diff --git a/-8mPXAsX3DY.txt b/-8mPXAsX3DY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4ccf2cacbd6d12c0506454ae66e9a932118cbe82
--- /dev/null
+++ b/-8mPXAsX3DY.txt
@@ -0,0 +1,1928 @@
+align:start position:0%
+ 
+the simplest quantum system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+so in order to decide what could be the
+
+ align:start position:0%
+so in order to decide what could be the
+ 
+
+ align:start position:0%
+so in order to decide what could be the
+simplest quantum system you could say
+
+ align:start position:0%
+simplest quantum system you could say
+ 
+
+ align:start position:0%
+simplest quantum system you could say
+well particle in a box it's very simple
+
+ align:start position:0%
+well particle in a box it's very simple
+ 
+
+ align:start position:0%
+well particle in a box it's very simple
+but in a sense it's not all that simple
+
+ align:start position:0%
+but in a sense it's not all that simple
+ 
+
+ align:start position:0%
+but in a sense it's not all that simple
+it has
+
+ align:start position:0%
+it has
+ 
+
+ align:start position:0%
+it has
+infinitely many states
+
+ align:start position:0%
+infinitely many states
+ 
+
+ align:start position:0%
+infinitely many states
+all these functions on an interval and
+
+ align:start position:0%
+all these functions on an interval and
+ 
+
+ align:start position:0%
+all these functions on an interval and
+then the energion says were infinitely
+
+ align:start position:0%
+then the energion says were infinitely
+ 
+
+ align:start position:0%
+then the energion says were infinitely
+many of them so not that simple okay so
+
+ align:start position:0%
+many of them so not that simple okay so
+ 
+
+ align:start position:0%
+many of them so not that simple okay so
+infinite bound states something with one
+
+ align:start position:0%
+infinite bound states something with one
+ 
+
+ align:start position:0%
+infinite bound states something with one
+bouncing okay a delta function potential
+
+ align:start position:0%
+bouncing okay a delta function potential
+ 
+
+ align:start position:0%
+bouncing okay a delta function potential
+just one bound state but it has
+
+ align:start position:0%
+just one bound state but it has
+ 
+
+ align:start position:0%
+just one bound state but it has
+infinitely many scattering States but
+
+ align:start position:0%
+infinitely many scattering States but
+ 
+
+ align:start position:0%
+infinitely many scattering States but
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+complicated so what is it what could be
+
+ align:start position:0%
+complicated so what is it what could be
+ 
+
+ align:start position:0%
+complicated so what is it what could be
+simpler well suppose you have the
+
+ align:start position:0%
+simpler well suppose you have the
+ 
+
+ align:start position:0%
+simpler well suppose you have the
+Schrodinger equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H sy and
+
+ align:start position:0%
+H sy and
+ 
+
+ align:start position:0%
+H sy and
+we work in general we know that this
+
+ align:start position:0%
+we work in general we know that this
+ 
+
+ align:start position:0%
+we work in general we know that this
+thing has energy eigenstates and
+
+ align:start position:0%
+thing has energy eigenstates and
+ 
+
+ align:start position:0%
+thing has energy eigenstates and
+probably we should focus on them
+
+ align:start position:0%
+probably we should focus on them
+ 
+
+ align:start position:0%
+probably we should focus on them
+subsequent to the minus I P over H bar
+
+ align:start position:0%
+subsequent to the minus I P over H bar
+ 
+
+ align:start position:0%
+subsequent to the minus I P over H bar
+little sy and then you have h sy equal
+
+ align:start position:0%
+little sy and then you have h sy equal
+ 
+
+ align:start position:0%
+little sy and then you have h sy equal
+each side
+
+ align:start position:0%
+each side
+ 
+
+ align:start position:0%
+each side
+so that is quantum mechanics and you
+
+ align:start position:0%
+so that is quantum mechanics and you
+ 
+
+ align:start position:0%
+so that is quantum mechanics and you
+could say well you know it's up to me to
+
+ align:start position:0%
+could say well you know it's up to me to
+ 
+
+ align:start position:0%
+could say well you know it's up to me to
+decide what the Hamiltonian is if I want
+
+ align:start position:0%
+decide what the Hamiltonian is if I want
+ 
+
+ align:start position:0%
+decide what the Hamiltonian is if I want
+to invent the simplest quantum
+
+ align:start position:0%
+to invent the simplest quantum
+ 
+
+ align:start position:0%
+to invent the simplest quantum
+mechanical system on the other hand
+
+ align:start position:0%
+mechanical system on the other hand
+ 
+
+ align:start position:0%
+mechanical system on the other hand
+there are some things that should be
+
+ align:start position:0%
+there are some things that should be
+ 
+
+ align:start position:0%
+there are some things that should be
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+these are complex numbers
+
+ align:start position:0%
+these are complex numbers
+ 
+
+ align:start position:0%
+these are complex numbers
+energies H must be an operator that has
+
+ align:start position:0%
+energies H must be an operator that has
+ 
+
+ align:start position:0%
+energies H must be an operator that has
+units of energy
+
+ align:start position:0%
+units of energy
+ 
+
+ align:start position:0%
+units of energy
+and we also saw that if we want
+
+ align:start position:0%
+and we also saw that if we want
+ 
+
+ align:start position:0%
+and we also saw that if we want
+probabilities that are going to be
+
+ align:start position:0%
+probabilities that are going to be
+ 
+
+ align:start position:0%
+probabilities that are going to be
+associated with size squared
+
+ align:start position:0%
+associated with size squared
+ 
+
+ align:start position:0%
+associated with size squared
+to be conserved we need H to be
+
+ align:start position:0%
+to be conserved we need H to be
+ 
+
+ align:start position:0%
+to be conserved we need H to be
+hermitian so there should be some notion
+
+ align:start position:0%
+hermitian so there should be some notion
+ 
+
+ align:start position:0%
+hermitian so there should be some notion
+of inner product some sort of
+
+ align:start position:0%
+of inner product some sort of
+ 
+
+ align:start position:0%
+of inner product some sort of
+operation that gives us numbers we used
+
+ align:start position:0%
+operation that gives us numbers we used
+ 
+
+ align:start position:0%
+operation that gives us numbers we used
+to defy psy that gives a number
+
+ align:start position:0%
+to defy psy that gives a number
+ 
+
+ align:start position:0%
+to defy psy that gives a number
+also complex numbers in general and it
+
+ align:start position:0%
+also complex numbers in general and it
+ 
+
+ align:start position:0%
+also complex numbers in general and it
+has the property at some point
+
+ align:start position:0%
+has the property at some point
+ 
+
+ align:start position:0%
+has the property at some point
+conjugates this thing it has this and
+
+ align:start position:0%
+conjugates this thing it has this and
+ 
+
+ align:start position:0%
+conjugates this thing it has this and
+integrates but maybe if you're doing the
+
+ align:start position:0%
+integrates but maybe if you're doing the
+ 
+
+ align:start position:0%
+integrates but maybe if you're doing the
+simplest quantum mechanical system in
+
+ align:start position:0%
+simplest quantum mechanical system in
+ 
+
+ align:start position:0%
+simplest quantum mechanical system in
+the world it will be simpler than at
+
+ align:start position:0%
+the world it will be simpler than at
+ 
+
+ align:start position:0%
+the world it will be simpler than at
+integral integrals are complicated but
+
+ align:start position:0%
+integral integrals are complicated but
+ 
+
+ align:start position:0%
+integral integrals are complicated but
+anyway we have something like that and
+
+ align:start position:0%
+anyway we have something like that and
+ 
+
+ align:start position:0%
+anyway we have something like that and
+we want
+
+ align:start position:0%
+we want
+ 
+
+ align:start position:0%
+we want
+H to
+
+ align:start position:0%
+H to
+ 
+
+ align:start position:0%
+H to
+be hermitian so let me write the same
+
+ align:start position:0%
+be hermitian so let me write the same
+ 
+
+ align:start position:0%
+be hermitian so let me write the same
+for any operator a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is equal to a dagger
+
+ align:start position:0%
+this is equal to a dagger
+ 
+
+ align:start position:0%
+this is equal to a dagger
+sy and
+
+ align:start position:0%
+sy and
+ 
+
+ align:start position:0%
+sy and
+that's a hermitian conjugate that's a
+
+ align:start position:0%
+that's a hermitian conjugate that's a
+ 
+
+ align:start position:0%
+that's a hermitian conjugate that's a
+general definition and we want H to be
+
+ align:start position:0%
+general definition and we want H to be
+ 
+
+ align:start position:0%
+general definition and we want H to be
+hermitian so H
+
+ align:start position:0%
+hermitian so H
+ 
+
+ align:start position:0%
+hermitian so H
+dagger equal H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so in some sense you could say
+
+ align:start position:0%
+okay so in some sense you could say
+ 
+
+ align:start position:0%
+okay so in some sense you could say
+there that's quantum mechanics for you
+
+ align:start position:0%
+there that's quantum mechanics for you
+ 
+
+ align:start position:0%
+there that's quantum mechanics for you
+it's a Schrodinger equation a
+
+ align:start position:0%
+it's a Schrodinger equation a
+ 
+
+ align:start position:0%
+it's a Schrodinger equation a
+Hamiltonian an inner product a notion of
+
+ align:start position:0%
+Hamiltonian an inner product a notion of
+ 
+
+ align:start position:0%
+Hamiltonian an inner product a notion of
+hermitian operators and then you're
+
+ align:start position:0%
+hermitian operators and then you're
+ 
+
+ align:start position:0%
+hermitian operators and then you're
+supposed to solve it and what we've done
+
+ align:start position:0%
+supposed to solve it and what we've done
+ 
+
+ align:start position:0%
+supposed to solve it and what we've done
+is solved this for a whole semester and
+
+ align:start position:0%
+is solved this for a whole semester and
+ 
+
+ align:start position:0%
+is solved this for a whole semester and
+try to understand
+
+ align:start position:0%
+try to understand
+ 
+
+ align:start position:0%
+try to understand
+some physics out of it
+
+ align:start position:0%
+some physics out of it
+ 
+
+ align:start position:0%
+some physics out of it
+but we started with the notion that
+
+ align:start position:0%
+but we started with the notion that
+ 
+
+ align:start position:0%
+but we started with the notion that
+something simple would be a particle
+
+ align:start position:0%
+something simple would be a particle
+ 
+
+ align:start position:0%
+something simple would be a particle
+living in one dimension and that's a
+
+ align:start position:0%
+living in one dimension and that's a
+ 
+
+ align:start position:0%
+living in one dimension and that's a
+very reasonable thought
+
+ align:start position:0%
+very reasonable thought
+ 
+
+ align:start position:0%
+very reasonable thought
+motivated from classical mechanics
+
+ align:start position:0%
+motivated from classical mechanics
+ 
+
+ align:start position:0%
+motivated from classical mechanics
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+surely we have particles that move and
+
+ align:start position:0%
+surely we have particles that move and
+ 
+
+ align:start position:0%
+surely we have particles that move and
+moving in three dimensions is more
+
+ align:start position:0%
+moving in three dimensions is more
+ 
+
+ align:start position:0%
+moving in three dimensions is more
+complicated so we waited towards the end
+
+ align:start position:0%
+complicated so we waited towards the end
+ 
+
+ align:start position:0%
+complicated so we waited towards the end
+of the semester to do three dimensions
+
+ align:start position:0%
+of the semester to do three dimensions
+ 
+
+ align:start position:0%
+of the semester to do three dimensions
+but moving in one dimension is already
+
+ align:start position:0%
+but moving in one dimension is already
+ 
+
+ align:start position:0%
+but moving in one dimension is already
+kind of interesting and complicated so
+
+ align:start position:0%
+kind of interesting and complicated so
+ 
+
+ align:start position:0%
+kind of interesting and complicated so
+we had size of X that represented the
+
+ align:start position:0%
+we had size of X that represented the
+ 
+
+ align:start position:0%
+we had size of X that represented the
+fact that the particle could be anywhere
+
+ align:start position:0%
+fact that the particle could be anywhere
+ 
+
+ align:start position:0%
+fact that the particle could be anywhere
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how can I simplify this well the key to
+
+ align:start position:0%
+how can I simplify this well the key to
+ 
+
+ align:start position:0%
+how can I simplify this well the key to
+simplifying this is maybe
+
+ align:start position:0%
+simplifying this is maybe
+ 
+
+ align:start position:0%
+simplifying this is maybe
+not to be too attached to the physics
+
+ align:start position:0%
+not to be too attached to the physics
+ 
+
+ align:start position:0%
+not to be too attached to the physics
+for a while and try to visualize what
+
+ align:start position:0%
+for a while and try to visualize what
+ 
+
+ align:start position:0%
+for a while and try to visualize what
+could you describe that was simpler so
+
+ align:start position:0%
+could you describe that was simpler so
+ 
+
+ align:start position:0%
+could you describe that was simpler so
+suppose the particle could only live at
+
+ align:start position:0%
+suppose the particle could only live at
+ 
+
+ align:start position:0%
+suppose the particle could only live at
+two points X 1 and X 2
+
+ align:start position:0%
+two points X 1 and X 2
+ 
+
+ align:start position:0%
+two points X 1 and X 2
+the particle can be here or here
+
+ align:start position:0%
+the particle can be here or here
+ 
+
+ align:start position:0%
+the particle can be here or here
+now if cut the real line down to just
+
+ align:start position:0%
+now if cut the real line down to just
+ 
+
+ align:start position:0%
+now if cut the real line down to just
+two points you can only be in this point
+
+ align:start position:0%
+two points you can only be in this point
+ 
+
+ align:start position:0%
+two points you can only be in this point
+or that point
+
+ align:start position:0%
+or that point
+ 
+
+ align:start position:0%
+or that point
+and you say that's very in physical but
+
+ align:start position:0%
+and you say that's very in physical but
+ 
+
+ align:start position:0%
+and you say that's very in physical but
+let's wait a second and think of this
+
+ align:start position:0%
+let's wait a second and think of this
+ 
+
+ align:start position:0%
+let's wait a second and think of this
+what does that mean well we used to have
+
+ align:start position:0%
+what does that mean well we used to have
+ 
+
+ align:start position:0%
+what does that mean well we used to have
+a sigh of X that could be anywhere and
+
+ align:start position:0%
+a sigh of X that could be anywhere and
+ 
+
+ align:start position:0%
+a sigh of X that could be anywhere and
+we wrote it as a function but now that
+
+ align:start position:0%
+we wrote it as a function but now that
+ 
+
+ align:start position:0%
+we wrote it as a function but now that
+it can if I think of this the simplest
+
+ align:start position:0%
+it can if I think of this the simplest
+ 
+
+ align:start position:0%
+it can if I think of this the simplest
+thing ok the simplest thing is a
+
+ align:start position:0%
+thing ok the simplest thing is a
+ 
+
+ align:start position:0%
+thing ok the simplest thing is a
+particle is just at one point there's
+
+ align:start position:0%
+particle is just at one point there's
+ 
+
+ align:start position:0%
+particle is just at one point there's
+only one point the whole world for the
+
+ align:start position:0%
+only one point the whole world for the
+ 
+
+ align:start position:0%
+only one point the whole world for the
+particle is one point and it's there but
+
+ align:start position:0%
+particle is one point and it's there but
+ 
+
+ align:start position:0%
+particle is one point and it's there but
+that probably is not too interesting
+
+ align:start position:0%
+that probably is not too interesting
+ 
+
+ align:start position:0%
+that probably is not too interesting
+because the particle is there the
+
+ align:start position:0%
+because the particle is there the
+ 
+
+ align:start position:0%
+because the particle is there the
+probability to find it there is always 1
+
+ align:start position:0%
+probability to find it there is always 1
+ 
+
+ align:start position:0%
+probability to find it there is always 1
+and what can you do with it oh but if
+
+ align:start position:0%
+and what can you do with it oh but if
+ 
+
+ align:start position:0%
+and what can you do with it oh but if
+you have two points there's room for
+
+ align:start position:0%
+you have two points there's room for
+ 
+
+ align:start position:0%
+you have two points there's room for
+funny things to happen so we'll assume
+
+ align:start position:0%
+funny things to happen so we'll assume
+ 
+
+ align:start position:0%
+funny things to happen so we'll assume
+that the particle can be in two points
+
+ align:start position:0%
+that the particle can be in two points
+ 
+
+ align:start position:0%
+that the particle can be in two points
+so from all of this sigh effects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will go to a new PI of X that has
+
+ align:start position:0%
+will go to a new PI of X that has
+ 
+
+ align:start position:0%
+will go to a new PI of X that has
+two pieces of information the value of y
+
+ align:start position:0%
+two pieces of information the value of y
+ 
+
+ align:start position:0%
+two pieces of information the value of y
+at X 1 and the value of y at X 2 and
+
+ align:start position:0%
+at X 1 and the value of y at X 2 and
+ 
+
+ align:start position:0%
+at X 1 and the value of y at X 2 and
+those are two numbers alpha and beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alpha squared would be
+
+ align:start position:0%
+alpha squared would be
+ 
+
+ align:start position:0%
+alpha squared would be
+the probability to
+
+ align:start position:0%
+the probability to
+ 
+
+ align:start position:0%
+the probability to
+be at X 1
+
+ align:start position:0%
+be at X 1
+ 
+
+ align:start position:0%
+be at X 1
+beta squared would be the probability to
+
+ align:start position:0%
+beta squared would be the probability to
+ 
+
+ align:start position:0%
+beta squared would be the probability to
+be at X 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this may remind you already of something
+
+ align:start position:0%
+this may remind you already of something
+ 
+
+ align:start position:0%
+this may remind you already of something
+we're doing with interferometers in
+
+ align:start position:0%
+we're doing with interferometers in
+ 
+
+ align:start position:0%
+we're doing with interferometers in
+which the photon could be in the upper
+
+ align:start position:0%
+which the photon could be in the upper
+ 
+
+ align:start position:0%
+which the photon could be in the upper
+branch or the lower branch and you had
+
+ align:start position:0%
+branch or the lower branch and you had
+ 
+
+ align:start position:0%
+branch or the lower branch and you had
+two numbers so this is somewhat
+
+ align:start position:0%
+two numbers so this is somewhat
+ 
+
+ align:start position:0%
+two numbers so this is somewhat
+analogous except that the interferometer
+
+ align:start position:0%
+analogous except that the interferometer
+ 
+
+ align:start position:0%
+analogous except that the interferometer
+you could eventually
+
+ align:start position:0%
+you could eventually
+ 
+
+ align:start position:0%
+you could eventually
+put more beam splitters and have maybe
+
+ align:start position:0%
+put more beam splitters and have maybe
+ 
+
+ align:start position:0%
+put more beam splitters and have maybe
+later 3 branches or 4 branches or things
+
+ align:start position:0%
+later 3 branches or 4 branches or things
+ 
+
+ align:start position:0%
+later 3 branches or 4 branches or things
+like that here I want to consider two
+
+ align:start position:0%
+like that here I want to consider two
+ 
+
+ align:start position:0%
+like that here I want to consider two
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+particle there so one thing that this
+
+ align:start position:0%
+particle there so one thing that this
+ 
+
+ align:start position:0%
+particle there so one thing that this
+could be could be strictly that but now
+
+ align:start position:0%
+could be could be strictly that but now
+ 
+
+ align:start position:0%
+could be could be strictly that but now
+let's relax our
+
+ align:start position:0%
+let's relax our
+ 
+
+ align:start position:0%
+let's relax our
+assumption so you could also mean for
+
+ align:start position:0%
+assumption so you could also mean for
+ 
+
+ align:start position:0%
+assumption so you could also mean for
+example that you have a box and a
+
+ align:start position:0%
+example that you have a box and a
+ 
+
+ align:start position:0%
+example that you have a box and a
+partition and there's the left side of
+
+ align:start position:0%
+partition and there's the left side of
+ 
+
+ align:start position:0%
+partition and there's the left side of
+the box and the right side of the box
+
+ align:start position:0%
+the box and the right side of the box
+ 
+
+ align:start position:0%
+the box and the right side of the box
+and the molecule can either be on the
+
+ align:start position:0%
+and the molecule can either be on the
+ 
+
+ align:start position:0%
+and the molecule can either be on the
+left side or on the right side
+
+ align:start position:0%
+left side or on the right side
+ 
+
+ align:start position:0%
+left side or on the right side
+that's a fairly physical
+
+ align:start position:0%
+that's a fairly physical
+ 
+
+ align:start position:0%
+that's a fairly physical
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+so here you could be probability
+
+ align:start position:0%
+so here you could be probability
+ 
+
+ align:start position:0%
+so here you could be probability
+the amplitude
+
+ align:start position:0%
+the amplitude
+ 
+
+ align:start position:0%
+the amplitude
+amplitude to be on the left or amplitude
+
+ align:start position:0%
+amplitude to be on the left or amplitude
+ 
+
+ align:start position:0%
+amplitude to be on the left or amplitude
+to be on right two component vector just
+
+ align:start position:0%
+to be on right two component vector just
+ 
+
+ align:start position:0%
+to be on right two component vector just
+like that one would be the amplitude to
+
+ align:start position:0%
+like that one would be the amplitude to
+ 
+
+ align:start position:0%
+like that one would be the amplitude to
+be in either one and maybe the template
+
+ align:start position:0%
+be in either one and maybe the template
+ 
+
+ align:start position:0%
+be in either one and maybe the template
+changes in time or it could be that you
+
+ align:start position:0%
+changes in time or it could be that you
+ 
+
+ align:start position:0%
+changes in time or it could be that you
+have a particle
+
+ align:start position:0%
+have a particle
+ 
+
+ align:start position:0%
+have a particle
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+suddenly you discover that yeah the
+
+ align:start position:0%
+suddenly you discover that yeah the
+ 
+
+ align:start position:0%
+suddenly you discover that yeah the
+particle is at rest it's not moving it's
+
+ align:start position:0%
+particle is at rest it's not moving it's
+ 
+
+ align:start position:0%
+particle is at rest it's not moving it's
+not doing anything it's at one single
+
+ align:start position:0%
+not doing anything it's at one single
+ 
+
+ align:start position:0%
+not doing anything it's at one single
+point not two points but actually this
+
+ align:start position:0%
+point not two points but actually this
+ 
+
+ align:start position:0%
+point not two points but actually this
+particle has maybe something called spin
+
+ align:start position:0%
+particle has maybe something called spin
+ 
+
+ align:start position:0%
+particle has maybe something called spin
+and the spin can be up or the spin can
+
+ align:start position:0%
+and the spin can be up or the spin can
+ 
+
+ align:start position:0%
+and the spin can be up or the spin can
+be down
+
+ align:start position:0%
+be down
+ 
+
+ align:start position:0%
+be down
+well we could invent something we could
+
+ align:start position:0%
+well we could invent something we could
+ 
+
+ align:start position:0%
+well we could invent something we could
+call it spin or a particle
+
+ align:start position:0%
+call it spin or a particle
+ 
+
+ align:start position:0%
+call it spin or a particle
+could be in this state or in that state
+
+ align:start position:0%
+could be in this state or in that state
+ 
+
+ align:start position:0%
+could be in this state or in that state
+even if that's possible for a particle
+
+ align:start position:0%
+even if that's possible for a particle
+ 
+
+ align:start position:0%
+even if that's possible for a particle
+you could have here the amplitude
+
+ align:start position:0%
+you could have here the amplitude
+ 
+
+ align:start position:0%
+you could have here the amplitude
+for up
+
+ align:start position:0%
+for up
+ 
+
+ align:start position:0%
+for up
+spin and the amplitude for down
+
+ align:start position:0%
+spin and the amplitude for down
+ 
+
+ align:start position:0%
+spin and the amplitude for down
+spin and
+
+ align:start position:0%
+spin and
+ 
+
+ align:start position:0%
+spin and
+those would be the two numbers so you
+
+ align:start position:0%
+those would be the two numbers so you
+ 
+
+ align:start position:0%
+those would be the two numbers so you
+know it's lots of possibilities in a
+
+ align:start position:0%
+know it's lots of possibilities in a
+ 
+
+ align:start position:0%
+know it's lots of possibilities in a
+sense this is a
+
+ align:start position:0%
+sense this is a
+ 
+
+ align:start position:0%
+sense this is a
+classic problem waiting for a physical
+
+ align:start position:0%
+classic problem waiting for a physical
+ 
+
+ align:start position:0%
+classic problem waiting for a physical
+application in quantum mechanics so
+
+ align:start position:0%
+application in quantum mechanics so
+ 
+
+ align:start position:0%
+application in quantum mechanics so
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+push it a little more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how would we do inner products you know
+
+ align:start position:0%
+how would we do inner products you know
+ 
+
+ align:start position:0%
+how would we do inner products you know
+we decided okay you need to do inner
+
+ align:start position:0%
+we decided okay you need to do inner
+ 
+
+ align:start position:0%
+we decided okay you need to do inner
+products and
+
+ align:start position:0%
+products and
+ 
+
+ align:start position:0%
+products and
+what was the inner product of two
+
+ align:start position:0%
+what was the inner product of two
+ 
+
+ align:start position:0%
+what was the inner product of two
+functions Phi and psi was the integral
+
+ align:start position:0%
+functions Phi and psi was the integral
+ 
+
+ align:start position:0%
+functions Phi and psi was the integral
+DX of Phi star of X 1 times a 5 star of
+
+ align:start position:0%
+DX of Phi star of X 1 times a 5 star of
+ 
+
+ align:start position:0%
+DX of Phi star of X 1 times a 5 star of
+X times Phi of X and what you're really
+
+ align:start position:0%
+X times Phi of X and what you're really
+ 
+
+ align:start position:0%
+X times Phi of X and what you're really
+doing is taking the values of the first
+
+ align:start position:0%
+doing is taking the values of the first
+ 
+
+ align:start position:0%
+doing is taking the values of the first
+wave function at one point complex
+
+ align:start position:0%
+wave function at one point complex
+ 
+
+ align:start position:0%
+wave function at one point complex
+conjugate and you take the value of the
+
+ align:start position:0%
+conjugate and you take the value of the
+ 
+
+ align:start position:0%
+conjugate and you take the value of the
+second wave function at the same point
+
+ align:start position:0%
+second wave function at the same point
+ 
+
+ align:start position:0%
+second wave function at the same point
+compress conjugating it so if you would
+
+ align:start position:0%
+compress conjugating it so if you would
+ 
+
+ align:start position:0%
+compress conjugating it so if you would
+have two vectors like this
+
+ align:start position:0%
+have two vectors like this
+ 
+
+ align:start position:0%
+have two vectors like this
+alpha and
+
+ align:start position:0%
+alpha and
+ 
+
+ align:start position:0%
+alpha and
+beta the
+
+ align:start position:0%
+beta the
+ 
+
+ align:start position:0%
+beta the
+first wave function alpha 1 beta 1 and
+
+ align:start position:0%
+first wave function alpha 1 beta 1 and
+ 
+
+ align:start position:0%
+first wave function alpha 1 beta 1 and
+the second wave function alpha 2 beta 2
+
+ align:start position:0%
+the second wave function alpha 2 beta 2
+ 
+
+ align:start position:0%
+the second wave function alpha 2 beta 2
+the inner product psy 1 psy
+
+ align:start position:0%
+the inner product psy 1 psy
+ 
+
+ align:start position:0%
+the inner product psy 1 psy
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+should be the analog of this thing which
+
+ align:start position:0%
+should be the analog of this thing which
+ 
+
+ align:start position:0%
+should be the analog of this thing which
+is multiplied things at the same point
+
+ align:start position:0%
+is multiplied things at the same point
+ 
+
+ align:start position:0%
+is multiplied things at the same point
+so you should do the alpha 1 star that's
+
+ align:start position:0%
+so you should do the alpha 1 star that's
+ 
+
+ align:start position:0%
+so you should do the alpha 1 star that's
+alpha 2
+
+ align:start position:0%
+alpha 2
+ 
+
+ align:start position:0%
+alpha 2
+plus beta 1 star and beta 2
+
+ align:start position:0%
+plus beta 1 star and beta 2
+ 
+
+ align:start position:0%
+plus beta 1 star and beta 2
+that would be the nice way to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could think of this as having
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transposed this alpha 1 and complex
+
+ align:start position:0%
+transposed this alpha 1 and complex
+ 
+
+ align:start position:0%
+transposed this alpha 1 and complex
+conjugated it beta 1 and then the matrix
+
+ align:start position:0%
+conjugated it beta 1 and then the matrix
+ 
+
+ align:start position:0%
+conjugated it beta 1 and then the matrix
+product with alpha 1 beta 1
+
+ align:start position:0%
+product with alpha 1 beta 1
+ 
+
+ align:start position:0%
+product with alpha 1 beta 1
+so u transpose complex conjugate the
+
+ align:start position:0%
+so u transpose complex conjugate the
+ 
+
+ align:start position:0%
+so u transpose complex conjugate the
+first and
+
+ align:start position:0%
+first and
+ 
+
+ align:start position:0%
+first and
+you do that with a second you know
+
+ align:start position:0%
+you do that with a second you know
+ 
+
+ align:start position:0%
+you do that with a second you know
+when you study a little more mechanics
+
+ align:start position:0%
+when you study a little more mechanics
+ 
+
+ align:start position:0%
+when you study a little more mechanics
+in 805 you will explore this analogy
+
+ align:start position:0%
+in 805 you will explore this analogy
+ 
+
+ align:start position:0%
+in 805 you will explore this analogy
+even more in that you will think of a
+
+ align:start position:0%
+even more in that you will think of a
+ 
+
+ align:start position:0%
+even more in that you will think of a
+way function as a column vector infinite
+
+ align:start position:0%
+way function as a column vector infinite
+ 
+
+ align:start position:0%
+way function as a column vector infinite
+one side at zero PI epsilon Phi 2
+
+ align:start position:0%
+one side at zero PI epsilon Phi 2
+ 
+
+ align:start position:0%
+one side at zero PI epsilon Phi 2
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+sired minus epsilon so you've
+
+ align:start position:0%
+sired minus epsilon so you've
+ 
+
+ align:start position:0%
+sired minus epsilon so you've
+sliced the x-axis and a certain infinite
+
+ align:start position:0%
+sliced the x-axis and a certain infinite
+ 
+
+ align:start position:0%
+sliced the x-axis and a certain infinite
+vector and that's your old way function
+
+ align:start position:0%
+vector and that's your old way function
+ 
+
+ align:start position:0%
+vector and that's your old way function
+so it's not so unnatural to do this and
+
+ align:start position:0%
+so it's not so unnatural to do this and
+ 
+
+ align:start position:0%
+so it's not so unnatural to do this and
+this will be our inner product
+
+ align:start position:0%
+this will be our inner product
+ 
+
+ align:start position:0%
+this will be our inner product
+so how about H being hermitian
+
+ align:start position:0%
+so how about H being hermitian
+ 
+
+ align:start position:0%
+so how about H being hermitian
+median
+
+ align:start position:0%
+median
+ 
+
+ align:start position:0%
+median
+that just means for matrices that age
+
+ align:start position:0%
+that just means for matrices that age
+ 
+
+ align:start position:0%
+that just means for matrices that age
+transpose complex conjugated that's
+
+ align:start position:0%
+transpose complex conjugated that's
+ 
+
+ align:start position:0%
+transpose complex conjugated that's
+dagger hermitian is equal to h and
+
+ align:start position:0%
+dagger hermitian is equal to h and
+ 
+
+ align:start position:0%
+dagger hermitian is equal to h and
+you may have seen that that's what
+
+ align:start position:0%
+you may have seen that that's what
+ 
+
+ align:start position:0%
+you may have seen that that's what
+dagger means you transpose on her and
+
+ align:start position:0%
+dagger means you transpose on her and
+ 
+
+ align:start position:0%
+dagger means you transpose on her and
+complex conjugate if you haven't seen it
+
+ align:start position:0%
+complex conjugate if you haven't seen it
+ 
+
+ align:start position:0%
+complex conjugate if you haven't seen it
+you could prove it now using this rule
+
+ align:start position:0%
+you could prove it now using this rule
+ 
+
+ align:start position:0%
+you could prove it now using this rule
+for the inner product because the inner
+
+ align:start position:0%
+for the inner product because the inner
+ 
+
+ align:start position:0%
+for the inner product because the inner
+product will tell you how to construct
+
+ align:start position:0%
+product will tell you how to construct
+ 
+
+ align:start position:0%
+product will tell you how to construct
+the complex the dagger of any operator
+
+ align:start position:0%
+the complex the dagger of any operator
+ 
+
+ align:start position:0%
+the complex the dagger of any operator
+and you will find that indeed the dagger
+
+ align:start position:0%
+and you will find that indeed the dagger
+ 
+
+ align:start position:0%
+and you will find that indeed the dagger
+what it does is transpose this and
+
+ align:start position:0%
+what it does is transpose this and
+ 
+
+ align:start position:0%
+what it does is transpose this and
+complex conjugates and it's sort of
+
+ align:start position:0%
+complex conjugates and it's sort of
+ 
+
+ align:start position:0%
+complex conjugates and it's sort of
+comes because the inner product
+
+ align:start position:0%
+comes because the inner product
+ 
+
+ align:start position:0%
+comes because the inner product
+transposes and complex conjugates the
+
+ align:start position:0%
+transposes and complex conjugates the
+ 
+
+ align:start position:0%
+transposes and complex conjugates the
+first object
\ No newline at end of file
diff --git a/-IWKPe6X6Vs.txt b/-IWKPe6X6Vs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0006f9fa69a5b6e05a60df4de4a340780a407663
--- /dev/null
+++ b/-IWKPe6X6Vs.txt
@@ -0,0 +1,2627 @@
+align:start position:0%
+ 
+after flipping a coin 100 times you
+
+ align:start position:0%
+after flipping a coin 100 times you
+ 
+
+ align:start position:0%
+after flipping a coin 100 times you
+tally out 42 heads and 58
+
+ align:start position:0%
+tally out 42 heads and 58
+ 
+
+ align:start position:0%
+tally out 42 heads and 58
+tails you expected a 50/50
+
+ align:start position:0%
+tails you expected a 50/50
+ 
+
+ align:start position:0%
+tails you expected a 50/50
+distribution does this mean the coin is
+
+ align:start position:0%
+distribution does this mean the coin is
+ 
+
+ align:start position:0%
+distribution does this mean the coin is
+unfair this video is part of the
+
+ align:start position:0%
+unfair this video is part of the
+ 
+
+ align:start position:0%
+unfair this video is part of the
+probability and statistics video
+
+ align:start position:0%
+probability and statistics video
+ 
+
+ align:start position:0%
+probability and statistics video
+series many events and phenomena are
+
+ align:start position:0%
+series many events and phenomena are
+ 
+
+ align:start position:0%
+series many events and phenomena are
+probabilistic Engineers designers and
+
+ align:start position:0%
+probabilistic Engineers designers and
+ 
+
+ align:start position:0%
+probabilistic Engineers designers and
+Architects often use probability
+
+ align:start position:0%
+Architects often use probability
+ 
+
+ align:start position:0%
+Architects often use probability
+distributions to predict system
+
+ align:start position:0%
+distributions to predict system
+ 
+
+ align:start position:0%
+distributions to predict system
+Behavior hi my name is lorda salaman and
+
+ align:start position:0%
+Behavior hi my name is lorda salaman and
+ 
+
+ align:start position:0%
+Behavior hi my name is lorda salaman and
+I'm a research scientist in the hhmi
+
+ align:start position:0%
+I'm a research scientist in the hhmi
+ 
+
+ align:start position:0%
+I'm a research scientist in the hhmi
+education group in the biology
+
+ align:start position:0%
+education group in the biology
+ 
+
+ align:start position:0%
+education group in the biology
+department at MIT I also work in the MIT
+
+ align:start position:0%
+department at MIT I also work in the MIT
+ 
+
+ align:start position:0%
+department at MIT I also work in the MIT
+office of educational Innovation and
+
+ align:start position:0%
+office of educational Innovation and
+ 
+
+ align:start position:0%
+office of educational Innovation and
+Technology I helped de velop the star
+
+ align:start position:0%
+Technology I helped de velop the star
+ 
+
+ align:start position:0%
+Technology I helped de velop the star
+genetic software feature in this
+
+ align:start position:0%
+genetic software feature in this
+ 
+
+ align:start position:0%
+genetic software feature in this
+video before watching this video you
+
+ align:start position:0%
+video before watching this video you
+ 
+
+ align:start position:0%
+video before watching this video you
+should know what a probability
+
+ align:start position:0%
+should know what a probability
+ 
+
+ align:start position:0%
+should know what a probability
+distribution is and be familiar with
+
+ align:start position:0%
+distribution is and be familiar with
+ 
+
+ align:start position:0%
+distribution is and be familiar with
+basic genetics vocabulary including
+
+ align:start position:0%
+basic genetics vocabulary including
+ 
+
+ align:start position:0%
+basic genetics vocabulary including
+genotype phenotype homozygous and
+
+ align:start position:0%
+genotype phenotype homozygous and
+ 
+
+ align:start position:0%
+genotype phenotype homozygous and
+heterozygous you should also know how to
+
+ align:start position:0%
+heterozygous you should also know how to
+ 
+
+ align:start position:0%
+heterozygous you should also know how to
+use punet squares to predict the
+
+ align:start position:0%
+use punet squares to predict the
+ 
+
+ align:start position:0%
+use punet squares to predict the
+expected results of melan crosses
+
+ align:start position:0%
+expected results of melan crosses
+ 
+
+ align:start position:0%
+expected results of melan crosses
+after watching this video you will be
+
+ align:start position:0%
+after watching this video you will be
+ 
+
+ align:start position:0%
+after watching this video you will be
+able to apply Ki Square hypothesis
+
+ align:start position:0%
+able to apply Ki Square hypothesis
+ 
+
+ align:start position:0%
+able to apply Ki Square hypothesis
+testing to experimental data obtained
+
+ align:start position:0%
+testing to experimental data obtained
+ 
+
+ align:start position:0%
+testing to experimental data obtained
+from genetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiments going back to the question
+
+ align:start position:0%
+experiments going back to the question
+ 
+
+ align:start position:0%
+experiments going back to the question
+of whether or not our coin is fair it
+
+ align:start position:0%
+of whether or not our coin is fair it
+ 
+
+ align:start position:0%
+of whether or not our coin is fair it
+turns out there is statistical tool that
+
+ align:start position:0%
+turns out there is statistical tool that
+ 
+
+ align:start position:0%
+turns out there is statistical tool that
+can help
+
+ align:start position:0%
+can help
+ 
+
+ align:start position:0%
+can help
+us statistical tests can be used to
+
+ align:start position:0%
+us statistical tests can be used to
+ 
+
+ align:start position:0%
+us statistical tests can be used to
+determ determined if sample data can be
+
+ align:start position:0%
+determ determined if sample data can be
+ 
+
+ align:start position:0%
+determ determined if sample data can be
+assumed to come from a population that
+
+ align:start position:0%
+assumed to come from a population that
+ 
+
+ align:start position:0%
+assumed to come from a population that
+has a certain
+
+ align:start position:0%
+has a certain
+ 
+
+ align:start position:0%
+has a certain
+distribution today we will use the
+
+ align:start position:0%
+distribution today we will use the
+ 
+
+ align:start position:0%
+distribution today we will use the
+statistical test called the kai Square
+
+ align:start position:0%
+statistical test called the kai Square
+ 
+
+ align:start position:0%
+statistical test called the kai Square
+test for goodness of
+
+ align:start position:0%
+test for goodness of
+ 
+
+ align:start position:0%
+test for goodness of
+fit the Ki Square test is used to
+
+ align:start position:0%
+fit the Ki Square test is used to
+ 
+
+ align:start position:0%
+fit the Ki Square test is used to
+analyze categorical data in other words
+
+ align:start position:0%
+analyze categorical data in other words
+ 
+
+ align:start position:0%
+analyze categorical data in other words
+the test Compares a sample of data
+
+ align:start position:0%
+the test Compares a sample of data
+ 
+
+ align:start position:0%
+the test Compares a sample of data
+collected about an event to expected
+
+ align:start position:0%
+collected about an event to expected
+ 
+
+ align:start position:0%
+collected about an event to expected
+values in our coin flipping example our
+
+ align:start position:0%
+values in our coin flipping example our
+ 
+
+ align:start position:0%
+values in our coin flipping example our
+categories are heads and
+
+ align:start position:0%
+categories are heads and
+ 
+
+ align:start position:0%
+categories are heads and
+tails an event is one coin
+
+ align:start position:0%
+tails an event is one coin
+ 
+
+ align:start position:0%
+tails an event is one coin
+flip our sample is 100
+
+ align:start position:0%
+flip our sample is 100
+ 
+
+ align:start position:0%
+flip our sample is 100
+events we expect that the coin should
+
+ align:start position:0%
+events we expect that the coin should
+ 
+
+ align:start position:0%
+events we expect that the coin should
+have a 5050 chance of being heads or
+
+ align:start position:0%
+have a 5050 chance of being heads or
+ 
+
+ align:start position:0%
+have a 5050 chance of being heads or
+tails in any given event
+
+ align:start position:0%
+tails in any given event
+ 
+
+ align:start position:0%
+tails in any given event
+the question we are trying to answer is
+
+ align:start position:0%
+the question we are trying to answer is
+ 
+
+ align:start position:0%
+the question we are trying to answer is
+does our sample come from the 5050
+
+ align:start position:0%
+does our sample come from the 5050
+ 
+
+ align:start position:0%
+does our sample come from the 5050
+population distribution we
+
+ align:start position:0%
+population distribution we
+ 
+
+ align:start position:0%
+population distribution we
+expect what we have just done is State
+
+ align:start position:0%
+expect what we have just done is State
+ 
+
+ align:start position:0%
+expect what we have just done is State
+our null hypothesis about the coin
+
+ align:start position:0%
+our null hypothesis about the coin
+ 
+
+ align:start position:0%
+our null hypothesis about the coin
+flipping
+
+ align:start position:0%
+flipping
+ 
+
+ align:start position:0%
+flipping
+experiment the kai Square statistics
+
+ align:start position:0%
+experiment the kai Square statistics
+ 
+
+ align:start position:0%
+experiment the kai Square statistics
+tests this null
+
+ align:start position:0%
+tests this null
+ 
+
+ align:start position:0%
+tests this null
+hypothesis we also need to State an
+
+ align:start position:0%
+hypothesis we also need to State an
+ 
+
+ align:start position:0%
+hypothesis we also need to State an
+alternative
+
+ align:start position:0%
+alternative
+ 
+
+ align:start position:0%
+alternative
+hypothesis the alternative hypothesis is
+
+ align:start position:0%
+hypothesis the alternative hypothesis is
+ 
+
+ align:start position:0%
+hypothesis the alternative hypothesis is
+simply that the data do not come from
+
+ align:start position:0%
+simply that the data do not come from
+ 
+
+ align:start position:0%
+simply that the data do not come from
+the specify 50/50 population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution before we can test our
+
+ align:start position:0%
+distribution before we can test our
+ 
+
+ align:start position:0%
+distribution before we can test our
+hypothesis we need to calculate a Kai
+
+ align:start position:0%
+hypothesis we need to calculate a Kai
+ 
+
+ align:start position:0%
+hypothesis we need to calculate a Kai
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+statistic this statistic measures the
+
+ align:start position:0%
+statistic this statistic measures the
+ 
+
+ align:start position:0%
+statistic this statistic measures the
+discrepancy between observed counts and
+
+ align:start position:0%
+discrepancy between observed counts and
+ 
+
+ align:start position:0%
+discrepancy between observed counts and
+expected counts
+
+ align:start position:0%
+expected counts
+ 
+
+ align:start position:0%
+expected counts
+each term in our summation finds the
+
+ align:start position:0%
+each term in our summation finds the
+ 
+
+ align:start position:0%
+each term in our summation finds the
+deviation or error between observed and
+
+ align:start position:0%
+deviation or error between observed and
+ 
+
+ align:start position:0%
+deviation or error between observed and
+expected values for each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+category this deviation is squared to
+
+ align:start position:0%
+category this deviation is squared to
+ 
+
+ align:start position:0%
+category this deviation is squared to
+obtain positive values otherwise
+
+ align:start position:0%
+obtain positive values otherwise
+ 
+
+ align:start position:0%
+obtain positive values otherwise
+everything will sum to zero because both
+
+ align:start position:0%
+everything will sum to zero because both
+ 
+
+ align:start position:0%
+everything will sum to zero because both
+are observed and expected outcomes sum
+
+ align:start position:0%
+are observed and expected outcomes sum
+ 
+
+ align:start position:0%
+are observed and expected outcomes sum
+to the same
+
+ align:start position:0%
+to the same
+ 
+
+ align:start position:0%
+to the same
+value each term in the summation is
+
+ align:start position:0%
+value each term in the summation is
+ 
+
+ align:start position:0%
+value each term in the summation is
+divided by the expected value of the
+
+ align:start position:0%
+divided by the expected value of the
+ 
+
+ align:start position:0%
+divided by the expected value of the
+outcome as a way of normalizing each
+
+ align:start position:0%
+outcome as a way of normalizing each
+ 
+
+ align:start position:0%
+outcome as a way of normalizing each
+difference the kai Square statistic
+
+ align:start position:0%
+difference the kai Square statistic
+ 
+
+ align:start position:0%
+difference the kai Square statistic
+lives in a
+
+ align:start position:0%
+lives in a
+ 
+
+ align:start position:0%
+lives in a
+distribution this is the kai Square
+
+ align:start position:0%
+distribution this is the kai Square
+ 
+
+ align:start position:0%
+distribution this is the kai Square
+distribution for any sample that has two
+
+ align:start position:0%
+distribution for any sample that has two
+ 
+
+ align:start position:0%
+distribution for any sample that has two
+categories of data or in other words one
+
+ align:start position:0%
+categories of data or in other words one
+ 
+
+ align:start position:0%
+categories of data or in other words one
+degree of
+
+ align:start position:0%
+degree of
+ 
+
+ align:start position:0%
+degree of
+Freedom if the outut come of an event
+
+ align:start position:0%
+Freedom if the outut come of an event
+ 
+
+ align:start position:0%
+Freedom if the outut come of an event
+can only fall into one of two categories
+
+ align:start position:0%
+can only fall into one of two categories
+ 
+
+ align:start position:0%
+can only fall into one of two categories
+we only need to know how many events
+
+ align:start position:0%
+we only need to know how many events
+ 
+
+ align:start position:0%
+we only need to know how many events
+fell into one category in order to
+
+ align:start position:0%
+fell into one category in order to
+ 
+
+ align:start position:0%
+fell into one category in order to
+determine how many fell into the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+category the Ki squar distribution is
+
+ align:start position:0%
+category the Ki squar distribution is
+ 
+
+ align:start position:0%
+category the Ki squar distribution is
+actually a set of distributions each for
+
+ align:start position:0%
+actually a set of distributions each for
+ 
+
+ align:start position:0%
+actually a set of distributions each for
+a different number of degrees of
+
+ align:start position:0%
+a different number of degrees of
+ 
+
+ align:start position:0%
+a different number of degrees of
+freedom if we look at these
+
+ align:start position:0%
+freedom if we look at these
+ 
+
+ align:start position:0%
+freedom if we look at these
+distributions the x axis is Kai Square
+
+ align:start position:0%
+distributions the x axis is Kai Square
+ 
+
+ align:start position:0%
+distributions the x axis is Kai Square
+values and the y axis is relative
+
+ align:start position:0%
+values and the y axis is relative
+ 
+
+ align:start position:0%
+values and the y axis is relative
+frequency you might also notice that
+
+ align:start position:0%
+frequency you might also notice that
+ 
+
+ align:start position:0%
+frequency you might also notice that
+these distributions are positively
+
+ align:start position:0%
+these distributions are positively
+ 
+
+ align:start position:0%
+these distributions are positively
+skewed this makes sense for a couple of
+
+ align:start position:0%
+skewed this makes sense for a couple of
+ 
+
+ align:start position:0%
+skewed this makes sense for a couple of
+reasons the Ki Square statistic is
+
+ align:start position:0%
+reasons the Ki Square statistic is
+ 
+
+ align:start position:0%
+reasons the Ki Square statistic is
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+positive larger and larger Ki Square
+
+ align:start position:0%
+positive larger and larger Ki Square
+ 
+
+ align:start position:0%
+positive larger and larger Ki Square
+values indicate larger discrepancies
+
+ align:start position:0%
+values indicate larger discrepancies
+ 
+
+ align:start position:0%
+values indicate larger discrepancies
+between observed and expected
+
+ align:start position:0%
+between observed and expected
+ 
+
+ align:start position:0%
+between observed and expected
+values while possible these large
+
+ align:start position:0%
+values while possible these large
+ 
+
+ align:start position:0%
+values while possible these large
+discrepancies are less probable if the
+
+ align:start position:0%
+discrepancies are less probable if the
+ 
+
+ align:start position:0%
+discrepancies are less probable if the
+null hypothesis is
+
+ align:start position:0%
+null hypothesis is
+ 
+
+ align:start position:0%
+null hypothesis is
+true if we calculate the Ki Square test
+
+ align:start position:0%
+true if we calculate the Ki Square test
+ 
+
+ align:start position:0%
+true if we calculate the Ki Square test
+statistic for the coin flipping
+
+ align:start position:0%
+statistic for the coin flipping
+ 
+
+ align:start position:0%
+statistic for the coin flipping
+experiment we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2.56 how do we interpret this
+
+ align:start position:0%
+2.56 how do we interpret this
+ 
+
+ align:start position:0%
+2.56 how do we interpret this
+number by first we need to look at the
+
+ align:start position:0%
+number by first we need to look at the
+ 
+
+ align:start position:0%
+number by first we need to look at the
+appropriate Kai Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution in the coin flipping
+
+ align:start position:0%
+distribution in the coin flipping
+ 
+
+ align:start position:0%
+distribution in the coin flipping
+experiment there are two possible
+
+ align:start position:0%
+experiment there are two possible
+ 
+
+ align:start position:0%
+experiment there are two possible
+outcomes heads or
+
+ align:start position:0%
+outcomes heads or
+ 
+
+ align:start position:0%
+outcomes heads or
+tails if we know how many heads were
+
+ align:start position:0%
+tails if we know how many heads were
+ 
+
+ align:start position:0%
+tails if we know how many heads were
+flipped we can calculate the number of
+
+ align:start position:0%
+flipped we can calculate the number of
+ 
+
+ align:start position:0%
+flipped we can calculate the number of
+Tails flipped so we only have one degree
+
+ align:start position:0%
+Tails flipped so we only have one degree
+ 
+
+ align:start position:0%
+Tails flipped so we only have one degree
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Freedom let's refer to the kai Square
+
+ align:start position:0%
+Freedom let's refer to the kai Square
+ 
+
+ align:start position:0%
+Freedom let's refer to the kai Square
+distribution tions for one degree of
+
+ align:start position:0%
+distribution tions for one degree of
+ 
+
+ align:start position:0%
+distribution tions for one degree of
+Freedom we can compare our test
+
+ align:start position:0%
+Freedom we can compare our test
+ 
+
+ align:start position:0%
+Freedom we can compare our test
+statistic to the distribution to see if
+
+ align:start position:0%
+statistic to the distribution to see if
+ 
+
+ align:start position:0%
+statistic to the distribution to see if
+we have support for our n hypothesis or
+
+ align:start position:0%
+we have support for our n hypothesis or
+ 
+
+ align:start position:0%
+we have support for our n hypothesis or
+if we need to reject
+
+ align:start position:0%
+if we need to reject
+ 
+
+ align:start position:0%
+if we need to reject
+it what will our Criterion for support
+
+ align:start position:0%
+it what will our Criterion for support
+ 
+
+ align:start position:0%
+it what will our Criterion for support
+or rejection of our null hypothesis
+
+ align:start position:0%
+or rejection of our null hypothesis
+ 
+
+ align:start position:0%
+or rejection of our null hypothesis
+be while this is a fairly arbitrary
+
+ align:start position:0%
+be while this is a fairly arbitrary
+ 
+
+ align:start position:0%
+be while this is a fairly arbitrary
+choice in many fields a result result is
+
+ align:start position:0%
+choice in many fields a result result is
+ 
+
+ align:start position:0%
+choice in many fields a result result is
+said not to differ significantly from
+
+ align:start position:0%
+said not to differ significantly from
+ 
+
+ align:start position:0%
+said not to differ significantly from
+expectations if it has a one in 20
+
+ align:start position:0%
+expectations if it has a one in 20
+ 
+
+ align:start position:0%
+expectations if it has a one in 20
+chance of
+
+ align:start position:0%
+chance of
+ 
+
+ align:start position:0%
+chance of
+happening in other words if the
+
+ align:start position:0%
+happening in other words if the
+ 
+
+ align:start position:0%
+happening in other words if the
+difference between the observed result
+
+ align:start position:0%
+difference between the observed result
+ 
+
+ align:start position:0%
+difference between the observed result
+and the expected result is small enough
+
+ align:start position:0%
+and the expected result is small enough
+ 
+
+ align:start position:0%
+and the expected result is small enough
+we would expect to see it one in 20
+
+ align:start position:0%
+we would expect to see it one in 20
+ 
+
+ align:start position:0%
+we would expect to see it one in 20
+times which is a probability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.05 this probability is called called
+
+ align:start position:0%
+0.05 this probability is called called
+ 
+
+ align:start position:0%
+0.05 this probability is called called
+the level of
+
+ align:start position:0%
+the level of
+ 
+
+ align:start position:0%
+the level of
+significance if a Kai Square value has a
+
+ align:start position:0%
+significance if a Kai Square value has a
+ 
+
+ align:start position:0%
+significance if a Kai Square value has a
+probability of occurring that is greater
+
+ align:start position:0%
+probability of occurring that is greater
+ 
+
+ align:start position:0%
+probability of occurring that is greater
+than our level of significance it lends
+
+ align:start position:0%
+than our level of significance it lends
+ 
+
+ align:start position:0%
+than our level of significance it lends
+support to our null
+
+ align:start position:0%
+support to our null
+ 
+
+ align:start position:0%
+support to our null
+hypothesis if a Kai Square value has a
+
+ align:start position:0%
+hypothesis if a Kai Square value has a
+ 
+
+ align:start position:0%
+hypothesis if a Kai Square value has a
+probability of occurring that is less
+
+ align:start position:0%
+probability of occurring that is less
+ 
+
+ align:start position:0%
+probability of occurring that is less
+than our level of significance we should
+
+ align:start position:0%
+than our level of significance we should
+ 
+
+ align:start position:0%
+than our level of significance we should
+reject the null
+
+ align:start position:0%
+reject the null
+ 
+
+ align:start position:0%
+reject the null
+hypothesis using the kai Square
+
+ align:start position:0%
+hypothesis using the kai Square
+ 
+
+ align:start position:0%
+hypothesis using the kai Square
+distribution for one degree of Freedom a
+
+ align:start position:0%
+distribution for one degree of Freedom a
+ 
+
+ align:start position:0%
+distribution for one degree of Freedom a
+Kai Square value of
+
+ align:start position:0%
+Kai Square value of
+ 
+
+ align:start position:0%
+Kai Square value of
+2.56 has greater than the 5% probability
+
+ align:start position:0%
+2.56 has greater than the 5% probability
+ 
+
+ align:start position:0%
+2.56 has greater than the 5% probability
+of occurring that we have set as our
+
+ align:start position:0%
+of occurring that we have set as our
+ 
+
+ align:start position:0%
+of occurring that we have set as our
+minimum this means that we fail to
+
+ align:start position:0%
+minimum this means that we fail to
+ 
+
+ align:start position:0%
+minimum this means that we fail to
+reject our null
+
+ align:start position:0%
+reject our null
+ 
+
+ align:start position:0%
+reject our null
+hypothesis in other words what we
+
+ align:start position:0%
+hypothesis in other words what we
+ 
+
+ align:start position:0%
+hypothesis in other words what we
+observe is close enough to what we
+
+ align:start position:0%
+observe is close enough to what we
+ 
+
+ align:start position:0%
+observe is close enough to what we
+expect that we have confidence that our
+
+ align:start position:0%
+expect that we have confidence that our
+ 
+
+ align:start position:0%
+expect that we have confidence that our
+coin is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fair
+
+ align:start position:0%
+fair
+ 
+
+ align:start position:0%
+fair
+now suppose you're planning an
+
+ align:start position:0%
+now suppose you're planning an
+ 
+
+ align:start position:0%
+now suppose you're planning an
+experiment where you will cross mutant
+
+ align:start position:0%
+experiment where you will cross mutant
+ 
+
+ align:start position:0%
+experiment where you will cross mutant
+flies that are heterozygous for a
+
+ align:start position:0%
+flies that are heterozygous for a
+ 
+
+ align:start position:0%
+flies that are heterozygous for a
+wingless phenotype to each
+
+ align:start position:0%
+wingless phenotype to each
+ 
+
+ align:start position:0%
+wingless phenotype to each
+other the wingless phenotype is dominant
+
+ align:start position:0%
+other the wingless phenotype is dominant
+ 
+
+ align:start position:0%
+other the wingless phenotype is dominant
+relative to the wild type winged
+
+ align:start position:0%
+relative to the wild type winged
+ 
+
+ align:start position:0%
+relative to the wild type winged
+phenotype let's use the notation Big G
+
+ align:start position:0%
+phenotype let's use the notation Big G
+ 
+
+ align:start position:0%
+phenotype let's use the notation Big G
+little G for the genotype of the parent
+
+ align:start position:0%
+little G for the genotype of the parent
+ 
+
+ align:start position:0%
+little G for the genotype of the parent
+mutant
+
+ align:start position:0%
+mutant
+ 
+
+ align:start position:0%
+mutant
+flies in this case the F typee winged
+
+ align:start position:0%
+flies in this case the F typee winged
+ 
+
+ align:start position:0%
+flies in this case the F typee winged
+flies are homozygous
+
+ align:start position:0%
+flies are homozygous
+ 
+
+ align:start position:0%
+flies are homozygous
+recessive what percentage of flies
+
+ align:start position:0%
+recessive what percentage of flies
+ 
+
+ align:start position:0%
+recessive what percentage of flies
+resulting from a cross of two heterosis
+
+ align:start position:0%
+resulting from a cross of two heterosis
+ 
+
+ align:start position:0%
+resulting from a cross of two heterosis
+wingless mutants would you expect to be
+
+ align:start position:0%
+wingless mutants would you expect to be
+ 
+
+ align:start position:0%
+wingless mutants would you expect to be
+wild type versus mutant pause the video
+
+ align:start position:0%
+wild type versus mutant pause the video
+ 
+
+ align:start position:0%
+wild type versus mutant pause the video
+here and use a punet square to justify
+
+ align:start position:0%
+here and use a punet square to justify
+ 
+
+ align:start position:0%
+here and use a punet square to justify
+your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+performing this cross using a punet
+
+ align:start position:0%
+performing this cross using a punet
+ 
+
+ align:start position:0%
+performing this cross using a punet
+square you would expect a 3:1 ratio of
+
+ align:start position:0%
+square you would expect a 3:1 ratio of
+ 
+
+ align:start position:0%
+square you would expect a 3:1 ratio of
+mutant to Wild type
+
+ align:start position:0%
+mutant to Wild type
+ 
+
+ align:start position:0%
+mutant to Wild type
+flies you perform the cross with the
+
+ align:start position:0%
+flies you perform the cross with the
+ 
+
+ align:start position:0%
+flies you perform the cross with the
+parental mutant flies the cross produces
+
+ align:start position:0%
+parental mutant flies the cross produces
+ 
+
+ align:start position:0%
+parental mutant flies the cross produces
+50 progyny 32 are mutant and 18 are wild
+
+ align:start position:0%
+50 progyny 32 are mutant and 18 are wild
+ 
+
+ align:start position:0%
+50 progyny 32 are mutant and 18 are wild
+type so only 64% of our flies are mutant
+
+ align:start position:0%
+type so only 64% of our flies are mutant
+ 
+
+ align:start position:0%
+type so only 64% of our flies are mutant
+even though you expected
+
+ align:start position:0%
+even though you expected
+ 
+
+ align:start position:0%
+even though you expected
+75% of them to be
+
+ align:start position:0%
+75% of them to be
+ 
+
+ align:start position:0%
+75% of them to be
+mutant although it is not what you
+
+ align:start position:0%
+mutant although it is not what you
+ 
+
+ align:start position:0%
+mutant although it is not what you
+expected it doesn't seem that far off
+
+ align:start position:0%
+expected it doesn't seem that far off
+ 
+
+ align:start position:0%
+expected it doesn't seem that far off
+either you decide to continue mating
+
+ align:start position:0%
+either you decide to continue mating
+ 
+
+ align:start position:0%
+either you decide to continue mating
+your parental mutant flies until you
+
+ align:start position:0%
+your parental mutant flies until you
+ 
+
+ align:start position:0%
+your parental mutant flies until you
+have a th
+
+ align:start position:0%
+have a th
+ 
+
+ align:start position:0%
+have a th
+progyny surely with this large a sample
+
+ align:start position:0%
+progyny surely with this large a sample
+ 
+
+ align:start position:0%
+progyny surely with this large a sample
+size the ratio of mutant to Wild type
+
+ align:start position:0%
+size the ratio of mutant to Wild type
+ 
+
+ align:start position:0%
+size the ratio of mutant to Wild type
+flies will be closer to what you
+
+ align:start position:0%
+flies will be closer to what you
+ 
+
+ align:start position:0%
+flies will be closer to what you
+expect voila oh wait a minute even with
+
+ align:start position:0%
+expect voila oh wait a minute even with
+ 
+
+ align:start position:0%
+expect voila oh wait a minute even with
+a thousand progyny our experiments still
+
+ align:start position:0%
+a thousand progyny our experiments still
+ 
+
+ align:start position:0%
+a thousand progyny our experiments still
+produce 68% mutant and 32% wild type
+
+ align:start position:0%
+produce 68% mutant and 32% wild type
+ 
+
+ align:start position:0%
+produce 68% mutant and 32% wild type
+flies now you're really starting to
+
+ align:start position:0%
+flies now you're really starting to
+ 
+
+ align:start position:0%
+flies now you're really starting to
+wonder if you can call the results close
+
+ align:start position:0%
+wonder if you can call the results close
+ 
+
+ align:start position:0%
+wonder if you can call the results close
+enough to the expected
+
+ align:start position:0%
+enough to the expected
+ 
+
+ align:start position:0%
+enough to the expected
+outcome we can use the kai Square test
+
+ align:start position:0%
+outcome we can use the kai Square test
+ 
+
+ align:start position:0%
+outcome we can use the kai Square test
+to evaluate whether the sample that had
+
+ align:start position:0%
+to evaluate whether the sample that had
+ 
+
+ align:start position:0%
+to evaluate whether the sample that had
+is 68 to 32 ratio could have come from
+
+ align:start position:0%
+is 68 to 32 ratio could have come from
+ 
+
+ align:start position:0%
+is 68 to 32 ratio could have come from
+the 3:1 population distribution that we
+
+ align:start position:0%
+the 3:1 population distribution that we
+ 
+
+ align:start position:0%
+the 3:1 population distribution that we
+expected pause the video here calculate
+
+ align:start position:0%
+expected pause the video here calculate
+ 
+
+ align:start position:0%
+expected pause the video here calculate
+the Ki Square test statistic and
+
+ align:start position:0%
+the Ki Square test statistic and
+ 
+
+ align:start position:0%
+the Ki Square test statistic and
+determine the degrees of freedom in your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data you should have obtained
+
+ align:start position:0%
+data you should have obtained
+ 
+
+ align:start position:0%
+data you should have obtained
+29.2 for your Kai Square
+
+ align:start position:0%
+29.2 for your Kai Square
+ 
+
+ align:start position:0%
+29.2 for your Kai Square
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+because there are only two phenotypic
+
+ align:start position:0%
+because there are only two phenotypic
+ 
+
+ align:start position:0%
+because there are only two phenotypic
+outcomes for your cross there is only
+
+ align:start position:0%
+outcomes for your cross there is only
+ 
+
+ align:start position:0%
+outcomes for your cross there is only
+one degree of Freedom any fly that isn't
+
+ align:start position:0%
+one degree of Freedom any fly that isn't
+ 
+
+ align:start position:0%
+one degree of Freedom any fly that isn't
+a mutant is wild type and vice
+
+ align:start position:0%
+a mutant is wild type and vice
+ 
+
+ align:start position:0%
+a mutant is wild type and vice
+versa the Ki Square distribution can
+
+ align:start position:0%
+versa the Ki Square distribution can
+ 
+
+ align:start position:0%
+versa the Ki Square distribution can
+also be presented in tabular
+
+ align:start position:0%
+also be presented in tabular
+ 
+
+ align:start position:0%
+also be presented in tabular
+form if you look at this table our
+
+ align:start position:0%
+form if you look at this table our
+ 
+
+ align:start position:0%
+form if you look at this table our
+experiment with one degree of freedom
+
+ align:start position:0%
+experiment with one degree of freedom
+ 
+
+ align:start position:0%
+experiment with one degree of freedom
+and a Kai Square value of 29 .2
+
+ align:start position:0%
+and a Kai Square value of 29 .2
+ 
+
+ align:start position:0%
+and a Kai Square value of 29 .2
+corresponds to a probability that is
+
+ align:start position:0%
+corresponds to a probability that is
+ 
+
+ align:start position:0%
+corresponds to a probability that is
+much smaller than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.05 do you have support for the null
+
+ align:start position:0%
+0.05 do you have support for the null
+ 
+
+ align:start position:0%
+0.05 do you have support for the null
+hypothesis or should you reject
+
+ align:start position:0%
+hypothesis or should you reject
+ 
+
+ align:start position:0%
+hypothesis or should you reject
+it pause the video here and take a
+
+ align:start position:0%
+it pause the video here and take a
+ 
+
+ align:start position:0%
+it pause the video here and take a
+moment to think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it because the ratio of progyny the you
+
+ align:start position:0%
+it because the ratio of progyny the you
+ 
+
+ align:start position:0%
+it because the ratio of progyny the you
+obtained in your experiment has a
+
+ align:start position:0%
+obtained in your experiment has a
+ 
+
+ align:start position:0%
+obtained in your experiment has a
+probability of happening that is less
+
+ align:start position:0%
+probability of happening that is less
+ 
+
+ align:start position:0%
+probability of happening that is less
+than our level of significance you
+
+ align:start position:0%
+than our level of significance you
+ 
+
+ align:start position:0%
+than our level of significance you
+should reject our null
+
+ align:start position:0%
+should reject our null
+ 
+
+ align:start position:0%
+should reject our null
+hypothesis this indicates that our
+
+ align:start position:0%
+hypothesis this indicates that our
+ 
+
+ align:start position:0%
+hypothesis this indicates that our
+discrepant results are due to something
+
+ align:start position:0%
+discrepant results are due to something
+ 
+
+ align:start position:0%
+discrepant results are due to something
+more than just random
+
+ align:start position:0%
+more than just random
+ 
+
+ align:start position:0%
+more than just random
+chance a multitude of other factors
+
+ align:start position:0%
+chance a multitude of other factors
+ 
+
+ align:start position:0%
+chance a multitude of other factors
+could be contributing to our results for
+
+ align:start position:0%
+could be contributing to our results for
+ 
+
+ align:start position:0%
+could be contributing to our results for
+example there might be interactions with
+
+ align:start position:0%
+example there might be interactions with
+ 
+
+ align:start position:0%
+example there might be interactions with
+other genes that you are not aware of or
+
+ align:start position:0%
+other genes that you are not aware of or
+ 
+
+ align:start position:0%
+other genes that you are not aware of or
+environmental factors could be playing a
+
+ align:start position:0%
+environmental factors could be playing a
+ 
+
+ align:start position:0%
+environmental factors could be playing a
+role all we know is there are null
+
+ align:start position:0%
+role all we know is there are null
+ 
+
+ align:start position:0%
+role all we know is there are null
+hypothesis of a 3:1 ratio of mutant to
+
+ align:start position:0%
+hypothesis of a 3:1 ratio of mutant to
+ 
+
+ align:start position:0%
+hypothesis of a 3:1 ratio of mutant to
+Wild type flies is
+
+ align:start position:0%
+Wild type flies is
+ 
+
+ align:start position:0%
+Wild type flies is
+incorrect as a Next Step you decide to
+
+ align:start position:0%
+incorrect as a Next Step you decide to
+ 
+
+ align:start position:0%
+incorrect as a Next Step you decide to
+go back and review your notes to see if
+
+ align:start position:0%
+go back and review your notes to see if
+ 
+
+ align:start position:0%
+go back and review your notes to see if
+you can formulate another plausible
+
+ align:start position:0%
+you can formulate another plausible
+ 
+
+ align:start position:0%
+you can formulate another plausible
+hypothesis reviewing your punet Square
+
+ align:start position:0%
+hypothesis reviewing your punet Square
+ 
+
+ align:start position:0%
+hypothesis reviewing your punet Square
+you expected to obtain this genotypic
+
+ align:start position:0%
+you expected to obtain this genotypic
+ 
+
+ align:start position:0%
+you expected to obtain this genotypic
+ratio in the F1 progeny if you were to
+
+ align:start position:0%
+ratio in the F1 progeny if you were to
+ 
+
+ align:start position:0%
+ratio in the F1 progeny if you were to
+select a big G Big G mutant from the F1
+
+ align:start position:0%
+select a big G Big G mutant from the F1
+ 
+
+ align:start position:0%
+select a big G Big G mutant from the F1
+progeny and cross it with a little G
+
+ align:start position:0%
+progeny and cross it with a little G
+ 
+
+ align:start position:0%
+progeny and cross it with a little G
+little G wild type fly you would expect
+
+ align:start position:0%
+little G wild type fly you would expect
+ 
+
+ align:start position:0%
+little G wild type fly you would expect
+that all of the progyny will be
+
+ align:start position:0%
+that all of the progyny will be
+ 
+
+ align:start position:0%
+that all of the progyny will be
+mutants after attempting this cross with
+
+ align:start position:0%
+mutants after attempting this cross with
+ 
+
+ align:start position:0%
+mutants after attempting this cross with
+a variety of flies from the F1 progyny
+
+ align:start position:0%
+a variety of flies from the F1 progyny
+ 
+
+ align:start position:0%
+a variety of flies from the F1 progyny
+that have a mutant phenotype
+
+ align:start position:0%
+that have a mutant phenotype
+ 
+
+ align:start position:0%
+that have a mutant phenotype
+it becomes clear that you cannot find a
+
+ align:start position:0%
+it becomes clear that you cannot find a
+ 
+
+ align:start position:0%
+it becomes clear that you cannot find a
+mutant fly that when crossed with a wild
+
+ align:start position:0%
+mutant fly that when crossed with a wild
+ 
+
+ align:start position:0%
+mutant fly that when crossed with a wild
+type fly produces all mutant
+
+ align:start position:0%
+type fly produces all mutant
+ 
+
+ align:start position:0%
+type fly produces all mutant
+progyny somehow you keep selecting
+
+ align:start position:0%
+progyny somehow you keep selecting
+ 
+
+ align:start position:0%
+progyny somehow you keep selecting
+heteros
+
+ align:start position:0%
+heteros
+ 
+
+ align:start position:0%
+heteros
+mutants you begin to suspect that the F1
+
+ align:start position:0%
+mutants you begin to suspect that the F1
+ 
+
+ align:start position:0%
+mutants you begin to suspect that the F1
+population does not contain the expected
+
+ align:start position:0%
+population does not contain the expected
+ 
+
+ align:start position:0%
+population does not contain the expected
+number of Big G Big G
+
+ align:start position:0%
+number of Big G Big G
+ 
+
+ align:start position:0%
+number of Big G Big G
+flies checking your lap no book you see
+
+ align:start position:0%
+flies checking your lap no book you see
+ 
+
+ align:start position:0%
+flies checking your lap no book you see
+a note about an observation that you
+
+ align:start position:0%
+a note about an observation that you
+ 
+
+ align:start position:0%
+a note about an observation that you
+barely paid attention to at the time
+
+ align:start position:0%
+barely paid attention to at the time
+ 
+
+ align:start position:0%
+barely paid attention to at the time
+when you made it the two parental mutant
+
+ align:start position:0%
+when you made it the two parental mutant
+ 
+
+ align:start position:0%
+when you made it the two parental mutant
+flies there were a number of dead
+
+ align:start position:0%
+flies there were a number of dead
+ 
+
+ align:start position:0%
+flies there were a number of dead
+embryos in your
+
+ align:start position:0%
+embryos in your
+ 
+
+ align:start position:0%
+embryos in your
+vial a new hypothesis is forming in your
+
+ align:start position:0%
+vial a new hypothesis is forming in your
+ 
+
+ align:start position:0%
+vial a new hypothesis is forming in your
+mind can you come up with a hypothesis
+
+ align:start position:0%
+mind can you come up with a hypothesis
+ 
+
+ align:start position:0%
+mind can you come up with a hypothesis
+that may explain the observations you
+
+ align:start position:0%
+that may explain the observations you
+ 
+
+ align:start position:0%
+that may explain the observations you
+have made through these
+
+ align:start position:0%
+have made through these
+ 
+
+ align:start position:0%
+have made through these
+experiments pause the video here
+
+ align:start position:0%
+experiments pause the video here
+ 
+
+ align:start position:0%
+experiments pause the video here
+discuss and justify your hypothesis with
+
+ align:start position:0%
+discuss and justify your hypothesis with
+ 
+
+ align:start position:0%
+discuss and justify your hypothesis with
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+classmate while there are many possible
+
+ align:start position:0%
+classmate while there are many possible
+ 
+
+ align:start position:0%
+classmate while there are many possible
+hypotheses one possible hypotheses is
+
+ align:start position:0%
+hypotheses one possible hypotheses is
+ 
+
+ align:start position:0%
+hypotheses one possible hypotheses is
+that the dead embryos in your vial were
+
+ align:start position:0%
+that the dead embryos in your vial were
+ 
+
+ align:start position:0%
+that the dead embryos in your vial were
+the missing Big G Big G
+
+ align:start position:0%
+the missing Big G Big G
+ 
+
+ align:start position:0%
+the missing Big G Big G
+mutants it may be that the wingless
+
+ align:start position:0%
+mutants it may be that the wingless
+ 
+
+ align:start position:0%
+mutants it may be that the wingless
+trait when homozygous results in
+
+ align:start position:0%
+trait when homozygous results in
+ 
+
+ align:start position:0%
+trait when homozygous results in
+lethality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this will result in a phenotypic ratio
+
+ align:start position:0%
+this will result in a phenotypic ratio
+ 
+
+ align:start position:0%
+this will result in a phenotypic ratio
+of 2: one mutant to Wild type flies in
+
+ align:start position:0%
+of 2: one mutant to Wild type flies in
+ 
+
+ align:start position:0%
+of 2: one mutant to Wild type flies in
+the F1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+progyny again you can use the K Square
+
+ align:start position:0%
+progyny again you can use the K Square
+ 
+
+ align:start position:0%
+progyny again you can use the K Square
+test for goodness of fit to test your
+
+ align:start position:0%
+test for goodness of fit to test your
+ 
+
+ align:start position:0%
+test for goodness of fit to test your
+new null
+
+ align:start position:0%
+new null
+ 
+
+ align:start position:0%
+new null
+hypothesis going back to your data of a
+
+ align:start position:0%
+hypothesis going back to your data of a
+ 
+
+ align:start position:0%
+hypothesis going back to your data of a
+thousand progyny use the test to
+
+ align:start position:0%
+thousand progyny use the test to
+ 
+
+ align:start position:0%
+thousand progyny use the test to
+evaluate the no
+
+ align:start position:0%
+evaluate the no
+ 
+
+ align:start position:0%
+evaluate the no
+hypothesis pause the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+video you should have obtained a Ki
+
+ align:start position:0%
+video you should have obtained a Ki
+ 
+
+ align:start position:0%
+video you should have obtained a Ki
+Square value of
+
+ align:start position:0%
+Square value of
+ 
+
+ align:start position:0%
+Square value of
+0.36 for one degree of Freedom you
+
+ align:start position:0%
+0.36 for one degree of Freedom you
+ 
+
+ align:start position:0%
+0.36 for one degree of Freedom you
+cannot reject your no
+
+ align:start position:0%
+cannot reject your no
+ 
+
+ align:start position:0%
+cannot reject your no
+hypothesis while you have support for
+
+ align:start position:0%
+hypothesis while you have support for
+ 
+
+ align:start position:0%
+hypothesis while you have support for
+your null hypothesis more experiments
+
+ align:start position:0%
+your null hypothesis more experiments
+ 
+
+ align:start position:0%
+your null hypothesis more experiments
+are needed to confirm the idea
+
+ align:start position:0%
+are needed to confirm the idea
+ 
+
+ align:start position:0%
+are needed to confirm the idea
+that the Big G Big G genotype is lethal
+
+ align:start position:0%
+that the Big G Big G genotype is lethal
+ 
+
+ align:start position:0%
+that the Big G Big G genotype is lethal
+as you
+
+ align:start position:0%
+as you
+ 
+
+ align:start position:0%
+as you
+suspect the results from our K Square
+
+ align:start position:0%
+suspect the results from our K Square
+ 
+
+ align:start position:0%
+suspect the results from our K Square
+test have led us to a reasonable next
+
+ align:start position:0%
+test have led us to a reasonable next
+ 
+
+ align:start position:0%
+test have led us to a reasonable next
+experiment to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perform in this video you saw how the
+
+ align:start position:0%
+perform in this video you saw how the
+ 
+
+ align:start position:0%
+perform in this video you saw how the
+kai Square statistic can help us
+
+ align:start position:0%
+kai Square statistic can help us
+ 
+
+ align:start position:0%
+kai Square statistic can help us
+determine if our experimental genetic
+
+ align:start position:0%
+determine if our experimental genetic
+ 
+
+ align:start position:0%
+determine if our experimental genetic
+data came from the expected population
+
+ align:start position:0%
+data came from the expected population
+ 
+
+ align:start position:0%
+data came from the expected population
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+distribution comparing observed values
+
+ align:start position:0%
+distribution comparing observed values
+ 
+
+ align:start position:0%
+distribution comparing observed values
+to expected values helped us determine
+
+ align:start position:0%
+to expected values helped us determine
+ 
+
+ align:start position:0%
+to expected values helped us determine
+if deviations in our data could be
+
+ align:start position:0%
+if deviations in our data could be
+ 
+
+ align:start position:0%
+if deviations in our data could be
+explained by random chance or if a
+
+ align:start position:0%
+explained by random chance or if a
+ 
+
+ align:start position:0%
+explained by random chance or if a
+hypothesis needed
+
+ align:start position:0%
+hypothesis needed
+ 
+
+ align:start position:0%
+hypothesis needed
+revision the Ki Square test for goodness
+
+ align:start position:0%
+revision the Ki Square test for goodness
+ 
+
+ align:start position:0%
+revision the Ki Square test for goodness
+of fit is just one statistical test of
+
+ align:start position:0%
+of fit is just one statistical test of
+ 
+
+ align:start position:0%
+of fit is just one statistical test of
+many that allows us to determine how
+
+ align:start position:0%
+many that allows us to determine how
+ 
+
+ align:start position:0%
+many that allows us to determine how
+confident we are that a sample of data
+
+ align:start position:0%
+confident we are that a sample of data
+ 
+
+ align:start position:0%
+confident we are that a sample of data
+comes from a population with a certain
+
+ align:start position:0%
+comes from a population with a certain
+ 
+
+ align:start position:0%
+comes from a population with a certain
+distribution it is important to
+
+ align:start position:0%
+distribution it is important to
+ 
+
+ align:start position:0%
+distribution it is important to
+understand what these tests mean and how
+
+ align:start position:0%
+understand what these tests mean and how
+ 
+
+ align:start position:0%
+understand what these tests mean and how
+to interpret their results so that you
+
+ align:start position:0%
+to interpret their results so that you
+ 
+
+ align:start position:0%
+to interpret their results so that you
+know their limitations and can make
+
+ align:start position:0%
+know their limitations and can make
+ 
+
+ align:start position:0%
+know their limitations and can make
+inform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decisions
\ No newline at end of file
diff --git a/-Km2237G0P8.txt b/-Km2237G0P8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..00381adf2664fef099791692ba56cd4b6aaaa631
--- /dev/null
+++ b/-Km2237G0P8.txt
@@ -0,0 +1,491 @@
+align:start position:0%
+ 
+assessing student work uh as a team um
+
+ align:start position:0%
+assessing student work uh as a team um
+ 
+
+ align:start position:0%
+assessing student work uh as a team um
+has different challenges of of course
+
+ align:start position:0%
+has different challenges of of course
+ 
+
+ align:start position:0%
+has different challenges of of course
+the first thing you do is assess the
+
+ align:start position:0%
+the first thing you do is assess the
+ 
+
+ align:start position:0%
+the first thing you do is assess the
+output of the team's work uh whether
+
+ align:start position:0%
+output of the team's work uh whether
+ 
+
+ align:start position:0%
+output of the team's work uh whether
+that's a requirement set whether it's a
+
+ align:start position:0%
+that's a requirement set whether it's a
+ 
+
+ align:start position:0%
+that's a requirement set whether it's a
+set of initial Concepts whether it's a
+
+ align:start position:0%
+set of initial Concepts whether it's a
+ 
+
+ align:start position:0%
+set of initial Concepts whether it's a
+presentation that's given at a
+
+ align:start position:0%
+presentation that's given at a
+ 
+
+ align:start position:0%
+presentation that's given at a
+preliminary design review uh whether
+
+ align:start position:0%
+preliminary design review uh whether
+ 
+
+ align:start position:0%
+preliminary design review uh whether
+it's a physical prototype that they
+
+ align:start position:0%
+it's a physical prototype that they
+ 
+
+ align:start position:0%
+it's a physical prototype that they
+present as as a team um so that always
+
+ align:start position:0%
+present as as a team um so that always
+ 
+
+ align:start position:0%
+present as as a team um so that always
+should be the first um thing that is
+
+ align:start position:0%
+should be the first um thing that is
+ 
+
+ align:start position:0%
+should be the first um thing that is
+assessed is what is the net output that
+
+ align:start position:0%
+assessed is what is the net output that
+ 
+
+ align:start position:0%
+assessed is what is the net output that
+that the team has produced um within
+
+ align:start position:0%
+that the team has produced um within
+ 
+
+ align:start position:0%
+that the team has produced um within
+that uh it is not always easy to discern
+
+ align:start position:0%
+that uh it is not always easy to discern
+ 
+
+ align:start position:0%
+that uh it is not always easy to discern
+what has been the individual
+
+ align:start position:0%
+what has been the individual
+ 
+
+ align:start position:0%
+what has been the individual
+contribution since the the whole purpose
+
+ align:start position:0%
+contribution since the the whole purpose
+ 
+
+ align:start position:0%
+contribution since the the whole purpose
+of a team is that you know the the sum
+
+ align:start position:0%
+of a team is that you know the the sum
+ 
+
+ align:start position:0%
+of a team is that you know the the sum
+that comes out is greater than the
+
+ align:start position:0%
+that comes out is greater than the
+ 
+
+ align:start position:0%
+that comes out is greater than the
+individual parts so in the best
+
+ align:start position:0%
+individual parts so in the best
+ 
+
+ align:start position:0%
+individual parts so in the best
+functioning teams there's a magic that
+
+ align:start position:0%
+functioning teams there's a magic that
+ 
+
+ align:start position:0%
+functioning teams there's a magic that
+happens there there's a Synergy that
+
+ align:start position:0%
+happens there there's a Synergy that
+ 
+
+ align:start position:0%
+happens there there's a Synergy that
+happens there's an output that's only
+
+ align:start position:0%
+happens there's an output that's only
+ 
+
+ align:start position:0%
+happens there's an output that's only
+produced by these synergistic
+
+ align:start position:0%
+produced by these synergistic
+ 
+
+ align:start position:0%
+produced by these synergistic
+interactions of all the team members in
+
+ align:start position:0%
+interactions of all the team members in
+ 
+
+ align:start position:0%
+interactions of all the team members in
+in a sense
+
+ align:start position:0%
+in a sense
+ 
+
+ align:start position:0%
+in a sense
+um trying to dissect you know what's the
+
+ align:start position:0%
+um trying to dissect you know what's the
+ 
+
+ align:start position:0%
+um trying to dissect you know what's the
+individual piece that everybody did is
+
+ align:start position:0%
+individual piece that everybody did is
+ 
+
+ align:start position:0%
+individual piece that everybody did is
+counter this idea of Team Synergy that
+
+ align:start position:0%
+counter this idea of Team Synergy that
+ 
+
+ align:start position:0%
+counter this idea of Team Synergy that
+being said we also need to um assess
+
+ align:start position:0%
+being said we also need to um assess
+ 
+
+ align:start position:0%
+being said we also need to um assess
+individually the contributions and the
+
+ align:start position:0%
+individually the contributions and the
+ 
+
+ align:start position:0%
+individually the contributions and the
+learnings of students and we do this
+
+ align:start position:0%
+learnings of students and we do this
+ 
+
+ align:start position:0%
+learnings of students and we do this
+through a couple of mechanisms for
+
+ align:start position:0%
+through a couple of mechanisms for
+ 
+
+ align:start position:0%
+through a couple of mechanisms for
+example a peer review uh so you can do a
+
+ align:start position:0%
+example a peer review uh so you can do a
+ 
+
+ align:start position:0%
+example a peer review uh so you can do a
+peer review process uh it's trickier in
+
+ align:start position:0%
+peer review process uh it's trickier in
+ 
+
+ align:start position:0%
+peer review process uh it's trickier in
+smaller teams than in larger teams but
+
+ align:start position:0%
+smaller teams than in larger teams but
+ 
+
+ align:start position:0%
+smaller teams than in larger teams but
+um if it's done properly peer review can
+
+ align:start position:0%
+um if it's done properly peer review can
+ 
+
+ align:start position:0%
+um if it's done properly peer review can
+be very effective in in not only helping
+
+ align:start position:0%
+be very effective in in not only helping
+ 
+
+ align:start position:0%
+be very effective in in not only helping
+one understand you know who who um who
+
+ align:start position:0%
+one understand you know who who um who
+ 
+
+ align:start position:0%
+one understand you know who who um who
+are the
+
+ align:start position:0%
+are the
+ 
+
+ align:start position:0%
+are the
+contributors and who are the Free Riders
+
+ align:start position:0%
+contributors and who are the Free Riders
+ 
+
+ align:start position:0%
+contributors and who are the Free Riders
+this is always a big issue in teams is
+
+ align:start position:0%
+this is always a big issue in teams is
+ 
+
+ align:start position:0%
+this is always a big issue in teams is
+that the free riter syndrome where uh
+
+ align:start position:0%
+that the free riter syndrome where uh
+ 
+
+ align:start position:0%
+that the free riter syndrome where uh
+some team members contribute
+
+ align:start position:0%
+some team members contribute
+ 
+
+ align:start position:0%
+some team members contribute
+significantly less than others and this
+
+ align:start position:0%
+significantly less than others and this
+ 
+
+ align:start position:0%
+significantly less than others and this
+is often The Source can be a source of
+
+ align:start position:0%
+is often The Source can be a source of
+ 
+
+ align:start position:0%
+is often The Source can be a source of
+conflict
+
+ align:start position:0%
+conflict
+ 
+
+ align:start position:0%
+conflict
+and so understanding this is important
+
+ align:start position:0%
+and so understanding this is important
+ 
+
+ align:start position:0%
+and so understanding this is important
+but also having other mechanisms in the
+
+ align:start position:0%
+but also having other mechanisms in the
+ 
+
+ align:start position:0%
+but also having other mechanisms in the
+class such as an individual final exam
+
+ align:start position:0%
+class such as an individual final exam
+ 
+
+ align:start position:0%
+class such as an individual final exam
+and then the other uh written exam which
+
+ align:start position:0%
+and then the other uh written exam which
+ 
+
+ align:start position:0%
+and then the other uh written exam which
+is administered online and the other
+
+ align:start position:0%
+is administered online and the other
+ 
+
+ align:start position:0%
+is administered online and the other
+thing we started doing is oral exams
+
+ align:start position:0%
+thing we started doing is oral exams
+ 
+
+ align:start position:0%
+thing we started doing is oral exams
+which seems oldfashioned but I have to
+
+ align:start position:0%
+which seems oldfashioned but I have to
+ 
+
+ align:start position:0%
+which seems oldfashioned but I have to
+tell you in 15 to 20 minutes of a
+
+ align:start position:0%
+tell you in 15 to 20 minutes of a
+ 
+
+ align:start position:0%
+tell you in 15 to 20 minutes of a
+one-on-one conversation with a student
+
+ align:start position:0%
+one-on-one conversation with a student
+ 
+
+ align:start position:0%
+one-on-one conversation with a student
+at the end of the class you really learn
+
+ align:start position:0%
+at the end of the class you really learn
+ 
+
+ align:start position:0%
+at the end of the class you really learn
+a lot you learn a lot about what they've
+
+ align:start position:0%
+a lot you learn a lot about what they've
+ 
+
+ align:start position:0%
+a lot you learn a lot about what they've
+learned uh where they may still have
+
+ align:start position:0%
+learned uh where they may still have
+ 
+
+ align:start position:0%
+learned uh where they may still have
+confusion or misconceptions and also the
+
+ align:start position:0%
+confusion or misconceptions and also the
+ 
+
+ align:start position:0%
+confusion or misconceptions and also the
+feedback that they give you so I highly
+
+ align:start position:0%
+feedback that they give you so I highly
+ 
+
+ align:start position:0%
+feedback that they give you so I highly
+recommend to do oral exams if it's
+
+ align:start position:0%
+recommend to do oral exams if it's
+ 
+
+ align:start position:0%
+recommend to do oral exams if it's
+possible
\ No newline at end of file
diff --git a/0su7rM_7_DM.txt b/0su7rM_7_DM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..78824eea273b85097eb25c37f49dff3f167975a7
--- /dev/null
+++ b/0su7rM_7_DM.txt
@@ -0,0 +1,9797 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu you'll recall the last class
+
+ align:start position:0%
+ocw.mit.edu you'll recall the last class
+ 
+
+ align:start position:0%
+ocw.mit.edu you'll recall the last class
+was the third
+
+ align:start position:0%
+was the third
+ 
+
+ align:start position:0%
+was the third
+of conception models this one dealing
+
+ align:start position:0%
+of conception models this one dealing
+ 
+
+ align:start position:0%
+of conception models this one dealing
+with the organic shape of Nature and its
+
+ align:start position:0%
+with the organic shape of Nature and its
+ 
+
+ align:start position:0%
+with the organic shape of Nature and its
+replication
+
+ align:start position:0%
+replication
+ 
+
+ align:start position:0%
+replication
+in patterning of
+
+ align:start position:0%
+in patterning of
+ 
+
+ align:start position:0%
+in patterning of
+cities we focused
+
+ align:start position:0%
+cities we focused
+ 
+
+ align:start position:0%
+cities we focused
+on a number of
+
+ align:start position:0%
+on a number of
+ 
+
+ align:start position:0%
+on a number of
+examples one of which
+
+ align:start position:0%
+examples one of which
+ 
+
+ align:start position:0%
+examples one of which
+was uh the work of Patrick GES the
+
+ align:start position:0%
+was uh the work of Patrick GES the
+ 
+
+ align:start position:0%
+was uh the work of Patrick GES the
+second one was the work of ebena Harden
+
+ align:start position:0%
+second one was the work of ebena Harden
+ 
+
+ align:start position:0%
+second one was the work of ebena Harden
+the Garden City movement the third was
+
+ align:start position:0%
+the Garden City movement the third was
+ 
+
+ align:start position:0%
+the Garden City movement the third was
+the work of Claren Stein and hry Wright
+
+ align:start position:0%
+the work of Claren Stein and hry Wright
+ 
+
+ align:start position:0%
+the work of Claren Stein and hry Wright
+in the United
+
+ align:start position:0%
+in the United
+ 
+
+ align:start position:0%
+in the United
+States and
+
+ align:start position:0%
+States and
+ 
+
+ align:start position:0%
+States and
+the and then I did a short run through
+
+ align:start position:0%
+the and then I did a short run through
+ 
+
+ align:start position:0%
+the and then I did a short run through
+of uh a piece that I wrote last year for
+
+ align:start position:0%
+of uh a piece that I wrote last year for
+ 
+
+ align:start position:0%
+of uh a piece that I wrote last year for
+conference in Athens on nature and the
+
+ align:start position:0%
+conference in Athens on nature and the
+ 
+
+ align:start position:0%
+conference in Athens on nature and the
+city in which I argued that there was
+
+ align:start position:0%
+city in which I argued that there was
+ 
+
+ align:start position:0%
+city in which I argued that there was
+the most dynamic thing about cities is
+
+ align:start position:0%
+the most dynamic thing about cities is
+ 
+
+ align:start position:0%
+the most dynamic thing about cities is
+it's it's is our human capacity to learn
+
+ align:start position:0%
+it's it's is our human capacity to learn
+ 
+
+ align:start position:0%
+it's it's is our human capacity to learn
+and to adapt to change and I try to show
+
+ align:start position:0%
+and to adapt to change and I try to show
+ 
+
+ align:start position:0%
+and to adapt to change and I try to show
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh that in the life
+
+ align:start position:0%
+uh that in the life
+ 
+
+ align:start position:0%
+uh that in the life
+of 70 years of
+
+ align:start position:0%
+of 70 years of
+ 
+
+ align:start position:0%
+of 70 years of
+the Tennessee Valley
+
+ align:start position:0%
+the Tennessee Valley
+ 
+
+ align:start position:0%
+the Tennessee Valley
+Authority the capacity to change the
+
+ align:start position:0%
+Authority the capacity to change the
+ 
+
+ align:start position:0%
+Authority the capacity to change the
+perspective about what
+
+ align:start position:0%
+perspective about what
+ 
+
+ align:start position:0%
+perspective about what
+nature
+
+ align:start position:0%
+nature
+ 
+
+ align:start position:0%
+nature
+is uh nature is no static phenomenon
+
+ align:start position:0%
+is uh nature is no static phenomenon
+ 
+
+ align:start position:0%
+is uh nature is no static phenomenon
+it's uh it's a pro it's a learning of
+
+ align:start position:0%
+it's uh it's a pro it's a learning of
+ 
+
+ align:start position:0%
+it's uh it's a pro it's a learning of
+patterns as previously identified in
+
+ align:start position:0%
+patterns as previously identified in
+ 
+
+ align:start position:0%
+patterns as previously identified in
+organic systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+selectively so it's requires the human
+
+ align:start position:0%
+selectively so it's requires the human
+ 
+
+ align:start position:0%
+selectively so it's requires the human
+brain and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the Tennessee Valley Authority built
+
+ align:start position:0%
+uh the Tennessee Valley Authority built
+ 
+
+ align:start position:0%
+uh the Tennessee Valley Authority built
+28 Dam
+
+ align:start position:0%
+28 Dam
+ 
+
+ align:start position:0%
+28 Dam
+on the concept that dams that water
+
+ align:start position:0%
+on the concept that dams that water
+ 
+
+ align:start position:0%
+on the concept that dams that water
+power was more
+
+ align:start position:0%
+power was more
+ 
+
+ align:start position:0%
+power was more
+hygienic and would be sufficient for
+
+ align:start position:0%
+hygienic and would be sufficient for
+ 
+
+ align:start position:0%
+hygienic and would be sufficient for
+creating a new industrial Zone in the
+
+ align:start position:0%
+creating a new industrial Zone in the
+ 
+
+ align:start position:0%
+creating a new industrial Zone in the
+eight states of this of the Tennessee
+
+ align:start position:0%
+eight states of this of the Tennessee
+ 
+
+ align:start position:0%
+eight states of this of the Tennessee
+Valley 65% of the power now is not
+
+ align:start position:0%
+Valley 65% of the power now is not
+ 
+
+ align:start position:0%
+Valley 65% of the power now is not
+generated by
+
+ align:start position:0%
+generated by
+ 
+
+ align:start position:0%
+generated by
+water the prediction of the economic
+
+ align:start position:0%
+water the prediction of the economic
+ 
+
+ align:start position:0%
+water the prediction of the economic
+growth in this region is was very low
+
+ align:start position:0%
+growth in this region is was very low
+ 
+
+ align:start position:0%
+growth in this region is was very low
+also the capacity of the water to
+
+ align:start position:0%
+also the capacity of the water to
+ 
+
+ align:start position:0%
+also the capacity of the water to
+produce enough energy was low
+
+ align:start position:0%
+produce enough energy was low
+ 
+
+ align:start position:0%
+produce enough energy was low
+so what happened
+
+ align:start position:0%
+so what happened
+ 
+
+ align:start position:0%
+so what happened
+coal became the substitute coal led to
+
+ align:start position:0%
+coal became the substitute coal led to
+ 
+
+ align:start position:0%
+coal became the substitute coal led to
+strip mining which is as
+
+ align:start position:0%
+strip mining which is as
+ 
+
+ align:start position:0%
+strip mining which is as
+anti-natural phenomenon as you can
+
+ align:start position:0%
+anti-natural phenomenon as you can
+ 
+
+ align:start position:0%
+anti-natural phenomenon as you can
+imagine the largest environmental
+
+ align:start position:0%
+imagine the largest environmental
+ 
+
+ align:start position:0%
+imagine the largest environmental
+disaster in the United States happened
+
+ align:start position:0%
+disaster in the United States happened
+ 
+
+ align:start position:0%
+disaster in the United States happened
+in the Cal spill from one of the coal
+
+ align:start position:0%
+in the Cal spill from one of the coal
+ 
+
+ align:start position:0%
+in the Cal spill from one of the coal
+generating plants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so on and so on and we went through
+
+ align:start position:0%
+and so on and so on and we went through
+ 
+
+ align:start position:0%
+and so on and so on and we went through
+uh an argument which suggests that
+
+ align:start position:0%
+uh an argument which suggests that
+ 
+
+ align:start position:0%
+uh an argument which suggests that
+nature is still a phenomenon which is
+
+ align:start position:0%
+nature is still a phenomenon which is
+ 
+
+ align:start position:0%
+nature is still a phenomenon which is
+understood through the process of the
+
+ align:start position:0%
+understood through the process of the
+ 
+
+ align:start position:0%
+understood through the process of the
+human
+
+ align:start position:0%
+human
+ 
+
+ align:start position:0%
+human
+brain there's no absolute
+
+ align:start position:0%
+brain there's no absolute
+ 
+
+ align:start position:0%
+brain there's no absolute
+correctness of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nature biomorphism is a foolish project
+
+ align:start position:0%
+nature biomorphism is a foolish project
+ 
+
+ align:start position:0%
+nature biomorphism is a foolish project
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+architects who should understand a much
+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+on Fifth Avenue New
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+
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+ align:start position:0%
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+
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+
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+
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+
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+
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+ 
+
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+problematic what I've given you
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
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+ align:start position:0%
+ 
+ 
+
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+um are some functional descriptive
+
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+ 
+
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+
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+ 
+
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+
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+ 
+
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+
+ align:start position:0%
+with an example
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
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+
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+it proposes what its weaknesses are this
+ 
+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
+semester in City Planning education it's
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
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+
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+classical theories which no longer are
+ 
+
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+
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+interesting to anybody um the second
+ 
+
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+
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+page the first page deals with the
+ 
+
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+application of one of the these theories
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+
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+
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+ho to
+ 
+
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+Atlanta you can see the sector theory in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Atlanta indicating the location of High
+
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+Atlanta indicating the location of High
+ 
+
+ align:start position:0%
+Atlanta indicating the location of High
+income white
+
+ align:start position:0%
+income white
+ 
+
+ align:start position:0%
+income white
+housing um as opposed to lwi income
+
+ align:start position:0%
+housing um as opposed to lwi income
+ 
+
+ align:start position:0%
+housing um as opposed to lwi income
+housing um following a model purported
+
+ align:start position:0%
+housing um following a model purported
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+
+ align:start position:0%
+housing um following a model purported
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+
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+
+ align:start position:0%
+by H hoit in
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+the next page deals with uh examination
+
+ align:start position:0%
+the next page deals with uh examination
+ 
+
+ align:start position:0%
+the next page deals with uh examination
+of
+
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+of
+ 
+
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+two figures in in Great Britain who
+
+ align:start position:0%
+two figures in in Great Britain who
+ 
+
+ align:start position:0%
+two figures in in Great Britain who
+lived more or less at the same time John
+
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+lived more or less at the same time John
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+
+ align:start position:0%
+lived more or less at the same time John
+Rus and
+
+ align:start position:0%
+Rus and
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+
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+Rus and
+the theorist of AR theorist of
+
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+the theorist of AR theorist of
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+
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+the theorist of AR theorist of
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+
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+Engles um who we will discuss more fully
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+
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+Engles um who we will discuss more fully
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+
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+
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+
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+Manifesto and
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+
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+
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+uh in 1845 at the age of 25 he wrote one
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+
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+uh in 1845 at the age of 25 he wrote one
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+
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+
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+
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+
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+when we talk about the origins the
+ 
+
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+industrial city the next
+
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+industrial city the next
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+
+ align:start position:0%
+industrial city the next
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+
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+page is from a diagram by Mal Weber in a
+ 
+
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+page is from a diagram by Mal Weber in a
+book called urban place and non-place
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+book called urban place and non-place
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+
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+
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+ 
+
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+
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+
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+
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+
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+
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+
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+conventional uh economic models uh or
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+
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+conventional uh economic models uh or
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+
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+even physical models of
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+
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+even physical models of
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+interaction uh and an old model
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+
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+interaction uh and an old model
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+ 
+
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+uh a book called A Communications theory
+
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+uh a book called A Communications theory
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+
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+uh a book called A Communications theory
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+
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+ 
+
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+
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+
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+
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+ 
+
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+last this the next
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+ 
+
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+ 
+page is from economic
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+
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+geography and
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+
+ align:start position:0%
+ 
+ 
+
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+ 
+diagrams and then next we'll finish with
+
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+diagrams and then next we'll finish with
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+
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+diagrams and then next we'll finish with
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+
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+cont a very recent piece from The New
+ 
+
+ align:start position:0%
+cont a very recent piece from The New
+York
+
+ align:start position:0%
+York
+ 
+
+ align:start position:0%
+York
+Times uh in which a physicist solves the
+
+ align:start position:0%
+Times uh in which a physicist solves the
+ 
+
+ align:start position:0%
+Times uh in which a physicist solves the
+city
+
+ align:start position:0%
+city
+ 
+
+ align:start position:0%
+city
+uh this is hopefully what we will finish
+
+ align:start position:0%
+uh this is hopefully what we will finish
+ 
+
+ align:start position:0%
+uh this is hopefully what we will finish
+with the question is does it really make
+
+ align:start position:0%
+with the question is does it really make
+ 
+
+ align:start position:0%
+with the question is does it really make
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+
+ align:start position:0%
+any sense at
+ 
+
+ align:start position:0%
+any sense at
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+
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+all but we'll look at the work
+ 
+
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+all but we'll look at the work
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+
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+of these people dealing with models of
+ 
+
+ align:start position:0%
+of these people dealing with models of
+complex Theory at the
+
+ align:start position:0%
+complex Theory at the
+ 
+
+ align:start position:0%
+complex Theory at the
+moment the first let's go through these
+
+ align:start position:0%
+moment the first let's go through these
+ 
+
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+moment the first let's go through these
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+
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+very quickly
+ 
+
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+
+ align:start position:0%
+the
+ 
+
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+the
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+first by the way these breakdowns were
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+
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+created in this class with Kevin Lynch
+ 
+
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+created in this class with Kevin Lynch
+and follows them to some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extent cities are you seen as unique
+
+ align:start position:0%
+extent cities are you seen as unique
+ 
+
+ align:start position:0%
+extent cities are you seen as unique
+historical
+
+ align:start position:0%
+historical
+ 
+
+ align:start position:0%
+historical
+processes uh each city is a unique
+
+ align:start position:0%
+processes uh each city is a unique
+ 
+
+ align:start position:0%
+processes uh each city is a unique
+cumulative historical process a city can
+
+ align:start position:0%
+cumulative historical process a city can
+ 
+
+ align:start position:0%
+cumulative historical process a city can
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+
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+only be explained by telling a
+ 
+
+ align:start position:0%
+only be explained by telling a
+story you cannot generalize ize very
+
+ align:start position:0%
+story you cannot generalize ize very
+ 
+
+ align:start position:0%
+story you cannot generalize ize very
+much about cities what you can
+
+ align:start position:0%
+much about cities what you can
+ 
+
+ align:start position:0%
+much about cities what you can
+generalize about is the way of reading a
+
+ align:start position:0%
+generalize about is the way of reading a
+ 
+
+ align:start position:0%
+generalize about is the way of reading a
+city you you have to learn a standard
+
+ align:start position:0%
+city you you have to learn a standard
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+
+ align:start position:0%
+city you you have to learn a standard
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+
+ align:start position:0%
+way of looking at them so for instance
+ 
+
+ align:start position:0%
+way of looking at them so for instance
+rasmusen says Two Chief types are
+
+ align:start position:0%
+rasmusen says Two Chief types are
+ 
+
+ align:start position:0%
+rasmusen says Two Chief types are
+distinguishable among among large cities
+
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+distinguishable among among large cities
+ 
+
+ align:start position:0%
+distinguishable among among large cities
+the concentrated and the scattered the
+
+ align:start position:0%
+the concentrated and the scattered the
+ 
+
+ align:start position:0%
+the concentrated and the scattered the
+former is the more common on the
+
+ align:start position:0%
+former is the more common on the
+ 
+
+ align:start position:0%
+former is the more common on the
+continent is clearly represented by the
+
+ align:start position:0%
+continent is clearly represented by the
+ 
+
+ align:start position:0%
+continent is clearly represented by the
+big government seats of Paris and Vienna
+
+ align:start position:0%
+big government seats of Paris and Vienna
+ 
+
+ align:start position:0%
+big government seats of Paris and Vienna
+and so on the second type is represented
+
+ align:start position:0%
+and so on the second type is represented
+ 
+
+ align:start position:0%
+and so on the second type is represented
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+
+ align:start position:0%
+by the English town which now to many of
+ 
+
+ align:start position:0%
+by the English town which now to many of
+us seems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideal the question of what is unique and
+
+ align:start position:0%
+ideal the question of what is unique and
+ 
+
+ align:start position:0%
+ideal the question of what is unique and
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+generalized is a difference in some of
+
+ align:start position:0%
+generalized is a difference in some of
+ 
+
+ align:start position:0%
+generalized is a difference in some of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+propositions even within this
+
+ align:start position:0%
+propositions even within this
+ 
+
+ align:start position:0%
+propositions even within this
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+
+ align:start position:0%
+proposition of this the the unique
+ 
+
+ align:start position:0%
+proposition of this the the unique
+historic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process you have a book like Alan
+
+ align:start position:0%
+process you have a book like Alan
+ 
+
+ align:start position:0%
+process you have a book like Alan
+jacobs's book on
+
+ align:start position:0%
+jacobs's book on
+ 
+
+ align:start position:0%
+jacobs's book on
+streets which by the way doesn't include
+
+ align:start position:0%
+streets which by the way doesn't include
+ 
+
+ align:start position:0%
+streets which by the way doesn't include
+the nki prospect which is one of the
+
+ align:start position:0%
+the nki prospect which is one of the
+ 
+
+ align:start position:0%
+the nki prospect which is one of the
+great streets in the world it's only
+
+ align:start position:0%
+great streets in the world it's only
+ 
+
+ align:start position:0%
+great streets in the world it's only
+streets that Alan Jacobs has visited in
+
+ align:start position:0%
+streets that Alan Jacobs has visited in
+ 
+
+ align:start position:0%
+streets that Alan Jacobs has visited in
+science I don't know if you can
+
+ align:start position:0%
+science I don't know if you can
+ 
+
+ align:start position:0%
+science I don't know if you can
+do experimentation on the basis of only
+
+ align:start position:0%
+do experimentation on the basis of only
+ 
+
+ align:start position:0%
+do experimentation on the basis of only
+what you have visited but it's okay we
+
+ align:start position:0%
+what you have visited but it's okay we
+ 
+
+ align:start position:0%
+what you have visited but it's okay we
+are we we we
+
+ align:start position:0%
+are we we we
+ 
+
+ align:start position:0%
+are we we we
+handicapped uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the cities the streets that he
+
+ align:start position:0%
+but the cities the streets that he
+ 
+
+ align:start position:0%
+but the cities the streets that he
+identifies uh are un each is unique it
+
+ align:start position:0%
+identifies uh are un each is unique it
+ 
+
+ align:start position:0%
+identifies uh are un each is unique it
+gives measurements of its width it give
+
+ align:start position:0%
+gives measurements of its width it give
+ 
+
+ align:start position:0%
+gives measurements of its width it give
+dimensions of the density around the
+
+ align:start position:0%
+dimensions of the density around the
+ 
+
+ align:start position:0%
+dimensions of the density around the
+street whereas bia's propositions which
+
+ align:start position:0%
+street whereas bia's propositions which
+ 
+
+ align:start position:0%
+street whereas bia's propositions which
+I'll discuss next Tuesday amongst others
+
+ align:start position:0%
+I'll discuss next Tuesday amongst others
+ 
+
+ align:start position:0%
+I'll discuss next Tuesday amongst others
+space syntax looks at streets merely as
+
+ align:start position:0%
+space syntax looks at streets merely as
+ 
+
+ align:start position:0%
+space syntax looks at streets merely as
+linkages in a topological environment in
+
+ align:start position:0%
+linkages in a topological environment in
+ 
+
+ align:start position:0%
+linkages in a topological environment in
+which if you understand the GE geometry
+
+ align:start position:0%
+which if you understand the GE geometry
+ 
+
+ align:start position:0%
+which if you understand the GE geometry
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+ align:start position:0%
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+ 
+
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+
+ align:start position:0%
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+
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+
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+
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+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+for a small town which had had no
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+student excuse me proposed to start a
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+
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+
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+ 
+ 
+
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+
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+anyway was that there wasn't much debate
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+
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+
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+
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+ 
+
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+
+ align:start position:0%
+but it wasn't uh it was in New York and
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+
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+but it wasn't uh it was in New York and
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+
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+I felt like a provincial from Boston so
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+
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+
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+I had nothing to say um but it was a
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+
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+
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+
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+
+ align:start position:0%
+withstand Notions of change and
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+
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+
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+
+ align:start position:0%
+of cases used by the John Carlo De Carlo
+ 
+
+ align:start position:0%
+of cases used by the John Carlo De Carlo
+in the El schools in uh in Italy um and
+
+ align:start position:0%
+in the El schools in uh in Italy um and
+ 
+
+ align:start position:0%
+in the El schools in uh in Italy um and
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+
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+so I took two examples by two great men
+ 
+
+ align:start position:0%
+so I took two examples by two great men
+John
+
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+ 
+ 
+
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+
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+
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+
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+ 
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+
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+
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+uh Li there was nothing to do so look
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+
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+
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+
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+
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+
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+
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+
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+
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+ align:start position:0%
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+ 
+
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+
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+
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+
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+ 
+
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+
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+
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+Oxford he says that reading is an
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+ 
+ 
+
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+
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+
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+
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+ 
+
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+
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+ 
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+
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+
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+
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+
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+ 
+ 
+
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+implications it's interesting that under
+
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+implications it's interesting that under
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+
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+
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+
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+ 
+
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+
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+1917 cities were not considered as
+ 
+
+ align:start position:0%
+1917 cities were not considered as
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+dialogue there were larger issues at
+
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+dialogue there were larger issues at
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+
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+dialogue there were larger issues at
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+
+ align:start position:0%
+hand you had to change the structure of
+ 
+
+ align:start position:0%
+hand you had to change the structure of
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+
+ align:start position:0%
+society and in as a byproduct cities
+ 
+
+ align:start position:0%
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+would change
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+automatically they doesn't work that way
+
+ align:start position:0%
+automatically they doesn't work that way
+ 
+
+ align:start position:0%
+automatically they doesn't work that way
+but so was the doctrine of early Marxist
+
+ align:start position:0%
+but so was the doctrine of early Marxist
+ 
+
+ align:start position:0%
+but so was the doctrine of early Marxist
+so Soviet
+
+ align:start position:0%
+so Soviet
+ 
+
+ align:start position:0%
+so Soviet
+Marxism and Engles himself
+
+ align:start position:0%
+Marxism and Engles himself
+ 
+
+ align:start position:0%
+Marxism and Engles himself
+changed uh there's a wonderful book
+
+ align:start position:0%
+changed uh there's a wonderful book
+ 
+
+ align:start position:0%
+changed uh there's a wonderful book
+called Marx's General recently published
+
+ align:start position:0%
+called Marx's General recently published
+ 
+
+ align:start position:0%
+called Marx's General recently published
+by an English writer which discusses
+
+ align:start position:0%
+by an English writer which discusses
+ 
+
+ align:start position:0%
+by an English writer which discusses
+engel's
+
+ align:start position:0%
+engel's
+ 
+
+ align:start position:0%
+engel's
+history uh in relation to Hegel and
+
+ align:start position:0%
+history uh in relation to Hegel and
+ 
+
+ align:start position:0%
+history uh in relation to Hegel and
+the Engles attended was in the Army in
+
+ align:start position:0%
+the Engles attended was in the Army in
+ 
+
+ align:start position:0%
+the Engles attended was in the Army in
+Berlin doing nothing so he attended a CL
+
+ align:start position:0%
+Berlin doing nothing so he attended a CL
+ 
+
+ align:start position:0%
+Berlin doing nothing so he attended a CL
+and religious philosophy taught at the
+
+ align:start position:0%
+and religious philosophy taught at the
+ 
+
+ align:start position:0%
+and religious philosophy taught at the
+University at that time religion was a
+
+ align:start position:0%
+University at that time religion was a
+ 
+
+ align:start position:0%
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+fundamental component of the study of
+
+ align:start position:0%
+fundamental component of the study of
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+philosophy in his class was nor was
+ 
+
+ align:start position:0%
+philosophy in his class was nor was
+skot bakunin the Russian
+
+ align:start position:0%
+skot bakunin the Russian
+ 
+
+ align:start position:0%
+skot bakunin the Russian
+Anarchist uh uh I forget the names of
+
+ align:start position:0%
+Anarchist uh uh I forget the names of
+ 
+
+ align:start position:0%
+Anarchist uh uh I forget the names of
+the others people who were there at the
+
+ align:start position:0%
+the others people who were there at the
+ 
+
+ align:start position:0%
+the others people who were there at the
+same time questioning whether
+
+ align:start position:0%
+same time questioning whether
+ 
+
+ align:start position:0%
+same time questioning whether
+Hegel hegel's work had just been started
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+to be
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+
+ align:start position:0%
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Engles
+
+ align:start position:0%
+Engles
+ 
+
+ align:start position:0%
+Engles
+again started
+
+ align:start position:0%
+again started
+ 
+
+ align:start position:0%
+again started
+adapting the pur purist Marxist
+
+ align:start position:0%
+adapting the pur purist Marxist
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+facing uh in different parts of Europe
+ 
+
+ align:start position:0%
+facing uh in different parts of Europe
+as he
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+traveled the notion
+
+ align:start position:0%
+traveled the notion
+ 
+
+ align:start position:0%
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+of historians who claim the uniqueness
+
+ align:start position:0%
+of historians who claim the uniqueness
+ 
+
+ align:start position:0%
+of historians who claim the uniqueness
+of cities is
+
+ align:start position:0%
+of cities is
+ 
+
+ align:start position:0%
+of cities is
+widespread um writing about
+
+ align:start position:0%
+widespread um writing about
+ 
+
+ align:start position:0%
+widespread um writing about
+Venice um Mary McCarthy says there's
+
+ align:start position:0%
+Venice um Mary McCarthy says there's
+ 
+
+ align:start position:0%
+Venice um Mary McCarthy says there's
+nothing more to be said about Venice and
+
+ align:start position:0%
+nothing more to be said about Venice and
+ 
+
+ align:start position:0%
+nothing more to be said about Venice and
+quotes Napoleon Rasen Shelly PR all
+
+ align:start position:0%
+quotes Napoleon Rasen Shelly PR all
+ 
+
+ align:start position:0%
+quotes Napoleon Rasen Shelly PR all
+saying the same
+
+ align:start position:0%
+saying the same
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+
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+Venice says the newcomer I pity you says
+
+ align:start position:0%
+Venice says the newcomer I pity you says
+ 
+
+ align:start position:0%
+Venice says the newcomer I pity you says
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+
+ align:start position:0%
+the old hand there's something a little
+ 
+
+ align:start position:0%
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+boring about saying the same things
+
+ align:start position:0%
+boring about saying the same things
+ 
+
+ align:start position:0%
+boring about saying the same things
+about a city uh Walter Benjamin is a
+
+ align:start position:0%
+about a city uh Walter Benjamin is a
+ 
+
+ align:start position:0%
+about a city uh Walter Benjamin is a
+much more lively character a German
+
+ align:start position:0%
+much more lively character a German
+ 
+
+ align:start position:0%
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+philosopher who died in 1940 but wrote
+
+ align:start position:0%
+philosopher who died in 1940 but wrote
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+
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+particularly
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+interesting never nevertheless no City
+
+ align:start position:0%
+interesting never nevertheless no City
+ 
+
+ align:start position:0%
+interesting never nevertheless no City
+can fade in the few hours of Sunday rest
+
+ align:start position:0%
+can fade in the few hours of Sunday rest
+ 
+
+ align:start position:0%
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+more rapidly than
+
+ align:start position:0%
+more rapidly than
+ 
+
+ align:start position:0%
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+Naples here's a theory of the speed at
+
+ align:start position:0%
+Naples here's a theory of the speed at
+ 
+
+ align:start position:0%
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+which a city changes its form from
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+which a city changes its form from
+working to rest I don't know if any
+
+ align:start position:0%
+working to rest I don't know if any
+ 
+
+ align:start position:0%
+working to rest I don't know if any
+other person who's ever observed the
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+another he
+
+ align:start position:0%
+another he
+ 
+
+ align:start position:0%
+another he
+says the well-known list of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the seven deadly sins located pride
+
+ align:start position:0%
+of the seven deadly sins located pride
+ 
+
+ align:start position:0%
+of the seven deadly sins located pride
+in Genoa aest in Florence voluptuousness
+
+ align:start position:0%
+in Genoa aest in Florence voluptuousness
+ 
+
+ align:start position:0%
+in Genoa aest in Florence voluptuousness
+in Venice anger in bolognia greed in
+
+ align:start position:0%
+in Venice anger in bolognia greed in
+ 
+
+ align:start position:0%
+in Venice anger in bolognia greed in
+Milan Envy in Rome and indolence in
+
+ align:start position:0%
+Milan Envy in Rome and indolence in
+ 
+
+ align:start position:0%
+Milan Envy in Rome and indolence in
+Naples he
+
+ align:start position:0%
+Naples he
+ 
+
+ align:start position:0%
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+then he then you know goes on to talk
+
+ align:start position:0%
+then he then you know goes on to talk
+ 
+
+ align:start position:0%
+then he then you know goes on to talk
+about uh uh what indolence means and
+
+ align:start position:0%
+about uh uh what indolence means and
+ 
+
+ align:start position:0%
+about uh uh what indolence means and
+paracity of buildings and Builds an
+
+ align:start position:0%
+paracity of buildings and Builds an
+ 
+
+ align:start position:0%
+paracity of buildings and Builds an
+incredible Cent natur structure of this
+
+ align:start position:0%
+incredible Cent natur structure of this
+ 
+
+ align:start position:0%
+incredible Cent natur structure of this
+place what you do with it is not
+
+ align:start position:0%
+place what you do with it is not
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+important it's that a city is something
+ 
+
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+as particular as the gestures that
+
+ align:start position:0%
+as particular as the gestures that
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+people make with their hands he claims
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+that the gestures that people make with
+ 
+
+ align:start position:0%
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+their hands with their nose with their
+
+ align:start position:0%
+their hands with their nose with their
+ 
+
+ align:start position:0%
+their hands with their nose with their
+eyes with their breasts in Naples is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unique
+
+ align:start position:0%
+unique
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+so it g
+ 
+
+ align:start position:0%
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+you the extraordinary thing about B
+
+ align:start position:0%
+you the extraordinary thing about B
+ 
+
+ align:start position:0%
+you the extraordinary thing about B
+Walter Benjamin
+
+ align:start position:0%
+Walter Benjamin
+ 
+
+ align:start position:0%
+Walter Benjamin
+who is the tension between this attitude
+
+ align:start position:0%
+who is the tension between this attitude
+ 
+
+ align:start position:0%
+who is the tension between this attitude
+of finding the Deep structure of
+
+ align:start position:0%
+of finding the Deep structure of
+ 
+
+ align:start position:0%
+of finding the Deep structure of
+explanation of cities and being a
+
+ align:start position:0%
+explanation of cities and being a
+ 
+
+ align:start position:0%
+explanation of cities and being a
+Marxist
+
+ align:start position:0%
+Marxist
+ 
+
+ align:start position:0%
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+himself as a Marxist like Engles he
+
+ align:start position:0%
+himself as a Marxist like Engles he
+ 
+
+ align:start position:0%
+himself as a Marxist like Engles he
+would only see Naples as a generalized
+
+ align:start position:0%
+would only see Naples as a generalized
+ 
+
+ align:start position:0%
+would only see Naples as a generalized
+phenomenon of Human
+
+ align:start position:0%
+phenomenon of Human
+ 
+
+ align:start position:0%
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+Experience he would he would look for
+
+ align:start position:0%
+Experience he would he would look for
+ 
+
+ align:start position:0%
+Experience he would he would look for
+where poor people lived and where the
+
+ align:start position:0%
+where poor people lived and where the
+ 
+
+ align:start position:0%
+where poor people lived and where the
+forces of production were and so on
+
+ align:start position:0%
+forces of production were and so on
+ 
+
+ align:start position:0%
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+instead he's attracted by this
+
+ align:start position:0%
+instead he's attracted by this
+ 
+
+ align:start position:0%
+instead he's attracted by this
+uniqueness phenomenon everything is
+
+ align:start position:0%
+uniqueness phenomenon everything is
+ 
+
+ align:start position:0%
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+unique he writes about Paris in similar
+
+ align:start position:0%
+unique he writes about Paris in similar
+ 
+
+ align:start position:0%
+unique he writes about Paris in similar
+ways um much less interesting than alter
+
+ align:start position:0%
+ways um much less interesting than alter
+ 
+
+ align:start position:0%
+ways um much less interesting than alter
+Benjamin of whom I'm a big fan so I
+
+ align:start position:0%
+Benjamin of whom I'm a big fan so I
+ 
+
+ align:start position:0%
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+
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+ 
+
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+
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+ 
+
+ align:start position:0%
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+uh the architectural critic Nook Schulz
+
+ align:start position:0%
+uh the architectural critic Nook Schulz
+ 
+
+ align:start position:0%
+uh the architectural critic Nook Schulz
+the no
+
+ align:start position:0%
+the no
+ 
+
+ align:start position:0%
+the no
+Norwegian uh critic who has made a who
+
+ align:start position:0%
+Norwegian uh critic who has made a who
+ 
+
+ align:start position:0%
+Norwegian uh critic who has made a who
+wrote a book called genius
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+locai which suggests again that every
+
+ align:start position:0%
+locai which suggests again that every
+ 
+
+ align:start position:0%
+locai which suggests again that every
+town has a genius not every town he only
+
+ align:start position:0%
+town has a genius not every town he only
+ 
+
+ align:start position:0%
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+selects a couple uh and then tries to
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+selects a couple uh and then tries to
+explain what is the genius is so in
+
+ align:start position:0%
+explain what is the genius is so in
+ 
+
+ align:start position:0%
+explain what is the genius is so in
+Prague we read the following the
+
+ align:start position:0%
+Prague we read the following the
+ 
+
+ align:start position:0%
+Prague we read the following the
+fascination of Prague resides first of
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+all in a strong sense of mystery big
+ 
+
+ align:start position:0%
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+
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+ 
+
+ align:start position:0%
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+um you have the feeling that it's
+
+ align:start position:0%
+um you have the feeling that it's
+ 
+
+ align:start position:0%
+um you have the feeling that it's
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+possible to penetrate ever deeper into
+things streets Gates Courtyards have an
+
+ align:start position:0%
+things streets Gates Courtyards have an
+ 
+
+ align:start position:0%
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+endless inside now that is maybe a
+
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+endless inside now that is maybe a
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+Prague but as a theory it says terribly
+
+ align:start position:0%
+Prague but as a theory it says terribly
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much in carum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he says those who visit carum are
+
+ align:start position:0%
+he says those who visit carum are
+ 
+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
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+well am I not struck by a strong quality
+
+ align:start position:0%
+well am I not struck by a strong quality
+ 
+
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+well am I not struck by a strong quality
+of place if I enter
+
+ align:start position:0%
+of place if I enter
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+
+ align:start position:0%
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+Leon or is there measurement of the
+
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+
+ align:start position:0%
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+
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+carum as opposed to Leon there's no
+
+ align:start position:0%
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+ 
+
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+attempt to generalize about cities
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+whatsoever if s sence is about
+ 
+
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+generalization this is not anywhere near
+
+ align:start position:0%
+generalization this is not anywhere near
+ 
+
+ align:start position:0%
+generalization this is not anywhere near
+scientific it maybe what Architects do
+
+ align:start position:0%
+scientific it maybe what Architects do
+ 
+
+ align:start position:0%
+scientific it maybe what Architects do
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+reading or artists do which raises a
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+very big unresolved conflict in urbanism
+ 
+
+ align:start position:0%
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+
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+
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+
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+
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+
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+
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+
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+
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+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+urbanism it may be that the distinction
+ 
+
+ align:start position:0%
+urbanism it may be that the distinction
+is between learning about cities
+
+ align:start position:0%
+is between learning about cities
+ 
+
+ align:start position:0%
+is between learning about cities
+throughout history because youve look at
+
+ align:start position:0%
+throughout history because youve look at
+ 
+
+ align:start position:0%
+throughout history because youve look at
+Prague you think of of looking at Sean
+
+ align:start position:0%
+Prague you think of of looking at Sean
+ 
+
+ align:start position:0%
+Prague you think of of looking at Sean
+and although rudol AR the gal
+
+ align:start position:0%
+and although rudol AR the gal
+ 
+
+ align:start position:0%
+and although rudol AR the gal
+psychologist says that if you look at
+
+ align:start position:0%
+psychologist says that if you look at
+ 
+
+ align:start position:0%
+psychologist says that if you look at
+Sean you should follow the following
+
+ align:start position:0%
+Sean you should follow the following
+ 
+
+ align:start position:0%
+Sean you should follow the following
+path with your eyes from red to Yellow
+
+ align:start position:0%
+path with your eyes from red to Yellow
+ 
+
+ align:start position:0%
+path with your eyes from red to Yellow
+back to green and these forms all fit
+
+ align:start position:0%
+back to green and these forms all fit
+ 
+
+ align:start position:0%
+back to green and these forms all fit
+into a a scientific explanation of what
+
+ align:start position:0%
+into a a scientific explanation of what
+ 
+
+ align:start position:0%
+into a a scientific explanation of what
+you see that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ um we accept certain truths
+
+ align:start position:0%
+ um we accept certain truths
+ 
+
+ align:start position:0%
+ um we accept certain truths
+through ART the patterning of music
+
+ align:start position:0%
+through ART the patterning of music
+ 
+
+ align:start position:0%
+through ART the patterning of music
+is studied and available for
+
+ align:start position:0%
+is studied and available for
+ 
+
+ align:start position:0%
+is studied and available for
+your understanding but it is an
+
+ align:start position:0%
+your understanding but it is an
+ 
+
+ align:start position:0%
+your understanding but it is an
+intuitive experiential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phenomenon much of
+
+ align:start position:0%
+phenomenon much of
+ 
+
+ align:start position:0%
+phenomenon much of
+this these explanations are of that
+
+ align:start position:0%
+this these explanations are of that
+ 
+
+ align:start position:0%
+this these explanations are of that
+order they don't attempt to compare the
+
+ align:start position:0%
+order they don't attempt to compare the
+ 
+
+ align:start position:0%
+order they don't attempt to compare the
+amount of mystery in Rome versus the
+
+ align:start position:0%
+amount of mystery in Rome versus the
+ 
+
+ align:start position:0%
+amount of mystery in Rome versus the
+amount of mystery in carum or in
+
+ align:start position:0%
+amount of mystery in carum or in
+ 
+
+ align:start position:0%
+amount of mystery in carum or in
+Prague let's look go on very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quickly we've got half an
+
+ align:start position:0%
+quickly we've got half an
+ 
+
+ align:start position:0%
+quickly we've got half an
+hour there's a lot of reading available
+
+ align:start position:0%
+hour there's a lot of reading available
+ 
+
+ align:start position:0%
+hour there's a lot of reading available
+about each of these sectors so I
+
+ align:start position:0%
+about each of these sectors so I
+ 
+
+ align:start position:0%
+about each of these sectors so I
+will propose that if you're interested
+
+ align:start position:0%
+will propose that if you're interested
+ 
+
+ align:start position:0%
+will propose that if you're interested
+in any of these bodies of work uh either
+
+ align:start position:0%
+in any of these bodies of work uh either
+ 
+
+ align:start position:0%
+in any of these bodies of work uh either
+contact me and I'll give you more
+
+ align:start position:0%
+contact me and I'll give you more
+ 
+
+ align:start position:0%
+contact me and I'll give you more
+reading that if you need to do more
+
+ align:start position:0%
+reading that if you need to do more
+ 
+
+ align:start position:0%
+reading that if you need to do more
+reading
+
+ align:start position:0%
+reading
+ 
+
+ align:start position:0%
+reading
+is enough in this class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the next group of work is is number
+
+ align:start position:0%
+um the next group of work is is number
+ 
+
+ align:start position:0%
+um the next group of work is is number
+two Ecology of
+
+ align:start position:0%
+two Ecology of
+ 
+
+ align:start position:0%
+two Ecology of
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+um the idea that people as a group
+
+ align:start position:0%
+um the idea that people as a group
+ 
+
+ align:start position:0%
+um the idea that people as a group
+behave in in ways which pattern the
+
+ align:start position:0%
+behave in in ways which pattern the
+ 
+
+ align:start position:0%
+behave in in ways which pattern the
+city is most
+
+ align:start position:0%
+city is most
+ 
+
+ align:start position:0%
+city is most
+likely to be associated in the first
+
+ align:start position:0%
+likely to be associated in the first
+ 
+
+ align:start position:0%
+likely to be associated in the first
+instance with the work of the German
+
+ align:start position:0%
+instance with the work of the German
+ 
+
+ align:start position:0%
+instance with the work of the German
+sociologists from about 1900 to
+
+ align:start position:0%
+sociologists from about 1900 to
+ 
+
+ align:start position:0%
+sociologists from about 1900 to
+1950 um I'll just briefly mention them
+
+ align:start position:0%
+1950 um I'll just briefly mention them
+ 
+
+ align:start position:0%
+1950 um I'll just briefly mention them
+and talk a little bit about what their
+
+ align:start position:0%
+and talk a little bit about what their
+ 
+
+ align:start position:0%
+and talk a little bit about what their
+fundamental thinking about the nature of
+
+ align:start position:0%
+fundamental thinking about the nature of
+ 
+
+ align:start position:0%
+fundamental thinking about the nature of
+cities
+
+ align:start position:0%
+cities
+ 
+
+ align:start position:0%
+cities
+was Max
+
+ align:start position:0%
+was Max
+ 
+
+ align:start position:0%
+was Max
+Weber 19 five the three of Max Weber yor
+
+ align:start position:0%
+Weber 19 five the three of Max Weber yor
+ 
+
+ align:start position:0%
+Weber 19 five the three of Max Weber yor
+siml s i m m
+
+ align:start position:0%
+siml s i m m
+ 
+
+ align:start position:0%
+siml s i m m
+l and oswal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Spangler for
+
+ align:start position:0%
+Spangler for
+ 
+
+ align:start position:0%
+Spangler for
+them cities were relatively
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+new must remember that cities only grew
+
+ align:start position:0%
+new must remember that cities only grew
+ 
+
+ align:start position:0%
+new must remember that cities only grew
+at about 1% perom in your central in
+
+ align:start position:0%
+at about 1% perom in your central in
+ 
+
+ align:start position:0%
+at about 1% perom in your central in
+Europe until about then until 1930
+
+ align:start position:0%
+Europe until about then until 1930
+ 
+
+ align:start position:0%
+Europe until about then until 1930
+when parts of England grew urbanistic at
+
+ align:start position:0%
+when parts of England grew urbanistic at
+ 
+
+ align:start position:0%
+when parts of England grew urbanistic at
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+10%
+
+ align:start position:0%
+10%
+ 
+
+ align:start position:0%
+10%
+um but it involved a change in
+
+ align:start position:0%
+um but it involved a change in
+ 
+
+ align:start position:0%
+um but it involved a change in
+character uh for ver a city is
+
+ align:start position:0%
+character uh for ver a city is
+ 
+
+ align:start position:0%
+character uh for ver a city is
+essentially a human settlement which
+
+ align:start position:0%
+essentially a human settlement which
+ 
+
+ align:start position:0%
+essentially a human settlement which
+could be called comp
+
+ align:start position:0%
+could be called comp
+ 
+
+ align:start position:0%
+could be called comp
+Cosmopolitan it contains a variety of
+
+ align:start position:0%
+Cosmopolitan it contains a variety of
+ 
+
+ align:start position:0%
+Cosmopolitan it contains a variety of
+LIF Styles and different sorts of
+
+ align:start position:0%
+LIF Styles and different sorts of
+ 
+
+ align:start position:0%
+LIF Styles and different sorts of
+individuals which have to
+
+ align:start position:0%
+individuals which have to
+ 
+
+ align:start position:0%
+individuals which have to
+coexist he argues that the best way for
+
+ align:start position:0%
+coexist he argues that the best way for
+ 
+
+ align:start position:0%
+coexist he argues that the best way for
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+coexisting is to establish ideal typical
+
+ align:start position:0%
+coexisting is to establish ideal typical
+ 
+
+ align:start position:0%
+coexisting is to establish ideal typical
+conditions in which each state of urban
+
+ align:start position:0%
+conditions in which each state of urban
+ 
+
+ align:start position:0%
+conditions in which each state of urban
+life most neatly fulfills the social
+
+ align:start position:0%
+life most neatly fulfills the social
+ 
+
+ align:start position:0%
+life most neatly fulfills the social
+capacities in the in inherent in any of
+
+ align:start position:0%
+capacities in the in inherent in any of
+ 
+
+ align:start position:0%
+capacities in the in inherent in any of
+the one
+
+ align:start position:0%
+the one
+ 
+
+ align:start position:0%
+the one
+groups so for him an ideal city would be
+
+ align:start position:0%
+groups so for him an ideal city would be
+ 
+
+ align:start position:0%
+groups so for him an ideal city would be
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the creation of a a a a a a a
+
+ align:start position:0%
+the creation of a a a a a a a
+ 
+
+ align:start position:0%
+the creation of a a a a a a a
+phenomenon which has a large amount of
+
+ align:start position:0%
+phenomenon which has a large amount of
+ 
+
+ align:start position:0%
+phenomenon which has a large amount of
+Distinction in it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh the maintenance of these struct
+
+ align:start position:0%
+and uh the maintenance of these struct
+ 
+
+ align:start position:0%
+and uh the maintenance of these struct
+social structures competing social
+
+ align:start position:0%
+social structures competing social
+ 
+
+ align:start position:0%
+social structures competing social
+structures the capacity to understand
+
+ align:start position:0%
+structures the capacity to understand
+ 
+
+ align:start position:0%
+structures the capacity to understand
+when they change and when they
+
+ align:start position:0%
+when they change and when they
+ 
+
+ align:start position:0%
+when they change and when they
+don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he believes
+
+ align:start position:0%
+he believes
+ 
+
+ align:start position:0%
+he believes
+in in the kind of city that he was
+
+ align:start position:0%
+in in the kind of city that he was
+ 
+
+ align:start position:0%
+in in the kind of city that he was
+examining in Germany at the time George
+
+ align:start position:0%
+examining in Germany at the time George
+ 
+
+ align:start position:0%
+examining in Germany at the time George
+siml noticed another phenomenon of the
+
+ align:start position:0%
+siml noticed another phenomenon of the
+ 
+
+ align:start position:0%
+siml noticed another phenomenon of the
+emerging City form and that is that it
+
+ align:start position:0%
+emerging City form and that is that it
+ 
+
+ align:start position:0%
+emerging City form and that is that it
+put pressure on the individual
+
+ align:start position:0%
+put pressure on the individual
+ 
+
+ align:start position:0%
+put pressure on the individual
+existence the excess of psychic
+
+ align:start position:0%
+existence the excess of psychic
+ 
+
+ align:start position:0%
+existence the excess of psychic
+stimulation in a large city
+
+ align:start position:0%
+stimulation in a large city
+ 
+
+ align:start position:0%
+stimulation in a large city
+would cause
+
+ align:start position:0%
+would cause
+ 
+
+ align:start position:0%
+would cause
+withdrawal uh this is a strange
+
+ align:start position:0%
+withdrawal uh this is a strange
+ 
+
+ align:start position:0%
+withdrawal uh this is a strange
+concept uh
+
+ align:start position:0%
+concept uh
+ 
+
+ align:start position:0%
+concept uh
+it it maybe Associates it itself with
+
+ align:start position:0%
+it it maybe Associates it itself with
+ 
+
+ align:start position:0%
+it it maybe Associates it itself with
+people like Richard s Senate who's
+
+ align:start position:0%
+people like Richard s Senate who's
+ 
+
+ align:start position:0%
+people like Richard s Senate who's
+spoken about the the fall of public man
+
+ align:start position:0%
+spoken about the the fall of public man
+ 
+
+ align:start position:0%
+spoken about the the fall of public man
+in similar ways that
+
+ align:start position:0%
+in similar ways that
+ 
+
+ align:start position:0%
+in similar ways that
+the if in Sim Sim's case it was the
+
+ align:start position:0%
+the if in Sim Sim's case it was the
+ 
+
+ align:start position:0%
+the if in Sim Sim's case it was the
+withdraw all of people from the
+
+ align:start position:0%
+withdraw all of people from the
+ 
+
+ align:start position:0%
+withdraw all of people from the
+excessive stimulation of the city in
+
+ align:start position:0%
+excessive stimulation of the city in
+ 
+
+ align:start position:0%
+excessive stimulation of the city in
+Richard Senate's case it's the changing
+
+ align:start position:0%
+Richard Senate's case it's the changing
+ 
+
+ align:start position:0%
+Richard Senate's case it's the changing
+the capacity of people to from
+
+ align:start position:0%
+the capacity of people to from
+ 
+
+ align:start position:0%
+the capacity of people to from
+maintaining a state of publicness to a
+
+ align:start position:0%
+maintaining a state of publicness to a
+ 
+
+ align:start position:0%
+maintaining a state of publicness to a
+preference for a state of privacy I
+
+ align:start position:0%
+preference for a state of privacy I
+ 
+
+ align:start position:0%
+preference for a state of privacy I
+disagree with Senate to some extent
+
+ align:start position:0%
+disagree with Senate to some extent
+ 
+
+ align:start position:0%
+disagree with Senate to some extent
+about that
+
+ align:start position:0%
+about that
+ 
+
+ align:start position:0%
+about that
+observation uh as I'll deal with in the
+
+ align:start position:0%
+observation uh as I'll deal with in the
+ 
+
+ align:start position:0%
+observation uh as I'll deal with in the
+subsequent class uh the notion of
+
+ align:start position:0%
+subsequent class uh the notion of
+ 
+
+ align:start position:0%
+subsequent class uh the notion of
+privacy was foreign
+
+ align:start position:0%
+privacy was foreign
+ 
+
+ align:start position:0%
+privacy was foreign
+to people until the middle of the Middle
+
+ align:start position:0%
+to people until the middle of the Middle
+ 
+
+ align:start position:0%
+to people until the middle of the Middle
+Ages
+
+ align:start position:0%
+Ages
+ 
+
+ align:start position:0%
+Ages
+uh but
+
+ align:start position:0%
+uh but
+ 
+
+ align:start position:0%
+uh but
+simil
+
+ align:start position:0%
+simil
+ 
+
+ align:start position:0%
+simil
+uh talks of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this whenever large s numbers of people
+
+ align:start position:0%
+this whenever large s numbers of people
+ 
+
+ align:start position:0%
+this whenever large s numbers of people
+live
+
+ align:start position:0%
+live
+ 
+
+ align:start position:0%
+live
+together there's a selfhood a human
+
+ align:start position:0%
+together there's a selfhood a human
+ 
+
+ align:start position:0%
+together there's a selfhood a human
+identity which tries to project itself
+
+ align:start position:0%
+identity which tries to project itself
+ 
+
+ align:start position:0%
+identity which tries to project itself
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+process just as an example of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phenomenon if you would wish to withdraw
+
+ align:start position:0%
+phenomenon if you would wish to withdraw
+ 
+
+ align:start position:0%
+phenomenon if you would wish to withdraw
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+Manhattan from the
+
+ align:start position:0%
+Manhattan from the
+ 
+
+ align:start position:0%
+Manhattan from the
+intense energy that the city has
+
+ align:start position:0%
+intense energy that the city has
+ 
+
+ align:start position:0%
+intense energy that the city has
+produced
+
+ align:start position:0%
+produced
+ 
+
+ align:start position:0%
+produced
+um why would you have glass on the
+
+ align:start position:0%
+um why would you have glass on the
+ 
+
+ align:start position:0%
+um why would you have glass on the
+Windows of your
+
+ align:start position:0%
+Windows of your
+ 
+
+ align:start position:0%
+Windows of your
+apartment there's been some study of the
+
+ align:start position:0%
+apartment there's been some study of the
+ 
+
+ align:start position:0%
+apartment there's been some study of the
+amount of Glass on residential
+
+ align:start position:0%
+amount of Glass on residential
+ 
+
+ align:start position:0%
+amount of Glass on residential
+accommodation even to the extent that
+
+ align:start position:0%
+accommodation even to the extent that
+ 
+
+ align:start position:0%
+accommodation even to the extent that
+what is the form
+
+ align:start position:0%
+what is the form
+ 
+
+ align:start position:0%
+what is the form
+of old
+
+ align:start position:0%
+of old
+ 
+
+ align:start position:0%
+of old
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+where this man is in his apartment and
+
+ align:start position:0%
+where this man is in his apartment and
+ 
+
+ align:start position:0%
+where this man is in his apartment and
+he's hurt his legs so he can't move rear
+
+ align:start position:0%
+he's hurt his legs so he can't move rear
+ 
+
+ align:start position:0%
+he's hurt his legs so he can't move rear
+window yes who was the actor uh Jimmy
+
+ align:start position:0%
+window yes who was the actor uh Jimmy
+ 
+
+ align:start position:0%
+window yes who was the actor uh Jimmy
+Stewart Jimmy Stewart yeah yeah I'm
+
+ align:start position:0%
+Stewart Jimmy Stewart yeah yeah I'm
+ 
+
+ align:start position:0%
+Stewart Jimmy Stewart yeah yeah I'm
+sorry my memory is is falling
+
+ align:start position:0%
+sorry my memory is is falling
+ 
+
+ align:start position:0%
+sorry my memory is is falling
+apart um the phenomenon that you can use
+
+ align:start position:0%
+apart um the phenomenon that you can use
+ 
+
+ align:start position:0%
+apart um the phenomenon that you can use
+glass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as glass gives you both the option of
+
+ align:start position:0%
+as glass gives you both the option of
+ 
+
+ align:start position:0%
+as glass gives you both the option of
+withdrawing and being
+
+ align:start position:0%
+withdrawing and being
+ 
+
+ align:start position:0%
+withdrawing and being
+public it's an extraordinary
+
+ align:start position:0%
+public it's an extraordinary
+ 
+
+ align:start position:0%
+public it's an extraordinary
+idea that if you really if siml were
+
+ align:start position:0%
+idea that if you really if siml were
+ 
+
+ align:start position:0%
+idea that if you really if siml were
+absolutely
+
+ align:start position:0%
+absolutely
+ 
+
+ align:start position:0%
+absolutely
+correct we would all live in turrets or
+
+ align:start position:0%
+correct we would all live in turrets or
+ 
+
+ align:start position:0%
+correct we would all live in turrets or
+in gardens or anything establishing
+
+ align:start position:0%
+in gardens or anything establishing
+ 
+
+ align:start position:0%
+in gardens or anything establishing
+ourselves outside of the turmoil of
+
+ align:start position:0%
+ourselves outside of the turmoil of
+ 
+
+ align:start position:0%
+ourselves outside of the turmoil of
+urbanism the glass apartment Block in
+
+ align:start position:0%
+urbanism the glass apartment Block in
+ 
+
+ align:start position:0%
+urbanism the glass apartment Block in
+manhatton allowing people to see you on
+
+ align:start position:0%
+manhatton allowing people to see you on
+ 
+
+ align:start position:0%
+manhatton allowing people to see you on
+when you're ready to be
+
+ align:start position:0%
+when you're ready to be
+ 
+
+ align:start position:0%
+when you're ready to be
+seen But most mostly available is a
+
+ align:start position:0%
+seen But most mostly available is a
+ 
+
+ align:start position:0%
+seen But most mostly available is a
+curious
+
+ align:start position:0%
+curious
+ 
+
+ align:start position:0%
+curious
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+phenomenon siml might have had something
+
+ align:start position:0%
+phenomenon siml might have had something
+ 
+
+ align:start position:0%
+phenomenon siml might have had something
+to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about osal Spangler had a a
+
+ align:start position:0%
+about osal Spangler had a a
+ 
+
+ align:start position:0%
+about osal Spangler had a a
+typical negative view of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the future of the emerging large
+
+ align:start position:0%
+the future of the emerging large
+ 
+
+ align:start position:0%
+the future of the emerging large
+city uh he said that it has very
+
+ align:start position:0%
+city uh he said that it has very
+ 
+
+ align:start position:0%
+city uh he said that it has very
+popularly understood at the time that
+
+ align:start position:0%
+popularly understood at the time that
+ 
+
+ align:start position:0%
+popularly understood at the time that
+there was something wrong that it needed
+
+ align:start position:0%
+there was something wrong that it needed
+ 
+
+ align:start position:0%
+there was something wrong that it needed
+to be ciled in size
+
+ align:start position:0%
+to be ciled in size
+ 
+
+ align:start position:0%
+to be ciled in size
+that uh its inre increasing hom
+
+ align:start position:0%
+that uh its inre increasing hom
+ 
+
+ align:start position:0%
+that uh its inre increasing hom
+heterogeneity was a phenomenon which was
+
+ align:start position:0%
+heterogeneity was a phenomenon which was
+ 
+
+ align:start position:0%
+heterogeneity was a phenomenon which was
+dangerous
+
+ align:start position:0%
+dangerous
+ 
+
+ align:start position:0%
+dangerous
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh he believed that cities would go
+
+ align:start position:0%
+uh he believed that cities would go
+ 
+
+ align:start position:0%
+uh he believed that cities would go
+would be destroyed and I don't know what
+
+ align:start position:0%
+would be destroyed and I don't know what
+ 
+
+ align:start position:0%
+would be destroyed and I don't know what
+would replace them but he had the
+
+ align:start position:0%
+would replace them but he had the
+ 
+
+ align:start position:0%
+would replace them but he had the
+similar idea to others in England that
+
+ align:start position:0%
+similar idea to others in England that
+ 
+
+ align:start position:0%
+similar idea to others in England that
+London would be
+
+ align:start position:0%
+London would be
+ 
+
+ align:start position:0%
+London would be
+dispersed and into small communities
+
+ align:start position:0%
+dispersed and into small communities
+ 
+
+ align:start position:0%
+dispersed and into small communities
+largely in the rural areas of
+
+ align:start position:0%
+largely in the rural areas of
+ 
+
+ align:start position:0%
+largely in the rural areas of
+England uh completely an
+
+ align:start position:0%
+England uh completely an
+ 
+
+ align:start position:0%
+England uh completely an
+that complete nonsense of an idea but
+
+ align:start position:0%
+that complete nonsense of an idea but
+ 
+
+ align:start position:0%
+that complete nonsense of an idea but
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which the none of these
+
+ align:start position:0%
+which the none of these
+ 
+
+ align:start position:0%
+which the none of these
+people attempted to understand the
+
+ align:start position:0%
+people attempted to understand the
+ 
+
+ align:start position:0%
+people attempted to understand the
+sociology of an actual City they General
+
+ align:start position:0%
+sociology of an actual City they General
+ 
+
+ align:start position:0%
+sociology of an actual City they General
+they were
+
+ align:start position:0%
+they were
+ 
+
+ align:start position:0%
+they were
+generalists uh I'm reminded a little in
+
+ align:start position:0%
+generalists uh I'm reminded a little in
+ 
+
+ align:start position:0%
+generalists uh I'm reminded a little in
+reading of this to of a book which is
+
+ align:start position:0%
+reading of this to of a book which is
+ 
+
+ align:start position:0%
+reading of this to of a book which is
+recently published by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um Edward Glazer at Harvard called
+
+ align:start position:0%
+um Edward Glazer at Harvard called
+ 
+
+ align:start position:0%
+um Edward Glazer at Harvard called
+the triph of the city Triumph of the
+
+ align:start position:0%
+the triph of the city Triumph of the
+ 
+
+ align:start position:0%
+the triph of the city Triumph of the
+city
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+um there isn't really time to discuss
+
+ align:start position:0%
+um there isn't really time to discuss
+ 
+
+ align:start position:0%
+um there isn't really time to discuss
+this book at length but it's sometime in
+
+ align:start position:0%
+this book at length but it's sometime in
+ 
+
+ align:start position:0%
+this book at length but it's sometime in
+this class I would like to so ask me a
+
+ align:start position:0%
+this class I would like to so ask me a
+ 
+
+ align:start position:0%
+this class I would like to so ask me a
+question about it when we have more time
+
+ align:start position:0%
+question about it when we have more time
+ 
+
+ align:start position:0%
+question about it when we have more time
+uh its analysis is very much in the old
+
+ align:start position:0%
+uh its analysis is very much in the old
+ 
+
+ align:start position:0%
+uh its analysis is very much in the old
+school
+
+ align:start position:0%
+school
+ 
+
+ align:start position:0%
+school
+manner uh
+
+ align:start position:0%
+manner uh
+ 
+
+ align:start position:0%
+manner uh
+but if spingler proposes the cities will
+
+ align:start position:0%
+but if spingler proposes the cities will
+ 
+
+ align:start position:0%
+but if spingler proposes the cities will
+disappear because they are too crude and
+
+ align:start position:0%
+disappear because they are too crude and
+ 
+
+ align:start position:0%
+disappear because they are too crude and
+too they've deviated from decent human
+
+ align:start position:0%
+too they've deviated from decent human
+ 
+
+ align:start position:0%
+too they've deviated from decent human
+principles
+
+ align:start position:0%
+principles
+ 
+
+ align:start position:0%
+principles
+uh Glazer sees the future of interaction
+
+ align:start position:0%
+uh Glazer sees the future of interaction
+ 
+
+ align:start position:0%
+uh Glazer sees the future of interaction
+in the modern
+
+ align:start position:0%
+in the modern
+ 
+
+ align:start position:0%
+in the modern
+city as the essence of its
+
+ align:start position:0%
+city as the essence of its
+ 
+
+ align:start position:0%
+city as the essence of its
+being U he proposes that a good City
+
+ align:start position:0%
+being U he proposes that a good City
+ 
+
+ align:start position:0%
+being U he proposes that a good City
+would have would intensify
+
+ align:start position:0%
+would have would intensify
+ 
+
+ align:start position:0%
+would have would intensify
+interaction because it's economically
+
+ align:start position:0%
+interaction because it's economically
+ 
+
+ align:start position:0%
+interaction because it's economically
+important and so on and so on and so
+
+ align:start position:0%
+important and so on and so on and so
+ 
+
+ align:start position:0%
+important and so on and so on and so
+on um he's not an architect so he's P
+
+ align:start position:0%
+on um he's not an architect so he's P
+ 
+
+ align:start position:0%
+on um he's not an architect so he's P
+for tall buildings residential buildings
+
+ align:start position:0%
+for tall buildings residential buildings
+ 
+
+ align:start position:0%
+for tall buildings residential buildings
+um indiscriminate of how they are
+
+ align:start position:0%
+um indiscriminate of how they are
+ 
+
+ align:start position:0%
+um indiscriminate of how they are
+designed and how they are model
+
+ align:start position:0%
+designed and how they are model
+ 
+
+ align:start position:0%
+designed and how they are model
+modulated and so reminds me of what is
+
+ align:start position:0%
+modulated and so reminds me of what is
+ 
+
+ align:start position:0%
+modulated and so reminds me of what is
+happening in
+
+ align:start position:0%
+happening in
+ 
+
+ align:start position:0%
+happening in
+China uh amongst other places
+
+ align:start position:0%
+China uh amongst other places
+ 
+
+ align:start position:0%
+China uh amongst other places
+um The Chicago School were a bunch
+
+ align:start position:0%
+um The Chicago School were a bunch
+ 
+
+ align:start position:0%
+um The Chicago School were a bunch
+of sociologist who took a look at the
+
+ align:start position:0%
+of sociologist who took a look at the
+ 
+
+ align:start position:0%
+of sociologist who took a look at the
+American city for the first time
+
+ align:start position:0%
+American city for the first time
+ 
+
+ align:start position:0%
+American city for the first time
+analytically the concentric model uh of
+
+ align:start position:0%
+analytically the concentric model uh of
+ 
+
+ align:start position:0%
+analytically the concentric model uh of
+Park burges and
+
+ align:start position:0%
+Park burges and
+ 
+
+ align:start position:0%
+Park burges and
+McKenzie uh postulated a city
+
+ align:start position:0%
+McKenzie uh postulated a city
+ 
+
+ align:start position:0%
+McKenzie uh postulated a city
+which is much like a plant phenomenon
+
+ align:start position:0%
+which is much like a plant phenomenon
+ 
+
+ align:start position:0%
+which is much like a plant phenomenon
+that it increased and changed as it
+
+ align:start position:0%
+that it increased and changed as it
+ 
+
+ align:start position:0%
+that it increased and changed as it
+expanded outwards that the city
+
+ align:start position:0%
+expanded outwards that the city
+ 
+
+ align:start position:0%
+expanded outwards that the city
+consisted Rings annular rings of
+
+ align:start position:0%
+consisted Rings annular rings of
+ 
+
+ align:start position:0%
+consisted Rings annular rings of
+social
+
+ align:start position:0%
+social
+ 
+
+ align:start position:0%
+social
+classes um in which the dynamic was that
+
+ align:start position:0%
+classes um in which the dynamic was that
+ 
+
+ align:start position:0%
+classes um in which the dynamic was that
+you would move from the center to the
+
+ align:start position:0%
+you would move from the center to the
+ 
+
+ align:start position:0%
+you would move from the center to the
+outwards in the inner ring is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+center the central business district
+
+ align:start position:0%
+center the central business district
+ 
+
+ align:start position:0%
+center the central business district
+immediately surrounding it is something
+
+ align:start position:0%
+immediately surrounding it is something
+ 
+
+ align:start position:0%
+immediately surrounding it is something
+called The Zone in
+
+ align:start position:0%
+called The Zone in
+ 
+
+ align:start position:0%
+called The Zone in
+transition beyond that is
+
+ align:start position:0%
+transition beyond that is
+ 
+
+ align:start position:0%
+transition beyond that is
+the zone
+
+ align:start position:0%
+the zone
+ 
+
+ align:start position:0%
+the zone
+of uh working men's houses beyond that
+
+ align:start position:0%
+of uh working men's houses beyond that
+ 
+
+ align:start position:0%
+of uh working men's houses beyond that
+is the zone of better residences beyond
+
+ align:start position:0%
+is the zone of better residences beyond
+ 
+
+ align:start position:0%
+is the zone of better residences beyond
+that is the commuter Zone The Zone of
+
+ align:start position:0%
+that is the commuter Zone The Zone of
+ 
+
+ align:start position:0%
+that is the commuter Zone The Zone of
+transition that immediate Zone around
+
+ align:start position:0%
+transition that immediate Zone around
+ 
+
+ align:start position:0%
+transition that immediate Zone around
+the central bu area is of
+
+ align:start position:0%
+the central bu area is of
+ 
+
+ align:start position:0%
+the central bu area is of
+Interest what distinguishes the American
+
+ align:start position:0%
+Interest what distinguishes the American
+ 
+
+ align:start position:0%
+Interest what distinguishes the American
+American city from the European city in
+
+ align:start position:0%
+American city from the European city in
+ 
+
+ align:start position:0%
+American city from the European city in
+the grossest sense is the American city
+
+ align:start position:0%
+the grossest sense is the American city
+ 
+
+ align:start position:0%
+the grossest sense is the American city
+is a city of immigration European city
+
+ align:start position:0%
+is a city of immigration European city
+ 
+
+ align:start position:0%
+is a city of immigration European city
+is quite the opposite it's only been
+
+ align:start position:0%
+is quite the opposite it's only been
+ 
+
+ align:start position:0%
+is quite the opposite it's only been
+open to reation recently and is
+
+ align:start position:0%
+open to reation recently and is
+ 
+
+ align:start position:0%
+open to reation recently and is
+struggling like hell to deal with it
+
+ align:start position:0%
+struggling like hell to deal with it
+ 
+
+ align:start position:0%
+struggling like hell to deal with it
+America's gone through a couple of
+
+ align:start position:0%
+America's gone through a couple of
+ 
+
+ align:start position:0%
+America's gone through a couple of
+hundred years if not
+
+ align:start position:0%
+hundred years if not
+ 
+
+ align:start position:0%
+hundred years if not
+forever uh dealing with a problem of
+
+ align:start position:0%
+forever uh dealing with a problem of
+ 
+
+ align:start position:0%
+forever uh dealing with a problem of
+immigration and the zone of transition
+
+ align:start position:0%
+immigration and the zone of transition
+ 
+
+ align:start position:0%
+immigration and the zone of transition
+in the American city was that under
+
+ align:start position:0%
+in the American city was that under
+ 
+
+ align:start position:0%
+in the American city was that under
+determined Zone before the settled
+
+ align:start position:0%
+determined Zone before the settled
+ 
+
+ align:start position:0%
+determined Zone before the settled
+residential population took place a Zone
+
+ align:start position:0%
+residential population took place a Zone
+ 
+
+ align:start position:0%
+residential population took place a Zone
+in transition the obvious phenomenon was
+
+ align:start position:0%
+in transition the obvious phenomenon was
+ 
+
+ align:start position:0%
+in transition the obvious phenomenon was
+that this is Zone which had
+
+ align:start position:0%
+that this is Zone which had
+ 
+
+ align:start position:0%
+that this is Zone which had
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+a more rapid turnover than any other
+
+ align:start position:0%
+a more rapid turnover than any other
+ 
+
+ align:start position:0%
+a more rapid turnover than any other
+Zone in the city and this has actually
+
+ align:start position:0%
+Zone in the city and this has actually
+ 
+
+ align:start position:0%
+Zone in the city and this has actually
+been the The Zone which has been a zone
+
+ align:start position:0%
+been the The Zone which has been a zone
+ 
+
+ align:start position:0%
+been the The Zone which has been a zone
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+immigration a zone of building of
+
+ align:start position:0%
+immigration a zone of building of
+ 
+
+ align:start position:0%
+immigration a zone of building of
+bypasses past the central buiness this
+
+ align:start position:0%
+bypasses past the central buiness this
+ 
+
+ align:start position:0%
+bypasses past the central buiness this
+area in fact if anything it's a better
+
+ align:start position:0%
+area in fact if anything it's a better
+ 
+
+ align:start position:0%
+area in fact if anything it's a better
+Flex Zone around the center of the city
+
+ align:start position:0%
+Flex Zone around the center of the city
+ 
+
+ align:start position:0%
+Flex Zone around the center of the city
+than the park system of Adelaide which
+
+ align:start position:0%
+than the park system of Adelaide which
+ 
+
+ align:start position:0%
+than the park system of Adelaide which
+the organic model so enthused about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um there was a gentleman called hom hoit
+
+ align:start position:0%
+um there was a gentleman called hom hoit
+ 
+
+ align:start position:0%
+um there was a gentleman called hom hoit
+who during the Depression years in
+
+ align:start position:0%
+who during the Depression years in
+ 
+
+ align:start position:0%
+who during the Depression years in
+Washington did nothing else that be
+
+ align:start position:0%
+Washington did nothing else that be
+ 
+
+ align:start position:0%
+Washington did nothing else that be
+without a computer calculated rent
+
+ align:start position:0%
+without a computer calculated rent
+ 
+
+ align:start position:0%
+without a computer calculated rent
+payments in cities in the United States
+
+ align:start position:0%
+payments in cities in the United States
+ 
+
+ align:start position:0%
+payments in cities in the United States
+particularly in Chicago written a book
+
+ align:start position:0%
+particularly in Chicago written a book
+ 
+
+ align:start position:0%
+particularly in Chicago written a book
+about Chicago from which he developed a
+
+ align:start position:0%
+about Chicago from which he developed a
+ 
+
+ align:start position:0%
+about Chicago from which he developed a
+an alternative model to the concentric
+
+ align:start position:0%
+an alternative model to the concentric
+ 
+
+ align:start position:0%
+an alternative model to the concentric
+model that is he claims that a city is
+
+ align:start position:0%
+model that is he claims that a city is
+ 
+
+ align:start position:0%
+model that is he claims that a city is
+really patented on the basis of
+
+ align:start position:0%
+really patented on the basis of
+ 
+
+ align:start position:0%
+really patented on the basis of
+sectors sectors Dev allow people to move
+
+ align:start position:0%
+sectors sectors Dev allow people to move
+ 
+
+ align:start position:0%
+sectors sectors Dev allow people to move
+towards higher income areas towards open
+
+ align:start position:0%
+towards higher income areas towards open
+ 
+
+ align:start position:0%
+towards higher income areas towards open
+space towards mountains towards higher
+
+ align:start position:0%
+space towards mountains towards higher
+ 
+
+ align:start position:0%
+space towards mountains towards higher
+natural food
+
+ align:start position:0%
+natural food
+ 
+
+ align:start position:0%
+natural food
+phenomenon uh and therefore you get a
+
+ align:start position:0%
+phenomenon uh and therefore you get a
+ 
+
+ align:start position:0%
+phenomenon uh and therefore you get a
+division of
+
+ align:start position:0%
+division of
+ 
+
+ align:start position:0%
+division of
+people rather than occupying space
+
+ align:start position:0%
+people rather than occupying space
+ 
+
+ align:start position:0%
+people rather than occupying space
+concentrically occupying space through
+
+ align:start position:0%
+concentrically occupying space through
+ 
+
+ align:start position:0%
+concentrically occupying space through
+wedges now if you look at the diagram of
+
+ align:start position:0%
+wedges now if you look at the diagram of
+ 
+
+ align:start position:0%
+wedges now if you look at the diagram of
+Atlanta you'll see some just Justice for
+
+ align:start position:0%
+Atlanta you'll see some just Justice for
+ 
+
+ align:start position:0%
+Atlanta you'll see some just Justice for
+his
+
+ align:start position:0%
+his
+ 
+
+ align:start position:0%
+his
+phenomenon it applies equally well to
+
+ align:start position:0%
+phenomenon it applies equally well to
+ 
+
+ align:start position:0%
+phenomenon it applies equally well to
+Johannesburg when I do a case study with
+
+ align:start position:0%
+Johannesburg when I do a case study with
+ 
+
+ align:start position:0%
+Johannesburg when I do a case study with
+you of Johannesburg you will see how the
+
+ align:start position:0%
+you of Johannesburg you will see how the
+ 
+
+ align:start position:0%
+you of Johannesburg you will see how the
+sector theory worked very well up to a
+
+ align:start position:0%
+sector theory worked very well up to a
+ 
+
+ align:start position:0%
+sector theory worked very well up to a
+certain point in the construction of in
+
+ align:start position:0%
+certain point in the construction of in
+ 
+
+ align:start position:0%
+certain point in the construction of in
+the organization of the city um in the
+
+ align:start position:0%
+the organization of the city um in the
+ 
+
+ align:start position:0%
+the organization of the city um in the
+case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of Atlanta you have as I've said before
+
+ align:start position:0%
+of Atlanta you have as I've said before
+ 
+
+ align:start position:0%
+of Atlanta you have as I've said before
+U the phenomenon
+
+ align:start position:0%
+U the phenomenon
+ 
+
+ align:start position:0%
+U the phenomenon
+here uh based on rent
+
+ align:start position:0%
+here uh based on rent
+ 
+
+ align:start position:0%
+here uh based on rent
+payments
+
+ align:start position:0%
+payments
+ 
+
+ align:start position:0%
+payments
+um justifying the white
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model these The Chicago
+
+ align:start position:0%
+model these The Chicago
+ 
+
+ align:start position:0%
+model these The Chicago
+School took
+
+ align:start position:0%
+School took
+ 
+
+ align:start position:0%
+School took
+place in the great City of
+
+ align:start position:0%
+place in the great City of
+ 
+
+ align:start position:0%
+place in the great City of
+Chicago Chicago has been called the
+
+ align:start position:0%
+Chicago Chicago has been called the
+ 
+
+ align:start position:0%
+Chicago Chicago has been called the
+shock City
+
+ align:start position:0%
+shock City
+ 
+
+ align:start position:0%
+shock City
+because of its rapid
+
+ align:start position:0%
+because of its rapid
+ 
+
+ align:start position:0%
+because of its rapid
+emergence Chicago didn't exist in
+
+ align:start position:0%
+emergence Chicago didn't exist in
+ 
+
+ align:start position:0%
+emergence Chicago didn't exist in
+1830 and in 1893 at the time of the
+
+ align:start position:0%
+1830 and in 1893 at the time of the
+ 
+
+ align:start position:0%
+1830 and in 1893 at the time of the
+Chicago World's
+
+ align:start position:0%
+Chicago World's
+ 
+
+ align:start position:0%
+Chicago World's
+Fair 125th of all the world's railroads
+
+ align:start position:0%
+Fair 125th of all the world's railroads
+ 
+
+ align:start position:0%
+Fair 125th of all the world's railroads
+pass through
+
+ align:start position:0%
+pass through
+ 
+
+ align:start position:0%
+pass through
+kaga it's the most
+
+ align:start position:0%
+kaga it's the most
+ 
+
+ align:start position:0%
+kaga it's the most
+rapidly and
+
+ align:start position:0%
+rapidly and
+ 
+
+ align:start position:0%
+rapidly and
+be and by virtue of its rapid growth
+
+ align:start position:0%
+be and by virtue of its rapid growth
+ 
+
+ align:start position:0%
+be and by virtue of its rapid growth
+which wasn't accompanied by
+
+ align:start position:0%
+which wasn't accompanied by
+ 
+
+ align:start position:0%
+which wasn't accompanied by
+government or good
+
+ align:start position:0%
+government or good
+ 
+
+ align:start position:0%
+government or good
+government uh you have the phenomenon
+
+ align:start position:0%
+government uh you have the phenomenon
+ 
+
+ align:start position:0%
+government uh you have the phenomenon
+which I look into more carefully when we
+
+ align:start position:0%
+which I look into more carefully when we
+ 
+
+ align:start position:0%
+which I look into more carefully when we
+discuss the case of Chicago Chicago is
+
+ align:start position:0%
+discuss the case of Chicago Chicago is
+ 
+
+ align:start position:0%
+discuss the case of Chicago Chicago is
+the is the most phenomenal 19th century
+
+ align:start position:0%
+the is the most phenomenal 19th century
+ 
+
+ align:start position:0%
+the is the most phenomenal 19th century
+city of
+
+ align:start position:0%
+city of
+ 
+
+ align:start position:0%
+city of
+all and uh it's interesting that Chicago
+
+ align:start position:0%
+all and uh it's interesting that Chicago
+ 
+
+ align:start position:0%
+all and uh it's interesting that Chicago
+was the place where the first academic
+
+ align:start position:0%
+was the place where the first academic
+ 
+
+ align:start position:0%
+was the place where the first academic
+study of the social grouping of cities
+
+ align:start position:0%
+study of the social grouping of cities
+ 
+
+ align:start position:0%
+study of the social grouping of cities
+should take
+
+ align:start position:0%
+should take
+ 
+
+ align:start position:0%
+should take
+place
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a lot of things happened for the first
+
+ align:start position:0%
+a lot of things happened for the first
+ 
+
+ align:start position:0%
+a lot of things happened for the first
+time in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chicago economics has paid a serious but
+
+ align:start position:0%
+Chicago economics has paid a serious but
+ 
+
+ align:start position:0%
+Chicago economics has paid a serious but
+very scant interes in location as Paul
+
+ align:start position:0%
+very scant interes in location as Paul
+ 
+
+ align:start position:0%
+very scant interes in location as Paul
+Krugman put points
+
+ align:start position:0%
+Krugman put points
+ 
+
+ align:start position:0%
+Krugman put points
+out the new textbook by Joseph stigle at
+
+ align:start position:0%
+out the new textbook by Joseph stigle at
+ 
+
+ align:start position:0%
+out the new textbook by Joseph stigle at
+Harvard which is a thousand pages in L
+
+ align:start position:0%
+Harvard which is a thousand pages in L
+ 
+
+ align:start position:0%
+Harvard which is a thousand pages in L
+as the word City mentioned once and the
+
+ align:start position:0%
+as the word City mentioned once and the
+ 
+
+ align:start position:0%
+as the word City mentioned once and the
+word location mentioned
+
+ align:start position:0%
+word location mentioned
+ 
+
+ align:start position:0%
+word location mentioned
+once if you want to read about greed
+
+ align:start position:0%
+once if you want to read about greed
+ 
+
+ align:start position:0%
+once if you want to read about greed
+krugman's views on why economics is not
+
+ align:start position:0%
+krugman's views on why economics is not
+ 
+
+ align:start position:0%
+krugman's views on why economics is not
+included location as a serious input
+
+ align:start position:0%
+included location as a serious input
+ 
+
+ align:start position:0%
+included location as a serious input
+read the pieces that I've suggested you
+
+ align:start position:0%
+read the pieces that I've suggested you
+ 
+
+ align:start position:0%
+read the pieces that I've suggested you
+read They're two pieces by Krugman
+
+ align:start position:0%
+read They're two pieces by Krugman
+ 
+
+ align:start position:0%
+read They're two pieces by Krugman
+um explaining why the modern economics
+
+ align:start position:0%
+um explaining why the modern economics
+ 
+
+ align:start position:0%
+um explaining why the modern economics
+after
+
+ align:start position:0%
+after
+ 
+
+ align:start position:0%
+after
+Marshall uh managed very well on
+
+ align:start position:0%
+Marshall uh managed very well on
+ 
+
+ align:start position:0%
+Marshall uh managed very well on
+optimization theories without including
+
+ align:start position:0%
+optimization theories without including
+ 
+
+ align:start position:0%
+optimization theories without including
+the cost of Transportation or the cost
+
+ align:start position:0%
+the cost of Transportation or the cost
+ 
+
+ align:start position:0%
+the cost of Transportation or the cost
+the cost and benefits of
+
+ align:start position:0%
+the cost and benefits of
+ 
+
+ align:start position:0%
+the cost and benefits of
+location um he claims there's been a
+
+ align:start position:0%
+location um he claims there's been a
+ 
+
+ align:start position:0%
+location um he claims there's been a
+weakness in economic geography which has
+
+ align:start position:0%
+weakness in economic geography which has
+ 
+
+ align:start position:0%
+weakness in economic geography which has
+tried to measure up to the purity of
+
+ align:start position:0%
+tried to measure up to the purity of
+ 
+
+ align:start position:0%
+tried to measure up to the purity of
+Economics of modern economics and uh
+
+ align:start position:0%
+Economics of modern economics and uh
+ 
+
+ align:start position:0%
+Economics of modern economics and uh
+give some suggestions for maybe a new
+
+ align:start position:0%
+give some suggestions for maybe a new
+ 
+
+ align:start position:0%
+give some suggestions for maybe a new
+in post real estate study of location
+
+ align:start position:0%
+in post real estate study of location
+ 
+
+ align:start position:0%
+in post real estate study of location
+the classical location models
+
+ align:start position:0%
+the classical location models
+ 
+
+ align:start position:0%
+the classical location models
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+still number one at a regional level the
+
+ align:start position:0%
+still number one at a regional level the
+ 
+
+ align:start position:0%
+still number one at a regional level the
+more work of Von
+
+ align:start position:0%
+more work of Von
+ 
+
+ align:start position:0%
+more work of Von
+tunin the German
+
+ align:start position:0%
+tunin the German
+ 
+
+ align:start position:0%
+tunin the German
+agronomist who argued that look that the
+
+ align:start position:0%
+agronomist who argued that look that the
+ 
+
+ align:start position:0%
+agronomist who argued that look that the
+cost of Transportation was a phenomenon
+
+ align:start position:0%
+cost of Transportation was a phenomenon
+ 
+
+ align:start position:0%
+cost of Transportation was a phenomenon
+in allocating land use
+
+ align:start position:0%
+in allocating land use
+ 
+
+ align:start position:0%
+in allocating land use
+he claims
+
+ align:start position:0%
+he claims
+ 
+
+ align:start position:0%
+he claims
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh as I've said
+
+ align:start position:0%
+uh as I've said
+ 
+
+ align:start position:0%
+uh as I've said
+before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh this around around the center the
+
+ align:start position:0%
+uh this around around the center the
+ 
+
+ align:start position:0%
+uh this around around the center the
+spatial distribution of crops occurs
+
+ align:start position:0%
+spatial distribution of crops occurs
+ 
+
+ align:start position:0%
+spatial distribution of crops occurs
+according to the yield per unit or area
+
+ align:start position:0%
+according to the yield per unit or area
+ 
+
+ align:start position:0%
+according to the yield per unit or area
+around the central town
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you end up
+
+ align:start position:0%
+you end up
+ 
+
+ align:start position:0%
+you end up
+with dairy in the center orchards in
+
+ align:start position:0%
+with dairy in the center orchards in
+ 
+
+ align:start position:0%
+with dairy in the center orchards in
+this next ring grain in the next ring
+
+ align:start position:0%
+this next ring grain in the next ring
+ 
+
+ align:start position:0%
+this next ring grain in the next ring
+Earth cattle in the next ring and
+
+ align:start position:0%
+Earth cattle in the next ring and
+ 
+
+ align:start position:0%
+Earth cattle in the next ring and
+Forestry farther furthest from the
+
+ align:start position:0%
+Forestry farther furthest from the
+ 
+
+ align:start position:0%
+Forestry farther furthest from the
+center this is not only a function of
+
+ align:start position:0%
+center this is not only a function of
+ 
+
+ align:start position:0%
+center this is not only a function of
+land values but a function of the cost
+
+ align:start position:0%
+land values but a function of the cost
+ 
+
+ align:start position:0%
+land values but a function of the cost
+of transporting goods to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+center Southern Germany where
+
+ align:start position:0%
+center Southern Germany where
+ 
+
+ align:start position:0%
+center Southern Germany where
+Von tun and and Christal and people like
+
+ align:start position:0%
+Von tun and and Christal and people like
+ 
+
+ align:start position:0%
+Von tun and and Christal and people like
+that economic geographers work was
+
+ align:start position:0%
+that economic geographers work was
+ 
+
+ align:start position:0%
+that economic geographers work was
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+flat and with population growth
+
+ align:start position:0%
+flat and with population growth
+ 
+
+ align:start position:0%
+flat and with population growth
+occurring at a very low
+
+ align:start position:0%
+occurring at a very low
+ 
+
+ align:start position:0%
+occurring at a very low
+rate uh the notion of a single Centered
+
+ align:start position:0%
+rate uh the notion of a single Centered
+ 
+
+ align:start position:0%
+rate uh the notion of a single Centered
+City or a distributed pattern of cities
+
+ align:start position:0%
+City or a distributed pattern of cities
+ 
+
+ align:start position:0%
+City or a distributed pattern of cities
+at regular intervals was
+
+ align:start position:0%
+at regular intervals was
+ 
+
+ align:start position:0%
+at regular intervals was
+appropriate
+
+ align:start position:0%
+appropriate
+ 
+
+ align:start position:0%
+appropriate
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+crystala base
+
+ align:start position:0%
+crystala base
+ 
+
+ align:start position:0%
+crystala base
+East economic geography on the idea that
+
+ align:start position:0%
+East economic geography on the idea that
+ 
+
+ align:start position:0%
+East economic geography on the idea that
+there were Central places uh and uh you
+
+ align:start position:0%
+there were Central places uh and uh you
+ 
+
+ align:start position:0%
+there were Central places uh and uh you
+can see this phenomenon in Northern
+
+ align:start position:0%
+can see this phenomenon in Northern
+ 
+
+ align:start position:0%
+can see this phenomenon in Northern
+Italy
+
+ align:start position:0%
+Italy
+ 
+
+ align:start position:0%
+Italy
+today from if you move Eastward from
+
+ align:start position:0%
+today from if you move Eastward from
+ 
+
+ align:start position:0%
+today from if you move Eastward from
+Milan you 30 miles from Milan is Pria 30
+
+ align:start position:0%
+Milan you 30 miles from Milan is Pria 30
+ 
+
+ align:start position:0%
+Milan you 30 miles from Milan is Pria 30
+miles from Pria Verona Venza is 30 m
+
+ align:start position:0%
+miles from Pria Verona Venza is 30 m
+ 
+
+ align:start position:0%
+miles from Pria Verona Venza is 30 m
+from V
+
+ align:start position:0%
+from V
+ 
+
+ align:start position:0%
+from V
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+pav Padova is 30 mil and Venice at the
+
+ align:start position:0%
+pav Padova is 30 mil and Venice at the
+ 
+
+ align:start position:0%
+pav Padova is 30 mil and Venice at the
+end of this horizontal East West
+
+ align:start position:0%
+end of this horizontal East West
+ 
+
+ align:start position:0%
+end of this horizontal East West
+axis if you go from Milan Milano to
+
+ align:start position:0%
+axis if you go from Milan Milano to
+ 
+
+ align:start position:0%
+axis if you go from Milan Milano to
+bolognia you have 30 miles to pava then
+
+ align:start position:0%
+bolognia you have 30 miles to pava then
+ 
+
+ align:start position:0%
+bolognia you have 30 miles to pava then
+30 m to Parma 30 mil to reio 30 mil to
+
+ align:start position:0%
+30 m to Parma 30 mil to reio 30 mil to
+ 
+
+ align:start position:0%
+30 m to Parma 30 mil to reio 30 mil to
+Moda and 30 miles to Bologna on the axis
+
+ align:start position:0%
+Moda and 30 miles to Bologna on the axis
+ 
+
+ align:start position:0%
+Moda and 30 miles to Bologna on the axis
+from bologna in the big triangle to
+
+ align:start position:0%
+from bologna in the big triangle to
+ 
+
+ align:start position:0%
+from bologna in the big triangle to
+Venice Yia Ferrara which is about 30 mi
+
+ align:start position:0%
+Venice Yia Ferrara which is about 30 mi
+ 
+
+ align:start position:0%
+Venice Yia Ferrara which is about 30 mi
+from bolognia and then historical land
+
+ align:start position:0%
+from bolognia and then historical land
+ 
+
+ align:start position:0%
+from bolognia and then historical land
+patterns didn't allow this phenomenon to
+
+ align:start position:0%
+patterns didn't allow this phenomenon to
+ 
+
+ align:start position:0%
+patterns didn't allow this phenomenon to
+take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place there was a big exhibition in
+
+ align:start position:0%
+place there was a big exhibition in
+ 
+
+ align:start position:0%
+place there was a big exhibition in
+Italy entitled the culture of
+
+ align:start position:0%
+Italy entitled the culture of
+ 
+
+ align:start position:0%
+Italy entitled the culture of
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+cities what is interesting about
+
+ align:start position:0%
+cities what is interesting about
+ 
+
+ align:start position:0%
+cities what is interesting about
+Christal's interpretation for contemp
+
+ align:start position:0%
+Christal's interpretation for contemp
+ 
+
+ align:start position:0%
+Christal's interpretation for contemp
+times is that a place like
+
+ align:start position:0%
+times is that a place like
+ 
+
+ align:start position:0%
+times is that a place like
+Mona produces the headquarters of
+
+ align:start position:0%
+Mona produces the headquarters of
+ 
+
+ align:start position:0%
+Mona produces the headquarters of
+Lamborghini Ferrari and
+
+ align:start position:0%
+Lamborghini Ferrari and
+ 
+
+ align:start position:0%
+Lamborghini Ferrari and
+Maserati and still is a relatively small
+
+ align:start position:0%
+Maserati and still is a relatively small
+ 
+
+ align:start position:0%
+Maserati and still is a relatively small
+population Center you go to Cortona near
+
+ align:start position:0%
+population Center you go to Cortona near
+ 
+
+ align:start position:0%
+population Center you go to Cortona near
+areto it
+
+ align:start position:0%
+areto it
+ 
+
+ align:start position:0%
+areto it
+has a bunch of things almost every small
+
+ align:start position:0%
+has a bunch of things almost every small
+ 
+
+ align:start position:0%
+has a bunch of things almost every small
+town has a center and a condition of
+
+ align:start position:0%
+town has a center and a condition of
+ 
+
+ align:start position:0%
+town has a center and a condition of
+uniqueness
+
+ align:start position:0%
+uniqueness
+ 
+
+ align:start position:0%
+uniqueness
+The Genius of the Italian landscape is
+
+ align:start position:0%
+The Genius of the Italian landscape is
+ 
+
+ align:start position:0%
+The Genius of the Italian landscape is
+in not
+
+ align:start position:0%
+in not
+ 
+
+ align:start position:0%
+in not
+developing well so they they argue they
+
+ align:start position:0%
+developing well so they they argue they
+ 
+
+ align:start position:0%
+developing well so they they argue they
+haven't developed large cities Milano is
+
+ align:start position:0%
+haven't developed large cities Milano is
+ 
+
+ align:start position:0%
+haven't developed large cities Milano is
+not a village uh but the Italians are
+
+ align:start position:0%
+not a village uh but the Italians are
+ 
+
+ align:start position:0%
+not a village uh but the Italians are
+free to interpret things very freely uh
+
+ align:start position:0%
+free to interpret things very freely uh
+ 
+
+ align:start position:0%
+free to interpret things very freely uh
+but the genius of being able to be small
+
+ align:start position:0%
+but the genius of being able to be small
+ 
+
+ align:start position:0%
+but the genius of being able to be small
+and yet to be unique and
+
+ align:start position:0%
+and yet to be unique and
+ 
+
+ align:start position:0%
+and yet to be unique and
+to I was asked to come to Ferrara
+
+ align:start position:0%
+to I was asked to come to Ferrara
+ 
+
+ align:start position:0%
+to I was asked to come to Ferrara
+once uh because the the they started New
+
+ align:start position:0%
+once uh because the the they started New
+ 
+
+ align:start position:0%
+once uh because the the they started New
+School of Architecture run by a friend
+
+ align:start position:0%
+School of Architecture run by a friend
+ 
+
+ align:start position:0%
+School of Architecture run by a friend
+of mine and the city was going to give
+
+ align:start position:0%
+of mine and the city was going to give
+ 
+
+ align:start position:0%
+of mine and the city was going to give
+them a
+
+ align:start position:0%
+them a
+ 
+
+ align:start position:0%
+them a
+building and they wanted this small
+
+ align:start position:0%
+building and they wanted this small
+ 
+
+ align:start position:0%
+building and they wanted this small
+group of people to choose the building
+
+ align:start position:0%
+group of people to choose the building
+ 
+
+ align:start position:0%
+group of people to choose the building
+they CH took us to a building which
+
+ align:start position:0%
+they CH took us to a building which
+ 
+
+ align:start position:0%
+they CH took us to a building which
+they' given to the
+
+ align:start position:0%
+they' given to the
+ 
+
+ align:start position:0%
+they' given to the
+man who developed the first electronic
+
+ align:start position:0%
+man who developed the first electronic
+ 
+
+ align:start position:0%
+man who developed the first electronic
+system for the movies and it made a film
+
+ align:start position:0%
+system for the movies and it made a film
+ 
+
+ align:start position:0%
+system for the movies and it made a film
+which was very popular at the time
+
+ align:start position:0%
+which was very popular at the time
+ 
+
+ align:start position:0%
+which was very popular at the time
+possible prior to all of this computer
+
+ align:start position:0%
+possible prior to all of this computer
+ 
+
+ align:start position:0%
+possible prior to all of this computer
+stuff there was a sense in this town
+
+ align:start position:0%
+stuff there was a sense in this town
+ 
+
+ align:start position:0%
+stuff there was a sense in this town
+that there was an appreciation of his
+
+ align:start position:0%
+that there was an appreciation of his
+ 
+
+ align:start position:0%
+that there was an appreciation of his
+capacity to be located
+
+ align:start position:0%
+capacity to be located
+ 
+
+ align:start position:0%
+capacity to be located
+locally you bought food from the shop on
+
+ align:start position:0%
+locally you bought food from the shop on
+ 
+
+ align:start position:0%
+locally you bought food from the shop on
+the corner but yet he had an
+
+ align:start position:0%
+the corner but yet he had an
+ 
+
+ align:start position:0%
+the corner but yet he had an
+international aspiration and put
+
+ align:start position:0%
+international aspiration and put
+ 
+
+ align:start position:0%
+international aspiration and put
+together all of these places constant to
+
+ align:start position:0%
+together all of these places constant to
+ 
+
+ align:start position:0%
+together all of these places constant to
+the Italian Urban
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+culture it's an strange phenomenon but
+
+ align:start position:0%
+culture it's an strange phenomenon but
+ 
+
+ align:start position:0%
+culture it's an strange phenomenon but
+it's the phenomen
+
+ align:start position:0%
+it's the phenomen
+ 
+
+ align:start position:0%
+it's the phenomen
+phenomenon which is worth noticing and
+
+ align:start position:0%
+phenomenon which is worth noticing and
+ 
+
+ align:start position:0%
+phenomenon which is worth noticing and
+it's a phenomenon which organizes the
+
+ align:start position:0%
+it's a phenomenon which organizes the
+ 
+
+ align:start position:0%
+it's a phenomenon which organizes the
+city and the country in a different way
+
+ align:start position:0%
+city and the country in a different way
+ 
+
+ align:start position:0%
+city and the country in a different way
+than the very large city and the very
+
+ align:start position:0%
+than the very large city and the very
+ 
+
+ align:start position:0%
+than the very large city and the very
+large spatial
+
+ align:start position:0%
+large spatial
+ 
+
+ align:start position:0%
+large spatial
+interland
+
+ align:start position:0%
+interland
+ 
+
+ align:start position:0%
+interland
+uh it's worth talking about in as we
+
+ align:start position:0%
+uh it's worth talking about in as we
+ 
+
+ align:start position:0%
+uh it's worth talking about in as we
+develop this class a bit further but it
+
+ align:start position:0%
+develop this class a bit further but it
+ 
+
+ align:start position:0%
+develop this class a bit further but it
+emanates from Christal's work c h r i s
+
+ align:start position:0%
+emanates from Christal's work c h r i s
+ 
+
+ align:start position:0%
+emanates from Christal's work c h r i s
+t a l l e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r the third application of the classical
+
+ align:start position:0%
+r the third application of the classical
+ 
+
+ align:start position:0%
+r the third application of the classical
+economic model is in the distribution of
+
+ align:start position:0%
+economic model is in the distribution of
+ 
+
+ align:start position:0%
+economic model is in the distribution of
+activities in the
+
+ align:start position:0%
+activities in the
+ 
+
+ align:start position:0%
+activities in the
+center uh in in
+
+ align:start position:0%
+center uh in in
+ 
+
+ align:start position:0%
+center uh in in
+the Central City itself here you will
+
+ align:start position:0%
+the Central City itself here you will
+ 
+
+ align:start position:0%
+the Central City itself here you will
+have the phenomenon which seems very
+
+ align:start position:0%
+have the phenomenon which seems very
+ 
+
+ align:start position:0%
+have the phenomenon which seems very
+crude still at the moment that what are
+
+ align:start position:0%
+crude still at the moment that what are
+ 
+
+ align:start position:0%
+crude still at the moment that what are
+there are two variables the one is the
+
+ align:start position:0%
+there are two variables the one is the
+ 
+
+ align:start position:0%
+there are two variables the one is the
+amount of rent the money you want to pay
+
+ align:start position:0%
+amount of rent the money you want to pay
+ 
+
+ align:start position:0%
+amount of rent the money you want to pay
+in rent at one access and another AIS
+
+ align:start position:0%
+in rent at one access and another AIS
+ 
+
+ align:start position:0%
+in rent at one access and another AIS
+which says the distance that you can be
+
+ align:start position:0%
+which says the distance that you can be
+ 
+
+ align:start position:0%
+which says the distance that you can be
+from the center the argument being that
+
+ align:start position:0%
+from the center the argument being that
+ 
+
+ align:start position:0%
+from the center the argument being that
+in the center you pay higher rents and
+
+ align:start position:0%
+in the center you pay higher rents and
+ 
+
+ align:start position:0%
+in the center you pay higher rents and
+the further out you go the lower rents
+
+ align:start position:0%
+the further out you go the lower rents
+ 
+
+ align:start position:0%
+the further out you go the lower rents
+you pay but you have have to pay the
+
+ align:start position:0%
+you pay but you have have to pay the
+ 
+
+ align:start position:0%
+you pay but you have have to pay the
+increased Transportation costs so that
+
+ align:start position:0%
+increased Transportation costs so that
+ 
+
+ align:start position:0%
+increased Transportation costs so that
+balance
+
+ align:start position:0%
+balance
+ 
+
+ align:start position:0%
+balance
+will produce suburban and then exurban
+
+ align:start position:0%
+will produce suburban and then exurban
+ 
+
+ align:start position:0%
+will produce suburban and then exurban
+locations depending on the Improvement
+
+ align:start position:0%
+locations depending on the Improvement
+ 
+
+ align:start position:0%
+locations depending on the Improvement
+of the transportation system outwards
+
+ align:start position:0%
+of the transportation system outwards
+ 
+
+ align:start position:0%
+of the transportation system outwards
+that you'll get movements of
+
+ align:start position:0%
+that you'll get movements of
+ 
+
+ align:start position:0%
+that you'll get movements of
+people as
+
+ align:start position:0%
+people as
+ 
+
+ align:start position:0%
+people as
+they classically make more income from
+
+ align:start position:0%
+they classically make more income from
+ 
+
+ align:start position:0%
+they classically make more income from
+the center outwards and this
+
+ align:start position:0%
+the center outwards and this
+ 
+
+ align:start position:0%
+the center outwards and this
+is the workingclass people in the in
+
+ align:start position:0%
+is the workingclass people in the in
+ 
+
+ align:start position:0%
+is the workingclass people in the in
+this graph come in the form a curve in
+
+ align:start position:0%
+this graph come in the form a curve in
+ 
+
+ align:start position:0%
+this graph come in the form a curve in
+the center where they
+
+ align:start position:0%
+the center where they
+ 
+
+ align:start position:0%
+the center where they
+balance minimum costs of
+
+ align:start position:0%
+balance minimum costs of
+ 
+
+ align:start position:0%
+balance minimum costs of
+Transportation in public transportation
+
+ align:start position:0%
+Transportation in public transportation
+ 
+
+ align:start position:0%
+Transportation in public transportation
+with low medium RS and so on and so on
+
+ align:start position:0%
+with low medium RS and so on and so on
+ 
+
+ align:start position:0%
+with low medium RS and so on and so on
+what I saw do was otm it in the father
+
+ align:start position:0%
+what I saw do was otm it in the father
+ 
+
+ align:start position:0%
+what I saw do was otm it in the father
+Regional
+
+ align:start position:0%
+Regional
+ 
+
+ align:start position:0%
+Regional
+science uh is one of the formulators of
+
+ align:start position:0%
+science uh is one of the formulators of
+ 
+
+ align:start position:0%
+science uh is one of the formulators of
+this Theory uh Alonso at Harvard did
+
+ align:start position:0%
+this Theory uh Alonso at Harvard did
+ 
+
+ align:start position:0%
+this Theory uh Alonso at Harvard did
+versions of it Wingo M and
+
+ align:start position:0%
+versions of it Wingo M and
+ 
+
+ align:start position:0%
+versions of it Wingo M and
+others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let me just say a few words about the
+
+ align:start position:0%
+um let me just say a few words about the
+ 
+
+ align:start position:0%
+um let me just say a few words about the
+others in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+list
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there have been attempts to modulate to
+
+ align:start position:0%
+there have been attempts to modulate to
+ 
+
+ align:start position:0%
+there have been attempts to modulate to
+modulate the form of cities by analogies
+
+ align:start position:0%
+modulate the form of cities by analogies
+ 
+
+ align:start position:0%
+modulate the form of cities by analogies
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+physics population potential being
+
+ align:start position:0%
+physics population potential being
+ 
+
+ align:start position:0%
+physics population potential being
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let me get this correct I often make
+
+ align:start position:0%
+uh let me get this correct I often make
+ 
+
+ align:start position:0%
+uh let me get this correct I often make
+a mistake
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with well I'll forget about
+
+ align:start position:0%
+with well I'll forget about
+ 
+
+ align:start position:0%
+with well I'll forget about
+it we haven't got time to go into the
+
+ align:start position:0%
+it we haven't got time to go into the
+ 
+
+ align:start position:0%
+it we haven't got time to go into the
+great difference into the population
+
+ align:start position:0%
+great difference into the population
+ 
+
+ align:start position:0%
+great difference into the population
+potential model gravity models
+
+ align:start position:0%
+potential model gravity models
+ 
+
+ align:start position:0%
+potential model gravity models
+Communications networks and topology I
+
+ align:start position:0%
+Communications networks and topology I
+ 
+
+ align:start position:0%
+Communications networks and topology I
+should add to that more current work in
+
+ align:start position:0%
+should add to that more current work in
+ 
+
+ align:start position:0%
+should add to that more current work in
+fractal and Chaos
+
+ align:start position:0%
+fractal and Chaos
+ 
+
+ align:start position:0%
+fractal and Chaos
+Theory um which if you want to read
+
+ align:start position:0%
+Theory um which if you want to read
+ 
+
+ align:start position:0%
+Theory um which if you want to read
+about fractals read Gavin
+
+ align:start position:0%
+about fractals read Gavin
+ 
+
+ align:start position:0%
+about fractals read Gavin
+batty uh
+
+ align:start position:0%
+batty uh
+ 
+
+ align:start position:0%
+batty uh
+but I estimate these as having less of a
+
+ align:start position:0%
+but I estimate these as having less of a
+ 
+
+ align:start position:0%
+but I estimate these as having less of a
+life in determining current practice in
+
+ align:start position:0%
+life in determining current practice in
+ 
+
+ align:start position:0%
+life in determining current practice in
+urbanism than any of the others they
+
+ align:start position:0%
+urbanism than any of the others they
+ 
+
+ align:start position:0%
+urbanism than any of the others they
+somewhat academic gravity models
+
+ align:start position:0%
+somewhat academic gravity models
+ 
+
+ align:start position:0%
+somewhat academic gravity models
+Foresters Urban systems all of these
+
+ align:start position:0%
+Foresters Urban systems all of these
+ 
+
+ align:start position:0%
+Foresters Urban systems all of these
+form an attempt to
+
+ align:start position:0%
+form an attempt to
+ 
+
+ align:start position:0%
+form an attempt to
+use uh uh Notions of proximity not
+
+ align:start position:0%
+use uh uh Notions of proximity not
+ 
+
+ align:start position:0%
+use uh uh Notions of proximity not
+Notions of
+
+ align:start position:0%
+Notions of
+ 
+
+ align:start position:0%
+Notions of
+income uh to locate shopping centers to
+
+ align:start position:0%
+income uh to locate shopping centers to
+ 
+
+ align:start position:0%
+income uh to locate shopping centers to
+make modifications to the American city
+
+ align:start position:0%
+make modifications to the American city
+ 
+
+ align:start position:0%
+make modifications to the American city
+um the question of
+
+ align:start position:0%
+um the question of
+ 
+
+ align:start position:0%
+um the question of
+decisions link
+
+ align:start position:0%
+decisions link
+ 
+
+ align:start position:0%
+decisions link
+decisions uh again you we have to look
+
+ align:start position:0%
+decisions uh again you we have to look
+ 
+
+ align:start position:0%
+decisions uh again you we have to look
+at the work of people like Forester who
+
+ align:start position:0%
+at the work of people like Forester who
+ 
+
+ align:start position:0%
+at the work of people like Forester who
+claims that we'll see the same phenomen
+
+ align:start position:0%
+claims that we'll see the same phenomen
+ 
+
+ align:start position:0%
+claims that we'll see the same phenomen
+in the work of John Haren on
+
+ align:start position:0%
+in the work of John Haren on
+ 
+
+ align:start position:0%
+in the work of John Haren on
+Tuesday uh John
+
+ align:start position:0%
+Tuesday uh John
+ 
+
+ align:start position:0%
+Tuesday uh John
+Haren claim is that the built world is
+
+ align:start position:0%
+Haren claim is that the built world is
+ 
+
+ align:start position:0%
+Haren claim is that the built world is
+the fun is really the outcome of
+
+ align:start position:0%
+the fun is really the outcome of
+ 
+
+ align:start position:0%
+the fun is really the outcome of
+agreements that are made between
+
+ align:start position:0%
+agreements that are made between
+ 
+
+ align:start position:0%
+agreements that are made between
+different people there's no City but one
+
+ align:start position:0%
+different people there's no City but one
+ 
+
+ align:start position:0%
+different people there's no City but one
+that rests on made agreements and tries
+
+ align:start position:0%
+that rests on made agreements and tries
+ 
+
+ align:start position:0%
+that rests on made agreements and tries
+to determine from made agreements what
+
+ align:start position:0%
+to determine from made agreements what
+ 
+
+ align:start position:0%
+to determine from made agreements what
+could be the form of a city which takes
+
+ align:start position:0%
+could be the form of a city which takes
+ 
+
+ align:start position:0%
+could be the form of a city which takes
+that into account J
+
+ align:start position:0%
+that into account J
+ 
+
+ align:start position:0%
+that into account J
+Forester
+
+ align:start position:0%
+Forester
+ 
+
+ align:start position:0%
+Forester
+uh argues that social systems are count
+
+ align:start position:0%
+uh argues that social systems are count
+ 
+
+ align:start position:0%
+uh argues that social systems are count
+very complex and single answers are not
+
+ align:start position:0%
+very complex and single answers are not
+ 
+
+ align:start position:0%
+very complex and single answers are not
+predictable or not should not be
+
+ align:start position:0%
+predictable or not should not be
+ 
+
+ align:start position:0%
+predictable or not should not be
+expected um Urban systems are based on
+
+ align:start position:0%
+expected um Urban systems are based on
+ 
+
+ align:start position:0%
+expected um Urban systems are based on
+information about the importance thing
+
+ align:start position:0%
+information about the importance thing
+ 
+
+ align:start position:0%
+information about the importance thing
+decisions that largely businessman make
+
+ align:start position:0%
+decisions that largely businessman make
+ 
+
+ align:start position:0%
+decisions that largely businessman make
+in the American
+
+ align:start position:0%
+in the American
+ 
+
+ align:start position:0%
+in the American
+city uh he hasn't asked anybody or
+
+ align:start position:0%
+city uh he hasn't asked anybody or
+ 
+
+ align:start position:0%
+city uh he hasn't asked anybody or
+studied data of any significance he
+
+ align:start position:0%
+studied data of any significance he
+ 
+
+ align:start position:0%
+studied data of any significance he
+comes to
+
+ align:start position:0%
+comes to
+ 
+
+ align:start position:0%
+comes to
+simplistics resolutions that the more in
+
+ align:start position:0%
+simplistics resolutions that the more in
+ 
+
+ align:start position:0%
+simplistics resolutions that the more in
+the more the economy grows the more poor
+
+ align:start position:0%
+the more the economy grows the more poor
+ 
+
+ align:start position:0%
+the more the economy grows the more poor
+people you will have and things of this
+
+ align:start position:0%
+people you will have and things of this
+ 
+
+ align:start position:0%
+people you will have and things of this
+kind in um I'm not doing him just
+
+ align:start position:0%
+kind in um I'm not doing him just
+ 
+
+ align:start position:0%
+kind in um I'm not doing him just
+Justice in one
+
+ align:start position:0%
+Justice in one
+ 
+
+ align:start position:0%
+Justice in one
+sentence um then the arena of conflict
+
+ align:start position:0%
+sentence um then the arena of conflict
+ 
+
+ align:start position:0%
+sentence um then the arena of conflict
+which is really quite an interesting
+
+ align:start position:0%
+which is really quite an interesting
+ 
+
+ align:start position:0%
+which is really quite an interesting
+phenomenon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um much of the models that I've gone
+
+ align:start position:0%
+um much of the models that I've gone
+ 
+
+ align:start position:0%
+um much of the models that I've gone
+through have
+
+ align:start position:0%
+through have
+ 
+
+ align:start position:0%
+through have
+assumed that the city is composed of
+
+ align:start position:0%
+assumed that the city is composed of
+ 
+
+ align:start position:0%
+assumed that the city is composed of
+benign people making benign agreements
+
+ align:start position:0%
+benign people making benign agreements
+ 
+
+ align:start position:0%
+benign people making benign agreements
+amongst each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other Park and burgess's model of
+
+ align:start position:0%
+other Park and burgess's model of
+ 
+
+ align:start position:0%
+other Park and burgess's model of
+concentric circles means that it all
+
+ align:start position:0%
+concentric circles means that it all
+ 
+
+ align:start position:0%
+concentric circles means that it all
+like a plant takes place without the
+
+ align:start position:0%
+like a plant takes place without the
+ 
+
+ align:start position:0%
+like a plant takes place without the
+plant having any items of conflict or
+
+ align:start position:0%
+plant having any items of conflict or
+ 
+
+ align:start position:0%
+plant having any items of conflict or
+conflict as a phenomenon whereas in fact
+
+ align:start position:0%
+conflict as a phenomenon whereas in fact
+ 
+
+ align:start position:0%
+conflict as a phenomenon whereas in fact
+for long for many centuries the
+
+ align:start position:0%
+for long for many centuries the
+ 
+
+ align:start position:0%
+for long for many centuries the
+resolution of conflict to the building
+
+ align:start position:0%
+resolution of conflict to the building
+ 
+
+ align:start position:0%
+resolution of conflict to the building
+of walls was a fundamental aspect of
+
+ align:start position:0%
+of walls was a fundamental aspect of
+ 
+
+ align:start position:0%
+of walls was a fundamental aspect of
+City form
+
+ align:start position:0%
+City form
+ 
+
+ align:start position:0%
+City form
+vong
+
+ align:start position:0%
+vong
+ 
+
+ align:start position:0%
+vong
+the end of the 17th century the
+
+ align:start position:0%
+the end of the 17th century the
+ 
+
+ align:start position:0%
+the end of the 17th century the
+beginning of the 18th
+
+ align:start position:0%
+beginning of the 18th
+ 
+
+ align:start position:0%
+beginning of the 18th
+century uh could design a town which
+
+ align:start position:0%
+century uh could design a town which
+ 
+
+ align:start position:0%
+century uh could design a town which
+could not be penetrated so it his
+
+ align:start position:0%
+could not be penetrated so it his
+ 
+
+ align:start position:0%
+could not be penetrated so it his
+reputation was blond
+
+ align:start position:0%
+reputation was blond
+ 
+
+ align:start position:0%
+reputation was blond
+taught
+
+ align:start position:0%
+taught
+ 
+
+ align:start position:0%
+taught
+fortification to architecture students
+
+ align:start position:0%
+fortification to architecture students
+ 
+
+ align:start position:0%
+fortification to architecture students
+at the the academy in
+
+ align:start position:0%
+at the the academy in
+ 
+
+ align:start position:0%
+at the the academy in
+Paris
+
+ align:start position:0%
+Paris
+ 
+
+ align:start position:0%
+Paris
+um the people have taken up
+
+ align:start position:0%
+um the people have taken up
+ 
+
+ align:start position:0%
+um the people have taken up
+conflict really exist on the left
+
+ align:start position:0%
+conflict really exist on the left
+ 
+
+ align:start position:0%
+conflict really exist on the left
+there's David Gordon who explains
+
+ align:start position:0%
+there's David Gordon who explains
+ 
+
+ align:start position:0%
+there's David Gordon who explains
+American Suburbia by the movement of
+
+ align:start position:0%
+American Suburbia by the movement of
+ 
+
+ align:start position:0%
+American Suburbia by the movement of
+bosses to get away from workers in labor
+
+ align:start position:0%
+bosses to get away from workers in labor
+ 
+
+ align:start position:0%
+bosses to get away from workers in labor
+Strife you get money castels in his pre
+
+ align:start position:0%
+Strife you get money castels in his pre
+ 
+
+ align:start position:0%
+Strife you get money castels in his pre
+communication theory model mode who was
+
+ align:start position:0%
+communication theory model mode who was
+ 
+
+ align:start position:0%
+communication theory model mode who was
+a Spanish young Spanish
+
+ align:start position:0%
+a Spanish young Spanish
+ 
+
+ align:start position:0%
+a Spanish young Spanish
+Marxist uh who wrote something called
+
+ align:start position:0%
+Marxist uh who wrote something called
+ 
+
+ align:start position:0%
+Marxist uh who wrote something called
+The Wild City in which he claims that
+
+ align:start position:0%
+The Wild City in which he claims that
+ 
+
+ align:start position:0%
+The Wild City in which he claims that
+suburbanization is the function of
+
+ align:start position:0%
+suburbanization is the function of
+ 
+
+ align:start position:0%
+suburbanization is the function of
+surplus Commodities rather than of any
+
+ align:start position:0%
+surplus Commodities rather than of any
+ 
+
+ align:start position:0%
+surplus Commodities rather than of any
+any other form of
+
+ align:start position:0%
+any other form of
+ 
+
+ align:start position:0%
+any other form of
+economy uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh um
+
+ align:start position:0%
+uh um
+ 
+
+ align:start position:0%
+uh um
+David
+
+ align:start position:0%
+David
+ 
+
+ align:start position:0%
+David
+Harvey arguing that it's very difficult
+
+ align:start position:0%
+Harvey arguing that it's very difficult
+ 
+
+ align:start position:0%
+Harvey arguing that it's very difficult
+to produce social equity and counter
+
+ align:start position:0%
+to produce social equity and counter
+ 
+
+ align:start position:0%
+to produce social equity and counter
+capitalism because there will always be
+
+ align:start position:0%
+capitalism because there will always be
+ 
+
+ align:start position:0%
+capitalism because there will always be
+obstacles in the way of
+
+ align:start position:0%
+obstacles in the way of
+ 
+
+ align:start position:0%
+obstacles in the way of
+maximizing return on
+
+ align:start position:0%
+maximizing return on
+ 
+
+ align:start position:0%
+maximizing return on
+Capital
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh Leo the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+French sociologist who who ran a journal
+
+ align:start position:0%
+French sociologist who who ran a journal
+ 
+
+ align:start position:0%
+French sociologist who who ran a journal
+called Le SP
+
+ align:start position:0%
+called Le SP
+ 
+
+ align:start position:0%
+called Le SP
+soci uh I was editor of
+
+ align:start position:0%
+soci uh I was editor of
+ 
+
+ align:start position:0%
+soci uh I was editor of
+spio space and society which was uh I
+
+ align:start position:0%
+spio space and society which was uh I
+ 
+
+ align:start position:0%
+spio space and society which was uh I
+was part
+
+ align:start position:0%
+was part
+ 
+
+ align:start position:0%
+was part
+editor following the F's
+
+ align:start position:0%
+editor following the F's
+ 
+
+ align:start position:0%
+editor following the F's
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+um all of these are looking at the way
+
+ align:start position:0%
+um all of these are looking at the way
+ 
+
+ align:start position:0%
+um all of these are looking at the way
+in which conflict can be assumed and
+
+ align:start position:0%
+in which conflict can be assumed and
+ 
+
+ align:start position:0%
+in which conflict can be assumed and
+resolved as part of the real existence
+
+ align:start position:0%
+resolved as part of the real existence
+ 
+
+ align:start position:0%
+resolved as part of the real existence
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+city
+
+ align:start position:0%
+city
+ 
+
+ align:start position:0%
+city
+uh John car dealo the Italian architect
+
+ align:start position:0%
+uh John car dealo the Italian architect
+ 
+
+ align:start position:0%
+uh John car dealo the Italian architect
+used to argue
+
+ align:start position:0%
+used to argue
+ 
+
+ align:start position:0%
+used to argue
+that one of the functions
+
+ align:start position:0%
+that one of the functions
+ 
+
+ align:start position:0%
+that one of the functions
+of one of the ways of displaying
+
+ align:start position:0%
+of one of the ways of displaying
+ 
+
+ align:start position:0%
+of one of the ways of displaying
+conflict was
+
+ align:start position:0%
+conflict was
+ 
+
+ align:start position:0%
+conflict was
+to allow architecture to build in its
+
+ align:start position:0%
+to allow architecture to build in its
+ 
+
+ align:start position:0%
+to allow architecture to build in its
+appropriate fashion but to depict the of
+
+ align:start position:0%
+appropriate fashion but to depict the of
+ 
+
+ align:start position:0%
+appropriate fashion but to depict the of
+conflict that are available and to
+
+ align:start position:0%
+conflict that are available and to
+ 
+
+ align:start position:0%
+conflict that are available and to
+heighten the sense of conflict in the
+
+ align:start position:0%
+heighten the sense of conflict in the
+ 
+
+ align:start position:0%
+heighten the sense of conflict in the
+city but also to make it possible in a
+
+ align:start position:0%
+city but also to make it possible in a
+ 
+
+ align:start position:0%
+city but also to make it possible in a
+kind of anarchic sense for that
+
+ align:start position:0%
+kind of anarchic sense for that
+ 
+
+ align:start position:0%
+kind of anarchic sense for that
+City's resolutions to be made within a
+
+ align:start position:0%
+City's resolutions to be made within a
+ 
+
+ align:start position:0%
+City's resolutions to be made within a
+framework of understood conflict
+
+ align:start position:0%
+framework of understood conflict
+ 
+
+ align:start position:0%
+framework of understood conflict
+resolvable conflict not
+
+ align:start position:0%
+resolvable conflict not
+ 
+
+ align:start position:0%
+resolvable conflict not
+Revolution uh so these attempts at
+
+ align:start position:0%
+Revolution uh so these attempts at
+ 
+
+ align:start position:0%
+Revolution uh so these attempts at
+plans uh
+
+ align:start position:0%
+plans uh
+ 
+
+ align:start position:0%
+plans uh
+sometimes Manifest this or at
+
+ align:start position:0%
+sometimes Manifest this or at
+ 
+
+ align:start position:0%
+sometimes Manifest this or at
+least if you look at the workers's
+
+ align:start position:0%
+least if you look at the workers's
+ 
+
+ align:start position:0%
+least if you look at the workers's
+housing interally for
+
+ align:start position:0%
+housing interally for
+ 
+
+ align:start position:0%
+housing interally for
+instance uh you can see elements of this
+
+ align:start position:0%
+instance uh you can see elements of this
+ 
+
+ align:start position:0%
+instance uh you can see elements of this
+proposition but it's very vague and very
+
+ align:start position:0%
+proposition but it's very vague and very
+ 
+
+ align:start position:0%
+proposition but it's very vague and very
+generalized and not really powerful
+
+ align:start position:0%
+generalized and not really powerful
+ 
+
+ align:start position:0%
+generalized and not really powerful
+Theory um the marxists have not produced
+
+ align:start position:0%
+Theory um the marxists have not produced
+ 
+
+ align:start position:0%
+Theory um the marxists have not produced
+cities
+
+ align:start position:0%
+cities
+ 
+
+ align:start position:0%
+cities
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+externalized the conflict Notions which
+
+ align:start position:0%
+externalized the conflict Notions which
+ 
+
+ align:start position:0%
+externalized the conflict Notions which
+they examined in the ear the CI are much
+
+ align:start position:0%
+they examined in the ear the CI are much
+ 
+
+ align:start position:0%
+they examined in the ear the CI are much
+like any city in the world and Chinese
+
+ align:start position:0%
+like any city in the world and Chinese
+ 
+
+ align:start position:0%
+like any city in the world and Chinese
+Marxism is certainly not producing very
+
+ align:start position:0%
+Marxism is certainly not producing very
+ 
+
+ align:start position:0%
+Marxism is certainly not producing very
+much from which we can learn uh about
+
+ align:start position:0%
+much from which we can learn uh about
+ 
+
+ align:start position:0%
+much from which we can learn uh about
+New City
+
+ align:start position:0%
+New City
+ 
+
+ align:start position:0%
+New City
+growth
+
+ align:start position:0%
+growth
+ 
+
+ align:start position:0%
+growth
+uh so this particular theory is waiting
+
+ align:start position:0%
+uh so this particular theory is waiting
+ 
+
+ align:start position:0%
+uh so this particular theory is waiting
+to most of these
+
+ align:start position:0%
+to most of these
+ 
+
+ align:start position:0%
+to most of these
+theories let me just end off in
+
+ align:start position:0%
+theories let me just end off in
+ 
+
+ align:start position:0%
+theories let me just end off in
+one with this piece I gave
+
+ align:start position:0%
+one with this piece I gave
+ 
+
+ align:start position:0%
+one with this piece I gave
+you on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physics H the work of Jeffrey West yes
+
+ align:start position:0%
+physics H the work of Jeffrey West yes
+ 
+
+ align:start position:0%
+physics H the work of Jeffrey West yes
+do you know his work yeah what do you
+
+ align:start position:0%
+do you know his work yeah what do you
+ 
+
+ align:start position:0%
+do you know his work yeah what do you
+think of
+
+ align:start position:0%
+think of
+ 
+
+ align:start position:0%
+think of
+it I think I think it brings in an
+
+ align:start position:0%
+it I think I think it brings in an
+ 
+
+ align:start position:0%
+it I think I think it brings in an
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+perspective uh someone is
+
+ align:start position:0%
+perspective uh someone is
+ 
+
+ align:start position:0%
+perspective uh someone is
+finding on the
+
+ align:start position:0%
+finding on the
+ 
+
+ align:start position:0%
+finding on the
+the efficiency of CI and the ratios of
+
+ align:start position:0%
+the efficiency of CI and the ratios of
+ 
+
+ align:start position:0%
+the efficiency of CI and the ratios of
+investment versus how the population
+
+ align:start position:0%
+investment versus how the population
+ 
+
+ align:start position:0%
+investment versus how the population
+grows at the same time the per capital
+
+ align:start position:0%
+grows at the same time the per capital
+ 
+
+ align:start position:0%
+grows at the same time the per capital
+world that
+
+ align:start position:0%
+world that
+ 
+
+ align:start position:0%
+world that
+generat but it seems to be bit
+
+ align:start position:0%
+generat but it seems to be bit
+ 
+
+ align:start position:0%
+generat but it seems to be bit
+reductionist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+view you know it
+
+ align:start position:0%
+view you know it
+ 
+
+ align:start position:0%
+view you know it
+starts yeah it starts separating
+
+ align:start position:0%
+starts yeah it starts separating
+ 
+
+ align:start position:0%
+starts yeah it starts separating
+out what optimizes the functioning of a
+
+ align:start position:0%
+out what optimizes the functioning of a
+ 
+
+ align:start position:0%
+out what optimizes the functioning of a
+city in terms of transportation land use
+
+ align:start position:0%
+city in terms of transportation land use
+ 
+
+ align:start position:0%
+city in terms of transportation land use
+crime and so on which are important
+
+ align:start position:0%
+crime and so on which are important
+ 
+
+ align:start position:0%
+crime and so on which are important
+components to understand but he doesn't
+
+ align:start position:0%
+components to understand but he doesn't
+ 
+
+ align:start position:0%
+components to understand but he doesn't
+accept the city as an environment which
+
+ align:start position:0%
+accept the city as an environment which
+ 
+
+ align:start position:0%
+accept the city as an environment which
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+spatiality or experience or any of the
+
+ align:start position:0%
+spatiality or experience or any of the
+ 
+
+ align:start position:0%
+spatiality or experience or any of the
+things that art
+
+ align:start position:0%
+things that art
+ 
+
+ align:start position:0%
+things that art
+history I'm beginning to think more and
+
+ align:start position:0%
+history I'm beginning to think more and
+ 
+
+ align:start position:0%
+history I'm beginning to think more and
+more that in order to understand
+
+ align:start position:0%
+more that in order to understand
+ 
+
+ align:start position:0%
+more that in order to understand
+urbanism you need to study art
+
+ align:start position:0%
+urbanism you need to study art
+ 
+
+ align:start position:0%
+urbanism you need to study art
+history and perhaps forg about all of
+
+ align:start position:0%
+history and perhaps forg about all of
+ 
+
+ align:start position:0%
+history and perhaps forg about all of
+this stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we all know that every city is
+
+ align:start position:0%
+but we all know that every city is
+ 
+
+ align:start position:0%
+but we all know that every city is
+unique that's all we talk about when we
+
+ align:start position:0%
+unique that's all we talk about when we
+ 
+
+ align:start position:0%
+unique that's all we talk about when we
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+cities by but focusing on those
+
+ align:start position:0%
+cities by but focusing on those
+ 
+
+ align:start position:0%
+cities by but focusing on those
+differences misses the point sure there
+
+ align:start position:0%
+differences misses the point sure there
+ 
+
+ align:start position:0%
+differences misses the point sure there
+are differences but different from what
+
+ align:start position:0%
+are differences but different from what
+ 
+
+ align:start position:0%
+are differences but different from what
+we found the
+
+ align:start position:0%
+we found the
+ 
+
+ align:start position:0%
+we found the
+what there's an
+
+ align:start position:0%
+what there's an
+ 
+
+ align:start position:0%
+what there's an
+arrogance about the security of physics
+
+ align:start position:0%
+arrogance about the security of physics
+ 
+
+ align:start position:0%
+arrogance about the security of physics
+has applied to complex phenomena such as
+
+ align:start position:0%
+has applied to complex phenomena such as
+ 
+
+ align:start position:0%
+has applied to complex phenomena such as
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+city um it may be that this is a new
+
+ align:start position:0%
+city um it may be that this is a new
+ 
+
+ align:start position:0%
+city um it may be that this is a new
+generation of thinking I mean they're
+
+ align:start position:0%
+generation of thinking I mean they're
+ 
+
+ align:start position:0%
+generation of thinking I mean they're
+doing it at Oxford in Santa Fe and the
+
+ align:start position:0%
+doing it at Oxford in Santa Fe and the
+ 
+
+ align:start position:0%
+doing it at Oxford in Santa Fe and the
+more and more groups of complex
+
+ align:start position:0%
+more and more groups of complex
+ 
+
+ align:start position:0%
+more and more groups of complex
+theorists
+
+ align:start position:0%
+theorists
+ 
+
+ align:start position:0%
+theorists
+emerging I have my doubts and I'll be
+
+ align:start position:0%
+emerging I have my doubts and I'll be
+ 
+
+ align:start position:0%
+emerging I have my doubts and I'll be
+too old to see any of this anyway so I
+
+ align:start position:0%
+too old to see any of this anyway so I
+ 
+
+ align:start position:0%
+too old to see any of this anyway so I
+leave it for you on Tuesday we will look
+
+ align:start position:0%
+leave it for you on Tuesday we will look
+ 
+
+ align:start position:0%
+leave it for you on Tuesday we will look
+at for the last time in part one of this
+
+ align:start position:0%
+at for the last time in part one of this
+ 
+
+ align:start position:0%
+at for the last time in part one of this
+subject at four or five theories of
+
+ align:start position:0%
+subject at four or five theories of
+ 
+
+ align:start position:0%
+subject at four or five theories of
+Architects contemporary Architects or
+
+ align:start position:0%
+Architects contemporary Architects or
+ 
+
+ align:start position:0%
+Architects contemporary Architects or
+recently deceased Architects who've made
+
+ align:start position:0%
+recently deceased Architects who've made
+ 
+
+ align:start position:0%
+recently deceased Architects who've made
+attempts such as space
+
+ align:start position:0%
+attempts such as space
+ 
+
+ align:start position:0%
+attempts such as space
+syntax so on and so on um and then start
+
+ align:start position:0%
+syntax so on and so on um and then start
+ 
+
+ align:start position:0%
+syntax so on and so on um and then start
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+scratch with the Industrial Revolution
+
+ align:start position:0%
+scratch with the Industrial Revolution
+ 
+
+ align:start position:0%
+scratch with the Industrial Revolution
+and see what we can learn by looking
+
+ align:start position:0%
+and see what we can learn by looking
+ 
+
+ align:start position:0%
+and see what we can learn by looking
+carefully at
+
+ align:start position:0%
+carefully at
+ 
+
+ align:start position:0%
+carefully at
+phenomena
\ No newline at end of file
diff --git a/12K3PlcicZE.txt b/12K3PlcicZE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0c78ff0052f768aa042364a18060a4c24db52801
--- /dev/null
+++ b/12K3PlcicZE.txt
@@ -0,0 +1,2147 @@
+align:start position:0%
+ 
+i won't tile this in with the discount
+
+ align:start position:0%
+i won't tile this in with the discount
+ 
+
+ align:start position:0%
+i won't tile this in with the discount
+rate here
+
+ align:start position:0%
+rate here
+ 
+
+ align:start position:0%
+rate here
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+when the demand for capacity is growing
+
+ align:start position:0%
+when the demand for capacity is growing
+ 
+
+ align:start position:0%
+when the demand for capacity is growing
+say for electricity
+
+ align:start position:0%
+say for electricity
+ 
+
+ align:start position:0%
+say for electricity
+you have two choices you can build a big
+
+ align:start position:0%
+you have two choices you can build a big
+ 
+
+ align:start position:0%
+you have two choices you can build a big
+plant now for many years ahead so i'm
+
+ align:start position:0%
+plant now for many years ahead so i'm
+ 
+
+ align:start position:0%
+plant now for many years ahead so i'm
+going to okay i'm going to build a plant
+
+ align:start position:0%
+going to okay i'm going to build a plant
+ 
+
+ align:start position:0%
+going to okay i'm going to build a plant
+for the next uh 20 years my father had
+
+ align:start position:0%
+for the next uh 20 years my father had
+ 
+
+ align:start position:0%
+for the next uh 20 years my father had
+this experience working actually in
+
+ align:start position:0%
+this experience working actually in
+ 
+
+ align:start position:0%
+this experience working actually in
+india on the when they were building the
+
+ align:start position:0%
+india on the when they were building the
+ 
+
+ align:start position:0%
+india on the when they were building the
+original steel mills about 30 or 40
+
+ align:start position:0%
+original steel mills about 30 or 40
+ 
+
+ align:start position:0%
+original steel mills about 30 or 40
+years ago the whole pressure was build
+
+ align:start position:0%
+years ago the whole pressure was build
+ 
+
+ align:start position:0%
+years ago the whole pressure was build
+big plants get them really efficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's one approach and the other
+
+ align:start position:0%
+that's one approach and the other
+ 
+
+ align:start position:0%
+that's one approach and the other
+approach is to build small now and some
+
+ align:start position:0%
+approach is to build small now and some
+ 
+
+ align:start position:0%
+approach is to build small now and some
+more smaller units later on as you phase
+
+ align:start position:0%
+more smaller units later on as you phase
+ 
+
+ align:start position:0%
+more smaller units later on as you phase
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+capacity according to the growth of the
+
+ align:start position:0%
+capacity according to the growth of the
+ 
+
+ align:start position:0%
+capacity according to the growth of the
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+so the choice a is based on economies of
+
+ align:start position:0%
+so the choice a is based on economies of
+ 
+
+ align:start position:0%
+so the choice a is based on economies of
+scale
+
+ align:start position:0%
+scale
+ 
+
+ align:start position:0%
+scale
+and the choice b
+
+ align:start position:0%
+and the choice b
+ 
+
+ align:start position:0%
+and the choice b
+has this particular feature which i want
+
+ align:start position:0%
+has this particular feature which i want
+ 
+
+ align:start position:0%
+has this particular feature which i want
+to emphasize here
+
+ align:start position:0%
+to emphasize here
+ 
+
+ align:start position:0%
+to emphasize here
+is that if you decide to build a
+
+ align:start position:0%
+is that if you decide to build a
+ 
+
+ align:start position:0%
+is that if you decide to build a
+capacity when you need it that is not
+
+ align:start position:0%
+capacity when you need it that is not
+ 
+
+ align:start position:0%
+capacity when you need it that is not
+all now
+
+ align:start position:0%
+all now
+ 
+
+ align:start position:0%
+all now
+because you're if you're building for
+
+ align:start position:0%
+because you're if you're building for
+ 
+
+ align:start position:0%
+because you're if you're building for
+the next 10 years or 15 years but maybe
+
+ align:start position:0%
+the next 10 years or 15 years but maybe
+ 
+
+ align:start position:0%
+the next 10 years or 15 years but maybe
+in three or four years
+
+ align:start position:0%
+in three or four years
+ 
+
+ align:start position:0%
+in three or four years
+that extra addition if your money is
+
+ align:start position:0%
+that extra addition if your money is
+ 
+
+ align:start position:0%
+that extra addition if your money is
+expensive you have a discount rate of
+
+ align:start position:0%
+expensive you have a discount rate of
+ 
+
+ align:start position:0%
+expensive you have a discount rate of
+ten percent or eight percent or whatever
+
+ align:start position:0%
+ten percent or eight percent or whatever
+ 
+
+ align:start position:0%
+ten percent or eight percent or whatever
+it might be
+
+ align:start position:0%
+it might be
+ 
+
+ align:start position:0%
+it might be
+might be say oh three three years later
+
+ align:start position:0%
+might be say oh three three years later
+ 
+
+ align:start position:0%
+might be say oh three three years later
+if i build that same plant
+
+ align:start position:0%
+if i build that same plant
+ 
+
+ align:start position:0%
+if i build that same plant
+i don't pay a hundred units because 100
+
+ align:start position:0%
+i don't pay a hundred units because 100
+ 
+
+ align:start position:0%
+i don't pay a hundred units because 100
+of what i paid the first year well your
+
+ align:start position:0%
+of what i paid the first year well your
+ 
+
+ align:start position:0%
+of what i paid the first year well your
+check may be 400 percent but the present
+
+ align:start position:0%
+check may be 400 percent but the present
+ 
+
+ align:start position:0%
+check may be 400 percent but the present
+value of it would be discounted over
+
+ align:start position:0%
+value of it would be discounted over
+ 
+
+ align:start position:0%
+value of it would be discounted over
+three years and come in roughly speaking
+
+ align:start position:0%
+three years and come in roughly speaking
+ 
+
+ align:start position:0%
+three years and come in roughly speaking
+for orders of magnitude would be thirty
+
+ align:start position:0%
+for orders of magnitude would be thirty
+ 
+
+ align:start position:0%
+for orders of magnitude would be thirty
+percent uh less or if the discount rate
+
+ align:start position:0%
+percent uh less or if the discount rate
+ 
+
+ align:start position:0%
+percent uh less or if the discount rate
+was eight be about 25 percent less so
+
+ align:start position:0%
+was eight be about 25 percent less so
+ 
+
+ align:start position:0%
+was eight be about 25 percent less so
+the point is that by deferring the cost
+
+ align:start position:0%
+the point is that by deferring the cost
+ 
+
+ align:start position:0%
+the point is that by deferring the cost
+you counter balance the cost of the
+
+ align:start position:0%
+you counter balance the cost of the
+ 
+
+ align:start position:0%
+you counter balance the cost of the
+effective economy of scale
+
+ align:start position:0%
+effective economy of scale
+ 
+
+ align:start position:0%
+effective economy of scale
+if the argument is if i build it big
+
+ align:start position:0%
+if the argument is if i build it big
+ 
+
+ align:start position:0%
+if the argument is if i build it big
+it's cheaper per unit
+
+ align:start position:0%
+it's cheaper per unit
+ 
+
+ align:start position:0%
+it's cheaper per unit
+but if you delay
+
+ align:start position:0%
+but if you delay
+ 
+
+ align:start position:0%
+but if you delay
+the investments those other additions
+
+ align:start position:0%
+the investments those other additions
+ 
+
+ align:start position:0%
+the investments those other additions
+occur later in time
+
+ align:start position:0%
+occur later in time
+ 
+
+ align:start position:0%
+occur later in time
+and their cost is discounted so that
+
+ align:start position:0%
+and their cost is discounted so that
+ 
+
+ align:start position:0%
+and their cost is discounted so that
+the advantage of building large in the
+
+ align:start position:0%
+the advantage of building large in the
+ 
+
+ align:start position:0%
+the advantage of building large in the
+beginning are counter balanced so the
+
+ align:start position:0%
+beginning are counter balanced so the
+ 
+
+ align:start position:0%
+beginning are counter balanced so the
+discount rate counterbalance the economy
+
+ align:start position:0%
+discount rate counterbalance the economy
+ 
+
+ align:start position:0%
+discount rate counterbalance the economy
+the scale
+
+ align:start position:0%
+the scale
+ 
+
+ align:start position:0%
+the scale
+that is what you might gain
+
+ align:start position:0%
+that is what you might gain
+ 
+
+ align:start position:0%
+that is what you might gain
+by using
+
+ align:start position:0%
+by using
+ 
+
+ align:start position:0%
+by using
+economies of scale um in
+
+ align:start position:0%
+economies of scale um in
+ 
+
+ align:start position:0%
+economies of scale um in
+the control the productivity of the
+
+ align:start position:0%
+the control the productivity of the
+ 
+
+ align:start position:0%
+the control the productivity of the
+plant and principle you can lose by the
+
+ align:start position:0%
+plant and principle you can lose by the
+ 
+
+ align:start position:0%
+plant and principle you can lose by the
+economics
+
+ align:start position:0%
+economics
+ 
+
+ align:start position:0%
+economics
+now if you consider that economies of
+
+ align:start position:0%
+now if you consider that economies of
+ 
+
+ align:start position:0%
+now if you consider that economies of
+scale is a driver of the engineering
+
+ align:start position:0%
+scale is a driver of the engineering
+ 
+
+ align:start position:0%
+scale is a driver of the engineering
+design
+
+ align:start position:0%
+design
+ 
+
+ align:start position:0%
+design
+recognize the same point that many
+
+ align:start position:0%
+recognize the same point that many
+ 
+
+ align:start position:0%
+recognize the same point that many
+engineering designs what is the best
+
+ align:start position:0%
+engineering designs what is the best
+ 
+
+ align:start position:0%
+engineering designs what is the best
+technical design
+
+ align:start position:0%
+technical design
+ 
+
+ align:start position:0%
+technical design
+uh don't really factor in the economics
+
+ align:start position:0%
+uh don't really factor in the economics
+ 
+
+ align:start position:0%
+uh don't really factor in the economics
+of it they'll look at the
+
+ align:start position:0%
+of it they'll look at the
+ 
+
+ align:start position:0%
+of it they'll look at the
+all right you asked me to provide
+
+ align:start position:0%
+all right you asked me to provide
+ 
+
+ align:start position:0%
+all right you asked me to provide
+capacity this is the cheapest way to do
+
+ align:start position:0%
+capacity this is the cheapest way to do
+ 
+
+ align:start position:0%
+capacity this is the cheapest way to do
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this ties in this discussion ties in
+
+ align:start position:0%
+this ties in this discussion ties in
+ 
+
+ align:start position:0%
+this ties in this discussion ties in
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+mit text
+
+ align:start position:0%
+mit text
+ 
+
+ align:start position:0%
+mit text
+simple case that i gave you a homework
+
+ align:start position:0%
+simple case that i gave you a homework
+ 
+
+ align:start position:0%
+simple case that i gave you a homework
+two that i've given you that you're
+
+ align:start position:0%
+two that i've given you that you're
+ 
+
+ align:start position:0%
+two that i've given you that you're
+turning in soon
+
+ align:start position:0%
+turning in soon
+ 
+
+ align:start position:0%
+turning in soon
+that you know if you look at it i've
+
+ align:start position:0%
+that you know if you look at it i've
+ 
+
+ align:start position:0%
+that you know if you look at it i've
+given you some particular numbers
+
+ align:start position:0%
+given you some particular numbers
+ 
+
+ align:start position:0%
+given you some particular numbers
+and of course your numbers depend on
+
+ align:start position:0%
+and of course your numbers depend on
+ 
+
+ align:start position:0%
+and of course your numbers depend on
+your special factors your own uh
+
+ align:start position:0%
+your special factors your own uh
+ 
+
+ align:start position:0%
+your special factors your own uh
+but very often the things with economy
+
+ align:start position:0%
+but very often the things with economy
+ 
+
+ align:start position:0%
+but very often the things with economy
+that scale just isn't a good design
+
+ align:start position:0%
+that scale just isn't a good design
+ 
+
+ align:start position:0%
+that scale just isn't a good design
+because on an economic basis from a
+
+ align:start position:0%
+because on an economic basis from a
+ 
+
+ align:start position:0%
+because on an economic basis from a
+productivity basis purely technically it
+
+ align:start position:0%
+productivity basis purely technically it
+ 
+
+ align:start position:0%
+productivity basis purely technically it
+looks great from a economic basis it may
+
+ align:start position:0%
+looks great from a economic basis it may
+ 
+
+ align:start position:0%
+looks great from a economic basis it may
+not there's x counter balancing of the
+
+ align:start position:0%
+not there's x counter balancing of the
+ 
+
+ align:start position:0%
+not there's x counter balancing of the
+of the discount rate counterbalances the
+
+ align:start position:0%
+of the discount rate counterbalances the
+ 
+
+ align:start position:0%
+of the discount rate counterbalances the
+economies of scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is compounded by this thing of
+
+ align:start position:0%
+now this is compounded by this thing of
+ 
+
+ align:start position:0%
+now this is compounded by this thing of
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+what is this thing
+
+ align:start position:0%
+what is this thing
+ 
+
+ align:start position:0%
+what is this thing
+so learning is an experiment an
+
+ align:start position:0%
+so learning is an experiment an
+ 
+
+ align:start position:0%
+so learning is an experiment an
+empirical observation the production of
+
+ align:start position:0%
+empirical observation the production of
+ 
+
+ align:start position:0%
+empirical observation the production of
+more units
+
+ align:start position:0%
+more units
+ 
+
+ align:start position:0%
+more units
+uh gives a lower unit cost
+
+ align:start position:0%
+uh gives a lower unit cost
+ 
+
+ align:start position:0%
+uh gives a lower unit cost
+why is this
+
+ align:start position:0%
+why is this
+ 
+
+ align:start position:0%
+why is this
+well the first time for those of you who
+
+ align:start position:0%
+well the first time for those of you who
+ 
+
+ align:start position:0%
+well the first time for those of you who
+have ever gone camping and have had to
+
+ align:start position:0%
+have ever gone camping and have had to
+ 
+
+ align:start position:0%
+have ever gone camping and have had to
+raise a tent the first time you put your
+
+ align:start position:0%
+raise a tent the first time you put your
+ 
+
+ align:start position:0%
+raise a tent the first time you put your
+tent together you probably
+
+ align:start position:0%
+tent together you probably
+ 
+
+ align:start position:0%
+tent together you probably
+took a long time you had to figure out
+
+ align:start position:0%
+took a long time you had to figure out
+ 
+
+ align:start position:0%
+took a long time you had to figure out
+where part a went to part c and so forth
+
+ align:start position:0%
+where part a went to part c and so forth
+ 
+
+ align:start position:0%
+where part a went to part c and so forth
+and you hadn't done it before
+
+ align:start position:0%
+and you hadn't done it before
+ 
+
+ align:start position:0%
+and you hadn't done it before
+and by the time you've done it 10 or 15
+
+ align:start position:0%
+and by the time you've done it 10 or 15
+ 
+
+ align:start position:0%
+and by the time you've done it 10 or 15
+times you can probably do it much faster
+
+ align:start position:0%
+times you can probably do it much faster
+ 
+
+ align:start position:0%
+times you can probably do it much faster
+that is you've learned something about
+
+ align:start position:0%
+that is you've learned something about
+ 
+
+ align:start position:0%
+that is you've learned something about
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
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+
+ align:start position:0%
+it's a
+ 
+
+ align:start position:0%
+it's a
+common kind of exp of
+
+ align:start position:0%
+common kind of exp of
+ 
+
+ align:start position:0%
+common kind of exp of
+industrial analysis to compare the cost
+
+ align:start position:0%
+industrial analysis to compare the cost
+ 
+
+ align:start position:0%
+industrial analysis to compare the cost
+of producing a unit whether it's a ship
+
+ align:start position:0%
+of producing a unit whether it's a ship
+ 
+
+ align:start position:0%
+of producing a unit whether it's a ship
+or a car or an oil platform
+
+ align:start position:0%
+or a car or an oil platform
+ 
+
+ align:start position:0%
+or a car or an oil platform
+by looking at what was the cost of first
+
+ align:start position:0%
+by looking at what was the cost of first
+ 
+
+ align:start position:0%
+by looking at what was the cost of first
+design was
+
+ align:start position:0%
+design was
+ 
+
+ align:start position:0%
+design was
+the cost of the second one like the
+
+ align:start position:0%
+the cost of the second one like the
+ 
+
+ align:start position:0%
+the cost of the second one like the
+first the stir and so forth
+
+ align:start position:0%
+first the stir and so forth
+ 
+
+ align:start position:0%
+first the stir and so forth
+and it's called learning on the basis
+
+ align:start position:0%
+and it's called learning on the basis
+ 
+
+ align:start position:0%
+and it's called learning on the basis
+that you on the idea that you've learned
+
+ align:start position:0%
+that you on the idea that you've learned
+ 
+
+ align:start position:0%
+that you on the idea that you've learned
+something how to do it better bet uh
+
+ align:start position:0%
+something how to do it better bet uh
+ 
+
+ align:start position:0%
+something how to do it better bet uh
+better it also may reflect frankly not
+
+ align:start position:0%
+better it also may reflect frankly not
+ 
+
+ align:start position:0%
+better it also may reflect frankly not
+just learning
+
+ align:start position:0%
+just learning
+ 
+
+ align:start position:0%
+just learning
+but also that you've
+
+ align:start position:0%
+but also that you've
+ 
+
+ align:start position:0%
+but also that you've
+changed the design somewhat you've
+
+ align:start position:0%
+changed the design somewhat you've
+ 
+
+ align:start position:0%
+changed the design somewhat you've
+tweaked it somehow so it's now more
+
+ align:start position:0%
+tweaked it somehow so it's now more
+ 
+
+ align:start position:0%
+tweaked it somehow so it's now more
+efficient
+
+ align:start position:0%
+efficient
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+
+ align:start position:0%
+efficient
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+collectively it's known as the learning
+
+ align:start position:0%
+collectively it's known as the learning
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+
+ align:start position:0%
+collectively it's known as the learning
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+
+ align:start position:0%
+phenomenon and this can be very
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+
+ align:start position:0%
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+
+ align:start position:0%
+important i was working with bp at one
+ 
+
+ align:start position:0%
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+time and for reasons which was counter
+
+ align:start position:0%
+time and for reasons which was counter
+ 
+
+ align:start position:0%
+time and for reasons which was counter
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+
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+there to their culture
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+
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+ align:start position:0%
+um
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+
+ align:start position:0%
+um
+when they were doing some drilling in
+
+ align:start position:0%
+when they were doing some drilling in
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+
+ align:start position:0%
+when they were doing some drilling in
+azerbaijan
+
+ align:start position:0%
+azerbaijan
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+
+ align:start position:0%
+azerbaijan
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that uh their
+
+ align:start position:0%
+that uh their
+ 
+
+ align:start position:0%
+that uh their
+standard practice was to uh have bespoke
+
+ align:start position:0%
+standard practice was to uh have bespoke
+ 
+
+ align:start position:0%
+standard practice was to uh have bespoke
+designs as designs particularly suited
+
+ align:start position:0%
+designs as designs particularly suited
+ 
+
+ align:start position:0%
+designs as designs particularly suited
+to the location the depth of water
+
+ align:start position:0%
+to the location the depth of water
+ 
+
+ align:start position:0%
+to the location the depth of water
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+that didn't work for a variety of
+
+ align:start position:0%
+that didn't work for a variety of
+ 
+
+ align:start position:0%
+that didn't work for a variety of
+reasons so they made they actually
+
+ align:start position:0%
+reasons so they made they actually
+ 
+
+ align:start position:0%
+reasons so they made they actually
+implemented three platforms which were
+
+ align:start position:0%
+implemented three platforms which were
+ 
+
+ align:start position:0%
+implemented three platforms which were
+copies of each other
+
+ align:start position:0%
+copies of each other
+ 
+
+ align:start position:0%
+copies of each other
+and what they found was huge
+
+ align:start position:0%
+and what they found was huge
+ 
+
+ align:start position:0%
+and what they found was huge
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+savings through this learning in that
+
+ align:start position:0%
+savings through this learning in that
+ 
+
+ align:start position:0%
+savings through this learning in that
+case particularly because
+
+ align:start position:0%
+case particularly because
+ 
+
+ align:start position:0%
+case particularly because
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+
+ align:start position:0%
+by the time the teams came to do the
+ 
+
+ align:start position:0%
+by the time the teams came to do the
+second and third one they knew better
+
+ align:start position:0%
+second and third one they knew better
+ 
+
+ align:start position:0%
+second and third one they knew better
+how to sequence their
+
+ align:start position:0%
+how to sequence their
+ 
+
+ align:start position:0%
+how to sequence their
+use of labor and materials
+
+ align:start position:0%
+use of labor and materials
+ 
+
+ align:start position:0%
+use of labor and materials
+when to time things how to time things
+
+ align:start position:0%
+when to time things how to time things
+ 
+
+ align:start position:0%
+when to time things how to time things
+what was the better way of putting the
+
+ align:start position:0%
+what was the better way of putting the
+ 
+
+ align:start position:0%
+what was the better way of putting the
+pieces together just like learning how
+
+ align:start position:0%
+pieces together just like learning how
+ 
+
+ align:start position:0%
+pieces together just like learning how
+to put up a tent when you go camping
+
+ align:start position:0%
+to put up a tent when you go camping
+ 
+
+ align:start position:0%
+to put up a tent when you go camping
+so this effect which basically says if
+
+ align:start position:0%
+so this effect which basically says if
+ 
+
+ align:start position:0%
+so this effect which basically says if
+you build modules that are the same you
+
+ align:start position:0%
+you build modules that are the same you
+ 
+
+ align:start position:0%
+you build modules that are the same you
+can make it less expensive
+
+ align:start position:0%
+can make it less expensive
+ 
+
+ align:start position:0%
+can make it less expensive
+adds on in increases the effect of the
+
+ align:start position:0%
+adds on in increases the effect of the
+ 
+
+ align:start position:0%
+adds on in increases the effect of the
+discount rate insofar as it makes future
+
+ align:start position:0%
+discount rate insofar as it makes future
+ 
+
+ align:start position:0%
+discount rate insofar as it makes future
+investments of a series of modules uh
+
+ align:start position:0%
+investments of a series of modules uh
+ 
+
+ align:start position:0%
+investments of a series of modules uh
+cheaper
+
+ align:start position:0%
+cheaper
+ 
+
+ align:start position:0%
+cheaper
+so it is another add-on to the
+
+ align:start position:0%
+so it is another add-on to the
+ 
+
+ align:start position:0%
+so it is another add-on to the
+importance of
+
+ align:start position:0%
+importance of
+ 
+
+ align:start position:0%
+importance of
+the discount rate in terms of
+
+ align:start position:0%
+the discount rate in terms of
+ 
+
+ align:start position:0%
+the discount rate in terms of
+counterbalancing economies of scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right so i've just sort of said it but
+
+ align:start position:0%
+right so i've just sort of said it but
+ 
+
+ align:start position:0%
+right so i've just sort of said it but
+i'm calling it again
+
+ align:start position:0%
+i'm calling it again
+ 
+
+ align:start position:0%
+i'm calling it again
+learning is in quotes because it's not
+
+ align:start position:0%
+learning is in quotes because it's not
+ 
+
+ align:start position:0%
+learning is in quotes because it's not
+only learning you may have some
+
+ align:start position:0%
+only learning you may have some
+ 
+
+ align:start position:0%
+only learning you may have some
+technological
+
+ align:start position:0%
+technological
+ 
+
+ align:start position:0%
+technological
+improvements over time also you didn't
+
+ align:start position:0%
+improvements over time also you didn't
+ 
+
+ align:start position:0%
+improvements over time also you didn't
+have to have that piece as thick as the
+
+ align:start position:0%
+have to have that piece as thick as the
+ 
+
+ align:start position:0%
+have to have that piece as thick as the
+other ones because you found out you
+
+ align:start position:0%
+other ones because you found out you
+ 
+
+ align:start position:0%
+other ones because you found out you
+didn't need it and so forth so there are
+
+ align:start position:0%
+didn't need it and so forth so there are
+ 
+
+ align:start position:0%
+didn't need it and so forth so there are
+various ways you can improve on the
+
+ align:start position:0%
+various ways you can improve on the
+ 
+
+ align:start position:0%
+various ways you can improve on the
+design but it reflects the empirical
+
+ align:start position:0%
+design but it reflects the empirical
+ 
+
+ align:start position:0%
+design but it reflects the empirical
+understanding that as you an observable
+
+ align:start position:0%
+understanding that as you an observable
+ 
+
+ align:start position:0%
+understanding that as you an observable
+understanding as you make the same thing
+
+ align:start position:0%
+understanding as you make the same thing
+ 
+
+ align:start position:0%
+understanding as you make the same thing
+again and again you can do it
+
+ align:start position:0%
+again and again you can do it
+ 
+
+ align:start position:0%
+again and again you can do it
+less expensively and this can be
+
+ align:start position:0%
+less expensively and this can be
+ 
+
+ align:start position:0%
+less expensively and this can be
+quite important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the uh next one here is this notion
+
+ align:start position:0%
+now the uh next one here is this notion
+ 
+
+ align:start position:0%
+now the uh next one here is this notion
+of competitive gaming
+
+ align:start position:0%
+of competitive gaming
+ 
+
+ align:start position:0%
+of competitive gaming
+which is that
+
+ align:start position:0%
+which is that
+ 
+
+ align:start position:0%
+which is that
+it's not so easy to define
+
+ align:start position:0%
+it's not so easy to define
+ 
+
+ align:start position:0%
+it's not so easy to define
+directly but it basically says sometimes
+
+ align:start position:0%
+directly but it basically says sometimes
+ 
+
+ align:start position:0%
+directly but it basically says sometimes
+it's important to make a decision
+
+ align:start position:0%
+it's important to make a decision
+ 
+
+ align:start position:0%
+it's important to make a decision
+make a commitment in advance as a signal
+
+ align:start position:0%
+make a commitment in advance as a signal
+ 
+
+ align:start position:0%
+make a commitment in advance as a signal
+to competitors
+
+ align:start position:0%
+to competitors
+ 
+
+ align:start position:0%
+to competitors
+so the example i guess relate to here is
+
+ align:start position:0%
+so the example i guess relate to here is
+ 
+
+ align:start position:0%
+so the example i guess relate to here is
+when cortez invaded mexico
+
+ align:start position:0%
+when cortez invaded mexico
+ 
+
+ align:start position:0%
+when cortez invaded mexico
+and he came there by ship
+
+ align:start position:0%
+and he came there by ship
+ 
+
+ align:start position:0%
+and he came there by ship
+he deliberately burned his ship
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so he could not go back the implication
+
+ align:start position:0%
+so he could not go back the implication
+ 
+
+ align:start position:0%
+so he could not go back the implication
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+i am committed if you work with me i
+
+ align:start position:0%
+i am committed if you work with me i
+ 
+
+ align:start position:0%
+i am committed if you work with me i
+will be here because i am not going
+
+ align:start position:0%
+will be here because i am not going
+ 
+
+ align:start position:0%
+will be here because i am not going
+anywhere else i'm not going to uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decide to go home and leave you alone if
+
+ align:start position:0%
+decide to go home and leave you alone if
+ 
+
+ align:start position:0%
+decide to go home and leave you alone if
+you if you revolt against the aztec
+
+ align:start position:0%
+you if you revolt against the aztec
+ 
+
+ align:start position:0%
+you if you revolt against the aztec
+rulers
+
+ align:start position:0%
+rulers
+ 
+
+ align:start position:0%
+rulers
+i'm going to be here because i can't go
+
+ align:start position:0%
+i'm going to be here because i can't go
+ 
+
+ align:start position:0%
+i'm going to be here because i can't go
+anywhere else so
+
+ align:start position:0%
+anywhere else so
+ 
+
+ align:start position:0%
+anywhere else so
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+attributed by some people that this was
+
+ align:start position:0%
+attributed by some people that this was
+ 
+
+ align:start position:0%
+attributed by some people that this was
+a an important aspect competitive aspect
+
+ align:start position:0%
+a an important aspect competitive aspect
+ 
+
+ align:start position:0%
+a an important aspect competitive aspect
+of saying we're not going to have any
+
+ align:start position:0%
+of saying we're not going to have any
+ 
+
+ align:start position:0%
+of saying we're not going to have any
+flexibility we're going to commit right
+
+ align:start position:0%
+flexibility we're going to commit right
+ 
+
+ align:start position:0%
+flexibility we're going to commit right
+now it's important
+
+ align:start position:0%
+now it's important
+ 
+
+ align:start position:0%
+now it's important
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i'm now working with a company in
+
+ align:start position:0%
+i'm now working with a company in
+ 
+
+ align:start position:0%
+i'm now working with a company in
+morocco which produces phosphate and
+
+ align:start position:0%
+morocco which produces phosphate and
+ 
+
+ align:start position:0%
+morocco which produces phosphate and
+their view is
+
+ align:start position:0%
+their view is
+ 
+
+ align:start position:0%
+their view is
+somewhat similar
+
+ align:start position:0%
+somewhat similar
+ 
+
+ align:start position:0%
+somewhat similar
+they have uh they're committed to have
+
+ align:start position:0%
+they have uh they're committed to have
+ 
+
+ align:start position:0%
+they have uh they're committed to have
+bm
+
+ align:start position:0%
+bm
+ 
+
+ align:start position:0%
+bm
+to add on capacity to their production
+
+ align:start position:0%
+to add on capacity to their production
+ 
+
+ align:start position:0%
+to add on capacity to their production
+and it's a signal to everybody else that
+
+ align:start position:0%
+and it's a signal to everybody else that
+ 
+
+ align:start position:0%
+and it's a signal to everybody else that
+we are going to we intend to be the big
+
+ align:start position:0%
+we are going to we intend to be the big
+ 
+
+ align:start position:0%
+we are going to we intend to be the big
+uh producers on the block we intend to
+
+ align:start position:0%
+uh producers on the block we intend to
+ 
+
+ align:start position:0%
+uh producers on the block we intend to
+be the world's uh dominant producers and
+
+ align:start position:0%
+be the world's uh dominant producers and
+ 
+
+ align:start position:0%
+be the world's uh dominant producers and
+if you want to build your capacity and
+
+ align:start position:0%
+if you want to build your capacity and
+ 
+
+ align:start position:0%
+if you want to build your capacity and
+compete with us you're going to lose
+
+ align:start position:0%
+compete with us you're going to lose
+ 
+
+ align:start position:0%
+compete with us you're going to lose
+because we're going to have more of it
+
+ align:start position:0%
+because we're going to have more of it
+ 
+
+ align:start position:0%
+because we're going to have more of it
+we're going to be cheaper and we're
+
+ align:start position:0%
+we're going to be cheaper and we're
+ 
+
+ align:start position:0%
+we're going to be cheaper and we're
+going to dominate so
+
+ align:start position:0%
+going to dominate so
+ 
+
+ align:start position:0%
+going to dominate so
+that kind of thinking or very variance
+
+ align:start position:0%
+that kind of thinking or very variance
+ 
+
+ align:start position:0%
+that kind of thinking or very variance
+on this kind of thinking suggests
+
+ align:start position:0%
+on this kind of thinking suggests
+ 
+
+ align:start position:0%
+on this kind of thinking suggests
+illustrates tries to illustrate the
+
+ align:start position:0%
+illustrates tries to illustrate the
+ 
+
+ align:start position:0%
+illustrates tries to illustrate the
+point that
+
+ align:start position:0%
+point that
+ 
+
+ align:start position:0%
+point that
+eliminating flexibility it can be a good
+
+ align:start position:0%
+eliminating flexibility it can be a good
+ 
+
+ align:start position:0%
+eliminating flexibility it can be a good
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the tendency of these principle drivers
+
+ align:start position:0%
+the tendency of these principle drivers
+ 
+
+ align:start position:0%
+the tendency of these principle drivers
+which i just referred to are the
+
+ align:start position:0%
+which i just referred to are the
+ 
+
+ align:start position:0%
+which i just referred to are the
+following first uncertainty
+
+ align:start position:0%
+following first uncertainty
+ 
+
+ align:start position:0%
+following first uncertainty
+emphasizes
+
+ align:start position:0%
+emphasizes
+ 
+
+ align:start position:0%
+emphasizes
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+flexibility the cons is scaled against
+
+ align:start position:0%
+flexibility the cons is scaled against
+ 
+
+ align:start position:0%
+flexibility the cons is scaled against
+the discount rate is four the learning
+
+ align:start position:0%
+the discount rate is four the learning
+ 
+
+ align:start position:0%
+the discount rate is four the learning
+is four and the competitive again is
+
+ align:start position:0%
+is four and the competitive again is
+ 
+
+ align:start position:0%
+is four and the competitive again is
+against
+
+ align:start position:0%
+against
+ 
+
+ align:start position:0%
+against
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh this is where i want to
+
+ align:start position:0%
+uh this is where i want to
+ 
+
+ align:start position:0%
+uh this is where i want to
+let you think about it that when you're
+
+ align:start position:0%
+let you think about it that when you're
+ 
+
+ align:start position:0%
+let you think about it that when you're
+thinking about
+
+ align:start position:0%
+thinking about
+ 
+
+ align:start position:0%
+thinking about
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+where are the pros and cons for having
+
+ align:start position:0%
+where are the pros and cons for having
+ 
+
+ align:start position:0%
+where are the pros and cons for having
+economies of scale there are a number of
+
+ align:start position:0%
+economies of scale there are a number of
+ 
+
+ align:start position:0%
+economies of scale there are a number of
+issues to take into consideration
+
+ align:start position:0%
+issues to take into consideration
+ 
+
+ align:start position:0%
+issues to take into consideration
+it's not all
+
+ align:start position:0%
+it's not all
+ 
+
+ align:start position:0%
+it's not all
+if there's uncertainty you have to have
+
+ align:start position:0%
+if there's uncertainty you have to have
+ 
+
+ align:start position:0%
+if there's uncertainty you have to have
+a flexibility
+
+ align:start position:0%
+a flexibility
+ 
+
+ align:start position:0%
+a flexibility
+maybe maybe not you have to do the
+
+ align:start position:0%
+maybe maybe not you have to do the
+ 
+
+ align:start position:0%
+maybe maybe not you have to do the
+calculations and explore it to get it
+
+ align:start position:0%
+calculations and explore it to get it
+ 
+
+ align:start position:0%
+calculations and explore it to get it
+right but it's not clear what the answer
+
+ align:start position:0%
+right but it's not clear what the answer
+ 
+
+ align:start position:0%
+right but it's not clear what the answer
+has to be there's not one possible
+
+ align:start position:0%
+has to be there's not one possible
+ 
+
+ align:start position:0%
+has to be there's not one possible
+answer
\ No newline at end of file
diff --git a/1R4IzkWSNgI.txt b/1R4IzkWSNgI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..302a8b4291b6ebed21cc3f6dff2caec2b3dda9b1
--- /dev/null
+++ b/1R4IzkWSNgI.txt
@@ -0,0 +1,1435 @@
+align:start position:0%
+ 
+after our warmup we can now come to the
+
+ align:start position:0%
+after our warmup we can now come to the
+ 
+
+ align:start position:0%
+after our warmup we can now come to the
+real problem we have again a random
+
+ align:start position:0%
+real problem we have again a random
+ 
+
+ align:start position:0%
+real problem we have again a random
+variable theta with a known prior
+
+ align:start position:0%
+variable theta with a known prior
+ 
+
+ align:start position:0%
+variable theta with a known prior
+distribution and we're interested in a
+
+ align:start position:0%
+distribution and we're interested in a
+ 
+
+ align:start position:0%
+distribution and we're interested in a
+point estimate what will be different
+
+ align:start position:0%
+point estimate what will be different
+ 
+
+ align:start position:0%
+point estimate what will be different
+this time however is that we now have an
+
+ align:start position:0%
+this time however is that we now have an
+ 
+
+ align:start position:0%
+this time however is that we now have an
+observation and we also have a model of
+
+ align:start position:0%
+observation and we also have a model of
+ 
+
+ align:start position:0%
+observation and we also have a model of
+that observation as a conditional
+
+ align:start position:0%
+that observation as a conditional
+ 
+
+ align:start position:0%
+that observation as a conditional
+distribution given the value of the true
+
+ align:start position:0%
+distribution given the value of the true
+ 
+
+ align:start position:0%
+distribution given the value of the true
+parameter we observe a value of that
+
+ align:start position:0%
+parameter we observe a value of that
+ 
+
+ align:start position:0%
+parameter we observe a value of that
+random variable that values little X and
+
+ align:start position:0%
+random variable that values little X and
+ 
+
+ align:start position:0%
+random variable that values little X and
+on the basis of that value we would like
+
+ align:start position:0%
+on the basis of that value we would like
+ 
+
+ align:start position:0%
+on the basis of that value we would like
+to now come up with a point estimate of
+
+ align:start position:0%
+to now come up with a point estimate of
+ 
+
+ align:start position:0%
+to now come up with a point estimate of
+the unknown random variable theta how do
+
+ align:start position:0%
+the unknown random variable theta how do
+ 
+
+ align:start position:0%
+the unknown random variable theta how do
+we proceed we can of course use the
+
+ align:start position:0%
+we proceed we can of course use the
+ 
+
+ align:start position:0%
+we proceed we can of course use the
+Bayes rule and the Bayes rule is going
+
+ align:start position:0%
+Bayes rule and the Bayes rule is going
+ 
+
+ align:start position:0%
+Bayes rule and the Bayes rule is going
+to give us a distribution for the
+
+ align:start position:0%
+to give us a distribution for the
+ 
+
+ align:start position:0%
+to give us a distribution for the
+unknown random variable given the
+
+ align:start position:0%
+unknown random variable given the
+ 
+
+ align:start position:0%
+unknown random variable given the
+observation that we have obtained and
+
+ align:start position:0%
+observation that we have obtained and
+ 
+
+ align:start position:0%
+observation that we have obtained and
+that distribution could be discrete or
+
+ align:start position:0%
+that distribution could be discrete or
+ 
+
+ align:start position:0%
+that distribution could be discrete or
+continuous let me just plot something as
+
+ align:start position:0%
+continuous let me just plot something as
+ 
+
+ align:start position:0%
+continuous let me just plot something as
+if it's continuous and now that we have
+
+ align:start position:0%
+if it's continuous and now that we have
+ 
+
+ align:start position:0%
+if it's continuous and now that we have
+the posterior distribution of theta we
+
+ align:start position:0%
+the posterior distribution of theta we
+ 
+
+ align:start position:0%
+the posterior distribution of theta we
+would like to come up with a point
+
+ align:start position:0%
+would like to come up with a point
+ 
+
+ align:start position:0%
+would like to come up with a point
+estimate how do we do it remember our
+
+ align:start position:0%
+estimate how do we do it remember our
+ 
+
+ align:start position:0%
+estimate how do we do it remember our
+earlier conclusion if we do not have any
+
+ align:start position:0%
+earlier conclusion if we do not have any
+ 
+
+ align:start position:0%
+earlier conclusion if we do not have any
+observations if we live in a universe
+
+ align:start position:0%
+observations if we live in a universe
+ 
+
+ align:start position:0%
+observations if we live in a universe
+where we have a distribution of theta
+
+ align:start position:0%
+where we have a distribution of theta
+ 
+
+ align:start position:0%
+where we have a distribution of theta
+and we want a point estimate the optimal
+
+ align:start position:0%
+and we want a point estimate the optimal
+ 
+
+ align:start position:0%
+and we want a point estimate the optimal
+one the one that minimizes the mean
+
+ align:start position:0%
+one the one that minimizes the mean
+ 
+
+ align:start position:0%
+one the one that minimizes the mean
+squared error is the expected value of
+
+ align:start position:0%
+squared error is the expected value of
+ 
+
+ align:start position:0%
+squared error is the expected value of
+our random variable but now we live in a
+
+ align:start position:0%
+our random variable but now we live in a
+ 
+
+ align:start position:0%
+our random variable but now we live in a
+different universe in a universe where
+
+ align:start position:0%
+different universe in a universe where
+ 
+
+ align:start position:0%
+different universe in a universe where
+we have a conditional distribution of
+
+ align:start position:0%
+we have a conditional distribution of
+ 
+
+ align:start position:0%
+we have a conditional distribution of
+theta we want to minimize the
+
+ align:start position:0%
+theta we want to minimize the
+ 
+
+ align:start position:0%
+theta we want to minimize the
+conditional mean squared error because
+
+ align:start position:0%
+conditional mean squared error because
+ 
+
+ align:start position:0%
+conditional mean squared error because
+this is the mean squared error that
+
+ align:start position:0%
+this is the mean squared error that
+ 
+
+ align:start position:0%
+this is the mean squared error that
+applies to this conditional universe in
+
+ align:start position:0%
+applies to this conditional universe in
+ 
+
+ align:start position:0%
+applies to this conditional universe in
+which we have obtained a particular
+
+ align:start position:0%
+which we have obtained a particular
+ 
+
+ align:start position:0%
+which we have obtained a particular
+observation what is going to be the
+
+ align:start position:0%
+observation what is going to be the
+ 
+
+ align:start position:0%
+observation what is going to be the
+result of this minimization well this is
+
+ align:start position:0%
+result of this minimization well this is
+ 
+
+ align:start position:0%
+result of this minimization well this is
+a problem that's identical to the
+
+ align:start position:0%
+a problem that's identical to the
+ 
+
+ align:start position:0%
+a problem that's identical to the
+problem of minimizing this quantity
+
+ align:start position:0%
+problem of minimizing this quantity
+ 
+
+ align:start position:0%
+problem of minimizing this quantity
+except that now this problem is posed in
+
+ align:start position:0%
+except that now this problem is posed in
+ 
+
+ align:start position:0%
+except that now this problem is posed in
+a conditional universe so we just follow
+
+ align:start position:0%
+a conditional universe so we just follow
+ 
+
+ align:start position:0%
+a conditional universe so we just follow
+the same steps and obtain the same
+
+ align:start position:0%
+the same steps and obtain the same
+ 
+
+ align:start position:0%
+the same steps and obtain the same
+solution the solution is going to be the
+
+ align:start position:0%
+solution the solution is going to be the
+ 
+
+ align:start position:0%
+solution the solution is going to be the
+expected value of the unknown random
+
+ align:start position:0%
+expected value of the unknown random
+ 
+
+ align:start position:0%
+expected value of the unknown random
+variable except that now we live in a
+
+ align:start position:0%
+variable except that now we live in a
+ 
+
+ align:start position:0%
+variable except that now we live in a
+conditional universe and therefore we
+
+ align:start position:0%
+conditional universe and therefore we
+ 
+
+ align:start position:0%
+conditional universe and therefore we
+should take the relevant expected value
+
+ align:start position:0%
+should take the relevant expected value
+ 
+
+ align:start position:0%
+should take the relevant expected value
+which is the conditional expectation
+
+ align:start position:0%
+which is the conditional expectation
+ 
+
+ align:start position:0%
+which is the conditional expectation
+given the information that we have
+
+ align:start position:0%
+given the information that we have
+ 
+
+ align:start position:0%
+given the information that we have
+available in our hands so to summarize
+
+ align:start position:0%
+available in our hands so to summarize
+ 
+
+ align:start position:0%
+available in our hands so to summarize
+what we obtain is that the optimal
+
+ align:start position:0%
+what we obtain is that the optimal
+ 
+
+ align:start position:0%
+what we obtain is that the optimal
+estimate is the conditional expectation
+
+ align:start position:0%
+estimate is the conditional expectation
+ 
+
+ align:start position:0%
+estimate is the conditional expectation
+and this is a relation between numbers
+
+ align:start position:0%
+and this is a relation between numbers
+ 
+
+ align:start position:0%
+and this is a relation between numbers
+but if we want to think about it more
+
+ align:start position:0%
+but if we want to think about it more
+ 
+
+ align:start position:0%
+but if we want to think about it more
+abstractly we have designed an estimator
+
+ align:start position:0%
+abstractly we have designed an estimator
+ 
+
+ align:start position:0%
+abstractly we have designed an estimator
+which is based on a random variable
+
+ align:start position:0%
+which is based on a random variable
+ 
+
+ align:start position:0%
+which is based on a random variable
+capital X and calculates the expected
+
+ align:start position:0%
+capital X and calculates the expected
+ 
+
+ align:start position:0%
+capital X and calculates the expected
+value of our random variable that we're
+
+ align:start position:0%
+value of our random variable that we're
+ 
+
+ align:start position:0%
+value of our random variable that we're
+trying to estimate namely theta on the
+
+ align:start position:0%
+trying to estimate namely theta on the
+ 
+
+ align:start position:0%
+trying to estimate namely theta on the
+basis of X let us now continue with some
+
+ align:start position:0%
+basis of X let us now continue with some
+ 
+
+ align:start position:0%
+basis of X let us now continue with some
+observations remember that the expected
+
+ align:start position:0%
+observations remember that the expected
+ 
+
+ align:start position:0%
+observations remember that the expected
+value of theta minimizes this quantity
+
+ align:start position:0%
+value of theta minimizes this quantity
+ 
+
+ align:start position:0%
+value of theta minimizes this quantity
+and we can write this more explicitly in
+
+ align:start position:0%
+and we can write this more explicitly in
+ 
+
+ align:start position:0%
+and we can write this more explicitly in
+terms of the following inequality that
+
+ align:start position:0%
+terms of the following inequality that
+ 
+
+ align:start position:0%
+terms of the following inequality that
+if we use the expected value as an
+
+ align:start position:0%
+if we use the expected value as an
+ 
+
+ align:start position:0%
+if we use the expected value as an
+estimate the resulting mean squared
+
+ align:start position:0%
+estimate the resulting mean squared
+ 
+
+ align:start position:0%
+estimate the resulting mean squared
+error is less than or equal to the mean
+
+ align:start position:0%
+error is less than or equal to the mean
+ 
+
+ align:start position:0%
+error is less than or equal to the mean
+squared error that we would have
+
+ align:start position:0%
+squared error that we would have
+ 
+
+ align:start position:0%
+squared error that we would have
+obtained if we had used any other
+
+ align:start position:0%
+obtained if we had used any other
+ 
+
+ align:start position:0%
+obtained if we had used any other
+estimate see so this is a relation
+
+ align:start position:0%
+estimate see so this is a relation
+ 
+
+ align:start position:0%
+estimate see so this is a relation
+that's true for all see now let us take
+
+ align:start position:0%
+that's true for all see now let us take
+ 
+
+ align:start position:0%
+that's true for all see now let us take
+this inequality and translate it into
+
+ align:start position:0%
+this inequality and translate it into
+ 
+
+ align:start position:0%
+this inequality and translate it into
+our more interesting context where we
+
+ align:start position:0%
+our more interesting context where we
+ 
+
+ align:start position:0%
+our more interesting context where we
+have an observation available once more
+
+ align:start position:0%
+have an observation available once more
+ 
+
+ align:start position:0%
+have an observation available once more
+the conditional expectation minimizes
+
+ align:start position:0%
+the conditional expectation minimizes
+ 
+
+ align:start position:0%
+the conditional expectation minimizes
+the mean squared error let us write out
+
+ align:start position:0%
+the mean squared error let us write out
+ 
+
+ align:start position:0%
+the mean squared error let us write out
+explicitly what this means in a form
+
+ align:start position:0%
+explicitly what this means in a form
+ 
+
+ align:start position:0%
+explicitly what this means in a form
+analogous to what we wrote down earlier
+
+ align:start position:0%
+analogous to what we wrote down earlier
+ 
+
+ align:start position:0%
+analogous to what we wrote down earlier
+what it means is that the expected value
+
+ align:start position:0%
+what it means is that the expected value
+ 
+
+ align:start position:0%
+what it means is that the expected value
+of theta minus the estimate namely the
+
+ align:start position:0%
+of theta minus the estimate namely the
+ 
+
+ align:start position:0%
+of theta minus the estimate namely the
+conditional expectation squared in this
+
+ align:start position:0%
+conditional expectation squared in this
+ 
+
+ align:start position:0%
+conditional expectation squared in this
+conditional universe in which we live
+
+ align:start position:0%
+conditional universe in which we live
+ 
+
+ align:start position:0%
+conditional universe in which we live
+this is less than or equal to the mean
+
+ align:start position:0%
+this is less than or equal to the mean
+ 
+
+ align:start position:0%
+this is less than or equal to the mean
+squared error that we would have
+
+ align:start position:0%
+squared error that we would have
+ 
+
+ align:start position:0%
+squared error that we would have
+obtained if we had used any other
+
+ align:start position:0%
+obtained if we had used any other
+ 
+
+ align:start position:0%
+obtained if we had used any other
+estimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the place of the conditional
+
+ align:start position:0%
+in the place of the conditional
+ 
+
+ align:start position:0%
+in the place of the conditional
+expectation so for any value G of X that
+
+ align:start position:0%
+expectation so for any value G of X that
+ 
+
+ align:start position:0%
+expectation so for any value G of X that
+we might have used the error would have
+
+ align:start position:0%
+we might have used the error would have
+ 
+
+ align:start position:0%
+we might have used the error would have
+been at least as large why am I using
+
+ align:start position:0%
+been at least as large why am I using
+ 
+
+ align:start position:0%
+been at least as large why am I using
+this notation G here let us go back to
+
+ align:start position:0%
+this notation G here let us go back to
+ 
+
+ align:start position:0%
+this notation G here let us go back to
+the bigger picture what we have is that
+
+ align:start position:0%
+the bigger picture what we have is that
+ 
+
+ align:start position:0%
+the bigger picture what we have is that
+we are obtaining a numerical value X we
+
+ align:start position:0%
+we are obtaining a numerical value X we
+ 
+
+ align:start position:0%
+we are obtaining a numerical value X we
+do some processing to it which
+
+ align:start position:0%
+do some processing to it which
+ 
+
+ align:start position:0%
+do some processing to it which
+corresponds to some function G and we
+
+ align:start position:0%
+corresponds to some function G and we
+ 
+
+ align:start position:0%
+corresponds to some function G and we
+come up with an estimate which is a
+
+ align:start position:0%
+come up with an estimate which is a
+ 
+
+ align:start position:0%
+come up with an estimate which is a
+function of the little X that we have
+
+ align:start position:0%
+function of the little X that we have
+ 
+
+ align:start position:0%
+function of the little X that we have
+observed so no matter what estimate we
+
+ align:start position:0%
+observed so no matter what estimate we
+ 
+
+ align:start position:0%
+observed so no matter what estimate we
+use the mean squared error is going to
+
+ align:start position:0%
+use the mean squared error is going to
+ 
+
+ align:start position:0%
+use the mean squared error is going to
+be at least as large as the mean squared
+
+ align:start position:0%
+be at least as large as the mean squared
+ 
+
+ align:start position:0%
+be at least as large as the mean squared
+error that we obtain if we use the
+
+ align:start position:0%
+error that we obtain if we use the
+ 
+
+ align:start position:0%
+error that we obtain if we use the
+conditional expectation now let us take
+
+ align:start position:0%
+conditional expectation now let us take
+ 
+
+ align:start position:0%
+conditional expectation now let us take
+this inequality here and write it in a
+
+ align:start position:0%
+this inequality here and write it in a
+ 
+
+ align:start position:0%
+this inequality here and write it in a
+more abstract form suppose that we have
+
+ align:start position:0%
+more abstract form suppose that we have
+ 
+
+ align:start position:0%
+more abstract form suppose that we have
+settled on some particular estimator and
+
+ align:start position:0%
+settled on some particular estimator and
+ 
+
+ align:start position:0%
+settled on some particular estimator and
+we want to compare this estimator with
+
+ align:start position:0%
+we want to compare this estimator with
+ 
+
+ align:start position:0%
+we want to compare this estimator with
+the expected value estimator then we are
+
+ align:start position:0%
+the expected value estimator then we are
+ 
+
+ align:start position:0%
+the expected value estimator then we are
+going to get the following inequality if
+
+ align:start position:0%
+going to get the following inequality if
+ 
+
+ align:start position:0%
+going to get the following inequality if
+we use the conditional expectation as an
+
+ align:start position:0%
+we use the conditional expectation as an
+ 
+
+ align:start position:0%
+we use the conditional expectation as an
+estimator in a conditional universe
+
+ align:start position:0%
+estimator in a conditional universe
+ 
+
+ align:start position:0%
+estimator in a conditional universe
+where we know the value of the random
+
+ align:start position:0%
+where we know the value of the random
+ 
+
+ align:start position:0%
+where we know the value of the random
+variable X the corresponding mean
+
+ align:start position:0%
+variable X the corresponding mean
+ 
+
+ align:start position:0%
+variable X the corresponding mean
+squared error is going to be less than
+
+ align:start position:0%
+squared error is going to be less than
+ 
+
+ align:start position:0%
+squared error is going to be less than
+or equal to the mean squared error
+
+ align:start position:0%
+or equal to the mean squared error
+ 
+
+ align:start position:0%
+or equal to the mean squared error
+obtained by the alternative estimator G
+
+ align:start position:0%
+obtained by the alternative estimator G
+ 
+
+ align:start position:0%
+obtained by the alternative estimator G
+what does this inequality say this
+
+ align:start position:0%
+what does this inequality say this
+ 
+
+ align:start position:0%
+what does this inequality say this
+inequality is simply an abstract version
+
+ align:start position:0%
+inequality is simply an abstract version
+ 
+
+ align:start position:0%
+inequality is simply an abstract version
+of the previous inequality the previous
+
+ align:start position:0%
+of the previous inequality the previous
+ 
+
+ align:start position:0%
+of the previous inequality the previous
+inequality is true for all little X here
+
+ align:start position:0%
+inequality is true for all little X here
+ 
+
+ align:start position:0%
+inequality is true for all little X here
+we have an inequality between random
+
+ align:start position:0%
+we have an inequality between random
+ 
+
+ align:start position:0%
+we have an inequality between random
+variables this random variable here is
+
+ align:start position:0%
+variables this random variable here is
+ 
+
+ align:start position:0%
+variables this random variable here is
+the random variable that takes this
+
+ align:start position:0%
+the random variable that takes this
+ 
+
+ align:start position:0%
+the random variable that takes this
+specific numerical value whenever
+
+ align:start position:0%
+specific numerical value whenever
+ 
+
+ align:start position:0%
+specific numerical value whenever
+capital X takes the value little X when
+
+ align:start position:0%
+capital X takes the value little X when
+ 
+
+ align:start position:0%
+capital X takes the value little X when
+X takes the value little X were
+
+ align:start position:0%
+X takes the value little X were
+ 
+
+ align:start position:0%
+X takes the value little X were
+auditioning on this event and when X is
+
+ align:start position:0%
+auditioning on this event and when X is
+ 
+
+ align:start position:0%
+auditioning on this event and when X is
+equal to little X this quantity takes on
+
+ align:start position:0%
+equal to little X this quantity takes on
+ 
+
+ align:start position:0%
+equal to little X this quantity takes on
+this particular numerical value and
+
+ align:start position:0%
+this particular numerical value and
+ 
+
+ align:start position:0%
+this particular numerical value and
+similarly on the other side this is a
+
+ align:start position:0%
+similarly on the other side this is a
+ 
+
+ align:start position:0%
+similarly on the other side this is a
+random variable that takes this
+
+ align:start position:0%
+random variable that takes this
+ 
+
+ align:start position:0%
+random variable that takes this
+particular numerical value whenever
+
+ align:start position:0%
+particular numerical value whenever
+ 
+
+ align:start position:0%
+particular numerical value whenever
+capital X is equal to little X now that
+
+ align:start position:0%
+capital X is equal to little X now that
+ 
+
+ align:start position:0%
+capital X is equal to little X now that
+we have an inequality between random
+
+ align:start position:0%
+we have an inequality between random
+ 
+
+ align:start position:0%
+we have an inequality between random
+variables actually between conditional
+
+ align:start position:0%
+variables actually between conditional
+ 
+
+ align:start position:0%
+variables actually between conditional
+expectations we can take expectations of
+
+ align:start position:0%
+expectations we can take expectations of
+ 
+
+ align:start position:0%
+expectations we can take expectations of
+both sides and we use the law of
+
+ align:start position:0%
+both sides and we use the law of
+ 
+
+ align:start position:0%
+both sides and we use the law of
+iterated expectations the expectation of
+
+ align:start position:0%
+iterated expectations the expectation of
+ 
+
+ align:start position:0%
+iterated expectations the expectation of
+a conditional expectation is an
+
+ align:start position:0%
+a conditional expectation is an
+ 
+
+ align:start position:0%
+a conditional expectation is an
+unconditional expectation so we obtain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this as the expected value of this
+
+ align:start position:0%
+this as the expected value of this
+ 
+
+ align:start position:0%
+this as the expected value of this
+quantity and it's less than or equal to
+
+ align:start position:0%
+quantity and it's less than or equal to
+ 
+
+ align:start position:0%
+quantity and it's less than or equal to
+the expected value of this quantity
+
+ align:start position:0%
+the expected value of this quantity
+ 
+
+ align:start position:0%
+the expected value of this quantity
+using again the law of iterated
+
+ align:start position:0%
+using again the law of iterated
+ 
+
+ align:start position:0%
+using again the law of iterated
+expectations we obtain this relation
+
+ align:start position:0%
+expectations we obtain this relation
+ 
+
+ align:start position:0%
+expectations we obtain this relation
+here and what this inequality is saying
+
+ align:start position:0%
+here and what this inequality is saying
+ 
+
+ align:start position:0%
+here and what this inequality is saying
+is that the overall mean squared error
+
+ align:start position:0%
+is that the overall mean squared error
+ 
+
+ align:start position:0%
+is that the overall mean squared error
+if we use the conditional expectation
+
+ align:start position:0%
+if we use the conditional expectation
+ 
+
+ align:start position:0%
+if we use the conditional expectation
+now as an estimator is less than or
+
+ align:start position:0%
+now as an estimator is less than or
+ 
+
+ align:start position:0%
+now as an estimator is less than or
+equal to the mean squared error that we
+
+ align:start position:0%
+equal to the mean squared error that we
+ 
+
+ align:start position:0%
+equal to the mean squared error that we
+would obtain if we had used any other
+
+ align:start position:0%
+would obtain if we had used any other
+ 
+
+ align:start position:0%
+would obtain if we had used any other
+estimator so this inequality refers to
+
+ align:start position:0%
+estimator so this inequality refers to
+ 
+
+ align:start position:0%
+estimator so this inequality refers to
+the following picture we obtain an
+
+ align:start position:0%
+the following picture we obtain an
+ 
+
+ align:start position:0%
+the following picture we obtain an
+observation which is a random variable
+
+ align:start position:0%
+observation which is a random variable
+ 
+
+ align:start position:0%
+observation which is a random variable
+we process that random variable to come
+
+ align:start position:0%
+we process that random variable to come
+ 
+
+ align:start position:0%
+we process that random variable to come
+up with an estimator which is a function
+
+ align:start position:0%
+up with an estimator which is a function
+ 
+
+ align:start position:0%
+up with an estimator which is a function
+of the random variable that we observe
+
+ align:start position:0%
+of the random variable that we observe
+ 
+
+ align:start position:0%
+of the random variable that we observe
+and so is itself a random variable so
+
+ align:start position:0%
+and so is itself a random variable so
+ 
+
+ align:start position:0%
+and so is itself a random variable so
+when we use this random variable to
+
+ align:start position:0%
+when we use this random variable to
+ 
+
+ align:start position:0%
+when we use this random variable to
+estimate theta we obtain a certain mean
+
+ align:start position:0%
+estimate theta we obtain a certain mean
+ 
+
+ align:start position:0%
+estimate theta we obtain a certain mean
+squared error this is going to be at
+
+ align:start position:0%
+squared error this is going to be at
+ 
+
+ align:start position:0%
+squared error this is going to be at
+least as large as the mean squared error
+
+ align:start position:0%
+least as large as the mean squared error
+ 
+
+ align:start position:0%
+least as large as the mean squared error
+that we obtain if we use the conditional
+
+ align:start position:0%
+that we obtain if we use the conditional
+ 
+
+ align:start position:0%
+that we obtain if we use the conditional
+expectation as our estimator
+
+ align:start position:0%
+expectation as our estimator
+ 
+
+ align:start position:0%
+expectation as our estimator
+so to summarize the conditional
+
+ align:start position:0%
+so to summarize the conditional
+ 
+
+ align:start position:0%
+so to summarize the conditional
+expectation of theta viewed as a random
+
+ align:start position:0%
+expectation of theta viewed as a random
+ 
+
+ align:start position:0%
+expectation of theta viewed as a random
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+as an estimator what we call the LMS
+
+ align:start position:0%
+as an estimator what we call the LMS
+ 
+
+ align:start position:0%
+as an estimator what we call the LMS
+estimator of theta has the property that
+
+ align:start position:0%
+estimator of theta has the property that
+ 
+
+ align:start position:0%
+estimator of theta has the property that
+it minimizes the mean squared error over
+
+ align:start position:0%
+it minimizes the mean squared error over
+ 
+
+ align:start position:0%
+it minimizes the mean squared error over
+all possible alternative estimators so
+
+ align:start position:0%
+all possible alternative estimators so
+ 
+
+ align:start position:0%
+all possible alternative estimators so
+if you want to design this box using
+
+ align:start position:0%
+if you want to design this box using
+ 
+
+ align:start position:0%
+if you want to design this box using
+some other function G you're going to
+
+ align:start position:0%
+some other function G you're going to
+ 
+
+ align:start position:0%
+some other function G you're going to
+obtain a mean squared error that's going
+
+ align:start position:0%
+obtain a mean squared error that's going
+ 
+
+ align:start position:0%
+obtain a mean squared error that's going
+to be no better than what you obtain if
+
+ align:start position:0%
+to be no better than what you obtain if
+ 
+
+ align:start position:0%
+to be no better than what you obtain if
+you were to use the conditional
+
+ align:start position:0%
+you were to use the conditional
+ 
+
+ align:start position:0%
+you were to use the conditional
+expectation
\ No newline at end of file
diff --git a/1jDBM9UM9xk.txt b/1jDBM9UM9xk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..900294257426c0cc86f1d061ee51ea3d98bb49b5
--- /dev/null
+++ b/1jDBM9UM9xk.txt
@@ -0,0 +1,2399 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: It involves real
+phenomena out there.
+
+So we have real stuff
+that happens.
+
+So it might be an arrival
+process to a bank that we're
+
+trying to model.
+
+This is a reality, but
+this is what we have
+
+been doing so far.
+
+We have been playing
+with models of
+
+probabilistic phenomena.
+
+And somehow we need to
+tie the two together.
+
+The way these are tied is that
+we observe the real world and
+
+this gives us data.
+
+And then based on these data, we
+try to come up with a model
+
+of what exactly is going on.
+
+For example, for an arrival
+process, you might ask the
+
+model in question, is my arrival
+process Poisson or is
+
+it something different?
+
+If it is Poisson, what is the
+rate of the arrival process?
+
+Once you come up with your model
+and you come up with the
+
+parameters of the model, then
+you can use it to make
+
+predictions about reality or to
+figure out certain hidden
+
+things, certain hidden aspects
+of reality, that you do not
+
+observe directly, but you try
+to infer what they are.
+
+So that's where the usefulness
+of the model comes in.
+
+Now this field is of course
+tremendously useful.
+
+And it shows up pretty
+much everywhere.
+
+So we talked about the polling
+examples in the
+
+last couple of lectures.
+
+This is, of course, a
+real application.
+
+You sample and on the basis of
+the sample that you have, you
+
+try to make some inferences
+about, let's say, the
+
+preferences in a given
+population.
+
+Let's say in the medical field,
+you want to try whether
+
+a certain drug makes a
+difference or not.
+
+So people would do medical
+trials, get some results, and
+
+then from the data somehow you
+need to make sense of them and
+
+make a decision.
+
+Is the new drug useful
+or is it not?
+
+How do we go systematically
+about the
+
+question of this type?
+
+A sexier, more recent topic,
+there's this famous Netflix
+
+competition where Netflix gives
+you a huge table of
+
+movies and people.
+
+And people have rated the
+movies, but not everyone has
+
+watched all of the
+movies in there.
+
+You have some of the ratings.
+
+For example, this person gave a
+4 to that particular movie.
+
+So you get the table that's
+partially filled.
+
+And the Netflix asks
+you to make
+
+recommendations to people.
+
+So this means trying to guess.
+
+This person here, how much
+would they like this
+
+particular movie?
+
+And you can start thinking,
+well, maybe this person has
+
+given somewhat similar ratings
+with another person.
+
+And if that other person has
+also seen that movie, maybe
+
+the rating of that other
+person is relevant.
+
+But of course it's a lot more
+complicated than that.
+
+And this has been a serious
+competition where people have
+
+been using every heavy, wet
+machinery that there is in
+
+statistics, trying to
+come up with good
+
+recommendation systems.
+
+Then the other people, of
+course, are trying to analyze
+
+financial data.
+
+Somebody gives you the sequence
+of the values, let's
+
+say of the SMP index.
+
+You look at something like this
+
+and you can ask questions.
+
+How do I model these data using
+any of the models that
+
+we have in our bag of tools?
+
+How can I make predictions about
+what's going to happen
+
+afterwards, and so on?
+
+On the engineering side,
+anywhere where you have noise
+
+inference comes in.
+
+Signal processing, in
+some sense, is just
+
+an inference problem.
+
+You observe signals that are
+noisy and you try to figure
+
+out exactly what's happening
+out there or what kind of
+
+signal has been sent.
+
+Maybe the beginning of the field
+could be traced a few
+
+hundred years ago where people
+would observe, make
+
+astronomical observations
+of the position of the
+
+planets in the sky.
+
+They would have some beliefs
+that perhaps the orbits of
+
+planets is an ellipse.
+
+Or if it's a comet, maybe it's
+a parabola, hyperbola, don't
+
+know what it is.
+
+But they would have
+a model of that.
+
+But, of course, astronomical
+measurements would not be
+
+perfectly exact.
+
+And they would try to find the
+curve that fits these data.
+
+How do you go about choosing
+this particular curve on the
+
+base of noisy data and
+try to do it in a
+
+somewhat principled way?
+
+OK, so questions of this
+type-- clearly the
+
+applications are all
+over the place.
+
+But how is this related
+conceptually with what we have
+
+been doing so far?
+
+What's the relation between the
+field of inference and the
+
+field of probability
+as we have been
+
+practicing until now?
+
+Well, mathematically speaking,
+what's going to happen in the
+
+next few lectures could be just
+exercises or homework
+
+problems in the class in based
+on what we have done so far.
+
+That means you're not going
+to get any new facts about
+
+probability theory.
+
+Everything we're going to do
+will be simple applications of
+
+things that you already
+do know.
+
+So in some sense, statistics
+and inference is just an
+
+applied exercise
+in probability.
+
+But actually, things are
+not that simple in
+
+the following sense.
+
+If you get a probability
+problem,
+
+there's a correct answer.
+
+There's a correct solution.
+
+And that correct solution
+is unique.
+
+There's no ambiguity.
+
+The theory of probability has
+clearly defined rules.
+
+These are the axioms.
+
+You're given some information
+about probability
+
+distributions.
+
+You're asked to calculate
+certain other things.
+
+There's no ambiguity.
+
+Answers are always unique.
+
+In statistical questions, it's
+no longer the case that the
+
+question has a unique answer.
+
+If I give you data and I ask
+you what's the best way of
+
+estimating the motion of that
+planet, reasonable people can
+
+come up with different
+methods.
+
+And reasonable people will try
+to argue that's my method has
+
+these desirable properties but
+somebody else may say, here's
+
+another method that has certain
+desirable properties.
+
+And it's not clear what
+the best method is.
+
+So it's good to have some
+understanding of what the
+
+issues are and to know at least
+what is the general
+
+class of methods that one tries
+to consider, how does
+
+one go about such problems.
+
+So we're going to see
+lots and lots of
+
+different inference methods.
+
+We're not going to tell
+you that one is
+
+better than the other.
+
+But it's important to understand
+what are the
+
+concepts between those
+different methods.
+
+And finally, statistics can
+be misused really badly.
+
+That is, one can come up with
+methods that you think are
+
+sound, but in fact they're
+not quite that.
+
+I will bring some examples next
+time and talk a little
+
+more about this.
+
+So, they want to say, you have
+some data, you want to make
+
+some inference from them, what
+many people will do is to go
+
+to Wikipedia, find a statistical
+test that they
+
+think it applies to that
+situation, plug in numbers,
+
+and present results.
+
+Are the conclusions that they
+get really justified or are
+
+they misusing statistical
+methods?
+
+Well, too many people actually
+do misuse statistics and
+
+conclusions that people
+get are often false.
+
+So it's important to, besides
+just being able to copy
+
+statistical tests and use them,
+to understand what are
+
+the assumptions between the
+different methods and what
+
+kind of guarantees they
+have, if any.
+
+All right, so we'll try to do a
+quick tour through the field
+
+of inference in this lecture and
+the next few lectures that
+
+we have left this semester and
+try to highlight at the very
+
+high level the main concept
+skills, and
+
+techniques that come in.
+
+Let's start with some
+generalities and some general
+
+statements.
+
+One first statement is that
+statistics or inference
+
+problems come up in very
+different guises.
+
+And they may look as if they are
+of very different forms.
+
+Although, at some fundamental
+level, the basic issues turn
+
+out to be always pretty
+much the same.
+
+So let's look at this example.
+
+There's an unknown signal
+that's being sent.
+
+It's sent through some medium,
+and that medium just takes the
+
+signal and amplifies it
+by a certain number.
+
+So you can think of
+somebody shouting.
+
+There's the air out there.
+
+What you shouted will be
+attenuated through the air
+
+until it gets to a receiver.
+
+And that receiver then observes
+this, but together
+
+with some random noise.
+
+Here I meant S. S is the signal
+that's being sent.
+
+And what you observe is an X.
+
+You observe X, so what kind
+of inference problems
+
+could we have here?
+
+In some cases, you want to build
+a model of the physical
+
+phenomenon that you're
+dealing with.
+
+So for example, you don't know
+the attenuation of your signal
+
+and you try to find out what
+this number is based on the
+
+observations that you have.
+
+So the way this is done in
+engineering systems is that
+
+you design a certain signal, you
+know what it is, you shout
+
+a particular word, and then
+the receiver listens.
+
+And based on the intensity of
+the signal that they get, they
+
+try to make a guess about A. So
+you don't know A, but you
+
+know S. And by observing X,
+you get some information
+
+about what A is.
+
+So in this case, you're trying
+to build a model of the medium
+
+through which your signal
+is propagating.
+
+So sometimes one would call
+problems of this kind, let's
+
+say, system identification.
+
+In a different version of an
+inference problem that comes
+
+with this picture, you've
+done your modeling.
+
+You know your A. You know the
+medium through which the
+
+signal is going, but it's
+a communication system.
+
+This person is trying
+to communicate
+
+something to that person.
+
+So you send the signal S, but
+that person receives a noisy
+
+version of S. So that person
+tries to reconstruct S based
+
+on X.
+
+So in both cases, we have a
+linear relation between X and
+
+the unknown quantity.
+
+In one version, A is the unknown
+and we know S. In the
+
+other version, A is known,
+and so we try to infer S.
+
+Mathematically, you can see that
+this is essentially the
+
+same kind of problem
+in both cases.
+
+Although, the kind of practical
+problem that you're
+
+trying to solve is a
+little different.
+
+So we will not be making any
+distinctions between problems
+
+of the model building type as
+opposed to models where you
+
+try to estimate some unknown
+signal and so on.
+
+Because conceptually, the tools
+that one uses for both
+
+types of problems are
+essentially the same.
+
+OK, next a very useful
+classification
+
+of inference problems--
+
+the unknown quantity that you're
+trying to estimate
+
+could be either a discrete
+one that takes a
+
+small number of values.
+
+So this could be discrete
+problems, such as the airplane
+
+radar problem we encountered
+back a long
+
+time ago in this class.
+
+So there's two possibilities--
+
+an airplane is out there or an
+airplane is not out there.
+
+And you're trying to
+make a decision
+
+between these two options.
+
+Or you can have other problems
+would you have, let's say,
+
+four possible options.
+
+You don't know which one is
+true, but you get data and you
+
+try to figure out which
+one is true.
+
+In problems of these kind,
+usually you want to make a
+
+decision based on your data.
+
+And you're interested in the
+probability of making a
+
+correct decision.
+
+You would like that
+probability to
+
+be as high as possible.
+
+Estimation problems are
+a little different.
+
+Here you have some continuous
+quantity that's not known.
+
+And you try to make a good
+guess of that quantity.
+
+And you would like your guess to
+be as close as possible to
+
+the true quantity.
+
+So the polling problem
+was of this type.
+
+There was an unknown fraction
+f of the population that had
+
+some property.
+
+And you try to estimate f as
+accurately as you can.
+
+So the distinction here is that
+usually here the unknown
+
+quantity takes on discrete
+set of values.
+
+Here the unknown quantity
+takes a
+
+continuous set of values.
+
+Here we're interested in the
+probability of error.
+
+Here we're interested in
+the size of the error.
+
+Broadly speaking, most inference
+problems fall either
+
+in this category or
+in that category.
+
+Although, if you want to
+complicate life, you can also
+
+think or construct problems
+where both of these aspects
+
+are simultaneously present.
+
+OK, finally since we're in
+classification mode, there is
+
+a very big, important dichotomy
+into how one goes
+
+about inference problems.
+
+And here there's two
+fundamentally different
+
+philosophical points of view,
+which is how do we model the
+
+quantity that is unknown?
+
+In one approach, you say there's
+a certain quantity
+
+that has a definite value.
+
+It just happens that
+they don't know it.
+
+But it's a number.
+
+There's nothing random
+about it.
+
+So think of trying to estimate
+some physical quantity.
+
+You're making measurements, you
+try to estimate the mass
+
+of an electron, which
+is a sort of
+
+universal physical constant.
+
+There's nothing random
+about it.
+
+It's a fixed number.
+
+You get data, because you have
+some measuring apparatus.
+
+And that measuring apparatus,
+depending on what that results
+
+that you get are affected by the
+true mass of the electron,
+
+but there's also some noise.
+
+You take the data out of your
+measuring apparatus and you
+
+try to come up with
+some estimate of
+
+that quantity theta.
+
+So this is definitely a
+legitimate picture, but the
+
+important thing in this picture
+is that this theta is
+
+written as lowercase.
+
+And that's to make the point
+that it's a real number, not a
+
+random variable.
+
+There's a different
+philosophical approach which
+
+says, well, anything that I
+don't know I should model it
+
+as a random variable.
+
+Yes, I know.
+
+The mass of the electron
+is not really random.
+
+It's a constant.
+
+But I don't know what it is.
+
+I have some vague sense,
+perhaps, what it is perhaps
+
+because of the experiments
+that some other
+
+people carried out.
+
+So perhaps I have a prior
+distribution on the possible
+
+values of Theta.
+
+And that prior distribution
+doesn't mean that the nature
+
+is random, but it's more of a
+subjective description of my
+
+subjective beliefs of where do
+I think this constant number
+
+happens to be.
+
+So even though it's not truly
+random, I model my initial
+
+beliefs before the experiment
+starts.
+
+In terms of a prior
+distribution, I view it as a
+
+random variable.
+
+Then I observe another related
+random variable through some
+
+measuring apparatus.
+
+And then I use this again
+to create an estimate.
+
+So these two pictures
+philosophically are very
+
+different from each other.
+
+Here we treat the unknown
+quantities as unknown numbers.
+
+Here we treat them as
+random variables.
+
+When we treat them as a random
+variables, then we know pretty
+
+much already what we
+should be doing.
+
+We should just use
+the Bayes rule.
+
+Based on X, find
+the conditional
+
+distribution of Theta.
+
+And that's what we will be doing
+mostly over this lecture
+
+and the next lecture.
+
+Now in both cases, what you end
+up getting at the end is
+
+an estimate.
+
+But actually, that estimate is
+what kind of object is it?
+
+It's a random variable
+in both cases.
+
+Why?
+
+Even in this case where
+theta was a
+
+constant, my data are random.
+
+I do my data processing.
+
+So I calculate a function
+of the data, the
+
+data are random variables.
+
+So out here we output something
+which is a function
+
+of a random variable.
+
+So this quantity here
+will be also random.
+
+It's affected by the noise and
+the experiment that I have
+
+been doing.
+
+That's why these estimators
+will be denoted
+
+by uppercase Thetas.
+
+And we will be using hats.
+
+Hat, usually in estimation,
+means
+
+an estimate of something.
+
+All right, so this is
+the big picture.
+
+We're going to start with
+the Bayesian version.
+
+And then the last few lectures
+we're going to talk about the
+
+non-Bayesian version or
+the classical one.
+
+By the way, I should say that
+statisticians have been
+
+debating fiercely for 100 years
+whether the right way to
+
+approach statistics is to go
+the classical way or the
+
+Bayesian way.
+
+And there have been tides going
+back and forth between
+
+the two sides.
+
+These days, Bayesian methods
+tend to become a little more
+
+popular for various reasons.
+
+We're going to come back
+to this later.
+
+All right, so in Bayesian
+estimation, what we got in our
+
+hands is Bayes rule.
+
+And if you have Bayes rule,
+there's not a lot
+
+that's left to do.
+
+We have different forms of the
+Bayes rule, depending on
+
+whether we're dealing with
+discrete data, And discrete
+
+quantities to estimate, or
+continuous data, and so on.
+
+In the hypothesis testing
+problem, the unknown quantity
+
+Theta is discrete.
+
+So in both cases here,
+we have a P of Theta.
+
+We obtain data, the X's.
+
+And on the basis of the X that
+we observe, we can calculate
+
+the posterior distribution
+of Theta, given the data.
+
+So to use Bayesian inference,
+what do we start with?
+
+We start with some priors.
+
+These are our initial
+beliefs about what
+
+Theta that might be.
+
+That's before we do
+the experiment.
+
+We have a model of the
+experimental aparatus.
+
+And the model of the
+experimental apparatus tells
+
+us if this Theta is true, I'm
+going to see X's of that kind.
+
+If that other Theta is true, I'm
+going to see X's that they
+
+are somewhere else.
+
+That models my apparatus.
+
+And based on that knowledge,
+once I observe I have these
+
+two functions in my hands, we
+have already seen that if you
+
+know those two functions, you
+can also calculate the
+
+denominator here.
+
+So all of these functions are
+available, so you can compute,
+
+you can find a formula for
+this function as well.
+
+And as soon as you observe the
+data, that X's, you plug in
+
+here the numerical value
+of those X's.
+
+And you get a function
+of Theta.
+
+And this is the posterior
+distribution of Theta, given
+
+the data that you have seen.
+
+So you've already done
+a fair number of
+
+exercises of these kind.
+
+So we not say more about this.
+
+And there's a similar formula as
+you know for the case where
+
+we have continuous data.
+
+If the X's are continuous random
+variable, then the
+
+formula is the same, except
+that X's are described by
+
+densities instead of being
+described by a probability
+
+mass functions.
+
+OK, now if Theta is continuous,
+then we're dealing
+
+with estimation problems.
+
+But the story is once
+more the same.
+
+You're going to use the Bayes
+rule to come up with the
+
+posterior density of Theta,
+given the data
+
+that you have observed.
+
+Now just for the sake of the
+example, let's come back to
+
+this picture here.
+
+Suppose that something is flying
+in the air, and maybe
+
+this is just an object in the
+air close to the Earth.
+
+So because of gravity, the
+trajectory that it's going to
+
+follow it's going to
+be a parabola.
+
+So this is the general equation
+of a parabola.
+
+Zt is the position of my
+objects at time t.
+
+But I don't know exactly
+which parabola it is.
+
+So the parameters of the
+parabola are unknown
+
+quantities.
+
+What I can do is to go and
+measure the position of my
+
+objects at different times.
+
+But unfortunately, my
+measurements are noisy.
+
+What I want to do is to model
+the motion of my object.
+
+So I guess in the picture, the
+axis would be t going this way
+
+and Z going this way.
+
+And on the basis of the
+data that they get,
+
+these are my X's.
+
+I want to figure
+out the Thetas.
+
+That is, I want to figure
+out the exact
+
+equation of this parabola.
+
+Now if somebody gives you
+probability distributions for
+
+Theta, these would
+be your priors.
+
+So this is given.
+
+We need the conditional
+distribution of the X's given
+
+the Thetas.
+
+Well, we have the conditional
+distribution of Z, given the
+
+Thetas from this equation.
+
+And then by playing with this
+equation, you can also find
+
+how is X distributed if Theta
+takes a particular value.
+
+So you do have all of the
+densities that you might need.
+
+And you can apply
+the Bayes rule.
+
+And at the end, your end result
+would be a formula for
+
+the distribution of Theta,
+given to the X
+
+that you have observed--
+
+except for one sort of
+computation, or to make things
+
+more interesting.
+
+Instead of these X's and Theta's
+being single random
+
+variables that we have here,
+typically those X's and
+
+Theta's will be
+multi-dimensional random
+
+variables or will correspond
+to multiple ones.
+
+So this little Theta here
+actually stands for a triplet
+
+of Theta0, Theta1, and Theta2.
+
+And that X here stands here for
+the entire sequence of X's
+
+that we have observed.
+
+So in reality, the object that
+you're going to get at to the
+
+end after inference is done is
+a function that you plug in
+
+the values of the data and you
+get the function of the
+
+Theta's that tells you the
+relative likelihoods of
+
+different Theta triplets.
+
+So what I'm saying is that this
+is no harder than the
+
+problems that you have dealt
+with so far, except perhaps
+
+for the complication that's
+usually in interesting
+
+inference problems.
+
+Your Theta's and X's are often
+the vectors of random
+
+variables instead of individual
+random variables.
+
+Now if you are to do estimation
+in a case where you
+
+have discrete data, again the
+situation is no different.
+
+We still have a Bayes rule of
+the same kind, except that
+
+densities gets replaced
+by PMF's.
+
+If X is discrete, you put a P
+here instead of putting an f.
+
+So an example of an estimation
+problem with discrete data is
+
+similar to the polling
+problem.
+
+You have a coin.
+
+It has an unknown
+parameter Theta.
+
+This is the probability
+of obtaining heads.
+
+You flip the coin many times.
+
+What can you tell me about
+the true value of Theta?
+
+A classical statistician, at
+this point, would say, OK, I'm
+
+going to use an estimator,
+the most reasonable
+
+one, which is this.
+
+How many heads did they
+obtain in n trials?
+
+Divide by the total
+number of trials.
+
+This is my estimate of
+the bias of my coin.
+
+And then the classical
+statistician would continue
+
+from here and try to prove some
+properties and argue that
+
+this estimate is a good one.
+
+For example, we have the weak
+law of large numbers that
+
+tells us that this particular
+estimate converges in
+
+probability to the
+true parameter.
+
+This is a kind of guarantee
+that's useful to have.
+
+And the classical statistician
+would pretty much close the
+
+subject in this way.
+
+What would the Bayesian
+person do differently?
+
+The Bayesian person would start
+by assuming a prior
+
+distribution of Theta.
+
+Instead of treating Theta as
+an unknown constant, they
+
+would say that Theta would speak
+randomly or pretend that
+
+it would speak randomly
+and assume a
+
+distribution on Theta.
+
+So for example, if you don't
+know they need anything more,
+
+you might assume that any value
+for the bias of the coin
+
+is as likely as any other value
+of the bias of the coin.
+
+And this way so the probability
+distribution
+
+that's uniform.
+
+Or if you have a little more
+faith in the manufacturing
+
+processes that's created that
+coin, you might choose your
+
+prior to be a distribution
+that's centered around 1/2 and
+
+sits fairly narrowly centered
+around 1/2.
+
+That would be a prior
+distribution in which you say,
+
+well, I believe that the
+manufacturer tried to make my
+
+coin to be fair.
+
+But they often makes some
+mistakes, so it's going to be,
+
+I believe, it's approximately
+1/2 but not quite.
+
+So depending on your beliefs,
+you would choose an
+
+appropriate prior for the
+distribution of Theta.
+
+And then you would use the
+Bayes rule to find the
+
+probabilities of different
+values of Theta, based on the
+
+data that you have observed.
+
+So no matter which version of
+the Bayes rule that you use,
+
+the end product of the Bayes
+rule is going to be either a
+
+plot of this kind or a
+plot of that kind.
+
+So what am I plotting here?
+
+This axis is the Theta axis.
+
+These are the possible values
+of the unknown quantity that
+
+we're trying to estimate.
+
+In the continuous
+case, theta is a
+
+continuous random variable.
+
+I obtain my data.
+
+And I plot for the posterior
+probability distribution after
+
+observing my data.
+
+And I'm plotting here the
+probability density for Theta.
+
+So this is a plot
+of that density.
+
+In the discrete case, theta can
+take finitely many values
+
+or a discrete set of values.
+
+And for each one of those
+values, I'm telling you how
+
+likely is that the value to be
+the correct one, given the
+
+data that I have observed.
+
+And in general, what you would
+go back to your boss and
+
+report after you've done all
+your inference work would be
+
+either a plot of this kinds
+or of that kind.
+
+So you go to your boss
+who asks you, what is
+
+the value of Theta?
+
+And you say, well, I only
+have limited data.
+
+That I don't know what it is.
+
+It could be this, with
+so much probability.
+
+There's probability.
+
+OK, let's throw in some
+numbers here.
+
+There's probability 0.3 that
+Theta is this value.
+
+There's probability 0.2 that
+Theta is this value, 0.1 that
+
+it's this one, 0.1 that it's
+this one, 0.2 that it's that
+
+one, and so on.
+
+OK, now bosses often want
+simple answers.
+
+They say, OK, you're
+talking too much.
+
+What do you think Theta is?
+
+And now you're forced
+to make a decision.
+
+If that was the situation and
+you have to make a decision,
+
+how would you make it?
+
+Well, I'm going to make a
+decision that's most likely to
+
+be correct.
+
+If I make this decision,
+what's going to happen?
+
+Theta is this value with
+probability 0.2, which means
+
+there's probably 0.8 that
+they make an error
+
+if I make that guess.
+
+If I make that decision, this
+decision has probably 0.3 of
+
+being the correct one.
+
+So I have probably
+of error 0.7.
+
+So if you want to just maximize
+the probability of
+
+giving the correct decision, or
+if you want to minimize the
+
+probability of making an
+incorrect decision, what
+
+you're going to choose to report
+is that value of Theta
+
+for which the probability
+is highest.
+
+So in this case, I would
+choose to report this
+
+particular value, the most
+likely value of Theta, given
+
+what I have observed.
+
+And that value is called them
+maximum a posteriori
+
+probability estimate.
+
+It's going to be this
+one in our case.
+
+So picking the point in the
+posterior PMF that has the
+
+highest probability.
+
+That's the reasonable
+thing to do.
+
+This is the optimal thing to do
+if you want to minimize the
+
+probability of an incorrect
+inference.
+
+And that's what people do
+usually if they need to report
+
+a single answer, if they need
+to report a single decision.
+
+How about in the estimation
+context?
+
+If that's what you know about
+Theta, Theta could be around
+
+here, but there's also some
+sharp probability that it is
+
+around here.
+
+What's the single answer that
+you would give to your boss?
+
+One option is to use the same
+philosophy and say, OK, I'm
+
+going to find the Theta at which
+this posterior density
+
+is highest.
+
+So I would pick this point
+here and report this
+
+particular Theta.
+
+So this would be my Theta,
+again, Theta MAP, the Theta
+
+that has the highest a
+posteriori probability, just
+
+because it corresponds to
+the peak of the density.
+
+But in this context, the
+maximum a posteriori
+
+probability theta was the
+one that was most
+
+likely to be true.
+
+In the continuous case, you
+cannot really say that this is
+
+the most likely value
+of Theta.
+
+In a continuous setting, any
+value of Theta has zero
+
+probability, so when we
+talk about densities.
+
+So it's not the most likely.
+
+It's the one for which the
+density, so the probabilities
+
+of that neighborhoods,
+are highest.
+
+So the rationale for picking
+this particular estimate in
+
+the continuous case is much
+less compelling than the
+
+rationale that we had in here.
+
+So in this case, reasonable
+people might choose different
+
+quantities to report.
+
+And the very popular one would
+be to report instead the
+
+conditional expectation.
+
+So I don't know quite
+what Theta is.
+
+Given the data that I have,
+Theta has this distribution.
+
+Let me just report the average
+over that distribution.
+
+Let me report to the center
+of gravity of this figure.
+
+And in this figure, the center
+of gravity would probably be
+
+somewhere around here.
+
+And that would be a different
+estimate that you
+
+might choose to report.
+
+So center of gravity is
+something around here.
+
+And this is a conditional
+expectation of Theta, given
+
+the data that you have.
+
+So these are two, in some sense,
+fairly reasonable ways
+
+of choosing what to report
+to your boss.
+
+Some people might choose
+to report this.
+
+Some people might choose
+to report that.
+
+And a priori, if there's no
+compelling reason why one
+
+would be preferable than other
+one, unless you set some rules
+
+for the game and you describe
+a little more precisely what
+
+your objectives are.
+
+But no matter which one you
+report, a single answer, a
+
+point estimate, doesn't really
+tell you the whole story.
+
+There's a lot more information
+conveyed by this posterior
+
+distribution plot than
+any single number
+
+that you might report.
+
+So in general, you may wish to
+convince your boss that's it's
+
+worth their time to look at the
+entire plot, because that
+
+plot sort of covers all
+the possibilities.
+
+It tells your boss most likely
+we're in that range, but
+
+there's also a distinct change
+that our Theta happens to lie
+
+in that range.
+
+All right, now let us try to
+perhaps differentiate between
+
+these two and see under what
+circumstances this one might
+
+be the better estimate
+to perform.
+
+Better with respect to what?
+
+We need some rules.
+
+So we're going to throw
+in some rules.
+
+As a warm up, we're going to
+deal with the problem of
+
+making an estimation if you
+had no information at all,
+
+except for a prior
+distribution.
+
+So this is a warm up for what's
+coming next, which
+
+would be estimation that takes
+into account some information.
+
+So we have a Theta.
+
+And because of your subjective
+beliefs or models by others,
+
+you believe that Theta is
+uniformly distributed between,
+
+let's say, 4 and 10.
+
+You want to come up with
+a point estimate.
+
+Let's try to look
+for an estimate.
+
+Call it c, in this case.
+
+I want to pick a number
+with which to estimate
+
+the value of Theta.
+
+I will be interested in the size
+of the error that I make.
+
+And I really dislike large
+errors, so I'm going to focus
+
+on the square of the error
+that they make.
+
+So I pick c.
+
+Theta that has a random value
+that I don't know.
+
+But whatever it is, once it
+becomes known, it results into
+
+a squared error between
+what it is and what I
+
+guessed that it was.
+
+And I'm interested in making
+a small air on the average,
+
+where the average is taken
+with respect to all the
+
+possible and unknown
+values of Theta.
+
+So the problem, this is a least
+squares formulation of
+
+the problem, where we
+try to minimize the
+
+least squares errors.
+
+How do you find the optimal c?
+
+Well, we take that expression
+and expand it.
+
+And it is, using linearity
+of expectations--
+
+square minus 2c expected
+Theta plus c squared--
+
+that's the quantity that
+we want to minimize,
+
+with respect to c.
+
+To do the minimization, take the
+derivative with respect to
+
+c and set it to 0.
+
+So that differentiation gives us
+from here minus 2 expected
+
+value of Theta plus
+2c is equal to 0.
+
+And the answer that you get by
+solving this equation is that
+
+c is the expected
+value of Theta.
+
+So when you do this
+optimization, you find that
+
+the optimal estimate, the
+things you should be
+
+reporting, is the expected
+value of Theta.
+
+So in this particular example,
+you would choose your estimate
+
+c to be just the middle
+of these values,
+
+which would be 7.
+
+OK, and in case your
+boss asks you, how
+
+good is your estimate?
+
+How big is your error
+going to be?
+
+What you could report is the
+average size of the estimation
+
+error that you are making.
+
+We picked our estimates to be
+the expected value of Theta.
+
+So for this particular way that
+I'm choosing to do my
+
+estimation, this is the mean
+squared error that I get.
+
+And this is a familiar
+quantity.
+
+It's just the variance
+of the distribution.
+
+So the expectation is that
+best way to estimate a
+
+quantity, if you're interested
+in the mean squared error.
+
+And the resulting mean squared
+error is the variance itself.
+
+How will this story change if
+we now have data as well?
+
+Now having data means that
+we can compute posterior
+
+distributions or conditional
+distributions.
+
+So we get transported into a new
+universe where instead the
+
+working with the original
+distribution of Theta, the
+
+prior distribution, now we work
+with the condition of
+
+distribution of Theta,
+given the data
+
+that we have observed.
+
+Now remember our old slogan that
+conditional models and
+
+conditional probabilities are
+no different than ordinary
+
+probabilities, except that we
+live now in a new universe
+
+where the new information has
+been taken into account.
+
+So if you use that philosophy
+and you're asked to minimize
+
+the squared error but now that
+you live in a new universe
+
+where X has been fixed to
+something, what would the
+
+optimal solution be?
+
+It would again be the
+expectation of theta, but
+
+which expectation?
+
+It's the expectation which
+applies in the new conditional
+
+universe in which we
+live right now.
+
+So because of what we did
+before, by the same
+
+calculation, we would find that
+the optimal estimates is
+
+the expected value of X of
+Theta, but the optimal
+
+estimate that takes
+into account the
+
+information that we have.
+
+So the conclusion, once you get
+your data, if you want to
+
+minimize the mean squared error,
+you should just report
+
+the conditional estimation of
+this unknown quantity based on
+
+the data that you have.
+
+So the picture here is that
+Theta is unknown.
+
+You have your apparatus that
+creates measurements.
+
+So this creates an X. You take
+an X, and here you have a box
+
+that does calculations.
+
+It does calculations and it
+spits out the conditional
+
+expectation of Theta, given the
+particular data that you
+
+have observed.
+
+And what we have done in this
+class so far is, to some
+
+extent, developing the
+computational tools and skills
+
+to do with this particular
+calculation--
+
+how to calculate the posterior
+density for Theta and how to
+
+calculate expectations,
+conditional expectations.
+
+So in principle, we know
+how to do this.
+
+In principle, we can program a
+computer to take the data and
+
+to spit out condition
+expectations.
+
+Somebody who doesn't think like
+us might instead design a
+
+calculating machine that does
+something differently and
+
+produces some other estimate.
+
+So we went through this argument
+and we decided to
+
+program our computer to
+calculate conditional
+
+expectations.
+
+Somebody else came up with some
+other crazy idea for how
+
+to estimate the random
+variable.
+
+They came up with some function
+g and the programmed
+
+it, and they designed a machine
+that estimates Theta's
+
+by outputting a certain
+g of X.
+
+That could be an alternative
+estimator.
+
+Which one is better?
+
+Well, we convinced ourselves
+that this is the optimal one
+
+in a universe where we have
+fixed the particular
+
+value of the data.
+
+So what we have proved so far
+is a relation of this kind.
+
+In this conditional universe,
+the mean squared
+
+error that I get--
+
+I'm the one who's using
+this estimator--
+
+is less than or equal than the
+mean squared error that this
+
+person will get, the person
+who uses that estimator.
+
+For any particular value of
+the data, I'm going to do
+
+better than the other person.
+
+Now the data themselves
+are random.
+
+If I average over all possible
+values of the data, I should
+
+still be better off.
+
+If I'm better off for any
+possible value X, then I
+
+should be better off on the
+average over all possible
+
+values of X.
+
+So let us average both sides of
+this quantity with respect
+
+to the probability distribution
+of X. If you want
+
+to do it formally, you can write
+this inequality between
+
+numbers as an inequality between
+random variables.
+
+And it tells that no matter
+what that random variable
+
+turns out to be, this quantity
+is better than that quantity.
+
+Take expectations of both
+sides, and you get this
+
+inequality between expectations
+overall.
+
+And this last inequality tells
+me that the person who's using
+
+this estimator who produces
+estimates according to this
+
+machine will have a mean squared
+estimation error
+
+that's less than or equal to
+the estimation error that's
+
+produced by the other person.
+
+In a few words, the conditional
+expectation
+
+estimator is the optimal
+estimator.
+
+It's the ultimate estimating
+machine.
+
+That's how you should solve
+estimation problems and report
+
+a single value.
+
+If you're forced to report a
+single value and if you're
+
+interested in estimation
+errors.
+
+OK, while we could have told you
+that story, of course, a
+
+month or two ago, this is really
+about interpretation --
+
+about realizing that conditional
+expectations have
+
+a very nice property.
+
+But other than that, any
+probabilistic skills that come
+
+into this business are just the
+probabilistic skills of
+
+being able to calculate
+conditional expectations,
+
+which you already
+know how to do.
+
+So conclusion, all of optimal
+Bayesian estimation just means
+
+calculating and reporting
+conditional expectations.
+
+Well, if the world were that
+simple, then statisticians
+
+wouldn't be able to find jobs
+if life is that simple.
+
+So real life is not
+that simple.
+
+There are complications.
+
+And that perhaps makes their
+life a little more
+
+interesting.
+
+OK, one complication is that we
+would deal with the vectors
+
+instead of just single
+random variables.
+
+I use the notation here
+as if X was a
+
+single random variable.
+
+In real life, you get
+several data.
+
+Does our story change?
+
+Not really, same argument--
+
+given all the data that you
+have observed, you should
+
+still report the conditional
+expectation of Theta.
+
+But what kind of work does it
+take in order to report this
+
+conditional expectation?
+
+One issue is that you need to
+cook up a plausible prior
+
+distribution for Theta.
+
+How do you do that?
+
+In a given application , this
+is a bit of a judgment call,
+
+what prior would you
+be working with.
+
+And there's a certain
+skill there of not
+
+making silly choices.
+
+A more pragmatic, practical
+issue is that this is a
+
+formula that's extremely nice
+and compact and simple that
+
+you can write with
+minimal ink.
+
+But the behind it there could
+be hidden a huge amount of
+
+calculation.
+
+So doing any sort of
+calculations that involve
+
+multiple random variables really
+involves calculating
+
+multi-dimensional integrals.
+
+And the multi-dimensional
+integrals are hard to compute.
+
+So implementing actually this
+calculating machine here may
+
+not be easy, might be
+complicated computationally.
+
+It's also complicated in terms
+of not being able to derive
+
+intuition about it.
+
+So perhaps you might want to
+have a simpler version, a
+
+simpler alternative to this
+formula that's easier to work
+
+with and easier to calculate.
+
+We will be talking about
+one such simpler
+
+alternative next time.
+
+So again, to conclude, at
+the high level, Bayesian
+
+estimation is very, very simple,
+given that you have
+
+mastered everything that
+has happened in
+
+this course so far.
+
+There are certain practical
+issues and it's also good to
+
+be familiar with the concepts
+and the issues that in
+
+general, you would prefer to
+report that complete posterior
+
+distribution.
+
+But if you're forced to report a
+point estimate, then there's
+
+a number of reasonable
+ways to do it.
+
+And perhaps the most reasonable
+one is to just the
+
+report the conditional
+expectation itself.
\ No newline at end of file
diff --git a/1pkoBetgo7s.txt b/1pkoBetgo7s.txt
new file mode 100644
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+++ b/1pkoBetgo7s.txt
@@ -0,0 +1,12419 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
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+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu good so before we start do
+
+ align:start position:0%
+ocw.mit.edu good so before we start do
+ 
+
+ align:start position:0%
+ocw.mit.edu good so before we start do
+you have any questions on what we did uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we have
+
+ align:start position:0%
+okay so we have
+ 
+
+ align:start position:0%
+okay so we have
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+discussed that black hole can be
+
+ align:start position:0%
+discussed that black hole can be
+ 
+
+ align:start position:0%
+discussed that black hole can be
+considered as a sumal
+
+ align:start position:0%
+considered as a sumal
+ 
+
+ align:start position:0%
+considered as a sumal
+object and that actually black hoes
+
+ align:start position:0%
+object and that actually black hoes
+ 
+
+ align:start position:0%
+object and that actually black hoes
+oreas the the standard law of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thermodynamics and
+
+ align:start position:0%
+thermodynamics and
+ 
+
+ align:start position:0%
+thermodynamics and
+now we also mention that the
+
+ align:start position:0%
+now we also mention that the
+ 
+
+ align:start position:0%
+now we also mention that the
+um it's a Lal question to ask whether
+
+ align:start position:0%
+um it's a Lal question to ask whether
+ 
+
+ align:start position:0%
+um it's a Lal question to ask whether
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+ho should be considered as ordinary qu
+
+ align:start position:0%
+ho should be considered as ordinary qu
+ 
+
+ align:start position:0%
+ho should be considered as ordinary qu
+mechanical
+
+ align:start position:0%
+mechanical
+ 
+
+ align:start position:0%
+mechanical
+object and so this is related to the
+
+ align:start position:0%
+object and so this is related to the
+ 
+
+ align:start position:0%
+object and so this is related to the
+issue of information
+
+ align:start position:0%
+issue of information
+ 
+
+ align:start position:0%
+issue of information
+Paradox so but if when disregard this
+
+ align:start position:0%
+Paradox so but if when disregard this
+ 
+
+ align:start position:0%
+Paradox so but if when disregard this
+information Paradox uh which I think now
+
+ align:start position:0%
+information Paradox uh which I think now
+ 
+
+ align:start position:0%
+information Paradox uh which I think now
+have a very good
+
+ align:start position:0%
+have a very good
+ 
+
+ align:start position:0%
+have a very good
+um in principle have a a rasonable
+
+ align:start position:0%
+um in principle have a a rasonable
+ 
+
+ align:start position:0%
+um in principle have a a rasonable
+resolution which we talk about
+
+ align:start position:0%
+resolution which we talk about
+ 
+
+ align:start position:0%
+resolution which we talk about
+later but if we do treat the black ho as
+
+ align:start position:0%
+later but if we do treat the black ho as
+ 
+
+ align:start position:0%
+later but if we do treat the black ho as
+ordinary Quantum mechanic mechanical
+
+ align:start position:0%
+ordinary Quantum mechanic mechanical
+ 
+
+ align:start position:0%
+ordinary Quantum mechanic mechanical
+object then then they actually um very
+
+ align:start position:0%
+object then then they actually um very
+ 
+
+ align:start position:0%
+object then then they actually um very
+important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implications so one imp one implications
+
+ align:start position:0%
+implications so one imp one implications
+ 
+
+ align:start position:0%
+implications so one imp one implications
+this called the holographic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principle so holographic principle by
+
+ align:start position:0%
+principle so holographic principle by
+ 
+
+ align:start position:0%
+principle so holographic principle by
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+of is in some in some sense a rather
+
+ align:start position:0%
+of is in some in some sense a rather
+ 
+
+ align:start position:0%
+of is in some in some sense a rather
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um theistic concept at the
+
+ align:start position:0%
+um theistic concept at the
+ 
+
+ align:start position:0%
+um theistic concept at the
+moment and and I will also not to make
+
+ align:start position:0%
+moment and and I will also not to make
+ 
+
+ align:start position:0%
+moment and and I will also not to make
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+uh and I will also only give you a very
+
+ align:start position:0%
+uh and I will also only give you a very
+ 
+
+ align:start position:0%
+uh and I will also only give you a very
+humanistic discussion and it's possible
+
+ align:start position:0%
+humanistic discussion and it's possible
+ 
+
+ align:start position:0%
+humanistic discussion and it's possible
+to make it a little bit more rigorous
+
+ align:start position:0%
+to make it a little bit more rigorous
+ 
+
+ align:start position:0%
+to make it a little bit more rigorous
+but I will uh do it at the other um
+
+ align:start position:0%
+but I will uh do it at the other um
+ 
+
+ align:start position:0%
+but I will uh do it at the other um
+heuristic level just to give you a
+
+ align:start position:0%
+heuristic level just to give you a
+ 
+
+ align:start position:0%
+heuristic level just to give you a
+Feeling
+
+ align:start position:0%
+Feeling
+ 
+
+ align:start position:0%
+Feeling
+that there's something profound going
+
+ align:start position:0%
+that there's something profound going
+ 
+
+ align:start position:0%
+that there's something profound going
+on uh in quantum gravity because of the
+
+ align:start position:0%
+on uh in quantum gravity because of the
+ 
+
+ align:start position:0%
+on uh in quantum gravity because of the
+black holes because of black
+
+ align:start position:0%
+black holes because of black
+ 
+
+ align:start position:0%
+black holes because of black
+holes
+
+ align:start position:0%
+holes
+ 
+
+ align:start position:0%
+holes
+um so let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider isolated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+mass say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e and say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entropy S
+
+ align:start position:0%
+entropy S
+ 
+
+ align:start position:0%
+entropy S
+zero say in a sympotic flat space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then me also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+denote a as the
+
+ align:start position:0%
+denote a as the
+ 
+
+ align:start position:0%
+denote a as the
+area of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smallest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sphere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that say en closes the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then and also let let me
+
+ align:start position:0%
+okay and then and also let let me
+ 
+
+ align:start position:0%
+okay and then and also let let me
+introduce let
+
+ align:start position:0%
+introduce let
+ 
+
+ align:start position:0%
+introduce let
+ma be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the mass of the black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hole of the same Horizon
+
+ align:start position:0%
+hole of the same Horizon
+ 
+
+ align:start position:0%
+hole of the same Horizon
+area
+
+ align:start position:0%
+area
+ 
+
+ align:start position:0%
+area
+yeah say
+
+ align:start position:0%
+yeah say
+ 
+
+ align:start position:0%
+yeah say
+with black
+
+ align:start position:0%
+with black
+ 
+
+ align:start position:0%
+with black
+ho
+
+ align:start position:0%
+ho
+ 
+
+ align:start position:0%
+ho
+with Horizon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gr anything which is sufficiently
+
+ align:start position:0%
+gr anything which is sufficiently
+ 
+
+ align:start position:0%
+gr anything which is sufficiently
+massive will eventually collapse form a
+
+ align:start position:0%
+massive will eventually collapse form a
+ 
+
+ align:start position:0%
+massive will eventually collapse form a
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+hole because of
+
+ align:start position:0%
+hole because of
+ 
+
+ align:start position:0%
+hole because of
+that so we might must
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have e is smaller than
+
+ align:start position:0%
+have e is smaller than
+ 
+
+ align:start position:0%
+have e is smaller than
+ma
+
+ align:start position:0%
+ma
+ 
+
+ align:start position:0%
+ma
+okay so we must have e so whatever
+
+ align:start position:0%
+okay so we must have e so whatever
+ 
+
+ align:start position:0%
+okay so we must have e so whatever
+energe you can put in this region
+
+ align:start position:0%
+energe you can put in this region
+ 
+
+ align:start position:0%
+energe you can put in this region
+surrounded by area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a must be smaller than the mass of a
+
+ align:start position:0%
+a must be smaller than the mass of a
+ 
+
+ align:start position:0%
+a must be smaller than the mass of a
+black hole which you can put in that
+
+ align:start position:0%
+black hole which you can put in that
+ 
+
+ align:start position:0%
+black hole which you can put in that
+region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay because otherwise if we have a more
+
+ align:start position:0%
+okay because otherwise if we have a more
+ 
+
+ align:start position:0%
+okay because otherwise if we have a more
+mass will already be a black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hole Yeah say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal so now let's suppose e is smaller
+
+ align:start position:0%
+equal so now let's suppose e is smaller
+ 
+
+ align:start position:0%
+equal so now let's suppose e is smaller
+than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ma so we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose e is smaller than ma now we
+
+ align:start position:0%
+so suppose e is smaller than ma now we
+ 
+
+ align:start position:0%
+so suppose e is smaller than ma now we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+add this amount of
+
+ align:start position:0%
+add this amount of
+ 
+
+ align:start position:0%
+add this amount of
+energy say ma minus
+
+ align:start position:0%
+energy say ma minus
+ 
+
+ align:start position:0%
+energy say ma minus
+E amount of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+okay suppose we can do that keep a fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we can do that keep it
+
+ align:start position:0%
+okay so we can do that keep it
+ 
+
+ align:start position:0%
+okay so we can do that keep it
+fixed and then then this will reach a
+
+ align:start position:0%
+fixed and then then this will reach a
+ 
+
+ align:start position:0%
+fixed and then then this will reach a
+black hole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass then the final system will have a
+
+ align:start position:0%
+mass then the final system will have a
+ 
+
+ align:start position:0%
+mass then the final system will have a
+then the final system will be um we have
+
+ align:start position:0%
+then the final system will be um we have
+ 
+
+ align:start position:0%
+then the final system will be um we have
+the a black hole we have the black hole
+
+ align:start position:0%
+the a black hole we have the black hole
+ 
+
+ align:start position:0%
+the a black hole we have the black hole
+we have the energ given by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ma and that object must be a black hole
+
+ align:start position:0%
+Ma and that object must be a black hole
+ 
+
+ align:start position:0%
+Ma and that object must be a black hole
+because the uh
+
+ align:start position:0%
+because the uh
+ 
+
+ align:start position:0%
+because the uh
+um because the um yeah yeah because
+
+ align:start position:0%
+um because the um yeah yeah because
+ 
+
+ align:start position:0%
+um because the um yeah yeah because
+that's the black hole with the same
+
+ align:start position:0%
+that's the black hole with the same
+ 
+
+ align:start position:0%
+that's the black hole with the same
+Horizon area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay
+
+ align:start position:0%
+Okay
+ 
+
+ align:start position:0%
+Okay
+U so so
+
+ align:start position:0%
+U so so
+ 
+
+ align:start position:0%
+U so so
+that's because of this process also
+
+ align:start position:0%
+that's because of this process also
+ 
+
+ align:start position:0%
+that's because of this process also
+tells you that the blacko
+
+ align:start position:0%
+tells you that the blacko
+ 
+
+ align:start position:0%
+tells you that the blacko
+entropy much greater than the s0 the
+
+ align:start position:0%
+entropy much greater than the s0 the
+ 
+
+ align:start position:0%
+entropy much greater than the s0 the
+initial entropy of this system plus the
+
+ align:start position:0%
+initial entropy of this system plus the
+ 
+
+ align:start position:0%
+initial entropy of this system plus the
+S
+
+ align:start position:0%
+S
+ 
+
+ align:start position:0%
+S
+Prime uh uh S Prime is the entropy of
+
+ align:start position:0%
+Prime uh uh S Prime is the entropy of
+ 
+
+ align:start position:0%
+Prime uh uh S Prime is the entropy of
+added
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy okay so just because of the
+
+ align:start position:0%
+energy okay so just because of the
+ 
+
+ align:start position:0%
+energy okay so just because of the
+second L of thermodynamics your entropy
+
+ align:start position:0%
+second L of thermodynamics your entropy
+ 
+
+ align:start position:0%
+second L of thermodynamics your entropy
+should not
+
+ align:start position:0%
+should not
+ 
+
+ align:start position:0%
+should not
+decrease so so the
+
+ align:start position:0%
+decrease so so the
+ 
+
+ align:start position:0%
+decrease so so the
+final so you keep so you add this amount
+
+ align:start position:0%
+final so you keep so you add this amount
+ 
+
+ align:start position:0%
+final so you keep so you add this amount
+of energy so that this to to Ma so then
+
+ align:start position:0%
+of energy so that this to to Ma so then
+ 
+
+ align:start position:0%
+of energy so that this to to Ma so then
+you will precisely form a black hole of
+
+ align:start position:0%
+you will precisely form a black hole of
+ 
+
+ align:start position:0%
+you will precisely form a black hole of
+the mass Ma and with the Horizon area a
+
+ align:start position:0%
+the mass Ma and with the Horizon area a
+ 
+
+ align:start position:0%
+the mass Ma and with the Horizon area a
+and uh but this P entropy should be
+
+ align:start position:0%
+and uh but this P entropy should be
+ 
+
+ align:start position:0%
+and uh but this P entropy should be
+greater than s z plus the uh the entropy
+
+ align:start position:0%
+greater than s z plus the uh the entropy
+ 
+
+ align:start position:0%
+greater than s z plus the uh the entropy
+you added this is from the second L of
+
+ align:start position:0%
+you added this is from the second L of
+ 
+
+ align:start position:0%
+you added this is from the second L of
+some dyamics
+
+ align:start position:0%
+some dyamics
+ 
+
+ align:start position:0%
+some dyamics
+okay so then that
+
+ align:start position:0%
+okay so then that
+ 
+
+ align:start position:0%
+okay so then that
+means your initial en your initial
+
+ align:start position:0%
+means your initial en your initial
+ 
+
+ align:start position:0%
+means your initial en your initial
+entropy must be smaller than
+
+ align:start position:0%
+entropy must be smaller than
+ 
+
+ align:start position:0%
+entropy must be smaller than
+the black entropy
+
+ align:start position:0%
+the black entropy
+ 
+
+ align:start position:0%
+the black entropy
+okay must be smaller than a divided by 4
+
+ align:start position:0%
+okay must be smaller than a divided by 4
+ 
+
+ align:start position:0%
+okay must be smaller than a divided by 4
+H bar G
+
+ align:start position:0%
+H bar G
+ 
+
+ align:start position:0%
+H bar G
+Newton
+
+ align:start position:0%
+Newton
+ 
+
+ align:start position:0%
+Newton
+okay so this argument tells
+
+ align:start position:0%
+okay so this argument tells
+ 
+
+ align:start position:0%
+okay so this argument tells
+you that the maximal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entropy
+
+ align:start position:0%
+entropy
+ 
+
+ align:start position:0%
+entropy
+inside a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region bounded by area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so so we keeping a fixed at extra
+
+ align:start position:0%
+yes so so we keeping a fixed at extra
+ 
+
+ align:start position:0%
+yes so so we keeping a fixed at extra
+INRI to the system yeah uh so in that
+
+ align:start position:0%
+INRI to the system yeah uh so in that
+ 
+
+ align:start position:0%
+INRI to the system yeah uh so in that
+case uh why we don't have such a term
+
+ align:start position:0%
+case uh why we don't have such a term
+ 
+
+ align:start position:0%
+case uh why we don't have such a term
+sorry so so you said but we want to keep
+
+ align:start position:0%
+sorry so so you said but we want to keep
+ 
+
+ align:start position:0%
+sorry so so you said but we want to keep
+a fixed will that add actra entropy to
+
+ align:start position:0%
+a fixed will that add actra entropy to
+ 
+
+ align:start position:0%
+a fixed will that add actra entropy to
+the system yes uh so so according to the
+
+ align:start position:0%
+the system yes uh so so according to the
+ 
+
+ align:start position:0%
+the system yes uh so so according to the
+second La
+
+ align:start position:0%
+second La
+ 
+
+ align:start position:0%
+second La
+ofam
+
+ align:start position:0%
+ofam
+ 
+
+ align:start position:0%
+ofam
+why we we claim that the andri black ho
+
+ align:start position:0%
+why we we claim that the andri black ho
+ 
+
+ align:start position:0%
+why we we claim that the andri black ho
+is greater than or equal than S not plus
+
+ align:start position:0%
+is greater than or equal than S not plus
+ 
+
+ align:start position:0%
+is greater than or equal than S not plus
+s yeah uh uh okay add yeah because yeah
+
+ align:start position:0%
+s yeah uh uh okay add yeah because yeah
+ 
+
+ align:start position:0%
+s yeah uh uh okay add yeah because yeah
+this is the energy of added energ how
+
+ align:start position:0%
+this is the energy of added energ how
+ 
+
+ align:start position:0%
+this is the energy of added energ how
+about the actual energy that might be
+
+ align:start position:0%
+about the actual energy that might be
+ 
+
+ align:start position:0%
+about the actual energy that might be
+introduced by keeping a fixed like
+
+ align:start position:0%
+introduced by keeping a fixed like
+ 
+
+ align:start position:0%
+introduced by keeping a fixed like
+because it's not yeah whatever it is uh
+
+ align:start position:0%
+because it's not yeah whatever it is uh
+ 
+
+ align:start position:0%
+because it's not yeah whatever it is uh
+whatever it is suppose you can keep a
+
+ align:start position:0%
+whatever it is suppose you can keep a
+ 
+
+ align:start position:0%
+whatever it is suppose you can keep a
+fixed uh suppose you can keep a fixed
+
+ align:start position:0%
+fixed uh suppose you can keep a fixed
+ 
+
+ align:start position:0%
+fixed uh suppose you can keep a fixed
+then whatever uh uh things you added to
+
+ align:start position:0%
+then whatever uh uh things you added to
+ 
+
+ align:start position:0%
+then whatever uh uh things you added to
+that that total
+
+ align:start position:0%
+that that total
+ 
+
+ align:start position:0%
+that that total
+entropy must be smaller than the black
+
+ align:start position:0%
+entropy must be smaller than the black
+ 
+
+ align:start position:0%
+entropy must be smaller than the black
+entropy because black is the fow State
+
+ align:start position:0%
+entropy because black is the fow State
+ 
+
+ align:start position:0%
+entropy because black is the fow State
+you said uh it's an isolated system so
+
+ align:start position:0%
+you said uh it's an isolated system so
+ 
+
+ align:start position:0%
+you said uh it's an isolated system so
+with that uh how can you make sure that
+
+ align:start position:0%
+with that uh how can you make sure that
+ 
+
+ align:start position:0%
+with that uh how can you make sure that
+a is fixed why is yeah I'm just saying
+
+ align:start position:0%
+a is fixed why is yeah I'm just saying
+ 
+
+ align:start position:0%
+a is fixed why is yeah I'm just saying
+uh we are doing a thought experiment
+
+ align:start position:0%
+uh we are doing a thought experiment
+ 
+
+ align:start position:0%
+uh we are doing a thought experiment
+imagine you can do this by keeping a
+
+ align:start position:0%
+imagine you can do this by keeping a
+ 
+
+ align:start position:0%
+imagine you can do this by keeping a
+fixed yeah just say uh you you just put
+
+ align:start position:0%
+fixed yeah just say uh you you just put
+ 
+
+ align:start position:0%
+fixed yeah just say uh you you just put
+stuff in uh uh into this region uh so
+
+ align:start position:0%
+stuff in uh uh into this region uh so
+ 
+
+ align:start position:0%
+stuff in uh uh into this region uh so
+that stuff does not uh uh does not come
+
+ align:start position:0%
+that stuff does not uh uh does not come
+ 
+
+ align:start position:0%
+that stuff does not uh uh does not come
+out yeah just we have some region
+
+ align:start position:0%
+out yeah just we have some region
+ 
+
+ align:start position:0%
+out yeah just we have some region
+a uh maybe let me do it here you have
+
+ align:start position:0%
+a uh maybe let me do it here you have
+ 
+
+ align:start position:0%
+a uh maybe let me do it here you have
+some region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a and there's some Mass inside here some
+
+ align:start position:0%
+a and there's some Mass inside here some
+ 
+
+ align:start position:0%
+a and there's some Mass inside here some
+energ stuff inside here so this is the
+
+ align:start position:0%
+energ stuff inside here so this is the
+ 
+
+ align:start position:0%
+energ stuff inside here so this is the
+region a and then you just keep putting
+
+ align:start position:0%
+region a and then you just keep putting
+ 
+
+ align:start position:0%
+region a and then you just keep putting
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+in just keeping keep putting stuff in so
+
+ align:start position:0%
+in just keeping keep putting stuff in so
+ 
+
+ align:start position:0%
+in just keeping keep putting stuff in so
+that those things don't come out of a
+
+ align:start position:0%
+that those things don't come out of a
+ 
+
+ align:start position:0%
+that those things don't come out of a
+don't come out of this region uh uh that
+
+ align:start position:0%
+don't come out of this region uh uh that
+ 
+
+ align:start position:0%
+don't come out of this region uh uh that
+what this
+
+ align:start position:0%
+what this
+ 
+
+ align:start position:0%
+what this
+means then a is not smallest sphere then
+
+ align:start position:0%
+means then a is not smallest sphere then
+ 
+
+ align:start position:0%
+means then a is not smallest sphere then
+a is not smallest sphere to a is what
+
+ align:start position:0%
+a is not smallest sphere to a is what
+ 
+
+ align:start position:0%
+a is not smallest sphere to a is what
+not the smallest sphere that includ the
+
+ align:start position:0%
+not the smallest sphere that includ the
+ 
+
+ align:start position:0%
+not the smallest sphere that includ the
+system so that's it's not no no a is not
+
+ align:start position:0%
+system so that's it's not no no a is not
+ 
+
+ align:start position:0%
+system so that's it's not no no a is not
+the smallest to be increase system a
+
+ align:start position:0%
+the smallest to be increase system a
+ 
+
+ align:start position:0%
+the smallest to be increase system a
+just yeah maybe I should call it this A
+
+ align:start position:0%
+just yeah maybe I should call it this A
+ 
+
+ align:start position:0%
+just yeah maybe I should call it this A
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+area of a sphere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah sorry uh uh uh yeah uh thanks so so
+
+ align:start position:0%
+yeah sorry uh uh uh yeah uh thanks so so
+ 
+
+ align:start position:0%
+yeah sorry uh uh uh yeah uh thanks so so
+so just enough a to be a to be a sphere
+
+ align:start position:0%
+so just enough a to be a to be a sphere
+ 
+
+ align:start position:0%
+so just enough a to be a to be a sphere
+that enclose the system yeah yeah sorry
+
+ align:start position:0%
+that enclose the system yeah yeah sorry
+ 
+
+ align:start position:0%
+that enclose the system yeah yeah sorry
+I should not put the smallest there for
+
+ align:start position:0%
+I should not put the smallest there for
+ 
+
+ align:start position:0%
+I should not put the smallest there for
+some reason um for some reason uh yeah
+
+ align:start position:0%
+some reason um for some reason uh yeah
+ 
+
+ align:start position:0%
+some reason um for some reason uh yeah
+no no no no a yeah should not be
+
+ align:start position:0%
+no no no no a yeah should not be
+ 
+
+ align:start position:0%
+no no no no a yeah should not be
+smallest just a is any sphere uh uh yeah
+
+ align:start position:0%
+smallest just a is any sphere uh uh yeah
+ 
+
+ align:start position:0%
+smallest just a is any sphere uh uh yeah
+just some sphere which encos the
+
+ align:start position:0%
+just some sphere which encos the
+ 
+
+ align:start position:0%
+just some sphere which encos the
+region okay yes so it seems that this
+
+ align:start position:0%
+region okay yes so it seems that this
+ 
+
+ align:start position:0%
+region okay yes so it seems that this
+argument implicitly assumes that in
+
+ align:start position:0%
+argument implicitly assumes that in
+ 
+
+ align:start position:0%
+argument implicitly assumes that in
+order to add entropy that sort of
+
+ align:start position:0%
+order to add entropy that sort of
+ 
+
+ align:start position:0%
+order to add entropy that sort of
+corresponds to adding some amount of
+
+ align:start position:0%
+corresponds to adding some amount of
+ 
+
+ align:start position:0%
+corresponds to adding some amount of
+energy but is it possible to add entropy
+
+ align:start position:0%
+energy but is it possible to add entropy
+ 
+
+ align:start position:0%
+energy but is it possible to add entropy
+to the system without adding energy to
+
+ align:start position:0%
+to the system without adding energy to
+ 
+
+ align:start position:0%
+to the system without adding energy to
+the system oh you can you can that just
+
+ align:start position:0%
+the system oh you can you can that just
+ 
+
+ align:start position:0%
+the system oh you can you can that just
+make it even more whatever it is this is
+
+ align:start position:0%
+make it even more whatever it is this is
+ 
+
+ align:start position:0%
+make it even more whatever it is this is
+a final
+
+ align:start position:0%
+a final
+ 
+
+ align:start position:0%
+a final
+state so so the based Assumption of this
+
+ align:start position:0%
+state so so the based Assumption of this
+ 
+
+ align:start position:0%
+state so so the based Assumption of this
+is that if if you can put stuff inside
+
+ align:start position:0%
+is that if if you can put stuff inside
+ 
+
+ align:start position:0%
+is that if if you can put stuff inside
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+region uh or whatever is
+
+ align:start position:0%
+region uh or whatever is
+ 
+
+ align:start position:0%
+region uh or whatever is
+inside uh
+
+ align:start position:0%
+inside uh
+ 
+
+ align:start position:0%
+inside uh
+yeah the Su says the maximum stuff you
+
+ align:start position:0%
+yeah the Su says the maximum stuff you
+ 
+
+ align:start position:0%
+yeah the Su says the maximum stuff you
+can put inside the region is a black ho
+
+ align:start position:0%
+can put inside the region is a black ho
+ 
+
+ align:start position:0%
+can put inside the region is a black ho
+with the Horizon
+
+ align:start position:0%
+with the Horizon
+ 
+
+ align:start position:0%
+with the Horizon
+area well I guess what I'm confused
+
+ align:start position:0%
+area well I guess what I'm confused
+ 
+
+ align:start position:0%
+area well I guess what I'm confused
+about is that it seems that I certainly
+
+ align:start position:0%
+about is that it seems that I certainly
+ 
+
+ align:start position:0%
+about is that it seems that I certainly
+believe when you say that you you can't
+
+ align:start position:0%
+believe when you say that you you can't
+ 
+
+ align:start position:0%
+believe when you say that you you can't
+have a certain amount of energy in an
+
+ align:start position:0%
+have a certain amount of energy in an
+ 
+
+ align:start position:0%
+have a certain amount of energy in an
+area but I'm not sure why you can't have
+
+ align:start position:0%
+area but I'm not sure why you can't have
+ 
+
+ align:start position:0%
+area but I'm not sure why you can't have
+a certain amount of entropy in an area
+
+ align:start position:0%
+a certain amount of entropy in an area
+ 
+
+ align:start position:0%
+a certain amount of entropy in an area
+if energy and entropy are not oh no no
+
+ align:start position:0%
+if energy and entropy are not oh no no
+ 
+
+ align:start position:0%
+if energy and entropy are not oh no no
+we I'm not making that assumption the
+
+ align:start position:0%
+we I'm not making that assumption the
+ 
+
+ align:start position:0%
+we I'm not making that assumption the
+entropy the entropy is just a
+
+ align:start position:0%
+entropy the entropy is just a
+ 
+
+ align:start position:0%
+entropy the entropy is just a
+consequence of that this is a final
+
+ align:start position:0%
+consequence of that this is a final
+ 
+
+ align:start position:0%
+consequence of that this is a final
+State entropy the the final State
+
+ align:start position:0%
+State entropy the the final State
+ 
+
+ align:start position:0%
+State entropy the the final State
+entropy is always
+
+ align:start position:0%
+entropy is always
+ 
+
+ align:start position:0%
+entropy is always
+ner than the than entropy of your
+
+ align:start position:0%
+ner than the than entropy of your
+ 
+
+ align:start position:0%
+ner than the than entropy of your
+initial State okay yeah yeah entropy is
+
+ align:start position:0%
+initial State okay yeah yeah entropy is
+ 
+
+ align:start position:0%
+initial State okay yeah yeah entropy is
+a derived this equation is not
+
+ align:start position:0%
+a derived this equation is not
+ 
+
+ align:start position:0%
+a derived this equation is not
+assumption is derived okay yeah the
+
+ align:start position:0%
+assumption is derived okay yeah the
+ 
+
+ align:start position:0%
+assumption is derived okay yeah the
+assumption is that the the black hole is
+
+ align:start position:0%
+assumption is that the the black hole is
+ 
+
+ align:start position:0%
+assumption is that the the black hole is
+the maximal uh is the most massive
+
+ align:start position:0%
+the maximal uh is the most massive
+ 
+
+ align:start position:0%
+the maximal uh is the most massive
+object you can put inside this
+
+ align:start position:0%
+object you can put inside this
+ 
+
+ align:start position:0%
+object you can put inside this
+region sure
+
+ align:start position:0%
+region sure
+ 
+
+ align:start position:0%
+region sure
+yeah but but you can't have a less
+
+ align:start position:0%
+yeah but but you can't have a less
+ 
+
+ align:start position:0%
+yeah but but you can't have a less
+massive object with more than that
+
+ align:start position:0%
+massive object with more than that
+ 
+
+ align:start position:0%
+massive object with more than that
+entropy
+
+ align:start position:0%
+entropy
+ 
+
+ align:start position:0%
+entropy
+you can't have a less massive object
+
+ align:start position:0%
+you can't have a less massive object
+ 
+
+ align:start position:0%
+you can't have a less massive object
+with entropy that is more than that
+
+ align:start position:0%
+with entropy that is more than that
+ 
+
+ align:start position:0%
+with entropy that is more than that
+value inside the same region uh uh this
+
+ align:start position:0%
+value inside the same region uh uh this
+ 
+
+ align:start position:0%
+value inside the same region uh uh this
+is ruled out by this uh
+
+ align:start position:0%
+is ruled out by this uh
+ 
+
+ align:start position:0%
+is ruled out by this uh
+uh once you get this equation then you
+
+ align:start position:0%
+uh once you get this equation then you
+ 
+
+ align:start position:0%
+uh once you get this equation then you
+don't ask about the
+
+ align:start position:0%
+don't ask about the
+ 
+
+ align:start position:0%
+don't ask about the
+mass uh it just n eny must be smaller
+
+ align:start position:0%
+mass uh it just n eny must be smaller
+ 
+
+ align:start position:0%
+mass uh it just n eny must be smaller
+than this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value any other questions yes how do we
+
+ align:start position:0%
+value any other questions yes how do we
+ 
+
+ align:start position:0%
+value any other questions yes how do we
+keep track of of the area I mean doesn't
+
+ align:start position:0%
+keep track of of the area I mean doesn't
+ 
+
+ align:start position:0%
+keep track of of the area I mean doesn't
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so that's why I say this is a
+
+ align:start position:0%
+right so that's why I say this is a
+ 
+
+ align:start position:0%
+right so that's why I say this is a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+bit heuristic argument and that's why I
+
+ align:start position:0%
+bit heuristic argument and that's why I
+ 
+
+ align:start position:0%
+bit heuristic argument and that's why I
+say this is holistic argument yeah yeah
+
+ align:start position:0%
+say this is holistic argument yeah yeah
+ 
+
+ align:start position:0%
+say this is holistic argument yeah yeah
+indeed you have to be a little bit more
+
+ align:start position:0%
+indeed you have to be a little bit more
+ 
+
+ align:start position:0%
+indeed you have to be a little bit more
+careful about that uh
+
+ align:start position:0%
+careful about that uh
+ 
+
+ align:start position:0%
+careful about that uh
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um yeah but uh
+
+ align:start position:0%
+um yeah but uh
+ 
+
+ align:start position:0%
+um yeah but uh
+um say if you
+
+ align:start position:0%
+um say if you
+ 
+
+ align:start position:0%
+um say if you
+um if you uh
+
+ align:start position:0%
+um if you uh
+ 
+
+ align:start position:0%
+um if you uh
+um the keying is about the area and this
+
+ align:start position:0%
+um the keying is about the area and this
+ 
+
+ align:start position:0%
+um the keying is about the area and this
+order one Cent one maybe have to think
+
+ align:start position:0%
+order one Cent one maybe have to think
+ 
+
+ align:start position:0%
+order one Cent one maybe have to think
+about it uh we include the quantum
+
+ align:start position:0%
+about it uh we include the quantum
+ 
+
+ align:start position:0%
+about it uh we include the quantum
+Corrections Etc the back reaction Etc
+
+ align:start position:0%
+Corrections Etc the back reaction Etc
+ 
+
+ align:start position:0%
+Corrections Etc the back reaction Etc
+yeah but the keying is the area the
+
+ align:start position:0%
+yeah but the keying is the area the
+ 
+
+ align:start position:0%
+yeah but the keying is the area the
+black ho must be proportional to the
+
+ align:start position:0%
+black ho must be proportional to the
+ 
+
+ align:start position:0%
+black ho must be proportional to the
+area well uh it's St on assumption that
+
+ align:start position:0%
+area well uh it's St on assumption that
+ 
+
+ align:start position:0%
+area well uh it's St on assumption that
+the arrow of the arrow of the Horizon
+
+ align:start position:0%
+the arrow of the arrow of the Horizon
+ 
+
+ align:start position:0%
+the arrow of the arrow of the Horizon
+gra is is only based on the
+
+ align:start position:0%
+gra is is only based on the
+ 
+
+ align:start position:0%
+gra is is only based on the
+mass oh yeah yeah yeah yeah so the let
+
+ align:start position:0%
+mass oh yeah yeah yeah yeah so the let
+ 
+
+ align:start position:0%
+mass oh yeah yeah yeah yeah so the let
+me again there's a two nature of this
+
+ align:start position:0%
+me again there's a two nature of this
+ 
+
+ align:start position:0%
+me again there's a two nature of this
+argument the first nature of the
+
+ align:start position:0%
+argument the first nature of the
+ 
+
+ align:start position:0%
+argument the first nature of the
+argument is the the the maximal energe
+
+ align:start position:0%
+argument is the the the maximal energe
+ 
+
+ align:start position:0%
+argument is the the the maximal energe
+you can put inside the region is a black
+
+ align:start position:0%
+you can put inside the region is a black
+ 
+
+ align:start position:0%
+you can put inside the region is a black
+hole who whose Horizon area is given by
+
+ align:start position:0%
+hole who whose Horizon area is given by
+ 
+
+ align:start position:0%
+hole who whose Horizon area is given by
+the area of this region this is
+
+ align:start position:0%
+the area of this region this is
+ 
+
+ align:start position:0%
+the area of this region this is
+assumption yeah this is assumption yeah
+
+ align:start position:0%
+assumption yeah this is assumption yeah
+ 
+
+ align:start position:0%
+assumption yeah this is assumption yeah
+because we know in the gr any
+
+ align:start position:0%
+because we know in the gr any
+ 
+
+ align:start position:0%
+because we know in the gr any
+sufficiently massive thing will collapse
+
+ align:start position:0%
+sufficiently massive thing will collapse
+ 
+
+ align:start position:0%
+sufficiently massive thing will collapse
+to form black hole yeah and if you have
+
+ align:start position:0%
+to form black hole yeah and if you have
+ 
+
+ align:start position:0%
+to form black hole yeah and if you have
+more mass then the Horizon area will be
+
+ align:start position:0%
+more mass then the Horizon area will be
+ 
+
+ align:start position:0%
+more mass then the Horizon area will be
+outside and then you will be outside
+
+ align:start position:0%
+outside and then you will be outside
+ 
+
+ align:start position:0%
+outside and then you will be outside
+this area you you can no longer keep
+
+ align:start position:0%
+this area you you can no longer keep
+ 
+
+ align:start position:0%
+this area you you can no longer keep
+this a fixed yeah so that's the first
+
+ align:start position:0%
+this a fixed yeah so that's the first
+ 
+
+ align:start position:0%
+this a fixed yeah so that's the first
+assumption so with that
+
+ align:start position:0%
+assumption so with that
+ 
+
+ align:start position:0%
+assumption so with that
+assumption uh then with that assumption
+
+ align:start position:0%
+assumption uh then with that assumption
+ 
+
+ align:start position:0%
+assumption uh then with that assumption
+then just follows from the second no of
+
+ align:start position:0%
+then just follows from the second no of
+ 
+
+ align:start position:0%
+then just follows from the second no of
+Dynamics because this is whatever uh uh
+
+ align:start position:0%
+Dynamics because this is whatever uh uh
+ 
+
+ align:start position:0%
+Dynamics because this is whatever uh uh
+the entropy of the matter inside then
+
+ align:start position:0%
+the entropy of the matter inside then
+ 
+
+ align:start position:0%
+the entropy of the matter inside then
+this is whatever the initial entropy you
+
+ align:start position:0%
+this is whatever the initial entropy you
+ 
+
+ align:start position:0%
+this is whatever the initial entropy you
+do of the energy you need put it in to
+
+ align:start position:0%
+do of the energy you need put it in to
+ 
+
+ align:start position:0%
+do of the energy you need put it in to
+make it into a black hole and then that
+
+ align:start position:0%
+make it into a black hole and then that
+ 
+
+ align:start position:0%
+make it into a black hole and then that
+must be smaller than the entropy of the
+
+ align:start position:0%
+must be smaller than the entropy of the
+ 
+
+ align:start position:0%
+must be smaller than the entropy of the
+final state which is the entropy of the
+
+ align:start position:0%
+final state which is the entropy of the
+ 
+
+ align:start position:0%
+final state which is the entropy of the
+black hole
+
+ align:start position:0%
+black hole
+ 
+
+ align:start position:0%
+black hole
+but my question is that by keeping a
+
+ align:start position:0%
+but my question is that by keeping a
+ 
+
+ align:start position:0%
+but my question is that by keeping a
+fixed you might introduce actual entropy
+
+ align:start position:0%
+fixed you might introduce actual entropy
+ 
+
+ align:start position:0%
+fixed you might introduce actual entropy
+into the system H yeah it doesn't matter
+
+ align:start position:0%
+into the system H yeah it doesn't matter
+ 
+
+ align:start position:0%
+into the system H yeah it doesn't matter
+as far as the uh uh black ho is a final
+
+ align:start position:0%
+as far as the uh uh black ho is a final
+ 
+
+ align:start position:0%
+as far as the uh uh black ho is a final
+entropy State uh what you are saying is
+
+ align:start position:0%
+entropy State uh what you are saying is
+ 
+
+ align:start position:0%
+entropy State uh what you are saying is
+that there might be some other things
+
+ align:start position:0%
+that there might be some other things
+ 
+
+ align:start position:0%
+that there might be some other things
+here it's fine that does not change the
+
+ align:start position:0%
+here it's fine that does not change the
+ 
+
+ align:start position:0%
+here it's fine that does not change the
+the the direction of this um might be
+
+ align:start position:0%
+the the direction of this um might be
+ 
+
+ align:start position:0%
+the the direction of this um might be
+negative uh I'm not sure
+
+ align:start position:0%
+negative uh I'm not sure
+ 
+
+ align:start position:0%
+negative uh I'm not sure
+just no no whatever it is uh whatever it
+
+ align:start position:0%
+just no no whatever it is uh whatever it
+ 
+
+ align:start position:0%
+just no no whatever it is uh whatever it
+is this is my initial so that's why this
+
+ align:start position:0%
+is this is my initial so that's why this
+ 
+
+ align:start position:0%
+is this is my initial so that's why this
+is inequality here this is not equality
+
+ align:start position:0%
+is inequality here this is not equality
+ 
+
+ align:start position:0%
+is inequality here this is not equality
+inequality and and uh we are just using
+
+ align:start position:0%
+inequality and and uh we are just using
+ 
+
+ align:start position:0%
+inequality and and uh we are just using
+the second L of thermodynamics this is
+
+ align:start position:0%
+the second L of thermodynamics this is
+ 
+
+ align:start position:0%
+the second L of thermodynamics this is
+your initial State entropy this is my
+
+ align:start position:0%
+your initial State entropy this is my
+ 
+
+ align:start position:0%
+your initial State entropy this is my
+final State entropy this must be greater
+
+ align:start position:0%
+final State entropy this must be greater
+ 
+
+ align:start position:0%
+final State entropy this must be greater
+than that we're not asking the specific
+
+ align:start position:0%
+than that we're not asking the specific
+ 
+
+ align:start position:0%
+than that we're not asking the specific
+process we're not asking the specific
+
+ align:start position:0%
+process we're not asking the specific
+ 
+
+ align:start position:0%
+process we're not asking the specific
+process yeah just the final State have
+
+ align:start position:0%
+process yeah just the final State have
+ 
+
+ align:start position:0%
+process yeah just the final State have
+be greater than initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good okay so now let's see what we
+
+ align:start position:0%
+good okay so now let's see what we
+ 
+
+ align:start position:0%
+good okay so now let's see what we
+can try to go a little bit further from
+
+ align:start position:0%
+can try to go a little bit further from
+ 
+
+ align:start position:0%
+can try to go a little bit further from
+here so now let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recall so now we really treat the black
+
+ align:start position:0%
+recall so now we really treat the black
+ 
+
+ align:start position:0%
+recall so now we really treat the black
+ho as a Quantum statistical object so
+
+ align:start position:0%
+ho as a Quantum statistical object so
+ 
+
+ align:start position:0%
+ho as a Quantum statistical object so
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+recall definition of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in Quantum statistical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if you say I have some
+
+ align:start position:0%
+okay so if you say I have some
+ 
+
+ align:start position:0%
+okay so if you say I have some
+system and the state of and the state of
+
+ align:start position:0%
+system and the state of and the state of
+ 
+
+ align:start position:0%
+system and the state of and the state of
+that system is described by some density
+
+ align:start position:0%
+that system is described by some density
+ 
+
+ align:start position:0%
+that system is described by some density
+operator or density Matrix and then then
+
+ align:start position:0%
+operator or density Matrix and then then
+ 
+
+ align:start position:0%
+operator or density Matrix and then then
+the entropy of that system is just given
+
+ align:start position:0%
+the entropy of that system is just given
+ 
+
+ align:start position:0%
+the entropy of that system is just given
+by this formula that's given by this
+
+ align:start position:0%
+by this formula that's given by this
+ 
+
+ align:start position:0%
+by this formula that's given by this
+formula okay in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particular in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particular for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system with n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimensional c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the n dimensional h
+
+ align:start position:0%
+okay so this is the n dimensional h
+ 
+
+ align:start position:0%
+okay so this is the n dimensional h
+space okay this is a a dimension of the
+
+ align:start position:0%
+space okay this is a a dimension of the
+ 
+
+ align:start position:0%
+space okay this is a a dimension of the
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+space that s
+
+ align:start position:0%
+space that s
+ 
+
+ align:start position:0%
+space that s
+Max is no n so the maximum possible
+
+ align:start position:0%
+Max is no n so the maximum possible
+ 
+
+ align:start position:0%
+Max is no n so the maximum possible
+entropy you can have is no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n okay is this fact familiar to
+
+ align:start position:0%
+n okay is this fact familiar to
+ 
+
+ align:start position:0%
+n okay is this fact familiar to
+you so so you can convince yourself the
+
+ align:start position:0%
+you so so you can convince yourself the
+ 
+
+ align:start position:0%
+you so so you can convince yourself the
+maximal entropy is realized when row is
+
+ align:start position:0%
+maximal entropy is realized when row is
+ 
+
+ align:start position:0%
+maximal entropy is realized when row is
+just given by one over n times identity
+
+ align:start position:0%
+just given by one over n times identity
+ 
+
+ align:start position:0%
+just given by one over n times identity
+Matrix okay and so uh so this is the so
+
+ align:start position:0%
+Matrix okay and so uh so this is the so
+ 
+
+ align:start position:0%
+Matrix okay and so uh so this is the so
+this is the density Matrix which have
+
+ align:start position:0%
+this is the density Matrix which have
+ 
+
+ align:start position:0%
+this is the density Matrix which have
+low information because every state
+
+ align:start position:0%
+low information because every state
+ 
+
+ align:start position:0%
+low information because every state
+plays the same role and this state then
+
+ align:start position:0%
+plays the same role and this state then
+ 
+
+ align:start position:0%
+plays the same role and this state then
+you can plug in here and give you log n
+
+ align:start position:0%
+you can plug in here and give you log n
+ 
+
+ align:start position:0%
+you can plug in here and give you log n
+and the maximum m means you have minimal
+
+ align:start position:0%
+and the maximum m means you have minimal
+ 
+
+ align:start position:0%
+and the maximum m means you have minimal
+information okay and that is the state
+
+ align:start position:0%
+information okay and that is the state
+ 
+
+ align:start position:0%
+information okay and that is the state
+with minimal
+
+ align:start position:0%
+with minimal
+ 
+
+ align:start position:0%
+with minimal
+information and you can also just prove
+
+ align:start position:0%
+information and you can also just prove
+ 
+
+ align:start position:0%
+information and you can also just prove
+yourself youing using the um yeah using
+
+ align:start position:0%
+yourself youing using the um yeah using
+ 
+
+ align:start position:0%
+yourself youing using the um yeah using
+some algebra but this is a
+
+ align:start position:0%
+some algebra but this is a
+ 
+
+ align:start position:0%
+some algebra but this is a
+physic a physical argument for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so now if we compare with this two
+
+ align:start position:0%
+this so now if we compare with this two
+ 
+
+ align:start position:0%
+this so now if we compare with this two
+formula then we can draw a
+
+ align:start position:0%
+formula then we can draw a
+ 
+
+ align:start position:0%
+formula then we can draw a
+conclusion is
+
+ align:start position:0%
+conclusion is
+ 
+
+ align:start position:0%
+conclusion is
+that the so let me add a word called
+
+ align:start position:0%
+that the so let me add a word called
+ 
+
+ align:start position:0%
+that the so let me add a word called
+effective effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimension of the h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system inside the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is bonded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by log
+
+ align:start position:0%
+by log
+ 
+
+ align:start position:0%
+by log
+n must be smaller than a h bar
+
+ align:start position:0%
+n must be smaller than a h bar
+ 
+
+ align:start position:0%
+n must be smaller than a h bar
+GN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that tells you so what you can
+
+ align:start position:0%
+okay so that tells you so what you can
+ 
+
+ align:start position:0%
+okay so that tells you so what you can
+put inside this region of area a that's
+
+ align:start position:0%
+put inside this region of area a that's
+ 
+
+ align:start position:0%
+put inside this region of area a that's
+the maximum entropy you can
+
+ align:start position:0%
+the maximum entropy you can
+ 
+
+ align:start position:0%
+the maximum entropy you can
+have so and and if you have n deg
+
+ align:start position:0%
+have so and and if you have n deg
+ 
+
+ align:start position:0%
+have so and and if you have n deg
+Freedom then the maximum entropy you can
+
+ align:start position:0%
+Freedom then the maximum entropy you can
+ 
+
+ align:start position:0%
+Freedom then the maximum entropy you can
+have for this n deg is is log n then
+
+ align:start position:0%
+have for this n deg is is log n then
+ 
+
+ align:start position:0%
+have for this n deg is is log n then
+that tells you that log n must be
+
+ align:start position:0%
+that tells you that log n must be
+ 
+
+ align:start position:0%
+that tells you that log n must be
+smaller than this okay smaller or equal
+
+ align:start position:0%
+smaller than this okay smaller or equal
+ 
+
+ align:start position:0%
+smaller than this okay smaller or equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+that and so let me write this in terms
+
+ align:start position:0%
+that and so let me write this in terms
+ 
+
+ align:start position:0%
+that and so let me write this in terms
+of the so this can also for H bar and is
+
+ align:start position:0%
+of the so this can also for H bar and is
+ 
+
+ align:start position:0%
+of the so this can also for H bar and is
+also a plank n Square so it's also four
+
+ align:start position:0%
+also a plank n Square so it's also four
+ 
+
+ align:start position:0%
+also a plank n Square so it's also four
+times the pl lens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Square sorry for this
+
+ align:start position:0%
+Square sorry for this
+ 
+
+ align:start position:0%
+Square sorry for this
+part P space it can be even infinite
+
+ align:start position:0%
+part P space it can be even infinite
+ 
+
+ align:start position:0%
+part P space it can be even infinite
+yeah let me see that that's why really
+
+ align:start position:0%
+yeah let me see that that's why really
+ 
+
+ align:start position:0%
+yeah let me see that that's why really
+defective so so now let me make some
+
+ align:start position:0%
+defective so so now let me make some
+ 
+
+ align:start position:0%
+defective so so now let me make some
+remarks now let me some make some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remarks
+
+ align:start position:0%
+remarks
+ 
+
+ align:start position:0%
+remarks
+so zero
+
+ align:start position:0%
+so zero
+ 
+
+ align:start position:0%
+so zero
+remarks is that for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system of n
+
+ align:start position:0%
+system of n
+ 
+
+ align:start position:0%
+system of n
+spins say n Spin half particle so when I
+
+ align:start position:0%
+spins say n Spin half particle so when I
+ 
+
+ align:start position:0%
+spins say n Spin half particle so when I
+say spins I always mean spin
+
+ align:start position:0%
+say spins I always mean spin
+ 
+
+ align:start position:0%
+say spins I always mean spin
+half then the dimension of the h space
+
+ align:start position:0%
+half then the dimension of the h space
+ 
+
+ align:start position:0%
+half then the dimension of the h space
+is 2 to the^ n
+
+ align:start position:0%
+is 2 to the^ n
+ 
+
+ align:start position:0%
+is 2 to the^ n
+okay just remind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you but T but the dimension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+H the h space so normally I use script H
+
+ align:start position:0%
+H the h space so normally I use script H
+ 
+
+ align:start position:0%
+H the h space so normally I use script H
+to to to Delo the h space for a single
+
+ align:start position:0%
+to to to Delo the h space for a single
+ 
+
+ align:start position:0%
+to to to Delo the h space for a single
+harmonic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oscillator so the
+
+ align:start position:0%
+oscillator so the
+ 
+
+ align:start position:0%
+oscillator so the
+next so the simply system is spin then
+
+ align:start position:0%
+next so the simply system is spin then
+ 
+
+ align:start position:0%
+next so the simply system is spin then
+the next simply system is essentially
+
+ align:start position:0%
+the next simply system is essentially
+ 
+
+ align:start position:0%
+the next simply system is essentially
+harmonic
+
+ align:start position:0%
+harmonic
+ 
+
+ align:start position:0%
+harmonic
+oscillator and for for even for single
+
+ align:start position:0%
+oscillator and for for even for single
+ 
+
+ align:start position:0%
+oscillator and for for even for single
+harmonic
+
+ align:start position:0%
+harmonic
+ 
+
+ align:start position:0%
+harmonic
+oscillator and the dimension of H is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinite okay and then you ask what I'm
+
+ align:start position:0%
+infinite okay and then you ask what I'm
+ 
+
+ align:start position:0%
+infinite okay and then you ask what I'm
+talking about here because here I say
+
+ align:start position:0%
+talking about here because here I say
+ 
+
+ align:start position:0%
+talking about here because here I say
+the uh the h space should be smaller
+
+ align:start position:0%
+the uh the h space should be smaller
+ 
+
+ align:start position:0%
+the uh the h space should be smaller
+than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+but okay so even though even for single
+
+ align:start position:0%
+but okay so even though even for single
+ 
+
+ align:start position:0%
+but okay so even though even for single
+harmonic oate the H is
+
+ align:start position:0%
+harmonic oate the H is
+ 
+
+ align:start position:0%
+harmonic oate the H is
+infinite but
+
+ align:start position:0%
+infinite but
+ 
+
+ align:start position:0%
+infinite but
+for but for a Quantum mechanic system
+
+ align:start position:0%
+for but for a Quantum mechanic system
+ 
+
+ align:start position:0%
+for but for a Quantum mechanic system
+for Quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system with a finite number deg
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Freedom by fin number de freedom for
+
+ align:start position:0%
+Freedom by fin number de freedom for
+ 
+
+ align:start position:0%
+Freedom by fin number de freedom for
+example you can interpret as for example
+
+ align:start position:0%
+example you can interpret as for example
+ 
+
+ align:start position:0%
+example you can interpret as for example
+five number of harmonic oscillators
+
+ align:start position:0%
+five number of harmonic oscillators
+ 
+
+ align:start position:0%
+five number of harmonic oscillators
+okay the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimension of the h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+below some
+
+ align:start position:0%
+below some
+ 
+
+ align:start position:0%
+below some
+finite energy
+
+ align:start position:0%
+finite energy
+ 
+
+ align:start position:0%
+finite energy
+scale
+
+ align:start position:0%
+scale
+ 
+
+ align:start position:0%
+scale
+energy is always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite okay it's always
+
+ align:start position:0%
+finite okay it's always
+ 
+
+ align:start position:0%
+finite okay it's always
+finite and uh so that's why I used the
+
+ align:start position:0%
+finite and uh so that's why I used the
+ 
+
+ align:start position:0%
+finite and uh so that's why I used the
+the word effective there and because
+
+ align:start position:0%
+the word effective there and because
+ 
+
+ align:start position:0%
+the word effective there and because
+because normally if you normally we all
+
+ align:start position:0%
+because normally if you normally we all
+ 
+
+ align:start position:0%
+because normally if you normally we all
+consider the fight energy yeah because
+
+ align:start position:0%
+consider the fight energy yeah because
+ 
+
+ align:start position:0%
+consider the fight energy yeah because
+the system all have fight energy and
+
+ align:start position:0%
+the system all have fight energy and
+ 
+
+ align:start position:0%
+the system all have fight energy and
+then you have effective you have a fight
+
+ align:start position:0%
+then you have effective you have a fight
+ 
+
+ align:start position:0%
+then you have effective you have a fight
+dimensional h space
+
+ align:start position:0%
+dimensional h space
+ 
+
+ align:start position:0%
+dimensional h space
+okay so so uh so this equation is not
+
+ align:start position:0%
+okay so so uh so this equation is not
+ 
+
+ align:start position:0%
+okay so so uh so this equation is not
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crazy so and in
+
+ align:start position:0%
+crazy so and in
+ 
+
+ align:start position:0%
+crazy so and in
+typical so actually in typical physical
+
+ align:start position:0%
+typical so actually in typical physical
+ 
+
+ align:start position:0%
+typical so actually in typical physical
+systems even for harmonic oscillators
+
+ align:start position:0%
+systems even for harmonic oscillators
+ 
+
+ align:start position:0%
+systems even for harmonic oscillators
+both for spin or harmonic oscillators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially number of degrees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is of all the log n yeah is the n is the
+
+ align:start position:0%
+is of all the log n yeah is the n is the
+ 
+
+ align:start position:0%
+is of all the log n yeah is the n is the
+effective dimension of your h space
+
+ align:start position:0%
+effective dimension of your h space
+ 
+
+ align:start position:0%
+effective dimension of your h space
+okay yeah this is obvious from the
+
+ align:start position:0%
+okay yeah this is obvious from the
+ 
+
+ align:start position:0%
+okay yeah this is obvious from the
+spin okay this is also of
+
+ align:start position:0%
+spin okay this is also of
+ 
+
+ align:start position:0%
+spin okay this is also of
+obvious if you have a harmonic
+
+ align:start position:0%
+obvious if you have a harmonic
+ 
+
+ align:start position:0%
+obvious if you have a harmonic
+oscillator so each harmonic oscillator
+
+ align:start position:0%
+oscillator so each harmonic oscillator
+ 
+
+ align:start position:0%
+oscillator so each harmonic oscillator
+is fitly
+
+ align:start position:0%
+is fitly
+ 
+
+ align:start position:0%
+is fitly
+excited and then again roughly the uh
+
+ align:start position:0%
+excited and then again roughly the uh
+ 
+
+ align:start position:0%
+excited and then again roughly the uh
+log n is the number of harmonic
+
+ align:start position:0%
+log n is the number of harmonic
+ 
+
+ align:start position:0%
+log n is the number of harmonic
+oscillators
+
+ align:start position:0%
+oscillators
+ 
+
+ align:start position:0%
+oscillators
+okay so so be because of this we can
+
+ align:start position:0%
+okay so so be because of this we can
+ 
+
+ align:start position:0%
+okay so so be because of this we can
+also write this equation
+
+ align:start position:0%
+also write this equation
+ 
+
+ align:start position:0%
+also write this equation
+as the L of degre
+
+ align:start position:0%
+as the L of degre
+ 
+
+ align:start position:0%
+as the L of degre
+Freedom over
+
+ align:start position:0%
+Freedom over
+ 
+
+ align:start position:0%
+Freedom over
+any quantum gravity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system inside the region a can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be should be smaller than should be
+
+ align:start position:0%
+be should be smaller than should be
+ 
+
+ align:start position:0%
+be should be smaller than should be
+bounded by the area of that region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bond is certainly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+valate in non-gravitational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay because in non gravitation systems
+
+ align:start position:0%
+okay because in non gravitation systems
+ 
+
+ align:start position:0%
+okay because in non gravitation systems
+whose number with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+freedom and
+
+ align:start position:0%
+freedom and
+ 
+
+ align:start position:0%
+freedom and
+S the log n the log of your dimensional
+
+ align:start position:0%
+S the log n the log of your dimensional
+ 
+
+ align:start position:0%
+S the log n the log of your dimensional
+your space is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proportional to the
+
+ align:start position:0%
+proportional to the
+ 
+
+ align:start position:0%
+proportional to the
+volume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rather than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area so when the region is big
+
+ align:start position:0%
+area so when the region is big
+ 
+
+ align:start position:0%
+area so when the region is big
+enough then you're guaranteed to uh to
+
+ align:start position:0%
+enough then you're guaranteed to uh to
+ 
+
+ align:start position:0%
+enough then you're guaranteed to uh to
+violate this Bond because of course the
+
+ align:start position:0%
+violate this Bond because of course the
+ 
+
+ align:start position:0%
+violate this Bond because of course the
+volume grows faster than the area if you
+
+ align:start position:0%
+volume grows faster than the area if you
+ 
+
+ align:start position:0%
+volume grows faster than the area if you
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+sufficiently larger region so so for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example can just a lace of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spins say three dimensional lace of
+
+ align:start position:0%
+spins say three dimensional lace of
+ 
+
+ align:start position:0%
+spins say three dimensional lace of
+spins of La spacing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a say of latis spacing
+
+ align:start position:0%
+a say of latis spacing
+ 
+
+ align:start position:0%
+a say of latis spacing
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+okay then the total number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spins then the total number of
+
+ align:start position:0%
+spins then the total number of
+ 
+
+ align:start position:0%
+spins then the total number of
+spins
+
+ align:start position:0%
+spins
+ 
+
+ align:start position:0%
+spins
+then it's given by volume ID by a
+
+ align:start position:0%
+then it's given by volume ID by a
+ 
+
+ align:start position:0%
+then it's given by volume ID by a
+cube okay so this is essentially the
+
+ align:start position:0%
+cube okay so this is essentially the
+ 
+
+ align:start position:0%
+cube okay so this is essentially the
+number of deg freedom and this is given
+
+ align:start position:0%
+number of deg freedom and this is given
+ 
+
+ align:start position:0%
+number of deg freedom and this is given
+by a the area divide by a
+
+ align:start position:0%
+by a the area divide by a
+ 
+
+ align:start position:0%
+by a the area divide by a
+squ Time L divide by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a and this can be much much greater
+
+ align:start position:0%
+a and this can be much much greater
+ 
+
+ align:start position:0%
+a and this can be much much greater
+than a ided by plank
+
+ align:start position:0%
+than a ided by plank
+ 
+
+ align:start position:0%
+than a ided by plank
+Square plank length Square for l so
+
+ align:start position:0%
+Square plank length Square for l so
+ 
+
+ align:start position:0%
+Square plank length Square for l so
+efficientcy large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay they are large
+
+ align:start position:0%
+okay they are large
+ 
+
+ align:start position:0%
+okay they are large
+enough so so if you have a long
+
+ align:start position:0%
+enough so so if you have a long
+ 
+
+ align:start position:0%
+enough so so if you have a long
+gravitational
+
+ align:start position:0%
+gravitational
+ 
+
+ align:start position:0%
+gravitational
+system then this B can be easily
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+violated in
+
+ align:start position:0%
+violated in
+ 
+
+ align:start position:0%
+violated in
+particular this equation can also be
+
+ align:start position:0%
+particular this equation can also be
+ 
+
+ align:start position:0%
+particular this equation can also be
+violated because the because the um
+
+ align:start position:0%
+violated because the because the um
+ 
+
+ align:start position:0%
+violated because the because the um
+the dimension of the h
+
+ align:start position:0%
+the dimension of the h
+ 
+
+ align:start position:0%
+the dimension of the h
+space then in this case would be 2 to
+
+ align:start position:0%
+space then in this case would be 2 to
+ 
+
+ align:start position:0%
+space then in this case would be 2 to
+the power a
+
+ align:start position:0%
+the power a
+ 
+
+ align:start position:0%
+the power a
+cub and similarly so
+
+ align:start position:0%
+cub and similarly so
+ 
+
+ align:start position:0%
+cub and similarly so
+a so so the maximum
+
+ align:start position:0%
+a so so the maximum
+ 
+
+ align:start position:0%
+a so so the maximum
+entropy would be say V / a CU log two
+
+ align:start position:0%
+entropy would be say V / a CU log two
+ 
+
+ align:start position:0%
+entropy would be say V / a CU log two
+log two because it's a spin two system
+
+ align:start position:0%
+log two because it's a spin two system
+ 
+
+ align:start position:0%
+log two because it's a spin two system
+spin half system so this can be ner than
+
+ align:start position:0%
+spin half system so this can be ner than
+ 
+
+ align:start position:0%
+spin half system so this can be ner than
+entropy of a black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hole
+
+ align:start position:0%
+hole
+ 
+
+ align:start position:0%
+hole
+so so it's
+
+ align:start position:0%
+so so it's
+ 
+
+ align:start position:0%
+so so it's
+key that we can see the gravitational
+
+ align:start position:0%
+key that we can see the gravitational
+ 
+
+ align:start position:0%
+key that we can see the gravitational
+systems okay only in gravitational
+
+ align:start position:0%
+systems okay only in gravitational
+ 
+
+ align:start position:0%
+systems okay only in gravitational
+systems you have this remarkable feature
+
+ align:start position:0%
+systems you have this remarkable feature
+ 
+
+ align:start position:0%
+systems you have this remarkable feature
+that if few uh since will
+
+ align:start position:0%
+that if few uh since will
+ 
+
+ align:start position:0%
+that if few uh since will
+collapse okay since will collapse uh
+
+ align:start position:0%
+collapse okay since will collapse uh
+ 
+
+ align:start position:0%
+collapse okay since will collapse uh
+will collapse and then you will have
+
+ align:start position:0%
+will collapse and then you will have
+ 
+
+ align:start position:0%
+will collapse and then you will have
+this uh upper limit provided by the
+
+ align:start position:0%
+this uh upper limit provided by the
+ 
+
+ align:start position:0%
+this uh upper limit provided by the
+black hole yes so in the real world
+
+ align:start position:0%
+black hole yes so in the real world
+ 
+
+ align:start position:0%
+black hole yes so in the real world
+every system is a gravitational system
+
+ align:start position:0%
+every system is a gravitational system
+ 
+
+ align:start position:0%
+every system is a gravitational system
+yeah so this is just in some sense this
+
+ align:start position:0%
+yeah so this is just in some sense this
+ 
+
+ align:start position:0%
+yeah so this is just in some sense this
+is not actually correct
+
+ align:start position:0%
+is not actually correct
+ 
+
+ align:start position:0%
+is not actually correct
+real yeah but you need this L to be not
+
+ align:start position:0%
+real yeah but you need this L to be not
+ 
+
+ align:start position:0%
+real yeah but you need this L to be not
+enough I see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes so right in real world this
+
+ align:start position:0%
+yeah yes so right in real world this
+ 
+
+ align:start position:0%
+yeah yes so right in real world this
+bound has to be obeyed by systems so
+
+ align:start position:0%
+bound has to be obeyed by systems so
+ 
+
+ align:start position:0%
+bound has to be obeyed by systems so
+does that put some like bounds on UFT UV
+
+ align:start position:0%
+does that put some like bounds on UFT UV
+ 
+
+ align:start position:0%
+does that put some like bounds on UFT UV
+completions so in the real world this
+
+ align:start position:0%
+completions so in the real world this
+ 
+
+ align:start position:0%
+completions so in the real world this
+bound has to be aate by everything yeah
+
+ align:start position:0%
+bound has to be aate by everything yeah
+ 
+
+ align:start position:0%
+bound has to be aate by everything yeah
+so does that put some kind of
+
+ align:start position:0%
+so does that put some kind of
+ 
+
+ align:start position:0%
+so does that put some kind of
+restrictions on like Q of UV completion
+
+ align:start position:0%
+restrictions on like Q of UV completion
+ 
+
+ align:start position:0%
+restrictions on like Q of UV completion
+cuz we usually say it's you know
+
+ align:start position:0%
+cuz we usually say it's you know
+ 
+
+ align:start position:0%
+cuz we usually say it's you know
+infinite density degrees of freedom uh
+
+ align:start position:0%
+infinite density degrees of freedom uh
+ 
+
+ align:start position:0%
+infinite density degrees of freedom uh
+no because the because UV completion of
+
+ align:start position:0%
+no because the because UV completion of
+ 
+
+ align:start position:0%
+no because the because UV completion of
+qft is provided by gravity cor any Q I
+
+ align:start position:0%
+qft is provided by gravity cor any Q I
+ 
+
+ align:start position:0%
+qft is provided by gravity cor any Q I
+just mean like a scalar
+
+ align:start position:0%
+just mean like a scalar
+ 
+
+ align:start position:0%
+just mean like a scalar
+field then that's then that's not a
+
+ align:start position:0%
+field then that's then that's not a
+ 
+
+ align:start position:0%
+field then that's then that's not a
+theory of gravity right but if you have
+
+ align:start position:0%
+theory of gravity right but if you have
+ 
+
+ align:start position:0%
+theory of gravity right but if you have
+a scalar field in A Spacetime which has
+
+ align:start position:0%
+a scalar field in A Spacetime which has
+ 
+
+ align:start position:0%
+a scalar field in A Spacetime which has
+GR in it what is otherwise like FL yeah
+
+ align:start position:0%
+GR in it what is otherwise like FL yeah
+ 
+
+ align:start position:0%
+GR in it what is otherwise like FL yeah
+then the gr then the gravity will
+
+ align:start position:0%
+then the gr then the gravity will
+ 
+
+ align:start position:0%
+then the gr then the gravity will
+provide the UV completion of that scalar
+
+ align:start position:0%
+provide the UV completion of that scalar
+ 
+
+ align:start position:0%
+provide the UV completion of that scalar
+Fields
+
+ align:start position:0%
+Fields
+ 
+
+ align:start position:0%
+Fields
+yeah um
+
+ align:start position:0%
+yeah um
+ 
+
+ align:start position:0%
+yeah um
+right um I was going to say something
+
+ align:start position:0%
+right um I was going to say something
+ 
+
+ align:start position:0%
+right um I was going to say something
+else but I forgot
+
+ align:start position:0%
+else but I forgot
+ 
+
+ align:start position:0%
+else but I forgot
+um what about the ones that argue be
+
+ align:start position:0%
+um what about the ones that argue be
+ 
+
+ align:start position:0%
+um what about the ones that argue be
+complete what about the theories that RB
+
+ align:start position:0%
+complete what about the theories that RB
+ 
+
+ align:start position:0%
+complete what about the theories that RB
+complete at least
+
+ align:start position:0%
+complete at least
+ 
+
+ align:start position:0%
+complete at least
+formally uh sorry say it again uh the
+
+ align:start position:0%
+formally uh sorry say it again uh the
+ 
+
+ align:start position:0%
+formally uh sorry say it again uh the
+qfts that areg be complete yeah they
+
+ align:start position:0%
+qfts that areg be complete yeah they
+ 
+
+ align:start position:0%
+qfts that areg be complete yeah they
+still limited by gravity yeah the
+
+ align:start position:0%
+still limited by gravity yeah the
+ 
+
+ align:start position:0%
+still limited by gravity yeah the
+gravity will still provide something
+
+ align:start position:0%
+gravity will still provide something
+ 
+
+ align:start position:0%
+gravity will still provide something
+because qf have infinite number deg
+
+ align:start position:0%
+because qf have infinite number deg
+ 
+
+ align:start position:0%
+because qf have infinite number deg
+Freedom
+
+ align:start position:0%
+Freedom
+ 
+
+ align:start position:0%
+Freedom
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+so so example of this for example you
+
+ align:start position:0%
+so so example of this for example you
+ 
+
+ align:start position:0%
+so so example of this for example you
+can sync a
+
+ align:start position:0%
+can sync a
+ 
+
+ align:start position:0%
+can sync a
+classroom say four or
+
+ align:start position:0%
+classroom say four or
+ 
+
+ align:start position:0%
+classroom say four or
+photons and then you can calculate
+
+ align:start position:0%
+photons and then you can calculate
+ 
+
+ align:start position:0%
+photons and then you can calculate
+entropy again that entropy will
+
+ align:start position:0%
+entropy again that entropy will
+ 
+
+ align:start position:0%
+entropy again that entropy will
+proportional to the volume so if you
+
+ align:start position:0%
+proportional to the volume so if you
+ 
+
+ align:start position:0%
+proportional to the volume so if you
+make the the classroom big enough then
+
+ align:start position:0%
+make the the classroom big enough then
+ 
+
+ align:start position:0%
+make the the classroom big enough then
+that will evate this
+
+ align:start position:0%
+that will evate this
+ 
+
+ align:start position:0%
+that will evate this
+bounds but it's a simple exercise for
+
+ align:start position:0%
+bounds but it's a simple exercise for
+ 
+
+ align:start position:0%
+bounds but it's a simple exercise for
+you to do yourself that if you put the
+
+ align:start position:0%
+you to do yourself that if you put the
+ 
+
+ align:start position:0%
+you to do yourself that if you put the
+classroom at the finite temperature
+
+ align:start position:0%
+classroom at the finite temperature
+ 
+
+ align:start position:0%
+classroom at the finite temperature
+Photon then when the room Bigg enough
+
+ align:start position:0%
+Photon then when the room Bigg enough
+ 
+
+ align:start position:0%
+Photon then when the room Bigg enough
+there always a
+
+ align:start position:0%
+there always a
+ 
+
+ align:start position:0%
+there always a
+radius uh uh that will collapse form a
+
+ align:start position:0%
+radius uh uh that will collapse form a
+ 
+
+ align:start position:0%
+radius uh uh that will collapse form a
+black hole before this SP is violated
+
+ align:start position:0%
+black hole before this SP is violated
+ 
+
+ align:start position:0%
+black hole before this SP is violated
+okay I think maybe I have this problem
+
+ align:start position:0%
+okay I think maybe I have this problem
+ 
+
+ align:start position:0%
+okay I think maybe I have this problem
+in the P forgot whether I have it or not
+
+ align:start position:0%
+in the P forgot whether I have it or not
+ 
+
+ align:start position:0%
+in the P forgot whether I have it or not
+yeah you can do this simple exercise
+
+ align:start position:0%
+yeah you can do this simple exercise
+ 
+
+ align:start position:0%
+yeah you can do this simple exercise
+yourself yeah just imagine you have a
+
+ align:start position:0%
+yourself yeah just imagine you have a
+ 
+
+ align:start position:0%
+yourself yeah just imagine you have a
+box of photons as some at any non zero
+
+ align:start position:0%
+box of photons as some at any non zero
+ 
+
+ align:start position:0%
+box of photons as some at any non zero
+temperature T and then when you put the
+
+ align:start position:0%
+temperature T and then when you put the
+ 
+
+ align:start position:0%
+temperature T and then when you put the
+Box big enough then then at certain
+
+ align:start position:0%
+Box big enough then then at certain
+ 
+
+ align:start position:0%
+Box big enough then then at certain
+point the uh this this whole box of
+
+ align:start position:0%
+point the uh this this whole box of
+ 
+
+ align:start position:0%
+point the uh this this whole box of
+photon will collapse form a black
+
+ align:start position:0%
+photon will collapse form a black
+ 
+
+ align:start position:0%
+photon will collapse form a black
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+um uh and that's when it form and that's
+
+ align:start position:0%
+um uh and that's when it form and that's
+ 
+
+ align:start position:0%
+um uh and that's when it form and that's
+within to make this bond to be
+
+ align:start position:0%
+within to make this bond to be
+ 
+
+ align:start position:0%
+within to make this bond to be
+satisfied so so what this
+
+ align:start position:0%
+satisfied so so what this
+ 
+
+ align:start position:0%
+satisfied so so what this
+means that if you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity the quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity leads to a huge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reduction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of L
+
+ align:start position:0%
+of L
+ 
+
+ align:start position:0%
+of L
+Freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's really bounded by by your
+
+ align:start position:0%
+okay it's really bounded by by your
+ 
+
+ align:start position:0%
+okay it's really bounded by by your
+area now in previous
+
+ align:start position:0%
+area now in previous
+ 
+
+ align:start position:0%
+area now in previous
+AR you have a com
+
+ align:start position:0%
+AR you have a com
+ 
+
+ align:start position:0%
+AR you have a com
+F and so this Al
+
+ align:start position:0%
+F and so this Al
+ 
+
+ align:start position:0%
+F and so this Al
+apply we don't need to have
+
+ align:start position:0%
+apply we don't need to have
+ 
+
+ align:start position:0%
+apply we don't need to have
+a no yeah as I was uh uh
+
+ align:start position:0%
+a no yeah as I was uh uh
+ 
+
+ align:start position:0%
+a no yeah as I was uh uh
+power before uh if you have a conformal
+
+ align:start position:0%
+power before uh if you have a conformal
+ 
+
+ align:start position:0%
+power before uh if you have a conformal
+field Ser just by itself then there's no
+
+ align:start position:0%
+field Ser just by itself then there's no
+ 
+
+ align:start position:0%
+field Ser just by itself then there's no
+bound then there's no bound but if you
+
+ align:start position:0%
+bound then there's no bound but if you
+ 
+
+ align:start position:0%
+bound then there's no bound but if you
+couple this conformal F to gravity then
+
+ align:start position:0%
+couple this conformal F to gravity then
+ 
+
+ align:start position:0%
+couple this conformal F to gravity then
+as sufficiently high energy and then the
+
+ align:start position:0%
+as sufficiently high energy and then the
+ 
+
+ align:start position:0%
+as sufficiently high energy and then the
+degre freedom of this conformal filter
+
+ align:start position:0%
+degre freedom of this conformal filter
+ 
+
+ align:start position:0%
+degre freedom of this conformal filter
+must be reduced but if you just have a
+
+ align:start position:0%
+must be reduced but if you just have a
+ 
+
+ align:start position:0%
+must be reduced but if you just have a
+fter there's no bound no bound yeah yeah
+
+ align:start position:0%
+fter there's no bound no bound yeah yeah
+ 
+
+ align:start position:0%
+fter there's no bound no bound yeah yeah
+but you can ask what happens if we
+
+ align:start position:0%
+but you can ask what happens if we
+ 
+
+ align:start position:0%
+but you can ask what happens if we
+couple conformal F to gravity
+
+ align:start position:0%
+couple conformal F to gravity
+ 
+
+ align:start position:0%
+couple conformal F to gravity
+not even conformal fi just any Quantum
+
+ align:start position:0%
+not even conformal fi just any Quantum
+ 
+
+ align:start position:0%
+not even conformal fi just any Quantum
+field because any Quantum field have
+
+ align:start position:0%
+field because any Quantum field have
+ 
+
+ align:start position:0%
+field because any Quantum field have
+infinite number deg freedom and the
+
+ align:start position:0%
+infinite number deg freedom and the
+ 
+
+ align:start position:0%
+infinite number deg freedom and the
+number de is also proportional to the
+
+ align:start position:0%
+number de is also proportional to the
+ 
+
+ align:start position:0%
+number de is also proportional to the
+volume and uh um if you cou to gravity
+
+ align:start position:0%
+volume and uh um if you cou to gravity
+ 
+
+ align:start position:0%
+volume and uh um if you cou to gravity
+then this reduction must happen this
+
+ align:start position:0%
+then this reduction must happen this
+ 
+
+ align:start position:0%
+then this reduction must happen this
+reduction must happen
+
+ align:start position:0%
+reduction must happen
+ 
+
+ align:start position:0%
+reduction must happen
+Okay so now if we take a a small de of
+
+ align:start position:0%
+Okay so now if we take a a small de of
+ 
+
+ align:start position:0%
+Okay so now if we take a a small de of
+phase so we already have taken some Le
+
+ align:start position:0%
+phase so we already have taken some Le
+ 
+
+ align:start position:0%
+phase so we already have taken some Le
+of phase but let's take one more St Le
+
+ align:start position:0%
+of phase but let's take one more St Le
+ 
+
+ align:start position:0%
+of phase but let's take one more St Le
+phas then you can for formulate
+
+ align:start position:0%
+phas then you can for formulate
+ 
+
+ align:start position:0%
+phas then you can for formulate
+something called holographic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principle so given that the number de
+
+ align:start position:0%
+principle so given that the number de
+ 
+
+ align:start position:0%
+principle so given that the number de
+Freedom inside the region is always
+
+ align:start position:0%
+Freedom inside the region is always
+ 
+
+ align:start position:0%
+Freedom inside the region is always
+bonded by the
+
+ align:start position:0%
+bonded by the
+ 
+
+ align:start position:0%
+bonded by the
+area and this area actually have a very
+
+ align:start position:0%
+area and this area actually have a very
+ 
+
+ align:start position:0%
+area and this area actually have a very
+nice way is area in the unit of a plank
+
+ align:start position:0%
+nice way is area in the unit of a plank
+ 
+
+ align:start position:0%
+nice way is area in the unit of a plank
+lens it look like you have a minimal
+
+ align:start position:0%
+lens it look like you have a minimal
+ 
+
+ align:start position:0%
+lens it look like you have a minimal
+lens minimal area which is a plank
+
+ align:start position:0%
+lens minimal area which is a plank
+ 
+
+ align:start position:0%
+lens minimal area which is a plank
+Square lens and just the area divided by
+
+ align:start position:0%
+Square lens and just the area divided by
+ 
+
+ align:start position:0%
+Square lens and just the area divided by
+that give you the total L Freedom okay
+
+ align:start position:0%
+that give you the total L Freedom okay
+ 
+
+ align:start position:0%
+that give you the total L Freedom okay
+so so if you try to uh extrapolate a
+
+ align:start position:0%
+so so if you try to uh extrapolate a
+ 
+
+ align:start position:0%
+so so if you try to uh extrapolate a
+little bit further then we have
+
+ align:start position:0%
+little bit further then we have
+ 
+
+ align:start position:0%
+little bit further then we have
+so-called holographic principle is said
+
+ align:start position:0%
+so-called holographic principle is said
+ 
+
+ align:start position:0%
+so-called holographic principle is said
+in quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravity a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a can
+
+ align:start position:0%
+a can
+ 
+
+ align:start position:0%
+a can
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+fully
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+described can be fully
+
+ align:start position:0%
+described can be fully
+ 
+
+ align:start position:0%
+described can be fully
+described
+
+ align:start position:0%
+described
+ 
+
+ align:start position:0%
+described
+by no more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than so essentially just very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a h
+
+ align:start position:0%
+a h
+ 
+
+ align:start position:0%
+a h
+hn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a de
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+freedom in other
+
+ align:start position:0%
+freedom in other
+ 
+
+ align:start position:0%
+freedom in other
+words one degree of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Freedom per plunk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+the uh yeah just a rough formulation of
+
+ align:start position:0%
+the uh yeah just a rough formulation of
+ 
+
+ align:start position:0%
+the uh yeah just a rough formulation of
+the holographic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+so what we just
+
+ align:start position:0%
+so what we just
+ 
+
+ align:start position:0%
+so what we just
+said it just
+
+ align:start position:0%
+said it just
+ 
+
+ align:start position:0%
+said it just
+highlights a point we made
+
+ align:start position:0%
+highlights a point we made
+ 
+
+ align:start position:0%
+highlights a point we made
+earlier is that even though like from
+
+ align:start position:0%
+earlier is that even though like from
+ 
+
+ align:start position:0%
+earlier is that even though like from
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+analysis that the quantum gravity is
+
+ align:start position:0%
+analysis that the quantum gravity is
+ 
+
+ align:start position:0%
+analysis that the quantum gravity is
+always is only operating say at plank
+
+ align:start position:0%
+always is only operating say at plank
+ 
+
+ align:start position:0%
+always is only operating say at plank
+scale say at plank mass or plank length
+
+ align:start position:0%
+scale say at plank mass or plank length
+ 
+
+ align:start position:0%
+scale say at plank mass or plank length
+Etc but we see that the black
+
+ align:start position:0%
+Etc but we see that the black
+ 
+
+ align:start position:0%
+Etc but we see that the black
+hole actually brings the Quant gravity
+
+ align:start position:0%
+hole actually brings the Quant gravity
+ 
+
+ align:start position:0%
+hole actually brings the Quant gravity
+really to microscopic level okay because
+
+ align:start position:0%
+really to microscopic level okay because
+ 
+
+ align:start position:0%
+really to microscopic level okay because
+these are the really microscopic
+
+ align:start position:0%
+these are the really microscopic
+ 
+
+ align:start position:0%
+these are the really microscopic
+statement uh can apply to regions of
+
+ align:start position:0%
+statement uh can apply to regions of
+ 
+
+ align:start position:0%
+statement uh can apply to regions of
+arbitrary sides but some somehow they
+
+ align:start position:0%
+arbitrary sides but some somehow they
+ 
+
+ align:start position:0%
+arbitrary sides but some somehow they
+limited by constraint of con gravity
+
+ align:start position:0%
+limited by constraint of con gravity
+ 
+
+ align:start position:0%
+limited by constraint of con gravity
+okay so this is the a remarkable um um
+
+ align:start position:0%
+okay so this is the a remarkable um um
+ 
+
+ align:start position:0%
+okay so this is the a remarkable um um
+manifestation of the quantum
+
+ align:start position:0%
+manifestation of the quantum
+ 
+
+ align:start position:0%
+manifestation of the quantum
+effect any questions on this yes about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimensiones oh yeah yeah this you can
+
+ align:start position:0%
+dimensiones oh yeah yeah this you can
+ 
+
+ align:start position:0%
+dimensiones oh yeah yeah this you can
+generalize to any Dimension just always
+
+ align:start position:0%
+generalize to any Dimension just always
+ 
+
+ align:start position:0%
+generalize to any Dimension just always
+Co Dimension
+
+ align:start position:0%
+Co Dimension
+ 
+
+ align:start position:0%
+Co Dimension
+two so if you leave in five
+
+ align:start position:0%
+two so if you leave in five
+ 
+
+ align:start position:0%
+two so if you leave in five
+dimension then become three dimension
+
+ align:start position:0%
+dimension then become three dimension
+ 
+
+ align:start position:0%
+dimension then become three dimension
+yeah it's always core Dimension One in
+
+ align:start position:0%
+yeah it's always core Dimension One in
+ 
+
+ align:start position:0%
+yeah it's always core Dimension One in
+the spatial
+
+ align:start position:0%
+the spatial
+ 
+
+ align:start position:0%
+the spatial
+region because the black
+
+ align:start position:0%
+region because the black
+ 
+
+ align:start position:0%
+region because the black
+hole Yeah black hole just area of the
+
+ align:start position:0%
+hole Yeah black hole just area of the
+ 
+
+ align:start position:0%
+hole Yeah black hole just area of the
+black hole is always C Dimension One in
+
+ align:start position:0%
+black hole is always C Dimension One in
+ 
+
+ align:start position:0%
+black hole is always C Dimension One in
+term spatial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diere yeah 10 dimensional space the
+
+ align:start position:0%
+diere yeah 10 dimensional space the
+ 
+
+ align:start position:0%
+diere yeah 10 dimensional space the
+naivity this would be constrained by
+
+ align:start position:0%
+naivity this would be constrained by
+ 
+
+ align:start position:0%
+naivity this would be constrained by
+eight
+
+ align:start position:0%
+eight
+ 
+
+ align:start position:0%
+eight
+dimensional surface
+
+ align:start position:0%
+dimensional surface
+ 
+
+ align:start position:0%
+dimensional surface
+yeah yeah just no matter what dimension
+
+ align:start position:0%
+yeah yeah just no matter what dimension
+ 
+
+ align:start position:0%
+yeah yeah just no matter what dimension
+it's always constrained by the surface
+
+ align:start position:0%
+it's always constrained by the surface
+ 
+
+ align:start position:0%
+it's always constrained by the surface
+not constrained by the volume no matter
+
+ align:start position:0%
+not constrained by the volume no matter
+ 
+
+ align:start position:0%
+not constrained by the volume no matter
+in what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimension other
+
+ align:start position:0%
+dimension other
+ 
+
+ align:start position:0%
+dimension other
+questions there yeah so it seems like we
+
+ align:start position:0%
+questions there yeah so it seems like we
+ 
+
+ align:start position:0%
+questions there yeah so it seems like we
+must we are like constraining a system
+
+ align:start position:0%
+must we are like constraining a system
+ 
+
+ align:start position:0%
+must we are like constraining a system
+ACC the that it's number of states for
+
+ align:start position:0%
+ACC the that it's number of states for
+ 
+
+ align:start position:0%
+ACC the that it's number of states for
+given energy must grow slower some
+
+ align:start position:0%
+given energy must grow slower some
+ 
+
+ align:start position:0%
+given energy must grow slower some
+because must be
+
+ align:start position:0%
+because must be
+ 
+
+ align:start position:0%
+because must be
+lower yeah the number
+
+ align:start position:0%
+lower yeah the number
+ 
+
+ align:start position:0%
+lower yeah the number
+must yeah just say it just say
+
+ align:start position:0%
+must yeah just say it just say
+ 
+
+ align:start position:0%
+must yeah just say it just say
+um uh essentially what we said earlier
+
+ align:start position:0%
+um uh essentially what we said earlier
+ 
+
+ align:start position:0%
+um uh essentially what we said earlier
+is said if you're in the serial quantum
+
+ align:start position:0%
+is said if you're in the serial quantum
+ 
+
+ align:start position:0%
+is said if you're in the serial quantum
+gravity there's a cut off on the maximum
+
+ align:start position:0%
+gravity there's a cut off on the maximum
+ 
+
+ align:start position:0%
+gravity there's a cut off on the maximum
+energy you can have and uh and and
+
+ align:start position:0%
+energy you can have and uh and and
+ 
+
+ align:start position:0%
+energy you can have and uh and and
+there's a cut also on the maximum energy
+
+ align:start position:0%
+there's a cut also on the maximum energy
+ 
+
+ align:start position:0%
+there's a cut also on the maximum energy
+you can have because otherwise you form
+
+ align:start position:0%
+you can have because otherwise you form
+ 
+
+ align:start position:0%
+you can have because otherwise you form
+a black hole and then and then that's
+
+ align:start position:0%
+a black hole and then and then that's
+ 
+
+ align:start position:0%
+a black hole and then and then that's
+that cut off trans translate into the
+
+ align:start position:0%
+that cut off trans translate into the
+ 
+
+ align:start position:0%
+that cut off trans translate into the
+statement about the entropy and and the
+
+ align:start position:0%
+statement about the entropy and and the
+ 
+
+ align:start position:0%
+statement about the entropy and and the
+into the number Freedom yes I mean
+
+ align:start position:0%
+into the number Freedom yes I mean
+ 
+
+ align:start position:0%
+into the number Freedom yes I mean
+because much easier yeah yeah for
+
+ align:start position:0%
+because much easier yeah yeah for
+ 
+
+ align:start position:0%
+because much easier yeah yeah for
+example we have a first we start with a
+
+ align:start position:0%
+example we have a first we start with a
+ 
+
+ align:start position:0%
+example we have a first we start with a
+simple series L maybe for example we add
+
+ align:start position:0%
+simple series L maybe for example we add
+ 
+
+ align:start position:0%
+simple series L maybe for example we add
+for example stand model then we add
+
+ align:start position:0%
+for example stand model then we add
+ 
+
+ align:start position:0%
+for example stand model then we add
+super symmetry then the energy Spectrum
+
+ align:start position:0%
+super symmetry then the energy Spectrum
+ 
+
+ align:start position:0%
+super symmetry then the energy Spectrum
+the the limiting energy is there but the
+
+ align:start position:0%
+the the limiting energy is there but the
+ 
+
+ align:start position:0%
+the the limiting energy is there but the
+number of her space state is more and we
+
+ align:start position:0%
+number of her space state is more and we
+ 
+
+ align:start position:0%
+number of her space state is more and we
+can keep doing things like that
+
+ align:start position:0%
+can keep doing things like that
+ 
+
+ align:start position:0%
+can keep doing things like that
+yeah but we can't because it must be
+
+ align:start position:0%
+yeah but we can't because it must be
+ 
+
+ align:start position:0%
+yeah but we can't because it must be
+below this value yeah but but you see
+
+ align:start position:0%
+below this value yeah but but you see
+ 
+
+ align:start position:0%
+below this value yeah but but you see
+there's something about the volume here
+
+ align:start position:0%
+there's something about the volume here
+ 
+
+ align:start position:0%
+there's something about the volume here
+uh uh you have to talk about the within
+
+ align:start position:0%
+uh uh you have to talk about the within
+ 
+
+ align:start position:0%
+uh uh you have to talk about the within
+some region uh uh of course abstractly
+
+ align:start position:0%
+some region uh uh of course abstractly
+ 
+
+ align:start position:0%
+some region uh uh of course abstractly
+you can uh you can put some yeah maybe
+
+ align:start position:0%
+you can uh you can put some yeah maybe
+ 
+
+ align:start position:0%
+you can uh you can put some yeah maybe
+I'm not getting your
+
+ align:start position:0%
+I'm not getting your
+ 
+
+ align:start position:0%
+I'm not getting your
+question I you say not I always think we
+
+ align:start position:0%
+question I you say not I always think we
+ 
+
+ align:start position:0%
+question I you say not I always think we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+just um for example say the energy bound
+
+ align:start position:0%
+just um for example say the energy bound
+ 
+
+ align:start position:0%
+just um for example say the energy bound
+is here and below this how many St we
+
+ align:start position:0%
+is here and below this how many St we
+ 
+
+ align:start position:0%
+is here and below this how many St we
+could have no no no this is not the dire
+
+ align:start position:0%
+could have no no no this is not the dire
+ 
+
+ align:start position:0%
+could have no no no this is not the dire
+in ter the enty energy Bond uh this is
+
+ align:start position:0%
+in ter the enty energy Bond uh this is
+ 
+
+ align:start position:0%
+in ter the enty energy Bond uh this is
+in the end is the is the is the bound on
+
+ align:start position:0%
+in the end is the is the is the bound on
+ 
+
+ align:start position:0%
+in the end is the is the is the bound on
+the on the
+
+ align:start position:0%
+the on the
+ 
+
+ align:start position:0%
+the on the
+um on the lung body F you can put inside
+
+ align:start position:0%
+um on the lung body F you can put inside
+ 
+
+ align:start position:0%
+um on the lung body F you can put inside
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+region if you put too many deg F inside
+
+ align:start position:0%
+region if you put too many deg F inside
+ 
+
+ align:start position:0%
+region if you put too many deg F inside
+the region then you need to enlarge the
+
+ align:start position:0%
+the region then you need to enlarge the
+ 
+
+ align:start position:0%
+the region then you need to enlarge the
+region yeah just say it's look like the
+
+ align:start position:0%
+region yeah just say it's look like the
+ 
+
+ align:start position:0%
+region yeah just say it's look like the
+number of is incomparable something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+yeah understand shouldn't isolated
+
+ align:start position:0%
+yeah understand shouldn't isolated
+ 
+
+ align:start position:0%
+yeah understand shouldn't isolated
+system means also included the Machinery
+
+ align:start position:0%
+system means also included the Machinery
+ 
+
+ align:start position:0%
+system means also included the Machinery
+to do this things no I'm just saying you
+
+ align:start position:0%
+to do this things no I'm just saying you
+ 
+
+ align:start position:0%
+to do this things no I'm just saying you
+start with isolated system then you can
+
+ align:start position:0%
+start with isolated system then you can
+ 
+
+ align:start position:0%
+start with isolated system then you can
+add something to that isolated
+
+ align:start position:0%
+add something to that isolated
+ 
+
+ align:start position:0%
+add something to that isolated
+system but what about we take matters
+
+ align:start position:0%
+system but what about we take matters
+ 
+
+ align:start position:0%
+system but what about we take matters
+out of the black
+
+ align:start position:0%
+out of the black
+ 
+
+ align:start position:0%
+out of the black
+this no no you take it no that's thing
+
+ align:start position:0%
+this no no you take it no that's thing
+ 
+
+ align:start position:0%
+this no no you take it no that's thing
+that that actually see does not have to
+
+ align:start position:0%
+that that actually see does not have to
+ 
+
+ align:start position:0%
+that that actually see does not have to
+be a black
+
+ align:start position:0%
+be a black
+ 
+
+ align:start position:0%
+be a black
+hole it can be anything it just can be
+
+ align:start position:0%
+hole it can be anything it just can be
+ 
+
+ align:start position:0%
+hole it can be anything it just can be
+anything so if we instead putting energy
+
+ align:start position:0%
+anything so if we instead putting energy
+ 
+
+ align:start position:0%
+anything so if we instead putting energy
+inside we take energy out yeah you take
+
+ align:start position:0%
+inside we take energy out yeah you take
+ 
+
+ align:start position:0%
+inside we take energy out yeah you take
+entropy will decrease yeah just take
+
+ align:start position:0%
+entropy will decrease yeah just take
+ 
+
+ align:start position:0%
+entropy will decrease yeah just take
+entropy out
+
+ align:start position:0%
+entropy out
+ 
+
+ align:start position:0%
+entropy out
+yeah then this spond will be even more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfied a question there that the the
+
+ align:start position:0%
+satisfied a question there that the the
+ 
+
+ align:start position:0%
+satisfied a question there that the the
+the degree of freen yeah I mean l of no
+
+ align:start position:0%
+the degree of freen yeah I mean l of no
+ 
+
+ align:start position:0%
+the degree of freen yeah I mean l of no
+no n is the dimension of the h
+
+ align:start position:0%
+no n is the dimension of the h
+ 
+
+ align:start position:0%
+no n is the dimension of the h
+space n is the dimension of the h space
+
+ align:start position:0%
+space n is the dimension of the h space
+ 
+
+ align:start position:0%
+space n is the dimension of the h space
+that's what I call n here n Dimension h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space typically the L of the dimension
+
+ align:start position:0%
+space typically the L of the dimension
+ 
+
+ align:start position:0%
+space typically the L of the dimension
+of h space is exponential of the L
+
+ align:start position:0%
+of h space is exponential of the L
+ 
+
+ align:start position:0%
+of h space is exponential of the L
+Freedom okay just look at here just look
+
+ align:start position:0%
+Freedom okay just look at here just look
+ 
+
+ align:start position:0%
+Freedom okay just look at here just look
+at here
+
+ align:start position:0%
+at here
+ 
+
+ align:start position:0%
+at here
+yeah any other
+
+ align:start position:0%
+yeah any other
+ 
+
+ align:start position:0%
+yeah any other
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay um in
+
+ align:start position:0%
+okay um in
+ 
+
+ align:start position:0%
+okay um in
+the if we have a Quantum field Theory it
+
+ align:start position:0%
+the if we have a Quantum field Theory it
+ 
+
+ align:start position:0%
+the if we have a Quantum field Theory it
+has C vacuum energy right and then if
+
+ align:start position:0%
+has C vacuum energy right and then if
+ 
+
+ align:start position:0%
+has C vacuum energy right and then if
+you now like you know consider that to
+
+ align:start position:0%
+you now like you know consider that to
+ 
+
+ align:start position:0%
+you now like you know consider that to
+be the vacuum energy and you expand it
+
+ align:start position:0%
+be the vacuum energy and you expand it
+ 
+
+ align:start position:0%
+be the vacuum energy and you expand it
+at some point it will actually collapse
+
+ align:start position:0%
+at some point it will actually collapse
+ 
+
+ align:start position:0%
+at some point it will actually collapse
+into a black hole so like if you take
+
+ align:start position:0%
+into a black hole so like if you take
+ 
+
+ align:start position:0%
+into a black hole so like if you take
+the vacuum energy to be that predicted
+
+ align:start position:0%
+the vacuum energy to be that predicted
+ 
+
+ align:start position:0%
+the vacuum energy to be that predicted
+by T of then uh for like the universe it
+
+ align:start position:0%
+by T of then uh for like the universe it
+ 
+
+ align:start position:0%
+by T of then uh for like the universe it
+would not work even theoretically I mean
+
+ align:start position:0%
+would not work even theoretically I mean
+ 
+
+ align:start position:0%
+would not work even theoretically I mean
+I know the cosmological constant is like
+
+ align:start position:0%
+I know the cosmological constant is like
+ 
+
+ align:start position:0%
+I know the cosmological constant is like
+120 orders less but yeah that's a bit
+
+ align:start position:0%
+120 orders less but yeah that's a bit
+ 
+
+ align:start position:0%
+120 orders less but yeah that's a bit
+tricky uh because the um yeah so the
+
+ align:start position:0%
+tricky uh because the um yeah so the
+ 
+
+ align:start position:0%
+tricky uh because the um yeah so the
+vacuum energy will make it in to say
+
+ align:start position:0%
+vacuum energy will make it in to say
+ 
+
+ align:start position:0%
+vacuum energy will make it in to say
+depend on whether vacuum energy is
+
+ align:start position:0%
+depend on whether vacuum energy is
+ 
+
+ align:start position:0%
+depend on whether vacuum energy is
+positive or netive make it into de anti
+
+ align:start position:0%
+positive or netive make it into de anti
+ 
+
+ align:start position:0%
+positive or netive make it into de anti
+deer then then yeah then you try to see
+
+ align:start position:0%
+deer then then yeah then you try to see
+ 
+
+ align:start position:0%
+deer then then yeah then you try to see
+whether yeah um it depend on
+
+ align:start position:0%
+whether yeah um it depend on
+ 
+
+ align:start position:0%
+whether yeah um it depend on
+details but if you go big enough it's
+
+ align:start position:0%
+details but if you go big enough it's
+ 
+
+ align:start position:0%
+details but if you go big enough it's
+going to collapse for or no no not
+
+ align:start position:0%
+going to collapse for or no no not
+ 
+
+ align:start position:0%
+going to collapse for or no no not
+necess I'm just saying that you have to
+
+ align:start position:0%
+necess I'm just saying that you have to
+ 
+
+ align:start position:0%
+necess I'm just saying that you have to
+formulate a little bit differently
+
+ align:start position:0%
+formulate a little bit differently
+ 
+
+ align:start position:0%
+formulate a little bit differently
+you're talking about a particular state
+
+ align:start position:0%
+you're talking about a particular state
+ 
+
+ align:start position:0%
+you're talking about a particular state
+of certain energy to cap to gravity then
+
+ align:start position:0%
+of certain energy to cap to gravity then
+ 
+
+ align:start position:0%
+of certain energy to cap to gravity then
+you just take that state cap to gravity
+
+ align:start position:0%
+you just take that state cap to gravity
+ 
+
+ align:start position:0%
+you just take that state cap to gravity
+to see what you get
+
+ align:start position:0%
+to see what you get
+ 
+
+ align:start position:0%
+to see what you get
+yeah then ask questions from
+
+ align:start position:0%
+yeah then ask questions from
+ 
+
+ align:start position:0%
+yeah then ask questions from
+there yeah good so now let's move to a
+
+ align:start position:0%
+there yeah good so now let's move to a
+ 
+
+ align:start position:0%
+there yeah good so now let's move to a
+topic still is in the
+
+ align:start position:0%
+topic still is in the
+ 
+
+ align:start position:0%
+topic still is in the
+preparation to go to the to go to The
+
+ align:start position:0%
+preparation to go to the to go to The
+ 
+
+ align:start position:0%
+preparation to go to the to go to The
+Duality but we need the a lot piece of
+
+ align:start position:0%
+Duality but we need the a lot piece of
+ 
+
+ align:start position:0%
+Duality but we need the a lot piece of
+important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intuition in order to fully appreciate
+
+ align:start position:0%
+intuition in order to fully appreciate
+ 
+
+ align:start position:0%
+intuition in order to fully appreciate
+the duality
+
+ align:start position:0%
+the duality
+ 
+
+ align:start position:0%
+the duality
+and and this piece of
+
+ align:start position:0%
+and and this piece of
+ 
+
+ align:start position:0%
+and and this piece of
+intuition is n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Series yeah let me call it n Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+okay so now we want to look at the now
+
+ align:start position:0%
+okay so now we want to look at the now
+ 
+
+ align:start position:0%
+okay so now we want to look at the now
+we try to look at the uh hint for gra uh
+
+ align:start position:0%
+we try to look at the uh hint for gra uh
+ 
+
+ align:start position:0%
+we try to look at the uh hint for gra uh
+for holographic duality from the FI
+
+ align:start position:0%
+for holographic duality from the FI
+ 
+
+ align:start position:0%
+for holographic duality from the FI
+series side okay from the FI series side
+
+ align:start position:0%
+series side okay from the FI series side
+ 
+
+ align:start position:0%
+series side okay from the FI series side
+so so so far we have been talking about
+
+ align:start position:0%
+so so so far we have been talking about
+ 
+
+ align:start position:0%
+so so so far we have been talking about
+the hint
+
+ align:start position:0%
+the hint
+ 
+
+ align:start position:0%
+the hint
+photography from the gravity
+
+ align:start position:0%
+photography from the gravity
+ 
+
+ align:start position:0%
+photography from the gravity
+side uh and now we look at it from the
+
+ align:start position:0%
+side uh and now we look at it from the
+ 
+
+ align:start position:0%
+side uh and now we look at it from the
+field series side to see actually from
+
+ align:start position:0%
+field series side to see actually from
+ 
+
+ align:start position:0%
+field series side to see actually from
+fi series side there's also some hint to
+
+ align:start position:0%
+fi series side there's also some hint to
+ 
+
+ align:start position:0%
+fi series side there's also some hint to
+relate a long gravity system to a
+
+ align:start position:0%
+relate a long gravity system to a
+ 
+
+ align:start position:0%
+relate a long gravity system to a
+gravity system okay so let's start with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qcd uh
+
+ align:start position:0%
+qcd uh
+ 
+
+ align:start position:0%
+qcd uh
+um so qcd is su3 gauge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quar
+
+ align:start position:0%
+quar
+ 
+
+ align:start position:0%
+quar
+okay so we can so let me just write down
+
+ align:start position:0%
+okay so we can so let me just write down
+ 
+
+ align:start position:0%
+okay so we can so let me just write down
+it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ground
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this
+
+ align:start position:0%
+okay so this
+ 
+
+ align:start position:0%
+okay so this
+F describe the gluon field and this side
+
+ align:start position:0%
+F describe the gluon field and this side
+ 
+
+ align:start position:0%
+F describe the gluon field and this side
+describe the clocks okay so this a so
+
+ align:start position:0%
+describe the clocks okay so this a so
+ 
+
+ align:start position:0%
+describe the clocks okay so this a so
+this F is built
+
+ align:start position:0%
+this F is built
+ 
+
+ align:start position:0%
+this F is built
+out of the standard partial mu a mu
+
+ align:start position:0%
+out of the standard partial mu a mu
+ 
+
+ align:start position:0%
+out of the standard partial mu a mu
+minus partial mu a mu
+
+ align:start position:0%
+minus partial mu a mu
+ 
+
+ align:start position:0%
+minus partial mu a mu
+minus a mu a
+
+ align:start position:0%
+minus a mu a
+ 
+
+ align:start position:0%
+minus a mu a
+mu and May and a mu each gaug
+
+ align:start position:0%
+mu and May and a mu each gaug
+ 
+
+ align:start position:0%
+mu and May and a mu each gaug
+field is a 3X3 commission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix okay so this are 3 * 3 mission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix so this is using the Matrix
+
+ align:start position:0%
+Matrix so this is using the Matrix
+ 
+
+ align:start position:0%
+Matrix so this is using the Matrix
+notation so f is also a matrix so
+
+ align:start position:0%
+notation so f is also a matrix so
+ 
+
+ align:start position:0%
+notation so f is also a matrix so
+there's a trace here
+
+ align:start position:0%
+there's a trace here
+ 
+
+ align:start position:0%
+there's a trace here
+okay permission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix and the TA is just the generators
+
+ align:start position:0%
+Matrix and the TA is just the generators
+ 
+
+ align:start position:0%
+Matrix and the TA is just the generators
+of su
+
+ align:start position:0%
+of su
+ 
+
+ align:start position:0%
+of su
+su3
+
+ align:start position:0%
+su3
+ 
+
+ align:start position:0%
+su3
+okay so it doesn't matter if you don't
+
+ align:start position:0%
+okay so it doesn't matter if you don't
+ 
+
+ align:start position:0%
+okay so it doesn't matter if you don't
+know qcd it doesn't matter if you have
+
+ align:start position:0%
+know qcd it doesn't matter if you have
+ 
+
+ align:start position:0%
+know qcd it doesn't matter if you have
+not seen qcd before the only thing
+
+ align:start position:0%
+not seen qcd before the only thing
+ 
+
+ align:start position:0%
+not seen qcd before the only thing
+matters is just to remember that qcd is
+
+ align:start position:0%
+matters is just to remember that qcd is
+ 
+
+ align:start position:0%
+matters is just to remember that qcd is
+a theory of
+
+ align:start position:0%
+a theory of
+ 
+
+ align:start position:0%
+a theory of
+matrices PD is a theory of three 3x3
+
+ align:start position:0%
+matrices PD is a theory of three 3x3
+ 
+
+ align:start position:0%
+matrices PD is a theory of three 3x3
+matrices okay so the Gran field it's a
+
+ align:start position:0%
+matrices okay so the Gran field it's a
+ 
+
+ align:start position:0%
+matrices okay so the Gran field it's a
+3X3 matrices it's it's it's it's a
+
+ align:start position:0%
+3X3 matrices it's it's it's it's a
+ 
+
+ align:start position:0%
+3X3 matrices it's it's it's it's a
+described by
+
+ align:start position:0%
+described by
+ 
+
+ align:start position:0%
+described by
+matrices so of course the one of the
+
+ align:start position:0%
+matrices so of course the one of the
+ 
+
+ align:start position:0%
+matrices so of course the one of the
+remarkable thing about the
+
+ align:start position:0%
+remarkable thing about the
+ 
+
+ align:start position:0%
+remarkable thing about the
+qcd what's the most remarkable thing
+
+ align:start position:0%
+qcd what's the most remarkable thing
+ 
+
+ align:start position:0%
+qcd what's the most remarkable thing
+about qcd do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know yeah that's
+
+ align:start position:0%
+know yeah that's
+ 
+
+ align:start position:0%
+know yeah that's
+one and what other remarkable thing
+
+ align:start position:0%
+one and what other remarkable thing
+ 
+
+ align:start position:0%
+one and what other remarkable thing
+about the Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's related to that conf yeah
+
+ align:start position:0%
+yeah it's related to that conf yeah
+ 
+
+ align:start position:0%
+yeah it's related to that conf yeah
+confinement is also related to that it's
+
+ align:start position:0%
+confinement is also related to that it's
+ 
+
+ align:start position:0%
+confinement is also related to that it's
+just yeah one of the one of most
+
+ align:start position:0%
+just yeah one of the one of most
+ 
+
+ align:start position:0%
+just yeah one of the one of most
+remarkable one of the most remarkable
+
+ align:start position:0%
+remarkable one of the most remarkable
+ 
+
+ align:start position:0%
+remarkable one of the most remarkable
+thing about QD is still not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solvable and the reason it's not
+
+ align:start position:0%
+solvable and the reason it's not
+ 
+
+ align:start position:0%
+solvable and the reason it's not
+solvable is is because when you go to
+
+ align:start position:0%
+solvable is is because when you go to
+ 
+
+ align:start position:0%
+solvable is is because when you go to
+low energies the company becomes strong
+
+ align:start position:0%
+low energies the company becomes strong
+ 
+
+ align:start position:0%
+low energies the company becomes strong
+then we don't know how to deal with it
+
+ align:start position:0%
+then we don't know how to deal with it
+ 
+
+ align:start position:0%
+then we don't know how to deal with it
+okay um so we still don't know how to
+
+ align:start position:0%
+okay um so we still don't know how to
+ 
+
+ align:start position:0%
+okay um so we still don't know how to
+calculated from first principle of
+
+ align:start position:0%
+calculated from first principle of
+ 
+
+ align:start position:0%
+calculated from first principle of
+course we can put it on the computer but
+
+ align:start position:0%
+course we can put it on the computer but
+ 
+
+ align:start position:0%
+course we can put it on the computer but
+uh but just from the um uh in terms of
+
+ align:start position:0%
+uh but just from the um uh in terms of
+ 
+
+ align:start position:0%
+uh but just from the um uh in terms of
+theoretical understanding it's
+
+ align:start position:0%
+theoretical understanding it's
+ 
+
+ align:start position:0%
+theoretical understanding it's
+hard so in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1974 so this is old
+
+ align:start position:0%
+1974 so this is old
+ 
+
+ align:start position:0%
+1974 so this is old
+problem so starting in 1974 people
+
+ align:start position:0%
+problem so starting in 1974 people
+ 
+
+ align:start position:0%
+problem so starting in 1974 people
+starting 1971 people already tried to
+
+ align:start position:0%
+starting 1971 people already tried to
+ 
+
+ align:start position:0%
+starting 1971 people already tried to
+solve
+
+ align:start position:0%
+solve
+ 
+
+ align:start position:0%
+solve
+it so in 1974 so the big problem of this
+
+ align:start position:0%
+it so in 1974 so the big problem of this
+ 
+
+ align:start position:0%
+it so in 1974 so the big problem of this
+thing is that in Quantum fil normally we
+
+ align:start position:0%
+thing is that in Quantum fil normally we
+ 
+
+ align:start position:0%
+thing is that in Quantum fil normally we
+do expansions okay say we find some
+
+ align:start position:0%
+do expansions okay say we find some
+ 
+
+ align:start position:0%
+do expansions okay say we find some
+starting point so in physics that we
+
+ align:start position:0%
+starting point so in physics that we
+ 
+
+ align:start position:0%
+starting point so in physics that we
+always do we find a starting point which
+
+ align:start position:0%
+always do we find a starting point which
+ 
+
+ align:start position:0%
+always do we find a starting point which
+can be solved then we expand around that
+
+ align:start position:0%
+can be solved then we expand around that
+ 
+
+ align:start position:0%
+can be solved then we expand around that
+starting point and that starting point
+
+ align:start position:0%
+starting point and that starting point
+ 
+
+ align:start position:0%
+starting point and that starting point
+is often a free
+
+ align:start position:0%
+is often a free
+ 
+
+ align:start position:0%
+is often a free
+Theory and uh then we we expand about
+
+ align:start position:0%
+Theory and uh then we we expand about
+ 
+
+ align:start position:0%
+Theory and uh then we we expand about
+the free
+
+ align:start position:0%
+the free
+ 
+
+ align:start position:0%
+the free
+Theory so so the difficult thing about
+
+ align:start position:0%
+Theory so so the difficult thing about
+ 
+
+ align:start position:0%
+Theory so so the difficult thing about
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+theory is that first it's it's hard when
+
+ align:start position:0%
+theory is that first it's it's hard when
+ 
+
+ align:start position:0%
+theory is that first it's it's hard when
+you go to low energies first it's hard
+
+ align:start position:0%
+you go to low energies first it's hard
+ 
+
+ align:start position:0%
+you go to low energies first it's hard
+to find the starting point and the
+
+ align:start position:0%
+to find the starting point and the
+ 
+
+ align:start position:0%
+to find the starting point and the
+second is that there's nothing to expand
+
+ align:start position:0%
+second is that there's nothing to expand
+ 
+
+ align:start position:0%
+second is that there's nothing to expand
+because there's no small parameters okay
+
+ align:start position:0%
+because there's no small parameters okay
+ 
+
+ align:start position:0%
+because there's no small parameters okay
+there's no small parameters uh uh when
+
+ align:start position:0%
+there's no small parameters uh uh when
+ 
+
+ align:start position:0%
+there's no small parameters uh uh when
+you need to expand you always need a
+
+ align:start position:0%
+you need to expand you always need a
+ 
+
+ align:start position:0%
+you need to expand you always need a
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+parameter so so in 1974 to H come up
+
+ align:start position:0%
+parameter so so in 1974 to H come up
+ 
+
+ align:start position:0%
+parameter so so in 1974 to H come up
+with a a very nice idea he say this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+su3 he said let's just think take the
+
+ align:start position:0%
+su3 he said let's just think take the
+ 
+
+ align:start position:0%
+su3 he said let's just think take the
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+color
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is n equal
+
+ align:start position:0%
+which is n equal
+ 
+
+ align:start position:0%
+which is n equal
+3 as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameter so even even though in real
+
+ align:start position:0%
+parameter so even even though in real
+ 
+
+ align:start position:0%
+parameter so even even though in real
+life he said there
+
+ align:start position:0%
+life he said there
+ 
+
+ align:start position:0%
+life he said there
+only three yeah there's only three type
+
+ align:start position:0%
+only three yeah there's only three type
+ 
+
+ align:start position:0%
+only three yeah there's only three type
+of colors but let's imagine uh we treat
+
+ align:start position:0%
+of colors but let's imagine uh we treat
+ 
+
+ align:start position:0%
+of colors but let's imagine uh we treat
+it as a three parameter okay so which
+
+ align:start position:0%
+it as a three parameter okay so which
+ 
+
+ align:start position:0%
+it as a three parameter okay so which
+this just implies say you
+
+ align:start position:0%
+this just implies say you
+ 
+
+ align:start position:0%
+this just implies say you
+promote the gauge
+
+ align:start position:0%
+promote the gauge
+ 
+
+ align:start position:0%
+promote the gauge
+field to M byn matrices M byn commission
+
+ align:start position:0%
+field to M byn matrices M byn commission
+ 
+
+ align:start position:0%
+field to M byn matrices M byn commission
+matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay you say let's just treat this
+
+ align:start position:0%
+okay okay you say let's just treat this
+ 
+
+ align:start position:0%
+okay okay you say let's just treat this
+by in terms of M by m
+
+ align:start position:0%
+by in terms of M by m
+ 
+
+ align:start position:0%
+by in terms of M by m
+matrices and then let's consider angle
+
+ align:start position:0%
+matrices and then let's consider angle
+ 
+
+ align:start position:0%
+matrices and then let's consider angle
+to Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's consider Ang go Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mid so so he reasoned if in the infinite
+
+ align:start position:0%
+mid so so he reasoned if in the infinite
+ 
+
+ align:start position:0%
+mid so so he reasoned if in the infinite
+limit is sufficiently simple then maybe
+
+ align:start position:0%
+limit is sufficiently simple then maybe
+ 
+
+ align:start position:0%
+limit is sufficiently simple then maybe
+maybe we can solve that limit and then
+
+ align:start position:0%
+maybe we can solve that limit and then
+ 
+
+ align:start position:0%
+maybe we can solve that limit and then
+do one/
+
+ align:start position:0%
+do one/
+ 
+
+ align:start position:0%
+do one/
+expansion one n then it's a small
+
+ align:start position:0%
+expansion one n then it's a small
+ 
+
+ align:start position:0%
+expansion one n then it's a small
+parameter then we can Tre One n as a
+
+ align:start position:0%
+parameter then we can Tre One n as a
+ 
+
+ align:start position:0%
+parameter then we can Tre One n as a
+small parameter and then do one
+
+ align:start position:0%
+small parameter and then do one
+ 
+
+ align:start position:0%
+small parameter and then do one
+expansion
+
+ align:start position:0%
+expansion
+ 
+
+ align:start position:0%
+expansion
+okay so that's the rough idea and then
+
+ align:start position:0%
+okay so that's the rough idea and then
+ 
+
+ align:start position:0%
+okay so that's the rough idea and then
+you get a small paret one/ n so in real
+
+ align:start position:0%
+you get a small paret one/ n so in real
+ 
+
+ align:start position:0%
+you get a small paret one/ n so in real
+life n will be three so one over three
+
+ align:start position:0%
+life n will be three so one over three
+ 
+
+ align:start position:0%
+life n will be three so one over three
+um it's not very small but it's at least
+
+ align:start position:0%
+um it's not very small but it's at least
+ 
+
+ align:start position:0%
+um it's not very small but it's at least
+smaller than
+
+ align:start position:0%
+smaller than
+ 
+
+ align:start position:0%
+smaller than
+one okay so so this turns out to be an
+
+ align:start position:0%
+one okay so so this turns out to be an
+ 
+
+ align:start position:0%
+one okay so so this turns out to be an
+ingenious idea
+
+ align:start position:0%
+ingenious idea
+ 
+
+ align:start position:0%
+ingenious idea
+T out to be ingenious idea but
+
+ align:start position:0%
+T out to be ingenious idea but
+ 
+
+ align:start position:0%
+T out to be ingenious idea but
+unfortunately qcd still cannot be solved
+
+ align:start position:0%
+unfortunately qcd still cannot be solved
+ 
+
+ align:start position:0%
+unfortunately qcd still cannot be solved
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way but there's a surprise but there's a
+
+ align:start position:0%
+way but there's a surprise but there's a
+ 
+
+ align:start position:0%
+way but there's a surprise but there's a
+surprise so still you cannot solve this
+
+ align:start position:0%
+surprise so still you cannot solve this
+ 
+
+ align:start position:0%
+surprise so still you cannot solve this
+way uh even angle to infite limit turns
+
+ align:start position:0%
+way uh even angle to infite limit turns
+ 
+
+ align:start position:0%
+way uh even angle to infite limit turns
+out to be too hot but this a surprise it
+
+ align:start position:0%
+out to be too hot but this a surprise it
+ 
+
+ align:start position:0%
+out to be too hot but this a surprise it
+turns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out out this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion give you a string
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theory
+
+ align:start position:0%
+theory
+ 
+
+ align:start position:0%
+theory
+okay so I will now explain this
+
+ align:start position:0%
+okay so I will now explain this
+ 
+
+ align:start position:0%
+okay so I will now explain this
+okay so not explain this so so this a
+
+ align:start position:0%
+okay so not explain this so so this a
+ 
+
+ align:start position:0%
+okay so not explain this so so this a
+byproduct of his lar expansion is said
+
+ align:start position:0%
+byproduct of his lar expansion is said
+ 
+
+ align:start position:0%
+byproduct of his lar expansion is said
+you find that this
+
+ align:start position:0%
+you find that this
+ 
+
+ align:start position:0%
+you find that this
+actually such a gaug series actually
+
+ align:start position:0%
+actually such a gaug series actually
+ 
+
+ align:start position:0%
+actually such a gaug series actually
+secretly a string series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+key is that this field are matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so the key reason this emerges
+
+ align:start position:0%
+okay so so the key reason this emerges
+ 
+
+ align:start position:0%
+okay so so the key reason this emerges
+is because we are working with field
+
+ align:start position:0%
+is because we are working with field
+ 
+
+ align:start position:0%
+is because we are working with field
+which are
+
+ align:start position:0%
+which are
+ 
+
+ align:start position:0%
+which are
+matrices so so I will uh so to to
+
+ align:start position:0%
+matrices so so I will uh so to to
+ 
+
+ align:start position:0%
+matrices so so I will uh so to to
+illustrate
+
+ align:start position:0%
+illustrate
+ 
+
+ align:start position:0%
+illustrate
+this I will not do the qcd it's a little
+
+ align:start position:0%
+this I will not do the qcd it's a little
+ 
+
+ align:start position:0%
+this I will not do the qcd it's a little
+bit complicated we just do a simple
+
+ align:start position:0%
+bit complicated we just do a simple
+ 
+
+ align:start position:0%
+bit complicated we just do a simple
+scale of field Theory
+
+ align:start position:0%
+scale of field Theory
+ 
+
+ align:start position:0%
+scale of field Theory
+okay so we just do a simple scal of
+
+ align:start position:0%
+okay so we just do a simple scal of
+ 
+
+ align:start position:0%
+okay so we just do a simple scal of
+field the as a
+
+ align:start position:0%
+field the as a
+ 
+
+ align:start position:0%
+field the as a
+illustration so let's consider the
+
+ align:start position:0%
+illustration so let's consider the
+ 
+
+ align:start position:0%
+illustration so let's consider the
+following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this G is still coupling
+
+ align:start position:0%
+okay so this G is still coupling
+ 
+
+ align:start position:0%
+okay so this G is still coupling
+constant for what we do it's actually
+
+ align:start position:0%
+constant for what we do it's actually
+ 
+
+ align:start position:0%
+constant for what we do it's actually
+convenient to put it in the
+
+ align:start position:0%
+convenient to put it in the
+ 
+
+ align:start position:0%
+convenient to put it in the
+front of course you can rescale it I'm
+
+ align:start position:0%
+front of course you can rescale it I'm
+ 
+
+ align:start position:0%
+front of course you can rescale it I'm
+sure you you can rescale it to put it
+
+ align:start position:0%
+sure you you can rescale it to put it
+ 
+
+ align:start position:0%
+sure you you can rescale it to put it
+here which is normal place but I put it
+
+ align:start position:0%
+here which is normal place but I put it
+ 
+
+ align:start position:0%
+here which is normal place but I put it
+in the front just like what we normally
+
+ align:start position:0%
+in the front just like what we normally
+ 
+
+ align:start position:0%
+in the front just like what we normally
+do also for qcd okay so this G is cing
+
+ align:start position:0%
+do also for qcd okay so this G is cing
+ 
+
+ align:start position:0%
+do also for qcd okay so this G is cing
+con which we put in the front
+
+ align:start position:0%
+con which we put in the front
+ 
+
+ align:start position:0%
+con which we put in the front
+and then each five again I take it to be
+
+ align:start position:0%
+and then each five again I take it to be
+ 
+
+ align:start position:0%
+and then each five again I take it to be
+M byn commission
+
+ align:start position:0%
+M byn commission
+ 
+
+ align:start position:0%
+M byn commission
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+5x each one is a matrix a b so have two
+
+ align:start position:0%
+5x each one is a matrix a b so have two
+ 
+
+ align:start position:0%
+5x each one is a matrix a b so have two
+index so this m by m commission
+
+ align:start position:0%
+index so this m by m commission
+ 
+
+ align:start position:0%
+index so this m by m commission
+Matrix yeah M by Mission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix so which yeah which means that 5
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+Star equal to
+
+ align:start position:0%
+Star equal to
+ 
+
+ align:start position:0%
+Star equal to
+5ba
+
+ align:start position:0%
+5ba
+ 
+
+ align:start position:0%
+5ba
+okay so there's a
+
+ align:start position:0%
+okay so there's a
+ 
+
+ align:start position:0%
+okay so there's a
+um so there's a difference between the
+
+ align:start position:0%
+um so there's a difference between the
+ 
+
+ align:start position:0%
+um so there's a difference between the
+up and lower indices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I can write it more explicit in
+
+ align:start position:0%
+okay so I can write it more explicit in
+ 
+
+ align:start position:0%
+okay so I can write it more explicit in
+terms of
+
+ align:start position:0%
+terms of
+ 
+
+ align:start position:0%
+terms of
+components so just to give you in case
+
+ align:start position:0%
+components so just to give you in case
+ 
+
+ align:start position:0%
+components so just to give you in case
+some of you are not familiar with this
+
+ align:start position:0%
+some of you are not familiar with this
+ 
+
+ align:start position:0%
+some of you are not familiar with this
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+kind of field
+
+ align:start position:0%
+kind of field
+ 
+
+ align:start position:0%
+kind of field
+Theory so let me just also write it in
+
+ align:start position:0%
+Theory so let me just also write it in
+ 
+
+ align:start position:0%
+Theory so let me just also write it in
+terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+component so right in terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components it's 12 partial mu by
+
+ align:start position:0%
+components it's 12 partial mu by
+ 
+
+ align:start position:0%
+components it's 12 partial mu by
+a then partial mu by
+
+ align:start position:0%
+a then partial mu by
+ 
+
+ align:start position:0%
+a then partial mu by
+ba then
+
+ align:start position:0%
+ba then
+ 
+
+ align:start position:0%
+ba then
+Plus one
+
+ align:start position:0%
+Plus one
+ 
+
+ align:start position:0%
+Plus one
+quter 5 a
+
+ align:start position:0%
+quter 5 a
+ 
+
+ align:start position:0%
+quter 5 a
+b 5 b
+
+ align:start position:0%
+b 5 b
+ 
+
+ align:start position:0%
+b 5 b
+c 5
+
+ align:start position:0%
+c 5
+ 
+
+ align:start position:0%
+c 5
+CA
+
+ align:start position:0%
+CA
+ 
+
+ align:start position:0%
+CA
+five No 5
+
+ align:start position:0%
+five No 5
+ 
+
+ align:start position:0%
+five No 5
+CD 5
+
+ align:start position:0%
+CD 5
+ 
+
+ align:start position:0%
+CD 5
+da
+
+ align:start position:0%
+da
+ 
+
+ align:start position:0%
+da
+okay okay so this is the just having
+
+ align:start position:0%
+okay okay so this is the just having
+ 
+
+ align:start position:0%
+okay okay so this is the just having
+writing down the explicit using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+component so so this L by
+
+ align:start position:0%
+component so so this L by
+ 
+
+ align:start position:0%
+component so so this L by
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+is invariant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+under in addition to the usual
+
+ align:start position:0%
+under in addition to the usual
+ 
+
+ align:start position:0%
+under in addition to the usual
+translation rotation symmetries Etc has
+
+ align:start position:0%
+translation rotation symmetries Etc has
+ 
+
+ align:start position:0%
+translation rotation symmetries Etc has
+also a um internal
+
+ align:start position:0%
+also a um internal
+ 
+
+ align:start position:0%
+also a um internal
+symmetry under un Global
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry okay so uh
+
+ align:start position:0%
+symmetry okay so uh
+ 
+
+ align:start position:0%
+symmetry okay so uh
+um say 5x goes to U 5x U
+
+ align:start position:0%
+um say 5x goes to U 5x U
+ 
+
+ align:start position:0%
+um say 5x goes to U 5x U
+dagger for any
+
+ align:start position:0%
+dagger for any
+ 
+
+ align:start position:0%
+dagger for any
+U any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+is U
+
+ align:start position:0%
+is U
+ 
+
+ align:start position:0%
+is U
+Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this series in warant under so
+
+ align:start position:0%
+okay so this series in warant under so
+ 
+
+ align:start position:0%
+okay so this series in warant under so
+this is obvious from here because of
+
+ align:start position:0%
+this is obvious from here because of
+ 
+
+ align:start position:0%
+this is obvious from here because of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+Chace so this is in Waring on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let me just make some remarks
+
+ align:start position:0%
+okay so let me just make some remarks
+ 
+
+ align:start position:0%
+okay so let me just make some remarks
+before proceed to talk about the
+
+ align:start position:0%
+before proceed to talk about the
+ 
+
+ align:start position:0%
+before proceed to talk about the
+features of this series let me just make
+
+ align:start position:0%
+features of this series let me just make
+ 
+
+ align:start position:0%
+features of this series let me just make
+some quick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remark zero you said this is a Ser of n
+
+ align:start position:0%
+remark zero you said this is a Ser of n
+ 
+
+ align:start position:0%
+remark zero you said this is a Ser of n
+Square scalar
+
+ align:start position:0%
+Square scalar
+ 
+
+ align:start position:0%
+Square scalar
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+field okay so if this is intuitive to
+
+ align:start position:0%
+field okay so if this is intuitive to
+ 
+
+ align:start position:0%
+field okay so if this is intuitive to
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+then this is just means you have many
+
+ align:start position:0%
+then this is just means you have many
+ 
+
+ align:start position:0%
+then this is just means you have many
+many fields coupled together in some
+
+ align:start position:0%
+many fields coupled together in some
+ 
+
+ align:start position:0%
+many fields coupled together in some
+specific way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh also we don't have to
+
+ align:start position:0%
+okay and uh also we don't have to
+ 
+
+ align:start position:0%
+okay and uh also we don't have to
+consider her Mission matrices to
+
+ align:start position:0%
+consider her Mission matrices to
+ 
+
+ align:start position:0%
+consider her Mission matrices to
+consider her Mission Matrix just for
+
+ align:start position:0%
+consider her Mission Matrix just for
+ 
+
+ align:start position:0%
+consider her Mission Matrix just for
+Simplicity when can also
+
+ align:start position:0%
+Simplicity when can also
+ 
+
+ align:start position:0%
+Simplicity when can also
+consider can
+
+ align:start position:0%
+consider can
+ 
+
+ align:start position:0%
+consider can
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+other type of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrices for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+real say symmetric
+
+ align:start position:0%
+real say symmetric
+ 
+
+ align:start position:0%
+real say symmetric
+Matrix say it's real symmetric or
+
+ align:start position:0%
+Matrix say it's real symmetric or
+ 
+
+ align:start position:0%
+Matrix say it's real symmetric or
+antisymmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matri so in those cases if you consider
+
+ align:start position:0%
+matri so in those cases if you consider
+ 
+
+ align:start position:0%
+matri so in those cases if you consider
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+real matri then symmetric or anti
+
+ align:start position:0%
+real matri then symmetric or anti
+ 
+
+ align:start position:0%
+real matri then symmetric or anti
+symmetric Matrix in that case this
+
+ align:start position:0%
+symmetric Matrix in that case this
+ 
+
+ align:start position:0%
+symmetric Matrix in that case this
+Global syat become s o
+
+ align:start position:0%
+Global syat become s o
+ 
+
+ align:start position:0%
+Global syat become s o
+n okay rather than unu n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in here this U is a global SYM just U
+
+ align:start position:0%
+so in here this U is a global SYM just U
+ 
+
+ align:start position:0%
+so in here this U is a global SYM just U
+has beant cannot depend on X you see it
+
+ align:start position:0%
+has beant cannot depend on X you see it
+ 
+
+ align:start position:0%
+has beant cannot depend on X you see it
+from here cannot depend on X but you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also introduce GA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fields to make
+
+ align:start position:0%
+fields to make
+ 
+
+ align:start position:0%
+fields to make
+this un symm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+local
+
+ align:start position:0%
+local
+ 
+
+ align:start position:0%
+local
+okay so I will not do it now but this
+
+ align:start position:0%
+okay so I will not do it now but this
+ 
+
+ align:start position:0%
+okay so I will not do it now but this
+will be important a little bit later so
+
+ align:start position:0%
+will be important a little bit later so
+ 
+
+ align:start position:0%
+will be important a little bit later so
+later we will indeed make it into a
+
+ align:start position:0%
+later we will indeed make it into a
+ 
+
+ align:start position:0%
+later we will indeed make it into a
+local gaug symmetry but for now uh let
+
+ align:start position:0%
+local gaug symmetry but for now uh let
+ 
+
+ align:start position:0%
+local gaug symmetry but for now uh let
+me just consider this simple example
+
+ align:start position:0%
+me just consider this simple example
+ 
+
+ align:start position:0%
+me just consider this simple example
+okay because I don't want to introduce
+
+ align:start position:0%
+okay because I don't want to introduce
+ 
+
+ align:start position:0%
+okay because I don't want to introduce
+too many fields exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so any questions regarding the setup of
+
+ align:start position:0%
+so any questions regarding the setup of
+ 
+
+ align:start position:0%
+so any questions regarding the setup of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+the yes can you explain the last point
+
+ align:start position:0%
+the yes can you explain the last point
+ 
+
+ align:start position:0%
+the yes can you explain the last point
+so so what do you mean that if you how
+
+ align:start position:0%
+so so what do you mean that if you how
+ 
+
+ align:start position:0%
+so so what do you mean that if you how
+does introducing gauge Fields make the
+
+ align:start position:0%
+does introducing gauge Fields make the
+ 
+
+ align:start position:0%
+does introducing gauge Fields make the
+Symmetry local
+
+ align:start position:0%
+Symmetry local
+ 
+
+ align:start position:0%
+Symmetry local
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um yeah you have to take 832
+
+ align:start position:0%
+um yeah you have to take 832
+ 
+
+ align:start position:0%
+um yeah you have to take 832
+4 to know that but the simple way to
+
+ align:start position:0%
+4 to know that but the simple way to
+ 
+
+ align:start position:0%
+4 to know that but the simple way to
+explain
+
+ align:start position:0%
+explain
+ 
+
+ align:start position:0%
+explain
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+um yeah there's no simple way to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explain yeah yeah just say just
+
+ align:start position:0%
+explain yeah yeah just say just
+ 
+
+ align:start position:0%
+explain yeah yeah just say just
+say let me just explain the
+
+ align:start position:0%
+say let me just explain the
+ 
+
+ align:start position:0%
+say let me just explain the
+statement if you introduce some gauge
+
+ align:start position:0%
+statement if you introduce some gauge
+ 
+
+ align:start position:0%
+statement if you introduce some gauge
+field then you can make this U to be
+
+ align:start position:0%
+field then you can make this U to be
+ 
+
+ align:start position:0%
+field then you can make this U to be
+some arbitary function of X rather than
+
+ align:start position:0%
+some arbitary function of X rather than
+ 
+
+ align:start position:0%
+some arbitary function of X rather than
+a constant so that's the statement of a
+
+ align:start position:0%
+a constant so that's the statement of a
+ 
+
+ align:start position:0%
+a constant so that's the statement of a
+local yeah yeah just I can generalize
+
+ align:start position:0%
+local yeah yeah just I can generalize
+ 
+
+ align:start position:0%
+local yeah yeah just I can generalize
+this Theory so that this symmetry become
+
+ align:start position:0%
+this Theory so that this symmetry become
+ 
+
+ align:start position:0%
+this Theory so that this symmetry become
+a local ah be become a symmetry so that
+
+ align:start position:0%
+a local ah be become a symmetry so that
+ 
+
+ align:start position:0%
+a local ah be become a symmetry so that
+you can have arbitary X dependence uh
+
+ align:start position:0%
+you can have arbitary X dependence uh
+ 
+
+ align:start position:0%
+you can have arbitary X dependence uh
+can have arbitary SpaceTime dependence
+
+ align:start position:0%
+can have arbitary SpaceTime dependence
+ 
+
+ align:start position:0%
+can have arbitary SpaceTime dependence
+yeah so right now you must be a
+
+ align:start position:0%
+yeah so right now you must be a
+ 
+
+ align:start position:0%
+yeah so right now you must be a
+constant any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+good okay so
+
+ align:start position:0%
+good okay so
+ 
+
+ align:start position:0%
+good okay so
+now let's just try try to do peration
+
+ align:start position:0%
+now let's just try try to do peration
+ 
+
+ align:start position:0%
+now let's just try try to do peration
+Theory think g s small try to do
+
+ align:start position:0%
+Theory think g s small try to do
+ 
+
+ align:start position:0%
+Theory think g s small try to do
+peration Theory okay so the first thing
+
+ align:start position:0%
+peration Theory okay so the first thing
+ 
+
+ align:start position:0%
+peration Theory okay so the first thing
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+do of course is to write down the fan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rules say first you have look at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+propagator okay look at the
+
+ align:start position:0%
+propagator okay look at the
+ 
+
+ align:start position:0%
+propagator okay look at the
+propagator so you can essentially uh uh
+
+ align:start position:0%
+propagator so you can essentially uh uh
+ 
+
+ align:start position:0%
+propagator so you can essentially uh uh
+uh you are all Fields your exper so just
+
+ align:start position:0%
+uh you are all Fields your exper so just
+ 
+
+ align:start position:0%
+uh you are all Fields your exper so just
+by looking at that grounding then you
+
+ align:start position:0%
+by looking at that grounding then you
+ 
+
+ align:start position:0%
+by looking at that grounding then you
+can immediately write down this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+propagator we can just write down xus
+
+ align:start position:0%
+propagator we can just write down xus
+ 
+
+ align:start position:0%
+propagator we can just write down xus
+y okay so whatever propagator whatever
+
+ align:start position:0%
+y okay so whatever propagator whatever
+ 
+
+ align:start position:0%
+y okay so whatever propagator whatever
+space time dependence let me just call
+
+ align:start position:0%
+space time dependence let me just call
+ 
+
+ align:start position:0%
+space time dependence let me just call
+xus Y but also there's Anri index
+
+ align:start position:0%
+xus Y but also there's Anri index
+ 
+
+ align:start position:0%
+xus Y but also there's Anri index
+structure first there's also g
+
+ align:start position:0%
+structure first there's also g
+ 
+
+ align:start position:0%
+structure first there's also g
+s okay because there's a prefa one of G
+
+ align:start position:0%
+s okay because there's a prefa one of G
+ 
+
+ align:start position:0%
+s okay because there's a prefa one of G
+Square so when you invert the ktic this
+
+ align:start position:0%
+Square so when you invert the ktic this
+ 
+
+ align:start position:0%
+Square so when you invert the ktic this
+G
+
+ align:start position:0%
+G
+ 
+
+ align:start position:0%
+G
+sare and but the index structure is at
+
+ align:start position:0%
+sare and but the index structure is at
+ 
+
+ align:start position:0%
+sare and but the index structure is at
+AB b a so that a must contract with c
+
+ align:start position:0%
+AB b a so that a must contract with c
+ 
+
+ align:start position:0%
+AB b a so that a must contract with c
+and b must be the same as C so that
+
+ align:start position:0%
+and b must be the same as C so that
+ 
+
+ align:start position:0%
+and b must be the same as C so that
+means we have Delta a d and the Delta CB
+
+ align:start position:0%
+means we have Delta a d and the Delta CB
+ 
+
+ align:start position:0%
+means we have Delta a d and the Delta CB
+BC
+
+ align:start position:0%
+BC
+ 
+
+ align:start position:0%
+BC
+okay okay because in the L ground you
+
+ align:start position:0%
+okay okay because in the L ground you
+ 
+
+ align:start position:0%
+okay okay because in the L ground you
+only those field are PA so the
+
+ align:start position:0%
+only those field are PA so the
+ 
+
+ align:start position:0%
+only those field are PA so the
+propagator must have this
+
+ align:start position:0%
+propagator must have this
+ 
+
+ align:start position:0%
+propagator must have this
+structure so same we can write down
+
+ align:start position:0%
+structure so same we can write down
+ 
+
+ align:start position:0%
+structure so same we can write down
+the so there's a four particle
+
+ align:start position:0%
+the so there's a four particle
+ 
+
+ align:start position:0%
+the so there's a four particle
+interaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertex so so each particle have two
+
+ align:start position:0%
+vertex so so each particle have two
+ 
+
+ align:start position:0%
+vertex so so each particle have two
+index so this is
+
+ align:start position:0%
+index so this is
+ 
+
+ align:start position:0%
+index so this is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+CD
+
+ align:start position:0%
+CD
+ 
+
+ align:start position:0%
+CD
+EF oh yeah right sorry let me add one
+
+ align:start position:0%
+EF oh yeah right sorry let me add one
+ 
+
+ align:start position:0%
+EF oh yeah right sorry let me add one
+more and then I can Delo this
+
+ align:start position:0%
+more and then I can Delo this
+ 
+
+ align:start position:0%
+more and then I can Delo this
+diagrammatically just as AB c
+
+ align:start position:0%
+diagrammatically just as AB c
+ 
+
+ align:start position:0%
+diagrammatically just as AB c
+d okay just load this diagrammatic ially
+
+ align:start position:0%
+d okay just load this diagrammatic ially
+ 
+
+ align:start position:0%
+d okay just load this diagrammatic ially
+as the propagator which is W line ABCD
+
+ align:start position:0%
+as the propagator which is W line ABCD
+ 
+
+ align:start position:0%
+as the propagator which is W line ABCD
+okay and now also we have this Quantic
+
+ align:start position:0%
+okay and now also we have this Quantic
+ 
+
+ align:start position:0%
+okay and now also we have this Quantic
+interaction vertices which involve in
+
+ align:start position:0%
+interaction vertices which involve in
+ 
+
+ align:start position:0%
+interaction vertices which involve in
+four Fields so each field have two index
+
+ align:start position:0%
+four Fields so each field have two index
+ 
+
+ align:start position:0%
+four Fields so each field have two index
+because a so a b c d e f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+GH but this is not arital inaction they
+
+ align:start position:0%
+GH but this is not arital inaction they
+ 
+
+ align:start position:0%
+GH but this is not arital inaction they
+have contracted in the inaction
+
+ align:start position:0%
+have contracted in the inaction
+ 
+
+ align:start position:0%
+have contracted in the inaction
+contracted in the specific way so you
+
+ align:start position:0%
+contracted in the specific way so you
+ 
+
+ align:start position:0%
+contracted in the specific way so you
+get 1/ G squ because overall Factor G
+
+ align:start position:0%
+get 1/ G squ because overall Factor G
+ 
+
+ align:start position:0%
+get 1/ G squ because overall Factor G
+square and then you have do
+
+ align:start position:0%
+square and then you have do
+ 
+
+ align:start position:0%
+square and then you have do
+BC do
+
+ align:start position:0%
+BC do
+ 
+
+ align:start position:0%
+BC do
+D DOTA
+
+ align:start position:0%
+D DOTA
+ 
+
+ align:start position:0%
+D DOTA
+FG ha okay because they have to be
+
+ align:start position:0%
+FG ha okay because they have to be
+ 
+
+ align:start position:0%
+FG ha okay because they have to be
+contracted okay better to write it as AB
+
+ align:start position:0%
+contracted okay better to write it as AB
+ 
+
+ align:start position:0%
+contracted okay better to write it as AB
+this way
+
+ align:start position:0%
+this way
+ 
+
+ align:start position:0%
+this way
+AB okay so so a b contracted with c d
+
+ align:start position:0%
+AB okay so so a b contracted with c d
+ 
+
+ align:start position:0%
+AB okay so so a b contracted with c d
+contract with e e contract with g h
+
+ align:start position:0%
+contract with e e contract with g h
+ 
+
+ align:start position:0%
+contract with e e contract with g h
+contract with a so this give you a
+
+ align:start position:0%
+contract with a so this give you a
+ 
+
+ align:start position:0%
+contract with a so this give you a
+matrix product so uh just like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+H um
+
+ align:start position:0%
+H um
+ 
+
+ align:start position:0%
+H um
+a yeah let me just call DC that's right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a fman rule so now you
+
+ align:start position:0%
+okay so this is a fman rule so now you
+ 
+
+ align:start position:0%
+okay so this is a fman rule so now you
+can start
+
+ align:start position:0%
+can start
+ 
+
+ align:start position:0%
+can start
+calculating
+
+ align:start position:0%
+calculating
+ 
+
+ align:start position:0%
+calculating
+okay so if you have calculated this for
+
+ align:start position:0%
+okay so if you have calculated this for
+ 
+
+ align:start position:0%
+okay so if you have calculated this for
+a while then you find this is a little
+
+ align:start position:0%
+a while then you find this is a little
+ 
+
+ align:start position:0%
+a while then you find this is a little
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+tedious with all these indices is it's
+
+ align:start position:0%
+tedious with all these indices is it's
+ 
+
+ align:start position:0%
+tedious with all these indices is it's
+quite a
+
+ align:start position:0%
+quite a
+ 
+
+ align:start position:0%
+quite a
+ling and um but to this a smart to was a
+
+ align:start position:0%
+ling and um but to this a smart to was a
+ 
+
+ align:start position:0%
+ling and um but to this a smart to was a
+smart FAL so he say let me find a way so
+
+ align:start position:0%
+smart FAL so he say let me find a way so
+ 
+
+ align:start position:0%
+smart FAL so he say let me find a way so
+that I don't have to keep track of all
+
+ align:start position:0%
+that I don't have to keep track of all
+ 
+
+ align:start position:0%
+that I don't have to keep track of all
+this indices okay then he invented the
+
+ align:start position:0%
+this indices okay then he invented the
+ 
+
+ align:start position:0%
+this indices okay then he invented the
+very nice way so this is called double
+
+ align:start position:0%
+very nice way so this is called double
+ 
+
+ align:start position:0%
+very nice way so this is called double
+line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation so first
+
+ align:start position:0%
+notation so first
+ 
+
+ align:start position:0%
+notation so first
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+propagator AB B C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D since that a is contracted with c c is
+
+ align:start position:0%
+D since that a is contracted with c c is
+ 
+
+ align:start position:0%
+D since that a is contracted with c c is
+contracted with B separately he said
+
+ align:start position:0%
+contracted with B separately he said
+ 
+
+ align:start position:0%
+contracted with B separately he said
+let's just write it as a double
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line but since there's a difference
+
+ align:start position:0%
+line but since there's a difference
+ 
+
+ align:start position:0%
+line but since there's a difference
+between the upper and lower indices so
+
+ align:start position:0%
+between the upper and lower indices so
+ 
+
+ align:start position:0%
+between the upper and lower indices so
+let's define a direction for this double
+
+ align:start position:0%
+let's define a direction for this double
+ 
+
+ align:start position:0%
+let's define a direction for this double
+line so this should be go so this Define
+
+ align:start position:0%
+line so this should be go so this Define
+ 
+
+ align:start position:0%
+line so this should be go so this Define
+the direction to go from the upper index
+
+ align:start position:0%
+the direction to go from the upper index
+ 
+
+ align:start position:0%
+the direction to go from the upper index
+to the lower index then you will have a
+
+ align:start position:0%
+to the lower index then you will have a
+ 
+
+ align:start position:0%
+to the lower index then you will have a
+then you have D then CB okay because for
+
+ align:start position:0%
+then you have D then CB okay because for
+ 
+
+ align:start position:0%
+then you have D then CB okay because for
+C is upper to lower index you go from CD
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now you have now you don't have
+
+ align:start position:0%
+okay so now you have now you don't have
+ 
+
+ align:start position:0%
+okay so now you have now you don't have
+to worry about this uh Contra this
+
+ align:start position:0%
+to worry about this uh Contra this
+ 
+
+ align:start position:0%
+to worry about this uh Contra this
+anymore because it's automatically taken
+
+ align:start position:0%
+anymore because it's automatically taken
+ 
+
+ align:start position:0%
+anymore because it's automatically taken
+care by this
+
+ align:start position:0%
+care by this
+ 
+
+ align:start position:0%
+care by this
+notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+similarly this one is it's also
+
+ align:start position:0%
+similarly this one is it's also
+ 
+
+ align:start position:0%
+similarly this one is it's also
+automatically taken care
+
+ align:start position:0%
+automatically taken care
+ 
+
+ align:start position:0%
+automatically taken care
+of because each one if you replace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it by the double line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation then you just make it a b then
+
+ align:start position:0%
+rotation then you just make it a b then
+ 
+
+ align:start position:0%
+rotation then you just make it a b then
+B is equal to c b equal to here c equal
+
+ align:start position:0%
+B is equal to c b equal to here c equal
+ 
+
+ align:start position:0%
+B is equal to c b equal to here c equal
+to C D equal to D and a to
+
+ align:start position:0%
+to C D equal to D and a to
+ 
+
+ align:start position:0%
+to C D equal to D and a to
+a okay and then we have g s
+
+ align:start position:0%
+a okay and then we have g s
+ 
+
+ align:start position:0%
+a okay and then we have g s
+here you have G
+
+ align:start position:0%
+here you have G
+ 
+
+ align:start position:0%
+here you have G
+Square okay so once you draw the double
+
+ align:start position:0%
+Square okay so once you draw the double
+ 
+
+ align:start position:0%
+Square okay so once you draw the double
+line notation so let me also draw the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arrow once you have a double annotation
+
+ align:start position:0%
+arrow once you have a double annotation
+ 
+
+ align:start position:0%
+arrow once you have a double annotation
+then all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those the LA in delas they automatic
+
+ align:start position:0%
+those the LA in delas they automatic
+ 
+
+ align:start position:0%
+those the LA in delas they automatic
+taken care
+
+ align:start position:0%
+taken care
+ 
+
+ align:start position:0%
+taken care
+of okay
+
+ align:start position:0%
+of okay
+ 
+
+ align:start position:0%
+of okay
+on the left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+to sorry which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+that if you write oh okay
+
+ align:start position:0%
+that if you write oh okay
+ 
+
+ align:start position:0%
+that if you write oh okay
+um BC that's right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+BC good good
+
+ align:start position:0%
+BC good good
+ 
+
+ align:start position:0%
+BC good good
+good so so now let us give you some
+
+ align:start position:0%
+good so so now let us give you some
+ 
+
+ align:start position:0%
+good so so now let us give you some
+examples of using this diagram to
+
+ align:start position:0%
+examples of using this diagram to
+ 
+
+ align:start position:0%
+examples of using this diagram to
+calculate
+
+ align:start position:0%
+calculate
+ 
+
+ align:start position:0%
+calculate
+things and also try to calculate the
+
+ align:start position:0%
+things and also try to calculate the
+ 
+
+ align:start position:0%
+things and also try to calculate the
+independence because eventually we want
+
+ align:start position:0%
+independence because eventually we want
+ 
+
+ align:start position:0%
+independence because eventually we want
+to take a lar limit okay so we want to
+
+ align:start position:0%
+to take a lar limit okay so we want to
+ 
+
+ align:start position:0%
+to take a lar limit okay so we want to
+keep track of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independence yes uh the four point
+
+ align:start position:0%
+independence yes uh the four point
+ 
+
+ align:start position:0%
+independence yes uh the four point
+coupling uh does it come from the
+
+ align:start position:0%
+coupling uh does it come from the
+ 
+
+ align:start position:0%
+coupling uh does it come from the
+commutator in the F menu and the gaug
+
+ align:start position:0%
+commutator in the F menu and the gaug
+ 
+
+ align:start position:0%
+commutator in the F menu and the gaug
+here no I just rot done by myself okay
+
+ align:start position:0%
+here no I just rot done by myself okay
+ 
+
+ align:start position:0%
+here no I just rot done by myself okay
+so it's an additional thing yeah yeah
+
+ align:start position:0%
+so it's an additional thing yeah yeah
+ 
+
+ align:start position:0%
+so it's an additional thing yeah yeah
+it's it's
+
+ align:start position:0%
+it's it's
+ 
+
+ align:start position:0%
+it's it's
+AR yeah just arbitary field the yeah
+
+ align:start position:0%
+AR yeah just arbitary field the yeah
+ 
+
+ align:start position:0%
+AR yeah just arbitary field the yeah
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example okay so now let's try uh start
+
+ align:start position:0%
+example okay so now let's try uh start
+ 
+
+ align:start position:0%
+example okay so now let's try uh start
+calculating you have already have the
+
+ align:start position:0%
+calculating you have already have the
+ 
+
+ align:start position:0%
+calculating you have already have the
+for f rule what you wait
+
+ align:start position:0%
+for f rule what you wait
+ 
+
+ align:start position:0%
+for f rule what you wait
+for so let's just let's just to
+
+ align:start position:0%
+for so let's just let's just to
+ 
+
+ align:start position:0%
+for so let's just let's just to
+calculate so the first thing let's look
+
+ align:start position:0%
+calculate so the first thing let's look
+ 
+
+ align:start position:0%
+calculate so the first thing let's look
+at the vacuum
+
+ align:start position:0%
+at the vacuum
+ 
+
+ align:start position:0%
+at the vacuum
+energy okay so that's this the first
+
+ align:start position:0%
+energy okay so that's this the first
+ 
+
+ align:start position:0%
+energy okay so that's this the first
+thing to calculate so what's the vacuum
+
+ align:start position:0%
+thing to calculate so what's the vacuum
+ 
+
+ align:start position:0%
+thing to calculate so what's the vacuum
+energy the vacuum energy is all the
+
+ align:start position:0%
+energy the vacuum energy is all the
+ 
+
+ align:start position:0%
+energy the vacuum energy is all the
+diagrams it's a summation of all the
+
+ align:start position:0%
+diagrams it's a summation of all the
+ 
+
+ align:start position:0%
+diagrams it's a summation of all the
+diagram without external LS
+
+ align:start position:0%
+diagram without external LS
+ 
+
+ align:start position:0%
+diagram without external LS
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um yeah let's just so so the so the
+
+ align:start position:0%
+um yeah let's just so so the so the
+ 
+
+ align:start position:0%
+um yeah let's just so so the so the
+simplest
+
+ align:start position:0%
+simplest
+ 
+
+ align:start position:0%
+simplest
+diagram is just the the uh uh the with
+
+ align:start position:0%
+diagram is just the the uh uh the with
+ 
+
+ align:start position:0%
+diagram is just the the uh uh the with
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a simplest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram but
+
+ align:start position:0%
+diagram but
+ 
+
+ align:start position:0%
+diagram but
+now so if you do Lambda 54 series then
+
+ align:start position:0%
+now so if you do Lambda 54 series then
+ 
+
+ align:start position:0%
+now so if you do Lambda 54 series then
+that will be the end of the
+
+ align:start position:0%
+that will be the end of the
+ 
+
+ align:start position:0%
+that will be the end of the
+story
+
+ align:start position:0%
+story
+ 
+
+ align:start position:0%
+story
+okay you just contract of them but
+
+ align:start position:0%
+okay you just contract of them but
+ 
+
+ align:start position:0%
+okay you just contract of them but
+now the Matrix because we are
+
+ align:start position:0%
+now the Matrix because we are
+ 
+
+ align:start position:0%
+now the Matrix because we are
+Contracting
+
+ align:start position:0%
+Contracting
+ 
+
+ align:start position:0%
+Contracting
+matrices okay so this is like
+
+ align:start position:0%
+matrices okay so this is like
+ 
+
+ align:start position:0%
+matrices okay so this is like
+contracting two four matrices when you
+
+ align:start position:0%
+contracting two four matrices when you
+ 
+
+ align:start position:0%
+contracting two four matrices when you
+trting matrices but matrices don't
+
+ align:start position:0%
+trting matrices but matrices don't
+ 
+
+ align:start position:0%
+trting matrices but matrices don't
+commute so actually there's a
+
+ align:start position:0%
+commute so actually there's a
+ 
+
+ align:start position:0%
+commute so actually there's a
+difference so you you should convince
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yourself there's a difference which I
+
+ align:start position:0%
+yourself there's a difference which I
+ 
+
+ align:start position:0%
+yourself there's a difference which I
+actually connect this two this two
+
+ align:start position:0%
+actually connect this two this two
+ 
+
+ align:start position:0%
+actually connect this two this two
+from which I connect this two and this
+
+ align:start position:0%
+from which I connect this two and this
+ 
+
+ align:start position:0%
+from which I connect this two and this
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+okay because this this corresponding I
+
+ align:start position:0%
+okay because this this corresponding I
+ 
+
+ align:start position:0%
+okay because this this corresponding I
+connect the labeling ones and this one I
+
+ align:start position:0%
+connect the labeling ones and this one I
+ 
+
+ align:start position:0%
+connect the labeling ones and this one I
+connect the diagonal ones and the order
+
+ align:start position:0%
+connect the diagonal ones and the order
+ 
+
+ align:start position:0%
+connect the diagonal ones and the order
+actually matters okay the order actually
+
+ align:start position:0%
+actually matters okay the order actually
+ 
+
+ align:start position:0%
+actually matters okay the order actually
+matters because Matrix is don't
+
+ align:start position:0%
+matters because Matrix is don't
+ 
+
+ align:start position:0%
+matters because Matrix is don't
+commute so if I call this
+
+ align:start position:0%
+commute so if I call this
+ 
+
+ align:start position:0%
+commute so if I call this
+a and
+
+ align:start position:0%
+a and
+ 
+
+ align:start position:0%
+a and
+b and a not equal to
+
+ align:start position:0%
+b and a not equal to
+ 
+
+ align:start position:0%
+b and a not equal to
+B because the matrices don't commute
+
+ align:start position:0%
+B because the matrices don't commute
+ 
+
+ align:start position:0%
+B because the matrices don't commute
+okay so now let's do the end
+
+ align:start position:0%
+okay so now let's do the end
+ 
+
+ align:start position:0%
+okay so now let's do the end
+Counting
+
+ align:start position:0%
+Counting
+ 
+
+ align:start position:0%
+Counting
+so do the end counting is actually much
+
+ align:start position:0%
+so do the end counting is actually much
+ 
+
+ align:start position:0%
+so do the end counting is actually much
+simpler we use this double line notation
+
+ align:start position:0%
+simpler we use this double line notation
+ 
+
+ align:start position:0%
+simpler we use this double line notation
+so let's now use the double line
+
+ align:start position:0%
+so let's now use the double line
+ 
+
+ align:start position:0%
+so let's now use the double line
+notation because all this n so when you
+
+ align:start position:0%
+notation because all this n so when you
+ 
+
+ align:start position:0%
+notation because all this n so when you
+do the
+
+ align:start position:0%
+do the
+ 
+
+ align:start position:0%
+do the
+contractions you have all these
+
+ align:start position:0%
+contractions you have all these
+ 
+
+ align:start position:0%
+contractions you have all these
+indices you sum of all those indices
+
+ align:start position:0%
+indices you sum of all those indices
+ 
+
+ align:start position:0%
+indices you sum of all those indices
+when you sum all those indes you get
+
+ align:start position:0%
+when you sum all those indes you get
+ 
+
+ align:start position:0%
+when you sum all those indes you get
+some factors of n so that's how n will
+
+ align:start position:0%
+some factors of n so that's how n will
+ 
+
+ align:start position:0%
+some factors of n so that's how n will
+come will come into this
+
+ align:start position:0%
+come will come into this
+ 
+
+ align:start position:0%
+come will come into this
+the and uh but the but double notation
+
+ align:start position:0%
+the and uh but the but double notation
+ 
+
+ align:start position:0%
+the and uh but the but double notation
+makes makes the constraint all manifest
+
+ align:start position:0%
+makes makes the constraint all manifest
+ 
+
+ align:start position:0%
+makes makes the constraint all manifest
+so the contraction will be automatic you
+
+ align:start position:0%
+so the contraction will be automatic you
+ 
+
+ align:start position:0%
+so the contraction will be automatic you
+don't have to worry about all those
+
+ align:start position:0%
+don't have to worry about all those
+ 
+
+ align:start position:0%
+don't have to worry about all those
+delas so so let's just do that let's
+
+ align:start position:0%
+delas so so let's just do that let's
+ 
+
+ align:start position:0%
+delas so so let's just do that let's
+draw this four point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertex for this one we just Contracting
+
+ align:start position:0%
+vertex for this one we just Contracting
+ 
+
+ align:start position:0%
+vertex for this one we just Contracting
+laboring
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ones for this one we do the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing we
+
+ align:start position:0%
+thing we
+ 
+
+ align:start position:0%
+thing we
+contract nor bring
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once yeah I did not draw very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+okay so so this one should be contracted
+
+ align:start position:0%
+okay so so this one should be contracted
+ 
+
+ align:start position:0%
+okay so so this one should be contracted
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+one this one should be contracted with
+
+ align:start position:0%
+one this one should be contracted with
+ 
+
+ align:start position:0%
+one this one should be contracted with
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and this one contract with this one this
+
+ align:start position:0%
+and this one contract with this one this
+ 
+
+ align:start position:0%
+and this one contract with this one this
+one is contract with that okay this some
+
+ align:start position:0%
+one is contract with that okay this some
+ 
+
+ align:start position:0%
+one is contract with that okay this some
+intersection so now let's come to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+end okay so now here is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+key each
+
+ align:start position:0%
+key each
+ 
+
+ align:start position:0%
+key each
+noop corresponding to a contracted
+
+ align:start position:0%
+noop corresponding to a contracted
+ 
+
+ align:start position:0%
+noop corresponding to a contracted
+indices okay so for example in here this
+
+ align:start position:0%
+indices okay so for example in here this
+ 
+
+ align:start position:0%
+indices okay so for example in here this
+is already a and a and then if you
+
+ align:start position:0%
+is already a and a and then if you
+ 
+
+ align:start position:0%
+is already a and a and then if you
+contract this two then you sum over this
+
+ align:start position:0%
+contract this two then you sum over this
+ 
+
+ align:start position:0%
+contract this two then you sum over this
+a when you calculate the propagator and
+
+ align:start position:0%
+a when you calculate the propagator and
+ 
+
+ align:start position:0%
+a when you calculate the propagator and
+then that give you a fact of n so each
+
+ align:start position:0%
+then that give you a fact of n so each
+ 
+
+ align:start position:0%
+then that give you a fact of n so each
+contract each closed loop essentially
+
+ align:start position:0%
+contract each closed loop essentially
+ 
+
+ align:start position:0%
+contract each closed loop essentially
+give you a factor of n okay it's just
+
+ align:start position:0%
+give you a factor of n okay it's just
+ 
+
+ align:start position:0%
+give you a factor of n okay it's just
+because you contract yeah so there's
+
+ align:start position:0%
+because you contract yeah so there's
+ 
+
+ align:start position:0%
+because you contract yeah so there's
+three Loops here three contracted Loops
+
+ align:start position:0%
+three Loops here three contracted Loops
+ 
+
+ align:start position:0%
+three Loops here three contracted Loops
+so this give you
+
+ align:start position:0%
+so this give you
+ 
+
+ align:start position:0%
+so this give you
+NQ
+
+ align:start position:0%
+NQ
+ 
+
+ align:start position:0%
+NQ
+okay and if you look at the G Square
+
+ align:start position:0%
+okay and if you look at the G Square
+ 
+
+ align:start position:0%
+okay and if you look at the G Square
+dependence so you have two propagators
+
+ align:start position:0%
+dependence so you have two propagators
+ 
+
+ align:start position:0%
+dependence so you have two propagators
+here two pro you have two propagators
+
+ align:start position:0%
+here two pro you have two propagators
+ 
+
+ align:start position:0%
+here two pro you have two propagators
+each propagator give you a g Square then
+
+ align:start position:0%
+each propagator give you a g Square then
+ 
+
+ align:start position:0%
+each propagator give you a g Square then
+you have one vertex each vertex give you
+
+ align:start position:0%
+you have one vertex each vertex give you
+ 
+
+ align:start position:0%
+you have one vertex each vertex give you
+a one of G Square so you have G
+
+ align:start position:0%
+a one of G Square so you have G
+ 
+
+ align:start position:0%
+a one of G Square so you have G
+squ
+
+ align:start position:0%
+squ
+ 
+
+ align:start position:0%
+squ
+okay so now let's look at this
+
+ align:start position:0%
+okay so now let's look at this
+ 
+
+ align:start position:0%
+okay so now let's look at this
+one this one let's just follow this line
+
+ align:start position:0%
+one this one let's just follow this line
+ 
+
+ align:start position:0%
+one this one let's just follow this line
+you should also draw the arrow because
+
+ align:start position:0%
+you should also draw the arrow because
+ 
+
+ align:start position:0%
+you should also draw the arrow because
+the arrow should
+
+ align:start position:0%
+the arrow should
+ 
+
+ align:start position:0%
+the arrow should
+follow okay I did not dra the arrow but
+
+ align:start position:0%
+follow okay I did not dra the arrow but
+ 
+
+ align:start position:0%
+follow okay I did not dra the arrow but
+uh but Arrow should all follow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+follow okay the arrow should be
+
+ align:start position:0%
+follow okay the arrow should be
+ 
+
+ align:start position:0%
+follow okay the arrow should be
+consistent similarly here so here if you
+
+ align:start position:0%
+consistent similarly here so here if you
+ 
+
+ align:start position:0%
+consistent similarly here so here if you
+go around you find there's only a single
+
+ align:start position:0%
+go around you find there's only a single
+ 
+
+ align:start position:0%
+go around you find there's only a single
+contracted N9 so this only a fact of n
+
+ align:start position:0%
+contracted N9 so this only a fact of n
+ 
+
+ align:start position:0%
+contracted N9 so this only a fact of n
+of course G square dependenc is the same
+
+ align:start position:0%
+of course G square dependenc is the same
+ 
+
+ align:start position:0%
+of course G square dependenc is the same
+so you have G
+
+ align:start position:0%
+so you have G
+ 
+
+ align:start position:0%
+so you have G
+Square okay so now you already see the
+
+ align:start position:0%
+Square okay so now you already see the
+ 
+
+ align:start position:0%
+Square okay so now you already see the
+difference between these two diagrams
+
+ align:start position:0%
+difference between these two diagrams
+ 
+
+ align:start position:0%
+difference between these two diagrams
+and uh um why is proportional to n one
+
+ align:start position:0%
+and uh um why is proportional to n one
+ 
+
+ align:start position:0%
+and uh um why is proportional to n one
+is propor to n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cube
+
+ align:start position:0%
+Cube
+ 
+
+ align:start position:0%
+Cube
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+a diagram
+
+ align:start position:0%
+a diagram
+ 
+
+ align:start position:0%
+a diagram
+a can be
+
+ align:start position:0%
+a can be
+ 
+
+ align:start position:0%
+a can be
+drawn on the plane we are joining it on
+
+ align:start position:0%
+drawn on the plane we are joining it on
+ 
+
+ align:start position:0%
+drawn on the plane we are joining it on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+plane without
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crossing without course
+
+ align:start position:0%
+crossing without course
+ 
+
+ align:start position:0%
+crossing without course
+9 so we call it a planner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram and B cannot
+
+ align:start position:0%
+diagram and B cannot
+ 
+
+ align:start position:0%
+diagram and B cannot
+be draw on the plane without causing
+
+ align:start position:0%
+be draw on the plane without causing
+ 
+
+ align:start position:0%
+be draw on the plane without causing
+nines so we call L plan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram
+
+ align:start position:0%
+diagram
+ 
+
+ align:start position:0%
+diagram
+okay so so let's do do one more step so
+
+ align:start position:0%
+okay so so let's do do one more step so
+ 
+
+ align:start position:0%
+okay so so let's do do one more step so
+let's do one more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram so let's do one more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram
+
+ align:start position:0%
+diagram
+ 
+
+ align:start position:0%
+diagram
+okay so select
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order you just get two next all the
+
+ align:start position:0%
+order you just get two next all the
+ 
+
+ align:start position:0%
+order you just get two next all the
+vacum without any external L you have
+
+ align:start position:0%
+vacum without any external L you have
+ 
+
+ align:start position:0%
+vacum without any external L you have
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+vertices okay so you can connect this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way okay so this is one diagram you can
+
+ align:start position:0%
+way okay so this is one diagram you can
+ 
+
+ align:start position:0%
+way okay so this is one diagram you can
+also have plan L plan
+
+ align:start position:0%
+also have plan L plan
+ 
+
+ align:start position:0%
+also have plan L plan
+diagram yeah let me just draw the
+
+ align:start position:0%
+diagram yeah let me just draw the
+ 
+
+ align:start position:0%
+diagram yeah let me just draw the
+straight line rather than wavy line just
+
+ align:start position:0%
+straight line rather than wavy line just
+ 
+
+ align:start position:0%
+straight line rather than wavy line just
+to save
+
+ align:start position:0%
+to save
+ 
+
+ align:start position:0%
+to save
+trouble you can for example you can draw
+
+ align:start position:0%
+trouble you can for example you can draw
+ 
+
+ align:start position:0%
+trouble you can for example you can draw
+like this so This Is A L plan diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now give you a
+
+ align:start position:0%
+okay so now give you a
+ 
+
+ align:start position:0%
+okay so now give you a
+exercise today when you go home turn
+
+ align:start position:0%
+exercise today when you go home turn
+ 
+
+ align:start position:0%
+exercise today when you go home turn
+turn those into a plan uh into a double
+
+ align:start position:0%
+turn those into a plan uh into a double
+ 
+
+ align:start position:0%
+turn those into a plan uh into a double
+line uh diagrams then you should find
+
+ align:start position:0%
+line uh diagrams then you should find
+ 
+
+ align:start position:0%
+line uh diagrams then you should find
+yourself that this is n to the power 4
+
+ align:start position:0%
+yourself that this is n to the power 4
+ 
+
+ align:start position:0%
+yourself that this is n to the power 4
+yeah maybe I should do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um um yeah let me do this one for you so
+
+ align:start position:0%
+um um yeah let me do this one for you so
+ 
+
+ align:start position:0%
+um um yeah let me do this one for you so
+let me just do this one quickly for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but that will allow to draw the arrows
+
+ align:start position:0%
+but that will allow to draw the arrows
+ 
+
+ align:start position:0%
+but that will allow to draw the arrows
+just to save
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay so this
+
+ align:start position:0%
+okay so this
+ 
+
+ align:start position:0%
+okay so this
+one you count how many contracted nines
+
+ align:start position:0%
+one you count how many contracted nines
+ 
+
+ align:start position:0%
+one you count how many contracted nines
+one 2 3 four so this give you an Force
+
+ align:start position:0%
+one 2 3 four so this give you an Force
+ 
+
+ align:start position:0%
+one 2 3 four so this give you an Force
+behavior and this I will not do it now
+
+ align:start position:0%
+behavior and this I will not do it now
+ 
+
+ align:start position:0%
+behavior and this I will not do it now
+you do it yourself so also if you count
+
+ align:start position:0%
+you do it yourself so also if you count
+ 
+
+ align:start position:0%
+you do it yourself so also if you count
+the G dependence this give you g to the
+
+ align:start position:0%
+the G dependence this give you g to the
+ 
+
+ align:start position:0%
+the G dependence this give you g to the
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+4 and this give you n
+
+ align:start position:0%
+4 and this give you n
+ 
+
+ align:start position:0%
+4 and this give you n
+sare g s or G to the power
+
+ align:start position:0%
+sare g s or G to the power
+ 
+
+ align:start position:0%
+sare g s or G to the power
+4 is it g to the power 4 maybe I'm
+
+ align:start position:0%
+4 is it g to the power 4 maybe I'm
+ 
+
+ align:start position:0%
+4 is it g to the power 4 maybe I'm
+counting wrong 1 2 3 4 four propagators
+
+ align:start position:0%
+counting wrong 1 2 3 4 four propagators
+ 
+
+ align:start position:0%
+counting wrong 1 2 3 4 four propagators
+is g s yeah g to the^ 4
+
+ align:start position:0%
+is g s yeah g to the^ 4
+ 
+
+ align:start position:0%
+is g s yeah g to the^ 4
+yeah yes so in general the more is like
+
+ align:start position:0%
+yeah yes so in general the more is like
+ 
+
+ align:start position:0%
+yeah yes so in general the more is like
+the more like Crossings with that
+
+ align:start position:0%
+the more like Crossings with that
+ 
+
+ align:start position:0%
+the more like Crossings with that
+decrease and yeah that's
+
+ align:start position:0%
+decrease and yeah that's
+ 
+
+ align:start position:0%
+decrease and yeah that's
+right okay so now you can just
+
+ align:start position:0%
+right okay so now you can just
+ 
+
+ align:start position:0%
+right okay so now you can just
+continue with three vertices with four
+
+ align:start position:0%
+continue with three vertices with four
+ 
+
+ align:start position:0%
+continue with three vertices with four
+vertices
+
+ align:start position:0%
+vertices
+ 
+
+ align:start position:0%
+vertices
+Etc but of course the smart fellows will
+
+ align:start position:0%
+Etc but of course the smart fellows will
+ 
+
+ align:start position:0%
+Etc but of course the smart fellows will
+not stop and they ask H can I find some
+
+ align:start position:0%
+not stop and they ask H can I find some
+ 
+
+ align:start position:0%
+not stop and they ask H can I find some
+rules in doing this
+
+ align:start position:0%
+rules in doing this
+ 
+
+ align:start position:0%
+rules in doing this
+say how do you get the general en
+
+ align:start position:0%
+say how do you get the general en
+ 
+
+ align:start position:0%
+say how do you get the general en
+counting and whether does the all long
+
+ align:start position:0%
+counting and whether does the all long
+ 
+
+ align:start position:0%
+counting and whether does the all long
+plan the diagram will the same or or one
+
+ align:start position:0%
+plan the diagram will the same or or one
+ 
+
+ align:start position:0%
+plan the diagram will the same or or one
+need to classify them further okay so
+
+ align:start position:0%
+need to classify them further okay so
+ 
+
+ align:start position:0%
+need to classify them further okay so
+these are the obvious questions so let
+
+ align:start position:0%
+these are the obvious questions so let
+ 
+
+ align:start position:0%
+these are the obvious questions so let
+me just tell you some observations then
+
+ align:start position:0%
+me just tell you some observations then
+ 
+
+ align:start position:0%
+me just tell you some observations then
+I will close for
+
+ align:start position:0%
+I will close for
+ 
+
+ align:start position:0%
+I will close for
+today then I will close for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today so the first observation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just from those examples let me just
+
+ align:start position:0%
+so just from those examples let me just
+ 
+
+ align:start position:0%
+so just from those examples let me just
+draw some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observations observation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so this one requires a little bit
+
+ align:start position:0%
+one so this one requires a little bit
+ 
+
+ align:start position:0%
+one so this one requires a little bit
+Inu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ingenuity is said even A and
+
+ align:start position:0%
+Ingenuity is said even A and
+ 
+
+ align:start position:0%
+Ingenuity is said even A and
+B so this A and B they cannot be drawn
+
+ align:start position:0%
+B so this A and B they cannot be drawn
+ 
+
+ align:start position:0%
+B so this A and B they cannot be drawn
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+plane they cannot be they cannot be
+
+ align:start position:0%
+plane they cannot be they cannot be
+ 
+
+ align:start position:0%
+plane they cannot be they cannot be
+drawn on the plane without Crossing
+
+ align:start position:0%
+drawn on the plane without Crossing
+ 
+
+ align:start position:0%
+drawn on the plane without Crossing
+Lines But A and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B can be
+
+ align:start position:0%
+B can be
+ 
+
+ align:start position:0%
+B can be
+drawn on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Taurus without Crossing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lines
+
+ align:start position:0%
+Lines
+ 
+
+ align:start position:0%
+Lines
+okay so so now let me show it to
+
+ align:start position:0%
+okay so so now let me show it to
+ 
+
+ align:start position:0%
+okay so so now let me show it to
+you so so what is a
+
+ align:start position:0%
+you so so what is a
+ 
+
+ align:start position:0%
+you so so what is a
+Taurus so we can draw a taus on the
+
+ align:start position:0%
+Taurus so we can draw a taus on the
+ 
+
+ align:start position:0%
+Taurus so we can draw a taus on the
+plane like follows so we draw a square
+
+ align:start position:0%
+plane like follows so we draw a square
+ 
+
+ align:start position:0%
+plane like follows so we draw a square
+then we identify this side with that
+
+ align:start position:0%
+then we identify this side with that
+ 
+
+ align:start position:0%
+then we identify this side with that
+side identify this side with that side
+
+ align:start position:0%
+side identify this side with that side
+ 
+
+ align:start position:0%
+side identify this side with that side
+then then this give us a Taurus okay so
+
+ align:start position:0%
+then then this give us a Taurus okay so
+ 
+
+ align:start position:0%
+then then this give us a Taurus okay so
+because when you do that then give you a
+
+ align:start position:0%
+because when you do that then give you a
+ 
+
+ align:start position:0%
+because when you do that then give you a
+cylinder and then you do that again then
+
+ align:start position:0%
+cylinder and then you do that again then
+ 
+
+ align:start position:0%
+cylinder and then you do that again then
+give you a taus okay so but on the plane
+
+ align:start position:0%
+give you a taus okay so but on the plane
+ 
+
+ align:start position:0%
+give you a taus okay so but on the plane
+just simple
+
+ align:start position:0%
+just simple
+ 
+
+ align:start position:0%
+just simple
+identification so let's try to see this
+
+ align:start position:0%
+identification so let's try to see this
+ 
+
+ align:start position:0%
+identification so let's try to see this
+diagram now let me show this diagram can
+
+ align:start position:0%
+diagram now let me show this diagram can
+ 
+
+ align:start position:0%
+diagram now let me show this diagram can
+be draw on the turos without
+
+ align:start position:0%
+be draw on the turos without
+ 
+
+ align:start position:0%
+be draw on the turos without
+Crossing because the Vex is like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this we want to contract this guy with
+
+ align:start position:0%
+this we want to contract this guy with
+ 
+
+ align:start position:0%
+this we want to contract this guy with
+that guy and that guy with that guy
+
+ align:start position:0%
+that guy and that guy with that guy
+ 
+
+ align:start position:0%
+that guy and that guy with that guy
+right nonlabeling ones but now I can
+
+ align:start position:0%
+right nonlabeling ones but now I can
+ 
+
+ align:start position:0%
+right nonlabeling ones but now I can
+just go
+
+ align:start position:0%
+just go
+ 
+
+ align:start position:0%
+just go
+up and now this is identified with here
+
+ align:start position:0%
+up and now this is identified with here
+ 
+
+ align:start position:0%
+up and now this is identified with here
+that can come back here can go here come
+
+ align:start position:0%
+that can come back here can go here come
+ 
+
+ align:start position:0%
+that can come back here can go here come
+back here okay so this is contracted and
+
+ align:start position:0%
+back here okay so this is contracted and
+ 
+
+ align:start position:0%
+back here okay so this is contracted and
+I don't have to cross
+
+ align:start position:0%
+I don't have to cross
+ 
+
+ align:start position:0%
+I don't have to cross
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+yes good similarly let me do that
+
+ align:start position:0%
+yes good similarly let me do that
+ 
+
+ align:start position:0%
+yes good similarly let me do that
+one yeah that why maybe I will let you
+
+ align:start position:0%
+one yeah that why maybe I will let you
+ 
+
+ align:start position:0%
+one yeah that why maybe I will let you
+to do it yourself yeah do the so this is
+
+ align:start position:0%
+to do it yourself yeah do the so this is
+ 
+
+ align:start position:0%
+to do it yourself yeah do the so this is
+a this is oh no this is not a and b this
+
+ align:start position:0%
+a this is oh no this is not a and b this
+ 
+
+ align:start position:0%
+a this is oh no this is not a and b this
+is B and D let me call this B this this
+
+ align:start position:0%
+is B and D let me call this B this this
+ 
+
+ align:start position:0%
+is B and D let me call this B this this
+is let me call sorry let me call C and D
+
+ align:start position:0%
+is let me call sorry let me call C and D
+ 
+
+ align:start position:0%
+is let me call sorry let me call C and D
+so A and C are Planet
+
+ align:start position:0%
+so A and C are Planet
+ 
+
+ align:start position:0%
+so A and C are Planet
+diagrams and B and D are long plan
+
+ align:start position:0%
+diagrams and B and D are long plan
+ 
+
+ align:start position:0%
+diagrams and B and D are long plan
+diagrams
+
+ align:start position:0%
+diagrams
+ 
+
+ align:start position:0%
+diagrams
+okay so this is
+
+ align:start position:0%
+okay so this is
+ 
+
+ align:start position:0%
+okay so this is
+p so try to do yourself the
+
+ align:start position:0%
+p so try to do yourself the
+ 
+
+ align:start position:0%
+p so try to do yourself the
+D so essentially you have two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertex how to make that n planner
+
+ align:start position:0%
+vertex how to make that n planner
+ 
+
+ align:start position:0%
+vertex how to make that n planner
+diagram to be Planner on
+
+ align:start position:0%
+diagram to be Planner on
+ 
+
+ align:start position:0%
+diagram to be Planner on
+the on this taus when you identify here
+
+ align:start position:0%
+the on this taus when you identify here
+ 
+
+ align:start position:0%
+the on this taus when you identify here
+with there there is there okay so this
+
+ align:start position:0%
+with there there is there okay so this
+ 
+
+ align:start position:0%
+with there there is there okay so this
+is observation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one actually let me just do it for
+
+ align:start position:0%
+one actually let me just do it for
+ 
+
+ align:start position:0%
+one actually let me just do it for
+you so so we connect because I
+
+ align:start position:0%
+you so so we connect because I
+ 
+
+ align:start position:0%
+you so so we connect because I
+didn't because I it's better I have this
+
+ align:start position:0%
+didn't because I it's better I have this
+ 
+
+ align:start position:0%
+didn't because I it's better I have this
+example to make my second
+
+ align:start position:0%
+example to make my second
+ 
+
+ align:start position:0%
+example to make my second
+point so so now I need to connect this
+
+ align:start position:0%
+point so so now I need to connect this
+ 
+
+ align:start position:0%
+point so so now I need to connect this
+to that guy but I can do it by going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up I can this guy I can go here and then
+
+ align:start position:0%
+up I can this guy I can go here and then
+ 
+
+ align:start position:0%
+up I can this guy I can go here and then
+can go there similar in okay and then
+
+ align:start position:0%
+can go there similar in okay and then
+ 
+
+ align:start position:0%
+can go there similar in okay and then
+this is I can connect them without
+
+ align:start position:0%
+this is I can connect them without
+ 
+
+ align:start position:0%
+this is I can connect them without
+Crossing Lines so this is the
+
+ align:start position:0%
+Crossing Lines so this is the
+ 
+
+ align:start position:0%
+Crossing Lines so this is the
+observation
+
+ align:start position:0%
+observation
+ 
+
+ align:start position:0%
+observation
+one so now the observation
+
+ align:start position:0%
+one so now the observation
+ 
+
+ align:start position:0%
+one so now the observation
+two again is a little bit
+
+ align:start position:0%
+two again is a little bit
+ 
+
+ align:start position:0%
+two again is a little bit
+ingenious but maybe the slightly
+
+ align:start position:0%
+ingenious but maybe the slightly
+ 
+
+ align:start position:0%
+ingenious but maybe the slightly
+easier if you have done it long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enough for all the a to d the following
+
+ align:start position:0%
+enough for all the a to d the following
+ 
+
+ align:start position:0%
+enough for all the a to d the following
+rule is
+
+ align:start position:0%
+rule is
+ 
+
+ align:start position:0%
+rule is
+two the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power of
+
+ align:start position:0%
+power of
+ 
+
+ align:start position:0%
+power of
+n is equal
+
+ align:start position:0%
+n is equal
+ 
+
+ align:start position:0%
+n is equal
+to number of faces so so so this one we
+
+ align:start position:0%
+to number of faces so so so this one we
+ 
+
+ align:start position:0%
+to number of faces so so so this one we
+call so even though there cannot be
+
+ align:start position:0%
+call so even though there cannot be
+ 
+
+ align:start position:0%
+call so even though there cannot be
+cross the the cross lines on the plane
+
+ align:start position:0%
+cross the the cross lines on the plane
+ 
+
+ align:start position:0%
+cross the the cross lines on the plane
+but we can actually straighten them out
+
+ align:start position:0%
+but we can actually straighten them out
+ 
+
+ align:start position:0%
+but we can actually straighten them out
+on the Taurus okay so here we call we
+
+ align:start position:0%
+on the Taurus okay so here we call we
+ 
+
+ align:start position:0%
+on the Taurus okay so here we call we
+can straighten them out on the Taurus so
+
+ align:start position:0%
+can straighten them out on the Taurus so
+ 
+
+ align:start position:0%
+can straighten them out on the Taurus so
+so the second observ is the power N is a
+
+ align:start position:0%
+so the second observ is the power N is a
+ 
+
+ align:start position:0%
+so the second observ is the power N is a
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+faces in each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram
+
+ align:start position:0%
+diagram
+ 
+
+ align:start position:0%
+diagram
+after we stressing it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out okay first let's look at this
+
+ align:start position:0%
+out okay first let's look at this
+ 
+
+ align:start position:0%
+out okay first let's look at this
+diagram this is a planet diagram so
+
+ align:start position:0%
+diagram this is a planet diagram so
+ 
+
+ align:start position:0%
+diagram this is a planet diagram so
+there's one phas
+
+ align:start position:0%
+there's one phas
+ 
+
+ align:start position:0%
+there's one phas
+there's two face and then there's a face
+
+ align:start position:0%
+there's two face and then there's a face
+ 
+
+ align:start position:0%
+there's two face and then there's a face
+outside because this a whole plane so
+
+ align:start position:0%
+outside because this a whole plane so
+ 
+
+ align:start position:0%
+outside because this a whole plane so
+there's three faces so this is n
+
+ align:start position:0%
+there's three faces so this is n
+ 
+
+ align:start position:0%
+there's three faces so this is n
+Cube and the
+
+ align:start position:0%
+Cube and the
+ 
+
+ align:start position:0%
+Cube and the
+B on the
+
+ align:start position:0%
+B on the
+ 
+
+ align:start position:0%
+B on the
+Taurus there's only one face because
+
+ align:start position:0%
+Taurus there's only one face because
+ 
+
+ align:start position:0%
+Taurus there's only one face because
+each region is connected to each other
+
+ align:start position:0%
+each region is connected to each other
+ 
+
+ align:start position:0%
+each region is connected to each other
+okay so there's only one face you see
+
+ align:start position:0%
+okay so there's only one face you see
+ 
+
+ align:start position:0%
+okay so there's only one face you see
+the power
+
+ align:start position:0%
+the power
+ 
+
+ align:start position:0%
+the power
+n so now in C you have one phas you have
+
+ align:start position:0%
+n so now in C you have one phas you have
+ 
+
+ align:start position:0%
+n so now in C you have one phas you have
+two phas you have three phas you have
+
+ align:start position:0%
+two phas you have three phas you have
+ 
+
+ align:start position:0%
+two phas you have three phas you have
+four phas okay so this is n to the^
+
+ align:start position:0%
+four phas okay so this is n to the^
+ 
+
+ align:start position:0%
+four phas okay so this is n to the^
+4 and for this
+
+ align:start position:0%
+4 and for this
+ 
+
+ align:start position:0%
+4 and for this
+one you have one pH corresponding to
+
+ align:start position:0%
+one you have one pH corresponding to
+ 
+
+ align:start position:0%
+one you have one pH corresponding to
+here and then you easily convince
+
+ align:start position:0%
+here and then you easily convince
+ 
+
+ align:start position:0%
+here and then you easily convince
+yourself everything outside everything
+
+ align:start position:0%
+yourself everything outside everything
+ 
+
+ align:start position:0%
+yourself everything outside everything
+outside this region they're connected
+
+ align:start position:0%
+outside this region they're connected
+ 
+
+ align:start position:0%
+outside this region they're connected
+through the identification so you so you
+
+ align:start position:0%
+through the identification so you so you
+ 
+
+ align:start position:0%
+through the identification so you so you
+get n
+
+ align:start position:0%
+get n
+ 
+
+ align:start position:0%
+get n
+Square okay you get n
+
+ align:start position:0%
+Square okay you get n
+ 
+
+ align:start position:0%
+Square okay you get n
+Square so so these two observations so
+
+ align:start position:0%
+Square so so these two observations so
+ 
+
+ align:start position:0%
+Square so so these two observations so
+so let me stop here and then then from
+
+ align:start position:0%
+so let me stop here and then then from
+ 
+
+ align:start position:0%
+so let me stop here and then then from
+here you can figure out the general
+
+ align:start position:0%
+here you can figure out the general
+ 
+
+ align:start position:0%
+here you can figure out the general
+rules for for uh uh for yeah for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everything
\ No newline at end of file
diff --git a/2XraaWefBd8.txt b/2XraaWefBd8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6c83e7c4b7c07073799ac7718fc11ce510a4100f
--- /dev/null
+++ b/2XraaWefBd8.txt
@@ -0,0 +1,7315 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay so remember last
+
+ align:start position:0%
+ocw.mit.edu okay so remember last
+ 
+
+ align:start position:0%
+ocw.mit.edu okay so remember last
+time on Tuesday we learned about the
+
+ align:start position:0%
+time on Tuesday we learned about the
+ 
+
+ align:start position:0%
+time on Tuesday we learned about the
+chain hole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so for example we saw that if we
+
+ align:start position:0%
+and so for example we saw that if we
+ 
+
+ align:start position:0%
+and so for example we saw that if we
+have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function that
+
+ align:start position:0%
+function that
+ 
+
+ align:start position:0%
+function that
+depends sorry on three variables XY Z
+
+ align:start position:0%
+depends sorry on three variables XY Z
+ 
+
+ align:start position:0%
+depends sorry on three variables XY Z
+but XYZ themselves depends depend on
+
+ align:start position:0%
+but XYZ themselves depends depend on
+ 
+
+ align:start position:0%
+but XYZ themselves depends depend on
+some variable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T then you can find a formula for DW DT
+
+ align:start position:0%
+T then you can find a formula for DW DT
+ 
+
+ align:start position:0%
+T then you can find a formula for DW DT
+by writing down w subx DX
+
+ align:start position:0%
+by writing down w subx DX
+ 
+
+ align:start position:0%
+by writing down w subx DX
+DT plus W suby Dy
+
+ align:start position:0%
+DT plus W suby Dy
+ 
+
+ align:start position:0%
+DT plus W suby Dy
+DT plus W subz DZ DT and the meaning of
+
+ align:start position:0%
+DT plus W subz DZ DT and the meaning of
+ 
+
+ align:start position:0%
+DT plus W subz DZ DT and the meaning of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+formula is that well the change in W is
+
+ align:start position:0%
+formula is that well the change in W is
+ 
+
+ align:start position:0%
+formula is that well the change in W is
+caused by changes in X Y and Z x y and z
+
+ align:start position:0%
+caused by changes in X Y and Z x y and z
+ 
+
+ align:start position:0%
+caused by changes in X Y and Z x y and z
+change at rates dxdt dydt dzdt and this
+
+ align:start position:0%
+change at rates dxdt dydt dzdt and this
+ 
+
+ align:start position:0%
+change at rates dxdt dydt dzdt and this
+causes the function to change
+
+ align:start position:0%
+causes the function to change
+ 
+
+ align:start position:0%
+causes the function to change
+accordingly using the in terms of the
+
+ align:start position:0%
+accordingly using the in terms of the
+ 
+
+ align:start position:0%
+accordingly using the in terms of the
+partial well the partial derivatives
+
+ align:start position:0%
+partial well the partial derivatives
+ 
+
+ align:start position:0%
+partial well the partial derivatives
+tell you how sensitive W is to changes
+
+ align:start position:0%
+tell you how sensitive W is to changes
+ 
+
+ align:start position:0%
+tell you how sensitive W is to changes
+in each
+
+ align:start position:0%
+in each
+ 
+
+ align:start position:0%
+in each
+variable okay so we're going to just
+
+ align:start position:0%
+variable okay so we're going to just
+ 
+
+ align:start position:0%
+variable okay so we're going to just
+revite this in a new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation so I'm going to revite this in
+
+ align:start position:0%
+notation so I'm going to revite this in
+ 
+
+ align:start position:0%
+notation so I'm going to revite this in
+a more concise form
+
+ align:start position:0%
+a more concise form
+ 
+
+ align:start position:0%
+a more concise form
+as gradient of w product with the
+
+ align:start position:0%
+as gradient of w product with the
+ 
+
+ align:start position:0%
+as gradient of w product with the
+velocity Vector
+
+ align:start position:0%
+velocity Vector
+ 
+
+ align:start position:0%
+velocity Vector
+drdt
+
+ align:start position:0%
+drdt
+ 
+
+ align:start position:0%
+drdt
+where so the gradient of w is a vector
+
+ align:start position:0%
+where so the gradient of w is a vector
+ 
+
+ align:start position:0%
+where so the gradient of w is a vector
+formed by putting together all of the
+
+ align:start position:0%
+formed by putting together all of the
+ 
+
+ align:start position:0%
+formed by putting together all of the
+partial
+
+ align:start position:0%
+partial
+ 
+
+ align:start position:0%
+partial
+derivatives okay so it's the vector
+
+ align:start position:0%
+derivatives okay so it's the vector
+ 
+
+ align:start position:0%
+derivatives okay so it's the vector
+whose components are the partials and of
+
+ align:start position:0%
+whose components are the partials and of
+ 
+
+ align:start position:0%
+whose components are the partials and of
+course it's a vector that depends on X Y
+
+ align:start position:0%
+course it's a vector that depends on X Y
+ 
+
+ align:start position:0%
+course it's a vector that depends on X Y
+and Z right these guys depend on XYZ so
+
+ align:start position:0%
+and Z right these guys depend on XYZ so
+ 
+
+ align:start position:0%
+and Z right these guys depend on XYZ so
+it's actually one vector for each point
+
+ align:start position:0%
+it's actually one vector for each point
+ 
+
+ align:start position:0%
+it's actually one vector for each point
+XYZ you can talk about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradient
+
+ align:start position:0%
+gradient
+ 
+
+ align:start position:0%
+gradient
+of w at some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+XYZ so at each point it gives you a
+
+ align:start position:0%
+XYZ so at each point it gives you a
+ 
+
+ align:start position:0%
+XYZ so at each point it gives you a
+vector that actually is what we will
+
+ align:start position:0%
+vector that actually is what we will
+ 
+
+ align:start position:0%
+vector that actually is what we will
+call later a vector
+
+ align:start position:0%
+call later a vector
+ 
+
+ align:start position:0%
+call later a vector
+field but we'll get we'll get back to
+
+ align:start position:0%
+field but we'll get we'll get back to
+ 
+
+ align:start position:0%
+field but we'll get we'll get back to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+later and
+
+ align:start position:0%
+later and
+ 
+
+ align:start position:0%
+later and
+drdt is just the velocity vector
+
+ align:start position:0%
+drdt is just the velocity vector
+ 
+
+ align:start position:0%
+drdt is just the velocity vector
+dxdt dydt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT okay
+
+ align:start position:0%
+DT okay
+ 
+
+ align:start position:0%
+DT okay
+so the new definition for
+
+ align:start position:0%
+so the new definition for
+ 
+
+ align:start position:0%
+so the new definition for
+today is the definition of the gradient
+
+ align:start position:0%
+today is the definition of the gradient
+ 
+
+ align:start position:0%
+today is the definition of the gradient
+vector and our goal will be to
+
+ align:start position:0%
+vector and our goal will be to
+ 
+
+ align:start position:0%
+vector and our goal will be to
+understand a bit better what does this
+
+ align:start position:0%
+understand a bit better what does this
+ 
+
+ align:start position:0%
+understand a bit better what does this
+Vector mean what does it measure and
+
+ align:start position:0%
+Vector mean what does it measure and
+ 
+
+ align:start position:0%
+Vector mean what does it measure and
+what can we do with
+
+ align:start position:0%
+what can we do with
+ 
+
+ align:start position:0%
+what can we do with
+it but you see that in terms of
+
+ align:start position:0%
+it but you see that in terms of
+ 
+
+ align:start position:0%
+it but you see that in terms of
+information content it's really the same
+
+ align:start position:0%
+information content it's really the same
+ 
+
+ align:start position:0%
+information content it's really the same
+information that's already in the
+
+ align:start position:0%
+information that's already in the
+ 
+
+ align:start position:0%
+information that's already in the
+partial derivative
+
+ align:start position:0%
+partial derivative
+ 
+
+ align:start position:0%
+partial derivative
+are in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yes and I should say of course you
+
+ align:start position:0%
+so yes and I should say of course you
+ 
+
+ align:start position:0%
+so yes and I should say of course you
+can also use the gradient in other
+
+ align:start position:0%
+can also use the gradient in other
+ 
+
+ align:start position:0%
+can also use the gradient in other
+things like approximation formulas and
+
+ align:start position:0%
+things like approximation formulas and
+ 
+
+ align:start position:0%
+things like approximation formulas and
+so on it's just so far it's just
+
+ align:start position:0%
+so on it's just so far it's just
+ 
+
+ align:start position:0%
+so on it's just so far it's just
+notation it's a way to rewrite things
+
+ align:start position:0%
+notation it's a way to rewrite things
+ 
+
+ align:start position:0%
+notation it's a way to rewrite things
+but so here's the first pool property of
+
+ align:start position:0%
+but so here's the first pool property of
+ 
+
+ align:start position:0%
+but so here's the first pool property of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradient so
+
+ align:start position:0%
+gradient so
+ 
+
+ align:start position:0%
+gradient so
+so I claim that the gradient Vector is
+
+ align:start position:0%
+so I claim that the gradient Vector is
+ 
+
+ align:start position:0%
+so I claim that the gradient Vector is
+perpendicular to the level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface corresponding
+
+ align:start position:0%
+surface corresponding
+ 
+
+ align:start position:0%
+surface corresponding
+to setting the function W equal to a
+
+ align:start position:0%
+to setting the function W equal to a
+ 
+
+ align:start position:0%
+to setting the function W equal to a
+constant okay
+
+ align:start position:0%
+constant okay
+ 
+
+ align:start position:0%
+constant okay
+so if I draw a contour
+
+ align:start position:0%
+so if I draw a contour
+ 
+
+ align:start position:0%
+so if I draw a contour
+plot of my function so I'm going to
+
+ align:start position:0%
+plot of my function so I'm going to
+ 
+
+ align:start position:0%
+plot of my function so I'm going to
+actually forget about Z because I want
+
+ align:start position:0%
+actually forget about Z because I want
+ 
+
+ align:start position:0%
+actually forget about Z because I want
+to draw a two variable contol plot so
+
+ align:start position:0%
+to draw a two variable contol plot so
+ 
+
+ align:start position:0%
+to draw a two variable contol plot so
+say I have a function of two variables X
+
+ align:start position:0%
+say I have a function of two variables X
+ 
+
+ align:start position:0%
+say I have a function of two variables X
+and Y then maybe it has some Contour
+
+ align:start position:0%
+and Y then maybe it has some Contour
+ 
+
+ align:start position:0%
+and Y then maybe it has some Contour
+plot and I'm saying if I take the
+
+ align:start position:0%
+plot and I'm saying if I take the
+ 
+
+ align:start position:0%
+plot and I'm saying if I take the
+gradient of the function at this point
+
+ align:start position:0%
+gradient of the function at this point
+ 
+
+ align:start position:0%
+gradient of the function at this point
+XY so I will have a vector well if I
+
+ align:start position:0%
+XY so I will have a vector well if I
+ 
+
+ align:start position:0%
+XY so I will have a vector well if I
+draw that Vector on top of a contour
+
+ align:start position:0%
+draw that Vector on top of a contour
+ 
+
+ align:start position:0%
+draw that Vector on top of a contour
+plot it's going to end up being
+
+ align:start position:0%
+plot it's going to end up being
+ 
+
+ align:start position:0%
+plot it's going to end up being
+perpendicular to the level curve at this
+
+ align:start position:0%
+perpendicular to the level curve at this
+ 
+
+ align:start position:0%
+perpendicular to the level curve at this
+point same thing if I have a function of
+
+ align:start position:0%
+point same thing if I have a function of
+ 
+
+ align:start position:0%
+point same thing if I have a function of
+three variables then I can try to draw
+
+ align:start position:0%
+three variables then I can try to draw
+ 
+
+ align:start position:0%
+three variables then I can try to draw
+its Contour plot of course I can't
+
+ align:start position:0%
+its Contour plot of course I can't
+ 
+
+ align:start position:0%
+its Contour plot of course I can't
+really do it because the Contour plot
+
+ align:start position:0%
+really do it because the Contour plot
+ 
+
+ align:start position:0%
+really do it because the Contour plot
+would be you know living in space with X
+
+ align:start position:0%
+would be you know living in space with X
+ 
+
+ align:start position:0%
+would be you know living in space with X
+Y and Z but it would be a bunch of level
+
+ align:start position:0%
+Y and Z but it would be a bunch of level
+ 
+
+ align:start position:0%
+Y and Z but it would be a bunch of level
+surfaces and the gradient Vector would
+
+ align:start position:0%
+surfaces and the gradient Vector would
+ 
+
+ align:start position:0%
+surfaces and the gradient Vector would
+be a vector in space that Vector is
+
+ align:start position:0%
+be a vector in space that Vector is
+ 
+
+ align:start position:0%
+be a vector in space that Vector is
+perpendicular to the level
+
+ align:start position:0%
+perpendicular to the level
+ 
+
+ align:start position:0%
+perpendicular to the level
+surfaces so let's try to see that on a
+
+ align:start position:0%
+surfaces so let's try to see that on a
+ 
+
+ align:start position:0%
+surfaces so let's try to see that on a
+couple of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples so let's do a first example
+
+ align:start position:0%
+examples so let's do a first example
+ 
+
+ align:start position:0%
+examples so let's do a first example
+let's do
+
+ align:start position:0%
+let's do
+ 
+
+ align:start position:0%
+let's do
+things you know what's the easiest case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take a linear function of X Y and
+
+ align:start position:0%
+let's take a linear function of X Y and
+ 
+
+ align:start position:0%
+let's take a linear function of X Y and
+Z so I will take W equals A1 * X Plus A2
+
+ align:start position:0%
+Z so I will take W equals A1 * X Plus A2
+ 
+
+ align:start position:0%
+Z so I will take W equals A1 * X Plus A2
+* y plus A3 *
+
+ align:start position:0%
+* y plus A3 *
+ 
+
+ align:start position:0%
+* y plus A3 *
+Z
+
+ align:start position:0%
+Z
+ 
+
+ align:start position:0%
+Z
+well so what's the gradient of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function well the first component will
+
+ align:start position:0%
+function well the first component will
+ 
+
+ align:start position:0%
+function well the first component will
+be A1 that's partial W partial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X then A2 that's partial W partial Y and
+
+ align:start position:0%
+X then A2 that's partial W partial Y and
+ 
+
+ align:start position:0%
+X then A2 that's partial W partial Y and
+A3 partial W partial Z okay
+
+ align:start position:0%
+A3 partial W partial Z okay
+ 
+
+ align:start position:0%
+A3 partial W partial Z okay
+now what are the level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surfaces well if I set W equal to some
+
+ align:start position:0%
+surfaces well if I set W equal to some
+ 
+
+ align:start position:0%
+surfaces well if I set W equal to some
+constant C that means I look at the
+
+ align:start position:0%
+constant C that means I look at the
+ 
+
+ align:start position:0%
+constant C that means I look at the
+points where a1x + A2 y plus f p z
+
+ align:start position:0%
+points where a1x + A2 y plus f p z
+ 
+
+ align:start position:0%
+points where a1x + A2 y plus f p z
+equals c what kind of surface is that
+
+ align:start position:0%
+equals c what kind of surface is that
+ 
+
+ align:start position:0%
+equals c what kind of surface is that
+it's a plane
+
+ align:start position:0%
+it's a plane
+ 
+
+ align:start position:0%
+it's a plane
+and we know how to find a normal Vector
+
+ align:start position:0%
+and we know how to find a normal Vector
+ 
+
+ align:start position:0%
+and we know how to find a normal Vector
+to this plane just by looking at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coefficients so it's a plane with normal
+
+ align:start position:0%
+coefficients so it's a plane with normal
+ 
+
+ align:start position:0%
+coefficients so it's a plane with normal
+Vector exactly this
+
+ align:start position:0%
+Vector exactly this
+ 
+
+ align:start position:0%
+Vector exactly this
+gradient and in fact you know in a way
+
+ align:start position:0%
+gradient and in fact you know in a way
+ 
+
+ align:start position:0%
+gradient and in fact you know in a way
+this is the only case you need to check
+
+ align:start position:0%
+this is the only case you need to check
+ 
+
+ align:start position:0%
+this is the only case you need to check
+because of linear approximation if you
+
+ align:start position:0%
+because of linear approximation if you
+ 
+
+ align:start position:0%
+because of linear approximation if you
+replace a function by its linear
+
+ align:start position:0%
+replace a function by its linear
+ 
+
+ align:start position:0%
+replace a function by its linear
+approximation that means you will
+
+ align:start position:0%
+approximation that means you will
+ 
+
+ align:start position:0%
+approximation that means you will
+replace the level surfaces by their
+
+ align:start position:0%
+replace the level surfaces by their
+ 
+
+ align:start position:0%
+replace the level surfaces by their
+tangent planes and then you will
+
+ align:start position:0%
+tangent planes and then you will
+ 
+
+ align:start position:0%
+tangent planes and then you will
+actually end up in this situation but
+
+ align:start position:0%
+actually end up in this situation but
+ 
+
+ align:start position:0%
+actually end up in this situation but
+maybe that's not very convincing so
+
+ align:start position:0%
+maybe that's not very convincing so
+ 
+
+ align:start position:0%
+maybe that's not very convincing so
+let's do another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+so let's do a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example let's say we look at the
+
+ align:start position:0%
+example let's say we look at the
+ 
+
+ align:start position:0%
+example let's say we look at the
+function x² + y^2 okay so now it's a
+
+ align:start position:0%
+function x² + y^2 okay so now it's a
+ 
+
+ align:start position:0%
+function x² + y^2 okay so now it's a
+function of just two variables because
+
+ align:start position:0%
+function of just two variables because
+ 
+
+ align:start position:0%
+function of just two variables because
+that way I will be able to actually draw
+
+ align:start position:0%
+that way I will be able to actually draw
+ 
+
+ align:start position:0%
+that way I will be able to actually draw
+a picture for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you okay so what are the level sets of
+
+ align:start position:0%
+you okay so what are the level sets of
+ 
+
+ align:start position:0%
+you okay so what are the level sets of
+this function well they're going to be
+
+ align:start position:0%
+this function well they're going to be
+ 
+
+ align:start position:0%
+this function well they're going to be
+circles
+
+ align:start position:0%
+circles
+ 
+
+ align:start position:0%
+circles
+right wal C is a
+
+ align:start position:0%
+right wal C is a
+ 
+
+ align:start position:0%
+right wal C is a
+circle X2 + Y2 =
+
+ align:start position:0%
+circle X2 + Y2 =
+ 
+
+ align:start position:0%
+circle X2 + Y2 =
+C so you should say maybe sorry say the
+
+ align:start position:0%
+C so you should say maybe sorry say the
+ 
+
+ align:start position:0%
+C so you should say maybe sorry say the
+level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve is a circle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the Contour plot looks something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that now what's the gradient
+
+ align:start position:0%
+that now what's the gradient
+ 
+
+ align:start position:0%
+that now what's the gradient
+Vector well the gradient of this
+
+ align:start position:0%
+Vector well the gradient of this
+ 
+
+ align:start position:0%
+Vector well the gradient of this
+function so partial W partial X
+
+ align:start position:0%
+function so partial W partial X
+ 
+
+ align:start position:0%
+function so partial W partial X
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+2X and Par W par Y is 2 y so let's say I
+
+ align:start position:0%
+2X and Par W par Y is 2 y so let's say I
+ 
+
+ align:start position:0%
+2X and Par W par Y is 2 y so let's say I
+take a point x comma y
+
+ align:start position:0%
+take a point x comma y
+ 
+
+ align:start position:0%
+take a point x comma y
+and I try to draw my gradiant Vector so
+
+ align:start position:0%
+and I try to draw my gradiant Vector so
+ 
+
+ align:start position:0%
+and I try to draw my gradiant Vector so
+here at
+
+ align:start position:0%
+here at
+ 
+
+ align:start position:0%
+here at
+XY so I have to draw the vector 2x 2 Y
+
+ align:start position:0%
+XY so I have to draw the vector 2x 2 Y
+ 
+
+ align:start position:0%
+XY so I have to draw the vector 2x 2 Y
+what does it look
+
+ align:start position:0%
+what does it look
+ 
+
+ align:start position:0%
+what does it look
+like well it's going in that direction
+
+ align:start position:0%
+like well it's going in that direction
+ 
+
+ align:start position:0%
+like well it's going in that direction
+it's parallel to the
+
+ align:start position:0%
+it's parallel to the
+ 
+
+ align:start position:0%
+it's parallel to the
+position Vector for this point and it's
+
+ align:start position:0%
+position Vector for this point and it's
+ 
+
+ align:start position:0%
+position Vector for this point and it's
+actually twice the position Vector so I
+
+ align:start position:0%
+actually twice the position Vector so I
+ 
+
+ align:start position:0%
+actually twice the position Vector so I
+guess it goes more or less like
+
+ align:start position:0%
+guess it goes more or less like
+ 
+
+ align:start position:0%
+guess it goes more or less like
+this what's interesting to us is it is
+
+ align:start position:0%
+this what's interesting to us is it is
+ 
+
+ align:start position:0%
+this what's interesting to us is it is
+perpendicular to this
+
+ align:start position:0%
+perpendicular to this
+ 
+
+ align:start position:0%
+perpendicular to this
+circle okay so it's a general feature
+
+ align:start position:0%
+circle okay so it's a general feature
+ 
+
+ align:start position:0%
+circle okay so it's a general feature
+let me show
+
+ align:start position:0%
+let me show
+ 
+
+ align:start position:0%
+let me show
+you more
+
+ align:start position:0%
+you more
+ 
+
+ align:start position:0%
+you more
+examples oops not the one I
+
+ align:start position:0%
+examples oops not the one I
+ 
+
+ align:start position:0%
+examples oops not the one I
+want so I don't know if you can see it
+
+ align:start position:0%
+want so I don't know if you can see it
+ 
+
+ align:start position:0%
+want so I don't know if you can see it
+so well well hopefully you can so here I
+
+ align:start position:0%
+so well well hopefully you can so here I
+ 
+
+ align:start position:0%
+so well well hopefully you can so here I
+have a contour plot of a function and I
+
+ align:start position:0%
+have a contour plot of a function and I
+ 
+
+ align:start position:0%
+have a contour plot of a function and I
+have a blue Vector that's the gradient
+
+ align:start position:0%
+have a blue Vector that's the gradient
+ 
+
+ align:start position:0%
+have a blue Vector that's the gradient
+Vector at the pink point on the plot so
+
+ align:start position:0%
+Vector at the pink point on the plot so
+ 
+
+ align:start position:0%
+Vector at the pink point on the plot so
+can see I can move the pink point and
+
+ align:start position:0%
+can see I can move the pink point and
+ 
+
+ align:start position:0%
+can see I can move the pink point and
+the gradient Vector of course changes
+
+ align:start position:0%
+the gradient Vector of course changes
+ 
+
+ align:start position:0%
+the gradient Vector of course changes
+because the gradient depends on X and Y
+
+ align:start position:0%
+because the gradient depends on X and Y
+ 
+
+ align:start position:0%
+because the gradient depends on X and Y
+but what doesn't change is that it's
+
+ align:start position:0%
+but what doesn't change is that it's
+ 
+
+ align:start position:0%
+but what doesn't change is that it's
+always perpendicular to the level
+
+ align:start position:0%
+always perpendicular to the level
+ 
+
+ align:start position:0%
+always perpendicular to the level
+curves anywhere where I
+
+ align:start position:0%
+curves anywhere where I
+ 
+
+ align:start position:0%
+curves anywhere where I
+am my gradient stays
+
+ align:start position:0%
+am my gradient stays
+ 
+
+ align:start position:0%
+am my gradient stays
+perpendicular to the level
+
+ align:start position:0%
+perpendicular to the level
+ 
+
+ align:start position:0%
+perpendicular to the level
+curve okay is that convincing is that
+
+ align:start position:0%
+curve okay is that convincing is that
+ 
+
+ align:start position:0%
+curve okay is that convincing is that
+visible even for people who can see
+
+ align:start position:0%
+visible even for people who can see
+ 
+
+ align:start position:0%
+visible even for people who can see
+blue okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay so we have a lot of evidence but
+
+ align:start position:0%
+so okay so we have a lot of evidence but
+ 
+
+ align:start position:0%
+so okay so we have a lot of evidence but
+you know let's try to prove the theorem
+
+ align:start position:0%
+you know let's try to prove the theorem
+ 
+
+ align:start position:0%
+you know let's try to prove the theorem
+because it will
+
+ align:start position:0%
+because it will
+ 
+
+ align:start position:0%
+because it will
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so oh first of all sorry any questions
+
+ align:start position:0%
+so oh first of all sorry any questions
+ 
+
+ align:start position:0%
+so oh first of all sorry any questions
+about the statement the examples
+
+ align:start position:0%
+about the statement the examples
+ 
+
+ align:start position:0%
+about the statement the examples
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah very good question does the gradient
+
+ align:start position:0%
+ah very good question does the gradient
+ 
+
+ align:start position:0%
+ah very good question does the gradient
+Vector why is the gradient Vector
+
+ align:start position:0%
+Vector why is the gradient Vector
+ 
+
+ align:start position:0%
+Vector why is the gradient Vector
+perpendicular in One Direction rather
+
+ align:start position:0%
+perpendicular in One Direction rather
+ 
+
+ align:start position:0%
+perpendicular in One Direction rather
+than the other so we'll see the answer
+
+ align:start position:0%
+than the other so we'll see the answer
+ 
+
+ align:start position:0%
+than the other so we'll see the answer
+to that in a few minutes but let me just
+
+ align:start position:0%
+to that in a few minutes but let me just
+ 
+
+ align:start position:0%
+to that in a few minutes but let me just
+tell you
+
+ align:start position:0%
+tell you
+ 
+
+ align:start position:0%
+tell you
+immediately uh to decide which side it's
+
+ align:start position:0%
+immediately uh to decide which side it's
+ 
+
+ align:start position:0%
+immediately uh to decide which side it's
+pointing to it's always pointing towards
+
+ align:start position:0%
+pointing to it's always pointing towards
+ 
+
+ align:start position:0%
+pointing to it's always pointing towards
+higher values of a function okay and
+
+ align:start position:0%
+higher values of a function okay and
+ 
+
+ align:start position:0%
+higher values of a function okay and
+we'll see that maybe in about half an
+
+ align:start position:0%
+we'll see that maybe in about half an
+ 
+
+ align:start position:0%
+we'll see that maybe in about half an
+hour
+
+ align:start position:0%
+hour
+ 
+
+ align:start position:0%
+hour
+so well let me say actually
+
+ align:start position:0%
+so well let me say actually
+ 
+
+ align:start position:0%
+so well let me say actually
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+towards higher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+w okay any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions I don't see any questions so
+
+ align:start position:0%
+questions I don't see any questions so
+ 
+
+ align:start position:0%
+questions I don't see any questions so
+okay so let's try to prove this theorem
+
+ align:start position:0%
+okay so let's try to prove this theorem
+ 
+
+ align:start position:0%
+okay so let's try to prove this theorem
+at least this part of the theorem we are
+
+ align:start position:0%
+at least this part of the theorem we are
+ 
+
+ align:start position:0%
+at least this part of the theorem we are
+not going to prove that just yet that
+
+ align:start position:0%
+not going to prove that just yet that
+ 
+
+ align:start position:0%
+not going to prove that just yet that
+will come in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+while
+
+ align:start position:0%
+while
+ 
+
+ align:start position:0%
+while
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+well maybe we want to understand first
+
+ align:start position:0%
+well maybe we want to understand first
+ 
+
+ align:start position:0%
+well maybe we want to understand first
+what happens if we move inside the level
+
+ align:start position:0%
+what happens if we move inside the level
+ 
+
+ align:start position:0%
+what happens if we move inside the level
+curve okay so let's imagine that we're
+
+ align:start position:0%
+curve okay so let's imagine that we're
+ 
+
+ align:start position:0%
+curve okay so let's imagine that we're
+taking a moving point that stays on the
+
+ align:start position:0%
+taking a moving point that stays on the
+ 
+
+ align:start position:0%
+taking a moving point that stays on the
+level curve or on the level
+
+ align:start position:0%
+level curve or on the level
+ 
+
+ align:start position:0%
+level curve or on the level
+surface and then we know well what
+
+ align:start position:0%
+surface and then we know well what
+ 
+
+ align:start position:0%
+surface and then we know well what
+happens is that the function stays
+
+ align:start position:0%
+happens is that the function stays
+ 
+
+ align:start position:0%
+happens is that the function stays
+constant but we can also know how
+
+ align:start position:0%
+constant but we can also know how
+ 
+
+ align:start position:0%
+constant but we can also know how
+quickly the function changes using the
+
+ align:start position:0%
+quickly the function changes using the
+ 
+
+ align:start position:0%
+quickly the function changes using the
+chain rule up there so maybe the chain
+
+ align:start position:0%
+chain rule up there so maybe the chain
+ 
+
+ align:start position:0%
+chain rule up there so maybe the chain
+rule will actually be the key to
+
+ align:start position:0%
+rule will actually be the key to
+ 
+
+ align:start position:0%
+rule will actually be the key to
+understanding how the gradient vector
+
+ align:start position:0%
+understanding how the gradient vector
+ 
+
+ align:start position:0%
+understanding how the gradient vector
+and a motion on the level surface
+
+ align:start position:0%
+and a motion on the level surface
+ 
+
+ align:start position:0%
+and a motion on the level surface
+relate so let's take a
+
+ align:start position:0%
+relate so let's take a
+ 
+
+ align:start position:0%
+relate so let's take a
+curve rals R of
+
+ align:start position:0%
+curve rals R of
+ 
+
+ align:start position:0%
+curve rals R of
+T that
+
+ align:start position:0%
+T that
+ 
+
+ align:start position:0%
+T that
+stays
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inside well maybe I should say on the
+
+ align:start position:0%
+inside well maybe I should say on the
+ 
+
+ align:start position:0%
+inside well maybe I should say on the
+level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface W equals
+
+ align:start position:0%
+surface W equals
+ 
+
+ align:start position:0%
+surface W equals
+c okay
+
+ align:start position:0%
+c okay
+ 
+
+ align:start position:0%
+c okay
+so let's think about what that means so
+
+ align:start position:0%
+so let's think about what that means so
+ 
+
+ align:start position:0%
+so let's think about what that means so
+just to get you used to this idea I'm
+
+ align:start position:0%
+just to get you used to this idea I'm
+ 
+
+ align:start position:0%
+just to get you used to this idea I'm
+going to draw a level surface of a
+
+ align:start position:0%
+going to draw a level surface of a
+ 
+
+ align:start position:0%
+going to draw a level surface of a
+function of three variables okay so it's
+
+ align:start position:0%
+function of three variables okay so it's
+ 
+
+ align:start position:0%
+function of three variables okay so it's
+some surface given by the equation W of
+
+ align:start position:0%
+some surface given by the equation W of
+ 
+
+ align:start position:0%
+some surface given by the equation W of
+XYZ equals some constant
+
+ align:start position:0%
+XYZ equals some constant
+ 
+
+ align:start position:0%
+XYZ equals some constant
+C and so now I'm going to have a point
+
+ align:start position:0%
+C and so now I'm going to have a point
+ 
+
+ align:start position:0%
+C and so now I'm going to have a point
+on that and it's going to move on that
+
+ align:start position:0%
+on that and it's going to move on that
+ 
+
+ align:start position:0%
+on that and it's going to move on that
+surface so I will have you know some
+
+ align:start position:0%
+surface so I will have you know some
+ 
+
+ align:start position:0%
+surface so I will have you know some
+parametric
+
+ align:start position:0%
+parametric
+ 
+
+ align:start position:0%
+parametric
+curve that lives on this
+
+ align:start position:0%
+curve that lives on this
+ 
+
+ align:start position:0%
+curve that lives on this
+surface so the question
+
+ align:start position:0%
+surface so the question
+ 
+
+ align:start position:0%
+surface so the question
+is what's going to
+
+ align:start position:0%
+is what's going to
+ 
+
+ align:start position:0%
+is what's going to
+happen at any given time well the first
+
+ align:start position:0%
+happen at any given time well the first
+ 
+
+ align:start position:0%
+happen at any given time well the first
+observation is that the velocity Vector
+
+ align:start position:0%
+observation is that the velocity Vector
+ 
+
+ align:start position:0%
+observation is that the velocity Vector
+what can I say about the velocity
+
+ align:start position:0%
+what can I say about the velocity
+ 
+
+ align:start position:0%
+what can I say about the velocity
+Vector of this motion it's going to be
+
+ align:start position:0%
+Vector of this motion it's going to be
+ 
+
+ align:start position:0%
+Vector of this motion it's going to be
+tangent to the level surface right if I
+
+ align:start position:0%
+tangent to the level surface right if I
+ 
+
+ align:start position:0%
+tangent to the level surface right if I
+move on a Surface then at any point my
+
+ align:start position:0%
+move on a Surface then at any point my
+ 
+
+ align:start position:0%
+move on a Surface then at any point my
+velocity is tangent to the curve but if
+
+ align:start position:0%
+velocity is tangent to the curve but if
+ 
+
+ align:start position:0%
+velocity is tangent to the curve but if
+it's tangent to the curve then it's also
+
+ align:start position:0%
+it's tangent to the curve then it's also
+ 
+
+ align:start position:0%
+it's tangent to the curve then it's also
+tangent to the
+
+ align:start position:0%
+tangent to the
+ 
+
+ align:start position:0%
+tangent to the
+surface because the curve is inside the
+
+ align:start position:0%
+surface because the curve is inside the
+ 
+
+ align:start position:0%
+surface because the curve is inside the
+surface so okay it's getting a bit
+
+ align:start position:0%
+surface so okay it's getting a bit
+ 
+
+ align:start position:0%
+surface so okay it's getting a bit
+cluttered maybe I should draw a bigger
+
+ align:start position:0%
+cluttered maybe I should draw a bigger
+ 
+
+ align:start position:0%
+cluttered maybe I should draw a bigger
+picture let me do that right away here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I have my level surface wal C I have
+
+ align:start position:0%
+so I have my level surface wal C I have
+ 
+
+ align:start position:0%
+so I have my level surface wal C I have
+a curve on
+
+ align:start position:0%
+a curve on
+ 
+
+ align:start position:0%
+a curve on
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and at some
+
+ align:start position:0%
+and at some
+ 
+
+ align:start position:0%
+and at some
+point I'm going to have a certain
+
+ align:start position:0%
+point I'm going to have a certain
+ 
+
+ align:start position:0%
+point I'm going to have a certain
+velocity so the claim is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+V equals
+
+ align:start position:0%
+V equals
+ 
+
+ align:start position:0%
+V equals
+drdt is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tangent to the level W equals
+
+ align:start position:0%
+tangent to the level W equals
+ 
+
+ align:start position:0%
+tangent to the level W equals
+c because it's tangent to the curve and
+
+ align:start position:0%
+c because it's tangent to the curve and
+ 
+
+ align:start position:0%
+c because it's tangent to the curve and
+the curve is inside the level okay now
+
+ align:start position:0%
+the curve is inside the level okay now
+ 
+
+ align:start position:0%
+the curve is inside the level okay now
+what else can we say
+
+ align:start position:0%
+what else can we say
+ 
+
+ align:start position:0%
+what else can we say
+well we have the chain rule to tell us
+
+ align:start position:0%
+well we have the chain rule to tell us
+ 
+
+ align:start position:0%
+well we have the chain rule to tell us
+how the Val of w
+
+ align:start position:0%
+how the Val of w
+ 
+
+ align:start position:0%
+how the Val of w
+changes so by the chain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rule we have DW
+
+ align:start position:0%
+rule we have DW
+ 
+
+ align:start position:0%
+rule we have DW
+DT so the rate of change of the value of
+
+ align:start position:0%
+DT so the rate of change of the value of
+ 
+
+ align:start position:0%
+DT so the rate of change of the value of
+w as I move along this curve is given by
+
+ align:start position:0%
+w as I move along this curve is given by
+ 
+
+ align:start position:0%
+w as I move along this curve is given by
+the dot product between the
+
+ align:start position:0%
+the dot product between the
+ 
+
+ align:start position:0%
+the dot product between the
+gradient and the velocity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so well maybe I can rewrite it as NE
+
+ align:start position:0%
+and so well maybe I can rewrite it as NE
+ 
+
+ align:start position:0%
+and so well maybe I can rewrite it as NE
+W sorry uh d
+
+ align:start position:0%
+W sorry uh d
+ 
+
+ align:start position:0%
+W sorry uh d
+w
+
+ align:start position:0%
+w
+ 
+
+ align:start position:0%
+w
+v um and that should be well what should
+
+ align:start position:0%
+v um and that should be well what should
+ 
+
+ align:start position:0%
+v um and that should be well what should
+it be what happens to the value of w as
+
+ align:start position:0%
+it be what happens to the value of w as
+ 
+
+ align:start position:0%
+it be what happens to the value of w as
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+changes well it stays constant because
+
+ align:start position:0%
+changes well it stays constant because
+ 
+
+ align:start position:0%
+changes well it stays constant because
+we are moving on a curve that curve
+
+ align:start position:0%
+we are moving on a curve that curve
+ 
+
+ align:start position:0%
+we are moving on a curve that curve
+might be complicated but it stays always
+
+ align:start position:0%
+might be complicated but it stays always
+ 
+
+ align:start position:0%
+might be complicated but it stays always
+on the level W equals
+
+ align:start position:0%
+on the level W equals
+ 
+
+ align:start position:0%
+on the level W equals
+c so it's zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because W of T equals c which is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant okay is that
+
+ align:start position:0%
+constant okay is that
+ 
+
+ align:start position:0%
+constant okay is that
+convincing y okay so now if we have a
+
+ align:start position:0%
+convincing y okay so now if we have a
+ 
+
+ align:start position:0%
+convincing y okay so now if we have a
+DOT product that's zero that tells us
+
+ align:start position:0%
+DOT product that's zero that tells us
+ 
+
+ align:start position:0%
+DOT product that's zero that tells us
+that these two guys are
+
+ align:start position:0%
+that these two guys are
+ 
+
+ align:start position:0%
+that these two guys are
+perpendicular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the gradient Vector is perpendicular
+
+ align:start position:0%
+so the gradient Vector is perpendicular
+ 
+
+ align:start position:0%
+so the gradient Vector is perpendicular
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V okay that's a good start we know that
+
+ align:start position:0%
+V okay that's a good start we know that
+ 
+
+ align:start position:0%
+V okay that's a good start we know that
+the gradient is perpendicular to this
+
+ align:start position:0%
+the gradient is perpendicular to this
+ 
+
+ align:start position:0%
+the gradient is perpendicular to this
+Vector tangent that's tangent to the
+
+ align:start position:0%
+Vector tangent that's tangent to the
+ 
+
+ align:start position:0%
+Vector tangent that's tangent to the
+level surface what about other vectors
+
+ align:start position:0%
+level surface what about other vectors
+ 
+
+ align:start position:0%
+level surface what about other vectors
+tangent to the level
+
+ align:start position:0%
+tangent to the level
+ 
+
+ align:start position:0%
+tangent to the level
+surface well in fact I could use any
+
+ align:start position:0%
+surface well in fact I could use any
+ 
+
+ align:start position:0%
+surface well in fact I could use any
+curve drawn on the level wal C
+
+ align:start position:0%
+curve drawn on the level wal C
+ 
+
+ align:start position:0%
+curve drawn on the level wal C
+so I could move really any way I wanted
+
+ align:start position:0%
+so I could move really any way I wanted
+ 
+
+ align:start position:0%
+so I could move really any way I wanted
+on that
+
+ align:start position:0%
+on that
+ 
+
+ align:start position:0%
+on that
+surface in
+
+ align:start position:0%
+surface in
+ 
+
+ align:start position:0%
+surface in
+particular I claim that I could have
+
+ align:start position:0%
+particular I claim that I could have
+ 
+
+ align:start position:0%
+particular I claim that I could have
+chosen my velocity Vector to be any
+
+ align:start position:0%
+chosen my velocity Vector to be any
+ 
+
+ align:start position:0%
+chosen my velocity Vector to be any
+Vector tangent to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface okay so let's write this so this
+
+ align:start position:0%
+surface okay so let's write this so this
+ 
+
+ align:start position:0%
+surface okay so let's write this so this
+is true
+
+ align:start position:0%
+is true
+ 
+
+ align:start position:0%
+is true
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+curve well say for any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion on
+
+ align:start position:0%
+motion on
+ 
+
+ align:start position:0%
+motion on
+the level surface W equal C so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means V can
+
+ align:start position:0%
+means V can
+ 
+
+ align:start position:0%
+means V can
+be any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector
+
+ align:start position:0%
+Vector
+ 
+
+ align:start position:0%
+Vector
+tangent to the
+
+ align:start position:0%
+tangent to the
+ 
+
+ align:start position:0%
+tangent to the
+surface tangent
+
+ align:start position:0%
+surface tangent
+ 
+
+ align:start position:0%
+surface tangent
+to the level um see for example let me
+
+ align:start position:0%
+to the level um see for example let me
+ 
+
+ align:start position:0%
+to the level um see for example let me
+draw one more
+
+ align:start position:0%
+draw one more
+ 
+
+ align:start position:0%
+draw one more
+picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I have my level surface so I'm
+
+ align:start position:0%
+okay so I have my level surface so I'm
+ 
+
+ align:start position:0%
+okay so I have my level surface so I'm
+drawing more and more levels and the
+
+ align:start position:0%
+drawing more and more levels and the
+ 
+
+ align:start position:0%
+drawing more and more levels and the
+Never quite look the same but and I have
+
+ align:start position:0%
+Never quite look the same but and I have
+ 
+
+ align:start position:0%
+Never quite look the same but and I have
+a point and at this point I have the
+
+ align:start position:0%
+a point and at this point I have the
+ 
+
+ align:start position:0%
+a point and at this point I have the
+tangent plane to the level surface okay
+
+ align:start position:0%
+tangent plane to the level surface okay
+ 
+
+ align:start position:0%
+tangent plane to the level surface okay
+so this
+
+ align:start position:0%
+so this
+ 
+
+ align:start position:0%
+so this
+is tangent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane to the
+
+ align:start position:0%
+plane to the
+ 
+
+ align:start position:0%
+plane to the
+level then if I choose any VOR in that
+
+ align:start position:0%
+level then if I choose any VOR in that
+ 
+
+ align:start position:0%
+level then if I choose any VOR in that
+tangent plane let's say I choose and no
+
+ align:start position:0%
+tangent plane let's say I choose and no
+ 
+
+ align:start position:0%
+tangent plane let's say I choose and no
+but when that goes in that
+
+ align:start position:0%
+but when that goes in that
+ 
+
+ align:start position:0%
+but when that goes in that
+direction then I can actually find a
+
+ align:start position:0%
+direction then I can actually find a
+ 
+
+ align:start position:0%
+direction then I can actually find a
+curve that goes in that direction and
+
+ align:start position:0%
+curve that goes in that direction and
+ 
+
+ align:start position:0%
+curve that goes in that direction and
+stays on the level so here that would be
+
+ align:start position:0%
+stays on the level so here that would be
+ 
+
+ align:start position:0%
+stays on the level so here that would be
+a curve that somehow goes from the right
+
+ align:start position:0%
+a curve that somehow goes from the right
+ 
+
+ align:start position:0%
+a curve that somehow goes from the right
+to the left and of course it has to end
+
+ align:start position:0%
+to the left and of course it has to end
+ 
+
+ align:start position:0%
+to the left and of course it has to end
+up going up or something like
+
+ align:start position:0%
+up going up or something like
+ 
+
+ align:start position:0%
+up going up or something like
+that okay so
+
+ align:start position:0%
+that okay so
+ 
+
+ align:start position:0%
+that okay so
+given any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tangent let's call that vector v tangent
+
+ align:start position:0%
+tangent let's call that vector v tangent
+ 
+
+ align:start position:0%
+tangent let's call that vector v tangent
+to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level we get that the gradient is
+
+ align:start position:0%
+level we get that the gradient is
+ 
+
+ align:start position:0%
+level we get that the gradient is
+perpendicular to V so the gradient is
+
+ align:start position:0%
+perpendicular to V so the gradient is
+ 
+
+ align:start position:0%
+perpendicular to V so the gradient is
+perpendicular to this Vector tangent to
+
+ align:start position:0%
+perpendicular to this Vector tangent to
+ 
+
+ align:start position:0%
+perpendicular to this Vector tangent to
+this curve but also to you know any
+
+ align:start position:0%
+this curve but also to you know any
+ 
+
+ align:start position:0%
+this curve but also to you know any
+Vector I can draw that's tangent to my
+
+ align:start position:0%
+Vector I can draw that's tangent to my
+ 
+
+ align:start position:0%
+Vector I can draw that's tangent to my
+Surface so what does that mean well that
+
+ align:start position:0%
+Surface so what does that mean well that
+ 
+
+ align:start position:0%
+Surface so what does that mean well that
+means the gradient is actually
+
+ align:start position:0%
+means the gradient is actually
+ 
+
+ align:start position:0%
+means the gradient is actually
+perpendicular to the tangent plane or to
+
+ align:start position:0%
+perpendicular to the tangent plane or to
+ 
+
+ align:start position:0%
+perpendicular to the tangent plane or to
+the surface at this
+
+ align:start position:0%
+the surface at this
+ 
+
+ align:start position:0%
+the surface at this
+point so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradient is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perpendicular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and well here I've Illustrated things
+
+ align:start position:0%
+and well here I've Illustrated things
+ 
+
+ align:start position:0%
+and well here I've Illustrated things
+with a threedimensional example but
+
+ align:start position:0%
+with a threedimensional example but
+ 
+
+ align:start position:0%
+with a threedimensional example but
+really it works the same if you have
+
+ align:start position:0%
+really it works the same if you have
+ 
+
+ align:start position:0%
+really it works the same if you have
+only two variables when you have a level
+
+ align:start position:0%
+only two variables when you have a level
+ 
+
+ align:start position:0%
+only two variables when you have a level
+curve it has a tangent line and the
+
+ align:start position:0%
+curve it has a tangent line and the
+ 
+
+ align:start position:0%
+curve it has a tangent line and the
+gradient is perpendicular to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line okay any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's see that's actually pretty neat
+
+ align:start position:0%
+so let's see that's actually pretty neat
+ 
+
+ align:start position:0%
+so let's see that's actually pretty neat
+because there's a nice application of
+
+ align:start position:0%
+because there's a nice application of
+ 
+
+ align:start position:0%
+because there's a nice application of
+this which is to try to figure out now
+
+ align:start position:0%
+this which is to try to figure out now
+ 
+
+ align:start position:0%
+this which is to try to figure out now
+we know actually how to find the tangent
+
+ align:start position:0%
+we know actually how to find the tangent
+ 
+
+ align:start position:0%
+we know actually how to find the tangent
+plane to anything pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's
+
+ align:start position:0%
+so let's
+ 
+
+ align:start position:0%
+so let's
+see so let's say that for example I want
+
+ align:start position:0%
+see so let's say that for example I want
+ 
+
+ align:start position:0%
+see so let's say that for example I want
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+the tensent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+surface with
+
+ align:start position:0%
+surface with
+ 
+
+ align:start position:0%
+surface with
+equation let's say X2 + y^ 2us z^2 =
+
+ align:start position:0%
+equation let's say X2 + y^ 2us z^2 =
+ 
+
+ align:start position:0%
+equation let's say X2 + y^ 2us z^2 =
+4 at the point 21 1 let me write
+
+ align:start position:0%
+4 at the point 21 1 let me write
+ 
+
+ align:start position:0%
+4 at the point 21 1 let me write
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how do we do that well one way that
+
+ align:start position:0%
+so how do we do that well one way that
+ 
+
+ align:start position:0%
+so how do we do that well one way that
+we already
+
+ align:start position:0%
+we already
+ 
+
+ align:start position:0%
+we already
+know if we solve this for Z so we can
+
+ align:start position:0%
+know if we solve this for Z so we can
+ 
+
+ align:start position:0%
+know if we solve this for Z so we can
+write z equals function of X and Y then
+
+ align:start position:0%
+write z equals function of X and Y then
+ 
+
+ align:start position:0%
+write z equals function of X and Y then
+we know tangent plane
+
+ align:start position:0%
+we know tangent plane
+ 
+
+ align:start position:0%
+we know tangent plane
+approximation for the graph of a
+
+ align:start position:0%
+approximation for the graph of a
+ 
+
+ align:start position:0%
+approximation for the graph of a
+function Z equals some function of X and
+
+ align:start position:0%
+function Z equals some function of X and
+ 
+
+ align:start position:0%
+function Z equals some function of X and
+Y but that doesn't look like it's the
+
+ align:start position:0%
+Y but that doesn't look like it's the
+ 
+
+ align:start position:0%
+Y but that doesn't look like it's the
+best way to do it okay the best way to
+
+ align:start position:0%
+best way to do it okay the best way to
+ 
+
+ align:start position:0%
+best way to do it okay the best way to
+do it now that we have the gradient
+
+ align:start position:0%
+do it now that we have the gradient
+ 
+
+ align:start position:0%
+do it now that we have the gradient
+Vector is actually to directly say oh we
+
+ align:start position:0%
+Vector is actually to directly say oh we
+ 
+
+ align:start position:0%
+Vector is actually to directly say oh we
+we know the normal Vector to this plane
+
+ align:start position:0%
+we know the normal Vector to this plane
+ 
+
+ align:start position:0%
+we know the normal Vector to this plane
+the normal Vector will just be the
+
+ align:start position:0%
+the normal Vector will just be the
+ 
+
+ align:start position:0%
+the normal Vector will just be the
+gradient oh I think I have a cool
+
+ align:start position:0%
+gradient oh I think I have a cool
+ 
+
+ align:start position:0%
+gradient oh I think I have a cool
+picture to show
+
+ align:start position:0%
+picture to show
+ 
+
+ align:start position:0%
+picture to show
+so okay so that's what it looks
+
+ align:start position:0%
+so okay so that's what it looks
+ 
+
+ align:start position:0%
+so okay so that's what it looks
+like okay so here you have the surface
+
+ align:start position:0%
+like okay so here you have the surface
+ 
+
+ align:start position:0%
+like okay so here you have the surface
+x² + y sare - zare = 4 that's called a
+
+ align:start position:0%
+x² + y sare - zare = 4 that's called a
+ 
+
+ align:start position:0%
+x² + y sare - zare = 4 that's called a
+hyperboloid because it looks like what
+
+ align:start position:0%
+hyperboloid because it looks like what
+ 
+
+ align:start position:0%
+hyperboloid because it looks like what
+you get when you spin a hyperbola around
+
+ align:start position:0%
+you get when you spin a hyperbola around
+ 
+
+ align:start position:0%
+you get when you spin a hyperbola around
+an axis and here's its tangent plane at
+
+ align:start position:0%
+an axis and here's its tangent plane at
+ 
+
+ align:start position:0%
+an axis and here's its tangent plane at
+the given point so it doesn't look very
+
+ align:start position:0%
+the given point so it doesn't look very
+ 
+
+ align:start position:0%
+the given point so it doesn't look very
+tangent because it crosses the surface
+
+ align:start position:0%
+tangent because it crosses the surface
+ 
+
+ align:start position:0%
+tangent because it crosses the surface
+but it's really I mean if you think
+
+ align:start position:0%
+but it's really I mean if you think
+ 
+
+ align:start position:0%
+but it's really I mean if you think
+about it you'll see that's really the
+
+ align:start position:0%
+about it you'll see that's really the
+ 
+
+ align:start position:0%
+about it you'll see that's really the
+plane that's approximating the
+
+ align:start position:0%
+plane that's approximating the
+ 
+
+ align:start position:0%
+plane that's approximating the
+surface in the best way that you can at
+
+ align:start position:0%
+surface in the best way that you can at
+ 
+
+ align:start position:0%
+surface in the best way that you can at
+this given point it is really the
+
+ align:start position:0%
+this given point it is really the
+ 
+
+ align:start position:0%
+this given point it is really the
+tangent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how do we find this
+
+ align:start position:0%
+so how do we find this
+ 
+
+ align:start position:0%
+so how do we find this
+plane well you can plot it on a computer
+
+ align:start position:0%
+plane well you can plot it on a computer
+ 
+
+ align:start position:0%
+plane well you can plot it on a computer
+but that's not exactly
+
+ align:start position:0%
+but that's not exactly
+ 
+
+ align:start position:0%
+but that's not exactly
+you know how you would look for it in
+
+ align:start position:0%
+you know how you would look for it in
+ 
+
+ align:start position:0%
+you know how you would look for it in
+the first place so the way to do it is
+
+ align:start position:0%
+the first place so the way to do it is
+ 
+
+ align:start position:0%
+the first place so the way to do it is
+that we compute the gradient so the
+
+ align:start position:0%
+that we compute the gradient so the
+ 
+
+ align:start position:0%
+that we compute the gradient so the
+gradient of what well the gradient of
+
+ align:start position:0%
+gradient of what well the gradient of
+ 
+
+ align:start position:0%
+gradient of what well the gradient of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+function okay
+
+ align:start position:0%
+function okay
+ 
+
+ align:start position:0%
+function okay
+so so it should say this is the level
+
+ align:start position:0%
+so so it should say this is the level
+ 
+
+ align:start position:0%
+so so it should say this is the level
+set W = 4
+
+ align:start position:0%
+set W = 4
+ 
+
+ align:start position:0%
+set W = 4
+where W is x² + y^ 2us z^
+
+ align:start position:0%
+where W is x² + y^ 2us z^
+ 
+
+ align:start position:0%
+where W is x² + y^ 2us z^
+2 and so we know that the gradient of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this well what is
+
+ align:start position:0%
+this well what is
+ 
+
+ align:start position:0%
+this well what is
+it 2x then 2 Y and then -2
+
+ align:start position:0%
+it 2x then 2 Y and then -2
+ 
+
+ align:start position:0%
+it 2x then 2 Y and then -2
+Z so at this given
+
+ align:start position:0%
+Z so at this given
+ 
+
+ align:start position:0%
+Z so at this given
+point I guess we're at xal 2 so that's
+
+ align:start position:0%
+point I guess we're at xal 2 so that's
+ 
+
+ align:start position:0%
+point I guess we're at xal 2 so that's
+four and then y and z are 1 so 2
+
+ align:start position:0%
+four and then y and z are 1 so 2
+ 
+
+ align:start position:0%
+four and then y and z are 1 so 2
+-2 okay and that's going to be the
+
+ align:start position:0%
+-2 okay and that's going to be the
+ 
+
+ align:start position:0%
+-2 okay and that's going to be the
+normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector to the surface or to the tangent
+
+ align:start position:0%
+Vector to the surface or to the tangent
+ 
+
+ align:start position:0%
+Vector to the surface or to the tangent
+plane and that's one way to define the
+
+ align:start position:0%
+plane and that's one way to define the
+ 
+
+ align:start position:0%
+plane and that's one way to define the
+tangent plane right it has the same
+
+ align:start position:0%
+tangent plane right it has the same
+ 
+
+ align:start position:0%
+tangent plane right it has the same
+normal Vector as the surface or that's
+
+ align:start position:0%
+normal Vector as the surface or that's
+ 
+
+ align:start position:0%
+normal Vector as the surface or that's
+one way to define the normal Vector to
+
+ align:start position:0%
+one way to define the normal Vector to
+ 
+
+ align:start position:0%
+one way to define the normal Vector to
+the surface if you prefer being
+
+ align:start position:0%
+the surface if you prefer being
+ 
+
+ align:start position:0%
+the surface if you prefer being
+perpendicular to the surface means that
+
+ align:start position:0%
+perpendicular to the surface means that
+ 
+
+ align:start position:0%
+perpendicular to the surface means that
+you're perpendicular to its tangent
+
+ align:start position:0%
+you're perpendicular to its tangent
+ 
+
+ align:start position:0%
+you're perpendicular to its tangent
+plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the
+
+ align:start position:0%
+okay so the
+ 
+
+ align:start position:0%
+okay so the
+equation is well
+
+ align:start position:0%
+equation is well
+ 
+
+ align:start position:0%
+equation is well
+4x + 2
+
+ align:start position:0%
+4x + 2
+ 
+
+ align:start position:0%
+4x + 2
+y - 2 Z equals
+
+ align:start position:0%
+y - 2 Z equals
+ 
+
+ align:start position:0%
+y - 2 Z equals
+something where something is well we
+
+ align:start position:0%
+something where something is well we
+ 
+
+ align:start position:0%
+something where something is well we
+should just plug in that point we'll get
+
+ align:start position:0%
+should just plug in that point we'll get
+ 
+
+ align:start position:0%
+should just plug in that point we'll get
+8 + 2us 2 looks like we'll get
+
+ align:start position:0%
+8 + 2us 2 looks like we'll get
+ 
+
+ align:start position:0%
+8 + 2us 2 looks like we'll get
+eight and of course we could simplify by
+
+ align:start position:0%
+eight and of course we could simplify by
+ 
+
+ align:start position:0%
+eight and of course we could simplify by
+dividing everything by two two but it's
+
+ align:start position:0%
+dividing everything by two two but it's
+ 
+
+ align:start position:0%
+dividing everything by two two but it's
+not very important
+
+ align:start position:0%
+not very important
+ 
+
+ align:start position:0%
+not very important
+here okay so now if you have a surface
+
+ align:start position:0%
+here okay so now if you have a surface
+ 
+
+ align:start position:0%
+here okay so now if you have a surface
+given by an evil equation and a point on
+
+ align:start position:0%
+given by an evil equation and a point on
+ 
+
+ align:start position:0%
+given by an evil equation and a point on
+the surface well you know how to find
+
+ align:start position:0%
+the surface well you know how to find
+ 
+
+ align:start position:0%
+the surface well you know how to find
+the tangent plane to the surface at that
+
+ align:start position:0%
+the tangent plane to the surface at that
+ 
+
+ align:start position:0%
+the tangent plane to the surface at that
+point okay any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay let me give just
+
+ align:start position:0%
+no okay let me give just
+ 
+
+ align:start position:0%
+no okay let me give just
+another reason why you know another way
+
+ align:start position:0%
+another reason why you know another way
+ 
+
+ align:start position:0%
+another reason why you know another way
+that we could have seen this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I claim in fact we could have done
+
+ align:start position:0%
+so I claim in fact we could have done
+ 
+
+ align:start position:0%
+so I claim in fact we could have done
+this without the gradient when using the
+
+ align:start position:0%
+this without the gradient when using the
+ 
+
+ align:start position:0%
+this without the gradient when using the
+gradient in somehow a disguised way so
+
+ align:start position:0%
+gradient in somehow a disguised way so
+ 
+
+ align:start position:0%
+gradient in somehow a disguised way so
+here's another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so the other way to do it would be
+
+ align:start position:0%
+way so the other way to do it would be
+ 
+
+ align:start position:0%
+way so the other way to do it would be
+to start with a
+
+ align:start position:0%
+to start with a
+ 
+
+ align:start position:0%
+to start with a
+differential okay DW well it's pretty
+
+ align:start position:0%
+differential okay DW well it's pretty
+ 
+
+ align:start position:0%
+differential okay DW well it's pretty
+much the same content but let me write
+
+ align:start position:0%
+much the same content but let me write
+ 
+
+ align:start position:0%
+much the same content but let me write
+it as a differential DW is 2x DX minus 2
+
+ align:start position:0%
+it as a differential DW is 2x DX minus 2
+ 
+
+ align:start position:0%
+it as a differential DW is 2x DX minus 2
+y sorry plus 2 y d y minus 2 Z DZ so at
+
+ align:start position:0%
+y sorry plus 2 y d y minus 2 Z DZ so at
+ 
+
+ align:start position:0%
+y sorry plus 2 y d y minus 2 Z DZ so at
+the given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point at 211 this is 4 DX +
+
+ align:start position:0%
+point at 211 this is 4 DX +
+ 
+
+ align:start position:0%
+point at 211 this is 4 DX +
+2dy minus 2
+
+ align:start position:0%
+2dy minus 2
+ 
+
+ align:start position:0%
+2dy minus 2
+DZ now if we want to change this into an
+
+ align:start position:0%
+DZ now if we want to change this into an
+ 
+
+ align:start position:0%
+DZ now if we want to change this into an
+approximation formula we can we know
+
+ align:start position:0%
+approximation formula we can we know
+ 
+
+ align:start position:0%
+approximation formula we can we know
+that the change in w
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is approximately equal to 4 Delta X plus
+
+ align:start position:0%
+is approximately equal to 4 Delta X plus
+ 
+
+ align:start position:0%
+is approximately equal to 4 Delta X plus
+2 Delta
+
+ align:start position:0%
+2 Delta
+ 
+
+ align:start position:0%
+2 Delta
+Yus 2 Delta
+
+ align:start position:0%
+Yus 2 Delta
+ 
+
+ align:start position:0%
+Yus 2 Delta
+Z
+
+ align:start position:0%
+Z
+ 
+
+ align:start position:0%
+Z
+okay so when do we stay on the level
+
+ align:start position:0%
+okay so when do we stay on the level
+ 
+
+ align:start position:0%
+okay so when do we stay on the level
+surface well we stay on the level
+
+ align:start position:0%
+surface well we stay on the level
+ 
+
+ align:start position:0%
+surface well we stay on the level
+surface when w doesn't change so when
+
+ align:start position:0%
+surface when w doesn't change so when
+ 
+
+ align:start position:0%
+surface when w doesn't change so when
+this becomes
+
+ align:start position:0%
+this becomes
+ 
+
+ align:start position:0%
+this becomes
+zero okay now what does this
+
+ align:start position:0%
+zero okay now what does this
+ 
+
+ align:start position:0%
+zero okay now what does this
+approximation sign mean well it means
+
+ align:start position:0%
+approximation sign mean well it means
+ 
+
+ align:start position:0%
+approximation sign mean well it means
+that for small changes in XYZ this guy
+
+ align:start position:0%
+that for small changes in XYZ this guy
+ 
+
+ align:start position:0%
+that for small changes in XYZ this guy
+will be close to that guy it also means
+
+ align:start position:0%
+will be close to that guy it also means
+ 
+
+ align:start position:0%
+will be close to that guy it also means
+something else remember these
+
+ align:start position:0%
+something else remember these
+ 
+
+ align:start position:0%
+something else remember these
+approximation formulas they are linear
+
+ align:start position:0%
+approximation formulas they are linear
+ 
+
+ align:start position:0%
+approximation formulas they are linear
+approximation they mean that we replace
+
+ align:start position:0%
+approximation they mean that we replace
+ 
+
+ align:start position:0%
+approximation they mean that we replace
+the function actually by some closest
+
+ align:start position:0%
+the function actually by some closest
+ 
+
+ align:start position:0%
+the function actually by some closest
+linear formula that will be nearby and
+
+ align:start position:0%
+linear formula that will be nearby and
+ 
+
+ align:start position:0%
+linear formula that will be nearby and
+so in
+
+ align:start position:0%
+so in
+ 
+
+ align:start position:0%
+so in
+particular if we set face equal to zero
+
+ align:start position:0%
+particular if we set face equal to zero
+ 
+
+ align:start position:0%
+particular if we set face equal to zero
+instead of you know approximately zero
+
+ align:start position:0%
+instead of you know approximately zero
+ 
+
+ align:start position:0%
+instead of you know approximately zero
+it means we'll actually be moving on the
+
+ align:start position:0%
+it means we'll actually be moving on the
+ 
+
+ align:start position:0%
+it means we'll actually be moving on the
+tangent plane to the level set if you
+
+ align:start position:0%
+tangent plane to the level set if you
+ 
+
+ align:start position:0%
+tangent plane to the level set if you
+want setting equality is in
+
+ align:start position:0%
+want setting equality is in
+ 
+
+ align:start position:0%
+want setting equality is in
+approximations means that we replace the
+
+ align:start position:0%
+approximations means that we replace the
+ 
+
+ align:start position:0%
+approximations means that we replace the
+function by its tangent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the level corresponds
+
+ align:start position:0%
+so the level corresponds
+ 
+
+ align:start position:0%
+so the level corresponds
+to Delta W equal 0 and its tensent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane corresponds
+
+ align:start position:0%
+plane corresponds
+ 
+
+ align:start position:0%
+plane corresponds
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+4 Delta x + 2 Delta Yus 2 Delta Z equal
+
+ align:start position:0%
+4 Delta x + 2 Delta Yus 2 Delta Z equal
+ 
+
+ align:start position:0%
+4 Delta x + 2 Delta Yus 2 Delta Z equal
+Z that's what I'm trying to say
+
+ align:start position:0%
+Z that's what I'm trying to say
+ 
+
+ align:start position:0%
+Z that's what I'm trying to say
+basically and what's Delta X well that
+
+ align:start position:0%
+basically and what's Delta X well that
+ 
+
+ align:start position:0%
+basically and what's Delta X well that
+means it's the change in X so what's the
+
+ align:start position:0%
+means it's the change in X so what's the
+ 
+
+ align:start position:0%
+means it's the change in X so what's the
+change in X here that means well we
+
+ align:start position:0%
+change in X here that means well we
+ 
+
+ align:start position:0%
+change in X here that means well we
+started with xal 2 and we moved to some
+
+ align:start position:0%
+started with xal 2 and we moved to some
+ 
+
+ align:start position:0%
+started with xal 2 and we moved to some
+other value X so that's actually xus
+
+ align:start position:0%
+other value X so that's actually xus
+ 
+
+ align:start position:0%
+other value X so that's actually xus
+2 right that's how much X has changed
+
+ align:start position:0%
+2 right that's how much X has changed
+ 
+
+ align:start position:0%
+2 right that's how much X has changed
+compared to two and 2 * y - 1 - 2 * Z -1
+
+ align:start position:0%
+compared to two and 2 * y - 1 - 2 * Z -1
+ 
+
+ align:start position:0%
+compared to two and 2 * y - 1 - 2 * Z -1
+= 0 that's the equation of the tangent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane it's the same equation as the one
+
+ align:start position:0%
+plane it's the same equation as the one
+ 
+
+ align:start position:0%
+plane it's the same equation as the one
+over there these are just two different
+
+ align:start position:0%
+over there these are just two different
+ 
+
+ align:start position:0%
+over there these are just two different
+methods to get it okay so this one
+
+ align:start position:0%
+methods to get it okay so this one
+ 
+
+ align:start position:0%
+methods to get it okay so this one
+explains to you what's going on in terms
+
+ align:start position:0%
+explains to you what's going on in terms
+ 
+
+ align:start position:0%
+explains to you what's going on in terms
+of approximation formulas this one goes
+
+ align:start position:0%
+of approximation formulas this one goes
+ 
+
+ align:start position:0%
+of approximation formulas this one goes
+you know right away to the end by using
+
+ align:start position:0%
+you know right away to the end by using
+ 
+
+ align:start position:0%
+you know right away to the end by using
+the gradient
+
+ align:start position:0%
+the gradient
+ 
+
+ align:start position:0%
+the gradient
+Vector so in a way with this one you
+
+ align:start position:0%
+Vector so in a way with this one you
+ 
+
+ align:start position:0%
+Vector so in a way with this one you
+have you don't have to think nearly as
+
+ align:start position:0%
+have you don't have to think nearly as
+ 
+
+ align:start position:0%
+have you don't have to think nearly as
+much but you can use either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions no okay so let's move on with
+
+ align:start position:0%
+questions no okay so let's move on with
+ 
+
+ align:start position:0%
+questions no okay so let's move on with
+let's move on to a new
+
+ align:start position:0%
+let's move on to a new
+ 
+
+ align:start position:0%
+let's move on to a new
+topic which is another application of a
+
+ align:start position:0%
+topic which is another application of a
+ 
+
+ align:start position:0%
+topic which is another application of a
+gradient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+and that is directional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivatives okay so let's say that we
+
+ align:start position:0%
+derivatives okay so let's say that we
+ 
+
+ align:start position:0%
+derivatives okay so let's say that we
+have a function of two
+
+ align:start position:0%
+have a function of two
+ 
+
+ align:start position:0%
+have a function of two
+variables X and
+
+ align:start position:0%
+variables X and
+ 
+
+ align:start position:0%
+variables X and
+Y well we
+
+ align:start position:0%
+Y well we
+ 
+
+ align:start position:0%
+Y well we
+know how to compute partial W partial X
+
+ align:start position:0%
+know how to compute partial W partial X
+ 
+
+ align:start position:0%
+know how to compute partial W partial X
+or partial W partial Y which which
+
+ align:start position:0%
+or partial W partial Y which which
+ 
+
+ align:start position:0%
+or partial W partial Y which which
+measure how W changes if I move in the
+
+ align:start position:0%
+measure how W changes if I move in the
+ 
+
+ align:start position:0%
+measure how W changes if I move in the
+direction of the x-axis or in the
+
+ align:start position:0%
+direction of the x-axis or in the
+ 
+
+ align:start position:0%
+direction of the x-axis or in the
+direction of the y
+
+ align:start position:0%
+direction of the y
+ 
+
+ align:start position:0%
+direction of the y
+axis so what about moving in other
+
+ align:start position:0%
+axis so what about moving in other
+ 
+
+ align:start position:0%
+axis so what about moving in other
+directions well of course we've seen
+
+ align:start position:0%
+directions well of course we've seen
+ 
+
+ align:start position:0%
+directions well of course we've seen
+approximation formulas and so on but you
+
+ align:start position:0%
+approximation formulas and so on but you
+ 
+
+ align:start position:0%
+approximation formulas and so on but you
+know we can still ask is there a
+
+ align:start position:0%
+know we can still ask is there a
+ 
+
+ align:start position:0%
+know we can still ask is there a
+derivative in every direction and that's
+
+ align:start position:0%
+derivative in every direction and that's
+ 
+
+ align:start position:0%
+derivative in every direction and that's
+basically yes that's the directional
+
+ align:start position:0%
+basically yes that's the directional
+ 
+
+ align:start position:0%
+basically yes that's the directional
+derivative okay so these are derivatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction of I hat or J hat the vectors
+
+ align:start position:0%
+direction of I hat or J hat the vectors
+ 
+
+ align:start position:0%
+direction of I hat or J hat the vectors
+that go along the x or the y-
+
+ align:start position:0%
+that go along the x or the y-
+ 
+
+ align:start position:0%
+that go along the x or the y-
+axis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what if we
+
+ align:start position:0%
+so what if we
+ 
+
+ align:start position:0%
+so what if we
+move in another Direction let's say in
+
+ align:start position:0%
+move in another Direction let's say in
+ 
+
+ align:start position:0%
+move in another Direction let's say in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+direction of some unit
+
+ align:start position:0%
+direction of some unit
+ 
+
+ align:start position:0%
+direction of some unit
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+let's call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U okay so if I give you a unit Vector
+
+ align:start position:0%
+U okay so if I give you a unit Vector
+ 
+
+ align:start position:0%
+U okay so if I give you a unit Vector
+you can ask yourself if I move in that
+
+ align:start position:0%
+you can ask yourself if I move in that
+ 
+
+ align:start position:0%
+you can ask yourself if I move in that
+direction how quickly will my function
+
+ align:start position:0%
+direction how quickly will my function
+ 
+
+ align:start position:0%
+direction how quickly will my function
+change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so let's look at the straight
+
+ align:start position:0%
+so so let's look at the straight
+ 
+
+ align:start position:0%
+so so let's look at the straight
+trajectory what what this should mean is
+
+ align:start position:0%
+trajectory what what this should mean is
+ 
+
+ align:start position:0%
+trajectory what what this should mean is
+I start at some value
+
+ align:start position:0%
+I start at some value
+ 
+
+ align:start position:0%
+I start at some value
+XY and there I have my Vector U and I'm
+
+ align:start position:0%
+XY and there I have my Vector U and I'm
+ 
+
+ align:start position:0%
+XY and there I have my Vector U and I'm
+going to move in a straight line in the
+
+ align:start position:0%
+going to move in a straight line in the
+ 
+
+ align:start position:0%
+going to move in a straight line in the
+direction of U and I have the graph of
+
+ align:start position:0%
+direction of U and I have the graph of
+ 
+
+ align:start position:0%
+direction of U and I have the graph of
+my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function and I'm asking myself how
+
+ align:start position:0%
+function and I'm asking myself how
+ 
+
+ align:start position:0%
+function and I'm asking myself how
+quickly does the value change when I
+
+ align:start position:0%
+quickly does the value change when I
+ 
+
+ align:start position:0%
+quickly does the value change when I
+move on the
+
+ align:start position:0%
+move on the
+ 
+
+ align:start position:0%
+move on the
+graph you know in that direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's look at a straight line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trajectory so we have a position Vector
+
+ align:start position:0%
+trajectory so we have a position Vector
+ 
+
+ align:start position:0%
+trajectory so we have a position Vector
+r that will depend on some parameter
+
+ align:start position:0%
+r that will depend on some parameter
+ 
+
+ align:start position:0%
+r that will depend on some parameter
+which I will call S um you'll see why
+
+ align:start position:0%
+which I will call S um you'll see why
+ 
+
+ align:start position:0%
+which I will call S um you'll see why
+very soon in such a way that the
+
+ align:start position:0%
+very soon in such a way that the
+ 
+
+ align:start position:0%
+very soon in such a way that the
+derivative is this given unit Vector you
+
+ align:start position:0%
+derivative is this given unit Vector you
+ 
+
+ align:start position:0%
+derivative is this given unit Vector you
+had so why do I use S for my parameter
+
+ align:start position:0%
+had so why do I use S for my parameter
+ 
+
+ align:start position:0%
+had so why do I use S for my parameter
+rather than T well it's a convention I'm
+
+ align:start position:0%
+rather than T well it's a convention I'm
+ 
+
+ align:start position:0%
+rather than T well it's a convention I'm
+M I'm moving at I'm moving at unit speed
+
+ align:start position:0%
+M I'm moving at I'm moving at unit speed
+ 
+
+ align:start position:0%
+M I'm moving at I'm moving at unit speed
+along this line so that means that
+
+ align:start position:0%
+along this line so that means that
+ 
+
+ align:start position:0%
+along this line so that means that
+actually I'm parameterizing things by
+
+ align:start position:0%
+actually I'm parameterizing things by
+ 
+
+ align:start position:0%
+actually I'm parameterizing things by
+the distance that I've traveled along
+
+ align:start position:0%
+the distance that I've traveled along
+ 
+
+ align:start position:0%
+the distance that I've traveled along
+the curve sorry along this line so here
+
+ align:start position:0%
+the curve sorry along this line so here
+ 
+
+ align:start position:0%
+the curve sorry along this line so here
+it's called s in the sense of you know
+
+ align:start position:0%
+it's called s in the sense of you know
+ 
+
+ align:start position:0%
+it's called s in the sense of you know
+Arc Length or actually it's not really
+
+ align:start position:0%
+Arc Length or actually it's not really
+ 
+
+ align:start position:0%
+Arc Length or actually it's not really
+an arc because it's straight line so
+
+ align:start position:0%
+an arc because it's straight line so
+ 
+
+ align:start position:0%
+an arc because it's straight line so
+it's the
+
+ align:start position:0%
+it's the
+ 
+
+ align:start position:0%
+it's the
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+along the
+
+ align:start position:0%
+along the
+ 
+
+ align:start position:0%
+along the
+line okay so because we parameterizing
+
+ align:start position:0%
+line okay so because we parameterizing
+ 
+
+ align:start position:0%
+line okay so because we parameterizing
+by distance we're just using S as a
+
+ align:start position:0%
+by distance we're just using S as a
+ 
+
+ align:start position:0%
+by distance we're just using S as a
+convention just to distinguish it
+
+ align:start position:0%
+convention just to distinguish it
+ 
+
+ align:start position:0%
+convention just to distinguish it
+with distinguish this from other
+
+ align:start position:0%
+with distinguish this from other
+ 
+
+ align:start position:0%
+with distinguish this from other
+situations and so now the question will
+
+ align:start position:0%
+situations and so now the question will
+ 
+
+ align:start position:0%
+situations and so now the question will
+be what
+
+ align:start position:0%
+be what
+ 
+
+ align:start position:0%
+be what
+is dwds
+
+ align:start position:0%
+is dwds
+ 
+
+ align:start position:0%
+is dwds
+what's the rate of change of w when I
+
+ align:start position:0%
+what's the rate of change of w when I
+ 
+
+ align:start position:0%
+what's the rate of change of w when I
+move like
+
+ align:start position:0%
+move like
+ 
+
+ align:start position:0%
+move like
+that well of course we know the answer
+
+ align:start position:0%
+that well of course we know the answer
+ 
+
+ align:start position:0%
+that well of course we know the answer
+because that's a special case of a chain
+
+ align:start position:0%
+because that's a special case of a chain
+ 
+
+ align:start position:0%
+because that's a special case of a chain
+rle so that's how we will actually
+
+ align:start position:0%
+rle so that's how we will actually
+ 
+
+ align:start position:0%
+rle so that's how we will actually
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+it but in terms of what it means it
+
+ align:start position:0%
+it but in terms of what it means it
+ 
+
+ align:start position:0%
+it but in terms of what it means it
+really means we are asking ourselves we
+
+ align:start position:0%
+really means we are asking ourselves we
+ 
+
+ align:start position:0%
+really means we are asking ourselves we
+start at a point and we change the
+
+ align:start position:0%
+start at a point and we change the
+ 
+
+ align:start position:0%
+start at a point and we change the
+variables in a certain direction which
+
+ align:start position:0%
+variables in a certain direction which
+ 
+
+ align:start position:0%
+variables in a certain direction which
+is not necessarily the x or the Y
+
+ align:start position:0%
+is not necessarily the x or the Y
+ 
+
+ align:start position:0%
+is not necessarily the x or the Y
+Direction but really any Direction and
+
+ align:start position:0%
+Direction but really any Direction and
+ 
+
+ align:start position:0%
+Direction but really any Direction and
+then what's the derivative in that
+
+ align:start position:0%
+then what's the derivative in that
+ 
+
+ align:start position:0%
+then what's the derivative in that
+direction okay does that make sense as a
+
+ align:start position:0%
+direction okay does that make sense as a
+ 
+
+ align:start position:0%
+direction okay does that make sense as a
+concept kind of I see some faces that
+
+ align:start position:0%
+concept kind of I see some faces that
+ 
+
+ align:start position:0%
+concept kind of I see some faces that
+are not completely convinced so maybe I
+
+ align:start position:0%
+are not completely convinced so maybe I
+ 
+
+ align:start position:0%
+are not completely convinced so maybe I
+should show more pictures well let me
+
+ align:start position:0%
+should show more pictures well let me
+ 
+
+ align:start position:0%
+should show more pictures well let me
+first write down a bit more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll show you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I just want to give you the actual
+
+ align:start position:0%
+so I just want to give you the actual
+ 
+
+ align:start position:0%
+so I just want to give you the actual
+definition so sorry so first of all in
+
+ align:start position:0%
+definition so sorry so first of all in
+ 
+
+ align:start position:0%
+definition so sorry so first of all in
+case you wonder what this is all
+
+ align:start position:0%
+case you wonder what this is all
+ 
+
+ align:start position:0%
+case you wonder what this is all
+about so let's say that the components
+
+ align:start position:0%
+about so let's say that the components
+ 
+
+ align:start position:0%
+about so let's say that the components
+of our unit Vector are two numbers A and
+
+ align:start position:0%
+of our unit Vector are two numbers A and
+ 
+
+ align:start position:0%
+of our unit Vector are two numbers A and
+B okay then it means that we'll move
+
+ align:start position:0%
+B okay then it means that we'll move
+ 
+
+ align:start position:0%
+B okay then it means that we'll move
+along the line X of s equals some
+
+ align:start position:0%
+along the line X of s equals some
+ 
+
+ align:start position:0%
+along the line X of s equals some
+initial value the point where we're
+
+ align:start position:0%
+initial value the point where we're
+ 
+
+ align:start position:0%
+initial value the point where we're
+actually looking at the directional
+
+ align:start position:0%
+actually looking at the directional
+ 
+
+ align:start position:0%
+actually looking at the directional
+derivative plus s *
+
+ align:start position:0%
+derivative plus s *
+ 
+
+ align:start position:0%
+derivative plus s *
+a we say plus a *
+
+ align:start position:0%
+a we say plus a *
+ 
+
+ align:start position:0%
+a we say plus a *
+s and Y of s equal y0 + B * s and then
+
+ align:start position:0%
+s and Y of s equal y0 + B * s and then
+ 
+
+ align:start position:0%
+s and Y of s equal y0 + B * s and then
+we plug that into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+w
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we take the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative so we have a notation for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that which is going to be
+
+ align:start position:0%
+that which is going to be
+ 
+
+ align:start position:0%
+that which is going to be
+dwds with a
+
+ align:start position:0%
+dwds with a
+ 
+
+ align:start position:0%
+dwds with a
+subscript in the direction of U to
+
+ align:start position:0%
+subscript in the direction of U to
+ 
+
+ align:start position:0%
+subscript in the direction of U to
+indicate you know in which direction
+
+ align:start position:0%
+indicate you know in which direction
+ 
+
+ align:start position:0%
+indicate you know in which direction
+we're actually going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+move and that's called that's the
+
+ align:start position:0%
+move and that's called that's the
+ 
+
+ align:start position:0%
+move and that's called that's the
+directional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative in the direction of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U okay so let's see what it means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+geometrically
+
+ align:start position:0%
+geometrically
+ 
+
+ align:start position:0%
+geometrically
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+remember we've seen things about partial
+
+ align:start position:0%
+remember we've seen things about partial
+ 
+
+ align:start position:0%
+remember we've seen things about partial
+derivatives and we've seen that the
+
+ align:start position:0%
+derivatives and we've seen that the
+ 
+
+ align:start position:0%
+derivatives and we've seen that the
+partial derivatives are the slopes of
+
+ align:start position:0%
+partial derivatives are the slopes of
+ 
+
+ align:start position:0%
+partial derivatives are the slopes of
+slices of the graph by vertical planes
+
+ align:start position:0%
+slices of the graph by vertical planes
+ 
+
+ align:start position:0%
+slices of the graph by vertical planes
+that are parallel to the x or the Y
+
+ align:start position:0%
+that are parallel to the x or the Y
+ 
+
+ align:start position:0%
+that are parallel to the x or the Y
+directions okay so if I have a point you
+
+ align:start position:0%
+directions okay so if I have a point you
+ 
+
+ align:start position:0%
+directions okay so if I have a point you
+know at any point I can slice the graph
+
+ align:start position:0%
+know at any point I can slice the graph
+ 
+
+ align:start position:0%
+know at any point I can slice the graph
+of my function by two planes one that's
+
+ align:start position:0%
+of my function by two planes one that's
+ 
+
+ align:start position:0%
+of my function by two planes one that's
+going along the X One along the y
+
+ align:start position:0%
+going along the X One along the y
+ 
+
+ align:start position:0%
+going along the X One along the y
+direction and then I can look at
+
+ align:start position:0%
+direction and then I can look at
+ 
+
+ align:start position:0%
+direction and then I can look at
+the slices of the graph let me see if I
+
+ align:start position:0%
+the slices of the graph let me see if I
+ 
+
+ align:start position:0%
+the slices of the graph let me see if I
+can use that thing so we can look at the
+
+ align:start position:0%
+can use that thing so we can look at the
+ 
+
+ align:start position:0%
+can use that thing so we can look at the
+slices of the graph they drawn here and
+
+ align:start position:0%
+slices of the graph they drawn here and
+ 
+
+ align:start position:0%
+slices of the graph they drawn here and
+then we look at the tangent lines to
+
+ align:start position:0%
+then we look at the tangent lines to
+ 
+
+ align:start position:0%
+then we look at the tangent lines to
+these slices and we look at their slope
+
+ align:start position:0%
+these slices and we look at their slope
+ 
+
+ align:start position:0%
+these slices and we look at their slope
+and that gives us the partial
+
+ align:start position:0%
+and that gives us the partial
+ 
+
+ align:start position:0%
+and that gives us the partial
+derivatives in case you're on that side
+
+ align:start position:0%
+derivatives in case you're on that side
+ 
+
+ align:start position:0%
+derivatives in case you're on that side
+you want to see also the pointer was
+
+ align:start position:0%
+you want to see also the pointer was
+ 
+
+ align:start position:0%
+you want to see also the pointer was
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so now similarly the directional
+
+ align:start position:0%
+okay so now similarly the directional
+ 
+
+ align:start position:0%
+okay so now similarly the directional
+derivative means actually we'll be
+
+ align:start position:0%
+derivative means actually we'll be
+ 
+
+ align:start position:0%
+derivative means actually we'll be
+slicing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll be slicing our graph by a vertical
+
+ align:start position:0%
+we'll be slicing our graph by a vertical
+ 
+
+ align:start position:0%
+we'll be slicing our graph by a vertical
+plane it's not really colorful something
+
+ align:start position:0%
+plane it's not really colorful something
+ 
+
+ align:start position:0%
+plane it's not really colorful something
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+colorful we'll be slicing things by a
+
+ align:start position:0%
+colorful we'll be slicing things by a
+ 
+
+ align:start position:0%
+colorful we'll be slicing things by a
+plane that is now in the direction of
+
+ align:start position:0%
+plane that is now in the direction of
+ 
+
+ align:start position:0%
+plane that is now in the direction of
+this Vector U and we'll be looking at
+
+ align:start position:0%
+this Vector U and we'll be looking at
+ 
+
+ align:start position:0%
+this Vector U and we'll be looking at
+the slope of the slice of the graph so
+
+ align:start position:0%
+the slope of the slice of the graph so
+ 
+
+ align:start position:0%
+the slope of the slice of the graph so
+what that looks like
+
+ align:start position:0%
+what that looks like
+ 
+
+ align:start position:0%
+what that looks like
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so so that's the same applet by the way
+
+ align:start position:0%
+so so that's the same applet by the way
+ 
+
+ align:start position:0%
+so so that's the same applet by the way
+that you've used on your problem set in
+
+ align:start position:0%
+that you've used on your problem set in
+ 
+
+ align:start position:0%
+that you've used on your problem set in
+case you're
+
+ align:start position:0%
+case you're
+ 
+
+ align:start position:0%
+case you're
+wondering so now I'm picking a
+
+ align:start position:0%
+wondering so now I'm picking a
+ 
+
+ align:start position:0%
+wondering so now I'm picking a
+point on the Contour plot and at that
+
+ align:start position:0%
+point on the Contour plot and at that
+ 
+
+ align:start position:0%
+point on the Contour plot and at that
+point I slice the graph so here I'm
+
+ align:start position:0%
+point I slice the graph so here I'm
+ 
+
+ align:start position:0%
+point I slice the graph so here I'm
+starting by slicing in the direction of
+
+ align:start position:0%
+starting by slicing in the direction of
+ 
+
+ align:start position:0%
+starting by slicing in the direction of
+the xaxis so in fact what I'm measuring
+
+ align:start position:0%
+the xaxis so in fact what I'm measuring
+ 
+
+ align:start position:0%
+the xaxis so in fact what I'm measuring
+here by the slope of this slice is the
+
+ align:start position:0%
+here by the slope of this slice is the
+ 
+
+ align:start position:0%
+here by the slope of this slice is the
+partial in the X Direction it's really
+
+ align:start position:0%
+partial in the X Direction it's really
+ 
+
+ align:start position:0%
+partial in the X Direction it's really
+partial F partial X which is also the
+
+ align:start position:0%
+partial F partial X which is also the
+ 
+
+ align:start position:0%
+partial F partial X which is also the
+directional derivative in the direction
+
+ align:start position:0%
+directional derivative in the direction
+ 
+
+ align:start position:0%
+directional derivative in the direction
+of X of I sorry and now if I rotate the
+
+ align:start position:0%
+of X of I sorry and now if I rotate the
+ 
+
+ align:start position:0%
+of X of I sorry and now if I rotate the
+slice then I have all of these planes so
+
+ align:start position:0%
+slice then I have all of these planes so
+ 
+
+ align:start position:0%
+slice then I have all of these planes so
+you see at the bottom left I have the
+
+ align:start position:0%
+you see at the bottom left I have the
+ 
+
+ align:start position:0%
+you see at the bottom left I have the
+direction in which I'm going there's
+
+ align:start position:0%
+direction in which I'm going there's
+ 
+
+ align:start position:0%
+direction in which I'm going there's
+this like rotating line that tells you
+
+ align:start position:0%
+this like rotating line that tells you
+ 
+
+ align:start position:0%
+this like rotating line that tells you
+in which direction I'm going to be
+
+ align:start position:0%
+in which direction I'm going to be
+ 
+
+ align:start position:0%
+in which direction I'm going to be
+moving and for each Direction I have a
+
+ align:start position:0%
+moving and for each Direction I have a
+ 
+
+ align:start position:0%
+moving and for each Direction I have a
+plane and when I slice by that plane I
+
+ align:start position:0%
+plane and when I slice by that plane I
+ 
+
+ align:start position:0%
+plane and when I slice by that plane I
+will get so I have this direction here
+
+ align:start position:0%
+will get so I have this direction here
+ 
+
+ align:start position:0%
+will get so I have this direction here
+going maybe to the Southwest so that
+
+ align:start position:0%
+going maybe to the Southwest so that
+ 
+
+ align:start position:0%
+going maybe to the Southwest so that
+gives me a slice of My Graph by a
+
+ align:start position:0%
+gives me a slice of My Graph by a
+ 
+
+ align:start position:0%
+gives me a slice of My Graph by a
+vertical plane and the slice has a
+
+ align:start position:0%
+vertical plane and the slice has a
+ 
+
+ align:start position:0%
+vertical plane and the slice has a
+certain slope and the slope is going to
+
+ align:start position:0%
+certain slope and the slope is going to
+ 
+
+ align:start position:0%
+certain slope and the slope is going to
+be the directional derivative in that
+
+ align:start position:0%
+be the directional derivative in that
+ 
+
+ align:start position:0%
+be the directional derivative in that
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+okay I think that's as graphic as I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+okay any questions about
+
+ align:start position:0%
+okay any questions about
+ 
+
+ align:start position:0%
+okay any questions about
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+no okay so let's see how we compute that
+
+ align:start position:0%
+no okay so let's see how we compute that
+ 
+
+ align:start position:0%
+no okay so let's see how we compute that
+guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me just wrp again just in case
+
+ align:start position:0%
+so let me just wrp again just in case
+ 
+
+ align:start position:0%
+so let me just wrp again just in case
+you want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to case you didn't hear me it's the
+
+ align:start position:0%
+to case you didn't hear me it's the
+ 
+
+ align:start position:0%
+to case you didn't hear me it's the
+slope of the slice of the
+
+ align:start position:0%
+slope of the slice of the
+ 
+
+ align:start position:0%
+slope of the slice of the
+graph by a vertical
+
+ align:start position:0%
+graph by a vertical
+ 
+
+ align:start position:0%
+graph by a vertical
+plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that contains the given Direction U
+
+ align:start position:0%
+that contains the given Direction U
+ 
+
+ align:start position:0%
+that contains the given Direction U
+that's parallel to the direction
+
+ align:start position:0%
+that's parallel to the direction
+ 
+
+ align:start position:0%
+that's parallel to the direction
+U so how do we compute it well we can
+
+ align:start position:0%
+U so how do we compute it well we can
+ 
+
+ align:start position:0%
+U so how do we compute it well we can
+use the chain rule the chain
+
+ align:start position:0%
+use the chain rule the chain
+ 
+
+ align:start position:0%
+use the chain rule the chain
+rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implies that DW
+
+ align:start position:0%
+implies that DW
+ 
+
+ align:start position:0%
+implies that DW
+DS is actually the gradient of w do
+
+ align:start position:0%
+DS is actually the gradient of w do
+ 
+
+ align:start position:0%
+DS is actually the gradient of w do
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+the velocity Vector drds but remember we
+
+ align:start position:0%
+the velocity Vector drds but remember we
+ 
+
+ align:start position:0%
+the velocity Vector drds but remember we
+said that we are going to be moving at
+
+ align:start position:0%
+said that we are going to be moving at
+ 
+
+ align:start position:0%
+said that we are going to be moving at
+unit speed in the direction of U so in
+
+ align:start position:0%
+unit speed in the direction of U so in
+ 
+
+ align:start position:0%
+unit speed in the direction of U so in
+fact that's just gradient W do product
+
+ align:start position:0%
+fact that's just gradient W do product
+ 
+
+ align:start position:0%
+fact that's just gradient W do product
+with the unit Vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U okay so the formula that we remember
+
+ align:start position:0%
+U okay so the formula that we remember
+ 
+
+ align:start position:0%
+U okay so the formula that we remember
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+really d by DS in the direction of U is
+
+ align:start position:0%
+really d by DS in the direction of U is
+ 
+
+ align:start position:0%
+really d by DS in the direction of U is
+gradient W product with
+
+ align:start position:0%
+gradient W product with
+ 
+
+ align:start position:0%
+gradient W product with
+you and maybe I should also say in words
+
+ align:start position:0%
+you and maybe I should also say in words
+ 
+
+ align:start position:0%
+you and maybe I should also say in words
+this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+component of the gradient in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction of
+
+ align:start position:0%
+direction of
+ 
+
+ align:start position:0%
+direction of
+U and maybe that makes more sense so for
+
+ align:start position:0%
+U and maybe that makes more sense so for
+ 
+
+ align:start position:0%
+U and maybe that makes more sense so for
+example the directional derivative in
+
+ align:start position:0%
+example the directional derivative in
+ 
+
+ align:start position:0%
+example the directional derivative in
+the direction of IH hat is the component
+
+ align:start position:0%
+the direction of IH hat is the component
+ 
+
+ align:start position:0%
+the direction of IH hat is the component
+along the xaxis that's the same as
+
+ align:start position:0%
+along the xaxis that's the same as
+ 
+
+ align:start position:0%
+along the xaxis that's the same as
+indeed the partial derivative in the X
+
+ align:start position:0%
+indeed the partial derivative in the X
+ 
+
+ align:start position:0%
+indeed the partial derivative in the X
+Direction things make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense dwds the direction of IH hat
+
+ align:start position:0%
+sense dwds the direction of IH hat
+ 
+
+ align:start position:0%
+sense dwds the direction of IH hat
+is oh sorry what am I
+
+ align:start position:0%
+is oh sorry what am I
+ 
+
+ align:start position:0%
+is oh sorry what am I
+doing radi w. I hat which is W subx
+
+ align:start position:0%
+doing radi w. I hat which is W subx
+ 
+
+ align:start position:0%
+doing radi w. I hat which is W subx
+maybe I should find partial W partial X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so that's basically what we need to
+
+ align:start position:0%
+now so that's basically what we need to
+ 
+
+ align:start position:0%
+now so that's basically what we need to
+know to compute these
+
+ align:start position:0%
+know to compute these
+ 
+
+ align:start position:0%
+know to compute these
+guys so now let's go back to the
+
+ align:start position:0%
+guys so now let's go back to the
+ 
+
+ align:start position:0%
+guys so now let's go back to the
+gradient and see what this tells us
+
+ align:start position:0%
+gradient and see what this tells us
+ 
+
+ align:start position:0%
+gradient and see what this tells us
+about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I see you guys are having
+
+ align:start position:0%
+I see you guys are having
+ 
+
+ align:start position:0%
+I see you guys are having
+fun
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay let's do a little bit of
+
+ align:start position:0%
+okay okay let's do a little bit of
+ 
+
+ align:start position:0%
+okay okay let's do a little bit of
+geometry
+
+ align:start position:0%
+geometry
+ 
+
+ align:start position:0%
+geometry
+here that should calm you
+
+ align:start position:0%
+here that should calm you
+ 
+
+ align:start position:0%
+here that should calm you
+down so
+
+ align:start position:0%
+down so
+ 
+
+ align:start position:0%
+down so
+so we said dwds in the direction of U is
+
+ align:start position:0%
+so we said dwds in the direction of U is
+ 
+
+ align:start position:0%
+so we said dwds in the direction of U is
+gradient w. U that's the same as the
+
+ align:start position:0%
+gradient w. U that's the same as the
+ 
+
+ align:start position:0%
+gradient w. U that's the same as the
+length of gradient W Times the length of
+
+ align:start position:0%
+length of gradient W Times the length of
+ 
+
+ align:start position:0%
+length of gradient W Times the length of
+U well that happens to be one because
+
+ align:start position:0%
+U well that happens to be one because
+ 
+
+ align:start position:0%
+U well that happens to be one because
+we're taking a unit Vector times the
+
+ align:start position:0%
+we're taking a unit Vector times the
+ 
+
+ align:start position:0%
+we're taking a unit Vector times the
+cosine of the
+
+ align:start position:0%
+cosine of the
+ 
+
+ align:start position:0%
+cosine of the
+angle between the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradient and the given unit vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U so have this angle
+
+ align:start position:0%
+U so have this angle
+ 
+
+ align:start position:0%
+U so have this angle
+feta okay that's another way of saying
+
+ align:start position:0%
+feta okay that's another way of saying
+ 
+
+ align:start position:0%
+feta okay that's another way of saying
+we're taking the component of the
+
+ align:start position:0%
+we're taking the component of the
+ 
+
+ align:start position:0%
+we're taking the component of the
+gradient in the direction of U but now
+
+ align:start position:0%
+gradient in the direction of U but now
+ 
+
+ align:start position:0%
+gradient in the direction of U but now
+what does that tell us well let's try to
+
+ align:start position:0%
+what does that tell us well let's try to
+ 
+
+ align:start position:0%
+what does that tell us well let's try to
+figure out in which directions W changes
+
+ align:start position:0%
+figure out in which directions W changes
+ 
+
+ align:start position:0%
+figure out in which directions W changes
+the fastest in which direction it
+
+ align:start position:0%
+the fastest in which direction it
+ 
+
+ align:start position:0%
+the fastest in which direction it
+increases the most or decreases the most
+
+ align:start position:0%
+increases the most or decreases the most
+ 
+
+ align:start position:0%
+increases the most or decreases the most
+or doesn't actually
+
+ align:start position:0%
+or doesn't actually
+ 
+
+ align:start position:0%
+or doesn't actually
+change so this is when is this going to
+
+ align:start position:0%
+change so this is when is this going to
+ 
+
+ align:start position:0%
+change so this is when is this going to
+be the largest if I fix you if I fix a
+
+ align:start position:0%
+be the largest if I fix you if I fix a
+ 
+
+ align:start position:0%
+be the largest if I fix you if I fix a
+point if I set a point then the gradient
+
+ align:start position:0%
+point if I set a point then the gradient
+ 
+
+ align:start position:0%
+point if I set a point then the gradient
+Vector at that point is given to me but
+
+ align:start position:0%
+Vector at that point is given to me but
+ 
+
+ align:start position:0%
+Vector at that point is given to me but
+question is in which direction does it
+
+ align:start position:0%
+question is in which direction does it
+ 
+
+ align:start position:0%
+question is in which direction does it
+change the most quickly well what I can
+
+ align:start position:0%
+change the most quickly well what I can
+ 
+
+ align:start position:0%
+change the most quickly well what I can
+change is the direction and this will be
+
+ align:start position:0%
+change is the direction and this will be
+ 
+
+ align:start position:0%
+change is the direction and this will be
+the largest when the cosine is
+
+ align:start position:0%
+the largest when the cosine is
+ 
+
+ align:start position:0%
+the largest when the cosine is
+one so this is larest when cosine of the
+
+ align:start position:0%
+one so this is larest when cosine of the
+ 
+
+ align:start position:0%
+one so this is larest when cosine of the
+angle is one
+
+ align:start position:0%
+angle is one
+ 
+
+ align:start position:0%
+angle is one
+that means the angle is
+
+ align:start position:0%
+that means the angle is
+ 
+
+ align:start position:0%
+that means the angle is
+zero that means U is actually in the
+
+ align:start position:0%
+zero that means U is actually in the
+ 
+
+ align:start position:0%
+zero that means U is actually in the
+direction of the
+
+ align:start position:0%
+direction of the
+ 
+
+ align:start position:0%
+direction of the
+gradient okay so that's a new way to
+
+ align:start position:0%
+gradient okay so that's a new way to
+ 
+
+ align:start position:0%
+gradient okay so that's a new way to
+think about the direction of the
+
+ align:start position:0%
+think about the direction of the
+ 
+
+ align:start position:0%
+think about the direction of the
+gradient the gradient is the direction
+
+ align:start position:0%
+gradient the gradient is the direction
+ 
+
+ align:start position:0%
+gradient the gradient is the direction
+in which the function increases the most
+
+ align:start position:0%
+in which the function increases the most
+ 
+
+ align:start position:0%
+in which the function increases the most
+quickly at that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+direction of gradient W is the
+
+ align:start position:0%
+direction of gradient W is the
+ 
+
+ align:start position:0%
+direction of gradient W is the
+direction of fastest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+increase of w at the given point and
+
+ align:start position:0%
+increase of w at the given point and
+ 
+
+ align:start position:0%
+increase of w at the given point and
+what is the
+
+ align:start position:0%
+what is the
+ 
+
+ align:start position:0%
+what is the
+magnitude of w well it's actually the
+
+ align:start position:0%
+magnitude of w well it's actually the
+ 
+
+ align:start position:0%
+magnitude of w well it's actually the
+directional derivative in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if I go in that direction which
+
+ align:start position:0%
+okay so if I go in that direction which
+ 
+
+ align:start position:0%
+okay so if I go in that direction which
+gives me the fastest increase then the
+
+ align:start position:0%
+gives me the fastest increase then the
+ 
+
+ align:start position:0%
+gives me the fastest increase then the
+corresponding slope will be the length
+
+ align:start position:0%
+corresponding slope will be the length
+ 
+
+ align:start position:0%
+corresponding slope will be the length
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what's the direction of fastest
+
+ align:start position:0%
+and what's the direction of fastest
+ 
+
+ align:start position:0%
+and what's the direction of fastest
+decrease it's going in the opposite
+
+ align:start position:0%
+decrease it's going in the opposite
+ 
+
+ align:start position:0%
+decrease it's going in the opposite
+direction right I mean if you're a
+
+ align:start position:0%
+direction right I mean if you're a
+ 
+
+ align:start position:0%
+direction right I mean if you're a
+mountain and you know that you're facing
+
+ align:start position:0%
+mountain and you know that you're facing
+ 
+
+ align:start position:0%
+mountain and you know that you're facing
+the mountain uh that's the direction of
+
+ align:start position:0%
+the mountain uh that's the direction of
+ 
+
+ align:start position:0%
+the mountain uh that's the direction of
+fastest increase the direction of
+
+ align:start position:0%
+fastest increase the direction of
+ 
+
+ align:start position:0%
+fastest increase the direction of
+fastest decrease is behind you straight
+
+ align:start position:0%
+fastest decrease is behind you straight
+ 
+
+ align:start position:0%
+fastest decrease is behind you straight
+down okay
+
+ align:start position:0%
+down okay
+ 
+
+ align:start position:0%
+down okay
+so uh the minimal value of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dwds is achieved when cosine of theta is
+
+ align:start position:0%
+dwds is achieved when cosine of theta is
+ 
+
+ align:start position:0%
+dwds is achieved when cosine of theta is
+minus one that means Theta equal
+
+ align:start position:0%
+minus one that means Theta equal
+ 
+
+ align:start position:0%
+minus one that means Theta equal
+180° that means U is in the
+
+ align:start position:0%
+180° that means U is in the
+ 
+
+ align:start position:0%
+180° that means U is in the
+direction of minus the
+
+ align:start position:0%
+direction of minus the
+ 
+
+ align:start position:0%
+direction of minus the
+gradient head points opposite to the
+
+ align:start position:0%
+gradient head points opposite to the
+ 
+
+ align:start position:0%
+gradient head points opposite to the
+gradient
+
+ align:start position:0%
+gradient
+ 
+
+ align:start position:0%
+gradient
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+finally
+
+ align:start position:0%
+finally
+ 
+
+ align:start position:0%
+finally
+when do we have
+
+ align:start position:0%
+when do we have
+ 
+
+ align:start position:0%
+when do we have
+dwds equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero so in which direction does the
+
+ align:start position:0%
+zero so in which direction does the
+ 
+
+ align:start position:0%
+zero so in which direction does the
+function not
+
+ align:start position:0%
+function not
+ 
+
+ align:start position:0%
+function not
+change well we have two answers to that
+
+ align:start position:0%
+change well we have two answers to that
+ 
+
+ align:start position:0%
+change well we have two answers to that
+one is to just use that formula so
+
+ align:start position:0%
+one is to just use that formula so
+ 
+
+ align:start position:0%
+one is to just use that formula so
+that's when cosine Theta equal 0 that
+
+ align:start position:0%
+that's when cosine Theta equal 0 that
+ 
+
+ align:start position:0%
+that's when cosine Theta equal 0 that
+means Theta equal
+
+ align:start position:0%
+means Theta equal
+ 
+
+ align:start position:0%
+means Theta equal
+90° that means that U is perpendicular
+
+ align:start position:0%
+90° that means that U is perpendicular
+ 
+
+ align:start position:0%
+90° that means that U is perpendicular
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+gradient the other way to think about it
+
+ align:start position:0%
+gradient the other way to think about it
+ 
+
+ align:start position:0%
+gradient the other way to think about it
+a direction in which the value doesn't
+
+ align:start position:0%
+a direction in which the value doesn't
+ 
+
+ align:start position:0%
+a direction in which the value doesn't
+change is a Direction that's tangent to
+
+ align:start position:0%
+change is a Direction that's tangent to
+ 
+
+ align:start position:0%
+change is a Direction that's tangent to
+the level surface if we're not changing
+
+ align:start position:0%
+the level surface if we're not changing
+ 
+
+ align:start position:0%
+the level surface if we're not changing
+it means we're moving along the
+
+ align:start position:0%
+it means we're moving along the
+ 
+
+ align:start position:0%
+it means we're moving along the
+level and that's the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+as being tangent to the level so let me
+
+ align:start position:0%
+as being tangent to the level so let me
+ 
+
+ align:start position:0%
+as being tangent to the level so let me
+just show that on the picture
+
+ align:start position:0%
+just show that on the picture
+ 
+
+ align:start position:0%
+just show that on the picture
+here so if I actually show you the
+
+ align:start position:0%
+here so if I actually show you the
+ 
+
+ align:start position:0%
+here so if I actually show you the
+gradient uh you can't really see it here
+
+ align:start position:0%
+gradient uh you can't really see it here
+ 
+
+ align:start position:0%
+gradient uh you can't really see it here
+I need to move a bit okay so the
+
+ align:start position:0%
+I need to move a bit okay so the
+ 
+
+ align:start position:0%
+I need to move a bit okay so the
+gradient here is pointing straight up at
+
+ align:start position:0%
+gradient here is pointing straight up at
+ 
+
+ align:start position:0%
+gradient here is pointing straight up at
+the point that I've chosen now if I
+
+ align:start position:0%
+the point that I've chosen now if I
+ 
+
+ align:start position:0%
+the point that I've chosen now if I
+choose a slice that's
+
+ align:start position:0%
+choose a slice that's
+ 
+
+ align:start position:0%
+choose a slice that's
+perpendicular you know in a Direction
+
+ align:start position:0%
+perpendicular you know in a Direction
+ 
+
+ align:start position:0%
+perpendicular you know in a Direction
+that's perpendicular to the gradient so
+
+ align:start position:0%
+that's perpendicular to the gradient so
+ 
+
+ align:start position:0%
+that's perpendicular to the gradient so
+that's actually tangent to the level
+
+ align:start position:0%
+that's actually tangent to the level
+ 
+
+ align:start position:0%
+that's actually tangent to the level
+curve then you see that my slice is flat
+
+ align:start position:0%
+curve then you see that my slice is flat
+ 
+
+ align:start position:0%
+curve then you see that my slice is flat
+I don't actually have any slope the
+
+ align:start position:0%
+I don't actually have any slope the
+ 
+
+ align:start position:0%
+I don't actually have any slope the
+directional derivative in a Direction
+
+ align:start position:0%
+directional derivative in a Direction
+ 
+
+ align:start position:0%
+directional derivative in a Direction
+that's perpendicular to the gradient is
+
+ align:start position:0%
+that's perpendicular to the gradient is
+ 
+
+ align:start position:0%
+that's perpendicular to the gradient is
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+zero now if I rotate then the slope
+
+ align:start position:0%
+zero now if I rotate then the slope
+ 
+
+ align:start position:0%
+zero now if I rotate then the slope
+slowly increases increases increases and
+
+ align:start position:0%
+slowly increases increases increases and
+ 
+
+ align:start position:0%
+slowly increases increases increases and
+it becomes the largest when I'm going in
+
+ align:start position:0%
+it becomes the largest when I'm going in
+ 
+
+ align:start position:0%
+it becomes the largest when I'm going in
+the direction of the gradient so here I
+
+ align:start position:0%
+the direction of the gradient so here I
+ 
+
+ align:start position:0%
+the direction of the gradient so here I
+have actually a pretty big slope and now
+
+ align:start position:0%
+have actually a pretty big slope and now
+ 
+
+ align:start position:0%
+have actually a pretty big slope and now
+if I keep rotating then the slope will
+
+ align:start position:0%
+if I keep rotating then the slope will
+ 
+
+ align:start position:0%
+if I keep rotating then the slope will
+decrease again then it becomes zero when
+
+ align:start position:0%
+decrease again then it becomes zero when
+ 
+
+ align:start position:0%
+decrease again then it becomes zero when
+I'm perpendicular and then it becomes
+
+ align:start position:0%
+I'm perpendicular and then it becomes
+ 
+
+ align:start position:0%
+I'm perpendicular and then it becomes
+negative it's the most negative when I'm
+
+ align:start position:0%
+negative it's the most negative when I'm
+ 
+
+ align:start position:0%
+negative it's the most negative when I'm
+point away from the gradient and then
+
+ align:start position:0%
+point away from the gradient and then
+ 
+
+ align:start position:0%
+point away from the gradient and then
+become zero again when I'm back
+
+ align:start position:0%
+become zero again when I'm back
+ 
+
+ align:start position:0%
+become zero again when I'm back
+perpendicular okay so for example if I
+
+ align:start position:0%
+perpendicular okay so for example if I
+ 
+
+ align:start position:0%
+perpendicular okay so for example if I
+give you a contour plot and I ask you to
+
+ align:start position:0%
+give you a contour plot and I ask you to
+ 
+
+ align:start position:0%
+give you a contour plot and I ask you to
+draw the direction of the gradient
+
+ align:start position:0%
+draw the direction of the gradient
+ 
+
+ align:start position:0%
+draw the direction of the gradient
+Vector well at this point for example
+
+ align:start position:0%
+Vector well at this point for example
+ 
+
+ align:start position:0%
+Vector well at this point for example
+you would look at the picture the
+
+ align:start position:0%
+you would look at the picture the
+ 
+
+ align:start position:0%
+you would look at the picture the
+gradient Vector would be going
+
+ align:start position:0%
+gradient Vector would be going
+ 
+
+ align:start position:0%
+gradient Vector would be going
+perpendicular to the level and it would
+
+ align:start position:0%
+perpendicular to the level and it would
+ 
+
+ align:start position:0%
+perpendicular to the level and it would
+be going towards higher values of the
+
+ align:start position:0%
+be going towards higher values of the
+ 
+
+ align:start position:0%
+be going towards higher values of the
+function and I don't know if you can see
+
+ align:start position:0%
+function and I don't know if you can see
+ 
+
+ align:start position:0%
+function and I don't know if you can see
+the labels but the thing in the middle
+
+ align:start position:0%
+the labels but the thing in the middle
+ 
+
+ align:start position:0%
+the labels but the thing in the middle
+is minimum so it would actually be
+
+ align:start position:0%
+is minimum so it would actually be
+ 
+
+ align:start position:0%
+is minimum so it would actually be
+pointing in this kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction okay so that's it for
+
+ align:start position:0%
+Direction okay so that's it for
+ 
+
+ align:start position:0%
+Direction okay so that's it for
+today
\ No newline at end of file
diff --git a/2__KumJsGXc.txt b/2__KumJsGXc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5ce964811c20d9b0c9647152b1585a5b14f33fe0
--- /dev/null
+++ b/2__KumJsGXc.txt
@@ -0,0 +1,435 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu we
+
+ align:start position:0%
+ocw.mit.edu we
+ 
+
+ align:start position:0%
+ocw.mit.edu we
+have this definition for the class
+
+ align:start position:0%
+have this definition for the class
+ 
+
+ align:start position:0%
+have this definition for the class
+object I've
+
+ align:start position:0%
+object I've
+ 
+
+ align:start position:0%
+object I've
+um I've created the init for you and
+
+ align:start position:0%
+um I've created the init for you and
+ 
+
+ align:start position:0%
+um I've created the init for you and
+here I'm giving itself which is the
+
+ align:start position:0%
+here I'm giving itself which is the
+ 
+
+ align:start position:0%
+here I'm giving itself which is the
+first thing that you have to give it and
+
+ align:start position:0%
+first thing that you have to give it and
+ 
+
+ align:start position:0%
+first thing that you have to give it and
+then two parameters W and
+
+ align:start position:0%
+then two parameters W and
+ 
+
+ align:start position:0%
+then two parameters W and
+d and for for an instance of a car I'm
+
+ align:start position:0%
+d and for for an instance of a car I'm
+ 
+
+ align:start position:0%
+d and for for an instance of a car I'm
+going to assign the data attribute named
+
+ align:start position:0%
+going to assign the data attribute named
+ 
+
+ align:start position:0%
+going to assign the data attribute named
+Wheels to whatever is passed in for w so
+
+ align:start position:0%
+Wheels to whatever is passed in for w so
+ 
+
+ align:start position:0%
+Wheels to whatever is passed in for w so
+notice that they're not the same name
+
+ align:start position:0%
+notice that they're not the same name
+ 
+
+ align:start position:0%
+notice that they're not the same name
+and the data attribute for doors is
+
+ align:start position:0%
+and the data attribute for doors is
+ 
+
+ align:start position:0%
+and the data attribute for doors is
+going to be the value that's passed in
+
+ align:start position:0%
+going to be the value that's passed in
+ 
+
+ align:start position:0%
+going to be the value that's passed in
+for D okay and also notice that inside
+
+ align:start position:0%
+for D okay and also notice that inside
+ 
+
+ align:start position:0%
+for D okay and also notice that inside
+the init I can do any other sort of
+
+ align:start position:0%
+the init I can do any other sort of
+ 
+
+ align:start position:0%
+the init I can do any other sort of
+initializations that I'd like so it's
+
+ align:start position:0%
+initializations that I'd like so it's
+ 
+
+ align:start position:0%
+initializations that I'd like so it's
+not just assigning variables from the
+
+ align:start position:0%
+not just assigning variables from the
+ 
+
+ align:start position:0%
+not just assigning variables from the
+parameters to local to um to variables
+
+ align:start position:0%
+parameters to local to um to variables
+ 
+
+ align:start position:0%
+parameters to local to um to variables
+for for my objects so in this case I'm
+
+ align:start position:0%
+for for my objects so in this case I'm
+ 
+
+ align:start position:0%
+for for my objects so in this case I'm
+ass I'm creating a new data attribute
+
+ align:start position:0%
+ass I'm creating a new data attribute
+ 
+
+ align:start position:0%
+ass I'm creating a new data attribute
+named color and I'm going to just create
+
+ align:start position:0%
+named color and I'm going to just create
+ 
+
+ align:start position:0%
+named color and I'm going to just create
+it to be an empty string okay notice
+
+ align:start position:0%
+it to be an empty string okay notice
+ 
+
+ align:start position:0%
+it to be an empty string okay notice
+because I didn't even even though I
+
+ align:start position:0%
+because I didn't even even though I
+ 
+
+ align:start position:0%
+because I didn't even even though I
+didn't pass in any color to my uh to my
+
+ align:start position:0%
+didn't pass in any color to my uh to my
+ 
+
+ align:start position:0%
+didn't pass in any color to my uh to my
+object so the question says using the
+
+ align:start position:0%
+object so the question says using the
+ 
+
+ align:start position:0%
+object so the question says using the
+class definition above which line
+
+ align:start position:0%
+class definition above which line
+ 
+
+ align:start position:0%
+class definition above which line
+creates a new car object with four
+
+ align:start position:0%
+creates a new car object with four
+ 
+
+ align:start position:0%
+creates a new car object with four
+wheels and two doors okay so this
+
+ align:start position:0%
+wheels and two doors okay so this
+ 
+
+ align:start position:0%
+wheels and two doors okay so this
+um this first
+
+ align:start position:0%
+um this first
+ 
+
+ align:start position:0%
+um this first
+one is not right because it's trying to
+
+ align:start position:0%
+one is not right because it's trying to
+ 
+
+ align:start position:0%
+one is not right because it's trying to
+call the class with a variable my car so
+
+ align:start position:0%
+call the class with a variable my car so
+ 
+
+ align:start position:0%
+call the class with a variable my car so
+for self which isn't quite right so when
+
+ align:start position:0%
+for self which isn't quite right so when
+ 
+
+ align:start position:0%
+for self which isn't quite right so when
+you're creating a when you're creating
+
+ align:start position:0%
+you're creating a when you're creating
+ 
+
+ align:start position:0%
+you're creating a when you're creating
+your object you have to give it one less
+
+ align:start position:0%
+your object you have to give it one less
+ 
+
+ align:start position:0%
+your object you have to give it one less
+parameter than what you have so here
+
+ align:start position:0%
+parameter than what you have so here
+ 
+
+ align:start position:0%
+parameter than what you have so here
+we're just going to have to create it
+
+ align:start position:0%
+we're just going to have to create it
+ 
+
+ align:start position:0%
+we're just going to have to create it
+with the w and the
+
+ align:start position:0%
+with the w and the
+ 
+
+ align:start position:0%
+with the w and the
+D so we're going to create this
+
+ align:start position:0%
+D so we're going to create this
+ 
+
+ align:start position:0%
+D so we're going to create this
+the these variable this variable my car
+
+ align:start position:0%
+the these variable this variable my car
+ 
+
+ align:start position:0%
+the these variable this variable my car
+and we're going to assign it four for
+
+ align:start position:0%
+and we're going to assign it four for
+ 
+
+ align:start position:0%
+and we're going to assign it four for
+the number of uh wheels and two for the
+
+ align:start position:0%
+the number of uh wheels and two for the
+ 
+
+ align:start position:0%
+the number of uh wheels and two for the
+number of doors and the number of Wheels
+
+ align:start position:0%
+number of doors and the number of Wheels
+ 
+
+ align:start position:0%
+number of doors and the number of Wheels
+is the first parameter and the number of
+
+ align:start position:0%
+is the first parameter and the number of
+ 
+
+ align:start position:0%
+is the first parameter and the number of
+doors is the second one so it should be
+
+ align:start position:0%
+doors is the second one so it should be
+ 
+
+ align:start position:0%
+doors is the second one so it should be
+this one here car 4 comma 2 so that's
+
+ align:start position:0%
+this one here car 4 comma 2 so that's
+ 
+
+ align:start position:0%
+this one here car 4 comma 2 so that's
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+perfect
\ No newline at end of file
diff --git a/2guwjwIHmGg.txt b/2guwjwIHmGg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4b2f71439cfbfdf93820927cb016ab6d34710080
--- /dev/null
+++ b/2guwjwIHmGg.txt
@@ -0,0 +1,1011 @@
+align:start position:0%
+ 
+when we used our energy principle
+
+ align:start position:0%
+when we used our energy principle
+ 
+
+ align:start position:0%
+when we used our energy principle
+suppose we have an object that starts at
+
+ align:start position:0%
+suppose we have an object that starts at
+ 
+
+ align:start position:0%
+suppose we have an object that starts at
+a height H naught and this object is
+
+ align:start position:0%
+a height H naught and this object is
+ 
+
+ align:start position:0%
+a height H naught and this object is
+dropped and when it gets to the ground
+
+ align:start position:0%
+dropped and when it gets to the ground
+ 
+
+ align:start position:0%
+dropped and when it gets to the ground
+it has some final velocity and when we
+
+ align:start position:0%
+it has some final velocity and when we
+ 
+
+ align:start position:0%
+it has some final velocity and when we
+applied our energy principle assuming
+
+ align:start position:0%
+applied our energy principle assuming
+ 
+
+ align:start position:0%
+applied our energy principle assuming
+that there was no air resistance what we
+
+ align:start position:0%
+that there was no air resistance what we
+ 
+
+ align:start position:0%
+that there was no air resistance what we
+saw was that the change in kinetic
+
+ align:start position:0%
+saw was that the change in kinetic
+ 
+
+ align:start position:0%
+saw was that the change in kinetic
+energy plus the change a potential
+
+ align:start position:0%
+energy plus the change a potential
+ 
+
+ align:start position:0%
+energy plus the change a potential
+energy was zero so we had zero was equal
+
+ align:start position:0%
+energy was zero so we had zero was equal
+ 
+
+ align:start position:0%
+energy was zero so we had zero was equal
+to Delta K plus Delta U and we saw that
+
+ align:start position:0%
+to Delta K plus Delta U and we saw that
+ 
+
+ align:start position:0%
+to Delta K plus Delta U and we saw that
+the kinetic energy changed by one-half
+
+ align:start position:0%
+the kinetic energy changed by one-half
+ 
+
+ align:start position:0%
+the kinetic energy changed by one-half
+MV squared and the potential energy
+
+ align:start position:0%
+MV squared and the potential energy
+ 
+
+ align:start position:0%
+MV squared and the potential energy
+changed by minus MGH not so we can
+
+ align:start position:0%
+changed by minus MGH not so we can
+ 
+
+ align:start position:0%
+changed by minus MGH not so we can
+compute the velocity of the object as
+
+ align:start position:0%
+compute the velocity of the object as
+ 
+
+ align:start position:0%
+compute the velocity of the object as
+its falling given by square root of 2gh
+
+ align:start position:0%
+its falling given by square root of 2gh
+ 
+
+ align:start position:0%
+its falling given by square root of 2gh
+not now now that we're considering
+
+ align:start position:0%
+not now now that we're considering
+ 
+
+ align:start position:0%
+not now now that we're considering
+kinetic energy of rotation
+
+ align:start position:0%
+kinetic energy of rotation
+ 
+
+ align:start position:0%
+kinetic energy of rotation
+recall that we showed that the kinetic
+
+ align:start position:0%
+recall that we showed that the kinetic
+ 
+
+ align:start position:0%
+recall that we showed that the kinetic
+energy of rotate of a pure rotation
+
+ align:start position:0%
+energy of rotate of a pure rotation
+ 
+
+ align:start position:0%
+energy of rotate of a pure rotation
+about a fixed axis was one-half the
+
+ align:start position:0%
+about a fixed axis was one-half the
+ 
+
+ align:start position:0%
+about a fixed axis was one-half the
+moment of inertia about that axis times
+
+ align:start position:0%
+moment of inertia about that axis times
+ 
+
+ align:start position:0%
+moment of inertia about that axis times
+the angular speed squared we now would
+
+ align:start position:0%
+the angular speed squared we now would
+ 
+
+ align:start position:0%
+the angular speed squared we now would
+like to apply our energy principle to
+
+ align:start position:0%
+like to apply our energy principle to
+ 
+
+ align:start position:0%
+like to apply our energy principle to
+include rotational kinetic energy along
+
+ align:start position:0%
+include rotational kinetic energy along
+ 
+
+ align:start position:0%
+include rotational kinetic energy along
+with the translational kinetic energy
+
+ align:start position:0%
+with the translational kinetic energy
+ 
+
+ align:start position:0%
+with the translational kinetic energy
+and the example that we want to look at
+
+ align:start position:0%
+and the example that we want to look at
+ 
+
+ align:start position:0%
+and the example that we want to look at
+is something very simple suppose we have
+
+ align:start position:0%
+is something very simple suppose we have
+ 
+
+ align:start position:0%
+is something very simple suppose we have
+a pulley
+
+ align:start position:0%
+a pulley
+ 
+
+ align:start position:0%
+a pulley
+now our pulley has a mass P and we'll
+
+ align:start position:0%
+now our pulley has a mass P and we'll
+ 
+
+ align:start position:0%
+now our pulley has a mass P and we'll
+say it has a moment of inertia of the
+
+ align:start position:0%
+say it has a moment of inertia of the
+ 
+
+ align:start position:0%
+say it has a moment of inertia of the
+pulley about the fixed axis passing
+
+ align:start position:0%
+pulley about the fixed axis passing
+ 
+
+ align:start position:0%
+pulley about the fixed axis passing
+through the center of the pulley and we
+
+ align:start position:0%
+through the center of the pulley and we
+ 
+
+ align:start position:0%
+through the center of the pulley and we
+have a mass one and another block two
+
+ align:start position:0%
+have a mass one and another block two
+ 
+
+ align:start position:0%
+have a mass one and another block two
+and let's suppose that we release this
+
+ align:start position:0%
+and let's suppose that we release this
+ 
+
+ align:start position:0%
+and let's suppose that we release this
+system and for the moment let's make
+
+ align:start position:0%
+system and for the moment let's make
+ 
+
+ align:start position:0%
+system and for the moment let's make
+this surface frictionless and suppose
+
+ align:start position:0%
+this surface frictionless and suppose
+ 
+
+ align:start position:0%
+this surface frictionless and suppose
+that block two falls down a certain
+
+ align:start position:0%
+that block two falls down a certain
+ 
+
+ align:start position:0%
+that block two falls down a certain
+distance so in the final state block two
+
+ align:start position:0%
+distance so in the final state block two
+ 
+
+ align:start position:0%
+distance so in the final state block two
+will have dropped the distance H final
+
+ align:start position:0%
+will have dropped the distance H final
+ 
+
+ align:start position:0%
+will have dropped the distance H final
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+it's initial position and what we'd like
+
+ align:start position:0%
+it's initial position and what we'd like
+ 
+
+ align:start position:0%
+it's initial position and what we'd like
+to consider is find the velocity final
+
+ align:start position:0%
+to consider is find the velocity final
+ 
+
+ align:start position:0%
+to consider is find the velocity final
+of block two so we begin in the same way
+
+ align:start position:0%
+of block two so we begin in the same way
+ 
+
+ align:start position:0%
+of block two so we begin in the same way
+that we've done this before by
+
+ align:start position:0%
+that we've done this before by
+ 
+
+ align:start position:0%
+that we've done this before by
+considering our energy diagrams and so
+
+ align:start position:0%
+considering our energy diagrams and so
+ 
+
+ align:start position:0%
+considering our energy diagrams and so
+we'll have an initial state and in our
+
+ align:start position:0%
+we'll have an initial state and in our
+ 
+
+ align:start position:0%
+we'll have an initial state and in our
+initial state what we'll do is we'll
+
+ align:start position:0%
+initial state what we'll do is we'll
+ 
+
+ align:start position:0%
+initial state what we'll do is we'll
+just have the initial one two and I'm
+
+ align:start position:0%
+just have the initial one two and I'm
+ 
+
+ align:start position:0%
+just have the initial one two and I'm
+going to choose u equals zero here's my
+
+ align:start position:0%
+going to choose u equals zero here's my
+ 
+
+ align:start position:0%
+going to choose u equals zero here's my
+pulley and everything is at rest and so
+
+ align:start position:0%
+pulley and everything is at rest and so
+ 
+
+ align:start position:0%
+pulley and everything is at rest and so
+in the initial state the initial energy
+
+ align:start position:0%
+in the initial state the initial energy
+ 
+
+ align:start position:0%
+in the initial state the initial energy
+initial K initial plus u initial is zero
+
+ align:start position:0%
+initial K initial plus u initial is zero
+ 
+
+ align:start position:0%
+initial K initial plus u initial is zero
+and in our final state we have the
+
+ align:start position:0%
+and in our final state we have the
+ 
+
+ align:start position:0%
+and in our final state we have the
+pulley is rotating with Omega final
+
+ align:start position:0%
+pulley is rotating with Omega final
+ 
+
+ align:start position:0%
+pulley is rotating with Omega final
+block one is moving with the velocity V
+
+ align:start position:0%
+block one is moving with the velocity V
+ 
+
+ align:start position:0%
+block one is moving with the velocity V
+final one and block two is also moving
+
+ align:start position:0%
+final one and block two is also moving
+ 
+
+ align:start position:0%
+final one and block two is also moving
+with v2 final and let's just suppose
+
+ align:start position:0%
+with v2 final and let's just suppose
+ 
+
+ align:start position:0%
+with v2 final and let's just suppose
+that this was our u equals zero position
+
+ align:start position:0%
+that this was our u equals zero position
+ 
+
+ align:start position:0%
+that this was our u equals zero position
+and although it's so clear on the
+
+ align:start position:0%
+and although it's so clear on the
+ 
+
+ align:start position:0%
+and although it's so clear on the
+diagram u final it has moved down height
+
+ align:start position:0%
+diagram u final it has moved down height
+ 
+
+ align:start position:0%
+diagram u final it has moved down height
+H final so what is the energy in our
+
+ align:start position:0%
+H final so what is the energy in our
+ 
+
+ align:start position:0%
+H final so what is the energy in our
+final state well we have to consider all
+
+ align:start position:0%
+final state well we have to consider all
+ 
+
+ align:start position:0%
+final state well we have to consider all
+the different pieces we have block one
+
+ align:start position:0%
+the different pieces we have block one
+ 
+
+ align:start position:0%
+the different pieces we have block one
+one-half m1 v1 final squared we have the
+
+ align:start position:0%
+one-half m1 v1 final squared we have the
+ 
+
+ align:start position:0%
+one-half m1 v1 final squared we have the
+motion of block 2 one-half m2 v2 final
+
+ align:start position:0%
+motion of block 2 one-half m2 v2 final
+ 
+
+ align:start position:0%
+motion of block 2 one-half m2 v2 final
+squared and we also have the kinetic
+
+ align:start position:0%
+squared and we also have the kinetic
+ 
+
+ align:start position:0%
+squared and we also have the kinetic
+energy of the pulley which is given by
+
+ align:start position:0%
+energy of the pulley which is given by
+ 
+
+ align:start position:0%
+energy of the pulley which is given by
+1/2 I about the pulley Omega final
+
+ align:start position:0%
+1/2 I about the pulley Omega final
+ 
+
+ align:start position:0%
+1/2 I about the pulley Omega final
+square and what about our final
+
+ align:start position:0%
+square and what about our final
+ 
+
+ align:start position:0%
+square and what about our final
+potential energy well we dropped the
+
+ align:start position:0%
+potential energy well we dropped the
+ 
+
+ align:start position:0%
+potential energy well we dropped the
+height H final so we have block two has
+
+ align:start position:0%
+height H final so we have block two has
+ 
+
+ align:start position:0%
+height H final so we have block two has
+moved minus em 2 gee H final and now we
+
+ align:start position:0%
+moved minus em 2 gee H final and now we
+ 
+
+ align:start position:0%
+moved minus em 2 gee H final and now we
+have our two energy states
+
+ align:start position:0%
+have our two energy states
+ 
+
+ align:start position:0%
+have our two energy states
+and what we'd like to consider is apply
+
+ align:start position:0%
+and what we'd like to consider is apply
+ 
+
+ align:start position:0%
+and what we'd like to consider is apply
+the energy principle just like we
+
+ align:start position:0%
+the energy principle just like we
+ 
+
+ align:start position:0%
+the energy principle just like we
+applied it for this simple case but
+
+ align:start position:0%
+applied it for this simple case but
+ 
+
+ align:start position:0%
+applied it for this simple case but
+before we do that there is a constraint
+
+ align:start position:0%
+before we do that there is a constraint
+ 
+
+ align:start position:0%
+before we do that there is a constraint
+condition that because the Rope is fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in length as block one moves the pulley
+
+ align:start position:0%
+in length as block one moves the pulley
+ 
+
+ align:start position:0%
+in length as block one moves the pulley
+is rotating and block 2 is moving what
+
+ align:start position:0%
+is rotating and block 2 is moving what
+ 
+
+ align:start position:0%
+is rotating and block 2 is moving what
+we'll have is fixed and not slipping so
+
+ align:start position:0%
+we'll have is fixed and not slipping so
+ 
+
+ align:start position:0%
+we'll have is fixed and not slipping so
+as the Rope moves around the pulley the
+
+ align:start position:0%
+as the Rope moves around the pulley the
+ 
+
+ align:start position:0%
+as the Rope moves around the pulley the
+pulley is moving with the same motion is
+
+ align:start position:0%
+pulley is moving with the same motion is
+ 
+
+ align:start position:0%
+pulley is moving with the same motion is
+the rope and the Rope is moving with the
+
+ align:start position:0%
+the rope and the Rope is moving with the
+ 
+
+ align:start position:0%
+the rope and the Rope is moving with the
+speeds of block 1 and 2 so we see that V
+
+ align:start position:0%
+speeds of block 1 and 2 so we see that V
+ 
+
+ align:start position:0%
+speeds of block 1 and 2 so we see that V
+1 final is equal to B 2 final and now
+
+ align:start position:0%
+1 final is equal to B 2 final and now
+ 
+
+ align:start position:0%
+1 final is equal to B 2 final and now
+what about the pulley if this is radius
+
+ align:start position:0%
+what about the pulley if this is radius
+ 
+
+ align:start position:0%
+what about the pulley if this is radius
+R we know that the velocity of a point
+
+ align:start position:0%
+R we know that the velocity of a point
+ 
+
+ align:start position:0%
+R we know that the velocity of a point
+on the rim of a disc is moving with the
+
+ align:start position:0%
+on the rim of a disc is moving with the
+ 
+
+ align:start position:0%
+on the rim of a disc is moving with the
+speed of the rope which is the speed of
+
+ align:start position:0%
+speed of the rope which is the speed of
+ 
+
+ align:start position:0%
+speed of the rope which is the speed of
+block 1 and block 2 so that's our Omega
+
+ align:start position:0%
+block 1 and block 2 so that's our Omega
+ 
+
+ align:start position:0%
+block 1 and block 2 so that's our Omega
+final and so that makes our final energy
+
+ align:start position:0%
+final and so that makes our final energy
+ 
+
+ align:start position:0%
+final and so that makes our final energy
+that's now gather terms the velocities
+
+ align:start position:0%
+that's now gather terms the velocities
+ 
+
+ align:start position:0%
+that's now gather terms the velocities
+are the same so we have one-half m1 plus
+
+ align:start position:0%
+are the same so we have one-half m1 plus
+ 
+
+ align:start position:0%
+are the same so we have one-half m1 plus
+m2 and we'll just call this V final for
+
+ align:start position:0%
+m2 and we'll just call this V final for
+ 
+
+ align:start position:0%
+m2 and we'll just call this V final for
+simplicity one-half m2 times V final
+
+ align:start position:0%
+simplicity one-half m2 times V final
+ 
+
+ align:start position:0%
+simplicity one-half m2 times V final
+squared that accounts for these two
+
+ align:start position:0%
+squared that accounts for these two
+ 
+
+ align:start position:0%
+squared that accounts for these two
+terms and we have the moment of inertia
+
+ align:start position:0%
+terms and we have the moment of inertia
+ 
+
+ align:start position:0%
+terms and we have the moment of inertia
+kinetic energy associated with the wheel
+
+ align:start position:0%
+kinetic energy associated with the wheel
+ 
+
+ align:start position:0%
+kinetic energy associated with the wheel
+which is one-half I Omega final squared
+
+ align:start position:0%
+which is one-half I Omega final squared
+ 
+
+ align:start position:0%
+which is one-half I Omega final squared
+which is V final squared over R squared
+
+ align:start position:0%
+which is V final squared over R squared
+ 
+
+ align:start position:0%
+which is V final squared over R squared
+minus em 2 gee H final and so now we can
+
+ align:start position:0%
+minus em 2 gee H final and so now we can
+ 
+
+ align:start position:0%
+minus em 2 gee H final and so now we can
+solve our energy principle which is
+
+ align:start position:0%
+solve our energy principle which is
+ 
+
+ align:start position:0%
+solve our energy principle which is
+because we're assuming everything is
+
+ align:start position:0%
+because we're assuming everything is
+ 
+
+ align:start position:0%
+because we're assuming everything is
+frictionless we have 0 equals e final
+
+ align:start position:0%
+frictionless we have 0 equals e final
+ 
+
+ align:start position:0%
+frictionless we have 0 equals e final
+minus initial implies that a final
+
+ align:start position:0%
+minus initial implies that a final
+ 
+
+ align:start position:0%
+minus initial implies that a final
+equals the initial and we chose our
+
+ align:start position:0%
+equals the initial and we chose our
+ 
+
+ align:start position:0%
+equals the initial and we chose our
+initial potential energy to be zero so
+
+ align:start position:0%
+initial potential energy to be zero so
+ 
+
+ align:start position:0%
+initial potential energy to be zero so
+of course that's just a choice of
+
+ align:start position:0%
+of course that's just a choice of
+ 
+
+ align:start position:0%
+of course that's just a choice of
+constant so I can now solve this
+
+ align:start position:0%
+constant so I can now solve this
+ 
+
+ align:start position:0%
+constant so I can now solve this
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+by setting a final equal to zero that's
+
+ align:start position:0%
+by setting a final equal to zero that's
+ 
+
+ align:start position:0%
+by setting a final equal to zero that's
+the same statement and then you can see
+
+ align:start position:0%
+the same statement and then you can see
+ 
+
+ align:start position:0%
+the same statement and then you can see
+algebraically I can solve for V final
+
+ align:start position:0%
+algebraically I can solve for V final
+ 
+
+ align:start position:0%
+algebraically I can solve for V final
+and what I get is I'm just going to
+
+ align:start position:0%
+and what I get is I'm just going to
+ 
+
+ align:start position:0%
+and what I get is I'm just going to
+write all these terms over I get em 2
+
+ align:start position:0%
+write all these terms over I get em 2
+ 
+
+ align:start position:0%
+write all these terms over I get em 2
+gee H final I'm gonna divide by this
+
+ align:start position:0%
+gee H final I'm gonna divide by this
+ 
+
+ align:start position:0%
+gee H final I'm gonna divide by this
+common coefficient 1/2 + 1 + M 2 plus
+
+ align:start position:0%
+common coefficient 1/2 + 1 + M 2 plus
+ 
+
+ align:start position:0%
+common coefficient 1/2 + 1 + M 2 plus
+the moment of inertia divided by radius
+
+ align:start position:0%
+the moment of inertia divided by radius
+ 
+
+ align:start position:0%
+the moment of inertia divided by radius
+squared and I now have to take the
+
+ align:start position:0%
+squared and I now have to take the
+ 
+
+ align:start position:0%
+squared and I now have to take the
+square root of the whole thing and
+
+ align:start position:0%
+square root of the whole thing and
+ 
+
+ align:start position:0%
+square root of the whole thing and
+that's how I can find the velocity of
+
+ align:start position:0%
+that's how I can find the velocity of
+ 
+
+ align:start position:0%
+that's how I can find the velocity of
+block 2 when it's dropped down a certain
+
+ align:start position:0%
+block 2 when it's dropped down a certain
+ 
+
+ align:start position:0%
+block 2 when it's dropped down a certain
+distance H final so here we've
+
+ align:start position:0%
+distance H final so here we've
+ 
+
+ align:start position:0%
+distance H final so here we've
+generalized our energy approach to
+
+ align:start position:0%
+generalized our energy approach to
+ 
+
+ align:start position:0%
+generalized our energy approach to
+include rotational kinetic energy
\ No newline at end of file
diff --git a/2hNfJwfEvkA.txt b/2hNfJwfEvkA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fb0754afbf68954fafa7a93df45436dc877a148a
--- /dev/null
+++ b/2hNfJwfEvkA.txt
@@ -0,0 +1,15659 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu but let me mention again the
+
+ align:start position:0%
+ocw.mit.edu but let me mention again the
+ 
+
+ align:start position:0%
+ocw.mit.edu but let me mention again the
+tremendous importance uh of for for the
+
+ align:start position:0%
+tremendous importance uh of for for the
+ 
+
+ align:start position:0%
+tremendous importance uh of for for the
+for your understanding of the subject
+
+ align:start position:0%
+for your understanding of the subject
+ 
+
+ align:start position:0%
+for your understanding of the subject
+matter of the course uh of your watching
+
+ align:start position:0%
+matter of the course uh of your watching
+ 
+
+ align:start position:0%
+matter of the course uh of your watching
+as much television as possible not only
+
+ align:start position:0%
+as much television as possible not only
+ 
+
+ align:start position:0%
+as much television as possible not only
+the new prime time schedule that's about
+
+ align:start position:0%
+the new prime time schedule that's about
+ 
+
+ align:start position:0%
+the new prime time schedule that's about
+to start next week uh watch as much of
+
+ align:start position:0%
+to start next week uh watch as much of
+ 
+
+ align:start position:0%
+to start next week uh watch as much of
+it as you can make time for and we'll
+
+ align:start position:0%
+it as you can make time for and we'll
+ 
+
+ align:start position:0%
+it as you can make time for and we'll
+single out certain programs that I hope
+
+ align:start position:0%
+single out certain programs that I hope
+ 
+
+ align:start position:0%
+single out certain programs that I hope
+everyone will watch so we'll have some
+
+ align:start position:0%
+everyone will watch so we'll have some
+ 
+
+ align:start position:0%
+everyone will watch so we'll have some
+some uh shared experience of
+
+ align:start position:0%
+some uh shared experience of
+ 
+
+ align:start position:0%
+some uh shared experience of
+contemporary television that will uh
+
+ align:start position:0%
+contemporary television that will uh
+ 
+
+ align:start position:0%
+contemporary television that will uh
+create a kind of ballast for our
+
+ align:start position:0%
+create a kind of ballast for our
+ 
+
+ align:start position:0%
+create a kind of ballast for our
+argument and complicate our argument and
+
+ align:start position:0%
+argument and complicate our argument and
+ 
+
+ align:start position:0%
+argument and complicate our argument and
+allow us to draw on some common examples
+
+ align:start position:0%
+allow us to draw on some common examples
+ 
+
+ align:start position:0%
+allow us to draw on some common examples
+but even more important than that are
+
+ align:start position:0%
+but even more important than that are
+ 
+
+ align:start position:0%
+but even more important than that are
+the reruns that are on during the day on
+
+ align:start position:0%
+the reruns that are on during the day on
+ 
+
+ align:start position:0%
+the reruns that are on during the day on
+many channels and are especially
+
+ align:start position:0%
+many channels and are especially
+ 
+
+ align:start position:0%
+many channels and are especially
+available on Nick at night and TV Land
+
+ align:start position:0%
+available on Nick at night and TV Land
+ 
+
+ align:start position:0%
+available on Nick at night and TV Land
+and those of you who get who have access
+
+ align:start position:0%
+and those of you who get who have access
+ 
+
+ align:start position:0%
+and those of you who get who have access
+to Cable Systems should really watch
+
+ align:start position:0%
+to Cable Systems should really watch
+ 
+
+ align:start position:0%
+to Cable Systems should really watch
+those programs you can they they
+
+ align:start position:0%
+those programs you can they they
+ 
+
+ align:start position:0%
+those programs you can they they
+constitute over the course of a week or
+
+ align:start position:0%
+constitute over the course of a week or
+ 
+
+ align:start position:0%
+constitute over the course of a week or
+so a kind of mini history of the medium
+
+ align:start position:0%
+so a kind of mini history of the medium
+ 
+
+ align:start position:0%
+so a kind of mini history of the medium
+and we're going to be trying to
+
+ align:start position:0%
+and we're going to be trying to
+ 
+
+ align:start position:0%
+and we're going to be trying to
+construct a history of the medium that
+
+ align:start position:0%
+construct a history of the medium that
+ 
+
+ align:start position:0%
+construct a history of the medium that
+takes account of the external the
+
+ align:start position:0%
+takes account of the external the
+ 
+
+ align:start position:0%
+takes account of the external the
+political soci social forces that are
+
+ align:start position:0%
+political soci social forces that are
+ 
+
+ align:start position:0%
+political soci social forces that are
+shaping the medium but also take account
+
+ align:start position:0%
+shaping the medium but also take account
+ 
+
+ align:start position:0%
+shaping the medium but also take account
+of what we might call the internal
+
+ align:start position:0%
+of what we might call the internal
+ 
+
+ align:start position:0%
+of what we might call the internal
+Dynamic whereby a media system once it
+
+ align:start position:0%
+Dynamic whereby a media system once it
+ 
+
+ align:start position:0%
+Dynamic whereby a media system once it
+is stabilized in a society uh um uh
+
+ align:start position:0%
+is stabilized in a society uh um uh
+ 
+
+ align:start position:0%
+is stabilized in a society uh um uh
+elaborates itself and evolves in certain
+
+ align:start position:0%
+elaborates itself and evolves in certain
+ 
+
+ align:start position:0%
+elaborates itself and evolves in certain
+ways that I hope I can dramatize in a
+
+ align:start position:0%
+ways that I hope I can dramatize in a
+ 
+
+ align:start position:0%
+ways that I hope I can dramatize in a
+very in a very U credible and and and uh
+
+ align:start position:0%
+very in a very U credible and and and uh
+ 
+
+ align:start position:0%
+very in a very U credible and and and uh
+useful way for you as I suggested a few
+
+ align:start position:0%
+useful way for you as I suggested a few
+ 
+
+ align:start position:0%
+useful way for you as I suggested a few
+times in earlier classes one advantage
+
+ align:start position:0%
+times in earlier classes one advantage
+ 
+
+ align:start position:0%
+times in earlier classes one advantage
+of the perspective I try to suggest in
+
+ align:start position:0%
+of the perspective I try to suggest in
+ 
+
+ align:start position:0%
+of the perspective I try to suggest in
+this course is that it isn't limited to
+
+ align:start position:0%
+this course is that it isn't limited to
+ 
+
+ align:start position:0%
+this course is that it isn't limited to
+television that the that the framework
+
+ align:start position:0%
+television that the that the framework
+ 
+
+ align:start position:0%
+television that the that the framework
+theoretically I believe the framework
+
+ align:start position:0%
+theoretically I believe the framework
+ 
+
+ align:start position:0%
+theoretically I believe the framework
+could be used for virtually any media
+
+ align:start position:0%
+could be used for virtually any media
+ 
+
+ align:start position:0%
+could be used for virtually any media
+system with you have to be flexible and
+
+ align:start position:0%
+system with you have to be flexible and
+ 
+
+ align:start position:0%
+system with you have to be flexible and
+apply it in a flexible way but there's a
+
+ align:start position:0%
+apply it in a flexible way but there's a
+ 
+
+ align:start position:0%
+apply it in a flexible way but there's a
+process of of there's a process of what
+
+ align:start position:0%
+process of of there's a process of what
+ 
+
+ align:start position:0%
+process of of there's a process of what
+we might in a narrow in a in a in a
+
+ align:start position:0%
+we might in a narrow in a in a in a
+ 
+
+ align:start position:0%
+we might in a narrow in a in a in a
+broad sense called self-discovery
+
+ align:start position:0%
+broad sense called self-discovery
+ 
+
+ align:start position:0%
+broad sense called self-discovery
+wherein the new medium adapt to the
+
+ align:start position:0%
+wherein the new medium adapt to the
+ 
+
+ align:start position:0%
+wherein the new medium adapt to the
+particular economic and
+
+ align:start position:0%
+particular economic and
+ 
+
+ align:start position:0%
+particular economic and
+Technical and environmental constraints
+
+ align:start position:0%
+Technical and environmental constraints
+ 
+
+ align:start position:0%
+Technical and environmental constraints
+that it faces and also begins to explore
+
+ align:start position:0%
+that it faces and also begins to explore
+ 
+
+ align:start position:0%
+that it faces and also begins to explore
+the features and aspects of its nature
+
+ align:start position:0%
+the features and aspects of its nature
+ 
+
+ align:start position:0%
+the features and aspects of its nature
+that are unique to it what distinguishes
+
+ align:start position:0%
+that are unique to it what distinguishes
+ 
+
+ align:start position:0%
+that are unique to it what distinguishes
+it from its ancestors this exploration
+
+ align:start position:0%
+it from its ancestors this exploration
+ 
+
+ align:start position:0%
+it from its ancestors this exploration
+is always partial and
+
+ align:start position:0%
+is always partial and
+ 
+
+ align:start position:0%
+is always partial and
+incomplete a most dramatic example of
+
+ align:start position:0%
+incomplete a most dramatic example of
+ 
+
+ align:start position:0%
+incomplete a most dramatic example of
+that in the terms of the television
+
+ align:start position:0%
+that in the terms of the television
+ 
+
+ align:start position:0%
+that in the terms of the television
+medium is in some ways the most powerful
+
+ align:start position:0%
+medium is in some ways the most powerful
+ 
+
+ align:start position:0%
+medium is in some ways the most powerful
+and distinctive feature of television as
+
+ align:start position:0%
+and distinctive feature of television as
+ 
+
+ align:start position:0%
+and distinctive feature of television as
+a medium is a feature that was barely
+
+ align:start position:0%
+a medium is a feature that was barely
+ 
+
+ align:start position:0%
+a medium is a feature that was barely
+exploited by its fiction programming and
+
+ align:start position:0%
+exploited by its fiction programming and
+ 
+
+ align:start position:0%
+exploited by its fiction programming and
+really hasn't been much exploited uh by
+
+ align:start position:0%
+really hasn't been much exploited uh by
+ 
+
+ align:start position:0%
+really hasn't been much exploited uh by
+television by by by the medium more
+
+ align:start position:0%
+television by by by the medium more
+ 
+
+ align:start position:0%
+television by by by the medium more
+generally except in moments of Crisis
+
+ align:start position:0%
+generally except in moments of Crisis
+ 
+
+ align:start position:0%
+generally except in moments of Crisis
+and that is its power to allow to
+
+ align:start position:0%
+and that is its power to allow to
+ 
+
+ align:start position:0%
+and that is its power to allow to
+connect people all over the globe
+
+ align:start position:0%
+connect people all over the globe
+ 
+
+ align:start position:0%
+connect people all over the globe
+simultaneously to an event that's taking
+
+ align:start position:0%
+simultaneously to an event that's taking
+ 
+
+ align:start position:0%
+simultaneously to an event that's taking
+place now its power of simultaneous
+
+ align:start position:0%
+place now its power of simultaneous
+ 
+
+ align:start position:0%
+place now its power of simultaneous
+transmission uh in it's a very powerful
+
+ align:start position:0%
+transmission uh in it's a very powerful
+ 
+
+ align:start position:0%
+transmission uh in it's a very powerful
+and unique feature of Television no
+
+ align:start position:0%
+and unique feature of Television no
+ 
+
+ align:start position:0%
+and unique feature of Television no
+prior techn radio in some sense was
+
+ align:start position:0%
+prior techn radio in some sense was
+ 
+
+ align:start position:0%
+prior techn radio in some sense was
+capable of doing this but without
+
+ align:start position:0%
+capable of doing this but without
+ 
+
+ align:start position:0%
+capable of doing this but without
+pictures right uh uh but but that
+
+ align:start position:0%
+pictures right uh uh but but that
+ 
+
+ align:start position:0%
+pictures right uh uh but but that
+feature of Television was really not
+
+ align:start position:0%
+feature of Television was really not
+ 
+
+ align:start position:0%
+feature of Television was really not
+very much exploited and certainly not
+
+ align:start position:0%
+very much exploited and certainly not
+ 
+
+ align:start position:0%
+very much exploited and certainly not
+exploited at all in the fiction
+
+ align:start position:0%
+exploited at all in the fiction
+ 
+
+ align:start position:0%
+exploited at all in the fiction
+programming that developed which took
+
+ align:start position:0%
+programming that developed which took
+ 
+
+ align:start position:0%
+programming that developed which took
+place which were M programs were filmed
+
+ align:start position:0%
+place which were M programs were filmed
+ 
+
+ align:start position:0%
+place which were M programs were filmed
+and they and uh did not uh even attempt
+
+ align:start position:0%
+and they and uh did not uh even attempt
+ 
+
+ align:start position:0%
+and they and uh did not uh even attempt
+to exploit this this I'm not sure that
+
+ align:start position:0%
+to exploit this this I'm not sure that
+ 
+
+ align:start position:0%
+to exploit this this I'm not sure that
+as a that that it's a feature that is
+
+ align:start position:0%
+as a that that it's a feature that is
+ 
+
+ align:start position:0%
+as a that that it's a feature that is
+like likely to be of permanent and
+
+ align:start position:0%
+like likely to be of permanent and
+ 
+
+ align:start position:0%
+like likely to be of permanent and
+extensive use to fiction anyway to to
+
+ align:start position:0%
+extensive use to fiction anyway to to
+ 
+
+ align:start position:0%
+extensive use to fiction anyway to to
+narrative but it's certainly a feature
+
+ align:start position:0%
+narrative but it's certainly a feature
+ 
+
+ align:start position:0%
+narrative but it's certainly a feature
+of Television that in small ways is
+
+ align:start position:0%
+of Television that in small ways is
+ 
+
+ align:start position:0%
+of Television that in small ways is
+exploited every and of course we can
+
+ align:start position:0%
+exploited every and of course we can
+ 
+
+ align:start position:0%
+exploited every and of course we can
+feel uh the power of that that aspect
+
+ align:start position:0%
+feel uh the power of that that aspect
+ 
+
+ align:start position:0%
+feel uh the power of that that aspect
+the power of that aspect of the medium
+
+ align:start position:0%
+the power of that aspect of the medium
+ 
+
+ align:start position:0%
+the power of that aspect of the medium
+very strongly right now because of those
+
+ align:start position:0%
+very strongly right now because of those
+ 
+
+ align:start position:0%
+very strongly right now because of those
+uh images that we were able to see of of
+
+ align:start position:0%
+uh images that we were able to see of of
+ 
+
+ align:start position:0%
+uh images that we were able to see of of
+uh things going on in New York while it
+
+ align:start position:0%
+uh things going on in New York while it
+ 
+
+ align:start position:0%
+uh things going on in New York while it
+while it was happening uh but of course
+
+ align:start position:0%
+while it was happening uh but of course
+ 
+
+ align:start position:0%
+while it was happening uh but of course
+that's not its only Power and and it's
+
+ align:start position:0%
+that's not its only Power and and it's
+ 
+
+ align:start position:0%
+that's not its only Power and and it's
+its power to repeat and show things
+
+ align:start position:0%
+its power to repeat and show things
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+
+ align:start position:0%
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+again and again is also an extraordinary
+
+ align:start position:0%
+again and again is also an extraordinary
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+ align:start position:0%
+again and again is also an extraordinary
+aspect of of what it's in words its
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+ align:start position:0%
+aspect of of what it's in words its
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+
+ align:start position:0%
+aspect of of what it's in words its
+power both to record and preserve events
+
+ align:start position:0%
+power both to record and preserve events
+ 
+
+ align:start position:0%
+power both to record and preserve events
+and also to register events as they are
+
+ align:start position:0%
+and also to register events as they are
+ 
+
+ align:start position:0%
+and also to register events as they are
+happening uh that no medium has such a
+
+ align:start position:0%
+happening uh that no medium has such a
+ 
+
+ align:start position:0%
+happening uh that no medium has such a
+simultaneous power to do both at the
+
+ align:start position:0%
+simultaneous power to do both at the
+ 
+
+ align:start position:0%
+simultaneous power to do both at the
+same time and one can feel those the the
+
+ align:start position:0%
+same time and one can feel those the the
+ 
+
+ align:start position:0%
+same time and one can feel those the the
+the extraordinary uh importance and and
+
+ align:start position:0%
+the extraordinary uh importance and and
+ 
+
+ align:start position:0%
+the extraordinary uh importance and and
+uh extensiveness of those of those
+
+ align:start position:0%
+uh extensiveness of those of those
+ 
+
+ align:start position:0%
+uh extensiveness of those of those
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+ align:start position:0%
+defining features of the medium in in
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+
+ align:start position:0%
+defining features of the medium in in
+what we've been watching on television
+
+ align:start position:0%
+what we've been watching on television
+ 
+
+ align:start position:0%
+what we've been watching on television
+over the past over the past week and
+
+ align:start position:0%
+over the past over the past week and
+ 
+
+ align:start position:0%
+over the past over the past week and
+more uh it's a reminder of of what what
+
+ align:start position:0%
+more uh it's a reminder of of what what
+ 
+
+ align:start position:0%
+more uh it's a reminder of of what what
+an uniquely significant and unique
+
+ align:start position:0%
+an uniquely significant and unique
+ 
+
+ align:start position:0%
+an uniquely significant and unique
+uniquely
+
+ align:start position:0%
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+ align:start position:0%
+uniquely
+defining defi uniquely defining
+
+ align:start position:0%
+defining defi uniquely defining
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+
+ align:start position:0%
+defining defi uniquely defining
+instrument uh television is for the
+
+ align:start position:0%
+instrument uh television is for the
+ 
+
+ align:start position:0%
+instrument uh television is for the
+modern age for the for the 20th and the
+
+ align:start position:0%
+modern age for the for the 20th and the
+ 
+
+ align:start position:0%
+modern age for the for the 20th and the
+21st century it's probably the
+
+ align:start position:0%
+21st century it's probably the
+ 
+
+ align:start position:0%
+21st century it's probably the
+distinctive technology of the second
+
+ align:start position:0%
+distinctive technology of the second
+ 
+
+ align:start position:0%
+distinctive technology of the second
+certainly the distinctive technology of
+
+ align:start position:0%
+certainly the distinctive technology of
+ 
+
+ align:start position:0%
+certainly the distinctive technology of
+the second half of the 20th century and
+
+ align:start position:0%
+the second half of the 20th century and
+ 
+
+ align:start position:0%
+the second half of the 20th century and
+continues to be a dominant will will
+
+ align:start position:0%
+continues to be a dominant will will
+ 
+
+ align:start position:0%
+continues to be a dominant will will
+continue to be a dominant technology in
+
+ align:start position:0%
+continue to be a dominant technology in
+ 
+
+ align:start position:0%
+continue to be a dominant technology in
+the new century um so to come back to my
+
+ align:start position:0%
+the new century um so to come back to my
+ 
+
+ align:start position:0%
+the new century um so to come back to my
+uh original idea the framework that I'm
+
+ align:start position:0%
+uh original idea the framework that I'm
+ 
+
+ align:start position:0%
+uh original idea the framework that I'm
+proposing in the course about the way
+
+ align:start position:0%
+proposing in the course about the way
+ 
+
+ align:start position:0%
+proposing in the course about the way
+television uh uh in in the United States
+
+ align:start position:0%
+television uh uh in in the United States
+ 
+
+ align:start position:0%
+television uh uh in in the United States
+evolved and developed uh is a framework
+
+ align:start position:0%
+evolved and developed uh is a framework
+ 
+
+ align:start position:0%
+evolved and developed uh is a framework
+for uh I hope uh is a framework with
+
+ align:start position:0%
+for uh I hope uh is a framework with
+ 
+
+ align:start position:0%
+for uh I hope uh is a framework with
+applications to other to other media
+
+ align:start position:0%
+applications to other to other media
+ 
+
+ align:start position:0%
+applications to other to other media
+histories and uh the truth is I think in
+
+ align:start position:0%
+histories and uh the truth is I think in
+ 
+
+ align:start position:0%
+histories and uh the truth is I think in
+fact that the basic framework would is
+
+ align:start position:0%
+fact that the basic framework would is
+ 
+
+ align:start position:0%
+fact that the basic framework would is
+probably useful even for such recent
+
+ align:start position:0%
+probably useful even for such recent
+ 
+
+ align:start position:0%
+probably useful even for such recent
+Technologies as the computer uh although
+
+ align:start position:0%
+Technologies as the computer uh although
+ 
+
+ align:start position:0%
+Technologies as the computer uh although
+it's much harder to see the various
+
+ align:start position:0%
+it's much harder to see the various
+ 
+
+ align:start position:0%
+it's much harder to see the various
+phases through which Computing uh the
+
+ align:start position:0%
+phases through which Computing uh the
+ 
+
+ align:start position:0%
+phases through which Computing uh the
+computer as an object is uh likely to uh
+
+ align:start position:0%
+computer as an object is uh likely to uh
+ 
+
+ align:start position:0%
+computer as an object is uh likely to uh
+uh evolve uh it's clear that in certain
+
+ align:start position:0%
+uh evolve uh it's clear that in certain
+ 
+
+ align:start position:0%
+uh evolve uh it's clear that in certain
+broad ways the the development of the
+
+ align:start position:0%
+broad ways the the development of the
+ 
+
+ align:start position:0%
+broad ways the the development of the
+computer resembles uh the way it's
+
+ align:start position:0%
+computer resembles uh the way it's
+ 
+
+ align:start position:0%
+computer resembles uh the way it's
+deployed in society and the way and the
+
+ align:start position:0%
+deployed in society and the way and the
+ 
+
+ align:start position:0%
+deployed in society and the way and the
+way it has been used by by by the
+
+ align:start position:0%
+way it has been used by by by the
+ 
+
+ align:start position:0%
+way it has been used by by by the
+culture resembles in certain respects
+
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+culture resembles in certain respects
+ 
+
+ align:start position:0%
+culture resembles in certain respects
+the development of earlier media and
+
+ align:start position:0%
+the development of earlier media and
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+
+ align:start position:0%
+the development of earlier media and
+it's very useful to know that just as
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+ align:start position:0%
+it's very useful to know that just as
+ 
+
+ align:start position:0%
+it's very useful to know that just as
+the development of television in certain
+
+ align:start position:0%
+the development of television in certain
+ 
+
+ align:start position:0%
+the development of television in certain
+fundamental ways resembles the devel the
+
+ align:start position:0%
+fundamental ways resembles the devel the
+ 
+
+ align:start position:0%
+fundamental ways resembles the devel the
+evolution the development of American
+
+ align:start position:0%
+evolution the development of American
+ 
+
+ align:start position:0%
+evolution the development of American
+movies which in turn mirror although in
+
+ align:start position:0%
+movies which in turn mirror although in
+ 
+
+ align:start position:0%
+movies which in turn mirror although in
+a in a less decisively uh exact way the
+
+ align:start position:0%
+a in a less decisively uh exact way the
+ 
+
+ align:start position:0%
+a in a less decisively uh exact way the
+the uh process whereby earlier
+
+ align:start position:0%
+the uh process whereby earlier
+ 
+
+ align:start position:0%
+the uh process whereby earlier
+Technologies such as the printing press
+
+ align:start position:0%
+Technologies such as the printing press
+ 
+
+ align:start position:0%
+Technologies such as the printing press
+were absorbed into society and used by
+
+ align:start position:0%
+were absorbed into society and used by
+ 
+
+ align:start position:0%
+were absorbed into society and used by
+Society so the broad perspectives I
+
+ align:start position:0%
+Society so the broad perspectives I
+ 
+
+ align:start position:0%
+Society so the broad perspectives I
+think are useful beyond the question of
+
+ align:start position:0%
+think are useful beyond the question of
+ 
+
+ align:start position:0%
+think are useful beyond the question of
+Television but I
+
+ align:start position:0%
+Television but I
+ 
+
+ align:start position:0%
+Television but I
+hope in addition that that you'll come
+
+ align:start position:0%
+hope in addition that that you'll come
+ 
+
+ align:start position:0%
+hope in addition that that you'll come
+away from the course with a much more
+
+ align:start position:0%
+away from the course with a much more
+ 
+
+ align:start position:0%
+away from the course with a much more
+systematic and and uh nuanced structured
+
+ align:start position:0%
+systematic and and uh nuanced structured
+ 
+
+ align:start position:0%
+systematic and and uh nuanced structured
+um thick description uh of what uh
+
+ align:start position:0%
+um thick description uh of what uh
+ 
+
+ align:start position:0%
+um thick description uh of what uh
+American television is and has been and
+
+ align:start position:0%
+American television is and has been and
+ 
+
+ align:start position:0%
+American television is and has been and
+especially what it has what it has been
+
+ align:start position:0%
+especially what it has what it has been
+ 
+
+ align:start position:0%
+especially what it has what it has been
+so today is our last day without Clips
+
+ align:start position:0%
+so today is our last day without Clips
+ 
+
+ align:start position:0%
+so today is our last day without Clips
+but you might be thinking about some of
+
+ align:start position:0%
+but you might be thinking about some of
+ 
+
+ align:start position:0%
+but you might be thinking about some of
+the clips that you saw on Wednesday
+
+ align:start position:0%
+the clips that you saw on Wednesday
+ 
+
+ align:start position:0%
+the clips that you saw on Wednesday
+night uh uh to U complicate the things
+
+ align:start position:0%
+night uh uh to U complicate the things
+ 
+
+ align:start position:0%
+night uh uh to U complicate the things
+I'm going to say one last thing about
+
+ align:start position:0%
+I'm going to say one last thing about
+ 
+
+ align:start position:0%
+I'm going to say one last thing about
+you notice I said I I I made the
+
+ align:start position:0%
+you notice I said I I I made the
+ 
+
+ align:start position:0%
+you notice I said I I I made the
+Wasteland mythology a plural now to
+
+ align:start position:0%
+Wasteland mythology a plural now to
+ 
+
+ align:start position:0%
+Wasteland mythology a plural now to
+remind you of the fact that there are a
+
+ align:start position:0%
+remind you of the fact that there are a
+ 
+
+ align:start position:0%
+remind you of the fact that there are a
+series of mythologies the astonishing
+
+ align:start position:0%
+series of mythologies the astonishing
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+
+ align:start position:0%
+series of mythologies the astonishing
+thing is how is how powerful they remain
+
+ align:start position:0%
+thing is how is how powerful they remain
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+
+ align:start position:0%
+thing is how is how powerful they remain
+even in an era when television is
+
+ align:start position:0%
+even in an era when television is
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+
+ align:start position:0%
+even in an era when television is
+undergoing this transmogrification and
+
+ align:start position:0%
+undergoing this transmogrification and
+ 
+
+ align:start position:0%
+undergoing this transmogrification and
+is altering its relation to the society
+
+ align:start position:0%
+is altering its relation to the society
+ 
+
+ align:start position:0%
+is altering its relation to the society
+and such dramatic ways uh but it struck
+
+ align:start position:0%
+and such dramatic ways uh but it struck
+ 
+
+ align:start position:0%
+and such dramatic ways uh but it struck
+me that there was one further thing to
+
+ align:start position:0%
+me that there was one further thing to
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+
+ align:start position:0%
+me that there was one further thing to
+remind you about the basic term
+
+ align:start position:0%
+remind you about the basic term
+ 
+
+ align:start position:0%
+remind you about the basic term
+Wasteland of course as I as I've already
+
+ align:start position:0%
+Wasteland of course as I as I've already
+ 
+
+ align:start position:0%
+Wasteland of course as I as I've already
+mentioned comes from a famous speech
+
+ align:start position:0%
+mentioned comes from a famous speech
+ 
+
+ align:start position:0%
+mentioned comes from a famous speech
+made by the newly appointed John
+
+ align:start position:0%
+made by the newly appointed John
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+
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+made by the newly appointed John
+Kennedy's newly appointed head of the
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+Kennedy's newly appointed head of the
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+
+ align:start position:0%
+Kennedy's newly appointed head of the
+Federal Communications Commission to a
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+Federal Communications Commission to a
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+
+ align:start position:0%
+Federal Communications Commission to a
+gathering of broadcasters who expected
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+ align:start position:0%
+gathering of broadcasters who expected
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+
+ align:start position:0%
+gathering of broadcasters who expected
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+
+ align:start position:0%
+uh the the usual P pum from a from a
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+
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+uh the the usual P pum from a from a
+government uh uh official and instead
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+government uh uh official and instead
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+government uh uh official and instead
+receiv received this violent attack from
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+receiv received this violent attack from
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+receiv received this violent attack from
+the from the from this Young new
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+the from the from this Young new
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+
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+the from the from this Young new
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+ align:start position:0%
+Frontiersman and it was an attack in
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+
+ align:start position:0%
+Frontiersman and it was an attack in
+which he called television a vast
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+which he called television a vast
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+
+ align:start position:0%
+which he called television a vast
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+Wasteland if we look back at the
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+
+ align:start position:0%
+Wasteland if we look back at the
+television of the early 60s the
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+television of the early 60s the
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+
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+television of the early 60s the
+television of 1961 when he was speaking
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+television of 1961 when he was speaking
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+
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+television of 1961 when he was speaking
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+
+ align:start position:0%
+I think we could we could now in
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+
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+I think we could we could now in
+retrospect see that it was a very unfair
+
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+retrospect see that it was a very unfair
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+
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+retrospect see that it was a very unfair
+and foolish description that there were
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+and foolish description that there were
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+
+ align:start position:0%
+and foolish description that there were
+many banal and foolish things on
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+many banal and foolish things on
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+
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+many banal and foolish things on
+television but television was already a
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+television but television was already a
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+
+ align:start position:0%
+television but television was already a
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+very complex instrument of popular
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+
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+very complex instrument of popular
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+culture and was doing a a multitude of
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+culture and was doing a a multitude of
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+ align:start position:0%
+functions uh one of the things that's
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+
+ align:start position:0%
+functions uh one of the things that's
+wrong with the Wasteland mythology
+
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+wrong with the Wasteland mythology
+ 
+
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+wrong with the Wasteland mythology
+broadly is that people continue to
+
+ align:start position:0%
+broadly is that people continue to
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+
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+broadly is that people continue to
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+generalize about the medium as if it's a
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+generalize about the medium as if it's a
+single thing when of course it performs
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+single thing when of course it performs
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+single thing when of course it performs
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+so many different and and and F and and
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+
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+so many different and and and F and and
+fundamentally distinctive functions in
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+fundamentally distinctive functions in
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+
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+fundamentally distinctive functions in
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+the society that it's necessary to to
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+
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+the society that it's necessary to to
+distinguish it nobody nobody would
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+distinguish it nobody nobody would
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+distinguish it nobody nobody would
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+generalize about the book the way people
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+
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+generalize about the book the way people
+generalize about television I mean there
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+ align:start position:0%
+generalize about television I mean there
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+
+ align:start position:0%
+generalize about television I mean there
+are all kinds of books there's there are
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+are all kinds of books there's there are
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+are all kinds of books there's there are
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+
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+books and wonderful novels and great and
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+books and wonderful novels and great and
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+
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+and works of history no one would say
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+
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+and works of history no one would say
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+
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+generally say the book is utterly
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+
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+contemptible look at this horrible piece
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+contemptible look at this horrible piece
+ 
+
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+contemptible look at this horrible piece
+of pornography
+
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+of pornography
+ 
+
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+of pornography
+right the technology is evil the medium
+
+ align:start position:0%
+right the technology is evil the medium
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+
+ align:start position:0%
+right the technology is evil the medium
+the medium is beneath contempt because
+
+ align:start position:0%
+the medium is beneath contempt because
+ 
+
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+the medium is beneath contempt because
+of because Jerry fowell publishes this
+
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+of because Jerry fowell publishes this
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+
+ align:start position:0%
+of because Jerry fowell publishes this
+book no no no even if you have contempt
+
+ align:start position:0%
+book no no no even if you have contempt
+ 
+
+ align:start position:0%
+book no no no even if you have contempt
+for Jerry falwell's book it doesn't mean
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+for Jerry falwell's book it doesn't mean
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+for Jerry falwell's book it doesn't mean
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+that all books fall into it's such an
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+obvious thing to say and yet people
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+
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+obvious thing to say and yet people
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+continue to talk about television as if
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+
+ align:start position:0%
+continue to talk about television as if
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+it's this monolith it was never a
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+
+ align:start position:0%
+it's this monolith it was never a
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+monolith it always provided news and
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+monolith it always provided news and
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+ align:start position:0%
+variety programs and daytime serials and
+interviews and V various other forms of
+
+ align:start position:0%
+interviews and V various other forms of
+ 
+
+ align:start position:0%
+interviews and V various other forms of
+prime time fiction so even from the
+
+ align:start position:0%
+prime time fiction so even from the
+ 
+
+ align:start position:0%
+prime time fiction so even from the
+start it was a multi it was a
+
+ align:start position:0%
+start it was a multi it was a
+ 
+
+ align:start position:0%
+start it was a multi it was a
+multitudinous medium and to generalize
+
+ align:start position:0%
+multitudinous medium and to generalize
+ 
+
+ align:start position:0%
+multitudinous medium and to generalize
+so that's another objection to the what
+
+ align:start position:0%
+so that's another objection to the what
+ 
+
+ align:start position:0%
+so that's another objection to the what
+we'll call the Wasteland mythology the
+
+ align:start position:0%
+we'll call the Wasteland mythology the
+ 
+
+ align:start position:0%
+we'll call the Wasteland mythology the
+way it the way it reduces television to
+
+ align:start position:0%
+way it the way it reduces television to
+ 
+
+ align:start position:0%
+way it the way it reduces television to
+a monolithic experience which is true
+
+ align:start position:0%
+a monolithic experience which is true
+ 
+
+ align:start position:0%
+a monolithic experience which is true
+for no human being I mean no person who
+
+ align:start position:0%
+for no human being I mean no person who
+ 
+
+ align:start position:0%
+for no human being I mean no person who
+watches television experiences it
+
+ align:start position:0%
+watches television experiences it
+ 
+
+ align:start position:0%
+watches television experiences it
+monolithically and that doesn't even
+
+ align:start position:0%
+monolithically and that doesn't even
+ 
+
+ align:start position:0%
+monolithically and that doesn't even
+take account of the Fantastic variation
+
+ align:start position:0%
+take account of the Fantastic variation
+ 
+
+ align:start position:0%
+take account of the Fantastic variation
+and variety that one might acknowledge
+
+ align:start position:0%
+and variety that one might acknowledge
+ 
+
+ align:start position:0%
+and variety that one might acknowledge
+within particular single categories of
+
+ align:start position:0%
+within particular single categories of
+ 
+
+ align:start position:0%
+within particular single categories of
+programming I mean just to just to
+
+ align:start position:0%
+programming I mean just to just to
+ 
+
+ align:start position:0%
+programming I mean just to just to
+generalize in a persuasive way about the
+
+ align:start position:0%
+generalize in a persuasive way about the
+ 
+
+ align:start position:0%
+generalize in a persuasive way about the
+News broadcasting and and narrowcasting
+
+ align:start position:0%
+News broadcasting and and narrowcasting
+ 
+
+ align:start position:0%
+News broadcasting and and narrowcasting
+that's going on on television today is
+
+ align:start position:0%
+that's going on on television today is
+ 
+
+ align:start position:0%
+that's going on on television today is
+an immensely complicated job because
+
+ align:start position:0%
+an immensely complicated job because
+ 
+
+ align:start position:0%
+an immensely complicated job because
+there's so many kinds of news broadcast
+
+ align:start position:0%
+there's so many kinds of news broadcast
+ 
+
+ align:start position:0%
+there's so many kinds of news broadcast
+yes I was just thinking of the irony
+
+ align:start position:0%
+yes I was just thinking of the irony
+ 
+
+ align:start position:0%
+yes I was just thinking of the irony
+because that same Communications manager
+
+ align:start position:0%
+because that same Communications manager
+ 
+
+ align:start position:0%
+because that same Communications manager
+probably helped utilize television to
+
+ align:start position:0%
+probably helped utilize television to
+ 
+
+ align:start position:0%
+probably helped utilize television to
+completely sculpt and promote Kennedy's
+
+ align:start position:0%
+completely sculpt and promote Kennedy's
+ 
+
+ align:start position:0%
+completely sculpt and promote Kennedy's
+image I mean Kennedy was so good on
+
+ align:start position:0%
+image I mean Kennedy was so good on
+ 
+
+ align:start position:0%
+image I mean Kennedy was so good on
+television yes that's right and it was
+
+ align:start position:0%
+television yes that's right and it was
+ 
+
+ align:start position:0%
+television yes that's right and it was
+really important part of his legazy that
+
+ align:start position:0%
+really important part of his legazy that
+ 
+
+ align:start position:0%
+really important part of his legazy that
+is an interesting irony and I think
+
+ align:start position:0%
+is an interesting irony and I think
+ 
+
+ align:start position:0%
+is an interesting irony and I think
+that's right I mean the new uh was the
+
+ align:start position:0%
+that's right I mean the new uh was the
+ 
+
+ align:start position:0%
+that's right I mean the new uh was the
+was in some respects was the first
+
+ align:start position:0%
+was in some respects was the first
+ 
+
+ align:start position:0%
+was in some respects was the first
+television President and utilized
+
+ align:start position:0%
+television President and utilized
+ 
+
+ align:start position:0%
+television President and utilized
+television in a way that none of his
+
+ align:start position:0%
+television in a way that none of his
+ 
+
+ align:start position:0%
+television in a way that none of his
+predecessors had done there there are
+
+ align:start position:0%
+predecessors had done there there are
+ 
+
+ align:start position:0%
+predecessors had done there there are
+even arguments to the effect that the
+
+ align:start position:0%
+even arguments to the effect that the
+ 
+
+ align:start position:0%
+even arguments to the effect that the
+debates he had with Nixon which were
+
+ align:start position:0%
+debates he had with Nixon which were
+ 
+
+ align:start position:0%
+debates he had with Nixon which were
+televised debates were the secret to
+
+ align:start position:0%
+televised debates were the secret to
+ 
+
+ align:start position:0%
+televised debates were the secret to
+were the were the reason he was elected
+
+ align:start position:0%
+were the were the reason he was elected
+ 
+
+ align:start position:0%
+were the were the reason he was elected
+that he was better on television that he
+
+ align:start position:0%
+that he was better on television that he
+ 
+
+ align:start position:0%
+that he was better on television that he
+looked he looked more persuasive on
+
+ align:start position:0%
+looked he looked more persuasive on
+ 
+
+ align:start position:0%
+looked he looked more persuasive on
+television he was he he was U better at
+
+ align:start position:0%
+television he was he he was U better at
+ 
+
+ align:start position:0%
+television he was he he was U better at
+sound bites than his than his opponent
+
+ align:start position:0%
+sound bites than his than his opponent
+ 
+
+ align:start position:0%
+sound bites than his than his opponent
+was and so I think that's
+
+ align:start position:0%
+was and so I think that's
+ 
+
+ align:start position:0%
+was and so I think that's
+a a helpful and complicating point one
+
+ align:start position:0%
+a a helpful and complicating point one
+ 
+
+ align:start position:0%
+a a helpful and complicating point one
+one final point about the Wasteland
+
+ align:start position:0%
+one final point about the Wasteland
+ 
+
+ align:start position:0%
+one final point about the Wasteland
+mythology there's there's another kind
+
+ align:start position:0%
+mythology there's there's another kind
+ 
+
+ align:start position:0%
+mythology there's there's another kind
+of resonance that the term Wasteland has
+
+ align:start position:0%
+of resonance that the term Wasteland has
+ 
+
+ align:start position:0%
+of resonance that the term Wasteland has
+uh and some of you with literary
+
+ align:start position:0%
+uh and some of you with literary
+ 
+
+ align:start position:0%
+uh and some of you with literary
+backgrounds will pick up on it
+
+ align:start position:0%
+backgrounds will pick up on it
+ 
+
+ align:start position:0%
+backgrounds will pick up on it
+immediately and and I think it partly
+
+ align:start position:0%
+immediately and and I think it partly
+ 
+
+ align:start position:0%
+immediately and and I think it partly
+explains why the metaphor was so
+
+ align:start position:0%
+explains why the metaphor was so
+ 
+
+ align:start position:0%
+explains why the metaphor was so
+powerful especially among the educated
+
+ align:start position:0%
+powerful especially among the educated
+ 
+
+ align:start position:0%
+powerful especially among the educated
+classes the defining and in many ways
+
+ align:start position:0%
+classes the defining and in many ways
+ 
+
+ align:start position:0%
+classes the defining and in many ways
+ridiculously simplifying poem of the
+
+ align:start position:0%
+ridiculously simplifying poem of the
+ 
+
+ align:start position:0%
+ridiculously simplifying poem of the
+20th century in the English language is
+
+ align:start position:0%
+20th century in the English language is
+ 
+
+ align:start position:0%
+20th century in the English language is
+a poem by TS Elliott titled the
+
+ align:start position:0%
+a poem by TS Elliott titled the
+ 
+
+ align:start position:0%
+a poem by TS Elliott titled the
+Wasteland published in 1922 it purported
+
+ align:start position:0%
+Wasteland published in 1922 it purported
+ 
+
+ align:start position:0%
+Wasteland published in 1922 it purported
+to describe the debased and destructive
+
+ align:start position:0%
+to describe the debased and destructive
+ 
+
+ align:start position:0%
+to describe the debased and destructive
+uh conditions of Modern Life uh a world
+
+ align:start position:0%
+uh conditions of Modern Life uh a world
+ 
+
+ align:start position:0%
+uh conditions of Modern Life uh a world
+a world that was in Elliot's view an
+
+ align:start position:0%
+a world that was in Elliot's view an
+ 
+
+ align:start position:0%
+a world that was in Elliot's view an
+horrific moral and spiritual Wasteland a
+
+ align:start position:0%
+horrific moral and spiritual Wasteland a
+ 
+
+ align:start position:0%
+horrific moral and spiritual Wasteland a
+place of a place of Despair and
+
+ align:start position:0%
+place of a place of Despair and
+ 
+
+ align:start position:0%
+place of a place of Despair and
+emptiness and uh uh and and and human
+
+ align:start position:0%
+emptiness and uh uh and and and human
+ 
+
+ align:start position:0%
+emptiness and uh uh and and and human
+negativity uh in its day it was Pro
+
+ align:start position:0%
+negativity uh in its day it was Pro
+ 
+
+ align:start position:0%
+negativity uh in its day it was Pro
+unquestionably the most influential and
+
+ align:start position:0%
+unquestionably the most influential and
+ 
+
+ align:start position:0%
+unquestionably the most influential and
+important uh uh poem in the English
+
+ align:start position:0%
+important uh uh poem in the English
+ 
+
+ align:start position:0%
+important uh uh poem in the English
+language and for several Generations it
+
+ align:start position:0%
+language and for several Generations it
+ 
+
+ align:start position:0%
+language and for several Generations it
+was taken to be the definitive
+
+ align:start position:0%
+was taken to be the definitive
+ 
+
+ align:start position:0%
+was taken to be the definitive
+description uh of mod life of life in
+
+ align:start position:0%
+description uh of mod life of life in
+ 
+
+ align:start position:0%
+description uh of mod life of life in
+the mass democracies of Modern Life
+
+ align:start position:0%
+the mass democracies of Modern Life
+ 
+
+ align:start position:0%
+the mass democracies of Modern Life
+after the death of of of of of religious
+
+ align:start position:0%
+after the death of of of of of religious
+ 
+
+ align:start position:0%
+after the death of of of of of religious
+observance uh and uh it's only in in
+
+ align:start position:0%
+observance uh and uh it's only in in
+ 
+
+ align:start position:0%
+observance uh and uh it's only in in
+relatively recent times over the past
+
+ align:start position:0%
+relatively recent times over the past
+ 
+
+ align:start position:0%
+relatively recent times over the past
+quarter of a century and a bit more that
+
+ align:start position:0%
+quarter of a century and a bit more that
+ 
+
+ align:start position:0%
+quarter of a century and a bit more that
+the poem has been recognized for the
+
+ align:start position:0%
+the poem has been recognized for the
+ 
+
+ align:start position:0%
+the poem has been recognized for the
+much more personal and in many ways not
+
+ align:start position:0%
+much more personal and in many ways not
+ 
+
+ align:start position:0%
+much more personal and in many ways not
+just eccentric but perhaps neurotic
+
+ align:start position:0%
+just eccentric but perhaps neurotic
+ 
+
+ align:start position:0%
+just eccentric but perhaps neurotic
+expression that in fact it was and uh
+
+ align:start position:0%
+expression that in fact it was and uh
+ 
+
+ align:start position:0%
+expression that in fact it was and uh
+and uh there are many other texts
+
+ align:start position:0%
+and uh there are many other texts
+ 
+
+ align:start position:0%
+and uh there are many other texts
+including Jo Joyce's great novel ulyses
+
+ align:start position:0%
+including Jo Joyce's great novel ulyses
+ 
+
+ align:start position:0%
+including Jo Joyce's great novel ulyses
+uh which
+
+ align:start position:0%
+uh which
+ 
+
+ align:start position:0%
+uh which
+which Define and encompass modern
+
+ align:start position:0%
+which Define and encompass modern
+ 
+
+ align:start position:0%
+which Define and encompass modern
+experience 20th century experience in
+
+ align:start position:0%
+experience 20th century experience in
+ 
+
+ align:start position:0%
+experience 20th century experience in
+much more uh uh uh complex and uh
+
+ align:start position:0%
+much more uh uh uh complex and uh
+ 
+
+ align:start position:0%
+much more uh uh uh complex and uh
+unsimplified ways but the but the cache
+
+ align:start position:0%
+unsimplified ways but the but the cache
+ 
+
+ align:start position:0%
+unsimplified ways but the but the cache
+that the term has the feeling that the
+
+ align:start position:0%
+that the term has the feeling that the
+ 
+
+ align:start position:0%
+that the term has the feeling that the
+term the Wasteland uh uh uh uh would
+
+ align:start position:0%
+term the Wasteland uh uh uh uh would
+ 
+
+ align:start position:0%
+term the Wasteland uh uh uh uh would
+have implicitly had for many educated
+
+ align:start position:0%
+have implicitly had for many educated
+ 
+
+ align:start position:0%
+have implicitly had for many educated
+people also explains I think something
+
+ align:start position:0%
+people also explains I think something
+ 
+
+ align:start position:0%
+people also explains I think something
+of the power of the metaphor uh in our
+
+ align:start position:0%
+of the power of the metaphor uh in our
+ 
+
+ align:start position:0%
+of the power of the metaphor uh in our
+in its uh use as a descri as a as a
+
+ align:start position:0%
+in its uh use as a descri as a as a
+ 
+
+ align:start position:0%
+in its uh use as a descri as a as a
+descriptor for what became the dominant
+
+ align:start position:0%
+descriptor for what became the dominant
+ 
+
+ align:start position:0%
+descriptor for what became the dominant
+ium of communication in the in the
+
+ align:start position:0%
+ium of communication in the in the
+ 
+
+ align:start position:0%
+ium of communication in the in the
+country
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Susanna there's something that's um been
+
+ align:start position:0%
+Susanna there's something that's um been
+ 
+
+ align:start position:0%
+Susanna there's something that's um been
+haunting me I guess about uh the
+
+ align:start position:0%
+haunting me I guess about uh the
+ 
+
+ align:start position:0%
+haunting me I guess about uh the
+discussion of this Wasteland metaphor
+
+ align:start position:0%
+discussion of this Wasteland metaphor
+ 
+
+ align:start position:0%
+discussion of this Wasteland metaphor
+and if this point doesn't seem a good
+
+ align:start position:0%
+and if this point doesn't seem a good
+ 
+
+ align:start position:0%
+and if this point doesn't seem a good
+one to discuss now then um perhaps we
+
+ align:start position:0%
+one to discuss now then um perhaps we
+ 
+
+ align:start position:0%
+one to discuss now then um perhaps we
+can come back to it later but but I I
+
+ align:start position:0%
+can come back to it later but but I I
+ 
+
+ align:start position:0%
+can come back to it later but but I I
+hope we can take it up again um we've
+
+ align:start position:0%
+hope we can take it up again um we've
+ 
+
+ align:start position:0%
+hope we can take it up again um we've
+been discussing this this metaphor as if
+
+ align:start position:0%
+been discussing this this metaphor as if
+ 
+
+ align:start position:0%
+been discussing this this metaphor as if
+it were solely imposed on as a
+
+ align:start position:0%
+it were solely imposed on as a
+ 
+
+ align:start position:0%
+it were solely imposed on as a
+description of the medium and everyone
+
+ align:start position:0%
+description of the medium and everyone
+ 
+
+ align:start position:0%
+description of the medium and everyone
+who watches it by politicians perhaps by
+
+ align:start position:0%
+who watches it by politicians perhaps by
+ 
+
+ align:start position:0%
+who watches it by politicians perhaps by
+academics and intellectuals
+
+ align:start position:0%
+academics and intellectuals
+ 
+
+ align:start position:0%
+academics and intellectuals
+on the other hand people seem to have a
+
+ align:start position:0%
+on the other hand people seem to have a
+ 
+
+ align:start position:0%
+on the other hand people seem to have a
+very complicated relationship with
+
+ align:start position:0%
+very complicated relationship with
+ 
+
+ align:start position:0%
+very complicated relationship with
+television and as we can pick up by
+
+ align:start position:0%
+television and as we can pick up by
+ 
+
+ align:start position:0%
+television and as we can pick up by
+reading some of the essays we've been
+
+ align:start position:0%
+reading some of the essays we've been
+ 
+
+ align:start position:0%
+reading some of the essays we've been
+reading for example the Paul Klein essay
+
+ align:start position:0%
+reading for example the Paul Klein essay
+ 
+
+ align:start position:0%
+reading for example the Paul Klein essay
+Begins by quoting people who say that
+
+ align:start position:0%
+Begins by quoting people who say that
+ 
+
+ align:start position:0%
+Begins by quoting people who say that
+it's the self-loathing that people
+
+ align:start position:0%
+it's the self-loathing that people
+ 
+
+ align:start position:0%
+it's the self-loathing that people
+Express when they watch TV which they
+
+ align:start position:0%
+Express when they watch TV which they
+ 
+
+ align:start position:0%
+Express when they watch TV which they
+did at that time I see and which they
+
+ align:start position:0%
+did at that time I see and which they
+ 
+
+ align:start position:0%
+did at that time I see and which they
+certainly do now I suppose one way of
+
+ align:start position:0%
+certainly do now I suppose one way of
+ 
+
+ align:start position:0%
+certainly do now I suppose one way of
+looking at it is by saying that people
+
+ align:start position:0%
+looking at it is by saying that people
+ 
+
+ align:start position:0%
+looking at it is by saying that people
+only pretend to be disturbed by their
+
+ align:start position:0%
+only pretend to be disturbed by their
+ 
+
+ align:start position:0%
+only pretend to be disturbed by their
+own relationship with television or that
+
+ align:start position:0%
+own relationship with television or that
+ 
+
+ align:start position:0%
+own relationship with television or that
+we've been brainwashed into thinking
+
+ align:start position:0%
+we've been brainwashed into thinking
+ 
+
+ align:start position:0%
+we've been brainwashed into thinking
+that we're addicted to it and not really
+
+ align:start position:0%
+that we're addicted to it and not really
+ 
+
+ align:start position:0%
+that we're addicted to it and not really
+interacting with it in an stimulating
+
+ align:start position:0%
+interacting with it in an stimulating
+ 
+
+ align:start position:0%
+interacting with it in an stimulating
+sense but I do know that many people
+
+ align:start position:0%
+sense but I do know that many people
+ 
+
+ align:start position:0%
+sense but I do know that many people
+seem to be seem to find television
+
+ align:start position:0%
+seem to be seem to find television
+ 
+
+ align:start position:0%
+seem to be seem to find television
+addicting seem say I get up after a
+
+ align:start position:0%
+addicting seem say I get up after a
+ 
+
+ align:start position:0%
+addicting seem say I get up after a
+couple of hours and I don't feel that
+
+ align:start position:0%
+couple of hours and I don't feel that
+ 
+
+ align:start position:0%
+couple of hours and I don't feel that
+I've used my time well and I know that
+
+ align:start position:0%
+I've used my time well and I know that
+ 
+
+ align:start position:0%
+I've used my time well and I know that
+my own relationship to TV is very very
+
+ align:start position:0%
+my own relationship to TV is very very
+ 
+
+ align:start position:0%
+my own relationship to TV is very very
+complicated we haven't really discussed
+
+ align:start position:0%
+complicated we haven't really discussed
+ 
+
+ align:start position:0%
+complicated we haven't really discussed
+this question whether that's solely a
+
+ align:start position:0%
+this question whether that's solely a
+ 
+
+ align:start position:0%
+this question whether that's solely a
+function of something which we've all
+
+ align:start position:0%
+function of something which we've all
+ 
+
+ align:start position:0%
+function of something which we've all
+been told or whether on a personal level
+
+ align:start position:0%
+been told or whether on a personal level
+ 
+
+ align:start position:0%
+been told or whether on a personal level
+people also have this ambivalent
+
+ align:start position:0%
+people also have this ambivalent
+ 
+
+ align:start position:0%
+people also have this ambivalent
+relationship to TV in which case maybe
+
+ align:start position:0%
+relationship to TV in which case maybe
+ 
+
+ align:start position:0%
+relationship to TV in which case maybe
+there is some value in the our our
+
+ align:start position:0%
+there is some value in the our our
+ 
+
+ align:start position:0%
+there is some value in the our our
+suspicions of it well I think there
+
+ align:start position:0%
+suspicions of it well I think there
+ 
+
+ align:start position:0%
+suspicions of it well I think there
+there's certain look I I I haven't meant
+
+ align:start position:0%
+there's certain look I I I haven't meant
+ 
+
+ align:start position:0%
+there's certain look I I I haven't meant
+to suggest that there aren't all kinds
+
+ align:start position:0%
+to suggest that there aren't all kinds
+ 
+
+ align:start position:0%
+to suggest that there aren't all kinds
+of reasons to be incredibly suspicious
+
+ align:start position:0%
+of reasons to be incredibly suspicious
+ 
+
+ align:start position:0%
+of reasons to be incredibly suspicious
+of Television I mean I think television
+
+ align:start position:0%
+of Television I mean I think television
+ 
+
+ align:start position:0%
+of Television I mean I think television
+promulgates all kinds of attitudes and
+
+ align:start position:0%
+promulgates all kinds of attitudes and
+ 
+
+ align:start position:0%
+promulgates all kinds of attitudes and
+Views that are dubious and questionable
+
+ align:start position:0%
+Views that are dubious and questionable
+ 
+
+ align:start position:0%
+Views that are dubious and questionable
+uh I and and I I also think of course
+
+ align:start position:0%
+uh I and and I I also think of course
+ 
+
+ align:start position:0%
+uh I and and I I also think of course
+it's the case that particular viewers
+
+ align:start position:0%
+it's the case that particular viewers
+ 
+
+ align:start position:0%
+it's the case that particular viewers
+can use television in ways that are not
+
+ align:start position:0%
+can use television in ways that are not
+ 
+
+ align:start position:0%
+can use television in ways that are not
+not healthy for them you're certainly
+
+ align:start position:0%
+not healthy for them you're certainly
+ 
+
+ align:start position:0%
+not healthy for them you're certainly
+right I think that many people exper exp
+
+ align:start position:0%
+right I think that many people exper exp
+ 
+
+ align:start position:0%
+right I think that many people exper exp
+erience the medium in a in a in a way
+
+ align:start position:0%
+erience the medium in a in a in a way
+ 
+
+ align:start position:0%
+erience the medium in a in a in a way
+that encourages their own that
+
+ align:start position:0%
+that encourages their own that
+ 
+
+ align:start position:0%
+that encourages their own that
+encourages them to feel negative toward
+
+ align:start position:0%
+encourages them to feel negative toward
+ 
+
+ align:start position:0%
+encourages them to feel negative toward
+it although it's a complicated an
+
+ align:start position:0%
+it although it's a complicated an
+ 
+
+ align:start position:0%
+it although it's a complicated an
+ambivalent relation as you suggest
+
+ align:start position:0%
+ambivalent relation as you suggest
+ 
+
+ align:start position:0%
+ambivalent relation as you suggest
+because they often are also uh uh
+
+ align:start position:0%
+because they often are also uh uh
+ 
+
+ align:start position:0%
+because they often are also uh uh
+yielding to the medium in a certain way
+
+ align:start position:0%
+yielding to the medium in a certain way
+ 
+
+ align:start position:0%
+yielding to the medium in a certain way
+or allowing themselves to vegge out as
+
+ align:start position:0%
+or allowing themselves to vegge out as
+ 
+
+ align:start position:0%
+or allowing themselves to vegge out as
+they often say when they when they look
+
+ align:start position:0%
+they often say when they when they look
+ 
+
+ align:start position:0%
+they often say when they when they look
+at the medium but I think your your the
+
+ align:start position:0%
+at the medium but I think your your the
+ 
+
+ align:start position:0%
+at the medium but I think your your the
+C your central point is very important
+
+ align:start position:0%
+C your central point is very important
+ 
+
+ align:start position:0%
+C your central point is very important
+and I haven't haven't meant to imply
+
+ align:start position:0%
+and I haven't haven't meant to imply
+ 
+
+ align:start position:0%
+and I haven't haven't meant to imply
+that I disagree with it in fact I I
+
+ align:start position:0%
+that I disagree with it in fact I I
+ 
+
+ align:start position:0%
+that I disagree with it in fact I I
+think it's absolutely right uh one of
+
+ align:start position:0%
+think it's absolutely right uh one of
+ 
+
+ align:start position:0%
+think it's absolutely right uh one of
+the reasons for the power of the
+
+ align:start position:0%
+the reasons for the power of the
+ 
+
+ align:start position:0%
+the reasons for the power of the
+Wasteland mythology is that it was so
+
+ align:start position:0%
+Wasteland mythology is that it was so
+ 
+
+ align:start position:0%
+Wasteland mythology is that it was so
+widely accepted by people who engaged in
+
+ align:start position:0%
+widely accepted by people who engaged in
+ 
+
+ align:start position:0%
+widely accepted by people who engaged in
+a kind of cognitive dissonance in their
+
+ align:start position:0%
+a kind of cognitive dissonance in their
+ 
+
+ align:start position:0%
+a kind of cognitive dissonance in their
+own attitudes toward the media they
+
+ align:start position:0%
+own attitudes toward the media they
+ 
+
+ align:start position:0%
+own attitudes toward the media they
+would on the one hand actually watch
+
+ align:start position:0%
+would on the one hand actually watch
+ 
+
+ align:start position:0%
+would on the one hand actually watch
+television all the time and get a lot
+
+ align:start position:0%
+television all the time and get a lot
+ 
+
+ align:start position:0%
+television all the time and get a lot
+out of it and actually enjoy it but on
+
+ align:start position:0%
+out of it and actually enjoy it but on
+ 
+
+ align:start position:0%
+out of it and actually enjoy it but on
+the other hand they would also feel that
+
+ align:start position:0%
+the other hand they would also feel that
+ 
+
+ align:start position:0%
+the other hand they would also feel that
+it was dangerous and bad some of that
+
+ align:start position:0%
+it was dangerous and bad some of that
+ 
+
+ align:start position:0%
+it was dangerous and bad some of that
+was a form of condescension uh in which
+
+ align:start position:0%
+was a form of condescension uh in which
+ 
+
+ align:start position:0%
+was a form of condescension uh in which
+C uh in which people would would in some
+
+ align:start position:0%
+C uh in which people would would in some
+ 
+
+ align:start position:0%
+C uh in which people would would in some
+sense exempt themselves from the dire
+
+ align:start position:0%
+sense exempt themselves from the dire
+ 
+
+ align:start position:0%
+sense exempt themselves from the dire
+effects that they felt were were likely
+
+ align:start position:0%
+effects that they felt were were likely
+ 
+
+ align:start position:0%
+effects that they felt were were likely
+to be visited on others and there is a
+
+ align:start position:0%
+to be visited on others and there is a
+ 
+
+ align:start position:0%
+to be visited on others and there is a
+is a kind of there's a kind of class
+
+ align:start position:0%
+is a kind of there's a kind of class
+ 
+
+ align:start position:0%
+is a kind of there's a kind of class
+Warfare Dimension to certain aspects of
+
+ align:start position:0%
+Warfare Dimension to certain aspects of
+ 
+
+ align:start position:0%
+Warfare Dimension to certain aspects of
+the way the mythology is deployed has
+
+ align:start position:0%
+the way the mythology is deployed has
+ 
+
+ align:start position:0%
+the way the mythology is deployed has
+been deployed in the past for example in
+
+ align:start position:0%
+been deployed in the past for example in
+ 
+
+ align:start position:0%
+been deployed in the past for example in
+uh uh in which uh there's a a large
+
+ align:start position:0%
+uh uh in which uh there's a a large
+ 
+
+ align:start position:0%
+uh uh in which uh there's a a large
+discourse about the danger of Television
+
+ align:start position:0%
+discourse about the danger of Television
+ 
+
+ align:start position:0%
+discourse about the danger of Television
+to children and a good deal of that has
+
+ align:start position:0%
+to children and a good deal of that has
+ 
+
+ align:start position:0%
+to children and a good deal of that has
+to do is specifically devoted to
+
+ align:start position:0%
+to do is specifically devoted to
+ 
+
+ align:start position:0%
+to do is specifically devoted to
+children to latch key kids right to kids
+
+ align:start position:0%
+children to latch key kids right to kids
+ 
+
+ align:start position:0%
+children to latch key kids right to kids
+to ghetto children to Children whose
+
+ align:start position:0%
+to ghetto children to Children whose
+ 
+
+ align:start position:0%
+to ghetto children to Children whose
+parents have to work so if you the
+
+ align:start position:0%
+parents have to work so if you the
+ 
+
+ align:start position:0%
+parents have to work so if you the
+children come home and television's the
+
+ align:start position:0%
+children come home and television's the
+ 
+
+ align:start position:0%
+children come home and television's the
+only babysitter and and the people who
+
+ align:start position:0%
+only babysitter and and the people who
+ 
+
+ align:start position:0%
+only babysitter and and the people who
+make these arguments of course are in
+
+ align:start position:0%
+make these arguments of course are in
+ 
+
+ align:start position:0%
+make these arguments of course are in
+effect exempting their own families and
+
+ align:start position:0%
+effect exempting their own families and
+ 
+
+ align:start position:0%
+effect exempting their own families and
+their own children from the baleful
+
+ align:start position:0%
+their own children from the baleful
+ 
+
+ align:start position:0%
+their own children from the baleful
+effects of a medium that they think is
+
+ align:start position:0%
+effects of a medium that they think is
+ 
+
+ align:start position:0%
+effects of a medium that they think is
+going to harm others so that's also an
+
+ align:start position:0%
+going to harm others so that's also an
+ 
+
+ align:start position:0%
+going to harm others so that's also an
+aspect of the of the case but I but I'm
+
+ align:start position:0%
+aspect of the of the case but I but I'm
+ 
+
+ align:start position:0%
+aspect of the of the case but I but I'm
+I'm in a in a way that's not uh uh
+
+ align:start position:0%
+I'm in a in a way that's not uh uh
+ 
+
+ align:start position:0%
+I'm in a in a way that's not uh uh
+exactly what you were saying Susanna and
+
+ align:start position:0%
+exactly what you were saying Susanna and
+ 
+
+ align:start position:0%
+exactly what you were saying Susanna and
+and and I agree with what you're saying
+
+ align:start position:0%
+and and I agree with what you're saying
+ 
+
+ align:start position:0%
+and and I agree with what you're saying
+it seems to me that that one reason for
+
+ align:start position:0%
+it seems to me that that one reason for
+ 
+
+ align:start position:0%
+it seems to me that that one reason for
+the power of the Wasteland mythology is
+
+ align:start position:0%
+the power of the Wasteland mythology is
+ 
+
+ align:start position:0%
+the power of the Wasteland mythology is
+that at some level many people in their
+
+ align:start position:0%
+that at some level many people in their
+ 
+
+ align:start position:0%
+that at some level many people in their
+experience of Television have the have
+
+ align:start position:0%
+experience of Television have the have
+ 
+
+ align:start position:0%
+experience of Television have the have
+the mythology ratified they see a
+
+ align:start position:0%
+the mythology ratified they see a
+ 
+
+ align:start position:0%
+the mythology ratified they see a
+tremendous amount of Bal programming
+
+ align:start position:0%
+tremendous amount of Bal programming
+ 
+
+ align:start position:0%
+tremendous amount of Bal programming
+they see incredible foolishness and
+
+ align:start position:0%
+they see incredible foolishness and
+ 
+
+ align:start position:0%
+they see incredible foolishness and
+silliness on the medium and they even
+
+ align:start position:0%
+silliness on the medium and they even
+ 
+
+ align:start position:0%
+silliness on the medium and they even
+see that there's a certain sense in
+
+ align:start position:0%
+see that there's a certain sense in
+ 
+
+ align:start position:0%
+see that there's a certain sense in
+which they can sort of just relax in
+
+ align:start position:0%
+which they can sort of just relax in
+ 
+
+ align:start position:0%
+which they can sort of just relax in
+front of it and allow the words and
+
+ align:start position:0%
+front of it and allow the words and
+ 
+
+ align:start position:0%
+front of it and allow the words and
+images to pour over them in a way that's
+
+ align:start position:0%
+images to pour over them in a way that's
+ 
+
+ align:start position:0%
+images to pour over them in a way that's
+very relaxing and mind-numbing and they
+
+ align:start position:0%
+very relaxing and mind-numbing and they
+ 
+
+ align:start position:0%
+very relaxing and mind-numbing and they
+and and they and they draw from that the
+
+ align:start position:0%
+and and they and they draw from that the
+ 
+
+ align:start position:0%
+and and they and they draw from that the
+conclusion that that that that that the
+
+ align:start position:0%
+conclusion that that that that that the
+ 
+
+ align:start position:0%
+conclusion that that that that that the
+uh arguments against television and
+
+ align:start position:0%
+uh arguments against television and
+ 
+
+ align:start position:0%
+uh arguments against television and
+especially against its narcotizing
+
+ align:start position:0%
+especially against its narcotizing
+ 
+
+ align:start position:0%
+especially against its narcotizing
+effects have some have some uh Power uh
+
+ align:start position:0%
+effects have some have some uh Power uh
+ 
+
+ align:start position:0%
+effects have some have some uh Power uh
+I think it is true that people can allow
+
+ align:start position:0%
+I think it is true that people can allow
+ 
+
+ align:start position:0%
+I think it is true that people can allow
+themselves to fall into such a relation
+
+ align:start position:0%
+themselves to fall into such a relation
+ 
+
+ align:start position:0%
+themselves to fall into such a relation
+to the medium but there's no evidence to
+
+ align:start position:0%
+to the medium but there's no evidence to
+ 
+
+ align:start position:0%
+to the medium but there's no evidence to
+suggest that in fact those are features
+
+ align:start position:0%
+suggest that in fact those are features
+ 
+
+ align:start position:0%
+suggest that in fact those are features
+that are that are uh unique to
+
+ align:start position:0%
+that are that are uh unique to
+ 
+
+ align:start position:0%
+that are that are uh unique to
+television people there are there are
+
+ align:start position:0%
+television people there are there are
+ 
+
+ align:start position:0%
+television people there are there are
+there are other uh
+
+ align:start position:0%
+there are other uh
+ 
+
+ align:start position:0%
+there are other uh
+narot not exactly narcotizing experience
+
+ align:start position:0%
+narot not exactly narcotizing experience
+ 
+
+ align:start position:0%
+narot not exactly narcotizing experience
+there are other other experiences in in
+
+ align:start position:0%
+there are other other experiences in in
+ 
+
+ align:start position:0%
+there are other other experiences in in
+our lives that that can cause us to sort
+
+ align:start position:0%
+our lives that that can cause us to sort
+ 
+
+ align:start position:0%
+our lives that that can cause us to sort
+of veg out or fall or fall half asleep
+
+ align:start position:0%
+of veg out or fall or fall half asleep
+ 
+
+ align:start position:0%
+of veg out or fall or fall half asleep
+and and it's not intrinsic in the medium
+
+ align:start position:0%
+and and it's not intrinsic in the medium
+ 
+
+ align:start position:0%
+and and it's not intrinsic in the medium
+because of course you can also re
+
+ align:start position:0%
+because of course you can also re
+ 
+
+ align:start position:0%
+because of course you can also re
+interact with television in in much more
+
+ align:start position:0%
+interact with television in in much more
+ 
+
+ align:start position:0%
+interact with television in in much more
+alert and complex ways one might
+
+ align:start position:0%
+alert and complex ways one might
+ 
+
+ align:start position:0%
+alert and complex ways one might
+actually turn the argument on its head
+
+ align:start position:0%
+actually turn the argument on its head
+ 
+
+ align:start position:0%
+actually turn the argument on its head
+if one wanted to say that one of the
+
+ align:start position:0%
+if one wanted to say that one of the
+ 
+
+ align:start position:0%
+if one wanted to say that one of the
+most remarkable things about the medium
+
+ align:start position:0%
+most remarkable things about the medium
+ 
+
+ align:start position:0%
+most remarkable things about the medium
+is that is that it allows this this
+
+ align:start position:0%
+is that is that it allows this this
+ 
+
+ align:start position:0%
+is that is that it allows this this
+level of semiconscious interaction with
+
+ align:start position:0%
+level of semiconscious interaction with
+ 
+
+ align:start position:0%
+level of semiconscious interaction with
+it uh as well as allowing a much more
+
+ align:start position:0%
+it uh as well as allowing a much more
+ 
+
+ align:start position:0%
+it uh as well as allowing a much more
+complex active kind of relation uh to
+
+ align:start position:0%
+complex active kind of relation uh to
+ 
+
+ align:start position:0%
+complex active kind of relation uh to
+the medium the only the only uh place
+
+ align:start position:0%
+the medium the only the only uh place
+ 
+
+ align:start position:0%
+the medium the only the only uh place
+that I would hesitate uh the only place
+
+ align:start position:0%
+that I would hesitate uh the only place
+ 
+
+ align:start position:0%
+that I would hesitate uh the only place
+the only area in which I I would descent
+
+ align:start position:0%
+the only area in which I I would descent
+ 
+
+ align:start position:0%
+the only area in which I I would descent
+from the implications of your remark
+
+ align:start position:0%
+from the implications of your remark
+ 
+
+ align:start position:0%
+from the implications of your remark
+Susanna is is here and although you
+
+ align:start position:0%
+Susanna is is here and although you
+ 
+
+ align:start position:0%
+Susanna is is here and although you
+didn't actually say this so I wouldn't
+
+ align:start position:0%
+didn't actually say this so I wouldn't
+ 
+
+ align:start position:0%
+didn't actually say this so I wouldn't
+shouldn't attribute this view to you is
+
+ align:start position:0%
+shouldn't attribute this view to you is
+ 
+
+ align:start position:0%
+shouldn't attribute this view to you is
+the notion that there are negative
+
+ align:start position:0%
+the notion that there are negative
+ 
+
+ align:start position:0%
+the notion that there are negative
+long-term effects from this kind of
+
+ align:start position:0%
+long-term effects from this kind of
+ 
+
+ align:start position:0%
+long-term effects from this kind of
+vegging out there's no real evidence for
+
+ align:start position:0%
+vegging out there's no real evidence for
+ 
+
+ align:start position:0%
+vegging out there's no real evidence for
+that even though it is taken for granted
+
+ align:start position:0%
+that even though it is taken for granted
+ 
+
+ align:start position:0%
+that even though it is taken for granted
+that the uh by by by the by the
+
+ align:start position:0%
+that the uh by by by the by the
+ 
+
+ align:start position:0%
+that the uh by by by the by the
+wastelanders that there are uh negative
+
+ align:start position:0%
+wastelanders that there are uh negative
+ 
+
+ align:start position:0%
+wastelanders that there are uh negative
+negative effects from it uh there's no
+
+ align:start position:0%
+negative effects from it uh there's no
+ 
+
+ align:start position:0%
+negative effects from it uh there's no
+there's no and and and even the even the
+
+ align:start position:0%
+there's no and and and even the even the
+ 
+
+ align:start position:0%
+there's no and and and even the even the
+metaphor of addiction seems
+
+ align:start position:0%
+metaphor of addiction seems
+ 
+
+ align:start position:0%
+metaphor of addiction seems
+inappropriate because because it is not
+
+ align:start position:0%
+inappropriate because because it is not
+ 
+
+ align:start position:0%
+inappropriate because because it is not
+in fact a chemical addiction it is not
+
+ align:start position:0%
+in fact a chemical addiction it is not
+ 
+
+ align:start position:0%
+in fact a chemical addiction it is not
+the equivalent of tobacco addiction
+
+ align:start position:0%
+the equivalent of tobacco addiction
+ 
+
+ align:start position:0%
+the equivalent of tobacco addiction
+which we know actually affects the
+
+ align:start position:0%
+which we know actually affects the
+ 
+
+ align:start position:0%
+which we know actually affects the
+chemistry of the of the body or heroin
+
+ align:start position:0%
+chemistry of the of the body or heroin
+ 
+
+ align:start position:0%
+chemistry of the of the body or heroin
+addiction which again is a biological
+
+ align:start position:0%
+addiction which again is a biological
+ 
+
+ align:start position:0%
+addiction which again is a biological
+experience
+
+ align:start position:0%
+experience
+ 
+
+ align:start position:0%
+experience
+in a way that does not that does not
+
+ align:start position:0%
+in a way that does not that does not
+ 
+
+ align:start position:0%
+in a way that does not that does not
+seem to be true and people people go
+
+ align:start position:0%
+seem to be true and people people go
+ 
+
+ align:start position:0%
+seem to be true and people people go
+cold turkey off television all the time
+
+ align:start position:0%
+cold turkey off television all the time
+ 
+
+ align:start position:0%
+cold turkey off television all the time
+without any apparent negative
+
+ align:start position:0%
+without any apparent negative
+ 
+
+ align:start position:0%
+without any apparent negative
+consequences one more comment we'll go
+
+ align:start position:0%
+consequences one more comment we'll go
+ 
+
+ align:start position:0%
+consequences one more comment we'll go
+move
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on I don't plan to pursue this much much
+
+ align:start position:0%
+on I don't plan to pursue this much much
+ 
+
+ align:start position:0%
+on I don't plan to pursue this much much
+further I I just wanted to complicate
+
+ align:start position:0%
+further I I just wanted to complicate
+ 
+
+ align:start position:0%
+further I I just wanted to complicate
+that a little by mentioning that there
+
+ align:start position:0%
+that a little by mentioning that there
+ 
+
+ align:start position:0%
+that a little by mentioning that there
+are other one kind of addiction
+
+ align:start position:0%
+are other one kind of addiction
+ 
+
+ align:start position:0%
+are other one kind of addiction
+currently under debate for example is
+
+ align:start position:0%
+currently under debate for example is
+ 
+
+ align:start position:0%
+currently under debate for example is
+the question of whether gambling is an
+
+ align:start position:0%
+the question of whether gambling is an
+ 
+
+ align:start position:0%
+the question of whether gambling is an
+addiction for some people I just wanted
+
+ align:start position:0%
+addiction for some people I just wanted
+ 
+
+ align:start position:0%
+addiction for some people I just wanted
+to complicate the point by noting that
+
+ align:start position:0%
+to complicate the point by noting that
+ 
+
+ align:start position:0%
+to complicate the point by noting that
+addiction is you know obviously not
+
+ align:start position:0%
+addiction is you know obviously not
+ 
+
+ align:start position:0%
+addiction is you know obviously not
+always Us in the purely physical sense
+
+ align:start position:0%
+always Us in the purely physical sense
+ 
+
+ align:start position:0%
+always Us in the purely physical sense
+and I I think that that is presumably it
+
+ align:start position:0%
+and I I think that that is presumably it
+ 
+
+ align:start position:0%
+and I I think that that is presumably it
+must be what people have in mind when
+
+ align:start position:0%
+must be what people have in mind when
+ 
+
+ align:start position:0%
+must be what people have in mind when
+they talk of the television addiction
+
+ align:start position:0%
+they talk of the television addiction
+ 
+
+ align:start position:0%
+they talk of the television addiction
+okay I mean I think those are very
+
+ align:start position:0%
+okay I mean I think those are very
+ 
+
+ align:start position:0%
+okay I mean I think those are very
+dubious extensions of of of the notion
+
+ align:start position:0%
+dubious extensions of of of the notion
+ 
+
+ align:start position:0%
+dubious extensions of of of the notion
+of addiction just as they're under
+
+ align:start position:0%
+of addiction just as they're under
+ 
+
+ align:start position:0%
+of addiction just as they're under
+debate you know they just just as you
+
+ align:start position:0%
+debate you know they just just as you
+ 
+
+ align:start position:0%
+debate you know they just just as you
+know just as we're in our in the current
+
+ align:start position:0%
+know just as we're in our in the current
+ 
+
+ align:start position:0%
+know just as we're in our in the current
+moment that we're in the United States
+
+ align:start position:0%
+moment that we're in the United States
+ 
+
+ align:start position:0%
+moment that we're in the United States
+now there are very dubious extensions of
+
+ align:start position:0%
+now there are very dubious extensions of
+ 
+
+ align:start position:0%
+now there are very dubious extensions of
+Notions of therapy to uh and and and uh
+
+ align:start position:0%
+Notions of therapy to uh and and and uh
+ 
+
+ align:start position:0%
+Notions of therapy to uh and and and uh
+uh trauma the idea of the idea of trauma
+
+ align:start position:0%
+uh trauma the idea of the idea of trauma
+ 
+
+ align:start position:0%
+uh trauma the idea of the idea of trauma
+is now being extended Much More Much
+
+ align:start position:0%
+is now being extended Much More Much
+ 
+
+ align:start position:0%
+is now being extended Much More Much
+More widely and broadly than is probably
+
+ align:start position:0%
+More widely and broadly than is probably
+ 
+
+ align:start position:0%
+More widely and broadly than is probably
+uh medically or biologically accurate
+
+ align:start position:0%
+uh medically or biologically accurate
+ 
+
+ align:start position:0%
+uh medically or biologically accurate
+and it may not be an entirely uh helpful
+
+ align:start position:0%
+and it may not be an entirely uh helpful
+ 
+
+ align:start position:0%
+and it may not be an entirely uh helpful
+extension in in the case of these
+
+ align:start position:0%
+extension in in the case of these
+ 
+
+ align:start position:0%
+extension in in the case of these
+definition I mean look there are people
+
+ align:start position:0%
+definition I mean look there are people
+ 
+
+ align:start position:0%
+definition I mean look there are people
+who say that that's that uh there are
+
+ align:start position:0%
+who say that that's that uh there are
+ 
+
+ align:start position:0%
+who say that that's that uh there are
+there are people who extend the notion
+
+ align:start position:0%
+there are people who extend the notion
+ 
+
+ align:start position:0%
+there are people who extend the notion
+of addiction to to people to to uh to uh
+
+ align:start position:0%
+of addiction to to people to to uh to uh
+ 
+
+ align:start position:0%
+of addiction to to people to to uh to uh
+to sexual behavior and people say oh I I
+
+ align:start position:0%
+to sexual behavior and people say oh I I
+ 
+
+ align:start position:0%
+to sexual behavior and people say oh I I
+have to confess I'm I'm an adulter
+
+ align:start position:0%
+have to confess I'm I'm an adulter
+ 
+
+ align:start position:0%
+have to confess I'm I'm an adulter
+because I'm a sex addict and uh one can
+
+ align:start position:0%
+because I'm a sex addict and uh one can
+ 
+
+ align:start position:0%
+because I'm a sex addict and uh one can
+one can easily see that in that instance
+
+ align:start position:0%
+one can easily see that in that instance
+ 
+
+ align:start position:0%
+one can easily see that in that instance
+of why why the notion of it's very
+
+ align:start position:0%
+of why why the notion of it's very
+ 
+
+ align:start position:0%
+of why why the notion of it's very
+dangerous I think to extend the notion
+
+ align:start position:0%
+dangerous I think to extend the notion
+ 
+
+ align:start position:0%
+dangerous I think to extend the notion
+of addiction uh to to non-biological
+
+ align:start position:0%
+of addiction uh to to non-biological
+ 
+
+ align:start position:0%
+of addiction uh to to non-biological
+base to to to to Notions of you know
+
+ align:start position:0%
+base to to to to Notions of you know
+ 
+
+ align:start position:0%
+base to to to to Notions of you know
+there preferences that people have
+
+ align:start position:0%
+there preferences that people have
+ 
+
+ align:start position:0%
+there preferences that people have
+trouble breaking that's a very different
+
+ align:start position:0%
+trouble breaking that's a very different
+ 
+
+ align:start position:0%
+trouble breaking that's a very different
+kind of thing I I acknowledge you're
+
+ align:start position:0%
+kind of thing I I acknowledge you're
+ 
+
+ align:start position:0%
+kind of thing I I acknowledge you're
+right that it that it is part of the
+
+ align:start position:0%
+right that it that it is part of the
+ 
+
+ align:start position:0%
+right that it that it is part of the
+discourse of the society but I think
+
+ align:start position:0%
+discourse of the society but I think
+ 
+
+ align:start position:0%
+discourse of the society but I think
+it's a discourse that we might want to
+
+ align:start position:0%
+it's a discourse that we might want to
+ 
+
+ align:start position:0%
+it's a discourse that we might want to
+want to uh look on very skeptically but
+
+ align:start position:0%
+want to uh look on very skeptically but
+ 
+
+ align:start position:0%
+want to uh look on very skeptically but
+let me let me continue here because I I
+
+ align:start position:0%
+let me let me continue here because I I
+ 
+
+ align:start position:0%
+let me let me continue here because I I
+I don't want to keep doing this wind up
+
+ align:start position:0%
+I don't want to keep doing this wind up
+ 
+
+ align:start position:0%
+I don't want to keep doing this wind up
+and not actually get to our to to the
+
+ align:start position:0%
+and not actually get to our to to the
+ 
+
+ align:start position:0%
+and not actually get to our to to the
+core of the course which is the reading
+
+ align:start position:0%
+core of the course which is the reading
+ 
+
+ align:start position:0%
+core of the course which is the reading
+of programs in some kind of a systematic
+
+ align:start position:0%
+of programs in some kind of a systematic
+ 
+
+ align:start position:0%
+of programs in some kind of a systematic
+way the next step we make in the
+
+ align:start position:0%
+way the next step we make in the
+ 
+
+ align:start position:0%
+way the next step we make in the
+argument is to say okay if the Wasteland
+
+ align:start position:0%
+argument is to say okay if the Wasteland
+ 
+
+ align:start position:0%
+argument is to say okay if the Wasteland
+mythology these various simplified uh
+
+ align:start position:0%
+mythology these various simplified uh
+ 
+
+ align:start position:0%
+mythology these various simplified uh
+ways of of of understanding television
+
+ align:start position:0%
+ways of of of understanding television
+ 
+
+ align:start position:0%
+ways of of of understanding television
+are inadequate what would be an adequate
+
+ align:start position:0%
+are inadequate what would be an adequate
+ 
+
+ align:start position:0%
+are inadequate what would be an adequate
+way and what I what what I've suggested
+
+ align:start position:0%
+way and what I what what I've suggested
+ 
+
+ align:start position:0%
+way and what I what what I've suggested
+to you is of course is uh is not that we
+
+ align:start position:0%
+to you is of course is uh is not that we
+ 
+
+ align:start position:0%
+to you is of course is uh is not that we
+suddenly begin to tell some kind of a
+
+ align:start position:0%
+suddenly begin to tell some kind of a
+ 
+
+ align:start position:0%
+suddenly begin to tell some kind of a
+noble or triumphal story about the
+
+ align:start position:0%
+noble or triumphal story about the
+ 
+
+ align:start position:0%
+noble or triumphal story about the
+mediev and all but we simply acknowledge
+
+ align:start position:0%
+mediev and all but we simply acknowledge
+ 
+
+ align:start position:0%
+mediev and all but we simply acknowledge
+that it is a cultural formation that
+
+ align:start position:0%
+that it is a cultural formation that
+ 
+
+ align:start position:0%
+that it is a cultural formation that
+that a cultural formation which has
+
+ align:start position:0%
+that a cultural formation which has
+ 
+
+ align:start position:0%
+that a cultural formation which has
+ancestors and that we can learn
+
+ align:start position:0%
+ancestors and that we can learn
+ 
+
+ align:start position:0%
+ancestors and that we can learn
+something about the development of this
+
+ align:start position:0%
+something about the development of this
+ 
+
+ align:start position:0%
+something about the development of this
+new medium by or what was once a new
+
+ align:start position:0%
+new medium by or what was once a new
+ 
+
+ align:start position:0%
+new medium by or what was once a new
+medium by looking at its ancestors and
+
+ align:start position:0%
+medium by looking at its ancestors and
+ 
+
+ align:start position:0%
+medium by looking at its ancestors and
+by looking at the development of other
+
+ align:start position:0%
+by looking at the development of other
+ 
+
+ align:start position:0%
+by looking at the development of other
+of other media by recognizing that
+
+ align:start position:0%
+of other media by recognizing that
+ 
+
+ align:start position:0%
+of other media by recognizing that
+certain kinds of historical comparisons
+
+ align:start position:0%
+certain kinds of historical comparisons
+ 
+
+ align:start position:0%
+certain kinds of historical comparisons
+might be Illuminating granting that even
+
+ align:start position:0%
+might be Illuminating granting that even
+ 
+
+ align:start position:0%
+might be Illuminating granting that even
+granting the notion that that the medium
+
+ align:start position:0%
+granting the notion that that the medium
+ 
+
+ align:start position:0%
+granting the notion that that the medium
+itself might have a history that is
+
+ align:start position:0%
+itself might have a history that is
+ 
+
+ align:start position:0%
+itself might have a history that is
+valuable one aspect of the uh Wasteland
+
+ align:start position:0%
+valuable one aspect of the uh Wasteland
+ 
+
+ align:start position:0%
+valuable one aspect of the uh Wasteland
+mythology that I find I think is still
+
+ align:start position:0%
+mythology that I find I think is still
+ 
+
+ align:start position:0%
+mythology that I find I think is still
+the case and is that people talk about
+
+ align:start position:0%
+the case and is that people talk about
+ 
+
+ align:start position:0%
+the case and is that people talk about
+television as if it is unchanged over
+
+ align:start position:0%
+television as if it is unchanged over
+ 
+
+ align:start position:0%
+television as if it is unchanged over
+its 50-year history they make no or
+
+ align:start position:0%
+its 50-year history they make no or
+ 
+
+ align:start position:0%
+its 50-year history they make no or
+virtually so they they will sometimes
+
+ align:start position:0%
+virtually so they they will sometimes
+ 
+
+ align:start position:0%
+virtually so they they will sometimes
+talk about an alleged golden age of live
+
+ align:start position:0%
+talk about an alleged golden age of live
+ 
+
+ align:start position:0%
+talk about an alleged golden age of live
+television after which everything is
+
+ align:start position:0%
+television after which everything is
+ 
+
+ align:start position:0%
+television after which everything is
+terrible but for the most part they talk
+
+ align:start position:0%
+terrible but for the most part they talk
+ 
+
+ align:start position:0%
+terrible but for the most part they talk
+about television as if it's as if it did
+
+ align:start position:0%
+about television as if it's as if it did
+ 
+
+ align:start position:0%
+about television as if it's as if it did
+not itself have phases and and and and
+
+ align:start position:0%
+not itself have phases and and and and
+ 
+
+ align:start position:0%
+not itself have phases and and and and
+as if the programs of the 90s are
+
+ align:start position:0%
+as if the programs of the 90s are
+ 
+
+ align:start position:0%
+as if the programs of the 90s are
+identical to the programs of the 50s one
+
+ align:start position:0%
+identical to the programs of the 50s one
+ 
+
+ align:start position:0%
+identical to the programs of the 50s one
+can see the same mistake uh even more
+
+ align:start position:0%
+can see the same mistake uh even more
+ 
+
+ align:start position:0%
+can see the same mistake uh even more
+dramatically being made by by the film
+
+ align:start position:0%
+dramatically being made by by the film
+ 
+
+ align:start position:0%
+dramatically being made by by the film
+Scholars and the film historians who
+
+ align:start position:0%
+Scholars and the film historians who
+ 
+
+ align:start position:0%
+Scholars and the film historians who
+really many of whom continue to speak
+
+ align:start position:0%
+really many of whom continue to speak
+ 
+
+ align:start position:0%
+really many of whom continue to speak
+about the movies as if they are a
+
+ align:start position:0%
+about the movies as if they are a
+ 
+
+ align:start position:0%
+about the movies as if they are a
+continuous experience from the silent
+
+ align:start position:0%
+continuous experience from the silent
+ 
+
+ align:start position:0%
+continuous experience from the silent
+era to to the present day when there are
+
+ align:start position:0%
+era to to the present day when there are
+ 
+
+ align:start position:0%
+era to to the present day when there are
+at least two deci Ive moments in which
+
+ align:start position:0%
+at least two deci Ive moments in which
+ 
+
+ align:start position:0%
+at least two deci Ive moments in which
+the movies fundamentally alter their
+
+ align:start position:0%
+the movies fundamentally alter their
+ 
+
+ align:start position:0%
+the movies fundamentally alter their
+relation to the society one is at the
+
+ align:start position:0%
+relation to the society one is at the
+ 
+
+ align:start position:0%
+relation to the society one is at the
+Advent of sound at the end of the 20s
+
+ align:start position:0%
+Advent of sound at the end of the 20s
+ 
+
+ align:start position:0%
+Advent of sound at the end of the 20s
+and the other even more dramatic a
+
+ align:start position:0%
+and the other even more dramatic a
+ 
+
+ align:start position:0%
+and the other even more dramatic a
+fundamental transformation in the
+
+ align:start position:0%
+fundamental transformation in the
+ 
+
+ align:start position:0%
+fundamental transformation in the
+relationship between movies and American
+
+ align:start position:0%
+relationship between movies and American
+ 
+
+ align:start position:0%
+relationship between movies and American
+society occurs with the Advent of
+
+ align:start position:0%
+society occurs with the Advent of
+ 
+
+ align:start position:0%
+society occurs with the Advent of
+television and by by the late 50s or
+
+ align:start position:0%
+television and by by the late 50s or
+ 
+
+ align:start position:0%
+television and by by the late 50s or
+early 60s the relationship between the
+
+ align:start position:0%
+early 60s the relationship between the
+ 
+
+ align:start position:0%
+early 60s the relationship between the
+movie industry in so far as it's still
+
+ align:start position:0%
+movie industry in so far as it's still
+ 
+
+ align:start position:0%
+movie industry in so far as it's still
+an industry and the public is totally
+
+ align:start position:0%
+an industry and the public is totally
+ 
+
+ align:start position:0%
+an industry and the public is totally
+different from what it was and the movie
+
+ align:start position:0%
+different from what it was and the movie
+ 
+
+ align:start position:0%
+different from what it was and the movie
+industry as we've under as we had
+
+ align:start position:0%
+industry as we've under as we had
+ 
+
+ align:start position:0%
+industry as we've under as we had
+understood it before no longer exists
+
+ align:start position:0%
+understood it before no longer exists
+ 
+
+ align:start position:0%
+understood it before no longer exists
+there are no longer vast movie studios
+
+ align:start position:0%
+there are no longer vast movie studios
+ 
+
+ align:start position:0%
+there are no longer vast movie studios
+employing hundreds and sometimes
+
+ align:start position:0%
+employing hundreds and sometimes
+ 
+
+ align:start position:0%
+employing hundreds and sometimes
+thousands of people producing Mass
+
+ align:start position:0%
+thousands of people producing Mass
+ 
+
+ align:start position:0%
+thousands of people producing Mass
+producing stories on a regular basis
+
+ align:start position:0%
+producing stories on a regular basis
+ 
+
+ align:start position:0%
+producing stories on a regular basis
+that that that movie industry is gone
+
+ align:start position:0%
+that that that movie industry is gone
+ 
+
+ align:start position:0%
+that that that movie industry is gone
+the that that idea of the movies is
+
+ align:start position:0%
+the that that idea of the movies is
+ 
+
+ align:start position:0%
+the that that idea of the movies is
+finished and each individual film
+
+ align:start position:0%
+finished and each individual film
+ 
+
+ align:start position:0%
+finished and each individual film
+becomes not only a Blockbuster
+
+ align:start position:0%
+becomes not only a Blockbuster
+ 
+
+ align:start position:0%
+becomes not only a Blockbuster
+experience but the but the creation of
+
+ align:start position:0%
+experience but the but the creation of
+ 
+
+ align:start position:0%
+experience but the but the creation of
+the film The putting together of the
+
+ align:start position:0%
+the film The putting together of the
+ 
+
+ align:start position:0%
+the film The putting together of the
+film becomes an a vast elaborate problem
+
+ align:start position:0%
+film becomes an a vast elaborate problem
+ 
+
+ align:start position:0%
+film becomes an a vast elaborate problem
+in Deal making in which you go and get a
+
+ align:start position:0%
+in Deal making in which you go and get a
+ 
+
+ align:start position:0%
+in Deal making in which you go and get a
+star to who's bankable and you go to and
+
+ align:start position:0%
+star to who's bankable and you go to and
+ 
+
+ align:start position:0%
+star to who's bankable and you go to and
+you go to money backers who will Who
+
+ align:start position:0%
+you go to money backers who will Who
+ 
+
+ align:start position:0%
+you go to money backers who will Who
+will will have in words the production
+
+ align:start position:0%
+will will have in words the production
+ 
+
+ align:start position:0%
+will will have in words the production
+companies are are simply affect Bankers
+
+ align:start position:0%
+companies are are simply affect Bankers
+ 
+
+ align:start position:0%
+companies are are simply affect Bankers
+they're no they're no longer they no
+
+ align:start position:0%
+they're no they're no longer they no
+ 
+
+ align:start position:0%
+they're no they're no longer they no
+longer make a kind of creative
+
+ align:start position:0%
+longer make a kind of creative
+ 
+
+ align:start position:0%
+longer make a kind of creative
+contribution to the movie and the movies
+
+ align:start position:0%
+contribution to the movie and the movies
+ 
+
+ align:start position:0%
+contribution to the movie and the movies
+are a fundamentally different artifact
+
+ align:start position:0%
+are a fundamentally different artifact
+ 
+
+ align:start position:0%
+are a fundamentally different artifact
+they're made differently they have a
+
+ align:start position:0%
+they're made differently they have a
+ 
+
+ align:start position:0%
+they're made differently they have a
+different Their audience has a different
+
+ align:start position:0%
+different Their audience has a different
+ 
+
+ align:start position:0%
+different Their audience has a different
+demographic their relation to the
+
+ align:start position:0%
+demographic their relation to the
+ 
+
+ align:start position:0%
+demographic their relation to the
+society is different and and it is
+
+ align:start position:0%
+society is different and and it is
+ 
+
+ align:start position:0%
+society is different and and it is
+actually an intellectual mistake of a of
+
+ align:start position:0%
+actually an intellectual mistake of a of
+ 
+
+ align:start position:0%
+actually an intellectual mistake of a of
+a very large sort to pretend that the
+
+ align:start position:0%
+a very large sort to pretend that the
+ 
+
+ align:start position:0%
+a very large sort to pretend that the
+movies of the 1980s or 1990s are the
+
+ align:start position:0%
+movies of the 1980s or 1990s are the
+ 
+
+ align:start position:0%
+movies of the 1980s or 1990s are the
+same kind of object uh uh in in in
+
+ align:start position:0%
+same kind of object uh uh in in in
+ 
+
+ align:start position:0%
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+
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+sort of lack of awareness of the of even
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+
+ align:start position:0%
+sort of lack of awareness of the of even
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+
+ align:start position:0%
+what we might call the internal history
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+of a particular medium especially
+ 
+
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+of a particular medium especially
+afflicts discourse about television even
+
+ align:start position:0%
+afflicts discourse about television even
+ 
+
+ align:start position:0%
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+to this day although some of the
+
+ align:start position:0%
+to this day although some of the
+ 
+
+ align:start position:0%
+to this day although some of the
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+
+ align:start position:0%
+readings that I've asked you to do show
+ 
+
+ align:start position:0%
+readings that I've asked you to do show
+that there is now a nent uh historical
+
+ align:start position:0%
+that there is now a nent uh historical
+ 
+
+ align:start position:0%
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+scholarship being being developed about
+
+ align:start position:0%
+scholarship being being developed about
+ 
+
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+
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+
+ align:start position:0%
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+
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+I've asked you to read um by by a young
+
+ align:start position:0%
+I've asked you to read um by by a young
+ 
+
+ align:start position:0%
+I've asked you to read um by by a young
+scholar named Anderson who uh writes
+
+ align:start position:0%
+scholar named Anderson who uh writes
+ 
+
+ align:start position:0%
+scholar named Anderson who uh writes
+about the relation between Hollywood uh
+
+ align:start position:0%
+about the relation between Hollywood uh
+ 
+
+ align:start position:0%
+about the relation between Hollywood uh
+and and uh Hollywood systems and
+
+ align:start position:0%
+and and uh Hollywood systems and
+ 
+
+ align:start position:0%
+and and uh Hollywood systems and
+television who's done very very
+
+ align:start position:0%
+television who's done very very
+ 
+
+ align:start position:0%
+television who's done very very
+interesting work and the excerpt from
+
+ align:start position:0%
+interesting work and the excerpt from
+ 
+
+ align:start position:0%
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+his book that I've asked you to read
+
+ align:start position:0%
+his book that I've asked you to read
+ 
+
+ align:start position:0%
+his book that I've asked you to read
+That's reprinted in Nukem is about the
+
+ align:start position:0%
+That's reprinted in Nukem is about the
+ 
+
+ align:start position:0%
+That's reprinted in Nukem is about the
+relation between the Disney company and
+
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+relation between the Disney company and
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+the way early 50s television undergos a
+
+ align:start position:0%
+the way early 50s television undergos a
+ 
+
+ align:start position:0%
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+kind of radical transformation once the
+
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+kind of radical transformation once the
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+
+ align:start position:0%
+kind of radical transformation once the
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+
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+American movie industry uh acknowledges
+ 
+
+ align:start position:0%
+American movie industry uh acknowledges
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+
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+ 
+
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+to supply product to it uh and so so
+
+ align:start position:0%
+to supply product to it uh and so so
+ 
+
+ align:start position:0%
+to supply product to it uh and so so
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+
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+there is some historical work being done
+ 
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+
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+ 
+
+ align:start position:0%
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+about television in the public Realm
+
+ align:start position:0%
+about television in the public Realm
+ 
+
+ align:start position:0%
+about television in the public Realm
+still continues to be afflicted by this
+
+ align:start position:0%
+still continues to be afflicted by this
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+
+ align:start position:0%
+still continues to be afflicted by this
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+
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+ahistoricism it's a double ahistoricism
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+
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+
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+then it's an ahistoricism about the
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+
+ align:start position:0%
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+
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+
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+
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+other media forms so so when we
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+
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+
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+acknowledge that it's a cultural
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+
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+
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+
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+
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+and uh there are a couple of ways in
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+
+ align:start position:0%
+and uh there are a couple of ways in
+which uh we we we can uh um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+
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+um complicate and deepen our
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+
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+wonderfully helpful and in many ways
+still um
+
+ align:start position:0%
+still um
+ 
+
+ align:start position:0%
+still um
+uh FR immensely fruitful Rich
+
+ align:start position:0%
+uh FR immensely fruitful Rich
+ 
+
+ align:start position:0%
+uh FR immensely fruitful Rich
+distinction that James KY uh offers us
+
+ align:start position:0%
+distinction that James KY uh offers us
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+
+ align:start position:0%
+distinction that James KY uh offers us
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+
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+in the essay I asked you to read for one
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+
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+
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+
+ align:start position:0%
+you've all read it I'm not going to go
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+through it in detail I want to pull one
+ 
+
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+
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+
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+
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+
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+this to older societies as well there
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+
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+have been two in some degree competing
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+
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+
+ align:start position:0%
+imagining that only one of them is
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+
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+
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+
+ align:start position:0%
+communication systems not just
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+communication systems not just
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+
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+communication if we don't acknowledge
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+the aspect of what Carrie calls a
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+
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+another right the telegraph is a classic
+
+ align:start position:0%
+another right the telegraph is a classic
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+
+ align:start position:0%
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+
+ align:start position:0%
+instance of this of this process and and
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+
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+notion of communication uh the
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+useful for such things as commercial
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+
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+
+ align:start position:0%
+across a geographical area so that if
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+
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+
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+
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+York have an advantage over you right so
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+although for other reasons as well the
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+telegraph was understood as especially
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+movement of financial information
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+it's also been and such things of course
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+it's also been and such things of course
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+ align:start position:0%
+have been the milit military uh uh
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+
+ align:start position:0%
+institutions of all societies are
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+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+Transportation perspective for obvious
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+Transportation perspective for obvious
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+reasons it was a the quick communication
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+utilitarian uh and and functional use uh
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+something else uh it's to it's to engage
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+
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+
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+ 
+
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+
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+
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+ 
+
+ align:start position:0%
+is lying bleeding on the ground and
+Sancho comes over to him and says well
+
+ align:start position:0%
+Sancho comes over to him and says well
+ 
+
+ align:start position:0%
+Sancho comes over to him and says well
+and then and often often Sancho Panza
+
+ align:start position:0%
+and then and often often Sancho Panza
+ 
+
+ align:start position:0%
+and then and often often Sancho Panza
+his his his realistic counterpart right
+
+ align:start position:0%
+his his his realistic counterpart right
+ 
+
+ align:start position:0%
+his his his realistic counterpart right
+the ideal and the real riding together
+
+ align:start position:0%
+the ideal and the real riding together
+ 
+
+ align:start position:0%
+the ideal and the real riding together
+into the world the material and the
+
+ align:start position:0%
+into the world the material and the
+ 
+
+ align:start position:0%
+into the world the material and the
+spiritual join together as they ride
+
+ align:start position:0%
+spiritual join together as they ride
+ 
+
+ align:start position:0%
+spiritual join together as they ride
+into the uh into experience uh the the
+
+ align:start position:0%
+into the uh into experience uh the the
+ 
+
+ align:start position:0%
+into the uh into experience uh the the
+realistic side of the of the equation
+
+ align:start position:0%
+realistic side of the of the equation
+ 
+
+ align:start position:0%
+realistic side of the of the equation
+says well it's never so dark as before
+
+ align:start position:0%
+says well it's never so dark as before
+ 
+
+ align:start position:0%
+says well it's never so dark as before
+the dawn and he repeats all these boring
+
+ align:start position:0%
+the dawn and he repeats all these boring
+ 
+
+ align:start position:0%
+the dawn and he repeats all these boring
+stupid cliches but and and and kiot will
+
+ align:start position:0%
+stupid cliches but and and and kiot will
+ 
+
+ align:start position:0%
+stupid cliches but and and and kiot will
+sometimes respond oh Sono you bore me to
+
+ align:start position:0%
+sometimes respond oh Sono you bore me to
+ 
+
+ align:start position:0%
+sometimes respond oh Sono you bore me to
+death with your stupid cliche the very
+
+ align:start position:0%
+death with your stupid cliche the very
+ 
+
+ align:start position:0%
+death with your stupid cliche the very
+fact that they talk makes makes the
+
+ align:start position:0%
+fact that they talk makes makes the
+ 
+
+ align:start position:0%
+fact that they talk makes makes the
+bleeding from his ears less terrible
+
+ align:start position:0%
+bleeding from his ears less terrible
+ 
+
+ align:start position:0%
+bleeding from his ears less terrible
+right conversation itself in that novel
+
+ align:start position:0%
+right conversation itself in that novel
+ 
+
+ align:start position:0%
+right conversation itself in that novel
+and in our in our lives is a form of
+
+ align:start position:0%
+and in our in our lives is a form of
+ 
+
+ align:start position:0%
+and in our in our lives is a form of
+reparation so it's a it's a brilliant
+
+ align:start position:0%
+reparation so it's a it's a brilliant
+ 
+
+ align:start position:0%
+reparation so it's a it's a brilliant
+and and obviously right way of
+
+ align:start position:0%
+and and obviously right way of
+ 
+
+ align:start position:0%
+and and obviously right way of
+understanding what communication is we
+
+ align:start position:0%
+understanding what communication is we
+ 
+
+ align:start position:0%
+understanding what communication is we
+we don't so so we don't read the
+
+ align:start position:0%
+we don't so so we don't read the
+ 
+
+ align:start position:0%
+we don't so so we don't read the
+newspapers we don't watch we don't watch
+
+ align:start position:0%
+newspapers we don't watch we don't watch
+ 
+
+ align:start position:0%
+newspapers we don't watch we don't watch
+NYPD Blue we don't even watch the news
+
+ align:start position:0%
+NYPD Blue we don't even watch the news
+ 
+
+ align:start position:0%
+NYPD Blue we don't even watch the news
+on television uh necessarily or
+
+ align:start position:0%
+on television uh necessarily or
+ 
+
+ align:start position:0%
+on television uh necessarily or
+primarily in order to find something out
+
+ align:start position:0%
+primarily in order to find something out
+ 
+
+ align:start position:0%
+primarily in order to find something out
+right a transmission a a a functional
+
+ align:start position:0%
+right a transmission a a a functional
+ 
+
+ align:start position:0%
+right a transmission a a a functional
+use of the medium we watch it in part to
+
+ align:start position:0%
+use of the medium we watch it in part to
+ 
+
+ align:start position:0%
+use of the medium we watch it in part to
+share with our fellow citizens an
+
+ align:start position:0%
+share with our fellow citizens an
+ 
+
+ align:start position:0%
+share with our fellow citizens an
+experience that helps us in the process
+
+ align:start position:0%
+experience that helps us in the process
+ 
+
+ align:start position:0%
+experience that helps us in the process
+in the in the continuous process that we
+
+ align:start position:0%
+in the in the continuous process that we
+ 
+
+ align:start position:0%
+in the in the continuous process that we
+engage in in doing so uh that helps us
+
+ align:start position:0%
+engage in in doing so uh that helps us
+ 
+
+ align:start position:0%
+engage in in doing so uh that helps us
+to repair and recreate and rehearse the
+
+ align:start position:0%
+to repair and recreate and rehearse the
+ 
+
+ align:start position:0%
+to repair and recreate and rehearse the
+nature of our society that Society
+
+ align:start position:0%
+nature of our society that Society
+ 
+
+ align:start position:0%
+nature of our society that Society
+itself is a continuous process of this
+
+ align:start position:0%
+itself is a continuous process of this
+ 
+
+ align:start position:0%
+itself is a continuous process of this
+sort of reparation and maintenance work
+
+ align:start position:0%
+sort of reparation and maintenance work
+ 
+
+ align:start position:0%
+sort of reparation and maintenance work
+that communication systems perform for
+
+ align:start position:0%
+that communication systems perform for
+ 
+
+ align:start position:0%
+that communication systems perform for
+us the anthropological or sociological
+
+ align:start position:0%
+us the anthropological or sociological
+ 
+
+ align:start position:0%
+us the anthropological or sociological
+function of communication systems under
+
+ align:start position:0%
+function of communication systems under
+ 
+
+ align:start position:0%
+function of communication systems under
+the ritual view is this maintenance and
+
+ align:start position:0%
+the ritual view is this maintenance and
+ 
+
+ align:start position:0%
+the ritual view is this maintenance and
+reparation of the social fabric yes
+
+ align:start position:0%
+reparation of the social fabric yes
+ 
+
+ align:start position:0%
+reparation of the social fabric yes
+question uh the made you wait so long
+
+ align:start position:0%
+question uh the made you wait so long
+ 
+
+ align:start position:0%
+question uh the made you wait so long
+that's okay the the one thing I don't
+
+ align:start position:0%
+that's okay the the one thing I don't
+ 
+
+ align:start position:0%
+that's okay the the one thing I don't
+understand when I was reading it is if
+
+ align:start position:0%
+understand when I was reading it is if
+ 
+
+ align:start position:0%
+understand when I was reading it is if
+like I understand both views but what
+
+ align:start position:0%
+like I understand both views but what
+ 
+
+ align:start position:0%
+like I understand both views but what
+confuses me is that the ritual model
+
+ align:start position:0%
+confuses me is that the ritual model
+ 
+
+ align:start position:0%
+confuses me is that the ritual model
+seems like just an extension of the
+
+ align:start position:0%
+seems like just an extension of the
+ 
+
+ align:start position:0%
+seems like just an extension of the
+transmission model like you can't have
+
+ align:start position:0%
+transmission model like you can't have
+ 
+
+ align:start position:0%
+transmission model like you can't have
+like I I don't know how to explain it
+
+ align:start position:0%
+like I I don't know how to explain it
+ 
+
+ align:start position:0%
+like I I don't know how to explain it
+but even in the ritual model if we're
+
+ align:start position:0%
+but even in the ritual model if we're
+ 
+
+ align:start position:0%
+but even in the ritual model if we're
+all sitting around watching the news
+
+ align:start position:0%
+all sitting around watching the news
+ 
+
+ align:start position:0%
+all sitting around watching the news
+simply to have a common uh a common
+
+ align:start position:0%
+simply to have a common uh a common
+ 
+
+ align:start position:0%
+simply to have a common uh a common
+sense you know state of mind watching
+
+ align:start position:0%
+sense you know state of mind watching
+ 
+
+ align:start position:0%
+sense you know state of mind watching
+the planes drop over and over again uh
+
+ align:start position:0%
+the planes drop over and over again uh
+ 
+
+ align:start position:0%
+the planes drop over and over again uh
+we're still receiving that information
+
+ align:start position:0%
+we're still receiving that information
+ 
+
+ align:start position:0%
+we're still receiving that information
+and like by by receiving the information
+
+ align:start position:0%
+and like by by receiving the information
+ 
+
+ align:start position:0%
+and like by by receiving the information
+it is because of the information that we
+
+ align:start position:0%
+it is because of the information that we
+ 
+
+ align:start position:0%
+it is because of the information that we
+are uh connected on the same level so
+
+ align:start position:0%
+are uh connected on the same level so
+ 
+
+ align:start position:0%
+are uh connected on the same level so
+how is the ritual model significantly
+
+ align:start position:0%
+how is the ritual model significantly
+ 
+
+ align:start position:0%
+how is the ritual model significantly
+different than the transmission model
+
+ align:start position:0%
+different than the transmission model
+ 
+
+ align:start position:0%
+different than the transmission model
+and how can we only look at how can how
+
+ align:start position:0%
+and how can we only look at how can how
+ 
+
+ align:start position:0%
+and how can we only look at how can how
+can one be dominant over the other okay
+
+ align:start position:0%
+can one be dominant over the other okay
+ 
+
+ align:start position:0%
+can one be dominant over the other okay
+well I don't think it's a question of
+
+ align:start position:0%
+well I don't think it's a question of
+ 
+
+ align:start position:0%
+well I don't think it's a question of
+one dominating inica they're sort of
+
+ align:start position:0%
+one dominating inica they're sort of
+ 
+
+ align:start position:0%
+one dominating inica they're sort of
+competing ways of understanding what
+
+ align:start position:0%
+competing ways of understanding what
+ 
+
+ align:start position:0%
+competing ways of understanding what
+communication is but I think there are a
+
+ align:start position:0%
+communication is but I think there are a
+ 
+
+ align:start position:0%
+communication is but I think there are a
+couple of answers to what you're saying
+
+ align:start position:0%
+couple of answers to what you're saying
+ 
+
+ align:start position:0%
+couple of answers to what you're saying
+one is that you're you're you're not
+
+ align:start position:0%
+one is that you're you're you're not
+ 
+
+ align:start position:0%
+one is that you're you're you're not
+problematizing the word information
+
+ align:start position:0%
+problematizing the word information
+ 
+
+ align:start position:0%
+problematizing the word information
+enough what makes you think that what
+
+ align:start position:0%
+enough what makes you think that what
+ 
+
+ align:start position:0%
+enough what makes you think that what
+you're getting is actually always
+
+ align:start position:0%
+you're getting is actually always
+ 
+
+ align:start position:0%
+you're getting is actually always
+information in the case of the images of
+
+ align:start position:0%
+information in the case of the images of
+ 
+
+ align:start position:0%
+information in the case of the images of
+the planes crashing into the tower I
+
+ align:start position:0%
+the planes crashing into the tower I
+ 
+
+ align:start position:0%
+the planes crashing into the tower I
+suppose there is a level of of of
+
+ align:start position:0%
+suppose there is a level of of of
+ 
+
+ align:start position:0%
+suppose there is a level of of of
+information involved but suppose we
+
+ align:start position:0%
+information involved but suppose we
+ 
+
+ align:start position:0%
+information involved but suppose we
+change things and and suppose we're
+
+ align:start position:0%
+change things and and suppose we're
+ 
+
+ align:start position:0%
+change things and and suppose we're
+talking about uh the watching of a
+
+ align:start position:0%
+talking about uh the watching of a
+ 
+
+ align:start position:0%
+talking about uh the watching of a
+situation comedy uh this the situation
+
+ align:start position:0%
+situation comedy uh this the situation
+ 
+
+ align:start position:0%
+situation comedy uh this the situation
+comedy is a fantasy what's happening and
+
+ align:start position:0%
+comedy is a fantasy what's happening and
+ 
+
+ align:start position:0%
+comedy is a fantasy what's happening and
+in fact even the even the account of
+
+ align:start position:0%
+in fact even the even the account of
+ 
+
+ align:start position:0%
+in fact even the even the account of
+family life that television may be
+
+ align:start position:0%
+family life that television may be
+ 
+
+ align:start position:0%
+family life that television may be
+provide that you may be get provided by
+
+ align:start position:0%
+provide that you may be get provided by
+ 
+
+ align:start position:0%
+provide that you may be get provided by
+is not in fact is not in a narrow or
+
+ align:start position:0%
+is not in fact is not in a narrow or
+ 
+
+ align:start position:0%
+is not in fact is not in a narrow or
+objective sense an a reality it's a
+
+ align:start position:0%
+objective sense an a reality it's a
+ 
+
+ align:start position:0%
+objective sense an a reality it's a
+construction an interpretation right so
+
+ align:start position:0%
+construction an interpretation right so
+ 
+
+ align:start position:0%
+construction an interpretation right so
+so so and and one could and of course
+
+ align:start position:0%
+so so and and one could and of course
+ 
+
+ align:start position:0%
+so so and and one could and of course
+one could argue that news itself that
+
+ align:start position:0%
+one could argue that news itself that
+ 
+
+ align:start position:0%
+one could argue that news itself that
+what we call information is really a
+
+ align:start position:0%
+what we call information is really a
+ 
+
+ align:start position:0%
+what we call information is really a
+kind of construction it's one way of
+
+ align:start position:0%
+kind of construction it's one way of
+ 
+
+ align:start position:0%
+kind of construction it's one way of
+understanding uh What uh um uh
+
+ align:start position:0%
+understanding uh What uh um uh
+ 
+
+ align:start position:0%
+understanding uh What uh um uh
+particular details so that so that the
+
+ align:start position:0%
+particular details so that so that the
+ 
+
+ align:start position:0%
+particular details so that so that the
+narratives that and it the information
+
+ align:start position:0%
+narratives that and it the information
+ 
+
+ align:start position:0%
+narratives that and it the information
+that we get when the planes crash into
+
+ align:start position:0%
+that we get when the planes crash into
+ 
+
+ align:start position:0%
+that we get when the planes crash into
+the world Trade Center uh isn't simply
+
+ align:start position:0%
+the world Trade Center uh isn't simply
+ 
+
+ align:start position:0%
+the world Trade Center uh isn't simply
+the visual image imagine how someone how
+
+ align:start position:0%
+the visual image imagine how someone how
+ 
+
+ align:start position:0%
+the visual image imagine how someone how
+a member of the
+
+ align:start position:0%
+a member of the
+ 
+
+ align:start position:0%
+a member of the
+Hamas right the the Palestinian
+
+ align:start position:0%
+Hamas right the the Palestinian
+ 
+
+ align:start position:0%
+Hamas right the the Palestinian
+organization that
+
+ align:start position:0%
+organization that
+ 
+
+ align:start position:0%
+organization that
+we in America and the Israelis label a
+
+ align:start position:0%
+we in America and the Israelis label a
+ 
+
+ align:start position:0%
+we in America and the Israelis label a
+terrorist
+
+ align:start position:0%
+terrorist
+ 
+
+ align:start position:0%
+terrorist
+organization I'm being too neat I think
+
+ align:start position:0%
+organization I'm being too neat I think
+ 
+
+ align:start position:0%
+organization I'm being too neat I think
+it is a terrorist organization by me
+
+ align:start position:0%
+it is a terrorist organization by me
+ 
+
+ align:start position:0%
+it is a terrorist organization by me
+it's a terrorist organization but but
+
+ align:start position:0%
+it's a terrorist organization but but
+ 
+
+ align:start position:0%
+it's a terrorist organization but but
+imagine the Hamas watching that and
+
+ align:start position:0%
+imagine the Hamas watching that and
+ 
+
+ align:start position:0%
+imagine the Hamas watching that and
+imagine a commentator from the Hamas
+
+ align:start position:0%
+imagine a commentator from the Hamas
+ 
+
+ align:start position:0%
+imagine a commentator from the Hamas
+commenting on it or imagine the Syrian
+
+ align:start position:0%
+commenting on it or imagine the Syrian
+ 
+
+ align:start position:0%
+commenting on it or imagine the Syrian
+newspaper that Carri an editorial the
+
+ align:start position:0%
+newspaper that Carri an editorial the
+ 
+
+ align:start position:0%
+newspaper that Carri an editorial the
+day after the uh World Trade Center uh
+
+ align:start position:0%
+day after the uh World Trade Center uh
+ 
+
+ align:start position:0%
+day after the uh World Trade Center uh
+catastrophe saying uh the days of
+
+ align:start position:0%
+catastrophe saying uh the days of
+ 
+
+ align:start position:0%
+catastrophe saying uh the days of
+American hegemony are over and that
+
+ align:start position:0%
+American hegemony are over and that
+ 
+
+ align:start position:0%
+American hegemony are over and that
+finally America is no the America's in
+
+ align:start position:0%
+finally America is no the America's in
+ 
+
+ align:start position:0%
+finally America is no the America's in
+the Twilight of its power okay on the
+
+ align:start position:0%
+the Twilight of its power okay on the
+ 
+
+ align:start position:0%
+the Twilight of its power okay on the
+basis of the World Trade Center so that
+
+ align:start position:0%
+basis of the World Trade Center so that
+ 
+
+ align:start position:0%
+basis of the World Trade Center so that
+uh the the meaning the meaning of those
+
+ align:start position:0%
+uh the the meaning the meaning of those
+ 
+
+ align:start position:0%
+uh the the meaning the meaning of those
+planes crashing into the way World Trade
+
+ align:start position:0%
+planes crashing into the way World Trade
+ 
+
+ align:start position:0%
+planes crashing into the way World Trade
+Center is is not obvious it depends on
+
+ align:start position:0%
+Center is is not obvious it depends on
+ 
+
+ align:start position:0%
+Center is is not obvious it depends on
+it depends on the constructions that are
+
+ align:start position:0%
+it depends on the constructions that are
+ 
+
+ align:start position:0%
+it depends on the constructions that are
+put upon those events by the narratives
+
+ align:start position:0%
+put upon those events by the narratives
+ 
+
+ align:start position:0%
+put upon those events by the narratives
+that surround it and those narratives
+
+ align:start position:0%
+that surround it and those narratives
+ 
+
+ align:start position:0%
+that surround it and those narratives
+are going to differ from one kind of
+
+ align:start position:0%
+are going to differ from one kind of
+ 
+
+ align:start position:0%
+are going to differ from one kind of
+culture and one one ideological Center
+
+ align:start position:0%
+culture and one one ideological Center
+ 
+
+ align:start position:0%
+culture and one one ideological Center
+to another the process of doing that of
+
+ align:start position:0%
+to another the process of doing that of
+ 
+
+ align:start position:0%
+to another the process of doing that of
+of of of surrounding the event with
+
+ align:start position:0%
+of of of surrounding the event with
+ 
+
+ align:start position:0%
+of of of surrounding the event with
+commentary with talk with with with
+
+ align:start position:0%
+commentary with talk with with with
+ 
+
+ align:start position:0%
+commentary with talk with with with
+constructions right of constructing the
+
+ align:start position:0%
+constructions right of constructing the
+ 
+
+ align:start position:0%
+constructions right of constructing the
+meaning of those of those events is
+
+ align:start position:0%
+meaning of those of those events is
+ 
+
+ align:start position:0%
+meaning of those of those events is
+partly even maybe largely a ritualizing
+
+ align:start position:0%
+partly even maybe largely a ritualizing
+ 
+
+ align:start position:0%
+partly even maybe largely a ritualizing
+process and it may not really have to do
+
+ align:start position:0%
+process and it may not really have to do
+ 
+
+ align:start position:0%
+process and it may not really have to do
+with anything that we might label in
+
+ align:start position:0%
+with anything that we might label in
+ 
+
+ align:start position:0%
+with anything that we might label in
+quotes objective I'm not sure that there
+
+ align:start position:0%
+quotes objective I'm not sure that there
+ 
+
+ align:start position:0%
+quotes objective I'm not sure that there
+is such a such a thing but in other
+
+ align:start position:0%
+is such a such a thing but in other
+ 
+
+ align:start position:0%
+is such a such a thing but in other
+words the the because because because
+
+ align:start position:0%
+words the the because because because
+ 
+
+ align:start position:0%
+words the the because because because
+one might say that there is no single
+
+ align:start position:0%
+one might say that there is no single
+ 
+
+ align:start position:0%
+one might say that there is no single
+meaning to such a in and and and and
+
+ align:start position:0%
+meaning to such a in and and and and
+ 
+
+ align:start position:0%
+meaning to such a in and and and and
+decisive event that that the meanings of
+
+ align:start position:0%
+decisive event that that the meanings of
+ 
+
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+Lucy to the Dick Van djk
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+show
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+to Mary Tyler Moore The Mary Tyler Moore
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+to Mary Tyler Moore The Mary Tyler Moore
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+Rosanne right we could we could go on
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+ 
+
+ align:start position:0%
+because it's not actually a perfect
+situation comedy oh we might we could
+
+ align:start position:0%
+situation comedy oh we might we could
+ 
+
+ align:start position:0%
+situation comedy oh we might we could
+put friends in here if you want because
+
+ align:start position:0%
+put friends in here if you want because
+ 
+
+ align:start position:0%
+put friends in here if you want because
+something happens in the 80s and 90s
+
+ align:start position:0%
+something happens in the 80s and 90s
+ 
+
+ align:start position:0%
+something happens in the 80s and 90s
+families begin to disappear well what
+
+ align:start position:0%
+families begin to disappear well what
+ 
+
+ align:start position:0%
+families begin to disappear well what
+does this I mean many other things are
+
+ align:start position:0%
+does this I mean many other things are
+ 
+
+ align:start position:0%
+does this I mean many other things are
+going on and we'd have to surr this this
+
+ align:start position:0%
+going on and we'd have to surr this this
+ 
+
+ align:start position:0%
+going on and we'd have to surr this this
+progression oversimplifies because there
+
+ align:start position:0%
+progression oversimplifies because there
+ 
+
+ align:start position:0%
+progression oversimplifies because there
+are dozens and dozens of situation
+
+ align:start position:0%
+are dozens and dozens of situation
+ 
+
+ align:start position:0%
+are dozens and dozens of situation
+comedies in each year right uh but still
+
+ align:start position:0%
+comedies in each year right uh but still
+ 
+
+ align:start position:0%
+comedies in each year right uh but still
+let's say these are in certain ways
+
+ align:start position:0%
+let's say these are in certain ways
+ 
+
+ align:start position:0%
+let's say these are in certain ways
+representative what's going on here
+
+ align:start position:0%
+representative what's going on here
+ 
+
+ align:start position:0%
+representative what's going on here
+right uh Lucy constrained in the house
+
+ align:start position:0%
+right uh Lucy constrained in the house
+ 
+
+ align:start position:0%
+right uh Lucy constrained in the house
+all the time the basic plot of The Lucy
+
+ align:start position:0%
+all the time the basic plot of The Lucy
+ 
+
+ align:start position:0%
+all the time the basic plot of The Lucy
+Show is Lucy wants to get out of her
+
+ align:start position:0%
+Show is Lucy wants to get out of her
+ 
+
+ align:start position:0%
+Show is Lucy wants to get out of her
+domestic constraints and in the court
+
+ align:start position:0%
+domestic constraints and in the court
+ 
+
+ align:start position:0%
+domestic constraints and in the court
+and and and the basic plot is a
+
+ align:start position:0%
+and and and the basic plot is a
+ 
+
+ align:start position:0%
+and and and the basic plot is a
+humiliation plot in which Lucy tries to
+
+ align:start position:0%
+humiliation plot in which Lucy tries to
+ 
+
+ align:start position:0%
+humiliation plot in which Lucy tries to
+become uh to get into Ricky's show or
+
+ align:start position:0%
+become uh to get into Ricky's show or
+ 
+
+ align:start position:0%
+become uh to get into Ricky's show or
+tries to get onto a quiz show or tries
+
+ align:start position:0%
+tries to get onto a quiz show or tries
+ 
+
+ align:start position:0%
+tries to get onto a quiz show or tries
+to or tries to uh become an entrepreneur
+
+ align:start position:0%
+to or tries to uh become an entrepreneur
+ 
+
+ align:start position:0%
+to or tries to uh become an entrepreneur
+by producing vitamins right uh and in
+
+ align:start position:0%
+by producing vitamins right uh and in
+ 
+
+ align:start position:0%
+by producing vitamins right uh and in
+every case she suffers a horrific
+
+ align:start position:0%
+every case she suffers a horrific
+ 
+
+ align:start position:0%
+every case she suffers a horrific
+humiliation horrific comic humiliation
+
+ align:start position:0%
+humiliation horrific comic humiliation
+ 
+
+ align:start position:0%
+humiliation horrific comic humiliation
+at the end right uh so uh the notion
+
+ align:start position:0%
+at the end right uh so uh the notion
+ 
+
+ align:start position:0%
+at the end right uh so uh the notion
+here is that the norm is women belong in
+
+ align:start position:0%
+here is that the norm is women belong in
+ 
+
+ align:start position:0%
+here is that the norm is women belong in
+the home and that Lucy's comic lovable
+
+ align:start position:0%
+the home and that Lucy's comic lovable
+ 
+
+ align:start position:0%
+the home and that Lucy's comic lovable
+but comic desires to escape the home are
+
+ align:start position:0%
+but comic desires to escape the home are
+ 
+
+ align:start position:0%
+but comic desires to escape the home are
+just that lovable and comic and not to
+
+ align:start position:0%
+just that lovable and comic and not to
+ 
+
+ align:start position:0%
+just that lovable and comic and not to
+be taken seriously but we go we move to
+
+ align:start position:0%
+be taken seriously but we go we move to
+ 
+
+ align:start position:0%
+be taken seriously but we go we move to
+the Dick Van djk show uh uh we've moved
+
+ align:start position:0%
+the Dick Van djk show uh uh we've moved
+ 
+
+ align:start position:0%
+the Dick Van djk show uh uh we've moved
+from the city to the suburbs which is an
+
+ align:start position:0%
+from the city to the suburbs which is an
+ 
+
+ align:start position:0%
+from the city to the suburbs which is an
+interesting move in itself that tells us
+
+ align:start position:0%
+interesting move in itself that tells us
+ 
+
+ align:start position:0%
+interesting move in itself that tells us
+something about the family right but
+
+ align:start position:0%
+something about the family right but
+ 
+
+ align:start position:0%
+something about the family right but
+children the CH children play a slightly
+
+ align:start position:0%
+children the CH children play a slightly
+ 
+
+ align:start position:0%
+children the CH children play a slightly
+more important role and there are other
+
+ align:start position:0%
+more important role and there are other
+ 
+
+ align:start position:0%
+more important role and there are other
+shows we could mention where that's more
+
+ align:start position:0%
+shows we could mention where that's more
+ 
+
+ align:start position:0%
+shows we could mention where that's more
+important but the wife here is a woman
+
+ align:start position:0%
+important but the wife here is a woman
+ 
+
+ align:start position:0%
+important but the wife here is a woman
+who had a career before her her her uh
+
+ align:start position:0%
+who had a career before her her her uh
+ 
+
+ align:start position:0%
+who had a career before her her her uh
+her uh marriage began and there are
+
+ align:start position:0%
+her uh marriage began and there are
+ 
+
+ align:start position:0%
+her uh marriage began and there are
+various moments in the show where she
+
+ align:start position:0%
+various moments in the show where she
+ 
+
+ align:start position:0%
+various moments in the show where she
+returns to her career in certain ways
+
+ align:start position:0%
+returns to her career in certain ways
+ 
+
+ align:start position:0%
+returns to her career in certain ways
+that seem to threaten the F the the
+
+ align:start position:0%
+that seem to threaten the F the the
+ 
+
+ align:start position:0%
+that seem to threaten the F the the
+fabric by the time we get to the Mary
+
+ align:start position:0%
+fabric by the time we get to the Mary
+ 
+
+ align:start position:0%
+fabric by the time we get to the Mary
+Tyler Moore Show what's happened the
+
+ align:start position:0%
+Tyler Moore Show what's happened the
+ 
+
+ align:start position:0%
+Tyler Moore Show what's happened the
+same actress who is the mother here and
+
+ align:start position:0%
+same actress who is the mother here and
+ 
+
+ align:start position:0%
+same actress who is the mother here and
+that makes it further complicates the
+
+ align:start position:0%
+that makes it further complicates the
+ 
+
+ align:start position:0%
+that makes it further complicates the
+continuity right uh make and makes the
+
+ align:start position:0%
+continuity right uh make and makes the
+ 
+
+ align:start position:0%
+continuity right uh make and makes the
+argument even more explicit that that
+
+ align:start position:0%
+argument even more explicit that that
+ 
+
+ align:start position:0%
+argument even more explicit that that
+that we the same actress who who was the
+
+ align:start position:0%
+that we the same actress who who was the
+ 
+
+ align:start position:0%
+that we the same actress who who was the
+homebody Suburban mother frequently in
+
+ align:start position:0%
+homebody Suburban mother frequently in
+ 
+
+ align:start position:0%
+homebody Suburban mother frequently in
+the Dick Van Dyk show she's given an
+
+ align:start position:0%
+the Dick Van Dyk show she's given an
+ 
+
+ align:start position:0%
+the Dick Van Dyk show she's given an
+opportunity to become the dancer that
+
+ align:start position:0%
+opportunity to become the dancer that
+ 
+
+ align:start position:0%
+opportunity to become the dancer that
+she was before she was married and she
+
+ align:start position:0%
+she was before she was married and she
+ 
+
+ align:start position:0%
+she was before she was married and she
+turns it down because because she loves
+
+ align:start position:0%
+turns it down because because she loves
+ 
+
+ align:start position:0%
+turns it down because because she loves
+the Domesticity of of uh uh being a
+
+ align:start position:0%
+the Domesticity of of uh uh being a
+ 
+
+ align:start position:0%
+the Domesticity of of uh uh being a
+being a Suburban housewife right there's
+
+ align:start position:0%
+being a Suburban housewife right there's
+ 
+
+ align:start position:0%
+being a Suburban housewife right there's
+an even more dramatic example of this
+
+ align:start position:0%
+an even more dramatic example of this
+ 
+
+ align:start position:0%
+an even more dramatic example of this
+that we'll talk about briefly when we
+
+ align:start position:0%
+that we'll talk about briefly when we
+ 
+
+ align:start position:0%
+that we'll talk about briefly when we
+start looking at actual programs uh it's
+
+ align:start position:0%
+start looking at actual programs uh it's
+ 
+
+ align:start position:0%
+start looking at actual programs uh it's
+a magical show how many of you know the
+
+ align:start position:0%
+a magical show how many of you know the
+ 
+
+ align:start position:0%
+a magical show how many of you know the
+show I Dream of
+
+ align:start position:0%
+show I Dream of
+ 
+
+ align:start position:0%
+show I Dream of
+Genie almost everyone and that's a
+
+ align:start position:0%
+Genie almost everyone and that's a
+ 
+
+ align:start position:0%
+Genie almost everyone and that's a
+measure of how it's still a how how how
+
+ align:start position:0%
+measure of how it's still a how how how
+ 
+
+ align:start position:0%
+measure of how it's still a how how how
+how the TV is a universal a universal
+
+ align:start position:0%
+how the TV is a universal a universal
+ 
+
+ align:start position:0%
+how the TV is a universal a universal
+show uh can you think of another magical
+
+ align:start position:0%
+show uh can you think of another magical
+ 
+
+ align:start position:0%
+show uh can you think of another magical
+show like that Bewitched Bewitched may
+
+ align:start position:0%
+show like that Bewitched Bewitched may
+ 
+
+ align:start position:0%
+show like that Bewitched Bewitched may
+be even a better example but in both
+
+ align:start position:0%
+be even a better example but in both
+ 
+
+ align:start position:0%
+be even a better example but in both
+those cases what's interesting about
+
+ align:start position:0%
+those cases what's interesting about
+ 
+
+ align:start position:0%
+those cases what's interesting about
+them the women have magical powers in
+
+ align:start position:0%
+them the women have magical powers in
+ 
+
+ align:start position:0%
+them the women have magical powers in
+those show they're they're superhuman
+
+ align:start position:0%
+those show they're they're superhuman
+ 
+
+ align:start position:0%
+those show they're they're superhuman
+they're not they're not human beings in
+
+ align:start position:0%
+they're not they're not human beings in
+ 
+
+ align:start position:0%
+they're not they're not human beings in
+one case it's a witch and Genie is a
+
+ align:start position:0%
+one case it's a witch and Genie is a
+ 
+
+ align:start position:0%
+one case it's a witch and Genie is a
+genie right uh they have they have total
+
+ align:start position:0%
+genie right uh they have they have total
+ 
+
+ align:start position:0%
+genie right uh they have they have total
+power how do they choose to use their
+
+ align:start position:0%
+power how do they choose to use their
+ 
+
+ align:start position:0%
+power how do they choose to use their
+power totally subordinating themselves
+
+ align:start position:0%
+power totally subordinating themselves
+ 
+
+ align:start position:0%
+power totally subordinating themselves
+right they she can um the the mother in
+
+ align:start position:0%
+right they she can um the the mother in
+ 
+
+ align:start position:0%
+right they she can um the the mother in
+Bewitched uh could twitch her nose and
+
+ align:start position:0%
+Bewitched uh could twitch her nose and
+ 
+
+ align:start position:0%
+Bewitched uh could twitch her nose and
+clean the house but she prefers to use a
+
+ align:start position:0%
+clean the house but she prefers to use a
+ 
+
+ align:start position:0%
+clean the house but she prefers to use a
+broom and a dust mop because because her
+
+ align:start position:0%
+broom and a dust mop because because her
+ 
+
+ align:start position:0%
+broom and a dust mop because because her
+hubby prefers it right she could she
+
+ align:start position:0%
+hubby prefers it right she could she
+ 
+
+ align:start position:0%
+hubby prefers it right she could she
+could by the twitch of her nose travel
+
+ align:start position:0%
+could by the twitch of her nose travel
+ 
+
+ align:start position:0%
+could by the twitch of her nose travel
+to Paris with her mother and have a
+
+ align:start position:0%
+to Paris with her mother and have a
+ 
+
+ align:start position:0%
+to Paris with her mother and have a
+delicious meal at the fanciest Parisian
+
+ align:start position:0%
+delicious meal at the fanciest Parisian
+ 
+
+ align:start position:0%
+delicious meal at the fanciest Parisian
+Restaurant but she chooses to make pot
+
+ align:start position:0%
+Restaurant but she chooses to make pot
+ 
+
+ align:start position:0%
+Restaurant but she chooses to make pot
+roast for her husband who comes home
+
+ align:start position:0%
+roast for her husband who comes home
+ 
+
+ align:start position:0%
+roast for her husband who comes home
+from a hard day at the office right
+
+ align:start position:0%
+from a hard day at the office right
+ 
+
+ align:start position:0%
+from a hard day at the office right
+there think of the think of the the Fant
+
+ align:start position:0%
+there think of the think of the the Fant
+ 
+
+ align:start position:0%
+there think of the think of the the Fant
+the fantast the fantasy that the
+
+ align:start position:0%
+the fantast the fantasy that the
+ 
+
+ align:start position:0%
+the fantast the fantasy that the
+patriarchal culture is Eng engaging in
+
+ align:start position:0%
+patriarchal culture is Eng engaging in
+ 
+
+ align:start position:0%
+patriarchal culture is Eng engaging in
+here but still you can think of it as
+
+ align:start position:0%
+here but still you can think of it as
+ 
+
+ align:start position:0%
+here but still you can think of it as
+this it's comic but it's still engaging
+
+ align:start position:0%
+this it's comic but it's still engaging
+ 
+
+ align:start position:0%
+this it's comic but it's still engaging
+in a kind of discourse about the about
+
+ align:start position:0%
+in a kind of discourse about the about
+ 
+
+ align:start position:0%
+in a kind of discourse about the about
+gender relations and about the power
+
+ align:start position:0%
+gender relations and about the power
+ 
+
+ align:start position:0%
+gender relations and about the power
+relations uh uh in families right by the
+
+ align:start position:0%
+relations uh uh in families right by the
+ 
+
+ align:start position:0%
+relations uh uh in families right by the
+time we get to the mar Mary Tyler Mo
+
+ align:start position:0%
+time we get to the mar Mary Tyler Mo
+ 
+
+ align:start position:0%
+time we get to the mar Mary Tyler Mo
+show what's happened the woman has been
+
+ align:start position:0%
+show what's happened the woman has been
+ 
+
+ align:start position:0%
+show what's happened the woman has been
+liberated right it's a single woman
+
+ align:start position:0%
+liberated right it's a single woman
+ 
+
+ align:start position:0%
+liberated right it's a single woman
+she's trying to make it on her own right
+
+ align:start position:0%
+she's trying to make it on her own right
+ 
+
+ align:start position:0%
+she's trying to make it on her own right
+but in an odd way and know because
+
+ align:start position:0%
+but in an odd way and know because
+ 
+
+ align:start position:0%
+but in an odd way and know because
+television is always conservative as
+
+ align:start position:0%
+television is always conservative as
+ 
+
+ align:start position:0%
+television is always conservative as
+well as because because this Pro this
+
+ align:start position:0%
+well as because because this Pro this
+ 
+
+ align:start position:0%
+well as because because this Pro this
+ritualized process is complicated and
+
+ align:start position:0%
+ritualized process is complicated and
+ 
+
+ align:start position:0%
+ritualized process is complicated and
+what uh and and uh new or emergent ideas
+
+ align:start position:0%
+what uh and and uh new or emergent ideas
+ 
+
+ align:start position:0%
+what uh and and uh new or emergent ideas
+are treated very gingerly and nervously
+
+ align:start position:0%
+are treated very gingerly and nervously
+ 
+
+ align:start position:0%
+are treated very gingerly and nervously
+in a conservative consensus medium which
+
+ align:start position:0%
+in a conservative consensus medium which
+ 
+
+ align:start position:0%
+in a conservative consensus medium which
+is what television was what hap what
+
+ align:start position:0%
+is what television was what hap what
+ 
+
+ align:start position:0%
+is what television was what hap what
+happens the
+
+ align:start position:0%
+happens the
+ 
+
+ align:start position:0%
+happens the
+there is a family there isn't it the
+
+ align:start position:0%
+there is a family there isn't it the
+ 
+
+ align:start position:0%
+there is a family there isn't it the
+workplace is reconstituted as a kind of
+
+ align:start position:0%
+workplace is reconstituted as a kind of
+ 
+
+ align:start position:0%
+workplace is reconstituted as a kind of
+family and the and in fact it resembles
+
+ align:start position:0%
+family and the and in fact it resembles
+ 
+
+ align:start position:0%
+family and the and in fact it resembles
+a lot of the families of situation
+
+ align:start position:0%
+a lot of the families of situation
+ 
+
+ align:start position:0%
+a lot of the families of situation
+comedies of the past right so that so
+
+ align:start position:0%
+comedies of the past right so that so
+ 
+
+ align:start position:0%
+comedies of the past right so that so
+that uh uh Ted Baxter is the sort of is
+
+ align:start position:0%
+that uh uh Ted Baxter is the sort of is
+ 
+
+ align:start position:0%
+that uh uh Ted Baxter is the sort of is
+is the sort of foolish silly
+
+ align:start position:0%
+is the sort of foolish silly
+ 
+
+ align:start position:0%
+is the sort of foolish silly
+embarrassing uh brother figure right and
+
+ align:start position:0%
+embarrassing uh brother figure right and
+ 
+
+ align:start position:0%
+embarrassing uh brother figure right and
+and and Lou Grant is the benign Father
+
+ align:start position:0%
+and and Lou Grant is the benign Father
+ 
+
+ align:start position:0%
+and and Lou Grant is the benign Father
+Figure right uh and and and the
+
+ align:start position:0%
+Figure right uh and and and the
+ 
+
+ align:start position:0%
+Figure right uh and and and the
+workplace replaces the family but there
+
+ align:start position:0%
+workplace replaces the family but there
+ 
+
+ align:start position:0%
+workplace replaces the family but there
+but but in ways that make sort of
+
+ align:start position:0%
+but but in ways that make sort of
+ 
+
+ align:start position:0%
+but but in ways that make sort of
+explicit that the values that we had
+
+ align:start position:0%
+explicit that the values that we had
+ 
+
+ align:start position:0%
+explicit that the values that we had
+associated with Family Life are somehow
+
+ align:start position:0%
+associated with Family Life are somehow
+ 
+
+ align:start position:0%
+associated with Family Life are somehow
+still alive in this new environment
+
+ align:start position:0%
+still alive in this new environment
+ 
+
+ align:start position:0%
+still alive in this new environment
+what's going on in a certain sense is
+
+ align:start position:0%
+what's going on in a certain sense is
+ 
+
+ align:start position:0%
+what's going on in a certain sense is
+exactly this ritualizing process in
+
+ align:start position:0%
+exactly this ritualizing process in
+ 
+
+ align:start position:0%
+exactly this ritualizing process in
+which the society is responding and so
+
+ align:start position:0%
+which the society is responding and so
+ 
+
+ align:start position:0%
+which the society is responding and so
+if we think of situ the discourses of
+
+ align:start position:0%
+if we think of situ the discourses of
+ 
+
+ align:start position:0%
+if we think of situ the discourses of
+situation comedy as a whole we're not
+
+ align:start position:0%
+situation comedy as a whole we're not
+ 
+
+ align:start position:0%
+situation comedy as a whole we're not
+we're not talking in an artistic or
+
+ align:start position:0%
+we're not talking in an artistic or
+ 
+
+ align:start position:0%
+we're not talking in an artistic or
+aesthetic mode now right we're talking
+
+ align:start position:0%
+aesthetic mode now right we're talking
+ 
+
+ align:start position:0%
+aesthetic mode now right we're talking
+in an anthropological or cultural mode
+
+ align:start position:0%
+in an anthropological or cultural mode
+ 
+
+ align:start position:0%
+in an anthropological or cultural mode
+we're saying what cultural work do
+
+ align:start position:0%
+we're saying what cultural work do
+ 
+
+ align:start position:0%
+we're saying what cultural work do
+television programs play they play a
+
+ align:start position:0%
+television programs play they play a
+ 
+
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+culture itself is not fixed it's not
+
+ align:start position:0%
+culture itself is not fixed it's not
+ 
+
+ align:start position:0%
+culture itself is not fixed it's not
+finished it's continually in process and
+
+ align:start position:0%
+finished it's continually in process and
+ 
+
+ align:start position:0%
+finished it's continually in process and
+it's in and he he identifies what might
+
+ align:start position:0%
+it's in and he he identifies what might
+ 
+
+ align:start position:0%
+it's in and he he identifies what might
+be called three basic strands in the
+
+ align:start position:0%
+be called three basic strands in the
+ 
+
+ align:start position:0%
+be called three basic strands in the
+conversation of
+
+ align:start position:0%
+conversation of
+ 
+
+ align:start position:0%
+conversation of
+culture one strand is what might be
+
+ align:start position:0%
+culture one strand is what might be
+ 
+
+ align:start position:0%
+culture one strand is what might be
+called the residual Strand and that's
+
+ align:start position:0%
+called the residual Strand and that's
+ 
+
+ align:start position:0%
+called the residual Strand and that's
+the strand of of the set of values and
+
+ align:start position:0%
+the strand of of the set of values and
+ 
+
+ align:start position:0%
+the strand of of the set of values and
+beliefs that belong to the older to to
+
+ align:start position:0%
+beliefs that belong to the older to to
+ 
+
+ align:start position:0%
+beliefs that belong to the older to to
+an older time to an Era to the eras that
+
+ align:start position:0%
+an older time to an Era to the eras that
+ 
+
+ align:start position:0%
+an older time to an Era to the eras that
+are ending right we might think of
+
+ align:start position:0%
+are ending right we might think of
+ 
+
+ align:start position:0%
+are ending right we might think of
+certain kinds of U certain kinds of uh
+
+ align:start position:0%
+certain kinds of U certain kinds of uh
+ 
+
+ align:start position:0%
+certain kinds of U certain kinds of uh
+uh in our own Society c c certain
+
+ align:start position:0%
+uh in our own Society c c certain
+ 
+
+ align:start position:0%
+uh in our own Society c c certain
+Notions about about Rural America and
+
+ align:start position:0%
+Notions about about Rural America and
+ 
+
+ align:start position:0%
+Notions about about Rural America and
+about the values of small town America
+
+ align:start position:0%
+about the values of small town America
+ 
+
+ align:start position:0%
+about the values of small town America
+as having uh or or or or certain forms
+
+ align:start position:0%
+as having uh or or or or certain forms
+ 
+
+ align:start position:0%
+as having uh or or or or certain forms
+of religious fundamentalism in the
+
+ align:start position:0%
+of religious fundamentalism in the
+ 
+
+ align:start position:0%
+of religious fundamentalism in the
+United States as having as belonging to
+
+ align:start position:0%
+United States as having as belonging to
+ 
+
+ align:start position:0%
+United States as having as belonging to
+this residual discourse then there's the
+
+ align:start position:0%
+this residual discourse then there's the
+ 
+
+ align:start position:0%
+this residual discourse then there's the
+dominant discourse the discourse of the
+
+ align:start position:0%
+dominant discourse the discourse of the
+ 
+
+ align:start position:0%
+dominant discourse the discourse of the
+majority at the very center of what the
+
+ align:start position:0%
+majority at the very center of what the
+ 
+
+ align:start position:0%
+majority at the very center of what the
+culture thinks of itself and then on the
+
+ align:start position:0%
+culture thinks of itself and then on the
+ 
+
+ align:start position:0%
+culture thinks of itself and then on the
+other side there's what might be called
+
+ align:start position:0%
+other side there's what might be called
+ 
+
+ align:start position:0%
+other side there's what might be called
+emergent discourses discourses of ideas
+
+ align:start position:0%
+emergent discourses discourses of ideas
+ 
+
+ align:start position:0%
+emergent discourses discourses of ideas
+and perspectives and value systems value
+
+ align:start position:0%
+and perspectives and value systems value
+ 
+
+ align:start position:0%
+and perspectives and value systems value
+structures that are not yet fully
+
+ align:start position:0%
+structures that are not yet fully
+ 
+
+ align:start position:0%
+structures that are not yet fully
+established but are but are emerging and
+
+ align:start position:0%
+established but are but are emerging and
+ 
+
+ align:start position:0%
+established but are but are emerging and
+are likely to become important we might
+
+ align:start position:0%
+are likely to become important we might
+ 
+
+ align:start position:0%
+are likely to become important we might
+think for example of the ecology
+
+ align:start position:0%
+think for example of the ecology
+ 
+
+ align:start position:0%
+think for example of the ecology
+discourse today the the the the uh the
+
+ align:start position:0%
+discourse today the the the the uh the
+ 
+
+ align:start position:0%
+discourse today the the the the uh the
+or or the animal rights discourse today
+
+ align:start position:0%
+or or the animal rights discourse today
+ 
+
+ align:start position:0%
+or or the animal rights discourse today
+as part of an emergent discourse not yet
+
+ align:start position:0%
+as part of an emergent discourse not yet
+ 
+
+ align:start position:0%
+as part of an emergent discourse not yet
+at the center of uh cultural values but
+
+ align:start position:0%
+at the center of uh cultural values but
+ 
+
+ align:start position:0%
+at the center of uh cultural values but
+I think likely to become so certainly
+
+ align:start position:0%
+I think likely to become so certainly
+ 
+
+ align:start position:0%
+I think likely to become so certainly
+the ecological argument is be we can in
+
+ align:start position:0%
+the ecological argument is be we can in
+ 
+
+ align:start position:0%
+the ecological argument is be we can in
+your own lifetime has moved more and
+
+ align:start position:0%
+your own lifetime has moved more and
+ 
+
+ align:start position:0%
+your own lifetime has moved more and
+more toward toward the center maybe it's
+
+ align:start position:0%
+more toward toward the center maybe it's
+ 
+
+ align:start position:0%
+more toward toward the center maybe it's
+not yet acted at utterly at the center
+
+ align:start position:0%
+not yet acted at utterly at the center
+ 
+
+ align:start position:0%
+not yet acted at utterly at the center
+but it's much closer to the center than
+
+ align:start position:0%
+but it's much closer to the center than
+ 
+
+ align:start position:0%
+but it's much closer to the center than
+it was uh 15 or 20 years ago and there's
+
+ align:start position:0%
+it was uh 15 or 20 years ago and there's
+ 
+
+ align:start position:0%
+it was uh 15 or 20 years ago and there's
+an example of so and so we can think of
+
+ align:start position:0%
+an example of so and so we can think of
+ 
+
+ align:start position:0%
+an example of so and so we can think of
+culture as as as as a process in which
+
+ align:start position:0%
+culture as as as as a process in which
+ 
+
+ align:start position:0%
+culture as as as as a process in which
+these three kinds of voices of strains
+
+ align:start position:0%
+these three kinds of voices of strains
+ 
+
+ align:start position:0%
+these three kinds of voices of strains
+of value systems of beliefs of attitudes
+
+ align:start position:0%
+of value systems of beliefs of attitudes
+ 
+
+ align:start position:0%
+of value systems of beliefs of attitudes
+are in a kind of constant uh uh
+
+ align:start position:0%
+are in a kind of constant uh uh
+ 
+
+ align:start position:0%
+are in a kind of constant uh uh
+alternating flux or conversation and and
+
+ align:start position:0%
+alternating flux or conversation and and
+ 
+
+ align:start position:0%
+alternating flux or conversation and and
+and and it means that they shift in what
+
+ align:start position:0%
+and and it means that they shift in what
+ 
+
+ align:start position:0%
+and and it means that they shift in what
+what was once dominant can become
+
+ align:start position:0%
+what was once dominant can become
+ 
+
+ align:start position:0%
+what was once dominant can become
+residual and what was once what is now
+
+ align:start position:0%
+residual and what was once what is now
+ 
+
+ align:start position:0%
+residual and what was once what is now
+emergent can become part of the dominant
+
+ align:start position:0%
+emergent can become part of the dominant
+ 
+
+ align:start position:0%
+emergent can become part of the dominant
+value structure well the process whereby
+
+ align:start position:0%
+value structure well the process whereby
+ 
+
+ align:start position:0%
+value structure well the process whereby
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+happens is the process of communication
+
+ align:start position:0%
+happens is the process of communication
+ 
+
+ align:start position:0%
+happens is the process of communication
+and it specifically happens on the
+
+ align:start position:0%
+and it specifically happens on the
+ 
+
+ align:start position:0%
+and it specifically happens on the
+consensus medium that I've been talking
+
+ align:start position:0%
+consensus medium that I've been talking
+ 
+
+ align:start position:0%
+consensus medium that I've been talking
+about which will differ from different
+
+ align:start position:0%
+about which will differ from different
+ 
+
+ align:start position:0%
+about which will differ from different
+in different societies uh and I think
+
+ align:start position:0%
+in different societies uh and I think
+ 
+
+ align:start position:0%
+in different societies uh and I think
+one of the things one of the interesting
+
+ align:start position:0%
+one of the things one of the interesting
+ 
+
+ align:start position:0%
+one of the things one of the interesting
+things about our current moment is that
+
+ align:start position:0%
+things about our current moment is that
+ 
+
+ align:start position:0%
+things about our current moment is that
+television still performs in a in a in
+
+ align:start position:0%
+television still performs in a in a in
+ 
+
+ align:start position:0%
+television still performs in a in a in
+at least in a in a in a partial way the
+
+ align:start position:0%
+at least in a in a in a partial way the
+ 
+
+ align:start position:0%
+at least in a in a in a partial way the
+the the the the Great Central consensus
+
+ align:start position:0%
+the the the the Great Central consensus
+ 
+
+ align:start position:0%
+the the the the Great Central consensus
+role that had played through the late
+
+ align:start position:0%
+role that had played through the late
+ 
+
+ align:start position:0%
+role that had played through the late
+50s through the through the 80s sometime
+
+ align:start position:0%
+50s through the through the 80s sometime
+ 
+
+ align:start position:0%
+50s through the through the 80s sometime
+although it had already been aent by the
+
+ align:start position:0%
+although it had already been aent by the
+ 
+
+ align:start position:0%
+although it had already been aent by the
+end of the 70s you can see the system
+
+ align:start position:0%
+end of the 70s you can see the system
+ 
+
+ align:start position:0%
+end of the 70s you can see the system
+the consensus system beginning to fray
+
+ align:start position:0%
+the consensus system beginning to fray
+ 
+
+ align:start position:0%
+the consensus system beginning to fray
+and break down somewhat and we that's
+
+ align:start position:0%
+and break down somewhat and we that's
+ 
+
+ align:start position:0%
+and break down somewhat and we that's
+what we're going to study is that
+
+ align:start position:0%
+what we're going to study is that
+ 
+
+ align:start position:0%
+what we're going to study is that
+process whereby television becomes the
+
+ align:start position:0%
+process whereby television becomes the
+ 
+
+ align:start position:0%
+process whereby television becomes the
+consensus medium in the society uh
+
+ align:start position:0%
+consensus medium in the society uh
+ 
+
+ align:start position:0%
+consensus medium in the society uh
+articulates what are consensus values uh
+
+ align:start position:0%
+articulates what are consensus values uh
+ 
+
+ align:start position:0%
+articulates what are consensus values uh
+we can see the consensus values
+
+ align:start position:0%
+we can see the consensus values
+ 
+
+ align:start position:0%
+we can see the consensus values
+undergoing some radical threats and
+
+ align:start position:0%
+undergoing some radical threats and
+ 
+
+ align:start position:0%
+undergoing some radical threats and
+changes and then we can see the
+
+ align:start position:0%
+changes and then we can see the
+ 
+
+ align:start position:0%
+changes and then we can see the
+consensus function itself beginning to
+
+ align:start position:0%
+consensus function itself beginning to
+ 
+
+ align:start position:0%
+consensus function itself beginning to
+break down uh by the by by by some time
+
+ align:start position:0%
+break down uh by the by by by some time
+ 
+
+ align:start position:0%
+break down uh by the by by by some time
+at really begins to break down by the
+
+ align:start position:0%
+at really begins to break down by the
+ 
+
+ align:start position:0%
+at really begins to break down by the
+end of the 70s and it's a pro but it's a
+
+ align:start position:0%
+end of the 70s and it's a pro but it's a
+ 
+
+ align:start position:0%
+end of the 70s and it's a pro but it's a
+slow process it doesn't happen overnight
+
+ align:start position:0%
+slow process it doesn't happen overnight
+ 
+
+ align:start position:0%
+slow process it doesn't happen overnight
+and and uh these you know historical
+
+ align:start position:0%
+and and uh these you know historical
+ 
+
+ align:start position:0%
+and and uh these you know historical
+generalizations never have the neatness
+
+ align:start position:0%
+generalizations never have the neatness
+ 
+
+ align:start position:0%
+generalizations never have the neatness
+of of mathematical equations so it's not
+
+ align:start position:0%
+of of mathematical equations so it's not
+ 
+
+ align:start position:0%
+of of mathematical equations so it's not
+the case that one could say okay the
+
+ align:start position:0%
+the case that one could say okay the
+ 
+
+ align:start position:0%
+the case that one could say okay the
+consensus function of Television is
+
+ align:start position:0%
+consensus function of Television is
+ 
+
+ align:start position:0%
+consensus function of Television is
+completely gone now in 2001 but it's
+
+ align:start position:0%
+completely gone now in 2001 but it's
+ 
+
+ align:start position:0%
+completely gone now in 2001 but it's
+it's it's becoming it's it's becoming
+
+ align:start position:0%
+it's it's becoming it's it's becoming
+ 
+
+ align:start position:0%
+it's it's becoming it's it's becoming
+residual the reason that I gave out this
+
+ align:start position:0%
+residual the reason that I gave out this
+ 
+
+ align:start position:0%
+residual the reason that I gave out this
+uh uh piece from The New York Times is
+
+ align:start position:0%
+uh uh piece from The New York Times is
+ 
+
+ align:start position:0%
+uh uh piece from The New York Times is
+is that this moment we've been going
+
+ align:start position:0%
+is that this moment we've been going
+ 
+
+ align:start position:0%
+is that this moment we've been going
+through is a reminder of the extent to
+
+ align:start position:0%
+through is a reminder of the extent to
+ 
+
+ align:start position:0%
+through is a reminder of the extent to
+which television still performs
+
+ align:start position:0%
+which television still performs
+ 
+
+ align:start position:0%
+which television still performs
+especially at certain moments of
+
+ align:start position:0%
+especially at certain moments of
+ 
+
+ align:start position:0%
+especially at certain moments of
+cultural crisis the old consensus
+
+ align:start position:0%
+cultural crisis the old consensus
+ 
+
+ align:start position:0%
+cultural crisis the old consensus
+function that had performed in all of
+
+ align:start position:0%
+function that had performed in all of
+ 
+
+ align:start position:0%
+function that had performed in all of
+its in all ways through the 60s and 70s
+
+ align:start position:0%
+its in all ways through the 60s and 70s
+ 
+
+ align:start position:0%
+its in all ways through the 60s and 70s
+uh and uh the kind the kind of comfort
+
+ align:start position:0%
+uh and uh the kind the kind of comfort
+ 
+
+ align:start position:0%
+uh and uh the kind the kind of comfort
+and Solace that this country gut by
+
+ align:start position:0%
+and Solace that this country gut by
+ 
+
+ align:start position:0%
+and Solace that this country gut by
+watching Dan Rather BL fall into tears
+
+ align:start position:0%
+watching Dan Rather BL fall into tears
+ 
+
+ align:start position:0%
+watching Dan Rather BL fall into tears
+on the screen a Sentimental creature
+
+ align:start position:0%
+on the screen a Sentimental creature
+ 
+
+ align:start position:0%
+on the screen a Sentimental creature
+that he is he was on the he went on the
+
+ align:start position:0%
+that he is he was on the he went on the
+ 
+
+ align:start position:0%
+that he is he was on the he went on the
+David Letterman show and he broke down
+
+ align:start position:0%
+David Letterman show and he broke down
+ 
+
+ align:start position:0%
+David Letterman show and he broke down
+three times
+
+ align:start position:0%
+three times
+ 
+
+ align:start position:0%
+three times
+weeping I'm not I'm not much taken by
+
+ align:start position:0%
+weeping I'm not I'm not much taken by
+ 
+
+ align:start position:0%
+weeping I'm not I'm not much taken by
+that but but it's maybe part of the
+
+ align:start position:0%
+that but but it's maybe part of the
+ 
+
+ align:start position:0%
+that but but it's maybe part of the
+explanation for why Dan Rather has such
+
+ align:start position:0%
+explanation for why Dan Rather has such
+ 
+
+ align:start position:0%
+explanation for why Dan Rather has such
+an intimate connection to the audience
+
+ align:start position:0%
+an intimate connection to the audience
+ 
+
+ align:start position:0%
+an intimate connection to the audience
+that they they they sense How Deeply
+
+ align:start position:0%
+that they they they sense How Deeply
+ 
+
+ align:start position:0%
+that they they they sense How Deeply
+engaged he is by this by this uh story
+
+ align:start position:0%
+engaged he is by this by this uh story
+ 
+
+ align:start position:0%
+engaged he is by this by this uh story
+but in any case the network news
+
+ align:start position:0%
+but in any case the network news
+ 
+
+ align:start position:0%
+but in any case the network news
+programs uh performed a function during
+
+ align:start position:0%
+programs uh performed a function during
+ 
+
+ align:start position:0%
+programs uh performed a function during
+this crisis that was like the function
+
+ align:start position:0%
+this crisis that was like the function
+ 
+
+ align:start position:0%
+this crisis that was like the function
+they performed earlier when they when
+
+ align:start position:0%
+they performed earlier when they when
+ 
+
+ align:start position:0%
+they performed earlier when they when
+the Kennedy assassination was a dramatic
+
+ align:start position:0%
+the Kennedy assassination was a dramatic
+ 
+
+ align:start position:0%
+the Kennedy assassination was a dramatic
+example of it but there have been others
+
+ align:start position:0%
+example of it but there have been others
+ 
+
+ align:start position:0%
+example of it but there have been others
+uh and in those times the consensus uh
+
+ align:start position:0%
+uh and in those times the consensus uh
+ 
+
+ align:start position:0%
+uh and in those times the consensus uh
+reparative function the ritual function
+
+ align:start position:0%
+reparative function the ritual function
+ 
+
+ align:start position:0%
+reparative function the ritual function
+of Television becomes explicit
+
+ align:start position:0%
+of Television becomes explicit
+ 
+
+ align:start position:0%
+of Television becomes explicit
+impossible to miss but the argument but
+
+ align:start position:0%
+impossible to miss but the argument but
+ 
+
+ align:start position:0%
+impossible to miss but the argument but
+our argument in this course is is that
+
+ align:start position:0%
+our argument in this course is is that
+ 
+
+ align:start position:0%
+our argument in this course is is that
+that process that that function is
+
+ align:start position:0%
+that process that that function is
+ 
+
+ align:start position:0%
+that process that that function is
+always implicit and that that's always
+
+ align:start position:0%
+always implicit and that that's always
+ 
+
+ align:start position:0%
+always implicit and that that's always
+one aspect of what television has been
+
+ align:start position:0%
+one aspect of what television has been
+ 
+
+ align:start position:0%
+one aspect of what television has been
+doing and continues in some partial way
+
+ align:start position:0%
+doing and continues in some partial way
+ 
+
+ align:start position:0%
+doing and continues in some partial way
+to do in American societ so let me say a
+
+ align:start position:0%
+to do in American societ so let me say a
+ 
+
+ align:start position:0%
+to do in American societ so let me say a
+little bit more then about about um uh
+
+ align:start position:0%
+little bit more then about about um uh
+ 
+
+ align:start position:0%
+little bit more then about about um uh
+what my notion of consensus narrative
+
+ align:start position:0%
+what my notion of consensus narrative
+ 
+
+ align:start position:0%
+what my notion of consensus narrative
+and again I'm drawing out strains that
+
+ align:start position:0%
+and again I'm drawing out strains that
+ 
+
+ align:start position:0%
+and again I'm drawing out strains that
+are fully defined in the essay I hope
+
+ align:start position:0%
+are fully defined in the essay I hope
+ 
+
+ align:start position:0%
+are fully defined in the essay I hope
+you have read and will will reread
+
+ align:start position:0%
+you have read and will will reread
+ 
+
+ align:start position:0%
+you have read and will will reread
+closely these consensus systems have
+
+ align:start position:0%
+closely these consensus systems have
+ 
+
+ align:start position:0%
+closely these consensus systems have
+particular qualities that are worth
+
+ align:start position:0%
+particular qualities that are worth
+ 
+
+ align:start position:0%
+particular qualities that are worth
+emphasizing and they have three features
+
+ align:start position:0%
+emphasizing and they have three features
+ 
+
+ align:start position:0%
+emphasizing and they have three features
+in particular they are accessible
+
+ align:start position:0%
+in particular they are accessible
+ 
+
+ align:start position:0%
+in particular they are accessible
+they're conservative and they're
+
+ align:start position:0%
+they're conservative and they're
+ 
+
+ align:start position:0%
+they're conservative and they're
+collaborative let me talk about each in
+
+ align:start position:0%
+collaborative let me talk about each in
+ 
+
+ align:start position:0%
+collaborative let me talk about each in
+turn and I I Define these much more
+
+ align:start position:0%
+turn and I I Define these much more
+ 
+
+ align:start position:0%
+turn and I I Define these much more
+elaborately and fully in in in the essay
+
+ align:start position:0%
+elaborately and fully in in in the essay
+ 
+
+ align:start position:0%
+elaborately and fully in in in the essay
+uh let's start with the middle one
+
+ align:start position:0%
+uh let's start with the middle one
+ 
+
+ align:start position:0%
+uh let's start with the middle one
+conservative because it may be the most
+
+ align:start position:0%
+conservative because it may be the most
+ 
+
+ align:start position:0%
+conservative because it may be the most
+important they're deeply conservative
+
+ align:start position:0%
+important they're deeply conservative
+ 
+
+ align:start position:0%
+important they're deeply conservative
+media because they have to be if they're
+
+ align:start position:0%
+media because they have to be if they're
+ 
+
+ align:start position:0%
+media because they have to be if they're
+at the center of the society if
+
+ align:start position:0%
+at the center of the society if
+ 
+
+ align:start position:0%
+at the center of the society if
+everybody quote it's not really
+
+ align:start position:0%
+everybody quote it's not really
+ 
+
+ align:start position:0%
+everybody quote it's not really
+everybody at a certain point the the
+
+ align:start position:0%
+everybody at a certain point the the
+ 
+
+ align:start position:0%
+everybody at a certain point the the
+dominant consensus in American society
+
+ align:start position:0%
+dominant consensus in American society
+ 
+
+ align:start position:0%
+dominant consensus in American society
+in the 1950s did not acknowledge people
+
+ align:start position:0%
+in the 1950s did not acknowledge people
+ 
+
+ align:start position:0%
+in the 1950s did not acknowledge people
+of color so so the consensus and and so
+
+ align:start position:0%
+of color so so the consensus and and so
+ 
+
+ align:start position:0%
+of color so so the consensus and and so
+one of the reasons we want to look at
+
+ align:start position:0%
+one of the reasons we want to look at
+ 
+
+ align:start position:0%
+one of the reasons we want to look at
+consensus media is not because not
+
+ align:start position:0%
+consensus media is not because not
+ 
+
+ align:start position:0%
+consensus media is not because not
+because the values they articulate are
+
+ align:start position:0%
+because the values they articulate are
+ 
+
+ align:start position:0%
+because the values they articulate are
+are necessarily ones we would Embrace
+
+ align:start position:0%
+are necessarily ones we would Embrace
+ 
+
+ align:start position:0%
+are necessarily ones we would Embrace
+but because they can also tell us how
+
+ align:start position:0%
+but because they can also tell us how
+ 
+
+ align:start position:0%
+but because they can also tell us how
+the society defines itself what the they
+
+ align:start position:0%
+the society defines itself what the they
+ 
+
+ align:start position:0%
+the society defines itself what the they
+they're they're incredibly important
+
+ align:start position:0%
+they're they're incredibly important
+ 
+
+ align:start position:0%
+they're they're incredibly important
+media for cultural
+
+ align:start position:0%
+media for cultural
+ 
+
+ align:start position:0%
+media for cultural
+historians uh They Also may have
+
+ align:start position:0%
+historians uh They Also may have
+ 
+
+ align:start position:0%
+historians uh They Also may have
+artistic value at a certain point but
+
+ align:start position:0%
+artistic value at a certain point but
+ 
+
+ align:start position:0%
+artistic value at a certain point but
+they're but but from a historical or
+
+ align:start position:0%
+they're but but from a historical or
+ 
+
+ align:start position:0%
+they're but but from a historical or
+anthropological perspective they are
+
+ align:start position:0%
+anthropological perspective they are
+ 
+
+ align:start position:0%
+anthropological perspective they are
+really interesting to study they tell us
+
+ align:start position:0%
+really interesting to study they tell us
+ 
+
+ align:start position:0%
+really interesting to study they tell us
+more about Society uh the society they
+
+ align:start position:0%
+more about Society uh the society they
+ 
+
+ align:start position:0%
+more about Society uh the society they
+represent and and embody then the
+
+ align:start position:0%
+represent and and embody then the
+ 
+
+ align:start position:0%
+represent and and embody then the
+subcultural forms do the subcultural
+
+ align:start position:0%
+subcultural forms do the subcultural
+ 
+
+ align:start position:0%
+subcultural forms do the subcultural
+forms reveal things about Society too
+
+ align:start position:0%
+forms reveal things about Society too
+ 
+
+ align:start position:0%
+forms reveal things about Society too
+but not in the same way that consensus
+
+ align:start position:0%
+but not in the same way that consensus
+ 
+
+ align:start position:0%
+but not in the same way that consensus
+systems do so that's one of the great
+
+ align:start position:0%
+systems do so that's one of the great
+ 
+
+ align:start position:0%
+systems do so that's one of the great
+justifications for studying television
+
+ align:start position:0%
+justifications for studying television
+ 
+
+ align:start position:0%
+justifications for studying television
+closely is that it is a it tells us a
+
+ align:start position:0%
+closely is that it is a it tells us a
+ 
+
+ align:start position:0%
+closely is that it is a it tells us a
+lot if we study it intelligently and
+
+ align:start position:0%
+lot if we study it intelligently and
+ 
+
+ align:start position:0%
+lot if we study it intelligently and
+with the proper degree of skepticism and
+
+ align:start position:0%
+with the proper degree of skepticism and
+ 
+
+ align:start position:0%
+with the proper degree of skepticism and
+theoretical sophistication we can learn
+
+ align:start position:0%
+theoretical sophistication we can learn
+ 
+
+ align:start position:0%
+theoretical sophistication we can learn
+a great deal about the society embodied
+
+ align:start position:0%
+a great deal about the society embodied
+ 
+
+ align:start position:0%
+a great deal about the society embodied
+in it mirrored in its stories it's not a
+
+ align:start position:0%
+in it mirrored in its stories it's not a
+ 
+
+ align:start position:0%
+in it mirrored in its stories it's not a
+onetoone simple mirroring and and that's
+
+ align:start position:0%
+onetoone simple mirroring and and that's
+ 
+
+ align:start position:0%
+onetoone simple mirroring and and that's
+why I want to put the word consensus in
+
+ align:start position:0%
+why I want to put the word consensus in
+ 
+
+ align:start position:0%
+why I want to put the word consensus in
+quotations right I don't mean that it's
+
+ align:start position:0%
+quotations right I don't mean that it's
+ 
+
+ align:start position:0%
+quotations right I don't mean that it's
+a true consensus I don't mean everyone's
+
+ align:start position:0%
+a true consensus I don't mean everyone's
+ 
+
+ align:start position:0%
+a true consensus I don't mean everyone's
+voice is really there but I mean the
+
+ align:start position:0%
+voice is really there but I mean the
+ 
+
+ align:start position:0%
+voice is really there but I mean the
+society pretends that everyone's voice
+
+ align:start position:0%
+society pretends that everyone's voice
+ 
+
+ align:start position:0%
+society pretends that everyone's voice
+is there the society pretends that the
+
+ align:start position:0%
+is there the society pretends that the
+ 
+
+ align:start position:0%
+is there the society pretends that the
+values that are promulgated and taken
+
+ align:start position:0%
+values that are promulgated and taken
+ 
+
+ align:start position:0%
+values that are promulgated and taken
+for granted the values that are embedded
+
+ align:start position:0%
+for granted the values that are embedded
+ 
+
+ align:start position:0%
+for granted the values that are embedded
+in the consensus system are the values
+
+ align:start position:0%
+in the consensus system are the values
+ 
+
+ align:start position:0%
+in the consensus system are the values
+of the whole society and we can
+
+ align:start position:0%
+of the whole society and we can
+ 
+
+ align:start position:0%
+of the whole society and we can
+recognize the limitations of those
+
+ align:start position:0%
+recognize the limitations of those
+ 
+
+ align:start position:0%
+recognize the limitations of those
+values if we look closely at at those at
+
+ align:start position:0%
+values if we look closely at at those at
+ 
+
+ align:start position:0%
+values if we look closely at at those at
+those stories imagine what uh we might
+
+ align:start position:0%
+those stories imagine what uh we might
+ 
+
+ align:start position:0%
+those stories imagine what uh we might
+learn then if we went into the consensus
+
+ align:start position:0%
+learn then if we went into the consensus
+ 
+
+ align:start position:0%
+learn then if we went into the consensus
+what would it be radio or some form of
+
+ align:start position:0%
+what would it be radio or some form of
+ 
+
+ align:start position:0%
+what would it be radio or some form of
+some some combination of print media in
+
+ align:start position:0%
+some some combination of print media in
+ 
+
+ align:start position:0%
+some some combination of print media in
+the in the in in Nazi Germany in the in
+
+ align:start position:0%
+the in the in in Nazi Germany in the in
+ 
+
+ align:start position:0%
+the in the in in Nazi Germany in the in
+the in in the late 30s and 40s what we
+
+ align:start position:0%
+the in in the late 30s and 40s what we
+ 
+
+ align:start position:0%
+the in in the late 30s and 40s what we
+would find is a consensus that agreed
+
+ align:start position:0%
+would find is a consensus that agreed
+ 
+
+ align:start position:0%
+would find is a consensus that agreed
+that Jews were vermin
+
+ align:start position:0%
+that Jews were vermin
+ 
+
+ align:start position:0%
+that Jews were vermin
+right so I I don't mean to suggest that
+
+ align:start position:0%
+right so I I don't mean to suggest that
+ 
+
+ align:start position:0%
+right so I I don't mean to suggest that
+I don't want to I don't want to put a a
+
+ align:start position:0%
+I don't want to I don't want to put a a
+ 
+
+ align:start position:0%
+I don't want to I don't want to put a a
+a moral valuation on the term consensus
+
+ align:start position:0%
+a moral valuation on the term consensus
+ 
+
+ align:start position:0%
+a moral valuation on the term consensus
+for our purposes I want it to be a
+
+ align:start position:0%
+for our purposes I want it to be a
+ 
+
+ align:start position:0%
+for our purposes I want it to be a
+descriptor right not a not a valuation
+
+ align:start position:0%
+descriptor right not a not a valuation
+ 
+
+ align:start position:0%
+descriptor right not a not a valuation
+but just a descriptive a way of
+
+ align:start position:0%
+but just a descriptive a way of
+ 
+
+ align:start position:0%
+but just a descriptive a way of
+describing the role that these media
+
+ align:start position:0%
+describing the role that these media
+ 
+
+ align:start position:0%
+describing the role that these media
+play in a particular culture okay so
+
+ align:start position:0%
+play in a particular culture okay so
+ 
+
+ align:start position:0%
+play in a particular culture okay so
+let's talk about its conservative
+
+ align:start position:0%
+let's talk about its conservative
+ 
+
+ align:start position:0%
+let's talk about its conservative
+function it has to be conservative
+
+ align:start position:0%
+function it has to be conservative
+ 
+
+ align:start position:0%
+function it has to be conservative
+because it has to appeal across so many
+
+ align:start position:0%
+because it has to appeal across so many
+ 
+
+ align:start position:0%
+because it has to appeal across so many
+boundaries and that means that certain
+
+ align:start position:0%
+boundaries and that means that certain
+ 
+
+ align:start position:0%
+boundaries and that means that certain
+kinds of emergent or radical Notions
+
+ align:start position:0%
+kinds of emergent or radical Notions
+ 
+
+ align:start position:0%
+kinds of emergent or radical Notions
+which would offend large proportions of
+
+ align:start position:0%
+which would offend large proportions of
+ 
+
+ align:start position:0%
+which would offend large proportions of
+the population won't won't work on the
+
+ align:start position:0%
+the population won't won't work on the
+ 
+
+ align:start position:0%
+the population won't won't work on the
+meeting so it's conservative in terms of
+
+ align:start position:0%
+meeting so it's conservative in terms of
+ 
+
+ align:start position:0%
+meeting so it's conservative in terms of
+its content in terms of the belief
+
+ align:start position:0%
+its content in terms of the belief
+ 
+
+ align:start position:0%
+its content in terms of the belief
+systems and values that it will
+
+ align:start position:0%
+systems and values that it will
+ 
+
+ align:start position:0%
+systems and values that it will
+promulgate right and that's why in the
+
+ align:start position:0%
+promulgate right and that's why in the
+ 
+
+ align:start position:0%
+promulgate right and that's why in the
+early 50s the idea of the F of the
+
+ align:start position:0%
+early 50s the idea of the F of the
+ 
+
+ align:start position:0%
+early 50s the idea of the F of the
+nuclear family with the husband who
+
+ align:start position:0%
+nuclear family with the husband who
+ 
+
+ align:start position:0%
+nuclear family with the husband who
+works and the wife who stays at home was
+
+ align:start position:0%
+works and the wife who stays at home was
+ 
+
+ align:start position:0%
+works and the wife who stays at home was
+a was a staple a standard feature and
+
+ align:start position:0%
+a was a staple a standard feature and
+ 
+
+ align:start position:0%
+a was a staple a standard feature and
+even though there was a kind of
+
+ align:start position:0%
+even though there was a kind of
+ 
+
+ align:start position:0%
+even though there was a kind of
+subversive energy in the comic ways in
+
+ align:start position:0%
+subversive energy in the comic ways in
+ 
+
+ align:start position:0%
+subversive energy in the comic ways in
+which in many of those families The Lucy
+
+ align:start position:0%
+which in many of those families The Lucy
+ 
+
+ align:start position:0%
+which in many of those families The Lucy
+Show being a dramatic example of it the
+
+ align:start position:0%
+Show being a dramatic example of it the
+ 
+
+ align:start position:0%
+Show being a dramatic example of it the
+wife seemed the plot seemed again and
+
+ align:start position:0%
+wife seemed the plot seemed again and
+ 
+
+ align:start position:0%
+wife seemed the plot seemed again and
+again to dramatize a kind of discontent
+
+ align:start position:0%
+again to dramatize a kind of discontent
+ 
+
+ align:start position:0%
+again to dramatize a kind of discontent
+with that Arrangement the truth of the
+
+ align:start position:0%
+with that Arrangement the truth of the
+ 
+
+ align:start position:0%
+with that Arrangement the truth of the
+matter is that it was exact comedy
+
+ align:start position:0%
+matter is that it was exact comedy
+ 
+
+ align:start position:0%
+matter is that it was exact comedy
+always depends upon what are thought to
+
+ align:start position:0%
+always depends upon what are thought to
+ 
+
+ align:start position:0%
+always depends upon what are thought to
+be departures from the norm right uh if
+
+ align:start position:0%
+be departures from the norm right uh if
+ 
+
+ align:start position:0%
+be departures from the norm right uh if
+the norm is violated it seemed to be it
+
+ align:start position:0%
+the norm is violated it seemed to be it
+ 
+
+ align:start position:0%
+the norm is violated it seemed to be it
+seemed to be comical and funny another
+
+ align:start position:0%
+seemed to be comical and funny another
+ 
+
+ align:start position:0%
+seemed to be comical and funny another
+kind of situation comedy from this early
+
+ align:start position:0%
+kind of situation comedy from this early
+ 
+
+ align:start position:0%
+kind of situation comedy from this early
+period is a situation comedy in which
+
+ align:start position:0%
+period is a situation comedy in which
+ 
+
+ align:start position:0%
+period is a situation comedy in which
+the wife is missing we can call them uh
+
+ align:start position:0%
+the wife is missing we can call them uh
+ 
+
+ align:start position:0%
+the wife is missing we can call them uh
+and and in which the female figure is
+
+ align:start position:0%
+and and in which the female figure is
+ 
+
+ align:start position:0%
+and and in which the female figure is
+replaced the the the wife and mother
+
+ align:start position:0%
+replaced the the the wife and mother
+ 
+
+ align:start position:0%
+replaced the the the wife and mother
+figure is replaced by a comical often
+
+ align:start position:0%
+figure is replaced by a comical often
+ 
+
+ align:start position:0%
+figure is replaced by a comical often
+desexualized male figure can you can you
+
+ align:start position:0%
+desexualized male figure can you can you
+ 
+
+ align:start position:0%
+desexualized male figure can you can you
+think of shows like
+
+ align:start position:0%
+think of shows like
+ 
+
+ align:start position:0%
+think of shows like
+that my three sons is a terrific example
+
+ align:start position:0%
+that my three sons is a terrific example
+ 
+
+ align:start position:0%
+that my three sons is a terrific example
+and it ran for a long time another how
+
+ align:start position:0%
+and it ran for a long time another how
+ 
+
+ align:start position:0%
+and it ran for a long time another how
+many of you have seen my three sons a
+
+ align:start position:0%
+many of you have seen my three sons a
+ 
+
+ align:start position:0%
+many of you have seen my three sons a
+couple of you uh it's available it's an
+
+ align:start position:0%
+couple of you uh it's available it's an
+ 
+
+ align:start position:0%
+couple of you uh it's available it's an
+incredibly silly show in many ways but
+
+ align:start position:0%
+incredibly silly show in many ways but
+ 
+
+ align:start position:0%
+incredibly silly show in many ways but
+what what makes it interesting in a
+
+ align:start position:0%
+what what makes it interesting in a
+ 
+
+ align:start position:0%
+what what makes it interesting in a
+certain sense it it it draws a lot of
+
+ align:start position:0%
+certain sense it it it draws a lot of
+ 
+
+ align:start position:0%
+certain sense it it it draws a lot of
+its comedy from the absence of a of the
+
+ align:start position:0%
+its comedy from the absence of a of the
+ 
+
+ align:start position:0%
+its comedy from the absence of a of the
+female figure and the and the the the
+
+ align:start position:0%
+female figure and the and the the the
+ 
+
+ align:start position:0%
+female figure and the and the the the
+male figure who often is seen in wearing
+
+ align:start position:0%
+male figure who often is seen in wearing
+ 
+
+ align:start position:0%
+male figure who often is seen in wearing
+aprons and doing and cooking badly and
+
+ align:start position:0%
+aprons and doing and cooking badly and
+ 
+
+ align:start position:0%
+aprons and doing and cooking badly and
+so forth who replace inadequately
+
+ align:start position:0%
+so forth who replace inadequately
+ 
+
+ align:start position:0%
+so forth who replace inadequately
+replaces another such show is called
+
+ align:start position:0%
+replaces another such show is called
+ 
+
+ align:start position:0%
+replaces another such show is called
+Bachelor Father there are series of them
+
+ align:start position:0%
+Bachelor Father there are series of them
+ 
+
+ align:start position:0%
+Bachelor Father there are series of them
+another one a little bit later on was
+
+ align:start position:0%
+another one a little bit later on was
+ 
+
+ align:start position:0%
+another one a little bit later on was
+called uh um um
+
+ align:start position:0%
+called uh um um
+ 
+
+ align:start position:0%
+called uh um um
+full Full House Full House well that's a
+
+ align:start position:0%
+full Full House Full House well that's a
+ 
+
+ align:start position:0%
+full Full House Full House well that's a
+very late one yes full house but but see
+
+ align:start position:0%
+very late one yes full house but but see
+ 
+
+ align:start position:0%
+very late one yes full house but but see
+but by the time we get to Full House or
+
+ align:start position:0%
+but by the time we get to Full House or
+ 
+
+ align:start position:0%
+but by the time we get to Full House or
+my three dads we're in a different
+
+ align:start position:0%
+my three dads we're in a different
+ 
+
+ align:start position:0%
+my three dads we're in a different
+cultural dispensation and the the there
+
+ align:start position:0%
+cultural dispensation and the the there
+ 
+
+ align:start position:0%
+cultural dispensation and the the there
+it's there the absence of the female
+
+ align:start position:0%
+it's there the absence of the female
+ 
+
+ align:start position:0%
+it's there the absence of the female
+figure has a different cultural meaning
+
+ align:start position:0%
+figure has a different cultural meaning
+ 
+
+ align:start position:0%
+figure has a different cultural meaning
+from what it had in the 50s and early
+
+ align:start position:0%
+from what it had in the 50s and early
+ 
+
+ align:start position:0%
+from what it had in the 50s and early
+60s there there because what's happened
+
+ align:start position:0%
+60s there there because what's happened
+ 
+
+ align:start position:0%
+60s there there because what's happened
+is the nuclear family is no longer the
+
+ align:start position:0%
+is the nuclear family is no longer the
+ 
+
+ align:start position:0%
+is the nuclear family is no longer the
+norm by the time we get to a show like
+
+ align:start position:0%
+norm by the time we get to a show like
+ 
+
+ align:start position:0%
+norm by the time we get to a show like
+my three dads right
+
+ align:start position:0%
+my three dads right
+ 
+
+ align:start position:0%
+my three dads right
+so yes Wally put on your put on your uh
+
+ align:start position:0%
+so yes Wally put on your put on your uh
+ 
+
+ align:start position:0%
+so yes Wally put on your put on your uh
+my question is actually when was the uh
+
+ align:start position:0%
+my question is actually when was the uh
+ 
+
+ align:start position:0%
+my question is actually when was the uh
+when is when did the play The Odd Couple
+
+ align:start position:0%
+when is when did the play The Odd Couple
+ 
+
+ align:start position:0%
+when is when did the play The Odd Couple
+was it written I I don't know I assume
+
+ align:start position:0%
+was it written I I don't know I assume
+ 
+
+ align:start position:0%
+was it written I I don't know I assume
+the play came before the show yes the
+
+ align:start position:0%
+the play came before the show yes the
+ 
+
+ align:start position:0%
+the play came before the show yes the
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+
+ align:start position:0%
+play precedes the precedes the
+ 
+
+ align:start position:0%
+play precedes the precedes the
+television show I don't know the date
+
+ align:start position:0%
+television show I don't know the date
+ 
+
+ align:start position:0%
+television show I don't know the date
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+uh late 50s early 60s is my
+
+ align:start position:0%
+uh late 50s early 60s is my
+ 
+
+ align:start position:0%
+uh late 50s early 60s is my
+guess my guess but let me come back to
+
+ align:start position:0%
+guess my guess but let me come back to
+ 
+
+ align:start position:0%
+guess my guess but let me come back to
+this for so so what I'm going saying is
+
+ align:start position:0%
+this for so so what I'm going saying is
+ 
+
+ align:start position:0%
+this for so so what I'm going saying is
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+
+ align:start position:0%
+that in the early in the early phase the
+ 
+
+ align:start position:0%
+that in the early in the early phase the
+the the situation comedy with the absent
+
+ align:start position:0%
+the the situation comedy with the absent
+ 
+
+ align:start position:0%
+the the situation comedy with the absent
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+the notion that there's a discontent in
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+
+ align:start position:0%
+the notion that there's a discontent in
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+
+ align:start position:0%
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+ 
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+ align:start position:0%
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+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+comical what what is a continuous source
+ 
+
+ align:start position:0%
+comical what what is a continuous source
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+
+ align:start position:0%
+of Comedy is this failure to meet what
+ 
+
+ align:start position:0%
+of Comedy is this failure to meet what
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+
+ align:start position:0%
+the Norms of society assume and one
+ 
+
+ align:start position:0%
+the Norms of society assume and one
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+ align:start position:0%
+or is are violations of what is thought
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+
+ align:start position:0%
+or is are violations of what is thought
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+
+ align:start position:0%
+to be an utter Norm in other words what
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
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+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
+understood so deeply to be a part of
+ 
+
+ align:start position:0%
+understood so deeply to be a part of
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+
+ align:start position:0%
+nature to be not not not a construction
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+something that could change but a but a
+ 
+
+ align:start position:0%
+something that could change but a but a
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+
+ align:start position:0%
+but a part of the natural order of the
+ 
+
+ align:start position:0%
+but a part of the natural order of the
+world not part of a particular social
+
+ align:start position:0%
+world not part of a particular social
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+system that variations from it were seen
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+only later that the variations begin to
+ 
+
+ align:start position:0%
+only later that the variations begin to
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+
+ align:start position:0%
+take on uh a a conscious sense that wait
+ 
+
+ align:start position:0%
+take on uh a a conscious sense that wait
+a minute this is a constructed relation
+
+ align:start position:0%
+a minute this is a constructed relation
+ 
+
+ align:start position:0%
+a minute this is a constructed relation
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+
+ align:start position:0%
+and many many many many families are
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+
+ align:start position:0%
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+
+ align:start position:0%
+actually not organized on the on the
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+nuclear family model isn't so isn't so
+ 
+
+ align:start position:0%
+nuclear family model isn't so isn't so
+isn't so Universal and isn't so is isn't
+
+ align:start position:0%
+isn't so Universal and isn't so is isn't
+ 
+
+ align:start position:0%
+isn't so Universal and isn't so is isn't
+isn't so natural as we had originally
+
+ align:start position:0%
+isn't so natural as we had originally
+ 
+
+ align:start position:0%
+isn't so natural as we had originally
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+
+ align:start position:0%
+thought but that's a process that's a
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+process that actually in a certain sense
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+
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+could be said to be articulated or
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+
+ align:start position:0%
+enacted that that recognition that the
+ 
+
+ align:start position:0%
+enacted that that recognition that the
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+
+ align:start position:0%
+nuclear family is not the only way we
+ 
+
+ align:start position:0%
+nuclear family is not the only way we
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+
+ align:start position:0%
+can think about families or the that the
+ 
+
+ align:start position:0%
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+housewife is not the only role we can
+
+ align:start position:0%
+housewife is not the only role we can
+ 
+
+ align:start position:0%
+housewife is not the only role we can
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+ align:start position:0%
+think of for women that's a process
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+
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
+course of the development of particular
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+
+ align:start position:0%
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+
+ align:start position:0%
+genres on Tel so that we so that so that
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+
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+
+ align:start position:0%
+what I'm saying in a certain sense is
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+
+ align:start position:0%
+what I'm saying in a certain sense is
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+
+ align:start position:0%
+that is that um the conservative
+ 
+
+ align:start position:0%
+that is that um the conservative
+features of consensus Medi of of a
+
+ align:start position:0%
+features of consensus Medi of of a
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+
+ align:start position:0%
+features of consensus Medi of of a
+consensus medium are are particularly
+
+ align:start position:0%
+consensus medium are are particularly
+ 
+
+ align:start position:0%
+consensus medium are are particularly
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+
+ align:start position:0%
+important because when we see those
+ 
+
+ align:start position:0%
+important because when we see those
+those uh that belief structure changing
+
+ align:start position:0%
+those uh that belief structure changing
+ 
+
+ align:start position:0%
+those uh that belief structure changing
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+ align:start position:0%
+in certain ways certain basic
+ 
+
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+ align:start position:0%
+assumptions that the media might be
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+
+ align:start position:0%
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+ align:start position:0%
+making about essential features of the
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+
+ align:start position:0%
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+
+ align:start position:0%
+society we can say that those changes
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+
+ align:start position:0%
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+are really signified in a way that would
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+ 
+
+ align:start position:0%
+not be true if we were looking at a
+medium that that that was U defined only
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+ align:start position:0%
+medium that that that was U defined only
+ 
+
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+
+ align:start position:0%
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+society it would sign it signifies much
+ 
+
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+
+ align:start position:0%
+less uh uh if if the avangard novel
+ 
+
+ align:start position:0%
+less uh uh if if the avangard novel
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+
+ align:start position:0%
+doesn't respect the nuclear family than
+ 
+
+ align:start position:0%
+doesn't respect the nuclear family than
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+
+ align:start position:0%
+it does if the if the television system
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+is beginning to say wait a minute I can
+ 
+
+ align:start position:0%
+is beginning to say wait a minute I can
+imagine families where the woman is
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+ align:start position:0%
+imagine families where the woman is
+ 
+
+ align:start position:0%
+imagine families where the woman is
+dominant I can imagine families in which
+
+ align:start position:0%
+dominant I can imagine families in which
+ 
+
+ align:start position:0%
+dominant I can imagine families in which
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+
+ align:start position:0%
+there is no father I can imagine I can
+ 
+
+ align:start position:0%
+there is no father I can imagine I can
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+ align:start position:0%
+imagine families in which the children
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+
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+ align:start position:0%
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+
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+
+ align:start position:0%
+one of the things that begins to in a
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+
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+disturbing way happen at a certain point
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+
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+in the history of of of family sitcoms
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+ align:start position:0%
+in the history of of of family sitcoms
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+
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+in the history of of of family sitcoms
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+ align:start position:0%
+right so so there so so a consensus
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+
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+right so so there so so a consensus
+system is conservative in content but
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+system is conservative in content but
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+
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+system is conservative in content but
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+
+ align:start position:0%
+it's it's also conservative in form in
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
+format that is to say the basic you it
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+
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+format that is to say the basic you it
+will not it will not engage in what we
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+ align:start position:0%
+will not it will not engage in what we
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+
+ align:start position:0%
+will not it will not engage in what we
+might think of as modernist or avangard
+
+ align:start position:0%
+might think of as modernist or avangard
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+
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+might think of as modernist or avangard
+or uh narrative strategies it's it's
+
+ align:start position:0%
+or uh narrative strategies it's it's
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+
+ align:start position:0%
+or uh narrative strategies it's it's
+aesthetically
+
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+aesthetically
+ 
+
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+aesthetically
+conservative right formally conservative
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+
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+
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+as well as conservative in content as
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+
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+as well as conservative in content as
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+ align:start position:0%
+well as conservative in ide for exactly
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+
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+well as conservative in ide for exactly
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+ align:start position:0%
+the same reason uh and that's why it
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+
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+the same reason uh and that's why it
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+signifies very greatly that at a certain
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+
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+signifies very greatly that at a certain
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+
+ align:start position:0%
+point in the late 70s or early 80s we
+ 
+
+ align:start position:0%
+point in the late 70s or early 80s we
+begin to get television shows that use
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+ align:start position:0%
+begin to get television shows that use
+ 
+
+ align:start position:0%
+begin to get television shows that use
+complex flashback structures that make
+
+ align:start position:0%
+complex flashback structures that make
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+
+ align:start position:0%
+complex flashback structures that make
+it much more difficult to follow the
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+it much more difficult to follow the
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+
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+it much more difficult to follow the
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+ align:start position:0%
+narrative instead of having a
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+
+ align:start position:0%
+narrative instead of having a
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+ align:start position:0%
+straightforward narrative which is
+ 
+
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+straightforward narrative which is
+organized chronologically you begin to
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+ align:start position:0%
+organized chronologically you begin to
+ 
+
+ align:start position:0%
+organized chronologically you begin to
+get television programs in which the
+
+ align:start position:0%
+get television programs in which the
+ 
+
+ align:start position:0%
+get television programs in which the
+chronology is disrupted in the way that
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+ align:start position:0%
+chronology is disrupted in the way that
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+
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+chronology is disrupted in the way that
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+ align:start position:0%
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+
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+the modern novel did at turn of the
+century right but but when television
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+ align:start position:0%
+century right but but when television
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+
+ align:start position:0%
+century right but but when television
+narrative begins to show modernist
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+narrative begins to show modernist
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+Tendencies it suggests something among
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+Tendencies it suggests something among
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+
+ align:start position:0%
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+ align:start position:0%
+other things about the breakdown of the
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+
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+other things about the breakdown of the
+consensus function that television had
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+consensus function that television had
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+
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+been performing in American so it's
+
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+aesthetically it's accessible and this
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+aesthetically it's accessible and this
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+
+ align:start position:0%
+that is to say it speaks this is an
+ 
+
+ align:start position:0%
+that is to say it speaks this is an
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+ align:start position:0%
+aspect of its conservatism it's
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+
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+aspect of its conservatism it's
+accessible because to be a consensus
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+accessible because to be a consensus
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+
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+accessible because to be a consensus
+medium it has to speak broadly to
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+ align:start position:0%
+medium it has to speak broadly to
+ 
+
+ align:start position:0%
+medium it has to speak broadly to
+everyone it has to use it has to use a
+
+ align:start position:0%
+everyone it has to use it has to use a
+ 
+
+ align:start position:0%
+everyone it has to use it has to use a
+common a shared language it will embody
+
+ align:start position:0%
+common a shared language it will embody
+ 
+
+ align:start position:0%
+common a shared language it will embody
+it will talk and and and utilize the
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+ align:start position:0%
+it will talk and and and utilize the
+ 
+
+ align:start position:0%
+it will talk and and and utilize the
+myths and stories that are at the heart
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+ align:start position:0%
+myths and stories that are at the heart
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+
+ align:start position:0%
+myths and stories that are at the heart
+of the culture and it will communicate
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+ align:start position:0%
+of the culture and it will communicate
+ 
+
+ align:start position:0%
+of the culture and it will communicate
+them and rehearse them again and again
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+ align:start position:0%
+them and rehearse them again and again
+ 
+
+ align:start position:0%
+them and rehearse them again and again
+uh it's it and finally it's a
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+ align:start position:0%
+uh it's it and finally it's a
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+
+ align:start position:0%
+uh it's it and finally it's a
+collaborative medium in in the deepest
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+ align:start position:0%
+collaborative medium in in the deepest
+ 
+
+ align:start position:0%
+collaborative medium in in the deepest
+possible sense it's collaborative first
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+ align:start position:0%
+possible sense it's collaborative first
+ 
+
+ align:start position:0%
+possible sense it's collaborative first
+be uh in the case of movies or theater
+
+ align:start position:0%
+be uh in the case of movies or theater
+ 
+
+ align:start position:0%
+be uh in the case of movies or theater
+or television because many people
+
+ align:start position:0%
+or television because many people
+ 
+
+ align:start position:0%
+or television because many people
+collaborate to make the text there's no
+
+ align:start position:0%
+collaborate to make the text there's no
+ 
+
+ align:start position:0%
+collaborate to make the text there's no
+single author right no television
+
+ align:start position:0%
+single author right no television
+ 
+
+ align:start position:0%
+single author right no television
+program or movie actually has a single
+
+ align:start position:0%
+program or movie actually has a single
+ 
+
+ align:start position:0%
+program or movie actually has a single
+author the author is uh a writer a
+
+ align:start position:0%
+author the author is uh a writer a
+ 
+
+ align:start position:0%
+author the author is uh a writer a
+director the actors the there's that
+
+ align:start position:0%
+director the actors the there's that
+ 
+
+ align:start position:0%
+director the actors the there's that
+there's that kind of collaboration invol
+
+ align:start position:0%
+there's that kind of collaboration invol
+ 
+
+ align:start position:0%
+there's that kind of collaboration invol
+but that's the smallest aspect of the
+
+ align:start position:0%
+but that's the smallest aspect of the
+ 
+
+ align:start position:0%
+but that's the smallest aspect of the
+collaboration what else does it
+
+ align:start position:0%
+collaboration what else does it
+ 
+
+ align:start position:0%
+collaboration what else does it
+collaborate with the m the system also
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+ align:start position:0%
+collaborate with the m the system also
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+
+ align:start position:0%
+collaborate with the m the system also
+coll the the the story also collaborates
+
+ align:start position:0%
+coll the the the story also collaborates
+ 
+
+ align:start position:0%
+coll the the the story also collaborates
+with the understanding that the audience
+
+ align:start position:0%
+with the understanding that the audience
+ 
+
+ align:start position:0%
+with the understanding that the audience
+has of this material the audience is a
+
+ align:start position:0%
+has of this material the audience is a
+ 
+
+ align:start position:0%
+has of this material the audience is a
+is an active collaborator the audience
+
+ align:start position:0%
+is an active collaborator the audience
+ 
+
+ align:start position:0%
+is an active collaborator the audience
+is prior understanding of the generic
+
+ align:start position:0%
+is prior understanding of the generic
+ 
+
+ align:start position:0%
+is prior understanding of the generic
+forms that are that that they're
+
+ align:start position:0%
+forms that are that that they're
+ 
+
+ align:start position:0%
+forms that are that that they're
+watching the audience's prior
+
+ align:start position:0%
+watching the audience's prior
+ 
+
+ align:start position:0%
+watching the audience's prior
+understanding of the characters inside
+
+ align:start position:0%
+understanding of the characters inside
+ 
+
+ align:start position:0%
+understanding of the characters inside
+the story as a part of the collaboration
+
+ align:start position:0%
+the story as a part of the collaboration
+ 
+
+ align:start position:0%
+the story as a part of the collaboration
+but even more deeply than that there's a
+
+ align:start position:0%
+but even more deeply than that there's a
+ 
+
+ align:start position:0%
+but even more deeply than that there's a
+notion that that the wisdom the larger
+
+ align:start position:0%
+notion that that the wisdom the larger
+ 
+
+ align:start position:0%
+notion that that the wisdom the larger
+wisdom or wisdom system of the culture
+
+ align:start position:0%
+wisdom or wisdom system of the culture
+ 
+
+ align:start position:0%
+wisdom or wisdom system of the culture
+the larger story systems and myth
+
+ align:start position:0%
+the larger story systems and myth
+ 
+
+ align:start position:0%
+the larger story systems and myth
+systems of the culture are also lie
+
+ align:start position:0%
+systems of the culture are also lie
+ 
+
+ align:start position:0%
+systems of the culture are also lie
+behind and help to explain the content
+
+ align:start position:0%
+behind and help to explain the content
+ 
+
+ align:start position:0%
+behind and help to explain the content
+of consensus narrative so that uh if
+
+ align:start position:0%
+of consensus narrative so that uh if
+ 
+
+ align:start position:0%
+of consensus narrative so that uh if
+there are traditional Notions of
+
+ align:start position:0%
+there are traditional Notions of
+ 
+
+ align:start position:0%
+there are traditional Notions of
+individualism that have organized
+
+ align:start position:0%
+individualism that have organized
+ 
+
+ align:start position:0%
+individualism that have organized
+American society since the re
+
+ align:start position:0%
+American society since the re
+ 
+
+ align:start position:0%
+American society since the re
+evolutionary War those Notions of
+
+ align:start position:0%
+evolutionary War those Notions of
+ 
+
+ align:start position:0%
+evolutionary War those Notions of
+individualism are going to feed into and
+
+ align:start position:0%
+individualism are going to feed into and
+ 
+
+ align:start position:0%
+individualism are going to feed into and
+help to shape the stories that are told
+
+ align:start position:0%
+help to shape the stories that are told
+ 
+
+ align:start position:0%
+help to shape the stories that are told
+on its on the on the system's consensus
+
+ align:start position:0%
+on its on the on the system's consensus
+ 
+
+ align:start position:0%
+on its on the on the system's consensus
+medium so so this so the texts on a
+
+ align:start position:0%
+medium so so this so the texts on a
+ 
+
+ align:start position:0%
+medium so so this so the texts on a
+consensus medium collaborate not only
+
+ align:start position:0%
+consensus medium collaborate not only
+ 
+
+ align:start position:0%
+consensus medium collaborate not only
+with their own immediate ancestor texts
+
+ align:start position:0%
+with their own immediate ancestor texts
+ 
+
+ align:start position:0%
+with their own immediate ancestor texts
+and with but also with the older
+
+ align:start position:0%
+and with but also with the older
+ 
+
+ align:start position:0%
+and with but also with the older
+ancestor media and ancestor stories that
+
+ align:start position:0%
+ancestor media and ancestor stories that
+ 
+
+ align:start position:0%
+ancestor media and ancestor stories that
+are the
+
+ align:start position:0%
+are the
+ 
+
+ align:start position:0%
+are the
+shared that are the that are the shared
+
+ align:start position:0%
+shared that are the that are the shared
+ 
+
+ align:start position:0%
+shared that are the that are the shared
+possession of the of of the culture as a
+
+ align:start position:0%
+possession of the of of the culture as a
+ 
+
+ align:start position:0%
+possession of the of of the culture as a
+whole so in that sense consensus medium
+
+ align:start position:0%
+whole so in that sense consensus medium
+ 
+
+ align:start position:0%
+whole so in that sense consensus medium
+is a deeply collaborative system I try
+
+ align:start position:0%
+is a deeply collaborative system I try
+ 
+
+ align:start position:0%
+is a deeply collaborative system I try
+to embody this idea in that passage I in
+
+ align:start position:0%
+to embody this idea in that passage I in
+ 
+
+ align:start position:0%
+to embody this idea in that passage I in
+which I conclude the essay on television
+
+ align:start position:0%
+which I conclude the essay on television
+ 
+
+ align:start position:0%
+which I conclude the essay on television
+as an aesthetic medium in which I talk
+
+ align:start position:0%
+as an aesthetic medium in which I talk
+ 
+
+ align:start position:0%
+as an aesthetic medium in which I talk
+about that astonishing wonderful moment
+
+ align:start position:0%
+about that astonishing wonderful moment
+ 
+
+ align:start position:0%
+about that astonishing wonderful moment
+in Shakespeare from simine when the when
+
+ align:start position:0%
+in Shakespeare from simine when the when
+ 
+
+ align:start position:0%
+in Shakespeare from simine when the when
+when when uh standing over a dead body
+
+ align:start position:0%
+when when uh standing over a dead body
+ 
+
+ align:start position:0%
+when when uh standing over a dead body
+they sing This Magnificent durge to a
+
+ align:start position:0%
+they sing This Magnificent durge to a
+ 
+
+ align:start position:0%
+they sing This Magnificent durge to a
+person who appears to be dead it's one
+
+ align:start position:0%
+person who appears to be dead it's one
+ 
+
+ align:start position:0%
+person who appears to be dead it's one
+of the great elegies uh in in in English
+
+ align:start position:0%
+of the great elegies uh in in in English
+ 
+
+ align:start position:0%
+of the great elegies uh in in in English
+literature and The crucial lines are
+
+ align:start position:0%
+literature and The crucial lines are
+ 
+
+ align:start position:0%
+literature and The crucial lines are
+golden Lads and girls almost must as
+
+ align:start position:0%
+golden Lads and girls almost must as
+ 
+
+ align:start position:0%
+golden Lads and girls almost must as
+chimney sweepers come to dust and they
+
+ align:start position:0%
+chimney sweepers come to dust and they
+ 
+
+ align:start position:0%
+chimney sweepers come to dust and they
+are beautiful and magnificent lines
+
+ align:start position:0%
+are beautiful and magnificent lines
+ 
+
+ align:start position:0%
+are beautiful and magnificent lines
+aren't they and they are consoling lines
+
+ align:start position:0%
+aren't they and they are consoling lines
+ 
+
+ align:start position:0%
+aren't they and they are consoling lines
+in a certain way the lines take on a
+
+ align:start position:0%
+in a certain way the lines take on a
+ 
+
+ align:start position:0%
+in a certain way the lines take on a
+kind of richness in resonance when we
+
+ align:start position:0%
+kind of richness in resonance when we
+ 
+
+ align:start position:0%
+kind of richness in resonance when we
+recognize that the term in Shakespeare's
+
+ align:start position:0%
+recognize that the term in Shakespeare's
+ 
+
+ align:start position:0%
+recognize that the term in Shakespeare's
+native
+
+ align:start position:0%
+native
+ 
+
+ align:start position:0%
+native
+Warwickshire the term golden Lads refers
+
+ align:start position:0%
+Warwickshire the term golden Lads refers
+ 
+
+ align:start position:0%
+Warwickshire the term golden Lads refers
+literally to the flower we call the
+
+ align:start position:0%
+literally to the flower we call the
+ 
+
+ align:start position:0%
+literally to the flower we call the
+dandelion which has a golden cap when
+
+ align:start position:0%
+dandelion which has a golden cap when
+ 
+
+ align:start position:0%
+dandelion which has a golden cap when
+it's young and strong and then when it
+
+ align:start position:0%
+it's young and strong and then when it
+ 
+
+ align:start position:0%
+it's young and strong and then when it
+ages when it's about to when it goes to
+
+ align:start position:0%
+ages when it's about to when it goes to
+ 
+
+ align:start position:0%
+ages when it's about to when it goes to
+seed that cap turns into those they're
+
+ align:start position:0%
+seed that cap turns into those they're
+ 
+
+ align:start position:0%
+seed that cap turns into those they're
+very common here in New England right
+
+ align:start position:0%
+very common here in New England right
+ 
+
+ align:start position:0%
+very common here in New England right
+turns into a kind of set of white
+
+ align:start position:0%
+turns into a kind of set of white
+ 
+
+ align:start position:0%
+turns into a kind of set of white
+filaments and kids pick them and if they
+
+ align:start position:0%
+filaments and kids pick them and if they
+ 
+
+ align:start position:0%
+filaments and kids pick them and if they
+blow on them the seeds can be blown away
+
+ align:start position:0%
+blow on them the seeds can be blown away
+ 
+
+ align:start position:0%
+blow on them the seeds can be blown away
+right well so they they're golden Lads
+
+ align:start position:0%
+right well so they they're golden Lads
+ 
+
+ align:start position:0%
+right well so they they're golden Lads
+when they're young and they C why are
+
+ align:start position:0%
+when they're young and they C why are
+ 
+
+ align:start position:0%
+when they're young and they C why are
+they called chimney sweepers because
+
+ align:start position:0%
+they called chimney sweepers because
+ 
+
+ align:start position:0%
+they called chimney sweepers because
+chimney sweepers brooms in Shakespeare's
+
+ align:start position:0%
+chimney sweepers brooms in Shakespeare's
+ 
+
+ align:start position:0%
+chimney sweepers brooms in Shakespeare's
+day looked like those looked like those
+
+ align:start position:0%
+day looked like those looked like those
+ 
+
+ align:start position:0%
+day looked like those looked like those
+flowers when they've gone to seed and
+
+ align:start position:0%
+flowers when they've gone to seed and
+ 
+
+ align:start position:0%
+flowers when they've gone to seed and
+were actually they they had a rounded
+
+ align:start position:0%
+were actually they they had a rounded
+ 
+
+ align:start position:0%
+were actually they they had a rounded
+top like that and they were they because
+
+ align:start position:0%
+top like that and they were they because
+ 
+
+ align:start position:0%
+top like that and they were they because
+they were it was easier to clean
+
+ align:start position:0%
+they were it was easier to clean
+ 
+
+ align:start position:0%
+they were it was easier to clean
+chimneys with such a rounded brush so
+
+ align:start position:0%
+chimneys with such a rounded brush so
+ 
+
+ align:start position:0%
+chimneys with such a rounded brush so
+they called dandelions golden Lads when
+
+ align:start position:0%
+they called dandelions golden Lads when
+ 
+
+ align:start position:0%
+they called dandelions golden Lads when
+they were young and chimney sweepers
+
+ align:start position:0%
+they were young and chimney sweepers
+ 
+
+ align:start position:0%
+they were young and chimney sweepers
+when they were are close to death well
+
+ align:start position:0%
+when they were are close to death well
+ 
+
+ align:start position:0%
+when they were are close to death well
+that why is that so wonderful two
+
+ align:start position:0%
+that why is that so wonderful two
+ 
+
+ align:start position:0%
+that why is that so wonderful two
+reasons it's a it gives a kind of poetic
+
+ align:start position:0%
+reasons it's a it gives a kind of poetic
+ 
+
+ align:start position:0%
+reasons it's a it gives a kind of poetic
+resonance to the line because it links
+
+ align:start position:0%
+resonance to the line because it links
+ 
+
+ align:start position:0%
+resonance to the line because it links
+human human death with a cycle of the
+
+ align:start position:0%
+human human death with a cycle of the
+ 
+
+ align:start position:0%
+human human death with a cycle of the
+seasons golden Lads and girls all must
+
+ align:start position:0%
+seasons golden Lads and girls all must
+ 
+
+ align:start position:0%
+seasons golden Lads and girls all must
+as chimney sweepers come to dust the
+
+ align:start position:0%
+as chimney sweepers come to dust the
+ 
+
+ align:start position:0%
+as chimney sweepers come to dust the
+rich and the poor the Highborn and the
+
+ align:start position:0%
+rich and the poor the Highborn and the
+ 
+
+ align:start position:0%
+rich and the poor the Highborn and the
+low all die we share that with each
+
+ align:start position:0%
+low all die we share that with each
+ 
+
+ align:start position:0%
+low all die we share that with each
+other not just that we share that with
+
+ align:start position:0%
+other not just that we share that with
+ 
+
+ align:start position:0%
+other not just that we share that with
+nature with the natural process so it's
+
+ align:start position:0%
+nature with the natural process so it's
+ 
+
+ align:start position:0%
+nature with the natural process so it's
+a brilliant line but the most important
+
+ align:start position:0%
+a brilliant line but the most important
+ 
+
+ align:start position:0%
+a brilliant line but the most important
+thing for me is How Deeply collaborative
+
+ align:start position:0%
+thing for me is How Deeply collaborative
+ 
+
+ align:start position:0%
+thing for me is How Deeply collaborative
+it is because Shakespeare didn't invent
+
+ align:start position:0%
+it is because Shakespeare didn't invent
+ 
+
+ align:start position:0%
+it is because Shakespeare didn't invent
+the metaphor
+
+ align:start position:0%
+the metaphor
+ 
+
+ align:start position:0%
+the metaphor
+what grants the authority to the line is
+
+ align:start position:0%
+what grants the authority to the line is
+ 
+
+ align:start position:0%
+what grants the authority to the line is
+the common wisdom of the Elizabethan
+
+ align:start position:0%
+the common wisdom of the Elizabethan
+ 
+
+ align:start position:0%
+the common wisdom of the Elizabethan
+culture in which Shakespeare was born
+
+ align:start position:0%
+culture in which Shakespeare was born
+ 
+
+ align:start position:0%
+culture in which Shakespeare was born
+and the culture behind that because it
+
+ align:start position:0%
+and the culture behind that because it
+ 
+
+ align:start position:0%
+and the culture behind that because it
+was the native farmers in warshire who
+
+ align:start position:0%
+was the native farmers in warshire who
+ 
+
+ align:start position:0%
+was the native farmers in warshire who
+never read blank verse in their lives
+
+ align:start position:0%
+never read blank verse in their lives
+ 
+
+ align:start position:0%
+never read blank verse in their lives
+who came to call the dandelion golden
+
+ align:start position:0%
+who came to call the dandelion golden
+ 
+
+ align:start position:0%
+who came to call the dandelion golden
+Lads and chimney sweepers so what
+
+ align:start position:0%
+Lads and chimney sweepers so what
+ 
+
+ align:start position:0%
+Lads and chimney sweepers so what
+Shakespeare is doing there in a way is
+
+ align:start position:0%
+Shakespeare is doing there in a way is
+ 
+
+ align:start position:0%
+Shakespeare is doing there in a way is
+he's collaborating with his culture he's
+
+ align:start position:0%
+he's collaborating with his culture he's
+ 
+
+ align:start position:0%
+he's collaborating with his culture he's
+seizing on what we might call the common
+
+ align:start position:0%
+seizing on what we might call the common
+ 
+
+ align:start position:0%
+seizing on what we might call the common
+wisdom of his culture in order to
+
+ align:start position:0%
+wisdom of his culture in order to
+ 
+
+ align:start position:0%
+wisdom of his culture in order to
+express a comp an immensely complex Rich
+
+ align:start position:0%
+express a comp an immensely complex Rich
+ 
+
+ align:start position:0%
+express a comp an immensely complex Rich
+idea which in part belongs to the
+
+ align:start position:0%
+idea which in part belongs to the
+ 
+
+ align:start position:0%
+idea which in part belongs to the
+culture that's a very dramatic and
+
+ align:start position:0%
+culture that's a very dramatic and
+ 
+
+ align:start position:0%
+culture that's a very dramatic and
+poetic instance of this principle of
+
+ align:start position:0%
+poetic instance of this principle of
+ 
+
+ align:start position:0%
+poetic instance of this principle of
+collaboration that I think is operative
+
+ align:start position:0%
+collaboration that I think is operative
+ 
+
+ align:start position:0%
+collaboration that I think is operative
+on our on our popular media all the time
+
+ align:start position:0%
+on our on our popular media all the time
+ 
+
+ align:start position:0%
+on our on our popular media all the time
+and we are going to have occasions as we
+
+ align:start position:0%
+and we are going to have occasions as we
+ 
+
+ align:start position:0%
+and we are going to have occasions as we
+go on in this course to see one
+
+ align:start position:0%
+go on in this course to see one
+ 
+
+ align:start position:0%
+go on in this course to see one
+instances of such collaboration and of
+
+ align:start position:0%
+instances of such collaboration and of
+ 
+
+ align:start position:0%
+instances of such collaboration and of
+such of such U
+
+ align:start position:0%
+such of such U
+ 
+
+ align:start position:0%
+such of such U
+self-consciousness in our in our popular
+
+ align:start position:0%
+self-consciousness in our in our popular
+ 
+
+ align:start position:0%
+self-consciousness in our in our popular
+television programs that I think are at
+
+ align:start position:0%
+television programs that I think are at
+ 
+
+ align:start position:0%
+television programs that I think are at
+least the equal of the subtlety of those
+
+ align:start position:0%
+least the equal of the subtlety of those
+ 
+
+ align:start position:0%
+least the equal of the subtlety of those
+wonderful Shakespearean lines we're
+
+ align:start position:0%
+wonderful Shakespearean lines we're
+ 
+
+ align:start position:0%
+wonderful Shakespearean lines we're
+finished see you next time
\ No newline at end of file
diff --git a/2ieG1ka5pBw.txt b/2ieG1ka5pBw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0e070f23c70dea44f0c72733eb54092892685cd6
--- /dev/null
+++ b/2ieG1ka5pBw.txt
@@ -0,0 +1,3115 @@
+align:start position:0%
+ 
+hi welcome back to recitation in lecture
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+ 
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+you've been learning about Stokes
+
+ align:start position:0%
+you've been learning about Stokes
+ 
+
+ align:start position:0%
+you've been learning about Stokes
+theorem and I have a nice question here
+
+ align:start position:0%
+theorem and I have a nice question here
+ 
+
+ align:start position:0%
+theorem and I have a nice question here
+for you that can put Stokes theorem to
+
+ align:start position:0%
+for you that can put Stokes theorem to
+ 
+
+ align:start position:0%
+for you that can put Stokes theorem to
+the test so what I'd like you to do is
+
+ align:start position:0%
+the test so what I'd like you to do is
+ 
+
+ align:start position:0%
+the test so what I'd like you to do is
+I'd like you to consider this field F so
+
+ align:start position:0%
+I'd like you to consider this field F so
+ 
+
+ align:start position:0%
+I'd like you to consider this field F so
+its components are 2z X and Y and the
+
+ align:start position:0%
+its components are 2z X and Y and the
+ 
+
+ align:start position:0%
+its components are 2z X and Y and the
+surface s that's the top half of the
+
+ align:start position:0%
+surface s that's the top half of the
+ 
+
+ align:start position:0%
+surface s that's the top half of the
+unit sphere so it's the sphere of radius
+
+ align:start position:0%
+unit sphere so it's the sphere of radius
+ 
+
+ align:start position:0%
+unit sphere so it's the sphere of radius
+one centered at the origin but only its
+
+ align:start position:0%
+one centered at the origin but only its
+ 
+
+ align:start position:0%
+one centered at the origin but only its
+top half only the part where Z is
+
+ align:start position:0%
+top half only the part where Z is
+ 
+
+ align:start position:0%
+top half only the part where Z is
+greater than or equal to zero so what
+
+ align:start position:0%
+greater than or equal to zero so what
+ 
+
+ align:start position:0%
+greater than or equal to zero so what
+I'd like you to do is to verify Stokes
+
+ align:start position:0%
+I'd like you to do is to verify Stokes
+ 
+
+ align:start position:0%
+I'd like you to do is to verify Stokes
+theorem for this surface so that is I'd
+
+ align:start position:0%
+theorem for this surface so that is I'd
+ 
+
+ align:start position:0%
+theorem for this surface so that is I'd
+like you to compute the surface integral
+
+ align:start position:0%
+like you to compute the surface integral
+ 
+
+ align:start position:0%
+like you to compute the surface integral
+that comes from Stokes theorem for this
+
+ align:start position:0%
+that comes from Stokes theorem for this
+ 
+
+ align:start position:0%
+that comes from Stokes theorem for this
+surface and the line integral that comes
+
+ align:start position:0%
+surface and the line integral that comes
+ 
+
+ align:start position:0%
+surface and the line integral that comes
+from Stokes theorem for this surface and
+
+ align:start position:0%
+from Stokes theorem for this surface and
+ 
+
+ align:start position:0%
+from Stokes theorem for this surface and
+check that they're really equal to each
+
+ align:start position:0%
+check that they're really equal to each
+ 
+
+ align:start position:0%
+check that they're really equal to each
+other now before we start we should just
+
+ align:start position:0%
+other now before we start we should just
+ 
+
+ align:start position:0%
+other now before we start we should just
+say one brief thing about compatible
+
+ align:start position:0%
+say one brief thing about compatible
+ 
+
+ align:start position:0%
+say one brief thing about compatible
+orientation so I didn't give you any
+
+ align:start position:0%
+orientation so I didn't give you any
+ 
+
+ align:start position:0%
+orientation so I didn't give you any
+orientations but of course it doesn't
+
+ align:start position:0%
+orientations but of course it doesn't
+ 
+
+ align:start position:0%
+orientations but of course it doesn't
+matter as long as you choose ones that
+
+ align:start position:0%
+matter as long as you choose ones that
+ 
+
+ align:start position:0%
+matter as long as you choose ones that
+are compatible so if you if you think
+
+ align:start position:0%
+are compatible so if you if you think
+ 
+
+ align:start position:0%
+are compatible so if you if you think
+about your rules that you have for
+
+ align:start position:0%
+about your rules that you have for
+ 
+
+ align:start position:0%
+about your rules that you have for
+finding them so if you imagine yourself
+
+ align:start position:0%
+finding them so if you imagine yourself
+ 
+
+ align:start position:0%
+finding them so if you imagine yourself
+walking along this boundary circle with
+
+ align:start position:0%
+walking along this boundary circle with
+ 
+
+ align:start position:0%
+walking along this boundary circle with
+your left hand out over that sphere so
+
+ align:start position:0%
+your left hand out over that sphere so
+ 
+
+ align:start position:0%
+your left hand out over that sphere so
+you'll be walking in this
+
+ align:start position:0%
+you'll be walking in this
+ 
+
+ align:start position:0%
+you'll be walking in this
+counterclockwise Direction when your
+
+ align:start position:0%
+counterclockwise Direction when your
+ 
+
+ align:start position:0%
+counterclockwise Direction when your
+head is sticking out of the sphere all
+
+ align:start position:0%
+head is sticking out of the sphere all
+ 
+
+ align:start position:0%
+head is sticking out of the sphere all
+right so in other words the outward
+
+ align:start position:0%
+right so in other words the outward
+ 
+
+ align:start position:0%
+right so in other words the outward
+orientation on the sphere is compatible
+
+ align:start position:0%
+orientation on the sphere is compatible
+ 
+
+ align:start position:0%
+orientation on the sphere is compatible
+with the counterclockwise orientation on
+
+ align:start position:0%
+with the counterclockwise orientation on
+ 
+
+ align:start position:0%
+with the counterclockwise orientation on
+the on the circle that is the that is
+
+ align:start position:0%
+the on the circle that is the that is
+ 
+
+ align:start position:0%
+the on the circle that is the that is
+the boundary so let's actually put in a
+
+ align:start position:0%
+the boundary so let's actually put in a
+ 
+
+ align:start position:0%
+the boundary so let's actually put in a
+little arrow here to just indicate
+
+ align:start position:0%
+little arrow here to just indicate
+ 
+
+ align:start position:0%
+little arrow here to just indicate
+that's our orientation for the circle
+
+ align:start position:0%
+that's our orientation for the circle
+ 
+
+ align:start position:0%
+that's our orientation for the circle
+and and our normal is an outward
+
+ align:start position:0%
+and and our normal is an outward
+ 
+
+ align:start position:0%
+and and our normal is an outward
+pointing normal and let's call our
+
+ align:start position:0%
+pointing normal and let's call our
+ 
+
+ align:start position:0%
+pointing normal and let's call our
+Circle C and our s is our sphere is our
+
+ align:start position:0%
+Circle C and our s is our sphere is our
+ 
+
+ align:start position:0%
+Circle C and our s is our sphere is our
+surface okay so just so we have the same
+
+ align:start position:0%
+surface okay so just so we have the same
+ 
+
+ align:start position:0%
+surface okay so just so we have the same
+notation um good so why don't you work
+
+ align:start position:0%
+notation um good so why don't you work
+ 
+
+ align:start position:0%
+notation um good so why don't you work
+this out compute the line integral
+
+ align:start position:0%
+this out compute the line integral
+ 
+
+ align:start position:0%
+this out compute the line integral
+compute the surface integral come back
+
+ align:start position:0%
+compute the surface integral come back
+ 
+
+ align:start position:0%
+compute the surface integral come back
+and we can work them out together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hopefully you had some luck working on
+
+ align:start position:0%
+hopefully you had some luck working on
+ 
+
+ align:start position:0%
+hopefully you had some luck working on
+this problem we have two things to
+
+ align:start position:0%
+this problem we have two things to
+ 
+
+ align:start position:0%
+this problem we have two things to
+compute I think I'm going to start with
+
+ align:start position:0%
+compute I think I'm going to start with
+ 
+
+ align:start position:0%
+compute I think I'm going to start with
+the with the line integral so to compute
+
+ align:start position:0%
+the with the line integral so to compute
+ 
+
+ align:start position:0%
+the with the line integral so to compute
+the line so let me write that down line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral so what I need to do to compute
+
+ align:start position:0%
+integral so what I need to do to compute
+ 
+
+ align:start position:0%
+integral so what I need to do to compute
+the line integral is I need to compute
+
+ align:start position:0%
+the line integral is I need to compute
+ 
+
+ align:start position:0%
+the line integral is I need to compute
+so I want the
+
+ align:start position:0%
+so I want the
+ 
+
+ align:start position:0%
+so I want the
+integral over the curve
+
+ align:start position:0%
+integral over the curve
+ 
+
+ align:start position:0%
+integral over the curve
+C of f do
+
+ align:start position:0%
+C of f do
+ 
+
+ align:start position:0%
+C of f do
+Dr and so I know what f is on the on
+
+ align:start position:0%
+Dr and so I know what f is on the on
+ 
+
+ align:start position:0%
+Dr and so I know what f is on the on
+that Circle so I need to know what Dr is
+
+ align:start position:0%
+that Circle so I need to know what Dr is
+ 
+
+ align:start position:0%
+that Circle so I need to know what Dr is
+I so I need to know what R is I need a
+
+ align:start position:0%
+I so I need to know what R is I need a
+ 
+
+ align:start position:0%
+I so I need to know what R is I need a
+parameterization of that Circle well you
+
+ align:start position:0%
+parameterization of that Circle well you
+ 
+
+ align:start position:0%
+parameterization of that Circle well you
+know that's a pretty easy Circle to
+
+ align:start position:0%
+know that's a pretty easy Circle to
+ 
+
+ align:start position:0%
+know that's a pretty easy Circle to
+parameterize it's the unit circle in the
+
+ align:start position:0%
+parameterize it's the unit circle in the
+ 
+
+ align:start position:0%
+parameterize it's the unit circle in the
+XY plane so we have for C we have and
+
+ align:start position:0%
+XY plane so we have for C we have and
+ 
+
+ align:start position:0%
+XY plane so we have for C we have and
+it's and we're and we're wandering
+
+ align:start position:0%
+it's and we're and we're wandering
+ 
+
+ align:start position:0%
+it's and we're and we're wandering
+around it counterclockwise so it's it's
+
+ align:start position:0%
+around it counterclockwise so it's it's
+ 
+
+ align:start position:0%
+around it counterclockwise so it's it's
+our usual parameterization it's the one
+
+ align:start position:0%
+our usual parameterization it's the one
+ 
+
+ align:start position:0%
+our usual parameterization it's the one
+we like so we have x = cosine
+
+ align:start position:0%
+we like so we have x = cosine
+ 
+
+ align:start position:0%
+we like so we have x = cosine
+t y = sin t z where T goes from
+
+ align:start position:0%
+t y = sin t z where T goes from
+ 
+
+ align:start position:0%
+t y = sin t z where T goes from
+zero to 2 pi oh and this is in three
+
+ align:start position:0%
+zero to 2 pi oh and this is in three
+ 
+
+ align:start position:0%
+zero to 2 pi oh and this is in three
+dimensions so the other part of the
+
+ align:start position:0%
+dimensions so the other part of the
+ 
+
+ align:start position:0%
+dimensions so the other part of the
+parameterization is z equals z so this
+
+ align:start position:0%
+parameterization is z equals z so this
+ 
+
+ align:start position:0%
+parameterization is z equals z so this
+is my parameterization of this of this
+
+ align:start position:0%
+is my parameterization of this of this
+ 
+
+ align:start position:0%
+is my parameterization of this of this
+circle um okay so so let's go ahead and
+
+ align:start position:0%
+circle um okay so so let's go ahead and
+ 
+
+ align:start position:0%
+circle um okay so so let's go ahead and
+put that in so
+
+ align:start position:0%
+put that in so
+ 
+
+ align:start position:0%
+put that in so
+so the integral over
+
+ align:start position:0%
+so the integral over
+ 
+
+ align:start position:0%
+so the integral over
+C of f
+
+ align:start position:0%
+C of f
+ 
+
+ align:start position:0%
+C of f
+dot
+
+ align:start position:0%
+dot
+ 
+
+ align:start position:0%
+dot
+Dr well so it's the integral from 0 to 2
+
+ align:start position:0%
+Dr well so it's the integral from 0 to 2
+ 
+
+ align:start position:0%
+Dr well so it's the integral from 0 to 2
+pi so we've got three parts so the first
+
+ align:start position:0%
+pi so we've got three parts so the first
+ 
+
+ align:start position:0%
+pi so we've got three parts so the first
+part so f is going to be we have to go
+
+ align:start position:0%
+part so f is going to be we have to go
+ 
+
+ align:start position:0%
+part so f is going to be we have to go
+let's see so it's 2 Z XY so it's 2z DX
+
+ align:start position:0%
+let's see so it's 2 Z XY so it's 2z DX
+ 
+
+ align:start position:0%
+let's see so it's 2 Z XY so it's 2z DX
+plus X Dy + y DZ but Z is zero on this
+
+ align:start position:0%
+plus X Dy + y DZ but Z is zero on this
+ 
+
+ align:start position:0%
+plus X Dy + y DZ but Z is zero on this
+whole circle so so that piece just dies
+
+ align:start position:0%
+whole circle so so that piece just dies
+ 
+
+ align:start position:0%
+whole circle so so that piece just dies
+and DZ is also zero so that piece just
+
+ align:start position:0%
+and DZ is also zero so that piece just
+ 
+
+ align:start position:0%
+and DZ is also zero so that piece just
+dies so we're just left with xdy so this
+
+ align:start position:0%
+dies so we're just left with xdy so this
+ 
+
+ align:start position:0%
+dies so we're just left with xdy so this
+is equal to the integral of
+
+ align:start position:0%
+is equal to the integral of
+ 
+
+ align:start position:0%
+is equal to the integral of
+x Dy oh so I guess this is not from 0 to
+
+ align:start position:0%
+x Dy oh so I guess this is not from 0 to
+ 
+
+ align:start position:0%
+x Dy oh so I guess this is not from 0 to
+2 pi this is still over C sorry about
+
+ align:start position:0%
+2 pi this is still over C sorry about
+ 
+
+ align:start position:0%
+2 pi this is still over C sorry about
+that okay and now when I
+
+ align:start position:0%
+that okay and now when I
+ 
+
+ align:start position:0%
+that okay and now when I
+change to
+
+ align:start position:0%
+change to
+ 
+
+ align:start position:0%
+change to
+my parameterization okay yes right so
+
+ align:start position:0%
+my parameterization okay yes right so
+ 
+
+ align:start position:0%
+my parameterization okay yes right so
+we're this is still in DX Dy d form so
+
+ align:start position:0%
+we're this is still in DX Dy d form so
+ 
+
+ align:start position:0%
+we're this is still in DX Dy d form so
+it's it's still over C now we switch to
+
+ align:start position:0%
+it's it's still over C now we switch to
+ 
+
+ align:start position:0%
+it's it's still over C now we switch to
+the DT form so now T is going from 0 to
+
+ align:start position:0%
+the DT form so now T is going from 0 to
+ 
+
+ align:start position:0%
+the DT form so now T is going from 0 to
+2 pi okay so now we have xdy so X is
+
+ align:start position:0%
+2 pi okay so now we have xdy so X is
+ 
+
+ align:start position:0%
+2 pi okay so now we have xdy so X is
+cosine T and Dy so Y is sin T So Dy is
+
+ align:start position:0%
+cosine T and Dy so Y is sin T So Dy is
+ 
+
+ align:start position:0%
+cosine T and Dy so Y is sin T So Dy is
+cosine T DT so this is cosine T * cosine
+
+ align:start position:0%
+cosine T DT so this is cosine T * cosine
+ 
+
+ align:start position:0%
+cosine T DT so this is cosine T * cosine
+T is cosine 2qu
+
+ align:start position:0%
+T is cosine 2qu
+ 
+
+ align:start position:0%
+T is cosine 2qu
+T DT gosh so now you have to remember
+
+ align:start position:0%
+T DT gosh so now you have to remember
+ 
+
+ align:start position:0%
+T DT gosh so now you have to remember
+way back in 1801 when you learned how to
+
+ align:start position:0%
+way back in 1801 when you learned how to
+ 
+
+ align:start position:0%
+way back in 1801 when you learned how to
+compute trig integrals like this so I
+
+ align:start position:0%
+compute trig integrals like this so I
+ 
+
+ align:start position:0%
+compute trig integrals like this so I
+think the thing that we do when we have
+
+ align:start position:0%
+think the thing that we do when we have
+ 
+
+ align:start position:0%
+think the thing that we do when we have
+a cosine Square t is we use a half angle
+
+ align:start position:0%
+a cosine Square t is we use a half angle
+ 
+
+ align:start position:0%
+a cosine Square t is we use a half angle
+formula so let me come back down here
+
+ align:start position:0%
+formula so let me come back down here
+ 
+
+ align:start position:0%
+formula so let me come back down here
+just to finish this off in one board
+
+ align:start position:0%
+just to finish this off in one board
+ 
+
+ align:start position:0%
+just to finish this off in one board
+okay so cosine squ T so that's the
+
+ align:start position:0%
+okay so cosine squ T so that's the
+ 
+
+ align:start position:0%
+okay so cosine squ T so that's the
+integral from 0 to 2 pi so cosine 2qu T
+
+ align:start position:0%
+integral from 0 to 2 pi so cosine 2qu T
+ 
+
+ align:start position:0%
+integral from 0 to 2 pi so cosine 2qu T
+is 1 + cosine 2T /
+
+ align:start position:0%
+is 1 + cosine 2T /
+ 
+
+ align:start position:0%
+is 1 + cosine 2T /
+2 DT and now cosine 2T as T goes between
+
+ align:start position:0%
+2 DT and now cosine 2T as T goes between
+ 
+
+ align:start position:0%
+2 DT and now cosine 2T as T goes between
+0 and 2 pi well that's two whole Loops
+
+ align:start position:0%
+0 and 2 pi well that's two whole Loops
+ 
+
+ align:start position:0%
+0 and 2 pi well that's two whole Loops
+of it right two whole periods of Co 2T
+
+ align:start position:0%
+of it right two whole periods of Co 2T
+ 
+
+ align:start position:0%
+of it right two whole periods of Co 2T
+and you know it's a trig function it's a
+
+ align:start position:0%
+and you know it's a trig function it's a
+ 
+
+ align:start position:0%
+and you know it's a trig function it's a
+nice cosine function so the positive
+
+ align:start position:0%
+nice cosine function so the positive
+ 
+
+ align:start position:0%
+nice cosine function so the positive
+parts and the negative Parts cancel so
+
+ align:start position:0%
+parts and the negative Parts cancel so
+ 
+
+ align:start position:0%
+parts and the negative Parts cancel so
+the cosine 2T part when we integrate it
+
+ align:start position:0%
+the cosine 2T part when we integrate it
+ 
+
+ align:start position:0%
+the cosine 2T part when we integrate it
+from 0 to 2 pi that gives us zero so
+
+ align:start position:0%
+from 0 to 2 pi that gives us zero so
+ 
+
+ align:start position:0%
+from 0 to 2 pi that gives us zero so
+we're left with 1
+
+ align:start position:0%
+we're left with 1
+ 
+
+ align:start position:0%
+we're left with 1
+12 integrated from 0 to 2 pi and that's
+
+ align:start position:0%
+12 integrated from 0 to 2 pi and that's
+ 
+
+ align:start position:0%
+12 integrated from 0 to 2 pi and that's
+just going to give us 1 12 of 2 pi so
+
+ align:start position:0%
+just going to give us 1 12 of 2 pi so
+ 
+
+ align:start position:0%
+just going to give us 1 12 of 2 pi so
+that's Pi all right so good so that was
+
+ align:start position:0%
+that's Pi all right so good so that was
+ 
+
+ align:start position:0%
+that's Pi all right so good so that was
+the line integral very straightforward
+
+ align:start position:0%
+the line integral very straightforward
+ 
+
+ align:start position:0%
+the line integral very straightforward
+thing we had our Circle back here we had
+
+ align:start position:0%
+thing we had our Circle back here we had
+ 
+
+ align:start position:0%
+thing we had our Circle back here we had
+our Circle we had our field so we
+
+ align:start position:0%
+our Circle we had our field so we
+ 
+
+ align:start position:0%
+our Circle we had our field so we
+parameterized the curve that is the
+
+ align:start position:0%
+parameterized the curve that is the
+ 
+
+ align:start position:0%
+parameterized the curve that is the
+circle that is the boundary and then we
+
+ align:start position:0%
+circle that is the boundary and then we
+ 
+
+ align:start position:0%
+circle that is the boundary and then we
+just computed the line integral and it
+
+ align:start position:0%
+just computed the line integral and it
+ 
+
+ align:start position:0%
+just computed the line integral and it
+was a nice easy one to do you had to
+
+ align:start position:0%
+was a nice easy one to do you had to
+ 
+
+ align:start position:0%
+was a nice easy one to do you had to
+remember one little trig identity in
+
+ align:start position:0%
+remember one little trig identity in
+ 
+
+ align:start position:0%
+remember one little trig identity in
+order to do it all right that's the
+
+ align:start position:0%
+order to do it all right that's the
+ 
+
+ align:start position:0%
+order to do it all right that's the
+first one so let's
+
+ align:start position:0%
+first one so let's
+ 
+
+ align:start position:0%
+first one so let's
+uh let's go on to the surface
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral so the surface integral that
+
+ align:start position:0%
+integral so the surface integral that
+ 
+
+ align:start position:0%
+integral so the surface integral that
+you have to compute in Stokes theorem is
+
+ align:start position:0%
+you have to compute in Stokes theorem is
+ 
+
+ align:start position:0%
+you have to compute in Stokes theorem is
+you have to compute the double
+
+ align:start position:0%
+you have to compute the double
+ 
+
+ align:start position:0%
+you have to compute the double
+integral over your
+
+ align:start position:0%
+integral over your
+ 
+
+ align:start position:0%
+integral over your
+surface of the curl of
+
+ align:start position:0%
+surface of the curl of
+ 
+
+ align:start position:0%
+surface of the curl of
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+dotn with respect to surface area so
+
+ align:start position:0%
+dotn with respect to surface area so
+ 
+
+ align:start position:0%
+dotn with respect to surface area so
+this is the this is the integral we want
+
+ align:start position:0%
+this is the this is the integral we want
+ 
+
+ align:start position:0%
+this is the this is the integral we want
+to compute here this so okay so first
+
+ align:start position:0%
+to compute here this so okay so first
+ 
+
+ align:start position:0%
+to compute here this so okay so first
+thing we're going to need we're going to
+
+ align:start position:0%
+thing we're going to need we're going to
+ 
+
+ align:start position:0%
+thing we're going to need we're going to
+we're going to need to find the curl of
+
+ align:start position:0%
+we're going to need to find the curl of
+ 
+
+ align:start position:0%
+we're going to need to find the curl of
+F Well let's see so F let's let me just
+
+ align:start position:0%
+F Well let's see so F let's let me just
+ 
+
+ align:start position:0%
+F Well let's see so F let's let me just
+write it here so we don't have to walk
+
+ align:start position:0%
+write it here so we don't have to walk
+ 
+
+ align:start position:0%
+write it here so we don't have to walk
+all the way back over there so f is what
+
+ align:start position:0%
+all the way back over there so f is what
+ 
+
+ align:start position:0%
+all the way back over there so f is what
+is it it's
+
+ align:start position:0%
+is it it's
+ 
+
+ align:start position:0%
+is it it's
+2z
+
+ align:start position:0%
+2z
+ 
+
+ align:start position:0%
+2z
+X Y so curl of f okay you should have
+
+ align:start position:0%
+X Y so curl of f okay you should have
+ 
+
+ align:start position:0%
+X Y so curl of f okay you should have
+lots of experience Computing Curls by
+
+ align:start position:0%
+lots of experience Computing Curls by
+ 
+
+ align:start position:0%
+lots of experience Computing Curls by
+now but let's see okay so it's going to
+
+ align:start position:0%
+now but let's see okay so it's going to
+ 
+
+ align:start position:0%
+now but let's see okay so it's going to
+be this I I always think of it so we've
+
+ align:start position:0%
+be this I I always think of it so we've
+ 
+
+ align:start position:0%
+be this I I always think of it so we've
+got these little 2 by two determinants
+
+ align:start position:0%
+got these little 2 by two determinants
+ 
+
+ align:start position:0%
+got these little 2 by two determinants
+with the partial derivatives in them but
+
+ align:start position:0%
+with the partial derivatives in them but
+ 
+
+ align:start position:0%
+with the partial derivatives in them but
+most of those are going to be zero we've
+
+ align:start position:0%
+most of those are going to be zero we've
+ 
+
+ align:start position:0%
+most of those are going to be zero we've
+got a dxx term that's coming up in k and
+
+ align:start position:0%
+got a dxx term that's coming up in k and
+ 
+
+ align:start position:0%
+got a dxx term that's coming up in k and
+a Dy y term that's coming up in I and a
+
+ align:start position:0%
+a Dy y term that's coming up in I and a
+ 
+
+ align:start position:0%
+a Dy y term that's coming up in I and a
+DZ 2z term term that's coming up in in J
+
+ align:start position:0%
+DZ 2z term term that's coming up in in J
+ 
+
+ align:start position:0%
+DZ 2z term term that's coming up in in J
+so okay so almost all half the terms are
+
+ align:start position:0%
+so okay so almost all half the terms are
+ 
+
+ align:start position:0%
+so okay so almost all half the terms are
+zero the others are really easy to
+
+ align:start position:0%
+zero the others are really easy to
+ 
+
+ align:start position:0%
+zero the others are really easy to
+compute I trust that you can also
+
+ align:start position:0%
+compute I trust that you can also
+ 
+
+ align:start position:0%
+compute I trust that you can also
+compute and get that the curl is one 12
+
+ align:start position:0%
+compute and get that the curl is one 12
+ 
+
+ align:start position:0%
+compute and get that the curl is one 12
+one here okay so this is F this is curl
+
+ align:start position:0%
+one here okay so this is F this is curl
+ 
+
+ align:start position:0%
+one here okay so this is F this is curl
+of f great so okay so that's curl of f
+
+ align:start position:0%
+of f great so okay so that's curl of f
+ 
+
+ align:start position:0%
+of f great so okay so that's curl of f
+so now we need
+
+ align:start position:0%
+so now we need
+ 
+
+ align:start position:0%
+so now we need
+n well let's think so we need we need
+
+ align:start position:0%
+n well let's think so we need we need
+ 
+
+ align:start position:0%
+n well let's think so we need we need
+the unit normal to our surface and we
+
+ align:start position:0%
+the unit normal to our surface and we
+ 
+
+ align:start position:0%
+the unit normal to our surface and we
+said all right so back at the beginning
+
+ align:start position:0%
+said all right so back at the beginning
+ 
+
+ align:start position:0%
+said all right so back at the beginning
+before before we started we said it was
+
+ align:start position:0%
+before before we started we said it was
+ 
+
+ align:start position:0%
+before before we started we said it was
+the outward point normal so we need the
+
+ align:start position:0%
+the outward point normal so we need the
+ 
+
+ align:start position:0%
+the outward point normal so we need the
+outward pointing normal well this is a
+
+ align:start position:0%
+outward pointing normal well this is a
+ 
+
+ align:start position:0%
+outward pointing normal well this is a
+sphere right so so the normal is
+
+ align:start position:0%
+sphere right so so the normal is
+ 
+
+ align:start position:0%
+sphere right so so the normal is
+parallel to the position Vector so that
+
+ align:start position:0%
+parallel to the position Vector so that
+ 
+
+ align:start position:0%
+parallel to the position Vector so that
+means n should be parallel
+
+ align:start position:0%
+means n should be parallel
+ 
+
+ align:start position:0%
+means n should be parallel
+to should be parallel to the vector XYZ
+
+ align:start position:0%
+to should be parallel to the vector XYZ
+ 
+
+ align:start position:0%
+to should be parallel to the vector XYZ
+the position Vector so n should be
+
+ align:start position:0%
+the position Vector so n should be
+ 
+
+ align:start position:0%
+the position Vector so n should be
+parallel to this Vector XYZ but in fact
+
+ align:start position:0%
+parallel to this Vector XYZ but in fact
+ 
+
+ align:start position:0%
+parallel to this Vector XYZ but in fact
+it we're even better than that we're on
+
+ align:start position:0%
+it we're even better than that we're on
+ 
+
+ align:start position:0%
+it we're even better than that we're on
+a unit sphere so the the position Vector
+
+ align:start position:0%
+a unit sphere so the the position Vector
+ 
+
+ align:start position:0%
+a unit sphere so the the position Vector
+has length one so n should be pointing
+
+ align:start position:0%
+has length one so n should be pointing
+ 
+
+ align:start position:0%
+has length one so n should be pointing
+in the same direction is this vector and
+
+ align:start position:0%
+in the same direction is this vector and
+ 
+
+ align:start position:0%
+in the same direction is this vector and
+they both have length one so they better
+
+ align:start position:0%
+they both have length one so they better
+ 
+
+ align:start position:0%
+they both have length one so they better
+be equal to each
+
+ align:start position:0%
+be equal to each
+ 
+
+ align:start position:0%
+be equal to each
+other great so so this unit normal n is
+
+ align:start position:0%
+other great so so this unit normal n is
+ 
+
+ align:start position:0%
+other great so so this unit normal n is
+is just this very simple Vector XYZ you
+
+ align:start position:0%
+is just this very simple Vector XYZ you
+ 
+
+ align:start position:0%
+is just this very simple Vector XYZ you
+know if it had been a bigger sphere then
+
+ align:start position:0%
+know if it had been a bigger sphere then
+ 
+
+ align:start position:0%
+know if it had been a bigger sphere then
+you might have to you would have to
+
+ align:start position:0%
+you might have to you would have to
+ 
+
+ align:start position:0%
+you might have to you would have to
+divide this by by the radius to scale it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+appropriately all right so we've got
+
+ align:start position:0%
+appropriately all right so we've got
+ 
+
+ align:start position:0%
+appropriately all right so we've got
+curl F we've got n so the thing that we
+
+ align:start position:0%
+curl F we've got n so the thing that we
+ 
+
+ align:start position:0%
+curl F we've got n so the thing that we
+want okay so the integral that we
+
+ align:start position:0%
+want okay so the integral that we
+ 
+
+ align:start position:0%
+want okay so the integral that we
+want is
+
+ align:start position:0%
+want is
+ 
+
+ align:start position:0%
+want is
+this double
+
+ align:start position:0%
+this double
+ 
+
+ align:start position:0%
+this double
+integral over the surface okay of curl
+
+ align:start position:0%
+integral over the surface okay of curl
+ 
+
+ align:start position:0%
+integral over the surface okay of curl
+f.n so that's x + 2 y +
+
+ align:start position:0%
+f.n so that's x + 2 y +
+ 
+
+ align:start position:0%
+f.n so that's x + 2 y +
+z with respect to surface
+
+ align:start position:0%
+z with respect to surface
+ 
+
+ align:start position:0%
+z with respect to surface
+area okay well now we've just got a
+
+ align:start position:0%
+area okay well now we've just got a
+ 
+
+ align:start position:0%
+area okay well now we've just got a
+surface integral it's over a sphere not
+
+ align:start position:0%
+surface integral it's over a sphere not
+ 
+
+ align:start position:0%
+surface integral it's over a sphere not
+a Terri well a hemisphere not a terrible
+
+ align:start position:0%
+a Terri well a hemisphere not a terrible
+ 
+
+ align:start position:0%
+a Terri well a hemisphere not a terrible
+thing to parameterize so okay so that's
+
+ align:start position:0%
+thing to parameterize so okay so that's
+ 
+
+ align:start position:0%
+thing to parameterize so okay so that's
+what we should do we should go in we
+
+ align:start position:0%
+what we should do we should go in we
+ 
+
+ align:start position:0%
+what we should do we should go in we
+should parameterize it and then we
+
+ align:start position:0%
+should parameterize it and then we
+ 
+
+ align:start position:0%
+should parameterize it and then we
+should you know just compute it like a
+
+ align:start position:0%
+should you know just compute it like a
+ 
+
+ align:start position:0%
+should you know just compute it like a
+surface integral like we like we know
+
+ align:start position:0%
+surface integral like we like we know
+ 
+
+ align:start position:0%
+surface integral like we like we know
+how to do so um before we start though I
+
+ align:start position:0%
+how to do so um before we start though I
+ 
+
+ align:start position:0%
+how to do so um before we start though I
+want to make one little observation well
+
+ align:start position:0%
+want to make one little observation well
+ 
+
+ align:start position:0%
+want to make one little observation well
+maybe two little observations so we can
+
+ align:start position:0%
+maybe two little observations so we can
+ 
+
+ align:start position:0%
+maybe two little observations so we can
+simplify this all right
+
+ align:start position:0%
+simplify this all right
+ 
+
+ align:start position:0%
+simplify this all right
+X we're integrating X over the surface
+
+ align:start position:0%
+X we're integrating X over the surface
+ 
+
+ align:start position:0%
+X we're integrating X over the surface
+of a hemisphere centered at the origin
+
+ align:start position:0%
+of a hemisphere centered at the origin
+ 
+
+ align:start position:0%
+of a hemisphere centered at the origin
+this hemisphere is really symmetric and
+
+ align:start position:0%
+this hemisphere is really symmetric and
+ 
+
+ align:start position:0%
+this hemisphere is really symmetric and
+on the Nega the back side the part where
+
+ align:start position:0%
+on the Nega the back side the part where
+ 
+
+ align:start position:0%
+on the Nega the back side the part where
+X is negative we're getting negative
+
+ align:start position:0%
+X is negative we're getting negative
+ 
+
+ align:start position:0%
+X is negative we're getting negative
+contributions from X and on the front
+
+ align:start position:0%
+contributions from X and on the front
+ 
+
+ align:start position:0%
+contributions from X and on the front
+side where X is positive we're getting
+
+ align:start position:0%
+side where X is positive we're getting
+ 
+
+ align:start position:0%
+side where X is positive we're getting
+positive contributions from X and
+
+ align:start position:0%
+positive contributions from X and
+ 
+
+ align:start position:0%
+positive contributions from X and
+because this sphere is totally symmetric
+
+ align:start position:0%
+because this sphere is totally symmetric
+ 
+
+ align:start position:0%
+because this sphere is totally symmetric
+those just cancel out
+
+ align:start position:0%
+those just cancel out
+ 
+
+ align:start position:0%
+those just cancel out
+completely so when we integrate x over
+
+ align:start position:0%
+completely so when we integrate x over
+ 
+
+ align:start position:0%
+completely so when we integrate x over
+the whole
+
+ align:start position:0%
+the whole
+ 
+
+ align:start position:0%
+the whole
+sphere over the whole
+
+ align:start position:0%
+sphere over the whole
+ 
+
+ align:start position:0%
+sphere over the whole
+hemisphere it just it just kills itself
+
+ align:start position:0%
+hemisphere it just it just kills itself
+ 
+
+ align:start position:0%
+hemisphere it just it just kills itself
+I mean the negative Parts kill the
+
+ align:start position:0%
+I mean the negative Parts kill the
+ 
+
+ align:start position:0%
+I mean the negative Parts kill the
+positive parts we just get zero
+
+ align:start position:0%
+positive parts we just get zero
+ 
+
+ align:start position:0%
+positive parts we just get zero
+similarly this hemisphere is symmetric
+
+ align:start position:0%
+similarly this hemisphere is symmetric
+ 
+
+ align:start position:0%
+similarly this hemisphere is symmetric
+between its left side and its right side
+
+ align:start position:0%
+between its left side and its right side
+ 
+
+ align:start position:0%
+between its left side and its right side
+and so the parts where y are negative
+
+ align:start position:0%
+and so the parts where y are negative
+ 
+
+ align:start position:0%
+and so the parts where y are negative
+cancel out exactly where the parts where
+
+ align:start position:0%
+cancel out exactly where the parts where
+ 
+
+ align:start position:0%
+cancel out exactly where the parts where
+y are positive so a simplifying step we
+
+ align:start position:0%
+y are positive so a simplifying step we
+ 
+
+ align:start position:0%
+y are positive so a simplifying step we
+can realize right at the beginning that
+
+ align:start position:0%
+can realize right at the beginning that
+ 
+
+ align:start position:0%
+can realize right at the beginning that
+this is actually just the integral over
+
+ align:start position:0%
+this is actually just the integral over
+ 
+
+ align:start position:0%
+this is actually just the integral over
+s of
+
+ align:start position:0%
+s of
+ 
+
+ align:start position:0%
+s of
+Z with respect to surface area now if
+
+ align:start position:0%
+Z with respect to surface area now if
+ 
+
+ align:start position:0%
+Z with respect to surface area now if
+you didn't realize that that's okay what
+
+ align:start position:0%
+you didn't realize that that's okay what
+ 
+
+ align:start position:0%
+you didn't realize that that's okay what
+you would have done is you would have
+
+ align:start position:0%
+you would have done is you would have
+ 
+
+ align:start position:0%
+you would have done is you would have
+done the parameterization that we're
+
+ align:start position:0%
+done the parameterization that we're
+ 
+
+ align:start position:0%
+done the parameterization that we're
+about to do and in doing that
+
+ align:start position:0%
+about to do and in doing that
+ 
+
+ align:start position:0%
+about to do and in doing that
+parameterization you would have found
+
+ align:start position:0%
+parameterization you would have found
+ 
+
+ align:start position:0%
+parameterization you would have found
+that you were integrating something like
+
+ align:start position:0%
+that you were integrating something like
+ 
+
+ align:start position:0%
+that you were integrating something like
+cosine Theta between 0 and 2 pi or
+
+ align:start position:0%
+cosine Theta between 0 and 2 pi or
+ 
+
+ align:start position:0%
+cosine Theta between 0 and 2 pi or
+something like this and that would have
+
+ align:start position:0%
+something like this and that would have
+ 
+
+ align:start position:0%
+something like this and that would have
+given you zero so you would have you
+
+ align:start position:0%
+given you zero so you would have you
+ 
+
+ align:start position:0%
+given you zero so you would have you
+would have found this simp
+
+ align:start position:0%
+would have found this simp
+ 
+
+ align:start position:0%
+would have found this simp
+syry even if you didn't realize it right
+
+ align:start position:0%
+syry even if you didn't realize it right
+ 
+
+ align:start position:0%
+syry even if you didn't realize it right
+now you would have found it in the
+
+ align:start position:0%
+now you would have found it in the
+ 
+
+ align:start position:0%
+now you would have found it in the
+process of computing this this integral
+
+ align:start position:0%
+process of computing this this integral
+ 
+
+ align:start position:0%
+process of computing this this integral
+but but it's a little bit easier on us
+
+ align:start position:0%
+but but it's a little bit easier on us
+ 
+
+ align:start position:0%
+but but it's a little bit easier on us
+if we if we sort of can recognize that
+
+ align:start position:0%
+if we if we sort of can recognize that
+ 
+
+ align:start position:0%
+if we if we sort of can recognize that
+symmetry first now notice that Z doesn't
+
+ align:start position:0%
+symmetry first now notice that Z doesn't
+ 
+
+ align:start position:0%
+symmetry first now notice that Z doesn't
+cancel because this is just the top
+
+ align:start position:0%
+cancel because this is just the top
+ 
+
+ align:start position:0%
+cancel because this is just the top
+hemisphere so it doesn't have a bottom
+
+ align:start position:0%
+hemisphere so it doesn't have a bottom
+ 
+
+ align:start position:0%
+hemisphere so it doesn't have a bottom
+half to cancel out with right so the Z
+
+ align:start position:0%
+half to cancel out with right so the Z
+ 
+
+ align:start position:0%
+half to cancel out with right so the Z
+part we can't use this this easy
+
+ align:start position:0%
+part we can't use this this easy
+ 
+
+ align:start position:0%
+part we can't use this this easy
+analysis on if we were if we integrated
+
+ align:start position:0%
+analysis on if we were if we integrated
+ 
+
+ align:start position:0%
+analysis on if we were if we integrated
+this Z over the whole sphere if we had
+
+ align:start position:0%
+this Z over the whole sphere if we had
+ 
+
+ align:start position:0%
+this Z over the whole sphere if we had
+the other half of the sphere well then
+
+ align:start position:0%
+the other half of the sphere well then
+ 
+
+ align:start position:0%
+the other half of the sphere well then
+that would also give us zero but but we
+
+ align:start position:0%
+that would also give us zero but but we
+ 
+
+ align:start position:0%
+that would also give us zero but but we
+only have the half of the sphere the top
+
+ align:start position:0%
+only have the half of the sphere the top
+ 
+
+ align:start position:0%
+only have the half of the sphere the top
+half of the sphere so it's going to give
+
+ align:start position:0%
+half of the sphere so it's going to give
+ 
+
+ align:start position:0%
+half of the sphere so it's going to give
+us something positive because Z is
+
+ align:start position:0%
+us something positive because Z is
+ 
+
+ align:start position:0%
+us something positive because Z is
+always positive up there okay so let's
+
+ align:start position:0%
+always positive up there okay so let's
+ 
+
+ align:start position:0%
+always positive up there okay so let's
+let's actually set about parameterizing
+
+ align:start position:0%
+let's actually set about parameterizing
+ 
+
+ align:start position:0%
+let's actually set about parameterizing
+it we want to parameterize the unit
+
+ align:start position:0%
+it we want to parameterize the unit
+ 
+
+ align:start position:0%
+it we want to parameterize the unit
+sphere well okay so we have our standard
+
+ align:start position:0%
+sphere well okay so we have our standard
+ 
+
+ align:start position:0%
+sphere well okay so we have our standard
+parameterization that comes from
+
+ align:start position:0%
+parameterization that comes from
+ 
+
+ align:start position:0%
+parameterization that comes from
+spherical coordinates so row is just one
+
+ align:start position:0%
+spherical coordinates so row is just one
+ 
+
+ align:start position:0%
+spherical coordinates so row is just one
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+X is equal to it's going to
+
+ align:start position:0%
+X is equal to it's going to
+ 
+
+ align:start position:0%
+X is equal to it's going to
+be cosine you know what I always get a
+
+ align:start position:0%
+be cosine you know what I always get a
+ 
+
+ align:start position:0%
+be cosine you know what I always get a
+little confused so I'm just going to
+
+ align:start position:0%
+little confused so I'm just going to
+ 
+
+ align:start position:0%
+little confused so I'm just going to
+check carefully that I'm doing doing
+
+ align:start position:0%
+check carefully that I'm doing doing
+ 
+
+ align:start position:0%
+check carefully that I'm doing doing
+this perfectly right X is going to be
+
+ align:start position:0%
+this perfectly right X is going to be
+ 
+
+ align:start position:0%
+this perfectly right X is going to be
+yes cosine Theta sin V good Y is going
+
+ align:start position:0%
+yes cosine Theta sin V good Y is going
+ 
+
+ align:start position:0%
+yes cosine Theta sin V good Y is going
+to be sin
+
+ align:start position:0%
+to be sin
+ 
+
+ align:start position:0%
+to be sin
+Theta sinine V and
+
+ align:start position:0%
+Theta sinine V and
+ 
+
+ align:start position:0%
+Theta sinine V and
+Z is going to be
+
+ align:start position:0%
+Z is going to be
+ 
+
+ align:start position:0%
+Z is going to be
+cosine Fe so that's our parameterization
+
+ align:start position:0%
+cosine Fe so that's our parameterization
+ 
+
+ align:start position:0%
+cosine Fe so that's our parameterization
+okay but this this we need bounds of
+
+ align:start position:0%
+okay but this this we need bounds of
+ 
+
+ align:start position:0%
+okay but this this we need bounds of
+course on Theta and v in order to
+
+ align:start position:0%
+course on Theta and v in order to
+ 
+
+ align:start position:0%
+course on Theta and v in order to
+properly describe just this hemisphere
+
+ align:start position:0%
+properly describe just this hemisphere
+ 
+
+ align:start position:0%
+properly describe just this hemisphere
+so let's think so Fe we want the
+
+ align:start position:0%
+so let's think so Fe we want the
+ 
+
+ align:start position:0%
+so let's think so Fe we want the
+hemisphere that goes from the Z axis
+
+ align:start position:0%
+hemisphere that goes from the Z axis
+ 
+
+ align:start position:0%
+hemisphere that goes from the Z axis
+down to the XY plane so that means we
+
+ align:start position:0%
+down to the XY plane so that means we
+ 
+
+ align:start position:0%
+down to the XY plane so that means we
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+0o to be less than or equal to F to be
+
+ align:start position:0%
+0o to be less than or equal to F to be
+ 
+
+ align:start position:0%
+0o to be less than or equal to F to be
+less than or equal to Pi / 2 right
+
+ align:start position:0%
+less than or equal to Pi / 2 right
+ 
+
+ align:start position:0%
+less than or equal to Pi / 2 right
+that'll give us that just that top half
+
+ align:start position:0%
+that'll give us that just that top half
+ 
+
+ align:start position:0%
+that'll give us that just that top half
+and we want the whole thing we want to
+
+ align:start position:0%
+and we want the whole thing we want to
+ 
+
+ align:start position:0%
+and we want the whole thing we want to
+go all the way around so we want zero
+
+ align:start position:0%
+go all the way around so we want zero
+ 
+
+ align:start position:0%
+go all the way around so we want zero
+less than or equal to Theta less than or
+
+ align:start position:0%
+less than or equal to Theta less than or
+ 
+
+ align:start position:0%
+less than or equal to Theta less than or
+equal to 2
+
+ align:start position:0%
+equal to 2
+ 
+
+ align:start position:0%
+equal to 2
+pi so this is okay so this is our what x
+
+ align:start position:0%
+pi so this is okay so this is our what x
+ 
+
+ align:start position:0%
+pi so this is okay so this is our what x
+y and z are these are the bounds for our
+
+ align:start position:0%
+y and z are these are the bounds for our
+ 
+
+ align:start position:0%
+y and z are these are the bounds for our
+parameters the and Theta um now the only
+
+ align:start position:0%
+parameters the and Theta um now the only
+ 
+
+ align:start position:0%
+parameters the and Theta um now the only
+other thing we need is we need to know
+
+ align:start position:0%
+other thing we need is we need to know
+ 
+
+ align:start position:0%
+other thing we need is we need to know
+what DS is so in spherical coordinates
+
+ align:start position:0%
+what DS is so in spherical coordinates
+ 
+
+ align:start position:0%
+what DS is so in spherical coordinates
+we know that
+
+ align:start position:0%
+we know that
+ 
+
+ align:start position:0%
+we know that
+DS I'll put it right above here so DS is
+
+ align:start position:0%
+DS I'll put it right above here so DS is
+ 
+
+ align:start position:0%
+DS I'll put it right above here so DS is
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+to sin
+
+ align:start position:0%
+to sin
+ 
+
+ align:start position:0%
+to sin
+v d Fe D Theta let me again just double
+
+ align:start position:0%
+v d Fe D Theta let me again just double
+ 
+
+ align:start position:0%
+v d Fe D Theta let me again just double
+check that that I'm not doing anything
+
+ align:start position:0%
+check that that I'm not doing anything
+ 
+
+ align:start position:0%
+check that that I'm not doing anything
+silly so DS is equal to sin v d v d
+
+ align:start position:0%
+silly so DS is equal to sin v d v d
+ 
+
+ align:start position:0%
+silly so DS is equal to sin v d v d
+Theta so we've got our parameterization
+
+ align:start position:0%
+Theta so we've got our parameterization
+ 
+
+ align:start position:0%
+Theta so we've got our parameterization
+we've got our bounds on our parameters
+
+ align:start position:0%
+we've got our bounds on our parameters
+ 
+
+ align:start position:0%
+we've got our bounds on our parameters
+we know what DS is and we have the
+
+ align:start position:0%
+we know what DS is and we have the
+ 
+
+ align:start position:0%
+we know what DS is and we have the
+integral that we want to compute so now
+
+ align:start position:0%
+integral that we want to compute so now
+ 
+
+ align:start position:0%
+integral that we want to compute so now
+we just have to substitute everything in
+
+ align:start position:0%
+we just have to substitute everything in
+ 
+
+ align:start position:0%
+we just have to substitute everything in
+and actually compute it as an iterated
+
+ align:start position:0%
+and actually compute it as an iterated
+ 
+
+ align:start position:0%
+and actually compute it as an iterated
+integral great so let's do that so this
+
+ align:start position:0%
+integral great so let's do that so this
+ 
+
+ align:start position:0%
+integral great so let's do that so this
+integral that we want I'm going to write
+
+ align:start position:0%
+integral that we want I'm going to write
+ 
+
+ align:start position:0%
+integral that we want I'm going to write
+a big equal sign that's going to carry
+
+ align:start position:0%
+a big equal sign that's going to carry
+ 
+
+ align:start position:0%
+a big equal sign that's going to carry
+me all the way up here
+
+ align:start position:0%
+me all the way up here
+ 
+
+ align:start position:0%
+me all the way up here
+that's an equal sign all right so our
+
+ align:start position:0%
+that's an equal sign all right so our
+ 
+
+ align:start position:0%
+that's an equal sign all right so our
+integral the integral over s of Z with
+
+ align:start position:0%
+integral the integral over s of Z with
+ 
+
+ align:start position:0%
+integral the integral over s of Z with
+respect to surface area so Z becomes
+
+ align:start position:0%
+respect to surface area so Z becomes
+ 
+
+ align:start position:0%
+respect to surface area so Z becomes
+cosine V so we've got our double
+
+ align:start position:0%
+cosine V so we've got our double
+ 
+
+ align:start position:0%
+cosine V so we've got our double
+integral becomes an iterated integral Z
+
+ align:start position:0%
+integral becomes an iterated integral Z
+ 
+
+ align:start position:0%
+integral becomes an iterated integral Z
+becomes cosine V DS becomes sin Fe d f d
+
+ align:start position:0%
+becomes cosine V DS becomes sin Fe d f d
+ 
+
+ align:start position:0%
+becomes cosine V DS becomes sin Fe d f d
+Theta sin
+
+ align:start position:0%
+Theta sin
+ 
+
+ align:start position:0%
+Theta sin
+v d
+
+ align:start position:0%
+v d
+ 
+
+ align:start position:0%
+v d
+v d Theta and our bound so let's see V
+
+ align:start position:0%
+v d Theta and our bound so let's see V
+ 
+
+ align:start position:0%
+v d Theta and our bound so let's see V
+we said is going from 0 to Pi / 2 0 to
+
+ align:start position:0%
+we said is going from 0 to Pi / 2 0 to
+ 
+
+ align:start position:0%
+we said is going from 0 to Pi / 2 0 to
+Pi / 2 and Theta is going from 0 to 2
+
+ align:start position:0%
+Pi / 2 and Theta is going from 0 to 2
+ 
+
+ align:start position:0%
+Pi / 2 and Theta is going from 0 to 2
+pi okay so now we just have a nice
+
+ align:start position:0%
+pi okay so now we just have a nice
+ 
+
+ align:start position:0%
+pi okay so now we just have a nice
+straightforward iterated integral here
+
+ align:start position:0%
+straightforward iterated integral here
+ 
+
+ align:start position:0%
+straightforward iterated integral here
+to compute so let's do the inner one
+
+ align:start position:0%
+to compute so let's do the inner one
+ 
+
+ align:start position:0%
+to compute so let's do the inner one
+first so we're
+
+ align:start position:0%
+first so we're
+ 
+
+ align:start position:0%
+first so we're
+Computing the inner integral is the
+
+ align:start position:0%
+Computing the inner integral is the
+ 
+
+ align:start position:0%
+Computing the inner integral is the
+integral from
+
+ align:start position:0%
+integral from
+ 
+
+ align:start position:0%
+integral from
+0 to Pi / 2 of cosine
+
+ align:start position:0%
+0 to Pi / 2 of cosine
+ 
+
+ align:start position:0%
+0 to Pi / 2 of cosine
+F sin
+
+ align:start position:0%
+F sin
+ 
+
+ align:start position:0%
+F sin
+f d Fe and okay so this is you know
+
+ align:start position:0%
+f d Fe and okay so this is you know
+ 
+
+ align:start position:0%
+f d Fe and okay so this is you know
+bunch of different ways you could do
+
+ align:start position:0%
+bunch of different ways you could do
+ 
+
+ align:start position:0%
+bunch of different ways you could do
+this if you wanted to get fancy you
+
+ align:start position:0%
+this if you wanted to get fancy you
+ 
+
+ align:start position:0%
+this if you wanted to get fancy you
+could do a double angle formula here but
+
+ align:start position:0%
+could do a double angle formula here but
+ 
+
+ align:start position:0%
+could do a double angle formula here but
+that's really more fancy than you need
+
+ align:start position:0%
+that's really more fancy than you need
+ 
+
+ align:start position:0%
+that's really more fancy than you need
+because this is like sinine Fe time D
+
+ align:start position:0%
+because this is like sinine Fe time D
+ 
+
+ align:start position:0%
+because this is like sinine Fe time D
+sin Fe right so this is equal to you
+
+ align:start position:0%
+sin Fe right so this is equal to you
+ 
+
+ align:start position:0%
+sin Fe right so this is equal to you
+know you could another way of saying
+
+ align:start position:0%
+know you could another way of saying
+ 
+
+ align:start position:0%
+know you could another way of saying
+that is you can make the substitution U
+
+ align:start position:0%
+that is you can make the substitution U
+ 
+
+ align:start position:0%
+that is you can make the substitution U
+equals sin V anyhow you this is all Cal
+
+ align:start position:0%
+equals sin V anyhow you this is all Cal
+ 
+
+ align:start position:0%
+equals sin V anyhow you this is all Cal
+one stuff that hopefully you're pretty
+
+ align:start position:0%
+one stuff that hopefully you're pretty
+ 
+
+ align:start position:0%
+one stuff that hopefully you're pretty
+familiar with so okay so this is equal
+
+ align:start position:0%
+familiar with so okay so this is equal
+ 
+
+ align:start position:0%
+familiar with so okay so this is equal
+to all right so in the end we get sin^2
+
+ align:start position:0%
+to all right so in the end we get sin^2
+ 
+
+ align:start position:0%
+to all right so in the end we get sin^2
+F / 2 between 0 and pi/ 2 okay so we
+
+ align:start position:0%
+F / 2 between 0 and pi/ 2 okay so we
+ 
+
+ align:start position:0%
+F / 2 between 0 and pi/ 2 okay so we
+plug this in so sin^2 Pi / 2 that's 12
+
+ align:start position:0%
+plug this in so sin^2 Pi / 2 that's 12
+ 
+
+ align:start position:0%
+plug this in so sin^2 Pi / 2 that's 12
+minus sin^2 0/ 2 is 0 over 2 so it's
+
+ align:start position:0%
+minus sin^2 0/ 2 is 0 over 2 so it's
+ 
+
+ align:start position:0%
+minus sin^2 0/ 2 is 0 over 2 so it's
+just 1/2 right so the inner integral is
+
+ align:start position:0%
+just 1/2 right so the inner integral is
+ 
+
+ align:start position:0%
+just 1/2 right so the inner integral is
+1/2 so let's see about the outer one
+
+ align:start position:0%
+1/2 so let's see about the outer one
+ 
+
+ align:start position:0%
+1/2 so let's see about the outer one
+outer integral is just the integral from
+
+ align:start position:0%
+outer integral is just the integral from
+ 
+
+ align:start position:0%
+outer integral is just the integral from
+0 to 2 pi D Theta of whatever the inner
+
+ align:start position:0%
+0 to 2 pi D Theta of whatever the inner
+ 
+
+ align:start position:0%
+0 to 2 pi D Theta of whatever the inner
+integral was well the inner integral was
+
+ align:start position:0%
+integral was well the inner integral was
+ 
+
+ align:start position:0%
+integral was well the inner integral was
+1/2 so the integral from 0 to 2 pi of
+
+ align:start position:0%
+1/2 so the integral from 0 to 2 pi of
+ 
+
+ align:start position:0%
+1/2 so the integral from 0 to 2 pi of
+1/2 is pi straight forward good so okay
+
+ align:start position:0%
+1/2 is pi straight forward good so okay
+ 
+
+ align:start position:0%
+1/2 is pi straight forward good so okay
+so that's what the service integral
+
+ align:start position:0%
+so that's what the service integral
+ 
+
+ align:start position:0%
+so that's what the service integral
+gives us so let's go back here and
+
+ align:start position:0%
+gives us so let's go back here and
+ 
+
+ align:start position:0%
+gives us so let's go back here and
+compare so way back at the
+
+ align:start position:0%
+compare so way back at the
+ 
+
+ align:start position:0%
+compare so way back at the
+beginning of this recitation we did the
+
+ align:start position:0%
+beginning of this recitation we did the
+ 
+
+ align:start position:0%
+beginning of this recitation we did the
+line inter integral for this for this
+
+ align:start position:0%
+line inter integral for this for this
+ 
+
+ align:start position:0%
+line inter integral for this for this
+circle that's the boundary of this
+
+ align:start position:0%
+circle that's the boundary of this
+ 
+
+ align:start position:0%
+circle that's the boundary of this
+Hemisphere and we got pi and just now
+
+ align:start position:0%
+Hemisphere and we got pi and just now
+ 
+
+ align:start position:0%
+Hemisphere and we got pi and just now
+what we did is we had the surface
+
+ align:start position:0%
+what we did is we had the surface
+ 
+
+ align:start position:0%
+what we did is we had the surface
+integral the associated surface integral
+
+ align:start position:0%
+integral the associated surface integral
+ 
+
+ align:start position:0%
+integral the associated surface integral
+that we get from Stokes theorem this
+
+ align:start position:0%
+that we get from Stokes theorem this
+ 
+
+ align:start position:0%
+that we get from Stokes theorem this
+curl f.n DS so we had okay we computed F
+
+ align:start position:0%
+curl f.n DS so we had okay we computed F
+ 
+
+ align:start position:0%
+curl f.n DS so we had okay we computed F
+and curl F and N and then we' we'
+
+ align:start position:0%
+and curl F and N and then we' we'
+ 
+
+ align:start position:0%
+and curl F and N and then we' we'
+noticed a little nice symmetry here
+
+ align:start position:0%
+noticed a little nice symmetry here
+ 
+
+ align:start position:0%
+noticed a little nice symmetry here
+although if you didn't notice it you
+
+ align:start position:0%
+although if you didn't notice it you
+ 
+
+ align:start position:0%
+although if you didn't notice it you
+should have been had no trouble
+
+ align:start position:0%
+should have been had no trouble
+ 
+
+ align:start position:0%
+should have been had no trouble
+Computing the the extra terms in the
+
+ align:start position:0%
+Computing the the extra terms in the
+ 
+
+ align:start position:0%
+Computing the the extra terms in the
+integral that you actually ended up with
+
+ align:start position:0%
+integral that you actually ended up with
+ 
+
+ align:start position:0%
+integral that you actually ended up with
+it would have been you know another
+
+ align:start position:0%
+it would have been you know another
+ 
+
+ align:start position:0%
+it would have been you know another
+couple of trig terms there after you
+
+ align:start position:0%
+couple of trig terms there after you
+ 
+
+ align:start position:0%
+couple of trig terms there after you
+made the substitution so we
+
+ align:start position:0%
+made the substitution so we
+ 
+
+ align:start position:0%
+made the substitution so we
+parameterized our surface nicely because
+
+ align:start position:0%
+parameterized our surface nicely because
+ 
+
+ align:start position:0%
+parameterized our surface nicely because
+it's a sphere it's easy to do um and
+
+ align:start position:0%
+it's a sphere it's easy to do um and
+ 
+
+ align:start position:0%
+it's a sphere it's easy to do um and
+then we computed the double integral and
+
+ align:start position:0%
+then we computed the double integral and
+ 
+
+ align:start position:0%
+then we computed the double integral and
+we also came out with pi and we better
+
+ align:start position:0%
+we also came out with pi and we better
+ 
+
+ align:start position:0%
+we also came out with pi and we better
+have also come out with pi because
+
+ align:start position:0%
+have also come out with pi because
+ 
+
+ align:start position:0%
+have also come out with pi because
+Stokes theorem tells us that the line
+
+ align:start position:0%
+Stokes theorem tells us that the line
+ 
+
+ align:start position:0%
+Stokes theorem tells us that the line
+integral and the surface integral have
+
+ align:start position:0%
+integral and the surface integral have
+ 
+
+ align:start position:0%
+integral and the surface integral have
+to give us the same value so that's
+
+ align:start position:0%
+to give us the same value so that's
+ 
+
+ align:start position:0%
+to give us the same value so that's
+great so that's that's exactly what we
+
+ align:start position:0%
+great so that's that's exactly what we
+ 
+
+ align:start position:0%
+great so that's that's exactly what we
+were hoping would happen and now we've
+
+ align:start position:0%
+were hoping would happen and now we've
+ 
+
+ align:start position:0%
+were hoping would happen and now we've
+sort of convinced ourselves hopefully
+
+ align:start position:0%
+sort of convinced ourselves hopefully
+ 
+
+ align:start position:0%
+sort of convinced ourselves hopefully
+that that you know through a through an
+
+ align:start position:0%
+that that you know through a through an
+ 
+
+ align:start position:0%
+that that you know through a through an
+example now we have a maybe feel for
+
+ align:start position:0%
+example now we have a maybe feel for
+ 
+
+ align:start position:0%
+example now we have a maybe feel for
+what sorts of things Stokes theorem can
+
+ align:start position:0%
+what sorts of things Stokes theorem can
+ 
+
+ align:start position:0%
+what sorts of things Stokes theorem can
+do for us I'll end there
\ No newline at end of file
diff --git a/3SkCNpFOshk.txt b/3SkCNpFOshk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9981758b64efd48dc0f6fcd7f0591144d3a3695d
--- /dev/null
+++ b/3SkCNpFOshk.txt
@@ -0,0 +1,2090 @@
+align:start position:0%
+ 
+hi welcome back to recitation in the
+
+ align:start position:0%
+hi welcome back to recitation in the
+ 
+
+ align:start position:0%
+hi welcome back to recitation in the
+lecture we've learned very important
+
+ align:start position:0%
+lecture we've learned very important
+ 
+
+ align:start position:0%
+lecture we've learned very important
+Concepts linear space and linear
+
+ align:start position:0%
+Concepts linear space and linear
+ 
+
+ align:start position:0%
+Concepts linear space and linear
+Subspace well as you can imagine if we
+
+ align:start position:0%
+Subspace well as you can imagine if we
+ 
+
+ align:start position:0%
+Subspace well as you can imagine if we
+call something a space we're putting a
+
+ align:start position:0%
+call something a space we're putting a
+ 
+
+ align:start position:0%
+call something a space we're putting a
+lot of things a lot of objects into one
+
+ align:start position:0%
+lot of things a lot of objects into one
+ 
+
+ align:start position:0%
+lot of things a lot of objects into one
+set but for linear space we want to put
+
+ align:start position:0%
+set but for linear space we want to put
+ 
+
+ align:start position:0%
+set but for linear space we want to put
+them in according to a particular manner
+
+ align:start position:0%
+them in according to a particular manner
+ 
+
+ align:start position:0%
+them in according to a particular manner
+so can you recall what are the
+
+ align:start position:0%
+so can you recall what are the
+ 
+
+ align:start position:0%
+so can you recall what are the
+conditions for a set to be a linear
+
+ align:start position:0%
+conditions for a set to be a linear
+ 
+
+ align:start position:0%
+conditions for a set to be a linear
+space you take any two elements from
+
+ align:start position:0%
+space you take any two elements from
+ 
+
+ align:start position:0%
+space you take any two elements from
+that set take the sum of them you want
+
+ align:start position:0%
+that set take the sum of them you want
+ 
+
+ align:start position:0%
+that set take the sum of them you want
+the sum to be still in the same set
+
+ align:start position:0%
+the sum to be still in the same set
+ 
+
+ align:start position:0%
+the sum to be still in the same set
+that's the first condition second you
+
+ align:start position:0%
+that's the first condition second you
+ 
+
+ align:start position:0%
+that's the first condition second you
+take any multiple of any element from
+
+ align:start position:0%
+take any multiple of any element from
+ 
+
+ align:start position:0%
+take any multiple of any element from
+that set the result will still be in
+
+ align:start position:0%
+that set the result will still be in
+ 
+
+ align:start position:0%
+that set the result will still be in
+that set well that's the second
+
+ align:start position:0%
+that set well that's the second
+ 
+
+ align:start position:0%
+that set well that's the second
+condition okay and if within a linear
+
+ align:start position:0%
+condition okay and if within a linear
+ 
+
+ align:start position:0%
+condition okay and if within a linear
+space you can find a subset set which
+
+ align:start position:0%
+space you can find a subset set which
+ 
+
+ align:start position:0%
+space you can find a subset set which
+also satisfy the two conditions then
+
+ align:start position:0%
+also satisfy the two conditions then
+ 
+
+ align:start position:0%
+also satisfy the two conditions then
+that will give you a
+
+ align:start position:0%
+that will give you a
+ 
+
+ align:start position:0%
+that will give you a
+Subspace today we're going to look at
+
+ align:start position:0%
+Subspace today we're going to look at
+ 
+
+ align:start position:0%
+Subspace today we're going to look at
+this example to review these two
+
+ align:start position:0%
+this example to review these two
+ 
+
+ align:start position:0%
+this example to review these two
+important properties of linear space and
+
+ align:start position:0%
+important properties of linear space and
+ 
+
+ align:start position:0%
+important properties of linear space and
+Subspace okay I have two vectors X1 and
+
+ align:start position:0%
+Subspace okay I have two vectors X1 and
+ 
+
+ align:start position:0%
+Subspace okay I have two vectors X1 and
+X2 both of them are vectors in R3 so as
+
+ align:start position:0%
+X2 both of them are vectors in R3 so as
+ 
+
+ align:start position:0%
+X2 both of them are vectors in R3 so as
+you can see I've drawn them here this is
+
+ align:start position:0%
+you can see I've drawn them here this is
+ 
+
+ align:start position:0%
+you can see I've drawn them here this is
+X1 and this is X2
+
+ align:start position:0%
+X1 and this is X2
+ 
+
+ align:start position:0%
+X1 and this is X2
+so first we want to find the Subspace
+
+ align:start position:0%
+so first we want to find the Subspace
+ 
+
+ align:start position:0%
+so first we want to find the Subspace
+generated by X1 I call it V1 let me say
+
+ align:start position:0%
+generated by X1 I call it V1 let me say
+ 
+
+ align:start position:0%
+generated by X1 I call it V1 let me say
+a word about this generated by so what
+
+ align:start position:0%
+a word about this generated by so what
+ 
+
+ align:start position:0%
+a word about this generated by so what
+do I mean by a Subspace generated by
+
+ align:start position:0%
+do I mean by a Subspace generated by
+ 
+
+ align:start position:0%
+do I mean by a Subspace generated by
+X1 I'm looking for the smallest Subspace
+
+ align:start position:0%
+X1 I'm looking for the smallest Subspace
+ 
+
+ align:start position:0%
+X1 I'm looking for the smallest Subspace
+that contains X1 as small as you can get
+
+ align:start position:0%
+that contains X1 as small as you can get
+ 
+
+ align:start position:0%
+that contains X1 as small as you can get
+okay similarly I want to find out the
+
+ align:start position:0%
+okay similarly I want to find out the
+ 
+
+ align:start position:0%
+okay similarly I want to find out the
+Subspace generated by X 2 call it
+
+ align:start position:0%
+Subspace generated by X 2 call it
+ 
+
+ align:start position:0%
+Subspace generated by X 2 call it
+V2 okay then we want to say something
+
+ align:start position:0%
+V2 okay then we want to say something
+ 
+
+ align:start position:0%
+V2 okay then we want to say something
+about the intersection of V1 and V2
+
+ align:start position:0%
+about the intersection of V1 and V2
+ 
+
+ align:start position:0%
+about the intersection of V1 and V2
+that's the first question and the second
+
+ align:start position:0%
+that's the first question and the second
+ 
+
+ align:start position:0%
+that's the first question and the second
+question we want to put Vector X1 and X2
+
+ align:start position:0%
+question we want to put Vector X1 and X2
+ 
+
+ align:start position:0%
+question we want to put Vector X1 and X2
+together and look at the Subspace
+
+ align:start position:0%
+together and look at the Subspace
+ 
+
+ align:start position:0%
+together and look at the Subspace
+generated by X1 and X2 at the same time
+
+ align:start position:0%
+generated by X1 and X2 at the same time
+ 
+
+ align:start position:0%
+generated by X1 and X2 at the same time
+so I call it
+
+ align:start position:0%
+so I call it
+ 
+
+ align:start position:0%
+so I call it
+V3 and a good question to be asked here
+
+ align:start position:0%
+V3 and a good question to be asked here
+ 
+
+ align:start position:0%
+V3 and a good question to be asked here
+is what is the relation of V3 to V1 un
+
+ align:start position:0%
+is what is the relation of V3 to V1 un
+ 
+
+ align:start position:0%
+is what is the relation of V3 to V1 un
+V2 do you think they're
+
+ align:start position:0%
+V2 do you think they're
+ 
+
+ align:start position:0%
+V2 do you think they're
+equal um within the second question I
+
+ align:start position:0%
+equal um within the second question I
+ 
+
+ align:start position:0%
+equal um within the second question I
+would also like you to find a Subspace
+
+ align:start position:0%
+would also like you to find a Subspace
+ 
+
+ align:start position:0%
+would also like you to find a Subspace
+call it s of V3 such that neither X1 nor
+
+ align:start position:0%
+call it s of V3 such that neither X1 nor
+ 
+
+ align:start position:0%
+call it s of V3 such that neither X1 nor
+X2 is in
+
+ align:start position:0%
+X2 is in
+ 
+
+ align:start position:0%
+X2 is in
+s and the last question is I'd like you
+
+ align:start position:0%
+s and the last question is I'd like you
+ 
+
+ align:start position:0%
+s and the last question is I'd like you
+to say something about the intersection
+
+ align:start position:0%
+to say something about the intersection
+ 
+
+ align:start position:0%
+to say something about the intersection
+of V3 with the XY plane
+
+ align:start position:0%
+of V3 with the XY plane
+ 
+
+ align:start position:0%
+of V3 with the XY plane
+so notice that of course XY plane is
+
+ align:start position:0%
+so notice that of course XY plane is
+ 
+
+ align:start position:0%
+so notice that of course XY plane is
+also a Subspace of R3 so again I'm
+
+ align:start position:0%
+also a Subspace of R3 so again I'm
+ 
+
+ align:start position:0%
+also a Subspace of R3 so again I'm
+looking at the intersection of two
+
+ align:start position:0%
+looking at the intersection of two
+ 
+
+ align:start position:0%
+looking at the intersection of two
+subspaces all right why don't you hit
+
+ align:start position:0%
+subspaces all right why don't you hit
+ 
+
+ align:start position:0%
+subspaces all right why don't you hit
+the pause now and try to solve these
+
+ align:start position:0%
+the pause now and try to solve these
+ 
+
+ align:start position:0%
+the pause now and try to solve these
+three problems on your own and i' like
+
+ align:start position:0%
+three problems on your own and i' like
+ 
+
+ align:start position:0%
+three problems on your own and i' like
+you to identify your answers in this
+
+ align:start position:0%
+you to identify your answers in this
+ 
+
+ align:start position:0%
+you to identify your answers in this
+picture whenever you can I'll come back
+
+ align:start position:0%
+picture whenever you can I'll come back
+ 
+
+ align:start position:0%
+picture whenever you can I'll come back
+later and continue working with
+
+ align:start position:0%
+later and continue working with
+ 
+
+ align:start position:0%
+later and continue working with
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay how did our drawing go let's look
+
+ align:start position:0%
+okay how did our drawing go let's look
+ 
+
+ align:start position:0%
+okay how did our drawing go let's look
+at this together first we want to find
+
+ align:start position:0%
+at this together first we want to find
+ 
+
+ align:start position:0%
+at this together first we want to find
+Subspace generated by X1 so here is X1
+
+ align:start position:0%
+Subspace generated by X1 so here is X1
+ 
+
+ align:start position:0%
+Subspace generated by X1 so here is X1
+let's keep in mind the two conditions
+
+ align:start position:0%
+let's keep in mind the two conditions
+ 
+
+ align:start position:0%
+let's keep in mind the two conditions
+that a Subspace has to satisfy well if I
+
+ align:start position:0%
+that a Subspace has to satisfy well if I
+ 
+
+ align:start position:0%
+that a Subspace has to satisfy well if I
+want to obtain the Subspace at least I
+
+ align:start position:0%
+want to obtain the Subspace at least I
+ 
+
+ align:start position:0%
+want to obtain the Subspace at least I
+have to be able to take any multi
+
+ align:start position:0%
+have to be able to take any multi
+ 
+
+ align:start position:0%
+have to be able to take any multi
+multiple of X1 right so that means at
+
+ align:start position:0%
+multiple of X1 right so that means at
+ 
+
+ align:start position:0%
+multiple of X1 right so that means at
+least I have to include the straight
+
+ align:start position:0%
+least I have to include the straight
+ 
+
+ align:start position:0%
+least I have to include the straight
+line that contains X1 so I'm going to
+
+ align:start position:0%
+line that contains X1 so I'm going to
+ 
+
+ align:start position:0%
+line that contains X1 so I'm going to
+try to draw this straight line here so
+
+ align:start position:0%
+try to draw this straight line here so
+ 
+
+ align:start position:0%
+try to draw this straight line here so
+I'm just simply going to extend this X1
+
+ align:start position:0%
+I'm just simply going to extend this X1
+ 
+
+ align:start position:0%
+I'm just simply going to extend this X1
+along to both directions so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X1 I will try very hard to make it
+
+ align:start position:0%
+X1 I will try very hard to make it
+ 
+
+ align:start position:0%
+X1 I will try very hard to make it
+straight but to be honest it's really
+
+ align:start position:0%
+straight but to be honest it's really
+ 
+
+ align:start position:0%
+straight but to be honest it's really
+hard for me to draw straight lines on
+
+ align:start position:0%
+hard for me to draw straight lines on
+ 
+
+ align:start position:0%
+hard for me to draw straight lines on
+the board okay is that straight seems
+
+ align:start position:0%
+the board okay is that straight seems
+ 
+
+ align:start position:0%
+the board okay is that straight seems
+fine all right so this entire line
+
+ align:start position:0%
+fine all right so this entire line
+ 
+
+ align:start position:0%
+fine all right so this entire line
+contains X1 so at least this line has to
+
+ align:start position:0%
+contains X1 so at least this line has to
+ 
+
+ align:start position:0%
+contains X1 so at least this line has to
+be in V1 is there any anything else
+
+ align:start position:0%
+be in V1 is there any anything else
+ 
+
+ align:start position:0%
+be in V1 is there any anything else
+Beyond this line now let's turn to the
+
+ align:start position:0%
+Beyond this line now let's turn to the
+ 
+
+ align:start position:0%
+Beyond this line now let's turn to the
+second condition the second condition
+
+ align:start position:0%
+second condition the second condition
+ 
+
+ align:start position:0%
+second condition the second condition
+says that we have to be able to take any
+
+ align:start position:0%
+says that we have to be able to take any
+ 
+
+ align:start position:0%
+says that we have to be able to take any
+two elements take the sum and the sum
+
+ align:start position:0%
+two elements take the sum and the sum
+ 
+
+ align:start position:0%
+two elements take the sum and the sum
+will remain in that set does it work for
+
+ align:start position:0%
+will remain in that set does it work for
+ 
+
+ align:start position:0%
+will remain in that set does it work for
+this line you take any
+
+ align:start position:0%
+this line you take any
+ 
+
+ align:start position:0%
+this line you take any
+two vectors on this line or you can say
+
+ align:start position:0%
+two vectors on this line or you can say
+ 
+
+ align:start position:0%
+two vectors on this line or you can say
+any two points on this line and then you
+
+ align:start position:0%
+any two points on this line and then you
+ 
+
+ align:start position:0%
+any two points on this line and then you
+take the sum of them of course you still
+
+ align:start position:0%
+take the sum of them of course you still
+ 
+
+ align:start position:0%
+take the sum of them of course you still
+get something on this line you won't be
+
+ align:start position:0%
+get something on this line you won't be
+ 
+
+ align:start position:0%
+get something on this line you won't be
+able to escape from it right which means
+
+ align:start position:0%
+able to escape from it right which means
+ 
+
+ align:start position:0%
+able to escape from it right which means
+this line is a perfect set that satisfy
+
+ align:start position:0%
+this line is a perfect set that satisfy
+ 
+
+ align:start position:0%
+this line is a perfect set that satisfy
+the two conditions so this line simply
+
+ align:start position:0%
+the two conditions so this line simply
+ 
+
+ align:start position:0%
+the two conditions so this line simply
+gives me
+
+ align:start position:0%
+gives me
+ 
+
+ align:start position:0%
+gives me
+V1 that is the smallest Subspace that
+
+ align:start position:0%
+V1 that is the smallest Subspace that
+ 
+
+ align:start position:0%
+V1 that is the smallest Subspace that
+contains X1 so in other words the
+
+ align:start position:0%
+contains X1 so in other words the
+ 
+
+ align:start position:0%
+contains X1 so in other words the
+Subspace generated by X1 is V1 so
+
+ align:start position:0%
+Subspace generated by X1 is V1 so
+ 
+
+ align:start position:0%
+Subspace generated by X1 is V1 so
+similarly let's look at X2 what is the
+
+ align:start position:0%
+similarly let's look at X2 what is the
+ 
+
+ align:start position:0%
+similarly let's look at X2 what is the
+Subspace generated by X2 again you get
+
+ align:start position:0%
+Subspace generated by X2 again you get
+ 
+
+ align:start position:0%
+Subspace generated by X2 again you get
+the entire straight line that contains
+
+ align:start position:0%
+the entire straight line that contains
+ 
+
+ align:start position:0%
+the entire straight line that contains
+X2 so I'm going to ex extend
+
+ align:start position:0%
+X2 so I'm going to ex extend
+ 
+
+ align:start position:0%
+X2 so I'm going to ex extend
+x2 in both
+
+ align:start position:0%
+x2 in both
+ 
+
+ align:start position:0%
+x2 in both
+directions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I hope it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+straight not too
+
+ align:start position:0%
+straight not too
+ 
+
+ align:start position:0%
+straight not too
+bad that will give me V2 all right V1 V2
+
+ align:start position:0%
+bad that will give me V2 all right V1 V2
+ 
+
+ align:start position:0%
+bad that will give me V2 all right V1 V2
+both of them are subspaces of
+
+ align:start position:0%
+both of them are subspaces of
+ 
+
+ align:start position:0%
+both of them are subspaces of
+R3 now let's look at the intersection of
+
+ align:start position:0%
+R3 now let's look at the intersection of
+ 
+
+ align:start position:0%
+R3 now let's look at the intersection of
+V1 and V2 so we know that both of them
+
+ align:start position:0%
+V1 and V2 so we know that both of them
+ 
+
+ align:start position:0%
+V1 and V2 so we know that both of them
+are straight lines and clearly they're
+
+ align:start position:0%
+are straight lines and clearly they're
+ 
+
+ align:start position:0%
+are straight lines and clearly they're
+not parallel because X1 and X2 are not
+
+ align:start position:0%
+not parallel because X1 and X2 are not
+ 
+
+ align:start position:0%
+not parallel because X1 and X2 are not
+parallel right so what is the
+
+ align:start position:0%
+parallel right so what is the
+ 
+
+ align:start position:0%
+parallel right so what is the
+intersection of V1 and
+
+ align:start position:0%
+intersection of V1 and
+ 
+
+ align:start position:0%
+intersection of V1 and
+vs2 the intersection of V1 and
+
+ align:start position:0%
+vs2 the intersection of V1 and
+ 
+
+ align:start position:0%
+vs2 the intersection of V1 and
+V2 is the only
+
+ align:start position:0%
+V2 is the only
+ 
+
+ align:start position:0%
+V2 is the only
+point at which they cross and where is
+
+ align:start position:0%
+point at which they cross and where is
+ 
+
+ align:start position:0%
+point at which they cross and where is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+point it's here right at the origin
+
+ align:start position:0%
+point it's here right at the origin
+ 
+
+ align:start position:0%
+point it's here right at the origin
+because both of them pass the origin so
+
+ align:start position:0%
+because both of them pass the origin so
+ 
+
+ align:start position:0%
+because both of them pass the origin so
+that's I'm going to use o to denote
+
+ align:start position:0%
+that's I'm going to use o to denote
+ 
+
+ align:start position:0%
+that's I'm going to use o to denote
+that's the intersection of V1 and
+
+ align:start position:0%
+that's the intersection of V1 and
+ 
+
+ align:start position:0%
+that's the intersection of V1 and
+vs2 this is a set with only one element
+
+ align:start position:0%
+vs2 this is a set with only one element
+ 
+
+ align:start position:0%
+vs2 this is a set with only one element
+what can you say about this
+
+ align:start position:0%
+what can you say about this
+ 
+
+ align:start position:0%
+what can you say about this
+set I claim this is also a Subspace of
+
+ align:start position:0%
+set I claim this is also a Subspace of
+ 
+
+ align:start position:0%
+set I claim this is also a Subspace of
+R3 although by saying space we usually
+
+ align:start position:0%
+R3 although by saying space we usually
+ 
+
+ align:start position:0%
+R3 although by saying space we usually
+mean a lot of objects together but look
+
+ align:start position:0%
+mean a lot of objects together but look
+ 
+
+ align:start position:0%
+mean a lot of objects together but look
+at this set this set fits perfectly into
+
+ align:start position:0%
+at this set this set fits perfectly into
+ 
+
+ align:start position:0%
+at this set this set fits perfectly into
+the conditions of being a linear space
+
+ align:start position:0%
+the conditions of being a linear space
+ 
+
+ align:start position:0%
+the conditions of being a linear space
+you take any multiple of zero
+
+ align:start position:0%
+you take any multiple of zero
+ 
+
+ align:start position:0%
+you take any multiple of zero
+again you get zero 0 + 0 you get zero so
+
+ align:start position:0%
+again you get zero 0 + 0 you get zero so
+ 
+
+ align:start position:0%
+again you get zero 0 + 0 you get zero so
+that's a perfectly fine Subspace of R3
+
+ align:start position:0%
+that's a perfectly fine Subspace of R3
+ 
+
+ align:start position:0%
+that's a perfectly fine Subspace of R3
+all right so what we have got here is I
+
+ align:start position:0%
+all right so what we have got here is I
+ 
+
+ align:start position:0%
+all right so what we have got here is I
+take the intersection of V1 and V2 and
+
+ align:start position:0%
+take the intersection of V1 and V2 and
+ 
+
+ align:start position:0%
+take the intersection of V1 and V2 and
+the result again becomes a Subspace
+
+ align:start position:0%
+the result again becomes a Subspace
+ 
+
+ align:start position:0%
+the result again becomes a Subspace
+which only contains the
+
+ align:start position:0%
+which only contains the
+ 
+
+ align:start position:0%
+which only contains the
+origin that completes the first question
+
+ align:start position:0%
+origin that completes the first question
+ 
+
+ align:start position:0%
+origin that completes the first question
+let's look at the second one in the
+
+ align:start position:0%
+let's look at the second one in the
+ 
+
+ align:start position:0%
+let's look at the second one in the
+second question I want to put X1 and X2
+
+ align:start position:0%
+second question I want to put X1 and X2
+ 
+
+ align:start position:0%
+second question I want to put X1 and X2
+together and look at the Subspace
+
+ align:start position:0%
+together and look at the Subspace
+ 
+
+ align:start position:0%
+together and look at the Subspace
+generated by X1 and
+
+ align:start position:0%
+generated by X1 and
+ 
+
+ align:start position:0%
+generated by X1 and
+X2 and I would also like you to say
+
+ align:start position:0%
+X2 and I would also like you to say
+ 
+
+ align:start position:0%
+X2 and I would also like you to say
+something about the relation between V1
+
+ align:start position:0%
+something about the relation between V1
+ 
+
+ align:start position:0%
+something about the relation between V1
+Union V2 to the sub space generated by
+
+ align:start position:0%
+Union V2 to the sub space generated by
+ 
+
+ align:start position:0%
+Union V2 to the sub space generated by
+x1x2 let's try to answer the second
+
+ align:start position:0%
+x1x2 let's try to answer the second
+ 
+
+ align:start position:0%
+x1x2 let's try to answer the second
+question first is there a chance that V1
+
+ align:start position:0%
+question first is there a chance that V1
+ 
+
+ align:start position:0%
+question first is there a chance that V1
+Union V2 equal to
+
+ align:start position:0%
+Union V2 equal to
+ 
+
+ align:start position:0%
+Union V2 equal to
+V3 okay so what is V1 unit V2 that's
+
+ align:start position:0%
+V3 okay so what is V1 unit V2 that's
+ 
+
+ align:start position:0%
+V3 okay so what is V1 unit V2 that's
+clearly just two lines right this line
+
+ align:start position:0%
+clearly just two lines right this line
+ 
+
+ align:start position:0%
+clearly just two lines right this line
+Union this
+
+ align:start position:0%
+Union this
+ 
+
+ align:start position:0%
+Union this
+line is there a chance that this Union
+
+ align:start position:0%
+line is there a chance that this Union
+ 
+
+ align:start position:0%
+line is there a chance that this Union
+will be a
+
+ align:start position:0%
+will be a
+ 
+
+ align:start position:0%
+will be a
+Subspace let's check the two conditions
+
+ align:start position:0%
+Subspace let's check the two conditions
+ 
+
+ align:start position:0%
+Subspace let's check the two conditions
+first you take any multiple of the
+
+ align:start position:0%
+first you take any multiple of the
+ 
+
+ align:start position:0%
+first you take any multiple of the
+elements in this
+
+ align:start position:0%
+elements in this
+ 
+
+ align:start position:0%
+elements in this
+Union it's either on V it's either on
+
+ align:start position:0%
+Union it's either on V it's either on
+ 
+
+ align:start position:0%
+Union it's either on V it's either on
+this line or on this line since that the
+
+ align:start position:0%
+this line or on this line since that the
+ 
+
+ align:start position:0%
+this line or on this line since that the
+multiple is still going to stay inside
+
+ align:start position:0%
+multiple is still going to stay inside
+ 
+
+ align:start position:0%
+multiple is still going to stay inside
+the union so the first condition is
+
+ align:start position:0%
+the union so the first condition is
+ 
+
+ align:start position:0%
+the union so the first condition is
+actually satisfied what about the second
+
+ align:start position:0%
+actually satisfied what about the second
+ 
+
+ align:start position:0%
+actually satisfied what about the second
+one the second one says that I have to
+
+ align:start position:0%
+one the second one says that I have to
+ 
+
+ align:start position:0%
+one the second one says that I have to
+be able to take any sum the sum of any
+
+ align:start position:0%
+be able to take any sum the sum of any
+ 
+
+ align:start position:0%
+be able to take any sum the sum of any
+two elements from these two lines let's
+
+ align:start position:0%
+two elements from these two lines let's
+ 
+
+ align:start position:0%
+two elements from these two lines let's
+just try a simple sum X1 + X2 so what is
+
+ align:start position:0%
+just try a simple sum X1 + X2 so what is
+ 
+
+ align:start position:0%
+just try a simple sum X1 + X2 so what is
+X1 +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X2 you just sum up each coordinate that
+
+ align:start position:0%
+X2 you just sum up each coordinate that
+ 
+
+ align:start position:0%
+X2 you just sum up each coordinate that
+will give you
+
+ align:start position:0%
+will give you
+ 
+
+ align:start position:0%
+will give you
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 in this picture can I draw it in this
+
+ align:start position:0%
+3 in this picture can I draw it in this
+ 
+
+ align:start position:0%
+3 in this picture can I draw it in this
+picture it's going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somewhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay that's
+
+ align:start position:0%
+here okay that's
+ 
+
+ align:start position:0%
+here okay that's
+X1 plus
+
+ align:start position:0%
+X1 plus
+ 
+
+ align:start position:0%
+X1 plus
+X3 did you notice
+
+ align:start position:0%
+X3 did you notice
+ 
+
+ align:start position:0%
+X3 did you notice
+something you clearly have got out of
+
+ align:start position:0%
+something you clearly have got out of
+ 
+
+ align:start position:0%
+something you clearly have got out of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+Union so this sum is not
+
+ align:start position:0%
+Union so this sum is not
+ 
+
+ align:start position:0%
+Union so this sum is not
+inside V1 Union
+
+ align:start position:0%
+inside V1 Union
+ 
+
+ align:start position:0%
+inside V1 Union
+V2 which means V1 Union V2 is not a
+
+ align:start position:0%
+V2 which means V1 Union V2 is not a
+ 
+
+ align:start position:0%
+V2 which means V1 Union V2 is not a
+Subspace then it's impossible that this
+
+ align:start position:0%
+Subspace then it's impossible that this
+ 
+
+ align:start position:0%
+Subspace then it's impossible that this
+Union will equal to
+
+ align:start position:0%
+Union will equal to
+ 
+
+ align:start position:0%
+Union will equal to
+V3 so the second question the answer to
+
+ align:start position:0%
+V3 so the second question the answer to
+ 
+
+ align:start position:0%
+V3 so the second question the answer to
+the second question is no V3 is not
+
+ align:start position:0%
+the second question is no V3 is not
+ 
+
+ align:start position:0%
+the second question is no V3 is not
+equal to V1 un V2 now now let's identify
+
+ align:start position:0%
+equal to V1 un V2 now now let's identify
+ 
+
+ align:start position:0%
+equal to V1 un V2 now now let's identify
+V3 well as you can see since we have
+
+ align:start position:0%
+V3 well as you can see since we have
+ 
+
+ align:start position:0%
+V3 well as you can see since we have
+seen from this argument that we have to
+
+ align:start position:0%
+seen from this argument that we have to
+ 
+
+ align:start position:0%
+seen from this argument that we have to
+be included to be able to include this
+
+ align:start position:0%
+be included to be able to include this
+ 
+
+ align:start position:0%
+be included to be able to include this
+diagonal Vector here but in fact as you
+
+ align:start position:0%
+diagonal Vector here but in fact as you
+ 
+
+ align:start position:0%
+diagonal Vector here but in fact as you
+can see since we can take any elements
+
+ align:start position:0%
+can see since we can take any elements
+ 
+
+ align:start position:0%
+can see since we can take any elements
+from these two lines we're actually
+
+ align:start position:0%
+from these two lines we're actually
+ 
+
+ align:start position:0%
+from these two lines we're actually
+including every Vector on the plane
+
+ align:start position:0%
+including every Vector on the plane
+ 
+
+ align:start position:0%
+including every Vector on the plane
+spent by V1 and V2 so in other words I'm
+
+ align:start position:0%
+spent by V1 and V2 so in other words I'm
+ 
+
+ align:start position:0%
+spent by V1 and V2 so in other words I'm
+actually looking at this huge
+
+ align:start position:0%
+actually looking at this huge
+ 
+
+ align:start position:0%
+actually looking at this huge
+plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is spent by
+
+ align:start position:0%
+that is spent by
+ 
+
+ align:start position:0%
+that is spent by
+V1 and
+
+ align:start position:0%
+V1 and
+ 
+
+ align:start position:0%
+V1 and
+V2 that will give me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B3 okay so that's reasonable I'm looking
+
+ align:start position:0%
+B3 okay so that's reasonable I'm looking
+ 
+
+ align:start position:0%
+B3 okay so that's reasonable I'm looking
+at the Subspace generated by two line in
+
+ align:start position:0%
+at the Subspace generated by two line in
+ 
+
+ align:start position:0%
+at the Subspace generated by two line in
+R3 and that two line will be able to
+
+ align:start position:0%
+R3 and that two line will be able to
+ 
+
+ align:start position:0%
+R3 and that two line will be able to
+spend a plane in
+
+ align:start position:0%
+spend a plane in
+ 
+
+ align:start position:0%
+spend a plane in
+R3 okay now um for the last part of
+
+ align:start position:0%
+R3 okay now um for the last part of
+ 
+
+ align:start position:0%
+R3 okay now um for the last part of
+question two I want to find a Subspace
+
+ align:start position:0%
+question two I want to find a Subspace
+ 
+
+ align:start position:0%
+question two I want to find a Subspace
+is s of V3 so I want to find the
+
+ align:start position:0%
+is s of V3 so I want to find the
+ 
+
+ align:start position:0%
+is s of V3 so I want to find the
+Subspace of this plane such that X1 is
+
+ align:start position:0%
+Subspace of this plane such that X1 is
+ 
+
+ align:start position:0%
+Subspace of this plane such that X1 is
+not in s X2 is not in s either so I want
+
+ align:start position:0%
+not in s X2 is not in s either so I want
+ 
+
+ align:start position:0%
+not in s X2 is not in s either so I want
+to stay away from this line and this
+
+ align:start position:0%
+to stay away from this line and this
+ 
+
+ align:start position:0%
+to stay away from this line and this
+line can you find such a Subspace of
+
+ align:start position:0%
+line can you find such a Subspace of
+ 
+
+ align:start position:0%
+line can you find such a Subspace of
+V3 it's right here right because if you
+
+ align:start position:0%
+V3 it's right here right because if you
+ 
+
+ align:start position:0%
+V3 it's right here right because if you
+look at this Vector X1 + X2 sorry that
+
+ align:start position:0%
+look at this Vector X1 + X2 sorry that
+ 
+
+ align:start position:0%
+look at this Vector X1 + X2 sorry that
+should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X2
+
+ align:start position:0%
+X2
+ 
+
+ align:start position:0%
+X2
+if you look at this vector and if you
+
+ align:start position:0%
+if you look at this vector and if you
+ 
+
+ align:start position:0%
+if you look at this vector and if you
+look at the Subspace generated by this
+
+ align:start position:0%
+look at the Subspace generated by this
+ 
+
+ align:start position:0%
+look at the Subspace generated by this
+Vector again you know it's going to be a
+
+ align:start position:0%
+Vector again you know it's going to be a
+ 
+
+ align:start position:0%
+Vector again you know it's going to be a
+line and this line is right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this line forms a perfect Subspace
+
+ align:start position:0%
+here this line forms a perfect Subspace
+ 
+
+ align:start position:0%
+here this line forms a perfect Subspace
+of V3 but neither X1 nor X2 is inside
+
+ align:start position:0%
+of V3 but neither X1 nor X2 is inside
+ 
+
+ align:start position:0%
+of V3 but neither X1 nor X2 is inside
+the Subspace so let's just
+
+ align:start position:0%
+the Subspace so let's just
+ 
+
+ align:start position:0%
+the Subspace so let's just
+make it
+
+ align:start position:0%
+make it
+ 
+
+ align:start position:0%
+make it
+s of course the choice is not unique you
+
+ align:start position:0%
+s of course the choice is not unique you
+ 
+
+ align:start position:0%
+s of course the choice is not unique you
+can take twice X1 plus X2 or X1 + twice
+
+ align:start position:0%
+can take twice X1 plus X2 or X1 + twice
+ 
+
+ align:start position:0%
+can take twice X1 plus X2 or X1 + twice
+X2 okay we have completed the second
+
+ align:start position:0%
+X2 okay we have completed the second
+ 
+
+ align:start position:0%
+X2 okay we have completed the second
+problem the last problems ask us to find
+
+ align:start position:0%
+problem the last problems ask us to find
+ 
+
+ align:start position:0%
+problem the last problems ask us to find
+the intersection of V3 with XY plane
+
+ align:start position:0%
+the intersection of V3 with XY plane
+ 
+
+ align:start position:0%
+the intersection of V3 with XY plane
+well just think about that we have
+
+ align:start position:0%
+well just think about that we have
+ 
+
+ align:start position:0%
+well just think about that we have
+identified X V3 as this plane spent by
+
+ align:start position:0%
+identified X V3 as this plane spent by
+ 
+
+ align:start position:0%
+identified X V3 as this plane spent by
+line V1 and V2
+
+ align:start position:0%
+line V1 and V2
+ 
+
+ align:start position:0%
+line V1 and V2
+and XY is also plane so we're talking
+
+ align:start position:0%
+and XY is also plane so we're talking
+ 
+
+ align:start position:0%
+and XY is also plane so we're talking
+about the intersection of two planes in
+
+ align:start position:0%
+about the intersection of two planes in
+ 
+
+ align:start position:0%
+about the intersection of two planes in
+R3 what would that be so you have two
+
+ align:start position:0%
+R3 what would that be so you have two
+ 
+
+ align:start position:0%
+R3 what would that be so you have two
+planes intersect the intersection will
+
+ align:start position:0%
+planes intersect the intersection will
+ 
+
+ align:start position:0%
+planes intersect the intersection will
+be a straight line again right so let's
+
+ align:start position:0%
+be a straight line again right so let's
+ 
+
+ align:start position:0%
+be a straight line again right so let's
+Lo locate that straight line we want to
+
+ align:start position:0%
+Lo locate that straight line we want to
+ 
+
+ align:start position:0%
+Lo locate that straight line we want to
+find something that is inside V3 and XY
+
+ align:start position:0%
+find something that is inside V3 and XY
+ 
+
+ align:start position:0%
+find something that is inside V3 and XY
+plane at the same time what can you say
+
+ align:start position:0%
+plane at the same time what can you say
+ 
+
+ align:start position:0%
+plane at the same time what can you say
+about lines in X what can you say about
+
+ align:start position:0%
+about lines in X what can you say about
+ 
+
+ align:start position:0%
+about lines in X what can you say about
+the points in XY plan
+
+ align:start position:0%
+the points in XY plan
+ 
+
+ align:start position:0%
+the points in XY plan
+the Z coordinate has to be zero okay and
+
+ align:start position:0%
+the Z coordinate has to be zero okay and
+ 
+
+ align:start position:0%
+the Z coordinate has to be zero okay and
+at the same time we know that at least
+
+ align:start position:0%
+at the same time we know that at least
+ 
+
+ align:start position:0%
+at the same time we know that at least
+X1 and X2 are in V3 so did you notice
+
+ align:start position:0%
+X1 and X2 are in V3 so did you notice
+ 
+
+ align:start position:0%
+X1 and X2 are in V3 so did you notice
+that X2 is a vector that lies in V3 but
+
+ align:start position:0%
+that X2 is a vector that lies in V3 but
+ 
+
+ align:start position:0%
+that X2 is a vector that lies in V3 but
+at the same time the Z coordinate of X2
+
+ align:start position:0%
+at the same time the Z coordinate of X2
+ 
+
+ align:start position:0%
+at the same time the Z coordinate of X2
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+zero that is what we're looking for so
+
+ align:start position:0%
+zero that is what we're looking for so
+ 
+
+ align:start position:0%
+zero that is what we're looking for so
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+intersection of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V3 with XY plane will simply
+
+ align:start position:0%
+V3 with XY plane will simply
+ 
+
+ align:start position:0%
+V3 with XY plane will simply
+be the line that contains X2 and here
+
+ align:start position:0%
+be the line that contains X2 and here
+ 
+
+ align:start position:0%
+be the line that contains X2 and here
+we've identified that as
+
+ align:start position:0%
+we've identified that as
+ 
+
+ align:start position:0%
+we've identified that as
+V2 that's it this is a Subspace of R3
+
+ align:start position:0%
+V2 that's it this is a Subspace of R3
+ 
+
+ align:start position:0%
+V2 that's it this is a Subspace of R3
+and this is the sub of R3 the
+
+ align:start position:0%
+and this is the sub of R3 the
+ 
+
+ align:start position:0%
+and this is the sub of R3 the
+intersection is again a Subspace of
+
+ align:start position:0%
+intersection is again a Subspace of
+ 
+
+ align:start position:0%
+intersection is again a Subspace of
+R3 okay I hope you've learned a way to
+
+ align:start position:0%
+R3 okay I hope you've learned a way to
+ 
+
+ align:start position:0%
+R3 okay I hope you've learned a way to
+somehow visualize this linear space and
+
+ align:start position:0%
+somehow visualize this linear space and
+ 
+
+ align:start position:0%
+somehow visualize this linear space and
+Subspace through this
+
+ align:start position:0%
+Subspace through this
+ 
+
+ align:start position:0%
+Subspace through this
+exercise okay thank you for watching and
+
+ align:start position:0%
+exercise okay thank you for watching and
+ 
+
+ align:start position:0%
+exercise okay thank you for watching and
+I'll see you next
+
+ align:start position:0%
+I'll see you next
+ 
+
+ align:start position:0%
+I'll see you next
+time
\ No newline at end of file
diff --git a/3cN7bSffVm4.txt b/3cN7bSffVm4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1df0c8251546a873bc4924055ed2ca921cc45f63
--- /dev/null
+++ b/3cN7bSffVm4.txt
@@ -0,0 +1,411 @@
+align:start position:0%
+ 
+in the previous video we generated a
+
+ align:start position:0%
+in the previous video we generated a
+ 
+
+ align:start position:0%
+in the previous video we generated a
+cart tree with three splits but why not
+
+ align:start position:0%
+cart tree with three splits but why not
+ 
+
+ align:start position:0%
+cart tree with three splits but why not
+two or four or even five there are
+
+ align:start position:0%
+two or four or even five there are
+ 
+
+ align:start position:0%
+two or four or even five there are
+different ways to control how many
+
+ align:start position:0%
+different ways to control how many
+ 
+
+ align:start position:0%
+different ways to control how many
+splits are generated one way is by
+
+ align:start position:0%
+splits are generated one way is by
+ 
+
+ align:start position:0%
+splits are generated one way is by
+setting a lower bound for the number of
+
+ align:start position:0%
+setting a lower bound for the number of
+ 
+
+ align:start position:0%
+setting a lower bound for the number of
+data points in each subset in R this is
+
+ align:start position:0%
+data points in each subset in R this is
+ 
+
+ align:start position:0%
+data points in each subset in R this is
+called the min bucket parameter for the
+
+ align:start position:0%
+called the min bucket parameter for the
+ 
+
+ align:start position:0%
+called the min bucket parameter for the
+minimum number of observations in each
+
+ align:start position:0%
+minimum number of observations in each
+ 
+
+ align:start position:0%
+minimum number of observations in each
+bucket or subset the smaller min bucket
+
+ align:start position:0%
+bucket or subset the smaller min bucket
+ 
+
+ align:start position:0%
+bucket or subset the smaller min bucket
+is the more splits will be generated but
+
+ align:start position:0%
+is the more splits will be generated but
+ 
+
+ align:start position:0%
+is the more splits will be generated but
+if it's too small overfitting will occur
+
+ align:start position:0%
+if it's too small overfitting will occur
+ 
+
+ align:start position:0%
+if it's too small overfitting will occur
+this means that cart will fit the
+
+ align:start position:0%
+this means that cart will fit the
+ 
+
+ align:start position:0%
+this means that cart will fit the
+training set almost perfectly but this
+
+ align:start position:0%
+training set almost perfectly but this
+ 
+
+ align:start position:0%
+training set almost perfectly but this
+is bad because then the model will
+
+ align:start position:0%
+is bad because then the model will
+ 
+
+ align:start position:0%
+is bad because then the model will
+probably not perform well on test set
+
+ align:start position:0%
+probably not perform well on test set
+ 
+
+ align:start position:0%
+probably not perform well on test set
+data or new data on the other hand if
+
+ align:start position:0%
+data or new data on the other hand if
+ 
+
+ align:start position:0%
+data or new data on the other hand if
+the min bucket parameter is too large
+
+ align:start position:0%
+the min bucket parameter is too large
+ 
+
+ align:start position:0%
+the min bucket parameter is too large
+the model will be too simple and the
+
+ align:start position:0%
+the model will be too simple and the
+ 
+
+ align:start position:0%
+the model will be too simple and the
+accuracy will be poor later in the
+
+ align:start position:0%
+accuracy will be poor later in the
+ 
+
+ align:start position:0%
+accuracy will be poor later in the
+lecture we'll learn about a nice method
+
+ align:start position:0%
+lecture we'll learn about a nice method
+ 
+
+ align:start position:0%
+lecture we'll learn about a nice method
+for selecting the stopping parameter in
+
+ align:start position:0%
+for selecting the stopping parameter in
+ 
+
+ align:start position:0%
+for selecting the stopping parameter in
+each subset of a cart tree we have a
+
+ align:start position:0%
+each subset of a cart tree we have a
+ 
+
+ align:start position:0%
+each subset of a cart tree we have a
+bucket of observations which may contain
+
+ align:start position:0%
+bucket of observations which may contain
+ 
+
+ align:start position:0%
+bucket of observations which may contain
+both possible outcomes in the small
+
+ align:start position:0%
+both possible outcomes in the small
+ 
+
+ align:start position:0%
+both possible outcomes in the small
+example we showed in the previous video
+
+ align:start position:0%
+example we showed in the previous video
+ 
+
+ align:start position:0%
+example we showed in the previous video
+we classify each subset as either red or
+
+ align:start position:0%
+we classify each subset as either red or
+ 
+
+ align:start position:0%
+we classify each subset as either red or
+gray depending on the majority in that
+
+ align:start position:0%
+gray depending on the majority in that
+ 
+
+ align:start position:0%
+gray depending on the majority in that
+subset in the Supreme Court case we'll
+
+ align:start position:0%
+subset in the Supreme Court case we'll
+ 
+
+ align:start position:0%
+subset in the Supreme Court case we'll
+be classifying observations as either
+
+ align:start position:0%
+be classifying observations as either
+ 
+
+ align:start position:0%
+be classifying observations as either
+affirm or reverse instead of just taking
+
+ align:start position:0%
+affirm or reverse instead of just taking
+ 
+
+ align:start position:0%
+affirm or reverse instead of just taking
+the majority outcome to be the
+
+ align:start position:0%
+the majority outcome to be the
+ 
+
+ align:start position:0%
+the majority outcome to be the
+prediction we can compute the percentage
+
+ align:start position:0%
+prediction we can compute the percentage
+ 
+
+ align:start position:0%
+prediction we can compute the percentage
+of data in a subset of each type of
+
+ align:start position:0%
+of data in a subset of each type of
+ 
+
+ align:start position:0%
+of data in a subset of each type of
+outcome as an example if we have a
+
+ align:start position:0%
+outcome as an example if we have a
+ 
+
+ align:start position:0%
+outcome as an example if we have a
+subset with ten affirms and two reverses
+
+ align:start position:0%
+subset with ten affirms and two reverses
+ 
+
+ align:start position:0%
+subset with ten affirms and two reverses
+then 87% of the data is affirmed then
+
+ align:start position:0%
+then 87% of the data is affirmed then
+ 
+
+ align:start position:0%
+then 87% of the data is affirmed then
+just like in logistic regression we can
+
+ align:start position:0%
+just like in logistic regression we can
+ 
+
+ align:start position:0%
+just like in logistic regression we can
+use a threshold value to obtain our
+
+ align:start position:0%
+use a threshold value to obtain our
+ 
+
+ align:start position:0%
+use a threshold value to obtain our
+prediction for this example we would
+
+ align:start position:0%
+prediction for this example we would
+ 
+
+ align:start position:0%
+prediction for this example we would
+predict a firm with a threshold of 0.5
+
+ align:start position:0%
+predict a firm with a threshold of 0.5
+ 
+
+ align:start position:0%
+predict a firm with a threshold of 0.5
+since the majority is affirmed but if we
+
+ align:start position:0%
+since the majority is affirmed but if we
+ 
+
+ align:start position:0%
+since the majority is affirmed but if we
+increase that threshold to 0.9 we would
+
+ align:start position:0%
+increase that threshold to 0.9 we would
+ 
+
+ align:start position:0%
+increase that threshold to 0.9 we would
+predict reverse for this example then by
+
+ align:start position:0%
+predict reverse for this example then by
+ 
+
+ align:start position:0%
+predict reverse for this example then by
+varying the threat
+
+ align:start position:0%
+varying the threat
+ 
+
+ align:start position:0%
+varying the threat
+shoulde value we can compute an ROC
+
+ align:start position:0%
+shoulde value we can compute an ROC
+ 
+
+ align:start position:0%
+shoulde value we can compute an ROC
+curve and compute an AUC value to
+
+ align:start position:0%
+curve and compute an AUC value to
+ 
+
+ align:start position:0%
+curve and compute an AUC value to
+evaluate our model in the next video
+
+ align:start position:0%
+evaluate our model in the next video
+ 
+
+ align:start position:0%
+evaluate our model in the next video
+we'll build a cart tree in our to
+
+ align:start position:0%
+we'll build a cart tree in our to
+ 
+
+ align:start position:0%
+we'll build a cart tree in our to
+predict the decisions of justice Stevens
+
+ align:start position:0%
+predict the decisions of justice Stevens
+ 
+
+ align:start position:0%
+predict the decisions of justice Stevens
+and evaluate our model using an ROC
+
+ align:start position:0%
+and evaluate our model using an ROC
+ 
+
+ align:start position:0%
+and evaluate our model using an ROC
+curve
\ No newline at end of file
diff --git a/4PlHFcfB8DA.txt b/4PlHFcfB8DA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b8ea035f72f6340c6fd61c60050bcc1061e1dd56
--- /dev/null
+++ b/4PlHFcfB8DA.txt
@@ -0,0 +1,8616 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+okay so last time the idea was to think
+
+ align:start position:0%
+okay so last time the idea was to think
+ 
+
+ align:start position:0%
+okay so last time the idea was to think
+through a different way or in fact
+
+ align:start position:0%
+through a different way or in fact
+ 
+
+ align:start position:0%
+through a different way or in fact
+several different
+
+ align:start position:0%
+several different
+ 
+
+ align:start position:0%
+several different
+ways to think about discreet time
+
+ align:start position:0%
+ways to think about discreet time
+ 
+
+ align:start position:0%
+ways to think about discreet time
+systems today is a crash
+
+ align:start position:0%
+systems today is a crash
+ 
+
+ align:start position:0%
+systems today is a crash
+course to do the same thing in CT
+
+ align:start position:0%
+course to do the same thing in CT
+ 
+
+ align:start position:0%
+course to do the same thing in CT
+systems so last time for the last week
+
+ align:start position:0%
+systems so last time for the last week
+ 
+
+ align:start position:0%
+systems so last time for the last week
+we've been looking at different kinds of
+
+ align:start position:0%
+we've been looking at different kinds of
+ 
+
+ align:start position:0%
+we've been looking at different kinds of
+representations for DT
+
+ align:start position:0%
+representations for DT
+ 
+
+ align:start position:0%
+representations for DT
+systems difference equations because
+
+ align:start position:0%
+systems difference equations because
+ 
+
+ align:start position:0%
+systems difference equations because
+they're concise and precise block
+
+ align:start position:0%
+they're concise and precise block
+ 
+
+ align:start position:0%
+they're concise and precise block
+diagrams because they let you visualize
+
+ align:start position:0%
+diagrams because they let you visualize
+ 
+
+ align:start position:0%
+diagrams because they let you visualize
+the signal flow paths and operator
+
+ align:start position:0%
+the signal flow paths and operator
+ 
+
+ align:start position:0%
+the signal flow paths and operator
+Expressions because it lets you treat
+
+ align:start position:0%
+Expressions because it lets you treat
+ 
+
+ align:start position:0%
+Expressions because it lets you treat
+systems like
+
+ align:start position:0%
+systems like
+ 
+
+ align:start position:0%
+systems like
+pols what we'll see today is that that
+
+ align:start position:0%
+pols what we'll see today is that that
+ 
+
+ align:start position:0%
+pols what we'll see today is that that
+same kind of strategy Works precisely
+
+ align:start position:0%
+same kind of strategy Works precisely
+ 
+
+ align:start position:0%
+same kind of strategy Works precisely
+the strategy not the answers the same
+
+ align:start position:0%
+the strategy not the answers the same
+ 
+
+ align:start position:0%
+the strategy not the answers the same
+strategy Works precisely for
+
+ align:start position:0%
+strategy Works precisely for
+ 
+
+ align:start position:0%
+strategy Works precisely for
+CT we'll have a concise precise
+
+ align:start position:0%
+CT we'll have a concise precise
+ 
+
+ align:start position:0%
+CT we'll have a concise precise
+representation in terms of differential
+
+ align:start position:0%
+representation in terms of differential
+ 
+
+ align:start position:0%
+representation in terms of differential
+equations which I'm sure you already
+
+ align:start position:0%
+equations which I'm sure you already
+ 
+
+ align:start position:0%
+equations which I'm sure you already
+know all all
+
+ align:start position:0%
+know all all
+ 
+
+ align:start position:0%
+know all all
+about but we will also develop the
+
+ align:start position:0%
+about but we will also develop the
+ 
+
+ align:start position:0%
+about but we will also develop the
+notion of a block diagram so you can
+
+ align:start position:0%
+notion of a block diagram so you can
+ 
+
+ align:start position:0%
+notion of a block diagram so you can
+visualize signal flow
+
+ align:start position:0%
+visualize signal flow
+ 
+
+ align:start position:0%
+visualize signal flow
+paths and we'll have an analogous
+
+ align:start position:0%
+paths and we'll have an analogous
+ 
+
+ align:start position:0%
+paths and we'll have an analogous
+operator the a operator that will let us
+
+ align:start position:0%
+operator the a operator that will let us
+ 
+
+ align:start position:0%
+operator the a operator that will let us
+treat the systems as pols so that's the
+
+ align:start position:0%
+treat the systems as pols so that's the
+ 
+
+ align:start position:0%
+treat the systems as pols so that's the
+overview because it's so similar we'll
+
+ align:start position:0%
+overview because it's so similar we'll
+ 
+
+ align:start position:0%
+overview because it's so similar we'll
+be able to do all of this in one lecture
+
+ align:start position:0%
+be able to do all of this in one lecture
+ 
+
+ align:start position:0%
+be able to do all of this in one lecture
+okay so this is what that's what I mean
+
+ align:start position:0%
+okay so this is what that's what I mean
+ 
+
+ align:start position:0%
+okay so this is what that's what I mean
+by a crash course so this is
+
+ align:start position:0%
+by a crash course so this is
+ 
+
+ align:start position:0%
+by a crash course so this is
+Introduction to CT in 50
+
+ align:start position:0%
+Introduction to CT in 50
+ 
+
+ align:start position:0%
+Introduction to CT in 50
+minutes so you already know a lot about
+
+ align:start position:0%
+minutes so you already know a lot about
+ 
+
+ align:start position:0%
+minutes so you already know a lot about
+how you would represent systems as
+
+ align:start position:0%
+how you would represent systems as
+ 
+
+ align:start position:0%
+how you would represent systems as
+differential equations you've seen this
+
+ align:start position:0%
+differential equations you've seen this
+ 
+
+ align:start position:0%
+differential equations you've seen this
+in other classes uh you should have seen
+
+ align:start position:0%
+in other classes uh you should have seen
+ 
+
+ align:start position:0%
+in other classes uh you should have seen
+this sort of approach in physics you
+
+ align:start position:0%
+this sort of approach in physics you
+ 
+
+ align:start position:0%
+this sort of approach in physics you
+should have seen this sort of approach
+
+ align:start position:0%
+should have seen this sort of approach
+ 
+
+ align:start position:0%
+should have seen this sort of approach
+in math in
+
+ align:start position:0%
+in math in
+ 
+
+ align:start position:0%
+in math in
+1803 uh so we're going to assume that
+
+ align:start position:0%
+1803 uh so we're going to assume that
+ 
+
+ align:start position:0%
+1803 uh so we're going to assume that
+you already know how to think about
+
+ align:start position:0%
+you already know how to think about
+ 
+
+ align:start position:0%
+you already know how to think about
+differential equations and what we're
+
+ align:start position:0%
+differential equations and what we're
+ 
+
+ align:start position:0%
+differential equations and what we're
+going to do is Skip ahead and think
+
+ align:start position:0%
+going to do is Skip ahead and think
+ 
+
+ align:start position:0%
+going to do is Skip ahead and think
+about the alternative representations
+
+ align:start position:0%
+about the alternative representations
+ 
+
+ align:start position:0%
+about the alternative representations
+instead so just like in DT where we
+
+ align:start position:0%
+instead so just like in DT where we
+ 
+
+ align:start position:0%
+instead so just like in DT where we
+thought about block diagrams which gave
+
+ align:start position:0%
+thought about block diagrams which gave
+ 
+
+ align:start position:0%
+thought about block diagrams which gave
+us a way of thinking about signal flow
+
+ align:start position:0%
+us a way of thinking about signal flow
+ 
+
+ align:start position:0%
+us a way of thinking about signal flow
+paths we'll have the same sort of idea
+
+ align:start position:0%
+paths we'll have the same sort of idea
+ 
+
+ align:start position:0%
+paths we'll have the same sort of idea
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+CT the big difference you can anticipate
+
+ align:start position:0%
+CT the big difference you can anticipate
+ 
+
+ align:start position:0%
+CT the big difference you can anticipate
+I mean if the uh CT so in the D in the
+
+ align:start position:0%
+I mean if the uh CT so in the D in the
+ 
+
+ align:start position:0%
+I mean if the uh CT so in the D in the
+difference equation the fundamental
+
+ align:start position:0%
+difference equation the fundamental
+ 
+
+ align:start position:0%
+difference equation the fundamental
+operation in the difference equation was
+
+ align:start position:0%
+operation in the difference equation was
+ 
+
+ align:start position:0%
+operation in the difference equation was
+a delay
+
+ align:start position:0%
+a delay
+ 
+
+ align:start position:0%
+a delay
+operation if you contrast that to a CT
+
+ align:start position:0%
+operation if you contrast that to a CT
+ 
+
+ align:start position:0%
+operation if you contrast that to a CT
+system the fundamental operation is not
+
+ align:start position:0%
+system the fundamental operation is not
+ 
+
+ align:start position:0%
+system the fundamental operation is not
+delay you know from 1803 you know from
+
+ align:start position:0%
+delay you know from 1803 you know from
+ 
+
+ align:start position:0%
+delay you know from 1803 you know from
+physics you know from lots of uh other
+
+ align:start position:0%
+physics you know from lots of uh other
+ 
+
+ align:start position:0%
+physics you know from lots of uh other
+exposures that the fundamental operation
+
+ align:start position:0%
+exposures that the fundamental operation
+ 
+
+ align:start position:0%
+exposures that the fundamental operation
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+differentiation and so the blocks will
+
+ align:start position:0%
+differentiation and so the blocks will
+ 
+
+ align:start position:0%
+differentiation and so the blocks will
+not be built out of delays but will
+
+ align:start position:0%
+not be built out of delays but will
+ 
+
+ align:start position:0%
+not be built out of delays but will
+instead be built out of
+
+ align:start position:0%
+instead be built out of
+ 
+
+ align:start position:0%
+instead be built out of
+integrators apart from that the block
+
+ align:start position:0%
+integrators apart from that the block
+ 
+
+ align:start position:0%
+integrators apart from that the block
+diagram structure looks extremely
+
+ align:start position:0%
+diagram structure looks extremely
+ 
+
+ align:start position:0%
+diagram structure looks extremely
+similar and we'll be able to apply the
+
+ align:start position:0%
+similar and we'll be able to apply the
+ 
+
+ align:start position:0%
+similar and we'll be able to apply the
+same idea that we did in
+
+ align:start position:0%
+same idea that we did in
+ 
+
+ align:start position:0%
+same idea that we did in
+DT to simplify the representation of the
+
+ align:start position:0%
+DT to simplify the representation of the
+ 
+
+ align:start position:0%
+DT to simplify the representation of the
+block diagram by thinking in terms of
+
+ align:start position:0%
+block diagram by thinking in terms of
+ 
+
+ align:start position:0%
+block diagram by thinking in terms of
+operators the operator has to similarly
+
+ align:start position:0%
+operators the operator has to similarly
+ 
+
+ align:start position:0%
+operators the operator has to similarly
+change so the new operator the operator
+
+ align:start position:0%
+change so the new operator the operator
+ 
+
+ align:start position:0%
+change so the new operator the operator
+that we use to represent a CT system
+
+ align:start position:0%
+that we use to represent a CT system
+ 
+
+ align:start position:0%
+that we use to represent a CT system
+we'll call the a operator a is intended
+
+ align:start position:0%
+we'll call the a operator a is intended
+ 
+
+ align:start position:0%
+we'll call the a operator a is intended
+to mean
+
+ align:start position:0%
+to mean
+ 
+
+ align:start position:0%
+to mean
+accumulator the thing that's in my mind
+
+ align:start position:0%
+accumulator the thing that's in my mind
+ 
+
+ align:start position:0%
+accumulator the thing that's in my mind
+when I say the I the a operator is this
+
+ align:start position:0%
+when I say the I the a operator is this
+ 
+
+ align:start position:0%
+when I say the I the a operator is this
+tank this tank accumulates water and you
+
+ align:start position:0%
+tank this tank accumulates water and you
+ 
+
+ align:start position:0%
+tank this tank accumulates water and you
+can think about the relationship between
+
+ align:start position:0%
+can think about the relationship between
+ 
+
+ align:start position:0%
+can think about the relationship between
+the height of the water and the input
+
+ align:start position:0%
+the height of the water and the input
+ 
+
+ align:start position:0%
+the height of the water and the input
+and output rates by some differential
+
+ align:start position:0%
+and output rates by some differential
+ 
+
+ align:start position:0%
+and output rates by some differential
+equation but the point is that the tank
+
+ align:start position:0%
+equation but the point is that the tank
+ 
+
+ align:start position:0%
+equation but the point is that the tank
+itself the
+
+ align:start position:0%
+itself the
+ 
+
+ align:start position:0%
+itself the
+system accumulates and that's what we
+
+ align:start position:0%
+system accumulates and that's what we
+ 
+
+ align:start position:0%
+system accumulates and that's what we
+want to have in our heads when we think
+
+ align:start position:0%
+want to have in our heads when we think
+ 
+
+ align:start position:0%
+want to have in our heads when we think
+about the a oper op Ator so the a
+
+ align:start position:0%
+about the a oper op Ator so the a
+ 
+
+ align:start position:0%
+about the a oper op Ator so the a
+operator is going to be like the r
+
+ align:start position:0%
+operator is going to be like the r
+ 
+
+ align:start position:0%
+operator is going to be like the r
+operator you'll apply the r operator to
+
+ align:start position:0%
+operator you'll apply the r operator to
+ 
+
+ align:start position:0%
+operator you'll apply the r operator to
+a discrete time signal to generate a new
+
+ align:start position:0%
+a discrete time signal to generate a new
+ 
+
+ align:start position:0%
+a discrete time signal to generate a new
+discrete time signal that was shifted to
+
+ align:start position:0%
+discrete time signal that was shifted to
+ 
+
+ align:start position:0%
+discrete time signal that was shifted to
+the right that's what R meant R was
+
+ align:start position:0%
+the right that's what R meant R was
+ 
+
+ align:start position:0%
+the right that's what R meant R was
+right so right shift
+
+ align:start position:0%
+right so right shift
+ 
+
+ align:start position:0%
+right so right shift
+operator here you'll apply the a
+
+ align:start position:0%
+operator here you'll apply the a
+ 
+
+ align:start position:0%
+operator here you'll apply the a
+operator to the X signal X is now CT
+
+ align:start position:0%
+operator to the X signal X is now CT
+ 
+
+ align:start position:0%
+operator to the X signal X is now CT
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+time and when you apply the a operator
+
+ align:start position:0%
+time and when you apply the a operator
+ 
+
+ align:start position:0%
+time and when you apply the a operator
+to a signal X it generates a whole new
+
+ align:start position:0%
+to a signal X it generates a whole new
+ 
+
+ align:start position:0%
+to a signal X it generates a whole new
+signal y that is everywhere equal to the
+
+ align:start position:0%
+signal y that is everywhere equal to the
+ 
+
+ align:start position:0%
+signal y that is everywhere equal to the
+indefinite integral of the input signal
+
+ align:start position:0%
+indefinite integral of the input signal
+ 
+
+ align:start position:0%
+indefinite integral of the input signal
+so the a operator is start with the
+
+ align:start position:0%
+so the a operator is start with the
+ 
+
+ align:start position:0%
+so the a operator is start with the
+input signal X and integrate it with
+
+ align:start position:0%
+input signal X and integrate it with
+ 
+
+ align:start position:0%
+input signal X and integrate it with
+regard to time starting at minus
+
+ align:start position:0%
+regard to time starting at minus
+ 
+
+ align:start position:0%
+regard to time starting at minus
+infinity and going up to T that's the
+
+ align:start position:0%
+infinity and going up to T that's the
+ 
+
+ align:start position:0%
+infinity and going up to T that's the
+teeth
+
+ align:start position:0%
+teeth
+ 
+
+ align:start position:0%
+teeth
+value of the output
+
+ align:start position:0%
+value of the output
+ 
+
+ align:start position:0%
+value of the output
+signal okay
+
+ align:start position:0%
+signal okay
+ 
+
+ align:start position:0%
+signal okay
+simple so let's see how simple
+
+ align:start position:0%
+simple so let's see how simple
+ 
+
+ align:start position:0%
+simple so let's see how simple
+so here's a bunch of block diagrams
+
+ align:start position:0%
+so here's a bunch of block diagrams
+ 
+
+ align:start position:0%
+so here's a bunch of block diagrams
+written in terms of a here's a here's a
+
+ align:start position:0%
+written in terms of a here's a here's a
+ 
+
+ align:start position:0%
+written in terms of a here's a here's a
+bunch of differential equations figure
+
+ align:start position:0%
+bunch of differential equations figure
+ 
+
+ align:start position:0%
+bunch of differential equations figure
+out the correspondence if
+
+ align:start position:0%
+out the correspondence if
+ 
+
+ align:start position:0%
+out the correspondence if
+any okay traditionally it seems that
+
+ align:start position:0%
+any okay traditionally it seems that
+ 
+
+ align:start position:0%
+any okay traditionally it seems that
+people are quiet so before you start say
+
+ align:start position:0%
+people are quiet so before you start say
+ 
+
+ align:start position:0%
+people are quiet so before you start say
+something that has nothing to do with3
+
+ align:start position:0%
+something that has nothing to do with3
+ 
+
+ align:start position:0%
+something that has nothing to do with3
+to your next door neighbor it has to
+
+ align:start position:0%
+to your next door neighbor it has to
+ 
+
+ align:start position:0%
+to your next door neighbor it has to
+have nothing to do
+
+ align:start position:0%
+have nothing to do
+ 
+
+ align:start position:0%
+have nothing to do
+with3 and then figure out which of these
+
+ align:start position:0%
+with3 and then figure out which of these
+ 
+
+ align:start position:0%
+with3 and then figure out which of these
+bottom diagrams number 1 2 3 4 or none
+
+ align:start position:0%
+bottom diagrams number 1 2 3 4 or none
+ 
+
+ align:start position:0%
+bottom diagrams number 1 2 3 4 or none
+of them corresponds best to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correspondence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you've got 30 seconds to answer the
+
+ align:start position:0%
+okay you've got 30 seconds to answer the
+ 
+
+ align:start position:0%
+okay you've got 30 seconds to answer the
+question now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that killed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay everybody raise your hand and tell
+
+ align:start position:0%
+okay everybody raise your hand and tell
+ 
+
+ align:start position:0%
+okay everybody raise your hand and tell
+me which of the five available answers
+
+ align:start position:0%
+me which of the five available answers
+ 
+
+ align:start position:0%
+me which of the five available answers
+one through five best illustrates the
+
+ align:start position:0%
+one through five best illustrates the
+ 
+
+ align:start position:0%
+one through five best illustrates the
+correspondence raise your hands let me
+
+ align:start position:0%
+correspondence raise your hands let me
+ 
+
+ align:start position:0%
+correspondence raise your hands let me
+see how many of you figured it
+
+ align:start position:0%
+see how many of you figured it
+ 
+
+ align:start position:0%
+see how many of you figured it
+out remember if you're wrong you can
+
+ align:start position:0%
+out remember if you're wrong you can
+ 
+
+ align:start position:0%
+out remember if you're wrong you can
+blame it on your partner
+
+ align:start position:0%
+blame it on your partner
+ 
+
+ align:start position:0%
+blame it on your partner
+okay it's more than 95% correct how do
+
+ align:start position:0%
+okay it's more than 95% correct how do
+ 
+
+ align:start position:0%
+okay it's more than 95% correct how do
+you think about it what do I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first equation write an so which what do
+
+ align:start position:0%
+first equation write an so which what do
+ 
+
+ align:start position:0%
+first equation write an so which what do
+you want me to look at first this
+
+ align:start position:0%
+you want me to look at first this
+ 
+
+ align:start position:0%
+you want me to look at first this
+diagram that equation this diagram that
+
+ align:start position:0%
+diagram that equation this diagram that
+ 
+
+ align:start position:0%
+diagram that equation this diagram that
+equation write an equation for each of
+
+ align:start position:0%
+equation write an equation for each of
+ 
+
+ align:start position:0%
+equation write an equation for each of
+the diagrams how would I figure out an
+
+ align:start position:0%
+the diagrams how would I figure out an
+ 
+
+ align:start position:0%
+the diagrams how would I figure out an
+equation for that
+
+ align:start position:0%
+equation for that
+ 
+
+ align:start position:0%
+equation for that
+diagram yeah at what coming in out sign
+
+ align:start position:0%
+diagram yeah at what coming in out sign
+ 
+
+ align:start position:0%
+diagram yeah at what coming in out sign
+so look at what's coming in and out of
+
+ align:start position:0%
+so look at what's coming in and out of
+ 
+
+ align:start position:0%
+so look at what's coming in and out of
+the plus sign that's very good so so
+
+ align:start position:0%
+the plus sign that's very good so so
+ 
+
+ align:start position:0%
+the plus sign that's very good so so
+let's focus on the coming out first
+
+ align:start position:0%
+let's focus on the coming out first
+ 
+
+ align:start position:0%
+let's focus on the coming out first
+what's the name of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signal well I can think of two names
+
+ align:start position:0%
+signal well I can think of two names
+ 
+
+ align:start position:0%
+signal well I can think of two names
+right that's why it's a good idea to
+
+ align:start position:0%
+right that's why it's a good idea to
+ 
+
+ align:start position:0%
+right that's why it's a good idea to
+look at what's coming in and
+
+ align:start position:0%
+look at what's coming in and
+ 
+
+ align:start position:0%
+look at what's coming in and
+out one way that I could name this would
+
+ align:start position:0%
+out one way that I could name this would
+ 
+
+ align:start position:0%
+out one way that I could name this would
+be with reference to the a
+
+ align:start position:0%
+be with reference to the a
+ 
+
+ align:start position:0%
+be with reference to the a
+operator if I know that what comes out
+
+ align:start position:0%
+operator if I know that what comes out
+ 
+
+ align:start position:0%
+operator if I know that what comes out
+of the a operator is capital Y what goes
+
+ align:start position:0%
+of the a operator is capital Y what goes
+ 
+
+ align:start position:0%
+of the a operator is capital Y what goes
+into the a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator the
+
+ align:start position:0%
+operator the
+ 
+
+ align:start position:0%
+operator the
+derivative so if I know that what comes
+
+ align:start position:0%
+derivative so if I know that what comes
+ 
+
+ align:start position:0%
+derivative so if I know that what comes
+out is y then that what goes in must
+
+ align:start position:0%
+out is y then that what goes in must
+ 
+
+ align:start position:0%
+out is y then that what goes in must
+have been y
+
+ align:start position:0%
+have been y
+ 
+
+ align:start position:0%
+have been y
+dot right but that also has to be the
+
+ align:start position:0%
+dot right but that also has to be the
+ 
+
+ align:start position:0%
+dot right but that also has to be the
+output of the adder so what were the two
+
+ align:start position:0%
+output of the adder so what were the two
+ 
+
+ align:start position:0%
+output of the adder so what were the two
+inputs of the
+
+ align:start position:0%
+inputs of the
+ 
+
+ align:start position:0%
+inputs of the
+adder X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+py
+
+ align:start position:0%
+py
+ 
+
+ align:start position:0%
+py
+right so y dot the thing that goes into
+
+ align:start position:0%
+right so y dot the thing that goes into
+ 
+
+ align:start position:0%
+right so y dot the thing that goes into
+the accumulator has to be the same as X
+
+ align:start position:0%
+the accumulator has to be the same as X
+ 
+
+ align:start position:0%
+the accumulator has to be the same as X
+Plus py okay so y dot is X Plus py so
+
+ align:start position:0%
+Plus py okay so y dot is X Plus py so
+ 
+
+ align:start position:0%
+Plus py okay so y dot is X Plus py so
+there's a correspondence between these
+
+ align:start position:0%
+there's a correspondence between these
+ 
+
+ align:start position:0%
+there's a correspondence between these
+two everybody sort of get the
+
+ align:start position:0%
+two everybody sort of get the
+ 
+
+ align:start position:0%
+two everybody sort of get the
+idea we can do the same sort of thing
+
+ align:start position:0%
+idea we can do the same sort of thing
+ 
+
+ align:start position:0%
+idea we can do the same sort of thing
+here what's the name of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signal
+
+ align:start position:0%
+signal
+ 
+
+ align:start position:0%
+signal
+sh y do over P exactly so that that
+
+ align:start position:0%
+sh y do over P exactly so that that
+ 
+
+ align:start position:0%
+sh y do over P exactly so that that
+one's going to be y dot over p and
+
+ align:start position:0%
+one's going to be y dot over p and
+ 
+
+ align:start position:0%
+one's going to be y dot over p and
+that's going to have to be the same as
+
+ align:start position:0%
+that's going to have to be the same as
+ 
+
+ align:start position:0%
+that's going to have to be the same as
+uh X Plus
+
+ align:start position:0%
+uh X Plus
+ 
+
+ align:start position:0%
+uh X Plus
+y so if you cleared the fraction here
+
+ align:start position:0%
+y so if you cleared the fraction here
+ 
+
+ align:start position:0%
+y so if you cleared the fraction here
+you would find that y dot is PX plus py
+
+ align:start position:0%
+you would find that y dot is PX plus py
+ 
+
+ align:start position:0%
+you would find that y dot is PX plus py
+so there's a correspondence that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+right and you can do the same sort of
+
+ align:start position:0%
+right and you can do the same sort of
+ 
+
+ align:start position:0%
+right and you can do the same sort of
+thing down here right it's it looks a
+
+ align:start position:0%
+thing down here right it's it looks a
+ 
+
+ align:start position:0%
+thing down here right it's it looks a
+little bit different what's this this
+
+ align:start position:0%
+little bit different what's this this
+ 
+
+ align:start position:0%
+little bit different what's this this
+says that the output of the adder
+
+ align:start position:0%
+says that the output of the adder
+ 
+
+ align:start position:0%
+says that the output of the adder
+y right the output of the adder here is
+
+ align:start position:0%
+y right the output of the adder here is
+ 
+
+ align:start position:0%
+y right the output of the adder here is
+y so y must have been X Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what so P * the
+
+ align:start position:0%
+what so P * the
+ 
+
+ align:start position:0%
+what so P * the
+integral of
+
+ align:start position:0%
+integral of
+ 
+
+ align:start position:0%
+integral of
+Y right and I'd like to write that in a
+
+ align:start position:0%
+Y right and I'd like to write that in a
+ 
+
+ align:start position:0%
+Y right and I'd like to write that in a
+differential form so I could
+
+ align:start position:0%
+differential form so I could
+ 
+
+ align:start position:0%
+differential form so I could
+differentiate term by term to say that
+
+ align:start position:0%
+differentiate term by term to say that
+ 
+
+ align:start position:0%
+differentiate term by term to say that
+that's the same thing as y dot is X do
+
+ align:start position:0%
+that's the same thing as y dot is X do
+ 
+
+ align:start position:0%
+that's the same thing as y dot is X do
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+py uh so y dot is x dot plus py so those
+
+ align:start position:0%
+py uh so y dot is x dot plus py so those
+ 
+
+ align:start position:0%
+py uh so y dot is x dot plus py so those
+correspondence that way so the answer is
+
+ align:start position:0%
+correspondence that way so the answer is
+ 
+
+ align:start position:0%
+correspondence that way so the answer is
+one okay everybody's happy with that so
+
+ align:start position:0%
+one okay everybody's happy with that so
+ 
+
+ align:start position:0%
+one okay everybody's happy with that so
+the point is that the differential
+
+ align:start position:0%
+the point is that the differential
+ 
+
+ align:start position:0%
+the point is that the differential
+operators look very much the same you
+
+ align:start position:0%
+operators look very much the same you
+ 
+
+ align:start position:0%
+operators look very much the same you
+can use the same kind of reasoning that
+
+ align:start position:0%
+can use the same kind of reasoning that
+ 
+
+ align:start position:0%
+can use the same kind of reasoning that
+you did for difference equations with
+
+ align:start position:0%
+you did for difference equations with
+ 
+
+ align:start position:0%
+you did for difference equations with
+r of course the operators are
+
+ align:start position:0%
+r of course the operators are
+ 
+
+ align:start position:0%
+r of course the operators are
+different and just like
+
+ align:start position:0%
+different and just like
+ 
+
+ align:start position:0%
+different and just like
+R you can think about these things as
+
+ align:start position:0%
+R you can think about these things as
+ 
+
+ align:start position:0%
+R you can think about these things as
+pols so if you think about this feed
+
+ align:start position:0%
+pols so if you think about this feed
+ 
+
+ align:start position:0%
+pols so if you think about this feed
+forward
+
+ align:start position:0%
+forward
+ 
+
+ align:start position:0%
+forward
+system that's now CT not DT the feed
+
+ align:start position:0%
+system that's now CT not DT the feed
+ 
+
+ align:start position:0%
+system that's now CT not DT the feed
+forward system says that I could
+
+ align:start position:0%
+forward system says that I could
+ 
+
+ align:start position:0%
+forward system says that I could
+construct W by taking uh X plus a x X
+
+ align:start position:0%
+construct W by taking uh X plus a x X
+ 
+
+ align:start position:0%
+construct W by taking uh X plus a x X
+Plus ax or that's X plus the derivative
+
+ align:start position:0%
+Plus ax or that's X plus the derivative
+ 
+
+ align:start position:0%
+Plus ax or that's X plus the derivative
+the integral of x
+
+ align:start position:0%
+the integral of x
+ 
+
+ align:start position:0%
+the integral of x
+right then I could think about the Y
+
+ align:start position:0%
+right then I could think about the Y
+ 
+
+ align:start position:0%
+right then I could think about the Y
+signal as W plus the integral of
+
+ align:start position:0%
+signal as W plus the integral of
+ 
+
+ align:start position:0%
+signal as W plus the integral of
+w so that's this one y is W plus the
+
+ align:start position:0%
+w so that's this one y is W plus the
+ 
+
+ align:start position:0%
+w so that's this one y is W plus the
+integral of w and now I can substitute
+
+ align:start position:0%
+integral of w and now I can substitute
+ 
+
+ align:start position:0%
+integral of w and now I can substitute
+instances of this into
+
+ align:start position:0%
+instances of this into
+ 
+
+ align:start position:0%
+instances of this into
+here right so this W expression could go
+
+ align:start position:0%
+here right so this W expression could go
+ 
+
+ align:start position:0%
+here right so this W expression could go
+in there and that gives me
+
+ align:start position:0%
+in there and that gives me
+ 
+
+ align:start position:0%
+in there and that gives me
+this if I integrated this W expression
+
+ align:start position:0%
+this if I integrated this W expression
+ 
+
+ align:start position:0%
+this if I integrated this W expression
+once then I would get the integral of
+
+ align:start position:0%
+once then I would get the integral of
+ 
+
+ align:start position:0%
+once then I would get the integral of
+that plus the double integral of that so
+
+ align:start position:0%
+that plus the double integral of that so
+ 
+
+ align:start position:0%
+that plus the double integral of that so
+that gives me
+
+ align:start position:0%
+that gives me
+ 
+
+ align:start position:0%
+that gives me
+these and now I think about those things
+
+ align:start position:0%
+these and now I think about those things
+ 
+
+ align:start position:0%
+these and now I think about those things
+in terms of A's and I get precisely the
+
+ align:start position:0%
+in terms of A's and I get precisely the
+ 
+
+ align:start position:0%
+in terms of A's and I get precisely the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+expression so the idea is just like R
+
+ align:start position:0%
+expression so the idea is just like R
+ 
+
+ align:start position:0%
+expression so the idea is just like R
+you can manipulate
+
+ align:start position:0%
+you can manipulate
+ 
+
+ align:start position:0%
+you can manipulate
+operator U expressions in R like they
+
+ align:start position:0%
+operator U expressions in R like they
+ 
+
+ align:start position:0%
+operator U expressions in R like they
+were pols you can you can um manipulate
+
+ align:start position:0%
+were pols you can you can um manipulate
+ 
+
+ align:start position:0%
+were pols you can you can um manipulate
+operator expressions in
+
+ align:start position:0%
+operator expressions in
+ 
+
+ align:start position:0%
+operator expressions in
+a just like they were
+
+ align:start position:0%
+a just like they were
+ 
+
+ align:start position:0%
+a just like they were
+polinomial and the reason I can say that
+
+ align:start position:0%
+polinomial and the reason I can say that
+ 
+
+ align:start position:0%
+polinomial and the reason I can say that
+is that if I think through all the
+
+ align:start position:0%
+is that if I think through all the
+ 
+
+ align:start position:0%
+is that if I think through all the
+properties of polinomial I can draw an
+
+ align:start position:0%
+properties of polinomial I can draw an
+ 
+
+ align:start position:0%
+properties of polinomial I can draw an
+isomorphism between the way the system
+
+ align:start position:0%
+isomorphism between the way the system
+ 
+
+ align:start position:0%
+isomorphism between the way the system
+would have behaved and the way the
+
+ align:start position:0%
+would have behaved and the way the
+ 
+
+ align:start position:0%
+would have behaved and the way the
+polinomial would have behaved and in
+
+ align:start position:0%
+polinomial would have behaved and in
+ 
+
+ align:start position:0%
+polinomial would have behaved and in
+particular here's three statements that
+
+ align:start position:0%
+particular here's three statements that
+ 
+
+ align:start position:0%
+particular here's three statements that
+have to be
+
+ align:start position:0%
+have to be
+ 
+
+ align:start position:0%
+have to be
+true if the operator Expressions were
+
+ align:start position:0%
+true if the operator Expressions were
+ 
+
+ align:start position:0%
+true if the operator Expressions were
+supposed to behave like polinomial
+
+ align:start position:0%
+supposed to behave like polinomial
+ 
+
+ align:start position:0%
+supposed to behave like polinomial
+polinomial have the property that the
+
+ align:start position:0%
+polinomial have the property that the
+ 
+
+ align:start position:0%
+polinomial have the property that the
+the that uh polinomial in a should
+
+ align:start position:0%
+the that uh polinomial in a should
+ 
+
+ align:start position:0%
+the that uh polinomial in a should
+commute polinomial should have the the a
+
+ align:start position:0%
+commute polinomial should have the the a
+ 
+
+ align:start position:0%
+commute polinomial should have the the a
+should have the distributive property
+
+ align:start position:0%
+should have the distributive property
+ 
+
+ align:start position:0%
+should have the distributive property
+multiplication over addition
+
+ align:start position:0%
+multiplication over addition
+ 
+
+ align:start position:0%
+multiplication over addition
+and uh polinomial should associate and
+
+ align:start position:0%
+and uh polinomial should associate and
+ 
+
+ align:start position:0%
+and uh polinomial should associate and
+if you think about each of those in
+
+ align:start position:0%
+if you think about each of those in
+ 
+
+ align:start position:0%
+if you think about each of those in
+detail the operations that would
+
+ align:start position:0%
+detail the operations that would
+ 
+
+ align:start position:0%
+detail the operations that would
+correspond to what you put in the block
+
+ align:start position:0%
+correspond to what you put in the block
+ 
+
+ align:start position:0%
+correspond to what you put in the block
+diagram have precisely those same
+
+ align:start position:0%
+diagram have precisely those same
+ 
+
+ align:start position:0%
+diagram have precisely those same
+relations so that's the the outline of
+
+ align:start position:0%
+relations so that's the the outline of
+ 
+
+ align:start position:0%
+relations so that's the the outline of
+how you would go about proving something
+
+ align:start position:0%
+how you would go about proving something
+ 
+
+ align:start position:0%
+how you would go about proving something
+like this but the takeaway message is
+
+ align:start position:0%
+like this but the takeaway message is
+ 
+
+ align:start position:0%
+like this but the takeaway message is
+the operator expressions in
+
+ align:start position:0%
+the operator expressions in
+ 
+
+ align:start position:0%
+the operator expressions in
+a obey all the rules that you would
+
+ align:start position:0%
+a obey all the rules that you would
+ 
+
+ align:start position:0%
+a obey all the rules that you would
+expect from a
+
+ align:start position:0%
+expect from a
+ 
+
+ align:start position:0%
+expect from a
+polinomial so
+
+ align:start position:0%
+polinomial so
+ 
+
+ align:start position:0%
+polinomial so
+second question think about these two
+
+ align:start position:0%
+second question think about these two
+ 
+
+ align:start position:0%
+second question think about these two
+systems and think about the notion of
+
+ align:start position:0%
+systems and think about the notion of
+ 
+
+ align:start position:0%
+systems and think about the notion of
+equivalent equivalent
+
+ align:start position:0%
+equivalent equivalent
+ 
+
+ align:start position:0%
+equivalent equivalent
+here is going to be just the same as it
+
+ align:start position:0%
+here is going to be just the same as it
+ 
+
+ align:start position:0%
+here is going to be just the same as it
+was in D in DT and DT equivalent meant
+
+ align:start position:0%
+was in D in DT and DT equivalent meant
+ 
+
+ align:start position:0%
+was in D in DT and DT equivalent meant
+if all of the right shift operators
+
+ align:start position:0%
+if all of the right shift operators
+ 
+
+ align:start position:0%
+if all of the right shift operators
+started at rest that is to say their
+
+ align:start position:0%
+started at rest that is to say their
+ 
+
+ align:start position:0%
+started at rest that is to say their
+output was Zero we will have the same
+
+ align:start position:0%
+output was Zero we will have the same
+ 
+
+ align:start position:0%
+output was Zero we will have the same
+kind of notion
+
+ align:start position:0%
+kind of notion
+ 
+
+ align:start position:0%
+kind of notion
+here at rest is going to mean all the
+
+ align:start position:0%
+here at rest is going to mean all the
+ 
+
+ align:start position:0%
+here at rest is going to mean all the
+integrators integrators have a starting
+
+ align:start position:0%
+integrators integrators have a starting
+ 
+
+ align:start position:0%
+integrators integrators have a starting
+value an initial value
+
+ align:start position:0%
+value an initial value
+ 
+
+ align:start position:0%
+value an initial value
+if those initial values are all zero
+
+ align:start position:0%
+if those initial values are all zero
+ 
+
+ align:start position:0%
+if those initial values are all zero
+then we say that the system started at
+
+ align:start position:0%
+then we say that the system started at
+ 
+
+ align:start position:0%
+then we say that the system started at
+rest we have that same kind of Proviso
+
+ align:start position:0%
+rest we have that same kind of Proviso
+ 
+
+ align:start position:0%
+rest we have that same kind of Proviso
+given that Proviso then all of the
+
+ align:start position:0%
+given that Proviso then all of the
+ 
+
+ align:start position:0%
+given that Proviso then all of the
+operator Expressions behave like pols so
+
+ align:start position:0%
+operator Expressions behave like pols so
+ 
+
+ align:start position:0%
+operator Expressions behave like pols so
+tell me uh determine K1 so that these
+
+ align:start position:0%
+tell me uh determine K1 so that these
+ 
+
+ align:start position:0%
+tell me uh determine K1 so that these
+two systems are equivalent given that
+
+ align:start position:0%
+two systems are equivalent given that
+ 
+
+ align:start position:0%
+two systems are equivalent given that
+definition of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equivalence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so anyone have an
+
+ align:start position:0%
+so anyone have an
+ 
+
+ align:start position:0%
+so anyone have an
+answer so how should I choose K1 if I
+
+ align:start position:0%
+answer so how should I choose K1 if I
+ 
+
+ align:start position:0%
+answer so how should I choose K1 if I
+want those two systems to be equivalent
+
+ align:start position:0%
+want those two systems to be equivalent
+ 
+
+ align:start position:0%
+want those two systems to be equivalent
+yes raise your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hands okay it was a trick question so
+
+ align:start position:0%
+hands okay it was a trick question so
+ 
+
+ align:start position:0%
+hands okay it was a trick question so
+now given the additional information
+
+ align:start position:0%
+now given the additional information
+ 
+
+ align:start position:0%
+now given the additional information
+that it was a trick question revise your
+
+ align:start position:0%
+that it was a trick question revise your
+ 
+
+ align:start position:0%
+that it was a trick question revise your
+answers ah excellent excellent instant
+
+ align:start position:0%
+answers ah excellent excellent instant
+ 
+
+ align:start position:0%
+answers ah excellent excellent instant
+revisions wonderful okay what was the
+
+ align:start position:0%
+revisions wonderful okay what was the
+ 
+
+ align:start position:0%
+revisions wonderful okay what was the
+trick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh come on you all got it what was the
+
+ align:start position:0%
+oh come on you all got it what was the
+ 
+
+ align:start position:0%
+oh come on you all got it what was the
+trick yeah beus 1.6 it should have been
+
+ align:start position:0%
+trick yeah beus 1.6 it should have been
+ 
+
+ align:start position:0%
+trick yeah beus 1.6 it should have been
+minus 1.6 yes so H how so what do you do
+
+ align:start position:0%
+minus 1.6 yes so H how so what do you do
+ 
+
+ align:start position:0%
+minus 1.6 yes so H how so what do you do
+what do I do first in order to answer a
+
+ align:start position:0%
+what do I do first in order to answer a
+ 
+
+ align:start position:0%
+what do I do first in order to answer a
+question like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this well come on right so translate the
+
+ align:start position:0%
+this well come on right so translate the
+ 
+
+ align:start position:0%
+this well come on right so translate the
+block diagrams into a differential
+
+ align:start position:0%
+block diagrams into a differential
+ 
+
+ align:start position:0%
+block diagrams into a differential
+equation that's a good approach right
+
+ align:start position:0%
+equation that's a good approach right
+ 
+
+ align:start position:0%
+equation that's a good approach right
+because what we like to do is figure out
+
+ align:start position:0%
+because what we like to do is figure out
+ 
+
+ align:start position:0%
+because what we like to do is figure out
+an equivalence
+
+ align:start position:0%
+an equivalence
+ 
+
+ align:start position:0%
+an equivalence
+the equivalence is not
+
+ align:start position:0%
+the equivalence is not
+ 
+
+ align:start position:0%
+the equivalence is not
+trivial so in fact the equivalence is
+
+ align:start position:0%
+trivial so in fact the equivalence is
+ 
+
+ align:start position:0%
+trivial so in fact the equivalence is
+easier to think about if you do
+
+ align:start position:0%
+easier to think about if you do
+ 
+
+ align:start position:0%
+easier to think about if you do
+polinomial you could try to manipulate
+
+ align:start position:0%
+polinomial you could try to manipulate
+ 
+
+ align:start position:0%
+polinomial you could try to manipulate
+the blocks to make them look the same
+
+ align:start position:0%
+the blocks to make them look the same
+ 
+
+ align:start position:0%
+the blocks to make them look the same
+that's actually
+
+ align:start position:0%
+that's actually
+ 
+
+ align:start position:0%
+that's actually
+hard but it's pretty easy to do it if
+
+ align:start position:0%
+hard but it's pretty easy to do it if
+ 
+
+ align:start position:0%
+hard but it's pretty easy to do it if
+you think about the um block diagrams
+
+ align:start position:0%
+you think about the um block diagrams
+ 
+
+ align:start position:0%
+you think about the um block diagrams
+being represented as um functional oper
+
+ align:start position:0%
+being represented as um functional oper
+ 
+
+ align:start position:0%
+being represented as um functional oper
+as operators so you can look at the
+
+ align:start position:0%
+as operators so you can look at the
+ 
+
+ align:start position:0%
+as operators so you can look at the
+first one and you can say Okay w is the
+
+ align:start position:0%
+first one and you can say Okay w is the
+ 
+
+ align:start position:0%
+first one and you can say Okay w is the
+signal that when that comes out of a
+
+ align:start position:0%
+signal that when that comes out of a
+ 
+
+ align:start position:0%
+signal that when that comes out of a
+operating on x
+
+ align:start position:0%
+operating on x
+ 
+
+ align:start position:0%
+operating on x
+minus 7 W right that's what that Adder
+
+ align:start position:0%
+minus 7 W right that's what that Adder
+ 
+
+ align:start position:0%
+minus 7 W right that's what that Adder
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+right and you can similarly do this box
+
+ align:start position:0%
+right and you can similarly do this box
+ 
+
+ align:start position:0%
+right and you can similarly do this box
+it looks the same treat them as pols and
+
+ align:start position:0%
+it looks the same treat them as pols and
+ 
+
+ align:start position:0%
+it looks the same treat them as pols and
+you can reduce it to some equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form everyone have the gist of what I'm
+
+ align:start position:0%
+form everyone have the gist of what I'm
+ 
+
+ align:start position:0%
+form everyone have the gist of what I'm
+what's going on same thing down here the
+
+ align:start position:0%
+what's going on same thing down here the
+ 
+
+ align:start position:0%
+what's going on same thing down here the
+equations look a little bit different
+
+ align:start position:0%
+equations look a little bit different
+ 
+
+ align:start position:0%
+equations look a little bit different
+but it's the same idea you figure out
+
+ align:start position:0%
+but it's the same idea you figure out
+ 
+
+ align:start position:0%
+but it's the same idea you figure out
+what are the constraints imposed by the
+
+ align:start position:0%
+what are the constraints imposed by the
+ 
+
+ align:start position:0%
+what are the constraints imposed by the
+blocks the output of every a has to be
+
+ align:start position:0%
+blocks the output of every a has to be
+ 
+
+ align:start position:0%
+blocks the output of every a has to be
+the integral of the thing that went into
+
+ align:start position:0%
+the integral of the thing that went into
+ 
+
+ align:start position:0%
+the integral of the thing that went into
+it the output of every Adder has to be
+
+ align:start position:0%
+it the output of every Adder has to be
+ 
+
+ align:start position:0%
+it the output of every Adder has to be
+the sum of the two things that went into
+
+ align:start position:0%
+the sum of the two things that went into
+ 
+
+ align:start position:0%
+the sum of the two things that went into
+it figure out all those constraints
+
+ align:start position:0%
+it figure out all those constraints
+ 
+
+ align:start position:0%
+it figure out all those constraints
+reduce them to pols and then manipulate
+
+ align:start position:0%
+reduce them to pols and then manipulate
+ 
+
+ align:start position:0%
+reduce them to pols and then manipulate
+them as though they were pols and the
+
+ align:start position:0%
+them as though they were pols and the
+ 
+
+ align:start position:0%
+them as though they were pols and the
+polinomial manipulation shows that minus
+
+ align:start position:0%
+polinomial manipulation shows that minus
+ 
+
+ align:start position:0%
+polinomial manipulation shows that minus
+K1 should be 1.6 so K1 should be minus
+
+ align:start position:0%
+K1 should be 1.6 so K1 should be minus
+ 
+
+ align:start position:0%
+K1 should be 1.6 so K1 should be minus
+1.6 right point is it's easy right if
+
+ align:start position:0%
+1.6 right point is it's easy right if
+ 
+
+ align:start position:0%
+1.6 right point is it's easy right if
+you know pols you know the answer that's
+
+ align:start position:0%
+you know pols you know the answer that's
+ 
+
+ align:start position:0%
+you know pols you know the answer that's
+pretty good right so we're doing
+
+ align:start position:0%
+pretty good right so we're doing
+ 
+
+ align:start position:0%
+pretty good right so we're doing
+something completely different from
+
+ align:start position:0%
+something completely different from
+ 
+
+ align:start position:0%
+something completely different from
+pols but we're able to use the
+
+ align:start position:0%
+pols but we're able to use the
+ 
+
+ align:start position:0%
+pols but we're able to use the
+intuitions that we get from polinomial
+
+ align:start position:0%
+intuitions that we get from polinomial
+ 
+
+ align:start position:0%
+intuitions that we get from polinomial
+in order to do the
+
+ align:start position:0%
+in order to do the
+ 
+
+ align:start position:0%
+in order to do the
+problem there's one remaining
+
+ align:start position:0%
+problem there's one remaining
+ 
+
+ align:start position:0%
+problem there's one remaining
+problem something that is harder than it
+
+ align:start position:0%
+problem something that is harder than it
+ 
+
+ align:start position:0%
+problem something that is harder than it
+is in DT probably the hardest part of CT
+
+ align:start position:0%
+is in DT probably the hardest part of CT
+ 
+
+ align:start position:0%
+is in DT probably the hardest part of CT
+and that involves thinking about what
+
+ align:start position:0%
+and that involves thinking about what
+ 
+
+ align:start position:0%
+and that involves thinking about what
+should be our basis
+
+ align:start position:0%
+should be our basis
+ 
+
+ align:start position:0%
+should be our basis
+signals in DT there was a really good
+
+ align:start position:0%
+signals in DT there was a really good
+ 
+
+ align:start position:0%
+signals in DT there was a really good
+candidate for that which we call the
+
+ align:start position:0%
+candidate for that which we call the
+ 
+
+ align:start position:0%
+candidate for that which we call the
+unit sample
+
+ align:start position:0%
+unit sample
+ 
+
+ align:start position:0%
+unit sample
+signal the unit sample signal is the
+
+ align:start position:0%
+signal the unit sample signal is the
+ 
+
+ align:start position:0%
+signal the unit sample signal is the
+simplest possible non-trivial DT signal
+
+ align:start position:0%
+simplest possible non-trivial DT signal
+ 
+
+ align:start position:0%
+simplest possible non-trivial DT signal
+by which I mean it is zero everywhere
+
+ align:start position:0%
+by which I mean it is zero everywhere
+ 
+
+ align:start position:0%
+by which I mean it is zero everywhere
+except one place if it were zero
+
+ align:start position:0%
+except one place if it were zero
+ 
+
+ align:start position:0%
+except one place if it were zero
+everywhere we would call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trivial so in order for it not to be
+
+ align:start position:0%
+trivial so in order for it not to be
+ 
+
+ align:start position:0%
+trivial so in order for it not to be
+trivial it has to be nonzero at least
+
+ align:start position:0%
+trivial it has to be nonzero at least
+ 
+
+ align:start position:0%
+trivial it has to be nonzero at least
+someplace the place is non-trivial is at
+
+ align:start position:0%
+someplace the place is non-trivial is at
+ 
+
+ align:start position:0%
+someplace the place is non-trivial is at
+n equal
+
+ align:start position:0%
+n equal
+ 
+
+ align:start position:0%
+n equal
+0 and the value that it is given that it
+
+ align:start position:0%
+0 and the value that it is given that it
+ 
+
+ align:start position:0%
+0 and the value that it is given that it
+can't be zero is one okay so the unit
+
+ align:start position:0%
+can't be zero is one okay so the unit
+ 
+
+ align:start position:0%
+can't be zero is one okay so the unit
+sample signal is the most simple
+
+ align:start position:0%
+sample signal is the most simple
+ 
+
+ align:start position:0%
+sample signal is the most simple
+non-trivial DT signal so what we need is
+
+ align:start position:0%
+non-trivial DT signal so what we need is
+ 
+
+ align:start position:0%
+non-trivial DT signal so what we need is
+the equivalent for
+
+ align:start position:0%
+the equivalent for
+ 
+
+ align:start position:0%
+the equivalent for
+CT so here it
+
+ align:start position:0%
+CT so here it
+ 
+
+ align:start position:0%
+CT so here it
+is Define a signal in
+
+ align:start position:0%
+is Define a signal in
+ 
+
+ align:start position:0%
+is Define a signal in
+CT that is zero everywhere except zero
+
+ align:start position:0%
+CT that is zero everywhere except zero
+ 
+
+ align:start position:0%
+CT that is zero everywhere except zero
+and that zero make it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so is that a good choice and I hope
+
+ align:start position:0%
+one so is that a good choice and I hope
+ 
+
+ align:start position:0%
+one so is that a good choice and I hope
+I've sort of biased my presentation
+
+ align:start position:0%
+I've sort of biased my presentation
+ 
+
+ align:start position:0%
+I've sort of biased my presentation
+enough so that the answer is
+
+ align:start position:0%
+enough so that the answer is
+ 
+
+ align:start position:0%
+enough so that the answer is
+obviously no so the real question is why
+
+ align:start position:0%
+obviously no so the real question is why
+ 
+
+ align:start position:0%
+obviously no so the real question is why
+not can somebody think of a good reason
+
+ align:start position:0%
+not can somebody think of a good reason
+ 
+
+ align:start position:0%
+not can somebody think of a good reason
+why this is a poor choice for a building
+
+ align:start position:0%
+why this is a poor choice for a building
+ 
+
+ align:start position:0%
+why this is a poor choice for a building
+block signal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so you you would need infinite gain
+
+ align:start position:0%
+yes so you you would need infinite gain
+ 
+
+ align:start position:0%
+yes so you you would need infinite gain
+to go from zero to one that's sort of
+
+ align:start position:0%
+to go from zero to one that's sort of
+ 
+
+ align:start position:0%
+to go from zero to one that's sort of
+true for the r thing
+
+ align:start position:0%
+true for the r thing
+ 
+
+ align:start position:0%
+true for the r thing
+two right you have to go from 0 to
+
+ align:start position:0%
+two right you have to go from 0 to
+ 
+
+ align:start position:0%
+two right you have to go from 0 to
+one it's in zero time that seems hard
+
+ align:start position:0%
+one it's in zero time that seems hard
+ 
+
+ align:start position:0%
+one it's in zero time that seems hard
+any other ideas
+
+ align:start position:0%
+any other ideas
+ 
+
+ align:start position:0%
+any other ideas
+yeah not
+
+ align:start position:0%
+yeah not
+ 
+
+ align:start position:0%
+yeah not
+continuous uh that's also
+
+ align:start position:0%
+continuous uh that's also
+ 
+
+ align:start position:0%
+continuous uh that's also
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+yes the integral is always zero that's a
+
+ align:start position:0%
+yes the integral is always zero that's a
+ 
+
+ align:start position:0%
+yes the integral is always zero that's a
+problem so what kind of so it's not it's
+
+ align:start position:0%
+problem so what kind of so it's not it's
+ 
+
+ align:start position:0%
+problem so what kind of so it's not it's
+just not going to be a very useful
+
+ align:start position:0%
+just not going to be a very useful
+ 
+
+ align:start position:0%
+just not going to be a very useful
+signal okay what am I doing I'm trying
+
+ align:start position:0%
+signal okay what am I doing I'm trying
+ 
+
+ align:start position:0%
+signal okay what am I doing I'm trying
+to figure out a basis
+
+ align:start position:0%
+to figure out a basis
+ 
+
+ align:start position:0%
+to figure out a basis
+signal that I would use in Block
+
+ align:start position:0%
+signal that I would use in Block
+ 
+
+ align:start position:0%
+signal that I would use in Block
+diagrams my basic block diagram is this
+
+ align:start position:0%
+diagrams my basic block diagram is this
+ 
+
+ align:start position:0%
+diagrams my basic block diagram is this
+integrator
+
+ align:start position:0%
+integrator
+ 
+
+ align:start position:0%
+integrator
+thing minus infinity to T on
+
+ align:start position:0%
+thing minus infinity to T on
+ 
+
+ align:start position:0%
+thing minus infinity to T on
+to so I'd like to put something in here
+
+ align:start position:0%
+to so I'd like to put something in here
+ 
+
+ align:start position:0%
+to so I'd like to put something in here
+but if I put that signal what did I call
+
+ align:start position:0%
+but if I put that signal what did I call
+ 
+
+ align:start position:0%
+but if I put that signal what did I call
+it w if I put
+
+ align:start position:0%
+it w if I put
+ 
+
+ align:start position:0%
+it w if I put
+W into an integrator what's the output
+
+ align:start position:0%
+W into an integrator what's the output
+ 
+
+ align:start position:0%
+W into an integrator what's the output
+of the integrator after you integrate
+
+ align:start position:0%
+of the integrator after you integrate
+ 
+
+ align:start position:0%
+of the integrator after you integrate
+W zero well that's a problem it's not a
+
+ align:start position:0%
+W zero well that's a problem it's not a
+ 
+
+ align:start position:0%
+W zero well that's a problem it's not a
+very good basis function if the very
+
+ align:start position:0%
+very good basis function if the very
+ 
+
+ align:start position:0%
+very good basis function if the very
+first operator I go through turns it
+
+ align:start position:0%
+first operator I go through turns it
+ 
+
+ align:start position:0%
+first operator I go through turns it
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+zero everyone see that that's kind of a
+
+ align:start position:0%
+zero everyone see that that's kind of a
+ 
+
+ align:start position:0%
+zero everyone see that that's kind of a
+problem this is the problem in CT if you
+
+ align:start position:0%
+problem this is the problem in CT if you
+ 
+
+ align:start position:0%
+problem this is the problem in CT if you
+guys figure out the next slide you're
+
+ align:start position:0%
+guys figure out the next slide you're
+ 
+
+ align:start position:0%
+guys figure out the next slide you're
+done CT is easy so what we
+
+ align:start position:0%
+done CT is easy so what we
+ 
+
+ align:start position:0%
+done CT is easy so what we
+do is think about defining a
+
+ align:start position:0%
+do is think about defining a
+ 
+
+ align:start position:0%
+do is think about defining a
+signal that would have the property that
+
+ align:start position:0%
+signal that would have the property that
+ 
+
+ align:start position:0%
+signal that would have the property that
+it behaved as though it had those
+
+ align:start position:0%
+it behaved as though it had those
+ 
+
+ align:start position:0%
+it behaved as though it had those
+desirable properties what would have to
+
+ align:start position:0%
+desirable properties what would have to
+ 
+
+ align:start position:0%
+desirable properties what would have to
+happen we'd like a signal that had some
+
+ align:start position:0%
+happen we'd like a signal that had some
+ 
+
+ align:start position:0%
+happen we'd like a signal that had some
+amount of area because that's what this
+
+ align:start position:0%
+amount of area because that's what this
+ 
+
+ align:start position:0%
+amount of area because that's what this
+thing is this is an area
+
+ align:start position:0%
+thing is this is an area
+ 
+
+ align:start position:0%
+thing is this is an area
+operator we would like a signal that
+
+ align:start position:0%
+operator we would like a signal that
+ 
+
+ align:start position:0%
+operator we would like a signal that
+didn't have zero area the the W signal
+
+ align:start position:0%
+didn't have zero area the the W signal
+ 
+
+ align:start position:0%
+didn't have zero area the the W signal
+has zero area
+
+ align:start position:0%
+has zero area
+ 
+
+ align:start position:0%
+has zero area
+bad we'd like a signal that doesn't have
+
+ align:start position:0%
+bad we'd like a signal that doesn't have
+ 
+
+ align:start position:0%
+bad we'd like a signal that doesn't have
+zero area in fact if we wanted it to be
+
+ align:start position:0%
+zero area in fact if we wanted it to be
+ 
+
+ align:start position:0%
+zero area in fact if we wanted it to be
+kind of the simplest possible thing it
+
+ align:start position:0%
+kind of the simplest possible thing it
+ 
+
+ align:start position:0%
+kind of the simplest possible thing it
+should have an area of one right but
+
+ align:start position:0%
+should have an area of one right but
+ 
+
+ align:start position:0%
+should have an area of one right but
+we'd like it to be zero almost
+
+ align:start position:0%
+we'd like it to be zero almost
+ 
+
+ align:start position:0%
+we'd like it to be zero almost
+everywhere how do you do that
+
+ align:start position:0%
+everywhere how do you do that
+ 
+
+ align:start position:0%
+everywhere how do you do that
+okay well the way you can do it and the
+
+ align:start position:0%
+okay well the way you can do it and the
+ 
+
+ align:start position:0%
+okay well the way you can do it and the
+way we will do it is think about a
+
+ align:start position:0%
+way we will do it is think about a
+ 
+
+ align:start position:0%
+way we will do it is think about a
+building a signal in a
+
+ align:start position:0%
+building a signal in a
+ 
+
+ align:start position:0%
+building a signal in a
+limit what if I had a a pulse signal
+
+ align:start position:0%
+limit what if I had a a pulse signal
+ 
+
+ align:start position:0%
+limit what if I had a a pulse signal
+that was 2 Epsilon wide and 1 over 2
+
+ align:start position:0%
+that was 2 Epsilon wide and 1 over 2
+ 
+
+ align:start position:0%
+that was 2 Epsilon wide and 1 over 2
+Epsilon High the area would be one
+
+ align:start position:0%
+Epsilon High the area would be one
+ 
+
+ align:start position:0%
+Epsilon High the area would be one
+regardless of the value of
+
+ align:start position:0%
+regardless of the value of
+ 
+
+ align:start position:0%
+regardless of the value of
+Epsilon and if I shrunk Epsilon to be a
+
+ align:start position:0%
+Epsilon and if I shrunk Epsilon to be a
+ 
+
+ align:start position:0%
+Epsilon and if I shrunk Epsilon to be a
+very small
+
+ align:start position:0%
+very small
+ 
+
+ align:start position:0%
+very small
+number say
+
+ align:start position:0%
+number say
+ 
+
+ align:start position:0%
+number say
+zero if I think about the limit as EPS
+
+ align:start position:0%
+zero if I think about the limit as EPS
+ 
+
+ align:start position:0%
+zero if I think about the limit as EPS
+get smaller small and smaller and
+
+ align:start position:0%
+get smaller small and smaller and
+ 
+
+ align:start position:0%
+get smaller small and smaller and
+smaller and smaller then I approach the
+
+ align:start position:0%
+smaller and smaller then I approach the
+ 
+
+ align:start position:0%
+smaller and smaller then I approach the
+condition I'd like to have the signal is
+
+ align:start position:0%
+condition I'd like to have the signal is
+ 
+
+ align:start position:0%
+condition I'd like to have the signal is
+zero everywhere except zero now it has a
+
+ align:start position:0%
+zero everywhere except zero now it has a
+ 
+
+ align:start position:0%
+zero everywhere except zero now it has a
+horrendous value at zero but oh well
+
+ align:start position:0%
+horrendous value at zero but oh well
+ 
+
+ align:start position:0%
+horrendous value at zero but oh well
+I'll sweep that under the rug the
+
+ align:start position:0%
+I'll sweep that under the rug the
+ 
+
+ align:start position:0%
+I'll sweep that under the rug the
+important thing is that when I integrate
+
+ align:start position:0%
+important thing is that when I integrate
+ 
+
+ align:start position:0%
+important thing is that when I integrate
+it I'd like it to give me one that's the
+
+ align:start position:0%
+it I'd like it to give me one that's the
+ 
+
+ align:start position:0%
+it I'd like it to give me one that's the
+important thing everyone with me that's
+
+ align:start position:0%
+important thing everyone with me that's
+ 
+
+ align:start position:0%
+important thing everyone with me that's
+the hardest part in this part of the
+
+ align:start position:0%
+the hardest part in this part of the
+ 
+
+ align:start position:0%
+the hardest part in this part of the
+course if you get this CT systems are a
+
+ align:start position:0%
+course if you get this CT systems are a
+ 
+
+ align:start position:0%
+course if you get this CT systems are a
+breeze so this is kind of a different
+
+ align:start position:0%
+breeze so this is kind of a different
+ 
+
+ align:start position:0%
+breeze so this is kind of a different
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+signal the idea is to incorporate in it
+
+ align:start position:0%
+signal the idea is to incorporate in it
+ 
+
+ align:start position:0%
+signal the idea is to incorporate in it
+two seemingly uh contradictory things it
+
+ align:start position:0%
+two seemingly uh contradictory things it
+ 
+
+ align:start position:0%
+two seemingly uh contradictory things it
+should be zero almost
+
+ align:start position:0%
+should be zero almost
+ 
+
+ align:start position:0%
+should be zero almost
+everywhere and the integral should be
+
+ align:start position:0%
+everywhere and the integral should be
+ 
+
+ align:start position:0%
+everywhere and the integral should be
+one so there is no such thing right this
+
+ align:start position:0%
+one so there is no such thing right this
+ 
+
+ align:start position:0%
+one so there is no such thing right this
+is an idealized signal this is something
+
+ align:start position:0%
+is an idealized signal this is something
+ 
+
+ align:start position:0%
+is an idealized signal this is something
+that we think about in the limit it
+
+ align:start position:0%
+that we think about in the limit it
+ 
+
+ align:start position:0%
+that we think about in the limit it
+turns out that we can get a lot of
+
+ align:start position:0%
+turns out that we can get a lot of
+ 
+
+ align:start position:0%
+turns out that we can get a lot of
+insight by thinking about this
+
+ align:start position:0%
+insight by thinking about this
+ 
+
+ align:start position:0%
+insight by thinking about this
+signal but it is important to realize
+
+ align:start position:0%
+signal but it is important to realize
+ 
+
+ align:start position:0%
+signal but it is important to realize
+that it only def is only defined in a
+
+ align:start position:0%
+that it only def is only defined in a
+ 
+
+ align:start position:0%
+that it only def is only defined in a
+limit so um we will write it since it's
+
+ align:start position:0%
+limit so um we will write it since it's
+ 
+
+ align:start position:0%
+limit so um we will write it since it's
+so useful we will write it this way
+
+ align:start position:0%
+so useful we will write it this way
+ 
+
+ align:start position:0%
+so useful we will write it this way
+we'll draw a little arrow the arrow is
+
+ align:start position:0%
+we'll draw a little arrow the arrow is
+ 
+
+ align:start position:0%
+we'll draw a little arrow the arrow is
+supposed to canote in your mind this
+
+ align:start position:0%
+supposed to canote in your mind this
+ 
+
+ align:start position:0%
+supposed to canote in your mind this
+thing goes really
+
+ align:start position:0%
+thing goes really
+ 
+
+ align:start position:0%
+thing goes really
+high it goes so high that telling you
+
+ align:start position:0%
+high it goes so high that telling you
+ 
+
+ align:start position:0%
+high it goes so high that telling you
+how high it is is meaningless so instead
+
+ align:start position:0%
+how high it is is meaningless so instead
+ 
+
+ align:start position:0%
+how high it is is meaningless so instead
+to the side we tell you what's the area
+
+ align:start position:0%
+to the side we tell you what's the area
+ 
+
+ align:start position:0%
+to the side we tell you what's the area
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+it what would come out if you integrated
+
+ align:start position:0%
+it what would come out if you integrated
+ 
+
+ align:start position:0%
+it what would come out if you integrated
+it yes for DT signal like decompose any
+
+ align:start position:0%
+it yes for DT signal like decompose any
+ 
+
+ align:start position:0%
+it yes for DT signal like decompose any
+DT signal into a series of can you do
+
+ align:start position:0%
+DT signal into a series of can you do
+ 
+
+ align:start position:0%
+DT signal into a series of can you do
+the same thing with yes and that will be
+
+ align:start position:0%
+the same thing with yes and that will be
+ 
+
+ align:start position:0%
+the same thing with yes and that will be
+something that we spend a lot of time on
+
+ align:start position:0%
+something that we spend a lot of time on
+ 
+
+ align:start position:0%
+something that we spend a lot of time on
+because that decomposition is not
+
+ align:start position:0%
+because that decomposition is not
+ 
+
+ align:start position:0%
+because that decomposition is not
+trivial but it is
+
+ align:start position:0%
+trivial but it is
+ 
+
+ align:start position:0%
+trivial but it is
+possible so the question was can we
+
+ align:start position:0%
+possible so the question was can we
+ 
+
+ align:start position:0%
+possible so the question was can we
+decompose arbitrary signals into sums of
+
+ align:start position:0%
+decompose arbitrary signals into sums of
+ 
+
+ align:start position:0%
+decompose arbitrary signals into sums of
+these things and the answer is
+
+ align:start position:0%
+these things and the answer is
+ 
+
+ align:start position:0%
+these things and the answer is
+absolutely
+
+ align:start position:0%
+absolutely
+ 
+
+ align:start position:0%
+absolutely
+yes that's why we like
+
+ align:start position:0%
+yes that's why we like
+ 
+
+ align:start position:0%
+yes that's why we like
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+okay uh so the first thing think about
+
+ align:start position:0%
+okay uh so the first thing think about
+ 
+
+ align:start position:0%
+okay uh so the first thing think about
+is what happens if you put now instead
+
+ align:start position:0%
+is what happens if you put now instead
+ 
+
+ align:start position:0%
+is what happens if you put now instead
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+w let's put Delta of
+
+ align:start position:0%
+w let's put Delta of
+ 
+
+ align:start position:0%
+w let's put Delta of
+T the unit impulse
+
+ align:start position:0%
+T the unit impulse
+ 
+
+ align:start position:0%
+T the unit impulse
+function what happens if you put the
+
+ align:start position:0%
+function what happens if you put the
+ 
+
+ align:start position:0%
+function what happens if you put the
+unit impulse function into an integrator
+
+ align:start position:0%
+unit impulse function into an integrator
+ 
+
+ align:start position:0%
+unit impulse function into an integrator
+well if you integrate the Delta of T so
+
+ align:start position:0%
+well if you integrate the Delta of T so
+ 
+
+ align:start position:0%
+well if you integrate the Delta of T so
+if my input X of T is Delta of T and if
+
+ align:start position:0%
+if my input X of T is Delta of T and if
+ 
+
+ align:start position:0%
+if my input X of T is Delta of T and if
+I want to think about y of T which is
+
+ align:start position:0%
+I want to think about y of T which is
+ 
+
+ align:start position:0%
+I want to think about y of T which is
+going to be a operating on x so think
+
+ align:start position:0%
+going to be a operating on x so think
+ 
+
+ align:start position:0%
+going to be a operating on x so think
+about what would be the answer to this
+
+ align:start position:0%
+about what would be the answer to this
+ 
+
+ align:start position:0%
+about what would be the answer to this
+integral for times less than zero well
+
+ align:start position:0%
+integral for times less than zero well
+ 
+
+ align:start position:0%
+integral for times less than zero well
+the system started at rest if the
+
+ align:start position:0%
+the system started at rest if the
+ 
+
+ align:start position:0%
+the system started at rest if the
+integrator turned on at
+
+ align:start position:0%
+integrator turned on at
+ 
+
+ align:start position:0%
+integrator turned on at
+zero What's the value of the answer of
+
+ align:start position:0%
+zero What's the value of the answer of
+ 
+
+ align:start position:0%
+zero What's the value of the answer of
+the integrator
+
+ align:start position:0%
+the integrator
+ 
+
+ align:start position:0%
+the integrator
+here zero it started at zero back at
+
+ align:start position:0%
+here zero it started at zero back at
+ 
+
+ align:start position:0%
+here zero it started at zero back at
+minus infinity sometime started at rest
+
+ align:start position:0%
+minus infinity sometime started at rest
+ 
+
+ align:start position:0%
+minus infinity sometime started at rest
+there was no
+
+ align:start position:0%
+there was no
+ 
+
+ align:start position:0%
+there was no
+input so the answer is zero so the
+
+ align:start position:0%
+input so the answer is zero so the
+ 
+
+ align:start position:0%
+input so the answer is zero so the
+answer is going to be zero up until
+
+ align:start position:0%
+answer is going to be zero up until
+ 
+
+ align:start position:0%
+answer is going to be zero up until
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+happens during that brief of
+
+ align:start position:0%
+happens during that brief of
+ 
+
+ align:start position:0%
+happens during that brief of
+time a unit of area went in so what's
+
+ align:start position:0%
+time a unit of area went in so what's
+ 
+
+ align:start position:0%
+time a unit of area went in so what's
+the output of the integrator
+
+ align:start position:0%
+the output of the integrator
+ 
+
+ align:start position:0%
+the output of the integrator
+become
+
+ align:start position:0%
+become
+ 
+
+ align:start position:0%
+become
+one so at that time it became
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and then what's the value as you go
+
+ align:start position:0%
+one and then what's the value as you go
+ 
+
+ align:start position:0%
+one and then what's the value as you go
+forward in
+
+ align:start position:0%
+forward in
+ 
+
+ align:start position:0%
+forward in
+time one right it got stuck at one so
+
+ align:start position:0%
+time one right it got stuck at one so
+ 
+
+ align:start position:0%
+time one right it got stuck at one so
+the most primitive signal that we'll
+
+ align:start position:0%
+the most primitive signal that we'll
+ 
+
+ align:start position:0%
+the most primitive signal that we'll
+think about is the unit impulse function
+
+ align:start position:0%
+think about is the unit impulse function
+ 
+
+ align:start position:0%
+think about is the unit impulse function
+we'll denote that by Delta of t
+
+ align:start position:0%
+we'll denote that by Delta of t
+ 
+
+ align:start position:0%
+we'll denote that by Delta of t
+and it has the property that it goes
+
+ align:start position:0%
+and it has the property that it goes
+ 
+
+ align:start position:0%
+and it has the property that it goes
+through our most primitive
+
+ align:start position:0%
+through our most primitive
+ 
+
+ align:start position:0%
+through our most primitive
+block Delta goes to a unit step and the
+
+ align:start position:0%
+block Delta goes to a unit step and the
+ 
+
+ align:start position:0%
+block Delta goes to a unit step and the
+unit step is so useful that we'll give
+
+ align:start position:0%
+unit step is so useful that we'll give
+ 
+
+ align:start position:0%
+unit step is so useful that we'll give
+it a special name U of T U means unit
+
+ align:start position:0%
+it a special name U of T U means unit
+ 
+
+ align:start position:0%
+it a special name U of T U means unit
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+okay and with that all of these systems
+
+ align:start position:0%
+okay and with that all of these systems
+ 
+
+ align:start position:0%
+okay and with that all of these systems
+now make sense in the same sense that uh
+
+ align:start position:0%
+now make sense in the same sense that uh
+ 
+
+ align:start position:0%
+now make sense in the same sense that uh
+DT systems did so for example if I have
+
+ align:start position:0%
+DT systems did so for example if I have
+ 
+
+ align:start position:0%
+DT systems did so for example if I have
+a feed forward
+
+ align:start position:0%
+a feed forward
+ 
+
+ align:start position:0%
+a feed forward
+system I can think about that as having
+
+ align:start position:0%
+system I can think about that as having
+ 
+
+ align:start position:0%
+system I can think about that as having
+several signal flow paths going
+
+ align:start position:0%
+several signal flow paths going
+ 
+
+ align:start position:0%
+several signal flow paths going
+forward and the output of the signal
+
+ align:start position:0%
+forward and the output of the signal
+ 
+
+ align:start position:0%
+forward and the output of the signal
+when stimulated with a Delta
+
+ align:start position:0%
+when stimulated with a Delta
+ 
+
+ align:start position:0%
+when stimulated with a Delta
+function is the sum of all those
+
+ align:start position:0%
+function is the sum of all those
+ 
+
+ align:start position:0%
+function is the sum of all those
+different signal paths that I can think
+
+ align:start position:0%
+different signal paths that I can think
+ 
+
+ align:start position:0%
+different signal paths that I can think
+of so I can express the input output
+
+ align:start position:0%
+of so I can express the input output
+ 
+
+ align:start position:0%
+of so I can express the input output
+relationship by this functional
+
+ align:start position:0%
+relationship by this functional
+ 
+
+ align:start position:0%
+relationship by this functional
+relationship right everybody sees
+
+ align:start position:0%
+relationship right everybody sees
+ 
+
+ align:start position:0%
+relationship right everybody sees
+that or I can just think about all the
+
+ align:start position:0%
+that or I can just think about all the
+ 
+
+ align:start position:0%
+that or I can just think about all the
+different signal flow paths through here
+
+ align:start position:0%
+different signal flow paths through here
+ 
+
+ align:start position:0%
+different signal flow paths through here
+what would happen if I had a Delta
+
+ align:start position:0%
+what would happen if I had a Delta
+ 
+
+ align:start position:0%
+what would happen if I had a Delta
+function here well here's a signal flow
+
+ align:start position:0%
+function here well here's a signal flow
+ 
+
+ align:start position:0%
+function here well here's a signal flow
+path here's another one here's another
+
+ align:start position:0%
+path here's another one here's another
+ 
+
+ align:start position:0%
+path here's another one here's another
+one here's one four signal flow paths I
+
+ align:start position:0%
+one here's one four signal flow paths I
+ 
+
+ align:start position:0%
+one here's one four signal flow paths I
+have to think about four ways the input
+
+ align:start position:0%
+have to think about four ways the input
+ 
+
+ align:start position:0%
+have to think about four ways the input
+could turn into the output if the input
+
+ align:start position:0%
+could turn into the output if the input
+ 
+
+ align:start position:0%
+could turn into the output if the input
+went through the top path the output
+
+ align:start position:0%
+went through the top path the output
+ 
+
+ align:start position:0%
+went through the top path the output
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+Delta if the input went through this
+
+ align:start position:0%
+Delta if the input went through this
+ 
+
+ align:start position:0%
+Delta if the input went through this
+path the output would
+
+ align:start position:0%
+path the output would
+ 
+
+ align:start position:0%
+path the output would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+U if the if the input went through this
+
+ align:start position:0%
+U if the if the input went through this
+ 
+
+ align:start position:0%
+U if the if the input went through this
+path
+
+ align:start position:0%
+path
+ 
+
+ align:start position:0%
+path
+you if the input went through this it
+
+ align:start position:0%
+you if the input went through this it
+ 
+
+ align:start position:0%
+you if the input went through this it
+turns into U and then it goes through
+
+ align:start position:0%
+turns into U and then it goes through
+ 
+
+ align:start position:0%
+turns into U and then it goes through
+another accumulator what happens if you
+
+ align:start position:0%
+another accumulator what happens if you
+ 
+
+ align:start position:0%
+another accumulator what happens if you
+integrate
+
+ align:start position:0%
+integrate
+ 
+
+ align:start position:0%
+integrate
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+t right if this is
+
+ align:start position:0%
+t right if this is
+ 
+
+ align:start position:0%
+t right if this is
+U and if you put that into an into an
+
+ align:start position:0%
+U and if you put that into an into an
+ 
+
+ align:start position:0%
+U and if you put that into an into an
+integrator that integrator like all the
+
+ align:start position:0%
+integrator that integrator like all the
+ 
+
+ align:start position:0%
+integrator that integrator like all the
+other integrators that we'll talk about
+
+ align:start position:0%
+other integrators that we'll talk about
+ 
+
+ align:start position:0%
+other integrators that we'll talk about
+unless we tell you otherwise is
+
+ align:start position:0%
+unless we tell you otherwise is
+ 
+
+ align:start position:0%
+unless we tell you otherwise is
+initially at rest therefore the output
+
+ align:start position:0%
+initially at rest therefore the output
+ 
+
+ align:start position:0%
+initially at rest therefore the output
+started at
+
+ align:start position:0%
+started at
+ 
+
+ align:start position:0%
+started at
+zero because U is z for T less than Z it
+
+ align:start position:0%
+zero because U is z for T less than Z it
+ 
+
+ align:start position:0%
+zero because U is z for T less than Z it
+zero until something happens at T equals
+
+ align:start position:0%
+zero until something happens at T equals
+ 
+
+ align:start position:0%
+zero until something happens at T equals
+z at which point the input becomes one
+
+ align:start position:0%
+z at which point the input becomes one
+ 
+
+ align:start position:0%
+z at which point the input becomes one
+and the integral of one is
+
+ align:start position:0%
+and the integral of one is
+ 
+
+ align:start position:0%
+and the integral of one is
+T so we will usually write that this
+
+ align:start position:0%
+T so we will usually write that this
+ 
+
+ align:start position:0%
+T so we will usually write that this
+way meaning it's t so we we will write
+
+ align:start position:0%
+way meaning it's t so we we will write
+ 
+
+ align:start position:0%
+way meaning it's t so we we will write
+as a short hand times U that's kind of a
+
+ align:start position:0%
+as a short hand times U that's kind of a
+ 
+
+ align:start position:0%
+as a short hand times U that's kind of a
+strange strange thing to do it's just
+
+ align:start position:0%
+strange strange thing to do it's just
+ 
+
+ align:start position:0%
+strange strange thing to do it's just
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+convenient it's convenient because
+
+ align:start position:0%
+convenient it's convenient because
+ 
+
+ align:start position:0%
+convenient it's convenient because
+normally when you have a function so
+
+ align:start position:0%
+normally when you have a function so
+ 
+
+ align:start position:0%
+normally when you have a function so
+that last
+
+ align:start position:0%
+that last
+ 
+
+ align:start position:0%
+that last
+function this one is a signal
+
+ align:start position:0%
+function this one is a signal
+ 
+
+ align:start position:0%
+function this one is a signal
+that does
+
+ align:start position:0%
+that does
+ 
+
+ align:start position:0%
+that does
+this so we will call that Tu of T
+
+ align:start position:0%
+this so we will call that Tu of T
+ 
+
+ align:start position:0%
+this so we will call that Tu of T
+because obviously T is that signal we
+
+ align:start position:0%
+because obviously T is that signal we
+ 
+
+ align:start position:0%
+because obviously T is that signal we
+don't mean that right we want to Lop off
+
+ align:start position:0%
+don't mean that right we want to Lop off
+ 
+
+ align:start position:0%
+don't mean that right we want to Lop off
+the part that came before zero U of T
+
+ align:start position:0%
+the part that came before zero U of T
+ 
+
+ align:start position:0%
+the part that came before zero U of T
+multiplying by U of T is a quick way of
+
+ align:start position:0%
+multiplying by U of T is a quick way of
+ 
+
+ align:start position:0%
+multiplying by U of T is a quick way of
+writing Lop off the stuff that came
+
+ align:start position:0%
+writing Lop off the stuff that came
+ 
+
+ align:start position:0%
+writing Lop off the stuff that came
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+zero that's all that means so we'll
+
+ align:start position:0%
+zero that's all that means so we'll
+ 
+
+ align:start position:0%
+zero that's all that means so we'll
+we'll write that that way and you can
+
+ align:start position:0%
+we'll write that that way and you can
+ 
+
+ align:start position:0%
+we'll write that that way and you can
+see that by thinking about signal flow
+
+ align:start position:0%
+see that by thinking about signal flow
+ 
+
+ align:start position:0%
+see that by thinking about signal flow
+path and by thinking about how this
+
+ align:start position:0%
+path and by thinking about how this
+ 
+
+ align:start position:0%
+path and by thinking about how this
+basic signal this basis function goes
+
+ align:start position:0%
+basic signal this basis function goes
+ 
+
+ align:start position:0%
+basic signal this basis function goes
+through the system it's easy to figure
+
+ align:start position:0%
+through the system it's easy to figure
+ 
+
+ align:start position:0%
+through the system it's easy to figure
+out U the the response of such a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system just like in DP feedback is
+
+ align:start position:0%
+system just like in DP feedback is
+ 
+
+ align:start position:0%
+system just like in DP feedback is
+different so now we have to think about
+
+ align:start position:0%
+different so now we have to think about
+ 
+
+ align:start position:0%
+different so now we have to think about
+what would happen if there's a feedback
+
+ align:start position:0%
+what would happen if there's a feedback
+ 
+
+ align:start position:0%
+what would happen if there's a feedback
+loop so it was crucial when I was doing
+
+ align:start position:0%
+loop so it was crucial when I was doing
+ 
+
+ align:start position:0%
+loop so it was crucial when I was doing
+this kind of an illustration that it was
+
+ align:start position:0%
+this kind of an illustration that it was
+ 
+
+ align:start position:0%
+this kind of an illustration that it was
+feed forward
+
+ align:start position:0%
+feed forward
+ 
+
+ align:start position:0%
+feed forward
+only I could I could I could decompose
+
+ align:start position:0%
+only I could I could I could decompose
+ 
+
+ align:start position:0%
+only I could I could I could decompose
+all of the signal flow paths into a
+
+ align:start position:0%
+all of the signal flow paths into a
+ 
+
+ align:start position:0%
+all of the signal flow paths into a
+finite number of forward goinging paths
+
+ align:start position:0%
+finite number of forward goinging paths
+ 
+
+ align:start position:0%
+finite number of forward goinging paths
+this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+harder so this happened in dt2 we had to
+
+ align:start position:0%
+harder so this happened in dt2 we had to
+ 
+
+ align:start position:0%
+harder so this happened in dt2 we had to
+figure out how the DT system was going
+
+ align:start position:0%
+figure out how the DT system was going
+ 
+
+ align:start position:0%
+figure out how the DT system was going
+to work when we had a feedback path and
+
+ align:start position:0%
+to work when we had a feedback path and
+ 
+
+ align:start position:0%
+to work when we had a feedback path and
+it was more complicated and we had to
+
+ align:start position:0%
+it was more complicated and we had to
+ 
+
+ align:start position:0%
+it was more complicated and we had to
+fall back on thinking about sample by
+
+ align:start position:0%
+fall back on thinking about sample by
+ 
+
+ align:start position:0%
+fall back on thinking about sample by
+sample propagation of the signal through
+
+ align:start position:0%
+sample propagation of the signal through
+ 
+
+ align:start position:0%
+sample propagation of the signal through
+the system and we'll do the same thing
+
+ align:start position:0%
+the system and we'll do the same thing
+ 
+
+ align:start position:0%
+the system and we'll do the same thing
+here in order to figure out how to think
+
+ align:start position:0%
+here in order to figure out how to think
+ 
+
+ align:start position:0%
+here in order to figure out how to think
+about signal flow through such a
+
+ align:start position:0%
+about signal flow through such a
+ 
+
+ align:start position:0%
+about signal flow through such a
+diagram through a diagram that has
+
+ align:start position:0%
+diagram through a diagram that has
+ 
+
+ align:start position:0%
+diagram through a diagram that has
+feedback
+
+ align:start position:0%
+feedback
+ 
+
+ align:start position:0%
+feedback
+we'll think about falling back to 1803
+
+ align:start position:0%
+we'll think about falling back to 1803
+ 
+
+ align:start position:0%
+we'll think about falling back to 1803
+right something we can trust something
+
+ align:start position:0%
+right something we can trust something
+ 
+
+ align:start position:0%
+right something we can trust something
+we all loved right nod nod your heads
+
+ align:start position:0%
+we all loved right nod nod your heads
+ 
+
+ align:start position:0%
+we all loved right nod nod your heads
+yes make me this reassures me right fond
+
+ align:start position:0%
+yes make me this reassures me right fond
+ 
+
+ align:start position:0%
+yes make me this reassures me right fond
+memories of 1803 right so it's pretty
+
+ align:start position:0%
+memories of 1803 right so it's pretty
+ 
+
+ align:start position:0%
+memories of 1803 right so it's pretty
+simple to think about how you would
+
+ align:start position:0%
+simple to think about how you would
+ 
+
+ align:start position:0%
+simple to think about how you would
+solve that system by using an 1803 type
+
+ align:start position:0%
+solve that system by using an 1803 type
+ 
+
+ align:start position:0%
+solve that system by using an 1803 type
+approach convert the system into a
+
+ align:start position:0%
+approach convert the system into a
+ 
+
+ align:start position:0%
+approach convert the system into a
+differential equation we've already done
+
+ align:start position:0%
+differential equation we've already done
+ 
+
+ align:start position:0%
+differential equation we've already done
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one then from the form well we will
+
+ align:start position:0%
+one then from the form well we will
+ 
+
+ align:start position:0%
+one then from the form well we will
+usually in this class use the uh method
+
+ align:start position:0%
+usually in this class use the uh method
+ 
+
+ align:start position:0%
+usually in this class use the uh method
+the general method of solving
+
+ align:start position:0%
+the general method of solving
+ 
+
+ align:start position:0%
+the general method of solving
+differential equations which
+
+ align:start position:0%
+differential equations which
+ 
+
+ align:start position:0%
+differential equations which
+is what's the general method for solving
+
+ align:start position:0%
+is what's the general method for solving
+ 
+
+ align:start position:0%
+is what's the general method for solving
+differential
+
+ align:start position:0%
+differential
+ 
+
+ align:start position:0%
+differential
+equations they may not have told you in
+
+ align:start position:0%
+equations they may not have told you in
+ 
+
+ align:start position:0%
+equations they may not have told you in
+1803 what's the what's the general
+
+ align:start position:0%
+1803 what's the what's the general
+ 
+
+ align:start position:0%
+1803 what's the what's the general
+method of solving differential
+
+ align:start position:0%
+method of solving differential
+ 
+
+ align:start position:0%
+method of solving differential
+equations guess yes so the general
+
+ align:start position:0%
+equations guess yes so the general
+ 
+
+ align:start position:0%
+equations guess yes so the general
+method is
+
+ align:start position:0%
+method is
+ 
+
+ align:start position:0%
+method is
+guess if you can guess plug it in and it
+
+ align:start position:0%
+guess if you can guess plug it in and it
+ 
+
+ align:start position:0%
+guess if you can guess plug it in and it
+works you're
+
+ align:start position:0%
+works you're
+ 
+
+ align:start position:0%
+works you're
+done the kinds of systems that we will
+
+ align:start position:0%
+done the kinds of systems that we will
+ 
+
+ align:start position:0%
+done the kinds of systems that we will
+look at will be linear systems they will
+
+ align:start position:0%
+look at will be linear systems they will
+ 
+
+ align:start position:0%
+look at will be linear systems they will
+have a single unique solution if you can
+
+ align:start position:0%
+have a single unique solution if you can
+ 
+
+ align:start position:0%
+have a single unique solution if you can
+find it by guessing you're done and we
+
+ align:start position:0%
+find it by guessing you're done and we
+ 
+
+ align:start position:0%
+find it by guessing you're done and we
+will prove later in the course that all
+
+ align:start position:0%
+will prove later in the course that all
+ 
+
+ align:start position:0%
+will prove later in the course that all
+systems of this class where I haven't
+
+ align:start position:0%
+systems of this class where I haven't
+ 
+
+ align:start position:0%
+systems of this class where I haven't
+really defined what this class is but if
+
+ align:start position:0%
+really defined what this class is but if
+ 
+
+ align:start position:0%
+really defined what this class is but if
+you made a system out of adders gains
+
+ align:start position:0%
+you made a system out of adders gains
+ 
+
+ align:start position:0%
+you made a system out of adders gains
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+integrators and only those
+
+ align:start position:0%
+integrators and only those
+ 
+
+ align:start position:0%
+integrators and only those
+parts then that system will always be
+
+ align:start position:0%
+parts then that system will always be
+ 
+
+ align:start position:0%
+parts then that system will always be
+linear and the solutions can always be
+
+ align:start position:0%
+linear and the solutions can always be
+ 
+
+ align:start position:0%
+linear and the solutions can always be
+written as complex exponentials
+
+ align:start position:0%
+written as complex exponentials
+ 
+
+ align:start position:0%
+written as complex exponentials
+we'll prove that later I'm not going to
+
+ align:start position:0%
+we'll prove that later I'm not going to
+ 
+
+ align:start position:0%
+we'll prove that later I'm not going to
+bother with it now for now you would say
+
+ align:start position:0%
+bother with it now for now you would say
+ 
+
+ align:start position:0%
+bother with it now for now you would say
+Okay first order linear differential
+
+ align:start position:0%
+Okay first order linear differential
+ 
+
+ align:start position:0%
+Okay first order linear differential
+equation with constant coefficiency
+
+ align:start position:0%
+equation with constant coefficiency
+ 
+
+ align:start position:0%
+equation with constant coefficiency
+obvious the answer is obviously an
+
+ align:start position:0%
+obvious the answer is obviously an
+ 
+
+ align:start position:0%
+obvious the answer is obviously an
+exponential
+
+ align:start position:0%
+exponential
+ 
+
+ align:start position:0%
+exponential
+function so you plug that into the
+
+ align:start position:0%
+function so you plug that into the
+ 
+
+ align:start position:0%
+function so you plug that into the
+differential equation you figure out the
+
+ align:start position:0%
+differential equation you figure out the
+ 
+
+ align:start position:0%
+differential equation you figure out the
+constraints that would have to be uh
+
+ align:start position:0%
+constraints that would have to be uh
+ 
+
+ align:start position:0%
+constraints that would have to be uh
+solved for this to be true and the
+
+ align:start position:0%
+solved for this to be true and the
+ 
+
+ align:start position:0%
+solved for this to be true and the
+answer is that y should be e to the PT U
+
+ align:start position:0%
+answer is that y should be e to the PT U
+ 
+
+ align:start position:0%
+answer is that y should be e to the PT U
+of T should start at
+
+ align:start position:0%
+of T should start at
+ 
+
+ align:start position:0%
+of T should start at
+zero and there it should be an
+
+ align:start position:0%
+zero and there it should be an
+ 
+
+ align:start position:0%
+zero and there it should be an
+exponential after that and the P shows
+
+ align:start position:0%
+exponential after that and the P shows
+ 
+
+ align:start position:0%
+exponential after that and the P shows
+up as the exponent in the
+
+ align:start position:0%
+up as the exponent in the
+ 
+
+ align:start position:0%
+up as the exponent in the
+exponential okay what we'd like to do is
+
+ align:start position:0%
+exponential okay what we'd like to do is
+ 
+
+ align:start position:0%
+exponential okay what we'd like to do is
+develop an alternative way of thinking
+
+ align:start position:0%
+develop an alternative way of thinking
+ 
+
+ align:start position:0%
+develop an alternative way of thinking
+about that using the operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approach so a completely different way
+
+ align:start position:0%
+approach so a completely different way
+ 
+
+ align:start position:0%
+approach so a completely different way
+to solve that problem would be to think
+
+ align:start position:0%
+to solve that problem would be to think
+ 
+
+ align:start position:0%
+to solve that problem would be to think
+about write an operator expression for
+
+ align:start position:0%
+about write an operator expression for
+ 
+
+ align:start position:0%
+about write an operator expression for
+this okay so Y is a times the signal
+
+ align:start position:0%
+this okay so Y is a times the signal
+ 
+
+ align:start position:0%
+this okay so Y is a times the signal
+that results when you add X to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+py
+
+ align:start position:0%
+py
+ 
+
+ align:start position:0%
+py
+solve for the ratio Y byx and you get an
+
+ align:start position:0%
+solve for the ratio Y byx and you get an
+ 
+
+ align:start position:0%
+solve for the ratio Y byx and you get an
+operator expression a over 1 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PA just like in DT we have to figure out
+
+ align:start position:0%
+PA just like in DT we have to figure out
+ 
+
+ align:start position:0%
+PA just like in DT we have to figure out
+how we would think about
+
+ align:start position:0%
+how we would think about
+ 
+
+ align:start position:0%
+how we would think about
+that it's an implicit operation right
+
+ align:start position:0%
+that it's an implicit operation right
+ 
+
+ align:start position:0%
+that it's an implicit operation right
+it's telling me that if I knew the
+
+ align:start position:0%
+it's telling me that if I knew the
+ 
+
+ align:start position:0%
+it's telling me that if I knew the
+answer the answer is the signal that
+
+ align:start position:0%
+answer the answer is the signal that
+ 
+
+ align:start position:0%
+answer the answer is the signal that
+when operated on by one minus p is the
+
+ align:start position:0%
+when operated on by one minus p is the
+ 
+
+ align:start position:0%
+when operated on by one minus p is the
+input is the integral of the input but I
+
+ align:start position:0%
+input is the integral of the input but I
+ 
+
+ align:start position:0%
+input is the integral of the input but I
+don't know the answer so that reasoning
+
+ align:start position:0%
+don't know the answer so that reasoning
+ 
+
+ align:start position:0%
+don't know the answer so that reasoning
+doesn't quite work the reasoning that I
+
+ align:start position:0%
+doesn't quite work the reasoning that I
+ 
+
+ align:start position:0%
+doesn't quite work the reasoning that I
+used to solve the feed forward question
+
+ align:start position:0%
+used to solve the feed forward question
+ 
+
+ align:start position:0%
+used to solve the feed forward question
+doesn't quite work so I have to think of
+
+ align:start position:0%
+doesn't quite work so I have to think of
+ 
+
+ align:start position:0%
+doesn't quite work so I have to think of
+a different way of doing it just like we
+
+ align:start position:0%
+a different way of doing it just like we
+ 
+
+ align:start position:0%
+a different way of doing it just like we
+did in
+
+ align:start position:0%
+did in
+ 
+
+ align:start position:0%
+did in
+DT and the same solution works not
+
+ align:start position:0%
+DT and the same solution works not
+ 
+
+ align:start position:0%
+DT and the same solution works not
+surprisingly right a behaves like a
+
+ align:start position:0%
+surprisingly right a behaves like a
+ 
+
+ align:start position:0%
+surprisingly right a behaves like a
+polinomial r behaves like a polom after
+
+ align:start position:0%
+polinomial r behaves like a polom after
+ 
+
+ align:start position:0%
+polinomial r behaves like a polom after
+you turn it into a
+
+ align:start position:0%
+you turn it into a
+ 
+
+ align:start position:0%
+you turn it into a
+polinomial you can't tell if you started
+
+ align:start position:0%
+polinomial you can't tell if you started
+ 
+
+ align:start position:0%
+polinomial you can't tell if you started
+with a or R it's a
+
+ align:start position:0%
+with a or R it's a
+ 
+
+ align:start position:0%
+with a or R it's a
+polom so for that reason exactly the
+
+ align:start position:0%
+polom so for that reason exactly the
+ 
+
+ align:start position:0%
+polom so for that reason exactly the
+same stuff that you didn't in DT works
+
+ align:start position:0%
+same stuff that you didn't in DT works
+ 
+
+ align:start position:0%
+same stuff that you didn't in DT works
+that's why we can solve everything in 50
+
+ align:start position:0%
+that's why we can solve everything in 50
+ 
+
+ align:start position:0%
+that's why we can solve everything in 50
+minutes it's all the
+
+ align:start position:0%
+minutes it's all the
+ 
+
+ align:start position:0%
+minutes it's all the
+same so in DT we thought about this as
+
+ align:start position:0%
+same so in DT we thought about this as
+ 
+
+ align:start position:0%
+same so in DT we thought about this as
+being a
+
+ align:start position:0%
+being a
+ 
+
+ align:start position:0%
+being a
+series you could figure out an ascending
+
+ align:start position:0%
+series you could figure out an ascending
+ 
+
+ align:start position:0%
+series you could figure out an ascending
+series a power series that's equivalent
+
+ align:start position:0%
+series a power series that's equivalent
+ 
+
+ align:start position:0%
+series a power series that's equivalent
+by thinking about something like
+
+ align:start position:0%
+by thinking about something like
+ 
+
+ align:start position:0%
+by thinking about something like
+synthetic division tailor series
+
+ align:start position:0%
+synthetic division tailor series
+ 
+
+ align:start position:0%
+synthetic division tailor series
+whatever you're comfortable with but
+
+ align:start position:0%
+whatever you're comfortable with but
+ 
+
+ align:start position:0%
+whatever you're comfortable with but
+whatever you're comfortable with this a
+
+ align:start position:0%
+whatever you're comfortable with this a
+ 
+
+ align:start position:0%
+whatever you're comfortable with this a
+over 1 minus PA Take the A out front
+
+ align:start position:0%
+over 1 minus PA Take the A out front
+ 
+
+ align:start position:0%
+over 1 minus PA Take the A out front
+then you're left with 1 over 1us
+
+ align:start position:0%
+then you're left with 1 over 1us
+ 
+
+ align:start position:0%
+then you're left with 1 over 1us
+PA you think about that as a tailor
+
+ align:start position:0%
+PA you think about that as a tailor
+ 
+
+ align:start position:0%
+PA you think about that as a tailor
+series that's 1 + PA a plus p s a s plus
+
+ align:start position:0%
+series that's 1 + PA a plus p s a s plus
+ 
+
+ align:start position:0%
+series that's 1 + PA a plus p s a s plus
+PB a cub Etc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done okay now I know what the system
+
+ align:start position:0%
+done okay now I know what the system
+ 
+
+ align:start position:0%
+done okay now I know what the system
+functional looks like now I've got a
+
+ align:start position:0%
+functional looks like now I've got a
+ 
+
+ align:start position:0%
+functional looks like now I've got a
+feed forward system so I can use the
+
+ align:start position:0%
+feed forward system so I can use the
+ 
+
+ align:start position:0%
+feed forward system so I can use the
+technique from the other side what
+
+ align:start position:0%
+technique from the other side what
+ 
+
+ align:start position:0%
+technique from the other side what
+happens if you put Delta into a system
+
+ align:start position:0%
+happens if you put Delta into a system
+ 
+
+ align:start position:0%
+happens if you put Delta into a system
+whose um functional representation is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a you get a so you get a u let me skip
+
+ align:start position:0%
+a you get a so you get a u let me skip
+ 
+
+ align:start position:0%
+a you get a so you get a u let me skip
+that one that's on the next p slide uh
+
+ align:start position:0%
+that one that's on the next p slide uh
+ 
+
+ align:start position:0%
+that one that's on the next p slide uh
+what happens if you put um uh so what if
+
+ align:start position:0%
+what happens if you put um uh so what if
+ 
+
+ align:start position:0%
+what happens if you put um uh so what if
+what happens if you put in a no that's
+
+ align:start position:0%
+what happens if you put in a no that's
+ 
+
+ align:start position:0%
+what happens if you put in a no that's
+right I did that right okay one U sorry
+
+ align:start position:0%
+right I did that right okay one U sorry
+ 
+
+ align:start position:0%
+right I did that right okay one U sorry
+I'm confusing
+
+ align:start position:0%
+I'm confusing
+ 
+
+ align:start position:0%
+I'm confusing
+myself this a turned into that
+
+ align:start position:0%
+myself this a turned into that
+ 
+
+ align:start position:0%
+myself this a turned into that
+U right what happens if you put it into
+
+ align:start position:0%
+U right what happens if you put it into
+ 
+
+ align:start position:0%
+U right what happens if you put it into
+PA a
+
+ align:start position:0%
+PA a
+ 
+
+ align:start position:0%
+PA a
+s well the first so the first a turned
+
+ align:start position:0%
+s well the first so the first a turned
+ 
+
+ align:start position:0%
+s well the first so the first a turned
+Delta into U the second a turns Delta
+
+ align:start position:0%
+Delta into U the second a turns Delta
+ 
+
+ align:start position:0%
+Delta into U the second a turns Delta
+turns U into
+
+ align:start position:0%
+turns U into
+ 
+
+ align:start position:0%
+turns U into
+Tu and so I get this term so the PA a s
+
+ align:start position:0%
+Tu and so I get this term so the PA a s
+ 
+
+ align:start position:0%
+Tu and so I get this term so the PA a s
+turns into
+
+ align:start position:0%
+turns into
+ 
+
+ align:start position:0%
+turns into
+PTU the p^ 2 a cubed turns into half p^2
+
+ align:start position:0%
+PTU the p^ 2 a cubed turns into half p^2
+ 
+
+ align:start position:0%
+PTU the p^ 2 a cubed turns into half p^2
+t^2 U
+
+ align:start position:0%
+t^2 U
+ 
+
+ align:start position:0%
+t^2 U
+Etc so what I've done is I've thought of
+
+ align:start position:0%
+Etc so what I've done is I've thought of
+ 
+
+ align:start position:0%
+Etc so what I've done is I've thought of
+a way of constructing this output signal
+
+ align:start position:0%
+a way of constructing this output signal
+ 
+
+ align:start position:0%
+a way of constructing this output signal
+from the input signal without ever using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculus okay I started with a solution
+
+ align:start position:0%
+calculus okay I started with a solution
+ 
+
+ align:start position:0%
+calculus okay I started with a solution
+based on 1803 that's strictly
+
+ align:start position:0%
+based on 1803 that's strictly
+ 
+
+ align:start position:0%
+based on 1803 that's strictly
+calculus I just redid the whole problem
+
+ align:start position:0%
+calculus I just redid the whole problem
+ 
+
+ align:start position:0%
+calculus I just redid the whole problem
+and didn't use any
+
+ align:start position:0%
+and didn't use any
+ 
+
+ align:start position:0%
+and didn't use any
+calculus and I and the method works just
+
+ align:start position:0%
+calculus and I and the method works just
+ 
+
+ align:start position:0%
+calculus and I and the method works just
+the same reason that the r method
+
+ align:start position:0%
+the same reason that the r method
+ 
+
+ align:start position:0%
+the same reason that the r method
+worked in the r method when we were
+
+ align:start position:0%
+worked in the r method when we were
+ 
+
+ align:start position:0%
+worked in the r method when we were
+thinking about the simple feedback with
+
+ align:start position:0%
+thinking about the simple feedback with
+ 
+
+ align:start position:0%
+thinking about the simple feedback with
+an our system system every loop around
+
+ align:start position:0%
+an our system system every loop around
+ 
+
+ align:start position:0%
+an our system system every loop around
+the feedback loop generated one new
+
+ align:start position:0%
+the feedback loop generated one new
+ 
+
+ align:start position:0%
+the feedback loop generated one new
+sample here every loop around the CT
+
+ align:start position:0%
+sample here every loop around the CT
+ 
+
+ align:start position:0%
+sample here every loop around the CT
+Loop generates one more contribution to
+
+ align:start position:0%
+Loop generates one more contribution to
+ 
+
+ align:start position:0%
+Loop generates one more contribution to
+the output you put uh a Delta function
+
+ align:start position:0%
+the output you put uh a Delta function
+ 
+
+ align:start position:0%
+the output you put uh a Delta function
+in it gets integrated once and you get a
+
+ align:start position:0%
+in it gets integrated once and you get a
+ 
+
+ align:start position:0%
+in it gets integrated once and you get a
+u function
+
+ align:start position:0%
+u function
+ 
+
+ align:start position:0%
+u function
+out so first in in the symbolic
+
+ align:start position:0%
+out so first in in the symbolic
+ 
+
+ align:start position:0%
+out so first in in the symbolic
+representation so the first thing that
+
+ align:start position:0%
+representation so the first thing that
+ 
+
+ align:start position:0%
+representation so the first thing that
+comes out is uh a times the
+
+ align:start position:0%
+comes out is uh a times the
+ 
+
+ align:start position:0%
+comes out is uh a times the
+input second thing that comes out is a
+
+ align:start position:0%
+input second thing that comes out is a
+ 
+
+ align:start position:0%
+input second thing that comes out is a
+squ p times the input third thing that
+
+ align:start position:0%
+squ p times the input third thing that
+ 
+
+ align:start position:0%
+squ p times the input third thing that
+comes out
+
+ align:start position:0%
+comes out
+ 
+
+ align:start position:0%
+comes out
+uh p^2 a cubed Etc every time you go
+
+ align:start position:0%
+uh p^2 a cubed Etc every time you go
+ 
+
+ align:start position:0%
+uh p^2 a cubed Etc every time you go
+through the loop you pick up one more
+
+ align:start position:0%
+through the loop you pick up one more
+ 
+
+ align:start position:0%
+through the loop you pick up one more
+term now think about it in the time
+
+ align:start position:0%
+term now think about it in the time
+ 
+
+ align:start position:0%
+term now think about it in the time
+domain you put in a Delta function the
+
+ align:start position:0%
+domain you put in a Delta function the
+ 
+
+ align:start position:0%
+domain you put in a Delta function the
+first thing that comes out is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+step the second thing that comes
+
+ align:start position:0%
+step the second thing that comes
+ 
+
+ align:start position:0%
+step the second thing that comes
+out and gets added to the first thing
+
+ align:start position:0%
+out and gets added to the first thing
+ 
+
+ align:start position:0%
+out and gets added to the first thing
+that comes
+
+ align:start position:0%
+that comes
+ 
+
+ align:start position:0%
+that comes
+out is integrate multiply by P and
+
+ align:start position:0%
+out is integrate multiply by P and
+ 
+
+ align:start position:0%
+out is integrate multiply by P and
+integrate again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's this term P *
+
+ align:start position:0%
+so that's this term P *
+ 
+
+ align:start position:0%
+so that's this term P *
+T so we get the unit step from the first
+
+ align:start position:0%
+T so we get the unit step from the first
+ 
+
+ align:start position:0%
+T so we get the unit step from the first
+term which looks like this we get the
+
+ align:start position:0%
+term which looks like this we get the
+ 
+
+ align:start position:0%
+term which looks like this we get the
+linear increase from the second term we
+
+ align:start position:0%
+linear increase from the second term we
+ 
+
+ align:start position:0%
+linear increase from the second term we
+get a squared term we get a cube
+
+ align:start position:0%
+get a squared term we get a cube
+ 
+
+ align:start position:0%
+get a squared term we get a cube
+term and
+
+ align:start position:0%
+term and
+ 
+
+ align:start position:0%
+term and
+voila we get the series expansion for e
+
+ align:start position:0%
+voila we get the series expansion for e
+ 
+
+ align:start position:0%
+voila we get the series expansion for e
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+PT no calculus right it's purely
+
+ align:start position:0%
+PT no calculus right it's purely
+ 
+
+ align:start position:0%
+PT no calculus right it's purely
+thinking about how you would think about
+
+ align:start position:0%
+thinking about how you would think about
+ 
+
+ align:start position:0%
+thinking about how you would think about
+constructing the system con constructing
+
+ align:start position:0%
+constructing the system con constructing
+ 
+
+ align:start position:0%
+constructing the system con constructing
+the system by u a series representation
+
+ align:start position:0%
+the system by u a series representation
+ 
+
+ align:start position:0%
+the system by u a series representation
+for spinning around the feedback
+
+ align:start position:0%
+for spinning around the feedback
+ 
+
+ align:start position:0%
+for spinning around the feedback
+loop okay so that's an Insight that
+
+ align:start position:0%
+loop okay so that's an Insight that
+ 
+
+ align:start position:0%
+loop okay so that's an Insight that
+comes from thinking about um the system
+
+ align:start position:0%
+comes from thinking about um the system
+ 
+
+ align:start position:0%
+comes from thinking about um the system
+as a um functional representation as a
+
+ align:start position:0%
+as a um functional representation as a
+ 
+
+ align:start position:0%
+as a um functional representation as a
+polom pols can be expanded in tailor
+
+ align:start position:0%
+polom pols can be expanded in tailor
+ 
+
+ align:start position:0%
+polom pols can be expanded in tailor
+series therefore systems can be expanded
+
+ align:start position:0%
+series therefore systems can be expanded
+ 
+
+ align:start position:0%
+series therefore systems can be expanded
+in tailor
+
+ align:start position:0%
+in tailor
+ 
+
+ align:start position:0%
+in tailor
+series if you change the sign of
+
+ align:start position:0%
+series if you change the sign of
+ 
+
+ align:start position:0%
+series if you change the sign of
+P you notice that that previous example
+
+ align:start position:0%
+P you notice that that previous example
+ 
+
+ align:start position:0%
+P you notice that that previous example
+exploded right so we got an increasing
+
+ align:start position:0%
+exploded right so we got an increasing
+ 
+
+ align:start position:0%
+exploded right so we got an increasing
+exponential if you change the sign of p
+
+ align:start position:0%
+exponential if you change the sign of p
+ 
+
+ align:start position:0%
+exponential if you change the sign of p
+is not too surprising that what will
+
+ align:start position:0%
+is not too surprising that what will
+ 
+
+ align:start position:0%
+is not too surprising that what will
+happen is that it will
+
+ align:start position:0%
+happen is that it will
+ 
+
+ align:start position:0%
+happen is that it will
+converge so here symbolically the first
+
+ align:start position:0%
+converge so here symbolically the first
+ 
+
+ align:start position:0%
+converge so here symbolically the first
+signal is a unit step just like
+
+ align:start position:0%
+signal is a unit step just like
+ 
+
+ align:start position:0%
+signal is a unit step just like
+before but now because of the minus sign
+
+ align:start position:0%
+before but now because of the minus sign
+ 
+
+ align:start position:0%
+before but now because of the minus sign
+there's a negative on this PT so you get
+
+ align:start position:0%
+there's a negative on this PT so you get
+ 
+
+ align:start position:0%
+there's a negative on this PT so you get
+sloping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+downward in the Square term it's still
+
+ align:start position:0%
+downward in the Square term it's still
+ 
+
+ align:start position:0%
+downward in the Square term it's still
+positive so that breaks up
+
+ align:start position:0%
+positive so that breaks up
+ 
+
+ align:start position:0%
+positive so that breaks up
+up but the cubic is now downward
+
+ align:start position:0%
+up but the cubic is now downward
+ 
+
+ align:start position:0%
+up but the cubic is now downward
+again and you add an infinite number of
+
+ align:start position:0%
+again and you add an infinite number of
+ 
+
+ align:start position:0%
+again and you add an infinite number of
+those and you get another exponential
+
+ align:start position:0%
+those and you get another exponential
+ 
+
+ align:start position:0%
+those and you get another exponential
+this time a convergent
+
+ align:start position:0%
+this time a convergent
+ 
+
+ align:start position:0%
+this time a convergent
+one so the point is that it works
+
+ align:start position:0%
+one so the point is that it works
+ 
+
+ align:start position:0%
+one so the point is that it works
+extremely like the way the DT stuff did
+
+ align:start position:0%
+extremely like the way the DT stuff did
+ 
+
+ align:start position:0%
+extremely like the way the DT stuff did
+except now the basis functions are
+
+ align:start position:0%
+except now the basis functions are
+ 
+
+ align:start position:0%
+except now the basis functions are
+different the basis functions are
+
+ align:start position:0%
+different the basis functions are
+ 
+
+ align:start position:0%
+different the basis functions are
+derived from this thing which is the
+
+ align:start position:0%
+derived from this thing which is the
+ 
+
+ align:start position:0%
+derived from this thing which is the
+unit impulse
+
+ align:start position:0%
+unit impulse
+ 
+
+ align:start position:0%
+unit impulse
+function and the things that come out of
+
+ align:start position:0%
+function and the things that come out of
+ 
+
+ align:start position:0%
+function and the things that come out of
+the integrator are steps and ramps and
+
+ align:start position:0%
+the integrator are steps and ramps and
+ 
+
+ align:start position:0%
+the integrator are steps and ramps and
+Par parabas and stuff like
+
+ align:start position:0%
+Par parabas and stuff like
+ 
+
+ align:start position:0%
+Par parabas and stuff like
+that so in R the basic input signal was
+
+ align:start position:0%
+that so in R the basic input signal was
+ 
+
+ align:start position:0%
+that so in R the basic input signal was
+the um unit sample
+
+ align:start position:0%
+the um unit sample
+ 
+
+ align:start position:0%
+the um unit sample
+signal and what came out on each uh
+
+ align:start position:0%
+signal and what came out on each uh
+ 
+
+ align:start position:0%
+signal and what came out on each uh
+revolution around um uh for each cycle
+
+ align:start position:0%
+revolution around um uh for each cycle
+ 
+
+ align:start position:0%
+revolution around um uh for each cycle
+in a feedback system what came out was a
+
+ align:start position:0%
+in a feedback system what came out was a
+ 
+
+ align:start position:0%
+in a feedback system what came out was a
+successive delay here we get a
+
+ align:start position:0%
+successive delay here we get a
+ 
+
+ align:start position:0%
+successive delay here we get a
+successive
+
+ align:start position:0%
+successive
+ 
+
+ align:start position:0%
+successive
+integration okay delay was the
+
+ align:start position:0%
+integration okay delay was the
+ 
+
+ align:start position:0%
+integration okay delay was the
+fundamental operator integration is the
+
+ align:start position:0%
+fundamental operator integration is the
+ 
+
+ align:start position:0%
+fundamental operator integration is the
+fundamental operator successive delays
+
+ align:start position:0%
+fundamental operator successive delays
+ 
+
+ align:start position:0%
+fundamental operator successive delays
+successive
+
+ align:start position:0%
+successive
+ 
+
+ align:start position:0%
+successive
+Integrations and we get the idea that we
+
+ align:start position:0%
+Integrations and we get the idea that we
+ 
+
+ align:start position:0%
+Integrations and we get the idea that we
+have convergence and Divergence just
+
+ align:start position:0%
+have convergence and Divergence just
+ 
+
+ align:start position:0%
+have convergence and Divergence just
+like we did in DT except now the shapes
+
+ align:start position:0%
+like we did in DT except now the shapes
+ 
+
+ align:start position:0%
+like we did in DT except now the shapes
+of the regions are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different so if the P which we will
+
+ align:start position:0%
+different so if the P which we will
+ 
+
+ align:start position:0%
+different so if the P which we will
+later call the
+
+ align:start position:0%
+later call the
+ 
+
+ align:start position:0%
+later call the
+pole by complete analogy to what we did
+
+ align:start position:0%
+pole by complete analogy to what we did
+ 
+
+ align:start position:0%
+pole by complete analogy to what we did
+in DT if the pole is in the right half
+
+ align:start position:0%
+in DT if the pole is in the right half
+ 
+
+ align:start position:0%
+in DT if the pole is in the right half
+plane then the systems response is
+
+ align:start position:0%
+plane then the systems response is
+ 
+
+ align:start position:0%
+plane then the systems response is
+Divergent if the pole is in the left
+
+ align:start position:0%
+Divergent if the pole is in the left
+ 
+
+ align:start position:0%
+Divergent if the pole is in the left
+half plane the system's response is
+
+ align:start position:0%
+half plane the system's response is
+ 
+
+ align:start position:0%
+half plane the system's response is
+convergent
+
+ align:start position:0%
+convergent
+ 
+
+ align:start position:0%
+convergent
+so it looks just like DT we think about
+
+ align:start position:0%
+so it looks just like DT we think about
+ 
+
+ align:start position:0%
+so it looks just like DT we think about
+this as signal flow pass we think about
+
+ align:start position:0%
+this as signal flow pass we think about
+ 
+
+ align:start position:0%
+this as signal flow pass we think about
+how feedback gives rise to an infinite
+
+ align:start position:0%
+how feedback gives rise to an infinite
+ 
+
+ align:start position:0%
+how feedback gives rise to an infinite
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+those in DT each time through it gave
+
+ align:start position:0%
+those in DT each time through it gave
+ 
+
+ align:start position:0%
+those in DT each time through it gave
+one unit of delay in CT it gave um one
+
+ align:start position:0%
+one unit of delay in CT it gave um one
+ 
+
+ align:start position:0%
+one unit of delay in CT it gave um one
+unit of
+
+ align:start position:0%
+unit of
+ 
+
+ align:start position:0%
+unit of
+integration the method is the same the
+
+ align:start position:0%
+integration the method is the same the
+ 
+
+ align:start position:0%
+integration the method is the same the
+answer is
+
+ align:start position:0%
+answer is
+ 
+
+ align:start position:0%
+answer is
+different so what we got is tremendous
+
+ align:start position:0%
+different so what we got is tremendous
+ 
+
+ align:start position:0%
+different so what we got is tremendous
+similarities differential equation
+
+ align:start position:0%
+similarities differential equation
+ 
+
+ align:start position:0%
+similarities differential equation
+compared to difference equation block
+
+ align:start position:0%
+compared to difference equation block
+ 
+
+ align:start position:0%
+compared to difference equation block
+diagram compared to block diagram
+
+ align:start position:0%
+diagram compared to block diagram
+ 
+
+ align:start position:0%
+diagram compared to block diagram
+integrators instead of
+
+ align:start position:0%
+integrators instead of
+ 
+
+ align:start position:0%
+integrators instead of
+delays functional functional A's instead
+
+ align:start position:0%
+delays functional functional A's instead
+ 
+
+ align:start position:0%
+delays functional functional A's instead
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+RS pole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pole mode mode fundamental
+
+ align:start position:0%
+pole mode mode fundamental
+ 
+
+ align:start position:0%
+pole mode mode fundamental
+mode here the fundamental mode was a a
+
+ align:start position:0%
+mode here the fundamental mode was a a
+ 
+
+ align:start position:0%
+mode here the fundamental mode was a a
+geometric sequence here it's an
+
+ align:start position:0%
+geometric sequence here it's an
+ 
+
+ align:start position:0%
+geometric sequence here it's an
+exponential function of time and we got
+
+ align:start position:0%
+exponential function of time and we got
+ 
+
+ align:start position:0%
+exponential function of time and we got
+different kinds of regional convergence
+
+ align:start position:0%
+different kinds of regional convergence
+ 
+
+ align:start position:0%
+different kinds of regional convergence
+signal converges for for poles and left
+
+ align:start position:0%
+signal converges for for poles and left
+ 
+
+ align:start position:0%
+signal converges for for poles and left
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+plane signals converge for poles inside
+
+ align:start position:0%
+plane signals converge for poles inside
+ 
+
+ align:start position:0%
+plane signals converge for poles inside
+the unit
+
+ align:start position:0%
+the unit
+ 
+
+ align:start position:0%
+the unit
+circle same
+
+ align:start position:0%
+circle same
+ 
+
+ align:start position:0%
+circle same
+idea but some
+
+ align:start position:0%
+idea but some
+ 
+
+ align:start position:0%
+idea but some
+differences okay
+
+ align:start position:0%
+differences okay
+ 
+
+ align:start position:0%
+differences okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh barely have time think about this for
+
+ align:start position:0%
+uh barely have time think about this for
+ 
+
+ align:start position:0%
+uh barely have time think about this for
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+seconds we now have two representations
+
+ align:start position:0%
+seconds we now have two representations
+ 
+
+ align:start position:0%
+seconds we now have two representations
+our pooms and a
+
+ align:start position:0%
+our pooms and a
+ 
+
+ align:start position:0%
+our pooms and a
+pooms I'm giving you four examples to
+
+ align:start position:0%
+pooms I'm giving you four examples to
+ 
+
+ align:start position:0%
+pooms I'm giving you four examples to
+think through and your job is to figure
+
+ align:start position:0%
+think through and your job is to figure
+ 
+
+ align:start position:0%
+think through and your job is to figure
+out which of those functionals
+
+ align:start position:0%
+out which of those functionals
+ 
+
+ align:start position:0%
+out which of those functionals
+correspond to
+
+ align:start position:0%
+correspond to
+ 
+
+ align:start position:0%
+correspond to
+convergent responses when excited by a
+
+ align:start position:0%
+convergent responses when excited by a
+ 
+
+ align:start position:0%
+convergent responses when excited by a
+unit sample or a unit impulse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how do I think about this how do I is
+
+ align:start position:0%
+so how do I think about this how do I is
+ 
+
+ align:start position:0%
+so how do I think about this how do I is
+this convergent or
+
+ align:start position:0%
+this convergent or
+ 
+
+ align:start position:0%
+this convergent or
+Divergent what do I think
+
+ align:start position:0%
+Divergent what do I think
+ 
+
+ align:start position:0%
+Divergent what do I think
+about step
+
+ align:start position:0%
+about step
+ 
+
+ align:start position:0%
+about step
+one convergent how' you get that yeah is
+
+ align:start position:0%
+one convergent how' you get that yeah is
+ 
+
+ align:start position:0%
+one convergent how' you get that yeah is
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so factor it's polinomial you get a
+
+ align:start position:0%
+one so factor it's polinomial you get a
+ 
+
+ align:start position:0%
+one so factor it's polinomial you get a
+pole at minus a half and a pole at plus
+
+ align:start position:0%
+pole at minus a half and a pole at plus
+ 
+
+ align:start position:0%
+pole at minus a half and a pole at plus
+a half they're both inside you in a
+
+ align:start position:0%
+a half they're both inside you in a
+ 
+
+ align:start position:0%
+a half they're both inside you in a
+circle they both
+
+ align:start position:0%
+circle they both
+ 
+
+ align:start position:0%
+circle they both
+converge how about this
+
+ align:start position:0%
+converge how about this
+ 
+
+ align:start position:0%
+converge how about this
+one same equations same
+
+ align:start position:0%
+one same equations same
+ 
+
+ align:start position:0%
+one same equations same
+answer kind
+
+ align:start position:0%
+answer kind
+ 
+
+ align:start position:0%
+answer kind
+of same poles minus a half and plus a
+
+ align:start position:0%
+of same poles minus a half and plus a
+ 
+
+ align:start position:0%
+of same poles minus a half and plus a
+half convergent or
+
+ align:start position:0%
+half convergent or
+ 
+
+ align:start position:0%
+half convergent or
+Divergent Divergent because the regions
+
+ align:start position:0%
+Divergent Divergent because the regions
+ 
+
+ align:start position:0%
+Divergent Divergent because the regions
+are different right one of the poles is
+
+ align:start position:0%
+are different right one of the poles is
+ 
+
+ align:start position:0%
+are different right one of the poles is
+in the right half
+
+ align:start position:0%
+in the right half
+ 
+
+ align:start position:0%
+in the right half
+plane Divergent how about this
+
+ align:start position:0%
+plane Divergent how about this
+ 
+
+ align:start position:0%
+plane Divergent how about this
+one where were the
+
+ align:start position:0%
+one where were the
+ 
+
+ align:start position:0%
+one where were the
+poles minus a half minus three
+
+ align:start position:0%
+poles minus a half minus three
+ 
+
+ align:start position:0%
+poles minus a half minus three
+halves outside the unit
+
+ align:start position:0%
+halves outside the unit
+ 
+
+ align:start position:0%
+halves outside the unit
+circle one of the poles is outside the
+
+ align:start position:0%
+circle one of the poles is outside the
+ 
+
+ align:start position:0%
+circle one of the poles is outside the
+UN Circle diverges because of that
+
+ align:start position:0%
+UN Circle diverges because of that
+ 
+
+ align:start position:0%
+UN Circle diverges because of that
+pole minus a half and minus three halves
+
+ align:start position:0%
+pole minus a half and minus three halves
+ 
+
+ align:start position:0%
+pole minus a half and minus three halves
+same poles both in the left half
+
+ align:start position:0%
+same poles both in the left half
+ 
+
+ align:start position:0%
+same poles both in the left half
+plane converges that's the point okay so
+
+ align:start position:0%
+plane converges that's the point okay so
+ 
+
+ align:start position:0%
+plane converges that's the point okay so
+they work very similar but there are
+
+ align:start position:0%
+they work very similar but there are
+ 
+
+ align:start position:0%
+they work very similar but there are
+differences and now in the last three
+
+ align:start position:0%
+differences and now in the last three
+ 
+
+ align:start position:0%
+differences and now in the last three
+minutes the last thing I want to tell
+
+ align:start position:0%
+minutes the last thing I want to tell
+ 
+
+ align:start position:0%
+minutes the last thing I want to tell
+you about is that even complex numbers
+
+ align:start position:0%
+you about is that even complex numbers
+ 
+
+ align:start position:0%
+you about is that even complex numbers
+work just the same as in
+
+ align:start position:0%
+work just the same as in
+ 
+
+ align:start position:0%
+work just the same as in
+DT so think about a system that's
+
+ align:start position:0%
+DT so think about a system that's
+ 
+
+ align:start position:0%
+DT so think about a system that's
+slightly harder here I can represent
+
+ align:start position:0%
+slightly harder here I can represent
+ 
+
+ align:start position:0%
+slightly harder here I can represent
+this by this kind of a relationship so
+
+ align:start position:0%
+this by this kind of a relationship so
+ 
+
+ align:start position:0%
+this by this kind of a relationship so
+FAL
+
+ align:start position:0%
+FAL
+ 
+
+ align:start position:0%
+FAL
+KX but f is
+
+ align:start position:0%
+KX but f is
+ 
+
+ align:start position:0%
+KX but f is
+ma right so
+
+ align:start position:0%
+ma right so
+ 
+
+ align:start position:0%
+ma right so
+801 and so I generate a block diagram or
+
+ align:start position:0%
+801 and so I generate a block diagram or
+ 
+
+ align:start position:0%
+801 and so I generate a block diagram or
+a differential equation or however I
+
+ align:start position:0%
+a differential equation or however I
+ 
+
+ align:start position:0%
+a differential equation or however I
+want to think about it and I can solve
+
+ align:start position:0%
+want to think about it and I can solve
+ 
+
+ align:start position:0%
+want to think about it and I can solve
+for the answer what I'd like to do is
+
+ align:start position:0%
+for the answer what I'd like to do is
+ 
+
+ align:start position:0%
+for the answer what I'd like to do is
+think about it in terms of the
+
+ align:start position:0%
+think about it in terms of the
+ 
+
+ align:start position:0%
+think about it in terms of the
+functional
+
+ align:start position:0%
+functional
+ 
+
+ align:start position:0%
+functional
+representation so I just think about
+
+ align:start position:0%
+representation so I just think about
+ 
+
+ align:start position:0%
+representation so I just think about
+take this system that you're familiar
+
+ align:start position:0%
+take this system that you're familiar
+ 
+
+ align:start position:0%
+take this system that you're familiar
+with we did this on on the first lecture
+
+ align:start position:0%
+with we did this on on the first lecture
+ 
+
+ align:start position:0%
+with we did this on on the first lecture
+turn it into a differential
+
+ align:start position:0%
+turn it into a differential
+ 
+
+ align:start position:0%
+turn it into a differential
+equation turn that into a functional
+
+ align:start position:0%
+equation turn that into a functional
+ 
+
+ align:start position:0%
+equation turn that into a functional
+representation and now I want to think
+
+ align:start position:0%
+representation and now I want to think
+ 
+
+ align:start position:0%
+representation and now I want to think
+about how you would solve the functional
+
+ align:start position:0%
+about how you would solve the functional
+ 
+
+ align:start position:0%
+about how you would solve the functional
+representation the idea is just like
+
+ align:start position:0%
+representation the idea is just like
+ 
+
+ align:start position:0%
+representation the idea is just like
+before Factor but now the trick
+
+ align:start position:0%
+before Factor but now the trick
+ 
+
+ align:start position:0%
+before Factor but now the trick
+is that the
+
+ align:start position:0%
+is that the
+ 
+
+ align:start position:0%
+is that the
+factors uh become
+
+ align:start position:0%
+factors uh become
+ 
+
+ align:start position:0%
+factors uh become
+complex so one way you can think about
+
+ align:start position:0%
+complex so one way you can think about
+ 
+
+ align:start position:0%
+complex so one way you can think about
+this is to force the second order system
+
+ align:start position:0%
+this is to force the second order system
+ 
+
+ align:start position:0%
+this is to force the second order system
+into a canonical form the canonical form
+
+ align:start position:0%
+into a canonical form the canonical form
+ 
+
+ align:start position:0%
+into a canonical form the canonical form
+for uh
+
+ align:start position:0%
+for uh
+ 
+
+ align:start position:0%
+for uh
+DT was 1 over 1us p r for CT is a over 1
+
+ align:start position:0%
+DT was 1 over 1us p r for CT is a over 1
+ 
+
+ align:start position:0%
+DT was 1 over 1us p r for CT is a over 1
+minus p a so I want to make factors that
+
+ align:start position:0%
+minus p a so I want to make factors that
+ 
+
+ align:start position:0%
+minus p a so I want to make factors that
+look like that because I know that here
+
+ align:start position:0%
+look like that because I know that here
+ 
+
+ align:start position:0%
+look like that because I know that here
+the response looks like P to the N here
+
+ align:start position:0%
+the response looks like P to the N here
+ 
+
+ align:start position:0%
+the response looks like P to the N here
+the response looks like e to the p t if
+
+ align:start position:0%
+the response looks like e to the p t if
+ 
+
+ align:start position:0%
+the response looks like e to the p t if
+I can coers it into that form I already
+
+ align:start position:0%
+I can coers it into that form I already
+ 
+
+ align:start position:0%
+I can coers it into that form I already
+know the
+
+ align:start position:0%
+know the
+ 
+
+ align:start position:0%
+know the
+answer so that's what's Illustrated here
+
+ align:start position:0%
+answer so that's what's Illustrated here
+ 
+
+ align:start position:0%
+answer so that's what's Illustrated here
+I coers this into that form
+
+ align:start position:0%
+I coers this into that form
+ 
+
+ align:start position:0%
+I coers this into that form
+and then I know uh then I'll know what
+
+ align:start position:0%
+and then I know uh then I'll know what
+ 
+
+ align:start position:0%
+and then I know uh then I'll know what
+the answer looks
+
+ align:start position:0%
+the answer looks
+ 
+
+ align:start position:0%
+the answer looks
+like just like we could in DT substitute
+
+ align:start position:0%
+like just like we could in DT substitute
+ 
+
+ align:start position:0%
+like just like we could in DT substitute
+R goes to one over Z in CT we can
+
+ align:start position:0%
+R goes to one over Z in CT we can
+ 
+
+ align:start position:0%
+R goes to one over Z in CT we can
+substitute a goes to one / s and solve
+
+ align:start position:0%
+substitute a goes to one / s and solve
+ 
+
+ align:start position:0%
+substitute a goes to one / s and solve
+for S we get the same answer same as we
+
+ align:start position:0%
+for S we get the same answer same as we
+ 
+
+ align:start position:0%
+for S we get the same answer same as we
+did in DT except now we call it
+
+ align:start position:0%
+did in DT except now we call it
+ 
+
+ align:start position:0%
+did in DT except now we call it
+s so the poles to this system are plus
+
+ align:start position:0%
+s so the poles to this system are plus
+ 
+
+ align:start position:0%
+s so the poles to this system are plus
+or minus J constant for convenience I'll
+
+ align:start position:0%
+or minus J constant for convenience I'll
+ 
+
+ align:start position:0%
+or minus J constant for convenience I'll
+call the constant Omega
+
+ align:start position:0%
+call the constant Omega
+ 
+
+ align:start position:0%
+call the constant Omega
+KN so then I have a pole at e to the J
+
+ align:start position:0%
+KN so then I have a pole at e to the J
+ 
+
+ align:start position:0%
+KN so then I have a pole at e to the J
+Omega kn
+
+ align:start position:0%
+Omega kn
+ 
+
+ align:start position:0%
+Omega kn
+and another one so I have a poll at J
+
+ align:start position:0%
+and another one so I have a poll at J
+ 
+
+ align:start position:0%
+and another one so I have a poll at J
+Omega KN and a second poll at minus J
+
+ align:start position:0%
+Omega KN and a second poll at minus J
+ 
+
+ align:start position:0%
+Omega KN and a second poll at minus J
+Omega KN by that
+
+ align:start position:0%
+Omega KN by that
+ 
+
+ align:start position:0%
+Omega KN by that
+argument the fundamental modes are e to
+
+ align:start position:0%
+argument the fundamental modes are e to
+ 
+
+ align:start position:0%
+argument the fundamental modes are e to
+the J Omega T and e to the minus J Omega
+
+ align:start position:0%
+the J Omega T and e to the minus J Omega
+ 
+
+ align:start position:0%
+the J Omega T and e to the minus J Omega
+T just like in DT the complex poles gave
+
+ align:start position:0%
+T just like in DT the complex poles gave
+ 
+
+ align:start position:0%
+T just like in DT the complex poles gave
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+modes here the complex pole J Omega KN
+
+ align:start position:0%
+modes here the complex pole J Omega KN
+ 
+
+ align:start position:0%
+modes here the complex pole J Omega KN
+gave a complex mode cos Omega t plus J
+
+ align:start position:0%
+gave a complex mode cos Omega t plus J
+ 
+
+ align:start position:0%
+gave a complex mode cos Omega t plus J
+sin Omega t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and just like DT the system
+
+ align:start position:0%
+and just like DT the system
+ 
+
+ align:start position:0%
+and just like DT the system
+conspires so that started out being a
+
+ align:start position:0%
+conspires so that started out being a
+ 
+
+ align:start position:0%
+conspires so that started out being a
+mass spring system obviously it's not
+
+ align:start position:0%
+mass spring system obviously it's not
+ 
+
+ align:start position:0%
+mass spring system obviously it's not
+going to have an imaginary
+
+ align:start position:0%
+going to have an imaginary
+ 
+
+ align:start position:0%
+going to have an imaginary
+output the system conspires so that the
+
+ align:start position:0%
+output the system conspires so that the
+ 
+
+ align:start position:0%
+output the system conspires so that the
+imaginary parts of the different
+
+ align:start position:0%
+imaginary parts of the different
+ 
+
+ align:start position:0%
+imaginary parts of the different
+fundamental modes kill each other off
+
+ align:start position:0%
+fundamental modes kill each other off
+ 
+
+ align:start position:0%
+fundamental modes kill each other off
+and the answer is U is a real number so
+
+ align:start position:0%
+and the answer is U is a real number so
+ 
+
+ align:start position:0%
+and the answer is U is a real number so
+even though the mode even though the
+
+ align:start position:0%
+even though the mode even though the
+ 
+
+ align:start position:0%
+even though the mode even though the
+pole is complex the multipliers are
+
+ align:start position:0%
+pole is complex the multipliers are
+ 
+
+ align:start position:0%
+pole is complex the multipliers are
+complex this sum is real and if you just
+
+ align:start position:0%
+complex this sum is real and if you just
+ 
+
+ align:start position:0%
+complex this sum is real and if you just
+think about what that sum is by thinking
+
+ align:start position:0%
+think about what that sum is by thinking
+ 
+
+ align:start position:0%
+think about what that sum is by thinking
+about uh uh how complex numbers work you
+
+ align:start position:0%
+about uh uh how complex numbers work you
+ 
+
+ align:start position:0%
+about uh uh how complex numbers work you
+get an expression that looks like Omega
+
+ align:start position:0%
+get an expression that looks like Omega
+ 
+
+ align:start position:0%
+get an expression that looks like Omega
+sin Omega
+
+ align:start position:0%
+sin Omega
+ 
+
+ align:start position:0%
+sin Omega
+T it's kind of a little more fun to
+
+ align:start position:0%
+T it's kind of a little more fun to
+ 
+
+ align:start position:0%
+T it's kind of a little more fun to
+think about how that evolves as a series
+
+ align:start position:0%
+think about how that evolves as a series
+ 
+
+ align:start position:0%
+think about how that evolves as a series
+if we do a tailor series for this we can
+
+ align:start position:0%
+if we do a tailor series for this we can
+ 
+
+ align:start position:0%
+if we do a tailor series for this we can
+represent it that
+
+ align:start position:0%
+represent it that
+ 
+
+ align:start position:0%
+represent it that
+way and the series then the first term
+
+ align:start position:0%
+way and the series then the first term
+ 
+
+ align:start position:0%
+way and the series then the first term
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T the second term is a t cubed which
+
+ align:start position:0%
+T the second term is a t cubed which
+ 
+
+ align:start position:0%
+T the second term is a t cubed which
+goes down
+
+ align:start position:0%
+goes down
+ 
+
+ align:start position:0%
+goes down
+then there's a
+
+ align:start position:0%
+then there's a
+ 
+
+ align:start position:0%
+then there's a
+fifth and a
+
+ align:start position:0%
+fifth and a
+ 
+
+ align:start position:0%
+fifth and a
+seventh and a
+
+ align:start position:0%
+seventh and a
+ 
+
+ align:start position:0%
+seventh and a
+ninth and if you keep adding up the
+
+ align:start position:0%
+ninth and if you keep adding up the
+ 
+
+ align:start position:0%
+ninth and if you keep adding up the
+terms amazingly enough the series
+
+ align:start position:0%
+terms amazingly enough the series
+ 
+
+ align:start position:0%
+terms amazingly enough the series
+representation for the operator
+
+ align:start position:0%
+representation for the operator
+ 
+
+ align:start position:0%
+representation for the operator
+expression is the tailor series
+
+ align:start position:0%
+expression is the tailor series
+ 
+
+ align:start position:0%
+expression is the tailor series
+expansion of a sine
+
+ align:start position:0%
+expansion of a sine
+ 
+
+ align:start position:0%
+expansion of a sine
+wave just like we would have expected
+
+ align:start position:0%
+wave just like we would have expected
+ 
+
+ align:start position:0%
+wave just like we would have expected
+again here the response looks like e to
+
+ align:start position:0%
+again here the response looks like e to
+ 
+
+ align:start position:0%
+again here the response looks like e to
+the p t if I can coer it into that form
+
+ align:start position:0%
+the p t if I can coer it into that form
+ 
+
+ align:start position:0%
+the p t if I can coer it into that form
+I already know the
+
+ align:start position:0%
+I already know the
+ 
+
+ align:start position:0%
+I already know the
+answer so that's what's Illustrated here
+
+ align:start position:0%
+answer so that's what's Illustrated here
+ 
+
+ align:start position:0%
+answer so that's what's Illustrated here
+I coers this into that
+
+ align:start position:0%
+I coers this into that
+ 
+
+ align:start position:0%
+I coers this into that
+form and then I know uh then I'll know
+
+ align:start position:0%
+form and then I know uh then I'll know
+ 
+
+ align:start position:0%
+form and then I know uh then I'll know
+what the answer looks
+
+ align:start position:0%
+what the answer looks
+ 
+
+ align:start position:0%
+what the answer looks
+like just like we could in DT substitute
+
+ align:start position:0%
+like just like we could in DT substitute
+ 
+
+ align:start position:0%
+like just like we could in DT substitute
+R goes to one over Z in CT we can
+
+ align:start position:0%
+R goes to one over Z in CT we can
+ 
+
+ align:start position:0%
+R goes to one over Z in CT we can
+substitute a goes to one/ S and solve
+
+ align:start position:0%
+substitute a goes to one/ S and solve
+ 
+
+ align:start position:0%
+substitute a goes to one/ S and solve
+for S we get the same answer same as we
+
+ align:start position:0%
+for S we get the same answer same as we
+ 
+
+ align:start position:0%
+for S we get the same answer same as we
+did in DT except now we call it
+
+ align:start position:0%
+did in DT except now we call it
+ 
+
+ align:start position:0%
+did in DT except now we call it
+s so the poles to this system are plus
+
+ align:start position:0%
+s so the poles to this system are plus
+ 
+
+ align:start position:0%
+s so the poles to this system are plus
+or minus J constant for convenience I'll
+
+ align:start position:0%
+or minus J constant for convenience I'll
+ 
+
+ align:start position:0%
+or minus J constant for convenience I'll
+call the constant Omega
+
+ align:start position:0%
+call the constant Omega
+ 
+
+ align:start position:0%
+call the constant Omega
+KN so then I have a pole at e to the J
+
+ align:start position:0%
+KN so then I have a pole at e to the J
+ 
+
+ align:start position:0%
+KN so then I have a pole at e to the J
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+KN and another one so I have a poll at J
+
+ align:start position:0%
+KN and another one so I have a poll at J
+ 
+
+ align:start position:0%
+KN and another one so I have a poll at J
+Omega KN and a second pole at minus J
+
+ align:start position:0%
+Omega KN and a second pole at minus J
+ 
+
+ align:start position:0%
+Omega KN and a second pole at minus J
+Omega by that
+
+ align:start position:0%
+Omega by that
+ 
+
+ align:start position:0%
+Omega by that
+argument the fundamental modes are e to
+
+ align:start position:0%
+argument the fundamental modes are e to
+ 
+
+ align:start position:0%
+argument the fundamental modes are e to
+the J Omega T and e to the minus J Omega
+
+ align:start position:0%
+the J Omega T and e to the minus J Omega
+ 
+
+ align:start position:0%
+the J Omega T and e to the minus J Omega
+T just like in DT the complex poles gave
+
+ align:start position:0%
+T just like in DT the complex poles gave
+ 
+
+ align:start position:0%
+T just like in DT the complex poles gave
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+modes here the complex pole J Omega KN
+
+ align:start position:0%
+modes here the complex pole J Omega KN
+ 
+
+ align:start position:0%
+modes here the complex pole J Omega KN
+gave a complex mode cos Omega t plus J
+
+ align:start position:0%
+gave a complex mode cos Omega t plus J
+ 
+
+ align:start position:0%
+gave a complex mode cos Omega t plus J
+sin Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T and just like DT the system
+
+ align:start position:0%
+T and just like DT the system
+ 
+
+ align:start position:0%
+T and just like DT the system
+conspires so that start without being a
+
+ align:start position:0%
+conspires so that start without being a
+ 
+
+ align:start position:0%
+conspires so that start without being a
+mass spring system obviously it's not
+
+ align:start position:0%
+mass spring system obviously it's not
+ 
+
+ align:start position:0%
+mass spring system obviously it's not
+going to have an imaginary
+
+ align:start position:0%
+going to have an imaginary
+ 
+
+ align:start position:0%
+going to have an imaginary
+output the system conspires so that the
+
+ align:start position:0%
+output the system conspires so that the
+ 
+
+ align:start position:0%
+output the system conspires so that the
+imaginary parts of the different
+
+ align:start position:0%
+imaginary parts of the different
+ 
+
+ align:start position:0%
+imaginary parts of the different
+fundamental modes kill each other off
+
+ align:start position:0%
+fundamental modes kill each other off
+ 
+
+ align:start position:0%
+fundamental modes kill each other off
+and the answer is um is a real number so
+
+ align:start position:0%
+and the answer is um is a real number so
+ 
+
+ align:start position:0%
+and the answer is um is a real number so
+even though the mode even though the
+
+ align:start position:0%
+even though the mode even though the
+ 
+
+ align:start position:0%
+even though the mode even though the
+poll is complex the multipliers are
+
+ align:start position:0%
+poll is complex the multipliers are
+ 
+
+ align:start position:0%
+poll is complex the multipliers are
+complex the sum is real and if you just
+
+ align:start position:0%
+complex the sum is real and if you just
+ 
+
+ align:start position:0%
+complex the sum is real and if you just
+think about what that sum is by thinking
+
+ align:start position:0%
+think about what that sum is by thinking
+ 
+
+ align:start position:0%
+think about what that sum is by thinking
+about uh uh how complex numbers work you
+
+ align:start position:0%
+about uh uh how complex numbers work you
+ 
+
+ align:start position:0%
+about uh uh how complex numbers work you
+get an expression that looks like Omega
+
+ align:start position:0%
+get an expression that looks like Omega
+ 
+
+ align:start position:0%
+get an expression that looks like Omega
+not sin Omega
+
+ align:start position:0%
+not sin Omega
+ 
+
+ align:start position:0%
+not sin Omega
+T it's kind of a little more fun to
+
+ align:start position:0%
+T it's kind of a little more fun to
+ 
+
+ align:start position:0%
+T it's kind of a little more fun to
+think about how that evolves as a series
+
+ align:start position:0%
+think about how that evolves as a series
+ 
+
+ align:start position:0%
+think about how that evolves as a series
+if we do a tailor series for this we can
+
+ align:start position:0%
+if we do a tailor series for this we can
+ 
+
+ align:start position:0%
+if we do a tailor series for this we can
+represent it that
+
+ align:start position:0%
+represent it that
+ 
+
+ align:start position:0%
+represent it that
+way and the series then the first term
+
+ align:start position:0%
+way and the series then the first term
+ 
+
+ align:start position:0%
+way and the series then the first term
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T the second term is a t cubed which
+
+ align:start position:0%
+T the second term is a t cubed which
+ 
+
+ align:start position:0%
+T the second term is a t cubed which
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+down then there's a
+
+ align:start position:0%
+down then there's a
+ 
+
+ align:start position:0%
+down then there's a
+fifth and a
+
+ align:start position:0%
+fifth and a
+ 
+
+ align:start position:0%
+fifth and a
+seventh and a
+
+ align:start position:0%
+seventh and a
+ 
+
+ align:start position:0%
+seventh and a
+ninth and if you keep adding up the
+
+ align:start position:0%
+ninth and if you keep adding up the
+ 
+
+ align:start position:0%
+ninth and if you keep adding up the
+terms amazingly enough the series
+
+ align:start position:0%
+terms amazingly enough the series
+ 
+
+ align:start position:0%
+terms amazingly enough the series
+representation for the operator
+
+ align:start position:0%
+representation for the operator
+ 
+
+ align:start position:0%
+representation for the operator
+expression is the tailor series
+
+ align:start position:0%
+expression is the tailor series
+ 
+
+ align:start position:0%
+expression is the tailor series
+expansion of a sine
+
+ align:start position:0%
+expansion of a sine
+ 
+
+ align:start position:0%
+expansion of a sine
+wave just like we would have expected
+
+ align:start position:0%
+wave just like we would have expected
+ 
+
+ align:start position:0%
+wave just like we would have expected
+again I solved a differential equation a
+
+ align:start position:0%
+again I solved a differential equation a
+ 
+
+ align:start position:0%
+again I solved a differential equation a
+second order differential equation this
+
+ align:start position:0%
+second order differential equation this
+ 
+
+ align:start position:0%
+second order differential equation this
+time without calculus all I did was
+
+ align:start position:0%
+time without calculus all I did was
+ 
+
+ align:start position:0%
+time without calculus all I did was
+polinomial math and so with that I'll
+
+ align:start position:0%
+polinomial math and so with that I'll
+ 
+
+ align:start position:0%
+polinomial math and so with that I'll
+finish just by saying today what we did
+
+ align:start position:0%
+finish just by saying today what we did
+ 
+
+ align:start position:0%
+finish just by saying today what we did
+was introduce and basically finish
+
+ align:start position:0%
+was introduce and basically finish
+ 
+
+ align:start position:0%
+was introduce and basically finish
+CT because there's such a strong analogy
+
+ align:start position:0%
+CT because there's such a strong analogy
+ 
+
+ align:start position:0%
+CT because there's such a strong analogy
+between what we did in DT and how we'll
+
+ align:start position:0%
+between what we did in DT and how we'll
+ 
+
+ align:start position:0%
+between what we did in DT and how we'll
+approach thinking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CT
\ No newline at end of file
diff --git a/4nXw-f6NJ9s.txt b/4nXw-f6NJ9s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1028880e0a6078df47d20895963dea8395a3616b
--- /dev/null
+++ b/4nXw-f6NJ9s.txt
@@ -0,0 +1,14266 @@
+align:start position:0%
+ 
+hi everybody
+
+ align:start position:0%
+hi everybody
+ 
+
+ align:start position:0%
+hi everybody
+uh welcome to the last lecture of 6006
+
+ align:start position:0%
+uh welcome to the last lecture of 6006
+ 
+
+ align:start position:0%
+uh welcome to the last lecture of 6006
+last lecture we talked about
+
+ align:start position:0%
+last lecture we talked about
+ 
+
+ align:start position:0%
+last lecture we talked about
+summing up this class and talking about
+
+ align:start position:0%
+summing up this class and talking about
+ 
+
+ align:start position:0%
+summing up this class and talking about
+future courses in the department
+
+ align:start position:0%
+future courses in the department
+ 
+
+ align:start position:0%
+future courses in the department
+that use this material um
+
+ align:start position:0%
+that use this material um
+ 
+
+ align:start position:0%
+that use this material um
+just as a pointer to some of those
+
+ align:start position:0%
+just as a pointer to some of those
+ 
+
+ align:start position:0%
+just as a pointer to some of those
+classes i have a little slide here i
+
+ align:start position:0%
+classes i have a little slide here i
+ 
+
+ align:start position:0%
+classes i have a little slide here i
+didn't get to
+
+ align:start position:0%
+didn't get to
+ 
+
+ align:start position:0%
+didn't get to
+uh at the last lecture talking about
+
+ align:start position:0%
+uh at the last lecture talking about
+ 
+
+ align:start position:0%
+uh at the last lecture talking about
+kind of what i was talking about the end
+
+ align:start position:0%
+kind of what i was talking about the end
+ 
+
+ align:start position:0%
+kind of what i was talking about the end
+of last lecture about
+
+ align:start position:0%
+of last lecture about
+ 
+
+ align:start position:0%
+of last lecture about
+different models uh different
+
+ align:start position:0%
+different models uh different
+ 
+
+ align:start position:0%
+different models uh different
+specialized classes
+
+ align:start position:0%
+specialized classes
+ 
+
+ align:start position:0%
+specialized classes
+on different aspects of o6 material
+
+ align:start position:0%
+on different aspects of o6 material
+ 
+
+ align:start position:0%
+on different aspects of o6 material
+for example more graph stuff
+
+ align:start position:0%
+for example more graph stuff
+ 
+
+ align:start position:0%
+for example more graph stuff
+different models of computation
+
+ align:start position:0%
+different models of computation
+ 
+
+ align:start position:0%
+different models of computation
+randomness
+
+ align:start position:0%
+randomness
+ 
+
+ align:start position:0%
+randomness
+uh complexity all of these things have
+
+ align:start position:0%
+uh complexity all of these things have
+ 
+
+ align:start position:0%
+uh complexity all of these things have
+their own specialized classes
+
+ align:start position:0%
+their own specialized classes
+ 
+
+ align:start position:0%
+their own specialized classes
+in the department uh as well as a lot of
+
+ align:start position:0%
+in the department uh as well as a lot of
+ 
+
+ align:start position:0%
+in the department uh as well as a lot of
+applications
+
+ align:start position:0%
+applications
+ 
+
+ align:start position:0%
+applications
+uh for this material in subjects like
+
+ align:start position:0%
+uh for this material in subjects like
+ 
+
+ align:start position:0%
+uh for this material in subjects like
+biology cryptography
+
+ align:start position:0%
+biology cryptography
+ 
+
+ align:start position:0%
+biology cryptography
+and in particular for your instructors
+
+ align:start position:0%
+and in particular for your instructors
+ 
+
+ align:start position:0%
+and in particular for your instructors
+uh the the realm of graphics and
+
+ align:start position:0%
+uh the the realm of graphics and
+ 
+
+ align:start position:0%
+uh the the realm of graphics and
+geometry
+
+ align:start position:0%
+geometry
+ 
+
+ align:start position:0%
+geometry
+okay so all of all of your instructors
+
+ align:start position:0%
+okay so all of all of your instructors
+ 
+
+ align:start position:0%
+okay so all of all of your instructors
+this term happen to be
+
+ align:start position:0%
+this term happen to be
+ 
+
+ align:start position:0%
+this term happen to be
+geometers and have uh be interested in
+
+ align:start position:0%
+geometers and have uh be interested in
+ 
+
+ align:start position:0%
+geometers and have uh be interested in
+geometry related problems um
+
+ align:start position:0%
+geometry related problems um
+ 
+
+ align:start position:0%
+geometry related problems um
+me in particular i didn't start out in
+
+ align:start position:0%
+me in particular i didn't start out in
+ 
+
+ align:start position:0%
+me in particular i didn't start out in
+computer science
+
+ align:start position:0%
+computer science
+ 
+
+ align:start position:0%
+computer science
+i started out in mechanical engineering
+
+ align:start position:0%
+i started out in mechanical engineering
+ 
+
+ align:start position:0%
+i started out in mechanical engineering
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and the thing that was my passion um
+
+ align:start position:0%
+and the thing that was my passion um
+ 
+
+ align:start position:0%
+and the thing that was my passion um
+coming into mit
+
+ align:start position:0%
+coming into mit
+ 
+
+ align:start position:0%
+coming into mit
+was origami and so here's a couple of
+
+ align:start position:0%
+was origami and so here's a couple of
+ 
+
+ align:start position:0%
+was origami and so here's a couple of
+uh pieces that uh i designed um
+
+ align:start position:0%
+uh pieces that uh i designed um
+ 
+
+ align:start position:0%
+uh pieces that uh i designed um
+origami pieces one square sheet of paper
+
+ align:start position:0%
+origami pieces one square sheet of paper
+ 
+
+ align:start position:0%
+origami pieces one square sheet of paper
+without cutting here's a
+
+ align:start position:0%
+without cutting here's a
+ 
+
+ align:start position:0%
+without cutting here's a
+a lobster and here's a
+
+ align:start position:0%
+a lobster and here's a
+ 
+
+ align:start position:0%
+a lobster and here's a
+you know a copyrighted dinosaur from a
+
+ align:start position:0%
+you know a copyrighted dinosaur from a
+ 
+
+ align:start position:0%
+you know a copyrighted dinosaur from a
+particular movie of the year that i
+
+ align:start position:0%
+particular movie of the year that i
+ 
+
+ align:start position:0%
+particular movie of the year that i
+designed it
+
+ align:start position:0%
+designed it
+ 
+
+ align:start position:0%
+designed it
+um i
+
+ align:start position:0%
+um i
+ 
+
+ align:start position:0%
+um i
+uh when i was young in high school i
+
+ align:start position:0%
+uh when i was young in high school i
+ 
+
+ align:start position:0%
+uh when i was young in high school i
+started designing my own origami models
+
+ align:start position:0%
+started designing my own origami models
+ 
+
+ align:start position:0%
+started designing my own origami models
+and what i didn't realize was the
+
+ align:start position:0%
+and what i didn't realize was the
+ 
+
+ align:start position:0%
+and what i didn't realize was the
+procedures
+
+ align:start position:0%
+procedures
+ 
+
+ align:start position:0%
+procedures
+that i went about designing these models
+
+ align:start position:0%
+that i went about designing these models
+ 
+
+ align:start position:0%
+that i went about designing these models
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+actually algorithms right i just didn't
+
+ align:start position:0%
+actually algorithms right i just didn't
+ 
+
+ align:start position:0%
+actually algorithms right i just didn't
+have the mathematical language
+
+ align:start position:0%
+have the mathematical language
+ 
+
+ align:start position:0%
+have the mathematical language
+to to understand exactly what i was
+
+ align:start position:0%
+to to understand exactly what i was
+ 
+
+ align:start position:0%
+to to understand exactly what i was
+doing but i could gain some intuition as
+
+ align:start position:0%
+doing but i could gain some intuition as
+ 
+
+ align:start position:0%
+doing but i could gain some intuition as
+an origami artist
+
+ align:start position:0%
+an origami artist
+ 
+
+ align:start position:0%
+an origami artist
+and design these things by using some of
+
+ align:start position:0%
+and design these things by using some of
+ 
+
+ align:start position:0%
+and design these things by using some of
+those algorithmic techniques it wasn't
+
+ align:start position:0%
+those algorithmic techniques it wasn't
+ 
+
+ align:start position:0%
+those algorithmic techniques it wasn't
+until
+
+ align:start position:0%
+until
+ 
+
+ align:start position:0%
+until
+grad school as a mechanical engineer
+
+ align:start position:0%
+grad school as a mechanical engineer
+ 
+
+ align:start position:0%
+grad school as a mechanical engineer
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+i started talking
+
+ align:start position:0%
+i started talking
+ 
+
+ align:start position:0%
+i started talking
+with uh our other instructor here
+
+ align:start position:0%
+with uh our other instructor here
+ 
+
+ align:start position:0%
+with uh our other instructor here
+professor domain
+
+ align:start position:0%
+professor domain
+ 
+
+ align:start position:0%
+professor domain
+about uh using algorithms in computer
+
+ align:start position:0%
+about uh using algorithms in computer
+ 
+
+ align:start position:0%
+about uh using algorithms in computer
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+to design not just origami
+
+ align:start position:0%
+to design not just origami
+ 
+
+ align:start position:0%
+to design not just origami
+uh which we both do but also uh
+
+ align:start position:0%
+uh which we both do but also uh
+ 
+
+ align:start position:0%
+uh which we both do but also uh
+folded structures that can be used for
+
+ align:start position:0%
+folded structures that can be used for
+ 
+
+ align:start position:0%
+folded structures that can be used for
+mechanical applications like space
+
+ align:start position:0%
+mechanical applications like space
+ 
+
+ align:start position:0%
+mechanical applications like space
+flight um uh deployable bridges
+
+ align:start position:0%
+flight um uh deployable bridges
+ 
+
+ align:start position:0%
+flight um uh deployable bridges
+in in like um in times when you
+
+ align:start position:0%
+in in like um in times when you
+ 
+
+ align:start position:0%
+in in like um in times when you
+you can't you need a temporary
+
+ align:start position:0%
+you can't you need a temporary
+ 
+
+ align:start position:0%
+you can't you need a temporary
+bridge or shelter or something like that
+
+ align:start position:0%
+bridge or shelter or something like that
+ 
+
+ align:start position:0%
+bridge or shelter or something like that
+deployable structures
+
+ align:start position:0%
+deployable structures
+ 
+
+ align:start position:0%
+deployable structures
+where you might need to make folded
+
+ align:start position:0%
+where you might need to make folded
+ 
+
+ align:start position:0%
+where you might need to make folded
+structures transformable structures
+
+ align:start position:0%
+structures transformable structures
+ 
+
+ align:start position:0%
+structures transformable structures
+that can have different applications
+
+ align:start position:0%
+that can have different applications
+ 
+
+ align:start position:0%
+that can have different applications
+for different purposes need to
+
+ align:start position:0%
+for different purposes need to
+ 
+
+ align:start position:0%
+for different purposes need to
+reconfigure the dream being that
+
+ align:start position:0%
+reconfigure the dream being that
+ 
+
+ align:start position:0%
+reconfigure the dream being that
+we have these powerful devices in our
+
+ align:start position:0%
+we have these powerful devices in our
+ 
+
+ align:start position:0%
+we have these powerful devices in our
+pockets right now
+
+ align:start position:0%
+pockets right now
+ 
+
+ align:start position:0%
+pockets right now
+cell phones uh which uh you know are
+
+ align:start position:0%
+cell phones uh which uh you know are
+ 
+
+ align:start position:0%
+cell phones uh which uh you know are
+really powerful because we can
+
+ align:start position:0%
+really powerful because we can
+ 
+
+ align:start position:0%
+really powerful because we can
+reconfigure
+
+ align:start position:0%
+reconfigure
+ 
+
+ align:start position:0%
+reconfigure
+the bits in them to make software of all
+
+ align:start position:0%
+the bits in them to make software of all
+ 
+
+ align:start position:0%
+the bits in them to make software of all
+different kinds right
+
+ align:start position:0%
+different kinds right
+ 
+
+ align:start position:0%
+different kinds right
+there's a there's a exponential number
+
+ align:start position:0%
+there's a there's a exponential number
+ 
+
+ align:start position:0%
+there's a there's a exponential number
+of different programs that we can write
+
+ align:start position:0%
+of different programs that we can write
+ 
+
+ align:start position:0%
+of different programs that we can write
+and that's part of why you're here is to
+
+ align:start position:0%
+and that's part of why you're here is to
+ 
+
+ align:start position:0%
+and that's part of why you're here is to
+write the next best one
+
+ align:start position:0%
+write the next best one
+ 
+
+ align:start position:0%
+write the next best one
+right so that's how to how to make uh
+
+ align:start position:0%
+right so that's how to how to make uh
+ 
+
+ align:start position:0%
+right so that's how to how to make uh
+kind of a universal a device uh
+
+ align:start position:0%
+kind of a universal a device uh
+ 
+
+ align:start position:0%
+kind of a universal a device uh
+at the electronic level what if we could
+
+ align:start position:0%
+at the electronic level what if we could
+ 
+
+ align:start position:0%
+at the electronic level what if we could
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+in a material from a material standpoint
+
+ align:start position:0%
+in a material from a material standpoint
+ 
+
+ align:start position:0%
+in a material from a material standpoint
+what if i could
+
+ align:start position:0%
+what if i could
+ 
+
+ align:start position:0%
+what if i could
+reprogram the matter in my phone so that
+
+ align:start position:0%
+reprogram the matter in my phone so that
+ 
+
+ align:start position:0%
+reprogram the matter in my phone so that
+not only
+
+ align:start position:0%
+not only
+ 
+
+ align:start position:0%
+not only
+uh could i reprogram the app that's on
+
+ align:start position:0%
+uh could i reprogram the app that's on
+ 
+
+ align:start position:0%
+uh could i reprogram the app that's on
+your phone
+
+ align:start position:0%
+your phone
+ 
+
+ align:start position:0%
+your phone
+but instead of having the say the iphone
+
+ align:start position:0%
+but instead of having the say the iphone
+ 
+
+ align:start position:0%
+but instead of having the say the iphone
+10 or whatever that you have and and you
+
+ align:start position:0%
+10 or whatever that you have and and you
+ 
+
+ align:start position:0%
+10 or whatever that you have and and you
+want to go buy the iphone 11 instead you
+
+ align:start position:0%
+want to go buy the iphone 11 instead you
+ 
+
+ align:start position:0%
+want to go buy the iphone 11 instead you
+you download a software app that then
+
+ align:start position:0%
+you download a software app that then
+ 
+
+ align:start position:0%
+you download a software app that then
+reconfigures the matter in your phone it
+
+ align:start position:0%
+reconfigures the matter in your phone it
+ 
+
+ align:start position:0%
+reconfigures the matter in your phone it
+folds or reconfigures
+
+ align:start position:0%
+folds or reconfigures
+ 
+
+ align:start position:0%
+folds or reconfigures
+into the next generation iphone
+
+ align:start position:0%
+into the next generation iphone
+ 
+
+ align:start position:0%
+into the next generation iphone
+you you don't have to throw away that
+
+ align:start position:0%
+you you don't have to throw away that
+ 
+
+ align:start position:0%
+you you don't have to throw away that
+old one you can essentially recycle the
+
+ align:start position:0%
+old one you can essentially recycle the
+ 
+
+ align:start position:0%
+old one you can essentially recycle the
+material that you have
+
+ align:start position:0%
+material that you have
+ 
+
+ align:start position:0%
+material that you have
+uh to potentially uh save material save
+
+ align:start position:0%
+uh to potentially uh save material save
+ 
+
+ align:start position:0%
+uh to potentially uh save material save
+cost
+
+ align:start position:0%
+cost
+ 
+
+ align:start position:0%
+cost
+and be better for the environment
+
+ align:start position:0%
+and be better for the environment
+ 
+
+ align:start position:0%
+and be better for the environment
+potentially so uh
+
+ align:start position:0%
+potentially so uh
+ 
+
+ align:start position:0%
+potentially so uh
+i started moving into computer science
+
+ align:start position:0%
+i started moving into computer science
+ 
+
+ align:start position:0%
+i started moving into computer science
+because i found that it was
+
+ align:start position:0%
+because i found that it was
+ 
+
+ align:start position:0%
+because i found that it was
+a really good way to model the world and
+
+ align:start position:0%
+a really good way to model the world and
+ 
+
+ align:start position:0%
+a really good way to model the world and
+solve some really interesting problems
+
+ align:start position:0%
+solve some really interesting problems
+ 
+
+ align:start position:0%
+solve some really interesting problems
+uh about folding that i i really enjoyed
+
+ align:start position:0%
+uh about folding that i i really enjoyed
+ 
+
+ align:start position:0%
+uh about folding that i i really enjoyed
+so um the the three of us today
+
+ align:start position:0%
+so um the the three of us today
+ 
+
+ align:start position:0%
+so um the the three of us today
+are going to spend some time talking a
+
+ align:start position:0%
+are going to spend some time talking a
+ 
+
+ align:start position:0%
+are going to spend some time talking a
+little bit about how we can use
+
+ align:start position:0%
+little bit about how we can use
+ 
+
+ align:start position:0%
+little bit about how we can use
+algorithms
+
+ align:start position:0%
+algorithms
+ 
+
+ align:start position:0%
+algorithms
+606 material and beyond in our own
+
+ align:start position:0%
+606 material and beyond in our own
+ 
+
+ align:start position:0%
+606 material and beyond in our own
+research
+
+ align:start position:0%
+research
+ 
+
+ align:start position:0%
+research
+and we're going to start off with
+
+ align:start position:0%
+and we're going to start off with
+ 
+
+ align:start position:0%
+and we're going to start off with
+professor domain
+
+ align:start position:0%
+professor domain
+ 
+
+ align:start position:0%
+professor domain
+and then professor solomon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sweet so why don't i just jump into
+
+ align:start position:0%
+sweet so why don't i just jump into
+ 
+
+ align:start position:0%
+sweet so why don't i just jump into
+uh computational origami and geometric
+
+ align:start position:0%
+uh computational origami and geometric
+ 
+
+ align:start position:0%
+uh computational origami and geometric
+folding algorithms is sort of a broader
+
+ align:start position:0%
+folding algorithms is sort of a broader
+ 
+
+ align:start position:0%
+folding algorithms is sort of a broader
+umbrella for folding
+
+ align:start position:0%
+umbrella for folding
+ 
+
+ align:start position:0%
+umbrella for folding
+related things which is encapsulated by
+
+ align:start position:0%
+related things which is encapsulated by
+ 
+
+ align:start position:0%
+related things which is encapsulated by
+this class 6.849
+
+ align:start position:0%
+this class 6.849
+ 
+
+ align:start position:0%
+this class 6.849
+which is happening next fall so you
+
+ align:start position:0%
+which is happening next fall so you
+ 
+
+ align:start position:0%
+which is happening next fall so you
+should all take it
+
+ align:start position:0%
+should all take it
+ 
+
+ align:start position:0%
+should all take it
+06 should be a reasonable background
+
+ align:start position:0%
+06 should be a reasonable background
+ 
+
+ align:start position:0%
+06 should be a reasonable background
+and in general we're interested in two
+
+ align:start position:0%
+and in general we're interested in two
+ 
+
+ align:start position:0%
+and in general we're interested in two
+kinds of problems one
+
+ align:start position:0%
+kinds of problems one
+ 
+
+ align:start position:0%
+kinds of problems one
+the big one is origami design or general
+
+ align:start position:0%
+the big one is origami design or general
+ 
+
+ align:start position:0%
+the big one is origami design or general
+folding design where you have some
+
+ align:start position:0%
+folding design where you have some
+ 
+
+ align:start position:0%
+folding design where you have some
+specifications of what you'd like to
+
+ align:start position:0%
+specifications of what you'd like to
+ 
+
+ align:start position:0%
+specifications of what you'd like to
+build
+
+ align:start position:0%
+build
+ 
+
+ align:start position:0%
+build
+in this case i wanted to make a logo for
+
+ align:start position:0%
+in this case i wanted to make a logo for
+ 
+
+ align:start position:0%
+in this case i wanted to make a logo for
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and i imagined extruding that text
+
+ align:start position:0%
+and i imagined extruding that text
+ 
+
+ align:start position:0%
+and i imagined extruding that text
+into third third dimension and then i
+
+ align:start position:0%
+into third third dimension and then i
+ 
+
+ align:start position:0%
+into third third dimension and then i
+wanted an algorithm
+
+ align:start position:0%
+wanted an algorithm
+ 
+
+ align:start position:0%
+wanted an algorithm
+to figure tell me how to fold that
+
+ align:start position:0%
+to figure tell me how to fold that
+ 
+
+ align:start position:0%
+to figure tell me how to fold that
+structure and so there is an algorithm
+
+ align:start position:0%
+structure and so there is an algorithm
+ 
+
+ align:start position:0%
+structure and so there is an algorithm
+which i'll talk about in a moment that
+
+ align:start position:0%
+which i'll talk about in a moment that
+ 
+
+ align:start position:0%
+which i'll talk about in a moment that
+gives you a crease pattern and then
+
+ align:start position:0%
+gives you a crease pattern and then
+ 
+
+ align:start position:0%
+gives you a crease pattern and then
+currently you fold it by hand the dream
+
+ align:start position:0%
+currently you fold it by hand the dream
+ 
+
+ align:start position:0%
+currently you fold it by hand the dream
+is we'll eventually have folding
+
+ align:start position:0%
+is we'll eventually have folding
+ 
+
+ align:start position:0%
+is we'll eventually have folding
+machines that do it all for us
+
+ align:start position:0%
+machines that do it all for us
+ 
+
+ align:start position:0%
+machines that do it all for us
+um and so that's the origami design
+
+ align:start position:0%
+um and so that's the origami design
+ 
+
+ align:start position:0%
+um and so that's the origami design
+where you go from the
+
+ align:start position:0%
+where you go from the
+ 
+
+ align:start position:0%
+where you go from the
+the target shape back to the
+
+ align:start position:0%
+the target shape back to the
+ 
+
+ align:start position:0%
+the target shape back to the
+um to the crease pattern the reverse
+
+ align:start position:0%
+um to the crease pattern the reverse
+ 
+
+ align:start position:0%
+um to the crease pattern the reverse
+direction is sort of foldability if i
+
+ align:start position:0%
+direction is sort of foldability if i
+ 
+
+ align:start position:0%
+direction is sort of foldability if i
+gave you a structure
+
+ align:start position:0%
+gave you a structure
+ 
+
+ align:start position:0%
+gave you a structure
+like this and i wanted to know does it
+
+ align:start position:0%
+like this and i wanted to know does it
+ 
+
+ align:start position:0%
+like this and i wanted to know does it
+fold
+
+ align:start position:0%
+fold
+ 
+
+ align:start position:0%
+fold
+that's a problem we call foldability in
+
+ align:start position:0%
+that's a problem we call foldability in
+ 
+
+ align:start position:0%
+that's a problem we call foldability in
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+a class of problems and sadly most of
+
+ align:start position:0%
+a class of problems and sadly most of
+ 
+
+ align:start position:0%
+a class of problems and sadly most of
+those problems are np hard
+
+ align:start position:0%
+those problems are np hard
+ 
+
+ align:start position:0%
+those problems are np hard
+jason and i proved that foldability is
+
+ align:start position:0%
+jason and i proved that foldability is
+ 
+
+ align:start position:0%
+jason and i proved that foldability is
+hard for a general given a crease
+
+ align:start position:0%
+hard for a general given a crease
+ 
+
+ align:start position:0%
+hard for a general given a crease
+pattern like that
+
+ align:start position:0%
+pattern like that
+ 
+
+ align:start position:0%
+pattern like that
+telling you whether it folds into
+
+ align:start position:0%
+telling you whether it folds into
+ 
+
+ align:start position:0%
+telling you whether it folds into
+anything it turns out to be np hard so
+
+ align:start position:0%
+anything it turns out to be np hard so
+ 
+
+ align:start position:0%
+anything it turns out to be np hard so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+bad news so we focus a lot on the design
+
+ align:start position:0%
+bad news so we focus a lot on the design
+ 
+
+ align:start position:0%
+bad news so we focus a lot on the design
+problem because that
+
+ align:start position:0%
+problem because that
+ 
+
+ align:start position:0%
+problem because that
+actually tends to be easier we can solve
+
+ align:start position:0%
+actually tends to be easier we can solve
+ 
+
+ align:start position:0%
+actually tends to be easier we can solve
+it with algorithms like
+
+ align:start position:0%
+it with algorithms like
+ 
+
+ align:start position:0%
+it with algorithms like
+that one you're seeing um and so
+
+ align:start position:0%
+that one you're seeing um and so
+ 
+
+ align:start position:0%
+that one you're seeing um and so
+a long time ago we proved that you can
+
+ align:start position:0%
+a long time ago we proved that you can
+ 
+
+ align:start position:0%
+a long time ago we proved that you can
+fold everything
+
+ align:start position:0%
+fold everything
+ 
+
+ align:start position:0%
+fold everything
+if i give you a square piece of paper
+
+ align:start position:0%
+if i give you a square piece of paper
+ 
+
+ align:start position:0%
+if i give you a square piece of paper
+and you take
+
+ align:start position:0%
+and you take
+ 
+
+ align:start position:0%
+and you take
+any polygon you want to make or maybe
+
+ align:start position:0%
+any polygon you want to make or maybe
+ 
+
+ align:start position:0%
+any polygon you want to make or maybe
+the paper's white on one side black on
+
+ align:start position:0%
+the paper's white on one side black on
+ 
+
+ align:start position:0%
+the paper's white on one side black on
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+you you want to fold some two color
+
+ align:start position:0%
+you you want to fold some two color
+ 
+
+ align:start position:0%
+you you want to fold some two color
+pattern like a zebra or in general some
+
+ align:start position:0%
+pattern like a zebra or in general some
+ 
+
+ align:start position:0%
+pattern like a zebra or in general some
+three-dimensional surface
+
+ align:start position:0%
+three-dimensional surface
+ 
+
+ align:start position:0%
+three-dimensional surface
+like these guys there is a way to fold
+
+ align:start position:0%
+like these guys there is a way to fold
+ 
+
+ align:start position:0%
+like these guys there is a way to fold
+it from a large enough square of paper
+
+ align:start position:0%
+it from a large enough square of paper
+ 
+
+ align:start position:0%
+it from a large enough square of paper
+and it's actually really easy to prove
+
+ align:start position:0%
+and it's actually really easy to prove
+ 
+
+ align:start position:0%
+and it's actually really easy to prove
+that with an algorithm i have
+
+ align:start position:0%
+that with an algorithm i have
+ 
+
+ align:start position:0%
+that with an algorithm i have
+a sketch of the two pages of proof that
+
+ align:start position:0%
+a sketch of the two pages of proof that
+ 
+
+ align:start position:0%
+a sketch of the two pages of proof that
+we go over in 6849
+
+ align:start position:0%
+we go over in 6849
+ 
+
+ align:start position:0%
+we go over in 6849
+but i'll just hand wave a little bit uh
+
+ align:start position:0%
+but i'll just hand wave a little bit uh
+ 
+
+ align:start position:0%
+but i'll just hand wave a little bit uh
+if you take a piece of paper
+
+ align:start position:0%
+if you take a piece of paper
+ 
+
+ align:start position:0%
+if you take a piece of paper
+like my lecture notes here the first
+
+ align:start position:0%
+like my lecture notes here the first
+ 
+
+ align:start position:0%
+like my lecture notes here the first
+thing you do
+
+ align:start position:0%
+thing you do
+ 
+
+ align:start position:0%
+thing you do
+is fold it down into a very long narrow
+
+ align:start position:0%
+is fold it down into a very long narrow
+ 
+
+ align:start position:0%
+is fold it down into a very long narrow
+strip
+
+ align:start position:0%
+strip
+ 
+
+ align:start position:0%
+strip
+much longer and narrower than this one
+
+ align:start position:0%
+much longer and narrower than this one
+ 
+
+ align:start position:0%
+much longer and narrower than this one
+wasting most of the material
+
+ align:start position:0%
+wasting most of the material
+ 
+
+ align:start position:0%
+wasting most of the material
+and then you take your strip and you
+
+ align:start position:0%
+and then you take your strip and you
+ 
+
+ align:start position:0%
+and then you take your strip and you
+just figure out how to
+
+ align:start position:0%
+just figure out how to
+ 
+
+ align:start position:0%
+just figure out how to
+turn it in some general way and then you
+
+ align:start position:0%
+turn it in some general way and then you
+ 
+
+ align:start position:0%
+turn it in some general way and then you
+just sort of zigzag back and forth along
+
+ align:start position:0%
+just sort of zigzag back and forth along
+ 
+
+ align:start position:0%
+just sort of zigzag back and forth along
+the surface
+
+ align:start position:0%
+the surface
+ 
+
+ align:start position:0%
+the surface
+so it's very cool in that you can prove
+
+ align:start position:0%
+so it's very cool in that you can prove
+ 
+
+ align:start position:0%
+so it's very cool in that you can prove
+with an algorithm in a very short amount
+
+ align:start position:0%
+with an algorithm in a very short amount
+ 
+
+ align:start position:0%
+with an algorithm in a very short amount
+of time
+
+ align:start position:0%
+of time
+ 
+
+ align:start position:0%
+of time
+to someone you can actually fold
+
+ align:start position:0%
+to someone you can actually fold
+ 
+
+ align:start position:0%
+to someone you can actually fold
+everything of course it's a terrible
+
+ align:start position:0%
+everything of course it's a terrible
+ 
+
+ align:start position:0%
+everything of course it's a terrible
+folding because in the very first step
+
+ align:start position:0%
+folding because in the very first step
+ 
+
+ align:start position:0%
+folding because in the very first step
+we throw away
+
+ align:start position:0%
+we throw away
+ 
+
+ align:start position:0%
+we throw away
+all but epsilon of the material but it's
+
+ align:start position:0%
+all but epsilon of the material but it's
+ 
+
+ align:start position:0%
+all but epsilon of the material but it's
+a starting point and then that was back
+
+ align:start position:0%
+a starting point and then that was back
+ 
+
+ align:start position:0%
+a starting point and then that was back
+in the 90s late 90s
+
+ align:start position:0%
+in the 90s late 90s
+ 
+
+ align:start position:0%
+in the 90s late 90s
+one of the first results in
+
+ align:start position:0%
+one of the first results in
+ 
+
+ align:start position:0%
+one of the first results in
+computational origami and
+
+ align:start position:0%
+computational origami and
+ 
+
+ align:start position:0%
+computational origami and
+in modern times we look for better
+
+ align:start position:0%
+in modern times we look for better
+ 
+
+ align:start position:0%
+in modern times we look for better
+algorithms that are more efficient that
+
+ align:start position:0%
+algorithms that are more efficient that
+ 
+
+ align:start position:0%
+algorithms that are more efficient that
+try to minimize the scale factor from
+
+ align:start position:0%
+try to minimize the scale factor from
+ 
+
+ align:start position:0%
+try to minimize the scale factor from
+how big of a piece of paper do i start
+
+ align:start position:0%
+how big of a piece of paper do i start
+ 
+
+ align:start position:0%
+how big of a piece of paper do i start
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+to how big of a model do i get um and
+
+ align:start position:0%
+to how big of a model do i get um and
+ 
+
+ align:start position:0%
+to how big of a model do i get um and
+one of the cool ways
+
+ align:start position:0%
+one of the cool ways
+ 
+
+ align:start position:0%
+one of the cool ways
+these days which was invented by
+
+ align:start position:0%
+these days which was invented by
+ 
+
+ align:start position:0%
+these days which was invented by
+tomihirotachi and then analyzed by the
+
+ align:start position:0%
+tomihirotachi and then analyzed by the
+ 
+
+ align:start position:0%
+tomihirotachi and then analyzed by the
+two of us
+
+ align:start position:0%
+two of us
+ 
+
+ align:start position:0%
+two of us
+it's called orgamizer it's free software
+
+ align:start position:0%
+it's called orgamizer it's free software
+ 
+
+ align:start position:0%
+it's called orgamizer it's free software
+you take a 3d model
+
+ align:start position:0%
+you take a 3d model
+ 
+
+ align:start position:0%
+you take a 3d model
+and you can it makes it into a crease
+
+ align:start position:0%
+and you can it makes it into a crease
+ 
+
+ align:start position:0%
+and you can it makes it into a crease
+pattern that you fold from a square in
+
+ align:start position:0%
+pattern that you fold from a square in
+ 
+
+ align:start position:0%
+pattern that you fold from a square in
+this case it uses 22 percent of the area
+
+ align:start position:0%
+this case it uses 22 percent of the area
+ 
+
+ align:start position:0%
+this case it uses 22 percent of the area
+which is pretty good
+
+ align:start position:0%
+which is pretty good
+ 
+
+ align:start position:0%
+which is pretty good
+um similar to these guys
+
+ align:start position:0%
+um similar to these guys
+ 
+
+ align:start position:0%
+um similar to these guys
+in terms of efficiency but very very
+
+ align:start position:0%
+in terms of efficiency but very very
+ 
+
+ align:start position:0%
+in terms of efficiency but very very
+different kind of folding
+
+ align:start position:0%
+different kind of folding
+ 
+
+ align:start position:0%
+different kind of folding
+than what you would get from more
+
+ align:start position:0%
+than what you would get from more
+ 
+
+ align:start position:0%
+than what you would get from more
+traditional origami design which uses
+
+ align:start position:0%
+traditional origami design which uses
+ 
+
+ align:start position:0%
+traditional origami design which uses
+different algorithms which i'm not going
+
+ align:start position:0%
+different algorithms which i'm not going
+ 
+
+ align:start position:0%
+different algorithms which i'm not going
+to talk about but you should take the
+
+ align:start position:0%
+to talk about but you should take the
+ 
+
+ align:start position:0%
+to talk about but you should take the
+class jason gives a lecture in the class
+
+ align:start position:0%
+class jason gives a lecture in the class
+ 
+
+ align:start position:0%
+class jason gives a lecture in the class
+that you can
+
+ align:start position:0%
+that you can
+ 
+
+ align:start position:0%
+that you can
+learn from him but the you know the
+
+ align:start position:0%
+learn from him but the you know the
+ 
+
+ align:start position:0%
+learn from him but the you know the
+vision is we can take any sheet of
+
+ align:start position:0%
+vision is we can take any sheet of
+ 
+
+ align:start position:0%
+vision is we can take any sheet of
+material that can hold a crease
+
+ align:start position:0%
+material that can hold a crease
+ 
+
+ align:start position:0%
+material that can hold a crease
+like this sheet of steel that tomohiro
+
+ align:start position:0%
+like this sheet of steel that tomohiro
+ 
+
+ align:start position:0%
+like this sheet of steel that tomohiro
+is folding i was cut
+
+ align:start position:0%
+is folding i was cut
+ 
+
+ align:start position:0%
+is folding i was cut
+by a big laser cutter at mit and this is
+
+ align:start position:0%
+by a big laser cutter at mit and this is
+ 
+
+ align:start position:0%
+by a big laser cutter at mit and this is
+him in this data center several years
+
+ align:start position:0%
+him in this data center several years
+ 
+
+ align:start position:0%
+him in this data center several years
+ago
+
+ align:start position:0%
+ago
+ 
+
+ align:start position:0%
+ago
+folding it into a steel bunny
+
+ align:start position:0%
+folding it into a steel bunny
+ 
+
+ align:start position:0%
+folding it into a steel bunny
+and so this is like a totally new way to
+
+ align:start position:0%
+and so this is like a totally new way to
+ 
+
+ align:start position:0%
+and so this is like a totally new way to
+manufacture
+
+ align:start position:0%
+manufacture
+ 
+
+ align:start position:0%
+manufacture
+3d objects and you can make particularly
+
+ align:start position:0%
+3d objects and you can make particularly
+ 
+
+ align:start position:0%
+3d objects and you can make particularly
+interesting objects that
+
+ align:start position:0%
+interesting objects that
+ 
+
+ align:start position:0%
+interesting objects that
+either collapse flat for uh
+
+ align:start position:0%
+either collapse flat for uh
+ 
+
+ align:start position:0%
+either collapse flat for uh
+transportation
+
+ align:start position:0%
+transportation
+ 
+
+ align:start position:0%
+transportation
+uh or transform like jason was talking
+
+ align:start position:0%
+uh or transform like jason was talking
+ 
+
+ align:start position:0%
+uh or transform like jason was talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+but i'm just giving you a flavor uh the
+
+ align:start position:0%
+but i'm just giving you a flavor uh the
+ 
+
+ align:start position:0%
+but i'm just giving you a flavor uh the
+i think the first paper we wrote
+
+ align:start position:0%
+i think the first paper we wrote
+ 
+
+ align:start position:0%
+i think the first paper we wrote
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+was on maize folding so this is an
+
+ align:start position:0%
+was on maize folding so this is an
+ 
+
+ align:start position:0%
+was on maize folding so this is an
+example of folding
+
+ align:start position:0%
+example of folding
+ 
+
+ align:start position:0%
+example of folding
+a maze from a rectangle of paper and you
+
+ align:start position:0%
+a maze from a rectangle of paper and you
+ 
+
+ align:start position:0%
+a maze from a rectangle of paper and you
+can all
+
+ align:start position:0%
+can all
+ 
+
+ align:start position:0%
+can all
+try this out you just
+
+ align:start position:0%
+try this out you just
+ 
+
+ align:start position:0%
+try this out you just
+google for our maze folder you can
+
+ align:start position:0%
+google for our maze folder you can
+ 
+
+ align:start position:0%
+google for our maze folder you can
+generate a random maze
+
+ align:start position:0%
+generate a random maze
+ 
+
+ align:start position:0%
+generate a random maze
+and this 3d structure can be folded
+
+ align:start position:0%
+and this 3d structure can be folded
+ 
+
+ align:start position:0%
+and this 3d structure can be folded
+from this crease pattern that's a really
+
+ align:start position:0%
+from this crease pattern that's a really
+ 
+
+ align:start position:0%
+from this crease pattern that's a really
+hard one so
+
+ align:start position:0%
+hard one so
+ 
+
+ align:start position:0%
+hard one so
+try maybe try something smaller you can
+
+ align:start position:0%
+try maybe try something smaller you can
+ 
+
+ align:start position:0%
+try maybe try something smaller you can
+also write your favorite message
+
+ align:start position:0%
+also write your favorite message
+ 
+
+ align:start position:0%
+also write your favorite message
+and fold this maze extruded graph
+
+ align:start position:0%
+and fold this maze extruded graph
+ 
+
+ align:start position:0%
+and fold this maze extruded graph
+from this crease pattern might want to
+
+ align:start position:0%
+from this crease pattern might want to
+ 
+
+ align:start position:0%
+from this crease pattern might want to
+start with something smaller
+
+ align:start position:0%
+start with something smaller
+ 
+
+ align:start position:0%
+start with something smaller
+but that's the general idea and it's
+
+ align:start position:0%
+but that's the general idea and it's
+ 
+
+ align:start position:0%
+but that's the general idea and it's
+actually quite easy to prove this
+
+ align:start position:0%
+actually quite easy to prove this
+ 
+
+ align:start position:0%
+actually quite easy to prove this
+algorithmically
+
+ align:start position:0%
+algorithmically
+ 
+
+ align:start position:0%
+algorithmically
+if you have a really good origamis like
+
+ align:start position:0%
+if you have a really good origamis like
+ 
+
+ align:start position:0%
+if you have a really good origamis like
+jason on your team
+
+ align:start position:0%
+jason on your team
+ 
+
+ align:start position:0%
+jason on your team
+what you do is design how to fold each
+
+ align:start position:0%
+what you do is design how to fold each
+ 
+
+ align:start position:0%
+what you do is design how to fold each
+type of vertex this is just a graph on a
+
+ align:start position:0%
+type of vertex this is just a graph on a
+ 
+
+ align:start position:0%
+type of vertex this is just a graph on a
+grid
+
+ align:start position:0%
+grid
+ 
+
+ align:start position:0%
+grid
+so there are you know some constant
+
+ align:start position:0%
+so there are you know some constant
+ 
+
+ align:start position:0%
+so there are you know some constant
+number of different ways that each
+
+ align:start position:0%
+number of different ways that each
+ 
+
+ align:start position:0%
+number of different ways that each
+vertex could look it could be degree
+
+ align:start position:0%
+vertex could look it could be degree
+ 
+
+ align:start position:0%
+vertex could look it could be degree
+four it could be degree three
+
+ align:start position:0%
+four it could be degree three
+ 
+
+ align:start position:0%
+four it could be degree three
+uh in as a t it could be degree two
+
+ align:start position:0%
+uh in as a t it could be degree two
+ 
+
+ align:start position:0%
+uh in as a t it could be degree two
+either as a turn or a straight
+
+ align:start position:0%
+either as a turn or a straight
+ 
+
+ align:start position:0%
+either as a turn or a straight
+and you design little gadgets little
+
+ align:start position:0%
+and you design little gadgets little
+ 
+
+ align:start position:0%
+and you design little gadgets little
+crease patterns that fold into each of
+
+ align:start position:0%
+crease patterns that fold into each of
+ 
+
+ align:start position:0%
+crease patterns that fold into each of
+those little structures
+
+ align:start position:0%
+those little structures
+ 
+
+ align:start position:0%
+those little structures
+and if you can do it in a way that these
+
+ align:start position:0%
+and if you can do it in a way that these
+ 
+
+ align:start position:0%
+and if you can do it in a way that these
+boundaries are compatible
+
+ align:start position:0%
+boundaries are compatible
+ 
+
+ align:start position:0%
+boundaries are compatible
+then to fold the whole thing you just
+
+ align:start position:0%
+then to fold the whole thing you just
+ 
+
+ align:start position:0%
+then to fold the whole thing you just
+sort of glue together those crease
+
+ align:start position:0%
+sort of glue together those crease
+ 
+
+ align:start position:0%
+sort of glue together those crease
+patterns and that's how that software
+
+ align:start position:0%
+patterns and that's how that software
+ 
+
+ align:start position:0%
+patterns and that's how that software
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+and so that was this is particularly
+
+ align:start position:0%
+and so that was this is particularly
+ 
+
+ align:start position:0%
+and so that was this is particularly
+interesting because you can fold an
+
+ align:start position:0%
+interesting because you can fold an
+ 
+
+ align:start position:0%
+interesting because you can fold an
+arbitrarily complicated graph
+
+ align:start position:0%
+arbitrarily complicated graph
+ 
+
+ align:start position:0%
+arbitrarily complicated graph
+uh arbitrarily complicated maze m by n
+
+ align:start position:0%
+uh arbitrarily complicated maze m by n
+ 
+
+ align:start position:0%
+uh arbitrarily complicated maze m by n
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+constant scale factor as long as the
+
+ align:start position:0%
+constant scale factor as long as the
+ 
+
+ align:start position:0%
+constant scale factor as long as the
+height that you're extruding that maze
+
+ align:start position:0%
+height that you're extruding that maze
+ 
+
+ align:start position:0%
+height that you're extruding that maze
+is constant
+
+ align:start position:0%
+is constant
+ 
+
+ align:start position:0%
+is constant
+then this is one family of shapes we
+
+ align:start position:0%
+then this is one family of shapes we
+ 
+
+ align:start position:0%
+then this is one family of shapes we
+know how to fold really well
+
+ align:start position:0%
+know how to fold really well
+ 
+
+ align:start position:0%
+know how to fold really well
+in general we're trying to understand
+
+ align:start position:0%
+in general we're trying to understand
+ 
+
+ align:start position:0%
+in general we're trying to understand
+you know what makes
+
+ align:start position:0%
+you know what makes
+ 
+
+ align:start position:0%
+you know what makes
+this lobster a nice shape in that it can
+
+ align:start position:0%
+this lobster a nice shape in that it can
+ 
+
+ align:start position:0%
+this lobster a nice shape in that it can
+be represented with a not too large
+
+ align:start position:0%
+be represented with a not too large
+ 
+
+ align:start position:0%
+be represented with a not too large
+piece of paper and we don't have general
+
+ align:start position:0%
+piece of paper and we don't have general
+ 
+
+ align:start position:0%
+piece of paper and we don't have general
+answers to that
+
+ align:start position:0%
+answers to that
+ 
+
+ align:start position:0%
+answers to that
+that problem i think that was a
+
+ align:start position:0%
+that problem i think that was a
+ 
+
+ align:start position:0%
+that problem i think that was a
+whirlwind tour of computational origami
+
+ align:start position:0%
+whirlwind tour of computational origami
+ 
+
+ align:start position:0%
+whirlwind tour of computational origami
+i also play a lot in the
+
+ align:start position:0%
+i also play a lot in the
+ 
+
+ align:start position:0%
+i also play a lot in the
+in algorithmic sculpture one of the
+
+ align:start position:0%
+in algorithmic sculpture one of the
+ 
+
+ align:start position:0%
+in algorithmic sculpture one of the
+leading edges in comp
+
+ align:start position:0%
+leading edges in comp
+ 
+
+ align:start position:0%
+leading edges in comp
+in origami and origami math is
+
+ align:start position:0%
+in origami and origami math is
+ 
+
+ align:start position:0%
+in origami and origami math is
+understanding how curved creases work
+
+ align:start position:0%
+understanding how curved creases work
+ 
+
+ align:start position:0%
+understanding how curved creases work
+and one of our favorite models is this
+
+ align:start position:0%
+and one of our favorite models is this
+ 
+
+ align:start position:0%
+and one of our favorite models is this
+one where you fold concentric circles
+
+ align:start position:0%
+one where you fold concentric circles
+ 
+
+ align:start position:0%
+one where you fold concentric circles
+alternating mountain and valley
+
+ align:start position:0%
+alternating mountain and valley
+ 
+
+ align:start position:0%
+alternating mountain and valley
+cut a circular hole out and it folds
+
+ align:start position:0%
+cut a circular hole out and it folds
+ 
+
+ align:start position:0%
+cut a circular hole out and it folds
+into this kind of
+
+ align:start position:0%
+into this kind of
+ 
+
+ align:start position:0%
+into this kind of
+pringle shape as a nice physics
+
+ align:start position:0%
+pringle shape as a nice physics
+ 
+
+ align:start position:0%
+pringle shape as a nice physics
+equilibrium thing and then you can turn
+
+ align:start position:0%
+equilibrium thing and then you can turn
+ 
+
+ align:start position:0%
+equilibrium thing and then you can turn
+it into fun sculptures like
+
+ align:start position:0%
+it into fun sculptures like
+ 
+
+ align:start position:0%
+it into fun sculptures like
+this these are done with my dad martin
+
+ align:start position:0%
+this these are done with my dad martin
+ 
+
+ align:start position:0%
+this these are done with my dad martin
+domain
+
+ align:start position:0%
+domain
+ 
+
+ align:start position:0%
+domain
+who's also here at mit or this guy this
+
+ align:start position:0%
+who's also here at mit or this guy this
+ 
+
+ align:start position:0%
+who's also here at mit or this guy this
+paper has been printed with a pattern
+
+ align:start position:0%
+paper has been printed with a pattern
+ 
+
+ align:start position:0%
+paper has been printed with a pattern
+according to
+
+ align:start position:0%
+according to
+ 
+
+ align:start position:0%
+according to
+getting burned by glass and then it gets
+
+ align:start position:0%
+getting burned by glass and then it gets
+ 
+
+ align:start position:0%
+getting burned by glass and then it gets
+folded and then put inside
+
+ align:start position:0%
+folded and then put inside
+ 
+
+ align:start position:0%
+folded and then put inside
+glass also made here at mit
+
+ align:start position:0%
+glass also made here at mit
+ 
+
+ align:start position:0%
+glass also made here at mit
+uh and so we use sculpture to try to
+
+ align:start position:0%
+uh and so we use sculpture to try to
+ 
+
+ align:start position:0%
+uh and so we use sculpture to try to
+explore and understand intuitively how
+
+ align:start position:0%
+explore and understand intuitively how
+ 
+
+ align:start position:0%
+explore and understand intuitively how
+curve creases work and then we get
+
+ align:start position:0%
+curve creases work and then we get
+ 
+
+ align:start position:0%
+curve creases work and then we get
+better and better
+
+ align:start position:0%
+better and better
+ 
+
+ align:start position:0%
+better and better
+understanding of the mathematics of even
+
+ align:start position:0%
+understanding of the mathematics of even
+ 
+
+ align:start position:0%
+understanding of the mathematics of even
+we don't even know whether this surface
+
+ align:start position:0%
+we don't even know whether this surface
+ 
+
+ align:start position:0%
+we don't even know whether this surface
+exists whether it's possible to fold in
+
+ align:start position:0%
+exists whether it's possible to fold in
+ 
+
+ align:start position:0%
+exists whether it's possible to fold in
+this way although
+
+ align:start position:0%
+this way although
+ 
+
+ align:start position:0%
+this way although
+getting close to proving it uh
+
+ align:start position:0%
+getting close to proving it uh
+ 
+
+ align:start position:0%
+getting close to proving it uh
+so that was sort of in the top level of
+
+ align:start position:0%
+so that was sort of in the top level of
+ 
+
+ align:start position:0%
+so that was sort of in the top level of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+hierarchy computational geometry is a
+
+ align:start position:0%
+hierarchy computational geometry is a
+ 
+
+ align:start position:0%
+hierarchy computational geometry is a
+bigger umbrella
+
+ align:start position:0%
+bigger umbrella
+ 
+
+ align:start position:0%
+bigger umbrella
+which is represented by another class
+
+ align:start position:0%
+which is represented by another class
+ 
+
+ align:start position:0%
+which is represented by another class
+6850 that's being taught this term
+
+ align:start position:0%
+6850 that's being taught this term
+ 
+
+ align:start position:0%
+6850 that's being taught this term
+and then i talked about geometric
+
+ align:start position:0%
+and then i talked about geometric
+ 
+
+ align:start position:0%
+and then i talked about geometric
+folding within that branch
+
+ align:start position:0%
+folding within that branch
+ 
+
+ align:start position:0%
+folding within that branch
+let me briefly tell you about another
+
+ align:start position:0%
+let me briefly tell you about another
+ 
+
+ align:start position:0%
+let me briefly tell you about another
+world of geometry very different
+
+ align:start position:0%
+world of geometry very different
+ 
+
+ align:start position:0%
+world of geometry very different
+in terms of model of computation oh i'm
+
+ align:start position:0%
+in terms of model of computation oh i'm
+ 
+
+ align:start position:0%
+in terms of model of computation oh i'm
+jumped ahead a little bit
+
+ align:start position:0%
+jumped ahead a little bit
+ 
+
+ align:start position:0%
+jumped ahead a little bit
+uh rewind let me show you one more fun
+
+ align:start position:0%
+uh rewind let me show you one more fun
+ 
+
+ align:start position:0%
+uh rewind let me show you one more fun
+demo
+
+ align:start position:0%
+demo
+ 
+
+ align:start position:0%
+demo
+which uh if i find my scissors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if i take a rectangle of paper and i
+
+ align:start position:0%
+so if i take a rectangle of paper and i
+ 
+
+ align:start position:0%
+so if i take a rectangle of paper and i
+fold it flat
+
+ align:start position:0%
+fold it flat
+ 
+
+ align:start position:0%
+fold it flat
+and make one straight cut what shapes
+
+ align:start position:0%
+and make one straight cut what shapes
+ 
+
+ align:start position:0%
+and make one straight cut what shapes
+can i get
+
+ align:start position:0%
+can i get
+ 
+
+ align:start position:0%
+can i get
+this is called the fold and cut problem
+
+ align:start position:0%
+this is called the fold and cut problem
+ 
+
+ align:start position:0%
+this is called the fold and cut problem
+hundreds of years old
+
+ align:start position:0%
+hundreds of years old
+ 
+
+ align:start position:0%
+hundreds of years old
+here for example i get a
+
+ align:start position:0%
+here for example i get a
+ 
+
+ align:start position:0%
+here for example i get a
+swan here i get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one straight cut i unfold and get
+
+ align:start position:0%
+one straight cut i unfold and get
+ 
+
+ align:start position:0%
+one straight cut i unfold and get
+an angelfish tough audience
+
+ align:start position:0%
+an angelfish tough audience
+ 
+
+ align:start position:0%
+an angelfish tough audience
+today i keep going i've seen all these
+
+ align:start position:0%
+today i keep going i've seen all these
+ 
+
+ align:start position:0%
+today i keep going i've seen all these
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+this is this one is um a particularly
+
+ align:start position:0%
+this is this one is um a particularly
+ 
+
+ align:start position:0%
+this is this one is um a particularly
+difficult one to fold
+
+ align:start position:0%
+difficult one to fold
+ 
+
+ align:start position:0%
+difficult one to fold
+only full and to cut yeah
+
+ align:start position:0%
+only full and to cut yeah
+ 
+
+ align:start position:0%
+only full and to cut yeah
+okay hopefully that works well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the mit logo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah go mit all right so
+
+ align:start position:0%
+yeah go mit all right so
+ 
+
+ align:start position:0%
+yeah go mit all right so
+um that's that's actually the first
+
+ align:start position:0%
+um that's that's actually the first
+ 
+
+ align:start position:0%
+um that's that's actually the first
+problem i worked on in computational
+
+ align:start position:0%
+problem i worked on in computational
+ 
+
+ align:start position:0%
+problem i worked on in computational
+origami it's a lot of fun
+
+ align:start position:0%
+origami it's a lot of fun
+ 
+
+ align:start position:0%
+origami it's a lot of fun
+and there's a really interesting
+
+ align:start position:0%
+and there's a really interesting
+ 
+
+ align:start position:0%
+and there's a really interesting
+algorithm here also for computing
+
+ align:start position:0%
+algorithm here also for computing
+ 
+
+ align:start position:0%
+algorithm here also for computing
+the crease pattern how to fold your
+
+ align:start position:0%
+the crease pattern how to fold your
+ 
+
+ align:start position:0%
+the crease pattern how to fold your
+piece of paper to align
+
+ align:start position:0%
+piece of paper to align
+ 
+
+ align:start position:0%
+piece of paper to align
+in fact any graph you draw on a piece of
+
+ align:start position:0%
+in fact any graph you draw on a piece of
+ 
+
+ align:start position:0%
+in fact any graph you draw on a piece of
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+you can align all those edges and
+
+ align:start position:0%
+you can align all those edges and
+ 
+
+ align:start position:0%
+you can align all those edges and
+nothing else so you cut along the line
+
+ align:start position:0%
+nothing else so you cut along the line
+ 
+
+ align:start position:0%
+nothing else so you cut along the line
+you get exactly what you want
+
+ align:start position:0%
+you get exactly what you want
+ 
+
+ align:start position:0%
+you get exactly what you want
+cool all right now i want to talk about
+
+ align:start position:0%
+cool all right now i want to talk about
+ 
+
+ align:start position:0%
+cool all right now i want to talk about
+something completely different which is
+
+ align:start position:0%
+something completely different which is
+ 
+
+ align:start position:0%
+something completely different which is
+self-assembly
+
+ align:start position:0%
+self-assembly
+ 
+
+ align:start position:0%
+self-assembly
+a fun thing you can do with dna which we
+
+ align:start position:0%
+a fun thing you can do with dna which we
+ 
+
+ align:start position:0%
+a fun thing you can do with dna which we
+all have
+
+ align:start position:0%
+all have
+ 
+
+ align:start position:0%
+all have
+just pick out some cool dna strands and
+
+ align:start position:0%
+just pick out some cool dna strands and
+ 
+
+ align:start position:0%
+just pick out some cool dna strands and
+design them in a clever way so they fit
+
+ align:start position:0%
+design them in a clever way so they fit
+ 
+
+ align:start position:0%
+design them in a clever way so they fit
+together to form a kind of square
+
+ align:start position:0%
+together to form a kind of square
+ 
+
+ align:start position:0%
+together to form a kind of square
+with dangling ends which i'll call glues
+
+ align:start position:0%
+with dangling ends which i'll call glues
+ 
+
+ align:start position:0%
+with dangling ends which i'll call glues
+and each of those dangling ends can have
+
+ align:start position:0%
+and each of those dangling ends can have
+ 
+
+ align:start position:0%
+and each of those dangling ends can have
+a particular pattern and only
+
+ align:start position:0%
+a particular pattern and only
+ 
+
+ align:start position:0%
+a particular pattern and only
+identical or complementary patterns will
+
+ align:start position:0%
+identical or complementary patterns will
+ 
+
+ align:start position:0%
+identical or complementary patterns will
+attach to each other
+
+ align:start position:0%
+attach to each other
+ 
+
+ align:start position:0%
+attach to each other
+and so you can use this to design your
+
+ align:start position:0%
+and so you can use this to design your
+ 
+
+ align:start position:0%
+and so you can use this to design your
+own self-assembling system
+
+ align:start position:0%
+own self-assembling system
+ 
+
+ align:start position:0%
+own self-assembling system
+like biology does but engineered for
+
+ align:start position:0%
+like biology does but engineered for
+ 
+
+ align:start position:0%
+like biology does but engineered for
+example to build a computer this is an
+
+ align:start position:0%
+example to build a computer this is an
+ 
+
+ align:start position:0%
+example to build a computer this is an
+example of taking a bunch of these
+
+ align:start position:0%
+example of taking a bunch of these
+ 
+
+ align:start position:0%
+example of taking a bunch of these
+square tiles
+
+ align:start position:0%
+square tiles
+ 
+
+ align:start position:0%
+square tiles
+and building a binary counter this thing
+
+ align:start position:0%
+and building a binary counter this thing
+ 
+
+ align:start position:0%
+and building a binary counter this thing
+is roughly counting in binary
+
+ align:start position:0%
+is roughly counting in binary
+ 
+
+ align:start position:0%
+is roughly counting in binary
+along the diagonal it's a little skewed
+
+ align:start position:0%
+along the diagonal it's a little skewed
+ 
+
+ align:start position:0%
+along the diagonal it's a little skewed
+so it's hard to see
+
+ align:start position:0%
+so it's hard to see
+ 
+
+ align:start position:0%
+so it's hard to see
+but the general model is
+
+ align:start position:0%
+but the general model is
+ 
+
+ align:start position:0%
+but the general model is
+you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squares this is sort of the
+
+ align:start position:0%
+squares this is sort of the
+ 
+
+ align:start position:0%
+squares this is sort of the
+computational model
+
+ align:start position:0%
+computational model
+ 
+
+ align:start position:0%
+computational model
+with four different glues and you can
+
+ align:start position:0%
+with four different glues and you can
+ 
+
+ align:start position:0%
+with four different glues and you can
+build any square you want
+
+ align:start position:0%
+build any square you want
+ 
+
+ align:start position:0%
+build any square you want
+but you don't have very many of these
+
+ align:start position:0%
+but you don't have very many of these
+ 
+
+ align:start position:0%
+but you don't have very many of these
+different glues ideally
+
+ align:start position:0%
+different glues ideally
+ 
+
+ align:start position:0%
+different glues ideally
+and then if you have two tiles with
+
+ align:start position:0%
+and then if you have two tiles with
+ 
+
+ align:start position:0%
+and then if you have two tiles with
+complementary glues they'll want to
+
+ align:start position:0%
+complementary glues they'll want to
+ 
+
+ align:start position:0%
+complementary glues they'll want to
+match together but it depends how strong
+
+ align:start position:0%
+match together but it depends how strong
+ 
+
+ align:start position:0%
+match together but it depends how strong
+this glue
+
+ align:start position:0%
+this glue
+ 
+
+ align:start position:0%
+this glue
+is how much affinity there is for how
+
+ align:start position:0%
+is how much affinity there is for how
+ 
+
+ align:start position:0%
+is how much affinity there is for how
+long those dna dangling ends are
+
+ align:start position:0%
+long those dna dangling ends are
+ 
+
+ align:start position:0%
+long those dna dangling ends are
+and also the temperature of your system
+
+ align:start position:0%
+and also the temperature of your system
+ 
+
+ align:start position:0%
+and also the temperature of your system
+if you have really high temperature
+
+ align:start position:0%
+if you have really high temperature
+ 
+
+ align:start position:0%
+if you have really high temperature
+nothing will stick together
+
+ align:start position:0%
+nothing will stick together
+ 
+
+ align:start position:0%
+nothing will stick together
+low temperature things will stick
+
+ align:start position:0%
+low temperature things will stick
+ 
+
+ align:start position:0%
+low temperature things will stick
+together even if they're not supposed to
+
+ align:start position:0%
+together even if they're not supposed to
+ 
+
+ align:start position:0%
+together even if they're not supposed to
+and so you can if you tune your system
+
+ align:start position:0%
+and so you can if you tune your system
+ 
+
+ align:start position:0%
+and so you can if you tune your system
+really well
+
+ align:start position:0%
+really well
+ 
+
+ align:start position:0%
+really well
+you can design uh a system so that maybe
+
+ align:start position:0%
+you can design uh a system so that maybe
+ 
+
+ align:start position:0%
+you can design uh a system so that maybe
+these guys
+
+ align:start position:0%
+these guys
+ 
+
+ align:start position:0%
+these guys
+these glues are really strong and so
+
+ align:start position:0%
+these glues are really strong and so
+ 
+
+ align:start position:0%
+these glues are really strong and so
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+i don't know right e here eric
+
+ align:start position:0%
+i don't know right e here eric
+ 
+
+ align:start position:0%
+i don't know right e here eric
+and so these tiles will always glue
+
+ align:start position:0%
+and so these tiles will always glue
+ 
+
+ align:start position:0%
+and so these tiles will always glue
+together but only when all three of
+
+ align:start position:0%
+together but only when all three of
+ 
+
+ align:start position:0%
+together but only when all three of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+are glued together can this tile which
+
+ align:start position:0%
+are glued together can this tile which
+ 
+
+ align:start position:0%
+are glued together can this tile which
+has c
+
+ align:start position:0%
+has c
+ 
+
+ align:start position:0%
+has c
+complement and f complement
+
+ align:start position:0%
+complement and f complement
+ 
+
+ align:start position:0%
+complement and f complement
+then it will if you set the temperatures
+
+ align:start position:0%
+then it will if you set the temperatures
+ 
+
+ align:start position:0%
+then it will if you set the temperatures
+just right only because both of these
+
+ align:start position:0%
+just right only because both of these
+ 
+
+ align:start position:0%
+just right only because both of these
+edges match
+
+ align:start position:0%
+edges match
+ 
+
+ align:start position:0%
+edges match
+will this style be able to come in and
+
+ align:start position:0%
+will this style be able to come in and
+ 
+
+ align:start position:0%
+will this style be able to come in and
+that's the basis for that
+
+ align:start position:0%
+that's the basis for that
+ 
+
+ align:start position:0%
+that's the basis for that
+building that binary counter and so this
+
+ align:start position:0%
+building that binary counter and so this
+ 
+
+ align:start position:0%
+building that binary counter and so this
+is a very different model of computation
+
+ align:start position:0%
+is a very different model of computation
+ 
+
+ align:start position:0%
+is a very different model of computation
+from what we're used to in this class
+
+ align:start position:0%
+from what we're used to in this class
+ 
+
+ align:start position:0%
+from what we're used to in this class
+where you think of instructions and they
+
+ align:start position:0%
+where you think of instructions and they
+ 
+
+ align:start position:0%
+where you think of instructions and they
+run one at a time here the
+
+ align:start position:0%
+run one at a time here the
+ 
+
+ align:start position:0%
+run one at a time here the
+model of computation is geometric it's
+
+ align:start position:0%
+model of computation is geometric it's
+ 
+
+ align:start position:0%
+model of computation is geometric it's
+these squares that are just floating
+
+ align:start position:0%
+these squares that are just floating
+ 
+
+ align:start position:0%
+these squares that are just floating
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+and gluing together and so your program
+
+ align:start position:0%
+and gluing together and so your program
+ 
+
+ align:start position:0%
+and gluing together and so your program
+at any moment is some
+
+ align:start position:0%
+at any moment is some
+ 
+
+ align:start position:0%
+at any moment is some
+conglomerate of squares and so i just
+
+ align:start position:0%
+conglomerate of squares and so i just
+ 
+
+ align:start position:0%
+conglomerate of squares and so i just
+wanted to mention it because it's a
+
+ align:start position:0%
+wanted to mention it because it's a
+ 
+
+ align:start position:0%
+wanted to mention it because it's a
+really fun model
+
+ align:start position:0%
+really fun model
+ 
+
+ align:start position:0%
+really fun model
+you can prove cool things in this model
+
+ align:start position:0%
+you can prove cool things in this model
+ 
+
+ align:start position:0%
+you can prove cool things in this model
+like how to build any shape
+
+ align:start position:0%
+like how to build any shape
+ 
+
+ align:start position:0%
+like how to build any shape
+by a sequence of pores mixings between
+
+ align:start position:0%
+by a sequence of pores mixings between
+ 
+
+ align:start position:0%
+by a sequence of pores mixings between
+tiles
+
+ align:start position:0%
+tiles
+ 
+
+ align:start position:0%
+tiles
+that you can execute in parallel and so
+
+ align:start position:0%
+that you can execute in parallel and so
+ 
+
+ align:start position:0%
+that you can execute in parallel and so
+it only takes log n time
+
+ align:start position:0%
+it only takes log n time
+ 
+
+ align:start position:0%
+it only takes log n time
+in parallel steps a linear number of
+
+ align:start position:0%
+in parallel steps a linear number of
+ 
+
+ align:start position:0%
+in parallel steps a linear number of
+different mix
+
+ align:start position:0%
+different mix
+ 
+
+ align:start position:0%
+different mix
+operations to make an arbitrary shape
+
+ align:start position:0%
+operations to make an arbitrary shape
+ 
+
+ align:start position:0%
+operations to make an arbitrary shape
+even using
+
+ align:start position:0%
+even using
+ 
+
+ align:start position:0%
+even using
+a constant number of different glues
+
+ align:start position:0%
+a constant number of different glues
+ 
+
+ align:start position:0%
+a constant number of different glues
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+cool and may be practical
+
+ align:start position:0%
+cool and may be practical
+ 
+
+ align:start position:0%
+cool and may be practical
+you can also use it to build a
+
+ align:start position:0%
+you can also use it to build a
+ 
+
+ align:start position:0%
+you can also use it to build a
+replicator where you're given an object
+
+ align:start position:0%
+replicator where you're given an object
+ 
+
+ align:start position:0%
+replicator where you're given an object
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+that you don't know the shape of like we
+
+ align:start position:0%
+that you don't know the shape of like we
+ 
+
+ align:start position:0%
+that you don't know the shape of like we
+don't know whether this exists
+
+ align:start position:0%
+don't know whether this exists
+ 
+
+ align:start position:0%
+don't know whether this exists
+and we can't model it mathematically
+
+ align:start position:0%
+and we can't model it mathematically
+ 
+
+ align:start position:0%
+and we can't model it mathematically
+very well and you would stick it in a
+
+ align:start position:0%
+very well and you would stick it in a
+ 
+
+ align:start position:0%
+very well and you would stick it in a
+vat and all these tiles would attach and
+
+ align:start position:0%
+vat and all these tiles would attach and
+ 
+
+ align:start position:0%
+vat and all these tiles would attach and
+basically build a mold
+
+ align:start position:0%
+basically build a mold
+ 
+
+ align:start position:0%
+basically build a mold
+and then start photocopying in 3d that
+
+ align:start position:0%
+and then start photocopying in 3d that
+ 
+
+ align:start position:0%
+and then start photocopying in 3d that
+mold and you can build that
+
+ align:start position:0%
+mold and you can build that
+ 
+
+ align:start position:0%
+mold and you can build that
+with a system with only two steps i
+
+ align:start position:0%
+with a system with only two steps i
+ 
+
+ align:start position:0%
+with a system with only two steps i
+believe
+
+ align:start position:0%
+believe
+ 
+
+ align:start position:0%
+believe
+and a constant number of tile types and
+
+ align:start position:0%
+and a constant number of tile types and
+ 
+
+ align:start position:0%
+and a constant number of tile types and
+it does all of that
+
+ align:start position:0%
+it does all of that
+ 
+
+ align:start position:0%
+it does all of that
+in this model in constant time in
+
+ align:start position:0%
+in this model in constant time in
+ 
+
+ align:start position:0%
+in this model in constant time in
+reality you'd have to feed this machine
+
+ align:start position:0%
+reality you'd have to feed this machine
+ 
+
+ align:start position:0%
+reality you'd have to feed this machine
+and wait for it to print out all these
+
+ align:start position:0%
+and wait for it to print out all these
+ 
+
+ align:start position:0%
+and wait for it to print out all these
+things and and these experiments take
+
+ align:start position:0%
+things and and these experiments take
+ 
+
+ align:start position:0%
+things and and these experiments take
+hours if not days to run but in theory
+
+ align:start position:0%
+hours if not days to run but in theory
+ 
+
+ align:start position:0%
+hours if not days to run but in theory
+it's really cool and you get some really
+
+ align:start position:0%
+it's really cool and you get some really
+ 
+
+ align:start position:0%
+it's really cool and you get some really
+fun models and very general results
+
+ align:start position:0%
+fun models and very general results
+ 
+
+ align:start position:0%
+fun models and very general results
+you can also use it to build a
+
+ align:start position:0%
+you can also use it to build a
+ 
+
+ align:start position:0%
+you can also use it to build a
+miniaturizer or a magnifier and
+
+ align:start position:0%
+miniaturizer or a magnifier and
+ 
+
+ align:start position:0%
+miniaturizer or a magnifier and
+other other fun stuff okay
+
+ align:start position:0%
+other other fun stuff okay
+ 
+
+ align:start position:0%
+other other fun stuff okay
+um so that was a brief tour of
+
+ align:start position:0%
+um so that was a brief tour of
+ 
+
+ align:start position:0%
+um so that was a brief tour of
+computational geometry
+
+ align:start position:0%
+computational geometry
+ 
+
+ align:start position:0%
+computational geometry
+i work mostly in four different areas of
+
+ align:start position:0%
+i work mostly in four different areas of
+ 
+
+ align:start position:0%
+i work mostly in four different areas of
+algorithms
+
+ align:start position:0%
+algorithms
+ 
+
+ align:start position:0%
+algorithms
+geometry data structures graph
+
+ align:start position:0%
+geometry data structures graph
+ 
+
+ align:start position:0%
+geometry data structures graph
+algorithms and what i call recreational
+
+ align:start position:0%
+algorithms and what i call recreational
+ 
+
+ align:start position:0%
+algorithms and what i call recreational
+algorithms
+
+ align:start position:0%
+algorithms
+ 
+
+ align:start position:0%
+algorithms
+i think i made up that term and
+
+ align:start position:0%
+i think i made up that term and
+ 
+
+ align:start position:0%
+i think i made up that term and
+let's go into data structures which is
+
+ align:start position:0%
+let's go into data structures which is
+ 
+
+ align:start position:0%
+let's go into data structures which is
+represented by this class 6851
+
+ align:start position:0%
+represented by this class 6851
+ 
+
+ align:start position:0%
+represented by this class 6851
+all of the classes i mentioned have
+
+ align:start position:0%
+all of the classes i mentioned have
+ 
+
+ align:start position:0%
+all of the classes i mentioned have
+online video lectures so especially for
+
+ align:start position:0%
+online video lectures so especially for
+ 
+
+ align:start position:0%
+online video lectures so especially for
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+watching at home on opencourseware most
+
+ align:start position:0%
+watching at home on opencourseware most
+ 
+
+ align:start position:0%
+watching at home on opencourseware most
+of these classes are on opencourseware
+
+ align:start position:0%
+of these classes are on opencourseware
+ 
+
+ align:start position:0%
+of these classes are on opencourseware
+and if not
+
+ align:start position:0%
+and if not
+ 
+
+ align:start position:0%
+and if not
+they're on my webpage so 6851 advanced
+
+ align:start position:0%
+they're on my webpage so 6851 advanced
+ 
+
+ align:start position:0%
+they're on my webpage so 6851 advanced
+data structures
+
+ align:start position:0%
+data structures
+ 
+
+ align:start position:0%
+data structures
+is an extension of the sorts of data
+
+ align:start position:0%
+is an extension of the sorts of data
+ 
+
+ align:start position:0%
+is an extension of the sorts of data
+structures you've seen in
+
+ align:start position:0%
+structures you've seen in
+ 
+
+ align:start position:0%
+structures you've seen in
+here in 06 and the ones you will see in
+
+ align:start position:0%
+here in 06 and the ones you will see in
+ 
+
+ align:start position:0%
+here in 06 and the ones you will see in
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+i thought i'd give you a flavor of one
+
+ align:start position:0%
+i thought i'd give you a flavor of one
+ 
+
+ align:start position:0%
+i thought i'd give you a flavor of one
+such result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a problem we've seen in this class
+
+ align:start position:0%
+a problem we've seen in this class
+ 
+
+ align:start position:0%
+a problem we've seen in this class
+done better so suppose you want to store
+
+ align:start position:0%
+done better so suppose you want to store
+ 
+
+ align:start position:0%
+done better so suppose you want to store
+a dynamic ordered set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the set interface dynamic in
+
+ align:start position:0%
+so this is the set interface dynamic in
+ 
+
+ align:start position:0%
+so this is the set interface dynamic in
+the sense that i have
+
+ align:start position:0%
+the sense that i have
+ 
+
+ align:start position:0%
+the sense that i have
+insert and delete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and ordered in the sense that i want to
+
+ align:start position:0%
+and ordered in the sense that i want to
+ 
+
+ align:start position:0%
+and ordered in the sense that i want to
+support find next and finds previous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so exactly which subset of the set
+
+ align:start position:0%
+okay so exactly which subset of the set
+ 
+
+ align:start position:0%
+okay so exactly which subset of the set
+interface you choose
+
+ align:start position:0%
+interface you choose
+ 
+
+ align:start position:0%
+interface you choose
+influences what what data structure
+
+ align:start position:0%
+influences what what data structure
+ 
+
+ align:start position:0%
+influences what what data structure
+you've seen we've seen for dynamic sets
+
+ align:start position:0%
+you've seen we've seen for dynamic sets
+ 
+
+ align:start position:0%
+you've seen we've seen for dynamic sets
+you want to use
+
+ align:start position:0%
+you want to use
+ 
+
+ align:start position:0%
+you want to use
+hashing if you don't care about find
+
+ align:start position:0%
+hashing if you don't care about find
+ 
+
+ align:start position:0%
+hashing if you don't care about find
+next if you just care about
+
+ align:start position:0%
+next if you just care about
+ 
+
+ align:start position:0%
+next if you just care about
+find then hashing is great constant
+
+ align:start position:0%
+find then hashing is great constant
+ 
+
+ align:start position:0%
+find then hashing is great constant
+expected
+
+ align:start position:0%
+expected
+ 
+
+ align:start position:0%
+expected
+you can prove stronger things about
+
+ align:start position:0%
+you can prove stronger things about
+ 
+
+ align:start position:0%
+you can prove stronger things about
+hashing we do in that class
+
+ align:start position:0%
+hashing we do in that class
+ 
+
+ align:start position:0%
+hashing we do in that class
+but if you want dynamic and ordered
+
+ align:start position:0%
+but if you want dynamic and ordered
+ 
+
+ align:start position:0%
+but if you want dynamic and ordered
+you cannot do constant time for
+
+ align:start position:0%
+you cannot do constant time for
+ 
+
+ align:start position:0%
+you cannot do constant time for
+operation you can prove that
+
+ align:start position:0%
+operation you can prove that
+ 
+
+ align:start position:0%
+operation you can prove that
+which is cool but and so what data
+
+ align:start position:0%
+which is cool but and so what data
+ 
+
+ align:start position:0%
+which is cool but and so what data
+structure have we seen that solves this
+
+ align:start position:0%
+structure have we seen that solves this
+ 
+
+ align:start position:0%
+structure have we seen that solves this
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+pretty well set avl trees which solve
+
+ align:start position:0%
+pretty well set avl trees which solve
+ 
+
+ align:start position:0%
+pretty well set avl trees which solve
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+in log n so log n
+
+ align:start position:0%
+in log n so log n
+ 
+
+ align:start position:0%
+in log n so log n
+one competitor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i am interested in this in the
+
+ align:start position:0%
+yeah i am interested in this in the
+ 
+
+ align:start position:0%
+yeah i am interested in this in the
+word ram model
+
+ align:start position:0%
+word ram model
+ 
+
+ align:start position:0%
+word ram model
+which is the only model we've seen in
+
+ align:start position:0%
+which is the only model we've seen in
+ 
+
+ align:start position:0%
+which is the only model we've seen in
+this class this happens to work in a
+
+ align:start position:0%
+this class this happens to work in a
+ 
+
+ align:start position:0%
+this class this happens to work in a
+stronger model
+
+ align:start position:0%
+stronger model
+ 
+
+ align:start position:0%
+stronger model
+um and we can do better than log n
+
+ align:start position:0%
+um and we can do better than log n
+ 
+
+ align:start position:0%
+um and we can do better than log n
+in the following it'll take me a while
+
+ align:start position:0%
+in the following it'll take me a while
+ 
+
+ align:start position:0%
+in the following it'll take me a while
+before i get better but here's at least
+
+ align:start position:0%
+before i get better but here's at least
+ 
+
+ align:start position:0%
+before i get better but here's at least
+a different bound we can get
+
+ align:start position:0%
+a different bound we can get
+ 
+
+ align:start position:0%
+a different bound we can get
+log w uh this is via a structure called
+
+ align:start position:0%
+log w uh this is via a structure called
+ 
+
+ align:start position:0%
+log w uh this is via a structure called
+venom nubos
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who's a person avl is two people
+
+ align:start position:0%
+who's a person avl is two people
+ 
+
+ align:start position:0%
+who's a person avl is two people
+ben under both i've actually met so log
+
+ align:start position:0%
+ben under both i've actually met so log
+ 
+
+ align:start position:0%
+ben under both i've actually met so log
+w
+
+ align:start position:0%
+w
+ 
+
+ align:start position:0%
+w
+remember w is our word size so this is a
+
+ align:start position:0%
+remember w is our word size so this is a
+ 
+
+ align:start position:0%
+remember w is our word size so this is a
+bit of a weird running time it's great
+
+ align:start position:0%
+bit of a weird running time it's great
+ 
+
+ align:start position:0%
+bit of a weird running time it's great
+if w is like log n
+
+ align:start position:0%
+if w is like log n
+ 
+
+ align:start position:0%
+if w is like log n
+then this is log log n and we know w is
+
+ align:start position:0%
+then this is log log n and we know w is
+ 
+
+ align:start position:0%
+then this is log log n and we know w is
+at least log n but it could be bigger
+
+ align:start position:0%
+at least log n but it could be bigger
+ 
+
+ align:start position:0%
+at least log n but it could be bigger
+we don't really have a sense of how big
+
+ align:start position:0%
+we don't really have a sense of how big
+ 
+
+ align:start position:0%
+we don't really have a sense of how big
+w can get maybe it's even
+
+ align:start position:0%
+w can get maybe it's even
+ 
+
+ align:start position:0%
+w can get maybe it's even
+n maybe it's big and then these are the
+
+ align:start position:0%
+n maybe it's big and then these are the
+ 
+
+ align:start position:0%
+n maybe it's big and then these are the
+same maybe it's bigger than n
+
+ align:start position:0%
+same maybe it's bigger than n
+ 
+
+ align:start position:0%
+same maybe it's bigger than n
+and then this is maybe worse but for
+
+ align:start position:0%
+and then this is maybe worse but for
+ 
+
+ align:start position:0%
+and then this is maybe worse but for
+most w's this is actually
+
+ align:start position:0%
+most w's this is actually
+ 
+
+ align:start position:0%
+most w's this is actually
+pretty good and indeed optimal
+
+ align:start position:0%
+pretty good and indeed optimal
+ 
+
+ align:start position:0%
+pretty good and indeed optimal
+but it's not strictly better in any
+
+ align:start position:0%
+but it's not strictly better in any
+ 
+
+ align:start position:0%
+but it's not strictly better in any
+sense yet on the other hand
+
+ align:start position:0%
+sense yet on the other hand
+ 
+
+ align:start position:0%
+sense yet on the other hand
+there's another data structure which
+
+ align:start position:0%
+there's another data structure which
+ 
+
+ align:start position:0%
+there's another data structure which
+runs in log n divided by log w
+
+ align:start position:0%
+runs in log n divided by log w
+ 
+
+ align:start position:0%
+runs in log n divided by log w
+this is called fusion trees this was
+
+ align:start position:0%
+this is called fusion trees this was
+ 
+
+ align:start position:0%
+this is called fusion trees this was
+invented around the time that cold
+
+ align:start position:0%
+invented around the time that cold
+ 
+
+ align:start position:0%
+invented around the time that cold
+fusion was in the news and so
+
+ align:start position:0%
+fusion was in the news and so
+ 
+
+ align:start position:0%
+fusion was in the news and so
+they wanted data structures to represent
+
+ align:start position:0%
+they wanted data structures to represent
+ 
+
+ align:start position:0%
+they wanted data structures to represent
+and so we can achieve this bound or we
+
+ align:start position:0%
+and so we can achieve this bound or we
+ 
+
+ align:start position:0%
+and so we can achieve this bound or we
+can achieve this bound
+
+ align:start position:0%
+can achieve this bound
+ 
+
+ align:start position:0%
+can achieve this bound
+and this bound as good is if w is large
+
+ align:start position:0%
+and this bound as good is if w is large
+ 
+
+ align:start position:0%
+and this bound as good is if w is large
+this bound is good if w is small and so
+
+ align:start position:0%
+this bound is good if w is small and so
+ 
+
+ align:start position:0%
+this bound is good if w is small and so
+you can always take the min
+
+ align:start position:0%
+you can always take the min
+ 
+
+ align:start position:0%
+you can always take the min
+of the two whatever's better and in
+
+ align:start position:0%
+of the two whatever's better and in
+ 
+
+ align:start position:0%
+of the two whatever's better and in
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+the min
+
+ align:start position:0%
+the min
+ 
+
+ align:start position:0%
+the min
+uh the min of those two things
+
+ align:start position:0%
+uh the min of those two things
+ 
+
+ align:start position:0%
+uh the min of those two things
+is at most i think it's square root log
+
+ align:start position:0%
+is at most i think it's square root log
+ 
+
+ align:start position:0%
+is at most i think it's square root log
+n over log log n
+
+ align:start position:0%
+n over log log n
+ 
+
+ align:start position:0%
+n over log log n
+if you want to bound just in terms of n
+
+ align:start position:0%
+if you want to bound just in terms of n
+ 
+
+ align:start position:0%
+if you want to bound just in terms of n
+then the crossover point between these
+
+ align:start position:0%
+then the crossover point between these
+ 
+
+ align:start position:0%
+then the crossover point between these
+two is this place and so you're always
+
+ align:start position:0%
+two is this place and so you're always
+ 
+
+ align:start position:0%
+two is this place and so you're always
+at most this which is
+
+ align:start position:0%
+at most this which is
+ 
+
+ align:start position:0%
+at most this which is
+quite a bit better than the log n of avl
+
+ align:start position:0%
+quite a bit better than the log n of avl
+ 
+
+ align:start position:0%
+quite a bit better than the log n of avl
+we've got a square root
+
+ align:start position:0%
+we've got a square root
+ 
+
+ align:start position:0%
+we've got a square root
+and we've got a slight thing in the
+
+ align:start position:0%
+and we've got a slight thing in the
+ 
+
+ align:start position:0%
+and we've got a slight thing in the
+denominator pretty tiny
+
+ align:start position:0%
+denominator pretty tiny
+ 
+
+ align:start position:0%
+denominator pretty tiny
+but the big thing is the square root and
+
+ align:start position:0%
+but the big thing is the square root and
+ 
+
+ align:start position:0%
+but the big thing is the square root and
+that's kind of cool and it turns out
+
+ align:start position:0%
+that's kind of cool and it turns out
+ 
+
+ align:start position:0%
+that's kind of cool and it turns out
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+pretty much optimal in terms of an n
+
+ align:start position:0%
+pretty much optimal in terms of an n
+ 
+
+ align:start position:0%
+pretty much optimal in terms of an n
+bound this is optimal
+
+ align:start position:0%
+bound this is optimal
+ 
+
+ align:start position:0%
+bound this is optimal
+the min of these two in general is
+
+ align:start position:0%
+the min of these two in general is
+ 
+
+ align:start position:0%
+the min of these two in general is
+roughly optimal up to like log log terms
+
+ align:start position:0%
+roughly optimal up to like log log terms
+ 
+
+ align:start position:0%
+roughly optimal up to like log log terms
+i for fun
+
+ align:start position:0%
+i for fun
+ 
+
+ align:start position:0%
+i for fun
+i threw up the actual formula for the
+
+ align:start position:0%
+i threw up the actual formula for the
+ 
+
+ align:start position:0%
+i threw up the actual formula for the
+right bound
+
+ align:start position:0%
+right bound
+ 
+
+ align:start position:0%
+right bound
+uh which is tight up to constant factors
+
+ align:start position:0%
+uh which is tight up to constant factors
+ 
+
+ align:start position:0%
+uh which is tight up to constant factors
+there's matching upper and lower bounds
+
+ align:start position:0%
+there's matching upper and lower bounds
+ 
+
+ align:start position:0%
+there's matching upper and lower bounds
+which we talk about it's min of three
+
+ align:start position:0%
+which we talk about it's min of three
+ 
+
+ align:start position:0%
+which we talk about it's min of three
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+four things uh including log of w over a
+
+ align:start position:0%
+four things uh including log of w over a
+ 
+
+ align:start position:0%
+four things uh including log of w over a
+divided by log of log w over a over log
+
+ align:start position:0%
+divided by log of log w over a over log
+ 
+
+ align:start position:0%
+divided by log of log w over a over log
+of log n over a
+
+ align:start position:0%
+of log n over a
+ 
+
+ align:start position:0%
+of log n over a
+uh that's the last term that i just read
+
+ align:start position:0%
+uh that's the last term that i just read
+ 
+
+ align:start position:0%
+uh that's the last term that i just read
+is messy
+
+ align:start position:0%
+is messy
+ 
+
+ align:start position:0%
+is messy
+uh surprisingly that is the right answer
+
+ align:start position:0%
+uh surprisingly that is the right answer
+ 
+
+ align:start position:0%
+uh surprisingly that is the right answer
+for this very
+
+ align:start position:0%
+for this very
+ 
+
+ align:start position:0%
+for this very
+particular problem a very natural
+
+ align:start position:0%
+particular problem a very natural
+ 
+
+ align:start position:0%
+particular problem a very natural
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+uh a is the log of the space you're
+
+ align:start position:0%
+uh a is the log of the space you're
+ 
+
+ align:start position:0%
+uh a is the log of the space you're
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+so it's the address size uh good
+
+ align:start position:0%
+so it's the address size uh good
+ 
+
+ align:start position:0%
+so it's the address size uh good
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+um if you throw so it depends if you
+
+ align:start position:0%
+um if you throw so it depends if you
+ 
+
+ align:start position:0%
+um if you throw so it depends if you
+have a polynomial space data structure
+
+ align:start position:0%
+have a polynomial space data structure
+ 
+
+ align:start position:0%
+have a polynomial space data structure
+then basically
+
+ align:start position:0%
+then basically
+ 
+
+ align:start position:0%
+then basically
+these are optimal and this is
+
+ align:start position:0%
+these are optimal and this is
+ 
+
+ align:start position:0%
+these are optimal and this is
+generalizing to beyond that
+
+ align:start position:0%
+generalizing to beyond that
+ 
+
+ align:start position:0%
+generalizing to beyond that
+maybe you have a little bit more than
+
+ align:start position:0%
+maybe you have a little bit more than
+ 
+
+ align:start position:0%
+maybe you have a little bit more than
+polynomial space
+
+ align:start position:0%
+polynomial space
+ 
+
+ align:start position:0%
+polynomial space
+cool um so that's data structures
+
+ align:start position:0%
+cool um so that's data structures
+ 
+
+ align:start position:0%
+cool um so that's data structures
+i'm going to jump ahead to graph
+
+ align:start position:0%
+i'm going to jump ahead to graph
+ 
+
+ align:start position:0%
+i'm going to jump ahead to graph
+algorithms
+
+ align:start position:0%
+algorithms
+ 
+
+ align:start position:0%
+algorithms
+which if you want to take this class i
+
+ align:start position:0%
+which if you want to take this class i
+ 
+
+ align:start position:0%
+which if you want to take this class i
+recommend a time travel device
+
+ align:start position:0%
+recommend a time travel device
+ 
+
+ align:start position:0%
+recommend a time travel device
+go back to fall 2011 it may never get
+
+ align:start position:0%
+go back to fall 2011 it may never get
+ 
+
+ align:start position:0%
+go back to fall 2011 it may never get
+taught again but
+
+ align:start position:0%
+taught again but
+ 
+
+ align:start position:0%
+taught again but
+it has videos so you can watch instead
+
+ align:start position:0%
+it has videos so you can watch instead
+ 
+
+ align:start position:0%
+it has videos so you can watch instead
+of time traveling
+
+ align:start position:0%
+of time traveling
+ 
+
+ align:start position:0%
+of time traveling
+if you don't want to watch it live you
+
+ align:start position:0%
+if you don't want to watch it live you
+ 
+
+ align:start position:0%
+if you don't want to watch it live you
+can just watch the recorded version
+
+ align:start position:0%
+can just watch the recorded version
+ 
+
+ align:start position:0%
+can just watch the recorded version
+it was taught by a bunch of postdocs
+
+ align:start position:0%
+it was taught by a bunch of postdocs
+ 
+
+ align:start position:0%
+it was taught by a bunch of postdocs
+that were here uh and and
+
+ align:start position:0%
+that were here uh and and
+ 
+
+ align:start position:0%
+that were here uh and and
+myself uh and so what i like to do with
+
+ align:start position:0%
+myself uh and so what i like to do with
+ 
+
+ align:start position:0%
+myself uh and so what i like to do with
+graphs
+
+ align:start position:0%
+graphs
+ 
+
+ align:start position:0%
+graphs
+is the world of planar graphs or near
+
+ align:start position:0%
+is the world of planar graphs or near
+ 
+
+ align:start position:0%
+is the world of planar graphs or near
+planar graphs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we've talked a lot about this class
+
+ align:start position:0%
+so we've talked a lot about this class
+ 
+
+ align:start position:0%
+so we've talked a lot about this class
+algorithms that work for arbitrary
+
+ align:start position:0%
+algorithms that work for arbitrary
+ 
+
+ align:start position:0%
+algorithms that work for arbitrary
+graphs
+
+ align:start position:0%
+graphs
+ 
+
+ align:start position:0%
+graphs
+and the algorithms we've seen in this
+
+ align:start position:0%
+and the algorithms we've seen in this
+ 
+
+ align:start position:0%
+and the algorithms we've seen in this
+class are pretty much the best we know
+
+ align:start position:0%
+class are pretty much the best we know
+ 
+
+ align:start position:0%
+class are pretty much the best we know
+for a lot of problems for
+
+ align:start position:0%
+for a lot of problems for
+ 
+
+ align:start position:0%
+for a lot of problems for
+for arbitrary graphs but if your graph
+
+ align:start position:0%
+for arbitrary graphs but if your graph
+ 
+
+ align:start position:0%
+for arbitrary graphs but if your graph
+has some structure like
+
+ align:start position:0%
+has some structure like
+ 
+
+ align:start position:0%
+has some structure like
+it's a road network and there aren't too
+
+ align:start position:0%
+it's a road network and there aren't too
+ 
+
+ align:start position:0%
+it's a road network and there aren't too
+many overpasses you can usually
+
+ align:start position:0%
+many overpasses you can usually
+ 
+
+ align:start position:0%
+many overpasses you can usually
+draw these graphs in the plane without
+
+ align:start position:0%
+draw these graphs in the plane without
+ 
+
+ align:start position:0%
+draw these graphs in the plane without
+crossings that's the meaning of planar
+
+ align:start position:0%
+crossings that's the meaning of planar
+ 
+
+ align:start position:0%
+crossings that's the meaning of planar
+maybe not exactly maybe just a few
+
+ align:start position:0%
+maybe not exactly maybe just a few
+ 
+
+ align:start position:0%
+maybe not exactly maybe just a few
+crossings there's a generalization of
+
+ align:start position:0%
+crossings there's a generalization of
+ 
+
+ align:start position:0%
+crossings there's a generalization of
+this which i won't get into
+
+ align:start position:0%
+this which i won't get into
+ 
+
+ align:start position:0%
+this which i won't get into
+but let's just think about planar graphs
+
+ align:start position:0%
+but let's just think about planar graphs
+ 
+
+ align:start position:0%
+but let's just think about planar graphs
+planar graphs have some nice features
+
+ align:start position:0%
+planar graphs have some nice features
+ 
+
+ align:start position:0%
+planar graphs have some nice features
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+they always have a linear number of
+
+ align:start position:0%
+they always have a linear number of
+ 
+
+ align:start position:0%
+they always have a linear number of
+edges they're always sparse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can immediately plug that into
+
+ align:start position:0%
+so you can immediately plug that into
+ 
+
+ align:start position:0%
+so you can immediately plug that into
+our existing bounds but even so you know
+
+ align:start position:0%
+our existing bounds but even so you know
+ 
+
+ align:start position:0%
+our existing bounds but even so you know
+dijkstra
+
+ align:start position:0%
+dijkstra
+ 
+
+ align:start position:0%
+dijkstra
+uh this would take in this such a graph
+
+ align:start position:0%
+uh this would take in this such a graph
+ 
+
+ align:start position:0%
+uh this would take in this such a graph
+would take
+
+ align:start position:0%
+would take
+ 
+
+ align:start position:0%
+would take
+v log v time for planar graphs you can
+
+ align:start position:0%
+v log v time for planar graphs you can
+ 
+
+ align:start position:0%
+v log v time for planar graphs you can
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+the equivalent of dijkstra meaning i can
+
+ align:start position:0%
+the equivalent of dijkstra meaning i can
+ 
+
+ align:start position:0%
+the equivalent of dijkstra meaning i can
+compute single source shortest paths
+
+ align:start position:0%
+compute single source shortest paths
+ 
+
+ align:start position:0%
+compute single source shortest paths
+with non-negative edge weights
+
+ align:start position:0%
+with non-negative edge weights
+ 
+
+ align:start position:0%
+with non-negative edge weights
+in linear time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no log okay not that impressive but
+
+ align:start position:0%
+no log okay not that impressive but
+ 
+
+ align:start position:0%
+no log okay not that impressive but
+remove a log more impressive is we can
+
+ align:start position:0%
+remove a log more impressive is we can
+ 
+
+ align:start position:0%
+remove a log more impressive is we can
+do the equivalent of bellman ford
+
+ align:start position:0%
+do the equivalent of bellman ford
+ 
+
+ align:start position:0%
+do the equivalent of bellman ford
+uh which is single source shortest paths
+
+ align:start position:0%
+uh which is single source shortest paths
+ 
+
+ align:start position:0%
+uh which is single source shortest paths
+with arbitrary edge weights
+
+ align:start position:0%
+with arbitrary edge weights
+ 
+
+ align:start position:0%
+with arbitrary edge weights
+in a planar graph in uh
+
+ align:start position:0%
+in a planar graph in uh
+ 
+
+ align:start position:0%
+in a planar graph in uh
+sometime almost linear time
+
+ align:start position:0%
+sometime almost linear time
+ 
+
+ align:start position:0%
+sometime almost linear time
+v log squared v over
+
+ align:start position:0%
+v log squared v over
+ 
+
+ align:start position:0%
+v log squared v over
+log log v okay so there's a couple log
+
+ align:start position:0%
+log log v okay so there's a couple log
+ 
+
+ align:start position:0%
+log log v okay so there's a couple log
+factors here
+
+ align:start position:0%
+factors here
+ 
+
+ align:start position:0%
+factors here
+but for the almost linear time whereas
+
+ align:start position:0%
+but for the almost linear time whereas
+ 
+
+ align:start position:0%
+but for the almost linear time whereas
+bellman ford would take v squared time
+
+ align:start position:0%
+bellman ford would take v squared time
+ 
+
+ align:start position:0%
+bellman ford would take v squared time
+so this is a huge improvement over what
+
+ align:start position:0%
+so this is a huge improvement over what
+ 
+
+ align:start position:0%
+so this is a huge improvement over what
+we've seen in the class
+
+ align:start position:0%
+we've seen in the class
+ 
+
+ align:start position:0%
+we've seen in the class
+these are quite complicated algorithms
+
+ align:start position:0%
+these are quite complicated algorithms
+ 
+
+ align:start position:0%
+these are quite complicated algorithms
+but they're covered in that class if
+
+ align:start position:0%
+but they're covered in that class if
+ 
+
+ align:start position:0%
+but they're covered in that class if
+you're interested in them
+
+ align:start position:0%
+you're interested in them
+ 
+
+ align:start position:0%
+you're interested in them
+then the the area i work in a lot is
+
+ align:start position:0%
+then the the area i work in a lot is
+ 
+
+ align:start position:0%
+then the the area i work in a lot is
+approximation algorithms for
+
+ align:start position:0%
+approximation algorithms for
+ 
+
+ align:start position:0%
+approximation algorithms for
+planar graphs and let me just give you a
+
+ align:start position:0%
+planar graphs and let me just give you a
+ 
+
+ align:start position:0%
+planar graphs and let me just give you a
+fun
+
+ align:start position:0%
+fun
+ 
+
+ align:start position:0%
+fun
+flavor using something we know which is
+
+ align:start position:0%
+flavor using something we know which is
+ 
+
+ align:start position:0%
+flavor using something we know which is
+uh breadth first search
+
+ align:start position:0%
+uh breadth first search
+ 
+
+ align:start position:0%
+uh breadth first search
+so breadth research you can think of as
+
+ align:start position:0%
+so breadth research you can think of as
+ 
+
+ align:start position:0%
+so breadth research you can think of as
+building these sort of rings around
+
+ align:start position:0%
+building these sort of rings around
+ 
+
+ align:start position:0%
+building these sort of rings around
+a single root node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's this general approach as
+
+ align:start position:0%
+and there's this general approach as
+ 
+
+ align:start position:0%
+and there's this general approach as
+introduced by baker in 1994
+
+ align:start position:0%
+introduced by baker in 1994
+ 
+
+ align:start position:0%
+introduced by baker in 1994
+we've used for lots of different
+
+ align:start position:0%
+we've used for lots of different
+ 
+
+ align:start position:0%
+we've used for lots of different
+problems you want to solve some
+
+ align:start position:0%
+problems you want to solve some
+ 
+
+ align:start position:0%
+problems you want to solve some
+np hard problem on on a graph so just
+
+ align:start position:0%
+np hard problem on on a graph so just
+ 
+
+ align:start position:0%
+np hard problem on on a graph so just
+run
+
+ align:start position:0%
+run
+ 
+
+ align:start position:0%
+run
+breadth first search from an arbitrary
+
+ align:start position:0%
+breadth first search from an arbitrary
+ 
+
+ align:start position:0%
+breadth first search from an arbitrary
+vertex and decompose your graph into
+
+ align:start position:0%
+vertex and decompose your graph into
+ 
+
+ align:start position:0%
+vertex and decompose your graph into
+these layers
+
+ align:start position:0%
+these layers
+ 
+
+ align:start position:0%
+these layers
+you could number them you know zero one
+
+ align:start position:0%
+you could number them you know zero one
+ 
+
+ align:start position:0%
+you could number them you know zero one
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+three these are the levels
+
+ align:start position:0%
+three these are the levels
+ 
+
+ align:start position:0%
+three these are the levels
+and let's just like delete some of those
+
+ align:start position:0%
+and let's just like delete some of those
+ 
+
+ align:start position:0%
+and let's just like delete some of those
+layers let's say let's delete every
+
+ align:start position:0%
+layers let's say let's delete every
+ 
+
+ align:start position:0%
+layers let's say let's delete every
+fourth layer
+
+ align:start position:0%
+fourth layer
+ 
+
+ align:start position:0%
+fourth layer
+so maybe i delete this one i delete all
+
+ align:start position:0%
+so maybe i delete this one i delete all
+ 
+
+ align:start position:0%
+so maybe i delete this one i delete all
+the vertices in that layer
+
+ align:start position:0%
+the vertices in that layer
+ 
+
+ align:start position:0%
+the vertices in that layer
+and then i delete all the things in
+
+ align:start position:0%
+and then i delete all the things in
+ 
+
+ align:start position:0%
+and then i delete all the things in
+layer 8 and layer 12
+
+ align:start position:0%
+layer 8 and layer 12
+ 
+
+ align:start position:0%
+layer 8 and layer 12
+and so on guessing
+
+ align:start position:0%
+and so on guessing
+ 
+
+ align:start position:0%
+and so on guessing
+i don't know which one to start with but
+
+ align:start position:0%
+i don't know which one to start with but
+ 
+
+ align:start position:0%
+i don't know which one to start with but
+from i'll just try them all
+
+ align:start position:0%
+from i'll just try them all
+ 
+
+ align:start position:0%
+from i'll just try them all
+and then i delete every fourth layer
+
+ align:start position:0%
+and then i delete every fourth layer
+ 
+
+ align:start position:0%
+and then i delete every fourth layer
+after that
+
+ align:start position:0%
+after that
+ 
+
+ align:start position:0%
+after that
+so i've deleted on average about a
+
+ align:start position:0%
+so i've deleted on average about a
+ 
+
+ align:start position:0%
+so i've deleted on average about a
+quarter of the graph
+
+ align:start position:0%
+quarter of the graph
+ 
+
+ align:start position:0%
+quarter of the graph
+and it turns out for a lot of problems
+
+ align:start position:0%
+and it turns out for a lot of problems
+ 
+
+ align:start position:0%
+and it turns out for a lot of problems
+that you care about
+
+ align:start position:0%
+that you care about
+ 
+
+ align:start position:0%
+that you care about
+like choosing where to place fire
+
+ align:start position:0%
+like choosing where to place fire
+ 
+
+ align:start position:0%
+like choosing where to place fire
+stations in this graph to minimize
+
+ align:start position:0%
+stations in this graph to minimize
+ 
+
+ align:start position:0%
+stations in this graph to minimize
+uh you know travel time for if there's a
+
+ align:start position:0%
+uh you know travel time for if there's a
+ 
+
+ align:start position:0%
+uh you know travel time for if there's a
+fire somewhere in the graph
+
+ align:start position:0%
+fire somewhere in the graph
+ 
+
+ align:start position:0%
+fire somewhere in the graph
+this happens you know fires and graphs
+
+ align:start position:0%
+this happens you know fires and graphs
+ 
+
+ align:start position:0%
+this happens you know fires and graphs
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+this will only hurt your solution by
+
+ align:start position:0%
+this will only hurt your solution by
+ 
+
+ align:start position:0%
+this will only hurt your solution by
+like a factor
+
+ align:start position:0%
+like a factor
+ 
+
+ align:start position:0%
+like a factor
+of uh one plus a quarter
+
+ align:start position:0%
+of uh one plus a quarter
+ 
+
+ align:start position:0%
+of uh one plus a quarter
+uh so you'll get a solution that's uh
+
+ align:start position:0%
+uh so you'll get a solution that's uh
+ 
+
+ align:start position:0%
+uh so you'll get a solution that's uh
+within
+
+ align:start position:0%
+within
+ 
+
+ align:start position:0%
+within
+25 of the optimal for a lot of problems
+
+ align:start position:0%
+25 of the optimal for a lot of problems
+ 
+
+ align:start position:0%
+25 of the optimal for a lot of problems
+um and uh
+
+ align:start position:0%
+um and uh
+ 
+
+ align:start position:0%
+um and uh
+that works for any value of four so i
+
+ align:start position:0%
+that works for any value of four so i
+ 
+
+ align:start position:0%
+that works for any value of four so i
+could do it for ten
+
+ align:start position:0%
+could do it for ten
+ 
+
+ align:start position:0%
+could do it for ten
+and then i'd get within ten percent of
+
+ align:start position:0%
+and then i'd get within ten percent of
+ 
+
+ align:start position:0%
+and then i'd get within ten percent of
+the optimal solution
+
+ align:start position:0%
+the optimal solution
+ 
+
+ align:start position:0%
+the optimal solution
+uh okay but how do i actually solve the
+
+ align:start position:0%
+uh okay but how do i actually solve the
+ 
+
+ align:start position:0%
+uh okay but how do i actually solve the
+problem once i delete every fourth
+
+ align:start position:0%
+problem once i delete every fourth
+ 
+
+ align:start position:0%
+problem once i delete every fourth
+layer well then your graph has this
+
+ align:start position:0%
+layer well then your graph has this
+ 
+
+ align:start position:0%
+layer well then your graph has this
+extra special structure
+
+ align:start position:0%
+extra special structure
+ 
+
+ align:start position:0%
+extra special structure
+which is a constant number of layers
+
+ align:start position:0%
+which is a constant number of layers
+ 
+
+ align:start position:0%
+which is a constant number of layers
+let's say a constant number of breadth
+
+ align:start position:0%
+let's say a constant number of breadth
+ 
+
+ align:start position:0%
+let's say a constant number of breadth
+first search layers if you just look at
+
+ align:start position:0%
+first search layers if you just look at
+ 
+
+ align:start position:0%
+first search layers if you just look at
+this portion this connected component
+
+ align:start position:0%
+this portion this connected component
+ 
+
+ align:start position:0%
+this portion this connected component
+or this connected component in here you
+
+ align:start position:0%
+or this connected component in here you
+ 
+
+ align:start position:0%
+or this connected component in here you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+your graph is almost like a cycle
+
+ align:start position:0%
+your graph is almost like a cycle
+ 
+
+ align:start position:0%
+your graph is almost like a cycle
+it's like four cycles kind of stacked up
+
+ align:start position:0%
+it's like four cycles kind of stacked up
+ 
+
+ align:start position:0%
+it's like four cycles kind of stacked up
+together with some connections between
+
+ align:start position:0%
+together with some connections between
+ 
+
+ align:start position:0%
+together with some connections between
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+and it turns out that's something you
+
+ align:start position:0%
+and it turns out that's something you
+ 
+
+ align:start position:0%
+and it turns out that's something you
+can solve with very fancy dynamic
+
+ align:start position:0%
+can solve with very fancy dynamic
+ 
+
+ align:start position:0%
+can solve with very fancy dynamic
+programming
+
+ align:start position:0%
+programming
+ 
+
+ align:start position:0%
+programming
+like the stuff we've seen before in this
+
+ align:start position:0%
+like the stuff we've seen before in this
+ 
+
+ align:start position:0%
+like the stuff we've seen before in this
+class which focuses on just a single
+
+ align:start position:0%
+class which focuses on just a single
+ 
+
+ align:start position:0%
+class which focuses on just a single
+path or a single cycle
+
+ align:start position:0%
+path or a single cycle
+ 
+
+ align:start position:0%
+path or a single cycle
+if you just have a constant number of
+
+ align:start position:0%
+if you just have a constant number of
+ 
+
+ align:start position:0%
+if you just have a constant number of
+cycles with more work you can still do
+
+ align:start position:0%
+cycles with more work you can still do
+ 
+
+ align:start position:0%
+cycles with more work you can still do
+everything in polynomial time
+
+ align:start position:0%
+everything in polynomial time
+ 
+
+ align:start position:0%
+everything in polynomial time
+and so this is a very general approach
+
+ align:start position:0%
+and so this is a very general approach
+ 
+
+ align:start position:0%
+and so this is a very general approach
+for getting
+
+ align:start position:0%
+for getting
+ 
+
+ align:start position:0%
+for getting
+arbitrarily good approximation
+
+ align:start position:0%
+arbitrarily good approximation
+ 
+
+ align:start position:0%
+arbitrarily good approximation
+algorithms we call these one plus
+
+ align:start position:0%
+algorithms we call these one plus
+ 
+
+ align:start position:0%
+algorithms we call these one plus
+epsilon approximation for any epsilon
+
+ align:start position:0%
+epsilon approximation for any epsilon
+ 
+
+ align:start position:0%
+epsilon approximation for any epsilon
+but the larger the epsilon the more time
+
+ align:start position:0%
+but the larger the epsilon the more time
+ 
+
+ align:start position:0%
+but the larger the epsilon the more time
+you take it's something like
+
+ align:start position:0%
+you take it's something like
+ 
+
+ align:start position:0%
+you take it's something like
+two to the order one over epsilon times
+
+ align:start position:0%
+two to the order one over epsilon times
+ 
+
+ align:start position:0%
+two to the order one over epsilon times
+polynomial and n so as long as epsilon's
+
+ align:start position:0%
+polynomial and n so as long as epsilon's
+ 
+
+ align:start position:0%
+polynomial and n so as long as epsilon's
+constant this is polynomial time
+
+ align:start position:0%
+constant this is polynomial time
+ 
+
+ align:start position:0%
+constant this is polynomial time
+this is called a p-tess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway those graph algorithms last topic
+
+ align:start position:0%
+anyway those graph algorithms last topic
+ 
+
+ align:start position:0%
+anyway those graph algorithms last topic
+is recreational algorithms which is
+
+ align:start position:0%
+is recreational algorithms which is
+ 
+
+ align:start position:0%
+is recreational algorithms which is
+maybe best encompassed by this class
+
+ align:start position:0%
+maybe best encompassed by this class
+ 
+
+ align:start position:0%
+maybe best encompassed by this class
+6892 is its latest name it changes names
+
+ align:start position:0%
+6892 is its latest name it changes names
+ 
+
+ align:start position:0%
+6892 is its latest name it changes names
+every once in a while
+
+ align:start position:0%
+every once in a while
+ 
+
+ align:start position:0%
+every once in a while
+and i mentioned it in the hardness
+
+ align:start position:0%
+and i mentioned it in the hardness
+ 
+
+ align:start position:0%
+and i mentioned it in the hardness
+complexity lecture because this class is
+
+ align:start position:0%
+complexity lecture because this class is
+ 
+
+ align:start position:0%
+complexity lecture because this class is
+all about
+
+ align:start position:0%
+all about
+ 
+
+ align:start position:0%
+all about
+hardness proofs analyzing fun games and
+
+ align:start position:0%
+hardness proofs analyzing fun games and
+ 
+
+ align:start position:0%
+hardness proofs analyzing fun games and
+puzzles we saw the tetris
+
+ align:start position:0%
+puzzles we saw the tetris
+ 
+
+ align:start position:0%
+puzzles we saw the tetris
+np hardness in that lecture but you can
+
+ align:start position:0%
+np hardness in that lecture but you can
+ 
+
+ align:start position:0%
+np hardness in that lecture but you can
+also prove
+
+ align:start position:0%
+also prove
+ 
+
+ align:start position:0%
+also prove
+super mario brothers is hard or portal
+
+ align:start position:0%
+super mario brothers is hard or portal
+ 
+
+ align:start position:0%
+super mario brothers is hard or portal
+is hard or mario kart is hard
+
+ align:start position:0%
+is hard or mario kart is hard
+ 
+
+ align:start position:0%
+is hard or mario kart is hard
+or the witness some modern video game is
+
+ align:start position:0%
+or the witness some modern video game is
+ 
+
+ align:start position:0%
+or the witness some modern video game is
+hard
+
+ align:start position:0%
+hard
+ 
+
+ align:start position:0%
+hard
+or one of our latest results is that
+
+ align:start position:0%
+or one of our latest results is that
+ 
+
+ align:start position:0%
+or one of our latest results is that
+recursed that game in the top right
+
+ align:start position:0%
+recursed that game in the top right
+ 
+
+ align:start position:0%
+recursed that game in the top right
+is undecidable there's no algorithm to
+
+ align:start position:0%
+is undecidable there's no algorithm to
+ 
+
+ align:start position:0%
+is undecidable there's no algorithm to
+play that game perfectly
+
+ align:start position:0%
+play that game perfectly
+ 
+
+ align:start position:0%
+play that game perfectly
+so and you can even download the level
+
+ align:start position:0%
+so and you can even download the level
+ 
+
+ align:start position:0%
+so and you can even download the level
+and an example of the level and play it
+
+ align:start position:0%
+and an example of the level and play it
+ 
+
+ align:start position:0%
+and an example of the level and play it
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+if you dare um so
+
+ align:start position:0%
+if you dare um so
+ 
+
+ align:start position:0%
+if you dare um so
+uh that's a lot of we have a lot of fun
+
+ align:start position:0%
+uh that's a lot of we have a lot of fun
+ 
+
+ align:start position:0%
+uh that's a lot of we have a lot of fun
+in that world
+
+ align:start position:0%
+in that world
+ 
+
+ align:start position:0%
+in that world
+of hardness of different games and
+
+ align:start position:0%
+of hardness of different games and
+ 
+
+ align:start position:0%
+of hardness of different games and
+puzzles
+
+ align:start position:0%
+puzzles
+ 
+
+ align:start position:0%
+puzzles
+uh where do i want to go next uh
+
+ align:start position:0%
+uh where do i want to go next uh
+ 
+
+ align:start position:0%
+uh where do i want to go next uh
+okay next topic is balloon twisting
+
+ align:start position:0%
+okay next topic is balloon twisting
+ 
+
+ align:start position:0%
+okay next topic is balloon twisting
+totally different
+
+ align:start position:0%
+totally different
+ 
+
+ align:start position:0%
+totally different
+this is recreational but not about
+
+ align:start position:0%
+this is recreational but not about
+ 
+
+ align:start position:0%
+this is recreational but not about
+hardness so this is an octahedron
+
+ align:start position:0%
+hardness so this is an octahedron
+ 
+
+ align:start position:0%
+hardness so this is an octahedron
+twisted from one balloon i mean another
+
+ align:start position:0%
+twisted from one balloon i mean another
+ 
+
+ align:start position:0%
+twisted from one balloon i mean another
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+on a stick and so each of these is made
+
+ align:start position:0%
+on a stick and so each of these is made
+ 
+
+ align:start position:0%
+on a stick and so each of these is made
+from one balloon what graphs can you
+
+ align:start position:0%
+from one balloon what graphs can you
+ 
+
+ align:start position:0%
+from one balloon what graphs can you
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+for one balloon well you should read our
+
+ align:start position:0%
+for one balloon well you should read our
+ 
+
+ align:start position:0%
+for one balloon well you should read our
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+and you can characterize how many
+
+ align:start position:0%
+and you can characterize how many
+ 
+
+ align:start position:0%
+and you can characterize how many
+balloons you need to make each
+
+ align:start position:0%
+balloons you need to make each
+ 
+
+ align:start position:0%
+balloons you need to make each
+each polyhedron and some of these
+
+ align:start position:0%
+each polyhedron and some of these
+ 
+
+ align:start position:0%
+each polyhedron and some of these
+problems are np hard
+
+ align:start position:0%
+problems are np hard
+ 
+
+ align:start position:0%
+problems are np hard
+and it's a lot of fun
+
+ align:start position:0%
+and it's a lot of fun
+ 
+
+ align:start position:0%
+and it's a lot of fun
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+cool i think that's the end of the
+
+ align:start position:0%
+cool i think that's the end of the
+ 
+
+ align:start position:0%
+cool i think that's the end of the
+slides uh the last thing i wanted to
+
+ align:start position:0%
+slides uh the last thing i wanted to
+ 
+
+ align:start position:0%
+slides uh the last thing i wanted to
+show you
+
+ align:start position:0%
+show you
+ 
+
+ align:start position:0%
+show you
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+problem a puzzle slash magic trick comes
+
+ align:start position:0%
+problem a puzzle slash magic trick comes
+ 
+
+ align:start position:0%
+problem a puzzle slash magic trick comes
+from the puzzle world
+
+ align:start position:0%
+from the puzzle world
+ 
+
+ align:start position:0%
+from the puzzle world
+called the picture hanging problem so
+
+ align:start position:0%
+called the picture hanging problem so
+ 
+
+ align:start position:0%
+called the picture hanging problem so
+imagine you have a picture
+
+ align:start position:0%
+imagine you have a picture
+ 
+
+ align:start position:0%
+imagine you have a picture
+you want to hang it on a wall so you
+
+ align:start position:0%
+you want to hang it on a wall so you
+ 
+
+ align:start position:0%
+you want to hang it on a wall so you
+invested in some nice rope
+
+ align:start position:0%
+invested in some nice rope
+ 
+
+ align:start position:0%
+invested in some nice rope
+and you hang it and then if the on a
+
+ align:start position:0%
+and you hang it and then if the on a
+ 
+
+ align:start position:0%
+and you hang it and then if the on a
+nail
+
+ align:start position:0%
+nail
+ 
+
+ align:start position:0%
+nail
+if the nail falls out the picture falls
+
+ align:start position:0%
+if the nail falls out the picture falls
+ 
+
+ align:start position:0%
+if the nail falls out the picture falls
+and you're set
+
+ align:start position:0%
+and you're set
+ 
+
+ align:start position:0%
+and you're set
+so you invest in two nails like i have
+
+ align:start position:0%
+so you invest in two nails like i have
+ 
+
+ align:start position:0%
+so you invest in two nails like i have
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and maybe you hang your picture on both
+
+ align:start position:0%
+and maybe you hang your picture on both
+ 
+
+ align:start position:0%
+and maybe you hang your picture on both
+those nails now if one of the nails
+
+ align:start position:0%
+those nails now if one of the nails
+ 
+
+ align:start position:0%
+those nails now if one of the nails
+falls out you still have a crookedly
+
+ align:start position:0%
+falls out you still have a crookedly
+ 
+
+ align:start position:0%
+falls out you still have a crookedly
+hung picture
+
+ align:start position:0%
+hung picture
+ 
+
+ align:start position:0%
+hung picture
+the other nail falls out okay it's gone
+
+ align:start position:0%
+the other nail falls out okay it's gone
+ 
+
+ align:start position:0%
+the other nail falls out okay it's gone
+i want to hang a picture on two nails
+
+ align:start position:0%
+i want to hang a picture on two nails
+ 
+
+ align:start position:0%
+i want to hang a picture on two nails
+such that if i remove either nail the
+
+ align:start position:0%
+such that if i remove either nail the
+ 
+
+ align:start position:0%
+such that if i remove either nail the
+picture falls so jason pick a nail left
+
+ align:start position:0%
+picture falls so jason pick a nail left
+ 
+
+ align:start position:0%
+picture falls so jason pick a nail left
+or right
+
+ align:start position:0%
+or right
+ 
+
+ align:start position:0%
+or right
+left we remove make sure this doesn't
+
+ align:start position:0%
+left we remove make sure this doesn't
+ 
+
+ align:start position:0%
+left we remove make sure this doesn't
+fall off
+
+ align:start position:0%
+fall off
+ 
+
+ align:start position:0%
+fall off
+and boom the picture falls same wrapping
+
+ align:start position:0%
+and boom the picture falls same wrapping
+ 
+
+ align:start position:0%
+and boom the picture falls same wrapping
+you can check you can rewind the video
+
+ align:start position:0%
+you can check you can rewind the video
+ 
+
+ align:start position:0%
+you can check you can rewind the video
+make sure i did the same wrapping
+
+ align:start position:0%
+make sure i did the same wrapping
+ 
+
+ align:start position:0%
+make sure i did the same wrapping
+okay take out the right one good choice
+
+ align:start position:0%
+okay take out the right one good choice
+ 
+
+ align:start position:0%
+okay take out the right one good choice
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then also the picture false
+
+ align:start position:0%
+then also the picture false
+ 
+
+ align:start position:0%
+then also the picture false
+uh and so this is a classic puzzle but
+
+ align:start position:0%
+uh and so this is a classic puzzle but
+ 
+
+ align:start position:0%
+uh and so this is a classic puzzle but
+you can generalize it so let me do it to
+
+ align:start position:0%
+you can generalize it so let me do it to
+ 
+
+ align:start position:0%
+you can generalize it so let me do it to
+for three nails which is all i have here
+
+ align:start position:0%
+for three nails which is all i have here
+ 
+
+ align:start position:0%
+for three nails which is all i have here
+this nail sagging a little bit uh y
+
+ align:start position:0%
+this nail sagging a little bit uh y
+ 
+
+ align:start position:0%
+this nail sagging a little bit uh y
+x and y inverse x inverse okay i think
+
+ align:start position:0%
+x and y inverse x inverse okay i think
+ 
+
+ align:start position:0%
+x and y inverse x inverse okay i think
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+uh so this is one way to hang a picture
+
+ align:start position:0%
+uh so this is one way to hang a picture
+ 
+
+ align:start position:0%
+uh so this is one way to hang a picture
+on three nails such as if i remove any
+
+ align:start position:0%
+on three nails such as if i remove any
+ 
+
+ align:start position:0%
+on three nails such as if i remove any
+of the nails
+
+ align:start position:0%
+of the nails
+ 
+
+ align:start position:0%
+of the nails
+picture falls uh just justin uh one two
+
+ align:start position:0%
+picture falls uh just justin uh one two
+ 
+
+ align:start position:0%
+picture falls uh just justin uh one two
+or three
+
+ align:start position:0%
+or three
+ 
+
+ align:start position:0%
+or three
+two two okay
+
+ align:start position:0%
+two two okay
+ 
+
+ align:start position:0%
+two two okay
+yeah i wanna get out of the way make
+
+ align:start position:0%
+yeah i wanna get out of the way make
+ 
+
+ align:start position:0%
+yeah i wanna get out of the way make
+sure make sure i don't go
+
+ align:start position:0%
+sure make sure i don't go
+ 
+
+ align:start position:0%
+sure make sure i don't go
+over the edge here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's a lot easier to make this one
+
+ align:start position:0%
+yeah it's a lot easier to make this one
+ 
+
+ align:start position:0%
+yeah it's a lot easier to make this one
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+but you can see boom picture falls there
+
+ align:start position:0%
+but you can see boom picture falls there
+ 
+
+ align:start position:0%
+but you can see boom picture falls there
+and of course
+
+ align:start position:0%
+and of course
+ 
+
+ align:start position:0%
+and of course
+imagine infinite gravity and the picture
+
+ align:start position:0%
+imagine infinite gravity and the picture
+ 
+
+ align:start position:0%
+imagine infinite gravity and the picture
+falls tada
+
+ align:start position:0%
+falls tada
+ 
+
+ align:start position:0%
+falls tada
+and so you can generalize this to do
+
+ align:start position:0%
+and so you can generalize this to do
+ 
+
+ align:start position:0%
+and so you can generalize this to do
+essentially any
+
+ align:start position:0%
+essentially any
+ 
+
+ align:start position:0%
+essentially any
+it's called a monotone boolean function
+
+ align:start position:0%
+it's called a monotone boolean function
+ 
+
+ align:start position:0%
+it's called a monotone boolean function
+on any set of nails
+
+ align:start position:0%
+on any set of nails
+ 
+
+ align:start position:0%
+on any set of nails
+i mean you can make any subset of the
+
+ align:start position:0%
+i mean you can make any subset of the
+ 
+
+ align:start position:0%
+i mean you can make any subset of the
+nails cause the picture to fall
+
+ align:start position:0%
+nails cause the picture to fall
+ 
+
+ align:start position:0%
+nails cause the picture to fall
+and any collection of subsets of nails
+
+ align:start position:0%
+and any collection of subsets of nails
+ 
+
+ align:start position:0%
+and any collection of subsets of nails
+to make it fall of course if you remove
+
+ align:start position:0%
+to make it fall of course if you remove
+ 
+
+ align:start position:0%
+to make it fall of course if you remove
+more nails it's still going to fall
+
+ align:start position:0%
+more nails it's still going to fall
+ 
+
+ align:start position:0%
+more nails it's still going to fall
+that's the monotone sense but otherwise
+
+ align:start position:0%
+that's the monotone sense but otherwise
+ 
+
+ align:start position:0%
+that's the monotone sense but otherwise
+you can do an arbitrary
+
+ align:start position:0%
+you can do an arbitrary
+ 
+
+ align:start position:0%
+you can do an arbitrary
+pattern which is fun that's actually
+
+ align:start position:0%
+pattern which is fun that's actually
+ 
+
+ align:start position:0%
+pattern which is fun that's actually
+result with ron rivest and a bunch of
+
+ align:start position:0%
+result with ron rivest and a bunch of
+ 
+
+ align:start position:0%
+result with ron rivest and a bunch of
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+other people um i think
+
+ align:start position:0%
+other people um i think
+ 
+
+ align:start position:0%
+other people um i think
+i'm approximately on time so that was a
+
+ align:start position:0%
+i'm approximately on time so that was a
+ 
+
+ align:start position:0%
+i'm approximately on time so that was a
+quick tour
+
+ align:start position:0%
+quick tour
+ 
+
+ align:start position:0%
+quick tour
+and there are obviously various classes
+
+ align:start position:0%
+and there are obviously various classes
+ 
+
+ align:start position:0%
+and there are obviously various classes
+here you can take
+
+ align:start position:0%
+here you can take
+ 
+
+ align:start position:0%
+here you can take
+6892 the hardness class was just offered
+
+ align:start position:0%
+6892 the hardness class was just offered
+ 
+
+ align:start position:0%
+6892 the hardness class was just offered
+last semester so probably won't be for a
+
+ align:start position:0%
+last semester so probably won't be for a
+ 
+
+ align:start position:0%
+last semester so probably won't be for a
+while
+
+ align:start position:0%
+while
+ 
+
+ align:start position:0%
+while
+all these classes are online watch the
+
+ align:start position:0%
+all these classes are online watch the
+ 
+
+ align:start position:0%
+all these classes are online watch the
+videos feel free to ask me questions
+
+ align:start position:0%
+videos feel free to ask me questions
+ 
+
+ align:start position:0%
+videos feel free to ask me questions
+and now we have justin i left you space
+
+ align:start position:0%
+and now we have justin i left you space
+ 
+
+ align:start position:0%
+and now we have justin i left you space
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+for your outline
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you don't have to
+
+ align:start position:0%
+you don't have to
+ 
+
+ align:start position:0%
+you don't have to
+but i'll put your name out thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so jess justin is also a jabiter yeah
+
+ align:start position:0%
+so jess justin is also a jabiter yeah
+ 
+
+ align:start position:0%
+so jess justin is also a jabiter yeah
+we've got a lot of geometry people in
+
+ align:start position:0%
+we've got a lot of geometry people in
+ 
+
+ align:start position:0%
+we've got a lot of geometry people in
+double six this semester thank you
+
+ align:start position:0%
+double six this semester thank you
+ 
+
+ align:start position:0%
+double six this semester thank you
+okay you know it's like i can't help but
+
+ align:start position:0%
+okay you know it's like i can't help but
+ 
+
+ align:start position:0%
+okay you know it's like i can't help but
+share that on our
+
+ align:start position:0%
+share that on our
+ 
+
+ align:start position:0%
+share that on our
+instructor chat eric was texting that he
+
+ align:start position:0%
+instructor chat eric was texting that he
+ 
+
+ align:start position:0%
+instructor chat eric was texting that he
+was going to be
+
+ align:start position:0%
+was going to be
+ 
+
+ align:start position:0%
+was going to be
+he was somehow nervous that the applied
+
+ align:start position:0%
+he was somehow nervous that the applied
+ 
+
+ align:start position:0%
+he was somehow nervous that the applied
+guy would have all the like the cool
+
+ align:start position:0%
+guy would have all the like the cool
+ 
+
+ align:start position:0%
+guy would have all the like the cool
+stuff to show off
+
+ align:start position:0%
+stuff to show off
+ 
+
+ align:start position:0%
+stuff to show off
+and now i feel totally boring uh
+
+ align:start position:0%
+and now i feel totally boring uh
+ 
+
+ align:start position:0%
+and now i feel totally boring uh
+right yeah so yeah we have three
+
+ align:start position:0%
+right yeah so yeah we have three
+ 
+
+ align:start position:0%
+right yeah so yeah we have three
+different geometry instructors uh
+
+ align:start position:0%
+different geometry instructors uh
+ 
+
+ align:start position:0%
+different geometry instructors uh
+in in this class we have many different
+
+ align:start position:0%
+in in this class we have many different
+ 
+
+ align:start position:0%
+in in this class we have many different
+flavors of geometry that are kind of
+
+ align:start position:0%
+flavors of geometry that are kind of
+ 
+
+ align:start position:0%
+flavors of geometry that are kind of
+represented in this this room here from
+
+ align:start position:0%
+represented in this this room here from
+ 
+
+ align:start position:0%
+represented in this this room here from
+mechanical engineering to
+
+ align:start position:0%
+mechanical engineering to
+ 
+
+ align:start position:0%
+mechanical engineering to
+theory plus lots of other cool stuff to
+
+ align:start position:0%
+theory plus lots of other cool stuff to
+ 
+
+ align:start position:0%
+theory plus lots of other cool stuff to
+uh whatever it is that i do
+
+ align:start position:0%
+uh whatever it is that i do
+ 
+
+ align:start position:0%
+uh whatever it is that i do
+um all right so i'm a professor also
+
+ align:start position:0%
+um all right so i'm a professor also
+ 
+
+ align:start position:0%
+um all right so i'm a professor also
+from brazil and lead a group that
+
+ align:start position:0%
+from brazil and lead a group that
+ 
+
+ align:start position:0%
+from brazil and lead a group that
+studies
+
+ align:start position:0%
+studies
+ 
+
+ align:start position:0%
+studies
+slightly more applied geometry problems
+
+ align:start position:0%
+slightly more applied geometry problems
+ 
+
+ align:start position:0%
+slightly more applied geometry problems
+in some sense
+
+ align:start position:0%
+in some sense
+ 
+
+ align:start position:0%
+in some sense
+in seasonal we kind of cross a lot of
+
+ align:start position:0%
+in seasonal we kind of cross a lot of
+ 
+
+ align:start position:0%
+in seasonal we kind of cross a lot of
+boundaries actually closer to the math
+
+ align:start position:0%
+boundaries actually closer to the math
+ 
+
+ align:start position:0%
+boundaries actually closer to the math
+department than to the theory group in
+
+ align:start position:0%
+department than to the theory group in
+ 
+
+ align:start position:0%
+department than to the theory group in
+computer science
+
+ align:start position:0%
+computer science
+ 
+
+ align:start position:0%
+computer science
+which i would argue is largely a
+
+ align:start position:0%
+which i would argue is largely a
+ 
+
+ align:start position:0%
+which i would argue is largely a
+historical artifact rather than anything
+
+ align:start position:0%
+historical artifact rather than anything
+ 
+
+ align:start position:0%
+historical artifact rather than anything
+interesting about computer science or
+
+ align:start position:0%
+interesting about computer science or
+ 
+
+ align:start position:0%
+interesting about computer science or
+math um
+
+ align:start position:0%
+math um
+ 
+
+ align:start position:0%
+math um
+so continuing in our whirlwind tour of
+
+ align:start position:0%
+so continuing in our whirlwind tour of
+ 
+
+ align:start position:0%
+so continuing in our whirlwind tour of
+interesting geometry classes here at mit
+
+ align:start position:0%
+interesting geometry classes here at mit
+ 
+
+ align:start position:0%
+interesting geometry classes here at mit
+uh i have some more fun things to to add
+
+ align:start position:0%
+uh i have some more fun things to to add
+ 
+
+ align:start position:0%
+uh i have some more fun things to to add
+to the list and we'll introduce some of
+
+ align:start position:0%
+to the list and we'll introduce some of
+ 
+
+ align:start position:0%
+to the list and we'll introduce some of
+the ideas in the next couple slides here
+
+ align:start position:0%
+the ideas in the next couple slides here
+ 
+
+ align:start position:0%
+the ideas in the next couple slides here
+uh so uh normally every fall i teach
+
+ align:start position:0%
+uh so uh normally every fall i teach
+ 
+
+ align:start position:0%
+uh so uh normally every fall i teach
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+uh which is the introduction to computer
+
+ align:start position:0%
+uh which is the introduction to computer
+ 
+
+ align:start position:0%
+uh which is the introduction to computer
+graphics course in fact my
+
+ align:start position:0%
+graphics course in fact my
+ 
+
+ align:start position:0%
+graphics course in fact my
+background was was working in an
+
+ align:start position:0%
+background was was working in an
+ 
+
+ align:start position:0%
+background was was working in an
+animation studio for a little bit of
+
+ align:start position:0%
+animation studio for a little bit of
+ 
+
+ align:start position:0%
+animation studio for a little bit of
+time and and
+
+ align:start position:0%
+time and and
+ 
+
+ align:start position:0%
+time and and
+uh got one movie credit out of it until
+
+ align:start position:0%
+uh got one movie credit out of it until
+ 
+
+ align:start position:0%
+uh got one movie credit out of it until
+they changed the standards for movie
+
+ align:start position:0%
+they changed the standards for movie
+ 
+
+ align:start position:0%
+they changed the standards for movie
+credits and then that stopped happening
+
+ align:start position:0%
+credits and then that stopped happening
+ 
+
+ align:start position:0%
+credits and then that stopped happening
+uh but but in any event uh if you watch
+
+ align:start position:0%
+uh but but in any event uh if you watch
+ 
+
+ align:start position:0%
+uh but but in any event uh if you watch
+what's that movie up with the old man
+
+ align:start position:0%
+what's that movie up with the old man
+ 
+
+ align:start position:0%
+what's that movie up with the old man
+if you hit pause at just the right
+
+ align:start position:0%
+if you hit pause at just the right
+ 
+
+ align:start position:0%
+if you hit pause at just the right
+moment you can find me right above the
+
+ align:start position:0%
+moment you can find me right above the
+ 
+
+ align:start position:0%
+moment you can find me right above the
+list of babies that were born during
+
+ align:start position:0%
+list of babies that were born during
+ 
+
+ align:start position:0%
+list of babies that were born during
+uh production uh but in any event um
+
+ align:start position:0%
+uh production uh but in any event um
+ 
+
+ align:start position:0%
+uh production uh but in any event um
+although computer graphics might not
+
+ align:start position:0%
+although computer graphics might not
+ 
+
+ align:start position:0%
+although computer graphics might not
+sound like an algorithmic discipline
+
+ align:start position:0%
+sound like an algorithmic discipline
+ 
+
+ align:start position:0%
+sound like an algorithmic discipline
+i'll try to convince you guys that
+
+ align:start position:0%
+i'll try to convince you guys that
+ 
+
+ align:start position:0%
+i'll try to convince you guys that
+in some sense you can take just about
+
+ align:start position:0%
+in some sense you can take just about
+ 
+
+ align:start position:0%
+in some sense you can take just about
+anybody in our department have them
+
+ align:start position:0%
+anybody in our department have them
+ 
+
+ align:start position:0%
+anybody in our department have them
+teach 606 and give a similar talk that
+
+ align:start position:0%
+teach 606 and give a similar talk that
+ 
+
+ align:start position:0%
+teach 606 and give a similar talk that
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+the material that you've encountered in
+
+ align:start position:0%
+the material that you've encountered in
+ 
+
+ align:start position:0%
+the material that you've encountered in
+this course is going to be relevant to
+
+ align:start position:0%
+this course is going to be relevant to
+ 
+
+ align:start position:0%
+this course is going to be relevant to
+your life
+
+ align:start position:0%
+your life
+ 
+
+ align:start position:0%
+your life
+uh the other course that i teach that
+
+ align:start position:0%
+uh the other course that i teach that
+ 
+
+ align:start position:0%
+uh the other course that i teach that
+might be of interest uh
+
+ align:start position:0%
+might be of interest uh
+ 
+
+ align:start position:0%
+might be of interest uh
+and actually is a little more
+
+ align:start position:0%
+and actually is a little more
+ 
+
+ align:start position:0%
+and actually is a little more
+theoretically flavored uh that i teach
+
+ align:start position:0%
+theoretically flavored uh that i teach
+ 
+
+ align:start position:0%
+theoretically flavored uh that i teach
+is a six eight three eight
+
+ align:start position:0%
+is a six eight three eight
+ 
+
+ align:start position:0%
+is a six eight three eight
+so since eric so kindly put my board my
+
+ align:start position:0%
+so since eric so kindly put my board my
+ 
+
+ align:start position:0%
+so since eric so kindly put my board my
+name on the board here i guess i can
+
+ align:start position:0%
+name on the board here i guess i can
+ 
+
+ align:start position:0%
+name on the board here i guess i can
+draw a picture
+
+ align:start position:0%
+draw a picture
+ 
+
+ align:start position:0%
+draw a picture
+so the main object of interest in six
+
+ align:start position:0%
+so the main object of interest in six
+ 
+
+ align:start position:0%
+so the main object of interest in six
+eight three eight
+
+ align:start position:0%
+eight three eight
+ 
+
+ align:start position:0%
+eight three eight
+is a particular thing called a
+
+ align:start position:0%
+is a particular thing called a
+ 
+
+ align:start position:0%
+is a particular thing called a
+simplicial complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um usually uh in 606 we spend a lot
+
+ align:start position:0%
+so um usually uh in 606 we spend a lot
+ 
+
+ align:start position:0%
+so um usually uh in 606 we spend a lot
+of time thinking about graphs
+
+ align:start position:0%
+of time thinking about graphs
+ 
+
+ align:start position:0%
+of time thinking about graphs
+so let me draw you a graph so i'm going
+
+ align:start position:0%
+so let me draw you a graph so i'm going
+ 
+
+ align:start position:0%
+so let me draw you a graph so i'm going
+to take a square
+
+ align:start position:0%
+to take a square
+ 
+
+ align:start position:0%
+to take a square
+and subdivide it and now let's say i put
+
+ align:start position:0%
+and subdivide it and now let's say i put
+ 
+
+ align:start position:0%
+and subdivide it and now let's say i put
+edges diagonally
+
+ align:start position:0%
+edges diagonally
+ 
+
+ align:start position:0%
+edges diagonally
+like that now
+
+ align:start position:0%
+like that now
+ 
+
+ align:start position:0%
+like that now
+and pick from the most important thing
+
+ align:start position:0%
+and pick from the most important thing
+ 
+
+ align:start position:0%
+and pick from the most important thing
+is a bunch of notes can
+
+ align:start position:0%
+is a bunch of notes can
+ 
+
+ align:start position:0%
+is a bunch of notes can
+connect my edges in fact if i took this
+
+ align:start position:0%
+connect my edges in fact if i took this
+ 
+
+ align:start position:0%
+connect my edges in fact if i took this
+edge and i like moved it down or
+
+ align:start position:0%
+edge and i like moved it down or
+ 
+
+ align:start position:0%
+edge and i like moved it down or
+something it would be the same graph
+
+ align:start position:0%
+something it would be the same graph
+ 
+
+ align:start position:0%
+something it would be the same graph
+uh but of course in a lot of uh computer
+
+ align:start position:0%
+uh but of course in a lot of uh computer
+ 
+
+ align:start position:0%
+uh but of course in a lot of uh computer
+graphics applications this thing also
+
+ align:start position:0%
+graphics applications this thing also
+ 
+
+ align:start position:0%
+graphics applications this thing also
+looks an awful lot like a square uh and
+
+ align:start position:0%
+looks an awful lot like a square uh and
+ 
+
+ align:start position:0%
+looks an awful lot like a square uh and
+the reason
+
+ align:start position:0%
+the reason
+ 
+
+ align:start position:0%
+the reason
+is that of course the graph here
+
+ align:start position:0%
+is that of course the graph here
+ 
+
+ align:start position:0%
+is that of course the graph here
+contains triangles inside of it
+
+ align:start position:0%
+contains triangles inside of it
+ 
+
+ align:start position:0%
+contains triangles inside of it
+uh and so for instance um maybe
+
+ align:start position:0%
+uh and so for instance um maybe
+ 
+
+ align:start position:0%
+uh and so for instance um maybe
+i think of my graph as a collection of
+
+ align:start position:0%
+i think of my graph as a collection of
+ 
+
+ align:start position:0%
+i think of my graph as a collection of
+vertices clutching edges this is the
+
+ align:start position:0%
+vertices clutching edges this is the
+ 
+
+ align:start position:0%
+vertices clutching edges this is the
+sort of notation we've seen before
+
+ align:start position:0%
+sort of notation we've seen before
+ 
+
+ align:start position:0%
+sort of notation we've seen before
+and then i add a third thing to my trip
+
+ align:start position:0%
+and then i add a third thing to my trip
+ 
+
+ align:start position:0%
+and then i add a third thing to my trip
+uh to my
+
+ align:start position:0%
+uh to my
+ 
+
+ align:start position:0%
+uh to my
+description which is a set of triplets
+
+ align:start position:0%
+description which is a set of triplets
+ 
+
+ align:start position:0%
+description which is a set of triplets
+uh that's a set of triangles here
+
+ align:start position:0%
+uh that's a set of triangles here
+ 
+
+ align:start position:0%
+uh that's a set of triangles here
+right and we can take a lot of the
+
+ align:start position:0%
+right and we can take a lot of the
+ 
+
+ align:start position:0%
+right and we can take a lot of the
+algorithms that we've talked about in
+
+ align:start position:0%
+algorithms that we've talked about in
+ 
+
+ align:start position:0%
+algorithms that we've talked about in
+this class and extend it to this case so
+
+ align:start position:0%
+this class and extend it to this case so
+ 
+
+ align:start position:0%
+this class and extend it to this case so
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+um here's a deceptively annoying one uh
+
+ align:start position:0%
+um here's a deceptively annoying one uh
+ 
+
+ align:start position:0%
+um here's a deceptively annoying one uh
+let's say that i want the shortest path
+
+ align:start position:0%
+let's say that i want the shortest path
+ 
+
+ align:start position:0%
+let's say that i want the shortest path
+between two vertices on my graph
+
+ align:start position:0%
+between two vertices on my graph
+ 
+
+ align:start position:0%
+between two vertices on my graph
+yeah so we certainly have learned
+
+ align:start position:0%
+yeah so we certainly have learned
+ 
+
+ align:start position:0%
+yeah so we certainly have learned
+dijkstra's algorithm as one technique to
+
+ align:start position:0%
+dijkstra's algorithm as one technique to
+ 
+
+ align:start position:0%
+dijkstra's algorithm as one technique to
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+and indeed common practice in computer
+
+ align:start position:0%
+and indeed common practice in computer
+ 
+
+ align:start position:0%
+and indeed common practice in computer
+graphics which is shameful
+
+ align:start position:0%
+graphics which is shameful
+ 
+
+ align:start position:0%
+graphics which is shameful
+uh is on your triangle mesh if you want
+
+ align:start position:0%
+uh is on your triangle mesh if you want
+ 
+
+ align:start position:0%
+uh is on your triangle mesh if you want
+the shortest path between two vertices
+
+ align:start position:0%
+the shortest path between two vertices
+ 
+
+ align:start position:0%
+the shortest path between two vertices
+run dijkstra's algorithm on the edges
+
+ align:start position:0%
+run dijkstra's algorithm on the edges
+ 
+
+ align:start position:0%
+run dijkstra's algorithm on the edges
+and let's see if that works really quick
+
+ align:start position:0%
+and let's see if that works really quick
+ 
+
+ align:start position:0%
+and let's see if that works really quick
+so let's say that i want the shortest
+
+ align:start position:0%
+so let's say that i want the shortest
+ 
+
+ align:start position:0%
+so let's say that i want the shortest
+path between
+
+ align:start position:0%
+path between
+ 
+
+ align:start position:0%
+path between
+and by the way i'm going to assume the
+
+ align:start position:0%
+and by the way i'm going to assume the
+ 
+
+ align:start position:0%
+and by the way i'm going to assume the
+lengths of my edges are like the lengths
+
+ align:start position:0%
+lengths of my edges are like the lengths
+ 
+
+ align:start position:0%
+lengths of my edges are like the lengths
+as i've drawn them on the board here so
+
+ align:start position:0%
+as i've drawn them on the board here so
+ 
+
+ align:start position:0%
+as i've drawn them on the board here so
+it's like 1
+
+ align:start position:0%
+it's like 1
+ 
+
+ align:start position:0%
+it's like 1
+1 square root of 2. okay so let's say i
+
+ align:start position:0%
+1 square root of 2. okay so let's say i
+ 
+
+ align:start position:0%
+1 square root of 2. okay so let's say i
+want the shortest path between the
+
+ align:start position:0%
+want the shortest path between the
+ 
+
+ align:start position:0%
+want the shortest path between the
+bottom left and the upper right
+
+ align:start position:0%
+bottom left and the upper right
+ 
+
+ align:start position:0%
+bottom left and the upper right
+for run dijkstra's algorithm we're in
+
+ align:start position:0%
+for run dijkstra's algorithm we're in
+ 
+
+ align:start position:0%
+for run dijkstra's algorithm we're in
+good shape right we could uh you can
+
+ align:start position:0%
+good shape right we could uh you can
+ 
+
+ align:start position:0%
+good shape right we could uh you can
+i'll let you do the computations at home
+
+ align:start position:0%
+i'll let you do the computations at home
+ 
+
+ align:start position:0%
+i'll let you do the computations at home
+you'll get the path
+
+ align:start position:0%
+you'll get the path
+ 
+
+ align:start position:0%
+you'll get the path
+that is these two edges but here's a
+
+ align:start position:0%
+that is these two edges but here's a
+ 
+
+ align:start position:0%
+that is these two edges but here's a
+really annoying thing
+
+ align:start position:0%
+really annoying thing
+ 
+
+ align:start position:0%
+really annoying thing
+let's say instead i wanted the shortest
+
+ align:start position:0%
+let's say instead i wanted the shortest
+ 
+
+ align:start position:0%
+let's say instead i wanted the shortest
+path from the upper
+
+ align:start position:0%
+path from the upper
+ 
+
+ align:start position:0%
+path from the upper
+left to the lower right if i run
+
+ align:start position:0%
+left to the lower right if i run
+ 
+
+ align:start position:0%
+left to the lower right if i run
+dijkstra's algorithm on this
+
+ align:start position:0%
+dijkstra's algorithm on this
+ 
+
+ align:start position:0%
+dijkstra's algorithm on this
+triangulated square
+
+ align:start position:0%
+triangulated square
+ 
+
+ align:start position:0%
+triangulated square
+what's going to be the shortest path
+
+ align:start position:0%
+what's going to be the shortest path
+ 
+
+ align:start position:0%
+what's going to be the shortest path
+yeah in fact there's a bunch of them
+
+ align:start position:0%
+yeah in fact there's a bunch of them
+ 
+
+ align:start position:0%
+yeah in fact there's a bunch of them
+one of them might go all the way down
+
+ align:start position:0%
+one of them might go all the way down
+ 
+
+ align:start position:0%
+one of them might go all the way down
+and then all the way to the right
+
+ align:start position:0%
+and then all the way to the right
+ 
+
+ align:start position:0%
+and then all the way to the right
+what's the length of this path one two
+
+ align:start position:0%
+what's the length of this path one two
+ 
+
+ align:start position:0%
+what's the length of this path one two
+three four
+
+ align:start position:0%
+three four
+ 
+
+ align:start position:0%
+three four
+is that the length of the shortest path
+
+ align:start position:0%
+is that the length of the shortest path
+ 
+
+ align:start position:0%
+is that the length of the shortest path
+well probably not well we'd like our
+
+ align:start position:0%
+well probably not well we'd like our
+ 
+
+ align:start position:0%
+well probably not well we'd like our
+shortest path
+
+ align:start position:0%
+shortest path
+ 
+
+ align:start position:0%
+shortest path
+to do something like that but graphs
+
+ align:start position:0%
+to do something like that but graphs
+ 
+
+ align:start position:0%
+to do something like that but graphs
+don't know how to talk to
+
+ align:start position:0%
+don't know how to talk to
+ 
+
+ align:start position:0%
+don't know how to talk to
+triangles and this is going to be a
+
+ align:start position:0%
+triangles and this is going to be a
+ 
+
+ align:start position:0%
+triangles and this is going to be a
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+in fact it wasn't until
+
+ align:start position:0%
+in fact it wasn't until
+ 
+
+ align:start position:0%
+in fact it wasn't until
+history terms that we were able to kind
+
+ align:start position:0%
+history terms that we were able to kind
+ 
+
+ align:start position:0%
+history terms that we were able to kind
+of work out the correct
+
+ align:start position:0%
+of work out the correct
+ 
+
+ align:start position:0%
+of work out the correct
+algorithm for a shortness of a
+
+ align:start position:0%
+algorithm for a shortness of a
+ 
+
+ align:start position:0%
+algorithm for a shortness of a
+triangulated domain like this um
+
+ align:start position:0%
+triangulated domain like this um
+ 
+
+ align:start position:0%
+triangulated domain like this um
+that's the runtime that we would expect
+
+ align:start position:0%
+that's the runtime that we would expect
+ 
+
+ align:start position:0%
+that's the runtime that we would expect
+this is called uh mnp
+
+ align:start position:0%
+this is called uh mnp
+ 
+
+ align:start position:0%
+this is called uh mnp
+i'm guessing eric and jason could do a
+
+ align:start position:0%
+i'm guessing eric and jason could do a
+ 
+
+ align:start position:0%
+i'm guessing eric and jason could do a
+better job describing it than i can
+
+ align:start position:0%
+better job describing it than i can
+ 
+
+ align:start position:0%
+better job describing it than i can
+but the basic idea of the mmp algorithm
+
+ align:start position:0%
+but the basic idea of the mmp algorithm
+ 
+
+ align:start position:0%
+but the basic idea of the mmp algorithm
+actually is a really
+
+ align:start position:0%
+actually is a really
+ 
+
+ align:start position:0%
+actually is a really
+happens to be a nice extension of the
+
+ align:start position:0%
+happens to be a nice extension of the
+ 
+
+ align:start position:0%
+happens to be a nice extension of the
+way that we taught uh dijkstra's
+
+ align:start position:0%
+way that we taught uh dijkstra's
+ 
+
+ align:start position:0%
+way that we taught uh dijkstra's
+algorithm in 6.06 because they really do
+
+ align:start position:0%
+algorithm in 6.06 because they really do
+ 
+
+ align:start position:0%
+algorithm in 6.06 because they really do
+keep track of these sort of level sets
+
+ align:start position:0%
+keep track of these sort of level sets
+ 
+
+ align:start position:0%
+keep track of these sort of level sets
+of the distance function
+
+ align:start position:0%
+of the distance function
+ 
+
+ align:start position:0%
+of the distance function
+but now the level sets have to like oops
+
+ align:start position:0%
+but now the level sets have to like oops
+ 
+
+ align:start position:0%
+but now the level sets have to like oops
+i have to window an
+
+ align:start position:0%
+i have to window an
+ 
+
+ align:start position:0%
+i have to window an
+edge like that when i uh compute short
+
+ align:start position:0%
+edge like that when i uh compute short
+ 
+
+ align:start position:0%
+edge like that when i uh compute short
+its path which is a giant headache
+
+ align:start position:0%
+its path which is a giant headache
+ 
+
+ align:start position:0%
+its path which is a giant headache
+this is one of these algorithms that was
+
+ align:start position:0%
+this is one of these algorithms that was
+ 
+
+ align:start position:0%
+this is one of these algorithms that was
+known in theory about 10 years before
+
+ align:start position:0%
+known in theory about 10 years before
+ 
+
+ align:start position:0%
+known in theory about 10 years before
+anybody bothered to implement it in a
+
+ align:start position:0%
+anybody bothered to implement it in a
+ 
+
+ align:start position:0%
+anybody bothered to implement it in a
+way that they could convince
+
+ align:start position:0%
+way that they could convince
+ 
+
+ align:start position:0%
+way that they could convince
+them themselves really random n log n
+
+ align:start position:0%
+them themselves really random n log n
+ 
+
+ align:start position:0%
+them themselves really random n log n
+time uh and nowadays is a cottage
+
+ align:start position:0%
+time uh and nowadays is a cottage
+ 
+
+ align:start position:0%
+time uh and nowadays is a cottage
+industry in
+
+ align:start position:0%
+industry in
+ 
+
+ align:start position:0%
+industry in
+in computer graphics research papers to
+
+ align:start position:0%
+in computer graphics research papers to
+ 
+
+ align:start position:0%
+in computer graphics research papers to
+implement this and then speed it up in
+
+ align:start position:0%
+implement this and then speed it up in
+ 
+
+ align:start position:0%
+implement this and then speed it up in
+different ways and
+
+ align:start position:0%
+different ways and
+ 
+
+ align:start position:0%
+different ways and
+sadly the reality is that a different
+
+ align:start position:0%
+sadly the reality is that a different
+ 
+
+ align:start position:0%
+sadly the reality is that a different
+number we cover in 6838 called fast
+
+ align:start position:0%
+number we cover in 6838 called fast
+ 
+
+ align:start position:0%
+number we cover in 6838 called fast
+marching which doesn't actually give you
+
+ align:start position:0%
+marching which doesn't actually give you
+ 
+
+ align:start position:0%
+marching which doesn't actually give you
+the shortest path but some approximation
+
+ align:start position:0%
+the shortest path but some approximation
+ 
+
+ align:start position:0%
+the shortest path but some approximation
+thereof
+
+ align:start position:0%
+thereof
+ 
+
+ align:start position:0%
+thereof
+uh is faster easier to use and basically
+
+ align:start position:0%
+uh is faster easier to use and basically
+ 
+
+ align:start position:0%
+uh is faster easier to use and basically
+indistinguishable um so in any event um
+
+ align:start position:0%
+indistinguishable um so in any event um
+ 
+
+ align:start position:0%
+indistinguishable um so in any event um
+in 683 we kind of have an interesting
+
+ align:start position:0%
+in 683 we kind of have an interesting
+ 
+
+ align:start position:0%
+in 683 we kind of have an interesting
+we'll talk about a lot of algorithms
+
+ align:start position:0%
+we'll talk about a lot of algorithms
+ 
+
+ align:start position:0%
+we'll talk about a lot of algorithms
+that look like what we've done
+
+ align:start position:0%
+that look like what we've done
+ 
+
+ align:start position:0%
+that look like what we've done
+in whatever this class it's uh 6.006
+
+ align:start position:0%
+in whatever this class it's uh 6.006
+ 
+
+ align:start position:0%
+in whatever this class it's uh 6.006
+um but at the same time start to have a
+
+ align:start position:0%
+um but at the same time start to have a
+ 
+
+ align:start position:0%
+um but at the same time start to have a
+more geometric flavor and we
+
+ align:start position:0%
+more geometric flavor and we
+ 
+
+ align:start position:0%
+more geometric flavor and we
+don't worry quite as much about uh so in
+
+ align:start position:0%
+don't worry quite as much about uh so in
+ 
+
+ align:start position:0%
+don't worry quite as much about uh so in
+our computation model oftentimes we're
+
+ align:start position:0%
+our computation model oftentimes we're
+ 
+
+ align:start position:0%
+our computation model oftentimes we're
+kind of okay with real numbers because
+
+ align:start position:0%
+kind of okay with real numbers because
+ 
+
+ align:start position:0%
+kind of okay with real numbers because
+that's not where
+
+ align:start position:0%
+that's not where
+ 
+
+ align:start position:0%
+that's not where
+the headache is and of course when you
+
+ align:start position:0%
+the headache is and of course when you
+ 
+
+ align:start position:0%
+the headache is and of course when you
+write your code in this class you use
+
+ align:start position:0%
+write your code in this class you use
+ 
+
+ align:start position:0%
+write your code in this class you use
+double precision floating point
+
+ align:start position:0%
+double precision floating point
+ 
+
+ align:start position:0%
+double precision floating point
+if you're more responsible like in in
+
+ align:start position:0%
+if you're more responsible like in in
+ 
+
+ align:start position:0%
+if you're more responsible like in in
+jason's previous lecture you should
+
+ align:start position:0%
+jason's previous lecture you should
+ 
+
+ align:start position:0%
+jason's previous lecture you should
+probably keep track of
+
+ align:start position:0%
+probably keep track of
+ 
+
+ align:start position:0%
+probably keep track of
+the number of operations to make sure
+
+ align:start position:0%
+the number of operations to make sure
+ 
+
+ align:start position:0%
+the number of operations to make sure
+that your error is bounded but no i'm
+
+ align:start position:0%
+that your error is bounded but no i'm
+ 
+
+ align:start position:0%
+that your error is bounded but no i'm
+not sure that we
+
+ align:start position:0%
+not sure that we
+ 
+
+ align:start position:0%
+not sure that we
+really bother with that um in any event
+
+ align:start position:0%
+really bother with that um in any event
+ 
+
+ align:start position:0%
+really bother with that um in any event
+this allows us to kind of have two
+
+ align:start position:0%
+this allows us to kind of have two
+ 
+
+ align:start position:0%
+this allows us to kind of have two
+different mindsets right there's one
+
+ align:start position:0%
+different mindsets right there's one
+ 
+
+ align:start position:0%
+different mindsets right there's one
+mindset which is discreet
+
+ align:start position:0%
+mindset which is discreet
+ 
+
+ align:start position:0%
+mindset which is discreet
+there's another mindset which is smooth
+
+ align:start position:0%
+there's another mindset which is smooth
+ 
+
+ align:start position:0%
+there's another mindset which is smooth
+right so we think about
+
+ align:start position:0%
+right so we think about
+ 
+
+ align:start position:0%
+right so we think about
+understanding geometry like these
+
+ align:start position:0%
+understanding geometry like these
+ 
+
+ align:start position:0%
+understanding geometry like these
+triangulated domains as an approximation
+
+ align:start position:0%
+triangulated domains as an approximation
+ 
+
+ align:start position:0%
+triangulated domains as an approximation
+of a smooth surface
+
+ align:start position:0%
+of a smooth surface
+ 
+
+ align:start position:0%
+of a smooth surface
+and then we might want to do stuff like
+
+ align:start position:0%
+and then we might want to do stuff like
+ 
+
+ align:start position:0%
+and then we might want to do stuff like
+compute curvature and so on which is
+
+ align:start position:0%
+compute curvature and so on which is
+ 
+
+ align:start position:0%
+compute curvature and so on which is
+really associated with computing
+
+ align:start position:0%
+really associated with computing
+ 
+
+ align:start position:0%
+really associated with computing
+derivatives
+
+ align:start position:0%
+derivatives
+ 
+
+ align:start position:0%
+derivatives
+which of course we don't have on these
+
+ align:start position:0%
+which of course we don't have on these
+ 
+
+ align:start position:0%
+which of course we don't have on these
+kinds of special objects
+
+ align:start position:0%
+kinds of special objects
+ 
+
+ align:start position:0%
+kinds of special objects
+and that leads to this really fun area
+
+ align:start position:0%
+and that leads to this really fun area
+ 
+
+ align:start position:0%
+and that leads to this really fun area
+of math computer science
+
+ align:start position:0%
+of math computer science
+ 
+
+ align:start position:0%
+of math computer science
+whatever called discrete differential
+
+ align:start position:0%
+whatever called discrete differential
+ 
+
+ align:start position:0%
+whatever called discrete differential
+geometry which sounds like a
+
+ align:start position:0%
+geometry which sounds like a
+ 
+
+ align:start position:0%
+geometry which sounds like a
+contradiction in terms
+
+ align:start position:0%
+contradiction in terms
+ 
+
+ align:start position:0%
+contradiction in terms
+um and it's something that we cover in
+
+ align:start position:0%
+um and it's something that we cover in
+ 
+
+ align:start position:0%
+um and it's something that we cover in
+quite some detail in this course so we
+
+ align:start position:0%
+quite some detail in this course so we
+ 
+
+ align:start position:0%
+quite some detail in this course so we
+build up
+
+ align:start position:0%
+build up
+ 
+
+ align:start position:0%
+build up
+all of calculus the only calculations
+
+ align:start position:0%
+all of calculus the only calculations
+ 
+
+ align:start position:0%
+all of calculus the only calculations
+you're allowed to do
+
+ align:start position:0%
+you're allowed to do
+ 
+
+ align:start position:0%
+you're allowed to do
+are on the vertices edges and triangles
+
+ align:start position:0%
+are on the vertices edges and triangles
+ 
+
+ align:start position:0%
+are on the vertices edges and triangles
+of a triangle mesh
+
+ align:start position:0%
+of a triangle mesh
+ 
+
+ align:start position:0%
+of a triangle mesh
+uh and get pretty far including some
+
+ align:start position:0%
+uh and get pretty far including some
+ 
+
+ align:start position:0%
+uh and get pretty far including some
+some constructions of topology like the
+
+ align:start position:0%
+some constructions of topology like the
+ 
+
+ align:start position:0%
+some constructions of topology like the
+durant complex and so on
+
+ align:start position:0%
+durant complex and so on
+ 
+
+ align:start position:0%
+durant complex and so on
+i would argue actually if you take our
+
+ align:start position:0%
+i would argue actually if you take our
+ 
+
+ align:start position:0%
+i would argue actually if you take our
+course and then the differential
+
+ align:start position:0%
+course and then the differential
+ 
+
+ align:start position:0%
+course and then the differential
+geometry courses in that department
+
+ align:start position:0%
+geometry courses in that department
+ 
+
+ align:start position:0%
+geometry courses in that department
+somehow some of the indices and
+
+ align:start position:0%
+somehow some of the indices and
+ 
+
+ align:start position:0%
+somehow some of the indices and
+headaches that you often encounter
+
+ align:start position:0%
+headaches that you often encounter
+ 
+
+ align:start position:0%
+headaches that you often encounter
+in that world are much more concrete
+
+ align:start position:0%
+in that world are much more concrete
+ 
+
+ align:start position:0%
+in that world are much more concrete
+when you try to make them work on a mesh
+
+ align:start position:0%
+when you try to make them work on a mesh
+ 
+
+ align:start position:0%
+when you try to make them work on a mesh
+in any event i think i've already spent
+
+ align:start position:0%
+in any event i think i've already spent
+ 
+
+ align:start position:0%
+in any event i think i've already spent
+all of my time i can tell you a little
+
+ align:start position:0%
+all of my time i can tell you a little
+ 
+
+ align:start position:0%
+all of my time i can tell you a little
+bit about uh
+
+ align:start position:0%
+bit about uh
+ 
+
+ align:start position:0%
+bit about uh
+research uh in our group um so i
+
+ align:start position:0%
+research uh in our group um so i
+ 
+
+ align:start position:0%
+research uh in our group um so i
+leave kind of a weird extremely broad
+
+ align:start position:0%
+leave kind of a weird extremely broad
+ 
+
+ align:start position:0%
+leave kind of a weird extremely broad
+group where some of our students are
+
+ align:start position:0%
+group where some of our students are
+ 
+
+ align:start position:0%
+group where some of our students are
+essentially theory students
+
+ align:start position:0%
+essentially theory students
+ 
+
+ align:start position:0%
+essentially theory students
+what's your keyboard i'm sorry it was a
+
+ align:start position:0%
+what's your keyboard i'm sorry it was a
+ 
+
+ align:start position:0%
+what's your keyboard i'm sorry it was a
+reflex
+
+ align:start position:0%
+reflex
+ 
+
+ align:start position:0%
+reflex
+um but it was fast uh all right so
+
+ align:start position:0%
+um but it was fast uh all right so
+ 
+
+ align:start position:0%
+um but it was fast uh all right so
+we have some students whose background
+
+ align:start position:0%
+we have some students whose background
+ 
+
+ align:start position:0%
+we have some students whose background
+is not other ones that like we're in
+
+ align:start position:0%
+is not other ones that like we're in
+ 
+
+ align:start position:0%
+is not other ones that like we're in
+autonomous driving industry and decided
+
+ align:start position:0%
+autonomous driving industry and decided
+ 
+
+ align:start position:0%
+autonomous driving industry and decided
+to come back and
+
+ align:start position:0%
+to come back and
+ 
+
+ align:start position:0%
+to come back and
+uh uh work in research and so
+
+ align:start position:0%
+uh uh work in research and so
+ 
+
+ align:start position:0%
+uh uh work in research and so
+because of that we have this extremely
+
+ align:start position:0%
+because of that we have this extremely
+ 
+
+ align:start position:0%
+because of that we have this extremely
+broad set of research problems
+
+ align:start position:0%
+broad set of research problems
+ 
+
+ align:start position:0%
+broad set of research problems
+everything from
+
+ align:start position:0%
+everything from
+ 
+
+ align:start position:0%
+everything from
+the sort of classic machine learning
+
+ align:start position:0%
+the sort of classic machine learning
+ 
+
+ align:start position:0%
+the sort of classic machine learning
+problems you might encounter in
+
+ align:start position:0%
+problems you might encounter in
+ 
+
+ align:start position:0%
+problems you might encounter in
+in geometry world like if i have a
+
+ align:start position:0%
+in geometry world like if i have a
+ 
+
+ align:start position:0%
+in geometry world like if i have a
+self-driving car and i want to identify
+
+ align:start position:0%
+self-driving car and i want to identify
+ 
+
+ align:start position:0%
+self-driving car and i want to identify
+pedestrians and
+
+ align:start position:0%
+pedestrians and
+ 
+
+ align:start position:0%
+pedestrians and
+other cars on the road in an efficient
+
+ align:start position:0%
+other cars on the road in an efficient
+ 
+
+ align:start position:0%
+other cars on the road in an efficient
+and accurate fashion
+
+ align:start position:0%
+and accurate fashion
+ 
+
+ align:start position:0%
+and accurate fashion
+um by the way part of that is machine
+
+ align:start position:0%
+um by the way part of that is machine
+ 
+
+ align:start position:0%
+um by the way part of that is machine
+learning and deep
+
+ align:start position:0%
+learning and deep
+ 
+
+ align:start position:0%
+learning and deep
+whatever but there's another part which
+
+ align:start position:0%
+whatever but there's another part which
+ 
+
+ align:start position:0%
+whatever but there's another part which
+is algorithms because actually what
+
+ align:start position:0%
+is algorithms because actually what
+ 
+
+ align:start position:0%
+is algorithms because actually what
+comes into your lidar scanner
+
+ align:start position:0%
+comes into your lidar scanner
+ 
+
+ align:start position:0%
+comes into your lidar scanner
+is on the order of like thousands of
+
+ align:start position:0%
+is on the order of like thousands of
+ 
+
+ align:start position:0%
+is on the order of like thousands of
+points and some
+
+ align:start position:0%
+points and some
+ 
+
+ align:start position:0%
+points and some
+minuscule fraction of time and time
+
+ align:start position:0%
+minuscule fraction of time and time
+ 
+
+ align:start position:0%
+minuscule fraction of time and time
+complexity
+
+ align:start position:0%
+complexity
+ 
+
+ align:start position:0%
+complexity
+of your learning algorithm actually is
+
+ align:start position:0%
+of your learning algorithm actually is
+ 
+
+ align:start position:0%
+of your learning algorithm actually is
+really critical to get right
+
+ align:start position:0%
+really critical to get right
+ 
+
+ align:start position:0%
+really critical to get right
+and something that there are a lot of
+
+ align:start position:0%
+and something that there are a lot of
+ 
+
+ align:start position:0%
+and something that there are a lot of
+open problems right now because it's
+
+ align:start position:0%
+open problems right now because it's
+ 
+
+ align:start position:0%
+open problems right now because it's
+really not compatible with the hardware
+
+ align:start position:0%
+really not compatible with the hardware
+ 
+
+ align:start position:0%
+really not compatible with the hardware
+architecture that
+
+ align:start position:0%
+architecture that
+ 
+
+ align:start position:0%
+architecture that
+these cars often use uh we also look at
+
+ align:start position:0%
+these cars often use uh we also look at
+ 
+
+ align:start position:0%
+these cars often use uh we also look at
+geometry problems like if i give you
+
+ align:start position:0%
+geometry problems like if i give you
+ 
+
+ align:start position:0%
+geometry problems like if i give you
+data can i find a geometric structure
+
+ align:start position:0%
+data can i find a geometric structure
+ 
+
+ align:start position:0%
+data can i find a geometric structure
+uh so a sort of classic example of
+
+ align:start position:0%
+uh so a sort of classic example of
+ 
+
+ align:start position:0%
+uh so a sort of classic example of
+natural language processing
+
+ align:start position:0%
+natural language processing
+ 
+
+ align:start position:0%
+natural language processing
+where we use words like near and far you
+
+ align:start position:0%
+where we use words like near and far you
+ 
+
+ align:start position:0%
+where we use words like near and far you
+know in terms of semantics and meaning
+
+ align:start position:0%
+know in terms of semantics and meaning
+ 
+
+ align:start position:0%
+know in terms of semantics and meaning
+all the time
+
+ align:start position:0%
+all the time
+ 
+
+ align:start position:0%
+all the time
+the question is can we actually find an
+
+ align:start position:0%
+the question is can we actually find an
+ 
+
+ align:start position:0%
+the question is can we actually find an
+embedding of our
+
+ align:start position:0%
+embedding of our
+ 
+
+ align:start position:0%
+embedding of our
+you know word data into a geometric
+
+ align:start position:0%
+you know word data into a geometric
+ 
+
+ align:start position:0%
+you know word data into a geometric
+space to facilitate the kind of
+
+ align:start position:0%
+space to facilitate the kind of
+ 
+
+ align:start position:0%
+space to facilitate the kind of
+statistical algorithms that we care
+
+ align:start position:0%
+statistical algorithms that we care
+ 
+
+ align:start position:0%
+statistical algorithms that we care
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+and of course we apply geometry to lots
+
+ align:start position:0%
+and of course we apply geometry to lots
+ 
+
+ align:start position:0%
+and of course we apply geometry to lots
+of practical problems everything from
+
+ align:start position:0%
+of practical problems everything from
+ 
+
+ align:start position:0%
+of practical problems everything from
+meshing and scientific computing which i
+
+ align:start position:0%
+meshing and scientific computing which i
+ 
+
+ align:start position:0%
+meshing and scientific computing which i
+think is sort of a classic
+
+ align:start position:0%
+think is sort of a classic
+ 
+
+ align:start position:0%
+think is sort of a classic
+uh one in fact i think we're the first
+
+ align:start position:0%
+uh one in fact i think we're the first
+ 
+
+ align:start position:0%
+uh one in fact i think we're the first
+group that sort of enumerated all the
+
+ align:start position:0%
+group that sort of enumerated all the
+ 
+
+ align:start position:0%
+group that sort of enumerated all the
+cool things that they happened to
+
+ align:start position:0%
+cool things that they happened to
+ 
+
+ align:start position:0%
+cool things that they happened to
+draw matches um which is the sort of
+
+ align:start position:0%
+draw matches um which is the sort of
+ 
+
+ align:start position:0%
+draw matches um which is the sort of
+bottom finger here i should share this
+
+ align:start position:0%
+bottom finger here i should share this
+ 
+
+ align:start position:0%
+bottom finger here i should share this
+with you because there's some fun things
+
+ align:start position:0%
+with you because there's some fun things
+ 
+
+ align:start position:0%
+with you because there's some fun things
+to look at there
+
+ align:start position:0%
+to look at there
+ 
+
+ align:start position:0%
+to look at there
+um to uh other practical problems like
+
+ align:start position:0%
+um to uh other practical problems like
+ 
+
+ align:start position:0%
+um to uh other practical problems like
+taking a
+
+ align:start position:0%
+taking a
+ 
+
+ align:start position:0%
+taking a
+you know eric took a zebra and folded it
+
+ align:start position:0%
+you know eric took a zebra and folded it
+ 
+
+ align:start position:0%
+you know eric took a zebra and folded it
+we can take a zebra and
+
+ align:start position:0%
+we can take a zebra and
+ 
+
+ align:start position:0%
+we can take a zebra and
+move its texture onto a cat or a pig or
+
+ align:start position:0%
+move its texture onto a cat or a pig or
+ 
+
+ align:start position:0%
+move its texture onto a cat or a pig or
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+off the side of the screen but if you
+
+ align:start position:0%
+off the side of the screen but if you
+ 
+
+ align:start position:0%
+off the side of the screen but if you
+download the paper is it all for the 3d
+
+ align:start position:0%
+download the paper is it all for the 3d
+ 
+
+ align:start position:0%
+download the paper is it all for the 3d
+scan
+
+ align:start position:0%
+scan
+ 
+
+ align:start position:0%
+scan
+of one of my gratitude um so
+
+ align:start position:0%
+of one of my gratitude um so
+ 
+
+ align:start position:0%
+of one of my gratitude um so
+in any event in uh my five minutes
+
+ align:start position:0%
+in any event in uh my five minutes
+ 
+
+ align:start position:0%
+in any event in uh my five minutes
+remaining here i thought
+
+ align:start position:0%
+remaining here i thought
+ 
+
+ align:start position:0%
+remaining here i thought
+i'd dig into a little bit of a detail of
+
+ align:start position:0%
+i'd dig into a little bit of a detail of
+ 
+
+ align:start position:0%
+i'd dig into a little bit of a detail of
+two or maybe one application depending
+
+ align:start position:0%
+two or maybe one application depending
+ 
+
+ align:start position:0%
+two or maybe one application depending
+on when jason and eric get bored uh
+
+ align:start position:0%
+on when jason and eric get bored uh
+ 
+
+ align:start position:0%
+on when jason and eric get bored uh
+uh and essentially my message for you
+
+ align:start position:0%
+uh and essentially my message for you
+ 
+
+ align:start position:0%
+uh and essentially my message for you
+guys is of course
+
+ align:start position:0%
+guys is of course
+ 
+
+ align:start position:0%
+guys is of course
+you know it's not broken i'm not really
+
+ align:start position:0%
+you know it's not broken i'm not really
+ 
+
+ align:start position:0%
+you know it's not broken i'm not really
+a central
+
+ align:start position:0%
+a central
+ 
+
+ align:start position:0%
+a central
+cs theory group member here at mit uh
+
+ align:start position:0%
+cs theory group member here at mit uh
+ 
+
+ align:start position:0%
+cs theory group member here at mit uh
+but unfortunately for you guys 6.06 is
+
+ align:start position:0%
+but unfortunately for you guys 6.06 is
+ 
+
+ align:start position:0%
+but unfortunately for you guys 6.06 is
+unavoidable even if you want to go into
+
+ align:start position:0%
+unavoidable even if you want to go into
+ 
+
+ align:start position:0%
+unavoidable even if you want to go into
+deep learning statistics whatever data
+
+ align:start position:0%
+deep learning statistics whatever data
+ 
+
+ align:start position:0%
+deep learning statistics whatever data
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+you're going to encounter the material
+
+ align:start position:0%
+you're going to encounter the material
+ 
+
+ align:start position:0%
+you're going to encounter the material
+that you've seen in this course and in
+
+ align:start position:0%
+that you've seen in this course and in
+ 
+
+ align:start position:0%
+that you've seen in this course and in
+fact it's really
+
+ align:start position:0%
+fact it's really
+ 
+
+ align:start position:0%
+fact it's really
+the bread and butter of just about
+
+ align:start position:0%
+the bread and butter of just about
+ 
+
+ align:start position:0%
+the bread and butter of just about
+everything everybody does here in this
+
+ align:start position:0%
+everything everybody does here in this
+ 
+
+ align:start position:0%
+everything everybody does here in this
+data center
+
+ align:start position:0%
+data center
+ 
+
+ align:start position:0%
+data center
+so i thought i'd give you two quick
+
+ align:start position:0%
+so i thought i'd give you two quick
+ 
+
+ align:start position:0%
+so i thought i'd give you two quick
+examples one of which lifted from my
+
+ align:start position:0%
+examples one of which lifted from my
+ 
+
+ align:start position:0%
+examples one of which lifted from my
+teaching one for my research
+
+ align:start position:0%
+teaching one for my research
+ 
+
+ align:start position:0%
+teaching one for my research
+so uh if you continue with me next fall
+
+ align:start position:0%
+so uh if you continue with me next fall
+ 
+
+ align:start position:0%
+so uh if you continue with me next fall
+uh we'll teach
+
+ align:start position:0%
+uh we'll teach
+ 
+
+ align:start position:0%
+uh we'll teach
+6837 which is the intro to computer
+
+ align:start position:0%
+6837 which is the intro to computer
+ 
+
+ align:start position:0%
+6837 which is the intro to computer
+graphics course
+
+ align:start position:0%
+graphics course
+ 
+
+ align:start position:0%
+graphics course
+one thing that's always amazing to
+
+ align:start position:0%
+one thing that's always amazing to
+ 
+
+ align:start position:0%
+one thing that's always amazing to
+students is these algorithms that
+
+ align:start position:0%
+students is these algorithms that
+ 
+
+ align:start position:0%
+students is these algorithms that
+produce these
+
+ align:start position:0%
+produce these
+ 
+
+ align:start position:0%
+produce these
+images can fit in about 10 20 lines of
+
+ align:start position:0%
+images can fit in about 10 20 lines of
+ 
+
+ align:start position:0%
+images can fit in about 10 20 lines of
+code um so a really
+
+ align:start position:0%
+code um so a really
+ 
+
+ align:start position:0%
+code um so a really
+this is totally facetious because if you
+
+ align:start position:0%
+this is totally facetious because if you
+ 
+
+ align:start position:0%
+this is totally facetious because if you
+want those beautiful images and you use
+
+ align:start position:0%
+want those beautiful images and you use
+ 
+
+ align:start position:0%
+want those beautiful images and you use
+those 20 lines of code
+
+ align:start position:0%
+those 20 lines of code
+ 
+
+ align:start position:0%
+those 20 lines of code
+you'll be waiting until the universe to
+
+ align:start position:0%
+you'll be waiting until the universe to
+ 
+
+ align:start position:0%
+you'll be waiting until the universe to
+actually compute these things but in any
+
+ align:start position:0%
+actually compute these things but in any
+ 
+
+ align:start position:0%
+actually compute these things but in any
+event uh one nice one for rendering so
+
+ align:start position:0%
+event uh one nice one for rendering so
+ 
+
+ align:start position:0%
+event uh one nice one for rendering so
+drawing a bunch of shapes on your screen
+
+ align:start position:0%
+drawing a bunch of shapes on your screen
+ 
+
+ align:start position:0%
+drawing a bunch of shapes on your screen
+something called ray casting
+
+ align:start position:0%
+something called ray casting
+ 
+
+ align:start position:0%
+something called ray casting
+um or it's better known cousin ray
+
+ align:start position:0%
+um or it's better known cousin ray
+ 
+
+ align:start position:0%
+um or it's better known cousin ray
+tracing
+
+ align:start position:0%
+tracing
+ 
+
+ align:start position:0%
+tracing
+typically the difference is whether your
+
+ align:start position:0%
+typically the difference is whether your
+ 
+
+ align:start position:0%
+typically the difference is whether your
+rays can bounce off of the surface and
+
+ align:start position:0%
+rays can bounce off of the surface and
+ 
+
+ align:start position:0%
+rays can bounce off of the surface and
+have a secondary thing
+
+ align:start position:0%
+have a secondary thing
+ 
+
+ align:start position:0%
+have a secondary thing
+uh right so here's the raycasting
+
+ align:start position:0%
+uh right so here's the raycasting
+ 
+
+ align:start position:0%
+uh right so here's the raycasting
+algorithm let's say i have a scene
+
+ align:start position:0%
+algorithm let's say i have a scene
+ 
+
+ align:start position:0%
+algorithm let's say i have a scene
+built out of spheres and cues i'm gonna
+
+ align:start position:0%
+built out of spheres and cues i'm gonna
+ 
+
+ align:start position:0%
+built out of spheres and cues i'm gonna
+have a for loop over every pixel
+
+ align:start position:0%
+have a for loop over every pixel
+ 
+
+ align:start position:0%
+have a for loop over every pixel
+on the computer screen for every pixel i
+
+ align:start position:0%
+on the computer screen for every pixel i
+ 
+
+ align:start position:0%
+on the computer screen for every pixel i
+got to discover what color that should
+
+ align:start position:0%
+got to discover what color that should
+ 
+
+ align:start position:0%
+got to discover what color that should
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+so i shoot a ray from my eyeball through
+
+ align:start position:0%
+so i shoot a ray from my eyeball through
+ 
+
+ align:start position:0%
+so i shoot a ray from my eyeball through
+that pixel
+
+ align:start position:0%
+that pixel
+ 
+
+ align:start position:0%
+that pixel
+and find the first object that it runs
+
+ align:start position:0%
+and find the first object that it runs
+ 
+
+ align:start position:0%
+and find the first object that it runs
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+it's not so hard to intersect a line
+
+ align:start position:0%
+it's not so hard to intersect a line
+ 
+
+ align:start position:0%
+it's not so hard to intersect a line
+with a sphere or a line in the cube
+
+ align:start position:0%
+with a sphere or a line in the cube
+ 
+
+ align:start position:0%
+with a sphere or a line in the cube
+so what is that algorithm well i've
+
+ align:start position:0%
+so what is that algorithm well i've
+ 
+
+ align:start position:0%
+so what is that algorithm well i've
+given it to you on the screen here
+
+ align:start position:0%
+given it to you on the screen here
+ 
+
+ align:start position:0%
+given it to you on the screen here
+not too bad to think about and i think
+
+ align:start position:0%
+not too bad to think about and i think
+ 
+
+ align:start position:0%
+not too bad to think about and i think
+you guys are all extremely well equipped
+
+ align:start position:0%
+you guys are all extremely well equipped
+ 
+
+ align:start position:0%
+you guys are all extremely well equipped
+to analyze the runtime of this
+
+ align:start position:0%
+to analyze the runtime of this
+ 
+
+ align:start position:0%
+to analyze the runtime of this
+which is roughly the uh number of pixels
+
+ align:start position:0%
+which is roughly the uh number of pixels
+ 
+
+ align:start position:0%
+which is roughly the uh number of pixels
+times the number of objects right
+
+ align:start position:0%
+times the number of objects right
+ 
+
+ align:start position:0%
+times the number of objects right
+because for every pixel
+
+ align:start position:0%
+because for every pixel
+ 
+
+ align:start position:0%
+because for every pixel
+i gotta decide what object the ray out
+
+ align:start position:0%
+i gotta decide what object the ray out
+ 
+
+ align:start position:0%
+i gotta decide what object the ray out
+of my eyeball hits first
+
+ align:start position:0%
+of my eyeball hits first
+ 
+
+ align:start position:0%
+of my eyeball hits first
+so i need a for loop over every object
+
+ align:start position:0%
+so i need a for loop over every object
+ 
+
+ align:start position:0%
+so i need a for loop over every object
+make sense
+
+ align:start position:0%
+make sense
+ 
+
+ align:start position:0%
+make sense
+cool so let's uh look at sort of a basic
+
+ align:start position:0%
+cool so let's uh look at sort of a basic
+ 
+
+ align:start position:0%
+cool so let's uh look at sort of a basic
+uh rendering
+
+ align:start position:0%
+uh rendering
+ 
+
+ align:start position:0%
+uh rendering
+problem in fact eric already uh secretly
+
+ align:start position:0%
+problem in fact eric already uh secretly
+ 
+
+ align:start position:0%
+problem in fact eric already uh secretly
+stuck this one
+
+ align:start position:0%
+stuck this one
+ 
+
+ align:start position:0%
+stuck this one
+in here so there's a very famous 3d
+
+ align:start position:0%
+in here so there's a very famous 3d
+ 
+
+ align:start position:0%
+in here so there's a very famous 3d
+model called the stanford bunny
+
+ align:start position:0%
+model called the stanford bunny
+ 
+
+ align:start position:0%
+model called the stanford bunny
+um the stanford bunny is actually a
+
+ align:start position:0%
+um the stanford bunny is actually a
+ 
+
+ align:start position:0%
+um the stanford bunny is actually a
+great example of a simplicial complex
+
+ align:start position:0%
+great example of a simplicial complex
+ 
+
+ align:start position:0%
+great example of a simplicial complex
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+in fact a manifold one triangulated
+
+ align:start position:0%
+in fact a manifold one triangulated
+ 
+
+ align:start position:0%
+in fact a manifold one triangulated
+surface
+
+ align:start position:0%
+surface
+ 
+
+ align:start position:0%
+surface
+um actually i'm not sure it's manifold
+
+ align:start position:0%
+um actually i'm not sure it's manifold
+ 
+
+ align:start position:0%
+um actually i'm not sure it's manifold
+in its original
+
+ align:start position:0%
+in its original
+ 
+
+ align:start position:0%
+in its original
+form but but usually it is uh and this
+
+ align:start position:0%
+form but but usually it is uh and this
+ 
+
+ align:start position:0%
+form but but usually it is uh and this
+uh innocent looking
+
+ align:start position:0%
+uh innocent looking
+ 
+
+ align:start position:0%
+uh innocent looking
+extremely famous 3d model uh is actually
+
+ align:start position:0%
+extremely famous 3d model uh is actually
+ 
+
+ align:start position:0%
+extremely famous 3d model uh is actually
+quite uh pernicious
+
+ align:start position:0%
+quite uh pernicious
+ 
+
+ align:start position:0%
+quite uh pernicious
+it's composed of 69 000
+
+ align:start position:0%
+it's composed of 69 000
+ 
+
+ align:start position:0%
+it's composed of 69 000
+triangles and if i wanted 1080p like you
+
+ align:start position:0%
+triangles and if i wanted 1080p like you
+ 
+
+ align:start position:0%
+triangles and if i wanted 1080p like you
+know a high def
+
+ align:start position:0%
+know a high def
+ 
+
+ align:start position:0%
+know a high def
+uh rendering of my triangle then of
+
+ align:start position:0%
+uh rendering of my triangle then of
+ 
+
+ align:start position:0%
+uh rendering of my triangle then of
+course there's there's two million
+
+ align:start position:0%
+course there's there's two million
+ 
+
+ align:start position:0%
+course there's there's two million
+pixels on the screen
+
+ align:start position:0%
+pixels on the screen
+ 
+
+ align:start position:0%
+pixels on the screen
+so if we look at our big o expression
+
+ align:start position:0%
+so if we look at our big o expression
+ 
+
+ align:start position:0%
+so if we look at our big o expression
+roughly our computation time scales like
+
+ align:start position:0%
+roughly our computation time scales like
+ 
+
+ align:start position:0%
+roughly our computation time scales like
+the product of those two big numbers
+
+ align:start position:0%
+the product of those two big numbers
+ 
+
+ align:start position:0%
+the product of those two big numbers
+uh so just to render this ugly gray
+
+ align:start position:0%
+uh so just to render this ugly gray
+ 
+
+ align:start position:0%
+uh so just to render this ugly gray
+bunny it takes me
+
+ align:start position:0%
+bunny it takes me
+ 
+
+ align:start position:0%
+bunny it takes me
+a pretty large amount of time yeah and
+
+ align:start position:0%
+a pretty large amount of time yeah and
+ 
+
+ align:start position:0%
+a pretty large amount of time yeah and
+in fact uh the real
+
+ align:start position:0%
+in fact uh the real
+ 
+
+ align:start position:0%
+in fact uh the real
+by the way the bunny is like this famous
+
+ align:start position:0%
+by the way the bunny is like this famous
+ 
+
+ align:start position:0%
+by the way the bunny is like this famous
+test case in computer graphics so if you
+
+ align:start position:0%
+test case in computer graphics so if you
+ 
+
+ align:start position:0%
+test case in computer graphics so if you
+take my class you'll be rendering
+
+ align:start position:0%
+take my class you'll be rendering
+ 
+
+ align:start position:0%
+take my class you'll be rendering
+bunnies all day
+
+ align:start position:0%
+bunnies all day
+ 
+
+ align:start position:0%
+bunnies all day
+um you know the reality is we don't want
+
+ align:start position:0%
+um you know the reality is we don't want
+ 
+
+ align:start position:0%
+um you know the reality is we don't want
+just like gray flat shaded bunnies we
+
+ align:start position:0%
+just like gray flat shaded bunnies we
+ 
+
+ align:start position:0%
+just like gray flat shaded bunnies we
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+bunnies that are transparent and
+
+ align:start position:0%
+bunnies that are transparent and
+ 
+
+ align:start position:0%
+bunnies that are transparent and
+reflecting stuff
+
+ align:start position:0%
+reflecting stuff
+ 
+
+ align:start position:0%
+reflecting stuff
+and you know i shoot my bunny with a
+
+ align:start position:0%
+and you know i shoot my bunny with a
+ 
+
+ align:start position:0%
+and you know i shoot my bunny with a
+bullet and it shatters into a million
+
+ align:start position:0%
+bullet and it shatters into a million
+ 
+
+ align:start position:0%
+bullet and it shatters into a million
+pieces and all these cool things
+
+ align:start position:0%
+pieces and all these cool things
+ 
+
+ align:start position:0%
+pieces and all these cool things
+so of course that raycasting algorithm
+
+ align:start position:0%
+so of course that raycasting algorithm
+ 
+
+ align:start position:0%
+so of course that raycasting algorithm
+and each one of these new graphics
+
+ align:start position:0%
+and each one of these new graphics
+ 
+
+ align:start position:0%
+and each one of these new graphics
+features i add
+
+ align:start position:0%
+features i add
+ 
+
+ align:start position:0%
+features i add
+only adds the time complexity of of the
+
+ align:start position:0%
+only adds the time complexity of of the
+ 
+
+ align:start position:0%
+only adds the time complexity of of the
+technique uh that i implemented
+
+ align:start position:0%
+technique uh that i implemented
+ 
+
+ align:start position:0%
+technique uh that i implemented
+so pretty quickly and indeed if you
+
+ align:start position:0%
+so pretty quickly and indeed if you
+ 
+
+ align:start position:0%
+so pretty quickly and indeed if you
+write your own ray tracer at home which
+
+ align:start position:0%
+write your own ray tracer at home which
+ 
+
+ align:start position:0%
+write your own ray tracer at home which
+i strongly encourage you to do
+
+ align:start position:0%
+i strongly encourage you to do
+ 
+
+ align:start position:0%
+i strongly encourage you to do
+what you'll discover uh is that a
+
+ align:start position:0%
+what you'll discover uh is that a
+ 
+
+ align:start position:0%
+what you'll discover uh is that a
+teleslope would be the
+
+ align:start position:0%
+teleslope would be the
+ 
+
+ align:start position:0%
+teleslope would be the
+technical phrase uh so what is our way
+
+ align:start position:0%
+technical phrase uh so what is our way
+ 
+
+ align:start position:0%
+technical phrase uh so what is our way
+out of this well
+
+ align:start position:0%
+out of this well
+ 
+
+ align:start position:0%
+out of this well
+if you take uh a37 you'll see that our
+
+ align:start position:0%
+if you take uh a37 you'll see that our
+ 
+
+ align:start position:0%
+if you take uh a37 you'll see that our
+way out of these problems and graphics
+
+ align:start position:0%
+way out of these problems and graphics
+ 
+
+ align:start position:0%
+way out of these problems and graphics
+is data structures and algorithms
+
+ align:start position:0%
+is data structures and algorithms
+ 
+
+ align:start position:0%
+is data structures and algorithms
+it's completely unavoidable so for
+
+ align:start position:0%
+it's completely unavoidable so for
+ 
+
+ align:start position:0%
+it's completely unavoidable so for
+instance obviously we spent
+
+ align:start position:0%
+instance obviously we spent
+ 
+
+ align:start position:0%
+instance obviously we spent
+quite a bit of time in this course uh
+
+ align:start position:0%
+quite a bit of time in this course uh
+ 
+
+ align:start position:0%
+quite a bit of time in this course uh
+talking about avl trees
+
+ align:start position:0%
+talking about avl trees
+ 
+
+ align:start position:0%
+talking about avl trees
+uh in age seven we'll spend a big chunk
+
+ align:start position:0%
+uh in age seven we'll spend a big chunk
+ 
+
+ align:start position:0%
+uh in age seven we'll spend a big chunk
+of our tours talking about space
+
+ align:start position:0%
+of our tours talking about space
+ 
+
+ align:start position:0%
+of our tours talking about space
+partitioning trees
+
+ align:start position:0%
+partitioning trees
+ 
+
+ align:start position:0%
+partitioning trees
+uh so here i've actually forgot what
+
+ align:start position:0%
+uh so here i've actually forgot what
+ 
+
+ align:start position:0%
+uh so here i've actually forgot what
+kind of tree this
+
+ align:start position:0%
+kind of tree this
+ 
+
+ align:start position:0%
+kind of tree this
+is i think it's a kg tree
+
+ align:start position:0%
+is i think it's a kg tree
+ 
+
+ align:start position:0%
+is i think it's a kg tree
+doesn't matter um in any event uh one
+
+ align:start position:0%
+doesn't matter um in any event uh one
+ 
+
+ align:start position:0%
+doesn't matter um in any event uh one
+thing i could do is take all the
+
+ align:start position:0%
+thing i could do is take all the
+ 
+
+ align:start position:0%
+thing i could do is take all the
+uh triangles in my bunny and i could put
+
+ align:start position:0%
+uh triangles in my bunny and i could put
+ 
+
+ align:start position:0%
+uh triangles in my bunny and i could put
+the entire bunny in a giant cube
+
+ align:start position:0%
+the entire bunny in a giant cube
+ 
+
+ align:start position:0%
+the entire bunny in a giant cube
+right then with the property that the
+
+ align:start position:0%
+right then with the property that the
+ 
+
+ align:start position:0%
+right then with the property that the
+cube is outside of my let's say i
+
+ align:start position:0%
+cube is outside of my let's say i
+ 
+
+ align:start position:0%
+cube is outside of my let's say i
+cast a ray and the ray doesn't touch the
+
+ align:start position:0%
+cast a ray and the ray doesn't touch the
+ 
+
+ align:start position:0%
+cast a ray and the ray doesn't touch the
+cube
+
+ align:start position:0%
+cube
+ 
+
+ align:start position:0%
+cube
+can the ray touch the bunny no right
+
+ align:start position:0%
+can the ray touch the bunny no right
+ 
+
+ align:start position:0%
+can the ray touch the bunny no right
+zing's right pass it
+
+ align:start position:0%
+zing's right pass it
+ 
+
+ align:start position:0%
+zing's right pass it
+right so suddenly i just saved myself a
+
+ align:start position:0%
+right so suddenly i just saved myself a
+ 
+
+ align:start position:0%
+right so suddenly i just saved myself a
+lot of computation time right i don't
+
+ align:start position:0%
+lot of computation time right i don't
+ 
+
+ align:start position:0%
+lot of computation time right i don't
+have to iterate over all the triangles
+
+ align:start position:0%
+have to iterate over all the triangles
+ 
+
+ align:start position:0%
+have to iterate over all the triangles
+inside of the bunny to see whether they
+
+ align:start position:0%
+inside of the bunny to see whether they
+ 
+
+ align:start position:0%
+inside of the bunny to see whether they
+hit the ray or not because i already
+
+ align:start position:0%
+hit the ray or not because i already
+ 
+
+ align:start position:0%
+hit the ray or not because i already
+convinced myself by this conservative
+
+ align:start position:0%
+convinced myself by this conservative
+ 
+
+ align:start position:0%
+convinced myself by this conservative
+test
+
+ align:start position:0%
+test
+ 
+
+ align:start position:0%
+test
+that i didn't hit even the bounding box
+
+ align:start position:0%
+that i didn't hit even the bounding box
+ 
+
+ align:start position:0%
+that i didn't hit even the bounding box
+of the whole body
+
+ align:start position:0%
+of the whole body
+ 
+
+ align:start position:0%
+of the whole body
+yeah well that's sort of a nice order
+
+ align:start position:0%
+yeah well that's sort of a nice order
+ 
+
+ align:start position:0%
+yeah well that's sort of a nice order
+one speed up but depending on how big
+
+ align:start position:0%
+one speed up but depending on how big
+ 
+
+ align:start position:0%
+one speed up but depending on how big
+the bunny
+
+ align:start position:0%
+the bunny
+ 
+
+ align:start position:0%
+the bunny
+is relative to the size of my rendered
+
+ align:start position:0%
+is relative to the size of my rendered
+ 
+
+ align:start position:0%
+is relative to the size of my rendered
+image that might not be a super useful
+
+ align:start position:0%
+image that might not be a super useful
+ 
+
+ align:start position:0%
+image that might not be a super useful
+uh efficiency test but of course what
+
+ align:start position:0%
+uh efficiency test but of course what
+ 
+
+ align:start position:0%
+uh efficiency test but of course what
+could i do i could take the
+
+ align:start position:0%
+could i do i could take the
+ 
+
+ align:start position:0%
+could i do i could take the
+box containing the bunny i could slice
+
+ align:start position:0%
+box containing the bunny i could slice
+ 
+
+ align:start position:0%
+box containing the bunny i could slice
+it in half and i would say it does my
+
+ align:start position:0%
+it in half and i would say it does my
+ 
+
+ align:start position:0%
+it in half and i would say it does my
+you know does my ray hit the front or
+
+ align:start position:0%
+you know does my ray hit the front or
+ 
+
+ align:start position:0%
+you know does my ray hit the front or
+the back of the bunny or maybe both
+
+ align:start position:0%
+the back of the bunny or maybe both
+ 
+
+ align:start position:0%
+the back of the bunny or maybe both
+that's where you got it that's where
+
+ align:start position:0%
+that's where you got it that's where
+ 
+
+ align:start position:0%
+that's where you got it that's where
+things get done
+
+ align:start position:0%
+things get done
+ 
+
+ align:start position:0%
+things get done
+um and and so on so now you have this
+
+ align:start position:0%
+um and and so on so now you have this
+ 
+
+ align:start position:0%
+um and and so on so now you have this
+nice recursive
+
+ align:start position:0%
+nice recursive
+ 
+
+ align:start position:0%
+nice recursive
+tree structure where i keep taking the
+
+ align:start position:0%
+tree structure where i keep taking the
+ 
+
+ align:start position:0%
+tree structure where i keep taking the
+box containing my bunny and chopping it
+
+ align:start position:0%
+box containing my bunny and chopping it
+ 
+
+ align:start position:0%
+box containing my bunny and chopping it
+in half
+
+ align:start position:0%
+in half
+ 
+
+ align:start position:0%
+in half
+and placing uh in some sense usually the
+
+ align:start position:0%
+and placing uh in some sense usually the
+ 
+
+ align:start position:0%
+and placing uh in some sense usually the
+the triangles maybe not the leaves of my
+
+ align:start position:0%
+the triangles maybe not the leaves of my
+ 
+
+ align:start position:0%
+the triangles maybe not the leaves of my
+tree but that's exactly that that's
+
+ align:start position:0%
+tree but that's exactly that that's
+ 
+
+ align:start position:0%
+tree but that's exactly that that's
+probably good enough
+
+ align:start position:0%
+probably good enough
+ 
+
+ align:start position:0%
+probably good enough
+and you get a structure like what you
+
+ align:start position:0%
+and you get a structure like what you
+ 
+
+ align:start position:0%
+and you get a structure like what you
+see on the uh the screen here
+
+ align:start position:0%
+see on the uh the screen here
+ 
+
+ align:start position:0%
+see on the uh the screen here
+and why should you do that well remember
+
+ align:start position:0%
+and why should you do that well remember
+ 
+
+ align:start position:0%
+and why should you do that well remember
+it takes sort of pn
+
+ align:start position:0%
+it takes sort of pn
+ 
+
+ align:start position:0%
+it takes sort of pn
+time to render my image of my bunny
+
+ align:start position:0%
+time to render my image of my bunny
+ 
+
+ align:start position:0%
+time to render my image of my bunny
+normally
+
+ align:start position:0%
+normally
+ 
+
+ align:start position:0%
+normally
+well now the picture is actually
+
+ align:start position:0%
+well now the picture is actually
+ 
+
+ align:start position:0%
+well now the picture is actually
+misleadingly suggestive
+
+ align:start position:0%
+misleadingly suggestive
+ 
+
+ align:start position:0%
+misleadingly suggestive
+but you might think that maybe it takes
+
+ align:start position:0%
+but you might think that maybe it takes
+ 
+
+ align:start position:0%
+but you might think that maybe it takes
+roughly remember and as
+
+ align:start position:0%
+roughly remember and as
+ 
+
+ align:start position:0%
+roughly remember and as
+the number of objects in my scene p
+
+ align:start position:0%
+the number of objects in my scene p
+ 
+
+ align:start position:0%
+the number of objects in my scene p
+login time to render my bunny now
+
+ align:start position:0%
+login time to render my bunny now
+ 
+
+ align:start position:0%
+login time to render my bunny now
+because i can kind of traverse
+
+ align:start position:0%
+because i can kind of traverse
+ 
+
+ align:start position:0%
+because i can kind of traverse
+this tree of objects in my scene of
+
+ align:start position:0%
+this tree of objects in my scene of
+ 
+
+ align:start position:0%
+this tree of objects in my scene of
+course notice i put a question mark here
+
+ align:start position:0%
+course notice i put a question mark here
+ 
+
+ align:start position:0%
+course notice i put a question mark here
+and and the devil's in the details here
+
+ align:start position:0%
+and and the devil's in the details here
+ 
+
+ align:start position:0%
+and and the devil's in the details here
+in fact i think computer graphics people
+
+ align:start position:0%
+in fact i think computer graphics people
+ 
+
+ align:start position:0%
+in fact i think computer graphics people
+often believe that the rendering
+
+ align:start position:0%
+often believe that the rendering
+ 
+
+ align:start position:0%
+often believe that the rendering
+algorithm takes
+
+ align:start position:0%
+algorithm takes
+ 
+
+ align:start position:0%
+algorithm takes
+p log in time that's often not possible
+
+ align:start position:0%
+p log in time that's often not possible
+ 
+
+ align:start position:0%
+p log in time that's often not possible
+although kind of there's an interesting
+
+ align:start position:0%
+although kind of there's an interesting
+ 
+
+ align:start position:0%
+although kind of there's an interesting
+question which is that
+
+ align:start position:0%
+question which is that
+ 
+
+ align:start position:0%
+question which is that
+the heuristics they use for building
+
+ align:start position:0%
+the heuristics they use for building
+ 
+
+ align:start position:0%
+the heuristics they use for building
+these sorts of trees often do on average
+
+ align:start position:0%
+these sorts of trees often do on average
+ 
+
+ align:start position:0%
+these sorts of trees often do on average
+give them lock-in time
+
+ align:start position:0%
+give them lock-in time
+ 
+
+ align:start position:0%
+give them lock-in time
+and so there's something about their
+
+ align:start position:0%
+and so there's something about their
+ 
+
+ align:start position:0%
+and so there's something about their
+data that's making this problem easier
+
+ align:start position:0%
+data that's making this problem easier
+ 
+
+ align:start position:0%
+data that's making this problem easier
+than it might seem
+
+ align:start position:0%
+than it might seem
+ 
+
+ align:start position:0%
+than it might seem
+so we'll dig into that a little bit in
+
+ align:start position:0%
+so we'll dig into that a little bit in
+ 
+
+ align:start position:0%
+so we'll dig into that a little bit in
+the graphics class of course you're not
+
+ align:start position:0%
+the graphics class of course you're not
+ 
+
+ align:start position:0%
+the graphics class of course you're not
+going to prove as many pounds as you
+
+ align:start position:0%
+going to prove as many pounds as you
+ 
+
+ align:start position:0%
+going to prove as many pounds as you
+might in a
+
+ align:start position:0%
+might in a
+ 
+
+ align:start position:0%
+might in a
+theory course um but we're certainly
+
+ align:start position:0%
+theory course um but we're certainly
+ 
+
+ align:start position:0%
+theory course um but we're certainly
+building on the intuition that you've
+
+ align:start position:0%
+building on the intuition that you've
+ 
+
+ align:start position:0%
+building on the intuition that you've
+seen in this class
+
+ align:start position:0%
+seen in this class
+ 
+
+ align:start position:0%
+seen in this class
+to build up practical data structures
+
+ align:start position:0%
+to build up practical data structures
+ 
+
+ align:start position:0%
+to build up practical data structures
+and these data structures appear
+
+ align:start position:0%
+and these data structures appear
+ 
+
+ align:start position:0%
+and these data structures appear
+everywhere in computer graphics so for
+
+ align:start position:0%
+everywhere in computer graphics so for
+ 
+
+ align:start position:0%
+everywhere in computer graphics so for
+instance directive a6
+
+ align:start position:0%
+instance directive a6
+ 
+
+ align:start position:0%
+instance directive a6
+black directed acyclic graphs appear
+
+ align:start position:0%
+black directed acyclic graphs appear
+ 
+
+ align:start position:0%
+black directed acyclic graphs appear
+all over the place in computer graphics
+
+ align:start position:0%
+all over the place in computer graphics
+ 
+
+ align:start position:0%
+all over the place in computer graphics
+literature to describe 3d
+
+ align:start position:0%
+literature to describe 3d
+ 
+
+ align:start position:0%
+literature to describe 3d
+scenes so for example this classroom is
+
+ align:start position:0%
+scenes so for example this classroom is
+ 
+
+ align:start position:0%
+scenes so for example this classroom is
+a stark reminder of why we need
+
+ align:start position:0%
+a stark reminder of why we need
+ 
+
+ align:start position:0%
+a stark reminder of why we need
+dags and computer graphics because we
+
+ align:start position:0%
+dags and computer graphics because we
+ 
+
+ align:start position:0%
+dags and computer graphics because we
+have all of these empty seats here
+
+ align:start position:0%
+have all of these empty seats here
+ 
+
+ align:start position:0%
+have all of these empty seats here
+and they're all copies of one another so
+
+ align:start position:0%
+and they're all copies of one another so
+ 
+
+ align:start position:0%
+and they're all copies of one another so
+would it make sense for me
+
+ align:start position:0%
+would it make sense for me
+ 
+
+ align:start position:0%
+would it make sense for me
+to store however many like 100 3d models
+
+ align:start position:0%
+to store however many like 100 3d models
+ 
+
+ align:start position:0%
+to store however many like 100 3d models
+of the same chair
+
+ align:start position:0%
+of the same chair
+ 
+
+ align:start position:0%
+of the same chair
+probably not right so instead what do i
+
+ align:start position:0%
+probably not right so instead what do i
+ 
+
+ align:start position:0%
+probably not right so instead what do i
+do i have
+
+ align:start position:0%
+do i have
+ 
+
+ align:start position:0%
+do i have
+i store one instance of a chair and then
+
+ align:start position:0%
+i store one instance of a chair and then
+ 
+
+ align:start position:0%
+i store one instance of a chair and then
+some instructions on how to tile it
+
+ align:start position:0%
+some instructions on how to tile it
+ 
+
+ align:start position:0%
+some instructions on how to tile it
+into my entire scene so one way that i
+
+ align:start position:0%
+into my entire scene so one way that i
+ 
+
+ align:start position:0%
+into my entire scene so one way that i
+can do that
+
+ align:start position:0%
+can do that
+ 
+
+ align:start position:0%
+can do that
+is to think of there being a node which
+
+ align:start position:0%
+is to think of there being a node which
+ 
+
+ align:start position:0%
+is to think of there being a node which
+in a graph which knows how to draw one
+
+ align:start position:0%
+in a graph which knows how to draw one
+ 
+
+ align:start position:0%
+in a graph which knows how to draw one
+chair and now i can have a bunch of
+
+ align:start position:0%
+chair and now i can have a bunch of
+ 
+
+ align:start position:0%
+chair and now i can have a bunch of
+different nodes in my scene for all the
+
+ align:start position:0%
+different nodes in my scene for all the
+ 
+
+ align:start position:0%
+different nodes in my scene for all the
+instances of the chair that store like a
+
+ align:start position:0%
+instances of the chair that store like a
+ 
+
+ align:start position:0%
+instances of the chair that store like a
+different transformation for each one
+
+ align:start position:0%
+different transformation for each one
+ 
+
+ align:start position:0%
+different transformation for each one
+so what if you think about the graph
+
+ align:start position:0%
+so what if you think about the graph
+ 
+
+ align:start position:0%
+so what if you think about the graph
+structure here each of those is going to
+
+ align:start position:0%
+structure here each of those is going to
+ 
+
+ align:start position:0%
+structure here each of those is going to
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+into the same 3d model of the chair for
+
+ align:start position:0%
+into the same 3d model of the chair for
+ 
+
+ align:start position:0%
+into the same 3d model of the chair for
+rendering
+
+ align:start position:0%
+rendering
+ 
+
+ align:start position:0%
+rendering
+and that makes a direct and acyclic
+
+ align:start position:0%
+and that makes a direct and acyclic
+ 
+
+ align:start position:0%
+and that makes a direct and acyclic
+graph structure um called a scene graph
+
+ align:start position:0%
+graph structure um called a scene graph
+ 
+
+ align:start position:0%
+graph structure um called a scene graph
+which we'll spend quite a bit of time
+
+ align:start position:0%
+which we'll spend quite a bit of time
+ 
+
+ align:start position:0%
+which we'll spend quite a bit of time
+talking about in a37 how to
+
+ align:start position:0%
+talking about in a37 how to
+ 
+
+ align:start position:0%
+talking about in a37 how to
+traverse construct all that good stuff
+
+ align:start position:0%
+traverse construct all that good stuff
+ 
+
+ align:start position:0%
+traverse construct all that good stuff
+um and there are lots of different
+
+ align:start position:0%
+um and there are lots of different
+ 
+
+ align:start position:0%
+um and there are lots of different
+models of computation
+
+ align:start position:0%
+models of computation
+ 
+
+ align:start position:0%
+models of computation
+in that universe as well um your
+
+ align:start position:0%
+in that universe as well um your
+ 
+
+ align:start position:0%
+in that universe as well um your
+graphics card
+
+ align:start position:0%
+graphics card
+ 
+
+ align:start position:0%
+graphics card
+is a very specific kind of parallel
+
+ align:start position:0%
+is a very specific kind of parallel
+ 
+
+ align:start position:0%
+is a very specific kind of parallel
+processor that's kind of like
+
+ align:start position:0%
+processor that's kind of like
+ 
+
+ align:start position:0%
+processor that's kind of like
+lucille ball on the conveyor belt you
+
+ align:start position:0%
+lucille ball on the conveyor belt you
+ 
+
+ align:start position:0%
+lucille ball on the conveyor belt you
+know hammering at the same object over
+
+ align:start position:0%
+know hammering at the same object over
+ 
+
+ align:start position:0%
+know hammering at the same object over
+and over again
+
+ align:start position:0%
+and over again
+ 
+
+ align:start position:0%
+and over again
+but if you ask it to do anything other
+
+ align:start position:0%
+but if you ask it to do anything other
+ 
+
+ align:start position:0%
+but if you ask it to do anything other
+than one thing it knows how to do it's a
+
+ align:start position:0%
+than one thing it knows how to do it's a
+ 
+
+ align:start position:0%
+than one thing it knows how to do it's a
+bunch of data at a time
+
+ align:start position:0%
+bunch of data at a time
+ 
+
+ align:start position:0%
+bunch of data at a time
+uh then all of your computation grants
+
+ align:start position:0%
+uh then all of your computation grants
+ 
+
+ align:start position:0%
+uh then all of your computation grants
+for health this is called
+
+ align:start position:0%
+for health this is called
+ 
+
+ align:start position:0%
+for health this is called
+single instruction multiple data
+
+ align:start position:0%
+single instruction multiple data
+ 
+
+ align:start position:0%
+single instruction multiple data
+parallelism sim d
+
+ align:start position:0%
+parallelism sim d
+ 
+
+ align:start position:0%
+parallelism sim d
+numerical algorithms matter a lot for
+
+ align:start position:0%
+numerical algorithms matter a lot for
+ 
+
+ align:start position:0%
+numerical algorithms matter a lot for
+things like fluid simulation
+
+ align:start position:0%
+things like fluid simulation
+ 
+
+ align:start position:0%
+things like fluid simulation
+in approximate approximation algorithms
+
+ align:start position:0%
+in approximate approximation algorithms
+ 
+
+ align:start position:0%
+in approximate approximation algorithms
+are quite critical too
+
+ align:start position:0%
+are quite critical too
+ 
+
+ align:start position:0%
+are quite critical too
+um in computer graphics the the
+
+ align:start position:0%
+um in computer graphics the the
+ 
+
+ align:start position:0%
+um in computer graphics the the
+complexity is kind of interesting
+
+ align:start position:0%
+complexity is kind of interesting
+ 
+
+ align:start position:0%
+complexity is kind of interesting
+because of course
+
+ align:start position:0%
+because of course
+ 
+
+ align:start position:0%
+because of course
+your eyeball is sensitive to about 29.97
+
+ align:start position:0%
+your eyeball is sensitive to about 29.97
+ 
+
+ align:start position:0%
+your eyeball is sensitive to about 29.97
+frames per second worth of material
+
+ align:start position:0%
+frames per second worth of material
+ 
+
+ align:start position:0%
+frames per second worth of material
+um you can choose that time to do like
+
+ align:start position:0%
+um you can choose that time to do like
+ 
+
+ align:start position:0%
+um you can choose that time to do like
+really well rendering one object but
+
+ align:start position:0%
+really well rendering one object but
+ 
+
+ align:start position:0%
+really well rendering one object but
+then you take out of the time rendering
+
+ align:start position:0%
+then you take out of the time rendering
+ 
+
+ align:start position:0%
+then you take out of the time rendering
+something else
+
+ align:start position:0%
+something else
+ 
+
+ align:start position:0%
+something else
+so there's kind of an interesting
+
+ align:start position:0%
+so there's kind of an interesting
+ 
+
+ align:start position:0%
+so there's kind of an interesting
+conservation law that you have to
+
+ align:start position:0%
+conservation law that you have to
+ 
+
+ align:start position:0%
+conservation law that you have to
+balance when you solve these kinds of
+
+ align:start position:0%
+balance when you solve these kinds of
+ 
+
+ align:start position:0%
+balance when you solve these kinds of
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+which is an interesting balance now
+
+ align:start position:0%
+which is an interesting balance now
+ 
+
+ align:start position:0%
+which is an interesting balance now
+between like complexity and runtime of
+
+ align:start position:0%
+between like complexity and runtime of
+ 
+
+ align:start position:0%
+between like complexity and runtime of
+your algorithm
+
+ align:start position:0%
+your algorithm
+ 
+
+ align:start position:0%
+your algorithm
+and perception like what things can you
+
+ align:start position:0%
+and perception like what things can you
+ 
+
+ align:start position:0%
+and perception like what things can you
+get away with when you draw a scene
+
+ align:start position:0%
+get away with when you draw a scene
+ 
+
+ align:start position:0%
+get away with when you draw a scene
+and maybe like i can do tons of extra
+
+ align:start position:0%
+and maybe like i can do tons of extra
+ 
+
+ align:start position:0%
+and maybe like i can do tons of extra
+computation to get that extra shadow but
+
+ align:start position:0%
+computation to get that extra shadow but
+ 
+
+ align:start position:0%
+computation to get that extra shadow but
+it's just not worth it so i'll quickly
+
+ align:start position:0%
+it's just not worth it so i'll quickly
+ 
+
+ align:start position:0%
+it's just not worth it so i'll quickly
+sketch out another
+
+ align:start position:0%
+sketch out another
+ 
+
+ align:start position:0%
+sketch out another
+uh completely different application of
+
+ align:start position:0%
+uh completely different application of
+ 
+
+ align:start position:0%
+uh completely different application of
+uh the material that we've covered in
+
+ align:start position:0%
+uh the material that we've covered in
+ 
+
+ align:start position:0%
+uh the material that we've covered in
+6006 from my own research uh
+
+ align:start position:0%
+6006 from my own research uh
+ 
+
+ align:start position:0%
+6006 from my own research uh
+again just like eric i guess in a funny
+
+ align:start position:0%
+again just like eric i guess in a funny
+ 
+
+ align:start position:0%
+again just like eric i guess in a funny
+way both of our groups i think are kind
+
+ align:start position:0%
+way both of our groups i think are kind
+ 
+
+ align:start position:0%
+way both of our groups i think are kind
+of raw in terms of subject material like
+
+ align:start position:0%
+of raw in terms of subject material like
+ 
+
+ align:start position:0%
+of raw in terms of subject material like
+rather than
+
+ align:start position:0%
+rather than
+ 
+
+ align:start position:0%
+rather than
+some of our colleagues have like really
+
+ align:start position:0%
+some of our colleagues have like really
+ 
+
+ align:start position:0%
+some of our colleagues have like really
+laser focused on one
+
+ align:start position:0%
+laser focused on one
+ 
+
+ align:start position:0%
+laser focused on one
+topic or another um another research
+
+ align:start position:0%
+topic or another um another research
+ 
+
+ align:start position:0%
+topic or another um another research
+area that i
+
+ align:start position:0%
+area that i
+ 
+
+ align:start position:0%
+area that i
+sort of backed into uh is the area of
+
+ align:start position:0%
+sort of backed into uh is the area of
+ 
+
+ align:start position:0%
+sort of backed into uh is the area of
+political redistricting um
+
+ align:start position:0%
+political redistricting um
+ 
+
+ align:start position:0%
+political redistricting um
+this is relevant in the united states uh
+
+ align:start position:0%
+this is relevant in the united states uh
+ 
+
+ align:start position:0%
+this is relevant in the united states uh
+recently i've been reading some
+
+ align:start position:0%
+recently i've been reading some
+ 
+
+ align:start position:0%
+recently i've been reading some
+proposals about other countries which is
+
+ align:start position:0%
+proposals about other countries which is
+ 
+
+ align:start position:0%
+proposals about other countries which is
+really interesting how they do this
+
+ align:start position:0%
+really interesting how they do this
+ 
+
+ align:start position:0%
+really interesting how they do this
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+so in the u.s when we vote for people uh
+
+ align:start position:0%
+so in the u.s when we vote for people uh
+ 
+
+ align:start position:0%
+so in the u.s when we vote for people uh
+in congress
+
+ align:start position:0%
+in congress
+ 
+
+ align:start position:0%
+in congress
+by the way not necessarily for president
+
+ align:start position:0%
+by the way not necessarily for president
+ 
+
+ align:start position:0%
+by the way not necessarily for president
+this is a common uh
+
+ align:start position:0%
+this is a common uh
+ 
+
+ align:start position:0%
+this is a common uh
+misconception but uh certainly for for
+
+ align:start position:0%
+misconception but uh certainly for for
+ 
+
+ align:start position:0%
+misconception but uh certainly for for
+congress
+
+ align:start position:0%
+congress
+ 
+
+ align:start position:0%
+congress
+um your state gets divided into little
+
+ align:start position:0%
+um your state gets divided into little
+ 
+
+ align:start position:0%
+um your state gets divided into little
+regions each of which elects one member
+
+ align:start position:0%
+regions each of which elects one member
+ 
+
+ align:start position:0%
+regions each of which elects one member
+of the house
+
+ align:start position:0%
+of the house
+ 
+
+ align:start position:0%
+of the house
+and this there's sort of a subtle
+
+ align:start position:0%
+and this there's sort of a subtle
+ 
+
+ align:start position:0%
+and this there's sort of a subtle
+problem if you're not used to thinking
+
+ align:start position:0%
+problem if you're not used to thinking
+ 
+
+ align:start position:0%
+problem if you're not used to thinking
+about it or one that's like staring you
+
+ align:start position:0%
+about it or one that's like staring you
+ 
+
+ align:start position:0%
+about it or one that's like staring you
+in the face and screaming depending on
+
+ align:start position:0%
+in the face and screaming depending on
+ 
+
+ align:start position:0%
+in the face and screaming depending on
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+how often you read the the news uh in
+
+ align:start position:0%
+how often you read the the news uh in
+ 
+
+ align:start position:0%
+how often you read the the news uh in
+politics which is an issue called
+
+ align:start position:0%
+politics which is an issue called
+ 
+
+ align:start position:0%
+politics which is an issue called
+gerrymandering
+
+ align:start position:0%
+gerrymandering
+ 
+
+ align:start position:0%
+gerrymandering
+where your legislature draws the lines
+
+ align:start position:0%
+where your legislature draws the lines
+ 
+
+ align:start position:0%
+where your legislature draws the lines
+for what area on the map elects
+
+ align:start position:0%
+for what area on the map elects
+ 
+
+ align:start position:0%
+for what area on the map elects
+a member of congress and depending on
+
+ align:start position:0%
+a member of congress and depending on
+ 
+
+ align:start position:0%
+a member of congress and depending on
+how you draw the lines
+
+ align:start position:0%
+how you draw the lines
+ 
+
+ align:start position:0%
+how you draw the lines
+you can engineer different results for
+
+ align:start position:0%
+you can engineer different results for
+ 
+
+ align:start position:0%
+you can engineer different results for
+who's likely to get elected
+
+ align:start position:0%
+who's likely to get elected
+ 
+
+ align:start position:0%
+who's likely to get elected
+so for instance maybe there's some
+
+ align:start position:0%
+so for instance maybe there's some
+ 
+
+ align:start position:0%
+so for instance maybe there's some
+minority i can cluster them all together
+
+ align:start position:0%
+minority i can cluster them all together
+ 
+
+ align:start position:0%
+minority i can cluster them all together
+into one voting district
+
+ align:start position:0%
+into one voting district
+ 
+
+ align:start position:0%
+into one voting district
+then they'll only get the opportunity to
+
+ align:start position:0%
+then they'll only get the opportunity to
+ 
+
+ align:start position:0%
+then they'll only get the opportunity to
+elect one person but
+
+ align:start position:0%
+elect one person but
+ 
+
+ align:start position:0%
+elect one person but
+maybe if i divide the space where they
+
+ align:start position:0%
+maybe if i divide the space where they
+ 
+
+ align:start position:0%
+maybe if i divide the space where they
+live into two i could manage to engineer
+
+ align:start position:0%
+live into two i could manage to engineer
+ 
+
+ align:start position:0%
+live into two i could manage to engineer
+two districts
+
+ align:start position:0%
+two districts
+ 
+
+ align:start position:0%
+two districts
+with a high probability of electing
+
+ align:start position:0%
+with a high probability of electing
+ 
+
+ align:start position:0%
+with a high probability of electing
+somebody with their political interests
+
+ align:start position:0%
+somebody with their political interests
+ 
+
+ align:start position:0%
+somebody with their political interests
+in mind
+
+ align:start position:0%
+in mind
+ 
+
+ align:start position:0%
+in mind
+so it turns out that uh political
+
+ align:start position:0%
+so it turns out that uh political
+ 
+
+ align:start position:0%
+so it turns out that uh political
+redistricting in a broad sense is a
+
+ align:start position:0%
+redistricting in a broad sense is a
+ 
+
+ align:start position:0%
+redistricting in a broad sense is a
+great problem
+
+ align:start position:0%
+great problem
+ 
+
+ align:start position:0%
+great problem
+computationally even if you're a totally
+
+ align:start position:0%
+computationally even if you're a totally
+ 
+
+ align:start position:0%
+computationally even if you're a totally
+heartless theorist there's some really
+
+ align:start position:0%
+heartless theorist there's some really
+ 
+
+ align:start position:0%
+heartless theorist there's some really
+fun problems here
+
+ align:start position:0%
+fun problems here
+ 
+
+ align:start position:0%
+fun problems here
+um so for example the state of iowa we
+
+ align:start position:0%
+um so for example the state of iowa we
+ 
+
+ align:start position:0%
+um so for example the state of iowa we
+all pick on iowa because
+
+ align:start position:0%
+all pick on iowa because
+ 
+
+ align:start position:0%
+all pick on iowa because
+it has a unique law which is that your
+
+ align:start position:0%
+it has a unique law which is that your
+ 
+
+ align:start position:0%
+it has a unique law which is that your
+districts have to be built out of
+
+ align:start position:0%
+districts have to be built out of
+ 
+
+ align:start position:0%
+districts have to be built out of
+counties which are much larger than the
+
+ align:start position:0%
+counties which are much larger than the
+ 
+
+ align:start position:0%
+counties which are much larger than the
+typical census unit so computationally
+
+ align:start position:0%
+typical census unit so computationally
+ 
+
+ align:start position:0%
+typical census unit so computationally
+is easier
+
+ align:start position:0%
+is easier
+ 
+
+ align:start position:0%
+is easier
+but even in iowa um which is a giant
+
+ align:start position:0%
+but even in iowa um which is a giant
+ 
+
+ align:start position:0%
+but even in iowa um which is a giant
+grid with the exception of one
+
+ align:start position:0%
+grid with the exception of one
+ 
+
+ align:start position:0%
+grid with the exception of one
+shift in the middle which is fascinating
+
+ align:start position:0%
+shift in the middle which is fascinating
+ 
+
+ align:start position:0%
+shift in the middle which is fascinating
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i know a lot of times this is a fun fact
+
+ align:start position:0%
+i know a lot of times this is a fun fact
+ 
+
+ align:start position:0%
+i know a lot of times this is a fun fact
+like literally people were
+
+ align:start position:0%
+like literally people were
+ 
+
+ align:start position:0%
+like literally people were
+making the map of iowa and they work
+
+ align:start position:0%
+making the map of iowa and they work
+ 
+
+ align:start position:0%
+making the map of iowa and they work
+from the bottom up and the top down and
+
+ align:start position:0%
+from the bottom up and the top down and
+ 
+
+ align:start position:0%
+from the bottom up and the top down and
+it meets in the middle and their grids
+
+ align:start position:0%
+it meets in the middle and their grids
+ 
+
+ align:start position:0%
+it meets in the middle and their grids
+were shifted and now we're stuck with
+
+ align:start position:0%
+were shifted and now we're stuck with
+ 
+
+ align:start position:0%
+were shifted and now we're stuck with
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and it has an interesting effect on the
+
+ align:start position:0%
+and it has an interesting effect on the
+ 
+
+ align:start position:0%
+and it has an interesting effect on the
+topology of your graph because it looks
+
+ align:start position:0%
+topology of your graph because it looks
+ 
+
+ align:start position:0%
+topology of your graph because it looks
+like squares although there's triangles
+
+ align:start position:0%
+like squares although there's triangles
+ 
+
+ align:start position:0%
+like squares although there's triangles
+in the middle
+
+ align:start position:0%
+in the middle
+ 
+
+ align:start position:0%
+in the middle
+uh but in any event um even though
+
+ align:start position:0%
+uh but in any event um even though
+ 
+
+ align:start position:0%
+uh but in any event um even though
+there's only 99 counties in four
+
+ align:start position:0%
+there's only 99 counties in four
+ 
+
+ align:start position:0%
+there's only 99 counties in four
+districts there's approximately
+
+ align:start position:0%
+districts there's approximately
+ 
+
+ align:start position:0%
+districts there's approximately
+quintillions of possible ways you can
+
+ align:start position:0%
+quintillions of possible ways you can
+ 
+
+ align:start position:0%
+quintillions of possible ways you can
+divide that state into four contiguous
+
+ align:start position:0%
+divide that state into four contiguous
+ 
+
+ align:start position:0%
+divide that state into four contiguous
+districts that satisfy the rules as they
+
+ align:start position:0%
+districts that satisfy the rules as they
+ 
+
+ align:start position:0%
+districts that satisfy the rules as they
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+at least if you read them kind of
+
+ align:start position:0%
+at least if you read them kind of
+ 
+
+ align:start position:0%
+at least if you read them kind of
+literally in the uh the the law
+
+ align:start position:0%
+literally in the uh the the law
+ 
+
+ align:start position:0%
+literally in the uh the the law
+um so it seems like computers are useful
+
+ align:start position:0%
+um so it seems like computers are useful
+ 
+
+ align:start position:0%
+um so it seems like computers are useful
+but unfortunately it's a little subtle
+
+ align:start position:0%
+but unfortunately it's a little subtle
+ 
+
+ align:start position:0%
+but unfortunately it's a little subtle
+how right so for instance
+
+ align:start position:0%
+how right so for instance
+ 
+
+ align:start position:0%
+how right so for instance
+there's no single best districting
+
+ align:start position:0%
+there's no single best districting
+ 
+
+ align:start position:0%
+there's no single best districting
+planner out there um
+
+ align:start position:0%
+planner out there um
+ 
+
+ align:start position:0%
+planner out there um
+i can't think of a single state with a
+
+ align:start position:0%
+i can't think of a single state with a
+ 
+
+ align:start position:0%
+i can't think of a single state with a
+law that gives you an objective function
+
+ align:start position:0%
+law that gives you an objective function
+ 
+
+ align:start position:0%
+law that gives you an objective function
+you know similar to
+
+ align:start position:0%
+you know similar to
+ 
+
+ align:start position:0%
+you know similar to
+you know whatever cute you know
+
+ align:start position:0%
+you know whatever cute you know
+ 
+
+ align:start position:0%
+you know whatever cute you know
+characters that we've had in 6706 you
+
+ align:start position:0%
+characters that we've had in 6706 you
+ 
+
+ align:start position:0%
+characters that we've had in 6706 you
+know they often have
+
+ align:start position:0%
+know they often have
+ 
+
+ align:start position:0%
+know they often have
+very clear objectives in life but
+
+ align:start position:0%
+very clear objectives in life but
+ 
+
+ align:start position:0%
+very clear objectives in life but
+unfortunately redistricting uh that's
+
+ align:start position:0%
+unfortunately redistricting uh that's
+ 
+
+ align:start position:0%
+unfortunately redistricting uh that's
+very rarely the case you know you have
+
+ align:start position:0%
+very rarely the case you know you have
+ 
+
+ align:start position:0%
+very rarely the case you know you have
+to balance continuity population balance
+
+ align:start position:0%
+to balance continuity population balance
+ 
+
+ align:start position:0%
+to balance continuity population balance
+compactness all these different things
+
+ align:start position:0%
+compactness all these different things
+ 
+
+ align:start position:0%
+compactness all these different things
+uh reality check number two is that
+
+ align:start position:0%
+uh reality check number two is that
+ 
+
+ align:start position:0%
+uh reality check number two is that
+even if somebody did give you an
+
+ align:start position:0%
+even if somebody did give you an
+ 
+
+ align:start position:0%
+even if somebody did give you an
+objective function for just about any
+
+ align:start position:0%
+objective function for just about any
+ 
+
+ align:start position:0%
+objective function for just about any
+interesting objective function it's very
+
+ align:start position:0%
+interesting objective function it's very
+ 
+
+ align:start position:0%
+interesting objective function it's very
+obvious that
+
+ align:start position:0%
+obvious that
+ 
+
+ align:start position:0%
+obvious that
+generating the best possible districting
+
+ align:start position:0%
+generating the best possible districting
+ 
+
+ align:start position:0%
+generating the best possible districting
+plan is empty hard
+
+ align:start position:0%
+plan is empty hard
+ 
+
+ align:start position:0%
+plan is empty hard
+um and by the way it doesn't even matter
+
+ align:start position:0%
+um and by the way it doesn't even matter
+ 
+
+ align:start position:0%
+um and by the way it doesn't even matter
+because the law
+
+ align:start position:0%
+because the law
+ 
+
+ align:start position:0%
+because the law
+doesn't say that computers have to draw
+
+ align:start position:0%
+doesn't say that computers have to draw
+ 
+
+ align:start position:0%
+doesn't say that computers have to draw
+the best district right so
+
+ align:start position:0%
+the best district right so
+ 
+
+ align:start position:0%
+the best district right so
+even if p equals np you really could
+
+ align:start position:0%
+even if p equals np you really could
+ 
+
+ align:start position:0%
+even if p equals np you really could
+extract the best possible districting
+
+ align:start position:0%
+extract the best possible districting
+ 
+
+ align:start position:0%
+extract the best possible districting
+plan using an algorithm
+
+ align:start position:0%
+plan using an algorithm
+ 
+
+ align:start position:0%
+plan using an algorithm
+um it doesn't mean you have to use it at
+
+ align:start position:0%
+um it doesn't mean you have to use it at
+ 
+
+ align:start position:0%
+um it doesn't mean you have to use it at
+least the way the law is written now
+
+ align:start position:0%
+least the way the law is written now
+ 
+
+ align:start position:0%
+least the way the law is written now
+interestingly this is not true in
+
+ align:start position:0%
+interestingly this is not true in
+ 
+
+ align:start position:0%
+interestingly this is not true in
+certain parts of mexico where they
+
+ align:start position:0%
+certain parts of mexico where they
+ 
+
+ align:start position:0%
+certain parts of mexico where they
+actually make you
+
+ align:start position:0%
+actually make you
+ 
+
+ align:start position:0%
+actually make you
+compare your districting plan against
+
+ align:start position:0%
+compare your districting plan against
+ 
+
+ align:start position:0%
+compare your districting plan against
+the computer-generated one which is
+
+ align:start position:0%
+the computer-generated one which is
+ 
+
+ align:start position:0%
+the computer-generated one which is
+philosophically really interesting
+
+ align:start position:0%
+philosophically really interesting
+ 
+
+ align:start position:0%
+philosophically really interesting
+although practice it doesn't work
+
+ align:start position:0%
+although practice it doesn't work
+ 
+
+ align:start position:0%
+although practice it doesn't work
+terribly
+
+ align:start position:0%
+terribly
+ 
+
+ align:start position:0%
+terribly
+um right so uh our research has studied
+
+ align:start position:0%
+um right so uh our research has studied
+ 
+
+ align:start position:0%
+um right so uh our research has studied
+analysis of distributing plans instead
+
+ align:start position:0%
+analysis of distributing plans instead
+ 
+
+ align:start position:0%
+analysis of distributing plans instead
+so instead of writing a piece of
+
+ align:start position:0%
+so instead of writing a piece of
+ 
+
+ align:start position:0%
+so instead of writing a piece of
+software that takes in your state
+
+ align:start position:0%
+software that takes in your state
+ 
+
+ align:start position:0%
+software that takes in your state
+draws your districts and then you're
+
+ align:start position:0%
+draws your districts and then you're
+ 
+
+ align:start position:0%
+draws your districts and then you're
+done uh instead we ask statistical
+
+ align:start position:0%
+done uh instead we ask statistical
+ 
+
+ align:start position:0%
+done uh instead we ask statistical
+questions about
+
+ align:start position:0%
+questions about
+ 
+
+ align:start position:0%
+questions about
+i propose a districting plan and what
+
+ align:start position:0%
+i propose a districting plan and what
+ 
+
+ align:start position:0%
+i propose a districting plan and what
+does it look like relative to the space
+
+ align:start position:0%
+does it look like relative to the space
+ 
+
+ align:start position:0%
+does it look like relative to the space
+of the uh
+
+ align:start position:0%
+of the uh
+ 
+
+ align:start position:0%
+of the uh
+possibilities um so that of course begs
+
+ align:start position:0%
+possibilities um so that of course begs
+ 
+
+ align:start position:0%
+possibilities um so that of course begs
+the question of what are the
+
+ align:start position:0%
+the question of what are the
+ 
+
+ align:start position:0%
+the question of what are the
+possibilities
+
+ align:start position:0%
+possibilities
+ 
+
+ align:start position:0%
+possibilities
+so these are like connected graph
+
+ align:start position:0%
+so these are like connected graph
+ 
+
+ align:start position:0%
+so these are like connected graph
+partitions meaning you have a graph
+
+ align:start position:0%
+partitions meaning you have a graph
+ 
+
+ align:start position:0%
+partitions meaning you have a graph
+and now you take the vertices and you
+
+ align:start position:0%
+and now you take the vertices and you
+ 
+
+ align:start position:0%
+and now you take the vertices and you
+cluster them together
+
+ align:start position:0%
+cluster them together
+ 
+
+ align:start position:0%
+cluster them together
+in a way where they're connected to one
+
+ align:start position:0%
+in a way where they're connected to one
+ 
+
+ align:start position:0%
+in a way where they're connected to one
+another the one thing that we all agree
+
+ align:start position:0%
+another the one thing that we all agree
+ 
+
+ align:start position:0%
+another the one thing that we all agree
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+actually philosophically it's
+
+ align:start position:0%
+actually philosophically it's
+ 
+
+ align:start position:0%
+actually philosophically it's
+questionable why um
+
+ align:start position:0%
+questionable why um
+ 
+
+ align:start position:0%
+questionable why um
+is that you should be able to start at
+
+ align:start position:0%
+is that you should be able to start at
+ 
+
+ align:start position:0%
+is that you should be able to start at
+any point in your district and walk to
+
+ align:start position:0%
+any point in your district and walk to
+ 
+
+ align:start position:0%
+any point in your district and walk to
+any other one without leaving
+
+ align:start position:0%
+any other one without leaving
+ 
+
+ align:start position:0%
+any other one without leaving
+these days with the internet it's not
+
+ align:start position:0%
+these days with the internet it's not
+ 
+
+ align:start position:0%
+these days with the internet it's not
+clear that that's actually the best
+
+ align:start position:0%
+clear that that's actually the best
+ 
+
+ align:start position:0%
+clear that that's actually the best
+criteria but that's a lot that i think
+
+ align:start position:0%
+criteria but that's a lot that i think
+ 
+
+ align:start position:0%
+criteria but that's a lot that i think
+is never going to get passed in
+
+ align:start position:0%
+is never going to get passed in
+ 
+
+ align:start position:0%
+is never going to get passed in
+in your future so anyway i think i'm out
+
+ align:start position:0%
+in your future so anyway i think i'm out
+ 
+
+ align:start position:0%
+in your future so anyway i think i'm out
+of time so i don't think i'll walk you
+
+ align:start position:0%
+of time so i don't think i'll walk you
+ 
+
+ align:start position:0%
+of time so i don't think i'll walk you
+guys through the
+
+ align:start position:0%
+guys through the
+ 
+
+ align:start position:0%
+guys through the
+the theory here um if maybe i'll leave
+
+ align:start position:0%
+the theory here um if maybe i'll leave
+ 
+
+ align:start position:0%
+the theory here um if maybe i'll leave
+it in the slides uh there's a
+
+ align:start position:0%
+it in the slides uh there's a
+ 
+
+ align:start position:0%
+it in the slides uh there's a
+very simple proof that can show that at
+
+ align:start position:0%
+very simple proof that can show that at
+ 
+
+ align:start position:0%
+very simple proof that can show that at
+least the very simplest thing you might
+
+ align:start position:0%
+least the very simplest thing you might
+ 
+
+ align:start position:0%
+least the very simplest thing you might
+think of for analyzing your districting
+
+ align:start position:0%
+think of for analyzing your districting
+ 
+
+ align:start position:0%
+think of for analyzing your districting
+plan which is to say
+
+ align:start position:0%
+plan which is to say
+ 
+
+ align:start position:0%
+plan which is to say
+you propose a plan and now i want your
+
+ align:start position:0%
+you propose a plan and now i want your
+ 
+
+ align:start position:0%
+you propose a plan and now i want your
+plan to be at least
+
+ align:start position:0%
+plan to be at least
+ 
+
+ align:start position:0%
+plan to be at least
+as good under some axis that's just a
+
+ align:start position:0%
+as good under some axis that's just a
+ 
+
+ align:start position:0%
+as good under some axis that's just a
+randomly drawn one from the space of all
+
+ align:start position:0%
+randomly drawn one from the space of all
+ 
+
+ align:start position:0%
+randomly drawn one from the space of all
+possible connected partitions
+
+ align:start position:0%
+possible connected partitions
+ 
+
+ align:start position:0%
+possible connected partitions
+all possible ways i could draw the lines
+
+ align:start position:0%
+all possible ways i could draw the lines
+ 
+
+ align:start position:0%
+all possible ways i could draw the lines
+well then it might be useful to have a
+
+ align:start position:0%
+well then it might be useful to have a
+ 
+
+ align:start position:0%
+well then it might be useful to have a
+piece of software that could just
+
+ align:start position:0%
+piece of software that could just
+ 
+
+ align:start position:0%
+piece of software that could just
+randomly draw such a thing so in other
+
+ align:start position:0%
+randomly draw such a thing so in other
+ 
+
+ align:start position:0%
+randomly draw such a thing so in other
+words to draw something where the
+
+ align:start position:0%
+words to draw something where the
+ 
+
+ align:start position:0%
+words to draw something where the
+probability of any one partition
+
+ align:start position:0%
+probability of any one partition
+ 
+
+ align:start position:0%
+probability of any one partition
+is one over the number of partitions um
+
+ align:start position:0%
+is one over the number of partitions um
+ 
+
+ align:start position:0%
+is one over the number of partitions um
+this seems innocent in fact actually
+
+ align:start position:0%
+this seems innocent in fact actually
+ 
+
+ align:start position:0%
+this seems innocent in fact actually
+there's a number of papers that claim to
+
+ align:start position:0%
+there's a number of papers that claim to
+ 
+
+ align:start position:0%
+there's a number of papers that claim to
+do things like this
+
+ align:start position:0%
+do things like this
+ 
+
+ align:start position:0%
+do things like this
+but it turns out that it's a
+
+ align:start position:0%
+but it turns out that it's a
+ 
+
+ align:start position:0%
+but it turns out that it's a
+computationally uh
+
+ align:start position:0%
+computationally uh
+ 
+
+ align:start position:0%
+computationally uh
+difficult uh assuming that you believe
+
+ align:start position:0%
+difficult uh assuming that you believe
+ 
+
+ align:start position:0%
+difficult uh assuming that you believe
+that p doesn't equal np
+
+ align:start position:0%
+that p doesn't equal np
+ 
+
+ align:start position:0%
+that p doesn't equal np
+so i'll maybe leave some suggestive
+
+ align:start position:0%
+so i'll maybe leave some suggestive
+ 
+
+ align:start position:0%
+so i'll maybe leave some suggestive
+pictures uh in the slides and we can
+
+ align:start position:0%
+pictures uh in the slides and we can
+ 
+
+ align:start position:0%
+pictures uh in the slides and we can
+if you guys text me or during if we have
+
+ align:start position:0%
+if you guys text me or during if we have
+ 
+
+ align:start position:0%
+if you guys text me or during if we have
+a you know professor student chat i'm
+
+ align:start position:0%
+a you know professor student chat i'm
+ 
+
+ align:start position:0%
+a you know professor student chat i'm
+happy to sketch it out to you then
+
+ align:start position:0%
+happy to sketch it out to you then
+ 
+
+ align:start position:0%
+happy to sketch it out to you then
+um there's a very nice easy proof uh
+
+ align:start position:0%
+um there's a very nice easy proof uh
+ 
+
+ align:start position:0%
+um there's a very nice easy proof uh
+that reduces the hamiltonian cycle
+
+ align:start position:0%
+that reduces the hamiltonian cycle
+ 
+
+ align:start position:0%
+that reduces the hamiltonian cycle
+um and shows you that maybe you
+
+ align:start position:0%
+um and shows you that maybe you
+ 
+
+ align:start position:0%
+um and shows you that maybe you
+shouldn't trust these tools uh
+
+ align:start position:0%
+shouldn't trust these tools uh
+ 
+
+ align:start position:0%
+shouldn't trust these tools uh
+as much as they're argued about
+
+ align:start position:0%
+as much as they're argued about
+ 
+
+ align:start position:0%
+as much as they're argued about
+literally the supreme court a couple
+
+ align:start position:0%
+literally the supreme court a couple
+ 
+
+ align:start position:0%
+literally the supreme court a couple
+months ago
+
+ align:start position:0%
+months ago
+ 
+
+ align:start position:0%
+months ago
+by the way it was it was pretty fun like
+
+ align:start position:0%
+by the way it was it was pretty fun like
+ 
+
+ align:start position:0%
+by the way it was it was pretty fun like
+our uh expert report was referenced in
+
+ align:start position:0%
+our uh expert report was referenced in
+ 
+
+ align:start position:0%
+our uh expert report was referenced in
+the descent of the the case last summer
+
+ align:start position:0%
+the descent of the the case last summer
+ 
+
+ align:start position:0%
+the descent of the the case last summer
+um and when you read the discussion like
+
+ align:start position:0%
+um and when you read the discussion like
+ 
+
+ align:start position:0%
+um and when you read the discussion like
+you can see the judges trying to talk
+
+ align:start position:0%
+you can see the judges trying to talk
+ 
+
+ align:start position:0%
+you can see the judges trying to talk
+their way around complexity and
+
+ align:start position:0%
+their way around complexity and
+ 
+
+ align:start position:0%
+their way around complexity and
+um it's an interesting if somewhat dry
+
+ align:start position:0%
+um it's an interesting if somewhat dry
+ 
+
+ align:start position:0%
+um it's an interesting if somewhat dry
+uh read
+
+ align:start position:0%
+uh read
+ 
+
+ align:start position:0%
+uh read
+so in any event that's just the starting
+
+ align:start position:0%
+so in any event that's just the starting
+ 
+
+ align:start position:0%
+so in any event that's just the starting
+point for our research which says that
+
+ align:start position:0%
+point for our research which says that
+ 
+
+ align:start position:0%
+point for our research which says that
+of course these
+
+ align:start position:0%
+of course these
+ 
+
+ align:start position:0%
+of course these
+sampling problems are really hard and
+
+ align:start position:0%
+sampling problems are really hard and
+ 
+
+ align:start position:0%
+sampling problems are really hard and
+the question is what can you do like you
+
+ align:start position:0%
+the question is what can you do like you
+ 
+
+ align:start position:0%
+the question is what can you do like you
+throw the baby out with bath water or
+
+ align:start position:0%
+throw the baby out with bath water or
+ 
+
+ align:start position:0%
+throw the baby out with bath water or
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+um but the uh the real message here is
+
+ align:start position:0%
+um but the uh the real message here is
+ 
+
+ align:start position:0%
+um but the uh the real message here is
+of course the
+
+ align:start position:0%
+of course the
+ 
+
+ align:start position:0%
+of course the
+this course is unavoidable even in these
+
+ align:start position:0%
+this course is unavoidable even in these
+ 
+
+ align:start position:0%
+this course is unavoidable even in these
+extremely applied problems showing up in
+
+ align:start position:0%
+extremely applied problems showing up in
+ 
+
+ align:start position:0%
+extremely applied problems showing up in
+court cases or on your graphics card
+
+ align:start position:0%
+court cases or on your graphics card
+ 
+
+ align:start position:0%
+court cases or on your graphics card
+uh you're still complexity and
+
+ align:start position:0%
+uh you're still complexity and
+ 
+
+ align:start position:0%
+uh you're still complexity and
+algorithms and data structures
+
+ align:start position:0%
+algorithms and data structures
+ 
+
+ align:start position:0%
+algorithms and data structures
+are going to come back to play um so
+
+ align:start position:0%
+are going to come back to play um so
+ 
+
+ align:start position:0%
+are going to come back to play um so
+with that
+
+ align:start position:0%
+with that
+ 
+
+ align:start position:0%
+with that
+uh find our other two instructors up
+
+ align:start position:0%
+uh find our other two instructors up
+ 
+
+ align:start position:0%
+uh find our other two instructors up
+here for our final uh farewell
+
+ align:start position:0%
+here for our final uh farewell
+ 
+
+ align:start position:0%
+here for our final uh farewell
+suitably distance so algorithms are
+
+ align:start position:0%
+suitably distance so algorithms are
+ 
+
+ align:start position:0%
+suitably distance so algorithms are
+everywhere
+
+ align:start position:0%
+everywhere
+ 
+
+ align:start position:0%
+everywhere
+i hope you enjoyed this class it's been
+
+ align:start position:0%
+i hope you enjoyed this class it's been
+ 
+
+ align:start position:0%
+i hope you enjoyed this class it's been
+a lot of fun teaching you and having you
+
+ align:start position:0%
+a lot of fun teaching you and having you
+ 
+
+ align:start position:0%
+a lot of fun teaching you and having you
+as students
+
+ align:start position:0%
+as students
+ 
+
+ align:start position:0%
+as students
+even though you're not here physically
+
+ align:start position:0%
+even though you're not here physically
+ 
+
+ align:start position:0%
+even though you're not here physically
+in the room we still feel your presence
+
+ align:start position:0%
+in the room we still feel your presence
+ 
+
+ align:start position:0%
+in the room we still feel your presence
+and uh i look forward to seeing you all
+
+ align:start position:0%
+and uh i look forward to seeing you all
+ 
+
+ align:start position:0%
+and uh i look forward to seeing you all
+soon
+
+ align:start position:0%
+soon
+ 
+
+ align:start position:0%
+soon
+thanks for being a part of this fun
+
+ align:start position:0%
+thanks for being a part of this fun
+ 
+
+ align:start position:0%
+thanks for being a part of this fun
+thing i want to thank our to uh my
+
+ align:start position:0%
+thing i want to thank our to uh my
+ 
+
+ align:start position:0%
+thing i want to thank our to uh my
+co-two co-instructors for an awesome
+
+ align:start position:0%
+co-two co-instructors for an awesome
+ 
+
+ align:start position:0%
+co-two co-instructors for an awesome
+time this semester it's been a lot of
+
+ align:start position:0%
+time this semester it's been a lot of
+ 
+
+ align:start position:0%
+time this semester it's been a lot of
+fun teaching to you guys and
+
+ align:start position:0%
+fun teaching to you guys and
+ 
+
+ align:start position:0%
+fun teaching to you guys and
+thanks for uh spending 006 with us this
+
+ align:start position:0%
+thanks for uh spending 006 with us this
+ 
+
+ align:start position:0%
+thanks for uh spending 006 with us this
+term yeah thank you and hopefully we'll
+
+ align:start position:0%
+term yeah thank you and hopefully we'll
+ 
+
+ align:start position:0%
+term yeah thank you and hopefully we'll
+see you again soon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bye
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/5a2Poe_N0sQ.txt b/5a2Poe_N0sQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..add5fd4da12b1092187506f76d69408a7a0e6f26
--- /dev/null
+++ b/5a2Poe_N0sQ.txt
@@ -0,0 +1,12032 @@
+align:start position:0%
+ 
+okay for lecture
+
+ align:start position:0%
+okay for lecture
+ 
+
+ align:start position:0%
+okay for lecture
+30 uh which is you could say special
+
+ align:start position:0%
+30 uh which is you could say special
+ 
+
+ align:start position:0%
+30 uh which is you could say special
+cases of linear programming you could
+
+ align:start position:0%
+cases of linear programming you could
+ 
+
+ align:start position:0%
+cases of linear programming you could
+say special cases of integer programming
+
+ align:start position:0%
+say special cases of integer programming
+ 
+
+ align:start position:0%
+say special cases of integer programming
+but you got to say that word special
+
+ align:start position:0%
+but you got to say that word special
+ 
+
+ align:start position:0%
+but you got to say that word special
+because these are
+
+ align:start position:0%
+because these are
+ 
+
+ align:start position:0%
+because these are
+problems which fit where the answers the
+
+ align:start position:0%
+problems which fit where the answers the
+ 
+
+ align:start position:0%
+problems which fit where the answers the
+the the the the options are zero and
+
+ align:start position:0%
+the the the the options are zero and
+ 
+
+ align:start position:0%
+the the the the options are zero and
+one for the unknown X's so that in that
+
+ align:start position:0%
+one for the unknown X's so that in that
+ 
+
+ align:start position:0%
+one for the unknown X's so that in that
+way they're integer problems
+
+ align:start position:0%
+way they're integer problems
+ 
+
+ align:start position:0%
+way they're integer problems
+you a uh um we're looking at a zero or
+
+ align:start position:0%
+you a uh um we're looking at a zero or
+ 
+
+ align:start position:0%
+you a uh um we're looking at a zero or
+one marriages people are matched or
+
+ align:start position:0%
+one marriages people are matched or
+ 
+
+ align:start position:0%
+one marriages people are matched or
+they're not matched and usually integer
+
+ align:start position:0%
+they're not matched and usually integer
+ 
+
+ align:start position:0%
+they're not matched and usually integer
+programs are much harder than linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+programs because uh the Simplex method
+
+ align:start position:0%
+programs because uh the Simplex method
+ 
+
+ align:start position:0%
+programs because uh the Simplex method
+for example for linear programs you you
+
+ align:start position:0%
+for example for linear programs you you
+ 
+
+ align:start position:0%
+for example for linear programs you you
+allowed all those fractions in between
+
+ align:start position:0%
+allowed all those fractions in between
+ 
+
+ align:start position:0%
+allowed all those fractions in between
+until you hit a corner and you didn't
+
+ align:start position:0%
+until you hit a corner and you didn't
+ 
+
+ align:start position:0%
+until you hit a corner and you didn't
+know whether that corner had integer
+
+ align:start position:0%
+know whether that corner had integer
+ 
+
+ align:start position:0%
+know whether that corner had integer
+values now it's true in the
+
+ align:start position:0%
+values now it's true in the
+ 
+
+ align:start position:0%
+values now it's true in the
+particular exam example I chose it
+
+ align:start position:0%
+particular exam example I chose it
+ 
+
+ align:start position:0%
+particular exam example I chose it
+turned out that the graduate student
+
+ align:start position:0%
+turned out that the graduate student
+ 
+
+ align:start position:0%
+turned out that the graduate student
+worked
+
+ align:start position:0%
+worked
+ 
+
+ align:start position:0%
+worked
+for 4 hours
+
+ align:start position:0%
+for 4 hours
+ 
+
+ align:start position:0%
+for 4 hours
+integer and the uh others worked for
+
+ align:start position:0%
+integer and the uh others worked for
+ 
+
+ align:start position:0%
+integer and the uh others worked for
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+hours but uh the general linear program
+
+ align:start position:0%
+hours but uh the general linear program
+ 
+
+ align:start position:0%
+hours but uh the general linear program
+with ax equal B is not integer at all
+
+ align:start position:0%
+with ax equal B is not integer at all
+ 
+
+ align:start position:0%
+with ax equal B is not integer at all
+and we don't have to think about that
+
+ align:start position:0%
+and we don't have to think about that
+ 
+
+ align:start position:0%
+and we don't have to think about that
+which makes life much easier we just
+
+ align:start position:0%
+which makes life much easier we just
+ 
+
+ align:start position:0%
+which makes life much easier we just
+solve ax equal B if I add the constraint
+
+ align:start position:0%
+solve ax equal B if I add the constraint
+ 
+
+ align:start position:0%
+solve ax equal B if I add the constraint
+that the X's have to be integers that is
+
+ align:start position:0%
+that the X's have to be integers that is
+ 
+
+ align:start position:0%
+that the X's have to be integers that is
+a normally a very serious difficulty I
+
+ align:start position:0%
+a normally a very serious difficulty I
+ 
+
+ align:start position:0%
+a normally a very serious difficulty I
+get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+exponential algorithms there aren't
+
+ align:start position:0%
+exponential algorithms there aren't
+ 
+
+ align:start position:0%
+exponential algorithms there aren't
+polinomial algorithms in fact the one of
+
+ align:start position:0%
+polinomial algorithms in fact the one of
+ 
+
+ align:start position:0%
+polinomial algorithms in fact the one of
+the million dooll problems
+
+ align:start position:0%
+the million dooll problems
+ 
+
+ align:start position:0%
+the million dooll problems
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+offered uh proposed by the clay math
+
+ align:start position:0%
+offered uh proposed by the clay math
+ 
+
+ align:start position:0%
+offered uh proposed by the clay math
+Institute uh one of the seven is this
+
+ align:start position:0%
+Institute uh one of the seven is this
+ 
+
+ align:start position:0%
+Institute uh one of the seven is this
+problem uh P whether P equals
+
+ align:start position:0%
+problem uh P whether P equals
+ 
+
+ align:start position:0%
+problem uh P whether P equals
+NP so that P stands for polinomial and
+
+ align:start position:0%
+NP so that P stands for polinomial and
+ 
+
+ align:start position:0%
+NP so that P stands for polinomial and
+the n p stands for non-p polinomial the
+
+ align:start position:0%
+the n p stands for non-p polinomial the
+ 
+
+ align:start position:0%
+the n p stands for non-p polinomial the
+question is to prove that there is no
+
+ align:start position:0%
+question is to prove that there is no
+ 
+
+ align:start position:0%
+question is to prove that there is no
+algorithm of polinomial time for certain
+
+ align:start position:0%
+algorithm of polinomial time for certain
+ 
+
+ align:start position:0%
+algorithm of polinomial time for certain
+integer
+
+ align:start position:0%
+integer
+ 
+
+ align:start position:0%
+integer
+programs and that's an outstanding
+
+ align:start position:0%
+programs and that's an outstanding
+ 
+
+ align:start position:0%
+programs and that's an outstanding
+problem everybody thinks well I won't
+
+ align:start position:0%
+problem everybody thinks well I won't
+ 
+
+ align:start position:0%
+problem everybody thinks well I won't
+say everybody most people think that
+
+ align:start position:0%
+say everybody most people think that
+ 
+
+ align:start position:0%
+say everybody most people think that
+probably P doesn't equal NP that there
+
+ align:start position:0%
+probably P doesn't equal NP that there
+ 
+
+ align:start position:0%
+probably P doesn't equal NP that there
+are some polinomial Pro there are some
+
+ align:start position:0%
+are some polinomial Pro there are some
+ 
+
+ align:start position:0%
+are some polinomial Pro there are some
+there are
+
+ align:start position:0%
+there are
+ 
+
+ align:start position:0%
+there are
+some of these standard problems that
+
+ align:start position:0%
+some of these standard problems that
+ 
+
+ align:start position:0%
+some of these standard problems that
+can't be solved you can't there is
+
+ align:start position:0%
+can't be solved you can't there is
+ 
+
+ align:start position:0%
+can't be solved you can't there is
+nobody there is no algorithm of
+
+ align:start position:0%
+nobody there is no algorithm of
+ 
+
+ align:start position:0%
+nobody there is no algorithm of
+polinomial length polinomial running
+
+ align:start position:0%
+polinomial length polinomial running
+ 
+
+ align:start position:0%
+polinomial length polinomial running
+time that would do it but to to consider
+
+ align:start position:0%
+time that would do it but to to consider
+ 
+
+ align:start position:0%
+time that would do it but to to consider
+all possible algorithms and show that
+
+ align:start position:0%
+all possible algorithms and show that
+ 
+
+ align:start position:0%
+all possible algorithms and show that
+they all let you down is an unsolved
+
+ align:start position:0%
+they all let you down is an unsolved
+ 
+
+ align:start position:0%
+they all let you down is an unsolved
+problem so
+
+ align:start position:0%
+problem so
+ 
+
+ align:start position:0%
+problem so
+um but we do know so what do we know we
+
+ align:start position:0%
+um but we do know so what do we know we
+ 
+
+ align:start position:0%
+um but we do know so what do we know we
+have some problems like linear
+
+ align:start position:0%
+have some problems like linear
+ 
+
+ align:start position:0%
+have some problems like linear
+programming that we know are polinomial
+
+ align:start position:0%
+programming that we know are polinomial
+ 
+
+ align:start position:0%
+programming that we know are polinomial
+this one is
+
+ align:start position:0%
+this one is
+ 
+
+ align:start position:0%
+this one is
+polinomial we have a bunch of other
+
+ align:start position:0%
+polinomial we have a bunch of other
+ 
+
+ align:start position:0%
+polinomial we have a bunch of other
+problems that we know if we could solve
+
+ align:start position:0%
+problems that we know if we could solve
+ 
+
+ align:start position:0%
+problems that we know if we could solve
+one of them they they're equivalent you
+
+ align:start position:0%
+one of them they they're equivalent you
+ 
+
+ align:start position:0%
+one of them they they're equivalent you
+could say if there was an for one of
+
+ align:start position:0%
+could say if there was an for one of
+ 
+
+ align:start position:0%
+could say if there was an for one of
+them in polinomial time then all the
+
+ align:start position:0%
+them in polinomial time then all the
+ 
+
+ align:start position:0%
+them in polinomial time then all the
+whole lot we could solve so that's a
+
+ align:start position:0%
+whole lot we could solve so that's a
+ 
+
+ align:start position:0%
+whole lot we could solve so that's a
+whole bunch of problems that we believe
+
+ align:start position:0%
+whole bunch of problems that we believe
+ 
+
+ align:start position:0%
+whole bunch of problems that we believe
+can't be solved in polinomial time and
+
+ align:start position:0%
+can't be solved in polinomial time and
+ 
+
+ align:start position:0%
+can't be solved in polinomial time and
+the best we've been able to do is to is
+
+ align:start position:0%
+the best we've been able to do is to is
+ 
+
+ align:start position:0%
+the best we've been able to do is to is
+to get them in a in a group and say if
+
+ align:start position:0%
+to get them in a in a group and say if
+ 
+
+ align:start position:0%
+to get them in a in a group and say if
+one could do it they all could do it if
+
+ align:start position:0%
+one could do it they all could do it if
+ 
+
+ align:start position:0%
+one could do it they all could do it if
+one can't none of them can okay now I'm
+
+ align:start position:0%
+one can't none of them can okay now I'm
+ 
+
+ align:start position:0%
+one can't none of them can okay now I'm
+want to speak about these special
+
+ align:start position:0%
+want to speak about these special
+ 
+
+ align:start position:0%
+want to speak about these special
+problems that's the subject and here
+
+ align:start position:0%
+problems that's the subject and here
+ 
+
+ align:start position:0%
+problems that's the subject and here
+I've picked a coup Three Special
+
+ align:start position:0%
+I've picked a coup Three Special
+ 
+
+ align:start position:0%
+I've picked a coup Three Special
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+one two and barely May a chance to
+
+ align:start position:0%
+one two and barely May a chance to
+ 
+
+ align:start position:0%
+one two and barely May a chance to
+mention number three uh so let me tell
+
+ align:start position:0%
+mention number three uh so let me tell
+ 
+
+ align:start position:0%
+mention number three uh so let me tell
+you the marriage
+
+ align:start position:0%
+you the marriage
+ 
+
+ align:start position:0%
+you the marriage
+problem first in
+
+ align:start position:0%
+problem first in
+ 
+
+ align:start position:0%
+problem first in
+words uh so the marriage
+
+ align:start position:0%
+words uh so the marriage
+ 
+
+ align:start position:0%
+words uh so the marriage
+problem you have uh bunch of shall I say
+
+ align:start position:0%
+problem you have uh bunch of shall I say
+ 
+
+ align:start position:0%
+problem you have uh bunch of shall I say
+girls this sounds a little quaint Right
+
+ align:start position:0%
+girls this sounds a little quaint Right
+ 
+
+ align:start position:0%
+girls this sounds a little quaint Right
+girls and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boys uh
+
+ align:start position:0%
+boys uh
+ 
+
+ align:start position:0%
+boys uh
+G1 G2
+
+ align:start position:0%
+G1 G2
+ 
+
+ align:start position:0%
+G1 G2
+G3 say four four and four boys I'll take
+
+ align:start position:0%
+G3 say four four and four boys I'll take
+ 
+
+ align:start position:0%
+G3 say four four and four boys I'll take
+the problem that is described uh I think
+
+ align:start position:0%
+the problem that is described uh I think
+ 
+
+ align:start position:0%
+the problem that is described uh I think
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+page 622 of the book I
+
+ align:start position:0%
+page 622 of the book I
+ 
+
+ align:start position:0%
+page 622 of the book I
+think okay now so certain marriages
+
+ align:start position:0%
+think okay now so certain marriages
+ 
+
+ align:start position:0%
+think okay now so certain marriages
+certain
+
+ align:start position:0%
+certain
+ 
+
+ align:start position:0%
+certain
+matchings are okay others are
+
+ align:start position:0%
+matchings are okay others are
+ 
+
+ align:start position:0%
+matchings are okay others are
+not so
+
+ align:start position:0%
+not so
+ 
+
+ align:start position:0%
+not so
+suppose all those matchings are okay in
+
+ align:start position:0%
+suppose all those matchings are okay in
+ 
+
+ align:start position:0%
+suppose all those matchings are okay in
+words all four boys are acceptable for
+
+ align:start position:0%
+words all four boys are acceptable for
+ 
+
+ align:start position:0%
+words all four boys are acceptable for
+this girl so any any matching is
+
+ align:start position:0%
+this girl so any any matching is
+ 
+
+ align:start position:0%
+this girl so any any matching is
+possible but now let me look and see
+
+ align:start position:0%
+possible but now let me look and see
+ 
+
+ align:start position:0%
+possible but now let me look and see
+what the others were in this
+
+ align:start position:0%
+what the others were in this
+ 
+
+ align:start position:0%
+what the others were in this
+example uh girl two only boy four maybe
+
+ align:start position:0%
+example uh girl two only boy four maybe
+ 
+
+ align:start position:0%
+example uh girl two only boy four maybe
+I use some yellow chalk so girl two only
+
+ align:start position:0%
+I use some yellow chalk so girl two only
+ 
+
+ align:start position:0%
+I use some yellow chalk so girl two only
+boy
+
+ align:start position:0%
+boy
+ 
+
+ align:start position:0%
+boy
+four girl
+
+ align:start position:0%
+four girl
+ 
+
+ align:start position:0%
+four girl
+three two and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four and girl four for
+
+ align:start position:0%
+four and girl four for
+ 
+
+ align:start position:0%
+four and girl four for
+only number
+
+ align:start position:0%
+only number
+ 
+
+ align:start position:0%
+only number
+two I'll make that a dash line not
+
+ align:start position:0%
+two I'll make that a dash line not
+ 
+
+ align:start position:0%
+two I'll make that a dash line not
+because it's different but just to just
+
+ align:start position:0%
+because it's different but just to just
+ 
+
+ align:start position:0%
+because it's different but just to just
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh so I of course I'd like to create a
+
+ align:start position:0%
+uh so I of course I'd like to create a
+ 
+
+ align:start position:0%
+uh so I of course I'd like to create a
+matrix that describes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this this uh it's sort of a graph right
+
+ align:start position:0%
+this this uh it's sort of a graph right
+ 
+
+ align:start position:0%
+this this uh it's sort of a graph right
+this this is called actually the
+
+ align:start position:0%
+this this is called actually the
+ 
+
+ align:start position:0%
+this this is called actually the
+official name for this would be a
+
+ align:start position:0%
+official name for this would be a
+ 
+
+ align:start position:0%
+official name for this would be a
+bipartite graph so so these are nodes in
+
+ align:start position:0%
+bipartite graph so so these are nodes in
+ 
+
+ align:start position:0%
+bipartite graph so so these are nodes in
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph and the word bipartite means
+
+ align:start position:0%
+graph and the word bipartite means
+ 
+
+ align:start position:0%
+graph and the word bipartite means
+that's it's got two parts the girls and
+
+ align:start position:0%
+that's it's got two parts the girls and
+ 
+
+ align:start position:0%
+that's it's got two parts the girls and
+the boys and all edges go between the
+
+ align:start position:0%
+the boys and all edges go between the
+ 
+
+ align:start position:0%
+the boys and all edges go between the
+two parts never anyway that's bipartite
+
+ align:start position:0%
+two parts never anyway that's bipartite
+ 
+
+ align:start position:0%
+two parts never anyway that's bipartite
+graphs this is these everything I say
+
+ align:start position:0%
+graphs this is these everything I say
+ 
+
+ align:start position:0%
+graphs this is these everything I say
+today there's a host of
+
+ align:start position:0%
+today there's a host of
+ 
+
+ align:start position:0%
+today there's a host of
+people that are just have the neck of
+
+ align:start position:0%
+people that are just have the neck of
+ 
+
+ align:start position:0%
+people that are just have the neck of
+these combinatorial questions that um
+
+ align:start position:0%
+these combinatorial questions that um
+ 
+
+ align:start position:0%
+these combinatorial questions that um
+that it's become uh a very significant
+
+ align:start position:0%
+that it's become uh a very significant
+ 
+
+ align:start position:0%
+that it's become uh a very significant
+part of modern modern mathematics pure
+
+ align:start position:0%
+part of modern modern mathematics pure
+ 
+
+ align:start position:0%
+part of modern modern mathematics pure
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+applied okay so let me Express the graph
+
+ align:start position:0%
+applied okay so let me Express the graph
+ 
+
+ align:start position:0%
+applied okay so let me Express the graph
+this way the first row will
+
+ align:start position:0%
+this way the first row will
+ 
+
+ align:start position:0%
+this way the first row will
+tell
+
+ align:start position:0%
+tell
+ 
+
+ align:start position:0%
+tell
+the that the all four boys are allowed
+
+ align:start position:0%
+the that the all four boys are allowed
+ 
+
+ align:start position:0%
+the that the all four boys are allowed
+the second row will tell us that only
+
+ align:start position:0%
+the second row will tell us that only
+ 
+
+ align:start position:0%
+the second row will tell us that only
+boy one is allow boy four the second
+
+ align:start position:0%
+boy one is allow boy four the second
+ 
+
+ align:start position:0%
+boy one is allow boy four the second
+will tell us that two and four four are
+
+ align:start position:0%
+will tell us that two and four four are
+ 
+
+ align:start position:0%
+will tell us that two and four four are
+allowed and the third that only two is
+
+ align:start position:0%
+allowed and the third that only two is
+ 
+
+ align:start position:0%
+allowed and the third that only two is
+allowed that would be the Matrix that so
+
+ align:start position:0%
+allowed that would be the Matrix that so
+ 
+
+ align:start position:0%
+allowed that would be the Matrix that so
+so AIG J equals 1 AI J equals 1 if girl
+
+ align:start position:0%
+so AIG J equals 1 AI J equals 1 if girl
+ 
+
+ align:start position:0%
+so AIG J equals 1 AI J equals 1 if girl
+I and boy J are okay and otherwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+right zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else if not okay okay no
+
+ align:start position:0%
+else if not okay okay no
+ 
+
+ align:start position:0%
+else if not okay okay no
+Edge and what's our job well a complete
+
+ align:start position:0%
+Edge and what's our job well a complete
+ 
+
+ align:start position:0%
+Edge and what's our job well a complete
+matching so let me introduce few of
+
+ align:start position:0%
+matching so let me introduce few of
+ 
+
+ align:start position:0%
+matching so let me introduce few of
+these words a complete matching would be
+
+ align:start position:0%
+these words a complete matching would be
+ 
+
+ align:start position:0%
+these words a complete matching would be
+get everybody o get everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+married and the marriage problem
+
+ align:start position:0%
+married and the marriage problem
+ 
+
+ align:start position:0%
+married and the marriage problem
+is when can that be done can it be done
+
+ align:start position:0%
+is when can that be done can it be done
+ 
+
+ align:start position:0%
+is when can that be done can it be done
+in this example and what's a necessary
+
+ align:start position:0%
+in this example and what's a necessary
+ 
+
+ align:start position:0%
+in this example and what's a necessary
+and sufficient condition for doing
+
+ align:start position:0%
+and sufficient condition for doing
+ 
+
+ align:start position:0%
+and sufficient condition for doing
+it okay so the the ma and and of course
+
+ align:start position:0%
+it okay so the the ma and and of course
+ 
+
+ align:start position:0%
+it okay so the the ma and and of course
+you'll want a after the last lecture
+
+ align:start position:0%
+you'll want a after the last lecture
+ 
+
+ align:start position:0%
+you'll want a after the last lecture
+you'll want a maximization problem
+
+ align:start position:0%
+you'll want a maximization problem
+ 
+
+ align:start position:0%
+you'll want a maximization problem
+really here so the maximization problem
+
+ align:start position:0%
+really here so the maximization problem
+ 
+
+ align:start position:0%
+really here so the maximization problem
+would be how many marriages can we get
+
+ align:start position:0%
+would be how many marriages can we get
+ 
+
+ align:start position:0%
+would be how many marriages can we get
+maximize the number of marriages a
+
+ align:start position:0%
+maximize the number of marriages a
+ 
+
+ align:start position:0%
+maximize the number of marriages a
+complete matching means all married our
+
+ align:start position:0%
+complete matching means all married our
+ 
+
+ align:start position:0%
+complete matching means all married our
+problem would be to our our if we can't
+
+ align:start position:0%
+problem would be to our our if we can't
+ 
+
+ align:start position:0%
+problem would be to our our if we can't
+our problem would be to maximize the
+
+ align:start position:0%
+our problem would be to maximize the
+ 
+
+ align:start position:0%
+our problem would be to maximize the
+number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matches so this is like a specific
+
+ align:start position:0%
+matches so this is like a specific
+ 
+
+ align:start position:0%
+matches so this is like a specific
+question can everybody get
+
+ align:start position:0%
+question can everybody get
+ 
+
+ align:start position:0%
+question can everybody get
+matched and then if not the optimization
+
+ align:start position:0%
+matched and then if not the optimization
+ 
+
+ align:start position:0%
+matched and then if not the optimization
+problem the maximum problem would be to
+
+ align:start position:0%
+problem the maximum problem would be to
+ 
+
+ align:start position:0%
+problem the maximum problem would be to
+maximize the number of matches and
+
+ align:start position:0%
+maximize the number of matches and
+ 
+
+ align:start position:0%
+maximize the number of matches and
+there's going to be some minimum problem
+
+ align:start position:0%
+there's going to be some minimum problem
+ 
+
+ align:start position:0%
+there's going to be some minimum problem
+and the max will match them in at uh
+
+ align:start position:0%
+and the max will match them in at uh
+ 
+
+ align:start position:0%
+and the max will match them in at uh
+Duality at at at the winners okay now
+
+ align:start position:0%
+Duality at at at the winners okay now
+ 
+
+ align:start position:0%
+Duality at at at the winners okay now
+for this specific I would like first to
+
+ align:start position:0%
+for this specific I would like first to
+ 
+
+ align:start position:0%
+for this specific I would like first to
+ask this question is a complete is a
+
+ align:start position:0%
+ask this question is a complete is a
+ 
+
+ align:start position:0%
+ask this question is a complete is a
+complete or when is a complete matching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+sorry uh let's see um oh good
+
+ align:start position:0%
+sorry uh let's see um oh good
+ 
+
+ align:start position:0%
+sorry uh let's see um oh good
+question because it certainly will have
+
+ align:start position:0%
+question because it certainly will have
+ 
+
+ align:start position:0%
+question because it certainly will have
+a matrix
+
+ align:start position:0%
+a matrix
+ 
+
+ align:start position:0%
+a matrix
+answer well of course the Matrix of all
+
+ align:start position:0%
+answer well of course the Matrix of all
+ 
+
+ align:start position:0%
+answer well of course the Matrix of all
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would so that would be a case where
+
+ align:start position:0%
+would so that would be a case where
+ 
+
+ align:start position:0%
+would so that would be a case where
+everybody's willing to marry everybody
+
+ align:start position:0%
+everybody's willing to marry everybody
+ 
+
+ align:start position:0%
+everybody's willing to marry everybody
+and the rank is
+
+ align:start position:0%
+and the rank is
+ 
+
+ align:start position:0%
+and the rank is
+one was my first thought was well what
+
+ align:start position:0%
+one was my first thought was well what
+ 
+
+ align:start position:0%
+one was my first thought was well what
+about the identity Matrix well the
+
+ align:start position:0%
+about the identity Matrix well the
+ 
+
+ align:start position:0%
+about the identity Matrix well the
+identity Matrix of course that's a
+
+ align:start position:0%
+identity Matrix of course that's a
+ 
+
+ align:start position:0%
+identity Matrix of course that's a
+perfect we have a perfect matching girl
+
+ align:start position:0%
+perfect we have a perfect matching girl
+ 
+
+ align:start position:0%
+perfect we have a perfect matching girl
+one on Bo only I mean they're match
+
+ align:start position:0%
+one on Bo only I mean they're match
+ 
+
+ align:start position:0%
+one on Bo only I mean they're match
+their match their match their match
+
+ align:start position:0%
+their match their match their match
+ 
+
+ align:start position:0%
+their match their match their match
+great um yeah so somehow rank is
+
+ align:start position:0%
+great um yeah so somehow rank is
+ 
+
+ align:start position:0%
+great um yeah so somehow rank is
+somewhere hiding here
+
+ align:start position:0%
+somewhere hiding here
+ 
+
+ align:start position:0%
+somewhere hiding here
+uh what about this specific
+
+ align:start position:0%
+uh what about this specific
+ 
+
+ align:start position:0%
+uh what about this specific
+example could I do a complete matching
+
+ align:start position:0%
+example could I do a complete matching
+ 
+
+ align:start position:0%
+example could I do a complete matching
+and and if you tell me why not we
+
+ align:start position:0%
+and and if you tell me why not we
+ 
+
+ align:start position:0%
+and and if you tell me why not we
+probably have a guess at the general
+
+ align:start position:0%
+probably have a guess at the general
+ 
+
+ align:start position:0%
+probably have a guess at the general
+theorem why not the answer is no no and
+
+ align:start position:0%
+theorem why not the answer is no no and
+ 
+
+ align:start position:0%
+theorem why not the answer is no no and
+what's tell me the reason not all
+
+ align:start position:0%
+what's tell me the reason not all
+ 
+
+ align:start position:0%
+what's tell me the reason not all
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+col well let's that's this question of
+
+ align:start position:0%
+col well let's that's this question of
+ 
+
+ align:start position:0%
+col well let's that's this question of
+rank uh
+
+ align:start position:0%
+rank uh
+ 
+
+ align:start position:0%
+rank uh
+I'll in these in this language here of
+
+ align:start position:0%
+I'll in these in this language here of
+ 
+
+ align:start position:0%
+I'll in these in this language here of
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+edges would be maybe the way I'm looking
+
+ align:start position:0%
+edges would be maybe the way I'm looking
+ 
+
+ align:start position:0%
+edges would be maybe the way I'm looking
+and the words I yeah logically girl two
+
+ align:start position:0%
+and the words I yeah logically girl two
+ 
+
+ align:start position:0%
+and the words I yeah logically girl two
+and boy four have you got to take them
+
+ align:start position:0%
+and boy four have you got to take them
+ 
+
+ align:start position:0%
+and boy four have you got to take them
+out then the next two roads one's gone
+
+ align:start position:0%
+out then the next two roads one's gone
+ 
+
+ align:start position:0%
+out then the next two roads one's gone
+and and you've got a competition for boy
+
+ align:start position:0%
+and and you've got a competition for boy
+ 
+
+ align:start position:0%
+and and you've got a competition for boy
+too at that point right okay so now can
+
+ align:start position:0%
+too at that point right okay so now can
+ 
+
+ align:start position:0%
+too at that point right okay so now can
+we express the that put that into a way
+
+ align:start position:0%
+we express the that put that into a way
+ 
+
+ align:start position:0%
+we express the that put that into a way
+that doesn't pick out girl two as like
+
+ align:start position:0%
+that doesn't pick out girl two as like
+ 
+
+ align:start position:0%
+that doesn't pick out girl two as like
+guilty or boy four of course I should
+
+ align:start position:0%
+guilty or boy four of course I should
+ 
+
+ align:start position:0%
+guilty or boy four of course I should
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+I let let me let me start this sentence
+
+ align:start position:0%
+I let let me let me start this sentence
+ 
+
+ align:start position:0%
+I let let me let me start this sentence
+the problem is that girls tooth three
+
+ align:start position:0%
+the problem is that girls tooth three
+ 
+
+ align:start position:0%
+the problem is that girls tooth three
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four say it again and louder two boys
+
+ align:start position:0%
+four say it again and louder two boys
+ 
+
+ align:start position:0%
+four say it again and louder two boys
+only like this only like two
+
+ align:start position:0%
+only like this only like two
+ 
+
+ align:start position:0%
+only like this only like two
+boys we got three girls
+
+ align:start position:0%
+boys we got three girls
+ 
+
+ align:start position:0%
+boys we got three girls
+there that only can
+
+ align:start position:0%
+there that only can
+ 
+
+ align:start position:0%
+there that only can
+match are only acceptable only the only
+
+ align:start position:0%
+match are only acceptable only the only
+ 
+
+ align:start position:0%
+match are only acceptable only the only
+only matches are with two boys so you
+
+ align:start position:0%
+only matches are with two boys so you
+ 
+
+ align:start position:0%
+only matches are with two boys so you
+can't do
+
+ align:start position:0%
+can't do
+ 
+
+ align:start position:0%
+can't do
+it there's something but but I I I'll
+
+ align:start position:0%
+it there's something but but I I I'll
+ 
+
+ align:start position:0%
+it there's something but but I I I'll
+stay with that language so my my my
+
+ align:start position:0%
+stay with that language so my my my
+ 
+
+ align:start position:0%
+stay with that language so my my my
+theorem will be complete matching as
+
+ align:start position:0%
+theorem will be complete matching as
+ 
+
+ align:start position:0%
+theorem will be complete matching as
+possible if and only
+
+ align:start position:0%
+possible if and only
+ 
+
+ align:start position:0%
+possible if and only
+if now how shall I express it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every set why don't better right
+
+ align:start position:0%
+every set why don't better right
+ 
+
+ align:start position:0%
+every set why don't better right
+right-handed here of
+
+ align:start position:0%
+right-handed here of
+ 
+
+ align:start position:0%
+right-handed here of
+girls
+
+ align:start position:0%
+girls
+ 
+
+ align:start position:0%
+girls
+say say k
+
+ align:start position:0%
+say say k
+ 
+
+ align:start position:0%
+say say k
+girls or R
+
+ align:start position:0%
+girls or R
+ 
+
+ align:start position:0%
+girls or R
+girls every set of girls every subset of
+
+ align:start position:0%
+girls every set of girls every subset of
+ 
+
+ align:start position:0%
+girls every set of girls every subset of
+girls whatever I'm thinking you take
+
+ align:start position:0%
+girls whatever I'm thinking you take
+ 
+
+ align:start position:0%
+girls whatever I'm thinking you take
+take any group of girls say k of them K
+
+ align:start position:0%
+take any group of girls say k of them K
+ 
+
+ align:start position:0%
+take any group of girls say k of them K
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them must
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what much match there must be at least K
+
+ align:start position:0%
+what much match there must be at least K
+ 
+
+ align:start position:0%
+what much match there must be at least K
+booys that's
+
+ align:start position:0%
+booys that's
+ 
+
+ align:start position:0%
+booys that's
+clearly
+
+ align:start position:0%
+clearly
+ 
+
+ align:start position:0%
+clearly
+necessary right if I have a set of K
+
+ align:start position:0%
+necessary right if I have a set of K
+ 
+
+ align:start position:0%
+necessary right if I have a set of K
+girls that among them like these three
+
+ align:start position:0%
+girls that among them like these three
+ 
+
+ align:start position:0%
+girls that among them like these three
+that among them only connect
+
+ align:start position:0%
+that among them only connect
+ 
+
+ align:start position:0%
+that among them only connect
+except two boys then I can't do it so
+
+ align:start position:0%
+except two boys then I can't do it so
+ 
+
+ align:start position:0%
+except two boys then I can't do it so
+I've got it it's like that Duality weak
+
+ align:start position:0%
+I've got it it's like that Duality weak
+ 
+
+ align:start position:0%
+I've got it it's like that Duality weak
+Duality that I had before in some way
+
+ align:start position:0%
+Duality that I had before in some way
+ 
+
+ align:start position:0%
+Duality that I had before in some way
+half of the theorem is going to be easy
+
+ align:start position:0%
+half of the theorem is going to be easy
+ 
+
+ align:start position:0%
+half of the theorem is going to be easy
+let me finish the statement every set of
+
+ align:start position:0%
+let me finish the statement every set of
+ 
+
+ align:start position:0%
+let me finish the statement every set of
+girls K of them
+
+ align:start position:0%
+girls K of them
+ 
+
+ align:start position:0%
+girls K of them
+likes together collectively
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collectively at
+
+ align:start position:0%
+collectively at
+ 
+
+ align:start position:0%
+collectively at
+least
+
+ align:start position:0%
+least
+ 
+
+ align:start position:0%
+least
+K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boys certainly
+
+ align:start position:0%
+boys certainly
+ 
+
+ align:start position:0%
+boys certainly
+necessary not clear at all that
+
+ align:start position:0%
+necessary not clear at all that
+ 
+
+ align:start position:0%
+necessary not clear at all that
+it's sufficient that
+
+ align:start position:0%
+it's sufficient that
+ 
+
+ align:start position:0%
+it's sufficient that
+if this worked if every set of girls did
+
+ align:start position:0%
+if this worked if every set of girls did
+ 
+
+ align:start position:0%
+if this worked if every set of girls did
+like at least K boys but that's the
+
+ align:start position:0%
+like at least K boys but that's the
+ 
+
+ align:start position:0%
+like at least K boys but that's the
+theorem and that's that's the solution
+
+ align:start position:0%
+theorem and that's that's the solution
+ 
+
+ align:start position:0%
+theorem and that's that's the solution
+to the marriage problem that that that
+
+ align:start position:0%
+to the marriage problem that that that
+ 
+
+ align:start position:0%
+to the marriage problem that that that
+this condition is certainly necessary if
+
+ align:start position:0%
+this condition is certainly necessary if
+ 
+
+ align:start position:0%
+this condition is certainly necessary if
+I have a set of girls that don't like
+
+ align:start position:0%
+I have a set of girls that don't like
+ 
+
+ align:start position:0%
+I have a set of girls that don't like
+enough boys there's no way I could
+
+ align:start position:0%
+enough boys there's no way I could
+ 
+
+ align:start position:0%
+enough boys there's no way I could
+complete the
+
+ align:start position:0%
+complete the
+ 
+
+ align:start position:0%
+complete the
+matching
+
+ align:start position:0%
+matching
+ 
+
+ align:start position:0%
+matching
+other uh the boy well these matches
+
+ align:start position:0%
+other uh the boy well these matches
+ 
+
+ align:start position:0%
+other uh the boy well these matches
+are made in heaven so to speak uh
+
+ align:start position:0%
+are made in heaven so to speak uh
+ 
+
+ align:start position:0%
+are made in heaven so to speak uh
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+yeah I I I could yeah I could put an
+
+ align:start position:0%
+yeah I I I could yeah I could put an
+ 
+
+ align:start position:0%
+yeah I I I could yeah I could put an
+equivalent statement I guess that might
+
+ align:start position:0%
+equivalent statement I guess that might
+ 
+
+ align:start position:0%
+equivalent statement I guess that might
+be look different but it hopefully it
+
+ align:start position:0%
+be look different but it hopefully it
+ 
+
+ align:start position:0%
+be look different but it hopefully it
+would tie up that if every set of K
+
+ align:start position:0%
+would tie up that if every set of K
+ 
+
+ align:start position:0%
+would tie up that if every set of K
+boys like collectively at least K girls
+
+ align:start position:0%
+boys like collectively at least K girls
+ 
+
+ align:start position:0%
+boys like collectively at least K girls
+then that would be enough yeah so I
+
+ align:start position:0%
+then that would be enough yeah so I
+ 
+
+ align:start position:0%
+then that would be enough yeah so I
+don't have to work both directions it's
+
+ align:start position:0%
+don't have to work both directions it's
+ 
+
+ align:start position:0%
+don't have to work both directions it's
+enough to put it only in this direction
+
+ align:start position:0%
+enough to put it only in this direction
+ 
+
+ align:start position:0%
+enough to put it only in this direction
+so so that's the theorem that that uh
+
+ align:start position:0%
+so so that's the theorem that that uh
+ 
+
+ align:start position:0%
+so so that's the theorem that that uh
+and we could create other examples
+
+ align:start position:0%
+and we could create other examples
+ 
+
+ align:start position:0%
+and we could create other examples
+here um of course if I fix this one by
+
+ align:start position:0%
+here um of course if I fix this one by
+ 
+
+ align:start position:0%
+here um of course if I fix this one by
+allowing by this this set of three girls
+
+ align:start position:0%
+allowing by this this set of three girls
+ 
+
+ align:start position:0%
+allowing by this this set of three girls
+by getting a third boy into the picture
+
+ align:start position:0%
+by getting a third boy into the picture
+ 
+
+ align:start position:0%
+by getting a third boy into the picture
+for those three girls then I won't have
+
+ align:start position:0%
+for those three girls then I won't have
+ 
+
+ align:start position:0%
+for those three girls then I won't have
+any trouble to complete a matching where
+
+ align:start position:0%
+any trouble to complete a matching where
+ 
+
+ align:start position:0%
+any trouble to complete a matching where
+shall I do it well I could connect girl
+
+ align:start position:0%
+shall I do it well I could connect girl
+ 
+
+ align:start position:0%
+shall I do it well I could connect girl
+two to somewhere else okay now a
+
+ align:start position:0%
+two to somewhere else okay now a
+ 
+
+ align:start position:0%
+two to somewhere else okay now a
+complete matching is certainly possible
+
+ align:start position:0%
+complete matching is certainly possible
+ 
+
+ align:start position:0%
+complete matching is certainly possible
+I just put a one in the position in the
+
+ align:start position:0%
+I just put a one in the position in the
+ 
+
+ align:start position:0%
+I just put a one in the position in the
+21 position I just put a one
+
+ align:start position:0%
+21 position I just put a one
+ 
+
+ align:start position:0%
+21 position I just put a one
+there by matching girl two and boy
+
+ align:start position:0%
+there by matching girl two and boy
+ 
+
+ align:start position:0%
+there by matching girl two and boy
+one and now um uh complete match a
+
+ align:start position:0%
+one and now um uh complete match a
+ 
+
+ align:start position:0%
+one and now um uh complete match a
+complete match so now what's the
+
+ align:start position:0%
+complete match so now what's the
+ 
+
+ align:start position:0%
+complete match so now what's the
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+matching uh how well this little set of
+
+ align:start position:0%
+matching uh how well this little set of
+ 
+
+ align:start position:0%
+matching uh how well this little set of
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+troublemakers is like they only like the
+
+ align:start position:0%
+troublemakers is like they only like the
+ 
+
+ align:start position:0%
+troublemakers is like they only like the
+only three boys there so I had better on
+
+ align:start position:0%
+only three boys there so I had better on
+ 
+
+ align:start position:0%
+only three boys there so I had better on
+that said I that probably uh I know that
+
+ align:start position:0%
+that said I that probably uh I know that
+ 
+
+ align:start position:0%
+that said I that probably uh I know that
+they have got to match for those three
+
+ align:start position:0%
+they have got to match for those three
+ 
+
+ align:start position:0%
+they have got to match for those three
+boys and the theorem will say I could do
+
+ align:start position:0%
+boys and the theorem will say I could do
+ 
+
+ align:start position:0%
+boys and the theorem will say I could do
+it so how can I do it I guess well let's
+
+ align:start position:0%
+it so how can I do it I guess well let's
+ 
+
+ align:start position:0%
+it so how can I do it I guess well let's
+use this new Edge girl three could
+
+ align:start position:0%
+use this new Edge girl three could
+ 
+
+ align:start position:0%
+use this new Edge girl three could
+connect with that
+
+ align:start position:0%
+connect with that
+ 
+
+ align:start position:0%
+connect with that
+one no it can't no it can't
+
+ align:start position:0%
+one no it can't no it can't
+ 
+
+ align:start position:0%
+one no it can't no it can't
+three has to go three has to go with
+
+ align:start position:0%
+three has to go three has to go with
+ 
+
+ align:start position:0%
+three has to go three has to go with
+four in this
+
+ align:start position:0%
+four in this
+ 
+
+ align:start position:0%
+four in this
+case four has to go with two good yeah
+
+ align:start position:0%
+case four has to go with two good yeah
+ 
+
+ align:start position:0%
+case four has to go with two good yeah
+put it that that's better okay so I got
+
+ align:start position:0%
+put it that that's better okay so I got
+ 
+
+ align:start position:0%
+put it that that's better okay so I got
+a match and then of course one who
+
+ align:start position:0%
+a match and then of course one who
+ 
+
+ align:start position:0%
+a match and then of course one who
+helped us out here is happy with
+
+ align:start position:0%
+helped us out here is happy with
+ 
+
+ align:start position:0%
+helped us out here is happy with
+three so is that have I
+
+ align:start position:0%
+three so is that have I
+ 
+
+ align:start position:0%
+three so is that have I
+now have I done it right I don't know
+
+ align:start position:0%
+now have I done it right I don't know
+ 
+
+ align:start position:0%
+now have I done it right I don't know
+I've colored it well oh because I used
+
+ align:start position:0%
+I've colored it well oh because I used
+ 
+
+ align:start position:0%
+I've colored it well oh because I used
+yellow for before before the optimum was
+
+ align:start position:0%
+yellow for before before the optimum was
+ 
+
+ align:start position:0%
+yellow for before before the optimum was
+written Brad yeah yeah it's like right
+
+ align:start position:0%
+written Brad yeah yeah it's like right
+ 
+
+ align:start position:0%
+written Brad yeah yeah it's like right
+that's right okay so uh so I could go
+
+ align:start position:0%
+that's right okay so uh so I could go
+ 
+
+ align:start position:0%
+that's right okay so uh so I could go
+through the proof which is quite neat
+
+ align:start position:0%
+through the proof which is quite neat
+ 
+
+ align:start position:0%
+through the proof which is quite neat
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+pleasant that oh I can outline the proof
+
+ align:start position:0%
+pleasant that oh I can outline the proof
+ 
+
+ align:start position:0%
+pleasant that oh I can outline the proof
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+you can I outline the proof that this
+
+ align:start position:0%
+you can I outline the proof that this
+ 
+
+ align:start position:0%
+you can I outline the proof that this
+that if this condition is satisfied for
+
+ align:start position:0%
+that if this condition is satisfied for
+ 
+
+ align:start position:0%
+that if this condition is satisfied for
+every it has to be satisfied for every
+
+ align:start position:0%
+every it has to be satisfied for every
+ 
+
+ align:start position:0%
+every it has to be satisfied for every
+set of girls so notice to check whether
+
+ align:start position:0%
+set of girls so notice to check whether
+ 
+
+ align:start position:0%
+set of girls so notice to check whether
+it's satisfied we haven't got a good way
+
+ align:start position:0%
+it's satisfied we haven't got a good way
+ 
+
+ align:start position:0%
+it's satisfied we haven't got a good way
+to do that yet but but if it's satisfied
+
+ align:start position:0%
+to do that yet but but if it's satisfied
+ 
+
+ align:start position:0%
+to do that yet but but if it's satisfied
+for every set of girls then I could
+
+ align:start position:0%
+for every set of girls then I could
+ 
+
+ align:start position:0%
+for every set of girls then I could
+match them
+
+ align:start position:0%
+match them
+ 
+
+ align:start position:0%
+match them
+all uh can I
+
+ align:start position:0%
+all uh can I
+ 
+
+ align:start position:0%
+all uh can I
+just mentally think of two cases one
+
+ align:start position:0%
+just mentally think of two cases one
+ 
+
+ align:start position:0%
+just mentally think of two cases one
+case would be where every set of girls
+
+ align:start position:0%
+case would be where every set of girls
+ 
+
+ align:start position:0%
+case would be where every set of girls
+likes more than kboys like so this is
+
+ align:start position:0%
+likes more than kboys like so this is
+ 
+
+ align:start position:0%
+likes more than kboys like so this is
+the room to maneuver case how how do you
+
+ align:start position:0%
+the room to maneuver case how how do you
+ 
+
+ align:start position:0%
+the room to maneuver case how how do you
+propose that I deal with that case in
+
+ align:start position:0%
+propose that I deal with that case in
+ 
+
+ align:start position:0%
+propose that I deal with that case in
+the room to maneuver case where every
+
+ align:start position:0%
+the room to maneuver case where every
+ 
+
+ align:start position:0%
+the room to maneuver case where every
+set of K girls likes I'm going to prove
+
+ align:start position:0%
+set of K girls likes I'm going to prove
+ 
+
+ align:start position:0%
+set of K girls likes I'm going to prove
+this by IND ction on the number here
+
+ align:start position:0%
+this by IND ction on the number here
+ 
+
+ align:start position:0%
+this by IND ction on the number here
+okay so if every set of girls likes more
+
+ align:start position:0%
+okay so if every set of girls likes more
+ 
+
+ align:start position:0%
+okay so if every set of girls likes more
+than enough
+
+ align:start position:0%
+than enough
+ 
+
+ align:start position:0%
+than enough
+boys what shall I
+
+ align:start position:0%
+boys what shall I
+ 
+
+ align:start position:0%
+boys what shall I
+do well set for every set full set yeah
+
+ align:start position:0%
+do well set for every set full set yeah
+ 
+
+ align:start position:0%
+do well set for every set full set yeah
+for every set well that's true the full
+
+ align:start position:0%
+for every set well that's true the full
+ 
+
+ align:start position:0%
+for every set well that's true the full
+set the full end girls will like exactly
+
+ align:start position:0%
+set the full end girls will like exactly
+ 
+
+ align:start position:0%
+set the full end girls will like exactly
+and boys but all subsets I've got give
+
+ align:start position:0%
+and boys but all subsets I've got give
+ 
+
+ align:start position:0%
+and boys but all subsets I've got give
+suppose that happens what shall I do
+
+ align:start position:0%
+suppose that happens what shall I do
+ 
+
+ align:start position:0%
+suppose that happens what shall I do
+well I just take the first girl she can
+
+ align:start position:0%
+well I just take the first girl she can
+ 
+
+ align:start position:0%
+well I just take the first girl she can
+marry anybody who's accept cble and then
+
+ align:start position:0%
+marry anybody who's accept cble and then
+ 
+
+ align:start position:0%
+marry anybody who's accept cble and then
+I look at the smaller the remaining n
+
+ align:start position:0%
+I look at the smaller the remaining n
+ 
+
+ align:start position:0%
+I look at the smaller the remaining n
+minus one problem and what's happening
+
+ align:start position:0%
+minus one problem and what's happening
+ 
+
+ align:start position:0%
+minus one problem and what's happening
+there now every set of those girls well
+
+ align:start position:0%
+there now every set of those girls well
+ 
+
+ align:start position:0%
+there now every set of those girls well
+I've only used up one boy and I I said
+
+ align:start position:0%
+I've only used up one boy and I I said
+ 
+
+ align:start position:0%
+I've only used up one boy and I I said
+in this case that I had room to maneuver
+
+ align:start position:0%
+in this case that I had room to maneuver
+ 
+
+ align:start position:0%
+in this case that I had room to maneuver
+so I still am okay all right with that
+
+ align:start position:0%
+so I still am okay all right with that
+ 
+
+ align:start position:0%
+so I still am okay all right with that
+that's the easy
+
+ align:start position:0%
+that's the easy
+ 
+
+ align:start position:0%
+that's the easy
+one then the harder case is when there's
+
+ align:start position:0%
+one then the harder case is when there's
+ 
+
+ align:start position:0%
+one then the harder case is when there's
+some I'm giving this proof you without
+
+ align:start position:0%
+some I'm giving this proof you without
+ 
+
+ align:start position:0%
+some I'm giving this proof you without
+writing here so should I write that case
+
+ align:start position:0%
+writing here so should I write that case
+ 
+
+ align:start position:0%
+writing here so should I write that case
+one which I just dealt with was uh that
+
+ align:start position:0%
+one which I just dealt with was uh that
+ 
+
+ align:start position:0%
+one which I just dealt with was uh that
+for K less than n that uh
+
+ align:start position:0%
+for K less than n that uh
+ 
+
+ align:start position:0%
+for K less than n that uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+subset has subset has uh uh more room to
+
+ align:start position:0%
+subset has subset has uh uh more room to
+ 
+
+ align:start position:0%
+subset has subset has uh uh more room to
+maneuver an extra boy or more is is okay
+
+ align:start position:0%
+maneuver an extra boy or more is is okay
+ 
+
+ align:start position:0%
+maneuver an extra boy or more is is okay
+and and then we can just make an
+
+ align:start position:0%
+and and then we can just make an
+ 
+
+ align:start position:0%
+and and then we can just make an
+assignment get to a smaller problem
+
+ align:start position:0%
+assignment get to a smaller problem
+ 
+
+ align:start position:0%
+assignment get to a smaller problem
+we're okay now this the harder case is
+
+ align:start position:0%
+we're okay now this the harder case is
+ 
+
+ align:start position:0%
+we're okay now this the harder case is
+some set
+
+ align:start position:0%
+some set
+ 
+
+ align:start position:0%
+some set
+of K
+
+ align:start position:0%
+of K
+ 
+
+ align:start position:0%
+of K
+girls some for some K less than n likes
+
+ align:start position:0%
+girls some for some K less than n likes
+ 
+
+ align:start position:0%
+girls some for some K less than n likes
+only n boys only exactly and boys okay
+
+ align:start position:0%
+only n boys only exactly and boys okay
+ 
+
+ align:start position:0%
+only n boys only exactly and boys okay
+how do I deal with that case k
+
+ align:start position:0%
+how do I deal with that case k
+ 
+
+ align:start position:0%
+how do I deal with that case k
+boys how do I deal with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case and and and still
+
+ align:start position:0%
+case and and and still
+ 
+
+ align:start position:0%
+case and and and still
+all you know what I'm doing so I'm
+
+ align:start position:0%
+all you know what I'm doing so I'm
+ 
+
+ align:start position:0%
+all you know what I'm doing so I'm
+assuming this true so all sets it's not
+
+ align:start position:0%
+assuming this true so all sets it's not
+ 
+
+ align:start position:0%
+assuming this true so all sets it's not
+enough just to check any single set all
+
+ align:start position:0%
+enough just to check any single set all
+ 
+
+ align:start position:0%
+enough just to check any single set all
+sets like enough and some particular
+
+ align:start position:0%
+sets like enough and some particular
+ 
+
+ align:start position:0%
+sets like enough and some particular
+subset likes just barely enough now what
+
+ align:start position:0%
+subset likes just barely enough now what
+ 
+
+ align:start position:0%
+subset likes just barely enough now what
+shall I do okay well the claim is that
+
+ align:start position:0%
+shall I do okay well the claim is that
+ 
+
+ align:start position:0%
+shall I do okay well the claim is that
+those K girls I can match them to those
+
+ align:start position:0%
+those K girls I can match them to those
+ 
+
+ align:start position:0%
+those K girls I can match them to those
+K boys which I better do now why am I
+
+ align:start position:0%
+K boys which I better do now why am I
+ 
+
+ align:start position:0%
+K boys which I better do now why am I
+able to do
+
+ align:start position:0%
+able to do
+ 
+
+ align:start position:0%
+able to do
+that that's the induction step
+
+ align:start position:0%
+that that's the induction step
+ 
+
+ align:start position:0%
+that that's the induction step
+that's this is a smaller than n
+
+ align:start position:0%
+that's this is a smaller than n
+ 
+
+ align:start position:0%
+that's this is a smaller than n
+group and it's the hypothesis is
+
+ align:start position:0%
+group and it's the hypothesis is
+ 
+
+ align:start position:0%
+group and it's the hypothesis is
+satisfied so
+
+ align:start position:0%
+satisfied so
+ 
+
+ align:start position:0%
+satisfied so
+by so it's a smaller problem and I'm
+
+ align:start position:0%
+by so it's a smaller problem and I'm
+ 
+
+ align:start position:0%
+by so it's a smaller problem and I'm
+assuming that I've solved all smaller
+
+ align:start position:0%
+assuming that I've solved all smaller
+ 
+
+ align:start position:0%
+assuming that I've solved all smaller
+problems and I'm now coming to n the
+
+ align:start position:0%
+problems and I'm now coming to n the
+ 
+
+ align:start position:0%
+problems and I'm now coming to n the
+case of n boys girls and boys okay so so
+
+ align:start position:0%
+case of n boys girls and boys okay so so
+ 
+
+ align:start position:0%
+case of n boys girls and boys okay so so
+a match them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off this was a smaller problem
+
+ align:start position:0%
+off this was a smaller problem
+ 
+
+ align:start position:0%
+off this was a smaller problem
+so already presumed solved and now I
+
+ align:start position:0%
+so already presumed solved and now I
+ 
+
+ align:start position:0%
+so already presumed solved and now I
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+to what do I have to do now I've got to
+
+ align:start position:0%
+to what do I have to do now I've got to
+ 
+
+ align:start position:0%
+to what do I have to do now I've got to
+I've got the rest the other n minus
+
+ align:start position:0%
+I've got the rest the other n minus
+ 
+
+ align:start position:0%
+I've got the rest the other n minus
+K other n minus K how do I deal with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them well I guess if I want to use
+
+ align:start position:0%
+them well I guess if I want to use
+ 
+
+ align:start position:0%
+them well I guess if I want to use
+that's a smaller problem
+
+ align:start position:0%
+that's a smaller problem
+ 
+
+ align:start position:0%
+that's a smaller problem
+too but I then I would have to check
+
+ align:start position:0%
+too but I then I would have to check
+ 
+
+ align:start position:0%
+too but I then I would have to check
+that this condition
+
+ align:start position:0%
+that this condition
+ 
+
+ align:start position:0%
+that this condition
+but K of the boys are now
+
+ align:start position:0%
+but K of the boys are now
+ 
+
+ align:start position:0%
+but K of the boys are now
+used so I have to check the other n
+
+ align:start position:0%
+used so I have to check the other n
+ 
+
+ align:start position:0%
+used so I have to check the other n
+minus K I have to check this condition
+
+ align:start position:0%
+minus K I have to check this condition
+ 
+
+ align:start position:0%
+minus K I have to check this condition
+can I call this Hall's condition there
+
+ align:start position:0%
+can I call this Hall's condition there
+ 
+
+ align:start position:0%
+can I call this Hall's condition there
+was a a guy named Hall who Halls
+
+ align:start position:0%
+was a a guy named Hall who Halls
+ 
+
+ align:start position:0%
+was a a guy named Hall who Halls
+condition I have to
+
+ align:start position:0%
+condition I have to
+ 
+
+ align:start position:0%
+condition I have to
+check
+
+ align:start position:0%
+check
+ 
+
+ align:start position:0%
+check
+check
+
+ align:start position:0%
+check
+ 
+
+ align:start position:0%
+check
+Hall on the these remaining on these on
+
+ align:start position:0%
+Hall on the these remaining on these on
+ 
+
+ align:start position:0%
+Hall on the these remaining on these on
+the on the unmarried
+
+ align:start position:0%
+the on the unmarried
+ 
+
+ align:start position:0%
+the on the unmarried
+ones isn't that the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see sorry isn't that the same as
+
+ align:start position:0%
+let's see sorry isn't that the same as
+ 
+
+ align:start position:0%
+let's see sorry isn't that the same as
+your there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+call for these other guys yeah let's see
+
+ align:start position:0%
+call for these other guys yeah let's see
+ 
+
+ align:start position:0%
+call for these other guys yeah let's see
+the thing
+
+ align:start position:0%
+the thing
+ 
+
+ align:start position:0%
+the thing
+is we we can't match them off with boys
+
+ align:start position:0%
+is we we can't match them off with boys
+ 
+
+ align:start position:0%
+is we we can't match them off with boys
+that were used right by the first case
+
+ align:start position:0%
+that were used right by the first case
+ 
+
+ align:start position:0%
+that were used right by the first case
+so we have to be darn sure that these
+
+ align:start position:0%
+so we have to be darn sure that these
+ 
+
+ align:start position:0%
+so we have to be darn sure that these
+remaining girls
+
+ align:start position:0%
+remaining girls
+ 
+
+ align:start position:0%
+remaining girls
+like new boys I guess that's what I was
+
+ align:start position:0%
+like new boys I guess that's what I was
+ 
+
+ align:start position:0%
+like new boys I guess that's what I was
+thinking that you Tagg the K boys
+
+ align:start position:0%
+thinking that you Tagg the K boys
+ 
+
+ align:start position:0%
+thinking that you Tagg the K boys
+they're out of the picture they're out
+
+ align:start position:0%
+they're out of the picture they're out
+ 
+
+ align:start position:0%
+they're out of the picture they're out
+of the picture so the other nus K girls
+
+ align:start position:0%
+of the picture so the other nus K girls
+ 
+
+ align:start position:0%
+of the picture so the other nus K girls
+yes like this was K girls and K boys
+
+ align:start position:0%
+yes like this was K girls and K boys
+ 
+
+ align:start position:0%
+yes like this was K girls and K boys
+like the remaining nus K boys so you
+
+ align:start position:0%
+like the remaining nus K boys so you
+ 
+
+ align:start position:0%
+like the remaining nus K boys so you
+know but do I know that how do I know
+
+ align:start position:0%
+know but do I know that how do I know
+ 
+
+ align:start position:0%
+know but do I know that how do I know
+that those remaining
+
+ align:start position:0%
+that those remaining
+ 
+
+ align:start position:0%
+that those remaining
+girls that's the condition I mean in
+
+ align:start position:0%
+girls that's the condition I mean in
+ 
+
+ align:start position:0%
+girls that's the condition I mean in
+other words if you don't have that you
+
+ align:start position:0%
+other words if you don't have that you
+ 
+
+ align:start position:0%
+other words if you don't have that you
+can't you can't continue I can't
+
+ align:start position:0%
+can't you can't continue I can't
+ 
+
+ align:start position:0%
+can't you can't continue I can't
+continue but I have to check that I have
+
+ align:start position:0%
+continue but I have to check that I have
+ 
+
+ align:start position:0%
+continue but I have to check that I have
+that somehow from the original from
+
+ align:start position:0%
+that somehow from the original from
+ 
+
+ align:start position:0%
+that somehow from the original from
+knowing on the original big set I'm um
+
+ align:start position:0%
+knowing on the original big set I'm um
+ 
+
+ align:start position:0%
+knowing on the original big set I'm um
+see what I mean what what I have to
+
+ align:start position:0%
+see what I mean what what I have to
+ 
+
+ align:start position:0%
+see what I mean what what I have to
+worry about is hey maybe some of these
+
+ align:start position:0%
+worry about is hey maybe some of these
+ 
+
+ align:start position:0%
+worry about is hey maybe some of these
+remaining girls only liked those same K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boys and there would be something
+
+ align:start position:0%
+boys and there would be something
+ 
+
+ align:start position:0%
+boys and there would be something
+well girls like boys and that would
+
+ align:start position:0%
+well girls like boys and that would
+ 
+
+ align:start position:0%
+well girls like boys and that would
+violate but did we assume that was the
+
+ align:start position:0%
+violate but did we assume that was the
+ 
+
+ align:start position:0%
+violate but did we assume that was the
+largest set of K girls no I haven't I
+
+ align:start position:0%
+largest set of K girls no I haven't I
+ 
+
+ align:start position:0%
+largest set of K girls no I haven't I
+haven't but but I if necessary I could
+
+ align:start position:0%
+haven't but but I if necessary I could
+ 
+
+ align:start position:0%
+haven't but but I if necessary I could
+have but I didn't yeah but I mean yeah
+
+ align:start position:0%
+have but I didn't yeah but I mean yeah
+ 
+
+ align:start position:0%
+have but I didn't yeah but I mean yeah
+we're we're right in the middle exactly
+
+ align:start position:0%
+we're we're right in the middle exactly
+ 
+
+ align:start position:0%
+we're we're right in the middle exactly
+cooking
+
+ align:start position:0%
+cooking
+ 
+
+ align:start position:0%
+cooking
+this that only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+already would have violated I mean
+
+ align:start position:0%
+already would have violated I mean
+ 
+
+ align:start position:0%
+already would have violated I mean
+there's you're you're in the I mean so
+
+ align:start position:0%
+there's you're you're in the I mean so
+ 
+
+ align:start position:0%
+there's you're you're in the I mean so
+basically vac
+
+ align:start position:0%
+basically vac
+ 
+
+ align:start position:0%
+basically vac
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+all that's right that's it that's it
+
+ align:start position:0%
+all that's right that's it that's it
+ 
+
+ align:start position:0%
+all that's right that's it that's it
+including this condition in has to hold
+
+ align:start position:0%
+including this condition in has to hold
+ 
+
+ align:start position:0%
+including this condition in has to hold
+for sets of girls which included these K
+
+ align:start position:0%
+for sets of girls which included these K
+ 
+
+ align:start position:0%
+for sets of girls which included these K
+and some of
+
+ align:start position:0%
+and some of
+ 
+
+ align:start position:0%
+and some of
+these and it's yeah then it becomes fun
+
+ align:start position:0%
+these and it's yeah then it becomes fun
+ 
+
+ align:start position:0%
+these and it's yeah then it becomes fun
+I won't like spoil everybody's fun here
+
+ align:start position:0%
+I won't like spoil everybody's fun here
+ 
+
+ align:start position:0%
+I won't like spoil everybody's fun here
+it's just beautiful that it works out
+
+ align:start position:0%
+it's just beautiful that it works out
+ 
+
+ align:start position:0%
+it's just beautiful that it works out
+that that if I if I look at a set of
+
+ align:start position:0%
+that that if I if I look at a set of
+ 
+
+ align:start position:0%
+that that if I if I look at a set of
+some of these remaining K and then I add
+
+ align:start position:0%
+some of these remaining K and then I add
+ 
+
+ align:start position:0%
+some of these remaining K and then I add
+in these original K and then I have then
+
+ align:start position:0%
+in these original K and then I have then
+ 
+
+ align:start position:0%
+in these original K and then I have then
+I look at the hypothesis on that and
+
+ align:start position:0%
+I look at the hypothesis on that and
+ 
+
+ align:start position:0%
+I look at the hypothesis on that and
+anyway it's
+
+ align:start position:0%
+anyway it's
+ 
+
+ align:start position:0%
+anyway it's
+beautiful it's beautiful I it's so I'll
+
+ align:start position:0%
+beautiful it's beautiful I it's so I'll
+ 
+
+ align:start position:0%
+beautiful it's beautiful I it's so I'll
+put it's check and and then we didn't
+
+ align:start position:0%
+put it's check and and then we didn't
+ 
+
+ align:start position:0%
+put it's check and and then we didn't
+maybe say all the words that need to be
+
+ align:start position:0%
+maybe say all the words that need to be
+ 
+
+ align:start position:0%
+maybe say all the words that need to be
+said but it's it's really nice it's
+
+ align:start position:0%
+said but it's it's really nice it's
+ 
+
+ align:start position:0%
+said but it's it's really nice it's
+really nice okay this is kind of off
+
+ align:start position:0%
+really nice okay this is kind of off
+ 
+
+ align:start position:0%
+really nice okay this is kind of off
+subject yes does it sort of relate like
+
+ align:start position:0%
+subject yes does it sort of relate like
+ 
+
+ align:start position:0%
+subject yes does it sort of relate like
+I'm looking at that 4x4 Matrix all right
+
+ align:start position:0%
+I'm looking at that 4x4 Matrix all right
+ 
+
+ align:start position:0%
+I'm looking at that 4x4 Matrix all right
+I'm ready to look back at that too think
+
+ align:start position:0%
+I'm ready to look back at that too think
+ 
+
+ align:start position:0%
+I'm ready to look back at that too think
+that the is non singular is that a
+
+ align:start position:0%
+that the is non singular is that a
+ 
+
+ align:start position:0%
+that the is non singular is that a
+factor for example if two of those rows
+
+ align:start position:0%
+factor for example if two of those rows
+ 
+
+ align:start position:0%
+factor for example if two of those rows
+of the Matrix had 0 1 0 Z yes there's no
+
+ align:start position:0%
+of the Matrix had 0 1 0 Z yes there's no
+ 
+
+ align:start position:0%
+of the Matrix had 0 1 0 Z yes there's no
+way you can satisfy the condition we
+
+ align:start position:0%
+way you can satisfy the condition we
+ 
+
+ align:start position:0%
+way you can satisfy the condition we
+just talking about that's
+
+ align:start position:0%
+just talking about that's
+ 
+
+ align:start position:0%
+just talking about that's
+true yeah and that's all they want right
+
+ align:start position:0%
+true yeah and that's all they want right
+ 
+
+ align:start position:0%
+true yeah and that's all they want right
+but I I don't
+
+ align:start position:0%
+but I I don't
+ 
+
+ align:start position:0%
+but I I don't
+totally yeah I don't I don't there isn't
+
+ align:start position:0%
+totally yeah I don't I don't there isn't
+ 
+
+ align:start position:0%
+totally yeah I don't I don't there isn't
+a perfect match between Singularity of
+
+ align:start position:0%
+a perfect match between Singularity of
+ 
+
+ align:start position:0%
+a perfect match between Singularity of
+the Matrix or or dependence of the rows
+
+ align:start position:0%
+the Matrix or or dependence of the rows
+ 
+
+ align:start position:0%
+the Matrix or or dependence of the rows
+and this and let me show you actually
+
+ align:start position:0%
+and this and let me show you actually
+ 
+
+ align:start position:0%
+and this and let me show you actually
+what comes in with this Matrix cuz it's
+
+ align:start position:0%
+what comes in with this Matrix cuz it's
+ 
+
+ align:start position:0%
+what comes in with this Matrix cuz it's
+quite fun uh imagine those ones are
+
+ align:start position:0%
+quite fun uh imagine those ones are
+ 
+
+ align:start position:0%
+quite fun uh imagine those ones are
+Rooks in a in a chess game or well let
+
+ align:start position:0%
+Rooks in a in a chess game or well let
+ 
+
+ align:start position:0%
+Rooks in a in a chess game or well let
+me here let me State the problem let me
+
+ align:start position:0%
+me here let me State the problem let me
+ 
+
+ align:start position:0%
+me here let me State the problem let me
+State the problem this way how many line
+
+ align:start position:0%
+State the problem this way how many line
+ 
+
+ align:start position:0%
+State the problem this way how many line
+can I go back to zero here my original
+
+ align:start position:0%
+can I go back to zero here my original
+ 
+
+ align:start position:0%
+can I go back to zero here my original
+one where it was trouble where I could
+
+ align:start position:0%
+one where it was trouble where I could
+ 
+
+ align:start position:0%
+one where it was trouble where I could
+only mat where I couldn't match all four
+
+ align:start position:0%
+only mat where I couldn't match all four
+ 
+
+ align:start position:0%
+only mat where I couldn't match all four
+then the question is how many could I
+
+ align:start position:0%
+then the question is how many could I
+ 
+
+ align:start position:0%
+then the question is how many could I
+match Ma so the maximum number of mat
+
+ align:start position:0%
+match Ma so the maximum number of mat
+ 
+
+ align:start position:0%
+match Ma so the maximum number of mat
+matching here here's the great theorem
+
+ align:start position:0%
+matching here here's the great theorem
+ 
+
+ align:start position:0%
+matching here here's the great theorem
+because maximum is going to equal a
+
+ align:start position:0%
+because maximum is going to equal a
+ 
+
+ align:start position:0%
+because maximum is going to equal a
+minimum in this thing is the minimum
+
+ align:start position:0%
+minimum in this thing is the minimum
+ 
+
+ align:start position:0%
+minimum in this thing is the minimum
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+lines that cover the ones
+
+ align:start position:0%
+lines that cover the ones
+ 
+
+ align:start position:0%
+lines that cover the ones
+to and I'll put this in yellow to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cover all the ones in the Matrix now
+
+ align:start position:0%
+cover all the ones in the Matrix now
+ 
+
+ align:start position:0%
+cover all the ones in the Matrix now
+what do I mean by that I mean we think
+
+ align:start position:0%
+what do I mean by that I mean we think
+ 
+
+ align:start position:0%
+what do I mean by that I mean we think
+how many do you think was the maximum
+
+ align:start position:0%
+how many do you think was the maximum
+ 
+
+ align:start position:0%
+how many do you think was the maximum
+number number of marriages in this
+
+ align:start position:0%
+number number of marriages in this
+ 
+
+ align:start position:0%
+number number of marriages in this
+original sorry that I've screwed up the
+
+ align:start position:0%
+original sorry that I've screwed up the
+ 
+
+ align:start position:0%
+original sorry that I've screwed up the
+picture you remember the original with
+
+ align:start position:0%
+picture you remember the original with
+ 
+
+ align:start position:0%
+picture you remember the original with
+that Matrix how many how many could we
+
+ align:start position:0%
+that Matrix how many how many could we
+ 
+
+ align:start position:0%
+that Matrix how many how many could we
+marry off three three right so I believe
+
+ align:start position:0%
+marry off three three right so I believe
+ 
+
+ align:start position:0%
+marry off three three right so I believe
+that I can
+
+ align:start position:0%
+that I can
+ 
+
+ align:start position:0%
+that I can
+cover all the ones with three
+
+ align:start position:0%
+cover all the ones with three
+ 
+
+ align:start position:0%
+cover all the ones with three
+lines lines are horizontals or verticals
+
+ align:start position:0%
+lines lines are horizontals or verticals
+ 
+
+ align:start position:0%
+lines lines are horizontals or verticals
+so that's where there's a Twist somehow
+
+ align:start position:0%
+so that's where there's a Twist somehow
+ 
+
+ align:start position:0%
+so that's where there's a Twist somehow
+both boys and girls are in this picture
+
+ align:start position:0%
+both boys and girls are in this picture
+ 
+
+ align:start position:0%
+both boys and girls are in this picture
+so how could I cover all those
+
+ align:start position:0%
+so how could I cover all those
+ 
+
+ align:start position:0%
+so how could I cover all those
+ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wouldn't be hard right first
+
+ align:start position:0%
+wouldn't be hard right first
+ 
+
+ align:start position:0%
+wouldn't be hard right first
+row and what column second and fourth
+
+ align:start position:0%
+row and what column second and fourth
+ 
+
+ align:start position:0%
+row and what column second and fourth
+column
+
+ align:start position:0%
+column
+ 
+
+ align:start position:0%
+column
+right and I bet you somehow that tells
+
+ align:start position:0%
+right and I bet you somehow that tells
+ 
+
+ align:start position:0%
+right and I bet you somehow that tells
+me who's making
+
+ align:start position:0%
+me who's making
+ 
+
+ align:start position:0%
+me who's making
+trouble or something or who isn't or
+
+ align:start position:0%
+trouble or something or who isn't or
+ 
+
+ align:start position:0%
+trouble or something or who isn't or
+whatever yeah maybe the oh yeah the
+
+ align:start position:0%
+whatever yeah maybe the oh yeah the
+ 
+
+ align:start position:0%
+whatever yeah maybe the oh yeah the
+zeros tell me who's making TR of course
+
+ align:start position:0%
+zeros tell me who's making TR of course
+ 
+
+ align:start position:0%
+zeros tell me who's making TR of course
+trouble's coming from zeros so where are
+
+ align:start position:0%
+trouble's coming from zeros so where are
+ 
+
+ align:start position:0%
+trouble's coming from zeros so where are
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+zeros the zeros are in Girls 2 three and
+
+ align:start position:0%
+zeros the zeros are in Girls 2 three and
+ 
+
+ align:start position:0%
+zeros the zeros are in Girls 2 three and
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+and boys one and
+
+ align:start position:0%
+and boys one and
+ 
+
+ align:start position:0%
+and boys one and
+three and what was the problem
+
+ align:start position:0%
+three and what was the problem
+ 
+
+ align:start position:0%
+three and what was the problem
+there I had three girls and there's two
+
+ align:start position:0%
+there I had three girls and there's two
+ 
+
+ align:start position:0%
+there I had three girls and there's two
+boys they won't don't
+
+ align:start position:0%
+boys they won't don't
+ 
+
+ align:start position:0%
+boys they won't don't
+marry and yeah so the zeros I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have yeah you you see it okay so yeah
+
+ align:start position:0%
+have yeah you you see it okay so yeah
+ 
+
+ align:start position:0%
+have yeah you you see it okay so yeah
+some so somehow that's the if I have a
+
+ align:start position:0%
+some so somehow that's the if I have a
+ 
+
+ align:start position:0%
+some so somehow that's the if I have a
+so there's now the general problem if I
+
+ align:start position:0%
+so there's now the general problem if I
+ 
+
+ align:start position:0%
+so there's now the general problem if I
+have a matrix of ones and zeros
+
+ align:start position:0%
+have a matrix of ones and zeros
+ 
+
+ align:start position:0%
+have a matrix of ones and zeros
+I can
+
+ align:start position:0%
+I can
+ 
+
+ align:start position:0%
+I can
+ask how many lines it takes to cover
+
+ align:start position:0%
+ask how many lines it takes to cover
+ 
+
+ align:start position:0%
+ask how many lines it takes to cover
+them shall we create I've never done
+
+ align:start position:0%
+them shall we create I've never done
+ 
+
+ align:start position:0%
+them shall we create I've never done
+this but should we just have another
+
+ align:start position:0%
+this but should we just have another
+ 
+
+ align:start position:0%
+this but should we just have another
+example up here of a bigger Matrix can I
+
+ align:start position:0%
+example up here of a bigger Matrix can I
+ 
+
+ align:start position:0%
+example up here of a bigger Matrix can I
+I'll just put in some ones and zeros at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+random sorry I'm just doing this totally
+
+ align:start position:0%
+random sorry I'm just doing this totally
+ 
+
+ align:start position:0%
+random sorry I'm just doing this totally
+at random without a without figur out
+
+ align:start position:0%
+at random without a without figur out
+ 
+
+ align:start position:0%
+at random without a without figur out
+ahead of time how many lines would cover
+
+ align:start position:0%
+ahead of time how many lines would cover
+ 
+
+ align:start position:0%
+ahead of time how many lines would cover
+them all right I don't know do you you
+
+ align:start position:0%
+them all right I don't know do you you
+ 
+
+ align:start position:0%
+them all right I don't know do you you
+think we could marry these get a perfect
+
+ align:start position:0%
+think we could marry these get a perfect
+ 
+
+ align:start position:0%
+think we could marry these get a perfect
+matching out of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+well I guess it's stupid for me to have
+
+ align:start position:0%
+well I guess it's stupid for me to have
+ 
+
+ align:start position:0%
+well I guess it's stupid for me to have
+started here because this 5x5 problem is
+
+ align:start position:0%
+started here because this 5x5 problem is
+ 
+
+ align:start position:0%
+started here because this 5x5 problem is
+not probably solvable in an instant time
+
+ align:start position:0%
+not probably solvable in an instant time
+ 
+
+ align:start position:0%
+not probably solvable in an instant time
+uh or could I cover it with less than
+
+ align:start position:0%
+uh or could I cover it with less than
+ 
+
+ align:start position:0%
+uh or could I cover it with less than
+four lines Well everybody's looking
+
+ align:start position:0%
+four lines Well everybody's looking
+ 
+
+ align:start position:0%
+four lines Well everybody's looking
+uh I bet none of us I bet got at least
+
+ align:start position:0%
+uh I bet none of us I bet got at least
+ 
+
+ align:start position:0%
+uh I bet none of us I bet got at least
+four horizontal lines
+
+ align:start position:0%
+four horizontal lines
+ 
+
+ align:start position:0%
+four horizontal lines
+right say I need at least four and
+
+ align:start position:0%
+right say I need at least four and
+ 
+
+ align:start position:0%
+right say I need at least four and
+probably I need five do I need five
+
+ align:start position:0%
+probably I need five do I need five
+ 
+
+ align:start position:0%
+probably I need five do I need five
+lines to cover that yeah maybe even six
+
+ align:start position:0%
+lines to cover that yeah maybe even six
+ 
+
+ align:start position:0%
+lines to cover that yeah maybe even six
+oh don't W take me six I mean even I can
+
+ align:start position:0%
+oh don't W take me six I mean even I can
+ 
+
+ align:start position:0%
+oh don't W take me six I mean even I can
+do it with five right yes right and that
+
+ align:start position:0%
+do it with five right yes right and that
+ 
+
+ align:start position:0%
+do it with five right yes right and that
+would mean that I could find a matching
+
+ align:start position:0%
+would mean that I could find a matching
+ 
+
+ align:start position:0%
+would mean that I could find a matching
+let's look for a matching hey there
+
+ align:start position:0%
+let's look for a matching hey there
+ 
+
+ align:start position:0%
+let's look for a matching hey there
+might be one of course what will a
+
+ align:start position:0%
+might be one of course what will a
+ 
+
+ align:start position:0%
+might be one of course what will a
+matching be a matching will be a
+
+ align:start position:0%
+matching be a matching will be a
+ 
+
+ align:start position:0%
+matching be a matching will be a
+marriage a set of marriages and that
+
+ align:start position:0%
+marriage a set of marriages and that
+ 
+
+ align:start position:0%
+marriage a set of marriages and that
+means that the ones have to come from
+
+ align:start position:0%
+means that the ones have to come from
+ 
+
+ align:start position:0%
+means that the ones have to come from
+different rows and columns CU each
+
+ align:start position:0%
+different rows and columns CU each
+ 
+
+ align:start position:0%
+different rows and columns CU each
+marriage is like unique so maybe suppose
+
+ align:start position:0%
+marriage is like unique so maybe suppose
+ 
+
+ align:start position:0%
+marriage is like unique so maybe suppose
+I yeah let me try to marry them marry
+
+ align:start position:0%
+I yeah let me try to marry them marry
+ 
+
+ align:start position:0%
+I yeah let me try to marry them marry
+them marry them oops better not let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see move the top one yes move that way
+
+ align:start position:0%
+see move the top one yes move that way
+ 
+
+ align:start position:0%
+see move the top one yes move that way
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+here then this is okay and all right
+
+ align:start position:0%
+here then this is okay and all right
+ 
+
+ align:start position:0%
+here then this is okay and all right
+yeah so there I
+
+ align:start position:0%
+yeah so there I
+ 
+
+ align:start position:0%
+yeah so there I
+see that uh I can marry all
+
+ align:start position:0%
+see that uh I can marry all
+ 
+
+ align:start position:0%
+see that uh I can marry all
+five and I believe that tells me it
+
+ align:start position:0%
+five and I believe that tells me it
+ 
+
+ align:start position:0%
+five and I believe that tells me it
+takes me five lines now somebody tell me
+
+ align:start position:0%
+takes me five lines now somebody tell me
+ 
+
+ align:start position:0%
+takes me five lines now somebody tell me
+the reasoning there how do I now know
+
+ align:start position:0%
+the reasoning there how do I now know
+ 
+
+ align:start position:0%
+the reasoning there how do I now know
+that I cannot cover
+
+ align:start position:0%
+that I cannot cover
+ 
+
+ align:start position:0%
+that I cannot cover
+those all the
+
+ align:start position:0%
+those all the
+ 
+
+ align:start position:0%
+those all the
+ones with less than five lines how do I
+
+ align:start position:0%
+ones with less than five lines how do I
+ 
+
+ align:start position:0%
+ones with less than five lines how do I
+now know that don't tell don't say it
+
+ align:start position:0%
+now know that don't tell don't say it
+ 
+
+ align:start position:0%
+now know that don't tell don't say it
+for a minute how do I now know so the
+
+ align:start position:0%
+for a minute how do I now know so the
+ 
+
+ align:start position:0%
+for a minute how do I now know so the
+the answer I claim was five
+
+ align:start position:0%
+the answer I claim was five
+ 
+
+ align:start position:0%
+the answer I claim was five
+I could get five matches and I showed
+
+ align:start position:0%
+I could get five matches and I showed
+ 
+
+ align:start position:0%
+I could get five matches and I showed
+what they were and I believe that the
+
+ align:start position:0%
+what they were and I believe that the
+ 
+
+ align:start position:0%
+what they were and I believe that the
+minimum number of lines so this is like
+
+ align:start position:0%
+minimum number of lines so this is like
+ 
+
+ align:start position:0%
+minimum number of lines so this is like
+weak Duality again the minimum is five I
+
+ align:start position:0%
+weak Duality again the minimum is five I
+ 
+
+ align:start position:0%
+weak Duality again the minimum is five I
+can't do it with less how do how do you
+
+ align:start position:0%
+can't do it with less how do how do you
+ 
+
+ align:start position:0%
+can't do it with less how do how do you
+see that I cannot cover those with five
+
+ align:start position:0%
+see that I cannot cover those with five
+ 
+
+ align:start position:0%
+see that I cannot cover those with five
+lines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay right that's right my line will
+
+ align:start position:0%
+okay right that's right my line will
+ 
+
+ align:start position:0%
+okay right that's right my line will
+have to my lines have to cover all five
+
+ align:start position:0%
+have to my lines have to cover all five
+ 
+
+ align:start position:0%
+have to my lines have to cover all five
+of those those circled ones I don't even
+
+ align:start position:0%
+of those those circled ones I don't even
+ 
+
+ align:start position:0%
+of those those circled ones I don't even
+care about I mean just to cover those
+
+ align:start position:0%
+care about I mean just to cover those
+ 
+
+ align:start position:0%
+care about I mean just to cover those
+five circled ones is going to take me
+
+ align:start position:0%
+five circled ones is going to take me
+ 
+
+ align:start position:0%
+five circled ones is going to take me
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+lines right so that's why that's the
+
+ align:start position:0%
+lines right so that's why that's the
+ 
+
+ align:start position:0%
+lines right so that's why that's the
+weak Duality that the number of matches
+
+ align:start position:0%
+weak Duality that the number of matches
+ 
+
+ align:start position:0%
+weak Duality that the number of matches
+is always less or
+
+ align:start position:0%
+is always less or
+ 
+
+ align:start position:0%
+is always less or
+equal the number of lines because
+
+ align:start position:0%
+equal the number of lines because
+ 
+
+ align:start position:0%
+equal the number of lines because
+anytime I've got a match I've got some
+
+ align:start position:0%
+anytime I've got a match I've got some
+ 
+
+ align:start position:0%
+anytime I've got a match I've got some
+ones that I need that many lines to
+
+ align:start position:0%
+ones that I need that many lines to
+ 
+
+ align:start position:0%
+ones that I need that many lines to
+cover because a line can't cover two in
+
+ align:start position:0%
+cover because a line can't cover two in
+ 
+
+ align:start position:0%
+cover because a line can't cover two in
+a match right a line no line could cover
+
+ align:start position:0%
+a match right a line no line could cover
+ 
+
+ align:start position:0%
+a match right a line no line could cover
+two of these at once a line could only
+
+ align:start position:0%
+two of these at once a line could only
+ 
+
+ align:start position:0%
+two of these at once a line could only
+cover one marriage and and maybe some
+
+ align:start position:0%
+cover one marriage and and maybe some
+ 
+
+ align:start position:0%
+cover one marriage and and maybe some
+extra stuff but it's going to take me
+
+ align:start position:0%
+extra stuff but it's going to take me
+ 
+
+ align:start position:0%
+extra stuff but it's going to take me
+five lines to cover five matches you see
+
+ align:start position:0%
+five lines to cover five matches you see
+ 
+
+ align:start position:0%
+five lines to cover five matches you see
+that weak Duality then has an easy
+
+ align:start position:0%
+that weak Duality then has an easy
+ 
+
+ align:start position:0%
+that weak Duality then has an easy
+argument but the equation the fact that
+
+ align:start position:0%
+argument but the equation the fact that
+ 
+
+ align:start position:0%
+argument but the equation the fact that
+the number of so I made it I made let's
+
+ align:start position:0%
+the number of so I made it I made let's
+ 
+
+ align:start position:0%
+the number of so I made it I made let's
+see let me let me can I change this
+
+ align:start position:0%
+see let me let me can I change this
+ 
+
+ align:start position:0%
+see let me let me can I change this
+problem by changing some of these to
+
+ align:start position:0%
+problem by changing some of these to
+ 
+
+ align:start position:0%
+problem by changing some of these to
+zeros does that now does that now
+
+ align:start position:0%
+zeros does that now does that now
+ 
+
+ align:start position:0%
+zeros does that now does that now
+prevent event five
+
+ align:start position:0%
+prevent event five
+ 
+
+ align:start position:0%
+prevent event five
+matches row fourth row okay let me make
+
+ align:start position:0%
+matches row fourth row okay let me make
+ 
+
+ align:start position:0%
+matches row fourth row okay let me make
+that a zero
+
+ align:start position:0%
+that a zero
+ 
+
+ align:start position:0%
+that a zero
+also all right no
+
+ align:start position:0%
+also all right no
+ 
+
+ align:start position:0%
+also all right no
+problem and the thir one goes the way to
+
+ align:start position:0%
+problem and the thir one goes the way to
+ 
+
+ align:start position:0%
+problem and the thir one goes the way to
+the right and the first one so what else
+
+ align:start position:0%
+the right and the first one so what else
+ 
+
+ align:start position:0%
+the right and the first one so what else
+do you want me to turn into a zero th
+
+ align:start position:0%
+do you want me to turn into a zero th
+ 
+
+ align:start position:0%
+do you want me to turn into a zero th
+this one yeah so if I make I make that a
+
+ align:start position:0%
+this one yeah so if I make I make that a
+ 
+
+ align:start position:0%
+this one yeah so if I make I make that a
+zero that's not a problem because
+
+ align:start position:0%
+zero that's not a problem because
+ 
+
+ align:start position:0%
+zero that's not a problem because
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+right so tell me what to make a zero
+
+ align:start position:0%
+right so tell me what to make a zero
+ 
+
+ align:start position:0%
+right so tell me what to make a zero
+that last that a zero oh if I put a zero
+
+ align:start position:0%
+that last that a zero oh if I put a zero
+ 
+
+ align:start position:0%
+that last that a zero oh if I put a zero
+there yeah but anybody can do that uh I
+
+ align:start position:0%
+there yeah but anybody can do that uh I
+ 
+
+ align:start position:0%
+there yeah but anybody can do that uh I
+want to put one somewhere else well all
+
+ align:start position:0%
+want to put one somewhere else well all
+ 
+
+ align:start position:0%
+want to put one somewhere else well all
+right I'll do one and then you'll tell
+
+ align:start position:0%
+right I'll do one and then you'll tell
+ 
+
+ align:start position:0%
+right I'll do one and then you'll tell
+me that that's not enough right that's
+
+ align:start position:0%
+me that that's not enough right that's
+ 
+
+ align:start position:0%
+me that that's not enough right that's
+definitely not enough definitely all
+
+ align:start position:0%
+definitely not enough definitely all
+ 
+
+ align:start position:0%
+definitely not enough definitely all
+right all right so you you say that's
+
+ align:start position:0%
+right all right so you you say that's
+ 
+
+ align:start position:0%
+right all right so you you say that's
+not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enough it is enough yeah I think so it's
+
+ align:start position:0%
+enough it is enough yeah I think so it's
+ 
+
+ align:start position:0%
+enough it is enough yeah I think so it's
+getting there I'm getting there I'm I'm
+
+ align:start position:0%
+getting there I'm getting there I'm I'm
+ 
+
+ align:start position:0%
+getting there I'm getting there I'm I'm
+removing uh remember the bottom row yeah
+
+ align:start position:0%
+removing uh remember the bottom row yeah
+ 
+
+ align:start position:0%
+removing uh remember the bottom row yeah
+this so this
+
+ align:start position:0%
+this so this
+ 
+
+ align:start position:0%
+this so this
+right okay is that is a match possible
+
+ align:start position:0%
+right okay is that is a match possible
+ 
+
+ align:start position:0%
+right okay is that is a match possible
+there yes still one over the way to the
+
+ align:start position:0%
+there yes still one over the way to the
+ 
+
+ align:start position:0%
+there yes still one over the way to the
+right it's you still got a way to match
+
+ align:start position:0%
+right it's you still got a way to match
+ 
+
+ align:start position:0%
+right it's you still got a way to match
+those all right I'll take another one
+
+ align:start position:0%
+those all right I'll take another one
+ 
+
+ align:start position:0%
+those all right I'll take another one
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+uh well which I'll take one of these
+
+ align:start position:0%
+uh well which I'll take one of these
+ 
+
+ align:start position:0%
+uh well which I'll take one of these
+away yeah like that one no no no that
+
+ align:start position:0%
+away yeah like that one no no no that
+ 
+
+ align:start position:0%
+away yeah like that one no no no that
+didn't hurt like that one the first or
+
+ align:start position:0%
+didn't hurt like that one the first or
+ 
+
+ align:start position:0%
+didn't hurt like that one the first or
+the all right now we've got it okay now
+
+ align:start position:0%
+the all right now we've got it okay now
+ 
+
+ align:start position:0%
+the all right now we've got it okay now
+we believe that only the four the the we
+
+ align:start position:0%
+we believe that only the four the the we
+ 
+
+ align:start position:0%
+we believe that only the four the the we
+can only marry off four
+
+ align:start position:0%
+can only marry off four
+ 
+
+ align:start position:0%
+can only marry off four
+right but now how do we prove it because
+
+ align:start position:0%
+right but now how do we prove it because
+ 
+
+ align:start position:0%
+right but now how do we prove it because
+because you got to find four lines that
+
+ align:start position:0%
+because you got to find four lines that
+ 
+
+ align:start position:0%
+because you got to find four lines that
+cover
+
+ align:start position:0%
+cover
+ 
+
+ align:start position:0%
+cover
+everybody and that would
+
+ align:start position:0%
+everybody and that would
+ 
+
+ align:start position:0%
+everybody and that would
+say now what are four lines first two
+
+ align:start position:0%
+say now what are four lines first two
+ 
+
+ align:start position:0%
+say now what are four lines first two
+columns yeah just let me ask this
+
+ align:start position:0%
+columns yeah just let me ask this
+ 
+
+ align:start position:0%
+columns yeah just let me ask this
+question well no I won't but so if I
+
+ align:start position:0%
+question well no I won't but so if I
+ 
+
+ align:start position:0%
+question well no I won't but so if I
+find four lines that cover everybody
+
+ align:start position:0%
+find four lines that cover everybody
+ 
+
+ align:start position:0%
+find four lines that cover everybody
+then there could only be four matches
+
+ align:start position:0%
+then there could only be four matches
+ 
+
+ align:start position:0%
+then there could only be four matches
+cuz if there were five matches I could
+
+ align:start position:0%
+cuz if there were five matches I could
+ 
+
+ align:start position:0%
+cuz if there were five matches I could
+not cover all five all right now you now
+
+ align:start position:0%
+not cover all five all right now you now
+ 
+
+ align:start position:0%
+not cover all five all right now you now
+I'm ready to listen what
+
+ align:start position:0%
+I'm ready to listen what
+ 
+
+ align:start position:0%
+I'm ready to listen what
+for sorry two columns first two
+
+ align:start position:0%
+for sorry two columns first two
+ 
+
+ align:start position:0%
+for sorry two columns first two
+columns and then two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rows okay and that left me a matrix of
+
+ align:start position:0%
+rows okay and that left me a matrix of
+ 
+
+ align:start position:0%
+rows okay and that left me a matrix of
+zeros a submatrix of zeros which should
+
+ align:start position:0%
+zeros a submatrix of zeros which should
+ 
+
+ align:start position:0%
+zeros a submatrix of zeros which should
+should tell me that trouble where the
+
+ align:start position:0%
+should tell me that trouble where the
+ 
+
+ align:start position:0%
+should tell me that trouble where the
+trouble is this this Matrix of zeros
+
+ align:start position:0%
+trouble is this this Matrix of zeros
+ 
+
+ align:start position:0%
+trouble is this this Matrix of zeros
+tells me that girls girls one 2 and four
+
+ align:start position:0%
+tells me that girls girls one 2 and four
+ 
+
+ align:start position:0%
+tells me that girls girls one 2 and four
+won't uh don't obviously tells me that
+
+ align:start position:0%
+won't uh don't obviously tells me that
+ 
+
+ align:start position:0%
+won't uh don't obviously tells me that
+boys three four and five are no good are
+
+ align:start position:0%
+boys three four and five are no good are
+ 
+
+ align:start position:0%
+boys three four and five are no good are
+not acceptable and
+
+ align:start position:0%
+not acceptable and
+ 
+
+ align:start position:0%
+not acceptable and
+therefore uh so the only boys that are
+
+ align:start position:0%
+therefore uh so the only boys that are
+ 
+
+ align:start position:0%
+therefore uh so the only boys that are
+acceptable for I have three girls and
+
+ align:start position:0%
+acceptable for I have three girls and
+ 
+
+ align:start position:0%
+acceptable for I have three girls and
+the only boys that are acceptable are
+
+ align:start position:0%
+the only boys that are acceptable are
+ 
+
+ align:start position:0%
+the only boys that are acceptable are
+the remaining one and two yeah which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is was this one two
+
+ align:start position:0%
+is was this one two
+ 
+
+ align:start position:0%
+is was this one two
+five girls
+
+ align:start position:0%
+five girls
+ 
+
+ align:start position:0%
+five girls
+one let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see I thought these zeros and these
+
+ align:start position:0%
+see I thought these zeros and these
+ 
+
+ align:start position:0%
+see I thought these zeros and these
+zeros and these zeros refer to oh yeah
+
+ align:start position:0%
+zeros and these zeros refer to oh yeah
+ 
+
+ align:start position:0%
+zeros and these zeros refer to oh yeah
+refers to girls 125 right right refers
+
+ align:start position:0%
+refers to girls 125 right right refers
+ 
+
+ align:start position:0%
+refers to girls 125 right right refers
+to girls 125 and they will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not match boys 345 they only match boys
+
+ align:start position:0%
+not match boys 345 they only match boys
+ 
+
+ align:start position:0%
+not match boys 345 they only match boys
+one two and here I have a set of three
+
+ align:start position:0%
+one two and here I have a set of three
+ 
+
+ align:start position:0%
+one two and here I have a set of three
+girls and only two boys one two and five
+
+ align:start position:0%
+girls and only two boys one two and five
+ 
+
+ align:start position:0%
+girls and only two boys one two and five
+the only two boys are these two
+
+ align:start position:0%
+the only two boys are these two
+ 
+
+ align:start position:0%
+the only two boys are these two
+boys yeah Haven you saw
+
+ align:start position:0%
+boys yeah Haven you saw
+ 
+
+ align:start position:0%
+boys yeah Haven you saw
+partition here yes yes I could express
+
+ align:start position:0%
+partition here yes yes I could express
+ 
+
+ align:start position:0%
+partition here yes yes I could express
+this in graph language too that's right
+
+ align:start position:0%
+this in graph language too that's right
+ 
+
+ align:start position:0%
+this in graph language too that's right
+that's right yeah uh it's it's yeah it's
+
+ align:start position:0%
+that's right yeah uh it's it's yeah it's
+ 
+
+ align:start position:0%
+that's right yeah uh it's it's yeah it's
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+a you know the problem sounds like a j
+
+ align:start position:0%
+a you know the problem sounds like a j
+ 
+
+ align:start position:0%
+a you know the problem sounds like a j
+problem but it appears all over the
+
+ align:start position:0%
+problem but it appears all over the
+ 
+
+ align:start position:0%
+problem but it appears all over the
+place as it's a very quite a fundamental
+
+ align:start position:0%
+place as it's a very quite a fundamental
+ 
+
+ align:start position:0%
+place as it's a very quite a fundamental
+matching so that's why matching is the
+
+ align:start position:0%
+matching so that's why matching is the
+ 
+
+ align:start position:0%
+matching so that's why matching is the
+or assign sometimes assignment problem
+
+ align:start position:0%
+or assign sometimes assignment problem
+ 
+
+ align:start position:0%
+or assign sometimes assignment problem
+is were used but matching is and a
+
+ align:start position:0%
+is were used but matching is and a
+ 
+
+ align:start position:0%
+is were used but matching is and a
+perfect matching is is complete matching
+
+ align:start position:0%
+perfect matching is is complete matching
+ 
+
+ align:start position:0%
+perfect matching is is complete matching
+yeah so it's uh so that's the matching
+
+ align:start position:0%
+yeah so it's uh so that's the matching
+ 
+
+ align:start position:0%
+yeah so it's uh so that's the matching
+problem so maybe I could and and it
+
+ align:start position:0%
+problem so maybe I could and and it
+ 
+
+ align:start position:0%
+problem so maybe I could and and it
+connects to this type of bipar I
+
+ align:start position:0%
+connects to this type of bipar I
+ 
+
+ align:start position:0%
+connects to this type of bipar I
+two-part graph okay um can I go to a
+
+ align:start position:0%
+two-part graph okay um can I go to a
+ 
+
+ align:start position:0%
+two-part graph okay um can I go to a
+second problem but any question on this
+
+ align:start position:0%
+second problem but any question on this
+ 
+
+ align:start position:0%
+second problem but any question on this
+one yeah yeah what happens if you like
+
+ align:start position:0%
+one yeah yeah what happens if you like
+ 
+
+ align:start position:0%
+one yeah yeah what happens if you like
+add
+
+ align:start position:0%
+add
+ 
+
+ align:start position:0%
+add
+another put three groups yes that so
+
+ align:start position:0%
+another put three groups yes that so
+ 
+
+ align:start position:0%
+another put three groups yes that so
+tripartite graph I don't
+
+ align:start position:0%
+tripartite graph I don't
+ 
+
+ align:start position:0%
+tripartite graph I don't
+know I don't know I mean it's that
+
+ align:start position:0%
+know I don't know I mean it's that
+ 
+
+ align:start position:0%
+know I don't know I mean it's that
+you're thinking like a graph theorist I
+
+ align:start position:0%
+you're thinking like a graph theorist I
+ 
+
+ align:start position:0%
+you're thinking like a graph theorist I
+mean this is how this subject
+
+ align:start position:0%
+mean this is how this subject
+ 
+
+ align:start position:0%
+mean this is how this subject
+grows um uh and uh and some directions
+
+ align:start position:0%
+grows um uh and uh and some directions
+ 
+
+ align:start position:0%
+grows um uh and uh and some directions
+lead to a beautiful theorem they're all
+
+ align:start position:0%
+lead to a beautiful theorem they're all
+ 
+
+ align:start position:0%
+lead to a beautiful theorem they're all
+going to lead to some Duality if you
+
+ align:start position:0%
+going to lead to some Duality if you
+ 
+
+ align:start position:0%
+going to lead to some Duality if you
+give me a linear program uh but
+
+ align:start position:0%
+give me a linear program uh but
+ 
+
+ align:start position:0%
+give me a linear program uh but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh as I say I could have formulated this
+
+ align:start position:0%
+uh as I say I could have formulated this
+ 
+
+ align:start position:0%
+uh as I say I could have formulated this
+problem as a linear programming problem
+
+ align:start position:0%
+problem as a linear programming problem
+ 
+
+ align:start position:0%
+problem as a linear programming problem
+but and what's special about it is the
+
+ align:start position:0%
+but and what's special about it is the
+ 
+
+ align:start position:0%
+but and what's special about it is the
+corners would have turned out to be
+
+ align:start position:0%
+corners would have turned out to be
+ 
+
+ align:start position:0%
+corners would have turned out to be
+integers so that I only really had to
+
+ align:start position:0%
+integers so that I only really had to
+ 
+
+ align:start position:0%
+integers so that I only really had to
+look at integers and of course that's
+
+ align:start position:0%
+look at integers and of course that's
+ 
+
+ align:start position:0%
+look at integers and of course that's
+all I did just zeros and ones okay could
+
+ align:start position:0%
+all I did just zeros and ones okay could
+ 
+
+ align:start position:0%
+all I did just zeros and ones okay could
+I try to tell you about this Max flow
+
+ align:start position:0%
+I try to tell you about this Max flow
+ 
+
+ align:start position:0%
+I try to tell you about this Max flow
+problem uh I'll take let me take the
+
+ align:start position:0%
+problem uh I'll take let me take the
+ 
+
+ align:start position:0%
+problem uh I'll take let me take the
+example so now I'm going to have a
+
+ align:start position:0%
+example so now I'm going to have a
+ 
+
+ align:start position:0%
+example so now I'm going to have a
+network so now I'm doing Max flow well
+
+ align:start position:0%
+network so now I'm doing Max flow well
+ 
+
+ align:start position:0%
+network so now I'm doing Max flow well
+trees and graphs and and the example
+
+ align:start position:0%
+trees and graphs and and the example
+ 
+
+ align:start position:0%
+trees and graphs and and the example
+will be Max flow okay so so so
+
+ align:start position:0%
+will be Max flow okay so so so
+ 
+
+ align:start position:0%
+will be Max flow okay so so so
+graphs networks really networks and
+
+ align:start position:0%
+graphs networks really networks and
+ 
+
+ align:start position:0%
+graphs networks really networks and
+maximum flow okay okay so I'm going to
+
+ align:start position:0%
+maximum flow okay okay so I'm going to
+ 
+
+ align:start position:0%
+maximum flow okay okay so I'm going to
+draw a network here and it will have
+
+ align:start position:0%
+draw a network here and it will have
+ 
+
+ align:start position:0%
+draw a network here and it will have
+have uh a
+
+ align:start position:0%
+have uh a
+ 
+
+ align:start position:0%
+have uh a
+source and then
+
+ align:start position:0%
+source and then
+ 
+
+ align:start position:0%
+source and then
+edges through the network maybe maybe
+
+ align:start position:0%
+edges through the network maybe maybe
+ 
+
+ align:start position:0%
+edges through the network maybe maybe
+some more intermediate nodes and maybe
+
+ align:start position:0%
+some more intermediate nodes and maybe
+ 
+
+ align:start position:0%
+some more intermediate nodes and maybe
+some more intermediate nodes and then
+
+ align:start position:0%
+some more intermediate nodes and then
+ 
+
+ align:start position:0%
+some more intermediate nodes and then
+coming maybe some more nodes coming down
+
+ align:start position:0%
+coming maybe some more nodes coming down
+ 
+
+ align:start position:0%
+coming maybe some more nodes coming down
+to a
+
+ align:start position:0%
+to a
+ 
+
+ align:start position:0%
+to a
+sync S
+
+ align:start position:0%
+sync S
+ 
+
+ align:start position:0%
+sync S
+Prime now and I could connect some more
+
+ align:start position:0%
+Prime now and I could connect some more
+ 
+
+ align:start position:0%
+Prime now and I could connect some more
+of those I've forgotten whether I do in
+
+ align:start position:0%
+of those I've forgotten whether I do in
+ 
+
+ align:start position:0%
+of those I've forgotten whether I do in
+the uh in the problem
+
+ align:start position:0%
+the uh in the problem
+ 
+
+ align:start position:0%
+the uh in the problem
+here uh let me just F I'm just going to
+
+ align:start position:0%
+here uh let me just F I'm just going to
+ 
+
+ align:start position:0%
+here uh let me just F I'm just going to
+take the example that's in the
+
+ align:start position:0%
+take the example that's in the
+ 
+
+ align:start position:0%
+take the example that's in the
+book yeah few more connections are in
+
+ align:start position:0%
+book yeah few more connections are in
+ 
+
+ align:start position:0%
+book yeah few more connections are in
+here here to here here to here there
+
+ align:start position:0%
+here here to here here to here there
+ 
+
+ align:start position:0%
+here here to here here to here there
+okay now the point is I'm going to give
+
+ align:start position:0%
+okay now the point is I'm going to give
+ 
+
+ align:start position:0%
+okay now the point is I'm going to give
+capacities all those
+
+ align:start position:0%
+capacities all those
+ 
+
+ align:start position:0%
+capacities all those
+edges the edges that are not in there
+
+ align:start position:0%
+edges the edges that are not in there
+ 
+
+ align:start position:0%
+edges the edges that are not in there
+have capacity zero can't send any flow
+
+ align:start position:0%
+have capacity zero can't send any flow
+ 
+
+ align:start position:0%
+have capacity zero can't send any flow
+and all the other edges I'm going to put
+
+ align:start position:0%
+and all the other edges I'm going to put
+ 
+
+ align:start position:0%
+and all the other edges I'm going to put
+in capacities and let me put those in in
+
+ align:start position:0%
+in capacities and let me put those in in
+ 
+
+ align:start position:0%
+in capacities and let me put those in in
+yellow so here here are the capacities
+
+ align:start position:0%
+yellow so here here are the capacities
+ 
+
+ align:start position:0%
+yellow so here here are the capacities
+of these edges five 7 and N so this was
+
+ align:start position:0%
+of these edges five 7 and N so this was
+ 
+
+ align:start position:0%
+of these edges five 7 and N so this was
+the sink the source
+
+ align:start position:0%
+the sink the source
+ 
+
+ align:start position:0%
+the sink the source
+source 57 9 2 two on those vertical
+
+ align:start position:0%
+source 57 9 2 two on those vertical
+ 
+
+ align:start position:0%
+source 57 9 2 two on those vertical
+edges 1 14 and
+
+ align:start position:0%
+edges 1 14 and
+ 
+
+ align:start position:0%
+edges 1 14 and
+1 one and one on those edges and 68 and
+
+ align:start position:0%
+1 one and one on those edges and 68 and
+ 
+
+ align:start position:0%
+1 one and one on those edges and 68 and
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+five on those
+
+ align:start position:0%
+five on those
+ 
+
+ align:start position:0%
+five on those
+edges and I'm just going to ask you send
+
+ align:start position:0%
+edges and I'm just going to ask you send
+ 
+
+ align:start position:0%
+edges and I'm just going to ask you send
+as much as possible from the sink source
+
+ align:start position:0%
+as much as possible from the sink source
+ 
+
+ align:start position:0%
+as much as possible from the sink source
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+sink how much flow so that's the maximum
+
+ align:start position:0%
+sink how much flow so that's the maximum
+ 
+
+ align:start position:0%
+sink how much flow so that's the maximum
+flow problem Max flow maximize flow
+
+ align:start position:0%
+flow problem Max flow maximize flow
+ 
+
+ align:start position:0%
+flow problem Max flow maximize flow
+from source to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sink and of course what's the
+
+ align:start position:0%
+sink and of course what's the
+ 
+
+ align:start position:0%
+sink and of course what's the
+constraint the flows have to be so
+
+ align:start position:0%
+constraint the flows have to be so
+ 
+
+ align:start position:0%
+constraint the flows have to be so
+there's a flow on these edges and the
+
+ align:start position:0%
+there's a flow on these edges and the
+ 
+
+ align:start position:0%
+there's a flow on these edges and the
+flows have to be non-
+
+ align:start position:0%
+flows have to be non-
+ 
+
+ align:start position:0%
+flows have to be non-
+negative let's say but they can't exceed
+
+ align:start position:0%
+negative let's say but they can't exceed
+ 
+
+ align:start position:0%
+negative let's say but they can't exceed
+the capacity the
+
+ align:start position:0%
+the capacity the
+ 
+
+ align:start position:0%
+the capacity the
+flow less or equal to the capacity
+
+ align:start position:0%
+flow less or equal to the capacity
+ 
+
+ align:start position:0%
+flow less or equal to the capacity
+that's where our inequality really comes
+
+ align:start position:0%
+that's where our inequality really comes
+ 
+
+ align:start position:0%
+that's where our inequality really comes
+on each Edge each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Edge the flow has to be less or equal
+
+ align:start position:0%
+Edge the flow has to be less or equal
+ 
+
+ align:start position:0%
+Edge the flow has to be less or equal
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacity
+
+ align:start position:0%
+capacity
+ 
+
+ align:start position:0%
+capacity
+uh I yes I I it's like steady state or
+
+ align:start position:0%
+uh I yes I I it's like steady state or
+ 
+
+ align:start position:0%
+uh I yes I I it's like steady state or
+something I I'm thinking of those yeah
+
+ align:start position:0%
+something I I'm thinking of those yeah
+ 
+
+ align:start position:0%
+something I I'm thinking of those yeah
+I've got a bunch of stuff at the
+
+ align:start position:0%
+I've got a bunch of stuff at the
+ 
+
+ align:start position:0%
+I've got a bunch of stuff at the
+source like um trucks or whatever and
+
+ align:start position:0%
+source like um trucks or whatever and
+ 
+
+ align:start position:0%
+source like um trucks or whatever and
+I've got to send them to the sink
+
+ align:start position:0%
+I've got to send them to the sink
+ 
+
+ align:start position:0%
+I've got to send them to the sink
+and I can't send more so for example I
+
+ align:start position:0%
+and I can't send more so for example I
+ 
+
+ align:start position:0%
+and I can't send more so for example I
+absolutely my my capacity is certainly
+
+ align:start position:0%
+absolutely my my capacity is certainly
+ 
+
+ align:start position:0%
+absolutely my my capacity is certainly
+my flow is less than what I certainly
+
+ align:start position:0%
+my flow is less than what I certainly
+ 
+
+ align:start position:0%
+my flow is less than what I certainly
+can't send more than 5 S9
+
+ align:start position:0%
+can't send more than 5 S9
+ 
+
+ align:start position:0%
+can't send more than 5 S9
+21 absolutely but can I send 21
+
+ align:start position:0%
+21 absolutely but can I send 21
+ 
+
+ align:start position:0%
+21 absolutely but can I send 21
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+not solving my problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+already at the sink I could only get 19
+
+ align:start position:0%
+already at the sink I could only get 19
+ 
+
+ align:start position:0%
+already at the sink I could only get 19
+to the sink
+
+ align:start position:0%
+to the sink
+ 
+
+ align:start position:0%
+to the sink
+okay I can't even send 19 across the
+
+ align:start position:0%
+okay I can't even send 19 across the
+ 
+
+ align:start position:0%
+okay I can't even send 19 across the
+middle I could send
+
+ align:start position:0%
+middle I could send
+ 
+
+ align:start position:0%
+middle I could send
+16 you but I can't get 16 through no
+
+ align:start position:0%
+16 you but I can't get 16 through no
+ 
+
+ align:start position:0%
+16 you but I can't get 16 through no
+yeah this is fun right yes
+
+ align:start position:0%
+yeah this is fun right yes
+ 
+
+ align:start position:0%
+yeah this is fun right yes
+basically what how so what's your since
+
+ align:start position:0%
+basically what how so what's your since
+ 
+
+ align:start position:0%
+basically what how so what's your since
+you spoke up first you one second across
+
+ align:start position:0%
+you spoke up first you one second across
+ 
+
+ align:start position:0%
+you spoke up first you one second across
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right up and one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down right so your total your Capa your
+
+ align:start position:0%
+down right so your total your Capa your
+ 
+
+ align:start position:0%
+down right so your total your Capa your
+maximum is 12 that looks all right I
+
+ align:start position:0%
+maximum is 12 that looks all right I
+ 
+
+ align:start position:0%
+maximum is 12 that looks all right I
+think that sounds right so just to
+
+ align:start position:0%
+think that sounds right so just to
+ 
+
+ align:start position:0%
+think that sounds right so just to
+repeat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the 's I'm going to create a
+
+ align:start position:0%
+the 's I'm going to create a
+ 
+
+ align:start position:0%
+the 's I'm going to create a
+cut and and make the whole point here
+
+ align:start position:0%
+cut and and make the whole point here
+ 
+
+ align:start position:0%
+cut and and make the whole point here
+there's a cut here if I cut the network
+
+ align:start position:0%
+there's a cut here if I cut the network
+ 
+
+ align:start position:0%
+there's a cut here if I cut the network
+along
+
+ align:start position:0%
+along
+ 
+
+ align:start position:0%
+along
+that line so these guys are with the
+
+ align:start position:0%
+that line so these guys are with the
+ 
+
+ align:start position:0%
+that line so these guys are with the
+source and these guys are with the
+
+ align:start position:0%
+source and these guys are with the
+ 
+
+ align:start position:0%
+source and these guys are with the
+sink then I'm going to look how many can
+
+ align:start position:0%
+sink then I'm going to look how many can
+ 
+
+ align:start position:0%
+sink then I'm going to look how many can
+I get across the cut because I have to
+
+ align:start position:0%
+I get across the cut because I have to
+ 
+
+ align:start position:0%
+I get across the cut because I have to
+get it across the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cut
+
+ align:start position:0%
+cut
+ 
+
+ align:start position:0%
+cut
+and if I can do it the what's so what's
+
+ align:start position:0%
+and if I can do it the what's so what's
+ 
+
+ align:start position:0%
+and if I can do it the what's so what's
+the capacity of that cut 12 12 the the
+
+ align:start position:0%
+the capacity of that cut 12 12 the the
+ 
+
+ align:start position:0%
+the capacity of that cut 12 12 the the
+total that can cross is if I Cross by
+
+ align:start position:0%
+total that can cross is if I Cross by
+ 
+
+ align:start position:0%
+total that can cross is if I Cross by
+that edge one can cross if I Cross by
+
+ align:start position:0%
+that edge one can cross if I Cross by
+ 
+
+ align:start position:0%
+that edge one can cross if I Cross by
+that edge one more this way eight this
+
+ align:start position:0%
+that edge one more this way eight this
+ 
+
+ align:start position:0%
+that edge one more this way eight this
+way one this way one so if I'm going
+
+ align:start position:0%
+way one this way one so if I'm going
+ 
+
+ align:start position:0%
+way one this way one so if I'm going
+from this side of the cut to that side I
+
+ align:start position:0%
+from this side of the cut to that side I
+ 
+
+ align:start position:0%
+from this side of the cut to that side I
+cannot get more than 12 just the way I
+
+ align:start position:0%
+cannot get more than 12 just the way I
+ 
+
+ align:start position:0%
+cannot get more than 12 just the way I
+couldn't get more than 21 I mean we did
+
+ align:start position:0%
+couldn't get more than 21 I mean we did
+ 
+
+ align:start position:0%
+couldn't get more than 21 I mean we did
+a and you see the weak
+
+ align:start position:0%
+a and you see the weak
+ 
+
+ align:start position:0%
+a and you see the weak
+Duality as soon as I say hey I can't get
+
+ align:start position:0%
+Duality as soon as I say hey I can't get
+ 
+
+ align:start position:0%
+Duality as soon as I say hey I can't get
+more than 21 obvious I can't get more
+
+ align:start position:0%
+more than 21 obvious I can't get more
+ 
+
+ align:start position:0%
+more than 21 obvious I can't get more
+than 19 almost as obvious I can't get
+
+ align:start position:0%
+than 19 almost as obvious I can't get
+ 
+
+ align:start position:0%
+than 19 almost as obvious I can't get
+more than 16 almost as obvious I can't
+
+ align:start position:0%
+more than 16 almost as obvious I can't
+ 
+
+ align:start position:0%
+more than 16 almost as obvious I can't
+get more than
+
+ align:start position:0%
+get more than
+ 
+
+ align:start position:0%
+get more than
+12 less
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+obvious sorry the way you dra
+
+ align:start position:0%
+obvious sorry the way you dra
+ 
+
+ align:start position:0%
+obvious sorry the way you dra
+yes that it's less
+
+ align:start position:0%
+yes that it's less
+ 
+
+ align:start position:0%
+yes that it's less
+obvious you could yeah
+
+ align:start position:0%
+obvious you could yeah
+ 
+
+ align:start position:0%
+obvious you could yeah
+yeah I could have made that cut jump out
+
+ align:start position:0%
+yeah I could have made that cut jump out
+ 
+
+ align:start position:0%
+yeah I could have made that cut jump out
+all right yes but of course to the
+
+ align:start position:0%
+all right yes but of course to the
+ 
+
+ align:start position:0%
+all right yes but of course to the
+computer nothing is going to jump out so
+
+ align:start position:0%
+computer nothing is going to jump out so
+ 
+
+ align:start position:0%
+computer nothing is going to jump out so
+so we so in the end uh to solve a big
+
+ align:start position:0%
+so we so in the end uh to solve a big
+ 
+
+ align:start position:0%
+so we so in the end uh to solve a big
+problem which would be beyond our
+
+ align:start position:0%
+problem which would be beyond our
+ 
+
+ align:start position:0%
+problem which would be beyond our
+capacity we're going to hand it to the
+
+ align:start position:0%
+capacity we're going to hand it to the
+ 
+
+ align:start position:0%
+capacity we're going to hand it to the
+computer so we're going to the
+
+ align:start position:0%
+computer so we're going to the
+ 
+
+ align:start position:0%
+computer so we're going to the
+computer's going to be given the
+
+ align:start position:0%
+computer's going to be given the
+ 
+
+ align:start position:0%
+computer's going to be given the
+statement will be the capacities on all
+
+ align:start position:0%
+statement will be the capacities on all
+ 
+
+ align:start position:0%
+statement will be the capacities on all
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+edges and zero zero capacity on the on
+
+ align:start position:0%
+edges and zero zero capacity on the on
+ 
+
+ align:start position:0%
+edges and zero zero capacity on the on
+the uh absent
+
+ align:start position:0%
+the uh absent
+ 
+
+ align:start position:0%
+the uh absent
+edges and and of course as you can
+
+ align:start position:0%
+edges and and of course as you can
+ 
+
+ align:start position:0%
+edges and and of course as you can
+imagine we could allow ow different
+
+ align:start position:0%
+imagine we could allow ow different
+ 
+
+ align:start position:0%
+imagine we could allow ow different
+capacities in the two directions which
+
+ align:start position:0%
+capacities in the two directions which
+ 
+
+ align:start position:0%
+capacities in the two directions which
+would make the problem a little harder
+
+ align:start position:0%
+would make the problem a little harder
+ 
+
+ align:start position:0%
+would make the problem a little harder
+it be twice as many
+
+ align:start position:0%
+it be twice as many
+ 
+
+ align:start position:0%
+it be twice as many
+input for the for the program to deal
+
+ align:start position:0%
+input for the for the program to deal
+ 
+
+ align:start position:0%
+input for the for the program to deal
+with but still it would be a
+
+ align:start position:0%
+with but still it would be a
+ 
+
+ align:start position:0%
+with but still it would be a
+inequality set of inequality constraints
+
+ align:start position:0%
+inequality set of inequality constraints
+ 
+
+ align:start position:0%
+inequality set of inequality constraints
+and that it'd be a linear
+
+ align:start position:0%
+and that it'd be a linear
+ 
+
+ align:start position:0%
+and that it'd be a linear
+program and the beauty so the what's
+
+ align:start position:0%
+program and the beauty so the what's
+ 
+
+ align:start position:0%
+program and the beauty so the what's
+what's my main theorem here well I've
+
+ align:start position:0%
+what's my main theorem here well I've
+ 
+
+ align:start position:0%
+what's my main theorem here well I've
+stated it that maximum flow equals
+
+ align:start position:0%
+stated it that maximum flow equals
+ 
+
+ align:start position:0%
+stated it that maximum flow equals
+minimum
+
+ align:start position:0%
+minimum
+ 
+
+ align:start position:0%
+minimum
+That's The
+
+ align:start position:0%
+That's The
+ 
+
+ align:start position:0%
+That's The
+Duality the fact that maximum flow is
+
+ align:start position:0%
+Duality the fact that maximum flow is
+ 
+
+ align:start position:0%
+Duality the fact that maximum flow is
+less or equal that every flow is less
+
+ align:start position:0%
+less or equal that every flow is less
+ 
+
+ align:start position:0%
+less or equal that every flow is less
+than or equal to any cut is clear that's
+
+ align:start position:0%
+than or equal to any cut is clear that's
+ 
+
+ align:start position:0%
+than or equal to any cut is clear that's
+the weak Duality that's easy I can't
+
+ align:start position:0%
+the weak Duality that's easy I can't
+ 
+
+ align:start position:0%
+the weak Duality that's easy I can't
+send more flow across
+
+ align:start position:0%
+send more flow across
+ 
+
+ align:start position:0%
+send more flow across
+that that barbwire fence than the
+
+ align:start position:0%
+that that barbwire fence than the
+ 
+
+ align:start position:0%
+that that barbwire fence than the
+capacity of all the edges that cross it
+
+ align:start position:0%
+capacity of all the edges that cross it
+ 
+
+ align:start position:0%
+capacity of all the edges that cross it
+you see what the capacity of the cut is
+
+ align:start position:0%
+you see what the capacity of the cut is
+ 
+
+ align:start position:0%
+you see what the capacity of the cut is
+so the Capac what's what do I mean by
+
+ align:start position:0%
+so the Capac what's what do I mean by
+ 
+
+ align:start position:0%
+so the Capac what's what do I mean by
+the capacity of a
+
+ align:start position:0%
+the capacity of a
+ 
+
+ align:start position:0%
+the capacity of a
+cut of a of a cut first of all what is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cut a cut is and it didn't look quite as
+
+ align:start position:0%
+cut a cut is and it didn't look quite as
+ 
+
+ align:start position:0%
+cut a cut is and it didn't look quite as
+neat as don't think I didn't you thought
+
+ align:start position:0%
+neat as don't think I didn't you thought
+ 
+
+ align:start position:0%
+neat as don't think I didn't you thought
+I made that picture hard but at least
+
+ align:start position:0%
+I made that picture hard but at least
+ 
+
+ align:start position:0%
+I made that picture hard but at least
+the cut looked reasonable so a cut is
+
+ align:start position:0%
+the cut looked reasonable so a cut is
+ 
+
+ align:start position:0%
+the cut looked reasonable so a cut is
+any any way of separating The Source
+
+ align:start position:0%
+any any way of separating The Source
+ 
+
+ align:start position:0%
+any any way of separating The Source
+from the sink anything that I have to
+
+ align:start position:0%
+from the sink anything that I have to
+ 
+
+ align:start position:0%
+from the sink anything that I have to
+Traverse any like boundary and the cap
+
+ align:start position:0%
+Traverse any like boundary and the cap
+ 
+
+ align:start position:0%
+Traverse any like boundary and the cap
+what's the capacity of a
+
+ align:start position:0%
+what's the capacity of a
+ 
+
+ align:start position:0%
+what's the capacity of a
+cut it's the sum across it's how much
+
+ align:start position:0%
+cut it's the sum across it's how much
+ 
+
+ align:start position:0%
+cut it's the sum across it's how much
+it's the sum I look at all the edges
+
+ align:start position:0%
+it's the sum I look at all the edges
+ 
+
+ align:start position:0%
+it's the sum I look at all the edges
+that cross the cut how much can I send
+
+ align:start position:0%
+that cross the cut how much can I send
+ 
+
+ align:start position:0%
+that cross the cut how much can I send
+that's the capacity of a cut and then
+
+ align:start position:0%
+that's the capacity of a cut and then
+ 
+
+ align:start position:0%
+that's the capacity of a cut and then
+I'm look for the cut that's tightest so
+
+ align:start position:0%
+I'm look for the cut that's tightest so
+ 
+
+ align:start position:0%
+I'm look for the cut that's tightest so
+then the Dual problem is of course is a
+
+ align:start position:0%
+then the Dual problem is of course is a
+ 
+
+ align:start position:0%
+then the Dual problem is of course is a
+minimum problem find the cut of smallest
+
+ align:start position:0%
+minimum problem find the cut of smallest
+ 
+
+ align:start position:0%
+minimum problem find the cut of smallest
+capacity so the capacity of the tightest
+
+ align:start position:0%
+capacity so the capacity of the tightest
+ 
+
+ align:start position:0%
+capacity so the capacity of the tightest
+cut equals
+
+ align:start position:0%
+cut equals
+ 
+
+ align:start position:0%
+cut equals
+the maximum flow I can send what about
+
+ align:start position:0%
+the maximum flow I can send what about
+ 
+
+ align:start position:0%
+the maximum flow I can send what about
+correction those up going always going
+
+ align:start position:0%
+correction those up going always going
+ 
+
+ align:start position:0%
+correction those up going always going
+up always going from from source to sync
+
+ align:start position:0%
+up always going from from source to sync
+ 
+
+ align:start position:0%
+up always going from from source to sync
+that's that's right if if the capacity
+
+ align:start position:0%
+that's that's right if if the capacity
+ 
+
+ align:start position:0%
+that's that's right if if the capacity
+was different both the two ways I'm only
+
+ align:start position:0%
+was different both the two ways I'm only
+ 
+
+ align:start position:0%
+was different both the two ways I'm only
+going to look at the capacity that's
+
+ align:start position:0%
+going to look at the capacity that's
+ 
+
+ align:start position:0%
+going to look at the capacity that's
+going from the S sink source side to the
+
+ align:start position:0%
+going from the S sink source side to the
+ 
+
+ align:start position:0%
+going from the S sink source side to the
+sink
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side why do you think is that always the
+
+ align:start position:0%
+side why do you think is that always the
+ 
+
+ align:start position:0%
+side why do you think is that always the
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+the CH those cap
+
+ align:start position:0%
+the CH those cap
+ 
+
+ align:start position:0%
+the CH those cap
+maybe oh yeah the optimal
+
+ align:start position:0%
+maybe oh yeah the optimal
+ 
+
+ align:start position:0%
+maybe oh yeah the optimal
+flow all I'm saying is that once I have
+
+ align:start position:0%
+flow all I'm saying is that once I have
+ 
+
+ align:start position:0%
+flow all I'm saying is that once I have
+found the minimal cut that's the that's
+
+ align:start position:0%
+found the minimal cut that's the that's
+ 
+
+ align:start position:0%
+found the minimal cut that's the that's
+the tight one and I better send
+
+ align:start position:0%
+the tight one and I better send
+ 
+
+ align:start position:0%
+the tight one and I better send
+everything I have to send to to to
+
+ align:start position:0%
+everything I have to send to to to
+ 
+
+ align:start position:0%
+everything I have to send to to to
+achieve so the claim is that there's
+
+ align:start position:0%
+achieve so the claim is that there's
+ 
+
+ align:start position:0%
+achieve so the claim is that there's
+some flow that that if this is the
+
+ align:start position:0%
+some flow that that if this is the
+ 
+
+ align:start position:0%
+some flow that that if this is the
+minimal cut that I can fix up stuff here
+
+ align:start position:0%
+minimal cut that I can fix up stuff here
+ 
+
+ align:start position:0%
+minimal cut that I can fix up stuff here
+which isn't doing the minimum and fix up
+
+ align:start position:0%
+which isn't doing the minimum and fix up
+ 
+
+ align:start position:0%
+which isn't doing the minimum and fix up
+stuff here and maybe send it whatever
+
+ align:start position:0%
+stuff here and maybe send it whatever
+ 
+
+ align:start position:0%
+stuff here and maybe send it whatever
+way you're right I I'm not I'm only
+
+ align:start position:0%
+way you're right I I'm not I'm only
+ 
+
+ align:start position:0%
+way you're right I I'm not I'm only
+saying that across the cut I'm going to
+
+ align:start position:0%
+saying that across the cut I'm going to
+ 
+
+ align:start position:0%
+saying that across the cut I'm going to
+go from source to sync I'm not saying
+
+ align:start position:0%
+go from source to sync I'm not saying
+ 
+
+ align:start position:0%
+go from source to sync I'm not saying
+which way or how much flow goes on these
+
+ align:start position:0%
+which way or how much flow goes on these
+ 
+
+ align:start position:0%
+which way or how much flow goes on these
+other edges because that's where things
+
+ align:start position:0%
+other edges because that's where things
+ 
+
+ align:start position:0%
+other edges because that's where things
+are slack I've got extra capacity it's
+
+ align:start position:0%
+are slack I've got extra capacity it's
+ 
+
+ align:start position:0%
+are slack I've got extra capacity it's
+like having extra ones here I don't you
+
+ align:start position:0%
+like having extra ones here I don't you
+ 
+
+ align:start position:0%
+like having extra ones here I don't you
+know they're there but I don't use them
+
+ align:start position:0%
+know they're there but I don't use them
+ 
+
+ align:start position:0%
+know they're there but I don't use them
+but the ones that the matching the ones
+
+ align:start position:0%
+but the ones that the matching the ones
+ 
+
+ align:start position:0%
+but the ones that the matching the ones
+that I needed I needed and the capacity
+
+ align:start position:0%
+that I needed I needed and the capacity
+ 
+
+ align:start position:0%
+that I needed I needed and the capacity
+across that cut I need
+
+ align:start position:0%
+across that cut I need
+ 
+
+ align:start position:0%
+across that cut I need
+it yeah if you made that capacity n
+
+ align:start position:0%
+it yeah if you made that capacity n
+ 
+
+ align:start position:0%
+it yeah if you made that capacity n
+instead of 14 all right let me change
+
+ align:start position:0%
+instead of 14 all right let me change
+ 
+
+ align:start position:0%
+instead of 14 all right let me change
+would that mean you can only get a
+
+ align:start position:0%
+would that mean you can only get a
+ 
+
+ align:start position:0%
+would that mean you can only get a
+maximum of
+
+ align:start position:0%
+maximum of
+ 
+
+ align:start position:0%
+maximum of
+11 well because you can't Supply 10 that
+
+ align:start position:0%
+11 well because you can't Supply 10 that
+ 
+
+ align:start position:0%
+11 well because you can't Supply 10 that
+looks so you're saying is the minimal
+
+ align:start position:0%
+looks so you're saying is the minimal
+ 
+
+ align:start position:0%
+looks so you're saying is the minimal
+cut
+
+ align:start position:0%
+cut
+ 
+
+ align:start position:0%
+cut
+now now this no I mean is is the maximum
+
+ align:start position:0%
+now now this no I mean is is the maximum
+ 
+
+ align:start position:0%
+now now this no I mean is is the maximum
+through put down to the think S Prime is
+
+ align:start position:0%
+through put down to the think S Prime is
+ 
+
+ align:start position:0%
+through put down to the think S Prime is
+that going to be 11 instead of well I I
+
+ align:start position:0%
+that going to be 11 instead of well I I
+ 
+
+ align:start position:0%
+that going to be 11 instead of well I I
+asked the same question yeah yeah yeah
+
+ align:start position:0%
+asked the same question yeah yeah yeah
+ 
+
+ align:start position:0%
+asked the same question yeah yeah yeah
+have have you have we reduced have we
+
+ align:start position:0%
+have have you have we reduced have we
+ 
+
+ align:start position:0%
+have have you have we reduced have we
+now found a cut whose capacity is only
+
+ align:start position:0%
+now found a cut whose capacity is only
+ 
+
+ align:start position:0%
+now found a cut whose capacity is only
+11 so the theorem would say if that's
+
+ align:start position:0%
+11 so the theorem would say if that's
+ 
+
+ align:start position:0%
+11 so the theorem would say if that's
+the smallest and probably it is the
+
+ align:start position:0%
+the smallest and probably it is the
+ 
+
+ align:start position:0%
+the smallest and probably it is the
+theorem would say well we can get 11
+
+ align:start position:0%
+theorem would say well we can get 11
+ 
+
+ align:start position:0%
+theorem would say well we can get 11
+through that's the the if that's the
+
+ align:start position:0%
+through that's the the if that's the
+ 
+
+ align:start position:0%
+through that's the the if that's the
+smallest capacity if the if the tight
+
+ align:start position:0%
+smallest capacity if the if the tight
+ 
+
+ align:start position:0%
+smallest capacity if the if the tight
+one now is is is this
+
+ align:start position:0%
+one now is is is this
+ 
+
+ align:start position:0%
+one now is is is this
+cut
+
+ align:start position:0%
+cut
+ 
+
+ align:start position:0%
+cut
+then the cap we can send no more than 11
+
+ align:start position:0%
+then the cap we can send no more than 11
+ 
+
+ align:start position:0%
+then the cap we can send no more than 11
+and the theorem would say yep we can get
+
+ align:start position:0%
+and the theorem would say yep we can get
+ 
+
+ align:start position:0%
+and the theorem would say yep we can get
+11 through if that's the tightest cut do
+
+ align:start position:0%
+11 through if that's the tightest cut do
+ 
+
+ align:start position:0%
+11 through if that's the tightest cut do
+you see that like the beauty of the the
+
+ align:start position:0%
+you see that like the beauty of the the
+ 
+
+ align:start position:0%
+you see that like the beauty of the the
+Elegance of the answer that that uh that
+
+ align:start position:0%
+Elegance of the answer that that uh that
+ 
+
+ align:start position:0%
+Elegance of the answer that that uh that
+tightest cut is exactly what you can get
+
+ align:start position:0%
+tightest cut is exactly what you can get
+ 
+
+ align:start position:0%
+tightest cut is exactly what you can get
+through and and and you see that is
+
+ align:start position:0%
+through and and and you see that is
+ 
+
+ align:start position:0%
+through and and and you see that is
+exactly constrain it's the tight
+
+ align:start position:0%
+exactly constrain it's the tight
+ 
+
+ align:start position:0%
+exactly constrain it's the tight
+constraint yeah that was a good idea to
+
+ align:start position:0%
+constraint yeah that was a good idea to
+ 
+
+ align:start position:0%
+constraint yeah that was a good idea to
+change a number should I change a a
+
+ align:start position:0%
+change a number should I change a a
+ 
+
+ align:start position:0%
+change a number should I change a a
+different number just solve the problem
+
+ align:start position:0%
+different number just solve the problem
+ 
+
+ align:start position:0%
+different number just solve the problem
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+more so let me go back to 14
+
+ align:start position:0%
+more so let me go back to 14
+ 
+
+ align:start position:0%
+more so let me go back to 14
+here and let me change a few other
+
+ align:start position:0%
+here and let me change a few other
+ 
+
+ align:start position:0%
+here and let me change a few other
+numbers let me increase this one to a
+
+ align:start position:0%
+numbers let me increase this one to a
+ 
+
+ align:start position:0%
+numbers let me increase this one to a
+three I'm just doing this at random and
+
+ align:start position:0%
+three I'm just doing this at random and
+ 
+
+ align:start position:0%
+three I'm just doing this at random and
+reduce that two to a one and this nine
+
+ align:start position:0%
+reduce that two to a one and this nine
+ 
+
+ align:start position:0%
+reduce that two to a one and this nine
+to a six
+
+ align:start position:0%
+to a six
+ 
+
+ align:start position:0%
+to a six
+okay is it clear enough can you see what
+
+ align:start position:0%
+okay is it clear enough can you see what
+ 
+
+ align:start position:0%
+okay is it clear enough can you see what
+those numbers are
+
+ align:start position:0%
+those numbers are
+ 
+
+ align:start position:0%
+those numbers are
+so that's still a
+
+ align:start position:0%
+so that's still a
+ 
+
+ align:start position:0%
+so that's still a
+one well I'm asking you to solve a
+
+ align:start position:0%
+one well I'm asking you to solve a
+ 
+
+ align:start position:0%
+one well I'm asking you to solve a
+problem on the Fly here but then you you
+
+ align:start position:0%
+problem on the Fly here but then you you
+ 
+
+ align:start position:0%
+problem on the Fly here but then you you
+think 12 is now the
+
+ align:start position:0%
+think 12 is now the
+ 
+
+ align:start position:0%
+think 12 is now the
+minimum have seven and which 12 where's
+
+ align:start position:0%
+minimum have seven and which 12 where's
+ 
+
+ align:start position:0%
+minimum have seven and which 12 where's
+the cut go through the seven
+
+ align:start position:0%
+the cut go through the seven
+ 
+
+ align:start position:0%
+the cut go through the seven
+and the seven one one to and oh through
+
+ align:start position:0%
+and the seven one one to and oh through
+ 
+
+ align:start position:0%
+and the seven one one to and oh through
+down here through that one through that
+
+ align:start position:0%
+down here through that one through that
+ 
+
+ align:start position:0%
+down here through that one through that
+seven through that two and that one yeah
+
+ align:start position:0%
+seven through that two and that one yeah
+ 
+
+ align:start position:0%
+seven through that two and that one yeah
+so 2 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+12 and that if that's a minimal cut then
+
+ align:start position:0%
+12 and that if that's a minimal cut then
+ 
+
+ align:start position:0%
+12 and that if that's a minimal cut then
+I can get 12 through minim C well you
+
+ align:start position:0%
+I can get 12 through minim C well you
+ 
+
+ align:start position:0%
+I can get 12 through minim C well you
+just added to the other cut that was the
+
+ align:start position:0%
+just added to the other cut that was the
+ 
+
+ align:start position:0%
+just added to the other cut that was the
+minimal cut so therefore that
+
+ align:start position:0%
+minimal cut so therefore that
+ 
+
+ align:start position:0%
+minimal cut so therefore that
+cut yeah let's see this old cut how many
+
+ align:start position:0%
+cut yeah let's see this old cut how many
+ 
+
+ align:start position:0%
+cut yeah let's see this old cut how many
+can get through there one and one and
+
+ align:start position:0%
+can get through there one and one and
+ 
+
+ align:start position:0%
+can get through there one and one and
+eight and three and one oh I did I leave
+
+ align:start position:0%
+eight and three and one oh I did I leave
+ 
+
+ align:start position:0%
+eight and three and one oh I did I leave
+no I I increased that didn't I yeah so
+
+ align:start position:0%
+no I I increased that didn't I yeah so
+ 
+
+ align:start position:0%
+no I I increased that didn't I yeah so
+14 was that old cut but now I by
+
+ align:start position:0%
+14 was that old cut but now I by
+ 
+
+ align:start position:0%
+14 was that old cut but now I by
+reducing this seven reducing oh reducing
+
+ align:start position:0%
+reducing this seven reducing oh reducing
+ 
+
+ align:start position:0%
+reducing this seven reducing oh reducing
+some of these others I reduce some other
+
+ align:start position:0%
+some of these others I reduce some other
+ 
+
+ align:start position:0%
+some of these others I reduce some other
+cut to 12 we said so then the theorem
+
+ align:start position:0%
+cut to 12 we said so then the theorem
+ 
+
+ align:start position:0%
+cut to 12 we said so then the theorem
+would say the and we don't see
+
+ align:start position:0%
+would say the and we don't see
+ 
+
+ align:start position:0%
+would say the and we don't see
+immediately how but with a little
+
+ align:start position:0%
+immediately how but with a little
+ 
+
+ align:start position:0%
+immediately how but with a little
+patience we would figure out a way to
+
+ align:start position:0%
+patience we would figure out a way to
+ 
+
+ align:start position:0%
+patience we would figure out a way to
+send 12 through if if that's really we
+
+ align:start position:0%
+send 12 through if if that's really we
+ 
+
+ align:start position:0%
+send 12 through if if that's really we
+couldn't send more than 12 that's for
+
+ align:start position:0%
+couldn't send more than 12 that's for
+ 
+
+ align:start position:0%
+couldn't send more than 12 that's for
+sure because you've identified a cut
+
+ align:start position:0%
+sure because you've identified a cut
+ 
+
+ align:start position:0%
+sure because you've identified a cut
+with capacity 12 and then
+
+ align:start position:0%
+with capacity 12 and then
+ 
+
+ align:start position:0%
+with capacity 12 and then
+we've got some so we would we certainly
+
+ align:start position:0%
+we've got some so we would we certainly
+ 
+
+ align:start position:0%
+we've got some so we would we certainly
+know then we we got to send full amount
+
+ align:start position:0%
+know then we we got to send full amount
+ 
+
+ align:start position:0%
+know then we we got to send full amount
+across that cut we've got to send you
+
+ align:start position:0%
+across that cut we've got to send you
+ 
+
+ align:start position:0%
+across that cut we've got to send you
+know we've got to start on the answer
+
+ align:start position:0%
+know we've got to start on the answer
+ 
+
+ align:start position:0%
+know we've got to start on the answer
+because we know that we have to send
+
+ align:start position:0%
+because we know that we have to send
+ 
+
+ align:start position:0%
+because we know that we have to send
+seven that way and so forth and and and
+
+ align:start position:0%
+seven that way and so forth and and and
+ 
+
+ align:start position:0%
+seven that way and so forth and and and
+you know we know what all these ones
+
+ align:start position:0%
+you know we know what all these ones
+ 
+
+ align:start position:0%
+you know we know what all these ones
+should be and then we can fix the others
+
+ align:start position:0%
+should be and then we can fix the others
+ 
+
+ align:start position:0%
+should be and then we can fix the others
+to supply them where there's extra
+
+ align:start position:0%
+to supply them where there's extra
+ 
+
+ align:start position:0%
+to supply them where there's extra
+capacity that's a beautiful theorem and
+
+ align:start position:0%
+capacity that's a beautiful theorem and
+ 
+
+ align:start position:0%
+capacity that's a beautiful theorem and
+uh it would follow from some general
+
+ align:start position:0%
+uh it would follow from some general
+ 
+
+ align:start position:0%
+uh it would follow from some general
+Duality theorem of linear programming
+
+ align:start position:0%
+Duality theorem of linear programming
+ 
+
+ align:start position:0%
+Duality theorem of linear programming
+but then there would also be some
+
+ align:start position:0%
+but then there would also be some
+ 
+
+ align:start position:0%
+but then there would also be some
+special
+
+ align:start position:0%
+special
+ 
+
+ align:start position:0%
+special
+um uh argument like
+
+ align:start position:0%
+um uh argument like
+ 
+
+ align:start position:0%
+um uh argument like
+Halls uh condition that would apply and
+
+ align:start position:0%
+Halls uh condition that would apply and
+ 
+
+ align:start position:0%
+Halls uh condition that would apply and
+maybe I mentioned the the this Max flow
+
+ align:start position:0%
+maybe I mentioned the the this Max flow
+ 
+
+ align:start position:0%
+maybe I mentioned the the this Max flow
+Min cut is associated with Ford and
+
+ align:start position:0%
+Min cut is associated with Ford and
+ 
+
+ align:start position:0%
+Min cut is associated with Ford and
+Fulkerson where the sort of like
+
+ align:start position:0%
+Fulkerson where the sort of like
+ 
+
+ align:start position:0%
+Fulkerson where the sort of like
+comori Sparks to uh identify that uh
+
+ align:start position:0%
+comori Sparks to uh identify that uh
+ 
+
+ align:start position:0%
+comori Sparks to uh identify that uh
+um problem is there some systematic way
+
+ align:start position:0%
+um problem is there some systematic way
+ 
+
+ align:start position:0%
+um problem is there some systematic way
+of determining what the cut is besides
+
+ align:start position:0%
+of determining what the cut is besides
+ 
+
+ align:start position:0%
+of determining what the cut is besides
+yes that there would be right yes so the
+
+ align:start position:0%
+yes that there would be right yes so the
+ 
+
+ align:start position:0%
+yes that there would be right yes so the
+book would speak about that uh I
+
+ align:start position:0%
+book would speak about that uh I
+ 
+
+ align:start position:0%
+book would speak about that uh I
+mean one way is say I could write the
+
+ align:start position:0%
+mean one way is say I could write the
+ 
+
+ align:start position:0%
+mean one way is say I could write the
+whole thing as a linear program and use
+
+ align:start position:0%
+whole thing as a linear program and use
+ 
+
+ align:start position:0%
+whole thing as a linear program and use
+a Simplex
+
+ align:start position:0%
+a Simplex
+ 
+
+ align:start position:0%
+a Simplex
+method but then somehow the Simplex
+
+ align:start position:0%
+method but then somehow the Simplex
+ 
+
+ align:start position:0%
+method but then somehow the Simplex
+method should specialize to this problem
+
+ align:start position:0%
+method should specialize to this problem
+ 
+
+ align:start position:0%
+method should specialize to this problem
+and and uh
+
+ align:start position:0%
+and and uh
+ 
+
+ align:start position:0%
+and and uh
+um you know those those corners and so
+
+ align:start position:0%
+um you know those those corners and so
+ 
+
+ align:start position:0%
+um you know those those corners and so
+on should have a specific meaning in
+
+ align:start position:0%
+on should have a specific meaning in
+ 
+
+ align:start position:0%
+on should have a specific meaning in
+terms of flows and cuts yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah particular example if you had one
+
+ align:start position:0%
+yeah particular example if you had one
+ 
+
+ align:start position:0%
+yeah particular example if you had one
+source and one sink yes you should only
+
+ align:start position:0%
+source and one sink yes you should only
+ 
+
+ align:start position:0%
+source and one sink yes you should only
+have one pipe so
+
+ align:start position:0%
+have one pipe so
+ 
+
+ align:start position:0%
+have one pipe so
+um well no think hey he I'm I'm a oil
+
+ align:start position:0%
+um well no think hey he I'm I'm a oil
+ 
+
+ align:start position:0%
+um well no think hey he I'm I'm a oil
+and gas I'm George Bush in a previous
+
+ align:start position:0%
+and gas I'm George Bush in a previous
+ 
+
+ align:start position:0%
+and gas I'm George Bush in a previous
+Incarnation yeah oh yeah I've got I'm
+
+ align:start position:0%
+Incarnation yeah oh yeah I've got I'm
+ 
+
+ align:start position:0%
+Incarnation yeah oh yeah I've got I'm
+getting natural gas off the G out of the
+
+ align:start position:0%
+getting natural gas off the G out of the
+ 
+
+ align:start position:0%
+getting natural gas off the G out of the
+Gulf of Mexico I've got pipelines going
+
+ align:start position:0%
+Gulf of Mexico I've got pipelines going
+ 
+
+ align:start position:0%
+Gulf of Mexico I've got pipelines going
+into the mainland and I've got
+
+ align:start position:0%
+into the mainland and I've got
+ 
+
+ align:start position:0%
+into the mainland and I've got
+refineries there with capacities and
+
+ align:start position:0%
+refineries there with capacities and
+ 
+
+ align:start position:0%
+refineries there with capacities and
+those pipelines are a real network of
+
+ align:start position:0%
+those pipelines are a real network of
+ 
+
+ align:start position:0%
+those pipelines are a real network of
+pipelines about yeah Elric yeah yeah
+
+ align:start position:0%
+pipelines about yeah Elric yeah yeah
+ 
+
+ align:start position:0%
+pipelines about yeah Elric yeah yeah
+that's sending electricity believe
+
+ align:start position:0%
+that's sending electricity believe
+ 
+
+ align:start position:0%
+that's sending electricity believe
+absolutely sending electricity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+California in this problem yeah oh I so
+
+ align:start position:0%
+California in this problem yeah oh I so
+ 
+
+ align:start position:0%
+California in this problem yeah oh I so
+I'm not claiming that's most General
+
+ align:start position:0%
+I'm not claiming that's most General
+ 
+
+ align:start position:0%
+I'm not claiming that's most General
+that this problem would fit every need
+
+ align:start position:0%
+that this problem would fit every need
+ 
+
+ align:start position:0%
+that this problem would fit every need
+no but you could make become a sync and
+
+ align:start position:0%
+no but you could make become a sync and
+ 
+
+ align:start position:0%
+no but you could make become a sync and
+then you could ask the same question I
+
+ align:start position:0%
+then you could ask the same question I
+ 
+
+ align:start position:0%
+then you could ask the same question I
+could have multiple sources and syncs
+
+ align:start position:0%
+could have multiple sources and syncs
+ 
+
+ align:start position:0%
+could have multiple sources and syncs
+and make the problem more General but
+
+ align:start position:0%
+and make the problem more General but
+ 
+
+ align:start position:0%
+and make the problem more General but
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difficult
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true true
+
+ align:start position:0%
+true true
+ 
+
+ align:start position:0%
+true true
+true from York California
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so it could be phone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calls but if if you're calling one
+
+ align:start position:0%
+calls but if if you're calling one
+ 
+
+ align:start position:0%
+calls but if if you're calling one
+person in California then and you're
+
+ align:start position:0%
+person in California then and you're
+ 
+
+ align:start position:0%
+person in California then and you're
+sending a packet which can get split up
+
+ align:start position:0%
+sending a packet which can get split up
+ 
+
+ align:start position:0%
+sending a packet which can get split up
+in different ways and gets in fact isn't
+
+ align:start position:0%
+in different ways and gets in fact isn't
+ 
+
+ align:start position:0%
+in different ways and gets in fact isn't
+that what what AT&T is doing it's taking
+
+ align:start position:0%
+that what what AT&T is doing it's taking
+ 
+
+ align:start position:0%
+that what what AT&T is doing it's taking
+your phone message splitting it up into
+
+ align:start position:0%
+your phone message splitting it up into
+ 
+
+ align:start position:0%
+your phone message splitting it up into
+the packet sending them cheap ways and
+
+ align:start position:0%
+the packet sending them cheap ways and
+ 
+
+ align:start position:0%
+the packet sending them cheap ways and
+uh of course it's sending other packets
+
+ align:start position:0%
+uh of course it's sending other packets
+ 
+
+ align:start position:0%
+uh of course it's sending other packets
+at the same time so there there's
+
+ align:start position:0%
+at the same time so there there's
+ 
+
+ align:start position:0%
+at the same time so there there's
+another generalization we've got a bunch
+
+ align:start position:0%
+another generalization we've got a bunch
+ 
+
+ align:start position:0%
+another generalization we've got a bunch
+of different pairs Source sync pairs
+
+ align:start position:0%
+of different pairs Source sync pairs
+ 
+
+ align:start position:0%
+of different pairs Source sync pairs
+simultaneously trying to get their uh
+
+ align:start position:0%
+simultaneously trying to get their uh
+ 
+
+ align:start position:0%
+simultaneously trying to get their uh
+message through and then there's what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the right yeah that's my
+
+ align:start position:0%
+the right yeah that's my
+ 
+
+ align:start position:0%
+the right yeah that's my
+network yes obviously whoever designed
+
+ align:start position:0%
+network yes obviously whoever designed
+ 
+
+ align:start position:0%
+network yes obviously whoever designed
+this network right put too many put yeah
+
+ align:start position:0%
+this network right put too many put yeah
+ 
+
+ align:start position:0%
+this network right put too many put yeah
+whoever that that network isn't perfect
+
+ align:start position:0%
+whoever that that network isn't perfect
+ 
+
+ align:start position:0%
+whoever that that network isn't perfect
+because somebody paid extra for this
+
+ align:start position:0%
+because somebody paid extra for this
+ 
+
+ align:start position:0%
+because somebody paid extra for this
+paid for extra capacity that can't be
+
+ align:start position:0%
+paid for extra capacity that can't be
+ 
+
+ align:start position:0%
+paid for extra capacity that can't be
+used oh yeah that's right but actually
+
+ align:start position:0%
+used oh yeah that's right but actually
+ 
+
+ align:start position:0%
+used oh yeah that's right but actually
+in reality that happens all the time
+
+ align:start position:0%
+in reality that happens all the time
+ 
+
+ align:start position:0%
+in reality that happens all the time
+right if I mean a new pipeline is built
+
+ align:start position:0%
+right if I mean a new pipeline is built
+ 
+
+ align:start position:0%
+right if I mean a new pipeline is built
+from from Iraq to through turkey or
+
+ align:start position:0%
+from from Iraq to through turkey or
+ 
+
+ align:start position:0%
+from from Iraq to through turkey or
+wherever uh adds more capacity well then
+
+ align:start position:0%
+wherever uh adds more capacity well then
+ 
+
+ align:start position:0%
+wherever uh adds more capacity well then
+it turns out that that maybe you know
+
+ align:start position:0%
+it turns out that that maybe you know
+ 
+
+ align:start position:0%
+it turns out that that maybe you know
+now they've got excess Capac it but the
+
+ align:start position:0%
+now they've got excess Capac it but the
+ 
+
+ align:start position:0%
+now they've got excess Capac it but the
+minimum cut is what's determining how
+
+ align:start position:0%
+minimum cut is what's determining how
+ 
+
+ align:start position:0%
+minimum cut is what's determining how
+much flow gets you know from the oil
+
+ align:start position:0%
+much flow gets you know from the oil
+ 
+
+ align:start position:0%
+much flow gets you know from the oil
+fields to the to the
+
+ align:start position:0%
+fields to the to the
+ 
+
+ align:start position:0%
+fields to the to the
+refineries yeah and I could add a cost
+
+ align:start position:0%
+refineries yeah and I could add a cost
+ 
+
+ align:start position:0%
+refineries yeah and I could add a cost
+per node to to to go through that node
+
+ align:start position:0%
+per node to to to go through that node
+ 
+
+ align:start position:0%
+per node to to to go through that node
+oh you can imagine that I as long as I
+
+ align:start position:0%
+oh you can imagine that I as long as I
+ 
+
+ align:start position:0%
+oh you can imagine that I as long as I
+stay linear I I I I can make these
+
+ align:start position:0%
+stay linear I I I I can make these
+ 
+
+ align:start position:0%
+stay linear I I I I can make these
+things more General yeah yeah so I mean
+
+ align:start position:0%
+things more General yeah yeah so I mean
+ 
+
+ align:start position:0%
+things more General yeah yeah so I mean
+this this is really a good discussion
+
+ align:start position:0%
+this this is really a good discussion
+ 
+
+ align:start position:0%
+this this is really a good discussion
+that you know this is a model problem
+
+ align:start position:0%
+that you know this is a model problem
+ 
+
+ align:start position:0%
+that you know this is a model problem
+but but uh if we think about natural
+
+ align:start position:0%
+but but uh if we think about natural
+ 
+
+ align:start position:0%
+but but uh if we think about natural
+ways to make it closer and closer to
+
+ align:start position:0%
+ways to make it closer and closer to
+ 
+
+ align:start position:0%
+ways to make it closer and closer to
+reality we still stay with we still stay
+
+ align:start position:0%
+reality we still stay with we still stay
+ 
+
+ align:start position:0%
+reality we still stay with we still stay
+with uh this linear programming
+
+ align:start position:0%
+with uh this linear programming
+ 
+
+ align:start position:0%
+with uh this linear programming
+framework we can we can get a lot in
+
+ align:start position:0%
+framework we can we can get a lot in
+ 
+
+ align:start position:0%
+framework we can we can get a lot in
+well now I have to say though that
+
+ align:start position:0%
+well now I have to say though that
+ 
+
+ align:start position:0%
+well now I have to say though that
+multi-purpose you know so optimizing for
+
+ align:start position:0%
+multi-purpose you know so optimizing for
+ 
+
+ align:start position:0%
+multi-purpose you know so optimizing for
+multiple uses there that's that is
+
+ align:start position:0%
+multiple uses there that's that is
+ 
+
+ align:start position:0%
+multiple uses there that's that is
+really a different problem you know know
+
+ align:start position:0%
+really a different problem you know know
+ 
+
+ align:start position:0%
+really a different problem you know know
+if if I'm optimizing if I'm choosing the
+
+ align:start position:0%
+if if I'm optimizing if I'm choosing the
+ 
+
+ align:start position:0%
+if if I'm optimizing if I'm choosing the
+X's that optimize some function for
+
+ align:start position:0%
+X's that optimize some function for
+ 
+
+ align:start position:0%
+X's that optimize some function for
+several purposes op optimize several
+
+ align:start position:0%
+several purposes op optimize several
+ 
+
+ align:start position:0%
+several purposes op optimize several
+functions at once in some way uh that
+
+ align:start position:0%
+functions at once in some way uh that
+ 
+
+ align:start position:0%
+functions at once in some way uh that
+there I'm uh getting in you know by the
+
+ align:start position:0%
+there I'm uh getting in you know by the
+ 
+
+ align:start position:0%
+there I'm uh getting in you know by the
+way game
+
+ align:start position:0%
+way game
+ 
+
+ align:start position:0%
+way game
+theory is another example of linear
+
+ align:start position:0%
+theory is another example of linear
+ 
+
+ align:start position:0%
+theory is another example of linear
+programming and and vanoyan discovered
+
+ align:start position:0%
+programming and and vanoyan discovered
+ 
+
+ align:start position:0%
+programming and and vanoyan discovered
+that slightly
+
+ align:start position:0%
+that slightly
+ 
+
+ align:start position:0%
+that slightly
+before uh linear programming was
+
+ align:start position:0%
+before uh linear programming was
+ 
+
+ align:start position:0%
+before uh linear programming was
+discovered but almost the same time and
+
+ align:start position:0%
+discovered but almost the same time and
+ 
+
+ align:start position:0%
+discovered but almost the same time and
+people in the First Years even V noyman
+
+ align:start position:0%
+people in the First Years even V noyman
+ 
+
+ align:start position:0%
+people in the First Years even V noyman
+didn't instantly know and he instantly
+
+ align:start position:0%
+didn't instantly know and he instantly
+ 
+
+ align:start position:0%
+didn't instantly know and he instantly
+knew everything uh whe that it was the
+
+ align:start position:0%
+knew everything uh whe that it was the
+ 
+
+ align:start position:0%
+knew everything uh whe that it was the
+same and you do you remember the name of
+
+ align:start position:0%
+same and you do you remember the name of
+ 
+
+ align:start position:0%
+same and you do you remember the name of
+the fundamentals well I could talk about
+
+ align:start position:0%
+the fundamentals well I could talk about
+ 
+
+ align:start position:0%
+the fundamentals well I could talk about
+Game Theory I mean next time if you
+
+ align:start position:0%
+Game Theory I mean next time if you
+ 
+
+ align:start position:0%
+Game Theory I mean next time if you
+wanted among other problems uh the
+
+ align:start position:0%
+wanted among other problems uh the
+ 
+
+ align:start position:0%
+wanted among other problems uh the
+fundamental Duality there is called the
+
+ align:start position:0%
+fundamental Duality there is called the
+ 
+
+ align:start position:0%
+fundamental Duality there is called the
+Minimax theorem there's a Minimax equals
+
+ align:start position:0%
+Minimax theorem there's a Minimax equals
+ 
+
+ align:start position:0%
+Minimax theorem there's a Minimax equals
+a maxim
+
+ align:start position:0%
+a maxim
+ 
+
+ align:start position:0%
+a maxim
+Min in the in the world of Game Theory
+
+ align:start position:0%
+Min in the in the world of Game Theory
+ 
+
+ align:start position:0%
+Min in the in the world of Game Theory
+proved by V noyman the Minx theorem a
+
+ align:start position:0%
+proved by V noyman the Minx theorem a
+ 
+
+ align:start position:0%
+proved by V noyman the Minx theorem a
+minimum of a maximum of something is the
+
+ align:start position:0%
+minimum of a maximum of something is the
+ 
+
+ align:start position:0%
+minimum of a maximum of something is the
+maximum of the minimum of of something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh in two in the twers game theory
+
+ align:start position:0%
+and uh in two in the twers game theory
+ 
+
+ align:start position:0%
+and uh in two in the twers game theory
+that vanman
+
+ align:start position:0%
+that vanman
+ 
+
+ align:start position:0%
+that vanman
+was about that would match a linear so
+
+ align:start position:0%
+was about that would match a linear so
+ 
+
+ align:start position:0%
+was about that would match a linear so
+that would match a linear program I
+
+ align:start position:0%
+that would match a linear program I
+ 
+
+ align:start position:0%
+that would match a linear program I
+could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think this uh probably not
+
+ align:start position:0%
+think this uh probably not
+ 
+
+ align:start position:0%
+think this uh probably not
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah I well
+
+ align:start position:0%
+yeah yeah I well
+ 
+
+ align:start position:0%
+yeah yeah I well
+um the answer is yeah there's a duality
+
+ align:start position:0%
+um the answer is yeah there's a duality
+ 
+
+ align:start position:0%
+um the answer is yeah there's a duality
+in nonlinear
+
+ align:start position:0%
+in nonlinear
+ 
+
+ align:start position:0%
+in nonlinear
+programming there is but to tell you
+
+ align:start position:0%
+programming there is but to tell you
+ 
+
+ align:start position:0%
+programming there is but to tell you
+what the if you tell me one of the
+
+ align:start position:0%
+what the if you tell me one of the
+ 
+
+ align:start position:0%
+what the if you tell me one of the
+functions to tell you what the other is
+
+ align:start position:0%
+functions to tell you what the other is
+ 
+
+ align:start position:0%
+functions to tell you what the other is
+it's going to take me next week to do it
+
+ align:start position:0%
+it's going to take me next week to do it
+ 
+
+ align:start position:0%
+it's going to take me next week to do it
+uh it's not just like easy you see I I
+
+ align:start position:0%
+uh it's not just like easy you see I I
+ 
+
+ align:start position:0%
+uh it's not just like easy you see I I
+came up with that dual problem out of
+
+ align:start position:0%
+came up with that dual problem out of
+ 
+
+ align:start position:0%
+came up with that dual problem out of
+the blue really and but it wasn't
+
+ align:start position:0%
+the blue really and but it wasn't
+ 
+
+ align:start position:0%
+the blue really and but it wasn't
+totally out of the blue there was a
+
+ align:start position:0%
+totally out of the blue there was a
+ 
+
+ align:start position:0%
+totally out of the blue there was a
+there was a method there that could
+
+ align:start position:0%
+there was a method there that could
+ 
+
+ align:start position:0%
+there was a method there that could
+apply in nonlinear cases but not obvious
+
+ align:start position:0%
+apply in nonlinear cases but not obvious
+ 
+
+ align:start position:0%
+apply in nonlinear cases but not obvious
+anyway Game Theory two-person Game
+
+ align:start position:0%
+anyway Game Theory two-person Game
+ 
+
+ align:start position:0%
+anyway Game Theory two-person Game
+Theory would fit this U this setup and
+
+ align:start position:0%
+Theory would fit this U this setup and
+ 
+
+ align:start position:0%
+Theory would fit this U this setup and
+so the Minimax theorem is a is The
+
+ align:start position:0%
+so the Minimax theorem is a is The
+ 
+
+ align:start position:0%
+so the Minimax theorem is a is The
+Duality theorem threepers
+
+ align:start position:0%
+Duality theorem threepers
+ 
+
+ align:start position:0%
+Duality theorem threepers
+games you you know that's what John Nash
+
+ align:start position:0%
+games you you know that's what John Nash
+ 
+
+ align:start position:0%
+games you you know that's what John Nash
+won the Nobel Prize for he wrote a
+
+ align:start position:0%
+won the Nobel Prize for he wrote a
+ 
+
+ align:start position:0%
+won the Nobel Prize for he wrote a
+thesis so I didn't mention the other key
+
+ align:start position:0%
+thesis so I didn't mention the other key
+ 
+
+ align:start position:0%
+thesis so I didn't mention the other key
+names the this optimality condition is
+
+ align:start position:0%
+names the this optimality condition is
+ 
+
+ align:start position:0%
+names the this optimality condition is
+associated with and Tucker and now
+
+ align:start position:0%
+associated with and Tucker and now
+ 
+
+ align:start position:0%
+associated with and Tucker and now
+I've written down the great names in
+
+ align:start position:0%
+I've written down the great names in
+ 
+
+ align:start position:0%
+I've written down the great names in
+this subject and then uh John Nash who
+
+ align:start position:0%
+this subject and then uh John Nash who
+ 
+
+ align:start position:0%
+this subject and then uh John Nash who
+uh wrote his PhD ceases at Princeton
+
+ align:start position:0%
+uh wrote his PhD ceases at Princeton
+ 
+
+ align:start position:0%
+uh wrote his PhD ceases at Princeton
+under Tucker to everybody's surprise
+
+ align:start position:0%
+under Tucker to everybody's surprise
+ 
+
+ align:start position:0%
+under Tucker to everybody's surprise
+because Nash was a real character have
+
+ align:start position:0%
+because Nash was a real character have
+ 
+
+ align:start position:0%
+because Nash was a real character have
+you do you know this book The Beautiful
+
+ align:start position:0%
+you do you know this book The Beautiful
+ 
+
+ align:start position:0%
+you do you know this book The Beautiful
+a beautiful mind about John Nash who uh
+
+ align:start position:0%
+a beautiful mind about John Nash who uh
+ 
+
+ align:start position:0%
+a beautiful mind about John Nash who uh
+it's it may become a movie also movie
+
+ align:start position:0%
+it's it may become a movie also movie
+ 
+
+ align:start position:0%
+it's it may become a movie also movie
+movie rights have been B purchased um
+
+ align:start position:0%
+movie rights have been B purchased um
+ 
+
+ align:start position:0%
+movie rights have been B purchased um
+it's by Sylvia Nassar and it was on the
+
+ align:start position:0%
+it's by Sylvia Nassar and it was on the
+ 
+
+ align:start position:0%
+it's by Sylvia Nassar and it was on the
+best seller list so it's a biography of
+
+ align:start position:0%
+best seller list so it's a biography of
+ 
+
+ align:start position:0%
+best seller list so it's a biography of
+John Nash called A Beautiful
+
+ align:start position:0%
+John Nash called A Beautiful
+ 
+
+ align:start position:0%
+John Nash called A Beautiful
+Mind
+
+ align:start position:0%
+Mind
+ 
+
+ align:start position:0%
+Mind
+um uh so he won the Nobel Prize a few
+
+ align:start position:0%
+um uh so he won the Nobel Prize a few
+ 
+
+ align:start position:0%
+um uh so he won the Nobel Prize a few
+years ago but his life was a tra tragic
+
+ align:start position:0%
+years ago but his life was a tra tragic
+ 
+
+ align:start position:0%
+years ago but his life was a tra tragic
+story um well he was brilliant and
+
+ align:start position:0%
+story um well he was brilliant and
+ 
+
+ align:start position:0%
+story um well he was brilliant and
+actually for most mathem acian for all
+
+ align:start position:0%
+actually for most mathem acian for all
+ 
+
+ align:start position:0%
+actually for most mathem acian for all
+mathematicians the the what he got the
+
+ align:start position:0%
+mathematicians the the what he got the
+ 
+
+ align:start position:0%
+mathematicians the the what he got the
+his PhD thesis that he got the Nobel
+
+ align:start position:0%
+his PhD thesis that he got the Nobel
+ 
+
+ align:start position:0%
+his PhD thesis that he got the Nobel
+Prize for was not in any way the most
+
+ align:start position:0%
+Prize for was not in any way the most
+ 
+
+ align:start position:0%
+Prize for was not in any way the most
+deep and difficult work he did he went
+
+ align:start position:0%
+deep and difficult work he did he went
+ 
+
+ align:start position:0%
+deep and difficult work he did he went
+on to do prove
+
+ align:start position:0%
+on to do prove
+ 
+
+ align:start position:0%
+on to do prove
+remarkable facts in in high
+
+ align:start position:0%
+remarkable facts in in high
+ 
+
+ align:start position:0%
+remarkable facts in in high
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+analysis and then uh
+
+ align:start position:0%
+analysis and then uh
+ 
+
+ align:start position:0%
+analysis and then uh
+schizophrenia uh took over so he had
+
+ align:start position:0%
+schizophrenia uh took over so he had
+ 
+
+ align:start position:0%
+schizophrenia uh took over so he had
+many many years when he was first around
+
+ align:start position:0%
+many many years when he was first around
+ 
+
+ align:start position:0%
+many many years when he was first around
+the MIT math department and then around
+
+ align:start position:0%
+the MIT math department and then around
+ 
+
+ align:start position:0%
+the MIT math department and then around
+around the longest time around the
+
+ align:start position:0%
+around the longest time around the
+ 
+
+ align:start position:0%
+around the longest time around the
+Princeton math department but really out
+
+ align:start position:0%
+Princeton math department but really out
+ 
+
+ align:start position:0%
+Princeton math department but really out
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+U communication with people uh it was
+
+ align:start position:0%
+U communication with people uh it was
+ 
+
+ align:start position:0%
+U communication with people uh it was
+difficult and then incredibly um
+
+ align:start position:0%
+difficult and then incredibly um
+ 
+
+ align:start position:0%
+difficult and then incredibly um
+recovered so he gave a lecture at MIT a
+
+ align:start position:0%
+recovered so he gave a lecture at MIT a
+ 
+
+ align:start position:0%
+recovered so he gave a lecture at MIT a
+few weeks ago in fact which uh where he
+
+ align:start position:0%
+few weeks ago in fact which uh where he
+ 
+
+ align:start position:0%
+few weeks ago in fact which uh where he
+had a standing room only audience
+
+ align:start position:0%
+had a standing room only audience
+ 
+
+ align:start position:0%
+had a standing room only audience
+um I I think people would feel he hasn't
+
+ align:start position:0%
+um I I think people would feel he hasn't
+ 
+
+ align:start position:0%
+um I I think people would feel he hasn't
+recovered to the incredible that he had
+
+ align:start position:0%
+recovered to the incredible that he had
+ 
+
+ align:start position:0%
+recovered to the incredible that he had
+reached before his illness but uh still
+
+ align:start position:0%
+reached before his illness but uh still
+ 
+
+ align:start position:0%
+reached before his illness but uh still
+amazing to have recovered so he was able
+
+ align:start position:0%
+amazing to have recovered so he was able
+ 
+
+ align:start position:0%
+amazing to have recovered so he was able
+to go to the Nobel Prize ceremony and
+
+ align:start position:0%
+to go to the Nobel Prize ceremony and
+ 
+
+ align:start position:0%
+to go to the Nobel Prize ceremony and
+the book is quite
+
+ align:start position:0%
+the book is quite
+ 
+
+ align:start position:0%
+the book is quite
+uh really uh good reporting uh I think
+
+ align:start position:0%
+uh really uh good reporting uh I think
+ 
+
+ align:start position:0%
+uh really uh good reporting uh I think
+um by Sylvia
+
+ align:start position:0%
+um by Sylvia
+ 
+
+ align:start position:0%
+um by Sylvia
+Nassar
+
+ align:start position:0%
+Nassar
+ 
+
+ align:start position:0%
+Nassar
+um so that's the story of uh Ora few
+
+ align:start position:0%
+um so that's the story of uh Ora few
+ 
+
+ align:start position:0%
+um so that's the story of uh Ora few
+words about John Nash and then the
+
+ align:start position:0%
+words about John Nash and then the
+ 
+
+ align:start position:0%
+words about John Nash and then the
+reason I mentioned it is that he the
+
+ align:start position:0%
+reason I mentioned it is that he the
+ 
+
+ align:start position:0%
+reason I mentioned it is that he the
+problem he
+
+ align:start position:0%
+problem he
+ 
+
+ align:start position:0%
+problem he
+studied
+
+ align:start position:0%
+studied
+ 
+
+ align:start position:0%
+studied
+was nerson
+
+ align:start position:0%
+was nerson
+ 
+
+ align:start position:0%
+was nerson
+games so if you have n
+
+ align:start position:0%
+games so if you have n
+ 
+
+ align:start position:0%
+games so if you have n
+people three people is enough trying
+
+ align:start position:0%
+people three people is enough trying
+ 
+
+ align:start position:0%
+people three people is enough trying
+to maximize
+
+ align:start position:0%
+to maximize
+ 
+
+ align:start position:0%
+to maximize
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+profits
+
+ align:start position:0%
+profits
+ 
+
+ align:start position:0%
+profits
+that's much much harder than linear
+
+ align:start position:0%
+that's much much harder than linear
+ 
+
+ align:start position:0%
+that's much much harder than linear
+programming uh because they can form
+
+ align:start position:0%
+programming uh because they can form
+ 
+
+ align:start position:0%
+programming uh because they can form
+coalitions you know any two could join
+
+ align:start position:0%
+coalitions you know any two could join
+ 
+
+ align:start position:0%
+coalitions you know any two could join
+up and say okay we'll we'll be a team
+
+ align:start position:0%
+up and say okay we'll we'll be a team
+ 
+
+ align:start position:0%
+up and say okay we'll we'll be a team
+but then if you if then it may after a
+
+ align:start position:0%
+but then if you if then it may after a
+ 
+
+ align:start position:0%
+but then if you if then it may after a
+little while a person says as they do in
+
+ align:start position:0%
+little while a person says as they do in
+ 
+
+ align:start position:0%
+little while a person says as they do in
+reality hey I'd be better off this other
+
+ align:start position:0%
+reality hey I'd be better off this other
+ 
+
+ align:start position:0%
+reality hey I'd be better off this other
+person will bribe me to join him and uh
+
+ align:start position:0%
+person will bribe me to join him and uh
+ 
+
+ align:start position:0%
+person will bribe me to join him and uh
+so Coalition changes and what's the best
+
+ align:start position:0%
+so Coalition changes and what's the best
+ 
+
+ align:start position:0%
+so Coalition changes and what's the best
+what's the optimal strategy it's so I
+
+ align:start position:0%
+what's the optimal strategy it's so I
+ 
+
+ align:start position:0%
+what's the optimal strategy it's so I
+could speak if you send me an email
+
+ align:start position:0%
+could speak if you send me an email
+ 
+
+ align:start position:0%
+could speak if you send me an email
+choose maybe two person games I couldn't
+
+ align:start position:0%
+choose maybe two person games I couldn't
+ 
+
+ align:start position:0%
+choose maybe two person games I couldn't
+do three person games uh next it's next
+
+ align:start position:0%
+do three person games uh next it's next
+ 
+
+ align:start position:0%
+do three person games uh next it's next
+Wednesday morning at 99: uh it's the
+
+ align:start position:0%
+Wednesday morning at 99: uh it's the
+ 
+
+ align:start position:0%
+Wednesday morning at 99: uh it's the
+final pair of lectures and uh if you're
+
+ align:start position:0%
+final pair of lectures and uh if you're
+ 
+
+ align:start position:0%
+final pair of lectures and uh if you're
+willing to stay one more minute can I
+
+ align:start position:0%
+willing to stay one more minute can I
+ 
+
+ align:start position:0%
+willing to stay one more minute can I
+tell you about a problem which maybe
+
+ align:start position:0%
+tell you about a problem which maybe
+ 
+
+ align:start position:0%
+tell you about a problem which maybe
+will be solved by next Wednesday but
+
+ align:start position:0%
+will be solved by next Wednesday but
+ 
+
+ align:start position:0%
+will be solved by next Wednesday but
+maybe not uh it's a commentator thing
+
+ align:start position:0%
+maybe not uh it's a commentator thing
+ 
+
+ align:start position:0%
+maybe not uh it's a commentator thing
+and and I'll just put it in the record
+
+ align:start position:0%
+and and I'll just put it in the record
+ 
+
+ align:start position:0%
+and and I'll just put it in the record
+even though I'm I don't know how this is
+
+ align:start position:0%
+even though I'm I don't know how this is
+ 
+
+ align:start position:0%
+even though I'm I don't know how this is
+going to come out so the question is I
+
+ align:start position:0%
+going to come out so the question is I
+ 
+
+ align:start position:0%
+going to come out so the question is I
+got into this in a discussion this week
+
+ align:start position:0%
+got into this in a discussion this week
+ 
+
+ align:start position:0%
+got into this in a discussion this week
+I'd like to know if I if I knew some
+
+ align:start position:0%
+I'd like to know if I if I knew some
+ 
+
+ align:start position:0%
+I'd like to know if I if I knew some
+entries in a
+
+ align:start position:0%
+entries in a
+ 
+
+ align:start position:0%
+entries in a
+matrix could I complete the rest of the
+
+ align:start position:0%
+matrix could I complete the rest of the
+ 
+
+ align:start position:0%
+matrix could I complete the rest of the
+entries say so that the Matrix had rank
+
+ align:start position:0%
+entries say so that the Matrix had rank
+ 
+
+ align:start position:0%
+entries say so that the Matrix had rank
+one so suppose I
+
+ align:start position:0%
+one so suppose I
+ 
+
+ align:start position:0%
+one so suppose I
+knew suppose I knew
+
+ align:start position:0%
+knew suppose I knew
+ 
+
+ align:start position:0%
+knew suppose I knew
+these oh let me make my life easy
+
+ align:start position:0%
+these oh let me make my life easy
+ 
+
+ align:start position:0%
+these oh let me make my life easy
+suppose I knew those entries in a matrix
+
+ align:start position:0%
+suppose I knew those entries in a matrix
+ 
+
+ align:start position:0%
+suppose I knew those entries in a matrix
+I let me say
+
+ align:start position:0%
+I let me say
+ 
+
+ align:start position:0%
+I let me say
+those suppose I know well let me yeah
+
+ align:start position:0%
+those suppose I know well let me yeah
+ 
+
+ align:start position:0%
+those suppose I know well let me yeah
+well let me let me put in another entry
+
+ align:start position:0%
+well let me let me put in another entry
+ 
+
+ align:start position:0%
+well let me let me put in another entry
+okay suppose I know those those say
+
+ align:start position:0%
+okay suppose I know those those say
+ 
+
+ align:start position:0%
+okay suppose I know those those say
+those six entries could be anything
+
+ align:start position:0%
+those six entries could be anything
+ 
+
+ align:start position:0%
+those six entries could be anything
+could I finish the other
+
+ align:start position:0%
+could I finish the other
+ 
+
+ align:start position:0%
+could I finish the other
+three so that the Matrix was rank
+
+ align:start position:0%
+three so that the Matrix was rank
+ 
+
+ align:start position:0%
+three so that the Matrix was rank
+one what does rank one mean means every
+
+ align:start position:0%
+one what does rank one mean means every
+ 
+
+ align:start position:0%
+one what does rank one mean means every
+row is a multiple of every other row it
+
+ align:start position:0%
+row is a multiple of every other row it
+ 
+
+ align:start position:0%
+row is a multiple of every other row it
+means every 2x two determinant is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero every 2x two determinant because
+
+ align:start position:0%
+zero every 2x two determinant because
+ 
+
+ align:start position:0%
+zero every 2x two determinant because
+typical rank one Matrix let's see let me
+
+ align:start position:0%
+typical rank one Matrix let's see let me
+ 
+
+ align:start position:0%
+typical rank one Matrix let's see let me
+draw just write down a typical rank one
+
+ align:start position:0%
+draw just write down a typical rank one
+ 
+
+ align:start position:0%
+draw just write down a typical rank one
+Matrix a 132 and then some multiple of
+
+ align:start position:0%
+Matrix a 132 and then some multiple of
+ 
+
+ align:start position:0%
+Matrix a 132 and then some multiple of
+that and then some other multiple of
+
+ align:start position:0%
+that and then some other multiple of
+ 
+
+ align:start position:0%
+that and then some other multiple of
+that say
+
+ align:start position:0%
+that say
+ 
+
+ align:start position:0%
+that say
+396 okay every row is a multiple of the
+
+ align:start position:0%
+396 okay every row is a multiple of the
+ 
+
+ align:start position:0%
+396 okay every row is a multiple of the
+same row every column is a multiple of
+
+ align:start position:0%
+same row every column is a multiple of
+ 
+
+ align:start position:0%
+same row every column is a multiple of
+the same column the rank is one and
+
+ align:start position:0%
+the same column the rank is one and
+ 
+
+ align:start position:0%
+the same column the rank is one and
+every 2x two determinant say 3 2 9 6 is
+
+ align:start position:0%
+every 2x two determinant say 3 2 9 6 is
+ 
+
+ align:start position:0%
+every 2x two determinant say 3 2 9 6 is
+18 - 18
+
+ align:start position:0%
+18 - 18
+ 
+
+ align:start position:0%
+18 - 18
+every 2x two determinant has to be zero
+
+ align:start position:0%
+every 2x two determinant has to be zero
+ 
+
+ align:start position:0%
+every 2x two determinant has to be zero
+so if I give if if I'm if I'm given any
+
+ align:start position:0%
+so if I give if if I'm if I'm given any
+ 
+
+ align:start position:0%
+so if I give if if I'm if I'm given any
+six numbers here can I finish the
+
+ align:start position:0%
+six numbers here can I finish the
+ 
+
+ align:start position:0%
+six numbers here can I finish the
+remaining
+
+ align:start position:0%
+remaining
+ 
+
+ align:start position:0%
+remaining
+three to be rank one I don't think so
+
+ align:start position:0%
+three to be rank one I don't think so
+ 
+
+ align:start position:0%
+three to be rank one I don't think so
+why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not this
+
+ align:start position:0%
+not this
+ 
+
+ align:start position:0%
+not this
+guy right right okay so this guy would
+
+ align:start position:0%
+guy right right okay so this guy would
+ 
+
+ align:start position:0%
+guy right right okay so this guy would
+be trouble right because he's the
+
+ align:start position:0%
+be trouble right because he's the
+ 
+
+ align:start position:0%
+be trouble right because he's the
+determined by making that 2 x two
+
+ align:start position:0%
+determined by making that 2 x two
+ 
+
+ align:start position:0%
+determined by making that 2 x two
+determinant and also by making this
+
+ align:start position:0%
+determinant and also by making this
+ 
+
+ align:start position:0%
+determinant and also by making this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+oh last row get a 2 by DET oh here I've
+
+ align:start position:0%
+oh last row get a 2 by DET oh here I've
+ 
+
+ align:start position:0%
+oh last row get a 2 by DET oh here I've
+got a 2 by two determin oh yeah I'm
+
+ align:start position:0%
+got a 2 by two determin oh yeah I'm
+ 
+
+ align:start position:0%
+got a 2 by two determin oh yeah I'm
+already in trouble okay so let's take
+
+ align:start position:0%
+already in trouble okay so let's take
+ 
+
+ align:start position:0%
+already in trouble okay so let's take
+out this
+
+ align:start position:0%
+out this
+ 
+
+ align:start position:0%
+out this
+guy okay got to have other conditions
+
+ align:start position:0%
+guy okay got to have other conditions
+ 
+
+ align:start position:0%
+guy okay got to have other conditions
+about that that these aren't already
+
+ align:start position:0%
+about that that these aren't already
+ 
+
+ align:start position:0%
+about that that these aren't already
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+okay somehow right so now yeah so like
+
+ align:start position:0%
+okay somehow right so now yeah so like
+ 
+
+ align:start position:0%
+okay somehow right so now yeah so like
+our our marriage problem okay what about
+
+ align:start position:0%
+our our marriage problem okay what about
+ 
+
+ align:start position:0%
+our our marriage problem okay what about
+those five could I do it in that
+
+ align:start position:0%
+those five could I do it in that
+ 
+
+ align:start position:0%
+those five could I do it in that
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+and or not let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see many optim oh yeah I mean if so if I
+
+ align:start position:0%
+see many optim oh yeah I mean if so if I
+ 
+
+ align:start position:0%
+see many optim oh yeah I mean if so if I
+think of it big picture I'm given the
+
+ align:start position:0%
+think of it big picture I'm given the
+ 
+
+ align:start position:0%
+think of it big picture I'm given the
+first row yeah so then I take the second
+
+ align:start position:0%
+first row yeah so then I take the second
+ 
+
+ align:start position:0%
+first row yeah so then I take the second
+row the right multiple to make that come
+
+ align:start position:0%
+row the right multiple to make that come
+ 
+
+ align:start position:0%
+row the right multiple to make that come
+out right yeah and the third row to make
+
+ align:start position:0%
+out right yeah and the third row to make
+ 
+
+ align:start position:0%
+out right yeah and the third row to make
+that come out right or in terms of 2x
+
+ align:start position:0%
+that come out right or in terms of 2x
+ 
+
+ align:start position:0%
+that come out right or in terms of 2x
+two determinants which you can see I'm
+
+ align:start position:0%
+two determinants which you can see I'm
+ 
+
+ align:start position:0%
+two determinants which you can see I'm
+plugging away there's a little 2x two so
+
+ align:start position:0%
+plugging away there's a little 2x two so
+ 
+
+ align:start position:0%
+plugging away there's a little 2x two so
+that's determined there's a little 2 by
+
+ align:start position:0%
+that's determined there's a little 2 by
+ 
+
+ align:start position:0%
+that's determined there's a little 2 by
+two so that's determined then that's
+
+ align:start position:0%
+two so that's determined then that's
+ 
+
+ align:start position:0%
+two so that's determined then that's
+determined then that's determined once
+
+ align:start position:0%
+determined then that's determined once
+ 
+
+ align:start position:0%
+determined then that's determined once
+you deter that you still have problems
+
+ align:start position:0%
+you deter that you still have problems
+ 
+
+ align:start position:0%
+you deter that you still have problems
+with the first two entries in the First
+
+ align:start position:0%
+with the first two entries in the First
+ 
+
+ align:start position:0%
+with the first two entries in the First
+Column and the first two let's see uh
+
+ align:start position:0%
+Column and the first two let's see uh
+ 
+
+ align:start position:0%
+Column and the first two let's see uh
+should I erase these yellow ones
+
+ align:start position:0%
+should I erase these yellow ones
+ 
+
+ align:start position:0%
+should I erase these yellow ones
+and listen that the first the last one
+
+ align:start position:0%
+and listen that the first the last one
+ 
+
+ align:start position:0%
+and listen that the first the last one
+you eras
+
+ align:start position:0%
+you eras
+ 
+
+ align:start position:0%
+you eras
+you say that was
+
+ align:start position:0%
+you say that was
+ 
+
+ align:start position:0%
+you say that was
+deted row two column row two column 3
+
+ align:start position:0%
+deted row two column row two column 3
+ 
+
+ align:start position:0%
+deted row two column row two column 3
+that seems determined by this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah has to satisfy two conditions but
+
+ align:start position:0%
+yeah has to satisfy two conditions but
+ 
+
+ align:start position:0%
+yeah has to satisfy two conditions but
+but it might luck out it might be that
+
+ align:start position:0%
+but it might luck out it might be that
+ 
+
+ align:start position:0%
+but it might luck out it might be that
+the number we needed in there was the
+
+ align:start position:0%
+the number we needed in there was the
+ 
+
+ align:start position:0%
+the number we needed in there was the
+number that yeah so I mean this is
+
+ align:start position:0%
+number that yeah so I mean this is
+ 
+
+ align:start position:0%
+number that yeah so I mean this is
+exactly the reasoning we went through we
+
+ align:start position:0%
+exactly the reasoning we went through we
+ 
+
+ align:start position:0%
+exactly the reasoning we went through we
+thought oh we're lost lost but then we
+
+ align:start position:0%
+thought oh we're lost lost but then we
+ 
+
+ align:start position:0%
+thought oh we're lost lost but then we
+recovered yeah so I think actually it
+
+ align:start position:0%
+recovered yeah so I think actually it
+ 
+
+ align:start position:0%
+recovered yeah so I think actually it
+would work I mean because it what we put
+
+ align:start position:0%
+would work I mean because it what we put
+ 
+
+ align:start position:0%
+would work I mean because it what we put
+in there made that a multiple of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and
+
+ align:start position:0%
+that and
+ 
+
+ align:start position:0%
+that and
+then it's got to
+
+ align:start position:0%
+then it's got to
+ 
+
+ align:start position:0%
+then it's got to
+satisfy two you're right the first
+
+ align:start position:0%
+satisfy two you're right the first
+ 
+
+ align:start position:0%
+satisfy two you're right the first
+square and the and the second square and
+
+ align:start position:0%
+square and the and the second square and
+ 
+
+ align:start position:0%
+square and the and the second square and
+I'm saying
+
+ align:start position:0%
+I'm saying
+ 
+
+ align:start position:0%
+I'm saying
+that when we put that number in to make
+
+ align:start position:0%
+that when we put that number in to make
+ 
+
+ align:start position:0%
+that when we put that number in to make
+this Square okay we put in the right
+
+ align:start position:0%
+this Square okay we put in the right
+ 
+
+ align:start position:0%
+this Square okay we put in the right
+number so that
+
+ align:start position:0%
+number so that
+ 
+
+ align:start position:0%
+number so that
+it'll it'll be it'll be kosher with both
+
+ align:start position:0%
+it'll it'll be it'll be kosher with both
+ 
+
+ align:start position:0%
+it'll it'll be it'll be kosher with both
+but you're absolutely right that's the
+
+ align:start position:0%
+but you're absolutely right that's the
+ 
+
+ align:start position:0%
+but you're absolutely right that's the
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+thinking so yeah so that number that we
+
+ align:start position:0%
+thinking so yeah so that number that we
+ 
+
+ align:start position:0%
+thinking so yeah so that number that we
+put in
+
+ align:start position:0%
+put in
+ 
+
+ align:start position:0%
+put in
+there made these two made these two
+
+ align:start position:0%
+there made these two made these two
+ 
+
+ align:start position:0%
+there made these two made these two
+little vectors in the same direction so
+
+ align:start position:0%
+little vectors in the same direction so
+ 
+
+ align:start position:0%
+little vectors in the same direction so
+that we can get a number in
+
+ align:start position:0%
+that we can get a number in
+ 
+
+ align:start position:0%
+that we can get a number in
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now you see the problem so how do
+
+ align:start position:0%
+so so now you see the problem so how do
+ 
+
+ align:start position:0%
+so so now you see the problem so how do
+you find what are the conditions under
+
+ align:start position:0%
+you find what are the conditions under
+ 
+
+ align:start position:0%
+you find what are the conditions under
+which you can do it or can't do it
+
+ align:start position:0%
+which you can do it or can't do it
+ 
+
+ align:start position:0%
+which you can do it or can't do it
+should I do one more
+
+ align:start position:0%
+should I do one more
+ 
+
+ align:start position:0%
+should I do one more
+example uh at least I the you're really
+
+ align:start position:0%
+example uh at least I the you're really
+ 
+
+ align:start position:0%
+example uh at least I the you're really
+seeing this just as it's being done so
+
+ align:start position:0%
+seeing this just as it's being done so
+ 
+
+ align:start position:0%
+seeing this just as it's being done so
+we don't know let's see well I better
+
+ align:start position:0%
+we don't know let's see well I better
+ 
+
+ align:start position:0%
+we don't know let's see well I better
+stay with
+
+ align:start position:0%
+stay with
+ 
+
+ align:start position:0%
+stay with
+3x3 I think I can't get six I can't
+
+ align:start position:0%
+3x3 I think I can't get six I can't
+ 
+
+ align:start position:0%
+3x3 I think I can't get six I can't
+specify six this is first step of my
+
+ align:start position:0%
+specify six this is first step of my
+ 
+
+ align:start position:0%
+specify six this is first step of my
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have an undetermined one right but but
+
+ align:start position:0%
+have an undetermined one right but but
+ 
+
+ align:start position:0%
+have an undetermined one right but but
+now I think I can't here's let's see so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's okay there's six how many inde 2
+
+ align:start position:0%
+here's okay there's six how many inde 2
+ 
+
+ align:start position:0%
+here's okay there's six how many inde 2
+by are well that's sort of the question
+
+ align:start position:0%
+by are well that's sort of the question
+ 
+
+ align:start position:0%
+by are well that's sort of the question
+yeah how many independent 2 by tws that
+
+ align:start position:0%
+yeah how many independent 2 by tws that
+ 
+
+ align:start position:0%
+yeah how many independent 2 by tws that
+that is maybe the question and I claim
+
+ align:start position:0%
+that is maybe the question and I claim
+ 
+
+ align:start position:0%
+that is maybe the question and I claim
+there aren't six I think that one I
+
+ align:start position:0%
+there aren't six I think that one I
+ 
+
+ align:start position:0%
+there aren't six I think that one I
+can't do but now tell me why oh maybe
+
+ align:start position:0%
+can't do but now tell me why oh maybe
+ 
+
+ align:start position:0%
+can't do but now tell me why oh maybe
+you can see why I
+
+ align:start position:0%
+you can see why I
+ 
+
+ align:start position:0%
+you can see why I
+can't
+
+ align:start position:0%
+can't
+ 
+
+ align:start position:0%
+can't
+why if you use your thinking now I'll
+
+ align:start position:0%
+why if you use your thinking now I'll
+ 
+
+ align:start position:0%
+why if you use your thinking now I'll
+I'll have to give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this guy is determined by this one
+
+ align:start position:0%
+in this guy is determined by this one
+ 
+
+ align:start position:0%
+in this guy is determined by this one
+but is there anybody fighting it right
+
+ align:start position:0%
+but is there anybody fighting it right
+ 
+
+ align:start position:0%
+but is there anybody fighting it right
+yes the
+
+ align:start position:0%
+yes the
+ 
+
+ align:start position:0%
+yes the
+last oh and these guys are fighting it
+
+ align:start position:0%
+last oh and these guys are fighting it
+ 
+
+ align:start position:0%
+last oh and these guys are fighting it
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+bottom as well well as this yeah okay
+
+ align:start position:0%
+bottom as well well as this yeah okay
+ 
+
+ align:start position:0%
+bottom as well well as this yeah okay
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so so at this point we conjecture we
+
+ align:start position:0%
+so so at this point we conjecture we
+ 
+
+ align:start position:0%
+so so at this point we conjecture we
+can't get six in there we can't specify
+
+ align:start position:0%
+can't get six in there we can't specify
+ 
+
+ align:start position:0%
+can't get six in there we can't specify
+six so that would be my guess I they
+
+ align:start position:0%
+six so that would be my guess I they
+ 
+
+ align:start position:0%
+six so that would be my guess I they
+couldn't couldn't specify
+
+ align:start position:0%
+couldn't couldn't specify
+ 
+
+ align:start position:0%
+couldn't couldn't specify
+six yeah this is this won't work but
+
+ align:start position:0%
+six yeah this is this won't work but
+ 
+
+ align:start position:0%
+six yeah this is this won't work but
+five could work but five won't
+
+ align:start position:0%
+five could work but five won't
+ 
+
+ align:start position:0%
+five could work but five won't
+necessarily work right you could give me
+
+ align:start position:0%
+necessarily work right you could give me
+ 
+
+ align:start position:0%
+necessarily work right you could give me
+five that where I couldn't do it
+
+ align:start position:0%
+five that where I couldn't do it
+ 
+
+ align:start position:0%
+five that where I couldn't do it
+right if I had a 2 by two in there it
+
+ align:start position:0%
+right if I had a 2 by two in there it
+ 
+
+ align:start position:0%
+right if I had a 2 by two in there it
+would fail so you see it's one of these
+
+ align:start position:0%
+would fail so you see it's one of these
+ 
+
+ align:start position:0%
+would fail so you see it's one of these
+cases where you where every size or the
+
+ align:start position:0%
+cases where you where every size or the
+ 
+
+ align:start position:0%
+cases where you where every size or the
+condition is that every size has to be
+
+ align:start position:0%
+condition is that every size has to be
+ 
+
+ align:start position:0%
+condition is that every size has to be
+okay so here's my theorem half proved
+
+ align:start position:0%
+okay so here's my theorem half proved
+ 
+
+ align:start position:0%
+okay so here's my theorem half proved
+that can be done marriage or whatever
+
+ align:start position:0%
+that can be done marriage or whatever
+ 
+
+ align:start position:0%
+that can be done marriage or whatever
+let's rank one as possible if um
+
+ align:start position:0%
+let's rank one as possible if um
+ 
+
+ align:start position:0%
+let's rank one as possible if um
+every uh K by K submatrix has less or
+
+ align:start position:0%
+every uh K by K submatrix has less or
+ 
+
+ align:start position:0%
+every uh K by K submatrix has less or
+equal to 2 K - one uh specified
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x's in other words when K was three and
+
+ align:start position:0%
+x's in other words when K was three and
+ 
+
+ align:start position:0%
+x's in other words when K was three and
+I was looking at the whole Matrix five
+
+ align:start position:0%
+I was looking at the whole Matrix five
+ 
+
+ align:start position:0%
+I was looking at the whole Matrix five
+was the maximum but then I also have to
+
+ align:start position:0%
+was the maximum but then I also have to
+ 
+
+ align:start position:0%
+was the maximum but then I also have to
+look at smaller matrices 2 by tws and be
+
+ align:start position:0%
+look at smaller matrices 2 by tws and be
+ 
+
+ align:start position:0%
+look at smaller matrices 2 by tws and be
+sure
+
+ align:start position:0%
+sure
+ 
+
+ align:start position:0%
+sure
+that I have less or equal three of
+
+ align:start position:0%
+that I have less or equal three of
+ 
+
+ align:start position:0%
+that I have less or equal three of
+those in any 2 by two I'm only allowed
+
+ align:start position:0%
+those in any 2 by two I'm only allowed
+ 
+
+ align:start position:0%
+those in any 2 by two I'm only allowed
+to specify three not all four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm I offer a prize I guess for the
+
+ align:start position:0%
+so I'm I offer a prize I guess for the
+ 
+
+ align:start position:0%
+so I'm I offer a prize I guess for the
+proof that so I can prove that this is
+
+ align:start position:0%
+proof that so I can prove that this is
+ 
+
+ align:start position:0%
+proof that so I can prove that this is
+required I can prove that in a k byk i
+
+ align:start position:0%
+required I can prove that in a k byk i
+ 
+
+ align:start position:0%
+required I can prove that in a k byk i
+can't fit in 2K of them it has to be
+
+ align:start position:0%
+can't fit in 2K of them it has to be
+ 
+
+ align:start position:0%
+can't fit in 2K of them it has to be
+less or equal 2K minus one so this would
+
+ align:start position:0%
+less or equal 2K minus one so this would
+ 
+
+ align:start position:0%
+less or equal 2K minus one so this would
+be an example I can't fit six in but
+
+ align:start position:0%
+be an example I can't fit six in but
+ 
+
+ align:start position:0%
+be an example I can't fit six in but
+five I can fit right that that would be
+
+ align:start position:0%
+five I can fit right that that would be
+ 
+
+ align:start position:0%
+five I can fit right that that would be
+no problem can can we just do that case
+
+ align:start position:0%
+no problem can can we just do that case
+ 
+
+ align:start position:0%
+no problem can can we just do that case
+doesn't mean any five would work but
+
+ align:start position:0%
+doesn't mean any five would work but
+ 
+
+ align:start position:0%
+doesn't mean any five would work but
+these five will work because there's no
+
+ align:start position:0%
+these five will work because there's no
+ 
+
+ align:start position:0%
+these five will work because there's no
+reason they shouldn't that's what that's
+
+ align:start position:0%
+reason they shouldn't that's what that's
+ 
+
+ align:start position:0%
+reason they shouldn't that's what that's
+what this Duality is it works if there's
+
+ align:start position:0%
+what this Duality is it works if there's
+ 
+
+ align:start position:0%
+what this Duality is it works if there's
+no reason why
+
+ align:start position:0%
+no reason why
+ 
+
+ align:start position:0%
+no reason why
+not do you see that that would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work yes because well anyway you see it
+
+ align:start position:0%
+work yes because well anyway you see it
+ 
+
+ align:start position:0%
+work yes because well anyway you see it
+the these two these three would
+
+ align:start position:0%
+the these two these three would
+ 
+
+ align:start position:0%
+the these two these three would
+determine that these three would
+
+ align:start position:0%
+determine that these three would
+ 
+
+ align:start position:0%
+determine that these three would
+determine that these three would
+
+ align:start position:0%
+determine that these three would
+ 
+
+ align:start position:0%
+determine that these three would
+determine that these three would
+
+ align:start position:0%
+determine that these three would
+ 
+
+ align:start position:0%
+determine that these three would
+determine that and then true enough
+
+ align:start position:0%
+determine that and then true enough
+ 
+
+ align:start position:0%
+determine that and then true enough
+these would determine it but it we got a
+
+ align:start position:0%
+these would determine it but it we got a
+ 
+
+ align:start position:0%
+these would determine it but it we got a
+good chance and it well it just has to
+
+ align:start position:0%
+good chance and it well it just has to
+ 
+
+ align:start position:0%
+good chance and it well it just has to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+there's to determined by
+
+ align:start position:0%
+there's to determined by
+ 
+
+ align:start position:0%
+there's to determined by
+one of given of of given ones yeah
+
+ align:start position:0%
+one of given of of given ones yeah
+ 
+
+ align:start position:0%
+one of given of of given ones yeah
+that's right that's right the condition
+
+ align:start position:0%
+that's right that's right the condition
+ 
+
+ align:start position:0%
+that's right that's right the condition
+because otherwise all the other are
+
+ align:start position:0%
+because otherwise all the other are
+ 
+
+ align:start position:0%
+because otherwise all the other are
+specified in terms how many yeah so how
+
+ align:start position:0%
+specified in terms how many yeah so how
+ 
+
+ align:start position:0%
+specified in terms how many yeah so how
+many does that give you you have K by K
+
+ align:start position:0%
+many does that give you you have K by K
+ 
+
+ align:start position:0%
+many does that give you you have K by K
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+many if I have a 10x10
+
+ align:start position:0%
+many if I have a 10x10
+ 
+
+ align:start position:0%
+many if I have a 10x10
+Matrix the max maximum number I could
+
+ align:start position:0%
+Matrix the max maximum number I could
+ 
+
+ align:start position:0%
+Matrix the max maximum number I could
+specify would be
+
+ align:start position:0%
+specify would be
+ 
+
+ align:start position:0%
+specify would be
+19 but then those 19 that I specify I
+
+ align:start position:0%
+19 but then those 19 that I specify I
+ 
+
+ align:start position:0%
+19 but then those 19 that I specify I
+can't specify any 19 any 9 by9 Matrix in
+
+ align:start position:0%
+can't specify any 19 any 9 by9 Matrix in
+ 
+
+ align:start position:0%
+can't specify any 19 any 9 by9 Matrix in
+that Matrix can only have 17 of them and
+
+ align:start position:0%
+that Matrix can only have 17 of them and
+ 
+
+ align:start position:0%
+that Matrix can only have 17 of them and
+any 5x5 Matrix could only have nine of
+
+ align:start position:0%
+any 5x5 Matrix could only have nine of
+ 
+
+ align:start position:0%
+any 5x5 Matrix could only have nine of
+them and any 2x two Matrix could only
+
+ align:start position:0%
+them and any 2x two Matrix could only
+ 
+
+ align:start position:0%
+them and any 2x two Matrix could only
+have three of them otherwise I'd be dead
+
+ align:start position:0%
+have three of them otherwise I'd be dead
+ 
+
+ align:start position:0%
+have three of them otherwise I'd be dead
+at that lower level like the marriage
+
+ align:start position:0%
+at that lower level like the marriage
+ 
+
+ align:start position:0%
+at that lower level like the marriage
+problem it's where where that smaller
+
+ align:start position:0%
+problem it's where where that smaller
+ 
+
+ align:start position:0%
+problem it's where where that smaller
+set of
+
+ align:start position:0%
+set of
+ 
+
+ align:start position:0%
+set of
+or like the maximum cut problem where a
+
+ align:start position:0%
+or like the maximum cut problem where a
+ 
+
+ align:start position:0%
+or like the maximum cut problem where a
+small number smaller subset was was uh
+
+ align:start position:0%
+small number smaller subset was was uh
+ 
+
+ align:start position:0%
+small number smaller subset was was uh
+putting the limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on no if I think we had a case where
+
+ align:start position:0%
+on no if I think we had a case where
+ 
+
+ align:start position:0%
+on no if I think we had a case where
+there were no 2 by
+
+ align:start position:0%
+there were no 2 by
+ 
+
+ align:start position:0%
+there were no 2 by
+tws but that was a case with no no 2 x
+
+ align:start position:0%
+tws but that was a case with no no 2 x
+ 
+
+ align:start position:0%
+tws but that was a case with no no 2 x
+two screw-ups but a 3X3 screw
+
+ align:start position:0%
+two screw-ups but a 3X3 screw
+ 
+
+ align:start position:0%
+two screw-ups but a 3X3 screw
+up and so you have to check screw up at
+
+ align:start position:0%
+up and so you have to check screw up at
+ 
+
+ align:start position:0%
+up and so you have to check screw up at
+every size then the theorem is if you
+
+ align:start position:0%
+every size then the theorem is if you
+ 
+
+ align:start position:0%
+every size then the theorem is if you
+don't screw up at any size just in
+
+ align:start position:0%
+don't screw up at any size just in
+ 
+
+ align:start position:0%
+don't screw up at any size just in
+counting numbers then you can do it so
+
+ align:start position:0%
+counting numbers then you can do it so
+ 
+
+ align:start position:0%
+counting numbers then you can do it so
+what's the what's the question what's
+
+ align:start position:0%
+what's the what's the question what's
+ 
+
+ align:start position:0%
+what's the what's the question what's
+what the
+
+ align:start position:0%
+what the
+ 
+
+ align:start position:0%
+what the
+proof if if I could I don't know how to
+
+ align:start position:0%
+proof if if I could I don't know how to
+ 
+
+ align:start position:0%
+proof if if I could I don't know how to
+put in the X's right I don't know how to
+
+ align:start position:0%
+put in the X's right I don't know how to
+ 
+
+ align:start position:0%
+put in the X's right I don't know how to
+show yet anyway hopefully next Wednesday
+
+ align:start position:0%
+show yet anyway hopefully next Wednesday
+ 
+
+ align:start position:0%
+show yet anyway hopefully next Wednesday
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+different situation that if that if all
+
+ align:start position:0%
+different situation that if that if all
+ 
+
+ align:start position:0%
+different situation that if that if all
+these if I don't have too many of any in
+
+ align:start position:0%
+these if I don't have too many of any in
+ 
+
+ align:start position:0%
+these if I don't have too many of any in
+any size submatrix then I can do
+
+ align:start position:0%
+any size submatrix then I can do
+ 
+
+ align:start position:0%
+any size submatrix then I can do
+it both of the examples you showed it
+
+ align:start position:0%
+it both of the examples you showed it
+ 
+
+ align:start position:0%
+it both of the examples you showed it
+was easier to verify you could do it
+
+ align:start position:0%
+was easier to verify you could do it
+ 
+
+ align:start position:0%
+was easier to verify you could do it
+true by looking at the rows as multiple
+
+ align:start position:0%
+true by looking at the rows as multiple
+ 
+
+ align:start position:0%
+true by looking at the rows as multiple
+of other rows that true but that was
+
+ align:start position:0%
+of other rows that true but that was
+ 
+
+ align:start position:0%
+of other rows that true but that was
+because those were little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples you're not believing my theorem
+
+ align:start position:0%
+examples you're not believing my theorem
+ 
+
+ align:start position:0%
+examples you're not believing my theorem
+right well that's the best way actually
+
+ align:start position:0%
+right well that's the best way actually
+ 
+
+ align:start position:0%
+right well that's the best way actually
+no no I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm well yeah it's so it's like the
+
+ align:start position:0%
+I'm well yeah it's so it's like the
+ 
+
+ align:start position:0%
+I'm well yeah it's so it's like the
+marriage it's exactly like the marriage
+
+ align:start position:0%
+marriage it's exactly like the marriage
+ 
+
+ align:start position:0%
+marriage it's exactly like the marriage
+problem and that I have some condition
+
+ align:start position:0%
+problem and that I have some condition
+ 
+
+ align:start position:0%
+problem and that I have some condition
+which I hope is the right one that just
+
+ align:start position:0%
+which I hope is the right one that just
+ 
+
+ align:start position:0%
+which I hope is the right one that just
+involves a little
+
+ align:start position:0%
+involves a little
+ 
+
+ align:start position:0%
+involves a little
+counting and then the conclusion is that
+
+ align:start position:0%
+counting and then the conclusion is that
+ 
+
+ align:start position:0%
+counting and then the conclusion is that
+the whole thing can be completed the
+
+ align:start position:0%
+the whole thing can be completed the
+ 
+
+ align:start position:0%
+the whole thing can be completed the
+whole puzzle whole puzzle can be
+
+ align:start position:0%
+whole puzzle whole puzzle can be
+ 
+
+ align:start position:0%
+whole puzzle whole puzzle can be
+completed and uh
+
+ align:start position:0%
+completed and uh
+ 
+
+ align:start position:0%
+completed and uh
+it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly why is it different yeah I mean
+
+ align:start position:0%
+exactly why is it different yeah I mean
+ 
+
+ align:start position:0%
+exactly why is it different yeah I mean
+soor maybe it could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be turned into the marriage problem I
+
+ align:start position:0%
+be turned into the marriage problem I
+ 
+
+ align:start position:0%
+be turned into the marriage problem I
+don't know I don't know how to do
+
+ align:start position:0%
+don't know I don't know how to do
+ 
+
+ align:start position:0%
+don't know I don't know how to do
+that I haven't actually I mean I
+
+ align:start position:0%
+that I haven't actually I mean I
+ 
+
+ align:start position:0%
+that I haven't actually I mean I
+realized right away that the condition
+
+ align:start position:0%
+realized right away that the condition
+ 
+
+ align:start position:0%
+realized right away that the condition
+we have is is a marriage
+
+ align:start position:0%
+we have is is a marriage
+ 
+
+ align:start position:0%
+we have is is a marriage
+likee marriage problem like matching
+
+ align:start position:0%
+likee marriage problem like matching
+ 
+
+ align:start position:0%
+likee marriage problem like matching
+like condition so there ought to be a
+
+ align:start position:0%
+like condition so there ought to be a
+ 
+
+ align:start position:0%
+like condition so there ought to be a
+way but I haven't seen it yet haven't
+
+ align:start position:0%
+way but I haven't seen it yet haven't
+ 
+
+ align:start position:0%
+way but I haven't seen it yet haven't
+had time to tell the truth I'm uh
+
+ align:start position:0%
+had time to tell the truth I'm uh
+ 
+
+ align:start position:0%
+had time to tell the truth I'm uh
+normally I wouldn't reveal half prooved
+
+ align:start position:0%
+normally I wouldn't reveal half prooved
+ 
+
+ align:start position:0%
+normally I wouldn't reveal half prooved
+theorem uh but
+
+ align:start position:0%
+theorem uh but
+ 
+
+ align:start position:0%
+theorem uh but
+uh it seemed appropriate here if I have
+
+ align:start position:0%
+uh it seemed appropriate here if I have
+ 
+
+ align:start position:0%
+uh it seemed appropriate here if I have
+a 2 by two Matrix in the upper corner
+
+ align:start position:0%
+a 2 by two Matrix in the upper corner
+ 
+
+ align:start position:0%
+a 2 by two Matrix in the upper corner
+doesn't have zero determinator AR a 2 by
+
+ align:start position:0%
+doesn't have zero determinator AR a 2 by
+ 
+
+ align:start position:0%
+doesn't have zero determinator AR a 2 by
+two Matrix that the upper the upper left
+
+ align:start position:0%
+two Matrix that the upper the upper left
+ 
+
+ align:start position:0%
+two Matrix that the upper the upper left
+hand corner 2 by two 2 by two you know I
+
+ align:start position:0%
+hand corner 2 by two 2 by two you know I
+ 
+
+ align:start position:0%
+hand corner 2 by two 2 by two you know I
+fill in
+
+ align:start position:0%
+fill in
+ 
+
+ align:start position:0%
+fill in
+the first two entries and the first two
+
+ align:start position:0%
+the first two entries and the first two
+ 
+
+ align:start position:0%
+the first two entries and the first two
+rows wait a minute how big is this it's
+
+ align:start position:0%
+rows wait a minute how big is this it's
+ 
+
+ align:start position:0%
+rows wait a minute how big is this it's
+a 3 by3 3 by3 okay four in the
+
+ align:start position:0%
+a 3 by3 3 by3 okay four in the
+ 
+
+ align:start position:0%
+a 3 by3 3 by3 okay four in the
+upper the upper left corner 3x3 put
+
+ align:start position:0%
+upper the upper left corner 3x3 put
+ 
+
+ align:start position:0%
+upper the upper left corner 3x3 put
+in sorry tell me where to put so you're
+
+ align:start position:0%
+in sorry tell me where to put so you're
+ 
+
+ align:start position:0%
+in sorry tell me where to put so you're
+specifying these yeah those four then
+
+ align:start position:0%
+specifying these yeah those four then
+ 
+
+ align:start position:0%
+specifying these yeah those four then
+you're dead yeah right okay okay I'm
+
+ align:start position:0%
+you're dead yeah right okay okay I'm
+ 
+
+ align:start position:0%
+you're dead yeah right okay okay I'm
+saying you're dead because there's a
+
+ align:start position:0%
+saying you're dead because there's a
+ 
+
+ align:start position:0%
+saying you're dead because there's a
+because there's a submatrix of size two
+
+ align:start position:0%
+because there's a submatrix of size two
+ 
+
+ align:start position:0%
+because there's a submatrix of size two
+with two
+
+ align:start position:0%
+with two
+ 
+
+ align:start position:0%
+with two
+with too many specified yeah right you
+
+ align:start position:0%
+with too many specified yeah right you
+ 
+
+ align:start position:0%
+with too many specified yeah right you
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+toy
+
+ align:start position:0%
+toy
+ 
+
+ align:start position:0%
+toy
+youy the by I mean in these cases in all
+
+ align:start position:0%
+youy the by I mean in these cases in all
+ 
+
+ align:start position:0%
+youy the by I mean in these cases in all
+the cases that we found two maor that
+
+ align:start position:0%
+the cases that we found two maor that
+ 
+
+ align:start position:0%
+the cases that we found two maor that
+specify the same point
+
+ align:start position:0%
+specify the same point
+ 
+
+ align:start position:0%
+specify the same point
+yes everybody is free to leave it's 10
+
+ align:start position:0%
+yes everybody is free to leave it's 10
+ 
+
+ align:start position:0%
+yes everybody is free to leave it's 10
+to five now right uh uh yeah so let's
+
+ align:start position:0%
+to five now right uh uh yeah so let's
+ 
+
+ align:start position:0%
+to five now right uh uh yeah so let's
+let's come back to this hopefully with
+
+ align:start position:0%
+let's come back to this hopefully with
+ 
+
+ align:start position:0%
+let's come back to this hopefully with
+some new idea uh 9:00 Wednesday okay
+
+ align:start position:0%
+some new idea uh 9:00 Wednesday okay
+ 
+
+ align:start position:0%
+some new idea uh 9:00 Wednesday okay
+thanks oh that's answer actually
\ No newline at end of file
diff --git a/5qTCy2wTL_s.txt b/5qTCy2wTL_s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..36b5ef7f8a0b9ed014fee91a30bd62c6a066e1af
--- /dev/null
+++ b/5qTCy2wTL_s.txt
@@ -0,0 +1,2831 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: All right.
+
+It's 12:05, so why don't you
+go ahead and take 10 more
+
+seconds on the clicker
+question today.
+
+This is about the periodic
+trends that we
+
+discussed on Wednesday.
+
+So specifically, what we're
+asking here is as we go across
+
+the periodic table, we want to
+consider which has the smaller
+
+ionization energy.
+
+All right.
+
+So, let's focus our attention
+up here now, whether it's
+
+between aluminum or whether
+it's between phosphorous.
+
+And I also wanted you to
+identify why it's also
+
+important to understand why we
+have these trends, not just to
+
+memorize the trend itself.
+
+So, it turns out that the
+majority of you got the
+
+correct answer, which is
+that it's aluminum.
+
+The reason it's aluminum is
+because aluminum has a lower z
+
+effective, so it's not being
+pulled in as tightly by the
+
+nucleus, and if it's not being
+pulled in as tightly, you're
+
+going to have to put in less
+energy in order to ionize it,
+
+so that's why it's actually
+going to have the smaller
+
+ionization energy.
+
+So it looks like not too many
+more than half of you got this
+
+correct, so make sure you can
+look at your periodic table
+
+and figure out how to think
+about ionization energy in
+
+terms of z effective, not just
+in terms of memorizing what
+
+that trend is.
+
+All right, so we can go to
+today's notes, and in terms of
+
+the notes, what we're going
+to start with is finishing
+
+material that's going to be
+relevant for exam 1, and I
+
+told you on Wednesday that
+actually I'd give you some
+
+information today in terms of
+what you need to do to prepare
+
+for exam 1.
+
+So you should have gotten two
+handouts as you came in, and
+
+if you didn't, please raise your
+hand and a TA will come
+
+to you and get you that
+second handout.
+
+But the second one says "exam
+instructions and logistics."
+
+So, if everyone can
+pull that out.
+
+So this is going to tell you
+pretty much everything you
+
+need to know in terms of getting
+ready for the exam,
+
+which is next Wednesday.
+
+So when you go home today or
+some time this weekend, make
+
+sure you read this
+page in detail.
+
+I'm just going to go over a few
+of the main points here.
+
+So, the first is that what we're
+going over notes today
+
+and also on Monday, the exam
+material ends at the end
+
+lecture notes from lecture 9.
+
+So that was Wednesday's class
+-- not at the end of
+
+Wednesday's class, but at the
+end of the lecture notes.
+
+So we're going to finish
+up with those today.
+
+I'll be really, really clear
+when we get through them, and
+
+that's where you can stop in
+terms of studying for this.
+
+Also, on everything that was on
+problem-sets 1 through 3.
+
+So, you turned in p-set 3 today,
+but we'll have the
+
+answers posted for you this
+afternoon, so you can start
+
+studying from p-set 3, even as
+early as tonight, if you want
+
+to, because those answers
+will be there for you.
+
+So, in terms of what it is that
+you need to prepare and
+
+bring with you for the exam, you
+need to bring your MIT ID,
+
+especially if you haven't been
+showing up regularly to your
+
+recitations and you aren't 100%
+sure if your TA knows
+
+exactly who you are, you need to
+make sure you have your MIT
+
+ID with you.
+
+You can't take the exam unless
+you're registered for the
+
+class, and we need to make
+sure we can verify that.
+
+You also need to bring a
+calculator, of course, because
+
+we'll be solving problems that
+involve calculations.
+
+You can bring any calculator
+you want, we don't actually
+
+have restrictions for calculator
+types here, but
+
+what you can't do, is you can't
+program any relevant
+
+chemical or information about
+constants in there.
+
+It's OK to use certain
+fundamental constants that
+
+come in a lot of calculators,
+so there's nothing we can do
+
+about that.
+
+That's OK.
+
+If you're wondering what's OK
+or what's not OK, it's very
+
+clearly written out in this
+handout, so make sure you read
+
+through it, because it is your
+responsibility to make sure
+
+that your calculator does
+not have anything extra
+
+programmed in it.
+
+And if you have your calculator
+all set up as you
+
+love and you don't want to
+change it, then maybe you
+
+should just go and get an $8.00
+scientific calculator
+
+that doesn't have any of the
+graphing functions, because
+
+you don't actually need them, so
+that's a better option for
+
+you, you can do that as well.
+
+And I had mentioned several
+times that you do not need to
+
+memorize the majority of the
+equations and you don't need
+
+to memorize any physical
+constants.
+
+So if you flip the info page
+over on the back here, what
+
+you'll see is the periodic
+table, this is the same one
+
+that I've handed out in the
+last two lectures -- the
+
+periodic table without any
+electron configurations.
+
+This is exactly the sheet here,
+it's exactly what you'll
+
+get on exam day.
+
+You'll also see that they have
+all the physical constants
+
+that you're going to need, and
+also a bunch of the actual
+
+equations that we've been using
+in the first couple
+
+weeks here.
+
+So you don't need to memorize
+any of this, you're actually
+
+going to be handed this.
+
+There are a few equations that
+you need to memorize -- those
+
+are the very simple -- very,
+very simple equations, such as
+
+e equals h times nu -- hopefully
+you don't have to
+
+sit down and try to memorize
+that, hopefully we all know
+
+that already.
+
+But just to be really clear,
+I've written out exactly which
+
+equations you do have to
+memorize on the front here, so
+
+long as you know those, the
+rest you can just look up.
+
+And in terms of using these
+equations in solving problems
+
+on the exam, and also using
+these constants, make sure if
+
+you think there might be any
+chance you're going to get any
+
+little part of a problem wrong
+or do a calculation
+
+inaccurately, you need to write
+out every single step of
+
+your thinking as you write out
+these problems. We can't give
+
+you any partial credit
+whatsoever if we can't see
+
+your thought process.
+
+So it's important to write out
+the equation you use, you need
+
+to write out the constants
+that you use to
+
+fill in that equation.
+
+And that we need to see your
+work to get full credit, and
+
+then especially if you get
+things wrong, we need to know
+
+where it went wrong, because
+we do try to give as much
+
+partial credit as possible in
+these exams, since there are a
+
+lot of places where small
+mistakes can result in the
+
+wrong answer.
+
+So also, along those lines in
+terms of test taking, make
+
+sure you also box your answers
+and that you keep track of
+
+significant figures and that you
+also remember to include
+
+your units.
+
+These are just little things
+that can add up, so you just
+
+want to make sure you're
+on top of those.
+
+And your TAs on Tuesday are
+going to share a lot of other
+
+types of sort of exam strategies
+in thinking about
+
+how you can approach an exam
+when we're in a time situation
+
+like we are, so they'll share
+some of their experience with
+
+you in terms of taking
+these timed exams.
+
+So, in terms of practicing this
+weekend, I mentioned that
+
+instead of getting a problem-set
+today, what I am
+
+going to be posting is optional
+extra problems. So
+
+they're optional, but they're
+very, very, very highly
+
+encouraged that you do these,
+because this is going to give
+
+you practice for the types of
+problems that are going to be
+
+on the exam.
+
+We're also posting a practice
+exam for you to take, so after
+
+you're completely done your
+studying, it's good to have
+
+everything done before you take
+the practice exam, and
+
+then sit down just with this
+sheet here and your
+
+calculator, and ideally a timer,
+and make sure you can
+
+do the practice exam in the
+allotted amount of time.
+
+So that way you can have an
+idea if, oh, I do really
+
+understand this but I'm a little
+bit slow, maybe I need
+
+to practice this one type of
+problem a little bit longer so
+
+I can get up to speed so I'm
+going to be able to get
+
+through all this in terms
+of the exam time.
+
+All right.
+
+So let's move on to
+today's topics.
+
+So, as I said, we're finishing
+up with what we left off with
+
+yesterday -- or excuse
+me, on Wednesday.
+
+This includes atomic radius and
+the idea of isoelectronic
+
+atoms. So that's going to
+be the end of the exam 1
+
+material, and then we'll move
+on to exam 2 material, which
+
+is kind of exciting, because
+we've been talking about just
+
+individual atoms and ions up to
+this point, and now we can
+
+talk about molecules, so
+we're going to start
+
+talking about bonding.
+
+So for some you that are less
+interested in maybe the
+
+physical structure of an
+individual atom, now some more
+
+exciting material for you might
+be coming up if you like
+
+to think about how, instead,
+molecules behave, either
+
+within bonding, within
+themselves, or with other
+
+molecules, that's what we're
+going to be heading to
+
+in this next unit.
+
+So, we need to finish up
+with periodic trends.
+
+And first, on your
+lecture notes, I
+
+start with atomic radius.
+
+I was so proud of myself getting
+the lecture notes
+
+finished early and handing them
+in to CopyTech, and then
+
+I realized we didn't do
+
+electronegativity on Wednesday.
+
+So, if you can flip your lecture
+notes over and just
+
+write on the blank space,
+we're going to cover
+
+electronegativity first here,
+and specifically, you can go
+
+back and fill this in to your
+lecture 9 notes, if you want
+
+to stay organized, but I just
+suggest just writing it on
+
+lecture 10 notes now
+and going back.
+
+You can still keep organized,
+which hopefully most of you
+
+like to do, and get it in the
+right place in the notes.
+
+So, when we're talking about the
+idea of electronegativity,
+
+essentially what we're talking
+about is the ability for an
+
+atom to attract electron density
+from another atom.
+
+So it's just a measure of how
+much does one given atom want
+
+to pull away electron
+density from, let's
+
+say, an adjacent atom.
+
+So it's actually very related
+to what we're talking about
+
+when we said electron affinity,
+and it's also
+
+related to ionization energy,
+and we can call
+
+electronegativity by symbol
+here, and it turns out that
+
+it's going to be proportional
+to 1/2 of the electron
+
+affinity of a given atom, plus
+the ionization energy.
+
+So, in other words, we
+can just think of
+
+electronegativity as being the
+average of that ionization
+
+energy and the electron
+affinity.
+
+This should make sense, because
+if an atom has a very
+
+high electron affinity, that
+means it's really happy taking
+
+an electron from another atom,
+or taking a free electron --
+
+that that's very favorable.
+
+If something has a high
+ionization energy, it means
+
+that it really, really,
+really does not want
+
+to give up an electron.
+
+So you can think about how these
+2 things combined are
+
+going to be electronegativity,
+which is a measure of how much
+
+an atom wants to pull electron
+density away
+
+from another atom.
+
+So, if we think about
+electronegativity as a
+
+periodic trend, we can just draw
+our nice periodic table
+
+here, and let's separate
+it into quadrants.
+
+So if we think about the upper
+right hand part of the
+
+quadrant, well, this is where
+we're going to have high
+
+electron affinity and high
+ionization energy, so we're
+
+also going to see high
+electronegativity here.
+
+And in contrast, in the lower
+left hand part of the periodic
+
+table, these 2 quantities are
+low, so also what we're going
+
+to see is low electronegativity.
+
+And if we talk about what's
+going on in areas, or with
+
+atoms that have high
+electronegativity, and we
+
+think about whether they're
+electron donors or electron
+
+acceptors, what would you expect
+for an atom that has
+
+high electronegativity?
+
+Is it going to be an electron
+donor or acceptor?
+
+Great.
+
+Yup, it's going to be an
+electron acceptor, it wants to
+
+accept electrons, it wants to
+accept electron density.
+
+So, in contrast, if it has a
+low electronegativity, this
+
+then is going to be
+an electron donor.
+
+All right, so it's very
+common to talk about
+
+electronegativity of different
+atoms, and you can look up
+
+tables of these.
+
+Often what you'll see is not
+a table based on this
+
+definition, but something that's
+called the Pauling
+
+definition of electronegativity,
+but it's
+
+exactly the same idea and the
+same trend as this more
+
+numerical way to think about
+what the meaning of
+
+electronegativity is.
+
+All right, so now we can move
+on to the start of today's
+
+notes, which is atomic radius.
+
+So this, in fact, is going to
+be our last principle that
+
+we're going to talk about in
+terms of periodic trends.
+
+So this is actually the most
+straightforward, so sometimes
+
+it's nice to end with the
+easiest concept, and that's
+
+what we're doing here.
+
+And if we're talking about
+atomic radius, essentially
+
+we're talking about
+atomic size.
+
+And immediately it should
+probably come into your head
+
+that we don't actually have an
+atomic radius that we can talk
+
+about, right?
+
+What I just spent many lectures
+discussing is the
+
+fact that we can not know how
+far away an electron is from
+
+the nucleus, so we can't
+actually know the radius of a
+
+certain atom.
+
+And that's true.
+
+An atom's not a defined
+sphere, for example.
+
+We can't define it as an exact
+radius in terms of the
+
+definition we might think
+of classically.
+
+So, keep that in mind when we're
+talking about atomic
+
+radius, I'm not suddenly
+changing my story and saying,
+
+yes, we do have a
+distinct radius.
+
+Instead, what people have done
+is come up with different ways
+
+to think about how they
+can define a radius.
+
+And one common way to think
+about it, is to think about
+
+the value of r, or the radius,
+below which 90% of that
+
+electron density is going
+to be contained.
+
+So we're not saying it's
+all the electron
+
+density, it's just 90%.
+
+Because we know as we go to
+infinity, even though the
+
+density gets smaller and smaller
+and smaller, we still
+
+have electron density very far
+away from the nucleus.
+
+So, what we're going to define
+is just let's just capture 90%
+
+of that electron density.
+
+So, that's one way to think
+about it, and there's also
+
+another way, and this
+is the way that your
+
+book presents it.
+
+If you, in fact, have two of
+the same atom right next to
+
+each other, let's say you have a
+crystal, or let's say you're
+
+talking about a metal, what you
+can do is just look at the
+
+distance between the two nuclei,
+and split that in 1/2,
+
+and take the atomic
+radius that way.
+
+So, these are two different
+definitions of how to think
+
+about atomic radius, but really
+what you find when
+
+these are measured is they
+come up with almost the
+
+identical values, so there are
+tables you can look up of
+
+atomic radii and see these
+values, and you can trust them
+
+that, yes, they work for both
+this definition and for this
+
+definition here,
+in most cases.
+
+And what we've been talking
+about with all of these
+
+properties are, of course, how
+can we figure out what that is
+
+for a certain atom by looking
+at the periodic table, so we
+
+want to think about
+the periodic
+
+trend for atomic radius.
+
+And we know as we go across a
+row in the periodic table,
+
+what's happening is that z
+effective or the effective
+
+pull on the nucleus
+is increasing.
+
+So would you expect, therefore,
+as we go across a
+
+row for the atomic radius, to
+increase or to decrease?
+
+Good.
+
+OK, yes.
+
+We are expecting to see that
+it decreases because it's
+
+feeling a stronger pull, all the
+electrons are being pulled
+
+in closer to the nucleus, so
+that atomic size is going to
+
+get smaller.
+
+This is in contrast to what's
+happening as we go down a
+
+periodic table.
+
+So as we go down we're now
+adding electrons to further
+
+and further away shells, so
+what we're going to see is
+
+that the atomic radius is going
+to increase as we're
+
+going down the periodic table.
+
+And we can look at
+an example here.
+
+If we start in the upper left
+hand corner of the periodic
+
+table with lithium, you can
+see that as we go down the
+
+table, what you're seeing is
+that that atomic radius is
+
+actually increasing,
+as we would expect.
+
+Whereas, if we go across a row,
+what we see is that the
+
+atomic radius is decreasing.
+
+So, again, this is one of the
+more straightforward trends.
+
+You just need to remember
+what's happening to z
+
+effective, which really tells
+us what's happening with all
+
+the trends, and once you know
+z effective, you can figure
+
+out, for example, what direction
+the atomic radius
+
+should be going into.
+
+So, that's it for
+periodic trends.
+
+We have talked about four
+different ones.
+
+We talked about ionization
+energy, electron affinity, we
+
+talked about electronegativity,
+which is
+
+just kind of a combination of
+the first two, and then ended
+
+with atomic radius here.
+
+And what you might have noted
+is although we described how
+
+to make predictions about these
+properties, I didn't
+
+talk too much about what it
+actually means, what the
+
+ramifications of these different
+properties are.
+
+And the reason we didn't do that
+is because we're actually
+
+going to spend much of the rest
+of the course relating
+
+these different properties to
+the properties of molecules in
+
+terms of bonding, and also in
+terms of chemical reactions.
+
+So, for example, if we have a
+very electronegative atom
+
+within a certain molecule, what
+you'll actually find is
+
+that it does affect how the
+molecule is going to take part
+
+in different chemical or
+biological reactions.
+
+And this will become more and
+more clear as we actually talk
+
+about these reactions and
+talk about bonding.
+
+But you need to be able to
+predict what kind of
+
+properties a certain atom's
+going to have within a
+
+molecule, whether you're talking
+about something, for
+
+example, that's very
+electronegative, or something
+
+that is not electronegative at
+all, it is going to make a
+
+difference in terms of thinking
+about how molecules
+
+are structured and
+also how they
+
+interact with other molecules.
+
+However, I can give you at least
+one example while we're
+
+still on just talking about
+atoms. So we haven't gotten to
+
+molecules yet, we're just
+talking about single atoms or
+
+single ions, but what's nice
+is just talking about this
+
+very straightforward principle
+of atomic radius.
+
+We can already use that in terms
+of single ions to think
+
+about a really complex
+biological issue, which is to
+
+talk about ion channels.
+
+So, that is just a quick example
+for some of you, you
+
+might be very familiar with ion
+channels, others might not
+
+know what these are, so I'll
+just tell you quite briefly
+
+that ion channels are
+these very massive
+
+transmembrane proteins.
+
+Essentially, what they are is
+it's a protein that spans the
+
+membrane of a cell.
+
+And what they do is they
+regulate the influx of ions
+
+across that cell.
+
+So the influx of ions from the
+outside of the cell to the
+
+inside of the cell,
+for example.
+
+And you can think of ion
+channels as being gated, by
+
+gated it means the gate can be
+closed and no ions are going
+
+through, as in this case here.
+
+Or you can talk about the gate
+being open, and in this case,
+
+you can see that you will
+have an influx of ions.
+
+So, ion channels are important
+for maintaining a voltage
+
+difference between the inside of
+the cell and outside of the
+
+cell, and they're found in all
+sorts of cell types in your
+
+body, but if you think about
+where they're most prevalent,
+
+it turns out that they're most
+prevalent in muscle cells and
+
+also in nerve cells,
+so in your neurons.
+
+And essentially, what they do
+in neurons is they underlie
+
+those nerve impulses, or those,
+essentially what we
+
+call electrical signaling
+between neurons -- you might
+
+also call that the action
+potential of the neurons.
+
+So essentially, they regulate
+this action potential, and
+
+they do so by helping to
+establish and then control the
+
+voltage gradient within the
+cells. so, essentially,
+
+they're establishing or
+controlling or changing the
+
+difference between the charge
+inside the cell and the charge
+
+outside cell.
+
+And when we talk about any type
+of ion channel, there are
+
+just tons of different kinds of
+ion channels, and you can
+
+characterize them in a
+few different ways.
+
+So, for example, you could
+characterize them in terms of
+
+how they're gated, and basically
+how they open or
+
+close -- that's one way to talk
+about different types.
+
+Another way to talk about
+different types is to think
+
+about which ion they're
+selected for.
+
+And all ion channels are
+selective for a single type of
+
+ion, and we can think about
+how that selectivity takes
+
+place, and that's where this
+idea of atomic radius is going
+
+to become very important.
+
+So, for example, if we look at
+sodium channels, and sodium
+
+channels are some of the
+particularly prevalent ones
+
+when we're talking about
+neurons, if you think about
+
+the cell membrane, and this
+little green cartoon is me
+
+trying to show a sodium channel
+here, and in this
+
+case, you can see that it's
+closed, such that no ions are
+
+getting through.
+
+However, when that gate is
+opened, the sodium channel is
+
+now going to be incredibly
+selective and only let through
+
+sodium ions and no other
+type of ion.
+
+And this is really interesting
+to think about because you can
+
+imagine in our body we have
+concentrations of all types of
+
+ions, and specifically, some
+seem very, very similar to
+
+each other.
+
+So we could think about
+comparing the potassium ion to
+
+a sodium ion.
+
+They have the same charge
+of plus one.
+
+The only thing that's different
+is that they're one
+
+down on the periodic table,
+potassium is down one row, so
+
+it's going to be a little
+bigger, but when we're
+
+thinking about size, it maybe
+does not seem that significant
+
+to talk about the size.
+
+But what we find out
+is that it is.
+
+So, what happens, this is
+another view of a sodium
+
+channel, so this is actually
+looking a little bit more at
+
+the protein structure.
+
+What all of these channels
+have is what's called a
+
+selectivity filter, so this
+filter filters out the type of
+
+ion that's going to be
+allowed through.
+
+And there's two parts
+of the filter.
+
+First we need to select
+for actual charge.
+
+So the way that it does this
+is the filter is actually
+
+lined with all of this negative
+charge, and for those
+
+of you that are more into
+biology or biochemistry,
+
+that's because of negatively
+charged amino acid residues,
+
+but all you need to think about
+is that it has negative
+
+charge in the inside of this
+pore, and what happens then is
+
+that if something has a positive
+charge, it's going to
+
+be stabilized to enter this
+pore, whereas any negative
+
+ions are going to be repelled.
+
+So that's the first step in
+being selective, but now how
+
+do we differentiate between
+these sodium
+
+and potassium ions.
+
+And the answer is just really
+beautifully simple, and it's
+
+just that the pore gets really,
+really tiny, to the
+
+point that it gets so small that
+all that can fit through
+
+this pore is one a single ion,
+one single sodium ion,
+
+solvated by one single
+water molecule.
+
+And that's all that's big enough
+to pass through or
+
+small enough to pass through.
+
+And if we go up even just one
+row on the periodic table to
+
+potassium, what we actually see
+is now that it's going to
+
+be too large, and, in fact, a
+potassium solvated with one
+
+water molecule won't go
+through our channel.
+
+So, this is just one example
+of how these properties can
+
+already, even our understanding
+just talking
+
+about single atoms, can already
+make an impact in
+
+these biological systems. And
+actually, a question that
+
+might come up, I just explained,
+the sodium channel,
+
+you might say, well, how do
+potassium channels work then,
+
+because I can understand how you
+can filter something big
+
+out, but how do you filter
+out something small.
+
+And it turns out that size
+exclusion is also the
+
+principle that's in play with
+potassium channels as well,
+
+but in this case it's a little
+more complex, because what
+
+happens is these negative
+residues the are in the pore
+
+need to stabilize the potassium
+as it goes through,
+
+and the potassium is large
+enough to make all the
+
+contacts it needs, but the
+sodium, which you can picture
+
+being smaller, actually can't
+reach all of the stabilizing
+
+charges that it needs to to
+get through the pore.
+
+So, again, it is based on size,
+it's a little bit less
+
+intuitive than the idea of just
+straining out all of the
+
+potassium ions.
+
+But again, many of these ion
+channels have this size
+
+exclusion pore, it's a very
+important part of them.
+
+All right, so that was a quick
+aside on thinking about how
+
+these properties can,
+in fact, relate to
+
+something in our body.
+
+Let's move on to the last topic
+in terms of this first
+
+exam, which is thinking about
+the idea of isoelectronic
+
+atoms, or isoelectronic ions.
+
+And isoelectronic is very
+straightforward, it just means
+
+having the same electron
+configuration.
+
+The easiest way to look at this
+is just to do an example.
+
+So let's take the
+example of neon.
+
+This has the electron
+configuration of 1 s 2, 2
+
+s 2, and 2 p 6.
+
+It looks like we're cut off the
+screen a little bit here,
+
+but you can see I've just
+circled it there.
+
+So we can go ahead and think
+about, well, are there any
+
+other atoms that are going
+to have the same electron
+
+configuration?
+
+The answer to that is definitely
+no -- if they had
+
+the same electron configuration,
+they would, in
+
+fact, be neon.
+
+But we can think about different
+ions that have this
+
+electron configuration.
+
+So for example, if we think
+about fluorine, that has an
+
+electron configuration of 1 s
+2, 2 s 2, 2 p 5, so all we
+
+would need to do is add one more
+electron to get the same
+
+configuration as for neon.
+
+So if we want to write out what
+that would be, it would
+
+just be to say that f minus is
+isoelectronic with neon.
+
+So, we can say that -- if we
+have neon here and we want to
+
+think about what's
+isoelectronic, f minus would
+
+be isoelectronic.
+
+We also have oxygen -- what
+would the charge on oxygen be?
+
+Um-hmm, right.
+
+2 minus.
+
+Then also, nitrogen, 3 minus --
+these are all going to be
+
+isoelectronic with neon.
+
+We can go in the other
+direction, so let's go to
+
+sodium, but we would need to
+take away an electron to make
+
+it isoelectronic.
+
+So we would say sodium plus,
+or magnesium 2 plus, we can
+
+just keep going -- aluminum 3
+plus, silicone 4 plus, and we
+
+can go on and on in either
+direction all the way across
+
+and down the periodic table.
+
+So, that's the idea of
+isoelectronic ions.
+
+These are all isoelectronic,
+they all have the same
+
+electron configuration.
+
+And we can also think
+about going back to
+
+atomic size for a second.
+
+What the relationship is between
+these ions and their
+
+parent atoms. So, for example,
+if we think of the fluorine
+
+minus case, would you expect
+fluorine minus to be larger or
+
+smaller than neutral fluorine?
+
+Okay.
+
+I heard mostly larger, but a
+little bit of a mix in there,
+
+and it turns out that
+larger is correct.
+
+And we can think about why --
+essentially we have fluorine
+
+and now we're adding
+another electron.
+
+So you can picture that fluorine
+is going to get
+
+larger in this case.
+
+And that would be true
+for all of the
+
+negatively charged ions.
+
+So, by the same logic, that
+means that all of our
+
+positively charged ions are, in
+fact, going to be smaller
+
+in terms of radius, compared
+to their neutral parents.
+
+Not only are we taking away an
+electron here, but we're also
+
+going to decrease shielding,
+so the electrons that are
+
+already in there are going to
+feel a higher z effective and
+
+will be pulling and the atom
+will be getting smaller.
+
+And this is just a picture
+showing some of these sizes
+
+with their parent.
+
+So, for example, a lithium here,
+you can see how lithium
+
+plus is smaller than the actual
+lithium atom in its
+
+neutral state.
+
+Whereas for fluorine, fluorine
+is smaller than f minus is the
+
+one that's the outer
+shell shown here.
+
+So, let's do a clicker question
+on isoelectronic
+
+atoms. And now we're asking you
+to look at krypton, so the
+
+atomic mass is 36.
+
+You can actually just grab
+that handout, the second
+
+handout on the exam and look at
+the periodic table there.
+
+So, which of the following ions
+listed is isoelectronic
+
+with krypton?
+
+OK, let's take 10
+seconds on that.
+
+OK, good.
+
+This might be our all-time
+high, 89% got this right.
+
+This is great.
+
+So, selenium 2 minus is what's
+going to be isoelectronic,
+
+because if you add two electrons
+to selenium, you'll
+
+get the same electron
+configuration that you have
+
+for krypton here.
+
+OK, I think we can safely
+go back to notes.
+
+So, I said I would announce
+it, that's the
+
+end of exam 1 material.
+
+So, if you compartmentalize
+things in your brain in
+
+certain ways, put that off into
+the end of the exam 1
+
+part of your brain, and
+now we're going to
+
+move on to exam 2.
+
+Remember, for exam 2, you
+still need to know and
+
+understand everything you
+learned in exam 1, but you can
+
+put off learning it completely
+until we get through, at
+
+least, next Wednesday before we
+start maybe spending time
+
+on these concepts outside
+of class.
+
+So, we're going to start with
+talking about bonding, and any
+
+time we have a chemical bond,
+basically what we're talking
+
+about is having two atoms where
+the arrangement of their
+
+nuclei and they're electrons are
+such that the bonded atoms
+
+results in a lower energy than
+for the separate atoms. So we
+
+know we always want to have
+our systems in as low an
+
+energy as possible, so it makes
+sense that a bond would
+
+happen any time we got a lower
+energy when we combine two
+
+atoms, versus when we
+keep them separate.
+
+So specifically, today
+we're going to talk
+
+about covalent bonds.
+
+A covalent bond is any time we
+have a pair of electrons that
+
+is shared between two different
+atoms. And the key
+
+word for covalent bonds is
+the idea of being shared.
+
+The two electrons, for example,
+we see in the h 2
+
+molecule, they don't belong to
+one or the other atom, they're
+
+actually shared.
+
+And what we'll see later, is
+that the sharing is not always
+
+equal -- in the case
+of h 2, it is
+
+completely equal sharing.
+
+In some cases, because of things
+like electronegativity,
+
+one atom will take away more of
+the electron density than
+
+the other atom, but they're
+still shared, even if they're
+
+not always evenly shared.
+
+So, in talking about covalent
+bonds, we should be able to
+
+still apply a more general
+definition of a chemical bond,
+
+which should tell us that the
+h 2 molecule is going to be
+
+lower in energy than if we
+looked at 2 separate hydrogen
+
+atom molecules.
+
+So, let's see if that's
+actually the case.
+
+So if I tell you that the energy
+for single hydrogen
+
+atom is negative 13 12
+kilojoules per mole.
+
+If we want to talk about two
+hydrogen atoms, then we just
+
+need to double that, so that's
+going to be negative 2 6 2 4
+
+kilojoules per mole that we're
+talking about in terms of a
+
+single hydrogen atom.
+
+So, let's compare this to the
+energy of the h 2 molecule,
+
+and we find that that's
+negative 3,048
+
+kilojoules per mole.
+
+So, in fact, yes, we did confirm
+that these covalent
+
+bond, at least in the case of
+hydrogen, we have confirmed by
+
+the numbers that we are at a
+lower energy state when we
+
+talk about the bonded atom
+versus the individual atom.
+
+And when we talk about covalent
+bonds, there's 2
+
+properties that we'll mostly
+focus on, and that's going to
+
+be thinking about the bond
+strength or the energy by
+
+which it stabilized
+when it bonds.
+
+And we can also talk about the
+bond length, so we might be
+
+interested in what the bond
+length is, what the distance
+
+between these two nuclei are.
+
+And we can actually better
+visualize this if we plot how
+
+that energy changes
+as a function of
+
+internuclear distance.
+
+And when I say internuclear
+distance, we actually call
+
+this r here.
+
+It's kind of ironic that we put
+this in the same lecture
+
+as we talk about atomic radii,
+which we also call r, but
+
+they're two different r's,
+so you need to keep them
+
+separated in terms of what
+you're talking about.
+
+When we're talking about r for
+internuclear distance, we're
+
+talking about the distance
+between two different nuclei
+
+in a bond, in a covalent bond.
+
+So, if we look at this graph
+where what we're charting is
+
+the internuclear distance, so
+the distance between these two
+
+hydrogen atoms, as a function
+of energy, what we are going
+
+to see is a curve that looks
+like this -- this is the
+
+general curve that you'll see
+for any covalent bond, and
+
+we'll explain where that
+comes from in a minute.
+
+I want to point out that the
+zero energy is defined as when
+
+you have a naked proton where
+the electron has popped out --
+
+that's what we've defined as
+zero energy up to this point
+
+when we're talking about single
+atoms. So, for starters
+
+we'll keep that as our zero
+energy, we're going to change
+
+it soon to make something that
+makes more sense in terms of
+
+bonding, but we'll keep
+that as zero for now.
+
+So, we see that the two h atoms
+separate have a certain
+
+energy that's lower than
+when the electron's
+
+not with the atom.
+
+And then even lower
+down, we have our
+
+bonded hydrogen molecule.
+
+So, we can think about the
+different kinds of
+
+interactions that are
+taking place.
+
+I said what hold the bonds
+together, what holds two atoms
+
+together is the attractive force
+we have between each
+
+electron and the
+other nucleus.
+
+That's the huge force that we're
+talking about in terms
+
+of making a bond stable, but
+there are also repulsive
+
+forces, so you can imagine
+we're going to have
+
+electron-electron repulsion
+between the two electrons if
+
+we're bringing them
+closer together.
+
+And the real killer is if we get
+too close we're even going
+
+to have nuclear-nuclear
+repulsion between the nuclei
+
+of the two atoms.
+
+So, this makes this chart shown
+in pink make a lot more
+
+sense, because if we're way
+out at very far distances,
+
+essentially what we have here
+is we're talking about two
+
+separate atoms. They're not
+interacting at all so that's
+
+why the energy is the same as
+that for two individual atoms,
+
+that's what we're
+dealing with.
+
+As we get closer together,
+we start get lower
+
+and lower in energy.
+
+The reason is because the
+predominant force at this
+
+point is going to be the
+attraction that's being felt
+
+between the nuclei and the
+electrons in each of the
+
+atoms. At some point you're
+going to hit a well here,
+
+which is the point where it's
+most stabilized or at it's
+
+lowest energy.
+
+So, when we think about a bond
+length, this is going to be
+
+the length of our bond here,
+that makes sense because it's
+
+going to want to be at
+that distance that
+
+minimizes the energy.
+
+But as we keep getting closer,
+even though as we get closer,
+
+the attraction is going to get
+stronger between the two
+
+nuclei and the electrons.
+
+We're also going to start to
+have the repulsive forces
+
+become more prominent here, and,
+in fact, they take over
+
+at some point, becoming the more
+prevalent of the forces,
+
+so as you get closer, the
+electron-electron repulsions,
+
+and eventually the
+nucleus-nucleus repulsion is
+
+going to mean that your energy
+is just absolutely
+
+skyrocketing, so it just keeps
+going up and up as you get
+
+closer to zero here.
+
+So, when we want to talk about
+the information that we can
+
+get out of looking at a chart
+like this, well, the first
+
+thing I did tell you was that
+this is going to be the bond
+
+length, so the distance r where
+the energy is lowest,
+
+but we can also talk about
+something called dissociation
+
+energy, that's going to be this
+distance right here or
+
+the energy that is this value.
+
+And the dissociation energy is
+very intuitive in terms of
+
+what it means, it means how much
+energy you need to put
+
+into the molecule in order to
+disassociate it into its
+
+individual atoms. And so we can
+actually think about how
+
+do we calculate what the
+dissociation energy should be
+
+for h 2, so let's go
+ahead and do this.
+
+So, if we talk about
+dissociating h 2, we're going
+
+from the h 2 molecule, and
+breaking this bond right in
+
+half, so we now have
+two individual
+
+hydrogen atoms here.
+
+So we need to take the energy
+for the two atoms, which we
+
+know is -- so let's take our
+dissociation energy is going
+
+to be equal to negative 2 6 2 4
+kilojoules per mole, and we
+
+want to subtract the energy of
+the hydrogen molecule itself,
+
+so that's going to be negative
+3 0 4 8 kilojoules per mole.
+
+So, what we get for the
+disassociation energy for a
+
+hydrogen atom is 424 kilojoules
+per mole.
+
+So what that means is that's how
+much energy we would have
+
+to put in to a hydrogen molecule
+in order to get it to
+
+split apart into
+its two atoms.
+
+So, another way to talk about
+dissociation energy is simply
+
+to call it bond strength, it's
+the same thing, they're equal
+
+to each other.
+
+If we know that this is it the
+dissociation energy for a
+
+hydrogen atom, we can also say
+the bond strength for hydrogen
+
+molecule is 424.
+
+So, there's actually another way
+to graph it where we can
+
+directly graph the dissociation
+energy or the
+
+bond strengths.
+
+So I said before when we were
+talking about single atoms, we
+
+always define the zero energy
+as when an electron was
+
+actually ejected, but now, when
+we talk about chemical
+
+reactions taking place, it's
+very, very rare that we're
+
+actually going to be talking
+about anything that gets to
+
+this point here.
+
+It's much more relevant to set
+our zero point energy as the
+
+separation of a bond in terms of
+talking about the reactions
+
+that we'll usually be
+dealing with here.
+
+So, let's change our graph where
+we now have this zero
+
+point set as the two individuals
+hydrogen atoms,
+
+and then we see that our h 2
+molecule is at the negative of
+
+the dissociation energy, or the
+negative what that bond
+
+strength is.
+
+So we know what that number
+would be, it would be negative
+
+424 kilojoules per mole
+that we see here.
+
+So, what this let's us do now
+is directly compare, for
+
+example, the strength of a bond
+in terms of a hydrogen
+
+atom and hydrogen molecule,
+compared to any kind of
+
+molecule that we want to
+graph on top of it.
+
+So, let's, for example,
+look at nitrogen.
+
+So n 2, we can do the chart
+here in green, so it's the
+
+green dotted line, and what
+we see is that we have now
+
+defined this energy
+as where the 2
+
+nitrogen atoms are separated.
+
+So what we can actually directly
+compare is the
+
+dissociation energy or the
+bond strength of nitrogen
+
+versus hydrogen.
+
+So, if we think about this,
+which would you say has a
+
+stronger bond?
+
+Is it going to be hydrogen
+or nitrogen?
+
+Yup, it's going to
+be nitrogen.
+
+And the reason we can see that
+by looking at this graph is
+
+that we see that nitrogen when
+it's bonded is in an even
+
+lower well than we
+saw for hydrogen.
+
+It's going to be a stronger
+bond because it's more
+
+stabilized when it when it comes
+together as a molecule.
+
+We can also think about the
+distance, the bond distance.
+
+So, which would you
+say is going to be
+
+shorter in this case?
+
+Is a hydrogen bond shorter, or
+is a nitrogen-nitrogen triple
+
+bond going to be shorter?
+
+Um-hmm, again, we can
+get this information
+
+directly from our graph.
+
+We see that the radius is
+shorter, so that means that
+
+the nitrogen-nitrogen bond
+is going to be shorter.
+
+We can know this information
+even if we just knew that the
+
+bond was stronger, we wouldn't
+need to look at a graph here,
+
+because it turns out that if you
+have a stronger bond, that
+
+also means that you have a
+shorter bond -- those ywo are
+
+correlated.
+
+And something that we'll see
+later on is that triple bonds,
+
+for example, are going to be
+stronger than a corresponding
+
+double bond or a corresponding
+single bond.
+
+So, if we talked about a
+nitrogen-nitrogen single
+
+versus double versus triple
+bond, the triple bond will be
+
+the shortest and it will
+be the strongest.
+
+So, that's basically the idea
+of how we are going to be
+
+thinking about covalent bonds.
+
+It's also important, once we
+start talking about molecules,
+
+to have a way to represent them,
+and also to be able to
+
+look at a shorthand notation
+for a certain molecule and
+
+understand what the bond is.
+
+So, for example, down here I
+wrote that it was n 2 and that
+
+it was h 2, but when I re-wrote
+the molecules up
+
+here, you saw that it's an h
+h single bond where it's a
+
+nitrogen-nitrogen triple bond.
+
+So any chemist should be able
+to just look at n 2 and know
+
+that it's a triple bond, but
+that's not something that
+
+we've learned how did to do
+yet, so let's go ahead and
+
+start a new topic that's going
+to allow us to have some sort
+
+of sense of what the valence
+electron configuration, which
+
+includes whether something's a
+single or double or a triple
+
+bond can be figured out for
+any given molecule.
+
+So, to do this, what I'm going
+to do is introduce the topic
+
+of Lewis structures.
+
+We're going to really get into
+this next class, but I just
+
+want to introduce it to you to
+give us a start, and many of
+
+you have used Lewis structures
+in high school, but we'll be
+
+doing some much more challenging
+Lewis structures,
+
+I can assure you, in
+this class here.
+
+So, a Lewis structure is
+basically an organizing
+
+property of bonding, of
+molecules, which is the idea
+
+that when we're thinking about
+bonding, the key is to achieve
+
+a full valence shell in each of
+the individual atoms. So we
+
+want to have in an h h bond, for
+example, a full shell for
+
+each of the hydrogen atoms.
+And G.N. Lewis is the
+
+scientist that is credited, and
+who did, in fact, come up
+
+with this idea for the way to
+represent this, so the other
+
+parts of this idea, another way
+to phrase it is that the
+
+electrons are going to be
+distributed in such a way that
+
+we have what are called full
+octets for each of the atoms,
+
+and basically that's the same
+thing as saying we have a full
+
+valence shell, and this is
+something that Lewis was able
+
+to recognize very, very early,
+way before we had quantum
+
+mechanics to describe what these
+orbitals were, but it
+
+makes sense a full valence shell
+means for most atoms
+
+that we have a full s orbital
+plus a full p orbital, so
+
+we're going to have a total of
+four orbitals that are each
+
+filled with eight electrons, so
+that's why we see that we
+
+need an octet here.
+
+And the idea is that when you do
+these Lewis dot structures,
+
+we're representing electrons
+with dots, which we'll see in
+
+a minute, and each
+dot is going to
+
+represent a valence electron.
+
+So, hopefully, you remember
+what we mean by valence
+
+electrons versus
+core electrons.
+
+Core electrons are all those
+electrons held in really tight
+
+with the nucleus in the inner
+shells, whereas the valence
+
+electrons are only those
+electrons that are in the
+
+outer-most shell, or at your
+highest value of n of the
+
+principal quantum number.
+
+So, Lewis structures are really
+a model for a way to
+
+think about what the valence
+electron configuration is, and
+
+as I said, it's not based on
+quantum mechanics, it's
+
+something that Lewis observed
+far, far before quantum
+
+mechanics were discovered.
+
+So he came up with the ideas
+that led to the idea of Lewis
+
+structures in the very
+early 1900's.
+
+So you might ask well, why are
+we using this model if it
+
+clearly doesn't take into
+account quantum mechanics?
+
+And the reason that we use it
+is that it is incredibly
+
+accurate, and allows us to very,
+very quickly predict and
+
+to predict accurately, in most
+cases, what the electron
+
+configuration of molecules
+are going to be.
+
+So this is really useful.
+
+We don't always want to go
+and solve the Schrodinger
+
+equation, and in fact, once we
+start talking about molecules,
+
+I can imagine none of you, as
+much as you love math or
+
+physics, want to be trying
+to solve this Schrodinger
+
+equation in that case either.
+
+So, what Lewis structures allow
+us to do is over 90% of
+
+the time be correct in terms
+of figuring out what the
+
+electron configuration is.
+
+And we won't just use
+them in this class.
+
+If you actually go to any of the
+chemistry labs at MIT, if
+
+you go over to building 18 and
+look in the organic labs where
+
+they're synthesizing new
+molecules or making up new
+
+reactions, what you'll see if
+you open anyone's notebook,
+
+their lab notebook, assuming
+they keep a nice lab notebook,
+
+is that they will have Lewis
+structures drawn in there that
+
+explain the reactions that
+they're going to be
+
+doing for that day.
+
+And I mean this means way past
+all the chemistry they've
+
+taken, they're now graduate
+students or they're now
+
+professors, and they're still
+writing out Lewis structures.
+
+Now they're writing a more
+abbreviated form, which you'll
+
+probably get to if you take
+organic chemistry, but really
+
+it's the exact same idea.
+
+And this goes all the
+way back to 1902.
+
+In fact, Lewis was an American
+scientist, so he was trained
+
+in America, and he actually was
+a professor here at MIT
+
+from 1905 all the way to about
+1911 or 1912, and these are
+
+some notes from 1902, and you
+can't see them very well, but
+
+this was essentially an early
+form of Lewis structures, and
+
+this was called the
+cubicle atom.
+
+So, basically what he's showing
+in these cubes is that
+
+there are eight spaces that
+need to be filled up
+
+to have a full cube.
+
+So in order to fill them, he
+would have to have eight
+
+electrons or an octet
+around the cubes.
+
+So what we're seeing is this
+is notes from 1902 -- he
+
+actually didn't publish any of
+this work or these ideas that
+
+led to Lewis structures until
+1916, but his early class
+
+notes were used as evidence
+about how long ago he actually
+
+came up with the idea of it.
+
+So it's really neat to think
+that your counterparts 100
+
+years ago right here at MIT
+could have been sitting in a
+
+class where they had Lewis as
+their lecturer, and he's
+
+putting forth these ideas --
+these are actually his lecture
+
+notes, even though it wasn't
+even published yet, and giving
+
+this idea of Lewis structure,
+which is exactly what we keep
+
+using today in order to make
+a lot of these predictions.
+
+So, let's see how some of this
+works, and hopefully your
+
+counterparts from 100 years
+ago would also be able to
+
+think about how this works, even
+if they don't have the
+
+quantum mechanics behind
+the individual electron
+
+configurations for atoms. So
+I said that we want to be
+
+talking about valence electrons
+here, so that means
+
+if we're talking about, for
+example, the octet rule for an
+
+f f molecule where we have two
+fluorine atoms, we need to
+
+write the valence electrons
+as dots around them.
+
+So let's do a quick clicker
+question, and you tell me how
+
+many valence electrons
+does fluorine have?
+
+Remember, valence electrons
+are different from core,
+
+they're only the outer-most
+electrons in
+
+the outer-most shell.
+
+So, 10 seconds on this,
+this should
+
+be fast. OK, great.
+
+Good job on the clicker
+questions today.
+
+So we have seven valence
+electrons.
+
+So, let's go back to the notes,
+and let's fill these
+
+in, seven electrons.
+
+Another way you could have
+known them was to look at
+
+Lewis' notes here, where if look
+at this box carefully you
+
+see there are seven dots around
+the cube, so there are
+
+his seven valence electrons.
+
+So, we see is when we use the
+octet rule to look at fluorine
+
+molecule, we're combining two
+fluorine atoms, and what we
+
+end up with is an f f molecule
+where they're sharing two
+
+electrons, so making
+that covalent bond.
+
+But that each individual
+fluorine atom has eight
+
+electrons, or full
+octet around it.
+
+We can think about where those
+electrons came from, so we got
+
+seven from the blue electrons
+here, seven as shown in green
+
+here, but each individual
+fluorine atom has eight, even
+
+though two of those are being
+shared between both of them.
+
+So, the octet rule is a general
+rule that you'll for
+
+all of the atoms. There are some
+exceptions, which we'll
+
+get to later, but the only a
+big exception here is with
+
+hydrogen, which has a special
+stability that's associated
+
+with two electrons.
+
+This should make a lot of sense,
+because we know that a
+
+hydrogen has 1 s as it's
+outer-most or valence orbital,
+
+so it can be filled up just
+with two 1 s electrons.
+
+And we give different names,
+depending on what kind of
+
+electrons we're dealing with,
+so, for example, with h c l
+
+here, we can talk about
+having bonded
+
+versus lone pair electrons.
+
+So, in terms of the c l atom,
+we need to talk about each
+
+atom individually.
+
+How many bonding electrons
+does c l have?
+
+All right.
+
+Let's see, we've got a mixed
+response here, it turns out it
+
+has two bonding electrons.
+
+I heard some people say one,
+and that's a good guess,
+
+remember they're actually
+sharing.
+
+So these two electrons, they
+belong to chlorine, they also
+
+belong to hydrogen, but they
+do, in fact, belong to
+
+chlorine as well.
+
+There's no one person owning
+them, so they both have two
+
+electrons here that
+are bonding.
+
+So how many lone pair electrons
+do we have?
+
+OK.
+
+I hear six and three, so both
+are sort of right, we have 6
+
+lone pair electrons,
+which means that we
+
+have three lone pairs.
+
+So, in terms of thinking about
+how to draw a Lewis structure,
+
+I won't go through this today
+or any day in terms of just
+
+reading through the rules, you
+can read that yourself.
+
+But what we'll do is go through
+each of these rules in
+
+terms of an example.
+
+So, what will start with on
+Monday is doing the most
+
+simple example of methane
+using these
+
+Lewis structure rules.
+
+So, don't forget to study this
+weekend and get those extra
+
+practice problems from
+the course website.
\ No newline at end of file
diff --git a/5wCZqdCDafc.txt b/5wCZqdCDafc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..17432bdb79966a6d839689886fb44d38ac2c8b2c
--- /dev/null
+++ b/5wCZqdCDafc.txt
@@ -0,0 +1,1499 @@
+align:start position:0%
+ 
+so connectivity is more than just an All
+
+ align:start position:0%
+so connectivity is more than just an All
+ 
+
+ align:start position:0%
+so connectivity is more than just an All
+or Nothing Affair we can talk about how
+
+ align:start position:0%
+or Nothing Affair we can talk about how
+ 
+
+ align:start position:0%
+or Nothing Affair we can talk about how
+connected a graph is so let's begin with
+
+ align:start position:0%
+connected a graph is so let's begin with
+ 
+
+ align:start position:0%
+connected a graph is so let's begin with
+two vertices two vertices are said to be
+
+ align:start position:0%
+two vertices two vertices are said to be
+ 
+
+ align:start position:0%
+two vertices two vertices are said to be
+K Edge connected if they remain
+
+ align:start position:0%
+K Edge connected if they remain
+ 
+
+ align:start position:0%
+K Edge connected if they remain
+connected if you remove fewer than K
+
+ align:start position:0%
+connected if you remove fewer than K
+ 
+
+ align:start position:0%
+connected if you remove fewer than K
+edges from the
+
+ align:start position:0%
+edges from the
+ 
+
+ align:start position:0%
+edges from the
+graph let's look at an example so here's
+
+ align:start position:0%
+graph let's look at an example so here's
+ 
+
+ align:start position:0%
+graph let's look at an example so here's
+a graph and let's focus on those two
+
+ align:start position:0%
+a graph and let's focus on those two
+ 
+
+ align:start position:0%
+a graph and let's focus on those two
+vertices that I've highlighted in
+
+ align:start position:0%
+vertices that I've highlighted in
+ 
+
+ align:start position:0%
+vertices that I've highlighted in
+magenta they are one EDG connected
+
+ align:start position:0%
+magenta they are one EDG connected
+ 
+
+ align:start position:0%
+magenta they are one EDG connected
+because they're connected and if you
+
+ align:start position:0%
+because they're connected and if you
+ 
+
+ align:start position:0%
+because they're connected and if you
+remove one Edge they become disconnected
+
+ align:start position:0%
+remove one Edge they become disconnected
+ 
+
+ align:start position:0%
+remove one Edge they become disconnected
+so they're one Edge connected but
+
+ align:start position:0%
+so they're one Edge connected but
+ 
+
+ align:start position:0%
+so they're one Edge connected but
+they're not two Edge connected if in
+
+ align:start position:0%
+they're not two Edge connected if in
+ 
+
+ align:start position:0%
+they're not two Edge connected if in
+particular if I delete that edge um then
+
+ align:start position:0%
+particular if I delete that edge um then
+ 
+
+ align:start position:0%
+particular if I delete that edge um then
+they no longer is a path between the two
+
+ align:start position:0%
+they no longer is a path between the two
+ 
+
+ align:start position:0%
+they no longer is a path between the two
+magenta
+
+ align:start position:0%
+magenta
+ 
+
+ align:start position:0%
+magenta
+vertices um here's an example of two
+
+ align:start position:0%
+vertices um here's an example of two
+ 
+
+ align:start position:0%
+vertices um here's an example of two
+vertices these two green vertices that
+
+ align:start position:0%
+vertices these two green vertices that
+ 
+
+ align:start position:0%
+vertices these two green vertices that
+are two Edge connected that means that I
+
+ align:start position:0%
+are two Edge connected that means that I
+ 
+
+ align:start position:0%
+are two Edge connected that means that I
+can remove any number of edges less than
+
+ align:start position:0%
+can remove any number of edges less than
+ 
+
+ align:start position:0%
+can remove any number of edges less than
+two which is to say one Edge and they'll
+
+ align:start position:0%
+two which is to say one Edge and they'll
+ 
+
+ align:start position:0%
+two which is to say one Edge and they'll
+stay connected so I could try but if if
+
+ align:start position:0%
+stay connected so I could try but if if
+ 
+
+ align:start position:0%
+stay connected so I could try but if if
+I do remove two vertices they become
+
+ align:start position:0%
+I do remove two vertices they become
+ 
+
+ align:start position:0%
+I do remove two vertices they become
+disconnected so with those two vertices
+
+ align:start position:0%
+disconnected so with those two vertices
+ 
+
+ align:start position:0%
+disconnected so with those two vertices
+now I uh those two edges judiciously
+
+ align:start position:0%
+now I uh those two edges judiciously
+ 
+
+ align:start position:0%
+now I uh those two edges judiciously
+selected there will no longer be a path
+
+ align:start position:0%
+selected there will no longer be a path
+ 
+
+ align:start position:0%
+selected there will no longer be a path
+between the two green
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertices uh for a three-edge connected
+
+ align:start position:0%
+vertices uh for a three-edge connected
+ 
+
+ align:start position:0%
+vertices uh for a three-edge connected
+example we can look at these two uh
+
+ align:start position:0%
+example we can look at these two uh
+ 
+
+ align:start position:0%
+example we can look at these two uh
+vertices highlighted in purple and
+
+ align:start position:0%
+vertices highlighted in purple and
+ 
+
+ align:start position:0%
+vertices highlighted in purple and
+discover that we can remove any two
+
+ align:start position:0%
+discover that we can remove any two
+ 
+
+ align:start position:0%
+discover that we can remove any two
+edges and they're still going to be
+
+ align:start position:0%
+edges and they're still going to be
+ 
+
+ align:start position:0%
+edges and they're still going to be
+stuck together you can kind of see that
+
+ align:start position:0%
+stuck together you can kind of see that
+ 
+
+ align:start position:0%
+stuck together you can kind of see that
+because they're in a cycle here and in a
+
+ align:start position:0%
+because they're in a cycle here and in a
+ 
+
+ align:start position:0%
+because they're in a cycle here and in a
+cycle there and in order to break them
+
+ align:start position:0%
+cycle there and in order to break them
+ 
+
+ align:start position:0%
+cycle there and in order to break them
+you're going to have to break both
+
+ align:start position:0%
+you're going to have to break both
+ 
+
+ align:start position:0%
+you're going to have to break both
+Cycles um which means uh breaking uh two
+
+ align:start position:0%
+Cycles um which means uh breaking uh two
+ 
+
+ align:start position:0%
+Cycles um which means uh breaking uh two
+edges to break two
+
+ align:start position:0%
+edges to break two
+ 
+
+ align:start position:0%
+edges to break two
+cycles
+
+ align:start position:0%
+cycles
+ 
+
+ align:start position:0%
+cycles
+and uh if you remove three on the other
+
+ align:start position:0%
+and uh if you remove three on the other
+ 
+
+ align:start position:0%
+and uh if you remove three on the other
+hand you can't separate them so if I cut
+
+ align:start position:0%
+hand you can't separate them so if I cut
+ 
+
+ align:start position:0%
+hand you can't separate them so if I cut
+these three
+
+ align:start position:0%
+these three
+ 
+
+ align:start position:0%
+these three
+edges um I might have been more obvious
+
+ align:start position:0%
+edges um I might have been more obvious
+ 
+
+ align:start position:0%
+edges um I might have been more obvious
+to cut that one but I'm doing it this
+
+ align:start position:0%
+to cut that one but I'm doing it this
+ 
+
+ align:start position:0%
+to cut that one but I'm doing it this
+way to make it interesting if I cut
+
+ align:start position:0%
+way to make it interesting if I cut
+ 
+
+ align:start position:0%
+way to make it interesting if I cut
+these three edges then in fact I wind up
+
+ align:start position:0%
+these three edges then in fact I wind up
+ 
+
+ align:start position:0%
+these three edges then in fact I wind up
+with no path between those two vertices
+
+ align:start position:0%
+with no path between those two vertices
+ 
+
+ align:start position:0%
+with no path between those two vertices
+so they are two Edge connected um uh
+
+ align:start position:0%
+so they are two Edge connected um uh
+ 
+
+ align:start position:0%
+so they are two Edge connected um uh
+they are three Edge connected but not
+
+ align:start position:0%
+they are three Edge connected but not
+ 
+
+ align:start position:0%
+they are three Edge connected but not
+four Edge connected meaning you can
+
+ align:start position:0%
+four Edge connected meaning you can
+ 
+
+ align:start position:0%
+four Edge connected meaning you can
+remove two but you can't remove three
+
+ align:start position:0%
+remove two but you can't remove three
+ 
+
+ align:start position:0%
+remove two but you can't remove three
+and keep them connected for a whole
+
+ align:start position:0%
+and keep them connected for a whole
+ 
+
+ align:start position:0%
+and keep them connected for a whole
+graph um a whole graph is kedge
+
+ align:start position:0%
+graph um a whole graph is kedge
+ 
+
+ align:start position:0%
+graph um a whole graph is kedge
+connected if every two vertices are
+
+ align:start position:0%
+connected if every two vertices are
+ 
+
+ align:start position:0%
+connected if every two vertices are
+kedge connected um uh and the point of
+
+ align:start position:0%
+kedge connected um uh and the point of
+ 
+
+ align:start position:0%
+kedge connected um uh and the point of
+this degree of connectivity is to
+
+ align:start position:0%
+this degree of connectivity is to
+ 
+
+ align:start position:0%
+this degree of connectivity is to
+measure one one motivation of it is it
+
+ align:start position:0%
+measure one one motivation of it is it
+ 
+
+ align:start position:0%
+measure one one motivation of it is it
+if you think of this graph as indicating
+
+ align:start position:0%
+if you think of this graph as indicating
+ 
+
+ align:start position:0%
+if you think of this graph as indicating
+uh a communication Network where
+
+ align:start position:0%
+uh a communication Network where
+ 
+
+ align:start position:0%
+uh a communication Network where
+vertices are centers that are sending
+
+ align:start position:0%
+vertices are centers that are sending
+ 
+
+ align:start position:0%
+vertices are centers that are sending
+and receiving data and an edge
+
+ align:start position:0%
+and receiving data and an edge
+ 
+
+ align:start position:0%
+and receiving data and an edge
+corresponds to having some kind of a
+
+ align:start position:0%
+corresponds to having some kind of a
+ 
+
+ align:start position:0%
+corresponds to having some kind of a
+Channel or cable between uh adjacent
+
+ align:start position:0%
+Channel or cable between uh adjacent
+ 
+
+ align:start position:0%
+Channel or cable between uh adjacent
+centers then connectivity is a measure
+
+ align:start position:0%
+centers then connectivity is a measure
+ 
+
+ align:start position:0%
+centers then connectivity is a measure
+of how many of your channels or cables
+
+ align:start position:0%
+of how many of your channels or cables
+ 
+
+ align:start position:0%
+of how many of your channels or cables
+can go down and still have the property
+
+ align:start position:0%
+can go down and still have the property
+ 
+
+ align:start position:0%
+can go down and still have the property
+that every Center of information can
+
+ align:start position:0%
+that every Center of information can
+ 
+
+ align:start position:0%
+that every Center of information can
+communicate with every other Center of
+
+ align:start position:0%
+communicate with every other Center of
+ 
+
+ align:start position:0%
+communicate with every other Center of
+information so how many connections can
+
+ align:start position:0%
+information so how many connections can
+ 
+
+ align:start position:0%
+information so how many connections can
+fail without cutting off
+
+ align:start position:0%
+fail without cutting off
+ 
+
+ align:start position:0%
+fail without cutting off
+communication here's an example of a
+
+ align:start position:0%
+communication here's an example of a
+ 
+
+ align:start position:0%
+communication here's an example of a
+graph that globally this is was the
+
+ align:start position:0%
+graph that globally this is was the
+ 
+
+ align:start position:0%
+graph that globally this is was the
+graph that we saw before that has some
+
+ align:start position:0%
+graph that we saw before that has some
+ 
+
+ align:start position:0%
+graph that we saw before that has some
+vertices that are one Edge connected
+
+ align:start position:0%
+vertices that are one Edge connected
+ 
+
+ align:start position:0%
+vertices that are one Edge connected
+others that are two other others that
+
+ align:start position:0%
+others that are two other others that
+ 
+
+ align:start position:0%
+others that are two other others that
+are three but the graph as a whole is
+
+ align:start position:0%
+are three but the graph as a whole is
+ 
+
+ align:start position:0%
+are three but the graph as a whole is
+only one Edge connected because there's
+
+ align:start position:0%
+only one Edge connected because there's
+ 
+
+ align:start position:0%
+only one Edge connected because there's
+this one Edge that can be removed that
+
+ align:start position:0%
+this one Edge that can be removed that
+ 
+
+ align:start position:0%
+this one Edge that can be removed that
+splits it in
+
+ align:start position:0%
+splits it in
+ 
+
+ align:start position:0%
+splits it in
+two this graph on the other hand a
+
+ align:start position:0%
+two this graph on the other hand a
+ 
+
+ align:start position:0%
+two this graph on the other hand a
+modification of it is two Edge connected
+
+ align:start position:0%
+modification of it is two Edge connected
+ 
+
+ align:start position:0%
+modification of it is two Edge connected
+now I can remove any one Edge and no
+
+ align:start position:0%
+now I can remove any one Edge and no
+ 
+
+ align:start position:0%
+now I can remove any one Edge and no
+matter what single edge I remove this
+
+ align:start position:0%
+matter what single edge I remove this
+ 
+
+ align:start position:0%
+matter what single edge I remove this
+will remain a connected graph which
+
+ align:start position:0%
+will remain a connected graph which
+ 
+
+ align:start position:0%
+will remain a connected graph which
+makes it two Edge connected now there's
+
+ align:start position:0%
+makes it two Edge connected now there's
+ 
+
+ align:start position:0%
+makes it two Edge connected now there's
+a corresponding definition of vertex
+
+ align:start position:0%
+a corresponding definition of vertex
+ 
+
+ align:start position:0%
+a corresponding definition of vertex
+connected uh meaning it's K vertex
+
+ align:start position:0%
+connected uh meaning it's K vertex
+ 
+
+ align:start position:0%
+connected uh meaning it's K vertex
+connected if you can remove any number
+
+ align:start position:0%
+connected if you can remove any number
+ 
+
+ align:start position:0%
+connected if you can remove any number
+of vertices up to uh K and it will stay
+
+ align:start position:0%
+of vertices up to uh K and it will stay
+ 
+
+ align:start position:0%
+of vertices up to uh K and it will stay
+connected if it's K vertex connected
+
+ align:start position:0%
+connected if it's K vertex connected
+ 
+
+ align:start position:0%
+connected if it's K vertex connected
+it's certainly K Edge connected but not
+
+ align:start position:0%
+it's certainly K Edge connected but not
+ 
+
+ align:start position:0%
+it's certainly K Edge connected but not
+conversely um if here's a graph that is
+
+ align:start position:0%
+conversely um if here's a graph that is
+ 
+
+ align:start position:0%
+conversely um if here's a graph that is
+two uh Edge vertex connected but one
+
+ align:start position:0%
+two uh Edge vertex connected but one
+ 
+
+ align:start position:0%
+two uh Edge vertex connected but one
+vertex connected if you remove uh one
+
+ align:start position:0%
+vertex connected if you remove uh one
+ 
+
+ align:start position:0%
+vertex connected if you remove uh one
+vertex it breaks if you remove that
+
+ align:start position:0%
+vertex it breaks if you remove that
+ 
+
+ align:start position:0%
+vertex it breaks if you remove that
+vertex it breaks but on the other hand
+
+ align:start position:0%
+vertex it breaks but on the other hand
+ 
+
+ align:start position:0%
+vertex it breaks but on the other hand
+it needs two edges to be cut in order to
+
+ align:start position:0%
+it needs two edges to be cut in order to
+ 
+
+ align:start position:0%
+it needs two edges to be cut in order to
+uh split the graph in
+
+ align:start position:0%
+uh split the graph in
+ 
+
+ align:start position:0%
+uh split the graph in
+two the complete graph on N vertices um
+
+ align:start position:0%
+two the complete graph on N vertices um
+ 
+
+ align:start position:0%
+two the complete graph on N vertices um
+is uh uh to cut it up it
+
+ align:start position:0%
+is uh uh to cut it up it
+ 
+
+ align:start position:0%
+is uh uh to cut it up it
+requires cutting uh n minus one edges
+
+ align:start position:0%
+requires cutting uh n minus one edges
+ 
+
+ align:start position:0%
+requires cutting uh n minus one edges
+and in fact n minus one vertices to
+
+ align:start position:0%
+and in fact n minus one vertices to
+ 
+
+ align:start position:0%
+and in fact n minus one vertices to
+break it up because everything is
+
+ align:start position:0%
+break it up because everything is
+ 
+
+ align:start position:0%
+break it up because everything is
+connected to everything else so knen is
+
+ align:start position:0%
+connected to everything else so knen is
+ 
+
+ align:start position:0%
+connected to everything else so knen is
+as a connected a graph on N vertices as
+
+ align:start position:0%
+as a connected a graph on N vertices as
+ 
+
+ align:start position:0%
+as a connected a graph on N vertices as
+you can possibly have but of course it's
+
+ align:start position:0%
+you can possibly have but of course it's
+ 
+
+ align:start position:0%
+you can possibly have but of course it's
+got a lot of edges it's got n choose two
+
+ align:start position:0%
+got a lot of edges it's got n choose two
+ 
+
+ align:start position:0%
+got a lot of edges it's got n choose two
+edges or about n * n minus one over two
+
+ align:start position:0%
+edges or about n * n minus one over two
+ 
+
+ align:start position:0%
+edges or about n * n minus one over two
+edges another interesting structure is
+
+ align:start position:0%
+edges another interesting structure is
+ 
+
+ align:start position:0%
+edges another interesting structure is
+the n-dimensional hyper Cube so the
+
+ align:start position:0%
+the n-dimensional hyper Cube so the
+ 
+
+ align:start position:0%
+the n-dimensional hyper Cube so the
+square is a two-dimensional and the cube
+
+ align:start position:0%
+square is a two-dimensional and the cube
+ 
+
+ align:start position:0%
+square is a two-dimensional and the cube
+the the ordinary cube is the H3 has uh
+
+ align:start position:0%
+the the ordinary cube is the H3 has uh
+ 
+
+ align:start position:0%
+the the ordinary cube is the H3 has uh
+has eight vertices and looks like a cube
+
+ align:start position:0%
+has eight vertices and looks like a cube
+ 
+
+ align:start position:0%
+has eight vertices and looks like a cube
+uh and in enal the way we Define hn is
+
+ align:start position:0%
+uh and in enal the way we Define hn is
+ 
+
+ align:start position:0%
+uh and in enal the way we Define hn is
+that its vertices are the binary strings
+
+ align:start position:0%
+that its vertices are the binary strings
+ 
+
+ align:start position:0%
+that its vertices are the binary strings
+of length n and two vertices are
+
+ align:start position:0%
+of length n and two vertices are
+ 
+
+ align:start position:0%
+of length n and two vertices are
+adjacent if they differ in one bit
+
+ align:start position:0%
+adjacent if they differ in one bit
+ 
+
+ align:start position:0%
+adjacent if they differ in one bit
+they're the same except that in one
+
+ align:start position:0%
+they're the same except that in one
+ 
+
+ align:start position:0%
+they're the same except that in one
+coordinate one of them has a one and the
+
+ align:start position:0%
+coordinate one of them has a one and the
+ 
+
+ align:start position:0%
+coordinate one of them has a one and the
+other has a zero in that case you can
+
+ align:start position:0%
+other has a zero in that case you can
+ 
+
+ align:start position:0%
+other has a zero in that case you can
+make the edges
+
+ align:start position:0%
+make the edges
+ 
+
+ align:start position:0%
+make the edges
+adjacent um it turns out that the uh the
+
+ align:start position:0%
+adjacent um it turns out that the uh the
+ 
+
+ align:start position:0%
+adjacent um it turns out that the uh the
+n-dimensional hypergraph is n vertex
+
+ align:start position:0%
+n-dimensional hypergraph is n vertex
+ 
+
+ align:start position:0%
+n-dimensional hypergraph is n vertex
+connected and this is worked out in a
+
+ align:start position:0%
+connected and this is worked out in a
+ 
+
+ align:start position:0%
+connected and this is worked out in a
+homework or class problem so to
+
+ align:start position:0%
+homework or class problem so to
+ 
+
+ align:start position:0%
+homework or class problem so to
+summarize um well actually before we
+
+ align:start position:0%
+summarize um well actually before we
+ 
+
+ align:start position:0%
+summarize um well actually before we
+summarize there's a basic theorem that
+
+ align:start position:0%
+summarize there's a basic theorem that
+ 
+
+ align:start position:0%
+summarize there's a basic theorem that
+we're not going to prove it's just a
+
+ align:start position:0%
+we're not going to prove it's just a
+ 
+
+ align:start position:0%
+we're not going to prove it's just a
+little bit too much of a challenge for
+
+ align:start position:0%
+little bit too much of a challenge for
+ 
+
+ align:start position:0%
+little bit too much of a challenge for
+us to get into uh would take maybe a
+
+ align:start position:0%
+us to get into uh would take maybe a
+ 
+
+ align:start position:0%
+us to get into uh would take maybe a
+couple of lectures is to prove manger
+
+ align:start position:0%
+couple of lectures is to prove manger
+ 
+
+ align:start position:0%
+couple of lectures is to prove manger
+theorem uh which says that um a graph is
+
+ align:start position:0%
+theorem uh which says that um a graph is
+ 
+
+ align:start position:0%
+theorem uh which says that um a graph is
+K uh vertex
+
+ align:start position:0%
+K uh vertex
+ 
+
+ align:start position:0%
+K uh vertex
+connected uh if and only if uh you can
+
+ align:start position:0%
+connected uh if and only if uh you can
+ 
+
+ align:start position:0%
+connected uh if and only if uh you can
+connect any two vertices with completely
+
+ align:start position:0%
+connect any two vertices with completely
+ 
+
+ align:start position:0%
+connect any two vertices with completely
+nonoverlapping different paths K of them
+
+ align:start position:0%
+nonoverlapping different paths K of them
+ 
+
+ align:start position:0%
+nonoverlapping different paths K of them
+so um if two vertices are K connected
+
+ align:start position:0%
+so um if two vertices are K connected
+ 
+
+ align:start position:0%
+so um if two vertices are K connected
+then they're are uh completely separate
+
+ align:start position:0%
+then they're are uh completely separate
+ 
+
+ align:start position:0%
+then they're are uh completely separate
+K separate paths connecting them which
+
+ align:start position:0%
+K separate paths connecting them which
+ 
+
+ align:start position:0%
+K separate paths connecting them which
+means of course that you have to cut
+
+ align:start position:0%
+means of course that you have to cut
+ 
+
+ align:start position:0%
+means of course that you have to cut
+each of the paths in order to separate
+
+ align:start position:0%
+each of the paths in order to separate
+ 
+
+ align:start position:0%
+each of the paths in order to separate
+them and a similar theorem goes for Edge
+
+ align:start position:0%
+them and a similar theorem goes for Edge
+ 
+
+ align:start position:0%
+them and a similar theorem goes for Edge
+connected so to summarize uh about some
+
+ align:start position:0%
+connected so to summarize uh about some
+ 
+
+ align:start position:0%
+connected so to summarize uh about some
+graphs that we know about uh if given
+
+ align:start position:0%
+graphs that we know about uh if given
+ 
+
+ align:start position:0%
+graphs that we know about uh if given
+that connectivity measures fa tolerance
+
+ align:start position:0%
+that connectivity measures fa tolerance
+ 
+
+ align:start position:0%
+that connectivity measures fa tolerance
+in a network we're interested in well
+
+ align:start position:0%
+in a network we're interested in well
+ 
+
+ align:start position:0%
+in a network we're interested in well
+how many edges did it take to a achieve
+
+ align:start position:0%
+how many edges did it take to a achieve
+ 
+
+ align:start position:0%
+how many edges did it take to a achieve
+this level of connectivity so the number
+
+ align:start position:0%
+this level of connectivity so the number
+ 
+
+ align:start position:0%
+this level of connectivity so the number
+of edges is kind of a measure of the
+
+ align:start position:0%
+of edges is kind of a measure of the
+ 
+
+ align:start position:0%
+of edges is kind of a measure of the
+cost and the complete graph on N
+
+ align:start position:0%
+cost and the complete graph on N
+ 
+
+ align:start position:0%
+cost and the complete graph on N
+vertices is n minus one connected but it
+
+ align:start position:0%
+vertices is n minus one connected but it
+ 
+
+ align:start position:0%
+vertices is n minus one connected but it
+has about n^2 over two edges the hyper
+
+ align:start position:0%
+has about n^2 over two edges the hyper
+ 
+
+ align:start position:0%
+has about n^2 over two edges the hyper
+Cube now if we're going to be talking
+
+ align:start position:0%
+Cube now if we're going to be talking
+ 
+
+ align:start position:0%
+Cube now if we're going to be talking
+about graphs of size n to be uniform the
+
+ align:start position:0%
+about graphs of size n to be uniform the
+ 
+
+ align:start position:0%
+about graphs of size n to be uniform the
+hyper Cube on hn has two to the N
+
+ align:start position:0%
+hyper Cube on hn has two to the N
+ 
+
+ align:start position:0%
+hyper Cube on hn has two to the N
+vertices so if we want an N vertex
+
+ align:start position:0%
+vertices so if we want an N vertex
+ 
+
+ align:start position:0%
+vertices so if we want an N vertex
+version we're talking about H sub log n
+
+ align:start position:0%
+version we're talking about H sub log n
+ 
+
+ align:start position:0%
+version we're talking about H sub log n
+which has n vertices uh and then it has
+
+ align:start position:0%
+which has n vertices uh and then it has
+ 
+
+ align:start position:0%
+which has n vertices uh and then it has
+about n log n over two edges so it's got
+
+ align:start position:0%
+about n log n over two edges so it's got
+ 
+
+ align:start position:0%
+about n log n over two edges so it's got
+fewer edges than the complete graph but
+
+ align:start position:0%
+fewer edges than the complete graph but
+ 
+
+ align:start position:0%
+fewer edges than the complete graph but
+uh a significantly less um exponentially
+
+ align:start position:0%
+uh a significantly less um exponentially
+ 
+
+ align:start position:0%
+uh a significantly less um exponentially
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+connectivity the grid is simply um uh
+
+ align:start position:0%
+connectivity the grid is simply um uh
+ 
+
+ align:start position:0%
+connectivity the grid is simply um uh
+like the XY uh axis uh or the XY plane
+
+ align:start position:0%
+like the XY uh axis uh or the XY plane
+ 
+
+ align:start position:0%
+like the XY uh axis uh or the XY plane
+with points at integers so that every
+
+ align:start position:0%
+with points at integers so that every
+ 
+
+ align:start position:0%
+with points at integers so that every
+node is connected to every uh to four
+
+ align:start position:0%
+node is connected to every uh to four
+ 
+
+ align:start position:0%
+node is connected to every uh to four
+adjacent nodes to one up one down one
+
+ align:start position:0%
+adjacent nodes to one up one down one
+ 
+
+ align:start position:0%
+adjacent nodes to one up one down one
+right and one left now of course when
+
+ align:start position:0%
+right and one left now of course when
+ 
+
+ align:start position:0%
+right and one left now of course when
+you get to the the edge of it if you
+
+ align:start position:0%
+you get to the the edge of it if you
+ 
+
+ align:start position:0%
+you get to the the edge of it if you
+make it finite the ones on the edge are
+
+ align:start position:0%
+make it finite the ones on the edge are
+ 
+
+ align:start position:0%
+make it finite the ones on the edge are
+only going to be two connected so you
+
+ align:start position:0%
+only going to be two connected so you
+ 
+
+ align:start position:0%
+only going to be two connected so you
+have to wrap it around in the shape of a
+
+ align:start position:0%
+have to wrap it around in the shape of a
+ 
+
+ align:start position:0%
+have to wrap it around in the shape of a
+donut to really make it work with a
+
+ align:start position:0%
+donut to really make it work with a
+ 
+
+ align:start position:0%
+donut to really make it work with a
+finite graph but if you do that then the
+
+ align:start position:0%
+finite graph but if you do that then the
+ 
+
+ align:start position:0%
+finite graph but if you do that then the
+thing is four connected um four uh Edge
+
+ align:start position:0%
+thing is four connected um four uh Edge
+ 
+
+ align:start position:0%
+thing is four connected um four uh Edge
+connected but and only has two n edges
+
+ align:start position:0%
+connected but and only has two n edges
+ 
+
+ align:start position:0%
+connected but and only has two n edges
+and then a cycle is two connected a
+
+ align:start position:0%
+and then a cycle is two connected a
+ 
+
+ align:start position:0%
+and then a cycle is two connected a
+cycle of size n is two connected with n
+
+ align:start position:0%
+cycle of size n is two connected with n
+ 
+
+ align:start position:0%
+cycle of size n is two connected with n
+vertices and finally trees which we'll
+
+ align:start position:0%
+vertices and finally trees which we'll
+ 
+
+ align:start position:0%
+vertices and finally trees which we'll
+talk about next time um are the smallest
+
+ align:start position:0%
+talk about next time um are the smallest
+ 
+
+ align:start position:0%
+talk about next time um are the smallest
+possible connected graphs they are one
+
+ align:start position:0%
+possible connected graphs they are one
+ 
+
+ align:start position:0%
+possible connected graphs they are one
+connected indeed everything is in a tree
+
+ align:start position:0%
+connected indeed everything is in a tree
+ 
+
+ align:start position:0%
+connected indeed everything is in a tree
+is connected um and they only have n
+
+ align:start position:0%
+is connected um and they only have n
+ 
+
+ align:start position:0%
+is connected um and they only have n
+minus one edges but if you remove one
+
+ align:start position:0%
+minus one edges but if you remove one
+ 
+
+ align:start position:0%
+minus one edges but if you remove one
+Edge it splits and that's sort of the
+
+ align:start position:0%
+Edge it splits and that's sort of the
+ 
+
+ align:start position:0%
+Edge it splits and that's sort of the
+summary of the K connectivity story
\ No newline at end of file
diff --git a/62FdhX-zS2Y.txt b/62FdhX-zS2Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..449024cbc049d4cb5578939018eb911953d489ec
--- /dev/null
+++ b/62FdhX-zS2Y.txt
@@ -0,0 +1,7003 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu I want to discuss with you
+
+ align:start position:0%
+ocw.mit.edu I want to discuss with you
+ 
+
+ align:start position:0%
+ocw.mit.edu I want to discuss with you
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+a very topical and interesting
+
+ align:start position:0%
+a very topical and interesting
+ 
+
+ align:start position:0%
+a very topical and interesting
+question which is the notion of stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells in fact I'm going to discuss two
+
+ align:start position:0%
+cells in fact I'm going to discuss two
+ 
+
+ align:start position:0%
+cells in fact I'm going to discuss two
+things the first of which is another
+
+ align:start position:0%
+things the first of which is another
+ 
+
+ align:start position:0%
+things the first of which is another
+concept that you need following on from
+
+ align:start position:0%
+concept that you need following on from
+ 
+
+ align:start position:0%
+concept that you need following on from
+the concepts we had right at the
+
+ align:start position:0%
+the concepts we had right at the
+ 
+
+ align:start position:0%
+the concepts we had right at the
+beginning of
+
+ align:start position:0%
+beginning of
+ 
+
+ align:start position:0%
+beginning of
+lecture I feel like this
+
+ align:start position:0%
+lecture I feel like this
+ 
+
+ align:start position:0%
+lecture I feel like this
+microphone
+
+ align:start position:0%
+microphone
+ 
+
+ align:start position:0%
+microphone
+the first is a concept that you'll need
+
+ align:start position:0%
+the first is a concept that you'll need
+ 
+
+ align:start position:0%
+the first is a concept that you'll need
+in addition to the ones we started
+
+ align:start position:0%
+in addition to the ones we started
+ 
+
+ align:start position:0%
+in addition to the ones we started
+lecture with and then we'll talk about
+
+ align:start position:0%
+lecture with and then we'll talk about
+ 
+
+ align:start position:0%
+lecture with and then we'll talk about
+stem cells so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today we'll talk about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potency and then we'll talk about stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells potency along with fate
+
+ align:start position:0%
+cells potency along with fate
+ 
+
+ align:start position:0%
+cells potency along with fate
+determination and differentiation ation
+
+ align:start position:0%
+determination and differentiation ation
+ 
+
+ align:start position:0%
+determination and differentiation ation
+is one of those terms that you need to
+
+ align:start position:0%
+is one of those terms that you need to
+ 
+
+ align:start position:0%
+is one of those terms that you need to
+know and you need to understand in order
+
+ align:start position:0%
+know and you need to understand in order
+ 
+
+ align:start position:0%
+know and you need to understand in order
+to understand stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells potency refers to the number of
+
+ align:start position:0%
+cells potency refers to the number of
+ 
+
+ align:start position:0%
+cells potency refers to the number of
+possible fates that a cell can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acquire number of possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+open to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell and this is a very important
+
+ align:start position:0%
+cell and this is a very important
+ 
+
+ align:start position:0%
+cell and this is a very important
+concept of development because in
+
+ align:start position:0%
+concept of development because in
+ 
+
+ align:start position:0%
+concept of development because in
+general potency decreases with age and
+
+ align:start position:0%
+general potency decreases with age and
+ 
+
+ align:start position:0%
+general potency decreases with age and
+decreases as different parts of the
+
+ align:start position:0%
+decreases as different parts of the
+ 
+
+ align:start position:0%
+decreases as different parts of the
+organism become
+
+ align:start position:0%
+organism become
+ 
+
+ align:start position:0%
+organism become
+specialized so in general potency
+
+ align:start position:0%
+specialized so in general potency
+ 
+
+ align:start position:0%
+specialized so in general potency
+decreases with age
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I will put in here and we'll explore
+
+ align:start position:0%
+but I will put in here and we'll explore
+ 
+
+ align:start position:0%
+but I will put in here and we'll explore
+this more in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment
+
+ align:start position:0%
+moment
+ 
+
+ align:start position:0%
+moment
+except
+
+ align:start position:0%
+except
+ 
+
+ align:start position:0%
+except
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some stem
+
+ align:start position:0%
+some stem
+ 
+
+ align:start position:0%
+some stem
+cells and we haven't defined a stem cell
+
+ align:start position:0%
+cells and we haven't defined a stem cell
+ 
+
+ align:start position:0%
+cells and we haven't defined a stem cell
+yet but we
+
+ align:start position:0%
+yet but we
+ 
+
+ align:start position:0%
+yet but we
+will what kinds of potencies are there
+
+ align:start position:0%
+will what kinds of potencies are there
+ 
+
+ align:start position:0%
+will what kinds of potencies are there
+there's the big one to poy
+
+ align:start position:0%
+there's the big one to poy
+ 
+
+ align:start position:0%
+there's the big one to poy
+potent where a cell can become
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orates and there's really only one cell
+
+ align:start position:0%
+orates and there's really only one cell
+ 
+
+ align:start position:0%
+orates and there's really only one cell
+that can do this in the normal animal
+
+ align:start position:0%
+that can do this in the normal animal
+ 
+
+ align:start position:0%
+that can do this in the normal animal
+and that is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zygote and in most animals even as the
+
+ align:start position:0%
+zygote and in most animals even as the
+ 
+
+ align:start position:0%
+zygote and in most animals even as the
+zygote becomes just two cells or a few
+
+ align:start position:0%
+zygote becomes just two cells or a few
+ 
+
+ align:start position:0%
+zygote becomes just two cells or a few
+cells that full potency is
+
+ align:start position:0%
+cells that full potency is
+ 
+
+ align:start position:0%
+cells that full potency is
+lost and cells instead
+
+ align:start position:0%
+lost and cells instead
+ 
+
+ align:start position:0%
+lost and cells instead
+in the embryo are multi or plur
+
+ align:start position:0%
+in the embryo are multi or plur
+ 
+
+ align:start position:0%
+in the embryo are multi or plur
+potent which means that they can acquire
+
+ align:start position:0%
+potent which means that they can acquire
+ 
+
+ align:start position:0%
+potent which means that they can acquire
+many Fates but not all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fates or embryonic cells especially in
+
+ align:start position:0%
+Fates or embryonic cells especially in
+ 
+
+ align:start position:0%
+Fates or embryonic cells especially in
+the early
+
+ align:start position:0%
+the early
+ 
+
+ align:start position:0%
+the early
+embryo and many stem cells can also
+
+ align:start position:0%
+embryo and many stem cells can also
+ 
+
+ align:start position:0%
+embryo and many stem cells can also
+become are also multi poent or Pur poent
+
+ align:start position:0%
+become are also multi poent or Pur poent
+ 
+
+ align:start position:0%
+become are also multi poent or Pur poent
+and then as time progresses is that a
+
+ align:start position:0%
+and then as time progresses is that a
+ 
+
+ align:start position:0%
+and then as time progresses is that a
+hand up yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sir that's a great question the question
+
+ align:start position:0%
+sir that's a great question the question
+ 
+
+ align:start position:0%
+sir that's a great question the question
+is how do I reconcile what I'm telling
+
+ align:start position:0%
+is how do I reconcile what I'm telling
+ 
+
+ align:start position:0%
+is how do I reconcile what I'm telling
+you with the fact that you can get
+
+ align:start position:0%
+you with the fact that you can get
+ 
+
+ align:start position:0%
+you with the fact that you can get
+identical sex tlets or octuplets
+
+ align:start position:0%
+identical sex tlets or octuplets
+ 
+
+ align:start position:0%
+identical sex tlets or octuplets
+actually it's a good question that's
+
+ align:start position:0%
+actually it's a good question that's
+ 
+
+ align:start position:0%
+actually it's a good question that's
+true in different animals the ear very
+
+ align:start position:0%
+true in different animals the ear very
+ 
+
+ align:start position:0%
+true in different animals the ear very
+early embryonic cells are sometimes
+
+ align:start position:0%
+early embryonic cells are sometimes
+ 
+
+ align:start position:0%
+early embryonic cells are sometimes
+times toy potent up to a while okay and
+
+ align:start position:0%
+times toy potent up to a while okay and
+ 
+
+ align:start position:0%
+times toy potent up to a while okay and
+so for example in armadillo here's a
+
+ align:start position:0%
+so for example in armadillo here's a
+ 
+
+ align:start position:0%
+so for example in armadillo here's a
+piece of you know fact for your back
+
+ align:start position:0%
+piece of you know fact for your back
+ 
+
+ align:start position:0%
+piece of you know fact for your back
+pockets in the armadillo the eight cell
+
+ align:start position:0%
+pockets in the armadillo the eight cell
+ 
+
+ align:start position:0%
+pockets in the armadillo the eight cell
+embryo almost always splits into eight
+
+ align:start position:0%
+embryo almost always splits into eight
+ 
+
+ align:start position:0%
+embryo almost always splits into eight
+single cells Each of which becomes a
+
+ align:start position:0%
+single cells Each of which becomes a
+ 
+
+ align:start position:0%
+single cells Each of which becomes a
+baby armadillo okay so those cells are
+
+ align:start position:0%
+baby armadillo okay so those cells are
+ 
+
+ align:start position:0%
+baby armadillo okay so those cells are
+toy potent in mice even at the two cell
+
+ align:start position:0%
+toy potent in mice even at the two cell
+ 
+
+ align:start position:0%
+toy potent in mice even at the two cell
+stage the two mouth cells are probably
+
+ align:start position:0%
+stage the two mouth cells are probably
+ 
+
+ align:start position:0%
+stage the two mouth cells are probably
+not equivalently potent and they're not
+
+ align:start position:0%
+not equivalently potent and they're not
+ 
+
+ align:start position:0%
+not equivalently potent and they're not
+to potent so you very very seldom almost
+
+ align:start position:0%
+to potent so you very very seldom almost
+ 
+
+ align:start position:0%
+to potent so you very very seldom almost
+never get identical Mouse
+
+ align:start position:0%
+never get identical Mouse
+ 
+
+ align:start position:0%
+never get identical Mouse
+twins okay so it's you know it's it's
+
+ align:start position:0%
+twins okay so it's you know it's it's
+ 
+
+ align:start position:0%
+twins okay so it's you know it's it's
+one of these generalities and if you ask
+
+ align:start position:0%
+one of these generalities and if you ask
+ 
+
+ align:start position:0%
+one of these generalities and if you ask
+me you get the specifics are a bit
+
+ align:start position:0%
+me you get the specifics are a bit
+ 
+
+ align:start position:0%
+me you get the specifics are a bit
+different as cell fate restriction
+
+ align:start position:0%
+different as cell fate restriction
+ 
+
+ align:start position:0%
+different as cell fate restriction
+continues cells can become bip poent or
+
+ align:start position:0%
+continues cells can become bip poent or
+ 
+
+ align:start position:0%
+continues cells can become bip poent or
+uni
+
+ align:start position:0%
+uni
+ 
+
+ align:start position:0%
+uni
+poent
+
+ align:start position:0%
+poent
+ 
+
+ align:start position:0%
+poent
+whereby one or just two Fates are open
+
+ align:start position:0%
+whereby one or just two Fates are open
+ 
+
+ align:start position:0%
+whereby one or just two Fates are open
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+them and so if we
+
+ align:start position:0%
+them and so if we
+ 
+
+ align:start position:0%
+them and so if we
+look taking this concept let's now start
+
+ align:start position:0%
+look taking this concept let's now start
+ 
+
+ align:start position:0%
+look taking this concept let's now start
+the lecture about stem
+
+ align:start position:0%
+the lecture about stem
+ 
+
+ align:start position:0%
+the lecture about stem
+cells you're going to need this concept
+
+ align:start position:0%
+cells you're going to need this concept
+ 
+
+ align:start position:0%
+cells you're going to need this concept
+stem cells I'll point out whatever they
+
+ align:start position:0%
+stem cells I'll point out whatever they
+ 
+
+ align:start position:0%
+stem cells I'll point out whatever they
+are got almost 3,000 hits yesterday on
+
+ align:start position:0%
+are got almost 3,000 hits yesterday on
+ 
+
+ align:start position:0%
+are got almost 3,000 hits yesterday on
+Google News this is way below baseball
+
+ align:start position:0%
+Google News this is way below baseball
+ 
+
+ align:start position:0%
+Google News this is way below baseball
+which got 45,000 I checked but still you
+
+ align:start position:0%
+which got 45,000 I checked but still you
+ 
+
+ align:start position:0%
+which got 45,000 I checked but still you
+know as science topics go stem cells are
+
+ align:start position:0%
+know as science topics go stem cells are
+ 
+
+ align:start position:0%
+know as science topics go stem cells are
+really up there and they're on the
+
+ align:start position:0%
+really up there and they're on the
+ 
+
+ align:start position:0%
+really up there and they're on the
+covers of magazines over and over again
+
+ align:start position:0%
+covers of magazines over and over again
+ 
+
+ align:start position:0%
+covers of magazines over and over again
+and we'll talk more about why that is
+
+ align:start position:0%
+and we'll talk more about why that is
+ 
+
+ align:start position:0%
+and we'll talk more about why that is
+here's a diagram it's not on your
+
+ align:start position:0%
+here's a diagram it's not on your
+ 
+
+ align:start position:0%
+here's a diagram it's not on your
+handouts that I drew for you let's not
+
+ align:start position:0%
+handouts that I drew for you let's not
+ 
+
+ align:start position:0%
+handouts that I drew for you let's not
+dwell on it but let's now move on to
+
+ align:start position:0%
+dwell on it but let's now move on to
+ 
+
+ align:start position:0%
+dwell on it but let's now move on to
+topic number
+
+ align:start position:0%
+topic number
+ 
+
+ align:start position:0%
+topic number
+two which will fold in this concept of
+
+ align:start position:0%
+two which will fold in this concept of
+ 
+
+ align:start position:0%
+two which will fold in this concept of
+potency and the concepts of Fate
+
+ align:start position:0%
+potency and the concepts of Fate
+ 
+
+ align:start position:0%
+potency and the concepts of Fate
+determination and
+
+ align:start position:0%
+determination and
+ 
+
+ align:start position:0%
+determination and
+differentiation and talk about stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's do as is our custom let's
+
+ align:start position:0%
+and let's do as is our custom let's
+ 
+
+ align:start position:0%
+and let's do as is our custom let's
+define what a stem cell is I think that
+
+ align:start position:0%
+define what a stem cell is I think that
+ 
+
+ align:start position:0%
+define what a stem cell is I think that
+a stem cell can be defined as a cell of
+
+ align:start position:0%
+a stem cell can be defined as a cell of
+ 
+
+ align:start position:0%
+a stem cell can be defined as a cell of
+variable potency that has the capacity
+
+ align:start position:0%
+variable potency that has the capacity
+ 
+
+ align:start position:0%
+variable potency that has the capacity
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+self-renew
+
+ align:start position:0%
+self-renew
+ 
+
+ align:start position:0%
+self-renew
+cells of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+potency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that can
+
+ align:start position:0%
+that can
+ 
+
+ align:start position:0%
+that can
+self-renew they can make more of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+themselves despite the hype despite
+
+ align:start position:0%
+themselves despite the hype despite
+ 
+
+ align:start position:0%
+themselves despite the hype despite
+covers of Time Magazine and almost every
+
+ align:start position:0%
+covers of Time Magazine and almost every
+ 
+
+ align:start position:0%
+covers of Time Magazine and almost every
+front page of every newspaper across the
+
+ align:start position:0%
+front page of every newspaper across the
+ 
+
+ align:start position:0%
+front page of every newspaper across the
+world stem cells are normally found in
+
+ align:start position:0%
+world stem cells are normally found in
+ 
+
+ align:start position:0%
+world stem cells are normally found in
+our bodies and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normally
+
+ align:start position:0%
+normally
+ 
+
+ align:start position:0%
+normally
+as we'll explore they're used for organ
+
+ align:start position:0%
+as we'll explore they're used for organ
+ 
+
+ align:start position:0%
+as we'll explore they're used for organ
+maintenance and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+repair organ maintenance and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+repair but the thing you know that has
+
+ align:start position:0%
+repair but the thing you know that has
+ 
+
+ align:start position:0%
+repair but the thing you know that has
+everyone fired up is that you can
+
+ align:start position:0%
+everyone fired up is that you can
+ 
+
+ align:start position:0%
+everyone fired up is that you can
+somehow harness these cells for
+
+ align:start position:0%
+somehow harness these cells for
+ 
+
+ align:start position:0%
+somehow harness these cells for
+therapeutic purposes and that you can
+
+ align:start position:0%
+therapeutic purposes and that you can
+ 
+
+ align:start position:0%
+therapeutic purposes and that you can
+repair
+
+ align:start position:0%
+repair
+ 
+
+ align:start position:0%
+repair
+what the body cannot by being clever and
+
+ align:start position:0%
+what the body cannot by being clever and
+ 
+
+ align:start position:0%
+what the body cannot by being clever and
+using the power of these
+
+ align:start position:0%
+using the power of these
+ 
+
+ align:start position:0%
+using the power of these
+cells as they normally have it or as you
+
+ align:start position:0%
+cells as they normally have it or as you
+ 
+
+ align:start position:0%
+cells as they normally have it or as you
+can give it to them and so there's this
+
+ align:start position:0%
+can give it to them and so there's this
+ 
+
+ align:start position:0%
+can give it to them and so there's this
+question of therapy and therapeutic stem
+
+ align:start position:0%
+question of therapy and therapeutic stem
+ 
+
+ align:start position:0%
+question of therapy and therapeutic stem
+cells where the idea again is that you
+
+ align:start position:0%
+cells where the idea again is that you
+ 
+
+ align:start position:0%
+cells where the idea again is that you
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+repair a damaged
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+organ
+
+ align:start position:0%
+organ
+ 
+
+ align:start position:0%
+organ
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+introducing somehow injecting or
+
+ align:start position:0%
+introducing somehow injecting or
+ 
+
+ align:start position:0%
+introducing somehow injecting or
+otherwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+introducing extra or somehow special
+
+ align:start position:0%
+introducing extra or somehow special
+ 
+
+ align:start position:0%
+introducing extra or somehow special
+stem cells which I am going to
+
+ align:start position:0%
+stem cells which I am going to
+ 
+
+ align:start position:0%
+stem cells which I am going to
+abbreviate here to for as SC by indu by
+
+ align:start position:0%
+abbreviate here to for as SC by indu by
+ 
+
+ align:start position:0%
+abbreviate here to for as SC by indu by
+introducing extra stem cells into a
+
+ align:start position:0%
+introducing extra stem cells into a
+ 
+
+ align:start position:0%
+introducing extra stem cells into a
+damaged
+
+ align:start position:0%
+damaged
+ 
+
+ align:start position:0%
+damaged
+body does this work it does work it
+
+ align:start position:0%
+body does this work it does work it
+ 
+
+ align:start position:0%
+body does this work it does work it
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+for the hematopoetic system as in bone
+
+ align:start position:0%
+for the hematopoetic system as in bone
+ 
+
+ align:start position:0%
+for the hematopoetic system as in bone
+marrow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transplants and it also works for skin
+
+ align:start position:0%
+transplants and it also works for skin
+ 
+
+ align:start position:0%
+transplants and it also works for skin
+cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transplants um what is just put skin
+
+ align:start position:0%
+transplants um what is just put skin
+ 
+
+ align:start position:0%
+transplants um what is just put skin
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+skin stem cells can be grown from your
+
+ align:start position:0%
+skin stem cells can be grown from your
+ 
+
+ align:start position:0%
+skin stem cells can be grown from your
+own skin and in the case of burn victims
+
+ align:start position:0%
+own skin and in the case of burn victims
+ 
+
+ align:start position:0%
+own skin and in the case of burn victims
+this has really saved countless lives
+
+ align:start position:0%
+this has really saved countless lives
+ 
+
+ align:start position:0%
+this has really saved countless lives
+the original technology began to be
+
+ align:start position:0%
+the original technology began to be
+ 
+
+ align:start position:0%
+the original technology began to be
+developed here at MIT by Professor
+
+ align:start position:0%
+developed here at MIT by Professor
+ 
+
+ align:start position:0%
+developed here at MIT by Professor
+Howard green who's now at Harvard but
+
+ align:start position:0%
+Howard green who's now at Harvard but
+ 
+
+ align:start position:0%
+Howard green who's now at Harvard but
+the idea is to take your skin and grow
+
+ align:start position:0%
+the idea is to take your skin and grow
+ 
+
+ align:start position:0%
+the idea is to take your skin and grow
+it on something like G or some kind of
+
+ align:start position:0%
+it on something like G or some kind of
+ 
+
+ align:start position:0%
+it on something like G or some kind of
+solid support and then to cover a burn
+
+ align:start position:0%
+solid support and then to cover a burn
+ 
+
+ align:start position:0%
+solid support and then to cover a burn
+patient
+
+ align:start position:0%
+patient
+ 
+
+ align:start position:0%
+patient
+with layers of support on which there
+
+ align:start position:0%
+with layers of support on which there
+ 
+
+ align:start position:0%
+with layers of support on which there
+are some stem cells and these stem cells
+
+ align:start position:0%
+are some stem cells and these stem cells
+ 
+
+ align:start position:0%
+are some stem cells and these stem cells
+will help fill in the holes in the skin
+
+ align:start position:0%
+will help fill in the holes in the skin
+ 
+
+ align:start position:0%
+will help fill in the holes in the skin
+left by the burn normally when a wound
+
+ align:start position:0%
+left by the burn normally when a wound
+ 
+
+ align:start position:0%
+left by the burn normally when a wound
+heals as I'm sure you've noticed it
+
+ align:start position:0%
+heals as I'm sure you've noticed it
+ 
+
+ align:start position:0%
+heals as I'm sure you've noticed it
+heals from the sides the only way a
+
+ align:start position:0%
+heals from the sides the only way a
+ 
+
+ align:start position:0%
+heals from the sides the only way a
+wound can heal is from the side and if
+
+ align:start position:0%
+wound can heal is from the side and if
+ 
+
+ align:start position:0%
+wound can heal is from the side and if
+it's a big wound it can take a very very
+
+ align:start position:0%
+it's a big wound it can take a very very
+ 
+
+ align:start position:0%
+it's a big wound it can take a very very
+long time to heal and you can get
+
+ align:start position:0%
+long time to heal and you can get
+ 
+
+ align:start position:0%
+long time to heal and you can get
+infections and so on while the healing
+
+ align:start position:0%
+infections and so on while the healing
+ 
+
+ align:start position:0%
+infections and so on while the healing
+process is going on so seeding the
+
+ align:start position:0%
+process is going on so seeding the
+ 
+
+ align:start position:0%
+process is going on so seeding the
+inside of a wound with stem cells that
+
+ align:start position:0%
+inside of a wound with stem cells that
+ 
+
+ align:start position:0%
+inside of a wound with stem cells that
+can start the skin regeneration process
+
+ align:start position:0%
+can start the skin regeneration process
+ 
+
+ align:start position:0%
+can start the skin regeneration process
+and seal up the body against infection
+
+ align:start position:0%
+and seal up the body against infection
+ 
+
+ align:start position:0%
+and seal up the body against infection
+has been incredibly useful and we'll
+
+ align:start position:0%
+has been incredibly useful and we'll
+ 
+
+ align:start position:0%
+has been incredibly useful and we'll
+talk more about bone marrow transplants
+
+ align:start position:0%
+talk more about bone marrow transplants
+ 
+
+ align:start position:0%
+talk more about bone marrow transplants
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+moment
+
+ align:start position:0%
+moment
+ 
+
+ align:start position:0%
+moment
+okay we previously talked about this
+
+ align:start position:0%
+okay we previously talked about this
+ 
+
+ align:start position:0%
+okay we previously talked about this
+process by which cells decide or
+
+ align:start position:0%
+process by which cells decide or
+ 
+
+ align:start position:0%
+process by which cells decide or
+undecided initially they decide what
+
+ align:start position:0%
+undecided initially they decide what
+ 
+
+ align:start position:0%
+undecided initially they decide what
+they're going to become and then they
+
+ align:start position:0%
+they're going to become and then they
+ 
+
+ align:start position:0%
+they're going to become and then they
+differentiate into their final function
+
+ align:start position:0%
+differentiate into their final function
+ 
+
+ align:start position:0%
+differentiate into their final function
+stem cells fit into this litany
+
+ align:start position:0%
+stem cells fit into this litany
+ 
+
+ align:start position:0%
+stem cells fit into this litany
+somewhere between the commitment stage
+
+ align:start position:0%
+somewhere between the commitment stage
+ 
+
+ align:start position:0%
+somewhere between the commitment stage
+and the differentiation stage and in
+
+ align:start position:0%
+and the differentiation stage and in
+ 
+
+ align:start position:0%
+and the differentiation stage and in
+this diagram these multiple arrows are
+
+ align:start position:0%
+this diagram these multiple arrows are
+ 
+
+ align:start position:0%
+this diagram these multiple arrows are
+there for a reason there are multiple
+
+ align:start position:0%
+there for a reason there are multiple
+ 
+
+ align:start position:0%
+there for a reason there are multiple
+steps between commitment and
+
+ align:start position:0%
+steps between commitment and
+ 
+
+ align:start position:0%
+steps between commitment and
+differentiation and somewhere along the
+
+ align:start position:0%
+differentiation and somewhere along the
+ 
+
+ align:start position:0%
+differentiation and somewhere along the
+way a group of cells with capacities
+
+ align:start position:0%
+way a group of cells with capacities
+ 
+
+ align:start position:0%
+way a group of cells with capacities
+will talk
+
+ align:start position:0%
+will talk
+ 
+
+ align:start position:0%
+will talk
+about Le leaves this lineage and sits
+
+ align:start position:0%
+about Le leaves this lineage and sits
+ 
+
+ align:start position:0%
+about Le leaves this lineage and sits
+around and waits partially determined so
+
+ align:start position:0%
+around and waits partially determined so
+ 
+
+ align:start position:0%
+around and waits partially determined so
+that it can go on and make more
+
+ align:start position:0%
+that it can go on and make more
+ 
+
+ align:start position:0%
+that it can go on and make more
+differentiated cells when they're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+needed and I've added on there the
+
+ align:start position:0%
+needed and I've added on there the
+ 
+
+ align:start position:0%
+needed and I've added on there the
+potency timeline decreasing with age
+
+ align:start position:0%
+potency timeline decreasing with age
+ 
+
+ align:start position:0%
+potency timeline decreasing with age
+of the developing
+
+ align:start position:0%
+of the developing
+ 
+
+ align:start position:0%
+of the developing
+animal but let's Di diagram the notion
+
+ align:start position:0%
+animal but let's Di diagram the notion
+ 
+
+ align:start position:0%
+animal but let's Di diagram the notion
+of stem cells on the
+
+ align:start position:0%
+of stem cells on the
+ 
+
+ align:start position:0%
+of stem cells on the
+board stem cells generally divide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slowly here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one it's a variable potency it may be
+
+ align:start position:0%
+one it's a variable potency it may be
+ 
+
+ align:start position:0%
+one it's a variable potency it may be
+multi potent it may be bip
+
+ align:start position:0%
+multi potent it may be bip
+ 
+
+ align:start position:0%
+multi potent it may be bip
+potential and it is somewhat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+committed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is a slightly difficult concept
+
+ align:start position:0%
+which is a slightly difficult concept
+ 
+
+ align:start position:0%
+which is a slightly difficult concept
+because last time we talked about
+
+ align:start position:0%
+because last time we talked about
+ 
+
+ align:start position:0%
+because last time we talked about
+committed versus uncommitted but now I'm
+
+ align:start position:0%
+committed versus uncommitted but now I'm
+ 
+
+ align:start position:0%
+committed versus uncommitted but now I'm
+telling you something can be somewhat
+
+ align:start position:0%
+telling you something can be somewhat
+ 
+
+ align:start position:0%
+telling you something can be somewhat
+committed and that gets to this multiple
+
+ align:start position:0%
+committed and that gets to this multiple
+ 
+
+ align:start position:0%
+committed and that gets to this multiple
+arrows there where as cells progress in
+
+ align:start position:0%
+arrows there where as cells progress in
+ 
+
+ align:start position:0%
+arrows there where as cells progress in
+their fate decisions they change their
+
+ align:start position:0%
+their fate decisions they change their
+ 
+
+ align:start position:0%
+their fate decisions they change their
+molecular signature and they really do
+
+ align:start position:0%
+molecular signature and they really do
+ 
+
+ align:start position:0%
+molecular signature and they really do
+become closer and closer to a cell
+
+ align:start position:0%
+become closer and closer to a cell
+ 
+
+ align:start position:0%
+become closer and closer to a cell
+that's made a decision but it's kind of
+
+ align:start position:0%
+that's made a decision but it's kind of
+ 
+
+ align:start position:0%
+that's made a decision but it's kind of
+like you know if you weighing up going
+
+ align:start position:0%
+like you know if you weighing up going
+ 
+
+ align:start position:0%
+like you know if you weighing up going
+to med school or going to graduate
+
+ align:start position:0%
+to med school or going to graduate
+ 
+
+ align:start position:0%
+to med school or going to graduate
+school in bioengineering you know you've
+
+ align:start position:0%
+school in bioengineering you know you've
+ 
+
+ align:start position:0%
+school in bioengineering you know you've
+decided that it'll be one or the other
+
+ align:start position:0%
+decided that it'll be one or the other
+ 
+
+ align:start position:0%
+decided that it'll be one or the other
+but you haven't decided which you're
+
+ align:start position:0%
+but you haven't decided which you're
+ 
+
+ align:start position:0%
+but you haven't decided which you're
+somewhat committed and then when you
+
+ align:start position:0%
+somewhat committed and then when you
+ 
+
+ align:start position:0%
+somewhat committed and then when you
+make the decision to go to graduate
+
+ align:start position:0%
+make the decision to go to graduate
+ 
+
+ align:start position:0%
+make the decision to go to graduate
+school you've now become committed okay
+
+ align:start position:0%
+school you've now become committed okay
+ 
+
+ align:start position:0%
+school you've now become committed okay
+so the cell is doing the same kind of
+
+ align:start position:0%
+so the cell is doing the same kind of
+ 
+
+ align:start position:0%
+so the cell is doing the same kind of
+notion
+
+ align:start position:0%
+notion
+ 
+
+ align:start position:0%
+notion
+there there's your stem cell variable
+
+ align:start position:0%
+there there's your stem cell variable
+ 
+
+ align:start position:0%
+there there's your stem cell variable
+potency under the correct stimulus that
+
+ align:start position:0%
+potency under the correct stimulus that
+ 
+
+ align:start position:0%
+potency under the correct stimulus that
+stem cell will
+
+ align:start position:0%
+stem cell will
+ 
+
+ align:start position:0%
+stem cell will
+divide to give rise to two different
+
+ align:start position:0%
+divide to give rise to two different
+ 
+
+ align:start position:0%
+divide to give rise to two different
+cells one is another stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell and the other is something we'll
+
+ align:start position:0%
+cell and the other is something we'll
+ 
+
+ align:start position:0%
+cell and the other is something we'll
+call a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+progenitor the progenitor is more
+
+ align:start position:0%
+progenitor the progenitor is more
+ 
+
+ align:start position:0%
+progenitor the progenitor is more
+committed than the stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell the progenitor cell is going to go
+
+ align:start position:0%
+cell the progenitor cell is going to go
+ 
+
+ align:start position:0%
+cell the progenitor cell is going to go
+on and divide usually a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lot so progenitors divide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rapidly and their progeny will
+
+ align:start position:0%
+rapidly and their progeny will
+ 
+
+ align:start position:0%
+rapidly and their progeny will
+eventually go on and
+
+ align:start position:0%
+eventually go on and
+ 
+
+ align:start position:0%
+eventually go on and
+differentiate into one or more different
+
+ align:start position:0%
+differentiate into one or more different
+ 
+
+ align:start position:0%
+differentiate into one or more different
+kinds of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+maybe a stripey cell and a spotted cell
+
+ align:start position:0%
+maybe a stripey cell and a spotted cell
+ 
+
+ align:start position:0%
+maybe a stripey cell and a spotted cell
+type and a cell type with
+
+ align:start position:0%
+type and a cell type with
+ 
+
+ align:start position:0%
+type and a cell type with
+squiggles and so here are the
+
+ align:start position:0%
+squiggles and so here are the
+ 
+
+ align:start position:0%
+squiggles and so here are the
+differentiated cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+types and the number of different
+
+ align:start position:0%
+types and the number of different
+ 
+
+ align:start position:0%
+types and the number of different
+differentiated cells that comes out of
+
+ align:start position:0%
+differentiated cells that comes out of
+ 
+
+ align:start position:0%
+differentiated cells that comes out of
+this process is a reflection of the
+
+ align:start position:0%
+this process is a reflection of the
+ 
+
+ align:start position:0%
+this process is a reflection of the
+potency of the stem cell okay so here
+
+ align:start position:0%
+potency of the stem cell okay so here
+ 
+
+ align:start position:0%
+potency of the stem cell okay so here
+you've got these progenitors the idea is
+
+ align:start position:0%
+you've got these progenitors the idea is
+ 
+
+ align:start position:0%
+you've got these progenitors the idea is
+that these
+
+ align:start position:0%
+that these
+ 
+
+ align:start position:0%
+that these
+progenitors will have similar potency
+
+ align:start position:0%
+progenitors will have similar potency
+ 
+
+ align:start position:0%
+progenitors will have similar potency
+but as I'll show you there's a whole
+
+ align:start position:0%
+but as I'll show you there's a whole
+ 
+
+ align:start position:0%
+but as I'll show you there's a whole
+variation on this but here the
+
+ align:start position:0%
+variation on this but here the
+ 
+
+ align:start position:0%
+variation on this but here the
+number of differentiated cell
+
+ align:start position:0%
+number of differentiated cell
+ 
+
+ align:start position:0%
+number of differentiated cell
+types the number of cell types
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reflects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potency of the stem
+
+ align:start position:0%
+potency of the stem
+ 
+
+ align:start position:0%
+potency of the stem
+cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this kind of diagram is called a
+
+ align:start position:0%
+okay this kind of diagram is called a
+ 
+
+ align:start position:0%
+okay this kind of diagram is called a
+lineage diagram it tells you what not
+
+ align:start position:0%
+lineage diagram it tells you what not
+ 
+
+ align:start position:0%
+lineage diagram it tells you what not
+only what the final fate of the cell is
+
+ align:start position:0%
+only what the final fate of the cell is
+ 
+
+ align:start position:0%
+only what the final fate of the cell is
+it tells you something about the
+
+ align:start position:0%
+it tells you something about the
+ 
+
+ align:start position:0%
+it tells you something about the
+progress towards that final fate so a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lineage we can Define as the set of cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+types
+
+ align:start position:0%
+types
+ 
+
+ align:start position:0%
+types
+arising from a stem cell or a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+progenitor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's talk about the discovery of
+
+ align:start position:0%
+okay let's talk about the discovery of
+ 
+
+ align:start position:0%
+okay let's talk about the discovery of
+stem cells because this is something
+
+ align:start position:0%
+stem cells because this is something
+ 
+
+ align:start position:0%
+stem cells because this is something
+that really was pivotal in helping
+
+ align:start position:0%
+that really was pivotal in helping
+ 
+
+ align:start position:0%
+that really was pivotal in helping
+understand whether or not there was some
+
+ align:start position:0%
+understand whether or not there was some
+ 
+
+ align:start position:0%
+understand whether or not there was some
+way that the body normally repaired
+
+ align:start position:0%
+way that the body normally repaired
+ 
+
+ align:start position:0%
+way that the body normally repaired
+itself it was clear that during early
+
+ align:start position:0%
+itself it was clear that during early
+ 
+
+ align:start position:0%
+itself it was clear that during early
+development there was lots of cell
+
+ align:start position:0%
+development there was lots of cell
+ 
+
+ align:start position:0%
+development there was lots of cell
+division and lots of changes cell types
+
+ align:start position:0%
+division and lots of changes cell types
+ 
+
+ align:start position:0%
+division and lots of changes cell types
+were formed and organs were formed but
+
+ align:start position:0%
+were formed and organs were formed but
+ 
+
+ align:start position:0%
+were formed and organs were formed but
+it really wasn't clear in the adult how
+
+ align:start position:0%
+it really wasn't clear in the adult how
+ 
+
+ align:start position:0%
+it really wasn't clear in the adult how
+much repair there was how much turnover
+
+ align:start position:0%
+much repair there was how much turnover
+ 
+
+ align:start position:0%
+much repair there was how much turnover
+of tissues there were and really what
+
+ align:start position:0%
+of tissues there were and really what
+ 
+
+ align:start position:0%
+of tissues there were and really what
+the whole dynamic process of maintaining
+
+ align:start position:0%
+the whole dynamic process of maintaining
+ 
+
+ align:start position:0%
+the whole dynamic process of maintaining
+the adult
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Wars
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the discovery of stem cells came
+
+ align:start position:0%
+and the discovery of stem cells came
+ 
+
+ align:start position:0%
+and the discovery of stem cells came
+about because people looked to see how
+
+ align:start position:0%
+about because people looked to see how
+ 
+
+ align:start position:0%
+about because people looked to see how
+long cells lived and what they
+
+ align:start position:0%
+long cells lived and what they
+ 
+
+ align:start position:0%
+long cells lived and what they
+found was found using a turnover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assay that measures the half life of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells and they found that in all almost
+
+ align:start position:0%
+cells and they found that in all almost
+ 
+
+ align:start position:0%
+cells and they found that in all almost
+all organs in fact probably in all
+
+ align:start position:0%
+all organs in fact probably in all
+ 
+
+ align:start position:0%
+all organs in fact probably in all
+organs cells did not live forever they
+
+ align:start position:0%
+organs cells did not live forever they
+ 
+
+ align:start position:0%
+organs cells did not live forever they
+turned over they died and they were
+
+ align:start position:0%
+turned over they died and they were
+ 
+
+ align:start position:0%
+turned over they died and they were
+replaced by new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells and this turnover assay implied
+
+ align:start position:0%
+cells and this turnover assay implied
+ 
+
+ align:start position:0%
+cells and this turnover assay implied
+that there was some kind of
+
+ align:start position:0%
+that there was some kind of
+ 
+
+ align:start position:0%
+that there was some kind of
+replacement and the cells doing the
+
+ align:start position:0%
+replacement and the cells doing the
+ 
+
+ align:start position:0%
+replacement and the cells doing the
+replacement were called stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells you find this by a pulse Chase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assay which will go over on your handout
+
+ align:start position:0%
+assay which will go over on your handout
+ 
+
+ align:start position:0%
+assay which will go over on your handout
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+moment and what was found was really
+
+ align:start position:0%
+moment and what was found was really
+ 
+
+ align:start position:0%
+moment and what was found was really
+variable for different organs
+
+ align:start position:0%
+variable for different organs
+ 
+
+ align:start position:0%
+variable for different organs
+firstly all organs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about show cell
+
+ align:start position:0%
+about show cell
+ 
+
+ align:start position:0%
+about show cell
+turnover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+red blood cells have a half life of
+
+ align:start position:0%
+red blood cells have a half life of
+ 
+
+ align:start position:0%
+red blood cells have a half life of
+about 120
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+days there are a lot of red blood cells
+
+ align:start position:0%
+days there are a lot of red blood cells
+ 
+
+ align:start position:0%
+days there are a lot of red blood cells
+in your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+body and in fact that implies that there
+
+ align:start position:0%
+body and in fact that implies that there
+ 
+
+ align:start position:0%
+body and in fact that implies that there
+are about 10 to the 7th new red blood
+
+ align:start position:0%
+are about 10 to the 7th new red blood
+ 
+
+ align:start position:0%
+are about 10 to the 7th new red blood
+cells made a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+day
+
+ align:start position:0%
+day
+ 
+
+ align:start position:0%
+day
+in your intestine the half life of cells
+
+ align:start position:0%
+in your intestine the half life of cells
+ 
+
+ align:start position:0%
+in your intestine the half life of cells
+is 3 to 5 days in the small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intestine and the hair on your
+
+ align:start position:0%
+intestine and the hair on your
+ 
+
+ align:start position:0%
+intestine and the hair on your
+head has a half life of about four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+years so it's variable for different
+
+ align:start position:0%
+years so it's variable for different
+ 
+
+ align:start position:0%
+years so it's variable for different
+kinds of
+
+ align:start position:0%
+kinds of
+ 
+
+ align:start position:0%
+kinds of
+cells if you look at your your first
+
+ align:start position:0%
+cells if you look at your your first
+ 
+
+ align:start position:0%
+cells if you look at your your first
+handout it diagrams a pulse Chase assay
+
+ align:start position:0%
+handout it diagrams a pulse Chase assay
+ 
+
+ align:start position:0%
+handout it diagrams a pulse Chase assay
+where a cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+population is labeled with a nucleotide
+
+ align:start position:0%
+population is labeled with a nucleotide
+ 
+
+ align:start position:0%
+population is labeled with a nucleotide
+analog it's a normal nucleotide but it's
+
+ align:start position:0%
+analog it's a normal nucleotide but it's
+ 
+
+ align:start position:0%
+analog it's a normal nucleotide but it's
+got a bromine added to it and it acts
+
+ align:start position:0%
+got a bromine added to it and it acts
+ 
+
+ align:start position:0%
+got a bromine added to it and it acts
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+deoxythymidine gets incorporated into
+
+ align:start position:0%
+deoxythymidine gets incorporated into
+ 
+
+ align:start position:0%
+deoxythymidine gets incorporated into
+DNA and you give just a short pulse of
+
+ align:start position:0%
+DNA and you give just a short pulse of
+ 
+
+ align:start position:0%
+DNA and you give just a short pulse of
+this nucleotide analog so only some of
+
+ align:start position:0%
+this nucleotide analog so only some of
+ 
+
+ align:start position:0%
+this nucleotide analog so only some of
+the cells get labeled and you only give
+
+ align:start position:0%
+the cells get labeled and you only give
+ 
+
+ align:start position:0%
+the cells get labeled and you only give
+it for a short time so you get a labeled
+
+ align:start position:0%
+it for a short time so you get a labeled
+ 
+
+ align:start position:0%
+it for a short time so you get a labeled
+cell population and then you stop the
+
+ align:start position:0%
+cell population and then you stop the
+ 
+
+ align:start position:0%
+cell population and then you stop the
+labeling by adding lots of unlabeled
+
+ align:start position:0%
+labeling by adding lots of unlabeled
+ 
+
+ align:start position:0%
+labeling by adding lots of unlabeled
+thymidine and that's called a Chase and
+
+ align:start position:0%
+thymidine and that's called a Chase and
+ 
+
+ align:start position:0%
+thymidine and that's called a Chase and
+you follow the cells over this long
+
+ align:start position:0%
+you follow the cells over this long
+ 
+
+ align:start position:0%
+you follow the cells over this long
+Chase period and then you can watch and
+
+ align:start position:0%
+Chase period and then you can watch and
+ 
+
+ align:start position:0%
+Chase period and then you can watch and
+see what happens to those cells that you
+
+ align:start position:0%
+see what happens to those cells that you
+ 
+
+ align:start position:0%
+see what happens to those cells that you
+initially labeled over a very short time
+
+ align:start position:0%
+initially labeled over a very short time
+ 
+
+ align:start position:0%
+initially labeled over a very short time
+and so in this example I've got four
+
+ align:start position:0%
+and so in this example I've got four
+ 
+
+ align:start position:0%
+and so in this example I've got four
+cells initially labeled over time there
+
+ align:start position:0%
+cells initially labeled over time there
+ 
+
+ align:start position:0%
+cells initially labeled over time there
+are only two cells left and if if you
+
+ align:start position:0%
+are only two cells left and if if you
+ 
+
+ align:start position:0%
+are only two cells left and if if you
+measure the time from going from four
+
+ align:start position:0%
+measure the time from going from four
+ 
+
+ align:start position:0%
+measure the time from going from four
+cells to two cells you can get to the
+
+ align:start position:0%
+cells to two cells you can get to the
+ 
+
+ align:start position:0%
+cells to two cells you can get to the
+half life of that cell
+
+ align:start position:0%
+half life of that cell
+ 
+
+ align:start position:0%
+half life of that cell
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+okay you can also you don't have a
+
+ align:start position:0%
+okay you can also you don't have a
+ 
+
+ align:start position:0%
+okay you can also you don't have a
+handout for this just look on the screen
+
+ align:start position:0%
+handout for this just look on the screen
+ 
+
+ align:start position:0%
+handout for this just look on the screen
+you can also follow this labeled cell
+
+ align:start position:0%
+you can also follow this labeled cell
+ 
+
+ align:start position:0%
+you can also follow this labeled cell
+population and see what those cells
+
+ align:start position:0%
+population and see what those cells
+ 
+
+ align:start position:0%
+population and see what those cells
+become and you can see that they go on
+
+ align:start position:0%
+become and you can see that they go on
+ 
+
+ align:start position:0%
+become and you can see that they go on
+to differentiate as particular cell
+
+ align:start position:0%
+to differentiate as particular cell
+ 
+
+ align:start position:0%
+to differentiate as particular cell
+types so this is a kind of way of
+
+ align:start position:0%
+types so this is a kind of way of
+ 
+
+ align:start position:0%
+types so this is a kind of way of
+labeling the lineage of these cells and
+
+ align:start position:0%
+labeling the lineage of these cells and
+ 
+
+ align:start position:0%
+labeling the lineage of these cells and
+that is useful too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this was the theory behind stem cell
+
+ align:start position:0%
+this was the theory behind stem cell
+ 
+
+ align:start position:0%
+this was the theory behind stem cell
+definition but what is a stem cell look
+
+ align:start position:0%
+definition but what is a stem cell look
+ 
+
+ align:start position:0%
+definition but what is a stem cell look
+like and how do you isolate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one it turns out that that's really
+
+ align:start position:0%
+one it turns out that that's really
+ 
+
+ align:start position:0%
+one it turns out that that's really
+difficult so isolation and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assay in the adult stem cells are very
+
+ align:start position:0%
+assay in the adult stem cells are very
+ 
+
+ align:start position:0%
+assay in the adult stem cells are very
+very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rare and that is one of the
+
+ align:start position:0%
+rare and that is one of the
+ 
+
+ align:start position:0%
+rare and that is one of the
+issues with using stem cells for therapy
+
+ align:start position:0%
+issues with using stem cells for therapy
+ 
+
+ align:start position:0%
+issues with using stem cells for therapy
+there are very few of them and they're
+
+ align:start position:0%
+there are very few of them and they're
+ 
+
+ align:start position:0%
+there are very few of them and they're
+hard to isolate hematopoetic stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells comprise about 0 1% of the bone
+
+ align:start position:0%
+cells comprise about 0 1% of the bone
+ 
+
+ align:start position:0%
+cells comprise about 0 1% of the bone
+marrow which is where the stem cells
+
+ align:start position:0%
+marrow which is where the stem cells
+ 
+
+ align:start position:0%
+marrow which is where the stem cells
+reside and where the precursors of your
+
+ align:start position:0%
+reside and where the precursors of your
+ 
+
+ align:start position:0%
+reside and where the precursors of your
+whole blood and immune system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reside the way that this was dealt with
+
+ align:start position:0%
+reside the way that this was dealt with
+ 
+
+ align:start position:0%
+reside the way that this was dealt with
+was through a really clever technique
+
+ align:start position:0%
+was through a really clever technique
+ 
+
+ align:start position:0%
+was through a really clever technique
+that has the acronym of fact I'll give
+
+ align:start position:0%
+that has the acronym of fact I'll give
+ 
+
+ align:start position:0%
+that has the acronym of fact I'll give
+you a slide in a moment it stands for
+
+ align:start position:0%
+you a slide in a moment it stands for
+ 
+
+ align:start position:0%
+you a slide in a moment it stands for
+fluoresence activated cell sorting we'll
+
+ align:start position:0%
+fluoresence activated cell sorting we'll
+ 
+
+ align:start position:0%
+fluoresence activated cell sorting we'll
+go to a slide in a moment so we don't
+
+ align:start position:0%
+go to a slide in a moment so we don't
+ 
+
+ align:start position:0%
+go to a slide in a moment so we don't
+have to spell it out and the idea behind
+
+ align:start position:0%
+have to spell it out and the idea behind
+ 
+
+ align:start position:0%
+have to spell it out and the idea behind
+facts is that you
+
+ align:start position:0%
+facts is that you
+ 
+
+ align:start position:0%
+facts is that you
+label stem cells and you might be
+
+ align:start position:0%
+label stem cells and you might be
+ 
+
+ align:start position:0%
+label stem cells and you might be
+guessing what to label them with but you
+
+ align:start position:0%
+guessing what to label them with but you
+ 
+
+ align:start position:0%
+guessing what to label them with but you
+label them usually via their cell
+
+ align:start position:0%
+label them usually via their cell
+ 
+
+ align:start position:0%
+label them usually via their cell
+surface
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proteins with some kind of
+
+ align:start position:0%
+proteins with some kind of
+ 
+
+ align:start position:0%
+proteins with some kind of
+tag often an antibody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tag and then you can use that tag to
+
+ align:start position:0%
+tag and then you can use that tag to
+ 
+
+ align:start position:0%
+tag and then you can use that tag to
+make them different colors and you can
+
+ align:start position:0%
+make them different colors and you can
+ 
+
+ align:start position:0%
+make them different colors and you can
+then sort them cell by cell through this
+
+ align:start position:0%
+then sort them cell by cell through this
+ 
+
+ align:start position:0%
+then sort them cell by cell through this
+special fluorescent activated cell
+
+ align:start position:0%
+special fluorescent activated cell
+ 
+
+ align:start position:0%
+special fluorescent activated cell
+sorder sort individual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells and then you can
+
+ align:start position:0%
+cells and then you can
+ 
+
+ align:start position:0%
+cells and then you can
+assay individual cells or small groups
+
+ align:start position:0%
+assay individual cells or small groups
+ 
+
+ align:start position:0%
+assay individual cells or small groups
+of them for stem cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties let's look at a slide of how
+
+ align:start position:0%
+properties let's look at a slide of how
+ 
+
+ align:start position:0%
+properties let's look at a slide of how
+the facts the fluorescence activated
+
+ align:start position:0%
+the facts the fluorescence activated
+ 
+
+ align:start position:0%
+the facts the fluorescence activated
+cell sort of works no let's not I've
+
+ align:start position:0%
+cell sort of works no let's not I've
+ 
+
+ align:start position:0%
+cell sort of works no let's not I've
+really gotten ahead of myself here and
+
+ align:start position:0%
+really gotten ahead of myself here and
+ 
+
+ align:start position:0%
+really gotten ahead of myself here and
+I'm going to to go back because I want
+
+ align:start position:0%
+I'm going to to go back because I want
+ 
+
+ align:start position:0%
+I'm going to to go back because I want
+to show you
+
+ align:start position:0%
+to show you
+ 
+
+ align:start position:0%
+to show you
+this hold on to that thought and let's
+
+ align:start position:0%
+this hold on to that thought and let's
+ 
+
+ align:start position:0%
+this hold on to that thought and let's
+go back to this notion of a pulse Chase
+
+ align:start position:0%
+go back to this notion of a pulse Chase
+ 
+
+ align:start position:0%
+go back to this notion of a pulse Chase
+assay I forgot that I had this here this
+
+ align:start position:0%
+assay I forgot that I had this here this
+ 
+
+ align:start position:0%
+assay I forgot that I had this here this
+is really important this is a pulse
+
+ align:start position:0%
+is really important this is a pulse
+ 
+
+ align:start position:0%
+is really important this is a pulse
+Chase assay of intestinal cells and so
+
+ align:start position:0%
+Chase assay of intestinal cells and so
+ 
+
+ align:start position:0%
+Chase assay of intestinal cells and so
+your small
+
+ align:start position:0%
+your small
+ 
+
+ align:start position:0%
+your small
+intestine
+
+ align:start position:0%
+intestine
+ 
+
+ align:start position:0%
+intestine
+lies inside your
+
+ align:start position:0%
+lies inside your
+ 
+
+ align:start position:0%
+lies inside your
+belly and if you look at its Anatomy it
+
+ align:start position:0%
+belly and if you look at its Anatomy it
+ 
+
+ align:start position:0%
+belly and if you look at its Anatomy it
+contains many tubes
+
+ align:start position:0%
+contains many tubes
+ 
+
+ align:start position:0%
+contains many tubes
+whose folds are throw whose whose
+
+ align:start position:0%
+whose folds are throw whose whose
+ 
+
+ align:start position:0%
+whose folds are throw whose whose
+surface is thrown into folds to increase
+
+ align:start position:0%
+surface is thrown into folds to increase
+ 
+
+ align:start position:0%
+surface is thrown into folds to increase
+the surface area for food absorption and
+
+ align:start position:0%
+the surface area for food absorption and
+ 
+
+ align:start position:0%
+the surface area for food absorption and
+if you look at these folds they are very
+
+ align:start position:0%
+if you look at these folds they are very
+ 
+
+ align:start position:0%
+if you look at these folds they are very
+closely packed so you get a huge surface
+
+ align:start position:0%
+closely packed so you get a huge surface
+ 
+
+ align:start position:0%
+closely packed so you get a huge surface
+area increase and the cells of these
+
+ align:start position:0%
+area increase and the cells of these
+ 
+
+ align:start position:0%
+area increase and the cells of these
+folds that are doing the food absorption
+
+ align:start position:0%
+folds that are doing the food absorption
+ 
+
+ align:start position:0%
+folds that are doing the food absorption
+turn over every 3 to 5 days those are
+
+ align:start position:0%
+turn over every 3 to 5 days those are
+ 
+
+ align:start position:0%
+turn over every 3 to 5 days those are
+the ones I was talking about so if you
+
+ align:start position:0%
+the ones I was talking about so if you
+ 
+
+ align:start position:0%
+the ones I was talking about so if you
+blow up one of these folds which is
+
+ align:start position:0%
+blow up one of these folds which is
+ 
+
+ align:start position:0%
+blow up one of these folds which is
+called a villis there's the part that's
+
+ align:start position:0%
+called a villis there's the part that's
+ 
+
+ align:start position:0%
+called a villis there's the part that's
+sticking up into the cavity into the
+
+ align:start position:0%
+sticking up into the cavity into the
+ 
+
+ align:start position:0%
+sticking up into the cavity into the
+Lumen of the small intestine and then
+
+ align:start position:0%
+Lumen of the small intestine and then
+ 
+
+ align:start position:0%
+Lumen of the small intestine and then
+there's this part that kind of dips down
+
+ align:start position:0%
+there's this part that kind of dips down
+ 
+
+ align:start position:0%
+there's this part that kind of dips down
+into the lining of the intestine which
+
+ align:start position:0%
+into the lining of the intestine which
+ 
+
+ align:start position:0%
+into the lining of the intestine which
+is called a crypt the stem cells lie
+
+ align:start position:0%
+is called a crypt the stem cells lie
+ 
+
+ align:start position:0%
+is called a crypt the stem cells lie
+somewhere at the base of the crypt it's
+
+ align:start position:0%
+somewhere at the base of the crypt it's
+ 
+
+ align:start position:0%
+somewhere at the base of the crypt it's
+not exactly clear where but if you but
+
+ align:start position:0%
+not exactly clear where but if you but
+ 
+
+ align:start position:0%
+not exactly clear where but if you but
+the idea is that somewhere at the bottom
+
+ align:start position:0%
+the idea is that somewhere at the bottom
+ 
+
+ align:start position:0%
+the idea is that somewhere at the bottom
+of this Crypt there these stem cells
+
+ align:start position:0%
+of this Crypt there these stem cells
+ 
+
+ align:start position:0%
+of this Crypt there these stem cells
+that under specific conditions will
+
+ align:start position:0%
+that under specific conditions will
+ 
+
+ align:start position:0%
+that under specific conditions will
+start to proliferate and they will move
+
+ align:start position:0%
+start to proliferate and they will move
+ 
+
+ align:start position:0%
+start to proliferate and they will move
+up into the villis and replace the
+
+ align:start position:0%
+up into the villis and replace the
+ 
+
+ align:start position:0%
+up into the villis and replace the
+villis cells that are dying you can
+
+ align:start position:0%
+villis cells that are dying you can
+ 
+
+ align:start position:0%
+villis cells that are dying you can
+monitor this by doing a pulse Chase
+
+ align:start position:0%
+monitor this by doing a pulse Chase
+ 
+
+ align:start position:0%
+monitor this by doing a pulse Chase
+experiment so here's the Crypt and
+
+ align:start position:0%
+experiment so here's the Crypt and
+ 
+
+ align:start position:0%
+experiment so here's the Crypt and
+they've given in this experiment a pulse
+
+ align:start position:0%
+they've given in this experiment a pulse
+ 
+
+ align:start position:0%
+they've given in this experiment a pulse
+of thymidine has been given and you're
+
+ align:start position:0%
+of thymidine has been given and you're
+ 
+
+ align:start position:0%
+of thymidine has been given and you're
+looking kind of at time zero right after
+
+ align:start position:0%
+looking kind of at time zero right after
+ 
+
+ align:start position:0%
+looking kind of at time zero right after
+the pulse of of thymidine has been given
+
+ align:start position:0%
+the pulse of of thymidine has been given
+ 
+
+ align:start position:0%
+the pulse of of thymidine has been given
+here are the cells the black cells in
+
+ align:start position:0%
+here are the cells the black cells in
+ 
+
+ align:start position:0%
+here are the cells the black cells in
+the cryp they're labeled and then if you
+
+ align:start position:0%
+the cryp they're labeled and then if you
+ 
+
+ align:start position:0%
+the cryp they're labeled and then if you
+look over time you can see that these
+
+ align:start position:0%
+look over time you can see that these
+ 
+
+ align:start position:0%
+look over time you can see that these
+black cells move away from the Crypt
+
+ align:start position:0%
+black cells move away from the Crypt
+ 
+
+ align:start position:0%
+black cells move away from the Crypt
+they're moving up into the villa and
+
+ align:start position:0%
+they're moving up into the villa and
+ 
+
+ align:start position:0%
+they're moving up into the villa and
+here they are actually right on top of
+
+ align:start position:0%
+here they are actually right on top of
+ 
+
+ align:start position:0%
+here they are actually right on top of
+the villis replacing the cells that were
+
+ align:start position:0%
+the villis replacing the cells that were
+ 
+
+ align:start position:0%
+the villis replacing the cells that were
+turning over so that's a really
+
+ align:start position:0%
+turning over so that's a really
+ 
+
+ align:start position:0%
+turning over so that's a really
+beautiful demonstration of a pulse Chase
+
+ align:start position:0%
+beautiful demonstration of a pulse Chase
+ 
+
+ align:start position:0%
+beautiful demonstration of a pulse Chase
+assay okay now we can go to our
+
+ align:start position:0%
+assay okay now we can go to our
+ 
+
+ align:start position:0%
+assay okay now we can go to our
+fluorescence activated cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorder the idea is that you take a mix
+
+ align:start position:0%
+sorder the idea is that you take a mix
+ 
+
+ align:start position:0%
+sorder the idea is that you take a mix
+of cells you don't have this on your
+
+ align:start position:0%
+of cells you don't have this on your
+ 
+
+ align:start position:0%
+of cells you don't have this on your
+handout just look on the screen the
+
+ align:start position:0%
+handout just look on the screen the
+ 
+
+ align:start position:0%
+handout just look on the screen the
+cells are labeled with fluorescent
+
+ align:start position:0%
+cells are labeled with fluorescent
+ 
+
+ align:start position:0%
+cells are labeled with fluorescent
+antibodies and you put them into a
+
+ align:start position:0%
+antibodies and you put them into a
+ 
+
+ align:start position:0%
+antibodies and you put them into a
+reservoir and droplet Generator and the
+
+ align:start position:0%
+reservoir and droplet Generator and the
+ 
+
+ align:start position:0%
+reservoir and droplet Generator and the
+cells drop out of this reservoir one at
+
+ align:start position:0%
+cells drop out of this reservoir one at
+ 
+
+ align:start position:0%
+cells drop out of this reservoir one at
+a time and as they drop out they go past
+
+ align:start position:0%
+a time and as they drop out they go past
+ 
+
+ align:start position:0%
+a time and as they drop out they go past
+a laser and you can tune the laser to
+
+ align:start position:0%
+a laser and you can tune the laser to
+ 
+
+ align:start position:0%
+a laser and you can tune the laser to
+whatever wavelengths you want it excites
+
+ align:start position:0%
+whatever wavelengths you want it excites
+ 
+
+ align:start position:0%
+whatever wavelengths you want it excites
+the cells and if the cells emit in the
+
+ align:start position:0%
+the cells and if the cells emit in the
+ 
+
+ align:start position:0%
+the cells and if the cells emit in the
+particular wavelength you're interested
+
+ align:start position:0%
+particular wavelength you're interested
+ 
+
+ align:start position:0%
+particular wavelength you're interested
+in the detector will detect that and
+
+ align:start position:0%
+in the detector will detect that and
+ 
+
+ align:start position:0%
+in the detector will detect that and
+then it actually gives a charge to the
+
+ align:start position:0%
+then it actually gives a charge to the
+ 
+
+ align:start position:0%
+then it actually gives a charge to the
+cell that it is the correct fluoresence
+
+ align:start position:0%
+cell that it is the correct fluoresence
+ 
+
+ align:start position:0%
+cell that it is the correct fluoresence
+and as the cells are dropping down the
+
+ align:start position:0%
+and as the cells are dropping down the
+ 
+
+ align:start position:0%
+and as the cells are dropping down the
+cells of the correct color are deflected
+
+ align:start position:0%
+cells of the correct color are deflected
+ 
+
+ align:start position:0%
+cells of the correct color are deflected
+by an electric charge and different
+
+ align:start position:0%
+by an electric charge and different
+ 
+
+ align:start position:0%
+by an electric charge and different
+color cells can be collected into
+
+ align:start position:0%
+color cells can be collected into
+ 
+
+ align:start position:0%
+color cells can be collected into
+different flasks okay this really works
+
+ align:start position:0%
+different flasks okay this really works
+ 
+
+ align:start position:0%
+different flasks okay this really works
+it's a fantastic machine you can collect
+
+ align:start position:0%
+it's a fantastic machine you can collect
+ 
+
+ align:start position:0%
+it's a fantastic machine you can collect
+cells about you know you can collect
+
+ align:start position:0%
+cells about you know you can collect
+ 
+
+ align:start position:0%
+cells about you know you can collect
+millions of cells an hour it's pretty
+
+ align:start position:0%
+millions of cells an hour it's pretty
+ 
+
+ align:start position:0%
+millions of cells an hour it's pretty
+quick but you do it one cell at a time
+
+ align:start position:0%
+quick but you do it one cell at a time
+ 
+
+ align:start position:0%
+quick but you do it one cell at a time
+and in that way you can isolate cells
+
+ align:start position:0%
+and in that way you can isolate cells
+ 
+
+ align:start position:0%
+and in that way you can isolate cells
+which have got stem cell properties
+
+ align:start position:0%
+which have got stem cell properties
+ 
+
+ align:start position:0%
+which have got stem cell properties
+okay so you've used your fax machine
+
+ align:start position:0%
+okay so you've used your fax machine
+ 
+
+ align:start position:0%
+okay so you've used your fax machine
+you've got cells that look as though
+
+ align:start position:0%
+you've got cells that look as though
+ 
+
+ align:start position:0%
+you've got cells that look as though
+they've got stem cell properties and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's look at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assays that may be used and there are
+
+ align:start position:0%
+assays that may be used and there are
+ 
+
+ align:start position:0%
+assays that may be used and there are
+three assays that you should know one is
+
+ align:start position:0%
+three assays that you should know one is
+ 
+
+ align:start position:0%
+three assays that you should know one is
+a repopulation
+
+ align:start position:0%
+a repopulation
+ 
+
+ align:start position:0%
+a repopulation
+assay to test stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cellus and this is a transplant assay
+
+ align:start position:0%
+cellus and this is a transplant assay
+ 
+
+ align:start position:0%
+cellus and this is a transplant assay
+where you're
+
+ align:start position:0%
+where you're
+ 
+
+ align:start position:0%
+where you're
+transplanting
+
+ align:start position:0%
+transplanting
+ 
+
+ align:start position:0%
+transplanting
+test cells test stem
+
+ align:start position:0%
+test cells test stem
+ 
+
+ align:start position:0%
+test cells test stem
+cells into the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adult and you have removed from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adult endogenous cells that might be
+
+ align:start position:0%
+adult endogenous cells that might be
+ 
+
+ align:start position:0%
+adult endogenous cells that might be
+competing with those stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells that would include the stem cells
+
+ align:start position:0%
+cells that would include the stem cells
+ 
+
+ align:start position:0%
+cells that would include the stem cells
+we'll go through a slide in a moment I'm
+
+ align:start position:0%
+we'll go through a slide in a moment I'm
+ 
+
+ align:start position:0%
+we'll go through a slide in a moment I'm
+going to list them here another one is
+
+ align:start position:0%
+going to list them here another one is
+ 
+
+ align:start position:0%
+going to list them here another one is
+an invitro induction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assay where you're going to take
+
+ align:start position:0%
+assay where you're going to take
+ 
+
+ align:start position:0%
+assay where you're going to take
+isolated
+
+ align:start position:0%
+isolated
+ 
+
+ align:start position:0%
+isolated
+cells and you're going to treat them
+
+ align:start position:0%
+cells and you're going to treat them
+ 
+
+ align:start position:0%
+cells and you're going to treat them
+with various inducers various signaling
+
+ align:start position:0%
+with various inducers various signaling
+ 
+
+ align:start position:0%
+with various inducers various signaling
+molecules and you're going to test and
+
+ align:start position:0%
+molecules and you're going to test and
+ 
+
+ align:start position:0%
+molecules and you're going to test and
+see what Fates those cells can
+
+ align:start position:0%
+see what Fates those cells can
+ 
+
+ align:start position:0%
+see what Fates those cells can
+acquire and a third assay is called an
+
+ align:start position:0%
+acquire and a third assay is called an
+ 
+
+ align:start position:0%
+acquire and a third assay is called an
+embryo incorporation assay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where you're going to take cells that
+
+ align:start position:0%
+where you're going to take cells that
+ 
+
+ align:start position:0%
+where you're going to take cells that
+may be stem
+
+ align:start position:0%
+may be stem
+ 
+
+ align:start position:0%
+may be stem
+cells and you're going to test
+
+ align:start position:0%
+cells and you're going to test
+ 
+
+ align:start position:0%
+cells and you're going to test
+them in a chimeric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+embryo let's go through your next
+
+ align:start position:0%
+embryo let's go through your next
+ 
+
+ align:start position:0%
+embryo let's go through your next
+slides to discuss each of these
+
+ align:start position:0%
+slides to discuss each of these
+ 
+
+ align:start position:0%
+slides to discuss each of these
+points bone marrow transplants resulted
+
+ align:start position:0%
+points bone marrow transplants resulted
+ 
+
+ align:start position:0%
+points bone marrow transplants resulted
+in a Nobel Prize in 1990 for Eon Thomas
+
+ align:start position:0%
+in a Nobel Prize in 1990 for Eon Thomas
+ 
+
+ align:start position:0%
+in a Nobel Prize in 1990 for Eon Thomas
+and Joseph Murray it's a technique that
+
+ align:start position:0%
+and Joseph Murray it's a technique that
+ 
+
+ align:start position:0%
+and Joseph Murray it's a technique that
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+millions of lives and here how it works
+
+ align:start position:0%
+millions of lives and here how it works
+ 
+
+ align:start position:0%
+millions of lives and here how it works
+in a mouse you take the mouse and you
+
+ align:start position:0%
+in a mouse you take the mouse and you
+ 
+
+ align:start position:0%
+in a mouse you take the mouse and you
+irradiate the mouse to destroy the bone
+
+ align:start position:0%
+irradiate the mouse to destroy the bone
+ 
+
+ align:start position:0%
+irradiate the mouse to destroy the bone
+marrow and the stem cells associated
+
+ align:start position:0%
+marrow and the stem cells associated
+ 
+
+ align:start position:0%
+marrow and the stem cells associated
+with the bone marrow if it's a person to
+
+ align:start position:0%
+with the bone marrow if it's a person to
+ 
+
+ align:start position:0%
+with the bone marrow if it's a person to
+destroy the diseased burnt bone
+
+ align:start position:0%
+destroy the diseased burnt bone
+ 
+
+ align:start position:0%
+destroy the diseased burnt bone
+marrow and then you replace that bone
+
+ align:start position:0%
+marrow and then you replace that bone
+ 
+
+ align:start position:0%
+marrow and then you replace that bone
+marrow with normal bone marrow to either
+
+ align:start position:0%
+marrow with normal bone marrow to either
+ 
+
+ align:start position:0%
+marrow with normal bone marrow to either
+try to make the person better or in this
+
+ align:start position:0%
+try to make the person better or in this
+ 
+
+ align:start position:0%
+try to make the person better or in this
+case to test something about stem cells
+
+ align:start position:0%
+case to test something about stem cells
+ 
+
+ align:start position:0%
+case to test something about stem cells
+the irradiated mouse or person would die
+
+ align:start position:0%
+the irradiated mouse or person would die
+ 
+
+ align:start position:0%
+the irradiated mouse or person would die
+but the normal bone marrow will cause
+
+ align:start position:0%
+but the normal bone marrow will cause
+ 
+
+ align:start position:0%
+but the normal bone marrow will cause
+the mouse to live and if you've put stem
+
+ align:start position:0%
+the mouse to live and if you've put stem
+ 
+
+ align:start position:0%
+the mouse to live and if you've put stem
+cells into that Mouse you can start
+
+ align:start position:0%
+cells into that Mouse you can start
+ 
+
+ align:start position:0%
+cells into that Mouse you can start
+getting them out of that Mouse whose
+
+ align:start position:0%
+getting them out of that Mouse whose
+ 
+
+ align:start position:0%
+getting them out of that Mouse whose
+life you've saved and isolate more stem
+
+ align:start position:0%
+life you've saved and isolate more stem
+ 
+
+ align:start position:0%
+life you've saved and isolate more stem
+cells those kinds of assays led to the
+
+ align:start position:0%
+cells those kinds of assays led to the
+ 
+
+ align:start position:0%
+cells those kinds of assays led to the
+definition of the hematopoetic stem cell
+
+ align:start position:0%
+definition of the hematopoetic stem cell
+ 
+
+ align:start position:0%
+definition of the hematopoetic stem cell
+here it is it's a plur poent stem cell
+
+ align:start position:0%
+here it is it's a plur poent stem cell
+ 
+
+ align:start position:0%
+here it is it's a plur poent stem cell
+that gives rise to all of these
+
+ align:start position:0%
+that gives rise to all of these
+ 
+
+ align:start position:0%
+that gives rise to all of these
+different kinds of cells the immune
+
+ align:start position:0%
+different kinds of cells the immune
+ 
+
+ align:start position:0%
+different kinds of cells the immune
+cells and all of the blood cells it's a
+
+ align:start position:0%
+cells and all of the blood cells it's a
+ 
+
+ align:start position:0%
+cells and all of the blood cells it's a
+very very powerful stem cell and the the
+
+ align:start position:0%
+very very powerful stem cell and the the
+ 
+
+ align:start position:0%
+very very powerful stem cell and the the
+ability to actually make this diagram
+
+ align:start position:0%
+ability to actually make this diagram
+ 
+
+ align:start position:0%
+ability to actually make this diagram
+and say that there was a single cell
+
+ align:start position:0%
+and say that there was a single cell
+ 
+
+ align:start position:0%
+and say that there was a single cell
+that gave rise to all these different
+
+ align:start position:0%
+that gave rise to all these different
+ 
+
+ align:start position:0%
+that gave rise to all these different
+lineages was because of a titration
+
+ align:start position:0%
+lineages was because of a titration
+ 
+
+ align:start position:0%
+lineages was because of a titration
+assay where you could take these
+
+ align:start position:0%
+assay where you could take these
+ 
+
+ align:start position:0%
+assay where you could take these
+putative hematopoetic stem cells that
+
+ align:start position:0%
+putative hematopoetic stem cells that
+ 
+
+ align:start position:0%
+putative hematopoetic stem cells that
+were difficult to isolate and still
+
+ align:start position:0%
+were difficult to isolate and still
+ 
+
+ align:start position:0%
+were difficult to isolate and still
+haven't been isolated in their purity
+
+ align:start position:0%
+haven't been isolated in their purity
+ 
+
+ align:start position:0%
+haven't been isolated in their purity
+but you can titrate them down and you
+
+ align:start position:0%
+but you can titrate them down and you
+ 
+
+ align:start position:0%
+but you can titrate them down and you
+can introduce what you think is one stem
+
+ align:start position:0%
+can introduce what you think is one stem
+ 
+
+ align:start position:0%
+can introduce what you think is one stem
+cell 10 stem cells 100 stem cells and so
+
+ align:start position:0%
+cell 10 stem cells 100 stem cells and so
+ 
+
+ align:start position:0%
+cell 10 stem cells 100 stem cells and so
+on into an irradiated Mouse and ask how
+
+ align:start position:0%
+on into an irradiated Mouse and ask how
+ 
+
+ align:start position:0%
+on into an irradiated Mouse and ask how
+many stem cells does it take to
+
+ align:start position:0%
+many stem cells does it take to
+ 
+
+ align:start position:0%
+many stem cells does it take to
+repopulate the entire blood system and
+
+ align:start position:0%
+repopulate the entire blood system and
+ 
+
+ align:start position:0%
+repopulate the entire blood system and
+immune system and it turns out you have
+
+ align:start position:0%
+immune system and it turns out you have
+ 
+
+ align:start position:0%
+immune system and it turns out you have
+to mix these cells with carrier cells
+
+ align:start position:0%
+to mix these cells with carrier cells
+ 
+
+ align:start position:0%
+to mix these cells with carrier cells
+otherwise it doesn't work but it turns
+
+ align:start position:0%
+otherwise it doesn't work but it turns
+ 
+
+ align:start position:0%
+otherwise it doesn't work but it turns
+out that one cell can repopulate the
+
+ align:start position:0%
+out that one cell can repopulate the
+ 
+
+ align:start position:0%
+out that one cell can repopulate the
+entire hematopoetic system which is
+
+ align:start position:0%
+entire hematopoetic system which is
+ 
+
+ align:start position:0%
+entire hematopoetic system which is
+really extraordinary and led to the
+
+ align:start position:0%
+really extraordinary and led to the
+ 
+
+ align:start position:0%
+really extraordinary and led to the
+diagram that I showed you in the slide
+
+ align:start position:0%
+diagram that I showed you in the slide
+ 
+
+ align:start position:0%
+diagram that I showed you in the slide
+before okay here's another assay this is
+
+ align:start position:0%
+before okay here's another assay this is
+ 
+
+ align:start position:0%
+before okay here's another assay this is
+an initro induction assay and the idea
+
+ align:start position:0%
+an initro induction assay and the idea
+ 
+
+ align:start position:0%
+an initro induction assay and the idea
+here is that you start off with
+
+ align:start position:0%
+here is that you start off with
+ 
+
+ align:start position:0%
+here is that you start off with
+something which you think might be stem
+
+ align:start position:0%
+something which you think might be stem
+ 
+
+ align:start position:0%
+something which you think might be stem
+cells by various criteria and then to
+
+ align:start position:0%
+cells by various criteria and then to
+ 
+
+ align:start position:0%
+cells by various criteria and then to
+test what these cells can do you put
+
+ align:start position:0%
+test what these cells can do you put
+ 
+
+ align:start position:0%
+test what these cells can do you put
+them into plastic tissue culture dishes
+
+ align:start position:0%
+them into plastic tissue culture dishes
+ 
+
+ align:start position:0%
+them into plastic tissue culture dishes
+and you add some nutrients and so on to
+
+ align:start position:0%
+and you add some nutrients and so on to
+ 
+
+ align:start position:0%
+and you add some nutrients and so on to
+allow the cells to divide and then you
+
+ align:start position:0%
+allow the cells to divide and then you
+ 
+
+ align:start position:0%
+allow the cells to divide and then you
+add some inducers and you remember a
+
+ align:start position:0%
+add some inducers and you remember a
+ 
+
+ align:start position:0%
+add some inducers and you remember a
+couple of lectures back inducers are
+
+ align:start position:0%
+couple of lectures back inducers are
+ 
+
+ align:start position:0%
+couple of lectures back inducers are
+just ligans for various signaling
+
+ align:start position:0%
+just ligans for various signaling
+ 
+
+ align:start position:0%
+just ligans for various signaling
+systems you might add fiberblast growth
+
+ align:start position:0%
+systems you might add fiberblast growth
+ 
+
+ align:start position:0%
+systems you might add fiberblast growth
+factor to this one and retinoic acid to
+
+ align:start position:0%
+factor to this one and retinoic acid to
+ 
+
+ align:start position:0%
+factor to this one and retinoic acid to
+that one and then you ask what happens
+
+ align:start position:0%
+that one and then you ask what happens
+ 
+
+ align:start position:0%
+that one and then you ask what happens
+to the cells they will go on in general
+
+ align:start position:0%
+to the cells they will go on in general
+ 
+
+ align:start position:0%
+to the cells they will go on in general
+to differentiate into different cell
+
+ align:start position:0%
+to differentiate into different cell
+ 
+
+ align:start position:0%
+to differentiate into different cell
+types and depending on what they
+
+ align:start position:0%
+types and depending on what they
+ 
+
+ align:start position:0%
+types and depending on what they
+differentiate into you can say something
+
+ align:start position:0%
+differentiate into you can say something
+ 
+
+ align:start position:0%
+differentiate into you can say something
+about the potency of these putative stem
+
+ align:start position:0%
+about the potency of these putative stem
+ 
+
+ align:start position:0%
+about the potency of these putative stem
+cells you can't test if they're really
+
+ align:start position:0%
+cells you can't test if they're really
+ 
+
+ align:start position:0%
+cells you can't test if they're really
+stem cells but you can say something
+
+ align:start position:0%
+stem cells but you can say something
+ 
+
+ align:start position:0%
+stem cells but you can say something
+about their
+
+ align:start position:0%
+about their
+ 
+
+ align:start position:0%
+about their
+potency can do a similar experiment but
+
+ align:start position:0%
+potency can do a similar experiment but
+ 
+
+ align:start position:0%
+potency can do a similar experiment but
+in a whole
+
+ align:start position:0%
+in a whole
+ 
+
+ align:start position:0%
+in a whole
+Mouse the mouse is made from the embryo
+
+ align:start position:0%
+Mouse the mouse is made from the embryo
+ 
+
+ align:start position:0%
+Mouse the mouse is made from the embryo
+is made from a part of the the very
+
+ align:start position:0%
+is made from a part of the the very
+ 
+
+ align:start position:0%
+is made from a part of the the very
+early embryo called the Inner Cell mass
+
+ align:start position:0%
+early embryo called the Inner Cell mass
+ 
+
+ align:start position:0%
+early embryo called the Inner Cell mass
+and you can inject labeled putative stem
+
+ align:start position:0%
+and you can inject labeled putative stem
+ 
+
+ align:start position:0%
+and you can inject labeled putative stem
+cells into an early Mouse embryo into
+
+ align:start position:0%
+cells into an early Mouse embryo into
+ 
+
+ align:start position:0%
+cells into an early Mouse embryo into
+this Inner Cell Mass part of the embryo
+
+ align:start position:0%
+this Inner Cell Mass part of the embryo
+ 
+
+ align:start position:0%
+this Inner Cell Mass part of the embryo
+put it into a um a mother a a recipient
+
+ align:start position:0%
+put it into a um a mother a a recipient
+ 
+
+ align:start position:0%
+put it into a um a mother a a recipient
+mother and then ask what comes out what
+
+ align:start position:0%
+mother and then ask what comes out what
+ 
+
+ align:start position:0%
+mother and then ask what comes out what
+kind of embryo comes out of that process
+
+ align:start position:0%
+kind of embryo comes out of that process
+ 
+
+ align:start position:0%
+kind of embryo comes out of that process
+and if you see that the baby that comes
+
+ align:start position:0%
+and if you see that the baby that comes
+ 
+
+ align:start position:0%
+and if you see that the baby that comes
+out of this chimic embryo
+
+ align:start position:0%
+out of this chimic embryo
+ 
+
+ align:start position:0%
+out of this chimic embryo
+has got a green liver and green ears and
+
+ align:start position:0%
+has got a green liver and green ears and
+ 
+
+ align:start position:0%
+has got a green liver and green ears and
+green whiskers you'll know that these
+
+ align:start position:0%
+green whiskers you'll know that these
+ 
+
+ align:start position:0%
+green whiskers you'll know that these
+cells that you put into the chimeric
+
+ align:start position:0%
+cells that you put into the chimeric
+ 
+
+ align:start position:0%
+cells that you put into the chimeric
+embryo that you made the chimeric embryo
+
+ align:start position:0%
+embryo that you made the chimeric embryo
+ 
+
+ align:start position:0%
+embryo that you made the chimeric embryo
+with had the capacity to give liver ears
+
+ align:start position:0%
+with had the capacity to give liver ears
+ 
+
+ align:start position:0%
+with had the capacity to give liver ears
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+whiskers okay so this is a powerful
+
+ align:start position:0%
+whiskers okay so this is a powerful
+ 
+
+ align:start position:0%
+whiskers okay so this is a powerful
+essay to again look at the potency of
+
+ align:start position:0%
+essay to again look at the potency of
+ 
+
+ align:start position:0%
+essay to again look at the potency of
+cells not in this case the stem cell of
+
+ align:start position:0%
+cells not in this case the stem cell of
+ 
+
+ align:start position:0%
+cells not in this case the stem cell of
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells one of the things about stem
+
+ align:start position:0%
+cells one of the things about stem
+ 
+
+ align:start position:0%
+cells one of the things about stem
+cells is that you only want them to work
+
+ align:start position:0%
+cells is that you only want them to work
+ 
+
+ align:start position:0%
+cells is that you only want them to work
+when you want them to work if you cut
+
+ align:start position:0%
+when you want them to work if you cut
+ 
+
+ align:start position:0%
+when you want them to work if you cut
+yourself in the normal process of
+
+ align:start position:0%
+yourself in the normal process of
+ 
+
+ align:start position:0%
+yourself in the normal process of
+keeping your liver the right size in the
+
+ align:start position:0%
+keeping your liver the right size in the
+ 
+
+ align:start position:0%
+keeping your liver the right size in the
+normal process of keeping your heart
+
+ align:start position:0%
+normal process of keeping your heart
+ 
+
+ align:start position:0%
+normal process of keeping your heart
+muscle correct you want your stem cells
+
+ align:start position:0%
+muscle correct you want your stem cells
+ 
+
+ align:start position:0%
+muscle correct you want your stem cells
+to be working and keeping everything
+
+ align:start position:0%
+to be working and keeping everything
+ 
+
+ align:start position:0%
+to be working and keeping everything
+homeostatic you don't want them to be
+
+ align:start position:0%
+homeostatic you don't want them to be
+ 
+
+ align:start position:0%
+homeostatic you don't want them to be
+dividing out of control because then
+
+ align:start position:0%
+dividing out of control because then
+ 
+
+ align:start position:0%
+dividing out of control because then
+you'll get cancer and so something has
+
+ align:start position:0%
+you'll get cancer and so something has
+ 
+
+ align:start position:0%
+you'll get cancer and so something has
+to control what stem cells do and when
+
+ align:start position:0%
+to control what stem cells do and when
+ 
+
+ align:start position:0%
+to control what stem cells do and when
+they do it and this is a question of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Regulation and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notion of a stem cell
+
+ align:start position:0%
+notion of a stem cell
+ 
+
+ align:start position:0%
+notion of a stem cell
+Niche stem cells are kept
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quiescent usually in
+
+ align:start position:0%
+quiescent usually in
+ 
+
+ align:start position:0%
+quiescent usually in
+g0 that we talked about in the cell
+
+ align:start position:0%
+g0 that we talked about in the cell
+ 
+
+ align:start position:0%
+g0 that we talked about in the cell
+cycle
+
+ align:start position:0%
+cycle
+ 
+
+ align:start position:0%
+cycle
+lecture and they're kept quiescent by
+
+ align:start position:0%
+lecture and they're kept quiescent by
+ 
+
+ align:start position:0%
+lecture and they're kept quiescent by
+signals from the surrounding cells so
+
+ align:start position:0%
+signals from the surrounding cells so
+ 
+
+ align:start position:0%
+signals from the surrounding cells so
+there's cell cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interaction and by
+
+ align:start position:0%
+interaction and by
+ 
+
+ align:start position:0%
+interaction and by
+signals
+
+ align:start position:0%
+signals
+ 
+
+ align:start position:0%
+signals
+from the surrounding cells and those are
+
+ align:start position:0%
+from the surrounding cells and those are
+ 
+
+ align:start position:0%
+from the surrounding cells and those are
+given a special name by stem cell
+
+ align:start position:0%
+given a special name by stem cell
+ 
+
+ align:start position:0%
+given a special name by stem cell
+biologists they're not that special but
+
+ align:start position:0%
+biologists they're not that special but
+ 
+
+ align:start position:0%
+biologists they're not that special but
+they're given a special
+
+ align:start position:0%
+they're given a special
+ 
+
+ align:start position:0%
+they're given a special
+name they're called Niche cells or the
+
+ align:start position:0%
+name they're called Niche cells or the
+ 
+
+ align:start position:0%
+name they're called Niche cells or the
+niche okay they're just surrounding
+
+ align:start position:0%
+niche okay they're just surrounding
+ 
+
+ align:start position:0%
+niche okay they're just surrounding
+cells that are secreting
+
+ align:start position:0%
+cells that are secreting
+ 
+
+ align:start position:0%
+cells that are secreting
+signals on some kind of activation you
+
+ align:start position:0%
+signals on some kind of activation you
+ 
+
+ align:start position:0%
+signals on some kind of activation you
+cut
+
+ align:start position:0%
+cut
+ 
+
+ align:start position:0%
+cut
+yourself your organ normally needs
+
+ align:start position:0%
+yourself your organ normally needs
+ 
+
+ align:start position:0%
+yourself your organ normally needs
+repair things change so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+activation by some kind of environmental
+
+ align:start position:0%
+activation by some kind of environmental
+ 
+
+ align:start position:0%
+activation by some kind of environmental
+input local or less
+
+ align:start position:0%
+input local or less
+ 
+
+ align:start position:0%
+input local or less
+local the niche
+
+ align:start position:0%
+local the niche
+ 
+
+ align:start position:0%
+local the niche
+cells induce the stem cells to
+
+ align:start position:0%
+cells induce the stem cells to
+ 
+
+ align:start position:0%
+cells induce the stem cells to
+divide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they do this and they induce the
+
+ align:start position:0%
+and they do this and they induce the
+ 
+
+ align:start position:0%
+and they do this and they induce the
+stem cells to divide into a stem cell
+
+ align:start position:0%
+stem cells to divide into a stem cell
+ 
+
+ align:start position:0%
+stem cells to divide into a stem cell
+plus a progenitor which then goes
+
+ align:start position:0%
+plus a progenitor which then goes
+ 
+
+ align:start position:0%
+plus a progenitor which then goes
+on to do all the things that I
+
+ align:start position:0%
+on to do all the things that I
+ 
+
+ align:start position:0%
+on to do all the things that I
+diagrammed that progenitors do on the
+
+ align:start position:0%
+diagrammed that progenitors do on the
+ 
+
+ align:start position:0%
+diagrammed that progenitors do on the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+board and the niche cells do this
+
+ align:start position:0%
+board and the niche cells do this
+ 
+
+ align:start position:0%
+board and the niche cells do this
+because they've changed their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signaling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is yet another use or very related
+
+ align:start position:0%
+this is yet another use or very related
+ 
+
+ align:start position:0%
+this is yet another use or very related
+use of the notion of cell cell signaling
+
+ align:start position:0%
+use of the notion of cell cell signaling
+ 
+
+ align:start position:0%
+use of the notion of cell cell signaling
+in controlling life here's a diagram
+
+ align:start position:0%
+in controlling life here's a diagram
+ 
+
+ align:start position:0%
+in controlling life here's a diagram
+here are Niche cells you don't have this
+
+ align:start position:0%
+here are Niche cells you don't have this
+ 
+
+ align:start position:0%
+here are Niche cells you don't have this
+just look on the screen surrounding
+
+ align:start position:0%
+just look on the screen surrounding
+ 
+
+ align:start position:0%
+just look on the screen surrounding
+cells maintaining stem cells quiet when
+
+ align:start position:0%
+cells maintaining stem cells quiet when
+ 
+
+ align:start position:0%
+cells maintaining stem cells quiet when
+there's an Environ environmental input
+
+ align:start position:0%
+there's an Environ environmental input
+ 
+
+ align:start position:0%
+there's an Environ environmental input
+the niche cells change they activate the
+
+ align:start position:0%
+the niche cells change they activate the
+ 
+
+ align:start position:0%
+the niche cells change they activate the
+stem cells to divide and form more stem
+
+ align:start position:0%
+stem cells to divide and form more stem
+ 
+
+ align:start position:0%
+stem cells to divide and form more stem
+cells and progenitor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells one really fantastic example of
+
+ align:start position:0%
+cells one really fantastic example of
+ 
+
+ align:start position:0%
+cells one really fantastic example of
+the niche and the interaction between
+
+ align:start position:0%
+the niche and the interaction between
+ 
+
+ align:start position:0%
+the niche and the interaction between
+stem cells and the niche is in the hair
+
+ align:start position:0%
+stem cells and the niche is in the hair
+ 
+
+ align:start position:0%
+stem cells and the niche is in the hair
+this is from my colleague elain fuches
+
+ align:start position:0%
+this is from my colleague elain fuches
+ 
+
+ align:start position:0%
+this is from my colleague elain fuches
+at Rockefeller who over many years has
+
+ align:start position:0%
+at Rockefeller who over many years has
+ 
+
+ align:start position:0%
+at Rockefeller who over many years has
+figured out that in the hair follicle
+
+ align:start position:0%
+figured out that in the hair follicle
+ 
+
+ align:start position:0%
+figured out that in the hair follicle
+this is the hair sticking out of the
+
+ align:start position:0%
+this is the hair sticking out of the
+ 
+
+ align:start position:0%
+this is the hair sticking out of the
+skin in the hair there is a small group
+
+ align:start position:0%
+skin in the hair there is a small group
+ 
+
+ align:start position:0%
+skin in the hair there is a small group
+of cells on one side of the hair shaft
+
+ align:start position:0%
+of cells on one side of the hair shaft
+ 
+
+ align:start position:0%
+of cells on one side of the hair shaft
+called The Bulge cells and these bulge
+
+ align:start position:0%
+called The Bulge cells and these bulge
+ 
+
+ align:start position:0%
+called The Bulge cells and these bulge
+cells are the stem
+
+ align:start position:0%
+cells are the stem
+ 
+
+ align:start position:0%
+cells are the stem
+cells her investigators isolated these
+
+ align:start position:0%
+cells her investigators isolated these
+ 
+
+ align:start position:0%
+cells her investigators isolated these
+bulge cells and did the following
+
+ align:start position:0%
+bulge cells and did the following
+ 
+
+ align:start position:0%
+bulge cells and did the following
+experiment to show that they were hair
+
+ align:start position:0%
+experiment to show that they were hair
+ 
+
+ align:start position:0%
+experiment to show that they were hair
+stem cells there's a kind of a mouse
+
+ align:start position:0%
+stem cells there's a kind of a mouse
+ 
+
+ align:start position:0%
+stem cells there's a kind of a mouse
+called a nude mouse that has a very bad
+
+ align:start position:0%
+called a nude mouse that has a very bad
+ 
+
+ align:start position:0%
+called a nude mouse that has a very bad
+immune system so it's useful for immune
+
+ align:start position:0%
+immune system so it's useful for immune
+ 
+
+ align:start position:0%
+immune system so it's useful for immune
+system experiments but it also has no
+
+ align:start position:0%
+system experiments but it also has no
+ 
+
+ align:start position:0%
+system experiments but it also has no
+hair and you can do a transplant into
+
+ align:start position:0%
+hair and you can do a transplant into
+ 
+
+ align:start position:0%
+hair and you can do a transplant into
+this mouse of these bulge cells and you
+
+ align:start position:0%
+this mouse of these bulge cells and you
+ 
+
+ align:start position:0%
+this mouse of these bulge cells and you
+get little Tufts of hair growing where
+
+ align:start position:0%
+get little Tufts of hair growing where
+ 
+
+ align:start position:0%
+get little Tufts of hair growing where
+the rest of the mouse is nude and you've
+
+ align:start position:0%
+the rest of the mouse is nude and you've
+ 
+
+ align:start position:0%
+the rest of the mouse is nude and you've
+done a careful experiment where you've
+
+ align:start position:0%
+done a careful experiment where you've
+ 
+
+ align:start position:0%
+done a careful experiment where you've
+labeled the cells you've transplanted in
+
+ align:start position:0%
+labeled the cells you've transplanted in
+ 
+
+ align:start position:0%
+labeled the cells you've transplanted in
+so that you can show that they actually
+
+ align:start position:0%
+so that you can show that they actually
+ 
+
+ align:start position:0%
+so that you can show that they actually
+came from the transplanted tissue and
+
+ align:start position:0%
+came from the transplanted tissue and
+ 
+
+ align:start position:0%
+came from the transplanted tissue and
+not from the mouse the nude Mouse tissue
+
+ align:start position:0%
+not from the mouse the nude Mouse tissue
+ 
+
+ align:start position:0%
+not from the mouse the nude Mouse tissue
+and you can do that because you label
+
+ align:start position:0%
+and you can do that because you label
+ 
+
+ align:start position:0%
+and you can do that because you label
+them with gfp and they're green so
+
+ align:start position:0%
+them with gfp and they're green so
+ 
+
+ align:start position:0%
+them with gfp and they're green so
+there's the green hair and it shows you
+
+ align:start position:0%
+there's the green hair and it shows you
+ 
+
+ align:start position:0%
+there's the green hair and it shows you
+that these bulge cells are stem
+
+ align:start position:0%
+that these bulge cells are stem
+ 
+
+ align:start position:0%
+that these bulge cells are stem
+cells during the life of a hair your
+
+ align:start position:0%
+cells during the life of a hair your
+ 
+
+ align:start position:0%
+cells during the life of a hair your
+hair has a life we discussed four years
+
+ align:start position:0%
+hair has a life we discussed four years
+ 
+
+ align:start position:0%
+hair has a life we discussed four years
+on your hair head during the life of a
+
+ align:start position:0%
+on your hair head during the life of a
+ 
+
+ align:start position:0%
+on your hair head during the life of a
+hair the Bulge cells and the niche cells
+
+ align:start position:0%
+hair the Bulge cells and the niche cells
+ 
+
+ align:start position:0%
+hair the Bulge cells and the niche cells
+are of different are in different places
+
+ align:start position:0%
+are of different are in different places
+ 
+
+ align:start position:0%
+are of different are in different places
+and depending on whether they're
+
+ align:start position:0%
+and depending on whether they're
+ 
+
+ align:start position:0%
+and depending on whether they're
+touching or far apart from one another
+
+ align:start position:0%
+touching or far apart from one another
+ 
+
+ align:start position:0%
+touching or far apart from one another
+there's induction of hair growth or not
+
+ align:start position:0%
+there's induction of hair growth or not
+ 
+
+ align:start position:0%
+there's induction of hair growth or not
+so at a particular stage of the hair
+
+ align:start position:0%
+so at a particular stage of the hair
+ 
+
+ align:start position:0%
+so at a particular stage of the hair
+cycle this is called the hair cycle look
+
+ align:start position:0%
+cycle this is called the hair cycle look
+ 
+
+ align:start position:0%
+cycle this is called the hair cycle look
+on the bottom of the screen here the
+
+ align:start position:0%
+on the bottom of the screen here the
+ 
+
+ align:start position:0%
+on the bottom of the screen here the
+Bulge cells and a group of cells called
+
+ align:start position:0%
+Bulge cells and a group of cells called
+ 
+
+ align:start position:0%
+Bulge cells and a group of cells called
+the dermal pillar that lies right at the
+
+ align:start position:0%
+the dermal pillar that lies right at the
+ 
+
+ align:start position:0%
+the dermal pillar that lies right at the
+bottom of the hair shaft are touch ing
+
+ align:start position:0%
+bottom of the hair shaft are touch ing
+ 
+
+ align:start position:0%
+bottom of the hair shaft are touch ing
+one another and at that point a
+
+ align:start position:0%
+one another and at that point a
+ 
+
+ align:start position:0%
+one another and at that point a
+particular signaling pathway called the
+
+ align:start position:0%
+particular signaling pathway called the
+ 
+
+ align:start position:0%
+particular signaling pathway called the
+wi pathway is activated and these dermal
+
+ align:start position:0%
+wi pathway is activated and these dermal
+ 
+
+ align:start position:0%
+wi pathway is activated and these dermal
+pil cells tell the buge Bulge cells to
+
+ align:start position:0%
+pil cells tell the buge Bulge cells to
+ 
+
+ align:start position:0%
+pil cells tell the buge Bulge cells to
+start dividing and start making a new
+
+ align:start position:0%
+start dividing and start making a new
+ 
+
+ align:start position:0%
+start dividing and start making a new
+hair shaft after that's happened the
+
+ align:start position:0%
+hair shaft after that's happened the
+ 
+
+ align:start position:0%
+hair shaft after that's happened the
+Bulge cells move away from the dermal
+
+ align:start position:0%
+Bulge cells move away from the dermal
+ 
+
+ align:start position:0%
+Bulge cells move away from the dermal
+pil cells here they are during growth
+
+ align:start position:0%
+pil cells here they are during growth
+ 
+
+ align:start position:0%
+pil cells here they are during growth
+the growth period you see the Bulge and
+
+ align:start position:0%
+the growth period you see the Bulge and
+ 
+
+ align:start position:0%
+the growth period you see the Bulge and
+the dermal pil cells are no longer
+
+ align:start position:0%
+the dermal pil cells are no longer
+ 
+
+ align:start position:0%
+the dermal pil cells are no longer
+touching at this point the stem cells
+
+ align:start position:0%
+touching at this point the stem cells
+ 
+
+ align:start position:0%
+touching at this point the stem cells
+become quiescent and there are enough
+
+ align:start position:0%
+become quiescent and there are enough
+ 
+
+ align:start position:0%
+become quiescent and there are enough
+progenitor cells in the hair shaft to
+
+ align:start position:0%
+progenitor cells in the hair shaft to
+ 
+
+ align:start position:0%
+progenitor cells in the hair shaft to
+give you formation of the hair and then
+
+ align:start position:0%
+give you formation of the hair and then
+ 
+
+ align:start position:0%
+give you formation of the hair and then
+the stem cells remain quiescent until
+
+ align:start position:0%
+the stem cells remain quiescent until
+ 
+
+ align:start position:0%
+the stem cells remain quiescent until
+the next hair cycle starts and they get
+
+ align:start position:0%
+the next hair cycle starts and they get
+ 
+
+ align:start position:0%
+the next hair cycle starts and they get
+in contact with the dommal pillar again
+
+ align:start position:0%
+in contact with the dommal pillar again
+ 
+
+ align:start position:0%
+in contact with the dommal pillar again
+and start making new hair this is a
+
+ align:start position:0%
+and start making new hair this is a
+ 
+
+ align:start position:0%
+and start making new hair this is a
+really beautiful story that's shown us
+
+ align:start position:0%
+really beautiful story that's shown us
+ 
+
+ align:start position:0%
+really beautiful story that's shown us
+quite clearly how the niche cells can
+
+ align:start position:0%
+quite clearly how the niche cells can
+ 
+
+ align:start position:0%
+quite clearly how the niche cells can
+control these stem
+
+ align:start position:0%
+control these stem
+ 
+
+ align:start position:0%
+control these stem
+cells all right so let's spend the last
+
+ align:start position:0%
+cells all right so let's spend the last
+ 
+
+ align:start position:0%
+cells all right so let's spend the last
+minutes talking about
+
+ align:start position:0%
+minutes talking about
+ 
+
+ align:start position:0%
+minutes talking about
+Therapeutics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the
+
+ align:start position:0%
+here's the
+ 
+
+ align:start position:0%
+here's the
+dream you know the dream is that you
+
+ align:start position:0%
+dream you know the dream is that you
+ 
+
+ align:start position:0%
+dream you know the dream is that you
+have a stem cell population for every
+
+ align:start position:0%
+have a stem cell population for every
+ 
+
+ align:start position:0%
+have a stem cell population for every
+organ in the
+
+ align:start position:0%
+organ in the
+ 
+
+ align:start position:0%
+organ in the
+body including things like
+
+ align:start position:0%
+body including things like
+ 
+
+ align:start position:0%
+body including things like
+limbs such that if your limb gets
+
+ align:start position:0%
+limbs such that if your limb gets
+ 
+
+ align:start position:0%
+limbs such that if your limb gets
+severed or your heart becomes really
+
+ align:start position:0%
+severed or your heart becomes really
+ 
+
+ align:start position:0%
+severed or your heart becomes really
+diseased Ed or your spinal cord is
+
+ align:start position:0%
+diseased Ed or your spinal cord is
+ 
+
+ align:start position:0%
+diseased Ed or your spinal cord is
+injured and you can't walk anymore that
+
+ align:start position:0%
+injured and you can't walk anymore that
+ 
+
+ align:start position:0%
+injured and you can't walk anymore that
+you can just inject into a patient the
+
+ align:start position:0%
+you can just inject into a patient the
+ 
+
+ align:start position:0%
+you can just inject into a patient the
+correct stem cells and everything gets
+
+ align:start position:0%
+correct stem cells and everything gets
+ 
+
+ align:start position:0%
+correct stem cells and everything gets
+repaired that's the dream and that's
+
+ align:start position:0%
+repaired that's the dream and that's
+ 
+
+ align:start position:0%
+repaired that's the dream and that's
+really the Holy Grail of what thousands
+
+ align:start position:0%
+really the Holy Grail of what thousands
+ 
+
+ align:start position:0%
+really the Holy Grail of what thousands
+and thousands of investigators are going
+
+ align:start position:0%
+and thousands of investigators are going
+ 
+
+ align:start position:0%
+and thousands of investigators are going
+after and it's given precedence by bone
+
+ align:start position:0%
+after and it's given precedence by bone
+ 
+
+ align:start position:0%
+after and it's given precedence by bone
+marrow transplants which really are very
+
+ align:start position:0%
+marrow transplants which really are very
+ 
+
+ align:start position:0%
+marrow transplants which really are very
+successful turns out that it's kind of
+
+ align:start position:0%
+successful turns out that it's kind of
+ 
+
+ align:start position:0%
+successful turns out that it's kind of
+tough it's tough because these are ad
+
+ align:start position:0%
+tough it's tough because these are ad
+ 
+
+ align:start position:0%
+tough it's tough because these are ad
+stem cells are really rare the
+
+ align:start position:0%
+stem cells are really rare the
+ 
+
+ align:start position:0%
+stem cells are really rare the
+hematopoetic stem cells are special
+
+ align:start position:0%
+hematopoetic stem cells are special
+ 
+
+ align:start position:0%
+hematopoetic stem cells are special
+because they're kind of liquid they're
+
+ align:start position:0%
+because they're kind of liquid they're
+ 
+
+ align:start position:0%
+because they're kind of liquid they're
+single cells they're not attached to
+
+ align:start position:0%
+single cells they're not attached to
+ 
+
+ align:start position:0%
+single cells they're not attached to
+anything and they are relatively easy to
+
+ align:start position:0%
+anything and they are relatively easy to
+ 
+
+ align:start position:0%
+anything and they are relatively easy to
+identify but other stem cells are very
+
+ align:start position:0%
+identify but other stem cells are very
+ 
+
+ align:start position:0%
+identify but other stem cells are very
+difficult so the
+
+ align:start position:0%
+difficult so the
+ 
+
+ align:start position:0%
+difficult so the
+idea is that you inject stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells to repair a damaged
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+organ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you need stem cells of the correct
+
+ align:start position:0%
+you need stem cells of the correct
+ 
+
+ align:start position:0%
+you need stem cells of the correct
+potency otherwise you're not going to
+
+ align:start position:0%
+potency otherwise you're not going to
+ 
+
+ align:start position:0%
+potency otherwise you're not going to
+repair the specific
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+organ but adult stem cells are very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rare and so the quest has been to find
+
+ align:start position:0%
+rare and so the quest has been to find
+ 
+
+ align:start position:0%
+rare and so the quest has been to find
+some kind of substitute for adult stem
+
+ align:start position:0%
+some kind of substitute for adult stem
+ 
+
+ align:start position:0%
+some kind of substitute for adult stem
+cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+substitutes come in two
+
+ align:start position:0%
+substitutes come in two
+ 
+
+ align:start position:0%
+substitutes come in two
+flavors one Are embryonic stem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells abbreviated
+
+ align:start position:0%
+cells abbreviated
+ 
+
+ align:start position:0%
+cells abbreviated
+esc's embryonic stem cells are cells
+
+ align:start position:0%
+esc's embryonic stem cells are cells
+ 
+
+ align:start position:0%
+esc's embryonic stem cells are cells
+that grow from the Inner Cell mass of an
+
+ align:start position:0%
+that grow from the Inner Cell mass of an
+ 
+
+ align:start position:0%
+that grow from the Inner Cell mass of an
+early mamalian embryo and you can grow
+
+ align:start position:0%
+early mamalian embryo and you can grow
+ 
+
+ align:start position:0%
+early mamalian embryo and you can grow
+from the them groups of cells that will
+
+ align:start position:0%
+from the them groups of cells that will
+ 
+
+ align:start position:0%
+from the them groups of cells that will
+keep growing in the laboratory for a
+
+ align:start position:0%
+keep growing in the laboratory for a
+ 
+
+ align:start position:0%
+keep growing in the laboratory for a
+long time and have variable potency so
+
+ align:start position:0%
+long time and have variable potency so
+ 
+
+ align:start position:0%
+long time and have variable potency so
+the embryon stem cells are
+
+ align:start position:0%
+the embryon stem cells are
+ 
+
+ align:start position:0%
+the embryon stem cells are
+derived from the Inner Cell
+
+ align:start position:0%
+derived from the Inner Cell
+ 
+
+ align:start position:0%
+derived from the Inner Cell
+mass of an early mamalian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+embryo human in the case of
+
+ align:start position:0%
+embryo human in the case of
+ 
+
+ align:start position:0%
+embryo human in the case of
+human
+
+ align:start position:0%
+human
+ 
+
+ align:start position:0%
+human
+and you grow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out so-called ESC
+
+ align:start position:0%
+out so-called ESC
+ 
+
+ align:start position:0%
+out so-called ESC
+lines which means that these cells grow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuously in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+culture and each embryonic stem cell
+
+ align:start position:0%
+culture and each embryonic stem cell
+ 
+
+ align:start position:0%
+culture and each embryonic stem cell
+line has a unique potency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and can be used to do different things
+
+ align:start position:0%
+and can be used to do different things
+ 
+
+ align:start position:0%
+and can be used to do different things
+in terms of theoretical repair if you
+
+ align:start position:0%
+in terms of theoretical repair if you
+ 
+
+ align:start position:0%
+in terms of theoretical repair if you
+look on your next handout the idea is
+
+ align:start position:0%
+look on your next handout the idea is
+ 
+
+ align:start position:0%
+look on your next handout the idea is
+that you take this Inner Cell Mass you
+
+ align:start position:0%
+that you take this Inner Cell Mass you
+ 
+
+ align:start position:0%
+that you take this Inner Cell Mass you
+plate the cells as single
+
+ align:start position:0%
+plate the cells as single
+ 
+
+ align:start position:0%
+plate the cells as single
+cells they grow and grow and
+
+ align:start position:0%
+cells they grow and grow and
+ 
+
+ align:start position:0%
+cells they grow and grow and
+grow and if you treat them with various
+
+ align:start position:0%
+grow and if you treat them with various
+ 
+
+ align:start position:0%
+grow and if you treat them with various
+indues you can get them to become hot or
+
+ align:start position:0%
+indues you can get them to become hot or
+ 
+
+ align:start position:0%
+indues you can get them to become hot or
+neuron genitors inject those into
+
+ align:start position:0%
+neuron genitors inject those into
+ 
+
+ align:start position:0%
+neuron genitors inject those into
+animals and make them better there's
+
+ align:start position:0%
+animals and make them better there's
+ 
+
+ align:start position:0%
+animals and make them better there's
+some issues with embryonic stem
+
+ align:start position:0%
+some issues with embryonic stem
+ 
+
+ align:start position:0%
+some issues with embryonic stem
+cells and the
+
+ align:start position:0%
+cells and the
+ 
+
+ align:start position:0%
+cells and the
+problems are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+twofold one is
+
+ align:start position:0%
+twofold one is
+ 
+
+ align:start position:0%
+twofold one is
+ethical in
+
+ align:start position:0%
+ethical in
+ 
+
+ align:start position:0%
+ethical in
+that you have to harest human embryos
+
+ align:start position:0%
+that you have to harest human embryos
+ 
+
+ align:start position:0%
+that you have to harest human embryos
+you have to obtain and harvest human
+
+ align:start position:0%
+you have to obtain and harvest human
+ 
+
+ align:start position:0%
+you have to obtain and harvest human
+embryos to get these human stem cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lines and currently you're really not
+
+ align:start position:0%
+lines and currently you're really not
+ 
+
+ align:start position:0%
+lines and currently you're really not
+allowed to do much human embryo work to
+
+ align:start position:0%
+allowed to do much human embryo work to
+ 
+
+ align:start position:0%
+allowed to do much human embryo work to
+obtain human stem cells but the second
+
+ align:start position:0%
+obtain human stem cells but the second
+ 
+
+ align:start position:0%
+obtain human stem cells but the second
+even if you were is that these cells are
+
+ align:start position:0%
+even if you were is that these cells are
+ 
+
+ align:start position:0%
+even if you were is that these cells are
+non
+
+ align:start position:0%
+non
+ 
+
+ align:start position:0%
+non
+autologous they do not
+
+ align:start position:0%
+autologous they do not
+ 
+
+ align:start position:0%
+autologous they do not
+match the
+
+ align:start position:0%
+match the
+ 
+
+ align:start position:0%
+match the
+person into which you're putting them
+
+ align:start position:0%
+person into which you're putting them
+ 
+
+ align:start position:0%
+person into which you're putting them
+they do not match the immune system of
+
+ align:start position:0%
+they do not match the immune system of
+ 
+
+ align:start position:0%
+they do not match the immune system of
+the recipient and so they'll be rejected
+
+ align:start position:0%
+the recipient and so they'll be rejected
+ 
+
+ align:start position:0%
+the recipient and so they'll be rejected
+and it's the same as an organ transplant
+
+ align:start position:0%
+and it's the same as an organ transplant
+ 
+
+ align:start position:0%
+and it's the same as an organ transplant
+you have lots of problems of
+
+ align:start position:0%
+you have lots of problems of
+ 
+
+ align:start position:0%
+you have lots of problems of
+rejection so the latest thing that is
+
+ align:start position:0%
+rejection so the latest thing that is
+ 
+
+ align:start position:0%
+rejection so the latest thing that is
+very exciting and wonderful and
+
+ align:start position:0%
+very exciting and wonderful and
+ 
+
+ align:start position:0%
+very exciting and wonderful and
+potentially might be very useful is the
+
+ align:start position:0%
+potentially might be very useful is the
+ 
+
+ align:start position:0%
+potentially might be very useful is the
+use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of things called IPS cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in which you convert adult
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells into stem
+
+ align:start position:0%
+cells into stem
+ 
+
+ align:start position:0%
+cells into stem
+cells and you do so as I'll Tell You by
+
+ align:start position:0%
+cells and you do so as I'll Tell You by
+ 
+
+ align:start position:0%
+cells and you do so as I'll Tell You by
+adding some transcription factors to
+
+ align:start position:0%
+adding some transcription factors to
+ 
+
+ align:start position:0%
+adding some transcription factors to
+them the advantage of these is that they
+
+ align:start position:0%
+them the advantage of these is that they
+ 
+
+ align:start position:0%
+them the advantage of these is that they
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+self cells you could do them from
+
+ align:start position:0%
+self cells you could do them from
+ 
+
+ align:start position:0%
+self cells you could do them from
+yourself the disadvantage is that
+
+ align:start position:0%
+yourself the disadvantage is that
+ 
+
+ align:start position:0%
+yourself the disadvantage is that
+they're really not proven
+
+ align:start position:0%
+they're really not proven
+ 
+
+ align:start position:0%
+they're really not proven
+and there are still I will just say lots
+
+ align:start position:0%
+and there are still I will just say lots
+ 
+
+ align:start position:0%
+and there are still I will just say lots
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems but there are a lot of people
+
+ align:start position:0%
+problems but there are a lot of people
+ 
+
+ align:start position:0%
+problems but there are a lot of people
+including some of the top investigators
+
+ align:start position:0%
+including some of the top investigators
+ 
+
+ align:start position:0%
+including some of the top investigators
+in the world working on these IPS cells
+
+ align:start position:0%
+in the world working on these IPS cells
+ 
+
+ align:start position:0%
+in the world working on these IPS cells
+so look at your last
+
+ align:start position:0%
+so look at your last
+ 
+
+ align:start position:0%
+so look at your last
+handout we will remove
+
+ align:start position:0%
+handout we will remove
+ 
+
+ align:start position:0%
+handout we will remove
+our interesting calendar reminders there
+
+ align:start position:0%
+our interesting calendar reminders there
+ 
+
+ align:start position:0%
+our interesting calendar reminders there
+adult differentiated cells which are
+
+ align:start position:0%
+adult differentiated cells which are
+ 
+
+ align:start position:0%
+adult differentiated cells which are
+unipotent can be treated with three or
+
+ align:start position:0%
+unipotent can be treated with three or
+ 
+
+ align:start position:0%
+unipotent can be treated with three or
+four transcription factors and finding
+
+ align:start position:0%
+four transcription factors and finding
+ 
+
+ align:start position:0%
+four transcription factors and finding
+these transcription factors was the key
+
+ align:start position:0%
+these transcription factors was the key
+ 
+
+ align:start position:0%
+these transcription factors was the key
+and once you express these transcription
+
+ align:start position:0%
+and once you express these transcription
+ 
+
+ align:start position:0%
+and once you express these transcription
+factors in these adult cells like magic
+
+ align:start position:0%
+factors in these adult cells like magic
+ 
+
+ align:start position:0%
+factors in these adult cells like magic
+they become stem cells it really was
+
+ align:start position:0%
+they become stem cells it really was
+ 
+
+ align:start position:0%
+they become stem cells it really was
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+magic you can test the potency of these
+
+ align:start position:0%
+magic you can test the potency of these
+ 
+
+ align:start position:0%
+magic you can test the potency of these
+stem cells in the same way we discussed
+
+ align:start position:0%
+stem cells in the same way we discussed
+ 
+
+ align:start position:0%
+stem cells in the same way we discussed
+and professor yamanaka in Japan and
+
+ align:start position:0%
+and professor yamanaka in Japan and
+ 
+
+ align:start position:0%
+and professor yamanaka in Japan and
+Professor yanish here have shown that
+
+ align:start position:0%
+Professor yanish here have shown that
+ 
+
+ align:start position:0%
+Professor yanish here have shown that
+these are really very powerful cells
+
+ align:start position:0%
+these are really very powerful cells
+ 
+
+ align:start position:0%
+these are really very powerful cells
+and those are the promise of the future
+
+ align:start position:0%
+and those are the promise of the future
+ 
+
+ align:start position:0%
+and those are the promise of the future
+and we'll stop there and meet on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Friday
\ No newline at end of file
diff --git a/6BPDK1b3jDg.txt b/6BPDK1b3jDg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f4d6f3f78d310de9a0a5a2e5629ad27bc5dd4226
--- /dev/null
+++ b/6BPDK1b3jDg.txt
@@ -0,0 +1,8651 @@
+align:start position:0%
+ 
+so the big issue that we're trying I was
+
+ align:start position:0%
+so the big issue that we're trying I was
+ 
+
+ align:start position:0%
+so the big issue that we're trying I was
+trying to take on yesterday and this is
+
+ align:start position:0%
+trying to take on yesterday and this is
+ 
+
+ align:start position:0%
+trying to take on yesterday and this is
+of really fundamental importance to
+
+ align:start position:0%
+of really fundamental importance to
+ 
+
+ align:start position:0%
+of really fundamental importance to
+biology is you saw from that that
+
+ align:start position:0%
+biology is you saw from that that
+ 
+
+ align:start position:0%
+biology is you saw from that that
+molecular composition of cells 80% water
+
+ align:start position:0%
+molecular composition of cells 80% water
+ 
+
+ align:start position:0%
+molecular composition of cells 80% water
+of the rest of it about 50% of what
+
+ align:start position:0%
+of the rest of it about 50% of what
+ 
+
+ align:start position:0%
+of the rest of it about 50% of what
+there what's there by mass is is protein
+
+ align:start position:0%
+there what's there by mass is is protein
+ 
+
+ align:start position:0%
+there what's there by mass is is protein
+proteins do most of the really
+
+ align:start position:0%
+proteins do most of the really
+ 
+
+ align:start position:0%
+proteins do most of the really
+interesting stuff in the cell they're
+
+ align:start position:0%
+interesting stuff in the cell they're
+ 
+
+ align:start position:0%
+interesting stuff in the cell they're
+the ones that are able to catalyze
+
+ align:start position:0%
+the ones that are able to catalyze
+ 
+
+ align:start position:0%
+the ones that are able to catalyze
+specific chemical reactions with lets
+
+ align:start position:0%
+specific chemical reactions with lets
+ 
+
+ align:start position:0%
+specific chemical reactions with lets
+all this amazing chemistry
+
+ align:start position:0%
+all this amazing chemistry
+ 
+
+ align:start position:0%
+all this amazing chemistry
+Tak uh that's needed for Life take place
+
+ align:start position:0%
+Tak uh that's needed for Life take place
+ 
+
+ align:start position:0%
+Tak uh that's needed for Life take place
+at physiological conditions um their
+
+ align:start position:0%
+at physiological conditions um their
+ 
+
+ align:start position:0%
+at physiological conditions um their
+structural components of the cells they
+
+ align:start position:0%
+structural components of the cells they
+ 
+
+ align:start position:0%
+structural components of the cells they
+are all kinds of amazing machines I've
+
+ align:start position:0%
+are all kinds of amazing machines I've
+ 
+
+ align:start position:0%
+are all kinds of amazing machines I've
+showed you the little flugel motor that
+
+ align:start position:0%
+showed you the little flugel motor that
+ 
+
+ align:start position:0%
+showed you the little flugel motor that
+turns it but that's just one of many
+
+ align:start position:0%
+turns it but that's just one of many
+ 
+
+ align:start position:0%
+turns it but that's just one of many
+many nanom machines that are necessary
+
+ align:start position:0%
+many nanom machines that are necessary
+ 
+
+ align:start position:0%
+many nanom machines that are necessary
+uh for life they have in Exquisite
+
+ align:start position:0%
+uh for life they have in Exquisite
+ 
+
+ align:start position:0%
+uh for life they have in Exquisite
+specificity when you get sick and you
+
+ align:start position:0%
+specificity when you get sick and you
+ 
+
+ align:start position:0%
+specificity when you get sick and you
+get an immune response you develop
+
+ align:start position:0%
+get an immune response you develop
+ 
+
+ align:start position:0%
+get an immune response you develop
+antibodies and other cells that are able
+
+ align:start position:0%
+antibodies and other cells that are able
+ 
+
+ align:start position:0%
+antibodies and other cells that are able
+to rec recognize exactly the some piece
+
+ align:start position:0%
+to rec recognize exactly the some piece
+ 
+
+ align:start position:0%
+to rec recognize exactly the some piece
+of that virus or or
+
+ align:start position:0%
+of that virus or or
+ 
+
+ align:start position:0%
+of that virus or or
+um or bacterium that's infected you and
+
+ align:start position:0%
+um or bacterium that's infected you and
+ 
+
+ align:start position:0%
+um or bacterium that's infected you and
+mount an immune response but all of the
+
+ align:start position:0%
+mount an immune response but all of the
+ 
+
+ align:start position:0%
+mount an immune response but all of the
+things that are doing that are
+
+ align:start position:0%
+things that are doing that are
+ 
+
+ align:start position:0%
+things that are doing that are
+proteins and the sort of most of you I
+
+ align:start position:0%
+proteins and the sort of most of you I
+ 
+
+ align:start position:0%
+proteins and the sort of most of you I
+think know that we've sort of said that
+
+ align:start position:0%
+think know that we've sort of said that
+ 
+
+ align:start position:0%
+think know that we've sort of said that
+amino acids are just a
+
+ align:start position:0%
+amino acids are just a
+ 
+
+ align:start position:0%
+amino acids are just a
+chain of one amino acid joined to
+
+ align:start position:0%
+chain of one amino acid joined to
+ 
+
+ align:start position:0%
+chain of one amino acid joined to
+another amino
+
+ align:start position:0%
+another amino
+ 
+
+ align:start position:0%
+another amino
+acid to another amino
+
+ align:start position:0%
+acid to another amino
+ 
+
+ align:start position:0%
+acid to another amino
+acid and then and and so on and the
+
+ align:start position:0%
+acid and then and and so on and the
+ 
+
+ align:start position:0%
+acid and then and and so on and the
+what's so the backbone that peptide bond
+
+ align:start position:0%
+what's so the backbone that peptide bond
+ 
+
+ align:start position:0%
+what's so the backbone that peptide bond
+that I showed the other day is
+
+ align:start position:0%
+that I showed the other day is
+ 
+
+ align:start position:0%
+that I showed the other day is
+absolutely regular piece of backbone and
+
+ align:start position:0%
+absolutely regular piece of backbone and
+ 
+
+ align:start position:0%
+absolutely regular piece of backbone and
+what gives the the
+
+ align:start position:0%
+what gives the the
+ 
+
+ align:start position:0%
+what gives the the
+uh the thing the amino acids their
+
+ align:start position:0%
+uh the thing the amino acids their
+ 
+
+ align:start position:0%
+uh the thing the amino acids their
+character is the side chain that hangs
+
+ align:start position:0%
+character is the side chain that hangs
+ 
+
+ align:start position:0%
+character is the side chain that hangs
+off and you'll have different side
+
+ align:start position:0%
+off and you'll have different side
+ 
+
+ align:start position:0%
+off and you'll have different side
+chains hanging off depending on what the
+
+ align:start position:0%
+chains hanging off depending on what the
+ 
+
+ align:start position:0%
+chains hanging off depending on what the
+amino acid is and and you will not have
+
+ align:start position:0%
+amino acid is and and you will not have
+ 
+
+ align:start position:0%
+amino acid is and and you will not have
+to memorize all of those uh structures
+
+ align:start position:0%
+to memorize all of those uh structures
+ 
+
+ align:start position:0%
+to memorize all of those uh structures
+but the important thing is that these
+
+ align:start position:0%
+but the important thing is that these
+ 
+
+ align:start position:0%
+but the important thing is that these
+various amino acids fit into chemical
+
+ align:start position:0%
+various amino acids fit into chemical
+ 
+
+ align:start position:0%
+various amino acids fit into chemical
+categories that give them properties
+
+ align:start position:0%
+categories that give them properties
+ 
+
+ align:start position:0%
+categories that give them properties
+they either have a plus charge and
+
+ align:start position:0%
+they either have a plus charge and
+ 
+
+ align:start position:0%
+they either have a plus charge and
+negative charge um they're hydrophobic
+
+ align:start position:0%
+negative charge um they're hydrophobic
+ 
+
+ align:start position:0%
+negative charge um they're hydrophobic
+they don't like to with water they're
+
+ align:start position:0%
+they don't like to with water they're
+ 
+
+ align:start position:0%
+they don't like to with water they're
+polar they can't interact with water and
+
+ align:start position:0%
+polar they can't interact with water and
+ 
+
+ align:start position:0%
+polar they can't interact with water and
+so on and it's clear to you clear from a
+
+ align:start position:0%
+so on and it's clear to you clear from a
+ 
+
+ align:start position:0%
+so on and it's clear to you clear from a
+couple of your comments some of you why
+
+ align:start position:0%
+couple of your comments some of you why
+ 
+
+ align:start position:0%
+couple of your comments some of you why
+are we going through all of this well
+
+ align:start position:0%
+are we going through all of this well
+ 
+
+ align:start position:0%
+are we going through all of this well
+the reason we're going through all of
+
+ align:start position:0%
+the reason we're going through all of
+ 
+
+ align:start position:0%
+the reason we're going through all of
+this is all amino acids look like this
+
+ align:start position:0%
+this is all amino acids look like this
+ 
+
+ align:start position:0%
+this is all amino acids look like this
+it doesn't matter if they're going to be
+
+ align:start position:0%
+it doesn't matter if they're going to be
+ 
+
+ align:start position:0%
+it doesn't matter if they're going to be
+an enzyme part of a motor a structural
+
+ align:start position:0%
+an enzyme part of a motor a structural
+ 
+
+ align:start position:0%
+an enzyme part of a motor a structural
+part of your cells they all consist of
+
+ align:start position:0%
+part of your cells they all consist of
+ 
+
+ align:start position:0%
+part of your cells they all consist of
+the same backbone made up of those 20
+
+ align:start position:0%
+the same backbone made up of those 20
+ 
+
+ align:start position:0%
+the same backbone made up of those 20
+amino acids and what gives the makes uh
+
+ align:start position:0%
+amino acids and what gives the makes uh
+ 
+
+ align:start position:0%
+amino acids and what gives the makes uh
+um the proteins so important is the
+
+ align:start position:0%
+um the proteins so important is the
+ 
+
+ align:start position:0%
+um the proteins so important is the
+ultimate three-dimensional structure I'm
+
+ align:start position:0%
+ultimate three-dimensional structure I'm
+ 
+
+ align:start position:0%
+ultimate three-dimensional structure I'm
+not sure what the sound
+
+ align:start position:0%
+not sure what the sound
+ 
+
+ align:start position:0%
+not sure what the sound
+is okay let's try standing back here um
+
+ align:start position:0%
+is okay let's try standing back here um
+ 
+
+ align:start position:0%
+is okay let's try standing back here um
+uh what gives the uh all these proteins
+
+ align:start position:0%
+uh what gives the uh all these proteins
+ 
+
+ align:start position:0%
+uh what gives the uh all these proteins
+their individual character is how this
+
+ align:start position:0%
+their individual character is how this
+ 
+
+ align:start position:0%
+their individual character is how this
+chain of amino acids you could just
+
+ align:start position:0%
+chain of amino acids you could just
+ 
+
+ align:start position:0%
+chain of amino acids you could just
+think of them like this folds up into
+
+ align:start position:0%
+think of them like this folds up into
+ 
+
+ align:start position:0%
+think of them like this folds up into
+some three-dimensional structure that
+
+ align:start position:0%
+some three-dimensional structure that
+ 
+
+ align:start position:0%
+some three-dimensional structure that
+ultimately is able to to do the
+
+ align:start position:0%
+ultimately is able to to do the
+ 
+
+ align:start position:0%
+ultimately is able to to do the
+biological function that we're um we're
+
+ align:start position:0%
+biological function that we're um we're
+ 
+
+ align:start position:0%
+biological function that we're um we're
+trying to understand and one of the real
+
+ align:start position:0%
+trying to understand and one of the real
+ 
+
+ align:start position:0%
+trying to understand and one of the real
+holy Grails still in biology is how to
+
+ align:start position:0%
+holy Grails still in biology is how to
+ 
+
+ align:start position:0%
+holy Grails still in biology is how to
+look at the sequence of amino acids that
+
+ align:start position:0%
+look at the sequence of amino acids that
+ 
+
+ align:start position:0%
+look at the sequence of amino acids that
+constitute a protein and figure out what
+
+ align:start position:0%
+constitute a protein and figure out what
+ 
+
+ align:start position:0%
+constitute a protein and figure out what
+the three-dimensional structure is it's
+
+ align:start position:0%
+the three-dimensional structure is it's
+ 
+
+ align:start position:0%
+the three-dimensional structure is it's
+one of the Holy Grails that hasn't been
+
+ align:start position:0%
+one of the Holy Grails that hasn't been
+ 
+
+ align:start position:0%
+one of the Holy Grails that hasn't been
+solved one of you may have a key Insight
+
+ align:start position:0%
+solved one of you may have a key Insight
+ 
+
+ align:start position:0%
+solved one of you may have a key Insight
+that that will solve this if we could do
+
+ align:start position:0%
+that that will solve this if we could do
+ 
+
+ align:start position:0%
+that that will solve this if we could do
+that uh would really be a huge Advance
+
+ align:start position:0%
+that uh would really be a huge Advance
+ 
+
+ align:start position:0%
+that uh would really be a huge Advance
+because what you can get out of the
+
+ align:start position:0%
+because what you can get out of the
+ 
+
+ align:start position:0%
+because what you can get out of the
+genome uh sequences is you can read the
+
+ align:start position:0%
+genome uh sequences is you can read the
+ 
+
+ align:start position:0%
+genome uh sequences is you can read the
+sequence of every Gene and you can
+
+ align:start position:0%
+sequence of every Gene and you can
+ 
+
+ align:start position:0%
+sequence of every Gene and you can
+predict the sequence of amino acids in
+
+ align:start position:0%
+predict the sequence of amino acids in
+ 
+
+ align:start position:0%
+predict the sequence of amino acids in
+the protein but all it tells you is the
+
+ align:start position:0%
+the protein but all it tells you is the
+ 
+
+ align:start position:0%
+the protein but all it tells you is the
+linear the linear sequence of the uh
+
+ align:start position:0%
+linear the linear sequence of the uh
+ 
+
+ align:start position:0%
+linear the linear sequence of the uh
+amino acids it doesn't tell you what the
+
+ align:start position:0%
+amino acids it doesn't tell you what the
+ 
+
+ align:start position:0%
+amino acids it doesn't tell you what the
+three-dimensional structure is and how
+
+ align:start position:0%
+three-dimensional structure is and how
+ 
+
+ align:start position:0%
+three-dimensional structure is and how
+it gets how an amino acid gets from a
+
+ align:start position:0%
+it gets how an amino acid gets from a
+ 
+
+ align:start position:0%
+it gets how an amino acid gets from a
+sort of floppy chain in the linear
+
+ align:start position:0%
+sort of floppy chain in the linear
+ 
+
+ align:start position:0%
+sort of floppy chain in the linear
+structure to the three-dimensional thing
+
+ align:start position:0%
+structure to the three-dimensional thing
+ 
+
+ align:start position:0%
+structure to the three-dimensional thing
+is complicated and you have to
+
+ align:start position:0%
+is complicated and you have to
+ 
+
+ align:start position:0%
+is complicated and you have to
+understand several kinds of of forces
+
+ align:start position:0%
+understand several kinds of of forces
+ 
+
+ align:start position:0%
+understand several kinds of of forces
+and so I introduced a few terms the when
+
+ align:start position:0%
+and so I introduced a few terms the when
+ 
+
+ align:start position:0%
+and so I introduced a few terms the when
+we think about protein structure the
+
+ align:start position:0%
+we think about protein structure the
+ 
+
+ align:start position:0%
+we think about protein structure the
+primary structure that's just the linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of amino acids so veiling followed by a
+
+ align:start position:0%
+of amino acids so veiling followed by a
+ 
+
+ align:start position:0%
+of amino acids so veiling followed by a
+tryptophane followed by a ProLine
+
+ align:start position:0%
+tryptophane followed by a ProLine
+ 
+
+ align:start position:0%
+tryptophane followed by a ProLine
+followed by a thine whatever it would be
+
+ align:start position:0%
+followed by a thine whatever it would be
+ 
+
+ align:start position:0%
+followed by a thine whatever it would be
+that doesn't tell you very much then the
+
+ align:start position:0%
+that doesn't tell you very much then the
+ 
+
+ align:start position:0%
+that doesn't tell you very much then the
+first key part of understanding how
+
+ align:start position:0%
+first key part of understanding how
+ 
+
+ align:start position:0%
+first key part of understanding how
+proteins get to a three-dimensional
+
+ align:start position:0%
+proteins get to a three-dimensional
+ 
+
+ align:start position:0%
+proteins get to a three-dimensional
+structure was the discovery of what's
+
+ align:start position:0%
+structure was the discovery of what's
+ 
+
+ align:start position:0%
+structure was the discovery of what's
+termed secondary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure and these are the things I
+
+ align:start position:0%
+structure and these are the things I
+ 
+
+ align:start position:0%
+structure and these are the things I
+introduced to the other day there's two
+
+ align:start position:0%
+introduced to the other day there's two
+ 
+
+ align:start position:0%
+introduced to the other day there's two
+important ones an Al Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Helix and a beta sheet and this is a
+
+ align:start position:0%
+Helix and a beta sheet and this is a
+ 
+
+ align:start position:0%
+Helix and a beta sheet and this is a
+propensity of a certain string of amino
+
+ align:start position:0%
+propensity of a certain string of amino
+ 
+
+ align:start position:0%
+propensity of a certain string of amino
+acids in this linear sequence to adopt
+
+ align:start position:0%
+acids in this linear sequence to adopt
+ 
+
+ align:start position:0%
+acids in this linear sequence to adopt
+one of
+
+ align:start position:0%
+one of
+ 
+
+ align:start position:0%
+one of
+two uh very common protein structures
+
+ align:start position:0%
+two uh very common protein structures
+ 
+
+ align:start position:0%
+two uh very common protein structures
+and then the important thing about these
+
+ align:start position:0%
+and then the important thing about these
+ 
+
+ align:start position:0%
+and then the important thing about these
+uh elements the the Alpha helices and
+
+ align:start position:0%
+uh elements the the Alpha helices and
+ 
+
+ align:start position:0%
+uh elements the the Alpha helices and
+the beta sheets is they are not not
+
+ align:start position:0%
+the beta sheets is they are not not
+ 
+
+ align:start position:0%
+the beta sheets is they are not not
+dependent on the side chain so they're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not they're instead dependent on
+
+ align:start position:0%
+not they're instead dependent on
+ 
+
+ align:start position:0%
+not they're instead dependent on
+hydrogen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+NH and and the uh carbon double bond
+
+ align:start position:0%
+NH and and the uh carbon double bond
+ 
+
+ align:start position:0%
+NH and and the uh carbon double bond
+oxygen in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+backbone and that was how um lonus
+
+ align:start position:0%
+backbone and that was how um lonus
+ 
+
+ align:start position:0%
+backbone and that was how um lonus
+Pauling figured out originally the alpha
+
+ align:start position:0%
+Pauling figured out originally the alpha
+ 
+
+ align:start position:0%
+Pauling figured out originally the alpha
+Helix he decided to ignore all the side
+
+ align:start position:0%
+Helix he decided to ignore all the side
+ 
+
+ align:start position:0%
+Helix he decided to ignore all the side
+chains and he worked out that you could
+
+ align:start position:0%
+chains and he worked out that you could
+ 
+
+ align:start position:0%
+chains and he worked out that you could
+arrange the backbone of a protein the
+
+ align:start position:0%
+arrange the backbone of a protein the
+ 
+
+ align:start position:0%
+arrange the backbone of a protein the
+peptide bonds into these repeating
+
+ align:start position:0%
+peptide bonds into these repeating
+ 
+
+ align:start position:0%
+peptide bonds into these repeating
+structures that would account for the
+
+ align:start position:0%
+structures that would account for the
+ 
+
+ align:start position:0%
+structures that would account for the
+reflections he'd seen when we get to
+
+ align:start position:0%
+reflections he'd seen when we get to
+ 
+
+ align:start position:0%
+reflections he'd seen when we get to
+talking about how Watson and Crick
+
+ align:start position:0%
+talking about how Watson and Crick
+ 
+
+ align:start position:0%
+talking about how Watson and Crick
+worked out the structure that's how they
+
+ align:start position:0%
+worked out the structure that's how they
+ 
+
+ align:start position:0%
+worked out the structure that's how they
+started out too they decided to ignore
+
+ align:start position:0%
+started out too they decided to ignore
+ 
+
+ align:start position:0%
+started out too they decided to ignore
+if you will the side chain which are the
+
+ align:start position:0%
+if you will the side chain which are the
+ 
+
+ align:start position:0%
+if you will the side chain which are the
+A and G's and C's and T's which turned
+
+ align:start position:0%
+A and G's and C's and T's which turned
+ 
+
+ align:start position:0%
+A and G's and C's and T's which turned
+out to be not a productive way to go
+
+ align:start position:0%
+out to be not a productive way to go
+ 
+
+ align:start position:0%
+out to be not a productive way to go
+after the structure of DNA but in any
+
+ align:start position:0%
+after the structure of DNA but in any
+ 
+
+ align:start position:0%
+after the structure of DNA but in any
+case that was part of
+
+ align:start position:0%
+case that was part of
+ 
+
+ align:start position:0%
+case that was part of
+what lonus Pauling did in working these
+
+ align:start position:0%
+what lonus Pauling did in working these
+ 
+
+ align:start position:0%
+what lonus Pauling did in working these
+out and so those little movies I I
+
+ align:start position:0%
+out and so those little movies I I
+ 
+
+ align:start position:0%
+out and so those little movies I I
+showed you this is an alpha Helix now
+
+ align:start position:0%
+showed you this is an alpha Helix now
+ 
+
+ align:start position:0%
+showed you this is an alpha Helix now
+what has what's been done in this
+
+ align:start position:0%
+what has what's been done in this
+ 
+
+ align:start position:0%
+what has what's been done in this
+picture is all the side chains have been
+
+ align:start position:0%
+picture is all the side chains have been
+ 
+
+ align:start position:0%
+picture is all the side chains have been
+taken off and so you can look at look at
+
+ align:start position:0%
+taken off and so you can look at look at
+ 
+
+ align:start position:0%
+taken off and so you can look at look at
+this in your textbook you'll you you'll
+
+ align:start position:0%
+this in your textbook you'll you you'll
+ 
+
+ align:start position:0%
+this in your textbook you'll you you'll
+see pictures but these hydrogen bonds
+
+ align:start position:0%
+see pictures but these hydrogen bonds
+ 
+
+ align:start position:0%
+see pictures but these hydrogen bonds
+are the the the amino acid is just in
+
+ align:start position:0%
+are the the the amino acid is just in
+ 
+
+ align:start position:0%
+are the the the amino acid is just in
+this Helix it's coiling around and at
+
+ align:start position:0%
+this Helix it's coiling around and at
+ 
+
+ align:start position:0%
+this Helix it's coiling around and at
+regular intervals there's the
+
+ align:start position:0%
+regular intervals there's the
+ 
+
+ align:start position:0%
+regular intervals there's the
+opportunity for forming a hydrogen bond
+
+ align:start position:0%
+opportunity for forming a hydrogen bond
+ 
+
+ align:start position:0%
+opportunity for forming a hydrogen bond
+and we can with some success but
+
+ align:start position:0%
+and we can with some success but
+ 
+
+ align:start position:0%
+and we can with some success but
+certainly not certainty predict that a
+
+ align:start position:0%
+certainly not certainty predict that a
+ 
+
+ align:start position:0%
+certainly not certainty predict that a
+particular sequence of amino acids is
+
+ align:start position:0%
+particular sequence of amino acids is
+ 
+
+ align:start position:0%
+particular sequence of amino acids is
+going to uh form an alpha Helix and part
+
+ align:start position:0%
+going to uh form an alpha Helix and part
+ 
+
+ align:start position:0%
+going to uh form an alpha Helix and part
+of what that's based on is there's some
+
+ align:start position:0%
+of what that's based on is there's some
+ 
+
+ align:start position:0%
+of what that's based on is there's some
+amino acids that don't fit easily into
+
+ align:start position:0%
+amino acids that don't fit easily into
+ 
+
+ align:start position:0%
+amino acids that don't fit easily into
+an alpha Helix so they'll disrupt one if
+
+ align:start position:0%
+an alpha Helix so they'll disrupt one if
+ 
+
+ align:start position:0%
+an alpha Helix so they'll disrupt one if
+it would ever tried to form so that's
+
+ align:start position:0%
+it would ever tried to form so that's
+ 
+
+ align:start position:0%
+it would ever tried to form so that's
+one of the elements of protein
+
+ align:start position:0%
+one of the elements of protein
+ 
+
+ align:start position:0%
+one of the elements of protein
+structures so what you might get from
+
+ align:start position:0%
+structures so what you might get from
+ 
+
+ align:start position:0%
+structures so what you might get from
+this is the idea that somewhere along
+
+ align:start position:0%
+this is the idea that somewhere along
+ 
+
+ align:start position:0%
+this is the idea that somewhere along
+here this little piece of the linear
+
+ align:start position:0%
+here this little piece of the linear
+ 
+
+ align:start position:0%
+here this little piece of the linear
+sequence is apt to be an alah Helix and
+
+ align:start position:0%
+sequence is apt to be an alah Helix and
+ 
+
+ align:start position:0%
+sequence is apt to be an alah Helix and
+you can represent that as this little
+
+ align:start position:0%
+you can represent that as this little
+ 
+
+ align:start position:0%
+you can represent that as this little
+sort of coil that you've seen in these
+
+ align:start position:0%
+sort of coil that you've seen in these
+ 
+
+ align:start position:0%
+sort of coil that you've seen in these
+three-dimensional structures the other
+
+ align:start position:0%
+three-dimensional structures the other
+ 
+
+ align:start position:0%
+three-dimensional structures the other
+one which is the beta sheet now that
+
+ align:start position:0%
+one which is the beta sheet now that
+ 
+
+ align:start position:0%
+one which is the beta sheet now that
+involves interactions between
+
+ align:start position:0%
+involves interactions between
+ 
+
+ align:start position:0%
+involves interactions between
+two pieces of uh two stretches of amino
+
+ align:start position:0%
+two pieces of uh two stretches of amino
+ 
+
+ align:start position:0%
+two pieces of uh two stretches of amino
+acids maybe there was a loop in
+
+ align:start position:0%
+acids maybe there was a loop in
+ 
+
+ align:start position:0%
+acids maybe there was a loop in
+between and then you can get
+
+ align:start position:0%
+between and then you can get
+ 
+
+ align:start position:0%
+between and then you can get
+interactions between them and that oh so
+
+ align:start position:0%
+interactions between them and that oh so
+ 
+
+ align:start position:0%
+interactions between them and that oh so
+let me just
+
+ align:start position:0%
+let me just
+ 
+
+ align:start position:0%
+let me just
+go there's the uh there's the the beta
+
+ align:start position:0%
+go there's the uh there's the the beta
+ 
+
+ align:start position:0%
+go there's the uh there's the the beta
+sheet interaction now those are
+
+ align:start position:0%
+sheet interaction now those are
+ 
+
+ align:start position:0%
+sheet interaction now those are
+represented as arrows you now it takes
+
+ align:start position:0%
+represented as arrows you now it takes
+ 
+
+ align:start position:0%
+represented as arrows you now it takes
+two of them to go so you got to have to
+
+ align:start position:0%
+two of them to go so you got to have to
+ 
+
+ align:start position:0%
+two of them to go so you got to have to
+to represent a beta sheet in a
+
+ align:start position:0%
+to represent a beta sheet in a
+ 
+
+ align:start position:0%
+to represent a beta sheet in a
+three-dimensional structure you have
+
+ align:start position:0%
+three-dimensional structure you have
+ 
+
+ align:start position:0%
+three-dimensional structure you have
+have to have two of those broad arrows
+
+ align:start position:0%
+have to have two of those broad arrows
+ 
+
+ align:start position:0%
+have to have two of those broad arrows
+and there was a question why were there
+
+ align:start position:0%
+and there was a question why were there
+ 
+
+ align:start position:0%
+and there was a question why were there
+arrows on them well one of the things I
+
+ align:start position:0%
+arrows on them well one of the things I
+ 
+
+ align:start position:0%
+arrows on them well one of the things I
+think you can see if you look at those
+
+ align:start position:0%
+think you can see if you look at those
+ 
+
+ align:start position:0%
+think you can see if you look at those
+backbones is that both nucleic acid and
+
+ align:start position:0%
+backbones is that both nucleic acid and
+ 
+
+ align:start position:0%
+backbones is that both nucleic acid and
+protein backbones there's a polarity if
+
+ align:start position:0%
+protein backbones there's a polarity if
+ 
+
+ align:start position:0%
+protein backbones there's a polarity if
+you start this direction say the the
+
+ align:start position:0%
+you start this direction say the the
+ 
+
+ align:start position:0%
+you start this direction say the the
+amino Terminus it's got a tri a
+
+ align:start position:0%
+amino Terminus it's got a tri a
+ 
+
+ align:start position:0%
+amino Terminus it's got a tri a
+particular direction it's not symmetric
+
+ align:start position:0%
+particular direction it's not symmetric
+ 
+
+ align:start position:0%
+particular direction it's not symmetric
+if you come back the other way you find
+
+ align:start position:0%
+if you come back the other way you find
+ 
+
+ align:start position:0%
+if you come back the other way you find
+carboxy Amino the alpha carbon and
+
+ align:start position:0%
+carboxy Amino the alpha carbon and
+ 
+
+ align:start position:0%
+carboxy Amino the alpha carbon and
+you'll find it in the opposite order if
+
+ align:start position:0%
+you'll find it in the opposite order if
+ 
+
+ align:start position:0%
+you'll find it in the opposite order if
+you come back the other way so there's
+
+ align:start position:0%
+you come back the other way so there's
+ 
+
+ align:start position:0%
+you come back the other way so there's
+an inherent polarity the arrows aren't
+
+ align:start position:0%
+an inherent polarity the arrows aren't
+ 
+
+ align:start position:0%
+an inherent polarity the arrows aren't
+represented on here but they are
+
+ align:start position:0%
+represented on here but they are
+ 
+
+ align:start position:0%
+represented on here but they are
+um they are um when you look at it in
+
+ align:start position:0%
+um they are um when you look at it in
+ 
+
+ align:start position:0%
+um they are um when you look at it in
+three three dimensions and you can
+
+ align:start position:0%
+three three dimensions and you can
+ 
+
+ align:start position:0%
+three three dimensions and you can
+either form beta sheets where the two
+
+ align:start position:0%
+either form beta sheets where the two
+ 
+
+ align:start position:0%
+either form beta sheets where the two
+strands have the same polarity or if in
+
+ align:start position:0%
+strands have the same polarity or if in
+ 
+
+ align:start position:0%
+strands have the same polarity or if in
+a case like that where they loop back
+
+ align:start position:0%
+a case like that where they loop back
+ 
+
+ align:start position:0%
+a case like that where they loop back
+then of course if if this one was
+
+ align:start position:0%
+then of course if if this one was
+ 
+
+ align:start position:0%
+then of course if if this one was
+pointing in this direction as it goes
+
+ align:start position:0%
+pointing in this direction as it goes
+ 
+
+ align:start position:0%
+pointing in this direction as it goes
+through the loop then the opposite
+
+ align:start position:0%
+through the loop then the opposite
+ 
+
+ align:start position:0%
+through the loop then the opposite
+strand will will be of the um pointing
+
+ align:start position:0%
+strand will will be of the um pointing
+ 
+
+ align:start position:0%
+strand will will be of the um pointing
+in the other polarity one going this way
+
+ align:start position:0%
+in the other polarity one going this way
+ 
+
+ align:start position:0%
+in the other polarity one going this way
+and one going that way um so
+
+ align:start position:0%
+and one going that way um so
+ 
+
+ align:start position:0%
+and one going that way um so
+the the this part is is sort of helpful
+
+ align:start position:0%
+the the this part is is sort of helpful
+ 
+
+ align:start position:0%
+the the this part is is sort of helpful
+you can make guesses that maybe this
+
+ align:start position:0%
+you can make guesses that maybe this
+ 
+
+ align:start position:0%
+you can make guesses that maybe this
+part has a tendency over here to form a
+
+ align:start position:0%
+part has a tendency over here to form a
+ 
+
+ align:start position:0%
+part has a tendency over here to form a
+beta
+
+ align:start position:0%
+beta
+ 
+
+ align:start position:0%
+beta
+sheet but you still haven't gotten very
+
+ align:start position:0%
+sheet but you still haven't gotten very
+ 
+
+ align:start position:0%
+sheet but you still haven't gotten very
+far towards understanding how you get to
+
+ align:start position:0%
+far towards understanding how you get to
+ 
+
+ align:start position:0%
+far towards understanding how you get to
+the threedimensional structure and I
+
+ align:start position:0%
+the threedimensional structure and I
+ 
+
+ align:start position:0%
+the threedimensional structure and I
+just by putting on um and superimposing
+
+ align:start position:0%
+just by putting on um and superimposing
+ 
+
+ align:start position:0%
+just by putting on um and superimposing
+some amino acids onto that um a sec here
+
+ align:start position:0%
+some amino acids onto that um a sec here
+ 
+
+ align:start position:0%
+some amino acids onto that um a sec here
+let's just get that onto that Alpha
+
+ align:start position:0%
+let's just get that onto that Alpha
+ 
+
+ align:start position:0%
+let's just get that onto that Alpha
+Helix then you can see what happens that
+
+ align:start position:0%
+Helix then you can see what happens that
+ 
+
+ align:start position:0%
+Helix then you can see what happens that
+if you form an alpha Helix what happen
+
+ align:start position:0%
+if you form an alpha Helix what happen
+ 
+
+ align:start position:0%
+if you form an alpha Helix what happen
+happens is all the side chains stick out
+
+ align:start position:0%
+happens is all the side chains stick out
+ 
+
+ align:start position:0%
+happens is all the side chains stick out
+and now I think you can see those of you
+
+ align:start position:0%
+and now I think you can see those of you
+ 
+
+ align:start position:0%
+and now I think you can see those of you
+Engineers anyway if you wanted to build
+
+ align:start position:0%
+Engineers anyway if you wanted to build
+ 
+
+ align:start position:0%
+Engineers anyway if you wanted to build
+something you have a cylinder and you
+
+ align:start position:0%
+something you have a cylinder and you
+ 
+
+ align:start position:0%
+something you have a cylinder and you
+can stick amino acids out that have
+
+ align:start position:0%
+can stick amino acids out that have
+ 
+
+ align:start position:0%
+can stick amino acids out that have
+particular chemical characteristics and
+
+ align:start position:0%
+particular chemical characteristics and
+ 
+
+ align:start position:0%
+particular chemical characteristics and
+depending on the characteristics of
+
+ align:start position:0%
+depending on the characteristics of
+ 
+
+ align:start position:0%
+depending on the characteristics of
+those amino acids whether they have
+
+ align:start position:0%
+those amino acids whether they have
+ 
+
+ align:start position:0%
+those amino acids whether they have
+charges on them or they hate water or
+
+ align:start position:0%
+charges on them or they hate water or
+ 
+
+ align:start position:0%
+charges on them or they hate water or
+something that will influence what
+
+ align:start position:0%
+something that will influence what
+ 
+
+ align:start position:0%
+something that will influence what
+happens to that component of the of the
+
+ align:start position:0%
+happens to that component of the of the
+ 
+
+ align:start position:0%
+happens to that component of the of the
+protein structure when it gets into a
+
+ align:start position:0%
+protein structure when it gets into a
+ 
+
+ align:start position:0%
+protein structure when it gets into a
+three-dimensional uh threedimensional
+
+ align:start position:0%
+three-dimensional uh threedimensional
+ 
+
+ align:start position:0%
+three-dimensional uh threedimensional
+thing and as I think I I showed you the
+
+ align:start position:0%
+thing and as I think I I showed you the
+ 
+
+ align:start position:0%
+thing and as I think I I showed you the
+other day when we caught it on looking
+
+ align:start position:0%
+other day when we caught it on looking
+ 
+
+ align:start position:0%
+other day when we caught it on looking
+down the end on this particular example
+
+ align:start position:0%
+down the end on this particular example
+ 
+
+ align:start position:0%
+down the end on this particular example
+here are a couple of aromatic amino
+
+ align:start position:0%
+here are a couple of aromatic amino
+ 
+
+ align:start position:0%
+here are a couple of aromatic amino
+acids right here they're on the same
+
+ align:start position:0%
+acids right here they're on the same
+ 
+
+ align:start position:0%
+acids right here they're on the same
+side of the Helix and they would hate
+
+ align:start position:0%
+side of the Helix and they would hate
+ 
+
+ align:start position:0%
+side of the Helix and they would hate
+water whereas some of the other amino
+
+ align:start position:0%
+water whereas some of the other amino
+ 
+
+ align:start position:0%
+water whereas some of the other amino
+acids up here are ones that have charges
+
+ align:start position:0%
+acids up here are ones that have charges
+ 
+
+ align:start position:0%
+acids up here are ones that have charges
+so those would love water so what this
+
+ align:start position:0%
+so those would love water so what this
+ 
+
+ align:start position:0%
+so those would love water so what this
+would look like is a cylinder part of
+
+ align:start position:0%
+would look like is a cylinder part of
+ 
+
+ align:start position:0%
+would look like is a cylinder part of
+which heat heated water and part of
+
+ align:start position:0%
+which heat heated water and part of
+ 
+
+ align:start position:0%
+which heat heated water and part of
+which loved water and you might guess as
+
+ align:start position:0%
+which loved water and you might guess as
+ 
+
+ align:start position:0%
+which loved water and you might guess as
+if it folded up in three-dimensional
+
+ align:start position:0%
+if it folded up in three-dimensional
+ 
+
+ align:start position:0%
+if it folded up in three-dimensional
+space the part that hat hated water
+
+ align:start position:0%
+space the part that hat hated water
+ 
+
+ align:start position:0%
+space the part that hat hated water
+might fold towards the inside of the
+
+ align:start position:0%
+might fold towards the inside of the
+ 
+
+ align:start position:0%
+might fold towards the inside of the
+protein and the part of the cylinder the
+
+ align:start position:0%
+protein and the part of the cylinder the
+ 
+
+ align:start position:0%
+protein and the part of the cylinder the
+loved water would face to the outside so
+
+ align:start position:0%
+loved water would face to the outside so
+ 
+
+ align:start position:0%
+loved water would face to the outside so
+that's sort of the underlying principle
+
+ align:start position:0%
+that's sort of the underlying principle
+ 
+
+ align:start position:0%
+that's sort of the underlying principle
+but so the rest of the the other forces
+
+ align:start position:0%
+but so the rest of the the other forces
+ 
+
+ align:start position:0%
+but so the rest of the the other forces
+that we had to
+
+ align:start position:0%
+that we had to
+ 
+
+ align:start position:0%
+that we had to
+understand in order to get to the terti
+
+ align:start position:0%
+understand in order to get to the terti
+ 
+
+ align:start position:0%
+understand in order to get to the terti
+What's called the tertiary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure this is the
+
+ align:start position:0%
+structure this is the
+ 
+
+ align:start position:0%
+structure this is the
+full
+
+ align:start position:0%
+full
+ 
+
+ align:start position:0%
+full
+3d structure which we can now determine
+
+ align:start position:0%
+3d structure which we can now determine
+ 
+
+ align:start position:0%
+3d structure which we can now determine
+by a variety of of methods x-ray
+
+ align:start position:0%
+by a variety of of methods x-ray
+ 
+
+ align:start position:0%
+by a variety of of methods x-ray
+crystallography of proteins is is the
+
+ align:start position:0%
+crystallography of proteins is is the
+ 
+
+ align:start position:0%
+crystallography of proteins is is the
+probably the most common but NMR for
+
+ align:start position:0%
+probably the most common but NMR for
+ 
+
+ align:start position:0%
+probably the most common but NMR for
+example can be used to derive a
+
+ align:start position:0%
+example can be used to derive a
+ 
+
+ align:start position:0%
+example can be used to derive a
+three-dimensional structure as well and
+
+ align:start position:0%
+three-dimensional structure as well and
+ 
+
+ align:start position:0%
+three-dimensional structure as well and
+the other forces then that go into this
+
+ align:start position:0%
+the other forces then that go into this
+ 
+
+ align:start position:0%
+the other forces then that go into this
+are ionic forces uh someone seemed
+
+ align:start position:0%
+are ionic forces uh someone seemed
+ 
+
+ align:start position:0%
+are ionic forces uh someone seemed
+confused by this but if you have a plus
+
+ align:start position:0%
+confused by this but if you have a plus
+ 
+
+ align:start position:0%
+confused by this but if you have a plus
+charge on this part of an amino acid and
+
+ align:start position:0%
+charge on this part of an amino acid and
+ 
+
+ align:start position:0%
+charge on this part of an amino acid and
+a minus charge here if in
+
+ align:start position:0%
+a minus charge here if in
+ 
+
+ align:start position:0%
+a minus charge here if in
+three-dimensional space the plus charge
+
+ align:start position:0%
+three-dimensional space the plus charge
+ 
+
+ align:start position:0%
+three-dimensional space the plus charge
+got somewhere near the the minus charge
+
+ align:start position:0%
+got somewhere near the the minus charge
+ 
+
+ align:start position:0%
+got somewhere near the the minus charge
+then that would form an ionic bond and I
+
+ align:start position:0%
+then that would form an ionic bond and I
+ 
+
+ align:start position:0%
+then that would form an ionic bond and I
+think most of you know enough
+
+ align:start position:0%
+think most of you know enough
+ 
+
+ align:start position:0%
+think most of you know enough
+electricity and magnetism that wouldn't
+
+ align:start position:0%
+electricity and magnetism that wouldn't
+ 
+
+ align:start position:0%
+electricity and magnetism that wouldn't
+surprise you that that those would those
+
+ align:start position:0%
+surprise you that that those would those
+ 
+
+ align:start position:0%
+surprise you that that those would those
+two would be attracted the one that I
+
+ align:start position:0%
+two would be attracted the one that I
+ 
+
+ align:start position:0%
+two would be attracted the one that I
+think is has been harder to understand
+
+ align:start position:0%
+think is has been harder to understand
+ 
+
+ align:start position:0%
+think is has been harder to understand
+um is the Vander
+
+ align:start position:0%
+um is the Vander
+ 
+
+ align:start position:0%
+um is the Vander
+bals interactions that we talked about
+
+ align:start position:0%
+bals interactions that we talked about
+ 
+
+ align:start position:0%
+bals interactions that we talked about
+which is the other day which is is
+
+ align:start position:0%
+which is the other day which is is
+ 
+
+ align:start position:0%
+which is the other day which is is
+tricky in the sense that it's I I don't
+
+ align:start position:0%
+tricky in the sense that it's I I don't
+ 
+
+ align:start position:0%
+tricky in the sense that it's I I don't
+for this course you don't particularly
+
+ align:start position:0%
+for this course you don't particularly
+ 
+
+ align:start position:0%
+for this course you don't particularly
+really need to understand understand the
+
+ align:start position:0%
+really need to understand understand the
+ 
+
+ align:start position:0%
+really need to understand understand the
+underlying chemistry but the principle
+
+ align:start position:0%
+underlying chemistry but the principle
+ 
+
+ align:start position:0%
+underlying chemistry but the principle
+of it is that if you have a non-polar
+
+ align:start position:0%
+of it is that if you have a non-polar
+ 
+
+ align:start position:0%
+of it is that if you have a non-polar
+Bond one that isn't got any particular
+
+ align:start position:0%
+Bond one that isn't got any particular
+ 
+
+ align:start position:0%
+Bond one that isn't got any particular
+attraction to it gets very very close to
+
+ align:start position:0%
+attraction to it gets very very close to
+ 
+
+ align:start position:0%
+attraction to it gets very very close to
+another one then the FL the transient
+
+ align:start position:0%
+another one then the FL the transient
+ 
+
+ align:start position:0%
+another one then the FL the transient
+fluctuations in one indu something in
+
+ align:start position:0%
+fluctuations in one indu something in
+ 
+
+ align:start position:0%
+fluctuations in one indu something in
+the other one that makes them stick
+
+ align:start position:0%
+the other one that makes them stick
+ 
+
+ align:start position:0%
+the other one that makes them stick
+together and the whole point about this
+
+ align:start position:0%
+together and the whole point about this
+ 
+
+ align:start position:0%
+together and the whole point about this
+is if you get two molecular surfaces
+
+ align:start position:0%
+is if you get two molecular surfaces
+ 
+
+ align:start position:0%
+is if you get two molecular surfaces
+that are very very close together about
+
+ align:start position:0%
+that are very very close together about
+ 
+
+ align:start position:0%
+that are very very close together about
+you know maybe two times the length of a
+
+ align:start position:0%
+you know maybe two times the length of a
+ 
+
+ align:start position:0%
+you know maybe two times the length of a
+of a calent bond or something then you
+
+ align:start position:0%
+of a calent bond or something then you
+ 
+
+ align:start position:0%
+of a calent bond or something then you
+can generate uh very powerful forces
+
+ align:start position:0%
+can generate uh very powerful forces
+ 
+
+ align:start position:0%
+can generate uh very powerful forces
+because even though the very each
+
+ align:start position:0%
+because even though the very each
+ 
+
+ align:start position:0%
+because even though the very each
+individual interaction is weak about a
+
+ align:start position:0%
+individual interaction is weak about a
+ 
+
+ align:start position:0%
+individual interaction is weak about a
+quarter or a third of a hydrogen bond
+
+ align:start position:0%
+quarter or a third of a hydrogen bond
+ 
+
+ align:start position:0%
+quarter or a third of a hydrogen bond
+summing them up can make them very very
+
+ align:start position:0%
+summing them up can make them very very
+ 
+
+ align:start position:0%
+summing them up can make them very very
+strong and so that's another kind of
+
+ align:start position:0%
+strong and so that's another kind of
+ 
+
+ align:start position:0%
+strong and so that's another kind of
+force that's important when a linear
+
+ align:start position:0%
+force that's important when a linear
+ 
+
+ align:start position:0%
+force that's important when a linear
+molecule is trying to figure out how in
+
+ align:start position:0%
+molecule is trying to figure out how in
+ 
+
+ align:start position:0%
+molecule is trying to figure out how in
+space it's going to fold up the point of
+
+ align:start position:0%
+space it's going to fold up the point of
+ 
+
+ align:start position:0%
+space it's going to fold up the point of
+the gecko thing was it's only recently
+
+ align:start position:0%
+the gecko thing was it's only recently
+ 
+
+ align:start position:0%
+the gecko thing was it's only recently
+relative recently been discovered that
+
+ align:start position:0%
+relative recently been discovered that
+ 
+
+ align:start position:0%
+relative recently been discovered that
+the reason those lizards can stick to
+
+ align:start position:0%
+the reason those lizards can stick to
+ 
+
+ align:start position:0%
+the reason those lizards can stick to
+walls is they have sort of incredible
+
+ align:start position:0%
+walls is they have sort of incredible
+ 
+
+ align:start position:0%
+walls is they have sort of incredible
+split
+
+ align:start position:0%
+split
+ 
+
+ align:start position:0%
+split
+ends noticed a couple of you came to the
+
+ align:start position:0%
+ends noticed a couple of you came to the
+ 
+
+ align:start position:0%
+ends noticed a couple of you came to the
+uh to Bob F's talk the other day and you
+
+ align:start position:0%
+uh to Bob F's talk the other day and you
+ 
+
+ align:start position:0%
+uh to Bob F's talk the other day and you
+got to hear the full treatment but
+
+ align:start position:0%
+got to hear the full treatment but
+ 
+
+ align:start position:0%
+got to hear the full treatment but
+because their hairs on their on their
+
+ align:start position:0%
+because their hairs on their on their
+ 
+
+ align:start position:0%
+because their hairs on their on their
+feet are so split they're very fine and
+
+ align:start position:0%
+feet are so split they're very fine and
+ 
+
+ align:start position:0%
+feet are so split they're very fine and
+these these uh the molecules are able to
+
+ align:start position:0%
+these these uh the molecules are able to
+ 
+
+ align:start position:0%
+these these uh the molecules are able to
+make very close interaction vender
+
+ align:start position:0%
+make very close interaction vender
+ 
+
+ align:start position:0%
+make very close interaction vender
+Fall's interactions with the surface and
+
+ align:start position:0%
+Fall's interactions with the surface and
+ 
+
+ align:start position:0%
+Fall's interactions with the surface and
+that's what's holding the gecko to the
+
+ align:start position:0%
+that's what's holding the gecko to the
+ 
+
+ align:start position:0%
+that's what's holding the gecko to the
+wall and there's just so many of of them
+
+ align:start position:0%
+wall and there's just so many of of them
+ 
+
+ align:start position:0%
+wall and there's just so many of of them
+that it can support a whole Gecko and
+
+ align:start position:0%
+that it can support a whole Gecko and
+ 
+
+ align:start position:0%
+that it can support a whole Gecko and
+that's what could be the basis he say
+
+ align:start position:0%
+that's what could be the basis he say
+ 
+
+ align:start position:0%
+that's what could be the basis he say
+said to me of a somewhere 30 to 50
+
+ align:start position:0%
+said to me of a somewhere 30 to 50
+ 
+
+ align:start position:0%
+said to me of a somewhere 30 to 50
+billion adhesive industry a
+
+ align:start position:0%
+billion adhesive industry a
+ 
+
+ align:start position:0%
+billion adhesive industry a
+self-cleaning dry adhesive and it's it's
+
+ align:start position:0%
+self-cleaning dry adhesive and it's it's
+ 
+
+ align:start position:0%
+self-cleaning dry adhesive and it's it's
+not something magic only the gecko hair
+
+ align:start position:0%
+not something magic only the gecko hair
+ 
+
+ align:start position:0%
+not something magic only the gecko hair
+will do you can design synthetic
+
+ align:start position:0%
+will do you can design synthetic
+ 
+
+ align:start position:0%
+will do you can design synthetic
+molecules that have the same property
+
+ align:start position:0%
+molecules that have the same property
+ 
+
+ align:start position:0%
+molecules that have the same property
+you're able to make these millions of
+
+ align:start position:0%
+you're able to make these millions of
+ 
+
+ align:start position:0%
+you're able to make these millions of
+Vander Falls interactions so that's two
+
+ align:start position:0%
+Vander Falls interactions so that's two
+ 
+
+ align:start position:0%
+Vander Falls interactions so that's two
+of the other things and the final thing
+
+ align:start position:0%
+of the other things and the final thing
+ 
+
+ align:start position:0%
+of the other things and the final thing
+was which isn't really a force but goes
+
+ align:start position:0%
+was which isn't really a force but goes
+ 
+
+ align:start position:0%
+was which isn't really a force but goes
+into this is this
+
+ align:start position:0%
+into this is this
+ 
+
+ align:start position:0%
+into this is this
+hydrophobic effect and that is that if
+
+ align:start position:0%
+hydrophobic effect and that is that if
+ 
+
+ align:start position:0%
+hydrophobic effect and that is that if
+we have things amino acids such as veine
+
+ align:start position:0%
+we have things amino acids such as veine
+ 
+
+ align:start position:0%
+we have things amino acids such as veine
+or something that doesn't like to mix
+
+ align:start position:0%
+or something that doesn't like to mix
+ 
+
+ align:start position:0%
+or something that doesn't like to mix
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+water then when the protein folds up the
+
+ align:start position:0%
+water then when the protein folds up the
+ 
+
+ align:start position:0%
+water then when the protein folds up the
+things that don't like to interact with
+
+ align:start position:0%
+things that don't like to interact with
+ 
+
+ align:start position:0%
+things that don't like to interact with
+water will kind of go together just the
+
+ align:start position:0%
+water will kind of go together just the
+ 
+
+ align:start position:0%
+water will kind of go together just the
+way if you put a lot of oil in the water
+
+ align:start position:0%
+way if you put a lot of oil in the water
+ 
+
+ align:start position:0%
+way if you put a lot of oil in the water
+it'll sort of pull together because
+
+ align:start position:0%
+it'll sort of pull together because
+ 
+
+ align:start position:0%
+it'll sort of pull together because
+anytime you have something that gets
+
+ align:start position:0%
+anytime you have something that gets
+ 
+
+ align:start position:0%
+anytime you have something that gets
+stuck in water it disrupts hydrogen
+
+ align:start position:0%
+stuck in water it disrupts hydrogen
+ 
+
+ align:start position:0%
+stuck in water it disrupts hydrogen
+bonds and and that's energetically
+
+ align:start position:0%
+bonds and and that's energetically
+ 
+
+ align:start position:0%
+bonds and and that's energetically
+unfavorable so the things that hate
+
+ align:start position:0%
+unfavorable so the things that hate
+ 
+
+ align:start position:0%
+unfavorable so the things that hate
+water will tend to Lump Lump together
+
+ align:start position:0%
+water will tend to Lump Lump together
+ 
+
+ align:start position:0%
+water will tend to Lump Lump together
+and you're all used to seeing little
+
+ align:start position:0%
+and you're all used to seeing little
+ 
+
+ align:start position:0%
+and you're all used to seeing little
+drops of of oil and stuff floating
+
+ align:start position:0%
+drops of of oil and stuff floating
+ 
+
+ align:start position:0%
+drops of of oil and stuff floating
+around and so um let me just switch over
+
+ align:start position:0%
+around and so um let me just switch over
+ 
+
+ align:start position:0%
+around and so um let me just switch over
+to this other thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so this was just showing you one of
+
+ align:start position:0%
+now so this was just showing you one of
+ 
+
+ align:start position:0%
+now so this was just showing you one of
+these protein chains that's folded up
+
+ align:start position:0%
+these protein chains that's folded up
+ 
+
+ align:start position:0%
+these protein chains that's folded up
+into a three-dimensional structure this
+
+ align:start position:0%
+into a three-dimensional structure this
+ 
+
+ align:start position:0%
+into a three-dimensional structure this
+happens to be uh something with with an
+
+ align:start position:0%
+happens to be uh something with with an
+ 
+
+ align:start position:0%
+happens to be uh something with with an
+enzymatic activity but the important
+
+ align:start position:0%
+enzymatic activity but the important
+ 
+
+ align:start position:0%
+enzymatic activity but the important
+thing for right now is what's been
+
+ align:start position:0%
+thing for right now is what's been
+ 
+
+ align:start position:0%
+thing for right now is what's been
+colored in here are the amino acids that
+
+ align:start position:0%
+colored in here are the amino acids that
+ 
+
+ align:start position:0%
+colored in here are the amino acids that
+if you looked back on the the list of
+
+ align:start position:0%
+if you looked back on the the list of
+ 
+
+ align:start position:0%
+if you looked back on the the list of
+amino acids and what categories are
+
+ align:start position:0%
+amino acids and what categories are
+ 
+
+ align:start position:0%
+amino acids and what categories are
+you'd see some of them are called said
+
+ align:start position:0%
+you'd see some of them are called said
+ 
+
+ align:start position:0%
+you'd see some of them are called said
+to have hydrophobic side chains and this
+
+ align:start position:0%
+to have hydrophobic side chains and this
+ 
+
+ align:start position:0%
+to have hydrophobic side chains and this
+is quite you can see quite strikingly
+
+ align:start position:0%
+is quite you can see quite strikingly
+ 
+
+ align:start position:0%
+is quite you can see quite strikingly
+how the amino acids in the interior part
+
+ align:start position:0%
+how the amino acids in the interior part
+ 
+
+ align:start position:0%
+how the amino acids in the interior part
+of this protein have clustered together
+
+ align:start position:0%
+of this protein have clustered together
+ 
+
+ align:start position:0%
+of this protein have clustered together
+they don't like to interact with water
+
+ align:start position:0%
+they don't like to interact with water
+ 
+
+ align:start position:0%
+they don't like to interact with water
+they interact very well with each other
+
+ align:start position:0%
+they interact very well with each other
+ 
+
+ align:start position:0%
+they interact very well with each other
+just like you can mix butter and oil
+
+ align:start position:0%
+just like you can mix butter and oil
+ 
+
+ align:start position:0%
+just like you can mix butter and oil
+they mix together together very well and
+
+ align:start position:0%
+they mix together together very well and
+ 
+
+ align:start position:0%
+they mix together together very well and
+so that is another factor that
+
+ align:start position:0%
+so that is another factor that
+ 
+
+ align:start position:0%
+so that is another factor that
+contributes to the three-dimensional
+
+ align:start position:0%
+contributes to the three-dimensional
+ 
+
+ align:start position:0%
+contributes to the three-dimensional
+structure of these uh of these proteins
+
+ align:start position:0%
+structure of these uh of these proteins
+ 
+
+ align:start position:0%
+structure of these uh of these proteins
+so understanding what proteins are all
+
+ align:start position:0%
+so understanding what proteins are all
+ 
+
+ align:start position:0%
+so understanding what proteins are all
+about means ultimately understanding
+
+ align:start position:0%
+about means ultimately understanding
+ 
+
+ align:start position:0%
+about means ultimately understanding
+their three-dimensional structure and as
+
+ align:start position:0%
+their three-dimensional structure and as
+ 
+
+ align:start position:0%
+their three-dimensional structure and as
+I say a big unsolved problem right at
+
+ align:start position:0%
+I say a big unsolved problem right at
+ 
+
+ align:start position:0%
+I say a big unsolved problem right at
+the moment is how do you get from a
+
+ align:start position:0%
+the moment is how do you get from a
+ 
+
+ align:start position:0%
+the moment is how do you get from a
+linear chain of amino acids to one of
+
+ align:start position:0%
+linear chain of amino acids to one of
+ 
+
+ align:start position:0%
+linear chain of amino acids to one of
+these uh three-dimensional structures
+
+ align:start position:0%
+these uh three-dimensional structures
+ 
+
+ align:start position:0%
+these uh three-dimensional structures
+and you can imagine with 20 different
+
+ align:start position:0%
+and you can imagine with 20 different
+ 
+
+ align:start position:0%
+and you can imagine with 20 different
+side chains there's
+
+ align:start position:0%
+side chains there's
+ 
+
+ align:start position:0%
+side chains there's
+unbelievable number of combinations that
+
+ align:start position:0%
+unbelievable number of combinations that
+ 
+
+ align:start position:0%
+unbelievable number of combinations that
+you can make yet almost every protein
+
+ align:start position:0%
+you can make yet almost every protein
+ 
+
+ align:start position:0%
+you can make yet almost every protein
+has that's in nature has one unique or
+
+ align:start position:0%
+has that's in nature has one unique or
+ 
+
+ align:start position:0%
+has that's in nature has one unique or
+one or two or something you uh
+
+ align:start position:0%
+one or two or something you uh
+ 
+
+ align:start position:0%
+one or two or something you uh
+confirmations that takes out out of all
+
+ align:start position:0%
+confirmations that takes out out of all
+ 
+
+ align:start position:0%
+confirmations that takes out out of all
+the kinds of things that you could do
+
+ align:start position:0%
+the kinds of things that you could do
+ 
+
+ align:start position:0%
+the kinds of things that you could do
+and it's this combination of forces that
+
+ align:start position:0%
+and it's this combination of forces that
+ 
+
+ align:start position:0%
+and it's this combination of forces that
+does that does that now the final let me
+
+ align:start position:0%
+does that does that now the final let me
+ 
+
+ align:start position:0%
+does that does that now the final let me
+just go back for one sec so the final
+
+ align:start position:0%
+just go back for one sec so the final
+ 
+
+ align:start position:0%
+just go back for one sec so the final
+thing that one talks about when you're
+
+ align:start position:0%
+thing that one talks about when you're
+ 
+
+ align:start position:0%
+thing that one talks about when you're
+talking about proteins are quaternary
+
+ align:start position:0%
+talking about proteins are quaternary
+ 
+
+ align:start position:0%
+talking about proteins are quaternary
+structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what that means is when you have
+
+ align:start position:0%
+and what that means is when you have
+ 
+
+ align:start position:0%
+and what that means is when you have
+more than
+
+ align:start position:0%
+more than
+ 
+
+ align:start position:0%
+more than
+one um poly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+peptide chain so if we have two
+
+ align:start position:0%
+peptide chain so if we have two
+ 
+
+ align:start position:0%
+peptide chain so if we have two
+different uh proteins that interact this
+
+ align:start position:0%
+different uh proteins that interact this
+ 
+
+ align:start position:0%
+different uh proteins that interact this
+is protein number one and this is
+
+ align:start position:0%
+is protein number one and this is
+ 
+
+ align:start position:0%
+is protein number one and this is
+protein number two then there has to be
+
+ align:start position:0%
+protein number two then there has to be
+ 
+
+ align:start position:0%
+protein number two then there has to be
+some sort of interaction between each of
+
+ align:start position:0%
+some sort of interaction between each of
+ 
+
+ align:start position:0%
+some sort of interaction between each of
+these three-dimensional structures in
+
+ align:start position:0%
+these three-dimensional structures in
+ 
+
+ align:start position:0%
+these three-dimensional structures in
+order for the proteins to stick together
+
+ align:start position:0%
+order for the proteins to stick together
+ 
+
+ align:start position:0%
+order for the proteins to stick together
+and something like that felar motor that
+
+ align:start position:0%
+and something like that felar motor that
+ 
+
+ align:start position:0%
+and something like that felar motor that
+makes let the bacteria swim has many
+
+ align:start position:0%
+makes let the bacteria swim has many
+ 
+
+ align:start position:0%
+makes let the bacteria swim has many
+many parts all of which have to fit
+
+ align:start position:0%
+many parts all of which have to fit
+ 
+
+ align:start position:0%
+many parts all of which have to fit
+together just the same way all the
+
+ align:start position:0%
+together just the same way all the
+ 
+
+ align:start position:0%
+together just the same way all the
+different parts of an engine have to fit
+
+ align:start position:0%
+different parts of an engine have to fit
+ 
+
+ align:start position:0%
+different parts of an engine have to fit
+together now this next one this next
+
+ align:start position:0%
+together now this next one this next
+ 
+
+ align:start position:0%
+together now this next one this next
+little movie is just a a dier it's
+
+ align:start position:0%
+little movie is just a a dier it's
+ 
+
+ align:start position:0%
+little movie is just a a dier it's
+actually a heterodimer so it's made of
+
+ align:start position:0%
+actually a heterodimer so it's made of
+ 
+
+ align:start position:0%
+actually a heterodimer so it's made of
+two proteins they're different but
+
+ align:start position:0%
+two proteins they're different but
+ 
+
+ align:start position:0%
+two proteins they're different but
+they're come they've come together and
+
+ align:start position:0%
+they're come they've come together and
+ 
+
+ align:start position:0%
+they're come they've come together and
+they're um they're interacting so what
+
+ align:start position:0%
+they're um they're interacting so what
+ 
+
+ align:start position:0%
+they're um they're interacting so what
+you will first see is the
+
+ align:start position:0%
+you will first see is the
+ 
+
+ align:start position:0%
+you will first see is the
+three-dimensional structure of the uh of
+
+ align:start position:0%
+three-dimensional structure of the uh of
+ 
+
+ align:start position:0%
+three-dimensional structure of the uh of
+each protein um showing the alpha heles
+
+ align:start position:0%
+each protein um showing the alpha heles
+ 
+
+ align:start position:0%
+each protein um showing the alpha heles
+the beta sheets and nothing else is
+
+ align:start position:0%
+the beta sheets and nothing else is
+ 
+
+ align:start position:0%
+the beta sheets and nothing else is
+shown the side chains aren't shown the
+
+ align:start position:0%
+shown the side chains aren't shown the
+ 
+
+ align:start position:0%
+shown the side chains aren't shown the
+other the molecular surfaces aren't
+
+ align:start position:0%
+other the molecular surfaces aren't
+ 
+
+ align:start position:0%
+other the molecular surfaces aren't
+shown you can just see the backbone
+
+ align:start position:0%
+shown you can just see the backbone
+ 
+
+ align:start position:0%
+shown you can just see the backbone
+you'll see Alpha Helix a turn some beta
+
+ align:start position:0%
+you'll see Alpha Helix a turn some beta
+ 
+
+ align:start position:0%
+you'll see Alpha Helix a turn some beta
+sheets just the kind of stuff you were
+
+ align:start position:0%
+sheets just the kind of stuff you were
+ 
+
+ align:start position:0%
+sheets just the kind of stuff you were
+seeing the other day but you'll see that
+
+ align:start position:0%
+seeing the other day but you'll see that
+ 
+
+ align:start position:0%
+seeing the other day but you'll see that
+the two proteins are together and this
+
+ align:start position:0%
+the two proteins are together and this
+ 
+
+ align:start position:0%
+the two proteins are together and this
+is actually a movie made by Tom Schwarz
+
+ align:start position:0%
+is actually a movie made by Tom Schwarz
+ 
+
+ align:start position:0%
+is actually a movie made by Tom Schwarz
+who's a crystallographer who just
+
+ align:start position:0%
+who's a crystallographer who just
+ 
+
+ align:start position:0%
+who's a crystallographer who just
+started you on our faculty this this
+
+ align:start position:0%
+started you on our faculty this this
+ 
+
+ align:start position:0%
+started you on our faculty this this
+fall in the biology department is one of
+
+ align:start position:0%
+fall in the biology department is one of
+ 
+
+ align:start position:0%
+fall in the biology department is one of
+the proteins he studied and then after
+
+ align:start position:0%
+the proteins he studied and then after
+ 
+
+ align:start position:0%
+the proteins he studied and then after
+that and he rotates it around so you can
+
+ align:start position:0%
+that and he rotates it around so you can
+ 
+
+ align:start position:0%
+that and he rotates it around so you can
+see it after that he then puts on the
+
+ align:start position:0%
+see it after that he then puts on the
+ 
+
+ align:start position:0%
+see it after that he then puts on the
+side chains and then traces the surface
+
+ align:start position:0%
+side chains and then traces the surface
+ 
+
+ align:start position:0%
+side chains and then traces the surface
+so this is what they call the Vander
+
+ align:start position:0%
+so this is what they call the Vander
+ 
+
+ align:start position:0%
+so this is what they call the Vander
+valal surface so this is what the
+
+ align:start position:0%
+valal surface so this is what the
+ 
+
+ align:start position:0%
+valal surface so this is what the
+protein would actually look like and
+
+ align:start position:0%
+protein would actually look like and
+ 
+
+ align:start position:0%
+protein would actually look like and
+what I'd like you to what I think you'll
+
+ align:start position:0%
+what I'd like you to what I think you'll
+ 
+
+ align:start position:0%
+what I'd like you to what I think you'll
+see from this is how incredibly well the
+
+ align:start position:0%
+see from this is how incredibly well the
+ 
+
+ align:start position:0%
+see from this is how incredibly well the
+proteins fit together I mean they by the
+
+ align:start position:0%
+proteins fit together I mean they by the
+ 
+
+ align:start position:0%
+proteins fit together I mean they by the
+theme of sort of probably keep saying
+
+ align:start position:0%
+theme of sort of probably keep saying
+ 
+
+ align:start position:0%
+theme of sort of probably keep saying
+all the way through the course is
+
+ align:start position:0%
+all the way through the course is
+ 
+
+ align:start position:0%
+all the way through the course is
+biology works from fitting shapes and
+
+ align:start position:0%
+biology works from fitting shapes and
+ 
+
+ align:start position:0%
+biology works from fitting shapes and
+things have to work incredibly well and
+
+ align:start position:0%
+things have to work incredibly well and
+ 
+
+ align:start position:0%
+things have to work incredibly well and
+that's also why these Vander valal
+
+ align:start position:0%
+that's also why these Vander valal
+ 
+
+ align:start position:0%
+that's also why these Vander valal
+forces become so important because
+
+ align:start position:0%
+forces become so important because
+ 
+
+ align:start position:0%
+forces become so important because
+Evolution has ended up making things
+
+ align:start position:0%
+Evolution has ended up making things
+ 
+
+ align:start position:0%
+Evolution has ended up making things
+that just go together just like a hand
+
+ align:start position:0%
+that just go together just like a hand
+ 
+
+ align:start position:0%
+that just go together just like a hand
+and a perfectly fit glove that's the way
+
+ align:start position:0%
+and a perfectly fit glove that's the way
+ 
+
+ align:start position:0%
+and a perfectly fit glove that's the way
+most of these interactions are so watch
+
+ align:start position:0%
+most of these interactions are so watch
+ 
+
+ align:start position:0%
+most of these interactions are so watch
+this little movie so you see the light
+
+ align:start position:0%
+this little movie so you see the light
+ 
+
+ align:start position:0%
+this little movie so you see the light
+blue is one of the proteins there's an
+
+ align:start position:0%
+blue is one of the proteins there's an
+ 
+
+ align:start position:0%
+blue is one of the proteins there's an
+alpha Helix there's a lot of alpha
+
+ align:start position:0%
+alpha Helix there's a lot of alpha
+ 
+
+ align:start position:0%
+alpha Helix there's a lot of alpha
+helices in this one the purple one's the
+
+ align:start position:0%
+helices in this one the purple one's the
+ 
+
+ align:start position:0%
+helices in this one the purple one's the
+other protein and you can see that in
+
+ align:start position:0%
+other protein and you can see that in
+ 
+
+ align:start position:0%
+other protein and you can see that in
+between them there's a there's an
+
+ align:start position:0%
+between them there's a there's an
+ 
+
+ align:start position:0%
+between them there's a there's an
+interface and so those must be
+
+ align:start position:0%
+interface and so those must be
+ 
+
+ align:start position:0%
+interface and so those must be
+interacting but when when he
+
+ align:start position:0%
+interacting but when when he
+ 
+
+ align:start position:0%
+interacting but when when he
+superimposes now
+
+ align:start position:0%
+superimposes now
+ 
+
+ align:start position:0%
+superimposes now
+the all the amino acids in the surface
+
+ align:start position:0%
+the all the amino acids in the surface
+ 
+
+ align:start position:0%
+the all the amino acids in the surface
+now what he's going to do he's going to
+
+ align:start position:0%
+now what he's going to do he's going to
+ 
+
+ align:start position:0%
+now what he's going to do he's going to
+pull those apart so you can see where
+
+ align:start position:0%
+pull those apart so you can see where
+ 
+
+ align:start position:0%
+pull those apart so you can see where
+they were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interacting you get the idea now of how
+
+ align:start position:0%
+interacting you get the idea now of how
+ 
+
+ align:start position:0%
+interacting you get the idea now of how
+beautifully these things have folded up
+
+ align:start position:0%
+beautifully these things have folded up
+ 
+
+ align:start position:0%
+beautifully these things have folded up
+in three-dimensional space and position
+
+ align:start position:0%
+in three-dimensional space and position
+ 
+
+ align:start position:0%
+in three-dimensional space and position
+so that they can fit together and work
+
+ align:start position:0%
+so that they can fit together and work
+ 
+
+ align:start position:0%
+so that they can fit together and work
+together as a machine just the same way
+
+ align:start position:0%
+together as a machine just the same way
+ 
+
+ align:start position:0%
+together as a machine just the same way
+if you were building a machine and you
+
+ align:start position:0%
+if you were building a machine and you
+ 
+
+ align:start position:0%
+if you were building a machine and you
+needed to have two parts that haded you
+
+ align:start position:0%
+needed to have two parts that haded you
+ 
+
+ align:start position:0%
+needed to have two parts that haded you
+had to Jo joing together you've got to
+
+ align:start position:0%
+had to Jo joing together you've got to
+ 
+
+ align:start position:0%
+had to Jo joing together you've got to
+Tool things so that the surfaces go
+
+ align:start position:0%
+Tool things so that the surfaces go
+ 
+
+ align:start position:0%
+Tool things so that the surfaces go
+exactly together that's what uh um
+
+ align:start position:0%
+exactly together that's what uh um
+ 
+
+ align:start position:0%
+exactly together that's what uh um
+nature does that's also why this why I'm
+
+ align:start position:0%
+nature does that's also why this why I'm
+ 
+
+ align:start position:0%
+nature does that's also why this why I'm
+making such a deal out of this
+
+ align:start position:0%
+making such a deal out of this
+ 
+
+ align:start position:0%
+making such a deal out of this
+three-dimensional structure of of
+
+ align:start position:0%
+three-dimensional structure of of
+ 
+
+ align:start position:0%
+three-dimensional structure of of
+proteins and how it got there I could
+
+ align:start position:0%
+proteins and how it got there I could
+ 
+
+ align:start position:0%
+proteins and how it got there I could
+just say it gets there by Magic but it
+
+ align:start position:0%
+just say it gets there by Magic but it
+ 
+
+ align:start position:0%
+just say it gets there by Magic but it
+doesn't it's determined by this set of
+
+ align:start position:0%
+doesn't it's determined by this set of
+ 
+
+ align:start position:0%
+doesn't it's determined by this set of
+forces and one of the things we can't do
+
+ align:start position:0%
+forces and one of the things we can't do
+ 
+
+ align:start position:0%
+forces and one of the things we can't do
+at this point is predict here's a linear
+
+ align:start position:0%
+at this point is predict here's a linear
+ 
+
+ align:start position:0%
+at this point is predict here's a linear
+sequence of amino acids here's the 3D
+
+ align:start position:0%
+sequence of amino acids here's the 3D
+ 
+
+ align:start position:0%
+sequence of amino acids here's the 3D
+structure that would be a huge advance
+
+ align:start position:0%
+structure that would be a huge advance
+ 
+
+ align:start position:0%
+structure that would be a huge advance
+in biology if one of you guys could
+
+ align:start position:0%
+in biology if one of you guys could
+ 
+
+ align:start position:0%
+in biology if one of you guys could
+figure figure out how to do that during
+
+ align:start position:0%
+figure figure out how to do that during
+ 
+
+ align:start position:0%
+figure figure out how to do that during
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+career
+
+ align:start position:0%
+career
+ 
+
+ align:start position:0%
+career
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+so just want
+
+ align:start position:0%
+so just want
+ 
+
+ align:start position:0%
+so just want
+to reiterate some of the things that
+
+ align:start position:0%
+to reiterate some of the things that
+ 
+
+ align:start position:0%
+to reiterate some of the things that
+proteins do because we'll be talking
+
+ align:start position:0%
+proteins do because we'll be talking
+ 
+
+ align:start position:0%
+proteins do because we'll be talking
+about them as we go
+
+ align:start position:0%
+about them as we go
+ 
+
+ align:start position:0%
+about them as we go
+along one thing they do they they act as
+
+ align:start position:0%
+along one thing they do they they act as
+ 
+
+ align:start position:0%
+along one thing they do they they act as
+enzymes which are
+
+ align:start position:0%
+enzymes which are
+ 
+
+ align:start position:0%
+enzymes which are
+catalysts for biological reactions that
+
+ align:start position:0%
+catalysts for biological reactions that
+ 
+
+ align:start position:0%
+catalysts for biological reactions that
+take place under physiological
+
+ align:start position:0%
+take place under physiological
+ 
+
+ align:start position:0%
+take place under physiological
+conditions and will give you a lot of of
+
+ align:start position:0%
+conditions and will give you a lot of of
+ 
+
+ align:start position:0%
+conditions and will give you a lot of of
+examples of those enzymes starting uh
+
+ align:start position:0%
+examples of those enzymes starting uh
+ 
+
+ align:start position:0%
+examples of those enzymes starting uh
+very soon um they play structural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roles our hair our fingernails made of
+
+ align:start position:0%
+roles our hair our fingernails made of
+ 
+
+ align:start position:0%
+roles our hair our fingernails made of
+protein are the the hairs on the gecko's
+
+ align:start position:0%
+protein are the the hairs on the gecko's
+ 
+
+ align:start position:0%
+protein are the the hairs on the gecko's
+feet are made of keratin which is the
+
+ align:start position:0%
+feet are made of keratin which is the
+ 
+
+ align:start position:0%
+feet are made of keratin which is the
+same stuff our hair is made of except
+
+ align:start position:0%
+same stuff our hair is made of except
+ 
+
+ align:start position:0%
+same stuff our hair is made of except
+they basically got a whole lot of split
+
+ align:start position:0%
+they basically got a whole lot of split
+ 
+
+ align:start position:0%
+they basically got a whole lot of split
+ends they're finer hairs to begin with
+
+ align:start position:0%
+ends they're finer hairs to begin with
+ 
+
+ align:start position:0%
+ends they're finer hairs to begin with
+and a lot of split ends and that's what
+
+ align:start position:0%
+and a lot of split ends and that's what
+ 
+
+ align:start position:0%
+and a lot of split ends and that's what
+makes these very very fine things that
+
+ align:start position:0%
+makes these very very fine things that
+ 
+
+ align:start position:0%
+makes these very very fine things that
+can make
+
+ align:start position:0%
+can make
+ 
+
+ align:start position:0%
+can make
+vendal interactions with with surfaces
+
+ align:start position:0%
+vendal interactions with with surfaces
+ 
+
+ align:start position:0%
+vendal interactions with with surfaces
+um they play roles
+
+ align:start position:0%
+um they play roles
+ 
+
+ align:start position:0%
+um they play roles
+in specificity for example mentioned the
+
+ align:start position:0%
+in specificity for example mentioned the
+ 
+
+ align:start position:0%
+in specificity for example mentioned the
+antibodies and we'll talk about the
+
+ align:start position:0%
+antibodies and we'll talk about the
+ 
+
+ align:start position:0%
+antibodies and we'll talk about the
+immune response in some detail at the
+
+ align:start position:0%
+immune response in some detail at the
+ 
+
+ align:start position:0%
+immune response in some detail at the
+end of
+
+ align:start position:0%
+end of
+ 
+
+ align:start position:0%
+end of
+the uh end of the uh course and one of
+
+ align:start position:0%
+the uh end of the uh course and one of
+ 
+
+ align:start position:0%
+the uh end of the uh course and one of
+the really magic things that we've come
+
+ align:start position:0%
+the really magic things that we've come
+ 
+
+ align:start position:0%
+the really magic things that we've come
+to understand in biology recently is how
+
+ align:start position:0%
+to understand in biology recently is how
+ 
+
+ align:start position:0%
+to understand in biology recently is how
+it is that your body has uh this immune
+
+ align:start position:0%
+it is that your body has uh this immune
+ 
+
+ align:start position:0%
+it is that your body has uh this immune
+system that's able to recognize
+
+ align:start position:0%
+system that's able to recognize
+ 
+
+ align:start position:0%
+system that's able to recognize
+literally any molecule any molecule
+
+ align:start position:0%
+literally any molecule any molecule
+ 
+
+ align:start position:0%
+literally any molecule any molecule
+doesn't matter whether it's existed or
+
+ align:start position:0%
+doesn't matter whether it's existed or
+ 
+
+ align:start position:0%
+doesn't matter whether it's existed or
+you in your PhD thesis and chemistry
+
+ align:start position:0%
+you in your PhD thesis and chemistry
+ 
+
+ align:start position:0%
+you in your PhD thesis and chemistry
+synthesize something the world has never
+
+ align:start position:0%
+synthesize something the world has never
+ 
+
+ align:start position:0%
+synthesize something the world has never
+seen before your immune system can
+
+ align:start position:0%
+seen before your immune system can
+ 
+
+ align:start position:0%
+seen before your immune system can
+create an antibody or something that
+
+ align:start position:0%
+create an antibody or something that
+ 
+
+ align:start position:0%
+create an antibody or something that
+will very very specifically recognize
+
+ align:start position:0%
+will very very specifically recognize
+ 
+
+ align:start position:0%
+will very very specifically recognize
+that particular shape and just the same
+
+ align:start position:0%
+that particular shape and just the same
+ 
+
+ align:start position:0%
+that particular shape and just the same
+sort of way that you saw the the shape
+
+ align:start position:0%
+sort of way that you saw the the shape
+ 
+
+ align:start position:0%
+sort of way that you saw the the shape
+on that uh on that movie and you might
+
+ align:start position:0%
+on that uh on that movie and you might
+ 
+
+ align:start position:0%
+on that uh on that movie and you might
+think You' need to Cod a zillion pieces
+
+ align:start position:0%
+think You' need to Cod a zillion pieces
+ 
+
+ align:start position:0%
+think You' need to Cod a zillion pieces
+of miles of DNA in order to do that but
+
+ align:start position:0%
+of miles of DNA in order to do that but
+ 
+
+ align:start position:0%
+of miles of DNA in order to do that but
+there's a trick using combination and uh
+
+ align:start position:0%
+there's a trick using combination and uh
+ 
+
+ align:start position:0%
+there's a trick using combination and uh
+combinatorial functions and uh and
+
+ align:start position:0%
+combinatorial functions and uh and
+ 
+
+ align:start position:0%
+combinatorial functions and uh and
+mutation that lets your body your body
+
+ align:start position:0%
+mutation that lets your body your body
+ 
+
+ align:start position:0%
+mutation that lets your body your body
+do that and final another example which
+
+ align:start position:0%
+do that and final another example which
+ 
+
+ align:start position:0%
+do that and final another example which
+I've was showing you
+
+ align:start position:0%
+I've was showing you
+ 
+
+ align:start position:0%
+I've was showing you
+where uh they can do all sorts of little
+
+ align:start position:0%
+where uh they can do all sorts of little
+ 
+
+ align:start position:0%
+where uh they can do all sorts of little
+Motors and machines i' showed you the
+
+ align:start position:0%
+Motors and machines i' showed you the
+ 
+
+ align:start position:0%
+Motors and machines i' showed you the
+bacteria uh swimming around these these
+
+ align:start position:0%
+bacteria uh swimming around these these
+ 
+
+ align:start position:0%
+bacteria uh swimming around these these
+are just eoli and you can't see the
+
+ align:start position:0%
+are just eoli and you can't see the
+ 
+
+ align:start position:0%
+are just eoli and you can't see the
+Feller Motors but you can see them
+
+ align:start position:0%
+Feller Motors but you can see them
+ 
+
+ align:start position:0%
+Feller Motors but you can see them
+buzzing around on uh just under a cover
+
+ align:start position:0%
+buzzing around on uh just under a cover
+ 
+
+ align:start position:0%
+buzzing around on uh just under a cover
+slip some of them are stuck to the cover
+
+ align:start position:0%
+slip some of them are stuck to the cover
+ 
+
+ align:start position:0%
+slip some of them are stuck to the cover
+slip and um well there we go uh in this
+
+ align:start position:0%
+slip and um well there we go uh in this
+ 
+
+ align:start position:0%
+slip and um well there we go uh in this
+one which was taken by Howard Berg who's
+
+ align:start position:0%
+one which was taken by Howard Berg who's
+ 
+
+ align:start position:0%
+one which was taken by Howard Berg who's
+a professor at Harvard this is on his
+
+ align:start position:0%
+a professor at Harvard this is on his
+ 
+
+ align:start position:0%
+a professor at Harvard this is on his
+web just took this off his website you
+
+ align:start position:0%
+web just took this off his website you
+ 
+
+ align:start position:0%
+web just took this off his website you
+can see the the bacteria Swimming by
+
+ align:start position:0%
+can see the the bacteria Swimming by
+ 
+
+ align:start position:0%
+can see the the bacteria Swimming by
+having these flagella which are
+
+ align:start position:0%
+having these flagella which are
+ 
+
+ align:start position:0%
+having these flagella which are
+basically like sort of propellers more
+
+ align:start position:0%
+basically like sort of propellers more
+ 
+
+ align:start position:0%
+basically like sort of propellers more
+or less that they turn um here's one
+
+ align:start position:0%
+or less that they turn um here's one
+ 
+
+ align:start position:0%
+or less that they turn um here's one
+where he used the strobe so you can get
+
+ align:start position:0%
+where he used the strobe so you can get
+ 
+
+ align:start position:0%
+where he used the strobe so you can get
+a little bit better view of it and I
+
+ align:start position:0%
+a little bit better view of it and I
+ 
+
+ align:start position:0%
+a little bit better view of it and I
+showed you this picture of or in the in
+
+ align:start position:0%
+showed you this picture of or in the in
+ 
+
+ align:start position:0%
+showed you this picture of or in the in
+the first lecture so that's a machine
+
+ align:start position:0%
+the first lecture so that's a machine
+ 
+
+ align:start position:0%
+the first lecture so that's a machine
+but every single part of that machine is
+
+ align:start position:0%
+but every single part of that machine is
+ 
+
+ align:start position:0%
+but every single part of that machine is
+is made of a protein that's got a very
+
+ align:start position:0%
+is made of a protein that's got a very
+ 
+
+ align:start position:0%
+is made of a protein that's got a very
+thre diim certain threedimensional space
+
+ align:start position:0%
+thre diim certain threedimensional space
+ 
+
+ align:start position:0%
+thre diim certain threedimensional space
+and we're going to start talking about
+
+ align:start position:0%
+and we're going to start talking about
+ 
+
+ align:start position:0%
+and we're going to start talking about
+energetics uh how does a cell get energy
+
+ align:start position:0%
+energetics uh how does a cell get energy
+ 
+
+ align:start position:0%
+energetics uh how does a cell get energy
+and one of the things you might wonder
+
+ align:start position:0%
+and one of the things you might wonder
+ 
+
+ align:start position:0%
+and one of the things you might wonder
+is if you were to design such a nanom
+
+ align:start position:0%
+is if you were to design such a nanom
+ 
+
+ align:start position:0%
+is if you were to design such a nanom
+machine how would you power
+
+ align:start position:0%
+machine how would you power
+ 
+
+ align:start position:0%
+machine how would you power
+it they exist I mean it's
+
+ align:start position:0%
+it they exist I mean it's
+ 
+
+ align:start position:0%
+it they exist I mean it's
+here uh but that's why in part part I'm
+
+ align:start position:0%
+here uh but that's why in part part I'm
+ 
+
+ align:start position:0%
+here uh but that's why in part part I'm
+going to start telling talking about
+
+ align:start position:0%
+going to start telling talking about
+ 
+
+ align:start position:0%
+going to start telling talking about
+energy and how cells make energy because
+
+ align:start position:0%
+energy and how cells make energy because
+ 
+
+ align:start position:0%
+energy and how cells make energy because
+this is one of the things they have to
+
+ align:start position:0%
+this is one of the things they have to
+ 
+
+ align:start position:0%
+this is one of the things they have to
+do and that was I said was a an averaged
+
+ align:start position:0%
+do and that was I said was a an averaged
+ 
+
+ align:start position:0%
+do and that was I said was a an averaged
+electron micrograph of a lot of those
+
+ align:start position:0%
+electron micrograph of a lot of those
+ 
+
+ align:start position:0%
+electron micrograph of a lot of those
+Motors so you can see that although um
+
+ align:start position:0%
+Motors so you can see that although um
+ 
+
+ align:start position:0%
+Motors so you can see that although um
+you know that's the textbook thing the
+
+ align:start position:0%
+you know that's the textbook thing the
+ 
+
+ align:start position:0%
+you know that's the textbook thing the
+actual thing uh is pretty much the same
+
+ align:start position:0%
+actual thing uh is pretty much the same
+ 
+
+ align:start position:0%
+actual thing uh is pretty much the same
+shape this is not at a resolution where
+
+ align:start position:0%
+shape this is not at a resolution where
+ 
+
+ align:start position:0%
+shape this is not at a resolution where
+you can make out the individual proteins
+
+ align:start position:0%
+you can make out the individual proteins
+ 
+
+ align:start position:0%
+you can make out the individual proteins
+that put it together but those are know
+
+ align:start position:0%
+that put it together but those are know
+ 
+
+ align:start position:0%
+that put it together but those are know
+some of those are starting to be known
+
+ align:start position:0%
+some of those are starting to be known
+ 
+
+ align:start position:0%
+some of those are starting to be known
+in three-dimensional detail and just I
+
+ align:start position:0%
+in three-dimensional detail and just I
+ 
+
+ align:start position:0%
+in three-dimensional detail and just I
+thought you might enjoy seeing this just
+
+ align:start position:0%
+thought you might enjoy seeing this just
+ 
+
+ align:start position:0%
+thought you might enjoy seeing this just
+to convince you at some motor in this
+
+ align:start position:0%
+to convince you at some motor in this
+ 
+
+ align:start position:0%
+to convince you at some motor in this
+thing what Howard Berg did was he stuck
+
+ align:start position:0%
+thing what Howard Berg did was he stuck
+ 
+
+ align:start position:0%
+thing what Howard Berg did was he stuck
+the propeller if you will the flagella
+
+ align:start position:0%
+the propeller if you will the flagella
+ 
+
+ align:start position:0%
+the propeller if you will the flagella
+to a cover slip using using an antibody
+
+ align:start position:0%
+to a cover slip using using an antibody
+ 
+
+ align:start position:0%
+to a cover slip using using an antibody
+and then um he let them do their thing
+
+ align:start position:0%
+and then um he let them do their thing
+ 
+
+ align:start position:0%
+and then um he let them do their thing
+and normally they would be turning the
+
+ align:start position:0%
+and normally they would be turning the
+ 
+
+ align:start position:0%
+and normally they would be turning the
+propeller and in swimming but if the
+
+ align:start position:0%
+propeller and in swimming but if the
+ 
+
+ align:start position:0%
+propeller and in swimming but if the
+propeller is attached the same thing
+
+ align:start position:0%
+propeller is attached the same thing
+ 
+
+ align:start position:0%
+propeller is attached the same thing
+would happen if you held on the
+
+ align:start position:0%
+would happen if you held on the
+ 
+
+ align:start position:0%
+would happen if you held on the
+propeller of a boat and turned on the
+
+ align:start position:0%
+propeller of a boat and turned on the
+ 
+
+ align:start position:0%
+propeller of a boat and turned on the
+motor the boat would start twirling
+
+ align:start position:0%
+motor the boat would start twirling
+ 
+
+ align:start position:0%
+motor the boat would start twirling
+around and what you seeing here is
+
+ align:start position:0%
+around and what you seeing here is
+ 
+
+ align:start position:0%
+around and what you seeing here is
+bacteria they're twirling around because
+
+ align:start position:0%
+bacteria they're twirling around because
+ 
+
+ align:start position:0%
+bacteria they're twirling around because
+they're fella are stuck on and those of
+
+ align:start position:0%
+they're fella are stuck on and those of
+ 
+
+ align:start position:0%
+they're fella are stuck on and those of
+you who are observant will notice even
+
+ align:start position:0%
+you who are observant will notice even
+ 
+
+ align:start position:0%
+you who are observant will notice even
+that they change direction and that's
+
+ align:start position:0%
+that they change direction and that's
+ 
+
+ align:start position:0%
+that they change direction and that's
+part of the way the part of the system
+
+ align:start position:0%
+part of the way the part of the system
+ 
+
+ align:start position:0%
+part of the way the part of the system
+that bacteria use so they can swim
+
+ align:start position:0%
+that bacteria use so they can swim
+ 
+
+ align:start position:0%
+that bacteria use so they can swim
+towards a food source or away from from
+
+ align:start position:0%
+towards a food source or away from from
+ 
+
+ align:start position:0%
+towards a food source or away from from
+uh another one okay here's just
+
+ align:start position:0%
+uh another one okay here's just
+ 
+
+ align:start position:0%
+uh another one okay here's just
+something to let you uh guys think about
+
+ align:start position:0%
+something to let you uh guys think about
+ 
+
+ align:start position:0%
+something to let you uh guys think about
+it if anybody can figure this one out
+
+ align:start position:0%
+it if anybody can figure this one out
+ 
+
+ align:start position:0%
+it if anybody can figure this one out
+send me an email here's something else
+
+ align:start position:0%
+send me an email here's something else
+ 
+
+ align:start position:0%
+send me an email here's something else
+the phenomenon I'm going to show you is
+
+ align:start position:0%
+the phenomenon I'm going to show you is
+ 
+
+ align:start position:0%
+the phenomenon I'm going to show you is
+due to a protein made by a soil
+
+ align:start position:0%
+due to a protein made by a soil
+ 
+
+ align:start position:0%
+due to a protein made by a soil
+bacterium it's called Pamona singi you
+
+ align:start position:0%
+bacterium it's called Pamona singi you
+ 
+
+ align:start position:0%
+bacterium it's called Pamona singi you
+don't need to know that it Associates
+
+ align:start position:0%
+don't need to know that it Associates
+ 
+
+ align:start position:0%
+don't need to know that it Associates
+with plants and uh what you're going to
+
+ align:start position:0%
+with plants and uh what you're going to
+ 
+
+ align:start position:0%
+with plants and uh what you're going to
+see is a little movie made by a couple
+
+ align:start position:0%
+see is a little movie made by a couple
+ 
+
+ align:start position:0%
+see is a little movie made by a couple
+of the posts in my lab where we they
+
+ align:start position:0%
+of the posts in my lab where we they
+ 
+
+ align:start position:0%
+of the posts in my lab where we they
+took pure water and if it's pure water
+
+ align:start position:0%
+took pure water and if it's pure water
+ 
+
+ align:start position:0%
+took pure water and if it's pure water
+you can cool it below freezing you can
+
+ align:start position:0%
+you can cool it below freezing you can
+ 
+
+ align:start position:0%
+you can cool it below freezing you can
+get it down to I don't know- 8°
+
+ align:start position:0%
+get it down to I don't know- 8°
+ 
+
+ align:start position:0%
+get it down to I don't know- 8°
+centigrade and it still will be a liquid
+
+ align:start position:0%
+centigrade and it still will be a liquid
+ 
+
+ align:start position:0%
+centigrade and it still will be a liquid
+even though you know water freezes at uh
+
+ align:start position:0%
+even though you know water freezes at uh
+ 
+
+ align:start position:0%
+even though you know water freezes at uh
+at 0° centigrade and what it has to do
+
+ align:start position:0%
+at 0° centigrade and what it has to do
+ 
+
+ align:start position:0%
+at 0° centigrade and what it has to do
+in in order to turn into ice somewhere
+
+ align:start position:0%
+in in order to turn into ice somewhere
+ 
+
+ align:start position:0%
+in in order to turn into ice somewhere
+you have to nucleate the formation of an
+
+ align:start position:0%
+you have to nucleate the formation of an
+ 
+
+ align:start position:0%
+you have to nucleate the formation of an
+Ice Crystal once it goes uh going so
+
+ align:start position:0%
+Ice Crystal once it goes uh going so
+ 
+
+ align:start position:0%
+Ice Crystal once it goes uh going so
+anyway what you're going to see is some
+
+ align:start position:0%
+anyway what you're going to see is some
+ 
+
+ align:start position:0%
+anyway what you're going to see is some
+super cooled water they've made you can
+
+ align:start position:0%
+super cooled water they've made you can
+ 
+
+ align:start position:0%
+super cooled water they've made you can
+see there's uh 0 degrees there and this
+
+ align:start position:0%
+see there's uh 0 degrees there and this
+ 
+
+ align:start position:0%
+see there's uh 0 degrees there and this
+is Mei taga one of the post dogs in my
+
+ align:start position:0%
+is Mei taga one of the post dogs in my
+ 
+
+ align:start position:0%
+is Mei taga one of the post dogs in my
+lab that's the super cooled water she's
+
+ align:start position:0%
+lab that's the super cooled water she's
+ 
+
+ align:start position:0%
+lab that's the super cooled water she's
+taking a little bit of culture of this
+
+ align:start position:0%
+taking a little bit of culture of this
+ 
+
+ align:start position:0%
+taking a little bit of culture of this
+uh Pamona singi and she's just going to
+
+ align:start position:0%
+uh Pamona singi and she's just going to
+ 
+
+ align:start position:0%
+uh Pamona singi and she's just going to
+put it in give a little tiny squirt of a
+
+ align:start position:0%
+put it in give a little tiny squirt of a
+ 
+
+ align:start position:0%
+put it in give a little tiny squirt of a
+few microliters into that uh
+
+ align:start position:0%
+few microliters into that uh
+ 
+
+ align:start position:0%
+few microliters into that uh
+water now it's going all cloudy you know
+
+ align:start position:0%
+water now it's going all cloudy you know
+ 
+
+ align:start position:0%
+water now it's going all cloudy you know
+you might wonder what's uh what's
+
+ align:start position:0%
+you might wonder what's uh what's
+ 
+
+ align:start position:0%
+you might wonder what's uh what's
+happening there but as you'll discover
+
+ align:start position:0%
+happening there but as you'll discover
+ 
+
+ align:start position:0%
+happening there but as you'll discover
+what happened is that what was liquid
+
+ align:start position:0%
+what happened is that what was liquid
+ 
+
+ align:start position:0%
+what happened is that what was liquid
+water is now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ice now that is due to one
+
+ align:start position:0%
+ice now that is due to one
+ 
+
+ align:start position:0%
+ice now that is due to one
+protein that this bacteria makes and
+
+ align:start position:0%
+protein that this bacteria makes and
+ 
+
+ align:start position:0%
+protein that this bacteria makes and
+displays on its surface here's a control
+
+ align:start position:0%
+displays on its surface here's a control
+ 
+
+ align:start position:0%
+displays on its surface here's a control
+experiment this is putting in a little
+
+ align:start position:0%
+experiment this is putting in a little
+ 
+
+ align:start position:0%
+experiment this is putting in a little
+bit of um Raz oium melotti another soil
+
+ align:start position:0%
+bit of um Raz oium melotti another soil
+ 
+
+ align:start position:0%
+bit of um Raz oium melotti another soil
+organism and same amount of bacteria
+
+ align:start position:0%
+organism and same amount of bacteria
+ 
+
+ align:start position:0%
+organism and same amount of bacteria
+didn't happen Okay so that's due to a
+
+ align:start position:0%
+didn't happen Okay so that's due to a
+ 
+
+ align:start position:0%
+didn't happen Okay so that's due to a
+protein uh that was on
+
+ align:start position:0%
+protein uh that was on
+ 
+
+ align:start position:0%
+protein uh that was on
+um uh on the surface of that bacterium
+
+ align:start position:0%
+um uh on the surface of that bacterium
+ 
+
+ align:start position:0%
+um uh on the surface of that bacterium
+anybody have any idea what that could do
+
+ align:start position:0%
+anybody have any idea what that could do
+ 
+
+ align:start position:0%
+anybody have any idea what that could do
+send me an
+
+ align:start position:0%
+send me an
+ 
+
+ align:start position:0%
+send me an
+email
+
+ align:start position:0%
+email
+ 
+
+ align:start position:0%
+email
+okay there's one last class of a bial
+
+ align:start position:0%
+okay there's one last class of a bial
+ 
+
+ align:start position:0%
+okay there's one last class of a bial
+Macro
+
+ align:start position:0%
+Macro
+ 
+
+ align:start position:0%
+Macro
+Molecule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those are
+
+ align:start position:0%
+those are
+ 
+
+ align:start position:0%
+those are
+lipids these
+
+ align:start position:0%
+lipids these
+ 
+
+ align:start position:0%
+lipids these
+are a little they're a little different
+
+ align:start position:0%
+are a little they're a little different
+ 
+
+ align:start position:0%
+are a little they're a little different
+in the sense that this is not now a long
+
+ align:start position:0%
+in the sense that this is not now a long
+ 
+
+ align:start position:0%
+in the sense that this is not now a long
+chain made by joining together subunits
+
+ align:start position:0%
+chain made by joining together subunits
+ 
+
+ align:start position:0%
+chain made by joining together subunits
+as we've seen with the proteins and
+
+ align:start position:0%
+as we've seen with the proteins and
+ 
+
+ align:start position:0%
+as we've seen with the proteins and
+nucleic acids but putting together the
+
+ align:start position:0%
+nucleic acids but putting together the
+ 
+
+ align:start position:0%
+nucleic acids but putting together the
+parts necessary to make uh a lipid
+
+ align:start position:0%
+parts necessary to make uh a lipid
+ 
+
+ align:start position:0%
+parts necessary to make uh a lipid
+involve the same principle that you end
+
+ align:start position:0%
+involve the same principle that you end
+ 
+
+ align:start position:0%
+involve the same principle that you end
+up splitting out water molecules that's
+
+ align:start position:0%
+up splitting out water molecules that's
+ 
+
+ align:start position:0%
+up splitting out water molecules that's
+a theme you've heard over and over again
+
+ align:start position:0%
+a theme you've heard over and over again
+ 
+
+ align:start position:0%
+a theme you've heard over and over again
+and if we take three lung chain three
+
+ align:start position:0%
+and if we take three lung chain three
+ 
+
+ align:start position:0%
+and if we take three lung chain three
+Three fatty acids
+
+ align:start position:0%
+Three fatty acids
+ 
+
+ align:start position:0%
+Three fatty acids
+uh some number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of some number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+carbons just some arbitrary
+
+ align:start position:0%
+carbons just some arbitrary
+ 
+
+ align:start position:0%
+carbons just some arbitrary
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+here and then we take a
+
+ align:start position:0%
+here and then we take a
+ 
+
+ align:start position:0%
+here and then we take a
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+carbon compound that has three hydroxy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+groups now this is not a carbohydrate
+
+ align:start position:0%
+groups now this is not a carbohydrate
+ 
+
+ align:start position:0%
+groups now this is not a carbohydrate
+because you'll notice there's not a
+
+ align:start position:0%
+because you'll notice there's not a
+ 
+
+ align:start position:0%
+because you'll notice there's not a
+double uh there's not a double bond
+
+ align:start position:0%
+double uh there's not a double bond
+ 
+
+ align:start position:0%
+double uh there's not a double bond
+oxygen um as we uh as you saw in the
+
+ align:start position:0%
+oxygen um as we uh as you saw in the
+ 
+
+ align:start position:0%
+oxygen um as we uh as you saw in the
+carbohydrates It's actually an alcohol
+
+ align:start position:0%
+carbohydrates It's actually an alcohol
+ 
+
+ align:start position:0%
+carbohydrates It's actually an alcohol
+it's known as glycerol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we split out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+water like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this what you get is a
+
+ align:start position:0%
+this what you get is a
+ 
+
+ align:start position:0%
+this what you get is a
+fat something you're you're familiar
+
+ align:start position:0%
+fat something you're you're familiar
+ 
+
+ align:start position:0%
+fat something you're you're familiar
+with from B fat or if you get something
+
+ align:start position:0%
+with from B fat or if you get something
+ 
+
+ align:start position:0%
+with from B fat or if you get something
+like olive oil you've heard the term
+
+ align:start position:0%
+like olive oil you've heard the term
+ 
+
+ align:start position:0%
+like olive oil you've heard the term
+unsaturated fats
+
+ align:start position:0%
+unsaturated fats
+ 
+
+ align:start position:0%
+unsaturated fats
+um maybe you recall from the second
+
+ align:start position:0%
+um maybe you recall from the second
+ 
+
+ align:start position:0%
+um maybe you recall from the second
+lecture that if we had a single calent
+
+ align:start position:0%
+lecture that if we had a single calent
+ 
+
+ align:start position:0%
+lecture that if we had a single calent
+Bond uh or if we had a double or a
+
+ align:start position:0%
+Bond uh or if we had a double or a
+ 
+
+ align:start position:0%
+Bond uh or if we had a double or a
+triple bond that was called an
+
+ align:start position:0%
+triple bond that was called an
+ 
+
+ align:start position:0%
+triple bond that was called an
+unsaturated uh fatty uh unsaturated Bond
+
+ align:start position:0%
+unsaturated uh fatty uh unsaturated Bond
+ 
+
+ align:start position:0%
+unsaturated uh fatty uh unsaturated Bond
+so if you have an
+
+ align:start position:0%
+so if you have an
+ 
+
+ align:start position:0%
+so if you have an
+unsaturated bond in here somewhere then
+
+ align:start position:0%
+unsaturated bond in here somewhere then
+ 
+
+ align:start position:0%
+unsaturated bond in here somewhere then
+you end up with an unsaturated fat and
+
+ align:start position:0%
+you end up with an unsaturated fat and
+ 
+
+ align:start position:0%
+you end up with an unsaturated fat and
+most of you know probably something like
+
+ align:start position:0%
+most of you know probably something like
+ 
+
+ align:start position:0%
+most of you know probably something like
+beef fat is solid if you put it in the
+
+ align:start position:0%
+beef fat is solid if you put it in the
+ 
+
+ align:start position:0%
+beef fat is solid if you put it in the
+refrigerator and something like peanut
+
+ align:start position:0%
+refrigerator and something like peanut
+ 
+
+ align:start position:0%
+refrigerator and something like peanut
+oil will stay liquid and that's because
+
+ align:start position:0%
+oil will stay liquid and that's because
+ 
+
+ align:start position:0%
+oil will stay liquid and that's because
+if you you have just
+
+ align:start position:0%
+if you you have just
+ 
+
+ align:start position:0%
+if you you have just
+saturated uh side chains on from this
+
+ align:start position:0%
+saturated uh side chains on from this
+ 
+
+ align:start position:0%
+saturated uh side chains on from this
+then they pack together very very
+
+ align:start position:0%
+then they pack together very very
+ 
+
+ align:start position:0%
+then they pack together very very
+tightly and they they will form a solid
+
+ align:start position:0%
+tightly and they they will form a solid
+ 
+
+ align:start position:0%
+tightly and they they will form a solid
+if you put a double bond in then there's
+
+ align:start position:0%
+if you put a double bond in then there's
+ 
+
+ align:start position:0%
+if you put a double bond in then there's
+a kink in the backbone and it's hard for
+
+ align:start position:0%
+a kink in the backbone and it's hard for
+ 
+
+ align:start position:0%
+a kink in the backbone and it's hard for
+these things to uh pack packed together
+
+ align:start position:0%
+these things to uh pack packed together
+ 
+
+ align:start position:0%
+these things to uh pack packed together
+and that's why they're called um called
+
+ align:start position:0%
+and that's why they're called um called
+ 
+
+ align:start position:0%
+and that's why they're called um called
+unsaturated uh unsaturated fats now
+
+ align:start position:0%
+unsaturated uh unsaturated fats now
+ 
+
+ align:start position:0%
+unsaturated uh unsaturated fats now
+there's a very particular kind of of
+
+ align:start position:0%
+there's a very particular kind of of
+ 
+
+ align:start position:0%
+there's a very particular kind of of
+lipid that's of unbelievable importance
+
+ align:start position:0%
+lipid that's of unbelievable importance
+ 
+
+ align:start position:0%
+lipid that's of unbelievable importance
+in bi ology and that's known as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phospho lipid and the reason that's so
+
+ align:start position:0%
+phospho lipid and the reason that's so
+ 
+
+ align:start position:0%
+phospho lipid and the reason that's so
+important is that that is the boundary
+
+ align:start position:0%
+important is that that is the boundary
+ 
+
+ align:start position:0%
+important is that that is the boundary
+that determines the outside of a of a
+
+ align:start position:0%
+that determines the outside of a of a
+ 
+
+ align:start position:0%
+that determines the outside of a of a
+cell so every cell every organism either
+
+ align:start position:0%
+cell so every cell every organism either
+ 
+
+ align:start position:0%
+cell so every cell every organism either
+is a single cell or is made up of
+
+ align:start position:0%
+is a single cell or is made up of
+ 
+
+ align:start position:0%
+is a single cell or is made up of
+multiple cells and I said it the in the
+
+ align:start position:0%
+multiple cells and I said it the in the
+ 
+
+ align:start position:0%
+multiple cells and I said it the in the
+first lecture that the one of the
+
+ align:start position:0%
+first lecture that the one of the
+ 
+
+ align:start position:0%
+first lecture that the one of the
+secrets to life is having a boundary
+
+ align:start position:0%
+secrets to life is having a boundary
+ 
+
+ align:start position:0%
+secrets to life is having a boundary
+that goes around your insides that
+
+ align:start position:0%
+that goes around your insides that
+ 
+
+ align:start position:0%
+that goes around your insides that
+separates your sides from all the rest
+
+ align:start position:0%
+separates your sides from all the rest
+ 
+
+ align:start position:0%
+separates your sides from all the rest
+of the of the universe and the way the
+
+ align:start position:0%
+of the of the universe and the way the
+ 
+
+ align:start position:0%
+of the of the universe and the way the
+these uh
+
+ align:start position:0%
+these uh
+ 
+
+ align:start position:0%
+these uh
+membranes is they're called are made
+
+ align:start position:0%
+membranes is they're called are made
+ 
+
+ align:start position:0%
+membranes is they're called are made
+of it's what's known as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phospho lipid by layer and it's the same
+
+ align:start position:0%
+phospho lipid by layer and it's the same
+ 
+
+ align:start position:0%
+phospho lipid by layer and it's the same
+Principle as before it uses a a
+
+ align:start position:0%
+Principle as before it uses a a
+ 
+
+ align:start position:0%
+Principle as before it uses a a
+glycerol except that one of
+
+ align:start position:0%
+glycerol except that one of
+ 
+
+ align:start position:0%
+glycerol except that one of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the fatty acids is replaced by a
+
+ align:start position:0%
+one of the fatty acids is replaced by a
+ 
+
+ align:start position:0%
+one of the fatty acids is replaced by a
+phosphate group that will have some kind
+
+ align:start position:0%
+phosphate group that will have some kind
+ 
+
+ align:start position:0%
+phosphate group that will have some kind
+of decoration uh added onto it and the
+
+ align:start position:0%
+of decoration uh added onto it and the
+ 
+
+ align:start position:0%
+of decoration uh added onto it and the
+other will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have fatty acids at the other two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positions
+
+ align:start position:0%
+positions
+ 
+
+ align:start position:0%
+positions
+now you'll notice by splitting out water
+
+ align:start position:0%
+now you'll notice by splitting out water
+ 
+
+ align:start position:0%
+now you'll notice by splitting out water
+here what we the kind of bond we have
+
+ align:start position:0%
+here what we the kind of bond we have
+ 
+
+ align:start position:0%
+here what we the kind of bond we have
+created the chemical name of this is an
+
+ align:start position:0%
+created the chemical name of this is an
+ 
+
+ align:start position:0%
+created the chemical name of this is an
+ester
+
+ align:start position:0%
+ester
+ 
+
+ align:start position:0%
+ester
+Bond if we wanted to add it uh break it
+
+ align:start position:0%
+Bond if we wanted to add it uh break it
+ 
+
+ align:start position:0%
+Bond if we wanted to add it uh break it
+we could add uh Add Water back across it
+
+ align:start position:0%
+we could add uh Add Water back across it
+ 
+
+ align:start position:0%
+we could add uh Add Water back across it
+um so what's important about the this
+
+ align:start position:0%
+um so what's important about the this
+ 
+
+ align:start position:0%
+um so what's important about the this
+molecule is this part of the
+
+ align:start position:0%
+molecule is this part of the
+ 
+
+ align:start position:0%
+molecule is this part of the
+molecule if you will
+
+ align:start position:0%
+molecule if you will
+ 
+
+ align:start position:0%
+molecule if you will
+is water loving because there the uh
+
+ align:start position:0%
+is water loving because there the uh
+ 
+
+ align:start position:0%
+is water loving because there the uh
+very polar bonds here the the oxygen had
+
+ align:start position:0%
+very polar bonds here the the oxygen had
+ 
+
+ align:start position:0%
+very polar bonds here the the oxygen had
+here would have a negative charge on it
+
+ align:start position:0%
+here would have a negative charge on it
+ 
+
+ align:start position:0%
+here would have a negative charge on it
+it under physiological
+
+ align:start position:0%
+it under physiological
+ 
+
+ align:start position:0%
+it under physiological
+conditions and this part is if you will
+
+ align:start position:0%
+conditions and this part is if you will
+ 
+
+ align:start position:0%
+conditions and this part is if you will
+is water
+
+ align:start position:0%
+is water
+ 
+
+ align:start position:0%
+is water
+hating so this is phospholipids are off
+
+ align:start position:0%
+hating so this is phospholipids are off
+ 
+
+ align:start position:0%
+hating so this is phospholipids are off
+opposite often represented in the
+
+ align:start position:0%
+opposite often represented in the
+ 
+
+ align:start position:0%
+opposite often represented in the
+following way where this is the water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+loving
+
+ align:start position:0%
+loving
+ 
+
+ align:start position:0%
+loving
+and then this would be the water hating
+
+ align:start position:0%
+and then this would be the water hating
+ 
+
+ align:start position:0%
+and then this would be the water hating
+part here and so if you take
+
+ align:start position:0%
+part here and so if you take
+ 
+
+ align:start position:0%
+part here and so if you take
+phospholipids and you just try and
+
+ align:start position:0%
+phospholipids and you just try and
+ 
+
+ align:start position:0%
+phospholipids and you just try and
+disperse them in water they
+
+ align:start position:0%
+disperse them in water they
+ 
+
+ align:start position:0%
+disperse them in water they
+spontaneously self assemble into
+
+ align:start position:0%
+spontaneously self assemble into
+ 
+
+ align:start position:0%
+spontaneously self assemble into
+structures that bring the
+
+ align:start position:0%
+structures that bring the
+ 
+
+ align:start position:0%
+structures that bring the
+water loving
+
+ align:start position:0%
+water loving
+ 
+
+ align:start position:0%
+water loving
+Parts together
+
+ align:start position:0%
+Parts together
+ 
+
+ align:start position:0%
+Parts together
+and the water hating Parts together and
+
+ align:start position:0%
+and the water hating Parts together and
+ 
+
+ align:start position:0%
+and the water hating Parts together and
+by so doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this they form what's known as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phospholipid by layer and that's what
+
+ align:start position:0%
+phospholipid by layer and that's what
+ 
+
+ align:start position:0%
+phospholipid by layer and that's what
+this membrane is made of membrane of a
+
+ align:start position:0%
+this membrane is made of membrane of a
+ 
+
+ align:start position:0%
+this membrane is made of membrane of a
+bacterial cell the membrane of our cells
+
+ align:start position:0%
+bacterial cell the membrane of our cells
+ 
+
+ align:start position:0%
+bacterial cell the membrane of our cells
+virtually the the same same thing it has
+
+ align:start position:0%
+virtually the the same same thing it has
+ 
+
+ align:start position:0%
+virtually the the same same thing it has
+the property that is not permeable to
+
+ align:start position:0%
+the property that is not permeable to
+ 
+
+ align:start position:0%
+the property that is not permeable to
+very much water can get across it a very
+
+ align:start position:0%
+very much water can get across it a very
+ 
+
+ align:start position:0%
+very much water can get across it a very
+limited number of of other chemical
+
+ align:start position:0%
+limited number of of other chemical
+ 
+
+ align:start position:0%
+limited number of of other chemical
+compounds but most things can't and so
+
+ align:start position:0%
+compounds but most things can't and so
+ 
+
+ align:start position:0%
+compounds but most things can't and so
+so what the cell by having this membrane
+
+ align:start position:0%
+so what the cell by having this membrane
+ 
+
+ align:start position:0%
+so what the cell by having this membrane
+what the what the cell is able to do
+
+ align:start position:0%
+what the what the cell is able to do
+ 
+
+ align:start position:0%
+what the what the cell is able to do
+then is control who comes in and who
+
+ align:start position:0%
+then is control who comes in and who
+ 
+
+ align:start position:0%
+then is control who comes in and who
+comes out and the way it does that is it
+
+ align:start position:0%
+comes out and the way it does that is it
+ 
+
+ align:start position:0%
+comes out and the way it does that is it
+has to put particular importers or
+
+ align:start position:0%
+has to put particular importers or
+ 
+
+ align:start position:0%
+has to put particular importers or
+exporters embedded in the membrane that
+
+ align:start position:0%
+exporters embedded in the membrane that
+ 
+
+ align:start position:0%
+exporters embedded in the membrane that
+can carry out those functions because as
+
+ align:start position:0%
+can carry out those functions because as
+ 
+
+ align:start position:0%
+can carry out those functions because as
+you would guess any system would have to
+
+ align:start position:0%
+you would guess any system would have to
+ 
+
+ align:start position:0%
+you would guess any system would have to
+bring stuff in get rid of waste you have
+
+ align:start position:0%
+bring stuff in get rid of waste you have
+ 
+
+ align:start position:0%
+bring stuff in get rid of waste you have
+to be able to go back and forth the
+
+ align:start position:0%
+to be able to go back and forth the
+ 
+
+ align:start position:0%
+to be able to go back and forth the
+things that do all those transports
+
+ align:start position:0%
+things that do all those transports
+ 
+
+ align:start position:0%
+things that do all those transports
+across the membrane what kind of
+
+ align:start position:0%
+across the membrane what kind of
+ 
+
+ align:start position:0%
+across the membrane what kind of
+molecule do you think it would likely to
+
+ align:start position:0%
+molecule do you think it would likely to
+ 
+
+ align:start position:0%
+molecule do you think it would likely to
+be if you were going to Nature was going
+
+ align:start position:0%
+be if you were going to Nature was going
+ 
+
+ align:start position:0%
+be if you were going to Nature was going
+to design something that was a pump to
+
+ align:start position:0%
+to design something that was a pump to
+ 
+
+ align:start position:0%
+to design something that was a pump to
+get something in or something that would
+
+ align:start position:0%
+get something in or something that would
+ 
+
+ align:start position:0%
+get something in or something that would
+get something out any
+
+ align:start position:0%
+get something out any
+ 
+
+ align:start position:0%
+get something out any
+idea what kind of
+
+ align:start position:0%
+idea what kind of
+ 
+
+ align:start position:0%
+idea what kind of
+molecule take a gas I've said so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far protein yeah absolutely and um let
+
+ align:start position:0%
+far protein yeah absolutely and um let
+ 
+
+ align:start position:0%
+far protein yeah absolutely and um let
+me just sort of show you a couple little
+
+ align:start position:0%
+me just sort of show you a couple little
+ 
+
+ align:start position:0%
+me just sort of show you a couple little
+pictures here so here's a representation
+
+ align:start position:0%
+pictures here so here's a representation
+ 
+
+ align:start position:0%
+pictures here so here's a representation
+of this phospholipid Bayer this is
+
+ align:start position:0%
+of this phospholipid Bayer this is
+ 
+
+ align:start position:0%
+of this phospholipid Bayer this is
+pretty standard stuff this is what you'd
+
+ align:start position:0%
+pretty standard stuff this is what you'd
+ 
+
+ align:start position:0%
+pretty standard stuff this is what you'd
+put on a Blackboard here's in Gray now
+
+ align:start position:0%
+put on a Blackboard here's in Gray now
+ 
+
+ align:start position:0%
+put on a Blackboard here's in Gray now
+the phospholipid and here's one of these
+
+ align:start position:0%
+the phospholipid and here's one of these
+ 
+
+ align:start position:0%
+the phospholipid and here's one of these
+proteins a picture one of these proteins
+
+ align:start position:0%
+proteins a picture one of these proteins
+ 
+
+ align:start position:0%
+proteins a picture one of these proteins
+that that functions to get things across
+
+ align:start position:0%
+that that functions to get things across
+ 
+
+ align:start position:0%
+that that functions to get things across
+the membrane and hopefully what you can
+
+ align:start position:0%
+the membrane and hopefully what you can
+ 
+
+ align:start position:0%
+the membrane and hopefully what you can
+see now is that it's made up of a whole
+
+ align:start position:0%
+see now is that it's made up of a whole
+ 
+
+ align:start position:0%
+see now is that it's made up of a whole
+lot of Alpha helices and they pack
+
+ align:start position:0%
+lot of Alpha helices and they pack
+ 
+
+ align:start position:0%
+lot of Alpha helices and they pack
+together to give sort of a cylinder made
+
+ align:start position:0%
+together to give sort of a cylinder made
+ 
+
+ align:start position:0%
+together to give sort of a cylinder made
+up of different Alpha helices that weave
+
+ align:start position:0%
+up of different Alpha helices that weave
+ 
+
+ align:start position:0%
+up of different Alpha helices that weave
+in and out of like this and then you by
+
+ align:start position:0%
+in and out of like this and then you by
+ 
+
+ align:start position:0%
+in and out of like this and then you by
+this sort of trick the protein is able
+
+ align:start position:0%
+this sort of trick the protein is able
+ 
+
+ align:start position:0%
+this sort of trick the protein is able
+to create a channel that runs up and
+
+ align:start position:0%
+to create a channel that runs up and
+ 
+
+ align:start position:0%
+to create a channel that runs up and
+down the middle of the of this Protein
+
+ align:start position:0%
+down the middle of the of this Protein
+ 
+
+ align:start position:0%
+down the middle of the of this Protein
+that's embedded in the membrane and then
+
+ align:start position:0%
+that's embedded in the membrane and then
+ 
+
+ align:start position:0%
+that's embedded in the membrane and then
+depending on the characteristics of that
+
+ align:start position:0%
+depending on the characteristics of that
+ 
+
+ align:start position:0%
+depending on the characteristics of that
+challenge it can of that channel it can
+
+ align:start position:0%
+challenge it can of that channel it can
+ 
+
+ align:start position:0%
+challenge it can of that channel it can
+either be used to bring stuff in or or
+
+ align:start position:0%
+either be used to bring stuff in or or
+ 
+
+ align:start position:0%
+either be used to bring stuff in or or
+or get rid of it now there is a a more
+
+ align:start position:0%
+or get rid of it now there is a a more
+ 
+
+ align:start position:0%
+or get rid of it now there is a a more
+fanciful depiction of it this is not
+
+ align:start position:0%
+fanciful depiction of it this is not
+ 
+
+ align:start position:0%
+fanciful depiction of it this is not
+reality but there you are with the water
+
+ align:start position:0%
+reality but there you are with the water
+ 
+
+ align:start position:0%
+reality but there you are with the water
+loving Parts here the fatty acids going
+
+ align:start position:0%
+loving Parts here the fatty acids going
+ 
+
+ align:start position:0%
+loving Parts here the fatty acids going
+in and this is supposed to be one of
+
+ align:start position:0%
+in and this is supposed to be one of
+ 
+
+ align:start position:0%
+in and this is supposed to be one of
+these membrane proteins now this next
+
+ align:start position:0%
+these membrane proteins now this next
+ 
+
+ align:start position:0%
+these membrane proteins now this next
+movie is
+
+ align:start position:0%
+movie is
+ 
+
+ align:start position:0%
+movie is
+trying to pretend here that it's looking
+
+ align:start position:0%
+trying to pretend here that it's looking
+ 
+
+ align:start position:0%
+trying to pretend here that it's looking
+at one of these membrane proteins
+
+ align:start position:0%
+at one of these membrane proteins
+ 
+
+ align:start position:0%
+at one of these membrane proteins
+colored here in red as it spans the
+
+ align:start position:0%
+colored here in red as it spans the
+ 
+
+ align:start position:0%
+colored here in red as it spans the
+membrane so here's looking from the
+
+ align:start position:0%
+membrane so here's looking from the
+ 
+
+ align:start position:0%
+membrane so here's looking from the
+membrane surface on and now it's going
+
+ align:start position:0%
+membrane surface on and now it's going
+ 
+
+ align:start position:0%
+membrane surface on and now it's going
+to dive into this thing as it crosses
+
+ align:start position:0%
+to dive into this thing as it crosses
+ 
+
+ align:start position:0%
+to dive into this thing as it crosses
+the membrane and it's basically what
+
+ align:start position:0%
+the membrane and it's basically what
+ 
+
+ align:start position:0%
+the membrane and it's basically what
+this movie is letting you do is feel
+
+ align:start position:0%
+this movie is letting you do is feel
+ 
+
+ align:start position:0%
+this movie is letting you do is feel
+like if you were the molecule that's
+
+ align:start position:0%
+like if you were the molecule that's
+ 
+
+ align:start position:0%
+like if you were the molecule that's
+being transported across the membrane
+
+ align:start position:0%
+being transported across the membrane
+ 
+
+ align:start position:0%
+being transported across the membrane
+you see how you'd go right down through
+
+ align:start position:0%
+you see how you'd go right down through
+ 
+
+ align:start position:0%
+you see how you'd go right down through
+uh a channel in the middle of the of the
+
+ align:start position:0%
+uh a channel in the middle of the of the
+ 
+
+ align:start position:0%
+uh a channel in the middle of the of the
+protein so
+
+ align:start position:0%
+protein so
+ 
+
+ align:start position:0%
+protein so
+that's one of the
+
+ align:start position:0%
+that's one of the
+ 
+
+ align:start position:0%
+that's one of the
+underlying principles then is
+
+ align:start position:0%
+underlying principles then is
+ 
+
+ align:start position:0%
+underlying principles then is
+that you have a phospholipid boundary
+
+ align:start position:0%
+that you have a phospholipid boundary
+ 
+
+ align:start position:0%
+that you have a phospholipid boundary
+that's that's critical for life but then
+
+ align:start position:0%
+that's that's critical for life but then
+ 
+
+ align:start position:0%
+that's that's critical for life but then
+to have everything else that needs to
+
+ align:start position:0%
+to have everything else that needs to
+ 
+
+ align:start position:0%
+to have everything else that needs to
+happen the the cell makes a series of
+
+ align:start position:0%
+happen the the cell makes a series of
+ 
+
+ align:start position:0%
+happen the the cell makes a series of
+proteins that function either to bring
+
+ align:start position:0%
+proteins that function either to bring
+ 
+
+ align:start position:0%
+proteins that function either to bring
+stuff in or to bring it out or in the
+
+ align:start position:0%
+stuff in or to bring it out or in the
+ 
+
+ align:start position:0%
+stuff in or to bring it out or in the
+case of something like the Feller motor
+
+ align:start position:0%
+case of something like the Feller motor
+ 
+
+ align:start position:0%
+case of something like the Feller motor
+uh that we talked about it has to embed
+
+ align:start position:0%
+uh that we talked about it has to embed
+ 
+
+ align:start position:0%
+uh that we talked about it has to embed
+part of the Machinery right in the in
+
+ align:start position:0%
+part of the Machinery right in the in
+ 
+
+ align:start position:0%
+part of the Machinery right in the in
+the membrane and one last picture I just
+
+ align:start position:0%
+the membrane and one last picture I just
+ 
+
+ align:start position:0%
+the membrane and one last picture I just
+want to show you usually uh even on that
+
+ align:start position:0%
+want to show you usually uh even on that
+ 
+
+ align:start position:0%
+want to show you usually uh even on that
+movie you tend to see the cell
+
+ align:start position:0%
+movie you tend to see the cell
+ 
+
+ align:start position:0%
+movie you tend to see the cell
+represented something like this with a
+
+ align:start position:0%
+represented something like this with a
+ 
+
+ align:start position:0%
+represented something like this with a
+membrane and every once in a while
+
+ align:start position:0%
+membrane and every once in a while
+ 
+
+ align:start position:0%
+membrane and every once in a while
+there's a protein this is a what it's a
+
+ align:start position:0%
+there's a protein this is a what it's a
+ 
+
+ align:start position:0%
+there's a protein this is a what it's a
+cartoon but it it is a much more much
+
+ align:start position:0%
+cartoon but it it is a much more much
+ 
+
+ align:start position:0%
+cartoon but it it is a much more much
+closer to um scale to scale drawing this
+
+ align:start position:0%
+closer to um scale to scale drawing this
+ 
+
+ align:start position:0%
+closer to um scale to scale drawing this
+is a back an eoli cell now they have an
+
+ align:start position:0%
+is a back an eoli cell now they have an
+ 
+
+ align:start position:0%
+is a back an eoli cell now they have an
+extra membrane that we won't worry about
+
+ align:start position:0%
+extra membrane that we won't worry about
+ 
+
+ align:start position:0%
+extra membrane that we won't worry about
+right for the moment but right there
+
+ align:start position:0%
+right for the moment but right there
+ 
+
+ align:start position:0%
+right for the moment but right there
+there's this little piece we can see
+
+ align:start position:0%
+there's this little piece we can see
+ 
+
+ align:start position:0%
+there's this little piece we can see
+little bits of is the the cell's
+
+ align:start position:0%
+little bits of is the the cell's
+ 
+
+ align:start position:0%
+little bits of is the the cell's
+membrane and what this picture is
+
+ align:start position:0%
+membrane and what this picture is
+ 
+
+ align:start position:0%
+membrane and what this picture is
+showing that this membrane is just
+
+ align:start position:0%
+showing that this membrane is just
+ 
+
+ align:start position:0%
+showing that this membrane is just
+absolutely studded with membrane
+
+ align:start position:0%
+absolutely studded with membrane
+ 
+
+ align:start position:0%
+absolutely studded with membrane
+proteins that are going to carry out
+
+ align:start position:0%
+proteins that are going to carry out
+ 
+
+ align:start position:0%
+proteins that are going to carry out
+very F various functions and here
+
+ align:start position:0%
+very F various functions and here
+ 
+
+ align:start position:0%
+very F various functions and here
+actually we're seeing that that motor
+
+ align:start position:0%
+actually we're seeing that that motor
+ 
+
+ align:start position:0%
+actually we're seeing that that motor
+which is embedded both in the inner and
+
+ align:start position:0%
+which is embedded both in the inner and
+ 
+
+ align:start position:0%
+which is embedded both in the inner and
+outer membrane and there's the the motor
+
+ align:start position:0%
+outer membrane and there's the the motor
+ 
+
+ align:start position:0%
+outer membrane and there's the the motor
+going off but a couple of things maybe
+
+ align:start position:0%
+going off but a couple of things maybe
+ 
+
+ align:start position:0%
+going off but a couple of things maybe
+you can take home from this there's a
+
+ align:start position:0%
+you can take home from this there's a
+ 
+
+ align:start position:0%
+you can take home from this there's a
+lot of membrane proteins a lot of
+
+ align:start position:0%
+lot of membrane proteins a lot of
+ 
+
+ align:start position:0%
+lot of membrane proteins a lot of
+proteins stuck in those membranes that
+
+ align:start position:0%
+proteins stuck in those membranes that
+ 
+
+ align:start position:0%
+proteins stuck in those membranes that
+control what goes in and out you also
+
+ align:start position:0%
+control what goes in and out you also
+ 
+
+ align:start position:0%
+control what goes in and out you also
+get a sense from here of how crowded the
+
+ align:start position:0%
+get a sense from here of how crowded the
+ 
+
+ align:start position:0%
+get a sense from here of how crowded the
+cytoplasm in is the proteins are really
+
+ align:start position:0%
+cytoplasm in is the proteins are really
+ 
+
+ align:start position:0%
+cytoplasm in is the proteins are really
+at amazingly high concentrations when
+
+ align:start position:0%
+at amazingly high concentrations when
+ 
+
+ align:start position:0%
+at amazingly high concentrations when
+they're in inside of the the uh the
+
+ align:start position:0%
+they're in inside of the the uh the
+ 
+
+ align:start position:0%
+they're in inside of the the uh the
+cytoplasm Okay so we've talked up till
+
+ align:start position:0%
+cytoplasm Okay so we've talked up till
+ 
+
+ align:start position:0%
+cytoplasm Okay so we've talked up till
+that's sort of a quick
+
+ align:start position:0%
+that's sort of a quick
+ 
+
+ align:start position:0%
+that's sort of a quick
+survey it's nothing more than a really
+
+ align:start position:0%
+survey it's nothing more than a really
+ 
+
+ align:start position:0%
+survey it's nothing more than a really
+superficial introduction to the four
+
+ align:start position:0%
+superficial introduction to the four
+ 
+
+ align:start position:0%
+superficial introduction to the four
+classes of of biomolecules but to go uh
+
+ align:start position:0%
+classes of of biomolecules but to go uh
+ 
+
+ align:start position:0%
+classes of of biomolecules but to go uh
+any further we're going to have to think
+
+ align:start position:0%
+any further we're going to have to think
+ 
+
+ align:start position:0%
+any further we're going to have to think
+a little bit about now the
+
+ align:start position:0%
+a little bit about now the
+ 
+
+ align:start position:0%
+a little bit about now the
+characteristics of living cells now I
+
+ align:start position:0%
+characteristics of living cells now I
+ 
+
+ align:start position:0%
+characteristics of living cells now I
+don't know if any of you know what this
+
+ align:start position:0%
+don't know if any of you know what this
+ 
+
+ align:start position:0%
+don't know if any of you know what this
+is but uh this is baker's yeast but you
+
+ align:start position:0%
+is but uh this is baker's yeast but you
+ 
+
+ align:start position:0%
+is but uh this is baker's yeast but you
+if you were making bread you know you
+
+ align:start position:0%
+if you were making bread you know you
+ 
+
+ align:start position:0%
+if you were making bread you know you
+put some yeast in it and it divides and
+
+ align:start position:0%
+put some yeast in it and it divides and
+ 
+
+ align:start position:0%
+put some yeast in it and it divides and
+it gives out carbon dioxide as a waste
+
+ align:start position:0%
+it gives out carbon dioxide as a waste
+ 
+
+ align:start position:0%
+it gives out carbon dioxide as a waste
+product and makes the the um the yeast
+
+ align:start position:0%
+product and makes the the um the yeast
+ 
+
+ align:start position:0%
+product and makes the the um the yeast
+uh makes the bread rise and what's
+
+ align:start position:0%
+uh makes the bread rise and what's
+ 
+
+ align:start position:0%
+uh makes the bread rise and what's
+happened in that little movie you just
+
+ align:start position:0%
+happened in that little movie you just
+ 
+
+ align:start position:0%
+happened in that little movie you just
+saw where two cells dividing to give
+
+ align:start position:0%
+saw where two cells dividing to give
+ 
+
+ align:start position:0%
+saw where two cells dividing to give
+four and four dividing to give eight and
+
+ align:start position:0%
+four and four dividing to give eight and
+ 
+
+ align:start position:0%
+four and four dividing to give eight and
+I don't know what we're up to here but
+
+ align:start position:0%
+I don't know what we're up to here but
+ 
+
+ align:start position:0%
+I don't know what we're up to here but
+um you can see a cell grow that's sped
+
+ align:start position:0%
+um you can see a cell grow that's sped
+ 
+
+ align:start position:0%
+um you can see a cell grow that's sped
+up it takes um probably something closer
+
+ align:start position:0%
+up it takes um probably something closer
+ 
+
+ align:start position:0%
+up it takes um probably something closer
+to an hour for a cell division to take
+
+ align:start position:0%
+to an hour for a cell division to take
+ 
+
+ align:start position:0%
+to an hour for a cell division to take
+place but this is the kind of thing that
+
+ align:start position:0%
+place but this is the kind of thing that
+ 
+
+ align:start position:0%
+place but this is the kind of thing that
+microorganisms do when they grow is you
+
+ align:start position:0%
+microorganisms do when they grow is you
+ 
+
+ align:start position:0%
+microorganisms do when they grow is you
+can start with a single
+
+ align:start position:0%
+can start with a single
+ 
+
+ align:start position:0%
+can start with a single
+cell and it will make two cells that are
+
+ align:start position:0%
+cell and it will make two cells that are
+ 
+
+ align:start position:0%
+cell and it will make two cells that are
+identical to
+
+ align:start position:0%
+identical to
+ 
+
+ align:start position:0%
+identical to
+itself and those will
+
+ align:start position:0%
+itself and those will
+ 
+
+ align:start position:0%
+itself and those will
+make four and what happen happens when
+
+ align:start position:0%
+make four and what happen happens when
+ 
+
+ align:start position:0%
+make four and what happen happens when
+we start out as a single cell we start
+
+ align:start position:0%
+we start out as a single cell we start
+ 
+
+ align:start position:0%
+we start out as a single cell we start
+out initially like this and we make
+
+ align:start position:0%
+out initially like this and we make
+ 
+
+ align:start position:0%
+out initially like this and we make
+cells that are identical at the
+
+ align:start position:0%
+cells that are identical at the
+ 
+
+ align:start position:0%
+cells that are identical at the
+beginning and those are the famous
+
+ align:start position:0%
+beginning and those are the famous
+ 
+
+ align:start position:0%
+beginning and those are the famous
+embryonic stem cells because at this
+
+ align:start position:0%
+embryonic stem cells because at this
+ 
+
+ align:start position:0%
+embryonic stem cells because at this
+point they can become any cell in your
+
+ align:start position:0%
+point they can become any cell in your
+ 
+
+ align:start position:0%
+point they can become any cell in your
+body and if if you're a yeast it doesn't
+
+ align:start position:0%
+body and if if you're a yeast it doesn't
+ 
+
+ align:start position:0%
+body and if if you're a yeast it doesn't
+matter everything you make is the same
+
+ align:start position:0%
+matter everything you make is the same
+ 
+
+ align:start position:0%
+matter everything you make is the same
+if it's if it's one of it's a human once
+
+ align:start position:0%
+if it's if it's one of it's a human once
+ 
+
+ align:start position:0%
+if it's if it's one of it's a human once
+you start dividing at some point cells
+
+ align:start position:0%
+you start dividing at some point cells
+ 
+
+ align:start position:0%
+you start dividing at some point cells
+are going to have to start making
+
+ align:start position:0%
+are going to have to start making
+ 
+
+ align:start position:0%
+are going to have to start making
+decisions and they're going to have to
+
+ align:start position:0%
+decisions and they're going to have to
+ 
+
+ align:start position:0%
+decisions and they're going to have to
+start the progyny will have to start to
+
+ align:start position:0%
+start the progyny will have to start to
+ 
+
+ align:start position:0%
+start the progyny will have to start to
+be different of each other so that you
+
+ align:start position:0%
+be different of each other so that you
+ 
+
+ align:start position:0%
+be different of each other so that you
+can have something that's an eye and
+
+ align:start position:0%
+can have something that's an eye and
+ 
+
+ align:start position:0%
+can have something that's an eye and
+another cell that's in the liver and so
+
+ align:start position:0%
+another cell that's in the liver and so
+ 
+
+ align:start position:0%
+another cell that's in the liver and so
+on and we'll talk a little bit about
+
+ align:start position:0%
+on and we'll talk a little bit about
+ 
+
+ align:start position:0%
+on and we'll talk a little bit about
+that as we go on but the major Point uh
+
+ align:start position:0%
+that as we go on but the major Point uh
+ 
+
+ align:start position:0%
+that as we go on but the major Point uh
+right at this point is that all of life
+
+ align:start position:0%
+right at this point is that all of life
+ 
+
+ align:start position:0%
+right at this point is that all of life
+involves one cell dividing and giving a
+
+ align:start position:0%
+involves one cell dividing and giving a
+ 
+
+ align:start position:0%
+involves one cell dividing and giving a
+couple of other cells and then those
+
+ align:start position:0%
+couple of other cells and then those
+ 
+
+ align:start position:0%
+couple of other cells and then those
+going on so um these cells as we said
+
+ align:start position:0%
+going on so um these cells as we said
+ 
+
+ align:start position:0%
+going on so um these cells as we said
+characteristics of of organisms which
+
+ align:start position:0%
+characteristics of of organisms which
+ 
+
+ align:start position:0%
+characteristics of of organisms which
+are to be true there at their cellular
+
+ align:start position:0%
+are to be true there at their cellular
+ 
+
+ align:start position:0%
+are to be true there at their cellular
+level as well is that they carry out
+
+ align:start position:0%
+level as well is that they carry out
+ 
+
+ align:start position:0%
+level as well is that they carry out
+metabolism they undergo regulated growth
+
+ align:start position:0%
+metabolism they undergo regulated growth
+ 
+
+ align:start position:0%
+metabolism they undergo regulated growth
+and you have a nice example of yeast
+
+ align:start position:0%
+and you have a nice example of yeast
+ 
+
+ align:start position:0%
+and you have a nice example of yeast
+undergoing regulated growth and they
+
+ align:start position:0%
+undergoing regulated growth and they
+ 
+
+ align:start position:0%
+undergoing regulated growth and they
+reproduce which in the case of a single
+
+ align:start position:0%
+reproduce which in the case of a single
+ 
+
+ align:start position:0%
+reproduce which in the case of a single
+celled organism is the same is the same
+
+ align:start position:0%
+celled organism is the same is the same
+ 
+
+ align:start position:0%
+celled organism is the same is the same
+as cell division for us reproducing is a
+
+ align:start position:0%
+as cell division for us reproducing is a
+ 
+
+ align:start position:0%
+as cell division for us reproducing is a
+lot more complicated because we have to
+
+ align:start position:0%
+lot more complicated because we have to
+ 
+
+ align:start position:0%
+lot more complicated because we have to
+make a whole other mic uh whole other uh
+
+ align:start position:0%
+make a whole other mic uh whole other uh
+ 
+
+ align:start position:0%
+make a whole other mic uh whole other uh
+multicellular organism where the the uh
+
+ align:start position:0%
+multicellular organism where the the uh
+ 
+
+ align:start position:0%
+multicellular organism where the the uh
+cells have differentiated functions but
+
+ align:start position:0%
+cells have differentiated functions but
+ 
+
+ align:start position:0%
+cells have differentiated functions but
+the point about that is there has to be
+
+ align:start position:0%
+the point about that is there has to be
+ 
+
+ align:start position:0%
+the point about that is there has to be
+an unbelievable amount of
+
+ align:start position:0%
+an unbelievable amount of
+ 
+
+ align:start position:0%
+an unbelievable amount of
+synthesis the DNA in our body we start
+
+ align:start position:0%
+synthesis the DNA in our body we start
+ 
+
+ align:start position:0%
+synthesis the DNA in our body we start
+out with two meters in a fertilized cell
+
+ align:start position:0%
+out with two meters in a fertilized cell
+ 
+
+ align:start position:0%
+out with two meters in a fertilized cell
+and we have uh 10 to the 14th cells by
+
+ align:start position:0%
+and we have uh 10 to the 14th cells by
+ 
+
+ align:start position:0%
+and we have uh 10 to the 14th cells by
+the time we're an adult so we've had to
+
+ align:start position:0%
+the time we're an adult so we've had to
+ 
+
+ align:start position:0%
+the time we're an adult so we've had to
+make a tremendous amount of DNA let
+
+ align:start position:0%
+make a tremendous amount of DNA let
+ 
+
+ align:start position:0%
+make a tremendous amount of DNA let
+alone protein and everything else and
+
+ align:start position:0%
+alone protein and everything else and
+ 
+
+ align:start position:0%
+alone protein and everything else and
+something almost all of you know from
+
+ align:start position:0%
+something almost all of you know from
+ 
+
+ align:start position:0%
+something almost all of you know from
+your engineering background at this
+
+ align:start position:0%
+your engineering background at this
+ 
+
+ align:start position:0%
+your engineering background at this
+place is that you need energy in order
+
+ align:start position:0%
+place is that you need energy in order
+ 
+
+ align:start position:0%
+place is that you need energy in order
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+synthesize uh synthesize uh material and
+
+ align:start position:0%
+synthesize uh synthesize uh material and
+ 
+
+ align:start position:0%
+synthesize uh synthesize uh material and
+what will uh start to to talk about in
+
+ align:start position:0%
+what will uh start to to talk about in
+ 
+
+ align:start position:0%
+what will uh start to to talk about in
+the in the next phase of this uh of this
+
+ align:start position:0%
+the in the next phase of this uh of this
+ 
+
+ align:start position:0%
+the in the next phase of this uh of this
+course then is how do cells make uh make
+
+ align:start position:0%
+course then is how do cells make uh make
+ 
+
+ align:start position:0%
+course then is how do cells make uh make
+energy and how do they uh carry out
+
+ align:start position:0%
+energy and how do they uh carry out
+ 
+
+ align:start position:0%
+energy and how do they uh carry out
+metabolism so I'm going to just before
+
+ align:start position:0%
+metabolism so I'm going to just before
+ 
+
+ align:start position:0%
+metabolism so I'm going to just before
+we do that I'll introduce to you very
+
+ align:start position:0%
+we do that I'll introduce to you very
+ 
+
+ align:start position:0%
+we do that I'll introduce to you very
+quickly to close out here two classes of
+
+ align:start position:0%
+quickly to close out here two classes of
+ 
+
+ align:start position:0%
+quickly to close out here two classes of
+cells of organisms we find in in nature
+
+ align:start position:0%
+cells of organisms we find in in nature
+ 
+
+ align:start position:0%
+cells of organisms we find in in nature
+we find uh organisms that are known as
+
+ align:start position:0%
+we find uh organisms that are known as
+ 
+
+ align:start position:0%
+we find uh organisms that are known as
+autot tropes these are certain
+
+ align:start position:0%
+autot tropes these are certain
+ 
+
+ align:start position:0%
+autot tropes these are certain
+bacteria and they're able to make
+
+ align:start position:0%
+bacteria and they're able to make
+ 
+
+ align:start position:0%
+bacteria and they're able to make
+everything they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need starting with
+
+ align:start position:0%
+need starting with
+ 
+
+ align:start position:0%
+need starting with
+CO2
+
+ align:start position:0%
+CO2
+ 
+
+ align:start position:0%
+CO2
+ammonia
+
+ align:start position:0%
+ammonia
+ 
+
+ align:start position:0%
+ammonia
+phosphate
+
+ align:start position:0%
+phosphate
+ 
+
+ align:start position:0%
+phosphate
+water a few things but that's all they
+
+ align:start position:0%
+water a few things but that's all they
+ 
+
+ align:start position:0%
+water a few things but that's all they
+need so for for example an organism that
+
+ align:start position:0%
+need so for for example an organism that
+ 
+
+ align:start position:0%
+need so for for example an organism that
+lives a bacterium that lives out in the
+
+ align:start position:0%
+lives a bacterium that lives out in the
+ 
+
+ align:start position:0%
+lives a bacterium that lives out in the
+open ocean is able to make everything
+
+ align:start position:0%
+open ocean is able to make everything
+ 
+
+ align:start position:0%
+open ocean is able to make everything
+from those very very simple basic uh
+
+ align:start position:0%
+from those very very simple basic uh
+ 
+
+ align:start position:0%
+from those very very simple basic uh
+building
+
+ align:start position:0%
+building
+ 
+
+ align:start position:0%
+building
+blocks heterotrofos
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eat some things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+made by other organisms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example of a heter trro uh that you're
+
+ align:start position:0%
+example of a heter trro uh that you're
+ 
+
+ align:start position:0%
+example of a heter trro uh that you're
+familiar with I'm familiar with is US
+
+ align:start position:0%
+familiar with I'm familiar with is US
+ 
+
+ align:start position:0%
+familiar with I'm familiar with is US
+probably remember your mother uh
+
+ align:start position:0%
+probably remember your mother uh
+ 
+
+ align:start position:0%
+probably remember your mother uh
+reminding you as you about to have yet
+
+ align:start position:0%
+reminding you as you about to have yet
+ 
+
+ align:start position:0%
+reminding you as you about to have yet
+another hot dog that it was important to
+
+ align:start position:0%
+another hot dog that it was important to
+ 
+
+ align:start position:0%
+another hot dog that it was important to
+eat your vitamins the reason you need to
+
+ align:start position:0%
+eat your vitamins the reason you need to
+ 
+
+ align:start position:0%
+eat your vitamins the reason you need to
+vitamins those are things we absolutely
+
+ align:start position:0%
+vitamins those are things we absolutely
+ 
+
+ align:start position:0%
+vitamins those are things we absolutely
+need for our life but we can't um make
+
+ align:start position:0%
+need for our life but we can't um make
+ 
+
+ align:start position:0%
+need for our life but we can't um make
+them ourselves uh vitamin C is one you
+
+ align:start position:0%
+them ourselves uh vitamin C is one you
+ 
+
+ align:start position:0%
+them ourselves uh vitamin C is one you
+probably know it has an interesting
+
+ align:start position:0%
+probably know it has an interesting
+ 
+
+ align:start position:0%
+probably know it has an interesting
+history how people figured this out it
+
+ align:start position:0%
+history how people figured this out it
+ 
+
+ align:start position:0%
+history how people figured this out it
+was Sailors at Sea got really really
+
+ align:start position:0%
+was Sailors at Sea got really really
+ 
+
+ align:start position:0%
+was Sailors at Sea got really really
+sick their teeth would start to loosen
+
+ align:start position:0%
+sick their teeth would start to loosen
+ 
+
+ align:start position:0%
+sick their teeth would start to loosen
+they would start to bleed and they would
+
+ align:start position:0%
+they would start to bleed and they would
+ 
+
+ align:start position:0%
+they would start to bleed and they would
+die um and some of the famous sea
+
+ align:start position:0%
+die um and some of the famous sea
+ 
+
+ align:start position:0%
+die um and some of the famous sea
+voyages you heard about in high in high
+
+ align:start position:0%
+voyages you heard about in high in high
+ 
+
+ align:start position:0%
+voyages you heard about in high in high
+school were very I think the Cape of
+
+ align:start position:0%
+school were very I think the Cape of
+ 
+
+ align:start position:0%
+school were very I think the Cape of
+Good Hope on the trip where that was
+
+ align:start position:0%
+Good Hope on the trip where that was
+ 
+
+ align:start position:0%
+Good Hope on the trip where that was
+discovered 100 out of the 160 Sailors
+
+ align:start position:0%
+discovered 100 out of the 160 Sailors
+ 
+
+ align:start position:0%
+discovered 100 out of the 160 Sailors
+died at Sea because of scurvy now scurvy
+
+ align:start position:0%
+died at Sea because of scurvy now scurvy
+ 
+
+ align:start position:0%
+died at Sea because of scurvy now scurvy
+turns out to be due to not not having
+
+ align:start position:0%
+turns out to be due to not not having
+ 
+
+ align:start position:0%
+turns out to be due to not not having
+vitamin C and there was uh finally a guy
+
+ align:start position:0%
+vitamin C and there was uh finally a guy
+ 
+
+ align:start position:0%
+vitamin C and there was uh finally a guy
+about the
+
+ align:start position:0%
+about the
+ 
+
+ align:start position:0%
+about the
+um Lind I'm just blanking on his first
+
+ align:start position:0%
+um Lind I'm just blanking on his first
+ 
+
+ align:start position:0%
+um Lind I'm just blanking on his first
+uh name uh at the moment uh about the
+
+ align:start position:0%
+uh name uh at the moment uh about the
+ 
+
+ align:start position:0%
+uh name uh at the moment uh about the
+1700s who was a naval surgeon in the
+
+ align:start position:0%
+1700s who was a naval surgeon in the
+ 
+
+ align:start position:0%
+1700s who was a naval surgeon in the
+British Navy and actually figured out
+
+ align:start position:0%
+British Navy and actually figured out
+ 
+
+ align:start position:0%
+British Navy and actually figured out
+that if you gave Sailors lemon juice
+
+ align:start position:0%
+that if you gave Sailors lemon juice
+ 
+
+ align:start position:0%
+that if you gave Sailors lemon juice
+that they didn't get scurvy it was a
+
+ align:start position:0%
+that they didn't get scurvy it was a
+ 
+
+ align:start position:0%
+that they didn't get scurvy it was a
+controlled experiment it took about uh
+
+ align:start position:0%
+controlled experiment it took about uh
+ 
+
+ align:start position:0%
+controlled experiment it took about uh
+50 years I think it was 1795 when they
+
+ align:start position:0%
+50 years I think it was 1795 when they
+ 
+
+ align:start position:0%
+50 years I think it was 1795 when they
+started to finally give the sailors
+
+ align:start position:0%
+started to finally give the sailors
+ 
+
+ align:start position:0%
+started to finally give the sailors
+lemon juice and stopped having this
+
+ align:start position:0%
+lemon juice and stopped having this
+ 
+
+ align:start position:0%
+lemon juice and stopped having this
+terrible sickness amongst their Sailors
+
+ align:start position:0%
+terrible sickness amongst their Sailors
+ 
+
+ align:start position:0%
+terrible sickness amongst their Sailors
+and then in about 1850 they substituted
+
+ align:start position:0%
+and then in about 1850 they substituted
+ 
+
+ align:start position:0%
+and then in about 1850 they substituted
+lime juice and some of you may still
+
+ align:start position:0%
+lime juice and some of you may still
+ 
+
+ align:start position:0%
+lime juice and some of you may still
+know the British Sailors are called
+
+ align:start position:0%
+know the British Sailors are called
+ 
+
+ align:start position:0%
+know the British Sailors are called
+called limes and that was because of of
+
+ align:start position:0%
+called limes and that was because of of
+ 
+
+ align:start position:0%
+called limes and that was because of of
+uh this solution they found to avoiding
+
+ align:start position:0%
+uh this solution they found to avoiding
+ 
+
+ align:start position:0%
+uh this solution they found to avoiding
+scurvy and what was really happening was
+
+ align:start position:0%
+scurvy and what was really happening was
+ 
+
+ align:start position:0%
+scurvy and what was really happening was
+they were finding a way to provide
+
+ align:start position:0%
+they were finding a way to provide
+ 
+
+ align:start position:0%
+they were finding a way to provide
+vitamin C which is in fresh fruits and
+
+ align:start position:0%
+vitamin C which is in fresh fruits and
+ 
+
+ align:start position:0%
+vitamin C which is in fresh fruits and
+vegetables which wasn't part of the
+
+ align:start position:0%
+vegetables which wasn't part of the
+ 
+
+ align:start position:0%
+vegetables which wasn't part of the
+classic sailor diet which was sort of
+
+ align:start position:0%
+classic sailor diet which was sort of
+ 
+
+ align:start position:0%
+classic sailor diet which was sort of
+biscuits and and dried meat during long
+
+ align:start position:0%
+biscuits and and dried meat during long
+ 
+
+ align:start position:0%
+biscuits and and dried meat during long
+voyages at Sea there's several other
+
+ align:start position:0%
+voyages at Sea there's several other
+ 
+
+ align:start position:0%
+voyages at Sea there's several other
+vitamins but the reason they're called
+
+ align:start position:0%
+vitamins but the reason they're called
+ 
+
+ align:start position:0%
+vitamins but the reason they're called
+vitamins are things that your body can't
+
+ align:start position:0%
+vitamins are things that your body can't
+ 
+
+ align:start position:0%
+vitamins are things that your body can't
+make but other organisms can the other
+
+ align:start position:0%
+make but other organisms can the other
+ 
+
+ align:start position:0%
+make but other organisms can the other
+thing that
+
+ align:start position:0%
+thing that
+ 
+
+ align:start position:0%
+thing that
+we that we can't make we can make some
+
+ align:start position:0%
+we that we can't make we can make some
+ 
+
+ align:start position:0%
+we that we can't make we can make some
+of our 20 amino acids but there are
+
+ align:start position:0%
+of our 20 amino acids but there are
+ 
+
+ align:start position:0%
+of our 20 amino acids but there are
+eight uh amino acids that um that we
+
+ align:start position:0%
+eight uh amino acids that um that we
+ 
+
+ align:start position:0%
+eight uh amino acids that um that we
+can't make um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lysine
+
+ align:start position:0%
+lysine
+ 
+
+ align:start position:0%
+lysine
+methionine
+
+ align:start position:0%
+methionine
+ 
+
+ align:start position:0%
+methionine
+Lucine
+
+ align:start position:0%
+Lucine
+ 
+
+ align:start position:0%
+Lucine
+isoline
+
+ align:start position:0%
+isoline
+ 
+
+ align:start position:0%
+isoline
+veine
+
+ align:start position:0%
+veine
+ 
+
+ align:start position:0%
+veine
+thine phenyalanine
+
+ align:start position:0%
+thine phenyalanine
+ 
+
+ align:start position:0%
+thine phenyalanine
+and tryptophane and this actually has
+
+ align:start position:0%
+and tryptophane and this actually has
+ 
+
+ align:start position:0%
+and tryptophane and this actually has
+consequences uh for us because um there
+
+ align:start position:0%
+consequences uh for us because um there
+ 
+
+ align:start position:0%
+consequences uh for us because um there
+are those of you who are vegetarians
+
+ align:start position:0%
+are those of you who are vegetarians
+ 
+
+ align:start position:0%
+are those of you who are vegetarians
+probably know you have to be kind of
+
+ align:start position:0%
+probably know you have to be kind of
+ 
+
+ align:start position:0%
+probably know you have to be kind of
+careful about your diet if you're eating
+
+ align:start position:0%
+careful about your diet if you're eating
+ 
+
+ align:start position:0%
+careful about your diet if you're eating
+animal protein um you're getting
+
+ align:start position:0%
+animal protein um you're getting
+ 
+
+ align:start position:0%
+animal protein um you're getting
+essentially all the different amino
+
+ align:start position:0%
+essentially all the different amino
+ 
+
+ align:start position:0%
+essentially all the different amino
+acids but if you uh if you're a
+
+ align:start position:0%
+acids but if you uh if you're a
+ 
+
+ align:start position:0%
+acids but if you uh if you're a
+vegetarian you have to be careful
+
+ align:start position:0%
+vegetarian you have to be careful
+ 
+
+ align:start position:0%
+vegetarian you have to be careful
+because the major
+
+ align:start position:0%
+because the major
+ 
+
+ align:start position:0%
+because the major
+uh food crops such as wheat and and rice
+
+ align:start position:0%
+uh food crops such as wheat and and rice
+ 
+
+ align:start position:0%
+uh food crops such as wheat and and rice
+for example are very low in lysing so if
+
+ align:start position:0%
+for example are very low in lysing so if
+ 
+
+ align:start position:0%
+for example are very low in lysing so if
+you just eat those you end up with uh a
+
+ align:start position:0%
+you just eat those you end up with uh a
+ 
+
+ align:start position:0%
+you just eat those you end up with uh a
+lysine deficiency that's that's not good
+
+ align:start position:0%
+lysine deficiency that's that's not good
+ 
+
+ align:start position:0%
+lysine deficiency that's that's not good
+but on the other hand beans lentils the
+
+ align:start position:0%
+but on the other hand beans lentils the
+ 
+
+ align:start position:0%
+but on the other hand beans lentils the
+various leguminous plants were also
+
+ align:start position:0%
+various leguminous plants were also
+ 
+
+ align:start position:0%
+various leguminous plants were also
+which also those ones that form the
+
+ align:start position:0%
+which also those ones that form the
+ 
+
+ align:start position:0%
+which also those ones that form the
+special associations with bacteria that
+
+ align:start position:0%
+special associations with bacteria that
+ 
+
+ align:start position:0%
+special associations with bacteria that
+let them convert atmospheric um nitrogen
+
+ align:start position:0%
+let them convert atmospheric um nitrogen
+ 
+
+ align:start position:0%
+let them convert atmospheric um nitrogen
+into ammonia those legumes are high in
+
+ align:start position:0%
+into ammonia those legumes are high in
+ 
+
+ align:start position:0%
+into ammonia those legumes are high in
+lysine but low in methionine so uh
+
+ align:start position:0%
+lysine but low in methionine so uh
+ 
+
+ align:start position:0%
+lysine but low in methionine so uh
+peoples all over the world figured this
+
+ align:start position:0%
+peoples all over the world figured this
+ 
+
+ align:start position:0%
+peoples all over the world figured this
+out by trial and error so um the Mexican
+
+ align:start position:0%
+out by trial and error so um the Mexican
+ 
+
+ align:start position:0%
+out by trial and error so um the Mexican
+diet is you know rice and beans there's
+
+ align:start position:0%
+diet is you know rice and beans there's
+ 
+
+ align:start position:0%
+diet is you know rice and beans there's
+a reason for it what's happening
+
+ align:start position:0%
+a reason for it what's happening
+ 
+
+ align:start position:0%
+a reason for it what's happening
+actually is you're just in the rice
+
+ align:start position:0%
+actually is you're just in the rice
+ 
+
+ align:start position:0%
+actually is you're just in the rice
+you're low and lysine but by having
+
+ align:start position:0%
+you're low and lysine but by having
+ 
+
+ align:start position:0%
+you're low and lysine but by having
+beans at the same time you're balancing
+
+ align:start position:0%
+beans at the same time you're balancing
+ 
+
+ align:start position:0%
+beans at the same time you're balancing
+out the two or the the native um
+
+ align:start position:0%
+out the two or the the native um
+ 
+
+ align:start position:0%
+out the two or the the native um
+Americans in in this part of of the
+
+ align:start position:0%
+Americans in in this part of of the
+ 
+
+ align:start position:0%
+Americans in in this part of of the
+country had the three sisters with the
+
+ align:start position:0%
+country had the three sisters with the
+ 
+
+ align:start position:0%
+country had the three sisters with the
+corn the squash and the beans and again
+
+ align:start position:0%
+corn the squash and the beans and again
+ 
+
+ align:start position:0%
+corn the squash and the beans and again
+they were balancing out the diet by
+
+ align:start position:0%
+they were balancing out the diet by
+ 
+
+ align:start position:0%
+they were balancing out the diet by
+making sure that they got the various
+
+ align:start position:0%
+making sure that they got the various
+ 
+
+ align:start position:0%
+making sure that they got the various
+amino acids uh a balance of all the
+
+ align:start position:0%
+amino acids uh a balance of all the
+ 
+
+ align:start position:0%
+amino acids uh a balance of all the
+amino acids that were necessary uh for
+
+ align:start position:0%
+amino acids that were necessary uh for
+ 
+
+ align:start position:0%
+amino acids that were necessary uh for
+life it also actually was really good
+
+ align:start position:0%
+life it also actually was really good
+ 
+
+ align:start position:0%
+life it also actually was really good
+gardening practice because the beans
+
+ align:start position:0%
+gardening practice because the beans
+ 
+
+ align:start position:0%
+gardening practice because the beans
+were able to convert atmospheric
+
+ align:start position:0%
+were able to convert atmospheric
+ 
+
+ align:start position:0%
+were able to convert atmospheric
+nitrogen into ammonia which was
+
+ align:start position:0%
+nitrogen into ammonia which was
+ 
+
+ align:start position:0%
+nitrogen into ammonia which was
+fertilizer and the squash leaves shaded
+
+ align:start position:0%
+fertilizer and the squash leaves shaded
+ 
+
+ align:start position:0%
+fertilizer and the squash leaves shaded
+the the ground so the ground didn't dry
+
+ align:start position:0%
+the the ground so the ground didn't dry
+ 
+
+ align:start position:0%
+the the ground so the ground didn't dry
+out and the corn could grow even when it
+
+ align:start position:0%
+out and the corn could grow even when it
+ 
+
+ align:start position:0%
+out and the corn could grow even when it
+was short on on
+
+ align:start position:0%
+was short on on
+ 
+
+ align:start position:0%
+was short on on
+uh on water but what was really
+
+ align:start position:0%
+uh on water but what was really
+ 
+
+ align:start position:0%
+uh on water but what was really
+happening in these as as people grew
+
+ align:start position:0%
+happening in these as as people grew
+ 
+
+ align:start position:0%
+happening in these as as people grew
+without even understanding the
+
+ align:start position:0%
+without even understanding the
+ 
+
+ align:start position:0%
+without even understanding the
+biochemistry they were compensating for
+
+ align:start position:0%
+biochemistry they were compensating for
+ 
+
+ align:start position:0%
+biochemistry they were compensating for
+the fact that were heterotrophs and
+
+ align:start position:0%
+the fact that were heterotrophs and
+ 
+
+ align:start position:0%
+the fact that were heterotrophs and
+needed to to do this so we'll start in
+
+ align:start position:0%
+needed to to do this so we'll start in
+ 
+
+ align:start position:0%
+needed to to do this so we'll start in
+uh at the next lecture on trying to talk
+
+ align:start position:0%
+uh at the next lecture on trying to talk
+ 
+
+ align:start position:0%
+uh at the next lecture on trying to talk
+about how cells make energy and how it
+
+ align:start position:0%
+about how cells make energy and how it
+ 
+
+ align:start position:0%
+about how cells make energy and how it
+makes some of this amazing stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen
\ No newline at end of file
diff --git a/6HrTfI8R_9A.txt b/6HrTfI8R_9A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..df170ef7844e31243cdeab0fb2d7d08de3777e98
--- /dev/null
+++ b/6HrTfI8R_9A.txt
@@ -0,0 +1,3061 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+OK, let's start.
+
+So let's go back to
+our starting point
+
+for the past couple of weeks.
+
+The square lattice, let's
+say, where each side
+
+we assign a binary variable
+sigma, which is minus 1.
+
+And a weight that tends
+to make subsequent nearest
+
+neighbors [? things ?] to
+be parallel to each other.
+
+So into the plus k,
+they are parallel.
+
+Penalized into the minus k
+if they are anti-parallel.
+
+And of course, over all
+pairs of nearest neighbors.
+
+And the partition function that
+is obtained by summing over 2
+
+to the n configurations.
+
+Let's make this up
+to give us a function
+
+of the rate of this
+coupling, which
+
+is some energy provided
+by temperature.
+
+And we expect this-- at least,
+in two and higher dimensions--
+
+to capture a phase transition.
+
+And the way that we have
+been proceeding with this
+
+to derive this factor as
+the hyperbolic cosine of k.
+
+1 plus r variable t, which is
+the hyperbolic [? sine ?] of k.
+
+Sigma i, sigma j.
+
+And then this becomes
+a cos k to the number
+
+of bonds, which is 2n
+on the square lattice.
+
+And then expanding
+these factors,
+
+we saw that we could get
+things that are either
+
+1 from each bond
+or a factor that
+
+was something like
+t sigma sigma.
+
+And then summing over
+the two values of sigma
+
+would give us 0 unless we
+added another factor of sigma
+
+through another bond.
+
+And going forth, we had to
+draw these kinds of diagrams
+
+where at each site, I have an
+even number of 1's selected.
+
+Then summing over the sigmas
+would give me a factor of 2
+
+to the n.
+
+And so then I have a sum over a
+whole bunch of configurations.
+
+[? There are ?]
+[? certainly ?] one.
+
+There are configurations
+that are composed
+
+of one way of drawing
+an object on the lattice
+
+such as this one,
+or objects that
+
+correspond to doing two of
+these loops, and so forth.
+
+So that's the expression
+for the partition function.
+
+And what we are
+really interested
+
+is the log of the partition
+function, which gives us
+
+the free energy in terms
+of thermodynamic quantities
+
+that potentially will tell
+us about phase transition.
+
+So here we will get
+a log 2 to the n.
+
+Well actually, you want
+to divide everything by n
+
+so that we get the
+intensive part.
+
+So here we get log 2
+hyperbolic cosine squared of k.
+
+And then I have to take the
+log of this expression that
+
+includes things
+that are one loop,
+
+disjointed loop, et cetera.
+
+And we've seen that
+the particular loop
+
+I can slide all over the place--
+so if you have a factor of n--
+
+whereas things that
+are multiple loops
+
+have factors of n
+squared, et cetera,
+
+which are incompatible
+with this.
+
+So it was very tempting for
+us to do the usual thing
+
+and say that the
+log of a sum that
+
+includes these multiple
+occurrences of the loops
+
+is the same thing as sum
+over the configurations
+
+that involve a single loop.
+
+And then we have to sum over
+all shapes of these loops.
+
+And each loop will
+get a factor of t
+
+per the number of bonds
+that are occurring in that.
+
+Of course, what we said was
+that this equality does not
+
+hold because if I
+exponentiate this term,
+
+I will generate things where
+the different loops will
+
+coincide with each
+other, and therefore
+
+create types of terms that are
+not created in the original sum
+
+that we had over there.
+
+So this sum over phantom
+loops neglected the condition
+
+that these loops, in some sense,
+have some material to them
+
+and don't want to
+intersect with each other.
+
+Nonetheless, it was
+useful, and we followed up
+
+this calculation.
+
+So that's repeat what the result
+of this incorrect calculation
+
+is.
+
+So we have log of 2 hyperbolic
+cosine squared k, 1 over n.
+
+Then we said the
+particular way to organize
+
+the sum over the
+loops is to sum over
+
+there the length of the loop.
+
+So I sum over the
+length of the loop
+
+and count the number of
+loops that have length l.
+
+All of them will be
+giving me a contribution
+
+that is t to the l.
+
+So then I said, well,
+let's, for example,
+
+pick a particular
+point on the lattice.
+
+Let's call it r.
+
+And I count the number of
+ways that I can start at r,
+
+do a walk of l steps,
+and end at r again.
+
+We saw that for
+these phantom loops,
+
+this w had a very
+nice structure.
+
+It was simply what
+was telling me
+
+about one step raised to the l.
+
+This was the Markovian property.
+
+There was, of course,
+an important thing here
+
+which said that I could have
+set the origin of this loop
+
+at any point along the loop.
+
+So there is an over-counting
+by a factor of l
+
+because the same loop
+would have been constructed
+
+with different points
+indicated as the origin.
+
+And actually, I can go the loop
+clockwise or anti-clockwise,
+
+so there was a factor of 2
+because of this degeneracy
+
+of going clockwise or
+anti-clockwise when
+
+I perform a walk.
+
+And then over here, there's
+also an implicit sum
+
+over this starting
+point and endpoint.
+
+If I always start and
+end at the origin,
+
+then I will get rid
+of the factor of n.
+
+But it is useful to
+explicitly include
+
+this sum over r because
+then you can explicitly
+
+see that sum over
+r of this object
+
+is the trace of that matrix.
+
+And I can actually
+[INAUDIBLE] the order,
+
+the trace, and the
+summation over l.
+
+And when that happens, I get
+log 2 cos squared k exactly
+
+as before.
+
+And then I have 1 over n.
+
+I have sum over r replaced
+by the trace operation.
+
+And then sum over l-- t, T
+raised to the l divided by
+
+l-- is the expansion for
+minus log of 1 minus t T.
+
+And there's the
+factor of 2 over there
+
+that I have to put over here.
+
+So note that this
+plus became minus
+
+because of the expansion
+for log of 1 minus
+
+x is minus x minus
+x squared over 2
+
+minus x cubed over 3, et cetera.
+
+And the final step
+that we did was
+
+to note that the trace I
+can calculate in any basis.
+
+And in particular, this
+matrix t is diagonalized
+
+by going to Fourier
+representation.
+
+In the Fourier representation,
+the trace operation
+
+becomes sum over all q values.
+
+Sum over all q values,
+I go to the continuum
+
+and write as n integral
+over q, so the n's cancel.
+
+I will get 2 integration over q.
+
+These are essentially each
+one of them, qz and qz,
+
+in the interval.
+
+Let's say 0 to 2 pi or minus
+pi to 2 pi, doesn't matter.
+
+Interval of size of 2pi.
+
+So that's the trace operation.
+
+Log of 1 minus t.
+
+Then the matrix that represents
+walking along the lattice
+
+represented in Fourier.
+
+And so basically at
+the particular site,
+
+we can step to the
+right or to the left.
+
+So that's e to the i qx, e to
+the minus i qx, e to the i qy,
+
+e to the minus i qy.
+
+Adding all of those up,
+you get 2 cosine of qz
+
+plus cosine of qy.
+
+So that was our expression.
+
+And then we realized,
+interestingly,
+
+that whereas this final
+expression certainly
+
+was not the Ising partition
+function that we were after,
+
+that it was, in
+fact, the partition
+
+function of a Gaussian
+model where at each site
+
+I had a variable
+whose variance was 1,
+
+and then I had this
+kind of coupling
+
+rather than with
+the sigma variable,
+
+with these Gaussian
+variables that
+
+will go from minus to infinity.
+
+But then we said, OK, we
+can do better than that.
+
+And we said that log
+z over n actually
+
+does equal a very similar sum.
+
+It is log 2 hyperbolic
+cosine squared k,
+
+and then I have 1 over n.
+
+Sum over all kinds
+of loops where
+
+I have a similar diagram that
+I draw, but I put a star.
+
+And this star
+implied two things--
+
+that just like before, I draw
+all kinds of individual loops,
+
+but I make sure
+that my loops never
+
+have a step that goes
+forward and backward.
+
+So there was no U-turn.
+
+And importantly, there
+was a factor of minus 1
+
+to the number of times that
+the walk crossed itself.
+
+And we showed that
+when we incorporate
+
+both of these conditions,
+the can indeed
+
+exponentiate this expression and
+get exactly the same diagrams
+
+as we had on the
+first line, all coming
+
+with the correct
+weights, and none
+
+of the diagrams that had
+multiple occurrences of a bond
+
+would occur.
+
+So then the question
+was, how do you
+
+calculate this
+given that we have
+
+this dependence on the number
+of crossings, which offhand may
+
+look as if it is something
+that requires memory?
+
+And then we saw that, indeed,
+just like the previous case,
+
+we could write the
+result as a sum over
+
+walks that have a
+particular length l.
+
+Right here, we have the
+factor of t to the l.
+
+Those walks could start and
+end at the particular point r.
+
+But we also specified
+the direction mu
+
+along which you started.
+
+So previously I only
+specified the origin.
+
+Now I have to specify the
+starting point as well
+
+as the direction.
+
+I have to end at the same point
+and along the same direction
+
+to complete the loop.
+
+And these were accomplished by
+having these factors of walks
+
+that are length l.
+
+So to do that, we can certainly
+incorporate this condition
+
+of no U-turn in the description
+of the steps that I take.
+
+So for each step, I
+know where I came from.
+
+I just make sure I don't
+step back, so that's easy.
+
+And we found that this
+minus 1 to the power of nc
+
+can be incorporated
+through a factor of e
+
+to the i sum over the changes of
+the orientation of the walker--
+
+as I step through the lattice--
+provided that I included also
+
+an additional factor of minus.
+
+So that factor of minus I
+could actually put out front.
+
+It's an important factor.
+
+And then there's
+the over-counting,
+
+but as before, the walk can go
+in either one of two directions
+
+and can have l starting points.
+
+OK, so now we can
+proceed just as before.
+
+log 2 hyperbolic
+cosine squared k,
+
+and then we have
+a sum over l here,
+
+which we can, again, represent
+as the log of 1 minus
+
+t-- this 4 by 4 matrix t star.
+
+Going through the log
+operation will change this sign
+
+from minus to plus.
+
+I have the 1 over 2n as before.
+
+And I have to sum over r and
+mu, which are the elements that
+
+characterize this
+4n by 4n matrix.
+
+So this amounts to doing
+the trace log operation.
+
+And then taking advantage of
+the fact that, just as before,
+
+Fourier transforms can
+at least partially block
+
+diagonalize this
+4n by 4n matrix.
+
+I go to that basis,
+and the trace
+
+becomes an integral over q.
+
+And then I would have to do
+the trace of a log of a 4
+
+by 4 matrix.
+
+And for that, I use the
+identity that a trace
+
+of log of any matrix is
+the log of the determinant
+
+of that same matrix.
+
+And so the thing that
+I have to integrate
+
+is the log of the
+determinant of a 4
+
+by 4 matrix that
+captures these steps
+
+that I take on the
+square lattice.
+
+And we saw that,
+for example, going
+
+in the horizontal direction
+would give me a factor of t
+
+e to the minus i qx.
+
+Going in the vertical
+direction-- up-- y qy.
+
+Going in the horizontal
+direction-- down.
+
+These are the diagonal elements.
+
+And then there were
+off-diagonal elements,
+
+so the next turn here was
+to go and then bend upward.
+
+So that gave me in addition
+to e to the minus i qx,
+
+which is the same
+forward step here.
+
+A factor of, let's
+call it omega so I
+
+don't have to write
+it all over the place.
+
+Omega is e to the pi pi over 4.
+
+And the next one was a U-turn.
+
+The next one was minus t
+e minus i qx omega star.
+
+And we could fill out similarly
+all of the other places
+
+in this 4 by 4 matrix.
+
+And then the whole problem comes
+down to having to evaluate a 4
+
+by 4 determinant,
+which you can do
+
+by hand with a couple of sheets
+of paper to do your algebra.
+
+And I wrote for you
+the final answer,
+
+is 1/2 2 integrals
+from minus pi 2 pi
+
+over qx and qy divided
+by 2 pi squared.
+
+And then the result of
+this, which is log of 1
+
+plus t squared squared minus 2t
+1 minus t squared cosine of qx
+
+plus cosine of qy.
+
+This was the expression
+for the partition function.
+
+OK, so this is where
+we ended up last time.
+
+Now the question is we
+have here on the board
+
+two expressions, the project
+one and the incorrect one--
+
+the Gaussian model and the
+2-dimensionalizing one.
+
+They look surprisingly
+similar, and that
+
+should start to worry us
+potentially because we expect
+
+that many when we
+have some functional
+
+form, that functional
+form carries
+
+within it certain singularities.
+
+And you say, well, these
+two functions, both of them
+
+are a double integral
+of log of something
+
+minus something
+cosine plus cosine.
+
+So after all of
+this work, did we
+
+end up with an expression
+that has the same singular
+
+behavior as the Gaussian model?
+
+OK, so let's go and look
+at things more carefully.
+
+So in both cases, what I need
+to do is to integrate A function
+
+a that appears inside the log.
+
+There is an A for the
+Gaussian, and then there
+
+is this object--
+let's call it A star--
+
+for the correct solution.
+
+So the thing that I have to
+integrate is, of course, q.
+
+So this is a function
+of the vector q,
+
+as well as the parameter that
+is a function of which I expect
+
+to have a phase
+transition, which is t.
+
+Now where could I potentially
+get some kind of a singularity?
+
+The only place that I
+can get a singularity
+
+is if the argument of the log
+goes to 0 because log of 0
+
+is something that's derivatives
+of singularities, et cetera.
+
+So you may say, OK, that's
+where I should be looking at.
+
+So where is it this
+most likely to happen
+
+when I'm integrating over q?
+
+So basically, I'm
+integrating over qx and qy
+
+over a [INAUDIBLE]
+[? zone ?] that
+
+goes from minus pi to
+pi in both directions.
+
+And potentially somewhere in
+this I encounter a singularity.
+
+Let's come from the site
+of high temperatures
+
+where t is close to 0.
+
+Then I have log
+of 1, no problem.
+
+As I go to lower and
+lower temperatures,
+
+the t becomes larger.
+
+Then from the 1, I start
+to subtract more and more
+
+with these cosines.
+
+And clearly the place
+that I'm subtracting
+
+most is right at the
+center of q equals to 0.
+
+So let's expand this
+in the vicinity of q
+
+goes to 0 in the
+vicinity of this place.
+
+And there what I see
+is it is 1 minus.
+
+Cosines are approximately
+1 minus q squared over 2.
+
+So I have 1 minus
+4t, and then I have
+
+plus t qx squared plus qy
+squared, which is essentially
+
+the net q squared.
+
+And then I have order of
+higher power z, qx and qy.
+
+Fine.
+
+So this part is
+positive, no problem.
+
+I see that this
+part goes through 0
+
+when I hit tc, which is 1/4.
+
+And this we had already
+seen, that basically this
+
+is the place where the
+exponentially increasing
+
+number of walks-- as 4
+to the number of steps--
+
+overcomes the
+exponentially decreasing
+
+fidelity of information carried
+through each walk, which
+
+was t to the l.
+
+So 4dt being 1, tc
+is of the order 1/4.
+
+We are interested
+in the singularities
+
+in the vicinity of
+this phase transition,
+
+so we additionally
+go and look at what
+
+happens when t approaches
+tc, but from this side above,
+
+because clearly if I go to
+t that is larger than 1/4,
+
+it doesn't make any sense.
+
+So t has to be less than 1/4.
+
+And so then what I have here is
+that I can write this as 4tc,
+
+so this is 4 times tc minus t.
+
+And this to the lowest order
+I can replace as tc-- q
+
+squared plus higher orders.
+
+This 4 I can write as 1 over tc.
+
+So the whole thing
+I can write as q
+
+squared plus delta t divided by
+tc, and there's a factor of 4.
+
+And delta t I have
+defined to be tc minus 10.
+
+How close I am to the location
+where this singularity takes
+
+places.
+
+So what I'm interested
+is not in the whole form
+
+of this function, but
+only the singularities
+
+that it expresses.
+
+So I focus on the singular part
+of this Gaussian expression.
+
+I don't have to worry
+about that term.
+
+So I have minus 1/2.
+
+I have double integral.
+
+The argument of
+the log, I expanded
+
+in the vicinity of
+the point that I
+
+see a singularity to take place.
+
+And I'll write the answer as q
+squared plus 4 delta t over tc.
+
+If I am sufficiently close in
+my integration to the origin
+
+so that the expansion
+in q is acceptable,
+
+there is an additional
+factor of tc.
+
+But if I take a log of
+tc, it's just a constant.
+
+I can integrate that out.
+
+It's going to not contribute
+to the singular part, just
+
+an additional regular component.
+
+Now if I am in the
+vicinity of q equals to 0
+
+where all of the action is,
+at this order, the thing
+
+that I'm integrating
+has circular symmetry so
+
+that 2-dimensional integration.
+
+I can write whether
+or not it's d qx, d qy
+
+as 2 pi q dq divided
+by 2 pi squared,
+
+which was the density of state.
+
+And this approximation
+of a thing being
+
+isotropic and
+circular only holds
+
+when I'm sufficiently
+close to the origin,
+
+let's say up to some value
+that I will call lambda.
+
+So I will impose
+some cut-off here,
+
+lambda, which is
+certainly less than one
+
+of the order of pi--
+let's say pi over 10.
+
+It doesn't matter what it is.
+
+As we will see,
+the singular part,
+
+it ultimately does not
+matter what I put for lambda.
+
+But the rest of the integration
+that I haven't exclusively
+
+written down from
+all of this-- again,
+
+in analogy to what we had seen
+before for the Landau-Ginzburg
+
+calculation will
+give me something
+
+that is perfectly analytic.
+
+So I have extracted from this
+expression the singular part.
+
+OK, now let's do this
+integral carefully.
+
+So what do I have?
+
+I have 1 over 2 pi with
+minus 1/2, so I have minus 1
+
+over 4 pi.
+
+If I call this whole
+object here x-- so x is q
+
+squared plus this
+something-- then
+
+we can see that dx is 2 q dq.
+
+So what I have to do is
+the integral of dx log x,
+
+which is x log x minus x.
+
+So essentially, let's keep the
+2 up there and make this 8 pi.
+
+And then what I have is
+x log x minus x itself,
+
+which I can write as log of e.
+
+And then this whole thing has
+to be evaluated between the two
+
+limits of integration,
+lambda and [INAUDIBLE].
+
+Now you explicitly see
+that if I substitute
+
+in this expression for q
+the upper part of lambda,
+
+it will give me
+something like lambda
+
+squared plus delta
+t-- an expandable
+
+and analytical function.
+
+Log of a constant plus delta t
+that I can start analytically
+
+expanding.
+
+So anything that I get
+from the other cut-off
+
+of the integration is
+perfectly analytic.
+
+I don't have to worry about it.
+
+If I'm interested in
+the singular part,
+
+I basically need to evaluate
+this as it's lower cut-off.
+
+So I evaluate it
+at q equals to 0.
+
+Well first off all, I
+will get a sign change
+
+because I'm at
+the lower cut-off.
+
+I will get from here
+4 delta t over tc.
+
+And from here, I will get
+log of a bunch of constants.
+
+It doesn't really matter.
+
+4 over e delta t over tc.
+
+What is the leading singularity?
+
+Is delta t log t-- log delta t?
+
+And so again, the
+leading singularity
+
+is delta t log of delta t.
+
+There's an overall factor of 1
+over pi. [? Doesn't match. ?]
+
+You take two derivatives.
+
+You find that the
+heat capacity, let's
+
+say that is proportion
+to two derivatives of log
+
+z by delta t squared.
+
+You take one derivative,
+it goes like the log.
+
+You take another
+derivative of the log,
+
+you find that the singularity
+is 1 over delta t.
+
+That corresponds to a
+heat capacity divergence
+
+with an exponent
+of unity, which is
+
+quite consistent with the
+generally Gaussian formula
+
+that we had in d dimensions,
+which was 2 minus t over 2.
+
+So that's the Gaussian.
+
+And of course, this
+whole theory breaks down
+
+for t that is greater than tc.
+
+Once I go beyond
+tc, my expressions
+
+just don't make sense.
+
+I can't integrate a lot
+of a negative number.
+
+And we understand why that is.
+
+That's because we are including
+all of these loops that
+
+can go over each
+other multiple times.
+
+The whole theory
+does not make sense.
+
+So we did this one to death.
+
+Will the exact result
+be any different?
+
+So let's carry out the
+corresponding procedure--
+
+for A star that is a
+function of q and t.
+
+And again, singularities
+should come from the place
+
+where this is most
+likely to go to 0.
+
+You can see it's 1
+something minus something.
+
+And clearly when the
+q's are close to 0
+
+is when you subtract
+most, and you're
+
+likely to become negative.
+
+So let's expand it around 0.
+
+This as q goes to 0 is 1
+plus t squared squared.
+
+And then I have minus.
+
+Each one of the cosines
+starts at unity,
+
+so I will have 4t
+1 minus t squared.
+
+And then from the qx squared
+over 2 qy squared over 2,
+
+I will get a plus
+t 1 minus t squared
+
+q squared-- qx squared plus
+qy squared-- plus order of q
+
+to the fourth.
+
+So the way that we identified
+the location of the singular
+
+part before was to focus
+on exactly q equals to 0.
+
+And what we find is that
+A star at q equals to 0
+
+is essentially this part.
+
+This part I'm going to rewrite
+the first end slightly.
+
+1 plus t squared squared
+is the same thing
+
+as 1 minus t squared
+squared plus 4t squared.
+
+The difference
+between the expansion
+
+of each one of
+these two terms is
+
+that this has plus 2t squared,
+this has minus 2t squared,
+
+which I have added here.
+
+And then minus 4t
+1 minus t squared.
+
+And the reason
+that I did that is
+
+that you can now see
+that this term is twice
+
+this times this when
+I take the square.
+
+So the whole thing is the same
+thing as 1 minus t squared
+
+minus 2t squared.
+
+So the first thing that gives
+us reassurance happens now,
+
+whereas previously for the
+Gaussian model 1 minus 4t could
+
+be both positive and
+negative, this you can see
+
+is always positive.
+
+So there is no
+problem with me not
+
+being able to go from one
+side of the phase transition
+
+to another side of
+the phase transition.
+
+This expression will
+encounter no difficulties.
+
+But there is a special
+point when this thing is 0.
+
+So there is a point when 1
+minus 2t c plus tc squared
+
+is equal to 0.
+
+The whole thing goes to 0.
+
+And you can figure
+out where that is.
+
+tc is 1.
+
+It's a quadratic form.
+
+It has two solutions-- 1
+minus plus square root of 2.
+
+A negative solution
+is not acceptable.
+
+Minus.
+
+I have to recast this slightly.
+
+Knowing the answer sometimes
+makes you go too fast.
+
+tc squared plus 2tc
+minus 1 equals to 0.
+
+tc is minus 1 plus or
+minus square root of 2.
+
+The minus solution
+is not acceptable.
+
+The plus solution would
+give me root 2 minus 1.
+
+Just to remind you,
+we calculated a value
+
+for the critical point
+based on duality.
+
+So let's just recap
+that duality argument.
+
+We saw that the series
+that we had calculated,
+
+which was an expansion in
+high temperatures times k,
+
+reproduced the expansion that
+we had for 0 temperature,
+
+including islands of
+minus in a sea of plus,
+
+where the contribution of each
+bond was going from e to the k
+
+to e to the minus k.
+
+So there was a correspondence
+between a dual coupling.
+
+And the actual coupling,
+that was like this.
+
+At a critical point,
+we said the two of them
+
+have to be the same.
+
+And what we had
+calculated based on that,
+
+since the hyperbolic
+tang I can write in terms
+
+of the exponentials was that
+the value of e to the minus
+
+e to the plus 2kc was, in
+fact, square root of 2 plus 1.
+
+And the inverse of this will
+be square root of 2 minus 1,
+
+and that's the same as the tang.
+
+That's the same
+thing as the things
+
+that we have already written.
+
+So the calculation
+that we had done
+
+before-- obtain this
+critical temperature based
+
+on this Kramers-Wannier
+duality--
+
+gave us a critical point here,
+which is precisely the place
+
+that we can identify as the
+origin of the singularity
+
+in this expression.
+
+So what did we do next?
+
+The next thing that we did
+was having identified up there
+
+where the critical point
+was-- which was at 14--
+
+was to expand our
+A, the integrand,
+
+inside the log in the
+vicinity of that point.
+
+So what I want to do
+is similarly expand
+
+a star of q for t that
+goes into vicinity of tc.
+
+And what do I have to do?
+
+So what I can do, let's write
+it as t is tc plus delta t
+
+and make an expansion
+for delta t small.
+
+So I have to make an expansion
+or delta t small, first
+
+of all, of this quantity.
+
+So if I make a
+small change in t,
+
+I'll have to take a
+derivative inside here.
+
+So I have minus 2t minus
+2, evaluate it at tc,
+
+times the change in delta t.
+
+So that's the change
+of this expression
+
+if I go slightly away from
+the point where it is 0.
+
+Yes?
+
+AUDIENCE: I have a question.
+
+T here is [? tangent ?]
+of k where we calculated
+
+the [INAUDIBLE] to
+[? be as ?] temperature.
+
+PROFESSOR: Now all
+of these things
+
+are analytical
+functions of each other.
+
+So the k is, in fact, some
+unit of energy divided by kt.
+
+So Really, the
+temperature is here.
+
+And my t is tang of
+the above objects,
+
+so it's tang of j divided by kt.
+
+So the point is
+that whenever I look
+
+at the delta in
+temperature, I can translate
+
+that delta in temperature to
+a delta int times the value
+
+of the derivative at
+the location of this,
+
+which is some finite number.
+
+Of basically up
+to some constant,
+
+taking derivatives with
+respect to temperature,
+
+with respect to k,
+with respect to tang k,
+
+with respect to beta.
+
+Evaluate it at the
+finite temperature,
+
+which is the location
+of the critical point.
+
+They're all the same up to
+proportionality constants,
+
+and that's why I wrote
+"proportionality" there.
+
+One thing that you
+have to make sure--
+
+and I spent actually half an
+hour this morning checking--
+
+is that the signs work out fine.
+
+So I didn't want to write
+an expression for the heat
+
+capacity that was negative.
+
+So proportionalities
+aside, that's
+
+the one thing that
+I better have,
+
+is that the sign of the heat
+capacity, that is positive.
+
+So that's the expansion of
+the term that corresponds to q
+
+equals to 0.
+
+The term that was
+proportional to q squared,
+
+look at what we did in
+the above expression
+
+for the Gaussian model.
+
+Since it was lower
+order, it was already
+
+proportional to q squared.
+
+We evaluated it at
+exactly t equals to tc.
+
+So I will put here tc 1
+minus tc squared q squared,
+
+and then I will
+have high orders.
+
+Now fortunately, we
+have a value for tc
+
+that we can substitute in
+a couple of places here.
+
+You can see that this is,
+in fact, twice tc plus 1,
+
+and tc plus 1 is root 2.
+
+So this is minus 2 root 2.
+
+I square that, and
+this whole thing
+
+becomes 8 delta t squared.
+
+This object here, 1
+minus tc squared--
+
+you can see if I put the 2 tc
+on the other side-- 1 minus tc
+
+squared' is the
+same thing as 2 tc.
+
+So I can write the whole thing
+here as 2 tc squared q squared.
+
+And the reason I
+do that is, like
+
+before, there's
+an overall factor
+
+that I can take out
+of this parentheses.
+
+And the answer will
+be q squared now
+
+plus 4 delta t over tc squared.
+
+It's very similar to
+what we had before,
+
+except that when we had q
+squared plus 4 delta t over tc,
+
+we have q squared plus 4
+delta t over tc squared.
+
+Now this square was very
+important for allowing
+
+us to go for both
+positive and negative,
+
+but let's see its consequence
+on the singularity.
+
+So now log z of the correct
+form divided by n-- the singular
+
+part-- and we calculate
+it just as before.
+
+First of all, rather than
+minus 1/2 I have a plus 1/2.
+
+I have the same integral, which
+in the vicinity of the origin
+
+is symmetric, so I will
+write it as 2 pi qd
+
+q divided by 4 pi squared.
+
+And then I have log.
+
+I will forget about this
+factor for consideration
+
+of singularities 4
+delta t over tc squared.
+
+And now again, it is
+exactly the same structure
+
+as x dx that I had before.
+
+So it's the same integral.
+
+And what you will find is that I
+evaluate it as 1/8 pi integral,
+
+essentially q squared plus
+4 delta t over tc squared,
+
+log of q squared plus 4
+delta t over tc squared
+
+over e evaluated
+between 0 and lambda.
+
+And the only singularity
+comes from the evaluation
+
+that we have at the origin.
+
+And so that I will
+get a factor of minus.
+
+So I will get 1/8 pi.
+
+Actually then, I
+substitute this factor.
+
+The 4 and the 8 will give me 2.
+
+And then I evaluate the
+log of delta t squared,
+
+so that's another factor of 2.
+
+So actually, only one
+factor of pi survives.
+
+I will have delta t over tc
+squared log of, let's say,
+
+absolute value of
+delta t over tc.
+
+So the only thing that
+changed was that whereas I
+
+had the linear term sitting
+in front of the log, now
+
+have a quadratic term.
+
+But now when I take two
+derivatives, and now
+
+we are sure that taking
+derivatives does not really
+
+matter whether I'm doing it with
+respect to temperature or delta
+
+t or any other variable.
+
+You can see that
+the leading behavior
+
+will come taking two
+derivatives out here
+
+and will be
+proportional to the log.
+
+So I will get minus 1 over
+pi log of delta t over tc.
+
+So that if I were to plug the
+heat capacity of the system,
+
+as a function of, let's
+say, this parameter t--
+
+which is also something that
+stands for temperature-- but t
+
+goes between, say, 0 and 1.
+
+It's a hyperbolic tangent.
+
+There's a location which is this
+tc, which is root 2 minus 1.
+
+And the singular part
+of the heat capacity--
+
+there will be some other
+part of the heat capacity
+
+that is regular-- but
+the singular part we see
+
+has a [INAUDIBLE] divergence.
+
+And furthermore, you can
+see that the amplitudes-- so
+
+essentially this
+goes approaching
+
+from different sides of the
+transition, A plus or A minus
+
+log of absolute
+value of delta a.
+
+And the ratio of the
+amplitudes, which we have also
+
+said is universal,
+is equal to 1.
+
+And you had
+anticipated that based
+
+on [? duality ?] [INAUDIBLE].
+
+All right, so indeed, there
+is a different behavior
+
+between the two models.
+
+The exact solution allows
+us to go both above
+
+and below, has this
+logarithmic singularity.
+
+And this expression was
+first written down-- well,
+
+first published Onsager in 1944.
+
+Even couple of
+years before that,
+
+he had written the expression on
+boards of various conferences,
+
+saying that this is
+the answer, but he
+
+didn't publish the paper.
+
+The way that he did it is based
+on the transfer matrix network,
+
+as we said.
+
+Basically, we can
+imagine that we
+
+have a lattice that is,
+let's say, I parallel
+
+in one direction,
+l perpendicular
+
+in the other direction.
+
+And then for the problems
+that you had to do,
+
+the transform matrix for
+one dimensional model,
+
+we can easy to do it
+for a [? ladder ?].
+
+It's a 4 by 4.
+
+For this, it becomes a 2 to
+the l by 2 to the l matrix.
+
+And of course, you are
+interested in the limit where
+
+l goes to infinity so that
+you can come 2-dimensional.
+
+And so he was able to sort
+of look at this structure
+
+of this matrix, recognize that
+the elements of this matrix
+
+could be represented in
+terms of other matrices
+
+that had some
+interesting algebra.
+
+And then he arguably
+could figure out
+
+what the diagonalization looked
+like in general for arbitrary
+
+l, and then calculate
+log z in terms
+
+of the log of the
+largest eigenvalue.
+
+I guess we have to
+multiply by l parallel.
+
+And showed that, indeed,
+it corresponds to this
+
+and has this phase transition.
+
+And before this solution,
+people were not even sure
+
+that when you sum an expression
+such as that for partition
+
+function if you ever get
+a singularity because,
+
+again, on the face
+of it, it's basically
+
+a sum of exponential functions.
+
+Each one of them is
+perfectly analytic,
+
+sums of analytical functions.
+
+It's supposed to be analytical.
+
+The whole key lies in the limit
+of taking, say, l to infinity
+
+and n to infinity,
+and then you'll
+
+be able to see these
+kinds of singularities.
+
+And then again,
+some people thought
+
+that the only type
+of singularities
+
+that you will be able to
+get are the kinds of things
+
+that we saw [INAUDIBLE] point.
+
+So to see a different
+type of singularity
+
+with a heat capacity that was
+actually divergent and could
+
+explicitly be shown
+through mathematics
+
+was quite an
+interesting revelation.
+
+So the kind of
+relative importance
+
+of that is that
+after the war-- you
+
+can see this is all around the
+time of World War II-- Casimir
+
+wrote to Pauli saying that I
+have been away from thinking
+
+about physics the past few years
+with the war and all of that.
+
+Anything interesting happening
+in theoretical physics?
+
+And Pauli responded, well,
+not much except that Onsager
+
+solved the
+2-dimensionalizing model.
+
+Of course, the solution that
+he has is quite obscure.
+
+And I don't think many
+people understand that.
+
+Then before, the form that
+people refer to was presented
+
+is actually kind of interesting,
+because this paper has
+
+something about
+crystal statistics,
+
+and then there's the following
+paper by a different author--
+
+Bruria Kaufman, 1949--
+has this same title
+
+except it goes from
+number two or something.
+
+So they were clearly
+talking to each other,
+
+but what she was able
+to show, Bruria Kaufman,
+
+was that the structure
+of these matrices
+
+can be simplified
+much further and can
+
+be made to look
+like spinners that
+
+are familiar from other
+branches of physics.
+
+And so this kind
+of 50-page paper
+
+was kind of reduced to
+something like a 20-page paper.
+
+And that's the solution that
+is reproduced in Wong's book.
+
+Chapter 15 of Wong has
+essentially a reproduction
+
+of this.
+
+I was looking at this
+because there aren't really
+
+that many women
+mathematical physicists,
+
+so I was kind of
+looking at her history,
+
+and she's quite
+an unusual person.
+
+So it turns out
+that for a while,
+
+she was mathematical
+assistant to Albert Einstein.
+
+She was first married to one of
+the most well known linguists
+
+of the 20th century.
+
+And for a while, they were
+both in Israel in a kibbutz
+
+where this important linguist
+was acting as a chauffeur
+
+and driving people around.
+
+And then later in life,
+she married briefly
+
+Willis Lamb, of Lamb shift.
+
+He turned out the term, 1949.
+
+She had done some calculation
+that if Lamb had paid attention
+
+to, he would have
+also potentially won
+
+a Nobel Prize for
+Mossbauer effect,
+
+but at that time
+didn't pay attention
+
+to it so somebody
+else got there first.
+
+So very interesting person.
+
+So to my mind, a good
+project for somebody
+
+is to write a biography
+for this person.
+
+It doesn't seem to exist.
+
+OK, so then both of these are
+based on this transfer matrix
+
+method.
+
+The method that
+I have given you,
+
+which is the graphical
+solution, was first
+
+presented by Kac
+and Ward in 1952.
+
+And it is reproduced
+in Feynman's book.
+
+So Feynman apparently also
+had one of these crucial steps
+
+of the conjecture with
+his factor of minus 1
+
+to the power of the
+number of crossings,
+
+giving you the correct
+factor to do the counting.
+
+Now it turns out that I also
+did not prove that statement,
+
+so there is a missing
+mathematical link
+
+to make my proof of this
+expression complete.
+
+And that was provided by a
+mathematician called Sherman,
+
+1960, that essentially
+shows very rigorously
+
+that these factors of minus
+1 to the number of crossings
+
+will work out and magically
+make everything happen.
+
+Now the question to
+ask is the following.
+
+We expect things to
+be exactly solvable
+
+when they are trivial
+in some sense.
+
+Gaussian model is
+exactly solvable
+
+because there is no
+interaction among the modes.
+
+So why is it that the
+2-dimensionalizing model
+
+is solvable?
+
+And one of the keys to
+that is a realization
+
+of another way of looking
+at the problem that
+
+appeared by Lieb, Mattis,
+and Schultz in 1964.
+
+And so basically what
+they said is let's
+
+take a look at these
+pictures that I
+
+have been drawing
+for the graphs.
+
+And so I have graphs
+that basically
+
+on a kind of coarse level, they
+look something like this maybe.
+
+And what they said was that
+if we look at the transfer
+
+matrix-- the one that
+Onsager and Bruria
+
+Kaufman were looking at.
+
+And the reason it was
+solvable, it looked very much
+
+like you had a
+system of fermions.
+
+And then the insight is that
+if we look at these pictures,
+
+you can regard this as
+a 1-dimensional system
+
+of fermions that is
+evolving in time.
+
+And what you are looking at
+these borderline histories
+
+of two particles
+that are propagating.
+
+Here they annihilate each other.
+
+Here they annihilate each other.
+
+Another pair gets
+created, et cetera.
+
+But in one dimensions, fermions
+you can regard two ways--
+
+either they cannot occupy the
+same site or you can say, well,
+
+let them occupy in same site,
+but then I introduce these
+
+factors of minus 1 for
+the exchange of fermions.
+
+So when two fermions cross
+each other in one dimension,
+
+their position
+has been exchanged
+
+so you have to put a
+minus 1 for crossing.
+
+And then when you sum over all
+histories for every crossing,
+
+there will be one that
+touches and goes away.
+
+And the sum total of
+the two of them is 0.
+
+So the point is that
+at the end of the day,
+
+this theory is a theory
+of three fermions.
+
+So we have not solved,
+in fact, an interacting
+
+complicated problem.
+
+It is.
+
+But in the right
+perspective, it looks
+
+like a bunch of fermions that
+completely non-interacting pass
+
+through each other
+as long as we're
+
+willing to put the minus 1 phase
+that you have for crossings.
+
+One last aspect to
+think about that you
+
+learn from this
+fermionic perspective.
+
+Look at this expression.
+
+Why did I say that this
+is a Gaussian model?
+
+We saw that we could
+get this, z Gaussian,
+
+by doing an integral
+essentially over weights
+
+that were continuous by i.
+
+And the weight I could click
+here as kij phi i phi j.
+
+Because in principle, if I
+only count an interaction once,
+
+let's say I count it twice.
+
+I could put a factor of 1/2
+if I allow i and j to be some.
+
+Especially I said the weight
+that I have to put here
+
+is something like
+phi i squared over 2.
+
+So this essentially you
+can see z of the Gaussian
+
+ultimately always
+becomes something like z
+
+of the Gaussian is going to
+be 1 over the square root
+
+of a determinant of whatever
+the quadratic form is up there.
+
+And when you take the log
+of the partition function,
+
+the square root of the
+determinant becomes minus 1/2
+
+of the log of the
+determinant, which
+
+is what we've been calculating.
+
+So that's obvious.
+
+You say this object
+over here that you
+
+write as an answer is also
+log of some determinant.
+
+So can I think of these as
+some kind of a rock that
+
+is prescribed according to
+these rules on a lattice,
+
+give weights to jump
+according to what I have,
+
+then do a kind of
+Gaussian integration
+
+and get the same answer?
+
+Well, the difficulty
+is precisely
+
+this 1/2 versus minus
+1/2, because when
+
+you do the Gaussian
+integration, you
+
+get the determinant
+in the denominator.
+
+So is there a trick to get the
+determinant in the numerator?
+
+And the answer is
+that people who
+
+do have integral formulations
+for fermionic systems
+
+rely on coherent
+states that involve
+
+anti-commuting variables,
+called Grassmann variables.
+
+And the very interesting thing
+about Grassmann variables
+
+is that if I do the analog
+of the Gaussian integration,
+
+the answer-- rather than
+being in the determinant,
+
+in the denominator--
+goes into the numerator.
+
+And so one can, in fact,
+rewrite this partition function,
+
+sort of working
+backward, in terms
+
+of an integration over
+Gaussian distributed
+
+Grassmannian variables
+on the lattice,
+
+which is also equivalent
+to another way of thinking
+
+about fermions.
+
+Let's see.
+
+What else is known
+about this model?
+
+So I said that the specific
+heat singularity is known,
+
+so we have this
+alpha which is 0 log.
+
+Given that the
+structure that we have
+
+involves inside the log
+something that is like this,
+
+you won't be surprised that if I
+think in terms of a correlation
+
+length-- so typically q's
+would be an inverse correlation
+
+length, some kind of a q
+at which I will be reaching
+
+appropriate saturation for
+a delta t-- I will arrive
+
+at a correlation range
+that diverge as delta t
+
+to the minus 1.
+
+Again, I can write it
+more precisely as b plus b
+
+minus to the minus mu minus.
+
+The ratio of the b's
+this is 1, and the mus
+
+are the same and equal to 1.
+
+So the correlation length
+diverges with an exponent 1,
+
+and one can [INAUDIBLE]
+this exactly.
+
+One can then also calculate
+actual correlations
+
+at criticality and show that
+that criticality correlations
+
+decay with separation
+between the points
+
+that you are looking at
+as 1 over r to the 1/4.
+
+So the exponent that we call
+mu is 1/4 in 2 dimensions.
+
+Once you have
+correlations, you certainly
+
+know that you can calculate
+the susceptibility
+
+as an integral of the
+correlation function.
+
+And so it's going to be an
+integral b 2r over r to the 1/4
+
+that is cut off at the
+correlation length.
+
+So that's going to give me c
+to the power of 2 minus 1/4,
+
+which is 7/4.
+
+So that's going to diverge as
+delta t 2 to the minus gamma.
+
+Gamma is, again, 7/4.
+
+So these things--
+correlations-- can
+
+be calculated like
+you saw already
+
+for the case of
+the Gaussian model
+
+with a appropriate modification.
+
+That is, I have to
+look at walks that
+
+don't come back and
+close on themselves,
+
+but walks that go from one
+point to another point.
+
+So the same types of techniques
+that is described here
+
+will allow you to get to
+all of these other results.
+
+AUDIENCE: Question?
+
+PROFESSOR: Yes?
+
+AUDIENCE: Do people try to
+experiment on the builds
+
+as things that should be
+[INAUDIBLE] to the Ising model?
+
+PROFESSOR: There are by now
+many experimental realizations
+
+of [INAUDIBLE] Ising model
+in which these exponents--
+
+actually, the next
+one that I will
+
+tell you have been
+confirmed very nicely.
+
+So there are a number of
+2-dimensional absorb, systems,
+
+a number of systems of
+mixtures in 2 dimensions
+
+that phase separate.
+
+So there's a huge number of
+experimental realizations.
+
+At that time, no, because
+we're talking about 70 years.
+
+So the last thing
+that I want to mention
+
+is, of course, when
+you go below tc,
+
+we expect that-- let's
+call it temperate--
+
+when I go below temperature,
+there will be a magnetization.
+
+That has always been our
+signature of symmetry breaking.
+
+And so the question is,
+what is the magnetization?
+
+And then this is another
+interesting story,
+
+that around 1950s in a
+couple of conferences,
+
+at the end of somebody's talk,
+Onsager went to the board
+
+and said that he
+and Bruria Kaufman
+
+have found this expression for
+the magnetization of the system
+
+at low temperature as a
+function of temperature
+
+or the coupling constant.
+
+But they never wrote the
+solution down until in 1952,
+
+actually CN Yang
+published a paper
+
+that has derived this result.
+
+And since this goes to 1
+at the critical point-- why
+
+duality [INAUDIBLE]
+2k [INAUDIBLE] 2k--
+
+[? dual ?] plus 1.
+
+This vanishes with
+an exponent beta,
+
+which is 1/8, which is the
+other exponent in this series.
+
+So as I said, there
+are many people
+
+who since the '50s and
+'60s devoted their life
+
+to looking at various
+generalizations, extensions
+
+of the Ising model.
+
+There are many people
+who try to solve it
+
+with a finite in 2 dimensions,
+a finite magnetic field.
+
+You can't do that.
+
+This magnetization
+is obtained only
+
+at the limit of
+[INAUDIBLE] going to 0.
+
+And clearly, people
+have thought a lot
+
+about doing things in 3
+dimensions or higher dimensions
+
+without much success.
+
+So this is basically
+the end of the portion
+
+that I had to give with
+discrete models and lattices.
+
+And as of next lecture, we
+will change our perspective
+
+one more time.
+
+We'll go back to
+the continuum and we
+
+will look at n component
+models in the low temperature
+
+expansion and see what
+happens over there.
+
+Are there any questions?
+
+OK, I will give you
+a preview of what
+
+I will be doing in
+the next few minutes.
+
+So we have been looking at these
+lattice models in the high t
+
+limit where expansion
+was graphical,
+
+such as the one that
+I have over there.
+
+But the partition
+function turned out
+
+to be something of
+two constants, as 1
+
+plus something that involves
+loops and things that
+
+involve multiple
+loops, et cetera.
+
+This was for the Ising model.
+
+It turns out that if I
+go from the Ising model
+
+to n component space.
+
+So at each side
+of the lattice, I
+
+put something that
+has n components
+
+subject to the condition
+that it's a unit vector.
+
+And I try to calculate
+the partition function
+
+by integrating over all
+of these unit vectors
+
+in n dimension of a
+weight that is just
+
+a generalization of the Ising,
+except that I would have
+
+the dot product of these things.
+
+And I start making appropriate
+high temperature expansions
+
+for these models.
+
+I will generate a
+very similar series,
+
+except that whenever
+I see a loop,
+
+I have to put a
+factor of n where
+
+n is the number of components.
+
+And this we already
+saw when we were
+
+doing Landau-Ginzburg
+expansions.
+
+We saw that the expansions
+that we had over here
+
+could be graphically
+interpreted as representations
+
+of the various terms that we
+had in the Landau-Ginzburg
+
+expansion.
+
+And essentially, this factor
+of n is the one difficulty.
+
+You can use the same methods
+for numerical expansions
+
+for all n models that are
+these n component models.
+
+You can't do anything
+exactly with them.
+
+Now the low temperature
+expansion for Ising
+
+like models we saw involved
+starting with some ground
+
+state-- for example, all up--
+and then including excitations
+
+that were islands of
+minus in a sea of plus.
+
+And so then there higher
+order in this series.
+
+Now for other discrete models,
+such as the Potts model,
+
+you can use the same procedure.
+
+And again, you see that
+in some of the problems
+
+that you've had to solve.
+
+But this will not work when we
+come to these continuous spin
+
+markets, because for
+continuous spin models,
+
+the ground state would be when
+everybody is pointing in one
+
+direction, but the excitations
+on this ground state
+
+are not islands that
+are flipped over.
+
+They are these long
+wavelength Goldstone modes,
+
+which we described
+earlier in class.
+
+So if we want to
+make an expansion
+
+to look at the low temperature
+[INAUDIBLE] for systems with n
+
+greater than 1, we have to
+make an expansion involving
+
+Goldstone modes
+and, as we will see,
+
+interactions among
+Goldstone modes.
+
+So you can no longer regard
+at that appropriate level
+
+of sophistication as the
+Goldstone modes maintain
+
+independence from each other.
+
+And very roughly, the main
+difference between discrete
+
+and these continuous symmetry
+models is captured as follows.
+
+Suppose I have a huge
+system that is L by L
+
+and I impose boundary conditions
+on one side where all of this
+
+spins in one
+direction, and ask what
+
+happens if I impose a different
+condition on the other side.
+
+Well, what would happen is you
+would have a domain boundary.
+
+And the cost of
+that domain boundary
+
+will be proportional to
+the area of the boundary
+
+in d dimensions.
+
+So the cost is
+proportional to some energy
+
+per bond times L
+to the d minus 1.
+
+Whereas if I try to do the same
+thing for a continuous spin
+
+system, if I align one side like
+this, the other side like this,
+
+but in-between I can gradually
+change from one direction
+
+to another direction.
+
+And the cost would
+be the gradient,
+
+which is 1 over L
+squared times integrated
+
+over the entire system.
+
+So the energy cost
+of this excitation
+
+will be some parameter
+j, 1 over L-- which
+
+is the shift-- squared-- which
+is the [? strain ?] squared--
+
+integrated over
+the entire volume,
+
+so it goes L to the d minus 2.
+
+So we can see that these
+systems are much softer
+
+than discrete systems.
+
+For discrete systems,
+thermal fluctuations
+
+are sufficient to destroy
+order at low temperature
+
+as soon as this cost is of the
+order of kt, which for large L
+
+can only happen in d
+[INAUDIBLE] 1 and lower.
+
+Whereas for these systems, it
+happens in d of 2 and lower.
+
+So the lower critical
+dimension for these models.
+
+With continuous symmetry,
+we already saw it's 2.
+
+For these models, it is 1.
+
+Now we are going to be
+interested in this class
+
+of models.
+
+I have told you that
+in 2 dimensions,
+
+they should not order.
+
+So presumably, the critical
+temperature-- if I continuously
+
+regard it as a
+function of dimension,
+
+will go to 0 as a function
+of dimension as d minus 2.
+
+So the insight of
+Polyakov was that maybe we
+
+can look at the interactions
+of these old Goldstone modes
+
+and do a systematic low
+temperature expansion that
+
+reaches the phase transition of
+a critical point systematically
+
+ind minus 2.
+
+And that's what we will
+attempt in the future.
\ No newline at end of file
diff --git a/6nDqY8MPLDM.txt b/6nDqY8MPLDM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c683f137831977b2dcf2df16fcac275a78c7930e
--- /dev/null
+++ b/6nDqY8MPLDM.txt
@@ -0,0 +1,7363 @@
+align:start position:0%
+ 
+the following content is provided under
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+ 
+
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+materials from hundreds of MIT courses
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+
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+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hope everyone had a great Veterans Day
+
+ align:start position:0%
+hope everyone had a great Veterans Day
+ 
+
+ align:start position:0%
+hope everyone had a great Veterans Day
+break yesterday spending it of course as
+
+ align:start position:0%
+break yesterday spending it of course as
+ 
+
+ align:start position:0%
+break yesterday spending it of course as
+I checked my tests on Ian's spending it
+
+ align:start position:0%
+I checked my tests on Ian's spending it
+ 
+
+ align:start position:0%
+I checked my tests on Ian's spending it
+mostly doing your opera research or
+
+ align:start position:0%
+mostly doing your opera research or
+ 
+
+ align:start position:0%
+mostly doing your opera research or
+psets but at least one person got to
+
+ align:start position:0%
+psets but at least one person got to
+ 
+
+ align:start position:0%
+psets but at least one person got to
+watch TV so at least one person got to
+
+ align:start position:0%
+watch TV so at least one person got to
+ 
+
+ align:start position:0%
+watch TV so at least one person got to
+have a real break and that's something
+
+ align:start position:0%
+have a real break and that's something
+ 
+
+ align:start position:0%
+have a real break and that's something
+truly amazing and special so now we're
+
+ align:start position:0%
+truly amazing and special so now we're
+ 
+
+ align:start position:0%
+truly amazing and special so now we're
+going to talk about svms
+
+ align:start position:0%
+going to talk about svms
+ 
+
+ align:start position:0%
+going to talk about svms
+they're pretty much the hardest thing in
+
+ align:start position:0%
+they're pretty much the hardest thing in
+ 
+
+ align:start position:0%
+they're pretty much the hardest thing in
+6:54 however in recent in recent years a
+
+ align:start position:0%
+6:54 however in recent in recent years a
+ 
+
+ align:start position:0%
+6:54 however in recent in recent years a
+few shortcuts have popped up that will
+
+ align:start position:0%
+few shortcuts have popped up that will
+ 
+
+ align:start position:0%
+few shortcuts have popped up that will
+sometimes allow you to solve the
+
+ align:start position:0%
+sometimes allow you to solve the
+ 
+
+ align:start position:0%
+sometimes allow you to solve the
+question depending on what they're
+
+ align:start position:0%
+question depending on what they're
+ 
+
+ align:start position:0%
+question depending on what they're
+asking for without solving some vast
+
+ align:start position:0%
+asking for without solving some vast
+ 
+
+ align:start position:0%
+asking for without solving some vast
+ugly set of equations with the vast
+
+ align:start position:0%
+ugly set of equations with the vast
+ 
+
+ align:start position:0%
+ugly set of equations with the vast
+Uglies number of unknowns so I'm going
+
+ align:start position:0%
+Uglies number of unknowns so I'm going
+ 
+
+ align:start position:0%
+Uglies number of unknowns so I'm going
+to show that to you guys
+
+ align:start position:0%
+to show that to you guys
+ 
+
+ align:start position:0%
+to show that to you guys
+I'm also going to try to explain all the
+
+ align:start position:0%
+I'm also going to try to explain all the
+ 
+
+ align:start position:0%
+I'm also going to try to explain all the
+alphabet soup that's in neural nets and
+
+ align:start position:0%
+alphabet soup that's in neural nets and
+ 
+
+ align:start position:0%
+alphabet soup that's in neural nets and
+what all the letters stand for because I
+
+ align:start position:0%
+what all the letters stand for because I
+ 
+
+ align:start position:0%
+what all the letters stand for because I
+took me a few times going to North go to
+
+ align:start position:0%
+took me a few times going to North go to
+ 
+
+ align:start position:0%
+took me a few times going to North go to
+the S campus it took me a few times
+
+ align:start position:0%
+the S campus it took me a few times
+ 
+
+ align:start position:0%
+the S campus it took me a few times
+going through SVM's to actually find out
+
+ align:start position:0%
+going through SVM's to actually find out
+ 
+
+ align:start position:0%
+going through SVM's to actually find out
+for sure what all those letters stood
+
+ align:start position:0%
+for sure what all those letters stood
+ 
+
+ align:start position:0%
+for sure what all those letters stood
+for and if you guys figure it out first
+
+ align:start position:0%
+for and if you guys figure it out first
+ 
+
+ align:start position:0%
+for and if you guys figure it out first
+try that's going to be great and you
+
+ align:start position:0%
+try that's going to be great and you
+ 
+
+ align:start position:0%
+try that's going to be great and you
+guys will be just fine so let's take a
+
+ align:start position:0%
+guys will be just fine so let's take a
+ 
+
+ align:start position:0%
+guys will be just fine so let's take a
+look at the problem is perhaps most
+
+ align:start position:0%
+look at the problem is perhaps most
+ 
+
+ align:start position:0%
+look at the problem is perhaps most
+optimized for using some of the
+
+ align:start position:0%
+optimized for using some of the
+ 
+
+ align:start position:0%
+optimized for using some of the
+shortcuts to solving it and not putting
+
+ align:start position:0%
+shortcuts to solving it and not putting
+ 
+
+ align:start position:0%
+shortcuts to solving it and not putting
+up all the equations then I will because
+
+ align:start position:0%
+up all the equations then I will because
+ 
+
+ align:start position:0%
+up all the equations then I will because
+I am not because I'm sadistic but
+
+ align:start position:0%
+I am not because I'm sadistic but
+ 
+
+ align:start position:0%
+I am not because I'm sadistic but
+because I'm being nice I will force you
+
+ align:start position:0%
+because I'm being nice I will force you
+ 
+
+ align:start position:0%
+because I'm being nice I will force you
+with me to solve some of the things they
+
+ align:start position:0%
+with me to solve some of the things they
+ 
+
+ align:start position:0%
+with me to solve some of the things they
+didn't ask for us to solve so that you
+
+ align:start position:0%
+didn't ask for us to solve so that you
+ 
+
+ align:start position:0%
+didn't ask for us to solve so that you
+can see that we can't get away with
+
+ align:start position:0%
+can see that we can't get away with
+ 
+
+ align:start position:0%
+can see that we can't get away with
+everything without doing some of the
+
+ align:start position:0%
+everything without doing some of the
+ 
+
+ align:start position:0%
+everything without doing some of the
+harder stuff and
+
+ align:start position:0%
+harder stuff and
+ 
+
+ align:start position:0%
+harder stuff and
+of course definitely ask questions as
+
+ align:start position:0%
+of course definitely ask questions as
+ 
+
+ align:start position:0%
+of course definitely ask questions as
+always but this time even more so you
+
+ align:start position:0%
+always but this time even more so you
+ 
+
+ align:start position:0%
+always but this time even more so you
+guys well if you were looking around you
+
+ align:start position:0%
+guys well if you were looking around you
+ 
+
+ align:start position:0%
+guys well if you were looking around you
+saw nobody in this entire lecture hall
+
+ align:start position:0%
+saw nobody in this entire lecture hall
+ 
+
+ align:start position:0%
+saw nobody in this entire lecture hall
+raise their hand that they're already
+
+ align:start position:0%
+raise their hand that they're already
+ 
+
+ align:start position:0%
+raise their hand that they're already
+set and ready and no svm so if you have
+
+ align:start position:0%
+set and ready and no svm so if you have
+ 
+
+ align:start position:0%
+set and ready and no svm so if you have
+a question maybe everybody else does
+
+ align:start position:0%
+a question maybe everybody else does
+ 
+
+ align:start position:0%
+a question maybe everybody else does
+so let's go
+
+ align:start position:0%
+so let's go
+ 
+
+ align:start position:0%
+so let's go
+you'll start right here as always
+
+ align:start position:0%
+you'll start right here as always
+ 
+
+ align:start position:0%
+you'll start right here as always
+pretend that I can draw and therefore
+
+ align:start position:0%
+pretend that I can draw and therefore
+ 
+
+ align:start position:0%
+pretend that I can draw and therefore
+all the pluses and minuses are only on
+
+ align:start position:0%
+all the pluses and minuses are only on
+ 
+
+ align:start position:0%
+all the pluses and minuses are only on
+integer coordinates so we are asked in
+
+ align:start position:0%
+integer coordinates so we are asked in
+ 
+
+ align:start position:0%
+integer coordinates so we are asked in
+this problem to circle the support
+
+ align:start position:0%
+this problem to circle the support
+ 
+
+ align:start position:0%
+this problem to circle the support
+vectors draw the edges of the street and
+
+ align:start position:0%
+vectors draw the edges of the street and
+ 
+
+ align:start position:0%
+vectors draw the edges of the street and
+then the dotted line in the middle that
+
+ align:start position:0%
+then the dotted line in the middle that
+ 
+
+ align:start position:0%
+then the dotted line in the middle that
+separates them the separator as a dashed
+
+ align:start position:0%
+separates them the separator as a dashed
+ 
+
+ align:start position:0%
+separates them the separator as a dashed
+line and then to give both W and B so
+
+ align:start position:0%
+line and then to give both W and B so
+ 
+
+ align:start position:0%
+line and then to give both W and B so
+what are W and B well there's a few
+
+ align:start position:0%
+what are W and B well there's a few
+ 
+
+ align:start position:0%
+what are W and B well there's a few
+important equations in in svms that we
+
+ align:start position:0%
+important equations in in svms that we
+ 
+
+ align:start position:0%
+important equations in in svms that we
+really hope and I'm going to tell you
+
+ align:start position:0%
+really hope and I'm going to tell you
+ 
+
+ align:start position:0%
+really hope and I'm going to tell you
+we're lucky in this because we don't
+
+ align:start position:0%
+we're lucky in this because we don't
+ 
+
+ align:start position:0%
+we're lucky in this because we don't
+have to but we really hope that we don't
+
+ align:start position:0%
+have to but we really hope that we don't
+ 
+
+ align:start position:0%
+have to but we really hope that we don't
+have to use because they provide a huge
+
+ align:start position:0%
+have to use because they provide a huge
+ 
+
+ align:start position:0%
+have to use because they provide a huge
+number of variables so one of those
+
+ align:start position:0%
+number of variables so one of those
+ 
+
+ align:start position:0%
+number of variables so one of those
+crucial equations is that for a spur a
+
+ align:start position:0%
+crucial equations is that for a spur a
+ 
+
+ align:start position:0%
+crucial equations is that for a spur a
+plus support vector W vector dot X plus
+
+ align:start position:0%
+plus support vector W vector dot X plus
+ 
+
+ align:start position:0%
+plus support vector W vector dot X plus
+the plus support vector plus B equals 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+WX minus plus B with minus 1 and W dot
+
+ align:start position:0%
+WX minus plus B with minus 1 and W dot
+ 
+
+ align:start position:0%
+WX minus plus B with minus 1 and W dot
+that dotted line I don't know we'll call
+
+ align:start position:0%
+that dotted line I don't know we'll call
+ 
+
+ align:start position:0%
+that dotted line I don't know we'll call
+it dot dot plus B equals 0 so what does
+
+ align:start position:0%
+it dot dot plus B equals 0 so what does
+ 
+
+ align:start position:0%
+it dot dot plus B equals 0 so what does
+this mean there are a lot of vectors
+
+ align:start position:0%
+this mean there are a lot of vectors
+ 
+
+ align:start position:0%
+this mean there are a lot of vectors
+well I mean we're usually in
+
+ align:start position:0%
+well I mean we're usually in
+ 
+
+ align:start position:0%
+well I mean we're usually in
+two-dimensional space so we can
+
+ align:start position:0%
+two-dimensional space so we can
+ 
+
+ align:start position:0%
+two-dimensional space so we can
+basically just say that there's two
+
+ align:start position:0%
+basically just say that there's two
+ 
+
+ align:start position:0%
+basically just say that there's two
+components of this W vector W 1 and W 2
+
+ align:start position:0%
+components of this W vector W 1 and W 2
+ 
+
+ align:start position:0%
+components of this W vector W 1 and W 2
+and they're just two coefficients and a
+
+ align:start position:0%
+and they're just two coefficients and a
+ 
+
+ align:start position:0%
+and they're just two coefficients and a
+linear equation so to get for instance
+
+ align:start position:0%
+linear equation so to get for instance
+ 
+
+ align:start position:0%
+linear equation so to get for instance
+what we're interested in finding this
+
+ align:start position:0%
+what we're interested in finding this
+ 
+
+ align:start position:0%
+what we're interested in finding this
+that dot line we'll just call that X
+
+ align:start position:0%
+that dot line we'll just call that X
+ 
+
+ align:start position:0%
+that dot line we'll just call that X
+with nothing on it actually maybe
+
+ align:start position:0%
+with nothing on it actually maybe
+ 
+
+ align:start position:0%
+with nothing on it actually maybe
+that'll be easier this is equivalent to
+
+ align:start position:0%
+that'll be easier this is equivalent to
+ 
+
+ align:start position:0%
+that'll be easier this is equivalent to
+saying W 1 X 1 plus W 2 X 2 plus B
+
+ align:start position:0%
+saying W 1 X 1 plus W 2 X 2 plus B
+ 
+
+ align:start position:0%
+saying W 1 X 1 plus W 2 X 2 plus B
+equals 0 where X 1 is this and X 2 is
+
+ align:start position:0%
+equals 0 where X 1 is this and X 2 is
+ 
+
+ align:start position:0%
+equals 0 where X 1 is this and X 2 is
+this we would possibly call them x and y
+
+ align:start position:0%
+this we would possibly call them x and y
+ 
+
+ align:start position:0%
+this we would possibly call them x and y
+so one way to think about it is you know
+
+ align:start position:0%
+so one way to think about it is you know
+ 
+
+ align:start position:0%
+so one way to think about it is you know
+W 1 we call a a x+ called W to be B Y oh
+
+ align:start position:0%
+W 1 we call a a x+ called W to be B Y oh
+ 
+
+ align:start position:0%
+W 1 we call a a x+ called W to be B Y oh
+don't call it B
+
+ align:start position:0%
+don't call it B
+ 
+
+ align:start position:0%
+don't call it B
+well a X plus CY plus B equals put this
+
+ align:start position:0%
+well a X plus CY plus B equals put this
+ 
+
+ align:start position:0%
+well a X plus CY plus B equals put this
+on parenthesis this is basically an
+
+ align:start position:0%
+on parenthesis this is basically an
+ 
+
+ align:start position:0%
+on parenthesis this is basically an
+equation like this or you know y equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative a over C X minus B over C it's
+
+ align:start position:0%
+negative a over C X minus B over C it's
+ 
+
+ align:start position:0%
+negative a over C X minus B over C it's
+basically y equals MX plus B does
+
+ align:start position:0%
+basically y equals MX plus B does
+ 
+
+ align:start position:0%
+basically y equals MX plus B does
+everyone see that this thing that we're
+
+ align:start position:0%
+everyone see that this thing that we're
+ 
+
+ align:start position:0%
+everyone see that this thing that we're
+looking for this w dot X plus B equals 0
+
+ align:start position:0%
+looking for this w dot X plus B equals 0
+ 
+
+ align:start position:0%
+looking for this w dot X plus B equals 0
+is the equation of a line on in
+
+ align:start position:0%
+is the equation of a line on in
+ 
+
+ align:start position:0%
+is the equation of a line on in
+Cartesian coordinates it just looks
+
+ align:start position:0%
+Cartesian coordinates it just looks
+ 
+
+ align:start position:0%
+Cartesian coordinates it just looks
+uglier normally when we're doing all
+
+ align:start position:0%
+uglier normally when we're doing all
+ 
+
+ align:start position:0%
+uglier normally when we're doing all
+this solving for W and B we'd have to
+
+ align:start position:0%
+this solving for W and B we'd have to
+ 
+
+ align:start position:0%
+this solving for W and B we'd have to
+put in equations with the you tons of
+
+ align:start position:0%
+put in equations with the you tons of
+ 
+
+ align:start position:0%
+put in equations with the you tons of
+equations plug in all the support
+
+ align:start position:0%
+equations plug in all the support
+ 
+
+ align:start position:0%
+equations plug in all the support
+vectors in there and we have to use
+
+ align:start position:0%
+vectors in there and we have to use
+ 
+
+ align:start position:0%
+vectors in there and we have to use
+these little devils called alphas which
+
+ align:start position:0%
+these little devils called alphas which
+ 
+
+ align:start position:0%
+these little devils called alphas which
+alphas essentially if it wasn't clear in
+
+ align:start position:0%
+alphas essentially if it wasn't clear in
+ 
+
+ align:start position:0%
+alphas essentially if it wasn't clear in
+the lecture which it usually isn't
+
+ align:start position:0%
+the lecture which it usually isn't
+ 
+
+ align:start position:0%
+the lecture which it usually isn't
+completely clear to everyone wasn't
+
+ align:start position:0%
+completely clear to everyone wasn't
+ 
+
+ align:start position:0%
+completely clear to everyone wasn't
+clear to me completely alphas way I'd
+
+ align:start position:0%
+clear to me completely alphas way I'd
+ 
+
+ align:start position:0%
+clear to me completely alphas way I'd
+like to think about them the Alpha is in
+
+ align:start position:0%
+like to think about them the Alpha is in
+ 
+
+ align:start position:0%
+like to think about them the Alpha is in
+this problem is they are the weight of
+
+ align:start position:0%
+this problem is they are the weight of
+ 
+
+ align:start position:0%
+this problem is they are the weight of
+how significant any particular point on
+
+ align:start position:0%
+how significant any particular point on
+ 
+
+ align:start position:0%
+how significant any particular point on
+the graph is towards creating the
+
+ align:start position:0%
+the graph is towards creating the
+ 
+
+ align:start position:0%
+the graph is towards creating the
+boundary this the higher the alpha is
+
+ align:start position:0%
+boundary this the higher the alpha is
+ 
+
+ align:start position:0%
+boundary this the higher the alpha is
+the more that that point narrows in the
+
+ align:start position:0%
+the more that that point narrows in the
+ 
+
+ align:start position:0%
+the more that that point narrows in the
+boundary the lower the alpha is the less
+
+ align:start position:0%
+boundary the lower the alpha is the less
+ 
+
+ align:start position:0%
+boundary the lower the alpha is the less
+at that point narrows in the boundary
+
+ align:start position:0%
+at that point narrows in the boundary
+ 
+
+ align:start position:0%
+at that point narrows in the boundary
+the wider the road can be and if that
+
+ align:start position:0%
+the wider the road can be and if that
+ 
+
+ align:start position:0%
+the wider the road can be and if that
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+do anything if that point is irrelevant
+
+ align:start position:0%
+do anything if that point is irrelevant
+ 
+
+ align:start position:0%
+do anything if that point is irrelevant
+and could be removed it wouldn't affect
+
+ align:start position:0%
+and could be removed it wouldn't affect
+ 
+
+ align:start position:0%
+and could be removed it wouldn't affect
+the boundary the Alpha is everyone zero
+
+ align:start position:0%
+the boundary the Alpha is everyone zero
+ 
+
+ align:start position:0%
+the boundary the Alpha is everyone zero
+well that was one person but you can
+
+ align:start position:0%
+well that was one person but you can
+ 
+
+ align:start position:0%
+well that was one person but you can
+suffice for everyone the Alpha is zero
+
+ align:start position:0%
+suffice for everyone the Alpha is zero
+ 
+
+ align:start position:0%
+suffice for everyone the Alpha is zero
+and that means if it's not a support
+
+ align:start position:0%
+and that means if it's not a support
+ 
+
+ align:start position:0%
+and that means if it's not a support
+vector if it's not one of the vectors on
+
+ align:start position:0%
+vector if it's not one of the vectors on
+ 
+
+ align:start position:0%
+vector if it's not one of the vectors on
+the boundary lines it will always have
+
+ align:start position:0%
+the boundary lines it will always have
+ 
+
+ align:start position:0%
+the boundary lines it will always have
+an alpha of zero because it doesn't
+
+ align:start position:0%
+an alpha of zero because it doesn't
+ 
+
+ align:start position:0%
+an alpha of zero because it doesn't
+affect so keeping that in mind there's a
+
+ align:start position:0%
+affect so keeping that in mind there's a
+ 
+
+ align:start position:0%
+affect so keeping that in mind there's a
+few fun and important equations about
+
+ align:start position:0%
+few fun and important equations about
+ 
+
+ align:start position:0%
+few fun and important equations about
+alphas that will mean if we're solving
+
+ align:start position:0%
+alphas that will mean if we're solving
+ 
+
+ align:start position:0%
+alphas that will mean if we're solving
+many equations for many unknowns which
+
+ align:start position:0%
+many equations for many unknowns which
+ 
+
+ align:start position:0%
+many equations for many unknowns which
+hopefully we won't have to do the sum
+
+ align:start position:0%
+hopefully we won't have to do the sum
+ 
+
+ align:start position:0%
+hopefully we won't have to do the sum
+over the positive alphas equals the sum
+
+ align:start position:0%
+over the positive alphas equals the sum
+ 
+
+ align:start position:0%
+over the positive alphas equals the sum
+over and the alphas of the negative
+
+ align:start position:0%
+over and the alphas of the negative
+ 
+
+ align:start position:0%
+over and the alphas of the negative
+points this is true over all the points
+
+ align:start position:0%
+points this is true over all the points
+ 
+
+ align:start position:0%
+points this is true over all the points
+but since all the alphas are 0 except
+
+ align:start position:0%
+but since all the alphas are 0 except
+ 
+
+ align:start position:0%
+but since all the alphas are 0 except
+for the support vectors it also means
+
+ align:start position:0%
+for the support vectors it also means
+ 
+
+ align:start position:0%
+for the support vectors it also means
+the alphas of the positive support
+
+ align:start position:0%
+the alphas of the positive support
+ 
+
+ align:start position:0%
+the alphas of the positive support
+vectors are equal to the alphas of the
+
+ align:start position:0%
+vectors are equal to the alphas of the
+ 
+
+ align:start position:0%
+vectors are equal to the alphas of the
+negative support vectors additionally
+
+ align:start position:0%
+negative support vectors additionally
+ 
+
+ align:start position:0%
+negative support vectors additionally
+our buddy the W vector is equal to the
+
+ align:start position:0%
+our buddy the W vector is equal to the
+ 
+
+ align:start position:0%
+our buddy the W vector is equal to the
+sum over the all I that R plus vectors
+
+ align:start position:0%
+sum over the all I that R plus vectors
+ 
+
+ align:start position:0%
+sum over the all I that R plus vectors
+of WI alpha I minus M over J minus
+
+ align:start position:0%
+of WI alpha I minus M over J minus
+ 
+
+ align:start position:0%
+of WI alpha I minus M over J minus
+vectors of W J alpha J now all these
+
+ align:start position:0%
+vectors of W J alpha J now all these
+ 
+
+ align:start position:0%
+vectors of W J alpha J now all these
+equations can be used in a bloody mess
+
+ align:start position:0%
+equations can be used in a bloody mess
+ 
+
+ align:start position:0%
+equations can be used in a bloody mess
+to figure out the answer to what we're
+
+ align:start position:0%
+to figure out the answer to what we're
+ 
+
+ align:start position:0%
+to figure out the answer to what we're
+trying to find which is circle as well
+
+ align:start position:0%
+trying to find which is circle as well
+ 
+
+ align:start position:0%
+trying to find which is circle as well
+actually they can't be used to circle of
+
+ align:start position:0%
+actually they can't be used to circle of
+ 
+
+ align:start position:0%
+actually they can't be used to circle of
+support vectors and draw the draw the
+
+ align:start position:0%
+support vectors and draw the draw the
+ 
+
+ align:start position:0%
+support vectors and draw the draw the
+dotted line but once we do that all
+
+ align:start position:0%
+dotted line but once we do that all
+ 
+
+ align:start position:0%
+dotted line but once we do that all
+these equations can be used in a bloody
+
+ align:start position:0%
+these equations can be used in a bloody
+ 
+
+ align:start position:0%
+these equations can be used in a bloody
+mess to give us the but the next thing
+
+ align:start position:0%
+mess to give us the but the next thing
+ 
+
+ align:start position:0%
+mess to give us the but the next thing
+that we want which is W and B so
+
+ align:start position:0%
+that we want which is W and B so
+ 
+
+ align:start position:0%
+that we want which is W and B so
+fortunately there's another way to get W
+
+ align:start position:0%
+fortunately there's another way to get W
+ 
+
+ align:start position:0%
+fortunately there's another way to get W
+and B if you guys really want at the at
+
+ align:start position:0%
+and B if you guys really want at the at
+ 
+
+ align:start position:0%
+and B if you guys really want at the at
+the end of the hour we can also try to
+
+ align:start position:0%
+the end of the hour we can also try to
+ 
+
+ align:start position:0%
+the end of the hour we can also try to
+get try to drive W and B using the many
+
+ align:start position:0%
+get try to drive W and B using the many
+ 
+
+ align:start position:0%
+get try to drive W and B using the many
+equations and many unknowns but it's a
+
+ align:start position:0%
+equations and many unknowns but it's a
+ 
+
+ align:start position:0%
+equations and many unknowns but it's a
+bit painful we'll try to do it the cool
+
+ align:start position:0%
+bit painful we'll try to do it the cool
+ 
+
+ align:start position:0%
+bit painful we'll try to do it the cool
+way so let's start
+
+ align:start position:0%
+way so let's start
+ 
+
+ align:start position:0%
+way so let's start
+this is the one we're looking at we need
+
+ align:start position:0%
+this is the one we're looking at we need
+ 
+
+ align:start position:0%
+this is the one we're looking at we need
+to find what the support vectors are so
+
+ align:start position:0%
+to find what the support vectors are so
+ 
+
+ align:start position:0%
+to find what the support vectors are so
+first thing we need to do is simply I it
+
+ align:start position:0%
+first thing we need to do is simply I it
+ 
+
+ align:start position:0%
+first thing we need to do is simply I it
+fortunately on the test there will
+
+ align:start position:0%
+fortunately on the test there will
+ 
+
+ align:start position:0%
+fortunately on the test there will
+always be ones that you can I if you're
+
+ align:start position:0%
+always be ones that you can I if you're
+ 
+
+ align:start position:0%
+always be ones that you can I if you're
+supposed to circle the support vectors
+
+ align:start position:0%
+supposed to circle the support vectors
+ 
+
+ align:start position:0%
+supposed to circle the support vectors
+there's obviously some number of pluses
+
+ align:start position:0%
+there's obviously some number of pluses
+ 
+
+ align:start position:0%
+there's obviously some number of pluses
+and some number of minuses I say
+
+ align:start position:0%
+and some number of minuses I say
+ 
+
+ align:start position:0%
+and some number of minuses I say
+obviously but maybe not but hopefully
+
+ align:start position:0%
+obviously but maybe not but hopefully
+ 
+
+ align:start position:0%
+obviously but maybe not but hopefully
+obviously and we'll find out because I'm
+
+ align:start position:0%
+obviously and we'll find out because I'm
+ 
+
+ align:start position:0%
+obviously and we'll find out because I'm
+going to call them random people so give
+
+ align:start position:0%
+going to call them random people so give
+ 
+
+ align:start position:0%
+going to call them random people so give
+me a positive support vector yeah
+
+ align:start position:0%
+me a positive support vector yeah
+ 
+
+ align:start position:0%
+me a positive support vector yeah
+perfect that's good all right that's
+
+ align:start position:0%
+perfect that's good all right that's
+ 
+
+ align:start position:0%
+perfect that's good all right that's
+what ah not give me a native support Oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+No ah that is a good question
+
+ align:start position:0%
+No ah that is a good question
+ 
+
+ align:start position:0%
+No ah that is a good question
+question is what is a support vector how
+
+ align:start position:0%
+question is what is a support vector how
+ 
+
+ align:start position:0%
+question is what is a support vector how
+many other people are will meant to
+
+ align:start position:0%
+many other people are will meant to
+ 
+
+ align:start position:0%
+many other people are will meant to
+having this question see you're not
+
+ align:start position:0%
+having this question see you're not
+ 
+
+ align:start position:0%
+having this question see you're not
+alone okay before I go on I'm going to
+
+ align:start position:0%
+alone okay before I go on I'm going to
+ 
+
+ align:start position:0%
+alone okay before I go on I'm going to
+assume guys make sure I'm correct money
+
+ align:start position:0%
+assume guys make sure I'm correct money
+ 
+
+ align:start position:0%
+assume guys make sure I'm correct money
+was uh just being served so I can tailor
+
+ align:start position:0%
+was uh just being served so I can tailor
+ 
+
+ align:start position:0%
+was uh just being served so I can tailor
+based on this Monday was the support
+
+ align:start position:0%
+based on this Monday was the support
+ 
+
+ align:start position:0%
+based on this Monday was the support
+vector machine lecture but it was also
+
+ align:start position:0%
+vector machine lecture but it was also
+ 
+
+ align:start position:0%
+vector machine lecture but it was also
+very difficult to follow that's what I
+
+ align:start position:0%
+very difficult to follow that's what I
+ 
+
+ align:start position:0%
+very difficult to follow that's what I
+that's what I usually expect so um what
+
+ align:start position:0%
+that's what I usually expect so um what
+ 
+
+ align:start position:0%
+that's what I usually expect so um what
+is a support vector well all these
+
+ align:start position:0%
+is a support vector well all these
+ 
+
+ align:start position:0%
+is a support vector well all these
+pluses and minuses if we were if we were
+
+ align:start position:0%
+pluses and minuses if we were if we were
+ 
+
+ align:start position:0%
+pluses and minuses if we were if we were
+me and we if I guess yeah if we were me
+
+ align:start position:0%
+me and we if I guess yeah if we were me
+ 
+
+ align:start position:0%
+me and we if I guess yeah if we were me
+and I was describing this problem the
+
+ align:start position:0%
+and I was describing this problem the
+ 
+
+ align:start position:0%
+and I was describing this problem the
+one that we work out in class I would
+
+ align:start position:0%
+one that we work out in class I would
+ 
+
+ align:start position:0%
+one that we work out in class I would
+call them points because they're on the
+
+ align:start position:0%
+call them points because they're on the
+ 
+
+ align:start position:0%
+call them points because they're on the
+graph their points their data points I
+
+ align:start position:0%
+graph their points their data points I
+ 
+
+ align:start position:0%
+graph their points their data points I
+would cut but however in more difficult
+
+ align:start position:0%
+would cut but however in more difficult
+ 
+
+ align:start position:0%
+would cut but however in more difficult
+versions of this problem that have n
+
+ align:start position:0%
+versions of this problem that have n
+ 
+
+ align:start position:0%
+versions of this problem that have n
+dimensions where n is some ridiculous
+
+ align:start position:0%
+dimensions where n is some ridiculous
+ 
+
+ align:start position:0%
+dimensions where n is some ridiculous
+number of dimension
+
+ align:start position:0%
+number of dimension
+ 
+
+ align:start position:0%
+number of dimension
+that you're never going to graph like
+
+ align:start position:0%
+that you're never going to graph like
+ 
+
+ align:start position:0%
+that you're never going to graph like
+say you know some of the research I'm
+
+ align:start position:0%
+say you know some of the research I'm
+ 
+
+ align:start position:0%
+say you know some of the research I'm
+doing now I could use support vector
+
+ align:start position:0%
+doing now I could use support vector
+ 
+
+ align:start position:0%
+doing now I could use support vector
+machines on some of these articles that
+
+ align:start position:0%
+machines on some of these articles that
+ 
+
+ align:start position:0%
+machines on some of these articles that
+I'm reading about cyber events to try to
+
+ align:start position:0%
+I'm reading about cyber events to try to
+ 
+
+ align:start position:0%
+I'm reading about cyber events to try to
+figure out if there's a real event or if
+
+ align:start position:0%
+figure out if there's a real event or if
+ 
+
+ align:start position:0%
+figure out if there's a real event or if
+it's just someone complaining about how
+
+ align:start position:0%
+it's just someone complaining about how
+ 
+
+ align:start position:0%
+it's just someone complaining about how
+we're really vulnerable or something
+
+ align:start position:0%
+we're really vulnerable or something
+ 
+
+ align:start position:0%
+we're really vulnerable or something
+like that and no event actually happened
+
+ align:start position:0%
+like that and no event actually happened
+ 
+
+ align:start position:0%
+like that and no event actually happened
+so the reason why they call these guys
+
+ align:start position:0%
+so the reason why they call these guys
+ 
+
+ align:start position:0%
+so the reason why they call these guys
+vectors is when you're not able to graph
+
+ align:start position:0%
+vectors is when you're not able to graph
+ 
+
+ align:start position:0%
+vectors is when you're not able to graph
+them on a Cartesian plane there's still
+
+ align:start position:0%
+them on a Cartesian plane there's still
+ 
+
+ align:start position:0%
+them on a Cartesian plane there's still
+this long you know vector of many
+
+ align:start position:0%
+this long you know vector of many
+ 
+
+ align:start position:0%
+this long you know vector of many
+different dimensions right now though
+
+ align:start position:0%
+different dimensions right now though
+ 
+
+ align:start position:0%
+different dimensions right now though
+these points represent the vectors it's
+
+ align:start position:0%
+these points represent the vectors it's
+ 
+
+ align:start position:0%
+these points represent the vectors it's
+very simple it's easier to view them
+
+ align:start position:0%
+very simple it's easier to view them
+ 
+
+ align:start position:0%
+very simple it's easier to view them
+this way but for instance that plus at
+
+ align:start position:0%
+this way but for instance that plus at
+ 
+
+ align:start position:0%
+this way but for instance that plus at
+negative 1/2 represents the fact that
+
+ align:start position:0%
+negative 1/2 represents the fact that
+ 
+
+ align:start position:0%
+negative 1/2 represents the fact that
+there's a vector going in the direction
+
+ align:start position:0%
+there's a vector going in the direction
+ 
+
+ align:start position:0%
+there's a vector going in the direction
+of negative 1/2 with the magnitudes such
+
+ align:start position:0%
+of negative 1/2 with the magnitudes such
+ 
+
+ align:start position:0%
+of negative 1/2 with the magnitudes such
+that it reaches negative 1/2 so all
+
+ align:start position:0%
+that it reaches negative 1/2 so all
+ 
+
+ align:start position:0%
+that it reaches negative 1/2 so all
+these points are just a point
+
+ align:start position:0%
+these points are just a point
+ 
+
+ align:start position:0%
+these points are just a point
+representation in vector you probably in
+
+ align:start position:0%
+representation in vector you probably in
+ 
+
+ align:start position:0%
+representation in vector you probably in
+any class that worked with vectors saw
+
+ align:start position:0%
+any class that worked with vectors saw
+ 
+
+ align:start position:0%
+any class that worked with vectors saw
+this saw vectors being represented as
+
+ align:start position:0%
+this saw vectors being represented as
+ 
+
+ align:start position:0%
+this saw vectors being represented as
+points question hi the question is all
+
+ align:start position:0%
+points question hi the question is all
+ 
+
+ align:start position:0%
+points question hi the question is all
+respect to the origin answers
+
+ align:start position:0%
+respect to the origin answers
+ 
+
+ align:start position:0%
+respect to the origin answers
+economically when directions are
+
+ align:start position:0%
+economically when directions are
+ 
+
+ align:start position:0%
+economically when directions are
+represented at points yes it's always
+
+ align:start position:0%
+represented at points yes it's always
+ 
+
+ align:start position:0%
+represented at points yes it's always
+good respect to the origin so that's the
+
+ align:start position:0%
+good respect to the origin so that's the
+ 
+
+ align:start position:0%
+good respect to the origin so that's the
+basic idea is that all these points are
+
+ align:start position:0%
+basic idea is that all these points are
+ 
+
+ align:start position:0%
+basic idea is that all these points are
+vectors so what are support vectors well
+
+ align:start position:0%
+vectors so what are support vectors well
+ 
+
+ align:start position:0%
+vectors so what are support vectors well
+we could call them support points for
+
+ align:start position:0%
+we could call them support points for
+ 
+
+ align:start position:0%
+we could call them support points for
+this case but the reason we call the
+
+ align:start position:0%
+this case but the reason we call the
+ 
+
+ align:start position:0%
+this case but the reason we call the
+support vectors is again in the
+
+ align:start position:0%
+support vectors is again in the
+ 
+
+ align:start position:0%
+support vectors is again in the
+generalized case that you might be doing
+
+ align:start position:0%
+generalized case that you might be doing
+ 
+
+ align:start position:0%
+generalized case that you might be doing
+in the real world with real AI you're
+
+ align:start position:0%
+in the real world with real AI you're
+ 
+
+ align:start position:0%
+in the real world with real AI you're
+going to have the giant vector it's not
+
+ align:start position:0%
+going to have the giant vector it's not
+ 
+
+ align:start position:0%
+going to have the giant vector it's not
+just going to be points on a graph well
+
+ align:start position:0%
+just going to be points on a graph well
+ 
+
+ align:start position:0%
+just going to be points on a graph well
+usually so the support vectors the
+
+ align:start position:0%
+usually so the support vectors the
+ 
+
+ align:start position:0%
+usually so the support vectors the
+support points we found one of them
+
+ align:start position:0%
+support points we found one of them
+ 
+
+ align:start position:0%
+support points we found one of them
+correctly
+
+ align:start position:0%
+correctly
+ 
+
+ align:start position:0%
+correctly
+it's this guy they're going to be the
+
+ align:start position:0%
+it's this guy they're going to be the
+ 
+
+ align:start position:0%
+it's this guy they're going to be the
+ones that again they don't have an alpha
+
+ align:start position:0%
+ones that again they don't have an alpha
+ 
+
+ align:start position:0%
+ones that again they don't have an alpha
+of 0 they're the ones that bind in the
+
+ align:start position:0%
+of 0 they're the ones that bind in the
+ 
+
+ align:start position:0%
+of 0 they're the ones that bind in the
+as petracles of the road the boundary
+
+ align:start position:0%
+as petracles of the road the boundary
+ 
+
+ align:start position:0%
+as petracles of the road the boundary
+lines they're going to be on the edge of
+
+ align:start position:0%
+lines they're going to be on the edge of
+ 
+
+ align:start position:0%
+lines they're going to be on the edge of
+plus whichever direction we draw it this
+
+ align:start position:0%
+plus whichever direction we draw it this
+ 
+
+ align:start position:0%
+plus whichever direction we draw it this
+plus is the edge of the plus region if
+
+ align:start position:0%
+plus is the edge of the plus region if
+ 
+
+ align:start position:0%
+plus is the edge of the plus region if
+we made this the edge of the plus region
+
+ align:start position:0%
+we made this the edge of the plus region
+ 
+
+ align:start position:0%
+we made this the edge of the plus region
+and everything on this side is plus
+
+ align:start position:0%
+and everything on this side is plus
+ 
+
+ align:start position:0%
+and everything on this side is plus
+everything on this size - we'd be
+
+ align:start position:0%
+everything on this size - we'd be
+ 
+
+ align:start position:0%
+everything on this size - we'd be
+screwed because there's two pluses on
+
+ align:start position:0%
+screwed because there's two pluses on
+ 
+
+ align:start position:0%
+screwed because there's two pluses on
+the on the other side of that generally
+
+ align:start position:0%
+the on the other side of that generally
+ 
+
+ align:start position:0%
+the on the other side of that generally
+when trying to find
+
+ align:start position:0%
+when trying to find
+ 
+
+ align:start position:0%
+when trying to find
+support vectors you do something a
+
+ align:start position:0%
+support vectors you do something a
+ 
+
+ align:start position:0%
+support vectors you do something a
+little bit similar to my crazy method of
+
+ align:start position:0%
+little bit similar to my crazy method of
+ 
+
+ align:start position:0%
+little bit similar to my crazy method of
+doing nearest neighbors and try to find
+
+ align:start position:0%
+doing nearest neighbors and try to find
+ 
+
+ align:start position:0%
+doing nearest neighbors and try to find
+a plus my excuse me a plus minus pair
+
+ align:start position:0%
+a plus my excuse me a plus minus pair
+ 
+
+ align:start position:0%
+a plus my excuse me a plus minus pair
+that's close to each other sometimes
+
+ align:start position:0%
+that's close to each other sometimes
+ 
+
+ align:start position:0%
+that's close to each other sometimes
+though it's not just two points because
+
+ align:start position:0%
+though it's not just two points because
+ 
+
+ align:start position:0%
+though it's not just two points because
+sometimes if you try to draw the
+
+ align:start position:0%
+sometimes if you try to draw the
+ 
+
+ align:start position:0%
+sometimes if you try to draw the
+simple-minded thing which is sort of the
+
+ align:start position:0%
+simple-minded thing which is sort of the
+ 
+
+ align:start position:0%
+simple-minded thing which is sort of the
+perpendicular bisector of the two points
+
+ align:start position:0%
+perpendicular bisector of the two points
+ 
+
+ align:start position:0%
+perpendicular bisector of the two points
+you get screwed because there's another
+
+ align:start position:0%
+you get screwed because there's another
+ 
+
+ align:start position:0%
+you get screwed because there's another
+point in your way so now that I've given
+
+ align:start position:0%
+point in your way so now that I've given
+ 
+
+ align:start position:0%
+point in your way so now that I've given
+away a clue let's go
+
+ align:start position:0%
+away a clue let's go
+ 
+
+ align:start position:0%
+away a clue let's go
+and hopefully that made sense to you
+
+ align:start position:0%
+and hopefully that made sense to you
+ 
+
+ align:start position:0%
+and hopefully that made sense to you
+guys the support vectors are the ones on
+
+ align:start position:0%
+guys the support vectors are the ones on
+ 
+
+ align:start position:0%
+guys the support vectors are the ones on
+the edges they're just barely a plus for
+
+ align:start position:0%
+the edges they're just barely a plus for
+ 
+
+ align:start position:0%
+the edges they're just barely a plus for
+sure but barely - for sure let's go back
+
+ align:start position:0%
+sure but barely - for sure let's go back
+ 
+
+ align:start position:0%
+sure but barely - for sure let's go back
+can you give me a negative support
+
+ align:start position:0%
+can you give me a negative support
+ 
+
+ align:start position:0%
+can you give me a negative support
+vector the one on Paulo yeah and does
+
+ align:start position:0%
+vector the one on Paulo yeah and does
+ 
+
+ align:start position:0%
+vector the one on Paulo yeah and does
+anyone think that there's a third
+
+ align:start position:0%
+anyone think that there's a third
+ 
+
+ align:start position:0%
+anyone think that there's a third
+support vector well let's simple-minded
+
+ align:start position:0%
+support vector well let's simple-minded
+ 
+
+ align:start position:0%
+support vector well let's simple-minded
+Lee try the thing that remember support
+
+ align:start position:0%
+Lee try the thing that remember support
+ 
+
+ align:start position:0%
+Lee try the thing that remember support
+vectors always attempt to have the
+
+ align:start position:0%
+vectors always attempt to have the
+ 
+
+ align:start position:0%
+vectors always attempt to have the
+widest possible space between the pluses
+
+ align:start position:0%
+widest possible space between the pluses
+ 
+
+ align:start position:0%
+widest possible space between the pluses
+and the minuses that they can so let's
+
+ align:start position:0%
+and the minuses that they can so let's
+ 
+
+ align:start position:0%
+and the minuses that they can so let's
+simple-minded Lee try to do the
+
+ align:start position:0%
+simple-minded Lee try to do the
+ 
+
+ align:start position:0%
+simple-minded Lee try to do the
+perpendicular bisector and see if it see
+
+ align:start position:0%
+perpendicular bisector and see if it see
+ 
+
+ align:start position:0%
+perpendicular bisector and see if it see
+if it screws us over so when we
+
+ align:start position:0%
+if it screws us over so when we
+ 
+
+ align:start position:0%
+if it screws us over so when we
+simple-minded Lee do the perpendicular
+
+ align:start position:0%
+simple-minded Lee do the perpendicular
+ 
+
+ align:start position:0%
+simple-minded Lee do the perpendicular
+bisector it goes through like here like
+
+ align:start position:0%
+bisector it goes through like here like
+ 
+
+ align:start position:0%
+bisector it goes through like here like
+this and it's just fine so these are the
+
+ align:start position:0%
+this and it's just fine so these are the
+ 
+
+ align:start position:0%
+this and it's just fine so these are the
+only two support vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's our divider line so we're on
+
+ align:start position:0%
+and there's our divider line so we're on
+ 
+
+ align:start position:0%
+and there's our divider line so we're on
+the homestretch but we have to find W
+
+ align:start position:0%
+the homestretch but we have to find W
+ 
+
+ align:start position:0%
+the homestretch but we have to find W
+and B in olden days we would find W and
+
+ align:start position:0%
+and B in olden days we would find W and
+ 
+
+ align:start position:0%
+and B in olden days we would find W and
+B by plugging in W dot the plus support
+
+ align:start position:0%
+B by plugging in W dot the plus support
+ 
+
+ align:start position:0%
+B by plugging in W dot the plus support
+vector plus B equals one that's very
+
+ align:start position:0%
+vector plus B equals one that's very
+ 
+
+ align:start position:0%
+vector plus B equals one that's very
+crucial these W dot X plus X minus our
+
+ align:start position:0%
+crucial these W dot X plus X minus our
+ 
+
+ align:start position:0%
+crucial these W dot X plus X minus our
+only true equaling one or negative one
+
+ align:start position:0%
+only true equaling one or negative one
+ 
+
+ align:start position:0%
+only true equaling one or negative one
+are only true for support vectors it's
+
+ align:start position:0%
+are only true for support vectors it's
+ 
+
+ align:start position:0%
+are only true for support vectors it's
+always true that W dot any positive
+
+ align:start position:0%
+always true that W dot any positive
+ 
+
+ align:start position:0%
+always true that W dot any positive
+point plus B will be some positive
+
+ align:start position:0%
+point plus B will be some positive
+ 
+
+ align:start position:0%
+point plus B will be some positive
+number but it won't always be supportive
+
+ align:start position:0%
+number but it won't always be supportive
+ 
+
+ align:start position:0%
+number but it won't always be supportive
+it don't won't always be one in fact it
+
+ align:start position:0%
+it don't won't always be one in fact it
+ 
+
+ align:start position:0%
+it don't won't always be one in fact it
+will always be the greater than one up
+
+ align:start position:0%
+will always be the greater than one up
+ 
+
+ align:start position:0%
+will always be the greater than one up
+over here it will always be less than
+
+ align:start position:0%
+over here it will always be less than
+ 
+
+ align:start position:0%
+over here it will always be less than
+negative one down over there
+
+ align:start position:0%
+negative one down over there
+ 
+
+ align:start position:0%
+negative one down over there
+so in olden days we would plug in
+
+ align:start position:0%
+so in olden days we would plug in
+ 
+
+ align:start position:0%
+so in olden days we would plug in
+negative 1/2 into this equation we plug
+
+ align:start position:0%
+negative 1/2 into this equation we plug
+ 
+
+ align:start position:0%
+negative 1/2 into this equation we plug
+in 3 negative 2 into this equation we
+
+ align:start position:0%
+in 3 negative 2 into this equation we
+ 
+
+ align:start position:0%
+in 3 negative 2 into this equation we
+plug in alpha plus equals alpha minus
+
+ align:start position:0%
+plug in alpha plus equals alpha minus
+ 
+
+ align:start position:0%
+plug in alpha plus equals alpha minus
+it's the sums and since there's only one
+
+ align:start position:0%
+it's the sums and since there's only one
+ 
+
+ align:start position:0%
+it's the sums and since there's only one
+plus or minus we know that they were
+
+ align:start position:0%
+plus or minus we know that they were
+ 
+
+ align:start position:0%
+plus or minus we know that they were
+equal and then we fidget around with
+
+ align:start position:0%
+equal and then we fidget around with
+ 
+
+ align:start position:0%
+equal and then we fidget around with
+this W equation however there is a
+
+ align:start position:0%
+this W equation however there is a
+ 
+
+ align:start position:0%
+this W equation however there is a
+better way to do it and so let's use
+
+ align:start position:0%
+better way to do it and so let's use
+ 
+
+ align:start position:0%
+better way to do it and so let's use
+this cheap strategy to solve to solve
+
+ align:start position:0%
+this cheap strategy to solve to solve
+ 
+
+ align:start position:0%
+this cheap strategy to solve to solve
+this version of the SVM here's how first
+
+ align:start position:0%
+this version of the SVM here's how first
+ 
+
+ align:start position:0%
+this version of the SVM here's how first
+and I know I didn't draw these
+
+ align:start position:0%
+and I know I didn't draw these
+ 
+
+ align:start position:0%
+and I know I didn't draw these
+completely straight sorry but can anyone
+
+ align:start position:0%
+completely straight sorry but can anyone
+ 
+
+ align:start position:0%
+completely straight sorry but can anyone
+by looking at the fact that this is 3
+
+ align:start position:0%
+by looking at the fact that this is 3
+ 
+
+ align:start position:0%
+by looking at the fact that this is 3
+negative 2 and this is negative 1/2 can
+
+ align:start position:0%
+negative 2 and this is negative 1/2 can
+ 
+
+ align:start position:0%
+negative 2 and this is negative 1/2 can
+anyone tell me what the equation uh if
+
+ align:start position:0%
+anyone tell me what the equation uh if
+ 
+
+ align:start position:0%
+anyone tell me what the equation uh if
+you can do y equals MX plus B can anyone
+
+ align:start position:0%
+you can do y equals MX plus B can anyone
+ 
+
+ align:start position:0%
+you can do y equals MX plus B can anyone
+tell me what the equation of that dotted
+
+ align:start position:0%
+tell me what the equation of that dotted
+ 
+
+ align:start position:0%
+tell me what the equation of that dotted
+line is supposed to be if I was a good
+
+ align:start position:0%
+line is supposed to be if I was a good
+ 
+
+ align:start position:0%
+line is supposed to be if I was a good
+at drawing you said Y minus 1 and I say
+
+ align:start position:0%
+at drawing you said Y minus 1 and I say
+ 
+
+ align:start position:0%
+at drawing you said Y minus 1 and I say
+yes why I'm just - why so therefore the
+
+ align:start position:0%
+yes why I'm just - why so therefore the
+ 
+
+ align:start position:0%
+yes why I'm just - why so therefore the
+pluses would be y is greater than or
+
+ align:start position:0%
+pluses would be y is greater than or
+ 
+
+ align:start position:0%
+pluses would be y is greater than or
+equal to X minus X minus 1
+
+ align:start position:0%
+equal to X minus X minus 1
+ 
+
+ align:start position:0%
+equal to X minus X minus 1
+indeed so we've already seen that WX
+
+ align:start position:0%
+indeed so we've already seen that WX
+ 
+
+ align:start position:0%
+indeed so we've already seen that WX
+plus B like somehow can be converted
+
+ align:start position:0%
+plus B like somehow can be converted
+ 
+
+ align:start position:0%
+plus B like somehow can be converted
+into this form right so therefore if we
+
+ align:start position:0%
+into this form right so therefore if we
+ 
+
+ align:start position:0%
+into this form right so therefore if we
+have y equals X minus 1 then we know
+
+ align:start position:0%
+have y equals X minus 1 then we know
+ 
+
+ align:start position:0%
+have y equals X minus 1 then we know
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+we have in w1 that we know that we have
+
+ align:start position:0%
+we have in w1 that we know that we have
+ 
+
+ align:start position:0%
+we have in w1 that we know that we have
+W X plus B equals zero let's do that
+
+ align:start position:0%
+W X plus B equals zero let's do that
+ 
+
+ align:start position:0%
+W X plus B equals zero let's do that
+here so we know that W 1 W 1 X 1 being
+
+ align:start position:0%
+here so we know that W 1 W 1 X 1 being
+ 
+
+ align:start position:0%
+here so we know that W 1 W 1 X 1 being
+even call it X and why I think it'll be
+
+ align:start position:0%
+even call it X and why I think it'll be
+ 
+
+ align:start position:0%
+even call it X and why I think it'll be
+fine no one will come after us
+
+ align:start position:0%
+fine no one will come after us
+ 
+
+ align:start position:0%
+fine no one will come after us
+w 2 y plus B equals 0 but we also know
+
+ align:start position:0%
+w 2 y plus B equals 0 but we also know
+ 
+
+ align:start position:0%
+w 2 y plus B equals 0 but we also know
+that y equals x minus 1 which means that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if y equals X minus 1 then that means
+
+ align:start position:0%
+if y equals X minus 1 then that means
+ 
+
+ align:start position:0%
+if y equals X minus 1 then that means
+that according to this thing that we
+
+ align:start position:0%
+that according to this thing that we
+ 
+
+ align:start position:0%
+that according to this thing that we
+have over here then negative w1 over w2
+
+ align:start position:0%
+have over here then negative w1 over w2
+ 
+
+ align:start position:0%
+have over here then negative w1 over w2
+equals so we know that negative w1 over
+
+ align:start position:0%
+equals so we know that negative w1 over
+ 
+
+ align:start position:0%
+equals so we know that negative w1 over
+w2 and we have negative negative B over
+
+ align:start position:0%
+w2 and we have negative negative B over
+ 
+
+ align:start position:0%
+w2 and we have negative negative B over
+w2 so y equals x minus 1 and if we solve
+
+ align:start position:0%
+w2 so y equals x minus 1 and if we solve
+ 
+
+ align:start position:0%
+w2 so y equals x minus 1 and if we solve
+this equation to make it look like this
+
+ align:start position:0%
+this equation to make it look like this
+ 
+
+ align:start position:0%
+this equation to make it look like this
+we would have y equals negative w1 over
+
+ align:start position:0%
+we would have y equals negative w1 over
+ 
+
+ align:start position:0%
+we would have y equals negative w1 over
+w2 minus B over w2 so we know that in
+
+ align:start position:0%
+w2 minus B over w2 so we know that in
+ 
+
+ align:start position:0%
+w2 minus B over w2 so we know that in
+some way shape or form that we know that
+
+ align:start position:0%
+some way shape or form that we know that
+ 
+
+ align:start position:0%
+some way shape or form that we know that
+Nick did then therefore w1 over w2 is
+
+ align:start position:0%
+Nick did then therefore w1 over w2 is
+ 
+
+ align:start position:0%
+Nick did then therefore w1 over w2 is
+some scalar multiple of minus 1 and we
+
+ align:start position:0%
+some scalar multiple of minus 1 and we
+ 
+
+ align:start position:0%
+some scalar multiple of minus 1 and we
+know that B over w2 is in fact some
+
+ align:start position:0%
+know that B over w2 is in fact some
+ 
+
+ align:start position:0%
+know that B over w2 is in fact some
+scalar multiple of positive one scalar
+
+ align:start position:0%
+scalar multiple of positive one scalar
+ 
+
+ align:start position:0%
+scalar multiple of positive one scalar
+multiple scalar multiple well why is it
+
+ align:start position:0%
+multiple scalar multiple well why is it
+ 
+
+ align:start position:0%
+multiple scalar multiple well why is it
+a scalar multiple why is it it just
+
+ align:start position:0%
+a scalar multiple why is it it just
+ 
+
+ align:start position:0%
+a scalar multiple why is it it just
+going to be negative 1 or positive 1
+
+ align:start position:0%
+going to be negative 1 or positive 1
+ 
+
+ align:start position:0%
+going to be negative 1 or positive 1
+because just because in this equation we
+
+ align:start position:0%
+because just because in this equation we
+ 
+
+ align:start position:0%
+because just because in this equation we
+can multiply the entire equation by any
+
+ align:start position:0%
+can multiply the entire equation by any
+ 
+
+ align:start position:0%
+can multiply the entire equation by any
+number and it will still have the same
+
+ align:start position:0%
+number and it will still have the same
+ 
+
+ align:start position:0%
+number and it will still have the same
+boundary line you guys see that if you
+
+ align:start position:0%
+boundary line you guys see that if you
+ 
+
+ align:start position:0%
+boundary line you guys see that if you
+know if X here if we multiplied
+
+ align:start position:0%
+know if X here if we multiplied
+ 
+
+ align:start position:0%
+know if X here if we multiplied
+everything since it's all divided by
+
+ align:start position:0%
+everything since it's all divided by
+ 
+
+ align:start position:0%
+everything since it's all divided by
+- if we double w - but also w BB and w1
+
+ align:start position:0%
+- if we double w - but also w BB and w1
+ 
+
+ align:start position:0%
+- if we double w - but also w BB and w1
+it would be the exact same question do
+
+ align:start position:0%
+it would be the exact same question do
+ 
+
+ align:start position:0%
+it would be the exact same question do
+you guys agree so there's in fact the
+
+ align:start position:0%
+you guys agree so there's in fact the
+ 
+
+ align:start position:0%
+you guys agree so there's in fact the
+infinitely many possible equations you
+
+ align:start position:0%
+infinitely many possible equations you
+ 
+
+ align:start position:0%
+infinitely many possible equations you
+say well great mark you figured out what
+
+ align:start position:0%
+say well great mark you figured out what
+ 
+
+ align:start position:0%
+say well great mark you figured out what
+form it is so you figured out that w1
+
+ align:start position:0%
+form it is so you figured out that w1
+ 
+
+ align:start position:0%
+form it is so you figured out that w1
+over w2 equals on some scalar multiple
+
+ align:start position:0%
+over w2 equals on some scalar multiple
+ 
+
+ align:start position:0%
+over w2 equals on some scalar multiple
+of negative one so it's negative one
+
+ align:start position:0%
+of negative one so it's negative one
+ 
+
+ align:start position:0%
+of negative one so it's negative one
+times what's everyone's favorite letter
+
+ align:start position:0%
+times what's everyone's favorite letter
+ 
+
+ align:start position:0%
+times what's everyone's favorite letter
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+negative 1 times K and we figured out
+
+ align:start position:0%
+negative 1 times K and we figured out
+ 
+
+ align:start position:0%
+negative 1 times K and we figured out
+that B over w2 is I guess we can just do
+
+ align:start position:0%
+that B over w2 is I guess we can just do
+ 
+
+ align:start position:0%
+that B over w2 is I guess we can just do
+negative K is positive K but what's K
+
+ align:start position:0%
+negative K is positive K but what's K
+ 
+
+ align:start position:0%
+negative K is positive K but what's K
+how are we going to figure it out well
+
+ align:start position:0%
+how are we going to figure it out well
+ 
+
+ align:start position:0%
+how are we going to figure it out well
+it's a good question I will tell you how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll assert the following fact as true
+
+ align:start position:0%
+I'll assert the following fact as true
+ 
+
+ align:start position:0%
+I'll assert the following fact as true
+without proof then I will not prove it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 over the magnitude of W which is this
+
+ align:start position:0%
+1 over the magnitude of W which is this
+ 
+
+ align:start position:0%
+1 over the magnitude of W which is this
+vector here duck with w1 w2 equals this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where this is that line that I just drew
+
+ align:start position:0%
+where this is that line that I just drew
+ 
+
+ align:start position:0%
+where this is that line that I just drew
+the line from here to this point 1 over
+
+ align:start position:0%
+the line from here to this point 1 over
+ 
+
+ align:start position:0%
+the line from here to this point 1 over
+the magnitude of W equals this therefore
+
+ align:start position:0%
+the magnitude of W equals this therefore
+ 
+
+ align:start position:0%
+the magnitude of W equals this therefore
+since 1 over the magnitude of W equals
+
+ align:start position:0%
+since 1 over the magnitude of W equals
+ 
+
+ align:start position:0%
+since 1 over the magnitude of W equals
+this and this equals I believe 2 root 2
+
+ align:start position:0%
+this and this equals I believe 2 root 2
+ 
+
+ align:start position:0%
+this and this equals I believe 2 root 2
+because we're going over to down to
+
+ align:start position:0%
+because we're going over to down to
+ 
+
+ align:start position:0%
+because we're going over to down to
+Pythagorean theorem 2 or 2 so therefore
+
+ align:start position:0%
+Pythagorean theorem 2 or 2 so therefore
+ 
+
+ align:start position:0%
+Pythagorean theorem 2 or 2 so therefore
+flip everything over magnitude of W
+
+ align:start position:0%
+flip everything over magnitude of W
+ 
+
+ align:start position:0%
+flip everything over magnitude of W
+equals 1 over 2 root 2 so therefore
+
+ align:start position:0%
+equals 1 over 2 root 2 so therefore
+ 
+
+ align:start position:0%
+equals 1 over 2 root 2 so therefore
+magnitude of W equals root 2 over 4 but
+
+ align:start position:0%
+magnitude of W equals root 2 over 4 but
+ 
+
+ align:start position:0%
+magnitude of W equals root 2 over 4 but
+why are we okay well how do we calculate
+
+ align:start position:0%
+why are we okay well how do we calculate
+ 
+
+ align:start position:0%
+why are we okay well how do we calculate
+the magnitude of W do people know in
+
+ align:start position:0%
+the magnitude of W do people know in
+ 
+
+ align:start position:0%
+the magnitude of W do people know in
+general magnitudes of vectors generally
+
+ align:start position:0%
+general magnitudes of vectors generally
+ 
+
+ align:start position:0%
+general magnitudes of vectors generally
+for these vectors we do it by thing the
+
+ align:start position:0%
+for these vectors we do it by thing the
+ 
+
+ align:start position:0%
+for these vectors we do it by thing the
+square root
+
+ align:start position:0%
+square root
+ 
+
+ align:start position:0%
+square root
+of the sum of the components squared so
+
+ align:start position:0%
+of the sum of the components squared so
+ 
+
+ align:start position:0%
+of the sum of the components squared so
+the square root of W 1 squared plus W 2
+
+ align:start position:0%
+the square root of W 1 squared plus W 2
+ 
+
+ align:start position:0%
+the square root of W 1 squared plus W 2
+squared equals root 2 over 4 but that's
+
+ align:start position:0%
+squared equals root 2 over 4 but that's
+ 
+
+ align:start position:0%
+squared equals root 2 over 4 but that's
+not all that's not all we say because we
+
+ align:start position:0%
+not all that's not all we say because we
+ 
+
+ align:start position:0%
+not all that's not all we say because we
+know from this over here that the ratio
+
+ align:start position:0%
+know from this over here that the ratio
+ 
+
+ align:start position:0%
+know from this over here that the ratio
+of W 1 and W 2 is yeah the ratio of the
+
+ align:start position:0%
+of W 1 and W 2 is yeah the ratio of the
+ 
+
+ align:start position:0%
+of W 1 and W 2 is yeah the ratio of the
+ratio of W 1 and W 2 is going to be
+
+ align:start position:0%
+ratio of W 1 and W 2 is going to be
+ 
+
+ align:start position:0%
+ratio of W 1 and W 2 is going to be
+actually sorry I shouldn't put a K here
+
+ align:start position:0%
+actually sorry I shouldn't put a K here
+ 
+
+ align:start position:0%
+actually sorry I shouldn't put a K here
+I realize I probably should have been
+
+ align:start position:0%
+I realize I probably should have been
+ 
+
+ align:start position:0%
+I realize I probably should have been
+confusing you guys a lot w1 over w2 is
+
+ align:start position:0%
+confusing you guys a lot w1 over w2 is
+ 
+
+ align:start position:0%
+confusing you guys a lot w1 over w2 is
+just negative 1 B over w2 is just 1
+
+ align:start position:0%
+just negative 1 B over w2 is just 1
+ 
+
+ align:start position:0%
+just negative 1 B over w2 is just 1
+that's just the fact there's no K the K
+
+ align:start position:0%
+that's just the fact there's no K the K
+ 
+
+ align:start position:0%
+that's just the fact there's no K the K
+is to determine what W 1 and W 2 is w1
+
+ align:start position:0%
+is to determine what W 1 and W 2 is w1
+ 
+
+ align:start position:0%
+is to determine what W 1 and W 2 is w1
+and w2 are so W 1 equals like negative K
+
+ align:start position:0%
+and w2 are so W 1 equals like negative K
+ 
+
+ align:start position:0%
+and w2 are so W 1 equals like negative K
+and W 2 equals positive K and then B
+
+ align:start position:0%
+and W 2 equals positive K and then B
+ 
+
+ align:start position:0%
+and W 2 equals positive K and then B
+equals also positive pay by the way
+
+ align:start position:0%
+equals also positive pay by the way
+ 
+
+ align:start position:0%
+equals also positive pay by the way
+here's a question for you could I have
+
+ align:start position:0%
+here's a question for you could I have
+ 
+
+ align:start position:0%
+here's a question for you could I have
+put the K the negative sign on a
+
+ align:start position:0%
+put the K the negative sign on a
+ 
+
+ align:start position:0%
+put the K the negative sign on a
+different I'm going to put the negative
+
+ align:start position:0%
+different I'm going to put the negative
+ 
+
+ align:start position:0%
+different I'm going to put the negative
+sign on W 2 and B instead of on W 1 so
+
+ align:start position:0%
+sign on W 2 and B instead of on W 1 so
+ 
+
+ align:start position:0%
+sign on W 2 and B instead of on W 1 so
+maybe people said yes that's a very
+
+ align:start position:0%
+maybe people said yes that's a very
+ 
+
+ align:start position:0%
+maybe people said yes that's a very
+strange actually not because of the fact
+
+ align:start position:0%
+strange actually not because of the fact
+ 
+
+ align:start position:0%
+strange actually not because of the fact
+that the pluses are on the negative
+
+ align:start position:0%
+that the pluses are on the negative
+ 
+
+ align:start position:0%
+that the pluses are on the negative
+x-axis it's just a little trick I picked
+
+ align:start position:0%
+x-axis it's just a little trick I picked
+ 
+
+ align:start position:0%
+x-axis it's just a little trick I picked
+up when one of them is negative in the
+
+ align:start position:0%
+up when one of them is negative in the
+ 
+
+ align:start position:0%
+up when one of them is negative in the
+other one is it follow the pluses so we
+
+ align:start position:0%
+other one is it follow the pluses so we
+ 
+
+ align:start position:0%
+other one is it follow the pluses so we
+know that W 1 is negative K W 2 is
+
+ align:start position:0%
+know that W 1 is negative K W 2 is
+ 
+
+ align:start position:0%
+know that W 1 is negative K W 2 is
+positive K and B is positive K w1 over
+
+ align:start position:0%
+positive K and B is positive K w1 over
+ 
+
+ align:start position:0%
+positive K and B is positive K w1 over
+w2 is negative 1 B over W 2 is positive
+
+ align:start position:0%
+w2 is negative 1 B over W 2 is positive
+ 
+
+ align:start position:0%
+w2 is negative 1 B over W 2 is positive
+1 so what do we know about the ratio of
+
+ align:start position:0%
+1 so what do we know about the ratio of
+ 
+
+ align:start position:0%
+1 so what do we know about the ratio of
+W 1 and W 2 it's equal to negative 1 and
+
+ align:start position:0%
+W 1 and W 2 it's equal to negative 1 and
+ 
+
+ align:start position:0%
+W 1 and W 2 it's equal to negative 1 and
+that means that when we square it W 1
+
+ align:start position:0%
+that means that when we square it W 1
+ 
+
+ align:start position:0%
+that means that when we square it W 1
+squared equals W 2 squared so therefore
+
+ align:start position:0%
+squared equals W 2 squared so therefore
+ 
+
+ align:start position:0%
+squared equals W 2 squared so therefore
+this is the square root of 2 W 1 squared
+
+ align:start position:0%
+this is the square root of 2 W 1 squared
+ 
+
+ align:start position:0%
+this is the square root of 2 W 1 squared
+which equals root 2 W 1 equivalently
+
+ align:start position:0%
+which equals root 2 W 1 equivalently
+ 
+
+ align:start position:0%
+which equals root 2 W 1 equivalently
+well actually
+
+ align:start position:0%
+well actually
+ 
+
+ align:start position:0%
+well actually
+no it doesn't equal root 2 w 1 because W
+
+ align:start position:0%
+no it doesn't equal root 2 w 1 because W
+ 
+
+ align:start position:0%
+no it doesn't equal root 2 w 1 because W
+1 is actually negative so it we you know
+
+ align:start position:0%
+1 is actually negative so it we you know
+ 
+
+ align:start position:0%
+1 is actually negative so it we you know
+it's negative 2 W when it doesn't matter
+
+ align:start position:0%
+it's negative 2 W when it doesn't matter
+ 
+
+ align:start position:0%
+it's negative 2 W when it doesn't matter
+the point is that if that equals root 2
+
+ align:start position:0%
+the point is that if that equals root 2
+ 
+
+ align:start position:0%
+the point is that if that equals root 2
+over 4 then W 1 is everyone negative 1/4
+
+ align:start position:0%
+over 4 then W 1 is everyone negative 1/4
+ 
+
+ align:start position:0%
+over 4 then W 1 is everyone negative 1/4
+bingo
+
+ align:start position:0%
+bingo
+ 
+
+ align:start position:0%
+bingo
+and if W 1 is negative 1/4 everything
+
+ align:start position:0%
+and if W 1 is negative 1/4 everything
+ 
+
+ align:start position:0%
+and if W 1 is negative 1/4 everything
+else falls into place
+
+ align:start position:0%
+else falls into place
+ 
+
+ align:start position:0%
+else falls into place
+butter W 2 and B everyone positive 1/4
+
+ align:start position:0%
+butter W 2 and B everyone positive 1/4
+ 
+
+ align:start position:0%
+butter W 2 and B everyone positive 1/4
+we got it we've done with this part of
+
+ align:start position:0%
+we got it we've done with this part of
+ 
+
+ align:start position:0%
+we got it we've done with this part of
+the problem however bonus let's do
+
+ align:start position:0%
+the problem however bonus let's do
+ 
+
+ align:start position:0%
+the problem however bonus let's do
+conquer the alphas which they didn't ask
+
+ align:start position:0%
+conquer the alphas which they didn't ask
+ 
+
+ align:start position:0%
+conquer the alphas which they didn't ask
+you to calculate actually you know what
+
+ align:start position:0%
+you to calculate actually you know what
+ 
+
+ align:start position:0%
+you to calculate actually you know what
+we'll do the office if we have enough
+
+ align:start position:0%
+we'll do the office if we have enough
+ 
+
+ align:start position:0%
+we'll do the office if we have enough
+time since they didn't actually ask you
+
+ align:start position:0%
+time since they didn't actually ask you
+ 
+
+ align:start position:0%
+time since they didn't actually ask you
+to calculate them however my
+
+ align:start position:0%
+to calculate them however my
+ 
+
+ align:start position:0%
+to calculate them however my
+recommendation is since there's only one
+
+ align:start position:0%
+recommendation is since there's only one
+ 
+
+ align:start position:0%
+recommendation is since there's only one
+alpha plus and 1 alpha minus they must
+
+ align:start position:0%
+alpha plus and 1 alpha minus they must
+ 
+
+ align:start position:0%
+alpha plus and 1 alpha minus they must
+be equal from this equation
+
+ align:start position:0%
+be equal from this equation
+ 
+
+ align:start position:0%
+be equal from this equation
+since this is some of the alpha plus
+
+ align:start position:0%
+since this is some of the alpha plus
+ 
+
+ align:start position:0%
+since this is some of the alpha plus
+equals the sum of the alpha minus and so
+
+ align:start position:0%
+equals the sum of the alpha minus and so
+ 
+
+ align:start position:0%
+equals the sum of the alpha minus and so
+therefore some of the W or say W equals
+
+ align:start position:0%
+therefore some of the W or say W equals
+ 
+
+ align:start position:0%
+therefore some of the W or say W equals
+the sum of W sorry should be an X of
+
+ align:start position:0%
+the sum of W sorry should be an X of
+ 
+
+ align:start position:0%
+the sum of W sorry should be an X of
+course there's not a million w's in this
+
+ align:start position:0%
+course there's not a million w's in this
+ 
+
+ align:start position:0%
+course there's not a million w's in this
+equation the sum of the points the
+
+ align:start position:0%
+equation the sum of the points the
+ 
+
+ align:start position:0%
+equation the sum of the points the
+positive data points times their alpha
+
+ align:start position:0%
+positive data points times their alpha
+ 
+
+ align:start position:0%
+positive data points times their alpha
+is minus the negative data points times
+
+ align:start position:0%
+is minus the negative data points times
+ 
+
+ align:start position:0%
+is minus the negative data points times
+their office so we're looking at here on
+
+ align:start position:0%
+their office so we're looking at here on
+ 
+
+ align:start position:0%
+their office so we're looking at here on
+negative 1/4 1/4 equals um what do we
+
+ align:start position:0%
+negative 1/4 1/4 equals um what do we
+ 
+
+ align:start position:0%
+negative 1/4 1/4 equals um what do we
+got here positive point negative 1/2 so
+
+ align:start position:0%
+got here positive point negative 1/2 so
+ 
+
+ align:start position:0%
+got here positive point negative 1/2 so
+we've got alpha plus or alpha of that
+
+ align:start position:0%
+we've got alpha plus or alpha of that
+ 
+
+ align:start position:0%
+we've got alpha plus or alpha of that
+point negative 1/2 minus alpha of that
+
+ align:start position:0%
+point negative 1/2 minus alpha of that
+ 
+
+ align:start position:0%
+point negative 1/2 minus alpha of that
+minus point and what is that it's 3
+
+ align:start position:0%
+minus point and what is that it's 3
+ 
+
+ align:start position:0%
+minus point and what is that it's 3
+negative 2 3 negative 2 so if both of
+
+ align:start position:0%
+negative 2 3 negative 2 so if both of
+ 
+
+ align:start position:0%
+negative 2 3 negative 2 so if both of
+the alphas which are equal were 1 we'd
+
+ align:start position:0%
+the alphas which are equal were 1 we'd
+ 
+
+ align:start position:0%
+the alphas which are equal were 1 we'd
+have negative 4 and we'd have negative 4
+
+ align:start position:0%
+have negative 4 and we'd have negative 4
+ 
+
+ align:start position:0%
+have negative 4 and we'd have negative 4
+4 but we want negative 1/4 1/4 so
+
+ align:start position:0%
+4 but we want negative 1/4 1/4 so
+ 
+
+ align:start position:0%
+4 but we want negative 1/4 1/4 so
+actually both of the alphas are 1/16 and
+
+ align:start position:0%
+actually both of the alphas are 1/16 and
+ 
+
+ align:start position:0%
+actually both of the alphas are 1/16 and
+that's the answer
+
+ align:start position:0%
+that's the answer
+ 
+
+ align:start position:0%
+that's the answer
+we'll do that boring gap if we have time
+
+ align:start position:0%
+we'll do that boring gap if we have time
+ 
+
+ align:start position:0%
+we'll do that boring gap if we have time
+but we won't so let's do number two so
+
+ align:start position:0%
+but we won't so let's do number two so
+ 
+
+ align:start position:0%
+but we won't so let's do number two so
+let's go into faster mode number two
+
+ align:start position:0%
+let's go into faster mode number two
+ 
+
+ align:start position:0%
+let's go into faster mode number two
+very similar to number one in many ways
+
+ align:start position:0%
+very similar to number one in many ways
+ 
+
+ align:start position:0%
+very similar to number one in many ways
+but as you can see one of the main
+
+ align:start position:0%
+but as you can see one of the main
+ 
+
+ align:start position:0%
+but as you can see one of the main
+things that they added an extra minus
+
+ align:start position:0%
+things that they added an extra minus
+ 
+
+ align:start position:0%
+things that they added an extra minus
+sign at two negative one so I think we
+
+ align:start position:0%
+sign at two negative one so I think we
+ 
+
+ align:start position:0%
+sign at two negative one so I think we
+can all agree that this will still be
+
+ align:start position:0%
+can all agree that this will still be
+ 
+
+ align:start position:0%
+can all agree that this will still be
+our plus actually add another plus sign
+
+ align:start position:0%
+our plus actually add another plus sign
+ 
+
+ align:start position:0%
+our plus actually add another plus sign
+there too so maybe this plus sign is a
+
+ align:start position:0%
+there too so maybe this plus sign is a
+ 
+
+ align:start position:0%
+there too so maybe this plus sign is a
+split vector but it's not this plus sign
+
+ align:start position:0%
+split vector but it's not this plus sign
+ 
+
+ align:start position:0%
+split vector but it's not this plus sign
+is the support vector what do you guys
+
+ align:start position:0%
+is the support vector what do you guys
+ 
+
+ align:start position:0%
+is the support vector what do you guys
+think about the new negative sign will
+
+ align:start position:0%
+think about the new negative sign will
+ 
+
+ align:start position:0%
+think about the new negative sign will
+it become the support vector since it is
+
+ align:start position:0%
+it become the support vector since it is
+ 
+
+ align:start position:0%
+it become the support vector since it is
+like strictly closer to the pluses yup
+
+ align:start position:0%
+like strictly closer to the pluses yup
+ 
+
+ align:start position:0%
+like strictly closer to the pluses yup
+you're right
+
+ align:start position:0%
+you're right
+ 
+
+ align:start position:0%
+you're right
+okay so this is a very beautiful
+
+ align:start position:0%
+okay so this is a very beautiful
+ 
+
+ align:start position:0%
+okay so this is a very beautiful
+division because if I do this correctly
+
+ align:start position:0%
+division because if I do this correctly
+ 
+
+ align:start position:0%
+division because if I do this correctly
+which I didn't but if we pretend that I
+
+ align:start position:0%
+which I didn't but if we pretend that I
+ 
+
+ align:start position:0%
+which I didn't but if we pretend that I
+did then the dotted line is y equals x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so with the dotted line at y equals
+
+ align:start position:0%
+okay so with the dotted line at y equals
+ 
+
+ align:start position:0%
+okay so with the dotted line at y equals
+x then we know that just like we did up
+
+ align:start position:0%
+x then we know that just like we did up
+ 
+
+ align:start position:0%
+x then we know that just like we did up
+here we know that if y equals x plus 0
+
+ align:start position:0%
+here we know that if y equals x plus 0
+ 
+
+ align:start position:0%
+here we know that if y equals x plus 0
+we know that first of all B equals 0
+
+ align:start position:0%
+we know that first of all B equals 0
+ 
+
+ align:start position:0%
+we know that first of all B equals 0
+second of all we know that we've got
+
+ align:start position:0%
+second of all we know that we've got
+ 
+
+ align:start position:0%
+second of all we know that we've got
+just with y equals x then we know that
+
+ align:start position:0%
+just with y equals x then we know that
+ 
+
+ align:start position:0%
+just with y equals x then we know that
+negative w1 over w2 equals 1 the plus
+
+ align:start position:0%
+negative w1 over w2 equals 1 the plus
+ 
+
+ align:start position:0%
+negative w1 over w2 equals 1 the plus
+are still on the left and up so we know
+
+ align:start position:0%
+are still on the left and up so we know
+ 
+
+ align:start position:0%
+are still on the left and up so we know
+that w1 is some negative number negative
+
+ align:start position:0%
+that w1 is some negative number negative
+ 
+
+ align:start position:0%
+that w1 is some negative number negative
+K w2 is some positive number K great how
+
+ align:start position:0%
+K w2 is some positive number K great how
+ 
+
+ align:start position:0%
+K w2 is some positive number K great how
+are we going to figure it out well let's
+
+ align:start position:0%
+are we going to figure it out well let's
+ 
+
+ align:start position:0%
+are we going to figure it out well let's
+call that this D for distance or
+
+ align:start position:0%
+call that this D for distance or
+ 
+
+ align:start position:0%
+call that this D for distance or
+whatever you want to call it so on over
+
+ align:start position:0%
+whatever you want to call it so on over
+ 
+
+ align:start position:0%
+whatever you want to call it so on over
+W equals D D in this case is not on 2
+
+ align:start position:0%
+W equals D D in this case is not on 2
+ 
+
+ align:start position:0%
+W equals D D in this case is not on 2
+root 2 can everyone tell what D is here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's actually so it goes over two and
+
+ align:start position:0%
+it's actually so it goes over two and
+ 
+
+ align:start position:0%
+it's actually so it goes over two and
+one so it should be one and a half root
+
+ align:start position:0%
+one so it should be one and a half root
+ 
+
+ align:start position:0%
+one so it should be one and a half root
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+since this with distance which is twice
+
+ align:start position:0%
+since this with distance which is twice
+ 
+
+ align:start position:0%
+since this with distance which is twice
+as much goes over 3 and 3 which is 3
+
+ align:start position:0%
+as much goes over 3 and 3 which is 3
+ 
+
+ align:start position:0%
+as much goes over 3 and 3 which is 3
+root 2 so it's one and a half root 2 I
+
+ align:start position:0%
+root 2 so it's one and a half root 2 I
+ 
+
+ align:start position:0%
+root 2 so it's one and a half root 2 I
+don't like putting in decimals and stuff
+
+ align:start position:0%
+don't like putting in decimals and stuff
+ 
+
+ align:start position:0%
+don't like putting in decimals and stuff
+there so we'll say that 2 over negative
+
+ align:start position:0%
+there so we'll say that 2 over negative
+ 
+
+ align:start position:0%
+there so we'll say that 2 over negative
+W equals to D equals 3 root 2 so
+
+ align:start position:0%
+W equals to D equals 3 root 2 so
+ 
+
+ align:start position:0%
+W equals to D equals 3 root 2 so
+therefore right high-diving 1 2 3 1 2 3
+
+ align:start position:0%
+therefore right high-diving 1 2 3 1 2 3
+ 
+
+ align:start position:0%
+therefore right high-diving 1 2 3 1 2 3
+3 root 2 so therefore magnitude of W
+
+ align:start position:0%
+3 root 2 so therefore magnitude of W
+ 
+
+ align:start position:0%
+3 root 2 so therefore magnitude of W
+equals let's see switch them over we
+
+ align:start position:0%
+equals let's see switch them over we
+ 
+
+ align:start position:0%
+equals let's see switch them over we
+should get root 2 over 3 and it's
+
+ align:start position:0%
+should get root 2 over 3 and it's
+ 
+
+ align:start position:0%
+should get root 2 over 3 and it's
+magnitude of W is root 2 over 3 we can
+
+ align:start position:0%
+magnitude of W is root 2 over 3 we can
+ 
+
+ align:start position:0%
+magnitude of W is root 2 over 3 we can
+do our same trick from before square
+
+ align:start position:0%
+do our same trick from before square
+ 
+
+ align:start position:0%
+do our same trick from before square
+root of 2 W 2 squared equals root 2 over
+
+ align:start position:0%
+root of 2 W 2 squared equals root 2 over
+ 
+
+ align:start position:0%
+root of 2 W 2 squared equals root 2 over
+3 and this is just root 2 times W 2
+
+ align:start position:0%
+3 and this is just root 2 times W 2
+ 
+
+ align:start position:0%
+3 and this is just root 2 times W 2
+equals root 2 over 3 so therefore W 2 is
+
+ align:start position:0%
+equals root 2 over 3 so therefore W 2 is
+ 
+
+ align:start position:0%
+equals root 2 over 3 so therefore W 2 is
+1/3 and W 1 is negative 1/3 bingo we've
+
+ align:start position:0%
+1/3 and W 1 is negative 1/3 bingo we've
+ 
+
+ align:start position:0%
+1/3 and W 1 is negative 1/3 bingo we've
+got W 1 we've got W - we know that B was
+
+ align:start position:0%
+got W 1 we've got W - we know that B was
+ 
+
+ align:start position:0%
+got W 1 we've got W - we know that B was
+0 because obviously at 0 its y equals x
+
+ align:start position:0%
+0 because obviously at 0 its y equals x
+ 
+
+ align:start position:0%
+0 because obviously at 0 its y equals x
+and we're done
+
+ align:start position:0%
+and we're done
+ 
+
+ align:start position:0%
+and we're done
+ah that was fast the alphas might have
+
+ align:start position:0%
+ah that was fast the alphas might have
+ 
+
+ align:start position:0%
+ah that was fast the alphas might have
+taken longer actually the alphas on this
+
+ align:start position:0%
+taken longer actually the alphas on this
+ 
+
+ align:start position:0%
+taken longer actually the alphas on this
+one or more of a pain in the ass than
+
+ align:start position:0%
+one or more of a pain in the ass than
+ 
+
+ align:start position:0%
+one or more of a pain in the ass than
+anywhere else because let's take a look
+
+ align:start position:0%
+anywhere else because let's take a look
+ 
+
+ align:start position:0%
+anywhere else because let's take a look
+at this one if you can see it we've
+
+ align:start position:0%
+at this one if you can see it we've
+ 
+
+ align:start position:0%
+at this one if you can see it we've
+added yet some new points we've got this
+
+ align:start position:0%
+added yet some new points we've got this
+ 
+
+ align:start position:0%
+added yet some new points we've got this
+point up here this point down there so I
+
+ align:start position:0%
+point up here this point down there so I
+ 
+
+ align:start position:0%
+point up here this point down there so I
+think pretty clearly these plus and
+
+ align:start position:0%
+think pretty clearly these plus and
+ 
+
+ align:start position:0%
+think pretty clearly these plus and
+minus are the closest to each other but
+
+ align:start position:0%
+minus are the closest to each other but
+ 
+
+ align:start position:0%
+minus are the closest to each other but
+what happens if we take the
+
+ align:start position:0%
+what happens if we take the
+ 
+
+ align:start position:0%
+what happens if we take the
+perpendicular bisector between these two
+
+ align:start position:0%
+perpendicular bisector between these two
+ 
+
+ align:start position:0%
+perpendicular bisector between these two
+and dude like this this plus is in the
+
+ align:start position:0%
+and dude like this this plus is in the
+ 
+
+ align:start position:0%
+and dude like this this plus is in the
+middle so we're going to have 2 feet so
+
+ align:start position:0%
+middle so we're going to have 2 feet so
+ 
+
+ align:start position:0%
+middle so we're going to have 2 feet so
+therefore this plus is going to have to
+
+ align:start position:0%
+therefore this plus is going to have to
+ 
+
+ align:start position:0%
+therefore this plus is going to have to
+also be support vector so we can't just
+
+ align:start position:0%
+also be support vector so we can't just
+ 
+
+ align:start position:0%
+also be support vector so we can't just
+draw this line we have to include this
+
+ align:start position:0%
+draw this line we have to include this
+ 
+
+ align:start position:0%
+draw this line we have to include this
+what's our best division
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertical lines that's right vertical
+
+ align:start position:0%
+vertical lines that's right vertical
+ 
+
+ align:start position:0%
+vertical lines that's right vertical
+lines just saw and that means that the
+
+ align:start position:0%
+lines just saw and that means that the
+ 
+
+ align:start position:0%
+lines just saw and that means that the
+equation of our equation of our boundary
+
+ align:start position:0%
+equation of our equation of our boundary
+ 
+
+ align:start position:0%
+equation of our equation of our boundary
+the dotted line here y-axis so the
+
+ align:start position:0%
+the dotted line here y-axis so the
+ 
+
+ align:start position:0%
+the dotted line here y-axis so the
+equation of the boundary of the y-axis
+
+ align:start position:0%
+equation of the boundary of the y-axis
+ 
+
+ align:start position:0%
+equation of the boundary of the y-axis
+then B equals zero and how W 2 equals
+
+ align:start position:0%
+then B equals zero and how W 2 equals
+ 
+
+ align:start position:0%
+then B equals zero and how W 2 equals
+zero so the only thing that is not W 2
+
+ align:start position:0%
+zero so the only thing that is not W 2
+ 
+
+ align:start position:0%
+zero so the only thing that is not W 2
+equals 0 so W 2 equals 0 B equals 0 but
+
+ align:start position:0%
+equals 0 so W 2 equals 0 B equals 0 but
+ 
+
+ align:start position:0%
+equals 0 so W 2 equals 0 B equals 0 but
+W 1 is not equal to 0 because it's just
+
+ align:start position:0%
+W 1 is not equal to 0 because it's just
+ 
+
+ align:start position:0%
+W 1 is not equal to 0 because it's just
+the equation of the y-axis so we
+
+ align:start position:0%
+the equation of the y-axis so we
+ 
+
+ align:start position:0%
+the equation of the y-axis so we
+therefore know that the equation is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W 1 times x equals 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if w1 times x equals zero and we know
+
+ align:start position:0%
+so if w1 times x equals zero and we know
+ 
+
+ align:start position:0%
+so if w1 times x equals zero and we know
+that that just means essentially that X
+
+ align:start position:0%
+that that just means essentially that X
+ 
+
+ align:start position:0%
+that that just means essentially that X
+is going to be some K it's also going to
+
+ align:start position:0%
+is going to be some K it's also going to
+ 
+
+ align:start position:0%
+is going to be some K it's also going to
+be negative because of the fact that
+
+ align:start position:0%
+be negative because of the fact that
+ 
+
+ align:start position:0%
+be negative because of the fact that
+that plus is our store on the left then
+
+ align:start position:0%
+that plus is our store on the left then
+ 
+
+ align:start position:0%
+that plus is our store on the left then
+we're going to figure out what that K is
+
+ align:start position:0%
+we're going to figure out what that K is
+ 
+
+ align:start position:0%
+we're going to figure out what that K is
+we'll use our old trick
+
+ align:start position:0%
+we'll use our old trick
+ 
+
+ align:start position:0%
+we'll use our old trick
+by this point old hopefully one over
+
+ align:start position:0%
+by this point old hopefully one over
+ 
+
+ align:start position:0%
+by this point old hopefully one over
+magnitude of W equals D this time D is
+
+ align:start position:0%
+magnitude of W equals D this time D is
+ 
+
+ align:start position:0%
+magnitude of W equals D this time D is
+just 1 so therefore magnitude of W
+
+ align:start position:0%
+just 1 so therefore magnitude of W
+ 
+
+ align:start position:0%
+just 1 so therefore magnitude of W
+equals one there's only one component in
+
+ align:start position:0%
+equals one there's only one component in
+ 
+
+ align:start position:0%
+equals one there's only one component in
+W so therefore W 1 is minus 1 because
+
+ align:start position:0%
+W so therefore W 1 is minus 1 because
+ 
+
+ align:start position:0%
+W so therefore W 1 is minus 1 because
+the plus is on the left people see that
+
+ align:start position:0%
+the plus is on the left people see that
+ 
+
+ align:start position:0%
+the plus is on the left people see that
+not too bad
+
+ align:start position:0%
+not too bad
+ 
+
+ align:start position:0%
+not too bad
+this one's easy to calculate a W but
+
+ align:start position:0%
+this one's easy to calculate a W but
+ 
+
+ align:start position:0%
+this one's easy to calculate a W but
+it's not as easy to get all the alphas
+
+ align:start position:0%
+it's not as easy to get all the alphas
+ 
+
+ align:start position:0%
+it's not as easy to get all the alphas
+but let's move on to a new and even more
+
+ align:start position:0%
+but let's move on to a new and even more
+ 
+
+ align:start position:0%
+but let's move on to a new and even more
+fun maybe not
+
+ align:start position:0%
+fun maybe not
+ 
+
+ align:start position:0%
+fun maybe not
+um question which is this guy as you can
+
+ align:start position:0%
+um question which is this guy as you can
+ 
+
+ align:start position:0%
+um question which is this guy as you can
+see this is a lease this well maybe not
+
+ align:start position:0%
+see this is a lease this well maybe not
+ 
+
+ align:start position:0%
+see this is a lease this well maybe not
+this is a one-dimensional vector these
+
+ align:start position:0%
+this is a one-dimensional vector these
+ 
+
+ align:start position:0%
+this is a one-dimensional vector these
+vectors only have a single dimension so
+
+ align:start position:0%
+vectors only have a single dimension so
+ 
+
+ align:start position:0%
+vectors only have a single dimension so
+it just looks like a number line here
+
+ align:start position:0%
+it just looks like a number line here
+ 
+
+ align:start position:0%
+it just looks like a number line here
+that dimension varies from it looks like
+
+ align:start position:0%
+that dimension varies from it looks like
+ 
+
+ align:start position:0%
+that dimension varies from it looks like
+negative 9 to positive 9 either just has
+
+ align:start position:0%
+negative 9 to positive 9 either just has
+ 
+
+ align:start position:0%
+negative 9 to positive 9 either just has
+one component you don't have to worry
+
+ align:start position:0%
+one component you don't have to worry
+ 
+
+ align:start position:0%
+one component you don't have to worry
+about any of these crazy magnitudes with
+
+ align:start position:0%
+about any of these crazy magnitudes with
+ 
+
+ align:start position:0%
+about any of these crazy magnitudes with
+two components just everything as a
+
+ align:start position:0%
+two components just everything as a
+ 
+
+ align:start position:0%
+two components just everything as a
+single component however it's obvious
+
+ align:start position:0%
+single component however it's obvious
+ 
+
+ align:start position:0%
+single component however it's obvious
+that a linear basis line is going to
+
+ align:start position:0%
+that a linear basis line is going to
+ 
+
+ align:start position:0%
+that a linear basis line is going to
+completely screw us up here since lines
+
+ align:start position:0%
+completely screw us up here since lines
+ 
+
+ align:start position:0%
+completely screw us up here since lines
+at this point are just like glump all
+
+ align:start position:0%
+at this point are just like glump all
+ 
+
+ align:start position:0%
+at this point are just like glump all
+these are pluses all these are Mises
+
+ align:start position:0%
+these are pluses all these are Mises
+ 
+
+ align:start position:0%
+these are pluses all these are Mises
+well not great that doesn't get them off
+
+ align:start position:0%
+well not great that doesn't get them off
+ 
+
+ align:start position:0%
+well not great that doesn't get them off
+so how are we going to do it well we're
+
+ align:start position:0%
+so how are we going to do it well we're
+ 
+
+ align:start position:0%
+so how are we going to do it well we're
+going to use what is usually perhaps the
+
+ align:start position:0%
+going to use what is usually perhaps the
+ 
+
+ align:start position:0%
+going to use what is usually perhaps the
+hardest thing in SVM's but in this case
+
+ align:start position:0%
+hardest thing in SVM's but in this case
+ 
+
+ align:start position:0%
+hardest thing in SVM's but in this case
+is not going to be too bad for us we're
+
+ align:start position:0%
+is not going to be too bad for us we're
+ 
+
+ align:start position:0%
+is not going to be too bad for us we're
+going to use a kernel now based on how
+
+ align:start position:0%
+going to use a kernel now based on how
+ 
+
+ align:start position:0%
+going to use a kernel now based on how
+little I understood kernels the first
+
+ align:start position:0%
+little I understood kernels the first
+ 
+
+ align:start position:0%
+little I understood kernels the first
+time I've took this class I'm guessing
+
+ align:start position:0%
+time I've took this class I'm guessing
+ 
+
+ align:start position:0%
+time I've took this class I'm guessing
+that you guys would like to have some
+
+ align:start position:0%
+that you guys would like to have some
+ 
+
+ align:start position:0%
+that you guys would like to have some
+explanation on these kernels you
+
+ align:start position:0%
+explanation on these kernels you
+ 
+
+ align:start position:0%
+explanation on these kernels you
+probably saw them you remember the
+
+ align:start position:0%
+probably saw them you remember the
+ 
+
+ align:start position:0%
+probably saw them you remember the
+kernels from Patrick's lecture vaguely
+
+ align:start position:0%
+kernels from Patrick's lecture vaguely
+ 
+
+ align:start position:0%
+kernels from Patrick's lecture vaguely
+they're like this Phi and then there's
+
+ align:start position:0%
+they're like this Phi and then there's
+ 
+
+ align:start position:0%
+they're like this Phi and then there's
+this K and then they get really
+
+ align:start position:0%
+this K and then they get really
+ 
+
+ align:start position:0%
+this K and then they get really
+complicated okay so here's how the
+
+ align:start position:0%
+complicated okay so here's how the
+ 
+
+ align:start position:0%
+complicated okay so here's how the
+kernel works the basic idea is this
+
+ align:start position:0%
+kernel works the basic idea is this
+ 
+
+ align:start position:0%
+kernel works the basic idea is this
+and I'll write it over here
+
+ align:start position:0%
+and I'll write it over here
+ 
+
+ align:start position:0%
+and I'll write it over here
+oh wow there's more stuff okay I'll
+
+ align:start position:0%
+oh wow there's more stuff okay I'll
+ 
+
+ align:start position:0%
+oh wow there's more stuff okay I'll
+write it right here the basic idea is
+
+ align:start position:0%
+write it right here the basic idea is
+ 
+
+ align:start position:0%
+write it right here the basic idea is
+this we're taking the normal space which
+
+ align:start position:0%
+this we're taking the normal space which
+ 
+
+ align:start position:0%
+this we're taking the normal space which
+is you know this number line or it could
+
+ align:start position:0%
+is you know this number line or it could
+ 
+
+ align:start position:0%
+is you know this number line or it could
+be any kind of normal space and we're
+
+ align:start position:0%
+be any kind of normal space and we're
+ 
+
+ align:start position:0%
+be any kind of normal space and we're
+going to take a vector we're going to
+
+ align:start position:0%
+going to take a vector we're going to
+ 
+
+ align:start position:0%
+going to take a vector we're going to
+put it into it of a function called Phi
+
+ align:start position:0%
+put it into it of a function called Phi
+ 
+
+ align:start position:0%
+put it into it of a function called Phi
+and Phi of vector X brings X into some
+
+ align:start position:0%
+and Phi of vector X brings X into some
+ 
+
+ align:start position:0%
+and Phi of vector X brings X into some
+new dimension Phi or fee if you like it
+
+ align:start position:0%
+new dimension Phi or fee if you like it
+ 
+
+ align:start position:0%
+new dimension Phi or fee if you like it
+better is usually a nasty piece of work
+
+ align:start position:0%
+better is usually a nasty piece of work
+ 
+
+ align:start position:0%
+better is usually a nasty piece of work
+and something that you'd never ever want
+
+ align:start position:0%
+and something that you'd never ever want
+ 
+
+ align:start position:0%
+and something that you'd never ever want
+to look at sometimes it's not too bad
+
+ align:start position:0%
+to look at sometimes it's not too bad
+ 
+
+ align:start position:0%
+to look at sometimes it's not too bad
+Phi is the function that brings it into
+
+ align:start position:0%
+Phi is the function that brings it into
+ 
+
+ align:start position:0%
+Phi is the function that brings it into
+the new dimension okay and when you
+
+ align:start position:0%
+the new dimension okay and when you
+ 
+
+ align:start position:0%
+the new dimension okay and when you
+brought the data into a new dimension
+
+ align:start position:0%
+brought the data into a new dimension
+ 
+
+ align:start position:0%
+brought the data into a new dimension
+sometimes you can just cut a straight
+
+ align:start position:0%
+sometimes you can just cut a straight
+ 
+
+ align:start position:0%
+sometimes you can just cut a straight
+line in that dimension and you'll just
+
+ align:start position:0%
+line in that dimension and you'll just
+ 
+
+ align:start position:0%
+line in that dimension and you'll just
+be happy however something that was
+
+ align:start position:0%
+be happy however something that was
+ 
+
+ align:start position:0%
+be happy however something that was
+noted by the very very smart inventor of
+
+ align:start position:0%
+noted by the very very smart inventor of
+ 
+
+ align:start position:0%
+noted by the very very smart inventor of
+support vector machines is that you
+
+ align:start position:0%
+support vector machines is that you
+ 
+
+ align:start position:0%
+support vector machines is that you
+don't actually need to to work with
+
+ align:start position:0%
+don't actually need to to work with
+ 
+
+ align:start position:0%
+don't actually need to to work with
+function Phi
+
+ align:start position:0%
+function Phi
+ 
+
+ align:start position:0%
+function Phi
+even if Phi is an absolutely horrible
+
+ align:start position:0%
+even if Phi is an absolutely horrible
+ 
+
+ align:start position:0%
+even if Phi is an absolutely horrible
+monstrosity because of the fact that you
+
+ align:start position:0%
+monstrosity because of the fact that you
+ 
+
+ align:start position:0%
+monstrosity because of the fact that you
+never need to know what the vector X
+
+ align:start position:0%
+never need to know what the vector X
+ 
+
+ align:start position:0%
+never need to know what the vector X
+what all these vectors X actually are in
+
+ align:start position:0%
+what all these vectors X actually are in
+ 
+
+ align:start position:0%
+what all these vectors X actually are in
+the new space at least not directly in
+
+ align:start position:0%
+the new space at least not directly in
+ 
+
+ align:start position:0%
+the new space at least not directly in
+none of these equations up here do we
+
+ align:start position:0%
+none of these equations up here do we
+ 
+
+ align:start position:0%
+none of these equations up here do we
+ever use X by itself however we do use X
+
+ align:start position:0%
+ever use X by itself however we do use X
+ 
+
+ align:start position:0%
+ever use X by itself however we do use X
+being dot product with something else so
+
+ align:start position:0%
+being dot product with something else so
+ 
+
+ align:start position:0%
+being dot product with something else so
+he figured out a very sneaky and
+
+ align:start position:0%
+he figured out a very sneaky and
+ 
+
+ align:start position:0%
+he figured out a very sneaky and
+excellent shortcut okay so I shouldn't
+
+ align:start position:0%
+excellent shortcut okay so I shouldn't
+ 
+
+ align:start position:0%
+excellent shortcut okay so I shouldn't
+use x1 x2 L use X and Z so if you have
+
+ align:start position:0%
+use x1 x2 L use X and Z so if you have
+ 
+
+ align:start position:0%
+use x1 x2 L use X and Z so if you have
+two vectors X and Z which are in a
+
+ align:start position:0%
+two vectors X and Z which are in a
+ 
+
+ align:start position:0%
+two vectors X and Z which are in a
+regular space you put them into this
+
+ align:start position:0%
+regular space you put them into this
+ 
+
+ align:start position:0%
+regular space you put them into this
+function called the kernel then it will
+
+ align:start position:0%
+function called the kernel then it will
+ 
+
+ align:start position:0%
+function called the kernel then it will
+tell you Phi of X dotted with 5z
+
+ align:start position:0%
+tell you Phi of X dotted with 5z
+ 
+
+ align:start position:0%
+tell you Phi of X dotted with 5z
+and if you have that you don't need five
+
+ align:start position:0%
+and if you have that you don't need five
+ 
+
+ align:start position:0%
+and if you have that you don't need five
+does everyone see that
+
+ align:start position:0%
+does everyone see that
+ 
+
+ align:start position:0%
+does everyone see that
+does everyone see why we don't need five
+
+ align:start position:0%
+does everyone see why we don't need five
+ 
+
+ align:start position:0%
+does everyone see why we don't need five
+look at all these equations up here we
+
+ align:start position:0%
+look at all these equations up here we
+ 
+
+ align:start position:0%
+look at all these equations up here we
+never look at X by itself in these in
+
+ align:start position:0%
+never look at X by itself in these in
+ 
+
+ align:start position:0%
+never look at X by itself in these in
+these vector equations at least now
+
+ align:start position:0%
+these vector equations at least now
+ 
+
+ align:start position:0%
+these vector equations at least now
+calculating alphas yeah that gets a
+
+ align:start position:0%
+calculating alphas yeah that gets a
+ 
+
+ align:start position:0%
+calculating alphas yeah that gets a
+little bit fuzzy but in the vector but
+
+ align:start position:0%
+little bit fuzzy but in the vector but
+ 
+
+ align:start position:0%
+little bit fuzzy but in the vector but
+in the vector equations also you get you
+
+ align:start position:0%
+in the vector equations also you get you
+ 
+
+ align:start position:0%
+in the vector equations also you get you
+may ask like why would you do this you
+
+ align:start position:0%
+may ask like why would you do this you
+ 
+
+ align:start position:0%
+may ask like why would you do this you
+can't complete the alphas it turns out
+
+ align:start position:0%
+can't complete the alphas it turns out
+ 
+
+ align:start position:0%
+can't complete the alphas it turns out
+we're um that actually other than for
+
+ align:start position:0%
+we're um that actually other than for
+ 
+
+ align:start position:0%
+we're um that actually other than for
+these very simple linear problems human
+
+ align:start position:0%
+these very simple linear problems human
+ 
+
+ align:start position:0%
+these very simple linear problems human
+minds cannot calculate the alphas in
+
+ align:start position:0%
+minds cannot calculate the alphas in
+ 
+
+ align:start position:0%
+minds cannot calculate the alphas in
+fact you run a very complicated
+
+ align:start position:0%
+fact you run a very complicated
+ 
+
+ align:start position:0%
+fact you run a very complicated
+quadratic optimization in fact finding
+
+ align:start position:0%
+quadratic optimization in fact finding
+ 
+
+ align:start position:0%
+quadratic optimization in fact finding
+out the best alphas is the thing that
+
+ align:start position:0%
+out the best alphas is the thing that
+ 
+
+ align:start position:0%
+out the best alphas is the thing that
+you will climb on when you're doing
+
+ align:start position:0%
+you will climb on when you're doing
+ 
+
+ align:start position:0%
+you will climb on when you're doing
+SVM's
+
+ align:start position:0%
+SVM's
+ 
+
+ align:start position:0%
+SVM's
+in the real world you say alright I'll
+
+ align:start position:0%
+in the real world you say alright I'll
+ 
+
+ align:start position:0%
+in the real world you say alright I'll
+run my algorithm and I know there's only
+
+ align:start position:0%
+run my algorithm and I know there's only
+ 
+
+ align:start position:0%
+run my algorithm and I know there's only
+one peak which is very very good because
+
+ align:start position:0%
+one peak which is very very good because
+ 
+
+ align:start position:0%
+one peak which is very very good because
+it's quadratic optimization let me
+
+ align:start position:0%
+it's quadratic optimization let me
+ 
+
+ align:start position:0%
+it's quadratic optimization let me
+figure out the office so in fact it
+
+ align:start position:0%
+figure out the office so in fact it
+ 
+
+ align:start position:0%
+figure out the office so in fact it
+doesn't matter that you can't do that
+
+ align:start position:0%
+doesn't matter that you can't do that
+ 
+
+ align:start position:0%
+doesn't matter that you can't do that
+use these alpha places to figure out the
+
+ align:start position:0%
+use these alpha places to figure out the
+ 
+
+ align:start position:0%
+use these alpha places to figure out the
+alphas um if you've gone into if you
+
+ align:start position:0%
+alphas um if you've gone into if you
+ 
+
+ align:start position:0%
+alphas um if you've gone into if you
+only know the kernel function out the
+
+ align:start position:0%
+only know the kernel function out the
+ 
+
+ align:start position:0%
+only know the kernel function out the
+Phi function because normally the
+
+ align:start position:0%
+Phi function because normally the
+ 
+
+ align:start position:0%
+Phi function because normally the
+computer figures out the alphas for you
+
+ align:start position:0%
+computer figures out the alphas for you
+ 
+
+ align:start position:0%
+computer figures out the alphas for you
+with quadratic optimization just in
+
+ align:start position:0%
+with quadratic optimization just in
+ 
+
+ align:start position:0%
+with quadratic optimization just in
+these simple problems we know you can
+
+ align:start position:0%
+these simple problems we know you can
+ 
+
+ align:start position:0%
+these simple problems we know you can
+calculate the alphas so we have the
+
+ align:start position:0%
+calculate the alphas so we have the
+ 
+
+ align:start position:0%
+calculate the alphas so we have the
+kernel which replaces that basically
+
+ align:start position:0%
+kernel which replaces that basically
+ 
+
+ align:start position:0%
+kernel which replaces that basically
+gives us the dot product of the things
+
+ align:start position:0%
+gives us the dot product of the things
+ 
+
+ align:start position:0%
+gives us the dot product of the things
+in the new space so being that as it may
+
+ align:start position:0%
+in the new space so being that as it may
+ 
+
+ align:start position:0%
+in the new space so being that as it may
+I'll give you the kernel here I'd like
+
+ align:start position:0%
+I'll give you the kernel here I'd like
+ 
+
+ align:start position:0%
+I'll give you the kernel here I'd like
+you to give me the Phi so a kernel for
+
+ align:start position:0%
+you to give me the Phi so a kernel for
+ 
+
+ align:start position:0%
+you to give me the Phi so a kernel for
+that someone got an idea whose name was
+
+ align:start position:0%
+that someone got an idea whose name was
+ 
+
+ align:start position:0%
+that someone got an idea whose name was
+Susan Q random student apparently she
+
+ align:start position:0%
+Susan Q random student apparently she
+ 
+
+ align:start position:0%
+Susan Q random student apparently she
+got an idea that if we had a kernel for
+
+ align:start position:0%
+got an idea that if we had a kernel for
+ 
+
+ align:start position:0%
+got an idea that if we had a kernel for
+X and Z actually they're not vectors I
+
+ align:start position:0%
+X and Z actually they're not vectors I
+ 
+
+ align:start position:0%
+X and Z actually they're not vectors I
+guess they're just single components and
+
+ align:start position:0%
+guess they're just single components and
+ 
+
+ align:start position:0%
+guess they're just single components and
+the kernel equals cosine PI over 4 x
+
+ align:start position:0%
+the kernel equals cosine PI over 4 x
+ 
+
+ align:start position:0%
+the kernel equals cosine PI over 4 x
+times cosine pi over 4z plus sine PI
+
+ align:start position:0%
+times cosine pi over 4z plus sine PI
+ 
+
+ align:start position:0%
+times cosine pi over 4z plus sine PI
+over 4 X plus
+
+ align:start position:0%
+over 4 X plus
+ 
+
+ align:start position:0%
+over 4 X plus
+pi over 4z so that is the new dot
+
+ align:start position:0%
+pi over 4z so that is the new dot
+ 
+
+ align:start position:0%
+pi over 4z so that is the new dot
+product cosine PI over 4x
+
+ align:start position:0%
+product cosine PI over 4x
+ 
+
+ align:start position:0%
+product cosine PI over 4x
+oh wait sorry I put one of the disease
+
+ align:start position:0%
+oh wait sorry I put one of the disease
+ 
+
+ align:start position:0%
+oh wait sorry I put one of the disease
+not inside the parenthesis that was
+
+ align:start position:0%
+not inside the parenthesis that was
+ 
+
+ align:start position:0%
+not inside the parenthesis that was
+still with me so cosine of the quantity
+
+ align:start position:0%
+still with me so cosine of the quantity
+ 
+
+ align:start position:0%
+still with me so cosine of the quantity
+PI over 4 x times cosine is upon T pi
+
+ align:start position:0%
+PI over 4 x times cosine is upon T pi
+ 
+
+ align:start position:0%
+PI over 4 x times cosine is upon T pi
+over 4z plus sine is upon T PI over 4 X
+
+ align:start position:0%
+over 4z plus sine is upon T PI over 4 X
+ 
+
+ align:start position:0%
+over 4z plus sine is upon T PI over 4 X
+plus sine of the quantity PI over 4 z is
+
+ align:start position:0%
+plus sine of the quantity PI over 4 z is
+ 
+
+ align:start position:0%
+plus sine of the quantity PI over 4 z is
+the new dot product so that begs the
+
+ align:start position:0%
+the new dot product so that begs the
+ 
+
+ align:start position:0%
+the new dot product so that begs the
+question in this one this is an easy one
+
+ align:start position:0%
+question in this one this is an easy one
+ 
+
+ align:start position:0%
+question in this one this is an easy one
+so we can calculate the 5 what is Phi of
+
+ align:start position:0%
+so we can calculate the 5 what is Phi of
+ 
+
+ align:start position:0%
+so we can calculate the 5 what is Phi of
+X we're actually taking it from one
+
+ align:start position:0%
+X we're actually taking it from one
+ 
+
+ align:start position:0%
+X we're actually taking it from one
+dimension and we may be playing around
+
+ align:start position:0%
+dimension and we may be playing around
+ 
+
+ align:start position:0%
+dimension and we may be playing around
+with it a lot to get this this thing has
+
+ align:start position:0%
+with it a lot to get this this thing has
+ 
+
+ align:start position:0%
+with it a lot to get this this thing has
+become a new dot product it replaces dot
+
+ align:start position:0%
+become a new dot product it replaces dot
+ 
+
+ align:start position:0%
+become a new dot product it replaces dot
+product now remember the dot part for
+
+ align:start position:0%
+product now remember the dot part for
+ 
+
+ align:start position:0%
+product now remember the dot part for
+scalars would have just been multiplying
+
+ align:start position:0%
+scalars would have just been multiplying
+ 
+
+ align:start position:0%
+scalars would have just been multiplying
+the two numbers together so it actually
+
+ align:start position:0%
+the two numbers together so it actually
+ 
+
+ align:start position:0%
+the two numbers together so it actually
+makes it a little bit more complicated
+
+ align:start position:0%
+makes it a little bit more complicated
+ 
+
+ align:start position:0%
+makes it a little bit more complicated
+does anyone think they know the Phi
+
+ align:start position:0%
+does anyone think they know the Phi
+ 
+
+ align:start position:0%
+does anyone think they know the Phi
+ah we got one what do you think you need
+
+ align:start position:0%
+ah we got one what do you think you need
+ 
+
+ align:start position:0%
+ah we got one what do you think you need
+to come back two dimensional absolutely
+
+ align:start position:0%
+to come back two dimensional absolutely
+ 
+
+ align:start position:0%
+to come back two dimensional absolutely
+that's exactly correct how would you
+
+ align:start position:0%
+that's exactly correct how would you
+ 
+
+ align:start position:0%
+that's exactly correct how would you
+solve this on the next whole quiz if
+
+ align:start position:0%
+solve this on the next whole quiz if
+ 
+
+ align:start position:0%
+solve this on the next whole quiz if
+you're not our brave volunteer
+
+ align:start position:0%
+you're not our brave volunteer
+ 
+
+ align:start position:0%
+you're not our brave volunteer
+well that K if you squint at it not very
+
+ align:start position:0%
+well that K if you squint at it not very
+ 
+
+ align:start position:0%
+well that K if you squint at it not very
+much actually it's pretty much a dot
+
+ align:start position:0%
+much actually it's pretty much a dot
+ 
+
+ align:start position:0%
+much actually it's pretty much a dot
+product between cosine PI over 4 s and
+
+ align:start position:0%
+product between cosine PI over 4 s and
+ 
+
+ align:start position:0%
+product between cosine PI over 4 s and
+sine PI over 4 is I mean look at it dot
+
+ align:start position:0%
+sine PI over 4 is I mean look at it dot
+ 
+
+ align:start position:0%
+sine PI over 4 is I mean look at it dot
+product is just remember if the dot
+
+ align:start position:0%
+product is just remember if the dot
+ 
+
+ align:start position:0%
+product is just remember if the dot
+product of X and Z vectors is X 1 is X 1
+
+ align:start position:0%
+product of X and Z vectors is X 1 is X 1
+ 
+
+ align:start position:0%
+product of X and Z vectors is X 1 is X 1
+Z 1 plus X 2 Z 2 so that basically is X
+
+ align:start position:0%
+Z 1 plus X 2 Z 2 so that basically is X
+ 
+
+ align:start position:0%
+Z 1 plus X 2 Z 2 so that basically is X
+1 Z 1 plus X 2 Z 2 o this should have
+
+ align:start position:0%
+1 Z 1 plus X 2 Z 2 o this should have
+ 
+
+ align:start position:0%
+1 Z 1 plus X 2 Z 2 o this should have
+been many times
+
+ align:start position:0%
+been many times
+ 
+
+ align:start position:0%
+been many times
+yeah there's trillion times sorry
+
+ align:start position:0%
+yeah there's trillion times sorry
+ 
+
+ align:start position:0%
+yeah there's trillion times sorry
+there's a plus there anyone who missed
+
+ align:start position:0%
+there's a plus there anyone who missed
+ 
+
+ align:start position:0%
+there's a plus there anyone who missed
+it because of that my bad that should
+
+ align:start position:0%
+it because of that my bad that should
+ 
+
+ align:start position:0%
+it because of that my bad that should
+have been a x there should've been times
+
+ align:start position:0%
+have been a x there should've been times
+ 
+
+ align:start position:0%
+have been a x there should've been times
+up there the plot only plus is its
+
+ align:start position:0%
+up there the plot only plus is its
+ 
+
+ align:start position:0%
+up there the plot only plus is its
+cosine PI over 4 X cosine 2 pi over 4z
+
+ align:start position:0%
+cosine PI over 4 X cosine 2 pi over 4z
+ 
+
+ align:start position:0%
+cosine PI over 4 X cosine 2 pi over 4z
+plus sine PI over 4 x times sine PI over
+
+ align:start position:0%
+plus sine PI over 4 x times sine PI over
+ 
+
+ align:start position:0%
+plus sine PI over 4 x times sine PI over
+4 Z so yeah it's basically the dot
+
+ align:start position:0%
+4 Z so yeah it's basically the dot
+ 
+
+ align:start position:0%
+4 Z so yeah it's basically the dot
+product between cosine PI over 4 X and
+
+ align:start position:0%
+product between cosine PI over 4 X and
+ 
+
+ align:start position:0%
+product between cosine PI over 4 X and
+sine PI
+
+ align:start position:0%
+sine PI
+ 
+
+ align:start position:0%
+sine PI
+for bingo all right last thing and then
+
+ align:start position:0%
+for bingo all right last thing and then
+ 
+
+ align:start position:0%
+for bingo all right last thing and then
+we well we're not done yet because we're
+
+ align:start position:0%
+we well we're not done yet because we're
+ 
+
+ align:start position:0%
+we well we're not done yet because we're
+going to maybe ask some questions and
+
+ align:start position:0%
+going to maybe ask some questions and
+ 
+
+ align:start position:0%
+going to maybe ask some questions and
+then we're going to see if we can
+
+ align:start position:0%
+then we're going to see if we can
+ 
+
+ align:start position:0%
+then we're going to see if we can
+conquer those alphas but last thing
+
+ align:start position:0%
+conquer those alphas but last thing
+ 
+
+ align:start position:0%
+conquer those alphas but last thing
+let's graph in this new dimension all
+
+ align:start position:0%
+let's graph in this new dimension all
+ 
+
+ align:start position:0%
+let's graph in this new dimension all
+the points
+
+ align:start position:0%
+the points
+ 
+
+ align:start position:0%
+the points
+so obviously cosines and sines so we're
+
+ align:start position:0%
+so obviously cosines and sines so we're
+ 
+
+ align:start position:0%
+so obviously cosines and sines so we're
+going to get results between 1 and minus
+
+ align:start position:0%
+going to get results between 1 and minus
+ 
+
+ align:start position:0%
+going to get results between 1 and minus
+1 let's see maybe I can graph it um can
+
+ align:start position:0%
+1 let's see maybe I can graph it um can
+ 
+
+ align:start position:0%
+1 let's see maybe I can graph it um can
+I write on all these wait maybe this one
+
+ align:start position:0%
+I write on all these wait maybe this one
+ 
+
+ align:start position:0%
+I write on all these wait maybe this one
+oh no people do weird stick figures
+
+ align:start position:0%
+oh no people do weird stick figures
+ 
+
+ align:start position:0%
+oh no people do weird stick figures
+there ok
+
+ align:start position:0%
+there ok
+ 
+
+ align:start position:0%
+there ok
+oh yeah this one's kind of messy but
+
+ align:start position:0%
+oh yeah this one's kind of messy but
+ 
+
+ align:start position:0%
+oh yeah this one's kind of messy but
+we'll do it on this ok so we've got this
+
+ align:start position:0%
+we'll do it on this ok so we've got this
+ 
+
+ align:start position:0%
+we'll do it on this ok so we've got this
+is 1 negative 1 1 half and 1 or so 1/2
+
+ align:start position:0%
+is 1 negative 1 1 half and 1 or so 1/2
+ 
+
+ align:start position:0%
+is 1 negative 1 1 half and 1 or so 1/2
+negative 1/2 1 negative 1 negative 1/2
+
+ align:start position:0%
+negative 1/2 1 negative 1 negative 1/2
+ 
+
+ align:start position:0%
+negative 1/2 1 negative 1 negative 1/2
+1/2
+
+ align:start position:0%
+1/2
+ 
+
+ align:start position:0%
+1/2
+ok so given that let's try to graph all
+
+ align:start position:0%
+ok so given that let's try to graph all
+ 
+
+ align:start position:0%
+ok so given that let's try to graph all
+these points on this number line into
+
+ align:start position:0%
+these points on this number line into
+ 
+
+ align:start position:0%
+these points on this number line into
+this new brave new dimension by using
+
+ align:start position:0%
+this new brave new dimension by using
+ 
+
+ align:start position:0%
+this new brave new dimension by using
+their cosine sine PI over 4 so all right
+
+ align:start position:0%
+their cosine sine PI over 4 so all right
+ 
+
+ align:start position:0%
+their cosine sine PI over 4 so all right
+great so let's do the pluses first what
+
+ align:start position:0%
+great so let's do the pluses first what
+ 
+
+ align:start position:0%
+great so let's do the pluses first what
+about the plus X 0 is cosine 0 sine 0 so
+
+ align:start position:0%
+about the plus X 0 is cosine 0 sine 0 so
+ 
+
+ align:start position:0%
+about the plus X 0 is cosine 0 sine 0 so
+what is that that's 1 0 that's right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in fact the 8 and the minus 8 are also
+
+ align:start position:0%
+in fact the 8 and the minus 8 are also
+ 
+
+ align:start position:0%
+in fact the 8 and the minus 8 are also
+that times 3 the eight of the minus 8
+
+ align:start position:0%
+that times 3 the eight of the minus 8
+ 
+
+ align:start position:0%
+that times 3 the eight of the minus 8
+are also that because then it's just 2
+
+ align:start position:0%
+are also that because then it's just 2
+ 
+
+ align:start position:0%
+are also that because then it's just 2
+pi n minus 2 pi which well cosine and
+
+ align:start position:0%
+pi n minus 2 pi which well cosine and
+ 
+
+ align:start position:0%
+pi n minus 2 pi which well cosine and
+sine are periodic ok great
+
+ align:start position:0%
+sine are periodic ok great
+ 
+
+ align:start position:0%
+sine are periodic ok great
+what about the one well that's cosine PI
+
+ align:start position:0%
+what about the one well that's cosine PI
+ 
+
+ align:start position:0%
+what about the one well that's cosine PI
+over 4 sine PI over 4 what's that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's root 2 over 2 root 2 over 2 so
+
+ align:start position:0%
+yeah it's root 2 over 2 root 2 over 2 so
+ 
+
+ align:start position:0%
+yeah it's root 2 over 2 root 2 over 2 so
+it's something like here we'll say and
+
+ align:start position:0%
+it's something like here we'll say and
+ 
+
+ align:start position:0%
+it's something like here we'll say and
+in fact the 9 and the 9 and the negative
+
+ align:start position:0%
+in fact the 9 and the 9 and the negative
+ 
+
+ align:start position:0%
+in fact the 9 and the 9 and the negative
+7 are also that so there's three of
+
+ align:start position:0%
+7 are also that so there's three of
+ 
+
+ align:start position:0%
+7 are also that so there's three of
+these two okay what about the negative
+
+ align:start position:0%
+these two okay what about the negative
+ 
+
+ align:start position:0%
+these two okay what about the negative
+one that's cosine negative PI over 4
+
+ align:start position:0%
+one that's cosine negative PI over 4
+ 
+
+ align:start position:0%
+one that's cosine negative PI over 4
+sine PI over 4 that's right the x value
+
+ align:start position:0%
+sine PI over 4 that's right the x value
+ 
+
+ align:start position:0%
+sine PI over 4 that's right the x value
+is positive root 2 over 2 and the y
+
+ align:start position:0%
+is positive root 2 over 2 and the y
+ 
+
+ align:start position:0%
+is positive root 2 over 2 and the y
+value is negative so and again there's
+
+ align:start position:0%
+value is negative so and again there's
+ 
+
+ align:start position:0%
+value is negative so and again there's
+three of them all right great now let's
+
+ align:start position:0%
+three of them all right great now let's
+ 
+
+ align:start position:0%
+three of them all right great now let's
+do the minuses
+
+ align:start position:0%
+do the minuses
+ 
+
+ align:start position:0%
+do the minuses
+there's the minus at 3 which is also the
+
+ align:start position:0%
+there's the minus at 3 which is also the
+ 
+
+ align:start position:0%
+there's the minus at 3 which is also the
+same as I minus at negative 7 minus at 3
+
+ align:start position:0%
+same as I minus at negative 7 minus at 3
+ 
+
+ align:start position:0%
+same as I minus at negative 7 minus at 3
+is cosine 3 PI over 4 sine 3 PI over 4
+
+ align:start position:0%
+is cosine 3 PI over 4 sine 3 PI over 4
+ 
+
+ align:start position:0%
+is cosine 3 PI over 4 sine 3 PI over 4
+which one is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's in a second ah yeah that's
+
+ align:start position:0%
+so that's in a second ah yeah that's
+ 
+
+ align:start position:0%
+so that's in a second ah yeah that's
+going to be the second quadrant we're
+
+ align:start position:0%
+going to be the second quadrant we're
+ 
+
+ align:start position:0%
+going to be the second quadrant we're
+going to have the cosine is going to be
+
+ align:start position:0%
+going to have the cosine is going to be
+ 
+
+ align:start position:0%
+going to have the cosine is going to be
+negative but the sine is going to be
+
+ align:start position:0%
+negative but the sine is going to be
+ 
+
+ align:start position:0%
+negative but the sine is going to be
+positive and so we get three points here
+
+ align:start position:0%
+positive and so we get three points here
+ 
+
+ align:start position:0%
+positive and so we get three points here
+and as you may predicted the other one
+
+ align:start position:0%
+and as you may predicted the other one
+ 
+
+ align:start position:0%
+and as you may predicted the other one
+the 5 PI over 4 is in the third quadrant
+
+ align:start position:0%
+the 5 PI over 4 is in the third quadrant
+ 
+
+ align:start position:0%
+the 5 PI over 4 is in the third quadrant
+we get three points here why are the
+
+ align:start position:0%
+we get three points here why are the
+ 
+
+ align:start position:0%
+we get three points here why are the
+support vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I understand where you're getting
+
+ align:start position:0%
+but I understand where you're getting
+ 
+
+ align:start position:0%
+but I understand where you're getting
+three of these of plus the person's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+already lonely to keep ah there's two
+
+ align:start position:0%
+already lonely to keep ah there's two
+ 
+
+ align:start position:0%
+already lonely to keep ah there's two
+negatives here and there's two natives
+
+ align:start position:0%
+negatives here and there's two natives
+ 
+
+ align:start position:0%
+negatives here and there's two natives
+here good cop doesn't change the problem
+
+ align:start position:0%
+here good cop doesn't change the problem
+ 
+
+ align:start position:0%
+here good cop doesn't change the problem
+in fact if we just grapple points there
+
+ align:start position:0%
+in fact if we just grapple points there
+ 
+
+ align:start position:0%
+in fact if we just grapple points there
+might have been more but there's a very
+
+ align:start position:0%
+might have been more but there's a very
+ 
+
+ align:start position:0%
+might have been more but there's a very
+subtle and important distinction there
+
+ align:start position:0%
+subtle and important distinction there
+ 
+
+ align:start position:0%
+subtle and important distinction there
+are two negatives but otherwise yeah
+
+ align:start position:0%
+are two negatives but otherwise yeah
+ 
+
+ align:start position:0%
+are two negatives but otherwise yeah
+these are grasped correctly does anyone
+
+ align:start position:0%
+these are grasped correctly does anyone
+ 
+
+ align:start position:0%
+these are grasped correctly does anyone
+see where the support vectors are some
+
+ align:start position:0%
+see where the support vectors are some
+ 
+
+ align:start position:0%
+see where the support vectors are some
+popular minus and plus will try to do
+
+ align:start position:0%
+popular minus and plus will try to do
+ 
+
+ align:start position:0%
+popular minus and plus will try to do
+the perpendicular bisector let's see it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that works but guess what these guys are
+
+ align:start position:0%
+that works but guess what these guys are
+ 
+
+ align:start position:0%
+that works but guess what these guys are
+on the same line so we'd better circle
+
+ align:start position:0%
+on the same line so we'd better circle
+ 
+
+ align:start position:0%
+on the same line so we'd better circle
+them so it's actually the question is
+
+ align:start position:0%
+them so it's actually the question is
+ 
+
+ align:start position:0%
+them so it's actually the question is
+what isn't a support vector only this
+
+ align:start position:0%
+what isn't a support vector only this
+ 
+
+ align:start position:0%
+what isn't a support vector only this
+only those big question this is one
+
+ align:start position:0%
+only those big question this is one
+ 
+
+ align:start position:0%
+only those big question this is one
+affection I mean you just proved that
+
+ align:start position:0%
+affection I mean you just proved that
+ 
+
+ align:start position:0%
+affection I mean you just proved that
+actually just show that those land on
+
+ align:start position:0%
+actually just show that those land on
+ 
+
+ align:start position:0%
+actually just show that those land on
+the same line so you really need like
+
+ align:start position:0%
+the same line so you really need like
+ 
+
+ align:start position:0%
+the same line so you really need like
+the cosine term and a side
+
+ align:start position:0%
+the cosine term and a side
+ 
+
+ align:start position:0%
+the cosine term and a side
+just the cosine alright classic is so
+
+ align:start position:0%
+just the cosine alright classic is so
+ 
+
+ align:start position:0%
+just the cosine alright classic is so
+then we've done this in one dimension
+
+ align:start position:0%
+then we've done this in one dimension
+ 
+
+ align:start position:0%
+then we've done this in one dimension
+all we do is do only the cosine so if we
+
+ align:start position:0%
+all we do is do only the cosine so if we
+ 
+
+ align:start position:0%
+all we do is do only the cosine so if we
+did only the cosine then they would have
+
+ align:start position:0%
+did only the cosine then they would have
+ 
+
+ align:start position:0%
+did only the cosine then they would have
+still been divided easily divisible the
+
+ align:start position:0%
+still been divided easily divisible the
+ 
+
+ align:start position:0%
+still been divided easily divisible the
+answer is absolutely we could have
+
+ align:start position:0%
+answer is absolutely we could have
+ 
+
+ align:start position:0%
+answer is absolutely we could have
+however the question did not because
+
+ align:start position:0%
+however the question did not because
+ 
+
+ align:start position:0%
+however the question did not because
+Susan Q random student decided to do
+
+ align:start position:0%
+Susan Q random student decided to do
+ 
+
+ align:start position:0%
+Susan Q random student decided to do
+cosine inside but yes if we had said you
+
+ align:start position:0%
+cosine inside but yes if we had said you
+ 
+
+ align:start position:0%
+cosine inside but yes if we had said you
+654 student find a fine that will work
+
+ align:start position:0%
+654 student find a fine that will work
+ 
+
+ align:start position:0%
+654 student find a fine that will work
+for this you could have found a Phi that
+
+ align:start position:0%
+for this you could have found a Phi that
+ 
+
+ align:start position:0%
+for this you could have found a Phi that
+was just cosine that would be easier
+
+ align:start position:0%
+was just cosine that would be easier
+ 
+
+ align:start position:0%
+was just cosine that would be easier
+however it's important to be able to
+
+ align:start position:0%
+however it's important to be able to
+ 
+
+ align:start position:0%
+however it's important to be able to
+work with what somebody else gives you
+
+ align:start position:0%
+work with what somebody else gives you
+ 
+
+ align:start position:0%
+work with what somebody else gives you
+in this case they gave you they give you
+
+ align:start position:0%
+in this case they gave you they give you
+ 
+
+ align:start position:0%
+in this case they gave you they give you
+that transformation which yeah was a
+
+ align:start position:0%
+that transformation which yeah was a
+ 
+
+ align:start position:0%
+that transformation which yeah was a
+wasteful with an extra dimension you
+
+ align:start position:0%
+wasteful with an extra dimension you
+ 
+
+ align:start position:0%
+wasteful with an extra dimension you
+didn't need the sine because you didn't
+
+ align:start position:0%
+didn't need the sine because you didn't
+ 
+
+ align:start position:0%
+didn't need the sine because you didn't
+need the y-axis really here you just
+
+ align:start position:0%
+need the y-axis really here you just
+ 
+
+ align:start position:0%
+need the y-axis really here you just
+needed the X does everyone see this how
+
+ align:start position:0%
+needed the X does everyone see this how
+ 
+
+ align:start position:0%
+needed the X does everyone see this how
+this works can maybe transform
+
+ align:start position:0%
+this works can maybe transform
+ 
+
+ align:start position:0%
+this works can maybe transform
+dimensions the main hardest part is
+
+ align:start position:0%
+dimensions the main hardest part is
+ 
+
+ align:start position:0%
+dimensions the main hardest part is
+they'll usually give you a K and ask for
+
+ align:start position:0%
+they'll usually give you a K and ask for
+ 
+
+ align:start position:0%
+they'll usually give you a K and ask for
+a fire or give you a fire ask for a K
+
+ align:start position:0%
+a fire or give you a fire ask for a K
+ 
+
+ align:start position:0%
+a fire or give you a fire ask for a K
+it's not too bad just remember if they
+
+ align:start position:0%
+it's not too bad just remember if they
+ 
+
+ align:start position:0%
+it's not too bad just remember if they
+give you a Phi do a dot product with it
+
+ align:start position:0%
+give you a Phi do a dot product with it
+ 
+
+ align:start position:0%
+give you a Phi do a dot product with it
+and if they give you a fire that's just
+
+ align:start position:0%
+and if they give you a fire that's just
+ 
+
+ align:start position:0%
+and if they give you a fire that's just
+one component dot product of one
+
+ align:start position:0%
+one component dot product of one
+ 
+
+ align:start position:0%
+one component dot product of one
+component just multiplying it together
+
+ align:start position:0%
+component just multiplying it together
+ 
+
+ align:start position:0%
+component just multiplying it together
+easy enough so they give you a K treat
+
+ align:start position:0%
+easy enough so they give you a K treat
+ 
+
+ align:start position:0%
+easy enough so they give you a K treat
+it as a dot product and try to
+
+ align:start position:0%
+it as a dot product and try to
+ 
+
+ align:start position:0%
+it as a dot product and try to
+reverse-engineer it's usually something
+
+ align:start position:0%
+reverse-engineer it's usually something
+ 
+
+ align:start position:0%
+reverse-engineer it's usually something
+like this that's easy to
+
+ align:start position:0%
+like this that's easy to
+ 
+
+ align:start position:0%
+like this that's easy to
+reverse-engineer I really haven't seen
+
+ align:start position:0%
+reverse-engineer I really haven't seen
+ 
+
+ align:start position:0%
+reverse-engineer I really haven't seen
+it where it's not so it may look it
+
+ align:start position:0%
+it where it's not so it may look it
+ 
+
+ align:start position:0%
+it where it's not so it may look it
+often looks like the scariest problem
+
+ align:start position:0%
+often looks like the scariest problem
+ 
+
+ align:start position:0%
+often looks like the scariest problem
+but it's usually not too bad to go
+
+ align:start position:0%
+but it's usually not too bad to go
+ 
+
+ align:start position:0%
+but it's usually not too bad to go
+between five and KS does anyone have any
+
+ align:start position:0%
+between five and KS does anyone have any
+ 
+
+ align:start position:0%
+between five and KS does anyone have any
+questions on anything that we did on
+
+ align:start position:0%
+questions on anything that we did on
+ 
+
+ align:start position:0%
+questions on anything that we did on
+spectrum change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but what is some what's the intuition
+
+ align:start position:0%
+but what is some what's the intuition
+ 
+
+ align:start position:0%
+but what is some what's the intuition
+behind the building like we solve it and
+
+ align:start position:0%
+behind the building like we solve it and
+ 
+
+ align:start position:0%
+behind the building like we solve it and
+figure out numbers integrations what is
+
+ align:start position:0%
+figure out numbers integrations what is
+ 
+
+ align:start position:0%
+figure out numbers integrations what is
+it but what is intuition what is w w is
+
+ align:start position:0%
+it but what is intuition what is w w is
+ 
+
+ align:start position:0%
+it but what is intuition what is w w is
+the dividing line it's the drop-dead
+
+ align:start position:0%
+the dividing line it's the drop-dead
+ 
+
+ align:start position:0%
+the dividing line it's the drop-dead
+dividing line when I say the drop-dead
+
+ align:start position:0%
+dividing line when I say the drop-dead
+ 
+
+ align:start position:0%
+dividing line when I say the drop-dead
+dividing line you like those big bold
+
+ align:start position:0%
+dividing line you like those big bold
+ 
+
+ align:start position:0%
+dividing line you like those big bold
+solid lines over there those are you're
+
+ align:start position:0%
+solid lines over there those are you're
+ 
+
+ align:start position:0%
+solid lines over there those are you're
+pretty certain lines everything passed
+
+ align:start position:0%
+pretty certain lines everything passed
+ 
+
+ align:start position:0%
+pretty certain lines everything passed
+that was a minus and you're doing your
+
+ align:start position:0%
+that was a minus and you're doing your
+ 
+
+ align:start position:0%
+that was a minus and you're doing your
+training is that everything has to plus
+
+ align:start position:0%
+training is that everything has to plus
+ 
+
+ align:start position:0%
+training is that everything has to plus
+the big bold line there was a plus in
+
+ align:start position:0%
+the big bold line there was a plus in
+ 
+
+ align:start position:0%
+the big bold line there was a plus in
+your training separate the dotted line
+
+ align:start position:0%
+your training separate the dotted line
+ 
+
+ align:start position:0%
+your training separate the dotted line
+is the one you're really going to use in
+
+ align:start position:0%
+is the one you're really going to use in
+ 
+
+ align:start position:0%
+is the one you're really going to use in
+the test data in the test data when push
+
+ align:start position:0%
+the test data in the test data when push
+ 
+
+ align:start position:0%
+the test data in the test data when push
+comes to shove you might get something
+
+ align:start position:0%
+comes to shove you might get something
+ 
+
+ align:start position:0%
+comes to shove you might get something
+that's inside of that gutter and if it's
+
+ align:start position:0%
+that's inside of that gutter and if it's
+ 
+
+ align:start position:0%
+that's inside of that gutter and if it's
+on the say of that one up there it's on
+
+ align:start position:0%
+on the say of that one up there it's on
+ 
+
+ align:start position:0%
+on the say of that one up there it's on
+the up left side that dotted line you're
+
+ align:start position:0%
+the up left side that dotted line you're
+ 
+
+ align:start position:0%
+the up left side that dotted line you're
+going to call it a plus so that dotted
+
+ align:start position:0%
+going to call it a plus so that dotted
+ 
+
+ align:start position:0%
+going to call it a plus so that dotted
+line is your decision boundary and that
+
+ align:start position:0%
+line is your decision boundary and that
+ 
+
+ align:start position:0%
+line is your decision boundary and that
+is that is basically the idea and in
+
+ align:start position:0%
+is that is basically the idea and in
+ 
+
+ align:start position:0%
+is that is basically the idea and in
+fact the way that the algorithm would do
+
+ align:start position:0%
+fact the way that the algorithm would do
+ 
+
+ align:start position:0%
+fact the way that the algorithm would do
+it on the computer is it would contract
+
+ align:start position:0%
+it on the computer is it would contract
+ 
+
+ align:start position:0%
+it on the computer is it would contract
+the optimize the Alfa's which messes
+
+ align:start position:0%
+the optimize the Alfa's which messes
+ 
+
+ align:start position:0%
+the optimize the Alfa's which messes
+around with the dotted line and by
+
+ align:start position:0%
+around with the dotted line and by
+ 
+
+ align:start position:0%
+around with the dotted line and by
+quadratically i'll math-amazing the out
+
+ align:start position:0%
+quadratically i'll math-amazing the out
+ 
+
+ align:start position:0%
+quadratically i'll math-amazing the out
+those alphas you see how the alphas add
+
+ align:start position:0%
+those alphas you see how the alphas add
+ 
+
+ align:start position:0%
+those alphas you see how the alphas add
+up to a w it just checks it around and
+
+ align:start position:0%
+up to a w it just checks it around and
+ 
+
+ align:start position:0%
+up to a w it just checks it around and
+eventually it finds Oh making the alpha
+
+ align:start position:0%
+eventually it finds Oh making the alpha
+ 
+
+ align:start position:0%
+eventually it finds Oh making the alpha
+of this one zero makes that that makes
+
+ align:start position:0%
+of this one zero makes that that makes
+ 
+
+ align:start position:0%
+of this one zero makes that that makes
+it a better optimization you're trying
+
+ align:start position:0%
+it a better optimization you're trying
+ 
+
+ align:start position:0%
+it a better optimization you're trying
+to get the widest possible road it would
+
+ align:start position:0%
+to get the widest possible road it would
+ 
+
+ align:start position:0%
+to get the widest possible road it would
+eventually come out to this this is
+
+ align:start position:0%
+eventually come out to this this is
+ 
+
+ align:start position:0%
+eventually come out to this this is
+trivial for a human to eyeball but some
+
+ align:start position:0%
+trivial for a human to eyeball but some
+ 
+
+ align:start position:0%
+trivial for a human to eyeball but some
+real problems with two hundred data
+
+ align:start position:0%
+real problems with two hundred data
+ 
+
+ align:start position:0%
+real problems with two hundred data
+points that have to get one or two of
+
+ align:start position:0%
+points that have to get one or two of
+ 
+
+ align:start position:0%
+points that have to get one or two of
+them wrong classified and so you may be
+
+ align:start position:0%
+them wrong classified and so you may be
+ 
+
+ align:start position:0%
+them wrong classified and so you may be
+using a quadratic kernel or something
+
+ align:start position:0%
+using a quadratic kernel or something
+ 
+
+ align:start position:0%
+using a quadratic kernel or something
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+you can't do that you just can't well
+
+ align:start position:0%
+you can't do that you just can't well
+ 
+
+ align:start position:0%
+you can't do that you just can't well
+maybe you can in which case you should
+
+ align:start position:0%
+maybe you can in which case you should
+ 
+
+ align:start position:0%
+maybe you can in which case you should
+be getting a MacArthur Fellowship or
+
+ align:start position:0%
+be getting a MacArthur Fellowship or
+ 
+
+ align:start position:0%
+be getting a MacArthur Fellowship or
+something like that but the computer
+
+ align:start position:0%
+something like that but the computer
+ 
+
+ align:start position:0%
+something like that but the computer
+can't and the basic idea is when it
+
+ align:start position:0%
+can't and the basic idea is when it
+ 
+
+ align:start position:0%
+can't and the basic idea is when it
+comes down to it it figures out the
+
+ align:start position:0%
+comes down to it it figures out the
+ 
+
+ align:start position:0%
+comes down to it it figures out the
+Alpha is to give it the bet the best W
+
+ align:start position:0%
+Alpha is to give it the bet the best W
+ 
+
+ align:start position:0%
+Alpha is to give it the bet the best W
+for widest road in the W is your
+
+ align:start position:0%
+for widest road in the W is your
+ 
+
+ align:start position:0%
+for widest road in the W is your
+decision about it good question any
+
+ align:start position:0%
+decision about it good question any
+ 
+
+ align:start position:0%
+decision about it good question any
+other questions about our old friend SVM
+
+ align:start position:0%
+other questions about our old friend SVM
+ 
+
+ align:start position:0%
+other questions about our old friend SVM
+I have a question for you um after
+
+ align:start position:0%
+I have a question for you um after
+ 
+
+ align:start position:0%
+I have a question for you um after
+seeing this and let's pretend that they
+
+ align:start position:0%
+seeing this and let's pretend that they
+ 
+
+ align:start position:0%
+seeing this and let's pretend that they
+only ask you to solve for WS B's you
+
+ align:start position:0%
+only ask you to solve for WS B's you
+ 
+
+ align:start position:0%
+only ask you to solve for WS B's you
+know these kind of criminals and Pfizer
+
+ align:start position:0%
+know these kind of criminals and Pfizer
+ 
+
+ align:start position:0%
+know these kind of criminals and Pfizer
+typical things how many people now think
+
+ align:start position:0%
+typical things how many people now think
+ 
+
+ align:start position:0%
+typical things how many people now think
+that you can go through and work an SVM
+
+ align:start position:0%
+that you can go through and work an SVM
+ 
+
+ align:start position:0%
+that you can go through and work an SVM
+problem alright we've got we've got a
+
+ align:start position:0%
+problem alright we've got we've got a
+ 
+
+ align:start position:0%
+problem alright we've got we've got a
+few we
+
+ align:start position:0%
+few we
+ 
+
+ align:start position:0%
+few we
+a happy few band of brothers maybe eight
+
+ align:start position:0%
+a happy few band of brothers maybe eight
+ 
+
+ align:start position:0%
+a happy few band of brothers maybe eight
+people raised their hand there that's
+
+ align:start position:0%
+people raised their hand there that's
+ 
+
+ align:start position:0%
+people raised their hand there that's
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+how many people know what a support
+
+ align:start position:0%
+how many people know what a support
+ 
+
+ align:start position:0%
+how many people know what a support
+vector is now that's really good because
+
+ align:start position:0%
+vector is now that's really good because
+ 
+
+ align:start position:0%
+vector is now that's really good because
+that if that's all you learn from
+
+ align:start position:0%
+that if that's all you learn from
+ 
+
+ align:start position:0%
+that if that's all you learn from
+today's minor sensation is still good
+
+ align:start position:0%
+today's minor sensation is still good
+ 
+
+ align:start position:0%
+today's minor sensation is still good
+it really is I'm telling you I had to
+
+ align:start position:0%
+it really is I'm telling you I had to
+ 
+
+ align:start position:0%
+it really is I'm telling you I had to
+take two classes on this and then ta it
+
+ align:start position:0%
+take two classes on this and then ta it
+ 
+
+ align:start position:0%
+take two classes on this and then ta it
+before I really really understood it so
+
+ align:start position:0%
+before I really really understood it so
+ 
+
+ align:start position:0%
+before I really really understood it so
+you guys are ahead of me all right take
+
+ align:start position:0%
+you guys are ahead of me all right take
+ 
+
+ align:start position:0%
+you guys are ahead of me all right take
+care have a great weekend and we'll see
+
+ align:start position:0%
+care have a great weekend and we'll see
+ 
+
+ align:start position:0%
+care have a great weekend and we'll see
+you for boosting and vampires next week
\ No newline at end of file
diff --git a/6uLKZSoHnrc.txt b/6uLKZSoHnrc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..735e59356fdc01ce48470e6259f0559b8bc6bc85
--- /dev/null
+++ b/6uLKZSoHnrc.txt
@@ -0,0 +1,1977 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR NELSON: Well, so last
+time we did a little bit
+
+more work on thermodynamic
+cycles, and basically went
+
+around a cycle and looked at
+some state functions, delta u
+
+and delta H. Saw that around
+a closed cycle those zero
+
+because they're state
+functions.
+
+So if you start and end at the
+same place, they've got end at
+
+the same place that
+they started.
+
+There's no change in them, and
+then we also looked at some at
+
+non-state functions, work and
+heat, and saw that those
+
+aren't zero going
+around a cycle.
+
+Of course you can do work in a
+cyclic process, and heat can
+
+be exchanged with the
+environment at the same time.
+
+So we calculated those
+values too.
+
+And we also looked at this other
+funny function that's
+
+our special function.
+
+We looked at this integral dq
+over T. It's so special that
+
+we called this derivative dS,
+and saw that at least for the
+
+cycle we looked at, it
+also behaved as a
+
+state function behaves.
+
+That is, going around the cycle,
+it had no net change,
+
+and we'll see this come
+back later on.
+
+Then we went on to look at
+thermochemistry, and that's
+
+what I want to continue today.
+
+So really, the main result that
+we saw last time is that
+
+we can describe the enthalpy
+of reaction, so if we have
+
+reactants going to products, and
+we'd like to know our heat
+
+of reaction or enthalpy of
+reaction, remember it's a
+
+constant pressure as we're
+considering it, so it's
+
+equivalent to heat of reaction,
+than the way we can
+
+do this is construct a cycle
+where we're going to express
+
+these in terms of their
+constituent elements.
+
+We're going to all the way
+back to the atoms.
+
+Right, so if we have the
+elements in their standard
+
+states, that is their most
+stable forms at room
+
+temperature and pressure, then
+what we're really doing is
+
+we're saying let's take the
+reactants and let's pull them
+
+all apart into their
+separate elements,
+
+they're separate atoms.
+
+And then put them back together
+this way, and we'll
+
+calculate the enthalpy
+of this process, the
+
+enthalpy of this process.
+
+It's a cycle, so that'll
+give us the enthalpy of
+
+reaction, all right?
+
+So this delta H is our sum for
+delta H of formation for the
+
+reactants, right.
+
+And this is our sum of
+the quantity for
+
+the products, right.
+
+And in this way, then we can
+express our delta H of
+
+reaction is just going to be
+given a sum of the heats of
+
+formation or the difference
+between the heats of formation
+
+of the products and the
+reactants, right?
+
+Now, of course, we have to
+weight this by the number of
+
+moles of each reactant
+to each product
+
+involved in the reaction.
+
+So to write this a little more
+carefully, it's, you want to
+
+write the sum over i of nu i
+delta H naught of formation of
+
+i summed over the products.
+
+This is per mole minus sum over
+i, nu i here over the
+
+reactants in the
+same quantity.
+
+Delta H per mole f i, right?
+
+So in other words, were taking
+each of the products and we're
+
+going to weight them by their
+stoichiomeric coefficients,
+
+and we're going to have in this
+delta H of reaction their
+
+heats of formation, and then
+we're going to have the
+
+negative heats of formation of
+the reactants, because that's
+
+being subtracted, okay?
+
+So, just to go through a basic
+example, let's just look at
+
+the burning of methane.
+
+So we've got methane gas,
+combining with oxygen gas, so
+
+you have carbon dioxide gas and
+liquid water, and we'll
+
+consider the whole thing
+at room temperature
+
+and pressure, right.
+
+So let's just undertake
+this set of processes.
+
+Let's decompose these
+to the elements.
+
+So in other words, our methane
+gas, we're going to write the
+
+chemical equilibrium between
+this and the solid carbon.
+
+That is to say let's specify
+graphite, it's not diamond,
+
+right, graphite is the stable
+form of carbon at room
+
+temperature and pressure.
+
+And then, hydrogen gas two
+moles of hydrogen gas and
+
+we're going to have a delta
+H of formation.
+
+This is for CH4 in the
+gas phase, right?
+
+And then over here, we have our
+oxygen but 2 O2 gas going
+
+to, well 2 O2 gas -- the point
+is oxygen already is in it's
+
+stable form at room temperature
+
+and pressure, right?
+
+That is the elemental form of
+oxygen, of course, is as
+
+oxygen molecules in the gas so
+there's no delta H formation
+
+for oxygen.
+
+The gas is zero, right.
+
+And then second phase of this,
+now we're going to take the
+
+elements that we've produced,
+and we're going to put them
+
+back to make products, right?
+
+So there we've got carbon as
+graphite, and a solid plus an
+
+oxygen gas goes to make
+CO2 gas, right.
+
+And we've got our positive
+delta H of formation
+
+associated with that.
+
+And finally we've got hydrogen
+gas plus oxygen gas giving us
+
+two water molecules and this
+is in the liquid phase, and
+
+there's some delta heat of
+formation associated with
+
+that, okay.
+
+So there is our set of
+individual processes that's
+
+going to constitute
+our cycle, right.
+
+If we take the combination of
+all those, which is to say we
+
+just take both steps in this
+cycle, then we'll have our net
+
+reaction, which is to say
+we'll have this, right.
+
+So what that says is our heat
+of reaction is our heat of
+
+formation per mole of
+CO2 gas, right.
+
+Plus 2 times the heat of
+reaction or heat of formation
+
+per mole of liquid water minus
+heat of formation per mole of
+
+methane, right.
+
+And things we can
+easily look up.
+
+So in a simple way, we can
+determine, we can calculate
+
+what the heat of
+reaction is for
+
+something like this, right.
+
+And you'll see in the back
+of your book, you'll see
+
+moderately extensive tables of
+heats of formation, and if you
+
+go online you'll see, you can
+find extremely extensive
+
+tabulated values of heats of
+formation, that have been
+
+measured for an enormous
+number of compounds.
+
+And from that, then you can look
+at enthalpies of reaction
+
+for countless numbers
+of reactions, right.
+
+So by using the tabulated data,
+we can really determined
+
+heats of formation for most
+reactions that you might
+
+contemplate, OK?
+
+Of course, the cyclic steps that
+we've taken to do this
+
+apply not just for breaking
+down reactants and product
+
+into the elements in their
+standards states, but of
+
+course we could also look at
+whole sets of reactions and
+
+write cycles as well, right.
+
+So for example, if we wanted
+to look at the reaction of
+
+something like carbon graphite
+plus oxygen gas to make carbon
+
+monoxide gas, well normally
+this isn't the way the
+
+reaction would work.
+
+Normally if you just tried to
+make this happen what you
+
+would wind up with the
+CO2, not CO, right.
+
+But one way to approach this
+is you could look at the
+
+individual reactions of going,
+you could go to CO2 and then
+
+you can go with CO2 and oxygen
+and combine, or combine CO and
+
+oxygen to get CO2, right?
+
+So normally, CO2 is formed, but
+you could calculate the
+
+heat of reaction.
+
+Of course you could go back to
+the elements, but you can also
+
+say well, let's just take a
+known heat of reaction for, or
+
+heat of formation for CO2, and
+then also combine that with
+
+the heat of reaction for CO plus
+oxygen forming CO2 and
+
+determine this that way, all
+right, OK, so once you have
+
+done this, once we've got the
+heat of reaction then there
+
+are a few simple results
+that are useful.
+
+One is we know immediately
+whether when we run a reaction
+
+heat is going to be released
+in the process out to the
+
+environment, or whether
+heat is going to
+
+be taken in, right.
+
+So, and of course if you ever
+used a hot pack or a chemical
+
+hot pack or cold pack, you've
+seen examples of the two of
+
+those, where the constituents
+are selected to give you
+
+either heat released or
+heat taken up, right.
+
+So in particular delta H of
+reaction less than zero, that
+
+means a negative amount of heat,
+which means that heat is
+
+released, right.
+
+Yes, that is it's exothermic.
+
+Positive enthalpy of reaction,
+which is to say a heat of
+
+reaction is positive.
+
+Remember the way we define heat
+is positive it means that
+
+there is heat that is coming
+from the environment into the
+
+system, right.
+
+In other words heat is absorbed
+or taken up by the
+
+reacting system.
+
+That's endothermic, okay.
+
+All right, one more important
+aspect of this that we need to
+
+be able to deal with, and that
+is the heats of formation that
+
+you'll find tabulated typically
+are going to be
+
+given for room temperature
+and pressure.
+
+And it's very common that you
+might want to know the
+
+thermodynamic condition for
+reactions, especially at other
+
+temperatures, very common,
+of course.
+
+And it's not hard to see how the
+heat of reaction at room
+
+temperature can be related to
+they heat of reaction at other
+
+temperatures.
+
+So let's just look at that.
+
+So remember your fundamental
+relation, dH, if you write
+
+that as a function of
+temperature and pressure,
+
+partial of H with respect to T,
+constant pressure, dT, plus
+
+partial of H with respect to p
+at constant temperature, dp.
+
+But if we're working
+at constant
+
+pressure then dp is zero.
+
+So we just got the derivative
+with respect to temperature.
+
+That's our heat capacity,
+right, Cp.
+
+And we may have tabulated values
+of Cp for an enormous
+
+number of materials.
+
+So now, if we look at the
+temperature dependence of
+
+delta H for reaction, really
+what we're going to need to do
+
+is look at how that heat
+capacity changes going from
+
+reactants to products, right?
+
+So in other words, d delta H of
+reaction, with respect to
+
+temperature.
+
+That's what we want to
+find out, right?
+
+So how does delta H change if
+we change the temperature?
+
+Well, it's just given by Cp dT
+for the reactants and the
+
+products, right?
+
+For the products minus the
+reaction, that is it's delta
+
+Cp, we need the sum
+over the products.
+
+Nu i, Cp i minus same
+sum over reactants,
+
+i, nu i Cp i, right.
+
+Similar to what we saw before.
+
+Now we need to integrate,
+right.
+
+So if we integrate between some
+pair of temperatures, T1
+
+and T2, we do this and we have
+this quantity, d delta H of
+
+reaction with respect to
+temperature, dT, all this is
+
+at constant pressure, right.
+
+Let's just be careful
+to specify that.
+
+Well, so of course, this is then
+just delta H of reaction
+
+at T2 minus delta H
+of reaction at T1.
+
+This is looking good.
+
+This is what we want to get,
+is our heat of reaction at
+
+some new temperature T2.
+
+If we already know it at some
+initial temperature, usually
+
+room temperature, T1.
+
+And it's just given by the
+integral from T1 to T2 of
+
+delta Cp dT.
+
+Now in general, this is as far
+as we can go, but at least if
+
+the temperature change isn't
+too big, for most materials
+
+that heat capacities doesn't
+depend very strongly on
+
+temperature, right.
+
+If you take some material, and
+you measure its heat capacity,
+
+right, how much heat do I have
+to put into it in order to
+
+change its temperature
+by a degree, right.
+
+And I make that measurement
+at room temperature.
+
+And then maybe I raise the
+temperature to whatever, room
+
+temperature, maybe 20 degrees
+hotter than room temperature.
+
+And I again say OK, now how much
+heat do I need to raise
+
+this thing's temperature
+by 1 degree?
+
+The amount of heat I need to put
+in to do that is not very
+
+different from what it was at
+room temperature right.
+
+In other words the
+heat capacity
+
+didn't change very much.
+
+So, the result of that is
+that at least for modest
+
+temperature excursions, it may
+be the case that we can
+
+simplify this and simply say
+it's just the difference in
+
+heat capacities times the
+temperature change.
+
+Again, we can't always be
+assured of that, but it's
+
+often the case.
+
+Any questions on any
+of this so far?
+
+OK, now what I want to do is
+just describe a little bit of
+
+how do you measure all
+this stuff, right?
+
+So what we've done so far is
+just lay out in principle how
+
+we should describe heats of
+reaction, and of course
+
+assuming that we've got
+everything in tables we can
+
+always look them up, but
+sometimes you want to make new
+
+compounds, right.
+
+Sometimes you'd like to know
+what the energetics are
+
+involved there, right, and so
+it's useful to be able to
+
+actually measure something.
+
+So how do we do It?
+
+This is what's called
+calorimetry.
+
+So we're going to make
+measurements to determine heat
+
+of reaction values.
+
+Actually, calorimetry is used
+for all sorts of things.
+
+It can be used to determine, for
+example, the energetics of
+
+phase transitions.
+
+Maybe you're not looking at a
+reaction, but you've got some
+
+new compound, and you're looking
+at it go from liquid
+
+to solid or to gas.
+
+And you can see what the heat
+involved in a process like
+
+that is as well.
+
+So what happens?
+
+Well, the objective in the case
+of a reaction, we have
+
+reactants at some temperature
+going to products at that
+
+temperature, and that is our
+heat of reaction at that
+
+temperature.
+
+That's how it's defined,
+right, at constant
+
+temperature.
+
+OK?
+
+What do we actually measure?
+
+Well, what we can really do is
+we can put the reactants in
+
+some container, put the whole
+thing in an insulated place,
+
+you know, hold things in
+a big insulated box.
+
+Run the reaction.
+
+Maybe it produces heat.
+
+If it does, then the whole thing
+will heat up, right?
+
+The stuff that's inside the
+reacting volume, and
+
+whatever's right around it there
+inside the big box, it's
+
+all going to heat up.
+
+So I'll start at some initial
+temperature, T1.
+
+I won't end up at the
+same temperature.
+
+It'll be hotter.
+
+How much hotter?
+
+Well, that depends on how
+much heat was produced.
+
+So in principle, if I measure
+how much hotter, I can
+
+determine how much heat was
+produced, and from that, I
+
+should be able to calculate
+delta H at T1.
+
+So let's think about how
+that's really working.
+
+I've really got reactants at T1,
+plus a calorimeter at T1,
+
+and I'm going to end up with
+products -- well let's let me
+
+just write that's over.
+
+In fact, let's start by just
+putting a little sketch of the
+
+whole thing up.
+
+So here's my reacting stuff,
+maybe it's a liquid.
+
+It's going to take
+place in there.
+
+It's going to be a constant
+pressure, it might be open to
+
+the air, or even if it isn't,
+there might be plenty of room,
+
+and it's a liquid anyway, so
+the pressure isn't going to
+
+change significantly.
+
+I want to measure
+the temperature.
+
+And the whole thing is
+insulated right.
+
+I don't want to have to deal
+with heat escaping to the
+
+outside environment in a way
+that might be difficult or
+
+complicated to measure
+or calculate.
+
+OK, so this, what I've sketched
+here would be a
+
+constant pressure calorimeter.
+
+There's a reaction.
+
+Normally this is used for a
+reaction in the condensed
+
+phases and liquid usually.
+
+So this is a constant pressure
+calorimeter.
+
+It's set up to be
+
+well-insulated so it's adiabatic.
+
+That's the set up.
+
+We're going to run the
+reactants, the reaction.
+
+The reactants are going
+to turn into products.
+
+Let's look at what happens.
+
+So what happens is my
+reactants at T1 plus
+
+calorimeter at T1 turn into
+products at T2 plus my
+
+calorimeter at T2, right.
+
+That's my process.
+
+That's what really happens.
+
+Now that, the enthalpy of that
+process isn't what I want,
+
+right, because the temperature
+has changed, also the
+
+calorimeter is heated up.
+
+So I need to relate this
+to what I do want.
+
+Let's label this one.
+
+It is adiabatic.
+
+It is taking place inside this
+thing, and it's a constant
+
+pressure, and we'll do
+it reversibly, right.
+
+So that's what we've got.
+
+Now, we can always take these
+things the products and the
+
+calorimeter at temperature T2
+and cool them or warm them to
+
+get to products plus calorimeter
+at T1, right.
+
+Let's label that two.
+
+It's still at constant
+pressure.
+
+It's reversible.
+
+It's a temperature change.
+
+Now to make that happen, it's
+not adiabatic, right.
+
+If I wanted to do that, I'd
+need a heating element or
+
+something to cool, so I could
+make that temperature change
+
+happen, right.
+
+Well, so now I can complete
+the cycle.
+
+I've got reactants and
+calorimeter at T1.
+
+Fewer products and calorimeter
+at T1, right.
+
+Calorimeter doesn't change
+in this process.
+
+So here I've got some delta H
+associated with changing the
+
+temperature.
+
+This delta H though, this
+is what I want.
+
+This is delta H of reaction
+at T1, right?
+
+It's isothermal, constant
+pressure, reversible.
+
+Just what I want.
+
+That's how I've defined
+delta H of reaction.
+
+This is what I'm after.
+
+All right, so now let's see how
+we execute it, and do the
+
+calculations that allow
+us to calculate this.
+
+So, one, what's delta
+H in step one?
+
+Yes, exactly, it's adiabatic,
+right constant pressure.
+
+it's zero.
+
+Delta H1 is zero, right.
+
+What we're really going to do in
+practice is we're going to
+
+measure, we're going to use our
+thermometer and say great,
+
+how much did the temperature
+change, right.
+
+So now, then we're going to use
+what we're going to learn
+
+from step two in order to
+calculate this part, what we
+
+could call step three.
+
+OK, so two, that's
+the crucial part.
+
+It's constant pressure.
+
+It's just given by the
+corresponding heat, and it's
+
+just a temperature
+change, right.
+
+So we know how to do this,
+integral from well it's T1 to
+
+T2, depending on which way
+we go of Cp for the
+
+whole system dT.
+
+OK?
+
+It's just how much heat is
+involved when we change the
+
+temperature.
+
+Now, the products have some heat
+capacity associated with
+
+them right, it takes a certain
+amount of heat if we make
+
+their temperature change, to
+either put it in or take it
+
+away, depending on which
+direction the
+
+temperature is changing.
+
+Same with the calorimeter, OK.
+
+In actual practice though, the
+calorimeter, is going to be
+
+this big hunk of metal, and
+really what's going to,
+
+there's going to be some stuff
+in here, right, they'll be a
+
+fluid, it will usually
+be some sort of oil.
+
+There's a pretty big
+thermal mass.
+
+Now we run the reaction
+and it produces heat.
+
+Most of the heat is going to
+warm up or cool off all that
+
+oil and stuff.
+
+There's a moderate amount
+of material
+
+in the actual reaction.
+
+You want to design the
+calorimeter to fulfill that
+
+condition,
+
+Of course, you can't make it
+so enormous that even for,
+
+that for any ordinary reaction
+there's not even a measurable
+
+temperature change, right,
+because if you have your
+
+enough oil to fill up this room,
+it would take a huge
+
+amount of heat to change it by
+even a tiny, it's temperature
+
+but even a tiny amount.
+
+So the calorimeter is designed
+sort of to scale to match the
+
+maybe the ordinary volume of
+reactants that you'll put in
+
+there, such that, pretty much
+all the heat's just going to
+
+heat up the calorimeter, and
+there's only a small amount
+
+that's going toward heating
+up the products, right.
+
+So in general, or at least
+usually it'll be the case,
+
+that this is approximately equal
+to integral from T1 to
+
+T2 Cp of just the
+calorimeter dT.
+
+And that generally is just given
+by the heat capacity the
+
+calorimeter times
+delta T, right..
+
+Because the heat capacity of the
+calorimeter just like this
+
+thing is not strongly
+temperature dependent, OK.
+
+So the point is we can calculate
+delta H associated
+
+with this process pretty
+readily, OK.
+
+That leaves three, right.
+
+But delta H for step three must
+just be the opposite of
+
+this delta H because this was
+zero and we know that were
+
+going around a cycle, right.
+
+And that's our heat
+of reaction.
+
+So we're going to be able
+to do this, right?
+
+OK, now this is one way to
+do calorimetry, and it's
+
+practical as long as all the
+materials are in condensed
+
+phases, solids and liquids.
+
+If gases are involved it can
+work, but it can be tricky to
+
+keep the pressure constant,
+right, because that means that
+
+now the moles of gas might be
+changing, and that means in
+
+some way the volume has
+to be adjustable.
+
+You'd need some sort of balloon
+or membrane that will
+
+allow that to happen.
+
+Could be done, but easier is to
+just do the whole thing at
+
+constant volume, right, and just
+run the reaction that way
+
+and redo the calculation to be
+a constant volume rather than
+
+constant pressure calorimeter,
+right.
+
+And it's not hard to do that.
+
+So let's just look at what
+happens in that case.
+
+It's almost the same.
+
+So let's see, just to finish the
+job here though, all this
+
+says is delta H of reaction is
+just negative Cp for the
+
+calorimeter times delta T, all
+right. so that's what we think
+
+we know in constant pressure
+calorimetry.
+
+Yes, and if we have gases
+involved, it's pretty similar,
+
+but now what will have is
+something like this.
+
+We'll have a reaction vessel
+that's sealed,
+
+it's constant volume.
+
+That'll be inside
+our calorimeter.
+
+It's insulated, and there's
+still a thermometer, so we can
+
+measure the temperature.
+
+So this is still adiabatic.
+
+It's insulated, but now it's
+constant volume, OK.
+
+Now, you know with constant
+volume, now it's not going to
+
+be delta H that's
+straightforward to measure,
+
+it's going to be dealt
+u, all right.
+
+But it's going to be almost
+the same, right?
+
+So let's just think about
+what happens here.
+
+Now it's the cycle that
+we've got will still
+
+basically look the same.
+
+That is its reactants at T1 plus
+calorimeter at T1, going
+
+to products at T2 plus
+calorimeter at T2, right?
+
+And it's still adiabatic, but
+now it's constant volume.
+
+And it's also reversal right.
+
+So this is our process one.
+
+Now, process two, we're going
+to end up here with our
+
+products, again at T1 plus our
+calorimeter at T1, right.
+
+So now we have a
+constant volume
+
+reversible temperature change.
+
+And so this part now isn't
+exactly what we want to
+
+determine delta H, because it's
+a isothermal constant
+
+volume, reversible products or
+reversible process that takes
+
+a reactant to T1 to
+a product of T1.
+
+What these are going to give
+us are delta u values.
+
+This'll give us delta u of
+reaction, right, T1, right.
+
+It's a constant volume.
+
+All right, so in the end, we're
+going to determine delta
+
+u here, and then in the end,
+we're going to have to relate
+
+that to delta H, but that's
+straight forward enough to do.
+
+So let's look at how we'll
+analyze what happens.
+
+So one adiabatic, constant
+volume process, right.
+
+What's zero in that case?
+
+In this case delta
+H was zero in the
+
+constant pressure example.
+
+Now we've got a constant
+volume process.
+
+What's zero?
+
+It's u, because u is to q plus
+w right, heat and work, but
+
+it's adiabatic.
+
+So there's no heat, exchange
+with the environment, and it's
+
+constant volume, so there's
+no p dV work, right.
+
+So q is zero adiabatic.
+
+Work is zero.
+
+Delta u1 is zero.
+
+And again just in the constant
+pressure case, what happens
+
+that we're going to measure in
+step one, which is to say in
+
+actually running the
+reaction is the
+
+temperature's going to change.
+
+Right?
+
+The whole thing's going to come
+to some new equilibrium
+
+temperature between the products
+and the oil or
+
+whatever's around it, and we're
+going to measure that.
+
+OK, two, now it's a temperature
+change, right?
+
+We know how to calculate delta
+u for a temperature change.
+
+It's very similar here, but
+what's going to be different
+
+from the case with constant
+pressure?
+
+There's a real important detail
+that's different if you
+
+want to calculate what happens
+at constant pressure when you
+
+change the temperature?
+
+What happens at constant
+volume?
+
+Looking at this expression,
+what's got to be different?
+
+Cv, right.
+
+We're not going to have the
+constant pressure heat
+
+capacity, we're going to have
+the constant volume heat
+
+capacity, right.
+
+So delta u for step two, that's
+our q under constant
+
+volume conditions, integral
+from T1 to T2 Cv for our
+
+whole system dT.
+
+Integral from T2 to T2, and now
+I can separate again the
+
+calorimeter from the product,
+and at least approximately,
+
+again, it'll be Cv for the
+calorimeter dT, which is to
+
+say then it's Cv of
+the calorimeter
+
+times delta T. Great.
+
+Three, well delta u1 was zero.
+
+Delta u2 was there Cv delta T,
+so now all we need since the
+
+whole thing is going around in
+a cycle, Since we know delta
+
+u3 must be negative delta u2,
+and that is our delta u of
+
+reaction, right?
+
+So delta u of reaction is
+approximately equal to
+
+negative Cv for the calorimeter
+times delta T. So,
+
+this is what we're going to
+measure, and this is what
+
+we're going to determine.
+
+And now we're almost done,
+except what we really want is
+
+delta H and not delta
+V, right.
+
+So now we're going to use the
+fact that H is u plus pV.
+
+Delta H is delta u plus delta
+pV, and now this is all at
+
+constant temperature
+in the end, right?
+
+We've determined delta u for
+some temperature T1, right.
+
+So what happens then
+we're going to use
+
+the ideal gas law.
+
+So it's approximately delta
+u plus delta nRT.
+
+That's a constant.
+
+That's a constant.
+
+So it's delta u plus RT, we can
+say T1 is the temperature
+
+we've used here, delta
+n of the gas.
+
+In other words, what matters
+here in changing the pressure
+
+volume product?
+
+What matters is we turned some
+reactants into some products.
+
+How many moles of gas are
+there in each case, in
+
+reactants and products?
+
+If that changes, of course you
+know that the pressure in
+
+there is going to change at
+constant volume if the amount
+
+of gas in there is changing.
+
+And nothing else is going
+to make a significant
+
+contribution to it, OK?
+
+So finally, then delta H of
+reaction for our temperature
+
+T1 is approximately minus Cv of
+the calorimeter times delta
+
+T plus R T1 delta n of gas.
+
+Change of the number of
+moles of gas, right.
+
+We're going to measure that,
+and now we're going to
+
+determine this.
+
+In practice, we'll already know
+the heat capacity of our
+
+calorimeter, when we
+buy it, right?
+
+So we don't really need to put
+in a certain amount of heat
+
+and change the temperature
+of the products and the
+
+calorimeter and so on.
+
+What we need to do is just
+measure how much the
+
+temperature changed, OK.
+
+It's worth getting just sort of
+roughly calibrated how big
+
+is this compared to the
+rest of this stuff.
+
+That is, how different
+is delta u from
+
+delta H, all right.
+
+And of course it's
+straightforward to do this,
+
+and I've written this out in the
+notes, so I won't re-write
+
+the numbers here.
+
+But I gave an example
+looking at combining
+
+HCl and oxygen right.
+
+So 4 HCl plus oxygen gas.
+
+This two in the gas going to
+water and the liquid, plus
+
+chlorine gas at room
+temperature.
+
+Well, what you find out is delta
+u of reaction is minus
+
+195 kilojoules for the
+reaction as written.
+
+And it turns out, as written, if
+you say OK, how much, what
+
+changed for the pV product?
+
+Well here we've got four moles
+of gas, five moles of gas.
+
+Here just two, so we changed
+the number of
+
+moles of gas by three.
+
+All right, how much did
+it matter, right?
+
+Well it matters.
+
+It's measurable.
+
+So now delta H of reaction
+turns out to be minus 202
+
+kilojoules.
+
+So, you know, seven out of a
+couple of a hundred, right, a
+
+few percent, kind of typical.
+
+In other words, if you look
+at energetics of ordinary
+
+reactions where you're, you
+know, you're making and
+
+breaking covalent bonds, there's
+a fair amount of
+
+energy stored in those, right?
+
+The additional change due to
+changing pressure volume is
+
+certainly measurable.
+
+You don't want to just ignore
+it, but in cases like that,
+
+it's usually a small fraction
+of the total.
+
+A few percent is
+typical, okay.
+
+All right, let me just go
+through one numerical example
+
+of a calorimetry calculation,
+OK.
+
+I won't put all the numbers up
+on the board because our time
+
+is running short, but I just
+want to outline it.
+
+All I really want to do is
+calibrate you a little bit for
+
+what happens with ordinary
+calorimeter heat capacities
+
+that makes the calculation
+turn out to be relatively
+
+easy, right.
+
+So let's just write it out.
+
+Let's take iron sulfide as a
+solid, plus 11 halves oxygen
+
+gas to make iron oxide,
+also a solid, plus
+
+sulphur dioxide gas.
+
+All right.
+
+We'll start at T1
+is 298 Kelvin.
+
+T2, maybe we don't know
+it yet, right.
+
+OK, so we know how to calculate
+what's going to
+
+happen, delta H and delta u,
+because we can look up the
+
+heats of formation and
+so forth of all
+
+the compounds, right.
+
+So if we do that, what we
+discover is that delta H of
+
+formation whoops, something's
+wrong here.
+
+This is sulphur -- what am I
+doing, boy, S and it's a two,
+
+sorry, and the heat of formation
+is minus 180
+
+kilojoules per mole, that's
+oxygen, it's zero.
+
+Boy, I'm, I don't know what is
+about this reaction that's
+
+vexing me but it's not
+that complicated.
+
+Here it's minus 824 kilojoules
+per mole minus 297 kilojoules
+
+per mole, right.
+
+So that's our input
+thermodynamic data.
+
+So first of all, let's just
+do a heat of reaction
+
+calculation, right.
+
+Taking the product minus
+the reaction, right.
+
+So it's minus 824 plus 4
+times minus 297 minus
+
+2 times minus 180.
+
+Right?
+
+In other words I've got the
+stoichiometric coefficients in
+
+there and the values, and I'm
+subtracting the reactants from
+
+products wind up with minus
+1652 kilojoules per mole.
+
+Well, it depends on what we
+write, what we consider mole,
+
+right, maybe I should just write
+kilojoules as written.
+
+OK, I'm going to skip the delta
+and get the change in
+
+moles of gas calculation.
+
+It's straightforward to do.
+
+What I really want to do is just
+give an example of what
+
+happens when you throw the
+thing, the material into a
+
+calorimeter and see how much
+the temperature changes.
+
+So let's imagine we start with
+0.1 moles of our iron sulfide,
+
+and then we have a
+stoichiometric amount of
+
+oxygen, and the whole thing is
+done in a constant volume
+
+calorimeter, and we
+see what happens.
+
+Now the crucial element is what
+is the heat capacity of
+
+the calorimeter, right?
+
+And it's, again it's a
+macroscopic pretty big thing,
+
+so typical might be 10
+kilojoules per Kelvin, and
+
+that's pretty big, right?
+
+Noticed that's not
+per mole, right.
+
+I mean the calorimeter is a big
+thing filled the little
+
+oil or whatever is
+inside it, right?
+
+And it's for that whole
+unit that you've
+
+got some heat capacity.
+
+How much heat does it take the
+warm the entire thing up or
+
+the insides of the thing
+up by a degree?
+
+It's that number right.
+
+Ordinary heat capacities are
+in Joule's per Kelvin mole,
+
+not kilojoules, right.
+
+And what that's telling you is
+probably your reactants and
+
+products, so the amount of
+heat that's involved in
+
+changing the air temperature
+is going to be negligible
+
+compared to what happens to
+the whole calorimeter.
+
+OK?
+
+So now if we say, OK, we we've
+done this calculation starting
+
+with 2 moles of this, but now
+we're going to be at 0.1 mole,
+
+so we're going to need to
+divide by 20, right.
+
+So instead of minus 1652, it's
+going to turn out delta u is
+
+minus 1648 kilojoules, so, and
+then divide by twenty, we end
+
+up with minus 82.4 kilojoules,
+that is, that's the delta u of
+
+reaction for what happens if
+you'd put in not two moles of
+
+this, but 0.1 mole
+of this, right.
+
+Practical amounts is the reason
+I'm using numbers like
+
+this, right.
+
+So now, what's delta T?
+
+Well here's Cv, right, so delta
+T is just our minus 10
+
+kilojoules per degree oh sorry,
+it's our minus 82.4
+
+kilojoules.
+
+That's the heat released,
+divided by minus 10 or 10
+
+kilojoules per Kelvin, right.
+
+It's 8.2 Kelvin.
+
+In other words, how much does
+the temperature of the whole
+
+thing change when you put an
+ordinary amount of material in
+
+there and run a reaction,
+right.
+
+Well, what do you do?
+
+You calculate how much heat is
+released in the reaction.
+
+And then what's going to matter
+is what's the heat
+
+capacity of the whole,
+of the calorimeter?
+
+I didn't even need to know
+that heat capacity of the
+
+product, right.
+
+Because it's effect the thermal
+mass of the product is
+
+negligible compared to the
+thermal mass of the
+
+calorimeter.
+
+Now in real practice, I'll do
+the calculation in reverse.
+
+I'll measure how much the
+temperature changed in the
+
+calorimeter, right.
+
+I'll know the heat capacity,
+and what I'll really be
+
+calculating is OK, how much heat
+must have been released
+
+in the reaction to make that
+temperature change happen?
+
+And that in the case of constant
+volume, in this case
+
+that's my delta u, and then
+I'll add my little delta n
+
+term to get delta H.
+
+Any questions on calorimetry?
+
+OK.
+
+See you Friday.
+
+We'll finish on calorimetry and
+thermochemistry and then
+
+we'll start in on one of the
+really most difficult topics
+
+that we'll deal with all
+semester, which is a second
+
+law and our special function
+that we've seen just a little
+
+bit so far.
\ No newline at end of file
diff --git a/75PZmUc0TK0.txt b/75PZmUc0TK0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..93d921ff6357d9b8aa5f13c6454336e0f91ea509
--- /dev/null
+++ b/75PZmUc0TK0.txt
@@ -0,0 +1,8739 @@
+align:start position:0%
+ 
+Uh last time we talked about the picard
+
+ align:start position:0%
+Uh last time we talked about the picard
+ 
+
+ align:start position:0%
+Uh last time we talked about the picard
+uh lindelof theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so this theorem is about uh
+
+ align:start position:0%
+And so this theorem is about uh
+ 
+
+ align:start position:0%
+And so this theorem is about uh
+solutions uh to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to ODEs.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so specifically it's it's asking
+
+ align:start position:0%
+And so specifically it's it's asking
+ 
+
+ align:start position:0%
+And so specifically it's it's asking
+that so you have a function uh f
+
+ align:start position:0%
+that so you have a function uh f
+ 
+
+ align:start position:0%
+that so you have a function uh f
+and a function g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh f here is is is differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the derivative of of f as well as g
+
+ align:start position:0%
+and the derivative of of f as well as g
+ 
+
+ align:start position:0%
+and the derivative of of f as well as g
+are continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the problem is that you're
+
+ align:start position:0%
+And then the problem is that you're
+ 
+
+ align:start position:0%
+And then the problem is that you're
+looking for solutions. So you want a
+
+ align:start position:0%
+looking for solutions. So you want a
+ 
+
+ align:start position:0%
+looking for solutions. So you want a
+solution. So looking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y to the OD
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where the and the OD is that the
+
+ align:start position:0%
+where the and the OD is that the
+ 
+
+ align:start position:0%
+where the and the OD is that the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+should be equal to f of y.
+
+ align:start position:0%
+should be equal to f of y.
+ 
+
+ align:start position:0%
+should be equal to f of y.
+So at some point uh x
+
+ align:start position:0%
+So at some point uh x
+ 
+
+ align:start position:0%
+So at some point uh x
+uh the derivative of y should be equal
+
+ align:start position:0%
+uh the derivative of y should be equal
+ 
+
+ align:start position:0%
+uh the derivative of y should be equal
+to f of y of x plus g of x
+
+ align:start position:0%
+to f of y of x plus g of x
+ 
+
+ align:start position:0%
+to f of y of x plus g of x
+and uh you are looking for that uh that
+
+ align:start position:0%
+and uh you are looking for that uh that
+ 
+
+ align:start position:0%
+and uh you are looking for that uh that
+this function that y of zero say is
+
+ align:start position:0%
+this function that y of zero say is
+ 
+
+ align:start position:0%
+this function that y of zero say is
+equal to a. Okay. So this is what's
+
+ align:start position:0%
+equal to a. Okay. So this is what's
+ 
+
+ align:start position:0%
+equal to a. Okay. So this is what's
+called the initial condition,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+right? And this is so the this is equal
+
+ align:start position:0%
+right? And this is so the this is equal
+ 
+
+ align:start position:0%
+right? And this is so the this is equal
+to that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so in order to uh so we want ex you
+
+ align:start position:0%
+And so in order to uh so we want ex you
+ 
+
+ align:start position:0%
+And so in order to uh so we want ex you
+uh existence. So want
+
+ align:start position:0%
+uh existence. So want
+ 
+
+ align:start position:0%
+uh existence. So want
+existence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uniqueness.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So existence just means that there is a
+
+ align:start position:0%
+So existence just means that there is a
+ 
+
+ align:start position:0%
+So existence just means that there is a
+solution for a given a there is a
+
+ align:start position:0%
+solution for a given a there is a
+ 
+
+ align:start position:0%
+solution for a given a there is a
+solution. Uniqueness means that if you
+
+ align:start position:0%
+solution. Uniqueness means that if you
+ 
+
+ align:start position:0%
+solution. Uniqueness means that if you
+have two solutions
+
+ align:start position:0%
+have two solutions
+ 
+
+ align:start position:0%
+have two solutions
+uh to this uh od then they will have to
+
+ align:start position:0%
+uh to this uh od then they will have to
+ 
+
+ align:start position:0%
+uh to this uh od then they will have to
+coincide.
+
+ align:start position:0%
+coincide.
+ 
+
+ align:start position:0%
+coincide.
+And so uh we uh the way we were setting
+
+ align:start position:0%
+And so uh we uh the way we were setting
+ 
+
+ align:start position:0%
+And so uh we uh the way we were setting
+it up was that we were using so using
+
+ align:start position:0%
+it up was that we were using so using
+ 
+
+ align:start position:0%
+it up was that we were using so using
+the contracting mapping theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the contracting mapping theorem is
+
+ align:start position:0%
+So the contracting mapping theorem is
+ 
+
+ align:start position:0%
+So the contracting mapping theorem is
+the following that if you take a metric
+
+ align:start position:0%
+the following that if you take a metric
+ 
+
+ align:start position:0%
+the following that if you take a metric
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+X and this metric space is so X comma D
+
+ align:start position:0%
+X and this metric space is so X comma D
+ 
+
+ align:start position:0%
+X and this metric space is so X comma D
+is a metric space is a cushy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh metric space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh then a contracting map. So a
+
+ align:start position:0%
+uh then a contracting map. So a
+ 
+
+ align:start position:0%
+uh then a contracting map. So a
+contracting map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um is a map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t from this metric space into itself.
+
+ align:start position:0%
+t from this metric space into itself.
+ 
+
+ align:start position:0%
+t from this metric space into itself.
+So that um um and a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C strictly less than one. So that if you
+
+ align:start position:0%
+C strictly less than one. So that if you
+ 
+
+ align:start position:0%
+C strictly less than one. So that if you
+measure the distance between the images,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the images are squeezed together. So
+
+ align:start position:0%
+the images are squeezed together. So
+ 
+
+ align:start position:0%
+the images are squeezed together. So
+this means that the the distance between
+
+ align:start position:0%
+this means that the the distance between
+ 
+
+ align:start position:0%
+this means that the the distance between
+the images is this constant that is
+
+ align:start position:0%
+the images is this constant that is
+ 
+
+ align:start position:0%
+the images is this constant that is
+strictly less than one times the
+
+ align:start position:0%
+strictly less than one times the
+ 
+
+ align:start position:0%
+strictly less than one times the
+distance between x and y. So this is a
+
+ align:start position:0%
+distance between x and y. So this is a
+ 
+
+ align:start position:0%
+distance between x and y. So this is a
+contracting map.
+
+ align:start position:0%
+contracting map.
+ 
+
+ align:start position:0%
+contracting map.
+And the contracting mapping theorem say.
+
+ align:start position:0%
+And the contracting mapping theorem say.
+ 
+
+ align:start position:0%
+And the contracting mapping theorem say.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the contracting mapping theorem uh is
+
+ align:start position:0%
+So the contracting mapping theorem uh is
+ 
+
+ align:start position:0%
+So the contracting mapping theorem uh is
+is the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh there exist if you have a cushy
+
+ align:start position:0%
+that uh there exist if you have a cushy
+ 
+
+ align:start position:0%
+that uh there exist if you have a cushy
+complete metric space and you have a
+
+ align:start position:0%
+complete metric space and you have a
+ 
+
+ align:start position:0%
+complete metric space and you have a
+contracting map like this then uh t
+
+ align:start position:0%
+contracting map like this then uh t
+ 
+
+ align:start position:0%
+contracting map like this then uh t
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+a unique
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fix point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and remember that a fixed point. So a
+
+ align:start position:0%
+and remember that a fixed point. So a
+ 
+
+ align:start position:0%
+and remember that a fixed point. So a
+fixed point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a x in this space so that t
+
+ align:start position:0%
+this is a x in this space so that t
+ 
+
+ align:start position:0%
+this is a x in this space so that t
+leaves it invariant.
+
+ align:start position:0%
+leaves it invariant.
+ 
+
+ align:start position:0%
+leaves it invariant.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And so we proved this we proved the
+
+ align:start position:0%
+And so we proved this we proved the
+ 
+
+ align:start position:0%
+And so we proved this we proved the
+contracting mapping theorem last time.
+
+ align:start position:0%
+contracting mapping theorem last time.
+ 
+
+ align:start position:0%
+contracting mapping theorem last time.
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+how were we going to use this for this
+
+ align:start position:0%
+how were we going to use this for this
+ 
+
+ align:start position:0%
+how were we going to use this for this
+OD?
+
+ align:start position:0%
+OD?
+ 
+
+ align:start position:0%
+OD?
+So we define so if if um if I here is an
+
+ align:start position:0%
+So we define so if if um if I here is an
+ 
+
+ align:start position:0%
+So we define so if if um if I here is an
+interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+containing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+containing uh
+
+ align:start position:0%
+containing uh
+ 
+
+ align:start position:0%
+containing uh
+a zero. Then we defined uh
+
+ align:start position:0%
+a zero. Then we defined uh
+ 
+
+ align:start position:0%
+a zero. Then we defined uh
+n u is a function. So n u and sorry y is
+
+ align:start position:0%
+n u is a function. So n u and sorry y is
+ 
+
+ align:start position:0%
+n u is a function. So n u and sorry y is
+a continuous function.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Then we defined t of y. So this is a
+
+ align:start position:0%
+Then we defined t of y. So this is a
+ 
+
+ align:start position:0%
+Then we defined t of y. So this is a
+continuous function on on the interval
+
+ align:start position:0%
+continuous function on on the interval
+ 
+
+ align:start position:0%
+continuous function on on the interval
+on i.
+
+ align:start position:0%
+on i.
+ 
+
+ align:start position:0%
+on i.
+Then we defined a another continuous
+
+ align:start position:0%
+Then we defined a another continuous
+ 
+
+ align:start position:0%
+Then we defined a another continuous
+function on the same interval as follow
+
+ align:start position:0%
+function on the same interval as follow
+ 
+
+ align:start position:0%
+function on the same interval as follow
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+t of y. So this is going to be a
+
+ align:start position:0%
+t of y. So this is going to be a
+ 
+
+ align:start position:0%
+t of y. So this is going to be a
+continuous function.
+
+ align:start position:0%
+continuous function.
+ 
+
+ align:start position:0%
+continuous function.
+So in in x
+
+ align:start position:0%
+So in in x
+ 
+
+ align:start position:0%
+So in in x
+this thing here is this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because we want it to have value at zero
+
+ align:start position:0%
+because we want it to have value at zero
+ 
+
+ align:start position:0%
+because we want it to have value at zero
+a and then we're integrating from zero
+
+ align:start position:0%
+a and then we're integrating from zero
+ 
+
+ align:start position:0%
+a and then we're integrating from zero
+to x of f
+
+ align:start position:0%
+to x of f
+ 
+
+ align:start position:0%
+to x of f
+of uh y of s
+
+ align:start position:0%
+of uh y of s
+ 
+
+ align:start position:0%
+of uh y of s
+plus g of s
+
+ align:start position:0%
+plus g of s
+ 
+
+ align:start position:0%
+plus g of s
+ds Right.
+
+ align:start position:0%
+ds Right.
+ 
+
+ align:start position:0%
+ds Right.
+And so this
+
+ align:start position:0%
+And so this
+ 
+
+ align:start position:0%
+And so this
+so this here gives you a map from t
+
+ align:start position:0%
+so this here gives you a map from t
+ 
+
+ align:start position:0%
+so this here gives you a map from t
+gives you a map from the continuous
+
+ align:start position:0%
+gives you a map from the continuous
+ 
+
+ align:start position:0%
+gives you a map from the continuous
+function on this interval into the
+
+ align:start position:0%
+function on this interval into the
+ 
+
+ align:start position:0%
+function on this interval into the
+continuous function on the interval.
+
+ align:start position:0%
+continuous function on the interval.
+ 
+
+ align:start position:0%
+continuous function on the interval.
+And it also has the property that if you
+
+ align:start position:0%
+And it also has the property that if you
+ 
+
+ align:start position:0%
+And it also has the property that if you
+take a function
+
+ align:start position:0%
+take a function
+ 
+
+ align:start position:0%
+take a function
+and you evaluate it at zero then you get
+
+ align:start position:0%
+and you evaluate it at zero then you get
+ 
+
+ align:start position:0%
+and you evaluate it at zero then you get
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+okay. And now we observe that in fact
+
+ align:start position:0%
+okay. And now we observe that in fact
+ 
+
+ align:start position:0%
+okay. And now we observe that in fact
+this the image here
+
+ align:start position:0%
+this the image here
+ 
+
+ align:start position:0%
+this the image here
+the image is if you define when you
+
+ align:start position:0%
+the image is if you define when you
+ 
+
+ align:start position:0%
+the image is if you define when you
+define it like this by the fundamental
+
+ align:start position:0%
+define it like this by the fundamental
+ 
+
+ align:start position:0%
+define it like this by the fundamental
+theorem of calculus this function here
+
+ align:start position:0%
+theorem of calculus this function here
+ 
+
+ align:start position:0%
+theorem of calculus this function here
+is differentiable.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this function is so it actually takes
+
+ align:start position:0%
+So this function is so it actually takes
+ 
+
+ align:start position:0%
+So this function is so it actually takes
+so t actually takes
+
+ align:start position:0%
+so t actually takes
+ 
+
+ align:start position:0%
+so t actually takes
+the space of continuous functions
+
+ align:start position:0%
+the space of continuous functions
+ 
+
+ align:start position:0%
+the space of continuous functions
+into the space of functions that are not
+
+ align:start position:0%
+into the space of functions that are not
+ 
+
+ align:start position:0%
+into the space of functions that are not
+just continuous but actually
+
+ align:start position:0%
+just continuous but actually
+ 
+
+ align:start position:0%
+just continuous but actually
+differentiable
+
+ align:start position:0%
+differentiable
+ 
+
+ align:start position:0%
+differentiable
+and even the derivative is continuous
+
+ align:start position:0%
+and even the derivative is continuous
+ 
+
+ align:start position:0%
+and even the derivative is continuous
+and the ones that are
+
+ align:start position:0%
+and the ones that are
+ 
+
+ align:start position:0%
+and the ones that are
+um so this here is a space of functions.
+
+ align:start position:0%
+um so this here is a space of functions.
+ 
+
+ align:start position:0%
+um so this here is a space of functions.
+So this is functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that are um that are where where the
+
+ align:start position:0%
+that are um that are where where the
+ 
+
+ align:start position:0%
+that are um that are where where the
+functions y so that y prime exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+right and so now what we saw last time
+
+ align:start position:0%
+right and so now what we saw last time
+ 
+
+ align:start position:0%
+right and so now what we saw last time
+was that by the fundamental theorem of
+
+ align:start position:0%
+was that by the fundamental theorem of
+ 
+
+ align:start position:0%
+was that by the fundamental theorem of
+calculus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of calculus.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So by the fundamental therm
+
+ align:start position:0%
+Right? So by the fundamental therm
+ 
+
+ align:start position:0%
+Right? So by the fundamental therm
+calculus the derivative of this function
+
+ align:start position:0%
+calculus the derivative of this function
+ 
+
+ align:start position:0%
+calculus the derivative of this function
+if you take y and you take t of it this
+
+ align:start position:0%
+if you take y and you take t of it this
+ 
+
+ align:start position:0%
+if you take y and you take t of it this
+is now a function and it's
+
+ align:start position:0%
+is now a function and it's
+ 
+
+ align:start position:0%
+is now a function and it's
+differentiable and the derivative is f
+
+ align:start position:0%
+differentiable and the derivative is f
+ 
+
+ align:start position:0%
+differentiable and the derivative is f
+of y.
+
+ align:start position:0%
+of y.
+ 
+
+ align:start position:0%
+of y.
+So at x it's f of y of x plus g of x.
+
+ align:start position:0%
+So at x it's f of y of x plus g of x.
+ 
+
+ align:start position:0%
+So at x it's f of y of x plus g of x.
+And so this means that if so if
+
+ align:start position:0%
+And so this means that if so if
+ 
+
+ align:start position:0%
+And so this means that if so if
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+is a fixed point
+
+ align:start position:0%
+is a fixed point
+ 
+
+ align:start position:0%
+is a fixed point
+for the map t. So if it's a fixed point,
+
+ align:start position:0%
+for the map t. So if it's a fixed point,
+ 
+
+ align:start position:0%
+for the map t. So if it's a fixed point,
+this just means that t of y is equal to
+
+ align:start position:0%
+this just means that t of y is equal to
+ 
+
+ align:start position:0%
+this just means that t of y is equal to
+y. Well then
+
+ align:start position:0%
+y. Well then
+ 
+
+ align:start position:0%
+y. Well then
+then this thing here is the derivative
+
+ align:start position:0%
+then this thing here is the derivative
+ 
+
+ align:start position:0%
+then this thing here is the derivative
+of y. So then it means that y here
+
+ align:start position:0%
+of y. So then it means that y here
+ 
+
+ align:start position:0%
+of y. So then it means that y here
+solves the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. We have already checked that the
+
+ align:start position:0%
+right. We have already checked that the
+ 
+
+ align:start position:0%
+right. We have already checked that the
+initial value we did that uh somewhere
+
+ align:start position:0%
+initial value we did that uh somewhere
+ 
+
+ align:start position:0%
+initial value we did that uh somewhere
+here we already checked that the initial
+
+ align:start position:0%
+here we already checked that the initial
+ 
+
+ align:start position:0%
+here we already checked that the initial
+value is what it should be and if it's a
+
+ align:start position:0%
+value is what it should be and if it's a
+ 
+
+ align:start position:0%
+value is what it should be and if it's a
+fixed point then the derivative is also
+
+ align:start position:0%
+fixed point then the derivative is also
+ 
+
+ align:start position:0%
+fixed point then the derivative is also
+what it should be. Right?
+
+ align:start position:0%
+what it should be. Right?
+ 
+
+ align:start position:0%
+what it should be. Right?
+Okay. So we want to find a fixed point
+
+ align:start position:0%
+Okay. So we want to find a fixed point
+ 
+
+ align:start position:0%
+Okay. So we want to find a fixed point
+and so what we did last time was that we
+
+ align:start position:0%
+and so what we did last time was that we
+ 
+
+ align:start position:0%
+and so what we did last time was that we
+saw that if we if we restrict the
+
+ align:start position:0%
+saw that if we if we restrict the
+ 
+
+ align:start position:0%
+saw that if we if we restrict the
+interval.
+
+ align:start position:0%
+interval.
+ 
+
+ align:start position:0%
+interval.
+So last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we proved is that if we restrict
+
+ align:start position:0%
+what we proved is that if we restrict
+ 
+
+ align:start position:0%
+what we proved is that if we restrict
+the interval. So last time we showed
+
+ align:start position:0%
+the interval. So last time we showed
+ 
+
+ align:start position:0%
+the interval. So last time we showed
+so we set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m here equal to a absolute value of a +
+
+ align:start position:0%
+m here equal to a absolute value of a +
+ 
+
+ align:start position:0%
+m here equal to a absolute value of a +
+2.
+
+ align:start position:0%
+2.
+ 
+
+ align:start position:0%
+2.
+And then we saw that there exist a delta
+
+ align:start position:0%
+And then we saw that there exist a delta
+ 
+
+ align:start position:0%
+And then we saw that there exist a delta
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at delta zero greater than zero. So that
+
+ align:start position:0%
+at delta zero greater than zero. So that
+ 
+
+ align:start position:0%
+at delta zero greater than zero. So that
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+if you restrict to the interval if
+
+ align:start position:0%
+if you restrict to the interval if
+ 
+
+ align:start position:0%
+if you restrict to the interval if
+you're looking at the interval of
+
+ align:start position:0%
+you're looking at the interval of
+ 
+
+ align:start position:0%
+you're looking at the interval of
+continuous function so the interval of
+
+ align:start position:0%
+continuous function so the interval of
+ 
+
+ align:start position:0%
+continuous function so the interval of
+continuous function on this little
+
+ align:start position:0%
+continuous function on this little
+ 
+
+ align:start position:0%
+continuous function on this little
+interval.
+
+ align:start position:0%
+interval.
+ 
+
+ align:start position:0%
+interval.
+So this is a interval around zero and
+
+ align:start position:0%
+So this is a interval around zero and
+ 
+
+ align:start position:0%
+So this is a interval around zero and
+you're looking at this map.
+
+ align:start position:0%
+you're looking at this map.
+ 
+
+ align:start position:0%
+you're looking at this map.
+Then this map here well first of all we
+
+ align:start position:0%
+Then this map here well first of all we
+ 
+
+ align:start position:0%
+Then this map here well first of all we
+already know that it takes this the
+
+ align:start position:0%
+already know that it takes this the
+ 
+
+ align:start position:0%
+already know that it takes this the
+space of continuous function into the
+
+ align:start position:0%
+space of continuous function into the
+ 
+
+ align:start position:0%
+space of continuous function into the
+space of continuous function. But we
+
+ align:start position:0%
+space of continuous function. But we
+ 
+
+ align:start position:0%
+space of continuous function. But we
+have something more that we have that if
+
+ align:start position:0%
+have something more that we have that if
+ 
+
+ align:start position:0%
+have something more that we have that if
+you're looking at the subspace of this
+
+ align:start position:0%
+you're looking at the subspace of this
+ 
+
+ align:start position:0%
+you're looking at the subspace of this
+which is a space of functions y that are
+
+ align:start position:0%
+which is a space of functions y that are
+ 
+
+ align:start position:0%
+which is a space of functions y that are
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you also require that the norm here
+
+ align:start position:0%
+and you also require that the norm here
+ 
+
+ align:start position:0%
+and you also require that the norm here
+is lesser equal to m.
+
+ align:start position:0%
+is lesser equal to m.
+ 
+
+ align:start position:0%
+is lesser equal to m.
+Then takes
+
+ align:start position:0%
+Then takes
+ 
+
+ align:start position:0%
+Then takes
+this space here into itself. Right? This
+
+ align:start position:0%
+this space here into itself. Right? This
+ 
+
+ align:start position:0%
+this space here into itself. Right? This
+is this lema that we proved last time,
+
+ align:start position:0%
+is this lema that we proved last time,
+ 
+
+ align:start position:0%
+is this lema that we proved last time,
+right? And and so okay.
+
+ align:start position:0%
+right? And and so okay.
+ 
+
+ align:start position:0%
+right? And and so okay.
+So so this this space here, right? You
+
+ align:start position:0%
+So so this this space here, right? You
+ 
+
+ align:start position:0%
+So so this this space here, right? You
+can think about this space here as we
+
+ align:start position:0%
+can think about this space here as we
+ 
+
+ align:start position:0%
+can think about this space here as we
+did last time as then we defined we
+
+ align:start position:0%
+did last time as then we defined we
+ 
+
+ align:start position:0%
+did last time as then we defined we
+defined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we define
+
+ align:start position:0%
+we define
+ 
+
+ align:start position:0%
+we define
+uh capital R equal to
+
+ align:start position:0%
+uh capital R equal to
+ 
+
+ align:start position:0%
+uh capital R equal to
+uh no actually so we we defined uh we
+
+ align:start position:0%
+uh no actually so we we defined uh we
+ 
+
+ align:start position:0%
+uh no actually so we we defined uh we
+looked at the balls I guess just on on
+
+ align:start position:0%
+looked at the balls I guess just on on
+ 
+
+ align:start position:0%
+looked at the balls I guess just on on
+this so we looked at the ball of
+
+ align:start position:0%
+this so we looked at the ball of
+ 
+
+ align:start position:0%
+this so we looked at the ball of
+freighers capital n
+
+ align:start position:0%
+freighers capital n
+ 
+
+ align:start position:0%
+freighers capital n
+in in in this around the zero function.
+
+ align:start position:0%
+in in in this around the zero function.
+ 
+
+ align:start position:0%
+in in in this around the zero function.
+So this thing here is the closed ball
+
+ align:start position:0%
+So this thing here is the closed ball
+ 
+
+ align:start position:0%
+So this thing here is the closed ball
+in the space of continuous function with
+
+ align:start position:0%
+in the space of continuous function with
+ 
+
+ align:start position:0%
+in the space of continuous function with
+the metric that we've been using and
+
+ align:start position:0%
+the metric that we've been using and
+ 
+
+ align:start position:0%
+the metric that we've been using and
+this set here we can think about if we
+
+ align:start position:0%
+this set here we can think about if we
+ 
+
+ align:start position:0%
+this set here we can think about if we
+want as this set. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now what we have is so we have
+
+ align:start position:0%
+Okay. So now what we have is so we have
+ 
+
+ align:start position:0%
+Okay. So now what we have is so we have
+so the setup now is that we want to find
+
+ align:start position:0%
+so the setup now is that we want to find
+ 
+
+ align:start position:0%
+so the setup now is that we want to find
+a fixed point for this map T right we
+
+ align:start position:0%
+a fixed point for this map T right we
+ 
+
+ align:start position:0%
+a fixed point for this map T right we
+have a space that we want to look at and
+
+ align:start position:0%
+have a space that we want to look at and
+ 
+
+ align:start position:0%
+have a space that we want to look at and
+the space is again now we're going to
+
+ align:start position:0%
+the space is again now we're going to
+ 
+
+ align:start position:0%
+the space is again now we're going to
+think about so just to so this is the
+
+ align:start position:0%
+think about so just to so this is the
+ 
+
+ align:start position:0%
+think about so just to so this is the
+space we're looking at but this is what
+
+ align:start position:0%
+space we're looking at but this is what
+ 
+
+ align:start position:0%
+space we're looking at but this is what
+we before have denoted like the ball in
+
+ align:start position:0%
+we before have denoted like the ball in
+ 
+
+ align:start position:0%
+we before have denoted like the ball in
+this metric space it's a centered at the
+
+ align:start position:0%
+this metric space it's a centered at the
+ 
+
+ align:start position:0%
+this metric space it's a centered at the
+function function that is constant zero
+
+ align:start position:0%
+function function that is constant zero
+ 
+
+ align:start position:0%
+function function that is constant zero
+and this is the radius right
+
+ align:start position:0%
+and this is the radius right
+ 
+
+ align:start position:0%
+and this is the radius right
+and so I'm I'm now looking at this
+
+ align:start position:0%
+and so I'm I'm now looking at this
+ 
+
+ align:start position:0%
+and so I'm I'm now looking at this
+this map so we have now shown that it
+
+ align:start position:0%
+this map so we have now shown that it
+ 
+
+ align:start position:0%
+this map so we have now shown that it
+take this metric ball into itself okay
+
+ align:start position:0%
+take this metric ball into itself okay
+ 
+
+ align:start position:0%
+take this metric ball into itself okay
+and I want to find a fixed point want to
+
+ align:start position:0%
+and I want to find a fixed point want to
+ 
+
+ align:start position:0%
+and I want to find a fixed point want to
+find a fix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixed point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of t.
+
+ align:start position:0%
+of t.
+ 
+
+ align:start position:0%
+of t.
+Okay. So I need to I need to show So we
+
+ align:start position:0%
+Okay. So I need to I need to show So we
+ 
+
+ align:start position:0%
+Okay. So I need to I need to show So we
+want to show
+
+ align:start position:0%
+want to show
+ 
+
+ align:start position:0%
+want to show
+want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that T
+
+ align:start position:0%
+that T
+ 
+
+ align:start position:0%
+that T
+is a contracting map,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? Because if it is a contracting
+
+ align:start position:0%
+right? Because if it is a contracting
+ 
+
+ align:start position:0%
+right? Because if it is a contracting
+map, then we already know that if you
+
+ align:start position:0%
+map, then we already know that if you
+ 
+
+ align:start position:0%
+map, then we already know that if you
+take a closed interval like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you equip it with the usual distance
+
+ align:start position:0%
+and you equip it with the usual distance
+ 
+
+ align:start position:0%
+and you equip it with the usual distance
+that we have, this here is this here is
+
+ align:start position:0%
+that we have, this here is this here is
+ 
+
+ align:start position:0%
+that we have, this here is this here is
+cushy complete,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? But now if you take a cushy
+
+ align:start position:0%
+right? But now if you take a cushy
+ 
+
+ align:start position:0%
+right? But now if you take a cushy
+complete space and you're taking a
+
+ align:start position:0%
+complete space and you're taking a
+ 
+
+ align:start position:0%
+complete space and you're taking a
+closed subset and this here is a closed
+
+ align:start position:0%
+closed subset and this here is a closed
+ 
+
+ align:start position:0%
+closed subset and this here is a closed
+subset then this here is also cushy
+
+ align:start position:0%
+subset then this here is also cushy
+ 
+
+ align:start position:0%
+subset then this here is also cushy
+complete this here is also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay. So if we could prove that t from
+
+ align:start position:0%
+okay. So if we could prove that t from
+ 
+
+ align:start position:0%
+okay. So if we could prove that t from
+this space into itself is a contracting
+
+ align:start position:0%
+this space into itself is a contracting
+ 
+
+ align:start position:0%
+this space into itself is a contracting
+map. So it means that the existence C
+
+ align:start position:0%
+map. So it means that the existence C
+ 
+
+ align:start position:0%
+map. So it means that the existence C
+strictly less than one. Then we would
+
+ align:start position:0%
+strictly less than one. Then we would
+ 
+
+ align:start position:0%
+strictly less than one. Then we would
+have a fixed point and we would have a
+
+ align:start position:0%
+have a fixed point and we would have a
+ 
+
+ align:start position:0%
+have a fixed point and we would have a
+solution to the OD. Right? The thing is
+
+ align:start position:0%
+solution to the OD. Right? The thing is
+ 
+
+ align:start position:0%
+solution to the OD. Right? The thing is
+that this is not quite going to do it.
+
+ align:start position:0%
+that this is not quite going to do it.
+ 
+
+ align:start position:0%
+that this is not quite going to do it.
+It's not quite a contracting map,
+
+ align:start position:0%
+It's not quite a contracting map,
+ 
+
+ align:start position:0%
+It's not quite a contracting map,
+but so so we will need so for it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+a contracting map.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We need to restrict
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+further.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So by that I mean that we so we
+
+ align:start position:0%
+Okay. So by that I mean that we so we
+ 
+
+ align:start position:0%
+Okay. So by that I mean that we so we
+need to find we need to
+
+ align:start position:0%
+need to find we need to
+ 
+
+ align:start position:0%
+need to find we need to
+we need a delta to be
+
+ align:start position:0%
+we need a delta to be
+ 
+
+ align:start position:0%
+we need a delta to be
+we need to show that there's some delta
+
+ align:start position:0%
+we need to show that there's some delta
+ 
+
+ align:start position:0%
+we need to show that there's some delta
+it will actually be less than so we need
+
+ align:start position:0%
+it will actually be less than so we need
+ 
+
+ align:start position:0%
+it will actually be less than so we need
+to show that there's some delta that is
+
+ align:start position:0%
+to show that there's some delta that is
+ 
+
+ align:start position:0%
+to show that there's some delta that is
+smaller than this delta zero and so that
+
+ align:start position:0%
+smaller than this delta zero and so that
+ 
+
+ align:start position:0%
+smaller than this delta zero and so that
+if you restrict to this space here now
+
+ align:start position:0%
+if you restrict to this space here now
+ 
+
+ align:start position:0%
+if you restrict to this space here now
+it's a continuous function I won't
+
+ align:start position:0%
+it's a continuous function I won't
+ 
+
+ align:start position:0%
+it's a continuous function I won't
+define the I won't I will denote the
+
+ align:start position:0%
+define the I won't I will denote the
+ 
+
+ align:start position:0%
+define the I won't I will denote the
+ball by the same but this here is
+
+ align:start position:0%
+ball by the same but this here is
+ 
+
+ align:start position:0%
+ball by the same but this here is
+actually a ball in a different metric
+
+ align:start position:0%
+actually a ball in a different metric
+ 
+
+ align:start position:0%
+actually a ball in a different metric
+space because this is now a ball in the
+
+ align:start position:0%
+space because this is now a ball in the
+ 
+
+ align:start position:0%
+space because this is now a ball in the
+continuous functions on this smaller
+
+ align:start position:0%
+continuous functions on this smaller
+ 
+
+ align:start position:0%
+continuous functions on this smaller
+interval.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, but it's for the same radius.
+
+ align:start position:0%
+Okay, but it's for the same radius.
+ 
+
+ align:start position:0%
+Okay, but it's for the same radius.
+Okay, so if we restrict the map to this
+
+ align:start position:0%
+Okay, so if we restrict the map to this
+ 
+
+ align:start position:0%
+Okay, so if we restrict the map to this
+space here then on this it is a
+
+ align:start position:0%
+space here then on this it is a
+ 
+
+ align:start position:0%
+space here then on this it is a
+contracting map. Okay. So we need to cut
+
+ align:start position:0%
+contracting map. Okay. So we need to cut
+ 
+
+ align:start position:0%
+contracting map. Okay. So we need to cut
+down the interval. Uh
+
+ align:start position:0%
+down the interval. Uh
+ 
+
+ align:start position:0%
+down the interval. Uh
+okay. So now how do we do that? So
+
+ align:start position:0%
+okay. So now how do we do that? So
+ 
+
+ align:start position:0%
+okay. So now how do we do that? So
+so we need a contracting property again.
+
+ align:start position:0%
+so we need a contracting property again.
+ 
+
+ align:start position:0%
+so we need a contracting property again.
+And so suppose you take two functions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+These are continuous maps
+
+ align:start position:0%
+These are continuous maps
+ 
+
+ align:start position:0%
+These are continuous maps
+on some interval say from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right here again delta is now that's the
+
+ align:start position:0%
+right here again delta is now that's the
+ 
+
+ align:start position:0%
+right here again delta is now that's the
+delta we're looking for and it would be
+
+ align:start position:0%
+delta we're looking for and it would be
+ 
+
+ align:start position:0%
+delta we're looking for and it would be
+smaller than delta zero so since it's
+
+ align:start position:0%
+smaller than delta zero so since it's
+ 
+
+ align:start position:0%
+smaller than delta zero so since it's
+smaller than delta zero we already know
+
+ align:start position:0%
+smaller than delta zero we already know
+ 
+
+ align:start position:0%
+smaller than delta zero we already know
+that t that so we have two maps like
+
+ align:start position:0%
+that t that so we have two maps like
+ 
+
+ align:start position:0%
+that t that so we have two maps like
+this they are both supposed to be in the
+
+ align:start position:0%
+this they are both supposed to be in the
+ 
+
+ align:start position:0%
+this they are both supposed to be in the
+ball so this means that this thing here
+
+ align:start position:0%
+ball so this means that this thing here
+ 
+
+ align:start position:0%
+ball so this means that this thing here
+is less than m and we know we have
+
+ align:start position:0%
+is less than m and we know we have
+ 
+
+ align:start position:0%
+is less than m and we know we have
+already proven just because delta is
+
+ align:start position:0%
+already proven just because delta is
+ 
+
+ align:start position:0%
+already proven just because delta is
+less than delta zero that t of this
+
+ align:start position:0%
+less than delta zero that t of this
+ 
+
+ align:start position:0%
+less than delta zero that t of this
+function here
+
+ align:start position:0%
+function here
+ 
+
+ align:start position:0%
+function here
+has norm less or equal to m. Okay. So,
+
+ align:start position:0%
+has norm less or equal to m. Okay. So,
+ 
+
+ align:start position:0%
+has norm less or equal to m. Okay. So,
+but now let's look at the difference.
+
+ align:start position:0%
+but now let's look at the difference.
+ 
+
+ align:start position:0%
+but now let's look at the difference.
+So, t of y1
+
+ align:start position:0%
+So, t of y1
+ 
+
+ align:start position:0%
+So, t of y1
+uh of x minus t of y2
+
+ align:start position:0%
+uh of x minus t of y2
+ 
+
+ align:start position:0%
+uh of x minus t of y2
+of x,
+
+ align:start position:0%
+of x,
+ 
+
+ align:start position:0%
+of x,
+right? And then we're interested in the
+
+ align:start position:0%
+right? And then we're interested in the
+ 
+
+ align:start position:0%
+right? And then we're interested in the
+norm here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I and now x here is in this smaller
+
+ align:start position:0%
+And I and now x here is in this smaller
+ 
+
+ align:start position:0%
+And I and now x here is in this smaller
+interval.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now let's just write down what
+
+ align:start position:0%
+Okay. So now let's just write down what
+ 
+
+ align:start position:0%
+Okay. So now let's just write down what
+the map is. So the map here is the
+
+ align:start position:0%
+the map is. So the map here is the
+ 
+
+ align:start position:0%
+the map is. So the map here is the
+integral. So it's a sorry it's a plus
+
+ align:start position:0%
+integral. So it's a sorry it's a plus
+ 
+
+ align:start position:0%
+integral. So it's a sorry it's a plus
+the integral from zero to x of f of y1
+
+ align:start position:0%
+the integral from zero to x of f of y1
+ 
+
+ align:start position:0%
+the integral from zero to x of f of y1
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+plus g of s
+
+ align:start position:0%
+plus g of s
+ 
+
+ align:start position:0%
+plus g of s
+d s
+
+ align:start position:0%
+d s
+ 
+
+ align:start position:0%
+d s
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+a + the integral from zero to x of f of
+
+ align:start position:0%
+a + the integral from zero to x of f of
+ 
+
+ align:start position:0%
+a + the integral from zero to x of f of
+y 2 s + G of S
+
+ align:start position:0%
+y 2 s + G of S
+ 
+
+ align:start position:0%
+y 2 s + G of S
+DS, right?
+
+ align:start position:0%
+DS, right?
+ 
+
+ align:start position:0%
+DS, right?
+And now you see that the A's cancel,
+
+ align:start position:0%
+And now you see that the A's cancel,
+ 
+
+ align:start position:0%
+And now you see that the A's cancel,
+right? The A's here cancel
+
+ align:start position:0%
+right? The A's here cancel
+ 
+
+ align:start position:0%
+right? The A's here cancel
+and the G of S that those also cancel
+
+ align:start position:0%
+and the G of S that those also cancel
+ 
+
+ align:start position:0%
+and the G of S that those also cancel
+out, right? So you left with that this
+
+ align:start position:0%
+out, right? So you left with that this
+ 
+
+ align:start position:0%
+out, right? So you left with that this
+thing here is the absolute value of the
+
+ align:start position:0%
+thing here is the absolute value of the
+ 
+
+ align:start position:0%
+thing here is the absolute value of the
+integral from 0 to x of f of um y1 of s
+
+ align:start position:0%
+integral from 0 to x of f of um y1 of s
+ 
+
+ align:start position:0%
+integral from 0 to x of f of um y1 of s
+minus uh um f of y2
+
+ align:start position:0%
+minus uh um f of y2
+ 
+
+ align:start position:0%
+minus uh um f of y2
+of s
+
+ align:start position:0%
+of s
+ 
+
+ align:start position:0%
+of s
+ds.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when we proved that at the map
+
+ align:start position:0%
+when we proved that at the map
+ 
+
+ align:start position:0%
+when we proved that at the map
+He takes this ball into this ball we
+
+ align:start position:0%
+He takes this ball into this ball we
+ 
+
+ align:start position:0%
+He takes this ball into this ball we
+used we defined. So let me just define
+
+ align:start position:0%
+used we defined. So let me just define
+ 
+
+ align:start position:0%
+used we defined. So let me just define
+that again. We defined L1
+
+ align:start position:0%
+that again. We defined L1
+ 
+
+ align:start position:0%
+that again. We defined L1
+and N1 was the the maximum
+
+ align:start position:0%
+and N1 was the the maximum
+ 
+
+ align:start position:0%
+and N1 was the the maximum
+of actually uh
+
+ align:start position:0%
+of actually uh
+ 
+
+ align:start position:0%
+of actually uh
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I don't remember whether it was called
+
+ align:start position:0%
+I don't remember whether it was called
+ 
+
+ align:start position:0%
+I don't remember whether it was called
+L1. Let me just call it L uh to not call
+
+ align:start position:0%
+L1. Let me just call it L uh to not call
+ 
+
+ align:start position:0%
+L1. Let me just call it L uh to not call
+it some. So uh L here is the maximum of
+
+ align:start position:0%
+it some. So uh L here is the maximum of
+ 
+
+ align:start position:0%
+it some. So uh L here is the maximum of
+FP prime
+
+ align:start position:0%
+FP prime
+ 
+
+ align:start position:0%
+FP prime
+um of of offset
+
+ align:start position:0%
+um of of offset
+ 
+
+ align:start position:0%
+um of of offset
+where set here
+
+ align:start position:0%
+where set here
+ 
+
+ align:start position:0%
+where set here
+has no less or equal to M. Okay.
+
+ align:start position:0%
+has no less or equal to M. Okay.
+ 
+
+ align:start position:0%
+has no less or equal to M. Okay.
+So this is so f prime exists and is
+
+ align:start position:0%
+So this is so f prime exists and is
+ 
+
+ align:start position:0%
+So this is so f prime exists and is
+continuous. So on this interval here it
+
+ align:start position:0%
+continuous. So on this interval here it
+ 
+
+ align:start position:0%
+continuous. So on this interval here it
+has a maximum. Okay. So it's a nice
+
+ align:start position:0%
+has a maximum. Okay. So it's a nice
+ 
+
+ align:start position:0%
+has a maximum. Okay. So it's a nice
+finite number. And so now we use the so
+
+ align:start position:0%
+finite number. And so now we use the so
+ 
+
+ align:start position:0%
+finite number. And so now we use the so
+by the mean value theorem
+
+ align:start position:0%
+by the mean value theorem
+ 
+
+ align:start position:0%
+by the mean value theorem
+the mean value theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+By the mean value theorem, we have that
+
+ align:start position:0%
+By the mean value theorem, we have that
+ 
+
+ align:start position:0%
+By the mean value theorem, we have that
+f of set one
+
+ align:start position:0%
+f of set one
+ 
+
+ align:start position:0%
+f of set one
+minus f of set 2. As long as set one and
+
+ align:start position:0%
+minus f of set 2. As long as set one and
+ 
+
+ align:start position:0%
+minus f of set 2. As long as set one and
+set two
+
+ align:start position:0%
+set two
+ 
+
+ align:start position:0%
+set two
+are uh are in the interval from minus m
+
+ align:start position:0%
+are uh are in the interval from minus m
+ 
+
+ align:start position:0%
+are uh are in the interval from minus m
+to m. Then we have that this difference
+
+ align:start position:0%
+to m. Then we have that this difference
+ 
+
+ align:start position:0%
+to m. Then we have that this difference
+here is equal to the derivative in some
+
+ align:start position:0%
+here is equal to the derivative in some
+ 
+
+ align:start position:0%
+here is equal to the derivative in some
+intermediate point set sigma
+
+ align:start position:0%
+intermediate point set sigma
+ 
+
+ align:start position:0%
+intermediate point set sigma
+s I guess s times the difference between
+
+ align:start position:0%
+s I guess s times the difference between
+ 
+
+ align:start position:0%
+s I guess s times the difference between
+the two set one minus set two. So we
+
+ align:start position:0%
+the two set one minus set two. So we
+ 
+
+ align:start position:0%
+the two set one minus set two. So we
+have this right this is the mean math
+
+ align:start position:0%
+have this right this is the mean math
+ 
+
+ align:start position:0%
+have this right this is the mean math
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+and so we have that uh therefore we have
+
+ align:start position:0%
+and so we have that uh therefore we have
+ 
+
+ align:start position:0%
+and so we have that uh therefore we have
+that the norm here of the difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bounded by this here when we take the
+
+ align:start position:0%
+is bounded by this here when we take the
+ 
+
+ align:start position:0%
+is bounded by this here when we take the
+absolute value of this we're getting the
+
+ align:start position:0%
+absolute value of this we're getting the
+ 
+
+ align:start position:0%
+absolute value of this we're getting the
+absolute value. So this here is is equal
+
+ align:start position:0%
+absolute value. So this here is is equal
+ 
+
+ align:start position:0%
+absolute value. So this here is is equal
+to the absolute value of frime sigma
+
+ align:start position:0%
+to the absolute value of frime sigma
+ 
+
+ align:start position:0%
+to the absolute value of frime sigma
+time z 1 minus z 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This thing here
+
+ align:start position:0%
+This thing here
+ 
+
+ align:start position:0%
+This thing here
+because these two are in this interval
+
+ align:start position:0%
+because these two are in this interval
+ 
+
+ align:start position:0%
+because these two are in this interval
+this is bounded by by capital L. So
+
+ align:start position:0%
+this is bounded by by capital L. So
+ 
+
+ align:start position:0%
+this is bounded by by capital L. So
+you're getting this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now if you use this fact here
+
+ align:start position:0%
+And so now if you use this fact here
+ 
+
+ align:start position:0%
+And so now if you use this fact here
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+and you use this on this. So this thing
+
+ align:start position:0%
+and you use this on this. So this thing
+ 
+
+ align:start position:0%
+and you use this on this. So this thing
+here is less or equal to the integral
+
+ align:start position:0%
+here is less or equal to the integral
+ 
+
+ align:start position:0%
+here is less or equal to the integral
+from zero to x and I can take the
+
+ align:start position:0%
+from zero to x and I can take the
+ 
+
+ align:start position:0%
+from zero to x and I can take the
+absolute value in under the integration
+
+ align:start position:0%
+absolute value in under the integration
+ 
+
+ align:start position:0%
+absolute value in under the integration
+sign. So I get f of y1
+
+ align:start position:0%
+sign. So I get f of y1
+ 
+
+ align:start position:0%
+sign. So I get f of y1
+s minus
+
+ align:start position:0%
+s minus
+ 
+
+ align:start position:0%
+s minus
+uh f of y2
+
+ align:start position:0%
+uh f of y2
+ 
+
+ align:start position:0%
+uh f of y2
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+ds right
+
+ align:start position:0%
+ds right
+ 
+
+ align:start position:0%
+ds right
+and so now I can continue this string so
+
+ align:start position:0%
+and so now I can continue this string so
+ 
+
+ align:start position:0%
+and so now I can continue this string so
+I have what I'm interested in is g of y1
+
+ align:start position:0%
+I have what I'm interested in is g of y1
+ 
+
+ align:start position:0%
+I have what I'm interested in is g of y1
+at x minus g of y2
+
+ align:start position:0%
+at x minus g of y2
+ 
+
+ align:start position:0%
+at x minus g of y2
+of x and I'm interested in the abs bound
+
+ align:start position:0%
+of x and I'm interested in the abs bound
+ 
+
+ align:start position:0%
+of x and I'm interested in the abs bound
+for the absolute value and I have that
+
+ align:start position:0%
+for the absolute value and I have that
+ 
+
+ align:start position:0%
+for the absolute value and I have that
+this is less or equal to the integral
+
+ align:start position:0%
+this is less or equal to the integral
+ 
+
+ align:start position:0%
+this is less or equal to the integral
+from 0 to x of f of y1
+
+ align:start position:0%
+from 0 to x of f of y1
+ 
+
+ align:start position:0%
+from 0 to x of f of y1
+s plus f of y 2
+
+ align:start position:0%
+s plus f of y 2
+ 
+
+ align:start position:0%
+s plus f of y 2
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+ds
+
+ align:start position:0%
+ds
+ 
+
+ align:start position:0%
+ds
+and now I know that this interval here
+
+ align:start position:0%
+and now I know that this interval here
+ 
+
+ align:start position:0%
+and now I know that this interval here
+right x is supposed to lie in this
+
+ align:start position:0%
+right x is supposed to lie in this
+ 
+
+ align:start position:0%
+right x is supposed to lie in this
+interval here so this means is that that
+
+ align:start position:0%
+interval here so this means is that that
+ 
+
+ align:start position:0%
+interval here so this means is that that
+this the length of this interval from
+
+ align:start position:0%
+this the length of this interval from
+ 
+
+ align:start position:0%
+this the length of this interval from
+zero to is at most delta. So delta and
+
+ align:start position:0%
+zero to is at most delta. So delta and
+ 
+
+ align:start position:0%
+zero to is at most delta. So delta and
+then I can take the maximum of this
+
+ align:start position:0%
+then I can take the maximum of this
+ 
+
+ align:start position:0%
+then I can take the maximum of this
+or I can take the uh that's right I can
+
+ align:start position:0%
+or I can take the uh that's right I can
+ 
+
+ align:start position:0%
+or I can take the uh that's right I can
+take the the maximum of this but you see
+
+ align:start position:0%
+take the the maximum of this but you see
+ 
+
+ align:start position:0%
+take the the maximum of this but you see
+that this thing here is bounded by so
+
+ align:start position:0%
+that this thing here is bounded by so
+ 
+
+ align:start position:0%
+that this thing here is bounded by so
+this is the maximum is the maximum
+
+ align:start position:0%
+this is the maximum is the maximum
+ 
+
+ align:start position:0%
+this is the maximum is the maximum
+and if I use this inequality here it's
+
+ align:start position:0%
+and if I use this inequality here it's
+ 
+
+ align:start position:0%
+and if I use this inequality here it's
+bounded by L and then it's applied this
+
+ align:start position:0%
+bounded by L and then it's applied this
+ 
+
+ align:start position:0%
+bounded by L and then it's applied this
+here you should think about as set one
+
+ align:start position:0%
+here you should think about as set one
+ 
+
+ align:start position:0%
+here you should think about as set one
+and this here for each x you can s you
+
+ align:start position:0%
+and this here for each x you can s you
+ 
+
+ align:start position:0%
+and this here for each x you can s you
+can think about this as set one and set
+
+ align:start position:0%
+can think about this as set one and set
+ 
+
+ align:start position:0%
+can think about this as set one and set
+two and so you're getting this thing
+
+ align:start position:0%
+two and so you're getting this thing
+ 
+
+ align:start position:0%
+two and so you're getting this thing
+here times y1
+
+ align:start position:0%
+here times y1
+ 
+
+ align:start position:0%
+here times y1
+s - y 2
+
+ align:start position:0%
+s - y 2
+ 
+
+ align:start position:0%
+s - y 2
+s and here s will now lie in the
+
+ align:start position:0%
+s and here s will now lie in the
+ 
+
+ align:start position:0%
+s and here s will now lie in the
+interval
+
+ align:start position:0%
+interval
+ 
+
+ align:start position:0%
+interval
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in this interval here
+
+ align:start position:0%
+in this interval here
+ 
+
+ align:start position:0%
+in this interval here
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+Right? And so now you see that this is
+
+ align:start position:0%
+Right? And so now you see that this is
+ 
+
+ align:start position:0%
+Right? And so now you see that this is
+just a constant. So this is equal to
+
+ align:start position:0%
+just a constant. So this is equal to
+ 
+
+ align:start position:0%
+just a constant. So this is equal to
+delta L. And then this maximum
+
+ align:start position:0%
+delta L. And then this maximum
+ 
+
+ align:start position:0%
+delta L. And then this maximum
+S lesser equal to delta
+
+ align:start position:0%
+S lesser equal to delta
+ 
+
+ align:start position:0%
+S lesser equal to delta
+Y1
+
+ align:start position:0%
+Y1
+ 
+
+ align:start position:0%
+Y1
+minus Y2
+
+ align:start position:0%
+minus Y2
+ 
+
+ align:start position:0%
+minus Y2
+like this. Right? This is evaluated in
+
+ align:start position:0%
+like this. Right? This is evaluated in
+ 
+
+ align:start position:0%
+like this. Right? This is evaluated in
+S. But I wouldn't I don't write that.
+
+ align:start position:0%
+S. But I wouldn't I don't write that.
+ 
+
+ align:start position:0%
+S. But I wouldn't I don't write that.
+Okay? And this thing here. But this is
+
+ align:start position:0%
+Okay? And this thing here. But this is
+ 
+
+ align:start position:0%
+Okay? And this thing here. But this is
+just delta L. This maximum here is just
+
+ align:start position:0%
+just delta L. This maximum here is just
+ 
+
+ align:start position:0%
+just delta L. This maximum here is just
+the distance between this function and
+
+ align:start position:0%
+the distance between this function and
+ 
+
+ align:start position:0%
+the distance between this function and
+that function. That's how we define this
+
+ align:start position:0%
+that function. That's how we define this
+ 
+
+ align:start position:0%
+that function. That's how we define this
+distance. Right?
+
+ align:start position:0%
+distance. Right?
+ 
+
+ align:start position:0%
+distance. Right?
+And so you see that this right hand side
+
+ align:start position:0%
+And so you see that this right hand side
+ 
+
+ align:start position:0%
+And so you see that this right hand side
+is now holds for all x. So this means
+
+ align:start position:0%
+is now holds for all x. So this means
+ 
+
+ align:start position:0%
+is now holds for all x. So this means
+that we have that the maximum of this
+
+ align:start position:0%
+that we have that the maximum of this
+ 
+
+ align:start position:0%
+that we have that the maximum of this
+thing here over x where x is in the
+
+ align:start position:0%
+thing here over x where x is in the
+ 
+
+ align:start position:0%
+thing here over x where x is in the
+interval between zero and delta. So this
+
+ align:start position:0%
+interval between zero and delta. So this
+ 
+
+ align:start position:0%
+interval between zero and delta. So this
+means that we have that the distance
+
+ align:start position:0%
+means that we have that the distance
+ 
+
+ align:start position:0%
+means that we have that the distance
+between t of y1
+
+ align:start position:0%
+between t of y1
+ 
+
+ align:start position:0%
+between t of y1
+and t of y2.
+
+ align:start position:0%
+and t of y2.
+ 
+
+ align:start position:0%
+and t of y2.
+This thing here is equal to the maximum.
+
+ align:start position:0%
+This thing here is equal to the maximum.
+ 
+
+ align:start position:0%
+This thing here is equal to the maximum.
+This is how we define that distance
+
+ align:start position:0%
+This is how we define that distance
+ 
+
+ align:start position:0%
+This is how we define that distance
+after all.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and then it's of this thing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry uh x
+
+ align:start position:0%
+sorry uh x
+ 
+
+ align:start position:0%
+sorry uh x
+minus t of y 2
+
+ align:start position:0%
+minus t of y 2
+ 
+
+ align:start position:0%
+minus t of y 2
+in x
+
+ align:start position:0%
+in x
+ 
+
+ align:start position:0%
+in x
+right so we have that this and this
+
+ align:start position:0%
+right so we have that this and this
+ 
+
+ align:start position:0%
+right so we have that this and this
+inequality say that it's less or equal
+
+ align:start position:0%
+inequality say that it's less or equal
+ 
+
+ align:start position:0%
+inequality say that it's less or equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+delta uh L D Y1 comma Y2
+
+ align:start position:0%
+delta uh L D Y1 comma Y2
+ 
+
+ align:start position:0%
+delta uh L D Y1 comma Y2
+and so you see that now if you so L here
+
+ align:start position:0%
+and so you see that now if you so L here
+ 
+
+ align:start position:0%
+and so you see that now if you so L here
+was just a fixed constant right if I now
+
+ align:start position:0%
+was just a fixed constant right if I now
+ 
+
+ align:start position:0%
+was just a fixed constant right if I now
+set delta just to make sure that there's
+
+ align:start position:0%
+set delta just to make sure that there's
+ 
+
+ align:start position:0%
+set delta just to make sure that there's
+no problem I'm setting delta equal to 1
+
+ align:start position:0%
+no problem I'm setting delta equal to 1
+ 
+
+ align:start position:0%
+no problem I'm setting delta equal to 1
+/ 2 L I don't really need the one but I
+
+ align:start position:0%
+/ 2 L I don't really need the one but I
+ 
+
+ align:start position:0%
+/ 2 L I don't really need the one but I
+I I'll just do it like this so I don't
+
+ align:start position:0%
+I I'll just do it like this so I don't
+ 
+
+ align:start position:0%
+I I'll just do it like this so I don't
+have zero in the denominator if I choose
+
+ align:start position:0%
+have zero in the denominator if I choose
+ 
+
+ align:start position:0%
+have zero in the denominator if I choose
+the delta to be equal to this. Right?
+
+ align:start position:0%
+the delta to be equal to this. Right?
+ 
+
+ align:start position:0%
+the delta to be equal to this. Right?
+Well, then you see that this thing here
+
+ align:start position:0%
+Well, then you see that this thing here
+ 
+
+ align:start position:0%
+Well, then you see that this thing here
+the the inner product of these two is
+
+ align:start position:0%
+the the inner product of these two is
+ 
+
+ align:start position:0%
+the the inner product of these two is
+less or the the product of these two is
+
+ align:start position:0%
+less or the the product of these two is
+ 
+
+ align:start position:0%
+less or the the product of these two is
+less than a half. So this is less or
+
+ align:start position:0%
+less than a half. So this is less or
+ 
+
+ align:start position:0%
+less than a half. So this is less or
+equal to I can just place it by a half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that. Right?
+
+ align:start position:0%
+like that. Right?
+ 
+
+ align:start position:0%
+like that. Right?
+And so you see this is exactly what it
+
+ align:start position:0%
+And so you see this is exactly what it
+ 
+
+ align:start position:0%
+And so you see this is exactly what it
+means to be a contracting mapping. In
+
+ align:start position:0%
+means to be a contracting mapping. In
+ 
+
+ align:start position:0%
+means to be a contracting mapping. In
+fact, it's a contracting mapping which
+
+ align:start position:0%
+fact, it's a contracting mapping which
+ 
+
+ align:start position:0%
+fact, it's a contracting mapping which
+is pretty nice
+
+ align:start position:0%
+is pretty nice
+ 
+
+ align:start position:0%
+is pretty nice
+that the constant it's not just strictly
+
+ align:start position:0%
+that the constant it's not just strictly
+ 
+
+ align:start position:0%
+that the constant it's not just strictly
+some constant strictly less than one but
+
+ align:start position:0%
+some constant strictly less than one but
+ 
+
+ align:start position:0%
+some constant strictly less than one but
+it's actually a half right. So it's a
+
+ align:start position:0%
+it's actually a half right. So it's a
+ 
+
+ align:start position:0%
+it's actually a half right. So it's a
+contracting mapping theorem a
+
+ align:start position:0%
+contracting mapping theorem a
+ 
+
+ align:start position:0%
+contracting mapping theorem a
+contracting map and so now by the
+
+ align:start position:0%
+contracting map and so now by the
+ 
+
+ align:start position:0%
+contracting map and so now by the
+contracting mapping theorem we have a
+
+ align:start position:0%
+contracting mapping theorem we have a
+ 
+
+ align:start position:0%
+contracting mapping theorem we have a
+fixed point. Okay.
+
+ align:start position:0%
+fixed point. Okay.
+ 
+
+ align:start position:0%
+fixed point. Okay.
+So this solve the OD. Okay. And it do
+
+ align:start position:0%
+So this solve the OD. Okay. And it do
+ 
+
+ align:start position:0%
+So this solve the OD. Okay. And it do
+does more than that because a
+
+ align:start position:0%
+does more than that because a
+ 
+
+ align:start position:0%
+does more than that because a
+contracting mapping theorem says that it
+
+ align:start position:0%
+contracting mapping theorem says that it
+ 
+
+ align:start position:0%
+contracting mapping theorem says that it
+has a unique
+
+ align:start position:0%
+has a unique
+ 
+
+ align:start position:0%
+has a unique
+uh unique fix point. Right? So this
+
+ align:start position:0%
+uh unique fix point. Right? So this
+ 
+
+ align:start position:0%
+uh unique fix point. Right? So this
+means that and and if you have a
+
+ align:start position:0%
+means that and and if you have a
+ 
+
+ align:start position:0%
+means that and and if you have a
+solution to this, right? If you have a
+
+ align:start position:0%
+solution to this, right? If you have a
+ 
+
+ align:start position:0%
+solution to this, right? If you have a
+solution to this, then we saw last time
+
+ align:start position:0%
+solution to this, then we saw last time
+ 
+
+ align:start position:0%
+solution to this, then we saw last time
+that if it is a solution, then it is a
+
+ align:start position:0%
+that if it is a solution, then it is a
+ 
+
+ align:start position:0%
+that if it is a solution, then it is a
+fixed point, right?
+
+ align:start position:0%
+fixed point, right?
+ 
+
+ align:start position:0%
+fixed point, right?
+Okay. So now we almost have existence
+
+ align:start position:0%
+Okay. So now we almost have existence
+ 
+
+ align:start position:0%
+Okay. So now we almost have existence
+and uniqueness.
+
+ align:start position:0%
+and uniqueness.
+ 
+
+ align:start position:0%
+and uniqueness.
+Uh let me explain what is missing to the
+
+ align:start position:0%
+Uh let me explain what is missing to the
+ 
+
+ align:start position:0%
+Uh let me explain what is missing to the
+existence of uniqueness.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So for that
+
+ align:start position:0%
+So for that
+ 
+
+ align:start position:0%
+So for that
+let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+backtrack a little bit and talk about
+
+ align:start position:0%
+backtrack a little bit and talk about
+ 
+
+ align:start position:0%
+backtrack a little bit and talk about
+something about metric spaces.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bases specifically uh about connected
+
+ align:start position:0%
+bases specifically uh about connected
+ 
+
+ align:start position:0%
+bases specifically uh about connected
+matrix bases.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So suppose you have a metric space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+It is connected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if um if x here is the only subset
+
+ align:start position:0%
+if um if x here is the only subset
+ 
+
+ align:start position:0%
+if um if x here is the only subset
+only subset. So, so the whole set itself
+
+ align:start position:0%
+only subset. So, so the whole set itself
+ 
+
+ align:start position:0%
+only subset. So, so the whole set itself
+is the only subset
+
+ align:start position:0%
+is the only subset
+ 
+
+ align:start position:0%
+is the only subset
+of of X that is
+
+ align:start position:0%
+of of X that is
+ 
+
+ align:start position:0%
+of of X that is
+is both open and closed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? Remember that if you take a
+
+ align:start position:0%
+Right? Remember that if you take a
+ 
+
+ align:start position:0%
+Right? Remember that if you take a
+metric space then the sorry if
+
+ align:start position:0%
+metric space then the sorry if
+ 
+
+ align:start position:0%
+metric space then the sorry if
+if X and sorry and and the empty set are
+
+ align:start position:0%
+if X and sorry and and the empty set are
+ 
+
+ align:start position:0%
+if X and sorry and and the empty set are
+the only
+
+ align:start position:0%
+the only
+ 
+
+ align:start position:0%
+the only
+uh subset of X that are both open and
+
+ align:start position:0%
+uh subset of X that are both open and
+ 
+
+ align:start position:0%
+uh subset of X that are both open and
+closed. Right? Remember that if you take
+
+ align:start position:0%
+closed. Right? Remember that if you take
+ 
+
+ align:start position:0%
+closed. Right? Remember that if you take
+a metric space and if you take the whole
+
+ align:start position:0%
+a metric space and if you take the whole
+ 
+
+ align:start position:0%
+a metric space and if you take the whole
+set or the empty set, those are all
+
+ align:start position:0%
+set or the empty set, those are all
+ 
+
+ align:start position:0%
+set or the empty set, those are all
+they're both always closed and open,
+
+ align:start position:0%
+they're both always closed and open,
+ 
+
+ align:start position:0%
+they're both always closed and open,
+right? And so it's connected if those
+
+ align:start position:0%
+right? And so it's connected if those
+ 
+
+ align:start position:0%
+right? And so it's connected if those
+are the only two subsets that are at the
+
+ align:start position:0%
+are the only two subsets that are at the
+ 
+
+ align:start position:0%
+are the only two subsets that are at the
+same time open and closed. Okay?
+
+ align:start position:0%
+same time open and closed. Okay?
+ 
+
+ align:start position:0%
+same time open and closed. Okay?
+And so now
+
+ align:start position:0%
+And so now
+ 
+
+ align:start position:0%
+And so now
+we have that we have the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have the following lema
+
+ align:start position:0%
+we have the following lema
+ 
+
+ align:start position:0%
+we have the following lema
+or theorem just call it theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if you take a interval here with a
+
+ align:start position:0%
+that if you take a interval here with a
+ 
+
+ align:start position:0%
+that if you take a interval here with a
+usual metric here so this is so I here
+
+ align:start position:0%
+usual metric here so this is so I here
+ 
+
+ align:start position:0%
+usual metric here so this is so I here
+is a interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then uh the theorem is that that that
+
+ align:start position:0%
+then uh the theorem is that that that
+ 
+
+ align:start position:0%
+then uh the theorem is that that that
+uh this metric space here so is
+
+ align:start position:0%
+uh this metric space here so is
+ 
+
+ align:start position:0%
+uh this metric space here so is
+connected.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So let's try to prove that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I take now a subset
+
+ align:start position:0%
+So I take now a subset
+ 
+
+ align:start position:0%
+So I take now a subset
+here uh that is
+
+ align:start position:0%
+here uh that is
+ 
+
+ align:start position:0%
+here uh that is
+is both open
+
+ align:start position:0%
+is both open
+ 
+
+ align:start position:0%
+is both open
+open and closed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we want to show
+
+ align:start position:0%
+And we want to show
+ 
+
+ align:start position:0%
+And we want to show
+want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if a here is non- empty
+
+ align:start position:0%
+if a here is non- empty
+ 
+
+ align:start position:0%
+if a here is non- empty
+then it implies that a
+
+ align:start position:0%
+then it implies that a
+ 
+
+ align:start position:0%
+then it implies that a
+is is everything. Right? So we're
+
+ align:start position:0%
+is is everything. Right? So we're
+ 
+
+ align:start position:0%
+is is everything. Right? So we're
+assuming that it's non- empty and then
+
+ align:start position:0%
+assuming that it's non- empty and then
+ 
+
+ align:start position:0%
+assuming that it's non- empty and then
+we should apply uh to try to prove that
+
+ align:start position:0%
+we should apply uh to try to prove that
+ 
+
+ align:start position:0%
+we should apply uh to try to prove that
+a is everything.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we let
+
+ align:start position:0%
+So we let
+ 
+
+ align:start position:0%
+So we let
+x0 be an element in a right but right
+
+ align:start position:0%
+x0 be an element in a right but right
+ 
+
+ align:start position:0%
+x0 be an element in a right but right
+we're assuming it's not empty so we can
+
+ align:start position:0%
+we're assuming it's not empty so we can
+ 
+
+ align:start position:0%
+we're assuming it's not empty so we can
+let x0 be an element in a
+
+ align:start position:0%
+let x0 be an element in a
+ 
+
+ align:start position:0%
+let x0 be an element in a
+and now I want to define
+
+ align:start position:0%
+and now I want to define
+ 
+
+ align:start position:0%
+and now I want to define
+um I want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I want to so I have here I have here my
+
+ align:start position:0%
+I want to so I have here I have here my
+ 
+
+ align:start position:0%
+I want to so I have here I have here my
+interval this is my interval I
+
+ align:start position:0%
+interval this is my interval I
+ 
+
+ align:start position:0%
+interval this is my interval I
+have here x0
+
+ align:start position:0%
+have here x0
+ 
+
+ align:start position:0%
+have here x0
+and I take uh and I'm looking at the the
+
+ align:start position:0%
+and I take uh and I'm looking at the the
+ 
+
+ align:start position:0%
+and I take uh and I'm looking at the the
+y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in
+
+ align:start position:0%
+uh in
+ 
+
+ align:start position:0%
+uh in
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+so that um
+
+ align:start position:0%
+so that um
+ 
+
+ align:start position:0%
+so that um
+that if you take everything
+
+ align:start position:0%
+that if you take everything
+ 
+
+ align:start position:0%
+that if you take everything
+uh so that so y is an a and I'm going to
+
+ align:start position:0%
+uh so that so y is an a and I'm going to
+ 
+
+ align:start position:0%
+uh so that so y is an a and I'm going to
+look at y in a with
+
+ align:start position:0%
+look at y in a with
+ 
+
+ align:start position:0%
+look at y in a with
+y bigger equal to x0 and I'm going to
+
+ align:start position:0%
+y bigger equal to x0 and I'm going to
+ 
+
+ align:start position:0%
+y bigger equal to x0 and I'm going to
+look at the y so that that this whole
+
+ align:start position:0%
+look at the y so that that this whole
+ 
+
+ align:start position:0%
+look at the y so that that this whole
+interval here from x0 to y
+
+ align:start position:0%
+interval here from x0 to y
+ 
+
+ align:start position:0%
+interval here from x0 to y
+is contained in a
+
+ align:start position:0%
+is contained in a
+ 
+
+ align:start position:0%
+is contained in a
+so I'm defining so
+
+ align:start position:0%
+so I'm defining so
+ 
+
+ align:start position:0%
+so I'm defining so
+so define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as subset here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+of of I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that uh it's the y this subset b is
+
+ align:start position:0%
+so that uh it's the y this subset b is
+ 
+
+ align:start position:0%
+so that uh it's the y this subset b is
+the y in a with a property that it is
+
+ align:start position:0%
+the y in a with a property that it is
+ 
+
+ align:start position:0%
+the y in a with a property that it is
+that y here is big or equal to x0 and
+
+ align:start position:0%
+that y here is big or equal to x0 and
+ 
+
+ align:start position:0%
+that y here is big or equal to x0 and
+and you have
+
+ align:start position:0%
+and you have
+ 
+
+ align:start position:0%
+and you have
+And this interval here
+
+ align:start position:0%
+And this interval here
+ 
+
+ align:start position:0%
+And this interval here
+is contained in a
+
+ align:start position:0%
+is contained in a
+ 
+
+ align:start position:0%
+is contained in a
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now I want to show that so let's say
+
+ align:start position:0%
+and now I want to show that so let's say
+ 
+
+ align:start position:0%
+and now I want to show that so let's say
+let's say for the sake of argument let
+
+ align:start position:0%
+let's say for the sake of argument let
+ 
+
+ align:start position:0%
+let's say for the sake of argument let
+me assume
+
+ align:start position:0%
+me assume
+ 
+
+ align:start position:0%
+me assume
+that this interval is a closed interval
+
+ align:start position:0%
+that this interval is a closed interval
+ 
+
+ align:start position:0%
+that this interval is a closed interval
+like this it works equally well the
+
+ align:start position:0%
+like this it works equally well the
+ 
+
+ align:start position:0%
+like this it works equally well the
+argument with obvious modification
+
+ align:start position:0%
+argument with obvious modification
+ 
+
+ align:start position:0%
+argument with obvious modification
+work each equally well if it's open or
+
+ align:start position:0%
+work each equally well if it's open or
+ 
+
+ align:start position:0%
+work each equally well if it's open or
+half open uh interval.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So I take some y here and I have
+
+ align:start position:0%
+Okay. So I take some y here and I have
+ 
+
+ align:start position:0%
+Okay. So I take some y here and I have
+so I have a y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I and y is so it's a set so that
+
+ align:start position:0%
+and I and y is so it's a set so that
+ 
+
+ align:start position:0%
+and I and y is so it's a set so that
+this whole interval is contained in a
+
+ align:start position:0%
+this whole interval is contained in a
+ 
+
+ align:start position:0%
+this whole interval is contained in a
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and what I want to show is so want to
+
+ align:start position:0%
+and what I want to show is so want to
+ 
+
+ align:start position:0%
+and what I want to show is so want to
+show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that y is in a And this is the first
+
+ align:start position:0%
+that y is in a And this is the first
+ 
+
+ align:start position:0%
+that y is in a And this is the first
+thing I want to show. One is that y is
+
+ align:start position:0%
+thing I want to show. One is that y is
+ 
+
+ align:start position:0%
+thing I want to show. One is that y is
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+and then I want the second thing I want
+
+ align:start position:0%
+and then I want the second thing I want
+ 
+
+ align:start position:0%
+and then I want the second thing I want
+to show is that y
+
+ align:start position:0%
+to show is that y
+ 
+
+ align:start position:0%
+to show is that y
+is equal to b.
+
+ align:start position:0%
+is equal to b.
+ 
+
+ align:start position:0%
+is equal to b.
+You see if I had proven both of these
+
+ align:start position:0%
+You see if I had proven both of these
+ 
+
+ align:start position:0%
+You see if I had proven both of these
+property right then it would be that so
+
+ align:start position:0%
+property right then it would be that so
+ 
+
+ align:start position:0%
+property right then it would be that so
+then um then
+
+ align:start position:0%
+then um then
+ 
+
+ align:start position:0%
+then um then
+um it would mean that everything here
+
+ align:start position:0%
+um it would mean that everything here
+ 
+
+ align:start position:0%
+um it would mean that everything here
+would be in a and including this last
+
+ align:start position:0%
+would be in a and including this last
+ 
+
+ align:start position:0%
+would be in a and including this last
+point right and so this means that we
+
+ align:start position:0%
+point right and so this means that we
+ 
+
+ align:start position:0%
+point right and so this means that we
+have this entire interval is in a is in
+
+ align:start position:0%
+have this entire interval is in a is in
+ 
+
+ align:start position:0%
+have this entire interval is in a is in
+I sorry and then likewise we could argue
+
+ align:start position:0%
+I sorry and then likewise we could argue
+ 
+
+ align:start position:0%
+I sorry and then likewise we could argue
+on the other side Okay.
+
+ align:start position:0%
+on the other side Okay.
+ 
+
+ align:start position:0%
+on the other side Okay.
+So now how do we prove this? So
+
+ align:start position:0%
+So now how do we prove this? So
+ 
+
+ align:start position:0%
+So now how do we prove this? So
+well the first thing is that if if um
+
+ align:start position:0%
+well the first thing is that if if um
+ 
+
+ align:start position:0%
+well the first thing is that if if um
+if we take so if we set
+
+ align:start position:0%
+if we take so if we set
+ 
+
+ align:start position:0%
+if we take so if we set
+sorry this is no sorry but that's this
+
+ align:start position:0%
+sorry this is no sorry but that's this
+ 
+
+ align:start position:0%
+sorry this is no sorry but that's this
+here should have been
+
+ align:start position:0%
+here should have been
+ 
+
+ align:start position:0%
+here should have been
+this here should have been y zero and
+
+ align:start position:0%
+this here should have been y zero and
+ 
+
+ align:start position:0%
+this here should have been y zero and
+this should have been the soup
+
+ align:start position:0%
+this should have been the soup
+ 
+
+ align:start position:0%
+this should have been the soup
+of y in Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So these guys
+
+ align:start position:0%
+So these guys
+ 
+
+ align:start position:0%
+So these guys
+and then this here and we want to prove
+
+ align:start position:0%
+and then this here and we want to prove
+ 
+
+ align:start position:0%
+and then this here and we want to prove
+that this thing here is in in a
+
+ align:start position:0%
+that this thing here is in in a
+ 
+
+ align:start position:0%
+that this thing here is in in a
+and uh and the second thing is we want
+
+ align:start position:0%
+and uh and the second thing is we want
+ 
+
+ align:start position:0%
+and uh and the second thing is we want
+to prove that this soup is actually
+
+ align:start position:0%
+to prove that this soup is actually
+ 
+
+ align:start position:0%
+to prove that this soup is actually
+equal to B. Okay, that's what we want to
+
+ align:start position:0%
+equal to B. Okay, that's what we want to
+ 
+
+ align:start position:0%
+equal to B. Okay, that's what we want to
+prove.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the soup of these well if you have if
+
+ align:start position:0%
+So the soup of these well if you have if
+ 
+
+ align:start position:0%
+So the soup of these well if you have if
+y z is a soup of elements then you have
+
+ align:start position:0%
+y z is a soup of elements then you have
+ 
+
+ align:start position:0%
+y z is a soup of elements then you have
+a sequence. So here you have y z and
+
+ align:start position:0%
+a sequence. So here you have y z and
+ 
+
+ align:start position:0%
+a sequence. So here you have y z and
+this means that you have a sequence of
+
+ align:start position:0%
+this means that you have a sequence of
+ 
+
+ align:start position:0%
+this means that you have a sequence of
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+which are then in elements in the set B.
+
+ align:start position:0%
+which are then in elements in the set B.
+ 
+
+ align:start position:0%
+which are then in elements in the set B.
+This is soup of B.
+
+ align:start position:0%
+This is soup of B.
+ 
+
+ align:start position:0%
+This is soup of B.
+Mine is the same as soup of B. Sorry,
+
+ align:start position:0%
+Mine is the same as soup of B. Sorry,
+ 
+
+ align:start position:0%
+Mine is the same as soup of B. Sorry,
+soup of B.
+
+ align:start position:0%
+soup of B.
+ 
+
+ align:start position:0%
+soup of B.
+I write like this.
+
+ align:start position:0%
+I write like this.
+ 
+
+ align:start position:0%
+I write like this.
+So I take this set and these are the Y
+
+ align:start position:0%
+So I take this set and these are the Y
+ 
+
+ align:start position:0%
+So I take this set and these are the Y
+so that this entire interval is
+
+ align:start position:0%
+so that this entire interval is
+ 
+
+ align:start position:0%
+so that this entire interval is
+contained in a right and then I take the
+
+ align:start position:0%
+contained in a right and then I take the
+ 
+
+ align:start position:0%
+contained in a right and then I take the
+soup of this set and I want to prove
+
+ align:start position:0%
+soup of this set and I want to prove
+ 
+
+ align:start position:0%
+soup of this set and I want to prove
+that this soup is in A. And then I want
+
+ align:start position:0%
+that this soup is in A. And then I want
+ 
+
+ align:start position:0%
+that this soup is in A. And then I want
+to prove that in fact the soup is B.
+
+ align:start position:0%
+to prove that in fact the soup is B.
+ 
+
+ align:start position:0%
+to prove that in fact the soup is B.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that it's a soup of of such
+
+ align:start position:0%
+So that it's a soup of of such
+ 
+
+ align:start position:0%
+So that it's a soup of of such
+elements in capital B means that there
+
+ align:start position:0%
+elements in capital B means that there
+ 
+
+ align:start position:0%
+elements in capital B means that there
+exists a sequence
+
+ align:start position:0%
+exists a sequence
+ 
+
+ align:start position:0%
+exists a sequence
+of elements
+
+ align:start position:0%
+of elements
+ 
+
+ align:start position:0%
+of elements
+in B.
+
+ align:start position:0%
+in B.
+ 
+
+ align:start position:0%
+in B.
+So, so that y here y0
+
+ align:start position:0%
+So, so that y here y0
+ 
+
+ align:start position:0%
+So, so that y here y0
+is the soup of b. This here implies that
+
+ align:start position:0%
+is the soup of b. This here implies that
+ 
+
+ align:start position:0%
+is the soup of b. This here implies that
+there exist a sequence y
+
+ align:start position:0%
+there exist a sequence y
+ 
+
+ align:start position:0%
+there exist a sequence y
+and these yn
+
+ align:start position:0%
+and these yn
+ 
+
+ align:start position:0%
+and these yn
+are in a and you have that
+
+ align:start position:0%
+are in a and you have that
+ 
+
+ align:start position:0%
+are in a and you have that
+x0
+
+ align:start position:0%
+x0
+ 
+
+ align:start position:0%
+x0
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+is contained in a and and then you have
+
+ align:start position:0%
+is contained in a and and then you have
+ 
+
+ align:start position:0%
+is contained in a and and then you have
+that these guys converge to y z.
+
+ align:start position:0%
+that these guys converge to y z.
+ 
+
+ align:start position:0%
+that these guys converge to y z.
+Right? This is what you get from that is
+
+ align:start position:0%
+Right? This is what you get from that is
+ 
+
+ align:start position:0%
+Right? This is what you get from that is
+a soup. Right? These two things are that
+
+ align:start position:0%
+a soup. Right? These two things are that
+ 
+
+ align:start position:0%
+a soup. Right? These two things are that
+the elements
+
+ align:start position:0%
+the elements
+ 
+
+ align:start position:0%
+the elements
+are in that these elements. So this here
+
+ align:start position:0%
+are in that these elements. So this here
+ 
+
+ align:start position:0%
+are in that these elements. So this here
+is just that's the y in on b.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now what you have so this here means
+
+ align:start position:0%
+So now what you have so this here means
+ 
+
+ align:start position:0%
+So now what you have so this here means
+so here I have x0
+
+ align:start position:0%
+so here I have x0
+ 
+
+ align:start position:0%
+so here I have x0
+here I have y z and I have these uh
+
+ align:start position:0%
+here I have y z and I have these uh
+ 
+
+ align:start position:0%
+here I have y z and I have these uh
+these elements
+
+ align:start position:0%
+these elements
+ 
+
+ align:start position:0%
+these elements
+y in
+
+ align:start position:0%
+y in
+ 
+
+ align:start position:0%
+y in
+and they are in particular they are in a
+
+ align:start position:0%
+and they are in particular they are in a
+ 
+
+ align:start position:0%
+and they are in particular they are in a
+okay but a is closed right since a is
+
+ align:start position:0%
+okay but a is closed right since a is
+ 
+
+ align:start position:0%
+okay but a is closed right since a is
+closed since
+
+ align:start position:0%
+closed since
+ 
+
+ align:start position:0%
+closed since
+y is in a
+
+ align:start position:0%
+y is in a
+ 
+
+ align:start position:0%
+y is in a
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+Y in and a is closed
+
+ align:start position:0%
+Y in and a is closed
+ 
+
+ align:start position:0%
+Y in and a is closed
+is a closed
+
+ align:start position:0%
+is a closed
+ 
+
+ align:start position:0%
+is a closed
+is a closed subset.
+
+ align:start position:0%
+is a closed subset.
+ 
+
+ align:start position:0%
+is a closed subset.
+This means that that the limit here the
+
+ align:start position:0%
+This means that that the limit here the
+ 
+
+ align:start position:0%
+This means that that the limit here the
+limit y z which is the limit this here
+
+ align:start position:0%
+limit y z which is the limit this here
+ 
+
+ align:start position:0%
+limit y z which is the limit this here
+must also be in a right.
+
+ align:start position:0%
+must also be in a right.
+ 
+
+ align:start position:0%
+must also be in a right.
+Okay. So we have proven the first
+
+ align:start position:0%
+Okay. So we have proven the first
+ 
+
+ align:start position:0%
+Okay. So we have proven the first
+property right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we proven that that right so well so
+
+ align:start position:0%
+we proven that that right so well so
+ 
+
+ align:start position:0%
+we proven that that right so well so
+we've proven that y0 is in a but now you
+
+ align:start position:0%
+we've proven that y0 is in a but now you
+ 
+
+ align:start position:0%
+we've proven that y0 is in a but now you
+see that we have that for each of the y
+
+ align:start position:0%
+see that we have that for each of the y
+ 
+
+ align:start position:0%
+see that we have that for each of the y
+in we have that this interval here lie
+
+ align:start position:0%
+in we have that this interval here lie
+ 
+
+ align:start position:0%
+in we have that this interval here lie
+in a right and they converge to this so
+
+ align:start position:0%
+in a right and they converge to this so
+ 
+
+ align:start position:0%
+in a right and they converge to this so
+it means that if you take anything to
+
+ align:start position:0%
+it means that if you take anything to
+ 
+
+ align:start position:0%
+it means that if you take anything to
+the left
+
+ align:start position:0%
+the left
+ 
+
+ align:start position:0%
+the left
+of y0. Well, then eventually there's
+
+ align:start position:0%
+of y0. Well, then eventually there's
+ 
+
+ align:start position:0%
+of y0. Well, then eventually there's
+some y in to the right of that and so
+
+ align:start position:0%
+some y in to the right of that and so
+ 
+
+ align:start position:0%
+some y in to the right of that and so
+this whole interval is in a right. So
+
+ align:start position:0%
+this whole interval is in a right. So
+ 
+
+ align:start position:0%
+this whole interval is in a right. So
+you see that this it now means that not
+
+ align:start position:0%
+you see that this it now means that not
+ 
+
+ align:start position:0%
+you see that this it now means that not
+only is y z in a but y z is really in
+
+ align:start position:0%
+only is y z in a but y z is really in
+ 
+
+ align:start position:0%
+only is y z in a but y z is really in
+the set b.
+
+ align:start position:0%
+the set b.
+ 
+
+ align:start position:0%
+the set b.
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this here only used that A was closed,
+
+ align:start position:0%
+this here only used that A was closed,
+ 
+
+ align:start position:0%
+this here only used that A was closed,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+So now we need to use that A is open,
+
+ align:start position:0%
+So now we need to use that A is open,
+ 
+
+ align:start position:0%
+So now we need to use that A is open,
+right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So now
+
+ align:start position:0%
+So now
+ 
+
+ align:start position:0%
+So now
+suppose we take a element
+
+ align:start position:0%
+suppose we take a element
+ 
+
+ align:start position:0%
+suppose we take a element
+suppose. So now here we have x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have here b and we want to show that
+
+ align:start position:0%
+we have here b and we want to show that
+ 
+
+ align:start position:0%
+we have here b and we want to show that
+this y0 we define to be the soup of this
+
+ align:start position:0%
+this y0 we define to be the soup of this
+ 
+
+ align:start position:0%
+this y0 we define to be the soup of this
+set capital b. We want to prove that
+
+ align:start position:0%
+set capital b. We want to prove that
+ 
+
+ align:start position:0%
+set capital b. We want to prove that
+this thing here is in fact y zero.
+
+ align:start position:0%
+this thing here is in fact y zero.
+ 
+
+ align:start position:0%
+this thing here is in fact y zero.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+Suppose not suppose that suppose not. So
+
+ align:start position:0%
+Suppose not suppose that suppose not. So
+ 
+
+ align:start position:0%
+Suppose not suppose that suppose not. So
+suppose that you have here strictly
+
+ align:start position:0%
+suppose that you have here strictly
+ 
+
+ align:start position:0%
+suppose that you have here strictly
+between these two this here is y z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we already know that y0
+
+ align:start position:0%
+now we already know that y0
+ 
+
+ align:start position:0%
+now we already know that y0
+is in a. This is what we proved here.
+
+ align:start position:0%
+is in a. This is what we proved here.
+ 
+
+ align:start position:0%
+is in a. This is what we proved here.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+So but since since
+
+ align:start position:0%
+So but since since
+ 
+
+ align:start position:0%
+So but since since
+um uh a here is open
+
+ align:start position:0%
+um uh a here is open
+ 
+
+ align:start position:0%
+um uh a here is open
+there exist some tiny little interval
+
+ align:start position:0%
+there exist some tiny little interval
+ 
+
+ align:start position:0%
+there exist some tiny little interval
+there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some interval here
+
+ align:start position:0%
+some interval here
+ 
+
+ align:start position:0%
+some interval here
+around this y z. So if you take y z and
+
+ align:start position:0%
+around this y z. So if you take y z and
+ 
+
+ align:start position:0%
+around this y z. So if you take y z and
+you subtract this epsilon
+
+ align:start position:0%
+you subtract this epsilon
+ 
+
+ align:start position:0%
+you subtract this epsilon
+so there exists some epsilon greater
+
+ align:start position:0%
+so there exists some epsilon greater
+ 
+
+ align:start position:0%
+so there exists some epsilon greater
+than zero. So that if you're looking at
+
+ align:start position:0%
+than zero. So that if you're looking at
+ 
+
+ align:start position:0%
+than zero. So that if you're looking at
+this tiny little interval centered at y
+
+ align:start position:0%
+this tiny little interval centered at y
+ 
+
+ align:start position:0%
+this tiny little interval centered at y
+z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then this here is contained in a. This
+
+ align:start position:0%
+then this here is contained in a. This
+ 
+
+ align:start position:0%
+then this here is contained in a. This
+is just because a was open right.
+
+ align:start position:0%
+is just because a was open right.
+ 
+
+ align:start position:0%
+is just because a was open right.
+But this means that that now you have
+
+ align:start position:0%
+But this means that that now you have
+ 
+
+ align:start position:0%
+But this means that that now you have
+that. So this here is you assume this is
+
+ align:start position:0%
+that. So this here is you assume this is
+ 
+
+ align:start position:0%
+that. So this here is you assume this is
+y z. So you have that this thing here
+
+ align:start position:0%
+y z. So you have that this thing here
+ 
+
+ align:start position:0%
+y z. So you have that this thing here
+lie in the set capital A and this here I
+
+ align:start position:0%
+lie in the set capital A and this here I
+ 
+
+ align:start position:0%
+lie in the set capital A and this here I
+guarantee you that you can actually go a
+
+ align:start position:0%
+guarantee you that you can actually go a
+ 
+
+ align:start position:0%
+guarantee you that you can actually go a
+little bit past it right that even if
+
+ align:start position:0%
+little bit past it right that even if
+ 
+
+ align:start position:0%
+little bit past it right that even if
+you go a little bit past it if you go a
+
+ align:start position:0%
+you go a little bit past it if you go a
+ 
+
+ align:start position:0%
+you go a little bit past it if you go a
+little bit past it here then these are
+
+ align:start position:0%
+little bit past it here then these are
+ 
+
+ align:start position:0%
+little bit past it here then these are
+still in A right so this means that this
+
+ align:start position:0%
+still in A right so this means that this
+ 
+
+ align:start position:0%
+still in A right so this means that this
+could not be the soup right so therefore
+
+ align:start position:0%
+could not be the soup right so therefore
+ 
+
+ align:start position:0%
+could not be the soup right so therefore
+this point here had to be B right it had
+
+ align:start position:0%
+this point here had to be B right it had
+ 
+
+ align:start position:0%
+this point here had to be B right it had
+to be the final point.
+
+ align:start position:0%
+to be the final point.
+ 
+
+ align:start position:0%
+to be the final point.
+Okay, so this proved these two property,
+
+ align:start position:0%
+Okay, so this proved these two property,
+ 
+
+ align:start position:0%
+Okay, so this proved these two property,
+right? And so once you have these two
+
+ align:start position:0%
+right? And so once you have these two
+ 
+
+ align:start position:0%
+right? And so once you have these two
+property, you have that the interval is
+
+ align:start position:0%
+property, you have that the interval is
+ 
+
+ align:start position:0%
+property, you have that the interval is
+connected, right? That the only non-enty
+
+ align:start position:0%
+connected, right? That the only non-enty
+ 
+
+ align:start position:0%
+connected, right? That the only non-enty
+subset of the interval that is both open
+
+ align:start position:0%
+subset of the interval that is both open
+ 
+
+ align:start position:0%
+subset of the interval that is both open
+and closed is itself. Okay.
+
+ align:start position:0%
+and closed is itself. Okay.
+ 
+
+ align:start position:0%
+and closed is itself. Okay.
+Now why is this related to what we want?
+
+ align:start position:0%
+Now why is this related to what we want?
+ 
+
+ align:start position:0%
+Now why is this related to what we want?
+So this is just so we have
+
+ align:start position:0%
+So this is just so we have
+ 
+
+ align:start position:0%
+So this is just so we have
+suppose you take two functions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So why is this related to the uniqueness
+
+ align:start position:0%
+So why is this related to the uniqueness
+ 
+
+ align:start position:0%
+So why is this related to the uniqueness
+for the OD?
+
+ align:start position:0%
+for the OD?
+ 
+
+ align:start position:0%
+for the OD?
+So this is the following lema.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Suppose you have a interval. So this is
+
+ align:start position:0%
+Suppose you have a interval. So this is
+ 
+
+ align:start position:0%
+Suppose you have a interval. So this is
+a interval
+
+ align:start position:0%
+a interval
+ 
+
+ align:start position:0%
+a interval
+in R and suppose you have two functions
+
+ align:start position:0%
+in R and suppose you have two functions
+ 
+
+ align:start position:0%
+in R and suppose you have two functions
+U1 and U2
+
+ align:start position:0%
+U1 and U2
+ 
+
+ align:start position:0%
+U1 and U2
+they're functions on the interval
+
+ align:start position:0%
+they're functions on the interval
+ 
+
+ align:start position:0%
+they're functions on the interval
+and they are both continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then assume that for some assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+for some X0 0
+
+ align:start position:0%
+for some X0 0
+ 
+
+ align:start position:0%
+for some X0 0
+in the interval
+
+ align:start position:0%
+in the interval
+ 
+
+ align:start position:0%
+in the interval
+uh u 1 of x0 is equal to u2 of x0. So
+
+ align:start position:0%
+uh u 1 of x0 is equal to u2 of x0. So
+ 
+
+ align:start position:0%
+uh u 1 of x0 is equal to u2 of x0. So
+they coincide in one point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And assume you have a second condition.
+
+ align:start position:0%
+And assume you have a second condition.
+ 
+
+ align:start position:0%
+And assume you have a second condition.
+And the second condition is
+
+ align:start position:0%
+And the second condition is
+ 
+
+ align:start position:0%
+And the second condition is
+that if
+
+ align:start position:0%
+that if
+ 
+
+ align:start position:0%
+that if
+uh if u
+
+ align:start position:0%
+uh if u
+ 
+
+ align:start position:0%
+uh if u
+uh of u1 of x is equal to u2
+
+ align:start position:0%
+uh of u1 of x is equal to u2
+ 
+
+ align:start position:0%
+uh of u1 of x is equal to u2
+of x then there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exist
+
+ align:start position:0%
+there exist
+ 
+
+ align:start position:0%
+there exist
+a neighborhood so a epsilon
+
+ align:start position:0%
+a neighborhood so a epsilon
+ 
+
+ align:start position:0%
+a neighborhood so a epsilon
+where this is allowed. not to depend on
+
+ align:start position:0%
+where this is allowed. not to depend on
+ 
+
+ align:start position:0%
+where this is allowed. not to depend on
+x.
+
+ align:start position:0%
+x.
+ 
+
+ align:start position:0%
+x.
+So that uh u 1 is equal to u2 in not
+
+ align:start position:0%
+So that uh u 1 is equal to u2 in not
+ 
+
+ align:start position:0%
+So that uh u 1 is equal to u2 in not
+just at x but actually uh on this little
+
+ align:start position:0%
+just at x but actually uh on this little
+ 
+
+ align:start position:0%
+just at x but actually uh on this little
+interval x minus epsilon x + epsilon.
+
+ align:start position:0%
+interval x minus epsilon x + epsilon.
+ 
+
+ align:start position:0%
+interval x minus epsilon x + epsilon.
+Okay. So you have these two properties.
+
+ align:start position:0%
+Okay. So you have these two properties.
+ 
+
+ align:start position:0%
+Okay. So you have these two properties.
+So you have two continuous functions on
+
+ align:start position:0%
+So you have two continuous functions on
+ 
+
+ align:start position:0%
+So you have two continuous functions on
+an interval. They agree at one point and
+
+ align:start position:0%
+an interval. They agree at one point and
+ 
+
+ align:start position:0%
+an interval. They agree at one point and
+if they agree at any point in this
+
+ align:start position:0%
+if they agree at any point in this
+ 
+
+ align:start position:0%
+if they agree at any point in this
+interval then they agree on a little
+
+ align:start position:0%
+interval then they agree on a little
+ 
+
+ align:start position:0%
+interval then they agree on a little
+neighborhood of that point. Okay. But
+
+ align:start position:0%
+neighborhood of that point. Okay. But
+ 
+
+ align:start position:0%
+neighborhood of that point. Okay. But
+the neighborhood may depend on the
+
+ align:start position:0%
+the neighborhood may depend on the
+ 
+
+ align:start position:0%
+the neighborhood may depend on the
+point. Okay. And then the statement is
+
+ align:start position:0%
+point. Okay. And then the statement is
+ 
+
+ align:start position:0%
+point. Okay. And then the statement is
+so the claim is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that U1
+
+ align:start position:0%
+that U1
+ 
+
+ align:start position:0%
+that U1
+is actually equal to U2 everywhere.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in in the interval where they defined.
+
+ align:start position:0%
+in in the interval where they defined.
+ 
+
+ align:start position:0%
+in in the interval where they defined.
+Okay, that's a claim. Okay. And so now
+
+ align:start position:0%
+Okay, that's a claim. Okay. And so now
+ 
+
+ align:start position:0%
+Okay, that's a claim. Okay. And so now
+you see that if you take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you're looking at so the proof of
+
+ align:start position:0%
+if you're looking at so the proof of
+ 
+
+ align:start position:0%
+if you're looking at so the proof of
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+that suppose so proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose you define a function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and this function here is u1 of x
+
+ align:start position:0%
+uh and this function here is u1 of x
+ 
+
+ align:start position:0%
+uh and this function here is u1 of x
+minus u2 of x. If you define it like
+
+ align:start position:0%
+minus u2 of x. If you define it like
+ 
+
+ align:start position:0%
+minus u2 of x. If you define it like
+this, u1 and u2 are continuous. So f
+
+ align:start position:0%
+this, u1 and u2 are continuous. So f
+ 
+
+ align:start position:0%
+this, u1 and u2 are continuous. So f
+here is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You also have that f of x0. Well, this
+
+ align:start position:0%
+You also have that f of x0. Well, this
+ 
+
+ align:start position:0%
+You also have that f of x0. Well, this
+is u1 of x0 minus u2 of x0.
+
+ align:start position:0%
+is u1 of x0 minus u2 of x0.
+ 
+
+ align:start position:0%
+is u1 of x0 minus u2 of x0.
+And these two function coincided at x0.
+
+ align:start position:0%
+And these two function coincided at x0.
+ 
+
+ align:start position:0%
+And these two function coincided at x0.
+So this is zero.
+
+ align:start position:0%
+So this is zero.
+ 
+
+ align:start position:0%
+So this is zero.
+You also have that if f ofx
+
+ align:start position:0%
+You also have that if f ofx
+ 
+
+ align:start position:0%
+You also have that if f ofx
+so if f of x is equal to zero.
+
+ align:start position:0%
+so if f of x is equal to zero.
+ 
+
+ align:start position:0%
+so if f of x is equal to zero.
+Well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now then then you have by this
+
+ align:start position:0%
+right now then then you have by this
+ 
+
+ align:start position:0%
+right now then then you have by this
+second property here this property here.
+
+ align:start position:0%
+second property here this property here.
+ 
+
+ align:start position:0%
+second property here this property here.
+So if f is zero this is just meaning
+
+ align:start position:0%
+So if f is zero this is just meaning
+ 
+
+ align:start position:0%
+So if f is zero this is just meaning
+that the two function coincided at that
+
+ align:start position:0%
+that the two function coincided at that
+ 
+
+ align:start position:0%
+that the two function coincided at that
+x just means that there exist they exist
+
+ align:start position:0%
+x just means that there exist they exist
+ 
+
+ align:start position:0%
+x just means that there exist they exist
+a delta
+
+ align:start position:0%
+a delta
+ 
+
+ align:start position:0%
+a delta
+epsilon sorry epsilon greater than zero
+
+ align:start position:0%
+epsilon sorry epsilon greater than zero
+ 
+
+ align:start position:0%
+epsilon sorry epsilon greater than zero
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+uh f
+
+ align:start position:0%
+uh f
+ 
+
+ align:start position:0%
+uh f
+um of um of y is equal to zero in this
+
+ align:start position:0%
+um of um of y is equal to zero in this
+ 
+
+ align:start position:0%
+um of um of y is equal to zero in this
+little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interval around
+
+ align:start position:0%
+interval around
+ 
+
+ align:start position:0%
+interval around
+X and so you have that
+
+ align:start position:0%
+X and so you have that
+ 
+
+ align:start position:0%
+X and so you have that
+and now I claim that so now the claim is
+
+ align:start position:0%
+and now I claim that so now the claim is
+ 
+
+ align:start position:0%
+and now I claim that so now the claim is
+that the zero set so the set where the
+
+ align:start position:0%
+that the zero set so the set where the
+ 
+
+ align:start position:0%
+that the zero set so the set where the
+function f is zero this is both open and
+
+ align:start position:0%
+function f is zero this is both open and
+ 
+
+ align:start position:0%
+function f is zero this is both open and
+closed.
+
+ align:start position:0%
+closed.
+ 
+
+ align:start position:0%
+closed.
+So the claim here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that that the set
+
+ align:start position:0%
+that that the set
+ 
+
+ align:start position:0%
+that that the set
+u capital a
+
+ align:start position:0%
+u capital a
+ 
+
+ align:start position:0%
+u capital a
+this is the set of x in the interval
+
+ align:start position:0%
+this is the set of x in the interval
+ 
+
+ align:start position:0%
+this is the set of x in the interval
+where f of x is equal to zero
+
+ align:start position:0%
+where f of x is equal to zero
+ 
+
+ align:start position:0%
+where f of x is equal to zero
+that this here is both
+
+ align:start position:0%
+that this here is both
+ 
+
+ align:start position:0%
+that this here is both
+open and closed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? We already know that this set
+
+ align:start position:0%
+Right? We already know that this set
+ 
+
+ align:start position:0%
+Right? We already know that this set
+this is follow up here that that x0 is
+
+ align:start position:0%
+this is follow up here that that x0 is
+ 
+
+ align:start position:0%
+this is follow up here that that x0 is
+so since
+
+ align:start position:0%
+so since
+ 
+
+ align:start position:0%
+so since
+since x0 is in this set then we have and
+
+ align:start position:0%
+since x0 is in this set then we have and
+ 
+
+ align:start position:0%
+since x0 is in this set then we have and
+the integral is connected and
+
+ align:start position:0%
+the integral is connected and
+ 
+
+ align:start position:0%
+the integral is connected and
+I is connected.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If this set is both open and closed,
+
+ align:start position:0%
+If this set is both open and closed,
+ 
+
+ align:start position:0%
+If this set is both open and closed,
+then we have that then uh a is equal to
+
+ align:start position:0%
+then we have that then uh a is equal to
+ 
+
+ align:start position:0%
+then we have that then uh a is equal to
+the whole interval. Right? So this means
+
+ align:start position:0%
+the whole interval. Right? So this means
+ 
+
+ align:start position:0%
+the whole interval. Right? So this means
+that the that f is constant zero which
+
+ align:start position:0%
+that the that f is constant zero which
+ 
+
+ align:start position:0%
+that the that f is constant zero which
+means that the two functions coincided
+
+ align:start position:0%
+means that the two functions coincided
+ 
+
+ align:start position:0%
+means that the two functions coincided
+everywhere. Right? And so we just need
+
+ align:start position:0%
+everywhere. Right? And so we just need
+ 
+
+ align:start position:0%
+everywhere. Right? And so we just need
+to prove that f is
+
+ align:start position:0%
+to prove that f is
+ 
+
+ align:start position:0%
+to prove that f is
+both uh open and closed. But the zero
+
+ align:start position:0%
+both uh open and closed. But the zero
+ 
+
+ align:start position:0%
+both uh open and closed. But the zero
+set if you take a continuous function
+
+ align:start position:0%
+set if you take a continuous function
+ 
+
+ align:start position:0%
+set if you take a continuous function
+right. So if if f here is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you have a sequence
+
+ align:start position:0%
+and you have a sequence
+ 
+
+ align:start position:0%
+and you have a sequence
+so that each element here in the
+
+ align:start position:0%
+so that each element here in the
+ 
+
+ align:start position:0%
+so that each element here in the
+sequence is zero and these xn converts
+
+ align:start position:0%
+sequence is zero and these xn converts
+ 
+
+ align:start position:0%
+sequence is zero and these xn converts
+to some x. Well then by continuity right
+
+ align:start position:0%
+to some x. Well then by continuity right
+ 
+
+ align:start position:0%
+to some x. Well then by continuity right
+by by continuity
+
+ align:start position:0%
+by by continuity
+ 
+
+ align:start position:0%
+by by continuity
+f of x would also be zero. This is by
+
+ align:start position:0%
+f of x would also be zero. This is by
+ 
+
+ align:start position:0%
+f of x would also be zero. This is by
+continuity
+
+ align:start position:0%
+continuity
+ 
+
+ align:start position:0%
+continuity
+right we already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this means that this set here is
+
+ align:start position:0%
+so this means that this set here is
+ 
+
+ align:start position:0%
+so this means that this set here is
+definitely closed right and the open
+
+ align:start position:0%
+definitely closed right and the open
+ 
+
+ align:start position:0%
+definitely closed right and the open
+thing with the open is just exactly this
+
+ align:start position:0%
+thing with the open is just exactly this
+ 
+
+ align:start position:0%
+thing with the open is just exactly this
+property that we're assuming that if you
+
+ align:start position:0%
+property that we're assuming that if you
+ 
+
+ align:start position:0%
+property that we're assuming that if you
+have an element in it each element is
+
+ align:start position:0%
+have an element in it each element is
+ 
+
+ align:start position:0%
+have an element in it each element is
+interior which means that there is this
+
+ align:start position:0%
+interior which means that there is this
+ 
+
+ align:start position:0%
+interior which means that there is this
+little interval around it right so you
+
+ align:start position:0%
+little interval around it right so you
+ 
+
+ align:start position:0%
+little interval around it right so you
+have we have proven that it's both uh
+
+ align:start position:0%
+have we have proven that it's both uh
+ 
+
+ align:start position:0%
+have we have proven that it's both uh
+closed. We prove that first and also
+
+ align:start position:0%
+closed. We prove that first and also
+ 
+
+ align:start position:0%
+closed. We prove that first and also
+open. And so we have that that if you
+
+ align:start position:0%
+open. And so we have that that if you
+ 
+
+ align:start position:0%
+open. And so we have that that if you
+have two such function
+
+ align:start position:0%
+have two such function
+ 
+
+ align:start position:0%
+have two such function
+defined both continuous and defined on
+
+ align:start position:0%
+defined both continuous and defined on
+ 
+
+ align:start position:0%
+defined both continuous and defined on
+an interval they coincide at one point
+
+ align:start position:0%
+an interval they coincide at one point
+ 
+
+ align:start position:0%
+an interval they coincide at one point
+and if they coincide at one point then
+
+ align:start position:0%
+and if they coincide at one point then
+ 
+
+ align:start position:0%
+and if they coincide at one point then
+they coincide in a little neighborhood.
+
+ align:start position:0%
+they coincide in a little neighborhood.
+ 
+
+ align:start position:0%
+they coincide in a little neighborhood.
+If you have two function with this
+
+ align:start position:0%
+If you have two function with this
+ 
+
+ align:start position:0%
+If you have two function with this
+property then they must be equal in the
+
+ align:start position:0%
+property then they must be equal in the
+ 
+
+ align:start position:0%
+property then they must be equal in the
+whole interval. Right? Okay. So now how
+
+ align:start position:0%
+whole interval. Right? Okay. So now how
+ 
+
+ align:start position:0%
+whole interval. Right? Okay. So now how
+does this relate to the the uniqueness
+
+ align:start position:0%
+does this relate to the the uniqueness
+ 
+
+ align:start position:0%
+does this relate to the the uniqueness
+that we wanted to prove?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we're starting again. So we have the
+
+ align:start position:0%
+So we're starting again. So we have the
+ 
+
+ align:start position:0%
+So we're starting again. So we have the
+so we have so this is again the picard
+
+ align:start position:0%
+so we have so this is again the picard
+ 
+
+ align:start position:0%
+so we have so this is again the picard
+linder theorem and this is the
+
+ align:start position:0%
+linder theorem and this is the
+ 
+
+ align:start position:0%
+linder theorem and this is the
+uniqueness part.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so you're looking at again you're
+
+ align:start position:0%
+And so you're looking at again you're
+ 
+
+ align:start position:0%
+And so you're looking at again you're
+looking at solutions
+
+ align:start position:0%
+looking at solutions
+ 
+
+ align:start position:0%
+looking at solutions
+to to this OD.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and we have that now we had that um
+
+ align:start position:0%
+Um and we have that now we had that um
+ 
+
+ align:start position:0%
+Um and we have that now we had that um
+in a we have that in a so and then we
+
+ align:start position:0%
+in a we have that in a so and then we
+ 
+
+ align:start position:0%
+in a we have that in a so and then we
+let sorry and let y1
+
+ align:start position:0%
+let sorry and let y1
+ 
+
+ align:start position:0%
+let sorry and let y1
+and y2 be solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's say that these two they may be
+
+ align:start position:0%
+and let's say that these two they may be
+ 
+
+ align:start position:0%
+and let's say that these two they may be
+defined on different interval of course
+
+ align:start position:0%
+defined on different interval of course
+ 
+
+ align:start position:0%
+defined on different interval of course
+you know but but you just take the
+
+ align:start position:0%
+you know but but you just take the
+ 
+
+ align:start position:0%
+you know but but you just take the
+intersection of the two intervals that
+
+ align:start position:0%
+intersection of the two intervals that
+ 
+
+ align:start position:0%
+intersection of the two intervals that
+they're defined. So suppose that they're
+
+ align:start position:0%
+they're defined. So suppose that they're
+ 
+
+ align:start position:0%
+they're defined. So suppose that they're
+both defined say on the same interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+and this interval here and I of course
+
+ align:start position:0%
+and this interval here and I of course
+ 
+
+ align:start position:0%
+and this interval here and I of course
+has to include the zero where we want
+
+ align:start position:0%
+has to include the zero where we want
+ 
+
+ align:start position:0%
+has to include the zero where we want
+this condition.
+
+ align:start position:0%
+this condition.
+ 
+
+ align:start position:0%
+this condition.
+Well then we have what do we have? So we
+
+ align:start position:0%
+Well then we have what do we have? So we
+ 
+
+ align:start position:0%
+Well then we have what do we have? So we
+have a interval and we have two
+
+ align:start position:0%
+have a interval and we have two
+ 
+
+ align:start position:0%
+have a interval and we have two
+continuous functions. They're actually
+
+ align:start position:0%
+continuous functions. They're actually
+ 
+
+ align:start position:0%
+continuous functions. They're actually
+better than continuous. They're
+
+ align:start position:0%
+better than continuous. They're
+ 
+
+ align:start position:0%
+better than continuous. They're
+differentiable
+
+ align:start position:0%
+differentiable
+ 
+
+ align:start position:0%
+differentiable
+and even the derivative is continuous.
+
+ align:start position:0%
+and even the derivative is continuous.
+ 
+
+ align:start position:0%
+and even the derivative is continuous.
+But but never mind that. Uh we have that
+
+ align:start position:0%
+But but never mind that. Uh we have that
+ 
+
+ align:start position:0%
+But but never mind that. Uh we have that
+we have that y1 of zero is equal to a
+
+ align:start position:0%
+we have that y1 of zero is equal to a
+ 
+
+ align:start position:0%
+we have that y1 of zero is equal to a
+and that's equal to y2 of zero. So they
+
+ align:start position:0%
+and that's equal to y2 of zero. So they
+ 
+
+ align:start position:0%
+and that's equal to y2 of zero. So they
+coincide at one point.
+
+ align:start position:0%
+coincide at one point.
+ 
+
+ align:start position:0%
+coincide at one point.
+And now the you the Picard Lindelof
+
+ align:start position:0%
+And now the you the Picard Lindelof
+ 
+
+ align:start position:0%
+And now the you the Picard Lindelof
+theorem said that because there were two
+
+ align:start position:0%
+theorem said that because there were two
+ 
+
+ align:start position:0%
+theorem said that because there were two
+solutions if you restrict the interval
+
+ align:start position:0%
+solutions if you restrict the interval
+ 
+
+ align:start position:0%
+solutions if you restrict the interval
+right to looking at this little interval
+
+ align:start position:0%
+right to looking at this little interval
+ 
+
+ align:start position:0%
+right to looking at this little interval
+around zero but then there was a unique
+
+ align:start position:0%
+around zero but then there was a unique
+ 
+
+ align:start position:0%
+around zero but then there was a unique
+fixed point right so it means that in a
+
+ align:start position:0%
+fixed point right so it means that in a
+ 
+
+ align:start position:0%
+fixed point right so it means that in a
+small neighborhood
+
+ align:start position:0%
+small neighborhood
+ 
+
+ align:start position:0%
+small neighborhood
+of the origin so two in a small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neighborhood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+origin. This is again this is thanks to
+
+ align:start position:0%
+origin. This is again this is thanks to
+ 
+
+ align:start position:0%
+origin. This is again this is thanks to
+that in the contracting mapping theorem
+
+ align:start position:0%
+that in the contracting mapping theorem
+ 
+
+ align:start position:0%
+that in the contracting mapping theorem
+you had a unique fixed point in a small
+
+ align:start position:0%
+you had a unique fixed point in a small
+ 
+
+ align:start position:0%
+you had a unique fixed point in a small
+neighborhood of the origin y1
+
+ align:start position:0%
+neighborhood of the origin y1
+ 
+
+ align:start position:0%
+neighborhood of the origin y1
+is equal to y2 right but actually the
+
+ align:start position:0%
+is equal to y2 right but actually the
+ 
+
+ align:start position:0%
+is equal to y2 right but actually the
+pical line the argument would work at
+
+ align:start position:0%
+pical line the argument would work at
+ 
+
+ align:start position:0%
+pical line the argument would work at
+any other point right suppose you take
+
+ align:start position:0%
+any other point right suppose you take
+ 
+
+ align:start position:0%
+any other point right suppose you take
+any other point then you and you take a
+
+ align:start position:0%
+any other point then you and you take a
+ 
+
+ align:start position:0%
+any other point then you and you take a
+solution to the OD well if If you take
+
+ align:start position:0%
+solution to the OD well if If you take
+ 
+
+ align:start position:0%
+solution to the OD well if If you take
+another point then the value so suppose
+
+ align:start position:0%
+another point then the value so suppose
+ 
+
+ align:start position:0%
+another point then the value so suppose
+so so if you take so take you any other
+
+ align:start position:0%
+so so if you take so take you any other
+ 
+
+ align:start position:0%
+so so if you take so take you any other
+point so here you have zero
+
+ align:start position:0%
+point so here you have zero
+ 
+
+ align:start position:0%
+point so here you have zero
+and so now take any other points let's
+
+ align:start position:0%
+and so now take any other points let's
+ 
+
+ align:start position:0%
+and so now take any other points let's
+call it x0
+
+ align:start position:0%
+call it x0
+ 
+
+ align:start position:0%
+call it x0
+and if you assume that these two
+
+ align:start position:0%
+and if you assume that these two
+ 
+
+ align:start position:0%
+and if you assume that these two
+functions coincide at this point so
+
+ align:start position:0%
+functions coincide at this point so
+ 
+
+ align:start position:0%
+functions coincide at this point so
+suppose that y1
+
+ align:start position:0%
+suppose that y1
+ 
+
+ align:start position:0%
+suppose that y1
+of x0 is equal to y2
+
+ align:start position:0%
+of x0 is equal to y2
+ 
+
+ align:start position:0%
+of x0 is equal to y2
+of x0. If you now restrict this
+
+ align:start position:0%
+of x0. If you now restrict this
+ 
+
+ align:start position:0%
+of x0. If you now restrict this
+interval,
+
+ align:start position:0%
+interval,
+ 
+
+ align:start position:0%
+interval,
+make it sufficiently small, then the
+
+ align:start position:0%
+make it sufficiently small, then the
+ 
+
+ align:start position:0%
+make it sufficiently small, then the
+argument of picard lindelof tells you
+
+ align:start position:0%
+argument of picard lindelof tells you
+ 
+
+ align:start position:0%
+argument of picard lindelof tells you
+that you had this unique fixed point. So
+
+ align:start position:0%
+that you had this unique fixed point. So
+ 
+
+ align:start position:0%
+that you had this unique fixed point. So
+you had a unique solution on this little
+
+ align:start position:0%
+you had a unique solution on this little
+ 
+
+ align:start position:0%
+you had a unique solution on this little
+interval. But since they coincide at
+
+ align:start position:0%
+interval. But since they coincide at
+ 
+
+ align:start position:0%
+interval. But since they coincide at
+this point, it means that they must be
+
+ align:start position:0%
+this point, it means that they must be
+ 
+
+ align:start position:0%
+this point, it means that they must be
+the same in this little interval. And so
+
+ align:start position:0%
+the same in this little interval. And so
+ 
+
+ align:start position:0%
+the same in this little interval. And so
+you see that now we have the condition
+
+ align:start position:0%
+you see that now we have the condition
+ 
+
+ align:start position:0%
+you see that now we have the condition
+for for the lema okay for the lema that
+
+ align:start position:0%
+for for the lema okay for the lema that
+ 
+
+ align:start position:0%
+for for the lema okay for the lema that
+said that so you have these two
+
+ align:start position:0%
+said that so you have these two
+ 
+
+ align:start position:0%
+said that so you have these two
+continuous function and they were equal
+
+ align:start position:0%
+continuous function and they were equal
+ 
+
+ align:start position:0%
+continuous function and they were equal
+at one point and if they're equal at a
+
+ align:start position:0%
+at one point and if they're equal at a
+ 
+
+ align:start position:0%
+at one point and if they're equal at a
+point then they're equal in a whole
+
+ align:start position:0%
+point then they're equal in a whole
+ 
+
+ align:start position:0%
+point then they're equal in a whole
+neighborhood. Okay so these two
+
+ align:start position:0%
+neighborhood. Okay so these two
+ 
+
+ align:start position:0%
+neighborhood. Okay so these two
+functions these two solutions are equal
+
+ align:start position:0%
+functions these two solutions are equal
+ 
+
+ align:start position:0%
+functions these two solutions are equal
+on the on the interval where they're
+
+ align:start position:0%
+on the on the interval where they're
+ 
+
+ align:start position:0%
+on the on the interval where they're
+both defined. Okay.
+
+ align:start position:0%
+both defined. Okay.
+ 
+
+ align:start position:0%
+both defined. Okay.
+Now Okay. Okay. So now you might and and
+
+ align:start position:0%
+Now Okay. Okay. So now you might and and
+ 
+
+ align:start position:0%
+Now Okay. Okay. So now you might and and
+then I want to do a little bit of review
+
+ align:start position:0%
+then I want to do a little bit of review
+ 
+
+ align:start position:0%
+then I want to do a little bit of review
+at the end. So at least say something
+
+ align:start position:0%
+at the end. So at least say something
+ 
+
+ align:start position:0%
+at the end. So at least say something
+about the the final. But before we get
+
+ align:start position:0%
+about the the final. But before we get
+ 
+
+ align:start position:0%
+about the the final. But before we get
+to that, let me just make one more
+
+ align:start position:0%
+to that, let me just make one more
+ 
+
+ align:start position:0%
+to that, let me just make one more
+observation
+
+ align:start position:0%
+observation
+ 
+
+ align:start position:0%
+observation
+about the picard line.
+
+ align:start position:0%
+about the picard line.
+ 
+
+ align:start position:0%
+about the picard line.
+So you may
+
+ align:start position:0%
+So you may
+ 
+
+ align:start position:0%
+So you may
+say that in the proof of the picard
+
+ align:start position:0%
+say that in the proof of the picard
+ 
+
+ align:start position:0%
+say that in the proof of the picard
+linder we kind of had to restrict the
+
+ align:start position:0%
+linder we kind of had to restrict the
+ 
+
+ align:start position:0%
+linder we kind of had to restrict the
+interval. Is that really necessary? Why
+
+ align:start position:0%
+interval. Is that really necessary? Why
+ 
+
+ align:start position:0%
+interval. Is that really necessary? Why
+should we restrict? Why should we only
+
+ align:start position:0%
+should we restrict? Why should we only
+ 
+
+ align:start position:0%
+should we restrict? Why should we only
+be able to say that we had a solution in
+
+ align:start position:0%
+be able to say that we had a solution in
+ 
+
+ align:start position:0%
+be able to say that we had a solution in
+a very small interval? And so if you're
+
+ align:start position:0%
+a very small interval? And so if you're
+ 
+
+ align:start position:0%
+a very small interval? And so if you're
+looking at the example, suppose you're
+
+ align:start position:0%
+looking at the example, suppose you're
+ 
+
+ align:start position:0%
+looking at the example, suppose you're
+looking at the example
+
+ align:start position:0%
+looking at the example
+ 
+
+ align:start position:0%
+looking at the example
+where y where f
+
+ align:start position:0%
+where y where f
+ 
+
+ align:start position:0%
+where y where f
+so f of y
+
+ align:start position:0%
+so f of y
+ 
+
+ align:start position:0%
+so f of y
+is equal to y 2 g of x is equal to zero.
+
+ align:start position:0%
+is equal to y 2 g of x is equal to zero.
+ 
+
+ align:start position:0%
+is equal to y 2 g of x is equal to zero.
+And so you're looking at the OD the
+
+ align:start position:0%
+And so you're looking at the OD the
+ 
+
+ align:start position:0%
+And so you're looking at the OD the
+solutions here y so that's uh y prime is
+
+ align:start position:0%
+solutions here y so that's uh y prime is
+ 
+
+ align:start position:0%
+solutions here y so that's uh y prime is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+y 2 and uh let's say equal to a
+
+ align:start position:0%
+y 2 and uh let's say equal to a
+ 
+
+ align:start position:0%
+y 2 and uh let's say equal to a
+uh form
+
+ align:start position:0%
+uh form
+ 
+
+ align:start position:0%
+uh form
+uh x
+
+ align:start position:0%
+uh x
+ 
+
+ align:start position:0%
+uh x
+uh equal to x0
+
+ align:start position:0%
+uh equal to x0
+ 
+
+ align:start position:0%
+uh equal to x0
+okay so suppose you're looking at a like
+
+ align:start position:0%
+okay so suppose you're looking at a like
+ 
+
+ align:start position:0%
+okay so suppose you're looking at a like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+right so at this x0 you want the value
+
+ align:start position:0%
+right so at this x0 you want the value
+ 
+
+ align:start position:0%
+right so at this x0 you want the value
+of the function to be so you want sorry
+
+ align:start position:0%
+of the function to be so you want sorry
+ 
+
+ align:start position:0%
+of the function to be so you want sorry
+y of uh x0
+
+ align:start position:0%
+y of uh x0
+ 
+
+ align:start position:0%
+y of uh x0
+uh equal to
+
+ align:start position:0%
+uh equal to
+ 
+
+ align:start position:0%
+uh equal to
+want maybe I should maybe this is a
+
+ align:start position:0%
+want maybe I should maybe this is a
+ 
+
+ align:start position:0%
+want maybe I should maybe this is a
+little bit bad notation so I want a a
+
+ align:start position:0%
+little bit bad notation so I want a a
+ 
+
+ align:start position:0%
+little bit bad notation so I want a a
+function so that y prime is equal to y^
+
+ align:start position:0%
+function so that y prime is equal to y^
+ 
+
+ align:start position:0%
+function so that y prime is equal to y^
+2 and I want y of x0 = a Right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now let's say that x0
+
+ align:start position:0%
+Okay. Now let's say that x0
+ 
+
+ align:start position:0%
+Okay. Now let's say that x0
+and a are both positive.
+
+ align:start position:0%
+and a are both positive.
+ 
+
+ align:start position:0%
+and a are both positive.
+So if you're looking at this OD
+
+ align:start position:0%
+So if you're looking at this OD
+ 
+
+ align:start position:0%
+So if you're looking at this OD
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+then you can just this one here is easy
+
+ align:start position:0%
+then you can just this one here is easy
+ 
+
+ align:start position:0%
+then you can just this one here is easy
+to solve
+
+ align:start position:0%
+to solve
+ 
+
+ align:start position:0%
+to solve
+because you have a function
+
+ align:start position:0%
+because you have a function
+ 
+
+ align:start position:0%
+because you have a function
+you have a function y prime
+
+ align:start position:0%
+you have a function y prime
+ 
+
+ align:start position:0%
+you have a function y prime
+equal to y²
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now let's try to find a solution in
+
+ align:start position:0%
+and now let's try to find a solution in
+ 
+
+ align:start position:0%
+and now let's try to find a solution in
+a neighborhood of x0 but there supposed
+
+ align:start position:0%
+a neighborhood of x0 but there supposed
+ 
+
+ align:start position:0%
+a neighborhood of x0 but there supposed
+to be positive. So in a small
+
+ align:start position:0%
+to be positive. So in a small
+ 
+
+ align:start position:0%
+to be positive. So in a small
+neighborhood it's positive. So I can
+
+ align:start position:0%
+neighborhood it's positive. So I can
+ 
+
+ align:start position:0%
+neighborhood it's positive. So I can
+divide by y^2. So I can looking at so
+
+ align:start position:0%
+divide by y^2. So I can looking at so
+ 
+
+ align:start position:0%
+divide by y^2. So I can looking at so
+this thing here is equivalent to that y
+
+ align:start position:0%
+this thing here is equivalent to that y
+ 
+
+ align:start position:0%
+this thing here is equivalent to that y
+prime over y^ 2 is equal to 1.
+
+ align:start position:0%
+prime over y^ 2 is equal to 1.
+ 
+
+ align:start position:0%
+prime over y^ 2 is equal to 1.
+And this thing here I can write as 1 / y
+
+ align:start position:0%
+And this thing here I can write as 1 / y
+ 
+
+ align:start position:0%
+And this thing here I can write as 1 / y
+prime * -1. this thing here, if you're
+
+ align:start position:0%
+prime * -1. this thing here, if you're
+ 
+
+ align:start position:0%
+prime * -1. this thing here, if you're
+looking at this function here by the
+
+ align:start position:0%
+looking at this function here by the
+ 
+
+ align:start position:0%
+looking at this function here by the
+chain rule, it's equal to that, right?
+
+ align:start position:0%
+chain rule, it's equal to that, right?
+ 
+
+ align:start position:0%
+chain rule, it's equal to that, right?
+And so this means that now you can apply
+
+ align:start position:0%
+And so this means that now you can apply
+ 
+
+ align:start position:0%
+And so this means that now you can apply
+the fundamental theorem of calculus. And
+
+ align:start position:0%
+the fundamental theorem of calculus. And
+ 
+
+ align:start position:0%
+the fundamental theorem of calculus. And
+if you're integrating this function here
+
+ align:start position:0%
+if you're integrating this function here
+ 
+
+ align:start position:0%
+if you're integrating this function here
+and you're integrating it from
+
+ align:start position:0%
+and you're integrating it from
+ 
+
+ align:start position:0%
+and you're integrating it from
+uh two values uh x0 to x
+
+ align:start position:0%
+uh two values uh x0 to x
+ 
+
+ align:start position:0%
+uh two values uh x0 to x
+uh d
+
+ align:start position:0%
+uh d
+ 
+
+ align:start position:0%
+uh d
+uh uh d of s sorry this is the prime.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then what you get is that this thing
+
+ align:start position:0%
+Then what you get is that this thing
+ 
+
+ align:start position:0%
+Then what you get is that this thing
+here is equal to well on one hand by the
+
+ align:start position:0%
+here is equal to well on one hand by the
+ 
+
+ align:start position:0%
+here is equal to well on one hand by the
+fundamental theorem of calculus it's 1 /
+
+ align:start position:0%
+fundamental theorem of calculus it's 1 /
+ 
+
+ align:start position:0%
+fundamental theorem of calculus it's 1 /
+y of x minus and then there's a minus
+
+ align:start position:0%
+y of x minus and then there's a minus
+ 
+
+ align:start position:0%
+y of x minus and then there's a minus
+sign sorry this here because of this
+
+ align:start position:0%
+sign sorry this here because of this
+ 
+
+ align:start position:0%
+sign sorry this here because of this
+minus sign. So it's minus this plus 1 /
+
+ align:start position:0%
+minus sign. So it's minus this plus 1 /
+ 
+
+ align:start position:0%
+minus sign. So it's minus this plus 1 /
+y of x0
+
+ align:start position:0%
+y of x0
+ 
+
+ align:start position:0%
+y of x0
+and on the other hand it's equal to this
+
+ align:start position:0%
+and on the other hand it's equal to this
+ 
+
+ align:start position:0%
+and on the other hand it's equal to this
+and when you're integrating this on this
+
+ align:start position:0%
+and when you're integrating this on this
+ 
+
+ align:start position:0%
+and when you're integrating this on this
+interval here so this also equal to x0 x
+
+ align:start position:0%
+interval here so this also equal to x0 x
+ 
+
+ align:start position:0%
+interval here so this also equal to x0 x
+um and then one d s this thing here is
+
+ align:start position:0%
+um and then one d s this thing here is
+ 
+
+ align:start position:0%
+um and then one d s this thing here is
+just x - x0
+
+ align:start position:0%
+just x - x0
+ 
+
+ align:start position:0%
+just x - x0
+x - x0
+
+ align:start position:0%
+x - x0
+ 
+
+ align:start position:0%
+x - x0
+okay So if you solve it then let me just
+
+ align:start position:0%
+okay So if you solve it then let me just
+ 
+
+ align:start position:0%
+okay So if you solve it then let me just
+write the result. If you check what this
+
+ align:start position:0%
+write the result. If you check what this
+ 
+
+ align:start position:0%
+write the result. If you check what this
+gives you,
+
+ align:start position:0%
+gives you,
+ 
+
+ align:start position:0%
+gives you,
+this gives you that um when you solve it
+
+ align:start position:0%
+this gives you that um when you solve it
+ 
+
+ align:start position:0%
+this gives you that um when you solve it
+like this, uh you're getting
+
+ align:start position:0%
+like this, uh you're getting
+ 
+
+ align:start position:0%
+like this, uh you're getting
+you're getting that y here is so you
+
+ align:start position:0%
+you're getting that y here is so you
+ 
+
+ align:start position:0%
+you're getting that y here is so you
+have this od here
+
+ align:start position:0%
+have this od here
+ 
+
+ align:start position:0%
+have this od here
+and you're assuming that these things
+
+ align:start position:0%
+and you're assuming that these things
+ 
+
+ align:start position:0%
+and you're assuming that these things
+here are positive and then the solutions
+
+ align:start position:0%
+here are positive and then the solutions
+ 
+
+ align:start position:0%
+here are positive and then the solutions
+are of the form y of x
+
+ align:start position:0%
+are of the form y of x
+ 
+
+ align:start position:0%
+are of the form y of x
+= a over 1 + a
+
+ align:start position:0%
+= a over 1 + a
+ 
+
+ align:start position:0%
+= a over 1 + a
+uh x0 - x right
+
+ align:start position:0%
+uh x0 - x right
+ 
+
+ align:start position:0%
+uh x0 - x right
+and so what you should observe here is
+
+ align:start position:0%
+and so what you should observe here is
+ 
+
+ align:start position:0%
+and so what you should observe here is
+that this thing here right as this is
+
+ align:start position:0%
+that this thing here right as this is
+ 
+
+ align:start position:0%
+that this thing here right as this is
+not defined. So this is note
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that y is not defined
+
+ align:start position:0%
+that y is not defined
+ 
+
+ align:start position:0%
+that y is not defined
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on all of r. But instead as x here goes
+
+ align:start position:0%
+on all of r. But instead as x here goes
+ 
+
+ align:start position:0%
+on all of r. But instead as x here goes
+to uh x0
+
+ align:start position:0%
+to uh x0
+ 
+
+ align:start position:0%
+to uh x0
+um + 1.
+
+ align:start position:0%
+um + 1.
+ 
+
+ align:start position:0%
+um + 1.
+As x0 goes to this, this thing here goes
+
+ align:start position:0%
+As x0 goes to this, this thing here goes
+ 
+
+ align:start position:0%
+As x0 goes to this, this thing here goes
+to minus one. So the denominator goes to
+
+ align:start position:0%
+to minus one. So the denominator goes to
+ 
+
+ align:start position:0%
+to minus one. So the denominator goes to
+zero. So the function blows up. Right?
+
+ align:start position:0%
+zero. So the function blows up. Right?
+ 
+
+ align:start position:0%
+zero. So the function blows up. Right?
+So this is so this here show you that it
+
+ align:start position:0%
+So this is so this here show you that it
+ 
+
+ align:start position:0%
+So this is so this here show you that it
+does in a neighborhood of this point. It
+
+ align:start position:0%
+does in a neighborhood of this point. It
+ 
+
+ align:start position:0%
+does in a neighborhood of this point. It
+has a solution but that neighborhood is
+
+ align:start position:0%
+has a solution but that neighborhood is
+ 
+
+ align:start position:0%
+has a solution but that neighborhood is
+not you know it's some relatively small
+
+ align:start position:0%
+not you know it's some relatively small
+ 
+
+ align:start position:0%
+not you know it's some relatively small
+neighborhoods and the function you
+
+ align:start position:0%
+neighborhoods and the function you
+ 
+
+ align:start position:0%
+neighborhoods and the function you
+cannot extend it past a you know past as
+
+ align:start position:0%
+cannot extend it past a you know past as
+ 
+
+ align:start position:0%
+cannot extend it past a you know past as
+a a certain value you can't extend it
+
+ align:start position:0%
+a a certain value you can't extend it
+ 
+
+ align:start position:0%
+a a certain value you can't extend it
+past in this case you can't extend it
+
+ align:start position:0%
+past in this case you can't extend it
+ 
+
+ align:start position:0%
+past in this case you can't extend it
+past this point here so to the left of
+
+ align:start position:0%
+past this point here so to the left of
+ 
+
+ align:start position:0%
+past this point here so to the left of
+this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the sorry to the to the right I guess
+
+ align:start position:0%
+to the sorry to the to the right I guess
+ 
+
+ align:start position:0%
+to the sorry to the to the right I guess
+of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay. So now I want to say a little bit
+
+ align:start position:0%
+Okay. So now I want to say a little bit
+ 
+
+ align:start position:0%
+Okay. So now I want to say a little bit
+about the the final. Yeah. Sorry.
+
+ align:start position:0%
+about the the final. Yeah. Sorry.
+ 
+
+ align:start position:0%
+about the the final. Yeah. Sorry.
+>> Why is it that you can't um once you
+
+ align:start position:0%
+>> Why is it that you can't um once you
+ 
+
+ align:start position:0%
+>> Why is it that you can't um once you
+reach that point where it blows up does
+
+ align:start position:0%
+reach that point where it blows up does
+ 
+
+ align:start position:0%
+reach that point where it blows up does
+it like it never solves differential
+
+ align:start position:0%
+it like it never solves differential
+ 
+
+ align:start position:0%
+it like it never solves differential
+equation past that point?
+
+ align:start position:0%
+equation past that point?
+ 
+
+ align:start position:0%
+equation past that point?
+>> Yeah, that's right. So so the thing is
+
+ align:start position:0%
+>> Yeah, that's right. So so the thing is
+ 
+
+ align:start position:0%
+>> Yeah, that's right. So so the thing is
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so right. So this here this OD is going
+
+ align:start position:0%
+so right. So this here this OD is going
+ 
+
+ align:start position:0%
+so right. So this here this OD is going
+to force it to once this here once Y
+
+ align:start position:0%
+to force it to once this here once Y
+ 
+
+ align:start position:0%
+to force it to once this here once Y
+become large then why become really
+
+ align:start position:0%
+become large then why become really
+ 
+
+ align:start position:0%
+become large then why become really
+really large so it become large too
+
+ align:start position:0%
+really large so it become large too
+ 
+
+ align:start position:0%
+really large so it become large too
+quickly so it becomes quickly so that so
+
+ align:start position:0%
+quickly so it becomes quickly so that so
+ 
+
+ align:start position:0%
+quickly so it becomes quickly so that so
+it would give you some sort of OD like
+
+ align:start position:0%
+it would give you some sort of OD like
+ 
+
+ align:start position:0%
+it would give you some sort of OD like
+this that you have some critical value
+
+ align:start position:0%
+this that you have some critical value
+ 
+
+ align:start position:0%
+this that you have some critical value
+where you couldn't extend it past that
+
+ align:start position:0%
+where you couldn't extend it past that
+ 
+
+ align:start position:0%
+where you couldn't extend it past that
+because it is it will have like a a
+
+ align:start position:0%
+because it is it will have like a a
+ 
+
+ align:start position:0%
+because it is it will have like a a
+tangent that is that is going vertical
+
+ align:start position:0%
+tangent that is that is going vertical
+ 
+
+ align:start position:0%
+tangent that is that is going vertical
+like this. Okay. And
+
+ align:start position:0%
+like this. Okay. And
+ 
+
+ align:start position:0%
+like this. Okay. And
+>> so you can't So, so this means that
+
+ align:start position:0%
+>> so you can't So, so this means that
+ 
+
+ align:start position:0%
+>> so you can't So, so this means that
+there's, you know, that's right. So, so
+
+ align:start position:0%
+there's, you know, that's right. So, so
+ 
+
+ align:start position:0%
+there's, you know, that's right. So, so
+um but so, so you have a solution that
+
+ align:start position:0%
+um but so, so you have a solution that
+ 
+
+ align:start position:0%
+um but so, so you have a solution that
+exists on some interval, but it doesn't
+
+ align:start position:0%
+exists on some interval, but it doesn't
+ 
+
+ align:start position:0%
+exists on some interval, but it doesn't
+exist past this point. So, you can't
+
+ align:start position:0%
+exist past this point. So, you can't
+ 
+
+ align:start position:0%
+exist past this point. So, you can't
+have a solution,
+
+ align:start position:0%
+have a solution,
+ 
+
+ align:start position:0%
+have a solution,
+uh, you know, on some interval larger
+
+ align:start position:0%
+uh, you know, on some interval larger
+ 
+
+ align:start position:0%
+uh, you know, on some interval larger
+than than this to the left. and and this
+
+ align:start position:0%
+than than this to the left. and and this
+ 
+
+ align:start position:0%
+than than this to the left. and and this
+is probably a similar phenomena on the
+
+ align:start position:0%
+is probably a similar phenomena on the
+ 
+
+ align:start position:0%
+is probably a similar phenomena on the
+other side, right?
+
+ align:start position:0%
+other side, right?
+ 
+
+ align:start position:0%
+other side, right?
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+But and it's like a kind of standard
+
+ align:start position:0%
+But and it's like a kind of standard
+ 
+
+ align:start position:0%
+But and it's like a kind of standard
+prop, you know, standard uh issue that
+
+ align:start position:0%
+prop, you know, standard uh issue that
+ 
+
+ align:start position:0%
+prop, you know, standard uh issue that
+for uh differential equations you can
+
+ align:start position:0%
+for uh differential equations you can
+ 
+
+ align:start position:0%
+for uh differential equations you can
+get blowups like this that that this is
+
+ align:start position:0%
+get blowups like this that that this is
+ 
+
+ align:start position:0%
+get blowups like this that that this is
+a particular simple examp. Any other
+
+ align:start position:0%
+a particular simple examp. Any other
+ 
+
+ align:start position:0%
+a particular simple examp. Any other
+questions?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um okay, great.
\ No newline at end of file
diff --git a/79GY-hI_emE.txt b/79GY-hI_emE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..46c4ee4176370b01bc39d2c898f0ab58bd64a6fe
--- /dev/null
+++ b/79GY-hI_emE.txt
@@ -0,0 +1,659 @@
+align:start position:0%
+ 
+there's one more property of this thing
+
+ align:start position:0%
+there's one more property of this thing
+ 
+
+ align:start position:0%
+there's one more property of this thing
+that is important and it's something
+
+ align:start position:0%
+that is important and it's something
+ 
+
+ align:start position:0%
+that is important and it's something
+called the correspondence principle
+
+ align:start position:0%
+called the correspondence principle
+ 
+
+ align:start position:0%
+called the correspondence principle
+which is another classical intuition and
+
+ align:start position:0%
+which is another classical intuition and
+ 
+
+ align:start position:0%
+which is another classical intuition and
+it says that the wave function and it
+
+ align:start position:0%
+it says that the wave function and it
+ 
+
+ align:start position:0%
+it says that the wave function and it
+addresses the question of what happens
+
+ align:start position:0%
+addresses the question of what happens
+ 
+
+ align:start position:0%
+addresses the question of what happens
+to the amplitude of the wave function it
+
+ align:start position:0%
+to the amplitude of the wave function it
+ 
+
+ align:start position:0%
+to the amplitude of the wave function it
+says that the wave function should be
+
+ align:start position:0%
+says that the wave function should be
+ 
+
+ align:start position:0%
+says that the wave function should be
+larger in the regions where the particle
+
+ align:start position:0%
+larger in the regions where the particle
+ 
+
+ align:start position:0%
+larger in the regions where the particle
+spends more time so in this problem you
+
+ align:start position:0%
+spends more time so in this problem you
+ 
+
+ align:start position:0%
+spends more time so in this problem you
+have the particle going here it's
+
+ align:start position:0%
+have the particle going here it's
+ 
+
+ align:start position:0%
+have the particle going here it's
+bouncing and it's going slowly here it's
+
+ align:start position:0%
+bouncing and it's going slowly here it's
+ 
+
+ align:start position:0%
+bouncing and it's going slowly here it's
+going very fast here so it's very small
+
+ align:start position:0%
+going very fast here so it's very small
+ 
+
+ align:start position:0%
+going very fast here so it's very small
+time here spent a lot of time here
+
+ align:start position:0%
+time here spent a lot of time here
+ 
+
+ align:start position:0%
+time here spent a lot of time here
+spends a lot of time here so it should
+
+ align:start position:0%
+spends a lot of time here so it should
+ 
+
+ align:start position:0%
+spends a lot of time here so it should
+be bigger in this region and smaller in
+
+ align:start position:0%
+be bigger in this region and smaller in
+ 
+
+ align:start position:0%
+be bigger in this region and smaller in
+the regions that spends little time so
+
+ align:start position:0%
+the regions that spends little time so
+ 
+
+ align:start position:0%
+the regions that spends little time so
+this was folded correspondence principle
+
+ align:start position:0%
+this was folded correspondence principle
+ 
+
+ align:start position:0%
+this was folded correspondence principle
+which is a big name for a somewhat vague
+
+ align:start position:0%
+which is a big name for a somewhat vague
+ 
+
+ align:start position:0%
+which is a big name for a somewhat vague
+idea and but nevertheless is a
+
+ align:start position:0%
+idea and but nevertheless is a
+ 
+
+ align:start position:0%
+idea and but nevertheless is a
+interesting thing and it's true as well
+
+ align:start position:0%
+interesting thing and it's true as well
+ 
+
+ align:start position:0%
+interesting thing and it's true as well
+so let me explain this a little more and
+
+ align:start position:0%
+so let me explain this a little more and
+ 
+
+ align:start position:0%
+so let me explain this a little more and
+get the key point about this so we say
+
+ align:start position:0%
+get the key point about this so we say
+ 
+
+ align:start position:0%
+get the key point about this so we say
+if you have a potential of X and X plus
+
+ align:start position:0%
+if you have a potential of X and X plus
+ 
+
+ align:start position:0%
+if you have a potential of X and X plus
+B X this is the X the probability to be
+
+ align:start position:0%
+B X this is the X the probability to be
+ 
+
+ align:start position:0%
+B X this is the X the probability to be
+found in the X is equal to Y square DX
+
+ align:start position:0%
+found in the X is equal to Y square DX
+ 
+
+ align:start position:0%
+found in the X is equal to Y square DX
+and it's proportional to the darling
+
+ align:start position:0%
+and it's proportional to the darling
+ 
+
+ align:start position:0%
+and it's proportional to the darling
+spent there so we'll say that it's will
+
+ align:start position:0%
+spent there so we'll say that it's will
+ 
+
+ align:start position:0%
+spent there so we'll say that it's will
+write it in the following way it's
+
+ align:start position:0%
+write it in the following way it's
+ 
+
+ align:start position:0%
+write it in the following way it's
+proportional to the fraction of time
+
+ align:start position:0%
+proportional to the fraction of time
+ 
+
+ align:start position:0%
+proportional to the fraction of time
+spent in DX and that we will call the
+
+ align:start position:0%
+spent in DX and that we will call the
+ 
+
+ align:start position:0%
+spent in DX and that we will call the
+little T over the period of the motion
+
+ align:start position:0%
+little T over the period of the motion
+ 
+
+ align:start position:0%
+little T over the period of the motion
+in this oscillation the classical
+
+ align:start position:0%
+in this oscillation the classical
+ 
+
+ align:start position:0%
+in this oscillation the classical
+particle is doing that's a fraction of
+
+ align:start position:0%
+particle is doing that's a fraction of
+ 
+
+ align:start position:0%
+particle is doing that's a fraction of
+time it spends there up to factors of
+
+ align:start position:0%
+time it spends there up to factors of
+ 
+
+ align:start position:0%
+time it spends there up to factors of
+two maybe because spends more in there
+
+ align:start position:0%
+two maybe because spends more in there
+ 
+
+ align:start position:0%
+two maybe because spends more in there
+and therefore o period doesn't matter
+
+ align:start position:0%
+and therefore o period doesn't matter
+ 
+
+ align:start position:0%
+and therefore o period doesn't matter
+anyway approximate it's a classical
+
+ align:start position:0%
+anyway approximate it's a classical
+ 
+
+ align:start position:0%
+anyway approximate it's a classical
+intuition expressed with the
+
+ align:start position:0%
+intuition expressed with the
+ 
+
+ align:start position:0%
+intuition expressed with the
+correspondence principle so this is
+
+ align:start position:0%
+correspondence principle so this is
+ 
+
+ align:start position:0%
+correspondence principle so this is
+equal to DX over V over the velocity the
+
+ align:start position:0%
+equal to DX over V over the velocity the
+ 
+
+ align:start position:0%
+equal to DX over V over the velocity the
+position dependent velocity T and this
+
+ align:start position:0%
+position dependent velocity T and this
+ 
+
+ align:start position:0%
+position dependent velocity T and this
+is therefore VX and the velocity is P
+
+ align:start position:0%
+is therefore VX and the velocity is P
+ 
+
+ align:start position:0%
+is therefore VX and the velocity is P
+over N so the mass over period and the
+
+ align:start position:0%
+over N so the mass over period and the
+ 
+
+ align:start position:0%
+over N so the mass over period and the
+momentum so here we go here is the
+
+ align:start position:0%
+momentum so here we go here is the
+ 
+
+ align:start position:0%
+momentum so here we go here is the
+interesting thing we found that the
+
+ align:start position:0%
+interesting thing we found that the
+ 
+
+ align:start position:0%
+interesting thing we found that the
+magnitude of the wave function should be
+
+ align:start position:0%
+magnitude of the wave function should be
+ 
+
+ align:start position:0%
+magnitude of the wave function should be
+proportional to 1 over P of X or lambda
+
+ align:start position:0%
+proportional to 1 over P of X or lambda
+ 
+
+ align:start position:0%
+proportional to 1 over P of X or lambda
+over H bar so then the key result is the
+
+ align:start position:0%
+over H bar so then the key result is the
+ 
+
+ align:start position:0%
+over H bar so then the key result is the
+magnitude of the wave function goes like
+
+ align:start position:0%
+magnitude of the wave function goes like
+ 
+
+ align:start position:0%
+magnitude of the wave function goes like
+the square root of the position
+
+ align:start position:0%
+the square root of the position
+ 
+
+ align:start position:0%
+the square root of the position
+dependent the Broglie wavelength so if
+
+ align:start position:0%
+dependent the Broglie wavelength so if
+ 
+
+ align:start position:0%
+dependent the Broglie wavelength so if
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the broadly away from is becoming
+
+ align:start position:0%
+then the broadly away from is becoming
+ 
+
+ align:start position:0%
+then the broadly away from is becoming
+bigger because the momentum is becoming
+
+ align:start position:0%
+bigger because the momentum is becoming
+ 
+
+ align:start position:0%
+bigger because the momentum is becoming
+smaller the logic here says that yes
+
+ align:start position:0%
+smaller the logic here says that yes
+ 
+
+ align:start position:0%
+smaller the logic here says that yes
+indeed in here the particle is spending
+
+ align:start position:0%
+indeed in here the particle is spending
+ 
+
+ align:start position:0%
+indeed in here the particle is spending
+more time here so actually I should be
+
+ align:start position:0%
+more time here so actually I should be
+ 
+
+ align:start position:0%
+more time here so actually I should be
+drawing it a little bigger so when I try
+
+ align:start position:0%
+drawing it a little bigger so when I try
+ 
+
+ align:start position:0%
+drawing it a little bigger so when I try
+to sketch a wave function in a potential
+
+ align:start position:0%
+to sketch a wave function in a potential
+ 
+
+ align:start position:0%
+to sketch a wave function in a potential
+this is my best guess of how it would be
+
+ align:start position:0%
+this is my best guess of how it would be
+ 
+
+ align:start position:0%
+this is my best guess of how it would be
+and you will be doing a lot of numerical
+
+ align:start position:0%
+and you will be doing a lot of numerical
+ 
+
+ align:start position:0%
+and you will be doing a lot of numerical
+experimentation with Mathematica and get
+
+ align:start position:0%
+experimentation with Mathematica and get
+ 
+
+ align:start position:0%
+experimentation with Mathematica and get
+that kind of insight they pose position
+
+ align:start position:0%
+that kind of insight they pose position
+ 
+
+ align:start position:0%
+that kind of insight they pose position
+dependent the broad new wave length as
+
+ align:start position:0%
+dependent the broad new wave length as
+ 
+
+ align:start position:0%
+dependent the broad new wave length as
+you have it is is a function of the
+
+ align:start position:0%
+you have it is is a function of the
+ 
+
+ align:start position:0%
+you have it is is a function of the
+canary the local kinetic energy and
+
+ align:start position:0%
+canary the local kinetic energy and
+ 
+
+ align:start position:0%
+canary the local kinetic energy and
+that's what it gives for you okay so
+
+ align:start position:0%
+that's what it gives for you okay so
+ 
+
+ align:start position:0%
+that's what it gives for you okay so
+that is one key insight into the plot of
+
+ align:start position:0%
+that is one key insight into the plot of
+ 
+
+ align:start position:0%
+that is one key insight into the plot of
+the wave function without solving
+
+ align:start position:0%
+the wave function without solving
+ 
+
+ align:start position:0%
+the wave function without solving
+anything you can estimate how the wave
+
+ align:start position:0%
+anything you can estimate how the wave
+ 
+
+ align:start position:0%
+anything you can estimate how the wave
+length goes and probably to what degree
+
+ align:start position:0%
+length goes and probably to what degree
+ 
+
+ align:start position:0%
+length goes and probably to what degree
+the amplitude goes what else do you know
+
+ align:start position:0%
+the amplitude goes what else do you know
+ 
+
+ align:start position:0%
+the amplitude goes what else do you know
+there's a node theorem that we mentioned
+
+ align:start position:0%
+there's a node theorem that we mentioned
+ 
+
+ align:start position:0%
+there's a node theorem that we mentioned
+again in the case of the square well the
+
+ align:start position:0%
+again in the case of the square well the
+ 
+
+ align:start position:0%
+again in the case of the square well the
+ground state the bound state the ground
+
+ align:start position:0%
+ground state the bound state the ground
+ 
+
+ align:start position:0%
+ground state the bound state the ground
+state bound state is a state without a
+
+ align:start position:0%
+state bound state is a state without a
+ 
+
+ align:start position:0%
+state bound state is a state without a
+node the first excited state has one now
+
+ align:start position:0%
+node the first excited state has one now
+ 
+
+ align:start position:0%
+node the first excited state has one now
+that makes excited state has two nodes
+
+ align:start position:0%
+that makes excited state has two nodes
+ 
+
+ align:start position:0%
+that makes excited state has two nodes
+and that's three nodes and the number of
+
+ align:start position:0%
+and that's three nodes and the number of
+ 
+
+ align:start position:0%
+and that's three nodes and the number of
+nodes increase with that information it
+
+ align:start position:0%
+nodes increase with that information it
+ 
+
+ align:start position:0%
+nodes increase with that information it
+already becomes kind of plausible that
+
+ align:start position:0%
+already becomes kind of plausible that
+ 
+
+ align:start position:0%
+already becomes kind of plausible that
+you can sketch a general wave function
\ No newline at end of file
diff --git a/7GF78YQz62w.txt b/7GF78YQz62w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..53a70013563d7880091bea441c2e2b135015ac0a
--- /dev/null
+++ b/7GF78YQz62w.txt
@@ -0,0 +1,891 @@
+align:start position:0%
+ 
+So Andrew, before the show, we asked you
+
+ align:start position:0%
+So Andrew, before the show, we asked you
+ 
+
+ align:start position:0%
+So Andrew, before the show, we asked you
+to respond to a question which we'll we
+
+ align:start position:0%
+to respond to a question which we'll we
+ 
+
+ align:start position:0%
+to respond to a question which we'll we
+will now reveal the answer to. So the
+
+ align:start position:0%
+will now reveal the answer to. So the
+ 
+
+ align:start position:0%
+will now reveal the answer to. So the
+question was, should I Sarah Hansen use
+
+ align:start position:0%
+question was, should I Sarah Hansen use
+ 
+
+ align:start position:0%
+question was, should I Sarah Hansen use
+chat GPT right now to plan my
+
+ align:start position:0%
+chat GPT right now to plan my
+ 
+
+ align:start position:0%
+chat GPT right now to plan my
+retirement? What's our answer?
+
+ align:start position:0%
+retirement? What's our answer?
+ 
+
+ align:start position:0%
+retirement? What's our answer?
+Not yet. Okay, please explain. Not yet.
+
+ align:start position:0%
+Not yet. Okay, please explain. Not yet.
+ 
+
+ align:start position:0%
+Not yet. Okay, please explain. Not yet.
+Because large language models are not
+
+ align:start position:0%
+Because large language models are not
+ 
+
+ align:start position:0%
+Because large language models are not
+yet ready to be able to do delegated
+
+ align:start position:0%
+yet ready to be able to do delegated
+ 
+
+ align:start position:0%
+yet ready to be able to do delegated
+financial decision-m for us. M turns out
+
+ align:start position:0%
+financial decision-m for us. M turns out
+ 
+
+ align:start position:0%
+financial decision-m for us. M turns out
+that saving for retirement is one set of
+
+ align:start position:0%
+that saving for retirement is one set of
+ 
+
+ align:start position:0%
+that saving for retirement is one set of
+activities but then spending while in
+
+ align:start position:0%
+activities but then spending while in
+ 
+
+ align:start position:0%
+activities but then spending while in
+retirement that's a whole different set
+
+ align:start position:0%
+retirement that's a whole different set
+ 
+
+ align:start position:0%
+retirement that's a whole different set
+of activities and many of us have become
+
+ align:start position:0%
+of activities and many of us have become
+ 
+
+ align:start position:0%
+of activities and many of us have become
+good at saving but you know we've been
+
+ align:start position:0%
+good at saving but you know we've been
+ 
+
+ align:start position:0%
+good at saving but you know we've been
+such good savers that we forget that at
+
+ align:start position:0%
+such good savers that we forget that at
+ 
+
+ align:start position:0%
+such good savers that we forget that at
+some point we need to spend and and we
+
+ align:start position:0%
+some point we need to spend and and we
+ 
+
+ align:start position:0%
+some point we need to spend and and we
+have to spend at the right rate for the
+
+ align:start position:0%
+have to spend at the right rate for the
+ 
+
+ align:start position:0%
+have to spend at the right rate for the
+right things at the right times. So what
+
+ align:start position:0%
+right things at the right times. So what
+ 
+
+ align:start position:0%
+right things at the right times. So what
+my colleagues and I are trying to
+
+ align:start position:0%
+my colleagues and I are trying to
+ 
+
+ align:start position:0%
+my colleagues and I are trying to
+understand now is not only what those
+
+ align:start position:0%
+understand now is not only what those
+ 
+
+ align:start position:0%
+understand now is not only what those
+optimal decisions are. I think we now
+
+ align:start position:0%
+optimal decisions are. I think we now
+ 
+
+ align:start position:0%
+optimal decisions are. I think we now
+have a lot of information about that.
+
+ align:start position:0%
+have a lot of information about that.
+ 
+
+ align:start position:0%
+have a lot of information about that.
+There's been a lot of research done on
+
+ align:start position:0%
+There's been a lot of research done on
+ 
+
+ align:start position:0%
+There's been a lot of research done on
+that. But the more challenging issue is
+
+ align:start position:0%
+that. But the more challenging issue is
+ 
+
+ align:start position:0%
+that. But the more challenging issue is
+how do we communicate that to people who
+
+ align:start position:0%
+how do we communicate that to people who
+ 
+
+ align:start position:0%
+how do we communicate that to people who
+don't have any finance background and
+
+ align:start position:0%
+don't have any finance background and
+ 
+
+ align:start position:0%
+don't have any finance background and
+and moreover can't afford to hire the
+
+ align:start position:0%
+and moreover can't afford to hire the
+ 
+
+ align:start position:0%
+and moreover can't afford to hire the
+financial adviserss that some of the
+
+ align:start position:0%
+financial adviserss that some of the
+ 
+
+ align:start position:0%
+financial adviserss that some of the
+higher net worth individuals have access
+
+ align:start position:0%
+higher net worth individuals have access
+ 
+
+ align:start position:0%
+higher net worth individuals have access
+to. So we're working on an AI solution
+
+ align:start position:0%
+to. So we're working on an AI solution
+ 
+
+ align:start position:0%
+to. So we're working on an AI solution
+uh an AI financial adviser that can
+
+ align:start position:0%
+uh an AI financial adviser that can
+ 
+
+ align:start position:0%
+uh an AI financial adviser that can
+satisfy the most important criterion of
+
+ align:start position:0%
+satisfy the most important criterion of
+ 
+
+ align:start position:0%
+satisfy the most important criterion of
+financial advice that regulators impose
+
+ align:start position:0%
+financial advice that regulators impose
+ 
+
+ align:start position:0%
+financial advice that regulators impose
+which is something called fiduciary
+
+ align:start position:0%
+which is something called fiduciary
+ 
+
+ align:start position:0%
+which is something called fiduciary
+duty. A fiduciary is somebody who is
+
+ align:start position:0%
+duty. A fiduciary is somebody who is
+ 
+
+ align:start position:0%
+duty. A fiduciary is somebody who is
+appointed to help you further your
+
+ align:start position:0%
+appointed to help you further your
+ 
+
+ align:start position:0%
+appointed to help you further your
+goals, will look out for your best
+
+ align:start position:0%
+goals, will look out for your best
+ 
+
+ align:start position:0%
+goals, will look out for your best
+interests uh above and beyond their own.
+
+ align:start position:0%
+interests uh above and beyond their own.
+ 
+
+ align:start position:0%
+interests uh above and beyond their own.
+And so very often people get a little
+
+ align:start position:0%
+And so very often people get a little
+ 
+
+ align:start position:0%
+And so very often people get a little
+bit concerned about you know financial
+
+ align:start position:0%
+bit concerned about you know financial
+ 
+
+ align:start position:0%
+bit concerned about you know financial
+planners and other people in the
+
+ align:start position:0%
+planners and other people in the
+ 
+
+ align:start position:0%
+planners and other people in the
+financial industry because they don't
+
+ align:start position:0%
+financial industry because they don't
+ 
+
+ align:start position:0%
+financial industry because they don't
+want to be taken advantage of. And you
+
+ align:start position:0%
+want to be taken advantage of. And you
+ 
+
+ align:start position:0%
+want to be taken advantage of. And you
+know there are many good financial
+
+ align:start position:0%
+know there are many good financial
+ 
+
+ align:start position:0%
+know there are many good financial
+planners out there but not everybody can
+
+ align:start position:0%
+planners out there but not everybody can
+ 
+
+ align:start position:0%
+planners out there but not everybody can
+afford one. So the question is can you
+
+ align:start position:0%
+afford one. So the question is can you
+ 
+
+ align:start position:0%
+afford one. So the question is can you
+for those people who can't afford
+
+ align:start position:0%
+for those people who can't afford
+ 
+
+ align:start position:0%
+for those people who can't afford
+financial planning and for the financial
+
+ align:start position:0%
+financial planning and for the financial
+ 
+
+ align:start position:0%
+financial planning and for the financial
+institutions that don't want to spend
+
+ align:start position:0%
+institutions that don't want to spend
+ 
+
+ align:start position:0%
+institutions that don't want to spend
+their resources of financial advice to
+
+ align:start position:0%
+their resources of financial advice to
+ 
+
+ align:start position:0%
+their resources of financial advice to
+those who aren't going to generate
+
+ align:start position:0%
+those who aren't going to generate
+ 
+
+ align:start position:0%
+those who aren't going to generate
+enough commissions for them for these
+
+ align:start position:0%
+enough commissions for them for these
+ 
+
+ align:start position:0%
+enough commissions for them for these
+people can we come up with uh financial
+
+ align:start position:0%
+people can we come up with uh financial
+ 
+
+ align:start position:0%
+people can we come up with uh financial
+advice from an AI platform that
+
+ align:start position:0%
+advice from an AI platform that
+ 
+
+ align:start position:0%
+advice from an AI platform that
+satisfies a definition of a fiduciary
+
+ align:start position:0%
+satisfies a definition of a fiduciary
+ 
+
+ align:start position:0%
+satisfies a definition of a fiduciary
+some some program that you can trust to
+
+ align:start position:0%
+some some program that you can trust to
+ 
+
+ align:start position:0%
+some some program that you can trust to
+look out for your best interest. We're
+
+ align:start position:0%
+look out for your best interest. We're
+ 
+
+ align:start position:0%
+look out for your best interest. We're
+not there yet. However, I believe that
+
+ align:start position:0%
+not there yet. However, I believe that
+ 
+
+ align:start position:0%
+not there yet. However, I believe that
+everybody should use large language
+
+ align:start position:0%
+everybody should use large language
+ 
+
+ align:start position:0%
+everybody should use large language
+models to help them think through
+
+ align:start position:0%
+models to help them think through
+ 
+
+ align:start position:0%
+models to help them think through
+retirement issues more seriously. For
+
+ align:start position:0%
+retirement issues more seriously. For
+ 
+
+ align:start position:0%
+retirement issues more seriously. For
+example, ask JBT, "What are the biggest
+
+ align:start position:0%
+example, ask JBT, "What are the biggest
+ 
+
+ align:start position:0%
+example, ask JBT, "What are the biggest
+issues that I need to focus on for my
+
+ align:start position:0%
+issues that I need to focus on for my
+ 
+
+ align:start position:0%
+issues that I need to focus on for my
+retirement? How much time do I have?
+
+ align:start position:0%
+retirement? How much time do I have?
+ 
+
+ align:start position:0%
+retirement? How much time do I have?
+What kind of ideas and products and
+
+ align:start position:0%
+What kind of ideas and products and
+ 
+
+ align:start position:0%
+What kind of ideas and products and
+services should I make use of? How do I
+
+ align:start position:0%
+services should I make use of? How do I
+ 
+
+ align:start position:0%
+services should I make use of? How do I
+get better financial information? How do
+
+ align:start position:0%
+get better financial information? How do
+ 
+
+ align:start position:0%
+get better financial information? How do
+I learn more about these problems?" All
+
+ align:start position:0%
+I learn more about these problems?" All
+ 
+
+ align:start position:0%
+I learn more about these problems?" All
+of those things I think ChatBT can do a
+
+ align:start position:0%
+of those things I think ChatBT can do a
+ 
+
+ align:start position:0%
+of those things I think ChatBT can do a
+pretty good job at, but I wouldn't let
+
+ align:start position:0%
+pretty good job at, but I wouldn't let
+ 
+
+ align:start position:0%
+pretty good job at, but I wouldn't let
+it make your decisions for you. Real
+
+ align:start position:0%
+it make your decisions for you. Real
+ 
+
+ align:start position:0%
+it make your decisions for you. Real
+question for you. I know a lot of times
+
+ align:start position:0%
+question for you. I know a lot of times
+ 
+
+ align:start position:0%
+question for you. I know a lot of times
+when I put in a prompt that's um within
+
+ align:start position:0%
+when I put in a prompt that's um within
+ 
+
+ align:start position:0%
+when I put in a prompt that's um within
+my domain of expertise, some of it will
+
+ align:start position:0%
+my domain of expertise, some of it will
+ 
+
+ align:start position:0%
+my domain of expertise, some of it will
+be good, but some of it's kind of
+
+ align:start position:0%
+be good, but some of it's kind of
+ 
+
+ align:start position:0%
+be good, but some of it's kind of
+garbage and not all that accurate. So,
+
+ align:start position:0%
+garbage and not all that accurate. So,
+ 
+
+ align:start position:0%
+garbage and not all that accurate. So,
+as a person who doesn't know finance,
+
+ align:start position:0%
+as a person who doesn't know finance,
+ 
+
+ align:start position:0%
+as a person who doesn't know finance,
+how do I know I can trust the answers
+
+ align:start position:0%
+how do I know I can trust the answers
+ 
+
+ align:start position:0%
+how do I know I can trust the answers
+that are coming back even about those
+
+ align:start position:0%
+that are coming back even about those
+ 
+
+ align:start position:0%
+that are coming back even about those
+general type of questions? Well, so
+
+ align:start position:0%
+general type of questions? Well, so
+ 
+
+ align:start position:0%
+general type of questions? Well, so
+that's really why you need to have
+
+ align:start position:0%
+that's really why you need to have
+ 
+
+ align:start position:0%
+that's really why you need to have
+additional time and effort employed in
+
+ align:start position:0%
+additional time and effort employed in
+ 
+
+ align:start position:0%
+additional time and effort employed in
+thinking through these issues, not just
+
+ align:start position:0%
+thinking through these issues, not just
+ 
+
+ align:start position:0%
+thinking through these issues, not just
+by yourself, but with friends and
+
+ align:start position:0%
+by yourself, but with friends and
+ 
+
+ align:start position:0%
+by yourself, but with friends and
+family. Yeah. So we need human support
+
+ align:start position:0%
+family. Yeah. So we need human support
+ 
+
+ align:start position:0%
+family. Yeah. So we need human support
+for thinking about how large language
+
+ align:start position:0%
+for thinking about how large language
+ 
+
+ align:start position:0%
+for thinking about how large language
+models can work either well or in some
+
+ align:start position:0%
+models can work either well or in some
+ 
+
+ align:start position:0%
+models can work either well or in some
+cases not so well. And in any case, if
+
+ align:start position:0%
+cases not so well. And in any case, if
+ 
+
+ align:start position:0%
+cases not so well. And in any case, if
+you are planning for your retirement, at
+
+ align:start position:0%
+you are planning for your retirement, at
+ 
+
+ align:start position:0%
+you are planning for your retirement, at
+some point or another, you're going to
+
+ align:start position:0%
+some point or another, you're going to
+ 
+
+ align:start position:0%
+some point or another, you're going to
+have to engage with people from the
+
+ align:start position:0%
+have to engage with people from the
+ 
+
+ align:start position:0%
+have to engage with people from the
+financial institutions. Yeah. They will
+
+ align:start position:0%
+financial institutions. Yeah. They will
+ 
+
+ align:start position:0%
+financial institutions. Yeah. They will
+be able to help deal with some of the
+
+ align:start position:0%
+be able to help deal with some of the
+ 
+
+ align:start position:0%
+be able to help deal with some of the
+so-called hallucination problems with
+
+ align:start position:0%
+so-called hallucination problems with
+ 
+
+ align:start position:0%
+so-called hallucination problems with
+these large language models. But the
+
+ align:start position:0%
+these large language models. But the
+ 
+
+ align:start position:0%
+these large language models. But the
+answer is like anything else that we do.
+
+ align:start position:0%
+answer is like anything else that we do.
+ 
+
+ align:start position:0%
+answer is like anything else that we do.
+You know, how do you know that your
+
+ align:start position:0%
+You know, how do you know that your
+ 
+
+ align:start position:0%
+You know, how do you know that your
+doctor is always giving you the best
+
+ align:start position:0%
+doctor is always giving you the best
+ 
+
+ align:start position:0%
+doctor is always giving you the best
+information? Doctors are very highly
+
+ align:start position:0%
+information? Doctors are very highly
+ 
+
+ align:start position:0%
+information? Doctors are very highly
+trained, but they do make mistakes. So
+
+ align:start position:0%
+trained, but they do make mistakes. So
+ 
+
+ align:start position:0%
+trained, but they do make mistakes. So
+get a second opinion, get a third
+
+ align:start position:0%
+get a second opinion, get a third
+ 
+
+ align:start position:0%
+get a second opinion, get a third
+opinion, talk to your family members.
+
+ align:start position:0%
+opinion, talk to your family members.
+ 
+
+ align:start position:0%
+opinion, talk to your family members.
+Ultimately, you're going to be
+
+ align:start position:0%
+Ultimately, you're going to be
+ 
+
+ align:start position:0%
+Ultimately, you're going to be
+responsible for your own decisions. But
+
+ align:start position:0%
+responsible for your own decisions. But
+ 
+
+ align:start position:0%
+responsible for your own decisions. But
+the more informed you can be and the
+
+ align:start position:0%
+the more informed you can be and the
+ 
+
+ align:start position:0%
+the more informed you can be and the
+more you can check the uh accuracy of
+
+ align:start position:0%
+more you can check the uh accuracy of
+ 
+
+ align:start position:0%
+more you can check the uh accuracy of
+the information and that information
+
+ align:start position:0%
+the information and that information
+ 
+
+ align:start position:0%
+the information and that information
+come from humans or from chat bots, I
+
+ align:start position:0%
+come from humans or from chat bots, I
+ 
+
+ align:start position:0%
+come from humans or from chat bots, I
+think those are the ways that we've
+
+ align:start position:0%
+think those are the ways that we've
+ 
+
+ align:start position:0%
+think those are the ways that we've
+developed for making sure that we make
+
+ align:start position:0%
+developed for making sure that we make
+ 
+
+ align:start position:0%
+developed for making sure that we make
+the best decisions possible.
\ No newline at end of file
diff --git a/7aNYj3zyVkc.txt b/7aNYj3zyVkc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c3894b4ebcb9a76f22fcd6450a1fdca5968b9842
--- /dev/null
+++ b/7aNYj3zyVkc.txt
@@ -0,0 +1,7571 @@
+align:start position:0%
+ 
+um I've emphasized in the first lecture
+
+ align:start position:0%
+um I've emphasized in the first lecture
+ 
+
+ align:start position:0%
+um I've emphasized in the first lecture
+you know that this is there's a lot of
+
+ align:start position:0%
+you know that this is there's a lot of
+ 
+
+ align:start position:0%
+you know that this is there's a lot of
+stuff that happens uh just in your
+
+ align:start position:0%
+stuff that happens uh just in your
+ 
+
+ align:start position:0%
+stuff that happens uh just in your
+ordinary life I saw two examples of this
+
+ align:start position:0%
+ordinary life I saw two examples of this
+ 
+
+ align:start position:0%
+ordinary life I saw two examples of this
+yesterday yesterday's Boston Globe just
+
+ align:start position:0%
+yesterday yesterday's Boston Globe just
+ 
+
+ align:start position:0%
+yesterday yesterday's Boston Globe just
+on the front page uh there was a
+
+ align:start position:0%
+on the front page uh there was a
+ 
+
+ align:start position:0%
+on the front page uh there was a
+discovery uh about heart cell Discovery
+
+ align:start position:0%
+discovery uh about heart cell Discovery
+ 
+
+ align:start position:0%
+discovery uh about heart cell Discovery
+raises treatment hopes scientists
+
+ align:start position:0%
+raises treatment hopes scientists
+ 
+
+ align:start position:0%
+raises treatment hopes scientists
+announced yesterday discovery of cells
+
+ align:start position:0%
+announced yesterday discovery of cells
+ 
+
+ align:start position:0%
+announced yesterday discovery of cells
+in the heart that can create new muscle
+
+ align:start position:0%
+in the heart that can create new muscle
+ 
+
+ align:start position:0%
+in the heart that can create new muscle
+cells raising hopes that doctors may
+
+ align:start position:0%
+cells raising hopes that doctors may
+ 
+
+ align:start position:0%
+cells raising hopes that doctors may
+find dramatic new ways to treat heart
+
+ align:start position:0%
+find dramatic new ways to treat heart
+ 
+
+ align:start position:0%
+find dramatic new ways to treat heart
+disease uh they're show the team showed
+
+ align:start position:0%
+disease uh they're show the team showed
+ 
+
+ align:start position:0%
+disease uh they're show the team showed
+that the cells which are similar to sem
+
+ align:start position:0%
+that the cells which are similar to sem
+ 
+
+ align:start position:0%
+that the cells which are similar to sem
+cells can be expanded from just a few
+
+ align:start position:0%
+cells can be expanded from just a few
+ 
+
+ align:start position:0%
+cells can be expanded from just a few
+hundred in a laboratory dish up to uh to
+
+ align:start position:0%
+hundred in a laboratory dish up to uh to
+ 
+
+ align:start position:0%
+hundred in a laboratory dish up to uh to
+more than a million and these can be
+
+ align:start position:0%
+more than a million and these can be
+ 
+
+ align:start position:0%
+more than a million and these can be
+guided into becoming the pulsing mus
+
+ align:start position:0%
+guided into becoming the pulsing mus
+ 
+
+ align:start position:0%
+guided into becoming the pulsing mus
+muscles that power the heart so we were
+
+ align:start position:0%
+muscles that power the heart so we were
+ 
+
+ align:start position:0%
+muscles that power the heart so we were
+talking about those yeast dividing and
+
+ align:start position:0%
+talking about those yeast dividing and
+ 
+
+ align:start position:0%
+talking about those yeast dividing and
+saying how one cell becomes two this is
+
+ align:start position:0%
+saying how one cell becomes two this is
+ 
+
+ align:start position:0%
+saying how one cell becomes two this is
+a general principle throughout life that
+
+ align:start position:0%
+a general principle throughout life that
+ 
+
+ align:start position:0%
+a general principle throughout life that
+cells come from other cells and they
+
+ align:start position:0%
+cells come from other cells and they
+ 
+
+ align:start position:0%
+cells come from other cells and they
+divide and you can will see the
+
+ align:start position:0%
+divide and you can will see the
+ 
+
+ align:start position:0%
+divide and you can will see the
+relationship to that with DNA
+
+ align:start position:0%
+relationship to that with DNA
+ 
+
+ align:start position:0%
+relationship to that with DNA
+replication as we go along case of a
+
+ align:start position:0%
+replication as we go along case of a
+ 
+
+ align:start position:0%
+replication as we go along case of a
+yeast as I said they're just always the
+
+ align:start position:0%
+yeast as I said they're just always the
+ 
+
+ align:start position:0%
+yeast as I said they're just always the
+same you're probably are always the same
+
+ align:start position:0%
+same you're probably are always the same
+ 
+
+ align:start position:0%
+same you're probably are always the same
+but in something like our own cells we
+
+ align:start position:0%
+but in something like our own cells we
+ 
+
+ align:start position:0%
+but in something like our own cells we
+start out as a single fertilized cell
+
+ align:start position:0%
+start out as a single fertilized cell
+ 
+
+ align:start position:0%
+start out as a single fertilized cell
+but somewhere along the way the cells
+
+ align:start position:0%
+but somewhere along the way the cells
+ 
+
+ align:start position:0%
+but somewhere along the way the cells
+have to become specialized so the very
+
+ align:start position:0%
+have to become specialized so the very
+ 
+
+ align:start position:0%
+have to become specialized so the very
+early ones are the embryonic stem cells
+
+ align:start position:0%
+early ones are the embryonic stem cells
+ 
+
+ align:start position:0%
+early ones are the embryonic stem cells
+they have the potential to become any
+
+ align:start position:0%
+they have the potential to become any
+ 
+
+ align:start position:0%
+they have the potential to become any
+cell in the body but at some point uh
+
+ align:start position:0%
+cell in the body but at some point uh
+ 
+
+ align:start position:0%
+cell in the body but at some point uh
+there's at one of these cell divisions
+
+ align:start position:0%
+there's at one of these cell divisions
+ 
+
+ align:start position:0%
+there's at one of these cell divisions
+the cells are going to have to start to
+
+ align:start position:0%
+the cells are going to have to start to
+ 
+
+ align:start position:0%
+the cells are going to have to start to
+become more specialized and for example
+
+ align:start position:0%
+become more specialized and for example
+ 
+
+ align:start position:0%
+become more specialized and for example
+this one might be a lineage that would
+
+ align:start position:0%
+this one might be a lineage that would
+ 
+
+ align:start position:0%
+this one might be a lineage that would
+lead to the heart muscle or to becom a
+
+ align:start position:0%
+lead to the heart muscle or to becom a
+ 
+
+ align:start position:0%
+lead to the heart muscle or to becom a
+nerve or something and at that point it
+
+ align:start position:0%
+nerve or something and at that point it
+ 
+
+ align:start position:0%
+nerve or something and at that point it
+loses its ability to become any cell in
+
+ align:start position:0%
+loses its ability to become any cell in
+ 
+
+ align:start position:0%
+loses its ability to become any cell in
+the body and in many cases by the time
+
+ align:start position:0%
+the body and in many cases by the time
+ 
+
+ align:start position:0%
+the body and in many cases by the time
+you get out ultimately to the
+
+ align:start position:0%
+you get out ultimately to the
+ 
+
+ align:start position:0%
+you get out ultimately to the
+final um cell that's making up the
+
+ align:start position:0%
+final um cell that's making up the
+ 
+
+ align:start position:0%
+final um cell that's making up the
+muscle or the nerve or something it has
+
+ align:start position:0%
+muscle or the nerve or something it has
+ 
+
+ align:start position:0%
+muscle or the nerve or something it has
+no capacity to regenerate so that's why
+
+ align:start position:0%
+no capacity to regenerate so that's why
+ 
+
+ align:start position:0%
+no capacity to regenerate so that's why
+for example spinal cord injuries are so
+
+ align:start position:0%
+for example spinal cord injuries are so
+ 
+
+ align:start position:0%
+for example spinal cord injuries are so
+damaging because nerves at this point
+
+ align:start position:0%
+damaging because nerves at this point
+ 
+
+ align:start position:0%
+damaging because nerves at this point
+can't be regenerated or heart disease
+
+ align:start position:0%
+can't be regenerated or heart disease
+ 
+
+ align:start position:0%
+can't be regenerated or heart disease
+you get a damaged heart or stuck this is
+
+ align:start position:0%
+you get a damaged heart or stuck this is
+ 
+
+ align:start position:0%
+you get a damaged heart or stuck this is
+why this result is exciting because
+
+ align:start position:0%
+why this result is exciting because
+ 
+
+ align:start position:0%
+why this result is exciting because
+there seem to be at least a few cells in
+
+ align:start position:0%
+there seem to be at least a few cells in
+ 
+
+ align:start position:0%
+there seem to be at least a few cells in
+the heart in the heart that have the
+
+ align:start position:0%
+the heart in the heart that have the
+ 
+
+ align:start position:0%
+the heart in the heart that have the
+capacity to regenerate more more heart
+
+ align:start position:0%
+capacity to regenerate more more heart
+ 
+
+ align:start position:0%
+capacity to regenerate more more heart
+heart muscle now this is early on it
+
+ align:start position:0%
+heart muscle now this is early on it
+ 
+
+ align:start position:0%
+heart muscle now this is early on it
+hasn't been rigorously shown to be a
+
+ align:start position:0%
+hasn't been rigorously shown to be a
+ 
+
+ align:start position:0%
+hasn't been rigorously shown to be a
+stem cell but there's an example from
+
+ align:start position:0%
+stem cell but there's an example from
+ 
+
+ align:start position:0%
+stem cell but there's an example from
+yesterday's front of yesterday's paper
+
+ align:start position:0%
+yesterday's front of yesterday's paper
+ 
+
+ align:start position:0%
+yesterday's front of yesterday's paper
+about something we were virtually
+
+ align:start position:0%
+about something we were virtually
+ 
+
+ align:start position:0%
+about something we were virtually
+alluding to in class there was oops
+
+ align:start position:0%
+alluding to in class there was oops
+ 
+
+ align:start position:0%
+alluding to in class there was oops
+there was also that an article about
+
+ align:start position:0%
+there was also that an article about
+ 
+
+ align:start position:0%
+there was also that an article about
+AIDS testing again you know that we'll
+
+ align:start position:0%
+AIDS testing again you know that we'll
+ 
+
+ align:start position:0%
+AIDS testing again you know that we'll
+talk more about the H hiv1 virus and
+
+ align:start position:0%
+talk more about the H hiv1 virus and
+ 
+
+ align:start position:0%
+talk more about the H hiv1 virus and
+then today on the on the front page AG
+
+ align:start position:0%
+then today on the on the front page AG
+ 
+
+ align:start position:0%
+then today on the on the front page AG
+of the Boston Globe yet again as Romney
+
+ align:start position:0%
+of the Boston Globe yet again as Romney
+ 
+
+ align:start position:0%
+of the Boston Globe yet again as Romney
+draws fire on stem cells and um you you
+
+ align:start position:0%
+draws fire on stem cells and um you you
+ 
+
+ align:start position:0%
+draws fire on stem cells and um you you
+you can look at this uh but you know
+
+ align:start position:0%
+you can look at this uh but you know
+ 
+
+ align:start position:0%
+you can look at this uh but you know
+he's sort of trying to straddle I guess
+
+ align:start position:0%
+he's sort of trying to straddle I guess
+ 
+
+ align:start position:0%
+he's sort of trying to straddle I guess
+between uh being supportive of research
+
+ align:start position:0%
+between uh being supportive of research
+ 
+
+ align:start position:0%
+between uh being supportive of research
+in the one hand and the concerns of uh
+
+ align:start position:0%
+in the one hand and the concerns of uh
+ 
+
+ align:start position:0%
+in the one hand and the concerns of uh
+the conservatives and religious right on
+
+ align:start position:0%
+the conservatives and religious right on
+ 
+
+ align:start position:0%
+the conservatives and religious right on
+the other hand and he's drawing fire
+
+ align:start position:0%
+the other hand and he's drawing fire
+ 
+
+ align:start position:0%
+the other hand and he's drawing fire
+from from both sides but it's an issue
+
+ align:start position:0%
+from from both sides but it's an issue
+ 
+
+ align:start position:0%
+from from both sides but it's an issue
+that is in our society today you're
+
+ align:start position:0%
+that is in our society today you're
+ 
+
+ align:start position:0%
+that is in our society today you're
+going to be expected to make decisions
+
+ align:start position:0%
+going to be expected to make decisions
+ 
+
+ align:start position:0%
+going to be expected to make decisions
+on it to know about it and understand
+
+ align:start position:0%
+on it to know about it and understand
+ 
+
+ align:start position:0%
+on it to know about it and understand
+just trying to drive home that this what
+
+ align:start position:0%
+just trying to drive home that this what
+ 
+
+ align:start position:0%
+just trying to drive home that this what
+we're talking about isn't taking place
+
+ align:start position:0%
+we're talking about isn't taking place
+ 
+
+ align:start position:0%
+we're talking about isn't taking place
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+vacuum um nobody emailed
+
+ align:start position:0%
+vacuum um nobody emailed
+ 
+
+ align:start position:0%
+vacuum um nobody emailed
+me um an idea as to what happened here I
+
+ align:start position:0%
+me um an idea as to what happened here I
+ 
+
+ align:start position:0%
+me um an idea as to what happened here I
+showed you this little movie this sing
+
+ align:start position:0%
+showed you this little movie this sing
+ 
+
+ align:start position:0%
+showed you this little movie this sing
+this uh is water that's cooled below the
+
+ align:start position:0%
+this uh is water that's cooled below the
+ 
+
+ align:start position:0%
+this uh is water that's cooled below the
+freezing point but it hasn't uh formed
+
+ align:start position:0%
+freezing point but it hasn't uh formed
+ 
+
+ align:start position:0%
+freezing point but it hasn't uh formed
+ice crystals but if we put a little bit
+
+ align:start position:0%
+ice crystals but if we put a little bit
+ 
+
+ align:start position:0%
+ice crystals but if we put a little bit
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+pomonis uh singi in it then it uh
+
+ align:start position:0%
+pomonis uh singi in it then it uh
+ 
+
+ align:start position:0%
+pomonis uh singi in it then it uh
+somehow that super cooled water turned
+
+ align:start position:0%
+somehow that super cooled water turned
+ 
+
+ align:start position:0%
+somehow that super cooled water turned
+into ice and I told you it was a protein
+
+ align:start position:0%
+into ice and I told you it was a protein
+ 
+
+ align:start position:0%
+into ice and I told you it was a protein
+on the surface nobody had any ideas so
+
+ align:start position:0%
+on the surface nobody had any ideas so
+ 
+
+ align:start position:0%
+on the surface nobody had any ideas so
+why don't you turn to whoever's close to
+
+ align:start position:0%
+why don't you turn to whoever's close to
+ 
+
+ align:start position:0%
+why don't you turn to whoever's close to
+you and you can talk about it for 30
+
+ align:start position:0%
+you and you can talk about it for 30
+ 
+
+ align:start position:0%
+you and you can talk about it for 30
+seconds see if anybody can come up with
+
+ align:start position:0%
+seconds see if anybody can come up with
+ 
+
+ align:start position:0%
+seconds see if anybody can come up with
+an idea as to why right I won't look you
+
+ align:start position:0%
+an idea as to why right I won't look you
+ 
+
+ align:start position:0%
+an idea as to why right I won't look you
+know just go ahead talk to somebody see
+
+ align:start position:0%
+know just go ahead talk to somebody see
+ 
+
+ align:start position:0%
+know just go ahead talk to somebody see
+what come up with an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay well let's see we manage to get any
+
+ align:start position:0%
+okay well let's see we manage to get any
+ 
+
+ align:start position:0%
+okay well let's see we manage to get any
+any ideas anybody got the courage to try
+
+ align:start position:0%
+any ideas anybody got the courage to try
+ 
+
+ align:start position:0%
+any ideas anybody got the courage to try
+and uh guess what that protein might be
+
+ align:start position:0%
+and uh guess what that protein might be
+ 
+
+ align:start position:0%
+and uh guess what that protein might be
+doing it's a molecule okay it's a
+
+ align:start position:0%
+doing it's a molecule okay it's a
+ 
+
+ align:start position:0%
+doing it's a molecule okay it's a
+nonpolar molecule it's disturbing the
+
+ align:start position:0%
+nonpolar molecule it's disturbing the
+ 
+
+ align:start position:0%
+nonpolar molecule it's disturbing the
+bonds it's a non-polar molecule it's not
+
+ align:start position:0%
+bonds it's a non-polar molecule it's not
+ 
+
+ align:start position:0%
+bonds it's a non-polar molecule it's not
+disturbing the
+
+ align:start position:0%
+disturbing the
+ 
+
+ align:start position:0%
+disturbing the
+bonds um it's interesting idea do you
+
+ align:start position:0%
+bonds um it's interesting idea do you
+ 
+
+ align:start position:0%
+bonds um it's interesting idea do you
+have an idea then able to extend that as
+
+ align:start position:0%
+have an idea then able to extend that as
+ 
+
+ align:start position:0%
+have an idea then able to extend that as
+to why then ice would start to
+
+ align:start position:0%
+to why then ice would start to
+ 
+
+ align:start position:0%
+to why then ice would start to
+form I mean certainly true that
+
+ align:start position:0%
+form I mean certainly true that
+ 
+
+ align:start position:0%
+form I mean certainly true that
+non-polar bonds sort of interfere with
+
+ align:start position:0%
+non-polar bonds sort of interfere with
+ 
+
+ align:start position:0%
+non-polar bonds sort of interfere with
+the water that's something we' we've
+
+ align:start position:0%
+the water that's something we' we've
+ 
+
+ align:start position:0%
+the water that's something we' we've
+talked about um let's see any other
+
+ align:start position:0%
+talked about um let's see any other
+ 
+
+ align:start position:0%
+talked about um let's see any other
+ideas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's that's a version of the same
+
+ align:start position:0%
+yeah that's that's a version of the same
+ 
+
+ align:start position:0%
+yeah that's that's a version of the same
+idea I think hydrophobic you think he
+
+ align:start position:0%
+idea I think hydrophobic you think he
+ 
+
+ align:start position:0%
+idea I think hydrophobic you think he
+wants to repel the water and push it
+
+ align:start position:0%
+wants to repel the water and push it
+ 
+
+ align:start position:0%
+wants to repel the water and push it
+together that's that's an interesting
+
+ align:start position:0%
+together that's that's an interesting
+ 
+
+ align:start position:0%
+together that's that's an interesting
+you're sort of getting closer on these
+
+ align:start position:0%
+you're sort of getting closer on these
+ 
+
+ align:start position:0%
+you're sort of getting closer on these
+yeah you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah there there it is if you were to
+
+ align:start position:0%
+yeah there there it is if you were to
+ 
+
+ align:start position:0%
+yeah there there it is if you were to
+design a protein that basically could
+
+ align:start position:0%
+design a protein that basically could
+ 
+
+ align:start position:0%
+design a protein that basically could
+bind water
+
+ align:start position:0%
+bind water
+ 
+
+ align:start position:0%
+bind water
+molecules in a lattice that mimicked
+
+ align:start position:0%
+molecules in a lattice that mimicked
+ 
+
+ align:start position:0%
+molecules in a lattice that mimicked
+what you found in ice then the water
+
+ align:start position:0%
+what you found in ice then the water
+ 
+
+ align:start position:0%
+what you found in ice then the water
+molecules coming up and binding to these
+
+ align:start position:0%
+molecules coming up and binding to these
+ 
+
+ align:start position:0%
+molecules coming up and binding to these
+little pockets in the protein would
+
+ align:start position:0%
+little pockets in the protein would
+ 
+
+ align:start position:0%
+little pockets in the protein would
+present then a little field of stable
+
+ align:start position:0%
+present then a little field of stable
+ 
+
+ align:start position:0%
+present then a little field of stable
+water molecules that looked to the next
+
+ align:start position:0%
+water molecules that looked to the next
+ 
+
+ align:start position:0%
+water molecules that looked to the next
+water molecule like it was an ice part
+
+ align:start position:0%
+water molecule like it was an ice part
+ 
+
+ align:start position:0%
+water molecule like it was an ice part
+of an Ice Crystal and that's that's
+
+ align:start position:0%
+of an Ice Crystal and that's that's
+ 
+
+ align:start position:0%
+of an Ice Crystal and that's that's
+indeed how that that bacterium does that
+
+ align:start position:0%
+indeed how that that bacterium does that
+ 
+
+ align:start position:0%
+indeed how that that bacterium does that
+trick it's called the ice nucleation
+
+ align:start position:0%
+trick it's called the ice nucleation
+ 
+
+ align:start position:0%
+trick it's called the ice nucleation
+protein and they do things like take
+
+ align:start position:0%
+protein and they do things like take
+ 
+
+ align:start position:0%
+protein and they do things like take
+this bacterium and they put it into
+
+ align:start position:0%
+this bacterium and they put it into
+ 
+
+ align:start position:0%
+this bacterium and they put it into
+things like when you're doing snow snow
+
+ align:start position:0%
+things like when you're doing snow snow
+ 
+
+ align:start position:0%
+things like when you're doing snow snow
+making um they can you put this in and
+
+ align:start position:0%
+making um they can you put this in and
+ 
+
+ align:start position:0%
+making um they can you put this in and
+then you spray the the cool the super
+
+ align:start position:0%
+then you spray the the cool the super
+ 
+
+ align:start position:0%
+then you spray the the cool the super
+cooled water and this makes it go into
+
+ align:start position:0%
+cooled water and this makes it go into
+ 
+
+ align:start position:0%
+cooled water and this makes it go into
+ice crystals and then it helps the the
+
+ align:start position:0%
+ice crystals and then it helps the the
+ 
+
+ align:start position:0%
+ice crystals and then it helps the the
+get nice snow for um
+
+ align:start position:0%
+get nice snow for um
+ 
+
+ align:start position:0%
+get nice snow for um
+for ski resorts and things that's that's
+
+ align:start position:0%
+for ski resorts and things that's that's
+ 
+
+ align:start position:0%
+for ski resorts and things that's that's
+at least one of the areas where it's
+
+ align:start position:0%
+at least one of the areas where it's
+ 
+
+ align:start position:0%
+at least one of the areas where it's
+where it's used okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so when I showed I'm just going to
+
+ align:start position:0%
+um so when I showed I'm just going to
+ 
+
+ align:start position:0%
+um so when I showed I'm just going to
+show you this movie again these are just
+
+ align:start position:0%
+show you this movie again these are just
+ 
+
+ align:start position:0%
+show you this movie again these are just
+baker's yeast sacr sis kind of single
+
+ align:start position:0%
+baker's yeast sacr sis kind of single
+ 
+
+ align:start position:0%
+baker's yeast sacr sis kind of single
+celled yeast that's used in in h baking
+
+ align:start position:0%
+celled yeast that's used in in h baking
+ 
+
+ align:start position:0%
+celled yeast that's used in in h baking
+bread or making beer and uh here we're
+
+ align:start position:0%
+bread or making beer and uh here we're
+ 
+
+ align:start position:0%
+bread or making beer and uh here we're
+seeing cells divide they and then this
+
+ align:start position:0%
+seeing cells divide they and then this
+ 
+
+ align:start position:0%
+seeing cells divide they and then this
+this particular kind of yeast uh has a
+
+ align:start position:0%
+this particular kind of yeast uh has a
+ 
+
+ align:start position:0%
+this particular kind of yeast uh has a
+way of doing it kind of buds the
+
+ align:start position:0%
+way of doing it kind of buds the
+ 
+
+ align:start position:0%
+way of doing it kind of buds the
+daughter off from the side some some
+
+ align:start position:0%
+daughter off from the side some some
+ 
+
+ align:start position:0%
+daughter off from the side some some
+double and then split down the middle
+
+ align:start position:0%
+double and then split down the middle
+ 
+
+ align:start position:0%
+double and then split down the middle
+but you can see what's going on there's
+
+ align:start position:0%
+but you can see what's going on there's
+ 
+
+ align:start position:0%
+but you can see what's going on there's
+a lot of cell growth going on and the
+
+ align:start position:0%
+a lot of cell growth going on and the
+ 
+
+ align:start position:0%
+a lot of cell growth going on and the
+issue that I I that we're going to
+
+ align:start position:0%
+issue that I I that we're going to
+ 
+
+ align:start position:0%
+issue that I I that we're going to
+address now is where does the energy
+
+ align:start position:0%
+address now is where does the energy
+ 
+
+ align:start position:0%
+address now is where does the energy
+come that's needed to do that you know
+
+ align:start position:0%
+come that's needed to do that you know
+ 
+
+ align:start position:0%
+come that's needed to do that you know
+from your own experience that to build
+
+ align:start position:0%
+from your own experience that to build
+ 
+
+ align:start position:0%
+from your own experience that to build
+things to make things takes takes energy
+
+ align:start position:0%
+things to make things takes takes energy
+ 
+
+ align:start position:0%
+things to make things takes takes energy
+you can't build put up a bridge you
+
+ align:start position:0%
+you can't build put up a bridge you
+ 
+
+ align:start position:0%
+you can't build put up a bridge you
+can't put up a building you can't design
+
+ align:start position:0%
+can't put up a building you can't design
+ 
+
+ align:start position:0%
+can't put up a building you can't design
+build a computer chip without some
+
+ align:start position:0%
+build a computer chip without some
+ 
+
+ align:start position:0%
+build a computer chip without some
+somehow putting energy in you're you're
+
+ align:start position:0%
+somehow putting energy in you're you're
+ 
+
+ align:start position:0%
+somehow putting energy in you're you're
+taking a bunch of matter in the universe
+
+ align:start position:0%
+taking a bunch of matter in the universe
+ 
+
+ align:start position:0%
+taking a bunch of matter in the universe
+and ordering it in a very uh specific
+
+ align:start position:0%
+and ordering it in a very uh specific
+ 
+
+ align:start position:0%
+and ordering it in a very uh specific
+way uh making new contacts didn't be
+
+ align:start position:0%
+way uh making new contacts didn't be
+ 
+
+ align:start position:0%
+way uh making new contacts didn't be
+there it's an energy requiring process
+
+ align:start position:0%
+there it's an energy requiring process
+ 
+
+ align:start position:0%
+there it's an energy requiring process
+and I'm going to talk today about where
+
+ align:start position:0%
+and I'm going to talk today about where
+ 
+
+ align:start position:0%
+and I'm going to talk today about where
+that energy comes from and and I want to
+
+ align:start position:0%
+that energy comes from and and I want to
+ 
+
+ align:start position:0%
+that energy comes from and and I want to
+tell you a little bit just very brief
+
+ align:start position:0%
+tell you a little bit just very brief
+ 
+
+ align:start position:0%
+tell you a little bit just very brief
+historical thing along the way because a
+
+ align:start position:0%
+historical thing along the way because a
+ 
+
+ align:start position:0%
+historical thing along the way because a
+point I've emphasized here is is biology
+
+ align:start position:0%
+point I've emphasized here is is biology
+ 
+
+ align:start position:0%
+point I've emphasized here is is biology
+is an experimental science and many of
+
+ align:start position:0%
+is an experimental science and many of
+ 
+
+ align:start position:0%
+is an experimental science and many of
+the greatest discoveries weren't because
+
+ align:start position:0%
+the greatest discoveries weren't because
+ 
+
+ align:start position:0%
+the greatest discoveries weren't because
+somebody had the idea and then and went
+
+ align:start position:0%
+somebody had the idea and then and went
+ 
+
+ align:start position:0%
+somebody had the idea and then and went
+out to prove it very often we didn't
+
+ align:start position:0%
+out to prove it very often we didn't
+ 
+
+ align:start position:0%
+out to prove it very often we didn't
+even understand how it worked and and
+
+ align:start position:0%
+even understand how it worked and and
+ 
+
+ align:start position:0%
+even understand how it worked and and
+somebody was investigating a phenomenon
+
+ align:start position:0%
+somebody was investigating a phenomenon
+ 
+
+ align:start position:0%
+somebody was investigating a phenomenon
+found some peculiar things and then
+
+ align:start position:0%
+found some peculiar things and then
+ 
+
+ align:start position:0%
+found some peculiar things and then
+began to get insights and the insights
+
+ align:start position:0%
+began to get insights and the insights
+ 
+
+ align:start position:0%
+began to get insights and the insights
+were what then
+
+ align:start position:0%
+were what then
+ 
+
+ align:start position:0%
+were what then
+um uh led to a fundamental uh increase
+
+ align:start position:0%
+um uh led to a fundamental uh increase
+ 
+
+ align:start position:0%
+um uh led to a fundamental uh increase
+in her understanding and this little bit
+
+ align:start position:0%
+in her understanding and this little bit
+ 
+
+ align:start position:0%
+in her understanding and this little bit
+of History involves some names that
+
+ align:start position:0%
+of History involves some names that
+ 
+
+ align:start position:0%
+of History involves some names that
+you've see on uh the MIT buildings
+
+ align:start position:0%
+you've see on uh the MIT buildings
+ 
+
+ align:start position:0%
+you've see on uh the MIT buildings
+around here one is laazer who is a
+
+ align:start position:0%
+around here one is laazer who is a
+ 
+
+ align:start position:0%
+around here one is laazer who is a
+French um
+
+ align:start position:0%
+French um
+ 
+
+ align:start position:0%
+French um
+a French scientist and he was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+studying what happened when
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grapes were converted into
+
+ align:start position:0%
+grapes were converted into
+ 
+
+ align:start position:0%
+grapes were converted into
+wine nice uh good topic for a French uh
+
+ align:start position:0%
+wine nice uh good topic for a French uh
+ 
+
+ align:start position:0%
+wine nice uh good topic for a French uh
+scientist to be studying so in essence
+
+ align:start position:0%
+scientist to be studying so in essence
+ 
+
+ align:start position:0%
+scientist to be studying so in essence
+what he was
+
+ align:start position:0%
+what he was
+ 
+
+ align:start position:0%
+what he was
+studying was
+
+ align:start position:0%
+studying was
+ 
+
+ align:start position:0%
+studying was
+glucose being converted to two two
+
+ align:start position:0%
+glucose being converted to two two
+ 
+
+ align:start position:0%
+glucose being converted to two two
+molecules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh excuse me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ethanol and two molecules of uh carbon
+
+ align:start position:0%
+ethanol and two molecules of uh carbon
+ 
+
+ align:start position:0%
+ethanol and two molecules of uh carbon
+dioxide this
+
+ align:start position:0%
+dioxide this
+ 
+
+ align:start position:0%
+dioxide this
+transformation there's C6
+
+ align:start position:0%
+transformation there's C6
+ 
+
+ align:start position:0%
+transformation there's C6
+h12 06 remember
+
+ align:start position:0%
+h12 06 remember
+ 
+
+ align:start position:0%
+h12 06 remember
+carbohydrates have the have that uh
+
+ align:start position:0%
+carbohydrates have the have that uh
+ 
+
+ align:start position:0%
+carbohydrates have the have that uh
+that um composition um and so he was he
+
+ align:start position:0%
+that um composition um and so he was he
+ 
+
+ align:start position:0%
+that um composition um and so he was he
+was studying that he managed to figure
+
+ align:start position:0%
+was studying that he managed to figure
+ 
+
+ align:start position:0%
+was studying that he managed to figure
+out that's what happened to the sugar
+
+ align:start position:0%
+out that's what happened to the sugar
+ 
+
+ align:start position:0%
+out that's what happened to the sugar
+when you were making wine and at that
+
+ align:start position:0%
+when you were making wine and at that
+ 
+
+ align:start position:0%
+when you were making wine and at that
+point he got beheaded that terminated
+
+ align:start position:0%
+point he got beheaded that terminated
+ 
+
+ align:start position:0%
+point he got beheaded that terminated
+that part of uh his investigation but
+
+ align:start position:0%
+that part of uh his investigation but
+ 
+
+ align:start position:0%
+that part of uh his investigation but
+this was this problem was then picked up
+
+ align:start position:0%
+this was this problem was then picked up
+ 
+
+ align:start position:0%
+this was this problem was then picked up
+by uh L pester who uh again his uh his
+
+ align:start position:0%
+by uh L pester who uh again his uh his
+ 
+
+ align:start position:0%
+by uh L pester who uh again his uh his
+name is on one of the MIT buildings um
+
+ align:start position:0%
+name is on one of the MIT buildings um
+ 
+
+ align:start position:0%
+name is on one of the MIT buildings um
+he worked in France as well there's a
+
+ align:start position:0%
+he worked in France as well there's a
+ 
+
+ align:start position:0%
+he worked in France as well there's a
+pastor Institute in Paris there's a nice
+
+ align:start position:0%
+pastor Institute in Paris there's a nice
+ 
+
+ align:start position:0%
+pastor Institute in Paris there's a nice
+museum in Le in northern France that has
+
+ align:start position:0%
+museum in Le in northern France that has
+ 
+
+ align:start position:0%
+museum in Le in northern France that has
+a lot of this but he grew up in in ARB
+
+ align:start position:0%
+a lot of this but he grew up in in ARB
+ 
+
+ align:start position:0%
+a lot of this but he grew up in in ARB
+which is a town in sort of Eastern
+
+ align:start position:0%
+which is a town in sort of Eastern
+ 
+
+ align:start position:0%
+which is a town in sort of Eastern
+France that as you can see from the the
+
+ align:start position:0%
+France that as you can see from the the
+ 
+
+ align:start position:0%
+France that as you can see from the the
+from the little picture of the village
+
+ align:start position:0%
+from the little picture of the village
+ 
+
+ align:start position:0%
+from the little picture of the village
+wine making was a major industry so he
+
+ align:start position:0%
+wine making was a major industry so he
+ 
+
+ align:start position:0%
+wine making was a major industry so he
+was was interested in that probably from
+
+ align:start position:0%
+was was interested in that probably from
+ 
+
+ align:start position:0%
+was was interested in that probably from
+when he was a small small kid although
+
+ align:start position:0%
+when he was a small small kid although
+ 
+
+ align:start position:0%
+when he was a small small kid although
+probably not dressed like that but
+
+ align:start position:0%
+probably not dressed like that but
+ 
+
+ align:start position:0%
+probably not dressed like that but
+anyway so he one of the issues that he
+
+ align:start position:0%
+anyway so he one of the issues that he
+ 
+
+ align:start position:0%
+anyway so he one of the issues that he
+he took on which was a real problem for
+
+ align:start position:0%
+he took on which was a real problem for
+ 
+
+ align:start position:0%
+he took on which was a real problem for
+the wine growers in in his little town
+
+ align:start position:0%
+the wine growers in in his little town
+ 
+
+ align:start position:0%
+the wine growers in in his little town
+and in France in general was sometimes
+
+ align:start position:0%
+and in France in general was sometimes
+ 
+
+ align:start position:0%
+and in France in general was sometimes
+wines would go bad they'd come out sour
+
+ align:start position:0%
+wines would go bad they'd come out sour
+ 
+
+ align:start position:0%
+wines would go bad they'd come out sour
+and they they couldn't be drunk and then
+
+ align:start position:0%
+and they they couldn't be drunk and then
+ 
+
+ align:start position:0%
+and they they couldn't be drunk and then
+you'd lose all the all the profit that
+
+ align:start position:0%
+you'd lose all the all the profit that
+ 
+
+ align:start position:0%
+you'd lose all the all the profit that
+would have come from from that wine so
+
+ align:start position:0%
+would have come from from that wine so
+ 
+
+ align:start position:0%
+would have come from from that wine so
+there's a lot of interest in trying to
+
+ align:start position:0%
+there's a lot of interest in trying to
+ 
+
+ align:start position:0%
+there's a lot of interest in trying to
+figure out how to prevent uh wines from
+
+ align:start position:0%
+figure out how to prevent uh wines from
+ 
+
+ align:start position:0%
+figure out how to prevent uh wines from
+going bad and so Louis pester started to
+
+ align:start position:0%
+going bad and so Louis pester started to
+ 
+
+ align:start position:0%
+going bad and so Louis pester started to
+to study this and he discovered
+
+ align:start position:0%
+to study this and he discovered
+ 
+
+ align:start position:0%
+to study this and he discovered
+that uh that the there was this
+
+ align:start position:0%
+that uh that the there was this
+ 
+
+ align:start position:0%
+that uh that the there was this
+conversion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that had been figured out now of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+ethanol to carbon dioxide so this was a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conversion and we now refer to it
+
+ align:start position:0%
+conversion and we now refer to it
+ 
+
+ align:start position:0%
+conversion and we now refer to it
+generally as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fermentation but what he discovered was
+
+ align:start position:0%
+fermentation but what he discovered was
+ 
+
+ align:start position:0%
+fermentation but what he discovered was
+this conversion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+occurred
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if yeast were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+present that the rate of this conversion
+
+ align:start position:0%
+present that the rate of this conversion
+ 
+
+ align:start position:0%
+present that the rate of this conversion
+varied as the number of yeast so it went
+
+ align:start position:0%
+varied as the number of yeast so it went
+ 
+
+ align:start position:0%
+varied as the number of yeast so it went
+faster if there were more yeast and the
+
+ align:start position:0%
+faster if there were more yeast and the
+ 
+
+ align:start position:0%
+faster if there were more yeast and the
+yeast stopped
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+growing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when the sugar ran
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out so what he discovered here was a
+
+ align:start position:0%
+out so what he discovered here was a
+ 
+
+ align:start position:0%
+out so what he discovered here was a
+correlation he hadn't proven anything he
+
+ align:start position:0%
+correlation he hadn't proven anything he
+ 
+
+ align:start position:0%
+correlation he hadn't proven anything he
+just saw that if you watch sugar go to
+
+ align:start position:0%
+just saw that if you watch sugar go to
+ 
+
+ align:start position:0%
+just saw that if you watch sugar go to
+ethanol there were yeast around if you
+
+ align:start position:0%
+ethanol there were yeast around if you
+ 
+
+ align:start position:0%
+ethanol there were yeast around if you
+had more yeast it went faster and when
+
+ align:start position:0%
+had more yeast it went faster and when
+ 
+
+ align:start position:0%
+had more yeast it went faster and when
+you ran out of sugar the yeast stopped
+
+ align:start position:0%
+you ran out of sugar the yeast stopped
+ 
+
+ align:start position:0%
+you ran out of sugar the yeast stopped
+growing it was something connected here
+
+ align:start position:0%
+growing it was something connected here
+ 
+
+ align:start position:0%
+growing it was something connected here
+so he came up with the idea that the
+
+ align:start position:0%
+so he came up with the idea that the
+ 
+
+ align:start position:0%
+so he came up with the idea that the
+yeast were responsible for this
+
+ align:start position:0%
+yeast were responsible for this
+ 
+
+ align:start position:0%
+yeast were responsible for this
+conversion was happening when you made
+
+ align:start position:0%
+conversion was happening when you made
+ 
+
+ align:start position:0%
+conversion was happening when you made
+wine and it was further uh helped out on
+
+ align:start position:0%
+wine and it was further uh helped out on
+ 
+
+ align:start position:0%
+wine and it was further uh helped out on
+this because he discovered an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alternative conversion in which C6
+
+ align:start position:0%
+alternative conversion in which C6
+ 
+
+ align:start position:0%
+alternative conversion in which C6
+h126 went instead to give two molecules
+
+ align:start position:0%
+h126 went instead to give two molecules
+ 
+
+ align:start position:0%
+h126 went instead to give two molecules
+of ch3 CH
+
+ align:start position:0%
+of ch3 CH
+ 
+
+ align:start position:0%
+of ch3 CH
+o
+
+ align:start position:0%
+o
+ 
+
+ align:start position:0%
+o
+this molecule which you
+
+ align:start position:0%
+this molecule which you
+ 
+
+ align:start position:0%
+this molecule which you
+know is lactic acid it too has C6
+
+ align:start position:0%
+know is lactic acid it too has C6
+ 
+
+ align:start position:0%
+know is lactic acid it too has C6
+h126 on both sides of the equation but
+
+ align:start position:0%
+h126 on both sides of the equation but
+ 
+
+ align:start position:0%
+h126 on both sides of the equation but
+it's a different molecule and what he
+
+ align:start position:0%
+it's a different molecule and what he
+ 
+
+ align:start position:0%
+it's a different molecule and what he
+found was that this is the lactic acid
+
+ align:start position:0%
+found was that this is the lactic acid
+ 
+
+ align:start position:0%
+found was that this is the lactic acid
+um you know it it's what's in yogurt
+
+ align:start position:0%
+um you know it it's what's in yogurt
+ 
+
+ align:start position:0%
+um you know it it's what's in yogurt
+that makes yogurt sour or if you
+
+ align:start position:0%
+that makes yogurt sour or if you
+ 
+
+ align:start position:0%
+that makes yogurt sour or if you
+exercise really hard and your muscles
+
+ align:start position:0%
+exercise really hard and your muscles
+ 
+
+ align:start position:0%
+exercise really hard and your muscles
+are sore that's because you accumulate
+
+ align:start position:0%
+are sore that's because you accumulate
+ 
+
+ align:start position:0%
+are sore that's because you accumulate
+lactic acid in your muscles and tell you
+
+ align:start position:0%
+lactic acid in your muscles and tell you
+ 
+
+ align:start position:0%
+lactic acid in your muscles and tell you
+why that is in the next lecture but what
+
+ align:start position:0%
+why that is in the next lecture but what
+ 
+
+ align:start position:0%
+why that is in the next lecture but what
+uh the other thing that uh pester
+
+ align:start position:0%
+uh the other thing that uh pester
+ 
+
+ align:start position:0%
+uh the other thing that uh pester
+realized that was when you got this
+
+ align:start position:0%
+realized that was when you got this
+ 
+
+ align:start position:0%
+realized that was when you got this
+alternative conversion you didn't have
+
+ align:start position:0%
+alternative conversion you didn't have
+ 
+
+ align:start position:0%
+alternative conversion you didn't have
+yeast present you had some other
+
+ align:start position:0%
+yeast present you had some other
+ 
+
+ align:start position:0%
+yeast present you had some other
+organism and so that was a huge Advance
+
+ align:start position:0%
+organism and so that was a huge Advance
+ 
+
+ align:start position:0%
+organism and so that was a huge Advance
+uh just and of practical value to the
+
+ align:start position:0%
+uh just and of practical value to the
+ 
+
+ align:start position:0%
+uh just and of practical value to the
+wine makers because they knew they had
+
+ align:start position:0%
+wine makers because they knew they had
+ 
+
+ align:start position:0%
+wine makers because they knew they had
+to have yeast in there to get wine and
+
+ align:start position:0%
+to have yeast in there to get wine and
+ 
+
+ align:start position:0%
+to have yeast in there to get wine and
+their problems were coming when some
+
+ align:start position:0%
+their problems were coming when some
+ 
+
+ align:start position:0%
+their problems were coming when some
+other organism that wasn't yeast got in
+
+ align:start position:0%
+other organism that wasn't yeast got in
+ 
+
+ align:start position:0%
+other organism that wasn't yeast got in
+there and it did something different
+
+ align:start position:0%
+there and it did something different
+ 
+
+ align:start position:0%
+there and it did something different
+with the sugar and made it into lactic
+
+ align:start position:0%
+with the sugar and made it into lactic
+ 
+
+ align:start position:0%
+with the sugar and made it into lactic
+acid and instead of making an end
+
+ align:start position:0%
+acid and instead of making an end
+ 
+
+ align:start position:0%
+acid and instead of making an end
+ethanol and and carbon dioxide so there
+
+ align:start position:0%
+ethanol and and carbon dioxide so there
+ 
+
+ align:start position:0%
+ethanol and and carbon dioxide so there
+was pastur working away on a on a
+
+ align:start position:0%
+was pastur working away on a on a
+ 
+
+ align:start position:0%
+was pastur working away on a on a
+practical problem and um it was a you
+
+ align:start position:0%
+practical problem and um it was a you
+ 
+
+ align:start position:0%
+practical problem and um it was a you
+know a really major advance to the wine
+
+ align:start position:0%
+know a really major advance to the wine
+ 
+
+ align:start position:0%
+know a really major advance to the wine
+making industry for him him to do this
+
+ align:start position:0%
+making industry for him him to do this
+ 
+
+ align:start position:0%
+making industry for him him to do this
+but it also then sort of
+
+ align:start position:0%
+but it also then sort of
+ 
+
+ align:start position:0%
+but it also then sort of
+unexpectedly led to uh another issue and
+
+ align:start position:0%
+unexpectedly led to uh another issue and
+ 
+
+ align:start position:0%
+unexpectedly led to uh another issue and
+that was why were the yeast doing this
+
+ align:start position:0%
+that was why were the yeast doing this
+ 
+
+ align:start position:0%
+that was why were the yeast doing this
+because one of the things that L not and
+
+ align:start position:0%
+because one of the things that L not and
+ 
+
+ align:start position:0%
+because one of the things that L not and
+Pastor noticed was that you you did this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conversion the two
+
+ align:start position:0%
+conversion the two
+ 
+
+ align:start position:0%
+conversion the two
+ethanol plus two carbon dioxide but you
+
+ align:start position:0%
+ethanol plus two carbon dioxide but you
+ 
+
+ align:start position:0%
+ethanol plus two carbon dioxide but you
+could account for virtually all of the
+
+ align:start position:0%
+could account for virtually all of the
+ 
+
+ align:start position:0%
+could account for virtually all of the
+the carbons and hydrogens and oxygens uh
+
+ align:start position:0%
+the carbons and hydrogens and oxygens uh
+ 
+
+ align:start position:0%
+the carbons and hydrogens and oxygens uh
+that started out of sugar seemed like
+
+ align:start position:0%
+that started out of sugar seemed like
+ 
+
+ align:start position:0%
+that started out of sugar seemed like
+virtually all of them showed up in the
+
+ align:start position:0%
+virtually all of them showed up in the
+ 
+
+ align:start position:0%
+virtually all of them showed up in the
+uh in the ethanol and carbon dioxide so
+
+ align:start position:0%
+uh in the ethanol and carbon dioxide so
+ 
+
+ align:start position:0%
+uh in the ethanol and carbon dioxide so
+why was the yeast doing this and the I
+
+ align:start position:0%
+why was the yeast doing this and the I
+ 
+
+ align:start position:0%
+why was the yeast doing this and the I
+idea began to develop out of that was
+
+ align:start position:0%
+idea began to develop out of that was
+ 
+
+ align:start position:0%
+idea began to develop out of that was
+that the uh rather than being used to
+
+ align:start position:0%
+that the uh rather than being used to
+ 
+
+ align:start position:0%
+that the uh rather than being used to
+make biomass in which case you would
+
+ align:start position:0%
+make biomass in which case you would
+ 
+
+ align:start position:0%
+make biomass in which case you would
+have expected to see a whole lot of mass
+
+ align:start position:0%
+have expected to see a whole lot of mass
+ 
+
+ align:start position:0%
+have expected to see a whole lot of mass
+in the yeast cells and not so much up
+
+ align:start position:0%
+in the yeast cells and not so much up
+ 
+
+ align:start position:0%
+in the yeast cells and not so much up
+here that instead most of this sugar was
+
+ align:start position:0%
+here that instead most of this sugar was
+ 
+
+ align:start position:0%
+here that instead most of this sugar was
+being used to make energy and that
+
+ align:start position:0%
+being used to make energy and that
+ 
+
+ align:start position:0%
+being used to make energy and that
+somehow the cell was getting the energy
+
+ align:start position:0%
+somehow the cell was getting the energy
+ 
+
+ align:start position:0%
+somehow the cell was getting the energy
+necessary to do all that synthetic work
+
+ align:start position:0%
+necessary to do all that synthetic work
+ 
+
+ align:start position:0%
+necessary to do all that synthetic work
+in that involved in cell division by
+
+ align:start position:0%
+in that involved in cell division by
+ 
+
+ align:start position:0%
+in that involved in cell division by
+carrying out uh this
+
+ align:start position:0%
+carrying out uh this
+ 
+
+ align:start position:0%
+carrying out uh this
+conversion and there's a fundamental uh
+
+ align:start position:0%
+conversion and there's a fundamental uh
+ 
+
+ align:start position:0%
+conversion and there's a fundamental uh
+relationship then between chemical
+
+ align:start position:0%
+relationship then between chemical
+ 
+
+ align:start position:0%
+relationship then between chemical
+energy and whether a reaction uh can
+
+ align:start position:0%
+energy and whether a reaction uh can
+ 
+
+ align:start position:0%
+energy and whether a reaction uh can
+proceed and I'll just uh take it through
+
+ align:start position:0%
+proceed and I'll just uh take it through
+ 
+
+ align:start position:0%
+proceed and I'll just uh take it through
+and in a sort of your typical
+
+ align:start position:0%
+and in a sort of your typical
+ 
+
+ align:start position:0%
+and in a sort of your typical
+introductory chemistry reaction a plus b
+
+ align:start position:0%
+introductory chemistry reaction a plus b
+ 
+
+ align:start position:0%
+introductory chemistry reaction a plus b
+going to C plus d now if this re there
+
+ align:start position:0%
+going to C plus d now if this re there
+ 
+
+ align:start position:0%
+going to C plus d now if this re there
+are certain classes of reactions that
+
+ align:start position:0%
+are certain classes of reactions that
+ 
+
+ align:start position:0%
+are certain classes of reactions that
+will go almost to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+completion
+
+ align:start position:0%
+completion
+ 
+
+ align:start position:0%
+completion
+probably an overstatement it say it's to
+
+ align:start position:0%
+probably an overstatement it say it's to
+ 
+
+ align:start position:0%
+probably an overstatement it say it's to
+go to completion but it's effectively
+
+ align:start position:0%
+go to completion but it's effectively
+ 
+
+ align:start position:0%
+go to completion but it's effectively
+over here those are termed irreversible
+
+ align:start position:0%
+over here those are termed irreversible
+ 
+
+ align:start position:0%
+over here those are termed irreversible
+reactions and there are certainly are
+
+ align:start position:0%
+reactions and there are certainly are
+ 
+
+ align:start position:0%
+reactions and there are certainly are
+are some of them if I have hydrogen and
+
+ align:start position:0%
+are some of them if I have hydrogen and
+ 
+
+ align:start position:0%
+are some of them if I have hydrogen and
+oxygen and I little light a little match
+
+ align:start position:0%
+oxygen and I little light a little match
+ 
+
+ align:start position:0%
+oxygen and I little light a little match
+we pretty much go all the way to making
+
+ align:start position:0%
+we pretty much go all the way to making
+ 
+
+ align:start position:0%
+we pretty much go all the way to making
+water with a great big boom and no
+
+ align:start position:0%
+water with a great big boom and no
+ 
+
+ align:start position:0%
+water with a great big boom and no
+hydrogen or not much hydrogen oxygen
+
+ align:start position:0%
+hydrogen or not much hydrogen oxygen
+ 
+
+ align:start position:0%
+hydrogen or not much hydrogen oxygen
+left on the other side however most
+
+ align:start position:0%
+left on the other side however most
+ 
+
+ align:start position:0%
+left on the other side however most
+reactions that one finds in nature don't
+
+ align:start position:0%
+reactions that one finds in nature don't
+ 
+
+ align:start position:0%
+reactions that one finds in nature don't
+have that quality instead they're going
+
+ align:start position:0%
+have that quality instead they're going
+ 
+
+ align:start position:0%
+have that quality instead they're going
+forward at some rate and back at another
+
+ align:start position:0%
+forward at some rate and back at another
+ 
+
+ align:start position:0%
+forward at some rate and back at another
+and they reach eventually an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium it's
+
+ align:start position:0%
+equilibrium it's
+ 
+
+ align:start position:0%
+equilibrium it's
+characterized by what's known as an
+
+ align:start position:0%
+characterized by what's known as an
+ 
+
+ align:start position:0%
+characterized by what's known as an
+equilibrium constant which is
+
+ align:start position:0%
+equilibrium constant which is
+ 
+
+ align:start position:0%
+equilibrium constant which is
+the product of the
+
+ align:start position:0%
+the product of the
+ 
+
+ align:start position:0%
+the product of the
+concentrations of the products over the
+
+ align:start position:0%
+concentrations of the products over the
+ 
+
+ align:start position:0%
+concentrations of the products over the
+product of the
+
+ align:start position:0%
+product of the
+ 
+
+ align:start position:0%
+product of the
+concentration of the reactants and
+
+ align:start position:0%
+concentration of the reactants and
+ 
+
+ align:start position:0%
+concentration of the reactants and
+that's a char eristic of every uh
+
+ align:start position:0%
+that's a char eristic of every uh
+ 
+
+ align:start position:0%
+that's a char eristic of every uh
+particular chemical reaction and we
+
+ align:start position:0%
+particular chemical reaction and we
+ 
+
+ align:start position:0%
+particular chemical reaction and we
+really have to worry about this uh in
+
+ align:start position:0%
+really have to worry about this uh in
+ 
+
+ align:start position:0%
+really have to worry about this uh in
+biology because if everything was
+
+ align:start position:0%
+biology because if everything was
+ 
+
+ align:start position:0%
+biology because if everything was
+irreversible that would fine but in
+
+ align:start position:0%
+irreversible that would fine but in
+ 
+
+ align:start position:0%
+irreversible that would fine but in
+order to do all this synthetic work you
+
+ align:start position:0%
+order to do all this synthetic work you
+ 
+
+ align:start position:0%
+order to do all this synthetic work you
+have to um deal with a lot of reactions
+
+ align:start position:0%
+have to um deal with a lot of reactions
+ 
+
+ align:start position:0%
+have to um deal with a lot of reactions
+that aren't going to go to completion
+
+ align:start position:0%
+that aren't going to go to completion
+ 
+
+ align:start position:0%
+that aren't going to go to completion
+and nature has had to figure out a way
+
+ align:start position:0%
+and nature has had to figure out a way
+ 
+
+ align:start position:0%
+and nature has had to figure out a way
+of uh of doing that just the same way
+
+ align:start position:0%
+of uh of doing that just the same way
+ 
+
+ align:start position:0%
+of uh of doing that just the same way
+that Bridges and buildings don't
+
+ align:start position:0%
+that Bridges and buildings don't
+ 
+
+ align:start position:0%
+that Bridges and buildings don't
+spontaneously assemble in Engineers on
+
+ align:start position:0%
+spontaneously assemble in Engineers on
+ 
+
+ align:start position:0%
+spontaneously assemble in Engineers on
+earth have had to work out ways of
+
+ align:start position:0%
+earth have had to work out ways of
+ 
+
+ align:start position:0%
+earth have had to work out ways of
+putting all of those things together so
+
+ align:start position:0%
+putting all of those things together so
+ 
+
+ align:start position:0%
+putting all of those things together so
+at some level you see the same kind of
+
+ align:start position:0%
+at some level you see the same kind of
+ 
+
+ align:start position:0%
+at some level you see the same kind of
+problem now there's a there's a a way of
+
+ align:start position:0%
+problem now there's a there's a a way of
+ 
+
+ align:start position:0%
+problem now there's a there's a a way of
+expressing this energy associated with a
+
+ align:start position:0%
+expressing this energy associated with a
+ 
+
+ align:start position:0%
+expressing this energy associated with a
+chemical reaction that can be used to
+
+ align:start position:0%
+chemical reaction that can be used to
+ 
+
+ align:start position:0%
+chemical reaction that can be used to
+directly calculate whether uh a reaction
+
+ align:start position:0%
+directly calculate whether uh a reaction
+ 
+
+ align:start position:0%
+directly calculate whether uh a reaction
+is going to go or and how far it will go
+
+ align:start position:0%
+is going to go or and how far it will go
+ 
+
+ align:start position:0%
+is going to go or and how far it will go
+and um the person who did this work is
+
+ align:start position:0%
+and um the person who did this work is
+ 
+
+ align:start position:0%
+and um the person who did this work is
+another person who's on uh um one of the
+
+ align:start position:0%
+another person who's on uh um one of the
+ 
+
+ align:start position:0%
+another person who's on uh um one of the
+MIT buildings uh it was josea Gibbs who
+
+ align:start position:0%
+MIT buildings uh it was josea Gibbs who
+ 
+
+ align:start position:0%
+MIT buildings uh it was josea Gibbs who
+was a uh faculty member uh chemist who
+
+ align:start position:0%
+was a uh faculty member uh chemist who
+ 
+
+ align:start position:0%
+was a uh faculty member uh chemist who
+worked at Yale in the
+
+ align:start position:0%
+worked at Yale in the
+ 
+
+ align:start position:0%
+worked at Yale in the
+1980s 18 excuse me 18 uh 1800s and he
+
+ align:start position:0%
+1980s 18 excuse me 18 uh 1800s and he
+ 
+
+ align:start position:0%
+1980s 18 excuse me 18 uh 1800s and he
+um came up with expression that's now
+
+ align:start position:0%
+um came up with expression that's now
+ 
+
+ align:start position:0%
+um came up with expression that's now
+known as Gibs free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy and this is what's important
+
+ align:start position:0%
+energy and this is what's important
+ 
+
+ align:start position:0%
+energy and this is what's important
+about this uh this way of talking about
+
+ align:start position:0%
+about this uh this way of talking about
+ 
+
+ align:start position:0%
+about this uh this way of talking about
+the energy ex um Associated change
+
+ align:start position:0%
+the energy ex um Associated change
+ 
+
+ align:start position:0%
+the energy ex um Associated change
+associated with the chemical reaction is
+
+ align:start position:0%
+associated with the chemical reaction is
+ 
+
+ align:start position:0%
+associated with the chemical reaction is
+it combines not only uh the considers
+
+ align:start position:0%
+it combines not only uh the considers
+ 
+
+ align:start position:0%
+it combines not only uh the considers
+not only the internal energy of the
+
+ align:start position:0%
+not only the internal energy of the
+ 
+
+ align:start position:0%
+not only the internal energy of the
+system but also the change in disorder
+
+ align:start position:0%
+system but also the change in disorder
+ 
+
+ align:start position:0%
+system but also the change in disorder
+or another way of saying that for those
+
+ align:start position:0%
+or another way of saying that for those
+ 
+
+ align:start position:0%
+or another way of saying that for those
+of you who've run into the laws of
+
+ align:start position:0%
+of you who've run into the laws of
+ 
+
+ align:start position:0%
+of you who've run into the laws of
+thermodynamics it combines the first and
+
+ align:start position:0%
+thermodynamics it combines the first and
+ 
+
+ align:start position:0%
+thermodynamics it combines the first and
+second laws of thermodynamics and you
+
+ align:start position:0%
+second laws of thermodynamics and you
+ 
+
+ align:start position:0%
+second laws of thermodynamics and you
+have to consider both of those you're
+
+ align:start position:0%
+have to consider both of those you're
+ 
+
+ align:start position:0%
+have to consider both of those you're
+going to consider whether a uh a
+
+ align:start position:0%
+going to consider whether a uh a
+ 
+
+ align:start position:0%
+going to consider whether a uh a
+reaction will go and and
+
+ align:start position:0%
+reaction will go and and
+ 
+
+ align:start position:0%
+reaction will go and and
+it's that you can't measure an absolute
+
+ align:start position:0%
+it's that you can't measure an absolute
+ 
+
+ align:start position:0%
+it's that you can't measure an absolute
+free energy but you can measure a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change and this was this is the equation
+
+ align:start position:0%
+change and this was this is the equation
+ 
+
+ align:start position:0%
+change and this was this is the equation
+it's uh the change associated with with
+
+ align:start position:0%
+it's uh the change associated with with
+ 
+
+ align:start position:0%
+it's uh the change associated with with
+a chemical reaction is is equal to the
+
+ align:start position:0%
+a chemical reaction is is equal to the
+ 
+
+ align:start position:0%
+a chemical reaction is is equal to the
+change associated with the chemical
+
+ align:start position:0%
+change associated with the chemical
+ 
+
+ align:start position:0%
+change associated with the chemical
+reaction under some set of standard
+
+ align:start position:0%
+reaction under some set of standard
+ 
+
+ align:start position:0%
+reaction under some set of standard
+conditions times RT times the log of the
+
+ align:start position:0%
+conditions times RT times the log of the
+ 
+
+ align:start position:0%
+conditions times RT times the log of the
+concentration of the products multiplied
+
+ align:start position:0%
+concentration of the products multiplied
+ 
+
+ align:start position:0%
+concentration of the products multiplied
+together over the concent ation of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reactants so if we just go to the same
+
+ align:start position:0%
+reactants so if we just go to the same
+ 
+
+ align:start position:0%
+reactants so if we just go to the same
+example we were just thinking about the
+
+ align:start position:0%
+example we were just thinking about the
+ 
+
+ align:start position:0%
+example we were just thinking about the
+assoc the energy change with that
+
+ align:start position:0%
+assoc the energy change with that
+ 
+
+ align:start position:0%
+assoc the energy change with that
+reaction that we were
+
+ align:start position:0%
+reaction that we were
+ 
+
+ align:start position:0%
+reaction that we were
+considering would have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+been
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so this is the energy chain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so associated with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concentrations the reactants and
+
+ align:start position:0%
+concentrations the reactants and
+ 
+
+ align:start position:0%
+concentrations the reactants and
+products that we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+considering this is the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change under
+
+ align:start position:0%
+change under
+ 
+
+ align:start position:0%
+change under
+standard what term standard
+
+ align:start position:0%
+standard what term standard
+ 
+
+ align:start position:0%
+standard what term standard
+conditions where every thing the each
+
+ align:start position:0%
+conditions where every thing the each
+ 
+
+ align:start position:0%
+conditions where every thing the each
+reactant each product is present under
+
+ align:start position:0%
+reactant each product is present under
+ 
+
+ align:start position:0%
+reactant each product is present under
+one molar concentrations so not
+
+ align:start position:0%
+one molar concentrations so not
+ 
+
+ align:start position:0%
+one molar concentrations so not
+something you'd ever find in most cases
+
+ align:start position:0%
+something you'd ever find in most cases
+ 
+
+ align:start position:0%
+something you'd ever find in most cases
+but it's a frame of reference and then
+
+ align:start position:0%
+but it's a frame of reference and then
+ 
+
+ align:start position:0%
+but it's a frame of reference and then
+this is the gas constant the universal
+
+ align:start position:0%
+this is the gas constant the universal
+ 
+
+ align:start position:0%
+this is the gas constant the universal
+gas
+
+ align:start position:0%
+gas
+ 
+
+ align:start position:0%
+gas
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is 2 *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10-3 kilo
+
+ align:start position:0%
+10-3 kilo
+ 
+
+ align:start position:0%
+10-3 kilo
+calories per mole per degree Kelvin the
+
+ align:start position:0%
+calories per mole per degree Kelvin the
+ 
+
+ align:start position:0%
+calories per mole per degree Kelvin the
+temperature in absolute this is the
+
+ align:start position:0%
+temperature in absolute this is the
+ 
+
+ align:start position:0%
+temperature in absolute this is the
+temp in degrees
+
+ align:start position:0%
+temp in degrees
+ 
+
+ align:start position:0%
+temp in degrees
+Kelvin and the temperature for most
+
+ align:start position:0%
+Kelvin and the temperature for most
+ 
+
+ align:start position:0%
+Kelvin and the temperature for most
+biology most life is around 25° Cen so
+
+ align:start position:0%
+biology most life is around 25° Cen so
+ 
+
+ align:start position:0%
+biology most life is around 25° Cen so
+that's equal to
+
+ align:start position:0%
+that's equal to
+ 
+
+ align:start position:0%
+that's equal to
+298°
+
+ align:start position:0%
+298°
+ 
+
+ align:start position:0%
+298°
+Kelvin which is about equal to 300°
+
+ align:start position:0%
+Kelvin which is about equal to 300°
+ 
+
+ align:start position:0%
+Kelvin which is about equal to 300°
+Kelvin so for most and since the range
+
+ align:start position:0%
+Kelvin so for most and since the range
+ 
+
+ align:start position:0%
+Kelvin so for most and since the range
+in which life can occur on an absolute
+
+ align:start position:0%
+in which life can occur on an absolute
+ 
+
+ align:start position:0%
+in which life can occur on an absolute
+temperature scale is really pretty small
+
+ align:start position:0%
+temperature scale is really pretty small
+ 
+
+ align:start position:0%
+temperature scale is really pretty small
+and sort of fluctuates in only very
+
+ align:start position:0%
+and sort of fluctuates in only very
+ 
+
+ align:start position:0%
+and sort of fluctuates in only very
+minor ways around 25° Centigrade then
+
+ align:start position:0%
+minor ways around 25° Centigrade then
+ 
+
+ align:start position:0%
+minor ways around 25° Centigrade then
+for most of the biological reactions
+
+ align:start position:0%
+for most of the biological reactions
+ 
+
+ align:start position:0%
+for most of the biological reactions
+we'll be thinking about this RT uh
+
+ align:start position:0%
+we'll be thinking about this RT uh
+ 
+
+ align:start position:0%
+we'll be thinking about this RT uh
+number number is is about 6 K
+
+ align:start position:0%
+number number is is about 6 K
+ 
+
+ align:start position:0%
+number number is is about 6 K
+Cals per per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mole now biochemists actually have a
+
+ align:start position:0%
+mole now biochemists actually have a
+ 
+
+ align:start position:0%
+mole now biochemists actually have a
+special form of free energy they use
+
+ align:start position:0%
+special form of free energy they use
+ 
+
+ align:start position:0%
+special form of free energy they use
+which we put a a Delta
+
+ align:start position:0%
+which we put a a Delta
+ 
+
+ align:start position:0%
+which we put a a Delta
+G Prime and that's in this case the
+
+ align:start position:0%
+G Prime and that's in this case the
+ 
+
+ align:start position:0%
+G Prime and that's in this case the
+Delta G Prime is equal to Delta G Prime
+
+ align:start position:0%
+Delta G Prime is equal to Delta G Prime
+ 
+
+ align:start position:0%
+Delta G Prime is equal to Delta G Prime
+under a set of standard conditions plus
+
+ align:start position:0%
+under a set of standard conditions plus
+ 
+
+ align:start position:0%
+under a set of standard conditions plus
+RT
+
+ align:start position:0%
+RT
+ 
+
+ align:start position:0%
+RT
+natural log of C
+
+ align:start position:0%
+natural log of C
+ 
+
+ align:start position:0%
+natural log of C
+products over the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reactants but the assumption is made
+
+ align:start position:0%
+reactants but the assumption is made
+ 
+
+ align:start position:0%
+reactants but the assumption is made
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+reactions the
+
+ align:start position:0%
+reactions the
+ 
+
+ align:start position:0%
+reactions the
+reaction is in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+water which is I mentioned the other day
+
+ align:start position:0%
+water which is I mentioned the other day
+ 
+
+ align:start position:0%
+water which is I mentioned the other day
+is 55 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is this is the degree celsius I've
+
+ align:start position:0%
+this is this is the degree celsius I've
+ 
+
+ align:start position:0%
+this is this is the degree celsius I've
+just expressed it in degrees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Kelvin sorry my
+
+ align:start position:0%
+Kelvin sorry my
+ 
+
+ align:start position:0%
+Kelvin sorry my
+mistake excuse
+
+ align:start position:0%
+mistake excuse
+ 
+
+ align:start position:0%
+mistake excuse
+me because I was wrong that's why okay
+
+ align:start position:0%
+me because I was wrong that's why okay
+ 
+
+ align:start position:0%
+me because I was wrong that's why okay
+um thanks for catching that uh all right
+
+ align:start position:0%
+um thanks for catching that uh all right
+ 
+
+ align:start position:0%
+um thanks for catching that uh all right
+so under the so water is very
+
+ align:start position:0%
+so under the so water is very
+ 
+
+ align:start position:0%
+so under the so water is very
+concentrated and so under these
+
+ align:start position:0%
+concentrated and so under these
+ 
+
+ align:start position:0%
+concentrated and so under these
+conditions the other convention is then
+
+ align:start position:0%
+conditions the other convention is then
+ 
+
+ align:start position:0%
+conditions the other convention is then
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+set the hydrogen ions to and and water
+
+ align:start position:0%
+set the hydrogen ions to and and water
+ 
+
+ align:start position:0%
+set the hydrogen ions to and and water
+molecules to one and you don't have to
+
+ align:start position:0%
+molecules to one and you don't have to
+ 
+
+ align:start position:0%
+molecules to one and you don't have to
+think about them when you're we're doing
+
+ align:start position:0%
+think about them when you're we're doing
+ 
+
+ align:start position:0%
+think about them when you're we're doing
+this this is a convention that that uh
+
+ align:start position:0%
+this this is a convention that that uh
+ 
+
+ align:start position:0%
+this this is a convention that that uh
+that bio that biochemists do now this
+
+ align:start position:0%
+that bio that biochemists do now this
+ 
+
+ align:start position:0%
+that bio that biochemists do now this
+free
+
+ align:start position:0%
+free
+ 
+
+ align:start position:0%
+free
+energy the the the Delta G gies free
+
+ align:start position:0%
+energy the the the Delta G gies free
+ 
+
+ align:start position:0%
+energy the the the Delta G gies free
+energy is a thermodynamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property and I I want to I'll just give
+
+ align:start position:0%
+property and I I want to I'll just give
+ 
+
+ align:start position:0%
+property and I I want to I'll just give
+share with you mean the same visual
+
+ align:start position:0%
+share with you mean the same visual
+ 
+
+ align:start position:0%
+share with you mean the same visual
+image I've had since I was in undergrad
+
+ align:start position:0%
+image I've had since I was in undergrad
+ 
+
+ align:start position:0%
+image I've had since I was in undergrad
+which I think is not a bad way of
+
+ align:start position:0%
+which I think is not a bad way of
+ 
+
+ align:start position:0%
+which I think is not a bad way of
+thinking about it trying to un
+
+ align:start position:0%
+thinking about it trying to un
+ 
+
+ align:start position:0%
+thinking about it trying to un
+understand what happens that if we have
+
+ align:start position:0%
+understand what happens that if we have
+ 
+
+ align:start position:0%
+understand what happens that if we have
+a a plot of
+
+ align:start position:0%
+a a plot of
+ 
+
+ align:start position:0%
+a a plot of
+the the free
+
+ align:start position:0%
+the the free
+ 
+
+ align:start position:0%
+the the free
+energy as a function of what happens as
+
+ align:start position:0%
+energy as a function of what happens as
+ 
+
+ align:start position:0%
+energy as a function of what happens as
+the reaction goes along so that we
+
+ align:start position:0%
+the reaction goes along so that we
+ 
+
+ align:start position:0%
+the reaction goes along so that we
+have a + b here and C+ D down here uh
+
+ align:start position:0%
+have a + b here and C+ D down here uh
+ 
+
+ align:start position:0%
+have a + b here and C+ D down here uh
+when you go from reaction to products
+
+ align:start position:0%
+when you go from reaction to products
+ 
+
+ align:start position:0%
+when you go from reaction to products
+way of of drawn it there's free en some
+
+ align:start position:0%
+way of of drawn it there's free en some
+ 
+
+ align:start position:0%
+way of of drawn it there's free en some
+kind of energy is given off in this kind
+
+ align:start position:0%
+kind of energy is given off in this kind
+ 
+
+ align:start position:0%
+kind of energy is given off in this kind
+of reaction and the if you know that if
+
+ align:start position:0%
+of reaction and the if you know that if
+ 
+
+ align:start position:0%
+of reaction and the if you know that if
+you know that you will know then that
+
+ align:start position:0%
+you know that you will know then that
+ 
+
+ align:start position:0%
+you know that you will know then that
+the the reaction will be able to go
+
+ align:start position:0%
+the the reaction will be able to go
+ 
+
+ align:start position:0%
+the the reaction will be able to go
+forward because it's able to give off
+
+ align:start position:0%
+forward because it's able to give off
+ 
+
+ align:start position:0%
+forward because it's able to give off
+energy just just the same way hydrogen
+
+ align:start position:0%
+energy just just the same way hydrogen
+ 
+
+ align:start position:0%
+energy just just the same way hydrogen
+and oxygen give off a lot of heat and
+
+ align:start position:0%
+and oxygen give off a lot of heat and
+ 
+
+ align:start position:0%
+and oxygen give off a lot of heat and
+stuff and you know that reaction really
+
+ align:start position:0%
+stuff and you know that reaction really
+ 
+
+ align:start position:0%
+stuff and you know that reaction really
+goes a long way to completion so it's
+
+ align:start position:0%
+goes a long way to completion so it's
+ 
+
+ align:start position:0%
+goes a long way to completion so it's
+kind of as if uh you were out here on
+
+ align:start position:0%
+kind of as if uh you were out here on
+ 
+
+ align:start position:0%
+kind of as if uh you were out here on
+your spring break on your
+
+ align:start position:0%
+your spring break on your
+ 
+
+ align:start position:0%
+your spring break on your
+skis are ready to go down the uh Black
+
+ align:start position:0%
+skis are ready to go down the uh Black
+ 
+
+ align:start position:0%
+skis are ready to go down the uh Black
+Diamond Hill and it you you can sort of
+
+ align:start position:0%
+Diamond Hill and it you you can sort of
+ 
+
+ align:start position:0%
+Diamond Hill and it you you can sort of
+see it what what happened now because
+
+ align:start position:0%
+see it what what happened now because
+ 
+
+ align:start position:0%
+see it what what happened now because
+it's a thermodynamic property it doesn't
+
+ align:start position:0%
+it's a thermodynamic property it doesn't
+ 
+
+ align:start position:0%
+it's a thermodynamic property it doesn't
+matter what route you take to get from
+
+ align:start position:0%
+matter what route you take to get from
+ 
+
+ align:start position:0%
+matter what route you take to get from
+the reactants to the products so if you
+
+ align:start position:0%
+the reactants to the products so if you
+ 
+
+ align:start position:0%
+the reactants to the products so if you
+go down the Double Diamond slope or you
+
+ align:start position:0%
+go down the Double Diamond slope or you
+ 
+
+ align:start position:0%
+go down the Double Diamond slope or you
+go down the the bunny slope you still
+
+ align:start position:0%
+go down the the bunny slope you still
+ 
+
+ align:start position:0%
+go down the the bunny slope you still
+end up with the same amount of energy
+
+ align:start position:0%
+end up with the same amount of energy
+ 
+
+ align:start position:0%
+end up with the same amount of energy
+coming out of the reaction and that's
+
+ align:start position:0%
+coming out of the reaction and that's
+ 
+
+ align:start position:0%
+coming out of the reaction and that's
+important because if if if that wasn't
+
+ align:start position:0%
+important because if if if that wasn't
+ 
+
+ align:start position:0%
+important because if if if that wasn't
+true you could make a perpetual motion
+
+ align:start position:0%
+true you could make a perpetual motion
+ 
+
+ align:start position:0%
+true you could make a perpetual motion
+machine and you'd be very rich um the
+
+ align:start position:0%
+machine and you'd be very rich um the
+ 
+
+ align:start position:0%
+machine and you'd be very rich um the
+second thing that's important is that
+
+ align:start position:0%
+second thing that's important is that
+ 
+
+ align:start position:0%
+second thing that's important is that
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the free energy will tell
+
+ align:start position:0%
+uh the free energy will tell
+ 
+
+ align:start position:0%
+uh the free energy will tell
+you what would happen if if the reaction
+
+ align:start position:0%
+you what would happen if if the reaction
+ 
+
+ align:start position:0%
+you what would happen if if the reaction
+went but it will not tell you whether it
+
+ align:start position:0%
+went but it will not tell you whether it
+ 
+
+ align:start position:0%
+went but it will not tell you whether it
+can go if I did a demo here and I
+
+ align:start position:0%
+can go if I did a demo here and I
+ 
+
+ align:start position:0%
+can go if I did a demo here and I
+brought some hydrogen and some oxygen
+
+ align:start position:0%
+brought some hydrogen and some oxygen
+ 
+
+ align:start position:0%
+brought some hydrogen and some oxygen
+and I mixed them together in a vessel in
+
+ align:start position:0%
+and I mixed them together in a vessel in
+ 
+
+ align:start position:0%
+and I mixed them together in a vessel in
+the front of the class we could all sit
+
+ align:start position:0%
+the front of the class we could all sit
+ 
+
+ align:start position:0%
+the front of the class we could all sit
+here waiting for it to explode but the
+
+ align:start position:0%
+here waiting for it to explode but the
+ 
+
+ align:start position:0%
+here waiting for it to explode but the
+likelihood is we would sit here for a
+
+ align:start position:0%
+likelihood is we would sit here for a
+ 
+
+ align:start position:0%
+likelihood is we would sit here for a
+very very long time and not see an
+
+ align:start position:0%
+very very long time and not see an
+ 
+
+ align:start position:0%
+very very long time and not see an
+explosion right and the reason is that
+
+ align:start position:0%
+explosion right and the reason is that
+ 
+
+ align:start position:0%
+explosion right and the reason is that
+in order to get that hydrogen oxygen to
+
+ align:start position:0%
+in order to get that hydrogen oxygen to
+ 
+
+ align:start position:0%
+in order to get that hydrogen oxygen to
+close enough together we had to give
+
+ align:start position:0%
+close enough together we had to give
+ 
+
+ align:start position:0%
+close enough together we had to give
+them some extra energy and push them so
+
+ align:start position:0%
+them some extra energy and push them so
+ 
+
+ align:start position:0%
+them some extra energy and push them so
+they overcome repulsion and stuff so if
+
+ align:start position:0%
+they overcome repulsion and stuff so if
+ 
+
+ align:start position:0%
+they overcome repulsion and stuff so if
+you were uh out here on your on your
+
+ align:start position:0%
+you were uh out here on your on your
+ 
+
+ align:start position:0%
+you were uh out here on your on your
+skis
+
+ align:start position:0%
+skis
+ 
+
+ align:start position:0%
+skis
+again getting all ready to go but in
+
+ align:start position:0%
+again getting all ready to go but in
+ 
+
+ align:start position:0%
+again getting all ready to go but in
+fact you got off at the wrong uh stop on
+
+ align:start position:0%
+fact you got off at the wrong uh stop on
+ 
+
+ align:start position:0%
+fact you got off at the wrong uh stop on
+the ski lift and you were there even
+
+ align:start position:0%
+the ski lift and you were there even
+ 
+
+ align:start position:0%
+the ski lift and you were there even
+though there would be energy getting
+
+ align:start position:0%
+though there would be energy getting
+ 
+
+ align:start position:0%
+though there would be energy getting
+down from here you're it's not going to
+
+ align:start position:0%
+down from here you're it's not going to
+ 
+
+ align:start position:0%
+down from here you're it's not going to
+happen at any discernable rate given the
+
+ align:start position:0%
+happen at any discernable rate given the
+ 
+
+ align:start position:0%
+happen at any discernable rate given the
+sort of little bounce and energy you
+
+ align:start position:0%
+sort of little bounce and energy you
+ 
+
+ align:start position:0%
+sort of little bounce and energy you
+have in your normal uh in your normal
+
+ align:start position:0%
+have in your normal uh in your normal
+ 
+
+ align:start position:0%
+have in your normal uh in your normal
+Liv so what we're doing doing when we do
+
+ align:start position:0%
+Liv so what we're doing doing when we do
+ 
+
+ align:start position:0%
+Liv so what we're doing doing when we do
+hydrogen oxygen we're giving by putting
+
+ align:start position:0%
+hydrogen oxygen we're giving by putting
+ 
+
+ align:start position:0%
+hydrogen oxygen we're giving by putting
+a match into it or something we're
+
+ align:start position:0%
+a match into it or something we're
+ 
+
+ align:start position:0%
+a match into it or something we're
+giving it enough energy that actually a
+
+ align:start position:0%
+giving it enough energy that actually a
+ 
+
+ align:start position:0%
+giving it enough energy that actually a
+few of the molecules get up here they
+
+ align:start position:0%
+few of the molecules get up here they
+ 
+
+ align:start position:0%
+few of the molecules get up here they
+drop down then they give up so much
+
+ align:start position:0%
+drop down then they give up so much
+ 
+
+ align:start position:0%
+drop down then they give up so much
+energy and heat that all the rest of
+
+ align:start position:0%
+energy and heat that all the rest of
+ 
+
+ align:start position:0%
+energy and heat that all the rest of
+them get pushed up and the thing goes
+
+ align:start position:0%
+them get pushed up and the thing goes
+ 
+
+ align:start position:0%
+them get pushed up and the thing goes
+but that's sort of a not a not a bad way
+
+ align:start position:0%
+but that's sort of a not a not a bad way
+ 
+
+ align:start position:0%
+but that's sort of a not a not a bad way
+of thinking about it and when we're
+
+ align:start position:0%
+of thinking about it and when we're
+ 
+
+ align:start position:0%
+of thinking about it and when we're
+going to talk in a minute about what
+
+ align:start position:0%
+going to talk in a minute about what
+ 
+
+ align:start position:0%
+going to talk in a minute about what
+determines how fast reactions go not how
+
+ align:start position:0%
+determines how fast reactions go not how
+ 
+
+ align:start position:0%
+determines how fast reactions go not how
+not whether they go or not and then of
+
+ align:start position:0%
+not whether they go or not and then of
+ 
+
+ align:start position:0%
+not whether they go or not and then of
+course we're going to have that point
+
+ align:start position:0%
+course we're going to have that point
+ 
+
+ align:start position:0%
+course we're going to have that point
+we're going to have to worry about this
+
+ align:start position:0%
+we're going to have to worry about this
+ 
+
+ align:start position:0%
+we're going to have to worry about this
+about this issue but before that um what
+
+ align:start position:0%
+about this issue but before that um what
+ 
+
+ align:start position:0%
+about this issue but before that um what
+I want to show you is that there's a
+
+ align:start position:0%
+I want to show you is that there's a
+ 
+
+ align:start position:0%
+I want to show you is that there's a
+direct
+
+ align:start position:0%
+direct
+ 
+
+ align:start position:0%
+direct
+relationship between this Gibs free uh
+
+ align:start position:0%
+relationship between this Gibs free uh
+ 
+
+ align:start position:0%
+relationship between this Gibs free uh
+Gibs free energy and the equilibrium
+
+ align:start position:0%
+Gibs free energy and the equilibrium
+ 
+
+ align:start position:0%
+Gibs free energy and the equilibrium
+constant so um so we have
+
+ align:start position:0%
+constant so um so we have
+ 
+
+ align:start position:0%
+constant so um so we have
+this well what we could do is we have
+
+ align:start position:0%
+this well what we could do is we have
+ 
+
+ align:start position:0%
+this well what we could do is we have
+you you have the reaction over there so
+
+ align:start position:0%
+you you have the reaction over there so
+ 
+
+ align:start position:0%
+you you have the reaction over there so
+let's consider that reaction has come to
+
+ align:start position:0%
+let's consider that reaction has come to
+ 
+
+ align:start position:0%
+let's consider that reaction has come to
+equilibrium and that means there'll be
+
+ align:start position:0%
+equilibrium and that means there'll be
+ 
+
+ align:start position:0%
+equilibrium and that means there'll be
+no further uh energy change
+
+ align:start position:0%
+no further uh energy change
+ 
+
+ align:start position:0%
+no further uh energy change
+uh so we'll just set the Delta G to zero
+
+ align:start position:0%
+uh so we'll just set the Delta G to zero
+ 
+
+ align:start position:0%
+uh so we'll just set the Delta G to zero
+and that would mean then that Delta G
+
+ align:start position:0%
+and that would mean then that Delta G
+ 
+
+ align:start position:0%
+and that would mean then that Delta G
+Prime 0 is equal to minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rtation C over D over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concentration a b um you'll recognize
+
+ align:start position:0%
+concentration a b um you'll recognize
+ 
+
+ align:start position:0%
+concentration a b um you'll recognize
+this that's the equilibrium constant
+
+ align:start position:0%
+this that's the equilibrium constant
+ 
+
+ align:start position:0%
+this that's the equilibrium constant
+right so oop sorry there's a natural log
+
+ align:start position:0%
+right so oop sorry there's a natural log
+ 
+
+ align:start position:0%
+right so oop sorry there's a natural log
+in here didn't get it
+
+ align:start position:0%
+in here didn't get it
+ 
+
+ align:start position:0%
+in here didn't get it
+in okay so which is equal to minus RT
+
+ align:start position:0%
+in okay so which is equal to minus RT
+ 
+
+ align:start position:0%
+in okay so which is equal to minus RT
+the natural
+
+ align:start position:0%
+the natural
+ 
+
+ align:start position:0%
+the natural
+log of the equilibrium constant or the
+
+ align:start position:0%
+log of the equilibrium constant or the
+ 
+
+ align:start position:0%
+log of the equilibrium constant or the
+natural log of the equilibrium constant
+
+ align:start position:0%
+natural log of the equilibrium constant
+ 
+
+ align:start position:0%
+natural log of the equilibrium constant
+is is equal to minus Delta G Prime 0/ RT
+
+ align:start position:0%
+is is equal to minus Delta G Prime 0/ RT
+ 
+
+ align:start position:0%
+is is equal to minus Delta G Prime 0/ RT
+or another way of saying that is the K
+
+ align:start position:0%
+or another way of saying that is the K
+ 
+
+ align:start position:0%
+or another way of saying that is the K
+equilibrium is equal e
+
+ align:start position:0%
+equilibrium is equal e
+ 
+
+ align:start position:0%
+equilibrium is equal e
+Theus Delta G Prime
+
+ align:start position:0%
+Theus Delta G Prime
+ 
+
+ align:start position:0%
+Theus Delta G Prime
+0 over RT
+
+ align:start position:0%
+0 over RT
+ 
+
+ align:start position:0%
+0 over RT
+so if you think back to the consequences
+
+ align:start position:0%
+so if you think back to the consequences
+ 
+
+ align:start position:0%
+so if you think back to the consequences
+of an equilibrium constant if the
+
+ align:start position:0%
+of an equilibrium constant if the
+ 
+
+ align:start position:0%
+of an equilibrium constant if the
+reaction is going to go almost all the
+
+ align:start position:0%
+reaction is going to go almost all the
+ 
+
+ align:start position:0%
+reaction is going to go almost all the
+way then they're going to be mostly re
+
+ align:start position:0%
+way then they're going to be mostly re
+ 
+
+ align:start position:0%
+way then they're going to be mostly re
+mostly products very few reactants so
+
+ align:start position:0%
+mostly products very few reactants so
+ 
+
+ align:start position:0%
+mostly products very few reactants so
+the K equilibrium will be large so if a
+
+ align:start position:0%
+the K equilibrium will be large so if a
+ 
+
+ align:start position:0%
+the K equilibrium will be large so if a
+reaction is going to go a long way then
+
+ align:start position:0%
+reaction is going to go a long way then
+ 
+
+ align:start position:0%
+reaction is going to go a long way then
+the the equilibrium constant will be
+
+ align:start position:0%
+the the equilibrium constant will be
+ 
+
+ align:start position:0%
+the the equilibrium constant will be
+large and in order for an equilibrium
+
+ align:start position:0%
+large and in order for an equilibrium
+ 
+
+ align:start position:0%
+large and in order for an equilibrium
+constant to be uh large large then this
+
+ align:start position:0%
+constant to be uh large large then this
+ 
+
+ align:start position:0%
+constant to be uh large large then this
+Delta G is going to have to have a large
+
+ align:start position:0%
+Delta G is going to have to have a large
+ 
+
+ align:start position:0%
+Delta G is going to have to have a large
+a large negative sign so if the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+favorable then K equilibrium will be
+
+ align:start position:0%
+favorable then K equilibrium will be
+ 
+
+ align:start position:0%
+favorable then K equilibrium will be
+large and uh the Delta G Prime Z will
+
+ align:start position:0%
+large and uh the Delta G Prime Z will
+ 
+
+ align:start position:0%
+large and uh the Delta G Prime Z will
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+at least within the scale of an
+
+ align:start position:0%
+at least within the scale of an
+ 
+
+ align:start position:0%
+at least within the scale of an
+activation energy a large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative value and let me give you a
+
+ align:start position:0%
+negative value and let me give you a
+ 
+
+ align:start position:0%
+negative value and let me give you a
+couple of
+
+ align:start position:0%
+couple of
+ 
+
+ align:start position:0%
+couple of
+examples when we talked
+
+ align:start position:0%
+examples when we talked
+ 
+
+ align:start position:0%
+examples when we talked
+about carbohydrates I briefly told you
+
+ align:start position:0%
+about carbohydrates I briefly told you
+ 
+
+ align:start position:0%
+about carbohydrates I briefly told you
+sucrose was a what we call a
+
+ align:start position:0%
+sucrose was a what we call a
+ 
+
+ align:start position:0%
+sucrose was a what we call a
+disaccharide Two Sugars join
+
+ align:start position:0%
+disaccharide Two Sugars join
+ 
+
+ align:start position:0%
+disaccharide Two Sugars join
+together how do we Jo what do we do when
+
+ align:start position:0%
+together how do we Jo what do we do when
+ 
+
+ align:start position:0%
+together how do we Jo what do we do when
+we join two things together pretty much
+
+ align:start position:0%
+we join two things together pretty much
+ 
+
+ align:start position:0%
+we join two things together pretty much
+usually in nature you split out a
+
+ align:start position:0%
+usually in nature you split out a
+ 
+
+ align:start position:0%
+usually in nature you split out a
+molecule of water so we take a molecule
+
+ align:start position:0%
+molecule of water so we take a molecule
+ 
+
+ align:start position:0%
+molecule of water so we take a molecule
+of glucose a molecule of fructose both
+
+ align:start position:0%
+of glucose a molecule of fructose both
+ 
+
+ align:start position:0%
+of glucose a molecule of fructose both
+carbohydrates both stick them together
+
+ align:start position:0%
+carbohydrates both stick them together
+ 
+
+ align:start position:0%
+carbohydrates both stick them together
+we get table sugar if we want to reverse
+
+ align:start position:0%
+we get table sugar if we want to reverse
+ 
+
+ align:start position:0%
+we get table sugar if we want to reverse
+that reaction we have to put in a
+
+ align:start position:0%
+that reaction we have to put in a
+ 
+
+ align:start position:0%
+that reaction we have to put in a
+molecule of water and we can run it the
+
+ align:start position:0%
+molecule of water and we can run it the
+ 
+
+ align:start position:0%
+molecule of water and we can run it the
+other way we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glucose plus fructose the K equilibrium
+
+ align:start position:0%
+glucose plus fructose the K equilibrium
+ 
+
+ align:start position:0%
+glucose plus fructose the K equilibrium
+for that reaction is
+
+ align:start position:0%
+for that reaction is
+ 
+
+ align:start position:0%
+for that reaction is
+140,000 the um
+
+ align:start position:0%
+140,000 the um
+ 
+
+ align:start position:0%
+140,000 the um
+the Delta G Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 is min - 7 kilo calories per
+
+ align:start position:0%
+0 is min - 7 kilo calories per
+ 
+
+ align:start position:0%
+0 is min - 7 kilo calories per
+mole if we think about so that's an
+
+ align:start position:0%
+mole if we think about so that's an
+ 
+
+ align:start position:0%
+mole if we think about so that's an
+example of what I was just telling a
+
+ align:start position:0%
+example of what I was just telling a
+ 
+
+ align:start position:0%
+example of what I was just telling a
+fairly large negative value we think
+
+ align:start position:0%
+fairly large negative value we think
+ 
+
+ align:start position:0%
+fairly large negative value we think
+about a reaction that's
+
+ align:start position:0%
+about a reaction that's
+ 
+
+ align:start position:0%
+about a reaction that's
+not uh
+
+ align:start position:0%
+not uh
+ 
+
+ align:start position:0%
+not uh
+favorable here's acetic
+
+ align:start position:0%
+favorable here's acetic
+ 
+
+ align:start position:0%
+favorable here's acetic
+acid that's what makes vinegar sour and
+
+ align:start position:0%
+acid that's what makes vinegar sour and
+ 
+
+ align:start position:0%
+acid that's what makes vinegar sour and
+it can the hydrogen ion can come off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here to give you a hydrogen ion and the
+
+ align:start position:0%
+here to give you a hydrogen ion and the
+ 
+
+ align:start position:0%
+here to give you a hydrogen ion and the
+negative ion of acetic acid or or
+
+ align:start position:0%
+negative ion of acetic acid or or
+ 
+
+ align:start position:0%
+negative ion of acetic acid or or
+acetate ion the uh equilibrium constant
+
+ align:start position:0%
+acetate ion the uh equilibrium constant
+ 
+
+ align:start position:0%
+acetate ion the uh equilibrium constant
+for that
+
+ align:start position:0%
+for that
+ 
+
+ align:start position:0%
+for that
+one is what is it two I
+
+ align:start position:0%
+one is what is it two I
+ 
+
+ align:start position:0%
+one is what is it two I
+think 2 *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10us five so only a little tiny bit of
+
+ align:start position:0%
+10us five so only a little tiny bit of
+ 
+
+ align:start position:0%
+10us five so only a little tiny bit of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+acidic acid actually ionizes and the K
+
+ align:start position:0%
+acidic acid actually ionizes and the K
+ 
+
+ align:start position:0%
+acidic acid actually ionizes and the K
+equilibrium constant then oh excuse me
+
+ align:start position:0%
+equilibrium constant then oh excuse me
+ 
+
+ align:start position:0%
+equilibrium constant then oh excuse me
+the um the uh Delta G Prime Z is plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+6.3 kilo calories uh per mole so it's
+
+ align:start position:0%
+6.3 kilo calories uh per mole so it's
+ 
+
+ align:start position:0%
+6.3 kilo calories uh per mole so it's
+some they're buried in this example is
+
+ align:start position:0%
+some they're buried in this example is
+ 
+
+ align:start position:0%
+some they're buried in this example is
+not only an showing you that a fav
+
+ align:start position:0%
+not only an showing you that a fav
+ 
+
+ align:start position:0%
+not only an showing you that a fav
+reaction that's unfavorable have a POS
+
+ align:start position:0%
+reaction that's unfavorable have a POS
+ 
+
+ align:start position:0%
+reaction that's unfavorable have a POS
+positive free energy associated with it
+
+ align:start position:0%
+positive free energy associated with it
+ 
+
+ align:start position:0%
+positive free energy associated with it
+whereas one that's favorable will have a
+
+ align:start position:0%
+whereas one that's favorable will have a
+ 
+
+ align:start position:0%
+whereas one that's favorable will have a
+negative free energy this is also sort
+
+ align:start position:0%
+negative free energy this is also sort
+ 
+
+ align:start position:0%
+negative free energy this is also sort
+of telling you why you're a you don't
+
+ align:start position:0%
+of telling you why you're a you don't
+ 
+
+ align:start position:0%
+of telling you why you're a you don't
+die when you put salad dressing on your
+
+ align:start position:0%
+die when you put salad dressing on your
+ 
+
+ align:start position:0%
+die when you put salad dressing on your
+salads because if if if acetic acid
+
+ align:start position:0%
+salads because if if if acetic acid
+ 
+
+ align:start position:0%
+salads because if if if acetic acid
+ionized as thoroughly as as sulfuric
+
+ align:start position:0%
+ionized as thoroughly as as sulfuric
+ 
+
+ align:start position:0%
+ionized as thoroughly as as sulfuric
+acid and you put an equivalent amount of
+
+ align:start position:0%
+acid and you put an equivalent amount of
+ 
+
+ align:start position:0%
+acid and you put an equivalent amount of
+sulfuric acid on your salads none of us
+
+ align:start position:0%
+sulfuric acid on your salads none of us
+ 
+
+ align:start position:0%
+sulfuric acid on your salads none of us
+would be here it's only a little tiny
+
+ align:start position:0%
+would be here it's only a little tiny
+ 
+
+ align:start position:0%
+would be here it's only a little tiny
+bit that's going and and
+
+ align:start position:0%
+bit that's going and and
+ 
+
+ align:start position:0%
+bit that's going and and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh it's happening so um what this really
+
+ align:start position:0%
+uh it's happening so um what this really
+ 
+
+ align:start position:0%
+uh it's happening so um what this really
+sets up for us though is this
+
+ align:start position:0%
+sets up for us though is this
+ 
+
+ align:start position:0%
+sets up for us though is this
+fundamental problem in biology and that
+
+ align:start position:0%
+fundamental problem in biology and that
+ 
+
+ align:start position:0%
+fundamental problem in biology and that
+is that this reaction here is you can
+
+ align:start position:0%
+is that this reaction here is you can
+ 
+
+ align:start position:0%
+is that this reaction here is you can
+see why it would go this one doesn't go
+
+ align:start position:0%
+see why it would go this one doesn't go
+ 
+
+ align:start position:0%
+see why it would go this one doesn't go
+but most of the reactions that you have
+
+ align:start position:0%
+but most of the reactions that you have
+ 
+
+ align:start position:0%
+but most of the reactions that you have
+to carry out in biology demand an energy
+
+ align:start position:0%
+to carry out in biology demand an energy
+ 
+
+ align:start position:0%
+to carry out in biology demand an energy
+input because they just won't go we
+
+ align:start position:0%
+input because they just won't go we
+ 
+
+ align:start position:0%
+input because they just won't go we
+could sort of force this a little bit we
+
+ align:start position:0%
+could sort of force this a little bit we
+ 
+
+ align:start position:0%
+could sort of force this a little bit we
+could raise the concentration of of the
+
+ align:start position:0%
+could raise the concentration of of the
+ 
+
+ align:start position:0%
+could raise the concentration of of the
+of the reactants would give us a little
+
+ align:start position:0%
+of the reactants would give us a little
+ 
+
+ align:start position:0%
+of the reactants would give us a little
+bit more product but that's not a useful
+
+ align:start position:0%
+bit more product but that's not a useful
+ 
+
+ align:start position:0%
+bit more product but that's not a useful
+solution to all the things so this was a
+
+ align:start position:0%
+solution to all the things so this was a
+ 
+
+ align:start position:0%
+solution to all the things so this was a
+really fundamental problem that had to
+
+ align:start position:0%
+really fundamental problem that had to
+ 
+
+ align:start position:0%
+really fundamental problem that had to
+be solved in evolution in order for life
+
+ align:start position:0%
+be solved in evolution in order for life
+ 
+
+ align:start position:0%
+be solved in evolution in order for life
+to um ever exist and I'll give you just
+
+ align:start position:0%
+to um ever exist and I'll give you just
+ 
+
+ align:start position:0%
+to um ever exist and I'll give you just
+an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example if we take let's consider taking
+
+ align:start position:0%
+example if we take let's consider taking
+ 
+
+ align:start position:0%
+example if we take let's consider taking
+a couple of molecules of
+
+ align:start position:0%
+a couple of molecules of
+ 
+
+ align:start position:0%
+a couple of molecules of
+glutamate which is an uh one of the Amo
+
+ align:start position:0%
+glutamate which is an uh one of the Amo
+ 
+
+ align:start position:0%
+glutamate which is an uh one of the Amo
+acids we talked about a couple of
+
+ align:start position:0%
+acids we talked about a couple of
+ 
+
+ align:start position:0%
+acids we talked about a couple of
+molecules of ammonia and making it into
+
+ align:start position:0%
+molecules of ammonia and making it into
+ 
+
+ align:start position:0%
+molecules of ammonia and making it into
+a couple of molecules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glutamine now this is an amino acid
+
+ align:start position:0%
+glutamine now this is an amino acid
+ 
+
+ align:start position:0%
+glutamine now this is an amino acid
+needed for making proteins this is an
+
+ align:start position:0%
+needed for making proteins this is an
+ 
+
+ align:start position:0%
+needed for making proteins this is an
+amino acid needed for making proteins
+
+ align:start position:0%
+amino acid needed for making proteins
+ 
+
+ align:start position:0%
+amino acid needed for making proteins
+cell has to have both of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+glutamate has two methylene groups and
+
+ align:start position:0%
+glutamate has two methylene groups and
+ 
+
+ align:start position:0%
+glutamate has two methylene groups and
+then a carboxy group it's one of
+
+ align:start position:0%
+then a carboxy group it's one of
+ 
+
+ align:start position:0%
+then a carboxy group it's one of
+the acidic amino acids and glutamine the
+
+ align:start position:0%
+the acidic amino acids and glutamine the
+ 
+
+ align:start position:0%
+the acidic amino acids and glutamine the
+side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chain is now an aid the Delta
+
+ align:start position:0%
+chain is now an aid the Delta
+ 
+
+ align:start position:0%
+chain is now an aid the Delta
+G from zero associated with this
+
+ align:start position:0%
+G from zero associated with this
+ 
+
+ align:start position:0%
+G from zero associated with this
+reaction is plus 7 kilo calories per
+
+ align:start position:0%
+reaction is plus 7 kilo calories per
+ 
+
+ align:start position:0%
+reaction is plus 7 kilo calories per
+mole so it's as unfavorable almost as
+
+ align:start position:0%
+mole so it's as unfavorable almost as
+ 
+
+ align:start position:0%
+mole so it's as unfavorable almost as
+the as that one we're looking at in it's
+
+ align:start position:0%
+the as that one we're looking at in it's
+ 
+
+ align:start position:0%
+the as that one we're looking at in it's
+worse than the one we're looking at over
+
+ align:start position:0%
+worse than the one we're looking at over
+ 
+
+ align:start position:0%
+worse than the one we're looking at over
+there the reason that this uh is sort of
+
+ align:start position:0%
+there the reason that this uh is sort of
+ 
+
+ align:start position:0%
+there the reason that this uh is sort of
+pushing the thing up uphill
+
+ align:start position:0%
+pushing the thing up uphill
+ 
+
+ align:start position:0%
+pushing the thing up uphill
+energetically is that this the electrons
+
+ align:start position:0%
+energetically is that this the electrons
+ 
+
+ align:start position:0%
+energetically is that this the electrons
+here actually distribute themselves back
+
+ align:start position:0%
+here actually distribute themselves back
+ 
+
+ align:start position:0%
+here actually distribute themselves back
+and forth so you can kind of think of
+
+ align:start position:0%
+and forth so you can kind of think of
+ 
+
+ align:start position:0%
+and forth so you can kind of think of
+the molecule as going back and forth
+
+ align:start position:0%
+the molecule as going back and forth
+ 
+
+ align:start position:0%
+the molecule as going back and forth
+between these two forms and that makes
+
+ align:start position:0%
+between these two forms and that makes
+ 
+
+ align:start position:0%
+between these two forms and that makes
+it more stable and when you stick on the
+
+ align:start position:0%
+it more stable and when you stick on the
+ 
+
+ align:start position:0%
+it more stable and when you stick on the
+am group to make the the amid it can't
+
+ align:start position:0%
+am group to make the the amid it can't
+ 
+
+ align:start position:0%
+am group to make the the amid it can't
+do that and so you're actually pushing
+
+ align:start position:0%
+do that and so you're actually pushing
+ 
+
+ align:start position:0%
+do that and so you're actually pushing
+everything energetically uphill so how
+
+ align:start position:0%
+everything energetically uphill so how
+ 
+
+ align:start position:0%
+everything energetically uphill so how
+does how does cell accomplish this
+
+ align:start position:0%
+does how does cell accomplish this
+ 
+
+ align:start position:0%
+does how does cell accomplish this
+there's energy available if we consider
+
+ align:start position:0%
+there's energy available if we consider
+ 
+
+ align:start position:0%
+there's energy available if we consider
+what happens
+
+ align:start position:0%
+what happens
+ 
+
+ align:start position:0%
+what happens
+with C6
+
+ align:start position:0%
+with C6
+ 
+
+ align:start position:0%
+with C6
+h206 going to two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lactate the Delta G Prime 0 associated
+
+ align:start position:0%
+lactate the Delta G Prime 0 associated
+ 
+
+ align:start position:0%
+lactate the Delta G Prime 0 associated
+with that is minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50 kilo calories per mole so the cells
+
+ align:start position:0%
+50 kilo calories per mole so the cells
+ 
+
+ align:start position:0%
+50 kilo calories per mole so the cells
+get a lot of energy out of making even
+
+ align:start position:0%
+get a lot of energy out of making even
+ 
+
+ align:start position:0%
+get a lot of energy out of making even
+that simple conversion of a sugar
+
+ align:start position:0%
+that simple conversion of a sugar
+ 
+
+ align:start position:0%
+that simple conversion of a sugar
+molecule into two
+
+ align:start position:0%
+molecule into two
+ 
+
+ align:start position:0%
+molecule into two
+lactate but you have to some somehow it
+
+ align:start position:0%
+lactate but you have to some somehow it
+ 
+
+ align:start position:0%
+lactate but you have to some somehow it
+has to figure out how to use that energy
+
+ align:start position:0%
+has to figure out how to use that energy
+ 
+
+ align:start position:0%
+has to figure out how to use that energy
+in order to drive these unfavorable
+
+ align:start position:0%
+in order to drive these unfavorable
+ 
+
+ align:start position:0%
+in order to drive these unfavorable
+reactions and the solution which is
+
+ align:start position:0%
+reactions and the solution which is
+ 
+
+ align:start position:0%
+reactions and the solution which is
+really one of the the secrets uh to life
+
+ align:start position:0%
+really one of the the secrets uh to life
+ 
+
+ align:start position:0%
+really one of the the secrets uh to life
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the is to use coupled
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reactions
+
+ align:start position:0%
+reactions
+ 
+
+ align:start position:0%
+reactions
+with a common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intermediate and if you look outside a
+
+ align:start position:0%
+intermediate and if you look outside a
+ 
+
+ align:start position:0%
+intermediate and if you look outside a
+cell as Lavoisier did or pester did this
+
+ align:start position:0%
+cell as Lavoisier did or pester did this
+ 
+
+ align:start position:0%
+cell as Lavoisier did or pester did this
+is what you see but if you could look
+
+ align:start position:0%
+is what you see but if you could look
+ 
+
+ align:start position:0%
+is what you see but if you could look
+inside the cell and see what's happening
+
+ align:start position:0%
+inside the cell and see what's happening
+ 
+
+ align:start position:0%
+inside the cell and see what's happening
+when that conversion is being made you
+
+ align:start position:0%
+when that conversion is being made you
+ 
+
+ align:start position:0%
+when that conversion is being made you
+discover that the the full reaction
+
+ align:start position:0%
+discover that the the full reaction
+ 
+
+ align:start position:0%
+discover that the the full reaction
+looks like this it's uh the sugar
+
+ align:start position:0%
+looks like this it's uh the sugar
+ 
+
+ align:start position:0%
+looks like this it's uh the sugar
+molecule plus two molecules of ADP Plus
+
+ align:start position:0%
+molecule plus two molecules of ADP Plus
+ 
+
+ align:start position:0%
+molecule plus two molecules of ADP Plus
+two molecules of inorganic phosphate
+
+ align:start position:0%
+two molecules of inorganic phosphate
+ 
+
+ align:start position:0%
+two molecules of inorganic phosphate
+going to give two molecules of
+
+ align:start position:0%
+going to give two molecules of
+ 
+
+ align:start position:0%
+going to give two molecules of
+lactate plus two molecules of
+
+ align:start position:0%
+lactate plus two molecules of
+ 
+
+ align:start position:0%
+lactate plus two molecules of
+ATP what's ATP it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ribonucleotide
+
+ align:start position:0%
+ribonucleotide
+ 
+
+ align:start position:0%
+ribonucleotide
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+0p and what happens when you make a TP
+
+ align:start position:0%
+0p and what happens when you make a TP
+ 
+
+ align:start position:0%
+0p and what happens when you make a TP
+is an extra phosphate gets added on to
+
+ align:start position:0%
+is an extra phosphate gets added on to
+ 
+
+ align:start position:0%
+is an extra phosphate gets added on to
+that end of the molecule so by having
+
+ align:start position:0%
+that end of the molecule so by having
+ 
+
+ align:start position:0%
+that end of the molecule so by having
+yet another phosphate on here we've got
+
+ align:start position:0%
+yet another phosphate on here we've got
+ 
+
+ align:start position:0%
+yet another phosphate on here we've got
+a whole row of negative charges this is
+
+ align:start position:0%
+a whole row of negative charges this is
+ 
+
+ align:start position:0%
+a whole row of negative charges this is
+a a molecule in which the various parts
+
+ align:start position:0%
+a a molecule in which the various parts
+ 
+
+ align:start position:0%
+a a molecule in which the various parts
+are not happy to be together because all
+
+ align:start position:0%
+are not happy to be together because all
+ 
+
+ align:start position:0%
+are not happy to be together because all
+these negative charges would like to
+
+ align:start position:0%
+these negative charges would like to
+ 
+
+ align:start position:0%
+these negative charges would like to
+push apart so when you break the bond of
+
+ align:start position:0%
+push apart so when you break the bond of
+ 
+
+ align:start position:0%
+push apart so when you break the bond of
+ATP then energy is released so using ATP
+
+ align:start position:0%
+ATP then energy is released so using ATP
+ 
+
+ align:start position:0%
+ATP then energy is released so using ATP
+key is a way of of sort of storing
+
+ align:start position:0%
+key is a way of of sort of storing
+ 
+
+ align:start position:0%
+key is a way of of sort of storing
+chemical energy so you can use it in in
+
+ align:start position:0%
+chemical energy so you can use it in in
+ 
+
+ align:start position:0%
+chemical energy so you can use it in in
+some other kind of context and so by uh
+
+ align:start position:0%
+some other kind of context and so by uh
+ 
+
+ align:start position:0%
+some other kind of context and so by uh
+Burning It by carrying out the reaction
+
+ align:start position:0%
+Burning It by carrying out the reaction
+ 
+
+ align:start position:0%
+Burning It by carrying out the reaction
+in this way a cell is able to not only
+
+ align:start position:0%
+in this way a cell is able to not only
+ 
+
+ align:start position:0%
+in this way a cell is able to not only
+make uh sugar molecule of sugar glucose
+
+ align:start position:0%
+make uh sugar molecule of sugar glucose
+ 
+
+ align:start position:0%
+make uh sugar molecule of sugar glucose
+into to lactate it's gener able to
+
+ align:start position:0%
+into to lactate it's gener able to
+ 
+
+ align:start position:0%
+into to lactate it's gener able to
+generate um ATP along the way and the
+
+ align:start position:0%
+generate um ATP along the way and the
+ 
+
+ align:start position:0%
+generate um ATP along the way and the
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+G Prime Z for this reaction is - 34 kilo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calories per mole so even though it's
+
+ align:start position:0%
+calories per mole so even though it's
+ 
+
+ align:start position:0%
+calories per mole so even though it's
+taking out some of that energy and
+
+ align:start position:0%
+taking out some of that energy and
+ 
+
+ align:start position:0%
+taking out some of that energy and
+putting it in ATP this is a reaction
+
+ align:start position:0%
+putting it in ATP this is a reaction
+ 
+
+ align:start position:0%
+putting it in ATP this is a reaction
+that goes very very efficiently then
+
+ align:start position:0%
+that goes very very efficiently then
+ 
+
+ align:start position:0%
+that goes very very efficiently then
+instead of trying to carry out just that
+
+ align:start position:0%
+instead of trying to carry out just that
+ 
+
+ align:start position:0%
+instead of trying to carry out just that
+reaction what the cell is actually doing
+
+ align:start position:0%
+reaction what the cell is actually doing
+ 
+
+ align:start position:0%
+reaction what the cell is actually doing
+is taking the
+
+ align:start position:0%
+is taking the
+ 
+
+ align:start position:0%
+is taking the
+two glutamate plus the
+
+ align:start position:0%
+two glutamate plus the
+ 
+
+ align:start position:0%
+two glutamate plus the
+two molecules of ammonia plus 2
+
+ align:start position:0%
+two molecules of ammonia plus 2
+ 
+
+ align:start position:0%
+two molecules of ammonia plus 2
+ATP and then this is converting it to
+
+ align:start position:0%
+ATP and then this is converting it to
+ 
+
+ align:start position:0%
+ATP and then this is converting it to
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glutamine plus two water I think I
+
+ align:start position:0%
+glutamine plus two water I think I
+ 
+
+ align:start position:0%
+glutamine plus two water I think I
+failed to put that in here
+
+ align:start position:0%
+failed to put that in here
+ 
+
+ align:start position:0%
+failed to put that in here
+so you can correct it back
+
+ align:start position:0%
+so you can correct it back
+ 
+
+ align:start position:0%
+so you can correct it back
+there plus
+
+ align:start position:0%
+there plus
+ 
+
+ align:start position:0%
+there plus
+280p plus two molecules of inorganic
+
+ align:start position:0%
+280p plus two molecules of inorganic
+ 
+
+ align:start position:0%
+280p plus two molecules of inorganic
+phosphate and so the P subi very
+
+ align:start position:0%
+phosphate and so the P subi very
+ 
+
+ align:start position:0%
+phosphate and so the P subi very
+commonly used in bi chemistry to denote
+
+ align:start position:0%
+commonly used in bi chemistry to denote
+ 
+
+ align:start position:0%
+commonly used in bi chemistry to denote
+just inorganic phosphate ion so that uh
+
+ align:start position:0%
+just inorganic phosphate ion so that uh
+ 
+
+ align:start position:0%
+just inorganic phosphate ion so that uh
+what's happened here then are these two
+
+ align:start position:0%
+what's happened here then are these two
+ 
+
+ align:start position:0%
+what's happened here then are these two
+reactions going on this reaction uh now
+
+ align:start position:0%
+reactions going on this reaction uh now
+ 
+
+ align:start position:0%
+reactions going on this reaction uh now
+because um
+
+ align:start position:0%
+because um
+ 
+
+ align:start position:0%
+because um
+ATP is involved is now uh now favorable
+
+ align:start position:0%
+ATP is involved is now uh now favorable
+ 
+
+ align:start position:0%
+ATP is involved is now uh now favorable
+and the Delta G for this reaction
+
+ align:start position:0%
+and the Delta G for this reaction
+ 
+
+ align:start position:0%
+and the Delta G for this reaction
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+m- 9 kilo calories per mole so by having
+
+ align:start position:0%
+m- 9 kilo calories per mole so by having
+ 
+
+ align:start position:0%
+m- 9 kilo calories per mole so by having
+an ATP hydrolized as part of the
+
+ align:start position:0%
+an ATP hydrolized as part of the
+ 
+
+ align:start position:0%
+an ATP hydrolized as part of the
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+mechanism this reaction that used to be
+
+ align:start position:0%
+mechanism this reaction that used to be
+ 
+
+ align:start position:0%
+mechanism this reaction that used to be
+unfavorable is now favorable and then
+
+ align:start position:0%
+unfavorable is now favorable and then
+ 
+
+ align:start position:0%
+unfavorable is now favorable and then
+the kind of cute thing then is if you
+
+ align:start position:0%
+the kind of cute thing then is if you
+ 
+
+ align:start position:0%
+the kind of cute thing then is if you
+sum this all up the atps and the atps
+
+ align:start position:0%
+sum this all up the atps and the atps
+ 
+
+ align:start position:0%
+sum this all up the atps and the atps
+are on both
+
+ align:start position:0%
+are on both
+ 
+
+ align:start position:0%
+are on both
+sides of the equation so they just drop
+
+ align:start position:0%
+sides of the equation so they just drop
+ 
+
+ align:start position:0%
+sides of the equation so they just drop
+drop out and what you're left
+
+ align:start position:0%
+drop out and what you're left
+ 
+
+ align:start position:0%
+drop out and what you're left
+with the C6
+
+ align:start position:0%
+with the C6
+ 
+
+ align:start position:0%
+with the C6
+h126 plus the two glutamines plus two
+
+ align:start position:0%
+h126 plus the two glutamines plus two
+ 
+
+ align:start position:0%
+h126 plus the two glutamines plus two
+ammonia is going to
+
+ align:start position:0%
+ammonia is going to
+ 
+
+ align:start position:0%
+ammonia is going to
+give two
+
+ align:start position:0%
+give two
+ 
+
+ align:start position:0%
+give two
+glutamines um excuse
+
+ align:start position:0%
+glutamines um excuse
+ 
+
+ align:start position:0%
+glutamines um excuse
+me two
+
+ align:start position:0%
+me two
+ 
+
+ align:start position:0%
+me two
+lactate plus two glutamines um plus the
+
+ align:start position:0%
+lactate plus two glutamines um plus the
+ 
+
+ align:start position:0%
+lactate plus two glutamines um plus the
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+waters and
+
+ align:start position:0%
+waters and
+ 
+
+ align:start position:0%
+waters and
+the Delta G Prime Z for this is minus
+
+ align:start position:0%
+the Delta G Prime Z for this is minus
+ 
+
+ align:start position:0%
+the Delta G Prime Z for this is minus
+43 kilo calories
+
+ align:start position:0%
+43 kilo calories
+ 
+
+ align:start position:0%
+43 kilo calories
+per mole so this is not an you can think
+
+ align:start position:0%
+per mole so this is not an you can think
+ 
+
+ align:start position:0%
+per mole so this is not an you can think
+of it of the using energy in the form of
+
+ align:start position:0%
+of it of the using energy in the form of
+ 
+
+ align:start position:0%
+of it of the using energy in the form of
+ATP like there a little the way we use
+
+ align:start position:0%
+ATP like there a little the way we use
+ 
+
+ align:start position:0%
+ATP like there a little the way we use
+money in our society um I do some work
+
+ align:start position:0%
+money in our society um I do some work
+ 
+
+ align:start position:0%
+money in our society um I do some work
+at MIT I don't get given food to eat or
+
+ align:start position:0%
+at MIT I don't get given food to eat or
+ 
+
+ align:start position:0%
+at MIT I don't get given food to eat or
+TV to watch the Super Bowl instead I get
+
+ align:start position:0%
+TV to watch the Super Bowl instead I get
+ 
+
+ align:start position:0%
+TV to watch the Super Bowl instead I get
+given money then I go to the store I
+
+ align:start position:0%
+given money then I go to the store I
+ 
+
+ align:start position:0%
+given money then I go to the store I
+give them the money I end up with the
+
+ align:start position:0%
+give them the money I end up with the
+ 
+
+ align:start position:0%
+give them the money I end up with the
+food or the the stuff and if you're
+
+ align:start position:0%
+food or the the stuff and if you're
+ 
+
+ align:start position:0%
+food or the the stuff and if you're
+watching it from the outside you see me
+
+ align:start position:0%
+watching it from the outside you see me
+ 
+
+ align:start position:0%
+watching it from the outside you see me
+do work at school and then food or TV or
+
+ align:start position:0%
+do work at school and then food or TV or
+ 
+
+ align:start position:0%
+do work at school and then food or TV or
+whatever shows up at home but what's
+
+ align:start position:0%
+whatever shows up at home but what's
+ 
+
+ align:start position:0%
+whatever shows up at home but what's
+happening is the money is serving as a
+
+ align:start position:0%
+happening is the money is serving as a
+ 
+
+ align:start position:0%
+happening is the money is serving as a
+common intermediate in those
+
+ align:start position:0%
+common intermediate in those
+ 
+
+ align:start position:0%
+common intermediate in those
+transactions and that's what basically
+
+ align:start position:0%
+transactions and that's what basically
+ 
+
+ align:start position:0%
+transactions and that's what basically
+ATP is in a Cell It's energy money and
+
+ align:start position:0%
+ATP is in a Cell It's energy money and
+ 
+
+ align:start position:0%
+ATP is in a Cell It's energy money and
+in making ATP the uh cell has to take
+
+ align:start position:0%
+in making ATP the uh cell has to take
+ 
+
+ align:start position:0%
+in making ATP the uh cell has to take
+this ribos with an adenine on it I think
+
+ align:start position:0%
+this ribos with an adenine on it I think
+ 
+
+ align:start position:0%
+this ribos with an adenine on it I think
+I didn't put the adenine on here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+realize uh and um
+
+ align:start position:0%
+realize uh and um
+ 
+
+ align:start position:0%
+realize uh and um
+the Adine sitting on the ribos now there
+
+ align:start position:0%
+the Adine sitting on the ribos now there
+ 
+
+ align:start position:0%
+the Adine sitting on the ribos now there
+there's two phosphates both of which
+
+ align:start position:0%
+there's two phosphates both of which
+ 
+
+ align:start position:0%
+there's two phosphates both of which
+have a negative charge on them and to
+
+ align:start position:0%
+have a negative charge on them and to
+ 
+
+ align:start position:0%
+have a negative charge on them and to
+create that third Bond it has to push it
+
+ align:start position:0%
+create that third Bond it has to push it
+ 
+
+ align:start position:0%
+create that third Bond it has to push it
+together so this very sort of unstable
+
+ align:start position:0%
+together so this very sort of unstable
+ 
+
+ align:start position:0%
+together so this very sort of unstable
+intrinsically unstable molecule when you
+
+ align:start position:0%
+intrinsically unstable molecule when you
+ 
+
+ align:start position:0%
+intrinsically unstable molecule when you
+break the bond it'll give you energy
+
+ align:start position:0%
+break the bond it'll give you energy
+ 
+
+ align:start position:0%
+break the bond it'll give you energy
+back and that's one of the the really uh
+
+ align:start position:0%
+back and that's one of the the really uh
+ 
+
+ align:start position:0%
+back and that's one of the the really uh
+amazing secrets to life and that's the
+
+ align:start position:0%
+amazing secrets to life and that's the
+ 
+
+ align:start position:0%
+amazing secrets to life and that's the
+the underlying principle of why it is
+
+ align:start position:0%
+the underlying principle of why it is
+ 
+
+ align:start position:0%
+the underlying principle of why it is
+that life can go can go forward now the
+
+ align:start position:0%
+that life can go can go forward now the
+ 
+
+ align:start position:0%
+that life can go can go forward now the
+second issue that we need to quick
+
+ align:start position:0%
+second issue that we need to quick
+ 
+
+ align:start position:0%
+second issue that we need to quick
+address here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is oops where did maybe it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is not only can a reaction go which is
+
+ align:start position:0%
+is not only can a reaction go which is
+ 
+
+ align:start position:0%
+is not only can a reaction go which is
+what thermodynamics tells us but how
+
+ align:start position:0%
+what thermodynamics tells us but how
+ 
+
+ align:start position:0%
+what thermodynamics tells us but how
+fast can it go and this epitomizes the
+
+ align:start position:0%
+fast can it go and this epitomizes the
+ 
+
+ align:start position:0%
+fast can it go and this epitomizes the
+problem that all chemical reactions face
+
+ align:start position:0%
+problem that all chemical reactions face
+ 
+
+ align:start position:0%
+problem that all chemical reactions face
+because literally every chemical
+
+ align:start position:0%
+because literally every chemical
+ 
+
+ align:start position:0%
+because literally every chemical
+reaction that you carry out involves
+
+ align:start position:0%
+reaction that you carry out involves
+ 
+
+ align:start position:0%
+reaction that you carry out involves
+bringing a couple of entities together
+
+ align:start position:0%
+bringing a couple of entities together
+ 
+
+ align:start position:0%
+bringing a couple of entities together
+and as they get closer and closer and
+
+ align:start position:0%
+and as they get closer and closer and
+ 
+
+ align:start position:0%
+and as they get closer and closer and
+closer it they don't want to be there so
+
+ align:start position:0%
+closer it they don't want to be there so
+ 
+
+ align:start position:0%
+closer it they don't want to be there so
+you have to sort of push them together
+
+ align:start position:0%
+you have to sort of push them together
+ 
+
+ align:start position:0%
+you have to sort of push them together
+in some kind of way or make sure they
+
+ align:start position:0%
+in some kind of way or make sure they
+ 
+
+ align:start position:0%
+in some kind of way or make sure they
+have enough energy to get together and
+
+ align:start position:0%
+have enough energy to get together and
+ 
+
+ align:start position:0%
+have enough energy to get together and
+that's what we see represented here and
+
+ align:start position:0%
+that's what we see represented here and
+ 
+
+ align:start position:0%
+that's what we see represented here and
+that's a special term called the
+
+ align:start position:0%
+that's a special term called the
+ 
+
+ align:start position:0%
+that's a special term called the
+activation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy it's given the term Delta G with
+
+ align:start position:0%
+energy it's given the term Delta G with
+ 
+
+ align:start position:0%
+energy it's given the term Delta G with
+a with a double dagger and that is what
+
+ align:start position:0%
+a with a double dagger and that is what
+ 
+
+ align:start position:0%
+a with a double dagger and that is what
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's the the size of that activation
+
+ align:start position:0%
+it's the the size of that activation
+ 
+
+ align:start position:0%
+it's the the size of that activation
+energy that limits how fast chemical
+
+ align:start position:0%
+energy that limits how fast chemical
+ 
+
+ align:start position:0%
+energy that limits how fast chemical
+reactions can go so the solution you use
+
+ align:start position:0%
+reactions can go so the solution you use
+ 
+
+ align:start position:0%
+reactions can go so the solution you use
+in chemistry most of you know it's a cat
+
+ align:start position:0%
+in chemistry most of you know it's a cat
+ 
+
+ align:start position:0%
+in chemistry most of you know it's a cat
+you use a catalyst the Catalyst doesn't
+
+ align:start position:0%
+you use a catalyst the Catalyst doesn't
+ 
+
+ align:start position:0%
+you use a catalyst the Catalyst doesn't
+change the outcome of the reaction it
+
+ align:start position:0%
+change the outcome of the reaction it
+ 
+
+ align:start position:0%
+change the outcome of the reaction it
+just changes how fast you get there so
+
+ align:start position:0%
+just changes how fast you get there so
+ 
+
+ align:start position:0%
+just changes how fast you get there so
+there are many reactions you heard about
+
+ align:start position:0%
+there are many reactions you heard about
+ 
+
+ align:start position:0%
+there are many reactions you heard about
+in chemistry just stick the thing at
+
+ align:start position:0%
+in chemistry just stick the thing at
+ 
+
+ align:start position:0%
+in chemistry just stick the thing at
+500° Centigrade put in a piece of
+
+ align:start position:0%
+500° Centigrade put in a piece of
+ 
+
+ align:start position:0%
+500° Centigrade put in a piece of
+platinum and some Platinum uh and now
+
+ align:start position:0%
+platinum and some Platinum uh and now
+ 
+
+ align:start position:0%
+platinum and some Platinum uh and now
+the reaction will go a whole lot faster
+
+ align:start position:0%
+the reaction will go a whole lot faster
+ 
+
+ align:start position:0%
+the reaction will go a whole lot faster
+by heating it up you the molecules have
+
+ align:start position:0%
+by heating it up you the molecules have
+ 
+
+ align:start position:0%
+by heating it up you the molecules have
+more energy so they have more energy
+
+ align:start position:0%
+more energy so they have more energy
+ 
+
+ align:start position:0%
+more energy so they have more energy
+they can get closer together just from
+
+ align:start position:0%
+they can get closer together just from
+ 
+
+ align:start position:0%
+they can get closer together just from
+that and then what the the Platinum
+
+ align:start position:0%
+that and then what the the Platinum
+ 
+
+ align:start position:0%
+that and then what the the Platinum
+surface would do would allow the
+
+ align:start position:0%
+surface would do would allow the
+ 
+
+ align:start position:0%
+surface would do would allow the
+molecules to both stick and it would
+
+ align:start position:0%
+molecules to both stick and it would
+ 
+
+ align:start position:0%
+molecules to both stick and it would
+bring them in proximity and also help
+
+ align:start position:0%
+bring them in proximity and also help
+ 
+
+ align:start position:0%
+bring them in proximity and also help
+them them come together we can't raise
+
+ align:start position:0%
+them them come together we can't raise
+ 
+
+ align:start position:0%
+them them come together we can't raise
+the temperature in a biological system
+
+ align:start position:0%
+the temperature in a biological system
+ 
+
+ align:start position:0%
+the temperature in a biological system
+but still you have to overcome this but
+
+ align:start position:0%
+but still you have to overcome this but
+ 
+
+ align:start position:0%
+but still you have to overcome this but
+the principle then what you have to do
+
+ align:start position:0%
+the principle then what you have to do
+ 
+
+ align:start position:0%
+the principle then what you have to do
+when you're carrying out a Catal what
+
+ align:start position:0%
+when you're carrying out a Catal what
+ 
+
+ align:start position:0%
+when you're carrying out a Catal what
+any Catalyst has would do is that it
+
+ align:start position:0%
+any Catalyst has would do is that it
+ 
+
+ align:start position:0%
+any Catalyst has would do is that it
+lowers
+
+ align:start position:0%
+lowers
+ 
+
+ align:start position:0%
+lowers
+this this activation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy and if you lower the activation
+
+ align:start position:0%
+energy and if you lower the activation
+ 
+
+ align:start position:0%
+energy and if you lower the activation
+energy then enough of the molecules just
+
+ align:start position:0%
+energy then enough of the molecules just
+ 
+
+ align:start position:0%
+energy then enough of the molecules just
+at whatever condition they're in will
+
+ align:start position:0%
+at whatever condition they're in will
+ 
+
+ align:start position:0%
+at whatever condition they're in will
+have enough energy to be able to go it
+
+ align:start position:0%
+have enough energy to be able to go it
+ 
+
+ align:start position:0%
+have enough energy to be able to go it
+won't change the size of the drop it
+
+ align:start position:0%
+won't change the size of the drop it
+ 
+
+ align:start position:0%
+won't change the size of the drop it
+just changes how fast you reach the that
+
+ align:start position:0%
+just changes how fast you reach the that
+ 
+
+ align:start position:0%
+just changes how fast you reach the that
+final equilibrium and there are two
+
+ align:start position:0%
+final equilibrium and there are two
+ 
+
+ align:start position:0%
+final equilibrium and there are two
+forms of U
+
+ align:start position:0%
+forms of U
+ 
+
+ align:start position:0%
+forms of U
+biological two molecules that are
+
+ align:start position:0%
+biological two molecules that are
+ 
+
+ align:start position:0%
+biological two molecules that are
+biological
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+catalysts one of the molecules you know
+
+ align:start position:0%
+catalysts one of the molecules you know
+ 
+
+ align:start position:0%
+catalysts one of the molecules you know
+is as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enzymes enzymes are made of a protein we
+
+ align:start position:0%
+enzymes enzymes are made of a protein we
+ 
+
+ align:start position:0%
+enzymes enzymes are made of a protein we
+spent a bunch of time um
+
+ align:start position:0%
+spent a bunch of time um
+ 
+
+ align:start position:0%
+spent a bunch of time um
+working at that one of the things I
+
+ align:start position:0%
+working at that one of the things I
+ 
+
+ align:start position:0%
+working at that one of the things I
+showed you the very first day uh this is
+
+ align:start position:0%
+showed you the very first day uh this is
+ 
+
+ align:start position:0%
+showed you the very first day uh this is
+a thing made by the anthrax bacterium
+
+ align:start position:0%
+a thing made by the anthrax bacterium
+ 
+
+ align:start position:0%
+a thing made by the anthrax bacterium
+Anthrax lethal Factor what it actually
+
+ align:start position:0%
+Anthrax lethal Factor what it actually
+ 
+
+ align:start position:0%
+Anthrax lethal Factor what it actually
+is it's a protein and it's an enzyme
+
+ align:start position:0%
+is it's a protein and it's an enzyme
+ 
+
+ align:start position:0%
+is it's a protein and it's an enzyme
+that's able to catalyze the cleavage of
+
+ align:start position:0%
+that's able to catalyze the cleavage of
+ 
+
+ align:start position:0%
+that's able to catalyze the cleavage of
+certain uh peptide bonds in proteins in
+
+ align:start position:0%
+certain uh peptide bonds in proteins in
+ 
+
+ align:start position:0%
+certain uh peptide bonds in proteins in
+our body and it particular it goes after
+
+ align:start position:0%
+our body and it particular it goes after
+ 
+
+ align:start position:0%
+our body and it particular it goes after
+molecules that are involved in in
+
+ align:start position:0%
+molecules that are involved in in
+ 
+
+ align:start position:0%
+molecules that are involved in in
+signaling processes inside of cells and
+
+ align:start position:0%
+signaling processes inside of cells and
+ 
+
+ align:start position:0%
+signaling processes inside of cells and
+we don't have those then we die more
+
+ align:start position:0%
+we don't have those then we die more
+ 
+
+ align:start position:0%
+we don't have those then we die more
+recently it was discovered that
+
+ align:start position:0%
+recently it was discovered that
+ 
+
+ align:start position:0%
+recently it was discovered that
+RNA can be a catalyst and these are
+
+ align:start position:0%
+RNA can be a catalyst and these are
+ 
+
+ align:start position:0%
+RNA can be a catalyst and these are
+called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um if you have an RNA that's a catalyst
+
+ align:start position:0%
+um if you have an RNA that's a catalyst
+ 
+
+ align:start position:0%
+um if you have an RNA that's a catalyst
+it's it's called a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ribosome and these seem pretty exotic
+
+ align:start position:0%
+ribosome and these seem pretty exotic
+ 
+
+ align:start position:0%
+ribosome and these seem pretty exotic
+for a little while when they first
+
+ align:start position:0%
+for a little while when they first
+ 
+
+ align:start position:0%
+for a little while when they first
+discovered the idea that a piece of RNA
+
+ align:start position:0%
+discovered the idea that a piece of RNA
+ 
+
+ align:start position:0%
+discovered the idea that a piece of RNA
+could serve as a catalyst in a
+
+ align:start position:0%
+could serve as a catalyst in a
+ 
+
+ align:start position:0%
+could serve as a catalyst in a
+biological system but uh it eventually
+
+ align:start position:0%
+biological system but uh it eventually
+ 
+
+ align:start position:0%
+biological system but uh it eventually
+turned out that the ribosome which we'll
+
+ align:start position:0%
+turned out that the ribosome which we'll
+ 
+
+ align:start position:0%
+turned out that the ribosome which we'll
+talk about in some detail which is a is
+
+ align:start position:0%
+talk about in some detail which is a is
+ 
+
+ align:start position:0%
+talk about in some detail which is a is
+the protein synthesizing Machinery that
+
+ align:start position:0%
+the protein synthesizing Machinery that
+ 
+
+ align:start position:0%
+the protein synthesizing Machinery that
+creates those peptide bonds between each
+
+ align:start position:0%
+creates those peptide bonds between each
+ 
+
+ align:start position:0%
+creates those peptide bonds between each
+of the amino acids to make the proteins
+
+ align:start position:0%
+of the amino acids to make the proteins
+ 
+
+ align:start position:0%
+of the amino acids to make the proteins
+it's a big conglomeration of RNA shown
+
+ align:start position:0%
+it's a big conglomeration of RNA shown
+ 
+
+ align:start position:0%
+it's a big conglomeration of RNA shown
+in Gray and a bunch of proteins
+
+ align:start position:0%
+in Gray and a bunch of proteins
+ 
+
+ align:start position:0%
+in Gray and a bunch of proteins
+different proteins that are shown in
+
+ align:start position:0%
+different proteins that are shown in
+ 
+
+ align:start position:0%
+different proteins that are shown in
+yellow but the actual formation of the
+
+ align:start position:0%
+yellow but the actual formation of the
+ 
+
+ align:start position:0%
+yellow but the actual formation of the
+peptide bond the thing that makes all
+
+ align:start position:0%
+peptide bond the thing that makes all
+ 
+
+ align:start position:0%
+peptide bond the thing that makes all
+proteins is actually catalyzed by a
+
+ align:start position:0%
+proteins is actually catalyzed by a
+ 
+
+ align:start position:0%
+proteins is actually catalyzed by a
+piece of RNA and so the ribosome is
+
+ align:start position:0%
+piece of RNA and so the ribosome is
+ 
+
+ align:start position:0%
+piece of RNA and so the ribosome is
+actually a ribozyme and it's ironic that
+
+ align:start position:0%
+actually a ribozyme and it's ironic that
+ 
+
+ align:start position:0%
+actually a ribozyme and it's ironic that
+that sense that a piece of RNA is
+
+ align:start position:0%
+that sense that a piece of RNA is
+ 
+
+ align:start position:0%
+that sense that a piece of RNA is
+catalyzing the bond that makes proteins
+
+ align:start position:0%
+catalyzing the bond that makes proteins
+ 
+
+ align:start position:0%
+catalyzing the bond that makes proteins
+possible so we'll finish this up and get
+
+ align:start position:0%
+possible so we'll finish this up and get
+ 
+
+ align:start position:0%
+possible so we'll finish this up and get
+in then to uh glycolysis which is the
+
+ align:start position:0%
+in then to uh glycolysis which is the
+ 
+
+ align:start position:0%
+in then to uh glycolysis which is the
+most evolutionary ancient of these uh
+
+ align:start position:0%
+most evolutionary ancient of these uh
+ 
+
+ align:start position:0%
+most evolutionary ancient of these uh
+energy producing systems on on Monday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
\ No newline at end of file
diff --git a/7xJJU5HDCVE.txt b/7xJJU5HDCVE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..adf664f4bf691c908552a8e9d886b854ba7d481e
--- /dev/null
+++ b/7xJJU5HDCVE.txt
@@ -0,0 +1,1293 @@
+The following
+content is provided
+
+under a Creative
+Commons License.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+SPEAKER 1: Welcome to
+this Vensim tutorial.
+
+As a group of students engaged
+in the system dynamics seminar
+
+at MIT Sloan, we
+will present how
+
+to estimate model parameters
+and the confidence interval
+
+in a dynamic model using Maximum
+Likelihood Estimation, MLE,
+
+Likelihood Ratio, LR method.
+
+First, the basics of MLE
+are described, as well as
+
+the advantages and
+underlying assumptions.
+
+Next, the different methods
+available for finding
+
+confidence intervals of
+the estimated parameters
+
+are discussed.
+
+Then, a step-by-step guide
+to a parameter estimation
+
+using MLE-- an assessment
+of the uncertainty
+
+around parameter estimates using
+Univariant Likelihood Ratio
+
+Method in Vensim-- is provided.
+
+This video is presented to you
+by William, George, Sergey,
+
+and Jim under the guidance of
+Professor Hazhir Rahmandad.
+
+The literature, Struben,
+Sterman, and Keith,
+
+highlight that estimating model
+parameters and the uncertainty
+
+of these parameters are central
+to good dynamic modeling
+
+practice.
+
+Models must be grounded
+in data if modelers
+
+are to provide reliable
+advice to policymakers.
+
+Ideally, one should
+estimate model parameters
+
+using data that are independent
+of the model behavior.
+
+Often, however, such
+direct estimation
+
+from independent
+data is not possible.
+
+In practice, modelers
+must frequently
+
+estimate at least
+some model parameters
+
+using historical data itself,
+finding the set of parameters
+
+that minimize the difference
+between the historical and
+
+simulated time series.
+
+Only then can estimations
+of model parameters
+
+and uncertainties
+of these estimations
+
+serve to test model
+hypotheses and quantify
+
+important uncertainties, which
+are crucial for decision-making
+
+based on modeling outcome.
+
+Therefore, when modeling
+a system in Vensim,
+
+if the purpose of this model
+involves numerical testing
+
+or projection, robust
+statistical parameter
+
+estimation is necessary.
+
+Confidence intervals also
+serve as an important tool
+
+for decision-making based
+on modeling outcomes.
+
+Various approaches are
+available to estimate parameters
+
+in confidence intervals in
+dynamic model, including,
+
+for estimation, the
+generalized methods of moments
+
+in maximum likelihood, and
+for confidence intervals,
+
+likelihood-based methods
+and bootstrapping.
+
+Maximum Likelihood Estimation
+is becoming increasingly
+
+important for
+nonlinear models when
+
+estimating nonlinear
+parameters that
+
+consist of non-normal,
+autocorrelated errors,
+
+and heteroscedasticity.
+
+It is simpler to understand
+the construct, yet
+
+at the same time,
+requires relatively little
+
+computational power.
+
+MLE is best suitable for
+using historical data
+
+to generate parameter
+estimation and confidence
+
+intervals as long as
+errors of estimation
+
+are independent and
+identically distributed.
+
+When using MLE in
+complex systems
+
+where these assumptions
+are violated,
+
+and/or the analytical
+likelihood function
+
+might be difficult
+to find, one should
+
+use more advanced methods.
+
+This tutorial will not
+address these cases.
+
+As the demonstration will
+show, the average laptop
+
+in use in 2014 is capable
+of running the analysis
+
+in a few minutes or less.
+
+This tutorial is based on the
+following four references--
+
+"Bootstrapping for confidence
+interval estimation
+
+and hypothesis testing for
+parameters of system dynamics
+
+models" by Dogan, "A behavioral
+approach to feedback loop
+
+dominance analysis" by
+Ford, "Modeling Managerial
+
+Behavior," also known as
+"The Beer Game" by Sterman,
+
+and a soon-to-be published text
+by Struben, Sterman, and Keith,
+
+"Parameter and Confidence
+Interval Estimation in Dynamic
+
+Models-- Maximum Likelihood
+and Bootstrapping Methods."
+
+More background and explanation
+on the theory of MLE
+
+can be found in these works.
+
+This tutorial will focus on the
+application of MLE in Vensim.
+
+The literature, Struben,
+Sterman, and Keith,
+
+stresses that
+modelers must not only
+
+estimate parameter values,
+but also the uncertainty
+
+in the estimates so they
+and others can determine
+
+how much confidence to
+place in the estimates
+
+and select appropriate ranges
+for sensitivity analysis
+
+in order to assess the
+robustness of the conclusions.
+
+Estimating confidence
+intervals can
+
+be thought of as
+finding the shape
+
+of the inverted bowl, Figure 2.
+
+If for a given data set,
+the likelihood function
+
+for a set of parameters
+falls off very steeply
+
+for even small departures
+from the best estimate,
+
+then one can have confidence
+that the true parameters
+
+are close to the
+estimated value.
+
+As always, assuming the
+model is correctly specified,
+
+another maintained
+hypothesis are satisfied.
+
+If the likelihood
+falls off only slowly,
+
+other values of the parameters
+are nearly as likely
+
+as the best estimates and one
+cannot have much confidence
+
+in the estimated values.
+
+MLE methods provides
+two major approaches
+
+to constructing confidence
+intervals or confidence
+
+regions.
+
+The first is the
+asymptotic method, AM,
+
+which assumes that the
+likelihood function can
+
+be approximated by a parabola
+around the estimated parameter.
+
+An assumption that is valid
+for a very large sample.
+
+The second is the
+likelihood ratio, LR method.
+
+The LR is the ratio of
+the likelihood for a given
+
+set of parameter values to the
+likelihood for the MLE values.
+
+The LR method involves searching
+the actual likelihood surface
+
+to find values of the
+likelihood function
+
+that yield a particular
+value for the LR.
+
+That value is derived for
+the probability distribution
+
+of the LR and the
+confidence level
+
+desired, such as 95% chance that
+the true parameter value lies
+
+within the confidence interval.
+
+This tutorial will use the
+Univariate Likelihood Ratio
+
+for determining the MLE
+competence interval in Vensim.
+
+The estimated parameter
+and competence interval
+
+mean that for a specific
+percentage of probability--
+
+usually 95 or 99% that
+the real parameter falls
+
+within the confidence interval
+with the designated percent
+
+possibility.
+
+This is consistent with
+general applications
+
+of statistics and probability.
+
+The LR our method of
+confidence interval
+
+estimation compared to the
+likelihood for the estimated
+
+parameter, theta hat, with
+that of an alternative set,
+
+theta star.
+
+The likelihood ratio is
+determined in equation one
+
+as R equals L theta hat
+divided by L theta star.
+
+Asymptotically, the
+likelihood ratio
+
+falls at chi square
+distribution, equation two.
+
+This is valuable, because the
+univariate method requires
+
+no new optimizations once
+the MLE has been found.
+
+The critical parameter
+value for all parameters
+
+is then simply using
+equation three.
+
+A disadvantage of univariate
+confidence interval estimates,
+
+however, is that the parameter
+space is not fully explored.
+
+Hence, the effect of interaction
+between the parameters on LL
+
+is ignored,
+
+The tutorial now switches
+to a real simulation
+
+using Vensim 6.1.
+
+It will show how the
+theory just described
+
+can be applied to estimating
+parameters of decision-making
+
+in the Beer Distribution Game.
+
+SPEAKER 2: Hello.
+
+This tutorial is now going
+to explore analytics,
+
+by estimating the parameters
+for a well-analyzed model
+
+of decision-making used in
+the Beer Distribution Game.
+
+The model is described in the
+paper, "Modeling Managerial
+
+Behavior-- Misperception
+of Feedback in a Dynamic
+
+Decision-Making Experiment" by
+Professor Sterman from 1989.
+
+Participants in the beer
+game choose how much beer
+
+to order each period in
+a simulated supply chain.
+
+The challenge is to estimate
+the parameters of a proposed
+
+decision rule for
+participant orders.
+
+The screen shows
+the simple model
+
+of beer game decision-making.
+
+The ordering decision rule
+proposed by Professor Sterman
+
+is the following.
+
+The orders placed every week
+are given by the maximum of zero
+
+and the sum of expected
+customer orders-- the orders
+
+that participants
+expect to receive
+
+next period from their
+immediate customer and inventory
+
+discrepancy.
+
+The inventory discrepancy
+is the difference
+
+between total desired
+inventory and some
+
+of actual on-hand
+inventory and supply
+
+line of on-order inventory.
+
+There are four
+parameters that are
+
+used in the model-- [INAUDIBLE],
+the weight on incoming orders
+
+in demand forecasting,
+S prime, the desired
+
+on-hand and on-order
+inventory, the fraction
+
+of the gap between desired and
+actual on-hand and on-order
+
+inventory ordered each
+week, and the fraction
+
+of the supply line the
+subject accounts for.
+
+As modelers, we don't
+know what the parameters
+
+of the actual game are.
+
+But we have the data for actual
+orders placed by participants.
+
+And this data is read
+from the Excel spreadsheet
+
+into the variable,
+actual orders.
+
+Let's start from
+some guesstimates
+
+and assign the following values.
+
+[INAUDIBLE], fraction
+of discrepancy
+
+between desired and
+actual inventory,
+
+and supply line fraction
+are all equal to 0.5.
+
+S prime, the total desired
+inventory, is 20 cases of beer.
+
+With these parameters, the
+model runs and generates
+
+some alias of the
+order placed, which
+
+can be seem on this graph.
+
+Let's compare them
+against the actual orders
+
+observed in the beer game.
+
+We can see that although
+the trend is generally
+
+correct at the high level, the
+shape is totally different.
+
+This necessitates the question,
+how can we effectively measure
+
+the fit of the data?
+
+The typical way is to calculate
+the sum of squared errors,
+
+which are differences between
+simulated and actual data
+
+points.
+
+Square, to make
+sure negative values
+
+don't reduce the total sum.
+
+The basic statistics
+of any variable
+
+can be found by
+using statistics to
+
+from either object
+output or bench tool.
+
+For this tutorial, I
+have already defined it.
+
+And in this case, we can see
+[INAUDIBLE] of sum of squares
+
+of residuals is 1700,
+with a mean of about 35.
+
+This is pretty far
+from a good fit,
+
+and we can confirm
+it officially.
+
+Now let's see how to
+run the optimization
+
+to find the parameters that
+will bring the values of orders
+
+placed as close to the
+actual orders as possible.
+
+The optimization
+control panel is
+
+invoked by using optimized
+tool on the toolbar.
+
+When you first open, you have
+to specify the file name here.
+
+Also, it is necessary to specify
+what type of optimization
+
+you're going to do.
+
+There are two types
+that can be used.
+
+They differ in the way they
+interpret and calculate
+
+the payoff value.
+
+A payoff is a single number
+that summarize the simulation.
+
+In the case of
+the simulation, it
+
+will be a measure
+of fit, which can
+
+be a sum of squared
+errors between the actual
+
+and the simulated
+values, or it can
+
+be a true electrical function.
+
+If you are only interested
+in finding the best
+
+fit without worrying about
+confidence intervals,
+
+you can use the
+calibration mode.
+
+For calibration, it is
+not necessary to define
+
+the payoff functional mode.
+
+Instead, choose the model
+variable and the data variable
+
+with which the model
+variable will be compared.
+
+In Vensim, then
+at each time step,
+
+the difference between the
+data and the model variable
+
+is multiplied by the
+weight specified.
+
+And this product
+is then squared.
+
+This number, which
+is always positive,
+
+is then subtracted
+from the payoff,
+
+so that the payoff
+is always negative.
+
+Maximizing the
+payoff means getting
+
+it to be as close
+to zero as possible.
+
+However, this is not a true
+log-likelihood function,
+
+so the results cannot be used to
+find the confidence intervals,
+
+which we need.
+
+Therefore, we're going
+to use the policy mode.
+
+For policy mode,
+the payoff function
+
+must be specified explicitly.
+
+At each time step, the
+value of the variable
+
+or presenting a payoff function
+is multiplied by the weight.
+
+Then it is multiplied by time
+step and added to the payoff.
+
+The optimizer is designed
+to maximize the payoff.
+
+So variables, for
+which more is better,
+
+should be given
+positive weights,
+
+and those, for which
+less is better,
+
+should be given
+negative weights.
+
+Here, [INAUDIBLE] are specified
+in the sum of squared errors.
+
+Residuals are calculated as
+the difference between orders
+
+placed and actual orders
+at each time step.
+
+This squared value
+is then accumulated
+
+in the stock sum
+of residual square.
+
+The tricky part is the variable,
+total sum of residual square.
+
+Please note that because
+Vensim, in the policy mode,
+
+multiplies the values
+of the payoff function
+
+by the time step,
+the payoff value
+
+is the weighted combination
+of the different payoff
+
+elements integrated
+over the simulation.
+
+This is not what
+we're looking for.
+
+We are interested in the final
+value of a variable instead
+
+of the integrated value, because
+the final value is exactly
+
+the total sum of squared
+errors the way we defined it.
+
+Here's an example to
+illustrate the concept.
+
+In this line is a
+stock variable level.
+
+It can be seen that, if we
+just use the stock of sum
+
+of residual squared in
+the payoff function,
+
+we get the value, which is equal
+to the area under the curve,
+
+instead of the final
+value that we need.
+
+[INAUDIBLE] look at
+only the final value.
+
+In a model, it is necessary
+to introduce new variable
+
+for the payoff function and
+use the following equation that
+
+makes its value to be
+zero at each time step,
+
+except for the final step.
+
+Add the current value of the
+residual squared to the stock
+
+level to account for the value
+of the current time step.
+
+This effectually ignores
+all the intermediate values
+
+and looks only at
+the final value.
+
+So far, this is
+nothing different
+
+from what Vensim was doing
+in the calibration mode.
+
+We simply replicated what it
+would be doing automatically.
+
+In order to get the true
+likelihood function-- assuming
+
+normal distribution
+of errors-- we
+
+need to divide the
+sum of squared errors
+
+by two variances.
+
+This is what you can see in the
+true low likelihood function
+
+variable.
+
+So far, in this
+demonstration, we
+
+don't know what the
+standard deviation of errors
+
+is going to be, because we
+haven't optimized anything yet,
+
+so we're going to leave
+this variable as 1.
+
+We are going to change
+it to the actual value
+
+of the standard deviation of
+errors later by the confidence
+
+interval.
+
+Now let's change the
+run name and go back
+
+to Optimization Setup.
+
+And let's use our log-likelihood
+function as the payoff element.
+
+Because this is
+policy mode, we don't
+
+need to specify anything
+in Compare To field.
+
+For the weight, because
+this is policy mode,
+
+it is necessary to
+assign a negative value.
+
+This tells Vensim
+that we're looking
+
+to minimize the payoff function.
+
+If there are multiple
+payoff functions,
+
+the weight value would
+have been important.
+
+For one function,
+it doesn't matter.
+
+But we don't want
+to change the values
+
+of the log-likelihood function
+to calculate true confidence
+
+internal values.
+
+Therefore, the log-likelihood
+function will not be scaled,
+
+and the weight is
+going to be minus 1.
+
+Next screen, the
+Optimization Control Panel,
+
+we have to specify
+the file name again.
+
+Then, make sure to
+use multiple starts.
+
+This means the
+analysis is less likely
+
+going to be stuck
+at a local optimum
+
+if the surface is not complete.
+
+If multiple starts is
+random, starting points
+
+for any optimizations are
+picked randomly and uniformly
+
+over the range of
+each parameter.
+
+Next field, optimizer, tells
+Vensim to use probable method
+
+to find local minimum
+function at each start.
+
+Technically, you could
+ignore this parameter
+
+and just rely on
+random starts to find
+
+the values of a payoff function.
+
+However, using multiple
+starts together
+
+with optimization
+of each time step
+
+produces better and
+faster convergence.
+
+The other values are left
+at the default levels.
+
+You can read more about these
+parameter in Vensim help,
+
+but generally, they
+control the optimization
+
+and are important for
+complicated models
+
+where simulation
+time is significant.
+
+Let's add now the parameters
+that Vensim will vary in order
+
+to minimize the payoff function.
+
+Next, make sure Payoff Report
+is selected and hit Finish.
+
+For random or other random
+values of multiple start,
+
+the optimizer will
+never stop unless you
+
+click on the Stop
+button to interrupt it.
+
+If you don't choose
+multiple starts,
+
+the next few steps
+are not necessary
+
+as Vensim would be able
+to complete optimization
+
+and sensitivity analysis,
+which is performed
+
+in the final step
+of optimization.
+
+However, as I mentioned,
+the optimization
+
+can be stuck at a
+local optimum, thus
+
+producing some optimal results.
+
+So it is recommended that you
+use multiple starts unless you
+
+know the shape of
+the payoff function
+
+and are sure that local optimum
+is equal to the global optimum.
+
+So having chosen
+random multiple starts,
+
+the question is, when to
+stop the optimization.
+
+This requires some
+experiments and depends
+
+on the shape of your
+payoff function.
+
+In this case, the
+values of the payoff
+
+have been changing quite
+fast in the beginning
+
+and are now at the same
+level for quite some time.
+
+So it's a good time to attempt
+to interrupt the optimization
+
+and see if you like the results.
+
+As you can see, the shape
+of the orders placed
+
+is much closer to the
+actual order values.
+
+The statistics shows
+a much better fit,
+
+with the total sum of squared
+error significantly lower
+
+at the level of just 279,
+with a mean of 5.813.
+
+The values of the rest of
+the optimized parameter
+
+can be looked up in the
+file with the same name
+
+as the run name and
+the extension out.
+
+We can open this file from
+Vensim using the Edit File
+
+command from File menu.
+
+So far, we only know the
+optimal values, but not
+
+the confidence intervals.
+
+We need now to tell Vensim to
+use the optimal values found
+
+and calculate the confidence
+intervals around them.
+
+We are going to do it by using
+the output of the optimization
+
+and changing
+optimization parameters.
+
+To do this, first, we have to
+modify the optimization control
+
+parameters and turn
+of multiple starts,
+
+and optimize them, and save
+it as the optimization control
+
+type file, BOC.
+
+Also, we need to change the
+value of standard deviation
+
+to the actual value
+to make sure we're
+
+looking at the true values of
+the log-likelihood function.
+
+This value can be found in the
+statistics [INAUDIBLE] again.
+
+We use it to change the
+variable in the model.
+
+Open the Optimization
+Control Panel again,
+
+and leave the payoff
+function as it is.
+
+But on the Optimization
+Control Screen,
+
+open the file that
+was just created
+
+and check that multiple starts
+and optimizer are turned off.
+
+In addition, specify [INAUDIBLE]
+by choosing payoff value
+
+and entering the value by
+which Vensim will change
+
+the optimal likelihood function
+in order to find the constants
+
+controls.
+
+Because for likelihood
+ratio method,
+
+the likelihood ratio
+is approximated
+
+by the chi-square
+distribution, it
+
+is necessary to find the value
+of chi-square distribution
+
+[INAUDIBLE] for 95th percentile
+for one degree of freedom,
+
+because we are doing
+the univariate analysis.
+
+A disadvantage of univariate
+confidence interval estimation
+
+is that the parameter space
+is not fully explored.
+
+Hence, the effect of
+interaction between parameters
+
+and log-likelihood
+function is ignored.
+
+The value of chi-squared,
+in this case,
+
+is approximately
+3.84146, which we're
+
+going to use in the
+sensitivity field.
+
+Now, the [INAUDIBLE] button.
+
+And as you see,
+this time, we don't
+
+have to wait as Vensim
+doesn't do any optimization.
+
+The results,
+allocated in the file
+
+that has the name of
+the run-- and the word
+
+sensitive with
+the extension tab.
+
+Let's open this file and
+see our estimated parameters
+
+and the confidence intervals.
+
+Since we are using too much
+more likelihood function,
+
+the confidence bounds are
+not necessarily symmetric.
+
+This is a very simple tutorial.
+
+I hope you are now more familiar
+with [INAUDIBLE] for estimating
+
+parameters and confidence
+intervals for your models.
+
+Thank you.
+
+SPEAKER 3: A summary of the
+seven key steps involved
+
+in determining the MLE in Vensim
+is contained on the slide.
+
+It can be printed and
+serve as a useful reference
+
+and check for those
+wishing to use the method.
+
+MLE has its advantages
+and disadvantages
+
+in estimating parameters and
+their confidence intervals
+
+when performing
+dynamic modeling.
+
+In conclusion,
+when the condition
+
+of errors being independent
+and identically distributed
+
+are met, then MLE is a simple
+and straightforward method
+
+for estimating
+parameters in determining
+
+their statistical fit in system
+dynamics models developed
+
+in Vensim.
\ No newline at end of file
diff --git a/7y67IP6XTPc.txt b/7y67IP6XTPc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2e08243896f3311eddcf381060c5fe3ea3972628
--- /dev/null
+++ b/7y67IP6XTPc.txt
@@ -0,0 +1,4538 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Hi everyone.
+
+So I am Esther Duflo.
+
+I am the other person who
+teaches this class.
+
+You had Abhijit for
+the first class.
+
+I am going to start by doing
+a bit of housekeeping.
+
+Keeping in mind that maybe
+some people are going to
+
+arrive, so it is your
+responsibility to inform
+
+everybody else of what
+I said today.
+
+I got some requests of
+clarifying what was the
+
+requirements for this
+class, so I'll just
+
+go through it once.
+
+So we are going to post
+essay topics.
+
+For 10 topics.
+
+And we are going to give
+three or four choices.
+
+You can also make
+your own essays.
+
+Whatever it is.
+
+You do have a chance to
+write up to 10 essays.
+
+But you don't need to
+write that many.
+
+You are going to be graded
+out of the best five.
+
+So you can write any between
+one and ten.
+
+And if you have one you're not
+going to have a very high
+
+grade but--
+
+Any between five and ten and
+then we'll just take
+
+the best five, OK?
+
+I think the syllabus said seven
+and Abhijit said five,
+
+so I went for the
+easier thing.
+
+So that's one thing.
+
+The syllabus also said that we
+might not grade all of them
+
+but, actually, we are going
+to grade all of them.
+
+So I would suggest that you do
+the first one so that you get
+
+used to it.
+
+Traditionally, it has been the
+case that when students can
+
+decide how to arrange their
+deadlines, they think that
+
+it's efficient to set all the
+
+deadlines late in the semester.
+
+I can tell you by experience
+that it's actually exposed not
+
+to be such a good idea.
+
+So if I were you, I would
+arrange things to do as many
+
+of them early as possible
+so you don't get
+
+panicked by the end.
+
+So that's one.
+
+The other component of the
+requirement for this class is
+
+to do the readings.
+
+And so to be prepared to
+discuss in the class.
+
+One way in which we're going
+to ensure that you're doing
+
+the reading is a very,
+very short pop-quizes
+
+every once in awhile.
+
+It also means you have
+to come to class.
+
+It's not a class that's
+very difficult.
+
+But one thing that it requires
+is that you actually come.
+
+And so we're going to have those
+at any random times.
+
+Very simple.
+
+2, 3, 4 questions just to check
+that you've actually
+
+read the thing.
+
+And today the questions for the
+first topic were already
+
+posted on Stellar.
+
+So you already have access to
+them as well as the deadline
+
+for the first thing.
+
+And that's it.
+
+Other than that, I think I gave
+a version of this spiel
+
+in 14.74 yesterday.
+
+There are two development
+classes.
+
+If you're wondering which one
+you should be in, this one is
+
+going to be more based
+on the readings and
+
+discussion and lectures.
+
+And the other one's going to go
+more in the detail of the
+
+techniques of papers and
+solving the models and
+
+replicating empirical
+papers, et cetera.
+
+So this one's a better
+introduction and the other one
+
+is better if you already have a
+fair amount of economics and
+
+econometrics.
+
+So that's the trade off.
+
+Other than that, obviously, the
+themes that are going to
+
+be covered are going to
+be pretty similar.
+
+So my sense is, probably, that
+you don't want to take both at
+
+the same time.
+
+Although you could think of
+taking them both in sequence.
+
+Then you would do 73
+first, 74 second.
+
+I don't recognize any 74
+students, but you shouldn't
+
+want to take 74 and then 73.
+
+That would be a bit boring.
+
+So you're welcome to shop a
+little bit for some time and
+
+then decide what's
+more appropriate.
+
+You're welcome to take both but
+I would have warned you
+
+that there will be some overlap
+between the two.
+
+That's it for housekeeping so if
+you have questions, that's
+
+a good time.
+
+I'm happy to answer questions by
+email also but chances are
+
+that if you have a question on
+the logistics, a lot of people
+
+share it as well.
+
+Any questions?
+
+No.
+
+The class is being recorded,
+that's for OpenCourseWare.
+
+But don't worry about saying
+anything embarrassing.
+
+That would be edited out.
+
+I'm the only one--
+
+and Abhijit--
+
+is going to be the only ones who
+are being recorded on tape
+
+saying things embarrassing.
+
+I'm assuming if you say
+something extremely smart we
+
+can keep it though.
+
+AUDIENCE: [LAUGHTER]
+
+PROFESSOR: So there
+is no danger.
+
+Feel free.
+
+Just ignore them.
+
+And hopefully, the idea is that
+if it works well, it will
+
+be one of these classes that
+people can take on their own
+
+down the line.
+
+Anything else?
+
+Any questions?
+
+No questions?
+
+When you speak, at the
+beginning, if you at least
+
+would state your name so
+that I can possibly
+
+get to know who are.
+
+I can address you
+by your name.
+
+That would be nice.
+
+And otherwise, we're
+ready to roll.
+
+Shall we dive in?
+
+Let's dive in.
+
+So, in the video that you saw
+last time, you saw quite a few
+
+people who were maybe trapped in
+some kind of poverty trap.
+
+So for example, there was this
+farmer who, before he was
+
+given fertilizer, had
+very low yield.
+
+And because he had
+very low yield he
+
+didn't have much money.
+
+Because he didn't have much
+money, he couldn't buy
+
+fertilizer and, therefore,
+he continued to
+
+have very low yield.
+
+And what the Millennium Village
+Project did is to give
+
+him the fertilizer.
+
+And the hope was, that with this
+first gift of fertilizer,
+
+his yield would increase by a
+sufficient amount that, down
+
+the line, he would be able to
+buy his own fertilizer.
+
+And grow more and more maize.
+
+And then, progressively, maybe
+start feeding his children
+
+better and buying them books
+and all of those things you
+
+want to think about.
+
+So in that video, the Sachs and
+Jolie video that you saw
+
+last time, this argument that
+there might be these poverty
+
+traps keep coming over
+and over again.
+
+So for example, in the Kennedy
+story with the farmers, you
+
+see it in the schools.
+
+The schools don't have computers
+so the kids cannot
+
+really learn well.
+
+You start putting computers
+and kids can learn better.
+
+They will then make
+more money.
+
+They will then be able to buy
+computers for their schools,
+
+et cetera, et cetera.
+
+So one of the things that we
+are going to do a lot of in
+
+this class is to try to
+understand when there are such
+
+poverty traps and
+when, in fact,
+
+maybe it's not so obvious.
+
+And for that, we have to
+understand what creates the
+
+conditions for such poverty
+traps to emerge.
+
+So what I want to do today--
+
+we are going to delve in on one
+example of one particular
+
+poverty trap and how
+that could work.
+
+Which is going to be the fact
+that we are physical,
+
+biological bodies.
+
+But what we're going to go
+over as a mechanism, it's
+
+going to carry us during
+the entire class.
+
+We are going to have to be
+looking for the same type of
+
+conditions.
+
+So I want to start with
+a story of someone
+
+that actually I met.
+
+I met some guy called
+Pak Solhin.
+
+Pak means mister.
+
+Mister Solhin.
+
+So people in Indonesia don't
+really have a first
+
+name and last name.
+
+They just have a name.
+
+And so, for example, Mrs.
+So-and-so is Ebu--
+
+I would be Ebu Esther,
+for example.
+
+So this guy is Pak Solhin.
+
+And I met him in a village
+in Indonesia--
+
+in Java, which is one of the
+richest parts of Indonesia.
+
+This is the main island, most
+densely populated--
+
+in the summer of 2008.
+
+In the summer of 2008, I was--
+
+probably for you it's already
+ancient history, it's before
+
+the great collapse of the
+world economy and stuff.
+
+--One of the key events at the
+time, for the developing
+
+countries in particular,
+was that the food
+
+prices were very high.
+
+Basically since 2005, food
+prices have increased
+
+enormously in the world for
+reasons that are not fully
+
+understood.
+
+And then they collapsed
+again when the whole
+
+economy went berserk.
+
+The world economy went away,
+the food prices also
+
+collapsed, and they have started
+to increase again.
+
+Part of the hunger that
+you see now--
+
+in Egypt, Tunisia, et cetera,
+all over the Middle East--
+
+part of it is fueled by a
+re-increase in the food prices
+
+which are almost reaching
+the 2008 level.
+
+For people in urban areas,
+this has, of course,
+
+immediately threatened
+their livelihood.
+
+Because they don't
+produce food.
+
+They buy food.
+
+So as soon as the food prices
+increase, that immediately
+
+affects them.
+
+So the beginning of 2008,
+2007 you observed this
+
+kind of food riots--
+
+nothing like we are seeing
+now in Egypt--
+
+but dis-content in various
+urban areas.
+
+And generally, people were
+wondering what was happening
+
+to food prices.
+
+What people have been thinking
+is that there are several
+
+factors that are responsible
+for the
+
+increase of the food prices.
+
+One is there are many more
+people in China and India
+
+making more money.
+
+And as they are making more
+money, not only they eat more
+
+but, more that that,
+they eat more meat.
+
+And it turns out that to produce
+1,000 calories of
+
+meat, you need much more
+grain than to produce
+
+1,000 calories of grain.
+
+That may sound strange, but it
+turns out that the cow is not
+
+a very efficient way to
+transform the calories from
+
+grain into calories
+that we eat.
+
+The cow has started by using
+a lot of it, et cetera.
+
+So to produce 1,000 calories
+of cows, you need much more
+
+than 1,000 calories
+worth of grain.
+
+So as China and India is
+becoming richer and eating
+
+more meat, then there is a
+demand for more grains.
+
+That's one.
+
+The second thing that is
+happening is bio-fuels.
+
+With the increase in the world
+prices of fuel there is more
+
+and more demand for bio-fuels,
+so entire strips of Brazil
+
+have been covered into
+maize that is being
+
+used to make ethanol.
+
+A third thing is oil is actually
+an input into the
+
+production of food.
+
+Because oil is a very important
+input into the
+
+production of fertilizer.
+
+So as the price of oil increase,
+the price of
+
+fertilizer increase,
+and therefore the
+
+price of food increases.
+
+So all of these factors are
+fundamental forces which
+
+explains why, after the short
+dip right after the crisis,
+
+the food prices again
+started to increase.
+
+So that's the backdrop
+of my visit to
+
+this village in Indonesia.
+
+And I met this guy.
+
+And he was all alone.
+
+He has a small, dingy,
+little house.
+
+And he was a bit depressed,
+or very depressed.
+
+And why was he depressed?
+
+Well he was depressed because
+he was all alone at home.
+
+And he was all alone at home
+because his wife had gone to
+
+the city to start working
+as a maid.
+
+His oldest son had also gone to
+the city to start working
+
+as an apprentice on a
+construction site.
+
+And the two young kids were
+with the grandparents.
+
+So he was all alone, he didn't
+have anything in his house, he
+
+didn't do all that much,
+and he wasn't happy.
+
+So the question is, why
+did that happen?
+
+Why was he not working?
+
+And what he explained to me
+is that he was not working
+
+because he didn't have a job.
+
+And he didn't have a job because
+when the fertilizer
+
+prices increased, the farmers
+that used to employ him
+
+decided that they had to do
+something to cut costs.
+
+They weren't very sure whether
+they were going to be able to
+
+sell their outputs and they were
+facing those increases in
+
+expenditure.
+
+So they decided they
+had to cut costs.
+
+And so they could have done
+one of two things.
+
+What could they have done?
+
+Yeah?
+
+AUDIENCE: They could have cut
+wages or cut the number of
+
+people employed.
+
+PROFESSOR: Right.
+
+They could have cut wages or
+they could have cut the number
+
+of people who worked for them.
+
+So of course, if they had
+cut wages, he still
+
+would have a job.
+
+But instead, they
+cut employment.
+
+And why did they cut employment
+
+rather than cut wages?
+
+Well his theory was that if they
+had cut wages, his wages
+
+would've been so low that he
+would not have been able to
+
+buy enough food--
+
+especially as the food prices
+were rising at the same time--
+
+with the equivalent of one day
+of wage that would have been
+
+too little to sustain himself
+to be strong enough to
+
+actually work for a whole day.
+
+So seeing that, the employer,
+instead of cutting the wage
+
+and therefore making him unable
+to work, then you give
+
+a wage of someone, let's
+say, 1,000 rupiahs--
+
+1,000 rupiahs is not enough to
+get yourself energetic for a
+
+full day of work.
+
+So you've spent your 1,000
+rupiahs but the person can't
+
+feed himself for
+a day of work.
+
+You get nothing out of him,
+so there's no point.
+
+Yes?
+
+AUDIENCE: The question that came
+to my mind was, is there
+
+any truth to his theory?
+
+Did you find any other examples
+that would back up
+
+that that's the reason why the
+farmer, that he used to work
+
+on his land, decided to cut
+jobs instead of wages?
+
+PROFESSOR: Right.
+
+What you're asking
+is whether--
+
+that's fine-- whether maybe
+it's a plausible theory.
+
+But is there any truth to it?
+
+We're going to spend a fair
+amount of time on this very
+
+question, not on Tuesday,
+but starting Thursday.
+
+In terms of the empirical truth
+of his theory, in terms
+
+of the biological soundness
+of it, it
+
+sounds plausible a priori.
+
+That you need to start with a
+certain number of calories
+
+just to get going, right?
+
+Your body needs maybe 1,000
+calories just to survive.
+
+So the first thousand calories
+that you're consuming are not
+
+very useful to you to help you
+to actually start exercising.
+
+Then, once you are alive,
+the next calories
+
+will start being useful.
+
+So a priori, maybe
+there was some
+
+plausibility to this theory.
+
+That's only one theory.
+
+So that means that he
+lost his job so he
+
+couldn't do much of anything.
+
+He was not doing nothing,
+otherwise I would
+
+not have met him.
+
+He would be dead.
+
+But he was doing things that
+was not taking too
+
+much effort for him.
+
+For example, he was sitting next
+to the bank of a lake and
+
+he was fishing.
+
+He was getting a little
+bit of rice from
+
+the government program.
+
+He was getting a little bit
+of meals from his brother.
+
+But he was not really
+living a full life.
+
+He was sort of surviving.
+
+So at the heart of
+his theory--
+
+and I think your question of
+whether this is true or not is
+
+a very interesting question
+which certainly came to my
+
+mind when I was talking
+to him--
+
+but at the heart of this
+theory was this purely
+
+biological mechanism.
+
+And then on top of this
+biological mechanism, other
+
+things crept up.
+
+One is the fact that he was not
+doing anything, and that
+
+his kids were gone.
+
+That made him depressed so
+then it gave him very low
+
+energy to actually
+you do anything.
+
+So even if his theory was
+wrong, he sort of became
+
+trapped in a poverty trap that
+may have been more of a
+
+psychological one.
+
+Because he was there, sitting
+all alone in his hut, unable
+
+to do anything, thinking that
+he was worthless, therefore,
+
+in some sense, becoming
+worthless.
+
+There are other parts of his
+stories where we start seeing
+
+other bits of poverty trap.
+
+For example, what happened
+with his kid.
+
+So the kid who had to drop out
+of school to start working as
+
+a construction worker was
+actually a bright kid.
+
+So that's another place
+where you see now an
+
+inter-generational
+poverty trap.
+
+Where because the parents are
+poor, the kid has to drop out
+
+of school because he has to go
+to work and therefore himself
+
+will probably make less
+money down the line.
+
+And that's another thing where
+we have to ask exactly the
+
+same question you were
+asking before.
+
+Is it an isolated example?
+
+Or is it something that
+is generalized.
+
+That it's actually something
+like the inability to work for
+
+the parents, or the lack of
+income, that forces kids to
+
+stay out of school that
+could have otherwise
+
+have gotten an education.
+
+That's another place where we
+can find, potentially, a
+
+poverty trap.
+
+Where the kid got
+some schools.
+
+He got a few years of school but
+maybe not enough for it to
+
+be sufficient for him to
+actually get a good
+
+job down the line.
+
+And for himself, he couldn't
+work as a construction worker
+
+because he was too weak for the
+basic jobs which require
+
+some strength, and too unskilled
+for the better jobs,
+
+and too old to be an apprentice
+like his kid.
+
+He was kind of trapped.
+
+So what is happening in this
+story that you would think--
+
+even if we accept the biological
+mechanism, which I
+
+want to go back into in
+detail in a moment--
+
+something else could
+have happened.
+
+So for example--
+
+if we're thinking that his
+being out of a job is a
+
+temporary phenomenon--
+
+maybe he could have gotten a
+loan to sustain his family so
+
+that the kid could at least stay
+in school until the time
+
+for him to graduate.
+
+Then at least you wouldn't
+have that
+
+inter-generational trap.
+
+So at the heart of it, we have
+this biological phenomenon and
+
+then other things sort of creep
+in that maintain him in
+
+this position that creates
+the poverty trap.
+
+So what I want to do now
+is go through the
+
+biological story in detail.
+
+And then we're going to see how
+the other things add up,
+
+creep in, and create
+that trap.
+
+So let's go through the
+biological poverty trap.
+
+I should say that it's
+one of the most
+
+ancient ideas in economics.
+
+A very old idea .
+
+It dates at least
+from the 1950s.
+
+And this is an old
+idea exactly in
+
+this form of the biology.
+
+So the idea is that the first
+few calories that you get to
+
+consume are used by your
+body just to survive.
+
+So they don't make you strong.
+
+And then, when you start eating
+enough to survive, the
+
+next calories start giving
+you strength.
+
+So that's when you can start
+working out or you can work.
+
+So someone who is very poor,
+like Pak Solhin, may not have
+
+enough to eat to be very
+productive but if he could eat
+
+more, then he would
+become productive.
+
+So at the heart of this is this
+idea of what they call a
+
+capacity curve.
+
+And a capacity curve has
+something like this shape.
+
+It relates how much effort you
+can exercise to how much
+
+income you have, and, of course,
+how much income you
+
+have is supposed to be related
+to how much you consume.
+
+So what is the assumption that
+is underlying the fact I have
+
+put income here on the x-axis?
+
+Yep?
+
+AUDIENCE: The more money you
+have the more you eat.
+
+PROFESSOR: Right.
+
+The more money you have
+the more you eat.
+
+So for example, the simplest
+case would be, all
+
+you have, you eat.
+
+Of course, we know that it's not
+true because you also need
+
+to take care of your
+basic needs.
+
+You need to clothe yourself.
+
+You need to pay your children's
+school fee.
+
+Maybe you need something
+for your housing.
+
+So maybe you will only consume
+a part of your income.
+
+But maybe some fraction
+of what you have,
+
+you're going to eat.
+
+So that creates a relationship
+between the income you have
+
+today and how much
+you get to eat.
+
+So instead of income here, we
+could have calories consumed.
+
+And one first big question that
+we'll have to answer next
+
+time is, how steep is this
+relationship between how much
+
+income people have and how
+much they are eating.
+
+Here we are assuming that there
+is some relationship and
+
+it's formidably steep enough.
+
+So whenever you have income,
+you start eating.
+
+And what we have here on the
+left, on the x-axis is the
+
+work capacity.
+
+So how many bushels of wheat
+are you able to harvest or
+
+something like that.
+
+How many trenches can you dig.
+
+So the work capacity,
+you think of
+
+it as physical output.
+
+But of course, there could be
+a relationship between this
+
+physical output and your
+income tomorrow.
+
+Because, for example, you could
+be paid by the piece.
+
+So if you're paid by the piece,
+however many bushel of
+
+wheat you harvest, you
+get that much income.
+
+That creates the work capacity
+and your income tomorrow are
+
+related one for one.
+
+Right?
+
+So here we have income
+today, work capacity.
+
+And instead, we could
+have income
+
+today and income tomorrow.
+
+OK?
+
+Now why is this shaped
+the way it is?
+
+What does the shape represent?
+
+AUDIENCE: The left part is the
+part where your body is just
+
+able to survive.
+
+And then afterwards he gets a
+chance to actually make more
+
+money tomorrow because
+[INAUDIBLE].
+
+PROFESSOR: Exactly.
+
+So the left part is the first
+part where you're just getting
+
+enough to survive.
+
+You are just eating
+enough to survive.
+
+So the first few calories are
+good because they keep you
+
+alive so you can actually
+move about.
+
+But after that it just keeps you
+at this kind of low level.
+
+Right?
+
+And then you start having, maybe
+1,200, 1,500 calories.
+
+And then suddenly, it's a good
+breakfast you're eating before
+
+going out for your run.
+
+It shoots up and then, why does
+it flatten out again?
+
+Yeah?
+
+AUDIENCE: Because after a while
+you're satisfied and it
+
+levels out once [INAUDIBLE].
+
+PROFESSOR: Right.
+
+After a while it satisfy
+and it levels out.
+
+And if we had continued the
+curve, what would happen?
+
+It would really go down.
+
+Just think of post-Thanksgiving
+slump and
+
+she probably gets a deep
+down going line.
+
+So that creates this kind of
+funny shape between you're
+
+income today and your work
+capacity and, therefore,
+
+between your income today and
+your income tomorrow.
+
+Or it could be within a week or
+something like that, right?
+
+Which seems to have a reasonable
+biological sense.
+
+Now what happened when the
+price of food went up?
+
+What does it do to the
+work capacity?
+
+Yeah?
+
+AUDIENCE: I suppose it goes down
+because those people have
+
+to spend more of their
+income on food and
+
+then buy less food.
+
+PROFESSOR: Exactly.
+
+So what happens when the price
+of food goes up is that, in
+
+terms of bushels of wheat,
+that's the same thing.
+
+But in terms of actual income
+that the bushel of wheat
+
+transform into-- how
+much income-- that
+
+creates a jump down.
+
+Because to go from income to
+work capacity, to create from
+
+income today to calorie,
+that's more expensive.
+
+So the curve shifts down because
+for every dollar that
+
+you spend, or rupiah that you
+spend on food, that's fewer
+
+calories and, therefore, that
+shifts down whatever you are
+
+able to achieve in terms
+of capacity, right?
+
+So if we have it in the form
+of income to work capacity,
+
+the prices of food going up
+makes the curve going down.
+
+Yeah?
+
+AUDIENCE: Could you also, if
+you were talking about
+
+students, instead of saying the
+word capacity, I'd put the
+
+way you pay attention?
+
+Would they pay more attention
+if they ate more?
+
+Or is it just physical spending
+that [INAUDIBLE]
+
+PROFESSOR: Right.
+
+Here, if we're thinking of Pak
+Solhin, we are thinking about
+
+physical [INAUDIBLE].
+
+But if we're thinking about
+Pak Solhin's children, for
+
+example, it could well be their
+
+capacity to focus in class.
+
+And it could easily have
+the same shape.
+
+In fact, there are other thing
+that competes also for
+
+calories for children.
+
+For example, whether or not they
+have intestinal worms.
+
+And the intestinal worms also
+shift your work capacity, your
+
+attention capacity,
+down because they
+
+are eating your food.
+
+Therefore, that tends to make
+the kids anemic and less
+
+likely to be listening.
+
+That's exactly right.
+
+Yeah?
+
+AUDIENCE: And so increase in
+food prices, does that cause a
+
+shift or a stretch?
+
+PROFESSOR: It specifically
+causes shift and a--
+
+how would you call it,
+west-southwest, right?--
+
+It is both a shift
+and a stretch.
+
+Which is, it will take more of
+your income today to have you
+
+switch to the--
+
+think of it going this way.
+
+And alternatively,
+what happens when
+
+the wages go down?
+
+That's another thing
+we can look at.
+
+What happens to the
+work capacity?
+
+Not to the work capacity, but if
+we put income on the y-axis
+
+now and the wages go down?
+
+AUDIENCE: It shifts lower.
+
+PROFESSOR: It again will do the
+same thing because now the
+
+same work capacity will
+translate into less income.
+
+So what was happening in
+Indonesia in 2008 was, on the
+
+one hand, food prices
+were going up.
+
+On the other hand, farmers were
+stressed out because the
+
+input prices were going up.
+
+So at the same time they wanted
+to reduce the wages
+
+when the prices were
+increased.
+
+And both of these phenomenon
+create this southwest shift in
+
+the capacity curve.
+
+Yeah?
+
+AUDIENCE: Why didn't the farmers
+just increase the
+
+prices they were selling the
+crops at [INAUDIBLE]?
+
+PROFESSOR: That's an excellent
+question, so why didn't the
+
+farmer just increase
+the prices?
+
+The thing is that with the
+agricultural cycle, you
+
+produce and then-- so you put
+your fertilizer in the ground,
+
+then you put your crop
+in the ground and
+
+then you wait around.
+
+Then the crop comes and
+you try to sell it.
+
+And you're exactly right, the
+fact that the input prices
+
+have gone up while the demand,
+in principal, would
+
+not have gone up.
+
+It would have meant that the
+food prices sold by the farmer
+
+would probably go up.
+
+But what happened is that they
+weren't very sure whether or
+
+not the food prices were going
+to go up by the time they sold
+
+their food in proportion
+to the input prices.
+
+So the situation that prevailed
+in 2008 is a lot of
+
+volatility.
+
+The prices were high but they
+were also increasing.
+
+And that was true for the input
+prices and that was true
+
+for the output prices.
+
+And when you were talking to
+the farmer, everybody felt
+
+that they were holding the
+short end of the stick.
+
+The farmers were saying,
+well, yes, the
+
+food prices will increase.
+
+But we don't know whether it
+will increase enough to cover
+
+our input prices.
+
+Moreover, the farmers found
+it difficult to
+
+get loans, for example.
+
+So even if they know that the
+prices are going to go up for
+
+that input in the future, in the
+meantime, they still have
+
+to buy the fertilizer.
+
+So they sort of had
+to cut costs now.
+
+So this is a little bit
+what was happening.
+
+It's a mismatch between the
+price you have to pay for the
+
+fertilizer today.
+
+And you're going to realize
+the output in the future.
+
+So that creates this uncertainty
+plus the fact that
+
+you need to finance it
+one way or the other.
+
+Which is why, at that time,
+there were two things going on
+
+which were both against
+the poor guy.
+
+So this is what we have with
+the capacity curve.
+
+So we've had this reasoning for
+food but let's think a bit
+
+about other reasons--
+
+forget that we are talking about
+physical work capacity.
+
+Think about other reasons why
+there might be a relationship
+
+between your income today
+and an income at some
+
+point in the future.
+
+Think of the next generation,
+think of next month, or
+
+anything like that.
+
+Can you think of other reasons
+why this kind of funnily
+
+shaped curve might appear?
+
+So food might be one.
+
+What would be other reasons why
+this funnily shaped curve
+
+might appear?
+
+Yeah?
+
+AUDIENCE: Over the long
+term, maybe education.
+
+PROFESSOR: So let's go through
+the education one.
+
+Why do you think--
+
+AUDIENCE: Before, the less long
+you can afford to keep
+
+you're children in school.
+
+And so their income capacity
+isn't as low as yours was.
+
+But the richer you are, the more
+schooling you can get and
+
+the higher income you
+can [INAUDIBLE].
+
+PROFESSOR: So this is right.
+
+That there is probably a
+relationship between how long
+
+you can keep the
+kid in school--
+
+because if there are school fees
+you might or might not be
+
+able to afford them.
+
+Or there might also be an
+opportunity cost for the child
+
+to be in school.
+
+Like Pak Solhin's son couldn't
+afford to be in school because
+
+he had to work.
+
+So I think it's not very
+controversial to say there
+
+might be a relationship between
+your income today and
+
+how long your kid will
+stay in school.
+
+And then, there is probably a
+relationship between how long
+
+your kids can stay in school
+and their income.
+
+Which will create a relationship
+between your
+
+income today and the income
+of the child.
+
+So that creates a relationship
+of some form or another.
+
+But what would be necessary for
+this relationship to have
+
+this S-shape?
+
+So what you have explained, I
+think and I think most people
+
+would agree--
+
+we can ask around-- but I think
+what you have explained
+
+clearly is that we might expect
+through education--
+
+a relationship between
+income today and
+
+income of the children.
+
+Now what else do you need for
+that relationship to have this
+
+funny shape?
+
+AUDIENCE: At the start, you
+need to invest more.
+
+So like if they just learn to
+fifth grade, or if they just
+
+learn to second grade, it isn't
+going to make that much
+
+of a difference.
+
+But as they finish middle school
+and high school, it's a
+
+much steeper curve.
+
+But then, going to college
+versus Ph.D. levels off.
+
+PROFESSOR: Yeah.
+
+Sadly, going to a Ph.D usually
+leads to a drop in income
+
+compared to having gone
+to a Master's.
+
+Especially if you choose
+the Master's properly.
+
+But this is exactly
+that, which is we
+
+need one more thing.
+
+What you're saying
+is exactly right.
+
+What's your name?
+
+AUDIENCE: Yousef.
+
+PROFESSOR: Yousef.
+
+But what she told us is you
+need one more thing.
+
+You also need for the benefits
+of the first few years of
+
+education to be relatively
+low.
+
+And that's an empirical question
+that goes back to the
+
+plausibility question that
+you were asking earlier.
+
+Is it the case that the first
+few years of education are
+
+useless, or not very useful?
+
+Or is it the case that every
+year of education
+
+is a year of education.
+
+And there will be an S-shaped
+based on education if the
+
+first few years of education
+are not that useful.
+
+And [INAUDIBLE], if in fact,
+even the first few years of
+
+education are that useful.
+
+I'm not going to answer
+this question now.
+
+But we are going to answer it in
+due course, whether or not
+
+this is the case.
+
+You see that this is not
+something that we can just
+
+think of in the abstract.
+
+We have to find out.
+
+There could be reasons
+the other way.
+
+You could feel, for example,
+that the first years of
+
+education are amazingly useful
+because this is when
+
+you learn to read.
+
+And once you know how to read,
+who cares about all of these
+
+things that I'm trying to teach
+you because you can
+
+teach yourself everything
+you need to know.
+
+Or you could think that
+education is not useful unless
+
+you have a secondary degree.
+
+Because that's what opens
+the door to you for
+
+various formal jobs.
+
+Right?
+
+It could easily cut one
+way or the other.
+
+I don't know if you guys
+have an insight.
+
+For example, what
+is your view?
+
+Do you think that this is likely
+that the first few
+
+years of education are
+not so useful or--
+
+AUDIENCE: I think the first
+few years are very useful
+
+because some people
+learn to develop,
+
+like, love for reading.
+
+And actually realize that they
+can learn things by reading
+
+[INAUDIBLE].
+
+PROFESSOR: So for example, you
+think that, the first few
+
+years of education
+are very useful.
+
+So there would be a relationship
+between income
+
+today and income
+of my children.
+
+But it wouldn't have this shape
+if that is the case.
+
+In fact, it might have a
+completely opposite shape
+
+where it's more like an inverted
+L as opposed to an S.
+
+So education would be one.
+
+What would be another
+possibility for this funnily
+
+looking shape to appear between
+income today and
+
+income at some point
+in the future?
+
+Is it on my income in the future
+or the income of my
+
+children or my income
+next year?
+
+What would be other sources
+of such shapes?
+
+Yeah?
+
+AUDIENCE: Access in knowledge
+of, like, the job market.
+
+In the sense that if you were
+raised in a family that's a
+
+higher income and so, therefore,
+your parents would
+
+teach you more from a younger
+age and would allow you to
+
+have a higher income.
+
+PROFESSOR: Right.
+
+So for example, for access
+to the job market, it is
+
+possible-- if I can rephrase
+what you are saying-- that
+
+people who live in a village,
+their horizon is the village.
+
+Where they are growing
+whatever.
+
+They are growing stuff and they
+are making some income.
+
+But they don't have the
+perspective in mind that they
+
+could go to the city where
+there a number
+
+of other jobs available.
+
+So in that case, for people who
+have very little money and
+
+live in the village, well, their
+children will again also
+
+live in the village and have
+very little money.
+
+If suddenly something opens the
+possibility to go to the
+
+city-- for example, someone
+comes into some money, gets
+
+the option to buy a train
+ticket, goes to the city and
+
+figures out the options there.
+
+Then suddenly you have access
+to a number of other
+
+opportunities, potentially
+much more rewarding, that
+
+would potentially create
+this S-shape.
+
+Where the fact of being poor
+means that you live in a
+
+relatively restricted
+environment.
+
+You stay there.
+
+And then when you become just a
+bit richer, that opens this
+
+opportunity that helps you
+you become much richer.
+
+That's a very nice example.
+
+Yeah?
+
+AUDIENCE: Another option is
+savings which depends on how
+
+much income you have.
+
+Because the more you save, the
+more you invest and the higher
+
+income producing activities.
+
+So the poor people have
+no money to save so
+
+they're stuck there.
+
+But as they get more income you
+can afford to save more
+
+and invest more and it pushes
+your future earnings.
+
+PROFESSOR: Right.
+
+So saving is a very interesting
+example.
+
+Again you could say-- well,
+suppose for example, that
+
+people saved some fixed fraction
+of their income.
+
+Then if I have more income
+today I will save more.
+
+Therefore, I will invest more,
+therefore, I will be richer in
+
+the future.
+
+Now if it was a fixed fraction
+of my income, again, I would
+
+definitely see a relationship
+between income today and
+
+income tomorrow just because
+I save more.
+
+But if it's a fixed fraction of
+my income, what else do I
+
+need for this S-shape to come?
+
+Yes?
+
+AUDIENCE: You need for poor
+people to not be able to save
+
+this fraction.
+
+Because they, for instance,
+spend their money on food or
+
+things that they need
+to buy today.
+
+And so are either a fraction
+of [INAUDIBLE]
+
+income or it's just lower
+for poor people.
+
+PROFESSOR: Right.
+
+So the first possibility for
+an S-shape to appear due to
+
+savings is that actually people
+do not save a fixed
+
+fraction of their income.
+
+Is that for some reason, the
+poor save less than the rich.
+
+So if that's the case-- and
+let's talk through whether we
+
+have reasons to think that
+the poor would save
+
+less than the rich--
+
+but let's first take it as given
+for a moment, and let's
+
+assume the poor save
+less than the rich.
+
+And if that's the case--
+
+assume the poor save nothing--
+
+then if you're very poor, you
+have no income tomorrow coming
+
+out of investments.
+
+And then if you start saving
+when you become a little
+
+richer and that money is
+invested, that starts creating
+
+some return for that money and
+you get into this steeper part
+
+of the S-shape.
+
+So that's a first mechanism
+through which savings could
+
+create a relationship between
+your income today and your
+
+income tomorrow that would
+have this S-shape.
+
+Now what we do have to explain
+is why is it the case that the
+
+poor would be able to save
+less than the rich?
+
+And that is something that, I
+think, we all have in mind.
+
+Say, yes, of course, the
+poor don't save because
+
+they have no money.
+
+But one thing I want you to keep
+in mind is that the poor
+
+have no money but they
+have a present
+
+and they have a future.
+
+So unless they think that they
+will have more money tomorrow
+
+or unless, for some reason, they
+are extremely impatient,
+
+then the poor should want
+to save as well.
+
+Because, of course, today
+they have very
+
+little money for food.
+
+But tomorrow they'll have very
+little for food as well.
+
+So we need to go a little
+further than to say, well, of
+
+course the poor save because
+they have no money.
+
+Right?
+
+Again, let's not go into
+the details of that.
+
+I think there are good reasons
+to think that the poor would
+
+be less able to save
+than the rich.
+
+And we're going to have
+a whole set of
+
+lectures about that.
+
+But just keep in mind that it's
+not so obvious that the
+
+poor would be less
+likely to save.
+
+Another--
+
+sorry, you wanted to talk.
+
+AUDIENCE: [INAUDIBLE]
+
+access to healthcare
+and medicine.
+
+PROFESSOR: Right.
+
+So let's go to health.
+
+Let's finish saving
+and then I'll go
+
+back to you for health.
+
+Another reason why there might
+be a relationship between
+
+income today and income
+tomorrow of
+
+this form due to savings.
+
+Suppose that the poor and the
+rich saved both a proportion
+
+of their income.
+
+There could still be a
+relationship like that.
+
+Yeah?
+
+AUDIENCE: The rich could be able
+to invest their savings
+
+more effectively.
+
+PROFESSOR: Exactly.
+
+It could be that the rich have
+access to better investment
+
+opportunity.
+
+For example, it could be that
+the bank is just not
+
+interested in very small
+saving accounts.
+
+And in fact, it's the case
+that the banks are not
+
+interested in very small
+saving accounts.
+
+Because as soon as you're a bank
+and you take the saving
+
+of someone, the government is on
+your back to make sure that
+
+you don't run away
+with the saving--
+
+which is a good idea--
+but that costs money.
+
+So maintaining a saving account
+for someone costs some
+
+amount of money.
+
+And regardless of the size of
+the account, it still costs
+
+the same money because you need
+to do all the paperwork.
+
+So as a result, if you come to a
+bank with your five rupiahs,
+
+the bank is going to say, thank
+you, but I don't want
+
+your five rupiahs.
+
+Whereas, if you come with your
+5,000 rupiahs they're, sure,
+
+I'm going to put it in this very
+nice account for you with
+
+a nice return.
+
+So that's one reason
+right there.
+
+That the poor might have to save
+under the mattress where
+
+the money might disappear.
+
+Where it might be stolen.
+
+And so the return on
+saving for the poor
+
+might be very low.
+
+It might even be negative.
+
+Whereas, the return for the rich
+might be higher, either
+
+because they have access to this
+savings account or they
+
+can, for example, start
+a small business.
+
+For example, when you want to
+start a small business, is it
+
+worthwhile starting a tiny
+business with almost nothing?
+
+Maybe not.
+
+Maybe it needs to be large
+enough for it to be
+
+worthwhile.
+
+So even if the poor and the
+rich were to save the same
+
+amount proportionally, there
+might still be something
+
+related, not to how much they
+save, but what's the
+
+productivity of those savings.
+
+You were talking about
+health care.
+
+Why don't you tell us what
+you're thinking about
+
+healthcare.
+
+AUDIENCE: So at lower incomes
+you can't really
+
+buy a lot of medicine.
+
+And maybe you can reach a point
+where you can start
+
+buying medicines or
+buying healthcare.
+
+And maybe towards the end when
+you have higher income, it
+
+levels off because you don't
+encounter the health problems
+
+that you might at low incomes
+in the first place.
+
+PROFESSOR: Right.
+
+So healthcare might be another
+source of that.
+
+For example, if you're very
+poor, you might not be able to
+
+purchase very simple, relatively
+cheap technologies
+
+that prevent you from
+getting sick.
+
+It could be a covering
+for your water.
+
+It could be a water filter.
+
+It could be a bed net to put on
+top of your kids when they
+
+sleep so that they don't
+get malaria.
+
+So all of these things might
+all be like some fixed
+
+investment that, if you
+can't afford them, you
+
+can't afford them.
+
+And then you are getting sick
+more, therefore you are less
+
+productive, therefore you make
+less money, et cetera.
+
+So that's another source where
+we would have this S-shape.
+
+Then we again have to think
+about these goods as things
+
+that are a little bit lumpy.
+
+Like a bed net, for example.
+
+Or a water filter.
+
+That you can either afford
+or not afford.
+
+So if you have enough money you
+afford it and then you can
+
+be generally healthier.
+
+You don't lose all your calories
+to diarrhea and other
+
+nice things like that.
+
+And if you're poor you would
+be sick all the time.
+
+Or paying for the doctors,
+for example.
+
+So for example, if someone is
+sick and very poor they might
+
+not be able to pay
+for the doctor.
+
+Then they'll stay sick so
+they can't earn money.
+
+And again, a doctor visit is one
+big lump investment which
+
+you may or may not be
+able to afford.
+
+That would be another source
+of an S-shape like that.
+
+So the reason why I went through
+all of these examples
+
+is that we are going to have a
+lot to say about the exact
+
+story that Pak Solhin told
+me about the food.
+
+Whether this was a real story
+in this case or whether it's
+
+some stuff that he was telling
+himself to explain the
+
+situation he was in but, really,
+there was something
+
+else behind his problems
+like depression or
+
+something like that.
+
+But the first time it was
+formalized was in this context
+
+of nutrition.
+
+And it's very natural to think
+of it in the context of
+
+nutrition but it could apply.
+
+And a very important part of the
+discussion that I want you
+
+to keep in mind is that it's not
+enough for there to be a
+
+relationship between income
+today and income tomorrow.
+
+To create a poverty
+trap it needs to
+
+have this funny shape.
+
+And I want to discuss why.
+
+So the way that we are going to
+think of it is we are going
+
+to think about what
+is the dynamic of
+
+someone's income over time.
+
+So let's start with this picture
+which brings inherited
+
+income on the x-axis--
+
+so think of it as
+income today--
+
+and income from work.
+
+What I have plotted here
+is this S-shaped curve.
+
+Think of it, for example, as
+coming from nutrition.
+
+But any of the examples that you
+talked about if you don't
+
+like the nutrition one.
+
+And the line that goes through
+the diagonal is
+
+the 45-degree line.
+
+So why is the 45-degree line
+relevant and interesting here
+
+is that, , on the 45-degree
+line, income today is the same
+
+as income tomorrow.
+
+Right, so we're going
+to make use of it.
+
+Now I want to try and look at
+the dynamic of someone's
+
+income over time.
+
+So suppose someone got this
+little income, y prime 0.
+
+Where do I read their income
+in period one?
+
+Yep?
+
+AUDIENCE: It would be going
+from curvy line to the
+
+45-degree line horizontally.
+
+PROFESSOR: Exactly.
+
+So to go from income y prime 0
+to y1, I go on the vertical
+
+line up to the curve.
+
+That tells me this is what
+someone who starts his life
+
+with some income, yi0, can make
+his decision about how
+
+much to eat, creates some
+calories, creates some work
+
+capacity, goes to work,
+generates an income that he
+
+takes home.
+
+That's the income that we
+have on the curvy line.
+
+And then I want to say, well,
+that becomes y1, right?
+
+And then y1 is going to become
+the y0 of tomorrow.
+
+So to find it, I'm doing exactly
+what you're saying
+
+which is I'm going
+horizontally to
+
+the 45-degree line.
+
+And I could go down again.
+
+So from y0, I go to y1.
+
+Then horizontally
+on the 45-degree
+
+line gives me y1 again.
+
+And then how do I find y2?
+
+I go vertical again,
+that gives me y2.
+
+I go horizontal again to
+the degree line and I
+
+continue like that.
+
+And where will I end up?
+
+AUDIENCE: Where the two
+curves intersect.
+
+PROFESSOR: I will end up at
+the intersection of the
+
+45-degree line and the
+S-shape curve, right?
+
+At the first intersection.
+
+Now what if I start with
+a higher income.
+
+If I start with the income
+y 0 double prime.
+
+I go vertical to the curve.
+
+That gives me y1 double prime.
+
+I have to go horizontally
+to find it when it
+
+becomes income tomorrow.
+
+Again vertically, et cetera.
+
+And I again end up at the
+intersection of the 45-degree
+
+line and the S-shape curve
+but now it's a higher
+
+intersection.
+
+Now what happens if I start at
+the sixth point in the middle
+
+over there?
+
+Which way will that go?
+
+AUDIENCE: That will go down.
+
+PROFESSOR: That will go down.
+
+If I go to the sixth point,
+I go vertical
+
+then left then down.
+
+So what is the key point after
+which I will start going to
+
+the high point?
+
+Yeah?
+
+AUDIENCE: Where it intersects
+the 45-degree line again.
+
+PROFESSOR: So the intersection
+from below.
+
+So at this point P where the
+capacity curve intersects the
+
+45-degree line from below.
+
+Anything to the right goes
+to the high steady state.
+
+Anything to the left goes
+to the low steady state.
+
+So this possibility that there
+are two steady states
+
+depending on where you start
+from is the formalization of
+
+the poverty curve.
+
+Which is anybody who is poorer
+than the unstable equilibrium
+
+over there--
+
+if someone starts with exactly
+this income, where do they go?
+
+If someone starts with exactly
+the intersection of the
+
+45-degree line and the S-shape
+curve, do they go down or do
+
+they go up?
+
+They just stay there.
+
+So it is also a steady state but
+it's a very unstable one.
+
+If anything happens, any
+small perturbation.
+
+If they go slightly
+to the left, they
+
+go all the way down.
+
+If they go slightly to the
+right, they go all the way up.
+
+So we call that an unstable
+statistic.
+
+So there is one unstable
+statistic and two stable ones.
+
+And those two stable ones is
+what we're talking about.
+
+They could be a poverty trap.
+
+Yes?
+
+AUDIENCE: Why are they moving
+toward that 45-degree line?
+
+PROFESSOR: Can someone
+explain that?
+
+You want to know why we are
+going horizontal to the
+
+45-degree line?
+
+Yeah.
+
+Can someone explain that once?
+
+And then I'll re-explain
+it as well.
+
+AUDIENCE: Because yesterday's
+income is going to be your
+
+today's income.
+
+And your today's income
+is going to be
+
+your tomorrow's income.
+
+So if we start with a value
+zero, so that value
+
+can come from work.
+
+It's going to be tomorrow's
+[INAUDIBLE].
+
+So if you get the income from
+work, the y-value of that will
+
+be your incurred income
+tomorrow.
+
+So you have to go to
+the 45-degree line.
+
+PROFESSOR: Exactly.
+
+The reason why we are using the
+horizontal line is that--
+
+so from y0, I know
+that I go to y1.
+
+And then I want to know,
+from y1 where do I go?
+
+For that I need to put
+y1 on the x-axis.
+
+And the 45-degree line allows
+me to do that because the
+
+45-degree line is where the
+vertical is equal to the
+
+horizontal.
+
+So I'm going right to find y1
+on the horizontal line which
+
+helps me to find it
+on the x-axis.
+
+And then I know that from
+y1, I go to y2.
+
+And then again horizontal, and
+then again vertical, and then
+
+again horizontal.
+
+That makes sense?
+
+Is it clear for everybody?
+
+It would be better if we were
+all on the same page.
+
+That we have that here.
+
+This is not obvious.
+
+It's not meant to be obvious.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+y0 or y1--
+
+PROFESSOR: So, the first
+one you mean?
+
+AUDIENCE: Oh, is that
+because that's the--
+
+PROFESSOR: That's the
+capacity curve.
+
+Exactly.
+
+Your y0 is what you
+start from.
+
+And then the curve gives us
+what is the relationship
+
+between income today and
+income tomorrow.
+
+So think of it with
+the food example.
+
+You start with some income.
+
+You decide how much to eat--
+let's say you eat
+
+80 percent of it--
+
+you eat it.
+
+That gives you some strength.
+
+You go work.
+
+That gives you some wage.
+
+That's your income from work.
+
+AUDIENCE: And then, when we're
+determining the distance
+
+between y0 and y1, is that
+determined just by the
+
+distance from the curve
+to the 45-degree line?
+
+PROFESSOR: Exactly.
+
+So y0 goes to y1.
+
+Do you understand the first
+vertical step here right?
+
+y0 goes to y1 for the
+first vertical step.
+
+And then we're looking for y1 on
+the vertical axis, but now
+
+we need to find a way
+to put it back on
+
+the horizontal axis.
+
+And the 45-degree line helps us
+to do that because on the
+
+45-degree line the vertical
+distance is the same as the
+
+horizontal distance.
+
+So the horizontal line is just
+a trick to help us find where
+
+is y1 on the horizontal axis,
+which helps us go to y2.
+
+That make sense?
+
+So from y0, I go to
+y1 vertically --
+
+that's just a capacity curve.
+
+Then the horizontal line
+is just to the left.
+
+Now what is the new y0?
+
+The new y0 is y1.
+
+And then again, we go
+vertically to y2.
+
+Horizontally to find it on
+the horizontal axis,
+
+vertically, et cetera.
+
+Yeah?
+
+AUDIENCE: What's the
+unit of time--
+
+PROFESSOR: The unit of time is
+whatever we think is the right
+
+unit of time depending on the
+problem we're looking at.
+
+So, for example, if it is food,
+that might be the date.
+
+If it's the income of your
+children, that may be a
+
+generation.
+
+In some sense, once we have
+decided what problem we are
+
+looking at, the unit of time
+doesn't really matter.
+
+We adjust to it.
+
+Yeah?
+
+AUDIENCE: How did you determine
+which states were
+
+stable and which ones
+were not stable?
+
+PROFESSOR: Well, look at it,
+and for any point, you're
+
+figuring out whether or not
+you're going to stay here.
+
+Whether things tend to bring you
+back here or things tend
+
+to pull you away from it.
+
+Think of it, for example,
+as magnets.
+
+Either they cling together or
+they are trying to go away.
+
+Or think of it as a stick.
+
+Does it stay vertical or
+does it fall down?
+
+Suppose that we start with
+income and the first income we
+
+are getting is y3.
+
+That's going to pull you.
+
+You're going to go vertical
+a little bit, horizontal a
+
+little bit, et cetera.
+
+That's going to pull
+you exactly
+
+at that first statistic.
+
+Right?
+
+So now, if you start from the
+first statistic and something
+
+slightly pushes you away from
+it, it is going to bring you
+
+back to it.
+
+If you are a little bit richer
+than the first statistic,
+
+you're going to, again, go back
+to the first statistic.
+
+If you're slightly richer,
+it's pulling you down.
+
+If you're slightly poorer,
+it's pulling you up.
+
+Now, if you're looking at the
+one that's here on top, that's
+
+the same thing.
+
+At the very top, if you're
+slightly poorer, it's pulling
+
+you up towards it.
+
+If you're slightly richer,
+it's pulling you
+
+down towards it.
+
+Now if you look at the one where
+the line intersects from
+
+below, if you're exactly
+at it, you stay at it.
+
+But if you're slightly poorer,
+where do you go?
+
+All the way down.
+
+If you're slightly richer,
+all the way up.
+
+So that one is not stable.
+
+So basically, you follow your
+arrows wherever they are going
+
+to take you.
+
+OK?
+
+Any more question?
+
+Yeah?
+
+AUDIENCE: What are the
+axis labels for it?
+
+Like income from work.
+
+I thought we were trying to
+connect on a time scale--
+
+PROFESSOR: Right, so it
+doesn't really matter.
+
+Think of it as income today
+versus income tomorrow.
+
+Or income that you inherited
+versus income
+
+that you create yourself.
+
+Whatever scales we are
+talking about.
+
+So in the food example, it would
+be the income you had at
+
+the end of today.
+
+And then, that would be
+inherited income you inherited
+
+from yesterday.
+
+And then the income from work
+would be the income of the end
+
+of the day.
+
+So here the scale would
+be one day.
+
+In the education example, you
+would go from your income to
+
+what your children will make.
+
+That's a whole generation.
+
+So the time scale, it depends
+on the problem.
+
+I think in the food example,
+it's useful to think of a day.
+
+In the health example
+it might be a month.
+
+AUDIENCE: Why is there a
+tendency to move to the
+
+intersections?
+
+PROFESSOR: Well, that's where
+the arrows are pulling you,
+
+aren't they?
+
+Because the closer of
+the intersection
+
+is where you are--
+
+first, you go from wherever
+you start to the curve.
+
+And then the curve is
+trying to go back to
+
+the 45-degree line.
+
+So the closer you are
+to the intersection,
+
+the less you move.
+
+Which is why this
+is, everything
+
+pulls you back there.
+
+--Not all the intersections.
+
+No, it's the stable ones.
+
+The one to the left and the
+one to the right, not the
+
+middle one.
+
+Which you have a tendency
+to go away from.
+
+Any other questions
+on how this works?
+
+Yeah?
+
+AUDIENCE: How do you guys
+actually gather the data to
+
+[INAUDIBLE]?
+
+PROFESSOR: So that's an
+excellent question.
+
+Right now, I've just
+asserted that it's
+
+the form of the curve.
+
+And then we have to go back to
+the question that a neighbor--
+
+whose name I don't know-- asked
+earlier, which is what
+
+is, actually, the shape
+of the curve?
+
+And that's a key question.
+
+That's going back to the
+questions we were asking in
+
+the case of education,
+for example.
+
+Is the relationship between
+income today and income
+
+tomorrow due to education?
+
+Is it really of this shape or
+is it of another shape?
+
+That's what we have to
+assert empirically.
+
+And it's going to have
+to be gathered on a
+
+case-by-case example.
+
+So for example, for food.
+
+To create this shape, to know
+what is the form of the shape,
+
+we are going to need
+to know two things.
+
+We need to know what is the
+relationship between how much
+
+income you have and how many
+calories you consume.
+
+And what is the relationship
+between the calories you
+
+consume and your
+work capacity?
+
+And the product of the two
+will be that curve.
+
+And the shape it has--
+
+God knows, I mean, actually even
+we know, but we're going
+
+to cover that next time.
+
+So this is assuming that
+the capacity curve
+
+indeed has this shape.
+
+Then we can see how the poverty
+trap can emerge.
+
+Now, if instead, the capacity
+curve had this shape--
+
+think of your example
+of education.
+
+And think that, in fact, the
+first few years of education
+
+are very valuable and the next
+years you guys are kind of
+
+wasting your time-- not to speak
+of me-- and the next
+
+years of education are
+not so valuable.
+
+What is really important is
+to learn how to read.
+
+Imagine that's the case.
+
+Then it means that the
+relationship between income
+
+today and income tomorrow
+is not as steep anymore.
+
+It starts very high and
+then it tapers off.
+
+And so we can play the same
+game again that we were
+
+playing before.
+
+We can say, well, let's draw
+the diagonal line.
+
+Let's start with some
+income, a1.
+
+To find out income tomorrow
+what do we do?
+
+We go vertical.
+
+We find income, a2.
+
+Then we have to go horizontal to
+the 45-degree line to find
+
+it on the horizontal line.
+
+We go vertical again to
+find it on the curve.
+
+Horizontal again,
+vertical again.
+
+Where do we end up?
+
+q.
+
+Now suppose we had started
+above q, where
+
+would we end up?
+
+q.
+
+Suppose we had started anywhere
+in between, where
+
+would we end up?
+
+q.
+
+So there is no poverty
+trap, in this case.
+
+If there is only one
+intersection because the
+
+returns are first high and then
+low, then there won't be
+
+a poverty trap.
+
+It doesn't mean that there is no
+relationship between income
+
+today and income tomorrow.
+
+There is one.
+
+But the point is, that
+relationship is first steep
+
+and then tapers off.
+
+So for example, imagine that
+the only type of businesses
+
+that you can run are businesses
+
+that you can run yourself.
+
+That for some reason, you are in
+a business where you can't
+
+really have employees.
+
+Imagine.
+
+So in that case, your first
+investment will be quite
+
+valuable, right?
+
+But then, eventually, you can't
+really add much more
+
+because you won't have
+enough time to sell
+
+all of these things.
+
+So your first dollars invested
+will have a very high return.
+
+And then less and less
+and less and less.
+
+And so in that case, everybody
+will end up at the same place.
+
+An example that could make it
+clear, is going back to our
+
+Kenyan farmer from the MTV
+video, Kennedy fertilizer.
+
+If you put fertilizer
+on your crop--
+
+well when you put just
+a little bit, the
+
+effects are very high.
+
+But when you start putting more,
+eventually, the soil
+
+can't absorb it so the
+effects are less and
+
+less and less high.
+
+So even if you don't have enough
+to put on your entire
+
+field to start with, you could
+imagine that you would first
+
+put it in the most productive
+part of your field.
+
+Because the first unit of
+fertilizer you are putting is
+
+very high return.
+
+The second, you need less
+because you're going to the
+
+place of your field that is
+less productive anyway.
+
+At the third, you
+need even less.
+
+The fourth is really not that
+productive because, now, you
+
+end up putting more where
+you started from
+
+in the first place.
+
+So that's not really
+helpful anymore.
+
+So in that case, the returns
+don't have this S-shape.
+
+They have this inverted
+L-shape.
+
+So in that case, there
+is no poverty trap.
+
+And so that is where the
+question that you were asking
+
+is essential.
+
+Which is, how do we know what
+the shape of this curve?
+
+Because the shape of this curve
+is going to crucially
+
+determine whether or
+not we have a trap.
+
+And what I want you to remember
+is that that's more
+
+than a relationship
+between income
+
+today and income tomorrow.
+
+It has to be this relationship
+of this shape.
+
+So that's the first thing, which
+is if the relationship
+
+is inverted--
+
+L-shaped like that, which
+is the canonical case in
+
+economics, most of our
+economics model--
+
+what you learn in 14.01--
+
+has production function
+of this form.
+
+Where this production function,
+which we called,
+
+have decreasing returns.
+
+Where the first unit invested is
+very profitable and then it
+
+becomes less and less
+profitable.
+
+We've already discussed a number
+of reasons why the
+
+returns might not would
+always be decreasing.
+
+For example, we discussed the
+case of calories where there
+
+might be an increasing zone and
+then a decreasing zone.
+
+We discussed education might
+or might not be that way.
+
+We got an interesting example
+about businesses where you
+
+might not have a very profitable
+opportunity for
+
+your business if you don't
+have enough money.
+
+We discussed savings, which may
+or may not have this form.
+
+Where nobody wants your
+small savings.
+
+So there are reasons
+why it may not
+
+always be inverted L-shaped.
+
+But if it is inverted L-shaped
+there won't be a poverty trap.
+
+--You might be very bored with
+me repeating the same thing
+
+for the fifth time now, but
+the reason why I insist is
+
+that this is a confusion that
+we hear over and over again
+
+among policy makers.
+
+In the policy discourse,
+whenever they're thinking of a
+
+double feedback loop--
+
+for example, kids who have
+less education, make less
+
+money, and parents who have
+less money send their kids
+
+less to school.
+
+Immediately, people think, ha!
+
+If there is a double feedback
+loop like that, that creates a
+
+poverty trap.
+
+And the point is, that that's
+not sufficient.
+
+That's necessary but that's
+not sufficient.
+
+Because if the double feedback
+loop gives you a nice inverted
+
+L-shape, eventually, everybody
+will end up
+
+nicely in the same place.
+
+OK?
+
+So there is more, which is, here
+is another case where we
+
+have an S-shaped curve.
+
+But the S-shaped curve is a
+little different, it's a
+
+little higher.
+
+So why would it be a little
+higher, for example?
+
+Why has it moved up compared
+to what we had before?
+
+Why could it have moved up?
+
+Go back to the food example.
+
+Sorry?
+
+AUDIENCE: Lower food prices.
+
+PROFESSOR: Lower food prices.
+
+So for example, the productivity
+of the land might
+
+have gone up.
+
+Maybe the government came and
+built some irrigation dams and
+
+the productivity of
+land has gone up.
+
+So to produce the same amount of
+food you need less effort.
+
+So the work capacity translates
+into a higher
+
+income for moi.
+
+So for whatever reason,
+the curve shifts up.
+
+So then what happened--
+
+we gave some person
+some income, y0.
+
+We find y1 by going vertical.
+
+We find it again on the
+horizontal line, y1.
+
+Going back to y2, horizontal
+again.
+
+Et cetera, et cetera.
+
+Where do we end up?
+
+At the intersection.
+
+And now there's only
+one intersection.
+
+So wherever we start, we are
+going to end up at the same
+
+intersection.
+
+In that case, is there going
+to be a poverty trap?
+
+No.
+
+In that case there is no poverty
+trap because, again,
+
+there is one statistic.
+
+So an S-shape is not even a
+sufficient condition for a
+
+poverty trap.
+
+It is necessary but it's
+not sufficient.
+
+Let's find another example,
+which is this one.
+
+Where in fact, now it's
+the opposite.
+
+There was some flood
+and the land is now
+
+completely washed out.
+
+So people are very
+unproductive.
+
+They have to work very hard
+to produce very little.
+
+So what happened to
+my poor S-shape?
+
+It's shifted to the
+southwest, right?
+
+So now if I start from y0--
+
+quite high-- where do I go?
+
+So I go up, but then
+it's not enough.
+
+The 45-degree line
+is to the left.
+
+I have to go left, down
+again, down again,
+
+down again, and again.
+
+I'm going to end up at the
+single intersection where I'm
+
+always pulled up, which
+is a very low income.
+
+So in a sense, there is no
+poverty trap here either.
+
+Because it's not that if you're
+poor, you'll stay poor,
+
+and if you're rich,
+you'll stay rich.
+
+Regardless, you're
+going to be poor.
+
+AUDIENCE: [LAUGHTER]
+
+PROFESSOR: So you could think
+it's a universal poverty trap
+
+or you can think that's
+just the way is.
+
+Because if you ignore the right
+side, we almost are in
+
+the inverted L-shape except
+there are stuff that are a
+
+little bit irrelevant
+to the right.
+
+The reason why they are
+irrelevant is that,
+
+eventually, everybody's
+becoming poor anyway.
+
+So again, we don't have
+a poverty trap.
+
+So let's look at those
+three examples.
+
+That's an example with
+a poverty trap.
+
+That's an example that
+doesn't have one.
+
+That's another example that
+doesn't have one.
+
+What is different between the
+one example with the poverty
+
+trap and the one which
+doesn't have one--
+
+or two?
+
+Yes.
+
+Can you tell me your name?
+
+AUDIENCE: Zachary--
+
+PROFESSOR: Zachary.
+
+AUDIENCE: --it crosses the
+45-degree line twice.
+
+PROFESSOR: Exactly.
+
+Well, twice or--
+
+AUDIENCE: Three times.
+
+PROFESSOR: Three times.
+
+It crosses the 45-degree
+line once from below.
+
+So the rule is that you're going
+to have a poverty trap
+
+if the capacity curve--
+
+or whatever is the curve between
+the income from work
+
+and the inherited income--
+
+crosses the 45-degree line,
+at least once, from below.
+
+That is, there is at least one
+unstable equilibrium where
+
+you're crossing from below.
+
+And that is necessary for
+having a poverty trap.
+
+So what you need, in other
+words, is to have a zone where
+
+income is accelerating.
+
+And this zone must to be at a
+place where the income was
+
+relatively low to start with.
+
+And it needs to accelerate
+enough that it's becoming high
+
+to start with.
+
+In other words, it needs to be
+a zone where, if you're below
+
+the zone, you're making
+less tomorrow than you
+
+started from today.
+
+And when you're on the right
+of the zone, you're making
+
+more tomorrow than you
+started from today.
+
+And you need to have
+this point.
+
+Otherwise, there is
+no poverty trap.
+
+All right?
+
+So that's the mathematical
+expression of it.
+
+And now, in a sense, the game
+that we're going to play all
+
+around this class is
+to be looking for--
+
+are we in this situation where
+whatever is the relationship
+
+between income today and income
+tomorrow crosses the
+
+45-degree line from below.
+
+Or are we not in
+this situation.
+
+And now we are in a much better
+position to ask the
+
+question that Zach asked at the
+beginning of the question
+
+which is, are we really
+believing that there could be
+
+a poverty trap based on food?
+
+I didn't want to answer his
+question to start with because
+
+I needed some time to specify
+the question in a much more
+
+precise way.
+
+Now we can re-ask the question
+and say, is it really possible
+
+that the relationship between
+the calories I consume and my
+
+strength has this specific form
+where it intersects the
+
+45-degree line from below?
+
+And how does that intersect with
+the fact that I choose
+
+how much to consume?
+
+Because, of course, if there
+is indeed a strong
+
+relationship between the
+calories consumed and the work
+
+capacity, then people should
+try and get out of it by
+
+eating as much as possible
+when they are very poor.
+
+So to the extent that people
+can choose how much to
+
+consume, how much food to eat,
+they should eat more when they
+
+are very poor in order to try
+and pull themselves to the
+
+right of this point.
+
+And when they are richer then
+it wouldn't really matter.
+
+So they would eat less.
+
+So that would create a force
+that goes against an S-shape
+
+for the capacity curve.
+
+So we have to see--
+
+and that goes back to
+your question, where
+
+do you get it from?
+
+Well, we get it from looking at
+the data and looking at--
+
+to what extent people who have
+more money eat so much more,
+
+and to what extent people who
+eat so much more are so much
+
+more productive.
+
+And that's what we
+are going to do.
+
+We are going to do
+it for food.
+
+But now that we understand the
+principle for food, we are
+
+going to do it for education.
+
+We are going to do it for
+health, we are going to do it
+
+for savings, for businesses,
+et cetera.
+
+Yeah?
+
+AUDIENCE: To go back to the
+example with the start of the
+
+class, would you say that--
+
+I forgot his name but-- that
+the man was at an unstable
+
+equilibrium since as soon as he
+lost his job, he seemed to
+
+go down and not be able
+to eat enough to get
+
+another job, et cetera?
+
+PROFESSOR: Right.
+
+So that's a very
+good question.
+
+What we can try now is to
+re-interpret Mister Solhin's
+
+story in the context of this.
+
+And you could say, well perhaps,
+it was exactly
+
+something like that.
+
+So what would have
+happened to him?
+
+Let's see, I want to--
+
+oops.
+
+What would have happened
+to him?
+
+So we discussed that one thing
+that might have happened to
+
+him is that something happened
+to the capacity curve, right?
+
+We were saying that coincident
+decrease in the wage and
+
+increase in the food prices
+means that the capacity curve
+
+tends to move to
+the southwest.
+
+So assume that Pak Solhin
+was at the high
+
+equilibrium up there.
+
+Right?
+
+But right there.
+
+And then the curve moves
+slightly to the right.
+
+Then, with the same income, he
+suddenly is now below what
+
+would correspond to the new
+equilibrium and it would start
+
+falling down, down,
+down, down.
+
+And once he starts going down,
+there is no going up again.
+
+It could also have
+eliminated--
+
+we might also be in a situation
+where, at the
+
+beginning there was just
+one equilibrium--
+
+so we were, for example
+in this situation--
+
+and then once the curve moves
+down, they are now two
+
+equilibria, including
+the unstable one.
+
+So we may have started, in the
+former situation, where people
+
+were productive enough that they
+were always moving up.
+
+And then, with the increase in
+food prices and the decrease
+
+in wages, that curve shifts down
+and now it creates two
+
+equilibria.
+
+So some people get trapped
+like he was.
+
+What was interesting in Pak
+Solhin's villages is that, in
+
+the same villages, I
+met people who were
+
+happily eating enough.
+
+So it seemed that there was both
+kinds, which makes you
+
+think that these two things
+were coexisting.
+
+So maybe what happened with him
+is that we started from a
+
+situation like that, and then
+we moved left and we end up
+
+with this double situation.
+
+That's possible
+
+So what we had in the
+Sachs-Jolie video is--
+
+we said when we just
+started the class--
+
+lots of examples of
+poverty traps.
+
+And in each case, we could try
+and think, well, what makes us
+
+think that there is indeed a
+poverty trap in this case?
+
+Or what makes us think that
+maybe there is no poverty trap
+
+in this case?
+
+So one example is what
+happened with the
+
+farmer that they meet.
+
+So they claim that there
+was a poverty trap.
+
+So what is the implicit argument
+that they had in mind
+
+that would help us think that,
+for a farmer, the decision to
+
+use fertilizer corresponds
+to that
+
+problem versus that problem?
+
+What do we need to know about
+fertilizer and fertilizer use
+
+to try and sort out whether we
+are in the situation that they
+
+talk about or in the
+other situation.
+
+Yeah?
+
+You go ahead, I have
+a problem.
+
+AUDIENCE: You need to know if
+there is some minimum of
+
+fertilizer used that becomes
+useful for the farmer.
+
+PROFESSOR: Right.
+
+So there could be that, minimum
+fertilizer used.
+
+But why would there be a minimum
+fertilizer used?
+
+Yeah?
+
+AUDIENCE: Maybe it's super
+difficult to acquire small
+
+quantities of fertilizer.
+
+PROFESSOR: So for example,
+it might be sold by
+
+the bag or 50 kg.
+
+So in that case, what we have
+is not so much S-shaped but
+
+something which is a degenerated
+S where you get
+
+nothing if you can't invest
+enough and then you get the
+
+return which are, potentially,
+very steep at the beginning.
+
+So instead of a nice little
+curvy S, we have a flat part
+
+and then an inverted L.
+
+But if we have a flat part and
+then the inverted L, it would
+
+still work like an S. Because
+there would still be an
+
+intersection where the curve
+intersects from above on the
+
+flat part, an intersection where
+it intersects from below
+
+at the beginning of the
+L-shape, and another
+
+intersection where it intersects
+from above at the
+
+end of the L-shape.
+
+So the S doesn't have to be a
+proper S. It could be a flat
+
+part and then an inverted L. So
+this example could be one,
+
+which is you can only buy
+fertilizer by the 50 kg.
+
+What other situation
+could we find?
+
+Yeah?
+
+AUDIENCE: The percentage of
+chance for success in using
+
+fertilizer.
+
+So if you only had [INAUDIBLE]
+over a small plot of land, it
+
+is, like, 20% chance
+of actually
+
+improving your crop yield.
+
+You would have to use a larger
+quantity to actually get an
+
+improved crop yield.
+
+PROFESSOR: So that could be a
+possibility if the chance of
+
+success depends on
+how much you use.
+
+I think it's not very likely
+that it would be a purely
+
+physical thing because
+fertilizer is quite scalable.
+
+But one way in which we could
+have your story is if, to use
+
+fertilizer it requires
+some learning.
+
+And there's no point doing
+all that learning--
+
+and asking all of your neighbors
+how they do it, and
+
+try to understand
+how they do it.
+
+Maybe experiment a little bit,
+maybe it won't work first.
+
+--Maybe there is no point to
+go through all of this
+
+learning if, at the end of the
+day, you know that, no matter
+
+what, you will always be able
+to use just a little bit.
+
+So that would be one way
+in which you would,
+
+again, create this.
+
+You're not going to use any
+fertilizer if you know that
+
+you, eventually, would be able
+to use it on the substantial
+
+part of your field.
+
+Yeah?
+
+AUDIENCE: I think that the main
+point they made in the
+
+video is that there needed
+to be an initial push.
+
+So they needed a lot of
+fertilizer and you needed to
+
+put it on all of the crops for
+it to make a big impact.
+
+And the fact is, if you have a
+little bit of fertilizer-- the
+
+point was why couldn't
+they invest?
+
+So save would be paying for a
+little bit of fertilizer.
+
+And then buy more fertilizer and
+then continue to grow it
+
+until [INAUDIBLE].
+
+You know, if you started off
+with a small amount, you
+
+couldn't really invest
+and grow your yield
+
+to make more money.
+
+PROFESSOR: Right.
+
+Then the third possibility is
+that if you invest just a
+
+little bit--
+
+let's say fertilizer scales
+nicely, so you can invest just
+
+a little bit and
+you can do it.
+
+But then, you're going to make
+just a little bit more money.
+
+And then we need some other
+mechanism which means that
+
+saving a little bit more money
+is not feasible, or people are
+
+not going to do it.
+
+So then we need to bring in
+something else which is along
+
+the line of what we
+were discussing
+
+earlier in the class.
+
+We need to bring in something
+else which is, the banks are
+
+not going to take your small
+amount of money.
+
+Or if you have a small amount
+of money, you are
+
+going to waste it.
+
+But if you have a lot, now
+that's enough money to be
+
+worthwhile and you're
+going to keep it.
+
+All right.
+
+So we are going to end
+here for today.
+
+So make sure you understand this
+because we are not ready
+
+to go back to it formally a lot,
+but this is going to be
+
+with us all the time.
+
+And on Tuesday, we are going
+to go through experiments.
\ No newline at end of file
diff --git a/84LF3ze7Yvw.txt b/84LF3ze7Yvw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fea06c2884ecb4a5198f7af189f6f0342e198993
--- /dev/null
+++ b/84LF3ze7Yvw.txt
@@ -0,0 +1,9707 @@
+align:start position:0%
+ 
+so today my plan is to finish the open
+
+ align:start position:0%
+so today my plan is to finish the open
+ 
+
+ align:start position:0%
+so today my plan is to finish the open
+economy part of the course and uh we
+
+ align:start position:0%
+economy part of the course and uh we
+ 
+
+ align:start position:0%
+economy part of the course and uh we
+will talk about exchange regimes but but
+
+ align:start position:0%
+will talk about exchange regimes but but
+ 
+
+ align:start position:0%
+will talk about exchange regimes but but
+before I do that I need to
+
+ align:start position:0%
+before I do that I need to
+ 
+
+ align:start position:0%
+before I do that I need to
+finish er a few things that we didn't in
+
+ align:start position:0%
+finish er a few things that we didn't in
+ 
+
+ align:start position:0%
+finish er a few things that we didn't in
+previous lecture and that will help us
+
+ align:start position:0%
+previous lecture and that will help us
+ 
+
+ align:start position:0%
+previous lecture and that will help us
+an introduction for the kind of things I
+
+ align:start position:0%
+an introduction for the kind of things I
+ 
+
+ align:start position:0%
+an introduction for the kind of things I
+want to talk about today and uh let me
+
+ align:start position:0%
+want to talk about today and uh let me
+ 
+
+ align:start position:0%
+want to talk about today and uh let me
+start just reviewing that last H slide
+
+ align:start position:0%
+start just reviewing that last H slide
+ 
+
+ align:start position:0%
+start just reviewing that last H slide
+that we discussed H which is the Mandel
+
+ align:start position:0%
+that we discussed H which is the Mandel
+ 
+
+ align:start position:0%
+that we discussed H which is the Mandel
+flaming model and the Mandel flaming
+
+ align:start position:0%
+flaming model and the Mandel flaming
+ 
+
+ align:start position:0%
+flaming model and the Mandel flaming
+model essentially is our old islm model
+
+ align:start position:0%
+model essentially is our old islm model
+ 
+
+ align:start position:0%
+model essentially is our old islm model
+in which the as is a little different
+
+ align:start position:0%
+in which the as is a little different
+ 
+
+ align:start position:0%
+in which the as is a little different
+because now we have a net exports term H
+
+ align:start position:0%
+because now we have a net exports term H
+ 
+
+ align:start position:0%
+because now we have a net exports term H
+which is a function of new things like
+
+ align:start position:0%
+which is a function of new things like
+ 
+
+ align:start position:0%
+which is a function of new things like
+foreign output foreign income and the
+
+ align:start position:0%
+foreign output foreign income and the
+ 
+
+ align:start position:0%
+foreign output foreign income and the
+and most importantly the real exchange
+
+ align:start position:0%
+and most importantly the real exchange
+ 
+
+ align:start position:0%
+and most importantly the real exchange
+rate and the real Exchange in itself
+
+ align:start position:0%
+rate and the real Exchange in itself
+ 
+
+ align:start position:0%
+rate and the real Exchange in itself
+because of the uip and coverity
+
+ align:start position:0%
+because of the uip and coverity
+ 
+
+ align:start position:0%
+because of the uip and coverity
+condition is a function of expected
+
+ align:start position:0%
+condition is a function of expected
+ 
+
+ align:start position:0%
+condition is a function of expected
+exchange rate the the intern foreign
+
+ align:start position:0%
+exchange rate the the intern foreign
+ 
+
+ align:start position:0%
+exchange rate the the intern foreign
+interest rate and it also gives yet
+
+ align:start position:0%
+interest rate and it also gives yet
+ 
+
+ align:start position:0%
+interest rate and it also gives yet
+another reason for why H the interest
+
+ align:start position:0%
+another reason for why H the interest
+ 
+
+ align:start position:0%
+another reason for why H the interest
+rate affects H domestic aggregate demand
+
+ align:start position:0%
+rate affects H domestic aggregate demand
+ 
+
+ align:start position:0%
+rate affects H domestic aggregate demand
+okay there's a there a there's a the
+
+ align:start position:0%
+okay there's a there a there's a the
+ 
+
+ align:start position:0%
+okay there's a there a there's a the
+traditional investment effect of an
+
+ align:start position:0%
+traditional investment effect of an
+ 
+
+ align:start position:0%
+traditional investment effect of an
+increase in interest rate but we also
+
+ align:start position:0%
+increase in interest rate but we also
+ 
+
+ align:start position:0%
+increase in interest rate but we also
+get um the appreciation effect of an
+
+ align:start position:0%
+get um the appreciation effect of an
+ 
+
+ align:start position:0%
+get um the appreciation effect of an
+increasing the interest rate which is
+
+ align:start position:0%
+increasing the interest rate which is
+ 
+
+ align:start position:0%
+increasing the interest rate which is
+contractionary from the point of view of
+
+ align:start position:0%
+contractionary from the point of view of
+ 
+
+ align:start position:0%
+contractionary from the point of view of
+agregate demand so but this is like that
+
+ align:start position:0%
+agregate demand so but this is like that
+ 
+
+ align:start position:0%
+agregate demand so but this is like that
+with this extra net export term and and
+
+ align:start position:0%
+with this extra net export term and and
+ 
+
+ align:start position:0%
+with this extra net export term and and
+in this diagram you know for this we
+
+ align:start position:0%
+in this diagram you know for this we
+ 
+
+ align:start position:0%
+in this diagram you know for this we
+have the same interest right here from
+
+ align:start position:0%
+have the same interest right here from
+ 
+
+ align:start position:0%
+have the same interest right here from
+this diagram which which portrays the
+
+ align:start position:0%
+this diagram which which portrays the
+ 
+
+ align:start position:0%
+this diagram which which portrays the
+uncovered interest by the condition we
+
+ align:start position:0%
+uncovered interest by the condition we
+ 
+
+ align:start position:0%
+uncovered interest by the condition we
+can get for any given International
+
+ align:start position:0%
+can get for any given International
+ 
+
+ align:start position:0%
+can get for any given International
+interest rate and expected exchange rate
+
+ align:start position:0%
+interest rate and expected exchange rate
+ 
+
+ align:start position:0%
+interest rate and expected exchange rate
+for next period uh we can get the
+
+ align:start position:0%
+for next period uh we can get the
+ 
+
+ align:start position:0%
+for next period uh we can get the
+current exchange okay so that was our
+
+ align:start position:0%
+current exchange okay so that was our
+ 
+
+ align:start position:0%
+current exchange okay so that was our
+model and we did a few experiments here
+
+ align:start position:0%
+model and we did a few experiments here
+ 
+
+ align:start position:0%
+model and we did a few experiments here
+the first one was well what happens if
+
+ align:start position:0%
+the first one was well what happens if
+ 
+
+ align:start position:0%
+the first one was well what happens if
+the spected exchang rate goes up the
+
+ align:start position:0%
+the spected exchang rate goes up the
+ 
+
+ align:start position:0%
+the spected exchang rate goes up the
+first thing is which curves move well if
+
+ align:start position:0%
+first thing is which curves move well if
+ 
+
+ align:start position:0%
+first thing is which curves move well if
+the expected exchange goes up then I
+
+ align:start position:0%
+the expected exchange goes up then I
+ 
+
+ align:start position:0%
+the expected exchange goes up then I
+know that for any given interest rate H
+
+ align:start position:0%
+know that for any given interest rate H
+ 
+
+ align:start position:0%
+know that for any given interest rate H
+the current exchanger will go up okay I
+
+ align:start position:0%
+the current exchanger will go up okay I
+ 
+
+ align:start position:0%
+the current exchanger will go up okay I
+know that this curve in other words will
+
+ align:start position:0%
+know that this curve in other words will
+ 
+
+ align:start position:0%
+know that this curve in other words will
+shift to the right why do I know that
+
+ align:start position:0%
+shift to the right why do I know that
+ 
+
+ align:start position:0%
+shift to the right why do I know that
+well because if the current exchange
+
+ align:start position:0%
+well because if the current exchange
+ 
+
+ align:start position:0%
+well because if the current exchange
+rate doesn't move by the same amount of
+
+ align:start position:0%
+rate doesn't move by the same amount of
+ 
+
+ align:start position:0%
+rate doesn't move by the same amount of
+expected exchange rate now I'm going to
+
+ align:start position:0%
+expected exchange rate now I'm going to
+ 
+
+ align:start position:0%
+expected exchange rate now I'm going to
+expect I'm going to have expected
+
+ align:start position:0%
+expect I'm going to have expected
+ 
+
+ align:start position:0%
+expect I'm going to have expected
+capital gain or loss which will be
+
+ align:start position:0%
+capital gain or loss which will be
+ 
+
+ align:start position:0%
+capital gain or loss which will be
+inconsistent with the previous parity of
+
+ align:start position:0%
+inconsistent with the previous parity of
+ 
+
+ align:start position:0%
+inconsistent with the previous parity of
+interest rate no so we had agreed that
+
+ align:start position:0%
+interest rate no so we had agreed that
+ 
+
+ align:start position:0%
+interest rate no so we had agreed that
+you know that we had certain expected
+
+ align:start position:0%
+you know that we had certain expected
+ 
+
+ align:start position:0%
+you know that we had certain expected
+appreciation let's make it very simple
+
+ align:start position:0%
+appreciation let's make it very simple
+ 
+
+ align:start position:0%
+appreciation let's make it very simple
+suppose that this interest rate happens
+
+ align:start position:0%
+suppose that this interest rate happens
+ 
+
+ align:start position:0%
+suppose that this interest rate happens
+to be equal to International interest
+
+ align:start position:0%
+to be equal to International interest
+ 
+
+ align:start position:0%
+to be equal to International interest
+rate then we know that this exchange
+
+ align:start position:0%
+rate then we know that this exchange
+ 
+
+ align:start position:0%
+rate then we know that this exchange
+rate has to be equal to the expected
+
+ align:start position:0%
+rate has to be equal to the expected
+ 
+
+ align:start position:0%
+rate has to be equal to the expected
+exchange rate because you cannot expect
+
+ align:start position:0%
+exchange rate because you cannot expect
+ 
+
+ align:start position:0%
+exchange rate because you cannot expect
+an appreciation or depreciation of the
+
+ align:start position:0%
+an appreciation or depreciation of the
+ 
+
+ align:start position:0%
+an appreciation or depreciation of the
+currency the interest rate that they
+
+ align:start position:0%
+currency the interest rate that they
+ 
+
+ align:start position:0%
+currency the interest rate that they
+same but if now the expected exchange
+
+ align:start position:0%
+same but if now the expected exchange
+ 
+
+ align:start position:0%
+same but if now the expected exchange
+Next Period goes up and it exchange rate
+
+ align:start position:0%
+Next Period goes up and it exchange rate
+ 
+
+ align:start position:0%
+Next Period goes up and it exchange rate
+today doesn't move that would mean that
+
+ align:start position:0%
+today doesn't move that would mean that
+ 
+
+ align:start position:0%
+today doesn't move that would mean that
+you expect also capital A an
+
+ align:start position:0%
+you expect also capital A an
+ 
+
+ align:start position:0%
+you expect also capital A an
+appreciation of the currency and which
+
+ align:start position:0%
+appreciation of the currency and which
+ 
+
+ align:start position:0%
+appreciation of the currency and which
+means that investing in domestic bonds
+
+ align:start position:0%
+means that investing in domestic bonds
+ 
+
+ align:start position:0%
+means that investing in domestic bonds
+would give you a higher return because
+
+ align:start position:0%
+would give you a higher return because
+ 
+
+ align:start position:0%
+would give you a higher return because
+the same interest rate plus expectation
+
+ align:start position:0%
+the same interest rate plus expectation
+ 
+
+ align:start position:0%
+the same interest rate plus expectation
+so we know that the uncovering condition
+
+ align:start position:0%
+so we know that the uncovering condition
+ 
+
+ align:start position:0%
+so we know that the uncovering condition
+will move to the right know as a result
+
+ align:start position:0%
+will move to the right know as a result
+ 
+
+ align:start position:0%
+will move to the right know as a result
+of the increase in expected exchange
+
+ align:start position:0%
+of the increase in expected exchange
+ 
+
+ align:start position:0%
+of the increase in expected exchange
+rate but that also means that any given
+
+ align:start position:0%
+rate but that also means that any given
+ 
+
+ align:start position:0%
+rate but that also means that any given
+interest rate you get a higher an an
+
+ align:start position:0%
+interest rate you get a higher an an
+ 
+
+ align:start position:0%
+interest rate you get a higher an an
+appreciated exchange relative to the
+
+ align:start position:0%
+appreciated exchange relative to the
+ 
+
+ align:start position:0%
+appreciated exchange relative to the
+previous one before the increase in the
+
+ align:start position:0%
+previous one before the increase in the
+ 
+
+ align:start position:0%
+previous one before the increase in the
+spected ex change rate which means that
+
+ align:start position:0%
+spected ex change rate which means that
+ 
+
+ align:start position:0%
+spected ex change rate which means that
+the is Will shift to the
+
+ align:start position:0%
+the is Will shift to the
+ 
+
+ align:start position:0%
+the is Will shift to the
+left so if the expected changer goes up
+
+ align:start position:0%
+left so if the expected changer goes up
+ 
+
+ align:start position:0%
+left so if the expected changer goes up
+that leads to an appreciation and that
+
+ align:start position:0%
+that leads to an appreciation and that
+ 
+
+ align:start position:0%
+that leads to an appreciation and that
+leads to contraction in aggregate
+
+ align:start position:0%
+leads to contraction in aggregate
+ 
+
+ align:start position:0%
+leads to contraction in aggregate
+demand okay
+
+ align:start position:0%
+demand okay
+ 
+
+ align:start position:0%
+demand okay
+good next experiment was well what
+
+ align:start position:0%
+good next experiment was well what
+ 
+
+ align:start position:0%
+good next experiment was well what
+happens if foreign output comes down
+
+ align:start position:0%
+happens if foreign output comes down
+ 
+
+ align:start position:0%
+happens if foreign output comes down
+well if foreign output comes down then
+
+ align:start position:0%
+well if foreign output comes down then
+ 
+
+ align:start position:0%
+well if foreign output comes down then
+that has nothing to do with the intar
+
+ align:start position:0%
+that has nothing to do with the intar
+ 
+
+ align:start position:0%
+that has nothing to do with the intar
+condition it's not doesn't show up in
+
+ align:start position:0%
+condition it's not doesn't show up in
+ 
+
+ align:start position:0%
+condition it's not doesn't show up in
+this expression but it does shift this
+
+ align:start position:0%
+this expression but it does shift this
+ 
+
+ align:start position:0%
+this expression but it does shift this
+no because it's usces our exports for
+
+ align:start position:0%
+no because it's usces our exports for
+ 
+
+ align:start position:0%
+no because it's usces our exports for
+any given level of interest rate and
+
+ align:start position:0%
+any given level of interest rate and
+ 
+
+ align:start position:0%
+any given level of interest rate and
+output and so they yes shift to the left
+
+ align:start position:0%
+output and so they yes shift to the left
+ 
+
+ align:start position:0%
+output and so they yes shift to the left
+that's contraction that's a way you
+
+ align:start position:0%
+that's contraction that's a way you
+ 
+
+ align:start position:0%
+that's contraction that's a way you
+import a recession from the rest of the
+
+ align:start position:0%
+import a recession from the rest of the
+ 
+
+ align:start position:0%
+import a recession from the rest of the
+world okay as I said before people
+
+ align:start position:0%
+world okay as I said before people
+ 
+
+ align:start position:0%
+world okay as I said before people
+around Asia and and Latin America are
+
+ align:start position:0%
+around Asia and and Latin America are
+ 
+
+ align:start position:0%
+around Asia and and Latin America are
+very very worried about the Chinese
+
+ align:start position:0%
+very very worried about the Chinese
+ 
+
+ align:start position:0%
+very very worried about the Chinese
+actually the Europeans as well because
+
+ align:start position:0%
+actually the Europeans as well because
+ 
+
+ align:start position:0%
+actually the Europeans as well because
+Germany exports a lot to China are very
+
+ align:start position:0%
+Germany exports a lot to China are very
+ 
+
+ align:start position:0%
+Germany exports a lot to China are very
+worried about contractions in China and
+
+ align:start position:0%
+worried about contractions in China and
+ 
+
+ align:start position:0%
+worried about contractions in China and
+so on because through that channel is
+
+ align:start position:0%
+so on because through that channel is
+ 
+
+ align:start position:0%
+so on because through that channel is
+contractionary as well now we're in the
+
+ align:start position:0%
+contractionary as well now we're in the
+ 
+
+ align:start position:0%
+contractionary as well now we're in the
+other part of the of the cycle because
+
+ align:start position:0%
+other part of the of the cycle because
+ 
+
+ align:start position:0%
+other part of the of the cycle because
+China is
+
+ align:start position:0%
+China is
+ 
+
+ align:start position:0%
+China is
+reopening and and that sort of gives
+
+ align:start position:0%
+reopening and and that sort of gives
+ 
+
+ align:start position:0%
+reopening and and that sort of gives
+lots of Hope to Europe and so on and and
+
+ align:start position:0%
+lots of Hope to Europe and so on and and
+ 
+
+ align:start position:0%
+lots of Hope to Europe and so on and and
+one of the reasons why the Euro has
+
+ align:start position:0%
+one of the reasons why the Euro has
+ 
+
+ align:start position:0%
+one of the reasons why the Euro has
+appreciated vaves the the dollar
+
+ align:start position:0%
+appreciated vaves the the dollar
+ 
+
+ align:start position:0%
+appreciated vaves the the dollar
+recently okay um and then the last
+
+ align:start position:0%
+recently okay um and then the last
+ 
+
+ align:start position:0%
+recently okay um and then the last
+experiment that I don't remember whether
+
+ align:start position:0%
+experiment that I don't remember whether
+ 
+
+ align:start position:0%
+experiment that I don't remember whether
+we finish or not I think I said it very
+
+ align:start position:0%
+we finish or not I think I said it very
+ 
+
+ align:start position:0%
+we finish or not I think I said it very
+quickly is well what happens if the
+
+ align:start position:0%
+quickly is well what happens if the
+ 
+
+ align:start position:0%
+quickly is well what happens if the
+international interest rate goes
+
+ align:start position:0%
+international interest rate goes
+ 
+
+ align:start position:0%
+international interest rate goes
+up what moves well the first thing that
+
+ align:start position:0%
+up what moves well the first thing that
+ 
+
+ align:start position:0%
+up what moves well the first thing that
+will move is this this was a parameter
+
+ align:start position:0%
+will move is this this was a parameter
+ 
+
+ align:start position:0%
+will move is this this was a parameter
+okay so what do I know that if I keep
+
+ align:start position:0%
+okay so what do I know that if I keep
+ 
+
+ align:start position:0%
+okay so what do I know that if I keep
+the interest rate constant and the
+
+ align:start position:0%
+the interest rate constant and the
+ 
+
+ align:start position:0%
+the interest rate constant and the
+international interest rate went up what
+
+ align:start position:0%
+international interest rate went up what
+ 
+
+ align:start position:0%
+international interest rate went up what
+has to happen to the exch and the
+
+ align:start position:0%
+has to happen to the exch and the
+ 
+
+ align:start position:0%
+has to happen to the exch and the
+spected exchange hasn't changed what has
+
+ align:start position:0%
+spected exchange hasn't changed what has
+ 
+
+ align:start position:0%
+spected exchange hasn't changed what has
+to happen to the exchanger today to be
+
+ align:start position:0%
+to happen to the exchanger today to be
+ 
+
+ align:start position:0%
+to happen to the exchanger today to be
+different between the two things the two
+
+ align:start position:0%
+different between the two things the two
+ 
+
+ align:start position:0%
+different between the two things the two
+bones so this is experiment suppose
+
+ align:start position:0%
+bones so this is experiment suppose
+ 
+
+ align:start position:0%
+bones so this is experiment suppose
+we're at any domestic interest rate we
+
+ align:start position:0%
+we're at any domestic interest rate we
+ 
+
+ align:start position:0%
+we're at any domestic interest rate we
+don't touch that now I increase
+
+ align:start position:0%
+don't touch that now I increase
+ 
+
+ align:start position:0%
+don't touch that now I increase
+International interest rate and I say
+
+ align:start position:0%
+International interest rate and I say
+ 
+
+ align:start position:0%
+International interest rate and I say
+the speed exchange rate is the same as
+
+ align:start position:0%
+the speed exchange rate is the same as
+ 
+
+ align:start position:0%
+the speed exchange rate is the same as
+it used to be what has to happen to the
+
+ align:start position:0%
+it used to be what has to happen to the
+ 
+
+ align:start position:0%
+it used to be what has to happen to the
+current exchange rate in order to be
+
+ align:start position:0%
+current exchange rate in order to be
+ 
+
+ align:start position:0%
+current exchange rate in order to be
+different between investing in the US
+
+ align:start position:0%
+different between investing in the US
+ 
+
+ align:start position:0%
+different between investing in the US
+Bond or the or the foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bond exactly as to depreciate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why that's correct but but why is that
+
+ align:start position:0%
+why that's correct but but why is that
+ 
+
+ align:start position:0%
+why that's correct but but why is that
+you need an a that the exchanger Falls
+
+ align:start position:0%
+you need an a that the exchanger Falls
+ 
+
+ align:start position:0%
+you need an a that the exchanger Falls
+today in order to restore to have the
+
+ align:start position:0%
+today in order to restore to have the
+ 
+
+ align:start position:0%
+today in order to restore to have the
+the interp condition
+
+ align:start position:0%
+the interp condition
+ 
+
+ align:start position:0%
+the interp condition
+holding okay so remember what happened
+
+ align:start position:0%
+holding okay so remember what happened
+ 
+
+ align:start position:0%
+holding okay so remember what happened
+is that you had the same interest rate
+
+ align:start position:0%
+is that you had the same interest rate
+ 
+
+ align:start position:0%
+is that you had the same interest rate
+and now the the international interest
+
+ align:start position:0%
+and now the the international interest
+ 
+
+ align:start position:0%
+and now the the international interest
+went up that means if nothing moves now
+
+ align:start position:0%
+went up that means if nothing moves now
+ 
+
+ align:start position:0%
+went up that means if nothing moves now
+you prefer you were indiffer before now
+
+ align:start position:0%
+you prefer you were indiffer before now
+ 
+
+ align:start position:0%
+you prefer you were indiffer before now
+you would prefer to invest in the
+
+ align:start position:0%
+you would prefer to invest in the
+ 
+
+ align:start position:0%
+you would prefer to invest in the
+international bond if I don't change the
+
+ align:start position:0%
+international bond if I don't change the
+ 
+
+ align:start position:0%
+international bond if I don't change the
+the US rate then I have to compensate
+
+ align:start position:0%
+the US rate then I have to compensate
+ 
+
+ align:start position:0%
+the US rate then I have to compensate
+you by some other mean the only way I
+
+ align:start position:0%
+you by some other mean the only way I
+ 
+
+ align:start position:0%
+you by some other mean the only way I
+can compensate you in this mod the only
+
+ align:start position:0%
+can compensate you in this mod the only
+ 
+
+ align:start position:0%
+can compensate you in this mod the only
+thing is endogenous is by an expected
+
+ align:start position:0%
+thing is endogenous is by an expected
+ 
+
+ align:start position:0%
+thing is endogenous is by an expected
+appreciation of the exchange rate
+
+ align:start position:0%
+appreciation of the exchange rate
+ 
+
+ align:start position:0%
+appreciation of the exchange rate
+because that would give you a capital
+
+ align:start position:0%
+because that would give you a capital
+ 
+
+ align:start position:0%
+because that would give you a capital
+gain from holding the bond the US Bond a
+
+ align:start position:0%
+gain from holding the bond the US Bond a
+ 
+
+ align:start position:0%
+gain from holding the bond the US Bond a
+currency capital gain now since expected
+
+ align:start position:0%
+currency capital gain now since expected
+ 
+
+ align:start position:0%
+currency capital gain now since expected
+change is given the only way I can give
+
+ align:start position:0%
+change is given the only way I can give
+ 
+
+ align:start position:0%
+change is given the only way I can give
+you that is depreciating the currency
+
+ align:start position:0%
+you that is depreciating the currency
+ 
+
+ align:start position:0%
+you that is depreciating the currency
+today so then you can expect an
+
+ align:start position:0%
+today so then you can expect an
+ 
+
+ align:start position:0%
+today so then you can expect an
+appreciation tomorrow from today to
+
+ align:start position:0%
+appreciation tomorrow from today to
+ 
+
+ align:start position:0%
+appreciation tomorrow from today to
+tomorrow okay that's that's the
+
+ align:start position:0%
+tomorrow okay that's that's the
+ 
+
+ align:start position:0%
+tomorrow okay that's that's the
+mechanism okay so that means that this
+
+ align:start position:0%
+mechanism okay so that means that this
+ 
+
+ align:start position:0%
+mechanism okay so that means that this
+curve here will shift to the right okay
+
+ align:start position:0%
+curve here will shift to the right okay
+ 
+
+ align:start position:0%
+curve here will shift to the right okay
+for any given interest rate you need a
+
+ align:start position:0%
+for any given interest rate you need a
+ 
+
+ align:start position:0%
+for any given interest rate you need a
+sorry to the left for any given I made
+
+ align:start position:0%
+sorry to the left for any given I made
+ 
+
+ align:start position:0%
+sorry to the left for any given I made
+that mistake in the previous lecture so
+
+ align:start position:0%
+that mistake in the previous lecture so
+ 
+
+ align:start position:0%
+that mistake in the previous lecture so
+for any given interest rate this Curve
+
+ align:start position:0%
+for any given interest rate this Curve
+ 
+
+ align:start position:0%
+for any given interest rate this Curve
+will have to move to the left okay so if
+
+ align:start position:0%
+will have to move to the left okay so if
+ 
+
+ align:start position:0%
+will have to move to the left okay so if
+the interest rate doesn't change and
+
+ align:start position:0%
+the interest rate doesn't change and
+ 
+
+ align:start position:0%
+the interest rate doesn't change and
+international interest is up you need an
+
+ align:start position:0%
+international interest is up you need an
+ 
+
+ align:start position:0%
+international interest is up you need an
+exchange rate today that is lower than
+
+ align:start position:0%
+exchange rate today that is lower than
+ 
+
+ align:start position:0%
+exchange rate today that is lower than
+it used to be so you can expect an
+
+ align:start position:0%
+it used to be so you can expect an
+ 
+
+ align:start position:0%
+it used to be so you can expect an
+appreciation from now to the next period
+
+ align:start position:0%
+appreciation from now to the next period
+ 
+
+ align:start position:0%
+appreciation from now to the next period
+okay so that's what moves to the left
+
+ align:start position:0%
+okay so that's what moves to the left
+ 
+
+ align:start position:0%
+okay so that's what moves to the left
+now what happens what else moves in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case and remember when I I'm asking the
+
+ align:start position:0%
+case and remember when I I'm asking the
+ 
+
+ align:start position:0%
+case and remember when I I'm asking the
+question what else
+
+ align:start position:0%
+question what else
+ 
+
+ align:start position:0%
+question what else
+moves I mean what curve moves what you
+
+ align:start position:0%
+moves I mean what curve moves what you
+ 
+
+ align:start position:0%
+moves I mean what curve moves what you
+need to do is just take something as
+
+ align:start position:0%
+need to do is just take something as
+ 
+
+ align:start position:0%
+need to do is just take something as
+given and then see what whether we get
+
+ align:start position:0%
+given and then see what whether we get
+ 
+
+ align:start position:0%
+given and then see what whether we get
+the same equilibrium output or not so
+
+ align:start position:0%
+the same equilibrium output or not so
+ 
+
+ align:start position:0%
+the same equilibrium output or not so
+take an interest r as given that's the
+
+ align:start position:0%
+take an interest r as given that's the
+ 
+
+ align:start position:0%
+take an interest r as given that's the
+easiest and then ask the question well
+
+ align:start position:0%
+easiest and then ask the question well
+ 
+
+ align:start position:0%
+easiest and then ask the question well
+will I get the same equilibrium output
+
+ align:start position:0%
+will I get the same equilibrium output
+ 
+
+ align:start position:0%
+will I get the same equilibrium output
+or not if I get the same equilibrium
+
+ align:start position:0%
+or not if I get the same equilibrium
+ 
+
+ align:start position:0%
+or not if I get the same equilibrium
+output that means that yes hasn't move
+
+ align:start position:0%
+output that means that yes hasn't move
+ 
+
+ align:start position:0%
+output that means that yes hasn't move
+but if I get a different equilibrium
+
+ align:start position:0%
+but if I get a different equilibrium
+ 
+
+ align:start position:0%
+but if I get a different equilibrium
+output it means that yes has move
+
+ align:start position:0%
+output it means that yes has move
+ 
+
+ align:start position:0%
+output it means that yes has move
+because for the same interest rate I'm
+
+ align:start position:0%
+because for the same interest rate I'm
+ 
+
+ align:start position:0%
+because for the same interest rate I'm
+getting a different equilibrium output
+
+ align:start position:0%
+getting a different equilibrium output
+ 
+
+ align:start position:0%
+getting a different equilibrium output
+so what happens in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case does say yes move or
+
+ align:start position:0%
+case does say yes move or
+ 
+
+ align:start position:0%
+case does say yes move or
+not when I star goes up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going to simplify the question yes it
+
+ align:start position:0%
+going to simplify the question yes it
+ 
+
+ align:start position:0%
+going to simplify the question yes it
+does which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way will I get more or less output when
+
+ align:start position:0%
+way will I get more or less output when
+ 
+
+ align:start position:0%
+way will I get more or less output when
+the international interest rate goes up
+
+ align:start position:0%
+the international interest rate goes up
+ 
+
+ align:start position:0%
+the international interest rate goes up
+and I'm taking look the kind of things
+
+ align:start position:0%
+and I'm taking look the kind of things
+ 
+
+ align:start position:0%
+and I'm taking look the kind of things
+I'm taking as even I'm also taking as
+
+ align:start position:0%
+I'm taking as even I'm also taking as
+ 
+
+ align:start position:0%
+I'm taking as even I'm also taking as
+given International output so I I'm not
+
+ align:start position:0%
+given International output so I I'm not
+ 
+
+ align:start position:0%
+given International output so I I'm not
+do y star I'm not not moving expected
+
+ align:start position:0%
+do y star I'm not not moving expected
+ 
+
+ align:start position:0%
+do y star I'm not not moving expected
+exchange rate ER and I'm asking the
+
+ align:start position:0%
+exchange rate ER and I'm asking the
+ 
+
+ align:start position:0%
+exchange rate ER and I'm asking the
+question if the domestic Central Bank
+
+ align:start position:0%
+question if the domestic Central Bank
+ 
+
+ align:start position:0%
+question if the domestic Central Bank
+the FED in the case of the US does not
+
+ align:start position:0%
+the FED in the case of the US does not
+ 
+
+ align:start position:0%
+the FED in the case of the US does not
+change the interest rate what happens to
+
+ align:start position:0%
+change the interest rate what happens to
+ 
+
+ align:start position:0%
+change the interest rate what happens to
+gum output does it go down or
+
+ align:start position:0%
+gum output does it go down or
+ 
+
+ align:start position:0%
+gum output does it go down or
+up if they other if the international
+
+ align:start position:0%
+up if they other if the international
+ 
+
+ align:start position:0%
+up if they other if the international
+interest rate goes up the domestic
+
+ align:start position:0%
+interest rate goes up the domestic
+ 
+
+ align:start position:0%
+interest rate goes up the domestic
+interest does not what has to happen to
+
+ align:start position:0%
+interest does not what has to happen to
+ 
+
+ align:start position:0%
+interest does not what has to happen to
+the exchange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate you answer it before has to go down
+
+ align:start position:0%
+rate you answer it before has to go down
+ 
+
+ align:start position:0%
+rate you answer it before has to go down
+that means it has to depreciate what
+
+ align:start position:0%
+that means it has to depreciate what
+ 
+
+ align:start position:0%
+that means it has to depreciate what
+happen to net exports when the exchange
+
+ align:start position:0%
+happen to net exports when the exchange
+ 
+
+ align:start position:0%
+happen to net exports when the exchange
+rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depreciates what does it mean that
+
+ align:start position:0%
+depreciates what does it mean that
+ 
+
+ align:start position:0%
+depreciates what does it mean that
+exchanger depreciate especially if we
+
+ align:start position:0%
+exchanger depreciate especially if we
+ 
+
+ align:start position:0%
+exchanger depreciate especially if we
+have the in this case we have the price
+
+ align:start position:0%
+have the in this case we have the price
+ 
+
+ align:start position:0%
+have the in this case we have the price
+is completely fixed so now if the
+
+ align:start position:0%
+is completely fixed so now if the
+ 
+
+ align:start position:0%
+is completely fixed so now if the
+nominal exchanger depreciates means that
+
+ align:start position:0%
+nominal exchanger depreciates means that
+ 
+
+ align:start position:0%
+nominal exchanger depreciates means that
+the real exchanger depreciates what does
+
+ align:start position:0%
+the real exchanger depreciates what does
+ 
+
+ align:start position:0%
+the real exchanger depreciates what does
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean what got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cheaper okay you need lot to study for
+
+ align:start position:0%
+cheaper okay you need lot to study for
+ 
+
+ align:start position:0%
+cheaper okay you need lot to study for
+the quiz and
+
+ align:start position:0%
+the quiz and
+ 
+
+ align:start position:0%
+the quiz and
+domestic goods are cheaper so so that
+
+ align:start position:0%
+domestic goods are cheaper so so that
+ 
+
+ align:start position:0%
+domestic goods are cheaper so so that
+means that the and equivalently foreign
+
+ align:start position:0%
+means that the and equivalently foreign
+ 
+
+ align:start position:0%
+means that the and equivalently foreign
+Goods got more expensive that means for
+
+ align:start position:0%
+Goods got more expensive that means for
+ 
+
+ align:start position:0%
+Goods got more expensive that means for
+any given level of domestic interest
+
+ align:start position:0%
+any given level of domestic interest
+ 
+
+ align:start position:0%
+any given level of domestic interest
+rate now there will be less Imports and
+
+ align:start position:0%
+rate now there will be less Imports and
+ 
+
+ align:start position:0%
+rate now there will be less Imports and
+More exports that means net export will
+
+ align:start position:0%
+More exports that means net export will
+ 
+
+ align:start position:0%
+More exports that means net export will
+be more which means the is Will shift to
+
+ align:start position:0%
+be more which means the is Will shift to
+ 
+
+ align:start position:0%
+be more which means the is Will shift to
+the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good so these things you you need
+
+ align:start position:0%
+okay good so these things you you need
+ 
+
+ align:start position:0%
+okay good so these things you you need
+to control I understand that it's a
+
+ align:start position:0%
+to control I understand that it's a
+ 
+
+ align:start position:0%
+to control I understand that it's a
+little confusing to think about exchange
+
+ align:start position:0%
+little confusing to think about exchange
+ 
+
+ align:start position:0%
+little confusing to think about exchange
+rates and so on but but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so anything that happens here with
+
+ align:start position:0%
+um so anything that happens here with
+ 
+
+ align:start position:0%
+um so anything that happens here with
+the exchange that is just a relative
+
+ align:start position:0%
+the exchange that is just a relative
+ 
+
+ align:start position:0%
+the exchange that is just a relative
+price the more expensive are your goods
+
+ align:start position:0%
+price the more expensive are your goods
+ 
+
+ align:start position:0%
+price the more expensive are your goods
+the harder it will be to sell them you
+
+ align:start position:0%
+the harder it will be to sell them you
+ 
+
+ align:start position:0%
+the harder it will be to sell them you
+and and the more tempted you will be to
+
+ align:start position:0%
+and and the more tempted you will be to
+ 
+
+ align:start position:0%
+and and the more tempted you will be to
+buy foreign Goods that's that's that's
+
+ align:start position:0%
+buy foreign Goods that's that's that's
+ 
+
+ align:start position:0%
+buy foreign Goods that's that's that's
+what it does it's so that's contraction
+
+ align:start position:0%
+what it does it's so that's contraction
+ 
+
+ align:start position:0%
+what it does it's so that's contraction
+appreciation are contraction here or not
+
+ align:start position:0%
+appreciation are contraction here or not
+ 
+
+ align:start position:0%
+appreciation are contraction here or not
+here the story is a little different
+
+ align:start position:0%
+here the story is a little different
+ 
+
+ align:start position:0%
+here the story is a little different
+it's all about equalizing expected
+
+ align:start position:0%
+it's all about equalizing expected
+ 
+
+ align:start position:0%
+it's all about equalizing expected
+returns so you need to have an movement
+
+ align:start position:0%
+returns so you need to have an movement
+ 
+
+ align:start position:0%
+returns so you need to have an movement
+in the chain rate today so that you are
+
+ align:start position:0%
+in the chain rate today so that you are
+ 
+
+ align:start position:0%
+in the chain rate today so that you are
+always indiff between investing in one
+
+ align:start position:0%
+always indiff between investing in one
+ 
+
+ align:start position:0%
+always indiff between investing in one
+side or the other it's about the return
+
+ align:start position:0%
+side or the other it's about the return
+ 
+
+ align:start position:0%
+side or the other it's about the return
+the expected exchange and the exchange
+
+ align:start position:0%
+the expected exchange and the exchange
+ 
+
+ align:start position:0%
+the expected exchange and the exchange
+rate so okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good okay I got it's a little unclear
+
+ align:start position:0%
+good okay I got it's a little unclear
+ 
+
+ align:start position:0%
+good okay I got it's a little unclear
+but we'll keep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trying is there anything particularly
+
+ align:start position:0%
+trying is there anything particularly
+ 
+
+ align:start position:0%
+trying is there anything particularly
+unclear oh it's all a blur here
+
+ align:start position:0%
+unclear oh it's all a blur here
+ 
+
+ align:start position:0%
+unclear oh it's all a blur here
+okay got
+
+ align:start position:0%
+okay got
+ 
+
+ align:start position:0%
+okay got
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+um well let me so all that I describe
+
+ align:start position:0%
+um well let me so all that I describe
+ 
+
+ align:start position:0%
+um well let me so all that I describe
+here is is
+
+ align:start position:0%
+here is is
+ 
+
+ align:start position:0%
+here is is
+um is allowing the exchanger to move
+
+ align:start position:0%
+um is allowing the exchanger to move
+ 
+
+ align:start position:0%
+um is allowing the exchanger to move
+we're saying look if we move something
+
+ align:start position:0%
+we're saying look if we move something
+ 
+
+ align:start position:0%
+we're saying look if we move something
+or the foreign foreigners move something
+
+ align:start position:0%
+or the foreign foreigners move something
+ 
+
+ align:start position:0%
+or the foreign foreigners move something
+then we ask the question well what does
+
+ align:start position:0%
+then we ask the question well what does
+ 
+
+ align:start position:0%
+then we ask the question well what does
+exchange it has to do today here okay
+
+ align:start position:0%
+exchange it has to do today here okay
+ 
+
+ align:start position:0%
+exchange it has to do today here okay
+and typically when when when that's done
+
+ align:start position:0%
+and typically when when when that's done
+ 
+
+ align:start position:0%
+and typically when when when that's done
+we call those regimes floating exchange
+
+ align:start position:0%
+we call those regimes floating exchange
+ 
+
+ align:start position:0%
+we call those regimes floating exchange
+rate systems meaning exchange rate can
+
+ align:start position:0%
+rate systems meaning exchange rate can
+ 
+
+ align:start position:0%
+rate systems meaning exchange rate can
+float that move around as interest rates
+
+ align:start position:0%
+float that move around as interest rates
+ 
+
+ align:start position:0%
+float that move around as interest rates
+in different parts of the world change
+
+ align:start position:0%
+in different parts of the world change
+ 
+
+ align:start position:0%
+in different parts of the world change
+then the exchange rate moves around okay
+
+ align:start position:0%
+then the exchange rate moves around okay
+ 
+
+ align:start position:0%
+then the exchange rate moves around okay
+typically call that flexible exchange
+
+ align:start position:0%
+typically call that flexible exchange
+ 
+
+ align:start position:0%
+typically call that flexible exchange
+rate I think the distinction is a lot
+
+ align:start position:0%
+rate I think the distinction is a lot
+ 
+
+ align:start position:0%
+rate I think the distinction is a lot
+harder to make in practice but for
+
+ align:start position:0%
+harder to make in practice but for
+ 
+
+ align:start position:0%
+harder to make in practice but for
+reasons I'll explain later but but
+
+ align:start position:0%
+reasons I'll explain later but but
+ 
+
+ align:start position:0%
+reasons I'll explain later but but
+that's what is meant as a as a floating
+
+ align:start position:0%
+that's what is meant as a as a floating
+ 
+
+ align:start position:0%
+that's what is meant as a as a floating
+exchange rate system one in which really
+
+ align:start position:0%
+exchange rate system one in which really
+ 
+
+ align:start position:0%
+exchange rate system one in which really
+you're doing your each country is doing
+
+ align:start position:0%
+you're doing your each country is doing
+ 
+
+ align:start position:0%
+you're doing your each country is doing
+its own policies and so on and the
+
+ align:start position:0%
+its own policies and so on and the
+ 
+
+ align:start position:0%
+its own policies and so on and the
+exchange it does what needs to do so so
+
+ align:start position:0%
+exchange it does what needs to do so so
+ 
+
+ align:start position:0%
+exchange it does what needs to do so so
+so the financial markets
+
+ align:start position:0%
+so the financial markets
+ 
+
+ align:start position:0%
+so the financial markets
+clear many countries however do
+
+ align:start position:0%
+clear many countries however do
+ 
+
+ align:start position:0%
+clear many countries however do
+something which is the polar opposite of
+
+ align:start position:0%
+something which is the polar opposite of
+ 
+
+ align:start position:0%
+something which is the polar opposite of
+that which is called a fixed exchange
+
+ align:start position:0%
+that which is called a fixed exchange
+ 
+
+ align:start position:0%
+that which is called a fixed exchange
+rate regime okay so some countries
+
+ align:start position:0%
+rate regime okay so some countries
+ 
+
+ align:start position:0%
+rate regime okay so some countries
+really Peg their currencies to a major
+
+ align:start position:0%
+really Peg their currencies to a major
+ 
+
+ align:start position:0%
+really Peg their currencies to a major
+currency an extreme case is the Euro
+
+ align:start position:0%
+currency an extreme case is the Euro
+ 
+
+ align:start position:0%
+currency an extreme case is the Euro
+Zone where they give up their individual
+
+ align:start position:0%
+Zone where they give up their individual
+ 
+
+ align:start position:0%
+Zone where they give up their individual
+currencies and they have a common
+
+ align:start position:0%
+currencies and they have a common
+ 
+
+ align:start position:0%
+currencies and they have a common
+currency okay so so Germany and and and
+
+ align:start position:0%
+currency okay so so Germany and and and
+ 
+
+ align:start position:0%
+currency okay so so Germany and and and
+and and and Italy have a Ultra Peg
+
+ align:start position:0%
+and and and Italy have a Ultra Peg
+ 
+
+ align:start position:0%
+and and and Italy have a Ultra Peg
+exchange rate because they have the same
+
+ align:start position:0%
+exchange rate because they have the same
+ 
+
+ align:start position:0%
+exchange rate because they have the same
+currency okay now most of the times
+
+ align:start position:0%
+currency okay now most of the times
+ 
+
+ align:start position:0%
+currency okay now most of the times
+fixed exchange rates are are are a
+
+ align:start position:0%
+fixed exchange rates are are are a
+ 
+
+ align:start position:0%
+fixed exchange rates are are are a
+little weaker than that for example the
+
+ align:start position:0%
+little weaker than that for example the
+ 
+
+ align:start position:0%
+little weaker than that for example the
+Hong Kong dollar has been ped to the
+
+ align:start position:0%
+Hong Kong dollar has been ped to the
+ 
+
+ align:start position:0%
+Hong Kong dollar has been ped to the
+dollar for a long time for the US dollar
+
+ align:start position:0%
+dollar for a long time for the US dollar
+ 
+
+ align:start position:0%
+dollar for a long time for the US dollar
+for a long time okay and I'll show you a
+
+ align:start position:0%
+for a long time okay and I'll show you a
+ 
+
+ align:start position:0%
+for a long time okay and I'll show you a
+few others many countries go through
+
+ align:start position:0%
+few others many countries go through
+ 
+
+ align:start position:0%
+few others many countries go through
+some phase where they try to pay the
+
+ align:start position:0%
+some phase where they try to pay the
+ 
+
+ align:start position:0%
+some phase where they try to pay the
+currency and it typically fails at some
+
+ align:start position:0%
+currency and it typically fails at some
+ 
+
+ align:start position:0%
+currency and it typically fails at some
+point but but they have periods in which
+
+ align:start position:0%
+point but but they have periods in which
+ 
+
+ align:start position:0%
+point but but they have periods in which
+the currency is is big but so let me
+
+ align:start position:0%
+the currency is is big but so let me
+ 
+
+ align:start position:0%
+the currency is is big but so let me
+suppose that you have a peg exchange
+
+ align:start position:0%
+suppose that you have a peg exchange
+ 
+
+ align:start position:0%
+suppose that you have a peg exchange
+rate let me show you some features of it
+
+ align:start position:0%
+rate let me show you some features of it
+ 
+
+ align:start position:0%
+rate let me show you some features of it
+suppose you are in a peg in a peg or a
+
+ align:start position:0%
+suppose you are in a peg in a peg or a
+ 
+
+ align:start position:0%
+suppose you are in a peg in a peg or a
+fixed exchanges regime P to another
+
+ align:start position:0%
+fixed exchanges regime P to another
+ 
+
+ align:start position:0%
+fixed exchanges regime P to another
+currency and suppose it's credible
+
+ align:start position:0%
+currency and suppose it's credible
+ 
+
+ align:start position:0%
+currency and suppose it's credible
+that's a big issue with fixed exchange
+
+ align:start position:0%
+that's a big issue with fixed exchange
+ 
+
+ align:start position:0%
+that's a big issue with fixed exchange
+rate but suppose it's credible there are
+
+ align:start position:0%
+rate but suppose it's credible there are
+ 
+
+ align:start position:0%
+rate but suppose it's credible there are
+some countries that have credible fixed
+
+ align:start position:0%
+some countries that have credible fixed
+ 
+
+ align:start position:0%
+some countries that have credible fixed
+exchange rate well if if you have a
+
+ align:start position:0%
+exchange rate well if if you have a
+ 
+
+ align:start position:0%
+exchange rate well if if you have a
+fixed exchange rate with respect to some
+
+ align:start position:0%
+fixed exchange rate with respect to some
+ 
+
+ align:start position:0%
+fixed exchange rate with respect to some
+other Cur currency and it's credible
+
+ align:start position:0%
+other Cur currency and it's credible
+ 
+
+ align:start position:0%
+other Cur currency and it's credible
+then you know that speced exchang it is
+
+ align:start position:0%
+then you know that speced exchang it is
+ 
+
+ align:start position:0%
+then you know that speced exchang it is
+equal to exchang and equal to a constant
+
+ align:start position:0%
+equal to exchang and equal to a constant
+ 
+
+ align:start position:0%
+equal to exchang and equal to a constant
+that's what it means to have a fixed
+
+ align:start position:0%
+that's what it means to have a fixed
+ 
+
+ align:start position:0%
+that's what it means to have a fixed
+exchange rate okay it's
+
+ align:start position:0%
+exchange rate okay it's
+ 
+
+ align:start position:0%
+exchange rate okay it's
+constant but if this is constant means
+
+ align:start position:0%
+constant but if this is constant means
+ 
+
+ align:start position:0%
+constant but if this is constant means
+you never can expect an appreciation or
+
+ align:start position:0%
+you never can expect an appreciation or
+ 
+
+ align:start position:0%
+you never can expect an appreciation or
+depreciation because it's constant it's
+
+ align:start position:0%
+depreciation because it's constant it's
+ 
+
+ align:start position:0%
+depreciation because it's constant it's
+fixed and if you can't expect an
+
+ align:start position:0%
+fixed and if you can't expect an
+ 
+
+ align:start position:0%
+fixed and if you can't expect an
+appreciation or appreciation the UN
+
+ align:start position:0%
+appreciation or appreciation the UN
+ 
+
+ align:start position:0%
+appreciation or appreciation the UN
+coverage disparity condition tells you
+
+ align:start position:0%
+coverage disparity condition tells you
+ 
+
+ align:start position:0%
+coverage disparity condition tells you
+that you know what does it tell you that
+
+ align:start position:0%
+that you know what does it tell you that
+ 
+
+ align:start position:0%
+that you know what does it tell you that
+your interest rate has to be the same as
+
+ align:start position:0%
+your interest rate has to be the same as
+ 
+
+ align:start position:0%
+your interest rate has to be the same as
+the foreign interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+why what would happen in a
+
+ align:start position:0%
+why what would happen in a
+ 
+
+ align:start position:0%
+why what would happen in a
+credible pay in a credible fixed
+
+ align:start position:0%
+credible pay in a credible fixed
+ 
+
+ align:start position:0%
+credible pay in a credible fixed
+exchange if the domestic interest rate
+
+ align:start position:0%
+exchange if the domestic interest rate
+ 
+
+ align:start position:0%
+exchange if the domestic interest rate
+is higher than International than the
+
+ align:start position:0%
+is higher than International than the
+ 
+
+ align:start position:0%
+is higher than International than the
+currency the interest rate of the
+
+ align:start position:0%
+currency the interest rate of the
+ 
+
+ align:start position:0%
+currency the interest rate of the
+country you're paying
+
+ align:start position:0%
+country you're paying
+ 
+
+ align:start position:0%
+country you're paying
+to what would happen suppose that I'm in
+
+ align:start position:0%
+to what would happen suppose that I'm in
+ 
+
+ align:start position:0%
+to what would happen suppose that I'm in
+a fixed exchange rate and and we have
+
+ align:start position:0%
+a fixed exchange rate and and we have
+ 
+
+ align:start position:0%
+a fixed exchange rate and and we have
+the same interest rate and now I
+
+ align:start position:0%
+the same interest rate and now I
+ 
+
+ align:start position:0%
+the same interest rate and now I
+unilaterally decide to raise interest
+
+ align:start position:0%
+unilaterally decide to raise interest
+ 
+
+ align:start position:0%
+unilaterally decide to raise interest
+rates what do you think would happen
+
+ align:start position:0%
+rates what do you think would happen
+ 
+
+ align:start position:0%
+rates what do you think would happen
+with capital flows what how what would
+
+ align:start position:0%
+with capital flows what how what would
+ 
+
+ align:start position:0%
+with capital flows what how what would
+you do to your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+portfolio if the C is the change it this
+
+ align:start position:0%
+portfolio if the C is the change it this
+ 
+
+ align:start position:0%
+portfolio if the C is the change it this
+Peg and is credible it is as if they
+
+ align:start position:0%
+Peg and is credible it is as if they
+ 
+
+ align:start position:0%
+Peg and is credible it is as if they
+were issuing the same currency because
+
+ align:start position:0%
+were issuing the same currency because
+ 
+
+ align:start position:0%
+were issuing the same currency because
+it's the same it's different currency
+
+ align:start position:0%
+it's the same it's different currency
+ 
+
+ align:start position:0%
+it's the same it's different currency
+different name but it has a constant in
+
+ align:start position:0%
+different name but it has a constant in
+ 
+
+ align:start position:0%
+different name but it has a constant in
+front of it okay so it's as if it was
+
+ align:start position:0%
+front of it okay so it's as if it was
+ 
+
+ align:start position:0%
+front of it okay so it's as if it was
+issuing the same currency two bonds that
+
+ align:start position:0%
+issuing the same currency two bonds that
+ 
+
+ align:start position:0%
+issuing the same currency two bonds that
+are identical and issuing the same
+
+ align:start position:0%
+are identical and issuing the same
+ 
+
+ align:start position:0%
+are identical and issuing the same
+currency cannot be paying different
+
+ align:start position:0%
+currency cannot be paying different
+ 
+
+ align:start position:0%
+currency cannot be paying different
+interest rate because you would all
+
+ align:start position:0%
+interest rate because you would all
+ 
+
+ align:start position:0%
+interest rate because you would all
+invest all your money you know in the in
+
+ align:start position:0%
+invest all your money you know in the in
+ 
+
+ align:start position:0%
+invest all your money you know in the in
+the bond that is paying a high interest
+
+ align:start position:0%
+the bond that is paying a high interest
+ 
+
+ align:start position:0%
+the bond that is paying a high interest
+rate and that's what happens here so is
+
+ align:start position:0%
+rate and that's what happens here so is
+ 
+
+ align:start position:0%
+rate and that's what happens here so is
+mechanically what would happen is for
+
+ align:start position:0%
+mechanically what would happen is for
+ 
+
+ align:start position:0%
+mechanically what would happen is for
+some crazy reason a country has a fixed
+
+ align:start position:0%
+some crazy reason a country has a fixed
+ 
+
+ align:start position:0%
+some crazy reason a country has a fixed
+exchange credible fixed exchange decides
+
+ align:start position:0%
+exchange credible fixed exchange decides
+ 
+
+ align:start position:0%
+exchange credible fixed exchange decides
+to have an interest rate higher than the
+
+ align:start position:0%
+to have an interest rate higher than the
+ 
+
+ align:start position:0%
+to have an interest rate higher than the
+currency the the interest rate in the
+
+ align:start position:0%
+currency the the interest rate in the
+ 
+
+ align:start position:0%
+currency the the interest rate in the
+currency is is being ped to then you
+
+ align:start position:0%
+currency is is being ped to then you
+ 
+
+ align:start position:0%
+currency is is being ped to then you
+would see massive Capital flows to that
+
+ align:start position:0%
+would see massive Capital flows to that
+ 
+
+ align:start position:0%
+would see massive Capital flows to that
+country so there would be ANM almost
+
+ align:start position:0%
+country so there would be ANM almost
+ 
+
+ align:start position:0%
+country so there would be ANM almost
+pressure for an appreciation of that
+
+ align:start position:0%
+pressure for an appreciation of that
+ 
+
+ align:start position:0%
+pressure for an appreciation of that
+currency okay but but the and what the
+
+ align:start position:0%
+currency okay but but the and what the
+ 
+
+ align:start position:0%
+currency okay but but the and what the
+central bank would have to do is start
+
+ align:start position:0%
+central bank would have to do is start
+ 
+
+ align:start position:0%
+central bank would have to do is start
+buying massive amounts of the supplying
+
+ align:start position:0%
+buying massive amounts of the supplying
+ 
+
+ align:start position:0%
+buying massive amounts of the supplying
+massive amounts of his currency for
+
+ align:start position:0%
+massive amounts of his currency for
+ 
+
+ align:start position:0%
+massive amounts of his currency for
+those that want to buy it because there
+
+ align:start position:0%
+those that want to buy it because there
+ 
+
+ align:start position:0%
+those that want to buy it because there
+would an infinite demand for that
+
+ align:start position:0%
+would an infinite demand for that
+ 
+
+ align:start position:0%
+would an infinite demand for that
+okay so in practice what that means and
+
+ align:start position:0%
+okay so in practice what that means and
+ 
+
+ align:start position:0%
+okay so in practice what that means and
+and sometimes you can do that for a
+
+ align:start position:0%
+and sometimes you can do that for a
+ 
+
+ align:start position:0%
+and sometimes you can do that for a
+little while but but but but not in in a
+
+ align:start position:0%
+little while but but but but not in in a
+ 
+
+ align:start position:0%
+little while but but but but not in in a
+sustained manner so what happens in
+
+ align:start position:0%
+sustained manner so what happens in
+ 
+
+ align:start position:0%
+sustained manner so what happens in
+practice is that if you really have a a
+
+ align:start position:0%
+practice is that if you really have a a
+ 
+
+ align:start position:0%
+practice is that if you really have a a
+a a peg exchange rate and you have free
+
+ align:start position:0%
+a a peg exchange rate and you have free
+ 
+
+ align:start position:0%
+a a peg exchange rate and you have free
+Capital Mobility which is people can
+
+ align:start position:0%
+Capital Mobility which is people can
+ 
+
+ align:start position:0%
+Capital Mobility which is people can
+move in and out of your bonds China
+
+ align:start position:0%
+move in and out of your bonds China
+ 
+
+ align:start position:0%
+move in and out of your bonds China
+doesn't for example so it can allow
+
+ align:start position:0%
+doesn't for example so it can allow
+ 
+
+ align:start position:0%
+doesn't for example so it can allow
+itself to both control a little with the
+
+ align:start position:0%
+itself to both control a little with the
+ 
+
+ align:start position:0%
+itself to both control a little with the
+currency and a mean be semi semi Peg and
+
+ align:start position:0%
+currency and a mean be semi semi Peg and
+ 
+
+ align:start position:0%
+currency and a mean be semi semi Peg and
+still can move it domestic interest rate
+
+ align:start position:0%
+still can move it domestic interest rate
+ 
+
+ align:start position:0%
+still can move it domestic interest rate
+because they have Capital controls but
+
+ align:start position:0%
+because they have Capital controls but
+ 
+
+ align:start position:0%
+because they have Capital controls but
+but if you don't have Capital controls
+
+ align:start position:0%
+but if you don't have Capital controls
+ 
+
+ align:start position:0%
+but if you don't have Capital controls
+and people can move money in and out it
+
+ align:start position:0%
+and people can move money in and out it
+ 
+
+ align:start position:0%
+and people can move money in and out it
+can do portfolio investment as it
+
+ align:start position:0%
+can do portfolio investment as it
+ 
+
+ align:start position:0%
+can do portfolio investment as it
+happened with most of the advanced
+
+ align:start position:0%
+happened with most of the advanced
+ 
+
+ align:start position:0%
+happened with most of the advanced
+economies then effectively ER you you
+
+ align:start position:0%
+economies then effectively ER you you
+ 
+
+ align:start position:0%
+economies then effectively ER you you
+give up domestic monetary policy okay
+
+ align:start position:0%
+give up domestic monetary policy okay
+ 
+
+ align:start position:0%
+give up domestic monetary policy okay
+because whatever the other country does
+
+ align:start position:0%
+because whatever the other country does
+ 
+
+ align:start position:0%
+because whatever the other country does
+the country you're pegging to does you
+
+ align:start position:0%
+the country you're pegging to does you
+ 
+
+ align:start position:0%
+the country you're pegging to does you
+have to follow
+
+ align:start position:0%
+have to follow
+ 
+
+ align:start position:0%
+have to follow
+that's what it means you Peg you give up
+
+ align:start position:0%
+that's what it means you Peg you give up
+ 
+
+ align:start position:0%
+that's what it means you Peg you give up
+your domestic monetary policy if you
+
+ align:start position:0%
+your domestic monetary policy if you
+ 
+
+ align:start position:0%
+your domestic monetary policy if you
+choose to Peg to another country a
+
+ align:start position:0%
+choose to Peg to another country a
+ 
+
+ align:start position:0%
+choose to Peg to another country a
+little later I'm going to tell you why
+
+ align:start position:0%
+little later I'm going to tell you why
+ 
+
+ align:start position:0%
+little later I'm going to tell you why
+countries may choose to do that but
+
+ align:start position:0%
+countries may choose to do that but
+ 
+
+ align:start position:0%
+countries may choose to do that but
+that's what you do okay and they and cpy
+
+ align:start position:0%
+that's what you do okay and they and cpy
+ 
+
+ align:start position:0%
+that's what you do okay and they and cpy
+tells you that's what you do you're not
+
+ align:start position:0%
+tells you that's what you do you're not
+ 
+
+ align:start position:0%
+tells you that's what you do you're not
+going to be able to deviate very
+
+ align:start position:0%
+going to be able to deviate very
+ 
+
+ align:start position:0%
+going to be able to deviate very
+significantly from the interest rate
+
+ align:start position:0%
+significantly from the interest rate
+ 
+
+ align:start position:0%
+significantly from the interest rate
+that the other country is setting if you
+
+ align:start position:0%
+that the other country is setting if you
+ 
+
+ align:start position:0%
+that the other country is setting if you
+want to maintain your fixed exchange
+
+ align:start position:0%
+want to maintain your fixed exchange
+ 
+
+ align:start position:0%
+want to maintain your fixed exchange
+rate now in practice there are many
+
+ align:start position:0%
+rate now in practice there are many
+ 
+
+ align:start position:0%
+rate now in practice there are many
+hybrid regimes there there are very very
+
+ align:start position:0%
+hybrid regimes there there are very very
+ 
+
+ align:start position:0%
+hybrid regimes there there are very very
+few pure float regimes H few I mean it's
+
+ align:start position:0%
+few pure float regimes H few I mean it's
+ 
+
+ align:start position:0%
+few pure float regimes H few I mean it's
+maybe five or something like that but
+
+ align:start position:0%
+maybe five or something like that but
+ 
+
+ align:start position:0%
+maybe five or something like that but
+but but but so there all sort of degrees
+
+ align:start position:0%
+but but but so there all sort of degrees
+ 
+
+ align:start position:0%
+but but but so there all sort of degrees
+of exchanges regimes and and which are
+
+ align:start position:0%
+of exchanges regimes and and which are
+ 
+
+ align:start position:0%
+of exchanges regimes and and which are
+hybrids between fixed exchange rates and
+
+ align:start position:0%
+hybrids between fixed exchange rates and
+ 
+
+ align:start position:0%
+hybrids between fixed exchange rates and
+and fully flexible exchange rates let me
+
+ align:start position:0%
+and fully flexible exchange rates let me
+ 
+
+ align:start position:0%
+and fully flexible exchange rates let me
+show you just a few just randomly more
+
+ align:start position:0%
+show you just a few just randomly more
+ 
+
+ align:start position:0%
+show you just a few just randomly more
+less randomly selected in Bloomberg H so
+
+ align:start position:0%
+less randomly selected in Bloomberg H so
+ 
+
+ align:start position:0%
+less randomly selected in Bloomberg H so
+there you have in in in in in white is
+
+ align:start position:0%
+there you have in in in in in white is
+ 
+
+ align:start position:0%
+there you have in in in in in white is
+the US Euro that's a float that's that's
+
+ align:start position:0%
+the US Euro that's a float that's that's
+ 
+
+ align:start position:0%
+the US Euro that's a float that's that's
+the cleanest float you can imagine I
+
+ align:start position:0%
+the cleanest float you can imagine I
+ 
+
+ align:start position:0%
+the cleanest float you can imagine I
+mean there's
+
+ align:start position:0%
+mean there's
+ 
+
+ align:start position:0%
+mean there's
+no then another which is a very clean
+
+ align:start position:0%
+no then another which is a very clean
+ 
+
+ align:start position:0%
+no then another which is a very clean
+float is the dollar Yen Japanese
+
+ align:start position:0%
+float is the dollar Yen Japanese
+ 
+
+ align:start position:0%
+float is the dollar Yen Japanese
+Yen now that's a currency that has that
+
+ align:start position:0%
+Yen now that's a currency that has that
+ 
+
+ align:start position:0%
+Yen now that's a currency that has that
+freely float but if there is a major
+
+ align:start position:0%
+freely float but if there is a major
+ 
+
+ align:start position:0%
+freely float but if there is a major
+dislocation central banks do intervene
+
+ align:start position:0%
+dislocation central banks do intervene
+ 
+
+ align:start position:0%
+dislocation central banks do intervene
+to money it means in normal
+
+ align:start position:0%
+to money it means in normal
+ 
+
+ align:start position:0%
+to money it means in normal
+circumstances they float and the same is
+
+ align:start position:0%
+circumstances they float and the same is
+ 
+
+ align:start position:0%
+circumstances they float and the same is
+true with the EUR but if as big
+
+ align:start position:0%
+true with the EUR but if as big
+ 
+
+ align:start position:0%
+true with the EUR but if as big
+dislocation some major Bank collapses or
+
+ align:start position:0%
+dislocation some major Bank collapses or
+ 
+
+ align:start position:0%
+dislocation some major Bank collapses or
+something like that then there are major
+
+ align:start position:0%
+something like that then there are major
+ 
+
+ align:start position:0%
+something like that then there are major
+dis dislocations in in financial markets
+
+ align:start position:0%
+dis dislocations in in financial markets
+ 
+
+ align:start position:0%
+dis dislocations in in financial markets
+they become very segmented Arbitrage is
+
+ align:start position:0%
+they become very segmented Arbitrage is
+ 
+
+ align:start position:0%
+they become very segmented Arbitrage is
+not that easy and so on then then then
+
+ align:start position:0%
+not that easy and so on then then then
+ 
+
+ align:start position:0%
+not that easy and so on then then then
+central banks intervene but but for the
+
+ align:start position:0%
+central banks intervene but but for the
+ 
+
+ align:start position:0%
+central banks intervene but but for the
+normal business cycle and so on they do
+
+ align:start position:0%
+normal business cycle and so on they do
+ 
+
+ align:start position:0%
+normal business cycle and so on they do
+not they don't intervene in the currency
+
+ align:start position:0%
+not they don't intervene in the currency
+ 
+
+ align:start position:0%
+not they don't intervene in the currency
+Market they intervene in different ways
+
+ align:start position:0%
+Market they intervene in different ways
+ 
+
+ align:start position:0%
+Market they intervene in different ways
+and that's the reason I'll get
+
+ align:start position:0%
+and that's the reason I'll get
+ 
+
+ align:start position:0%
+and that's the reason I'll get
+there and the other one is the the pound
+
+ align:start position:0%
+there and the other one is the the pound
+ 
+
+ align:start position:0%
+there and the other one is the the pound
+no the US dollar versus the British
+
+ align:start position:0%
+no the US dollar versus the British
+ 
+
+ align:start position:0%
+no the US dollar versus the British
+pound then then it's also that's a pure
+
+ align:start position:0%
+pound then then it's also that's a pure
+ 
+
+ align:start position:0%
+pound then then it's also that's a pure
+float
+
+ align:start position:0%
+float
+ 
+
+ align:start position:0%
+float
+these are also pure floats this is the
+
+ align:start position:0%
+these are also pure floats this is the
+ 
+
+ align:start position:0%
+these are also pure floats this is the
+US versus the OC
+
+ align:start position:0%
+US versus the OC
+ 
+
+ align:start position:0%
+US versus the OC
+dollar so and against the Canadian
+
+ align:start position:0%
+dollar so and against the Canadian
+ 
+
+ align:start position:0%
+dollar so and against the Canadian
+dollar and against the the Swedish Kona
+
+ align:start position:0%
+dollar and against the the Swedish Kona
+ 
+
+ align:start position:0%
+dollar and against the the Swedish Kona
+okay those are pretty
+
+ align:start position:0%
+okay those are pretty
+ 
+
+ align:start position:0%
+okay those are pretty
+floating regimes they are a little
+
+ align:start position:0%
+floating regimes they are a little
+ 
+
+ align:start position:0%
+floating regimes they are a little
+different from the previous ones I show
+
+ align:start position:0%
+different from the previous ones I show
+ 
+
+ align:start position:0%
+different from the previous ones I show
+you because these are currencies are
+
+ align:start position:0%
+you because these are currencies are
+ 
+
+ align:start position:0%
+you because these are currencies are
+much more prone to sell off during
+
+ align:start position:0%
+much more prone to sell off during
+ 
+
+ align:start position:0%
+much more prone to sell off during
+riskof environments and that's the
+
+ align:start position:0%
+riskof environments and that's the
+ 
+
+ align:start position:0%
+riskof environments and that's the
+reason you see this spikes here okay
+
+ align:start position:0%
+reason you see this spikes here okay
+ 
+
+ align:start position:0%
+reason you see this spikes here okay
+this was Co big spike you didn't see it
+
+ align:start position:0%
+this was Co big spike you didn't see it
+ 
+
+ align:start position:0%
+this was Co big spike you didn't see it
+in the in the dollar euro and so on so
+
+ align:start position:0%
+in the in the dollar euro and so on so
+ 
+
+ align:start position:0%
+in the in the dollar euro and so on so
+forth so these are currencies that are
+
+ align:start position:0%
+forth so these are currencies that are
+ 
+
+ align:start position:0%
+forth so these are currencies that are
+free floaters but they're very exposed
+
+ align:start position:0%
+free floaters but they're very exposed
+ 
+
+ align:start position:0%
+free floaters but they're very exposed
+to to risk the risk environment in the
+
+ align:start position:0%
+to to risk the risk environment in the
+ 
+
+ align:start position:0%
+to to risk the risk environment in the
+market but there still their free
+
+ align:start position:0%
+market but there still their free
+ 
+
+ align:start position:0%
+market but there still their free
+floaters
+
+ align:start position:0%
+floaters
+ 
+
+ align:start position:0%
+floaters
+um the SS are a little bit more of
+
+ align:start position:0%
+um the SS are a little bit more of
+ 
+
+ align:start position:0%
+um the SS are a little bit more of
+independent minded and and but they do
+
+ align:start position:0%
+independent minded and and but they do
+ 
+
+ align:start position:0%
+independent minded and and but they do
+control a bit more the currency but it's
+
+ align:start position:0%
+control a bit more the currency but it's
+ 
+
+ align:start position:0%
+control a bit more the currency but it's
+still I I consider
+
+ align:start position:0%
+still I I consider
+ 
+
+ align:start position:0%
+still I I consider
+those free floaters
+
+ align:start position:0%
+those free floaters
+ 
+
+ align:start position:0%
+those free floaters
+these currencies are a little different
+
+ align:start position:0%
+these currencies are a little different
+ 
+
+ align:start position:0%
+these currencies are a little different
+this is the Brazilian
+
+ align:start position:0%
+this is the Brazilian
+ 
+
+ align:start position:0%
+this is the Brazilian
+real H the Zar is the South African Rand
+
+ align:start position:0%
+real H the Zar is the South African Rand
+ 
+
+ align:start position:0%
+real H the Zar is the South African Rand
+and this is the Colombian Peso and you
+
+ align:start position:0%
+and this is the Colombian Peso and you
+ 
+
+ align:start position:0%
+and this is the Colombian Peso and you
+see several things here they they do
+
+ align:start position:0%
+see several things here they they do
+ 
+
+ align:start position:0%
+see several things here they they do
+move so so they have a big component of
+
+ align:start position:0%
+move so so they have a big component of
+ 
+
+ align:start position:0%
+move so so they have a big component of
+flexible exchange rate uh they do
+
+ align:start position:0%
+flexible exchange rate uh they do
+ 
+
+ align:start position:0%
+flexible exchange rate uh they do
+intervene a lot more though H because
+
+ align:start position:0%
+intervene a lot more though H because
+ 
+
+ align:start position:0%
+intervene a lot more though H because
+they are exposed to much more risk off
+
+ align:start position:0%
+they are exposed to much more risk off
+ 
+
+ align:start position:0%
+they are exposed to much more risk off
+type environment and so on and they need
+
+ align:start position:0%
+type environment and so on and they need
+ 
+
+ align:start position:0%
+type environment and so on and they need
+to intervene fairly frequently to
+
+ align:start position:0%
+to intervene fairly frequently to
+ 
+
+ align:start position:0%
+to intervene fairly frequently to
+control movements in the chain rate but
+
+ align:start position:0%
+control movements in the chain rate but
+ 
+
+ align:start position:0%
+control movements in the chain rate but
+but you also see a trend in this things
+
+ align:start position:0%
+but you also see a trend in this things
+ 
+
+ align:start position:0%
+but you also see a trend in this things
+so their currencies are becoming
+
+ align:start position:0%
+so their currencies are becoming
+ 
+
+ align:start position:0%
+so their currencies are becoming
+chronically weaker relative to the
+
+ align:start position:0%
+chronically weaker relative to the
+ 
+
+ align:start position:0%
+chronically weaker relative to the
+dollar and the reason for that is
+
+ align:start position:0%
+dollar and the reason for that is
+ 
+
+ align:start position:0%
+dollar and the reason for that is
+because there are countries that have
+
+ align:start position:0%
+because there are countries that have
+ 
+
+ align:start position:0%
+because there are countries that have
+higher inflation so if you want to
+
+ align:start position:0%
+higher inflation so if you want to
+ 
+
+ align:start position:0%
+higher inflation so if you want to
+maintain the real exchange rate Conant
+
+ align:start position:0%
+maintain the real exchange rate Conant
+ 
+
+ align:start position:0%
+maintain the real exchange rate Conant
+and you have higher inflation than the
+
+ align:start position:0%
+and you have higher inflation than the
+ 
+
+ align:start position:0%
+and you have higher inflation than the
+other country then your nominal exchange
+
+ align:start position:0%
+other country then your nominal exchange
+ 
+
+ align:start position:0%
+other country then your nominal exchange
+rate has to be
+
+ align:start position:0%
+rate has to be
+ 
+
+ align:start position:0%
+rate has to be
+depreciating okay because your prices
+
+ align:start position:0%
+depreciating okay because your prices
+ 
+
+ align:start position:0%
+depreciating okay because your prices
+are rising at a faster Pace than the
+
+ align:start position:0%
+are rising at a faster Pace than the
+ 
+
+ align:start position:0%
+are rising at a faster Pace than the
+other one well if the exchanger was not
+
+ align:start position:0%
+other one well if the exchanger was not
+ 
+
+ align:start position:0%
+other one well if the exchanger was not
+appreciating on a depreciating on
+
+ align:start position:0%
+appreciating on a depreciating on
+ 
+
+ align:start position:0%
+appreciating on a depreciating on
+average then it would mean that you
+
+ align:start position:0%
+average then it would mean that you
+ 
+
+ align:start position:0%
+average then it would mean that you
+would becoming more and more expensive
+
+ align:start position:0%
+would becoming more and more expensive
+ 
+
+ align:start position:0%
+would becoming more and more expensive
+okay so that's a reason countries that
+
+ align:start position:0%
+okay so that's a reason countries that
+ 
+
+ align:start position:0%
+okay so that's a reason countries that
+have higher inflation they tend to have
+
+ align:start position:0%
+have higher inflation they tend to have
+ 
+
+ align:start position:0%
+have higher inflation they tend to have
+these Trends as well okay but it's still
+
+ align:start position:0%
+these Trends as well okay but it's still
+ 
+
+ align:start position:0%
+these Trends as well okay but it's still
+fairly
+
+ align:start position:0%
+fairly
+ 
+
+ align:start position:0%
+fairly
+floating here these are all currencies
+
+ align:start position:0%
+floating here these are all currencies
+ 
+
+ align:start position:0%
+floating here these are all currencies
+that are H to a different
+
+ align:start position:0%
+that are H to a different
+ 
+
+ align:start position:0%
+that are H to a different
+degree er um targeted in the sense
+
+ align:start position:0%
+degree er um targeted in the sense
+ 
+
+ align:start position:0%
+degree er um targeted in the sense
+they're contained in in terms of they're
+
+ align:start position:0%
+they're contained in in terms of they're
+ 
+
+ align:start position:0%
+they're contained in in terms of they're
+not free to float at will H the scale
+
+ align:start position:0%
+not free to float at will H the scale
+ 
+
+ align:start position:0%
+not free to float at will H the scale
+here will mislead you if I had put it in
+
+ align:start position:0%
+here will mislead you if I had put it in
+ 
+
+ align:start position:0%
+here will mislead you if I had put it in
+the same scale as the the euro dollar or
+
+ align:start position:0%
+the same scale as the the euro dollar or
+ 
+
+ align:start position:0%
+the same scale as the the euro dollar or
+the the Euro Yen and the the dollar Yen
+
+ align:start position:0%
+the the Euro Yen and the the dollar Yen
+ 
+
+ align:start position:0%
+the the Euro Yen and the the dollar Yen
+or the Euro Yen as well then these
+
+ align:start position:0%
+or the Euro Yen as well then these
+ 
+
+ align:start position:0%
+or the Euro Yen as well then these
+things would have been look very small
+
+ align:start position:0%
+things would have been look very small
+ 
+
+ align:start position:0%
+things would have been look very small
+okay so I should have put a real floater
+
+ align:start position:0%
+okay so I should have put a real floater
+ 
+
+ align:start position:0%
+okay so I should have put a real floater
+there so you would have seen that these
+
+ align:start position:0%
+there so you would have seen that these
+ 
+
+ align:start position:0%
+there so you would have seen that these
+guys are moving a lot less and these are
+
+ align:start position:0%
+guys are moving a lot less and these are
+ 
+
+ align:start position:0%
+guys are moving a lot less and these are
+different kind of countries this is the
+
+ align:start position:0%
+different kind of countries this is the
+ 
+
+ align:start position:0%
+different kind of countries this is the
+Hong Kong
+
+ align:start position:0%
+Hong Kong
+ 
+
+ align:start position:0%
+Hong Kong
+dollar that for all practical purposes
+
+ align:start position:0%
+dollar that for all practical purposes
+ 
+
+ align:start position:0%
+dollar that for all practical purposes
+Peg okay this little Wiggles is just
+
+ align:start position:0%
+Peg okay this little Wiggles is just
+ 
+
+ align:start position:0%
+Peg okay this little Wiggles is just
+technical things that happen overnight
+
+ align:start position:0%
+technical things that happen overnight
+ 
+
+ align:start position:0%
+technical things that happen overnight
+and stuff like that but they're Peg to
+
+ align:start position:0%
+and stuff like that but they're Peg to
+ 
+
+ align:start position:0%
+and stuff like that but they're Peg to
+the dollar okay so Hong Kong dollar is
+
+ align:start position:0%
+the dollar okay so Hong Kong dollar is
+ 
+
+ align:start position:0%
+the dollar okay so Hong Kong dollar is
+Peg to the
+
+ align:start position:0%
+Peg to the
+ 
+
+ align:start position:0%
+Peg to the
+dollar H that means they really don't
+
+ align:start position:0%
+dollar H that means they really don't
+ 
+
+ align:start position:0%
+dollar H that means they really don't
+have independent monetary policy
+
+ align:start position:0%
+have independent monetary policy
+ 
+
+ align:start position:0%
+have independent monetary policy
+relative to the US is and Le the
+
+ align:start position:0%
+relative to the US is and Le the
+ 
+
+ align:start position:0%
+relative to the US is and Le the
+US the this is a CN this is the the
+
+ align:start position:0%
+US the this is a CN this is the the
+ 
+
+ align:start position:0%
+US the this is a CN this is the the
+the the Chinese rii and and and it's a
+
+ align:start position:0%
+the the Chinese rii and and and it's a
+ 
+
+ align:start position:0%
+the the Chinese rii and and and it's a
+currency again I should have put it with
+
+ align:start position:0%
+currency again I should have put it with
+ 
+
+ align:start position:0%
+currency again I should have put it with
+a float real floater there is a lot more
+
+ align:start position:0%
+a float real floater there is a lot more
+ 
+
+ align:start position:0%
+a float real floater there is a lot more
+control okay so it moves around around
+
+ align:start position:0%
+control okay so it moves around around
+ 
+
+ align:start position:0%
+control okay so it moves around around
+but but in a much tighter range and and
+
+ align:start position:0%
+but but in a much tighter range and and
+ 
+
+ align:start position:0%
+but but in a much tighter range and and
+and they are thinking about exchange
+
+ align:start position:0%
+and they are thinking about exchange
+ 
+
+ align:start position:0%
+and they are thinking about exchange
+rate when part of their policy program
+
+ align:start position:0%
+rate when part of their policy program
+ 
+
+ align:start position:0%
+rate when part of their policy program
+and so on the exchange that is something
+
+ align:start position:0%
+and so on the exchange that is something
+ 
+
+ align:start position:0%
+and so on the exchange that is something
+they're thinking
+
+ align:start position:0%
+they're thinking
+ 
+
+ align:start position:0%
+they're thinking
+about this one here the blue one is is
+
+ align:start position:0%
+about this one here the blue one is is
+ 
+
+ align:start position:0%
+about this one here the blue one is is
+an interesting one
+
+ align:start position:0%
+an interesting one
+ 
+
+ align:start position:0%
+an interesting one
+er
+
+ align:start position:0%
+er
+ 
+
+ align:start position:0%
+er
+um that's the the the the Singaporean
+
+ align:start position:0%
+um that's the the the the Singaporean
+ 
+
+ align:start position:0%
+um that's the the the the Singaporean
+dollar okay and the Singaporean dollar
+
+ align:start position:0%
+dollar okay and the Singaporean dollar
+ 
+
+ align:start position:0%
+dollar okay and the Singaporean dollar
+they have a very interesting regime they
+
+ align:start position:0%
+they have a very interesting regime they
+ 
+
+ align:start position:0%
+they have a very interesting regime they
+have a a a um a Target Zone meaning they
+
+ align:start position:0%
+have a a a um a Target Zone meaning they
+ 
+
+ align:start position:0%
+have a a a um a Target Zone meaning they
+let the exchange rate move within a
+
+ align:start position:0%
+let the exchange rate move within a
+ 
+
+ align:start position:0%
+let the exchange rate move within a
+range
+
+ align:start position:0%
+range
+ 
+
+ align:start position:0%
+range
+only but it's not Peg against a single
+
+ align:start position:0%
+only but it's not Peg against a single
+ 
+
+ align:start position:0%
+only but it's not Peg against a single
+currency is pay against a basket of of
+
+ align:start position:0%
+currency is pay against a basket of of
+ 
+
+ align:start position:0%
+currency is pay against a basket of of
+currencies okay and the the recipe is
+
+ align:start position:0%
+currencies okay and the the recipe is
+ 
+
+ align:start position:0%
+currencies okay and the the recipe is
+secret so everyone is always guessing
+
+ align:start position:0%
+secret so everyone is always guessing
+ 
+
+ align:start position:0%
+secret so everyone is always guessing
+what they're doing and so on They do
+
+ align:start position:0%
+what they're doing and so on They do
+ 
+
+ align:start position:0%
+what they're doing and so on They do
+change the weights a little bit to keep
+
+ align:start position:0%
+change the weights a little bit to keep
+ 
+
+ align:start position:0%
+change the weights a little bit to keep
+the markets confused but but the Curren
+
+ align:start position:0%
+the markets confused but but the Curren
+ 
+
+ align:start position:0%
+the markets confused but but the Curren
+is very stable we all understand it's a
+
+ align:start position:0%
+is very stable we all understand it's a
+ 
+
+ align:start position:0%
+is very stable we all understand it's a
+it's a weighted average of the Euro the
+
+ align:start position:0%
+it's a weighted average of the Euro the
+ 
+
+ align:start position:0%
+it's a weighted average of the Euro the
+Remi and the and the dollar but but they
+
+ align:start position:0%
+Remi and the and the dollar but but they
+ 
+
+ align:start position:0%
+Remi and the and the dollar but but they
+they don't disclose exactly the thing
+
+ align:start position:0%
+they don't disclose exactly the thing
+ 
+
+ align:start position:0%
+they don't disclose exactly the thing
+but you know you can filter out what
+
+ align:start position:0%
+but you know you can filter out what
+ 
+
+ align:start position:0%
+but you know you can filter out what
+they're doing and and they they keep
+
+ align:start position:0%
+they're doing and and they they keep
+ 
+
+ align:start position:0%
+they're doing and and they they keep
+things in a range and they occasionally
+
+ align:start position:0%
+things in a range and they occasionally
+ 
+
+ align:start position:0%
+things in a range and they occasionally
+change the slope of that range but but
+
+ align:start position:0%
+change the slope of that range but but
+ 
+
+ align:start position:0%
+change the slope of that range but but
+it's very regulated in that con and they
+
+ align:start position:0%
+it's very regulated in that con and they
+ 
+
+ align:start position:0%
+it's very regulated in that con and they
+in fact they State their monetary policy
+
+ align:start position:0%
+in fact they State their monetary policy
+ 
+
+ align:start position:0%
+in fact they State their monetary policy
+in terms of the effects they said that's
+
+ align:start position:0%
+in terms of the effects they said that's
+ 
+
+ align:start position:0%
+in terms of the effects they said that's
+our policy interest rate is whatever it
+
+ align:start position:0%
+our policy interest rate is whatever it
+ 
+
+ align:start position:0%
+our policy interest rate is whatever it
+needs to be so the exchange remains in
+
+ align:start position:0%
+needs to be so the exchange remains in
+ 
+
+ align:start position:0%
+needs to be so the exchange remains in
+that range that's that's that's the way
+
+ align:start position:0%
+that range that's that's that's the way
+ 
+
+ align:start position:0%
+that range that's that's that's the way
+they State monetary don't even think
+
+ align:start position:0%
+they State monetary don't even think
+ 
+
+ align:start position:0%
+they State monetary don't even think
+about so I let the markets determine the
+
+ align:start position:0%
+about so I let the markets determine the
+ 
+
+ align:start position:0%
+about so I let the markets determine the
+interest we determine the CH here in
+
+ align:start position:0%
+interest we determine the CH here in
+ 
+
+ align:start position:0%
+interest we determine the CH here in
+that range and it's a narrow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+range again I should have
+
+ align:start position:0%
+range again I should have
+ 
+
+ align:start position:0%
+range again I should have
+put um a real floater that you would
+
+ align:start position:0%
+put um a real floater that you would
+ 
+
+ align:start position:0%
+put um a real floater that you would
+have seen that okay so Al so the point
+
+ align:start position:0%
+have seen that okay so Al so the point
+ 
+
+ align:start position:0%
+have seen that okay so Al so the point
+is that everything goes there are all
+
+ align:start position:0%
+is that everything goes there are all
+ 
+
+ align:start position:0%
+is that everything goes there are all
+sort of Arrangements happening around
+
+ align:start position:0%
+sort of Arrangements happening around
+ 
+
+ align:start position:0%
+sort of Arrangements happening around
+the world this is these are different
+
+ align:start position:0%
+the world this is these are different
+ 
+
+ align:start position:0%
+the world this is these are different
+kind of currencies no uh this is the the
+
+ align:start position:0%
+kind of currencies no uh this is the the
+ 
+
+ align:start position:0%
+kind of currencies no uh this is the the
+the the Turkish lader okay and the
+
+ align:start position:0%
+the the Turkish lader okay and the
+ 
+
+ align:start position:0%
+the the Turkish lader okay and the
+Argentinian
+
+ align:start position:0%
+Argentinian
+ 
+
+ align:start position:0%
+Argentinian
+peso I think through the sample has have
+
+ align:start position:0%
+peso I think through the sample has have
+ 
+
+ align:start position:0%
+peso I think through the sample has have
+been called peso since since they have
+
+ align:start position:0%
+been called peso since since they have
+ 
+
+ align:start position:0%
+been called peso since since they have
+this very high inflations they keep
+
+ align:start position:0%
+this very high inflations they keep
+ 
+
+ align:start position:0%
+this very high inflations they keep
+changing the name of the currency and so
+
+ align:start position:0%
+changing the name of the currency and so
+ 
+
+ align:start position:0%
+changing the name of the currency and so
+on because they have to remove zeros
+
+ align:start position:0%
+on because they have to remove zeros
+ 
+
+ align:start position:0%
+on because they have to remove zeros
+from things so but but I think through
+
+ align:start position:0%
+from things so but but I think through
+ 
+
+ align:start position:0%
+from things so but but I think through
+all that period is still the Argentinian
+
+ align:start position:0%
+all that period is still the Argentinian
+ 
+
+ align:start position:0%
+all that period is still the Argentinian
+PES and uh so I mean look at the
+
+ align:start position:0%
+PES and uh so I mean look at the
+ 
+
+ align:start position:0%
+PES and uh so I mean look at the
+scale so you cannot see it but but all
+
+ align:start position:0%
+scale so you cannot see it but but all
+ 
+
+ align:start position:0%
+scale so you cannot see it but but all
+these two countries are all the time
+
+ align:start position:0%
+these two countries are all the time
+ 
+
+ align:start position:0%
+these two countries are all the time
+fighting against the exchange rate in
+
+ align:start position:0%
+fighting against the exchange rate in
+ 
+
+ align:start position:0%
+fighting against the exchange rate in
+fact Argentina today has like five
+
+ align:start position:0%
+fact Argentina today has like five
+ 
+
+ align:start position:0%
+fact Argentina today has like five
+different exchange rates there is the
+
+ align:start position:0%
+different exchange rates there is the
+ 
+
+ align:start position:0%
+different exchange rates there is the
+official exchange rate there is the blue
+
+ align:start position:0%
+official exchange rate there is the blue
+ 
+
+ align:start position:0%
+official exchange rate there is the blue
+exchange rate there is a purple
+
+ align:start position:0%
+exchange rate there is a purple
+ 
+
+ align:start position:0%
+exchange rate there is a purple
+exchanger there all sort of things you
+
+ align:start position:0%
+exchanger there all sort of things you
+ 
+
+ align:start position:0%
+exchanger there all sort of things you
+should never pay with a credit card if
+
+ align:start position:0%
+should never pay with a credit card if
+ 
+
+ align:start position:0%
+should never pay with a credit card if
+you go to Argentina if you do tourism
+
+ align:start position:0%
+you go to Argentina if you do tourism
+ 
+
+ align:start position:0%
+you go to Argentina if you do tourism
+because you don't want to pay the
+
+ align:start position:0%
+because you don't want to pay the
+ 
+
+ align:start position:0%
+because you don't want to pay the
+official exchange you can get three
+
+ align:start position:0%
+official exchange you can get three
+ 
+
+ align:start position:0%
+official exchange you can get three
+times that in the in the blue Market I
+
+ align:start position:0%
+times that in the in the blue Market I
+ 
+
+ align:start position:0%
+times that in the in the blue Market I
+call it the black market since everyone
+
+ align:start position:0%
+call it the black market since everyone
+ 
+
+ align:start position:0%
+call it the black market since everyone
+does it I think blue is fine but but so
+
+ align:start position:0%
+does it I think blue is fine but but so
+ 
+
+ align:start position:0%
+does it I think blue is fine but but so
+there are all sort of
+
+ align:start position:0%
+there are all sort of
+ 
+
+ align:start position:0%
+there are all sort of
+exchanges and but still this is the
+
+ align:start position:0%
+exchanges and but still this is the
+ 
+
+ align:start position:0%
+exchanges and but still this is the
+official one
+
+ align:start position:0%
+official one
+ 
+
+ align:start position:0%
+official one
+and even the official one you see sort
+
+ align:start position:0%
+and even the official one you see sort
+ 
+
+ align:start position:0%
+and even the official one you see sort
+of has completely
+
+ align:start position:0%
+of has completely
+ 
+
+ align:start position:0%
+of has completely
+exploded the Turkish leader looks pretty
+
+ align:start position:0%
+exploded the Turkish leader looks pretty
+ 
+
+ align:start position:0%
+exploded the Turkish leader looks pretty
+good here just because I put it next to
+
+ align:start position:0%
+good here just because I put it next to
+ 
+
+ align:start position:0%
+good here just because I put it next to
+argentin argentinan PES otherwise it
+
+ align:start position:0%
+argentin argentinan PES otherwise it
+ 
+
+ align:start position:0%
+argentin argentinan PES otherwise it
+also would look pretty bad okay but most
+
+ align:start position:0%
+also would look pretty bad okay but most
+ 
+
+ align:start position:0%
+also would look pretty bad okay but most
+of the these countries are all the time
+
+ align:start position:0%
+of the these countries are all the time
+ 
+
+ align:start position:0%
+of the these countries are all the time
+paying the exchange rate because they
+
+ align:start position:0%
+paying the exchange rate because they
+ 
+
+ align:start position:0%
+paying the exchange rate because they
+use that to stabilize inflation the
+
+ align:start position:0%
+use that to stabilize inflation the
+ 
+
+ align:start position:0%
+use that to stabilize inflation the
+whole thing breaks up and then boom they
+
+ align:start position:0%
+whole thing breaks up and then boom they
+ 
+
+ align:start position:0%
+whole thing breaks up and then boom they
+go through big spikes you see this where
+
+ align:start position:0%
+go through big spikes you see this where
+ 
+
+ align:start position:0%
+go through big spikes you see this where
+they're trying to stabilize there you
+
+ align:start position:0%
+they're trying to stabilize there you
+ 
+
+ align:start position:0%
+they're trying to stabilize there you
+see that they're trying to stabilize the
+
+ align:start position:0%
+see that they're trying to stabilize the
+ 
+
+ align:start position:0%
+see that they're trying to stabilize the
+currency they're not floating there that
+
+ align:start position:0%
+currency they're not floating there that
+ 
+
+ align:start position:0%
+currency they're not floating there that
+range and they were a little successful
+
+ align:start position:0%
+range and they were a little successful
+ 
+
+ align:start position:0%
+range and they were a little successful
+and and and and and that happens all the
+
+ align:start position:0%
+and and and and and that happens all the
+ 
+
+ align:start position:0%
+and and and and and that happens all the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay and now
+
+ align:start position:0%
+okay and now
+ 
+
+ align:start position:0%
+okay and now
+obviously I mean look at this the size
+
+ align:start position:0%
+obviously I mean look at this the size
+ 
+
+ align:start position:0%
+obviously I mean look at this the size
+of this this is an appreciation of the
+
+ align:start position:0%
+of this this is an appreciation of the
+ 
+
+ align:start position:0%
+of this this is an appreciation of the
+dollar so it's a depreciation of the
+
+ align:start position:0%
+dollar so it's a depreciation of the
+ 
+
+ align:start position:0%
+dollar so it's a depreciation of the
+Argentinian PES what do you think is
+
+ align:start position:0%
+Argentinian PES what do you think is
+ 
+
+ align:start position:0%
+Argentinian PES what do you think is
+happening
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here looks very smooth by the way it's
+
+ align:start position:0%
+here looks very smooth by the way it's
+ 
+
+ align:start position:0%
+here looks very smooth by the way it's
+not that it's moving around it's
+
+ align:start position:0%
+not that it's moving around it's
+ 
+
+ align:start position:0%
+not that it's moving around it's
+just what do you think is happening
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very high inflation the thousands and
+
+ align:start position:0%
+very high inflation the thousands and
+ 
+
+ align:start position:0%
+very high inflation the thousands and
+that's what that's what is happening
+
+ align:start position:0%
+that's what that's what is happening
+ 
+
+ align:start position:0%
+that's what that's what is happening
+here but but again this is a hybrid
+
+ align:start position:0%
+here but but again this is a hybrid
+ 
+
+ align:start position:0%
+here but but again this is a hybrid
+system they they try to stabilize
+
+ align:start position:0%
+system they they try to stabilize
+ 
+
+ align:start position:0%
+system they they try to stabilize
+frequently the exchange rate the thing
+
+ align:start position:0%
+frequently the exchange rate the thing
+ 
+
+ align:start position:0%
+frequently the exchange rate the thing
+goes and then they stabilize it again
+
+ align:start position:0%
+goes and then they stabilize it again
+ 
+
+ align:start position:0%
+goes and then they stabilize it again
+and and so on so forth but you can't
+
+ align:start position:0%
+and and so on so forth but you can't
+ 
+
+ align:start position:0%
+and and so on so forth but you can't
+fight just having much higher inflation
+
+ align:start position:0%
+fight just having much higher inflation
+ 
+
+ align:start position:0%
+fight just having much higher inflation
+than the rest of the world you have
+
+ align:start position:0%
+than the rest of the world you have
+ 
+
+ align:start position:0%
+than the rest of the world you have
+higher inflation then there's no way
+
+ align:start position:0%
+higher inflation then there's no way
+ 
+
+ align:start position:0%
+higher inflation then there's no way
+around that your currency they
+
+ align:start position:0%
+around that your currency they
+ 
+
+ align:start position:0%
+around that your currency they
+appreciate they try to but they
+
+ align:start position:0%
+appreciate they try to but they
+ 
+
+ align:start position:0%
+appreciate they try to but they
+can't anyways
+
+ align:start position:0%
+can't anyways
+ 
+
+ align:start position:0%
+can't anyways
+ER so let me let me go back to this
+
+ align:start position:0%
+ER so let me let me go back to this
+ 
+
+ align:start position:0%
+ER so let me let me go back to this
+model and and and and think a little bit
+
+ align:start position:0%
+model and and and and think a little bit
+ 
+
+ align:start position:0%
+model and and and and think a little bit
+more about the decision
+
+ align:start position:0%
+more about the decision
+ 
+
+ align:start position:0%
+more about the decision
+to have one kind of exchanger the other
+
+ align:start position:0%
+to have one kind of exchanger the other
+ 
+
+ align:start position:0%
+to have one kind of exchanger the other
+one and therefore everything that goes
+
+ align:start position:0%
+one and therefore everything that goes
+ 
+
+ align:start position:0%
+one and therefore everything that goes
+in between so remember I just to remind
+
+ align:start position:0%
+in between so remember I just to remind
+ 
+
+ align:start position:0%
+in between so remember I just to remind
+you that's that's a model we
+
+ align:start position:0%
+you that's that's a model we
+ 
+
+ align:start position:0%
+you that's that's a model we
+have um so let me think about policy
+
+ align:start position:0%
+have um so let me think about policy
+ 
+
+ align:start position:0%
+have um so let me think about policy
+first and then then let's think how how
+
+ align:start position:0%
+first and then then let's think how how
+ 
+
+ align:start position:0%
+first and then then let's think how how
+how do you deal with policy in the
+
+ align:start position:0%
+how do you deal with policy in the
+ 
+
+ align:start position:0%
+how do you deal with policy in the
+different exchanger regimes and and then
+
+ align:start position:0%
+different exchanger regimes and and then
+ 
+
+ align:start position:0%
+different exchanger regimes and and then
+we'll see why would countries would do
+
+ align:start position:0%
+we'll see why would countries would do
+ 
+
+ align:start position:0%
+we'll see why would countries would do
+one thing or other so suppose a country
+
+ align:start position:0%
+one thing or other so suppose a country
+ 
+
+ align:start position:0%
+one thing or other so suppose a country
+is in a recession we are in this
+
+ align:start position:0%
+is in a recession we are in this
+ 
+
+ align:start position:0%
+is in a recession we are in this
+Model H and suppose that we are in the
+
+ align:start position:0%
+Model H and suppose that we are in the
+ 
+
+ align:start position:0%
+Model H and suppose that we are in the
+flexible exchange regime so what should
+
+ align:start position:0%
+flexible exchange regime so what should
+ 
+
+ align:start position:0%
+flexible exchange regime so what should
+the F fiscal policy do suppose you're in
+
+ align:start position:0%
+the F fiscal policy do suppose you're in
+ 
+
+ align:start position:0%
+the F fiscal policy do suppose you're in
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+recession what what should F fiscal
+
+ align:start position:0%
+recession what what should F fiscal
+ 
+
+ align:start position:0%
+recession what what should F fiscal
+policy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to there's nothing unique of close
+
+ align:start position:0%
+to there's nothing unique of close
+ 
+
+ align:start position:0%
+to there's nothing unique of close
+economy here in open economy in closed
+
+ align:start position:0%
+economy here in open economy in closed
+ 
+
+ align:start position:0%
+economy here in open economy in closed
+economy you would have given me the same
+
+ align:start position:0%
+economy you would have given me the same
+ 
+
+ align:start position:0%
+economy you would have given me the same
+answer if you in a recession what will
+
+ align:start position:0%
+answer if you in a recession what will
+ 
+
+ align:start position:0%
+answer if you in a recession what will
+you do with fiscal policy
+
+ align:start position:0%
+you do with fiscal policy
+ 
+
+ align:start position:0%
+you do with fiscal policy
+have expansionary fiscal policy increase
+
+ align:start position:0%
+have expansionary fiscal policy increase
+ 
+
+ align:start position:0%
+have expansionary fiscal policy increase
+G so that means you move the yes to the
+
+ align:start position:0%
+G so that means you move the yes to the
+ 
+
+ align:start position:0%
+G so that means you move the yes to the
+right nothing changes in the open
+
+ align:start position:0%
+right nothing changes in the open
+ 
+
+ align:start position:0%
+right nothing changes in the open
+economy you'll keep doing that the only
+
+ align:start position:0%
+economy you'll keep doing that the only
+ 
+
+ align:start position:0%
+economy you'll keep doing that the only
+thing that you get is a little smaller
+
+ align:start position:0%
+thing that you get is a little smaller
+ 
+
+ align:start position:0%
+thing that you get is a little smaller
+multiplier because part of that will go
+
+ align:start position:0%
+multiplier because part of that will go
+ 
+
+ align:start position:0%
+multiplier because part of that will go
+to Imports but but still it moves in the
+
+ align:start position:0%
+to Imports but but still it moves in the
+ 
+
+ align:start position:0%
+to Imports but but still it moves in the
+right direction okay and and and yes
+
+ align:start position:0%
+right direction okay and and and yes
+ 
+
+ align:start position:0%
+right direction okay and and and yes
+countries rely on other countries doing
+
+ align:start position:0%
+countries rely on other countries doing
+ 
+
+ align:start position:0%
+countries rely on other countries doing
+also their own expansionary fiscal
+
+ align:start position:0%
+also their own expansionary fiscal
+ 
+
+ align:start position:0%
+also their own expansionary fiscal
+policy but suppose we're talking about a
+
+ align:start position:0%
+policy but suppose we're talking about a
+ 
+
+ align:start position:0%
+policy but suppose we're talking about a
+recession that is unique to this country
+
+ align:start position:0%
+recession that is unique to this country
+ 
+
+ align:start position:0%
+recession that is unique to this country
+then you're going to do an expansionary
+
+ align:start position:0%
+then you're going to do an expansionary
+ 
+
+ align:start position:0%
+then you're going to do an expansionary
+fiscal policy
+
+ align:start position:0%
+fiscal policy
+ 
+
+ align:start position:0%
+fiscal policy
+what would the Central Bank
+
+ align:start position:0%
+what would the Central Bank
+ 
+
+ align:start position:0%
+what would the Central Bank
+do in close
+
+ align:start position:0%
+do in close
+ 
+
+ align:start position:0%
+do in close
+economy what drop interest rate well in
+
+ align:start position:0%
+economy what drop interest rate well in
+ 
+
+ align:start position:0%
+economy what drop interest rate well in
+open economy does the same you just drop
+
+ align:start position:0%
+open economy does the same you just drop
+ 
+
+ align:start position:0%
+open economy does the same you just drop
+interest rate it turns out that that
+
+ align:start position:0%
+interest rate it turns out that that
+ 
+
+ align:start position:0%
+interest rate it turns out that that
+will depreciate your
+
+ align:start position:0%
+will depreciate your
+ 
+
+ align:start position:0%
+will depreciate your
+currency H which will help you as well
+
+ align:start position:0%
+currency H which will help you as well
+ 
+
+ align:start position:0%
+currency H which will help you as well
+so it's very expansionary because of
+
+ align:start position:0%
+so it's very expansionary because of
+ 
+
+ align:start position:0%
+so it's very expansionary because of
+that no because your currency
+
+ align:start position:0%
+that no because your currency
+ 
+
+ align:start position:0%
+that no because your currency
+depreciates so net export goes up as a
+
+ align:start position:0%
+depreciates so net export goes up as a
+ 
+
+ align:start position:0%
+depreciates so net export goes up as a
+result of that you get the investment
+
+ align:start position:0%
+result of that you get the investment
+ 
+
+ align:start position:0%
+result of that you get the investment
+kick you lose a little bit because part
+
+ align:start position:0%
+kick you lose a little bit because part
+ 
+
+ align:start position:0%
+kick you lose a little bit because part
+goes to import but then you also get the
+
+ align:start position:0%
+goes to import but then you also get the
+ 
+
+ align:start position:0%
+goes to import but then you also get the
+effect of net exports that come from The
+
+ align:start position:0%
+effect of net exports that come from The
+ 
+
+ align:start position:0%
+effect of net exports that come from The
+Exchange okay so monetary policy is a
+
+ align:start position:0%
+Exchange okay so monetary policy is a
+ 
+
+ align:start position:0%
+Exchange okay so monetary policy is a
+great policy in open economy because it
+
+ align:start position:0%
+great policy in open economy because it
+ 
+
+ align:start position:0%
+great policy in open economy because it
+gets reinforced by the exchange rate
+
+ align:start position:0%
+gets reinforced by the exchange rate
+ 
+
+ align:start position:0%
+gets reinforced by the exchange rate
+it's even better than fiscal other
+
+ align:start position:0%
+it's even better than fiscal other
+ 
+
+ align:start position:0%
+it's even better than fiscal other
+things equal when you compare the two
+
+ align:start position:0%
+things equal when you compare the two
+ 
+
+ align:start position:0%
+things equal when you compare the two
+the two policies lost power relative to
+
+ align:start position:0%
+the two policies lost power relative to
+ 
+
+ align:start position:0%
+the two policies lost power relative to
+the close economy because the multipli
+
+ align:start position:0%
+the close economy because the multipli
+ 
+
+ align:start position:0%
+the close economy because the multipli
+is smaller but the difference is that
+
+ align:start position:0%
+is smaller but the difference is that
+ 
+
+ align:start position:0%
+is smaller but the difference is that
+the interest rate policy gets the extra
+
+ align:start position:0%
+the interest rate policy gets the extra
+ 
+
+ align:start position:0%
+the interest rate policy gets the extra
+kick that comes from the depreciation of
+
+ align:start position:0%
+kick that comes from the depreciation of
+ 
+
+ align:start position:0%
+kick that comes from the depreciation of
+the currency okay so it's a very
+
+ align:start position:0%
+the currency okay so it's a very
+ 
+
+ align:start position:0%
+the currency okay so it's a very
+powerful tool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's what you do if you have a
+
+ align:start position:0%
+okay so that's what you do if you have a
+ 
+
+ align:start position:0%
+okay so that's what you do if you have a
+a flexible exchange rate and that's what
+
+ align:start position:0%
+a flexible exchange rate and that's what
+ 
+
+ align:start position:0%
+a flexible exchange rate and that's what
+countries do in practice when they are F
+
+ align:start position:0%
+countries do in practice when they are F
+ 
+
+ align:start position:0%
+countries do in practice when they are F
+floting suppose you have a fixed
+
+ align:start position:0%
+floting suppose you have a fixed
+ 
+
+ align:start position:0%
+floting suppose you have a fixed
+exchange rate
+
+ align:start position:0%
+exchange rate
+ 
+
+ align:start position:0%
+exchange rate
+regime okay so and it's a credible fixed
+
+ align:start position:0%
+regime okay so and it's a credible fixed
+ 
+
+ align:start position:0%
+regime okay so and it's a credible fixed
+exchange regime then I ask you again the
+
+ align:start position:0%
+exchange regime then I ask you again the
+ 
+
+ align:start position:0%
+exchange regime then I ask you again the
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+what what kind of fiscal policy would
+
+ align:start position:0%
+what what kind of fiscal policy would
+ 
+
+ align:start position:0%
+what what kind of fiscal policy would
+you run in that country
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the same expansionary that's what you
+
+ align:start position:0%
+the same expansionary that's what you
+ 
+
+ align:start position:0%
+the same expansionary that's what you
+would do and is effective as it was in
+
+ align:start position:0%
+would do and is effective as it was in
+ 
+
+ align:start position:0%
+would do and is effective as it was in
+close economy a little less because the
+
+ align:start position:0%
+close economy a little less because the
+ 
+
+ align:start position:0%
+close economy a little less because the
+multiply is a little less that's it but
+
+ align:start position:0%
+multiply is a little less that's it but
+ 
+
+ align:start position:0%
+multiply is a little less that's it but
+no difference in the
+
+ align:start position:0%
+no difference in the
+ 
+
+ align:start position:0%
+no difference in the
+analysis in fact fiscal policy has
+
+ align:start position:0%
+analysis in fact fiscal policy has
+ 
+
+ align:start position:0%
+analysis in fact fiscal policy has
+exactly the same effect as as a fiscal
+
+ align:start position:0%
+exactly the same effect as as a fiscal
+ 
+
+ align:start position:0%
+exactly the same effect as as a fiscal
+policy in the flexible exchange rate in
+
+ align:start position:0%
+policy in the flexible exchange rate in
+ 
+
+ align:start position:0%
+policy in the flexible exchange rate in
+this case because I haven't moved
+
+ align:start position:0%
+this case because I haven't moved
+ 
+
+ align:start position:0%
+this case because I haven't moved
+exchange rate in any event in either of
+
+ align:start position:0%
+exchange rate in any event in either of
+ 
+
+ align:start position:0%
+exchange rate in any event in either of
+the two cases okay what should the
+
+ align:start position:0%
+the two cases okay what should the
+ 
+
+ align:start position:0%
+the two cases okay what should the
+Central Bank do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a tricky
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question yes Central Bank knows so it
+
+ align:start position:0%
+question yes Central Bank knows so it
+ 
+
+ align:start position:0%
+question yes Central Bank knows so it
+will have to match yeah exactly so the
+
+ align:start position:0%
+will have to match yeah exactly so the
+ 
+
+ align:start position:0%
+will have to match yeah exactly so the
+Central Bank cannot do anything I'm
+
+ align:start position:0%
+Central Bank cannot do anything I'm
+ 
+
+ align:start position:0%
+Central Bank cannot do anything I'm
+saying suppose this is an EOS sycratic
+
+ align:start position:0%
+saying suppose this is an EOS sycratic
+ 
+
+ align:start position:0%
+saying suppose this is an EOS sycratic
+recession this countri is in
+
+ align:start position:0%
+recession this countri is in
+ 
+
+ align:start position:0%
+recession this countri is in
+recession now now it wants to use its
+
+ align:start position:0%
+recession now now it wants to use its
+ 
+
+ align:start position:0%
+recession now now it wants to use its
+policy tools to deal with that it has
+
+ align:start position:0%
+policy tools to deal with that it has
+ 
+
+ align:start position:0%
+policy tools to deal with that it has
+fiscal but it doesn't have monetary
+
+ align:start position:0%
+fiscal but it doesn't have monetary
+ 
+
+ align:start position:0%
+fiscal but it doesn't have monetary
+policy unless the cycle of the other
+
+ align:start position:0%
+policy unless the cycle of the other
+ 
+
+ align:start position:0%
+policy unless the cycle of the other
+country coincides with your cycle so
+
+ align:start position:0%
+country coincides with your cycle so
+ 
+
+ align:start position:0%
+country coincides with your cycle so
+it's a global recession or something
+
+ align:start position:0%
+it's a global recession or something
+ 
+
+ align:start position:0%
+it's a global recession or something
+like that then then you're doomed
+
+ align:start position:0%
+like that then then you're doomed
+ 
+
+ align:start position:0%
+like that then then you're doomed
+because other countries doing the
+
+ align:start position:0%
+because other countries doing the
+ 
+
+ align:start position:0%
+because other countries doing the
+monetary policy for what they're doing
+
+ align:start position:0%
+monetary policy for what they're doing
+ 
+
+ align:start position:0%
+monetary policy for what they're doing
+they need not for what you need and
+
+ align:start position:0%
+they need not for what you need and
+ 
+
+ align:start position:0%
+they need not for what you need and
+therefore you don't have monetary policy
+
+ align:start position:0%
+therefore you don't have monetary policy
+ 
+
+ align:start position:0%
+therefore you don't have monetary policy
+so that's a costly thing of a fixed
+
+ align:start position:0%
+so that's a costly thing of a fixed
+ 
+
+ align:start position:0%
+so that's a costly thing of a fixed
+exchange rate we already said it but you
+
+ align:start position:0%
+exchange rate we already said it but you
+ 
+
+ align:start position:0%
+exchange rate we already said it but you
+now we're making it very concrete
+
+ align:start position:0%
+now we're making it very concrete
+ 
+
+ align:start position:0%
+now we're making it very concrete
+because we are in a recession and you
+
+ align:start position:0%
+because we are in a recession and you
+ 
+
+ align:start position:0%
+because we are in a recession and you
+realize now that you don't have a tool
+
+ align:start position:0%
+realize now that you don't have a tool
+ 
+
+ align:start position:0%
+realize now that you don't have a tool
+that you had before okay so that's a
+
+ align:start position:0%
+that you had before okay so that's a
+ 
+
+ align:start position:0%
+that you had before okay so that's a
+cost of a physic
+
+ align:start position:0%
+cost of a physic
+ 
+
+ align:start position:0%
+cost of a physic
+sry here is an example here when I'm
+
+ align:start position:0%
+sry here is an example here when I'm
+ 
+
+ align:start position:0%
+sry here is an example here when I'm
+plotting is the the policy rate in the
+
+ align:start position:0%
+plotting is the the policy rate in the
+ 
+
+ align:start position:0%
+plotting is the the policy rate in the
+US that's the blue one and that's the
+
+ align:start position:0%
+US that's the blue one and that's the
+ 
+
+ align:start position:0%
+US that's the blue one and that's the
+policy rate in Hong Kong there are small
+
+ align:start position:0%
+policy rate in Hong Kong there are small
+ 
+
+ align:start position:0%
+policy rate in Hong Kong there are small
+difference but you can see that the
+
+ align:start position:0%
+difference but you can see that the
+ 
+
+ align:start position:0%
+difference but you can see that the
+these are technical things but you can
+
+ align:start position:0%
+these are technical things but you can
+ 
+
+ align:start position:0%
+these are technical things but you can
+see that that Hong Kong has to follow
+
+ align:start position:0%
+see that that Hong Kong has to follow
+ 
+
+ align:start position:0%
+see that that Hong Kong has to follow
+the US essentially it's exactly the same
+
+ align:start position:0%
+the US essentially it's exactly the same
+ 
+
+ align:start position:0%
+the US essentially it's exactly the same
+shape so Hong Kong doesn't have
+
+ align:start position:0%
+shape so Hong Kong doesn't have
+ 
+
+ align:start position:0%
+shape so Hong Kong doesn't have
+independent monetary policy okay again
+
+ align:start position:0%
+independent monetary policy okay again
+ 
+
+ align:start position:0%
+independent monetary policy okay again
+those are technical gaps are not really
+
+ align:start position:0%
+those are technical gaps are not really
+ 
+
+ align:start position:0%
+those are technical gaps are not really
+but just look at the shape it's exactly
+
+ align:start position:0%
+but just look at the shape it's exactly
+ 
+
+ align:start position:0%
+but just look at the shape it's exactly
+the same mov around so Hong Kong doesn't
+
+ align:start position:0%
+the same mov around so Hong Kong doesn't
+ 
+
+ align:start position:0%
+the same mov around so Hong Kong doesn't
+have monetary policy
+
+ align:start position:0%
+have monetary policy
+ 
+
+ align:start position:0%
+have monetary policy
+period not something they Happ they get
+
+ align:start position:0%
+period not something they Happ they get
+ 
+
+ align:start position:0%
+period not something they Happ they get
+a recession that has to do with their
+
+ align:start position:0%
+a recession that has to do with their
+ 
+
+ align:start position:0%
+a recession that has to do with their
+own cycle and that is not a result of
+
+ align:start position:0%
+own cycle and that is not a result of
+ 
+
+ align:start position:0%
+own cycle and that is not a result of
+something that is happening in the US
+
+ align:start position:0%
+something that is happening in the US
+ 
+
+ align:start position:0%
+something that is happening in the US
+they don't have the tool to deal with
+
+ align:start position:0%
+they don't have the tool to deal with
+ 
+
+ align:start position:0%
+they don't have the tool to deal with
+that of course during Co and and during
+
+ align:start position:0%
+that of course during Co and and during
+ 
+
+ align:start position:0%
+that of course during Co and and during
+the global financial crisis they were
+
+ align:start position:0%
+the global financial crisis they were
+ 
+
+ align:start position:0%
+the global financial crisis they were
+align so they you know they would have
+
+ align:start position:0%
+align so they you know they would have
+ 
+
+ align:start position:0%
+align so they you know they would have
+moved it in the same direction that
+
+ align:start position:0%
+moved it in the same direction that
+ 
+
+ align:start position:0%
+moved it in the same direction that
+worked but if there is a shock that is a
+
+ align:start position:0%
+worked but if there is a shock that is a
+ 
+
+ align:start position:0%
+worked but if there is a shock that is a
+Chinese Centric that is affecting Hong
+
+ align:start position:0%
+Chinese Centric that is affecting Hong
+ 
+
+ align:start position:0%
+Chinese Centric that is affecting Hong
+Kong the US monetary policy is not going
+
+ align:start position:0%
+Kong the US monetary policy is not going
+ 
+
+ align:start position:0%
+Kong the US monetary policy is not going
+to react to that
+
+ align:start position:0%
+to react to that
+ 
+
+ align:start position:0%
+to react to that
+and that that that's a problem for Hong
+
+ align:start position:0%
+and that that that's a problem for Hong
+ 
+
+ align:start position:0%
+and that that that's a problem for Hong
+Hong Kong still they choose to do it the
+
+ align:start position:0%
+Hong Kong still they choose to do it the
+ 
+
+ align:start position:0%
+Hong Kong still they choose to do it the
+good question is
+
+ align:start position:0%
+good question is
+ 
+
+ align:start position:0%
+good question is
+why Always There is politics there is
+
+ align:start position:0%
+why Always There is politics there is
+ 
+
+ align:start position:0%
+why Always There is politics there is
+more than than the kind of thing but
+
+ align:start position:0%
+more than than the kind of thing but
+ 
+
+ align:start position:0%
+more than than the kind of thing but
+there are also economic Arguments for
+
+ align:start position:0%
+there are also economic Arguments for
+ 
+
+ align:start position:0%
+there are also economic Arguments for
+why you may want to do this
+
+ align:start position:0%
+why you may want to do this
+ 
+
+ align:start position:0%
+why you may want to do this
+things another situation that I mention
+
+ align:start position:0%
+things another situation that I mention
+ 
+
+ align:start position:0%
+things another situation that I mention
+happens all the time every other day in
+
+ align:start position:0%
+happens all the time every other day in
+ 
+
+ align:start position:0%
+happens all the time every other day in
+Argentina for example is speculative
+
+ align:start position:0%
+Argentina for example is speculative
+ 
+
+ align:start position:0%
+Argentina for example is speculative
+attacks on the currency so you want to
+
+ align:start position:0%
+attacks on the currency so you want to
+ 
+
+ align:start position:0%
+attacks on the currency so you want to
+have a fixed exchange rate but the
+
+ align:start position:0%
+have a fixed exchange rate but the
+ 
+
+ align:start position:0%
+have a fixed exchange rate but the
+markets don't believe you that you're
+
+ align:start position:0%
+markets don't believe you that you're
+ 
+
+ align:start position:0%
+markets don't believe you that you're
+going to be able to keep in there and uh
+
+ align:start position:0%
+going to be able to keep in there and uh
+ 
+
+ align:start position:0%
+going to be able to keep in there and uh
+and so what happens so look at this
+
+ align:start position:0%
+and so what happens so look at this
+ 
+
+ align:start position:0%
+and so what happens so look at this
+equation here suppose that that that you
+
+ align:start position:0%
+equation here suppose that that that you
+ 
+
+ align:start position:0%
+equation here suppose that that that you
+have a fixed exchange rate but now the
+
+ align:start position:0%
+have a fixed exchange rate but now the
+ 
+
+ align:start position:0%
+have a fixed exchange rate but now the
+market think you're not going to be able
+
+ align:start position:0%
+market think you're not going to be able
+ 
+
+ align:start position:0%
+market think you're not going to be able
+to sustain it okay so that means suppose
+
+ align:start position:0%
+to sustain it okay so that means suppose
+ 
+
+ align:start position:0%
+to sustain it okay so that means suppose
+that this guy starts going down that
+
+ align:start position:0%
+that this guy starts going down that
+ 
+
+ align:start position:0%
+that this guy starts going down that
+happens again in Argentina every other
+
+ align:start position:0%
+happens again in Argentina every other
+ 
+
+ align:start position:0%
+happens again in Argentina every other
+day probably today every single day no
+
+ align:start position:0%
+day probably today every single day no
+ 
+
+ align:start position:0%
+day probably today every single day no
+you want to say that they went to saiz
+
+ align:start position:0%
+you want to say that they went to saiz
+ 
+
+ align:start position:0%
+you want to say that they went to saiz
+exchange rate but the markets don't
+
+ align:start position:0%
+exchange rate but the markets don't
+ 
+
+ align:start position:0%
+exchange rate but the markets don't
+believe you and they expect your
+
+ align:start position:0%
+believe you and they expect your
+ 
+
+ align:start position:0%
+believe you and they expect your
+currency to lose value in the next few
+
+ align:start position:0%
+currency to lose value in the next few
+ 
+
+ align:start position:0%
+currency to lose value in the next few
+hours in the case of Argentina
+
+ align:start position:0%
+hours in the case of Argentina
+ 
+
+ align:start position:0%
+hours in the case of Argentina
+so this guy is going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down what happens to the current to the
+
+ align:start position:0%
+down what happens to the current to the
+ 
+
+ align:start position:0%
+down what happens to the current to the
+to the current exchang so expector
+
+ align:start position:0%
+to the current exchang so expector
+ 
+
+ align:start position:0%
+to the current exchang so expector
+exchange goes
+
+ align:start position:0%
+exchange goes
+ 
+
+ align:start position:0%
+exchange goes
+down everyone expects your currency to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drop what what will tend to happen to
+
+ align:start position:0%
+drop what what will tend to happen to
+ 
+
+ align:start position:0%
+drop what what will tend to happen to
+the currency today to the P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today it drops but you have a fixed
+
+ align:start position:0%
+today it drops but you have a fixed
+ 
+
+ align:start position:0%
+today it drops but you have a fixed
+exchange rate you can't let it drop
+
+ align:start position:0%
+exchange rate you can't let it drop
+ 
+
+ align:start position:0%
+exchange rate you can't let it drop
+so if you're going to maintain an
+
+ align:start position:0%
+so if you're going to maintain an
+ 
+
+ align:start position:0%
+so if you're going to maintain an
+exchange a fixed exchange rate and now
+
+ align:start position:0%
+exchange a fixed exchange rate and now
+ 
+
+ align:start position:0%
+exchange a fixed exchange rate and now
+you have a speculative attack people
+
+ align:start position:0%
+you have a speculative attack people
+ 
+
+ align:start position:0%
+you have a speculative attack people
+think your currency is going to drop and
+
+ align:start position:0%
+think your currency is going to drop and
+ 
+
+ align:start position:0%
+think your currency is going to drop and
+you want to maintain your peeg that's
+
+ align:start position:0%
+you want to maintain your peeg that's
+ 
+
+ align:start position:0%
+you want to maintain your peeg that's
+called defending the peeg if you want to
+
+ align:start position:0%
+called defending the peeg if you want to
+ 
+
+ align:start position:0%
+called defending the peeg if you want to
+defend the peeg then the only option you
+
+ align:start position:0%
+defend the peeg then the only option you
+ 
+
+ align:start position:0%
+defend the peeg then the only option you
+have if this guy is dropping to keep the
+
+ align:start position:0%
+have if this guy is dropping to keep the
+ 
+
+ align:start position:0%
+have if this guy is dropping to keep the
+exchange it is to raise interest rates a
+
+ align:start position:0%
+exchange it is to raise interest rates a
+ 
+
+ align:start position:0%
+exchange it is to raise interest rates a
+lot that's the way you fight the main
+
+ align:start position:0%
+lot that's the way you fight the main
+ 
+
+ align:start position:0%
+lot that's the way you fight the main
+way you fight it I mean you fight it by
+
+ align:start position:0%
+way you fight it I mean you fight it by
+ 
+
+ align:start position:0%
+way you fight it I mean you fight it by
+closing capital accounts and so but
+
+ align:start position:0%
+closing capital accounts and so but
+ 
+
+ align:start position:0%
+closing capital accounts and so but
+that's the last result you first try to
+
+ align:start position:0%
+that's the last result you first try to
+ 
+
+ align:start position:0%
+that's the last result you first try to
+fight it with monetary policy so if this
+
+ align:start position:0%
+fight it with monetary policy so if this
+ 
+
+ align:start position:0%
+fight it with monetary policy so if this
+thing is dropping you fight it by
+
+ align:start position:0%
+thing is dropping you fight it by
+ 
+
+ align:start position:0%
+thing is dropping you fight it by
+increasing interest rate a lot and
+
+ align:start position:0%
+increasing interest rate a lot and
+ 
+
+ align:start position:0%
+increasing interest rate a lot and
+that's the way you stabilize the
+
+ align:start position:0%
+that's the way you stabilize the
+ 
+
+ align:start position:0%
+that's the way you stabilize the
+currency but what happens when you raise
+
+ align:start position:0%
+currency but what happens when you raise
+ 
+
+ align:start position:0%
+currency but what happens when you raise
+interest rate a lot to defend the parity
+
+ align:start position:0%
+interest rate a lot to defend the parity
+ 
+
+ align:start position:0%
+interest rate a lot to defend the parity
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+peg what's the problem of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah you generate a domestic
+
+ align:start position:0%
+that yeah you generate a domestic
+ 
+
+ align:start position:0%
+that yeah you generate a domestic
+recession okay because just to defend
+
+ align:start position:0%
+recession okay because just to defend
+ 
+
+ align:start position:0%
+recession okay because just to defend
+your currency your peg you have to raise
+
+ align:start position:0%
+your currency your peg you have to raise
+ 
+
+ align:start position:0%
+your currency your peg you have to raise
+interest rate a lot no so it means
+
+ align:start position:0%
+interest rate a lot no so it means
+ 
+
+ align:start position:0%
+interest rate a lot no so it means
+you're going to have a recession at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+home so that's another problem of fix
+
+ align:start position:0%
+home so that's another problem of fix
+ 
+
+ align:start position:0%
+home so that's another problem of fix
+exchange it's a problem that's not a
+
+ align:start position:0%
+exchange it's a problem that's not a
+ 
+
+ align:start position:0%
+exchange it's a problem that's not a
+problem for Hong Kong it was in 1997
+
+ align:start position:0%
+problem for Hong Kong it was in 1997
+ 
+
+ align:start position:0%
+problem for Hong Kong it was in 1997
+they did have a speculated attack
+
+ align:start position:0%
+they did have a speculated attack
+ 
+
+ align:start position:0%
+they did have a speculated attack
+despite the fact that they had twice the
+
+ align:start position:0%
+despite the fact that they had twice the
+ 
+
+ align:start position:0%
+despite the fact that they had twice the
+number of reserves relative to their
+
+ align:start position:0%
+number of reserves relative to their
+ 
+
+ align:start position:0%
+number of reserves relative to their
+money base but still they have specul
+
+ align:start position:0%
+money base but still they have specul
+ 
+
+ align:start position:0%
+money base but still they have specul
+that but it rarely happens in Hong Kong
+
+ align:start position:0%
+that but it rarely happens in Hong Kong
+ 
+
+ align:start position:0%
+that but it rarely happens in Hong Kong
+in Argentina again every other day but
+
+ align:start position:0%
+in Argentina again every other day but
+ 
+
+ align:start position:0%
+in Argentina again every other day but
+but in same in Turkey in Turkey is every
+
+ align:start position:0%
+but in same in Turkey in Turkey is every
+ 
+
+ align:start position:0%
+but in same in Turkey in Turkey is every
+15 days but but but uh but it's
+
+ align:start position:0%
+15 days but but but uh but it's
+ 
+
+ align:start position:0%
+15 days but but but uh but it's
+happening all the
+
+ align:start position:0%
+happening all the
+ 
+
+ align:start position:0%
+happening all the
+time so that's a problem as well because
+
+ align:start position:0%
+time so that's a problem as well because
+ 
+
+ align:start position:0%
+time so that's a problem as well because
+if you have to spend a lot of energy
+
+ align:start position:0%
+if you have to spend a lot of energy
+ 
+
+ align:start position:0%
+if you have to spend a lot of energy
+defending your peg then you're going to
+
+ align:start position:0%
+defending your peg then you're going to
+ 
+
+ align:start position:0%
+defending your peg then you're going to
+be causing lots of recessions at home
+
+ align:start position:0%
+be causing lots of recessions at home
+ 
+
+ align:start position:0%
+be causing lots of recessions at home
+just to stabilize the currency
+
+ align:start position:0%
+just to stabilize the currency
+ 
+
+ align:start position:0%
+just to stabilize the currency
+okay that's that's bigger economy say
+
+ align:start position:0%
+okay that's that's bigger economy say
+ 
+
+ align:start position:0%
+okay that's that's bigger economy say
+okay well Argentina turkey and so on
+
+ align:start position:0%
+okay well Argentina turkey and so on
+ 
+
+ align:start position:0%
+okay well Argentina turkey and so on
+know but these are bigger boys no here
+
+ align:start position:0%
+know but these are bigger boys no here
+ 
+
+ align:start position:0%
+know but these are bigger boys no here
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+have this is the ERM crisis so before
+
+ align:start position:0%
+have this is the ERM crisis so before
+ 
+
+ align:start position:0%
+have this is the ERM crisis so before
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+euro uh more or the Euro Zone plus the
+
+ align:start position:0%
+euro uh more or the Euro Zone plus the
+ 
+
+ align:start position:0%
+euro uh more or the Euro Zone plus the
+UK H had a system called the
+
+ align:start position:0%
+UK H had a system called the
+ 
+
+ align:start position:0%
+UK H had a system called the
+ERM em emsm ERM is the well anyway EMS
+
+ align:start position:0%
+ERM em emsm ERM is the well anyway EMS
+ 
+
+ align:start position:0%
+ERM em emsm ERM is the well anyway EMS
+is European monetary system ERM is
+
+ align:start position:0%
+is European monetary system ERM is
+ 
+
+ align:start position:0%
+is European monetary system ERM is
+exchang rates mechanism or something
+
+ align:start position:0%
+exchang rates mechanism or something
+ 
+
+ align:start position:0%
+exchang rates mechanism or something
+like that and they're both link but
+
+ align:start position:0%
+like that and they're both link but
+ 
+
+ align:start position:0%
+like that and they're both link but
+let's call it the the the European
+
+ align:start position:0%
+let's call it the the the European
+ 
+
+ align:start position:0%
+let's call it the the the European
+monetary system and the basic idea of
+
+ align:start position:0%
+monetary system and the basic idea of
+ 
+
+ align:start position:0%
+monetary system and the basic idea of
+the European monetary
+
+ align:start position:0%
+the European monetary
+ 
+
+ align:start position:0%
+the European monetary
+system was that
+
+ align:start position:0%
+system was that
+ 
+
+ align:start position:0%
+system was that
+that they behave very much like
+
+ align:start position:0%
+that they behave very much like
+ 
+
+ align:start position:0%
+that they behave very much like
+Singapore with respect to each other
+
+ align:start position:0%
+Singapore with respect to each other
+ 
+
+ align:start position:0%
+Singapore with respect to each other
+meaning they allow themselves to H move
+
+ align:start position:0%
+meaning they allow themselves to H move
+ 
+
+ align:start position:0%
+meaning they allow themselves to H move
+around but only in narrow bands the the
+
+ align:start position:0%
+around but only in narrow bands the the
+ 
+
+ align:start position:0%
+around but only in narrow bands the the
+countries that have the more
+
+ align:start position:0%
+countries that have the more
+ 
+
+ align:start position:0%
+countries that have the more
+stable um domestic monetary position
+
+ align:start position:0%
+stable um domestic monetary position
+ 
+
+ align:start position:0%
+stable um domestic monetary position
+like France Vis the Germany the Dutch
+
+ align:start position:0%
+like France Vis the Germany the Dutch
+ 
+
+ align:start position:0%
+like France Vis the Germany the Dutch
+Mark and the French Frank what they had
+
+ align:start position:0%
+Mark and the French Frank what they had
+ 
+
+ align:start position:0%
+Mark and the French Frank what they had
+is bands of Two and a half% up and down
+
+ align:start position:0%
+is bands of Two and a half% up and down
+ 
+
+ align:start position:0%
+is bands of Two and a half% up and down
+and they move within those those ranges
+
+ align:start position:0%
+and they move within those those ranges
+ 
+
+ align:start position:0%
+and they move within those those ranges
+they didn't have a full Peg but they
+
+ align:start position:0%
+they didn't have a full Peg but they
+ 
+
+ align:start position:0%
+they didn't have a full Peg but they
+allow themselves to move a little bit
+
+ align:start position:0%
+allow themselves to move a little bit
+ 
+
+ align:start position:0%
+allow themselves to move a little bit
+Portugal which was a little had little
+
+ align:start position:0%
+Portugal which was a little had little
+ 
+
+ align:start position:0%
+Portugal which was a little had little
+less discipline they had 5% for each
+
+ align:start position:0%
+less discipline they had 5% for each
+ 
+
+ align:start position:0%
+less discipline they had 5% for each
+side and stuff like that but the point
+
+ align:start position:0%
+side and stuff like that but the point
+ 
+
+ align:start position:0%
+side and stuff like that but the point
+is they would have narrow bands okay and
+
+ align:start position:0%
+is they would have narrow bands okay and
+ 
+
+ align:start position:0%
+is they would have narrow bands okay and
+they move around in those narrow bands
+
+ align:start position:0%
+they move around in those narrow bands
+ 
+
+ align:start position:0%
+they move around in those narrow bands
+and they kept there ER kept it for quite
+
+ align:start position:0%
+and they kept there ER kept it for quite
+ 
+
+ align:start position:0%
+and they kept there ER kept it for quite
+a while before the
+
+ align:start position:0%
+a while before the
+ 
+
+ align:start position:0%
+a while before the
+euro now here the whole system came
+
+ align:start position:0%
+euro now here the whole system came
+ 
+
+ align:start position:0%
+euro now here the whole system came
+under a speculative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attack what happened around
+
+ align:start position:0%
+attack what happened around
+ 
+
+ align:start position:0%
+attack what happened around
+there you probably have no
+
+ align:start position:0%
+there you probably have no
+ 
+
+ align:start position:0%
+there you probably have no
+idea maybe like the end of the
+
+ align:start position:0%
+idea maybe like the end of the
+ 
+
+ align:start position:0%
+idea maybe like the end of the
+well it's really linked to that
+
+ align:start position:0%
+well it's really linked to that
+ 
+
+ align:start position:0%
+well it's really linked to that
+yes yeah it's the German re
+
+ align:start position:0%
+yes yeah it's the German re
+ 
+
+ align:start position:0%
+yes yeah it's the German re
+reunification so what happened is when
+
+ align:start position:0%
+reunification so what happened is when
+ 
+
+ align:start position:0%
+reunification so what happened is when
+East Germany and West Germany unify they
+
+ align:start position:0%
+East Germany and West Germany unify they
+ 
+
+ align:start position:0%
+East Germany and West Germany unify they
+had to have a massive fiscal policy Mass
+
+ align:start position:0%
+had to have a massive fiscal policy Mass
+ 
+
+ align:start position:0%
+had to have a massive fiscal policy Mass
+expansionary fiscal policy and that big
+
+ align:start position:0%
+expansionary fiscal policy and that big
+ 
+
+ align:start position:0%
+expansionary fiscal policy and that big
+expansion put lots of upward pressure on
+
+ align:start position:0%
+expansion put lots of upward pressure on
+ 
+
+ align:start position:0%
+expansion put lots of upward pressure on
+Dom on on on on German interest rates
+
+ align:start position:0%
+Dom on on on on German interest rates
+ 
+
+ align:start position:0%
+Dom on on on on German interest rates
+and and that led to Big
+
+ align:start position:0%
+and and that led to Big
+ 
+
+ align:start position:0%
+and and that led to Big
+appreciations of the Dutch Market and
+
+ align:start position:0%
+appreciations of the Dutch Market and
+ 
+
+ align:start position:0%
+appreciations of the Dutch Market and
+and the other countries tried to fight
+
+ align:start position:0%
+and the other countries tried to fight
+ 
+
+ align:start position:0%
+and the other countries tried to fight
+it because they had to be in this very
+
+ align:start position:0%
+it because they had to be in this very
+ 
+
+ align:start position:0%
+it because they had to be in this very
+narrow band but they were experiencing
+
+ align:start position:0%
+narrow band but they were experiencing
+ 
+
+ align:start position:0%
+narrow band but they were experiencing
+this big speculative attacks and so they
+
+ align:start position:0%
+this big speculative attacks and so they
+ 
+
+ align:start position:0%
+this big speculative attacks and so they
+had to raise their interest rate
+
+ align:start position:0%
+had to raise their interest rate
+ 
+
+ align:start position:0%
+had to raise their interest rate
+enormously H the UK tried to do it for a
+
+ align:start position:0%
+enormously H the UK tried to do it for a
+ 
+
+ align:start position:0%
+enormously H the UK tried to do it for a
+while and I we give up and then they
+
+ align:start position:0%
+while and I we give up and then they
+ 
+
+ align:start position:0%
+while and I we give up and then they
+they they they abandoned the system the
+
+ align:start position:0%
+they they they abandoned the system the
+ 
+
+ align:start position:0%
+they they they abandoned the system the
+French tried to stay in there for quite
+
+ align:start position:0%
+French tried to stay in there for quite
+ 
+
+ align:start position:0%
+French tried to stay in there for quite
+a bit okay you can see the French Frank
+
+ align:start position:0%
+a bit okay you can see the French Frank
+ 
+
+ align:start position:0%
+a bit okay you can see the French Frank
+they didn't move they didn't move but it
+
+ align:start position:0%
+they didn't move they didn't move but it
+ 
+
+ align:start position:0%
+they didn't move they didn't move but it
+was extremely costly for them because
+
+ align:start position:0%
+was extremely costly for them because
+ 
+
+ align:start position:0%
+was extremely costly for them because
+the interest rate has to go up a lot and
+
+ align:start position:0%
+the interest rate has to go up a lot and
+ 
+
+ align:start position:0%
+the interest rate has to go up a lot and
+sort of they got into big recession and
+
+ align:start position:0%
+sort of they got into big recession and
+ 
+
+ align:start position:0%
+sort of they got into big recession and
+eventually the whole system broke up
+
+ align:start position:0%
+eventually the whole system broke up
+ 
+
+ align:start position:0%
+eventually the whole system broke up
+broke down I mean everyone left and
+
+ align:start position:0%
+broke down I mean everyone left and
+ 
+
+ align:start position:0%
+broke down I mean everyone left and
+eventually they rejoined but now in the
+
+ align:start position:0%
+eventually they rejoined but now in the
+ 
+
+ align:start position:0%
+eventually they rejoined but now in the
+Euro and the euro is a little different
+
+ align:start position:0%
+Euro and the euro is a little different
+ 
+
+ align:start position:0%
+Euro and the euro is a little different
+because in the Euro you gave up there's
+
+ align:start position:0%
+because in the Euro you gave up there's
+ 
+
+ align:start position:0%
+because in the Euro you gave up there's
+no space for speculative attacks because
+
+ align:start position:0%
+no space for speculative attacks because
+ 
+
+ align:start position:0%
+no space for speculative attacks because
+there's a single currency okay so that's
+
+ align:start position:0%
+there's a single currency okay so that's
+ 
+
+ align:start position:0%
+there's a single currency okay so that's
+that's the most extreme form speculative
+
+ align:start position:0%
+that's the most extreme form speculative
+ 
+
+ align:start position:0%
+that's the most extreme form speculative
+attacks nowadays in Europe happen
+
+ align:start position:0%
+attacks nowadays in Europe happen
+ 
+
+ align:start position:0%
+attacks nowadays in Europe happen
+through different
+
+ align:start position:0%
+through different
+ 
+
+ align:start position:0%
+through different
+means it's the well anyways let me not
+
+ align:start position:0%
+means it's the well anyways let me not
+ 
+
+ align:start position:0%
+means it's the well anyways let me not
+get into that but but but here you have
+
+ align:start position:0%
+get into that but but but here you have
+ 
+
+ align:start position:0%
+get into that but but but here you have
+so I'm saying having a fixed exchange is
+
+ align:start position:0%
+so I'm saying having a fixed exchange is
+ 
+
+ align:start position:0%
+so I'm saying having a fixed exchange is
+not easy even for countries that have
+
+ align:start position:0%
+not easy even for countries that have
+ 
+
+ align:start position:0%
+not easy even for countries that have
+sort of very welldeveloped financial
+
+ align:start position:0%
+sort of very welldeveloped financial
+ 
+
+ align:start position:0%
+sort of very welldeveloped financial
+markets and so on so
+
+ align:start position:0%
+markets and so on so
+ 
+
+ align:start position:0%
+markets and so on so
+forth now it would seem given all that I
+
+ align:start position:0%
+forth now it would seem given all that I
+ 
+
+ align:start position:0%
+forth now it would seem given all that I
+said that I mean there's no reason to
+
+ align:start position:0%
+said that I mean there's no reason to
+ 
+
+ align:start position:0%
+said that I mean there's no reason to
+have a fixed exchange is something you
+
+ align:start position:0%
+have a fixed exchange is something you
+ 
+
+ align:start position:0%
+have a fixed exchange is something you
+look give up an instrument and on top of
+
+ align:start position:0%
+look give up an instrument and on top of
+ 
+
+ align:start position:0%
+look give up an instrument and on top of
+that you are subject to speculative
+
+ align:start position:0%
+that you are subject to speculative
+ 
+
+ align:start position:0%
+that you are subject to speculative
+attacks all the time okay not all the
+
+ align:start position:0%
+attacks all the time okay not all the
+ 
+
+ align:start position:0%
+attacks all the time okay not all the
+time well it depends on how bad you are
+
+ align:start position:0%
+time well it depends on how bad you are
+ 
+
+ align:start position:0%
+time well it depends on how bad you are
+but but you know you have to be very
+
+ align:start position:0%
+but but you know you have to be very
+ 
+
+ align:start position:0%
+but but you know you have to be very
+well behave because otherwise you're
+
+ align:start position:0%
+well behave because otherwise you're
+ 
+
+ align:start position:0%
+well behave because otherwise you're
+subject to speculative attacks all the
+
+ align:start position:0%
+subject to speculative attacks all the
+ 
+
+ align:start position:0%
+subject to speculative attacks all the
+time so so why not do flexible exchange
+
+ align:start position:0%
+time so so why not do flexible exchange
+ 
+
+ align:start position:0%
+time so so why not do flexible exchange
+why why what is wrong with flexible
+
+ align:start position:0%
+why why what is wrong with flexible
+ 
+
+ align:start position:0%
+why why what is wrong with flexible
+exchange rate well I think the main
+
+ align:start position:0%
+exchange rate well I think the main
+ 
+
+ align:start position:0%
+exchange rate well I think the main
+problem of flexible exchange rate is
+
+ align:start position:0%
+problem of flexible exchange rate is
+ 
+
+ align:start position:0%
+problem of flexible exchange rate is
+that it tends to move a lot I mean we
+
+ align:start position:0%
+that it tends to move a lot I mean we
+ 
+
+ align:start position:0%
+that it tends to move a lot I mean we
+know that it moves a lot more than
+
+ align:start position:0%
+know that it moves a lot more than
+ 
+
+ align:start position:0%
+know that it moves a lot more than
+fundamental meaning you know
+
+ align:start position:0%
+fundamental meaning you know
+ 
+
+ align:start position:0%
+fundamental meaning you know
+productivity is a little higher in one
+
+ align:start position:0%
+productivity is a little higher in one
+ 
+
+ align:start position:0%
+productivity is a little higher in one
+country than the other demand is a
+
+ align:start position:0%
+country than the other demand is a
+ 
+
+ align:start position:0%
+country than the other demand is a
+little high in the the country but CH
+
+ align:start position:0%
+little high in the the country but CH
+ 
+
+ align:start position:0%
+little high in the the country but CH
+moves a lot more than those little
+
+ align:start position:0%
+moves a lot more than those little
+ 
+
+ align:start position:0%
+moves a lot more than those little
+differences justify
+
+ align:start position:0%
+differences justify
+ 
+
+ align:start position:0%
+differences justify
+and the reason one way of understanding
+
+ align:start position:0%
+and the reason one way of understanding
+ 
+
+ align:start position:0%
+and the reason one way of understanding
+this is the following and this will see
+
+ align:start position:0%
+this is the following and this will see
+ 
+
+ align:start position:0%
+this is the following and this will see
+serve as an introduction to the next
+
+ align:start position:0%
+serve as an introduction to the next
+ 
+
+ align:start position:0%
+serve as an introduction to the next
+topic of the course which will be asset
+
+ align:start position:0%
+topic of the course which will be asset
+ 
+
+ align:start position:0%
+topic of the course which will be asset
+pricing and things like that so let's
+
+ align:start position:0%
+pricing and things like that so let's
+ 
+
+ align:start position:0%
+pricing and things like that so let's
+look at revisit our interest parity
+
+ align:start position:0%
+look at revisit our interest parity
+ 
+
+ align:start position:0%
+look at revisit our interest parity
+condition but now let's not assume that
+
+ align:start position:0%
+condition but now let's not assume that
+ 
+
+ align:start position:0%
+condition but now let's not assume that
+that that the next the the the expected
+
+ align:start position:0%
+that that the next the the the expected
+ 
+
+ align:start position:0%
+that that the next the the the expected
+exchang is fixed I mean that was an
+
+ align:start position:0%
+exchang is fixed I mean that was an
+ 
+
+ align:start position:0%
+exchang is fixed I mean that was an
+assumption just to make our life simple
+
+ align:start position:0%
+assumption just to make our life simple
+ 
+
+ align:start position:0%
+assumption just to make our life simple
+but but needs not be so that's a that's
+
+ align:start position:0%
+but but needs not be so that's a that's
+ 
+
+ align:start position:0%
+but but needs not be so that's a that's
+the uncovering transparity condition is
+
+ align:start position:0%
+the uncovering transparity condition is
+ 
+
+ align:start position:0%
+the uncovering transparity condition is
+this well you see I can replace this guy
+
+ align:start position:0%
+this well you see I can replace this guy
+ 
+
+ align:start position:0%
+this well you see I can replace this guy
+here for what will happen next period
+
+ align:start position:0%
+here for what will happen next period
+ 
+
+ align:start position:0%
+here for what will happen next period
+it's the same thing shifted by a period
+
+ align:start position:0%
+it's the same thing shifted by a period
+ 
+
+ align:start position:0%
+it's the same thing shifted by a period
+with an expectation there so e+ one
+
+ align:start position:0%
+with an expectation there so e+ one
+ 
+
+ align:start position:0%
+with an expectation there so e+ one
+expected this guy here is equal to 1
+
+ align:start position:0%
+expected this guy here is equal to 1
+ 
+
+ align:start position:0%
+expected this guy here is equal to 1
+plus expected domestic interest rate one
+
+ align:start position:0%
+plus expected domestic interest rate one
+ 
+
+ align:start position:0%
+plus expected domestic interest rate one
+period from now divided by 1 plus
+
+ align:start position:0%
+period from now divided by 1 plus
+ 
+
+ align:start position:0%
+period from now divided by 1 plus
+International interest expected one
+
+ align:start position:0%
+International interest expected one
+ 
+
+ align:start position:0%
+International interest expected one
+period from now times the expector
+
+ align:start position:0%
+period from now times the expector
+ 
+
+ align:start position:0%
+period from now times the expector
+exchange it for t plus two two years
+
+ align:start position:0%
+exchange it for t plus two two years
+ 
+
+ align:start position:0%
+exchange it for t plus two two years
+from now and I can keep doing this I can
+
+ align:start position:0%
+from now and I can keep doing this I can
+ 
+
+ align:start position:0%
+from now and I can keep doing this I can
+replace this by something equivalent to
+
+ align:start position:0%
+replace this by something equivalent to
+ 
+
+ align:start position:0%
+replace this by something equivalent to
+that with all the sub index shift by one
+
+ align:start position:0%
+that with all the sub index shift by one
+ 
+
+ align:start position:0%
+that with all the sub index shift by one
+year blah blah blah blah blah and so I
+
+ align:start position:0%
+year blah blah blah blah blah and so I
+ 
+
+ align:start position:0%
+year blah blah blah blah blah and so I
+can end up writing this exchange rate as
+
+ align:start position:0%
+can end up writing this exchange rate as
+ 
+
+ align:start position:0%
+can end up writing this exchange rate as
+this product of lots of things that can
+
+ align:start position:0%
+this product of lots of things that can
+ 
+
+ align:start position:0%
+this product of lots of things that can
+happen in the future the the monetary
+
+ align:start position:0%
+happen in the future the the monetary
+ 
+
+ align:start position:0%
+happen in the future the the monetary
+policy path at home the monetary policy
+
+ align:start position:0%
+policy path at home the monetary policy
+ 
+
+ align:start position:0%
+policy path at home the monetary policy
+path not the next period the path for
+
+ align:start position:0%
+path not the next period the path for
+ 
+
+ align:start position:0%
+path not the next period the path for
+years to come of H monetary policy in
+
+ align:start position:0%
+years to come of H monetary policy in
+ 
+
+ align:start position:0%
+years to come of H monetary policy in
+the other country and there's always an
+
+ align:start position:0%
+the other country and there's always an
+ 
+
+ align:start position:0%
+the other country and there's always an
+expected exchange rate at the end there
+
+ align:start position:0%
+expected exchange rate at the end there
+ 
+
+ align:start position:0%
+expected exchange rate at the end there
+that that that is free can move
+
+ align:start position:0%
+that that that is free can move
+ 
+
+ align:start position:0%
+that that that is free can move
+around so the the problem of this
+
+ align:start position:0%
+around so the the problem of this
+ 
+
+ align:start position:0%
+around so the the problem of this
+exchang is that future matters too
+
+ align:start position:0%
+exchang is that future matters too
+ 
+
+ align:start position:0%
+exchang is that future matters too
+much in a sense and you know people have
+
+ align:start position:0%
+much in a sense and you know people have
+ 
+
+ align:start position:0%
+much in a sense and you know people have
+lots of imagination so all sort of weird
+
+ align:start position:0%
+lots of imagination so all sort of weird
+ 
+
+ align:start position:0%
+lots of imagination so all sort of weird
+things they imagine and and when people
+
+ align:start position:0%
+things they imagine and and when people
+ 
+
+ align:start position:0%
+things they imagine and and when people
+have lots of imagination then these
+
+ align:start position:0%
+have lots of imagination then these
+ 
+
+ align:start position:0%
+have lots of imagination then these
+things are moving a lot and that's the
+
+ align:start position:0%
+things are moving a lot and that's the
+ 
+
+ align:start position:0%
+things are moving a lot and that's the
+reason you see enormous fluctuations in
+
+ align:start position:0%
+reason you see enormous fluctuations in
+ 
+
+ align:start position:0%
+reason you see enormous fluctuations in
+nominal exchange rate
+
+ align:start position:0%
+nominal exchange rate
+ 
+
+ align:start position:0%
+nominal exchange rate
+now ER and that's a problem it's a
+
+ align:start position:0%
+now ER and that's a problem it's a
+ 
+
+ align:start position:0%
+now ER and that's a problem it's a
+problem to have a very volatile exchange
+
+ align:start position:0%
+problem to have a very volatile exchange
+ 
+
+ align:start position:0%
+problem to have a very volatile exchange
+rate because it it makes transactions
+
+ align:start position:0%
+rate because it it makes transactions
+ 
+
+ align:start position:0%
+rate because it it makes transactions
+more difficult I mean you know if the
+
+ align:start position:0%
+more difficult I mean you know if the
+ 
+
+ align:start position:0%
+more difficult I mean you know if the
+price of things are relative price of
+
+ align:start position:0%
+price of things are relative price of
+ 
+
+ align:start position:0%
+price of things are relative price of
+things are changing all the time it's a
+
+ align:start position:0%
+things are changing all the time it's a
+ 
+
+ align:start position:0%
+things are changing all the time it's a
+little bit more difficult to plan er
+
+ align:start position:0%
+little bit more difficult to plan er
+ 
+
+ align:start position:0%
+little bit more difficult to plan er
+Financial investment become more comp
+
+ align:start position:0%
+Financial investment become more comp
+ 
+
+ align:start position:0%
+Financial investment become more comp
+because you get all this exchange rate
+
+ align:start position:0%
+because you get all this exchange rate
+ 
+
+ align:start position:0%
+because you get all this exchange rate
+volatility in between so that's one of
+
+ align:start position:0%
+volatility in between so that's one of
+ 
+
+ align:start position:0%
+volatility in between so that's one of
+the main
+
+ align:start position:0%
+the main
+ 
+
+ align:start position:0%
+the main
+reasons you would prefer if you could to
+
+ align:start position:0%
+reasons you would prefer if you could to
+ 
+
+ align:start position:0%
+reasons you would prefer if you could to
+have a more managed exchange rate it's
+
+ align:start position:0%
+have a more managed exchange rate it's
+ 
+
+ align:start position:0%
+have a more managed exchange rate it's
+because you don't want this all this
+
+ align:start position:0%
+because you don't want this all this
+ 
+
+ align:start position:0%
+because you don't want this all this
+artificial volatility that comes from
+
+ align:start position:0%
+artificial volatility that comes from
+ 
+
+ align:start position:0%
+artificial volatility that comes from
+behavioral trades and things of that
+
+ align:start position:0%
+behavioral trades and things of that
+ 
+
+ align:start position:0%
+behavioral trades and things of that
+kind okay that's the main
+
+ align:start position:0%
+kind okay that's the main
+ 
+
+ align:start position:0%
+kind okay that's the main
+reason ER look at this example for
+
+ align:start position:0%
+reason ER look at this example for
+ 
+
+ align:start position:0%
+reason ER look at this example for
+example example for example sorry about
+
+ align:start position:0%
+example example for example sorry about
+ 
+
+ align:start position:0%
+example example for example sorry about
+that but the this is Russia during the
+
+ align:start position:0%
+that but the this is Russia during the
+ 
+
+ align:start position:0%
+that but the this is Russia during the
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+war this was the the the the rubble the
+
+ align:start position:0%
+war this was the the the the rubble the
+ 
+
+ align:start position:0%
+war this was the the the the rubble the
+the the the Russian
+
+ align:start position:0%
+the the the Russian
+ 
+
+ align:start position:0%
+the the the Russian
+currency and when they invaded of course
+
+ align:start position:0%
+currency and when they invaded of course
+ 
+
+ align:start position:0%
+currency and when they invaded of course
+the thing collapsed the currency
+
+ align:start position:0%
+the thing collapsed the currency
+ 
+
+ align:start position:0%
+the thing collapsed the currency
+collapsed
+
+ align:start position:0%
+collapsed
+ 
+
+ align:start position:0%
+collapsed
+okay H this period is a is a little
+
+ align:start position:0%
+okay H this period is a is a little
+ 
+
+ align:start position:0%
+okay H this period is a is a little
+longer than you think but but it
+
+ align:start position:0%
+longer than you think but but it
+ 
+
+ align:start position:0%
+longer than you think but but it
+collapsed for for quite a while and then
+
+ align:start position:0%
+collapsed for for quite a while and then
+ 
+
+ align:start position:0%
+collapsed for for quite a while and then
+you recover a lot actually overshot and
+
+ align:start position:0%
+you recover a lot actually overshot and
+ 
+
+ align:start position:0%
+you recover a lot actually overshot and
+came down so this is not because the
+
+ align:start position:0%
+came down so this is not because the
+ 
+
+ align:start position:0%
+came down so this is not because the
+Central Bank said you know we're going
+
+ align:start position:0%
+Central Bank said you know we're going
+ 
+
+ align:start position:0%
+Central Bank said you know we're going
+to devalue the Curren anything just
+
+ align:start position:0%
+to devalue the Curren anything just
+ 
+
+ align:start position:0%
+to devalue the Curren anything just
+people so wow this a country going into
+
+ align:start position:0%
+people so wow this a country going into
+ 
+
+ align:start position:0%
+people so wow this a country going into
+war it's going to be a mess so all that
+
+ align:start position:0%
+war it's going to be a mess so all that
+ 
+
+ align:start position:0%
+war it's going to be a mess so all that
+future I talk
+
+ align:start position:0%
+future I talk
+ 
+
+ align:start position:0%
+future I talk
+about er er essentially destroy the
+
+ align:start position:0%
+about er er essentially destroy the
+ 
+
+ align:start position:0%
+about er er essentially destroy the
+currency okay now a lot of that recovery
+
+ align:start position:0%
+currency okay now a lot of that recovery
+ 
+
+ align:start position:0%
+currency okay now a lot of that recovery
+happened there not because people now
+
+ align:start position:0%
+happened there not because people now
+ 
+
+ align:start position:0%
+happened there not because people now
+began to see the future as a better
+
+ align:start position:0%
+began to see the future as a better
+ 
+
+ align:start position:0%
+began to see the future as a better
+future or anything like that is because
+
+ align:start position:0%
+future or anything like that is because
+ 
+
+ align:start position:0%
+future or anything like that is because
+they have to hike interest rate
+
+ align:start position:0%
+they have to hike interest rate
+ 
+
+ align:start position:0%
+they have to hike interest rate
+massively they were around four or 5%
+
+ align:start position:0%
+massively they were around four or 5%
+ 
+
+ align:start position:0%
+massively they were around four or 5%
+and they had to go to 20% interest rate
+
+ align:start position:0%
+and they had to go to 20% interest rate
+ 
+
+ align:start position:0%
+and they had to go to 20% interest rate
+to defend exchange rate remember I told
+
+ align:start position:0%
+to defend exchange rate remember I told
+ 
+
+ align:start position:0%
+to defend exchange rate remember I told
+you I speculative attack and you have
+
+ align:start position:0%
+you I speculative attack and you have
+ 
+
+ align:start position:0%
+you I speculative attack and you have
+enormous pressure on your currency well
+
+ align:start position:0%
+enormous pressure on your currency well
+ 
+
+ align:start position:0%
+enormous pressure on your currency well
+the main tool you have toet that is to
+
+ align:start position:0%
+the main tool you have toet that is to
+ 
+
+ align:start position:0%
+the main tool you have toet that is to
+raise interest rate they had they had
+
+ align:start position:0%
+raise interest rate they had they had
+ 
+
+ align:start position:0%
+raise interest rate they had they had
+interest rate massively they do a lot of
+
+ align:start position:0%
+interest rate massively they do a lot of
+ 
+
+ align:start position:0%
+interest rate massively they do a lot of
+other things as well they put Capital
+
+ align:start position:0%
+other things as well they put Capital
+ 
+
+ align:start position:0%
+other things as well they put Capital
+controls and lots of things but but but
+
+ align:start position:0%
+controls and lots of things but but but
+ 
+
+ align:start position:0%
+controls and lots of things but but but
+this was the main thing they did and so
+
+ align:start position:0%
+this was the main thing they did and so
+ 
+
+ align:start position:0%
+this was the main thing they did and so
+they drag the recession the economy into
+
+ align:start position:0%
+they drag the recession the economy into
+ 
+
+ align:start position:0%
+they drag the recession the economy into
+recession for war related reasons and
+
+ align:start position:0%
+recession for war related reasons and
+ 
+
+ align:start position:0%
+recession for war related reasons and
+because of the monetary policy response
+
+ align:start position:0%
+because of the monetary policy response
+ 
+
+ align:start position:0%
+because of the monetary policy response
+they had to do with that okay so that's
+
+ align:start position:0%
+they had to do with that okay so that's
+ 
+
+ align:start position:0%
+they had to do with that okay so that's
+an extreme case of a war but but that's
+
+ align:start position:0%
+an extreme case of a war but but that's
+ 
+
+ align:start position:0%
+an extreme case of a war but but that's
+the kind of things that can
+
+ align:start position:0%
+the kind of things that can
+ 
+
+ align:start position:0%
+the kind of things that can
+happen in in in in in a floating
+
+ align:start position:0%
+happen in in in in in a floating
+ 
+
+ align:start position:0%
+happen in in in in in a floating
+exchange rate even
+
+ align:start position:0%
+exchange rate even
+ 
+
+ align:start position:0%
+exchange rate even
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+um I mean the main constraint in
+
+ align:start position:0%
+um I mean the main constraint in
+ 
+
+ align:start position:0%
+um I mean the main constraint in
+Argentina and turkey and so on is
+
+ align:start position:0%
+Argentina and turkey and so on is
+ 
+
+ align:start position:0%
+Argentina and turkey and so on is
+reserved they don't have enough reserves
+
+ align:start position:0%
+reserved they don't have enough reserves
+ 
+
+ align:start position:0%
+reserved they don't have enough reserves
+so if you have to defend your currency
+
+ align:start position:0%
+so if you have to defend your currency
+ 
+
+ align:start position:0%
+so if you have to defend your currency
+by intervening in the in the in the FX
+
+ align:start position:0%
+by intervening in the in the in the FX
+ 
+
+ align:start position:0%
+by intervening in the in the in the FX
+Market if you don't have enough then
+
+ align:start position:0%
+Market if you don't have enough then
+ 
+
+ align:start position:0%
+Market if you don't have enough then
+you're not credible I mean if you have
+
+ align:start position:0%
+you're not credible I mean if you have
+ 
+
+ align:start position:0%
+you're not credible I mean if you have
+massive capital outflows and you have
+
+ align:start position:0%
+massive capital outflows and you have
+ 
+
+ align:start position:0%
+massive capital outflows and you have
+have a few billion dollars there it's
+
+ align:start position:0%
+have a few billion dollars there it's
+ 
+
+ align:start position:0%
+have a few billion dollars there it's
+not going to work that's not the case of
+
+ align:start position:0%
+not going to work that's not the case of
+ 
+
+ align:start position:0%
+not going to work that's not the case of
+Russia they had massive amount of
+
+ align:start position:0%
+Russia they had massive amount of
+ 
+
+ align:start position:0%
+Russia they had massive amount of
+reserves so that that was not the issue
+
+ align:start position:0%
+reserves so that that was not the issue
+ 
+
+ align:start position:0%
+reserves so that that was not the issue
+it was all about expectations of things
+
+ align:start position:0%
+it was all about expectations of things
+ 
+
+ align:start position:0%
+it was all about expectations of things
+that happen in the future it was all
+
+ align:start position:0%
+that happen in the future it was all
+ 
+
+ align:start position:0%
+that happen in the future it was all
+about these kind of terms
+
+ align:start position:0%
+about these kind of terms
+ 
+
+ align:start position:0%
+about these kind of terms
+okay anyways so so that added to the
+
+ align:start position:0%
+okay anyways so so that added to the
+ 
+
+ align:start position:0%
+okay anyways so so that added to the
+cost they had
+
+ align:start position:0%
+cost they had
+ 
+
+ align:start position:0%
+cost they had
+so so how do we choose these things then
+
+ align:start position:0%
+so so how do we choose these things then
+ 
+
+ align:start position:0%
+so so how do we choose these things then
+in practice H again there are lots of
+
+ align:start position:0%
+in practice H again there are lots of
+ 
+
+ align:start position:0%
+in practice H again there are lots of
+things and politics play play role and
+
+ align:start position:0%
+things and politics play play role and
+ 
+
+ align:start position:0%
+things and politics play play role and
+so on
+
+ align:start position:0%
+so on
+ 
+
+ align:start position:0%
+so on
+ER but there there's a case so so so
+
+ align:start position:0%
+ER but there there's a case so so so
+ 
+
+ align:start position:0%
+ER but there there's a case so so so
+again I would put it even the other way
+
+ align:start position:0%
+again I would put it even the other way
+ 
+
+ align:start position:0%
+again I would put it even the other way
+around I think that if you could you
+
+ align:start position:0%
+around I think that if you could you
+ 
+
+ align:start position:0%
+around I think that if you could you
+would like to have a fixed exchange
+
+ align:start position:0%
+would like to have a fixed exchange
+ 
+
+ align:start position:0%
+would like to have a fixed exchange
+rate if you could you would like to have
+
+ align:start position:0%
+rate if you could you would like to have
+ 
+
+ align:start position:0%
+rate if you could you would like to have
+a fixed exchange rate because then you
+
+ align:start position:0%
+a fixed exchange rate because then you
+ 
+
+ align:start position:0%
+a fixed exchange rate because then you
+remove all this spous noise that happens
+
+ align:start position:0%
+remove all this spous noise that happens
+ 
+
+ align:start position:0%
+remove all this spous noise that happens
+every single day because of exchange
+
+ align:start position:0%
+every single day because of exchange
+ 
+
+ align:start position:0%
+every single day because of exchange
+volatility that complicates your
+
+ align:start position:0%
+volatility that complicates your
+ 
+
+ align:start position:0%
+volatility that complicates your
+life uh but so when can you do that well
+
+ align:start position:0%
+life uh but so when can you do that well
+ 
+
+ align:start position:0%
+life uh but so when can you do that well
+first you can do it with respect to some
+
+ align:start position:0%
+first you can do it with respect to some
+ 
+
+ align:start position:0%
+first you can do it with respect to some
+other country where the shocks are very
+
+ align:start position:0%
+other country where the shocks are very
+ 
+
+ align:start position:0%
+other country where the shocks are very
+similar no because you know if you know
+
+ align:start position:0%
+similar no because you know if you know
+ 
+
+ align:start position:0%
+similar no because you know if you know
+that that that say you're Mexico but or
+
+ align:start position:0%
+that that that say you're Mexico but or
+ 
+
+ align:start position:0%
+that that that say you're Mexico but or
+the north of Mexico something like that
+
+ align:start position:0%
+the north of Mexico something like that
+ 
+
+ align:start position:0%
+the north of Mexico something like that
+and you know that all your shocks are
+
+ align:start position:0%
+and you know that all your shocks are
+ 
+
+ align:start position:0%
+and you know that all your shocks are
+really shocks to the US then the US can
+
+ align:start position:0%
+really shocks to the US then the US can
+ 
+
+ align:start position:0%
+really shocks to the US then the US can
+do the monetary policy for you because
+
+ align:start position:0%
+do the monetary policy for you because
+ 
+
+ align:start position:0%
+do the monetary policy for you because
+you have the same shocks I'm
+
+ align:start position:0%
+you have the same shocks I'm
+ 
+
+ align:start position:0%
+you have the same shocks I'm
+exaggerating so if you're very
+
+ align:start position:0%
+exaggerating so if you're very
+ 
+
+ align:start position:0%
+exaggerating so if you're very
+similar then it makes sense to have a
+
+ align:start position:0%
+similar then it makes sense to have a
+ 
+
+ align:start position:0%
+similar then it makes sense to have a
+fix exchange because why pay for all
+
+ align:start position:0%
+fix exchange because why pay for all
+ 
+
+ align:start position:0%
+fix exchange because why pay for all
+that volatility when you're going to be
+
+ align:start position:0%
+that volatility when you're going to be
+ 
+
+ align:start position:0%
+that volatility when you're going to be
+doing the same policies in both
+
+ align:start position:0%
+doing the same policies in both
+ 
+
+ align:start position:0%
+doing the same policies in both
+countries more or less at the same time
+
+ align:start position:0%
+countries more or less at the same time
+ 
+
+ align:start position:0%
+countries more or less at the same time
+because you're exposed to the same
+
+ align:start position:0%
+because you're exposed to the same
+ 
+
+ align:start position:0%
+because you're exposed to the same
+shocks so that's one thing that's one
+
+ align:start position:0%
+shocks so that's one thing that's one
+ 
+
+ align:start position:0%
+shocks so that's one thing that's one
+reason why the Euro zone is the Euro
+
+ align:start position:0%
+reason why the Euro zone is the Euro
+ 
+
+ align:start position:0%
+reason why the Euro zone is the Euro
+Zone because they European countries
+
+ align:start position:0%
+Zone because they European countries
+ 
+
+ align:start position:0%
+Zone because they European countries
+that have very similar business cycles
+
+ align:start position:0%
+that have very similar business cycles
+ 
+
+ align:start position:0%
+that have very similar business cycles
+and so on Germany is a little different
+
+ align:start position:0%
+and so on Germany is a little different
+ 
+
+ align:start position:0%
+and so on Germany is a little different
+that's the reason they always have some
+
+ align:start position:0%
+that's the reason they always have some
+ 
+
+ align:start position:0%
+that's the reason they always have some
+problem I mean the North and the South
+
+ align:start position:0%
+problem I mean the North and the South
+ 
+
+ align:start position:0%
+problem I mean the North and the South
+they're a little different but but but
+
+ align:start position:0%
+they're a little different but but but
+ 
+
+ align:start position:0%
+they're a little different but but but
+they're much more similar than than
+
+ align:start position:0%
+they're much more similar than than
+ 
+
+ align:start position:0%
+they're much more similar than than
+other countries
+
+ align:start position:0%
+other countries
+ 
+
+ align:start position:0%
+other countries
+um so so that's that's what they have
+
+ align:start position:0%
+um so so that's that's what they have
+ 
+
+ align:start position:0%
+um so so that's that's what they have
+one another option is is is when you
+
+ align:start position:0%
+one another option is is is when you
+ 
+
+ align:start position:0%
+one another option is is is when you
+have lots of fiscal
+
+ align:start position:0%
+have lots of fiscal
+ 
+
+ align:start position:0%
+have lots of fiscal
+capacity because if you have lots of
+
+ align:start position:0%
+capacity because if you have lots of
+ 
+
+ align:start position:0%
+capacity because if you have lots of
+fiscal capacity then the cost of not
+
+ align:start position:0%
+fiscal capacity then the cost of not
+ 
+
+ align:start position:0%
+fiscal capacity then the cost of not
+having monetary polic is not that large
+
+ align:start position:0%
+having monetary polic is not that large
+ 
+
+ align:start position:0%
+having monetary polic is not that large
+because you can fight your business
+
+ align:start position:0%
+because you can fight your business
+ 
+
+ align:start position:0%
+because you can fight your business
+cycle with fiscal policy that's the case
+
+ align:start position:0%
+cycle with fiscal policy that's the case
+ 
+
+ align:start position:0%
+cycle with fiscal policy that's the case
+of Hong Kong for example Hong Kong Hong
+
+ align:start position:0%
+of Hong Kong for example Hong Kong Hong
+ 
+
+ align:start position:0%
+of Hong Kong for example Hong Kong Hong
+Kong first of all is not subject to
+
+ align:start position:0%
+Kong first of all is not subject to
+ 
+
+ align:start position:0%
+Kong first of all is not subject to
+speculative that because they have
+
+ align:start position:0%
+speculative that because they have
+ 
+
+ align:start position:0%
+speculative that because they have
+massive amount of reserves so anyone
+
+ align:start position:0%
+massive amount of reserves so anyone
+ 
+
+ align:start position:0%
+massive amount of reserves so anyone
+that dares attacking them is going to
+
+ align:start position:0%
+that dares attacking them is going to
+ 
+
+ align:start position:0%
+that dares attacking them is going to
+lose their share so so they're safe er
+
+ align:start position:0%
+lose their share so so they're safe er
+ 
+
+ align:start position:0%
+lose their share so so they're safe er
+um Soros tried many years back and he
+
+ align:start position:0%
+um Soros tried many years back and he
+ 
+
+ align:start position:0%
+um Soros tried many years back and he
+didn't do as well as he did attacking
+
+ align:start position:0%
+didn't do as well as he did attacking
+ 
+
+ align:start position:0%
+didn't do as well as he did attacking
+the British pound er um then then but
+
+ align:start position:0%
+the British pound er um then then but
+ 
+
+ align:start position:0%
+the British pound er um then then but
+they also have lots of fiscal resources
+
+ align:start position:0%
+they also have lots of fiscal resources
+ 
+
+ align:start position:0%
+they also have lots of fiscal resources
+so they can fight their domestic
+
+ align:start position:0%
+so they can fight their domestic
+ 
+
+ align:start position:0%
+so they can fight their domestic
+recessions and so on with fiscal policy
+
+ align:start position:0%
+recessions and so on with fiscal policy
+ 
+
+ align:start position:0%
+recessions and so on with fiscal policy
+the other factor which also applies to
+
+ align:start position:0%
+the other factor which also applies to
+ 
+
+ align:start position:0%
+the other factor which also applies to
+Hong Kong if you have very flexible
+
+ align:start position:0%
+Hong Kong if you have very flexible
+ 
+
+ align:start position:0%
+Hong Kong if you have very flexible
+factor market so if wages move very
+
+ align:start position:0%
+factor market so if wages move very
+ 
+
+ align:start position:0%
+factor market so if wages move very
+easily if prices move very easily
+
+ align:start position:0%
+easily if prices move very easily
+ 
+
+ align:start position:0%
+easily if prices move very easily
+domestically then you don't care about
+
+ align:start position:0%
+domestically then you don't care about
+ 
+
+ align:start position:0%
+domestically then you don't care about
+having a fixed nominal exchange rate
+
+ align:start position:0%
+having a fixed nominal exchange rate
+ 
+
+ align:start position:0%
+having a fixed nominal exchange rate
+because a fixed nominal exchange rate is
+
+ align:start position:0%
+because a fixed nominal exchange rate is
+ 
+
+ align:start position:0%
+because a fixed nominal exchange rate is
+not the same as a fixed real exchange
+
+ align:start position:0%
+not the same as a fixed real exchange
+ 
+
+ align:start position:0%
+not the same as a fixed real exchange
+rate which is what you really need to
+
+ align:start position:0%
+rate which is what you really need to
+ 
+
+ align:start position:0%
+rate which is what you really need to
+move around
+
+ align:start position:0%
+move around
+ 
+
+ align:start position:0%
+move around
+if your prices are flexible doesn't
+
+ align:start position:0%
+if your prices are flexible doesn't
+ 
+
+ align:start position:0%
+if your prices are flexible doesn't
+matter that the nominal exchange doesn't
+
+ align:start position:0%
+matter that the nominal exchange doesn't
+ 
+
+ align:start position:0%
+matter that the nominal exchange doesn't
+move because the prices are moving
+
+ align:start position:0%
+move because the prices are moving
+ 
+
+ align:start position:0%
+move because the prices are moving
+around and so you you still have lots of
+
+ align:start position:0%
+around and so you you still have lots of
+ 
+
+ align:start position:0%
+around and so you you still have lots of
+flexibility in the real exchange and
+
+ align:start position:0%
+flexibility in the real exchange and
+ 
+
+ align:start position:0%
+flexibility in the real exchange and
+that's the reason I would say is one of
+
+ align:start position:0%
+that's the reason I would say is one of
+ 
+
+ align:start position:0%
+that's the reason I would say is one of
+the reasons political reasons as well
+
+ align:start position:0%
+the reasons political reasons as well
+ 
+
+ align:start position:0%
+the reasons political reasons as well
+but but why they can afford it why I
+
+ align:start position:0%
+but but why they can afford it why I
+ 
+
+ align:start position:0%
+but but why they can afford it why I
+think in the case of H way around was
+
+ align:start position:0%
+think in the case of H way around was
+ 
+
+ align:start position:0%
+think in the case of H way around was
+some political
+
+ align:start position:0%
+some political
+ 
+
+ align:start position:0%
+some political
+reasons and and and and then they build
+
+ align:start position:0%
+reasons and and and and then they build
+ 
+
+ align:start position:0%
+reasons and and and and then they build
+a system so that it's it's a it's a
+
+ align:start position:0%
+a system so that it's it's a it's a
+ 
+
+ align:start position:0%
+a system so that it's it's a it's a
+coherent system because they have lots
+
+ align:start position:0%
+coherent system because they have lots
+ 
+
+ align:start position:0%
+coherent system because they have lots
+of fiscal capacity can defend the
+
+ align:start position:0%
+of fiscal capacity can defend the
+ 
+
+ align:start position:0%
+of fiscal capacity can defend the
+currency well they have very flexible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Market
+
+ align:start position:0%
+Market
+ 
+
+ align:start position:0%
+Market
+um this well this again this is what I
+
+ align:start position:0%
+um this well this again this is what I
+ 
+
+ align:start position:0%
+um this well this again this is what I
+said before if you if you if this is
+
+ align:start position:0%
+said before if you if you if this is
+ 
+
+ align:start position:0%
+said before if you if you if this is
+what I said before if you if you have
+
+ align:start position:0%
+what I said before if you if you have
+ 
+
+ align:start position:0%
+what I said before if you if you have
+you don't like that noise if you
+
+ align:start position:0%
+you don't like that noise if you
+ 
+
+ align:start position:0%
+you don't like that noise if you
+especially if you're going to be trading
+
+ align:start position:0%
+especially if you're going to be trading
+ 
+
+ align:start position:0%
+especially if you're going to be trading
+a lot with people and so on you know in
+
+ align:start position:0%
+a lot with people and so on you know in
+ 
+
+ align:start position:0%
+a lot with people and so on you know in
+Europe many people cross the border many
+
+ align:start position:0%
+Europe many people cross the border many
+ 
+
+ align:start position:0%
+Europe many people cross the border many
+times a day and you want to go shopping
+
+ align:start position:0%
+times a day and you want to go shopping
+ 
+
+ align:start position:0%
+times a day and you want to go shopping
+one way or the other it's a it's a pain
+
+ align:start position:0%
+one way or the other it's a it's a pain
+ 
+
+ align:start position:0%
+one way or the other it's a it's a pain
+if the exchange is moving all the time
+
+ align:start position:0%
+if the exchange is moving all the time
+ 
+
+ align:start position:0%
+if the exchange is moving all the time
+no it's much easier if things are table
+
+ align:start position:0%
+no it's much easier if things are table
+ 
+
+ align:start position:0%
+no it's much easier if things are table
+and the same appli to financial
+
+ align:start position:0%
+and the same appli to financial
+ 
+
+ align:start position:0%
+and the same appli to financial
+transactions people have deposits in
+
+ align:start position:0%
+transactions people have deposits in
+ 
+
+ align:start position:0%
+transactions people have deposits in
+different banks and stuff like that it's
+
+ align:start position:0%
+different banks and stuff like that it's
+ 
+
+ align:start position:0%
+different banks and stuff like that it's
+it's better if you don't have all that
+
+ align:start position:0%
+it's better if you don't have all that
+ 
+
+ align:start position:0%
+it's better if you don't have all that
+fluctuation and in the case of the Euro
+
+ align:start position:0%
+fluctuation and in the case of the Euro
+ 
+
+ align:start position:0%
+fluctuation and in the case of the Euro
+area they decided that ER that the
+
+ align:start position:0%
+area they decided that ER that the
+ 
+
+ align:start position:0%
+area they decided that ER that the
+advantage of having a very fixed
+
+ align:start position:0%
+advantage of having a very fixed
+ 
+
+ align:start position:0%
+advantage of having a very fixed
+exchange
+
+ align:start position:0%
+exchange
+ 
+
+ align:start position:0%
+exchange
+rate were more than the cost for
+
+ align:start position:0%
+rate were more than the cost for
+ 
+
+ align:start position:0%
+rate were more than the cost for
+individual countries of not having
+
+ align:start position:0%
+individual countries of not having
+ 
+
+ align:start position:0%
+individual countries of not having
+independent monetary
+
+ align:start position:0%
+independent monetary
+ 
+
+ align:start position:0%
+independent monetary
+policy this still a work in progress
+
+ align:start position:0%
+policy this still a work in progress
+ 
+
+ align:start position:0%
+policy this still a work in progress
+they're building that is not
+
+ align:start position:0%
+they're building that is not
+ 
+
+ align:start position:0%
+they're building that is not
+finished but but but they're working at
+
+ align:start position:0%
+finished but but but they're working at
+ 
+
+ align:start position:0%
+finished but but but they're working at
+it there another reason why countries
+
+ align:start position:0%
+it there another reason why countries
+ 
+
+ align:start position:0%
+it there another reason why countries
+fix exchange rate and that's the
+
+ align:start position:0%
+fix exchange rate and that's the
+ 
+
+ align:start position:0%
+fix exchange rate and that's the
+Argentinian reason and so on is is when
+
+ align:start position:0%
+Argentinian reason and so on is is when
+ 
+
+ align:start position:0%
+Argentinian reason and so on is is when
+when they have no control in inflation
+
+ align:start position:0%
+when they have no control in inflation
+ 
+
+ align:start position:0%
+when they have no control in inflation
+they have no credibility and so if you
+
+ align:start position:0%
+they have no credibility and so if you
+ 
+
+ align:start position:0%
+they have no credibility and so if you
+pck to another currency that has
+
+ align:start position:0%
+pck to another currency that has
+ 
+
+ align:start position:0%
+pck to another currency that has
+credibility then the idea the hope at
+
+ align:start position:0%
+credibility then the idea the hope at
+ 
+
+ align:start position:0%
+credibility then the idea the hope at
+least is that you will inherit the
+
+ align:start position:0%
+least is that you will inherit the
+ 
+
+ align:start position:0%
+least is that you will inherit the
+credibility of the other currency and
+
+ align:start position:0%
+credibility of the other currency and
+ 
+
+ align:start position:0%
+credibility of the other currency and
+that's what they try
+
+ align:start position:0%
+that's what they try
+ 
+
+ align:start position:0%
+that's what they try
+to Argentina had a currency board like
+
+ align:start position:0%
+to Argentina had a currency board like
+ 
+
+ align:start position:0%
+to Argentina had a currency board like
+Hong Kong for a while the whole idea was
+
+ align:start position:0%
+Hong Kong for a while the whole idea was
+ 
+
+ align:start position:0%
+Hong Kong for a while the whole idea was
+to control inflation well let's ECT to
+
+ align:start position:0%
+to control inflation well let's ECT to
+ 
+
+ align:start position:0%
+to control inflation well let's ECT to
+someone and and and if they if the
+
+ align:start position:0%
+someone and and and if they if the
+ 
+
+ align:start position:0%
+someone and and and if they if the
+markets believe you then it will work
+
+ align:start position:0%
+markets believe you then it will work
+ 
+
+ align:start position:0%
+markets believe you then it will work
+because then you inherit the The
+
+ align:start position:0%
+because then you inherit the The
+ 
+
+ align:start position:0%
+because then you inherit the The
+credibility of the you're saying when
+
+ align:start position:0%
+credibility of the you're saying when
+ 
+
+ align:start position:0%
+credibility of the you're saying when
+you take a fixed exchange it I'm not
+
+ align:start position:0%
+you take a fixed exchange it I'm not
+ 
+
+ align:start position:0%
+you take a fixed exchange it I'm not
+going to run monetary policy which is
+
+ align:start position:0%
+going to run monetary policy which is
+ 
+
+ align:start position:0%
+going to run monetary policy which is
+the main source of inflation so I'm
+
+ align:start position:0%
+the main source of inflation so I'm
+ 
+
+ align:start position:0%
+the main source of inflation so I'm
+going to let the credible country run
+
+ align:start position:0%
+going to let the credible country run
+ 
+
+ align:start position:0%
+going to let the credible country run
+the monetary policy for me that's what
+
+ align:start position:0%
+the monetary policy for me that's what
+ 
+
+ align:start position:0%
+the monetary policy for me that's what
+gives you credibility as long as
+
+ align:start position:0%
+gives you credibility as long as
+ 
+
+ align:start position:0%
+gives you credibility as long as
+somebody believes it you're not going to
+
+ align:start position:0%
+somebody believes it you're not going to
+ 
+
+ align:start position:0%
+somebody believes it you're not going to
+quit the thing but but but that's the
+
+ align:start position:0%
+quit the thing but but but that's the
+ 
+
+ align:start position:0%
+quit the thing but but but that's the
+reason countries do it often to
+
+ align:start position:0%
+reason countries do it often to
+ 
+
+ align:start position:0%
+reason countries do it often to
+stabilize inflation as
+
+ align:start position:0%
+stabilize inflation as
+ 
+
+ align:start position:0%
+stabilize inflation as
+well for
\ No newline at end of file
diff --git a/8Ji3Gkjqo5M.txt b/8Ji3Gkjqo5M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e8d7ce2edf3372c6f05a8a467480036793fcc93e
--- /dev/null
+++ b/8Ji3Gkjqo5M.txt
@@ -0,0 +1,10698 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay uh this is the next
+
+ align:start position:0%
+ocw.mit.edu okay uh this is the next
+ 
+
+ align:start position:0%
+ocw.mit.edu okay uh this is the next
+little last lecture you'll be happy to
+
+ align:start position:0%
+little last lecture you'll be happy to
+ 
+
+ align:start position:0%
+little last lecture you'll be happy to
+know uh and today we're going to talk
+
+ align:start position:0%
+know uh and today we're going to talk
+ 
+
+ align:start position:0%
+know uh and today we're going to talk
+about current regulatory safety issues I
+
+ align:start position:0%
+about current regulatory safety issues I
+ 
+
+ align:start position:0%
+about current regulatory safety issues I
+thought it would be really important for
+
+ align:start position:0%
+thought it would be really important for
+ 
+
+ align:start position:0%
+thought it would be really important for
+you to catch up on what the NRC thinks
+
+ align:start position:0%
+you to catch up on what the NRC thinks
+ 
+
+ align:start position:0%
+you to catch up on what the NRC thinks
+is important these days as it relates to
+
+ align:start position:0%
+is important these days as it relates to
+ 
+
+ align:start position:0%
+is important these days as it relates to
+their safety and Regulatory
+
+ align:start position:0%
+their safety and Regulatory
+ 
+
+ align:start position:0%
+their safety and Regulatory
+function so we're going to try to cover
+
+ align:start position:0%
+function so we're going to try to cover
+ 
+
+ align:start position:0%
+function so we're going to try to cover
+a few things relatively quickly and I
+
+ align:start position:0%
+a few things relatively quickly and I
+ 
+
+ align:start position:0%
+a few things relatively quickly and I
+went to the NRC website and I said what
+
+ align:start position:0%
+went to the NRC website and I said what
+ 
+
+ align:start position:0%
+went to the NRC website and I said what
+are your key current issues and the list
+
+ align:start position:0%
+are your key current issues and the list
+ 
+
+ align:start position:0%
+are your key current issues and the list
+is reactor vessel Integrity which as as
+
+ align:start position:0%
+is reactor vessel Integrity which as as
+ 
+
+ align:start position:0%
+is reactor vessel Integrity which as as
+you probably realize is now reactor
+
+ align:start position:0%
+you probably realize is now reactor
+ 
+
+ align:start position:0%
+you probably realize is now reactor
+vessel in berin pressurized water
+
+ align:start position:0%
+vessel in berin pressurized water
+ 
+
+ align:start position:0%
+vessel in berin pressurized water
+reactor some pump performance we'll look
+
+ align:start position:0%
+reactor some pump performance we'll look
+ 
+
+ align:start position:0%
+reactor some pump performance we'll look
+at that many of these issues have been
+
+ align:start position:0%
+at that many of these issues have been
+ 
+
+ align:start position:0%
+at that many of these issues have been
+around for 20
+
+ align:start position:0%
+around for 20
+ 
+
+ align:start position:0%
+around for 20
+years but they're still there the
+
+ align:start position:0%
+years but they're still there the
+ 
+
+ align:start position:0%
+years but they're still there the
+reactor coolant system weld issues they
+
+ align:start position:0%
+reactor coolant system weld issues they
+ 
+
+ align:start position:0%
+reactor coolant system weld issues they
+used uh and they're getting primary
+
+ align:start position:0%
+used uh and they're getting primary
+ 
+
+ align:start position:0%
+used uh and they're getting primary
+water stress corrosion cracking we've
+
+ align:start position:0%
+water stress corrosion cracking we've
+ 
+
+ align:start position:0%
+water stress corrosion cracking we've
+already talked about Davis Bessie head
+
+ align:start position:0%
+already talked about Davis Bessie head
+ 
+
+ align:start position:0%
+already talked about Davis Bessie head
+degradation so we're not going to talk
+
+ align:start position:0%
+degradation so we're not going to talk
+ 
+
+ align:start position:0%
+degradation so we're not going to talk
+about that but that's certainly related
+
+ align:start position:0%
+about that but that's certainly related
+ 
+
+ align:start position:0%
+about that but that's certainly related
+to uh certain weld issues we've never
+
+ align:start position:0%
+to uh certain weld issues we've never
+ 
+
+ align:start position:0%
+to uh certain weld issues we've never
+really talked about fire protection the
+
+ align:start position:0%
+really talked about fire protection the
+ 
+
+ align:start position:0%
+really talked about fire protection the
+fire protection is an old old
+
+ align:start position:0%
+fire protection is an old old
+ 
+
+ align:start position:0%
+fire protection is an old old
+rule uh that uh will briefly review and
+
+ align:start position:0%
+rule uh that uh will briefly review and
+ 
+
+ align:start position:0%
+rule uh that uh will briefly review and
+they've got some issues now with some
+
+ align:start position:0%
+they've got some issues now with some
+ 
+
+ align:start position:0%
+they've got some issues now with some
+insulation that doesn't meet certain
+
+ align:start position:0%
+insulation that doesn't meet certain
+ 
+
+ align:start position:0%
+insulation that doesn't meet certain
+standards and it's a difficult question
+
+ align:start position:0%
+standards and it's a difficult question
+ 
+
+ align:start position:0%
+standards and it's a difficult question
+for them and obviously the new issue
+
+ align:start position:0%
+for them and obviously the new issue
+ 
+
+ align:start position:0%
+for them and obviously the new issue
+since 9911 is planed security and
+
+ align:start position:0%
+since 9911 is planed security and
+ 
+
+ align:start position:0%
+since 9911 is planed security and
+terrorism uh we've seen some recent
+
+ align:start position:0%
+terrorism uh we've seen some recent
+ 
+
+ align:start position:0%
+terrorism uh we've seen some recent
+evidence of groundw contamination
+
+ align:start position:0%
+evidence of groundw contamination
+ 
+
+ align:start position:0%
+evidence of groundw contamination
+Mainely in the traum case and based on
+
+ align:start position:0%
+Mainely in the traum case and based on
+ 
+
+ align:start position:0%
+Mainely in the traum case and based on
+our last lecture I thought it' be good
+
+ align:start position:0%
+our last lecture I thought it' be good
+ 
+
+ align:start position:0%
+our last lecture I thought it' be good
+to update you on what they call the saf
+
+ align:start position:0%
+to update you on what they call the saf
+ 
+
+ align:start position:0%
+to update you on what they call the saf
+conscious work environment as a safety
+
+ align:start position:0%
+conscious work environment as a safety
+ 
+
+ align:start position:0%
+conscious work environment as a safety
+culture
+
+ align:start position:0%
+culture
+ 
+
+ align:start position:0%
+culture
+question so we'll go through them sort
+
+ align:start position:0%
+question so we'll go through them sort
+ 
+
+ align:start position:0%
+question so we'll go through them sort
+of one by
+
+ align:start position:0%
+of one by
+ 
+
+ align:start position:0%
+of one by
+one um the reactor vessel Integrity
+
+ align:start position:0%
+one um the reactor vessel Integrity
+ 
+
+ align:start position:0%
+one um the reactor vessel Integrity
+issue was in part driven by Yankee
+
+ align:start position:0%
+issue was in part driven by Yankee
+ 
+
+ align:start position:0%
+issue was in part driven by Yankee
+Atomic the Yankee Ro plant now what
+
+ align:start position:0%
+Atomic the Yankee Ro plant now what
+ 
+
+ align:start position:0%
+Atomic the Yankee Ro plant now what
+happened at Yankee was that when the
+
+ align:start position:0%
+happened at Yankee was that when the
+ 
+
+ align:start position:0%
+happened at Yankee was that when the
+Yankee plant was built back in the N
+
+ align:start position:0%
+Yankee plant was built back in the N
+ 
+
+ align:start position:0%
+Yankee plant was built back in the N
+late 50s each reactor was supposed to
+
+ align:start position:0%
+late 50s each reactor was supposed to
+ 
+
+ align:start position:0%
+late 50s each reactor was supposed to
+install a surveillance capsule of the
+
+ align:start position:0%
+install a surveillance capsule of the
+ 
+
+ align:start position:0%
+install a surveillance capsule of the
+material that the reactor vessel is made
+
+ align:start position:0%
+material that the reactor vessel is made
+ 
+
+ align:start position:0%
+material that the reactor vessel is made
+of and the material that the wells are
+
+ align:start position:0%
+of and the material that the wells are
+ 
+
+ align:start position:0%
+of and the material that the wells are
+made up and it's all very carefully
+
+ align:start position:0%
+made up and it's all very carefully
+ 
+
+ align:start position:0%
+made up and it's all very carefully
+tracked and monitored but in those days
+
+ align:start position:0%
+tracked and monitored but in those days
+ 
+
+ align:start position:0%
+tracked and monitored but in those days
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+50s um they weren't so scrupulous about
+
+ align:start position:0%
+50s um they weren't so scrupulous about
+ 
+
+ align:start position:0%
+50s um they weren't so scrupulous about
+making sure the capsules were the
+
+ align:start position:0%
+making sure the capsules were the
+ 
+
+ align:start position:0%
+making sure the capsules were the
+original vessel capsules and the well
+
+ align:start position:0%
+original vessel capsules and the well
+ 
+
+ align:start position:0%
+original vessel capsules and the well
+material was the original vessel
+
+ align:start position:0%
+material was the original vessel
+ 
+
+ align:start position:0%
+material was the original vessel
+material but luckily for Yankee at the
+
+ align:start position:0%
+material but luckily for Yankee at the
+ 
+
+ align:start position:0%
+material but luckily for Yankee at the
+time they did put capsules in and they
+
+ align:start position:0%
+time they did put capsules in and they
+ 
+
+ align:start position:0%
+time they did put capsules in and they
+did put weld capsules as well but
+
+ align:start position:0%
+did put weld capsules as well but
+ 
+
+ align:start position:0%
+did put weld capsules as well but
+unfortunately during the first or second
+
+ align:start position:0%
+unfortunately during the first or second
+ 
+
+ align:start position:0%
+unfortunately during the first or second
+year of operation the capsules were
+
+ align:start position:0%
+year of operation the capsules were
+ 
+
+ align:start position:0%
+year of operation the capsules were
+destroyed in other words the hold the
+
+ align:start position:0%
+destroyed in other words the hold the
+ 
+
+ align:start position:0%
+destroyed in other words the hold the
+holders cell uh broke and they they were
+
+ align:start position:0%
+holders cell uh broke and they they were
+ 
+
+ align:start position:0%
+holders cell uh broke and they they were
+able to retrieve some and they had
+
+ align:start position:0%
+able to retrieve some and they had
+ 
+
+ align:start position:0%
+able to retrieve some and they had
+limited amount of data upon which to
+
+ align:start position:0%
+limited amount of data upon which to
+ 
+
+ align:start position:0%
+limited amount of data upon which to
+base predictions and the way they made
+
+ align:start position:0%
+base predictions and the way they made
+ 
+
+ align:start position:0%
+base predictions and the way they made
+these predictions was they put them very
+
+ align:start position:0%
+these predictions was they put them very
+ 
+
+ align:start position:0%
+these predictions was they put them very
+close to the core and over a period of
+
+ align:start position:0%
+close to the core and over a period of
+ 
+
+ align:start position:0%
+close to the core and over a period of
+time they would take out specimens and
+
+ align:start position:0%
+time they would take out specimens and
+ 
+
+ align:start position:0%
+time they would take out specimens and
+determine what the degree of umbr it was
+
+ align:start position:0%
+determine what the degree of umbr it was
+ 
+
+ align:start position:0%
+determine what the degree of umbr it was
+and Yankee we had a number of specimens
+
+ align:start position:0%
+and Yankee we had a number of specimens
+ 
+
+ align:start position:0%
+and Yankee we had a number of specimens
+early in life and we had one really late
+
+ align:start position:0%
+early in life and we had one really late
+ 
+
+ align:start position:0%
+early in life and we had one really late
+in life and you couldn't really just
+
+ align:start position:0%
+in life and you couldn't really just
+ 
+
+ align:start position:0%
+in life and you couldn't really just
+draw a straight line curve to it but
+
+ align:start position:0%
+draw a straight line curve to it but
+ 
+
+ align:start position:0%
+draw a straight line curve to it but
+most reactors and pretty much all
+
+ align:start position:0%
+most reactors and pretty much all
+ 
+
+ align:start position:0%
+most reactors and pretty much all
+reactors today have these in incor
+
+ align:start position:0%
+reactors today have these in incor
+ 
+
+ align:start position:0%
+reactors today have these in incor
+specimens that they use to to determine
+
+ align:start position:0%
+specimens that they use to to determine
+ 
+
+ align:start position:0%
+specimens that they use to to determine
+whether or not the vessel is becoming
+
+ align:start position:0%
+whether or not the vessel is becoming
+ 
+
+ align:start position:0%
+whether or not the vessel is becoming
+overly embed and typically these are
+
+ align:start position:0%
+overly embed and typically these are
+ 
+
+ align:start position:0%
+overly embed and typically these are
+these are these are specimens in which
+
+ align:start position:0%
+these are these are specimens in which
+ 
+
+ align:start position:0%
+these are these are specimens in which
+the uh they're located in a place in the
+
+ align:start position:0%
+the uh they're located in a place in the
+ 
+
+ align:start position:0%
+the uh they're located in a place in the
+core a number places in the core where
+
+ align:start position:0%
+core a number places in the core where
+ 
+
+ align:start position:0%
+core a number places in the core where
+they can get IR radiations uh over time
+
+ align:start position:0%
+they can get IR radiations uh over time
+ 
+
+ align:start position:0%
+they can get IR radiations uh over time
+so what we what we have had at Yankee
+
+ align:start position:0%
+so what we what we have had at Yankee
+ 
+
+ align:start position:0%
+so what we what we have had at Yankee
+was that we were trying to go for a
+
+ align:start position:0%
+was that we were trying to go for a
+ 
+
+ align:start position:0%
+was that we were trying to go for a
+license renewal and one of the justif
+
+ align:start position:0%
+license renewal and one of the justif
+ 
+
+ align:start position:0%
+license renewal and one of the justif
+for continuing to operate past 40 Years
+
+ align:start position:0%
+for continuing to operate past 40 Years
+ 
+
+ align:start position:0%
+for continuing to operate past 40 Years
+of operation was that we need to show
+
+ align:start position:0%
+of operation was that we need to show
+ 
+
+ align:start position:0%
+of operation was that we need to show
+The Vessel with sound well in our
+
+ align:start position:0%
+The Vessel with sound well in our
+ 
+
+ align:start position:0%
+The Vessel with sound well in our
+attempt to try to defend it and
+
+ align:start position:0%
+attempt to try to defend it and
+ 
+
+ align:start position:0%
+attempt to try to defend it and
+obviously it depends on the well
+
+ align:start position:0%
+obviously it depends on the well
+ 
+
+ align:start position:0%
+obviously it depends on the well
+material and the metal because some of
+
+ align:start position:0%
+material and the metal because some of
+ 
+
+ align:start position:0%
+material and the metal because some of
+them depends upon your Chemistry of the
+
+ align:start position:0%
+them depends upon your Chemistry of the
+ 
+
+ align:start position:0%
+them depends upon your Chemistry of the
+metal you have more or less
+
+ align:start position:0%
+metal you have more or less
+ 
+
+ align:start position:0%
+metal you have more or less
+susceptibility to embrittlement and as I
+
+ align:start position:0%
+susceptibility to embrittlement and as I
+ 
+
+ align:start position:0%
+susceptibility to embrittlement and as I
+recall it was copper content and some
+
+ align:start position:0%
+recall it was copper content and some
+ 
+
+ align:start position:0%
+recall it was copper content and some
+nickel content and basically it it was
+
+ align:start position:0%
+nickel content and basically it it was
+ 
+
+ align:start position:0%
+nickel content and basically it it was
+very very very key to be able to
+
+ align:start position:0%
+very very very key to be able to
+ 
+
+ align:start position:0%
+very very very key to be able to
+understand what the vessel was in fact
+
+ align:start position:0%
+understand what the vessel was in fact
+ 
+
+ align:start position:0%
+understand what the vessel was in fact
+made of because the performance was
+
+ align:start position:0%
+made of because the performance was
+ 
+
+ align:start position:0%
+made of because the performance was
+significantly different well what
+
+ align:start position:0%
+significantly different well what
+ 
+
+ align:start position:0%
+significantly different well what
+happened at Yankee was we we spent
+
+ align:start position:0%
+happened at Yankee was we we spent
+ 
+
+ align:start position:0%
+happened at Yankee was we we spent
+probably over two years trying to
+
+ align:start position:0%
+probably over two years trying to
+ 
+
+ align:start position:0%
+probably over two years trying to
+convince the NRC that our vessel was
+
+ align:start position:0%
+convince the NRC that our vessel was
+ 
+
+ align:start position:0%
+convince the NRC that our vessel was
+fine based on the limited data that we
+
+ align:start position:0%
+fine based on the limited data that we
+ 
+
+ align:start position:0%
+fine based on the limited data that we
+had luckily for us we had a reactor in
+
+ align:start position:0%
+had luckily for us we had a reactor in
+ 
+
+ align:start position:0%
+had luckily for us we had a reactor in
+Belgium that was in fact also made of
+
+ align:start position:0%
+Belgium that was in fact also made of
+ 
+
+ align:start position:0%
+Belgium that was in fact also made of
+about the same time of the same type of
+
+ align:start position:0%
+about the same time of the same type of
+ 
+
+ align:start position:0%
+about the same time of the same type of
+metal and we had their radiation andent
+
+ align:start position:0%
+metal and we had their radiation andent
+ 
+
+ align:start position:0%
+metal and we had their radiation andent
+data the net result was the NRC didn't
+
+ align:start position:0%
+data the net result was the NRC didn't
+ 
+
+ align:start position:0%
+data the net result was the NRC didn't
+buy our
+
+ align:start position:0%
+buy our
+ 
+
+ align:start position:0%
+buy our
+story and
+
+ align:start position:0%
+story and
+ 
+
+ align:start position:0%
+story and
+um and and the key parameters basically
+
+ align:start position:0%
+um and and the key parameters basically
+ 
+
+ align:start position:0%
+um and and the key parameters basically
+that you have to look at is this uh n
+
+ align:start position:0%
+that you have to look at is this uh n
+ 
+
+ align:start position:0%
+that you have to look at is this uh n
+ductility transition temperature which I
+
+ align:start position:0%
+ductility transition temperature which I
+ 
+
+ align:start position:0%
+ductility transition temperature which I
+know you haven't had material so you
+
+ align:start position:0%
+know you haven't had material so you
+ 
+
+ align:start position:0%
+know you haven't had material so you
+wouldn't understand but it's a point
+
+ align:start position:0%
+wouldn't understand but it's a point
+ 
+
+ align:start position:0%
+wouldn't understand but it's a point
+after which at certain temperatures the
+
+ align:start position:0%
+after which at certain temperatures the
+ 
+
+ align:start position:0%
+after which at certain temperatures the
+reactor will uh lose a lot of its
+
+ align:start position:0%
+reactor will uh lose a lot of its
+ 
+
+ align:start position:0%
+reactor will uh lose a lot of its
+strength and in fact if you shock it
+
+ align:start position:0%
+strength and in fact if you shock it
+ 
+
+ align:start position:0%
+strength and in fact if you shock it
+under uh with cold water there a poti I
+
+ align:start position:0%
+under uh with cold water there a poti I
+ 
+
+ align:start position:0%
+under uh with cold water there a poti I
+should there be a flaw or crack in the
+
+ align:start position:0%
+should there be a flaw or crack in the
+ 
+
+ align:start position:0%
+should there be a flaw or crack in the
+vessel The Vessel can crack propagate
+
+ align:start position:0%
+vessel The Vessel can crack propagate
+ 
+
+ align:start position:0%
+vessel The Vessel can crack propagate
+that crack and that's why the NRC was
+
+ align:start position:0%
+that crack and that's why the NRC was
+ 
+
+ align:start position:0%
+that crack and that's why the NRC was
+really anxious about this particular
+
+ align:start position:0%
+really anxious about this particular
+ 
+
+ align:start position:0%
+really anxious about this particular
+event um and and the concern was and I
+
+ align:start position:0%
+event um and and the concern was and I
+ 
+
+ align:start position:0%
+event um and and the concern was and I
+believe we talked about it once in class
+
+ align:start position:0%
+believe we talked about it once in class
+ 
+
+ align:start position:0%
+believe we talked about it once in class
+the issue was what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressurized thermal shock
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and that that that phenomenon was if
+
+ align:start position:0%
+and and that that that phenomenon was if
+ 
+
+ align:start position:0%
+and and that that that phenomenon was if
+you're under high pressure say 2200
+
+ align:start position:0%
+you're under high pressure say 2200
+ 
+
+ align:start position:0%
+you're under high pressure say 2200
+lb and you hit a hot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vessel with cold water cold water being
+
+ align:start position:0%
+vessel with cold water cold water being
+ 
+
+ align:start position:0%
+vessel with cold water cold water being
+you know ambient temperature water like
+
+ align:start position:0%
+you know ambient temperature water like
+ 
+
+ align:start position:0%
+you know ambient temperature water like
+from the refueling storage pool which is
+
+ align:start position:0%
+from the refueling storage pool which is
+ 
+
+ align:start position:0%
+from the refueling storage pool which is
+obviously not this hot it could be
+
+ align:start position:0%
+obviously not this hot it could be
+ 
+
+ align:start position:0%
+obviously not this hot it could be
+typically um on the order of uh let's
+
+ align:start position:0%
+typically um on the order of uh let's
+ 
+
+ align:start position:0%
+typically um on the order of uh let's
+just say 60°
+
+ align:start position:0%
+just say 60°
+ 
+
+ align:start position:0%
+just say 60°
+F if there is a pre-existing flaw that
+
+ align:start position:0%
+F if there is a pre-existing flaw that
+ 
+
+ align:start position:0%
+F if there is a pre-existing flaw that
+shock would in fact cause that flaw to
+
+ align:start position:0%
+shock would in fact cause that flaw to
+ 
+
+ align:start position:0%
+shock would in fact cause that flaw to
+grow possibly rupturing The Vessel
+
+ align:start position:0%
+grow possibly rupturing The Vessel
+ 
+
+ align:start position:0%
+grow possibly rupturing The Vessel
+possibly rupturing The
+
+ align:start position:0%
+possibly rupturing The
+ 
+
+ align:start position:0%
+possibly rupturing The
+Vessel some compensatory actions that we
+
+ align:start position:0%
+Vessel some compensatory actions that we
+ 
+
+ align:start position:0%
+Vessel some compensatory actions that we
+had to take were and this is the eccs
+
+ align:start position:0%
+had to take were and this is the eccs
+ 
+
+ align:start position:0%
+had to take were and this is the eccs
+water that we rais this temperature to
+
+ align:start position:0%
+water that we rais this temperature to
+ 
+
+ align:start position:0%
+water that we rais this temperature to
+120° so that the shock would be less
+
+ align:start position:0%
+120° so that the shock would be less
+ 
+
+ align:start position:0%
+120° so that the shock would be less
+severe and um we showed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probabilistically that the likelihood of
+
+ align:start position:0%
+probabilistically that the likelihood of
+ 
+
+ align:start position:0%
+probabilistically that the likelihood of
+the event given this design of our
+
+ align:start position:0%
+the event given this design of our
+ 
+
+ align:start position:0%
+the event given this design of our
+system and given the failure rates of
+
+ align:start position:0%
+system and given the failure rates of
+ 
+
+ align:start position:0%
+system and given the failure rates of
+these certain compounds would be low
+
+ align:start position:0%
+these certain compounds would be low
+ 
+
+ align:start position:0%
+these certain compounds would be low
+enough such that the event was like a 10
+
+ align:start position:0%
+enough such that the event was like a 10
+ 
+
+ align:start position:0%
+enough such that the event was like a 10
+Theus 8 probability event but this was
+
+ align:start position:0%
+Theus 8 probability event but this was
+ 
+
+ align:start position:0%
+Theus 8 probability event but this was
+before the days of
+
+ align:start position:0%
+before the days of
+ 
+
+ align:start position:0%
+before the days of
+P Acceptance in the regulatory process
+
+ align:start position:0%
+P Acceptance in the regulatory process
+ 
+
+ align:start position:0%
+P Acceptance in the regulatory process
+but after all the s and done we were
+
+ align:start position:0%
+but after all the s and done we were
+ 
+
+ align:start position:0%
+but after all the s and done we were
+committing to inspections of the vessel
+
+ align:start position:0%
+committing to inspections of the vessel
+ 
+
+ align:start position:0%
+committing to inspections of the vessel
+to see if there's any calculated flaw LA
+
+ align:start position:0%
+to see if there's any calculated flaw LA
+ 
+
+ align:start position:0%
+to see if there's any calculated flaw LA
+but at that point we were going to spend
+
+ align:start position:0%
+but at that point we were going to spend
+ 
+
+ align:start position:0%
+but at that point we were going to spend
+roughly in those days $28
+
+ align:start position:0%
+roughly in those days $28
+ 
+
+ align:start position:0%
+roughly in those days $28
+million to do a vessel
+
+ align:start position:0%
+million to do a vessel
+ 
+
+ align:start position:0%
+million to do a vessel
+inspection and additional
+
+ align:start position:0%
+inspection and additional
+ 
+
+ align:start position:0%
+inspection and additional
+testing uh for a license renewal of 20
+
+ align:start position:0%
+testing uh for a license renewal of 20
+ 
+
+ align:start position:0%
+testing uh for a license renewal of 20
+years and there was no Assurance from
+
+ align:start position:0%
+years and there was no Assurance from
+ 
+
+ align:start position:0%
+years and there was no Assurance from
+the NRC that we'd actually be able to
+
+ align:start position:0%
+the NRC that we'd actually be able to
+ 
+
+ align:start position:0%
+the NRC that we'd actually be able to
+convince them that this is not a problem
+
+ align:start position:0%
+convince them that this is not a problem
+ 
+
+ align:start position:0%
+convince them that this is not a problem
+interestingly enough
+
+ align:start position:0%
+interestingly enough
+ 
+
+ align:start position:0%
+interestingly enough
+subsequently um the The Regulators did
+
+ align:start position:0%
+subsequently um the The Regulators did
+ 
+
+ align:start position:0%
+subsequently um the The Regulators did
+accept our but at that point was much
+
+ align:start position:0%
+accept our but at that point was much
+ 
+
+ align:start position:0%
+accept our but at that point was much
+too late to save the Ane plan so we shut
+
+ align:start position:0%
+too late to save the Ane plan so we shut
+ 
+
+ align:start position:0%
+too late to save the Ane plan so we shut
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+down but there's a lot of documentation
+
+ align:start position:0%
+down but there's a lot of documentation
+ 
+
+ align:start position:0%
+down but there's a lot of documentation
+there's this generic
+
+ align:start position:0%
+there's this generic
+ 
+
+ align:start position:0%
+there's this generic
+letter uh generic letter
+
+ align:start position:0%
+letter uh generic letter
+ 
+
+ align:start position:0%
+letter uh generic letter
+9201 you want some history on the
+
+ align:start position:0%
+9201 you want some history on the
+ 
+
+ align:start position:0%
+9201 you want some history on the
+case and um obviously there are lot lots
+
+ align:start position:0%
+case and um obviously there are lot lots
+ 
+
+ align:start position:0%
+case and um obviously there are lot lots
+of other correspondence between yankee
+
+ align:start position:0%
+of other correspondence between yankee
+ 
+
+ align:start position:0%
+of other correspondence between yankee
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+um the
+
+ align:start position:0%
+um the
+ 
+
+ align:start position:0%
+um the
+regulator but this is sort of the if you
+
+ align:start position:0%
+regulator but this is sort of the if you
+ 
+
+ align:start position:0%
+regulator but this is sort of the if you
+want to get more information on it
+
+ align:start position:0%
+want to get more information on it
+ 
+
+ align:start position:0%
+want to get more information on it
+that's a good place to start you could
+
+ align:start position:0%
+that's a good place to start you could
+ 
+
+ align:start position:0%
+that's a good place to start you could
+search um it was a difficult time for us
+
+ align:start position:0%
+search um it was a difficult time for us
+ 
+
+ align:start position:0%
+search um it was a difficult time for us
+a lot of reactors uh also had similar
+
+ align:start position:0%
+a lot of reactors uh also had similar
+ 
+
+ align:start position:0%
+a lot of reactors uh also had similar
+situations and they had to do a lot of
+
+ align:start position:0%
+situations and they had to do a lot of
+ 
+
+ align:start position:0%
+situations and they had to do a lot of
+vessel inspections identifying a lot of
+
+ align:start position:0%
+vessel inspections identifying a lot of
+ 
+
+ align:start position:0%
+vessel inspections identifying a lot of
+fracture toughness and I think if our
+
+ align:start position:0%
+fracture toughness and I think if our
+ 
+
+ align:start position:0%
+fracture toughness and I think if our
+department does a material science
+
+ align:start position:0%
+department does a material science
+ 
+
+ align:start position:0%
+department does a material science
+course for undergrads this is some this
+
+ align:start position:0%
+course for undergrads this is some this
+ 
+
+ align:start position:0%
+course for undergrads this is some this
+is going to be a major issue but the
+
+ align:start position:0%
+is going to be a major issue but the
+ 
+
+ align:start position:0%
+is going to be a major issue but the
+phenomenon is pressurized thermal shock
+
+ align:start position:0%
+phenomenon is pressurized thermal shock
+ 
+
+ align:start position:0%
+phenomenon is pressurized thermal shock
+in normal conditions you're not
+
+ align:start position:0%
+in normal conditions you're not
+ 
+
+ align:start position:0%
+in normal conditions you're not
+expecting the reactor vessel to fail
+
+ align:start position:0%
+expecting the reactor vessel to fail
+ 
+
+ align:start position:0%
+expecting the reactor vessel to fail
+because it's warm and hot but hit it
+
+ align:start position:0%
+because it's warm and hot but hit it
+ 
+
+ align:start position:0%
+because it's warm and hot but hit it
+with cold water it's a problem some
+
+ align:start position:0%
+with cold water it's a problem some
+ 
+
+ align:start position:0%
+with cold water it's a problem some
+reactors because you know some some of
+
+ align:start position:0%
+reactors because you know some some of
+ 
+
+ align:start position:0%
+reactors because you know some some of
+these reactors want to operate for 60
+
+ align:start position:0%
+these reactors want to operate for 60
+ 
+
+ align:start position:0%
+these reactors want to operate for 60
+years and fluence is a integrated
+
+ align:start position:0%
+years and fluence is a integrated
+ 
+
+ align:start position:0%
+years and fluence is a integrated
+phenomenon so what they've done and this
+
+ align:start position:0%
+phenomenon so what they've done and this
+ 
+
+ align:start position:0%
+phenomenon so what they've done and this
+gets back to our reactor physics and
+
+ align:start position:0%
+gets back to our reactor physics and
+ 
+
+ align:start position:0%
+gets back to our reactor physics and
+they've decided to do low leakage cores
+
+ align:start position:0%
+they've decided to do low leakage cores
+ 
+
+ align:start position:0%
+they've decided to do low leakage cores
+where they managed the core fuel
+
+ align:start position:0%
+where they managed the core fuel
+ 
+
+ align:start position:0%
+where they managed the core fuel
+management such that the amount of
+
+ align:start position:0%
+management such that the amount of
+ 
+
+ align:start position:0%
+management such that the amount of
+neutrons escaping from the reactor
+
+ align:start position:0%
+neutrons escaping from the reactor
+ 
+
+ align:start position:0%
+neutrons escaping from the reactor
+hitting the vessel is reduced so that's
+
+ align:start position:0%
+hitting the vessel is reduced so that's
+ 
+
+ align:start position:0%
+hitting the vessel is reduced so that's
+a major impact on on core design and in
+
+ align:start position:0%
+a major impact on on core design and in
+ 
+
+ align:start position:0%
+a major impact on on core design and in
+fact the reactor vessel is really the
+
+ align:start position:0%
+fact the reactor vessel is really the
+ 
+
+ align:start position:0%
+fact the reactor vessel is really the
+only major life limiting
+
+ align:start position:0%
+only major life limiting
+ 
+
+ align:start position:0%
+only major life limiting
+compound in the whole nuclear power
+
+ align:start position:0%
+compound in the whole nuclear power
+ 
+
+ align:start position:0%
+compound in the whole nuclear power
+plant you can replace turbines you
+
+ align:start position:0%
+plant you can replace turbines you
+ 
+
+ align:start position:0%
+plant you can replace turbines you
+replace condensers replace steam
+
+ align:start position:0%
+replace condensers replace steam
+ 
+
+ align:start position:0%
+replace condensers replace steam
+generators reactor vessel becomes a
+
+ align:start position:0%
+generators reactor vessel becomes a
+ 
+
+ align:start position:0%
+generators reactor vessel becomes a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+tricky we at Yankee were actually
+
+ align:start position:0%
+tricky we at Yankee were actually
+ 
+
+ align:start position:0%
+tricky we at Yankee were actually
+considering replacing a reactor vessel
+
+ align:start position:0%
+considering replacing a reactor vessel
+ 
+
+ align:start position:0%
+considering replacing a reactor vessel
+and we've done some preliminary studies
+
+ align:start position:0%
+and we've done some preliminary studies
+ 
+
+ align:start position:0%
+and we've done some preliminary studies
+but it became um for a plant of only 185
+
+ align:start position:0%
+but it became um for a plant of only 185
+ 
+
+ align:start position:0%
+but it became um for a plant of only 185
+megaw very difficult to justify but you
+
+ align:start position:0%
+megaw very difficult to justify but you
+ 
+
+ align:start position:0%
+megaw very difficult to justify but you
+theoretically can do it the other thing
+
+ align:start position:0%
+theoretically can do it the other thing
+ 
+
+ align:start position:0%
+theoretically can do it the other thing
+that you can do with this is called a
+
+ align:start position:0%
+that you can do with this is called a
+ 
+
+ align:start position:0%
+that you can do with this is called a
+kneeling and we look very hard at this
+
+ align:start position:0%
+kneeling and we look very hard at this
+ 
+
+ align:start position:0%
+kneeling and we look very hard at this
+concept of
+
+ align:start position:0%
+concept of
+ 
+
+ align:start position:0%
+concept of
+analing and this was done and has been
+
+ align:start position:0%
+analing and this was done and has been
+ 
+
+ align:start position:0%
+analing and this was done and has been
+done in uh reactors I in Russia for sure
+
+ align:start position:0%
+done in uh reactors I in Russia for sure
+ 
+
+ align:start position:0%
+done in uh reactors I in Russia for sure
+and I think in the Belgian reactor
+
+ align:start position:0%
+and I think in the Belgian reactor
+ 
+
+ align:start position:0%
+and I think in the Belgian reactor
+analing is basically taking and heating
+
+ align:start position:0%
+analing is basically taking and heating
+ 
+
+ align:start position:0%
+analing is basically taking and heating
+up the reactor vessel Wells or those
+
+ align:start position:0%
+up the reactor vessel Wells or those
+ 
+
+ align:start position:0%
+up the reactor vessel Wells or those
+heated those those zones where you have
+
+ align:start position:0%
+heated those those zones where you have
+ 
+
+ align:start position:0%
+heated those those zones where you have
+potentially EMB Britt conditions heating
+
+ align:start position:0%
+potentially EMB Britt conditions heating
+ 
+
+ align:start position:0%
+potentially EMB Britt conditions heating
+it up and allowing the material to relax
+
+ align:start position:0%
+it up and allowing the material to relax
+ 
+
+ align:start position:0%
+it up and allowing the material to relax
+and restore some of its original
+
+ align:start position:0%
+and restore some of its original
+ 
+
+ align:start position:0%
+and restore some of its original
+properties and this analing phenomenon
+
+ align:start position:0%
+properties and this analing phenomenon
+ 
+
+ align:start position:0%
+properties and this analing phenomenon
+allowed would could potentially allow
+
+ align:start position:0%
+allowed would could potentially allow
+ 
+
+ align:start position:0%
+allowed would could potentially allow
+you to get 10 more years of operating
+
+ align:start position:0%
+you to get 10 more years of operating
+ 
+
+ align:start position:0%
+you to get 10 more years of operating
+line and then allow it to reate so
+
+ align:start position:0%
+line and then allow it to reate so
+ 
+
+ align:start position:0%
+line and then allow it to reate so
+analing is another solution to reactive
+
+ align:start position:0%
+analing is another solution to reactive
+ 
+
+ align:start position:0%
+analing is another solution to reactive
+vessel Integrity issues if replacement
+
+ align:start position:0%
+vessel Integrity issues if replacement
+ 
+
+ align:start position:0%
+vessel Integrity issues if replacement
+is not an option but it's it's sort of
+
+ align:start position:0%
+is not an option but it's it's sort of
+ 
+
+ align:start position:0%
+is not an option but it's it's sort of
+like it doesn't fully recover and you
+
+ align:start position:0%
+like it doesn't fully recover and you
+ 
+
+ align:start position:0%
+like it doesn't fully recover and you
+need to do it more frequently as as as
+
+ align:start position:0%
+need to do it more frequently as as as
+ 
+
+ align:start position:0%
+need to do it more frequently as as as
+as as the more irradiation damage
+
+ align:start position:0%
+as as the more irradiation damage
+ 
+
+ align:start position:0%
+as as the more irradiation damage
+occurs and so these are some solutions
+
+ align:start position:0%
+occurs and so these are some solutions
+ 
+
+ align:start position:0%
+occurs and so these are some solutions
+that you might want to think about if
+
+ align:start position:0%
+that you might want to think about if
+ 
+
+ align:start position:0%
+that you might want to think about if
+you're ever faced in this
+
+ align:start position:0%
+you're ever faced in this
+ 
+
+ align:start position:0%
+you're ever faced in this
+situation the U the next issue do you
+
+ align:start position:0%
+situation the U the next issue do you
+ 
+
+ align:start position:0%
+situation the U the next issue do you
+have any questions on the reative vessel
+
+ align:start position:0%
+have any questions on the reative vessel
+ 
+
+ align:start position:0%
+have any questions on the reative vessel
+one by way before one it's a lot of a
+
+ align:start position:0%
+one by way before one it's a lot of a
+ 
+
+ align:start position:0%
+one by way before one it's a lot of a
+lot of stuff but I was I was prepared to
+
+ align:start position:0%
+lot of stuff but I was I was prepared to
+ 
+
+ align:start position:0%
+lot of stuff but I was I was prepared to
+give you some some discussions on the
+
+ align:start position:0%
+give you some some discussions on the
+ 
+
+ align:start position:0%
+give you some some discussions on the
+kinds of work that we did do uh to
+
+ align:start position:0%
+kinds of work that we did do uh to
+ 
+
+ align:start position:0%
+kinds of work that we did do uh to
+justify operation if you don't have the
+
+ align:start position:0%
+justify operation if you don't have the
+ 
+
+ align:start position:0%
+justify operation if you don't have the
+the Material Science Background it's pry
+
+ align:start position:0%
+the Material Science Background it's pry
+ 
+
+ align:start position:0%
+the Material Science Background it's pry
+hard to uh to discuss but the two key
+
+ align:start position:0%
+hard to uh to discuss but the two key
+ 
+
+ align:start position:0%
+hard to uh to discuss but the two key
+areas in this in this in this in this
+
+ align:start position:0%
+areas in this in this in this in this
+ 
+
+ align:start position:0%
+areas in this in this in this in this
+discussion is what is the maximum
+
+ align:start position:0%
+discussion is what is the maximum
+ 
+
+ align:start position:0%
+discussion is what is the maximum
+detectable flaw size and given that
+
+ align:start position:0%
+detectable flaw size and given that
+ 
+
+ align:start position:0%
+detectable flaw size and given that
+maximum detectable flaw size should you
+
+ align:start position:0%
+maximum detectable flaw size should you
+ 
+
+ align:start position:0%
+maximum detectable flaw size should you
+have a pts event would the reactive
+
+ align:start position:0%
+have a pts event would the reactive
+ 
+
+ align:start position:0%
+have a pts event would the reactive
+vessel fit or have a crack propagation
+
+ align:start position:0%
+vessel fit or have a crack propagation
+ 
+
+ align:start position:0%
+vessel fit or have a crack propagation
+such that the likelihood failure would
+
+ align:start position:0%
+such that the likelihood failure would
+ 
+
+ align:start position:0%
+such that the likelihood failure would
+be much higher and the inspections that
+
+ align:start position:0%
+be much higher and the inspections that
+ 
+
+ align:start position:0%
+be much higher and the inspections that
+you do inside these reactor vels mean
+
+ align:start position:0%
+you do inside these reactor vels mean
+ 
+
+ align:start position:0%
+you do inside these reactor vels mean
+you take all the fuel out of the reactor
+
+ align:start position:0%
+you take all the fuel out of the reactor
+ 
+
+ align:start position:0%
+you take all the fuel out of the reactor
+vessel and then you do uh uh some kind
+
+ align:start position:0%
+vessel and then you do uh uh some kind
+ 
+
+ align:start position:0%
+vessel and then you do uh uh some kind
+of inspection that will identify what
+
+ align:start position:0%
+of inspection that will identify what
+ 
+
+ align:start position:0%
+of inspection that will identify what
+you consider to be the maximum flaw size
+
+ align:start position:0%
+you consider to be the maximum flaw size
+ 
+
+ align:start position:0%
+you consider to be the maximum flaw size
+and and that that is the key driver and
+
+ align:start position:0%
+and and that that is the key driver and
+ 
+
+ align:start position:0%
+and and that that is the key driver and
+there's all kinds of analysis that you
+
+ align:start position:0%
+there's all kinds of analysis that you
+ 
+
+ align:start position:0%
+there's all kinds of analysis that you
+can do to show with a certain detectable
+
+ align:start position:0%
+can do to show with a certain detectable
+ 
+
+ align:start position:0%
+can do to show with a certain detectable
+fla size this thing is going to be a
+
+ align:start position:0%
+fla size this thing is going to be a
+ 
+
+ align:start position:0%
+fla size this thing is going to be a
+problem or not the other issue is this
+
+ align:start position:0%
+problem or not the other issue is this
+ 
+
+ align:start position:0%
+problem or not the other issue is this
+next issue that I want to talk about is
+
+ align:start position:0%
+next issue that I want to talk about is
+ 
+
+ align:start position:0%
+next issue that I want to talk about is
+some PP
+
+ align:start position:0%
+some PP
+ 
+
+ align:start position:0%
+some PP
+performance now this issue has been
+
+ align:start position:0%
+performance now this issue has been
+ 
+
+ align:start position:0%
+performance now this issue has been
+around found since the late
+
+ align:start position:0%
+around found since the late
+ 
+
+ align:start position:0%
+around found since the late
+1970s all right now why is this a
+
+ align:start position:0%
+1970s all right now why is this a
+ 
+
+ align:start position:0%
+1970s all right now why is this a
+problem well you remember in when we
+
+ align:start position:0%
+problem well you remember in when we
+ 
+
+ align:start position:0%
+problem well you remember in when we
+talked about um the need for
+
+ align:start position:0%
+talked about um the need for
+ 
+
+ align:start position:0%
+talked about um the need for
+recirculation all the water pretty much
+
+ align:start position:0%
+recirculation all the water pretty much
+ 
+
+ align:start position:0%
+recirculation all the water pretty much
+comes down into the lower uh containment
+
+ align:start position:0%
+comes down into the lower uh containment
+ 
+
+ align:start position:0%
+comes down into the lower uh containment
+section and is pumped back into either
+
+ align:start position:0%
+section and is pumped back into either
+ 
+
+ align:start position:0%
+section and is pumped back into either
+the core spray system or back into the
+
+ align:start position:0%
+the core spray system or back into the
+ 
+
+ align:start position:0%
+the core spray system or back into the
+reactor but when you have this stuff
+
+ align:start position:0%
+reactor but when you have this stuff
+ 
+
+ align:start position:0%
+reactor but when you have this stuff
+going on especially in the containment
+
+ align:start position:0%
+going on especially in the containment
+ 
+
+ align:start position:0%
+going on especially in the containment
+sprays or maybe in the major pipe Rak
+
+ align:start position:0%
+sprays or maybe in the major pipe Rak
+ 
+
+ align:start position:0%
+sprays or maybe in the major pipe Rak
+you you potentially can lose a lot of
+
+ align:start position:0%
+you you potentially can lose a lot of
+ 
+
+ align:start position:0%
+you you potentially can lose a lot of
+insulation a lot of debris ultimately
+
+ align:start position:0%
+insulation a lot of debris ultimately
+ 
+
+ align:start position:0%
+insulation a lot of debris ultimately
+end up in the bottom of the
+
+ align:start position:0%
+end up in the bottom of the
+ 
+
+ align:start position:0%
+end up in the bottom of the
+sun and it originally started with
+
+ align:start position:0%
+sun and it originally started with
+ 
+
+ align:start position:0%
+sun and it originally started with
+pressure with boiling water reactors
+
+ align:start position:0%
+pressure with boiling water reactors
+ 
+
+ align:start position:0%
+pressure with boiling water reactors
+back in the late late um
+
+ align:start position:0%
+back in the late late um
+ 
+
+ align:start position:0%
+back in the late late um
+1970s where they have for these pumps
+
+ align:start position:0%
+1970s where they have for these pumps
+ 
+
+ align:start position:0%
+1970s where they have for these pumps
+they had debris screens and the debris
+
+ align:start position:0%
+they had debris screens and the debris
+ 
+
+ align:start position:0%
+they had debris screens and the debris
+screens were were were intended to keep
+
+ align:start position:0%
+screens were were were intended to keep
+ 
+
+ align:start position:0%
+screens were were were intended to keep
+the debris from damaging the
+
+ align:start position:0%
+the debris from damaging the
+ 
+
+ align:start position:0%
+the debris from damaging the
+pump and possibly even going into the
+
+ align:start position:0%
+pump and possibly even going into the
+ 
+
+ align:start position:0%
+pump and possibly even going into the
+main cool pumps and Main cooling system
+
+ align:start position:0%
+main cool pumps and Main cooling system
+ 
+
+ align:start position:0%
+main cool pumps and Main cooling system
+and actually getting into the reactor
+
+ align:start position:0%
+and actually getting into the reactor
+ 
+
+ align:start position:0%
+and actually getting into the reactor
+vessel so the NRC had a a a big issue
+
+ align:start position:0%
+vessel so the NRC had a a a big issue
+ 
+
+ align:start position:0%
+vessel so the NRC had a a a big issue
+about identifying whether or not these
+
+ align:start position:0%
+about identifying whether or not these
+ 
+
+ align:start position:0%
+about identifying whether or not these
+bwrs debris screens would in fact block
+
+ align:start position:0%
+bwrs debris screens would in fact block
+ 
+
+ align:start position:0%
+bwrs debris screens would in fact block
+sufficient water from getting to the
+
+ align:start position:0%
+sufficient water from getting to the
+ 
+
+ align:start position:0%
+sufficient water from getting to the
+pumps and then not allowing water to be
+
+ align:start position:0%
+pumps and then not allowing water to be
+ 
+
+ align:start position:0%
+pumps and then not allowing water to be
+recirculated and this is this neet
+
+ align:start position:0%
+recirculated and this is this neet
+ 
+
+ align:start position:0%
+recirculated and this is this neet
+positive suction head and that was can
+
+ align:start position:0%
+positive suction head and that was can
+ 
+
+ align:start position:0%
+positive suction head and that was can
+you get enough water pumping through the
+
+ align:start position:0%
+you get enough water pumping through the
+ 
+
+ align:start position:0%
+you get enough water pumping through the
+pumps to be able to um get it to the
+
+ align:start position:0%
+pumps to be able to um get it to the
+ 
+
+ align:start position:0%
+pumps to be able to um get it to the
+appropriate places whether it be the
+
+ align:start position:0%
+appropriate places whether it be the
+ 
+
+ align:start position:0%
+appropriate places whether it be the
+reactor vessel or um or the sprays and
+
+ align:start position:0%
+reactor vessel or um or the sprays and
+ 
+
+ align:start position:0%
+reactor vessel or um or the sprays and
+it's it's basically the causing
+
+ align:start position:0%
+it's it's basically the causing
+ 
+
+ align:start position:0%
+it's it's basically the causing
+potentially a failure of the resarch
+
+ align:start position:0%
+potentially a failure of the resarch
+ 
+
+ align:start position:0%
+potentially a failure of the resarch
+pump or cavitation of these pumps both
+
+ align:start position:0%
+pump or cavitation of these pumps both
+ 
+
+ align:start position:0%
+pump or cavitation of these pumps both
+are not good things so initially as you
+
+ align:start position:0%
+are not good things so initially as you
+ 
+
+ align:start position:0%
+are not good things so initially as you
+look at it it's it's it's ass it was
+
+ align:start position:0%
+look at it it's it's it's ass it was
+ 
+
+ align:start position:0%
+look at it it's it's it's ass it was
+associated with insufficient cooling
+
+ align:start position:0%
+associated with insufficient cooling
+ 
+
+ align:start position:0%
+associated with insufficient cooling
+then in the early
+
+ align:start position:0%
+then in the early
+ 
+
+ align:start position:0%
+then in the early
+1990s um well there's a there's a red
+
+ align:start position:0%
+1990s um well there's a there's a red
+ 
+
+ align:start position:0%
+1990s um well there's a there's a red
+guide let me just write down the red
+
+ align:start position:0%
+guide let me just write down the red
+ 
+
+ align:start position:0%
+guide let me just write down the red
+guide so you can kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here there's a red guy that was
+
+ align:start position:0%
+here there's a red guy that was
+ 
+
+ align:start position:0%
+here there's a red guy that was
+issued it was on the sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question it was red
+
+ align:start position:0%
+question it was red
+ 
+
+ align:start position:0%
+question it was red
+guy
+
+ align:start position:0%
+guy
+ 
+
+ align:start position:0%
+guy
+1.82 and it was largely in response to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bwrs and they had a generic letter as
+
+ align:start position:0%
+bwrs and they had a generic letter as
+ 
+
+ align:start position:0%
+bwrs and they had a generic letter as
+well which was 85
+
+ align:start position:0%
+well which was 85
+ 
+
+ align:start position:0%
+well which was 85
+-22 so you can see how long ago this
+
+ align:start position:0%
+-22 so you can see how long ago this
+ 
+
+ align:start position:0%
+-22 so you can see how long ago this
+issue
+
+ align:start position:0%
+issue
+ 
+
+ align:start position:0%
+issue
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+and 1979 was the first time they got
+
+ align:start position:0%
+and 1979 was the first time they got
+ 
+
+ align:start position:0%
+and 1979 was the first time they got
+this thing gone under bre
+
+ align:start position:0%
+this thing gone under bre
+ 
+
+ align:start position:0%
+this thing gone under bre
+blockage uh they did some research they
+
+ align:start position:0%
+blockage uh they did some research they
+ 
+
+ align:start position:0%
+blockage uh they did some research they
+did some preliminary analysis and they
+
+ align:start position:0%
+did some preliminary analysis and they
+ 
+
+ align:start position:0%
+did some preliminary analysis and they
+basically had to bwr people fix certain
+
+ align:start position:0%
+basically had to bwr people fix certain
+ 
+
+ align:start position:0%
+basically had to bwr people fix certain
+things but they they concluded that it
+
+ align:start position:0%
+things but they they concluded that it
+ 
+
+ align:start position:0%
+things but they they concluded that it
+was kind of okay for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PW back at that
+
+ align:start position:0%
+PW back at that
+ 
+
+ align:start position:0%
+PW back at that
+time then they started looking at that
+
+ align:start position:0%
+time then they started looking at that
+ 
+
+ align:start position:0%
+time then they started looking at that
+and now now we're talking into the late
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1990s and they said well gee maybe pwrs
+
+ align:start position:0%
+1990s and they said well gee maybe pwrs
+ 
+
+ align:start position:0%
+1990s and they said well gee maybe pwrs
+are also susceptible to this
+
+ align:start position:0%
+are also susceptible to this
+ 
+
+ align:start position:0%
+are also susceptible to this
+problem and the the issue was very
+
+ align:start position:0%
+problem and the the issue was very
+ 
+
+ align:start position:0%
+problem and the the issue was very
+similar but they had uh the screens that
+
+ align:start position:0%
+similar but they had uh the screens that
+ 
+
+ align:start position:0%
+similar but they had uh the screens that
+they had were somewhat different in
+
+ align:start position:0%
+they had were somewhat different in
+ 
+
+ align:start position:0%
+they had were somewhat different in
+design than the BW was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they felt that initially the PWS
+
+ align:start position:0%
+and they felt that initially the PWS
+ 
+
+ align:start position:0%
+and they felt that initially the PWS
+screens were fine but then they had some
+
+ align:start position:0%
+screens were fine but then they had some
+ 
+
+ align:start position:0%
+screens were fine but then they had some
+experiments and they had some events
+
+ align:start position:0%
+experiments and they had some events
+ 
+
+ align:start position:0%
+experiments and they had some events
+that occurred that suggested that well
+
+ align:start position:0%
+that occurred that suggested that well
+ 
+
+ align:start position:0%
+that occurred that suggested that well
+we have a similar problem here and um
+
+ align:start position:0%
+we have a similar problem here and um
+ 
+
+ align:start position:0%
+we have a similar problem here and um
+they then began looking at it for PW now
+
+ align:start position:0%
+they then began looking at it for PW now
+ 
+
+ align:start position:0%
+they then began looking at it for PW now
+this is a current
+
+ align:start position:0%
+this is a current
+ 
+
+ align:start position:0%
+this is a current
+issue and they've done evaluations the
+
+ align:start position:0%
+issue and they've done evaluations the
+ 
+
+ align:start position:0%
+issue and they've done evaluations the
+NC has done
+
+ align:start position:0%
+NC has done
+ 
+
+ align:start position:0%
+NC has done
+evaluations and as has the
+
+ align:start position:0%
+evaluations and as has the
+ 
+
+ align:start position:0%
+evaluations and as has the
+industry and what they concluded was
+
+ align:start position:0%
+industry and what they concluded was
+ 
+
+ align:start position:0%
+industry and what they concluded was
+that some of this debris could pass
+
+ align:start position:0%
+that some of this debris could pass
+ 
+
+ align:start position:0%
+that some of this debris could pass
+through the
+
+ align:start position:0%
+through the
+ 
+
+ align:start position:0%
+through the
+screen and could get into the
+
+ align:start position:0%
+screen and could get into the
+ 
+
+ align:start position:0%
+screen and could get into the
+core and the issue basically is if it
+
+ align:start position:0%
+core and the issue basically is if it
+ 
+
+ align:start position:0%
+core and the issue basically is if it
+goes into the
+
+ align:start position:0%
+goes into the
+ 
+
+ align:start position:0%
+goes into the
+core it could obviously block some fuel
+
+ align:start position:0%
+core it could obviously block some fuel
+ 
+
+ align:start position:0%
+core it could obviously block some fuel
+pin Fuel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assends and the industry responded by by
+
+ align:start position:0%
+assends and the industry responded by by
+ 
+
+ align:start position:0%
+assends and the industry responded by by
+doing some analysis saying that yes if
+
+ align:start position:0%
+doing some analysis saying that yes if
+ 
+
+ align:start position:0%
+doing some analysis saying that yes if
+it blocks some fuel assemblies there are
+
+ align:start position:0%
+it blocks some fuel assemblies there are
+ 
+
+ align:start position:0%
+it blocks some fuel assemblies there are
+efficient number of
+
+ align:start position:0%
+efficient number of
+ 
+
+ align:start position:0%
+efficient number of
+holes in the core Barrel or areas where
+
+ align:start position:0%
+holes in the core Barrel or areas where
+ 
+
+ align:start position:0%
+holes in the core Barrel or areas where
+water can in fact come into the core
+
+ align:start position:0%
+water can in fact come into the core
+ 
+
+ align:start position:0%
+water can in fact come into the core
+that it is not a soal imminent
+
+ align:start position:0%
+that it is not a soal imminent
+ 
+
+ align:start position:0%
+that it is not a soal imminent
+problem which meant that they would be
+
+ align:start position:0%
+problem which meant that they would be
+ 
+
+ align:start position:0%
+problem which meant that they would be
+allowed to continue to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operate until this issue was technically
+
+ align:start position:0%
+operate until this issue was technically
+ 
+
+ align:start position:0%
+operate until this issue was technically
+resolved and the issue resolution was
+
+ align:start position:0%
+resolved and the issue resolution was
+ 
+
+ align:start position:0%
+resolved and the issue resolution was
+size of the screen
+
+ align:start position:0%
+size of the screen
+ 
+
+ align:start position:0%
+size of the screen
+mesh
+
+ align:start position:0%
+mesh
+ 
+
+ align:start position:0%
+mesh
+and the impact on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+core so we're fighting two things if you
+
+ align:start position:0%
+core so we're fighting two things if you
+ 
+
+ align:start position:0%
+core so we're fighting two things if you
+make it too fine a
+
+ align:start position:0%
+make it too fine a
+ 
+
+ align:start position:0%
+make it too fine a
+screen you're not going to get water to
+
+ align:start position:0%
+screen you're not going to get water to
+ 
+
+ align:start position:0%
+screen you're not going to get water to
+the pump if you make it too loose a
+
+ align:start position:0%
+the pump if you make it too loose a
+ 
+
+ align:start position:0%
+the pump if you make it too loose a
+screen you'll get debris into the
+
+ align:start position:0%
+screen you'll get debris into the
+ 
+
+ align:start position:0%
+screen you'll get debris into the
+core both are not good but there this is
+
+ align:start position:0%
+core both are not good but there this is
+ 
+
+ align:start position:0%
+core both are not good but there this is
+this is still a very active safety issue
+
+ align:start position:0%
+this is still a very active safety issue
+ 
+
+ align:start position:0%
+this is still a very active safety issue
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um the last bulletin I guess was
+
+ align:start position:0%
+um the last bulletin I guess was
+ 
+
+ align:start position:0%
+um the last bulletin I guess was
+bulletin on this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+2003-1 and it still requires lenses to
+
+ align:start position:0%
+2003-1 and it still requires lenses to
+ 
+
+ align:start position:0%
+2003-1 and it still requires lenses to
+demonstrate that they that this will not
+
+ align:start position:0%
+demonstrate that they that this will not
+ 
+
+ align:start position:0%
+demonstrate that they that this will not
+be a problem for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them okay now you remember the
+
+ align:start position:0%
+them okay now you remember the
+ 
+
+ align:start position:0%
+them okay now you remember the
+differences I I've written down a couple
+
+ align:start position:0%
+differences I I've written down a couple
+ 
+
+ align:start position:0%
+differences I I've written down a couple
+of things I've written down regulatory
+
+ align:start position:0%
+of things I've written down regulatory
+ 
+
+ align:start position:0%
+of things I've written down regulatory
+guides I've written down bulletins and
+
+ align:start position:0%
+guides I've written down bulletins and
+ 
+
+ align:start position:0%
+guides I've written down bulletins and
+I've written down generic letters do you
+
+ align:start position:0%
+I've written down generic letters do you
+ 
+
+ align:start position:0%
+I've written down generic letters do you
+recall the
+
+ align:start position:0%
+recall the
+ 
+
+ align:start position:0%
+recall the
+differences
+
+ align:start position:0%
+differences
+ 
+
+ align:start position:0%
+differences
+so the bulle have respond exactly the
+
+ align:start position:0%
+so the bulle have respond exactly the
+ 
+
+ align:start position:0%
+so the bulle have respond exactly the
+bulletins have to be responded to
+
+ align:start position:0%
+bulletins have to be responded to
+ 
+
+ align:start position:0%
+bulletins have to be responded to
+generic letters are heads up may may
+
+ align:start position:0%
+generic letters are heads up may may
+ 
+
+ align:start position:0%
+generic letters are heads up may may
+request some information red guides are
+
+ align:start position:0%
+request some information red guides are
+ 
+
+ align:start position:0%
+request some information red guides are
+this is a way to
+
+ align:start position:0%
+this is a way to
+ 
+
+ align:start position:0%
+this is a way to
+comply to this question so you've got
+
+ align:start position:0%
+comply to this question so you've got
+ 
+
+ align:start position:0%
+comply to this question so you've got
+all kinds of different approaches that
+
+ align:start position:0%
+all kinds of different approaches that
+ 
+
+ align:start position:0%
+all kinds of different approaches that
+the NRC has taken to allow the industry
+
+ align:start position:0%
+the NRC has taken to allow the industry
+ 
+
+ align:start position:0%
+the NRC has taken to allow the industry
+to be aware of a problem and how best to
+
+ align:start position:0%
+to be aware of a problem and how best to
+ 
+
+ align:start position:0%
+to be aware of a problem and how best to
+to get the solution of this problem and
+
+ align:start position:0%
+to get the solution of this problem and
+ 
+
+ align:start position:0%
+to get the solution of this problem and
+if you go if you go on the NRC website
+
+ align:start position:0%
+if you go if you go on the NRC website
+ 
+
+ align:start position:0%
+if you go if you go on the NRC website
+you'll see a lot of Industry
+
+ align:start position:0%
+you'll see a lot of Industry
+ 
+
+ align:start position:0%
+you'll see a lot of Industry
+presentations if you go under
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meetings you'll see sometimes anyi
+
+ align:start position:0%
+meetings you'll see sometimes anyi
+ 
+
+ align:start position:0%
+meetings you'll see sometimes anyi
+presentation and they'll see and you'll
+
+ align:start position:0%
+presentation and they'll see and you'll
+ 
+
+ align:start position:0%
+presentation and they'll see and you'll
+get from that website
+
+ align:start position:0%
+get from that website
+ 
+
+ align:start position:0%
+get from that website
+slides of what people have said from the
+
+ align:start position:0%
+slides of what people have said from the
+ 
+
+ align:start position:0%
+slides of what people have said from the
+industry's perspective now this one is
+
+ align:start position:0%
+industry's perspective now this one is
+ 
+
+ align:start position:0%
+industry's perspective now this one is
+in long-term core long-term core pooling
+
+ align:start position:0%
+in long-term core long-term core pooling
+ 
+
+ align:start position:0%
+in long-term core long-term core pooling
+on core Inlet flow blockage which
+
+ align:start position:0%
+on core Inlet flow blockage which
+ 
+
+ align:start position:0%
+on core Inlet flow blockage which
+basically said
+
+ align:start position:0%
+basically said
+ 
+
+ align:start position:0%
+basically said
+well we've got a lot of this debris
+
+ align:start position:0%
+well we've got a lot of this debris
+ 
+
+ align:start position:0%
+well we've got a lot of this debris
+coming through and it's going to impact
+
+ align:start position:0%
+coming through and it's going to impact
+ 
+
+ align:start position:0%
+coming through and it's going to impact
+the core and this is our analysis
+
+ align:start position:0%
+the core and this is our analysis
+ 
+
+ align:start position:0%
+the core and this is our analysis
+showing that we do not believe we have a
+
+ align:start position:0%
+showing that we do not believe we have a
+ 
+
+ align:start position:0%
+showing that we do not believe we have a
+problem under various
+
+ align:start position:0%
+problem under various
+ 
+
+ align:start position:0%
+problem under various
+scenarios could you open a
+
+ align:start position:0%
+scenarios could you open a
+ 
+
+ align:start position:0%
+scenarios could you open a
+window I'm warm as can
+
+ align:start position:0%
+window I'm warm as can
+ 
+
+ align:start position:0%
+window I'm warm as can
+be okay the the next issue is reactor
+
+ align:start position:0%
+be okay the the next issue is reactor
+ 
+
+ align:start position:0%
+be okay the the next issue is reactor
+cooling system weld issues now this
+
+ align:start position:0%
+cooling system weld issues now this
+ 
+
+ align:start position:0%
+cooling system weld issues now this
+graphic again comes from their
+
+ align:start position:0%
+graphic again comes from their
+ 
+
+ align:start position:0%
+graphic again comes from their
+website now these are all the are
+
+ align:start position:0%
+website now these are all the are
+ 
+
+ align:start position:0%
+website now these are all the are
+in which there are weld issue problems
+
+ align:start position:0%
+in which there are weld issue problems
+ 
+
+ align:start position:0%
+in which there are weld issue problems
+now you're looking at this like oh my
+
+ align:start position:0%
+now you're looking at this like oh my
+ 
+
+ align:start position:0%
+now you're looking at this like oh my
+goodness this is a this is this is not
+
+ align:start position:0%
+goodness this is a this is this is not
+ 
+
+ align:start position:0%
+goodness this is a this is this is not
+these things are kind of wearing out
+
+ align:start position:0%
+these things are kind of wearing out
+ 
+
+ align:start position:0%
+these things are kind of wearing out
+aren't they first you had we all know
+
+ align:start position:0%
+aren't they first you had we all know
+ 
+
+ align:start position:0%
+aren't they first you had we all know
+about the upper head control rod Drive
+
+ align:start position:0%
+about the upper head control rod Drive
+ 
+
+ align:start position:0%
+about the upper head control rod Drive
+um issues relative to Davis Bessie and
+
+ align:start position:0%
+um issues relative to Davis Bessie and
+ 
+
+ align:start position:0%
+um issues relative to Davis Bessie and
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+plants we vaguely or briefly mentioned
+
+ align:start position:0%
+plants we vaguely or briefly mentioned
+ 
+
+ align:start position:0%
+plants we vaguely or briefly mentioned
+pressurizer
+
+ align:start position:0%
+pressurizer
+ 
+
+ align:start position:0%
+pressurizer
+leaks Wells coming into or out of the um
+
+ align:start position:0%
+leaks Wells coming into or out of the um
+ 
+
+ align:start position:0%
+leaks Wells coming into or out of the um
+the reactor vessel and around the
+
+ align:start position:0%
+the reactor vessel and around the
+ 
+
+ align:start position:0%
+the reactor vessel and around the
+pressurizer around the main coolant
+
+ align:start position:0%
+pressurizer around the main coolant
+ 
+
+ align:start position:0%
+pressurizer around the main coolant
+pumps the lower reactor vessel head
+
+ align:start position:0%
+pumps the lower reactor vessel head
+ 
+
+ align:start position:0%
+pumps the lower reactor vessel head
+where in current plants all the
+
+ align:start position:0%
+where in current plants all the
+ 
+
+ align:start position:0%
+where in current plants all the
+instrumentation penetrations come
+
+ align:start position:0%
+instrumentation penetrations come
+ 
+
+ align:start position:0%
+instrumentation penetrations come
+through the bottom
+
+ align:start position:0%
+through the bottom
+ 
+
+ align:start position:0%
+through the bottom
+head and these areas are now becoming
+
+ align:start position:0%
+head and these areas are now becoming
+ 
+
+ align:start position:0%
+head and these areas are now becoming
+also very very important and they have a
+
+ align:start position:0%
+also very very important and they have a
+ 
+
+ align:start position:0%
+also very very important and they have a
+common common root
+
+ align:start position:0%
+common common root
+ 
+
+ align:start position:0%
+common common root
+cause and these the root cause is a
+
+ align:start position:0%
+cause and these the root cause is a
+ 
+
+ align:start position:0%
+cause and these the root cause is a
+certain type of alloy that's used in the
+
+ align:start position:0%
+certain type of alloy that's used in the
+ 
+
+ align:start position:0%
+certain type of alloy that's used in the
+wells and the butter in other words
+
+ align:start position:0%
+wells and the butter in other words
+ 
+
+ align:start position:0%
+wells and the butter in other words
+which is the uh materials that are uh
+
+ align:start position:0%
+which is the uh materials that are uh
+ 
+
+ align:start position:0%
+which is the uh materials that are uh
+associated with this alloy
+
+ align:start position:0%
+associated with this alloy
+ 
+
+ align:start position:0%
+associated with this alloy
+600 and it's it's primarily a primary
+
+ align:start position:0%
+600 and it's it's primarily a primary
+ 
+
+ align:start position:0%
+600 and it's it's primarily a primary
+stress water stress corrosion cracking
+
+ align:start position:0%
+stress water stress corrosion cracking
+ 
+
+ align:start position:0%
+stress water stress corrosion cracking
+which we talked about it's very clean
+
+ align:start position:0%
+which we talked about it's very clean
+ 
+
+ align:start position:0%
+which we talked about it's very clean
+water and the the determinant are
+
+ align:start position:0%
+water and the the determinant are
+ 
+
+ align:start position:0%
+water and the the determinant are
+temperature what the residual stresses
+
+ align:start position:0%
+temperature what the residual stresses
+ 
+
+ align:start position:0%
+temperature what the residual stresses
+are at those locations and how much of
+
+ align:start position:0%
+are at those locations and how much of
+ 
+
+ align:start position:0%
+are at those locations and how much of
+this nickel based Alo and how it was
+
+ align:start position:0%
+this nickel based Alo and how it was
+ 
+
+ align:start position:0%
+this nickel based Alo and how it was
+applied to these various Wells now I've
+
+ align:start position:0%
+applied to these various Wells now I've
+ 
+
+ align:start position:0%
+applied to these various Wells now I've
+just listed a few plants that have been
+
+ align:start position:0%
+just listed a few plants that have been
+ 
+
+ align:start position:0%
+just listed a few plants that have been
+affected now once you detect this
+
+ align:start position:0%
+affected now once you detect this
+ 
+
+ align:start position:0%
+affected now once you detect this
+problem there's a solution well first
+
+ align:start position:0%
+problem there's a solution well first
+ 
+
+ align:start position:0%
+problem there's a solution well first
+you got to detect which is a lot of
+
+ align:start position:0%
+you got to detect which is a lot of
+ 
+
+ align:start position:0%
+you got to detect which is a lot of
+measuring devices and you can imagine if
+
+ align:start position:0%
+measuring devices and you can imagine if
+ 
+
+ align:start position:0%
+measuring devices and you can imagine if
+you're in these areas it's probably a
+
+ align:start position:0%
+you're in these areas it's probably a
+ 
+
+ align:start position:0%
+you're in these areas it's probably a
+fair relatively High radiation zone so
+
+ align:start position:0%
+fair relatively High radiation zone so
+ 
+
+ align:start position:0%
+fair relatively High radiation zone so
+these are not easy to do but if you find
+
+ align:start position:0%
+these are not easy to do but if you find
+ 
+
+ align:start position:0%
+these are not easy to do but if you find
+these flaws you then the solution is
+
+ align:start position:0%
+these flaws you then the solution is
+ 
+
+ align:start position:0%
+these flaws you then the solution is
+grind it out and weld overlay take
+
+ align:start position:0%
+grind it out and weld overlay take
+ 
+
+ align:start position:0%
+grind it out and weld overlay take
+different weld metal and weld overlay so
+
+ align:start position:0%
+different weld metal and weld overlay so
+ 
+
+ align:start position:0%
+different weld metal and weld overlay so
+that you can avoid the leak that may
+
+ align:start position:0%
+that you can avoid the leak that may
+ 
+
+ align:start position:0%
+that you can avoid the leak that may
+occur
+
+ align:start position:0%
+occur
+ 
+
+ align:start position:0%
+occur
+now we also have in this case we have a
+
+ align:start position:0%
+now we also have in this case we have a
+ 
+
+ align:start position:0%
+now we also have in this case we have a
+different different type of
+
+ align:start position:0%
+different different type of
+ 
+
+ align:start position:0%
+different different type of
+response now the this
+
+ align:start position:0%
+response now the this
+ 
+
+ align:start position:0%
+response now the this
+alloy alloy 600 and 182 and and and
+
+ align:start position:0%
+alloy alloy 600 and 182 and and and
+ 
+
+ align:start position:0%
+alloy alloy 600 and 182 and and and
+82 are are basically the the the
+
+ align:start position:0%
+82 are are basically the the the
+ 
+
+ align:start position:0%
+82 are are basically the the the
+Structural Materials that keeps these
+
+ align:start position:0%
+Structural Materials that keeps these
+ 
+
+ align:start position:0%
+Structural Materials that keeps these
+pipes
+
+ align:start position:0%
+pipes
+ 
+
+ align:start position:0%
+pipes
+together and just just to get some
+
+ align:start position:0%
+together and just just to get some
+ 
+
+ align:start position:0%
+together and just just to get some
+perspective again on on timing and I
+
+ align:start position:0%
+perspective again on on timing and I
+ 
+
+ align:start position:0%
+perspective again on on timing and I
+think you're you're going to see a theme
+
+ align:start position:0%
+think you're you're going to see a theme
+ 
+
+ align:start position:0%
+think you're you're going to see a theme
+emerge from this discussion on the
+
+ align:start position:0%
+emerge from this discussion on the
+ 
+
+ align:start position:0%
+emerge from this discussion on the
+timing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question this was first
+
+ align:start position:0%
+question this was first
+ 
+
+ align:start position:0%
+question this was first
+detected in
+
+ align:start position:0%
+detected in
+ 
+
+ align:start position:0%
+detected in
+1989 at calber
+
+ align:start position:0%
+1989 at calber
+ 
+
+ align:start position:0%
+1989 at calber
+cliffs in um in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mar and the issue here was a pressurizer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's usually the hottest component and
+
+ align:start position:0%
+It's usually the hottest component and
+ 
+
+ align:start position:0%
+It's usually the hottest component and
+and during the fabrication it probably
+
+ align:start position:0%
+and during the fabrication it probably
+ 
+
+ align:start position:0%
+and during the fabrication it probably
+had a lot of stresses and it's on the
+
+ align:start position:0%
+had a lot of stresses and it's on the
+ 
+
+ align:start position:0%
+had a lot of stresses and it's on the
+heater
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sleeves which would the pressurizer
+
+ align:start position:0%
+sleeves which would the pressurizer
+ 
+
+ align:start position:0%
+sleeves which would the pressurizer
+heaters you know they get pretty hot and
+
+ align:start position:0%
+heaters you know they get pretty hot and
+ 
+
+ align:start position:0%
+heaters you know they get pretty hot and
+toasty and that's where the the the
+
+ align:start position:0%
+toasty and that's where the the the
+ 
+
+ align:start position:0%
+toasty and that's where the the the
+welds begin to start
+
+ align:start position:0%
+welds begin to start
+ 
+
+ align:start position:0%
+welds begin to start
+leaking and that resulted in information
+
+ align:start position:0%
+leaking and that resulted in information
+ 
+
+ align:start position:0%
+leaking and that resulted in information
+notice 90 D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10 then we saw I think you remember that
+
+ align:start position:0%
+10 then we saw I think you remember that
+ 
+
+ align:start position:0%
+10 then we saw I think you remember that
+chart timeline chart we had this thing
+
+ align:start position:0%
+chart timeline chart we had this thing
+ 
+
+ align:start position:0%
+chart timeline chart we had this thing
+at the bougie plant in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+France and that occurred roughly in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1991 and you recall the industry
+
+ align:start position:0%
+1991 and you recall the industry
+ 
+
+ align:start position:0%
+1991 and you recall the industry
+response to that event was different
+
+ align:start position:0%
+response to that event was different
+ 
+
+ align:start position:0%
+response to that event was different
+type of problem we don't have this
+
+ align:start position:0%
+type of problem we don't have this
+ 
+
+ align:start position:0%
+type of problem we don't have this
+design here our vessel's heads are made
+
+ align:start position:0%
+design here our vessel's heads are made
+ 
+
+ align:start position:0%
+design here our vessel's heads are made
+different differently and the NRC pretty
+
+ align:start position:0%
+different differently and the NRC pretty
+ 
+
+ align:start position:0%
+different differently and the NRC pretty
+much bought that argument based on Nei
+
+ align:start position:0%
+much bought that argument based on Nei
+ 
+
+ align:start position:0%
+much bought that argument based on Nei
+and every
+
+ align:start position:0%
+and every
+ 
+
+ align:start position:0%
+and every
+analysis and that bought some time but
+
+ align:start position:0%
+analysis and that bought some time but
+ 
+
+ align:start position:0%
+analysis and that bought some time but
+not a lot of
+
+ align:start position:0%
+not a lot of
+ 
+
+ align:start position:0%
+not a lot of
+time it then became interesting once
+
+ align:start position:0%
+time it then became interesting once
+ 
+
+ align:start position:0%
+time it then became interesting once
+again when people started looking
+
+ align:start position:0%
+again when people started looking
+ 
+
+ align:start position:0%
+again when people started looking
+at various inspections NRC Mand mandated
+
+ align:start position:0%
+at various inspections NRC Mand mandated
+ 
+
+ align:start position:0%
+at various inspections NRC Mand mandated
+some inspections
+
+ align:start position:0%
+some inspections
+ 
+
+ align:start position:0%
+some inspections
+of all of these types of welds as they
+
+ align:start position:0%
+of all of these types of welds as they
+ 
+
+ align:start position:0%
+of all of these types of welds as they
+in fact
+
+ align:start position:0%
+in fact
+ 
+
+ align:start position:0%
+in fact
+occurred and the sequence was well back
+
+ align:start position:0%
+occurred and the sequence was well back
+ 
+
+ align:start position:0%
+occurred and the sequence was well back
+in in
+
+ align:start position:0%
+in in
+ 
+
+ align:start position:0%
+in in
+1993 the conclusion was that the um
+
+ align:start position:0%
+1993 the conclusion was that the um
+ 
+
+ align:start position:0%
+1993 the conclusion was that the um
+these cracks were axial remember the
+
+ align:start position:0%
+these cracks were axial remember the
+ 
+
+ align:start position:0%
+these cracks were axial remember the
+axial
+
+ align:start position:0%
+axial
+ 
+
+ align:start position:0%
+axial
+discussion that they would result in
+
+ align:start position:0%
+discussion that they would result in
+ 
+
+ align:start position:0%
+discussion that they would result in
+detectable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leakage detectable leakage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and um you could be seen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+visually So based on their
+
+ align:start position:0%
+visually So based on their
+ 
+
+ align:start position:0%
+visually So based on their
+analysis and this was their basis that
+
+ align:start position:0%
+analysis and this was their basis that
+ 
+
+ align:start position:0%
+analysis and this was their basis that
+said oh it's okay it's not a problem for
+
+ align:start position:0%
+said oh it's okay it's not a problem for
+ 
+
+ align:start position:0%
+said oh it's okay it's not a problem for
+us CS if it's going to leak it's going
+
+ align:start position:0%
+us CS if it's going to leak it's going
+ 
+
+ align:start position:0%
+us CS if it's going to leak it's going
+to be axial it's not going to be
+
+ align:start position:0%
+to be axial it's not going to be
+ 
+
+ align:start position:0%
+to be axial it's not going to be
+circumferential which means the whole
+
+ align:start position:0%
+circumferential which means the whole
+ 
+
+ align:start position:0%
+circumferential which means the whole
+thing is apart and we can see it in
+
+ align:start position:0%
+thing is apart and we can see it in
+ 
+
+ align:start position:0%
+thing is apart and we can see it in
+terms of the detectable leakage because
+
+ align:start position:0%
+terms of the detectable leakage because
+ 
+
+ align:start position:0%
+terms of the detectable leakage because
+we don't and we can we can see it easily
+
+ align:start position:0%
+we don't and we can we can see it easily
+ 
+
+ align:start position:0%
+we don't and we can we can see it easily
+by simply taking a visual
+
+ align:start position:0%
+by simply taking a visual
+ 
+
+ align:start position:0%
+by simply taking a visual
+examination however when they started
+
+ align:start position:0%
+examination however when they started
+ 
+
+ align:start position:0%
+examination however when they started
+doing some of these inspections in
+
+ align:start position:0%
+doing some of these inspections in
+ 
+
+ align:start position:0%
+doing some of these inspections in
+1994 they found at Point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Beach
+
+ align:start position:0%
+Beach
+ 
+
+ align:start position:0%
+Beach
+that of the of the control rods the
+
+ align:start position:0%
+that of the of the control rods the
+ 
+
+ align:start position:0%
+that of the of the control rods the
+crdm they had lots of indications I
+
+ align:start position:0%
+crdm they had lots of indications I
+ 
+
+ align:start position:0%
+crdm they had lots of indications I
+think that I think that was 49
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indications and that sort of got got
+
+ align:start position:0%
+indications and that sort of got got
+ 
+
+ align:start position:0%
+indications and that sort of got got
+them going and they used what they
+
+ align:start position:0%
+them going and they used what they
+ 
+
+ align:start position:0%
+them going and they used what they
+called Ed current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+testing so it was not visual it was more
+
+ align:start position:0%
+testing so it was not visual it was more
+ 
+
+ align:start position:0%
+testing so it was not visual it was more
+scientific where they were looking for
+
+ align:start position:0%
+scientific where they were looking for
+ 
+
+ align:start position:0%
+scientific where they were looking for
+fors and in the process they also
+
+ align:start position:0%
+fors and in the process they also
+ 
+
+ align:start position:0%
+fors and in the process they also
+started looking at okone and you
+
+ align:start position:0%
+started looking at okone and you
+ 
+
+ align:start position:0%
+started looking at okone and you
+remember the okone okone unit one I
+
+ align:start position:0%
+remember the okone okone unit one I
+ 
+
+ align:start position:0%
+remember the okone okone unit one I
+think it was was it Aon
+
+ align:start position:0%
+think it was was it Aon
+ 
+
+ align:start position:0%
+think it was was it Aon
+one Aon one in 1994
+
+ align:start position:0%
+one Aon one in 1994
+ 
+
+ align:start position:0%
+one Aon one in 1994
+they also found 20
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indications and the sequence goes on and
+
+ align:start position:0%
+indications and the sequence goes on and
+ 
+
+ align:start position:0%
+indications and the sequence goes on and
+on and on until the NRC finally decided
+
+ align:start position:0%
+on and on until the NRC finally decided
+ 
+
+ align:start position:0%
+on and on until the NRC finally decided
+with a lot of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these findings that this stuff was fail
+
+ align:start position:0%
+these findings that this stuff was fail
+ 
+
+ align:start position:0%
+these findings that this stuff was fail
+and they give you they gave you generic
+
+ align:start position:0%
+and they give you they gave you generic
+ 
+
+ align:start position:0%
+and they give you they gave you generic
+letter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9701 which attempted to do a
+
+ align:start position:0%
+9701 which attempted to do a
+ 
+
+ align:start position:0%
+9701 which attempted to do a
+probabilistic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis of the
+
+ align:start position:0%
+analysis of the
+ 
+
+ align:start position:0%
+analysis of the
+likelihood and of these cracks occurring
+
+ align:start position:0%
+likelihood and of these cracks occurring
+ 
+
+ align:start position:0%
+likelihood and of these cracks occurring
+and potential damage in terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+growth what what what do you sense
+
+ align:start position:0%
+growth what what what do you sense
+ 
+
+ align:start position:0%
+growth what what what do you sense
+that's going on here growth what do you
+
+ align:start position:0%
+that's going on here growth what do you
+ 
+
+ align:start position:0%
+that's going on here growth what do you
+sense that's going on the NRC is trying
+
+ align:start position:0%
+sense that's going on the NRC is trying
+ 
+
+ align:start position:0%
+sense that's going on the NRC is trying
+to understand this
+
+ align:start position:0%
+to understand this
+ 
+
+ align:start position:0%
+to understand this
+problem they know it
+
+ align:start position:0%
+problem they know it
+ 
+
+ align:start position:0%
+problem they know it
+exists they're not prepared to shut down
+
+ align:start position:0%
+exists they're not prepared to shut down
+ 
+
+ align:start position:0%
+exists they're not prepared to shut down
+every plant to do visual inspections
+
+ align:start position:0%
+every plant to do visual inspections
+ 
+
+ align:start position:0%
+every plant to do visual inspections
+but they're saying to to the utilities
+
+ align:start position:0%
+but they're saying to to the utilities
+ 
+
+ align:start position:0%
+but they're saying to to the utilities
+you must give us a better case to
+
+ align:start position:0%
+you must give us a better case to
+ 
+
+ align:start position:0%
+you must give us a better case to
+justify why you should be operating and
+
+ align:start position:0%
+justify why you should be operating and
+ 
+
+ align:start position:0%
+justify why you should be operating and
+in order to do that we need to
+
+ align:start position:0%
+in order to do that we need to
+ 
+
+ align:start position:0%
+in order to do that we need to
+understand why these things are failing
+
+ align:start position:0%
+understand why these things are failing
+ 
+
+ align:start position:0%
+understand why these things are failing
+what is the history of this of this uh
+
+ align:start position:0%
+what is the history of this of this uh
+ 
+
+ align:start position:0%
+what is the history of this of this uh
+fabrication how was this stuff stress
+
+ align:start position:0%
+fabrication how was this stuff stress
+ 
+
+ align:start position:0%
+fabrication how was this stuff stress
+relieved was it
+
+ align:start position:0%
+relieved was it
+ 
+
+ align:start position:0%
+relieved was it
+um you know when they fabricated this
+
+ align:start position:0%
+um you know when they fabricated this
+ 
+
+ align:start position:0%
+um you know when they fabricated this
+particular nozzle this particular piece
+
+ align:start position:0%
+particular nozzle this particular piece
+ 
+
+ align:start position:0%
+particular nozzle this particular piece
+was it highly stressed when they
+
+ align:start position:0%
+was it highly stressed when they
+ 
+
+ align:start position:0%
+was it highly stressed when they
+assembled it and based on that
+
+ align:start position:0%
+assembled it and based on that
+ 
+
+ align:start position:0%
+assembled it and based on that
+information they were able to say the
+
+ align:start position:0%
+information they were able to say the
+ 
+
+ align:start position:0%
+information they were able to say the
+utility able to say we don't think these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+susceptible
+
+ align:start position:0%
+susceptible
+ 
+
+ align:start position:0%
+susceptible
+to to
+
+ align:start position:0%
+to to
+ 
+
+ align:start position:0%
+to to
+cracks or there was a function of
+
+ align:start position:0%
+cracks or there was a function of
+ 
+
+ align:start position:0%
+cracks or there was a function of
+time that people were able to say well
+
+ align:start position:0%
+time that people were able to say well
+ 
+
+ align:start position:0%
+time that people were able to say well
+we're not we don't expect to see this
+
+ align:start position:0%
+we're not we don't expect to see this
+ 
+
+ align:start position:0%
+we're not we don't expect to see this
+for another 5 years based on the
+
+ align:start position:0%
+for another 5 years based on the
+ 
+
+ align:start position:0%
+for another 5 years based on the
+environmental condition that that these
+
+ align:start position:0%
+environmental condition that that these
+ 
+
+ align:start position:0%
+environmental condition that that these
+um that these uh Wells had to
+
+ align:start position:0%
+um that these uh Wells had to
+ 
+
+ align:start position:0%
+um that these uh Wells had to
+experience but the evidence was fairly
+
+ align:start position:0%
+experience but the evidence was fairly
+ 
+
+ align:start position:0%
+experience but the evidence was fairly
+well uh mounting was mounting quite a
+
+ align:start position:0%
+well uh mounting was mounting quite a
+ 
+
+ align:start position:0%
+well uh mounting was mounting quite a
+bit but said there's a real problem and
+
+ align:start position:0%
+bit but said there's a real problem and
+ 
+
+ align:start position:0%
+bit but said there's a real problem and
+as you remember in France what they said
+
+ align:start position:0%
+as you remember in France what they said
+ 
+
+ align:start position:0%
+as you remember in France what they said
+was this is way too expensive to do all
+
+ align:start position:0%
+was this is way too expensive to do all
+ 
+
+ align:start position:0%
+was this is way too expensive to do all
+these visuals we're going to replace all
+
+ align:start position:0%
+these visuals we're going to replace all
+ 
+
+ align:start position:0%
+these visuals we're going to replace all
+the heads and stop the
+
+ align:start position:0%
+the heads and stop the
+ 
+
+ align:start position:0%
+the heads and stop the
+problem that stopped this problem but it
+
+ align:start position:0%
+problem that stopped this problem but it
+ 
+
+ align:start position:0%
+problem that stopped this problem but it
+didn't address necessarily any of these
+
+ align:start position:0%
+didn't address necessarily any of these
+ 
+
+ align:start position:0%
+didn't address necessarily any of these
+others so after they they they began to
+
+ align:start position:0%
+others so after they they they began to
+ 
+
+ align:start position:0%
+others so after they they they began to
+see more and more of these things out
+
+ align:start position:0%
+see more and more of these things out
+ 
+
+ align:start position:0%
+see more and more of these things out
+came bulletin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2001-01 and that basically said all
+
+ align:start position:0%
+2001-01 and that basically said all
+ 
+
+ align:start position:0%
+2001-01 and that basically said all
+right we're done with this looking we've
+
+ align:start position:0%
+right we're done with this looking we've
+ 
+
+ align:start position:0%
+right we're done with this looking we've
+seen evidence that of County one County
+
+ align:start position:0%
+seen evidence that of County one County
+ 
+
+ align:start position:0%
+seen evidence that of County one County
+3 Arkansas unit number one they actually
+
+ align:start position:0%
+3 Arkansas unit number one they actually
+ 
+
+ align:start position:0%
+3 Arkansas unit number one they actually
+saw Boron deposits at some of these
+
+ align:start position:0%
+saw Boron deposits at some of these
+ 
+
+ align:start position:0%
+saw Boron deposits at some of these
+plants remember that and said okay now
+
+ align:start position:0%
+plants remember that and said okay now
+ 
+
+ align:start position:0%
+plants remember that and said okay now
+we're going to have to do something very
+
+ align:start position:0%
+we're going to have to do something very
+ 
+
+ align:start position:0%
+we're going to have to do something very
+serious and in fact this is the first
+
+ align:start position:0%
+serious and in fact this is the first
+ 
+
+ align:start position:0%
+serious and in fact this is the first
+time that we've
+
+ align:start position:0%
+time that we've
+ 
+
+ align:start position:0%
+time that we've
+seen circumferential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ceds and this gave a lot of people a lot
+
+ align:start position:0%
+ceds and this gave a lot of people a lot
+ 
+
+ align:start position:0%
+ceds and this gave a lot of people a lot
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Paws because for the first time they
+
+ align:start position:0%
+Paws because for the first time they
+ 
+
+ align:start position:0%
+Paws because for the first time they
+were basically saying that these things
+
+ align:start position:0%
+were basically saying that these things
+ 
+
+ align:start position:0%
+were basically saying that these things
+could come apart quite more quite more
+
+ align:start position:0%
+could come apart quite more quite more
+ 
+
+ align:start position:0%
+could come apart quite more quite more
+dramatically than what we assume back in
+
+ align:start position:0%
+dramatically than what we assume back in
+ 
+
+ align:start position:0%
+dramatically than what we assume back in
+uh 1993
+
+ align:start position:0%
+uh 1993
+ 
+
+ align:start position:0%
+uh 1993
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+well after they did some more of these
+
+ align:start position:0%
+well after they did some more of these
+ 
+
+ align:start position:0%
+well after they did some more of these
+inspections up they came with bulletin
+
+ align:start position:0%
+inspections up they came with bulletin
+ 
+
+ align:start position:0%
+inspections up they came with bulletin
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+-01 and that kind of gave us the Davis
+
+ align:start position:0%
+-01 and that kind of gave us the Davis
+ 
+
+ align:start position:0%
+-01 and that kind of gave us the Davis
+Bessie
+
+ align:start position:0%
+Bessie
+ 
+
+ align:start position:0%
+Bessie
+finding and luckily as we saw there have
+
+ align:start position:0%
+finding and luckily as we saw there have
+ 
+
+ align:start position:0%
+finding and luckily as we saw there have
+been all kinds of um uh no no damage
+
+ align:start position:0%
+been all kinds of um uh no no damage
+ 
+
+ align:start position:0%
+been all kinds of um uh no no damage
+really was resulted from this but it
+
+ align:start position:0%
+really was resulted from this but it
+ 
+
+ align:start position:0%
+really was resulted from this but it
+gave the IND one of the closest near
+
+ align:start position:0%
+gave the IND one of the closest near
+ 
+
+ align:start position:0%
+gave the IND one of the closest near
+misses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ever the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so you know I don't know how much
+
+ align:start position:0%
+um so you know I don't know how much
+ 
+
+ align:start position:0%
+um so you know I don't know how much
+more to go into this but
+
+ align:start position:0%
+more to go into this but
+ 
+
+ align:start position:0%
+more to go into this but
+they they ultimately required a lot of
+
+ align:start position:0%
+they they ultimately required a lot of
+ 
+
+ align:start position:0%
+they they ultimately required a lot of
+lenses
+
+ align:start position:0%
+lenses
+ 
+
+ align:start position:0%
+lenses
+to um
+
+ align:start position:0%
+to um
+ 
+
+ align:start position:0%
+to um
+identify their highly susceptible
+
+ align:start position:0%
+identify their highly susceptible
+ 
+
+ align:start position:0%
+identify their highly susceptible
+plants and visual and nonvisual
+
+ align:start position:0%
+plants and visual and nonvisual
+ 
+
+ align:start position:0%
+plants and visual and nonvisual
+inspections were mandated to avoid any
+
+ align:start position:0%
+inspections were mandated to avoid any
+ 
+
+ align:start position:0%
+inspections were mandated to avoid any
+of this stuff in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+future and right now people are actually
+
+ align:start position:0%
+future and right now people are actually
+ 
+
+ align:start position:0%
+future and right now people are actually
+doing this the one thing I want to do
+
+ align:start position:0%
+doing this the one thing I want to do
+ 
+
+ align:start position:0%
+doing this the one thing I want to do
+talk about is what they now
+
+ align:start position:0%
+talk about is what they now
+ 
+
+ align:start position:0%
+talk about is what they now
+call I'll keep it on this board it's
+
+ align:start position:0%
+call I'll keep it on this board it's
+ 
+
+ align:start position:0%
+call I'll keep it on this board it's
+BMI bottom mounted
+
+ align:start position:0%
+BMI bottom mounted
+ 
+
+ align:start position:0%
+BMI bottom mounted
+instrumentation and this was found at
+
+ align:start position:0%
+instrumentation and this was found at
+ 
+
+ align:start position:0%
+instrumentation and this was found at
+the South Texas
+
+ align:start position:0%
+the South Texas
+ 
+
+ align:start position:0%
+the South Texas
+Project
+
+ align:start position:0%
+Project
+ 
+
+ align:start position:0%
+Project
+and it had this has to do with the same
+
+ align:start position:0%
+and it had this has to do with the same
+ 
+
+ align:start position:0%
+and it had this has to do with the same
+darn alloy 600 now just imagine a bottom
+
+ align:start position:0%
+darn alloy 600 now just imagine a bottom
+ 
+
+ align:start position:0%
+darn alloy 600 now just imagine a bottom
+mounted instrumentation to
+
+ align:start position:0%
+mounted instrumentation to
+ 
+
+ align:start position:0%
+mounted instrumentation to
+leak all
+
+ align:start position:0%
+leak all
+ 
+
+ align:start position:0%
+leak all
+right um it's it's a cold I mean it's a
+
+ align:start position:0%
+right um it's it's a cold I mean it's a
+ 
+
+ align:start position:0%
+right um it's it's a cold I mean it's a
+hot dark
+
+ align:start position:0%
+hot dark
+ 
+
+ align:start position:0%
+hot dark
+place and the core is right here you're
+
+ align:start position:0%
+place and the core is right here you're
+ 
+
+ align:start position:0%
+place and the core is right here you're
+not going in there during operation or
+
+ align:start position:0%
+not going in there during operation or
+ 
+
+ align:start position:0%
+not going in there during operation or
+even after it shut down of course I've
+
+ align:start position:0%
+even after it shut down of course I've
+ 
+
+ align:start position:0%
+even after it shut down of course I've
+be taken out to visually inspect and
+
+ align:start position:0%
+be taken out to visually inspect and
+ 
+
+ align:start position:0%
+be taken out to visually inspect and
+repair so this could be another major
+
+ align:start position:0%
+repair so this could be another major
+ 
+
+ align:start position:0%
+repair so this could be another major
+issues
+
+ align:start position:0%
+issues
+ 
+
+ align:start position:0%
+issues
+but so
+
+ align:start position:0%
+but so
+ 
+
+ align:start position:0%
+but so
+far they don't have they have not yet
+
+ align:start position:0%
+far they don't have they have not yet
+ 
+
+ align:start position:0%
+far they don't have they have not yet
+identified any other plants besides
+
+ align:start position:0%
+identified any other plants besides
+ 
+
+ align:start position:0%
+identified any other plants besides
+South Texas that has this
+
+ align:start position:0%
+South Texas that has this
+ 
+
+ align:start position:0%
+South Texas that has this
+problem that's not to say it's not
+
+ align:start position:0%
+problem that's not to say it's not
+ 
+
+ align:start position:0%
+problem that's not to say it's not
+occurring because there's no reason why
+
+ align:start position:0%
+occurring because there's no reason why
+ 
+
+ align:start position:0%
+occurring because there's no reason why
+it should only occur there and not
+
+ align:start position:0%
+it should only occur there and not
+ 
+
+ align:start position:0%
+it should only occur there and not
+anywhere
+
+ align:start position:0%
+anywhere
+ 
+
+ align:start position:0%
+anywhere
+else we already talked briefly about the
+
+ align:start position:0%
+else we already talked briefly about the
+ 
+
+ align:start position:0%
+else we already talked briefly about the
+pressurizer and some of these plants I I
+
+ align:start position:0%
+pressurizer and some of these plants I I
+ 
+
+ align:start position:0%
+pressurizer and some of these plants I I
+should I should say BMW
+
+ align:start position:0%
+should I should say BMW
+ 
+
+ align:start position:0%
+should I should say BMW
+everybody that manufactures these things
+
+ align:start position:0%
+everybody that manufactures these things
+ 
+
+ align:start position:0%
+everybody that manufactures these things
+do it in a different way and it really
+
+ align:start position:0%
+do it in a different way and it really
+ 
+
+ align:start position:0%
+do it in a different way and it really
+is related to the manufacturing how
+
+ align:start position:0%
+is related to the manufacturing how
+ 
+
+ align:start position:0%
+is related to the manufacturing how
+these components are made how the head
+
+ align:start position:0%
+these components are made how the head
+ 
+
+ align:start position:0%
+these components are made how the head
+is designed that affects stress
+
+ align:start position:0%
+is designed that affects stress
+ 
+
+ align:start position:0%
+is designed that affects stress
+levs so it is vendor unique and that's
+
+ align:start position:0%
+levs so it is vendor unique and that's
+ 
+
+ align:start position:0%
+levs so it is vendor unique and that's
+why some cases westing house isn't
+
+ align:start position:0%
+why some cases westing house isn't
+ 
+
+ align:start position:0%
+why some cases westing house isn't
+susceptible combustion engineering and
+
+ align:start position:0%
+susceptible combustion engineering and
+ 
+
+ align:start position:0%
+susceptible combustion engineering and
+BMW are in all of these different areas
+
+ align:start position:0%
+BMW are in all of these different areas
+ 
+
+ align:start position:0%
+BMW are in all of these different areas
+so you can't just blank it and say uh
+
+ align:start position:0%
+so you can't just blank it and say uh
+ 
+
+ align:start position:0%
+so you can't just blank it and say uh
+it's all PWS have this particular
+
+ align:start position:0%
+it's all PWS have this particular
+ 
+
+ align:start position:0%
+it's all PWS have this particular
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so I I think what you're going to be
+
+ align:start position:0%
+um so I I think what you're going to be
+ 
+
+ align:start position:0%
+um so I I think what you're going to be
+seeing in the in the near
+
+ align:start position:0%
+seeing in the in the near
+ 
+
+ align:start position:0%
+seeing in the in the near
+term uh is as more of these leaks
+
+ align:start position:0%
+term uh is as more of these leaks
+ 
+
+ align:start position:0%
+term uh is as more of these leaks
+develop this is a
+
+ align:start position:0%
+develop this is a
+ 
+
+ align:start position:0%
+develop this is a
+fix this can be fixed by weld overlays
+
+ align:start position:0%
+fix this can be fixed by weld overlays
+ 
+
+ align:start position:0%
+fix this can be fixed by weld overlays
+and relatively easy to inspect as can
+
+ align:start position:0%
+and relatively easy to inspect as can
+ 
+
+ align:start position:0%
+and relatively easy to inspect as can
+these be you can replace
+
+ align:start position:0%
+these be you can replace
+ 
+
+ align:start position:0%
+these be you can replace
+pressurizes this becomes a little
+
+ align:start position:0%
+pressurizes this becomes a little
+ 
+
+ align:start position:0%
+pressurizes this becomes a little
+trickier because that's there's a lot of
+
+ align:start position:0%
+trickier because that's there's a lot of
+ 
+
+ align:start position:0%
+trickier because that's there's a lot of
+incore instrumentation it's like a a
+
+ align:start position:0%
+incore instrumentation it's like a a
+ 
+
+ align:start position:0%
+incore instrumentation it's like a a
+forest down there heads can be
+
+ align:start position:0%
+forest down there heads can be
+ 
+
+ align:start position:0%
+forest down there heads can be
+replaced but the challenge and the
+
+ align:start position:0%
+replaced but the challenge and the
+ 
+
+ align:start position:0%
+replaced but the challenge and the
+additional cost and expense of doing
+
+ align:start position:0%
+additional cost and expense of doing
+ 
+
+ align:start position:0%
+additional cost and expense of doing
+these inspections is very very great any
+
+ align:start position:0%
+these inspections is very very great any
+ 
+
+ align:start position:0%
+these inspections is very very great any
+questions on on that one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no fire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protection um fire protection has an its
+
+ align:start position:0%
+protection um fire protection has an its
+ 
+
+ align:start position:0%
+protection um fire protection has an its
+own very interesting
+
+ align:start position:0%
+own very interesting
+ 
+
+ align:start position:0%
+own very interesting
+story this over Fire
+
+ align:start position:0%
+story this over Fire
+ 
+
+ align:start position:0%
+story this over Fire
+Protection
+
+ align:start position:0%
+Protection
+ 
+
+ align:start position:0%
+Protection
+um obviously the objective is to prevent
+
+ align:start position:0%
+um obviously the objective is to prevent
+ 
+
+ align:start position:0%
+um obviously the objective is to prevent
+fires now let's let's really go back to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+history how many of you remember the
+
+ align:start position:0%
+history how many of you remember the
+ 
+
+ align:start position:0%
+history how many of you remember the
+brown sper
+
+ align:start position:0%
+brown sper
+ 
+
+ align:start position:0%
+brown sper
+fire how many of you have heard of the
+
+ align:start position:0%
+fire how many of you have heard of the
+ 
+
+ align:start position:0%
+fire how many of you have heard of the
+brown Fair
+
+ align:start position:0%
+brown Fair
+ 
+
+ align:start position:0%
+brown Fair
+fire one okay we can start from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there what is anybody remember what
+
+ align:start position:0%
+there what is anybody remember what
+ 
+
+ align:start position:0%
+there what is anybody remember what
+plant they just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+restarted
+
+ align:start position:0%
+restarted
+ 
+
+ align:start position:0%
+restarted
+after about 10 15 years of being shut
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fair unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one now I don't know when this plant
+
+ align:start position:0%
+one now I don't know when this plant
+ 
+
+ align:start position:0%
+one now I don't know when this plant
+came actually started operation but they
+
+ align:start position:0%
+came actually started operation but they
+ 
+
+ align:start position:0%
+came actually started operation but they
+just spent I think was it actually $2
+
+ align:start position:0%
+just spent I think was it actually $2
+ 
+
+ align:start position:0%
+just spent I think was it actually $2
+billion that sounds right to bring the
+
+ align:start position:0%
+billion that sounds right to bring the
+ 
+
+ align:start position:0%
+billion that sounds right to bring the
+plant back into operating
+
+ align:start position:0%
+plant back into operating
+ 
+
+ align:start position:0%
+plant back into operating
+conditions but on March why is it always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+March
+
+ align:start position:0%
+March
+ 
+
+ align:start position:0%
+March
+1975 we had the Browns Fair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fire the plant was then in
+
+ align:start position:0%
+fire the plant was then in
+ 
+
+ align:start position:0%
+fire the plant was then in
+operation and they were trying to fix
+
+ align:start position:0%
+operation and they were trying to fix
+ 
+
+ align:start position:0%
+operation and they were trying to fix
+leaks
+
+ align:start position:0%
+leaks
+ 
+
+ align:start position:0%
+leaks
+in in the
+
+ align:start position:0%
+in in the
+ 
+
+ align:start position:0%
+in in the
+containment and between the containment
+
+ align:start position:0%
+containment and between the containment
+ 
+
+ align:start position:0%
+containment and between the containment
+and the outside and they were using a
+
+ align:start position:0%
+and the outside and they were using a
+ 
+
+ align:start position:0%
+and the outside and they were using a
+candle to see if any air was coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in well the candle worked they were able
+
+ align:start position:0%
+in well the candle worked they were able
+ 
+
+ align:start position:0%
+in well the candle worked they were able
+to detect air but the candle caught the
+
+ align:start position:0%
+to detect air but the candle caught the
+ 
+
+ align:start position:0%
+to detect air but the candle caught the
+insulation on
+
+ align:start position:0%
+insulation on
+ 
+
+ align:start position:0%
+insulation on
+fire which lasted
+
+ align:start position:0%
+fire which lasted
+ 
+
+ align:start position:0%
+fire which lasted
+for how many
+
+ align:start position:0%
+for how many
+ 
+
+ align:start position:0%
+for how many
+hours 7
+
+ align:start position:0%
+hours 7
+ 
+
+ align:start position:0%
+hours 7
+hours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+during that time as you might
+
+ align:start position:0%
+during that time as you might
+ 
+
+ align:start position:0%
+during that time as you might
+imagine and and they had this in the
+
+ align:start position:0%
+imagine and and they had this in the
+ 
+
+ align:start position:0%
+imagine and and they had this in the
+cable spreading
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+room now the cable spreading room we
+
+ align:start position:0%
+room now the cable spreading room we
+ 
+
+ align:start position:0%
+room now the cable spreading room we
+haven't really talked specifically about
+
+ align:start position:0%
+haven't really talked specifically about
+ 
+
+ align:start position:0%
+haven't really talked specifically about
+it but that's the place where all the
+
+ align:start position:0%
+it but that's the place where all the
+ 
+
+ align:start position:0%
+it but that's the place where all the
+power and instrumentation cables come to
+
+ align:start position:0%
+power and instrumentation cables come to
+ 
+
+ align:start position:0%
+power and instrumentation cables come to
+the plant control
+
+ align:start position:0%
+the plant control
+ 
+
+ align:start position:0%
+the plant control
+cables and they ended up
+
+ align:start position:0%
+cables and they ended up
+ 
+
+ align:start position:0%
+cables and they ended up
+burning 1,600 cables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about 628 of them were important to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+safy you can imagine what was going on
+
+ align:start position:0%
+safy you can imagine what was going on
+ 
+
+ align:start position:0%
+safy you can imagine what was going on
+in their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minds they essentially disabled many of
+
+ align:start position:0%
+minds they essentially disabled many of
+ 
+
+ align:start position:0%
+minds they essentially disabled many of
+the safety systems and they had to jury
+
+ align:start position:0%
+the safety systems and they had to jury
+ 
+
+ align:start position:0%
+the safety systems and they had to jury
+rig and as I remember using the cooling
+
+ align:start position:0%
+rig and as I remember using the cooling
+ 
+
+ align:start position:0%
+rig and as I remember using the cooling
+from the control rod Drive systems to
+
+ align:start position:0%
+from the control rod Drive systems to
+ 
+
+ align:start position:0%
+from the control rod Drive systems to
+cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's how we got Fire Protection in the
+
+ align:start position:0%
+that's how we got Fire Protection in the
+ 
+
+ align:start position:0%
+that's how we got Fire Protection in the
+US
+
+ align:start position:0%
+US
+ 
+
+ align:start position:0%
+US
+industry and as a result of that we have
+
+ align:start position:0%
+industry and as a result of that we have
+ 
+
+ align:start position:0%
+industry and as a result of that we have
+this some people call
+
+ align:start position:0%
+this some people call
+ 
+
+ align:start position:0%
+this some people call
+Infamous other people call Famous
+
+ align:start position:0%
+Infamous other people call Famous
+ 
+
+ align:start position:0%
+Infamous other people call Famous
+appendix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are since Brown's Ferry there has been
+
+ align:start position:0%
+are since Brown's Ferry there has been
+ 
+
+ align:start position:0%
+are since Brown's Ferry there has been
+another fire in the US industry
+
+ align:start position:0%
+another fire in the US industry
+ 
+
+ align:start position:0%
+another fire in the US industry
+affecting safe operation fires and turb
+
+ align:start position:0%
+affecting safe operation fires and turb
+ 
+
+ align:start position:0%
+affecting safe operation fires and turb
+and stuff like that nothing like like
+
+ align:start position:0%
+and stuff like that nothing like like
+ 
+
+ align:start position:0%
+and stuff like that nothing like like
+this so what do they
+
+ align:start position:0%
+this so what do they
+ 
+
+ align:start position:0%
+this so what do they
+require they required again these are
+
+ align:start position:0%
+require they required again these are
+ 
+
+ align:start position:0%
+require they required again these are
+for plants that have already been
+
+ align:start position:0%
+for plants that have already been
+ 
+
+ align:start position:0%
+for plants that have already been
+built and operated to the extent you
+
+ align:start position:0%
+built and operated to the extent you
+ 
+
+ align:start position:0%
+built and operated to the extent you
+could some people separated train a from
+
+ align:start position:0%
+could some people separated train a from
+ 
+
+ align:start position:0%
+could some people separated train a from
+train B Now you kind of know what train
+
+ align:start position:0%
+train B Now you kind of know what train
+ 
+
+ align:start position:0%
+train B Now you kind of know what train
+a and train b means and if you can't
+
+ align:start position:0%
+a and train b means and if you can't
+ 
+
+ align:start position:0%
+a and train b means and if you can't
+separate it because all these things
+
+ align:start position:0%
+separate it because all these things
+ 
+
+ align:start position:0%
+separate it because all these things
+come into the cable spreading room
+
+ align:start position:0%
+come into the cable spreading room
+ 
+
+ align:start position:0%
+come into the cable spreading room
+ultimately wires you have to have
+
+ align:start position:0%
+ultimately wires you have to have
+ 
+
+ align:start position:0%
+ultimately wires you have to have
+insulation specific ific insallation
+
+ align:start position:0%
+insulation specific ific insallation
+ 
+
+ align:start position:0%
+insulation specific ific insallation
+designed to keep to allow for a certain
+
+ align:start position:0%
+designed to keep to allow for a certain
+ 
+
+ align:start position:0%
+designed to keep to allow for a certain
+time before the fire can affect the
+
+ align:start position:0%
+time before the fire can affect the
+ 
+
+ align:start position:0%
+time before the fire can affect the
+wiring uh two 2hour wraps 6 hour wraps
+
+ align:start position:0%
+wiring uh two 2hour wraps 6 hour wraps
+ 
+
+ align:start position:0%
+wiring uh two 2hour wraps 6 hour wraps
+fire doors fire watches and obviously a
+
+ align:start position:0%
+fire doors fire watches and obviously a
+ 
+
+ align:start position:0%
+fire doors fire watches and obviously a
+lot
+
+ align:start position:0%
+lot
+ 
+
+ align:start position:0%
+lot
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+detection and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppression now with electrical fires
+
+ align:start position:0%
+suppression now with electrical fires
+ 
+
+ align:start position:0%
+suppression now with electrical fires
+you're probably not crazy about throwing
+
+ align:start position:0%
+you're probably not crazy about throwing
+ 
+
+ align:start position:0%
+you're probably not crazy about throwing
+water off them so they had Halon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems
+
+ align:start position:0%
+systems
+ 
+
+ align:start position:0%
+systems
+Halon and now they use some other type
+
+ align:start position:0%
+Halon and now they use some other type
+ 
+
+ align:start position:0%
+Halon and now they use some other type
+of material that's more environmentally
+
+ align:start position:0%
+of material that's more environmentally
+ 
+
+ align:start position:0%
+of material that's more environmentally
+friendly but this when this thing goes
+
+ align:start position:0%
+friendly but this when this thing goes
+ 
+
+ align:start position:0%
+friendly but this when this thing goes
+off you don't want to be in that room
+
+ align:start position:0%
+off you don't want to be in that room
+ 
+
+ align:start position:0%
+off you don't want to be in that room
+because you can't breathe it you
+
+ align:start position:0%
+because you can't breathe it you
+ 
+
+ align:start position:0%
+because you can't breathe it you
+got um some rooms don't have any
+
+ align:start position:0%
+got um some rooms don't have any
+ 
+
+ align:start position:0%
+got um some rooms don't have any
+equipment and they hand hand um hand
+
+ align:start position:0%
+equipment and they hand hand um hand
+ 
+
+ align:start position:0%
+equipment and they hand hand um hand
+fighting in some
+
+ align:start position:0%
+fighting in some
+ 
+
+ align:start position:0%
+fighting in some
+places but you do and end up doing
+
+ align:start position:0%
+places but you do and end up doing
+ 
+
+ align:start position:0%
+places but you do and end up doing
+as as the appendix art um approach
+
+ align:start position:0%
+as as the appendix art um approach
+ 
+
+ align:start position:0%
+as as the appendix art um approach
+changed they started using fire
+
+ align:start position:0%
+changed they started using fire
+ 
+
+ align:start position:0%
+changed they started using fire
+PR
+
+ align:start position:0%
+PR
+ 
+
+ align:start position:0%
+PR
+identifying how what the likelihood of a
+
+ align:start position:0%
+identifying how what the likelihood of a
+ 
+
+ align:start position:0%
+identifying how what the likelihood of a
+fire is and what the consequences of
+
+ align:start position:0%
+fire is and what the consequences of
+ 
+
+ align:start position:0%
+fire is and what the consequences of
+that fire may be the consequences are
+
+ align:start position:0%
+that fire may be the consequences are
+ 
+
+ align:start position:0%
+that fire may be the consequences are
+important so you're looking at a fire
+
+ align:start position:0%
+important so you're looking at a fire
+ 
+
+ align:start position:0%
+important so you're looking at a fire
+hazards
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis which
+
+ align:start position:0%
+analysis which
+ 
+
+ align:start position:0%
+analysis which
+includes likelihood and consequences of
+
+ align:start position:0%
+includes likelihood and consequences of
+ 
+
+ align:start position:0%
+includes likelihood and consequences of
+the fire on
+
+ align:start position:0%
+the fire on
+ 
+
+ align:start position:0%
+the fire on
+safety and obviously you have fire
+
+ align:start position:0%
+safety and obviously you have fire
+ 
+
+ align:start position:0%
+safety and obviously you have fire
+loading
+
+ align:start position:0%
+loading
+ 
+
+ align:start position:0%
+loading
+issues especially during outages I'm
+
+ align:start position:0%
+issues especially during outages I'm
+ 
+
+ align:start position:0%
+issues especially during outages I'm
+sure you're all familiar with these
+
+ align:start position:0%
+sure you're all familiar with these
+ 
+
+ align:start position:0%
+sure you're all familiar with these
+major fires that occur at churches
+
+ align:start position:0%
+major fires that occur at churches
+ 
+
+ align:start position:0%
+major fires that occur at churches
+people are doing repairs on the church
+
+ align:start position:0%
+people are doing repairs on the church
+ 
+
+ align:start position:0%
+people are doing repairs on the church
+they burn the whole church down well
+
+ align:start position:0%
+they burn the whole church down well
+ 
+
+ align:start position:0%
+they burn the whole church down well
+during outages this becomes very
+
+ align:start position:0%
+during outages this becomes very
+ 
+
+ align:start position:0%
+during outages this becomes very
+sensitive because you're this at this at
+
+ align:start position:0%
+sensitive because you're this at this at
+ 
+
+ align:start position:0%
+sensitive because you're this at this at
+this point you're in fact working
+
+ align:start position:0%
+this point you're in fact working
+ 
+
+ align:start position:0%
+this point you're in fact working
+potentially with uh welding equipment
+
+ align:start position:0%
+potentially with uh welding equipment
+ 
+
+ align:start position:0%
+potentially with uh welding equipment
+and stuff like that very very serious
+
+ align:start position:0%
+and stuff like that very very serious
+ 
+
+ align:start position:0%
+and stuff like that very very serious
+concern and people have done a lot to
+
+ align:start position:0%
+concern and people have done a lot to
+ 
+
+ align:start position:0%
+concern and people have done a lot to
+try to control fire loadings in these
+
+ align:start position:0%
+try to control fire loadings in these
+ 
+
+ align:start position:0%
+try to control fire loadings in these
+areas but to this to this day it's not a
+
+ align:start position:0%
+areas but to this to this day it's not a
+ 
+
+ align:start position:0%
+areas but to this to this day it's not a
+settled
+
+ align:start position:0%
+settled
+ 
+
+ align:start position:0%
+settled
+case um so they've replaced some of this
+
+ align:start position:0%
+case um so they've replaced some of this
+ 
+
+ align:start position:0%
+case um so they've replaced some of this
+deterministic analysis with a
+
+ align:start position:0%
+deterministic analysis with a
+ 
+
+ align:start position:0%
+deterministic analysis with a
+probabilistic analysis using the tool of
+
+ align:start position:0%
+probabilistic analysis using the tool of
+ 
+
+ align:start position:0%
+probabilistic analysis using the tool of
+fire hazards analysis identifying risk
+
+ align:start position:0%
+fire hazards analysis identifying risk
+ 
+
+ align:start position:0%
+fire hazards analysis identifying risk
+significant systems and then apply your
+
+ align:start position:0%
+significant systems and then apply your
+ 
+
+ align:start position:0%
+significant systems and then apply your
+uh mitigation or prevention system
+
+ align:start position:0%
+uh mitigation or prevention system
+ 
+
+ align:start position:0%
+uh mitigation or prevention system
+accordingly in the process the NRC is
+
+ align:start position:0%
+accordingly in the process the NRC is
+ 
+
+ align:start position:0%
+accordingly in the process the NRC is
+done some tests with some of this
+
+ align:start position:0%
+done some tests with some of this
+ 
+
+ align:start position:0%
+done some tests with some of this
+insulation it was supposed to be fire
+
+ align:start position:0%
+insulation it was supposed to be fire
+ 
+
+ align:start position:0%
+insulation it was supposed to be fire
+ra and I don't know if you were here we
+
+ align:start position:0%
+ra and I don't know if you were here we
+ 
+
+ align:start position:0%
+ra and I don't know if you were here we
+had one of the fellows from the NRC come
+
+ align:start position:0%
+had one of the fellows from the NRC come
+ 
+
+ align:start position:0%
+had one of the fellows from the NRC come
+by and a member asked about this hch
+
+ align:start position:0%
+by and a member asked about this hch
+ 
+
+ align:start position:0%
+by and a member asked about this hch
+insulation which was used routinely in
+
+ align:start position:0%
+insulation which was used routinely in
+ 
+
+ align:start position:0%
+insulation which was used routinely in
+many of these plants and when the NRC
+
+ align:start position:0%
+many of these plants and when the NRC
+ 
+
+ align:start position:0%
+many of these plants and when the NRC
+tested it they found that it didn't do
+
+ align:start position:0%
+tested it they found that it didn't do
+ 
+
+ align:start position:0%
+tested it they found that it didn't do
+its 2hour job it melted the covering of
+
+ align:start position:0%
+its 2hour job it melted the covering of
+ 
+
+ align:start position:0%
+its 2hour job it melted the covering of
+the insulation mounted allowing exposure
+
+ align:start position:0%
+the insulation mounted allowing exposure
+ 
+
+ align:start position:0%
+the insulation mounted allowing exposure
+to the actual cables which then would
+
+ align:start position:0%
+to the actual cables which then would
+ 
+
+ align:start position:0%
+to the actual cables which then would
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+burned um the NRC has has now dealing
+
+ align:start position:0%
+burned um the NRC has has now dealing
+ 
+
+ align:start position:0%
+burned um the NRC has has now dealing
+with this because this is again in many
+
+ align:start position:0%
+with this because this is again in many
+ 
+
+ align:start position:0%
+with this because this is again in many
+of the plants and I think the most
+
+ align:start position:0%
+of the plants and I think the most
+ 
+
+ align:start position:0%
+of the plants and I think the most
+recent
+
+ align:start position:0%
+recent
+ 
+
+ align:start position:0%
+recent
+determination is relative to this H mix
+
+ align:start position:0%
+determination is relative to this H mix
+ 
+
+ align:start position:0%
+determination is relative to this H mix
+stuff is that they and they issued
+
+ align:start position:0%
+stuff is that they and they issued
+ 
+
+ align:start position:0%
+stuff is that they and they issued
+another generic letter so you can see
+
+ align:start position:0%
+another generic letter so you can see
+ 
+
+ align:start position:0%
+another generic letter so you can see
+how recent this is generic letter 2006
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D3 for the lenses to evaluate this and
+
+ align:start position:0%
+D3 for the lenses to evaluate this and
+ 
+
+ align:start position:0%
+D3 for the lenses to evaluate this and
+take compensatory action should should
+
+ align:start position:0%
+take compensatory action should should
+ 
+
+ align:start position:0%
+take compensatory action should should
+they find a lot of this in key areas
+
+ align:start position:0%
+they find a lot of this in key areas
+ 
+
+ align:start position:0%
+they find a lot of this in key areas
+based on the fire hasard analysis and
+
+ align:start position:0%
+based on the fire hasard analysis and
+ 
+
+ align:start position:0%
+based on the fire hasard analysis and
+compensatory action could be putting
+
+ align:start position:0%
+compensatory action could be putting
+ 
+
+ align:start position:0%
+compensatory action could be putting
+somebody in the room where this
+
+ align:start position:0%
+somebody in the room where this
+ 
+
+ align:start position:0%
+somebody in the room where this
+insulation is and sitting there and
+
+ align:start position:0%
+insulation is and sitting there and
+ 
+
+ align:start position:0%
+insulation is and sitting there and
+watch it if there's a fire then you push
+
+ align:start position:0%
+watch it if there's a fire then you push
+ 
+
+ align:start position:0%
+watch it if there's a fire then you push
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+fire U that's a little more Draconian
+
+ align:start position:0%
+fire U that's a little more Draconian
+ 
+
+ align:start position:0%
+fire U that's a little more Draconian
+but that's a quick action but they
+
+ align:start position:0%
+but that's a quick action but they
+ 
+
+ align:start position:0%
+but that's a quick action but they
+conclude that in areas where there's
+
+ align:start position:0%
+conclude that in areas where there's
+ 
+
+ align:start position:0%
+conclude that in areas where there's
+both fire detection and automatic
+
+ align:start position:0%
+both fire detection and automatic
+ 
+
+ align:start position:0%
+both fire detection and automatic
+suppression even with you have this
+
+ align:start position:0%
+suppression even with you have this
+ 
+
+ align:start position:0%
+suppression even with you have this
+stuff the NRC remains I'm quoting
+
+ align:start position:0%
+stuff the NRC remains I'm quoting
+ 
+
+ align:start position:0%
+stuff the NRC remains I'm quoting
+assured that those plants overall fire
+
+ align:start position:0%
+assured that those plants overall fire
+ 
+
+ align:start position:0%
+assured that those plants overall fire
+protection scheme will ensure the safe
+
+ align:start position:0%
+protection scheme will ensure the safe
+ 
+
+ align:start position:0%
+protection scheme will ensure the safe
+shutdown of the reactor so if you have
+
+ align:start position:0%
+shutdown of the reactor so if you have
+ 
+
+ align:start position:0%
+shutdown of the reactor so if you have
+this stuff you would end up replacing it
+
+ align:start position:0%
+this stuff you would end up replacing it
+ 
+
+ align:start position:0%
+this stuff you would end up replacing it
+and you're probably if you don't have
+
+ align:start position:0%
+and you're probably if you don't have
+ 
+
+ align:start position:0%
+and you're probably if you don't have
+detection and suppression in that same
+
+ align:start position:0%
+detection and suppression in that same
+ 
+
+ align:start position:0%
+detection and suppression in that same
+mode you're going to have to do it
+
+ align:start position:0%
+mode you're going to have to do it
+ 
+
+ align:start position:0%
+mode you're going to have to do it
+so that's fire
+
+ align:start position:0%
+so that's fire
+ 
+
+ align:start position:0%
+so that's fire
+protection and the fire Pras is
+
+ align:start position:0%
+protection and the fire Pras is
+ 
+
+ align:start position:0%
+protection and the fire Pras is
+something still people are trying to
+
+ align:start position:0%
+something still people are trying to
+ 
+
+ align:start position:0%
+something still people are trying to
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+through they have other other types of
+
+ align:start position:0%
+through they have other other types of
+ 
+
+ align:start position:0%
+through they have other other types of
+fire uh protection equipment there's
+
+ align:start position:0%
+fire uh protection equipment there's
+ 
+
+ align:start position:0%
+fire uh protection equipment there's
+lots of thermal lag is another brand but
+
+ align:start position:0%
+lots of thermal lag is another brand but
+ 
+
+ align:start position:0%
+lots of thermal lag is another brand but
+that's sort of been resolved as best I
+
+ align:start position:0%
+that's sort of been resolved as best I
+ 
+
+ align:start position:0%
+that's sort of been resolved as best I
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+tell any questions on this
+
+ align:start position:0%
+tell any questions on this
+ 
+
+ align:start position:0%
+tell any questions on this
+one okay this is Ashley's
+
+ align:start position:0%
+one okay this is Ashley's
+ 
+
+ align:start position:0%
+one okay this is Ashley's
+fav Ashley did a study some years ago
+
+ align:start position:0%
+fav Ashley did a study some years ago
+ 
+
+ align:start position:0%
+fav Ashley did a study some years ago
+about an airplane crashing into a
+
+ align:start position:0%
+about an airplane crashing into a
+ 
+
+ align:start position:0%
+about an airplane crashing into a
+nuclear
+
+ align:start position:0%
+nuclear
+ 
+
+ align:start position:0%
+nuclear
+car and
+
+ align:start position:0%
+car and
+ 
+
+ align:start position:0%
+car and
+um as a result of 911 they have turned
+
+ align:start position:0%
+um as a result of 911 they have turned
+ 
+
+ align:start position:0%
+um as a result of 911 they have turned
+nuclear power
+
+ align:start position:0%
+nuclear power
+ 
+
+ align:start position:0%
+nuclear power
+plants into what does this remind you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of prison prison they' have turned
+
+ align:start position:0%
+of prison prison they' have turned
+ 
+
+ align:start position:0%
+of prison prison they' have turned
+nuclear power plants into prisons and
+
+ align:start position:0%
+nuclear power plants into prisons and
+ 
+
+ align:start position:0%
+nuclear power plants into prisons and
+this is probably normally you'd see
+
+ align:start position:0%
+this is probably normally you'd see
+ 
+
+ align:start position:0%
+this is probably normally you'd see
+razor wire here and a couple of
+
+ align:start position:0%
+razor wire here and a couple of
+ 
+
+ align:start position:0%
+razor wire here and a couple of
+fences and I think you see some razor
+
+ align:start position:0%
+fences and I think you see some razor
+ 
+
+ align:start position:0%
+fences and I think you see some razor
+wire here so there's at least an outer
+
+ align:start position:0%
+wire here so there's at least an outer
+ 
+
+ align:start position:0%
+wire here so there's at least an outer
+fence and inner fence separated by
+
+ align:start position:0%
+fence and inner fence separated by
+ 
+
+ align:start position:0%
+fence and inner fence separated by
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+detectors and uh electrified wire
+
+ align:start position:0%
+detectors and uh electrified wire
+ 
+
+ align:start position:0%
+detectors and uh electrified wire
+potentially and you have these pill
+
+ align:start position:0%
+potentially and you have these pill
+ 
+
+ align:start position:0%
+potentially and you have these pill
+boxes on the
+
+ align:start position:0%
+boxes on the
+ 
+
+ align:start position:0%
+boxes on the
+site now these pill boxes are
+
+ align:start position:0%
+site now these pill boxes are
+ 
+
+ align:start position:0%
+site now these pill boxes are
+positioned so that if anybody decides to
+
+ align:start position:0%
+positioned so that if anybody decides to
+ 
+
+ align:start position:0%
+positioned so that if anybody decides to
+come on the site with a gun and try to
+
+ align:start position:0%
+come on the site with a gun and try to
+ 
+
+ align:start position:0%
+come on the site with a gun and try to
+take over that facility this person
+
+ align:start position:0%
+take over that facility this person
+ 
+
+ align:start position:0%
+take over that facility this person
+or persons can kill that person anywhere
+
+ align:start position:0%
+or persons can kill that person anywhere
+ 
+
+ align:start position:0%
+or persons can kill that person anywhere
+on the property before they get
+
+ align:start position:0%
+on the property before they get
+ 
+
+ align:start position:0%
+on the property before they get
+endorsed so if you go to santrey the
+
+ align:start position:0%
+endorsed so if you go to santrey the
+ 
+
+ align:start position:0%
+endorsed so if you go to santrey the
+plant that I'm most familiar with in the
+
+ align:start position:0%
+plant that I'm most familiar with in the
+ 
+
+ align:start position:0%
+plant that I'm most familiar with in the
+states that where I observed this they
+
+ align:start position:0%
+states that where I observed this they
+ 
+
+ align:start position:0%
+states that where I observed this they
+have I don't know how many of these
+
+ align:start position:0%
+have I don't know how many of these
+ 
+
+ align:start position:0%
+have I don't know how many of these
+around but it's very clear it's lit up
+
+ align:start position:0%
+around but it's very clear it's lit up
+ 
+
+ align:start position:0%
+around but it's very clear it's lit up
+at night and you're not getting in this
+
+ align:start position:0%
+at night and you're not getting in this
+ 
+
+ align:start position:0%
+at night and you're not getting in this
+place and if if you think you're going
+
+ align:start position:0%
+place and if if you think you're going
+ 
+
+ align:start position:0%
+place and if if you think you're going
+to be carrying a gun in there you're
+
+ align:start position:0%
+to be carrying a gun in there you're
+ 
+
+ align:start position:0%
+to be carrying a gun in there you're
+going to die there's no there's no issue
+
+ align:start position:0%
+going to die there's no there's no issue
+ 
+
+ align:start position:0%
+going to die there's no there's no issue
+at Yankee our our security staff I was
+
+ align:start position:0%
+at Yankee our our security staff I was
+ 
+
+ align:start position:0%
+at Yankee our our security staff I was
+not comfortable with these guys having
+
+ align:start position:0%
+not comfortable with these guys having
+ 
+
+ align:start position:0%
+not comfortable with these guys having
+guns in the
+
+ align:start position:0%
+guns in the
+ 
+
+ align:start position:0%
+guns in the
+controller you never know when a worker
+
+ align:start position:0%
+controller you never know when a worker
+ 
+
+ align:start position:0%
+controller you never know when a worker
+got an issue even though you do all
+
+ align:start position:0%
+got an issue even though you do all
+ 
+
+ align:start position:0%
+got an issue even though you do all
+kinds of s profiling whatever a gun in
+
+ align:start position:0%
+kinds of s profiling whatever a gun in
+ 
+
+ align:start position:0%
+kinds of s profiling whatever a gun in
+the controling wasn't a good idea but
+
+ align:start position:0%
+the controling wasn't a good idea but
+ 
+
+ align:start position:0%
+the controling wasn't a good idea but
+the NC said you must have
+
+ align:start position:0%
+the NC said you must have
+ 
+
+ align:start position:0%
+the NC said you must have
+guns hand and you know it's it's it's
+
+ align:start position:0%
+guns hand and you know it's it's it's
+ 
+
+ align:start position:0%
+guns hand and you know it's it's it's
+really you look at some of these rifles
+
+ align:start position:0%
+really you look at some of these rifles
+ 
+
+ align:start position:0%
+really you look at some of these rifles
+they're well armed well so they had to
+
+ align:start position:0%
+they're well armed well so they had to
+ 
+
+ align:start position:0%
+they're well armed well so they had to
+upgrade the physical
+
+ align:start position:0%
+upgrade the physical
+ 
+
+ align:start position:0%
+upgrade the physical
+security it's not a welcoming place to
+
+ align:start position:0%
+security it's not a welcoming place to
+ 
+
+ align:start position:0%
+security it's not a welcoming place to
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+you have to show that your particular
+
+ align:start position:0%
+you have to show that your particular
+ 
+
+ align:start position:0%
+you have to show that your particular
+plant is capable of being you know
+
+ align:start position:0%
+plant is capable of being you know
+ 
+
+ align:start position:0%
+plant is capable of being you know
+withstand a aircraft impact and had we
+
+ align:start position:0%
+withstand a aircraft impact and had we
+ 
+
+ align:start position:0%
+withstand a aircraft impact and had we
+had more time we can show you some of
+
+ align:start position:0%
+had more time we can show you some of
+ 
+
+ align:start position:0%
+had more time we can show you some of
+the issues that we looked at with Ashley
+
+ align:start position:0%
+the issues that we looked at with Ashley
+ 
+
+ align:start position:0%
+the issues that we looked at with Ashley
+some years ago about it's not just about
+
+ align:start position:0%
+some years ago about it's not just about
+ 
+
+ align:start position:0%
+some years ago about it's not just about
+the containment it's about other things
+
+ align:start position:0%
+the containment it's about other things
+ 
+
+ align:start position:0%
+the containment it's about other things
+that could be
+
+ align:start position:0%
+that could be
+ 
+
+ align:start position:0%
+that could be
+damaged and then they have these the
+
+ align:start position:0%
+damaged and then they have these the
+ 
+
+ align:start position:0%
+damaged and then they have these the
+things called design bases threats which
+
+ align:start position:0%
+things called design bases threats which
+ 
+
+ align:start position:0%
+things called design bases threats which
+are imagine a certain type of intruder
+
+ align:start position:0%
+are imagine a certain type of intruder
+ 
+
+ align:start position:0%
+are imagine a certain type of intruder
+or intruder
+
+ align:start position:0%
+or intruder
+ 
+
+ align:start position:0%
+or intruder
+you have to be able to repel these
+
+ align:start position:0%
+you have to be able to repel these
+ 
+
+ align:start position:0%
+you have to be able to repel these
+people at least for a time until you get
+
+ align:start position:0%
+people at least for a time until you get
+ 
+
+ align:start position:0%
+people at least for a time until you get
+the Army Navy Marines airport whatever
+
+ align:start position:0%
+the Army Navy Marines airport whatever
+ 
+
+ align:start position:0%
+the Army Navy Marines airport whatever
+local police to
+
+ align:start position:0%
+local police to
+ 
+
+ align:start position:0%
+local police to
+come true and this design basis threat
+
+ align:start position:0%
+come true and this design basis threat
+ 
+
+ align:start position:0%
+come true and this design basis threat
+is continuing continuing to be evolv
+
+ align:start position:0%
+is continuing continuing to be evolv
+ 
+
+ align:start position:0%
+is continuing continuing to be evolv
+based on what the sophistication of the
+
+ align:start position:0%
+based on what the sophistication of the
+ 
+
+ align:start position:0%
+based on what the sophistication of the
+terrorist could be and they have not a
+
+ align:start position:0%
+terrorist could be and they have not a
+ 
+
+ align:start position:0%
+terrorist could be and they have not a
+lot of am of course but they do have
+
+ align:start position:0%
+lot of am of course but they do have
+ 
+
+ align:start position:0%
+lot of am of course but they do have
+people assaulting the plants and you do
+
+ align:start position:0%
+people assaulting the plants and you do
+ 
+
+ align:start position:0%
+people assaulting the plants and you do
+certain tests and drills every 3 to 5
+
+ align:start position:0%
+certain tests and drills every 3 to 5
+ 
+
+ align:start position:0%
+certain tests and drills every 3 to 5
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+uh the themee of this is not that we're
+
+ align:start position:0%
+uh the themee of this is not that we're
+ 
+
+ align:start position:0%
+uh the themee of this is not that we're
+going to be able to um it's it's not the
+
+ align:start position:0%
+going to be able to um it's it's not the
+ 
+
+ align:start position:0%
+going to be able to um it's it's not the
+utility's job to fend off the Intruder
+
+ align:start position:0%
+utility's job to fend off the Intruder
+ 
+
+ align:start position:0%
+utility's job to fend off the Intruder
+or or knock them out it's the it's the
+
+ align:start position:0%
+or or knock them out it's the it's the
+ 
+
+ align:start position:0%
+or or knock them out it's the it's the
+military's job and the police job to
+
+ align:start position:0%
+military's job and the police job to
+ 
+
+ align:start position:0%
+military's job and the police job to
+assist their job is only to hold off to
+
+ align:start position:0%
+assist their job is only to hold off to
+ 
+
+ align:start position:0%
+assist their job is only to hold off to
+avoid them getting into the critical
+
+ align:start position:0%
+avoid them getting into the critical
+ 
+
+ align:start position:0%
+avoid them getting into the critical
+areas of land and you know some people
+
+ align:start position:0%
+areas of land and you know some people
+ 
+
+ align:start position:0%
+areas of land and you know some people
+will say why don't we put missile
+
+ align:start position:0%
+will say why don't we put missile
+ 
+
+ align:start position:0%
+will say why don't we put missile
+batteries at some of these nuclear power
+
+ align:start position:0%
+batteries at some of these nuclear power
+ 
+
+ align:start position:0%
+batteries at some of these nuclear power
+to shoot down airplanes and the answer
+
+ align:start position:0%
+to shoot down airplanes and the answer
+ 
+
+ align:start position:0%
+to shoot down airplanes and the answer
+is that's not our job the job is that of
+
+ align:start position:0%
+is that's not our job the job is that of
+ 
+
+ align:start position:0%
+is that's not our job the job is that of
+the federal government to protect any
+
+ align:start position:0%
+the federal government to protect any
+ 
+
+ align:start position:0%
+the federal government to protect any
+installation
+
+ align:start position:0%
+installation
+ 
+
+ align:start position:0%
+installation
+incl so at this point this has been a
+
+ align:start position:0%
+incl so at this point this has been a
+ 
+
+ align:start position:0%
+incl so at this point this has been a
+hugely expensive operation the security
+
+ align:start position:0%
+hugely expensive operation the security
+ 
+
+ align:start position:0%
+hugely expensive operation the security
+staffs are larger than the operating
+
+ align:start position:0%
+staffs are larger than the operating
+ 
+
+ align:start position:0%
+staffs are larger than the operating
+staffs at these plants I'm talking They
+
+ align:start position:0%
+staffs at these plants I'm talking They
+ 
+
+ align:start position:0%
+staffs at these plants I'm talking They
+al also do 247
+
+ align:start position:0%
+al also do 247
+ 
+
+ align:start position:0%
+al also do 247
+365 so this is a huge new expense and
+
+ align:start position:0%
+365 so this is a huge new expense and
+ 
+
+ align:start position:0%
+365 so this is a huge new expense and
+these guys have to be TR and
+
+ align:start position:0%
+these guys have to be TR and
+ 
+
+ align:start position:0%
+these guys have to be TR and
+um wel train and you've seen some recent
+
+ align:start position:0%
+um wel train and you've seen some recent
+ 
+
+ align:start position:0%
+um wel train and you've seen some recent
+stories about guard sleeping on the job
+
+ align:start position:0%
+stories about guard sleeping on the job
+ 
+
+ align:start position:0%
+stories about guard sleeping on the job
+obviously that's not
+
+ align:start position:0%
+obviously that's not
+ 
+
+ align:start position:0%
+obviously that's not
+acceptable any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one groundwater
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contamination this is a surprising
+
+ align:start position:0%
+contamination this is a surprising
+ 
+
+ align:start position:0%
+contamination this is a surprising
+thing but it occurs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+typically I don't know if you remember
+
+ align:start position:0%
+typically I don't know if you remember
+ 
+
+ align:start position:0%
+typically I don't know if you remember
+but this is about five or six years ago
+
+ align:start position:0%
+but this is about five or six years ago
+ 
+
+ align:start position:0%
+but this is about five or six years ago
+Brook Haven National Lab had a I think
+
+ align:start position:0%
+Brook Haven National Lab had a I think
+ 
+
+ align:start position:0%
+Brook Haven National Lab had a I think
+it was in
+
+ align:start position:0%
+it was in
+ 
+
+ align:start position:0%
+it was in
+there um fueling water storage tank or
+
+ align:start position:0%
+there um fueling water storage tank or
+ 
+
+ align:start position:0%
+there um fueling water storage tank or
+some tank containing trated water leaked
+
+ align:start position:0%
+some tank containing trated water leaked
+ 
+
+ align:start position:0%
+some tank containing trated water leaked
+and Brook Haven is all on out in a nice
+
+ align:start position:0%
+and Brook Haven is all on out in a nice
+ 
+
+ align:start position:0%
+and Brook Haven is all on out in a nice
+area Mid Island other words Island 12
+
+ align:start position:0%
+area Mid Island other words Island 12
+ 
+
+ align:start position:0%
+area Mid Island other words Island 12
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+out in a in a nice residential area it's
+
+ align:start position:0%
+out in a in a nice residential area it's
+ 
+
+ align:start position:0%
+out in a in a nice residential area it's
+a nice research thatb they had a leap
+
+ align:start position:0%
+a nice research thatb they had a leap
+ 
+
+ align:start position:0%
+a nice research thatb they had a leap
+from one of their earlier operting rings
+
+ align:start position:0%
+from one of their earlier operting rings
+ 
+
+ align:start position:0%
+from one of their earlier operting rings
+and it was trigged very low
+
+ align:start position:0%
+and it was trigged very low
+ 
+
+ align:start position:0%
+and it was trigged very low
+level that you know did not exceed the
+
+ align:start position:0%
+level that you know did not exceed the
+ 
+
+ align:start position:0%
+level that you know did not exceed the
+drinking water standard but they had
+
+ align:start position:0%
+drinking water standard but they had
+ 
+
+ align:start position:0%
+drinking water standard but they had
+such a bruha they almost shut the laab
+
+ align:start position:0%
+such a bruha they almost shut the laab
+ 
+
+ align:start position:0%
+such a bruha they almost shut the laab
+down because of the public out Manny it
+
+ align:start position:0%
+down because of the public out Manny it
+ 
+
+ align:start position:0%
+down because of the public out Manny it
+be shut down and it changed the lab it
+
+ align:start position:0%
+be shut down and it changed the lab it
+ 
+
+ align:start position:0%
+be shut down and it changed the lab it
+used to be a nuclear energy lab story in
+
+ align:start position:0%
+used to be a nuclear energy lab story in
+ 
+
+ align:start position:0%
+used to be a nuclear energy lab story in
+part now it's pretty much a basic
+
+ align:start position:0%
+part now it's pretty much a basic
+ 
+
+ align:start position:0%
+part now it's pretty much a basic
+science level but they had a lot of
+
+ align:start position:0%
+science level but they had a lot of
+ 
+
+ align:start position:0%
+science level but they had a lot of
+reactors there they had high temperature
+
+ align:start position:0%
+reactors there they had high temperature
+ 
+
+ align:start position:0%
+reactors there they had high temperature
+uh fast flux
+
+ align:start position:0%
+uh fast flux
+ 
+
+ align:start position:0%
+uh fast flux
+reactor uh they also had some graphite
+
+ align:start position:0%
+reactor uh they also had some graphite
+ 
+
+ align:start position:0%
+reactor uh they also had some graphite
+reactors so they were one of early
+
+ align:start position:0%
+reactors so they were one of early
+ 
+
+ align:start position:0%
+reactors so they were one of early
+Pioneers because of this very low level
+
+ align:start position:0%
+Pioneers because of this very low level
+ 
+
+ align:start position:0%
+Pioneers because of this very low level
+of trium getting into the groundwater
+
+ align:start position:0%
+of trium getting into the groundwater
+ 
+
+ align:start position:0%
+of trium getting into the groundwater
+and migrating it shut it shut almost
+
+ align:start position:0%
+and migrating it shut it shut almost
+ 
+
+ align:start position:0%
+and migrating it shut it shut almost
+shut the re shut the laboratory
+
+ align:start position:0%
+shut the re shut the laboratory
+ 
+
+ align:start position:0%
+shut the re shut the laboratory
+down in the nuclear World we've had
+
+ align:start position:0%
+down in the nuclear World we've had
+ 
+
+ align:start position:0%
+down in the nuclear World we've had
+leaks at Indian Point Braidwood cage
+
+ align:start position:0%
+leaks at Indian Point Braidwood cage
+ 
+
+ align:start position:0%
+leaks at Indian Point Braidwood cage
+resin bar out in C and
+
+ align:start position:0%
+resin bar out in C and
+ 
+
+ align:start position:0%
+resin bar out in C and
+Cal again a lot of it coming from the
+
+ align:start position:0%
+Cal again a lot of it coming from the
+ 
+
+ align:start position:0%
+Cal again a lot of it coming from the
+spend fuel where you know trated water
+
+ align:start position:0%
+spend fuel where you know trated water
+ 
+
+ align:start position:0%
+spend fuel where you know trated water
+does does
+
+ align:start position:0%
+does does
+ 
+
+ align:start position:0%
+does does
+occur um and in some cases it came like
+
+ align:start position:0%
+occur um and in some cases it came like
+ 
+
+ align:start position:0%
+occur um and in some cases it came like
+in in Braidwood from um I think they had
+
+ align:start position:0%
+in in Braidwood from um I think they had
+ 
+
+ align:start position:0%
+in in Braidwood from um I think they had
+leakage in some of their vacuum valves
+
+ align:start position:0%
+leakage in some of their vacuum valves
+ 
+
+ align:start position:0%
+leakage in some of their vacuum valves
+on their on on the secondary side on the
+
+ align:start position:0%
+on their on on the secondary side on the
+ 
+
+ align:start position:0%
+on their on on the secondary side on the
+primary side of their
+
+ align:start position:0%
+primary side of their
+ 
+
+ align:start position:0%
+primary side of their
+plant uh and
+
+ align:start position:0%
+plant uh and
+ 
+
+ align:start position:0%
+plant uh and
+the the leakage was
+
+ align:start position:0%
+the the leakage was
+ 
+
+ align:start position:0%
+the the leakage was
+known not reported on time and when
+
+ align:start position:0%
+known not reported on time and when
+ 
+
+ align:start position:0%
+known not reported on time and when
+reported uh created a huge stir in the
+
+ align:start position:0%
+reported uh created a huge stir in the
+ 
+
+ align:start position:0%
+reported uh created a huge stir in the
+local
+
+ align:start position:0%
+local
+ 
+
+ align:start position:0%
+local
+population what they had to do at Brook
+
+ align:start position:0%
+population what they had to do at Brook
+ 
+
+ align:start position:0%
+population what they had to do at Brook
+Haven was drill monitoring
+
+ align:start position:0%
+Haven was drill monitoring
+ 
+
+ align:start position:0%
+Haven was drill monitoring
+Wells and suck up the
+
+ align:start position:0%
+Wells and suck up the
+ 
+
+ align:start position:0%
+Wells and suck up the
+water now trium you know you can't
+
+ align:start position:0%
+water now trium you know you can't
+ 
+
+ align:start position:0%
+water now trium you know you can't
+really do much with
+
+ align:start position:0%
+really do much with
+ 
+
+ align:start position:0%
+really do much with
+it what they did with that water I don't
+
+ align:start position:0%
+it what they did with that water I don't
+ 
+
+ align:start position:0%
+it what they did with that water I don't
+know but they were pumping the
+
+ align:start position:0%
+know but they were pumping the
+ 
+
+ align:start position:0%
+know but they were pumping the
+water uh
+
+ align:start position:0%
+water uh
+ 
+
+ align:start position:0%
+water uh
+and maybe storing it don't know they're
+
+ align:start position:0%
+and maybe storing it don't know they're
+ 
+
+ align:start position:0%
+and maybe storing it don't know they're
+apparently going to be doing the same at
+
+ align:start position:0%
+apparently going to be doing the same at
+ 
+
+ align:start position:0%
+apparently going to be doing the same at
+these Lees now this this rawood plant
+
+ align:start position:0%
+these Lees now this this rawood plant
+ 
+
+ align:start position:0%
+these Lees now this this rawood plant
+actually got a notice of
+
+ align:start position:0%
+actually got a notice of
+ 
+
+ align:start position:0%
+actually got a notice of
+violation this was issued in uh
+
+ align:start position:0%
+violation this was issued in uh
+ 
+
+ align:start position:0%
+violation this was issued in uh
+2006 and the violation basically cited
+
+ align:start position:0%
+2006 and the violation basically cited
+ 
+
+ align:start position:0%
+2006 and the violation basically cited
+them for under part 20 which is this
+
+ align:start position:0%
+them for under part 20 which is this
+ 
+
+ align:start position:0%
+them for under part 20 which is this
+radi electrical e part was they did not
+
+ align:start position:0%
+radi electrical e part was they did not
+ 
+
+ align:start position:0%
+radi electrical e part was they did not
+make the necessary surveys to identify
+
+ align:start position:0%
+make the necessary surveys to identify
+ 
+
+ align:start position:0%
+make the necessary surveys to identify
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+people uh
+
+ align:start position:0%
+people uh
+ 
+
+ align:start position:0%
+people uh
+um they were not assuring that the
+
+ align:start position:0%
+um they were not assuring that the
+ 
+
+ align:start position:0%
+um they were not assuring that the
+public got less
+
+ align:start position:0%
+public got less
+ 
+
+ align:start position:0%
+public got less
+than point one this number is REM
+
+ align:start position:0%
+than point one this number is REM
+ 
+
+ align:start position:0%
+than point one this number is REM
+perier had no way to assure even though
+
+ align:start position:0%
+perier had no way to assure even though
+ 
+
+ align:start position:0%
+perier had no way to assure even though
+I didn't get
+
+ align:start position:0%
+I didn't get
+ 
+
+ align:start position:0%
+I didn't get
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+um and there were failure their failure
+
+ align:start position:0%
+um and there were failure their failure
+ 
+
+ align:start position:0%
+um and there were failure their failure
+was largely to identify Le and deal with
+
+ align:start position:0%
+was largely to identify Le and deal with
+ 
+
+ align:start position:0%
+was largely to identify Le and deal with
+they just kind of ignored it they did
+
+ align:start position:0%
+they just kind of ignored it they did
+ 
+
+ align:start position:0%
+they just kind of ignored it they did
+release million gallons of
+
+ align:start position:0%
+release million gallons of
+ 
+
+ align:start position:0%
+release million gallons of
+water a lot a lot of water over
+
+ align:start position:0%
+water a lot a lot of water over
+ 
+
+ align:start position:0%
+water a lot a lot of water over
+time um and this went back from November
+
+ align:start position:0%
+time um and this went back from November
+ 
+
+ align:start position:0%
+time um and this went back from November
+1996 to March
+
+ align:start position:0%
+1996 to March
+ 
+
+ align:start position:0%
+1996 to March
+2006 so it's not that
+
+ align:start position:0%
+2006 so it's not that
+ 
+
+ align:start position:0%
+2006 so it's not that
+they didn't know was happen it's just
+
+ align:start position:0%
+they didn't know was happen it's just
+ 
+
+ align:start position:0%
+they didn't know was happen it's just
+that they failed to properly report it
+
+ align:start position:0%
+that they failed to properly report it
+ 
+
+ align:start position:0%
+that they failed to properly report it
+and failed to deal with it
+
+ align:start position:0%
+and failed to deal with it
+ 
+
+ align:start position:0%
+and failed to deal with it
+um and they had a numerous leaks over
+
+ align:start position:0%
+um and they had a numerous leaks over
+ 
+
+ align:start position:0%
+um and they had a numerous leaks over
+over that time period the largest of
+
+ align:start position:0%
+over that time period the largest of
+ 
+
+ align:start position:0%
+over that time period the largest of
+which was 3 3 million gallons to ground
+
+ align:start position:0%
+which was 3 3 million gallons to ground
+ 
+
+ align:start position:0%
+which was 3 3 million gallons to ground
+path ground path the industry of course
+
+ align:start position:0%
+path ground path the industry of course
+ 
+
+ align:start position:0%
+path ground path the industry of course
+responded to do this this the other
+
+ align:start position:0%
+responded to do this this the other
+ 
+
+ align:start position:0%
+responded to do this this the other
+things but most nuclear plants have
+
+ align:start position:0%
+things but most nuclear plants have
+ 
+
+ align:start position:0%
+things but most nuclear plants have
+monitoring R but not where apparently
+
+ align:start position:0%
+monitoring R but not where apparently
+ 
+
+ align:start position:0%
+monitoring R but not where apparently
+this particular Le occur and remember
+
+ align:start position:0%
+this particular Le occur and remember
+ 
+
+ align:start position:0%
+this particular Le occur and remember
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um the reactor oversight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process they got a white
+
+ align:start position:0%
+process they got a white
+ 
+
+ align:start position:0%
+process they got a white
+finding and that white finding triggered
+
+ align:start position:0%
+finding and that white finding triggered
+ 
+
+ align:start position:0%
+finding and that white finding triggered
+this investigation and they then also
+
+ align:start position:0%
+this investigation and they then also
+ 
+
+ align:start position:0%
+this investigation and they then also
+triggered this parent violation I don't
+
+ align:start position:0%
+triggered this parent violation I don't
+ 
+
+ align:start position:0%
+triggered this parent violation I don't
+know what the the fine
+
+ align:start position:0%
+know what the the fine
+ 
+
+ align:start position:0%
+know what the the fine
+was but my guess is they probably got
+
+ align:start position:0%
+was but my guess is they probably got
+ 
+
+ align:start position:0%
+was but my guess is they probably got
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay so here's what they what they
+
+ align:start position:0%
+so okay so here's what they what they
+ 
+
+ align:start position:0%
+so okay so here's what they what they
+had to do public got really
+
+ align:start position:0%
+had to do public got really
+ 
+
+ align:start position:0%
+had to do public got really
+outraged usual demands that trying to be
+
+ align:start position:0%
+outraged usual demands that trying to be
+ 
+
+ align:start position:0%
+outraged usual demands that trying to be
+shut down
+
+ align:start position:0%
+shut down
+ 
+
+ align:start position:0%
+shut down
+the report they didn't think that this
+
+ align:start position:0%
+the report they didn't think that this
+ 
+
+ align:start position:0%
+the report they didn't think that this
+leak was in within the reportable
+
+ align:start position:0%
+leak was in within the reportable
+ 
+
+ align:start position:0%
+leak was in within the reportable
+domain and unfortunately it was they
+
+ align:start position:0%
+domain and unfortunately it was they
+ 
+
+ align:start position:0%
+domain and unfortunately it was they
+have what they
+
+ align:start position:0%
+have what they
+ 
+
+ align:start position:0%
+have what they
+call radiological e textbooks rats and
+
+ align:start position:0%
+call radiological e textbooks rats and
+ 
+
+ align:start position:0%
+call radiological e textbooks rats and
+under those text specs they should have
+
+ align:start position:0%
+under those text specs they should have
+ 
+
+ align:start position:0%
+under those text specs they should have
+routinely reported even smalles which
+
+ align:start position:0%
+routinely reported even smalles which
+ 
+
+ align:start position:0%
+routinely reported even smalles which
+they chose not to
+
+ align:start position:0%
+they chose not to
+ 
+
+ align:start position:0%
+they chose not to
+do but even though the levels were low
+
+ align:start position:0%
+do but even though the levels were low
+ 
+
+ align:start position:0%
+do but even though the levels were low
+they had a problem let me take a minute
+
+ align:start position:0%
+they had a problem let me take a minute
+ 
+
+ align:start position:0%
+they had a problem let me take a minute
+to do the enforcement process which I
+
+ align:start position:0%
+to do the enforcement process which I
+ 
+
+ align:start position:0%
+to do the enforcement process which I
+think is is
+
+ align:start position:0%
+think is is
+ 
+
+ align:start position:0%
+think is is
+interesting for minor minor violations
+
+ align:start position:0%
+interesting for minor minor violations
+ 
+
+ align:start position:0%
+interesting for minor minor violations
+these are the things that were found in
+
+ align:start position:0%
+these are the things that were found in
+ 
+
+ align:start position:0%
+these are the things that were found in
+the inspection report still green no
+
+ align:start position:0%
+the inspection report still green no
+ 
+
+ align:start position:0%
+the inspection report still green no
+issues you self-identify they identify
+
+ align:start position:0%
+issues you self-identify they identify
+ 
+
+ align:start position:0%
+issues you self-identify they identify
+not a problem then you get a it says the
+
+ align:start position:0%
+not a problem then you get a it says the
+ 
+
+ align:start position:0%
+not a problem then you get a it says the
+non- escalated process severity level
+
+ align:start position:0%
+non- escalated process severity level
+ 
+
+ align:start position:0%
+non- escalated process severity level
+four they go from one to I think 1 to
+
+ align:start position:0%
+four they go from one to I think 1 to
+ 
+
+ align:start position:0%
+four they go from one to I think 1 to
+five and these are violations and
+
+ align:start position:0%
+five and these are violations and
+ 
+
+ align:start position:0%
+five and these are violations and
+related to Green s significance
+
+ align:start position:0%
+related to Green s significance
+ 
+
+ align:start position:0%
+related to Green s significance
+determination process s DP green
+
+ align:start position:0%
+determination process s DP green
+ 
+
+ align:start position:0%
+determination process s DP green
+findings you're okay but you got to
+
+ align:start position:0%
+findings you're okay but you got to
+ 
+
+ align:start position:0%
+findings you're okay but you got to
+viation did you fail to restore
+
+ align:start position:0%
+viation did you fail to restore
+ 
+
+ align:start position:0%
+viation did you fail to restore
+compliance yes you boom you get it okay
+
+ align:start position:0%
+compliance yes you boom you get it okay
+ 
+
+ align:start position:0%
+compliance yes you boom you get it okay
+we're not even talking you anymore if
+
+ align:start position:0%
+we're not even talking you anymore if
+ 
+
+ align:start position:0%
+we're not even talking you anymore if
+you did if if if if if you failed to
+
+ align:start position:0%
+you did if if if if if you failed to
+ 
+
+ align:start position:0%
+you did if if if if if you failed to
+restore no did you failed to put it in
+
+ align:start position:0%
+restore no did you failed to put it in
+ 
+
+ align:start position:0%
+restore no did you failed to put it in
+the corrective Action Program is it a
+
+ align:start position:0%
+the corrective Action Program is it a
+ 
+
+ align:start position:0%
+the corrective Action Program is it a
+repetitive finding is it
+
+ align:start position:0%
+repetitive finding is it
+ 
+
+ align:start position:0%
+repetitive finding is it
+willful if all these are no in other
+
+ align:start position:0%
+willful if all these are no in other
+ 
+
+ align:start position:0%
+willful if all these are no in other
+words you put in the corrective Action
+
+ align:start position:0%
+words you put in the corrective Action
+ 
+
+ align:start position:0%
+words you put in the corrective Action
+Program you dealt with it responsibly
+
+ align:start position:0%
+Program you dealt with it responsibly
+ 
+
+ align:start position:0%
+Program you dealt with it responsibly
+you're not going to get a violation
+
+ align:start position:0%
+you're not going to get a violation
+ 
+
+ align:start position:0%
+you're not going to get a violation
+it'll be it'll it'll be a violation but
+
+ align:start position:0%
+it'll be it'll it'll be a violation but
+ 
+
+ align:start position:0%
+it'll be it'll it'll be a violation but
+they call
+
+ align:start position:0%
+they call
+ 
+
+ align:start position:0%
+they call
+non-signed you won't get you won't get
+
+ align:start position:0%
+non-signed you won't get you won't get
+ 
+
+ align:start position:0%
+non-signed you won't get you won't get
+ding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for if um for other licenses namely I I
+
+ align:start position:0%
+for if um for other licenses namely I I
+ 
+
+ align:start position:0%
+for if um for other licenses namely I I
+would say that if this was something
+
+ align:start position:0%
+would say that if this was something
+ 
+
+ align:start position:0%
+would say that if this was something
+that you I don't know why this would be
+
+ align:start position:0%
+that you I don't know why this would be
+ 
+
+ align:start position:0%
+that you I don't know why this would be
+other lesson this we're not going to
+
+ align:start position:0%
+other lesson this we're not going to
+ 
+
+ align:start position:0%
+other lesson this we're not going to
+about but if you're an escalated process
+
+ align:start position:0%
+about but if you're an escalated process
+ 
+
+ align:start position:0%
+about but if you're an escalated process
+very level one and two and three
+
+ align:start position:0%
+very level one and two and three
+ 
+
+ align:start position:0%
+very level one and two and three
+violations related to white yellow
+
+ align:start position:0%
+violations related to white yellow
+ 
+
+ align:start position:0%
+violations related to white yellow
+red and a significance determination
+
+ align:start position:0%
+red and a significance determination
+ 
+
+ align:start position:0%
+red and a significance determination
+findings with actual consequence so you
+
+ align:start position:0%
+findings with actual consequence so you
+ 
+
+ align:start position:0%
+findings with actual consequence so you
+got a problem you got an impact and you
+
+ align:start position:0%
+got a problem you got an impact and you
+ 
+
+ align:start position:0%
+got a problem you got an impact and you
+could have a white with a
+
+ align:start position:0%
+could have a white with a
+ 
+
+ align:start position:0%
+could have a white with a
+consequence was it was it say first non
+
+ align:start position:0%
+consequence was it was it say first non
+ 
+
+ align:start position:0%
+consequence was it was it say first non
+willful uh level three in in this period
+
+ align:start position:0%
+willful uh level three in in this period
+ 
+
+ align:start position:0%
+willful uh level three in in this period
+of time yes credit for corrective action
+
+ align:start position:0%
+of time yes credit for corrective action
+ 
+
+ align:start position:0%
+of time yes credit for corrective action
+yes I guess it's it's notice of
+
+ align:start position:0%
+yes I guess it's it's notice of
+ 
+
+ align:start position:0%
+yes I guess it's it's notice of
+violation but no civil penalty civil
+
+ align:start position:0%
+violation but no civil penalty civil
+ 
+
+ align:start position:0%
+violation but no civil penalty civil
+penalty is the
+
+ align:start position:0%
+penalty is the
+ 
+
+ align:start position:0%
+penalty is the
+F from a public perspective getting a
+
+ align:start position:0%
+F from a public perspective getting a
+ 
+
+ align:start position:0%
+F from a public perspective getting a
+notice of violation is not a good thing
+
+ align:start position:0%
+notice of violation is not a good thing
+ 
+
+ align:start position:0%
+notice of violation is not a good thing
+from a public perspective getting a
+
+ align:start position:0%
+from a public perspective getting a
+ 
+
+ align:start position:0%
+from a public perspective getting a
+notice of violation and a civil penalty
+
+ align:start position:0%
+notice of violation and a civil penalty
+ 
+
+ align:start position:0%
+notice of violation and a civil penalty
+shows you're really really not doing
+
+ align:start position:0%
+shows you're really really not doing
+ 
+
+ align:start position:0%
+shows you're really really not doing
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+job so was if was not if it was if it
+
+ align:start position:0%
+job so was if was not if it was if it
+ 
+
+ align:start position:0%
+job so was if was not if it was if it
+was first non willful no did you get
+
+ align:start position:0%
+was first non willful no did you get
+ 
+
+ align:start position:0%
+was first non willful no did you get
+credit for identification then you can
+
+ align:start position:0%
+credit for identification then you can
+ 
+
+ align:start position:0%
+credit for identification then you can
+kind of play this as well
+
+ align:start position:0%
+kind of play this as well
+ 
+
+ align:start position:0%
+kind of play this as well
+if you if if you didn't identify it and
+
+ align:start position:0%
+if you if if you didn't identify it and
+ 
+
+ align:start position:0%
+if you if if you didn't identify it and
+you didn't correct it you're going to
+
+ align:start position:0%
+you didn't correct it you're going to
+ 
+
+ align:start position:0%
+you didn't correct it you're going to
+get hit twice with the base
+
+ align:start position:0%
+get hit twice with the base
+ 
+
+ align:start position:0%
+get hit twice with the base
+Baseline and uh violation right just
+
+ align:start position:0%
+Baseline and uh violation right just
+ 
+
+ align:start position:0%
+Baseline and uh violation right just
+basically just get a no of
+
+ align:start position:0%
+basically just get a no of
+ 
+
+ align:start position:0%
+basically just get a no of
+violation uh so you don't want to be on
+
+ align:start position:0%
+violation uh so you don't want to be on
+ 
+
+ align:start position:0%
+violation uh so you don't want to be on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+path for sure but this process has has
+
+ align:start position:0%
+path for sure but this process has has
+ 
+
+ align:start position:0%
+path for sure but this process has has
+been very effective at getting the
+
+ align:start position:0%
+been very effective at getting the
+ 
+
+ align:start position:0%
+been very effective at getting the
+utilities focus on trying to improve the
+
+ align:start position:0%
+utilities focus on trying to improve the
+ 
+
+ align:start position:0%
+utilities focus on trying to improve the
+situation um
+
+ align:start position:0%
+situation um
+ 
+
+ align:start position:0%
+situation um
+but violations and fines do
+
+ align:start position:0%
+but violations and fines do
+ 
+
+ align:start position:0%
+but violations and fines do
+occur I've picked up two recent
+
+ align:start position:0%
+occur I've picked up two recent
+ 
+
+ align:start position:0%
+occur I've picked up two recent
+enforcement actions this is
+
+ align:start position:0%
+enforcement actions this is
+ 
+
+ align:start position:0%
+enforcement actions this is
+airon just to give you a sense of what
+
+ align:start position:0%
+airon just to give you a sense of what
+ 
+
+ align:start position:0%
+airon just to give you a sense of what
+kinds of things they're they're citing
+
+ align:start position:0%
+kinds of things they're they're citing
+ 
+
+ align:start position:0%
+kinds of things they're they're citing
+you for now this was u a white
+
+ align:start position:0%
+you for now this was u a white
+ 
+
+ align:start position:0%
+you for now this was u a white
+finding part 50 appendix B which was
+
+ align:start position:0%
+finding part 50 appendix B which was
+ 
+
+ align:start position:0%
+finding part 50 appendix B which was
+really append quality insurance those
+
+ align:start position:0%
+really append quality insurance those
+ 
+
+ align:start position:0%
+really append quality insurance those
+were quity
+
+ align:start position:0%
+were quity
+ 
+
+ align:start position:0%
+were quity
+program and you didn't and this was in
+
+ align:start position:0%
+program and you didn't and this was in
+ 
+
+ align:start position:0%
+program and you didn't and this was in
+design control failed to take timely
+
+ align:start position:0%
+design control failed to take timely
+ 
+
+ align:start position:0%
+design control failed to take timely
+corrective action after identification
+
+ align:start position:0%
+corrective action after identification
+ 
+
+ align:start position:0%
+corrective action after identification
+of extensive corrosion essential to
+
+ align:start position:0%
+of extensive corrosion essential to
+ 
+
+ align:start position:0%
+of extensive corrosion essential to
+service water Riser and failed to verify
+
+ align:start position:0%
+service water Riser and failed to verify
+ 
+
+ align:start position:0%
+service water Riser and failed to verify
+the adequacy of the methodology and
+
+ align:start position:0%
+the adequacy of the methodology and
+ 
+
+ align:start position:0%
+the adequacy of the methodology and
+design inputs in calculations that
+
+ align:start position:0%
+design inputs in calculations that
+ 
+
+ align:start position:0%
+design inputs in calculations that
+supported the decision to accept three
+
+ align:start position:0%
+supported the decision to accept three
+ 
+
+ align:start position:0%
+supported the decision to accept three
+degraded essential service water pump
+
+ align:start position:0%
+degraded essential service water pump
+ 
+
+ align:start position:0%
+degraded essential service water pump
+GES for sech what does that say to you
+
+ align:start position:0%
+GES for sech what does that say to you
+ 
+
+ align:start position:0%
+GES for sech what does that say to you
+what message was NRC telling excellent
+
+ align:start position:0%
+what message was NRC telling excellent
+ 
+
+ align:start position:0%
+what message was NRC telling excellent
+about what they did from an engineering
+
+ align:start position:0%
+about what they did from an engineering
+ 
+
+ align:start position:0%
+about what they did from an engineering
+perspective
+
+ align:start position:0%
+perspective
+ 
+
+ align:start position:0%
+perspective
+they couldn't get you on a specific
+
+ align:start position:0%
+they couldn't get you on a specific
+ 
+
+ align:start position:0%
+they couldn't get you on a specific
+regulatory non-compliance item
+
+ align:start position:0%
+regulatory non-compliance item
+ 
+
+ align:start position:0%
+regulatory non-compliance item
+right but they got you on your
+
+ align:start position:0%
+right but they got you on your
+ 
+
+ align:start position:0%
+right but they got you on your
+corrective action quality control
+
+ align:start position:0%
+corrective action quality control
+ 
+
+ align:start position:0%
+corrective action quality control
+program which is sort of this catchall
+
+ align:start position:0%
+program which is sort of this catchall
+ 
+
+ align:start position:0%
+program which is sort of this catchall
+appendix B and appendix B says you
+
+ align:start position:0%
+appendix B and appendix B says you
+ 
+
+ align:start position:0%
+appendix B and appendix B says you
+didn't analyze this right and you made a
+
+ align:start position:0%
+didn't analyze this right and you made a
+ 
+
+ align:start position:0%
+didn't analyze this right and you made a
+crappy decision about why you should
+
+ align:start position:0%
+crappy decision about why you should
+ 
+
+ align:start position:0%
+crappy decision about why you should
+continue to operate with degraded
+
+ align:start position:0%
+continue to operate with degraded
+ 
+
+ align:start position:0%
+continue to operate with degraded
+service water
+
+ align:start position:0%
+service water
+ 
+
+ align:start position:0%
+service water
+pipes that's that that's that's a whole
+
+ align:start position:0%
+pipes that's that that's that's a whole
+ 
+
+ align:start position:0%
+pipes that's that that's that's a whole
+different thing where you failed to
+
+ align:start position:0%
+different thing where you failed to
+ 
+
+ align:start position:0%
+different thing where you failed to
+follow the text effects or fail to
+
+ align:start position:0%
+follow the text effects or fail to
+ 
+
+ align:start position:0%
+follow the text effects or fail to
+comply to a regulation you failed to
+
+ align:start position:0%
+comply to a regulation you failed to
+ 
+
+ align:start position:0%
+comply to a regulation you failed to
+follow good
+
+ align:start position:0%
+follow good
+ 
+
+ align:start position:0%
+follow good
+procedures and you made a lousy decision
+
+ align:start position:0%
+procedures and you made a lousy decision
+ 
+
+ align:start position:0%
+procedures and you made a lousy decision
+on how you decided that this this was
+
+ align:start position:0%
+on how you decided that this this was
+ 
+
+ align:start position:0%
+on how you decided that this this was
+still okay to
+
+ align:start position:0%
+still okay to
+ 
+
+ align:start position:0%
+still okay to
+run very significant in my
+
+ align:start position:0%
+run very significant in my
+ 
+
+ align:start position:0%
+run very significant in my
+op the next
+
+ align:start position:0%
+op the next
+ 
+
+ align:start position:0%
+op the next
+one this is a Kami
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Peak this is a kamach peak
+
+ align:start position:0%
+Peak this is a kamach peak
+ 
+
+ align:start position:0%
+Peak this is a kamach peak
+now this was an interesting one uh they
+
+ align:start position:0%
+now this was an interesting one uh they
+ 
+
+ align:start position:0%
+now this was an interesting one uh they
+had diesel generators supposed to supply
+
+ align:start position:0%
+had diesel generators supposed to supply
+ 
+
+ align:start position:0%
+had diesel generators supposed to supply
+back of
+
+ align:start position:0%
+back of
+ 
+
+ align:start position:0%
+back of
+power uh they had a white finding Tech
+
+ align:start position:0%
+power uh they had a white finding Tech
+ 
+
+ align:start position:0%
+power uh they had a white finding Tech
+spec violation and it says while the
+
+ align:start position:0%
+spec violation and it says while the
+ 
+
+ align:start position:0%
+spec violation and it says while the
+plan is in most one and two two diesel
+
+ align:start position:0%
+plan is in most one and two two diesel
+ 
+
+ align:start position:0%
+plan is in most one and two two diesel
+generators capable supplying offside
+
+ align:start position:0%
+generators capable supplying offside
+ 
+
+ align:start position:0%
+generators capable supplying offside
+power to one E Equipment which is the
+
+ align:start position:0%
+power to one E Equipment which is the
+ 
+
+ align:start position:0%
+power to one E Equipment which is the
+safety related buses have to be operable
+
+ align:start position:0%
+safety related buses have to be operable
+ 
+
+ align:start position:0%
+safety related buses have to be operable
+now from this perer no one to November
+
+ align:start position:0%
+now from this perer no one to November
+ 
+
+ align:start position:0%
+now from this perer no one to November
+21st while the plant was in operable
+
+ align:start position:0%
+21st while the plant was in operable
+ 
+
+ align:start position:0%
+21st while the plant was in operable
+condition supposed to blah blah blah
+
+ align:start position:0%
+condition supposed to blah blah blah
+ 
+
+ align:start position:0%
+condition supposed to blah blah blah
+power it was inoperable and action was
+
+ align:start position:0%
+power it was inoperable and action was
+ 
+
+ align:start position:0%
+power it was inoperable and action was
+not taken to restore operable status
+
+ align:start position:0%
+not taken to restore operable status
+ 
+
+ align:start position:0%
+not taken to restore operable status
+within 72 hours or be shut
+
+ align:start position:0%
+within 72 hours or be shut
+ 
+
+ align:start position:0%
+within 72 hours or be shut
+there specifically the complaint on the
+
+ align:start position:0%
+there specifically the complaint on the
+ 
+
+ align:start position:0%
+there specifically the complaint on the
+emergency diesel generator was made
+
+ align:start position:0%
+emergency diesel generator was made
+ 
+
+ align:start position:0%
+emergency diesel generator was made
+inoperable as a result of painting
+
+ align:start position:0%
+inoperable as a result of painting
+ 
+
+ align:start position:0%
+inoperable as a result of painting
+activities okay due to the paint having
+
+ align:start position:0%
+activities okay due to the paint having
+ 
+
+ align:start position:0%
+activities okay due to the paint having
+been deposited and remaining on at least
+
+ align:start position:0%
+been deposited and remaining on at least
+ 
+
+ align:start position:0%
+been deposited and remaining on at least
+one fuel rack in location that prevented
+
+ align:start position:0%
+one fuel rack in location that prevented
+ 
+
+ align:start position:0%
+one fuel rack in location that prevented
+motion required to support the operation
+
+ align:start position:0%
+motion required to support the operation
+ 
+
+ align:start position:0%
+motion required to support the operation
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+emergency this caused the the diesel
+
+ align:start position:0%
+emergency this caused the the diesel
+ 
+
+ align:start position:0%
+emergency this caused the the diesel
+generator fa to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start all right so who who's got the bow
+
+ align:start position:0%
+start all right so who who's got the bow
+ 
+
+ align:start position:0%
+start all right so who who's got the bow
+on this one the poor
+
+ align:start position:0%
+on this one the poor
+ 
+
+ align:start position:0%
+on this one the poor
+painter who's watching the
+
+ align:start position:0%
+painter who's watching the
+ 
+
+ align:start position:0%
+painter who's watching the
+store the point of this slidee is that
+
+ align:start position:0%
+store the point of this slidee is that
+ 
+
+ align:start position:0%
+store the point of this slidee is that
+even a tiny thing like painting can get
+
+ align:start position:0%
+even a tiny thing like painting can get
+ 
+
+ align:start position:0%
+even a tiny thing like painting can get
+you in trouble if you're not careful
+
+ align:start position:0%
+you in trouble if you're not careful
+ 
+
+ align:start position:0%
+you in trouble if you're not careful
+about what you're
+
+ align:start position:0%
+about what you're
+ 
+
+ align:start position:0%
+about what you're
+painting okay so those of you who start
+
+ align:start position:0%
+painting okay so those of you who start
+ 
+
+ align:start position:0%
+painting okay so those of you who start
+working in this industry you got to keep
+
+ align:start position:0%
+working in this industry you got to keep
+ 
+
+ align:start position:0%
+working in this industry you got to keep
+these things in mind and the reason I
+
+ align:start position:0%
+these things in mind and the reason I
+ 
+
+ align:start position:0%
+these things in mind and the reason I
+picked these because they're they're
+
+ align:start position:0%
+picked these because they're they're
+ 
+
+ align:start position:0%
+picked these because they're they're
+very different but they can mess you
+
+ align:start position:0%
+very different but they can mess you
+ 
+
+ align:start position:0%
+very different but they can mess you
+up right if this diesel generator fails
+
+ align:start position:0%
+up right if this diesel generator fails
+ 
+
+ align:start position:0%
+up right if this diesel generator fails
+to start it's a problem and the only
+
+ align:start position:0%
+to start it's a problem and the only
+ 
+
+ align:start position:0%
+to start it's a problem and the only
+reason they detected it was it failed to
+
+ align:start position:0%
+reason they detected it was it failed to
+ 
+
+ align:start position:0%
+reason they detected it was it failed to
+start then they started looking it's
+
+ align:start position:0%
+start then they started looking it's
+ 
+
+ align:start position:0%
+start then they started looking it's
+right through the F start oh this thing
+
+ align:start position:0%
+right through the F start oh this thing
+ 
+
+ align:start position:0%
+right through the F start oh this thing
+got stuck because somebody
+
+ align:start position:0%
+got stuck because somebody
+ 
+
+ align:start position:0%
+got stuck because somebody
+painted okay then they look back and say
+
+ align:start position:0%
+painted okay then they look back and say
+ 
+
+ align:start position:0%
+painted okay then they look back and say
+when was the painting
+
+ align:start position:0%
+when was the painting
+ 
+
+ align:start position:0%
+when was the painting
+job one that's how they they pick the
+
+ align:start position:0%
+job one that's how they they pick the
+ 
+
+ align:start position:0%
+job one that's how they they pick the
+time of
+
+ align:start position:0%
+time of
+ 
+
+ align:start position:0%
+time of
+infraction so it's not rocket science
+
+ align:start position:0%
+infraction so it's not rocket science
+ 
+
+ align:start position:0%
+infraction so it's not rocket science
+but very important okay I just want to
+
+ align:start position:0%
+but very important okay I just want to
+ 
+
+ align:start position:0%
+but very important okay I just want to
+stop you know we all talk about this
+
+ align:start position:0%
+stop you know we all talk about this
+ 
+
+ align:start position:0%
+stop you know we all talk about this
+great nuclear performing record 92%
+
+ align:start position:0%
+great nuclear performing record 92%
+ 
+
+ align:start position:0%
+great nuclear performing record 92%
+capacity Factor everything is great the
+
+ align:start position:0%
+capacity Factor everything is great the
+ 
+
+ align:start position:0%
+capacity Factor everything is great the
+industry is booming everybody's making
+
+ align:start position:0%
+industry is booming everybody's making
+ 
+
+ align:start position:0%
+industry is booming everybody's making
+money but as you saw from a little
+
+ align:start position:0%
+money but as you saw from a little
+ 
+
+ align:start position:0%
+money but as you saw from a little
+Litany of key safety issues they've been
+
+ align:start position:0%
+Litany of key safety issues they've been
+ 
+
+ align:start position:0%
+Litany of key safety issues they've been
+around for a very long
+
+ align:start position:0%
+around for a very long
+ 
+
+ align:start position:0%
+around for a very long
+time and when you start to start
+
+ align:start position:0%
+time and when you start to start
+ 
+
+ align:start position:0%
+time and when you start to start
+thinking about the pressure vessel
+
+ align:start position:0%
+thinking about the pressure vessel
+ 
+
+ align:start position:0%
+thinking about the pressure vessel
+integrity and the and the pipe welding
+
+ align:start position:0%
+integrity and the and the pipe welding
+ 
+
+ align:start position:0%
+integrity and the and the pipe welding
+and the primary system integrity
+
+ align:start position:0%
+and the primary system integrity
+ 
+
+ align:start position:0%
+and the primary system integrity
+itself these are going to be coming and
+
+ align:start position:0%
+itself these are going to be coming and
+ 
+
+ align:start position:0%
+itself these are going to be coming and
+continue to come unless people decide to
+
+ align:start position:0%
+continue to come unless people decide to
+ 
+
+ align:start position:0%
+continue to come unless people decide to
+fix fundamental problems and hopefully
+
+ align:start position:0%
+fix fundamental problems and hopefully
+ 
+
+ align:start position:0%
+fix fundamental problems and hopefully
+the new they will but these issues
+
+ align:start position:0%
+the new they will but these issues
+ 
+
+ align:start position:0%
+the new they will but these issues
+Remain the safe operation still requires
+
+ align:start position:0%
+Remain the safe operation still requires
+ 
+
+ align:start position:0%
+Remain the safe operation still requires
+this vigilance that we need attention to
+
+ align:start position:0%
+this vigilance that we need attention to
+ 
+
+ align:start position:0%
+this vigilance that we need attention to
+detail and in my opinion strong NRC
+
+ align:start position:0%
+detail and in my opinion strong NRC
+ 
+
+ align:start position:0%
+detail and in my opinion strong NRC
+oversight because had in my view had not
+
+ align:start position:0%
+oversight because had in my view had not
+ 
+
+ align:start position:0%
+oversight because had in my view had not
+the NRC been as as strong as it was and
+
+ align:start position:0%
+the NRC been as as strong as it was and
+ 
+
+ align:start position:0%
+the NRC been as as strong as it was and
+in some cases people argue it's not
+
+ align:start position:0%
+in some cases people argue it's not
+ 
+
+ align:start position:0%
+in some cases people argue it's not
+strong enough you'll fall into this
+
+ align:start position:0%
+strong enough you'll fall into this
+ 
+
+ align:start position:0%
+strong enough you'll fall into this
+complacency train as our friends at
+
+ align:start position:0%
+complacency train as our friends at
+ 
+
+ align:start position:0%
+complacency train as our friends at
+Exelon did at bra would have tolerated
+
+ align:start position:0%
+Exelon did at bra would have tolerated
+ 
+
+ align:start position:0%
+Exelon did at bra would have tolerated
+Le 3 million
+
+ align:start position:0%
+Le 3 million
+ 
+
+ align:start position:0%
+Le 3 million
+G even think
+
+ align:start position:0%
+G even think
+ 
+
+ align:start position:0%
+G even think
+about the role of the industry and Nei
+
+ align:start position:0%
+about the role of the industry and Nei
+ 
+
+ align:start position:0%
+about the role of the industry and Nei
+every are important because the NRC
+
+ align:start position:0%
+every are important because the NRC
+ 
+
+ align:start position:0%
+every are important because the NRC
+tends will tend to go to one extreme
+
+ align:start position:0%
+tends will tend to go to one extreme
+ 
+
+ align:start position:0%
+tends will tend to go to one extreme
+about uh what the solution ought to be
+
+ align:start position:0%
+about uh what the solution ought to be
+ 
+
+ align:start position:0%
+about uh what the solution ought to be
+and the industry said well let's be more
+
+ align:start position:0%
+and the industry said well let's be more
+ 
+
+ align:start position:0%
+and the industry said well let's be more
+reasonable and with the onset of
+
+ align:start position:0%
+reasonable and with the onset of
+ 
+
+ align:start position:0%
+reasonable and with the onset of
+probabilistic risk assessment risk
+
+ align:start position:0%
+probabilistic risk assessment risk
+ 
+
+ align:start position:0%
+probabilistic risk assessment risk
+inform performance-based
+
+ align:start position:0%
+inform performance-based
+ 
+
+ align:start position:0%
+inform performance-based
+uh safety determinations we have a shot
+
+ align:start position:0%
+uh safety determinations we have a shot
+ 
+
+ align:start position:0%
+uh safety determinations we have a shot
+at sort of maintaining that is this
+
+ align:start position:0%
+at sort of maintaining that is this
+ 
+
+ align:start position:0%
+at sort of maintaining that is this
+safety significant or not kind
+
+ align:start position:0%
+safety significant or not kind
+ 
+
+ align:start position:0%
+safety significant or not kind
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+so this is the one that that makes me a
+
+ align:start position:0%
+so this is the one that that makes me a
+ 
+
+ align:start position:0%
+so this is the one that that makes me a
+little nervous we're all bragging about
+
+ align:start position:0%
+little nervous we're all bragging about
+ 
+
+ align:start position:0%
+little nervous we're all bragging about
+the high capacity factors and yet when
+
+ align:start position:0%
+the high capacity factors and yet when
+ 
+
+ align:start position:0%
+the high capacity factors and yet when
+you think about the things that we just
+
+ align:start position:0%
+you think about the things that we just
+ 
+
+ align:start position:0%
+you think about the things that we just
+went through we're not done really in
+
+ align:start position:0%
+went through we're not done really in
+ 
+
+ align:start position:0%
+went through we're not done really in
+assuring the safety of these PL so any
+
+ align:start position:0%
+assuring the safety of these PL so any
+ 
+
+ align:start position:0%
+assuring the safety of these PL so any
+reactions or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comments
+
+ align:start position:0%
+comments
+ 
+
+ align:start position:0%
+comments
+no okay now next week's our last class
+
+ align:start position:0%
+no okay now next week's our last class
+ 
+
+ align:start position:0%
+no okay now next week's our last class
+uh scheduled is I'll do a quick review
+
+ align:start position:0%
+uh scheduled is I'll do a quick review
+ 
+
+ align:start position:0%
+uh scheduled is I'll do a quick review
+of the uh material that we
+
+ align:start position:0%
+of the uh material that we
+ 
+
+ align:start position:0%
+of the uh material that we
+covered during this term and also um
+
+ align:start position:0%
+covered during this term and also um
+ 
+
+ align:start position:0%
+covered during this term and also um
+provide some insights as to the advanced
+
+ align:start position:0%
+provide some insights as to the advanced
+ 
+
+ align:start position:0%
+provide some insights as to the advanced
+reactors that we're talking about uh
+
+ align:start position:0%
+reactors that we're talking about uh
+ 
+
+ align:start position:0%
+reactors that we're talking about uh
+please uh hand in the homework
+
+ align:start position:0%
+please uh hand in the homework
+ 
+
+ align:start position:0%
+please uh hand in the homework
+assignments so I can get them done and
+
+ align:start position:0%
+assignments so I can get them done and
+ 
+
+ align:start position:0%
+assignments so I can get them done and
+grade submitted um I think there are two
+
+ align:start position:0%
+grade submitted um I think there are two
+ 
+
+ align:start position:0%
+grade submitted um I think there are two
+two missing sets right now there's no
+
+ align:start position:0%
+two missing sets right now there's no
+ 
+
+ align:start position:0%
+two missing sets right now there's no
+homework for this class and there won't
+
+ align:start position:0%
+homework for this class and there won't
+ 
+
+ align:start position:0%
+homework for this class and there won't
+be any homework uh for the F class but I
+
+ align:start position:0%
+be any homework uh for the F class but I
+ 
+
+ align:start position:0%
+be any homework uh for the F class but I
+want you to spend the time to do
+
+ align:start position:0%
+want you to spend the time to do
+ 
+
+ align:start position:0%
+want you to spend the time to do
+that okay questions comments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suggestions good all right thank you
\ No newline at end of file
diff --git a/9CPA6WG6mRo.txt b/9CPA6WG6mRo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..17e3be292786d880385c06173002c222a8482412
--- /dev/null
+++ b/9CPA6WG6mRo.txt
@@ -0,0 +1,2950 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Well let's see
+if we can't get started.
+
+Everyone I trust can
+hear me adequately.
+
+Welcome back.
+
+It's Tuesday.
+
+For those of you who are not
+in my recitation section,
+
+I'm Dave Gossard, and I'll
+be your lecturer for the day.
+
+Professor Vandiver
+is out of town.
+
+It looks like some of
+you may be as well.
+
+We probably could have held this
+at the gate at Logan Airport
+
+and done a little better.
+
+But be that as it
+may, glad you came.
+
+This should be fun.
+
+Today we have a new topic
+and a demonstration,
+
+a real physical system.
+
+So unless there are any
+outstanding questions?
+
+Anybody have any
+questions or complaints
+
+to address to Vicente?
+
+No.
+
+All right, hearing none let's
+go ahead and get started then.
+
+Today the topic is multiple
+degree of freedom systems.
+
+Now to date, with a
+couple of exceptions,
+
+all of the systems
+that you've dealt with
+
+had a single degree of freedom,
+either a linear displacement
+
+x or an angular
+displacement theta.
+
+You know the concept
+of equations of motion,
+
+or I should say the
+equation of motion
+
+and the notion of undamped
+natural frequency.
+
+Well, today we're going to
+generalize, if you will,
+
+to systems that have not one
+but multiple degrees of freedom
+
+and see how those
+notions generalize.
+
+In particular, as
+you might expect,
+
+the system that has
+multiple degrees of freedom
+
+has multiple natural
+frequencies, also
+
+known as eigenvalues as we
+will explain here shortly.
+
+Multiple degrees
+of freedom systems
+
+have a new property,
+a new characteristic
+
+you haven't seen before.
+
+And that's what this
+lecture is all about,
+
+is to illustrate that to
+you and demonstrate it.
+
+It's the notion
+of natural modes,
+
+also called eigenvectors.
+
+And then the general response
+to initial conditions.
+
+So that is the plan for the day.
+
+And we'll start with this.
+
+This is kind of a
+classic textbook
+
+case, two springs, two masses.
+
+A straightforward extrapolation
+of what you've done before.
+
+You've got a spring K1,
+mass M1, spring K2, mass M2.
+
+And the displacements
+are indicated
+
+as shown there, X1 and X2.
+
+I want to hasten to point out
+that the displacements we speak
+
+of here are defined with respect
+to the static equilibrium
+
+position.
+
+This is a notion that Professor
+Vandiver went over at least
+
+once.
+
+And for those of you who've
+forgotten it or weren't there
+
+that day, I have for you a
+reference, essentially reprised
+
+that notion over there.
+
+So in the meantime,
+let me press on.
+
+If you have any questions, we
+can go back and cover that.
+
+But assuming you agree, let
+me simply say you've got
+
+two springs, two masses.
+
+The typical way we've
+taught you to do
+
+it is if you're
+going to generate
+
+the equations of motion
+by the direct method,
+
+you generate two free
+body diagrams, the sum
+
+forces in the x direction
+for each of the masses,
+
+get f equals MA and
+you'd get these.
+
+Conversely, you could
+also do it by Legrange.
+
+You could generate
+the expression
+
+for the kinetic energy,
+for the potential energy,
+
+for the Legrangian, do this
+Lagrange equation business,
+
+and you'd get the same thing.
+
+But either way you do it,
+what comes out the other side
+
+looks like this.
+
+And it's not a bad exercise
+for you to offline convince
+
+yourself that this is right.
+
+Not right now, but in
+the comfort and leisure
+
+of another time.
+
+So there you have it.
+
+That's what the two equations
+of motion would look like.
+
+Again, either by the direct
+method or by Legrange,
+
+you end up in the same
+place, so to speak.
+
+And now for today, we haven't
+asked you to do this much,
+
+but let me simply say
+the weapon of choice
+
+for multiple degrees
+of freedom system,
+
+because there's a certain
+repetitive quality to it,
+
+matrix notation is preferred.
+
+In these equations over
+here, written in matrix form
+
+would look like this.
+
+And that looks like this.
+
+There's two matrices,
+and let me hasten
+
+to point out that this is
+exactly this and nothing more.
+
+There's no magic, no
+additional derivation.
+
+This is simply a restructuring,
+and reorganization
+
+of these equations.
+
+And this may seem
+foreign to those
+
+of you who have not had any
+or very much linear algebra.
+
+Do not be dismayed.
+
+It is not a difficult
+thing to learn.
+
+As you probably know, a matrix
+multiplies by a vector--
+
+or multiplying a
+vector by a matrix--
+
+is done with two hands.
+
+The first item for example
+is M1 X1 dot plus 0.
+
+That gives you this
+term right here.
+
+Over here you get
+X1 times K1 plus K2.
+
+That's this one.
+
+And here you have minus
+K2 X2, that's that term.
+
+So matrix notation,
+this becomes that.
+
+No problem.
+
+It's like a model train set.
+
+It's great.
+
+Everyone should
+have one of these.
+
+All right, so what I would
+like to do for our example here
+
+is because we're going
+to be doing some algebra,
+
+for the express purpose of
+simplifying the algebra let
+
+me consider a special case
+where the masses are identical.
+
+And we can simply call
+them M. And similarly,
+
+the springs are identical,
+and we'll simply call them K.
+
+At that point, these
+equations become simplified.
+
+That's just M, that's
+just M. So this
+
+is the problem we're
+going to-- we're
+
+going to tackle this problem
+first, because as I say,
+
+it simplifies the algebra.
+
+Now here is-- this
+is not an assumption.
+
+This is a-- I would call
+this more a mechanism
+
+to get this job done here.
+
+Harmonic motion is
+one where we assume
+
+that the masses oscillate
+at the same frequency.
+
+So what this looks like is this.
+
+What we're basically saying
+is that X1 is actually
+
+equal-- X1 has
+amplitude A-- whoa.
+
+I'm being attacked here
+by the second board.
+
+Basically, the situation
+here is that we're
+
+assuming that both
+of these masses
+
+move-- I wouldn't call
+it exactly together.
+
+They're not in
+complete synchrony,
+
+as you'll see here in a moment.
+
+But what they are
+is they're going
+
+through a sinusoidal motion.
+
+And it is an oscillation
+at the same frequency.
+
+Both of them are oscillating
+at the same frequency.
+
+However, they differ
+in their magnitudes.
+
+They are not the same magnitude.
+
+But that assumption right
+there allows us to say this.
+
+If we differentiate those
+twice, we get the following.
+
+That comes back out.
+
+Douglas, where's
+that minus sign come?
+
+Can you-- first of all,
+can everybody read that?
+
+Can you guys read that
+in the back row here?
+
+For example, this says that X1
+double dot, if x1 is A1 cosine,
+
+then X1 double dot
+is A1 cosine preceded
+
+by a minus omega squared.
+
+Where does that come from?
+
+AUDIENCE: The minus sign came
+from when you differentiated
+
+the cosine in the first one.
+
+PROFESSOR: Exactly.
+
+And the cosine returns.
+
+And that's what you get.
+
+Well, here is, shall we say,
+the heart of the matter.
+
+When you substitute
+this into this--
+
+let me call this-- I'll try not
+to get too obsessive over this.
+
+But these are our
+equations of motion.
+
+So when we-- you
+get this, equals 0.
+
+Excuse me.
+
+Many people, I think,
+simply put a big 0 there,
+
+but I'll do it properly.
+
+It's two zeros, if you will.
+
+And forgive me for
+writing this out,
+
+but I would like you
+to be able to do this
+
+by yourself, to recreate
+this after the fact.
+
+This becomes-- dividing
+and collecting terms.
+
+OK, anybody unclear about
+how this is obtained?
+
+Yes, ma'am.
+
+Emma.
+
+AUDIENCE: I have a question
+about the previous one.
+
+PROFESSOR: Yeah?
+
+AUDIENCE: If the second
+term on the left hand side,
+
+should it also be
+multiplied by A1 A2?
+
+PROFESSOR: Yes it should.
+
+Thank you very much.
+
+Oh, hang on.
+
+Yes, thank you,
+that's exactly right.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Hang on a second.
+
+We're fighting the boards here.
+
+Let's see, one thing at a time.
+
+We've got A1, A2 cosine
+[INAUDIBLE] minus phi equals.
+
+Now Emma, does that
+take care of you?
+
+Yeah?
+
+And you said, Vicente?
+
+AUDIENCE: Diagonal terms--
+shouldn't there be a minus?
+
+PROFESSOR: I'm sorry,
+that's absolutely correct.
+
+Wonderful.
+
+So there we have it.
+
+Any other questions?
+
+I hope I got it right.
+
+Yes sir.
+
+AUDIENCE: Are they plus K?
+
+PROFESSOR: I'm sorry?
+
+AUDIENCE: Are they plus K?
+
+PROFESSOR: Plus K?
+
+No.
+
+They're minus.
+
+Yeah, why is that?
+
+Everybody see that?
+
+This is a straight-- there's
+less here than meets the eye.
+
+There's a straight segregation
+collecting of terms.
+
+The minus got added to the
+elements of the mass matrix,
+
+but not to the K metrics.
+
+The K metrics goes
+shows through as is.
+
+Now, the question on the
+floor is what we do with this?
+
+Can everybody appreciate
+that-- get out
+
+of the spring mass
+business and look at this
+
+from a math point of view?
+
+Does everyone
+appreciate that this
+
+is a set of linear equations?
+
+There's the old AX
+equal B kind of thing.
+
+And if you recall, to solve,
+what we're basically going
+
+to do is solve for A1 and A2.
+
+That's the game
+we're playing here.
+
+And if you recall from your math
+course, the determinant of this
+
+has got to equal 0.
+
+So let me simply repeat it here.
+
+The determinant of
+has got to equal 0.
+
+And you recall, the determinant
+is for at least the two
+
+by two you can do it
+by hand more or less.
+
+It's the cross products
+with appropriate sign.
+
+And I'm sparing you
+some algebra here,
+
+but trust me when you do
+this, this is what you get.
+
+M squared omega 4 minus
+3KM omega squared, plus K2.
+
+That's it right here.
+
+This little guy-- oh, all right.
+
+I can't do that anymore.
+
+I know, it's this one.
+
+That is called the
+characteristic equation.
+
+So here's the first answer.
+
+AUDIENCE: [INAUDIBLE]
+should that be K squared?
+
+PROFESSOR: I'm sorry.
+
+That's a typo.
+
+That's simply K.
+
+AUDIENCE: [INAUDIBLE] K squared?
+
+PROFESSOR: Or it's
+K squared, rather.
+
+Sorry.
+
+Thank you.
+
+AUDIENCE: I think
+in the above line,
+
+the determinant-- the upper
+left-- should had a 2K.
+
+PROFESSOR: Oh, this
+is 2K, absolutely.
+
+All right, 2K.
+
+Good enough?
+
+All right, thank you.
+
+So let's send this to the top.
+
+So the roots of
+the characteristic
+
+are the natural frequencies.
+
+Let's do this this way.
+
+Did I do that right?
+
+Yeah, plus or minus.
+
+So the situation is that when
+you apply the quadratic formula
+
+to that characteristic equation
+to find the values of omega
+
+for which that
+equation is satisfied,
+
+those omegas that come out
+are the natural frequencies.
+
+They are the quantities we seek.
+
+And what that yields, as you
+can see from the plus or minus
+
+here, there are two of them.
+
+I'll write the whole
+thing out here.
+
+And these are numerically.
+
+OK, everybody see that?
+
+So here are our two
+natural frequencies.
+
+Here's the first one-- excuse
+me, that's not right either.
+
+That's the square.
+
+OK So these are our natural
+frequencies, once again
+
+for this special case
+where the masses are equal
+
+and the springs are equal.
+
+Anybody recognize
+that number, 0.618,
+
+for all you fuss budgets?
+
+Ring any bells?
+
+Any number freaks here?
+
+No?
+
+I heard it.
+
+That's it.
+
+Exactly, nice job.
+
+The golden mean,
+the golden ratio.
+
+Also, let me simply
+say if there are--
+
+as far as the number
+of things-- if there
+
+are n degrees of freedom.
+
+There are n natural frequencies.
+
+What else?
+
+So that's that.
+
+So now it's time to get to this
+notion of the natural modes.
+
+Let me say, we've got
+to go all the way back
+
+to this set over here.
+
+If you take the first row
+of this matrix equation--
+
+that's the first of the
+equations of motion--
+
+and you make that assumption of
+the harmonic motion in there.
+
+Does everybody see that?
+
+What we've done is we've
+taken basically the first row
+
+of that expression
+right up there
+
+and formed the amplitude
+ratio A1 over A2.
+
+What we're doing is
+we've found the omegas.
+
+You remember, just
+review the bidding.
+
+Our original
+assumption was harmonic
+
+motion, that is to say
+all the displacements are
+
+moving in synchrony as it were.
+
+The same sinusoidal
+frequency, we've
+
+just found what
+frequencies those are.
+
+There are two of them,
+and they're right there.
+
+Now we're after these guys.
+
+Now we're after the
+relative magnitudes
+
+or the relative
+amplitudes of A1 and A2.
+
+And we from one of the
+equations isolated one of those.
+
+And let me just say, if
+you plug these back in,
+
+plug in the first one, you'll
+get oddly enough 1.618,
+
+These amplitude ratios.
+
+Are the so-called natural modes.
+
+And I think you can appreciate
+that this is the first one,
+
+and this is the second one.
+
+Any questions so far?
+
+Wonderful.
+
+Hearing none.
+
+Yes ma'am, Sara?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: You see
+this amplitude ratio.
+
+You saw how we got that.
+
+You see that the right hand side
+has got system parameter, Ks
+
+and Ms, and stuff like that.
+
+But this is the ringer, omega.
+
+This amplitude ratio
+is expressed in part
+
+in terms of omega.
+
+So what omega-- there's no
+ambiguity as to Ks and Ms,
+
+but what omega?
+
+Well the answer is, when
+we plug in this one,
+
+you get this answer.
+
+When you plug-in this
+one, you get this answer.
+
+So while we're at it-- Sara,
+want to hazard a guess?
+
+How many natural mode
+do you think we've got?
+
+Yeah, exactly.
+
+So you're going to
+have one of these
+
+for each degree of freedom.
+
+Let me just point out a
+couple of elements here,
+
+and then I'll show you a
+demonstration because we
+
+have to have some fun today.
+
+These are point of informations.
+
+They're ratios, not
+absolute magnitudes.
+
+That's number one.
+
+The second is-- I already told
+you, they got the same number.
+
+OK, each natural
+mode is associated
+
+with a particular
+natural frequency.
+
+This one goes with that one.
+
+And once again, they're
+associated with-- yeah,
+
+let me say that.
+
+I need another board.
+
+Let's just go over here.
+
+So in a sense--
+this is decouple.
+
+Decouple essentially into
+independent subsystems.
+
+So in general, what the system's
+response looks like is--
+
+I'm talking about the
+one in front of us here.
+
+This special case, where the
+masses and springs are equal.
+
+I think there's a
+minus sign in here.
+
+Does this come up?
+
+Wonderful.
+
+That's it.
+
+Does everybody see that?
+
+Yes, sir.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: I'm sorry?
+
+AUDIENCE: What does it say
+under that first bullet point?
+
+PROFESSOR: Here?
+
+AUDIENCE: These
+describe the situation.
+
+PROFESSOR: These
+describe the situation
+
+in which the entire
+system is oscillating at.
+
+It's the second bullet here.
+
+Thank you.
+
+AUDIENCE: At what?
+
+PROFESSOR: At one frequency.
+
+Sorry, I'm just getting a
+little tired of writing.
+
+So, any other questions,
+problems, complaints?
+
+All right.
+
+AUDIENCE: I have a question.
+
+PROFESSOR: Yes, sir.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: That's correct.
+
+Then, let's see.
+
+Then there's a
+mistake right here.
+
+Thank you.
+
+Yeah, because that's
+the way it came out.
+
+When you plug omega 2
+having this value into here,
+
+the amplitude ratio
+comes out minus.
+
+Fair enough?
+
+It threw me there for a minute.
+
+I thought you were going to say,
+why is the minus sign is there,
+
+rather than you could have
+had minus 1.618 and plus 1.
+
+And the answer is no reason,
+because these are ratios.
+
+Yeah, Kaitlin?
+
+AUDIENCE: But shouldn't-- when
+we go back and look at what you
+
+wrote down, it's [INAUDIBLE].
+
+I don't understand
+how that [INAUDIBLE].
+
+PROFESSOR: I'm sorry, say again?
+
+AUDIENCE: Never mind.
+
+PROFESSOR: Find it?
+
+Yeah, they're ratios, It's
+just as simple as that.
+
+So you multiply them by any
+number and it still works.
+
+I'll actually show
+you here in a second.
+
+At least, I believe
+that's the case.
+
+We'll just see here in a second.
+
+OK, questions?
+
+Comments?
+
+All right.
+
+Now is the time.
+
+Could I bring up
+the side board here?
+
+Let me show you--
+anybody here taken 2086?
+
+Wonderful.
+
+I've got one person?
+
+Great.
+
+Anyway, I believe in 2086,
+don't they teach you MATLAB?
+
+Isn't that the weapon of choice?
+
+OK, that's the program
+I'm using here, MATLAB.
+
+For those of you who
+haven't seen it yet,
+
+it is definitely a mixed bag.
+
+I don't know how
+you feel about it.
+
+It's very-- yeah--
+it's very powerful.
+
+It stands for Matrix Laboratory.
+
+It was written, I don't
+know, 20, 30 years ago here,
+
+I believe, at MIT by people who
+were into matrices, into matrix
+
+algebra.
+
+And it's kind of
+command line oriented.
+
+The good news,
+it's very powerful.
+
+Whatever you want to do,
+you can do in MATLAB.
+
+The bad news is, the
+user interface stinks.
+
+The language is very
+difficult to learn.
+
+It's even harder to remember.
+
+So with that
+rousing endorsement,
+
+let me show you
+what we've got here.
+
+This is a program I've-- is
+that font readable by you guys?
+
+No?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: I'm sorry?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yes.
+
+Well, I believe I can--
+here we go, fonts.
+
+Upping the fonts is
+kind of a mixed bag,
+
+because you get bigger
+letters but they're.
+
+OK, how's that?
+
+So here's the situation.
+
+This is a MATLAB program.
+
+And I'll explain to you
+what it does as we go.
+
+Let me see if my little
+cursor-- my cursor's here,
+
+but I can't see it.
+
+All right, here's the
+system parameters.
+
+Once again, we're doing
+a simple spring mass--
+
+this simplified spring mass
+system, exactly the one
+
+we've done here.
+
+When I wrote it, you'll see I
+generalized it to do this guy.
+
+So we got M1 and M2, K1 and K2.
+
+But if you'll notice, you see
+here their values are equal.
+
+We've got the mass
+at one kilogram each.
+
+And we've got 10 newtons per
+meter on each of the springs.
+
+Everybody appreciate that
+this system's numbers
+
+that we're putting in here
+match our case here, K over M?
+
+OK.
+
+And you can see
+here, we've defined--
+
+and again, let me
+just say I'm not
+
+trying to sell you on MATLAB.
+
+I don't want to leave
+you with the impression
+
+that we expect you to be
+able to instantly become
+
+a user of MATLAB.
+
+This is simply to illustrate
+the point of the lecture here.
+
+Here is the M,
+the system matrix.
+
+There's the K matrix.
+
+And I'll show you the eigenvalue
+and eigenvector thing later.
+
+But let me-- take
+my word for it.
+
+See this here?
+
+Ode45 is a cryptic allusion
+to the Runge-Kutta algorithm,
+
+fourth order Runge-Kutta that
+is the workhorse for integrating
+
+differential equations.
+
+And so let me just run this.
+
+And what I've got here
+is, here's the point
+
+I wanted you to get
+here, because I'll
+
+bet you can't see
+that cursor either.
+
+Yes, anyway, see
+this right here?
+
+tspan is the time scale and
+the time step, defined up here.
+
+But these are basically
+the initial conditions.
+
+See it here?
+
+X1, X1 dot, X2, X2 dot.
+
+So here's the first one.
+
+This is a 0.618 is for the X1.
+
+And 1 is for X2.
+
+Everybody appreciate that?
+
+Got it?
+
+OK.
+
+If these are the initial
+conditions, what I've done,
+
+I have artfully chosen
+the initial conditions
+
+to have the same ratio.
+
+What do you expect
+is going to happen?
+
+When I turn this thing--
+I've got a simulation here.
+
+I'm going to run this,
+and you're actually
+
+going to see it.
+
+What do you think
+you're going to see?
+
+It's a two spring,
+two mass system.
+
+What I've done is I've
+displaced the two masses.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: They'll certainly
+have an amplitude, because I'm
+
+putting it in there.
+
+That's the initial condition.
+
+The question is, what frequency
+you think they'll oscillate at?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Pardon?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Each of
+them will oscillate
+
+with the same frequency,
+for sure, but what
+
+do you think it's going to be?
+
+AUDIENCE: That one.
+
+PROFESSOR: It's
+going to be that one.
+
+So off we go.
+
+So let us hope that yours
+truly's program worked.
+
+Here we go.
+
+Oh, look at that.
+
+[INAUDIBLE], please
+interpret that for me.
+
+What do you see there?
+
+Hang on a second.
+
+Let me blow it up
+so you can see it.
+
+Ooh, isn't that pretty?
+
+And I believe the blue is
+X1 and the green is X2.
+
+See?
+
+Everybody agree?
+
+Everyone appreciate
+what's going on?
+
+You pull them both at
+slightly different--
+
+you basically used
+the first natural mode
+
+as the initial condition.
+
+And sure enough, they
+oscillate together.
+
+They oscillate at
+the same frequency.
+
+They oscillate at
+that frequency.
+
+Let me just see--
+I just want to make
+
+sure we get the full
+value out of this thing.
+
+Well, of course you
+can't see it anymore
+
+because our numbers are so big.
+
+Well, that's great.
+
+Anyway, take my word for
+it at-- oh, here it is.
+
+The period for the first
+natural frequency-- or I
+
+guess it's the second--
+it should be like 1.2.
+
+Or is it 3?
+
+Yeah, I'm sorry,
+the period is 3.2.
+
+And sure enough, there it is.
+
+It's about 3.
+
+3.2.
+
+Fabulous.
+
+Everybody got it?
+
+OK, now watch closely.
+
+Let me see if I can do this.
+
+This requires a little
+dexterity, which
+
+is always a short supply here.
+
+I have to hit this and this.
+
+Make sense?
+
+That's what it
+actually looks like.
+
+They're both oscillating at
+the same natural frequency,
+
+going up and down together.
+
+But they have
+different amplitudes.
+
+So one's bigger than the other.
+
+So that's what it looks like.
+
+Questions?
+
+Christina, you good?
+
+Clear enough?
+
+Wonderful.
+
+So let's go to our program.
+
+And instead of that set
+of initial conditions,
+
+we'll do the other.
+
+Read them to us here.
+
+What are the initial
+conditions here?
+
+AUDIENCE: It's 1.618.
+
+PROFESSOR: That's
+right, it's this guy.
+
+AUDIENCE: That guy.
+
+PROFESSOR: It's this guy.
+
+It's this ratio.
+
+So I basically
+arbitrarily chose, is it
+
+the negative first?
+
+No.
+
+I chose that one
+over there, 1.618.
+
+And then a minus 1
+for the second one.
+
+Fair enough?
+
+OK, there it goes.
+
+We've got to save it
+and make sure we got it.
+
+So again, you got a clue
+what's going to happen here?
+
+Here we go.
+
+Boom.
+
+Look at that.
+
+What's going on there?
+
+Yikes.
+
+Explain me.
+
+Is that good, bad, indifferent?
+
+Is it right?
+
+Wrong?
+
+AUDIENCE: The way
+the system acts,
+
+it has a higher frequency.
+
+PROFESSOR: Yeah, exactly.
+
+Two things.
+
+One is, they're out of phase.
+
+They're doing this.
+
+One's going this
+way, and the other's
+
+going the other at
+different amplitudes
+
+but the same frequency.
+
+But the frequency in question
+is higher than the previous.
+
+AUDIENCE: Why are
+they out of phase?
+
+PROFESSOR: I'm sorry?
+
+AUDIENCE: Why are they
+opposite of each other?
+
+PROFESSOR: [INAUDIBLE], why
+are they opposite each other?
+
+Because we made them that way.
+
+We said, that's the
+initial condition.
+
+Does that make sense?
+
+That minus sign does.
+
+One starts out,
+and one starts in.
+
+And they do that.
+
+Clear enough?
+
+Now what's going to happen
+if we plain just choose
+
+any old initial condition?
+
+These were special.
+
+We worked like a dog
+to compute these,
+
+so that the system would
+decouple in that way.
+
+So what if we-- now
+let me put that back.
+
+Now look at this one.
+
+All right, look at that.
+
+Read that to me.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah.
+
+So that says the initial
+condition for the first mass
+
+is 1 and whatever that is.
+
+One whatever that is.
+
+The second masses'
+initial condition is half
+
+that in the same direction.
+
+Both positive.
+
+So Christina, they're
+going to go together.
+
+But [INAUDIBLE],
+at what frequency?
+
+Any idea what it's
+going to look like?
+
+If you do, you're a
+better man than I,
+
+because what you're going
+to see here is that.
+
+It's this thing right here.
+
+It's that expression
+right there.
+
+And here's what it looks like.
+
+Did I stop the--
+oh, wait a minute.
+
+Did I ever show you that before?
+
+I think I forgot to
+show you the other.
+
+Anyway, not to worry.
+
+Hang on a second.
+
+I've got to stop this guy.
+
+First I have to find my finger.
+
+There it goes.
+
+That's the previous case.
+
+When they're out of phase,
+different magnitudes,
+
+going in opposite directions.
+
+And you can see, they're
+going at a higher frequency
+
+than before.
+
+Make sense?
+
+So now we are-- just to
+refresh your memory--
+
+now we're going for the
+third case, in which there's
+
+nothing special.
+
+We just picked a couple
+of initial conditions
+
+out of a hat.
+
+And here we go.
+
+Oops, I think not.
+
+I think that's
+the previous case.
+
+So let's go here.
+
+This is another wonderful
+thing about MATLAB
+
+is nothing happens
+until you save it.
+
+So we were just running
+the previous case.
+
+Nasty.
+
+Look at this.
+
+All right, can
+everybody see that?
+
+If you can interpret this,
+you're smarter than I am.
+
+But what this is, this is simply
+this expression over here.
+
+It's this expression
+for just some arbitrary
+
+initial condition.
+
+Do you see that that
+behavior though?
+
+Each of them, they're
+going together kind of,
+
+but they-- anyway, watch this.
+
+Here's what the simulation
+of that looks like.
+
+What the heck is that?
+
+Well anyway, the
+point of the story
+
+is that multiple
+degrees of freedom
+
+system in general's response
+can be arbitrarily complicated.
+
+It's not arbitrarily
+complicated,
+
+but pretty complicated.
+
+You'll get, in general if it's
+an nth order system, if you
+
+don't know anything
+about the worst case,
+
+you'll see four
+frequencies in there.
+
+And they're all mixed together
+in some mystical way that's
+
+unknown to you.
+
+Fair enough?
+
+And it's only when you reach the
+natural modes that you actually
+
+find out what is going on here.
+
+Well now I have to turn
+your attention to this guy.
+
+This is made by Professor
+Vandiver's machinist,
+
+a perfect example of
+a second order system.
+
+And I bring it to
+your attention here
+
+for two-- at the end of the
+day what we're going to do
+
+is I'm going to demonstrate
+exactly what I just
+
+did for the textbook
+case, the textbook system.
+
+I want to demonstrate exactly
+the same thing for this guy,
+
+only this is a real system.
+
+Very nice.
+
+We have a steel rod.
+
+It must be a half
+inch in diameter.
+
+The whole thing
+weighs several pounds.
+
+These sliding masses are right
+circular cylinders with a hole
+
+drilled through them.
+
+It's ever so slightly
+larger than these here.
+
+They're of different lengths.
+
+They're made of brass.
+
+They're serious masses.
+
+And the springs,
+which extend from here
+
+to here, and from here to
+here are wound on a lathe,
+
+and attached, and so forth.
+
+Pretty, no?
+
+Now look right off the bat.
+
+Did you see how
+that thing operates?
+
+Would you agree you have some
+complicated behavior here?
+
+Now also would you agree
+that this is it like that?
+
+Everybody see that?
+
+Before we go too far, this
+is a mixed message here.
+
+[INAUDIBLE], is this
+exactly like that?
+
+In what way is it
+similar to that?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Well, what is clear
+is that you've got two springs
+
+and you've got two masses.
+
+About that there is
+very little argument.
+
+AUDIENCE: It's damped.
+
+PROFESSOR: It's damped.
+
+Can everybody see that?
+
+How does [INAUDIBLE]
+know that it's damped?
+
+How's he know it's damped?
+
+I mean, that's just a wild
+guess on his part, but.
+
+AUDIENCE: You can hear
+it, and it slows down.
+
+And it slows down.
+
+This is the most important
+part is that it stops.
+
+Eventually if you come back
+in a minute or two, it's done.
+
+PROFESSOR: All
+right, [INAUDIBLE].
+
+You're on a roll.
+
+There's definitely
+damping there.
+
+What kind of damping?
+
+AUDIENCE: Friction.
+
+PROFESSOR: Friction, yeah.
+
+Does that have another
+name that you can think of?
+
+It's definitely friction.
+
+What it's not is
+viscous friction.
+
+What it is not is a damper or
+a dashpot which we've shown you
+
+before with the ideal expression
+that generate a force that
+
+opposes the-- generation of an
+opposing force that's linearly
+
+proportional to the velocity.
+
+What's going on
+here, do you think?
+
+What kind of damping
+do you think?
+
+It's called Coulomb.
+
+This is called Coulomb damping.
+
+And this is a digression.
+
+Now we're on the part where this
+is really-- everything that's
+
+on the board is what I
+wanted you to really come
+
+away from today with.
+
+So now we're out
+kind of in the, I
+
+would call it the
+winging it area
+
+right here, because this
+is the part where I simply
+
+had fun with the demo.
+
+This is viscous.
+
+And this has got the
+symbol-- well anyway,
+
+this is what it looks like.
+
+And this is the
+force of the damper.
+
+We'll call it B.
+
+And this is the velocity.
+
+And this is for constant
+of proportionality B.
+
+And it has this little
+symbol, like that.
+
+And when equations of motion
+are solved that contain that,
+
+the response looks like this.
+
+What we're talking about
+here, the force put out
+
+is a constant.
+
+That just comes
+from the sliding.
+
+And what it generates are
+distinctly non-linear equations
+
+of motion.
+
+And what you get here is you
+get this kind of behavior.
+
+If you really looked
+at it, what you'll see
+
+is there's definitely
+damping for large motions
+
+when the inertial forces and
+so forth are large compared
+
+to the friction forces.
+
+It'll look a lot like
+conventional viscous damping.
+
+It's just that when
+motions get really small,
+
+and the forces get down there
+to on the order of this,
+
+all a sudden you'll see on
+one cycle it'll just stop.
+
+And were you up here
+where you could see,
+
+or if we had a closeup of this--
+you can't see it, but just
+
+watch this thing stop.
+
+Right there.
+
+Do you see that?
+
+That's a little hard for you
+to see from there, but watch.
+
+Anyway, were you up
+here, you'd see this.
+
+That's what we're looking at.
+
+Well here we go.
+
+I need some help here.
+
+Who's in a volunteering
+frame of mind?
+
+Amy, all right.
+
+I appreciate the help here.
+
+Here's what I want to do.
+
+We just blew out some
+wonderful theory.
+
+All this is just
+solid as a rock.
+
+Yes, sir.
+
+AUDIENCE: For the Coulomb
+friction, is that a linear
+
+[INAUDIBLE]?
+
+Or is it still exponential?
+
+PROFESSOR: I'm sorry?
+
+Oh, no.
+
+If I'm not mistaken, I
+didn't really look this up,
+
+but I believe it's linear.
+
+I'd have to-- take that
+with a grain of salt,
+
+but I believe it's linear.
+
+Yes, Amy, here's the situation.
+
+We have all this
+marvelous theory.
+
+My goal is to-- and we have this
+fabulous demo apparatus, though
+
+inherited.
+
+And what I'd like to do-- oh,
+and we have computational means
+
+to.
+
+And in fact, we just went
+through the exercise.
+
+We already know those
+same equations that
+
+work for this work for this.
+
+Those are general.
+
+However, it's not my
+piece of apparatus.
+
+And well, here's the deal,
+what are the Ms and Ks.
+
+What are the values of-- I need
+M1, K1, M2, K2 to put into the.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, Yeah.
+
+That's what I'd like
+to do is I'd like to.
+
+AUDIENCE: Do I have
+to just determine
+
+the it by looking at it?
+
+PROFESSOR: Oh no, no, no.
+
+No, no.
+
+AUDIENCE: I'm not that good.
+
+PROFESSOR: You're my assistant.
+
+I guess the question
+is, how would
+
+you-- and I've got
+to tell you, that's
+
+the math part of a program.
+
+Now we're in the engineering
+part of the program,
+
+because somebody gave you
+a real live demo apparatus.
+
+Works like crazy, or appears to.
+
+And I'd love to take
+advantage of it,
+
+but I don't know
+any of the numbers.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: No.
+
+That's the constraint
+I'm operating on.
+
+It doesn't belong to me.
+
+I mean, I could take it apart.
+
+That's an absolutely
+appropriate thing to do.
+
+I would have liked to.
+
+It would be easier if you could.
+
+You just go, take a
+screwdriver to it.
+
+Here, put this on there
+and pull this out.
+
+I didn't have the luxury
+of any of that, so what's
+
+your next best suggestion?
+
+Nice suggestion, but no cigar.
+
+I'm sorry?
+
+AUDIENCE: Take it apart
+anyway, put it back together
+
+before the person notices.
+
+PROFESSOR: Well yeah.
+
+Yeah, no.
+
+That's fudging.
+
+Yeah, they notice.
+
+Have you ever taken
+apart anything made
+
+in modern manufacturing method?
+
+Oh, it's good because you
+can't put them back together.
+
+They're assembled by machine.
+
+And once upon a time you
+could disassemble one
+
+and reassemble things
+without detection.
+
+But anymore, once
+you take them apart,
+
+it's wicked hard to
+get them back together.
+
+OK, the floor is open.
+
+I need another suggestion.
+
+What are you going to do?
+
+AUDIENCE: Do you need to
+know the exact K and M,
+
+or do you just
+[INAUDIBLE] another ratio?
+
+PROFESSOR: I thought
+you were going
+
+to-- I need to know M or
+K. I need to know them all.
+
+AUDIENCE: Do you know
+the density of the--
+
+PROFESSOR: I was going
+to say, but I don't
+
+need to know anything exactly.
+
+All I need to know is as good a
+guess as you can come up with.
+
+It's all an estimate.
+
+AUDIENCE: If you know the
+density of the material,
+
+you can easily work
+up [INAUDIBLE].
+
+I'm assuming you're
+about [INAUDIBLE].
+
+PROFESSOR: Oh
+absolutely, absolutely.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Wonderful.
+
+Absolutely.
+
+She hit the jackpot,
+rang the magic buzzer.
+
+That's exactly what I did.
+
+Here's a little crummy sketch.
+
+Oh wait, you can't see that.
+
+Anyway, these are right circular
+cylinders with holes in them.
+
+And they've got
+measurements beside them.
+
+I can tell you, this
+is 75 millimeters.
+
+This is 35 millimeters.
+
+This one is 37 millimeters long.
+
+So I did that.
+
+That's great.
+
+That's an excellent suggestion.
+
+And after I did exactly that,
+I won't write out the formula.
+
+You know area, and
+volume, and all of that.
+
+Let me get you the
+right order here.
+
+M1 is 0.2929, and M2 is 0.5938.
+
+Everybody got that?
+
+This was obtained by taking
+a ruler to these things,
+
+taking diameters, lengths,
+and diameters of holes,
+
+multiply them times the density
+of brass taken out of the book.
+
+Do you believe that?
+
+Do you believe that number?
+
+Well, you're a trusting soul.
+
+I don't.
+
+To me, I believe that number.
+
+This was done with a ruler.
+
+The little millimeter thingies.
+
+So I just say, don't fall in
+the trap of false precision.
+
+OK Amy, you're on a roll.
+
+We've got the masses.
+
+What now?
+
+AUDIENCE: Free body diagram.
+
+PROFESSOR: Yeah,
+we got all that.
+
+AUDIENCE: Yeah, you've got that.
+
+But then what you can
+do for the spring,
+
+the forces of the
+spring when static.
+
+Don't move it.
+
+So take the top mast.
+
+It's not moving,
+which means that you
+
+know that the force going
+upwards-- which is the spring--
+
+is equal to the force going
+downward, which is [INAUDIBLE].
+
+So you can measure
+the displacement
+
+from the start of the spring
+to the bottom of the spring.
+
+Do you know the natural
+length of the spring?
+
+PROFESSOR: No Anyway,
+what I was going to say
+
+is, excellent idea.
+
+Can't do it.
+
+But what Amy was
+basically saying is,
+
+you know the masses now.
+
+Why not simply take
+from that expression
+
+right there, MH over K, right?
+
+What's the problem with that?
+
+How about it?
+
+Devin, how come I can't do that?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, I really don't
+know the no load position.
+
+Is that it, Amy?
+
+Right there?
+
+Maybe.
+
+Devin, you're the one
+that suggested it.
+
+Are those the no load
+positions of the masses?
+
+And if not, why not?
+
+I did mean to give
+you a clue there.
+
+Yeah, Nick?
+
+AUDIENCE: It can't be because
+there's static friction.
+
+PROFESSOR: Exactly.
+
+So Nick, you brought it up.
+
+What's that number?
+
+You don't know that either.
+
+No.
+
+Like I said, Amy, nice idea.
+
+No cigar.
+
+What else?
+
+We're running out of time?
+
+Here we go, Douglas.
+
+AUDIENCE: Could you
+displace each mast a certain
+
+[INAUDIBLE], and
+then measure the time
+
+it takes for them to stop
+and get the damping ratio?
+
+PROFESSOR: Hit
+the damping ratio.
+
+Well, I'll tell you what--
+you want to say that again?
+
+He said displace one or
+both count oscillations
+
+and get the damping ratio.
+
+Nick?
+
+AUDIENCE: Do we have anything
+like a force gauge or a spring
+
+scale?
+
+PROFESSOR: No.
+
+This is my living room
+I'm talking-- or my study.
+
+Anyway, Douglas said-- I
+forgot what you said now.
+
+He said-- oh, I know.
+
+You said, displace it and
+count the oscillations.
+
+Get the damping ratio.
+
+First off, the damping ratio is
+no help, even if we did get it.
+
+And the only formula for
+which we've ever given you--
+
+the only formula
+we've ever given
+
+you to do that with pertains
+to this kind of friction, which
+
+is not present.
+
+No cigar.
+
+Nick says, how
+about force gauge?
+
+Now, don't have it.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, we are.
+
+AUDIENCE: [INAUDIBLE]
+displace the other one
+
+and then find the frequency.
+
+PROFESSOR: Oh, what's your name?
+
+Sean?
+
+Or John?
+
+AUDIENCE: Sean.
+
+PROFESSOR: Say that out loud.
+
+Say it loud enough that
+Devin can hear you.
+
+AUDIENCE: You hold
+the first mass,
+
+and then you displace
+the second one.
+
+PROFESSOR: Hang on.
+
+He says, hold the first mass
+like this set screw right here.
+
+And?
+
+AUDIENCE: And then displace
+the other one then.
+
+PROFESSOR: Like that?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Actually,
+to answer your question
+
+Nick, the only instrument
+I have is a clock.
+
+Hang on a second.
+
+Here it is.
+
+Of course, this is the
+big task is finding it.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Count to 10,
+remember like Vandiver told you.
+
+Skip 1, 1, 2, 3, count to 10.
+
+Stop.
+
+Excellent, excellent, excellent.
+
+When you do that,
+that's the second one.
+
+I did that and right
+here, right here it's TP.
+
+The period of 10 of them--
+and then I divide to get 1--
+
+is 0.83 seconds.
+
+What does that tell you, Sean?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Well
+actually, these two--
+
+you can get the frequency.
+
+But what this does, because
+this gives you the frequency,
+
+you know in general
+that-- in particular, you
+
+know that this second natural
+frequency, which is just
+
+associated with this single
+spring and a mass here.
+
+It's just this guy.
+
+It's not both of them.
+
+Anyway, this turns out
+to-- I didn't graph that.
+
+That's square root of
+K over M. Trust me,
+
+you can put those two
+together, and you get
+
+K2 is equal to-- newton meters.
+
+This is exactly what you said.
+
+Freeze the first mass.
+
+Displace the second.
+
+Measure the period.
+
+You get the natural frequency
+for basically K2 over M2.
+
+So you got K2 out of it.
+
+Yeah, Douglas?
+
+AUDIENCE: So how come it gives
+you just the natural frequency
+
+and a damp natural frequency?
+
+PROFESSOR: Oh no.
+
+It absolutely is.
+
+It's all damped, no
+question about it.
+
+But again, what
+we're doing is we're
+
+going close enough, right?
+
+Because I have nothing.
+
+So even the damped
+natural frequency
+
+is better than nothing.
+
+All right, so Amy back to you.
+
+You're back in business.
+
+What now?
+
+So now we've got M2 and K2.
+
+AUDIENCE: You just need K1.
+
+PROFESSOR: Yeah.
+
+Now we need K1.
+
+What do we do now?
+
+AUDIENCE: We want to do
+the same thing that we just
+
+did for K2. [INAUDIBLE].
+
+PROFESSOR: Exactly.
+
+Well, not quite.
+
+Let's see, now I'm going
+to turn loose-- now we're
+
+back to our original system.
+
+It doesn't hurt anything.
+
+It's just ugly to look at.
+
+Now what?
+
+Sean, do that trick again.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Push this one up?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: I don't think so.
+
+Yeah, Nick.
+
+AUDIENCE: So just
+fix the second mass.
+
+PROFESSOR: Fix the second mass.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah, you
+see this frequency here?
+
+I'm going to overrule Chandler.
+
+I'm going to say, this is the
+natural frequency of that's
+
+mass and these two springs.
+
+Do that same trick again.
+
+You get the equivalent
+spring rate,
+
+subtract the second from it,
+and you get the other one.
+
+Devin, is that what
+you were going to say?
+
+Wonderful.
+
+That is exactly what I did.
+
+And you get out
+of it, you get K1
+
+is equal to 50.45
+newton per meter.
+
+In the interest of time, I'm
+going to short circuit this.
+
+I took exactly
+these parameters, I
+
+put them into that same
+computer program we had before,
+
+and what came out-- I have
+to have a place to put it.
+
+Ah, wonderful.
+
+And now I have to find it.
+
+Here we go.
+
+Here are the two modes.
+
+Actually, let me
+put it right here.
+
+For this system, because
+here's the first one.
+
+And here's the second one.
+
+0.9760 and minus 0.2177.
+
+Everybody appreciate that?
+
+This is by the same
+computational procedure
+
+we spoke of earlier.
+
+And sparing no expense,
+we have here a, made fresh
+
+from my basement, a custom
+made initial condition setting
+
+device, which I can hopefully
+avoid killing myself with.
+
+OK here's what we have.
+
+So I guess I didn't
+show you this first.
+
+If you can see it,
+what we have marked
+
+is the reference position.
+
+That's the rest position
+that we couldn't
+
+find by laying it down.
+
+Or excuse me, this is the
+static equilibrium position
+
+of mass number one,
+static equilibrium
+
+position of mass number two.
+
+Mode one or there.
+
+What they said over there, 0.4.
+
+And .97 is down here.
+
+Mode two is over here.
+
+So Devin, while I'm
+doing this, tell me
+
+how am I going to
+know if this is right
+
+or if this is all just bogus?
+
+What observable's going to
+tell me that I got it right?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: I'm sorry, speak up.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: How about it, Nick?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Exactly.
+
+And you ought to be able to
+see it from where you are.
+
+Can you appreciate that
+they're not at the moment?
+
+All right, now hang on.
+
+Here comes mode number one.
+
+This takes two hands to do it.
+
+All right, you ready?
+
+This is mode number one.
+
+Again, it's a those numbers.
+
+How about it?
+
+Can you see it?
+
+Very good.
+
+How about the other?
+
+And so here, this is number two.
+
+And this is a little
+more complicated,
+
+because the other one has
+to be done from the bottom.
+
+Hang on a second.
+
+Now this one we're doing
+is we're deflecting--
+
+this one is positive downward.
+
+So X1 is down, but
+X2 is negative.
+
+So it's displaced upward a bit.
+
+Are you ready?
+
+Nick, what do you
+expect to see this time?
+
+AUDIENCE: The frequency
+should be higher
+
+and they'll move in
+opposite directions.
+
+PROFESSOR: That's the key.
+
+Once again, they're going to
+move with the same frequency,
+
+albeit in different directions.
+
+But that new frequency is
+going to be higher than before.
+
+And sure enough, stand back.
+
+So there you go.
+
+What did that tell us?
+
+That told us that
+the first order
+
+we got the system parameters
+identified correctly
+
+and the theory holds up.
+
+Questions?
+
+Comments?
+
+Complaints?
+
+Devin?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: I'm sorry?
+
+AUDIENCE: What was the
+second set of conditions?
+
+PROFESSOR: The second
+set of initial conditions
+
+were right here.
+
+This is the second mode,
+X1, 0.97, X2, minus 0.2.
+
+OK, have a great
+Thanksgiving holiday.
\ No newline at end of file
diff --git a/9JhX_UNcQvE.txt b/9JhX_UNcQvE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5f3ad183d8a87ed2786ff9886dad3d14cfe6414e
--- /dev/null
+++ b/9JhX_UNcQvE.txt
@@ -0,0 +1,2603 @@
+align:start position:0%
+ 
+okay the generate perturbation theory
+
+ align:start position:0%
+okay the generate perturbation theory
+ 
+
+ align:start position:0%
+okay the generate perturbation theory
+okay we've done nicely our non
+
+ align:start position:0%
+okay we've done nicely our non
+ 
+
+ align:start position:0%
+okay we've done nicely our non
+degenerate case so we'll get none
+
+ align:start position:0%
+degenerate case so we'll get none
+ 
+
+ align:start position:0%
+degenerate case so we'll get none
+degenerate
+
+ align:start position:0%
+degenerate
+ 
+
+ align:start position:0%
+degenerate
+degenerate done in a very clear way I
+
+ align:start position:0%
+degenerate done in a very clear way I
+ 
+
+ align:start position:0%
+degenerate done in a very clear way I
+think so the first thing I want to say
+
+ align:start position:0%
+think so the first thing I want to say
+ 
+
+ align:start position:0%
+think so the first thing I want to say
+about the generate perturbation theories
+
+ align:start position:0%
+about the generate perturbation theories
+ 
+
+ align:start position:0%
+about the generate perturbation theories
+when it fails and why it fails and what
+
+ align:start position:0%
+when it fails and why it fails and what
+ 
+
+ align:start position:0%
+when it fails and why it fails and what
+goes wrong so so the generate
+
+ align:start position:0%
+goes wrong so so the generate
+ 
+
+ align:start position:0%
+goes wrong so so the generate
+perturbation theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trivial example to begin with why not H
+
+ align:start position:0%
+trivial example to begin with why not H
+ 
+
+ align:start position:0%
+trivial example to begin with why not H
+of lambda again is equal to H 0 plus
+
+ align:start position:0%
+of lambda again is equal to H 0 plus
+ 
+
+ align:start position:0%
+of lambda again is equal to H 0 plus
+lambda Delta H and for H 0 will take
+
+ align:start position:0%
+lambda Delta H and for H 0 will take
+ 
+
+ align:start position:0%
+lambda Delta H and for H 0 will take
+original Hamiltonian with energies 1 and
+
+ align:start position:0%
+original Hamiltonian with energies 1 and
+ 
+
+ align:start position:0%
+original Hamiltonian with energies 1 and
+1 and for Delta H I'll take off diagonal
+
+ align:start position:0%
+1 and for Delta H I'll take off diagonal
+ 
+
+ align:start position:0%
+1 and for Delta H I'll take off diagonal
+Hamiltonian a poly matrix and that's our
+
+ align:start position:0%
+Hamiltonian a poly matrix and that's our
+ 
+
+ align:start position:0%
+Hamiltonian a poly matrix and that's our
+Delta H and we say ok blindly not
+
+ align:start position:0%
+Delta H and we say ok blindly not
+ 
+
+ align:start position:0%
+Delta H and we say ok blindly not
+worried about this degeneracy and use
+
+ align:start position:0%
+worried about this degeneracy and use
+ 
+
+ align:start position:0%
+worried about this degeneracy and use
+the formulas that we had for non
+
+ align:start position:0%
+the formulas that we had for non
+ 
+
+ align:start position:0%
+the formulas that we had for non
+degenerate States and we would say well
+
+ align:start position:0%
+degenerate States and we would say well
+ 
+
+ align:start position:0%
+degenerate States and we would say well
+for the first date and the second state
+
+ align:start position:0%
+for the first date and the second state
+ 
+
+ align:start position:0%
+for the first date and the second state
+what do we have
+
+ align:start position:0%
+what do we have
+ 
+
+ align:start position:0%
+what do we have
+e I'll call them 1 and 2 not 0 and 1 so
+
+ align:start position:0%
+e I'll call them 1 and 2 not 0 and 1 so
+ 
+
+ align:start position:0%
+e I'll call them 1 and 2 not 0 and 1 so
+let's call them 1 of lambda will be
+
+ align:start position:0%
+let's call them 1 of lambda will be
+ 
+
+ align:start position:0%
+let's call them 1 of lambda will be
+equal to the first value 1 plus if the
+
+ align:start position:0%
+equal to the first value 1 plus if the
+ 
+
+ align:start position:0%
+equal to the first value 1 plus if the
+formula is Right Delta H times lambda 1
+
+ align:start position:0%
+formula is Right Delta H times lambda 1
+ 
+
+ align:start position:0%
+formula is Right Delta H times lambda 1
+1 the matrix element of the perturbation
+
+ align:start position:0%
+1 the matrix element of the perturbation
+ 
+
+ align:start position:0%
+1 the matrix element of the perturbation
+in the 1 1 state similarly e to the
+
+ align:start position:0%
+in the 1 1 state similarly e to the
+ 
+
+ align:start position:0%
+in the 1 1 state similarly e to the
+other eigenvalue should be 1 because the
+
+ align:start position:0%
+other eigenvalue should be 1 because the
+ 
+
+ align:start position:0%
+other eigenvalue should be 1 because the
+second eigenvalue plus lambda delta h 2
+
+ align:start position:0%
+second eigenvalue plus lambda delta h 2
+ 
+
+ align:start position:0%
+second eigenvalue plus lambda delta h 2
+2 that's what the formula would say but
+
+ align:start position:0%
+2 that's what the formula would say but
+ 
+
+ align:start position:0%
+2 that's what the formula would say but
+this is completely incorrect why because
+
+ align:start position:0%
+this is completely incorrect why because
+ 
+
+ align:start position:0%
+this is completely incorrect why because
+Delta H 1 1 is the 1 1 element of Delta
+
+ align:start position:0%
+Delta H 1 1 is the 1 1 element of Delta
+ 
+
+ align:start position:0%
+Delta H 1 1 is the 1 1 element of Delta
+H and it's 0 and the 2 2 element of
+
+ align:start position:0%
+H and it's 0 and the 2 2 element of
+ 
+
+ align:start position:0%
+H and it's 0 and the 2 2 element of
+Delta H is all
+
+ align:start position:0%
+Delta H is all
+ 
+
+ align:start position:0%
+Delta H is all
+zero and therefore this says one and one
+
+ align:start position:0%
+zero and therefore this says one and one
+ 
+
+ align:start position:0%
+zero and therefore this says one and one
+that the eigenvalues haven't changed on
+
+ align:start position:0%
+that the eigenvalues haven't changed on
+ 
+
+ align:start position:0%
+that the eigenvalues haven't changed on
+the other hand we know that the matrix
+
+ align:start position:0%
+the other hand we know that the matrix
+ 
+
+ align:start position:0%
+the other hand we know that the matrix
+the total matrix which is one lambda
+
+ align:start position:0%
+the total matrix which is one lambda
+ 
+
+ align:start position:0%
+the total matrix which is one lambda
+lambda 1 has eigenvectors 1 over square
+
+ align:start position:0%
+lambda 1 has eigenvectors 1 over square
+ 
+
+ align:start position:0%
+lambda 1 has eigenvectors 1 over square
+root of 2 1 1 and 1 over square root of
+
+ align:start position:0%
+root of 2 1 1 and 1 over square root of
+ 
+
+ align:start position:0%
+root of 2 1 1 and 1 over square root of
+2 1 minus 1 with eigenvalues this is our
+
+ align:start position:0%
+2 1 minus 1 with eigenvalues this is our
+ 
+
+ align:start position:0%
+2 1 minus 1 with eigenvalues this is our
+eigenvectors and eigenvalues 1 plus
+
+ align:start position:0%
+eigenvectors and eigenvalues 1 plus
+ 
+
+ align:start position:0%
+eigenvectors and eigenvalues 1 plus
+lambda and 1 minus lambda so the
+
+ align:start position:0%
+lambda and 1 minus lambda so the
+ 
+
+ align:start position:0%
+lambda and 1 minus lambda so the
+eigenvalues of the matrix are 1 plus
+
+ align:start position:0%
+eigenvalues of the matrix are 1 plus
+ 
+
+ align:start position:0%
+eigenvalues of the matrix are 1 plus
+lambda 1 minus lambda and this formula
+
+ align:start position:0%
+lambda 1 minus lambda and this formula
+ 
+
+ align:start position:0%
+lambda 1 minus lambda and this formula
+to first order in lambda gave us nothing
+
+ align:start position:0%
+to first order in lambda gave us nothing
+ 
+
+ align:start position:0%
+to first order in lambda gave us nothing
+it failed badly it's a disaster so you
+
+ align:start position:0%
+it failed badly it's a disaster so you
+ 
+
+ align:start position:0%
+it failed badly it's a disaster so you
+can say well what what happened and
+
+ align:start position:0%
+can say well what what happened and
+ 
+
+ align:start position:0%
+can say well what what happened and
+maybe a clue is on the fact of the
+
+ align:start position:0%
+maybe a clue is on the fact of the
+ 
+
+ align:start position:0%
+maybe a clue is on the fact of the
+eigenvectors eigenvectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are the eigenvectors of the total
+
+ align:start position:0%
+these are the eigenvectors of the total
+ 
+
+ align:start position:0%
+these are the eigenvectors of the total
+matrix these are in fact also the
+
+ align:start position:0%
+matrix these are in fact also the
+ 
+
+ align:start position:0%
+matrix these are in fact also the
+eigenvectors of the perturbation on the
+
+ align:start position:0%
+eigenvectors of the perturbation on the
+ 
+
+ align:start position:0%
+eigenvectors of the perturbation on the
+other hand when we said okay this is the
+
+ align:start position:0%
+other hand when we said okay this is the
+ 
+
+ align:start position:0%
+other hand when we said okay this is the
+first state the first eigenvector we
+
+ align:start position:0%
+first state the first eigenvector we
+ 
+
+ align:start position:0%
+first state the first eigenvector we
+thought of it as 1 0 and the hamiltonian
+
+ align:start position:0%
+thought of it as 1 0 and the hamiltonian
+ 
+
+ align:start position:0%
+thought of it as 1 0 and the hamiltonian
+on that eigenvector gave you the energy
+
+ align:start position:0%
+on that eigenvector gave you the energy
+ 
+
+ align:start position:0%
+on that eigenvector gave you the energy
+1 the second energy corresponds to the
+
+ align:start position:0%
+1 the second energy corresponds to the
+ 
+
+ align:start position:0%
+1 the second energy corresponds to the
+eigen vector 0 1 that's what we usually
+
+ align:start position:0%
+eigen vector 0 1 that's what we usually
+ 
+
+ align:start position:0%
+eigen vector 0 1 that's what we usually
+use for our matrices so here is the
+
+ align:start position:0%
+use for our matrices so here is the
+ 
+
+ align:start position:0%
+use for our matrices so here is the
+strange thing that seems to have
+
+ align:start position:0%
+strange thing that seems to have
+ 
+
+ align:start position:0%
+strange thing that seems to have
+happened for the original Hamiltonian
+
+ align:start position:0%
+happened for the original Hamiltonian
+ 
+
+ align:start position:0%
+happened for the original Hamiltonian
+did I ever a matrix we had this
+
+ align:start position:0%
+did I ever a matrix we had this
+ 
+
+ align:start position:0%
+did I ever a matrix we had this
+eigenvector and this eigenvector and
+
+ align:start position:0%
+eigenvector and this eigenvector and
+ 
+
+ align:start position:0%
+eigenvector and this eigenvector and
+then suddenly
+
+ align:start position:0%
+then suddenly
+ 
+
+ align:start position:0%
+then suddenly
+you turn on the perturbation and lambda
+
+ align:start position:0%
+you turn on the perturbation and lambda
+ 
+
+ align:start position:0%
+you turn on the perturbation and lambda
+can be 10 to the minus a thousand and
+
+ align:start position:0%
+can be 10 to the minus a thousand and
+ 
+
+ align:start position:0%
+can be 10 to the minus a thousand and
+already the eigenvectors jump and become
+
+ align:start position:0%
+already the eigenvectors jump and become
+ 
+
+ align:start position:0%
+already the eigenvectors jump and become
+this ones we go from this ones to that
+
+ align:start position:0%
+this ones we go from this ones to that
+ 
+
+ align:start position:0%
+this ones we go from this ones to that
+one you just add a perturbation that you
+
+ align:start position:0%
+one you just add a perturbation that you
+ 
+
+ align:start position:0%
+one you just add a perturbation that you
+even kind of measure in the eigenvectors
+
+ align:start position:0%
+even kind of measure in the eigenvectors
+ 
+
+ align:start position:0%
+even kind of measure in the eigenvectors
+change that's crazy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the explanation is this thing that we
+
+ align:start position:0%
+the explanation is this thing that we
+ 
+
+ align:start position:0%
+the explanation is this thing that we
+usually sometimes forget to say in a
+
+ align:start position:0%
+usually sometimes forget to say in a
+ 
+
+ align:start position:0%
+usually sometimes forget to say in a
+mathematically precise way these are not
+
+ align:start position:0%
+mathematically precise way these are not
+ 
+
+ align:start position:0%
+mathematically precise way these are not
+the eigenvectors of the original matrix
+
+ align:start position:0%
+the eigenvectors of the original matrix
+ 
+
+ align:start position:0%
+the eigenvectors of the original matrix
+since the original matrix is degenerate
+
+ align:start position:0%
+since the original matrix is degenerate
+ 
+
+ align:start position:0%
+since the original matrix is degenerate
+this is one possible choice of
+
+ align:start position:0%
+this is one possible choice of
+ 
+
+ align:start position:0%
+this is one possible choice of
+eigenvectors any linear combination of
+
+ align:start position:0%
+eigenvectors any linear combination of
+ 
+
+ align:start position:0%
+eigenvectors any linear combination of
+them is an eigenvector so this space of
+
+ align:start position:0%
+them is an eigenvector so this space of
+ 
+
+ align:start position:0%
+them is an eigenvector so this space of
+eigenvectors of this matrix is the span
+
+ align:start position:0%
+eigenvectors of this matrix is the span
+ 
+
+ align:start position:0%
+eigenvectors of this matrix is the span
+of these things so there was no reason
+
+ align:start position:0%
+of these things so there was no reason
+ 
+
+ align:start position:0%
+of these things so there was no reason
+to say all this where the eigenvectors
+
+ align:start position:0%
+to say all this where the eigenvectors
+ 
+
+ align:start position:0%
+to say all this where the eigenvectors
+before and now they've change there are
+
+ align:start position:0%
+before and now they've change there are
+ 
+
+ align:start position:0%
+before and now they've change there are
+this no before you don't know what are
+
+ align:start position:0%
+this no before you don't know what are
+ 
+
+ align:start position:0%
+this no before you don't know what are
+the eigenvectors are ambiguous there's
+
+ align:start position:0%
+the eigenvectors are ambiguous there's
+ 
+
+ align:start position:0%
+the eigenvectors are ambiguous there's
+no way to decide who they are these days
+
+ align:start position:0%
+no way to decide who they are these days
+ 
+
+ align:start position:0%
+no way to decide who they are these days
+or any linear combination remember when
+
+ align:start position:0%
+or any linear combination remember when
+ 
+
+ align:start position:0%
+or any linear combination remember when
+you have a degenerate eigen state any
+
+ align:start position:0%
+you have a degenerate eigen state any
+ 
+
+ align:start position:0%
+you have a degenerate eigen state any
+superposition of them is at the general
+
+ align:start position:0%
+superposition of them is at the general
+ 
+
+ align:start position:0%
+superposition of them is at the general
+die again say so so the explanation is
+
+ align:start position:0%
+die again say so so the explanation is
+ 
+
+ align:start position:0%
+die again say so so the explanation is
+that in some sense these eigenvectors of
+
+ align:start position:0%
+that in some sense these eigenvectors of
+ 
+
+ align:start position:0%
+that in some sense these eigenvectors of
+the perturb hamiltonian is one of the
+
+ align:start position:0%
+the perturb hamiltonian is one of the
+ 
+
+ align:start position:0%
+the perturb hamiltonian is one of the
+possible choices of a basis of
+
+ align:start position:0%
+possible choices of a basis of
+ 
+
+ align:start position:0%
+possible choices of a basis of
+eigenvectors for the original space and
+
+ align:start position:0%
+eigenvectors for the original space and
+ 
+
+ align:start position:0%
+eigenvectors for the original space and
+what the perturbation does is break the
+
+ align:start position:0%
+what the perturbation does is break the
+ 
+
+ align:start position:0%
+what the perturbation does is break the
+degeneracy all those equivalent
+
+ align:start position:0%
+degeneracy all those equivalent
+ 
+
+ align:start position:0%
+degeneracy all those equivalent
+eigenvectors suddenly are not all
+
+ align:start position:0%
+eigenvectors suddenly are not all
+ 
+
+ align:start position:0%
+eigenvectors suddenly are not all
+equivalent and there's some preferred
+
+ align:start position:0%
+equivalent and there's some preferred
+ 
+
+ align:start position:0%
+equivalent and there's some preferred
+ones so this is going to be so the fact
+
+ align:start position:0%
+ones so this is going to be so the fact
+ 
+
+ align:start position:0%
+ones so this is going to be so the fact
+is that the formulas are not working
+
+ align:start position:0%
+is that the formulas are not working
+ 
+
+ align:start position:0%
+is that the formulas are not working
+right and we have to do this again
+
+ align:start position:0%
+right and we have to do this again
+ 
+
+ align:start position:0%
+right and we have to do this again
+so here's what we're gonna do we're
+
+ align:start position:0%
+so here's what we're gonna do we're
+ 
+
+ align:start position:0%
+so here's what we're gonna do we're
+gonna set this up for a systematic
+
+ align:start position:0%
+gonna set this up for a systematic
+ 
+
+ align:start position:0%
+gonna set this up for a systematic
+analysis to get this right so systematic
+
+ align:start position:0%
+analysis to get this right so systematic
+ 
+
+ align:start position:0%
+analysis to get this right so systematic
+analysis so again we say h0 is known and
+
+ align:start position:0%
+analysis so again we say h0 is known and
+ 
+
+ align:start position:0%
+analysis so again we say h0 is known and
+it will have an e of say 1 0 and e 2 0
+
+ align:start position:0%
+it will have an e of say 1 0 and e 2 0
+ 
+
+ align:start position:0%
+it will have an e of say 1 0 and e 2 0
+like that until you encounter an e n 0
+
+ align:start position:0%
+like that until you encounter an e n 0
+ 
+
+ align:start position:0%
+like that until you encounter an e n 0
+that happens to be equal to the next one
+
+ align:start position:0%
+that happens to be equal to the next one
+ 
+
+ align:start position:0%
+that happens to be equal to the next one
+e n plus 1 0 and happens to be equal to
+
+ align:start position:0%
+e n plus 1 0 and happens to be equal to
+ 
+
+ align:start position:0%
+e n plus 1 0 and happens to be equal to
+the next one all the way to an e n plus
+
+ align:start position:0%
+the next one all the way to an e n plus
+ 
+
+ align:start position:0%
+the next one all the way to an e n plus
+capital n minus 1 0 which is then
+
+ align:start position:0%
+capital n minus 1 0 which is then
+ 
+
+ align:start position:0%
+capital n minus 1 0 which is then
+smaller than the next one which is e n
+
+ align:start position:0%
+smaller than the next one which is e n
+ 
+
+ align:start position:0%
+smaller than the next one which is e n
+plus N and then again so I'm saying in
+
+ align:start position:0%
+plus N and then again so I'm saying in
+ 
+
+ align:start position:0%
+plus N and then again so I'm saying in
+funny ways the fact that yes you had
+
+ align:start position:0%
+funny ways the fact that yes you had
+ 
+
+ align:start position:0%
+funny ways the fact that yes you had
+some states and suddenly you hit a
+
+ align:start position:0%
+some states and suddenly you hit a
+ 
+
+ align:start position:0%
+some states and suddenly you hit a
+collection of capital n energy
+
+ align:start position:0%
+collection of capital n energy
+ 
+
+ align:start position:0%
+collection of capital n energy
+eigenvalues that are identical they're
+
+ align:start position:0%
+eigenvalues that are identical they're
+ 
+
+ align:start position:0%
+eigenvalues that are identical they're
+all equal to en 0 all n states have
+
+ align:start position:0%
+all equal to en 0 all n states have
+ 
+
+ align:start position:0%
+all equal to en 0 all n states have
+energy e n 0 so it is as if you have
+
+ align:start position:0%
+energy e n 0 so it is as if you have
+ 
+
+ align:start position:0%
+energy e n 0 so it is as if you have
+this matrix H 0 and there are all kinds
+
+ align:start position:0%
+this matrix H 0 and there are all kinds
+ 
+
+ align:start position:0%
+this matrix H 0 and there are all kinds
+of numbers and then there's a whole
+
+ align:start position:0%
+of numbers and then there's a whole
+ 
+
+ align:start position:0%
+of numbers and then there's a whole
+block where all the entries of size n by
+
+ align:start position:0%
+block where all the entries of size n by
+ 
+
+ align:start position:0%
+block where all the entries of size n by
+n where all the entries are the same so
+
+ align:start position:0%
+n where all the entries are the same so
+ 
+
+ align:start position:0%
+n where all the entries are the same so
+n n plus 1 n plus 2 up to n n capital n
+
+ align:start position:0%
+n n plus 1 n plus 2 up to n n capital n
+ 
+
+ align:start position:0%
+n n plus 1 n plus 2 up to n n capital n
+minus 1 is n entries and they all have
+
+ align:start position:0%
+minus 1 is n entries and they all have
+ 
+
+ align:start position:0%
+minus 1 is n entries and they all have
+the same energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the corresponding eigen states are
+
+ align:start position:0%
+and the corresponding eigen states are
+ 
+
+ align:start position:0%
+and the corresponding eigen states are
+gonna be called and we're gonna use the
+
+ align:start position:0%
+gonna be called and we're gonna use the
+ 
+
+ align:start position:0%
+gonna be called and we're gonna use the
+label and for all of them even though
+
+ align:start position:0%
+label and for all of them even though
+ 
+
+ align:start position:0%
+label and for all of them even though
+they the energies are all the same so
+
+ align:start position:0%
+they the energies are all the same so
+ 
+
+ align:start position:0%
+they the energies are all the same so
+there's just an e/m energy so we have
+
+ align:start position:0%
+there's just an e/m energy so we have
+ 
+
+ align:start position:0%
+there's just an e/m energy so we have
+capital and state so there will be an N
+
+ align:start position:0%
+capital and state so there will be an N
+ 
+
+ align:start position:0%
+capital and state so there will be an N
+1 and n 2 up to an n capital n all those
+
+ align:start position:0%
+1 and n 2 up to an n capital n all those
+ 
+
+ align:start position:0%
+1 and n 2 up to an n capital n all those
+states are gonna form an orthonormal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basis for a space that we're gonna call
+
+ align:start position:0%
+basis for a space that we're gonna call
+ 
+
+ align:start position:0%
+basis for a space that we're gonna call
+VM so the space spanned by this states
+
+ align:start position:0%
+VM so the space spanned by this states
+ 
+
+ align:start position:0%
+VM so the space spanned by this states
+we're going to call VN with the n
+
+ align:start position:0%
+we're going to call VN with the n
+ 
+
+ align:start position:0%
+we're going to call VN with the n
+reminding you it has to do with it n
+
+ align:start position:0%
+reminding you it has to do with it n
+ 
+
+ align:start position:0%
+reminding you it has to do with it n
+states little and states with energy
+
+ align:start position:0%
+states little and states with energy
+ 
+
+ align:start position:0%
+states little and states with energy
+described by the label n so this is the
+
+ align:start position:0%
+described by the label n so this is the
+ 
+
+ align:start position:0%
+described by the label n so this is the
+degenerate subspace this is the space of
+
+ align:start position:0%
+degenerate subspace this is the space of
+ 
+
+ align:start position:0%
+degenerate subspace this is the space of
+all those states that have energy E and
+
+ align:start position:0%
+all those states that have energy E and
+ 
+
+ align:start position:0%
+all those states that have energy E and
+0 so I'll state that here so it's quite
+
+ align:start position:0%
+0 so I'll state that here so it's quite
+ 
+
+ align:start position:0%
+0 so I'll state that here so it's quite
+important to get our notation right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+otherwise we don't understand what's
+
+ align:start position:0%
+otherwise we don't understand what's
+ 
+
+ align:start position:0%
+otherwise we don't understand what's
+going on so H 0 and 0 K they all have
+
+ align:start position:0%
+going on so H 0 and 0 K they all have
+ 
+
+ align:start position:0%
+going on so H 0 and 0 K they all have
+energy e and 0 and 0 ok ok and this is
+
+ align:start position:0%
+energy e and 0 and 0 ok ok and this is
+ 
+
+ align:start position:0%
+energy e and 0 and 0 ok ok and this is
+for K equals 1 up to capital n now okay
+
+ align:start position:0%
+for K equals 1 up to capital n now okay
+ 
+
+ align:start position:0%
+for K equals 1 up to capital n now okay
+this is your degenerate subspace all
+
+ align:start position:0%
+this is your degenerate subspace all
+ 
+
+ align:start position:0%
+this is your degenerate subspace all
+these are all the states and we now want
+
+ align:start position:0%
+these are all the states and we now want
+ 
+
+ align:start position:0%
+these are all the states and we now want
+to know what happens to this space to
+
+ align:start position:0%
+to know what happens to this space to
+ 
+
+ align:start position:0%
+to know what happens to this space to
+all these states when the energy turns
+
+ align:start position:0%
+all these states when the energy turns
+ 
+
+ align:start position:0%
+all these states when the energy turns
+this is not just a theoretical construct
+
+ align:start position:0%
+this is not just a theoretical construct
+ 
+
+ align:start position:0%
+this is not just a theoretical construct
+when you start asking what happens to
+
+ align:start position:0%
+when you start asking what happens to
+ 
+
+ align:start position:0%
+when you start asking what happens to
+the first excited states in the hydrogen
+
+ align:start position:0%
+the first excited states in the hydrogen
+ 
+
+ align:start position:0%
+the first excited states in the hydrogen
+atom you already have four states there
+
+ align:start position:0%
+atom you already have four states there
+ 
+
+ align:start position:0%
+atom you already have four states there
+L equal 1 l equals 0 States at n equal 2
+
+ align:start position:0%
+L equal 1 l equals 0 States at n equal 2
+ 
+
+ align:start position:0%
+L equal 1 l equals 0 States at n equal 2
+and half degenerate States and
+
+ align:start position:0%
+and half degenerate States and
+ 
+
+ align:start position:0%
+and half degenerate States and
+immediately you're stuck in this
+
+ align:start position:0%
+immediately you're stuck in this
+ 
+
+ align:start position:0%
+immediately you're stuck in this
+situation so I will also use the
+
+ align:start position:0%
+situation so I will also use the
+ 
+
+ align:start position:0%
+situation so I will also use the
+notation that the total space space a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curly H is the sum of V and plus a V hot
+
+ align:start position:0%
+curly H is the sum of V and plus a V hot
+ 
+
+ align:start position:0%
+curly H is the sum of V and plus a V hot
+this is called the direct sum at this
+
+ align:start position:0%
+this is called the direct sum at this
+ 
+
+ align:start position:0%
+this is called the direct sum at this
+point it just doesn't matter too much
+
+ align:start position:0%
+point it just doesn't matter too much
+ 
+
+ align:start position:0%
+point it just doesn't matter too much
+these are linearly independent subspaces
+
+ align:start position:0%
+these are linearly independent subspaces
+ 
+
+ align:start position:0%
+these are linearly independent subspaces
+be and be hot and basically you think
+
+ align:start position:0%
+be and be hot and basically you think
+ 
+
+ align:start position:0%
+be and be hot and basically you think
+does V hot as all the other states yes
+
+ align:start position:0%
+does V hot as all the other states yes
+ 
+
+ align:start position:0%
+does V hot as all the other states yes
+there were this degenerate subspace and
+
+ align:start position:0%
+there were this degenerate subspace and
+ 
+
+ align:start position:0%
+there were this degenerate subspace and
+all the other states are we had so we
+
+ align:start position:0%
+all the other states are we had so we
+ 
+
+ align:start position:0%
+all the other states are we had so we
+had is the span of all other states and
+
+ align:start position:0%
+had is the span of all other states and
+ 
+
+ align:start position:0%
+had is the span of all other states and
+we'll call them p 0 or what letter are p
+
+ align:start position:0%
+we'll call them p 0 or what letter are p
+ 
+
+ align:start position:0%
+we'll call them p 0 or what letter are p
+0 with P equals some numbers so this is
+
+ align:start position:0%
+0 with P equals some numbers so this is
+ 
+
+ align:start position:0%
+0 with P equals some numbers so this is
+a good notation it allows you to
+
+ align:start position:0%
+a good notation it allows you to
+ 
+
+ align:start position:0%
+a good notation it allows you to
+distinguish the degenerate States use
+
+ align:start position:0%
+distinguish the degenerate States use
+ 
+
+ align:start position:0%
+distinguish the degenerate States use
+two labels maybe you only need at one
+
+ align:start position:0%
+two labels maybe you only need at one
+ 
+
+ align:start position:0%
+two labels maybe you only need at one
+label but you would get confused with
+
+ align:start position:0%
+label but you would get confused with
+ 
+
+ align:start position:0%
+label but you would get confused with
+the notation if you just use one labor
+
+ align:start position:0%
+the notation if you just use one labor
+ 
+
+ align:start position:0%
+the notation if you just use one labor
+so if that's the case the generate state
+
+ align:start position:0%
+so if that's the case the generate state
+ 
+
+ align:start position:0%
+so if that's the case the generate state
+but by putting the end here you now know
+
+ align:start position:0%
+but by putting the end here you now know
+ 
+
+ align:start position:0%
+but by putting the end here you now know
+you're talking at the generate state
+
+ align:start position:0%
+you're talking at the generate state
+ 
+
+ align:start position:0%
+you're talking at the generate state
+when you have a single label you're
+
+ align:start position:0%
+when you have a single label you're
+ 
+
+ align:start position:0%
+when you have a single label you're
+talking about the other states in the
+
+ align:start position:0%
+talking about the other states in the
+ 
+
+ align:start position:0%
+talking about the other states in the
+space so it's very good when your
+
+ align:start position:0%
+space so it's very good when your
+ 
+
+ align:start position:0%
+space so it's very good when your
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+makes it easy to think and recognize the
+
+ align:start position:0%
+makes it easy to think and recognize the
+ 
+
+ align:start position:0%
+makes it easy to think and recognize the
+equations that you have and V Hart and
+
+ align:start position:0%
+equations that you have and V Hart and
+ 
+
+ align:start position:0%
+equations that you have and V Hart and
+this are orthogonal spaces we've had is
+
+ align:start position:0%
+this are orthogonal spaces we've had is
+ 
+
+ align:start position:0%
+this are orthogonal spaces we've had is
+perpendicular to V n the inner product
+
+ align:start position:0%
+perpendicular to V n the inner product
+ 
+
+ align:start position:0%
+perpendicular to V n the inner product
+of any state outside the generate space
+
+ align:start position:0%
+of any state outside the generate space
+ 
+
+ align:start position:0%
+of any state outside the generate space
+with a state in the degenerate space is
+
+ align:start position:0%
+with a state in the degenerate space is
+ 
+
+ align:start position:0%
+with a state in the degenerate space is
+zero okay so let's up now do the
+
+ align:start position:0%
+zero okay so let's up now do the
+ 
+
+ align:start position:0%
+zero okay so let's up now do the
+important thing should I can do it here
+
+ align:start position:0%
+important thing should I can do it here
+ 
+
+ align:start position:0%
+important thing should I can do it here
+I think I'll do it here so what do we
+
+ align:start position:0%
+I think I'll do it here so what do we
+ 
+
+ align:start position:0%
+I think I'll do it here so what do we
+want to do what is the question here the
+
+ align:start position:0%
+want to do what is the question here the
+ 
+
+ align:start position:0%
+want to do what is the question here the
+question is the following we have a
+
+ align:start position:0%
+question is the following we have a
+ 
+
+ align:start position:0%
+question is the following we have a
+state and zero K we have capital n of
+
+ align:start position:0%
+state and zero K we have capital n of
+ 
+
+ align:start position:0%
+state and zero K we have capital n of
+those states and we want to figure out
+
+ align:start position:0%
+those states and we want to figure out
+ 
+
+ align:start position:0%
+those states and we want to figure out
+what they become as you turn on the
+
+ align:start position:0%
+what they become as you turn on the
+ 
+
+ align:start position:0%
+what they become as you turn on the
+perturbation so what using the old
+
+ align:start position:0%
+perturbation so what using the old
+ 
+
+ align:start position:0%
+perturbation so what using the old
+notation we'll say they become this and
+
+ align:start position:0%
+notation we'll say they become this and
+ 
+
+ align:start position:0%
+notation we'll say they become this and
+what is that gonna be it's gonna be M 0
+
+ align:start position:0%
+what is that gonna be it's gonna be M 0
+ 
+
+ align:start position:0%
+what is that gonna be it's gonna be M 0
+K the original state what it was plus
+
+ align:start position:0%
+K the original state what it was plus
+ 
+
+ align:start position:0%
+K the original state what it was plus
+order lambda the first correction so and
+
+ align:start position:0%
+order lambda the first correction so and
+ 
+
+ align:start position:0%
+order lambda the first correction so and
+one for this case state plus dot o dot
+
+ align:start position:0%
+one for this case state plus dot o dot
+ 
+
+ align:start position:0%
+one for this case state plus dot o dot
+for the energies we had em0 that was the
+
+ align:start position:0%
+for the energies we had em0 that was the
+ 
+
+ align:start position:0%
+for the energies we had em0 that was the
+energy of every state in the degenerate
+
+ align:start position:0%
+energy of every state in the degenerate
+ 
+
+ align:start position:0%
+energy of every state in the degenerate
+subspace now it's gonna become T and
+
+ align:start position:0%
+subspace now it's gonna become T and
+ 
+
+ align:start position:0%
+subspace now it's gonna become T and
+lambda P and lambda
+
+ align:start position:0%
+lambda P and lambda
+ 
+
+ align:start position:0%
+lambda P and lambda
+but if I say en and I'm already making a
+
+ align:start position:0%
+but if I say en and I'm already making a
+ 
+
+ align:start position:0%
+but if I say en and I'm already making a
+mistake
+
+ align:start position:0%
+mistake
+ 
+
+ align:start position:0%
+mistake
+because I'm looking at the fixed K and a
+
+ align:start position:0%
+because I'm looking at the fixed K and a
+ 
+
+ align:start position:0%
+because I'm looking at the fixed K and a
+fixed K means we chose one of the state
+
+ align:start position:0%
+fixed K means we chose one of the state
+ 
+
+ align:start position:0%
+fixed K means we chose one of the state
+and any single one of the state the
+
+ align:start position:0%
+and any single one of the state the
+ 
+
+ align:start position:0%
+and any single one of the state the
+energy can grow in a different way
+
+ align:start position:0%
+energy can grow in a different way
+ 
+
+ align:start position:0%
+energy can grow in a different way
+so I should call this emk because we're
+
+ align:start position:0%
+so I should call this emk because we're
+ 
+
+ align:start position:0%
+so I should call this emk because we're
+talking about this state will be equal
+
+ align:start position:0%
+talking about this state will be equal
+ 
+
+ align:start position:0%
+talking about this state will be equal
+to e and zero yes they all have the same
+
+ align:start position:0%
+to e and zero yes they all have the same
+ 
+
+ align:start position:0%
+to e and zero yes they all have the same
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+zeroth-order energy but then e MK 1 plus
+
+ align:start position:0%
+zeroth-order energy but then e MK 1 plus
+ 
+
+ align:start position:0%
+zeroth-order energy but then e MK 1 plus
+lambda squared e MK 2 and so on so this
+
+ align:start position:0%
+lambda squared e MK 2 and so on so this
+ 
+
+ align:start position:0%
+lambda squared e MK 2 and so on so this
+is the fate of the cave State and the
+
+ align:start position:0%
+is the fate of the cave State and the
+ 
+
+ align:start position:0%
+is the fate of the cave State and the
+degeneracy will be broken to first order
+
+ align:start position:0%
+degeneracy will be broken to first order
+ 
+
+ align:start position:0%
+degeneracy will be broken to first order
+if this e n case become different
+
+ align:start position:0%
+if this e n case become different
+ 
+
+ align:start position:0%
+if this e n case become different
+numbers because if they become different
+
+ align:start position:0%
+numbers because if they become different
+ 
+
+ align:start position:0%
+numbers because if they become different
+numbers in lambda they're going to start
+
+ align:start position:0%
+numbers in lambda they're going to start
+ 
+
+ align:start position:0%
+numbers in lambda they're going to start
+splitting the states remember this
+
+ align:start position:0%
+splitting the states remember this
+ 
+
+ align:start position:0%
+splitting the states remember this
+picture we had last time of several
+
+ align:start position:0%
+picture we had last time of several
+ 
+
+ align:start position:0%
+picture we had last time of several
+states at one point if the order lambda
+
+ align:start position:0%
+states at one point if the order lambda
+ 
+
+ align:start position:0%
+states at one point if the order lambda
+Corrections are different the state
+
+ align:start position:0%
+Corrections are different the state
+ 
+
+ align:start position:0%
+Corrections are different the state
+split the degeneracy is resolved and we
+
+ align:start position:0%
+split the degeneracy is resolved and we
+ 
+
+ align:start position:0%
+split the degeneracy is resolved and we
+can calculate things more easily if it's
+
+ align:start position:0%
+can calculate things more easily if it's
+ 
+
+ align:start position:0%
+can calculate things more easily if it's
+not resolved to first order it's harder
+
+ align:start position:0%
+not resolved to first order it's harder
+ 
+
+ align:start position:0%
+not resolved to first order it's harder
+it will be all of next lecture to figure
+
+ align:start position:0%
+it will be all of next lecture to figure
+ 
+
+ align:start position:0%
+it will be all of next lecture to figure
+out what happens in that case we
+
+ align:start position:0%
+out what happens in that case we
+ 
+
+ align:start position:0%
+out what happens in that case we
+discussed last time that the N one
+
+ align:start position:0%
+discussed last time that the N one
+ 
+
+ align:start position:0%
+discussed last time that the N one
+correction didn't have any component
+
+ align:start position:0%
+correction didn't have any component
+ 
+
+ align:start position:0%
+correction didn't have any component
+along the n zero vector we could always
+
+ align:start position:0%
+along the n zero vector we could always
+ 
+
+ align:start position:0%
+along the n zero vector we could always
+arrange that to happen here we can
+
+ align:start position:0%
+arrange that to happen here we can
+ 
+
+ align:start position:0%
+arrange that to happen here we can
+arrange something similar to happen so
+
+ align:start position:0%
+arrange something similar to happen so
+ 
+
+ align:start position:0%
+arrange something similar to happen so
+we will still assume assume and we can
+
+ align:start position:0%
+we will still assume assume and we can
+ 
+
+ align:start position:0%
+we will still assume assume and we can
+check that's always possible that the N
+
+ align:start position:0%
+check that's always possible that the N
+ 
+
+ align:start position:0%
+check that's always possible that the N
+P corrections to the state K at order P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for P equals 1 2 3 because it's not 0
+
+ align:start position:0%
+for P equals 1 2 3 because it's not 0
+ 
+
+ align:start position:0%
+for P equals 1 2 3 because it's not 0
+are orthogonal to n 0 K so this state
+
+ align:start position:0%
+are orthogonal to n 0 K so this state
+ 
+
+ align:start position:0%
+are orthogonal to n 0 K so this state
+doesn't have any component along n 0 K
+
+ align:start position:0%
+doesn't have any component along n 0 K
+ 
+
+ align:start position:0%
+doesn't have any component along n 0 K
+and this state doesn't have any company
+
+ align:start position:0%
+and this state doesn't have any company
+ 
+
+ align:start position:0%
+and this state doesn't have any company
+along the original one it's always
+
+ align:start position:0%
+along the original one it's always
+ 
+
+ align:start position:0%
+along the original one it's always
+possible to do that just like we did it
+
+ align:start position:0%
+possible to do that just like we did it
+ 
+
+ align:start position:0%
+possible to do that just like we did it
+in the degenerate non degenerate case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moreover but here is this is something I
+
+ align:start position:0%
+moreover but here is this is something I
+ 
+
+ align:start position:0%
+moreover but here is this is something I
+want you to notice we're saying that the
+
+ align:start position:0%
+want you to notice we're saying that the
+ 
+
+ align:start position:0%
+want you to notice we're saying that the
+state and one doesn't have any component
+
+ align:start position:0%
+state and one doesn't have any component
+ 
+
+ align:start position:0%
+state and one doesn't have any component
+along the state and 0 for a given K but
+
+ align:start position:0%
+along the state and 0 for a given K but
+ 
+
+ align:start position:0%
+along the state and 0 for a given K but
+the state and one can have components
+
+ align:start position:0%
+the state and one can have components
+ 
+
+ align:start position:0%
+the state and one can have components
+along and 0 for a different K so while
+
+ align:start position:0%
+along and 0 for a different K so while
+ 
+
+ align:start position:0%
+along and 0 for a different K so while
+the answer or a piece order correction
+
+ align:start position:0%
+the answer or a piece order correction
+ 
+
+ align:start position:0%
+the answer or a piece order correction
+doesn't have component along this it can
+
+ align:start position:0%
+doesn't have component along this it can
+ 
+
+ align:start position:0%
+doesn't have component along this it can
+have component for K for an L here where
+
+ align:start position:0%
+have component for K for an L here where
+ 
+
+ align:start position:0%
+have component for K for an L here where
+L is different from k so it means that n
+
+ align:start position:0%
+L is different from k so it means that n
+ 
+
+ align:start position:0%
+L is different from k so it means that n
+P K still can have a component in VN
+
+ align:start position:0%
+P K still can have a component in VN
+ 
+
+ align:start position:0%
+P K still can have a component in VN
+remember V n is this whole thing so if
+
+ align:start position:0%
+remember V n is this whole thing so if
+ 
+
+ align:start position:0%
+remember V n is this whole thing so if
+you're doing the case one well n 1k
+
+ align:start position:0%
+you're doing the case one well n 1k
+ 
+
+ align:start position:0%
+you're doing the case one well n 1k
+doesn't have a number along that one but
+
+ align:start position:0%
+doesn't have a number along that one but
+ 
+
+ align:start position:0%
+doesn't have a number along that one but
+it may have a component along all the
+
+ align:start position:0%
+it may have a component along all the
+ 
+
+ align:start position:0%
+it may have a component along all the
+others so it may still have a component
+
+ align:start position:0%
+others so it may still have a component
+ 
+
+ align:start position:0%
+others so it may still have a component
+that correction in VN in fact that's
+
+ align:start position:0%
+that correction in VN in fact that's
+ 
+
+ align:start position:0%
+that correction in VN in fact that's
+what will make the problem a little hard
+
+ align:start position:0%
+what will make the problem a little hard
+ 
+
+ align:start position:0%
+what will make the problem a little hard
+to do but it's a good thing to try to
+
+ align:start position:0%
+to do but it's a good thing to try to
+ 
+
+ align:start position:0%
+to do but it's a good thing to try to
+figure out this thing so what is the
+
+ align:start position:0%
+figure out this thing so what is the
+ 
+
+ align:start position:0%
+figure out this thing so what is the
+equation we want to solve the usual
+
+ align:start position:0%
+equation we want to solve the usual
+ 
+
+ align:start position:0%
+equation we want to solve the usual
+equation H of lambda on MK lambda is
+
+ align:start position:0%
+equation H of lambda on MK lambda is
+ 
+
+ align:start position:0%
+equation H of lambda on MK lambda is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+m'kay of lambda and K so we produce the
+
+ align:start position:0%
+m'kay of lambda and K so we produce the
+ 
+
+ align:start position:0%
+m'kay of lambda and K so we produce the
+general state that's its energy for the
+
+ align:start position:0%
+general state that's its energy for the
+ 
+
+ align:start position:0%
+general state that's its energy for the
+full final tone Ian that's our
+
+ align:start position:0%
+full final tone Ian that's our
+ 
+
+ align:start position:0%
+full final tone Ian that's our
+Schrodinger equation so what do we have
+
+ align:start position:0%
+Schrodinger equation so what do we have
+ 
+
+ align:start position:0%
+Schrodinger equation so what do we have
+to do we have to do exactly what we did
+
+ align:start position:0%
+to do we have to do exactly what we did
+ 
+
+ align:start position:0%
+to do we have to do exactly what we did
+before plugging that series separate the
+
+ align:start position:0%
+before plugging that series separate the
+ 
+
+ align:start position:0%
+before plugging that series separate the
+terms with various lambdas and see what
+
+ align:start position:0%
+terms with various lambdas and see what
+ 
+
+ align:start position:0%
+terms with various lambdas and see what
+we get so here is what we get to order
+
+ align:start position:0%
+we get so here is what we get to order
+ 
+
+ align:start position:0%
+we get so here is what we get to order
+lambda to the 0 you get H 0 minus M 0 on
+
+ align:start position:0%
+lambda to the 0 you get H 0 minus M 0 on
+ 
+
+ align:start position:0%
+lambda to the 0 you get H 0 minus M 0 on
+n 0 k equals 0 and that equation as it
+
+ align:start position:0%
+n 0 k equals 0 and that equation as it
+ 
+
+ align:start position:0%
+n 0 k equals 0 and that equation as it
+was the case for the non degenerate case
+
+ align:start position:0%
+was the case for the non degenerate case
+ 
+
+ align:start position:0%
+was the case for the non degenerate case
+sorry for the redundancy it's trivially
+
+ align:start position:0%
+sorry for the redundancy it's trivially
+ 
+
+ align:start position:0%
+sorry for the redundancy it's trivially
+satisfied we've stated that those are
+
+ align:start position:0%
+satisfied we've stated that those are
+ 
+
+ align:start position:0%
+satisfied we've stated that those are
+the energies in the top equation on that
+
+ align:start position:0%
+the energies in the top equation on that
+ 
+
+ align:start position:0%
+the energies in the top equation on that
+blackboard so this equation we don't
+
+ align:start position:0%
+blackboard so this equation we don't
+ 
+
+ align:start position:0%
+blackboard so this equation we don't
+need to worry about that's not too
+
+ align:start position:0%
+need to worry about that's not too
+ 
+
+ align:start position:0%
+need to worry about that's not too
+difficult lambda 1 H 0 minus e + 0 + 1 K
+
+ align:start position:0%
+difficult lambda 1 H 0 minus e + 0 + 1 K
+ 
+
+ align:start position:0%
+difficult lambda 1 H 0 minus e + 0 + 1 K
+will be equal to e MK 1 minus Delta H +
+
+ align:start position:0%
+will be equal to e MK 1 minus Delta H +
+ 
+
+ align:start position:0%
+will be equal to e MK 1 minus Delta H +
+0 K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+last equation starting to get lazy to
+
+ align:start position:0%
+last equation starting to get lazy to
+ 
+
+ align:start position:0%
+last equation starting to get lazy to
+write them out but we must and to K is
+
+ align:start position:0%
+write them out but we must and to K is
+ 
+
+ align:start position:0%
+write them out but we must and to K is
+equal to M e MK 1 minus Delta H and 1 k
+
+ align:start position:0%
+equal to M e MK 1 minus Delta H and 1 k
+ 
+
+ align:start position:0%
+equal to M e MK 1 minus Delta H and 1 k
+plus e MK 2 and 0 k ok and these
+
+ align:start position:0%
+plus e MK 2 and 0 k ok and these
+ 
+
+ align:start position:0%
+plus e MK 2 and 0 k ok and these
+equations are equations for K fixed but
+
+ align:start position:0%
+equations are equations for K fixed but
+ 
+
+ align:start position:0%
+equations are equations for K fixed but
+this every term in the equation has the
+
+ align:start position:0%
+this every term in the equation has the
+ 
+
+ align:start position:0%
+this every term in the equation has the
+same K but K then can run from 1 up to n
+
+ align:start position:0%
+same K but K then can run from 1 up to n
+ 
+
+ align:start position:0%
+same K but K then can run from 1 up to n
+so three equations terms n times there
+
+ align:start position:0%
+so three equations terms n times there
+ 
+
+ align:start position:0%
+so three equations terms n times there
+we go okay these are our equations this
+
+ align:start position:0%
+we go okay these are our equations this
+ 
+
+ align:start position:0%
+we go okay these are our equations this
+time and we need to understand them in
+
+ align:start position:0%
+time and we need to understand them in
+ 
+
+ align:start position:0%
+time and we need to understand them in
+fact we need to solve them what with
+
+ align:start position:0%
+fact we need to solve them what with
+ 
+
+ align:start position:0%
+fact we need to solve them what with
+getting experience with the non
+
+ align:start position:0%
+getting experience with the non
+ 
+
+ align:start position:0%
+getting experience with the non
+degenerate case is going to come very
+
+ align:start position:0%
+degenerate case is going to come very
+ 
+
+ align:start position:0%
+degenerate case is going to come very
+useful here although some things are not
+
+ align:start position:0%
+useful here although some things are not
+ 
+
+ align:start position:0%
+useful here although some things are not
+going to be exactly the same we're going
+
+ align:start position:0%
+going to be exactly the same we're going
+ 
+
+ align:start position:0%
+going to be exactly the same we're going
+to try to find the energy Corrections
+
+ align:start position:0%
+to try to find the energy Corrections
+ 
+
+ align:start position:0%
+to try to find the energy Corrections
+here but calculating the state and one
+
+ align:start position:0%
+here but calculating the state and one
+ 
+
+ align:start position:0%
+here but calculating the state and one
+is going to be a little harder we won't
+
+ align:start position:0%
+is going to be a little harder we won't
+ 
+
+ align:start position:0%
+is going to be a little harder we won't
+finish today we'll have much time left
+
+ align:start position:0%
+finish today we'll have much time left
+ 
+
+ align:start position:0%
+finish today we'll have much time left
+but what's going to happen is that you
+
+ align:start position:0%
+but what's going to happen is that you
+ 
+
+ align:start position:0%
+but what's going to happen is that you
+can calculate the state and one the part
+
+ align:start position:0%
+can calculate the state and one the part
+ 
+
+ align:start position:0%
+can calculate the state and one the part
+in the space we had but the part in the
+
+ align:start position:0%
+in the space we had but the part in the
+ 
+
+ align:start position:0%
+in the space we had but the part in the
+degenerate subspace where I said that n
+
+ align:start position:0%
+degenerate subspace where I said that n
+ 
+
+ align:start position:0%
+degenerate subspace where I said that n
+PK still can have a component in the
+
+ align:start position:0%
+PK still can have a component in the
+ 
+
+ align:start position:0%
+PK still can have a component in the
+degenerate subspace cannot be calculated
+
+ align:start position:0%
+degenerate subspace cannot be calculated
+ 
+
+ align:start position:0%
+degenerate subspace cannot be calculated
+from this equation so even when we
+
+ align:start position:0%
+from this equation so even when we
+ 
+
+ align:start position:0%
+from this equation so even when we
+finish doing this first equation
+
+ align:start position:0%
+finish doing this first equation
+ 
+
+ align:start position:0%
+finish doing this first equation
+you're gonna find the situation you
+
+ align:start position:0%
+you're gonna find the situation you
+ 
+
+ align:start position:0%
+you're gonna find the situation you
+still have not calculated all of the
+
+ align:start position:0%
+still have not calculated all of the
+ 
+
+ align:start position:0%
+still have not calculated all of the
+steps and one you're gonna have to go to
+
+ align:start position:0%
+steps and one you're gonna have to go to
+ 
+
+ align:start position:0%
+steps and one you're gonna have to go to
+the second equation to find the missing
+
+ align:start position:0%
+the second equation to find the missing
+ 
+
+ align:start position:0%
+the second equation to find the missing
+part of the state and one so it's gonna
+
+ align:start position:0%
+part of the state and one so it's gonna
+ 
+
+ align:start position:0%
+part of the state and one so it's gonna
+be pretty interesting
\ No newline at end of file
diff --git a/9Jry5-82I68.txt b/9Jry5-82I68.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b1e0a5def0dd5eb6c3873d3e788cd9875af92b7d
--- /dev/null
+++ b/9Jry5-82I68.txt
@@ -0,0 +1,2497 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Today's lecture
+is about a brand new data
+
+structure that you've
+probably seen before,
+
+and we've mentioned
+earlier in double 06,
+
+called a binary search tree.
+
+We've talked about
+binary search.
+
+It's a fundamental divide
+and conquer paradigm.
+
+There's a data structure
+associated with it,
+
+called the BST, a
+binary search tree.
+
+And what I want to do is
+motivate this data structure
+
+using a problem.
+
+It's a bit of a toy problem,
+but certainly a problem
+
+that you could imagine
+exists in all sorts
+
+of scheduling problems.
+
+It's a part of a runway
+reservation system
+
+that you can imagine building.
+
+And what I'll do is
+define this problem
+
+and talk about how we could
+possibly solve it with the data
+
+structures you've already seen--
+so lists and arrays, heaps
+
+as well as, which
+we saw last time--
+
+and hopefully motivate you into
+the reason behind the existence
+
+of binary search
+trees, because they
+
+are kind of the
+perfect data structure
+
+for this particular problem.
+
+So let's dive into what the
+runway reservation system looks
+
+like.
+
+And it's your basic
+scheduling problem.
+
+We'll assume an airport
+with a single runway.
+
+Now Logan has six runways.
+
+But the moment there's any sort
+of weather you're down to one.
+
+And of course, there's lots of
+airports with a single runway.
+
+And we can imagine that
+this runway is pretty busy.
+
+There's obviously safety issues
+associated with landing planes,
+
+and planes taking off.
+
+And so there are
+constraints associated
+
+with the system, that
+have to be obeyed.
+
+And you have to build these
+constraints in-- and the checks
+
+for these constraints--
+into your data structure.
+
+That's sort of the
+summary of the context.
+
+So reservations
+for future landings
+
+is really what this
+system is built for.
+
+There's a notion of time.
+
+We'll assume that
+time is continuous.
+
+So it could be represented
+by a real variable,
+
+or a real quantity.
+
+And what we'd like to do is
+reserve requests for landings.
+
+And these are going to
+specify landing time.
+
+Each of them is going to
+specify a landing time.
+
+We call it t.
+
+And in particular,
+we're going to add t
+
+to the set R of landing times if
+no other landings are scheduled
+
+within k minutes.
+
+And k is a parameter
+that could vary.
+
+I mean, it could be statically
+set to 3 minutes, or maybe 4.
+
+You can imagine it
+varying it dynamically
+
+depending on weather
+conditions, things like that.
+
+For the most of the examples
+we'll talk about today,
+
+we'll assume k is 3 minutes,
+or something like that.
+
+So this is about adding
+to the data structure.
+
+And so an insert
+operation, if you will,
+
+that has a constraint associated
+with it that you need to check.
+
+And so you wouldn't insert if
+the constraint was violated.
+
+You would if the
+constraint was satisfied.
+
+And time, as I
+said, is something
+
+that is part of the system.
+
+It needs to be modeled.
+
+You have the current
+notion of time.
+
+And every time you have a
+plane that's already landed,
+
+which means that
+you can essentially
+
+take this particular
+landing time away
+
+from the set R. So this
+removal, or delete-- we remove
+
+from set R, which is
+the set of landing times
+
+after the plane lands.
+
+So every once in awhile,
+as time increments,
+
+you're going to be checking
+the data structure.
+
+And you can do this, maybe,
+every minute, every 30 seconds.
+
+That isn't really important.
+
+But you have to be able
+to remove from this data
+
+structure.
+
+So fairly straightforward
+data structure.
+
+It's a set, R. We don't quite
+know how to implement it yet.
+
+But we'd like to do all of these
+operations in order log n time,
+
+where n is the size of the set.
+
+All right?
+
+So any questions about that?
+
+Any questions about
+the definition
+
+of the problem
+before we move on?
+
+Are we good on?
+
+OK.
+
+So let's look at a real
+straightforward example,
+
+and put this up here so you
+get a better sense of this.
+
+Let's say that, right
+now, we are at time 37.
+
+And the set R has
+41.2, 49, and 53 in it.
+
+And that's time.
+
+Now you may get a request
+for landing time 53.
+
+And-- I'm sorry.
+
+I want to call this
+56.3-- 41.2, 49, and 56.3.
+
+You may get a request
+for landing time 53.
+
+And right now the time is 37.
+
+It's in the future, and
+you say OK because you've
+
+done the check.
+
+And let's assume
+that k equals 3.
+
+And 53 is four ahead of 49, and
+3.3 before 56.3, so you're OK.
+
+44 is not allowed.
+
+It's too close to 41.2.
+
+And 20, just for
+completeness, is not
+
+allowed because it's passed.
+
+Can't schedule in the past.
+
+I mean, it could
+be the next day.
+
+But then you
+wouldn't call it 20.
+
+Let's assume that time is
+a monotonically increasing
+
+function.
+
+You have a 64-bit number.
+
+It can go to the end
+of the world, or 2012,
+
+or wherever you want.
+
+So you can keep the
+number a bit smaller,
+
+and do a little constant
+factor optimization, I guess.
+
+So that's sort of the set up.
+
+And hopefully you get a sense
+of what the requirements.
+
+And you guys know about a bunch
+of data structures already.
+
+And what I want to do is
+list each one of them,
+
+and essentially shoot
+them down with respect
+
+to not being able to make
+this efficiency requirement.
+
+And I'd like you guys to
+help me shoot them down.
+
+So let's talk about
+an easy one first.
+
+Let's say you have an unsorted
+list or an array corresponding
+
+to R. That's all you have.
+
+What's wrong with
+this data structure
+
+from an efficiency standpoint?
+
+Yeah.
+
+AUDIENCE: Pretty much everything
+you want to do to it is linear.
+
+PROFESSOR: That's exactly right.
+
+Pretty much everything you
+want to do to it is linear.
+
+And so you want to check
+the k minute check.
+
+You can certainly insert
+into it, and just add to it.
+
+So that part is not linear,
+that's constant time.
+
+But certainly,
+anything where you
+
+want to go check against
+other elements of the array,
+
+it's unsorted.
+
+You have no idea of where
+to find these elements.
+
+You have to scan
+through the entire array
+
+to check to see whether
+there's a landing time that's
+
+within k of the current time
+t that you're asking for.
+
+And that's going to
+take order n time.
+
+So you can insert in
+order 1 without a check.
+
+But sadly, the check
+takes order n time.
+
+All right?
+
+Let's do something that is
+a little more plausible.
+
+Let's talk about a sorted array.
+
+So this is a little
+more subtle question.
+
+Let's talk about a sorted array.
+
+What happens with
+a sorted array?
+
+Someone?
+
+What can you do
+with a sorted array?
+
+Yeah.
+
+AUDIENCE: Do a binary search
+to find the [INAUDIBLE].
+
+PROFESSOR: Binary search
+would find a bad insert.
+
+OK, good.
+
+So that's good.
+
+So if you have a sorted array,
+and just for argument's sake,
+
+it looks like 4, 20, 32, 37, 45.
+
+And it's increasing order.
+
+And if you get a particular time
+t, you can use binary search.
+
+And let's say, in particular,
+the time is, for example, 34.
+
+Then what you do is you go
+to the midpoint of the array,
+
+and maybe you just look at that.
+
+And you say oh, 34
+is greater than 32.
+
+So I'm going to go
+check and figure out
+
+if I need to move to
+the left or the right.
+
+And since it's greater I'm
+going to move to the right.
+
+And within logarithmic
+time, you'll
+
+find what we call the insertion
+point of the sorted array,
+
+where this 34 is
+supposed to sit.
+
+And you don't necessarily
+get to insert there.
+
+You need to look, once you've
+found the insertion point,
+
+to your left and to your right.
+
+And do the k minute check.
+
+So finish up the
+answer to the question,
+
+tell me how long it's going to
+take me to find the insertion
+
+point, how long it's going
+to take me to do the check,
+
+and how long it's going
+to take me to actually do
+
+the insertion.
+
+AUDIENCE: Log n in the search--
+
+PROFESSOR: Log n for the
+search, to find the point.
+
+AUDIENCE: Constant
+for the comparison?
+
+PROFESSOR: Constant
+to the comparison.
+
+And then the last step?
+
+AUDIENCE: Do the
+research [INAUDIBLE].
+
+PROFESSOR: Sorry, little louder.
+
+Sorry.
+
+AUDIENCE: The
+insertion is constant.
+
+PROFESSOR: Insertion
+is constant?
+
+Is that right?
+
+Do you people agree with him,
+that insertion is constant?
+
+AUDIENCE: You've got a
+maximum size up there, right?
+
+There must be a maximum.
+
+[INAUDIBLE]
+
+PROFESSOR: No, the indices--
+so right now the array
+
+has indices i.
+
+And if you start with 1, it's
+1, 2, 3, 4, 5, et cetera.
+
+So what do you
+mean by insertion?
+
+Someone explain to me
+what-- yeah, go ahead.
+
+AUDIENCE: When you
+put something in you
+
+have to shift
+every element over.
+
+PROFESSOR: That's exactly right.
+
+That's exactly right.
+
+Ok, good, that's great.
+
+I guess I should give
+you half a cushion.
+
+But I'll do the full one, right?
+
+And you get one, too.
+
+So the point here is
+this is pretty close.
+
+It's almost what we want.
+
+It's almost what we want.
+
+There's a little bit
+of a glitch here.
+
+We know about binary search.
+
+The binary search is
+going to allow us,
+
+if there's n elements
+here, to find the place--
+
+it's going to be able
+to find-- and I'm
+
+going to precise here-- the
+smallest i such that R of i
+
+is greater than or equal
+to t in order log n time.
+
+It's going to be
+able to do that.
+
+You're going to be able to
+compare R of i and R of i
+
+minus 1-- so the left
+and the right-- against t
+
+in order 1 time.
+
+But sadly, the actual insertion
+is going to require shifting.
+
+And that could take order n
+time, because it's an array.
+
+So that's the problem.
+
+Now you could imagine that
+you had a sorted list.
+
+And you could say, hey
+if I have a sorted list,
+
+then the list looks
+like this, and it's
+
+got a bunch of pointers in it.
+
+And if I've found
+the insertion point,
+
+then-- the list is nice,
+because you can insert something
+
+by moving pointers
+in constant time
+
+once you've found
+the insertion point.
+
+But what's the
+problem with the list?
+
+Yeah.
+
+AUDIENCE: You can't do
+binary search [INAUDIBLE].
+
+PROFESSOR: Well you can't
+do binary search on a list.
+
+There's no notion of
+going to the n by 2 index
+
+and doing random access on
+a conventional list, right?
+
+So the list does
+one thing right,
+
+but doesn't do the
+other thing right.
+
+The array does a
+couple things right,
+
+but doesn't do the
+shifting right.
+
+And so you see why we've
+constructed this toy problem.
+
+It's to motivate the
+binary search tree data
+
+structure, obviously.
+
+But you're close,
+but not quite there.
+
+What about heaps?
+
+We talked about heaps last time.
+
+What's the basic problem with
+the heap for this problem?
+
+The heaps are data
+arrays, but you
+
+can visualize them as trees.
+
+And obviously if we're talking
+about min heaps and max heaps.
+
+So in particular, what goes
+wrong with a min heap or a max
+
+heap for this problem?
+
+What takes a long time?
+
+Yeah.
+
+AUDIENCE: You have to scan every
+element, which [INAUDIBLE].
+
+PROFESSOR: That's right.
+
+I mean, sadly, you know when
+we talk about min heaps or max
+
+heaps, they actually have
+a fairly weak invariant.
+
+It turns out that-- I'm
+previewing a bit here--
+
+binary search
+trees are obviously
+
+similar to heaps in the
+sense that you visualize
+
+an array as a tree,
+in the case of a heap.
+
+And binary search
+trees are trees.
+
+But the invariant in a
+min heap or a max heap,
+
+is this kind of
+a week invariant.
+
+It essentially says,
+look at the min element.
+
+And the min element
+has to be the root,
+
+so you can do that one
+operation pretty quickly.
+
+But if you want to look
+for a k minute check,
+
+you want to see if there's
+an element in the heap that
+
+is less than or equal to k,
+or greater than or equal to k
+
+from t, this is going
+to take order n time.
+
+OK?
+
+Good.
+
+And finally, we haven't
+talked about dictionaries,
+
+but we will next week.
+
+Eric will talk about hash
+tables and dictionaries.
+
+And they have the same problem.
+
+So it's not like dictionaries
+are going to solve the problem,
+
+for those of you who know about
+hash tables and dictionaries.
+
+But you'll hear about
+them in some detail.
+
+They're very good
+at other things.
+
+So I don't want to say much more
+about that, because you're not
+
+supposed to know
+about dictionaries.
+
+Or at least we
+don't want to assume
+
+you do, though we
+have talked about them
+
+and alluded to
+dictionaries earlier.
+
+And so that's a story here.
+
+Yeah, back there, question.
+
+AUDIENCE: Yeah, can you explain
+why it's [INAUDIBLE] time?
+
+PROFESSOR: So what
+is a heap, right?
+
+A heap essentially-- a
+min heap, for example,
+
+or we talked about
+max heaps last time,
+
+has the property that
+you have an element k,
+
+and you're going to look
+at, let's say it's 21.
+
+Let's do min heaps, so this
+has to be less than what's
+
+here, 23, and what
+there, maybe it's
+
+30, and so on and so forth.
+
+And you have a
+recursive definition.
+
+And when you insert into a min
+heap, typically what happens
+
+is suppose you wanted to
+insert, for argument's sake,
+
+I want to insert 25.
+
+I want to insert 25 into this.
+
+The insertion algorithm
+for a min heap
+
+typically adds to the
+end of the min heap.
+
+So what you do is you
+would add 25 to this.
+
+And let's say that you
+had something out here.
+
+So you'd add to it.
+
+And you'd start flipping things.
+
+And you could work with
+just this part of the array
+
+to insert 25 in here.
+
+And you'd be able to satisfy
+the invariant of the min heap.
+
+And you'd get a
+legitimate min heap.
+
+But you'd never check the
+left part of it, which is 23.
+
+So it's quite possible--
+and this is a good example--
+
+that your basic insertion
+algorithm, which is essentially
+
+a version of max heap
+of i, or min heap of i,
+
+would simply insert
+at the end, and keep
+
+flipping until you get
+the min heap property,
+
+would be unable to check
+for the k minute check
+
+during the insertion.
+
+But what you'd have to do
+is to go look elsewhere.
+
+That min heap of i
+we'd never look at--
+
+or the insert algorithm we'd
+never look at-- and that
+
+would require order n time.
+
+All right?
+
+AUDIENCE: Thank you.
+
+PROFESSOR: So that's the
+story for the min heap.
+
+Thanks for the question.
+
+And it's similar for
+dictionaries, as I said.
+
+And so we're stuck.
+
+We have no data structure yet
+that can do all of the things
+
+that I put up on the board to
+the left, in order log n time.
+
+And as you can see, the
+sorted array got pretty close.
+
+And so if you could
+just solve this problem,
+
+if you could do fast insertion--
+and by fast I mean order log n
+
+time-- into a sorted
+array, we'd be in business.
+
+So that's what we'd like to
+do with binary search trees.
+
+Binary search trees
+are, as you can imagine,
+
+enable binary search.
+
+But the sorted arrays
+don't allow fast insertion,
+
+but BSTs do.
+
+So let me introduce BSTs.
+
+As with any data
+structure, there's
+
+a nice invariant
+associated with BSTs.
+
+The invariant is stronger
+than the heap invariant.
+
+And actually, that makes them
+a different data structure, not
+
+necessarily a better
+data structure.
+
+And I'll say why, but different.
+
+For this problem they're better.
+
+So one example of a binary
+search tree looks like this.
+
+And as a binary tree you have
+a node, and we call it x.
+
+Each of the nodes
+has a key of x.
+
+So 30 is the key for this node,
+17 for that one, et cetera.
+
+Unlike in a heap,
+your data structure
+
+is a little more complicated.
+
+The heap is simply
+an array, and you
+
+happen to visualize
+it as a tree.
+
+The binary search
+tree is actually
+
+a tree that has
+pointers, unlike a heap.
+
+So it's a more complicated
+data structure.
+
+You need a few more bytes for
+every node of the binary search
+
+tree, as opposed
+to the heap, which
+
+is simply an array element.
+
+And the pointers
+are parent of x.
+
+I haven't bothered
+showing the arrows here,
+
+because you could be going
+upwards or backwards.
+
+And you could imagine
+that you actually
+
+have a parent pointer
+that goes up this way,
+
+and you have a child
+pointer that goes this way.
+
+So there's really,
+potentially, three pointers
+
+for each node, the
+parent, the left child,
+
+and the right child.
+
+So pretty straightforward.
+
+That's the data
+structure in terms
+
+of what it needs to have
+so you can operate on it.
+
+And there's an
+invariant for a BST.
+
+What makes a BST
+is that you have
+
+an ordering of the
+key values that
+
+satisfy the invariant that
+for all nodes x if y is
+
+in the left subtree
+of x, we have--
+
+if it's in the left
+subtree then key of y
+
+is less than or
+equal to key of x.
+
+And if y is in the
+right subtree we
+
+have key of y is greater
+than or equal to key of x.
+
+So if we're talking
+about trees here,
+
+subtrees here,
+everything underneath--
+
+and that's the stronger part
+of the invariant in the BST,
+
+versus in the heap we were just
+talking about the children.
+
+And so you look at
+this BST, it is a BST
+
+because if I look to
+the right, from the root
+
+I only see values that
+are greater than 30.
+
+And if I look to the left,
+in the entire subtree,
+
+all the way down I only see
+values that are less than 30.
+
+And that has to be true for any
+intermediate node in the tree.
+
+And the only other
+nontrivial node here is 17.
+
+And you see that 14 is less than
+17, and 20 is greater than 17.
+
+OK?
+
+So that's the BST.
+
+That's the data structure.
+
+This is the invariant.
+
+So let's look at why BSTs
+are a possibility for solving
+
+our runway reservation problem.
+
+And what I'll do is
+I'll do the insert.
+
+So let's start with the
+nil set of elements,
+
+or null set of elements, R.
+And let's start inserting.
+
+So I insert 49.
+
+And all I do is make a node
+that has a key value of 49.
+
+This one is easy.
+
+Next insert, 79.
+
+And what happens here
+is I have to look at 49,
+
+and I compare 79 to 49.
+
+And because 79 is greater
+than 49 I go to the right
+
+and I attach 79 to
+the right child of 49.
+
+Then I want to insert 46.
+
+And when I want to
+insert 46 I look at this,
+
+I compare 49 and 46.
+
+46 is less, so I go to the left
+side and I put 46 in there.
+
+Next, let's say I
+want to insert 41.
+
+So far I haven't really talked
+about the k minute checks.
+
+And you could imagine
+that they're being done.
+
+I'll show you exactly, or
+talk about exactly how they're
+
+done in a second.
+
+It's not that hard.
+
+But let me go ahead
+and do one more.
+
+For 41, 41 is less
+than 49, so I go left.
+
+41 is less than 46, so
+I go left and attach it
+
+to the left child.
+
+All right?
+
+So that's what I have right now.
+
+Now let's talk about
+the k minute check.
+
+It's good to talk about
+the K minute check
+
+when there's
+actually a violation.
+
+And let's assume
+the k equals 3 here.
+
+And so, same thing here.
+
+You're essentially doing
+binary search here.
+
+And you're doing the checks as
+you're doing the binary search.
+
+So what you're
+going to be doing is
+
+you're going to check that--
+you're going to compare 42
+
+with 49, with the
+k minute check.
+
+And you realize they're 7 apart.
+
+So that's OK.
+
+And 42 is less than
+49, so you go left.
+
+And then you compare 42 with 46.
+
+And again, it's less than 46,
+but it's k away, more than 3
+
+away from 46.
+
+So that's cool.
+
+And you go left.
+
+And then you get to 41.
+
+And you compare 42 with 41.
+
+In this case is greater.
+
+But it's not k more than it.
+
+And so that means that if
+you didn't have the check,
+
+you would be putting 42 in here.
+
+But because you have
+the check, you fail.
+
+And you say, look,
+I mean this violates
+
+the safety property, violates
+the check I need to do.
+
+And therefore I'm
+not going to insert--
+
+I'm not going to reserve
+a request for you.
+
+All right?
+
+So what's happened here is
+it's basically a sorted array,
+
+except that you added
+a bunch of pointers
+
+associated with the tree.
+
+And so it's somewhere between a
+sorted list and a sorted array.
+
+And it does exactly
+the right thing
+
+with respect to
+being able to insert.
+
+Once you've found
+the place to insert,
+
+it's merely attaching
+this particular new node
+
+with it's appropriate
+key to the pointer.
+
+All right?
+
+So what's happened
+here is that if h
+
+is the height of the
+tree then insertion
+
+with or without the check
+is done in order h time.
+
+And that's what
+BSTs are good for.
+
+People buy that?
+
+Any questions about how they
+k minute check proceeded?
+
+Yeah, question.
+
+AUDIENCE: So, what's it called?
+
+The what check?
+
+PROFESSOR: The k minute check.
+
+Sorry, the k was 3 minutes k.
+
+I had this thing over
+here, add t to the set R
+
+if no other landings are
+scheduled within k minutes.
+
+So k was just a number.
+
+I want it to be a
+parameter because it
+
+doesn't matter what k is.
+
+As long as you know what it is
+when you do the binary search,
+
+you can add that in to an
+argument to your insert,
+
+and do the check.
+
+AUDIENCE: OK.
+
+PROFESSOR: So in this case,
+I set k to be 3 out here.
+
+And I was doing a check
+to see that the invariant,
+
+any elements in the BST
+already, on any nodes that
+
+had keys that were
+within 3 minutes--
+
+because I fixed k to be
+3-- to the actual time
+
+that I was trying to insert.
+
+All right?
+
+AUDIENCE: So there's
+no way [INAUDIBLE].
+
+PROFESSOR: I'm sorry,
+there's no way?
+
+AUDIENCE: There's
+no way you could
+
+insert the 42 into
+the tree then?
+
+PROFESSOR: Well, if
+the basic insertion
+
+method into a binary search tree
+doesn't have any constraints.
+
+But you can certainly
+augment the insertion method
+
+without changing the efficiency
+of the insertion method.
+
+So let's say that
+all you wanted to do
+
+was insert into a
+binary search tree,
+
+and it had nothing to do
+with the runway reservation.
+
+Then you would just insert
+the way I described to you.
+
+The beauty of the
+binary search tree
+
+is that while you're
+finding the place to insert,
+
+you can do these checks--
+the k minute checks.
+
+Yeah, question back there.
+
+AUDIENCE: What about 45?
+
+PROFESSOR: What about 45?
+
+So this is after-- we
+haven't inserted 42
+
+because it violated the check.
+
+So when you do 45,
+then what happens
+
+is you see that
+45 is less than 49
+
+and you pass, because you're
+more than 3 minutes away.
+
+We'll stick with that example.
+
+And then you get
+here and then you
+
+see that 45 is less than 46,
+and you'd fail right here.
+
+You would fail right here
+if you were doing the check,
+
+because 45 is not
+3 away from 46.
+
+All right?
+
+So that's the story.
+
+And so if you have h being
+the height of the tree,
+
+as you can see you're
+just following a path.
+
+And depending on
+what the height is
+
+you're going to do
+that many operations,
+
+times some constant factor.
+
+And so you can say that
+this is order h time.
+
+All right?
+
+Any other questions?
+
+Yeah, question back there.
+
+AUDIENCE: In a normal
+array [INAUDIBLE].
+
+PROFESSOR: Well, it's up to you.
+
+In a conventional binary search
+tree, or the vanilla binary
+
+search tree, typically
+what you're doing
+
+is you're doing
+either find or insert.
+
+And so what that means
+is that you would just
+
+return the pointer
+associated with that element.
+
+So if you're looking for find
+46, for example, on the tree
+
+that I have out there, typically
+46 is just the key value.
+
+And there may be a record
+associated with it.
+
+And you would get a
+pointer to that record
+
+because it's already in there.
+
+At that point you can
+say I want to override.
+
+Or if you want, you could
+have duplicate values.
+
+You could have this,
+what's called a multiset.
+
+A multiset is a set that
+has duplicate elements.
+
+In that case, you would need
+a little more sophistication
+
+to differentiate between
+two elements that
+
+have the same key values.
+
+So you'd have to
+call it 46a and 46b.
+
+And you'd have to have some
+way of differentiating.
+
+Any other questions?
+
+Yeah.
+
+AUDIENCE: Wouldn't
+it be a problem
+
+if the tree's not balanced?
+
+PROFESSOR: Ah, great question.
+
+Yes, stay tuned.
+
+So I was careful, right?
+
+I guess I kind of
+alluded to the fact
+
+that we'd solved the
+runway reservation system.
+
+Did I actually say that
+we'd solved the problem?
+
+Did I say we had
+solved the problem?
+
+OK, so I did not lie.
+
+I did not lie.
+
+I said that the height
+of the tree was h.
+
+And I said that this was
+accomplished in order h time,
+
+right?
+
+Which is not quite what I want,
+which is really your question.
+
+So we'll get to that.
+
+So we're not quite done yet.
+
+But before we do
+that, it turns out
+
+that today's lecture is
+really part one of two.
+
+You'll get a really good
+sense of BST operations
+
+in today's lecture.
+
+But there's going to be a few
+things that-- we can't cover
+
+all of double 6 in
+the lecture, right?
+
+We'd like to, and let you
+off for the entire fall,
+
+but that's not the way
+it works, all right?
+
+So it's a great question.
+
+I'll answer it towards the end.
+
+I just wanted you
+to say a little bit
+
+about other operations.
+
+There's many operations that
+you can do on a binary search
+
+tree, that can be
+done in order h time,
+
+and some even in constant time.
+
+And I'll put these in the notes.
+
+Some of these are
+fairly straightforward.
+
+Find min can be done
+in heap, in a min heap.
+
+If you want to find the minimum
+value, it's constant time.
+
+You just return the root.
+
+In the case of a binary search
+tree, how do you find the min?
+
+Someone?
+
+Worth a cushion.
+
+Yep.
+
+AUDIENCE: Keep
+going to the left?
+
+PROFESSOR: Keep
+going to the left.
+
+And how do you find the max?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Keep
+going to the right.
+
+All right great, thank you.
+
+And finally, what
+complexity is that?
+
+I sort gave it away, but I
+want to hear it from you.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Hm?
+
+AUDIENCE: It's the height
+
+PROFESSOR: It's the
+height, order h.
+
+All right, it's
+order h complexity.
+
+Go to the left until
+you hit a leaf,
+
+and until leaf
+order h complexity.
+
+Same thing for max.
+
+And then you can do
+a bunch of things.
+
+I'll put these in the notes.
+
+You can find things
+like next larger
+
+x, which is the next
+largest value beyond x.
+
+And you look at the key for
+x and you say, for example,
+
+if you put 46 in there, what's
+the next thing that's larger
+
+and that?
+
+In this tree here, it's 49.
+
+But that's something which was
+trivially done in this example.
+
+But in general you can do
+this in order h time as well.
+
+And you can see the pseudocode.
+
+And we'll probably cover
+that in section tomorrow.
+
+What I want to do today, for the
+rest of the time I have left,
+
+is actually talk about augmented
+binary search trees, which
+
+are things that can do more
+and have more data in them
+
+than just these pointers.
+
+And that's actually
+something which
+
+should give you a sense of the
+richness of the binary search
+
+tree structure, this
+notion of augmentation.
+
+And those of you, again,
+who have taken double 05,
+
+you know about
+design amendments.
+
+And so specifications
+never stay the same.
+
+I mean, you're
+working for someone,
+
+and they never really
+tell you what they want.
+
+They might, but they
+change their mind.
+
+So in this case, we're
+going to change our mind.
+
+And so we've done
+this to the extent
+
+that we can cover all of
+these in order h time.
+
+And let's say that now
+the problem specification
+
+changed on us.
+
+There's an additional
+requirement
+
+that we're asked to solve.
+
+And so you sort of
+committed to BST structures.
+
+But now we have an
+additional requirement.
+
+And the new requirement is that
+we be able to compute rank t.
+
+And rank t is how
+many planes are
+
+scheduled to land at times
+less than or equal to t.
+
+So perfectly
+reasonable question.
+
+It wasn't part of
+the original spec.
+
+You now have built your
+BST data structure,
+
+you thought you were done.
+
+Sorry, you aren't.
+
+You've got to do
+this extra stuff.
+
+So that's the notion
+of augmentation,
+
+which we're going to use this
+is an example of how we're
+
+going to augment
+the BST structure.
+
+And oh, by the way,
+I don't want you
+
+to change the
+complexity from order h.
+
+And we eventually will
+get to order log n,
+
+but don't go change something
+that was logarithmic to linear.
+
+That would be bad.
+
+So let's talk about
+how you do this.
+
+And I don't think we
+need this anymore.
+
+So the first thing we need to
+do is add a little bit more
+
+information to the
+node structure.
+
+And what we're going to do
+is augment the BST structure.
+
+And we're going to add one
+little number associated
+
+with each node, that looks at
+the number of nodes below it.
+
+So in particular,
+let's say that I
+
+have 49, 46, let's just
+say 49, 46 for now.
+
+And over here I
+have 79, 64, and 83.
+
+I'm going to modify--
+I'm going to have
+
+an extra number associated
+with each of these nodes.
+
+And I'm just going
+to write that number
+
+on the outside of the node.
+
+And you can just imagine
+that now the key value has
+
+two numbers associated
+with it-- the thing
+
+that I write inside the node,
+and what I write outside of it.
+
+So in particular, when
+I do insert or delete
+
+I'm going to be
+modifying these numbers.
+
+And these are size numbers.
+
+And what do I mean by that?
+
+Well these numbers
+correspond to subtree sizes.
+
+So the subtree size
+here is 1, 1, 1.
+
+So as I'm building
+this tree up I'm
+
+going to create an
+augmented BST structure,
+
+and I've modified
+insert and delete
+
+so they do some extra work.
+
+So let's say, for
+argument's sake,
+
+that I've added this in
+sort of a bottom up fashion.
+
+And what I have are these
+particular subtree sizes.
+
+All of these should make sense.
+
+This has just a single
+node, same thing here.
+
+So this subtree sizes associated
+with these nodes are all 1.
+
+The subtree size
+associated with 79
+
+is 3, because you're
+counting 79 and 64 and 83.
+
+And the subtree size
+associated with 49
+
+is 5, because you're counting
+everything underneath it.
+
+How did we get these numbers?
+
+Well you want to
+think about this
+
+as you started
+with an empty set,
+
+and you kept inserting into it.
+
+And you were doing a sequence
+of insert and delete operations.
+
+And if I explain to you how
+an insert operation modifies
+
+these numbers, that is
+pretty much all you need.
+
+And of course, analogously,
+for a delete operation.
+
+So what would happen for, let's
+say you wanted to insert 43?
+
+You would insert
+43 at this point.
+
+And what you'd do is you
+follow the insertion path
+
+just like you did before.
+
+But when you're
+following that path
+
+you're going to increment the
+nodes that you're seeing by 1.
+
+So you're going
+to add 43 to this.
+
+And you'd add 5 plus
+1, because you see 49.
+
+And then you would go
+down and you'd see 46.
+
+And so you'd add 1 to that.
+
+And then finally,
+you add 43 and you
+
+assign-- since
+it's a leaf-- you'd
+
+assign to value corresponding
+to the subtree size
+
+of this new node that you
+put in there, to be 1.
+
+It guess a little, teensy
+bit more complicated
+
+when you want to do
+the k minute check.
+
+But from a complexity
+standpoint,
+
+if you're not worried
+about constant factors,
+
+you can just say, you know what?
+
+I'm going to first run
+the regular insert,
+
+ignoring the subtree sizes.
+
+And if it fails, I'm done.
+
+Because I'm not going to
+modify the BST, and I'm done.
+
+I'm not going to have to
+modify the subtree sizes.
+
+If it succeeds, then
+I'm going to go in,
+
+and I know now that I can
+increment each of these nodes,
+
+because I know I'm
+going to be successful.
+
+So that's sort of a trivial
+way of solving this problem,
+
+that from an asymptotic
+complexity standpoint
+
+gives you your order
+h augmented insert.
+
+That make sense?
+
+Now you could do something
+better than that.
+
+I mean, I would urge you,
+if you had wrote something
+
+that-- we asked you to
+write something like this,
+
+to create a single procedure
+that essentially uses
+
+a recursion appropriately to
+do the right thing in one pass
+
+through the BST.
+
+And we'll talk about
+things like that
+
+as we go along in sections,
+and possibly in lectures.
+
+So that's the subtree
+insert delete.
+
+Everyone buy that?
+
+Yeah, question back there.
+
+AUDIENCE: If I wanted to delete
+a number, like let's say 79--
+
+PROFESSOR: Yep?
+
+AUDIENCE: --would we
+have to take it out
+
+and then rewrite the entire BST?
+
+PROFESSOR: What you'd have to
+do is a bubble up pointers.
+
+So you'd have to actually
+have 64 connected to-- what
+
+will happen is 83
+would actually come up,
+
+and you would essentially
+have some thing-- this
+
+is not quite how it works--
+but 83 would move up
+
+and you'd have 64 to the left.
+
+That's what would happened
+for delete in this case.
+
+So you would have to move
+pointers in the case of delete.
+
+And we're not done with
+binary search tree operations
+
+from a standpoint of
+teaching you about them.
+
+We'll talk about them not
+just in today's lecture,
+
+but later as well.
+
+So there's one
+thing missing here,
+
+though, which is I haven't
+quite figured out--
+
+I've told you how these
+subtree sizes work.
+
+But it's not
+completely clear, this
+
+is the last thing we have
+to do, is how are you
+
+going to compute rank t
+from the subtree sizes?
+
+So everyone understand
+subtree sizes?
+
+It's just the number of nodes
+that are underneath you.
+
+And you remember to count
+yourself, all right?
+
+Now what is rank t?
+
+Rank t is how many
+planes are scheduled
+
+to land at times less
+than or equal to t.
+
+So now I have a BST structure
+that looks like the one
+
+and I just ended up with.
+
+So I've added this 43.
+
+And so let me draw
+that out here,
+
+and see if we can
+answer this question.
+
+This is a subtle question.
+
+So I got 49, and that
+subtree size is 6.
+
+I got 46, subtree size is 2.
+
+43, 79, 64.
+
+and 83.
+
+So what I want is
+what lands before t?
+
+And how do I do that?
+
+Give me an algorithm
+that would allow
+
+me to compute in order h time.
+
+I want to do this
+in order h time.
+
+What lands before t?
+
+Someone?
+
+Yeah.
+
+AUDIENCE: So first
+you would have
+
+to find where to insert
+it, like we did before.
+
+PROFESSOR: Right, right.
+
+AUDIENCE: And then because we
+have the order of whatever it
+
+was before-- not
+the order, the--
+
+PROFESSOR: The sizes?
+
+The sizes?
+
+Yeah.
+
+AUDIENCE: And then we can
+look what's more than it
+
+on the right, we can
+subtract it and we get--
+
+PROFESSOR: What is more
+than it on the right.
+
+Do you want to say--
+
+AUDIENCE: Because, like--
+
+PROFESSOR: OK.
+
+AUDIENCE: --on the right--
+
+PROFESSOR: Right.
+
+AUDIENCE: --and then we
+can take this minus this
+
+and we get what's left.
+
+PROFESSOR: That's
+great, that's excellent.
+
+Excellent.
+
+So I'm going to do it a little
+bit differently from what
+
+you described.
+
+I'm going to
+actually do it in a,
+
+sort of, a more positive
+way, no offense intended.
+
+What we're going to
+do is we're going
+
+to add up the things
+that we want to add up.
+
+And what you have
+to do is walk--
+
+your first step was right on.
+
+I mean, your answer is correct.
+
+I'm just going to do it
+a little bit differently.
+
+You walk down the tree
+to find the desired time.
+
+This is just your search.
+
+We know how to do that.
+
+As you walk down you
+add in the nodes that
+
+is the subtree sizes-- you're
+just adding in the notes here.
+
+So if you see-- depending
+on the number of nodes
+
+that you see as you're
+going deeper in,
+
+you want to add in the nodes.
+
+And you're going to add
+one to that, corresponding
+
+to the nodes that are smaller.
+
+And we're going to add in the
+subtree sizes to the left,
+
+as opposed to subtracting.
+
+That may not make
+a lot of sense.
+
+But I guarantee you it
+will once we do an example.
+
+So what's going on here?
+
+I want to find a
+place to insert.
+
+I'm not actually going
+to do the insert.
+
+Think of it is doing a lookup.
+
+And along the way,
+I need to figure out
+
+the less than operator.
+
+I want to find all
+of the things that
+
+are less than this
+value I'm searching for.
+
+And so I have to do
+a bit of arithmetic.
+
+So let's say that I'm
+looking for what's
+
+less than or equal to 79.
+
+So t equals 79.
+
+So I'm going to look at 49.
+
+I'm going to walk down,
+I'm going to look at 49.
+
+And because I say I'm
+looking at 49-- and 49
+
+is clearly less than 79.
+
+So I'm going to add 1.
+
+And that's this check over here.
+
+I move on and what I need to
+do now is move to the right,
+
+because 79 is greater than 49.
+
+That's how my search would work.
+
+But because I've
+moved to the right,
+
+I'm going to add the subtree
+sizes that were to the left.
+
+Because I know that all
+of the things to the left
+
+are clearly less than 79.
+
+So I'm going to add 2,
+corresponding to a subtree 46.
+
+So I'm not actually
+looking there.
+
+But I'm going to add
+all of that stuff in.
+
+I'm going to move to the right,
+and now I'm going to see 79.
+
+At this point 79 is less
+than or equal to 79.
+
+So I'm going to see 79
+and I'm going to add 1.
+
+And because I've added 79,
+just like I did with 49,
+
+I have to add the subtree
+size to the left of 79.
+
+So the final addition
+is I add 1 corresponding
+
+to the subtree 64.
+
+And at this point
+I've discovered
+
+where I have to insert, I've
+essentially found the location,
+
+it matches 79.
+
+And there was no modification
+required in this algorithm.
+
+So if that was 78 you'd
+essentially do the same things.
+
+But you're done because you
+found the value, or the place
+
+that you want to insert.
+
+And you've done a
+bunch of additions.
+
+And you go look at add 1, add
+2, add 1, add 1, and you have 5.
+
+And that's the
+correct answer, as you
+
+can see from this example.
+
+So what's the bad news?
+
+The bad news was what
+this lady said up
+
+front, which was we haven't
+quite solved the problem.
+
+Because sadly, I could
+easily set things
+
+up such that the height h is
+order n, h could be order n.
+
+And if, for example, I
+gave you a sorted list,
+
+and I said insert into
+binary search tree
+
+that's originally null 43,
+and you put 43 in there.
+
+Then I say insert 46.
+
+And then I say instead of 48.
+
+And then I say
+insert 49, et cetera.
+
+And, you know, these
+could be any numbers.
+
+Then you see that what
+does this look like?
+
+Does it look like a tree?
+
+It looks like a list.
+
+That's the bad news.
+
+And I'll let Eric give
+you good news next week.
+
+We need to have this notion of
+balanced binary search trees.
+
+So everything I've said is true.
+
+I did not lie.
+
+But the one extra
+thing is we need
+
+to make sure these trees are
+balanced so h is order log n.
+
+And then everything
+I said works.
+
+All right?
+
+See you next time.
\ No newline at end of file
diff --git a/9NChLq-orAk.txt b/9NChLq-orAk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eb35a93a882f7b24f46e548642789dd5874166a6
--- /dev/null
+++ b/9NChLq-orAk.txt
@@ -0,0 +1,307 @@
+align:start position:0%
+ 
+so ours is a little different
+
+ align:start position:0%
+so ours is a little different
+ 
+
+ align:start position:0%
+so ours is a little different
+well it was actually very different from
+
+ align:start position:0%
+well it was actually very different from
+ 
+
+ align:start position:0%
+well it was actually very different from
+everyone else because ours is in 2d and
+
+ align:start position:0%
+everyone else because ours is in 2d and
+ 
+
+ align:start position:0%
+everyone else because ours is in 2d and
+everyone else's is in 3d but so all we
+
+ align:start position:0%
+everyone else's is in 3d but so all we
+ 
+
+ align:start position:0%
+everyone else's is in 3d but so all we
+have basically is like a background and
+
+ align:start position:0%
+have basically is like a background and
+ 
+
+ align:start position:0%
+have basically is like a background and
+then you have like a canvas and and then
+
+ align:start position:0%
+then you have like a canvas and and then
+ 
+
+ align:start position:0%
+then you have like a canvas and and then
+what you can do is if I can find the
+
+ align:start position:0%
+what you can do is if I can find the
+ 
+
+ align:start position:0%
+what you can do is if I can find the
+mouse you can like paint on here for
+
+ align:start position:0%
+mouse you can like paint on here for
+ 
+
+ align:start position:0%
+mouse you can like paint on here for
+example and then if you click on eraser
+
+ align:start position:0%
+example and then if you click on eraser
+ 
+
+ align:start position:0%
+example and then if you click on eraser
+and then go over that you can erase it
+
+ align:start position:0%
+and then go over that you can erase it
+ 
+
+ align:start position:0%
+and then go over that you can erase it
+so the main part of this was supposed to
+
+ align:start position:0%
+so the main part of this was supposed to
+ 
+
+ align:start position:0%
+so the main part of this was supposed to
+be that it's supposed to be able to
+
+ align:start position:0%
+be that it's supposed to be able to
+ 
+
+ align:start position:0%
+be that it's supposed to be able to
+connect with the Kinect and if you for
+
+ align:start position:0%
+connect with the Kinect and if you for
+ 
+
+ align:start position:0%
+connect with the Kinect and if you for
+example you use your but your right hand
+
+ align:start position:0%
+example you use your but your right hand
+ 
+
+ align:start position:0%
+example you use your but your right hand
+to move the mouse and like they did and
+
+ align:start position:0%
+to move the mouse and like they did and
+ 
+
+ align:start position:0%
+to move the mouse and like they did and
+then put like if your left hand goes up
+
+ align:start position:0%
+then put like if your left hand goes up
+ 
+
+ align:start position:0%
+then put like if your left hand goes up
+it clicks and then it supposed to draw
+
+ align:start position:0%
+it clicks and then it supposed to draw
+ 
+
+ align:start position:0%
+it clicks and then it supposed to draw
+but the Kinect would just not connect
+
+ align:start position:0%
+but the Kinect would just not connect
+ 
+
+ align:start position:0%
+but the Kinect would just not connect
+with the thing at all for some reason so
+
+ align:start position:0%
+with the thing at all for some reason so
+ 
+
+ align:start position:0%
+with the thing at all for some reason so
+we couldn't it wouldn't detect motion so
+
+ align:start position:0%
+we couldn't it wouldn't detect motion so
+ 
+
+ align:start position:0%
+we couldn't it wouldn't detect motion so
+we couldn't get it to work but
+
+ align:start position:0%
+we couldn't get it to work but
+ 
+
+ align:start position:0%
+we couldn't get it to work but
+essentially what it does is if you were
+
+ align:start position:0%
+essentially what it does is if you were
+ 
+
+ align:start position:0%
+essentially what it does is if you were
+to see when it's just painting it's
+
+ align:start position:0%
+to see when it's just painting it's
+ 
+
+ align:start position:0%
+to see when it's just painting it's
+creating a dot right so what it's
+
+ align:start position:0%
+creating a dot right so what it's
+ 
+
+ align:start position:0%
+creating a dot right so what it's
+basically doing is every time you click
+
+ align:start position:0%
+basically doing is every time you click
+ 
+
+ align:start position:0%
+basically doing is every time you click
+it creates a dot and then if you do it
+
+ align:start position:0%
+it creates a dot and then if you do it
+ 
+
+ align:start position:0%
+it creates a dot and then if you do it
+like a fluid motion it creates a bunch
+
+ align:start position:0%
+like a fluid motion it creates a bunch
+ 
+
+ align:start position:0%
+like a fluid motion it creates a bunch
+of dots where for example if you were to
+
+ align:start position:0%
+of dots where for example if you were to
+ 
+
+ align:start position:0%
+of dots where for example if you were to
+like you know draw a lot it's yeah you
+
+ align:start position:0%
+like you know draw a lot it's yeah you
+ 
+
+ align:start position:0%
+like you know draw a lot it's yeah you
+see like the dots down here we were like
+
+ align:start position:0%
+see like the dots down here we were like
+ 
+
+ align:start position:0%
+see like the dots down here we were like
+gonna do colors but we couldn't get that
+
+ align:start position:0%
+gonna do colors but we couldn't get that
+ 
+
+ align:start position:0%
+gonna do colors but we couldn't get that
+far but that's like the recent project
+
+ align:start position:0%
+far but that's like the recent project
+ 
+
+ align:start position:0%
+far but that's like the recent project
+we were gonna have something where you
+
+ align:start position:0%
+we were gonna have something where you
+ 
+
+ align:start position:0%
+we were gonna have something where you
+could like change the the canvas and
+
+ align:start position:0%
+could like change the the canvas and
+ 
+
+ align:start position:0%
+could like change the the canvas and
+then you can change the background so it
+
+ align:start position:0%
+then you can change the background so it
+ 
+
+ align:start position:0%
+then you can change the background so it
+looks like you're painting it like at
+
+ align:start position:0%
+looks like you're painting it like at
+ 
+
+ align:start position:0%
+looks like you're painting it like at
+the beach or something like that and so
+
+ align:start position:0%
+the beach or something like that and so
+ 
+
+ align:start position:0%
+the beach or something like that and so
+you know ascetically pleasing because
+
+ align:start position:0%
+you know ascetically pleasing because
+ 
+
+ align:start position:0%
+you know ascetically pleasing because
+this is as far as we could get for now
\ No newline at end of file
diff --git a/9i1sOSIccgw.txt b/9i1sOSIccgw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eec2d722806c647a511d8f8353d5653fd06057bb
--- /dev/null
+++ b/9i1sOSIccgw.txt
@@ -0,0 +1,915 @@
+align:start position:0%
+ 
+the topic of this recitation is election
+
+ align:start position:0%
+the topic of this recitation is election
+ 
+
+ align:start position:0%
+the topic of this recitation is election
+forecasting which is the art and science
+
+ align:start position:0%
+forecasting which is the art and science
+ 
+
+ align:start position:0%
+forecasting which is the art and science
+of predicting the winner of an election
+
+ align:start position:0%
+of predicting the winner of an election
+ 
+
+ align:start position:0%
+of predicting the winner of an election
+before any votes are actually cast using
+
+ align:start position:0%
+before any votes are actually cast using
+ 
+
+ align:start position:0%
+before any votes are actually cast using
+polling data from likely voters in this
+
+ align:start position:0%
+polling data from likely voters in this
+ 
+
+ align:start position:0%
+polling data from likely voters in this
+recitation we are going to look at the
+
+ align:start position:0%
+recitation we are going to look at the
+ 
+
+ align:start position:0%
+recitation we are going to look at the
+United States presidential election in
+
+ align:start position:0%
+United States presidential election in
+ 
+
+ align:start position:0%
+United States presidential election in
+the United States a president is elected
+
+ align:start position:0%
+the United States a president is elected
+ 
+
+ align:start position:0%
+the United States a president is elected
+every four years and while there are a
+
+ align:start position:0%
+every four years and while there are a
+ 
+
+ align:start position:0%
+every four years and while there are a
+number of different political parties in
+
+ align:start position:0%
+number of different political parties in
+ 
+
+ align:start position:0%
+number of different political parties in
+the u.s. generally there are only two
+
+ align:start position:0%
+the u.s. generally there are only two
+ 
+
+ align:start position:0%
+the u.s. generally there are only two
+competitive candidates there's the
+
+ align:start position:0%
+competitive candidates there's the
+ 
+
+ align:start position:0%
+competitive candidates there's the
+Republican candidate who tends to be
+
+ align:start position:0%
+Republican candidate who tends to be
+ 
+
+ align:start position:0%
+Republican candidate who tends to be
+more conservative and the Democratic
+
+ align:start position:0%
+more conservative and the Democratic
+ 
+
+ align:start position:0%
+more conservative and the Democratic
+candidate who's more liberal so for
+
+ align:start position:0%
+candidate who's more liberal so for
+ 
+
+ align:start position:0%
+candidate who's more liberal so for
+instance a recent Republican president
+
+ align:start position:0%
+instance a recent Republican president
+ 
+
+ align:start position:0%
+instance a recent Republican president
+was george w bush and a recent
+
+ align:start position:0%
+was george w bush and a recent
+ 
+
+ align:start position:0%
+was george w bush and a recent
+Democratic president was Barack Obama
+
+ align:start position:0%
+Democratic president was Barack Obama
+ 
+
+ align:start position:0%
+Democratic president was Barack Obama
+now while in many countries the leader
+
+ align:start position:0%
+now while in many countries the leader
+ 
+
+ align:start position:0%
+now while in many countries the leader
+of the country is elected using you know
+
+ align:start position:0%
+of the country is elected using you know
+ 
+
+ align:start position:0%
+of the country is elected using you know
+the simple candidate who receives the
+
+ align:start position:0%
+the simple candidate who receives the
+ 
+
+ align:start position:0%
+the simple candidate who receives the
+largest number of votes across the
+
+ align:start position:0%
+largest number of votes across the
+ 
+
+ align:start position:0%
+largest number of votes across the
+entire country is elected in the United
+
+ align:start position:0%
+entire country is elected in the United
+ 
+
+ align:start position:0%
+entire country is elected in the United
+States it's significantly more
+
+ align:start position:0%
+States it's significantly more
+ 
+
+ align:start position:0%
+States it's significantly more
+complicated there are 50 states in the
+
+ align:start position:0%
+complicated there are 50 states in the
+ 
+
+ align:start position:0%
+complicated there are 50 states in the
+United States and each is assigned a
+
+ align:start position:0%
+United States and each is assigned a
+ 
+
+ align:start position:0%
+United States and each is assigned a
+number of electoral votes based on its
+
+ align:start position:0%
+number of electoral votes based on its
+ 
+
+ align:start position:0%
+number of electoral votes based on its
+population so for instance the most
+
+ align:start position:0%
+population so for instance the most
+ 
+
+ align:start position:0%
+population so for instance the most
+populous state California in 2012 had
+
+ align:start position:0%
+populous state California in 2012 had
+ 
+
+ align:start position:0%
+populous state California in 2012 had
+nearly twenty times the number of
+
+ align:start position:0%
+nearly twenty times the number of
+ 
+
+ align:start position:0%
+nearly twenty times the number of
+electoral votes as the least populous
+
+ align:start position:0%
+electoral votes as the least populous
+ 
+
+ align:start position:0%
+electoral votes as the least populous
+states and these number of electoral
+
+ align:start position:0%
+states and these number of electoral
+ 
+
+ align:start position:0%
+states and these number of electoral
+votes are reassigned periodically based
+
+ align:start position:0%
+votes are reassigned periodically based
+ 
+
+ align:start position:0%
+votes are reassigned periodically based
+on changes of populations between states
+
+ align:start position:0%
+on changes of populations between states
+ 
+
+ align:start position:0%
+on changes of populations between states
+within a given state in general the
+
+ align:start position:0%
+within a given state in general the
+ 
+
+ align:start position:0%
+within a given state in general the
+system is winner-take-all in the sense
+
+ align:start position:0%
+system is winner-take-all in the sense
+ 
+
+ align:start position:0%
+system is winner-take-all in the sense
+that the candidate who receives the most
+
+ align:start position:0%
+that the candidate who receives the most
+ 
+
+ align:start position:0%
+that the candidate who receives the most
+votes in the state gets all of its
+
+ align:start position:0%
+votes in the state gets all of its
+ 
+
+ align:start position:0%
+votes in the state gets all of its
+electoral votes and then across the
+
+ align:start position:0%
+electoral votes and then across the
+ 
+
+ align:start position:0%
+electoral votes and then across the
+entire country the candidate who
+
+ align:start position:0%
+entire country the candidate who
+ 
+
+ align:start position:0%
+entire country the candidate who
+receives the most electoral votes wins
+
+ align:start position:0%
+receives the most electoral votes wins
+ 
+
+ align:start position:0%
+receives the most electoral votes wins
+the entire presidential election now
+
+ align:start position:0%
+the entire presidential election now
+ 
+
+ align:start position:0%
+the entire presidential election now
+while it seems like a somewhat subtle
+
+ align:start position:0%
+while it seems like a somewhat subtle
+ 
+
+ align:start position:0%
+while it seems like a somewhat subtle
+distinction the Electoral College versus
+
+ align:start position:0%
+distinction the Electoral College versus
+ 
+
+ align:start position:0%
+distinction the Electoral College versus
+the the simple popular vote model it can
+
+ align:start position:0%
+the the simple popular vote model it can
+ 
+
+ align:start position:0%
+the the simple popular vote model it can
+have very significant consequences on
+
+ align:start position:0%
+have very significant consequences on
+ 
+
+ align:start position:0%
+have very significant consequences on
+the outcome of the election as an
+
+ align:start position:0%
+the outcome of the election as an
+ 
+
+ align:start position:0%
+the outcome of the election as an
+example let's look at the 2000
+
+ align:start position:0%
+example let's look at the 2000
+ 
+
+ align:start position:0%
+example let's look at the 2000
+presidential election between George W
+
+ align:start position:0%
+presidential election between George W
+ 
+
+ align:start position:0%
+presidential election between George W
+Bush and Al Gore as we can see on the
+
+ align:start position:0%
+Bush and Al Gore as we can see on the
+ 
+
+ align:start position:0%
+Bush and Al Gore as we can see on the
+right here Al Gore received more than
+
+ align:start position:0%
+right here Al Gore received more than
+ 
+
+ align:start position:0%
+right here Al Gore received more than
+500,000 more votes across the entire
+
+ align:start position:0%
+500,000 more votes across the entire
+ 
+
+ align:start position:0%
+500,000 more votes across the entire
+country than george w bush in terms of
+
+ align:start position:0%
+country than george w bush in terms of
+ 
+
+ align:start position:0%
+country than george w bush in terms of
+the popular vote but in terms of the
+
+ align:start position:0%
+the popular vote but in terms of the
+ 
+
+ align:start position:0%
+the popular vote but in terms of the
+electoral vote because of how those
+
+ align:start position:0%
+electoral vote because of how those
+ 
+
+ align:start position:0%
+electoral vote because of how those
+votes were distributed George Bush
+
+ align:start position:0%
+votes were distributed George Bush
+ 
+
+ align:start position:0%
+votes were distributed George Bush
+actually won the election because he
+
+ align:start position:0%
+actually won the election because he
+ 
+
+ align:start position:0%
+actually won the election because he
+received five more elect
+
+ align:start position:0%
+received five more elect
+ 
+
+ align:start position:0%
+received five more elect
+votes than Al Gore so our goal will be
+
+ align:start position:0%
+votes than Al Gore so our goal will be
+ 
+
+ align:start position:0%
+votes than Al Gore so our goal will be
+to use polling data that's collected
+
+ align:start position:0%
+to use polling data that's collected
+ 
+
+ align:start position:0%
+to use polling data that's collected
+from likely voters before the election
+
+ align:start position:0%
+from likely voters before the election
+ 
+
+ align:start position:0%
+from likely voters before the election
+to predict the winner in each state and
+
+ align:start position:0%
+to predict the winner in each state and
+ 
+
+ align:start position:0%
+to predict the winner in each state and
+therefore to enable us to predict the
+
+ align:start position:0%
+therefore to enable us to predict the
+ 
+
+ align:start position:0%
+therefore to enable us to predict the
+winner of the entire election in the
+
+ align:start position:0%
+winner of the entire election in the
+ 
+
+ align:start position:0%
+winner of the entire election in the
+electoral college system
+
+ align:start position:0%
+electoral college system
+ 
+
+ align:start position:0%
+electoral college system
+why election prediction has long
+
+ align:start position:0%
+why election prediction has long
+ 
+
+ align:start position:0%
+why election prediction has long
+attracted some attention there's been a
+
+ align:start position:0%
+attracted some attention there's been a
+ 
+
+ align:start position:0%
+attracted some attention there's been a
+particular interest in the problem for
+
+ align:start position:0%
+particular interest in the problem for
+ 
+
+ align:start position:0%
+particular interest in the problem for
+the 2012 presidential election when then
+
+ align:start position:0%
+the 2012 presidential election when then
+ 
+
+ align:start position:0%
+the 2012 presidential election when then
+New York Times columnist Nate Silver
+
+ align:start position:0%
+New York Times columnist Nate Silver
+ 
+
+ align:start position:0%
+New York Times columnist Nate Silver
+took on the task of predicting the
+
+ align:start position:0%
+took on the task of predicting the
+ 
+
+ align:start position:0%
+took on the task of predicting the
+winner in each state to carry out this
+
+ align:start position:0%
+winner in each state to carry out this
+ 
+
+ align:start position:0%
+winner in each state to carry out this
+prediction task we're gonna use some
+
+ align:start position:0%
+prediction task we're gonna use some
+ 
+
+ align:start position:0%
+prediction task we're gonna use some
+data from Real Clear Politics calm that
+
+ align:start position:0%
+data from Real Clear Politics calm that
+ 
+
+ align:start position:0%
+data from Real Clear Politics calm that
+basically represents polling data that
+
+ align:start position:0%
+basically represents polling data that
+ 
+
+ align:start position:0%
+basically represents polling data that
+was collected in the months leading up
+
+ align:start position:0%
+was collected in the months leading up
+ 
+
+ align:start position:0%
+was collected in the months leading up
+to the 2004 2008 and 2012 US
+
+ align:start position:0%
+to the 2004 2008 and 2012 US
+ 
+
+ align:start position:0%
+to the 2004 2008 and 2012 US
+presidential elections each row in the
+
+ align:start position:0%
+presidential elections each row in the
+ 
+
+ align:start position:0%
+presidential elections each row in the
+dataset represents a state in a
+
+ align:start position:0%
+dataset represents a state in a
+ 
+
+ align:start position:0%
+dataset represents a state in a
+particular election year and the
+
+ align:start position:0%
+particular election year and the
+ 
+
+ align:start position:0%
+particular election year and the
+dependent variable which is called
+
+ align:start position:0%
+dependent variable which is called
+ 
+
+ align:start position:0%
+dependent variable which is called
+Republican is a binary outcome it's one
+
+ align:start position:0%
+Republican is a binary outcome it's one
+ 
+
+ align:start position:0%
+Republican is a binary outcome it's one
+if the Republican won that state in that
+
+ align:start position:0%
+if the Republican won that state in that
+ 
+
+ align:start position:0%
+if the Republican won that state in that
+particular election year and is zero if
+
+ align:start position:0%
+particular election year and is zero if
+ 
+
+ align:start position:0%
+particular election year and is zero if
+a Democrat won the independent variables
+
+ align:start position:0%
+a Democrat won the independent variables
+ 
+
+ align:start position:0%
+a Democrat won the independent variables
+again are related to polling data in
+
+ align:start position:0%
+again are related to polling data in
+ 
+
+ align:start position:0%
+again are related to polling data in
+that state so for instance the Rasmussen
+
+ align:start position:0%
+that state so for instance the Rasmussen
+ 
+
+ align:start position:0%
+that state so for instance the Rasmussen
+and survey u-s-a variables are related
+
+ align:start position:0%
+and survey u-s-a variables are related
+ 
+
+ align:start position:0%
+and survey u-s-a variables are related
+to two major polls that are that are
+
+ align:start position:0%
+to two major polls that are that are
+ 
+
+ align:start position:0%
+to two major polls that are that are
+assigned across many different states in
+
+ align:start position:0%
+assigned across many different states in
+ 
+
+ align:start position:0%
+assigned across many different states in
+the United States and it represents the
+
+ align:start position:0%
+the United States and it represents the
+ 
+
+ align:start position:0%
+the United States and it represents the
+percentage of voters who said they were
+
+ align:start position:0%
+percentage of voters who said they were
+ 
+
+ align:start position:0%
+percentage of voters who said they were
+likely to vote Republican - the
+
+ align:start position:0%
+likely to vote Republican - the
+ 
+
+ align:start position:0%
+likely to vote Republican - the
+percentage who said they were likely to
+
+ align:start position:0%
+percentage who said they were likely to
+ 
+
+ align:start position:0%
+percentage who said they were likely to
+vote Democrats so for instance if the
+
+ align:start position:0%
+vote Democrats so for instance if the
+ 
+
+ align:start position:0%
+vote Democrats so for instance if the
+variable survey u-s-a in our data set
+
+ align:start position:0%
+variable survey u-s-a in our data set
+ 
+
+ align:start position:0%
+variable survey u-s-a in our data set
+has value negative six it means that six
+
+ align:start position:0%
+has value negative six it means that six
+ 
+
+ align:start position:0%
+has value negative six it means that six
+percent more voters said they were
+
+ align:start position:0%
+percent more voters said they were
+ 
+
+ align:start position:0%
+percent more voters said they were
+likely to vote Democrat then said they
+
+ align:start position:0%
+likely to vote Democrat then said they
+ 
+
+ align:start position:0%
+likely to vote Democrat then said they
+were likely to vote Republican in that
+
+ align:start position:0%
+were likely to vote Republican in that
+ 
+
+ align:start position:0%
+were likely to vote Republican in that
+state we have two additional variables
+
+ align:start position:0%
+state we have two additional variables
+ 
+
+ align:start position:0%
+state we have two additional variables
+that capture polling data from a wider
+
+ align:start position:0%
+that capture polling data from a wider
+ 
+
+ align:start position:0%
+that capture polling data from a wider
+range of polls or as mucin and survey
+
+ align:start position:0%
+range of polls or as mucin and survey
+ 
+
+ align:start position:0%
+range of polls or as mucin and survey
+u-s-a are definitely not the only polls
+
+ align:start position:0%
+u-s-a are definitely not the only polls
+ 
+
+ align:start position:0%
+u-s-a are definitely not the only polls
+that are run on a state-by-state basis
+
+ align:start position:0%
+that are run on a state-by-state basis
+ 
+
+ align:start position:0%
+that are run on a state-by-state basis
+diff count counts the number of all the
+
+ align:start position:0%
+diff count counts the number of all the
+ 
+
+ align:start position:0%
+diff count counts the number of all the
+polls leading up to the election that
+
+ align:start position:0%
+polls leading up to the election that
+ 
+
+ align:start position:0%
+polls leading up to the election that
+predicted a Republican winner in the
+
+ align:start position:0%
+predicted a Republican winner in the
+ 
+
+ align:start position:0%
+predicted a Republican winner in the
+state - the number of poles that
+
+ align:start position:0%
+state - the number of poles that
+ 
+
+ align:start position:0%
+state - the number of poles that
+predicted a Democratic winner and prop R
+
+ align:start position:0%
+predicted a Democratic winner and prop R
+ 
+
+ align:start position:0%
+predicted a Democratic winner and prop R
+or proportion Republican Perez the
+
+ align:start position:0%
+or proportion Republican Perez the
+ 
+
+ align:start position:0%
+or proportion Republican Perez the
+proportion of all those polls leading up
+
+ align:start position:0%
+proportion of all those polls leading up
+ 
+
+ align:start position:0%
+proportion of all those polls leading up
+to the election that predicted a
+
+ align:start position:0%
+to the election that predicted a
+ 
+
+ align:start position:0%
+to the election that predicted a
+Republican winner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/AvvUQjoqOUU.txt b/AvvUQjoqOUU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d34d89bc7dbf1408ac66339995ecdfebf31cda48
--- /dev/null
+++ b/AvvUQjoqOUU.txt
@@ -0,0 +1,15939 @@
+align:start position:0%
+ 
+um okay anyway so online market so what
+
+ align:start position:0%
+um okay anyway so online market so what
+ 
+
+ align:start position:0%
+um okay anyway so online market so what
+I you know I've got uh several different
+
+ align:start position:0%
+I you know I've got uh several different
+ 
+
+ align:start position:0%
+I you know I've got uh several different
+papers to I was I figured I'd talk about
+
+ align:start position:0%
+papers to I was I figured I'd talk about
+ 
+
+ align:start position:0%
+papers to I was I figured I'd talk about
+today all of them are talking about uh
+
+ align:start position:0%
+today all of them are talking about uh
+ 
+
+ align:start position:0%
+today all of them are talking about uh
+online retail in one form or another um
+
+ align:start position:0%
+online retail in one form or another um
+ 
+
+ align:start position:0%
+online retail in one form or another um
+and and um just different issues in
+
+ align:start position:0%
+and and um just different issues in
+ 
+
+ align:start position:0%
+and and um just different issues in
+different issues in online retail trying
+
+ align:start position:0%
+different issues in online retail trying
+ 
+
+ align:start position:0%
+different issues in online retail trying
+to understand the industry um so the
+
+ align:start position:0%
+to understand the industry um so the
+ 
+
+ align:start position:0%
+to understand the industry um so the
+first uh paper I was going to talk about
+
+ align:start position:0%
+first uh paper I was going to talk about
+ 
+
+ align:start position:0%
+first uh paper I was going to talk about
+inov kler 11 C learning from seller
+
+ align:start position:0%
+inov kler 11 C learning from seller
+ 
+
+ align:start position:0%
+inov kler 11 C learning from seller
+experiments online markets um this is a
+
+ align:start position:0%
+experiments online markets um this is a
+ 
+
+ align:start position:0%
+experiments online markets um this is a
+paper uh studying
+
+ align:start position:0%
+paper uh studying
+ 
+
+ align:start position:0%
+paper uh studying
+eBay uh and you know while sort of eBay
+
+ align:start position:0%
+eBay uh and you know while sort of eBay
+ 
+
+ align:start position:0%
+eBay uh and you know while sort of eBay
+has been in a long run decline uh you
+
+ align:start position:0%
+has been in a long run decline uh you
+ 
+
+ align:start position:0%
+has been in a long run decline uh you
+know it's still an important way in
+
+ align:start position:0%
+know it's still an important way in
+ 
+
+ align:start position:0%
+know it's still an important way in
+which things get sold and I also just
+
+ align:start position:0%
+which things get sold and I also just
+ 
+
+ align:start position:0%
+which things get sold and I also just
+wanted to cover it because of the sort
+
+ align:start position:0%
+wanted to cover it because of the sort
+ 
+
+ align:start position:0%
+wanted to cover it because of the sort
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+um thought the method the methodology of
+
+ align:start position:0%
+um thought the method the methodology of
+ 
+
+ align:start position:0%
+um thought the method the methodology of
+the paper is interesting as an as a way
+
+ align:start position:0%
+the paper is interesting as an as a way
+ 
+
+ align:start position:0%
+the paper is interesting as an as a way
+to attack problems and these idea is
+
+ align:start position:0%
+to attack problems and these idea is
+ 
+
+ align:start position:0%
+to attack problems and these idea is
+that what they're sort of talking about
+
+ align:start position:0%
+that what they're sort of talking about
+ 
+
+ align:start position:0%
+that what they're sort of talking about
+is an alternative to sort of doing field
+
+ align:start position:0%
+is an alternative to sort of doing field
+ 
+
+ align:start position:0%
+is an alternative to sort of doing field
+experiments or setting up agreements to
+
+ align:start position:0%
+experiments or setting up agreements to
+ 
+
+ align:start position:0%
+experiments or setting up agreements to
+run experiments with online service
+
+ align:start position:0%
+run experiments with online service
+ 
+
+ align:start position:0%
+run experiments with online service
+providers is what they call
+
+ align:start position:0%
+providers is what they call
+ 
+
+ align:start position:0%
+providers is what they call
+opportunistic experiments you just find
+
+ align:start position:0%
+opportunistic experiments you just find
+ 
+
+ align:start position:0%
+opportunistic experiments you just find
+you know there are many many businesses
+
+ align:start position:0%
+you know there are many many businesses
+ 
+
+ align:start position:0%
+you know there are many many businesses
+in this world those businesses are
+
+ align:start position:0%
+in this world those businesses are
+ 
+
+ align:start position:0%
+in this world those businesses are
+trying to operate optimally they run
+
+ align:start position:0%
+trying to operate optimally they run
+ 
+
+ align:start position:0%
+trying to operate optimally they run
+lots of experiments themselves and so
+
+ align:start position:0%
+lots of experiments themselves and so
+ 
+
+ align:start position:0%
+lots of experiments themselves and so
+their idea is to take advantage of all
+
+ align:start position:0%
+their idea is to take advantage of all
+ 
+
+ align:start position:0%
+their idea is to take advantage of all
+these experiments that sellers are
+
+ align:start position:0%
+these experiments that sellers are
+ 
+
+ align:start position:0%
+these experiments that sellers are
+running on eBay and and analyze those
+
+ align:start position:0%
+running on eBay and and analyze those
+ 
+
+ align:start position:0%
+running on eBay and and analyze those
+and obviously you know you get less
+
+ align:start position:0%
+and obviously you know you get less
+ 
+
+ align:start position:0%
+and obviously you know you get less
+controlled experiments than if you were
+
+ align:start position:0%
+controlled experiments than if you were
+ 
+
+ align:start position:0%
+controlled experiments than if you were
+setting up the experiment yourself each
+
+ align:start position:0%
+setting up the experiment yourself each
+ 
+
+ align:start position:0%
+setting up the experiment yourself each
+experiment is not ideal but you know
+
+ align:start position:0%
+experiment is not ideal but you know
+ 
+
+ align:start position:0%
+experiment is not ideal but you know
+there has thousands and thousands of not
+
+ align:start position:0%
+there has thousands and thousands of not
+ 
+
+ align:start position:0%
+there has thousands and thousands of not
+ideal experiments maybe more informative
+
+ align:start position:0%
+ideal experiments maybe more informative
+ 
+
+ align:start position:0%
+ideal experiments maybe more informative
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+one or more informative and cheaper to
+
+ align:start position:0%
+one or more informative and cheaper to
+ 
+
+ align:start position:0%
+one or more informative and cheaper to
+run than just sort of one experiment you
+
+ align:start position:0%
+run than just sort of one experiment you
+ 
+
+ align:start position:0%
+run than just sort of one experiment you
+design yourself um so to start with a
+
+ align:start position:0%
+design yourself um so to start with a
+ 
+
+ align:start position:0%
+design yourself um so to start with a
+note that you know very few things on
+
+ align:start position:0%
+note that you know very few things on
+ 
+
+ align:start position:0%
+note that you know very few things on
+eBay are actually unique um they said
+
+ align:start position:0%
+eBay are actually unique um they said
+ 
+
+ align:start position:0%
+eBay are actually unique um they said
+you know it's a I guess interesting fact
+
+ align:start position:0%
+you know it's a I guess interesting fact
+ 
+
+ align:start position:0%
+you know it's a I guess interesting fact
+about eBay um for about a half of the
+
+ align:start position:0%
+about eBay um for about a half of the
+ 
+
+ align:start position:0%
+about eBay um for about a half of the
+items that are sold on eBay you can find
+
+ align:start position:0%
+items that are sold on eBay you can find
+ 
+
+ align:start position:0%
+items that are sold on eBay you can find
+a nearly identical item sold by exactly
+
+ align:start position:0%
+a nearly identical item sold by exactly
+ 
+
+ align:start position:0%
+a nearly identical item sold by exactly
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+seller and so when they're talking about
+
+ align:start position:0%
+seller and so when they're talking about
+ 
+
+ align:start position:0%
+seller and so when they're talking about
+an experiment they experiment meaning
+
+ align:start position:0%
+an experiment they experiment meaning
+ 
+
+ align:start position:0%
+an experiment they experiment meaning
+you have a seller you have exactly the
+
+ align:start position:0%
+you have a seller you have exactly the
+ 
+
+ align:start position:0%
+you have a seller you have exactly the
+same seller selling a product with
+
+ align:start position:0%
+same seller selling a product with
+ 
+
+ align:start position:0%
+same seller selling a product with
+exactly the same listing title listed in
+
+ align:start position:0%
+exactly the same listing title listed in
+ 
+
+ align:start position:0%
+exactly the same listing title listed in
+the same category and subtitle and they
+
+ align:start position:0%
+the same category and subtitle and they
+ 
+
+ align:start position:0%
+the same category and subtitle and they
+find 55 million seller experiments
+
+ align:start position:0%
+find 55 million seller experiments
+ 
+
+ align:start position:0%
+find 55 million seller experiments
+involving a total of 350 million
+
+ align:start position:0%
+involving a total of 350 million
+ 
+
+ align:start position:0%
+involving a total of 350 million
+listings um for much of their uh
+
+ align:start position:0%
+listings um for much of their uh
+ 
+
+ align:start position:0%
+listings um for much of their uh
+analysis they're restricting attention
+
+ align:start position:0%
+analysis they're restricting attention
+ 
+
+ align:start position:0%
+analysis they're restricting attention
+to experiments that have several
+
+ align:start position:0%
+to experiments that have several
+ 
+
+ align:start position:0%
+to experiments that have several
+different features there at least two
+
+ align:start position:0%
+different features there at least two
+ 
+
+ align:start position:0%
+different features there at least two
+items auctioned there's also at least
+
+ align:start position:0%
+items auctioned there's also at least
+ 
+
+ align:start position:0%
+items auctioned there's also at least
+one successful posted price sale they
+
+ align:start position:0%
+one successful posted price sale they
+ 
+
+ align:start position:0%
+one successful posted price sale they
+want a posted price sale because they're
+
+ align:start position:0%
+want a posted price sale because they're
+ 
+
+ align:start position:0%
+want a posted price sale because they're
+going to use that as sort of a reference
+
+ align:start position:0%
+going to use that as sort of a reference
+ 
+
+ align:start position:0%
+going to use that as sort of a reference
+for what's the market price of this if
+
+ align:start position:0%
+for what's the market price of this if
+ 
+
+ align:start position:0%
+for what's the market price of this if
+you just sell it so uh on on not through
+
+ align:start position:0%
+you just sell it so uh on on not through
+ 
+
+ align:start position:0%
+you just sell it so uh on on not through
+an auction and even with those
+
+ align:start position:0%
+an auction and even with those
+ 
+
+ align:start position:0%
+an auction and even with those
+restrictions they come up with you know
+
+ align:start position:0%
+restrictions they come up with you know
+ 
+
+ align:start position:0%
+restrictions they come up with you know
+244,000 experiments that have 7.6
+
+ align:start position:0%
+244,000 experiments that have 7.6
+ 
+
+ align:start position:0%
+244,000 experiments that have 7.6
+million listings so the idea is just
+
+ align:start position:0%
+million listings so the idea is just
+ 
+
+ align:start position:0%
+million listings so the idea is just
+that eBay sellers are just experimenting
+
+ align:start position:0%
+that eBay sellers are just experimenting
+ 
+
+ align:start position:0%
+that eBay sellers are just experimenting
+all the time with all kinds of things
+
+ align:start position:0%
+all the time with all kinds of things
+ 
+
+ align:start position:0%
+all the time with all kinds of things
+and this is something we can take
+
+ align:start position:0%
+and this is something we can take
+ 
+
+ align:start position:0%
+and this is something we can take
+advantage of the paper itself has like
+
+ align:start position:0%
+advantage of the paper itself has like
+ 
+
+ align:start position:0%
+advantage of the paper itself has like
+multiple different subp
+
+ align:start position:0%
+multiple different subp
+ 
+
+ align:start position:0%
+multiple different subp
+papers um discussing what to do with
+
+ align:start position:0%
+papers um discussing what to do with
+ 
+
+ align:start position:0%
+papers um discussing what to do with
+this so uh one of the subp papers is how
+
+ align:start position:0%
+this so uh one of the subp papers is how
+ 
+
+ align:start position:0%
+this so uh one of the subp papers is how
+to buy it now prices affect out comes
+
+ align:start position:0%
+to buy it now prices affect out comes
+ 
+
+ align:start position:0%
+to buy it now prices affect out comes
+you know on eBay if you have't never
+
+ align:start position:0%
+you know on eBay if you have't never
+ 
+
+ align:start position:0%
+you know on eBay if you have't never
+been on an eBay auction it's like it's
+
+ align:start position:0%
+been on an eBay auction it's like it's
+ 
+
+ align:start position:0%
+been on an eBay auction it's like it's
+classic English ascending bid auction uh
+
+ align:start position:0%
+classic English ascending bid auction uh
+ 
+
+ align:start position:0%
+classic English ascending bid auction uh
+but there's also this option of just
+
+ align:start position:0%
+but there's also this option of just
+ 
+
+ align:start position:0%
+but there's also this option of just
+click here to buy it for $125 and end
+
+ align:start position:0%
+click here to buy it for $125 and end
+ 
+
+ align:start position:0%
+click here to buy it for $125 and end
+the auction and so one of the papers
+
+ align:start position:0%
+the auction and so one of the papers
+ 
+
+ align:start position:0%
+the auction and so one of the papers
+they do is how does having a buy now
+
+ align:start position:0%
+they do is how does having a buy now
+ 
+
+ align:start position:0%
+they do is how does having a buy now
+price affect the outcome uh second is
+
+ align:start position:0%
+price affect the outcome uh second is
+ 
+
+ align:start position:0%
+price affect the outcome uh second is
+how does shipping fees affect outcomes
+
+ align:start position:0%
+how does shipping fees affect outcomes
+ 
+
+ align:start position:0%
+how does shipping fees affect outcomes
+there's this um you know interesting
+
+ align:start position:0%
+there's this um you know interesting
+ 
+
+ align:start position:0%
+there's this um you know interesting
+earlier paper by Hussein and Morgan that
+
+ align:start position:0%
+earlier paper by Hussein and Morgan that
+ 
+
+ align:start position:0%
+earlier paper by Hussein and Morgan that
+argued that um you know consumers are
+
+ align:start position:0%
+argued that um you know consumers are
+ 
+
+ align:start position:0%
+argued that um you know consumers are
+fairly naive in dealing with shipping
+
+ align:start position:0%
+fairly naive in dealing with shipping
+ 
+
+ align:start position:0%
+fairly naive in dealing with shipping
+fees and that you make more money by
+
+ align:start position:0%
+fees and that you make more money by
+ 
+
+ align:start position:0%
+fees and that you make more money by
+having good with 9.95 shipping than good
+
+ align:start position:0%
+having good with 9.95 shipping than good
+ 
+
+ align:start position:0%
+having good with 9.95 shipping than good
+with 595 shipping just you know somehow
+
+ align:start position:0%
+with 595 shipping just you know somehow
+ 
+
+ align:start position:0%
+with 595 shipping just you know somehow
+you offer the same good different
+
+ align:start position:0%
+you offer the same good different
+ 
+
+ align:start position:0%
+you offer the same good different
+shipping prices people somehow focus on
+
+ align:start position:0%
+shipping prices people somehow focus on
+ 
+
+ align:start position:0%
+shipping prices people somehow focus on
+the item price not on the shipping price
+
+ align:start position:0%
+the item price not on the shipping price
+ 
+
+ align:start position:0%
+the item price not on the shipping price
+and so the p shpp and handling you make
+
+ align:start position:0%
+and so the p shpp and handling you make
+ 
+
+ align:start position:0%
+and so the p shpp and handling you make
+more money selling with a high shipping
+
+ align:start position:0%
+more money selling with a high shipping
+ 
+
+ align:start position:0%
+more money selling with a high shipping
+and handling fee um anyway they're going
+
+ align:start position:0%
+and handling fee um anyway they're going
+ 
+
+ align:start position:0%
+and handling fee um anyway they're going
+to do an experiment on that or many
+
+ align:start position:0%
+to do an experiment on that or many
+ 
+
+ align:start position:0%
+to do an experiment on that or many
+sellers have done experiments on that
+
+ align:start position:0%
+sellers have done experiments on that
+ 
+
+ align:start position:0%
+sellers have done experiments on that
+and then they also have this sort of
+
+ align:start position:0%
+and then they also have this sort of
+ 
+
+ align:start position:0%
+and then they also have this sort of
+third paper about how and why to reserve
+
+ align:start position:0%
+third paper about how and why to reserve
+ 
+
+ align:start position:0%
+third paper about how and why to reserve
+prices affect revenues I'm just going to
+
+ align:start position:0%
+prices affect revenues I'm just going to
+ 
+
+ align:start position:0%
+prices affect revenues I'm just going to
+talk about the third one because it it
+
+ align:start position:0%
+talk about the third one because it it
+ 
+
+ align:start position:0%
+talk about the third one because it it
+sort of feeds back to sort of things I
+
+ align:start position:0%
+sort of feeds back to sort of things I
+ 
+
+ align:start position:0%
+sort of feeds back to sort of things I
+talked about in the auction literature
+
+ align:start position:0%
+talked about in the auction literature
+ 
+
+ align:start position:0%
+talked about in the auction literature
+about optimal Reserve prices and
+
+ align:start position:0%
+about optimal Reserve prices and
+ 
+
+ align:start position:0%
+about optimal Reserve prices and
+auctions okay here's just their
+
+ align:start position:0%
+auctions okay here's just their
+ 
+
+ align:start position:0%
+auctions okay here's just their
+motivating figure to explain eBay
+
+ align:start position:0%
+motivating figure to explain eBay
+ 
+
+ align:start position:0%
+motivating figure to explain eBay
+experiment ments you know like so they
+
+ align:start position:0%
+experiment ments you know like so they
+ 
+
+ align:start position:0%
+experiment ments you know like so they
+did a search for um Tailor Made Driver
+
+ align:start position:0%
+did a search for um Tailor Made Driver
+ 
+
+ align:start position:0%
+did a search for um Tailor Made Driver
+tailor made is a brand of of uh you know
+
+ align:start position:0%
+tailor made is a brand of of uh you know
+ 
+
+ align:start position:0%
+tailor made is a brand of of uh you know
+golf cob manufacturer you do a search
+
+ align:start position:0%
+golf cob manufacturer you do a search
+ 
+
+ align:start position:0%
+golf cob manufacturer you do a search
+for Tailor Made Driver on eBay and you
+
+ align:start position:0%
+for Tailor Made Driver on eBay and you
+ 
+
+ align:start position:0%
+for Tailor Made Driver on eBay and you
+just see a screen like this that's just
+
+ align:start position:0%
+just see a screen like this that's just
+ 
+
+ align:start position:0%
+just see a screen like this that's just
+full of um people selling new and used
+
+ align:start position:0%
+full of um people selling new and used
+ 
+
+ align:start position:0%
+full of um people selling new and used
+um golf clubs and it looks like there's
+
+ align:start position:0%
+um golf clubs and it looks like there's
+ 
+
+ align:start position:0%
+um golf clubs and it looks like there's
+just a zillion different golf clubs out
+
+ align:start position:0%
+just a zillion different golf clubs out
+ 
+
+ align:start position:0%
+just a zillion different golf clubs out
+there on eBay but if you do a more
+
+ align:start position:0%
+there on eBay but if you do a more
+ 
+
+ align:start position:0%
+there on eBay but if you do a more
+specific search um so for this specific
+
+ align:start position:0%
+specific search um so for this specific
+ 
+
+ align:start position:0%
+specific search um so for this specific
+search they typed in tailor made burner
+
+ align:start position:0%
+search they typed in tailor made burner
+ 
+
+ align:start position:0%
+search they typed in tailor made burner
+09 driver 2009 Golf Club new quote 10
+
+ align:start position:0%
+09 driver 2009 Golf Club new quote 10
+ 
+
+ align:start position:0%
+09 driver 2009 Golf Club new quote 10
+RH uh and so you do this very specific
+
+ align:start position:0%
+RH uh and so you do this very specific
+ 
+
+ align:start position:0%
+RH uh and so you do this very specific
+search and then what do you find you
+
+ align:start position:0%
+search and then what do you find you
+ 
+
+ align:start position:0%
+search and then what do you find you
+find that there is one seller who uses
+
+ align:start position:0%
+find that there is one seller who uses
+ 
+
+ align:start position:0%
+find that there is one seller who uses
+that as his title when he sells tailor
+
+ align:start position:0%
+that as his title when he sells tailor
+ 
+
+ align:start position:0%
+that as his title when he sells tailor
+made drivers online and so all the
+
+ align:start position:0%
+made drivers online and so all the
+ 
+
+ align:start position:0%
+made drivers online and so all the
+searches say tailor made burner 09
+
+ align:start position:0%
+searches say tailor made burner 09
+ 
+
+ align:start position:0%
+searches say tailor made burner 09
+driver 2009 Golf Club new 10.5 degrees
+
+ align:start position:0%
+driver 2009 Golf Club new 10.5 degrees
+ 
+
+ align:start position:0%
+driver 2009 Golf Club new 10.5 degrees
+right hand okay and what you'll notice
+
+ align:start position:0%
+right hand okay and what you'll notice
+ 
+
+ align:start position:0%
+right hand okay and what you'll notice
+in this thing is that the seller has
+
+ align:start position:0%
+in this thing is that the seller has
+ 
+
+ align:start position:0%
+in this thing is that the seller has
+these many many auctions this one's
+
+ align:start position:0%
+these many many auctions this one's
+ 
+
+ align:start position:0%
+these many many auctions this one's
+closing in 3 hours and 21 minutes this
+
+ align:start position:0%
+closing in 3 hours and 21 minutes this
+ 
+
+ align:start position:0%
+closing in 3 hours and 21 minutes this
+one closes in 3 hours and 22 minutes
+
+ align:start position:0%
+one closes in 3 hours and 22 minutes
+ 
+
+ align:start position:0%
+one closes in 3 hours and 22 minutes
+this one closes in 6 hours and 9 Minutes
+
+ align:start position:0%
+this one closes in 6 hours and 9 Minutes
+ 
+
+ align:start position:0%
+this one closes in 6 hours and 9 Minutes
+6 hours and 9 Minutes 8 hours 59
+
+ align:start position:0%
+6 hours and 9 Minutes 8 hours 59
+ 
+
+ align:start position:0%
+6 hours and 9 Minutes 8 hours 59
+941 you know so this seller is selling
+
+ align:start position:0%
+941 you know so this seller is selling
+ 
+
+ align:start position:0%
+941 you know so this seller is selling
+auctioning off eight of these in the
+
+ align:start position:0%
+auctioning off eight of these in the
+ 
+
+ align:start position:0%
+auctioning off eight of these in the
+next 12 hours and you can see this
+
+ align:start position:0%
+next 12 hours and you can see this
+ 
+
+ align:start position:0%
+next 12 hours and you can see this
+seller is conducting an experiment this
+
+ align:start position:0%
+seller is conducting an experiment this
+ 
+
+ align:start position:0%
+seller is conducting an experiment this
+golf club here maybe you can't see it I
+
+ align:start position:0%
+golf club here maybe you can't see it I
+ 
+
+ align:start position:0%
+golf club here maybe you can't see it I
+can uh this one has $799 shipping this
+
+ align:start position:0%
+can uh this one has $799 shipping this
+ 
+
+ align:start position:0%
+can uh this one has $799 shipping this
+one has $9.99 shipping uh this one is
+
+ align:start position:0%
+one has $9.99 shipping uh this one is
+ 
+
+ align:start position:0%
+one has $9.99 shipping uh this one is
+$9.99 shipping this one has $7.99
+
+ align:start position:0%
+$9.99 shipping this one has $7.99
+ 
+
+ align:start position:0%
+$9.99 shipping this one has $7.99
+shipping so you know here it's clear
+
+ align:start position:0%
+shipping so you know here it's clear
+ 
+
+ align:start position:0%
+shipping so you know here it's clear
+these have Buy It Now prices this is
+
+ align:start position:0%
+these have Buy It Now prices this is
+ 
+
+ align:start position:0%
+these have Buy It Now prices this is
+just $125 plus $9.99 this $125 plus $799
+
+ align:start position:0%
+just $125 plus $9.99 this $125 plus $799
+ 
+
+ align:start position:0%
+just $125 plus $9.99 this $125 plus $799
+if anyone saw these two listings
+
+ align:start position:0%
+if anyone saw these two listings
+ 
+
+ align:start position:0%
+if anyone saw these two listings
+obviously no one would buy this one but
+
+ align:start position:0%
+obviously no one would buy this one but
+ 
+
+ align:start position:0%
+obviously no one would buy this one but
+they're just mixed in with that big list
+
+ align:start position:0%
+they're just mixed in with that big list
+ 
+
+ align:start position:0%
+they're just mixed in with that big list
+people may only see one versus the other
+
+ align:start position:0%
+people may only see one versus the other
+ 
+
+ align:start position:0%
+people may only see one versus the other
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+unclear uh what's going to happen uh
+
+ align:start position:0%
+unclear uh what's going to happen uh
+ 
+
+ align:start position:0%
+unclear uh what's going to happen uh
+anyway so this is one sell's experiment
+
+ align:start position:0%
+anyway so this is one sell's experiment
+ 
+
+ align:start position:0%
+anyway so this is one sell's experiment
+and their ideaas that there are many
+
+ align:start position:0%
+and their ideaas that there are many
+ 
+
+ align:start position:0%
+and their ideaas that there are many
+many many of these experiments out there
+
+ align:start position:0%
+many many of these experiments out there
+ 
+
+ align:start position:0%
+many many of these experiments out there
+but this is sort of one of the 244,000
+
+ align:start position:0%
+but this is sort of one of the 244,000
+ 
+
+ align:start position:0%
+but this is sort of one of the 244,000
+they're analyzing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what where well so you know I guess
+
+ align:start position:0%
+okay what where well so you know I guess
+ 
+
+ align:start position:0%
+okay what where well so you know I guess
+you know the seller probably doesn't
+
+ align:start position:0%
+you know the seller probably doesn't
+ 
+
+ align:start position:0%
+you know the seller probably doesn't
+know whether a $799 shipping or a $999
+
+ align:start position:0%
+know whether a $799 shipping or a $999
+ 
+
+ align:start position:0%
+know whether a $799 shipping or a $999
+shipping produces better profits so
+
+ align:start position:0%
+shipping produces better profits so
+ 
+
+ align:start position:0%
+shipping produces better profits so
+they're probably just auctioning both of
+
+ align:start position:0%
+they're probably just auctioning both of
+ 
+
+ align:start position:0%
+they're probably just auctioning both of
+them off and they may have been doing
+
+ align:start position:0%
+them off and they may have been doing
+ 
+
+ align:start position:0%
+them off and they may have been doing
+this for a few weeks and then stopped
+
+ align:start position:0%
+this for a few weeks and then stopped
+ 
+
+ align:start position:0%
+this for a few weeks and then stopped
+and settled on whichever one was better
+
+ align:start position:0%
+and settled on whichever one was better
+ 
+
+ align:start position:0%
+and settled on whichever one was better
+um certainly this Buy It Now versus the
+
+ align:start position:0%
+um certainly this Buy It Now versus the
+ 
+
+ align:start position:0%
+um certainly this Buy It Now versus the
+auction there are probably some people
+
+ align:start position:0%
+auction there are probably some people
+ 
+
+ align:start position:0%
+auction there are probably some people
+who prefer one to the other and so you
+
+ align:start position:0%
+who prefer one to the other and so you
+ 
+
+ align:start position:0%
+who prefer one to the other and so you
+probably sell both ways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um but you know you definitely you
+
+ align:start position:0%
+um but you know you definitely you
+ 
+
+ align:start position:0%
+um but you know you definitely you
+actually see you know something you see
+
+ align:start position:0%
+actually see you know something you see
+ 
+
+ align:start position:0%
+actually see you know something you see
+in their data is you see people with
+
+ align:start position:0%
+in their data is you see people with
+ 
+
+ align:start position:0%
+in their data is you see people with
+conducting auctions where the starting
+
+ align:start position:0%
+conducting auctions where the starting
+ 
+
+ align:start position:0%
+conducting auctions where the starting
+price in the auction is above the Buy It
+
+ align:start position:0%
+price in the auction is above the Buy It
+ 
+
+ align:start position:0%
+price in the auction is above the Buy It
+Now price so it does seem like there are
+
+ align:start position:0%
+Now price so it does seem like there are
+ 
+
+ align:start position:0%
+Now price so it does seem like there are
+people who just see an auction and
+
+ align:start position:0%
+people who just see an auction and
+ 
+
+ align:start position:0%
+people who just see an auction and
+decide to enter it and other people who
+
+ align:start position:0%
+decide to enter it and other people who
+ 
+
+ align:start position:0%
+decide to enter it and other people who
+just are looking for a fixed price and
+
+ align:start position:0%
+just are looking for a fixed price and
+ 
+
+ align:start position:0%
+just are looking for a fixed price and
+buy it and not really paying attention
+
+ align:start position:0%
+buy it and not really paying attention
+ 
+
+ align:start position:0%
+buy it and not really paying attention
+to the opposite
+
+ align:start position:0%
+to the opposite
+ 
+
+ align:start position:0%
+to the opposite
+ones um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay anyway so um how do we think
+
+ align:start position:0%
+okay okay anyway so um how do we think
+ 
+
+ align:start position:0%
+okay okay anyway so um how do we think
+about effects of Reserve prices in ipv
+
+ align:start position:0%
+about effects of Reserve prices in ipv
+ 
+
+ align:start position:0%
+about effects of Reserve prices in ipv
+auctions if you remember you know a
+
+ align:start position:0%
+auctions if you remember you know a
+ 
+
+ align:start position:0%
+auctions if you remember you know a
+basic theory of of uh Reserve prices in
+
+ align:start position:0%
+basic theory of of uh Reserve prices in
+ 
+
+ align:start position:0%
+basic theory of of uh Reserve prices in
+English auction is the reserve price in
+
+ align:start position:0%
+English auction is the reserve price in
+ 
+
+ align:start position:0%
+English auction is the reserve price in
+English auction is the Monopoly price to
+
+ align:start position:0%
+English auction is the Monopoly price to
+ 
+
+ align:start position:0%
+English auction is the Monopoly price to
+one bidder and the logic was just you're
+
+ align:start position:0%
+one bidder and the logic was just you're
+ 
+
+ align:start position:0%
+one bidder and the logic was just you're
+selling this good once you found out
+
+ align:start position:0%
+selling this good once you found out
+ 
+
+ align:start position:0%
+selling this good once you found out
+what the second highest value is the
+
+ align:start position:0%
+what the second highest value is the
+ 
+
+ align:start position:0%
+what the second highest value is the
+value of the the willingness to pay of
+
+ align:start position:0%
+value of the the willingness to pay of
+ 
+
+ align:start position:0%
+value of the the willingness to pay of
+the high value bidder is just the
+
+ align:start position:0%
+the high value bidder is just the
+ 
+
+ align:start position:0%
+the high value bidder is just the
+distribution truncated at the point
+
+ align:start position:0%
+distribution truncated at the point
+ 
+
+ align:start position:0%
+distribution truncated at the point
+which you know their value is at least
+
+ align:start position:0%
+which you know their value is at least
+ 
+
+ align:start position:0%
+which you know their value is at least
+that and so you're just Monopoly pricing
+
+ align:start position:0%
+that and so you're just Monopoly pricing
+ 
+
+ align:start position:0%
+that and so you're just Monopoly pricing
+on the single bidder
+
+ align:start position:0%
+on the single bidder
+ 
+
+ align:start position:0%
+on the single bidder
+distribution uh and so it's just the
+
+ align:start position:0%
+distribution uh and so it's just the
+ 
+
+ align:start position:0%
+distribution uh and so it's just the
+optimal reserve price is the Monopoly
+
+ align:start position:0%
+optimal reserve price is the Monopoly
+ 
+
+ align:start position:0%
+optimal reserve price is the Monopoly
+price right you had
+
+ align:start position:0%
+price right you had
+ 
+
+ align:start position:0%
+price right you had
+this distribution of of values once
+
+ align:start position:0%
+this distribution of of values once
+ 
+
+ align:start position:0%
+this distribution of of values once
+everyone else has dropped out here all
+
+ align:start position:0%
+everyone else has dropped out here all
+ 
+
+ align:start position:0%
+everyone else has dropped out here all
+you know is that you're facing you're
+
+ align:start position:0%
+you know is that you're facing you're
+ 
+
+ align:start position:0%
+you know is that you're facing you're
+selling to someone whose draw is from
+
+ align:start position:0%
+selling to someone whose draw is from
+ 
+
+ align:start position:0%
+selling to someone whose draw is from
+you know this is
+
+ align:start position:0%
+you know this is
+ 
+
+ align:start position:0%
+you know this is
+the this is the second highest bid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nope um okay anyway so you have this
+
+ align:start position:0%
+nope um okay anyway so you have this
+ 
+
+ align:start position:0%
+nope um okay anyway so you have this
+distribution of the second highest bid
+
+ align:start position:0%
+distribution of the second highest bid
+ 
+
+ align:start position:0%
+distribution of the second highest bid
+you're pricing to that you set the
+
+ align:start position:0%
+you're pricing to that you set the
+ 
+
+ align:start position:0%
+you're pricing to that you set the
+Monopoly price on that demand
+
+ align:start position:0%
+Monopoly price on that demand
+ 
+
+ align:start position:0%
+Monopoly price on that demand
+curve they also note that if we want to
+
+ align:start position:0%
+curve they also note that if we want to
+ 
+
+ align:start position:0%
+curve they also note that if we want to
+sort of think about this empirically how
+
+ align:start position:0%
+sort of think about this empirically how
+ 
+
+ align:start position:0%
+sort of think about this empirically how
+does a reserve price effect um what's
+
+ align:start position:0%
+does a reserve price effect um what's
+ 
+
+ align:start position:0%
+does a reserve price effect um what's
+the optimal reserve price here's another
+
+ align:start position:0%
+the optimal reserve price here's another
+ 
+
+ align:start position:0%
+the optimal reserve price here's another
+good way to think about so this is
+
+ align:start position:0%
+good way to think about so this is
+ 
+
+ align:start position:0%
+good way to think about so this is
+density F of if you want to think about
+
+ align:start position:0%
+density F of if you want to think about
+ 
+
+ align:start position:0%
+density F of if you want to think about
+how does a reserve price affect things
+
+ align:start position:0%
+how does a reserve price affect things
+ 
+
+ align:start position:0%
+how does a reserve price affect things
+what I can do is just imagine an
+
+ align:start position:0%
+what I can do is just imagine an
+ 
+
+ align:start position:0%
+what I can do is just imagine an
+experiment where the seller has used
+
+ align:start position:0%
+experiment where the seller has used
+ 
+
+ align:start position:0%
+experiment where the seller has used
+many many different Reserve prices like
+
+ align:start position:0%
+many many different Reserve prices like
+ 
+
+ align:start position:0%
+many many different Reserve prices like
+they've used Reserve they've started the
+
+ align:start position:0%
+they've used Reserve they've started the
+ 
+
+ align:start position:0%
+they've used Reserve they've started the
+bidding at $1 $5 $10 20 30 40 50 for
+
+ align:start position:0%
+bidding at $1 $5 $10 20 30 40 50 for
+ 
+
+ align:start position:0%
+bidding at $1 $5 $10 20 30 40 50 for
+every reserve price you can just draw a
+
+ align:start position:0%
+every reserve price you can just draw a
+ 
+
+ align:start position:0%
+every reserve price you can just draw a
+graph which is if I res use a reserve
+
+ align:start position:0%
+graph which is if I res use a reserve
+ 
+
+ align:start position:0%
+graph which is if I res use a reserve
+price of you know 5% of the expected
+
+ align:start position:0%
+price of you know 5% of the expected
+ 
+
+ align:start position:0%
+price of you know 5% of the expected
+sale
+
+ align:start position:0%
+sale
+ 
+
+ align:start position:0%
+sale
+price what's the eventual um price at
+
+ align:start position:0%
+price what's the eventual um price at
+ 
+
+ align:start position:0%
+price what's the eventual um price at
+which I sell the
+
+ align:start position:0%
+which I sell the
+ 
+
+ align:start position:0%
+which I sell the
+good and what's the
+
+ align:start position:0%
+good and what's the
+ 
+
+ align:start position:0%
+good and what's the
+um if I if I use a very low reserve
+
+ align:start position:0%
+um if I if I use a very low reserve
+ 
+
+ align:start position:0%
+um if I if I use a very low reserve
+price I sell the good with probability
+
+ align:start position:0%
+price I sell the good with probability
+ 
+
+ align:start position:0%
+price I sell the good with probability
+0.9 or 0.95 but I get a fairly low
+
+ align:start position:0%
+0.9 or 0.95 but I get a fairly low
+ 
+
+ align:start position:0%
+0.9 or 0.95 but I get a fairly low
+average price and then if I sell it with
+
+ align:start position:0%
+average price and then if I sell it with
+ 
+
+ align:start position:0%
+average price and then if I sell it with
+a $20 Reserve maybe I sell the good with
+
+ align:start position:0%
+a $20 Reserve maybe I sell the good with
+ 
+
+ align:start position:0%
+a $20 Reserve maybe I sell the good with
+probability 08 and I get a higher
+
+ align:start position:0%
+probability 08 and I get a higher
+ 
+
+ align:start position:0%
+probability 08 and I get a higher
+average price and if I sell it with a
+
+ align:start position:0%
+average price and if I sell it with a
+ 
+
+ align:start position:0%
+average price and if I sell it with a
+reserve that's 120% of the average price
+
+ align:start position:0%
+reserve that's 120% of the average price
+ 
+
+ align:start position:0%
+reserve that's 120% of the average price
+for the good maybe I sell it with just
+
+ align:start position:0%
+for the good maybe I sell it with just
+ 
+
+ align:start position:0%
+for the good maybe I sell it with just
+some very small probability but I do get
+
+ align:start position:0%
+some very small probability but I do get
+ 
+
+ align:start position:0%
+some very small probability but I do get
+a very high price of selling so what you
+
+ align:start position:0%
+a very high price of selling so what you
+ 
+
+ align:start position:0%
+a very high price of selling so what you
+can basically do is just look at every
+
+ align:start position:0%
+can basically do is just look at every
+ 
+
+ align:start position:0%
+can basically do is just look at every
+reserve price the data and figure out
+
+ align:start position:0%
+reserve price the data and figure out
+ 
+
+ align:start position:0%
+reserve price the data and figure out
+what's the probability that the good
+
+ align:start position:0%
+what's the probability that the good
+ 
+
+ align:start position:0%
+what's the probability that the good
+sells and what's the expected price
+
+ align:start position:0%
+sells and what's the expected price
+ 
+
+ align:start position:0%
+sells and what's the expected price
+conditional on its selling and that's
+
+ align:start position:0%
+conditional on its selling and that's
+ 
+
+ align:start position:0%
+conditional on its selling and that's
+basically just your demand curve you can
+
+ align:start position:0%
+basically just your demand curve you can
+ 
+
+ align:start position:0%
+basically just your demand curve you can
+sort of view that as demand curve and
+
+ align:start position:0%
+sort of view that as demand curve and
+ 
+
+ align:start position:0%
+sort of view that as demand curve and
+you're just trying to Monopoly price on
+
+ align:start position:0%
+you're just trying to Monopoly price on
+ 
+
+ align:start position:0%
+you're just trying to Monopoly price on
+that curve so that's a second way to
+
+ align:start position:0%
+that curve so that's a second way to
+ 
+
+ align:start position:0%
+that curve so that's a second way to
+think about optimal pricing Reserve
+
+ align:start position:0%
+think about optimal pricing Reserve
+ 
+
+ align:start position:0%
+think about optimal pricing Reserve
+pricing is just draw this demand curve
+
+ align:start position:0%
+pricing is just draw this demand curve
+ 
+
+ align:start position:0%
+pricing is just draw this demand curve
+like object and think about what would
+
+ align:start position:0%
+like object and think about what would
+ 
+
+ align:start position:0%
+like object and think about what would
+be the Monopoly price on that and that
+
+ align:start position:0%
+be the Monopoly price on that and that
+ 
+
+ align:start position:0%
+be the Monopoly price on that and that
+would be the way to figure out what the
+
+ align:start position:0%
+would be the way to figure out what the
+ 
+
+ align:start position:0%
+would be the way to figure out what the
+optimal reserve price is so that would
+
+ align:start position:0%
+optimal reserve price is so that would
+ 
+
+ align:start position:0%
+optimal reserve price is so that would
+be an experimental way to figure out my
+
+ align:start position:0%
+be an experimental way to figure out my
+ 
+
+ align:start position:0%
+be an experimental way to figure out my
+op reserve price without you know
+
+ align:start position:0%
+op reserve price without you know
+ 
+
+ align:start position:0%
+op reserve price without you know
+theoretically you want to say what's the
+
+ align:start position:0%
+theoretically you want to say what's the
+ 
+
+ align:start position:0%
+theoretically you want to say what's the
+distribution from which the values are
+
+ align:start position:0%
+distribution from which the values are
+ 
+
+ align:start position:0%
+distribution from which the values are
+being drawn but without think about what
+
+ align:start position:0%
+being drawn but without think about what
+ 
+
+ align:start position:0%
+being drawn but without think about what
+the distribution from which values are
+
+ align:start position:0%
+the distribution from which values are
+ 
+
+ align:start position:0%
+the distribution from which values are
+being drawn you could just make this
+
+ align:start position:0%
+being drawn you could just make this
+ 
+
+ align:start position:0%
+being drawn you could just make this
+curve Monopoly price relative to
+
+ align:start position:0%
+curve Monopoly price relative to
+ 
+
+ align:start position:0%
+curve Monopoly price relative to
+it okay um you know there several
+
+ align:start position:0%
+it okay um you know there several
+ 
+
+ align:start position:0%
+it okay um you know there several
+reasons why this Simple Theory may not
+
+ align:start position:0%
+reasons why this Simple Theory may not
+ 
+
+ align:start position:0%
+reasons why this Simple Theory may not
+work in practice um one is entry costs
+
+ align:start position:0%
+work in practice um one is entry costs
+ 
+
+ align:start position:0%
+work in practice um one is entry costs
+if you imagine there's some cost to a
+
+ align:start position:0%
+if you imagine there's some cost to a
+ 
+
+ align:start position:0%
+if you imagine there's some cost to a
+bidder of starting to bid in an auction
+
+ align:start position:0%
+bidder of starting to bid in an auction
+ 
+
+ align:start position:0%
+bidder of starting to bid in an auction
+and look examining the good in detail
+
+ align:start position:0%
+and look examining the good in detail
+ 
+
+ align:start position:0%
+and look examining the good in detail
+if there's a low price they may be
+
+ align:start position:0%
+if there's a low price they may be
+ 
+
+ align:start position:0%
+if there's a low price they may be
+willing to pay the entry cost if they
+
+ align:start position:0%
+willing to pay the entry cost if they
+ 
+
+ align:start position:0%
+willing to pay the entry cost if they
+see that the reserve price is $110 they
+
+ align:start position:0%
+see that the reserve price is $110 they
+ 
+
+ align:start position:0%
+see that the reserve price is $110 they
+may not bother to read all the fine
+
+ align:start position:0%
+may not bother to read all the fine
+ 
+
+ align:start position:0%
+may not bother to read all the fine
+print and enter that auction um you know
+
+ align:start position:0%
+print and enter that auction um you know
+ 
+
+ align:start position:0%
+print and enter that auction um you know
+there could be some kind of common value
+
+ align:start position:0%
+there could be some kind of common value
+ 
+
+ align:start position:0%
+there could be some kind of common value
+component this theory was uh once I know
+
+ align:start position:0%
+component this theory was uh once I know
+ 
+
+ align:start position:0%
+component this theory was uh once I know
+everybody else's bid my bid is unchanged
+
+ align:start position:0%
+everybody else's bid my bid is unchanged
+ 
+
+ align:start position:0%
+everybody else's bid my bid is unchanged
+there common values the theory changes
+
+ align:start position:0%
+there common values the theory changes
+ 
+
+ align:start position:0%
+there common values the theory changes
+and then they also note that there could
+
+ align:start position:0%
+and then they also note that there could
+ 
+
+ align:start position:0%
+and then they also note that there could
+be you know speaking of this Theory and
+
+ align:start position:0%
+be you know speaking of this Theory and
+ 
+
+ align:start position:0%
+be you know speaking of this Theory and
+why this Theory may not work um you
+
+ align:start position:0%
+why this Theory may not work um you
+ 
+
+ align:start position:0%
+why this Theory may not work um you
+could also have sort of Behavioral
+
+ align:start position:0%
+could also have sort of Behavioral
+ 
+
+ align:start position:0%
+could also have sort of Behavioral
+preferences like loss Avers if you
+
+ align:start position:0%
+preferences like loss Avers if you
+ 
+
+ align:start position:0%
+preferences like loss Avers if you
+imagine you know the loss version is
+
+ align:start position:0%
+imagine you know the loss version is
+ 
+
+ align:start position:0%
+imagine you know the loss version is
+always like I feel bad losing something
+
+ align:start position:0%
+always like I feel bad losing something
+ 
+
+ align:start position:0%
+always like I feel bad losing something
+that I have if you sort of start the
+
+ align:start position:0%
+that I have if you sort of start the
+ 
+
+ align:start position:0%
+that I have if you sort of start the
+bidding at a very low price and people
+
+ align:start position:0%
+bidding at a very low price and people
+ 
+
+ align:start position:0%
+bidding at a very low price and people
+get used to the idea of owning this
+
+ align:start position:0%
+get used to the idea of owning this
+ 
+
+ align:start position:0%
+get used to the idea of owning this
+fancy golf club because they see it
+
+ align:start position:0%
+fancy golf club because they see it
+ 
+
+ align:start position:0%
+fancy golf club because they see it
+being bid for $20 once they've got used
+
+ align:start position:0%
+being bid for $20 once they've got used
+ 
+
+ align:start position:0%
+being bid for $20 once they've got used
+to the fact that they have this this
+
+ align:start position:0%
+to the fact that they have this this
+ 
+
+ align:start position:0%
+to the fact that they have this this
+fancy Golf Club then they may feel loss
+
+ align:start position:0%
+fancy Golf Club then they may feel loss
+ 
+
+ align:start position:0%
+fancy Golf Club then they may feel loss
+aversion if they don't win the golf club
+
+ align:start position:0%
+aversion if they don't win the golf club
+ 
+
+ align:start position:0%
+aversion if they don't win the golf club
+You by by getting people sort of tied up
+
+ align:start position:0%
+You by by getting people sort of tied up
+ 
+
+ align:start position:0%
+You by by getting people sort of tied up
+in the bidding they may get used to the
+
+ align:start position:0%
+in the bidding they may get used to the
+ 
+
+ align:start position:0%
+in the bidding they may get used to the
+thought of winning and then they may did
+
+ align:start position:0%
+thought of winning and then they may did
+ 
+
+ align:start position:0%
+thought of winning and then they may did
+more in the end um anyway to sort of to
+
+ align:start position:0%
+more in the end um anyway to sort of to
+ 
+
+ align:start position:0%
+more in the end um anyway to sort of to
+examine this uh what they do is uh they
+
+ align:start position:0%
+examine this uh what they do is uh they
+ 
+
+ align:start position:0%
+examine this uh what they do is uh they
+find a data set where they found 19,000
+
+ align:start position:0%
+find a data set where they found 19,000
+ 
+
+ align:start position:0%
+find a data set where they found 19,000
+experiments where there's several
+
+ align:start position:0%
+experiments where there's several
+ 
+
+ align:start position:0%
+experiments where there's several
+features uh one is there's variation in
+
+ align:start position:0%
+features uh one is there's variation in
+ 
+
+ align:start position:0%
+features uh one is there's variation in
+the start price uh there's free shipping
+
+ align:start position:0%
+the start price uh there's free shipping
+ 
+
+ align:start position:0%
+the start price uh there's free shipping
+which just simplifies things there's no
+
+ align:start position:0%
+which just simplifies things there's no
+ 
+
+ align:start position:0%
+which just simplifies things there's no
+secret reserve price no Buy It Now
+
+ align:start position:0%
+secret reserve price no Buy It Now
+ 
+
+ align:start position:0%
+secret reserve price no Buy It Now
+auction so these are just straight plain
+
+ align:start position:0%
+auction so these are just straight plain
+ 
+
+ align:start position:0%
+auction so these are just straight plain
+vanilla auctions of a good many
+
+ align:start position:0%
+vanilla auctions of a good many
+ 
+
+ align:start position:0%
+vanilla auctions of a good many
+different times okay uh and so these
+
+ align:start position:0%
+different times okay uh and so these
+ 
+
+ align:start position:0%
+different times okay uh and so these
+about 25 uh listings uh per experiment
+
+ align:start position:0%
+about 25 uh listings uh per experiment
+ 
+
+ align:start position:0%
+about 25 uh listings uh per experiment
+so again these are just sellers
+
+ align:start position:0%
+so again these are just sellers
+ 
+
+ align:start position:0%
+so again these are just sellers
+experimenting with you know sellers
+
+ align:start position:0%
+experimenting with you know sellers
+ 
+
+ align:start position:0%
+experimenting with you know sellers
+experimenting with what's what if I'm
+
+ align:start position:0%
+experimenting with what's what if I'm
+ 
+
+ align:start position:0%
+experimenting with what's what if I'm
+selling $125 Golf Club should I start
+
+ align:start position:0%
+selling $125 Golf Club should I start
+ 
+
+ align:start position:0%
+selling $125 Golf Club should I start
+the bidding at $5 or $100 or 50 or
+
+ align:start position:0%
+the bidding at $5 or $100 or 50 or
+ 
+
+ align:start position:0%
+the bidding at $5 or $100 or 50 or
+something in
+
+ align:start position:0%
+something in
+ 
+
+ align:start position:0%
+something in
+between uh figure five in the paper
+
+ align:start position:0%
+between uh figure five in the paper
+ 
+
+ align:start position:0%
+between uh figure five in the paper
+shows that yes sellers are doing this a
+
+ align:start position:0%
+shows that yes sellers are doing this a
+ 
+
+ align:start position:0%
+shows that yes sellers are doing this a
+lot so let's look at a typical category
+
+ align:start position:0%
+lot so let's look at a typical category
+ 
+
+ align:start position:0%
+lot so let's look at a typical category
+like Goods that cost between $30 and
+
+ align:start position:0%
+like Goods that cost between $30 and
+ 
+
+ align:start position:0%
+like Goods that cost between $30 and
+$100 and you can see Goods where the you
+
+ align:start position:0%
+$100 and you can see Goods where the you
+ 
+
+ align:start position:0%
+$100 and you can see Goods where the you
+know that cost between this is like the
+
+ align:start position:0%
+know that cost between this is like the
+ 
+
+ align:start position:0%
+know that cost between this is like the
+average price at which they're sold when
+
+ align:start position:0%
+average price at which they're sold when
+ 
+
+ align:start position:0%
+average price at which they're sold when
+they sell them through the through just
+
+ align:start position:0%
+they sell them through the through just
+ 
+
+ align:start position:0%
+they sell them through the through just
+a fixed price sale and you can see Goods
+
+ align:start position:0%
+a fixed price sale and you can see Goods
+ 
+
+ align:start position:0%
+a fixed price sale and you can see Goods
+that sell for $30 to $100 20% of the
+
+ align:start position:0%
+that sell for $30 to $100 20% of the
+ 
+
+ align:start position:0%
+that sell for $30 to $100 20% of the
+sellers start them out at zero in these
+
+ align:start position:0%
+sellers start them out at zero in these
+ 
+
+ align:start position:0%
+sellers start them out at zero in these
+experiments uh and then uh 37% start
+
+ align:start position:0%
+experiments uh and then uh 37% start
+ 
+
+ align:start position:0%
+experiments uh and then uh 37% start
+them out between 85 to 100% of the sort
+
+ align:start position:0%
+them out between 85 to 100% of the sort
+ 
+
+ align:start position:0%
+them out between 85 to 100% of the sort
+of average fixed price sale 17% choose
+
+ align:start position:0%
+of average fixed price sale 17% choose
+ 
+
+ align:start position:0%
+of average fixed price sale 17% choose
+60 to 80 133% are actually starting them
+
+ align:start position:0%
+60 to 80 133% are actually starting them
+ 
+
+ align:start position:0%
+60 to 80 133% are actually starting them
+off above the sort of average Buy It Now
+
+ align:start position:0%
+off above the sort of average Buy It Now
+ 
+
+ align:start position:0%
+off above the sort of average Buy It Now
+average fixed price sales um but we get
+
+ align:start position:0%
+average fixed price sales um but we get
+ 
+
+ align:start position:0%
+average fixed price sales um but we get
+the sort of Buy modal distribution
+
+ align:start position:0%
+the sort of Buy modal distribution
+ 
+
+ align:start position:0%
+the sort of Buy modal distribution
+notably there are very few sellers
+
+ align:start position:0%
+notably there are very few sellers
+ 
+
+ align:start position:0%
+notably there are very few sellers
+starting out in here it seems like if
+
+ align:start position:0%
+starting out in here it seems like if
+ 
+
+ align:start position:0%
+starting out in here it seems like if
+you're going to go low you just go all
+
+ align:start position:0%
+you're going to go low you just go all
+ 
+
+ align:start position:0%
+you're going to go low you just go all
+the way down to the bottom and start at
+
+ align:start position:0%
+the way down to the bottom and start at
+ 
+
+ align:start position:0%
+the way down to the bottom and start at
+almost
+
+ align:start position:0%
+almost
+ 
+
+ align:start position:0%
+almost
+zero okay and then the sort of this with
+
+ align:start position:0%
+zero okay and then the sort of this with
+ 
+
+ align:start position:0%
+zero okay and then the sort of this with
+a lot of within experiment variation so
+
+ align:start position:0%
+a lot of within experiment variation so
+ 
+
+ align:start position:0%
+a lot of within experiment variation so
+if you look at auctions in which there
+
+ align:start position:0%
+if you look at auctions in which there
+ 
+
+ align:start position:0%
+if you look at auctions in which there
+some sellers are sometimes selling it at
+
+ align:start position:0%
+some sellers are sometimes selling it at
+ 
+
+ align:start position:0%
+some sellers are sometimes selling it at
+less than 5% those same sellers were
+
+ align:start position:0%
+less than 5% those same sellers were
+ 
+
+ align:start position:0%
+less than 5% those same sellers were
+sometimes selling it at less than 5% are
+
+ align:start position:0%
+sometimes selling it at less than 5% are
+ 
+
+ align:start position:0%
+sometimes selling it at less than 5% are
+also sometimes selling 5 to 45 45 to 85
+
+ align:start position:0%
+also sometimes selling 5 to 45 45 to 85
+ 
+
+ align:start position:0%
+also sometimes selling 5 to 45 45 to 85
+85 to 100 100 to 120 greater than 120 so
+
+ align:start position:0%
+85 to 100 100 to 120 greater than 120 so
+ 
+
+ align:start position:0%
+85 to 100 100 to 120 greater than 120 so
+there just many experiments where
+
+ align:start position:0%
+there just many experiments where
+ 
+
+ align:start position:0%
+there just many experiments where
+sellers are trying out the whole range
+
+ align:start position:0%
+sellers are trying out the whole range
+ 
+
+ align:start position:0%
+sellers are trying out the whole range
+themselves this is sort of our
+
+ align:start position:0%
+themselves this is sort of our
+ 
+
+ align:start position:0%
+themselves this is sort of our
+experimental paper that we get to run
+
+ align:start position:0%
+experimental paper that we get to run
+ 
+
+ align:start position:0%
+experimental paper that we get to run
+without having to actually pay for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiments um okay so does the sort of
+
+ align:start position:0%
+experiments um okay so does the sort of
+ 
+
+ align:start position:0%
+experiments um okay so does the sort of
+standard uh auction demand Theory work
+
+ align:start position:0%
+standard uh auction demand Theory work
+ 
+
+ align:start position:0%
+standard uh auction demand Theory work
+uh and the answer is no um there's one
+
+ align:start position:0%
+uh and the answer is no um there's one
+ 
+
+ align:start position:0%
+uh and the answer is no um there's one
+interesting feature which is the demand
+
+ align:start position:0%
+interesting feature which is the demand
+ 
+
+ align:start position:0%
+interesting feature which is the demand
+curve turns up at very low prices so you
+
+ align:start position:0%
+curve turns up at very low prices so you
+ 
+
+ align:start position:0%
+curve turns up at very low prices so you
+know remember I I drew this curve for
+
+ align:start position:0%
+know remember I I drew this curve for
+ 
+
+ align:start position:0%
+know remember I I drew this curve for
+you saying if I start the good at only
+
+ align:start position:0%
+you saying if I start the good at only
+ 
+
+ align:start position:0%
+you saying if I start the good at only
+$5 if I start the good at
+
+ align:start position:0%
+$5 if I start the good at
+ 
+
+ align:start position:0%
+$5 if I start the good at
+$1 um you if I start the good at $1 I
+
+ align:start position:0%
+$1 um you if I start the good at $1 I
+ 
+
+ align:start position:0%
+$1 um you if I start the good at $1 I
+sell it almost entirely for sure but I'm
+
+ align:start position:0%
+sell it almost entirely for sure but I'm
+ 
+
+ align:start position:0%
+sell it almost entirely for sure but I'm
+going to have a lower average price than
+
+ align:start position:0%
+going to have a lower average price than
+ 
+
+ align:start position:0%
+going to have a lower average price than
+if I start the good at a higher price uh
+
+ align:start position:0%
+if I start the good at a higher price uh
+ 
+
+ align:start position:0%
+if I start the good at a higher price uh
+what they find is that the curve doesn't
+
+ align:start position:0%
+what they find is that the curve doesn't
+ 
+
+ align:start position:0%
+what they find is that the curve doesn't
+look like this um the curve looks like
+
+ align:start position:0%
+look like this um the curve looks like
+ 
+
+ align:start position:0%
+look like this um the curve looks like
+this um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so as I start at a lower and lower price
+
+ align:start position:0%
+so as I start at a lower and lower price
+ 
+
+ align:start position:0%
+so as I start at a lower and lower price
+not only do I sell for a higher with a
+
+ align:start position:0%
+not only do I sell for a higher with a
+ 
+
+ align:start position:0%
+not only do I sell for a higher with a
+higher probability I sell at a higher
+
+ align:start position:0%
+higher probability I sell at a higher
+ 
+
+ align:start position:0%
+higher probability I sell at a higher
+price conditional on selling so I'm up
+
+ align:start position:0%
+price conditional on selling so I'm up
+ 
+
+ align:start position:0%
+price conditional on selling so I'm up
+here I'm selling at 90% probability and
+
+ align:start position:0%
+here I'm selling at 90% probability and
+ 
+
+ align:start position:0%
+here I'm selling at 90% probability and
+I'm getting a higher price than I would
+
+ align:start position:0%
+I'm getting a higher price than I would
+ 
+
+ align:start position:0%
+I'm getting a higher price than I would
+get if I chose reserve price that only
+
+ align:start position:0%
+get if I chose reserve price that only
+ 
+
+ align:start position:0%
+get if I chose reserve price that only
+sold with 70%
+
+ align:start position:0%
+sold with 70%
+ 
+
+ align:start position:0%
+sold with 70%
+probability so the demand curve turns up
+
+ align:start position:0%
+probability so the demand curve turns up
+ 
+
+ align:start position:0%
+probability so the demand curve turns up
+you know it's suggesting that I put the
+
+ align:start position:0%
+you know it's suggesting that I put the
+ 
+
+ align:start position:0%
+you know it's suggesting that I put the
+$100 item out there started bidding at
+
+ align:start position:0%
+$100 item out there started bidding at
+ 
+
+ align:start position:0%
+$100 item out there started bidding at
+$1 lots of people see it at a dollar 10
+
+ align:start position:0%
+$1 lots of people see it at a dollar 10
+ 
+
+ align:start position:0%
+$1 lots of people see it at a dollar 10
+hours before the auction is over they
+
+ align:start position:0%
+hours before the auction is over they
+ 
+
+ align:start position:0%
+hours before the auction is over they
+all start following the auction they all
+
+ align:start position:0%
+all start following the auction they all
+ 
+
+ align:start position:0%
+all start following the auction they all
+start bidding I get more probably I get
+
+ align:start position:0%
+start bidding I get more probably I get
+ 
+
+ align:start position:0%
+start bidding I get more probably I get
+more entry than I would if I started it
+
+ align:start position:0%
+more entry than I would if I started it
+ 
+
+ align:start position:0%
+more entry than I would if I started it
+at uh $20 instead so the curve instead
+
+ align:start position:0%
+at uh $20 instead so the curve instead
+ 
+
+ align:start position:0%
+at uh $20 instead so the curve instead
+of looking like this you know looks like
+
+ align:start position:0%
+of looking like this you know looks like
+ 
+
+ align:start position:0%
+of looking like this you know looks like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead and if you you know you
+
+ align:start position:0%
+instead and if you you know you
+ 
+
+ align:start position:0%
+instead and if you you know you
+obviously how do we do Monopoly pricing
+
+ align:start position:0%
+obviously how do we do Monopoly pricing
+ 
+
+ align:start position:0%
+obviously how do we do Monopoly pricing
+you know like the way to think about
+
+ align:start position:0%
+you know like the way to think about
+ 
+
+ align:start position:0%
+you know like the way to think about
+Monopoly pricing is you do marginal
+
+ align:start position:0%
+Monopoly pricing is you do marginal
+ 
+
+ align:start position:0%
+Monopoly pricing is you do marginal
+revenue equals marginal cost so they
+
+ align:start position:0%
+revenue equals marginal cost so they
+ 
+
+ align:start position:0%
+revenue equals marginal cost so they
+take this demand curve they construct
+
+ align:start position:0%
+take this demand curve they construct
+ 
+
+ align:start position:0%
+take this demand curve they construct
+the marginal revenue curve and the
+
+ align:start position:0%
+the marginal revenue curve and the
+ 
+
+ align:start position:0%
+the marginal revenue curve and the
+marginal revenue curve also turns
+
+ align:start position:0%
+marginal revenue curve also turns
+ 
+
+ align:start position:0%
+marginal revenue curve also turns
+up so if you have a marginal you know
+
+ align:start position:0%
+up so if you have a marginal you know
+ 
+
+ align:start position:0%
+up so if you have a marginal you know
+like we're used to sort of marginal
+
+ align:start position:0%
+like we're used to sort of marginal
+ 
+
+ align:start position:0%
+like we're used to sort of marginal
+revenue is downward sloping you draw
+
+ align:start position:0%
+revenue is downward sloping you draw
+ 
+
+ align:start position:0%
+revenue is downward sloping you draw
+marginal cost across where marginal
+
+ align:start position:0%
+marginal cost across where marginal
+ 
+
+ align:start position:0%
+marginal cost across where marginal
+revenue hits marginal cost that's the
+
+ align:start position:0%
+revenue hits marginal cost that's the
+ 
+
+ align:start position:0%
+revenue hits marginal cost that's the
+that's the Monopoly price what do you do
+
+ align:start position:0%
+that's the Monopoly price what do you do
+ 
+
+ align:start position:0%
+that's the Monopoly price what do you do
+when marginal revenue turns up you know
+
+ align:start position:0%
+when marginal revenue turns up you know
+ 
+
+ align:start position:0%
+when marginal revenue turns up you know
+so if if
+
+ align:start position:0%
+so if if
+ 
+
+ align:start position:0%
+so if if
+um if this is my marginal revenue curve
+
+ align:start position:0%
+um if this is my marginal revenue curve
+ 
+
+ align:start position:0%
+um if this is my marginal revenue curve
+my marginal cost is flat that's my
+
+ align:start position:0%
+my marginal cost is flat that's my
+ 
+
+ align:start position:0%
+my marginal cost is flat that's my
+normal Monopoly pricing uh what do I do
+
+ align:start position:0%
+normal Monopoly pricing uh what do I do
+ 
+
+ align:start position:0%
+normal Monopoly pricing uh what do I do
+if marginal revenue turns
+
+ align:start position:0%
+if marginal revenue turns
+ 
+
+ align:start position:0%
+if marginal revenue turns
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+then I can draw the line across where
+
+ align:start position:0%
+then I can draw the line across where
+ 
+
+ align:start position:0%
+then I can draw the line across where
+marginal revenue equals marginal cost
+
+ align:start position:0%
+marginal revenue equals marginal cost
+ 
+
+ align:start position:0%
+marginal revenue equals marginal cost
+this is a local opt locally optimal
+
+ align:start position:0%
+this is a local opt locally optimal
+ 
+
+ align:start position:0%
+this is a local opt locally optimal
+Monopoly price but the solution is
+
+ align:start position:0%
+Monopoly price but the solution is
+ 
+
+ align:start position:0%
+Monopoly price but the solution is
+either going to be this point or this
+
+ align:start position:0%
+either going to be this point or this
+ 
+
+ align:start position:0%
+either going to be this point or this
+point right you know it doesn't have to
+
+ align:start position:0%
+point right you know it doesn't have to
+ 
+
+ align:start position:0%
+point right you know it doesn't have to
+intersect again it could be that you get
+
+ align:start position:0%
+intersect again it could be that you get
+ 
+
+ align:start position:0%
+intersect again it could be that you get
+a you know here your revenue is
+
+ align:start position:0%
+a you know here your revenue is
+ 
+
+ align:start position:0%
+a you know here your revenue is
+increasing so it may be that you want to
+
+ align:start position:0%
+increasing so it may be that you want to
+ 
+
+ align:start position:0%
+increasing so it may be that you want to
+sort of price there you know you may
+
+ align:start position:0%
+sort of price there you know you may
+ 
+
+ align:start position:0%
+sort of price there you know you may
+want a price here that may be the global
+
+ align:start position:0%
+want a price here that may be the global
+ 
+
+ align:start position:0%
+want a price here that may be the global
+Optimum or this could be the global
+
+ align:start position:0%
+Optimum or this could be the global
+ 
+
+ align:start position:0%
+Optimum or this could be the global
+Optimum but you're going to do one or
+
+ align:start position:0%
+Optimum but you're going to do one or
+ 
+
+ align:start position:0%
+Optimum but you're going to do one or
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+other uh anyway and so that's I guess in
+
+ align:start position:0%
+other uh anyway and so that's I guess in
+ 
+
+ align:start position:0%
+other uh anyway and so that's I guess in
+some sense the um you
+
+ align:start position:0%
+some sense the um you
+ 
+
+ align:start position:0%
+some sense the um you
+know this is sort of how they explain
+
+ align:start position:0%
+know this is sort of how they explain
+ 
+
+ align:start position:0%
+know this is sort of how they explain
+what's going on in the data if you
+
+ align:start position:0%
+what's going on in the data if you
+ 
+
+ align:start position:0%
+what's going on in the data if you
+remember in the data there was a lot of
+
+ align:start position:0%
+remember in the data there was a lot of
+ 
+
+ align:start position:0%
+remember in the data there was a lot of
+firms figure five you know like there
+
+ align:start position:0%
+firms figure five you know like there
+ 
+
+ align:start position:0%
+firms figure five you know like there
+were a lot of firms charging fairly High
+
+ align:start position:0%
+were a lot of firms charging fairly High
+ 
+
+ align:start position:0%
+were a lot of firms charging fairly High
+uh Reserve prices and then some firms
+
+ align:start position:0%
+uh Reserve prices and then some firms
+ 
+
+ align:start position:0%
+uh Reserve prices and then some firms
+charging very low Reserve prices and so
+
+ align:start position:0%
+charging very low Reserve prices and so
+ 
+
+ align:start position:0%
+charging very low Reserve prices and so
+you know their thought is that what's
+
+ align:start position:0%
+you know their thought is that what's
+ 
+
+ align:start position:0%
+you know their thought is that what's
+going on in the data is probably
+
+ align:start position:0%
+going on in the data is probably
+ 
+
+ align:start position:0%
+going on in the data is probably
+something like this where the marginal
+
+ align:start position:0%
+something like this where the marginal
+ 
+
+ align:start position:0%
+something like this where the marginal
+cost is pretty high so you
+
+ align:start position:0%
+cost is pretty high so you
+ 
+
+ align:start position:0%
+cost is pretty high so you
+either set a quite High reserve price
+
+ align:start position:0%
+either set a quite High reserve price
+ 
+
+ align:start position:0%
+either set a quite High reserve price
+and this is the optimum or you set this
+
+ align:start position:0%
+and this is the optimum or you set this
+ 
+
+ align:start position:0%
+and this is the optimum or you set this
+right end point and for different
+
+ align:start position:0%
+right end point and for different
+ 
+
+ align:start position:0%
+right end point and for different
+sellers different ones are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+optimal and you know in general if your
+
+ align:start position:0%
+optimal and you know in general if your
+ 
+
+ align:start position:0%
+optimal and you know in general if your
+marginal cost is high you're going to
+
+ align:start position:0%
+marginal cost is high you're going to
+ 
+
+ align:start position:0%
+marginal cost is high you're going to
+just set the high reserve price your
+
+ align:start position:0%
+just set the high reserve price your
+ 
+
+ align:start position:0%
+just set the high reserve price your
+marginal cost is low you're going to be
+
+ align:start position:0%
+marginal cost is low you're going to be
+ 
+
+ align:start position:0%
+marginal cost is low you're going to be
+setting the right end point
+
+ align:start position:0%
+setting the right end point
+ 
+
+ align:start position:0%
+setting the right end point
+you know and then the paper tries to do
+
+ align:start position:0%
+you know and then the paper tries to do
+ 
+
+ align:start position:0%
+you know and then the paper tries to do
+other predictions it tries to have a
+
+ align:start position:0%
+other predictions it tries to have a
+ 
+
+ align:start position:0%
+other predictions it tries to have a
+test of this sort of upper tail
+
+ align:start position:0%
+test of this sort of upper tail
+ 
+
+ align:start position:0%
+test of this sort of upper tail
+hypothesis of is the sort of does the
+
+ align:start position:0%
+hypothesis of is the sort of does the
+ 
+
+ align:start position:0%
+hypothesis of is the sort of does the
+upper tail of the price distribution
+
+ align:start position:0%
+upper tail of the price distribution
+ 
+
+ align:start position:0%
+upper tail of the price distribution
+look the same regardless of of what
+
+ align:start position:0%
+look the same regardless of of what
+ 
+
+ align:start position:0%
+look the same regardless of of what
+reserve price you use and that test only
+
+ align:start position:0%
+reserve price you use and that test only
+ 
+
+ align:start position:0%
+reserve price you use and that test only
+works so well so it it does seem like
+
+ align:start position:0%
+works so well so it it does seem like
+ 
+
+ align:start position:0%
+works so well so it it does seem like
+the sort of classic Theory this sort of
+
+ align:start position:0%
+the sort of classic Theory this sort of
+ 
+
+ align:start position:0%
+the sort of classic Theory this sort of
+upper tail distribution is is just what
+
+ align:start position:0%
+upper tail distribution is is just what
+ 
+
+ align:start position:0%
+upper tail distribution is is just what
+you get by truncating isn't quite right
+
+ align:start position:0%
+you get by truncating isn't quite right
+ 
+
+ align:start position:0%
+you get by truncating isn't quite right
+here um and it does seem to Ender this
+
+ align:start position:0%
+here um and it does seem to Ender this
+ 
+
+ align:start position:0%
+here um and it does seem to Ender this
+sort of it's entry costs are important
+
+ align:start position:0%
+sort of it's entry costs are important
+ 
+
+ align:start position:0%
+sort of it's entry costs are important
+for online auctions is the I think the
+
+ align:start position:0%
+for online auctions is the I think the
+ 
+
+ align:start position:0%
+for online auctions is the I think the
+main message
+
+ align:start position:0%
+main message
+ 
+
+ align:start position:0%
+main message
+there okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions yeah you know obviously I I
+
+ align:start position:0%
+questions yeah you know obviously I I
+ 
+
+ align:start position:0%
+questions yeah you know obviously I I
+think that's something you
+
+ align:start position:0%
+think that's something you
+ 
+
+ align:start position:0%
+think that's something you
+know uh uh that work was done inside
+
+ align:start position:0%
+know uh uh that work was done inside
+ 
+
+ align:start position:0%
+know uh uh that work was done inside
+eBay you know for a long time eBay
+
+ align:start position:0%
+eBay you know for a long time eBay
+ 
+
+ align:start position:0%
+eBay you know for a long time eBay
+actually had this sort of very very uh
+
+ align:start position:0%
+actually had this sort of very very uh
+ 
+
+ align:start position:0%
+actually had this sort of very very uh
+open policy to academics and we actually
+
+ align:start position:0%
+open policy to academics and we actually
+ 
+
+ align:start position:0%
+open policy to academics and we actually
+had several students like after they
+
+ align:start position:0%
+had several students like after they
+ 
+
+ align:start position:0%
+had several students like after they
+finish their phds here go to a postc for
+
+ align:start position:0%
+finish their phds here go to a postc for
+ 
+
+ align:start position:0%
+finish their phds here go to a postc for
+a year and sit at eBay because eBay
+
+ align:start position:0%
+a year and sit at eBay because eBay
+ 
+
+ align:start position:0%
+a year and sit at eBay because eBay
+would let you sit there and operate in
+
+ align:start position:0%
+would let you sit there and operate in
+ 
+
+ align:start position:0%
+would let you sit there and operate in
+inside the company and do all kinds of
+
+ align:start position:0%
+inside the company and do all kinds of
+ 
+
+ align:start position:0%
+inside the company and do all kinds of
+stuff with their full data set uh that
+
+ align:start position:0%
+stuff with their full data set uh that
+ 
+
+ align:start position:0%
+stuff with their full data set uh that
+seems to have faded away in you know
+
+ align:start position:0%
+seems to have faded away in you know
+ 
+
+ align:start position:0%
+seems to have faded away in you know
+three or four years ago um but obviously
+
+ align:start position:0%
+three or four years ago um but obviously
+ 
+
+ align:start position:0%
+three or four years ago um but obviously
+one could still scrape eBay and do the
+
+ align:start position:0%
+one could still scrape eBay and do the
+ 
+
+ align:start position:0%
+one could still scrape eBay and do the
+same kinds of
+
+ align:start position:0%
+same kinds of
+ 
+
+ align:start position:0%
+same kinds of
+things okay so then the
+
+ align:start position:0%
+things okay so then the
+ 
+
+ align:start position:0%
+things okay so then the
+um second topic that I guess is common
+
+ align:start position:0%
+um second topic that I guess is common
+ 
+
+ align:start position:0%
+um second topic that I guess is common
+to the rest of the papers I'm going to
+
+ align:start position:0%
+to the rest of the papers I'm going to
+ 
+
+ align:start position:0%
+to the rest of the papers I'm going to
+talk about is just
+
+ align:start position:0%
+talk about is just
+ 
+
+ align:start position:0%
+talk about is just
+understanding uh how online retail works
+
+ align:start position:0%
+understanding uh how online retail works
+ 
+
+ align:start position:0%
+understanding uh how online retail works
+and why why it's
+
+ align:start position:0%
+and why why it's
+ 
+
+ align:start position:0%
+and why why it's
+successful you know if you read people
+
+ align:start position:0%
+successful you know if you read people
+ 
+
+ align:start position:0%
+successful you know if you read people
+writing about uh e-commerce in the early
+
+ align:start position:0%
+writing about uh e-commerce in the early
+ 
+
+ align:start position:0%
+writing about uh e-commerce in the early
+in the internet era there's this
+
+ align:start position:0%
+in the internet era there's this
+ 
+
+ align:start position:0%
+in the internet era there's this
+question of is online retail ever going
+
+ align:start position:0%
+question of is online retail ever going
+ 
+
+ align:start position:0%
+question of is online retail ever going
+to really take off and displace
+
+ align:start position:0%
+to really take off and displace
+ 
+
+ align:start position:0%
+to really take off and displace
+traditional retail and the biggest
+
+ align:start position:0%
+traditional retail and the biggest
+ 
+
+ align:start position:0%
+traditional retail and the biggest
+argument against online retail taking
+
+ align:start position:0%
+argument against online retail taking
+ 
+
+ align:start position:0%
+argument against online retail taking
+off was that it's just much more
+
+ align:start position:0%
+off was that it's just much more
+ 
+
+ align:start position:0%
+off was that it's just much more
+expensive um you know like in if you
+
+ align:start position:0%
+expensive um you know like in if you
+ 
+
+ align:start position:0%
+expensive um you know like in if you
+look at the long history of retail in
+
+ align:start position:0%
+look at the long history of retail in
+ 
+
+ align:start position:0%
+look at the long history of retail in
+America you know in the8 1800s people
+
+ align:start position:0%
+America you know in the8 1800s people
+ 
+
+ align:start position:0%
+America you know in the8 1800s people
+shopped in department stores uh and then
+
+ align:start position:0%
+shopped in department stores uh and then
+ 
+
+ align:start position:0%
+shopped in department stores uh and then
+there was this Golden Era of catalog
+
+ align:start position:0%
+there was this Golden Era of catalog
+ 
+
+ align:start position:0%
+there was this Golden Era of catalog
+retail where like the Sears
+
+ align:start position:0%
+retail where like the Sears
+ 
+
+ align:start position:0%
+retail where like the Sears
+catalog you know in some sense brought
+
+ align:start position:0%
+catalog you know in some sense brought
+ 
+
+ align:start position:0%
+catalog you know in some sense brought
+products to the you know that were only
+
+ align:start position:0%
+products to the you know that were only
+ 
+
+ align:start position:0%
+products to the you know that were only
+formally available in cities to all of
+
+ align:start position:0%
+formally available in cities to all of
+ 
+
+ align:start position:0%
+formally available in cities to all of
+America and they had like this phone
+
+ align:start position:0%
+America and they had like this phone
+ 
+
+ align:start position:0%
+America and they had like this phone
+book well you know thousand page thick
+
+ align:start position:0%
+book well you know thousand page thick
+ 
+
+ align:start position:0%
+book well you know thousand page thick
+catalog that they would mail you you
+
+ align:start position:0%
+catalog that they would mail you you
+ 
+
+ align:start position:0%
+catalog that they would mail you you
+could buy anything from the Sears
+
+ align:start position:0%
+could buy anything from the Sears
+ 
+
+ align:start position:0%
+could buy anything from the Sears
+catalog you know Sears catalog just took
+
+ align:start position:0%
+catalog you know Sears catalog just took
+ 
+
+ align:start position:0%
+catalog you know Sears catalog just took
+off in the I think it's I guess it's
+
+ align:start position:0%
+off in the I think it's I guess it's
+ 
+
+ align:start position:0%
+off in the I think it's I guess it's
+late 1800s after there were sort of
+
+ align:start position:0%
+late 1800s after there were sort of
+ 
+
+ align:start position:0%
+late 1800s after there were sort of
+train or whatever they would bring
+
+ align:start position:0%
+train or whatever they would bring
+ 
+
+ align:start position:0%
+train or whatever they would bring
+packages to people uh when the car was
+
+ align:start position:0%
+packages to people uh when the car was
+ 
+
+ align:start position:0%
+packages to people uh when the car was
+invented the Sears catalog just went
+
+ align:start position:0%
+invented the Sears catalog just went
+ 
+
+ align:start position:0%
+invented the Sears catalog just went
+into a prolonged Decline and Sears
+
+ align:start position:0%
+into a prolonged Decline and Sears
+ 
+
+ align:start position:0%
+into a prolonged Decline and Sears
+opened you know massive you know not the
+
+ align:start position:0%
+opened you know massive you know not the
+ 
+
+ align:start position:0%
+opened you know massive you know not the
+size of a Walmart but you know massive
+
+ align:start position:0%
+size of a Walmart but you know massive
+ 
+
+ align:start position:0%
+size of a Walmart but you know massive
+department stores in many US cities and
+
+ align:start position:0%
+department stores in many US cities and
+ 
+
+ align:start position:0%
+department stores in many US cities and
+then again the catalog business declined
+
+ align:start position:0%
+then again the catalog business declined
+ 
+
+ align:start position:0%
+then again the catalog business declined
+the physical retail business took off
+
+ align:start position:0%
+the physical retail business took off
+ 
+
+ align:start position:0%
+the physical retail business took off
+you know thoughts on why that was
+
+ align:start position:0%
+you know thoughts on why that was
+ 
+
+ align:start position:0%
+you know thoughts on why that was
+catalog retail was just always much more
+
+ align:start position:0%
+catalog retail was just always much more
+ 
+
+ align:start position:0%
+catalog retail was just always much more
+expensive than traditional retail like
+
+ align:start position:0%
+expensive than traditional retail like
+ 
+
+ align:start position:0%
+expensive than traditional retail like
+if you look at
+
+ align:start position:0%
+if you look at
+ 
+
+ align:start position:0%
+if you look at
+Walmart uh Walmart's cost of selling
+
+ align:start position:0%
+Walmart uh Walmart's cost of selling
+ 
+
+ align:start position:0%
+Walmart uh Walmart's cost of selling
+Goods is
+
+ align:start position:0%
+Goods is
+ 
+
+ align:start position:0%
+Goods is
+roughly uh 20% of the merchandise that
+
+ align:start position:0%
+roughly uh 20% of the merchandise that
+ 
+
+ align:start position:0%
+roughly uh 20% of the merchandise that
+they sell um catalog retail had cost
+
+ align:start position:0%
+they sell um catalog retail had cost
+ 
+
+ align:start position:0%
+they sell um catalog retail had cost
+more like 40 or
+
+ align:start position:0%
+more like 40 or
+ 
+
+ align:start position:0%
+more like 40 or
+50% uh and why is it cost Walmart only
+
+ align:start position:0%
+50% uh and why is it cost Walmart only
+ 
+
+ align:start position:0%
+50% uh and why is it cost Walmart only
+20% when it cost catalog retail
+
+ align:start position:0%
+20% when it cost catalog retail
+ 
+
+ align:start position:0%
+20% when it cost catalog retail
+50% you know it's it's
+
+ align:start position:0%
+50% you know it's it's
+ 
+
+ align:start position:0%
+50% you know it's it's
+because catalog retail you know you need
+
+ align:start position:0%
+because catalog retail you know you need
+ 
+
+ align:start position:0%
+because catalog retail you know you need
+to have stuff in a warehouse every
+
+ align:start position:0%
+to have stuff in a warehouse every
+ 
+
+ align:start position:0%
+to have stuff in a warehouse every
+single item that gets sold someone needs
+
+ align:start position:0%
+single item that gets sold someone needs
+ 
+
+ align:start position:0%
+single item that gets sold someone needs
+to put it in a box put the box in the
+
+ align:start position:0%
+to put it in a box put the box in the
+ 
+
+ align:start position:0%
+to put it in a box put the box in the
+mail pay for the mail whereas you know
+
+ align:start position:0%
+mail pay for the mail whereas you know
+ 
+
+ align:start position:0%
+mail pay for the mail whereas you know
+Walmart's cost of putting you know like
+
+ align:start position:0%
+Walmart's cost of putting you know like
+ 
+
+ align:start position:0%
+Walmart's cost of putting you know like
+simplest example of like things never
+
+ align:start position:0%
+simplest example of like things never
+ 
+
+ align:start position:0%
+simplest example of like things never
+online like you know like a kitty
+
+ align:start position:0%
+online like you know like a kitty
+ 
+
+ align:start position:0%
+online like you know like a kitty
+swimming pool one of those plastic 4ot
+
+ align:start position:0%
+swimming pool one of those plastic 4ot
+ 
+
+ align:start position:0%
+swimming pool one of those plastic 4ot
+diameter swimming pools you can put a
+
+ align:start position:0%
+diameter swimming pools you can put a
+ 
+
+ align:start position:0%
+diameter swimming pools you can put a
+whole bunch of 4ot diameter plastic
+
+ align:start position:0%
+whole bunch of 4ot diameter plastic
+ 
+
+ align:start position:0%
+whole bunch of 4ot diameter plastic
+swimming pools stack them together put
+
+ align:start position:0%
+swimming pools stack them together put
+ 
+
+ align:start position:0%
+swimming pools stack them together put
+them in a truck take them to the Walmart
+
+ align:start position:0%
+them in a truck take them to the Walmart
+ 
+
+ align:start position:0%
+them in a truck take them to the Walmart
+and the cost of getting them there is is
+
+ align:start position:0%
+and the cost of getting them there is is
+ 
+
+ align:start position:0%
+and the cost of getting them there is is
+you know 50 cents or something like that
+
+ align:start position:0%
+you know 50 cents or something like that
+ 
+
+ align:start position:0%
+you know 50 cents or something like that
+you try to put a kitty swimming pool in
+
+ align:start position:0%
+you try to put a kitty swimming pool in
+ 
+
+ align:start position:0%
+you try to put a kitty swimming pool in
+the mail and send it to somebody you
+
+ align:start position:0%
+the mail and send it to somebody you
+ 
+
+ align:start position:0%
+the mail and send it to somebody you
+spent you know $30 mailing something
+
+ align:start position:0%
+spent you know $30 mailing something
+ 
+
+ align:start position:0%
+spent you know $30 mailing something
+that's only worth five or something and
+
+ align:start position:0%
+that's only worth five or something and
+ 
+
+ align:start position:0%
+that's only worth five or something and
+you know the putting things in a truck
+
+ align:start position:0%
+you know the putting things in a truck
+ 
+
+ align:start position:0%
+you know the putting things in a truck
+is just much much cheaper than packaging
+
+ align:start position:0%
+is just much much cheaper than packaging
+ 
+
+ align:start position:0%
+is just much much cheaper than packaging
+handling every package individually and
+
+ align:start position:0%
+handling every package individually and
+ 
+
+ align:start position:0%
+handling every package individually and
+you're getting some sense the Free Labor
+
+ align:start position:0%
+you're getting some sense the Free Labor
+ 
+
+ align:start position:0%
+you're getting some sense the Free Labor
+of people to just walk through the store
+
+ align:start position:0%
+of people to just walk through the store
+ 
+
+ align:start position:0%
+of people to just walk through the store
+and take it off the shelf and carry it
+
+ align:start position:0%
+and take it off the shelf and carry it
+ 
+
+ align:start position:0%
+and take it off the shelf and carry it
+home
+
+ align:start position:0%
+home
+ 
+
+ align:start position:0%
+home
+um anyway you know early on a Amazon was
+
+ align:start position:0%
+um anyway you know early on a Amazon was
+ 
+
+ align:start position:0%
+um anyway you know early on a Amazon was
+undercutting phys Barnes & Noble and
+
+ align:start position:0%
+undercutting phys Barnes & Noble and
+ 
+
+ align:start position:0%
+undercutting phys Barnes & Noble and
+selling books for lower than you would
+
+ align:start position:0%
+selling books for lower than you would
+ 
+
+ align:start position:0%
+selling books for lower than you would
+buy the books in a physical bookstore
+
+ align:start position:0%
+buy the books in a physical bookstore
+ 
+
+ align:start position:0%
+buy the books in a physical bookstore
+and there's a question of could could
+
+ align:start position:0%
+and there's a question of could could
+ 
+
+ align:start position:0%
+and there's a question of could could
+Amazon ever actually make a profit
+
+ align:start position:0%
+Amazon ever actually make a profit
+ 
+
+ align:start position:0%
+Amazon ever actually make a profit
+selling things not at a loss and sell if
+
+ align:start position:0%
+selling things not at a loss and sell if
+ 
+
+ align:start position:0%
+selling things not at a loss and sell if
+Amazon were pricing things at cost or
+
+ align:start position:0%
+Amazon were pricing things at cost or
+ 
+
+ align:start position:0%
+Amazon were pricing things at cost or
+above cost could it be competitive with
+
+ align:start position:0%
+above cost could it be competitive with
+ 
+
+ align:start position:0%
+above cost could it be competitive with
+traditional retail um one of the big
+
+ align:start position:0%
+traditional retail um one of the big
+ 
+
+ align:start position:0%
+traditional retail um one of the big
+arguments that was made early on was
+
+ align:start position:0%
+arguments that was made early on was
+ 
+
+ align:start position:0%
+arguments that was made early on was
+that yes Amazon doesn't need to have a
+
+ align:start position:0%
+that yes Amazon doesn't need to have a
+ 
+
+ align:start position:0%
+that yes Amazon doesn't need to have a
+cost advantage to sell things online it
+
+ align:start position:0%
+cost advantage to sell things online it
+ 
+
+ align:start position:0%
+cost advantage to sell things online it
+could be that you have a cost
+
+ align:start position:0%
+could be that you have a cost
+ 
+
+ align:start position:0%
+could be that you have a cost
+disadvantage but people buy online
+
+ align:start position:0%
+disadvantage but people buy online
+ 
+
+ align:start position:0%
+disadvantage but people buy online
+because of the product variety they
+
+ align:start position:0%
+because of the product variety they
+ 
+
+ align:start position:0%
+because of the product variety they
+product variety advantages are much
+
+ align:start position:0%
+product variety advantages are much
+ 
+
+ align:start position:0%
+product variety advantages are much
+bigger than the cost disad Vantage so
+
+ align:start position:0%
+bigger than the cost disad Vantage so
+ 
+
+ align:start position:0%
+bigger than the cost disad Vantage so
+therefore people buy online to get the
+
+ align:start position:0%
+therefore people buy online to get the
+ 
+
+ align:start position:0%
+therefore people buy online to get the
+book they want or whatever product they
+
+ align:start position:0%
+book they want or whatever product they
+ 
+
+ align:start position:0%
+book they want or whatever product they
+want that have a much bigger selection
+
+ align:start position:0%
+want that have a much bigger selection
+ 
+
+ align:start position:0%
+want that have a much bigger selection
+um and you know they note that when
+
+ align:start position:0%
+um and you know they note that when
+ 
+
+ align:start position:0%
+um and you know they note that when
+Amazon launched Amazon had 1 million
+
+ align:start position:0%
+Amazon launched Amazon had 1 million
+ 
+
+ align:start position:0%
+Amazon launched Amazon had 1 million
+titles obviously it later expanded to
+
+ align:start position:0%
+titles obviously it later expanded to
+ 
+
+ align:start position:0%
+titles obviously it later expanded to
+several million titles and a lot a very
+
+ align:start position:0%
+several million titles and a lot a very
+ 
+
+ align:start position:0%
+several million titles and a lot a very
+large physical bookstore at the time
+
+ align:start position:0%
+large physical bookstore at the time
+ 
+
+ align:start position:0%
+large physical bookstore at the time
+would have 100,000 titles your sort of
+
+ align:start position:0%
+would have 100,000 titles your sort of
+ 
+
+ align:start position:0%
+would have 100,000 titles your sort of
+typical bookstore might have 50,000
+
+ align:start position:0%
+typical bookstore might have 50,000
+ 
+
+ align:start position:0%
+typical bookstore might have 50,000
+titles in it uh you know perhaps there's
+
+ align:start position:0%
+titles in it uh you know perhaps there's
+ 
+
+ align:start position:0%
+titles in it uh you know perhaps there's
+some supert some super stores that would
+
+ align:start position:0%
+some supert some super stores that would
+ 
+
+ align:start position:0%
+some supert some super stores that would
+have 200,000 but Amazon had many many
+
+ align:start position:0%
+have 200,000 but Amazon had many many
+ 
+
+ align:start position:0%
+have 200,000 but Amazon had many many
+more books than uh even from the very
+
+ align:start position:0%
+more books than uh even from the very
+ 
+
+ align:start position:0%
+more books than uh even from the very
+beginning Than Physical bookstores did
+
+ align:start position:0%
+beginning Than Physical bookstores did
+ 
+
+ align:start position:0%
+beginning Than Physical bookstores did
+um and so what Bolson who and Smith try
+
+ align:start position:0%
+um and so what Bolson who and Smith try
+ 
+
+ align:start position:0%
+um and so what Bolson who and Smith try
+to do is just sort of say could we
+
+ align:start position:0%
+to do is just sort of say could we
+ 
+
+ align:start position:0%
+to do is just sort of say could we
+estimate how big the product variety
+
+ align:start position:0%
+estimate how big the product variety
+ 
+
+ align:start position:0%
+estimate how big the product variety
+benefit is by just in some sense looking
+
+ align:start position:0%
+benefit is by just in some sense looking
+ 
+
+ align:start position:0%
+benefit is by just in some sense looking
+at this demand curve like finding out um
+
+ align:start position:0%
+at this demand curve like finding out um
+ 
+
+ align:start position:0%
+at this demand curve like finding out um
+what fraction of the sales of Amazon are
+
+ align:start position:0%
+what fraction of the sales of Amazon are
+ 
+
+ align:start position:0%
+what fraction of the sales of Amazon are
+um to books that are beyond the 100
+
+ align:start position:0%
+um to books that are beyond the 100
+ 
+
+ align:start position:0%
+um to books that are beyond the 100
+100,000th book so so say there 100,000
+
+ align:start position:0%
+100,000th book so so say there 100,000
+ 
+
+ align:start position:0%
+100,000th book so so say there 100,000
+books that are available in your
+
+ align:start position:0%
+books that are available in your
+ 
+
+ align:start position:0%
+books that are available in your
+physical bookstore there are millions of
+
+ align:start position:0%
+physical bookstore there are millions of
+ 
+
+ align:start position:0%
+physical bookstore there are millions of
+other books that are not available in a
+
+ align:start position:0%
+other books that are not available in a
+ 
+
+ align:start position:0%
+other books that are not available in a
+physical bookstore how much utility to
+
+ align:start position:0%
+physical bookstore how much utility to
+ 
+
+ align:start position:0%
+physical bookstore how much utility to
+people get from buying all those books
+
+ align:start position:0%
+people get from buying all those books
+ 
+
+ align:start position:0%
+people get from buying all those books
+from 100,000 out to 2 million uh and the
+
+ align:start position:0%
+from 100,000 out to 2 million uh and the
+ 
+
+ align:start position:0%
+from 100,000 out to 2 million uh and the
+way they do that is to just
+
+ align:start position:0%
+way they do that is to just
+ 
+
+ align:start position:0%
+way they do that is to just
+basically you know convert Amazon sales
+
+ align:start position:0%
+basically you know convert Amazon sales
+ 
+
+ align:start position:0%
+basically you know convert Amazon sales
+ranks to quantities figure out how many
+
+ align:start position:0%
+ranks to quantities figure out how many
+ 
+
+ align:start position:0%
+ranks to quantities figure out how many
+copies of every book are being sold and
+
+ align:start position:0%
+copies of every book are being sold and
+ 
+
+ align:start position:0%
+copies of every book are being sold and
+then just count up how many book what
+
+ align:start position:0%
+then just count up how many book what
+ 
+
+ align:start position:0%
+then just count up how many book what
+fraction of Amazon sales or books
+
+ align:start position:0%
+fraction of Amazon sales or books
+ 
+
+ align:start position:0%
+fraction of Amazon sales or books
+outside the top 100 ,000 and then
+
+ align:start position:0%
+outside the top 100 ,000 and then
+ 
+
+ align:start position:0%
+outside the top 100 ,000 and then
+multiply them by just a consumer surplus
+
+ align:start position:0%
+multiply them by just a consumer surplus
+ 
+
+ align:start position:0%
+multiply them by just a consumer surplus
+estimate per title if you know if you
+
+ align:start position:0%
+estimate per title if you know if you
+ 
+
+ align:start position:0%
+estimate per title if you know if you
+have a general sense of the demand
+
+ align:start position:0%
+have a general sense of the demand
+ 
+
+ align:start position:0%
+have a general sense of the demand
+elasticity you know the average price
+
+ align:start position:0%
+elasticity you know the average price
+ 
+
+ align:start position:0%
+elasticity you know the average price
+you know the consumer you can just sort
+
+ align:start position:0%
+you know the consumer you can just sort
+ 
+
+ align:start position:0%
+you know the consumer you can just sort
+of guess what the consumer surplus is uh
+
+ align:start position:0%
+of guess what the consumer surplus is uh
+ 
+
+ align:start position:0%
+of guess what the consumer surplus is uh
+and estimate
+
+ align:start position:0%
+and estimate
+ 
+
+ align:start position:0%
+and estimate
+that and what they show in this figure
+
+ align:start position:0%
+that and what they show in this figure
+ 
+
+ align:start position:0%
+that and what they show in this figure
+is that uh if you look at books that are
+
+ align:start position:0%
+is that uh if you look at books that are
+ 
+
+ align:start position:0%
+is that uh if you look at books that are
+sort of outside the top 100,000 there
+
+ align:start position:0%
+sort of outside the top 100,000 there
+ 
+
+ align:start position:0%
+sort of outside the top 100,000 there
+seems to be this very very thick or very
+
+ align:start position:0%
+seems to be this very very thick or very
+ 
+
+ align:start position:0%
+seems to be this very very thick or very
+very slow decline in sales so you know
+
+ align:start position:0%
+very slow decline in sales so you know
+ 
+
+ align:start position:0%
+very slow decline in sales so you know
+book number 100,000 is selling one and a
+
+ align:start position:0%
+book number 100,000 is selling one and a
+ 
+
+ align:start position:0%
+book number 100,000 is selling one and a
+half cop a week uh book number 200,000
+
+ align:start position:0%
+half cop a week uh book number 200,000
+ 
+
+ align:start position:0%
+half cop a week uh book number 200,000
+is selling 8 book number 400 is selling
+
+ align:start position:0%
+is selling 8 book number 400 is selling
+ 
+
+ align:start position:0%
+is selling 8 book number 400 is selling
+6 copies a week book number six is spell
+
+ align:start position:0%
+6 copies a week book number six is spell
+ 
+
+ align:start position:0%
+6 copies a week book number six is spell
+selling like 04 but then when you get to
+
+ align:start position:0%
+selling like 04 but then when you get to
+ 
+
+ align:start position:0%
+selling like 04 but then when you get to
+book 2.2 million book 2.2 million is not
+
+ align:start position:0%
+book 2.2 million book 2.2 million is not
+ 
+
+ align:start position:0%
+book 2.2 million book 2.2 million is not
+selling that many fewer copies than book
+
+ align:start position:0%
+selling that many fewer copies than book
+ 
+
+ align:start position:0%
+selling that many fewer copies than book
+600,000 and so because this tale doesn't
+
+ align:start position:0%
+600,000 and so because this tale doesn't
+ 
+
+ align:start position:0%
+600,000 and so because this tale doesn't
+just sort of go to zero very quickly
+
+ align:start position:0%
+just sort of go to zero very quickly
+ 
+
+ align:start position:0%
+just sort of go to zero very quickly
+there are lots of sales on Amazon that
+
+ align:start position:0%
+there are lots of sales on Amazon that
+ 
+
+ align:start position:0%
+there are lots of sales on Amazon that
+are these extra books uh and the thought
+
+ align:start position:0%
+are these extra books uh and the thought
+ 
+
+ align:start position:0%
+are these extra books uh and the thought
+is that all these extra books are you
+
+ align:start position:0%
+is that all these extra books are you
+ 
+
+ align:start position:0%
+is that all these extra books are you
+know you know contributing a lot to
+
+ align:start position:0%
+know you know contributing a lot to
+ 
+
+ align:start position:0%
+know you know contributing a lot to
+consumer
+
+ align:start position:0%
+consumer
+ 
+
+ align:start position:0%
+consumer
+surplus what they estimate in their
+
+ align:start position:0%
+surplus what they estimate in their
+ 
+
+ align:start position:0%
+surplus what they estimate in their
+paper is that the sort of product
+
+ align:start position:0%
+paper is that the sort of product
+ 
+
+ align:start position:0%
+paper is that the sort of product
+variety back in 2000 when Amazon was
+
+ align:start position:0%
+variety back in 2000 when Amazon was
+ 
+
+ align:start position:0%
+variety back in 2000 when Amazon was
+still young was adding 700 million to a
+
+ align:start position:0%
+still young was adding 700 million to a
+ 
+
+ align:start position:0%
+still young was adding 700 million to a
+billion uh to consumer surplus and that
+
+ align:start position:0%
+billion uh to consumer surplus and that
+ 
+
+ align:start position:0%
+billion uh to consumer surplus and that
+was about you know Amazon was lowering
+
+ align:start position:0%
+was about you know Amazon was lowering
+ 
+
+ align:start position:0%
+was about you know Amazon was lowering
+prices I think it was by Amazon was 5 to
+
+ align:start position:0%
+prices I think it was by Amazon was 5 to
+ 
+
+ align:start position:0%
+prices I think it was by Amazon was 5 to
+10% cheaper than than physical
+
+ align:start position:0%
+10% cheaper than than physical
+ 
+
+ align:start position:0%
+10% cheaper than than physical
+bookstores at the time and what I find
+
+ align:start position:0%
+bookstores at the time and what I find
+ 
+
+ align:start position:0%
+bookstores at the time and what I find
+is that look at the gain from the lower
+
+ align:start position:0%
+is that look at the gain from the lower
+ 
+
+ align:start position:0%
+is that look at the gain from the lower
+prices the 5 to 10% lower prices look at
+
+ align:start position:0%
+prices the 5 to 10% lower prices look at
+ 
+
+ align:start position:0%
+prices the 5 to 10% lower prices look at
+the gains from the uh consumer surplus
+
+ align:start position:0%
+the gains from the uh consumer surplus
+ 
+
+ align:start position:0%
+the gains from the uh consumer surplus
+and the gains from the lower prices were
+
+ align:start position:0%
+and the gains from the lower prices were
+ 
+
+ align:start position:0%
+and the gains from the lower prices were
+only about 100 million a year the gains
+
+ align:start position:0%
+only about 100 million a year the gains
+ 
+
+ align:start position:0%
+only about 100 million a year the gains
+from the consumer surplus is like a
+
+ align:start position:0%
+from the consumer surplus is like a
+ 
+
+ align:start position:0%
+from the consumer surplus is like a
+billion dollars a year so consumer
+
+ align:start position:0%
+billion dollars a year so consumer
+ 
+
+ align:start position:0%
+billion dollars a year so consumer
+surplus is 10 times as important as the
+
+ align:start position:0%
+surplus is 10 times as important as the
+ 
+
+ align:start position:0%
+surplus is 10 times as important as the
+price cut and so if if you believe that
+
+ align:start position:0%
+price cut and so if if you believe that
+ 
+
+ align:start position:0%
+price cut and so if if you believe that
+if consumer surplus is 10 times as
+
+ align:start position:0%
+if consumer surplus is 10 times as
+ 
+
+ align:start position:0%
+if consumer surplus is 10 times as
+important there's a price cut you know
+
+ align:start position:0%
+important there's a price cut you know
+ 
+
+ align:start position:0%
+important there's a price cut you know
+you could take away the 100 million or
+
+ align:start position:0%
+you could take away the 100 million or
+ 
+
+ align:start position:0%
+you could take away the 100 million or
+even take have a negative 100 million or
+
+ align:start position:0%
+even take have a negative 100 million or
+ 
+
+ align:start position:0%
+even take have a negative 100 million or
+negative 200 million and they say that
+
+ align:start position:0%
+negative 200 million and they say that
+ 
+
+ align:start position:0%
+negative 200 million and they say that
+Amazon really could raise prices and
+
+ align:start position:0%
+Amazon really could raise prices and
+ 
+
+ align:start position:0%
+Amazon really could raise prices and
+still be a positive value for consumers
+
+ align:start position:0%
+still be a positive value for consumers
+ 
+
+ align:start position:0%
+still be a positive value for consumers
+because the product variety effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say it is a you know I mean it's a very
+
+ align:start position:0%
+say it is a you know I mean it's a very
+ 
+
+ align:start position:0%
+say it is a you know I mean it's a very
+nice paper it's a fairly the calculation
+
+ align:start position:0%
+nice paper it's a fairly the calculation
+ 
+
+ align:start position:0%
+nice paper it's a fairly the calculation
+itself is a little speculative in that
+
+ align:start position:0%
+itself is a little speculative in that
+ 
+
+ align:start position:0%
+itself is a little speculative in that
+you know it is uh you know we don't have
+
+ align:start position:0%
+you know it is uh you know we don't have
+ 
+
+ align:start position:0%
+you know it is uh you know we don't have
+a lot of EV you know like if you think
+
+ align:start position:0%
+a lot of EV you know like if you think
+ 
+
+ align:start position:0%
+a lot of EV you know like if you think
+about like you know any of these books
+
+ align:start position:0%
+about like you know any of these books
+ 
+
+ align:start position:0%
+about like you know any of these books
+that are sold very rarely it's very hard
+
+ align:start position:0%
+that are sold very rarely it's very hard
+ 
+
+ align:start position:0%
+that are sold very rarely it's very hard
+to get much evidence of what the demand
+
+ align:start position:0%
+to get much evidence of what the demand
+ 
+
+ align:start position:0%
+to get much evidence of what the demand
+curves look like for them because
+
+ align:start position:0%
+curves look like for them because
+ 
+
+ align:start position:0%
+curves look like for them because
+they're hardly selling any copies you
+
+ align:start position:0%
+they're hardly selling any copies you
+ 
+
+ align:start position:0%
+they're hardly selling any copies you
+are sort of extrapolating on some things
+
+ align:start position:0%
+are sort of extrapolating on some things
+ 
+
+ align:start position:0%
+are sort of extrapolating on some things
+there um okay so then the paper I want
+
+ align:start position:0%
+there um okay so then the paper I want
+ 
+
+ align:start position:0%
+there um okay so then the paper I want
+to talk about more is um uh Quan and
+
+ align:start position:0%
+to talk about more is um uh Quan and
+ 
+
+ align:start position:0%
+to talk about more is um uh Quan and
+Williams uh product iy market
+
+ align:start position:0%
+Williams uh product iy market
+ 
+
+ align:start position:0%
+Williams uh product iy market
+heterogenity and this is an argument
+
+ align:start position:0%
+heterogenity and this is an argument
+ 
+
+ align:start position:0%
+heterogenity and this is an argument
+that The bolon Who and Smith paper May
+
+ align:start position:0%
+that The bolon Who and Smith paper May
+ 
+
+ align:start position:0%
+that The bolon Who and Smith paper May
+really be
+
+ align:start position:0%
+really be
+ 
+
+ align:start position:0%
+really be
+overestimating uh product variety
+
+ align:start position:0%
+overestimating uh product variety
+ 
+
+ align:start position:0%
+overestimating uh product variety
+advantages and the reason they would
+
+ align:start position:0%
+advantages and the reason they would
+ 
+
+ align:start position:0%
+advantages and the reason they would
+argue this could be really overestimate
+
+ align:start position:0%
+argue this could be really overestimate
+ 
+
+ align:start position:0%
+argue this could be really overestimate
+profit variety advantages is because
+
+ align:start position:0%
+profit variety advantages is because
+ 
+
+ align:start position:0%
+profit variety advantages is because
+different physical bookstores carry
+
+ align:start position:0%
+different physical bookstores carry
+ 
+
+ align:start position:0%
+different physical bookstores carry
+different books so for instance you know
+
+ align:start position:0%
+different books so for instance you know
+ 
+
+ align:start position:0%
+different books so for instance you know
+people at the time needed to get
+
+ align:start position:0%
+people at the time needed to get
+ 
+
+ align:start position:0%
+people at the time needed to get
+textbooks for all of their graduate
+
+ align:start position:0%
+textbooks for all of their graduate
+ 
+
+ align:start position:0%
+textbooks for all of their graduate
+economics classes where would you get
+
+ align:start position:0%
+economics classes where would you get
+ 
+
+ align:start position:0%
+economics classes where would you get
+textbooks for graduate economics classes
+
+ align:start position:0%
+textbooks for graduate economics classes
+ 
+
+ align:start position:0%
+textbooks for graduate economics classes
+none of them are in the top 100,000 most
+
+ align:start position:0%
+none of them are in the top 100,000 most
+ 
+
+ align:start position:0%
+none of them are in the top 100,000 most
+popular books in the United States
+
+ align:start position:0%
+popular books in the United States
+ 
+
+ align:start position:0%
+popular books in the United States
+however you go to the MIT Coupe in the
+
+ align:start position:0%
+however you go to the MIT Coupe in the
+ 
+
+ align:start position:0%
+however you go to the MIT Coupe in the
+week before classes start and they would
+
+ align:start position:0%
+week before classes start and they would
+ 
+
+ align:start position:0%
+week before classes start and they would
+have all of The Graduate economics
+
+ align:start position:0%
+have all of The Graduate economics
+ 
+
+ align:start position:0%
+have all of The Graduate economics
+textbooks and all the other textbooks
+
+ align:start position:0%
+textbooks and all the other textbooks
+ 
+
+ align:start position:0%
+textbooks and all the other textbooks
+for all of your other classes would be
+
+ align:start position:0%
+for all of your other classes would be
+ 
+
+ align:start position:0%
+for all of your other classes would be
+in the MIT Coupe and you know not just
+
+ align:start position:0%
+in the MIT Coupe and you know not just
+ 
+
+ align:start position:0%
+in the MIT Coupe and you know not just
+the graduate economics textbooks to MIT
+
+ align:start position:0%
+the graduate economics textbooks to MIT
+ 
+
+ align:start position:0%
+the graduate economics textbooks to MIT
+Coupe but like the MIT Coupe also has a
+
+ align:start position:0%
+Coupe but like the MIT Coupe also has a
+ 
+
+ align:start position:0%
+Coupe but like the MIT Coupe also has a
+big selection of you know technical
+
+ align:start position:0%
+big selection of you know technical
+ 
+
+ align:start position:0%
+big selection of you know technical
+books and if you just want books about
+
+ align:start position:0%
+books and if you just want books about
+ 
+
+ align:start position:0%
+books and if you just want books about
+computer programming or whatever not for
+
+ align:start position:0%
+computer programming or whatever not for
+ 
+
+ align:start position:0%
+computer programming or whatever not for
+your classes they have lots of those
+
+ align:start position:0%
+your classes they have lots of those
+ 
+
+ align:start position:0%
+your classes they have lots of those
+books in that bookstores and then you
+
+ align:start position:0%
+books in that bookstores and then you
+ 
+
+ align:start position:0%
+books in that bookstores and then you
+know there are other bookstores in
+
+ align:start position:0%
+know there are other bookstores in
+ 
+
+ align:start position:0%
+know there are other bookstores in
+Boston where if you're interested in art
+
+ align:start position:0%
+Boston where if you're interested in art
+ 
+
+ align:start position:0%
+Boston where if you're interested in art
+that have lots of books about art and
+
+ align:start position:0%
+that have lots of books about art and
+ 
+
+ align:start position:0%
+that have lots of books about art and
+lots of big coffee table books or
+
+ align:start position:0%
+lots of big coffee table books or
+ 
+
+ align:start position:0%
+lots of big coffee table books or
+whatever and so their thought was that
+
+ align:start position:0%
+whatever and so their thought was that
+ 
+
+ align:start position:0%
+whatever and so their thought was that
+you know the qu Williams argument is
+
+ align:start position:0%
+you know the qu Williams argument is
+ 
+
+ align:start position:0%
+you know the qu Williams argument is
+that you really could be overestimating
+
+ align:start position:0%
+that you really could be overestimating
+ 
+
+ align:start position:0%
+that you really could be overestimating
+what Amazon is doing because there are
+
+ align:start position:0%
+what Amazon is doing because there are
+ 
+
+ align:start position:0%
+what Amazon is doing because there are
+many different bookstores the many
+
+ align:start position:0%
+many different bookstores the many
+ 
+
+ align:start position:0%
+many different bookstores the many
+different bookstores have many different
+
+ align:start position:0%
+different bookstores have many different
+ 
+
+ align:start position:0%
+different bookstores have many different
+books so the gain from
+
+ align:start position:0%
+books so the gain from
+ 
+
+ align:start position:0%
+books so the gain from
+the online over going to the bookstore
+
+ align:start position:0%
+the online over going to the bookstore
+ 
+
+ align:start position:0%
+the online over going to the bookstore
+that you know what have the books you
+
+ align:start position:0%
+that you know what have the books you
+ 
+
+ align:start position:0%
+that you know what have the books you
+want could be much smaller um they study
+
+ align:start position:0%
+want could be much smaller um they study
+ 
+
+ align:start position:0%
+want could be much smaller um they study
+this not in the case of books they they
+
+ align:start position:0%
+this not in the case of books they they
+ 
+
+ align:start position:0%
+this not in the case of books they they
+pick a different industry their industry
+
+ align:start position:0%
+pick a different industry their industry
+ 
+
+ align:start position:0%
+pick a different industry their industry
+is shoes um they don't say it one
+
+ align:start position:0%
+is shoes um they don't say it one
+ 
+
+ align:start position:0%
+is shoes um they don't say it one
+suspects that they have they had a
+
+ align:start position:0%
+suspects that they have they had a
+ 
+
+ align:start position:0%
+suspects that they have they had a
+friend who worked at zapo because they
+
+ align:start position:0%
+friend who worked at zapo because they
+ 
+
+ align:start position:0%
+friend who worked at zapo because they
+sort of are working with a uh very very
+
+ align:start position:0%
+sort of are working with a uh very very
+ 
+
+ align:start position:0%
+sort of are working with a uh very very
+what they describe as a very large
+
+ align:start position:0%
+what they describe as a very large
+ 
+
+ align:start position:0%
+what they describe as a very large
+online um shoe store in the year 2012
+
+ align:start position:0%
+online um shoe store in the year 2012
+ 
+
+ align:start position:0%
+online um shoe store in the year 2012
+2013 um and just here's one example of
+
+ align:start position:0%
+2013 um and just here's one example of
+ 
+
+ align:start position:0%
+2013 um and just here's one example of
+why we would think that physical shoe
+
+ align:start position:0%
+why we would think that physical shoe
+ 
+
+ align:start position:0%
+why we would think that physical shoe
+stores uh would carry different things
+
+ align:start position:0%
+stores uh would carry different things
+ 
+
+ align:start position:0%
+stores uh would carry different things
+this graph is this is entirely done with
+
+ align:start position:0%
+this graph is this is entirely done with
+ 
+
+ align:start position:0%
+this graph is this is entirely done with
+um sales on the on the uh online site
+
+ align:start position:0%
+um sales on the on the uh online site
+ 
+
+ align:start position:0%
+um sales on the on the uh online site
+what they graph is so this is a state
+
+ align:start position:0%
+what they graph is so this is a state
+ 
+
+ align:start position:0%
+what they graph is so this is a state
+level analysis for I think 49 states uh
+
+ align:start position:0%
+level analysis for I think 49 states uh
+ 
+
+ align:start position:0%
+level analysis for I think 49 states uh
+and what they put on this is just a DOT
+
+ align:start position:0%
+and what they put on this is just a DOT
+ 
+
+ align:start position:0%
+and what they put on this is just a DOT
+for every state of what fraction of the
+
+ align:start position:0%
+for every state of what fraction of the
+ 
+
+ align:start position:0%
+for every state of what fraction of the
+shoes that are sold to that state are
+
+ align:start position:0%
+shoes that are sold to that state are
+ 
+
+ align:start position:0%
+shoes that are sold to that state are
+boots and what fraction are
+
+ align:start position:0%
+boots and what fraction are
+ 
+
+ align:start position:0%
+boots and what fraction are
+sandals and you know what do you notice
+
+ align:start position:0%
+sandals and you know what do you notice
+ 
+
+ align:start position:0%
+sandals and you know what do you notice
+on the right side of this graph uh we
+
+ align:start position:0%
+on the right side of this graph uh we
+ 
+
+ align:start position:0%
+on the right side of this graph uh we
+take the two warmest US states which
+
+ align:start position:0%
+take the two warmest US states which
+ 
+
+ align:start position:0%
+take the two warmest US states which
+would be Hawaii and Florida and in
+
+ align:start position:0%
+would be Hawaii and Florida and in
+ 
+
+ align:start position:0%
+would be Hawaii and Florida and in
+Hawaii and Florida people don't buy a
+
+ align:start position:0%
+Hawaii and Florida people don't buy a
+ 
+
+ align:start position:0%
+Hawaii and Florida people don't buy a
+whole lot of boots uh and they buy a lot
+
+ align:start position:0%
+whole lot of boots uh and they buy a lot
+ 
+
+ align:start position:0%
+whole lot of boots uh and they buy a lot
+of sandals I guess especially in Florida
+
+ align:start position:0%
+of sandals I guess especially in Florida
+ 
+
+ align:start position:0%
+of sandals I guess especially in Florida
+people buy a lot of sandals uh and then
+
+ align:start position:0%
+people buy a lot of sandals uh and then
+ 
+
+ align:start position:0%
+people buy a lot of sandals uh and then
+you go down here and you look at what
+
+ align:start position:0%
+you go down here and you look at what
+ 
+
+ align:start position:0%
+you go down here and you look at what
+people are buying in you know the
+
+ align:start position:0%
+people are buying in you know the
+ 
+
+ align:start position:0%
+people are buying in you know the
+coldest States it's I don't know if
+
+ align:start position:0%
+coldest States it's I don't know if
+ 
+
+ align:start position:0%
+coldest States it's I don't know if
+that's North Dakota Wyoming Minnesota
+
+ align:start position:0%
+that's North Dakota Wyoming Minnesota
+ 
+
+ align:start position:0%
+that's North Dakota Wyoming Minnesota
+places like that people buy a lot of
+
+ align:start position:0%
+places like that people buy a lot of
+ 
+
+ align:start position:0%
+places like that people buy a lot of
+boots in North Dakota people buy fewer
+
+ align:start position:0%
+boots in North Dakota people buy fewer
+ 
+
+ align:start position:0%
+boots in North Dakota people buy fewer
+sandals in North
+
+ align:start position:0%
+sandals in North
+ 
+
+ align:start position:0%
+sandals in North
+Dakota um although I guess you know sort
+
+ align:start position:0%
+Dakota um although I guess you know sort
+ 
+
+ align:start position:0%
+Dakota um although I guess you know sort
+of surprising things you learn from this
+
+ align:start position:0%
+of surprising things you learn from this
+ 
+
+ align:start position:0%
+of surprising things you learn from this
+turns out people in North Dakota and
+
+ align:start position:0%
+turns out people in North Dakota and
+ 
+
+ align:start position:0%
+turns out people in North Dakota and
+Wyoming actually buy more sandals than
+
+ align:start position:0%
+Wyoming actually buy more sandals than
+ 
+
+ align:start position:0%
+Wyoming actually buy more sandals than
+people in Middle temperature States I
+
+ align:start position:0%
+people in Middle temperature States I
+ 
+
+ align:start position:0%
+people in Middle temperature States I
+guess it may be you know I don't know
+
+ align:start position:0%
+guess it may be you know I don't know
+ 
+
+ align:start position:0%
+guess it may be you know I don't know
+maybe if you live in a cold place you
+
+ align:start position:0%
+maybe if you live in a cold place you
+ 
+
+ align:start position:0%
+maybe if you live in a cold place you
+sort of go on vacation to Florida and
+
+ align:start position:0%
+sort of go on vacation to Florida and
+ 
+
+ align:start position:0%
+sort of go on vacation to Florida and
+you need to buy sandals or if you live
+
+ align:start position:0%
+you need to buy sandals or if you live
+ 
+
+ align:start position:0%
+you need to buy sandals or if you live
+in a medium temperature State you just
+
+ align:start position:0%
+in a medium temperature State you just
+ 
+
+ align:start position:0%
+in a medium temperature State you just
+you don't go on as many vacations to
+
+ align:start position:0%
+you don't go on as many vacations to
+ 
+
+ align:start position:0%
+you don't go on as many vacations to
+warm weather States I don't know but
+
+ align:start position:0%
+warm weather States I don't know but
+ 
+
+ align:start position:0%
+warm weather States I don't know but
+anyway you know but but you know their
+
+ align:start position:0%
+anyway you know but but you know their
+ 
+
+ align:start position:0%
+anyway you know but but you know their
+thought from this graph is if you look
+
+ align:start position:0%
+thought from this graph is if you look
+ 
+
+ align:start position:0%
+thought from this graph is if you look
+at if this is what happens for online
+
+ align:start position:0%
+at if this is what happens for online
+ 
+
+ align:start position:0%
+at if this is what happens for online
+retailers you imagine that you walk into
+
+ align:start position:0%
+retailers you imagine that you walk into
+ 
+
+ align:start position:0%
+retailers you imagine that you walk into
+you know even take a national chain
+
+ align:start position:0%
+you know even take a national chain
+ 
+
+ align:start position:0%
+you know even take a national chain
+store you imagine that the national
+
+ align:start position:0%
+store you imagine that the national
+ 
+
+ align:start position:0%
+store you imagine that the national
+chains in their North Dakota stores they
+
+ align:start position:0%
+chains in their North Dakota stores they
+ 
+
+ align:start position:0%
+chains in their North Dakota stores they
+have lots of boots on the on the shelves
+
+ align:start position:0%
+have lots of boots on the on the shelves
+ 
+
+ align:start position:0%
+have lots of boots on the on the shelves
+and in their Florida stores they have
+
+ align:start position:0%
+and in their Florida stores they have
+ 
+
+ align:start position:0%
+and in their Florida stores they have
+very few winter boots on the shelves uh
+
+ align:start position:0%
+very few winter boots on the shelves uh
+ 
+
+ align:start position:0%
+very few winter boots on the shelves uh
+and so this would just be an example
+
+ align:start position:0%
+and so this would just be an example
+ 
+
+ align:start position:0%
+and so this would just be an example
+that you know this doesn't this doesn't
+
+ align:start position:0%
+that you know this doesn't this doesn't
+ 
+
+ align:start position:0%
+that you know this doesn't this doesn't
+prove that local stores tailor
+
+ align:start position:0%
+prove that local stores tailor
+ 
+
+ align:start position:0%
+prove that local stores tailor
+their selections to what customers want
+
+ align:start position:0%
+their selections to what customers want
+ 
+
+ align:start position:0%
+their selections to what customers want
+but this at least suggests that local
+
+ align:start position:0%
+but this at least suggests that local
+ 
+
+ align:start position:0%
+but this at least suggests that local
+stores ought to tailor their selections
+
+ align:start position:0%
+stores ought to tailor their selections
+ 
+
+ align:start position:0%
+stores ought to tailor their selections
+to their customers and that ought to
+
+ align:start position:0%
+to their customers and that ought to
+ 
+
+ align:start position:0%
+to their customers and that ought to
+give you back some of the gains that we
+
+ align:start position:0%
+give you back some of the gains that we
+ 
+
+ align:start position:0%
+give you back some of the gains that we
+think is Amazon's gains from product
+
+ align:start position:0%
+think is Amazon's gains from product
+ 
+
+ align:start position:0%
+think is Amazon's gains from product
+variety should be gains from product
+
+ align:start position:0%
+variety should be gains from product
+ 
+
+ align:start position:0%
+variety should be gains from product
+variety at these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stores you know the paper actually has
+
+ align:start position:0%
+stores you know the paper actually has
+ 
+
+ align:start position:0%
+stores you know the paper actually has
+um it has a second data set where they
+
+ align:start position:0%
+um it has a second data set where they
+ 
+
+ align:start position:0%
+um it has a second data set where they
+they also got access to the
+
+ align:start position:0%
+they also got access to the
+ 
+
+ align:start position:0%
+they also got access to the
+inventories uh of local stores at Macy's
+
+ align:start position:0%
+inventories uh of local stores at Macy's
+ 
+
+ align:start position:0%
+inventories uh of local stores at Macy's
+and Payless shoe Payless Shoes which are
+
+ align:start position:0%
+and Payless shoe Payless Shoes which are
+ 
+
+ align:start position:0%
+and Payless shoe Payless Shoes which are
+just two chain retails stores and they
+
+ align:start position:0%
+just two chain retails stores and they
+ 
+
+ align:start position:0%
+just two chain retails stores and they
+find that there's substantial
+
+ align:start position:0%
+find that there's substantial
+ 
+
+ align:start position:0%
+find that there's substantial
+differences in the skus carried at the
+
+ align:start position:0%
+differences in the skus carried at the
+ 
+
+ align:start position:0%
+differences in the skus carried at the
+different stores now you know they don't
+
+ align:start position:0%
+different stores now you know they don't
+ 
+
+ align:start position:0%
+different stores now you know they don't
+know what they don't really have enough
+
+ align:start position:0%
+know what they don't really have enough
+ 
+
+ align:start position:0%
+know what they don't really have enough
+data to say whether it's just completely
+
+ align:start position:0%
+data to say whether it's just completely
+ 
+
+ align:start position:0%
+data to say whether it's just completely
+random or how much of it is this store
+
+ align:start position:0%
+random or how much of it is this store
+ 
+
+ align:start position:0%
+random or how much of it is this store
+carrying this store you know carrying
+
+ align:start position:0%
+carrying this store you know carrying
+ 
+
+ align:start position:0%
+carrying this store you know carrying
+boots and this one carrying sandals or
+
+ align:start position:0%
+boots and this one carrying sandals or
+ 
+
+ align:start position:0%
+boots and this one carrying sandals or
+this one having just different brands
+
+ align:start position:0%
+this one having just different brands
+ 
+
+ align:start position:0%
+this one having just different brands
+from the others but what they find is
+
+ align:start position:0%
+from the others but what they find is
+ 
+
+ align:start position:0%
+from the others but what they find is
+that like at especially at the Macy's
+
+ align:start position:0%
+that like at especially at the Macy's
+ 
+
+ align:start position:0%
+that like at especially at the Macy's
+there are almost no shoes that all the
+
+ align:start position:0%
+there are almost no shoes that all the
+ 
+
+ align:start position:0%
+there are almost no shoes that all the
+Macy's have different Macy's just have
+
+ align:start position:0%
+Macy's have different Macy's just have
+ 
+
+ align:start position:0%
+Macy's have different Macy's just have
+different shoes there are a lot of them
+
+ align:start position:0%
+different shoes there are a lot of them
+ 
+
+ align:start position:0%
+different shoes there are a lot of them
+that shoes that are only found in one or
+
+ align:start position:0%
+that shoes that are only found in one or
+ 
+
+ align:start position:0%
+that shoes that are only found in one or
+two stores very few that are found in
+
+ align:start position:0%
+two stores very few that are found in
+ 
+
+ align:start position:0%
+two stores very few that are found in
+100% of stores at the pays there are a
+
+ align:start position:0%
+100% of stores at the pays there are a
+ 
+
+ align:start position:0%
+100% of stores at the pays there are a
+lot of store shoes that are found in
+
+ align:start position:0%
+lot of store shoes that are found in
+ 
+
+ align:start position:0%
+lot of store shoes that are found in
+every pay and a lot of shoes that are
+
+ align:start position:0%
+every pay and a lot of shoes that are
+ 
+
+ align:start position:0%
+every pay and a lot of shoes that are
+found in like one or two pay lses
+
+ align:start position:0%
+found in like one or two pay lses
+ 
+
+ align:start position:0%
+found in like one or two pay lses
+um okay anyway so um how do they
+
+ align:start position:0%
+um okay anyway so um how do they
+ 
+
+ align:start position:0%
+um okay anyway so um how do they
+estimate you know so that what they want
+
+ align:start position:0%
+estimate you know so that what they want
+ 
+
+ align:start position:0%
+estimate you know so that what they want
+to do is
+
+ align:start position:0%
+to do is
+ 
+
+ align:start position:0%
+to do is
+estimate how important is this variation
+
+ align:start position:0%
+estimate how important is this variation
+ 
+
+ align:start position:0%
+estimate how important is this variation
+in consumer preferences and to estimate
+
+ align:start position:0%
+in consumer preferences and to estimate
+ 
+
+ align:start position:0%
+in consumer preferences and to estimate
+how important would it if if stores just
+
+ align:start position:0%
+how important would it if if stores just
+ 
+
+ align:start position:0%
+how important would it if if stores just
+match their local preferences would
+
+ align:start position:0%
+match their local preferences would
+ 
+
+ align:start position:0%
+match their local preferences would
+stores be able to sort of get most of
+
+ align:start position:0%
+stores be able to sort of get most of
+ 
+
+ align:start position:0%
+stores be able to sort of get most of
+the benefits that you get from Amazon
+
+ align:start position:0%
+the benefits that you get from Amazon
+ 
+
+ align:start position:0%
+the benefits that you get from Amazon
+um so what they do is a demand
+
+ align:start position:0%
+um so what they do is a demand
+ 
+
+ align:start position:0%
+um so what they do is a demand
+estimation it's going to be sort of a
+
+ align:start position:0%
+estimation it's going to be sort of a
+ 
+
+ align:start position:0%
+estimation it's going to be sort of a
+standard kind of nested Lo of demand so
+
+ align:start position:0%
+standard kind of nested Lo of demand so
+ 
+
+ align:start position:0%
+standard kind of nested Lo of demand so
+this is utility customer I location L
+
+ align:start position:0%
+this is utility customer I location L
+ 
+
+ align:start position:0%
+this is utility customer I location L
+buying product J it's going to be a mean
+
+ align:start position:0%
+buying product J it's going to be a mean
+ 
+
+ align:start position:0%
+buying product J it's going to be a mean
+utility of product J in location
+
+ align:start position:0%
+utility of product J in location
+ 
+
+ align:start position:0%
+utility of product J in location
+L um plus this sort of nestal loan
+
+ align:start position:0%
+L um plus this sort of nestal loan
+ 
+
+ align:start position:0%
+L um plus this sort of nestal loan
+models there's a shock uh you have this
+
+ align:start position:0%
+models there's a shock uh you have this
+ 
+
+ align:start position:0%
+models there's a shock uh you have this
+idiosyncratic preference of a customer
+
+ align:start position:0%
+idiosyncratic preference of a customer
+ 
+
+ align:start position:0%
+idiosyncratic preference of a customer
+for um all products in category J so if
+
+ align:start position:0%
+for um all products in category J so if
+ 
+
+ align:start position:0%
+for um all products in category J so if
+I'm looking for snow boots I have a snow
+
+ align:start position:0%
+I'm looking for snow boots I have a snow
+ 
+
+ align:start position:0%
+I'm looking for snow boots I have a snow
+boot specific shock and then a weight I
+
+ align:start position:0%
+boot specific shock and then a weight I
+ 
+
+ align:start position:0%
+boot specific shock and then a weight I
+have sort of two shocks one is the
+
+ align:start position:0%
+have sort of two shocks one is the
+ 
+
+ align:start position:0%
+have sort of two shocks one is the
+category specific shock and then one is
+
+ align:start position:0%
+category specific shock and then one is
+ 
+
+ align:start position:0%
+category specific shock and then one is
+the brand specific shock and they're
+
+ align:start position:0%
+the brand specific shock and they're
+ 
+
+ align:start position:0%
+the brand specific shock and they're
+going to estimate this Lambda parameter
+
+ align:start position:0%
+going to estimate this Lambda parameter
+ 
+
+ align:start position:0%
+going to estimate this Lambda parameter
+so they can tell whether people shocks
+
+ align:start position:0%
+so they can tell whether people shocks
+ 
+
+ align:start position:0%
+so they can tell whether people shocks
+are mostly category specific or mostly
+
+ align:start position:0%
+are mostly category specific or mostly
+ 
+
+ align:start position:0%
+are mostly category specific or mostly
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+specific and then what they're going to
+
+ align:start position:0%
+specific and then what they're going to
+ 
+
+ align:start position:0%
+specific and then what they're going to
+assume is that the um mean utility
+
+ align:start position:0%
+assume is that the um mean utility
+ 
+
+ align:start position:0%
+assume is that the um mean utility
+provided by product J and location L is
+
+ align:start position:0%
+provided by product J and location L is
+ 
+
+ align:start position:0%
+provided by product J and location L is
+a function of the product
+
+ align:start position:0%
+a function of the product
+ 
+
+ align:start position:0%
+a function of the product
+characteristics a function of the
+
+ align:start position:0%
+characteristics a function of the
+ 
+
+ align:start position:0%
+characteristics a function of the
+product price and then this other um Ze
+
+ align:start position:0%
+product price and then this other um Ze
+ 
+
+ align:start position:0%
+product price and then this other um Ze
+of LJ term which is
+
+ align:start position:0%
+of LJ term which is
+ 
+
+ align:start position:0%
+of LJ term which is
+the you know that's the sort of
+
+ align:start position:0%
+the you know that's the sort of
+ 
+
+ align:start position:0%
+the you know that's the sort of
+idiosyncratic preference for this
+
+ align:start position:0%
+idiosyncratic preference for this
+ 
+
+ align:start position:0%
+idiosyncratic preference for this
+product in location
+
+ align:start position:0%
+product in location
+ 
+
+ align:start position:0%
+product in location
+L uh they don't have the temperature
+
+ align:start position:0%
+L uh they don't have the temperature
+ 
+
+ align:start position:0%
+L uh they don't have the temperature
+here so like the people in Florida don't
+
+ align:start position:0%
+here so like the people in Florida don't
+ 
+
+ align:start position:0%
+here so like the people in Florida don't
+like boots would be here people in
+
+ align:start position:0%
+like boots would be here people in
+ 
+
+ align:start position:0%
+like boots would be here people in
+Hawaii like sandals would be here uh but
+
+ align:start position:0%
+Hawaii like sandals would be here uh but
+ 
+
+ align:start position:0%
+Hawaii like sandals would be here uh but
+then you know there's also you could
+
+ align:start position:0%
+then you know there's also you could
+ 
+
+ align:start position:0%
+then you know there's also you could
+imagine there's also just sort of these
+
+ align:start position:0%
+imagine there's also just sort of these
+ 
+
+ align:start position:0%
+imagine there's also just sort of these
+sort of mayonnaise like preferences like
+
+ align:start position:0%
+sort of mayonnaise like preferences like
+ 
+
+ align:start position:0%
+sort of mayonnaise like preferences like
+there's just Uggs boots are popular in
+
+ align:start position:0%
+there's just Uggs boots are popular in
+ 
+
+ align:start position:0%
+there's just Uggs boots are popular in
+New England they're unfashionable in
+
+ align:start position:0%
+New England they're unfashionable in
+ 
+
+ align:start position:0%
+New England they're unfashionable in
+California or this brand of shoes is
+
+ align:start position:0%
+California or this brand of shoes is
+ 
+
+ align:start position:0%
+California or this brand of shoes is
+popular here it's not popular here all
+
+ align:start position:0%
+popular here it's not popular here all
+ 
+
+ align:start position:0%
+popular here it's not popular here all
+of that would go into the
+
+ align:start position:0%
+of that would go into the
+ 
+
+ align:start position:0%
+of that would go into the
+zjs
+
+ align:start position:0%
+zjs
+ 
+
+ align:start position:0%
+zjs
+um uh a real challenge to estimating
+
+ align:start position:0%
+um uh a real challenge to estimating
+ 
+
+ align:start position:0%
+um uh a real challenge to estimating
+demand is that
+
+ align:start position:0%
+demand is that
+ 
+
+ align:start position:0%
+demand is that
+um most products you know like there's a
+
+ align:start position:0%
+um most products you know like there's a
+ 
+
+ align:start position:0%
+um most products you know like there's a
+very very large number of shoes in the
+
+ align:start position:0%
+very very large number of shoes in the
+ 
+
+ align:start position:0%
+very very large number of shoes in the
+world um and it turns out that most
+
+ align:start position:0%
+world um and it turns out that most
+ 
+
+ align:start position:0%
+world um and it turns out that most
+shoes in most cities in most months have
+
+ align:start position:0%
+shoes in most cities in most months have
+ 
+
+ align:start position:0%
+shoes in most cities in most months have
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+sales and so dealing with quantity data
+
+ align:start position:0%
+sales and so dealing with quantity data
+ 
+
+ align:start position:0%
+sales and so dealing with quantity data
+when you have zeros is very difficult
+
+ align:start position:0%
+when you have zeros is very difficult
+ 
+
+ align:start position:0%
+when you have zeros is very difficult
+you know like right if you remember that
+
+ align:start position:0%
+you know like right if you remember that
+ 
+
+ align:start position:0%
+you know like right if you remember that
+one of the things we you know standard
+
+ align:start position:0%
+one of the things we you know standard
+ 
+
+ align:start position:0%
+one of the things we you know standard
+approaches people do in the that like
+
+ align:start position:0%
+approaches people do in the that like
+ 
+
+ align:start position:0%
+approaches people do in the that like
+lit demand estimation is you sort of
+
+ align:start position:0%
+lit demand estimation is you sort of
+ 
+
+ align:start position:0%
+lit demand estimation is you sort of
+have you know log of the share product J
+
+ align:start position:0%
+have you know log of the share product J
+ 
+
+ align:start position:0%
+have you know log of the share product J
+minus log of the share the outside good
+
+ align:start position:0%
+minus log of the share the outside good
+ 
+
+ align:start position:0%
+minus log of the share the outside good
+was XJ beta minus Alpha PJ something
+
+ align:start position:0%
+was XJ beta minus Alpha PJ something
+ 
+
+ align:start position:0%
+was XJ beta minus Alpha PJ something
+like that you sort of invert the you
+
+ align:start position:0%
+like that you sort of invert the you
+ 
+
+ align:start position:0%
+like that you sort of invert the you
+sort of convert from the market sh you
+
+ align:start position:0%
+sort of convert from the market sh you
+ 
+
+ align:start position:0%
+sort of convert from the market sh you
+convert to the market shares to get back
+
+ align:start position:0%
+convert to the market shares to get back
+ 
+
+ align:start position:0%
+convert to the market shares to get back
+to the product characteristics and then
+
+ align:start position:0%
+to the product characteristics and then
+ 
+
+ align:start position:0%
+to the product characteristics and then
+you can run IV regressions to estimate
+
+ align:start position:0%
+you can run IV regressions to estimate
+ 
+
+ align:start position:0%
+you can run IV regressions to estimate
+demand you know you can't do these sort
+
+ align:start position:0%
+demand you know you can't do these sort
+ 
+
+ align:start position:0%
+demand you know you can't do these sort
+of log Transformations when you have a
+
+ align:start position:0%
+of log Transformations when you have a
+ 
+
+ align:start position:0%
+of log Transformations when you have a
+whole bunch of zeros in your data um and
+
+ align:start position:0%
+whole bunch of zeros in your data um and
+ 
+
+ align:start position:0%
+whole bunch of zeros in your data um and
+so what do you do when you have a whole
+
+ align:start position:0%
+so what do you do when you have a whole
+ 
+
+ align:start position:0%
+so what do you do when you have a whole
+bunch of zeros in your data anyway what
+
+ align:start position:0%
+bunch of zeros in your data anyway what
+ 
+
+ align:start position:0%
+bunch of zeros in your data anyway what
+they do in this paper is you know
+
+ align:start position:0%
+they do in this paper is you know
+ 
+
+ align:start position:0%
+they do in this paper is you know
+discuss a GMM approach to sort of try to
+
+ align:start position:0%
+discuss a GMM approach to sort of try to
+ 
+
+ align:start position:0%
+discuss a GMM approach to sort of try to
+deal with all the zeros and and you know
+
+ align:start position:0%
+deal with all the zeros and and you know
+ 
+
+ align:start position:0%
+deal with all the zeros and and you know
+you don't want to Al you know you also
+
+ align:start position:0%
+you don't want to Al you know you also
+ 
+
+ align:start position:0%
+you don't want to Al you know you also
+don't want to throw out another thing
+
+ align:start position:0%
+don't want to throw out another thing
+ 
+
+ align:start position:0%
+don't want to throw out another thing
+people do sometimes is just throw out
+
+ align:start position:0%
+people do sometimes is just throw out
+ 
+
+ align:start position:0%
+people do sometimes is just throw out
+all the zeros you clearly don't want to
+
+ align:start position:0%
+all the zeros you clearly don't want to
+ 
+
+ align:start position:0%
+all the zeros you clearly don't want to
+throw out all the zeros because like the
+
+ align:start position:0%
+throw out all the zeros because like the
+ 
+
+ align:start position:0%
+throw out all the zeros because like the
+goods that have zero sales in one month
+
+ align:start position:0%
+goods that have zero sales in one month
+ 
+
+ align:start position:0%
+goods that have zero sales in one month
+will have positive sales in the next
+
+ align:start position:0%
+will have positive sales in the next
+ 
+
+ align:start position:0%
+will have positive sales in the next
+month they all have positive mean
+
+ align:start position:0%
+month they all have positive mean
+ 
+
+ align:start position:0%
+month they all have positive mean
+utilities you don't want to remove them
+
+ align:start position:0%
+utilities you don't want to remove them
+ 
+
+ align:start position:0%
+utilities you don't want to remove them
+and say no one wants to buy from those
+
+ align:start position:0%
+and say no one wants to buy from those
+ 
+
+ align:start position:0%
+and say no one wants to buy from those
+goods um in particular what they note is
+
+ align:start position:0%
+goods um in particular what they note is
+ 
+
+ align:start position:0%
+goods um in particular what they note is
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+you know the number of shoes that are
+
+ align:start position:0%
+you know the number of shoes that are
+ 
+
+ align:start position:0%
+you know the number of shoes that are
+sold by this online website in in a
+
+ align:start position:0%
+sold by this online website in in a
+ 
+
+ align:start position:0%
+sold by this online website in in a
+particular City in a particular month is
+
+ align:start position:0%
+particular City in a particular month is
+ 
+
+ align:start position:0%
+particular City in a particular month is
+smaller than the inventory of a large
+
+ align:start position:0%
+smaller than the inventory of a large
+ 
+
+ align:start position:0%
+smaller than the inventory of a large
+shoe
+
+ align:start position:0%
+shoe
+ 
+
+ align:start position:0%
+shoe
+store so if you actually sort of were to
+
+ align:start position:0%
+store so if you actually sort of were to
+ 
+
+ align:start position:0%
+store so if you actually sort of were to
+take the realized shoe sales and say
+
+ align:start position:0%
+take the realized shoe sales and say
+ 
+
+ align:start position:0%
+take the realized shoe sales and say
+those people's Deltas are only based on
+
+ align:start position:0%
+those people's Deltas are only based on
+ 
+
+ align:start position:0%
+those people's Deltas are only based on
+the shoes that actually got bought what
+
+ align:start position:0%
+the shoes that actually got bought what
+ 
+
+ align:start position:0%
+the shoes that actually got bought what
+you'd conclude is that a single physical
+
+ align:start position:0%
+you'd conclude is that a single physical
+ 
+
+ align:start position:0%
+you'd conclude is that a single physical
+store could actually Supply the entire
+
+ align:start position:0%
+store could actually Supply the entire
+ 
+
+ align:start position:0%
+store could actually Supply the entire
+Market uh and so it's just it's very
+
+ align:start position:0%
+Market uh and so it's just it's very
+ 
+
+ align:start position:0%
+Market uh and so it's just it's very
+important to correctly deal with all of
+
+ align:start position:0%
+important to correctly deal with all of
+ 
+
+ align:start position:0%
+important to correctly deal with all of
+these shoes that are in the store and
+
+ align:start position:0%
+these shoes that are in the store and
+ 
+
+ align:start position:0%
+these shoes that are in the store and
+have zero sales in a month but you know
+
+ align:start position:0%
+have zero sales in a month but you know
+ 
+
+ align:start position:0%
+have zero sales in a month but you know
+people are buying like you just have
+
+ align:start position:0%
+people are buying like you just have
+ 
+
+ align:start position:0%
+people are buying like you just have
+these many products all with like a
+
+ align:start position:0%
+these many products all with like a
+ 
+
+ align:start position:0%
+these many products all with like a
+fraction of expected sales but those are
+
+ align:start position:0%
+fraction of expected sales but those are
+ 
+
+ align:start position:0%
+fraction of expected sales but those are
+what people buy among and so they have
+
+ align:start position:0%
+what people buy among and so they have
+ 
+
+ align:start position:0%
+what people buy among and so they have
+to deal with the zeros anyway you know
+
+ align:start position:0%
+to deal with the zeros anyway you know
+ 
+
+ align:start position:0%
+to deal with the zeros anyway you know
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+are one thing you'll notice in the paper
+
+ align:start position:0%
+are one thing you'll notice in the paper
+ 
+
+ align:start position:0%
+are one thing you'll notice in the paper
+like they spent a while talking about
+
+ align:start position:0%
+like they spent a while talking about
+ 
+
+ align:start position:0%
+like they spent a while talking about
+how to deal with demand estimation when
+
+ align:start position:0%
+how to deal with demand estimation when
+ 
+
+ align:start position:0%
+how to deal with demand estimation when
+you have lots of zeros uh if you ever
+
+ align:start position:0%
+you have lots of zeros uh if you ever
+ 
+
+ align:start position:0%
+you have lots of zeros uh if you ever
+have a paper you're trying to do demand
+
+ align:start position:0%
+have a paper you're trying to do demand
+ 
+
+ align:start position:0%
+have a paper you're trying to do demand
+estimation with lots of zeros I'd
+
+ align:start position:0%
+estimation with lots of zeros I'd
+ 
+
+ align:start position:0%
+estimation with lots of zeros I'd
+recommend read you know they discuss
+
+ align:start position:0%
+recommend read you know they discuss
+ 
+
+ align:start position:0%
+recommend read you know they discuss
+sort of their method and other methods
+
+ align:start position:0%
+sort of their method and other methods
+ 
+
+ align:start position:0%
+sort of their method and other methods
+of people able to deal with zeros I
+
+ align:start position:0%
+of people able to deal with zeros I
+ 
+
+ align:start position:0%
+of people able to deal with zeros I
+think theirs is thought to be a fairly
+
+ align:start position:0%
+think theirs is thought to be a fairly
+ 
+
+ align:start position:0%
+think theirs is thought to be a fairly
+good method for doing demand estimation
+
+ align:start position:0%
+good method for doing demand estimation
+ 
+
+ align:start position:0%
+good method for doing demand estimation
+when you have a whole bunch of zeros
+
+ align:start position:0%
+when you have a whole bunch of zeros
+ 
+
+ align:start position:0%
+when you have a whole bunch of zeros
+um but so anyway it it's the basic idea
+
+ align:start position:0%
+um but so anyway it it's the basic idea
+ 
+
+ align:start position:0%
+um but so anyway it it's the basic idea
+is they aggregate sales to the location
+
+ align:start position:0%
+is they aggregate sales to the location
+ 
+
+ align:start position:0%
+is they aggregate sales to the location
+month level they have 213
+
+ align:start position:0%
+month level they have 213
+ 
+
+ align:start position:0%
+month level they have 213
+locations uh most of the 213 locations
+
+ align:start position:0%
+locations uh most of the 213 locations
+ 
+
+ align:start position:0%
+locations uh most of the 213 locations
+are um metropolitan areas but then in
+
+ align:start position:0%
+are um metropolitan areas but then in
+ 
+
+ align:start position:0%
+are um metropolitan areas but then in
+addition they have sort of so they have
+
+ align:start position:0%
+addition they have sort of so they have
+ 
+
+ align:start position:0%
+addition they have sort of so they have
+sort of each metropolitan area as a
+
+ align:start position:0%
+sort of each metropolitan area as a
+ 
+
+ align:start position:0%
+sort of each metropolitan area as a
+location observation and then they have
+
+ align:start position:0%
+location observation and then they have
+ 
+
+ align:start position:0%
+location observation and then they have
+the rest of a state not in metropolitan
+
+ align:start position:0%
+the rest of a state not in metropolitan
+ 
+
+ align:start position:0%
+the rest of a state not in metropolitan
+areas as an observation uh anyway so
+
+ align:start position:0%
+areas as an observation uh anyway so
+ 
+
+ align:start position:0%
+areas as an observation uh anyway so
+they have 213 different
+
+ align:start position:0%
+they have 213 different
+ 
+
+ align:start position:0%
+they have 213 different
+locations they sort of do something
+
+ align:start position:0%
+locations they sort of do something
+ 
+
+ align:start position:0%
+locations they sort of do something
+that's kind of like a blp estimation
+
+ align:start position:0%
+that's kind of like a blp estimation
+ 
+
+ align:start position:0%
+that's kind of like a blp estimation
+except dealing with the zeros so they
+
+ align:start position:0%
+except dealing with the zeros so they
+ 
+
+ align:start position:0%
+except dealing with the zeros so they
+aggregate sales um they do something
+
+ align:start position:0%
+aggregate sales um they do something
+ 
+
+ align:start position:0%
+aggregate sales um they do something
+very much like you know these if you
+
+ align:start position:0%
+very much like you know these if you
+ 
+
+ align:start position:0%
+very much like you know these if you
+remember back in tobias's lecture your
+
+ align:start position:0%
+remember back in tobias's lecture your
+ 
+
+ align:start position:0%
+remember back in tobias's lecture your
+sort of blp instruments for Price are
+
+ align:start position:0%
+sort of blp instruments for Price are
+ 
+
+ align:start position:0%
+sort of blp instruments for Price are
+some function of the characteristics of
+
+ align:start position:0%
+some function of the characteristics of
+ 
+
+ align:start position:0%
+some function of the characteristics of
+all the competing Brands so they have
+
+ align:start position:0%
+all the competing Brands so they have
+ 
+
+ align:start position:0%
+all the competing Brands so they have
+like a you know I not a very convincing
+
+ align:start position:0%
+like a you know I not a very convincing
+ 
+
+ align:start position:0%
+like a you know I not a very convincing
+instrumentation strategy but that's what
+
+ align:start position:0%
+instrumentation strategy but that's what
+ 
+
+ align:start position:0%
+instrumentation strategy but that's what
+what's available so they have like a blp
+
+ align:start position:0%
+what's available so they have like a blp
+ 
+
+ align:start position:0%
+what's available so they have like a blp
+style instrumentation strategy dealing
+
+ align:start position:0%
+style instrumentation strategy dealing
+ 
+
+ align:start position:0%
+style instrumentation strategy dealing
+with the zeros and it is it's not a pure
+
+ align:start position:0%
+with the zeros and it is it's not a pure
+ 
+
+ align:start position:0%
+with the zeros and it is it's not a pure
+cross-section because you know there's
+
+ align:start position:0%
+cross-section because you know there's
+ 
+
+ align:start position:0%
+cross-section because you know there's
+price variation because the prices vary
+
+ align:start position:0%
+price variation because the prices vary
+ 
+
+ align:start position:0%
+price variation because the prices vary
+across months and you can see when this
+
+ align:start position:0%
+across months and you can see when this
+ 
+
+ align:start position:0%
+across months and you can see when this
+shoe is on sale and some month do sales
+
+ align:start position:0%
+shoe is on sale and some month do sales
+ 
+
+ align:start position:0%
+shoe is on sale and some month do sales
+go up um product reviews are also time
+
+ align:start position:0%
+go up um product reviews are also time
+ 
+
+ align:start position:0%
+go up um product reviews are also time
+varying shoes come out they have no
+
+ align:start position:0%
+varying shoes come out they have no
+ 
+
+ align:start position:0%
+varying shoes come out they have no
+reviews over time they build up reviews
+
+ align:start position:0%
+reviews over time they build up reviews
+ 
+
+ align:start position:0%
+reviews over time they build up reviews
+obviously higher reviews are good for
+
+ align:start position:0%
+obviously higher reviews are good for
+ 
+
+ align:start position:0%
+obviously higher reviews are good for
+sales it turns out though also um zero
+
+ align:start position:0%
+sales it turns out though also um zero
+ 
+
+ align:start position:0%
+sales it turns out though also um zero
+reviews are good for sale are positively
+
+ align:start position:0%
+reviews are good for sale are positively
+ 
+
+ align:start position:0%
+reviews are good for sale are positively
+associated with sales as well uh and
+
+ align:start position:0%
+associated with sales as well uh and
+ 
+
+ align:start position:0%
+associated with sales as well uh and
+this may be because zero sales means
+
+ align:start position:0%
+this may be because zero sales means
+ 
+
+ align:start position:0%
+this may be because zero sales means
+it's a zero reviews means it's a brand
+
+ align:start position:0%
+it's a zero reviews means it's a brand
+ 
+
+ align:start position:0%
+it's a zero reviews means it's a brand
+new product that's just being introduced
+
+ align:start position:0%
+new product that's just being introduced
+ 
+
+ align:start position:0%
+new product that's just being introduced
+with the latest fashion or that's being
+
+ align:start position:0%
+with the latest fashion or that's being
+ 
+
+ align:start position:0%
+with the latest fashion or that's being
+advertised or something like that um
+
+ align:start position:0%
+advertised or something like that um
+ 
+
+ align:start position:0%
+advertised or something like that um
+anyway and then the product set is also
+
+ align:start position:0%
+anyway and then the product set is also
+ 
+
+ align:start position:0%
+anyway and then the product set is also
+time varying um so anyway with all that
+
+ align:start position:0%
+time varying um so anyway with all that
+ 
+
+ align:start position:0%
+time varying um so anyway with all that
+they're able to sort of
+
+ align:start position:0%
+they're able to sort of
+ 
+
+ align:start position:0%
+they're able to sort of
+estimate all these C efficients and they
+
+ align:start position:0%
+estimate all these C efficients and they
+ 
+
+ align:start position:0%
+estimate all these C efficients and they
+can estimate sort of a distribution of
+
+ align:start position:0%
+can estimate sort of a distribution of
+ 
+
+ align:start position:0%
+can estimate sort of a distribution of
+the Delta
+
+ align:start position:0%
+the Delta
+ 
+
+ align:start position:0%
+the Delta
+ljs and the you know Delta ljs indicate
+
+ align:start position:0%
+ljs and the you know Delta ljs indicate
+ 
+
+ align:start position:0%
+ljs and the you know Delta ljs indicate
+that there is a lot of cross market
+
+ align:start position:0%
+that there is a lot of cross market
+ 
+
+ align:start position:0%
+that there is a lot of cross market
+heterogenity and preferences uh and you
+
+ align:start position:0%
+heterogenity and preferences uh and you
+ 
+
+ align:start position:0%
+heterogenity and preferences uh and you
+know I you you have to have faith that
+
+ align:start position:0%
+know I you you have to have faith that
+ 
+
+ align:start position:0%
+know I you you have to have faith that
+they're dealing with the zero appropri
+
+ align:start position:0%
+they're dealing with the zero appropri
+ 
+
+ align:start position:0%
+they're dealing with the zero appropri
+to deal with it it's not just in some
+
+ align:start position:0%
+to deal with it it's not just in some
+ 
+
+ align:start position:0%
+to deal with it it's not just in some
+markets people buy these these shoes
+
+ align:start position:0%
+markets people buy these these shoes
+ 
+
+ align:start position:0%
+markets people buy these these shoes
+actually have sales and some markets
+
+ align:start position:0%
+actually have sales and some markets
+ 
+
+ align:start position:0%
+actually have sales and some markets
+these have actually have sales but I
+
+ align:start position:0%
+these have actually have sales but I
+ 
+
+ align:start position:0%
+these have actually have sales but I
+think they've done a fairly good job of
+
+ align:start position:0%
+think they've done a fairly good job of
+ 
+
+ align:start position:0%
+think they've done a fairly good job of
+trying to argue that no there's
+
+ align:start position:0%
+trying to argue that no there's
+ 
+
+ align:start position:0%
+trying to argue that no there's
+underlying cross-sectional variation in
+
+ align:start position:0%
+underlying cross-sectional variation in
+ 
+
+ align:start position:0%
+underlying cross-sectional variation in
+the cities to purchase different shoes
+
+ align:start position:0%
+the cities to purchase different shoes
+ 
+
+ align:start position:0%
+the cities to purchase different shoes
+in different places and again I think
+
+ align:start position:0%
+in different places and again I think
+ 
+
+ align:start position:0%
+in different places and again I think
+some of that is like the Sho the boots
+
+ align:start position:0%
+some of that is like the Sho the boots
+ 
+
+ align:start position:0%
+some of that is like the Sho the boots
+versus sandals approach and some of that
+
+ align:start position:0%
+versus sandals approach and some of that
+ 
+
+ align:start position:0%
+versus sandals approach and some of that
+is just you know shoes are a fashion
+
+ align:start position:0%
+is just you know shoes are a fashion
+ 
+
+ align:start position:0%
+is just you know shoes are a fashion
+good and there are brands of sneakers
+
+ align:start position:0%
+good and there are brands of sneakers
+ 
+
+ align:start position:0%
+good and there are brands of sneakers
+brands of shoes brands of whatever that
+
+ align:start position:0%
+brands of shoes brands of whatever that
+ 
+
+ align:start position:0%
+brands of shoes brands of whatever that
+are more and less fashionable in
+
+ align:start position:0%
+are more and less fashionable in
+ 
+
+ align:start position:0%
+are more and less fashionable in
+different cities for whatever reason
+
+ align:start position:0%
+different cities for whatever reason
+ 
+
+ align:start position:0%
+different cities for whatever reason
+this has become something people wear
+
+ align:start position:0%
+this has become something people wear
+ 
+
+ align:start position:0%
+this has become something people wear
+and and people will to pay more for
+
+ align:start position:0%
+and and people will to pay more for
+ 
+
+ align:start position:0%
+and and people will to pay more for
+those okay um so how do they estimate
+
+ align:start position:0%
+those okay um so how do they estimate
+ 
+
+ align:start position:0%
+those okay um so how do they estimate
+the gains from product iety um to
+
+ align:start position:0%
+the gains from product iety um to
+ 
+
+ align:start position:0%
+the gains from product iety um to
+estimate gains from product variety this
+
+ align:start position:0%
+estimate gains from product variety this
+ 
+
+ align:start position:0%
+estimate gains from product variety this
+is done with a
+
+ align:start position:0%
+is done with a
+ 
+
+ align:start position:0%
+is done with a
+counterfactual so you know they know all
+
+ align:start position:0%
+counterfactual so you know they know all
+ 
+
+ align:start position:0%
+counterfactual so you know they know all
+the sales that zapo or whatever the
+
+ align:start position:0%
+the sales that zapo or whatever the
+ 
+
+ align:start position:0%
+the sales that zapo or whatever the
+retailer is made uh and then they think
+
+ align:start position:0%
+retailer is made uh and then they think
+ 
+
+ align:start position:0%
+retailer is made uh and then they think
+about a counterfactual world where
+
+ align:start position:0%
+about a counterfactual world where
+ 
+
+ align:start position:0%
+about a counterfactual world where
+instead of choosing from all the shoes
+
+ align:start position:0%
+instead of choosing from all the shoes
+ 
+
+ align:start position:0%
+instead of choosing from all the shoes
+at zapo people could only choose from a
+
+ align:start position:0%
+at zapo people could only choose from a
+ 
+
+ align:start position:0%
+at zapo people could only choose from a
+limited Supply uh what do they do for
+
+ align:start position:0%
+limited Supply uh what do they do for
+ 
+
+ align:start position:0%
+limited Supply uh what do they do for
+the limited Supply well the first thing
+
+ align:start position:0%
+the limited Supply well the first thing
+ 
+
+ align:start position:0%
+the limited Supply well the first thing
+they do is they use the data on the
+
+ align:start position:0%
+they do is they use the data on the
+ 
+
+ align:start position:0%
+they do is they use the data on the
+Macy's and Payless shoe stores to
+
+ align:start position:0%
+Macy's and Payless shoe stores to
+ 
+
+ align:start position:0%
+Macy's and Payless shoe stores to
+estimate the total number of products
+
+ align:start position:0%
+estimate the total number of products
+ 
+
+ align:start position:0%
+estimate the total number of products
+available in each market as a function
+
+ align:start position:0%
+available in each market as a function
+ 
+
+ align:start position:0%
+available in each market as a function
+of the population so they would be doing
+
+ align:start position:0%
+of the population so they would be doing
+ 
+
+ align:start position:0%
+of the population so they would be doing
+how many different brands of shoes are
+
+ align:start position:0%
+how many different brands of shoes are
+ 
+
+ align:start position:0%
+how many different brands of shoes are
+available in Boston which you get by
+
+ align:start position:0%
+available in Boston which you get by
+ 
+
+ align:start position:0%
+available in Boston which you get by
+looking at the overlap of all the Macy's
+
+ align:start position:0%
+looking at the overlap of all the Macy's
+ 
+
+ align:start position:0%
+looking at the overlap of all the Macy's
+in Boston and the overlap of the Macy's
+
+ align:start position:0%
+in Boston and the overlap of the Macy's
+ 
+
+ align:start position:0%
+in Boston and the overlap of the Macy's
+in Boston with the Payless shoe stores
+
+ align:start position:0%
+in Boston with the Payless shoe stores
+ 
+
+ align:start position:0%
+in Boston with the Payless shoe stores
+in Boston and then they have Census Data
+
+ align:start position:0%
+in Boston and then they have Census Data
+ 
+
+ align:start position:0%
+in Boston and then they have Census Data
+knowing how many and shoe stores there
+
+ align:start position:0%
+knowing how many and shoe stores there
+ 
+
+ align:start position:0%
+knowing how many and shoe stores there
+are in Boston how large they are in
+
+ align:start position:0%
+are in Boston how large they are in
+ 
+
+ align:start position:0%
+are in Boston how large they are in
+Boston they assume that they have the
+
+ align:start position:0%
+Boston they assume that they have the
+ 
+
+ align:start position:0%
+Boston they assume that they have the
+same overlap as as they're seeing in the
+
+ align:start position:0%
+same overlap as as they're seeing in the
+ 
+
+ align:start position:0%
+same overlap as as they're seeing in the
+May season pay lesses and there started
+
+ align:start position:0%
+May season pay lesses and there started
+ 
+
+ align:start position:0%
+May season pay lesses and there started
+trying to estimate how many total shoes
+
+ align:start position:0%
+trying to estimate how many total shoes
+ 
+
+ align:start position:0%
+trying to estimate how many total shoes
+are are there in the Boston area that
+
+ align:start position:0%
+are are there in the Boston area that
+ 
+
+ align:start position:0%
+are are there in the Boston area that
+you can buy at physical retail
+
+ align:start position:0%
+you can buy at physical retail
+ 
+
+ align:start position:0%
+you can buy at physical retail
+stores um obviously that's a bit of an
+
+ align:start position:0%
+stores um obviously that's a bit of an
+ 
+
+ align:start position:0%
+stores um obviously that's a bit of an
+aggressive assumption and that that
+
+ align:start position:0%
+aggressive assumption and that that
+ 
+
+ align:start position:0%
+aggressive assumption and that that
+assuming that people could actually know
+
+ align:start position:0%
+assuming that people could actually know
+ 
+
+ align:start position:0%
+assuming that people could actually know
+which local Boston shoe store to go to
+
+ align:start position:0%
+which local Boston shoe store to go to
+ 
+
+ align:start position:0%
+which local Boston shoe store to go to
+to buy whatever particular brand of
+
+ align:start position:0%
+to buy whatever particular brand of
+ 
+
+ align:start position:0%
+to buy whatever particular brand of
+boots they want um and then what they
+
+ align:start position:0%
+boots they want um and then what they
+ 
+
+ align:start position:0%
+boots they want um and then what they
+assume is that offline
+
+ align:start position:0%
+assume is that offline
+ 
+
+ align:start position:0%
+assume is that offline
+consumers have the choice of the NL
+
+ align:start position:0%
+consumers have the choice of the NL
+ 
+
+ align:start position:0%
+consumers have the choice of the NL
+products that have the highest Delta
+
+ align:start position:0%
+products that have the highest Delta
+ 
+
+ align:start position:0%
+products that have the highest Delta
+ljs uh to choose from so that the
+
+ align:start position:0%
+ljs uh to choose from so that the
+ 
+
+ align:start position:0%
+ljs uh to choose from so that the
+physical stores in each state or each
+
+ align:start position:0%
+physical stores in each state or each
+ 
+
+ align:start position:0%
+physical stores in each state or each
+City carry the most popular brands so
+
+ align:start position:0%
+City carry the most popular brands so
+ 
+
+ align:start position:0%
+City carry the most popular brands so
+again that's it's kind of an aggressive
+
+ align:start position:0%
+again that's it's kind of an aggressive
+ 
+
+ align:start position:0%
+again that's it's kind of an aggressive
+assumption in that you know local stores
+
+ align:start position:0%
+assumption in that you know local stores
+ 
+
+ align:start position:0%
+assumption in that you know local stores
+are tailoring their demand to what
+
+ align:start position:0%
+are tailoring their demand to what
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+
+ align:start position:0%
+are tailoring their demand to what
+people want and they're tailoring it
+
+ align:start position:0%
+people want and they're tailoring it
+ 
+
+ align:start position:0%
+people want and they're tailoring it
+perfectly they're picking the most
+
+ align:start position:0%
+perfectly they're picking the most
+ 
+
+ align:start position:0%
+perfectly they're picking the most
+popular brands and so it it's both you
+
+ align:start position:0%
+popular brands and so it it's both you
+ 
+
+ align:start position:0%
+popular brands and so it it's both you
+know it's both we
+
+ align:start position:0%
+know it's both we
+ 
+
+ align:start position:0%
+know it's both we
+observe it's both we know where in this
+
+ align:start position:0%
+observe it's both we know where in this
+ 
+
+ align:start position:0%
+observe it's both we know where in this
+in this where to buy shoes physically
+
+ align:start position:0%
+in this where to buy shoes physically
+ 
+
+ align:start position:0%
+in this where to buy shoes physically
+depending on what we want which store to
+
+ align:start position:0%
+depending on what we want which store to
+ 
+
+ align:start position:0%
+depending on what we want which store to
+go to and we and the shoe stores are
+
+ align:start position:0%
+go to and we and the shoe stores are
+ 
+
+ align:start position:0%
+go to and we and the shoe stores are
+doing perfect tailoring and carrying the
+
+ align:start position:0%
+doing perfect tailoring and carrying the
+ 
+
+ align:start position:0%
+doing perfect tailoring and carrying the
+most popular shoes not making
+
+ align:start position:0%
+most popular shoes not making
+ 
+
+ align:start position:0%
+most popular shoes not making
+mistakes um but anyway so subject to
+
+ align:start position:0%
+mistakes um but anyway so subject to
+ 
+
+ align:start position:0%
+mistakes um but anyway so subject to
+that caveat uh es the paper suggests the
+
+ align:start position:0%
+that caveat uh es the paper suggests the
+ 
+
+ align:start position:0%
+that caveat uh es the paper suggests the
+sort of online product variety benefits
+
+ align:start position:0%
+sort of online product variety benefits
+ 
+
+ align:start position:0%
+sort of online product variety benefits
+are are much smaller than what BR yelson
+
+ align:start position:0%
+are are much smaller than what BR yelson
+ 
+
+ align:start position:0%
+are are much smaller than what BR yelson
+who and Smith said and they're much
+
+ align:start position:0%
+who and Smith said and they're much
+ 
+
+ align:start position:0%
+who and Smith said and they're much
+smaller in two different senses um the
+
+ align:start position:0%
+smaller in two different senses um the
+ 
+
+ align:start position:0%
+smaller in two different senses um the
+first is that if you look at the gain
+
+ align:start position:0%
+first is that if you look at the gain
+ 
+
+ align:start position:0%
+first is that if you look at the gain
+from product variety they argue that
+
+ align:start position:0%
+from product variety they argue that
+ 
+
+ align:start position:0%
+from product variety they argue that
+about half of the gain from product
+
+ align:start position:0%
+about half of the gain from product
+ 
+
+ align:start position:0%
+about half of the gain from product
+variety would um be provided Anyway by
+
+ align:start position:0%
+variety would um be provided Anyway by
+ 
+
+ align:start position:0%
+variety would um be provided Anyway by
+local stores by just having heterogenea
+
+ align:start position:0%
+local stores by just having heterogenea
+ 
+
+ align:start position:0%
+local stores by just having heterogenea
+in local stores so you if you think
+
+ align:start position:0%
+in local stores so you if you think
+ 
+
+ align:start position:0%
+in local stores so you if you think
+about this sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Continuum you know let me do Brin nson
+
+ align:start position:0%
+Continuum you know let me do Brin nson
+ 
+
+ align:start position:0%
+Continuum you know let me do Brin nson
+who and Smith number so like you know so
+
+ align:start position:0%
+who and Smith number so like you know so
+ 
+
+ align:start position:0%
+who and Smith number so like you know so
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+have you know let's suppose we have so
+
+ align:start position:0%
+have you know let's suppose we have so
+ 
+
+ align:start position:0%
+have you know let's suppose we have so
+Brin holson who and Smith are looking at
+
+ align:start position:0%
+Brin holson who and Smith are looking at
+ 
+
+ align:start position:0%
+Brin holson who and Smith are looking at
+sort of what's the sort of consumer
+
+ align:start position:0%
+sort of what's the sort of consumer
+ 
+
+ align:start position:0%
+sort of what's the sort of consumer
+surplus from there being One Bookstore
+
+ align:start position:0%
+surplus from there being One Bookstore
+ 
+
+ align:start position:0%
+surplus from there being One Bookstore
+that has 100,000
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+titles and
+
+ align:start position:0%
+titles and
+ 
+
+ align:start position:0%
+titles and
+then we have this sort of
+
+ align:start position:0%
+then we have this sort of
+ 
+
+ align:start position:0%
+then we have this sort of
+Amazon with two million titles and
+
+ align:start position:0%
+Amazon with two million titles and
+ 
+
+ align:start position:0%
+Amazon with two million titles and
+they're arguing that you know this is 10
+
+ align:start position:0%
+they're arguing that you know this is 10
+ 
+
+ align:start position:0%
+they're arguing that you know this is 10
+that this is like if this is one this is
+
+ align:start position:0%
+that this is like if this is one this is
+ 
+
+ align:start position:0%
+that this is like if this is one this is
+you know 10 you get 10 times the I'm
+
+ align:start position:0%
+you know 10 you get 10 times the I'm
+ 
+
+ align:start position:0%
+you know 10 you get 10 times the I'm
+putting the consumer surplus in this
+
+ align:start position:0%
+putting the consumer surplus in this
+ 
+
+ align:start position:0%
+putting the consumer surplus in this
+axis
+
+ align:start position:0%
+axis
+ 
+
+ align:start position:0%
+axis
+um and then what uh Quan and Williams
+
+ align:start position:0%
+um and then what uh Quan and Williams
+ 
+
+ align:start position:0%
+um and then what uh Quan and Williams
+are saying is that we have so
+
+ align:start position:0%
+are saying is that we have so
+ 
+
+ align:start position:0%
+are saying is that we have so
+is quanon Williams saying well our
+
+ align:start position:0%
+is quanon Williams saying well our
+ 
+
+ align:start position:0%
+is quanon Williams saying well our
+Benchmark is going to be not One
+
+ align:start position:0%
+Benchmark is going to be not One
+ 
+
+ align:start position:0%
+Benchmark is going to be not One
+Bookstore
+
+ align:start position:0%
+Bookstore
+ 
+
+ align:start position:0%
+Bookstore
+uh but you know all Boston
+
+ align:start position:0%
+uh but you know all Boston
+ 
+
+ align:start position:0%
+uh but you know all Boston
+bookstores they don't know what all
+
+ align:start position:0%
+bookstores they don't know what all
+ 
+
+ align:start position:0%
+bookstores they don't know what all
+Boston bookstores have but they just
+
+ align:start position:0%
+Boston bookstores have but they just
+ 
+
+ align:start position:0%
+Boston bookstores have but they just
+assume that the Boston bookstores have
+
+ align:start position:0%
+assume that the Boston bookstores have
+ 
+
+ align:start position:0%
+assume that the Boston bookstores have
+these nonoverlapping sets of books and
+
+ align:start position:0%
+these nonoverlapping sets of books and
+ 
+
+ align:start position:0%
+these nonoverlapping sets of books and
+and the non-overlapping sets of books
+
+ align:start position:0%
+and the non-overlapping sets of books
+ 
+
+ align:start position:0%
+and the non-overlapping sets of books
+you know tailored to what the MIT
+
+ align:start position:0%
+you know tailored to what the MIT
+ 
+
+ align:start position:0%
+you know tailored to what the MIT
+students want tailored to what everybody
+
+ align:start position:0%
+students want tailored to what everybody
+ 
+
+ align:start position:0%
+students want tailored to what everybody
+else in Boston wants uh and what they
+
+ align:start position:0%
+else in Boston wants uh and what they
+ 
+
+ align:start position:0%
+else in Boston wants uh and what they
+find is that you know the all
+
+ align:start position:0%
+find is that you know the all
+ 
+
+ align:start position:0%
+find is that you know the all
+they're well they do all shoe stores but
+
+ align:start position:0%
+they're well they do all shoe stores but
+ 
+
+ align:start position:0%
+they're well they do all shoe stores but
+the all shoe stores thing compared to
+
+ align:start position:0%
+the all shoe stores thing compared to
+ 
+
+ align:start position:0%
+the all shoe stores thing compared to
+one shoe store they're arguing that all
+
+ align:start position:0%
+one shoe store they're arguing that all
+ 
+
+ align:start position:0%
+one shoe store they're arguing that all
+shoe stores get you about half of the
+
+ align:start position:0%
+shoe stores get you about half of the
+ 
+
+ align:start position:0%
+shoe stores get you about half of the
+half of the way to the Amazon ranking so
+
+ align:start position:0%
+half of the way to the Amazon ranking so
+ 
+
+ align:start position:0%
+half of the way to the Amazon ranking so
+in some sense that Quan and Williams may
+
+ align:start position:0%
+in some sense that Quan and Williams may
+ 
+
+ align:start position:0%
+in some sense that Quan and Williams may
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+overstating the gains by you know by
+
+ align:start position:0%
+overstating the gains by you know by
+ 
+
+ align:start position:0%
+overstating the gains by you know by
+100% or
+
+ align:start position:0%
+100% or
+ 
+
+ align:start position:0%
+100% or
+something and so that's one point then
+
+ align:start position:0%
+something and so that's one point then
+ 
+
+ align:start position:0%
+something and so that's one point then
+the second point of the paper that you
+
+ align:start position:0%
+the second point of the paper that you
+ 
+
+ align:start position:0%
+the second point of the paper that you
+know is not emphasized as much just in
+
+ align:start position:0%
+know is not emphasized as much just in
+ 
+
+ align:start position:0%
+know is not emphasized as much just in
+the title and Inter is that they also
+
+ align:start position:0%
+the title and Inter is that they also
+ 
+
+ align:start position:0%
+the title and Inter is that they also
+find that
+
+ align:start position:0%
+find that
+ 
+
+ align:start position:0%
+find that
+um they also find that the uh gains from
+
+ align:start position:0%
+um they also find that the uh gains from
+ 
+
+ align:start position:0%
+um they also find that the uh gains from
+product variety are just much
+
+ align:start position:0%
+product variety are just much
+ 
+
+ align:start position:0%
+product variety are just much
+smaller uh than are reported elsewhere
+
+ align:start position:0%
+smaller uh than are reported elsewhere
+ 
+
+ align:start position:0%
+smaller uh than are reported elsewhere
+um so that whereas you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know uh you
+
+ align:start position:0%
+know uh you
+ 
+
+ align:start position:0%
+know uh you
+know whereas um Bolson who and Smith are
+
+ align:start position:0%
+know whereas um Bolson who and Smith are
+ 
+
+ align:start position:0%
+know whereas um Bolson who and Smith are
+saying that sort of these gains are 10
+
+ align:start position:0%
+saying that sort of these gains are 10
+ 
+
+ align:start position:0%
+saying that sort of these gains are 10
+times the gain from a 5% price cut uh
+
+ align:start position:0%
+times the gain from a 5% price cut uh
+ 
+
+ align:start position:0%
+times the gain from a 5% price cut uh
+what they find is that the gains in the
+
+ align:start position:0%
+what they find is that the gains in the
+ 
+
+ align:start position:0%
+what they find is that the gains in the
+shoe store data uh look like they're uh
+
+ align:start position:0%
+shoe store data uh look like they're uh
+ 
+
+ align:start position:0%
+shoe store data uh look like they're uh
+you know two times uh the benefit of
+
+ align:start position:0%
+you know two times uh the benefit of
+ 
+
+ align:start position:0%
+you know two times uh the benefit of
+a so anyway sorry this
+
+ align:start position:0%
+a so anyway sorry this
+ 
+
+ align:start position:0%
+a so anyway sorry this
+is if I make this one this is two so the
+
+ align:start position:0%
+is if I make this one this is two so the
+ 
+
+ align:start position:0%
+is if I make this one this is two so the
+the gain is just equivalent to a f the
+
+ align:start position:0%
+the gain is just equivalent to a f the
+ 
+
+ align:start position:0%
+the gain is just equivalent to a f the
+gain is like equivalent to a a 5% price
+
+ align:start position:0%
+gain is like equivalent to a a 5% price
+ 
+
+ align:start position:0%
+gain is like equivalent to a a 5% price
+cut so it's like the this number is here
+
+ align:start position:0%
+cut so it's like the this number is here
+ 
+
+ align:start position:0%
+cut so it's like the this number is here
+this number is here so what they're
+
+ align:start position:0%
+this number is here so what they're
+ 
+
+ align:start position:0%
+this number is here so what they're
+arguing is that the sort of actually no
+
+ align:start position:0%
+arguing is that the sort of actually no
+ 
+
+ align:start position:0%
+arguing is that the sort of actually no
+sorry take that back um it's this one
+
+ align:start position:0%
+sorry take that back um it's this one
+ 
+
+ align:start position:0%
+sorry take that back um it's this one
+compared to this one I think is roughly
+
+ align:start position:0%
+compared to this one I think is roughly
+ 
+
+ align:start position:0%
+compared to this one I think is roughly
+equivalent to a 5% price
+
+ align:start position:0%
+equivalent to a 5% price
+ 
+
+ align:start position:0%
+equivalent to a 5% price
+cut so what they're finding is that the
+
+ align:start position:0%
+cut so what they're finding is that the
+ 
+
+ align:start position:0%
+cut so what they're finding is that the
+gains from product variety are just much
+
+ align:start position:0%
+gains from product variety are just much
+ 
+
+ align:start position:0%
+gains from product variety are just much
+much smaller in shoes than Bolson who
+
+ align:start position:0%
+much smaller in shoes than Bolson who
+ 
+
+ align:start position:0%
+much smaller in shoes than Bolson who
+and Smith said they were in books uh and
+
+ align:start position:0%
+and Smith said they were in books uh and
+ 
+
+ align:start position:0%
+and Smith said they were in books uh and
+because the gains are so much smaller uh
+
+ align:start position:0%
+because the gains are so much smaller uh
+ 
+
+ align:start position:0%
+because the gains are so much smaller uh
+and you take out this sort of this thing
+
+ align:start position:0%
+and you take out this sort of this thing
+ 
+
+ align:start position:0%
+and you take out this sort of this thing
+is halfway there already what you're
+
+ align:start position:0%
+is halfway there already what you're
+ 
+
+ align:start position:0%
+is halfway there already what you're
+getting is the product variety gains are
+
+ align:start position:0%
+getting is the product variety gains are
+ 
+
+ align:start position:0%
+getting is the product variety gains are
+are really only like equivalent to a 5%
+
+ align:start position:0%
+are really only like equivalent to a 5%
+ 
+
+ align:start position:0%
+are really only like equivalent to a 5%
+price cut
+
+ align:start position:0%
+price cut
+ 
+
+ align:start position:0%
+price cut
+um so it's saying in at least in the
+
+ align:start position:0%
+um so it's saying in at least in the
+ 
+
+ align:start position:0%
+um so it's saying in at least in the
+shoe sense um product variety gains are
+
+ align:start position:0%
+shoe sense um product variety gains are
+ 
+
+ align:start position:0%
+shoe sense um product variety gains are
+you know 10 times smaller than you would
+
+ align:start position:0%
+you know 10 times smaller than you would
+ 
+
+ align:start position:0%
+you know 10 times smaller than you would
+have might have thought from the the
+
+ align:start position:0%
+have might have thought from the the
+ 
+
+ align:start position:0%
+have might have thought from the the
+Brin yson who and Smith paper and
+
+ align:start position:0%
+Brin yson who and Smith paper and
+ 
+
+ align:start position:0%
+Brin yson who and Smith paper and
+obviously you know is that because shoes
+
+ align:start position:0%
+obviously you know is that because shoes
+ 
+
+ align:start position:0%
+obviously you know is that because shoes
+are very different from books that's one
+
+ align:start position:0%
+are very different from books that's one
+ 
+
+ align:start position:0%
+are very different from books that's one
+possibility you know right like every
+
+ align:start position:0%
+possibility you know right like every
+ 
+
+ align:start position:0%
+possibility you know right like every
+book is very very different from every
+
+ align:start position:0%
+book is very very different from every
+ 
+
+ align:start position:0%
+book is very very different from every
+other book you could imagine once you've
+
+ align:start position:0%
+other book you could imagine once you've
+ 
+
+ align:start position:0%
+other book you could imagine once you've
+got a million shoes the ability to make
+
+ align:start position:0%
+got a million shoes the ability to make
+ 
+
+ align:start position:0%
+got a million shoes the ability to make
+a million first shoe that's very
+
+ align:start position:0%
+a million first shoe that's very
+ 
+
+ align:start position:0%
+a million first shoe that's very
+different from all existing shoes is
+
+ align:start position:0%
+different from all existing shoes is
+ 
+
+ align:start position:0%
+different from all existing shoes is
+very hard whereas every new book is just
+
+ align:start position:0%
+very hard whereas every new book is just
+ 
+
+ align:start position:0%
+very hard whereas every new book is just
+completely different text from every
+
+ align:start position:0%
+completely different text from every
+ 
+
+ align:start position:0%
+completely different text from every
+other book there may be more inherent
+
+ align:start position:0%
+other book there may be more inherent
+ 
+
+ align:start position:0%
+other book there may be more inherent
+Variety in books than there are in shoes
+
+ align:start position:0%
+Variety in books than there are in shoes
+ 
+
+ align:start position:0%
+Variety in books than there are in shoes
+uh but you know I think it may also be
+
+ align:start position:0%
+uh but you know I think it may also be
+ 
+
+ align:start position:0%
+uh but you know I think it may also be
+that um they may have done a better job
+
+ align:start position:0%
+that um they may have done a better job
+ 
+
+ align:start position:0%
+that um they may have done a better job
+of dealing with estimating what's true
+
+ align:start position:0%
+of dealing with estimating what's true
+ 
+
+ align:start position:0%
+of dealing with estimating what's true
+product variety versus spous product
+
+ align:start position:0%
+product variety versus spous product
+ 
+
+ align:start position:0%
+product variety versus spous product
+variety you know like
+
+ align:start position:0%
+variety you know like
+ 
+
+ align:start position:0%
+variety you know like
+the I don't know if I remember like I've
+
+ align:start position:0%
+the I don't know if I remember like I've
+ 
+
+ align:start position:0%
+the I don't know if I remember like I've
+started discussed like when you're doing
+
+ align:start position:0%
+started discussed like when you're doing
+ 
+
+ align:start position:0%
+started discussed like when you're doing
+trying to estimate consumer Variety in
+
+ align:start position:0%
+trying to estimate consumer Variety in
+ 
+
+ align:start position:0%
+trying to estimate consumer Variety in
+demand like consumer welfare from demand
+
+ align:start position:0%
+demand like consumer welfare from demand
+ 
+
+ align:start position:0%
+demand like consumer welfare from demand
+and you have heterogeneous products you
+
+ align:start position:0%
+and you have heterogeneous products you
+ 
+
+ align:start position:0%
+and you have heterogeneous products you
+know everyone's always doing this
+
+ align:start position:0%
+know everyone's always doing this
+ 
+
+ align:start position:0%
+know everyone's always doing this
+um uh XJ beta minus Alpha PJ plus
+
+ align:start position:0%
+um uh XJ beta minus Alpha PJ plus
+ 
+
+ align:start position:0%
+um uh XJ beta minus Alpha PJ plus
+Epsilon i
+
+ align:start position:0%
+Epsilon i
+ 
+
+ align:start position:0%
+Epsilon i
+j and they're always assuming these
+
+ align:start position:0%
+j and they're always assuming these
+ 
+
+ align:start position:0%
+j and they're always assuming these
+Epsilon I JS are loit distributed which
+
+ align:start position:0%
+Epsilon I JS are loit distributed which
+ 
+
+ align:start position:0%
+Epsilon I JS are loit distributed which
+has a fairly thick tail and that every
+
+ align:start position:0%
+has a fairly thick tail and that every
+ 
+
+ align:start position:0%
+has a fairly thick tail and that every
+Epsilon i j is independent of every
+
+ align:start position:0%
+Epsilon i j is independent of every
+ 
+
+ align:start position:0%
+Epsilon i j is independent of every
+other Epsilon i j um again right once
+
+ align:start position:0%
+other Epsilon i j um again right once
+ 
+
+ align:start position:0%
+other Epsilon i j um again right once
+you get to the the millionth different
+
+ align:start position:0%
+you get to the the millionth different
+ 
+
+ align:start position:0%
+you get to the the millionth different
+shoe is it really an Epsilon i j that's
+
+ align:start position:0%
+shoe is it really an Epsilon i j that's
+ 
+
+ align:start position:0%
+shoe is it really an Epsilon i j that's
+completely independent of your taste for
+
+ align:start position:0%
+completely independent of your taste for
+ 
+
+ align:start position:0%
+completely independent of your taste for
+every other shoe out there
+
+ align:start position:0%
+every other shoe out there
+ 
+
+ align:start position:0%
+every other shoe out there
+it's highly likely those epsilons are
+
+ align:start position:0%
+it's highly likely those epsilons are
+ 
+
+ align:start position:0%
+it's highly likely those epsilons are
+highly correlated across shoes at least
+
+ align:start position:0%
+highly correlated across shoes at least
+ 
+
+ align:start position:0%
+highly correlated across shoes at least
+by having the sort of you know they've
+
+ align:start position:0%
+by having the sort of you know they've
+ 
+
+ align:start position:0%
+by having the sort of you know they've
+they've got the sort of those category
+
+ align:start position:0%
+they've got the sort of those category
+ 
+
+ align:start position:0%
+they've got the sort of those category
+specific shocks by putting in the
+
+ align:start position:0%
+specific shocks by putting in the
+ 
+
+ align:start position:0%
+specific shocks by putting in the
+category specific shocks esing the
+
+ align:start position:0%
+category specific shocks esing the
+ 
+
+ align:start position:0%
+category specific shocks esing the
+magnitude and doing a careful job of
+
+ align:start position:0%
+magnitude and doing a careful job of
+ 
+
+ align:start position:0%
+magnitude and doing a careful job of
+thinking about the zeros they may be
+
+ align:start position:0%
+thinking about the zeros they may be
+ 
+
+ align:start position:0%
+thinking about the zeros they may be
+sort of avoiding overstating how big all
+
+ align:start position:0%
+sort of avoiding overstating how big all
+ 
+
+ align:start position:0%
+sort of avoiding overstating how big all
+these Epsilon IGS are and all the
+
+ align:start position:0%
+these Epsilon IGS are and all the
+ 
+
+ align:start position:0%
+these Epsilon IGS are and all the
+Surplus we're getting from all these new
+
+ align:start position:0%
+Surplus we're getting from all these new
+ 
+
+ align:start position:0%
+Surplus we're getting from all these new
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+products um and I guess one other paper
+
+ align:start position:0%
+products um and I guess one other paper
+ 
+
+ align:start position:0%
+products um and I guess one other paper
+I thought I'd mention one other thing I
+
+ align:start position:0%
+I thought I'd mention one other thing I
+ 
+
+ align:start position:0%
+I thought I'd mention one other thing I
+thought i' mentioned in the paper is
+
+ align:start position:0%
+thought i' mentioned in the paper is
+ 
+
+ align:start position:0%
+thought i' mentioned in the paper is
+that um they do also you know they know
+
+ align:start position:0%
+that um they do also you know they know
+ 
+
+ align:start position:0%
+that um they do also you know they know
+that Macy's and PS carry different shoes
+
+ align:start position:0%
+that Macy's and PS carry different shoes
+ 
+
+ align:start position:0%
+that Macy's and PS carry different shoes
+in different stores they ask how
+
+ align:start position:0%
+in different stores they ask how
+ 
+
+ align:start position:0%
+in different stores they ask how
+important is it for stores to tailor
+
+ align:start position:0%
+important is it for stores to tailor
+ 
+
+ align:start position:0%
+important is it for stores to tailor
+their selections and what they find is
+
+ align:start position:0%
+their selections and what they find is
+ 
+
+ align:start position:0%
+their selections and what they find is
+that you know there's a gain that firms
+
+ align:start position:0%
+that you know there's a gain that firms
+ 
+
+ align:start position:0%
+that you know there's a gain that firms
+should do it it's not that large the
+
+ align:start position:0%
+should do it it's not that large the
+ 
+
+ align:start position:0%
+should do it it's not that large the
+gain from customizing stores is
+
+ align:start position:0%
+gain from customizing stores is
+ 
+
+ align:start position:0%
+gain from customizing stores is
+estimated to be about
+
+ align:start position:0%
+estimated to be about
+ 
+
+ align:start position:0%
+estimated to be about
+6% in Revenue so you could just carry
+
+ align:start position:0%
+6% in Revenue so you could just carry
+ 
+
+ align:start position:0%
+6% in Revenue so you could just carry
+all the standard shoes or you could
+
+ align:start position:0%
+all the standard shoes or you could
+ 
+
+ align:start position:0%
+all the standard shoes or you could
+tailor the demand in your city you
+
+ align:start position:0%
+tailor the demand in your city you
+ 
+
+ align:start position:0%
+tailor the demand in your city you
+tailor the man in your city you get like
+
+ align:start position:0%
+tailor the man in your city you get like
+ 
+
+ align:start position:0%
+tailor the man in your city you get like
+6% more profit so you know it seems like
+
+ align:start position:0%
+6% more profit so you know it seems like
+ 
+
+ align:start position:0%
+6% more profit so you know it seems like
+it's worth doing firms should want to do
+
+ align:start position:0%
+it's worth doing firms should want to do
+ 
+
+ align:start position:0%
+it's worth doing firms should want to do
+this especially if they have thin profit
+
+ align:start position:0%
+this especially if they have thin profit
+ 
+
+ align:start position:0%
+this especially if they have thin profit
+margins but it's only it's boundedly
+
+ align:start position:0%
+margins but it's only it's boundedly
+ 
+
+ align:start position:0%
+margins but it's only it's boundedly
+tailoring is is boundedly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+profitable okay yeah was this paper like
+
+ align:start position:0%
+profitable okay yeah was this paper like
+ 
+
+ align:start position:0%
+profitable okay yeah was this paper like
+actually response to Amazon paper or was
+
+ align:start position:0%
+actually response to Amazon paper or was
+ 
+
+ align:start position:0%
+actually response to Amazon paper or was
+it just kind of dint because couldn't
+
+ align:start position:0%
+it just kind of dint because couldn't
+ 
+
+ align:start position:0%
+it just kind of dint because couldn't
+you just do the same exercise they did
+
+ align:start position:0%
+you just do the same exercise they did
+ 
+
+ align:start position:0%
+you just do the same exercise they did
+the Amazon paper both
+
+ align:start position:0%
+the Amazon paper both
+ 
+
+ align:start position:0%
+the Amazon paper both
+shoes change yeah so certainly they
+
+ align:start position:0%
+shoes change yeah so certainly they
+ 
+
+ align:start position:0%
+shoes change yeah so certainly they
+could have um
+
+ align:start position:0%
+could have um
+ 
+
+ align:start position:0%
+could have um
+uh you know so they actually have I
+
+ align:start position:0%
+uh you know so they actually have I
+ 
+
+ align:start position:0%
+uh you know so they actually have I
+don't know they're several different
+
+ align:start position:0%
+don't know they're several different
+ 
+
+ align:start position:0%
+don't know they're several different
+they do several different calculations
+
+ align:start position:0%
+they do several different calculations
+ 
+
+ align:start position:0%
+they do several different calculations
+in the paper like suppose we estimate
+
+ align:start position:0%
+in the paper like suppose we estimate
+ 
+
+ align:start position:0%
+in the paper like suppose we estimate
+demand this way suppose we estimate
+
+ align:start position:0%
+demand this way suppose we estimate
+ 
+
+ align:start position:0%
+demand this way suppose we estimate
+demand this way suppose we estimate
+
+ align:start position:0%
+demand this way suppose we estimate
+ 
+
+ align:start position:0%
+demand this way suppose we estimate
+demand this way you know in in some
+
+ align:start position:0%
+demand this way you know in in some
+ 
+
+ align:start position:0%
+demand this way you know in in some
+sense doing demand worse and worse and
+
+ align:start position:0%
+sense doing demand worse and worse and
+ 
+
+ align:start position:0%
+sense doing demand worse and worse and
+wor doing worse and worse demand
+
+ align:start position:0%
+wor doing worse and worse demand
+ 
+
+ align:start position:0%
+wor doing worse and worse demand
+estimation and the they do present
+
+ align:start position:0%
+estimation and the they do present
+ 
+
+ align:start position:0%
+estimation and the they do present
+several things if You' done this
+
+ align:start position:0%
+several things if You' done this
+ 
+
+ align:start position:0%
+several things if You' done this
+estimate instead you'd get numbers that
+
+ align:start position:0%
+estimate instead you'd get numbers that
+ 
+
+ align:start position:0%
+estimate instead you'd get numbers that
+are two times as big if you do these
+
+ align:start position:0%
+are two times as big if you do these
+ 
+
+ align:start position:0%
+are two times as big if you do these
+estimates instead you get things that
+
+ align:start position:0%
+estimates instead you get things that
+ 
+
+ align:start position:0%
+estimates instead you get things that
+are five times as big so they do get um
+
+ align:start position:0%
+are five times as big so they do get um
+ 
+
+ align:start position:0%
+are five times as big so they do get um
+you know it it's it's not exactly the
+
+ align:start position:0%
+you know it it's it's not exactly the
+ 
+
+ align:start position:0%
+you know it it's it's not exactly the
+same calculation as the Amazon data but
+
+ align:start position:0%
+same calculation as the Amazon data but
+ 
+
+ align:start position:0%
+same calculation as the Amazon data but
+they do something that's sort of more
+
+ align:start position:0%
+they do something that's sort of more
+ 
+
+ align:start position:0%
+they do something that's sort of more
+like the naive calculations where you
+
+ align:start position:0%
+like the naive calculations where you
+ 
+
+ align:start position:0%
+like the naive calculations where you
+sort of treat everything as National
+
+ align:start position:0%
+sort of treat everything as National
+ 
+
+ align:start position:0%
+sort of treat everything as National
+market shares and use low jit models and
+
+ align:start position:0%
+market shares and use low jit models and
+ 
+
+ align:start position:0%
+market shares and use low jit models and
+show that you can get things many times
+
+ align:start position:0%
+show that you can get things many times
+ 
+
+ align:start position:0%
+show that you can get things many times
+bigger than the estimates they've
+
+ align:start position:0%
+bigger than the estimates they've
+ 
+
+ align:start position:0%
+bigger than the estimates they've
+gotten
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah I think you know these are the
+
+ align:start position:0%
+um yeah I think you know these are the
+ 
+
+ align:start position:0%
+um yeah I think you know these are the
+things that you know obviously you
+
+ align:start position:0%
+things that you know obviously you
+ 
+
+ align:start position:0%
+things that you know obviously you
+couldn't have done with the Amazon data
+
+ align:start position:0%
+couldn't have done with the Amazon data
+ 
+
+ align:start position:0%
+couldn't have done with the Amazon data
+like the the BR off didn't have anything
+
+ align:start position:0%
+like the the BR off didn't have anything
+ 
+
+ align:start position:0%
+like the the BR off didn't have anything
+about what is in local bookstores and
+
+ align:start position:0%
+about what is in local bookstores and
+ 
+
+ align:start position:0%
+about what is in local bookstores and
+how much overlap there is in local books
+
+ align:start position:0%
+how much overlap there is in local books
+ 
+
+ align:start position:0%
+how much overlap there is in local books
+across local bookstores and stuff like
+
+ align:start position:0%
+across local bookstores and stuff like
+ 
+
+ align:start position:0%
+across local bookstores and stuff like
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um but certainly you know paper is very
+
+ align:start position:0%
+um but certainly you know paper is very
+ 
+
+ align:start position:0%
+um but certainly you know paper is very
+much written in in response to
+
+ align:start position:0%
+much written in in response to
+ 
+
+ align:start position:0%
+much written in in response to
+literature saying there are these big
+
+ align:start position:0%
+literature saying there are these big
+ 
+
+ align:start position:0%
+literature saying there are these big
+really big private really big product
+
+ align:start position:0%
+really big private really big product
+ 
+
+ align:start position:0%
+really big private really big product
+variety benefits and and it was you know
+
+ align:start position:0%
+variety benefits and and it was you know
+ 
+
+ align:start position:0%
+variety benefits and and it was you know
+I think it the paper's more about more
+
+ align:start position:0%
+I think it the paper's more about more
+ 
+
+ align:start position:0%
+I think it the paper's more about more
+about the benefits are smaller if
+
+ align:start position:0%
+about the benefits are smaller if
+ 
+
+ align:start position:0%
+about the benefits are smaller if
+because of the variety in retail then
+
+ align:start position:0%
+because of the variety in retail then
+ 
+
+ align:start position:0%
+because of the variety in retail then
+the benefits are smaller if you just do
+
+ align:start position:0%
+the benefits are smaller if you just do
+ 
+
+ align:start position:0%
+the benefits are smaller if you just do
+the econometrics correctly but I think
+
+ align:start position:0%
+the econometrics correctly but I think
+ 
+
+ align:start position:0%
+the econometrics correctly but I think
+it is about both
+
+ align:start position:0%
+it is about both
+ 
+
+ align:start position:0%
+it is about both
+um okay um so anyway uh final paper I
+
+ align:start position:0%
+um okay um so anyway uh final paper I
+ 
+
+ align:start position:0%
+um okay um so anyway uh final paper I
+want to cover this is a working paper
+
+ align:start position:0%
+want to cover this is a working paper
+ 
+
+ align:start position:0%
+want to cover this is a working paper
+that Sarah and I have um which I guess
+
+ align:start position:0%
+that Sarah and I have um which I guess
+ 
+
+ align:start position:0%
+that Sarah and I have um which I guess
+has you know two different motivations
+
+ align:start position:0%
+has you know two different motivations
+ 
+
+ align:start position:0%
+has you know two different motivations
+you know one is also this is a paper
+
+ align:start position:0%
+you know one is also this is a paper
+ 
+
+ align:start position:0%
+you know one is also this is a paper
+about trying to estimate how big product
+
+ align:start position:0%
+about trying to estimate how big product
+ 
+
+ align:start position:0%
+about trying to estimate how big product
+variety CH benefits are and how big
+
+ align:start position:0%
+variety CH benefits are and how big
+ 
+
+ align:start position:0%
+variety CH benefits are and how big
+product variety benefits are in an area
+
+ align:start position:0%
+product variety benefits are in an area
+ 
+
+ align:start position:0%
+product variety benefits are in an area
+where we think the product variety
+
+ align:start position:0%
+where we think the product variety
+ 
+
+ align:start position:0%
+where we think the product variety
+benefits would be bigger um which is in
+
+ align:start position:0%
+benefits would be bigger um which is in
+ 
+
+ align:start position:0%
+benefits would be bigger um which is in
+used books and then the other is also uh
+
+ align:start position:0%
+used books and then the other is also uh
+ 
+
+ align:start position:0%
+used books and then the other is also uh
+you know some sense you can sort of say
+
+ align:start position:0%
+you know some sense you can sort of say
+ 
+
+ align:start position:0%
+you know some sense you can sort of say
+it as a you know uh Chicago School
+
+ align:start position:0%
+it as a you know uh Chicago School
+ 
+
+ align:start position:0%
+it as a you know uh Chicago School
+critique of our search and obfuscation
+
+ align:start position:0%
+critique of our search and obfuscation
+ 
+
+ align:start position:0%
+critique of our search and obfuscation
+paper or in the you know search and obus
+
+ align:start position:0%
+paper or in the you know search and obus
+ 
+
+ align:start position:0%
+paper or in the you know search and obus
+paper we argued that you see these sort
+
+ align:start position:0%
+paper we argued that you see these sort
+ 
+
+ align:start position:0%
+paper we argued that you see these sort
+of not super low and dispersed prices
+
+ align:start position:0%
+of not super low and dispersed prices
+ 
+
+ align:start position:0%
+of not super low and dispersed prices
+for computer components because the
+
+ align:start position:0%
+for computer components because the
+ 
+
+ align:start position:0%
+for computer components because the
+firms have an incentive to uh firms have
+
+ align:start position:0%
+firms have an incentive to uh firms have
+ 
+
+ align:start position:0%
+firms have an incentive to uh firms have
+an incentive to sort of obus gate what
+
+ align:start position:0%
+an incentive to sort of obus gate what
+ 
+
+ align:start position:0%
+an incentive to sort of obus gate what
+they're selling the prices at and invent
+
+ align:start position:0%
+they're selling the prices at and invent
+ 
+
+ align:start position:0%
+they're selling the prices at and invent
+these add-ons or invent complicated
+
+ align:start position:0%
+these add-ons or invent complicated
+ 
+
+ align:start position:0%
+these add-ons or invent complicated
+things that raise search costs and keep
+
+ align:start position:0%
+things that raise search costs and keep
+ 
+
+ align:start position:0%
+things that raise search costs and keep
+prices sort of high and disperse if they
+
+ align:start position:0%
+prices sort of high and disperse if they
+ 
+
+ align:start position:0%
+prices sort of high and disperse if they
+are in a search cost model rather than
+
+ align:start position:0%
+are in a search cost model rather than
+ 
+
+ align:start position:0%
+are in a search cost model rather than
+letting perfect competition come out
+
+ align:start position:0%
+letting perfect competition come out
+ 
+
+ align:start position:0%
+letting perfect competition come out
+here um this paper is sort of going to
+
+ align:start position:0%
+here um this paper is sort of going to
+ 
+
+ align:start position:0%
+here um this paper is sort of going to
+provide an alternate explanation for why
+
+ align:start position:0%
+provide an alternate explanation for why
+ 
+
+ align:start position:0%
+provide an alternate explanation for why
+prices can be high and dispersed it's
+
+ align:start position:0%
+prices can be high and dispersed it's
+ 
+
+ align:start position:0%
+prices can be high and dispersed it's
+going to be that um some sense prices
+
+ align:start position:0%
+going to be that um some sense prices
+ 
+
+ align:start position:0%
+going to be that um some sense prices
+are high in dispersed for two different
+
+ align:start position:0%
+are high in dispersed for two different
+ 
+
+ align:start position:0%
+are high in dispersed for two different
+reasons one is prices are high on the
+
+ align:start position:0%
+reasons one is prices are high on the
+ 
+
+ align:start position:0%
+reasons one is prices are high on the
+internet because the internet is so good
+
+ align:start position:0%
+internet because the internet is so good
+ 
+
+ align:start position:0%
+internet because the internet is so good
+at matching products to people and if
+
+ align:start position:0%
+at matching products to people and if
+ 
+
+ align:start position:0%
+at matching products to people and if
+you think about like you know like a
+
+ align:start position:0%
+you think about like you know like a
+ 
+
+ align:start position:0%
+you think about like you know like a
+used book like used book that you had as
+
+ align:start position:0%
+used book like used book that you had as
+ 
+
+ align:start position:0%
+used book like used book that you had as
+a child um you know and then you have
+
+ align:start position:0%
+a child um you know and then you have
+ 
+
+ align:start position:0%
+a child um you know and then you have
+used book as a child you now have a
+
+ align:start position:0%
+used book as a child you now have a
+ 
+
+ align:start position:0%
+used book as a child you now have a
+niece or nephew you want to buy them the
+
+ align:start position:0%
+niece or nephew you want to buy them the
+ 
+
+ align:start position:0%
+niece or nephew you want to buy them the
+same used book you same picture book
+
+ align:start position:0%
+same used book you same picture book
+ 
+
+ align:start position:0%
+same used book you same picture book
+that you remember from when you were a
+
+ align:start position:0%
+that you remember from when you were a
+ 
+
+ align:start position:0%
+that you remember from when you were a
+kid you're willing to pay many dollars
+
+ align:start position:0%
+kid you're willing to pay many dollars
+ 
+
+ align:start position:0%
+kid you're willing to pay many dollars
+for that book there are a million other
+
+ align:start position:0%
+for that book there are a million other
+ 
+
+ align:start position:0%
+for that book there are a million other
+people out there who didn't remember
+
+ align:start position:0%
+people out there who didn't remember
+ 
+
+ align:start position:0%
+people out there who didn't remember
+that book when they were kids there are
+
+ align:start position:0%
+that book when they were kids there are
+ 
+
+ align:start position:0%
+that book when they were kids there are
+probably hundreds of copies of it
+
+ align:start position:0%
+probably hundreds of copies of it
+ 
+
+ align:start position:0%
+probably hundreds of copies of it
+sitting in physical used book stores
+
+ align:start position:0%
+sitting in physical used book stores
+ 
+
+ align:start position:0%
+sitting in physical used book stores
+with 10 cents marked inside the cover
+
+ align:start position:0%
+with 10 cents marked inside the cover
+ 
+
+ align:start position:0%
+with 10 cents marked inside the cover
+that no one is ever buying if we get
+
+ align:start position:0%
+that no one is ever buying if we get
+ 
+
+ align:start position:0%
+that no one is ever buying if we get
+those books in the hands of the right
+
+ align:start position:0%
+those books in the hands of the right
+ 
+
+ align:start position:0%
+those books in the hands of the right
+people the willingness to pay is way way
+
+ align:start position:0%
+people the willingness to pay is way way
+ 
+
+ align:start position:0%
+people the willingness to pay is way way
+higher in fact actually you know we say
+
+ align:start position:0%
+higher in fact actually you know we say
+ 
+
+ align:start position:0%
+higher in fact actually you know we say
+the paper started when um Sarah was
+
+ align:start position:0%
+the paper started when um Sarah was
+ 
+
+ align:start position:0%
+the paper started when um Sarah was
+writing a paper on Pharmaceuticals and
+
+ align:start position:0%
+writing a paper on Pharmaceuticals and
+ 
+
+ align:start position:0%
+writing a paper on Pharmaceuticals and
+needed some
+
+ align:start position:0%
+needed some
+ 
+
+ align:start position:0%
+needed some
+obscure pharmaceutical book that someone
+
+ align:start position:0%
+obscure pharmaceutical book that someone
+ 
+
+ align:start position:0%
+obscure pharmaceutical book that someone
+had written in the 1970s the MIT
+
+ align:start position:0%
+had written in the 1970s the MIT
+ 
+
+ align:start position:0%
+had written in the 1970s the MIT
+libraries didn't carry uh you know uh
+
+ align:start position:0%
+libraries didn't carry uh you know uh
+ 
+
+ align:start position:0%
+libraries didn't carry uh you know uh
+website selling used books online were
+
+ align:start position:0%
+website selling used books online were
+ 
+
+ align:start position:0%
+website selling used books online were
+new she actually went on to uh website
+
+ align:start position:0%
+new she actually went on to uh website
+ 
+
+ align:start position:0%
+new she actually went on to uh website
+selling used books found the book and
+
+ align:start position:0%
+selling used books found the book and
+ 
+
+ align:start position:0%
+selling used books found the book and
+it's like you know wow I can find this
+
+ align:start position:0%
+it's like you know wow I can find this
+ 
+
+ align:start position:0%
+it's like you know wow I can find this
+book it's I've been trying to find this
+
+ align:start position:0%
+book it's I've been trying to find this
+ 
+
+ align:start position:0%
+book it's I've been trying to find this
+it's only $15 I can pay it out of my
+
+ align:start position:0%
+it's only $15 I can pay it out of my
+ 
+
+ align:start position:0%
+it's only $15 I can pay it out of my
+research account I'm thrilled to get it
+
+ align:start position:0%
+research account I'm thrilled to get it
+ 
+
+ align:start position:0%
+research account I'm thrilled to get it
+for 15 instead of 100 gets it and then
+
+ align:start position:0%
+for 15 instead of 100 gets it and then
+ 
+
+ align:start position:0%
+for 15 instead of 100 gets it and then
+sort of got the book in like 25 cents
+
+ align:start position:0%
+sort of got the book in like 25 cents
+ 
+
+ align:start position:0%
+sort of got the book in like 25 cents
+was penciled inside the front cover of
+
+ align:start position:0%
+was penciled inside the front cover of
+ 
+
+ align:start position:0%
+was penciled inside the front cover of
+it and like she you know it been sitting
+
+ align:start position:0%
+it and like she you know it been sitting
+ 
+
+ align:start position:0%
+it and like she you know it been sitting
+in a bookstore in Iowa City since some
+
+ align:start position:0%
+in a bookstore in Iowa City since some
+ 
+
+ align:start position:0%
+in a bookstore in Iowa City since some
+economics professor retired for the last
+
+ align:start position:0%
+economics professor retired for the last
+ 
+
+ align:start position:0%
+economics professor retired for the last
+decade and no one wanted to pay 25 cents
+
+ align:start position:0%
+decade and no one wanted to pay 25 cents
+ 
+
+ align:start position:0%
+decade and no one wanted to pay 25 cents
+for this and she was thrilled to get it
+
+ align:start position:0%
+for this and she was thrilled to get it
+ 
+
+ align:start position:0%
+for this and she was thrilled to get it
+for 15 bucks and realizing that this is
+
+ align:start position:0%
+for 15 bucks and realizing that this is
+ 
+
+ align:start position:0%
+for 15 bucks and realizing that this is
+sort of potential huge increase in
+
+ align:start position:0%
+sort of potential huge increase in
+ 
+
+ align:start position:0%
+sort of potential huge increase in
+social welfare of match quality
+
+ align:start position:0%
+social welfare of match quality
+ 
+
+ align:start position:0%
+social welfare of match quality
+okay anyway so part of what we're doing
+
+ align:start position:0%
+okay anyway so part of what we're doing
+ 
+
+ align:start position:0%
+okay anyway so part of what we're doing
+is sort
+
+ align:start position:0%
+is sort
+ 
+
+ align:start position:0%
+is sort
+of estimate that match quality and then
+
+ align:start position:0%
+of estimate that match quality and then
+ 
+
+ align:start position:0%
+of estimate that match quality and then
+the second thought on the paper is that
+
+ align:start position:0%
+the second thought on the paper is that
+ 
+
+ align:start position:0%
+the second thought on the paper is that
+you know it's it's nice to sort of
+
+ align:start position:0%
+you know it's it's nice to sort of
+ 
+
+ align:start position:0%
+you know it's it's nice to sort of
+explain two things with one story like
+
+ align:start position:0%
+explain two things with one story like
+ 
+
+ align:start position:0%
+explain two things with one story like
+price are high and dispersed because of
+
+ align:start position:0%
+price are high and dispersed because of
+ 
+
+ align:start position:0%
+price are high and dispersed because of
+search cost but we think there are two
+
+ align:start position:0%
+search cost but we think there are two
+ 
+
+ align:start position:0%
+search cost but we think there are two
+stories here price are high because of
+
+ align:start position:0%
+stories here price are high because of
+ 
+
+ align:start position:0%
+stories here price are high because of
+match quality and prices are dispersed
+
+ align:start position:0%
+match quality and prices are dispersed
+ 
+
+ align:start position:0%
+match quality and prices are dispersed
+because some websites are better at
+
+ align:start position:0%
+because some websites are better at
+ 
+
+ align:start position:0%
+because some websites are better at
+selling things than others and the
+
+ align:start position:0%
+selling things than others and the
+ 
+
+ align:start position:0%
+selling things than others and the
+websites that are better at selling
+
+ align:start position:0%
+websites that are better at selling
+ 
+
+ align:start position:0%
+websites that are better at selling
+things are going be able to command much
+
+ align:start position:0%
+things are going be able to command much
+ 
+
+ align:start position:0%
+things are going be able to command much
+higher prices than the ones that have
+
+ align:start position:0%
+higher prices than the ones that have
+ 
+
+ align:start position:0%
+higher prices than the ones that have
+limited uh attention anyway so the what
+
+ align:start position:0%
+limited uh attention anyway so the what
+ 
+
+ align:start position:0%
+limited uh attention anyway so the what
+what does paper do it's sort of a
+
+ align:start position:0%
+what does paper do it's sort of a
+ 
+
+ align:start position:0%
+what does paper do it's sort of a
+three-part paper first it's sort of
+
+ align:start position:0%
+three-part paper first it's sort of
+ 
+
+ align:start position:0%
+three-part paper first it's sort of
+developing uh simple models to basically
+
+ align:start position:0%
+developing uh simple models to basically
+ 
+
+ align:start position:0%
+developing uh simple models to basically
+illustrate the
+
+ align:start position:0%
+illustrate the
+ 
+
+ align:start position:0%
+illustrate the
+ideas you know one and two are really
+
+ align:start position:0%
+ideas you know one and two are really
+ 
+
+ align:start position:0%
+ideas you know one and two are really
+again just you know me always aspiring
+
+ align:start position:0%
+again just you know me always aspiring
+ 
+
+ align:start position:0%
+again just you know me always aspiring
+to be like Hendrick and Porter and
+
+ align:start position:0%
+to be like Hendrick and Porter and
+ 
+
+ align:start position:0%
+to be like Hendrick and Porter and
+having this Theory having predictions of
+
+ align:start position:0%
+having this Theory having predictions of
+ 
+
+ align:start position:0%
+having this Theory having predictions of
+the theory testing the predictions of
+
+ align:start position:0%
+the theory testing the predictions of
+ 
+
+ align:start position:0%
+the theory testing the predictions of
+theory to convince you that it's right
+
+ align:start position:0%
+theory to convince you that it's right
+ 
+
+ align:start position:0%
+theory to convince you that it's right
+and then the back part of the paper is
+
+ align:start position:0%
+and then the back part of the paper is
+ 
+
+ align:start position:0%
+and then the back part of the paper is
+structural estimates to try to say how
+
+ align:start position:0%
+structural estimates to try to say how
+ 
+
+ align:start position:0%
+structural estimates to try to say how
+big are the welfare gains from product
+
+ align:start position:0%
+big are the welfare gains from product
+ 
+
+ align:start position:0%
+big are the welfare gains from product
+from improved accessibility of usth
+
+ align:start position:0%
+from improved accessibility of usth
+ 
+
+ align:start position:0%
+from improved accessibility of usth
+books sold online versus in physical
+
+ align:start position:0%
+books sold online versus in physical
+ 
+
+ align:start position:0%
+books sold online versus in physical
+stor
+
+ align:start position:0%
+stor
+ 
+
+ align:start position:0%
+stor
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so first let me start with the basic
+
+ align:start position:0%
+um so first let me start with the basic
+ 
+
+ align:start position:0%
+um so first let me start with the basic
+Theory and this is a a you know simple
+
+ align:start position:0%
+Theory and this is a a you know simple
+ 
+
+ align:start position:0%
+Theory and this is a a you know simple
+model of dynamic Monopoly pricing of a
+
+ align:start position:0%
+model of dynamic Monopoly pricing of a
+ 
+
+ align:start position:0%
+model of dynamic Monopoly pricing of a
+variety that we don't I guess I never
+
+ align:start position:0%
+variety that we don't I guess I never
+ 
+
+ align:start position:0%
+variety that we don't I guess I never
+covered in the io class um but so
+
+ align:start position:0%
+covered in the io class um but so
+ 
+
+ align:start position:0%
+covered in the io class um but so
+imagine that you have a seller and the
+
+ align:start position:0%
+imagine that you have a seller and the
+ 
+
+ align:start position:0%
+imagine that you have a seller and the
+seller just has one unit to sell there's
+
+ align:start position:0%
+seller just has one unit to sell there's
+ 
+
+ align:start position:0%
+seller just has one unit to sell there's
+no production here so this is a unique
+
+ align:start position:0%
+no production here so this is a unique
+ 
+
+ align:start position:0%
+no production here so this is a unique
+item you're just trying to sell it and
+
+ align:start position:0%
+item you're just trying to sell it and
+ 
+
+ align:start position:0%
+item you're just trying to sell it and
+then you have customers who have values
+
+ align:start position:0%
+then you have customers who have values
+ 
+
+ align:start position:0%
+then you have customers who have values
+VJ drawn from some distribution F and
+
+ align:start position:0%
+VJ drawn from some distribution F and
+ 
+
+ align:start position:0%
+VJ drawn from some distribution F and
+they just arrive at some Plus on rate
+
+ align:start position:0%
+they just arrive at some Plus on rate
+ 
+
+ align:start position:0%
+they just arrive at some Plus on rate
+gamma they walk into your store when
+
+ align:start position:0%
+gamma they walk into your store when
+ 
+
+ align:start position:0%
+gamma they walk into your store when
+they walk into your store and are
+
+ align:start position:0%
+they walk into your store and are
+ 
+
+ align:start position:0%
+they walk into your store and are
+interested in this pharmaceutical
+
+ align:start position:0%
+interested in this pharmaceutical
+ 
+
+ align:start position:0%
+interested in this pharmaceutical
+textbook you have to either sell it to
+
+ align:start position:0%
+textbook you have to either sell it to
+ 
+
+ align:start position:0%
+textbook you have to either sell it to
+them immediately or not at all because
+
+ align:start position:0%
+them immediately or not at all because
+ 
+
+ align:start position:0%
+them immediately or not at all because
+if they you know they walk into your
+
+ align:start position:0%
+if they you know they walk into your
+ 
+
+ align:start position:0%
+if they you know they walk into your
+store they see the book they look at the
+
+ align:start position:0%
+store they see the book they look at the
+ 
+
+ align:start position:0%
+store they see the book they look at the
+price they don't want to buy it they
+
+ align:start position:0%
+price they don't want to buy it they
+ 
+
+ align:start position:0%
+price they don't want to buy it they
+walk out you'll never see them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again how should you set your prices
+
+ align:start position:0%
+again how should you set your prices
+ 
+
+ align:start position:0%
+again how should you set your prices
+well you know the demand from these
+
+ align:start position:0%
+well you know the demand from these
+ 
+
+ align:start position:0%
+well you know the demand from these
+These are onetime consumers who are my
+
+ align:start position:0%
+These are onetime consumers who are my
+ 
+
+ align:start position:0%
+These are onetime consumers who are my
+office so the demand at Price p is just
+
+ align:start position:0%
+office so the demand at Price p is just
+ 
+
+ align:start position:0%
+office so the demand at Price p is just
+1 minus capital F of P the probability
+
+ align:start position:0%
+1 minus capital F of P the probability
+ 
+
+ align:start position:0%
+1 minus capital F of P the probability
+that the consumer's value is above
+
+ align:start position:0%
+that the consumer's value is above
+ 
+
+ align:start position:0%
+that the consumer's value is above
+P so the expected profit is the
+
+ align:start position:0%
+P so the expected profit is the
+ 
+
+ align:start position:0%
+P so the expected profit is the
+expectation at setting a price of p and
+
+ align:start position:0%
+expectation at setting a price of p and
+ 
+
+ align:start position:0%
+expectation at setting a price of p and
+leaving it there is the expectation of p
+
+ align:start position:0%
+leaving it there is the expectation of p
+ 
+
+ align:start position:0%
+leaving it there is the expectation of p
+e to the minus RT where T is the uh
+
+ align:start position:0%
+e to the minus RT where T is the uh
+ 
+
+ align:start position:0%
+e to the minus RT where T is the uh
+random time at which you will sell the
+
+ align:start position:0%
+random time at which you will sell the
+ 
+
+ align:start position:0%
+random time at which you will sell the
+book in this model as long as you set
+
+ align:start position:0%
+book in this model as long as you set
+ 
+
+ align:start position:0%
+book in this model as long as you set
+any P that's less than the upper bound
+
+ align:start position:0%
+any P that's less than the upper bound
+ 
+
+ align:start position:0%
+any P that's less than the upper bound
+of f you'll always sell the book
+
+ align:start position:0%
+of f you'll always sell the book
+ 
+
+ align:start position:0%
+of f you'll always sell the book
+eventually you just may sell it a
+
+ align:start position:0%
+eventually you just may sell it a
+ 
+
+ align:start position:0%
+eventually you just may sell it a
+million years in the future and the Ed
+
+ align:start position:0%
+million years in the future and the Ed
+ 
+
+ align:start position:0%
+million years in the future and the Ed
+RT will eat up all your profits okay so
+
+ align:start position:0%
+RT will eat up all your profits okay so
+ 
+
+ align:start position:0%
+RT will eat up all your profits okay so
+what we're going to do is integrate P
+
+ align:start position:0%
+what we're going to do is integrate P
+ 
+
+ align:start position:0%
+what we're going to do is integrate P
+minus RT times the
+
+ align:start position:0%
+minus RT times the
+ 
+
+ align:start position:0%
+minus RT times the
+density of the probability of selling
+
+ align:start position:0%
+density of the probability of selling
+ 
+
+ align:start position:0%
+density of the probability of selling
+the book at in the interval TT plus
+
+ align:start position:0%
+the book at in the interval TT plus
+ 
+
+ align:start position:0%
+the book at in the interval TT plus
+DT
+
+ align:start position:0%
+DT
+ 
+
+ align:start position:0%
+DT
+um gamma is the Plus on arrival rate
+
+ align:start position:0%
+um gamma is the Plus on arrival rate
+ 
+
+ align:start position:0%
+um gamma is the Plus on arrival rate
+gamma D of p is the Plus on arrival rate
+
+ align:start position:0%
+gamma D of p is the Plus on arrival rate
+ 
+
+ align:start position:0%
+gamma D of p is the Plus on arrival rate
+of people willing to pay at least p and
+
+ align:start position:0%
+of people willing to pay at least p and
+ 
+
+ align:start position:0%
+of people willing to pay at least p and
+so the density of the time you sell it
+
+ align:start position:0%
+so the density of the time you sell it
+ 
+
+ align:start position:0%
+so the density of the time you sell it
+is uh gamma D of p e to minus gamma D of
+
+ align:start position:0%
+is uh gamma D of p e to minus gamma D of
+ 
+
+ align:start position:0%
+is uh gamma D of p e to minus gamma D of
+PT right and you may have seen like if
+
+ align:start position:0%
+PT right and you may have seen like if
+ 
+
+ align:start position:0%
+PT right and you may have seen like if
+you have a Plus on arrival rate gamma
+
+ align:start position:0%
+you have a Plus on arrival rate gamma
+ 
+
+ align:start position:0%
+you have a Plus on arrival rate gamma
+you know the density of arrivals is uh
+
+ align:start position:0%
+you know the density of arrivals is uh
+ 
+
+ align:start position:0%
+you know the density of arrivals is uh
+gamma e minus gamma
+
+ align:start position:0%
+gamma e minus gamma
+ 
+
+ align:start position:0%
+gamma e minus gamma
+T and so the act the arrival rate of
+
+ align:start position:0%
+T and so the act the arrival rate of
+ 
+
+ align:start position:0%
+T and so the act the arrival rate of
+people willing to pay p is this so this
+
+ align:start position:0%
+people willing to pay p is this so this
+ 
+
+ align:start position:0%
+people willing to pay p is this so this
+is the density of the um arrival
+
+ align:start position:0%
+is the density of the um arrival
+ 
+
+ align:start position:0%
+is the density of the um arrival
+distribution and it turns out this is a
+
+ align:start position:0%
+distribution and it turns out this is a
+ 
+
+ align:start position:0%
+distribution and it turns out this is a
+nice well behaved integral and so the uh
+
+ align:start position:0%
+nice well behaved integral and so the uh
+ 
+
+ align:start position:0%
+nice well behaved integral and so the uh
+price is a function of p is this
+
+ align:start position:0%
+price is a function of p is this
+ 
+
+ align:start position:0%
+price is a function of p is this
+expression it's p * gamma D of p over R
+
+ align:start position:0%
+expression it's p * gamma D of p over R
+ 
+
+ align:start position:0%
+expression it's p * gamma D of p over R
+plus gamma D of p and so you know as
+
+ align:start position:0%
+plus gamma D of p and so you know as
+ 
+
+ align:start position:0%
+plus gamma D of p and so you know as
+gamma D of p goes to
+
+ align:start position:0%
+gamma D of p goes to
+ 
+
+ align:start position:0%
+gamma D of p goes to
+one you're selling it almost instantly
+
+ align:start position:0%
+one you're selling it almost instantly
+ 
+
+ align:start position:0%
+one you're selling it almost instantly
+and you and your profit is p uh as gamma
+
+ align:start position:0%
+and you and your profit is p uh as gamma
+ 
+
+ align:start position:0%
+and you and your profit is p uh as gamma
+D of p goes to zero the
+
+ align:start position:0%
+D of p goes to zero the
+ 
+
+ align:start position:0%
+D of p goes to zero the
+r over outweighs the gamma D of p and
+
+ align:start position:0%
+r over outweighs the gamma D of p and
+ 
+
+ align:start position:0%
+r over outweighs the gamma D of p and
+you basically are getting something
+
+ align:start position:0%
+you basically are getting something
+ 
+
+ align:start position:0%
+you basically are getting something
+that's going towards zero U because just
+
+ align:start position:0%
+that's going towards zero U because just
+ 
+
+ align:start position:0%
+that's going towards zero U because just
+this is the discounting and this is the
+
+ align:start position:0%
+this is the discounting and this is the
+ 
+
+ align:start position:0%
+this is the discounting and this is the
+price that would you sell
+
+ align:start position:0%
+price that would you sell
+ 
+
+ align:start position:0%
+price that would you sell
+it and so we you know we can think of
+
+ align:start position:0%
+it and so we you know we can think of
+ 
+
+ align:start position:0%
+it and so we you know we can think of
+Monopoly pricing in two different ways
+
+ align:start position:0%
+Monopoly pricing in two different ways
+ 
+
+ align:start position:0%
+Monopoly pricing in two different ways
+one way to think about it is just the
+
+ align:start position:0%
+one way to think about it is just the
+ 
+
+ align:start position:0%
+one way to think about it is just the
+Monopoly price is the maximizer of this
+
+ align:start position:0%
+Monopoly price is the maximizer of this
+ 
+
+ align:start position:0%
+Monopoly price is the maximizer of this
+expression second way to think about is
+
+ align:start position:0%
+expression second way to think about is
+ 
+
+ align:start position:0%
+expression second way to think about is
+like a dynamic programming
+
+ align:start position:0%
+like a dynamic programming
+ 
+
+ align:start position:0%
+like a dynamic programming
+approach this good doesn't have any
+
+ align:start position:0%
+approach this good doesn't have any
+ 
+
+ align:start position:0%
+approach this good doesn't have any
+production cost but it has an
+
+ align:start position:0%
+production cost but it has an
+ 
+
+ align:start position:0%
+production cost but it has an
+opportunity cost because you can only
+
+ align:start position:0%
+opportunity cost because you can only
+ 
+
+ align:start position:0%
+opportunity cost because you can only
+sell it once and so if Pi
+
+ align:start position:0%
+sell it once and so if Pi
+ 
+
+ align:start position:0%
+sell it once and so if Pi
+star is your equilibrium expected profit
+
+ align:start position:0%
+star is your equilibrium expected profit
+ 
+
+ align:start position:0%
+star is your equilibrium expected profit
+from one unit of this good you're
+
+ align:start position:0%
+from one unit of this good you're
+ 
+
+ align:start position:0%
+from one unit of this good you're
+thinking about someone's in my store now
+
+ align:start position:0%
+thinking about someone's in my store now
+ 
+
+ align:start position:0%
+thinking about someone's in my store now
+what price should I quote
+
+ align:start position:0%
+what price should I quote
+ 
+
+ align:start position:0%
+what price should I quote
+them what I want to do is maximize P
+
+ align:start position:0%
+them what I want to do is maximize P
+ 
+
+ align:start position:0%
+them what I want to do is maximize P
+minus Pi star D of P I just I'm
+
+ align:start position:0%
+minus Pi star D of P I just I'm
+ 
+
+ align:start position:0%
+minus Pi star D of P I just I'm
+maximizing price minus opportunity cost
+
+ align:start position:0%
+maximizing price minus opportunity cost
+ 
+
+ align:start position:0%
+maximizing price minus opportunity cost
+times the demand and so another way to
+
+ align:start position:0%
+times the demand and so another way to
+ 
+
+ align:start position:0%
+times the demand and so another way to
+think about it is that pm has to solve
+
+ align:start position:0%
+think about it is that pm has to solve
+ 
+
+ align:start position:0%
+think about it is that pm has to solve
+this where Pi star is pi of
+
+ align:start position:0%
+this where Pi star is pi of
+ 
+
+ align:start position:0%
+this where Pi star is pi of
+PM okay so it's two different ways to
+
+ align:start position:0%
+PM okay so it's two different ways to
+ 
+
+ align:start position:0%
+PM okay so it's two different ways to
+think about Monopoly pricing for a
+
+ align:start position:0%
+think about Monopoly pricing for a
+ 
+
+ align:start position:0%
+think about Monopoly pricing for a
+unique item when you have customer rals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh observations from this Monopoly
+
+ align:start position:0%
+um uh observations from this Monopoly
+ 
+
+ align:start position:0%
+um uh observations from this Monopoly
+pricing model uh Monopoly price is
+
+ align:start position:0%
+pricing model uh Monopoly price is
+ 
+
+ align:start position:0%
+pricing model uh Monopoly price is
+increasing in the customer arrival rate
+
+ align:start position:0%
+increasing in the customer arrival rate
+ 
+
+ align:start position:0%
+increasing in the customer arrival rate
+right why is it increase in customer
+
+ align:start position:0%
+right why is it increase in customer
+ 
+
+ align:start position:0%
+right why is it increase in customer
+arrival rate because the higher is the
+
+ align:start position:0%
+arrival rate because the higher is the
+ 
+
+ align:start position:0%
+arrival rate because the higher is the
+customer arrival rate the higher is your
+
+ align:start position:0%
+customer arrival rate the higher is your
+ 
+
+ align:start position:0%
+customer arrival rate the higher is your
+opportunity cost um this is again a
+
+ align:start position:0%
+opportunity cost um this is again a
+ 
+
+ align:start position:0%
+opportunity cost um this is again a
+14121 exam standard exam question you
+
+ align:start position:0%
+14121 exam standard exam question you
+ 
+
+ align:start position:0%
+14121 exam standard exam question you
+know your Monopoly price is increasing
+
+ align:start position:0%
+know your Monopoly price is increasing
+ 
+
+ align:start position:0%
+know your Monopoly price is increasing
+in your cost um no full stop because of
+
+ align:start position:0%
+in your cost um no full stop because of
+ 
+
+ align:start position:0%
+in your cost um no full stop because of
+this function has increasing differences
+
+ align:start position:0%
+this function has increasing differences
+ 
+
+ align:start position:0%
+this function has increasing differences
+so Monopoly price is increasing
+
+ align:start position:0%
+so Monopoly price is increasing
+ 
+
+ align:start position:0%
+so Monopoly price is increasing
+opportunity cost therefore Monopoly
+
+ align:start position:0%
+opportunity cost therefore Monopoly
+ 
+
+ align:start position:0%
+opportunity cost therefore Monopoly
+price Dynamic Monopoly price increases
+
+ align:start position:0%
+price Dynamic Monopoly price increases
+ 
+
+ align:start position:0%
+price Dynamic Monopoly price increases
+in arrival rate because arrival rate
+
+ align:start position:0%
+in arrival rate because arrival rate
+ 
+
+ align:start position:0%
+in arrival rate because arrival rate
+increases your opportunity set
+
+ align:start position:0%
+increases your opportunity set
+ 
+
+ align:start position:0%
+increases your opportunity set
+opportunity cost goes up um so anyway if
+
+ align:start position:0%
+opportunity cost goes up um so anyway if
+ 
+
+ align:start position:0%
+opportunity cost goes up um so anyway if
+consumers start to arrive at higher
+
+ align:start position:0%
+consumers start to arrive at higher
+ 
+
+ align:start position:0%
+consumers start to arrive at higher
+rates online than they did in physical
+
+ align:start position:0%
+rates online than they did in physical
+ 
+
+ align:start position:0%
+rates online than they did in physical
+stores you're going to get higher prices
+
+ align:start position:0%
+stores you're going to get higher prices
+ 
+
+ align:start position:0%
+stores you're going to get higher prices
+and if there's a rival rate heterog and
+
+ align:start position:0%
+and if there's a rival rate heterog and
+ 
+
+ align:start position:0%
+and if there's a rival rate heterog and
+80 across online stores that's going to
+
+ align:start position:0%
+80 across online stores that's going to
+ 
+
+ align:start position:0%
+80 across online stores that's going to
+lead to price dispersion and stores that
+
+ align:start position:0%
+lead to price dispersion and stores that
+ 
+
+ align:start position:0%
+lead to price dispersion and stores that
+have are frequently visited by online
+
+ align:start position:0%
+have are frequently visited by online
+ 
+
+ align:start position:0%
+have are frequently visited by online
+consumers are going to be able to set
+
+ align:start position:0%
+consumers are going to be able to set
+ 
+
+ align:start position:0%
+consumers are going to be able to set
+higher prices because they're more
+
+ align:start position:0%
+higher prices because they're more
+ 
+
+ align:start position:0%
+higher prices because they're more
+patient those that have fewer visitors
+
+ align:start position:0%
+patient those that have fewer visitors
+ 
+
+ align:start position:0%
+patient those that have fewer visitors
+are going to set lower
+
+ align:start position:0%
+are going to set lower
+ 
+
+ align:start position:0%
+are going to set lower
+prices um how sensitive prices are to
+
+ align:start position:0%
+prices um how sensitive prices are to
+ 
+
+ align:start position:0%
+prices um how sensitive prices are to
+arrival rates depend on the thickness of
+
+ align:start position:0%
+arrival rates depend on the thickness of
+ 
+
+ align:start position:0%
+arrival rates depend on the thickness of
+the upper tail
+
+ align:start position:0%
+the upper tail
+ 
+
+ align:start position:0%
+the upper tail
+um if you have an extremely thick tail
+
+ align:start position:0%
+um if you have an extremely thick tail
+ 
+
+ align:start position:0%
+um if you have an extremely thick tail
+distribution like uh a constant times P
+
+ align:start position:0%
+distribution like uh a constant times P
+ 
+
+ align:start position:0%
+distribution like uh a constant times P
+the minus one then the Monopoly price
+
+ align:start position:0%
+the minus one then the Monopoly price
+ 
+
+ align:start position:0%
+the minus one then the Monopoly price
+increases almost linearly in arrival
+
+ align:start position:0%
+increases almost linearly in arrival
+ 
+
+ align:start position:0%
+increases almost linearly in arrival
+rates uh if you have a very thin tail
+
+ align:start position:0%
+rates uh if you have a very thin tail
+ 
+
+ align:start position:0%
+rates uh if you have a very thin tail
+distribution with a greater than one you
+
+ align:start position:0%
+distribution with a greater than one you
+ 
+
+ align:start position:0%
+distribution with a greater than one you
+know things increase more slowly with
+
+ align:start position:0%
+know things increase more slowly with
+ 
+
+ align:start position:0%
+know things increase more slowly with
+with with arrival rates um and then with
+
+ align:start position:0%
+with with arrival rates um and then with
+ 
+
+ align:start position:0%
+with with arrival rates um and then with
+if demand has this constant elasticity
+
+ align:start position:0%
+if demand has this constant elasticity
+ 
+
+ align:start position:0%
+if demand has this constant elasticity
+form uh like this then you get this very
+
+ align:start position:0%
+form uh like this then you get this very
+ 
+
+ align:start position:0%
+form uh like this then you get this very
+uh unusual theorem so the theorem is you
+
+ align:start position:0%
+uh unusual theorem so the theorem is you
+ 
+
+ align:start position:0%
+uh unusual theorem so the theorem is you
+know supposed the distribution of
+
+ align:start position:0%
+know supposed the distribution of
+ 
+
+ align:start position:0%
+know supposed the distribution of
+consumer valuations is such that demand
+
+ align:start position:0%
+consumer valuations is such that demand
+ 
+
+ align:start position:0%
+consumer valuations is such that demand
+has a truncated constant elasticity form
+
+ align:start position:0%
+has a truncated constant elasticity form
+ 
+
+ align:start position:0%
+has a truncated constant elasticity form
+suppose the Monopoly price is not at the
+
+ align:start position:0%
+suppose the Monopoly price is not at the
+ 
+
+ align:start position:0%
+suppose the Monopoly price is not at the
+Kink of this demand curve at one but
+
+ align:start position:0%
+Kink of this demand curve at one but
+ 
+
+ align:start position:0%
+Kink of this demand curve at one but
+it's on the sort of downward sloping
+
+ align:start position:0%
+it's on the sort of downward sloping
+ 
+
+ align:start position:0%
+it's on the sort of downward sloping
+part uh then the Monopoly price
+
+ align:start position:0%
+part uh then the Monopoly price
+ 
+
+ align:start position:0%
+part uh then the Monopoly price
+maximized is social welfare and social
+
+ align:start position:0%
+maximized is social welfare and social
+ 
+
+ align:start position:0%
+maximized is social welfare and social
+welfare is the price numer just
+
+ align:start position:0%
+welfare is the price numer just
+ 
+
+ align:start position:0%
+welfare is the price numer just
+numerically like I want to say what's
+
+ align:start position:0%
+numerically like I want to say what's
+ 
+
+ align:start position:0%
+numerically like I want to say what's
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+expected producer Surplus plus consumer
+
+ align:start position:0%
+expected producer Surplus plus consumer
+ 
+
+ align:start position:0%
+expected producer Surplus plus consumer
+surplus from selling this book the
+
+ align:start position:0%
+surplus from selling this book the
+ 
+
+ align:start position:0%
+surplus from selling this book the
+answer is if that book is being sold for
+
+ align:start position:0%
+answer is if that book is being sold for
+ 
+
+ align:start position:0%
+answer is if that book is being sold for
+$12 the answer expected welfare is $12
+
+ align:start position:0%
+$12 the answer expected welfare is $12
+ 
+
+ align:start position:0%
+$12 the answer expected welfare is $12
+so in some sense the like it's the most
+
+ align:start position:0%
+so in some sense the like it's the most
+ 
+
+ align:start position:0%
+so in some sense the like it's the most
+powerful structural estimation theorem
+
+ align:start position:0%
+powerful structural estimation theorem
+ 
+
+ align:start position:0%
+powerful structural estimation theorem
+of all time saying if you want to
+
+ align:start position:0%
+of all time saying if you want to
+ 
+
+ align:start position:0%
+of all time saying if you want to
+estimate the social welfare from Dynamic
+
+ align:start position:0%
+estimate the social welfare from Dynamic
+ 
+
+ align:start position:0%
+estimate the social welfare from Dynamic
+sales you just write down the price you
+
+ align:start position:0%
+sales you just write down the price you
+ 
+
+ align:start position:0%
+sales you just write down the price you
+don't need to compute the demand
+
+ align:start position:0%
+don't need to compute the demand
+ 
+
+ align:start position:0%
+don't need to compute the demand
+elasticities you don't need to out
+
+ align:start position:0%
+elasticities you don't need to out
+ 
+
+ align:start position:0%
+elasticities you don't need to out
+consumer surplus nothing you just write
+
+ align:start position:0%
+consumer surplus nothing you just write
+ 
+
+ align:start position:0%
+consumer surplus nothing you just write
+down the price and that is the welfare
+
+ align:start position:0%
+down the price and that is the welfare
+ 
+
+ align:start position:0%
+down the price and that is the welfare
+uh and then there's also this optimality
+
+ align:start position:0%
+uh and then there's also this optimality
+ 
+
+ align:start position:0%
+uh and then there's also this optimality
+theorem that there's no Monopoly
+
+ align:start position:0%
+theorem that there's no Monopoly
+ 
+
+ align:start position:0%
+theorem that there's no Monopoly
+Distortion um and you know so like why
+
+ align:start position:0%
+Distortion um and you know so like why
+ 
+
+ align:start position:0%
+Distortion um and you know so like why
+does this work
+
+ align:start position:0%
+does this work
+ 
+
+ align:start position:0%
+does this work
+out you know obviously the max Monopoly
+
+ align:start position:0%
+out you know obviously the max Monopoly
+ 
+
+ align:start position:0%
+out you know obviously the max Monopoly
+price
+
+ align:start position:0%
+price
+ 
+
+ align:start position:0%
+price
+maximizes uh Monopoly price
+
+ align:start position:0%
+maximizes uh Monopoly price
+ 
+
+ align:start position:0%
+maximizes uh Monopoly price
+maximizes monopolis
+
+ align:start position:0%
+maximizes monopolis
+ 
+
+ align:start position:0%
+maximizes monopolis
+profits um but what is consumer surplus
+
+ align:start position:0%
+profits um but what is consumer surplus
+ 
+
+ align:start position:0%
+profits um but what is consumer surplus
+if so if I have this distribution of
+
+ align:start position:0%
+if so if I have this distribution of
+ 
+
+ align:start position:0%
+if so if I have this distribution of
+consumer valuations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so I have this distribution of
+
+ align:start position:0%
+right so I have this distribution of
+ 
+
+ align:start position:0%
+right so I have this distribution of
+consumer valuations F of
+
+ align:start position:0%
+consumer valuations F of
+ 
+
+ align:start position:0%
+consumer valuations F of
+V uh and imagine it look something like
+
+ align:start position:0%
+V uh and imagine it look something like
+ 
+
+ align:start position:0%
+V uh and imagine it look something like
+that and suppose I set some price
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PM okay um when I sell the good there's
+
+ align:start position:0%
+PM okay um when I sell the good there's
+ 
+
+ align:start position:0%
+PM okay um when I sell the good there's
+some consumer
+
+ align:start position:0%
+some consumer
+ 
+
+ align:start position:0%
+some consumer
+surplus what's the consumer surplus you
+
+ align:start position:0%
+surplus what's the consumer surplus you
+ 
+
+ align:start position:0%
+surplus what's the consumer surplus you
+know it that's the expectation of V
+
+ align:start position:0%
+know it that's the expectation of V
+ 
+
+ align:start position:0%
+know it that's the expectation of V
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+PM conditional on V greater than pm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how does that vary with the Monopoly
+
+ align:start position:0%
+how does that vary with the Monopoly
+ 
+
+ align:start position:0%
+how does that vary with the Monopoly
+price okay like you know in a linear
+
+ align:start position:0%
+price okay like you know in a linear
+ 
+
+ align:start position:0%
+price okay like you know in a linear
+demand
+
+ align:start position:0%
+demand
+ 
+
+ align:start position:0%
+demand
+curve you know in a linear demand curve
+
+ align:start position:0%
+curve you know in a linear demand curve
+ 
+
+ align:start position:0%
+curve you know in a linear demand curve
+as as I set the price really high you
+
+ align:start position:0%
+as as I set the price really high you
+ 
+
+ align:start position:0%
+as as I set the price really high you
+know the expected value conditional
+
+ align:start position:0%
+know the expected value conditional
+ 
+
+ align:start position:0%
+know the expected value conditional
+being bigger than this is almost is
+
+ align:start position:0%
+being bigger than this is almost is
+ 
+
+ align:start position:0%
+being bigger than this is almost is
+almost nothing and so consumer surplus
+
+ align:start position:0%
+almost nothing and so consumer surplus
+ 
+
+ align:start position:0%
+almost nothing and so consumer surplus
+drops substantially with the Monopoly
+
+ align:start position:0%
+drops substantially with the Monopoly
+ 
+
+ align:start position:0%
+drops substantially with the Monopoly
+price uh but in a constant elasticity
+
+ align:start position:0%
+price uh but in a constant elasticity
+ 
+
+ align:start position:0%
+price uh but in a constant elasticity
+model the expected value of V minus pm
+
+ align:start position:0%
+model the expected value of V minus pm
+ 
+
+ align:start position:0%
+model the expected value of V minus pm
+conditional on V being bigger than PM is
+
+ align:start position:0%
+conditional on V being bigger than PM is
+ 
+
+ align:start position:0%
+conditional on V being bigger than PM is
+proportional to to
+
+ align:start position:0%
+proportional to to
+ 
+
+ align:start position:0%
+proportional to to
+PM so in a constant elasticity demand
+
+ align:start position:0%
+PM so in a constant elasticity demand
+ 
+
+ align:start position:0%
+PM so in a constant elasticity demand
+curve consumer surplus is proportional
+
+ align:start position:0%
+curve consumer surplus is proportional
+ 
+
+ align:start position:0%
+curve consumer surplus is proportional
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+price so if you set a really really high
+
+ align:start position:0%
+price so if you set a really really high
+ 
+
+ align:start position:0%
+price so if you set a really really high
+price you don't sell for a very long
+
+ align:start position:0%
+price you don't sell for a very long
+ 
+
+ align:start position:0%
+price you don't sell for a very long
+time and so the P to the minus RT part
+
+ align:start position:0%
+time and so the P to the minus RT part
+ 
+
+ align:start position:0%
+time and so the P to the minus RT part
+gets really small but when you do sell
+
+ align:start position:0%
+gets really small but when you do sell
+ 
+
+ align:start position:0%
+gets really small but when you do sell
+it the person because they willing to
+
+ align:start position:0%
+it the person because they willing to
+ 
+
+ align:start position:0%
+it the person because they willing to
+pay a million dollars for this book
+
+ align:start position:0%
+pay a million dollars for this book
+ 
+
+ align:start position:0%
+pay a million dollars for this book
+their expected Surplus is also on your
+
+ align:start position:0%
+their expected Surplus is also on your
+ 
+
+ align:start position:0%
+their expected Surplus is also on your
+order of a million
+
+ align:start position:0%
+order of a million
+ 
+
+ align:start position:0%
+order of a million
+dollars and so with constant elasticity
+
+ align:start position:0%
+dollars and so with constant elasticity
+ 
+
+ align:start position:0%
+dollars and so with constant elasticity
+demand the consumer surplus is just
+
+ align:start position:0%
+demand the consumer surplus is just
+ 
+
+ align:start position:0%
+demand the consumer surplus is just
+always proportional to the price being
+
+ align:start position:0%
+always proportional to the price being
+ 
+
+ align:start position:0%
+always proportional to the price being
+paid expected proportional to price
+
+ align:start position:0%
+paid expected proportional to price
+ 
+
+ align:start position:0%
+paid expected proportional to price
+therefore by maximizing expected price
+
+ align:start position:0%
+therefore by maximizing expected price
+ 
+
+ align:start position:0%
+therefore by maximizing expected price
+paid discount expected price you're also
+
+ align:start position:0%
+paid discount expected price you're also
+ 
+
+ align:start position:0%
+paid discount expected price you're also
+maximizing discounted expected social
+
+ align:start position:0%
+maximizing discounted expected social
+ 
+
+ align:start position:0%
+maximizing discounted expected social
+welfare um so you know I view this as
+
+ align:start position:0%
+welfare um so you know I view this as
+ 
+
+ align:start position:0%
+welfare um so you know I view this as
+more a I mean it's a it's a neat
+
+ align:start position:0%
+more a I mean it's a it's a neat
+ 
+
+ align:start position:0%
+more a I mean it's a it's a neat
+estimation trick or something but I view
+
+ align:start position:0%
+estimation trick or something but I view
+ 
+
+ align:start position:0%
+estimation trick or something but I view
+it more as a cautionary Tale the
+
+ align:start position:0%
+it more as a cautionary Tale the
+ 
+
+ align:start position:0%
+it more as a cautionary Tale the
+cautionary tale being if in this demand
+
+ align:start position:0%
+cautionary tale being if in this demand
+ 
+
+ align:start position:0%
+cautionary tale being if in this demand
+estimation you can't tell that the
+
+ align:start position:0%
+estimation you can't tell that the
+ 
+
+ align:start position:0%
+estimation you can't tell that the
+demand apart from if you can't tell the
+
+ align:start position:0%
+demand apart from if you can't tell the
+ 
+
+ align:start position:0%
+demand apart from if you can't tell the
+demand curve valuation curve apart from
+
+ align:start position:0%
+demand curve valuation curve apart from
+ 
+
+ align:start position:0%
+demand curve valuation curve apart from
+a constant elasticity demand curve then
+
+ align:start position:0%
+a constant elasticity demand curve then
+ 
+
+ align:start position:0%
+a constant elasticity demand curve then
+you're going to end up finding that the
+
+ align:start position:0%
+you're going to end up finding that the
+ 
+
+ align:start position:0%
+you're going to end up finding that the
+expected welfare is the price regardless
+
+ align:start position:0%
+expected welfare is the price regardless
+ 
+
+ align:start position:0%
+expected welfare is the price regardless
+of what the demand elasticities and
+
+ align:start position:0%
+of what the demand elasticities and
+ 
+
+ align:start position:0%
+of what the demand elasticities and
+everything else
+
+ align:start position:0%
+everything else
+ 
+
+ align:start position:0%
+everything else
+are so it it is you know can be a first
+
+ align:start position:0%
+are so it it is you know can be a first
+ 
+
+ align:start position:0%
+are so it it is you know can be a first
+approximation and it's also if you want
+
+ align:start position:0%
+approximation and it's also if you want
+ 
+
+ align:start position:0%
+approximation and it's also if you want
+a better approximation you need to be
+
+ align:start position:0%
+a better approximation you need to be
+ 
+
+ align:start position:0%
+a better approximation you need to be
+able to tell the shape of this curve
+
+ align:start position:0%
+able to tell the shape of this curve
+ 
+
+ align:start position:0%
+able to tell the shape of this curve
+apart from a constant elasticity one
+
+ align:start position:0%
+apart from a constant elasticity one
+ 
+
+ align:start position:0%
+apart from a constant elasticity one
+which is going to be hard to do in the
+
+ align:start position:0%
+which is going to be hard to do in the
+ 
+
+ align:start position:0%
+which is going to be hard to do in the
+upper tail because you don't see things
+
+ align:start position:0%
+upper tail because you don't see things
+ 
+
+ align:start position:0%
+upper tail because you don't see things
+in the upper tail very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+often um okay so now let me think about
+
+ align:start position:0%
+often um okay so now let me think about
+ 
+
+ align:start position:0%
+often um okay so now let me think about
+that's a monopoly model you again think
+
+ align:start position:0%
+that's a monopoly model you again think
+ 
+
+ align:start position:0%
+that's a monopoly model you again think
+about an oligopoly model so you have two
+
+ align:start position:0%
+about an oligopoly model so you have two
+ 
+
+ align:start position:0%
+about an oligopoly model so you have two
+types of consumers you have some people
+
+ align:start position:0%
+types of consumers you have some people
+ 
+
+ align:start position:0%
+types of consumers you have some people
+who just go stra like you know there's
+
+ align:start position:0%
+who just go stra like you know there's
+ 
+
+ align:start position:0%
+who just go stra like you know there's
+some they know some online bookstore
+
+ align:start position:0%
+some they know some online bookstore
+ 
+
+ align:start position:0%
+some they know some online bookstore
+like Better World Books or pows books
+
+ align:start position:0%
+like Better World Books or pows books
+ 
+
+ align:start position:0%
+like Better World Books or pows books
+and they just go directly to Powells
+
+ align:start position:0%
+and they just go directly to Powells
+ 
+
+ align:start position:0%
+and they just go directly to Powells
+books.com uh look for a book there
+
+ align:start position:0%
+books.com uh look for a book there
+ 
+
+ align:start position:0%
+books.com uh look for a book there
+uh we're going to have some consumers
+
+ align:start position:0%
+uh we're going to have some consumers
+ 
+
+ align:start position:0%
+uh we're going to have some consumers
+who sort of have this that or or you do
+
+ align:start position:0%
+who sort of have this that or or you do
+ 
+
+ align:start position:0%
+who sort of have this that or or you do
+a Google search Google search reveals
+
+ align:start position:0%
+a Google search Google search reveals
+ 
+
+ align:start position:0%
+a Google search Google search reveals
+the name of One Bookstore for the title
+
+ align:start position:0%
+the name of One Bookstore for the title
+ 
+
+ align:start position:0%
+the name of One Bookstore for the title
+you want you just go to that bookstore
+
+ align:start position:0%
+you want you just go to that bookstore
+ 
+
+ align:start position:0%
+you want you just go to that bookstore
+and you buy from the first the one
+
+ align:start position:0%
+and you buy from the first the one
+ 
+
+ align:start position:0%
+and you buy from the first the one
+that's highest ranked on Google okay and
+
+ align:start position:0%
+that's highest ranked on Google okay and
+ 
+
+ align:start position:0%
+that's highest ranked on Google okay and
+then we have other people who are going
+
+ align:start position:0%
+then we have other people who are going
+ 
+
+ align:start position:0%
+then we have other people who are going
+to be Shoppers uh who are going to
+
+ align:start position:0%
+to be Shoppers uh who are going to
+ 
+
+ align:start position:0%
+to be Shoppers uh who are going to
+arrive at a passon rate and they observe
+
+ align:start position:0%
+arrive at a passon rate and they observe
+ 
+
+ align:start position:0%
+arrive at a passon rate and they observe
+the prices at all the stores do I have a
+
+ align:start position:0%
+the prices at all the stores do I have a
+ 
+
+ align:start position:0%
+the prices at all the stores do I have a
+picture of a
+
+ align:start position:0%
+picture of a
+ 
+
+ align:start position:0%
+picture of a
+books I don't have a picture of a Books
+
+ align:start position:0%
+books I don't have a picture of a Books
+ 
+
+ align:start position:0%
+books I don't have a picture of a Books
+Okay anyway you know there are
+
+ align:start position:0%
+Okay anyway you know there are
+ 
+
+ align:start position:0%
+Okay anyway you know there are
+um we use data in the p in the uh in the
+
+ align:start position:0%
+um we use data in the p in the uh in the
+ 
+
+ align:start position:0%
+um we use data in the p in the uh in the
+paper from a website called a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+books.com um uh a books it was it's just
+
+ align:start position:0%
+books.com um uh a books it was it's just
+ 
+
+ align:start position:0%
+books.com um uh a books it was it's just
+a it's a used book aggregator site you
+
+ align:start position:0%
+a it's a used book aggregator site you
+ 
+
+ align:start position:0%
+a it's a used book aggregator site you
+can go on there you could type in any
+
+ align:start position:0%
+can go on there you could type in any
+ 
+
+ align:start position:0%
+can go on there you could type in any
+book you want that's out of print it
+
+ align:start position:0%
+book you want that's out of print it
+ 
+
+ align:start position:0%
+book you want that's out of print it
+will sort of find 100 online book stores
+
+ align:start position:0%
+will sort of find 100 online book stores
+ 
+
+ align:start position:0%
+will sort of find 100 online book stores
+that sell that particular used book okay
+
+ align:start position:0%
+that sell that particular used book okay
+ 
+
+ align:start position:0%
+that sell that particular used book okay
+um uh actually you know a books used to
+
+ align:start position:0%
+um uh actually you know a books used to
+ 
+
+ align:start position:0%
+um uh actually you know a books used to
+be an independent company it was
+
+ align:start position:0%
+be an independent company it was
+ 
+
+ align:start position:0%
+be an independent company it was
+purchased by Amazon so if you if you go
+
+ align:start position:0%
+purchased by Amazon so if you if you go
+ 
+
+ align:start position:0%
+purchased by Amazon so if you if you go
+to the Amazon bu used button Amazon buy
+
+ align:start position:0%
+to the Amazon bu used button Amazon buy
+ 
+
+ align:start position:0%
+to the Amazon bu used button Amazon buy
+used button is sort of the a books
+
+ align:start position:0%
+used button is sort of the a books
+ 
+
+ align:start position:0%
+used button is sort of the a books
+listings uh some sense Amazon invented
+
+ align:start position:0%
+listings uh some sense Amazon invented
+ 
+
+ align:start position:0%
+listings uh some sense Amazon invented
+the bu used button first when they
+
+ align:start position:0%
+the bu used button first when they
+ 
+
+ align:start position:0%
+the bu used button first when they
+invented the buus button there was
+
+ align:start position:0%
+invented the buus button there was
+ 
+
+ align:start position:0%
+invented the buus button there was
+nothing there under bued you'd click buy
+
+ align:start position:0%
+nothing there under bued you'd click buy
+ 
+
+ align:start position:0%
+nothing there under bued you'd click buy
+used and there were no copies available
+
+ align:start position:0%
+used and there were no copies available
+ 
+
+ align:start position:0%
+used and there were no copies available
+and so they realized well why don't we
+
+ align:start position:0%
+and so they realized well why don't we
+ 
+
+ align:start position:0%
+and so they realized well why don't we
+just buy a books that has 10 million
+
+ align:start position:0%
+just buy a books that has 10 million
+ 
+
+ align:start position:0%
+just buy a books that has 10 million
+Used Books listed and put all their
+
+ align:start position:0%
+Used Books listed and put all their
+ 
+
+ align:start position:0%
+Used Books listed and put all their
+listings under the by used button so now
+
+ align:start position:0%
+listings under the by used button so now
+ 
+
+ align:start position:0%
+listings under the by used button so now
+if you go to the buy used button you're
+
+ align:start position:0%
+if you go to the buy used button you're
+ 
+
+ align:start position:0%
+if you go to the buy used button you're
+seeing the same a books listings okay
+
+ align:start position:0%
+seeing the same a books listings okay
+ 
+
+ align:start position:0%
+seeing the same a books listings okay
+um anyway so our model is that sort of
+
+ align:start position:0%
+um anyway so our model is that sort of
+ 
+
+ align:start position:0%
+um anyway so our model is that sort of
+there these two types of customers the
+
+ align:start position:0%
+there these two types of customers the
+ 
+
+ align:start position:0%
+there these two types of customers the
+one's going to Amazon and clicking buy
+
+ align:start position:0%
+one's going to Amazon and clicking buy
+ 
+
+ align:start position:0%
+one's going to Amazon and clicking buy
+used and getting this curated list of
+
+ align:start position:0%
+used and getting this curated list of
+ 
+
+ align:start position:0%
+used and getting this curated list of
+all the things sorted by price and then
+
+ align:start position:0%
+all the things sorted by price and then
+ 
+
+ align:start position:0%
+all the things sorted by price and then
+the people who are sort of searching for
+
+ align:start position:0%
+the people who are sort of searching for
+ 
+
+ align:start position:0%
+the people who are sort of searching for
+a book by just typing it into Google or
+
+ align:start position:0%
+a book by just typing it into Google or
+ 
+
+ align:start position:0%
+a book by just typing it into Google or
+going directly to a used bookstore that
+
+ align:start position:0%
+going directly to a used bookstore that
+ 
+
+ align:start position:0%
+going directly to a used bookstore that
+they know online and finding it that way
+
+ align:start position:0%
+they know online and finding it that way
+ 
+
+ align:start position:0%
+they know online and finding it that way
+um you know we know that sort of this
+
+ align:start position:0%
+um you know we know that sort of this
+ 
+
+ align:start position:0%
+um you know we know that sort of this
+model can have pure strategy disperse
+
+ align:start position:0%
+model can have pure strategy disperse
+ 
+
+ align:start position:0%
+model can have pure strategy disperse
+price equilibria not so different from
+
+ align:start position:0%
+price equilibria not so different from
+ 
+
+ align:start position:0%
+price equilibria not so different from
+the dispersed price equilibria I did
+
+ align:start position:0%
+the dispersed price equilibria I did
+ 
+
+ align:start position:0%
+the dispersed price equilibria I did
+when I did differentiated product search
+
+ align:start position:0%
+when I did differentiated product search
+ 
+
+ align:start position:0%
+when I did differentiated product search
+models um you know the firms here the
+
+ align:start position:0%
+models um you know the firms here the
+ 
+
+ align:start position:0%
+models um you know the firms here the
+dispersion is going to be the firms that
+
+ align:start position:0%
+dispersion is going to be the firms that
+ 
+
+ align:start position:0%
+dispersion is going to be the firms that
+have the higher arrival rates are going
+
+ align:start position:0%
+have the higher arrival rates are going
+ 
+
+ align:start position:0%
+have the higher arrival rates are going
+to set high prices and mostly serve the
+
+ align:start position:0%
+to set high prices and mostly serve the
+ 
+
+ align:start position:0%
+to set high prices and mostly serve the
+non-shoppers if you don't have a lot of
+
+ align:start position:0%
+non-shoppers if you don't have a lot of
+ 
+
+ align:start position:0%
+non-shoppers if you don't have a lot of
+non-shoppers you're going to set a low
+
+ align:start position:0%
+non-shoppers you're going to set a low
+ 
+
+ align:start position:0%
+non-shoppers you're going to set a low
+price and compete for the
+
+ align:start position:0%
+price and compete for the
+ 
+
+ align:start position:0%
+price and compete for the
+Shoppers okay and when I'm thinking
+
+ align:start position:0%
+Shoppers okay and when I'm thinking
+ 
+
+ align:start position:0%
+Shoppers okay and when I'm thinking
+about like how does the online prices
+
+ align:start position:0%
+about like how does the online prices
+ 
+
+ align:start position:0%
+about like how does the online prices
+differ from the offline prices it helps
+
+ align:start position:0%
+differ from the offline prices it helps
+ 
+
+ align:start position:0%
+differ from the offline prices it helps
+think that there are two reasons one is
+
+ align:start position:0%
+think that there are two reasons one is
+ 
+
+ align:start position:0%
+think that there are two reasons one is
+the match quality reason the higher
+
+ align:start position:0%
+the match quality reason the higher
+ 
+
+ align:start position:0%
+the match quality reason the higher
+rival rates shift the distribution of
+
+ align:start position:0%
+rival rates shift the distribution of
+ 
+
+ align:start position:0%
+rival rates shift the distribution of
+Monopoly prices to the right um the
+
+ align:start position:0%
+Monopoly prices to the right um the
+ 
+
+ align:start position:0%
+Monopoly prices to the right um the
+second is a sort of competition effect
+
+ align:start position:0%
+second is a sort of competition effect
+ 
+
+ align:start position:0%
+second is a sort of competition effect
+which is there's a desire to attack
+
+ align:start position:0%
+which is there's a desire to attack
+ 
+
+ align:start position:0%
+which is there's a desire to attack
+attract the Shoppers so the firms that
+
+ align:start position:0%
+attract the Shoppers so the firms that
+ 
+
+ align:start position:0%
+attract the Shoppers so the firms that
+have low arrival rates of non-shoppers
+
+ align:start position:0%
+have low arrival rates of non-shoppers
+ 
+
+ align:start position:0%
+have low arrival rates of non-shoppers
+are going to sort of be competing
+
+ align:start position:0%
+are going to sort of be competing
+ 
+
+ align:start position:0%
+are going to sort of be competing
+against each other to try to sell in a
+
+ align:start position:0%
+against each other to try to sell in a
+ 
+
+ align:start position:0%
+against each other to try to sell in a
+more betrand likee environment to the
+
+ align:start position:0%
+more betrand likee environment to the
+ 
+
+ align:start position:0%
+more betrand likee environment to the
+people who using the search
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+engines so I think on the next page I
+
+ align:start position:0%
+engines so I think on the next page I
+ 
+
+ align:start position:0%
+engines so I think on the next page I
+have this illustration so here's a
+
+ align:start position:0%
+have this illustration so here's a
+ 
+
+ align:start position:0%
+have this illustration so here's a
+numerical simulation of the model so the
+
+ align:start position:0%
+numerical simulation of the model so the
+ 
+
+ align:start position:0%
+numerical simulation of the model so the
+this dashed Gray Line would be the
+
+ align:start position:0%
+this dashed Gray Line would be the
+ 
+
+ align:start position:0%
+this dashed Gray Line would be the
+distribution of Monopoly prices if
+
+ align:start position:0%
+distribution of Monopoly prices if
+ 
+
+ align:start position:0%
+distribution of Monopoly prices if
+they're exponentially distributed
+
+ align:start position:0%
+they're exponentially distributed
+ 
+
+ align:start position:0%
+they're exponentially distributed
+arrival rates and so the firms with High
+
+ align:start position:0%
+arrival rates and so the firms with High
+ 
+
+ align:start position:0%
+arrival rates and so the firms with High
+arrival rates at high prices those with
+
+ align:start position:0%
+arrival rates at high prices those with
+ 
+
+ align:start position:0%
+arrival rates at high prices those with
+low arrival rates at low
+
+ align:start position:0%
+low arrival rates at low
+ 
+
+ align:start position:0%
+low arrival rates at low
+prices if I
+
+ align:start position:0%
+prices if I
+ 
+
+ align:start position:0%
+prices if I
+increase uh the value of the good
+
+ align:start position:0%
+increase uh the value of the good
+ 
+
+ align:start position:0%
+increase uh the value of the good
+because people are getting a better
+
+ align:start position:0%
+because people are getting a better
+ 
+
+ align:start position:0%
+because people are getting a better
+matched good the Monopoly price
+
+ align:start position:0%
+matched good the Monopoly price
+ 
+
+ align:start position:0%
+matched good the Monopoly price
+distribution would shift to the right
+
+ align:start position:0%
+distribution would shift to the right
+ 
+
+ align:start position:0%
+distribution would shift to the right
+from the gray line to the Blue
+
+ align:start position:0%
+from the gray line to the Blue
+ 
+
+ align:start position:0%
+from the gray line to the Blue
+Line uh but then if I add in this atom
+
+ align:start position:0%
+Line uh but then if I add in this atom
+ 
+
+ align:start position:0%
+Line uh but then if I add in this atom
+of Shoppers who are just going to buy
+
+ align:start position:0%
+of Shoppers who are just going to buy
+ 
+
+ align:start position:0%
+of Shoppers who are just going to buy
+for the lowest price book and are fairly
+
+ align:start position:0%
+for the lowest price book and are fairly
+ 
+
+ align:start position:0%
+for the lowest price book and are fairly
+price insensitive what you get is the
+
+ align:start position:0%
+price insensitive what you get is the
+ 
+
+ align:start position:0%
+price insensitive what you get is the
+distribution of prices all the firms
+
+ align:start position:0%
+distribution of prices all the firms
+ 
+
+ align:start position:0%
+distribution of prices all the firms
+that are sort of going to be setting the
+
+ align:start position:0%
+that are sort of going to be setting the
+ 
+
+ align:start position:0%
+that are sort of going to be setting the
+lowest prices are now sort of betran
+
+ align:start position:0%
+lowest prices are now sort of betran
+ 
+
+ align:start position:0%
+lowest prices are now sort of betran
+competing against the other firms who
+
+ align:start position:0%
+competing against the other firms who
+ 
+
+ align:start position:0%
+competing against the other firms who
+are also going to set very low prices
+
+ align:start position:0%
+are also going to set very low prices
+ 
+
+ align:start position:0%
+are also going to set very low prices
+and so the low end of the price
+
+ align:start position:0%
+and so the low end of the price
+ 
+
+ align:start position:0%
+and so the low end of the price
+distribution gets pulled down the upper
+
+ align:start position:0%
+distribution gets pulled down the upper
+ 
+
+ align:start position:0%
+distribution gets pulled down the upper
+tail really doesn't get affected at all
+
+ align:start position:0%
+tail really doesn't get affected at all
+ 
+
+ align:start position:0%
+tail really doesn't get affected at all
+the upper tail doesn't get affected at
+
+ align:start position:0%
+the upper tail doesn't get affected at
+ 
+
+ align:start position:0%
+the upper tail doesn't get affected at
+all because these firms were just
+
+ align:start position:0%
+all because these firms were just
+ 
+
+ align:start position:0%
+all because these firms were just
+Monopoly pricing and serving the high
+
+ align:start position:0%
+Monopoly pricing and serving the high
+ 
+
+ align:start position:0%
+Monopoly pricing and serving the high
+value customers who who happen on their
+
+ align:start position:0%
+value customers who who happen on their
+ 
+
+ align:start position:0%
+value customers who who happen on their
+website occasionally they don't bother
+
+ align:start position:0%
+website occasionally they don't bother
+ 
+
+ align:start position:0%
+website occasionally they don't bother
+to compete for the Shoppers they just
+
+ align:start position:0%
+to compete for the Shoppers they just
+ 
+
+ align:start position:0%
+to compete for the Shoppers they just
+leave the high price and just exploit
+
+ align:start position:0%
+leave the high price and just exploit
+ 
+
+ align:start position:0%
+leave the high price and just exploit
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+non-shoppers uh and so what you get is
+
+ align:start position:0%
+non-shoppers uh and so what you get is
+ 
+
+ align:start position:0%
+non-shoppers uh and so what you get is
+this increase in dispersion uh which
+
+ align:start position:0%
+this increase in dispersion uh which
+ 
+
+ align:start position:0%
+this increase in dispersion uh which
+comes from the upper tail really having
+
+ align:start position:0%
+comes from the upper tail really having
+ 
+
+ align:start position:0%
+comes from the upper tail really having
+moved up because people have higher
+
+ align:start position:0%
+moved up because people have higher
+ 
+
+ align:start position:0%
+moved up because people have higher
+values and then the lower tail getting
+
+ align:start position:0%
+values and then the lower tail getting
+ 
+
+ align:start position:0%
+values and then the lower tail getting
+pulled down by the um competition and so
+
+ align:start position:0%
+pulled down by the um competition and so
+ 
+
+ align:start position:0%
+pulled down by the um competition and so
+we think those are the sort of two
+
+ align:start position:0%
+we think those are the sort of two
+ 
+
+ align:start position:0%
+we think those are the sort of two
+things you should expect is that the
+
+ align:start position:0%
+things you should expect is that the
+ 
+
+ align:start position:0%
+things you should expect is that the
+online price distribution has this
+
+ align:start position:0%
+online price distribution has this
+ 
+
+ align:start position:0%
+online price distribution has this
+thicker upper tail relative to the
+
+ align:start position:0%
+thicker upper tail relative to the
+ 
+
+ align:start position:0%
+thicker upper tail relative to the
+offline price distribution but then it
+
+ align:start position:0%
+offline price distribution but then it
+ 
+
+ align:start position:0%
+offline price distribution but then it
+also has a more mass and the lower tail
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perhaps um okay so how do we try to test
+
+ align:start position:0%
+perhaps um okay so how do we try to test
+ 
+
+ align:start position:0%
+perhaps um okay so how do we try to test
+this in the data um so we gathered a
+
+ align:start position:0%
+this in the data um so we gathered a
+ 
+
+ align:start position:0%
+this in the data um so we gathered a
+data set that had uh 335 books
+
+ align:start position:0%
+data set that had uh 335 books
+ 
+
+ align:start position:0%
+data set that had uh 335 books
+representative of traditional used
+
+ align:start position:0%
+representative of traditional used
+ 
+
+ align:start position:0%
+representative of traditional used
+bookstores inventories uh the way this
+
+ align:start position:0%
+bookstores inventories uh the way this
+ 
+
+ align:start position:0%
+bookstores inventories uh the way this
+worked is we just um actually Sarah did
+
+ align:start position:0%
+worked is we just um actually Sarah did
+ 
+
+ align:start position:0%
+worked is we just um actually Sarah did
+some of this herself we also just sent
+
+ align:start position:0%
+some of this herself we also just sent
+ 
+
+ align:start position:0%
+some of this herself we also just sent
+an RA to some physical bookstores with
+
+ align:start position:0%
+an RA to some physical bookstores with
+ 
+
+ align:start position:0%
+an RA to some physical bookstores with
+the instructions you know I want you to
+
+ align:start position:0%
+the instructions you know I want you to
+ 
+
+ align:start position:0%
+the instructions you know I want you to
+go to the physical bookstores and just
+
+ align:start position:0%
+go to the physical bookstores and just
+ 
+
+ align:start position:0%
+go to the physical bookstores and just
+go to the first shelf take every 17th
+
+ align:start position:0%
+go to the first shelf take every 17th
+ 
+
+ align:start position:0%
+go to the first shelf take every 17th
+book off the shelf take that book write
+
+ align:start position:0%
+book off the shelf take that book write
+ 
+
+ align:start position:0%
+book off the shelf take that book write
+down the title what it is write down the
+
+ align:start position:0%
+down the title what it is write down the
+ 
+
+ align:start position:0%
+down the title what it is write down the
+price and then just sort of go shelf to
+
+ align:start position:0%
+price and then just sort of go shelf to
+ 
+
+ align:start position:0%
+price and then just sort of go shelf to
+shelf to shelf picking out books um so
+
+ align:start position:0%
+shelf to shelf picking out books um so
+ 
+
+ align:start position:0%
+shelf to shelf picking out books um so
+we have a hundreds what we call Standard
+
+ align:start position:0%
+we have a hundreds what we call Standard
+ 
+
+ align:start position:0%
+we have a hundreds what we call Standard
+books in the data set we also
+
+ align:start position:0%
+books in the data set we also
+ 
+
+ align:start position:0%
+books in the data set we also
+oversampled what we call local interest
+
+ align:start position:0%
+oversampled what we call local interest
+ 
+
+ align:start position:0%
+oversampled what we call local interest
+books like if you go into a Boston
+
+ align:start position:0%
+books like if you go into a Boston
+ 
+
+ align:start position:0%
+books like if you go into a Boston
+bookstore you'll notice there's a shelf
+
+ align:start position:0%
+bookstore you'll notice there's a shelf
+ 
+
+ align:start position:0%
+bookstore you'll notice there's a shelf
+of books about Boston and Boston stuff
+
+ align:start position:0%
+of books about Boston and Boston stuff
+ 
+
+ align:start position:0%
+of books about Boston and Boston stuff
+uh and so what we would said is you know
+
+ align:start position:0%
+uh and so what we would said is you know
+ 
+
+ align:start position:0%
+uh and so what we would said is you know
+if there's a like a local interest
+
+ align:start position:0%
+if there's a like a local interest
+ 
+
+ align:start position:0%
+if there's a like a local interest
+section so there's a Boston shelf in the
+
+ align:start position:0%
+section so there's a Boston shelf in the
+ 
+
+ align:start position:0%
+section so there's a Boston shelf in the
+Boston bookstore one of the bookstores
+
+ align:start position:0%
+Boston bookstore one of the bookstores
+ 
+
+ align:start position:0%
+Boston bookstore one of the bookstores
+was in Atlanta there if there's a book
+
+ align:start position:0%
+was in Atlanta there if there's a book
+ 
+
+ align:start position:0%
+was in Atlanta there if there's a book
+about like Christmas in Georgia you know
+
+ align:start position:0%
+about like Christmas in Georgia you know
+ 
+
+ align:start position:0%
+about like Christmas in Georgia you know
+like find the shelf that has the Georgia
+
+ align:start position:0%
+like find the shelf that has the Georgia
+ 
+
+ align:start position:0%
+like find the shelf that has the Georgia
+books and and oversample those uh and
+
+ align:start position:0%
+books and and oversample those uh and
+ 
+
+ align:start position:0%
+books and and oversample those uh and
+then we also have sort of separate out
+
+ align:start position:0%
+then we also have sort of separate out
+ 
+
+ align:start position:0%
+then we also have sort of separate out
+popular books popular books are the
+
+ align:start position:0%
+popular books popular books are the
+ 
+
+ align:start position:0%
+popular books popular books are the
+things like I mean not not necessarily
+
+ align:start position:0%
+things like I mean not not necessarily
+ 
+
+ align:start position:0%
+things like I mean not not necessarily
+Harry Potter but things that are popular
+
+ align:start position:0%
+Harry Potter but things that are popular
+ 
+
+ align:start position:0%
+Harry Potter but things that are popular
+enough that every used bookstore is
+
+ align:start position:0%
+enough that every used bookstore is
+ 
+
+ align:start position:0%
+enough that every used bookstore is
+probably going to have a copy there are
+
+ align:start position:0%
+probably going to have a copy there are
+ 
+
+ align:start position:0%
+probably going to have a copy there are
+some things that these are former Mega
+
+ align:start position:0%
+some things that these are former Mega
+ 
+
+ align:start position:0%
+some things that these are former Mega
+bestsellers so it's not so rare to find
+
+ align:start position:0%
+bestsellers so it's not so rare to find
+ 
+
+ align:start position:0%
+bestsellers so it's not so rare to find
+these whereas the standard books are all
+
+ align:start position:0%
+these whereas the standard books are all
+ 
+
+ align:start position:0%
+these whereas the standard books are all
+going to be completely nonoverlapping
+
+ align:start position:0%
+going to be completely nonoverlapping
+ 
+
+ align:start position:0%
+going to be completely nonoverlapping
+across stores because just the average
+
+ align:start position:0%
+across stores because just the average
+ 
+
+ align:start position:0%
+across stores because just the average
+used book you know right there are
+
+ align:start position:0%
+used book you know right there are
+ 
+
+ align:start position:0%
+used book you know right there are
+millions of books the average used book
+
+ align:start position:0%
+millions of books the average used book
+ 
+
+ align:start position:0%
+millions of books the average used book
+is just not no one's going to have
+
+ align:start position:0%
+is just not no one's going to have
+ 
+
+ align:start position:0%
+is just not no one's going to have
+another copy of that you could search
+
+ align:start position:0%
+another copy of that you could search
+ 
+
+ align:start position:0%
+another copy of that you could search
+the bookstores all your life and
+
+ align:start position:0%
+the bookstores all your life and
+ 
+
+ align:start position:0%
+the bookstores all your life and
+probably not find another copy of a
+
+ align:start position:0%
+probably not find another copy of a
+ 
+
+ align:start position:0%
+probably not find another copy of a
+standard book okay uh anyway so we have
+
+ align:start position:0%
+standard book okay uh anyway so we have
+ 
+
+ align:start position:0%
+standard book okay uh anyway so we have
+four data collections we have what we
+
+ align:start position:0%
+four data collections we have what we
+ 
+
+ align:start position:0%
+four data collections we have what we
+did is we first just randomly selected
+
+ align:start position:0%
+did is we first just randomly selected
+ 
+
+ align:start position:0%
+did is we first just randomly selected
+these books from physical bookstores and
+
+ align:start position:0%
+these books from physical bookstores and
+ 
+
+ align:start position:0%
+these books from physical bookstores and
+then we went online and searched for
+
+ align:start position:0%
+then we went online and searched for
+ 
+
+ align:start position:0%
+then we went online and searched for
+those books at a
+
+ align:start position:0%
+those books at a
+ 
+
+ align:start position:0%
+those books at a
+books.com and then we noticed that uh in
+
+ align:start position:0%
+books.com and then we noticed that uh in
+ 
+
+ align:start position:0%
+books.com and then we noticed that uh in
+between the time we collected this and
+
+ align:start position:0%
+between the time we collected this and
+ 
+
+ align:start position:0%
+between the time we collected this and
+we and we wrote the paper Amazon bought
+
+ align:start position:0%
+we and we wrote the paper Amazon bought
+ 
+
+ align:start position:0%
+we and we wrote the paper Amazon bought
+uh a books and we thought wow that's a
+
+ align:start position:0%
+uh a books and we thought wow that's a
+ 
+
+ align:start position:0%
+uh a books and we thought wow that's a
+great second accidental uh opportunity
+
+ align:start position:0%
+great second accidental uh opportunity
+ 
+
+ align:start position:0%
+great second accidental uh opportunity
+here is that Amazon buying a books and
+
+ align:start position:0%
+here is that Amazon buying a books and
+ 
+
+ align:start position:0%
+here is that Amazon buying a books and
+putting the listings under by used
+
+ align:start position:0%
+putting the listings under by used
+ 
+
+ align:start position:0%
+putting the listings under by used
+probably just dramatically increased the
+
+ align:start position:0%
+probably just dramatically increased the
+ 
+
+ align:start position:0%
+probably just dramatically increased the
+number of people who are looking at the
+
+ align:start position:0%
+number of people who are looking at the
+ 
+
+ align:start position:0%
+number of people who are looking at the
+sort of curated the search engine
+
+ align:start position:0%
+sort of curated the search engine
+ 
+
+ align:start position:0%
+sort of curated the search engine
+listings for them and so then after
+
+ align:start position:0%
+listings for them and so then after
+ 
+
+ align:start position:0%
+listings for them and so then after
+Amazon bought and Incorporated the a
+
+ align:start position:0%
+Amazon bought and Incorporated the a
+ 
+
+ align:start position:0%
+Amazon bought and Incorporated the a
+books listings we went out and collected
+
+ align:start position:0%
+books listings we went out and collected
+ 
+
+ align:start position:0%
+books listings we went out and collected
+the data again a second time uh and we
+
+ align:start position:0%
+the data again a second time uh and we
+ 
+
+ align:start position:0%
+the data again a second time uh and we
+collected data again a second time so we
+
+ align:start position:0%
+collected data again a second time so we
+ 
+
+ align:start position:0%
+collected data again a second time so we
+would have before and after on prices
+
+ align:start position:0%
+would have before and after on prices
+ 
+
+ align:start position:0%
+would have before and after on prices
+before and after the a books listings uh
+
+ align:start position:0%
+before and after the a books listings uh
+ 
+
+ align:start position:0%
+before and after the a books listings uh
+and then we went and collected the data
+
+ align:start position:0%
+and then we went and collected the data
+ 
+
+ align:start position:0%
+and then we went and collected the data
+a fourth time a few months later we
+
+ align:start position:0%
+a fourth time a few months later we
+ 
+
+ align:start position:0%
+a fourth time a few months later we
+realized it would be useful to have
+
+ align:start position:0%
+realized it would be useful to have
+ 
+
+ align:start position:0%
+realized it would be useful to have
+quantity data and a way to get quantity
+
+ align:start position:0%
+quantity data and a way to get quantity
+ 
+
+ align:start position:0%
+quantity data and a way to get quantity
+data is to search a bookstore for the
+
+ align:start position:0%
+data is to search a bookstore for the
+ 
+
+ align:start position:0%
+data is to search a bookstore for the
+book search that same bookstore two
+
+ align:start position:0%
+book search that same bookstore two
+ 
+
+ align:start position:0%
+book search that same bookstore two
+months later see if they're still
+
+ align:start position:0%
+months later see if they're still
+ 
+
+ align:start position:0%
+months later see if they're still
+listing the book and infer if they don't
+
+ align:start position:0%
+listing the book and infer if they don't
+ 
+
+ align:start position:0%
+listing the book and infer if they don't
+they're not still listing the book two
+
+ align:start position:0%
+they're not still listing the book two
+ 
+
+ align:start position:0%
+they're not still listing the book two
+months later they may have sold the book
+
+ align:start position:0%
+months later they may have sold the book
+ 
+
+ align:start position:0%
+months later they may have sold the book
+now they may have just also just taken
+
+ align:start position:0%
+now they may have just also just taken
+ 
+
+ align:start position:0%
+now they may have just also just taken
+it down but it's it's a pain to take
+
+ align:start position:0%
+it down but it's it's a pain to take
+ 
+
+ align:start position:0%
+it down but it's it's a pain to take
+things down from your website you know
+
+ align:start position:0%
+things down from your website you know
+ 
+
+ align:start position:0%
+things down from your website you know
+you probably take them down when you
+
+ align:start position:0%
+you probably take them down when you
+ 
+
+ align:start position:0%
+you probably take them down when you
+sell them anyway so anyway that's so we
+
+ align:start position:0%
+sell them anyway so anyway that's so we
+ 
+
+ align:start position:0%
+sell them anyway so anyway that's so we
+have these four data Collections and
+
+ align:start position:0%
+have these four data Collections and
+ 
+
+ align:start position:0%
+have these four data Collections and
+last two is how we got quantity
+
+ align:start position:0%
+last two is how we got quantity
+ 
+
+ align:start position:0%
+last two is how we got quantity
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+um okay so what are the sort of
+
+ align:start position:0%
+um okay so what are the sort of
+ 
+
+ align:start position:0%
+um okay so what are the sort of
+predictions we're trying to test
+
+ align:start position:0%
+predictions we're trying to test
+ 
+
+ align:start position:0%
+predictions we're trying to test
+prediction one is that online prices
+
+ align:start position:0%
+prediction one is that online prices
+ 
+
+ align:start position:0%
+prediction one is that online prices
+should be more dispersed in offline
+
+ align:start position:0%
+should be more dispersed in offline
+ 
+
+ align:start position:0%
+should be more dispersed in offline
+prices and have a thicker upper
+
+ align:start position:0%
+prices and have a thicker upper
+ 
+
+ align:start position:0%
+prices and have a thicker upper
+tail um prediction two is local interest
+
+ align:start position:0%
+tail um prediction two is local interest
+ 
+
+ align:start position:0%
+tail um prediction two is local interest
+books may already be M well matched by
+
+ align:start position:0%
+books may already be M well matched by
+ 
+
+ align:start position:0%
+books may already be M well matched by
+the offline stores so the online offline
+
+ align:start position:0%
+the offline stores so the online offline
+ 
+
+ align:start position:0%
+the offline stores so the online offline
+Gap should be small for the local
+
+ align:start position:0%
+Gap should be small for the local
+ 
+
+ align:start position:0%
+Gap should be small for the local
+interest books in particular I put this
+
+ align:start position:0%
+interest books in particular I put this
+ 
+
+ align:start position:0%
+interest books in particular I put this
+uh quote up here you know I found this
+
+ align:start position:0%
+uh quote up here you know I found this
+ 
+
+ align:start position:0%
+uh quote up here you know I found this
+online review of one of the books in our
+
+ align:start position:0%
+online review of one of the books in our
+ 
+
+ align:start position:0%
+online review of one of the books in our
+data set the Mount Vernon Street
+
+ align:start position:0%
+data set the Mount Vernon Street
+ 
+
+ align:start position:0%
+data set the Mount Vernon Street
+Warren's a Boston story I don't know if
+
+ align:start position:0%
+Warren's a Boston story I don't know if
+ 
+
+ align:start position:0%
+Warren's a Boston story I don't know if
+you guys have been to Beacon Hill Mount
+
+ align:start position:0%
+you guys have been to Beacon Hill Mount
+ 
+
+ align:start position:0%
+you guys have been to Beacon Hill Mount
+Vernon is one of the streets on Beacon
+
+ align:start position:0%
+Vernon is one of the streets on Beacon
+ 
+
+ align:start position:0%
+Vernon is one of the streets on Beacon
+Hill uh you know it's a cute Street or
+
+ align:start position:0%
+Hill uh you know it's a cute Street or
+ 
+
+ align:start position:0%
+Hill uh you know it's a cute Street or
+whatever with the gas lamps and the
+
+ align:start position:0%
+whatever with the gas lamps and the
+ 
+
+ align:start position:0%
+whatever with the gas lamps and the
+brick sidewalks and stuff anyway if if
+
+ align:start position:0%
+brick sidewalks and stuff anyway if if
+ 
+
+ align:start position:0%
+brick sidewalks and stuff anyway if if
+you go into a local Boston bookstore you
+
+ align:start position:0%
+you go into a local Boston bookstore you
+ 
+
+ align:start position:0%
+you go into a local Boston bookstore you
+may some one of them some are already
+
+ align:start position:0%
+may some one of them some are already
+ 
+
+ align:start position:0%
+may some one of them some are already
+found a copy of this Mount Vernon Street
+
+ align:start position:0%
+found a copy of this Mount Vernon Street
+ 
+
+ align:start position:0%
+found a copy of this Mount Vernon Street
+Warren anyway if you read that book like
+
+ align:start position:0%
+Warren anyway if you read that book like
+ 
+
+ align:start position:0%
+Warren anyway if you read that book like
+what's your overwhelming thing of so
+
+ align:start position:0%
+what's your overwhelming thing of so
+ 
+
+ align:start position:0%
+what's your overwhelming thing of so
+this is a you know telling the stories
+
+ align:start position:0%
+this is a you know telling the stories
+ 
+
+ align:start position:0%
+this is a you know telling the stories
+of these children who became notable for
+
+ align:start position:0%
+of these children who became notable for
+ 
+
+ align:start position:0%
+of these children who became notable for
+eccentricity and philanthropy green
+
+ align:start position:0%
+eccentricity and philanthropy green
+ 
+
+ align:start position:0%
+eccentricity and philanthropy green
+focuses on Ned Warren homosexual and
+
+ align:start position:0%
+focuses on Ned Warren homosexual and
+ 
+
+ align:start position:0%
+focuses on Ned Warren homosexual and
+mover in the international movement of
+
+ align:start position:0%
+mover in the international movement of
+ 
+
+ align:start position:0%
+mover in the international movement of
+aestheticism who determined to lead a
+
+ align:start position:0%
+aestheticism who determined to lead a
+ 
+
+ align:start position:0%
+aestheticism who determined to lead a
+grand but blighted life the somewhat
+
+ align:start position:0%
+grand but blighted life the somewhat
+ 
+
+ align:start position:0%
+grand but blighted life the somewhat
+jumbled tale of a family thundering
+
+ align:start position:0%
+jumbled tale of a family thundering
+ 
+
+ align:start position:0%
+jumbled tale of a family thundering
+through greed and suicide you know
+
+ align:start position:0%
+through greed and suicide you know
+ 
+
+ align:start position:0%
+through greed and suicide you know
+basically I read this and I'm like I
+
+ align:start position:0%
+basically I read this and I'm like I
+ 
+
+ align:start position:0%
+basically I read this and I'm like I
+don't want to read that book I mean I
+
+ align:start position:0%
+don't want to read that book I mean I
+ 
+
+ align:start position:0%
+don't want to read that book I mean I
+don't I don't know so much about what
+
+ align:start position:0%
+don't I don't know so much about what
+ 
+
+ align:start position:0%
+don't I don't know so much about what
+aestheticism was but how much do I want
+
+ align:start position:0%
+aestheticism was but how much do I want
+ 
+
+ align:start position:0%
+aestheticism was but how much do I want
+to really read about greed and suicide
+
+ align:start position:0%
+to really read about greed and suicide
+ 
+
+ align:start position:0%
+to really read about greed and suicide
+in Boston in 19 C and the whole point is
+
+ align:start position:0%
+in Boston in 19 C and the whole point is
+ 
+
+ align:start position:0%
+in Boston in 19 C and the whole point is
+in fact nobody wants to read that book
+
+ align:start position:0%
+in fact nobody wants to read that book
+ 
+
+ align:start position:0%
+in fact nobody wants to read that book
+book so who's the high value purchaser
+
+ align:start position:0%
+book so who's the high value purchaser
+ 
+
+ align:start position:0%
+book so who's the high value purchaser
+of that book a tourist who's just been
+
+ align:start position:0%
+of that book a tourist who's just been
+ 
+
+ align:start position:0%
+of that book a tourist who's just been
+to Beacon Hill and seen Mount Vernon
+
+ align:start position:0%
+to Beacon Hill and seen Mount Vernon
+ 
+
+ align:start position:0%
+to Beacon Hill and seen Mount Vernon
+Street and finds a copy of a book about
+
+ align:start position:0%
+Street and finds a copy of a book about
+ 
+
+ align:start position:0%
+Street and finds a copy of a book about
+a family on Mount Vernon Street in the
+
+ align:start position:0%
+a family on Mount Vernon Street in the
+ 
+
+ align:start position:0%
+a family on Mount Vernon Street in the
+19th century and thinks oh wow this will
+
+ align:start position:0%
+19th century and thinks oh wow this will
+ 
+
+ align:start position:0%
+19th century and thinks oh wow this will
+be great to read my hotel room and then
+
+ align:start position:0%
+be great to read my hotel room and then
+ 
+
+ align:start position:0%
+be great to read my hotel room and then
+you know you get partway through the
+
+ align:start position:0%
+you know you get partway through the
+ 
+
+ align:start position:0%
+you know you get partway through the
+suicide are and you're like this is not
+
+ align:start position:0%
+suicide are and you're like this is not
+ 
+
+ align:start position:0%
+suicide are and you're like this is not
+my vacation reading and then you sort of
+
+ align:start position:0%
+my vacation reading and then you sort of
+ 
+
+ align:start position:0%
+my vacation reading and then you sort of
+leave it there and then the hotel turns
+
+ align:start position:0%
+leave it there and then the hotel turns
+ 
+
+ align:start position:0%
+leave it there and then the hotel turns
+back in and the sells it to the used
+
+ align:start position:0%
+back in and the sells it to the used
+ 
+
+ align:start position:0%
+back in and the sells it to the used
+bookstore and then they sell it again to
+
+ align:start position:0%
+bookstore and then they sell it again to
+ 
+
+ align:start position:0%
+bookstore and then they sell it again to
+the next tourist or something um uh but
+
+ align:start position:0%
+the next tourist or something um uh but
+ 
+
+ align:start position:0%
+the next tourist or something um uh but
+anyway but so you know for these books
+
+ align:start position:0%
+anyway but so you know for these books
+ 
+
+ align:start position:0%
+anyway but so you know for these books
+like the online prices not much higher
+
+ align:start position:0%
+like the online prices not much higher
+ 
+
+ align:start position:0%
+like the online prices not much higher
+because no one is out there searching
+
+ align:start position:0%
+because no one is out there searching
+ 
+
+ align:start position:0%
+because no one is out there searching
+for that book um but it is a good match
+
+ align:start position:0%
+for that book um but it is a good match
+ 
+
+ align:start position:0%
+for that book um but it is a good match
+to the local physical bookstore um uh
+
+ align:start position:0%
+to the local physical bookstore um uh
+ 
+
+ align:start position:0%
+to the local physical bookstore um uh
+anyway other predictions the online
+
+ align:start position:0%
+anyway other predictions the online
+ 
+
+ align:start position:0%
+anyway other predictions the online
+offline Gap should also be smaller for
+
+ align:start position:0%
+offline Gap should also be smaller for
+ 
+
+ align:start position:0%
+offline Gap should also be smaller for
+popular titles because there's a thinner
+
+ align:start position:0%
+popular titles because there's a thinner
+ 
+
+ align:start position:0%
+popular titles because there's a thinner
+upper tail for popular titles there's
+
+ align:start position:0%
+upper tail for popular titles there's
+ 
+
+ align:start position:0%
+upper tail for popular titles there's
+not the match quality issue and then
+
+ align:start position:0%
+not the match quality issue and then
+ 
+
+ align:start position:0%
+not the match quality issue and then
+Amazon's buy used feature should lead to
+
+ align:start position:0%
+Amazon's buy used feature should lead to
+ 
+
+ align:start position:0%
+Amazon's buy used feature should lead to
+more low prices in 2012 because it
+
+ align:start position:0%
+more low prices in 2012 because it
+ 
+
+ align:start position:0%
+more low prices in 2012 because it
+increases that competition for the lower
+
+ align:start position:0%
+increases that competition for the lower
+ 
+
+ align:start position:0%
+increases that competition for the lower
+tale any so those are the predictions we
+
+ align:start position:0%
+tale any so those are the predictions we
+ 
+
+ align:start position:0%
+tale any so those are the predictions we
+a test and let me sort of just say
+
+ align:start position:0%
+a test and let me sort of just say
+ 
+
+ align:start position:0%
+a test and let me sort of just say
+basically story is almost all of these
+
+ align:start position:0%
+basically story is almost all of these
+ 
+
+ align:start position:0%
+basically story is almost all of these
+things seem to be true in the data in
+
+ align:start position:0%
+things seem to be true in the data in
+ 
+
+ align:start position:0%
+things seem to be true in the data in
+each of these figures the left is the
+
+ align:start position:0%
+each of these figures the left is the
+ 
+
+ align:start position:0%
+each of these figures the left is the
+distribution of offline
+
+ align:start position:0%
+distribution of offline
+ 
+
+ align:start position:0%
+distribution of offline
+prices the right side is an estimate of
+
+ align:start position:0%
+prices the right side is an estimate of
+ 
+
+ align:start position:0%
+prices the right side is an estimate of
+the same object an estimate of the
+
+ align:start position:0%
+the same object an estimate of the
+ 
+
+ align:start position:0%
+the same object an estimate of the
+average across titles of the
+
+ align:start position:0%
+average across titles of the
+ 
+
+ align:start position:0%
+average across titles of the
+distribution of prices for that title um
+
+ align:start position:0%
+distribution of prices for that title um
+ 
+
+ align:start position:0%
+distribution of prices for that title um
+so these should be sort of estimates of
+
+ align:start position:0%
+so these should be sort of estimates of
+ 
+
+ align:start position:0%
+so these should be sort of estimates of
+the same of the estimates of the
+
+ align:start position:0%
+the same of the estimates of the
+ 
+
+ align:start position:0%
+the same of the estimates of the
+distribution of offline prices for these
+
+ align:start position:0%
+distribution of offline prices for these
+ 
+
+ align:start position:0%
+distribution of offline prices for these
+books and the distribution of online
+
+ align:start position:0%
+books and the distribution of online
+ 
+
+ align:start position:0%
+books and the distribution of online
+prices for these books and you see for
+
+ align:start position:0%
+prices for these books and you see for
+ 
+
+ align:start position:0%
+prices for these books and you see for
+the stand standard books there's just
+
+ align:start position:0%
+the stand standard books there's just
+ 
+
+ align:start position:0%
+the stand standard books there's just
+this massively higher upper tale of
+
+ align:start position:0%
+this massively higher upper tale of
+ 
+
+ align:start position:0%
+this massively higher upper tale of
+prices online uh than there was
+
+ align:start position:0%
+prices online uh than there was
+ 
+
+ align:start position:0%
+prices online uh than there was
+offline uh if you go to the local
+
+ align:start position:0%
+offline uh if you go to the local
+ 
+
+ align:start position:0%
+offline uh if you go to the local
+interest books the local interest books
+
+ align:start position:0%
+interest books the local interest books
+ 
+
+ align:start position:0%
+interest books the local interest books
+already had something of a tale um
+
+ align:start position:0%
+already had something of a tale um
+ 
+
+ align:start position:0%
+already had something of a tale um
+online because the ones that are well
+
+ align:start position:0%
+online because the ones that are well
+ 
+
+ align:start position:0%
+online because the ones that are well
+matched that that book that Finds Its
+
+ align:start position:0%
+matched that that book that Finds Its
+ 
+
+ align:start position:0%
+matched that that book that Finds Its
+way to the Beacon Hill bookstore is
+
+ align:start position:0%
+way to the Beacon Hill bookstore is
+ 
+
+ align:start position:0%
+way to the Beacon Hill bookstore is
+already well matched can charge a very
+
+ align:start position:0%
+already well matched can charge a very
+ 
+
+ align:start position:0%
+already well matched can charge a very
+high price offline and so the
+
+ align:start position:0%
+high price offline and so the
+ 
+
+ align:start position:0%
+high price offline and so the
+offline you know more of an upper tale
+
+ align:start position:0%
+offline you know more of an upper tale
+ 
+
+ align:start position:0%
+offline you know more of an upper tale
+offline and online offline Gap is
+
+ align:start position:0%
+offline and online offline Gap is
+ 
+
+ align:start position:0%
+offline and online offline Gap is
+smaller for those local interest books
+
+ align:start position:0%
+smaller for those local interest books
+ 
+
+ align:start position:0%
+smaller for those local interest books
+um popular ones also works but me skip
+
+ align:start position:0%
+um popular ones also works but me skip
+ 
+
+ align:start position:0%
+um popular ones also works but me skip
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um this is a
+
+ align:start position:0%
+um this is a
+ 
+
+ align:start position:0%
+um this is a
+200922 comparison 2009 2012
+
+ align:start position:0%
+200922 comparison 2009 2012
+ 
+
+ align:start position:0%
+200922 comparison 2009 2012
+comparison um the gray bars are the 2009
+
+ align:start position:0%
+comparison um the gray bars are the 2009
+ 
+
+ align:start position:0%
+comparison um the gray bars are the 2009
+price distribution the white outline
+
+ align:start position:0%
+price distribution the white outline
+ 
+
+ align:start position:0%
+price distribution the white outline
+bars are the
+
+ align:start position:0%
+bars are the
+ 
+
+ align:start position:0%
+bars are the
+2012 distribution and you see these
+
+ align:start position:0%
+2012 distribution and you see these
+ 
+
+ align:start position:0%
+2012 distribution and you see these
+distributions almost lie exactly on top
+
+ align:start position:0%
+distributions almost lie exactly on top
+ 
+
+ align:start position:0%
+distributions almost lie exactly on top
+of each other with the exception that
+
+ align:start position:0%
+of each other with the exception that
+ 
+
+ align:start position:0%
+of each other with the exception that
+like on the standard titles the number
+
+ align:start position:0%
+like on the standard titles the number
+ 
+
+ align:start position:0%
+like on the standard titles the number
+of standard titles sold at a very low
+
+ align:start position:0%
+of standard titles sold at a very low
+ 
+
+ align:start position:0%
+of standard titles sold at a very low
+price just shoots up in 2012 after the
+
+ align:start position:0%
+price just shoots up in 2012 after the
+ 
+
+ align:start position:0%
+price just shoots up in 2012 after the
+Amazon acquisition um and so this is if
+
+ align:start position:0%
+Amazon acquisition um and so this is if
+ 
+
+ align:start position:0%
+Amazon acquisition um and so this is if
+there are many more people searching and
+
+ align:start position:0%
+there are many more people searching and
+ 
+
+ align:start position:0%
+there are many more people searching and
+so that left tail just gets pushed down
+
+ align:start position:0%
+so that left tail just gets pushed down
+ 
+
+ align:start position:0%
+so that left tail just gets pushed down
+but it doesn't affect the upper tail at
+
+ align:start position:0%
+but it doesn't affect the upper tail at
+ 
+
+ align:start position:0%
+but it doesn't affect the upper tail at
+all and you see that in all three
+
+ align:start position:0%
+all and you see that in all three
+ 
+
+ align:start position:0%
+all and you see that in all three
+categories of books that the lower tail
+
+ align:start position:0%
+categories of books that the lower tail
+ 
+
+ align:start position:0%
+categories of books that the lower tail
+gets much thicker and it just seems to
+
+ align:start position:0%
+gets much thicker and it just seems to
+ 
+
+ align:start position:0%
+gets much thicker and it just seems to
+be drawing from these slightly higher
+
+ align:start position:0%
+be drawing from these slightly higher
+ 
+
+ align:start position:0%
+be drawing from these slightly higher
+prices uh as if it's competition is
+
+ align:start position:0%
+prices uh as if it's competition is
+ 
+
+ align:start position:0%
+prices uh as if it's competition is
+pulling down the bottom end
+
+ align:start position:0%
+pulling down the bottom end
+ 
+
+ align:start position:0%
+pulling down the bottom end
+and then uh you know paper also then
+
+ align:start position:0%
+and then uh you know paper also then
+ 
+
+ align:start position:0%
+and then uh you know paper also then
+develops a structural model to sort of
+
+ align:start position:0%
+develops a structural model to sort of
+ 
+
+ align:start position:0%
+develops a structural model to sort of
+estimate what are the welfare gains from
+
+ align:start position:0%
+estimate what are the welfare gains from
+ 
+
+ align:start position:0%
+estimate what are the welfare gains from
+selling books
+
+ align:start position:0%
+selling books
+ 
+
+ align:start position:0%
+selling books
+online and you know our answer is there
+
+ align:start position:0%
+online and you know our answer is there
+ 
+
+ align:start position:0%
+online and you know our answer is there
+seems to be a substantial welfare gain
+
+ align:start position:0%
+seems to be a substantial welfare gain
+ 
+
+ align:start position:0%
+seems to be a substantial welfare gain
+but even in This Used Books case it's
+
+ align:start position:0%
+but even in This Used Books case it's
+ 
+
+ align:start position:0%
+but even in This Used Books case it's
+not enormous so we're more with Quan and
+
+ align:start position:0%
+not enormous so we're more with Quan and
+ 
+
+ align:start position:0%
+not enormous so we're more with Quan and
+Williams than we are with brinol and who
+
+ align:start position:0%
+Williams than we are with brinol and who
+ 
+
+ align:start position:0%
+Williams than we are with brinol and who
+and Smith in terms of what the welfare
+
+ align:start position:0%
+and Smith in terms of what the welfare
+ 
+
+ align:start position:0%
+and Smith in terms of what the welfare
+gains what we find is that the
+
+ align:start position:0%
+gains what we find is that the
+ 
+
+ align:start position:0%
+gains what we find is that the
+estimated uh estimated social welfare
+
+ align:start position:0%
+estimated uh estimated social welfare
+ 
+
+ align:start position:0%
+estimated uh estimated social welfare
+from selling one of these 2009 books in
+
+ align:start position:0%
+from selling one of these 2009 books in
+ 
+
+ align:start position:0%
+from selling one of these 2009 books in
+the offline world was
+
+ align:start position:0%
+the offline world was
+ 
+
+ align:start position:0%
+the offline world was
+$7.7 estimated social welfare from
+
+ align:start position:0%
+$7.7 estimated social welfare from
+ 
+
+ align:start position:0%
+$7.7 estimated social welfare from
+selling it online was
+
+ align:start position:0%
+selling it online was
+ 
+
+ align:start position:0%
+selling it online was
+$16.87 so it's a more than doubling of
+
+ align:start position:0%
+$16.87 so it's a more than doubling of
+ 
+
+ align:start position:0%
+$16.87 so it's a more than doubling of
+welfare that comes from selling online
+
+ align:start position:0%
+welfare that comes from selling online
+ 
+
+ align:start position:0%
+welfare that comes from selling online
+uh but it's only a more than doubling of
+
+ align:start position:0%
+uh but it's only a more than doubling of
+ 
+
+ align:start position:0%
+uh but it's only a more than doubling of
+welfare it's not a massive you know not
+
+ align:start position:0%
+welfare it's not a massive you know not
+ 
+
+ align:start position:0%
+welfare it's not a massive you know not
+a 10 times increase in welfare from
+
+ align:start position:0%
+a 10 times increase in welfare from
+ 
+
+ align:start position:0%
+a 10 times increase in welfare from
+selling these things online and you know
+
+ align:start position:0%
+selling these things online and you know
+ 
+
+ align:start position:0%
+selling these things online and you know
+the if you look at the firm
+
+ align:start position:0%
+the if you look at the firm
+ 
+
+ align:start position:0%
+the if you look at the firm
+profits you know the profit is coming
+
+ align:start position:0%
+profits you know the profit is coming
+ 
+
+ align:start position:0%
+profits you know the profit is coming
+from two different dimensions it's like
+
+ align:start position:0%
+from two different dimensions it's like
+ 
+
+ align:start position:0%
+from two different dimensions it's like
+the average price is going from $12 to
+
+ align:start position:0%
+the average price is going from $12 to
+ 
+
+ align:start position:0%
+the average price is going from $12 to
+$16 when they're sold online and the
+
+ align:start position:0%
+$16 when they're sold online and the
+ 
+
+ align:start position:0%
+$16 when they're sold online and the
+books are being sold sooner so instead
+
+ align:start position:0%
+books are being sold sooner so instead
+ 
+
+ align:start position:0%
+books are being sold sooner so instead
+of the e to the minus RT being3 the e to
+
+ align:start position:0%
+of the e to the minus RT being3 the e to
+ 
+
+ align:start position:0%
+of the e to the minus RT being3 the e to
+the minus RT is 48 um so the books are
+
+ align:start position:0%
+the minus RT is 48 um so the books are
+ 
+
+ align:start position:0%
+the minus RT is 48 um so the books are
+getting sold for higher prices and
+
+ align:start position:0%
+getting sold for higher prices and
+ 
+
+ align:start position:0%
+getting sold for higher prices and
+they're getting sold sooner those two
+
+ align:start position:0%
+they're getting sold sooner those two
+ 
+
+ align:start position:0%
+they're getting sold sooner those two
+things both make profit more than double
+
+ align:start position:0%
+things both make profit more than double
+ 
+
+ align:start position:0%
+things both make profit more than double
+uh we're also estimating that the
+
+ align:start position:0%
+uh we're also estimating that the
+ 
+
+ align:start position:0%
+uh we're also estimating that the
+consumer surplus as best we can is is is
+
+ align:start position:0%
+consumer surplus as best we can is is is
+ 
+
+ align:start position:0%
+consumer surplus as best we can is is is
+also more than doubling and the consumer
+
+ align:start position:0%
+also more than doubling and the consumer
+ 
+
+ align:start position:0%
+also more than doubling and the consumer
+surplus is more than doubling because
+
+ align:start position:0%
+surplus is more than doubling because
+ 
+
+ align:start position:0%
+surplus is more than doubling because
+you know the people who are willing to
+
+ align:start position:0%
+you know the people who are willing to
+ 
+
+ align:start position:0%
+you know the people who are willing to
+buy $16 books get more utility than
+
+ align:start position:0%
+buy $16 books get more utility than
+ 
+
+ align:start position:0%
+buy $16 books get more utility than
+people will to buy $12 books and they're
+
+ align:start position:0%
+people will to buy $12 books and they're
+ 
+
+ align:start position:0%
+people will to buy $12 books and they're
+getting them sooner so the consumer
+
+ align:start position:0%
+getting them sooner so the consumer
+ 
+
+ align:start position:0%
+getting them sooner so the consumer
+surplus is discounted by this instead of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that sorry I'm out of time so anyone you
+
+ align:start position:0%
+that sorry I'm out of time so anyone you
+ 
+
+ align:start position:0%
+that sorry I'm out of time so anyone you
+say uh that's what I've got on retail
+
+ align:start position:0%
+say uh that's what I've got on retail
+ 
+
+ align:start position:0%
+say uh that's what I've got on retail
+for today and then um
\ No newline at end of file
diff --git a/AwjT1gJSsco.txt b/AwjT1gJSsco.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5c125362a81d54acc6da4c834dd4b12f7677ba46
--- /dev/null
+++ b/AwjT1gJSsco.txt
@@ -0,0 +1,4208 @@
+Walt Guy's biography is on the website.
+
+I hope you've had a chance to look at it.
+
+I will just say briefly that I guess, of all
+the lecturers coming, that Walt is the only
+
+one who is still actually working actively
+for NASA.
+
+He is head of the Automation, Robotics and
+Simulation Division, division chief at the
+
+Johnson Space Center.
+
+But that is not what he's talking about there.
+
+He's talking about the job that he used to
+do for about 20 years which was head of environmental
+
+thermal life support and crew systems.
+
+And, of course, the crew system includes all
+the space suits and the good stuff that I
+
+was fortunate enough to get to use.
+
+So I've got a personal debt of thanks to Walt.
+
+Aaron, I think you wanted to say a couple
+of things so I will pass the microphone to
+
+you.
+
+Yes, I would like to say a few words about
+Walt.
+
+We've worked together for many years.
+
+And Walt Guy has the very unique capability
+of being not only an outstanding engineer,
+
+a technical person, but he also has a very
+unique capability of being a great or outstanding
+
+project manager, program manager.
+
+No matter what task you gave Walt, he could
+deliver the product on performance, on schedule
+
+and on time.
+
+He has that unique capability.
+
+And he's done that from the Apollo Program
+through the Shuttle Program.
+
+And I think you're really in for a treat to
+hear Walt talk about the environmental control
+
+systems.
+
+He has a lot of information to offer you so,
+without further ado, let me turn it over to
+
+Walt.
+
+Thank you, Aaron.
+
+As Aaron said, we worked together over several
+programs over a long period of time.
+
+I was noticing the picture.
+
+I'm sure that wasn't put there for me.
+
+But my current responsibilities are the robotic
+arm you see there.
+
+That is a shuttle arm.
+
+Of course there are station arms also.
+
+Grapple fixture over here on the left.
+
+And the little jet pack on the tumbling crewman
+there is part of my current responsibilities.
+
+The 20 years that Jeff mentioned, I was responsible
+for the development of the Shuttle spacesuit.
+
+So it was like it was meant for me anyway.
+
+What I'd like to do is talk about the design.
+
+I know in the syllabus it said environmental
+control systems.
+
+So where did all the rest of the stuff come
+from?
+
+If you go back in perspective, the Mercury,
+Gemini, Apollo Program had the classical thing
+
+that aerospace calls environmental control
+systems.
+
+It was basically a cabin system.
+
+It took care of the living quarters for the
+crew.
+
+But in the Shuttle era the responsibility
+of that system expanded to include more than
+
+just the cabin and, thus, the very long hard
+to say name.
+
+These are the subsystem elements of the environmental
+thermal control and life support system.
+
+The first area I am going to -- These are
+the areas, the subsystems.
+
+The first area is the cabin atmospheric revitalization
+system.
+
+This is a long way of saying to take care
+of the atmosphere in the cabin.
+
+Humans are pollutants and this is the system
+that takes care of that.
+
+The cabin atmospheric pressure and composition,
+this is obviously to maintain the pressure
+
+and enough oxygen for breathing.
+
+The third is the cabin thermal control, and
+that is the classical environmental control
+
+system.
+
+But, for Shuttle, we've added some functions.
+
+One is the water and waste management subsystem.
+
+There are some hygiene functions required,
+there are some recharge of the spacesuit's
+
+backpack, management of the fuel cell water
+system, the fuel cells of the electrical power
+
+supply and provide a lot of extra water.
+
+Also, the vehicle at this point, has a dedicated
+active thermal control system that takes care
+
+of all of the systems in the vehicle, not
+just the cabin systems.
+
+And then last is the airlock support subsystem.
+
+This is the EVA crewman's portal to space.
+
+And so the environmental thermal control and
+life support system covers all these areas.
+
+What I will do is go through each one of those.
+
+The first is the cabin atmospheric revitalization
+system.
+
+Its functions are CO2 and trace gas removal,
+humidity control, environmental cooling and
+
+atmospheric circulation and ventilation.
+
+Again, I will talk each about these.
+
+But I do want to mention that there is a uniqueness
+about space and that there is no convection
+
+so circulation is important.
+
+Also, because of the fact that there is no
+convection, getting rid of the body heat,
+
+the latent heat requires a ventilation of
+the crew.
+
+So each of these areas ended up as part of
+the system design.
+
+This is an overview silhouette of the Orbiter.
+
+I will use this throughout the presentation.
+
+As you can see, part of the system we're talking
+about now, the atmospheric revitalization
+
+system is located upfront where the crew is.
+
+It is beneath the floor.
+
+And we will be talking about the systems in
+the remainder of the Orbiter as we go along.
+
+This is a simplified schematic.
+
+I would like to start at the cabin fans.
+
+These are redundant.
+
+Each fan will do the job.
+
+The next in line is the CO2 scrubber followed
+by the cooler, the cabin heat exchanger.
+
+There is a bypass around that for control
+of the amount of cooling that is needed.
+
+As you are aware, the Shuttle can fly with
+few or many crewmen.
+
+It turns out, as time has gone on, we fly
+pretty much a full compliment.
+
+But the original design was to fly a small
+number of crewmen.
+
+Also, this does give you temperature control.
+
+The same heat exchanger provides the condensation
+of the water from the atmosphere.
+
+Therefore, you get humidity control.
+
+And then that is collected.
+
+The gas continues on.
+
+It is now chilled and is provided out to the
+flight deck and the middeck to the crew.
+
+Then the gas from the cabin is then drawn
+back in through some flight deck avionics
+
+and back through the fans.
+
+So this is the basic systems schematic.
+
+I might pause here a moment to sort of explain
+the role of the government in the development
+
+of the Shuttle.
+
+As you know, the prime was Rockwell.
+
+It was their job to build the vehicle.
+
+But the government philosophy, management
+philosophy was to have ownership of the technical
+
+aspects of the design.
+
+So we had basically no excuse.
+
+If it didn't work it wasn't because the contractor
+did something wrong.
+
+We had to have ownership.
+
+In fact, Aaron, as the project manager, would
+probably look to us first as the reason for
+
+a problem as opposed to Rockwell because we
+were the conscience of the program so we should
+
+have made sure they didn't do it wrong and
+provided whatever technical insight to Aaron
+
+to make sure he made the programmatic decisions
+to make sure things were not done wrong.
+
+Very early in the Shuttle Program, I was responsible
+for an engineering organization.
+
+And that engineering organization wanted to
+own the design of the environmental thermal
+
+control and life support system.
+
+We acquired a chamber.
+
+This is a near atmospheric chamber.
+
+It is a square so it is obviously not shaped
+like the Orbiter cabin, but the volume was
+
+appropriate.
+
+And it did allow a sealed environment for
+testing.
+
+It would take a couple of PSI delta Ps.
+
+That's about all it would take.
+
+We developed a -- [COMMENT FROM HOFFMAN],
+No, that was a different one.
+
+OK.
+
+We developed an environmental control system
+or an atmospheric revitalization control system
+
+and placed it inside to do early testing.
+
+As you can see here, this is the fan package.
+
+The CO2 scrubbers are here.
+
+Heat exchange package over here.
+
+And you can tell we're not current in terms
+of calendar-wise.
+
+The CO2 and trace gas removal, the requirements
+were to maintain less than 7.6 millimeters
+
+of mercury.
+
+This is certainly to provide a habitable environment
+for the crew.
+
+This is higher than sea level but the medics
+agreed that that was a completely adequate
+
+level for CO2.
+
+The CO2 absorption came from the humidified
+cabin gas so the system had to accommodate
+
+that as a feed stream.
+
+The absorbent selected was lithium hydroxide.
+
+The equation was a lithium hydroxide reacted
+with the CO2 to produce lithium carbonate,
+
+water and heat.
+
+And this was a single use system.
+
+It turns out that the lithium hydroxide was
+an old solution.
+
+The previous spacecraft had used the same
+solution, but pretty much their solution was
+
+unique purchased production of lithium hydroxide.
+
+When we entered the Shuttle era, we were hoping
+for a long duration.
+
+And the idea was to use the commercial products
+to get away from special production.
+
+And so we looked around.
+
+And the Navy was producing a screened special
+production run for their submarines.
+
+So there was a lot of use there.
+
+And so the production was reasonably upo.
+
+We decided to use the Navy grade.
+
+And so we brought it in and put it in the
+test bed that I just showed you and did some
+
+tests, and it didn't work worth a darn.
+
+You notice the loops here show that our use
+of the canister was much more rapid that we
+
+had hoped for.
+
+The nice beautiful deep loops here are a process
+that we developed to screen the Navy LiOH
+
+so that we didn't have to create a new production
+capability but were able to test the LiOH
+
+that came off their production line and get
+a LiOH that was much more humidity tolerant.
+
+The key here turned out to be not the chemical
+itself but its ability to produce good performance
+
+over a wide humidity range.
+
+So we were able to screen that and make that
+a viable non-special production run LiOH.
+
+The lithium hydroxide, I said, was an old
+solution.
+
+All previous spacecraft have been pretty short
+mission.
+
+And even the Shuttle was a short mission.
+
+But the specification for Shuttle said that
+it should have a capability of going 28 days,
+
+and 28 days is not a short mission, at least
+not in Shuttle parlance.
+
+The engineering part of the organization said,
+well, why don't we go with a regenerative
+
+system?
+
+SkyLab had just been successfully flown with
+a regenerative system, something that wouldn't
+
+have all this expendables because 28 days
+worth of lithium hydroxide for seven crewmen
+
+fills everything up with lithium hydroxide.
+
+There is no room for anything else.
+
+So we began to look at a regenerative system
+that could be used.
+
+Actually, it was proposed as part of the original
+Shuttle development.
+
+But, at that point, the 28-day mission was
+considered a special case and the design case
+
+was the shorter missions.
+
+And, in fact, there were even projected to
+be a lot of short missions.
+
+The idea that the Shuttle was a space truck.
+
+It would take stuff up, dump it out and come
+home.
+
+And so the lithium hydroxide was a lighter
+system than a regenerative system.
+
+The lithium hydroxide was placed into the
+vehicle as a basic design.
+
+But, when the Space Lab era came along, we
+needed longer missions.
+
+We flew about four or five times in this 13
+to 16 day range, and those missions did require
+
+a lot of lithium hydroxide.
+
+And so it was proposed to use an absorbent
+that was regenerable, and the one that was
+
+selected was a solid amine.
+
+The absorbent is a polymerized ethyleneimine.
+
+Its designation is RNH, and I don't really
+know why.
+
+The absorption actually comes in, in two steps.
+
+First there is a reaction with water to create
+the Freon.
+
+And then that is then reactive with the CO2
+to give you another free ion, but the CO2
+
+is now captured.
+
+The desorption then with the heat and vacuum
+gives you back your original amine.
+
+So if you pack this in a bed, and what we
+used was an expanded metal foam heat exchanger
+
+that you could fill all the holes with the
+solid amine and put the passages adjacent
+
+to each other so that you could use the heat
+of absorption to do your desorption on your
+
+other side.
+
+And all you would need to do is expose it
+to vacuum.
+
+It was a very simple system.
+
+It worked fine for the three or four missions.
+
+I'm not sure how many missions it was used.
+
+But it was an adjunct.
+
+It was added in, put onto the floor, and then
+it was taken back out when it was no longer
+
+needed because it was just wasted load.
+
+Yes.
+
+For the lithium hydroxide, the product LiCO3,
+is that a solid form or a gas form?
+
+No, it's a solid lithium carbonate.
+
+And that goes in the canisters that you remove?
+
+Right.
+
+When you remove the canister it's a big lump.
+
+OK.
+
+Finishing up the CO2 and trace removal, we
+go to the trace removal and use the simple
+
+system of activated charcoal.
+
+And, in fact, it is packed into the same canister
+that the lithium hydroxide is packed into.
+
+It is a single use.
+
+There is a configuration, I believe, now operationally
+where the entire canister is activated charcoal
+
+so it can be used for cabin gas cleanup.
+
+So, if you had an issue that you needed to
+clean the cabin up, you could do that with
+
+a canister just of charcoal.
+
+The next area is the environmental cooling
+and humidity control.
+
+I mentioned on the schematic that we have
+a cabin heat exchanger.
+
+The front part of the heat exchanger basically
+is your reduced cabin gas temperature.
+
+The backend of the heat exchanger is where
+the condensing occurs because we get the gas
+
+below the dew point and, therefore, the water
+drops out.
+
+The heat exchanger has the characteristic
+that, as the water collects at the outlet
+
+of the heat exchanger, there were some holes
+drilled, actually, in the thin passages so
+
+the water can be sucked out.
+
+And it has the nickname "slurper." So it slurps
+the water out.
+
+It takes about 2% of the flow.
+
+So, as the cabin fan produces the flow through
+the heat exchanger, about 2% is siphoned off
+
+in the slurper.
+
+And that carries the water to the centripetal
+water gas separator.
+
+This is a device that basically spins the
+airstream.
+
+It's an airstream with water and trained.
+
+It spins the airstream.
+
+The water goes to the outside.
+
+It is collected in a trough and there is a
+pitot tube in the trough that the water impinges
+
+on, and we get about a 40 PSI delta head with
+that.
+
+It's just a pump basically, a pitot pump.
+
+The atmospheric circulation and ventilation
+is the next part of the system.
+
+As you know, we're still in atmospheric revitalization.
+
+There are the redundant fans that I mentioned.
+
+Each fan will do the job.
+
+There is also flight deck and mid deck duct
+system.
+
+It looks very complicated but there are only
+several points I want to make here.
+
+This is the atmospheric revitalization system
+I mentioned before.
+
+As you see, it is below the floor.
+
+This is the mid deck here.
+
+This is the flight deck.
+
+So it's below the floor of the mid deck.
+
+The gas exits the heat exchanger.
+
+It goes up.
+
+There is some aft mid deck ventilation exhaust.
+
+It goes on up to the flight deck and exhausts
+on the flight deck.
+
+Also there is a section that goes on the forward
+side of the cabin through the forward control
+
+console and blows in the face of the crew.
+
+The return is back through some avionic areas
+to provide cooling, and then back down to
+
+the system.
+
+This is a complicated picture, but really
+it is a very simple flow system.
+
+This becomes important later in our discussion
+because good mixing turned out to be a really
+
+important parameter.
+
+Not just cooling.
+
+OK.
+
+The second.
+
+Remember we had six?
+
+This is the second element.
+
+This is the atmospheric pressure and composition
+control.
+
+The first job is the 14.7.
+
+The Shuttle selected sea level, the idea being
+we could not have a lot of special designed
+
+equipment.
+
+Shuttle was intended to be a less expensive
+spacecraft than the previous ones.
+
+And so a sea level atmosphere gave us no questions
+about human survival and gave us a lot of
+
+opportunity for using more standard equipment
+and not specially designed equipment.
+
+There was a requirement, though, for a PSIA
+total control, but this was only for an emergency
+
+de-orbit.
+
+The problem statement is that you got a hole
+in your cabin.
+
+Don't know how you got it but you have it.
+
+And the idea is the system has to be able
+to sustain the crew for a de-orbit.
+
+And I don't know who made up the number but
+169 minutes is the number.
+
+We have an emergency return, 169 minutes.
+
+The system has to be able to accommodate that
+keeping the total pressure at or above 8 PSI.
+
+So there has to be enough flow capability,
+enough consumables to do that.
+
+The half-inch hole was a programmatic decision.
+
+I cannot speak for where the number exactly
+came from, but it probably had to do with
+
+meteoroid debris kind of analysis that said
+what type of hole you could expect.
+
+Anyway, that was the design for the system.
+
+The next aspect or element of the system is
+the O2/N2 partial pressure control.
+
+At the total pressure of 14.7, we wanted sea
+level which is about 3.2 PSI oxygen.
+
+At the 8 PSI, we wanted it to be survivable
+but the oxygen could be less.
+
+Obviously, people live in Denver so that works.
+
+There are also crew breathing masks which
+can be used in conjunction with low oxygen
+
+partial pressure.
+
+The cabin had to have both positive and negative
+relief.
+
+It had to store the oxygen and nitrogen, and
+it had to provide pressurization for the water
+
+management system.
+
+Remember earlier I talked about the more pervasive
+requirements?
+
+The water and waste management system now
+is placing requirements on the atmospheric
+
+pressure and composition control.
+
+This is a silhouette again where basically
+here you see the oxygen tank, which is 3300
+
+PSI oxygen tank.
+
+There are nitrogen tanks on both sides.
+
+These are high pressure tanks all 3300 PSI.
+
+The relief valves are shown here.
+
+And there is an O2/N2 supply panel which has
+all of the valves and regulators and everything
+
+on it.
+
+This system, however, though, gets most of
+its oxygen from the cryogenic tanks.
+
+So that is only just shown as an inlet.
+
+These tanks are basically part of the power
+control system.
+
+Electrical power is hydrogen and oxygen fuel
+cell.
+
+We use a lot less oxygen than they do so the
+storage was integrated.
+
+And then we use the oxygen for most of the
+uses.
+
+It comes from the main tanks.
+
+This is a schematic.
+
+I will start right there.
+
+This is the cryogenic system.
+
+This is the main cryogenic system.
+
+This is not part of the tankage of the pressure
+and composition control system.
+
+It goes through a restrictor.
+
+This is stored in a super critical state so
+the delivery is somewhat limited.
+
+And so this goes through a restrictor so that
+we don't decrease the pressure too fast in
+
+the cryogenic tank.
+
+It comes on down through a regulator that
+regulates down to 100 PSI.
+
+And that comes on down to two regulators.
+
+One is the normal regulator, the 14.7, and
+the other is the 8 PSI regulator, both of
+
+which are available depending on which cabin
+mode you're in.
+
+If you go over this way you will see the nitrogen.
+
+The nitrogen goes through its own regulator,
+and it is regulated at 200 PSI.
+
+And that's important because that is contrasted
+to the 100 here.
+
+Next the nitrogen goes through an on/off valve,
+a solenoid that is connected to partial pressure
+
+sensors of oxygen.
+
+And, if you're making up cabin gas, you have
+to make a choice as to whether you want nitrogen
+
+or oxygen.
+
+And that choice is made by this system and
+a simple on/off valve.
+
+There is no sophisticated control system.
+
+This is a simple on/off valve.
+
+If the cabin needs pressure but doesn't need
+oxygen then this valve is open and the 200
+
+PSI basically backs down the oxygen system.
+
+There is a check valve here, no oxygen flow
+because you get nitrogen.
+
+At the point that you need oxygen, this valve
+closes, then there is no 200 PSI anymore.
+
+Therefore, the 100 PSI provides oxygen to
+the regulators.
+
+It is a very simple design.
+
+Off the top of your head, what kind of failures
+did you have during qual test that really
+
+bothered you?
+
+The regulators were produced by Carlton, and
+the regulators were derivatives of regulators
+
+they had been building for years.
+
+So the regulator functions really were pretty
+good.
+
+But the early problem we had was the pressure
+tolerance wandered and didn't have as good
+
+a pressure tolerance.
+
+And they did make some mods to correct that.
+
+But the more significant issues got into flow
+issues.
+
+Their test capability was pretty limited.
+
+And when you're talking about very high flow
+cases you have to do something with the gas
+
+to make the regulator think that it is in
+an operational environment.
+
+And so we did a lot of testing, and I will
+show you that in just a second, for the high
+
+flow cases.
+
+Let's see.
+
+There is a redundant system.
+
+It is not shown in this schematic but there
+are two of these, just like this.
+
+This is the pressurization for the water and
+waste management system you see here.
+
+I would say there is a crossover to the redundant
+system so that you can do mix and match.
+
+If you have a problem in both systems, you
+can mix and match the capabilities.
+
+Also, the oxygen system provides the emergency
+breathing system.
+
+It also provides oxygen to the air lock for
+recharge of the backpack.
+
+We will talk about that later.
+
+And I believe that's it.
+
+So, for normal pressure, we have 14.7.
+
+And you have the automatic pressure regulator,
+basically on/off valve and the regulator.
+
+The partial pressure is controlled by the
+3.2 PSI which is the solenoid that controls
+
+that.
+
+It is a very simple system.
+
+The oxygen partial pressure does have another
+set point at the PSIA goes down to 2.45 PSI.
+
+And I will show you that in a minute.
+
+For cabin pressure relief, the problem statement
+really is why do you need relief?
+
+Well, what if one of those lines breaks?
+
+You've got 3300 PSI tankage.
+
+It is all plumed together.
+
+The crew, God forbid, step on a line and break
+it, and now you've got all this nitrogen rushing
+
+in.
+
+You don't want the cabin to explode, right?
+
+So you need a relief valve.
+
+And the relief valve was set at 16.2.
+
+And, again, that is one of the high flow cases
+that we ended up testing.
+
+The system was designed with three relief
+valves.
+
+Any tool will do the job.
+
+That is just a redundancy philosophy.
+
+Sometimes you will see two items where either
+one does the job.
+
+In this case, this is a very critical issue
+so there is a double redundancy here.
+
+For the negative pressure protection, there
+is an 8 PSI delta relief valve.
+
+In fact, there are three of those.
+
+You don't need the two to operate, but there
+are three.
+
+This is for the return that I just showed
+you.
+
+If you come back with a hole in the cabin,
+the cabin is at 8 PSI, you cannot reverse
+
+flow through that hole.
+
+That is not going to work.
+
+You don't want the cabin imploding on the
+crew so you've got to make up, as you come
+
+in the lower altitude, obviously the higher
+pressure, you've got to get that gas back
+
+in the cabin.
+
+So that's what that is for.
+
+OK.
+
+This is the other pressure vessel that was
+used as a test site.
+
+This was called the Environmental Test Article.
+
+Rockwell gave it that name.
+
+What they planned to do with this device,
+when they built it, was to do all the wiring
+
+runs and the plumbing runs in there.
+
+It was going to be a mockup.
+
+It turned out they built a rather beefy tank.
+
+In fact, maybe they got one very inexpensively.
+
+I'm not sure how they ended up with it, but
+they got it.
+
+They did do all the secondary structure, so
+it had the right shape inside.
+
+And so it turned out they didn't end up using
+it.
+
+They went onto other methods.
+
+And so it ended up leftover in the program.
+
+We convinced Aaron that he ought to give it
+to us, and he did.
+
+This is what it looks like in cutaway.
+
+You see here all the secondary structure,
+it was in boxes but we put it all in.
+
+Foamed it in so that the volume was right,
+so the cabin volume was essentially perfect.
+
+It had the flight deck.
+
+It had the mid deck.
+
+It had the lower deck for the environmental
+control system.
+
+But we also asked Aaron to give us the cert
+hardware, which he did.
+
+So we had the cert hardware underneath the
+floor.
+
+And the pressure control system we're talking
+about, actually, is on this back wall.
+
+That is a picture of it.
+
+What we did is faithfully run the lines.
+
+In fact, we even use the same line material,
+same fittings, same everything.
+
+So we faithfully duplicated inside this test
+article the volume and the geometry and the
+
+system.
+
+All the ventilation ducts you saw, all those
+were in place.
+
+We will come back to it later, but you'll
+notice on the back wall of this test facility
+
+there is an airlock hatch.
+
+And later on I will tell you where that goes.
+
+But this is the control panel and the nitrogen/oxygen
+system.
+
+This is test data.
+
+We did some testing to see how the system
+worked.
+
+This was testing of basically the on/off oxygen
+control system.
+
+Let me see if I can walk through this simply.
+
+We're working total pressure here, oxygen
+partial pressure here.
+
+During this first interval the oxygen is on.
+
+What we're doing here is we're breathing it
+down.
+
+And, when we hit the lower limit so that the
+regulator wants to do something, then the
+
+oxygen partial pressure starts up because
+the regulator comes on.
+
+Now, the total pressure is maintained because
+that is what the regulator is supposed to
+
+do, maintain total pressure.
+
+But as it maintains the total pressure it
+is doing it with oxygen and, therefore, the
+
+partial pressure is going up.
+
+When it is satisfied, that is enough partial
+pressure of oxygen, then the solenoid valve
+
+opens and you see the nitrogen come on.
+
+Now, you remember the nitrogen feed was at
+300 PSI versus 200 PSI.
+
+So there is a little jump.
+
+That is just a mechanical artifact of the
+regulator.
+
+If you change the inlet pressure it regulates
+slightly differently because it is a balance
+
+system.
+
+You see a little jump there.
+
+And then, during this period, the pressure
+is maintained.
+
+But we're breathing off the oxygen because
+we've got the oxygen fenced off now.
+
+And then when the pressure is satisfied and
+the solenoid goes back the other way then
+
+we again start the oxygen again.
+
+So the system worked quite well.
+
+If you notice the tolerance band spec-wise
+was pretty wide, the system operated on a
+
+very narrow brand so we were very pleased
+with that.
+
+Normally that is important.
+
+Not only because it shows you that you do
+have a good sensitive system, but you cannot
+
+-- Mechanical hardware, electrical hardware,
+either one never operates down the middle
+
+always.
+
+There is drift.
+
+You need a little tolerance in your band here
+to have a decent system design.
+
+Yes.
+
+Does this change a lot when you have the crew
+performing high metabolic activity?
+
+The cabin is so large that it really doesn't
+know.
+
+The cycles would be different, obviously,
+because you consume more oxygen, you would
+
+need more oxygen.
+
+So the on/off cycle would favor longer oxygen
+cycles.
+
+But, in the big picture, there is really not
+a lot of change.
+
+What was this time period?
+
+It looks like this was about three hours maybe.
+
+That might go to two hours for a cycle.
+
+I mean not really very much.
+
+Sorry.
+
+Does microgravity have much effect on circulation?
+
+There is no circulation in microgravity.
+
+It just lays there.
+
+You push it or it doesn't go.
+
+Diffusion is a driving force, so if you're
+really, really patient, even at zero G you
+
+can wait, but you cannot stay alive that way.
+
+But, yes, you do have to have ventilation.
+
+Still in the atmospheric pressure and composition
+control.
+
+This is the emergency breathing equipment.
+
+We used plug-in face masks.
+
+There are some uses for the mask that require
+a carry on bottle to give portability, but
+
+the vehicle does have plug-in capability.
+
+The masks were purge-type masks.
+
+You're probably not familiar much with masks,
+but there is a mask called a rebreather which
+
+basically your lung power does all the work
+and you only purge enough to keep the CO2
+
+down and you keep rebreathing.
+
+And then the purge-type is every breath is
+a fresh breath, and you then exhale and the
+
+gas goes out in the cabin.
+
+And that's the type that this is because the
+cabin needs the oxygen.
+
+I mean it's not going anywhere bad.
+
+It is OK that it's not completely spent.
+
+It's good.
+
+That's like a scuba mask, right?
+
+I don't scuba.
+
+Sorry.
+
+But I think the answer is yes.
+
+With scuba, you take in the air and then you
+blow it all out.
+
+I mean there are scuba rebreathing systems,
+but the typical scuba gear is not.
+
+Rather than raising your hand, if you make
+a noise of some kind.
+
+Sorry.
+
+I don't mean to ignore you.
+
+The mask can be used in a contaminated environment
+and the mask can be used if the concentration
+
+of O2 is low to give you a better oxygen level.
+
+This is the PSIA test that we did.
+
+Actually, a series of tests.
+
+But this is data from one.
+
+As you see, we started up in the 14.7 range.
+
+We simulated the hole.
+
+The pressure immediately starts down.
+
+The partial pressure of oxygen we let degrade
+to about the 2.2 range.
+
+This is a different set point.
+
+Remember I told you on the oxygen sensors
+we have two set points?
+
+This is the second set point.
+
+And so we have the lower oxygen partial pressure.
+
+The system came down.
+
+The PSIA regulator, which is always online,
+captured the pressure decay, caught it, and
+
+the solenoid valve popped back and forth to
+keep the oxygen OK because we're losing now.
+
+We're going out this half-inch hole.
+
+And the system worked just fine.
+
+This did have the crew on the masks because
+that is livable, you can live there, but the
+
+mask is a better environment.
+
+This is a mask case.
+
+This was a requirement that came on later.
+
+The design is the design now.
+
+The vehicle exists so we have to now operate
+the vehicle with accommodations for operationally
+
+what we want to do with it.
+
+And a new requirement developed and was imposed
+on the vehicle.
+
+And that requirement had to do with the space
+suit for the EVA operation.
+
+The Shuttle spacesuits are basically 100%
+O2.
+
+And the classical way of going EVA from a
+sea level environment was a four hour prebreathe.
+
+Actually, as much as six hours depending on
+how conservative the medics were at the time,
+
+that number varied around some, to prevent
+bends.
+
+But it was determined that if you accommodized
+at 9 PSI for about 12 hours then you only
+
+required a really short prebreathe.
+
+And the suit-up time, which gave you 30 to
+40 minutes, actually gave you sort of a free
+
+tune-up to your prebreathe as part of your
+suit-up operation.
+
+And so that was viewed as a much better way
+to do EVAs than the previous way.
+
+The masks are useful but are not very comfortable.
+
+So, if you have to keep them on for a long
+period of time, they're not very comfortable
+
+at all.
+
+Also the medics were very concerned about
+mask leakage, that if there was any nitrogen
+
+inflow that that could break the prebreathe.
+
+But our system isn't designed for 9.
+
+We have a 14.7 and an eight, but we don't
+have a 9, so we needed a manual procedure.
+
+But before that could be accepted there were
+some issues that had to be evaluated.
+
+And we had to do testing on each of these
+issues.
+
+The first is the flow rate acceptability at
+9 PSI.
+
+Obviously, the less dense gas you're not going
+to get the same mask flow rate.
+
+And we had to make sure that that ventilation
+was going to be adequate.
+
+And testing proved that it was.
+
+The next is a thermal acceptability.
+
+There are really two aspects to this.
+
+One is the fan itself is cooled by the environment,
+so if the environment doesn't provide as much
+
+cooling to fan itself it could overheat.
+
+Also, the electronic equipment, some of which
+is air cooled, the less dense gas could be
+
+a problem there.
+
+It turned out that could be controlled with
+load control.
+
+That could off load power and make that acceptable.
+
+The CO2 performance at 9 PSI, we needed to
+make sure that was OK.
+
+It turned out that, of course, the 9 PSI case,
+we don't care about the lithium hydroxide.
+
+The purge flow is so great there is no CO2
+problem.
+
+But at 9 PSI for 12 hours you have to get
+performance out of the lithium hydroxide.
+
+So we checked that and that worked out fine.
+
+And the last item was the ventilation adequacy.
+
+We do have a press and depress.
+
+You've got to come down to 9 and you've got
+to go back.
+
+And both of those adjust the gas mixture.
+
+And so we wanted to prove that that was OK.
+
+And so we went to the facility that we were
+talking about and ran this profile.
+
+Now, this profile was created by our-- yes?
+
+[AUDIENCE QUESTION]
+
+Well, that's what I just said.
+
+Yes, it does.
+
+The air-cooled equipment is going to run hot.
+
+If you want to cool that equipment, it will
+become a little clearer later, but the equipment
+
+is in equipment bays.
+
+And so, with the less dense gas, you need
+to have some of that equipment turned off
+
+so that the cooling that is available is adequate.
+
+So you do load control, get rid of some of
+the electronics.
+
+And, therefore, the air that's left, the atmosphere
+that is left can cool the equipment.
+
+And then when do you increase the pressure
+back to normal after the EVA?
+
+After the 12 hours.
+
+No, actually it's before the EVA.
+
+Well, I'm not sure what they do now.
+
+When you're all finished with your EVAs then
+you bring the cabin back.
+
+Because, typically, you do multiple EVAs.
+
+And so, from one day to the next, you just
+keep the cabin at, actually, we use 10.2 now
+
+rather than 9, but I think you have to certify
+it for 9, right?
+
+This was an early certification for 9.
+
+Yes.
+
+But wouldn't it have been easier to simply
+design the whole system for 9 from the beginning
+
+if you had [OVERLAPPING VOICES]?
+
+Well, this was not a Shuttle requirement.
+
+This was an operational requirement that occurred
+after the Shuttle specifications were set.
+
+You're correct.
+
+If we knew it ahead of time it would have
+been much easier to do it all for 9 PSIs,
+
+exactly.
+
+It would have just been a third condition.
+
+But, as Jeff pointed out, we changed our mind.
+
+The first was 9 and now we're at 10.2, so
+we're not consistent.
+
+As we learn, we change our mind.
+
+And the 10.2 was selected later.
+
+Our mission operations people that do the
+crew time lining and all, they created this
+
+procedure.
+
+And so we tested it.
+
+This has a simple depress cycle.
+
+You come from 14.7.
+
+You hesitate at about 11 and replenish the
+oxygen.
+
+You do that twice.
+
+You then do manual control down at the 9 psi
+level.
+
+You notice the oxygen partial pressure here
+is always maintained by these adjustments,
+
+and also during the manual period you select
+what you want.
+
+And then when you come back, the procedure
+was to increase the nitrogen and then finish
+
+the top off with oxygen.
+
+That was thought to be completely acceptable
+because the oxygen level, at this point, is
+
+completely viable.
+
+And so doing the nitrogen first and topping
+it off with oxygen was thought to be an acceptable
+
+way to operate.
+
+So we did the test and this is what happened.
+
+We were all nice and comfortable with our
+oxygen partial pressure.
+
+And you see the area next to where we were
+repressing.
+
+We depleted the oxygen substantially.
+
+And the mid deck and even the flight deck,
+we depleted the oxygen.
+
+And I've only shown you half the data.
+
+If you look at the rest of the data, you see
+where the oxygen went.
+
+These equipment bays that I mentioned earlier,
+the avionics bays and other equipment bays
+
+are basically isolated volumes from the cabin.
+
+So, as the pressure comes up, what you're
+doing is you're pressurizing these areas with
+
+cabin gas, which is oxygen and nitrogen, you're
+pressurizing these areas with nitrogen only.
+
+Basically, you are depleting the partial pressure
+here.
+
+You're increasing the partial pressure here.
+
+You remember partial pressure.
+
+You just count the molecules.
+
+That's all you have to do.
+
+Basically, we're putting more oxygen molecules
+here and we're taking them out of these areas.
+
+And, therefore, they are going down.
+
+This is just a picture of one of the bays.
+
+You see all the empty space around the equipment.
+
+That is where the gas is.
+
+We came up with an alternate procedure which
+is to simultaneously put the oxygen and nitrogen
+
+in together.
+
+And, of course, there is the 9 back to 14.7.
+
+And you notice that solved the problem.
+
+There is still some dip at the supply area
+because the mixture is lean.
+
+We need from 9 to 14.7, 5.7 PSI total pressure
+increase.
+
+But we only need 2.5 up to 3.2 oxygen.
+
+This is a mixture, but it's a lean mixture.
+
+So there is still some slight loss, but the
+only area that came under an issue is near
+
+the inlet where the O2/N2 supply panel is.
+
+And, of course, you can just avoid that area.
+
+Well, I should say that that area happens
+to be right around the bathroom.
+
+And so, before we repressurized the Shuttle,
+the commander would say anybody who has to
+
+use the bathroom use it now because for about
+ten, fifteen minutes, while we're depressurizing,
+
+it's off limits.
+
+OK.
+
+Next item.
+
+This is the water and waste management area.
+
+This is one of the six items.
+
+We have potable and waste water inventory
+management.
+
+We're continually producing potable water,
+as you know, and waste water.
+
+We have to dump them, we have to use them,
+so that is part of the requirement of this
+
+system.
+
+We have to store water for drinking, food
+prep and waste water storage.
+
+It has to be dumped to space.
+
+Commode and urinal for human waste collection.
+
+And we provide water for an evaporative heat
+sink, which we will talk about later, called
+
+the flash evaporator.
+
+Yes.
+
+This is an outstanding example of systems
+engineers, this total system that Walt is
+
+talking about.
+
+We can really see the interaction between
+all the systems and the spacecraft.
+
+This really is a systems engineering problem.
+
+Potable water, we take all the fuel cell byproduct
+water and use it.
+
+So it is basically in a fluent to the power
+system.
+
+We do have a launch storage capability for
+water and we do provide sterilization.
+
+The sterilization is iodine.
+
+We started out designing a silver ion system.
+
+It turned out that we had manufacturing problems
+and the company ended up going out of business,
+
+so we reverted to iodine.
+
+The Lunar Module used iodine.
+
+Waste water, the condensate from the cabin
+humidity control and urine and the urine pretreat.
+
+Urine has to be pretreated to bind the urea.
+
+If you don't, you get a lot of ammonia.
+
+It uses a chemical called Oxzone.
+
+It's an acid.
+
+I'm not really sure what it is.
+
+This is where the system is located.
+
+This is one of the simpler schematics.
+
+The water tanks are here.
+
+The water comes from the fuel cell.
+
+As I said, by the way, the delivery is about
+150 degrees and 60 psi.
+
+So there is a lot of hydrogen dissolved in
+the water.
+
+The water is collected in the fuel cells on
+the hydrogen side, so there is a lot of hydrogen.
+
+There is a hydrogen separator here.
+
+Otherwise, your tanks would end up full of
+hydrogen which is what you don't want.
+
+You will get water in the tanks.
+
+The hydrogen separator is a silver palladium
+metal.
+
+It is catalyzed.
+
+It is basically porous to hydrogen but not
+to water.
+
+If you expose the backside to the vacuum it
+pulls the hydrogen off and the water goes
+
+through just fine.
+
+I will say that there still is a rather high
+gas content in the water that you drink.
+
+And that gas, of course, evolves once it gets
+inside your stomach with predictable results.
+
+[LAUGHTER]
+
+Yes.
+
+In fact, all sorts of systems that Jeff could
+explain.
+
+They have slinger systems and all sorts of
+systems to get separation because it is not
+
+really possible to get all the gas out of
+the water.
+
+OK.
+
+There is a dump system.
+
+There is a potable waste dump to vacuum.
+
+There is also a vacuum vent, which I will
+show you what that is all about.
+
+And then the flash evaporator that I mentioned,
+and I will mention more later, is in the back
+
+of the vehicle and it has a redundant water
+feed system both sides.
+
+This is a schematic.
+
+Start at the same place.
+
+Water from the fuel cells goes through the
+hydrogen separator and then into this bank
+
+of tanks.
+
+The tanks are pressurized.
+
+They are yellow bellows tanks.
+
+On the back side of the bellows is nitrogen.
+
+On the forward side, of course, is the potable
+water.
+
+There is a hydrophobic filter on the downside
+of each tank.
+
+If a bellows were to leak, you don't want
+water into your nitrogen system.
+
+So this is a filter to prevent that.
+
+I mentioned the twin flash evaporator feeds.
+
+There they are.
+
+This is the dump nozzle here.
+
+The potable water system provides water to
+the crew so there is a regular water interface
+
+and a chilled water interface here.
+
+I believe that is it.
+
+I remember there were more problems with Apollo
+than there were with Shuttle.
+
+49:30 I don't have those sorted mentally.
+
+I'm sorry.
+
+I don't remember.
+
+I'm not sure.
+
+[AUDIENCE QUESTION]
+
+Maybe that was on Apollo.
+
+[AUDIENCE QUESTION]
+
+Basically that means you put your water into
+a plastic bag.
+
+And now you can actually swing it around like
+so.
+
+And so the water will go to the outside and
+the gas is in the inside.
+
+So that actually separates them and you can
+squeeze the gas out through a valve.
+
+On-orbit trash storage, there is an overboard
+bleed for odor control.
+
+It's a very small overboard bleed to vacuum.
+
+And the human solid waste collection and storage
+is also vacuum dried and stabilized.
+
+This is a waste management picture.
+
+The subject we were just talking about is
+the vacuum vent.
+
+That vacuum vent does vent the commode area
+where the feces are.
+
+That vent also provides a vent for the water
+separator.
+
+It also provides a vent for airlock depress
+for EVA.
+
+So this is the vacuum system.
+
+The urine is collected and trained in a liquid.
+
+Well, let me say that different.
+
+The urine, after it has been separated from
+the gas stream, is stored in a waste tank,
+
+as is the humidity from the cabin atmospheric
+revitalization system.
+
+And then that is pressurized from the pressured
+composition control system and is dumped overboard.
+
+This waster is not used for anything.
+
+It is basically dumped just to do inventory
+management.
+
+The next picture explains a little better
+about the commode and the urinals themselves.
+
+The urinal originally had a unisex interface
+cup.
+
+It turned out that didn't work very well,
+and so later flights there was a custom male/female.
+
+And later there were even some more customizing
+for the crew, I believe, but I don't have
+
+the details on that.
+
+The urinal itself, obviously for urination,
+there needs to be some way to make the urine
+
+go where you want it to go.
+
+And those were done in fan separators.
+
+So there is gas pulled in the cup.
+
+And in training the urine, the urine then
+comes down and goes through the separators.
+
+This is also a centrifugal-type separator.
+
+And then that is sent to the head that is
+created here.
+
+Then puts that waste water urine in the waste
+system.
+
+The EMU spacesuit, it also has a condensate
+drain after each EVA, and it also goes through
+
+this same system and into the waste tank.
+
+The commode.
+
+Basically there is a seat.
+
+The seat has a small opening.
+
+The commode itself is basically a cylinder
+or a tub.
+
+And there is a slinger in the bottom.
+
+So the slinger basically distributes the paper
+and the fecal matter on the outside wall in
+
+a thin layer.
+
+The vacuum then can dry that so that it deactivates
+it so it does not end up either any odor or
+
+creating any kind of bacteriological issues.
+
+But the entrainment of the fecal material
+so that it, in fact, hits the slinger, is
+
+done with an air flow.
+
+The air flow comes in around the seat itself.
+
+That requires good contact with the seat.
+
+It also requires positioning.
+
+Positioning turned out to be an early issue,
+or reliable positioning, and so a trainer
+
+was put together that had a camera here.
+
+And the trainer, I might add, was discretely
+located in a non-observable place so that
+
+it could be used in privacy, the comings and
+goings, and also the use of the facility itself.
+
+And they told us it was not hooked up to a
+tape recorder.
+
+[LAUGHTER]
+
+Just to elaborate on that.
+
+Basically, the problem is it really is a rather
+small opening.
+
+And it just doesn't feel natural to know where
+to put yourself down.
+
+And it actually did lead to significant messes
+on orbit.
+
+I won't go into any more detail.
+
+But the idea is that you would position yourself
+the way you thought it should be, and then
+
+you would turn on the lights.
+
+And there is a TV screen in front of you.
+
+I'm not making this up.
+
+[LAUGHTER]
+
+So that you could see how close you are to
+the bull's-eye.
+
+Enough said.
+
+The cabin thermal control is another one of
+the subsystem elements.
+
+It is a circulating liquid cooling system.
+
+It provides the heat sink for the atmosphere
+itself.
+
+It also provides the ability to reject that
+heat to the spacecraft cooling system because
+
+you've got to get rid of it out of the cabin.
+
+It has some avionics cold plates, some air
+cool avionics, support the crew in the airlock
+
+and a portable water chiller.
+
+This is the location.
+
+You will notice the avionics bays are listed
+here with their little circulation systems.
+
+The liquid system then services each of those,
+the chill or the condensing heat exchanger.
+
+And this is the place that the cabin system
+connects to the spacecraft system, on the
+
+aft bulkhead right here.
+
+We will see the other half of this system
+in a little bit.
+
+This is a schematic that is very complicated
+looking but it is fairly simple.
+
+Let me show you the air piece first.
+
+Look at the black lines.
+
+Those are twin fans.
+
+It goes through the air-cooled avionics through
+the heat exchanger to get rid of the heat.
+
+There are some cold plated avionics in each
+bay, so you take care of the cold plated and
+
+the air-cooled in this bay and in this bay
+and in this bay.
+
+Now you've got all of the electronics taken
+care of.
+
+I should have started this up at the pump.
+
+Sorry about that.
+
+Here is the pump and we will come down.
+
+It also takes care of the forward and overhead
+window mounts around the window for thermal
+
+control.
+
+And the hatch is just a way to keep those
+thermally stabilized.
+
+Back in the early flights, we had something
+called DFI, development flight instrumentation.
+
+It was a special instrumentation package.
+
+It was also liquid cooled.
+
+And then this is the heat exchanger to the
+spacecraft system.
+
+It is a Freon system.
+
+This is where the main heat is rejected right
+here.
+
+On the other side of this you've got cool
+liquid.
+
+It turns out this is water.
+
+We go through the liquid cooling garment which
+is the spacesuit cooling garment, the water
+
+chiller, go through the cabin heat exchanger
+to cool the cabin and condense the water out
+
+and then back to the pump.
+
+I failed to mention the IMU.
+
+It has triply redundant fans.
+
+It pulls air through it.
+
+And that is also cooled by this gas stream.
+
+Anyway, this is the cabin thermal control
+system.
+
+These functions, I just said each one of them
+so I won't repeat them.
+
+Cabins circulating liquid cooling loop.
+
+As I mentioned, water is the coolant.
+
+Water is actually a very good coolant.
+
+And, if you have any requirements that push
+you that way in your designing thermal control
+
+systems, you like water.
+
+Water is completely nontoxic so it can be
+around the crew.
+
+Leaks don't make any difference.
+
+It has a very high CP.
+
+It's a really good fluid.
+
+The problem with water is freezing.
+
+You don't want to freeze it and you don't
+want to get it so hot that it turns into steam.
+
+But if you can stay within the boundaries
+it is a good fluid.
+
+And that is what this is.
+
+Redundant pumps, I showed you that on the
+schematic.
+
+The liquid gas heat exchanger, I showed you
+that before.
+
+Cold plates for electronic cooling and the
+window hatch mount.
+
+The circulating gases that I mentioned for
+the avionics, the cabin gas was used as a
+
+coolant.
+
+You saw the redundant fans and the doubly
+redundant fans.
+
+I mentioned earlier, and someone commented
+on it, that the promise early on was the Shuttle
+
+could be a less expensive development activity
+if we used off the shelf avionics, the kind
+
+that aircraft use.
+
+And that's a good promise.
+
+It turned out that that's not a very good,
+not as good a solution for thermal control
+
+as liquid cooled.
+
+Liquid cooled is a much more efficient way
+of providing a heat sink to electrical equipment.
+
+When you blow the cabin gas through it then
+you end up with the problems of if you change
+
+the pressure in the cabin, which we talked
+about.
+
+That can effect cooling.
+
+Also you have to put out a lot more power.
+
+You have to blow a lot more gas than you do
+power to move the liquid around, so it's not
+
+a very good thermal solution.
+
+And actually the promise of less expensive
+avionics I don't think was actually fulfilled,
+
+although that's somebody else's topic and
+not mine, because I think everything was pretty
+
+well custom.
+
+It did potentially complicate the thermal
+control system for a good goal.
+
+And how well that goal was met, somebody else
+will have to speak for it.
+
+Another one of the subsystem elements of the
+spacecraft.
+
+Well, we usually take a two minute break when
+we're about halfway through.
+
+Certainly.
+
+Why don't we take our two minutes now and
+then we will pick it right back up?
+
+[AUDIENCE QUESTION]
+
+From an engineering standpoint, it is much
+better to cool with liquid.
+
+If you use cold plates, it is much more efficient.
+
+You get a good reliable heat sink.
+
+And you can then design your thermal conduction
+paths so that out of the avionics box you
+
+make sure the heat goes to the cold plate.
+
+And you use a lot less power.
+
+You can pump water a lot more efficiently
+for the cooling capability than you pump gas.
+
+Is that what happens on the Shuttle now or
+do you have a mixture?
+
+[AUDIENCE QUESTION]
+
+This is the air-cooled part of the loop and
+here are the cold plates.
+
+Let's get the class back.
+
+Thank you very much.
+
+I am sorry.
+
+Did you see what I was pointing at here?
+
+Yeah, you put both.
+
+Yeah, and this is one bay.
+
+And they have both cold plates and the air-cooled
+here, here and here.
+
+There they are.
+
+Of course, when you go outside the vehicle
+there is no more air so all the external equipment
+
+is cold plated.
+
+Was there another question?
+
+What kind of design changes would you have
+to make in order to go strictly to completely
+
+liquid cooled electronics?
+
+Well, if you're trying to use off-the-shelf
+and it is air-cooled already, there is a cabinet
+
+right there full of it.
+
+If it is air-cooled already then you have
+to stay with that concept.
+
+If you're custom designing then, from the
+very beginning, you say I'm custom designing
+
+this to be liquid cooled.
+
+And then the internal design is such that
+there are conduction pads to the base plate
+
+so that it can be cooled.
+
+OK.
+
+I guess previously to that all of our spacecraft
+were liquid cooled.
+
+Apollo was, wasn't it?
+
+Yes.
+
+Because you had to be able to take those spacecraft
+down the back?
+
+Right.
+
+We evacuated the cabin both in the Command
+Module and the Lunar Module.
+
+And Gemini, too.
+
+This is the spacecraft active thermal control
+system.
+
+This is the vehicle level.
+
+So now, even though we're still under this
+ETCLSS, we are not talking the classical environmental
+
+control anymore.
+
+This is a bigger picture.
+
+Also the reason the word active is stuck in
+here was a left over from previous programs,
+
+too.
+
+For example, on Apollo we had several heat
+rejection systems.
+
+Not a single one.
+
+And we also did a lot of passive thermal control
+on Apollo.
+
+We had a mission mode called "barbeque" which
+is basically you roll the vehicle very slowly
+
+so you normalize the environment.
+
+If you leave the same side toward the sun
+all the way to the moon that side gets really
+
+hot.
+
+This is the active system to get away from
+heaters and/or vehicle level control.
+
+There is an on-orbit.
+
+We have a radiative heat sink.
+
+We also have an evaporative heat sink on orbit.
+
+During ascent and entry we have two heat sinks,
+both of which are evaporative.
+
+We have a circulating liquid system.
+
+We take heat from the cabin, from the fuel
+cells, hydraulics, all the cold plate avionics
+
+and electronics, and payloads, we do cooling
+for payloads.
+
+All of these are the functions of the active
+thermal control system.
+
+This, as you notice, is a lot busier than
+some of the others have been.
+
+You will notice the radiators here on the
+side wall.
+
+This is the doors.
+
+When closed up there are no radiators.
+
+When opened the underside of the payload doors
+are your radiators.
+
+And this is on both side, obviously.
+
+That same heat exchanger that I showed you
+before that interfaces with the cabin is right
+
+here.
+
+The cabin load is dumped there.
+
+Fuel cell load is dumped here.
+
+The fluid is a Freon 21.
+
+There is a Freon 21 pump package.
+
+The payload heat exchanger is here, I believe.
+
+Mid body cold plates.
+
+Aft cold plates.
+
+Each radiator side has its own flow control
+system.
+
+The evaporative heat sinks, one is the flash
+evaporator that I've shown you a couple times
+
+before.
+
+I will describe it a little better in the
+minute.
+
+It is here.
+
+It uses water.
+
+There is an ammonia boiler here that is also
+an evaporative heat sink.
+
+And when we're on the ground there is a GSE
+connector for the GSE heat sink.
+
+[AUDIENCE QUESTION]
+
+More than you would ever know.
+
+In fact, this is the most complicated, integrated
+thermal test ever run at JSC.
+
+And I will show you a picture of it in a minute.
+
+We actually tested all of that together.
+
+And it all had to work together.
+
+And it gets worse as we go along.
+
+I will show you all the integration factors
+as we go along, but it changes from mission
+
+mode to mission mode.
+
+It changes within mission modes as to how
+the system works.
+
+And I will try to describe that.
+
+OK, so this sort of gives you the feel now.
+
+Keep in mind, geometry is going to play an
+effect here as to how you plum the system
+
+up.
+
+So Freon is running through all of those lines
+there to the radiators?
+
+It will be a little clearer in a minute.
+
+This is a schematic.
+
+Let's start at the radiators.
+
+On a good day, this is doing the job for you.
+
+All the radiators are getting you nice cool
+liquid.
+
+The radiator uses a bypass system, so you
+will see the bypass around the radiators.
+
+It is good to remind yourselves that heat
+load can be tremendously different.
+
+And the high level mission phases, a lot of
+electronics, a lot of crew activity, the vehicle
+
+is alive and pumping out the power and, therefore,
+pumping out the heat.
+
+If you ever did one of those 28 day missions
+we talked about, which was a spec requirement,
+
+you can imagine this vehicle is almost quiescent.
+
+It is doing very little.
+
+You're trying to link them the mission.
+
+So you're doing hopefully experiments or something
+in SpaceLab.
+
+You're doing something else.
+
+The vehicle is not working for you very hard.
+
+Just as an example, we have five computers.
+
+And we use all five during ascent and entry,
+the active phases for safety, but once you're
+
+on orbit, when you have a long mission like
+that, you actually power down all but two
+
+of the computers.
+
+That is just it.
+
+And there are a lot of other systems which
+you power down.
+
+And that way you're limited in missions by
+the electrical energy which is limited by
+
+the amount of hydrogen and oxygen you can
+carry for fuel cells.
+
+So, by powering down, you extend your mission.
+
+And, of course, you will also reduce the heat
+load.
+
+And, when you reduce the heat load, you've
+got to find some way to make that same radiator
+
+work for you at a very low heat load.
+
+So it has the capability of getting rid of
+a lot of heat.
+
+If you don't want it to get rid of that much
+heat, because you don't have it, then you
+
+have to go to bypass system.
+
+Anyway, the next thing in the loop is the
+GSE heat exchanger.
+
+On the ground you don't have radiators working
+so you use the GSE heat exchanger.
+
+Then there is the ammonia boiler.
+
+When you reenter the ammonia boiler gives
+you the ability to operate with an evaporative
+
+heat sink prior to the connection of the GSE,
+and so it is part of the thermal control system.
+
+The next is the flash evaporator.
+
+And you'll notice there are two flash chambers
+here.
+
+One is called the high load and one is called
+the topper.
+
+And I will talk about that a little more later.
+
+Then the nice cool liquid, however it was
+cooled, all these cool it.
+
+However it was cooled is then available for
+the vehicle.
+
+And there is one more little heat load, and
+that is the cryogenic oxygen that we're bringing
+
+in.
+
+We also warm it up with this coolant loop.
+
+So the flow then goes to the aft cold plates.
+
+And then the flow also goes to the cabin heat
+exchanger and the payload heat exchanger.
+
+You notice these are either or.
+
+And that's because sometimes you don't even
+have a payload heat exchanger use so you don't
+
+use it.
+
+Sometimes you have a lot of use for it.
+
+And maybe, for example, SpaceLab and Space
+Station have kind of an arrangement.
+
+You wouldn't be in the cabin as much so you
+can divert that.
+
+It allows you to use the capacity in either
+of two places here.
+
+Then you come on down and come through your
+pumping package, there are redundant pumps.
+
+Then you go the fuel cell heat exchanger because
+now you've used the nice cold fluid up.
+
+And so the fuel cell can stand the warmer
+temperatures.
+
+Also some cold plates.
+
+Now, it might have occurred to you, it occurred
+to me, why did we waste our nice cold fluid
+
+on these cold plates?
+
+Why didn't we put those cold plates down here
+so we could have had more cold fluid for our
+
+cabin heat exchangers?
+
+And the answer is geometry.
+
+Those are way in the back.
+
+The cabin is in the front.
+
+After you've come forward from the flash evaporator,
+which is in the back, to the cabin, you don't
+
+want to go back to pick this up.
+
+You wouldn't want to have to go back to the
+back of the vehicle and then back forward
+
+again, so this is a geometry problem.
+
+We have cold plates here.
+
+We also have cold plates here.
+
+They come forward.
+
+The hydraulics heat exchanger is the last
+thing on the loop and then back to the radiators.
+
+We will talk about that a little more.
+
+The functions of the active thermal control
+system.
+
+Collect the waste energy from all the systems.
+
+We just talked about that.
+
+And rejected radiatively to space.
+
+That is our first choice.
+
+Our first choice is to use the radiators.
+
+It turns out that the radiators in some heat
+load environments don't do the job.
+
+You have a high load and a bad environment,
+you cannot get rid of all the heat.
+
+Also, we are producing a lot of water, so
+something constructive has to be done with
+
+this water.
+
+The fuel cells are pumping it out because
+every time you make a kilowatt you've got
+
+more water to use.
+
+So we decided to augment the space radiators
+with the evaporative heat sink at these high
+
+load cases.
+
+This gives us an ability to accept a radiator
+system that cannot really do the job by itself
+
+but make it completely adequate for some of
+the low heat load cases, but in the high heat
+
+load cases then it is augmented by water.
+
+Now, when you want to get rid of water and
+you don't have some of this bad environment
+
+you can actually throttle the radiators down.
+
+And, if you throttle them down, then you force
+the evaporative heat sink to come online and
+
+do the job for you.
+
+In other words, you change the set point on
+the radiator.
+
+Normally we use 40 degrees set point.
+
+If you change it to 56 degrees and let the
+water take you from 56 back down to 40 then
+
+you artificially get rid of water.
+
+It is a good water dump system.
+
+During ascent, over 100,000 feet we use the
+water boiler.
+
+The flash evaporator.
+
+Not a water boiler.
+
+That's a Freudian slip, I guess.
+
+The Apollo had what's called a water boiler.
+
+It was a nightmare.
+
+We said never will we do that again, so we
+ended up with a different design for the Shuttle.
+
+The reentry system below 100,000 feet is ammonia.
+
+It will carry you all the way to the ground
+and on the ground until you get the GSE.
+
+Water won't carry you because water won't
+evaporate less than 100,000 feet, but the
+
+ammonia will so that's the reason it is there.
+
+Let's talk about the radiators themselves.
+
+The two payload bay doors are a mirror image
+of each other.
+
+They are radiators on each side that are exactly
+mirror image.
+
+I don't know what happened there.
+
+Anyway, this is supposed to say that the radiators
+on these two sides are mounted and are plumbed
+
+in two separate cooling loops.
+
+The reason for that is there is always a redundant
+loop.
+
+Obviously, you have to be able to take a failure
+and still have a good system.
+
+If you run both loops through both radiator
+sides and you took some sort of collision
+
+hit then you could wipe out both of your cooling
+loops in one hit.
+
+And so that is unacceptable.
+
+By plumbing the systems up with mirror image
+radiator systems on different loops then you
+
+can still use the capacity together.
+
+But if you lose one side you still have half
+your capacity left.
+
+And plus you have your evaporative heat sinks
+to make up the difference.
+
+So we can survive with a door out.
+
+I mentioned the dual set points before.
+
+I also mentioned the bypass thermal control.
+
+I mentioned the dual set points, 40 and 56.
+
+40 is our normal.
+
+If you're trying to burn up some water you
+go to 56 and you use the difference in water.
+
+The radiators, we have two different kinds
+of radiators.
+
+We have the single-sided that are on the back
+of the vehicle and some two-sided ones on
+
+the front of the vehicle.
+
+The reason for that is when you open the door
+you expose the underside of the door.
+
+If you have radiators on the underside of
+the door then you've exposed your radiators.
+
+But if you lift the radiator panel off the
+door, because the doors go way down, then
+
+you can see the underside.
+
+It's not as good, you don't get a full view
+of the heavens, but it does get rid of heat.
+
+And so we needed that extra capacity.
+
+On the front four panels they are the two-sided
+and on the back four they are single-sided.
+
+The radiators themselves are made out of a
+honeycomb aluminum structure.
+
+The tubes were imbedded in the structure so
+that the surface was smooth, and that was
+
+because we wanted to use a silver Teflon tape
+for our thermal control coding.
+
+For previous vehicles we always painted the
+radiators, painted them white.
+
+If you look at the alpha epsilon white paint,
+it is pretty good.
+
+I think Apollo was 0.18 alpha and epsilon
+about 0.92.
+
+That's pretty good.
+
+The market had moved along.
+
+Technology had advanced and there was not
+the silver Teflon out there.
+
+And what the silver Teflon does is the silver
+gives you the reflection which is good and
+
+the Teflon gives you the radiation which is
+good, so you get the best of both worlds.
+
+Silver Teflon was about 0.05 epsilon and about
+0.88, 0.9, something like that.
+
+You lost a slight amount in epsilon and gained
+a lot in alpha, so basically you could ignore
+
+the sun which is what you'd like to do, is
+ignore the sun.
+
+It turned out the silver Teflon had some issues.
+
+We tested the radiators.
+
+The radiator was not a slam dunk with eight
+panels, four of which are two-sided.
+
+Effectively you have 12 panels.
+
+You have fluid going through those in parallel
+tubes.
+
+You're trying to guaranty that the fluid all
+goes where it's supposed to go.
+
+And, therefore, the viscosity of Freon, which
+is very low, analytically said it was all
+
+right.
+
+But we wanted some testing to prove it so
+we did test the entire radiator system.
+
+And, in that test, all the silver Teflon fell
+off.
+
+It is a really good thermal coating but it
+doesn't seem to be very practical.
+
+It turned out that the problem was adhesive.
+
+We did a little adhesive work and the materials
+people came up with a Permacel that worked
+
+perfectly.
+
+They have never come off again.
+
+In fact, we get 10, 12 years out of the radiators,
+lots of time.
+
+The problem that the Permacel couldn't solve
+was beneath the tape you could get very small
+
+little out-gassing of the materials.
+
+Almost all materials outgas some.
+
+Basically, we would put bubbles underneath
+the tape.
+
+We went to a perforated.
+
+There are millions of little holes in this
+tape.
+
+And it is placed on the vehicle and it stayed
+on just fine.
+
+It wasn't very long, though, that people began
+to worry about the focusing of this silver,
+
+that the doors are curved upward.
+
+And so there is a focal point there that is
+a very, very hot point.
+
+And there was concern that that's really not
+a good thing to have.
+
+If we could make the surface less specular
+and more diffuse without losing the alpha
+
+and epsilon we would have a better design.
+
+And so they dimpled it.
+
+Now we have Permacel dimpled, perforated silver
+Teflon tape.
+
+It works great.
+
+The flash evaporator.
+
+Water is the flash evaporator's evaporant.
+
+This was a brand-new design.
+
+The water boiler on Apollo was no good.
+
+It was a problem.
+
+The flash evaporator is a very simple concept.
+
+You have a chamber.
+
+You run your coolant around the chamber that
+you want to be cooled.
+
+And you spray water on the walls of the chamber.
+
+And, if the pressures are all right, the water
+will flash.
+
+You won't get ice.
+
+It will go straight to steam.
+
+Steam will go overboard and it will all be
+wonderful.
+
+And if you can convince a program manager
+of that good luck.
+
+Anyway, the way to convince a program manager
+is to show him good test data.
+
+During the development, we developed this
+process of spraying the walls and not getting
+
+water carryover which will obviously freeze
+up your steam duct.
+
+Which you don't want.
+
+But, as the design evolved, we had to get
+more sophisticated because we needed this
+
+flash evaporator to burn up the extra water
+when we didn't need the fuel cell water.
+
+And we did that with that 40 to 56 set point.
+
+And so we needed a small evaporator that could
+handle that.
+
+It was called the "topper." It tops off the
+radiator.
+
+But when the doors are closed there is nothing
+else to get rid of your heat, now you need
+
+a loss of capacity.
+
+And so the second chamber was the hallowed
+chamber.
+
+Together they do the whole job.
+
+When the radiators are working only topper,
+you can come home with this system functional
+
+and make it home.
+
+It turns out we never did freeze up the steam
+duct so that part was good.
+
+It turns out that we had some freezing in
+the chamber.
+
+And, in fact, we had to develop a process
+that acknowledged that that could occur.
+
+And how would we flush it?
+
+It is called "flushing." And so we did develop
+a process.
+
+And it has never failed.
+
+The flushing process always works.
+
+And we have had on several occasions, I probably
+cannot count them for you, but four of five
+
+times maybe over the Shuttle flights we've
+had some freezing inside the cavities.
+
+There is a non-propulsive overboard vent.
+
+That was the one going out both sides for
+the topper because it could be used for very
+
+long times during the mission and you might
+be pointing or whatever you might be doing.
+
+But when you're coming home the high load
+is just a big out the side of the vehicle
+
+type duct.
+
+The ammonia boiler, its heat sink is ammonia.
+
+As I mentioned before, it evaporates all the
+way to the ground where the water won't.
+
+The redundant boiler is here.
+
+Up here there are no redundant boilers.
+
+These two chambers have redundant everything.
+
+They have redundant feed water systems and
+redundant control systems, redundant spray
+
+nozzles, redundant everything, but the chamber
+is a chamber.
+
+You get what you get.
+
+They are redundant boilers is the way the
+ammonia boiler gets its redundancy.
+
+It was designed to be utilized during entry
+and on the runway until the cooling is available.
+
+It turns out that we don't do that anymore.
+
+It turns out operationally we learned that
+if we cold soak the radiators before we shut
+
+the doors and then bypass them and come home
+on the flash evaporator that there is a lot
+
+of heat capacity still left in those radiators.
+
+There is a lot of fluid out there and it is
+cold.
+
+And so we can actually go all the way to wheel
+stop on the radiator.
+
+And so at 175,000 feet we start flowing the
+radiator.
+
+And at 100,000 feet the flash evaporator is
+off and we cold soak all the way home.
+
+And after wheel stop the ammonia boiler cranks
+up.
+
+I mentioned the Freon 21, the low viscosity.
+
+We got an excellent performance out of that.
+
+The low viscosity is really, really important,
+as much parallelism as we have.
+
+I didn't really give you the numbers.
+
+In the single panels we have 26 tubes.
+
+In the two-sided panels, I believe, there
+are 66 tubes.
+
+Lots of tubes.
+
+Lots of parallelism.
+
+It is awfully easy to get flow instability
+in a thermal system like that but the Freon
+
+loop does great.
+
+We have redundant pumps, all liquid heat exchangers
+and cold plates.
+
+This is that chamber that I told you.
+
+If you can look right down here, this is one
+person.
+
+In fact, there is a radiator panel.
+
+This was during buildup.
+
+Twice we tested the flash evaporator in this
+environment once as part of the integrated
+
+system with all the radiators and once by
+itself.
+
+And twice we tested the radiators, one as
+part of the integrated system and once by
+
+themselves.
+
+So we did essentially three large tests.
+
+And the one that had the entire system in
+it, had all the cold plates, had everything
+
+in it, as I said, is the most sophisticated
+thermal test we've ever done at JSC.
+
+And it proved that the system could work.
+
+It also proved that we had to tune the flash
+evaporator nozzle because it was wrong.
+
+But we did get the data, we did prove it was
+wrong and we got it re-machined.
+
+A machine out of columbium, somebody else
+will have to answer why.
+
+And so it was a problem for Aaron to go get
+us another one, but it fixed it and it was
+
+successful.
+
+[AUDIENCE QUESTION]
+
+You can have a command module and a service
+module and a stack configuration in side that
+
+chamber.
+
+And it had a solar and full vacuum.
+
+[AUDIENCE QUESTION]
+
+It was a manned chamber then.
+
+It is not now.
+
+After Apollo-Soyuz, it hasn't been manned
+since then.
+
+It's still available for testing but is not
+manned.
+
+It has a sister chamber 100 feet that way
+where all of the EVA testing is done.
+
+A good example, I think, of how the Shuttle
+Program built on a lot of Apollo-- The same
+
+thing at the Cape where a lot of the launch
+hardware was adapted is the Shuttle Program,
+
+you know, you heard about the budgetary constraints.
+
+The Shuttle Program never could have afforded
+to build something like that.
+
+But luckily a lot of this equipment was built
+during Apollo when the money was much more
+
+available.
+
+If you have been keeping count, we're getting
+toward the end here.
+
+I did want to mention, before we left the
+main orbiter systems, that there was some
+
+rotating equipment life testing that we did
+for the program.
+
+The equipment we're talking about here is
+the cabin fan, the water gas separators, the
+
+avionics bay fans, cabin coolant and the vehicle
+coolant pumps.
+
+The life requirement was 100 missions, and
+that was calculated by somebody to be 20,000
+
+hours.
+
+If you could show 20,000 hours of successful
+operation, you had the design life of the
+
+hardware.
+
+We set up a laboratory to run the equipment.
+
+It was obviously a low-maintenance lab.
+
+We collected data and checked in the room
+occasionally to see if everything was all
+
+right.
+
+It turned out that all the equipment passed
+the 20,000 hour requirement.
+
+We did learn something, though, that some
+of that stuff was so noisy.
+
+Oh, it was noisy.
+
+There was some work done on some muffling,
+but the hardware itself was all good.
+
+We are at the end.
+
+Yes.
+
+Were there noise requirements [AUDIENCE QUESTION]?
+
+Yes, there was a cabin noise spec.
+
+And, yes, it had to be met.
+
+And I don't remember how it was met.
+
+We put mufflers on some of the equipment.
+
+Maybe some insulation inside of the ducting,
+I'm not sure.
+
+If we have time, COHEN: I will tell a little
+anecdote here.
+
+I chaired the Change Control Board.
+
+[NOISE OBSCURES]
+
+The medical organization came to see me and
+said that the cabin was very, very noisy and
+
+it was going to really do a detriment to the
+astronauts.
+
+And it was very expensive in terms of dollars
+and weight to really get all the cabin fans
+
+and cabin environment down to the level they
+wanted.
+
+I thought for a moment.
+
+I go out to California a lot.
+
+I go out to Rockwell and stay in motels that
+are on the Los Angeles freeway.
+
+And I said you don't see me worried about
+my ears in staying in those freeways and not
+
+being able to sleep and having all that noise.
+
+And the doctor looked at me for a moment and
+said, well, you're already deaf.
+
+And I said what did you say?
+
+But we did have to make some modifications
+of it to actually reduce noise.
+
+Let me interject one item.
+
+I think somebody asked the issue about the
+IMU.
+
+We decided to pick the IMU off the shelves,
+and it was air-cooled, to really do it right.
+
+If we would have done it right, we would have
+picked an IMU which was compatible with liquid
+
+cooling rather than redesign it.
+
+But we decided to stick with the IMU that
+was air-cooled.
+
+Whether that was the right decision to make,
+I don't know.
+
+It seemed like it was because I think we've
+only had one problem with an IMU.
+
+I don't think we've had many problems with
+the IMU.
+
+But that is a little anecdote that I thought
+of.
+
+That's a program manager's trait.
+
+Probably the air-cooled IMU was a less expensive
+option.
+
+It might have cost a little in terms of thermal
+efficiency, but that is only energy power.
+
+And power was available so it was a good tradeoff.
+
+This is the last of the subsystem areas.
+
+This is the EVA airlock support.
+
+The Environmental Thermal Control and Life
+Support System does support the airlock.
+
+It maintains the cabin pressure and composition
+during the airlock repress and depress.
+
+This is really a requirement back on the ARS
+and the pressure and composition control system
+
+because airlock use basically dumps cabin
+gas and then you repress the airlock.
+
+It is a requirement that you cannot upset
+the cabin while you're doing the EVA function.
+
+We also provide the service and cooling umbilical.
+
+If you have any kind of mental picture of
+being in the airlock, the crew is connected
+
+with cooling and oxygen through an umbilical
+so they don't use the consumables in their
+
+spacesuit.
+
+And so that is provided by the ETCLSS.
+
+Heat rejection, the crew wears a liquid cooling
+garment.
+
+And the cooling for that is done by the vehicle
+until you go EVA, of course.
+
+Then the recharge.
+
+We supply the backpack O2 recharge from the
+900 PSI cryo.
+
+We supply the water to recharge for the sublimator.
+
+NASA is overrun with acronyms.
+
+EMU is extra vehicular mobility unit, which
+means nothing but spacesuit and backpack.
+
+So the spacesuit and backpack uses an evaporative
+heat sink and it uses a sublimator.
+
+And the idea there is it's a device that exposes
+a layer of ice to space and then it sublimates
+
+and you get your cooling from that as opposed
+to putting a liquid water on a surface and
+
+flashing it.
+
+Anyway, that has to be serviced.
+
+That water is provided from the system.
+
+And then the condensate that the crew brings
+back, EVA, that's a sweaty job.
+
+That condensate goes back into the system.
+
+So the airlock support is another part of
+this system.
+
+In fact, that is the sixth part.
+
+So we are through.
+
+This is a picture of the airlock.
+
+Not really the airlock.
+
+This is the test chamber that we built to
+put the equipment in.
+
+You'll notice it has the right hatch in it.
+
+And, if you can recall back an hour and a
+half ago, I showed you a picture where there
+
+was this hatch basically on the backside of
+the test chamber.
+
+We hook those together.
+
+Because, as I said, as you depress and repress
+the airlock it affects the cabin.
+
+So we needed a test environment that had both
+those simultaneously.
+
+But the difference is this has to go all the
+way to vacuum.
+
+So we connected this to our vacuum system.
+
+And, when the crew is inside this, it is a
+manned vacuum test.
+
+And when the crew is inside the other test
+chamber it is basically sea level or, at most,
+
+8 PSI would be the lowest it would ever be.
+
+And I think the last picture is a spacesuit
+inside the airlock.
+
+And this is just a little cutaway showing
+the airlock.
+
+This was mounted on the back of that chamber
+you saw earlier.
+
+If you bring that picture back up, I will
+talk to that for just a minute and then we
+
+will have some questions.
+
+Before every flight, one of the things that
+we do is that every EVA crewmember takes his
+
+or her spacesuit into that EVA test chamber,
+into the airlock test chamber so you actually
+
+get a chance to take your own suit down to
+vacuum.
+
+And particularly, before you do your very
+first EVA, it is really a confidence builder
+
+because the physical sensations that you get
+in a suit -- And remember you're at about
+
+a 4 PSI pure oxygen environment.
+
+Your body, the inside of your mouth feels
+a little different.
+
+There are funny sounds with the fans inside
+the suit.
+
+The sorts of things that you don't want to
+experience the first time when you actually
+
+go outside into space.
+
+It is much better to do it here in a controlled
+environment where if there is a problem -- Actually,
+
+you are supported because of the weight of
+the suit.
+
+It doesn't look like there is anybody in this
+suit.
+
+But, when you're in this suit, you're actually
+supported by a cable to the ceiling of the
+
+chamber which is on quick release bolts.
+
+You're suspended up here.
+
+And, if you ever have a problem, they can
+release this, repressurize the chamber within
+
+about 30 seconds.
+
+I think that's the limit for a manned rated
+chamber.
+
+You're going to be able to repress in about
+30 seconds and then just lift you out, suit
+
+and all from the top, and get you out of your
+suit and get you to the medics.
+
+This is just an inverted bell jar.
+
+The hatch is not sealed.
+
+When you depress it just like pulls it out
+and seals due to the pressure difference.
+
+You just lift the top off.
+
+Yet another example of the extensive testing
+that we go through before every mission.
+
+I might add one more thing, which I forgot
+actually to add earlier.
+
+The manned rating is a term used in manned
+spacecraft which means that you've specifically
+
+tested it and said that its design is worthy
+of supporting a human.
+
+The airlock had to provide that function.
+
+So Aaron was faced with man rating the airlock.
+
+And manned test capability is very scarce.
+
+In fact, JSC may be the only place anymore
+that can do it.
+
+Anyway, we volunteered to do that as part
+of our test program as a programmatic requirement.
+
+Not as testing or watching or confirming anything,
+but as a prime part of the test program was
+
+the manned rating of the airlock.
+
+And that was done in Houston.
+
+That is an interesting thought.
+
+If my memory serves me correctly, one of the
+problems we had in the early part of the Manned
+
+Space Program was doing some chamber runs
+McDonnell-Douglas with a two-gas system where
+
+we actually lost the heat [NOISE OBSCURES]
+
+in the chamber and almost lost a test subject.
+
+And that was when Apollo decided to go to
+100% oxygen.
+
+And that is what led up to the fire on the
+pad.
+
+It went to 100% oxygen at 16 pounds per square
+inch with an invert over the hatch for another
+
+reason.
+
+And that is really if you can realize that
+100% oxygen at 16 PSI everything burns.
+
+Stainless steel is not self-extinguishing
+at 16 PSI.
+
+And, of course, that's what we were up when
+we had the Apollo I fire on the pad.
+
+It was a function of doing some test work
+with the combined atmosphere.
+
+So you have got to be careful that sometimes
+you don't over-react the thing.
+
+Then we went back to a different type of atmosphere.
+
+Did you have a question?
+
+The systems you've been describing today seem
+to take up a lot of space in the Orbiter like
+
+other systems.
+
+How did you negotiate and manage other subsystems
+for the space and the volume in the way that
+
+you wanted?
+
+That is a good question but you're asking
+the wrong person.
+
+We are the government.
+
+We hired a contractor to design the vehicle.
+
+Now, the design aspects of it, the philosophy
+of it, the functionality of it we were very,
+
+very integral with.
+
+We watched, we audited, we said that looks
+smart, but we didn't go and say put that cold
+
+plate here and put that heat exchanger there.
+
+The vehicle integrated design was Rockwell's.
+
+Let me tell you how it was done.
+
+Actually, in those years we didn't have CAD/CAM
+systems.
+
+What we did is used everything on mockups.
+
+We did mockups.
+
+The system was laid out of what to do and
+the functions of what they had to do and the
+
+plumbing.
+
+And this was all laid out on a mockup.
+
+And basically that was how it was negotiated
+in terms of what you need.
+
+In today's environment you wouldn't do that.
+
+You would use electronic capability.
+
+You would use your CAD/CAM systems.
+
+You would actually draw it up on your computer.
+
+In fact, the 777 was built that way.
+
+The 777 at Boeing, they didn't use hard mockups.
+
+They used electronic mockups.
+
+And that is what we would do today.
+
+And it would be much easier.
+
+You would probably call all the engineers
+together.
+
+You would sit down and show how the equipment
+was laid out, get a satisfactory buyoff on
+
+it and do it much more rapidly and much more
+quickly.
+
+In the future, what you will be doing is actually
+use a CAD/CAM system or CAD system to actually
+
+negotiate the space you need for it.
+
+That is a good question.
+
+And it was based on purely that you would
+get drawings, mockups, go out and lay it out
+
+in a soft mockup or hard mockup.
+
+You would get the engineers to come out, the
+manufacturing people to come out and say this
+
+is how it is going to look and then get a
+buyoff on it.
+
+Today you wouldn't do it that way.
+
+You would do it all electronically so it would
+change.
+
+Well, let me ask you a question.
+
+Of all the work you've done in the Shuttle
+what was your biggest concern in getting ready
+
+to fly or during the flight?
+
+What did you have the biggest concern about?
+
+I was young and confident.
+
+I don't know that I had a specific area that
+I was really concerned about.
+
+Like these people right here, right?
+
+Young and confident.
+
+I did recognize, though, but it did result
+in the integrated tests that I showed.
+
+I did recognize that we had the most highly
+integrated thermal control system ever conceived.
+
+And it had, as I said, modes within modes.
+
+It changed modes with respect to the vehicle
+phases.
+
+It changed modes with respect to operation.
+
+We had 9 PSI that went to 10.2 PSI.
+
+We had 8 PSI.
+
+We had thermal control loops, ammonia boilers,
+flash evaporators, so I did recognize the
+
+sophistication.
+
+In fact, we proposed early on to use that
+large chamber in an integrated vehicle test.
+
+Not we, me, but the big we looked at an integrated
+test like the Command Service Module was tested.
+
+And that was viewed to be impractical.
+
+It was cut it off at the bulkhead.
+
+You could do the forward cabin part and then
+do the aft section, but that was viewed to
+
+be impractical.
+
+But it still was a very integrated design.
+
+All the systems engineering that was there
+created that inner-dependency.
+
+And I think I was smart enough to know that
+there was certainly some potential risks there.
+
+Remember in the very beginning of this I talked
+about ownership of all the technical aspects?
+
+We had ownership.
+
+We believed that what we had done was prudent,
+appropriate, and we believed it would work.
+
+It wasn't like you bought something and you
+hope it works.
+
+Can you say a word of what you think, this
+is looking in your crystal ball, about the
+
+CEV?
+
+Do you think it's going to have a very similar
+type system or have you thought about that?
+
+Well, we hope so.
+
+Our new administrator has sort of back to
+the grassroots philosophy, or at least right
+
+now.
+
+And so we hope that the CEV will be developed
+with a lot of government involvement, that
+
+the government will have ownership again of
+the technical aspects of the design.
+
+If that happens then I think a lot of the
+experience that is around and a lot of the
+
+free-thinking and the independence that the
+government can bring to that, there is another
+
+school of thought that says keep the government
+out of the way and let the contractor go do
+
+their thing.
+
+And, obviously, you wouldn't get that position
+from me but there are people that believe
+
+that's the right way to do it.
+
+Do you think the system will look pretty much
+like this or similar to it?
+
+Well, similar, yes, I do think so.
+
+I believe that the very tight schedule for
+the CEV is going to put a lot of pressure
+
+on the program manager to go with the tried
+and true.
+
+So I don't think there is going to be innovation
+that has risk with it.
+
+Maybe there will be innovation that is good
+engineering, but I think the innovation with
+
+risk will be very much minimized.
+
+Because taking Shuttle offline in 2010 there
+is going be a lot of pressure to get this
+
+vehicle finished.
+
+I think that is going to breed some conservatism
+on the design side.
+
+We talk about considering operation while
+you're doing the design, but there were always
+
+things once the design was made.
+
+Well, like you mention, once we came up with
+a requirement for a 10.2 cabin we had to develop
+
+workarounds.
+
+And one of the other things that after the
+system is designed, we then start to figure
+
+out how can it fail and work on malfunction
+procedures.
+
+And I know that the malfunction procedure
+for loss of two coolant loops that was probably
+
+the worst simulation case that we ever had
+to deal with.
+
+I am curious to get your opinion.
+
+Walt described how we have two independent
+cooling loops so that in principle one failure
+
+won't take them both out.
+
+Now, I don't remember what it was, but they
+did discover a single point failure somewhere
+
+in there which I think was corrected but where
+you could have lost both of the cooling loops
+
+with a single failure.
+
+The only failure I remember is one that John
+Young used to worry about.
+
+It had to do with if you did lose a radiator
+that that could bleed your accumulator down.
+
+And so they did add an isolation valve so
+they can isolate the radiator side.
+
+But the idea was to obviously not lose your
+fluid with a single hit.
+
+That even though you have a nice completely
+functional thermal control system it is useless
+
+because it has no fluid.
+
+We did have an emergency de-orbit procedure
+for loss of two Freon cooling loops.
+
+And, of all the things that we practices,
+that was the hairiest because it was absolutely
+
+time critical.
+
+At this point, you have no way of getting
+heat out of the cabin so you cannot ultimately
+
+cool your electronics.
+
+The cabin gets hot, your electronics get hot
+so you have to do an immediate de-orbit.
+
+Hopefully you're within range of a landing
+site.
+
+And then you turn off all the equipment that
+you can possibly turn off, including most
+
+of your computers.
+
+And, when you're riding down through entry,
+you basically watch the temperature of the
+
+computer.
+
+And, as each computer would get up to its
+failure temperature, you would then switch
+
+on the next computer, transfer the data, you
+know, turn off the computer which has just
+
+about failed, and hopefully you could make
+it to the ground.
+
+And I know the instructors that would lead
+us through this exercise said that the information
+
+they had gotten from the thermal analyst was
+that nobody was really sure whether we could
+
+make it.
+
+I don't know what your opinion was or not.
+
+We practiced it.
+
+But obviously, I think I've told you, nobody
+has ever died in a simulator.
+
+But you never know whether the thermal model
+that they use in the simulator is really going
+
+to duplicate the way the Shuttle is going
+to behave in an absolute emergency situation
+
+like that.
+
+We survived in the simulator but I don't know
+what your feeling is.
+
+Well, we do address the thermal model accuracy.
+
+We do specific testing to validate the thermal
+model so we do have pretty good confidence
+
+in those.
+
+But the real issue in overheat is that when
+does a piece of equipment stop working in
+
+an overheat situation?
+
+I mean there is no magic number.
+
+It is not like at 143 degrees it is OK and
+144 it is not OK.
+
+And it varies with age, it varies with equipment
+and it varies with a lot of things.
+
+So there wasn't really a precise answer as
+to how long you could keep everything functional
+
+and come home.
+
+Yes.
+
+You talked earlier a little about oxygen and
+nitrogen mixing in the cabin.
+
+I was wondering if there is a way to really
+study that on the ground since you're not
+
+in a DoD environment.
+
+How do you know there are not pockets of nitrogen
+sitting around that an astronaut can stick
+
+his heat into?
+
+Very good.
+
+I just forgot to mention that earlier.
+
+The testing that we ran, we had to set it
+up very carefully.
+
+If you notice, there is a flight deck and
+a mid-deck, so obviously buoyancy is going
+
+to mix that stuff for you.
+
+What we did is set up a thermal condition
+where less than one degree thermal gradient
+
+everywhere in there had to exist before we
+ran the test.
+
+And that was to guaranty that we had no help
+from the naturally induced circulation.
+
+But you are absolutely right.
+
+That test would have been a useless test without
+neutralizing the gravity effects.
+
+And actually the first time that I did the
+spacesuit test in there we actually used the
+
+10.2 protocol.
+
+So I actually had to go in the day before,
+take the cabin to 10.2, spend the night and
+
+then we could do just a 40 minute prebreathe.
+
+For most of the other tests, when you go in,
+in order to avoid the inconvenience and expense
+
+of staying through the night, you go in early
+in the morning.
+
+And then you're coming right from a sea level
+environment.
+
+So, before you go down to 4 PSI in the suit,
+you actually have to prebreathe pure oxygen
+
+for four hours.
+
+As Walt said, that was the alternative.
+
+You basically just get in your suit.
+
+You can either bring a book and read your
+book or they will pipe music into you if you
+
+want to give them a CD, or I guess there was
+an audiocassette in those days, or they have
+
+a little black and white TV monitor.
+
+And you just sort of sit there for four hours.
+
+And the problem is you're not allowed to go
+to sleep.
+
+That would be the easiest thing, but they
+want you actually to move around because when
+
+you're moving your muscles you're actually
+then doing a better job of de-nitrogenating.
+
+So you have to stay awake.
+
+And if you don't say anything for more than
+about 10 minutes they will pipe something
+
+in and say, Jeff, are you awake?
+
+But this was a very, very useful facility.
+
+I mean they used it for all different sorts
+of things.
+
+And I guess that was the one new facility
+which was built for the Shuttle specifically.
+
+Yes.
+
+Jeff mentioned several times the 10.2 and
+I talked about the 9.
+
+The 9 was the original design, but the issues
+with the 9 PSI had to do with the oxygen percentage
+
+got too high.
+
+And so there was much concern about flammability.
+
+The idea was if you could raise the pressure
+up some to 10.2 then that would be less of
+
+a flammability issue.
+
+But then the problem became at 10.2 that the
+suit at 4 PSI was too much of a drop.
+
+If you're in the bends while diving, somebody
+mentioned diving earlier, scuba, you could
+
+usually use a two to one.
+
+If you don't reduce pressure more than half
+you're probably OK.
+
+You're probably not going to get the bends,
+but half of 10.2 is not 4.
+
+And the suit is at 4, so there was that issue
+again.
+
+They raised and bumped the suit up a little
+bit and got it up to 4.3 and went to 10.2
+
+and developed the prebreathe protocols that
+made that acceptable.
+
+That is sort of how it balanced out.
+
+That was another operational move later.
+
+And, as Walt said, you're spending enough
+time, once you get in the suit and you purge
+
+all the nitrogen out, and so you're sitting
+in a pure oxygen environment, you've got to
+
+do a bunch of tests and check out communication
+tests and cooling tests.
+
+You basically are not losing much time by
+having to spend 40 minutes prebreathing.
+
+The whole thing worked out pretty well.
+
+And it will be an interesting question on
+how they designed the CEV because the CEV
+
+has to be compatible with docking to the Space
+Station which works at a sea level environment.
+
+But, on the other hand, if you're going to
+take the CEV into a situation where you want
+
+to do a lot of space walks, you probably want
+to be able to operate it at more like 8.5
+
+or 9 PSI so that you can go right into a spacesuit
+without an extensive prebreathe.
+
+And, of course, people are always trying to
+figure out could we design the spacesuit to
+
+work at a higher pressure?
+
+But then you give up maneuverability.
+
+We will talk about that in another lecture
+that I will be giving on EVA systems.
+
+Walt, thank you very much.
+
+I enjoyed it.
+
+[APPLAUSE]
\ No newline at end of file
diff --git a/B7iFcW8USjQ.txt b/B7iFcW8USjQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8bc249b166cc9563dfb0d9fb7da838b02461096b
--- /dev/null
+++ b/B7iFcW8USjQ.txt
@@ -0,0 +1,7427 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right so enzymes of
+
+ align:start position:0%
+ocw.mit.edu all right so enzymes of
+ 
+
+ align:start position:0%
+ocw.mit.edu all right so enzymes of
+course are catalysts and that leads us
+
+ align:start position:0%
+course are catalysts and that leads us
+ 
+
+ align:start position:0%
+course are catalysts and that leads us
+to our next unit which is kinetics and
+
+ align:start position:0%
+to our next unit which is kinetics and
+ 
+
+ align:start position:0%
+to our next unit which is kinetics and
+it's our next unit and in fact our last
+
+ align:start position:0%
+it's our next unit and in fact our last
+ 
+
+ align:start position:0%
+it's our next unit and in fact our last
+unit of the semester so we're going to
+
+ align:start position:0%
+unit of the semester so we're going to
+ 
+
+ align:start position:0%
+unit of the semester so we're going to
+be talking about kinetics uh for the
+
+ align:start position:0%
+be talking about kinetics uh for the
+ 
+
+ align:start position:0%
+be talking about kinetics uh for the
+rest of the semester which sounds like a
+
+ align:start position:0%
+rest of the semester which sounds like a
+ 
+
+ align:start position:0%
+rest of the semester which sounds like a
+long time but it really isn't all right
+
+ align:start position:0%
+long time but it really isn't all right
+ 
+
+ align:start position:0%
+long time but it really isn't all right
+so we'll switch to today's hand
+
+ align:start position:0%
+so we'll switch to today's hand
+ 
+
+ align:start position:0%
+so we'll switch to today's hand
+out so kinetics and thermodynamics is a
+
+ align:start position:0%
+out so kinetics and thermodynamics is a
+ 
+
+ align:start position:0%
+out so kinetics and thermodynamics is a
+sort of ying-yang you really have to
+
+ align:start position:0%
+sort of ying-yang you really have to
+ 
+
+ align:start position:0%
+sort of ying-yang you really have to
+think about both of them at the same
+
+ align:start position:0%
+think about both of them at the same
+ 
+
+ align:start position:0%
+think about both of them at the same
+time so when you're thinking about
+
+ align:start position:0%
+time so when you're thinking about
+ 
+
+ align:start position:0%
+time so when you're thinking about
+whether a reaction will go forward
+
+ align:start position:0%
+whether a reaction will go forward
+ 
+
+ align:start position:0%
+whether a reaction will go forward
+spontaneous ly you're thinking about
+
+ align:start position:0%
+spontaneous ly you're thinking about
+ 
+
+ align:start position:0%
+spontaneous ly you're thinking about
+thermodynamics and you're thinking about
+
+ align:start position:0%
+thermodynamics and you're thinking about
+ 
+
+ align:start position:0%
+thermodynamics and you're thinking about
+how fast that reaction is going to go
+
+ align:start position:0%
+how fast that reaction is going to go
+ 
+
+ align:start position:0%
+how fast that reaction is going to go
+you're thinking about
+
+ align:start position:0%
+you're thinking about
+ 
+
+ align:start position:0%
+you're thinking about
+kinetics so let's just do a little
+
+ align:start position:0%
+kinetics so let's just do a little
+ 
+
+ align:start position:0%
+kinetics so let's just do a little
+review we've talked about this before
+
+ align:start position:0%
+review we've talked about this before
+ 
+
+ align:start position:0%
+review we've talked about this before
+but it's a clicker challenge so today
+
+ align:start position:0%
+but it's a clicker challenge so today
+ 
+
+ align:start position:0%
+but it's a clicker challenge so today
+let's think back to
+
+ align:start position:0%
+let's think back to
+ 
+
+ align:start position:0%
+let's think back to
+thermodynamics and tell me what stable
+
+ align:start position:0%
+thermodynamics and tell me what stable
+ 
+
+ align:start position:0%
+thermodynamics and tell me what stable
+unstable refers to thinking about
+
+ align:start position:0%
+unstable refers to thinking about
+ 
+
+ align:start position:0%
+unstable refers to thinking about
+thermodynamics and kinetics now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so most people got stability um
+
+ align:start position:0%
+okay so most people got stability um
+ 
+
+ align:start position:0%
+okay so most people got stability um
+when you're talking about stable
+
+ align:start position:0%
+when you're talking about stable
+ 
+
+ align:start position:0%
+when you're talking about stable
+unstable you're not talking about rate
+
+ align:start position:0%
+unstable you're not talking about rate
+ 
+
+ align:start position:0%
+unstable you're not talking about rate
+you are talking about Delta G you're
+
+ align:start position:0%
+you are talking about Delta G you're
+ 
+
+ align:start position:0%
+you are talking about Delta G you're
+talking about the spontaneous tendency
+
+ align:start position:0%
+talking about the spontaneous tendency
+ 
+
+ align:start position:0%
+talking about the spontaneous tendency
+um a chemist if it's around a long time
+
+ align:start position:0%
+um a chemist if it's around a long time
+ 
+
+ align:start position:0%
+um a chemist if it's around a long time
+we're talking about not a being stable
+
+ align:start position:0%
+we're talking about not a being stable
+ 
+
+ align:start position:0%
+we're talking about not a being stable
+but being inert um and in uh in terms of
+
+ align:start position:0%
+but being inert um and in uh in terms of
+ 
+
+ align:start position:0%
+but being inert um and in uh in terms of
+of this one
+
+ align:start position:0%
+of this one
+ 
+
+ align:start position:0%
+of this one
+here for if you're thinking about the
+
+ align:start position:0%
+here for if you're thinking about the
+ 
+
+ align:start position:0%
+here for if you're thinking about the
+Delta G for the decomposition into its
+
+ align:start position:0%
+Delta G for the decomposition into its
+ 
+
+ align:start position:0%
+Delta G for the decomposition into its
+elements that versus the Delta G for
+
+ align:start position:0%
+elements that versus the Delta G for
+ 
+
+ align:start position:0%
+elements that versus the Delta G for
+formation if that's negative um then it
+
+ align:start position:0%
+formation if that's negative um then it
+ 
+
+ align:start position:0%
+formation if that's negative um then it
+would be stable but we want to be
+
+ align:start position:0%
+would be stable but we want to be
+ 
+
+ align:start position:0%
+would be stable but we want to be
+positive for the decomposition all right
+
+ align:start position:0%
+positive for the decomposition all right
+ 
+
+ align:start position:0%
+positive for the decomposition all right
+so let's just look at this up here so
+
+ align:start position:0%
+so let's just look at this up here so
+ 
+
+ align:start position:0%
+so let's just look at this up here so
+again it refers to Delta
+
+ align:start position:0%
+again it refers to Delta
+ 
+
+ align:start position:0%
+again it refers to Delta
+G and label um and inert aers to the
+
+ align:start position:0%
+G and label um and inert aers to the
+ 
+
+ align:start position:0%
+G and label um and inert aers to the
+rate and again when you have a negative
+
+ align:start position:0%
+rate and again when you have a negative
+ 
+
+ align:start position:0%
+rate and again when you have a negative
+Delta G of formation then that makes
+
+ align:start position:0%
+Delta G of formation then that makes
+ 
+
+ align:start position:0%
+Delta G of formation then that makes
+something um
+
+ align:start position:0%
+something um
+ 
+
+ align:start position:0%
+something um
+stable okay so thermodynamics kinetics
+
+ align:start position:0%
+stable okay so thermodynamics kinetics
+ 
+
+ align:start position:0%
+stable okay so thermodynamics kinetics
+we want to think about is the reaction
+
+ align:start position:0%
+we want to think about is the reaction
+ 
+
+ align:start position:0%
+we want to think about is the reaction
+spontaneous but we also need to think
+
+ align:start position:0%
+spontaneous but we also need to think
+ 
+
+ align:start position:0%
+spontaneous but we also need to think
+about how long it's going to take so
+
+ align:start position:0%
+about how long it's going to take so
+ 
+
+ align:start position:0%
+about how long it's going to take so
+rate is important and so if we think
+
+ align:start position:0%
+rate is important and so if we think
+ 
+
+ align:start position:0%
+rate is important and so if we think
+about the average weight uh or average
+
+ align:start position:0%
+about the average weight uh or average
+ 
+
+ align:start position:0%
+about the average weight uh or average
+rate of a ferris uh wheel um I looked it
+
+ align:start position:0%
+rate of a ferris uh wheel um I looked it
+ 
+
+ align:start position:0%
+rate of a ferris uh wheel um I looked it
+up it is uh 31 .4 seconds to spin around
+
+ align:start position:0%
+up it is uh 31 .4 seconds to spin around
+ 
+
+ align:start position:0%
+up it is uh 31 .4 seconds to spin around
+if you're at an amusement park and you
+
+ align:start position:0%
+if you're at an amusement park and you
+ 
+
+ align:start position:0%
+if you're at an amusement park and you
+can think about your experience um uh
+
+ align:start position:0%
+can think about your experience um uh
+ 
+
+ align:start position:0%
+can think about your experience um uh
+sorry that should say imagine one
+
+ align:start position:0%
+sorry that should say imagine one
+ 
+
+ align:start position:0%
+sorry that should say imagine one
+revolution every five seconds or every
+
+ align:start position:0%
+revolution every five seconds or every
+ 
+
+ align:start position:0%
+revolution every five seconds or every
+five hours would be a very different
+
+ align:start position:0%
+five hours would be a very different
+ 
+
+ align:start position:0%
+five hours would be a very different
+experience 5 seconds would be way too
+
+ align:start position:0%
+experience 5 seconds would be way too
+ 
+
+ align:start position:0%
+experience 5 seconds would be way too
+fast you'd probably be throwing up
+
+ align:start position:0%
+fast you'd probably be throwing up
+ 
+
+ align:start position:0%
+fast you'd probably be throwing up
+everywhere in five hours you'd be like
+
+ align:start position:0%
+everywhere in five hours you'd be like
+ 
+
+ align:start position:0%
+everywhere in five hours you'd be like
+oh my goodness get me off of this thing
+
+ align:start position:0%
+oh my goodness get me off of this thing
+ 
+
+ align:start position:0%
+oh my goodness get me off of this thing
+so rate matters and uh chemical kinetics
+
+ align:start position:0%
+so rate matters and uh chemical kinetics
+ 
+
+ align:start position:0%
+so rate matters and uh chemical kinetics
+doesn't measure the rate of ferris wheel
+
+ align:start position:0%
+doesn't measure the rate of ferris wheel
+ 
+
+ align:start position:0%
+doesn't measure the rate of ferris wheel
+except maybe it does if the ferris is
+
+ align:start position:0%
+except maybe it does if the ferris is
+ 
+
+ align:start position:0%
+except maybe it does if the ferris is
+Ferris iron then we might be talking
+
+ align:start position:0%
+Ferris iron then we might be talking
+ 
+
+ align:start position:0%
+Ferris iron then we might be talking
+about its rate if it's uh spinning
+
+ align:start position:0%
+about its rate if it's uh spinning
+ 
+
+ align:start position:0%
+about its rate if it's uh spinning
+around doing things in a chemical
+
+ align:start position:0%
+around doing things in a chemical
+ 
+
+ align:start position:0%
+around doing things in a chemical
+reaction so we might think about the
+
+ align:start position:0%
+reaction so we might think about the
+ 
+
+ align:start position:0%
+reaction so we might think about the
+concentration of Ferris iron changing
+
+ align:start position:0%
+concentration of Ferris iron changing
+ 
+
+ align:start position:0%
+concentration of Ferris iron changing
+with time so chemical kinetics
+
+ align:start position:0%
+with time so chemical kinetics
+ 
+
+ align:start position:0%
+with time so chemical kinetics
+experiments you measure concentrations
+
+ align:start position:0%
+experiments you measure concentrations
+ 
+
+ align:start position:0%
+experiments you measure concentrations
+and think about how fast they're
+
+ align:start position:0%
+and think about how fast they're
+ 
+
+ align:start position:0%
+and think about how fast they're
+changing with time so let's think about
+
+ align:start position:0%
+changing with time so let's think about
+ 
+
+ align:start position:0%
+changing with time so let's think about
+some of the factors that are going to
+
+ align:start position:0%
+some of the factors that are going to
+ 
+
+ align:start position:0%
+some of the factors that are going to
+affect the rates of chemical
+
+ align:start position:0%
+affect the rates of chemical
+ 
+
+ align:start position:0%
+affect the rates of chemical
+reactions and I will write some of these
+
+ align:start position:0%
+reactions and I will write some of these
+ 
+
+ align:start position:0%
+reactions and I will write some of these
+on the the board so what's one thing
+
+ align:start position:0%
+on the the board so what's one thing
+ 
+
+ align:start position:0%
+on the the board so what's one thing
+that you may have observed that will
+
+ align:start position:0%
+that you may have observed that will
+ 
+
+ align:start position:0%
+that you may have observed that will
+affect either speed up or slow down say
+
+ align:start position:0%
+affect either speed up or slow down say
+ 
+
+ align:start position:0%
+affect either speed up or slow down say
+a chemical reaction what's one thing you
+
+ align:start position:0%
+a chemical reaction what's one thing you
+ 
+
+ align:start position:0%
+a chemical reaction what's one thing you
+can think
+
+ align:start position:0%
+can think
+ 
+
+ align:start position:0%
+can think
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature what's another thing you can
+
+ align:start position:0%
+temperature what's another thing you can
+ 
+
+ align:start position:0%
+temperature what's another thing you can
+think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of Catal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+catalyst so right so changing the sort
+
+ align:start position:0%
+catalyst so right so changing the sort
+ 
+
+ align:start position:0%
+catalyst so right so changing the sort
+of in environment so it depends a little
+
+ align:start position:0%
+of in environment so it depends a little
+ 
+
+ align:start position:0%
+of in environment so it depends a little
+it could be it could be pressure it
+
+ align:start position:0%
+it could be it could be pressure it
+ 
+
+ align:start position:0%
+it could be it could be pressure it
+depends on um on what you're talking
+
+ align:start position:0%
+depends on um on what you're talking
+ 
+
+ align:start position:0%
+depends on um on what you're talking
+about what kind of uh nature of material
+
+ align:start position:0%
+about what kind of uh nature of material
+ 
+
+ align:start position:0%
+about what kind of uh nature of material
+you're talking about so possibly um
+
+ align:start position:0%
+you're talking about so possibly um
+ 
+
+ align:start position:0%
+you're talking about so possibly um
+pressure could have an effect and that
+
+ align:start position:0%
+pressure could have an effect and that
+ 
+
+ align:start position:0%
+pressure could have an effect and that
+brings us to the nature of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material whether it's gas or solid or
+
+ align:start position:0%
+material whether it's gas or solid or
+ 
+
+ align:start position:0%
+material whether it's gas or solid or
+other things um and that also comes to
+
+ align:start position:0%
+other things um and that also comes to
+ 
+
+ align:start position:0%
+other things um and that also comes to
+the other issue which is what is its
+
+ align:start position:0%
+the other issue which is what is its
+ 
+
+ align:start position:0%
+the other issue which is what is its
+mechanism oops sorry
+
+ align:start position:0%
+mechanism oops sorry
+ 
+
+ align:start position:0%
+mechanism oops sorry
+mechanism so does it have one step does
+
+ align:start position:0%
+mechanism so does it have one step does
+ 
+
+ align:start position:0%
+mechanism so does it have one step does
+it have many steps do the steps involve
+
+ align:start position:0%
+it have many steps do the steps involve
+ 
+
+ align:start position:0%
+it have many steps do the steps involve
+changes in Phase what's going on in the
+
+ align:start position:0%
+changes in Phase what's going on in the
+ 
+
+ align:start position:0%
+changes in Phase what's going on in the
+mechanism and so those are all some good
+
+ align:start position:0%
+mechanism and so those are all some good
+ 
+
+ align:start position:0%
+mechanism and so those are all some good
+things one other thing that I'll put on
+
+ align:start position:0%
+things one other thing that I'll put on
+ 
+
+ align:start position:0%
+things one other thing that I'll put on
+which also only applies um in some cases
+
+ align:start position:0%
+which also only applies um in some cases
+ 
+
+ align:start position:0%
+which also only applies um in some cases
+depending on the type of mechanism and
+
+ align:start position:0%
+depending on the type of mechanism and
+ 
+
+ align:start position:0%
+depending on the type of mechanism and
+type of reaction would be the
+
+ align:start position:0%
+type of reaction would be the
+ 
+
+ align:start position:0%
+type of reaction would be the
+concentration of the material which kind
+
+ align:start position:0%
+concentration of the material which kind
+ 
+
+ align:start position:0%
+concentration of the material which kind
+of also gets to this pressure idea um
+
+ align:start position:0%
+of also gets to this pressure idea um
+ 
+
+ align:start position:0%
+of also gets to this pressure idea um
+depending on what it is how much do you
+
+ align:start position:0%
+depending on what it is how much do you
+ 
+
+ align:start position:0%
+depending on what it is how much do you
+have in
+
+ align:start position:0%
+have in
+ 
+
+ align:start position:0%
+have in
+there all right so those are some of the
+
+ align:start position:0%
+there all right so those are some of the
+ 
+
+ align:start position:0%
+there all right so those are some of the
+things and we're going to talk about
+
+ align:start position:0%
+things and we're going to talk about
+ 
+
+ align:start position:0%
+things and we're going to talk about
+most of these in the next
+
+ align:start position:0%
+most of these in the next
+ 
+
+ align:start position:0%
+most of these in the next
+unit all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's now think about one example of
+
+ align:start position:0%
+so let's now think about one example of
+ 
+
+ align:start position:0%
+so let's now think about one example of
+a chemical reaction and this chemical
+
+ align:start position:0%
+a chemical reaction and this chemical
+ 
+
+ align:start position:0%
+a chemical reaction and this chemical
+reaction is called the oscillating clock
+
+ align:start position:0%
+reaction is called the oscillating clock
+ 
+
+ align:start position:0%
+reaction is called the oscillating clock
+and before we see the demo we're going
+
+ align:start position:0%
+and before we see the demo we're going
+ 
+
+ align:start position:0%
+and before we see the demo we're going
+to think about what's happening so this
+
+ align:start position:0%
+to think about what's happening so this
+ 
+
+ align:start position:0%
+to think about what's happening so this
+demo as with most chemical reactions
+
+ align:start position:0%
+demo as with most chemical reactions
+ 
+
+ align:start position:0%
+demo as with most chemical reactions
+involves thermodynamics chemical
+
+ align:start position:0%
+involves thermodynamics chemical
+ 
+
+ align:start position:0%
+involves thermodynamics chemical
+equilibrium kinetics it also has some
+
+ align:start position:0%
+equilibrium kinetics it also has some
+ 
+
+ align:start position:0%
+equilibrium kinetics it also has some
+acid base you have to have some acid in
+
+ align:start position:0%
+acid base you have to have some acid in
+ 
+
+ align:start position:0%
+acid base you have to have some acid in
+there to get it to go um it's also an
+
+ align:start position:0%
+there to get it to go um it's also an
+ 
+
+ align:start position:0%
+there to get it to go um it's also an
+oxidation reduction reaction and it has
+
+ align:start position:0%
+oxidation reduction reaction and it has
+ 
+
+ align:start position:0%
+oxidation reduction reaction and it has
+colors and we'll see that the colors
+
+ align:start position:0%
+colors and we'll see that the colors
+ 
+
+ align:start position:0%
+colors and we'll see that the colors
+change depending on what the oxidation
+
+ align:start position:0%
+change depending on what the oxidation
+ 
+
+ align:start position:0%
+change depending on what the oxidation
+state of the material is and also what
+
+ align:start position:0%
+state of the material is and also what
+ 
+
+ align:start position:0%
+state of the material is and also what
+its liganded state is so basically in
+
+ align:start position:0%
+its liganded state is so basically in
+ 
+
+ align:start position:0%
+its liganded state is so basically in
+one demo you get every unit that we've
+
+ align:start position:0%
+one demo you get every unit that we've
+ 
+
+ align:start position:0%
+one demo you get every unit that we've
+had in the second half of the course and
+
+ align:start position:0%
+had in the second half of the course and
+ 
+
+ align:start position:0%
+had in the second half of the course and
+that's kind of true about any chemical
+
+ align:start position:0%
+that's kind of true about any chemical
+ 
+
+ align:start position:0%
+that's kind of true about any chemical
+reaction every chem reaction if you're
+
+ align:start position:0%
+reaction every chem reaction if you're
+ 
+
+ align:start position:0%
+reaction every chem reaction if you're
+interested in it involves thinking about
+
+ align:start position:0%
+interested in it involves thinking about
+ 
+
+ align:start position:0%
+interested in it involves thinking about
+all of these things that we've been
+
+ align:start position:0%
+all of these things that we've been
+ 
+
+ align:start position:0%
+all of these things that we've been
+talking
+
+ align:start position:0%
+talking
+ 
+
+ align:start position:0%
+talking
+about all right so oscillating clock
+
+ align:start position:0%
+about all right so oscillating clock
+ 
+
+ align:start position:0%
+about all right so oscillating clock
+reaction um it's a fairly complicated
+
+ align:start position:0%
+reaction um it's a fairly complicated
+ 
+
+ align:start position:0%
+reaction um it's a fairly complicated
+reaction it has many steps and we're
+
+ align:start position:0%
+reaction it has many steps and we're
+ 
+
+ align:start position:0%
+reaction it has many steps and we're
+just going to break the overall reaction
+
+ align:start position:0%
+just going to break the overall reaction
+ 
+
+ align:start position:0%
+just going to break the overall reaction
+shown here down into two steps today as
+
+ align:start position:0%
+shown here down into two steps today as
+ 
+
+ align:start position:0%
+shown here down into two steps today as
+with many reaction mechanisms there are
+
+ align:start position:0%
+with many reaction mechanisms there are
+ 
+
+ align:start position:0%
+with many reaction mechanisms there are
+multiple steps but here is step one that
+
+ align:start position:0%
+multiple steps but here is step one that
+ 
+
+ align:start position:0%
+multiple steps but here is step one that
+we'll talk about and here is step two
+
+ align:start position:0%
+we'll talk about and here is step two
+ 
+
+ align:start position:0%
+we'll talk about and here is step two
+that we'll talk about
+
+ align:start position:0%
+that we'll talk about
+ 
+
+ align:start position:0%
+that we'll talk about
+and step one occurs when your I2
+
+ align:start position:0%
+and step one occurs when your I2
+ 
+
+ align:start position:0%
+and step one occurs when your I2
+concentration is low I2 here is a
+
+ align:start position:0%
+concentration is low I2 here is a
+ 
+
+ align:start position:0%
+concentration is low I2 here is a
+product of the reaction and when it
+
+ align:start position:0%
+product of the reaction and when it
+ 
+
+ align:start position:0%
+product of the reaction and when it
+builds up too much then that reaction
+
+ align:start position:0%
+builds up too much then that reaction
+ 
+
+ align:start position:0%
+builds up too much then that reaction
+will stop and so in this reaction we
+
+ align:start position:0%
+will stop and so in this reaction we
+ 
+
+ align:start position:0%
+will stop and so in this reaction we
+have acidic conditions you'll see our H+
+
+ align:start position:0%
+have acidic conditions you'll see our H+
+ 
+
+ align:start position:0%
+have acidic conditions you'll see our H+
+and under those acidic conditions we're
+
+ align:start position:0%
+and under those acidic conditions we're
+ 
+
+ align:start position:0%
+and under those acidic conditions we're
+going to change a clear solution so I
+
+ align:start position:0%
+going to change a clear solution so I
+ 
+
+ align:start position:0%
+going to change a clear solution so I
+iodide in its uh certain oxidation
+
+ align:start position:0%
+iodide in its uh certain oxidation
+ 
+
+ align:start position:0%
+iodide in its uh certain oxidation
+States is clear but when it goes to I2
+
+ align:start position:0%
+States is clear but when it goes to I2
+ 
+
+ align:start position:0%
+States is clear but when it goes to I2
+it turns in amber color in the second
+
+ align:start position:0%
+it turns in amber color in the second
+ 
+
+ align:start position:0%
+it turns in amber color in the second
+reaction which will only occur when I2
+
+ align:start position:0%
+reaction which will only occur when I2
+ 
+
+ align:start position:0%
+reaction which will only occur when I2
+is high so this will build up shutting
+
+ align:start position:0%
+is high so this will build up shutting
+ 
+
+ align:start position:0%
+is high so this will build up shutting
+off reaction a and starting reaction B
+
+ align:start position:0%
+off reaction a and starting reaction B
+ 
+
+ align:start position:0%
+off reaction a and starting reaction B
+in this reaction you have a complex
+
+ align:start position:0%
+in this reaction you have a complex
+ 
+
+ align:start position:0%
+in this reaction you have a complex
+being formed and that's going to change
+
+ align:start position:0%
+being formed and that's going to change
+ 
+
+ align:start position:0%
+being formed and that's going to change
+the color so we're going to go from
+
+ align:start position:0%
+the color so we're going to go from
+ 
+
+ align:start position:0%
+the color so we're going to go from
+Amber to a blue
+
+ align:start position:0%
+Amber to a blue
+ 
+
+ align:start position:0%
+Amber to a blue
+complex all right so before we see this
+
+ align:start position:0%
+complex all right so before we see this
+ 
+
+ align:start position:0%
+complex all right so before we see this
+happen and I should say that once you
+
+ align:start position:0%
+happen and I should say that once you
+ 
+
+ align:start position:0%
+happen and I should say that once you
+get over here you form the blue complex
+
+ align:start position:0%
+get over here you form the blue complex
+ 
+
+ align:start position:0%
+get over here you form the blue complex
+this will consume the I2 which will
+
+ align:start position:0%
+this will consume the I2 which will
+ 
+
+ align:start position:0%
+this will consume the I2 which will
+cause that to drop to be low again and
+
+ align:start position:0%
+cause that to drop to be low again and
+ 
+
+ align:start position:0%
+cause that to drop to be low again and
+then you're going to start reaction a
+
+ align:start position:0%
+then you're going to start reaction a
+ 
+
+ align:start position:0%
+then you're going to start reaction a
+again which then when it's gotten uh too
+
+ align:start position:0%
+again which then when it's gotten uh too
+ 
+
+ align:start position:0%
+again which then when it's gotten uh too
+when when your concentrations built up
+
+ align:start position:0%
+when when your concentrations built up
+ 
+
+ align:start position:0%
+when when your concentrations built up
+too much you'll start reaction B again
+
+ align:start position:0%
+too much you'll start reaction B again
+ 
+
+ align:start position:0%
+too much you'll start reaction B again
+and so reaction a then reaction B then
+
+ align:start position:0%
+and so reaction a then reaction B then
+ 
+
+ align:start position:0%
+and so reaction a then reaction B then
+reaction a reaction B um and you'll
+
+ align:start position:0%
+reaction a reaction B um and you'll
+ 
+
+ align:start position:0%
+reaction a reaction B um and you'll
+notice that the product of one of the
+
+ align:start position:0%
+notice that the product of one of the
+ 
+
+ align:start position:0%
+notice that the product of one of the
+reactions is a substrate here product
+
+ align:start position:0%
+reactions is a substrate here product
+ 
+
+ align:start position:0%
+reactions is a substrate here product
+here substrate here so this goes back
+
+ align:start position:0%
+here substrate here so this goes back
+ 
+
+ align:start position:0%
+here substrate here so this goes back
+and forth hence the name oscillating
+
+ align:start position:0%
+and forth hence the name oscillating
+ 
+
+ align:start position:0%
+and forth hence the name oscillating
+clock all right so before I show you
+
+ align:start position:0%
+clock all right so before I show you
+ 
+
+ align:start position:0%
+clock all right so before I show you
+something pretty I'm going to make you
+
+ align:start position:0%
+something pretty I'm going to make you
+ 
+
+ align:start position:0%
+something pretty I'm going to make you
+do work and think about the oxidation
+
+ align:start position:0%
+do work and think about the oxidation
+ 
+
+ align:start position:0%
+do work and think about the oxidation
+reduction reactions that are occurring
+
+ align:start position:0%
+reduction reactions that are occurring
+ 
+
+ align:start position:0%
+reduction reactions that are occurring
+that you're going to see that lead to
+
+ align:start position:0%
+that you're going to see that lead to
+ 
+
+ align:start position:0%
+that you're going to see that lead to
+these spectacular color changes all
+
+ align:start position:0%
+these spectacular color changes all
+ 
+
+ align:start position:0%
+these spectacular color changes all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so here we go clicker question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's just do 10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds all right so somebody asked once
+
+ align:start position:0%
+seconds all right so somebody asked once
+ 
+
+ align:start position:0%
+seconds all right so somebody asked once
+like how will I know that it's a
+
+ align:start position:0%
+like how will I know that it's a
+ 
+
+ align:start position:0%
+like how will I know that it's a
+peroxide so I tried to help you out and
+
+ align:start position:0%
+peroxide so I tried to help you out and
+ 
+
+ align:start position:0%
+peroxide so I tried to help you out and
+said reaction with hydrogen peroxide see
+
+ align:start position:0%
+said reaction with hydrogen peroxide see
+ 
+
+ align:start position:0%
+said reaction with hydrogen peroxide see
+how many people some people definitely
+
+ align:start position:0%
+how many people some people definitely
+ 
+
+ align:start position:0%
+how many people some people definitely
+notice that all right so let's just take
+
+ align:start position:0%
+notice that all right so let's just take
+ 
+
+ align:start position:0%
+notice that all right so let's just take
+a look over here at what's going on and
+
+ align:start position:0%
+a look over here at what's going on and
+ 
+
+ align:start position:0%
+a look over here at what's going on and
+fill in our chart so here the oxidation
+
+ align:start position:0%
+fill in our chart so here the oxidation
+ 
+
+ align:start position:0%
+fill in our chart so here the oxidation
+state is + five so we have now this
+
+ align:start position:0%
+state is + five so we have now this
+ 
+
+ align:start position:0%
+state is + five so we have now this
+oxygen is its normal -2 so -2 * 3 - 6
+
+ align:start position:0%
+oxygen is its normal -2 so -2 * 3 - 6
+ 
+
+ align:start position:0%
+oxygen is its normal -2 so -2 * 3 - 6
+equals the whole thing charge needs to
+
+ align:start position:0%
+equals the whole thing charge needs to
+ 
+
+ align:start position:0%
+equals the whole thing charge needs to
+equal minus one so we need plus five
+
+ align:start position:0%
+equal minus one so we need plus five
+ 
+
+ align:start position:0%
+equal minus one so we need plus five
+there and I2 is zero the next one I
+
+ align:start position:0%
+there and I2 is zero the next one I
+ 
+
+ align:start position:0%
+there and I2 is zero the next one I
+minus is being oxidized to I2 minus one
+
+ align:start position:0%
+minus is being oxidized to I2 minus one
+ 
+
+ align:start position:0%
+minus is being oxidized to I2 minus one
+to 0er the oxygen and hydrogen peroxide
+
+ align:start position:0%
+to 0er the oxygen and hydrogen peroxide
+ 
+
+ align:start position:0%
+to 0er the oxygen and hydrogen peroxide
+is being oxidized so it's minus um minus
+
+ align:start position:0%
+is being oxidized so it's minus um minus
+ 
+
+ align:start position:0%
+is being oxidized so it's minus um minus
+one here because we have plus two for H
+
+ align:start position:0%
+one here because we have plus two for H
+ 
+
+ align:start position:0%
+one here because we have plus two for H
+and two oxygen so that's minus one each
+
+ align:start position:0%
+and two oxygen so that's minus one each
+ 
+
+ align:start position:0%
+and two oxygen so that's minus one each
+to zero and then again minus one and
+
+ align:start position:0%
+to zero and then again minus one and
+ 
+
+ align:start position:0%
+to zero and then again minus one and
+oxygen and water is minus two so there's
+
+ align:start position:0%
+oxygen and water is minus two so there's
+ 
+
+ align:start position:0%
+oxygen and water is minus two so there's
+lots of oxidation reduction reactions
+
+ align:start position:0%
+lots of oxidation reduction reactions
+ 
+
+ align:start position:0%
+lots of oxidation reduction reactions
+going on and in fact this occurs in
+
+ align:start position:0%
+going on and in fact this occurs in
+ 
+
+ align:start position:0%
+going on and in fact this occurs in
+multiple different steps so there's even
+
+ align:start position:0%
+multiple different steps so there's even
+ 
+
+ align:start position:0%
+multiple different steps so there's even
+more different reactions going on that I
+
+ align:start position:0%
+more different reactions going on that I
+ 
+
+ align:start position:0%
+more different reactions going on that I
+didn't even show you all right so we
+
+ align:start position:0%
+didn't even show you all right so we
+ 
+
+ align:start position:0%
+didn't even show you all right so we
+have one more clicker question to answer
+
+ align:start position:0%
+have one more clicker question to answer
+ 
+
+ align:start position:0%
+have one more clicker question to answer
+before um we do the demo which is that
+
+ align:start position:0%
+before um we do the demo which is that
+ 
+
+ align:start position:0%
+before um we do the demo which is that
+if I told you you want to think about
+
+ align:start position:0%
+if I told you you want to think about
+ 
+
+ align:start position:0%
+if I told you you want to think about
+iodide you're using because it's
+
+ align:start position:0%
+iodide you're using because it's
+ 
+
+ align:start position:0%
+iodide you're using because it's
+changing color why are you using the
+
+ align:start position:0%
+changing color why are you using the
+ 
+
+ align:start position:0%
+changing color why are you using the
+hydrogen peroxide so tell me what uh is
+
+ align:start position:0%
+hydrogen peroxide so tell me what uh is
+ 
+
+ align:start position:0%
+hydrogen peroxide so tell me what uh is
+true about hydrogen peroxide using the
+
+ align:start position:0%
+true about hydrogen peroxide using the
+ 
+
+ align:start position:0%
+true about hydrogen peroxide using the
+information given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right so if we look over here the large
+
+ align:start position:0%
+right so if we look over here the large
+ 
+
+ align:start position:0%
+right so if we look over here the large
+positive value and again that's a large
+
+ align:start position:0%
+positive value and again that's a large
+ 
+
+ align:start position:0%
+positive value and again that's a large
+positive value of the standard reduction
+
+ align:start position:0%
+positive value of the standard reduction
+ 
+
+ align:start position:0%
+positive value of the standard reduction
+potential um is a big big palue which
+
+ align:start position:0%
+potential um is a big big palue which
+ 
+
+ align:start position:0%
+potential um is a big big palue which
+makes it a good oxidizing agent the
+
+ align:start position:0%
+makes it a good oxidizing agent the
+ 
+
+ align:start position:0%
+makes it a good oxidizing agent the
+reduction is spontaneous so if you have
+
+ align:start position:0%
+reduction is spontaneous so if you have
+ 
+
+ align:start position:0%
+reduction is spontaneous so if you have
+a large positive e that's going to for
+
+ align:start position:0%
+a large positive e that's going to for
+ 
+
+ align:start position:0%
+a large positive e that's going to for
+the reaction written as a reduction that
+
+ align:start position:0%
+the reaction written as a reduction that
+ 
+
+ align:start position:0%
+the reaction written as a reduction that
+means that Delta G for that reduction is
+
+ align:start position:0%
+means that Delta G for that reduction is
+ 
+
+ align:start position:0%
+means that Delta G for that reduction is
+going to be NE negative which means it's
+
+ align:start position:0%
+going to be NE negative which means it's
+ 
+
+ align:start position:0%
+going to be NE negative which means it's
+spontaneous so things that like to be
+
+ align:start position:0%
+spontaneous so things that like to be
+ 
+
+ align:start position:0%
+spontaneous so things that like to be
+reduced are good oxidizing agents
+
+ align:start position:0%
+reduced are good oxidizing agents
+ 
+
+ align:start position:0%
+reduced are good oxidizing agents
+actually hydrogen peroxide is a really
+
+ align:start position:0%
+actually hydrogen peroxide is a really
+ 
+
+ align:start position:0%
+actually hydrogen peroxide is a really
+good oxidizing agent and that's why it's
+
+ align:start position:0%
+good oxidizing agent and that's why it's
+ 
+
+ align:start position:0%
+good oxidizing agent and that's why it's
+used in a lot of things all right so
+
+ align:start position:0%
+used in a lot of things all right so
+ 
+
+ align:start position:0%
+used in a lot of things all right so
+let's look at this demo now so again
+
+ align:start position:0%
+let's look at this demo now so again
+ 
+
+ align:start position:0%
+let's look at this demo now so again
+clear to Amber Amber to Blue and the
+
+ align:start position:0%
+clear to Amber Amber to Blue and the
+ 
+
+ align:start position:0%
+clear to Amber Amber to Blue and the
+reaction rate is also sensitive to
+
+ align:start position:0%
+reaction rate is also sensitive to
+ 
+
+ align:start position:0%
+reaction rate is also sensitive to
+temperature and you told me temperature
+
+ align:start position:0%
+temperature and you told me temperature
+ 
+
+ align:start position:0%
+temperature and you told me temperature
+does affect reaction rates and it does
+
+ align:start position:0%
+does affect reaction rates and it does
+ 
+
+ align:start position:0%
+does affect reaction rates and it does
+in this case all right let's see it Okay
+
+ align:start position:0%
+in this case all right let's see it Okay
+ 
+
+ align:start position:0%
+in this case all right let's see it Okay
+so we've got the hydrogen peroxide
+
+ align:start position:0%
+so we've got the hydrogen peroxide
+ 
+
+ align:start position:0%
+so we've got the hydrogen peroxide
+Eric's got that in hand he's going to
+
+ align:start position:0%
+Eric's got that in hand he's going to
+ 
+
+ align:start position:0%
+Eric's got that in hand he's going to
+take the that off before he actually
+
+ align:start position:0%
+take the that off before he actually
+ 
+
+ align:start position:0%
+take the that off before he actually
+unscrews it yay okay hydrogen peroxide
+
+ align:start position:0%
+unscrews it yay okay hydrogen peroxide
+ 
+
+ align:start position:0%
+unscrews it yay okay hydrogen peroxide
+as we said it's a good um uh it gets
+
+ align:start position:0%
+as we said it's a good um uh it gets
+ 
+
+ align:start position:0%
+as we said it's a good um uh it gets
+reduced really easily which is actually
+
+ align:start position:0%
+reduced really easily which is actually
+ 
+
+ align:start position:0%
+reduced really easily which is actually
+the reason why we kept it in a plastic
+
+ align:start position:0%
+the reason why we kept it in a plastic
+ 
+
+ align:start position:0%
+the reason why we kept it in a plastic
+bag because even the presence of oxygen
+
+ align:start position:0%
+bag because even the presence of oxygen
+ 
+
+ align:start position:0%
+bag because even the presence of oxygen
+can uh can cause it to be uh can cause
+
+ align:start position:0%
+can uh can cause it to be uh can cause
+ 
+
+ align:start position:0%
+can uh can cause it to be uh can cause
+it to react so he's going to add uh
+
+ align:start position:0%
+it to react so he's going to add uh
+ 
+
+ align:start position:0%
+it to react so he's going to add uh
+solution B that was solution a solution
+
+ align:start position:0%
+solution B that was solution a solution
+ 
+
+ align:start position:0%
+solution B that was solution a solution
+B uh contains the iodate which is going
+
+ align:start position:0%
+B uh contains the iodate which is going
+ 
+
+ align:start position:0%
+B uh contains the iodate which is going
+to provide the um the huh yeah got a St
+
+ align:start position:0%
+to provide the um the huh yeah got a St
+ 
+
+ align:start position:0%
+to provide the um the huh yeah got a St
+um it's going to provide the the uh
+
+ align:start position:0%
+um it's going to provide the the uh
+ 
+
+ align:start position:0%
+um it's going to provide the the uh
+iodine for the solution and as you can
+
+ align:start position:0%
+iodine for the solution and as you can
+ 
+
+ align:start position:0%
+iodine for the solution and as you can
+see it's turning kind of yellowish which
+
+ align:start position:0%
+see it's turning kind of yellowish which
+ 
+
+ align:start position:0%
+see it's turning kind of yellowish which
+is what we were expecting so now the
+
+ align:start position:0%
+is what we were expecting so now the
+ 
+
+ align:start position:0%
+is what we were expecting so now the
+iodate is starting to produce the iodine
+
+ align:start position:0%
+iodate is starting to produce the iodine
+ 
+
+ align:start position:0%
+iodate is starting to produce the iodine
+and when he adds solution D we can see
+
+ align:start position:0%
+and when he adds solution D we can see
+ 
+
+ align:start position:0%
+and when he adds solution D we can see
+it changing yay it
+
+ align:start position:0%
+it changing yay it
+ 
+
+ align:start position:0%
+it changing yay it
+works it's always a struggle whether
+
+ align:start position:0%
+works it's always a struggle whether
+ 
+
+ align:start position:0%
+works it's always a struggle whether
+these things will actually work but this
+
+ align:start position:0%
+these things will actually work but this
+ 
+
+ align:start position:0%
+these things will actually work but this
+one this one's usually works very nicely
+
+ align:start position:0%
+one this one's usually works very nicely
+ 
+
+ align:start position:0%
+one this one's usually works very nicely
+I'm going to turn this up a little bit
+
+ align:start position:0%
+I'm going to turn this up a little bit
+ 
+
+ align:start position:0%
+I'm going to turn this up a little bit
+more and it will actually continue to do
+
+ align:start position:0%
+more and it will actually continue to do
+ 
+
+ align:start position:0%
+more and it will actually continue to do
+this uh for for quite a while I think
+
+ align:start position:0%
+this uh for for quite a while I think
+ 
+
+ align:start position:0%
+this uh for for quite a while I think
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+yeah yay awesome
+
+ align:start position:0%
+yeah yay awesome
+ 
+
+ align:start position:0%
+yeah yay awesome
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+awesome
+
+ align:start position:0%
+awesome
+ 
+
+ align:start position:0%
+awesome
+yeah so we can move this off to the side
+
+ align:start position:0%
+yeah so we can move this off to the side
+ 
+
+ align:start position:0%
+yeah so we can move this off to the side
+and now we're going to see the effect of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature actually we move that in a
+
+ align:start position:0%
+temperature actually we move that in a
+ 
+
+ align:start position:0%
+temperature actually we move that in a
+second so uh as Kathy mentioned uh
+
+ align:start position:0%
+second so uh as Kathy mentioned uh
+ 
+
+ align:start position:0%
+second so uh as Kathy mentioned uh
+affecting temperature will affect the
+
+ align:start position:0%
+affecting temperature will affect the
+ 
+
+ align:start position:0%
+affecting temperature will affect the
+rates of reaction so this guy will
+
+ align:start position:0%
+rates of reaction so this guy will
+ 
+
+ align:start position:0%
+rates of reaction so this guy will
+continue to go and what we have here is
+
+ align:start position:0%
+continue to go and what we have here is
+ 
+
+ align:start position:0%
+continue to go and what we have here is
+we have all three solutions again except
+
+ align:start position:0%
+we have all three solutions again except
+ 
+
+ align:start position:0%
+we have all three solutions again except
+they've been uh they've been put in ice
+
+ align:start position:0%
+they've been uh they've been put in ice
+ 
+
+ align:start position:0%
+they've been uh they've been put in ice
+so we're going to see if we've kept this
+
+ align:start position:0%
+so we're going to see if we've kept this
+ 
+
+ align:start position:0%
+so we're going to see if we've kept this
+a little bit cold again you should have
+
+ align:start position:0%
+a little bit cold again you should have
+ 
+
+ align:start position:0%
+a little bit cold again you should have
+taken this thing
+
+ align:start position:0%
+taken this thing
+ 
+
+ align:start position:0%
+taken this thing
+off all right so that's the
+
+ align:start position:0%
+off all right so that's the
+ 
+
+ align:start position:0%
+off all right so that's the
+peroxide we've got
+
+ align:start position:0%
+peroxide we've got
+ 
+
+ align:start position:0%
+peroxide we've got
+solution B you got
+
+ align:start position:0%
+solution B you got
+ 
+
+ align:start position:0%
+solution B you got
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+okay and yeah I'll get the St in a
+
+ align:start position:0%
+okay and yeah I'll get the St in a
+ 
+
+ align:start position:0%
+okay and yeah I'll get the St in a
+second after B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so as before you saw the temperature
+
+ align:start position:0%
+so as before you saw the temperature
+ 
+
+ align:start position:0%
+so as before you saw the temperature
+change kind of quickly um this time it's
+
+ align:start position:0%
+change kind of quickly um this time it's
+ 
+
+ align:start position:0%
+change kind of quickly um this time it's
+not really changing that much hold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on so before you saw the temperature
+
+ align:start position:0%
+on so before you saw the temperature
+ 
+
+ align:start position:0%
+on so before you saw the temperature
+change pretty quickly this is probably
+
+ align:start position:0%
+change pretty quickly this is probably
+ 
+
+ align:start position:0%
+change pretty quickly this is probably
+going to take a while to actually change
+
+ align:start position:0%
+going to take a while to actually change
+ 
+
+ align:start position:0%
+going to take a while to actually change
+it might not change at all it's because
+
+ align:start position:0%
+it might not change at all it's because
+ 
+
+ align:start position:0%
+it might not change at all it's because
+the reaction was so cold that you won't
+
+ align:start position:0%
+the reaction was so cold that you won't
+ 
+
+ align:start position:0%
+the reaction was so cold that you won't
+have that second step and also I can't
+
+ align:start position:0%
+have that second step and also I can't
+ 
+
+ align:start position:0%
+have that second step and also I can't
+there we go so it happens really really
+
+ align:start position:0%
+there we go so it happens really really
+ 
+
+ align:start position:0%
+there we go so it happens really really
+slowly as you can tell whereas this one
+
+ align:start position:0%
+slowly as you can tell whereas this one
+ 
+
+ align:start position:0%
+slowly as you can tell whereas this one
+happened very very quickly so yay yeah
+
+ align:start position:0%
+happened very very quickly so yay yeah
+ 
+
+ align:start position:0%
+happened very very quickly so yay yeah
+so example of many things so we had
+
+ align:start position:0%
+so example of many things so we had
+ 
+
+ align:start position:0%
+so example of many things so we had
+chemical equilibrium we had
+
+ align:start position:0%
+chemical equilibrium we had
+ 
+
+ align:start position:0%
+chemical equilibrium we had
+thermodynamics talking about which
+
+ align:start position:0%
+thermodynamics talking about which
+ 
+
+ align:start position:0%
+thermodynamics talking about which
+reactions were spontaneous so
+
+ align:start position:0%
+reactions were spontaneous so
+ 
+
+ align:start position:0%
+reactions were spontaneous so
+spontaneous until the making the Amber
+
+ align:start position:0%
+spontaneous until the making the Amber
+ 
+
+ align:start position:0%
+spontaneous until the making the Amber
+and then when it's made too much of the
+
+ align:start position:0%
+and then when it's made too much of the
+ 
+
+ align:start position:0%
+and then when it's made too much of the
+the iodide than the I2 then we see the
+
+ align:start position:0%
+the iodide than the I2 then we see the
+ 
+
+ align:start position:0%
+the iodide than the I2 then we see the
+next reaction going until we now have
+
+ align:start position:0%
+next reaction going until we now have
+ 
+
+ align:start position:0%
+next reaction going until we now have
+too little and then we switch back and
+
+ align:start position:0%
+too little and then we switch back and
+ 
+
+ align:start position:0%
+too little and then we switch back and
+forth and yeah this I think very clearly
+
+ align:start position:0%
+forth and yeah this I think very clearly
+ 
+
+ align:start position:0%
+forth and yeah this I think very clearly
+demonstrates that the uh the temperature
+
+ align:start position:0%
+demonstrates that the uh the temperature
+ 
+
+ align:start position:0%
+demonstrates that the uh the temperature
+is very different has a very different
+
+ align:start position:0%
+is very different has a very different
+ 
+
+ align:start position:0%
+is very different has a very different
+effect it's a much much slower
+
+ align:start position:0%
+effect it's a much much slower
+ 
+
+ align:start position:0%
+effect it's a much much slower
+reaction all right thank you we can
+
+ align:start position:0%
+reaction all right thank you we can
+ 
+
+ align:start position:0%
+reaction all right thank you we can
+leave them up do you want to just leave
+
+ align:start position:0%
+leave them up do you want to just leave
+ 
+
+ align:start position:0%
+leave them up do you want to just leave
+them up here I'm leave this yeah okay
+
+ align:start position:0%
+them up here I'm leave this yeah okay
+ 
+
+ align:start position:0%
+them up here I'm leave this yeah okay
+we'll leave the fast one up there it
+
+ align:start position:0%
+we'll leave the fast one up there it
+ 
+
+ align:start position:0%
+we'll leave the fast one up there it
+will eventually stop so uh it's good
+
+ align:start position:0%
+will eventually stop so uh it's good
+ 
+
+ align:start position:0%
+will eventually stop so uh it's good
+probably I don't know maybe F five
+
+ align:start position:0%
+probably I don't know maybe F five
+ 
+
+ align:start position:0%
+probably I don't know maybe F five
+minutes or more or a little longer and
+
+ align:start position:0%
+minutes or more or a little longer and
+ 
+
+ align:start position:0%
+minutes or more or a little longer and
+then eventually it just kind of stays
+
+ align:start position:0%
+then eventually it just kind of stays
+ 
+
+ align:start position:0%
+then eventually it just kind of stays
+this uh uh more dark brown maybe it's
+
+ align:start position:0%
+this uh uh more dark brown maybe it's
+ 
+
+ align:start position:0%
+this uh uh more dark brown maybe it's
+already happened we'll see if it
+
+ align:start position:0%
+already happened we'll see if it
+ 
+
+ align:start position:0%
+already happened we'll see if it
+switches
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again all right so let's talk about
+
+ align:start position:0%
+again all right so let's talk about
+ 
+
+ align:start position:0%
+again all right so let's talk about
+measuring reaction rates then because we
+
+ align:start position:0%
+measuring reaction rates then because we
+ 
+
+ align:start position:0%
+measuring reaction rates then because we
+just saw this reaction going in another
+
+ align:start position:0%
+just saw this reaction going in another
+ 
+
+ align:start position:0%
+just saw this reaction going in another
+reaction rate we saw the effect of
+
+ align:start position:0%
+reaction rate we saw the effect of
+ 
+
+ align:start position:0%
+reaction rate we saw the effect of
+temperature um and let's think about how
+
+ align:start position:0%
+temperature um and let's think about how
+ 
+
+ align:start position:0%
+temperature um and let's think about how
+we would actually go about measuring
+
+ align:start position:0%
+we would actually go about measuring
+ 
+
+ align:start position:0%
+we would actually go about measuring
+some of these so we can think about
+
+ align:start position:0%
+some of these so we can think about
+ 
+
+ align:start position:0%
+some of these so we can think about
+measuring two different kinds of rates
+
+ align:start position:0%
+measuring two different kinds of rates
+ 
+
+ align:start position:0%
+measuring two different kinds of rates
+an average rate and an instantaneous
+
+ align:start position:0%
+an average rate and an instantaneous
+ 
+
+ align:start position:0%
+an average rate and an instantaneous
+rate and so first let's talk about
+
+ align:start position:0%
+rate and so first let's talk about
+ 
+
+ align:start position:0%
+rate and so first let's talk about
+measuring average rate and to do that I
+
+ align:start position:0%
+measuring average rate and to do that I
+ 
+
+ align:start position:0%
+measuring average rate and to do that I
+should switch back over here okay so
+
+ align:start position:0%
+should switch back over here okay so
+ 
+
+ align:start position:0%
+should switch back over here okay so
+let's consider a different reaction now
+
+ align:start position:0%
+let's consider a different reaction now
+ 
+
+ align:start position:0%
+let's consider a different reaction now
+one that's a little less complicated and
+
+ align:start position:0%
+one that's a little less complicated and
+ 
+
+ align:start position:0%
+one that's a little less complicated and
+kind of made up but it's a good example
+
+ align:start position:0%
+kind of made up but it's a good example
+ 
+
+ align:start position:0%
+kind of made up but it's a good example
+um NO2 plus Co goes to no plus
+
+ align:start position:0%
+um NO2 plus Co goes to no plus
+ 
+
+ align:start position:0%
+um NO2 plus Co goes to no plus
+CO2 and so if you're measuring a rate
+
+ align:start position:0%
+CO2 and so if you're measuring a rate
+ 
+
+ align:start position:0%
+CO2 and so if you're measuring a rate
+you could think about measuring the
+
+ align:start position:0%
+you could think about measuring the
+ 
+
+ align:start position:0%
+you could think about measuring the
+decrease in either of the reactants or
+
+ align:start position:0%
+decrease in either of the reactants or
+ 
+
+ align:start position:0%
+decrease in either of the reactants or
+the increase in concentration of either
+
+ align:start position:0%
+the increase in concentration of either
+ 
+
+ align:start position:0%
+the increase in concentration of either
+of the products so in this case let's
+
+ align:start position:0%
+of the products so in this case let's
+ 
+
+ align:start position:0%
+of the products so in this case let's
+consider um that we're measuring the
+
+ align:start position:0%
+consider um that we're measuring the
+ 
+
+ align:start position:0%
+consider um that we're measuring the
+change in n
+
+ align:start position:0%
+change in n
+ 
+
+ align:start position:0%
+change in n
+and usually people pick the thing to
+
+ align:start position:0%
+and usually people pick the thing to
+ 
+
+ align:start position:0%
+and usually people pick the thing to
+measure based on what's easiest to
+
+ align:start position:0%
+measure based on what's easiest to
+ 
+
+ align:start position:0%
+measure based on what's easiest to
+measure what kind of handle you are does
+
+ align:start position:0%
+measure what kind of handle you are does
+ 
+
+ align:start position:0%
+measure what kind of handle you are does
+it have a spectroscopic signal or
+
+ align:start position:0%
+it have a spectroscopic signal or
+ 
+
+ align:start position:0%
+it have a spectroscopic signal or
+something else that you can easily
+
+ align:start position:0%
+something else that you can easily
+ 
+
+ align:start position:0%
+something else that you can easily
+measure so here we have concentration
+
+ align:start position:0%
+measure so here we have concentration
+ 
+
+ align:start position:0%
+measure so here we have concentration
+versus time and so we should see none in
+
+ align:start position:0%
+versus time and so we should see none in
+ 
+
+ align:start position:0%
+versus time and so we should see none in
+the beginning and then we should see it
+
+ align:start position:0%
+the beginning and then we should see it
+ 
+
+ align:start position:0%
+the beginning and then we should see it
+increase and then level off and we can
+
+ align:start position:0%
+increase and then level off and we can
+ 
+
+ align:start position:0%
+increase and then level off and we can
+calculate an average rate which is just
+
+ align:start position:0%
+calculate an average rate which is just
+ 
+
+ align:start position:0%
+calculate an average rate which is just
+going to be the change in concentration
+
+ align:start position:0%
+going to be the change in concentration
+ 
+
+ align:start position:0%
+going to be the change in concentration
+over the change in time we can also
+
+ align:start position:0%
+over the change in time we can also
+ 
+
+ align:start position:0%
+over the change in time we can also
+Express the average rate as Delta the
+
+ align:start position:0%
+Express the average rate as Delta the
+ 
+
+ align:start position:0%
+Express the average rate as Delta the
+concentration of no over delta T the
+
+ align:start position:0%
+concentration of no over delta T the
+ 
+
+ align:start position:0%
+concentration of no over delta T the
+change in
+
+ align:start position:0%
+change in
+ 
+
+ align:start position:0%
+change in
+time and we can calculate what that
+
+ align:start position:0%
+time and we can calculate what that
+ 
+
+ align:start position:0%
+time and we can calculate what that
+would be we can pick an interval say
+
+ align:start position:0%
+would be we can pick an interval say
+ 
+
+ align:start position:0%
+would be we can pick an interval say
+from 50 to 150 we can measure some
+
+ align:start position:0%
+from 50 to 150 we can measure some
+ 
+
+ align:start position:0%
+from 50 to 150 we can measure some
+concentrations there and then calculate
+
+ align:start position:0%
+concentrations there and then calculate
+ 
+
+ align:start position:0%
+concentrations there and then calculate
+the average rate the change in
+
+ align:start position:0%
+the average rate the change in
+ 
+
+ align:start position:0%
+the average rate the change in
+concentration from the time 150 to the
+
+ align:start position:0%
+concentration from the time 150 to the
+ 
+
+ align:start position:0%
+concentration from the time 150 to the
+time 50 concentration over that time
+
+ align:start position:0%
+time 50 concentration over that time
+ 
+
+ align:start position:0%
+time 50 concentration over that time
+interval and it will give us an answer
+
+ align:start position:0%
+interval and it will give us an answer
+ 
+
+ align:start position:0%
+interval and it will give us an answer
+in this case 1.3 * 10-4 molar per second
+
+ align:start position:0%
+in this case 1.3 * 10-4 molar per second
+ 
+
+ align:start position:0%
+in this case 1.3 * 10-4 molar per second
+all right well that could be useful to
+
+ align:start position:0%
+all right well that could be useful to
+ 
+
+ align:start position:0%
+all right well that could be useful to
+know but it really depends on the
+
+ align:start position:0%
+know but it really depends on the
+ 
+
+ align:start position:0%
+know but it really depends on the
+average rate depends on the time
+
+ align:start position:0%
+average rate depends on the time
+ 
+
+ align:start position:0%
+average rate depends on the time
+interval I picked if I picked a
+
+ align:start position:0%
+interval I picked if I picked a
+ 
+
+ align:start position:0%
+interval I picked if I picked a
+different time interval I might have
+
+ align:start position:0%
+different time interval I might have
+ 
+
+ align:start position:0%
+different time interval I might have
+gotten a different rate so instead of
+
+ align:start position:0%
+gotten a different rate so instead of
+ 
+
+ align:start position:0%
+gotten a different rate so instead of
+calculating average rate a lot of people
+
+ align:start position:0%
+calculating average rate a lot of people
+ 
+
+ align:start position:0%
+calculating average rate a lot of people
+want to Cal calculate instantaneous rate
+
+ align:start position:0%
+want to Cal calculate instantaneous rate
+ 
+
+ align:start position:0%
+want to Cal calculate instantaneous rate
+where you're asking what is the rate at
+
+ align:start position:0%
+where you're asking what is the rate at
+ 
+
+ align:start position:0%
+where you're asking what is the rate at
+a particular time point so now let's
+
+ align:start position:0%
+a particular time point so now let's
+ 
+
+ align:start position:0%
+a particular time point so now let's
+talk about instantaneous rate we'll have
+
+ align:start position:0%
+talk about instantaneous rate we'll have
+ 
+
+ align:start position:0%
+talk about instantaneous rate we'll have
+the same uh equation up there now
+
+ align:start position:0%
+the same uh equation up there now
+ 
+
+ align:start position:0%
+the same uh equation up there now
+instantaneous rate is uh defined as the
+
+ align:start position:0%
+instantaneous rate is uh defined as the
+ 
+
+ align:start position:0%
+instantaneous rate is uh defined as the
+rate where you have a limit of delta T
+
+ align:start position:0%
+rate where you have a limit of delta T
+ 
+
+ align:start position:0%
+rate where you have a limit of delta T
+the change in time going to zero you're
+
+ align:start position:0%
+the change in time going to zero you're
+ 
+
+ align:start position:0%
+the change in time going to zero you're
+comparing concentrations at time T and
+
+ align:start position:0%
+comparing concentrations at time T and
+ 
+
+ align:start position:0%
+comparing concentrations at time T and
+time t plus the interval
+
+ align:start position:0%
+time t plus the interval
+ 
+
+ align:start position:0%
+time t plus the interval
+DT over this time change again as you
+
+ align:start position:0%
+DT over this time change again as you
+ 
+
+ align:start position:0%
+DT over this time change again as you
+approach um zero you can also Express
+
+ align:start position:0%
+approach um zero you can also Express
+ 
+
+ align:start position:0%
+approach um zero you can also Express
+this as
+
+ align:start position:0%
+this as
+ 
+
+ align:start position:0%
+this as
+D change in concentration of n
+
+ align:start position:0%
+D change in concentration of n
+ 
+
+ align:start position:0%
+D change in concentration of n
+DT and so as that change in time
+
+ align:start position:0%
+DT and so as that change in time
+ 
+
+ align:start position:0%
+DT and so as that change in time
+approaches
+
+ align:start position:0%
+approaches
+ 
+
+ align:start position:0%
+approaches
+zero then the rate becomes the slope of
+
+ align:start position:0%
+zero then the rate becomes the slope of
+ 
+
+ align:start position:0%
+zero then the rate becomes the slope of
+a of the line tangent to the
+
+ align:start position:0%
+a of the line tangent to the
+ 
+
+ align:start position:0%
+a of the line tangent to the
+curve at time T so if we wanted to to
+
+ align:start position:0%
+curve at time T so if we wanted to to
+ 
+
+ align:start position:0%
+curve at time T so if we wanted to to
+say find the instantaneous rate at 150
+
+ align:start position:0%
+say find the instantaneous rate at 150
+ 
+
+ align:start position:0%
+say find the instantaneous rate at 150
+here's 150 we can draw a line tangent to
+
+ align:start position:0%
+here's 150 we can draw a line tangent to
+ 
+
+ align:start position:0%
+here's 150 we can draw a line tangent to
+the curve at
+
+ align:start position:0%
+the curve at
+ 
+
+ align:start position:0%
+the curve at
+that time so this would be the point at
+
+ align:start position:0%
+that time so this would be the point at
+ 
+
+ align:start position:0%
+that time so this would be the point at
+150 and then we can calculate the slope
+
+ align:start position:0%
+150 and then we can calculate the slope
+ 
+
+ align:start position:0%
+150 and then we can calculate the slope
+to tell us the instantaneous
+
+ align:start position:0%
+to tell us the instantaneous
+ 
+
+ align:start position:0%
+to tell us the instantaneous
+rate so let's do that we will calculate
+
+ align:start position:0%
+rate so let's do that we will calculate
+ 
+
+ align:start position:0%
+rate so let's do that we will calculate
+the slope we have to look at what the
+
+ align:start position:0%
+the slope we have to look at what the
+ 
+
+ align:start position:0%
+the slope we have to look at what the
+concentrations are what the times are
+
+ align:start position:0%
+concentrations are what the times are
+ 
+
+ align:start position:0%
+concentrations are what the times are
+and then the instantaneous rate at
+
+ align:start position:0%
+and then the instantaneous rate at
+ 
+
+ align:start position:0%
+and then the instantaneous rate at
+150 would be the slope of the line this
+
+ align:start position:0%
+150 would be the slope of the line this
+ 
+
+ align:start position:0%
+150 would be the slope of the line this
+change in concentration over that time
+
+ align:start position:0%
+change in concentration over that time
+ 
+
+ align:start position:0%
+change in concentration over that time
+interval and and to the correct
+
+ align:start position:0%
+interval and and to the correct
+ 
+
+ align:start position:0%
+interval and and to the correct
+significant figures there should be an
+
+ align:start position:0%
+significant figures there should be an
+ 
+
+ align:start position:0%
+significant figures there should be an
+extra zero in there um
+
+ align:start position:0%
+extra zero in there um
+ 
+
+ align:start position:0%
+extra zero in there um
+7.70 * 10- 5 molar per second so that
+
+ align:start position:0%
+7.70 * 10- 5 molar per second so that
+ 
+
+ align:start position:0%
+7.70 * 10- 5 molar per second so that
+would be the instantaneous rate again
+
+ align:start position:0%
+would be the instantaneous rate again
+ 
+
+ align:start position:0%
+would be the instantaneous rate again
+the slope of the line tangent to the
+
+ align:start position:0%
+the slope of the line tangent to the
+ 
+
+ align:start position:0%
+the slope of the line tangent to the
+curve at time 150 so you could ask what
+
+ align:start position:0%
+curve at time 150 so you could ask what
+ 
+
+ align:start position:0%
+curve at time 150 so you could ask what
+is the instantaneous rate at 100 seconds
+
+ align:start position:0%
+is the instantaneous rate at 100 seconds
+ 
+
+ align:start position:0%
+is the instantaneous rate at 100 seconds
+or 200 seconds um and get that
+
+ align:start position:0%
+or 200 seconds um and get that
+ 
+
+ align:start position:0%
+or 200 seconds um and get that
+instantaneous rate people are often
+
+ align:start position:0%
+instantaneous rate people are often
+ 
+
+ align:start position:0%
+instantaneous rate people are often
+talking about initial rate and by
+
+ align:start position:0%
+talking about initial rate and by
+ 
+
+ align:start position:0%
+talking about initial rate and by
+initial rate they mean the instantaneous
+
+ align:start position:0%
+initial rate they mean the instantaneous
+ 
+
+ align:start position:0%
+initial rate they mean the instantaneous
+rate at time equals zero so again we
+
+ align:start position:0%
+rate at time equals zero so again we
+ 
+
+ align:start position:0%
+rate at time equals zero so again we
+have two different rates we have average
+
+ align:start position:0%
+have two different rates we have average
+ 
+
+ align:start position:0%
+have two different rates we have average
+rate and instantaneous rate so now let's
+
+ align:start position:0%
+rate and instantaneous rate so now let's
+ 
+
+ align:start position:0%
+rate and instantaneous rate so now let's
+think about rate expressions and then
+
+ align:start position:0%
+think about rate expressions and then
+ 
+
+ align:start position:0%
+think about rate expressions and then
+rate laws all right so keeping with that
+
+ align:start position:0%
+rate laws all right so keeping with that
+ 
+
+ align:start position:0%
+rate laws all right so keeping with that
+same um
+
+ align:start position:0%
+same um
+ 
+
+ align:start position:0%
+same um
+reaction again we could monitor no
+
+ align:start position:0%
+reaction again we could monitor no
+ 
+
+ align:start position:0%
+reaction again we could monitor no
+forming or CO2 forming or we could
+
+ align:start position:0%
+forming or CO2 forming or we could
+ 
+
+ align:start position:0%
+forming or CO2 forming or we could
+monitor either of our reactants
+
+ align:start position:0%
+monitor either of our reactants
+ 
+
+ align:start position:0%
+monitor either of our reactants
+disappearing and if we assume that
+
+ align:start position:0%
+disappearing and if we assume that
+ 
+
+ align:start position:0%
+disappearing and if we assume that
+there's no intermediates or or very slow
+
+ align:start position:0%
+there's no intermediates or or very slow
+ 
+
+ align:start position:0%
+there's no intermediates or or very slow
+steps then we could say that the rate of
+
+ align:start position:0%
+steps then we could say that the rate of
+ 
+
+ align:start position:0%
+steps then we could say that the rate of
+the reaction should be equal to The
+
+ align:start position:0%
+the reaction should be equal to The
+ 
+
+ align:start position:0%
+the reaction should be equal to The
+Disappearance of the concentration of
+
+ align:start position:0%
+Disappearance of the concentration of
+ 
+
+ align:start position:0%
+Disappearance of the concentration of
+NO2 or decrease in NO2 one of our
+
+ align:start position:0%
+NO2 or decrease in NO2 one of our
+ 
+
+ align:start position:0%
+NO2 or decrease in NO2 one of our
+reactants over time it should also be
+
+ align:start position:0%
+reactants over time it should also be
+ 
+
+ align:start position:0%
+reactants over time it should also be
+equal to The Disappearance of Co our
+
+ align:start position:0%
+equal to The Disappearance of Co our
+ 
+
+ align:start position:0%
+equal to The Disappearance of Co our
+other reactant over time and also equal
+
+ align:start position:0%
+other reactant over time and also equal
+ 
+
+ align:start position:0%
+other reactant over time and also equal
+to the appearance of n o with time and
+
+ align:start position:0%
+to the appearance of n o with time and
+ 
+
+ align:start position:0%
+to the appearance of n o with time and
+also equal to the appearance of CO2 with
+
+ align:start position:0%
+also equal to the appearance of CO2 with
+ 
+
+ align:start position:0%
+also equal to the appearance of CO2 with
+time and again for these all to be equal
+
+ align:start position:0%
+time and again for these all to be equal
+ 
+
+ align:start position:0%
+time and again for these all to be equal
+to each other we are assuming here there
+
+ align:start position:0%
+to each other we are assuming here there
+ 
+
+ align:start position:0%
+to each other we are assuming here there
+are no intermediates being formed and or
+
+ align:start position:0%
+are no intermediates being formed and or
+ 
+
+ align:start position:0%
+are no intermediates being formed and or
+that if we are forming them then they're
+
+ align:start position:0%
+that if we are forming them then they're
+ 
+
+ align:start position:0%
+that if we are forming them then they're
+independent of time in other words if
+
+ align:start position:0%
+independent of time in other words if
+ 
+
+ align:start position:0%
+independent of time in other words if
+say there was a large slow step
+
+ align:start position:0%
+say there was a large slow step
+ 
+
+ align:start position:0%
+say there was a large slow step
+somewhere in here we might see all the
+
+ align:start position:0%
+somewhere in here we might see all the
+ 
+
+ align:start position:0%
+somewhere in here we might see all the
+reactants
+
+ align:start position:0%
+reactants
+ 
+
+ align:start position:0%
+reactants
+disappear but there'd be a lag before
+
+ align:start position:0%
+disappear but there'd be a lag before
+ 
+
+ align:start position:0%
+disappear but there'd be a lag before
+the products would appear because more
+
+ align:start position:0%
+the products would appear because more
+ 
+
+ align:start position:0%
+the products would appear because more
+steps and things are going on so these
+
+ align:start position:0%
+steps and things are going on so these
+ 
+
+ align:start position:0%
+steps and things are going on so these
+are all equal to each other if you have
+
+ align:start position:0%
+are all equal to each other if you have
+ 
+
+ align:start position:0%
+are all equal to each other if you have
+no intermediates or the intermediates
+
+ align:start position:0%
+no intermediates or the intermediates
+ 
+
+ align:start position:0%
+no intermediates or the intermediates
+are not affecting the overall
+
+ align:start position:0%
+are not affecting the overall
+ 
+
+ align:start position:0%
+are not affecting the overall
+rate so we could think about this for a
+
+ align:start position:0%
+rate so we could think about this for a
+ 
+
+ align:start position:0%
+rate so we could think about this for a
+generic equation so if we consider a
+
+ align:start position:0%
+generic equation so if we consider a
+ 
+
+ align:start position:0%
+generic equation so if we consider a
+plus b going to C plus d when we're
+
+ align:start position:0%
+plus b going to C plus d when we're
+ 
+
+ align:start position:0%
+plus b going to C plus d when we're
+talking about the rates of disappearance
+
+ align:start position:0%
+talking about the rates of disappearance
+ 
+
+ align:start position:0%
+talking about the rates of disappearance
+or appearance we have to remember the
+
+ align:start position:0%
+or appearance we have to remember the
+ 
+
+ align:start position:0%
+or appearance we have to remember the
+stochiometry of the reaction so if we
+
+ align:start position:0%
+stochiometry of the reaction so if we
+ 
+
+ align:start position:0%
+stochiometry of the reaction so if we
+have a stochiometry of little a then we
+
+ align:start position:0%
+have a stochiometry of little a then we
+ 
+
+ align:start position:0%
+have a stochiometry of little a then we
+would say minus1 over little a a d a DT
+
+ align:start position:0%
+would say minus1 over little a a d a DT
+ 
+
+ align:start position:0%
+would say minus1 over little a a d a DT
+stochiometry of little B for reactant B
+
+ align:start position:0%
+stochiometry of little B for reactant B
+ 
+
+ align:start position:0%
+stochiometry of little B for reactant B
+minus 1 over b b DB
+
+ align:start position:0%
+minus 1 over b b DB
+ 
+
+ align:start position:0%
+minus 1 over b b DB
+DT then formation of products 1 over C
+
+ align:start position:0%
+DT then formation of products 1 over C
+ 
+
+ align:start position:0%
+DT then formation of products 1 over C
+DC DT and our other product one over
+
+ align:start position:0%
+DC DT and our other product one over
+ 
+
+ align:start position:0%
+DC DT and our other product one over
+little d d d DT I got through it okay so
+
+ align:start position:0%
+little d d d DT I got through it okay so
+ 
+
+ align:start position:0%
+little d d d DT I got through it okay so
+let's look at an example reaction and
+
+ align:start position:0%
+let's look at an example reaction and
+ 
+
+ align:start position:0%
+let's look at an example reaction and
+why don't you tell me what the is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to why don't you look at the results
+
+ align:start position:0%
+to why don't you look at the results
+ 
+
+ align:start position:0%
+to why don't you look at the results
+make a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decision okay 10 seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right still haven't gotten much into the
+
+ align:start position:0%
+right still haven't gotten much into the
+ 
+
+ align:start position:0%
+right still haven't gotten much into the
+90s but still I'm happy all right so
+
+ align:start position:0%
+90s but still I'm happy all right so
+ 
+
+ align:start position:0%
+90s but still I'm happy all right so
+here again we're talking about The
+
+ align:start position:0%
+here again we're talking about The
+ 
+
+ align:start position:0%
+here again we're talking about The
+Disappearance of our um reactant so it
+
+ align:start position:0%
+Disappearance of our um reactant so it
+ 
+
+ align:start position:0%
+Disappearance of our um reactant so it
+would be minus one2 and the uh formation
+
+ align:start position:0%
+would be minus one2 and the uh formation
+ 
+
+ align:start position:0%
+would be minus one2 and the uh formation
+of one one of our products and the
+
+ align:start position:0%
+of one one of our products and the
+ 
+
+ align:start position:0%
+of one one of our products and the
+formation of the other product as well
+
+ align:start position:0%
+formation of the other product as well
+ 
+
+ align:start position:0%
+formation of the other product as well
+all right so don't forget about the sto
+
+ align:start position:0%
+all right so don't forget about the sto
+ 
+
+ align:start position:0%
+all right so don't forget about the sto
+geometry of the re action so these are
+
+ align:start position:0%
+geometry of the re action so these are
+ 
+
+ align:start position:0%
+geometry of the re action so these are
+called rate
+
+ align:start position:0%
+called rate
+ 
+
+ align:start position:0%
+called rate
+expressions and you don't want to get
+
+ align:start position:0%
+expressions and you don't want to get
+ 
+
+ align:start position:0%
+expressions and you don't want to get
+that confused with rate laws so a
+
+ align:start position:0%
+that confused with rate laws so a
+ 
+
+ align:start position:0%
+that confused with rate laws so a
+problem might ask write the rate
+
+ align:start position:0%
+problem might ask write the rate
+ 
+
+ align:start position:0%
+problem might ask write the rate
+expression this is what it's looking for
+
+ align:start position:0%
+expression this is what it's looking for
+ 
+
+ align:start position:0%
+expression this is what it's looking for
+if it says write the rate law it's going
+
+ align:start position:0%
+if it says write the rate law it's going
+ 
+
+ align:start position:0%
+if it says write the rate law it's going
+to be looking for the following thing so
+
+ align:start position:0%
+to be looking for the following thing so
+ 
+
+ align:start position:0%
+to be looking for the following thing so
+a rate law is a relationship between
+
+ align:start position:0%
+a rate law is a relationship between
+ 
+
+ align:start position:0%
+a rate law is a relationship between
+rate and
+
+ align:start position:0%
+rate and
+ 
+
+ align:start position:0%
+rate and
+concentration and they are related by a
+
+ align:start position:0%
+concentration and they are related by a
+ 
+
+ align:start position:0%
+concentration and they are related by a
+proportionality constant little K which
+
+ align:start position:0%
+proportionality constant little K which
+ 
+
+ align:start position:0%
+proportionality constant little K which
+is called the rate constant so big K is
+
+ align:start position:0%
+is called the rate constant so big K is
+ 
+
+ align:start position:0%
+is called the rate constant so big K is
+what equilibrium constant little K is a
+
+ align:start position:0%
+what equilibrium constant little K is a
+ 
+
+ align:start position:0%
+what equilibrium constant little K is a
+rate constant all right so let's look at
+
+ align:start position:0%
+rate constant all right so let's look at
+ 
+
+ align:start position:0%
+rate constant all right so let's look at
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+reaction and so reaction of a plus b c
+
+ align:start position:0%
+reaction and so reaction of a plus b c
+ 
+
+ align:start position:0%
+reaction and so reaction of a plus b c
+going to C plus d the rate law could be
+
+ align:start position:0%
+going to C plus d the rate law could be
+ 
+
+ align:start position:0%
+going to C plus d the rate law could be
+expressed rate equals rate constant K
+
+ align:start position:0%
+expressed rate equals rate constant K
+ 
+
+ align:start position:0%
+expressed rate equals rate constant K
+times the concentration of a to the m
+
+ align:start position:0%
+times the concentration of a to the m
+ 
+
+ align:start position:0%
+times the concentration of a to the m
+and B to the N where M and N are the
+
+ align:start position:0%
+and B to the N where M and N are the
+ 
+
+ align:start position:0%
+and B to the N where M and N are the
+order of the reaction in a and b
+
+ align:start position:0%
+order of the reaction in a and b
+ 
+
+ align:start position:0%
+order of the reaction in a and b
+respectively and K again is our rate
+
+ align:start position:0%
+respectively and K again is our rate
+ 
+
+ align:start position:0%
+respectively and K again is our rate
+constant all right so let's look at what
+
+ align:start position:0%
+constant all right so let's look at what
+ 
+
+ align:start position:0%
+constant all right so let's look at what
+I call the truth about rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+laws so the first thing you cannot just
+
+ align:start position:0%
+laws so the first thing you cannot just
+ 
+
+ align:start position:0%
+laws so the first thing you cannot just
+look at the stochiometry of the equation
+
+ align:start position:0%
+look at the stochiometry of the equation
+ 
+
+ align:start position:0%
+look at the stochiometry of the equation
+and say oh it's going to have this M for
+
+ align:start position:0%
+and say oh it's going to have this M for
+ 
+
+ align:start position:0%
+and say oh it's going to have this M for
+a based on its Doom omry unless it's
+
+ align:start position:0%
+a based on its Doom omry unless it's
+ 
+
+ align:start position:0%
+a based on its Doom omry unless it's
+what's called an elementary reaction and
+
+ align:start position:0%
+what's called an elementary reaction and
+ 
+
+ align:start position:0%
+what's called an elementary reaction and
+we're going to get to that on Wednesday
+
+ align:start position:0%
+we're going to get to that on Wednesday
+ 
+
+ align:start position:0%
+we're going to get to that on Wednesday
+after Thanksgiving make sure you come
+
+ align:start position:0%
+after Thanksgiving make sure you come
+ 
+
+ align:start position:0%
+after Thanksgiving make sure you come
+Wednesday after Thanksgiving that's the
+
+ align:start position:0%
+Wednesday after Thanksgiving that's the
+ 
+
+ align:start position:0%
+Wednesday after Thanksgiving that's the
+lecture on mechanism that's a really
+
+ align:start position:0%
+lecture on mechanism that's a really
+ 
+
+ align:start position:0%
+lecture on mechanism that's a really
+important lecture in kinetics so we'll
+
+ align:start position:0%
+important lecture in kinetics so we'll
+ 
+
+ align:start position:0%
+important lecture in kinetics so we'll
+learn about elementary reactions so you
+
+ align:start position:0%
+learn about elementary reactions so you
+ 
+
+ align:start position:0%
+learn about elementary reactions so you
+can't just look at the stochiometry and
+
+ align:start position:0%
+can't just look at the stochiometry and
+ 
+
+ align:start position:0%
+can't just look at the stochiometry and
+write the rate law you need
+
+ align:start position:0%
+write the rate law you need
+ 
+
+ align:start position:0%
+write the rate law you need
+experiment so the rate law is not just
+
+ align:start position:0%
+experiment so the rate law is not just
+ 
+
+ align:start position:0%
+experiment so the rate law is not just
+limited to reactants although largely um
+
+ align:start position:0%
+limited to reactants although largely um
+ 
+
+ align:start position:0%
+limited to reactants although largely um
+it's true that the rate laws will just
+
+ align:start position:0%
+it's true that the rate laws will just
+ 
+
+ align:start position:0%
+it's true that the rate laws will just
+have reactants it can also have a
+
+ align:start position:0%
+have reactants it can also have a
+ 
+
+ align:start position:0%
+have reactants it can also have a
+product term like C could appear in the
+
+ align:start position:0%
+product term like C could appear in the
+ 
+
+ align:start position:0%
+product term like C could appear in the
+rate law how would you know this well it
+
+ align:start position:0%
+rate law how would you know this well it
+ 
+
+ align:start position:0%
+rate law how would you know this well it
+would be experiment would tell you
+
+ align:start position:0%
+would be experiment would tell you
+ 
+
+ align:start position:0%
+would be experiment would tell you
+whether this was true or
+
+ align:start position:0%
+whether this was true or
+ 
+
+ align:start position:0%
+whether this was true or
+not so for this rate law we saw this
+
+ align:start position:0%
+not so for this rate law we saw this
+ 
+
+ align:start position:0%
+not so for this rate law we saw this
+already um the order of the reaction in
+
+ align:start position:0%
+already um the order of the reaction in
+ 
+
+ align:start position:0%
+already um the order of the reaction in
+a is
+
+ align:start position:0%
+a is
+ 
+
+ align:start position:0%
+a is
+um is M and the Order of the reaction in
+
+ align:start position:0%
+um is M and the Order of the reaction in
+ 
+
+ align:start position:0%
+um is M and the Order of the reaction in
+B is n and M and N can be integers they
+
+ align:start position:0%
+B is n and M and N can be integers they
+ 
+
+ align:start position:0%
+B is n and M and N can be integers they
+can be frac fractions or they can be
+
+ align:start position:0%
+can be frac fractions or they can be
+ 
+
+ align:start position:0%
+can be frac fractions or they can be
+positive and they can be
+
+ align:start position:0%
+positive and they can be
+ 
+
+ align:start position:0%
+positive and they can be
+negative so now we're going to think
+
+ align:start position:0%
+negative so now we're going to think
+ 
+
+ align:start position:0%
+negative so now we're going to think
+about all these different um orders of
+
+ align:start position:0%
+about all these different um orders of
+ 
+
+ align:start position:0%
+about all these different um orders of
+reaction and think about what and we'll
+
+ align:start position:0%
+reaction and think about what and we'll
+ 
+
+ align:start position:0%
+reaction and think about what and we'll
+do it just for a what m is equal to so
+
+ align:start position:0%
+do it just for a what m is equal to so
+ 
+
+ align:start position:0%
+do it just for a what m is equal to so
+we're going to fill in this table here
+
+ align:start position:0%
+we're going to fill in this table here
+ 
+
+ align:start position:0%
+we're going to fill in this table here
+and some of these things are in your
+
+ align:start position:0%
+and some of these things are in your
+ 
+
+ align:start position:0%
+and some of these things are in your
+notes some of them you need to fill in
+
+ align:start position:0%
+notes some of them you need to fill in
+ 
+
+ align:start position:0%
+notes some of them you need to fill in
+so we're going to start with m equals
+
+ align:start position:0%
+so we're going to start with m equals
+ 
+
+ align:start position:0%
+so we're going to start with m equals
+1 and this is called a firstorder
+
+ align:start position:0%
+1 and this is called a firstorder
+ 
+
+ align:start position:0%
+1 and this is called a firstorder
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+the rate law for this the rate would
+
+ align:start position:0%
+the rate law for this the rate would
+ 
+
+ align:start position:0%
+the rate law for this the rate would
+equal the rate constant times the
+
+ align:start position:0%
+equal the rate constant times the
+ 
+
+ align:start position:0%
+equal the rate constant times the
+concentration of a and now let's just
+
+ align:start position:0%
+concentration of a and now let's just
+ 
+
+ align:start position:0%
+concentration of a and now let's just
+think if this is a first order reaction
+
+ align:start position:0%
+think if this is a first order reaction
+ 
+
+ align:start position:0%
+think if this is a first order reaction
+that just depends on a if you double the
+
+ align:start position:0%
+that just depends on a if you double the
+ 
+
+ align:start position:0%
+that just depends on a if you double the
+concentration of a what do you expect
+
+ align:start position:0%
+concentration of a what do you expect
+ 
+
+ align:start position:0%
+concentration of a what do you expect
+will happen to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+what it will double right so in first
+
+ align:start position:0%
+what it will double right so in first
+ 
+
+ align:start position:0%
+what it will double right so in first
+order reaction you double the
+
+ align:start position:0%
+order reaction you double the
+ 
+
+ align:start position:0%
+order reaction you double the
+concentration of something and the rate
+
+ align:start position:0%
+concentration of something and the rate
+ 
+
+ align:start position:0%
+concentration of something and the rate
+will double and this is how you figure
+
+ align:start position:0%
+will double and this is how you figure
+ 
+
+ align:start position:0%
+will double and this is how you figure
+out what the order of the reaction is
+
+ align:start position:0%
+out what the order of the reaction is
+ 
+
+ align:start position:0%
+out what the order of the reaction is
+you double the concentration of
+
+ align:start position:0%
+you double the concentration of
+ 
+
+ align:start position:0%
+you double the concentration of
+something leaving everything else the
+
+ align:start position:0%
+something leaving everything else the
+ 
+
+ align:start position:0%
+something leaving everything else the
+same and see the effect on rate so again
+
+ align:start position:0%
+same and see the effect on rate so again
+ 
+
+ align:start position:0%
+same and see the effect on rate so again
+these are experimentally determined now
+
+ align:start position:0%
+these are experimentally determined now
+ 
+
+ align:start position:0%
+these are experimentally determined now
+let's consider m equal 2 and notice uh
+
+ align:start position:0%
+let's consider m equal 2 and notice uh
+ 
+
+ align:start position:0%
+let's consider m equal 2 and notice uh
+the blue went away here um and so but
+
+ align:start position:0%
+the blue went away here um and so but
+ 
+
+ align:start position:0%
+the blue went away here um and so but
+it's still there so you can see it all
+
+ align:start position:0%
+it's still there so you can see it all
+ 
+
+ align:start position:0%
+it's still there so you can see it all
+right second order what does the rate
+
+ align:start position:0%
+right second order what does the rate
+ 
+
+ align:start position:0%
+right second order what does the rate
+equal so it would equal K our rate
+
+ align:start position:0%
+equal so it would equal K our rate
+ 
+
+ align:start position:0%
+equal so it would equal K our rate
+constant times the concentration of a
+
+ align:start position:0%
+constant times the concentration of a
+ 
+
+ align:start position:0%
+constant times the concentration of a
+and now we have a two so it's raised to
+
+ align:start position:0%
+and now we have a two so it's raised to
+ 
+
+ align:start position:0%
+and now we have a two so it's raised to
+the power of M and that's two so that's
+
+ align:start position:0%
+the power of M and that's two so that's
+ 
+
+ align:start position:0%
+the power of M and that's two so that's
+how we would write the rate law for
+
+ align:start position:0%
+how we would write the rate law for
+ 
+
+ align:start position:0%
+how we would write the rate law for
+something that was second order in a so
+
+ align:start position:0%
+something that was second order in a so
+ 
+
+ align:start position:0%
+something that was second order in a so
+now let's think about if you double the
+
+ align:start position:0%
+now let's think about if you double the
+ 
+
+ align:start position:0%
+now let's think about if you double the
+concentration of a what would you ex
+
+ align:start position:0%
+concentration of a what would you ex
+ 
+
+ align:start position:0%
+concentration of a what would you ex
+observe for the con the rate what would
+
+ align:start position:0%
+observe for the con the rate what would
+ 
+
+ align:start position:0%
+observe for the con the rate what would
+happen it would quadruple
+
+ align:start position:0%
+happen it would quadruple
+ 
+
+ align:start position:0%
+happen it would quadruple
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+now what about if it triples why don't
+
+ align:start position:0%
+now what about if it triples why don't
+ 
+
+ align:start position:0%
+now what about if it triples why don't
+you tell me what would happen then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right 10 seconds very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fast 90% yes
+
+ align:start position:0%
+fast 90% yes
+ 
+
+ align:start position:0%
+fast 90% yes
+okay so yes nine
+
+ align:start position:0%
+okay so yes nine
+ 
+
+ align:start position:0%
+okay so yes nine
+times all right and in problem set nine
+
+ align:start position:0%
+times all right and in problem set nine
+ 
+
+ align:start position:0%
+times all right and in problem set nine
+which is already posted um there's all
+
+ align:start position:0%
+which is already posted um there's all
+ 
+
+ align:start position:0%
+which is already posted um there's all
+sorts of problems where you see the
+
+ align:start position:0%
+sorts of problems where you see the
+ 
+
+ align:start position:0%
+sorts of problems where you see the
+effects and you can figure out what the
+
+ align:start position:0%
+effects and you can figure out what the
+ 
+
+ align:start position:0%
+effects and you can figure out what the
+order of the reaction is all right so
+
+ align:start position:0%
+order of the reaction is all right so
+ 
+
+ align:start position:0%
+order of the reaction is all right so
+now let's consider minus1 over here
+
+ align:start position:0%
+now let's consider minus1 over here
+ 
+
+ align:start position:0%
+now let's consider minus1 over here
+which is often not referred to by any
+
+ align:start position:0%
+which is often not referred to by any
+ 
+
+ align:start position:0%
+which is often not referred to by any
+name um the rate here would be equal to
+
+ align:start position:0%
+name um the rate here would be equal to
+ 
+
+ align:start position:0%
+name um the rate here would be equal to
+K concentration of a to the minus
+
+ align:start position:0%
+K concentration of a to the minus
+ 
+
+ align:start position:0%
+K concentration of a to the minus
+one and if we double the concentration
+
+ align:start position:0%
+one and if we double the concentration
+ 
+
+ align:start position:0%
+one and if we double the concentration
+of this you can just yell out what would
+
+ align:start position:0%
+of this you can just yell out what would
+ 
+
+ align:start position:0%
+of this you can just yell out what would
+happen to the rate half
+
+ align:start position:0%
+happen to the rate half
+ 
+
+ align:start position:0%
+happen to the rate half
+yes all right now to m equal minus a
+
+ align:start position:0%
+yes all right now to m equal minus a
+ 
+
+ align:start position:0%
+yes all right now to m equal minus a
+half so the rate here would be k equals
+
+ align:start position:0%
+half so the rate here would be k equals
+ 
+
+ align:start position:0%
+half so the rate here would be k equals
+concentration of a raised to the minus
+
+ align:start position:0%
+concentration of a raised to the minus
+ 
+
+ align:start position:0%
+concentration of a raised to the minus
+one2 and now if we double that's um our
+
+ align:start position:0%
+one2 and now if we double that's um our
+ 
+
+ align:start position:0%
+one2 and now if we double that's um our
+last clicker question on this um sheet
+
+ align:start position:0%
+last clicker question on this um sheet
+ 
+
+ align:start position:0%
+last clicker question on this um sheet
+so why don't you tell me what happens
+
+ align:start position:0%
+so why don't you tell me what happens
+ 
+
+ align:start position:0%
+so why don't you tell me what happens
+and this should be fast too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right so going back um over here right
+
+ align:start position:0%
+right so going back um over here right
+ 
+
+ align:start position:0%
+right so going back um over here right
+we have Point uh 7even times which is 2
+
+ align:start position:0%
+we have Point uh 7even times which is 2
+ 
+
+ align:start position:0%
+we have Point uh 7even times which is 2
+to the minus
+
+ align:start position:0%
+to the minus
+ 
+
+ align:start position:0%
+to the minus
+one2 and when you're looking at the
+
+ align:start position:0%
+one2 and when you're looking at the
+ 
+
+ align:start position:0%
+one2 and when you're looking at the
+effects of the rate on concentration
+
+ align:start position:0%
+effects of the rate on concentration
+ 
+
+ align:start position:0%
+effects of the rate on concentration
+you'll see the concentration double and
+
+ align:start position:0%
+you'll see the concentration double and
+ 
+
+ align:start position:0%
+you'll see the concentration double and
+you're like what on Earth happened to
+
+ align:start position:0%
+you're like what on Earth happened to
+ 
+
+ align:start position:0%
+you're like what on Earth happened to
+the rate keep in mind this minus a half
+
+ align:start position:0%
+the rate keep in mind this minus a half
+ 
+
+ align:start position:0%
+the rate keep in mind this minus a half
+um because it's very hard to think about
+
+ align:start position:0%
+um because it's very hard to think about
+ 
+
+ align:start position:0%
+um because it's very hard to think about
+what the relationship is so again they
+
+ align:start position:0%
+what the relationship is so again they
+ 
+
+ align:start position:0%
+what the relationship is so again they
+can be fractions positive or
+
+ align:start position:0%
+can be fractions positive or
+ 
+
+ align:start position:0%
+can be fractions positive or
+negative all right so back up here now
+
+ align:start position:0%
+negative all right so back up here now
+ 
+
+ align:start position:0%
+negative all right so back up here now
+this actually is called half order um so
+
+ align:start position:0%
+this actually is called half order um so
+ 
+
+ align:start position:0%
+this actually is called half order um so
+we would have a rate that is equal to K
+
+ align:start position:0%
+we would have a rate that is equal to K
+ 
+
+ align:start position:0%
+we would have a rate that is equal to K
+times the concentration of a raised to
+
+ align:start position:0%
+times the concentration of a raised to
+ 
+
+ align:start position:0%
+times the concentration of a raised to
+the half and if we double that you can
+
+ align:start position:0%
+the half and if we double that you can
+ 
+
+ align:start position:0%
+the half and if we double that you can
+just yell out what would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen so 1.4 times the
+
+ align:start position:0%
+happen so 1.4 times the
+ 
+
+ align:start position:0%
+happen so 1.4 times the
+rate and
+
+ align:start position:0%
+rate and
+ 
+
+ align:start position:0%
+rate and
+finally m equals z what do you think uh
+
+ align:start position:0%
+finally m equals z what do you think uh
+ 
+
+ align:start position:0%
+finally m equals z what do you think uh
+that is likely to be
+
+ align:start position:0%
+that is likely to be
+ 
+
+ align:start position:0%
+that is likely to be
+called that is zero order so at least uh
+
+ align:start position:0%
+called that is zero order so at least uh
+ 
+
+ align:start position:0%
+called that is zero order so at least uh
+some things uh are pretty easy to uh to
+
+ align:start position:0%
+some things uh are pretty easy to uh to
+ 
+
+ align:start position:0%
+some things uh are pretty easy to uh to
+guess and if we think about the rate
+
+ align:start position:0%
+guess and if we think about the rate
+ 
+
+ align:start position:0%
+guess and if we think about the rate
+what would the rate be equal
+
+ align:start position:0%
+what would the rate be equal
+ 
+
+ align:start position:0%
+what would the rate be equal
+to just K right it's just going to be
+
+ align:start position:0%
+to just K right it's just going to be
+ 
+
+ align:start position:0%
+to just K right it's just going to be
+equal to K so it doesn't zero
+
+ align:start position:0%
+equal to K so it doesn't zero
+ 
+
+ align:start position:0%
+equal to K so it doesn't zero
+order the a term is not there so if we
+
+ align:start position:0%
+order the a term is not there so if we
+ 
+
+ align:start position:0%
+order the a term is not there so if we
+double the concentration of something
+
+ align:start position:0%
+double the concentration of something
+ 
+
+ align:start position:0%
+double the concentration of something
+that is zero order what happens to the
+
+ align:start position:0%
+that is zero order what happens to the
+ 
+
+ align:start position:0%
+that is zero order what happens to the
+rate nothing right no effect on rate the
+
+ align:start position:0%
+rate nothing right no effect on rate the
+ 
+
+ align:start position:0%
+rate nothing right no effect on rate the
+concentration term isn't part of the
+
+ align:start position:0%
+concentration term isn't part of the
+ 
+
+ align:start position:0%
+concentration term isn't part of the
+equation so the problem set nine will
+
+ align:start position:0%
+equation so the problem set nine will
+ 
+
+ align:start position:0%
+equation so the problem set nine will
+have a lot of experiments and you need
+
+ align:start position:0%
+have a lot of experiments and you need
+ 
+
+ align:start position:0%
+have a lot of experiments and you need
+to figure out by looking at what is
+
+ align:start position:0%
+to figure out by looking at what is
+ 
+
+ align:start position:0%
+to figure out by looking at what is
+happening um what the order of the
+
+ align:start position:0%
+happening um what the order of the
+ 
+
+ align:start position:0%
+happening um what the order of the
+reaction is is it doubling when you
+
+ align:start position:0%
+reaction is is it doubling when you
+ 
+
+ align:start position:0%
+reaction is is it doubling when you
+double the rate is it quadrupling is it
+
+ align:start position:0%
+double the rate is it quadrupling is it
+ 
+
+ align:start position:0%
+double the rate is it quadrupling is it
+doing some weird thing that seems to be
+
+ align:start position:0%
+doing some weird thing that seems to be
+ 
+
+ align:start position:0%
+doing some weird thing that seems to be
+a negative fra an inverse fraction um
+
+ align:start position:0%
+a negative fra an inverse fraction um
+ 
+
+ align:start position:0%
+a negative fra an inverse fraction um
+and that will allow you to figure figure
+
+ align:start position:0%
+and that will allow you to figure figure
+ 
+
+ align:start position:0%
+and that will allow you to figure figure
+out what the order is okay so once you
+
+ align:start position:0%
+out what the order is okay so once you
+ 
+
+ align:start position:0%
+out what the order is okay so once you
+figure out the order of the
+
+ align:start position:0%
+figure out the order of the
+ 
+
+ align:start position:0%
+figure out the order of the
+reaction then the next truth about rate
+
+ align:start position:0%
+reaction then the next truth about rate
+ 
+
+ align:start position:0%
+reaction then the next truth about rate
+laws is that the overall order of the
+
+ align:start position:0%
+laws is that the overall order of the
+ 
+
+ align:start position:0%
+laws is that the overall order of the
+reaction is just the sum of the
+
+ align:start position:0%
+reaction is just the sum of the
+ 
+
+ align:start position:0%
+reaction is just the sum of the
+exponents in the rate law so for example
+
+ align:start position:0%
+exponents in the rate law so for example
+ 
+
+ align:start position:0%
+exponents in the rate law so for example
+if we had this
+
+ align:start position:0%
+if we had this
+ 
+
+ align:start position:0%
+if we had this
+reaction what would be the overall order
+
+ align:start position:0%
+reaction what would be the overall order
+ 
+
+ align:start position:0%
+reaction what would be the overall order
+you can just yell it
+
+ align:start position:0%
+you can just yell it
+ 
+
+ align:start position:0%
+you can just yell it
+out yep it would be a third order the
+
+ align:start position:0%
+out yep it would be a third order the
+ 
+
+ align:start position:0%
+out yep it would be a third order the
+order would be three now you don't some
+
+ align:start position:0%
+order would be three now you don't some
+ 
+
+ align:start position:0%
+order would be three now you don't some
+people get this wrong on a test it's
+
+ align:start position:0%
+people get this wrong on a test it's
+ 
+
+ align:start position:0%
+people get this wrong on a test it's
+like no you want to save your points for
+
+ align:start position:0%
+like no you want to save your points for
+ 
+
+ align:start position:0%
+like no you want to save your points for
+something that's hard 2 + 1 is three so
+
+ align:start position:0%
+something that's hard 2 + 1 is three so
+ 
+
+ align:start position:0%
+something that's hard 2 + 1 is three so
+remember that okay and this would be
+
+ align:start position:0%
+remember that okay and this would be
+ 
+
+ align:start position:0%
+remember that okay and this would be
+then second order in a you would say
+
+ align:start position:0%
+then second order in a you would say
+ 
+
+ align:start position:0%
+then second order in a you would say
+that's first order in B overall third
+
+ align:start position:0%
+that's first order in B overall third
+ 
+
+ align:start position:0%
+that's first order in B overall third
+order so if you're going to lose points
+
+ align:start position:0%
+order so if you're going to lose points
+ 
+
+ align:start position:0%
+order so if you're going to lose points
+on an exam on this
+
+ align:start position:0%
+on an exam on this
+ 
+
+ align:start position:0%
+on an exam on this
+material I recommend losing them
+
+ align:start position:0%
+material I recommend losing them
+ 
+
+ align:start position:0%
+material I recommend losing them
+determining the UNS for the rate
+
+ align:start position:0%
+determining the UNS for the rate
+ 
+
+ align:start position:0%
+determining the UNS for the rate
+constant because that's much more
+
+ align:start position:0%
+constant because that's much more
+ 
+
+ align:start position:0%
+constant because that's much more
+complicated than figuring out the
+
+ align:start position:0%
+complicated than figuring out the
+ 
+
+ align:start position:0%
+complicated than figuring out the
+overall order of the reaction the
+
+ align:start position:0%
+overall order of the reaction the
+ 
+
+ align:start position:0%
+overall order of the reaction the
+units it depends on the order you can
+
+ align:start position:0%
+units it depends on the order you can
+ 
+
+ align:start position:0%
+units it depends on the order you can
+have squared you can have molar squared
+
+ align:start position:0%
+have squared you can have molar squared
+ 
+
+ align:start position:0%
+have squared you can have molar squared
+quadrupled molar to the minus fractions
+
+ align:start position:0%
+quadrupled molar to the minus fractions
+ 
+
+ align:start position:0%
+quadrupled molar to the minus fractions
+all sorts of crazy things happen in your
+
+ align:start position:0%
+all sorts of crazy things happen in your
+ 
+
+ align:start position:0%
+all sorts of crazy things happen in your
+units of Ray constants so save your
+
+ align:start position:0%
+units of Ray constants so save your
+ 
+
+ align:start position:0%
+units of Ray constants so save your
+points if you're going to lose some and
+
+ align:start position:0%
+points if you're going to lose some and
+ 
+
+ align:start position:0%
+points if you're going to lose some and
+I I think it would be great if you got
+
+ align:start position:0%
+I I think it would be great if you got
+ 
+
+ align:start position:0%
+I I think it would be great if you got
+aund everyone got 100 but if you're
+
+ align:start position:0%
+aund everyone got 100 but if you're
+ 
+
+ align:start position:0%
+aund everyone got 100 but if you're
+going to lose some lose them on that
+
+ align:start position:0%
+going to lose some lose them on that
+ 
+
+ align:start position:0%
+going to lose some lose them on that
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+harder Okay so so we'll end there for
+
+ align:start position:0%
+harder Okay so so we'll end there for
+ 
+
+ align:start position:0%
+harder Okay so so we'll end there for
+today and Wednesday we're going to be
+
+ align:start position:0%
+today and Wednesday we're going to be
+ 
+
+ align:start position:0%
+today and Wednesday we're going to be
+talking about um integrated rate laws
+
+ align:start position:0%
+talking about um integrated rate laws
+ 
+
+ align:start position:0%
+talking about um integrated rate laws
+half half life for first order nuclear
+
+ align:start position:0%
+half half life for first order nuclear
+ 
+
+ align:start position:0%
+half half life for first order nuclear
+chemistry it's going to be very exciting
+
+ align:start position:0%
+chemistry it's going to be very exciting
+ 
+
+ align:start position:0%
+chemistry it's going to be very exciting
+and slightly
+
+ align:start position:0%
+and slightly
+ 
+
+ align:start position:0%
+and slightly
+radioactive so where were we we were
+
+ align:start position:0%
+radioactive so where were we we were
+ 
+
+ align:start position:0%
+radioactive so where were we we were
+talking about the fact uh about how you
+
+ align:start position:0%
+talking about the fact uh about how you
+ 
+
+ align:start position:0%
+talking about the fact uh about how you
+measure instantaneous rates and average
+
+ align:start position:0%
+measure instantaneous rates and average
+ 
+
+ align:start position:0%
+measure instantaneous rates and average
+rates and and one of the uh the issues
+
+ align:start position:0%
+rates and and one of the uh the issues
+ 
+
+ align:start position:0%
+rates and and one of the uh the issues
+of doing itics experiments it's all
+
+ align:start position:0%
+of doing itics experiments it's all
+ 
+
+ align:start position:0%
+of doing itics experiments it's all
+experimental you want to measure things
+
+ align:start position:0%
+experimental you want to measure things
+ 
+
+ align:start position:0%
+experimental you want to measure things
+but it can be very challenging to
+
+ align:start position:0%
+but it can be very challenging to
+ 
+
+ align:start position:0%
+but it can be very challenging to
+measure initial rates because you're
+
+ align:start position:0%
+measure initial rates because you're
+ 
+
+ align:start position:0%
+measure initial rates because you're
+often talking about a very small change
+
+ align:start position:0%
+often talking about a very small change
+ 
+
+ align:start position:0%
+often talking about a very small change
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+concentration and so um it can be
+
+ align:start position:0%
+concentration and so um it can be
+ 
+
+ align:start position:0%
+concentration and so um it can be
+helpful sometimes um to use integrated
+
+ align:start position:0%
+helpful sometimes um to use integrated
+ 
+
+ align:start position:0%
+helpful sometimes um to use integrated
+rate laws which allow you to measure um
+
+ align:start position:0%
+rate laws which allow you to measure um
+ 
+
+ align:start position:0%
+rate laws which allow you to measure um
+a lot of different concentrations as
+
+ align:start position:0%
+a lot of different concentrations as
+ 
+
+ align:start position:0%
+a lot of different concentrations as
+times elapses and uh plot that data to
+
+ align:start position:0%
+times elapses and uh plot that data to
+ 
+
+ align:start position:0%
+times elapses and uh plot that data to
+to uh get out rate constants and things
+
+ align:start position:0%
+to uh get out rate constants and things
+ 
+
+ align:start position:0%
+to uh get out rate constants and things
+like that so we're going to talk about
+
+ align:start position:0%
+like that so we're going to talk about
+ 
+
+ align:start position:0%
+like that so we're going to talk about
+integrated rate
+
+ align:start position:0%
+integrated rate
+ 
+
+ align:start position:0%
+integrated rate
+laws and so this is uh the alternative
+
+ align:start position:0%
+laws and so this is uh the alternative
+ 
+
+ align:start position:0%
+laws and so this is uh the alternative
+then is to use this um integrated rate
+
+ align:start position:0%
+then is to use this um integrated rate
+ 
+
+ align:start position:0%
+then is to use this um integrated rate
+law again expresses concentrations
+
+ align:start position:0%
+law again expresses concentrations
+ 
+
+ align:start position:0%
+law again expresses concentrations
+directly as a function of time and gets
+
+ align:start position:0%
+directly as a function of time and gets
+ 
+
+ align:start position:0%
+directly as a function of time and gets
+at this small change changes problem all
+
+ align:start position:0%
+at this small change changes problem all
+ 
+
+ align:start position:0%
+at this small change changes problem all
+right so we're going to talk about first
+
+ align:start position:0%
+right so we're going to talk about first
+ 
+
+ align:start position:0%
+right so we're going to talk about first
+order now and then we'll talk about
+
+ align:start position:0%
+order now and then we'll talk about
+ 
+
+ align:start position:0%
+order now and then we'll talk about
+second order in a little bit so for a
+
+ align:start position:0%
+second order in a little bit so for a
+ 
+
+ align:start position:0%
+second order in a little bit so for a
+first order equation we have a going to
+
+ align:start position:0%
+first order equation we have a going to
+ 
+
+ align:start position:0%
+first order equation we have a going to
+B and we learned last time that we can
+
+ align:start position:0%
+B and we learned last time that we can
+ 
+
+ align:start position:0%
+B and we learned last time that we can
+write a rate
+
+ align:start position:0%
+write a rate
+ 
+
+ align:start position:0%
+write a rate
+expression for a first order process or
+
+ align:start position:0%
+expression for a first order process or
+ 
+
+ align:start position:0%
+expression for a first order process or
+for this process here so we could talk
+
+ align:start position:0%
+for this process here so we could talk
+ 
+
+ align:start position:0%
+for this process here so we could talk
+about the rate expression as The
+
+ align:start position:0%
+about the rate expression as The
+ 
+
+ align:start position:0%
+about the rate expression as The
+Disappearance of a minus D um
+
+ align:start position:0%
+Disappearance of a minus D um
+ 
+
+ align:start position:0%
+Disappearance of a minus D um
+concentration of a DT we can also write
+
+ align:start position:0%
+concentration of a DT we can also write
+ 
+
+ align:start position:0%
+concentration of a DT we can also write
+the rate law for a first order equation
+
+ align:start position:0%
+the rate law for a first order equation
+ 
+
+ align:start position:0%
+the rate law for a first order equation
+and that would be K our rate constant
+
+ align:start position:0%
+and that would be K our rate constant
+ 
+
+ align:start position:0%
+and that would be K our rate constant
+times our concentration so the rate
+
+ align:start position:0%
+times our concentration so the rate
+ 
+
+ align:start position:0%
+times our concentration so the rate
+expression has the DDT and the rate law
+
+ align:start position:0%
+expression has the DDT and the rate law
+ 
+
+ align:start position:0%
+expression has the DDT and the rate law
+has K our rate constant in it all right
+
+ align:start position:0%
+has K our rate constant in it all right
+ 
+
+ align:start position:0%
+has K our rate constant in it all right
+so using these two things that we
+
+ align:start position:0%
+so using these two things that we
+ 
+
+ align:start position:0%
+so using these two things that we
+learned last time we can do a derivation
+
+ align:start position:0%
+learned last time we can do a derivation
+ 
+
+ align:start position:0%
+learned last time we can do a derivation
+to get our integrated first order rate
+
+ align:start position:0%
+to get our integrated first order rate
+ 
+
+ align:start position:0%
+to get our integrated first order rate
+law so in this derivation we're going to
+
+ align:start position:0%
+law so in this derivation we're going to
+ 
+
+ align:start position:0%
+law so in this derivation we're going to
+separate our concentration terms on one
+
+ align:start position:0%
+separate our concentration terms on one
+ 
+
+ align:start position:0%
+separate our concentration terms on one
+side and our time terms on the other
+
+ align:start position:0%
+side and our time terms on the other
+ 
+
+ align:start position:0%
+side and our time terms on the other
+side so we're going to bring over our uh
+
+ align:start position:0%
+side so we're going to bring over our uh
+ 
+
+ align:start position:0%
+side so we're going to bring over our uh
+concentration of a over here so we'll
+
+ align:start position:0%
+concentration of a over here so we'll
+ 
+
+ align:start position:0%
+concentration of a over here so we'll
+divide by the concentration of a
+
+ align:start position:0%
+divide by the concentration of a
+ 
+
+ align:start position:0%
+divide by the concentration of a
+we have our D concentration of a term
+
+ align:start position:0%
+we have our D concentration of a term
+ 
+
+ align:start position:0%
+we have our D concentration of a term
+from here we're going to take our minus
+
+ align:start position:0%
+from here we're going to take our minus
+ 
+
+ align:start position:0%
+from here we're going to take our minus
+side put it on the other side and we're
+
+ align:start position:0%
+side put it on the other side and we're
+ 
+
+ align:start position:0%
+side put it on the other side and we're
+going to take our DT our time term and
+
+ align:start position:0%
+going to take our DT our time term and
+ 
+
+ align:start position:0%
+going to take our DT our time term and
+put it over there as well with our rate
+
+ align:start position:0%
+put it over there as well with our rate
+ 
+
+ align:start position:0%
+put it over there as well with our rate
+constant so we have the terms that have
+
+ align:start position:0%
+constant so we have the terms that have
+ 
+
+ align:start position:0%
+constant so we have the terms that have
+concentration of a on one side and we
+
+ align:start position:0%
+concentration of a on one side and we
+ 
+
+ align:start position:0%
+concentration of a on one side and we
+have our terms with rate constant and
+
+ align:start position:0%
+have our terms with rate constant and
+ 
+
+ align:start position:0%
+have our terms with rate constant and
+time on the other now we can integrate
+
+ align:start position:0%
+time on the other now we can integrate
+ 
+
+ align:start position:0%
+time on the other now we can integrate
+both sides and we will integrate from
+
+ align:start position:0%
+both sides and we will integrate from
+ 
+
+ align:start position:0%
+both sides and we will integrate from
+our original concentration of a so
+
+ align:start position:0%
+our original concentration of a so
+ 
+
+ align:start position:0%
+our original concentration of a so
+that's a to the O for for our original
+
+ align:start position:0%
+that's a to the O for for our original
+ 
+
+ align:start position:0%
+that's a to the O for for our original
+concentration um up to concentration at
+
+ align:start position:0%
+concentration um up to concentration at
+ 
+
+ align:start position:0%
+concentration um up to concentration at
+whatever time T we stopped the
+
+ align:start position:0%
+whatever time T we stopped the
+ 
+
+ align:start position:0%
+whatever time T we stopped the
+experiment and through all the times in
+
+ align:start position:0%
+experiment and through all the times in
+ 
+
+ align:start position:0%
+experiment and through all the times in
+between um over one over the
+
+ align:start position:0%
+between um over one over the
+ 
+
+ align:start position:0%
+between um over one over the
+concentration of a DA and on the other
+
+ align:start position:0%
+concentration of a DA and on the other
+ 
+
+ align:start position:0%
+concentration of a DA and on the other
+side we have our minus rate constant K
+
+ align:start position:0%
+side we have our minus rate constant K
+ 
+
+ align:start position:0%
+side we have our minus rate constant K
+and we're looking at the time from Time
+
+ align:start position:0%
+and we're looking at the time from Time
+ 
+
+ align:start position:0%
+and we're looking at the time from Time
+Zero to time T when we stopped the
+
+ align:start position:0%
+Zero to time T when we stopped the
+ 
+
+ align:start position:0%
+Zero to time T when we stopped the
+experiment all right so we can take this
+
+ align:start position:0%
+experiment all right so we can take this
+ 
+
+ align:start position:0%
+experiment all right so we can take this
+expression now and move it up because I
+
+ align:start position:0%
+expression now and move it up because I
+ 
+
+ align:start position:0%
+expression now and move it up because I
+have more derivations to go so I'm going
+
+ align:start position:0%
+have more derivations to go so I'm going
+ 
+
+ align:start position:0%
+have more derivations to go so I'm going
+to put it on the top of the screen and
+
+ align:start position:0%
+to put it on the top of the screen and
+ 
+
+ align:start position:0%
+to put it on the top of the screen and
+now I am going to solve it um so the
+
+ align:start position:0%
+now I am going to solve it um so the
+ 
+
+ align:start position:0%
+now I am going to solve it um so the
+this integral solves to the natural log
+
+ align:start position:0%
+this integral solves to the natural log
+ 
+
+ align:start position:0%
+this integral solves to the natural log
+of the concentration of a at time T
+
+ align:start position:0%
+of the concentration of a at time T
+ 
+
+ align:start position:0%
+of the concentration of a at time T
+minus the natural log of our original
+
+ align:start position:0%
+minus the natural log of our original
+ 
+
+ align:start position:0%
+minus the natural log of our original
+concentration of
+
+ align:start position:0%
+concentration of
+ 
+
+ align:start position:0%
+concentration of
+a on the other side minus KT our time so
+
+ align:start position:0%
+a on the other side minus KT our time so
+ 
+
+ align:start position:0%
+a on the other side minus KT our time so
+there are two ways we can rewrite this
+
+ align:start position:0%
+there are two ways we can rewrite this
+ 
+
+ align:start position:0%
+there are two ways we can rewrite this
+uh equation we can write it as the
+
+ align:start position:0%
+uh equation we can write it as the
+ 
+
+ align:start position:0%
+uh equation we can write it as the
+equation for a straight line and all I
+
+ align:start position:0%
+equation for a straight line and all I
+ 
+
+ align:start position:0%
+equation for a straight line and all I
+did was take this natural log of a z um
+
+ align:start position:0%
+did was take this natural log of a z um
+ 
+
+ align:start position:0%
+did was take this natural log of a z um
+or a original over
+
+ align:start position:0%
+or a original over
+ 
+
+ align:start position:0%
+or a original over
+here and we could also rearrange this
+
+ align:start position:0%
+here and we could also rearrange this
+ 
+
+ align:start position:0%
+here and we could also rearrange this
+term um instead of minus we have natural
+
+ align:start position:0%
+term um instead of minus we have natural
+ 
+
+ align:start position:0%
+term um instead of minus we have natural
+log of the concentration of a at time T
+
+ align:start position:0%
+log of the concentration of a at time T
+ 
+
+ align:start position:0%
+log of the concentration of a at time T
+over our original
+
+ align:start position:0%
+over our original
+ 
+
+ align:start position:0%
+over our original
+concentration and now we can take the
+
+ align:start position:0%
+concentration and now we can take the
+ 
+
+ align:start position:0%
+concentration and now we can take the
+inverse natur natural log of both sides
+
+ align:start position:0%
+inverse natur natural log of both sides
+ 
+
+ align:start position:0%
+inverse natur natural log of both sides
+and so uh we get rid of natural log here
+
+ align:start position:0%
+and so uh we get rid of natural log here
+ 
+
+ align:start position:0%
+and so uh we get rid of natural log here
+and on the other side we have e to the
+
+ align:start position:0%
+and on the other side we have e to the
+ 
+
+ align:start position:0%
+and on the other side we have e to the
+minus KT again the rate constant times
+
+ align:start position:0%
+minus KT again the rate constant times
+ 
+
+ align:start position:0%
+minus KT again the rate constant times
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+time and then then I can write it break
+
+ align:start position:0%
+time and then then I can write it break
+ 
+
+ align:start position:0%
+time and then then I can write it break
+this out here moving the original
+
+ align:start position:0%
+this out here moving the original
+ 
+
+ align:start position:0%
+this out here moving the original
+concentration of a to this side and now
+
+ align:start position:0%
+concentration of a to this side and now
+ 
+
+ align:start position:0%
+concentration of a to this side and now
+this is the equation for the integrated
+
+ align:start position:0%
+this is the equation for the integrated
+ 
+
+ align:start position:0%
+this is the equation for the integrated
+first order rate law where you have the
+
+ align:start position:0%
+first order rate law where you have the
+ 
+
+ align:start position:0%
+first order rate law where you have the
+concentration of a at some point T
+
+ align:start position:0%
+concentration of a at some point T
+ 
+
+ align:start position:0%
+concentration of a at some point T
+equals its original concentration time e
+
+ align:start position:0%
+equals its original concentration time e
+ 
+
+ align:start position:0%
+equals its original concentration time e
+to the minus K the rate constant times
+
+ align:start position:0%
+to the minus K the rate constant times
+ 
+
+ align:start position:0%
+to the minus K the rate constant times
+the time so if you know a rate constant
+
+ align:start position:0%
+the time so if you know a rate constant
+ 
+
+ align:start position:0%
+the time so if you know a rate constant
+how much time is elapse and you know how
+
+ align:start position:0%
+how much time is elapse and you know how
+ 
+
+ align:start position:0%
+how much time is elapse and you know how
+much you have of something originally
+
+ align:start position:0%
+much you have of something originally
+ 
+
+ align:start position:0%
+much you have of something originally
+you can figure out how much you should
+
+ align:start position:0%
+you can figure out how much you should
+ 
+
+ align:start position:0%
+you can figure out how much you should
+have now or if you figure out how the
+
+ align:start position:0%
+have now or if you figure out how the
+ 
+
+ align:start position:0%
+have now or if you figure out how the
+concentration changes um over time you
+
+ align:start position:0%
+concentration changes um over time you
+ 
+
+ align:start position:0%
+concentration changes um over time you
+can use and how much you had originally
+
+ align:start position:0%
+can use and how much you had originally
+ 
+
+ align:start position:0%
+can use and how much you had originally
+you can calculate um the rate constant
+
+ align:start position:0%
+you can calculate um the rate constant
+ 
+
+ align:start position:0%
+you can calculate um the rate constant
+for that particular material and you can
+
+ align:start position:0%
+for that particular material and you can
+ 
+
+ align:start position:0%
+for that particular material and you can
+do those calculations for rate constants
+
+ align:start position:0%
+do those calculations for rate constants
+ 
+
+ align:start position:0%
+do those calculations for rate constants
+by plotting using this equation for a
+
+ align:start position:0%
+by plotting using this equation for a
+ 
+
+ align:start position:0%
+by plotting using this equation for a
+straight line so here I'm going to plot
+
+ align:start position:0%
+straight line so here I'm going to plot
+ 
+
+ align:start position:0%
+straight line so here I'm going to plot
+natural log of a so I measured the
+
+ align:start position:0%
+natural log of a so I measured the
+ 
+
+ align:start position:0%
+natural log of a so I measured the
+concentration in a at various different
+
+ align:start position:0%
+concentration in a at various different
+ 
+
+ align:start position:0%
+concentration in a at various different
+times Against Time
+
+ align:start position:0%
+times Against Time
+ 
+
+ align:start position:0%
+times Against Time
+and we have an equation for a straight
+
+ align:start position:0%
+and we have an equation for a straight
+ 
+
+ align:start position:0%
+and we have an equation for a straight
+line so we should get a straight line if
+
+ align:start position:0%
+line so we should get a straight line if
+ 
+
+ align:start position:0%
+line so we should get a straight line if
+this is a first order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process and so what would uh this be up
+
+ align:start position:0%
+process and so what would uh this be up
+ 
+
+ align:start position:0%
+process and so what would uh this be up
+here what is the Y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intercept what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it yeah so that's a natural log of our
+
+ align:start position:0%
+it yeah so that's a natural log of our
+ 
+
+ align:start position:0%
+it yeah so that's a natural log of our
+original
+
+ align:start position:0%
+original
+ 
+
+ align:start position:0%
+original
+concentration and this you can yell more
+
+ align:start position:0%
+concentration and this you can yell more
+ 
+
+ align:start position:0%
+concentration and this you can yell more
+loudly uh what is our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slope yes it's a little bit easier to
+
+ align:start position:0%
+slope yes it's a little bit easier to
+ 
+
+ align:start position:0%
+slope yes it's a little bit easier to
+yell loudly minus
+
+ align:start position:0%
+yell loudly minus
+ 
+
+ align:start position:0%
+yell loudly minus
+K so you can experimentally determine
+
+ align:start position:0%
+K so you can experimentally determine
+ 
+
+ align:start position:0%
+K so you can experimentally determine
+the rate constant from this so if you
+
+ align:start position:0%
+the rate constant from this so if you
+ 
+
+ align:start position:0%
+the rate constant from this so if you
+measure how the concentration of a
+
+ align:start position:0%
+measure how the concentration of a
+ 
+
+ align:start position:0%
+measure how the concentration of a
+changes with time plot your data natural
+
+ align:start position:0%
+changes with time plot your data natural
+ 
+
+ align:start position:0%
+changes with time plot your data natural
+log of those concentrations versus time
+
+ align:start position:0%
+log of those concentrations versus time
+ 
+
+ align:start position:0%
+log of those concentrations versus time
+get a lot of data points from the slope
+
+ align:start position:0%
+get a lot of data points from the slope
+ 
+
+ align:start position:0%
+get a lot of data points from the slope
+you can measure the rate constant and so
+
+ align:start position:0%
+you can measure the rate constant and so
+ 
+
+ align:start position:0%
+you can measure the rate constant and so
+rate constants for a lot of different
+
+ align:start position:0%
+rate constants for a lot of different
+ 
+
+ align:start position:0%
+rate constants for a lot of different
+materials have already been measured in
+
+ align:start position:0%
+materials have already been measured in
+ 
+
+ align:start position:0%
+materials have already been measured in
+this kind of way way all right so for a
+
+ align:start position:0%
+this kind of way way all right so for a
+ 
+
+ align:start position:0%
+this kind of way way all right so for a
+first order process this is these are
+
+ align:start position:0%
+first order process this is these are
+ 
+
+ align:start position:0%
+first order process this is these are
+important equations but also for first
+
+ align:start position:0%
+important equations but also for first
+ 
+
+ align:start position:0%
+important equations but also for first
+order we spend a lot time talking about
+
+ align:start position:0%
+order we spend a lot time talking about
+ 
+
+ align:start position:0%
+order we spend a lot time talking about
+Half-Life so halflife is the time it
+
+ align:start position:0%
+Half-Life so halflife is the time it
+ 
+
+ align:start position:0%
+Half-Life so halflife is the time it
+takes for half of the original material
+
+ align:start position:0%
+takes for half of the original material
+ 
+
+ align:start position:0%
+takes for half of the original material
+to go away so it's a really easy thing
+
+ align:start position:0%
+to go away so it's a really easy thing
+ 
+
+ align:start position:0%
+to go away so it's a really easy thing
+it is I like it when things are called
+
+ align:start position:0%
+it is I like it when things are called
+ 
+
+ align:start position:0%
+it is I like it when things are called
+what they
+
+ align:start position:0%
+what they
+ 
+
+ align:start position:0%
+what they
+are and uh here the time involved has a
+
+ align:start position:0%
+are and uh here the time involved has a
+ 
+
+ align:start position:0%
+are and uh here the time involved has a
+little special abbreviation t a half so
+
+ align:start position:0%
+little special abbreviation t a half so
+ 
+
+ align:start position:0%
+little special abbreviation t a half so
+whenever you see t a half that's talking
+
+ align:start position:0%
+whenever you see t a half that's talking
+ 
+
+ align:start position:0%
+whenever you see t a half that's talking
+about a
+
+ align:start position:0%
+about a
+ 
+
+ align:start position:0%
+about a
+halflife so we can derive this
+
+ align:start position:0%
+halflife so we can derive this
+ 
+
+ align:start position:0%
+halflife so we can derive this
+expression as well for the first order
+
+ align:start position:0%
+expression as well for the first order
+ 
+
+ align:start position:0%
+expression as well for the first order
+halflife using the Expressions that we
+
+ align:start position:0%
+halflife using the Expressions that we
+ 
+
+ align:start position:0%
+halflife using the Expressions that we
+just looked
+
+ align:start position:0%
+just looked
+ 
+
+ align:start position:0%
+just looked
+at so from uh the expression we had
+
+ align:start position:0%
+at so from uh the expression we had
+ 
+
+ align:start position:0%
+at so from uh the expression we had
+above where we had the natural log of
+
+ align:start position:0%
+above where we had the natural log of
+ 
+
+ align:start position:0%
+above where we had the natural log of
+the concentration of a at time T over
+
+ align:start position:0%
+the concentration of a at time T over
+ 
+
+ align:start position:0%
+the concentration of a at time T over
+original concentration equals minus the
+
+ align:start position:0%
+original concentration equals minus the
+ 
+
+ align:start position:0%
+original concentration equals minus the
+rate constant K * time and now we can
+
+ align:start position:0%
+rate constant K * time and now we can
+ 
+
+ align:start position:0%
+rate constant K * time and now we can
+substitute in so we're not interested in
+
+ align:start position:0%
+substitute in so we're not interested in
+ 
+
+ align:start position:0%
+substitute in so we're not interested in
+just any old time we're interested in
+
+ align:start position:0%
+just any old time we're interested in
+ 
+
+ align:start position:0%
+just any old time we're interested in
+time a half so we're going to want to
+
+ align:start position:0%
+time a half so we're going to want to
+ 
+
+ align:start position:0%
+time a half so we're going to want to
+put a half in there and that is the time
+
+ align:start position:0%
+put a half in there and that is the time
+ 
+
+ align:start position:0%
+put a half in there and that is the time
+it takes for the original amount to go
+
+ align:start position:0%
+it takes for the original amount to go
+ 
+
+ align:start position:0%
+it takes for the original amount to go
+to half so to be divided by two so we
+
+ align:start position:0%
+to half so to be divided by two so we
+ 
+
+ align:start position:0%
+to half so to be divided by two so we
+can put that in so now our a t our
+
+ align:start position:0%
+can put that in so now our a t our
+ 
+
+ align:start position:0%
+can put that in so now our a t our
+concentration of a at times T is our
+
+ align:start position:0%
+concentration of a at times T is our
+ 
+
+ align:start position:0%
+concentration of a at times T is our
+original concentration divided by two
+
+ align:start position:0%
+original concentration divided by two
+ 
+
+ align:start position:0%
+original concentration divided by two
+and our T is t a half so you'll see that
+
+ align:start position:0%
+and our T is t a half so you'll see that
+ 
+
+ align:start position:0%
+and our T is t a half so you'll see that
+the a Zer terms are going to cancel out
+
+ align:start position:0%
+the a Zer terms are going to cancel out
+ 
+
+ align:start position:0%
+the a Zer terms are going to cancel out
+and you're going to end up with natural
+
+ align:start position:0%
+and you're going to end up with natural
+ 
+
+ align:start position:0%
+and you're going to end up with natural
+log of a half equal minus k
+
+ align:start position:0%
+log of a half equal minus k
+ 
+
+ align:start position:0%
+log of a half equal minus k
+times our half life T a half and so then
+
+ align:start position:0%
+times our half life T a half and so then
+ 
+
+ align:start position:0%
+times our half life T a half and so then
+we can uh put in our value for the
+
+ align:start position:0%
+we can uh put in our value for the
+ 
+
+ align:start position:0%
+we can uh put in our value for the
+natural log of a half and get rid of all
+
+ align:start position:0%
+natural log of a half and get rid of all
+ 
+
+ align:start position:0%
+natural log of a half and get rid of all
+those minus signs and rearrange it and
+
+ align:start position:0%
+those minus signs and rearrange it and
+ 
+
+ align:start position:0%
+those minus signs and rearrange it and
+so then our half life for this first
+
+ align:start position:0%
+so then our half life for this first
+ 
+
+ align:start position:0%
+so then our half life for this first
+order process is going to be equal to
+
+ align:start position:0%
+order process is going to be equal to
+ 
+
+ align:start position:0%
+order process is going to be equal to
+9631 divided K the rate constant so
+
+ align:start position:0%
+9631 divided K the rate constant so
+ 
+
+ align:start position:0%
+9631 divided K the rate constant so
+you'll note a couple of uh perhaps
+
+ align:start position:0%
+you'll note a couple of uh perhaps
+ 
+
+ align:start position:0%
+you'll note a couple of uh perhaps
+important things about this expression
+
+ align:start position:0%
+important things about this expression
+ 
+
+ align:start position:0%
+important things about this expression
+and one of the important things is that
+
+ align:start position:0%
+and one of the important things is that
+ 
+
+ align:start position:0%
+and one of the important things is that
+half life doesn't depend on the
+
+ align:start position:0%
+half life doesn't depend on the
+ 
+
+ align:start position:0%
+half life doesn't depend on the
+concentration so the concentration term
+
+ align:start position:0%
+concentration so the concentration term
+ 
+
+ align:start position:0%
+concentration so the concentration term
+has dropped out so what does halflife
+
+ align:start position:0%
+has dropped out so what does halflife
+ 
+
+ align:start position:0%
+has dropped out so what does halflife
+depend on then if it doesn't depend on
+
+ align:start position:0%
+depend on then if it doesn't depend on
+ 
+
+ align:start position:0%
+depend on then if it doesn't depend on
+the concentration again this is for
+
+ align:start position:0%
+the concentration again this is for
+ 
+
+ align:start position:0%
+the concentration again this is for
+first order so it's going to depend on K
+
+ align:start position:0%
+first order so it's going to depend on K
+ 
+
+ align:start position:0%
+first order so it's going to depend on K
+that's all that's in there there's only
+
+ align:start position:0%
+that's all that's in there there's only
+ 
+
+ align:start position:0%
+that's all that's in there there's only
+one thing that's in there there's a
+
+ align:start position:0%
+one thing that's in there there's a
+ 
+
+ align:start position:0%
+one thing that's in there there's a
+number a constant and there's K so
+
+ align:start position:0%
+number a constant and there's K so
+ 
+
+ align:start position:0%
+number a constant and there's K so
+halflife depends on K this rate constant
+
+ align:start position:0%
+halflife depends on K this rate constant
+ 
+
+ align:start position:0%
+halflife depends on K this rate constant
+and the rate constant depends on the
+
+ align:start position:0%
+and the rate constant depends on the
+ 
+
+ align:start position:0%
+and the rate constant depends on the
+material in question so different
+
+ align:start position:0%
+material in question so different
+ 
+
+ align:start position:0%
+material in question so different
+materials will have different values of
+
+ align:start position:0%
+materials will have different values of
+ 
+
+ align:start position:0%
+materials will have different values of
+rate constant and we just saw how you
+
+ align:start position:0%
+rate constant and we just saw how you
+ 
+
+ align:start position:0%
+rate constant and we just saw how you
+can calculate a rate constant you can
+
+ align:start position:0%
+can calculate a rate constant you can
+ 
+
+ align:start position:0%
+can calculate a rate constant you can
+measure it um from uh and get the slope
+
+ align:start position:0%
+measure it um from uh and get the slope
+ 
+
+ align:start position:0%
+measure it um from uh and get the slope
+of the line and tells you about what K
+
+ align:start position:0%
+of the line and tells you about what K
+ 
+
+ align:start position:0%
+of the line and tells you about what K
+is all right so let's use this
+
+ align:start position:0%
+is all right so let's use this
+ 
+
+ align:start position:0%
+is all right so let's use this
+expression now and why don't you tell me
+
+ align:start position:0%
+expression now and why don't you tell me
+ 
+
+ align:start position:0%
+expression now and why don't you tell me
+for the same material um which of these
+
+ align:start position:0%
+for the same material um which of these
+ 
+
+ align:start position:0%
+for the same material um which of these
+thing Pro which of these events will
+
+ align:start position:0%
+thing Pro which of these events will
+ 
+
+ align:start position:0%
+thing Pro which of these events will
+take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+longer all right 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it takes in fact the same amount of
+
+ align:start position:0%
+so it takes in fact the same amount of
+ 
+
+ align:start position:0%
+so it takes in fact the same amount of
+time because the concentration doesn't
+
+ align:start position:0%
+time because the concentration doesn't
+ 
+
+ align:start position:0%
+time because the concentration doesn't
+show up in there and it was the same
+
+ align:start position:0%
+show up in there and it was the same
+ 
+
+ align:start position:0%
+show up in there and it was the same
+material all right so before we move
+
+ align:start position:0%
+material all right so before we move
+ 
+
+ align:start position:0%
+material all right so before we move
+away from this you can write same amount
+
+ align:start position:0%
+away from this you can write same amount
+ 
+
+ align:start position:0%
+away from this you can write same amount
+of time in your notes let's take a look
+
+ align:start position:0%
+of time in your notes let's take a look
+ 
+
+ align:start position:0%
+of time in your notes let's take a look
+at this plot on the bottom of the page
+
+ align:start position:0%
+at this plot on the bottom of the page
+ 
+
+ align:start position:0%
+at this plot on the bottom of the page
+and just think about what's happening
+
+ align:start position:0%
+and just think about what's happening
+ 
+
+ align:start position:0%
+and just think about what's happening
+because you can talk about a first half
+
+ align:start position:0%
+because you can talk about a first half
+ 
+
+ align:start position:0%
+because you can talk about a first half
+life and a second half life and a third
+
+ align:start position:0%
+life and a second half life and a third
+ 
+
+ align:start position:0%
+life and a second half life and a third
+half life so we can just fill this right
+
+ align:start position:0%
+half life so we can just fill this right
+ 
+
+ align:start position:0%
+half life so we can just fill this right
+in so for a concentration at your first
+
+ align:start position:0%
+in so for a concentration at your first
+ 
+
+ align:start position:0%
+in so for a concentration at your first
+halflife how much is
+
+ align:start position:0%
+halflife how much is
+ 
+
+ align:start position:0%
+halflife how much is
+left so what's this number the
+
+ align:start position:0%
+left so what's this number the
+ 
+
+ align:start position:0%
+left so what's this number the
+concentration is what half second half
+
+ align:start position:0%
+concentration is what half second half
+ 
+
+ align:start position:0%
+concentration is what half second half
+life what do we
+
+ align:start position:0%
+life what do we
+ 
+
+ align:start position:0%
+life what do we
+got .25
+
+ align:start position:0%
+got .25
+ 
+
+ align:start position:0%
+got .25
+third .125 right so this is pretty easy
+
+ align:start position:0%
+third .125 right so this is pretty easy
+ 
+
+ align:start position:0%
+third .125 right so this is pretty easy
+to think about but sometimes when you
+
+ align:start position:0%
+to think about but sometimes when you
+ 
+
+ align:start position:0%
+to think about but sometimes when you
+have data and you're looking at it you
+
+ align:start position:0%
+have data and you're looking at it you
+ 
+
+ align:start position:0%
+have data and you're looking at it you
+have to remember what the sort of
+
+ align:start position:0%
+have to remember what the sort of
+ 
+
+ align:start position:0%
+have to remember what the sort of
+possibilities are okay so that's first
+
+ align:start position:0%
+possibilities are okay so that's first
+ 
+
+ align:start position:0%
+possibilities are okay so that's first
+order halflife and that's the end of
+
+ align:start position:0%
+order halflife and that's the end of
+ 
+
+ align:start position:0%
+order halflife and that's the end of
+this lecture but we're not really moving
+
+ align:start position:0%
+this lecture but we're not really moving
+ 
+
+ align:start position:0%
+this lecture but we're not really moving
+away from the topic because now we're
+
+ align:start position:0%
+away from the topic because now we're
+ 
+
+ align:start position:0%
+away from the topic because now we're
+going to talk about example of a first
+
+ align:start position:0%
+going to talk about example of a first
+ 
+
+ align:start position:0%
+going to talk about example of a first
+order process which is radioactive decay
\ No newline at end of file
diff --git a/BLExWo9Empk.txt b/BLExWo9Empk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..21049bc1c3d9986bbdd9e8b81ee72f8f559f745a
--- /dev/null
+++ b/BLExWo9Empk.txt
@@ -0,0 +1,3633 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation, or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Are you guys
+excited about Battlecode?
+
+I'm so excited to
+see this many-- Yeah!
+
+Yeah, let's hear a
+hurray-- no, no a yeah.
+
+Are you excited?
+
+AUDIENCE: Yeah!
+
+PROFESSOR: All right,
+that was a strong yeah.
+
+I actually mean that.
+
+I have a strange thing
+where when I say something
+
+it often comes out like I meant
+the opposite of what I said,
+
+like I didn't believe it.
+
+Like that time that Drew
+Houston-- from Dropbox,
+
+he's the Dropbox CEO-- do
+you guys remember this?
+
+He was giving his sponsor talk
+at the finals of Battlecode
+
+last year and he was
+just wrapping up,
+
+and everybody was
+applauding, and I
+
+came to the podium I was
+like, thanks, thanks Drew.
+
+That was really good.
+
+That made me want
+to work at Dropbox.
+
+If I didn't have a
+job already I would.
+
+And nobody believed
+me, they thought
+
+I was just being facetious.
+
+So, now he hates me.
+
+That's too bad.
+
+That happens to me.
+
+OK, let's get started soon.
+
+So you're all here
+because you're
+
+interested in Battlecode.
+
+These lectures are optional.
+
+They're geared at beginner
+to mid-level coders,
+
+but they'll be
+relevant even if you've
+
+had coding experience
+in a million languages.
+
+Because we're
+going to be talking
+
+a lot of the time about
+Battlecode, the game itself.
+
+And it could just be a
+way to keep yourself up
+
+to date on the latest
+metagame, for example.
+
+So we're going to go
+over the specs today.
+
+I'm going to introduce
+the competition.
+
+And then after
+lecture today, we'll
+
+be having a lab, during
+which we'll help you set up.
+
+So I see a lot of you brought
+your computers, that's
+
+fantastic.
+
+And that's also great because
+it means if you get bored,
+
+you can just watch
+YouTube videos.
+
+Yeah, so make sure to bring
+your ear plugs so that you don't
+
+bother the guy next to
+you, because he's already
+
+heard Gangnam Style.
+
+All right so be
+respectful of those guys.
+
+So here's our introduction.
+
+My name is Maxwell Mann, I'll
+be your lecturer for the next 10
+
+days.
+
+It actually is minus 4 days
+because of various things.
+
+So it's like the
+next two weeks, you
+
+can come here at this
+time-- or slightly earlier,
+
+so you can hear a lousy
+joke --you can come here,
+
+and you can hear me
+talk about the game,
+
+and hear what the
+devs think about what
+
+you might need to know.
+
+And then you can eat
+food at 6:00 PM, when
+
+we have massive
+quantities of food coming,
+
+and then from 6:00 to
+7:00, you have the option
+
+of staying for the lab session,
+which has been described,
+
+in anticipation,
+as a social utopia.
+
+And I really believe
+that it could be one,
+
+because everybody here has,
+sort of, some similar interests.
+
+So to introduce
+us, we developers,
+
+are students, or
+alums, who have worked
+
+on developing Battlecode.
+
+I'm Max.
+
+Sitting here in the
+front is Aaron Epstein
+
+and Steven Valdez.
+
+You'll be using them for help,
+all the time, if you need it,
+
+or just to bother them
+because you feel like it.
+
+They're here for
+no other reason,
+
+and to maintain the code base
+and these kinds of things.
+
+The website is battlecode.org
+and we have a forum there,
+
+where you could
+also go to get help.
+
+And I also,
+particularly, would like
+
+to direct your attention
+to the IRC channel.
+
+It's #battlecode on Freenode.
+
+So I don't know if
+you know what that is,
+
+but it's basically
+a way that you
+
+can talk to us on
+a real time chat.
+
+So you can do that at pretty
+much any hour of the day,
+
+because the way
+we're setting it up
+
+this year is we'll all
+be available, pretty
+
+much the whole time.
+
+OK, make sure that if
+you are an MIT student,
+
+and you want credit
+for this class--
+
+it's a six credit
+class --you just
+
+have to sign up on
+WebSIS for 6.S187.
+
+How many people have signed
+up on WebSIS already?
+
+All right, that's
+like everybody.
+
+Let's talk about the
+goals of the competition.
+
+What is a game?
+
+What are we doing?
+
+I'm sure a lot of you are
+thinking all right, well, here
+
+we go.
+
+I've got finals
+tomorrow but I have
+
+to decide what IAP
+classes to take.
+
+Gosh, this is a terrible
+combination of deadlines.
+
+Then you thought,
+should I take--
+
+should I to do battle code?
+
+Should I do one of these other
+things, like web programming,
+
+or game programming?
+
+What is the operating
+systems whatshumadoosits?
+
+Should I do this or that?
+
+And you're probably thinking
+to yourself, what is fun?
+
+What is valuable for me?
+
+What am I going to learn?
+
+And we ask ourselves
+the same question.
+
+A couple months
+before then was, what
+
+do we want the Battlecode
+competition to be like?
+
+And what we ended
+up deciding, was
+
+that the game needs
+to be fun and it
+
+needs to contain classic
+battle code areas of challenge
+
+in artificial intelligence.
+
+So this is a game that
+is a cross-- we've always
+
+said in the past that
+it is not StarCraft
+
+--but it is a cross between
+a real-time strategy
+
+game and an AI
+programming competition.
+
+So what we wanted was the
+game to be easy to learn,
+
+but hard to master.
+
+So what you'll see when I
+describe the game specs--
+
+and I'm going into it just
+momentarily --when I describe
+
+game specs you'll see ways
+to play the game, and then
+
+ways to excel at the game.
+
+So it's like you've got
+this infinite ramp, that you
+
+can run wild on, of
+how much effort you
+
+want to put into
+developing the best player.
+
+Or better yet, because
+what is the best?
+
+It's comparative.
+
+That's comparing
+to somebody else.
+
+But that's kind of irrelevant.
+
+What you want is to have fun.
+
+Anyway, you know that.
+
+So there we go.
+
+Our idea was to not
+have sort of skill caps
+
+and limiting factors,
+like maps that are just
+
+covered in maze so
+you can't do anything
+
+unless you can get
+past that maze.
+
+Like, OK, you didn't
+pass the test,
+
+I hope you enjoy
+your starting area.
+
+No, no.
+
+So not that.
+
+So let me show the game.
+
+How many of you have
+seen Battlecode before?
+
+A show of hands.
+
+So that's a good number,
+but it's not everybody.
+
+So I'm going to show you a game.
+
+So this is when
+you've made your code
+
+and you've put it
+into the client,
+
+you can run a game
+like this, and we'll
+
+go over how to do that.
+
+And I'll just hit
+play here, and you'll
+
+see the red team
+in the upper left,
+
+and the blue team
+in the bottom right,
+
+playing a game of
+Battlecode for this year.
+
+The player on the
+upper left, in red,
+
+is placing mines,
+and capturing bases.
+
+His soldiers are moving around
+and fighting with one another.
+
+Fighting the enemy, hopefully.
+
+And the blue player,
+here at the bottom right,
+
+is just sort of
+shooting his guys off
+
+to die at the enemy army.
+
+On the left you'll
+see indicators
+
+of various game constants
+and values that are changing.
+
+If I pause this
+for a second, you
+
+can see by clicking
+on any robot,
+
+you can see his ID number,
+what robot type it is.
+
+You can see his hit
+point level, which
+
+we have characteristically had
+a very difficult to remember
+
+name for.
+
+We always have different names
+for their energy and their head
+
+points this year it's going to
+be, "energon," for hit points.
+
+I think this flux number is
+actually no longer relevant,
+
+and you can ignore it.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: See,
+we worked so hard
+
+on making this
+polished and perfect,
+
+that we weren't finished
+until-- actually we're
+
+not finished yet, they're
+still fussing with something.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: The
+bytecodes used is going
+
+to be a key factor that you're
+going to look at so that you
+
+can determine how much
+computational energy
+
+those robots are spending.
+
+This year, there's
+a very big impact
+
+on the efficiency of your
+code, and the performance
+
+of your player.
+
+If you have efficient code, you
+could have twice as many robots
+
+on the field then
+you can sustain
+
+if your code is inefficient.
+
+Because the actual
+computational cost
+
+is recorded, and
+is then implemented
+
+into the upkeep of each unit.
+
+Finally, you'll see the
+location of the unit, and three
+
+indicator strings that you can
+use for debugging and control
+
+purposes.
+
+So what we'll do today is talk
+about what kinds of things
+
+are on this map, and how that's
+different and amazingly great,
+
+and how this year's new gameplay
+will be even more fun than it
+
+ever has been.
+
+And I can say that
+with some confidence,
+
+because it's quite different
+and demonstrably better.
+
+Yes.
+
+So what we think of
+as skill areas, areas
+
+that make a fun
+game for Battlecode,
+
+are, navigation-- but not
+that you so much require
+
+it --see, in this example,
+they didn't really
+
+need any complex maze
+solving algorithms.
+
+What they were just doing, is
+there are these neutral mines
+
+that are here, and you
+could either walk around
+
+the neutral minefield,
+or you could just
+
+clear yourself
+right on through it.
+
+So there's navigation,
+but you don't necessarily
+
+have to do it.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: There's
+group pathing--
+
+and that's a good point
+because, you know,
+
+OK, anybody can take one
+unit and after enough time,
+
+figure out how to implement
+any of the existing pathing
+
+algorithms.
+
+But let's say you've
+got multiple units.
+
+They start to get in
+one another's way.
+
+Let me give an example
+that's very concrete,
+
+and that hits really
+close to home, for me.
+
+I did this all the time--
+I've done Battlecode,
+
+I guess, like four years now.
+
+And so what I'd always
+have is, I'm here,
+
+and I want to go to ice
+cream-- something desirable
+
+--and I'm trying to
+get past this wall.
+
+So I go here, but then all my
+friends take up all this space
+
+because they're
+going the same way.
+
+And then I'm trying to
+turn around, and go back,
+
+and they're trying to
+go this way because they
+
+think it's closer
+to the ice cream.
+
+And we just end up here
+all day, and then the enemy
+
+comes by and shoots us.
+
+And then we've got
+holes in ourselves,
+
+how are we going to
+maintain that stomach
+
+area to keep the ice cream in?
+
+It's just not going to work.
+
+So we like navigation,
+we like group pathing.
+
+We like messaging.
+
+This year, the messaging
+system is totally new.
+
+In the past, what
+you'd need is--
+
+I'm going to go
+back to the screen
+
+here --is your
+robot would only be
+
+able to see a certain
+area around himself.
+
+And so every other
+robot would not
+
+know what's going on, on the
+whole map, except by messaging.
+
+But even then, they would
+have to receive messages
+
+that are broadcast
+within a certain range.
+
+So you end up having to make
+these chains where you'd
+
+say, all right,
+I've got, let's see,
+
+Joe, and James, and Jalopy.
+
+They're all in line, and these
+three robots are in line,
+
+and they each have
+some broadcast radius.
+
+And so maybe I can, sort
+of, set up a relay chain,
+
+and they're broadcasting back.
+
+And that was how you used
+to communicate information
+
+about where the enemy is.
+
+So here's the ice cream,
+here, and here's me.
+
+And I would have to hear
+it from these four guys.
+
+But that would end up
+being a lot of work
+
+for me to implement.
+
+And we like that, we
+think that's really cool.
+
+But at the same time
+it ended up meaning
+
+that if the ice
+cream were an enemy,
+
+and I needed to scout
+that the enemy were coming
+
+with some rush, that
+what would often happen
+
+is that there wouldn't
+be a chain established.
+
+Because this kind of
+stuff's kind of hard do.
+
+So this guy would see the enemy
+right here-- and here's me,
+
+back here, I'm just
+minding my own business.
+
+Maybe I'm building a staircase,
+which we did in one year.
+
+Or some other very useful
+expenditure of effort and time.
+
+So this guy sees the enemy
+and I don't know about it,
+
+I can't prepare
+until he comes back.
+
+OK, so then he comes back
+to within broadcast range--
+
+he's here --but by then
+the enemy is right there.
+
+I can't do anything.
+
+So what we've done
+this year, is we've
+
+said all right, realistically
+we've got these radios, right?
+
+Let's communicate, on these
+radios, across the whole map.
+
+So now your radio messages can
+be heard across the whole map.
+
+But, instead of being messages,
+like they used to be--
+
+and these messages
+were kind of annoying,
+
+they were these constructs
+that you had to assemble.
+
+You'd say, oh, I'm
+making a new message
+
+and I'm applying
+these parts to it.
+
+And not every message
+has every type of part.
+
+And not every part as
+every type of message.
+
+And every time I
+receive a message
+
+I can receive an
+infinity of messages.
+
+And then my robot
+explodes because he's
+
+being overloaded with messages.
+
+That's like spam, happens
+a lot, it happens to me.
+
+So what we get instead,
+is we said, all right,
+
+we've got a uniform
+message channel.
+
+We've got 10,000 channels.
+
+And any robot can
+post an integer
+
+to any one of those
+channels, at any time.
+
+So then my robot could be
+posting-- maybe my code
+
+is using frequency 567.
+
+And I'll be communicating on
+that frequency specifically
+
+where I'm going, or what
+direction I'm going,
+
+or something like that.
+
+And everybody on
+my team can see it.
+
+So that's a really useful
+sort of centralizing feature.
+
+So if the enemy is
+coming, I can just
+
+look on integer number 567, and
+if the enemy is coming, maybe
+
+that's a flag,
+maybe I make that, I
+
+guess, 666 because
+that's really bad.
+
+Right?
+
+So I make that my token for
+enemy is coming, and then bing,
+
+everybody can start preparing
+for the enemy coming.
+
+But there's more,
+I mean, let's say
+
+you're going to metagame them.
+
+You're going to think about what
+could happen from a high level.
+
+Like when would the
+enemy just invade?
+
+When would they attack me?
+
+I mean, I don't have to see them
+coming to know that they will.
+
+For example, maybe the
+map is really small.
+
+So this year, you can
+tell how big the map is.
+
+I mean, how does it make sense--
+this happened again and again
+
+in previous years --how
+does it make sense
+
+to have a game, where players
+are expected to operate
+
+intelligently, in the
+absence of information.
+
+OK, I understand that sometimes
+a little bit of uncertainty
+
+can be great.
+
+Like how great poker
+be if everybody
+
+knows what everybody
+else's hand is?
+
+That would be
+really lousy, right?
+
+But here, we just had
+almost no information,
+
+so you'd have
+build-order losses.
+
+This is sort of a big problem,
+in my eyes, with StarCraft.
+
+Which is that you'd start
+with a strategy that
+
+could lose before you have any
+information on how to fix that.
+
+So at least in StarCraft
+you know how big the map is.
+
+So here we're giving them
+the following centralized
+
+information.
+
+So here's what I'll do.
+
+I'm going to list out the
+centralized information
+
+that you can use, that
+you didn't really used
+
+to have access to.
+
+Now you might ask, all right
+I'm not going to memorize this,
+
+and I'm not taking
+notes-- even though I
+
+did bring a thingamabober, which
+is a computer, or a notebook.
+
+You might say, I'm not
+going to memorize this,
+
+I'm not interested,
+I'm here to have fun.
+
+Well look here, you can
+look in the Java docs
+
+and you can see all of
+the robot abilities.
+
+They're listed in
+this giant list here,
+
+and you'll have time
+to peruse those.
+
+And we'll sort of go
+over them over the course
+
+of the few lectures.
+
+But having them sort
+of in a condensed form
+
+or organized into
+topics, like what
+
+is centralized information?
+
+You know, what
+information can I use?
+
+Ends up probably being
+a bit of a convenience.
+
+So I have a couple of convenient
+organizations of data.
+
+And that's really all
+I'm here for is just--
+
+you can get all this information
+in our documentation,
+
+which we'll supply you when
+we help you set up the game.
+
+And/or you can sort of hear
+it from me, where I've got it
+
+sort of organized into a
+slightly different way.
+
+The centralized
+info that you get
+
+includes, you can sense the
+positions of all allied robots.
+
+So there's a function, and
+again, we have very good naming
+
+conventions so that all
+of the names that we pick
+
+let you know exactly
+what we're referring to.
+
+And for this function we call
+it-- it's a method called,
+
+"Sense Nearby Game Objects."
+
+And that's great because
+it can detect game objects
+
+across the map, anywhere,
+they don't have to be nearby.
+
+So that that's really nice.
+
+And it senses these things,
+which of course, you
+
+would want to sense.
+
+They're objects!
+
+You know, I was playing chess
+the other day with my friend
+
+Rick, and I said
+to him, you know
+
+what I could use more
+of is game objects.
+
+I can sense all of
+your game objects.
+
+And he didn't get it.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: So Sense
+Nearby Game Objects
+
+is an overloaded
+function, which means
+
+that you can call it
+with multiple arguments.
+
+And that really does help you.
+
+So the point is, this
+is a global function,
+
+because you can see any game
+object if that game object is
+
+of a certain type.
+
+So all of your allied
+robots you can see.
+
+Let's go back to our example,
+let's say that I am back here,
+
+that's me, over
+here at the bottom.
+
+And this guy up
+at the top, I can
+
+see where he is back from here.
+
+But my sight range is
+actually only here.
+
+So I've got different
+detection abilities.
+
+Allied robots, allied
+mines, and neutral mines,
+
+are all visible no
+matter where you are,
+
+but enemy robots are only
+visible within your sight
+
+radius.
+
+But it's within any
+allied robot site radius.
+
+It's harder to explain
+than it is to think about.
+
+In this picture, this
+robot can see these guys,
+
+because he's really close.
+
+But this guy can also see them,
+because this robot is nearby.
+
+Right, that's pretty
+straightforward.
+
+One person was nodding
+but he was also yawning,
+
+so he may have been nodding off.
+
+No, I'm only joking.
+
+Yeah, zing!
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: Sense
+Nearby Game Objects
+
+is a kind of useful
+thing to be able to do,
+
+but it's not always
+obvious how to use it.
+
+So, later on, I'll
+be talking about how
+
+one of the inputs to
+this is what type of game
+
+object you want.
+
+I still haven't-- I've been
+saying game object over
+
+and over, but none of you
+care about game objects.
+
+You care about
+enemy robots, I want
+
+to shoot at the enemy robots.
+
+So you would end up writing,
+oh, I want a robot please.
+
+So you tell it, give me game
+objects of type Robot.class.
+
+And you would say,
+all right, this
+
+is getting kind of confusing.
+
+I'm feeling a little
+bit overwhelmed.
+
+Well don't you worry about it,
+because here in the Java Docs,
+
+under package-- and you might
+notice that this is the Java
+
+docs version 7,
+for Java version 7.
+
+It's real sleek.
+
+We're distributing this
+at absolutely no cost.
+
+Yeah.
+
+Let's see here, oh, look!
+
+It's game object.
+
+There it is.
+
+And oh, look, subinterfaces
+include encampments and robots.
+
+Well that's great, that
+answers my question.
+
+So now I know that I can put
+Robot.class or Encampment.class
+
+and it will give me that
+type of game object.
+
+Yeah.
+
+Yeah!
+
+All right.
+
+[LAUGHS]
+
+So that's a piece of
+centralized information.
+
+Another piece of
+centralized info--
+
+so we've talked about
+how it's allied robots.
+
+There's allied mines.
+
+I'll talk about the mines and
+how you can lay them and defuse
+
+them, and how you get these
+things onto the game board.
+
+Allied robots, allied mines.
+
+You've got the radio system,
+which is entirely global.
+
+And that means that you can
+disrupt somebody else's radio
+
+program.
+
+I have a hunch that there are
+several people out there who
+
+would broadcast random numbers
+to my favorite channel, 567,
+
+and it would just
+totally ruin my player.
+
+I wouldn't be able
+to work at all.
+
+Now, in order to limit
+this sort of-- there's sort
+
+of a back and forth
+between sending messages
+
+that you want to send,
+receiving the messages
+
+with a certain amount of,
+sort of, redundancy in there,
+
+so you can be safe
+against message jamming,
+
+versus actual jamming itself.
+
+How do we assess the balance
+of these competing objectives?
+
+Well we've got a cost
+associated with everything.
+
+There's no free lunch.
+
+Except dinner for Battlecode.
+
+And that is actually free.
+
+We ordered so much
+pizza for today.
+
+Now I'm sure not many of you
+ordered that much pizza before.
+
+But let me tell
+you that I expected
+
+that-- there's like 120
+people here in the room,
+
+and we thought how much
+pizza does everybody eat?
+
+Well unfortunately Battlecode
+is a male dominated class.
+
+So we'll have slightly
+more pizza consumption
+
+than otherwise.
+
+Is that sexist?
+
+And so--
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: So we decided
+to get 50 pizzas.
+
+And we were like, well
+what's awesome pizza?
+
+We like Bertucci's.
+
+You guys don't like Bertucci's.
+
+Yeah!
+
+He likes Bertucci's.
+
+Yeah, so that was
+like $20 a pizza.
+
+So it was like $1000 for pizza.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: My goodness.
+
+Well anyway, it's going
+to be really good.
+
+And it's coming in
+like a half an hour.
+
+That's fantastic-- I've totally
+lost my train of thought.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: Right I was
+
+AUDIENCE: --message him.
+
+PROFESSOR: Yeah.
+
+I was saying that there's
+no free lunch, and as such,
+
+we have a bytecode cost.
+
+Now, I think in the past it's
+not been that obvious to me
+
+what the cost of doing a
+certain computation is.
+
+Can I jam the enemy?
+
+Is that really going to work, or
+am I going to run out of money?
+
+Is a question you could ask.
+
+So here, in the--
+let's see here,
+
+I have a place where I
+have installed Battlecode.
+
+And you're going to
+do something just
+
+like this, where you'll have
+that Battlecode-- that's OK,
+
+he had to go to the bathroom.
+
+Don't worry about him.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: Well it's a
+reasonable supposition,
+
+he is human, isn't he?
+
+All right, and so here, in
+the Battlecode directory
+
+where I've installed
+Battlecode, there's
+
+going to be a text file
+that's called method costs.
+
+Bingo.
+
+All right now it
+looks disorganized
+
+because everything-- the
+strings are different lengths.
+
+But each string represents
+a function that you can use.
+
+Like for example attack square.
+
+Or maybe broadcast a message.
+
+Ah, that was the one
+we were interested in.
+
+OK, let's look at that.
+
+Broadcast costs 25 bytecodes.
+
+All right, let's do a little
+bit of math-- arithmetic,
+
+it's not math, is it?
+
+25 bytecodes, all right?
+
+There are 10,000 strings,
+which I wrote and erased.
+
+10,000 places to
+write a message to.
+
+There are 25 bytecodes
+to broadcast a message.
+
+OK, so that means that I
+can broadcast 400 messages.
+
+Is that right?
+
+Is that this number divided by
+that number equals that number?
+
+Is that-- Yeah, yeah.
+
+Yeah, let's go with it.
+
+Yeah, let's go with that.
+
+So you have 400.
+
+No, but maybe you have more of
+your robots jamming signals.
+
+OK, how many robots
+can you have?
+
+All right, let's do
+that computation.
+
+I'm pretending that I'm you,
+and that I'm just like-- OK
+
+I'm not doing a very
+good impersonation.
+
+I recognize that.
+
+You'd be much faster at this.
+
+So you would want to find
+out how many robots you
+
+can sustain.
+
+Can I get somebody to
+suggest one way to figure out
+
+that number?
+
+Yes!
+
+You, you, you.
+
+Ah yes you could make a
+player and just spawn robots
+
+until they start dying.
+
+Let's say you wanted to
+do it in a different way.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: I have
+the example here.
+
+What is It?
+
+Game constants, there we are.
+
+So here I'm looking
+at the Java docs,
+
+and I can click
+on game constants.
+
+I'm looking at a
+different version of it
+
+that didn't actually show the
+game constants in the game
+
+constants page.
+
+But that's because we
+are well organized.
+
+And this is to show that we're
+indomitable, indefatigable,
+
+as it were.
+
+These constant values
+indicate, here,
+
+that your headquarters
+is capable of producing
+
+quite a few resources.
+
+This shows that it produces
+50 resources per turn.
+
+This resource
+production enables you
+
+to have an upkeep of robots.
+
+So in the past, we've had
+names like flux, and so on.
+
+This year, the name
+for it is power.
+
+That's tough though because
+we have time as well.
+
+And as you well know power
+times time is energy.
+
+And so now we have
+energon and energy,
+
+which is a multiple or a
+calculated quantity from power.
+
+But don't you worry
+too much about it.
+
+It's just a number.
+
+And the usage of this
+resource, or power, by robots,
+
+is displayed in unit upkeep.
+
+Which here, is
+written incorrectly.
+
+I'm going to be
+bring up the most
+
+recent version of this document.
+
+What's nice is that you
+guys will get one version,
+
+and then you'll have one
+version on your computer
+
+and not, like, 16.
+
+And your one version
+will be up to date.
+
+And when you want to
+update it, the client
+
+will automatically tell
+you that it needs updating.
+
+So you'll just have
+the one version,
+
+and you won't have
+disaster area.
+
+Yeah, constant value.
+
+So this is the more
+recently updated one.
+
+And you can see here the
+unit power upkeep is one.
+
+All right, fantastic.
+
+We're ready to do a computation.
+
+So I'm going to
+put here 40 divided
+
+by-- so this is the
+amount of energy,
+
+or the amount of
+power, that's produced
+
+per turn by your
+headquarters divided
+
+by the usage of that power.
+
+Now you're going to say,
+all right, I'm bored.
+
+I can do this in my head.
+
+Well maybe you can but some
+of us can't, all right?
+
+No, so that would be the number.
+
+But that would say that the
+number of robots you get
+
+is independent of how
+much work they're doing.
+
+And that doesn't make any sense.
+
+You should get to
+have more robots
+
+if you're doing
+less computation.
+
+So here you can see,
+there is a cost.
+
+Power cost per
+bytecode, which is here.
+
+And it's 10 to the minus 4.
+
+So let's say that I'm
+using-- 10 to the minus 4
+
+times the number bytecodes.
+
+Well, if I'm using zero
+byte codes, then I get 40.
+
+Because that would be 1 plus 0.
+
+And 40 over one is 40.
+
+OK and if I were
+using 10,000, which
+
+is also known as 10 to the 4.
+
+Then I would get 20.
+
+Wow, what a big difference.
+
+So that tells you that if
+you want to go ahead and spam
+
+the message system--
+let's say you're spamming,
+
+so you're using all of
+your bytecodes possible,
+
+and you have 20 robots.
+
+So 20 robots are spamming 400
+message integers per turn.
+
+So you're doing nothing
+but spamming the messages.
+
+And you're getting eight,
+zero, zero, ze-- Oh, ahh, ahh.
+
+Oh, it's not even enough.
+
+It's not enough.
+
+Well, so that shows that
+you could jam the enemy.
+
+And maybe you should, if you've
+got nothing better to do,
+
+if you derive a personal
+satisfaction from it.
+
+But this is worth saying.
+
+These kinds of calculations
+are important for strategy.
+
+But don't make them
+totally fixed in stone.
+
+Because we change
+the game, we tweak
+
+it a little bit for balance.
+
+So if it ends up being that
+10,000 is just so much radio
+
+space that we just would
+rather not have it,
+
+then it could just get
+knocked down to 1000.
+
+And then all of a sudden
+your player, which
+
+depends on this or that
+messaging construct,
+
+may have to be
+somewhat rethought.
+
+So this is a good time to
+talk about the organization
+
+of the competition.
+
+Is it?
+
+I think it is.
+
+Let's go to the
+Battlecode website.
+
+And let me show you something.
+
+I don't know I knew
+that you could do this.
+
+But previous years
+we've had like a list.
+
+And it'll be in
+text form, and it'll
+
+say on this date we have this
+competition, and this one.
+
+And then you have to
+open up a window of this.
+
+And then every single
+one of you opens up
+
+another window with
+Gmail or Google Calendar.
+
+And then you like manually enter
+in the-- do you not do that?
+
+Who has to do that whenever
+you have a competition,
+
+you want to know
+when things are?
+
+Yeah, yeah there's
+like two people who
+
+also have to do that.
+
+So I figured, in light of saving
+those two people some effort,
+
+we made this Google Calendar.
+
+And you could see, here's
+today's classroom session,
+
+here in 1-190 from
+5:00 to 6:00 PM.
+
+And it's got the
+lab written there.
+
+So the specs and software are
+released, as of 37 minutes ago,
+
+roughly speaking.
+
+And what we'll
+do, after this, is
+
+we'll talk about
+how to set it up.
+
+So there you go, specs
+and software are released.
+
+The sprint tournament
+is on the 14th.
+
+And what that means is you
+can submit a player for that,
+
+and you can be entered for a
+relatively small prize pool.
+
+Relatively small,
+the actual prize
+
+pool for the finals
+is I think $50,000.
+
+So relatively small
+is just some fraction
+
+of that which is
+still non-negligible.
+
+Anyway, so that's going to be
+really exciting because that
+
+will give you the opportunity
+to test your code out
+
+to see what other players
+are doing, because to
+
+some extent winning
+is going to be
+
+related to what other people do.
+
+But more importantly,
+having fun is
+
+related to what other
+people do, and talking
+
+to the other people.
+
+Like this social utopia of
+mine, the idea of this lab,
+
+is totally new-- as well
+as the Google Calendar
+
+--to try to make things more
+easy and fun and together,
+
+among us as Battlecoders.
+
+Because we do all
+share that common link.
+
+Yes.
+
+So the point is
+that if you didn't
+
+know you could do
+this, what you do
+
+is you go to-- if you want to
+add this to your own calendar,
+
+there's like a button where
+you can go and do that.
+
+I think the button isn't
+available because-- Yeah,
+
+there.
+
+There?
+
+At the bottom.
+
+At the bottom?
+
+Yeah, there you go.
+
+And then you just
+add it right in,
+
+so I've already got it here,
+in my personal calendar.
+
+And there you go, so
+you can see that I'm
+
+having lunch on the 24th.
+
+And OK, so you get the idea.
+
+So the sprint tournament
+is-- the submission deadline,
+
+you can see here,
+is on the 14th.
+
+On the 16th, on that
+Wednesday, in class,
+
+we'll show some of the games
+from the sprint tournament.
+
+I don't think we'll
+show all of them.
+
+See because what used to happen,
+is we would show all the games.
+
+And there's like 100 teams.
+
+And that ends up being
+a relatively large size
+
+round-robin bracket with, I
+think, double elimination.
+
+So it's a ton of games.
+
+I think it generally
+takes like five hours.
+
+But it ends up bumping up to
+six, seven, or eight hours
+
+because we end up
+showing up there,
+
+and the tournament code that
+sets it all up doesn't work.
+
+And so it takes forever.
+
+So we're going to
+do this year is
+
+we'll just sort to
+distill it down,
+
+we'll have something
+simple to show
+
+that's fantastic and
+exciting on the Wednesday.
+
+And in the future, when we
+have our later-- our seating
+
+tournament, which is sort
+of the same kind of thing,
+
+but it's more important, because
+it determines your positioning
+
+for the final tournament.
+
+When we have this
+seating tournament,
+
+we're going to live
+stream it on the internet,
+
+so that you don't
+even have to-- I mean,
+
+you guys all trekked out
+here in the dead of night
+
+and 5:00 or 6:00 PM
+in the freezing cold.
+
+I mean there could be people out
+there dying because they tried
+
+to make it here and
+they didn't make it.
+
+That would be horrible, that's
+not something to laugh at.
+
+So you came all
+the way out here,
+
+but we don't want to make you
+have to do that much work.
+
+Because we want you to have fun.
+
+So there you go.
+
+We've got a calendar to
+save you that effort.
+
+We have lab sessions to save
+you the effort of trying
+
+to make friends, and
+we'll have live streams
+
+in the future, which will
+make that much better.
+
+So as you can see here, it
+says the seating tournament
+
+submission deadline
+is on the 21st.
+
+And the seating tournament
+will be on the 22nd.
+
+So what that does, is it gets
+you your position in the finals
+
+tournament.
+
+The finals submission
+deadline is different, though.
+
+So you can continually
+update your player.
+
+My point is that you
+only have three weeks.
+
+It's the 7th today.
+
+And the finals submission
+deadline is the 28th.
+
+You have three weeks to
+make an amazing player.
+
+And each week, you'll
+have the chance
+
+to-- you could upload
+your player at any time,
+
+you can do scrimmage matches
+with other players at any time.
+
+And then finally, you'll be
+able to submit to the finals.
+
+I mean, I don't think it's
+worth getting too hyped up
+
+about this final thing because
+after all, in my experience,
+
+game changes at the last minute
+screw you over at the finals,
+
+and ends up being a crap shoot.
+
+No, no, I exaggerate.
+
+But the point is, the fun
+should be had as you go.
+
+And I am here to help with that.
+
+So what you need--
+so just one more
+
+thing about this
+administration is
+
+that I think that it's required
+that you upload a resume,
+
+and that you be an MIT student
+if you want to earn-- no,
+
+that's not right.
+
+We have international
+competitors, this year.
+
+We have sort of a thing going on
+with the University of Sussex.
+
+If you have friends
+at other universities,
+
+they can feel free to join you.
+
+And they don't have
+to be MIT students
+
+to either play or win money.
+
+And if they're in
+Honolulu, or Alaska,
+
+we'll fly them in
+here for the finals
+
+because we expect the finalists
+to show up at this dinner
+
+that we have at the Hyatt.
+
+We have this fantastically
+lavish dinner.
+
+I think we paid
+like $5,000 for it.
+
+Aaron, could you
+come up here and show
+
+what the sponsors
+are by just turning
+
+your back to the audience?
+
+No, actually there's a
+button here, I can do that.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah,
+that's a good point.
+
+OK, so here are our sponsors.
+
+We have these fancy company
+reps show up at this dinner.
+
+So if you're among
+the finalists,
+
+then you show up at
+the fancy reps dinner
+
+and they offer you
+jobs and stuff.
+
+It's apparently very
+nice, I've never been.
+
+AUDIENCE: [AUDIENCE LAUGHTER]
+
+Yeah, that's because I was busy.
+
+Yeah, that's why.
+
+Yeah, that's why.
+
+That's why.
+
+No.
+
+So these are some
+of the sponsors.
+
+Our main sponsors
+and some other ones.
+
+And you'll get a chance to meet
+them, as well, at the finals.
+
+So you don't have to be the best
+of the best by whatever stupid
+
+metric we come up with.
+
+What you have to
+be is-- anybody who
+
+does Battlecode is an attractive
+person to these employers who
+
+will meet you and give
+you business cards.
+
+And it'll be a good
+time for everyone.
+
+And so in that note
+you have, once again,
+
+on the calendar page, the finals
+are on the 2nd of February.
+
+So that'll be when that
+happens and it'll be in 26-100.
+
+It'll be a blast, and you
+should be looking forward
+
+to that very much.
+
+I feel like I've
+just been droning on,
+
+ranting about what I don't
+like about StarCraft.
+
+And I haven't talked enough
+about the things that
+
+are related to
+gameplay this year.
+
+This year, you
+have these robots.
+
+It's astounding to me, that I--
+Oh, is that why it didn't work?
+
+Because I was using this
+one instead of this one,
+
+and I meant to use
+this main client?
+
+Yeah, that's the one.
+
+OK, yeah.
+
+This was the point I was
+trying to make earlier.
+
+Where I was going to
+take compute time bot,
+
+playing against compute
+time bot, on this map.
+
+This is sort of how
+to do it, but it'll
+
+be done a little
+bit differently.
+
+And so the goal here is to see
+how many robots can be built.
+
+But this guy-- Ah!
+
+I think team A and
+B got switched.
+
+So what I'll do is I'll just
+briefly switch around the code.
+
+So this is sort of the
+structure of a robot controller.
+
+What happens is this code is
+run on each robot on your team,
+
+and that's what plays the game.
+
+I'm sure most of you
+know that already.
+
+And so what I'll do is I'll
+just check that the team is B.
+
+So I can switch the team,
+hit Save, run it again.
+
+Well it doesn't
+work as well as I
+
+was expecting because
+these guys are just
+
+dying when they go
+through the minefield.
+
+That's interesting.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: You know, you can
+make your own maps in this.
+
+This is a really good
+example of debugging.
+
+And you can say that
+I did this on purpose.
+
+Although if you have a
+strict adherence to honesty,
+
+you might not.
+
+So the maps are located where?
+
+You're looking at what, here?
+
+So you'll have a directory
+where you can see your maps.
+
+And you'll be also
+able to see them here.
+
+So here's simple.
+
+And what if I want
+to edit this map.
+
+Can I do that?
+
+Can I just double click it?
+
+It's an XML document.
+
+Oh, look.
+
+Is it?
+
+Oh, data, OK.
+
+Here's some data.
+
+I'm beginning to get
+to the part-- see,
+
+this would be really
+easy if I could just
+
+do edit with notepad.
+
+AUDIENCE: --source at the bottom
+
+PROFESSOR: Source!
+
+No.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Tab.
+
+AUDIENCE: No, down.
+
+PROFESSOR: Down?
+
+Down.
+
+AUDIENCE: Where design is.
+
+PROFESSOR: Oh!
+
+Bingo.
+
+All right!
+
+Yeah, thank you.
+
+So then, you can
+see that I can make
+
+my own maps using these codes.
+
+So the character "3"
+indicates a neutral mine.
+
+So I can just do like a find
+replace, were I'll replace "3"
+
+with ".", which is
+an open terrain.
+
+I'll just do replace all.
+
+And then I'll just
+make sure to change
+
+this one or else the
+whole map would be mines.
+
+I'm sure two of you thought
+that I wouldn't do that,
+
+but I assure you that I'm
+operating at full capacity.
+
+All right, so this is an
+example where you can see I've
+
+just built bunch of robots.
+
+And you can see that
+this is my power.
+
+Your power stored
+in a reserve bank.
+
+And what I'm going to do
+is suddenly at round 1,000,
+
+I'm going to start
+computing a lot.
+
+So right now you can
+see that this robot
+
+is using 38 bytecodes.
+
+Not very many.
+
+If you're amazing
+at counting you'll
+
+see that there
+are about 40 here.
+
+And the new robots-- oh, boom!
+
+Look at that.
+
+The new robots died because they
+don't have enough-- these guys
+
+don't have enough compute-- they
+don't have enough power to run.
+
+So they lose hit points
+until they're dead.
+
+And then if they all
+start using code,
+
+boom, when we cut down
+to half the number.
+
+And so you could
+see quite visually
+
+the effect of using 10,000
+bytecodes versus using
+
+no bytecodes at all.
+
+So from here, down to there.
+
+Bang.
+
+This power quantity can be
+affected by various things.
+
+So there are some equations that
+I could show for what that is.
+
+But maybe I've just gone
+a bit far field here
+
+because I've been talking
+about some details.
+
+Here's the general
+overview, right?
+
+You don't really need too
+many of the specifics,
+
+because all you've got
+to do is find the enemy.
+
+And there's a function
+that does that.
+
+Oh, look at that, I'll just
+add that to the global list.
+
+There's, "Sense Enemy
+Headquarters," bingo.
+
+Done.
+
+If you were interested in
+a little bit of masochism,
+
+coding masochism, and just
+doing something the hard way,
+
+you could do that.
+
+Because what we've
+also provided,
+
+is the dimensions
+of the map, and you
+
+know that the upper left
+corner of the map is 0,0.
+
+So with a symmetry
+operation you could say,
+
+my headquarters is here.
+
+The map size is this.
+
+My location is here.
+
+Therefore, the enemy must
+be at this other location.
+
+So more than one way to skin
+a cat, as the case may be.
+
+So you locate the enemy,
+and all you have to do
+
+is walk up to him.
+
+Because this year attacking
+happens automatically
+
+for soldiers.
+
+So right now there isn't
+any fighting going on.
+
+But I'll show an
+example that will
+
+show that all they've got to
+do is go near one another,
+
+and then their attack
+power is distributed
+
+among all of the
+robots they can see.
+
+So this is some old
+code that we were
+
+writing when we were
+testing the game.
+
+And what you'll
+find is that when
+
+robots come close
+to one another,
+
+they make these circles that
+indicate their attack range.
+
+So they're attacking-- this
+guy is distributing his attack
+
+among this one and that one.
+
+Similarly, this one is
+distributing among these three.
+
+So his attack power in
+this version of the game
+
+was different.
+
+But right now I believe
+the attack power is six.
+
+So he would be dealing two
+damage to each of these.
+
+What you also see in
+this picture, which
+
+I believe is quite instructive,
+is the shield robots.
+
+Yeah, any robot that's standing
+next to this shields robot
+
+will be given this
+additional shields parameter.
+
+And so you can see it here
+in the user interface.
+
+There's a green bar
+indicating health,
+
+and a blue bar
+indicating shields.
+
+In the latest implementation
+of Battlecode,
+
+shields serve as
+a protection only
+
+against a certain type of
+encampment that can be built.
+
+So is these encampments
+work in the following way.
+
+You start with just
+a headquarters,
+
+and that produces
+these soldiers.
+
+So you can produce a soldier
+at any tile around you,
+
+if that tile is unoccupied.
+
+That soldier can then be used
+to construct an encampment.
+
+And he can construct any of a
+number of types of encampment.
+
+So I've made this nice, handy,
+useful Battlecode data sheet.
+
+People from last
+year might remember
+
+that I made sort of a handy
+unit sheet at that time.
+
+But this year it's 100% more
+accurate than last year's.
+
+That's right.
+
+We've checked and
+double checked,
+
+but this is the latest version.
+
+So you can see here all of
+the different types of units.
+
+And there's a Boolean for
+whether it is an encampment,
+
+in terms of just a description.
+
+Although, you know, that's kind
+of not a fantastic description.
+
+Because all of these
+units-- you know,
+
+because we like to
+be straightforward.
+
+It's a realistic
+preparation for your life
+
+as a professional coder, that
+the database and documentation
+
+you receive will contain
+information opposite to the way
+
+that things are run.
+
+So you can see here that they're
+all listed-- some of these
+
+are listed as encampments.
+
+But in fact they are all robots.
+
+Yes, I believe that's correct.
+
+They are all robots.
+
+So the headquarters is
+what you start with.
+
+It generates 40 power turn, and
+it can spawn these soldiers.
+
+It takes 10 turns
+to spawn a soldier.
+
+Or it can research upgrades,
+and I'll talk about the upgrades
+
+below, in just a minute.
+
+The soldier has an upkeep
+of 1 to 2 power per turn,
+
+depending on byte code usage.
+
+It automatically
+distributes its attack power
+
+among adjacent enemy units.
+
+And it has the
+capability of laying
+
+mines, which take 25
+turns to lay a mine.
+
+Defusing mines, which take
+5 turns, and capturing
+
+encampments, which
+takes 50 turns.
+
+Now you might ask,
+all right, where
+
+am I getting these numbers?
+
+I'm assembling this
+sort of convenient
+
+diagram but what if
+the specs change?
+
+You know, where do
+I get these numbers?
+
+Well they're all under game
+constants under robot type
+
+enum, or the upgrade
+enum, and you'll
+
+find them all the Java docs.
+
+Alternatively, you
+could all always
+
+ask us where they are by
+going on our IRC chat,
+
+or talking to one
+of us in person.
+
+So you can see here they're
+laying mines, defusing mines,
+
+capturing encampments.
+
+And in the act of capturing
+one of these encampments, which
+
+is a pre-existing location on
+the map, these black circles.
+
+In the act of capturing
+one of those--
+
+there's nothing
+magical about it.
+
+Because here, among the
+robot controller methods,
+
+you'll find capture encampment.
+
+And what you'll do is
+you'll specify what type
+
+of enchantment
+you want it to be.
+
+And you might ask,
+what types are there?
+
+Well, you could either
+look at handy chart,
+
+or you could click
+here, under robot type.
+
+And this enum robot type
+will show you the types
+
+that you can build.
+
+You can build artillery,
+generator, medbay, shields,
+
+and supplier.
+
+The headquarters and
+soldier are different.
+
+They're not built
+from encampments.
+
+I don't know if that's written
+anywhere, but I've said it,
+
+so now you know it.
+
+Yeah.
+
+So that's how you're going to be
+able to build these units, that
+
+are shown here.
+
+So the medbay heals adjacent
+robots, 2 hit points per turn.
+
+You can see that's their quote,
+"attack power," because attack
+
+is a lot like healing.
+
+You know, modern surgery,
+you can use scalpel and such.
+
+These are also
+considered weapons.
+
+I'm sure you couldn't
+bring a scalpel on a plane.
+
+So attack is a really good word
+for healing-- a healing unit.
+
+And if you don't believe me talk
+to any medicine man you know.
+
+Shields will give
+all adjacent robots
+
+5 shield points per turn.
+
+So if you cluster 8
+units around them,
+
+then that'll go ahead and give
+40 shield points distributed
+
+among them, to the extent
+that 5 times 8 is 40.
+
+The shields only protect
+you from artillery, though.
+
+They don't protect you
+against other soldiers.
+
+Now, these robots
+that are shielded
+
+will lose 1 shield point
+per turn, as it wears off.
+
+But there's no cap on the
+amount of shields they can have.
+
+So they can have, I think,
+10 to the 8th shields.
+
+Which is like a lot more than
+their total hit points of 40.
+
+Right?
+
+So that's effectively infinite.
+
+The artillery is the one unit
+that can shoot at a far range.
+
+It could shoot at a range of 63.
+
+Now we always talk
+about squared ranges,
+
+because that makes it
+easier to do comparisons
+
+without having to
+take a square root.
+
+Although I guess if we
+did give you ranges,
+
+and not squared ranges, you
+could just square it and then
+
+compare it to the range that
+you had just calculated.
+
+this way works really well.
+
+So what I can do is I can
+demonstrate for you what that
+
+looks like by opening
+up-- oh my goodness,
+
+I'm almost out of time.
+
+I can open up this stockpiling--
+no, that's not right.
+
+I made it in the map
+maker program, down here.
+
+Yeah, so this shows
+you what 63 looks like.
+
+So if you're here in the middle,
+you can see all of these tiles
+
+but you can't see
+the ones outside.
+
+But its site range is only 14.
+
+Every robot has a site range
+of 14, As you can see here,
+
+in this document.
+
+So the attack range is
+63, the site range is 14.
+
+So, this is one of
+those cases where
+
+you'd need scouting units that
+would know what to shoot at.
+
+And it's really helpful that you
+have this global information.
+
+Because you don't
+need to post to radio
+
+to tell the artillery
+what to shoot at.
+
+Because he can already
+see all of the unit
+
+that your allies can see.
+
+He can't necessarily
+see the enemies,
+
+unless your guys are nearby.
+
+So, yes, the artillery does
+40 damage to the target
+
+that it specifies, and 20
+splash damage to adjacent tiles.
+
+And that does include
+friendly fire,
+
+so you've got to be careful
+about where you shoot.
+
+The generator generates
+10 resources per turn.
+
+And that resource is power.
+
+So that's added on to
+your headquarter power.
+
+So if you build a
+bunch of generators,
+
+you can support more soldiers.
+
+And finally, the
+supplier will reduce
+
+the build time for
+soldiers by 5%.
+
+And that's multiplicative.
+
+So if you have two
+suppliers, then it's
+
+0.95 squared times 10 turns.
+
+This year, we give
+you the opportunity
+
+of building upgrades as
+well, researching upgrades
+
+at your headquarters.
+
+So your headquarters
+is your central unit,
+
+the goal is to defeat
+the enemy headquarters.
+
+To do that, you could just
+walk your robots on over
+
+and kill them dead.
+
+It's not required that
+you research upgrades
+
+and built encampments.
+
+And that's one of
+the ways that we
+
+make the competition
+somewhat easier to enter,
+
+easier to get
+something that works.
+
+But if you want to
+research upgrades,
+
+to make a strategy
+that's tailored
+
+around a certain approach,
+then you can get these.
+
+The future upgrade
+reduces your energy decay
+
+because the way
+that you hold power,
+
+is that you can't just
+mass it up indefinitely.
+
+You get a power income
+from your headquarters,
+
+and you spend power to
+upkeep your soldiers.
+
+But we don't want that--
+if you have no soldiers
+
+and you're just
+getting income, we
+
+don't want that to
+go up indefinitely.
+
+So every turn that
+gets multiplied
+
+by a number that reduces it.
+
+So the energy decay,
+or the loss is 20%.
+
+But if you research fusion,
+the loss is only 1%.
+
+So then you might think
+of stockpiling energy
+
+and then spending it all
+at once to get a larger
+
+burst of robots, which couldn't
+be sustained for a long time.
+
+But then again, you only
+have to win one second.
+
+Finally, the-- OK, so then
+there's more upgrades.
+
+Vision upgrade extends your
+squared vision from 10 to 32.
+
+This should say 14, but
+as you know everything
+
+is always up to date
+100 percent of the time.
+
+So here's a demonstration of
+what that would look like.
+
+Here's 10 and here's 32.
+
+Boom, what a big difference.
+
+That's quite a lot more vision.
+
+That's important because
+you can defuse any mine
+
+within your site range if you
+have the diffusion ability.
+
+Which is not to be confused
+with chemical diffusion, which
+
+is something else.
+
+Yes, this is for
+defusing things,
+
+and it is spelled correctly.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: So yeah, that extends
+your mine defusing range.
+
+That's pretty important,
+but keep in mind
+
+that you can still only
+defuse one at a time.
+
+So you have to select which
+one you're going to defuse.
+
+And then you defuse that.
+
+Now, it's important
+to note that you
+
+can see where-- I've said that
+you see your allied mines.
+
+I haven't said that you can
+see your neutral mines as well.
+
+But you don't see enemy mines
+until one of your robots
+
+has stepped on it.
+
+So that means that you can't--
+I don't think you can defuse
+
+something you can't see.
+
+But actually I don't know,
+I'll have to check with that.
+
+Because it may be that
+you could just spam
+
+defuse on terrain
+that you don't know.
+
+And that might actually defuse
+things that you can't see.
+
+At the same time, that's
+not a fantastic strategy,
+
+because defused takes 5 turns.
+
+And during those 5
+turns you cannot attack.
+
+So that leaves you--
+or can you attack?
+
+I'm thinking maybe
+you can attack.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: You know what, you
+can't-- it's a very vulnerable
+
+position, to be
+defusing something.
+
+Because you're concentrating
+on something else.
+
+How do you going to
+perform as effectively
+
+on a different task?
+
+Pickaxe is the tool
+that you really
+
+need if you want to
+lay a ton of mines.
+
+Because instead of laying just
+one mine, where your robot is--
+
+I guess I'm going
+to have to come up
+
+with a system for
+describing robot--
+
+that's sort of like a robot.
+
+Maybe it's a Chinese character.
+
+So that's a robot,
+and ordinarily he
+
+would lay a mine here,
+but if you have pickaxe,
+
+he will lay mines in
+all of these positions
+
+for the same cost of
+laying just one mine.
+
+Pretty useful to have.
+
+And it takes the same amount.
+
+So laying a mine cost
+25 rounds, defusing
+
+a mine costs five rounds.
+
+So you could do the math.
+
+If you have pickaxe,
+you could lay them
+
+as fast as the other
+team can defuse them,
+
+provided you can get into an
+open space where you can do it.
+
+Realistically they might be
+able to encroach, and get you
+
+during that time.
+
+And why do you
+want to lay mines?
+
+Doesn't that slow the game down?
+
+Doesn't that mean
+that things will just
+
+move to slowly, make it
+a boring thing to watch?
+
+I would say no, because
+during that time
+
+you could be researching
+the nuclear missile.
+
+That's right.
+
+That's right, we
+knew that it would
+
+be interesting to watch
+players build nuclear missiles.
+
+If you research that,
+you win immediately.
+
+So--
+
+[AUDIENCE LAUGHTER]
+
+That's yet another
+fun way to win,
+
+and I'm going to show you an
+example of somebody attempting
+
+to win that way.
+
+This will only take as
+much time as it took me
+
+the last time I tried to do it.
+
+It's under-- golly, you won't
+have nearly-- oh, it's right
+
+here.
+
+It must be so hard to watch
+me, because it's like, oh man,
+
+he's looking right at it.
+
+Let's see, so let's
+put do nothing bot--
+
+because that's a decent
+match for the nuke bot.
+
+Where is he?
+
+Is he not here?
+
+AUDIENCE: No, he's
+in the middle.
+
+PROFESSOR: He's in the middle.
+
+Oh, I'm looking right at him.
+
+All right.
+
+All right, well it's by no
+means a foregone conclusion
+
+who wins this match.
+
+This is an old version
+of the code where
+
+nuking took 1,000 turns
+instead of 400 turns.
+
+But that's not to say that
+the red team will necessarily
+
+win on turn 1,000.
+
+Oh wait.
+
+It could only take 400
+turns wait a minute.
+
+Oh, that's 1,000 and
+this was-- OK yeah, hey!
+
+It happened.
+
+There you go.
+
+So yeah, the nuclear
+missile has-- I mean,
+
+it's not a very
+impressive graphic.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: It's
+technically the same one
+
+we use for every
+other explosion.
+
+[AUDIENCE LAUGHTER]
+
+PROFESSOR: But I think what
+we'll do is for the finals,
+
+we've got a new
+match visualizer.
+
+So this was an old
+version of the code,
+
+because of course I wouldn't
+show you something up to date.
+
+That would be that help
+you instead of hinder you.
+
+And what we're trying to do
+is train you to be amazing.
+
+And it's working, I swear.
+
+So what I'll do is I'll show
+this version of it, which
+
+is great, because it shows
+the thing researching.
+
+All right, well later
+versions of the client
+
+that you're going
+to receive will
+
+show what things are researching
+in the client window.
+
+And I think it really would
+not be in an excessive--
+
+the pizza should be
+arriving any moment,
+
+so I know that the
+gurgling of your stomachs
+
+is totally reasonable and
+will be resolved imminently.
+
+If I run this version,
+then I think-- let's see,
+
+is there-- so let's put do
+nothing against the nuke guy.
+
+Is the nuke guy still there?
+
+He is, OK.
+
+So this version of
+the map viewer shows
+
+researches that are going on.
+
+Yeah.
+
+And you can see he's researching
+pickaxe, diffusion, sight
+
+range, the fusion
+thing that reduces
+
+the amount of energy loss.
+
+He's researching everything.
+
+And whereas the other do
+nothing guy-- you know,
+
+you could describe
+him as a pacifist.
+
+The philosophy that
+he is developing,
+
+using three bytecodes per
+round, may change the world.
+
+So I see no reason to hate
+on his choice of vocation.
+
+I would definitely not--
+yeah, no, definitely.
+
+OK.
+
+So you can see here that
+nuke is researching.
+
+So in a tournament
+scenario we could all
+
+start getting excited
+and going ohhhhh!
+
+What's going to happen?
+
+Is it going to be close?
+
+And that sort of thing.
+
+I mean of course at
+the end it's going
+
+to be a bit of an
+anti-climax because it's
+
+going to show a
+little puff ball,
+
+like somebody made
+popcorn on one tile.
+
+But we'll be able to overcome
+that because we can just
+
+switch to YouTube
+and show a clip
+
+of some giant nuclear test.
+
+All right, that's all
+I have for you now.
+
+I mean to say that
+we're going to show
+
+you a whole bunch of things.
+
+You can get up and go,
+I know a lot of you
+
+have appointments with very
+attractive young women and men.
+
+And that's totally OK.
+
+But I recommend that you
+stick around, eat some pizza,
+
+hear about how to
+set up Battlecode.
+
+And know that we will have
+our developer testing code up.
+
+The team name, here on
+the Battlecode website.
+
+You can see here, team list.
+
+We just made a team that you can
+use to test your code against.
+
+That's down here at the bottom.
+
+It's test, somewhere.
+
+Yeah, Teh Devs
+Test, there you go.
+
+Did you guys make this many
+teams in the last 2 seconds?
+
+You must have.
+
+You know, it's
+important to multitask.
+
+Yeah, so you can
+upload your player
+
+and test it against
+Teh Devs test player.
+
+And that'll be
+available all the time,
+
+and that's probably
+sort of your first step
+
+on your road to success.
+
+Thank you very much for coming,
+and if you have any questions
+
+you can come to us after.
+
+[APPLAUSE]
\ No newline at end of file
diff --git a/BLb0l_K0MWM.txt b/BLb0l_K0MWM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..290afbdfe38f2ed44b06169327402eeae2aab1c9
--- /dev/null
+++ b/BLb0l_K0MWM.txt
@@ -0,0 +1,14811 @@
+align:start position:0%
+ 
+all right so welcome back been a bit of
+
+ align:start position:0%
+all right so welcome back been a bit of
+ 
+
+ align:start position:0%
+all right so welcome back been a bit of
+a break um you may yes exactly why are
+
+ align:start position:0%
+a break um you may yes exactly why are
+ 
+
+ align:start position:0%
+a break um you may yes exactly why are
+we here what are we doing with our lives
+
+ align:start position:0%
+we here what are we doing with our lives
+ 
+
+ align:start position:0%
+we here what are we doing with our lives
+we're learning about plasma Diagnostic
+
+ align:start position:0%
+we're learning about plasma Diagnostic
+ 
+
+ align:start position:0%
+we're learning about plasma Diagnostic
+and you may remember before uh we went
+
+ align:start position:0%
+and you may remember before uh we went
+ 
+
+ align:start position:0%
+and you may remember before uh we went
+away uh we spent a very enjoyable
+
+ align:start position:0%
+away uh we spent a very enjoyable
+ 
+
+ align:start position:0%
+away uh we spent a very enjoyable
+lecture drawing all sorts of diagrams
+
+ align:start position:0%
+lecture drawing all sorts of diagrams
+ 
+
+ align:start position:0%
+lecture drawing all sorts of diagrams
+like this where we had some energy
+
+ align:start position:0%
+like this where we had some energy
+ 
+
+ align:start position:0%
+like this where we had some energy
+levels here maybe this is
+
+ align:start position:0%
+levels here maybe this is
+ 
+
+ align:start position:0%
+levels here maybe this is
+ionization energy level this is maybe
+
+ align:start position:0%
+ionization energy level this is maybe
+ 
+
+ align:start position:0%
+ionization energy level this is maybe
+some lower energy level and something
+
+ align:start position:0%
+some lower energy level and something
+ 
+
+ align:start position:0%
+some lower energy level and something
+happened photons were flying around
+
+ align:start position:0%
+happened photons were flying around
+ 
+
+ align:start position:0%
+happened photons were flying around
+electrons were flying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around and we said that if we want to
+
+ align:start position:0%
+around and we said that if we want to
+ 
+
+ align:start position:0%
+around and we said that if we want to
+understand what the ionization state is
+
+ align:start position:0%
+understand what the ionization state is
+ 
+
+ align:start position:0%
+understand what the ionization state is
+in our plasma and also the excitation
+
+ align:start position:0%
+in our plasma and also the excitation
+ 
+
+ align:start position:0%
+in our plasma and also the excitation
+state which would be if you have some
+
+ align:start position:0%
+state which would be if you have some
+ 
+
+ align:start position:0%
+state which would be if you have some
+intermediate level here which I guess
+
+ align:start position:0%
+intermediate level here which I guess
+ 
+
+ align:start position:0%
+intermediate level here which I guess
+I've already used I so I have to come up
+
+ align:start position:0%
+I've already used I so I have to come up
+ 
+
+ align:start position:0%
+I've already used I so I have to come up
+with some other notation for it m like
+
+ align:start position:0%
+with some other notation for it m like
+ 
+
+ align:start position:0%
+with some other notation for it m like
+that maybe we want to know how many
+
+ align:start position:0%
+that maybe we want to know how many
+ 
+
+ align:start position:0%
+that maybe we want to know how many
+electrons are in this intermediate level
+
+ align:start position:0%
+electrons are in this intermediate level
+ 
+
+ align:start position:0%
+electrons are in this intermediate level
+in the lower level in the upper level
+
+ align:start position:0%
+in the lower level in the upper level
+ 
+
+ align:start position:0%
+in the lower level in the upper level
+because at the end of the day in
+
+ align:start position:0%
+because at the end of the day in
+ 
+
+ align:start position:0%
+because at the end of the day in
+spectroscopy what we're detecting is
+
+ align:start position:0%
+spectroscopy what we're detecting is
+ 
+
+ align:start position:0%
+spectroscopy what we're detecting is
+photons which are being emitted and the
+
+ align:start position:0%
+photons which are being emitted and the
+ 
+
+ align:start position:0%
+photons which are being emitted and the
+photons are being emitted when an
+
+ align:start position:0%
+photons are being emitted when an
+ 
+
+ align:start position:0%
+photons are being emitted when an
+electron drops down either from being a
+
+ align:start position:0%
+electron drops down either from being a
+ 
+
+ align:start position:0%
+electron drops down either from being a
+free electron into a bound state or
+
+ align:start position:0%
+free electron into a bound state or
+ 
+
+ align:start position:0%
+free electron into a bound state or
+between two bound States and we went
+
+ align:start position:0%
+between two bound States and we went
+ 
+
+ align:start position:0%
+between two bound States and we went
+through all these processes and we said
+
+ align:start position:0%
+through all these processes and we said
+ 
+
+ align:start position:0%
+through all these processes and we said
+you know if we really want to understand
+
+ align:start position:0%
+you know if we really want to understand
+ 
+
+ align:start position:0%
+you know if we really want to understand
+the plasma we need to model all of these
+
+ align:start position:0%
+the plasma we need to model all of these
+ 
+
+ align:start position:0%
+the plasma we need to model all of these
+processes and obviously that's an awful
+
+ align:start position:0%
+processes and obviously that's an awful
+ 
+
+ align:start position:0%
+processes and obviously that's an awful
+lot so today I'm going to go through and
+
+ align:start position:0%
+lot so today I'm going to go through and
+ 
+
+ align:start position:0%
+lot so today I'm going to go through and
+I'm going to present present a some
+
+ align:start position:0%
+I'm going to present present a some
+ 
+
+ align:start position:0%
+I'm going to present present a some
+simplified equilibria in which we do not
+
+ align:start position:0%
+simplified equilibria in which we do not
+ 
+
+ align:start position:0%
+simplified equilibria in which we do not
+need to include all of these processes
+
+ align:start position:0%
+need to include all of these processes
+ 
+
+ align:start position:0%
+need to include all of these processes
+and these are the equilibria which we
+
+ align:start position:0%
+and these are the equilibria which we
+ 
+
+ align:start position:0%
+and these are the equilibria which we
+tend to have a better chance of modeling
+
+ align:start position:0%
+tend to have a better chance of modeling
+ 
+
+ align:start position:0%
+tend to have a better chance of modeling
+and youone remember what this process
+
+ align:start position:0%
+and youone remember what this process
+ 
+
+ align:start position:0%
+and youone remember what this process
+was called here this is my personal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+favorite when you have two electrons in
+
+ align:start position:0%
+favorite when you have two electrons in
+ 
+
+ align:start position:0%
+favorite when you have two electrons in
+an excited state uh and one of them
+
+ align:start position:0%
+an excited state uh and one of them
+ 
+
+ align:start position:0%
+an excited state uh and one of them
+drops down and that provides enough
+
+ align:start position:0%
+drops down and that provides enough
+ 
+
+ align:start position:0%
+drops down and that provides enough
+energy for the other electron to ionize
+
+ align:start position:0%
+energy for the other electron to ionize
+ 
+
+ align:start position:0%
+energy for the other electron to ionize
+itself Auto ionization yes absolute
+
+ align:start position:0%
+itself Auto ionization yes absolute
+ 
+
+ align:start position:0%
+itself Auto ionization yes absolute
+favorite it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crazy okay good stuff so now let's go
+
+ align:start position:0%
+crazy okay good stuff so now let's go
+ 
+
+ align:start position:0%
+crazy okay good stuff so now let's go
+through some equilibria most of which do
+
+ align:start position:0%
+through some equilibria most of which do
+ 
+
+ align:start position:0%
+through some equilibria most of which do
+not involve Auto
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ionization and the reference for all of
+
+ align:start position:0%
+ionization and the reference for all of
+ 
+
+ align:start position:0%
+ionization and the reference for all of
+this um there are many textbooks on
+
+ align:start position:0%
+this um there are many textbooks on
+ 
+
+ align:start position:0%
+this um there are many textbooks on
+plasma spectroscopy a very famous
+
+ align:start position:0%
+plasma spectroscopy a very famous
+ 
+
+ align:start position:0%
+plasma spectroscopy a very famous
+textbook is green that's the name of the
+
+ align:start position:0%
+textbook is green that's the name of the
+ 
+
+ align:start position:0%
+textbook is green that's the name of the
+orer and the title of the book is plasma
+
+ align:start position:0%
+orer and the title of the book is plasma
+ 
+
+ align:start position:0%
+orer and the title of the book is plasma
+spectroscopy gream is not actually a
+
+ align:start position:0%
+spectroscopy gream is not actually a
+ 
+
+ align:start position:0%
+spectroscopy gream is not actually a
+particularly good book for learning
+
+ align:start position:0%
+particularly good book for learning
+ 
+
+ align:start position:0%
+particularly good book for learning
+spectroscopy it's a pretty good
+
+ align:start position:0%
+spectroscopy it's a pretty good
+ 
+
+ align:start position:0%
+spectroscopy it's a pretty good
+reference uh but you will find all this
+
+ align:start position:0%
+reference uh but you will find all this
+ 
+
+ align:start position:0%
+reference uh but you will find all this
+stuff in here if you want to know more
+
+ align:start position:0%
+stuff in here if you want to know more
+ 
+
+ align:start position:0%
+stuff in here if you want to know more
+Hutchinson has some of it uh in a
+
+ align:start position:0%
+Hutchinson has some of it uh in a
+ 
+
+ align:start position:0%
+Hutchinson has some of it uh in a
+slightly more fragmented fashion so I've
+
+ align:start position:0%
+slightly more fragmented fashion so I've
+ 
+
+ align:start position:0%
+slightly more fragmented fashion so I've
+been taking most of this from
+
+ align:start position:0%
+been taking most of this from
+ 
+
+ align:start position:0%
+been taking most of this from
+Green so the most simple
+
+ align:start position:0%
+Green so the most simple
+ 
+
+ align:start position:0%
+Green so the most simple
+equilibrium is an equilibrium where
+
+ align:start position:0%
+equilibrium is an equilibrium where
+ 
+
+ align:start position:0%
+equilibrium is an equilibrium where
+we're in complete thermodynamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium if we're we're in a
+
+ align:start position:0%
+equilibrium if we're we're in a
+ 
+
+ align:start position:0%
+equilibrium if we're we're in a
+thermodynamic equilibrium this implies
+
+ align:start position:0%
+thermodynamic equilibrium this implies
+ 
+
+ align:start position:0%
+thermodynamic equilibrium this implies
+straight away that we have a boltzman
+
+ align:start position:0%
+straight away that we have a boltzman
+ 
+
+ align:start position:0%
+straight away that we have a boltzman
+occupation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+States so our boltzman occupation of
+
+ align:start position:0%
+States so our boltzman occupation of
+ 
+
+ align:start position:0%
+States so our boltzman occupation of
+states is something like the occupation
+
+ align:start position:0%
+states is something like the occupation
+ 
+
+ align:start position:0%
+states is something like the occupation
+of the I State whether that's an
+
+ align:start position:0%
+of the I State whether that's an
+ 
+
+ align:start position:0%
+of the I State whether that's an
+ionization state or it's an excited
+
+ align:start position:0%
+ionization state or it's an excited
+ 
+
+ align:start position:0%
+ionization state or it's an excited
+state within an ion is proportional to
+
+ align:start position:0%
+state within an ion is proportional to
+ 
+
+ align:start position:0%
+state within an ion is proportional to
+exponential of minus the energy of that
+
+ align:start position:0%
+exponential of minus the energy of that
+ 
+
+ align:start position:0%
+exponential of minus the energy of that
+state over the temperature and the
+
+ align:start position:0%
+state over the temperature and the
+ 
+
+ align:start position:0%
+state over the temperature and the
+electrons and the ions and the radiation
+
+ align:start position:0%
+electrons and the ions and the radiation
+ 
+
+ align:start position:0%
+electrons and the ions and the radiation
+all share the same temperature so there
+
+ align:start position:0%
+all share the same temperature so there
+ 
+
+ align:start position:0%
+all share the same temperature so there
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+only one temperature for the electrons
+
+ align:start position:0%
+only one temperature for the electrons
+ 
+
+ align:start position:0%
+only one temperature for the electrons
+the ions and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+photons the other thing about a
+
+ align:start position:0%
+photons the other thing about a
+ 
+
+ align:start position:0%
+photons the other thing about a
+thermodynamic equilibrium is that all
+
+ align:start position:0%
+thermodynamic equilibrium is that all
+ 
+
+ align:start position:0%
+thermodynamic equilibrium is that all
+the processes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+balanced so all of the up processes that
+
+ align:start position:0%
+balanced so all of the up processes that
+ 
+
+ align:start position:0%
+balanced so all of the up processes that
+excite the system are exactly balanced
+
+ align:start position:0%
+excite the system are exactly balanced
+ 
+
+ align:start position:0%
+excite the system are exactly balanced
+by their counterparts that de excites
+
+ align:start position:0%
+by their counterparts that de excites
+ 
+
+ align:start position:0%
+by their counterparts that de excites
+the system so this is how we get into a
+
+ align:start position:0%
+the system so this is how we get into a
+ 
+
+ align:start position:0%
+the system so this is how we get into a
+steady state here that's actually not
+
+ align:start position:0%
+steady state here that's actually not
+ 
+
+ align:start position:0%
+steady state here that's actually not
+true in other equilibria there can be
+
+ align:start position:0%
+true in other equilibria there can be
+ 
+
+ align:start position:0%
+true in other equilibria there can be
+processes which excite and different
+
+ align:start position:0%
+processes which excite and different
+ 
+
+ align:start position:0%
+processes which excite and different
+processes that de exite as long as the
+
+ align:start position:0%
+processes that de exite as long as the
+ 
+
+ align:start position:0%
+processes that de exite as long as the
+rate is the same you're in an
+
+ align:start position:0%
+rate is the same you're in an
+ 
+
+ align:start position:0%
+rate is the same you're in an
+equilibrium and we'll talk about some of
+
+ align:start position:0%
+equilibrium and we'll talk about some of
+ 
+
+ align:start position:0%
+equilibrium and we'll talk about some of
+those uh later on but for thermodynamic
+
+ align:start position:0%
+those uh later on but for thermodynamic
+ 
+
+ align:start position:0%
+those uh later on but for thermodynamic
+equilibrium all processes balance with
+
+ align:start position:0%
+equilibrium all processes balance with
+ 
+
+ align:start position:0%
+equilibrium all processes balance with
+their opposite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+okay now how often do we think we get a
+
+ align:start position:0%
+okay now how often do we think we get a
+ 
+
+ align:start position:0%
+okay now how often do we think we get a
+thermodynamic equilibrium in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma maybe in space probably getting
+
+ align:start position:0%
+plasma maybe in space probably getting
+ 
+
+ align:start position:0%
+plasma maybe in space probably getting
+closer I mean a thermodynamic
+
+ align:start position:0%
+closer I mean a thermodynamic
+ 
+
+ align:start position:0%
+closer I mean a thermodynamic
+equilibrium is an infinite in uh system
+
+ align:start position:0%
+equilibrium is an infinite in uh system
+ 
+
+ align:start position:0%
+equilibrium is an infinite in uh system
+which is not changing in time so of
+
+ align:start position:0%
+which is not changing in time so of
+ 
+
+ align:start position:0%
+which is not changing in time so of
+course in reality we can never realize
+
+ align:start position:0%
+course in reality we can never realize
+ 
+
+ align:start position:0%
+course in reality we can never realize
+it the space plasma you might get close
+
+ align:start position:0%
+it the space plasma you might get close
+ 
+
+ align:start position:0%
+it the space plasma you might get close
+to thermodynamic equilibrium um but this
+
+ align:start position:0%
+to thermodynamic equilibrium um but this
+ 
+
+ align:start position:0%
+to thermodynamic equilibrium um but this
+also implies that you have to have your
+
+ align:start position:0%
+also implies that you have to have your
+ 
+
+ align:start position:0%
+also implies that you have to have your
+photons in Thal equilibrium with your
+
+ align:start position:0%
+photons in Thal equilibrium with your
+ 
+
+ align:start position:0%
+photons in Thal equilibrium with your
+gas which means that your system is
+
+ align:start position:0%
+gas which means that your system is
+ 
+
+ align:start position:0%
+gas which means that your system is
+optically thick and space plasmas at
+
+ align:start position:0%
+optically thick and space plasmas at
+ 
+
+ align:start position:0%
+optically thick and space plasmas at
+least Plasma in space in outter space is
+
+ align:start position:0%
+least Plasma in space in outter space is
+ 
+
+ align:start position:0%
+least Plasma in space in outter space is
+rarely optically thick maybe inside some
+
+ align:start position:0%
+rarely optically thick maybe inside some
+ 
+
+ align:start position:0%
+rarely optically thick maybe inside some
+astrophysical body it could be optically
+
+ align:start position:0%
+astrophysical body it could be optically
+ 
+
+ align:start position:0%
+astrophysical body it could be optically
+thick so this we don't really H get very
+
+ align:start position:0%
+thick so this we don't really H get very
+ 
+
+ align:start position:0%
+thick so this we don't really H get very
+often so this uh is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rare okay next one I want to talk about
+
+ align:start position:0%
+rare okay next one I want to talk about
+ 
+
+ align:start position:0%
+rare okay next one I want to talk about
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+local thermodynamic
+
+ align:start position:0%
+local thermodynamic
+ 
+
+ align:start position:0%
+local thermodynamic
+equilibrium I'll write as local te so
+
+ align:start position:0%
+equilibrium I'll write as local te so
+ 
+
+ align:start position:0%
+equilibrium I'll write as local te so
+people will often call this
+
+ align:start position:0%
+people will often call this
+ 
+
+ align:start position:0%
+people will often call this
+LT like this okay now in local
+
+ align:start position:0%
+LT like this okay now in local
+ 
+
+ align:start position:0%
+LT like this okay now in local
+thermodynamic equilibrium we make the
+
+ align:start position:0%
+thermodynamic equilibrium we make the
+ 
+
+ align:start position:0%
+thermodynamic equilibrium we make the
+assumption that our plasma is optically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thin which means that we can ignore the
+
+ align:start position:0%
+thin which means that we can ignore the
+ 
+
+ align:start position:0%
+thin which means that we can ignore the
+processes that involve photons being
+
+ align:start position:0%
+processes that involve photons being
+ 
+
+ align:start position:0%
+processes that involve photons being
+absorbed and emitted in terms of
+
+ align:start position:0%
+absorbed and emitted in terms of
+ 
+
+ align:start position:0%
+absorbed and emitted in terms of
+changing the levels so you think no I
+
+ align:start position:0%
+changing the levels so you think no I
+ 
+
+ align:start position:0%
+changing the levels so you think no I
+guess I'll call it radi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processes the rad processes still occur
+
+ align:start position:0%
+processes the rad processes still occur
+ 
+
+ align:start position:0%
+processes the rad processes still occur
+we can still observe the lines coming
+
+ align:start position:0%
+we can still observe the lines coming
+ 
+
+ align:start position:0%
+we can still observe the lines coming
+from them and do spectroscopy on them
+
+ align:start position:0%
+from them and do spectroscopy on them
+ 
+
+ align:start position:0%
+from them and do spectroscopy on them
+but they don't dominate the balance of
+
+ align:start position:0%
+but they don't dominate the balance of
+ 
+
+ align:start position:0%
+but they don't dominate the balance of
+the uh ex you know what determined what
+
+ align:start position:0%
+the uh ex you know what determined what
+ 
+
+ align:start position:0%
+the uh ex you know what determined what
+states are excited what are iron in fact
+
+ align:start position:0%
+states are excited what are iron in fact
+ 
+
+ align:start position:0%
+states are excited what are iron in fact
+that balance is then obviously dominated
+
+ align:start position:0%
+that balance is then obviously dominated
+ 
+
+ align:start position:0%
+that balance is then obviously dominated
+by the non- rative process so these are
+
+ align:start position:0%
+by the non- rative process so these are
+ 
+
+ align:start position:0%
+by the non- rative process so these are
+collisional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processes the collisional processes
+
+ align:start position:0%
+processes the collisional processes
+ 
+
+ align:start position:0%
+processes the collisional processes
+dominate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so this is collisional processes
+
+ align:start position:0%
+here so this is collisional processes
+ 
+
+ align:start position:0%
+here so this is collisional processes
+which excite from a lower state to an
+
+ align:start position:0%
+which excite from a lower state to an
+ 
+
+ align:start position:0%
+which excite from a lower state to an
+upper state but also collisional
+
+ align:start position:0%
+upper state but also collisional
+ 
+
+ align:start position:0%
+upper state but also collisional
+processes which de exite from the Upper
+
+ align:start position:0%
+processes which de exite from the Upper
+ 
+
+ align:start position:0%
+processes which de exite from the Upper
+State back down to the Lower State so
+
+ align:start position:0%
+State back down to the Lower State so
+ 
+
+ align:start position:0%
+State back down to the Lower State so
+our occupation of the upper and lower
+
+ align:start position:0%
+our occupation of the upper and lower
+ 
+
+ align:start position:0%
+our occupation of the upper and lower
+States is set purely by these
+
+ align:start position:0%
+States is set purely by these
+ 
+
+ align:start position:0%
+States is set purely by these
+collisional
+
+ align:start position:0%
+collisional
+ 
+
+ align:start position:0%
+collisional
+processes however we don't need to
+
+ align:start position:0%
+processes however we don't need to
+ 
+
+ align:start position:0%
+processes however we don't need to
+know the cross-section for these
+
+ align:start position:0%
+know the cross-section for these
+ 
+
+ align:start position:0%
+know the cross-section for these
+processes which we would do in our more
+
+ align:start position:0%
+processes which we would do in our more
+ 
+
+ align:start position:0%
+processes which we would do in our more
+detailed full model remember this Sigma
+
+ align:start position:0%
+detailed full model remember this Sigma
+ 
+
+ align:start position:0%
+detailed full model remember this Sigma
+i j is the cross-section for a process
+
+ align:start position:0%
+i j is the cross-section for a process
+ 
+
+ align:start position:0%
+i j is the cross-section for a process
+that takes us from State I to State J
+
+ align:start position:0%
+that takes us from State I to State J
+ 
+
+ align:start position:0%
+that takes us from State I to State J
+but they're unimportant in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LTE due to the balance so we keep the
+
+ align:start position:0%
+LTE due to the balance so we keep the
+ 
+
+ align:start position:0%
+LTE due to the balance so we keep the
+feature of a thermodynamic equilibrium
+
+ align:start position:0%
+feature of a thermodynamic equilibrium
+ 
+
+ align:start position:0%
+feature of a thermodynamic equilibrium
+that the process is a balance of the
+
+ align:start position:0%
+that the process is a balance of the
+ 
+
+ align:start position:0%
+that the process is a balance of the
+opposite process so the actual
+
+ align:start position:0%
+opposite process so the actual
+ 
+
+ align:start position:0%
+opposite process so the actual
+cross-section processes un
+
+ align:start position:0%
+cross-section processes un
+ 
+
+ align:start position:0%
+cross-section processes un
+important and that's what makes it a
+
+ align:start position:0%
+important and that's what makes it a
+ 
+
+ align:start position:0%
+important and that's what makes it a
+local thermodynamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibri and if
+
+ align:start position:0%
+equilibri and if
+ 
+
+ align:start position:0%
+equilibri and if
+you look at what this means and you work
+
+ align:start position:0%
+you look at what this means and you work
+ 
+
+ align:start position:0%
+you look at what this means and you work
+through the mathematics of
+
+ align:start position:0%
+through the mathematics of
+ 
+
+ align:start position:0%
+through the mathematics of
+your population balance you come up with
+
+ align:start position:0%
+your population balance you come up with
+ 
+
+ align:start position:0%
+your population balance you come up with
+the famous Saha equilibrium so a Saha
+
+ align:start position:0%
+the famous Saha equilibrium so a Saha
+ 
+
+ align:start position:0%
+the famous Saha equilibrium so a Saha
+equilibrium named after its discoverer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a form that says that the electron
+
+ align:start position:0%
+has a form that says that the electron
+ 
+
+ align:start position:0%
+has a form that says that the electron
+density times the
+
+ align:start position:0%
+density times the
+ 
+
+ align:start position:0%
+density times the
+ionization density for State Zed in its
+
+ align:start position:0%
+ionization density for State Zed in its
+ 
+
+ align:start position:0%
+ionization density for State Zed in its
+ground state over Zed minus one in its
+
+ align:start position:0%
+ground state over Zed minus one in its
+ 
+
+ align:start position:0%
+ground state over Zed minus one in its
+ground state so this is the density of
+
+ align:start position:0%
+ground state so this is the density of
+ 
+
+ align:start position:0%
+ground state so this is the density of
+atoms in ionization State Zed and their
+
+ align:start position:0%
+atoms in ionization State Zed and their
+ 
+
+ align:start position:0%
+atoms in ionization State Zed and their
+ground state atoms in ionization State Z
+
+ align:start position:0%
+ground state atoms in ionization State Z
+ 
+
+ align:start position:0%
+ground state atoms in ionization State Z
+minus one in their ground state Times by
+
+ align:start position:0%
+minus one in their ground state Times by
+ 
+
+ align:start position:0%
+minus one in their ground state Times by
+the electron density is
+
+ align:start position:0%
+the electron density is
+ 
+
+ align:start position:0%
+the electron density is
+equal to most
+
+ align:start position:0%
+equal to most
+ 
+
+ align:start position:0%
+equal to most
+importantly a factor to do with the
+
+ align:start position:0%
+importantly a factor to do with the
+ 
+
+ align:start position:0%
+importantly a factor to do with the
+ionization
+
+ align:start position:0%
+ionization
+ 
+
+ align:start position:0%
+ionization
+potential so this Kai Z here is the
+
+ align:start position:0%
+potential so this Kai Z here is the
+ 
+
+ align:start position:0%
+potential so this Kai Z here is the
+ionization to go from uh Zed minus one
+
+ align:start position:0%
+ionization to go from uh Zed minus one
+ 
+
+ align:start position:0%
+ionization to go from uh Zed minus one
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zed the change in energy there over the
+
+ align:start position:0%
+zed the change in energy there over the
+ 
+
+ align:start position:0%
+zed the change in energy there over the
+temperature and then there's a few other
+
+ align:start position:0%
+temperature and then there's a few other
+ 
+
+ align:start position:0%
+temperature and then there's a few other
+factors out front that come from the
+
+ align:start position:0%
+factors out front that come from the
+ 
+
+ align:start position:0%
+factors out front that come from the
+fact that we're going to be assuming l
+
+ align:start position:0%
+fact that we're going to be assuming l
+ 
+
+ align:start position:0%
+fact that we're going to be assuming l
+ations are maxwellian there's an ion
+
+ align:start position:0%
+ations are maxwellian there's an ion
+ 
+
+ align:start position:0%
+ations are maxwellian there's an ion
+Mass temperature over 2 pi H bar squared
+
+ align:start position:0%
+Mass temperature over 2 pi H bar squared
+ 
+
+ align:start position:0%
+Mass temperature over 2 pi H bar squared
+with three halves and then there's also
+
+ align:start position:0%
+with three halves and then there's also
+ 
+
+ align:start position:0%
+with three halves and then there's also
+a factor that's to do with the
+
+ align:start position:0%
+a factor that's to do with the
+ 
+
+ align:start position:0%
+a factor that's to do with the
+degeneracy of these levels and we talked
+
+ align:start position:0%
+degeneracy of these levels and we talked
+ 
+
+ align:start position:0%
+degeneracy of these levels and we talked
+about the degeneracy as being different
+
+ align:start position:0%
+about the degeneracy as being different
+ 
+
+ align:start position:0%
+about the degeneracy as being different
+ways to arrange electrons and still get
+
+ align:start position:0%
+ways to arrange electrons and still get
+ 
+
+ align:start position:0%
+ways to arrange electrons and still get
+out the same uh energy so this is g z
+
+ align:start position:0%
+out the same uh energy so this is g z
+ 
+
+ align:start position:0%
+out the same uh energy so this is g z
+for the Zer ionization State one over
+
+ align:start position:0%
+for the Zer ionization State one over
+ 
+
+ align:start position:0%
+for the Zer ionization State one over
+the degeneracy of the lower ionization
+
+ align:start position:0%
+the degeneracy of the lower ionization
+ 
+
+ align:start position:0%
+the degeneracy of the lower ionization
+state so the sah equilibrium doesn't
+
+ align:start position:0%
+state so the sah equilibrium doesn't
+ 
+
+ align:start position:0%
+state so the sah equilibrium doesn't
+tell you about how the excitation states
+
+ align:start position:0%
+tell you about how the excitation states
+ 
+
+ align:start position:0%
+tell you about how the excitation states
+are distributed within each ion but it
+
+ align:start position:0%
+are distributed within each ion but it
+ 
+
+ align:start position:0%
+are distributed within each ion but it
+does tell you what the ionization is and
+
+ align:start position:0%
+does tell you what the ionization is and
+ 
+
+ align:start position:0%
+does tell you what the ionization is and
+so this tells you for a given
+
+ align:start position:0%
+so this tells you for a given
+ 
+
+ align:start position:0%
+so this tells you for a given
+temperature how many particles you
+
+ align:start position:0%
+temperature how many particles you
+ 
+
+ align:start position:0%
+temperature how many particles you
+expect to be in each ionization State
+
+ align:start position:0%
+expect to be in each ionization State
+ 
+
+ align:start position:0%
+expect to be in each ionization State
+and because of this exponential Factor
+
+ align:start position:0%
+and because of this exponential Factor
+ 
+
+ align:start position:0%
+and because of this exponential Factor
+here which comes from a sort of Bolton
+
+ align:start position:0%
+here which comes from a sort of Bolton
+ 
+
+ align:start position:0%
+here which comes from a sort of Bolton
+like argument we're going to end up with
+
+ align:start position:0%
+like argument we're going to end up with
+ 
+
+ align:start position:0%
+like argument we're going to end up with
+most of our particles still being in
+
+ align:start position:0%
+most of our particles still being in
+ 
+
+ align:start position:0%
+most of our particles still being in
+lower ionization
+
+ align:start position:0%
+lower ionization
+ 
+
+ align:start position:0%
+lower ionization
+States okay any questions so far yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the radiation doesn't have to be the
+
+ align:start position:0%
+the radiation doesn't have to be the
+ 
+
+ align:start position:0%
+the radiation doesn't have to be the
+same because we it's optically thin and
+
+ align:start position:0%
+same because we it's optically thin and
+ 
+
+ align:start position:0%
+same because we it's optically thin and
+we don't care about it but the ions and
+
+ align:start position:0%
+we don't care about it but the ions and
+ 
+
+ align:start position:0%
+we don't care about it but the ions and
+the electrons are the same temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah so this notation here this uh
+
+ align:start position:0%
+yes yeah so this notation here this uh
+ 
+
+ align:start position:0%
+yes yeah so this notation here this uh
+lower number here is like if you have a
+
+ align:start position:0%
+lower number here is like if you have a
+ 
+
+ align:start position:0%
+lower number here is like if you have a
+series of levels within an atom that
+
+ align:start position:0%
+series of levels within an atom that
+ 
+
+ align:start position:0%
+series of levels within an atom that
+atom has a charge of plus Zed and then
+
+ align:start position:0%
+atom has a charge of plus Zed and then
+ 
+
+ align:start position:0%
+atom has a charge of plus Zed and then
+I've got these levels which I could
+
+ align:start position:0%
+I've got these levels which I could
+ 
+
+ align:start position:0%
+I've got these levels which I could
+label one two three four and so on like
+
+ align:start position:0%
+label one two three four and so on like
+ 
+
+ align:start position:0%
+label one two three four and so on like
+that this one refers to the energy level
+
+ align:start position:0%
+that this one refers to the energy level
+ 
+
+ align:start position:0%
+that this one refers to the energy level
+with an atom with charge plus Zed and
+
+ align:start position:0%
+with an atom with charge plus Zed and
+ 
+
+ align:start position:0%
+with an atom with charge plus Zed and
+the Zed here refers to that charge so
+
+ align:start position:0%
+the Zed here refers to that charge so
+ 
+
+ align:start position:0%
+the Zed here refers to that charge so
+these are atoms with different
+
+ align:start position:0%
+these are atoms with different
+ 
+
+ align:start position:0%
+these are atoms with different
+ionization states which means in general
+
+ align:start position:0%
+ionization states which means in general
+ 
+
+ align:start position:0%
+ionization states which means in general
+their energy levels will have different
+
+ align:start position:0%
+their energy levels will have different
+ 
+
+ align:start position:0%
+their energy levels will have different
+energies but here we're taking the ratio
+
+ align:start position:0%
+energies but here we're taking the ratio
+ 
+
+ align:start position:0%
+energies but here we're taking the ratio
+of the atoms of ionization State Zed in
+
+ align:start position:0%
+of the atoms of ionization State Zed in
+ 
+
+ align:start position:0%
+of the atoms of ionization State Zed in
+the ground state level one and the atoms
+
+ align:start position:0%
+the ground state level one and the atoms
+ 
+
+ align:start position:0%
+the ground state level one and the atoms
+of ionization State Zed minus one so
+
+ align:start position:0%
+of ionization State Zed minus one so
+ 
+
+ align:start position:0%
+of ionization State Zed minus one so
+they have one more electron and they're
+
+ align:start position:0%
+they have one more electron and they're
+ 
+
+ align:start position:0%
+they have one more electron and they're
+in their ground state one and the energy
+
+ align:start position:0%
+in their ground state one and the energy
+ 
+
+ align:start position:0%
+in their ground state one and the energy
+of that ground state will not in general
+
+ align:start position:0%
+of that ground state will not in general
+ 
+
+ align:start position:0%
+of that ground state will not in general
+be the same as the energy of the ion
+
+ align:start position:0%
+be the same as the energy of the ion
+ 
+
+ align:start position:0%
+be the same as the energy of the ion
+with one fewer electron because all the
+
+ align:start position:0%
+with one fewer electron because all the
+ 
+
+ align:start position:0%
+with one fewer electron because all the
+energy levels will shift when we reduce
+
+ align:start position:0%
+energy levels will shift when we reduce
+ 
+
+ align:start position:0%
+energy levels will shift when we reduce
+the number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yes yeah but you you could you could
+
+ align:start position:0%
+uh yes yeah but you you could you could
+ 
+
+ align:start position:0%
+uh yes yeah but you you could you could
+skip that by just taking ratios of this
+
+ align:start position:0%
+skip that by just taking ratios of this
+ 
+
+ align:start position:0%
+skip that by just taking ratios of this
+equation with unionized argon and then
+
+ align:start position:0%
+equation with unionized argon and then
+ 
+
+ align:start position:0%
+equation with unionized argon and then
+you get out the ionization to get to
+
+ align:start position:0%
+you get out the ionization to get to
+ 
+
+ align:start position:0%
+you get out the ionization to get to
+like the fifth ionization level so you
+
+ align:start position:0%
+like the fifth ionization level so you
+ 
+
+ align:start position:0%
+like the fifth ionization level so you
+don't actually have to do it with do it
+
+ align:start position:0%
+don't actually have to do it with do it
+ 
+
+ align:start position:0%
+don't actually have to do it with do it
+all in one you could also do it that way
+
+ align:start position:0%
+all in one you could also do it that way
+ 
+
+ align:start position:0%
+all in one you could also do it that way
+if you wanted but yeah in general these
+
+ align:start position:0%
+if you wanted but yeah in general these
+ 
+
+ align:start position:0%
+if you wanted but yeah in general these
+ionization potentials are tabulated
+
+ align:start position:0%
+ionization potentials are tabulated
+ 
+
+ align:start position:0%
+ionization potentials are tabulated
+there things that people know from an
+
+ align:start position:0%
+there things that people know from an
+ 
+
+ align:start position:0%
+there things that people know from an
+experiment you know it's 13.6 electron
+
+ align:start position:0%
+experiment you know it's 13.6 electron
+ 
+
+ align:start position:0%
+experiment you know it's 13.6 electron
+volts for hydrogen it's less for every
+
+ align:start position:0%
+volts for hydrogen it's less for every
+ 
+
+ align:start position:0%
+volts for hydrogen it's less for every
+subsequent uh element and so you need to
+
+ align:start position:0%
+subsequent uh element and so you need to
+ 
+
+ align:start position:0%
+subsequent uh element and so you need to
+put in the temperature of course of your
+
+ align:start position:0%
+put in the temperature of course of your
+ 
+
+ align:start position:0%
+put in the temperature of course of your
+plasma but then you can calculate this
+
+ align:start position:0%
+plasma but then you can calculate this
+ 
+
+ align:start position:0%
+plasma but then you can calculate this
+pretty quickly so this is a nice and
+
+ align:start position:0%
+pretty quickly so this is a nice and
+ 
+
+ align:start position:0%
+pretty quickly so this is a nice and
+simple relatively simple equilibria and
+
+ align:start position:0%
+simple relatively simple equilibria and
+ 
+
+ align:start position:0%
+simple relatively simple equilibria and
+so you know for example if you're doing
+
+ align:start position:0%
+so you know for example if you're doing
+ 
+
+ align:start position:0%
+so you know for example if you're doing
+spectroscopy and you see a line which
+
+ align:start position:0%
+spectroscopy and you see a line which
+ 
+
+ align:start position:0%
+spectroscopy and you see a line which
+has an energy which corresponds to The
+
+ align:start position:0%
+has an energy which corresponds to The
+ 
+
+ align:start position:0%
+has an energy which corresponds to The
+Zed ionization State you know you see a
+
+ align:start position:0%
+Zed ionization State you know you see a
+ 
+
+ align:start position:0%
+Zed ionization State you know you see a
+line that you know corresponds to argon
+
+ align:start position:0%
+line that you know corresponds to argon
+ 
+
+ align:start position:0%
+line that you know corresponds to argon
+5 plus then you know you have to be at
+
+ align:start position:0%
+5 plus then you know you have to be at
+ 
+
+ align:start position:0%
+5 plus then you know you have to be at
+at least the temperature that produces
+
+ align:start position:0%
+at least the temperature that produces
+ 
+
+ align:start position:0%
+at least the temperature that produces
+argon 5 plus you can't be at a
+
+ align:start position:0%
+argon 5 plus you can't be at a
+ 
+
+ align:start position:0%
+argon 5 plus you can't be at a
+temperature where argon is completely
+
+ align:start position:0%
+temperature where argon is completely
+ 
+
+ align:start position:0%
+temperature where argon is completely
+neutral or only singly ionized so
+
+ align:start position:0%
+neutral or only singly ionized so
+ 
+
+ align:start position:0%
+neutral or only singly ionized so
+straight away this sort of equilibrium
+
+ align:start position:0%
+straight away this sort of equilibrium
+ 
+
+ align:start position:0%
+straight away this sort of equilibrium
+is like uh if I see that line it must be
+
+ align:start position:0%
+is like uh if I see that line it must be
+ 
+
+ align:start position:0%
+is like uh if I see that line it must be
+at least this hot and you know that's
+
+ align:start position:0%
+at least this hot and you know that's
+ 
+
+ align:start position:0%
+at least this hot and you know that's
+often good enough for spectroscopy we'll
+
+ align:start position:0%
+often good enough for spectroscopy we'll
+ 
+
+ align:start position:0%
+often good enough for spectroscopy we'll
+talk about more advanced tactics using
+
+ align:start position:0%
+talk about more advanced tactics using
+ 
+
+ align:start position:0%
+talk about more advanced tactics using
+spectroscopy later on okay other
+
+ align:start position:0%
+spectroscopy later on okay other
+ 
+
+ align:start position:0%
+spectroscopy later on okay other
+questions any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online
+
+ align:start position:0%
+online
+ 
+
+ align:start position:0%
+online
+okay next equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is something called coronal
+
+ align:start position:0%
+is something called coronal
+ 
+
+ align:start position:0%
+is something called coronal
+equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coronal equilibrium is called coronal
+
+ align:start position:0%
+coronal equilibrium is called coronal
+ 
+
+ align:start position:0%
+coronal equilibrium is called coronal
+because it was first derived in the case
+
+ align:start position:0%
+because it was first derived in the case
+ 
+
+ align:start position:0%
+because it was first derived in the case
+of the solar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Corona sometimes this is also called a
+
+ align:start position:0%
+Corona sometimes this is also called a
+ 
+
+ align:start position:0%
+Corona sometimes this is also called a
+collisional radiative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium and that name radiative is
+
+ align:start position:0%
+equilibrium and that name radiative is
+ 
+
+ align:start position:0%
+equilibrium and that name radiative is
+much more descriptive and I wish we used
+
+ align:start position:0%
+much more descriptive and I wish we used
+ 
+
+ align:start position:0%
+much more descriptive and I wish we used
+it more but you'll still find most
+
+ align:start position:0%
+it more but you'll still find most
+ 
+
+ align:start position:0%
+it more but you'll still find most
+people calling it coronal equilibrium
+
+ align:start position:0%
+people calling it coronal equilibrium
+ 
+
+ align:start position:0%
+people calling it coronal equilibrium
+instead so it's called a collisional
+
+ align:start position:0%
+instead so it's called a collisional
+ 
+
+ align:start position:0%
+instead so it's called a collisional
+radiative equilibrium because we
+
+ align:start position:0%
+radiative equilibrium because we
+ 
+
+ align:start position:0%
+radiative equilibrium because we
+consider the
+
+ align:start position:0%
+consider the
+ 
+
+ align:start position:0%
+consider the
+excitation going from a lower state to
+
+ align:start position:0%
+excitation going from a lower state to
+ 
+
+ align:start position:0%
+excitation going from a lower state to
+an upper state only collisional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processes but for any D exitation going
+
+ align:start position:0%
+processes but for any D exitation going
+ 
+
+ align:start position:0%
+processes but for any D exitation going
+from an upper State back down to a lower
+
+ align:start position:0%
+from an upper State back down to a lower
+ 
+
+ align:start position:0%
+from an upper State back down to a lower
+State we consider only radiative
+
+ align:start position:0%
+State we consider only radiative
+ 
+
+ align:start position:0%
+State we consider only radiative
+process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a a slightly seemingly
+
+ align:start position:0%
+so this is a a slightly seemingly
+ 
+
+ align:start position:0%
+so this is a a slightly seemingly
+contrived setup that actually occurs a
+
+ align:start position:0%
+contrived setup that actually occurs a
+ 
+
+ align:start position:0%
+contrived setup that actually occurs a
+great deal of the time it's a setup in
+
+ align:start position:0%
+great deal of the time it's a setup in
+ 
+
+ align:start position:0%
+great deal of the time it's a setup in
+which our system is optically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thin and so we are very unlikely to have
+
+ align:start position:0%
+thin and so we are very unlikely to have
+ 
+
+ align:start position:0%
+thin and so we are very unlikely to have
+a photon wand by and suddenly excite our
+
+ align:start position:0%
+a photon wand by and suddenly excite our
+ 
+
+ align:start position:0%
+a photon wand by and suddenly excite our
+system because the photons mostly just
+
+ align:start position:0%
+system because the photons mostly just
+ 
+
+ align:start position:0%
+system because the photons mostly just
+stream through the plasma without being
+
+ align:start position:0%
+stream through the plasma without being
+ 
+
+ align:start position:0%
+stream through the plasma without being
+absorbed so this is opop Ean the photons
+
+ align:start position:0%
+absorbed so this is opop Ean the photons
+ 
+
+ align:start position:0%
+absorbed so this is opop Ean the photons
+Escape
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and yet it's also so collisionless the
+
+ align:start position:0%
+and yet it's also so collisionless the
+ 
+
+ align:start position:0%
+and yet it's also so collisionless the
+collisions happen so rarely um that
+
+ align:start position:0%
+collisions happen so rarely um that
+ 
+
+ align:start position:0%
+collisions happen so rarely um that
+although they're responsible for
+
+ align:start position:0%
+although they're responsible for
+ 
+
+ align:start position:0%
+although they're responsible for
+excitation before you have chance to
+
+ align:start position:0%
+excitation before you have chance to
+ 
+
+ align:start position:0%
+excitation before you have chance to
+have a collision de exite your system
+
+ align:start position:0%
+have a collision de exite your system
+ 
+
+ align:start position:0%
+have a collision de exite your system
+they will it will spontaneously emit a
+
+ align:start position:0%
+they will it will spontaneously emit a
+ 
+
+ align:start position:0%
+they will it will spontaneously emit a
+photon so that instead we'll have
+
+ align:start position:0%
+photon so that instead we'll have
+ 
+
+ align:start position:0%
+photon so that instead we'll have
+spontaneous emission taking us back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+so this uh
+
+ align:start position:0%
+so this uh
+ 
+
+ align:start position:0%
+so this uh
+works very well for low density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasmas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes exactly but and but we're not
+
+ align:start position:0%
+yeah yes exactly but and but we're not
+ 
+
+ align:start position:0%
+yeah yes exactly but and but we're not
+dealing with any rative processes that
+
+ align:start position:0%
+dealing with any rative processes that
+ 
+
+ align:start position:0%
+dealing with any rative processes that
+rely on there being a large number of
+
+ align:start position:0%
+rely on there being a large number of
+ 
+
+ align:start position:0%
+rely on there being a large number of
+photons like stimulated emission those
+
+ align:start position:0%
+photons like stimulated emission those
+ 
+
+ align:start position:0%
+photons like stimulated emission those
+will never happen it's just you know
+
+ align:start position:0%
+will never happen it's just you know
+ 
+
+ align:start position:0%
+will never happen it's just you know
+imagine you've got your Ion floating
+
+ align:start position:0%
+imagine you've got your Ion floating
+ 
+
+ align:start position:0%
+imagine you've got your Ion floating
+around uh lots of photons stream by they
+
+ align:start position:0%
+around uh lots of photons stream by they
+ 
+
+ align:start position:0%
+around uh lots of photons stream by they
+will never interact with it occasionally
+
+ align:start position:0%
+will never interact with it occasionally
+ 
+
+ align:start position:0%
+will never interact with it occasionally
+a collision will happen it excites and
+
+ align:start position:0%
+a collision will happen it excites and
+ 
+
+ align:start position:0%
+a collision will happen it excites and
+so now it's in an excited state then the
+
+ align:start position:0%
+so now it's in an excited state then the
+ 
+
+ align:start position:0%
+so now it's in an excited state then the
+clock is ticking two things could happen
+
+ align:start position:0%
+clock is ticking two things could happen
+ 
+
+ align:start position:0%
+clock is ticking two things could happen
+now another Collision could de exite it
+
+ align:start position:0%
+now another Collision could de exite it
+ 
+
+ align:start position:0%
+now another Collision could de exite it
+and non-radiatively take that energy
+
+ align:start position:0%
+and non-radiatively take that energy
+ 
+
+ align:start position:0%
+and non-radiatively take that energy
+away or spontaneous emission could occur
+
+ align:start position:0%
+away or spontaneous emission could occur
+ 
+
+ align:start position:0%
+away or spontaneous emission could occur
+and we've chosen oh this system works in
+
+ align:start position:0%
+and we've chosen oh this system works in
+ 
+
+ align:start position:0%
+and we've chosen oh this system works in
+a regime where the density is low enough
+
+ align:start position:0%
+a regime where the density is low enough
+ 
+
+ align:start position:0%
+a regime where the density is low enough
+remember these processes the collisional
+
+ align:start position:0%
+remember these processes the collisional
+ 
+
+ align:start position:0%
+remember these processes the collisional
+processes is all depend on density like
+
+ align:start position:0%
+processes is all depend on density like
+ 
+
+ align:start position:0%
+processes is all depend on density like
+that we've chosen a density which is low
+
+ align:start position:0%
+that we've chosen a density which is low
+ 
+
+ align:start position:0%
+that we've chosen a density which is low
+enough that there will never be a second
+
+ align:start position:0%
+enough that there will never be a second
+ 
+
+ align:start position:0%
+enough that there will never be a second
+Collision more quickly than we have
+
+ align:start position:0%
+Collision more quickly than we have
+ 
+
+ align:start position:0%
+Collision more quickly than we have
+spontaneous emission here this this
+
+ align:start position:0%
+spontaneous emission here this this
+ 
+
+ align:start position:0%
+spontaneous emission here this this
+occurs a lot in topmax and other plasmas
+
+ align:start position:0%
+occurs a lot in topmax and other plasmas
+ 
+
+ align:start position:0%
+occurs a lot in topmax and other plasmas
+so this and it's also relatively easy to
+
+ align:start position:0%
+so this and it's also relatively easy to
+ 
+
+ align:start position:0%
+so this and it's also relatively easy to
+solve for so this is a very favorite
+
+ align:start position:0%
+solve for so this is a very favorite
+ 
+
+ align:start position:0%
+solve for so this is a very favorite
+model in plasma
+
+ align:start position:0%
+model in plasma
+ 
+
+ align:start position:0%
+model in plasma
+spectroscopy okay so if you have that we
+
+ align:start position:0%
+spectroscopy okay so if you have that we
+ 
+
+ align:start position:0%
+spectroscopy okay so if you have that we
+can also write
+
+ align:start position:0%
+can also write
+ 
+
+ align:start position:0%
+can also write
+down the occupation of the excited
+
+ align:start position:0%
+down the occupation of the excited
+ 
+
+ align:start position:0%
+down the occupation of the excited
+States so this is some upper excited
+
+ align:start position:0%
+States so this is some upper excited
+ 
+
+ align:start position:0%
+States so this is some upper excited
+state number of atoms in that state
+
+ align:start position:0%
+state number of atoms in that state
+ 
+
+ align:start position:0%
+state number of atoms in that state
+compared to the ground state everything
+
+ align:start position:0%
+compared to the ground state everything
+ 
+
+ align:start position:0%
+compared to the ground state everything
+is being driven back to the ground state
+
+ align:start position:0%
+is being driven back to the ground state
+ 
+
+ align:start position:0%
+is being driven back to the ground state
+by spontaneous emission even if it takes
+
+ align:start position:0%
+by spontaneous emission even if it takes
+ 
+
+ align:start position:0%
+by spontaneous emission even if it takes
+multiple steps you'll eventually get to
+
+ align:start position:0%
+multiple steps you'll eventually get to
+ 
+
+ align:start position:0%
+multiple steps you'll eventually get to
+the ground state and you'll get there
+
+ align:start position:0%
+the ground state and you'll get there
+ 
+
+ align:start position:0%
+the ground state and you'll get there
+long before any Collision occurs so we
+
+ align:start position:0%
+long before any Collision occurs so we
+ 
+
+ align:start position:0%
+long before any Collision occurs so we
+are going to end up mostly in this
+
+ align:start position:0%
+are going to end up mostly in this
+ 
+
+ align:start position:0%
+are going to end up mostly in this
+ground state here and this ratio here is
+
+ align:start position:0%
+ground state here and this ratio here is
+ 
+
+ align:start position:0%
+ground state here and this ratio here is
+going to be equal to number of electrons
+
+ align:start position:0%
+going to be equal to number of electrons
+ 
+
+ align:start position:0%
+going to be equal to number of electrons
+doing the collisions pump it up to an
+
+ align:start position:0%
+doing the collisions pump it up to an
+ 
+
+ align:start position:0%
+doing the collisions pump it up to an
+excited state Times by The cross-section
+
+ align:start position:0%
+excited state Times by The cross-section
+ 
+
+ align:start position:0%
+excited state Times by The cross-section
+to go from the ground state to this
+
+ align:start position:0%
+to go from the ground state to this
+ 
+
+ align:start position:0%
+to go from the ground state to this
+excited
+
+ align:start position:0%
+excited
+ 
+
+ align:start position:0%
+excited
+state average over the velocity so
+
+ align:start position:0%
+state average over the velocity so
+ 
+
+ align:start position:0%
+state average over the velocity so
+that's our standard reaction rate here
+
+ align:start position:0%
+that's our standard reaction rate here
+ 
+
+ align:start position:0%
+that's our standard reaction rate here
+and it's going to be divided by the rate
+
+ align:start position:0%
+and it's going to be divided by the rate
+ 
+
+ align:start position:0%
+and it's going to be divided by the rate
+at which any process takes it from the
+
+ align:start position:0%
+at which any process takes it from the
+ 
+
+ align:start position:0%
+at which any process takes it from the
+Upper State down to the Lower State here
+
+ align:start position:0%
+Upper State down to the Lower State here
+ 
+
+ align:start position:0%
+Upper State down to the Lower State here
+and this could be by a chain of multiple
+
+ align:start position:0%
+and this could be by a chain of multiple
+ 
+
+ align:start position:0%
+and this could be by a chain of multiple
+processes so for example if this is the
+
+ align:start position:0%
+processes so for example if this is the
+ 
+
+ align:start position:0%
+processes so for example if this is the
+Upper State and there's some
+
+ align:start position:0%
+Upper State and there's some
+ 
+
+ align:start position:0%
+Upper State and there's some
+intermediate State and this is the Lower
+
+ align:start position:0%
+intermediate State and this is the Lower
+ 
+
+ align:start position:0%
+intermediate State and this is the Lower
+State we'd have to add up the processes
+
+ align:start position:0%
+State we'd have to add up the processes
+ 
+
+ align:start position:0%
+State we'd have to add up the processes
+that go straight down and the processes
+
+ align:start position:0%
+that go straight down and the processes
+ 
+
+ align:start position:0%
+that go straight down and the processes
+that go via some intermediate and any
+
+ align:start position:0%
+that go via some intermediate and any
+ 
+
+ align:start position:0%
+that go via some intermediate and any
+chain of these processes will happen
+
+ align:start position:0%
+chain of these processes will happen
+ 
+
+ align:start position:0%
+chain of these processes will happen
+more quickly than another quick so this
+
+ align:start position:0%
+more quickly than another quick so this
+ 
+
+ align:start position:0%
+more quickly than another quick so this
+is the the balance uh between these two
+
+ align:start position:0%
+is the the balance uh between these two
+ 
+
+ align:start position:0%
+is the the balance uh between these two
+here and we can write it very easily for
+
+ align:start position:0%
+here and we can write it very easily for
+ 
+
+ align:start position:0%
+here and we can write it very easily for
+this collisional radi
+
+ align:start position:0%
+this collisional radi
+ 
+
+ align:start position:0%
+this collisional radi
+Del but the up processes are no longer
+
+ align:start position:0%
+Del but the up processes are no longer
+ 
+
+ align:start position:0%
+Del but the up processes are no longer
+balanced by the down processes they're
+
+ align:start position:0%
+balanced by the down processes they're
+ 
+
+ align:start position:0%
+balanced by the down processes they're
+completely separate that's a big break
+
+ align:start position:0%
+completely separate that's a big break
+ 
+
+ align:start position:0%
+completely separate that's a big break
+from our local thermodynamic and our
+
+ align:start position:0%
+from our local thermodynamic and our
+ 
+
+ align:start position:0%
+from our local thermodynamic and our
+thermodynamic
+
+ align:start position:0%
+thermodynamic
+ 
+
+ align:start position:0%
+thermodynamic
+equilibria okay questions on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that that won't happen in this case
+
+ align:start position:0%
+that that won't happen in this case
+ 
+
+ align:start position:0%
+that that won't happen in this case
+because by before the second Collision
+
+ align:start position:0%
+because by before the second Collision
+ 
+
+ align:start position:0%
+because by before the second Collision
+happens it will have decayed right
+
+ align:start position:0%
+happens it will have decayed right
+ 
+
+ align:start position:0%
+happens it will have decayed right
+because because we're saying that these
+
+ align:start position:0%
+because because we're saying that these
+ 
+
+ align:start position:0%
+because because we're saying that these
+collisions are so infrequent so you can
+
+ align:start position:0%
+collisions are so infrequent so you can
+ 
+
+ align:start position:0%
+collisions are so infrequent so you can
+yeah really we just have collisions
+
+ align:start position:0%
+yeah really we just have collisions
+ 
+
+ align:start position:0%
+yeah really we just have collisions
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+up if the Collision only took goes up to
+
+ align:start position:0%
+up if the Collision only took goes up to
+ 
+
+ align:start position:0%
+up if the Collision only took goes up to
+here then before a second Collision
+
+ align:start position:0%
+here then before a second Collision
+ 
+
+ align:start position:0%
+here then before a second Collision
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+occur we'd have spontaneous emission and
+
+ align:start position:0%
+occur we'd have spontaneous emission and
+ 
+
+ align:start position:0%
+occur we'd have spontaneous emission and
+Decay if it goes up to here then there
+
+ align:start position:0%
+Decay if it goes up to here then there
+ 
+
+ align:start position:0%
+Decay if it goes up to here then there
+could be multiple Pathways back down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm sorry like you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said right so this is one of these
+
+ align:start position:0%
+said right so this is one of these
+ 
+
+ align:start position:0%
+said right so this is one of these
+things like when is this model valid
+
+ align:start position:0%
+things like when is this model valid
+ 
+
+ align:start position:0%
+things like when is this model valid
+right and so then there will be a
+
+ align:start position:0%
+right and so then there will be a
+ 
+
+ align:start position:0%
+right and so then there will be a
+dimensionless parameter which would be
+
+ align:start position:0%
+dimensionless parameter which would be
+ 
+
+ align:start position:0%
+dimensionless parameter which would be
+the ratio of those time scales and You'
+
+ align:start position:0%
+the ratio of those time scales and You'
+ 
+
+ align:start position:0%
+the ratio of those time scales and You'
+like that parameter to be like very
+
+ align:start position:0%
+like that parameter to be like very
+ 
+
+ align:start position:0%
+like that parameter to be like very
+large or very small depending on whether
+
+ align:start position:0%
+large or very small depending on whether
+ 
+
+ align:start position:0%
+large or very small depending on whether
+you write it one way up or the other way
+
+ align:start position:0%
+you write it one way up or the other way
+ 
+
+ align:start position:0%
+you write it one way up or the other way
+up what is very large and very small 10
+
+ align:start position:0%
+up what is very large and very small 10
+ 
+
+ align:start position:0%
+up what is very large and very small 10
+is pretty large number three can
+
+ align:start position:0%
+is pretty large number three can
+ 
+
+ align:start position:0%
+is pretty large number three can
+sometimes be large enough right so if
+
+ align:start position:0%
+sometimes be large enough right so if
+ 
+
+ align:start position:0%
+sometimes be large enough right so if
+you if you're using this model in a
+
+ align:start position:0%
+you if you're using this model in a
+ 
+
+ align:start position:0%
+you if you're using this model in a
+situation where the ratio is only three
+
+ align:start position:0%
+situation where the ratio is only three
+ 
+
+ align:start position:0%
+situation where the ratio is only three
+it will work roughly it won't be
+
+ align:start position:0%
+it will work roughly it won't be
+ 
+
+ align:start position:0%
+it will work roughly it won't be
+completely wrong there'll be a nice
+
+ align:start position:0%
+completely wrong there'll be a nice
+ 
+
+ align:start position:0%
+completely wrong there'll be a nice
+gentle transition from being right to
+
+ align:start position:0%
+gentle transition from being right to
+ 
+
+ align:start position:0%
+gentle transition from being right to
+being wrong and you'll be somewhere in
+
+ align:start position:0%
+being wrong and you'll be somewhere in
+ 
+
+ align:start position:0%
+being wrong and you'll be somewhere in
+the middle there and so a lot of the
+
+ align:start position:0%
+the middle there and so a lot of the
+ 
+
+ align:start position:0%
+the middle there and so a lot of the
+time we will use this model and if you
+
+ align:start position:0%
+time we will use this model and if you
+ 
+
+ align:start position:0%
+time we will use this model and if you
+go and look in Hutchinson's book and not
+
+ align:start position:0%
+go and look in Hutchinson's book and not
+ 
+
+ align:start position:0%
+go and look in Hutchinson's book and not
+covering it in the lecture today there
+
+ align:start position:0%
+covering it in the lecture today there
+ 
+
+ align:start position:0%
+covering it in the lecture today there
+are actually there's a limit to the
+
+ align:start position:0%
+are actually there's a limit to the
+ 
+
+ align:start position:0%
+are actually there's a limit to the
+energy levels for which CR works and so
+
+ align:start position:0%
+energy levels for which CR works and so
+ 
+
+ align:start position:0%
+energy levels for which CR works and so
+we find
+
+ align:start position:0%
+we find
+ 
+
+ align:start position:0%
+we find
+that uh transitions between the lower
+
+ align:start position:0%
+that uh transitions between the lower
+ 
+
+ align:start position:0%
+that uh transitions between the lower
+energy levels tend to be very rapid
+
+ align:start position:0%
+energy levels tend to be very rapid
+ 
+
+ align:start position:0%
+energy levels tend to be very rapid
+they're very favorable because of the
+
+ align:start position:0%
+they're very favorable because of the
+ 
+
+ align:start position:0%
+they're very favorable because of the
+overlap between the upper electron wave
+
+ align:start position:0%
+overlap between the upper electron wave
+ 
+
+ align:start position:0%
+overlap between the upper electron wave
+function and the lower electron wave
+
+ align:start position:0%
+function and the lower electron wave
+ 
+
+ align:start position:0%
+function and the lower electron wave
+functions and so you can actually use
+
+ align:start position:0%
+functions and so you can actually use
+ 
+
+ align:start position:0%
+functions and so you can actually use
+this coronal equilibrium to describe the
+
+ align:start position:0%
+this coronal equilibrium to describe the
+ 
+
+ align:start position:0%
+this coronal equilibrium to describe the
+first n energy levels and then you have
+
+ align:start position:0%
+first n energy levels and then you have
+ 
+
+ align:start position:0%
+first n energy levels and then you have
+to use a different
+
+ align:start position:0%
+to use a different
+ 
+
+ align:start position:0%
+to use a different
+equilibrium like maybe LTE to describe
+
+ align:start position:0%
+equilibrium like maybe LTE to describe
+ 
+
+ align:start position:0%
+equilibrium like maybe LTE to describe
+the upper energy level so you actually
+
+ align:start position:0%
+the upper energy level so you actually
+ 
+
+ align:start position:0%
+the upper energy level so you actually
+have like a transition between Which
+
+ align:start position:0%
+have like a transition between Which
+ 
+
+ align:start position:0%
+have like a transition between Which
+models are valid even within the same
+
+ align:start position:0%
+models are valid even within the same
+ 
+
+ align:start position:0%
+models are valid even within the same
+atom with the same ionization state so
+
+ align:start position:0%
+atom with the same ionization state so
+ 
+
+ align:start position:0%
+atom with the same ionization state so
+this stuff can get complicated um yeah
+
+ align:start position:0%
+this stuff can get complicated um yeah
+ 
+
+ align:start position:0%
+this stuff can get complicated um yeah
+that was probably too much information
+
+ align:start position:0%
+that was probably too much information
+ 
+
+ align:start position:0%
+that was probably too much information
+but still any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online okay and then the final thing
+
+ align:start position:0%
+online okay and then the final thing
+ 
+
+ align:start position:0%
+online okay and then the final thing
+after we've done
+
+ align:start position:0%
+after we've done
+ 
+
+ align:start position:0%
+after we've done
+um coronal equilibrium is really
+
+ align:start position:0%
+um coronal equilibrium is really
+ 
+
+ align:start position:0%
+um coronal equilibrium is really
+just having to actually solve those
+
+ align:start position:0%
+just having to actually solve those
+ 
+
+ align:start position:0%
+just having to actually solve those
+equations right so this is what we
+
+ align:start position:0%
+equations right so this is what we
+ 
+
+ align:start position:0%
+equations right so this is what we
+call non local
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thermodynamic equilibrium for many years
+
+ align:start position:0%
+thermodynamic equilibrium for many years
+ 
+
+ align:start position:0%
+thermodynamic equilibrium for many years
+I thought there was a hyphen here and
+
+ align:start position:0%
+I thought there was a hyphen here and
+ 
+
+ align:start position:0%
+I thought there was a hyphen here and
+this was non-local thermodynamic
+
+ align:start position:0%
+this was non-local thermodynamic
+ 
+
+ align:start position:0%
+this was non-local thermodynamic
+equilibrium so we have a thermodynamic
+
+ align:start position:0%
+equilibrium so we have a thermodynamic
+ 
+
+ align:start position:0%
+equilibrium so we have a thermodynamic
+equilibrium which mediated nonlocally it
+
+ align:start position:0%
+equilibrium which mediated nonlocally it
+ 
+
+ align:start position:0%
+equilibrium which mediated nonlocally it
+turns out I was wrong this is just not a
+
+ align:start position:0%
+turns out I was wrong this is just not a
+ 
+
+ align:start position:0%
+turns out I was wrong this is just not a
+local thermodynamic equilibrium which is
+
+ align:start position:0%
+local thermodynamic equilibrium which is
+ 
+
+ align:start position:0%
+local thermodynamic equilibrium which is
+a much less descriptive name but is much
+
+ align:start position:0%
+a much less descriptive name but is much
+ 
+
+ align:start position:0%
+a much less descriptive name but is much
+more valid and you'll often see this
+
+ align:start position:0%
+more valid and you'll often see this
+ 
+
+ align:start position:0%
+more valid and you'll often see this
+written as lowercase n
+
+ align:start position:0%
+written as lowercase n
+ 
+
+ align:start position:0%
+written as lowercase n
+LTE so in general you have to solve all
+
+ align:start position:0%
+LTE so in general you have to solve all
+ 
+
+ align:start position:0%
+LTE so in general you have to solve all
+of the different processes exciting and
+
+ align:start position:0%
+of the different processes exciting and
+ 
+
+ align:start position:0%
+of the different processes exciting and
+de exciting but for a specific nlte
+
+ align:start position:0%
+de exciting but for a specific nlte
+ 
+
+ align:start position:0%
+de exciting but for a specific nlte
+model for a specific plasma you're
+
+ align:start position:0%
+model for a specific plasma you're
+ 
+
+ align:start position:0%
+model for a specific plasma you're
+interested in you may still be able to
+
+ align:start position:0%
+interested in you may still be able to
+ 
+
+ align:start position:0%
+interested in you may still be able to
+restrict what those processes are so
+
+ align:start position:0%
+restrict what those processes are so
+ 
+
+ align:start position:0%
+restrict what those processes are so
+what you need to do is actually consider
+
+ align:start position:0%
+what you need to do is actually consider
+ 
+
+ align:start position:0%
+what you need to do is actually consider
+all the relevant
+
+ align:start position:0%
+all the relevant
+ 
+
+ align:start position:0%
+all the relevant
+processes because even in these models
+
+ align:start position:0%
+processes because even in these models
+ 
+
+ align:start position:0%
+processes because even in these models
+other processes are happening it's just
+
+ align:start position:0%
+other processes are happening it's just
+ 
+
+ align:start position:0%
+other processes are happening it's just
+we think the rate is very small and so
+
+ align:start position:0%
+we think the rate is very small and so
+ 
+
+ align:start position:0%
+we think the rate is very small and so
+those processes are not relevant so if
+
+ align:start position:0%
+those processes are not relevant so if
+ 
+
+ align:start position:0%
+those processes are not relevant so if
+you're doing an nlte model you simply
+
+ align:start position:0%
+you're doing an nlte model you simply
+ 
+
+ align:start position:0%
+you're doing an nlte model you simply
+have to think what calculate what
+
+ align:start position:0%
+have to think what calculate what
+ 
+
+ align:start position:0%
+have to think what calculate what
+processes are relevant to what aren't so
+
+ align:start position:0%
+processes are relevant to what aren't so
+ 
+
+ align:start position:0%
+processes are relevant to what aren't so
+I'll give you an example here if we're
+
+ align:start position:0%
+I'll give you an example here if we're
+ 
+
+ align:start position:0%
+I'll give you an example here if we're
+dealing with a photoionized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma so this is a for example I've got
+
+ align:start position:0%
+plasma so this is a for example I've got
+ 
+
+ align:start position:0%
+plasma so this is a for example I've got
+a gas
+
+ align:start position:0%
+a gas
+ 
+
+ align:start position:0%
+a gas
+cell chamber filled with gas and I've
+
+ align:start position:0%
+cell chamber filled with gas and I've
+ 
+
+ align:start position:0%
+cell chamber filled with gas and I've
+got Windows on it which are transparent
+
+ align:start position:0%
+got Windows on it which are transparent
+ 
+
+ align:start position:0%
+got Windows on it which are transparent
+to X-rays and I have an x-ray Source
+
+ align:start position:0%
+to X-rays and I have an x-ray Source
+ 
+
+ align:start position:0%
+to X-rays and I have an x-ray Source
+outside those x-rays will stream in and
+
+ align:start position:0%
+outside those x-rays will stream in and
+ 
+
+ align:start position:0%
+outside those x-rays will stream in and
+they will photo ionize the gas the uh
+
+ align:start position:0%
+they will photo ionize the gas the uh
+ 
+
+ align:start position:0%
+they will photo ionize the gas the uh
+photons will be absorbed and we'll have
+
+ align:start position:0%
+photons will be absorbed and we'll have
+ 
+
+ align:start position:0%
+photons will be absorbed and we'll have
+photo
+
+ align:start position:0%
+photo
+ 
+
+ align:start position:0%
+photo
+ionization and then the uh occupation
+
+ align:start position:0%
+ionization and then the uh occupation
+ 
+
+ align:start position:0%
+ionization and then the uh occupation
+levels will be set by those photo
+
+ align:start position:0%
+levels will be set by those photo
+ 
+
+ align:start position:0%
+levels will be set by those photo
+ionization processes we won't have to
+
+ align:start position:0%
+ionization processes we won't have to
+ 
+
+ align:start position:0%
+ionization processes we won't have to
+consider collisional processes because
+
+ align:start position:0%
+consider collisional processes because
+ 
+
+ align:start position:0%
+consider collisional processes because
+the photon field the strength of the
+
+ align:start position:0%
+the photon field the strength of the
+ 
+
+ align:start position:0%
+the photon field the strength of the
+X-ray Drive is so strong that the
+
+ align:start position:0%
+X-ray Drive is so strong that the
+ 
+
+ align:start position:0%
+X-ray Drive is so strong that the
+photons are much more likely to be
+
+ align:start position:0%
+photons are much more likely to be
+ 
+
+ align:start position:0%
+photons are much more likely to be
+involved than any collisions and so for
+
+ align:start position:0%
+involved than any collisions and so for
+ 
+
+ align:start position:0%
+involved than any collisions and so for
+a photon ionized system for example we
+
+ align:start position:0%
+a photon ionized system for example we
+ 
+
+ align:start position:0%
+a photon ionized system for example we
+can neglect collisional
+
+ align:start position:0%
+can neglect collisional
+ 
+
+ align:start position:0%
+can neglect collisional
+process so that reduces the number of
+
+ align:start position:0%
+process so that reduces the number of
+ 
+
+ align:start position:0%
+process so that reduces the number of
+equations that you need to solve uh and
+
+ align:start position:0%
+equations that you need to solve uh and
+ 
+
+ align:start position:0%
+equations that you need to solve uh and
+so you may be able to get away with a
+
+ align:start position:0%
+so you may be able to get away with a
+ 
+
+ align:start position:0%
+so you may be able to get away with a
+smaller set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations but if you calculate it and
+
+ align:start position:0%
+equations but if you calculate it and
+ 
+
+ align:start position:0%
+equations but if you calculate it and
+all your processes are roughly equal
+
+ align:start position:0%
+all your processes are roughly equal
+ 
+
+ align:start position:0%
+all your processes are roughly equal
+then you really do have to solve that
+
+ align:start position:0%
+then you really do have to solve that
+ 
+
+ align:start position:0%
+then you really do have to solve that
+big equation I put up on the board last
+
+ align:start position:0%
+big equation I put up on the board last
+ 
+
+ align:start position:0%
+big equation I put up on the board last
+time that was
+
+ align:start position:0%
+time that was
+ 
+
+ align:start position:0%
+time that was
+effectively zero because we're in steady
+
+ align:start position:0%
+effectively zero because we're in steady
+ 
+
+ align:start position:0%
+effectively zero because we're in steady
+state equals the sum over all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processes and as I mentioned people
+
+ align:start position:0%
+processes and as I mentioned people
+ 
+
+ align:start position:0%
+processes and as I mentioned people
+spend their lives writing codes to
+
+ align:start position:0%
+spend their lives writing codes to
+ 
+
+ align:start position:0%
+spend their lives writing codes to
+calculate these coefficients and to
+
+ align:start position:0%
+calculate these coefficients and to
+ 
+
+ align:start position:0%
+calculate these coefficients and to
+solve this balance um and it can get
+
+ align:start position:0%
+solve this balance um and it can get
+ 
+
+ align:start position:0%
+solve this balance um and it can get
+very very messy
+
+ align:start position:0%
+very very messy
+ 
+
+ align:start position:0%
+very very messy
+indeed so that's all I'm really going to
+
+ align:start position:0%
+indeed so that's all I'm really going to
+ 
+
+ align:start position:0%
+indeed so that's all I'm really going to
+say on
+
+ align:start position:0%
+say on
+ 
+
+ align:start position:0%
+say on
+NLP so in general if we're trying to do
+
+ align:start position:0%
+NLP so in general if we're trying to do
+ 
+
+ align:start position:0%
+NLP so in general if we're trying to do
+Spectros
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is a workflow that we might need
+
+ align:start position:0%
+there is a workflow that we might need
+ 
+
+ align:start position:0%
+there is a workflow that we might need
+to do so this is modeling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectr so first of all we're going to
+
+ align:start position:0%
+spectr so first of all we're going to
+ 
+
+ align:start position:0%
+spectr so first of all we're going to
+model the Spectra from a blob of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plasma little Cube like this it's got
+
+ align:start position:0%
+plasma little Cube like this it's got
+ 
+
+ align:start position:0%
+plasma little Cube like this it's got
+some mass density which is what
+
+ align:start position:0%
+some mass density which is what
+ 
+
+ align:start position:0%
+some mass density which is what
+spectroscopist often work in row and it
+
+ align:start position:0%
+spectroscopist often work in row and it
+ 
+
+ align:start position:0%
+spectroscopist often work in row and it
+has some temperature occasionally your
+
+ align:start position:0%
+has some temperature occasionally your
+ 
+
+ align:start position:0%
+has some temperature occasionally your
+spectroscopists might work in terms of
+
+ align:start position:0%
+spectroscopists might work in terms of
+ 
+
+ align:start position:0%
+spectroscopists might work in terms of
+ion density instead obviously these are
+
+ align:start position:0%
+ion density instead obviously these are
+ 
+
+ align:start position:0%
+ion density instead obviously these are
+same up to the ion Mass
+
+ align:start position:0%
+same up to the ion Mass
+ 
+
+ align:start position:0%
+same up to the ion Mass
+here then you need to determine what
+
+ align:start position:0%
+here then you need to determine what
+ 
+
+ align:start position:0%
+here then you need to determine what
+equilibrium is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+appropriate you know this could be a
+
+ align:start position:0%
+appropriate you know this could be a
+ 
+
+ align:start position:0%
+appropriate you know this could be a
+Saha type equilibrium or a collisional
+
+ align:start position:0%
+Saha type equilibrium or a collisional
+ 
+
+ align:start position:0%
+Saha type equilibrium or a collisional
+radiative equilibrium so maybe you know
+
+ align:start position:0%
+radiative equilibrium so maybe you know
+ 
+
+ align:start position:0%
+radiative equilibrium so maybe you know
+this by some back of the envelope
+
+ align:start position:0%
+this by some back of the envelope
+ 
+
+ align:start position:0%
+this by some back of the envelope
+calculations maybe you go through and
+
+ align:start position:0%
+calculations maybe you go through and
+ 
+
+ align:start position:0%
+calculations maybe you go through and
+calculate a load of rates and determine
+
+ align:start position:0%
+calculate a load of rates and determine
+ 
+
+ align:start position:0%
+calculate a load of rates and determine
+what's most important but you have to
+
+ align:start position:0%
+what's most important but you have to
+ 
+
+ align:start position:0%
+what's most important but you have to
+determine what your
+
+ align:start position:0%
+determine what your
+ 
+
+ align:start position:0%
+determine what your
+equilibriums so then you need to
+
+ align:start position:0%
+equilibriums so then you need to
+ 
+
+ align:start position:0%
+equilibriums so then you need to
+calculate the ionization
+
+ align:start position:0%
+calculate the ionization
+ 
+
+ align:start position:0%
+calculate the ionization
+States what ionizations are present in
+
+ align:start position:0%
+States what ionizations are present in
+ 
+
+ align:start position:0%
+States what ionizations are present in
+your system here so these are the
+
+ align:start position:0%
+your system here so these are the
+ 
+
+ align:start position:0%
+your system here so these are the
+density of ions with charge Z all the
+
+ align:start position:0%
+density of ions with charge Z all the
+ 
+
+ align:start position:0%
+density of ions with charge Z all the
+different Zs in some cases you may be
+
+ align:start position:0%
+different Zs in some cases you may be
+ 
+
+ align:start position:0%
+different Zs in some cases you may be
+very weakly ionized you may have a lot
+
+ align:start position:0%
+very weakly ionized you may have a lot
+ 
+
+ align:start position:0%
+very weakly ionized you may have a lot
+of neutrals and you may have just a few
+
+ align:start position:0%
+of neutrals and you may have just a few
+ 
+
+ align:start position:0%
+of neutrals and you may have just a few
+atoms which have an ionization of one in
+
+ align:start position:0%
+atoms which have an ionization of one in
+ 
+
+ align:start position:0%
+atoms which have an ionization of one in
+other cases you may go all the way from
+
+ align:start position:0%
+other cases you may go all the way from
+ 
+
+ align:start position:0%
+other cases you may go all the way from
+neutrals to fully stripped uh for
+
+ align:start position:0%
+neutrals to fully stripped uh for
+ 
+
+ align:start position:0%
+neutrals to fully stripped uh for
+something like tungsten which has 74
+
+ align:start position:0%
+something like tungsten which has 74
+ 
+
+ align:start position:0%
+something like tungsten which has 74
+electrons 76 electrons that's an awful
+
+ align:start position:0%
+electrons 76 electrons that's an awful
+ 
+
+ align:start position:0%
+electrons 76 electrons that's an awful
+lot of energy but you may well be able
+
+ align:start position:0%
+lot of energy but you may well be able
+ 
+
+ align:start position:0%
+lot of energy but you may well be able
+to get through plasma where you've got
+
+ align:start position:0%
+to get through plasma where you've got
+ 
+
+ align:start position:0%
+to get through plasma where you've got
+fly strip P so then you'd have to take
+
+ align:start position:0%
+fly strip P so then you'd have to take
+ 
+
+ align:start position:0%
+fly strip P so then you'd have to take
+into account all the other ionization
+
+ align:start position:0%
+into account all the other ionization
+ 
+
+ align:start position:0%
+into account all the other ionization
+St then you have to calculate the
+
+ align:start position:0%
+St then you have to calculate the
+ 
+
+ align:start position:0%
+St then you have to calculate the
+excited
+
+ align:start position:0%
+excited
+ 
+
+ align:start position:0%
+excited
+States and you have to calculate the
+
+ align:start position:0%
+States and you have to calculate the
+ 
+
+ align:start position:0%
+States and you have to calculate the
+excited States for each NZ so for all NZ
+
+ align:start position:0%
+excited States for each NZ so for all NZ
+ 
+
+ align:start position:0%
+excited States for each NZ so for all NZ
+you need NZ and then whatever the
+
+ align:start position:0%
+you need NZ and then whatever the
+ 
+
+ align:start position:0%
+you need NZ and then whatever the
+excitation
+
+ align:start position:0%
+excitation
+ 
+
+ align:start position:0%
+excitation
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay then you need to calculate the line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strengths these are these
+
+ align:start position:0%
+strengths these are these
+ 
+
+ align:start position:0%
+strengths these are these
+coefficients a i j and you'll remember
+
+ align:start position:0%
+coefficients a i j and you'll remember
+ 
+
+ align:start position:0%
+coefficients a i j and you'll remember
+that these had some hand wavy relevance
+
+ align:start position:0%
+that these had some hand wavy relevance
+ 
+
+ align:start position:0%
+that these had some hand wavy relevance
+to the overlap integral with the dipole
+
+ align:start position:0%
+to the overlap integral with the dipole
+ 
+
+ align:start position:0%
+to the overlap integral with the dipole
+operator between the upper and the Lower
+
+ align:start position:0%
+operator between the upper and the Lower
+ 
+
+ align:start position:0%
+operator between the upper and the Lower
+State but this is a dipole operator
+
+ align:start position:0%
+State but this is a dipole operator
+ 
+
+ align:start position:0%
+State but this is a dipole operator
+which is radiating away a photon of
+
+ align:start position:0%
+which is radiating away a photon of
+ 
+
+ align:start position:0%
+which is radiating away a photon of
+energy H bar Omega i j and that process
+
+ align:start position:0%
+energy H bar Omega i j and that process
+ 
+
+ align:start position:0%
+energy H bar Omega i j and that process
+has some probability to occur and so
+
+ align:start position:0%
+has some probability to occur and so
+ 
+
+ align:start position:0%
+has some probability to occur and so
+this tells you if you how many photons
+
+ align:start position:0%
+this tells you if you how many photons
+ 
+
+ align:start position:0%
+this tells you if you how many photons
+with that energy that you're going to
+
+ align:start position:0%
+with that energy that you're going to
+ 
+
+ align:start position:0%
+with that energy that you're going to
+see and you need to do that for every
+
+ align:start position:0%
+see and you need to do that for every
+ 
+
+ align:start position:0%
+see and you need to do that for every
+transition between
+
+ align:start position:0%
+transition between
+ 
+
+ align:start position:0%
+transition between
+every set of excited States for every
+
+ align:start position:0%
+every set of excited States for every
+ 
+
+ align:start position:0%
+every set of excited States for every
+ion in your system
+
+ align:start position:0%
+ion in your system
+ 
+
+ align:start position:0%
+ion in your system
+okay so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard once you've done that you can now
+
+ align:start position:0%
+hard once you've done that you can now
+ 
+
+ align:start position:0%
+hard once you've done that you can now
+predict the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Spectra this is
+
+ align:start position:0%
+Spectra this is
+ 
+
+ align:start position:0%
+Spectra this is
+predicting the intensity of radiation
+
+ align:start position:0%
+predicting the intensity of radiation
+ 
+
+ align:start position:0%
+predicting the intensity of radiation
+with frequency
+
+ align:start position:0%
+with frequency
+ 
+
+ align:start position:0%
+with frequency
+Omega for the very specific density and
+
+ align:start position:0%
+Omega for the very specific density and
+ 
+
+ align:start position:0%
+Omega for the very specific density and
+temperature that you started out with
+
+ align:start position:0%
+temperature that you started out with
+ 
+
+ align:start position:0%
+temperature that you started out with
+okay now if you're very very
+
+ align:start position:0%
+okay now if you're very very
+ 
+
+ align:start position:0%
+okay now if you're very very
+lucky your system is optically thin so
+
+ align:start position:0%
+lucky your system is optically thin so
+ 
+
+ align:start position:0%
+lucky your system is optically thin so
+tow less than one life is
+
+ align:start position:0%
+tow less than one life is
+ 
+
+ align:start position:0%
+tow less than one life is
+good if to is greater than one now you
+
+ align:start position:0%
+good if to is greater than one now you
+ 
+
+ align:start position:0%
+good if to is greater than one now you
+need to consider uh radiation
+
+ align:start position:0%
+need to consider uh radiation
+ 
+
+ align:start position:0%
+need to consider uh radiation
+transport so the fact that some of the
+
+ align:start position:0%
+transport so the fact that some of the
+ 
+
+ align:start position:0%
+transport so the fact that some of the
+radiation will be absorbed as it moves
+
+ align:start position:0%
+radiation will be absorbed as it moves
+ 
+
+ align:start position:0%
+radiation will be absorbed as it moves
+through your
+
+ align:start position:0%
+through your
+ 
+
+ align:start position:0%
+through your
+plasma and actually for both of these as
+
+ align:start position:0%
+plasma and actually for both of these as
+ 
+
+ align:start position:0%
+plasma and actually for both of these as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+you'll have to consider things like
+
+ align:start position:0%
+you'll have to consider things like
+ 
+
+ align:start position:0%
+you'll have to consider things like
+Reflections so the fact you've got metal
+
+ align:start position:0%
+Reflections so the fact you've got metal
+ 
+
+ align:start position:0%
+Reflections so the fact you've got metal
+walls on your toac or whatever it is
+
+ align:start position:0%
+walls on your toac or whatever it is
+ 
+
+ align:start position:0%
+walls on your toac or whatever it is
+means that some light going the other
+
+ align:start position:0%
+means that some light going the other
+ 
+
+ align:start position:0%
+means that some light going the other
+way will bounce back got my plasma here
+
+ align:start position:0%
+way will bounce back got my plasma here
+ 
+
+ align:start position:0%
+way will bounce back got my plasma here
+some of the light from this bit of
+
+ align:start position:0%
+some of the light from this bit of
+ 
+
+ align:start position:0%
+some of the light from this bit of
+plasma is going to be emitted this way
+
+ align:start position:0%
+plasma is going to be emitted this way
+ 
+
+ align:start position:0%
+plasma is going to be emitted this way
+and then it will bounce back into your
+
+ align:start position:0%
+and then it will bounce back into your
+ 
+
+ align:start position:0%
+and then it will bounce back into your
+detector and although it's being emitted
+
+ align:start position:0%
+detector and although it's being emitted
+ 
+
+ align:start position:0%
+detector and although it's being emitted
+from here it will look like it's been
+
+ align:start position:0%
+from here it will look like it's been
+ 
+
+ align:start position:0%
+from here it will look like it's been
+emitted along the line of sight hereit
+
+ align:start position:0%
+emitted along the line of sight hereit
+ 
+
+ align:start position:0%
+emitted along the line of sight hereit
+so if you don't take into account the
+
+ align:start position:0%
+so if you don't take into account the
+ 
+
+ align:start position:0%
+so if you don't take into account the
+reflections you will be thinking you've
+
+ align:start position:0%
+reflections you will be thinking you've
+ 
+
+ align:start position:0%
+reflections you will be thinking you've
+got lines from one bit of a plasma where
+
+ align:start position:0%
+got lines from one bit of a plasma where
+ 
+
+ align:start position:0%
+got lines from one bit of a plasma where
+in fact from another bit of a
+
+ align:start position:0%
+in fact from another bit of a
+ 
+
+ align:start position:0%
+in fact from another bit of a
+plasma you'll also need to model the
+
+ align:start position:0%
+plasma you'll also need to model the
+ 
+
+ align:start position:0%
+plasma you'll also need to model the
+response of your
+
+ align:start position:0%
+response of your
+ 
+
+ align:start position:0%
+response of your
+detector so there are no
+
+ align:start position:0%
+detector so there are no
+ 
+
+ align:start position:0%
+detector so there are no
+perfect spectrometers out there and they
+
+ align:start position:0%
+perfect spectrometers out there and they
+ 
+
+ align:start position:0%
+perfect spectrometers out there and they
+in general have a response curve to
+
+ align:start position:0%
+in general have a response curve to
+ 
+
+ align:start position:0%
+in general have a response curve to
+them which is like response as a
+
+ align:start position:0%
+them which is like response as a
+ 
+
+ align:start position:0%
+them which is like response as a
+frequency of Omega they're not flat they
+
+ align:start position:0%
+frequency of Omega they're not flat they
+ 
+
+ align:start position:0%
+frequency of Omega they're not flat they
+treat different frequencies differently
+
+ align:start position:0%
+treat different frequencies differently
+ 
+
+ align:start position:0%
+treat different frequencies differently
+they obsorb you know infrared photons
+
+ align:start position:0%
+they obsorb you know infrared photons
+ 
+
+ align:start position:0%
+they obsorb you know infrared photons
+more than visible
+
+ align:start position:0%
+more than visible
+ 
+
+ align:start position:0%
+more than visible
+photons and then finally you need to
+
+ align:start position:0%
+photons and then finally you need to
+ 
+
+ align:start position:0%
+photons and then finally you need to
+compare this to your experimental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data so for example if you had a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectrum that
+
+ align:start position:0%
+spectrum that
+ 
+
+ align:start position:0%
+spectrum that
+has two lines in it like that and you've
+
+ align:start position:0%
+has two lines in it like that and you've
+ 
+
+ align:start position:0%
+has two lines in it like that and you've
+done all of this process and you get out
+
+ align:start position:0%
+done all of this process and you get out
+ 
+
+ align:start position:0%
+done all of this process and you get out
+a spectrum that looks like this you have
+
+ align:start position:0%
+a spectrum that looks like this you have
+ 
+
+ align:start position:0%
+a spectrum that looks like this you have
+a choice you can even say it's close
+
+ align:start position:0%
+a choice you can even say it's close
+ 
+
+ align:start position:0%
+a choice you can even say it's close
+enough for today or you iterate and you
+
+ align:start position:0%
+enough for today or you iterate and you
+ 
+
+ align:start position:0%
+enough for today or you iterate and you
+do all of this again right and you pick
+
+ align:start position:0%
+do all of this again right and you pick
+ 
+
+ align:start position:0%
+do all of this again right and you pick
+a new density and temperature and you do
+
+ align:start position:0%
+a new density and temperature and you do
+ 
+
+ align:start position:0%
+a new density and temperature and you do
+some sort of gradient ense type thing
+
+ align:start position:0%
+some sort of gradient ense type thing
+ 
+
+ align:start position:0%
+some sort of gradient ense type thing
+until eventually your modeled Spectra
+
+ align:start position:0%
+until eventually your modeled Spectra
+ 
+
+ align:start position:0%
+until eventually your modeled Spectra
+matches up with your experimental
+
+ align:start position:0%
+matches up with your experimental
+ 
+
+ align:start position:0%
+matches up with your experimental
+Spectra and then you say
+
+ align:start position:0%
+Spectra and then you say
+ 
+
+ align:start position:0%
+Spectra and then you say
+aha now I finally
+
+ align:start position:0%
+aha now I finally
+ 
+
+ align:start position:0%
+aha now I finally
+know the density and temperature of my
+
+ align:start position:0%
+know the density and temperature of my
+ 
+
+ align:start position:0%
+know the density and temperature of my
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+now so it's a fair bit of work to do
+
+ align:start position:0%
+now so it's a fair bit of work to do
+ 
+
+ align:start position:0%
+now so it's a fair bit of work to do
+spectrally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so you can I will show you show you
+
+ align:start position:0%
+yeah so you can I will show you show you
+ 
+
+ align:start position:0%
+yeah so you can I will show you show you
+some tricks to narrow this parameter
+
+ align:start position:0%
+some tricks to narrow this parameter
+ 
+
+ align:start position:0%
+some tricks to narrow this parameter
+space in a moment this is the sort of
+
+ align:start position:0%
+space in a moment this is the sort of
+ 
+
+ align:start position:0%
+space in a moment this is the sort of
+most General case fact I had a page of
+
+ align:start position:0%
+most General case fact I had a page of
+ 
+
+ align:start position:0%
+most General case fact I had a page of
+notes on this and then my iPad hasn't
+
+ align:start position:0%
+notes on this and then my iPad hasn't
+ 
+
+ align:start position:0%
+notes on this and then my iPad hasn't
+updated them but I wrote the word line
+
+ align:start position:0%
+updated them but I wrote the word line
+ 
+
+ align:start position:0%
+updated them but I wrote the word line
+ratios and I'm gonna try and reconstruct
+
+ align:start position:0%
+ratios and I'm gonna try and reconstruct
+ 
+
+ align:start position:0%
+ratios and I'm gonna try and reconstruct
+the memory what exactly I was going to
+
+ align:start position:0%
+the memory what exactly I was going to
+ 
+
+ align:start position:0%
+the memory what exactly I was going to
+say so we'll see how it goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well other Diagnostics are can be
+
+ align:start position:0%
+well other Diagnostics are can be
+ 
+
+ align:start position:0%
+well other Diagnostics are can be
+expensive they can be limited to certain
+
+ align:start position:0%
+expensive they can be limited to certain
+ 
+
+ align:start position:0%
+expensive they can be limited to certain
+parameter ranges uh if you're doing
+
+ align:start position:0%
+parameter ranges uh if you're doing
+ 
+
+ align:start position:0%
+parameter ranges uh if you're doing
+astrophysics you can't do Thompson
+
+ align:start position:0%
+astrophysics you can't do Thompson
+ 
+
+ align:start position:0%
+astrophysics you can't do Thompson
+scattering on your black ho cor Corona
+
+ align:start position:0%
+scattering on your black ho cor Corona
+ 
+
+ align:start position:0%
+scattering on your black ho cor Corona
+so you have you're stuck with this sort
+
+ align:start position:0%
+so you have you're stuck with this sort
+ 
+
+ align:start position:0%
+so you have you're stuck with this sort
+of thing um spectroscopy does provide
+
+ align:start position:0%
+of thing um spectroscopy does provide
+ 
+
+ align:start position:0%
+of thing um spectroscopy does provide
+extremely detailed information on all of
+
+ align:start position:0%
+extremely detailed information on all of
+ 
+
+ align:start position:0%
+extremely detailed information on all of
+the atomic kinetics this is what people
+
+ align:start position:0%
+the atomic kinetics this is what people
+ 
+
+ align:start position:0%
+the atomic kinetics this is what people
+call this sort of distribution of
+
+ align:start position:0%
+call this sort of distribution of
+ 
+
+ align:start position:0%
+call this sort of distribution of
+different states of the atomic kinetics
+
+ align:start position:0%
+different states of the atomic kinetics
+ 
+
+ align:start position:0%
+different states of the atomic kinetics
+so if you're far from local
+
+ align:start position:0%
+so if you're far from local
+ 
+
+ align:start position:0%
+so if you're far from local
+thermodynamic equilibrium say you're
+
+ align:start position:0%
+thermodynamic equilibrium say you're
+ 
+
+ align:start position:0%
+thermodynamic equilibrium say you're
+looking at fast electrons in a toac the
+
+ align:start position:0%
+looking at fast electrons in a toac the
+ 
+
+ align:start position:0%
+looking at fast electrons in a toac the
+uh Spectra May provide information on
+
+ align:start position:0%
+uh Spectra May provide information on
+ 
+
+ align:start position:0%
+uh Spectra May provide information on
+those fast electrons that something like
+
+ align:start position:0%
+those fast electrons that something like
+ 
+
+ align:start position:0%
+those fast electrons that something like
+Thomson scattering doesn't because
+
+ align:start position:0%
+Thomson scattering doesn't because
+ 
+
+ align:start position:0%
+Thomson scattering doesn't because
+Thompson scattering maybe as sensitive
+
+ align:start position:0%
+Thompson scattering maybe as sensitive
+ 
+
+ align:start position:0%
+Thompson scattering maybe as sensitive
+just to the bulk of the plasma so you
+
+ align:start position:0%
+just to the bulk of the plasma so you
+ 
+
+ align:start position:0%
+just to the bulk of the plasma so you
+know this is a time honored time honored
+
+ align:start position:0%
+know this is a time honored time honored
+ 
+
+ align:start position:0%
+know this is a time honored time honored
+diagnostic we have a lot of knowledge
+
+ align:start position:0%
+diagnostic we have a lot of knowledge
+ 
+
+ align:start position:0%
+diagnostic we have a lot of knowledge
+about how to do it h it's just that it
+
+ align:start position:0%
+about how to do it h it's just that it
+ 
+
+ align:start position:0%
+about how to do it h it's just that it
+turns out to be very hard I'm sort of
+
+ align:start position:0%
+turns out to be very hard I'm sort of
+ 
+
+ align:start position:0%
+turns out to be very hard I'm sort of
+presented this in a slightly flippant
+
+ align:start position:0%
+presented this in a slightly flippant
+ 
+
+ align:start position:0%
+presented this in a slightly flippant
+way but this is what you need to do you
+
+ align:start position:0%
+way but this is what you need to do you
+ 
+
+ align:start position:0%
+way but this is what you need to do you
+actually want to solve all these things
+
+ align:start position:0%
+actually want to solve all these things
+ 
+
+ align:start position:0%
+actually want to solve all these things
+some of these steps have already been
+
+ align:start position:0%
+some of these steps have already been
+ 
+
+ align:start position:0%
+some of these steps have already been
+done for you right I mean a lot of this
+
+ align:start position:0%
+done for you right I mean a lot of this
+ 
+
+ align:start position:0%
+done for you right I mean a lot of this
+is now included in computer Packaging
+
+ align:start position:0%
+is now included in computer Packaging
+ 
+
+ align:start position:0%
+is now included in computer Packaging
+and so if you know what your equilibrium
+
+ align:start position:0%
+and so if you know what your equilibrium
+ 
+
+ align:start position:0%
+and so if you know what your equilibrium
+is um for example here this row T
+
+ align:start position:0%
+is um for example here this row T
+ 
+
+ align:start position:0%
+is um for example here this row T
+getting out some Spectra here there are
+
+ align:start position:0%
+getting out some Spectra here there are
+ 
+
+ align:start position:0%
+getting out some Spectra here there are
+large codes prism spec is a commercially
+
+ align:start position:0%
+large codes prism spec is a commercially
+ 
+
+ align:start position:0%
+large codes prism spec is a commercially
+available code you give it a density at
+
+ align:start position:0%
+available code you give it a density at
+ 
+
+ align:start position:0%
+available code you give it a density at
+a temperature and it will and the size
+
+ align:start position:0%
+a temperature and it will and the size
+ 
+
+ align:start position:0%
+a temperature and it will and the size
+of your plasma and it will do radiation
+
+ align:start position:0%
+of your plasma and it will do radiation
+ 
+
+ align:start position:0%
+of your plasma and it will do radiation
+transport through it and tell you what
+
+ align:start position:0%
+transport through it and tell you what
+ 
+
+ align:start position:0%
+transport through it and tell you what
+the Spectra is you run that for a few
+
+ align:start position:0%
+the Spectra is you run that for a few
+ 
+
+ align:start position:0%
+the Spectra is you run that for a few
+different rows and T's then and you
+
+ align:start position:0%
+different rows and T's then and you
+ 
+
+ align:start position:0%
+different rows and T's then and you
+create a table of Spectra of a different
+
+ align:start position:0%
+create a table of Spectra of a different
+ 
+
+ align:start position:0%
+create a table of Spectra of a different
+row and T you can very quickly fit that
+
+ align:start position:0%
+row and T you can very quickly fit that
+ 
+
+ align:start position:0%
+row and T you can very quickly fit that
+to your experimental Spectrum so um none
+
+ align:start position:0%
+to your experimental Spectrum so um none
+ 
+
+ align:start position:0%
+to your experimental Spectrum so um none
+of this stuff is impossible just if
+
+ align:start position:0%
+of this stuff is impossible just if
+ 
+
+ align:start position:0%
+of this stuff is impossible just if
+you're doing it from scrp be very hard
+
+ align:start position:0%
+you're doing it from scrp be very hard
+ 
+
+ align:start position:0%
+you're doing it from scrp be very hard
+yeah I'll just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+technical yeah that's a great question
+
+ align:start position:0%
+technical yeah that's a great question
+ 
+
+ align:start position:0%
+technical yeah that's a great question
+so you know what we talked about here is
+
+ align:start position:0%
+so you know what we talked about here is
+ 
+
+ align:start position:0%
+so you know what we talked about here is
+that there is some photon with some
+
+ align:start position:0%
+that there is some photon with some
+ 
+
+ align:start position:0%
+that there is some photon with some
+energy right so if we think that that is
+
+ align:start position:0%
+energy right so if we think that that is
+ 
+
+ align:start position:0%
+energy right so if we think that that is
+true Spectrum should look like a set of
+
+ align:start position:0%
+true Spectrum should look like a set of
+ 
+
+ align:start position:0%
+true Spectrum should look like a set of
+Delta functions right and those Delta
+
+ align:start position:0%
+Delta functions right and those Delta
+ 
+
+ align:start position:0%
+Delta functions right and those Delta
+functions should sit at Omega i j and I
+
+ align:start position:0%
+functions should sit at Omega i j and I
+ 
+
+ align:start position:0%
+functions should sit at Omega i j and I
+know the Delta functions that are
+
+ align:start position:0%
+know the Delta functions that are
+ 
+
+ align:start position:0%
+know the Delta functions that are
+infinite but they should have a height
+
+ align:start position:0%
+infinite but they should have a height
+ 
+
+ align:start position:0%
+infinite but they should have a height
+that is related to the strength of the
+
+ align:start position:0%
+that is related to the strength of the
+ 
+
+ align:start position:0%
+that is related to the strength of the
+transition
+
+ align:start position:0%
+transition
+ 
+
+ align:start position:0%
+transition
+here what we'll talk about next lecture
+
+ align:start position:0%
+here what we'll talk about next lecture
+ 
+
+ align:start position:0%
+here what we'll talk about next lecture
+is line broad so that is when these
+
+ align:start position:0%
+is line broad so that is when these
+ 
+
+ align:start position:0%
+is line broad so that is when these
+lines are broadened by other processes
+
+ align:start position:0%
+lines are broadened by other processes
+ 
+
+ align:start position:0%
+lines are broadened by other processes
+and we may be able to in some
+
+ align:start position:0%
+and we may be able to in some
+ 
+
+ align:start position:0%
+and we may be able to in some
+circumstances learn more about the
+
+ align:start position:0%
+circumstances learn more about the
+ 
+
+ align:start position:0%
+circumstances learn more about the
+plasma from the broadening for example
+
+ align:start position:0%
+plasma from the broadening for example
+ 
+
+ align:start position:0%
+plasma from the broadening for example
+if there's Doppler Broad will learn
+
+ align:start position:0%
+if there's Doppler Broad will learn
+ 
+
+ align:start position:0%
+if there's Doppler Broad will learn
+about the temperature there's Stark
+
+ align:start position:0%
+about the temperature there's Stark
+ 
+
+ align:start position:0%
+about the temperature there's Stark
+broadening we'll learn about the density
+
+ align:start position:0%
+broadening we'll learn about the density
+ 
+
+ align:start position:0%
+broadening we'll learn about the density
+uh and then there are other Zan
+
+ align:start position:0%
+uh and then there are other Zan
+ 
+
+ align:start position:0%
+uh and then there are other Zan
+splitting and things like that that may
+
+ align:start position:0%
+splitting and things like that that may
+ 
+
+ align:start position:0%
+splitting and things like that that may
+even be related to Magnetic but we'll
+
+ align:start position:0%
+even be related to Magnetic but we'll
+ 
+
+ align:start position:0%
+even be related to Magnetic but we'll
+get on to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later I would I would say yes in general
+
+ align:start position:0%
+later I would I would say yes in general
+ 
+
+ align:start position:0%
+later I would I would say yes in general
+and the worst uh case of this is the
+
+ align:start position:0%
+and the worst uh case of this is the
+ 
+
+ align:start position:0%
+and the worst uh case of this is the
+fact that this is line integrated so
+
+ align:start position:0%
+fact that this is line integrated so
+ 
+
+ align:start position:0%
+fact that this is line integrated so
+we're going through the plasma here and
+
+ align:start position:0%
+we're going through the plasma here and
+ 
+
+ align:start position:0%
+we're going through the plasma here and
+we're collecting all of that light and
+
+ align:start position:0%
+we're collecting all of that light and
+ 
+
+ align:start position:0%
+we're collecting all of that light and
+so if the plasma for
+
+ align:start position:0%
+so if the plasma for
+ 
+
+ align:start position:0%
+so if the plasma for
+example row or t changes along that
+
+ align:start position:0%
+example row or t changes along that
+ 
+
+ align:start position:0%
+example row or t changes along that
+curve then you you you can't say exactly
+
+ align:start position:0%
+curve then you you you can't say exactly
+ 
+
+ align:start position:0%
+curve then you you you can't say exactly
+how that density changes because there
+
+ align:start position:0%
+how that density changes because there
+ 
+
+ align:start position:0%
+how that density changes because there
+are a lots of different solutions you
+
+ align:start position:0%
+are a lots of different solutions you
+ 
+
+ align:start position:0%
+are a lots of different solutions you
+know that give you the same results so
+
+ align:start position:0%
+know that give you the same results so
+ 
+
+ align:start position:0%
+know that give you the same results so
+definitely not people do like arble
+
+ align:start position:0%
+definitely not people do like arble
+ 
+
+ align:start position:0%
+definitely not people do like arble
+inverted spectroscopy and very cool
+
+ align:start position:0%
+inverted spectroscopy and very cool
+ 
+
+ align:start position:0%
+inverted spectroscopy and very cool
+techniques like that when they measure
+
+ align:start position:0%
+techniques like that when they measure
+ 
+
+ align:start position:0%
+techniques like that when they measure
+lots of lines of sight and have symmetry
+
+ align:start position:0%
+lots of lines of sight and have symmetry
+ 
+
+ align:start position:0%
+lots of lines of sight and have symmetry
+assumption but that's quite tricky
+
+ align:start position:0%
+assumption but that's quite tricky
+ 
+
+ align:start position:0%
+assumption but that's quite tricky
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online okay I'm gonna try and do the
+
+ align:start position:0%
+online okay I'm gonna try and do the
+ 
+
+ align:start position:0%
+online okay I'm gonna try and do the
+line ratio thing let's see how this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goes you may have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectrum with some very well isolated
+
+ align:start position:0%
+spectrum with some very well isolated
+ 
+
+ align:start position:0%
+spectrum with some very well isolated
+lines so these lines could be
+
+ align:start position:0%
+lines so these lines could be
+ 
+
+ align:start position:0%
+lines so these lines could be
+ones that are some distance apart from
+
+ align:start position:0%
+ones that are some distance apart from
+ 
+
+ align:start position:0%
+ones that are some distance apart from
+any other lines they stand by themselves
+
+ align:start position:0%
+any other lines they stand by themselves
+ 
+
+ align:start position:0%
+any other lines they stand by themselves
+it's very clear what their wavelength is
+
+ align:start position:0%
+it's very clear what their wavelength is
+ 
+
+ align:start position:0%
+it's very clear what their wavelength is
+or their frequency is there's no
+
+ align:start position:0%
+or their frequency is there's no
+ 
+
+ align:start position:0%
+or their frequency is there's no
+confusing with anything else an example
+
+ align:start position:0%
+confusing with anything else an example
+ 
+
+ align:start position:0%
+confusing with anything else an example
+of a poorly separated line would be if
+
+ align:start position:0%
+of a poorly separated line would be if
+ 
+
+ align:start position:0%
+of a poorly separated line would be if
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+three lines all on top of each other
+
+ align:start position:0%
+three lines all on top of each other
+ 
+
+ align:start position:0%
+three lines all on top of each other
+like this because these lines are
+
+ align:start position:0%
+like this because these lines are
+ 
+
+ align:start position:0%
+like this because these lines are
+probably adding together in some
+
+ align:start position:0%
+probably adding together in some
+ 
+
+ align:start position:0%
+probably adding together in some
+way you can't exactly tell what the
+
+ align:start position:0%
+way you can't exactly tell what the
+ 
+
+ align:start position:0%
+way you can't exactly tell what the
+intensity of each of these is but if you
+
+ align:start position:0%
+intensity of each of these is but if you
+ 
+
+ align:start position:0%
+intensity of each of these is but if you
+have nice well separated lines then you
+
+ align:start position:0%
+have nice well separated lines then you
+ 
+
+ align:start position:0%
+have nice well separated lines then you
+have some intensity coefficient for this
+
+ align:start position:0%
+have some intensity coefficient for this
+ 
+
+ align:start position:0%
+have some intensity coefficient for this
+one some intensity coefficient for this
+
+ align:start position:0%
+one some intensity coefficient for this
+ 
+
+ align:start position:0%
+one some intensity coefficient for this
+one here so this line ratio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+technique you need to have strong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isolated and identified you need to
+
+ align:start position:0%
+isolated and identified you need to
+ 
+
+ align:start position:0%
+isolated and identified you need to
+know what these lines correspond to so
+
+ align:start position:0%
+know what these lines correspond to so
+ 
+
+ align:start position:0%
+know what these lines correspond to so
+identified in this case means we need to
+
+ align:start position:0%
+identified in this case means we need to
+ 
+
+ align:start position:0%
+identified in this case means we need to
+know what the ionization state is for it
+
+ align:start position:0%
+know what the ionization state is for it
+ 
+
+ align:start position:0%
+know what the ionization state is for it
+and we also need to know what upper
+
+ align:start position:0%
+and we also need to know what upper
+ 
+
+ align:start position:0%
+and we also need to know what upper
+level and lower level uh it corresponds
+
+ align:start position:0%
+level and lower level uh it corresponds
+ 
+
+ align:start position:0%
+level and lower level uh it corresponds
+to within that ionization state so we
+
+ align:start position:0%
+to within that ionization state so we
+ 
+
+ align:start position:0%
+to within that ionization state so we
+need to know the uh
+
+ align:start position:0%
+need to know the uh
+ 
+
+ align:start position:0%
+need to know the uh
+I guess we technically need to know the
+
+ align:start position:0%
+I guess we technically need to know the
+ 
+
+ align:start position:0%
+I guess we technically need to know the
+density of the Upper State
+
+ align:start position:0%
+density of the Upper State
+ 
+
+ align:start position:0%
+density of the Upper State
+here and so an example of this would be
+
+ align:start position:0%
+here and so an example of this would be
+ 
+
+ align:start position:0%
+here and so an example of this would be
+you know if I have a line that comes
+
+ align:start position:0%
+you know if I have a line that comes
+ 
+
+ align:start position:0%
+you know if I have a line that comes
+from aluminum that is twice ionized and
+
+ align:start position:0%
+from aluminum that is twice ionized and
+ 
+
+ align:start position:0%
+from aluminum that is twice ionized and
+aluminum which is three times ionized or
+
+ align:start position:0%
+aluminum which is three times ionized or
+ 
+
+ align:start position:0%
+aluminum which is three times ionized or
+something like that these two ions will
+
+ align:start position:0%
+something like that these two ions will
+ 
+
+ align:start position:0%
+something like that these two ions will
+have very strong lines for certain
+
+ align:start position:0%
+have very strong lines for certain
+ 
+
+ align:start position:0%
+have very strong lines for certain
+transitions you know you'll often have a
+
+ align:start position:0%
+transitions you know you'll often have a
+ 
+
+ align:start position:0%
+transitions you know you'll often have a
+very strong transition from some Upper
+
+ align:start position:0%
+very strong transition from some Upper
+ 
+
+ align:start position:0%
+very strong transition from some Upper
+State the lowest line up a state back
+
+ align:start position:0%
+State the lowest line up a state back
+ 
+
+ align:start position:0%
+State the lowest line up a state back
+down to the ground state because in
+
+ align:start position:0%
+down to the ground state because in
+ 
+
+ align:start position:0%
+down to the ground state because in
+general that's where you're going to end
+
+ align:start position:0%
+general that's where you're going to end
+ 
+
+ align:start position:0%
+general that's where you're going to end
+up and also in general you have like a
+
+ align:start position:0%
+up and also in general you have like a
+ 
+
+ align:start position:0%
+up and also in general you have like a
+large energy gap here so this is pretty
+
+ align:start position:0%
+large energy gap here so this is pretty
+ 
+
+ align:start position:0%
+large energy gap here so this is pretty
+favorable so maybe you've got some well
+
+ align:start position:0%
+favorable so maybe you've got some well
+ 
+
+ align:start position:0%
+favorable so maybe you've got some well
+isolated lines that you know correspond
+
+ align:start position:0%
+isolated lines that you know correspond
+ 
+
+ align:start position:0%
+isolated lines that you know correspond
+from a mission from an upper level to
+
+ align:start position:0%
+from a mission from an upper level to
+ 
+
+ align:start position:0%
+from a mission from an upper level to
+down to the ground level here and you
+
+ align:start position:0%
+down to the ground level here and you
+ 
+
+ align:start position:0%
+down to the ground level here and you
+can measure their intensity very well
+
+ align:start position:0%
+can measure their intensity very well
+ 
+
+ align:start position:0%
+can measure their intensity very well
+right so we now know the intensity of
+
+ align:start position:0%
+right so we now know the intensity of
+ 
+
+ align:start position:0%
+right so we now know the intensity of
+Omega one we know the intensity of Omega
+
+ align:start position:0%
+Omega one we know the intensity of Omega
+ 
+
+ align:start position:0%
+Omega one we know the intensity of Omega
+2 and this is what I mean by strong you
+
+ align:start position:0%
+2 and this is what I mean by strong you
+ 
+
+ align:start position:0%
+2 and this is what I mean by strong you
+don't want to be doing this on little
+
+ align:start position:0%
+don't want to be doing this on little
+ 
+
+ align:start position:0%
+don't want to be doing this on little
+lines that are down here in the noise
+
+ align:start position:0%
+lines that are down here in the noise
+ 
+
+ align:start position:0%
+lines that are down here in the noise
+because we can't measure their intensity
+
+ align:start position:0%
+because we can't measure their intensity
+ 
+
+ align:start position:0%
+because we can't measure their intensity
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+well so what you do with these lines is
+
+ align:start position:0%
+well so what you do with these lines is
+ 
+
+ align:start position:0%
+well so what you do with these lines is
+you say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+intensity of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line the intensity at some frequency
+
+ align:start position:0%
+line the intensity at some frequency
+ 
+
+ align:start position:0%
+line the intensity at some frequency
+corresponding to the transition from the
+
+ align:start position:0%
+corresponding to the transition from the
+ 
+
+ align:start position:0%
+corresponding to the transition from the
+upper state to the Lower State here
+
+ align:start position:0%
+upper state to the Lower State here
+ 
+
+ align:start position:0%
+upper state to the Lower State here
+is equal to the number of ions in the
+
+ align:start position:0%
+is equal to the number of ions in the
+ 
+
+ align:start position:0%
+is equal to the number of ions in the
+Upper
+
+ align:start position:0%
+Upper
+ 
+
+ align:start position:0%
+Upper
+State Times by the probability of
+
+ align:start position:0%
+State Times by the probability of
+ 
+
+ align:start position:0%
+State Times by the probability of
+transition from the upper state to the
+
+ align:start position:0%
+transition from the upper state to the
+ 
+
+ align:start position:0%
+transition from the upper state to the
+Lower State and then because this
+
+ align:start position:0%
+Lower State and then because this
+ 
+
+ align:start position:0%
+Lower State and then because this
+intensity often has units of energy here
+
+ align:start position:0%
+intensity often has units of energy here
+ 
+
+ align:start position:0%
+intensity often has units of energy here
+right this is like a power we obviously
+
+ align:start position:0%
+right this is like a power we obviously
+ 
+
+ align:start position:0%
+right this is like a power we obviously
+need to have an energy unit here so this
+
+ align:start position:0%
+need to have an energy unit here so this
+ 
+
+ align:start position:0%
+need to have an energy unit here so this
+is H bar Omega upper lower so if we have
+
+ align:start position:0%
+is H bar Omega upper lower so if we have
+ 
+
+ align:start position:0%
+is H bar Omega upper lower so if we have
+two lines here we can take the ratio of
+
+ align:start position:0%
+two lines here we can take the ratio of
+ 
+
+ align:start position:0%
+two lines here we can take the ratio of
+these so we could have intensity of
+
+ align:start position:0%
+these so we could have intensity of
+ 
+
+ align:start position:0%
+these so we could have intensity of
+Omega Zed Upp or
+
+ align:start position:0%
+Omega Zed Upp or
+ 
+
+ align:start position:0%
+Omega Zed Upp or
+lower over intensity of Omega Z minus
+
+ align:start position:0%
+lower over intensity of Omega Z minus
+ 
+
+ align:start position:0%
+lower over intensity of Omega Z minus
+one up or lower like that and we can see
+
+ align:start position:0%
+one up or lower like that and we can see
+ 
+
+ align:start position:0%
+one up or lower like that and we can see
+then that we're going to get out a zed
+
+ align:start position:0%
+then that we're going to get out a zed
+ 
+
+ align:start position:0%
+then that we're going to get out a zed
+upper Over N The Zed minus one
+
+ align:start position:0%
+upper Over N The Zed minus one
+ 
+
+ align:start position:0%
+upper Over N The Zed minus one
+upper a upper
+
+ align:start position:0%
+upper a upper
+ 
+
+ align:start position:0%
+upper a upper
+lower a upper lower I'll put little
+
+ align:start position:0%
+lower a upper lower I'll put little
+ 
+
+ align:start position:0%
+lower a upper lower I'll put little
+superscripts on these so we remember
+
+ align:start position:0%
+superscripts on these so we remember
+ 
+
+ align:start position:0%
+superscripts on these so we remember
+these are different coefficients for our
+
+ align:start position:0%
+these are different coefficients for our
+ 
+
+ align:start position:0%
+these are different coefficients for our
+different ionization States and then the
+
+ align:start position:0%
+different ionization States and then the
+ 
+
+ align:start position:0%
+different ionization States and then the
+H bars will can
+
+ align:start position:0%
+H bars will can
+ 
+
+ align:start position:0%
+H bars will can
+we'll have an Omega Z up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lower so these are things that we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculate look up in our Atomic
+
+ align:start position:0%
+calculate look up in our Atomic
+ 
+
+ align:start position:0%
+calculate look up in our Atomic
+database these are things that we have
+
+ align:start position:0%
+database these are things that we have
+ 
+
+ align:start position:0%
+database these are things that we have
+literally measured because our
+
+ align:start position:0%
+literally measured because our
+ 
+
+ align:start position:0%
+literally measured because our
+spectrometer is well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calibrated this line ratio we've also
+
+ align:start position:0%
+calibrated this line ratio we've also
+ 
+
+ align:start position:0%
+calibrated this line ratio we've also
+just measured
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infer the ratio between the number of
+
+ align:start position:0%
+infer the ratio between the number of
+ 
+
+ align:start position:0%
+infer the ratio between the number of
+atoms in one ionization State and
+
+ align:start position:0%
+atoms in one ionization State and
+ 
+
+ align:start position:0%
+atoms in one ionization State and
+another ionization State here I've done
+
+ align:start position:0%
+another ionization State here I've done
+ 
+
+ align:start position:0%
+another ionization State here I've done
+them as neighboring ionization States
+
+ align:start position:0%
+them as neighboring ionization States
+ 
+
+ align:start position:0%
+them as neighboring ionization States
+this could be like Zed minus two Zed
+
+ align:start position:0%
+this could be like Zed minus two Zed
+ 
+
+ align:start position:0%
+this could be like Zed minus two Zed
+minus 3 it doesn't really matter you
+
+ align:start position:0%
+minus 3 it doesn't really matter you
+ 
+
+ align:start position:0%
+minus 3 it doesn't really matter you
+don't generally get that because for a
+
+ align:start position:0%
+don't generally get that because for a
+ 
+
+ align:start position:0%
+don't generally get that because for a
+certain temperature you only have a few
+
+ align:start position:0%
+certain temperature you only have a few
+ 
+
+ align:start position:0%
+certain temperature you only have a few
+ionization States active at a time and
+
+ align:start position:0%
+ionization States active at a time and
+ 
+
+ align:start position:0%
+ionization States active at a time and
+because you've now inferred this
+
+ align:start position:0%
+because you've now inferred this
+ 
+
+ align:start position:0%
+because you've now inferred this
+quantity you can then use an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium such as
+
+ align:start position:0%
+equilibrium such as
+ 
+
+ align:start position:0%
+equilibrium such as
+Saha and you can get out the temperature
+
+ align:start position:0%
+Saha and you can get out the temperature
+ 
+
+ align:start position:0%
+Saha and you can get out the temperature
+so you can say your sah equilibrium says
+
+ align:start position:0%
+so you can say your sah equilibrium says
+ 
+
+ align:start position:0%
+so you can say your sah equilibrium says
+at a certain temperature I should have
+
+ align:start position:0%
+at a certain temperature I should have
+ 
+
+ align:start position:0%
+at a certain temperature I should have
+twice as many ions uh in the lower
+
+ align:start position:0%
+twice as many ions uh in the lower
+ 
+
+ align:start position:0%
+twice as many ions uh in the lower
+ionization State at the upper ionization
+
+ align:start position:0%
+ionization State at the upper ionization
+ 
+
+ align:start position:0%
+ionization State at the upper ionization
+State that's what I see therefore that
+
+ align:start position:0%
+State that's what I see therefore that
+ 
+
+ align:start position:0%
+State that's what I see therefore that
+is my temperature so just simply from
+
+ align:start position:0%
+is my temperature so just simply from
+ 
+
+ align:start position:0%
+is my temperature so just simply from
+looking at line ratios without doing all
+
+ align:start position:0%
+looking at line ratios without doing all
+ 
+
+ align:start position:0%
+looking at line ratios without doing all
+of this complicated modeling you may be
+
+ align:start position:0%
+of this complicated modeling you may be
+ 
+
+ align:start position:0%
+of this complicated modeling you may be
+able to get a handle on the temperature
+
+ align:start position:0%
+able to get a handle on the temperature
+ 
+
+ align:start position:0%
+able to get a handle on the temperature
+and that could be a first step that you
+
+ align:start position:0%
+and that could be a first step that you
+ 
+
+ align:start position:0%
+and that could be a first step that you
+then feed back into your algorithm where
+
+ align:start position:0%
+then feed back into your algorithm where
+ 
+
+ align:start position:0%
+then feed back into your algorithm where
+you say I know what the starting
+
+ align:start position:0%
+you say I know what the starting
+ 
+
+ align:start position:0%
+you say I know what the starting
+temperature roughly is so let's only
+
+ align:start position:0%
+temperature roughly is so let's only
+ 
+
+ align:start position:0%
+temperature roughly is so let's only
+look in the solution space surround it
+
+ align:start position:0%
+look in the solution space surround it
+ 
+
+ align:start position:0%
+look in the solution space surround it
+so this is quite a powerful technique
+
+ align:start position:0%
+so this is quite a powerful technique
+ 
+
+ align:start position:0%
+so this is quite a powerful technique
+and often this is as far as people go
+
+ align:start position:0%
+and often this is as far as people go
+ 
+
+ align:start position:0%
+and often this is as far as people go
+they'll do a line ratio they'll get a
+
+ align:start position:0%
+they'll do a line ratio they'll get a
+ 
+
+ align:start position:0%
+they'll do a line ratio they'll get a
+temperature out and I mentioned earlier
+
+ align:start position:0%
+temperature out and I mentioned earlier
+ 
+
+ align:start position:0%
+temperature out and I mentioned earlier
+the even simpler thing to do is just be
+
+ align:start position:0%
+the even simpler thing to do is just be
+ 
+
+ align:start position:0%
+the even simpler thing to do is just be
+like hey I've got a line that
+
+ align:start position:0%
+like hey I've got a line that
+ 
+
+ align:start position:0%
+like hey I've got a line that
+corresponds to uh aluminium 3 plus ions
+
+ align:start position:0%
+corresponds to uh aluminium 3 plus ions
+ 
+
+ align:start position:0%
+corresponds to uh aluminium 3 plus ions
+that only happens when the temperature
+
+ align:start position:0%
+that only happens when the temperature
+ 
+
+ align:start position:0%
+that only happens when the temperature
+in the plasma is like 10 electron volts
+
+ align:start position:0%
+in the plasma is like 10 electron volts
+ 
+
+ align:start position:0%
+in the plasma is like 10 electron volts
+maybe 12 maybe eight but that means like
+
+ align:start position:0%
+maybe 12 maybe eight but that means like
+ 
+
+ align:start position:0%
+maybe 12 maybe eight but that means like
+my plasma is probably 10 Els perfect and
+
+ align:start position:0%
+my plasma is probably 10 Els perfect and
+ 
+
+ align:start position:0%
+my plasma is probably 10 Els perfect and
+that's that's good enough for a lot of
+
+ align:start position:0%
+that's that's good enough for a lot of
+ 
+
+ align:start position:0%
+that's that's good enough for a lot of
+purposes okay questions on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah so no so absolutely like you're I
+
+ align:start position:0%
+yeah so no so absolutely like you're I
+ 
+
+ align:start position:0%
+yeah so no so absolutely like you're I
+say you're measuring it but you know it
+
+ align:start position:0%
+say you're measuring it but you know it
+ 
+
+ align:start position:0%
+say you're measuring it but you know it
+right it's close enough yes there may be
+
+ align:start position:0%
+right it's close enough yes there may be
+ 
+
+ align:start position:0%
+right it's close enough yes there may be
+some do the shift involved to it or some
+
+ align:start position:0%
+some do the shift involved to it or some
+ 
+
+ align:start position:0%
+some do the shift involved to it or some
+of these other line broadening
+
+ align:start position:0%
+of these other line broadening
+ 
+
+ align:start position:0%
+of these other line broadening
+mechanisms which means you don't know
+
+ align:start position:0%
+mechanisms which means you don't know
+ 
+
+ align:start position:0%
+mechanisms which means you don't know
+exactly where this is you may also have
+
+ align:start position:0%
+exactly where this is you may also have
+ 
+
+ align:start position:0%
+exactly where this is you may also have
+uncertainties in your Atomic code
+
+ align:start position:0%
+uncertainties in your Atomic code
+ 
+
+ align:start position:0%
+uncertainties in your Atomic code
+especially when you're working with
+
+ align:start position:0%
+especially when you're working with
+ 
+
+ align:start position:0%
+especially when you're working with
+x-rays uh the X-ray uh spectroscopy
+
+ align:start position:0%
+x-rays uh the X-ray uh spectroscopy
+ 
+
+ align:start position:0%
+x-rays uh the X-ray uh spectroscopy
+models can be quite unaccurate to within
+
+ align:start position:0%
+models can be quite unaccurate to within
+ 
+
+ align:start position:0%
+models can be quite unaccurate to within
+like 20% and that's still pretty good
+
+ align:start position:0%
+like 20% and that's still pretty good
+ 
+
+ align:start position:0%
+like 20% and that's still pretty good
+and so you say okay I thought it was
+
+ align:start position:0%
+and so you say okay I thought it was
+ 
+
+ align:start position:0%
+and so you say okay I thought it was
+going to be here there's nothing
+
+ align:start position:0%
+going to be here there's nothing
+ 
+
+ align:start position:0%
+going to be here there's nothing
+anywhere near here apart from this line
+
+ align:start position:0%
+anywhere near here apart from this line
+ 
+
+ align:start position:0%
+anywhere near here apart from this line
+so that is probably this line so making
+
+ align:start position:0%
+so that is probably this line so making
+ 
+
+ align:start position:0%
+so that is probably this line so making
+a line identification is like very tough
+
+ align:start position:0%
+a line identification is like very tough
+ 
+
+ align:start position:0%
+a line identification is like very tough
+and especially in a plasma in the
+
+ align:start position:0%
+and especially in a plasma in the
+ 
+
+ align:start position:0%
+and especially in a plasma in the
+laboratory you think my plasma is made
+
+ align:start position:0%
+laboratory you think my plasma is made
+ 
+
+ align:start position:0%
+laboratory you think my plasma is made
+out of aluminium because that's what
+
+ align:start position:0%
+out of aluminium because that's what
+ 
+
+ align:start position:0%
+out of aluminium because that's what
+you've made it out of but then you
+
+ align:start position:0%
+you've made it out of but then you
+ 
+
+ align:start position:0%
+you've made it out of but then you
+forget that the lenses are coated with
+
+ align:start position:0%
+forget that the lenses are coated with
+ 
+
+ align:start position:0%
+forget that the lenses are coated with
+magnesium chloride and so there may be
+
+ align:start position:0%
+magnesium chloride and so there may be
+ 
+
+ align:start position:0%
+magnesium chloride and so there may be
+magnesium chloride absorption lines when
+
+ align:start position:0%
+magnesium chloride absorption lines when
+ 
+
+ align:start position:0%
+magnesium chloride absorption lines when
+the x-rays from your experiment photoon
+
+ align:start position:0%
+the x-rays from your experiment photoon
+ 
+
+ align:start position:0%
+the x-rays from your experiment photoon
+or your electrode is made out of copper
+
+ align:start position:0%
+or your electrode is made out of copper
+ 
+
+ align:start position:0%
+or your electrode is made out of copper
+and now you've got copper lines as well
+
+ align:start position:0%
+and now you've got copper lines as well
+ 
+
+ align:start position:0%
+and now you've got copper lines as well
+or someone left their thumb print on one
+
+ align:start position:0%
+or someone left their thumb print on one
+ 
+
+ align:start position:0%
+or someone left their thumb print on one
+of the electrodes and now you have
+
+ align:start position:0%
+of the electrodes and now you have
+ 
+
+ align:start position:0%
+of the electrodes and now you have
+hydrocarbons and salt so you have sodium
+
+ align:start position:0%
+hydrocarbons and salt so you have sodium
+ 
+
+ align:start position:0%
+hydrocarbons and salt so you have sodium
+lines on there as well like all of this
+
+ align:start position:0%
+lines on there as well like all of this
+ 
+
+ align:start position:0%
+lines on there as well like all of this
+has happened to me very recently so so
+
+ align:start position:0%
+has happened to me very recently so so
+ 
+
+ align:start position:0%
+has happened to me very recently so so
+it's actually it's a nightmare you think
+
+ align:start position:0%
+it's actually it's a nightmare you think
+ 
+
+ align:start position:0%
+it's actually it's a nightmare you think
+like ah my plasma is made out of this
+
+ align:start position:0%
+like ah my plasma is made out of this
+ 
+
+ align:start position:0%
+like ah my plasma is made out of this
+and the answer is no your plasma is made
+
+ align:start position:0%
+and the answer is no your plasma is made
+ 
+
+ align:start position:0%
+and the answer is no your plasma is made
+out of whatever crap there is in the
+
+ align:start position:0%
+out of whatever crap there is in the
+ 
+
+ align:start position:0%
+out of whatever crap there is in the
+machine so yeah okay other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes I'm preferably negligible right
+
+ align:start position:0%
+yeah yes I'm preferably negligible right
+ 
+
+ align:start position:0%
+yeah yes I'm preferably negligible right
+so yeah this is this is definitely a
+
+ align:start position:0%
+so yeah this is this is definitely a
+ 
+
+ align:start position:0%
+so yeah this is this is definitely a
+technique that works best if it's
+
+ align:start position:0%
+technique that works best if it's
+ 
+
+ align:start position:0%
+technique that works best if it's
+optically thin you you could use it if
+
+ align:start position:0%
+optically thin you you could use it if
+ 
+
+ align:start position:0%
+optically thin you you could use it if
+you have very strong priers about what
+
+ align:start position:0%
+you have very strong priers about what
+ 
+
+ align:start position:0%
+you have very strong priers about what
+the density and temperature are so that
+
+ align:start position:0%
+the density and temperature are so that
+ 
+
+ align:start position:0%
+the density and temperature are so that
+you can calculate the opacity but if you
+
+ align:start position:0%
+you can calculate the opacity but if you
+ 
+
+ align:start position:0%
+you can calculate the opacity but if you
+have those strong priers then you don't
+
+ align:start position:0%
+have those strong priers then you don't
+ 
+
+ align:start position:0%
+have those strong priers then you don't
+need to do this technique you can sort
+
+ align:start position:0%
+need to do this technique you can sort
+ 
+
+ align:start position:0%
+need to do this technique you can sort
+of use it to confirm post talk
+
+ align:start position:0%
+of use it to confirm post talk
+ 
+
+ align:start position:0%
+of use it to confirm post talk
+afterwards that your technically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah well I mean that's that's really
+
+ align:start position:0%
+yeah well I mean that's that's really
+ 
+
+ align:start position:0%
+yeah well I mean that's that's really
+tricky if you're able to do an
+
+ align:start position:0%
+tricky if you're able to do an
+ 
+
+ align:start position:0%
+tricky if you're able to do an
+experiment where you can increase the
+
+ align:start position:0%
+experiment where you can increase the
+ 
+
+ align:start position:0%
+experiment where you can increase the
+depth of your plasma that would be one
+
+ align:start position:0%
+depth of your plasma that would be one
+ 
+
+ align:start position:0%
+depth of your plasma that would be one
+easy way to do it but of course if
+
+ align:start position:0%
+easy way to do it but of course if
+ 
+
+ align:start position:0%
+easy way to do it but of course if
+you're in a toac you can't just make the
+
+ align:start position:0%
+you're in a toac you can't just make the
+ 
+
+ align:start position:0%
+you're in a toac you can't just make the
+plasma twice as big just to see what
+
+ align:start position:0%
+plasma twice as big just to see what
+ 
+
+ align:start position:0%
+plasma twice as big just to see what
+would happen to the lines and so so um
+
+ align:start position:0%
+would happen to the lines and so so um
+ 
+
+ align:start position:0%
+would happen to the lines and so so um
+in some experiments you can you could
+
+ align:start position:0%
+in some experiments you can you could
+ 
+
+ align:start position:0%
+in some experiments you can you could
+use that technique otherwise yeah you'll
+
+ align:start position:0%
+use that technique otherwise yeah you'll
+ 
+
+ align:start position:0%
+use that technique otherwise yeah you'll
+have to use maybe other Diagnostics to
+
+ align:start position:0%
+have to use maybe other Diagnostics to
+ 
+
+ align:start position:0%
+have to use maybe other Diagnostics to
+give you ideas of density and
+
+ align:start position:0%
+give you ideas of density and
+ 
+
+ align:start position:0%
+give you ideas of density and
+temperature that you can then check how
+
+ align:start position:0%
+temperature that you can then check how
+ 
+
+ align:start position:0%
+temperature that you can then check how
+optically thick the various lines are
+
+ align:start position:0%
+optically thick the various lines are
+ 
+
+ align:start position:0%
+optically thick the various lines are
+and then um iterate from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there or simulation right as well give
+
+ align:start position:0%
+there or simulation right as well give
+ 
+
+ align:start position:0%
+there or simulation right as well give
+us some hints as what the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions what are we doing
+
+ align:start position:0%
+questions what are we doing
+ 
+
+ align:start position:0%
+questions what are we doing
+oh x-ray spectroscopy very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so the reason I'm talking about
+
+ align:start position:0%
+good so the reason I'm talking about
+ 
+
+ align:start position:0%
+good so the reason I'm talking about
+x-ray spectroscopy in particular is that
+
+ align:start position:0%
+x-ray spectroscopy in particular is that
+ 
+
+ align:start position:0%
+x-ray spectroscopy in particular is that
+quite a few people doing plasma physics
+
+ align:start position:0%
+quite a few people doing plasma physics
+ 
+
+ align:start position:0%
+quite a few people doing plasma physics
+end up using x-ray spectroscopy and also
+
+ align:start position:0%
+end up using x-ray spectroscopy and also
+ 
+
+ align:start position:0%
+end up using x-ray spectroscopy and also
+it's got it sort of Niche nomenclature
+
+ align:start position:0%
+it's got it sort of Niche nomenclature
+ 
+
+ align:start position:0%
+it's got it sort of Niche nomenclature
+uh that I wanted to introduce you to so
+
+ align:start position:0%
+uh that I wanted to introduce you to so
+ 
+
+ align:start position:0%
+uh that I wanted to introduce you to so
+that when people start talking about it
+
+ align:start position:0%
+that when people start talking about it
+ 
+
+ align:start position:0%
+that when people start talking about it
+you have some vague idea of what's going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on of course all forms of spectroscopy
+
+ align:start position:0%
+on of course all forms of spectroscopy
+ 
+
+ align:start position:0%
+on of course all forms of spectroscopy
+are valid lot of people do visible
+
+ align:start position:0%
+are valid lot of people do visible
+ 
+
+ align:start position:0%
+are valid lot of people do visible
+spectroscopy infrared ultraviolet but if
+
+ align:start position:0%
+spectroscopy infrared ultraviolet but if
+ 
+
+ align:start position:0%
+spectroscopy infrared ultraviolet but if
+you're working with plasmas at Fusion
+
+ align:start position:0%
+you're working with plasmas at Fusion
+ 
+
+ align:start position:0%
+you're working with plasmas at Fusion
+conditions which are like killer
+
+ align:start position:0%
+conditions which are like killer
+ 
+
+ align:start position:0%
+conditions which are like killer
+electron volt plasmas then you're going
+
+ align:start position:0%
+electron volt plasmas then you're going
+ 
+
+ align:start position:0%
+electron volt plasmas then you're going
+to be getting killer electron volt
+
+ align:start position:0%
+to be getting killer electron volt
+ 
+
+ align:start position:0%
+to be getting killer electron volt
+photons right and so that means they're
+
+ align:start position:0%
+photons right and so that means they're
+ 
+
+ align:start position:0%
+photons right and so that means they're
+in the X-ray regime and x-ray
+
+ align:start position:0%
+in the X-ray regime and x-ray
+ 
+
+ align:start position:0%
+in the X-ray regime and x-ray
+spectroscopy can be a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different so x-ray spectroscopy has very
+
+ align:start position:0%
+different so x-ray spectroscopy has very
+ 
+
+ align:start position:0%
+different so x-ray spectroscopy has very
+strong characteristic lines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these lines tend to have a high
+
+ align:start position:0%
+so these lines tend to have a high
+ 
+
+ align:start position:0%
+so these lines tend to have a high
+transition probability a i j and they
+
+ align:start position:0%
+transition probability a i j and they
+ 
+
+ align:start position:0%
+transition probability a i j and they
+tend to be
+
+ align:start position:0%
+tend to be
+ 
+
+ align:start position:0%
+tend to be
+narrow so they show up very very
+
+ align:start position:0%
+narrow so they show up very very
+ 
+
+ align:start position:0%
+narrow so they show up very very
+strongly they're easy to identify
+
+ align:start position:0%
+strongly they're easy to identify
+ 
+
+ align:start position:0%
+strongly they're easy to identify
+they're easy to work with and these
+
+ align:start position:0%
+they're easy to work with and these
+ 
+
+ align:start position:0%
+they're easy to work with and these
+lines corresponds to
+
+ align:start position:0%
+lines corresponds to
+ 
+
+ align:start position:0%
+lines corresponds to
+Transitions often between some of the
+
+ align:start position:0%
+Transitions often between some of the
+ 
+
+ align:start position:0%
+Transitions often between some of the
+lowest energy levels inside our atom
+
+ align:start position:0%
+lowest energy levels inside our atom
+ 
+
+ align:start position:0%
+lowest energy levels inside our atom
+so here this one is not referring to
+
+ align:start position:0%
+so here this one is not referring to
+ 
+
+ align:start position:0%
+so here this one is not referring to
+some abstract concept here this is
+
+ align:start position:0%
+some abstract concept here this is
+ 
+
+ align:start position:0%
+some abstract concept here this is
+literally n equals one right so this is
+
+ align:start position:0%
+literally n equals one right so this is
+ 
+
+ align:start position:0%
+literally n equals one right so this is
+the lowest energy level down there the
+
+ align:start position:0%
+the lowest energy level down there the
+ 
+
+ align:start position:0%
+the lowest energy level down there the
+energy level that your ground state
+
+ align:start position:0%
+energy level that your ground state
+ 
+
+ align:start position:0%
+energy level that your ground state
+hydrogen atom uh occupies here and these
+
+ align:start position:0%
+hydrogen atom uh occupies here and these
+ 
+
+ align:start position:0%
+hydrogen atom uh occupies here and these
+are the other excited stats because
+
+ align:start position:0%
+are the other excited stats because
+ 
+
+ align:start position:0%
+are the other excited stats because
+we're dealing with relatively High
+
+ align:start position:0%
+we're dealing with relatively High
+ 
+
+ align:start position:0%
+we're dealing with relatively High
+Energy Systems when we're doing EP
+
+ align:start position:0%
+Energy Systems when we're doing EP
+ 
+
+ align:start position:0%
+Energy Systems when we're doing EP
+spectroscopy our ion may be almost
+
+ align:start position:0%
+spectroscopy our ion may be almost
+ 
+
+ align:start position:0%
+spectroscopy our ion may be almost
+completely stripped there may be only
+
+ align:start position:0%
+completely stripped there may be only
+ 
+
+ align:start position:0%
+completely stripped there may be only
+two or three or one electrons here so
+
+ align:start position:0%
+two or three or one electrons here so
+ 
+
+ align:start position:0%
+two or three or one electrons here so
+and people start referring to these ions
+
+ align:start position:0%
+and people start referring to these ions
+ 
+
+ align:start position:0%
+and people start referring to these ions
+as helium like or lithium like so a
+
+ align:start position:0%
+as helium like or lithium like so a
+ 
+
+ align:start position:0%
+as helium like or lithium like so a
+helium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like unsurprisingly has two electrons
+
+ align:start position:0%
+like unsurprisingly has two electrons
+ 
+
+ align:start position:0%
+like unsurprisingly has two electrons
+and a lithium
+
+ align:start position:0%
+and a lithium
+ 
+
+ align:start position:0%
+and a lithium
+like has three
+
+ align:start position:0%
+like has three
+ 
+
+ align:start position:0%
+like has three
+electrons what they mean is this could
+
+ align:start position:0%
+electrons what they mean is this could
+ 
+
+ align:start position:0%
+electrons what they mean is this could
+be something like tungsten or aluminium
+
+ align:start position:0%
+be something like tungsten or aluminium
+ 
+
+ align:start position:0%
+be something like tungsten or aluminium
+or anything else like that but it's so
+
+ align:start position:0%
+or anything else like that but it's so
+ 
+
+ align:start position:0%
+or anything else like that but it's so
+ionized that there's only two or three
+
+ align:start position:0%
+ionized that there's only two or three
+ 
+
+ align:start position:0%
+ionized that there's only two or three
+electrons left and that means that you
+
+ align:start position:0%
+electrons left and that means that you
+ 
+
+ align:start position:0%
+electrons left and that means that you
+can use all of the
+
+ align:start position:0%
+can use all of the
+ 
+
+ align:start position:0%
+can use all of the
+spectroscopy all of the quantum physics
+
+ align:start position:0%
+spectroscopy all of the quantum physics
+ 
+
+ align:start position:0%
+spectroscopy all of the quantum physics
+that you do on helium which is a a
+
+ align:start position:0%
+that you do on helium which is a a
+ 
+
+ align:start position:0%
+that you do on helium which is a a
+relatively simple system to solve
+
+ align:start position:0%
+relatively simple system to solve
+ 
+
+ align:start position:0%
+relatively simple system to solve
+compared to something more complicated
+
+ align:start position:0%
+compared to something more complicated
+ 
+
+ align:start position:0%
+compared to something more complicated
+and all you have to do is replace the
+
+ align:start position:0%
+and all you have to do is replace the
+ 
+
+ align:start position:0%
+and all you have to do is replace the
+atomic charge the nucleus charge from
+
+ align:start position:0%
+atomic charge the nucleus charge from
+ 
+
+ align:start position:0%
+atomic charge the nucleus charge from
+two to whatever your actual nuclear
+
+ align:start position:0%
+two to whatever your actual nuclear
+ 
+
+ align:start position:0%
+two to whatever your actual nuclear
+charge is so you just take Zed from two
+
+ align:start position:0%
+charge is so you just take Zed from two
+ 
+
+ align:start position:0%
+charge is so you just take Zed from two
+to I don't know 13 for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aluminium but it means that you you have
+
+ align:start position:0%
+aluminium but it means that you you have
+ 
+
+ align:start position:0%
+aluminium but it means that you you have
+a pretty good idea of what these energy
+
+ align:start position:0%
+a pretty good idea of what these energy
+ 
+
+ align:start position:0%
+a pretty good idea of what these energy
+levels are because the quantum physics
+
+ align:start position:0%
+levels are because the quantum physics
+ 
+
+ align:start position:0%
+levels are because the quantum physics
+of low atomic number elements is pretty
+
+ align:start position:0%
+of low atomic number elements is pretty
+ 
+
+ align:start position:0%
+of low atomic number elements is pretty
+well understood so these characteristic
+
+ align:start position:0%
+well understood so these characteristic
+ 
+
+ align:start position:0%
+well understood so these characteristic
+lines will occur when there is some
+
+ align:start position:0%
+lines will occur when there is some
+ 
+
+ align:start position:0%
+lines will occur when there is some
+vacancy in a lower energy level so for
+
+ align:start position:0%
+vacancy in a lower energy level so for
+ 
+
+ align:start position:0%
+vacancy in a lower energy level so for
+example if we have an electron up here
+
+ align:start position:0%
+example if we have an electron up here
+ 
+
+ align:start position:0%
+example if we have an electron up here
+in the N equals 2 level and there's
+
+ align:start position:0%
+in the N equals 2 level and there's
+ 
+
+ align:start position:0%
+in the N equals 2 level and there's
+space in the N equals 1 level to drop
+
+ align:start position:0%
+space in the N equals 1 level to drop
+ 
+
+ align:start position:0%
+space in the N equals 1 level to drop
+down it
+
+ align:start position:0%
+down it
+ 
+
+ align:start position:0%
+down it
+will emit a photon here now why would
+
+ align:start position:0%
+will emit a photon here now why would
+ 
+
+ align:start position:0%
+will emit a photon here now why would
+there be space in this lower energy
+
+ align:start position:0%
+there be space in this lower energy
+ 
+
+ align:start position:0%
+there be space in this lower energy
+level I'd updated by notes and that also
+
+ align:start position:0%
+level I'd updated by notes and that also
+ 
+
+ align:start position:0%
+level I'd updated by notes and that also
+not as updated as well um this may be
+
+ align:start position:0%
+not as updated as well um this may be
+ 
+
+ align:start position:0%
+not as updated as well um this may be
+because of uh collisions or
+
+ align:start position:0%
+because of uh collisions or
+ 
+
+ align:start position:0%
+because of uh collisions or
+photoionization or something else like
+
+ align:start position:0%
+photoionization or something else like
+ 
+
+ align:start position:0%
+photoionization or something else like
+that if we're in a very hot plasma it's
+
+ align:start position:0%
+that if we're in a very hot plasma it's
+ 
+
+ align:start position:0%
+that if we're in a very hot plasma it's
+very reasonable to have hot electrons
+
+ align:start position:0%
+very reasonable to have hot electrons
+ 
+
+ align:start position:0%
+very reasonable to have hot electrons
+flying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around that
+
+ align:start position:0%
+around that
+ 
+
+ align:start position:0%
+around that
+collisionally ionize us or indeed just
+
+ align:start position:0%
+collisionally ionize us or indeed just
+ 
+
+ align:start position:0%
+collisionally ionize us or indeed just
+collisionally excite us up to some very
+
+ align:start position:0%
+collisionally excite us up to some very
+ 
+
+ align:start position:0%
+collisionally excite us up to some very
+high energy level like seven and that
+
+ align:start position:0%
+high energy level like seven and that
+ 
+
+ align:start position:0%
+high energy level like seven and that
+leaves a hole here and because this is
+
+ align:start position:0%
+leaves a hole here and because this is
+ 
+
+ align:start position:0%
+leaves a hole here and because this is
+energetically unfavorable to have a
+
+ align:start position:0%
+energetically unfavorable to have a
+ 
+
+ align:start position:0%
+energetically unfavorable to have a
+lower energy level unfilled one of these
+
+ align:start position:0%
+lower energy level unfilled one of these
+ 
+
+ align:start position:0%
+lower energy level unfilled one of these
+electrons in one of the higher energy
+
+ align:start position:0%
+electrons in one of the higher energy
+ 
+
+ align:start position:0%
+electrons in one of the higher energy
+levels will very rapidly drop down into
+
+ align:start position:0%
+levels will very rapidly drop down into
+ 
+
+ align:start position:0%
+levels will very rapidly drop down into
+here and these different transitions
+
+ align:start position:0%
+here and these different transitions
+ 
+
+ align:start position:0%
+here and these different transitions
+from down to the ground state from two
+
+ align:start position:0%
+from down to the ground state from two
+ 
+
+ align:start position:0%
+from down to the ground state from two
+two and three and so on have different
+
+ align:start position:0%
+two and three and so on have different
+ 
+
+ align:start position:0%
+two and three and so on have different
+names
+
+ align:start position:0%
+names
+ 
+
+ align:start position:0%
+names
+so first of all we have what I called
+
+ align:start position:0%
+so first of all we have what I called
+ 
+
+ align:start position:0%
+so first of all we have what I called
+the kshell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transitions this is transitions from or
+
+ align:start position:0%
+transitions this is transitions from or
+ 
+
+ align:start position:0%
+transitions this is transitions from or
+down to n equals one we have the K
+
+ align:start position:0%
+down to n equals one we have the K
+ 
+
+ align:start position:0%
+down to n equals one we have the K
+Alpha which is from Nal 2 to nals 1
+
+ align:start position:0%
+Alpha which is from Nal 2 to nals 1
+ 
+
+ align:start position:0%
+Alpha which is from Nal 2 to nals 1
+that's the one I've drawn here you have
+
+ align:start position:0%
+that's the one I've drawn here you have
+ 
+
+ align:start position:0%
+that's the one I've drawn here you have
+the K
+
+ align:start position:0%
+the K
+ 
+
+ align:start position:0%
+the K
+beta that's n equals
+
+ align:start position:0%
+beta that's n equals
+ 
+
+ align:start position:0%
+beta that's n equals
+three nals 1 and so on K gamma all that
+
+ align:start position:0%
+three nals 1 and so on K gamma all that
+ 
+
+ align:start position:0%
+three nals 1 and so on K gamma all that
+sort of thing now it turns out that the
+
+ align:start position:0%
+sort of thing now it turns out that the
+ 
+
+ align:start position:0%
+sort of thing now it turns out that the
+K Alpha is always the strongest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transition so you'll typically get an
+
+ align:start position:0%
+transition so you'll typically get an
+ 
+
+ align:start position:0%
+transition so you'll typically get an
+electron dropping down from two to one
+
+ align:start position:0%
+electron dropping down from two to one
+ 
+
+ align:start position:0%
+electron dropping down from two to one
+rather from three to one more quickly
+
+ align:start position:0%
+rather from three to one more quickly
+ 
+
+ align:start position:0%
+rather from three to one more quickly
+and this line will show up more strongly
+
+ align:start position:0%
+and this line will show up more strongly
+ 
+
+ align:start position:0%
+and this line will show up more strongly
+and it's strong again because of this
+
+ align:start position:0%
+and it's strong again because of this
+ 
+
+ align:start position:0%
+and it's strong again because of this
+overlap between the lowest energy state
+
+ align:start position:0%
+overlap between the lowest energy state
+ 
+
+ align:start position:0%
+overlap between the lowest energy state
+and the second highest n equals 2 energy
+
+ align:start position:0%
+and the second highest n equals 2 energy
+ 
+
+ align:start position:0%
+and the second highest n equals 2 energy
+State these wave functions look most
+
+ align:start position:0%
+State these wave functions look most
+ 
+
+ align:start position:0%
+State these wave functions look most
+similar as you start getting out to high
+
+ align:start position:0%
+similar as you start getting out to high
+ 
+
+ align:start position:0%
+similar as you start getting out to high
+ends these wave functions start to look
+
+ align:start position:0%
+ends these wave functions start to look
+ 
+
+ align:start position:0%
+ends these wave functions start to look
+really weird and when you do the overlap
+
+ align:start position:0%
+really weird and when you do the overlap
+ 
+
+ align:start position:0%
+really weird and when you do the overlap
+integral it's not particularly large so
+
+ align:start position:0%
+integral it's not particularly large so
+ 
+
+ align:start position:0%
+integral it's not particularly large so
+Quantum mechanically it's much easier
+
+ align:start position:0%
+Quantum mechanically it's much easier
+ 
+
+ align:start position:0%
+Quantum mechanically it's much easier
+for the electron to transition between
+
+ align:start position:0%
+for the electron to transition between
+ 
+
+ align:start position:0%
+for the electron to transition between
+these two wave functions here so the K
+
+ align:start position:0%
+these two wave functions here so the K
+ 
+
+ align:start position:0%
+these two wave functions here so the K
+Alpha is always
+
+ align:start position:0%
+Alpha is always
+ 
+
+ align:start position:0%
+Alpha is always
+strong we also then have the L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell this is transitions down to nals
+
+ align:start position:0%
+cell this is transitions down to nals
+ 
+
+ align:start position:0%
+cell this is transitions down to nals
+2 and you know you'll have L Alpha which
+
+ align:start position:0%
+2 and you know you'll have L Alpha which
+ 
+
+ align:start position:0%
+2 and you know you'll have L Alpha which
+is 3 to2 l beta which is four to2 then
+
+ align:start position:0%
+is 3 to2 l beta which is four to2 then
+ 
+
+ align:start position:0%
+is 3 to2 l beta which is four to2 then
+you also have the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mshell and so on but we tend to focus on
+
+ align:start position:0%
+mshell and so on but we tend to focus on
+ 
+
+ align:start position:0%
+mshell and so on but we tend to focus on
+the K shell because these lines are the
+
+ align:start position:0%
+the K shell because these lines are the
+ 
+
+ align:start position:0%
+the K shell because these lines are the
+highest energy Atomic lines you can get
+
+ align:start position:0%
+highest energy Atomic lines you can get
+ 
+
+ align:start position:0%
+highest energy Atomic lines you can get
+from the system because you're dropping
+
+ align:start position:0%
+from the system because you're dropping
+ 
+
+ align:start position:0%
+from the system because you're dropping
+down to the lowest energy level from
+
+ align:start position:0%
+down to the lowest energy level from
+ 
+
+ align:start position:0%
+down to the lowest energy level from
+somewhere else so these lines are very
+
+ align:start position:0%
+somewhere else so these lines are very
+ 
+
+ align:start position:0%
+somewhere else so these lines are very
+bright and they're very good signatures
+
+ align:start position:0%
+bright and they're very good signatures
+ 
+
+ align:start position:0%
+bright and they're very good signatures
+of what the plasma
+
+ align:start position:0%
+of what the plasma
+ 
+
+ align:start position:0%
+of what the plasma
+conditions are so just to give you an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example this is energy here and this is
+
+ align:start position:0%
+example this is energy here and this is
+ 
+
+ align:start position:0%
+example this is energy here and this is
+intensity and we have something like
+
+ align:start position:0%
+intensity and we have something like
+ 
+
+ align:start position:0%
+intensity and we have something like
+copper the copper Spectrum will have
+
+ align:start position:0%
+copper the copper Spectrum will have
+ 
+
+ align:start position:0%
+copper the copper Spectrum will have
+some remon component background here
+
+ align:start position:0%
+some remon component background here
+ 
+
+ align:start position:0%
+some remon component background here
+that you can never get rid of and then
+
+ align:start position:0%
+that you can never get rid of and then
+ 
+
+ align:start position:0%
+that you can never get rid of and then
+at sufficiently high energies we'll
+
+ align:start position:0%
+at sufficiently high energies we'll
+ 
+
+ align:start position:0%
+at sufficiently high energies we'll
+have two peaks like this this one is the
+
+ align:start position:0%
+have two peaks like this this one is the
+ 
+
+ align:start position:0%
+have two peaks like this this one is the
+K Alpha this is the K beta the K Alpha
+
+ align:start position:0%
+K Alpha this is the K beta the K Alpha
+ 
+
+ align:start position:0%
+K Alpha this is the K beta the K Alpha
+in this case is 8.1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KV and the K beta is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+8.9 and these lines are so narrow and so
+
+ align:start position:0%
+8.9 and these lines are so narrow and so
+ 
+
+ align:start position:0%
+8.9 and these lines are so narrow and so
+well defined that they form a very
+
+ align:start position:0%
+well defined that they form a very
+ 
+
+ align:start position:0%
+well defined that they form a very
+strong spectroscopic signature so if I'm
+
+ align:start position:0%
+strong spectroscopic signature so if I'm
+ 
+
+ align:start position:0%
+strong spectroscopic signature so if I'm
+looking inside my toac plasma that I
+
+ align:start position:0%
+looking inside my toac plasma that I
+ 
+
+ align:start position:0%
+looking inside my toac plasma that I
+want to be hydrogen and I look at these
+
+ align:start position:0%
+want to be hydrogen and I look at these
+ 
+
+ align:start position:0%
+want to be hydrogen and I look at these
+high energy killer electron volt ranges
+
+ align:start position:0%
+high energy killer electron volt ranges
+ 
+
+ align:start position:0%
+high energy killer electron volt ranges
+and I see Peaks there I can say straight
+
+ align:start position:0%
+and I see Peaks there I can say straight
+ 
+
+ align:start position:0%
+and I see Peaks there I can say straight
+away there is iron in my plasma there's
+
+ align:start position:0%
+away there is iron in my plasma there's
+ 
+
+ align:start position:0%
+away there is iron in my plasma there's
+tungsten in my plasma there's malum in
+
+ align:start position:0%
+tungsten in my plasma there's malum in
+ 
+
+ align:start position:0%
+tungsten in my plasma there's malum in
+my plasma and of course all of those
+
+ align:start position:0%
+my plasma and of course all of those
+ 
+
+ align:start position:0%
+my plasma and of course all of those
+impurities are radiating very strongly
+
+ align:start position:0%
+impurities are radiating very strongly
+ 
+
+ align:start position:0%
+impurities are radiating very strongly
+because these transitions are very
+
+ align:start position:0%
+because these transitions are very
+ 
+
+ align:start position:0%
+because these transitions are very
+strong and so that um really ruins your
+
+ align:start position:0%
+strong and so that um really ruins your
+ 
+
+ align:start position:0%
+strong and so that um really ruins your
+Power Balance reactor so a lot of
+
+ align:start position:0%
+Power Balance reactor so a lot of
+ 
+
+ align:start position:0%
+Power Balance reactor so a lot of
+spectroscopy early spectroscopy work at
+
+ align:start position:0%
+spectroscopy early spectroscopy work at
+ 
+
+ align:start position:0%
+spectroscopy early spectroscopy work at
+least in magnetic infi Fusion was
+
+ align:start position:0%
+least in magnetic infi Fusion was
+ 
+
+ align:start position:0%
+least in magnetic infi Fusion was
+looking for these signatures of
+
+ align:start position:0%
+looking for these signatures of
+ 
+
+ align:start position:0%
+looking for these signatures of
+impurities in the plasma here okay
+
+ align:start position:0%
+impurities in the plasma here okay
+ 
+
+ align:start position:0%
+impurities in the plasma here okay
+questions on all this the nure thing is
+
+ align:start position:0%
+questions on all this the nure thing is
+ 
+
+ align:start position:0%
+questions on all this the nure thing is
+basically knowing that K means
+
+ align:start position:0%
+basically knowing that K means
+ 
+
+ align:start position:0%
+basically knowing that K means
+transitions to one and Alpha and beta
+
+ align:start position:0%
+transitions to one and Alpha and beta
+ 
+
+ align:start position:0%
+transitions to one and Alpha and beta
+mean from the level above and the level
+
+ align:start position:0%
+mean from the level above and the level
+ 
+
+ align:start position:0%
+mean from the level above and the level
+above that and knowing that the K Alpha
+
+ align:start position:0%
+above that and knowing that the K Alpha
+ 
+
+ align:start position:0%
+above that and knowing that the K Alpha
+is much stronger than the others and
+
+ align:start position:0%
+is much stronger than the others and
+ 
+
+ align:start position:0%
+is much stronger than the others and
+maybe knowing that sometimes people were
+
+ align:start position:0%
+maybe knowing that sometimes people were
+ 
+
+ align:start position:0%
+maybe knowing that sometimes people were
+like this is a k Alpha transition in
+
+ align:start position:0%
+like this is a k Alpha transition in
+ 
+
+ align:start position:0%
+like this is a k Alpha transition in
+helium like aluminum and you're like ah
+
+ align:start position:0%
+helium like aluminum and you're like ah
+ 
+
+ align:start position:0%
+helium like aluminum and you're like ah
+cool um
+
+ align:start position:0%
+cool um
+ 
+
+ align:start position:0%
+cool um
+yeah right
+
+ align:start position:0%
+yeah right
+ 
+
+ align:start position:0%
+yeah right
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah I me absolutely brem stong is
+
+ align:start position:0%
+yes yeah I me absolutely brem stong is
+ 
+
+ align:start position:0%
+yes yeah I me absolutely brem stong is
+producing those wavelengths as well in
+
+ align:start position:0%
+producing those wavelengths as well in
+ 
+
+ align:start position:0%
+producing those wavelengths as well in
+general um but not lines so that's
+
+ align:start position:0%
+general um but not lines so that's
+ 
+
+ align:start position:0%
+general um but not lines so that's
+that's why they're so unique and you
+
+ align:start position:0%
+that's why they're so unique and you
+ 
+
+ align:start position:0%
+that's why they're so unique and you
+know maybe in some system you could have
+
+ align:start position:0%
+know maybe in some system you could have
+ 
+
+ align:start position:0%
+know maybe in some system you could have
+like synchron radiation or something
+
+ align:start position:0%
+like synchron radiation or something
+ 
+
+ align:start position:0%
+like synchron radiation or something
+like that or you know but in general
+
+ align:start position:0%
+like that or you know but in general
+ 
+
+ align:start position:0%
+like that or you know but in general
+these are very specific yeah and they
+
+ align:start position:0%
+these are very specific yeah and they
+ 
+
+ align:start position:0%
+these are very specific yeah and they
+they're slightly different energy so K
+
+ align:start position:0%
+they're slightly different energy so K
+ 
+
+ align:start position:0%
+they're slightly different energy so K
+Alpha for helium like is at a slightly
+
+ align:start position:0%
+Alpha for helium like is at a slightly
+ 
+
+ align:start position:0%
+Alpha for helium like is at a slightly
+higher energy than K Alpha for lithium
+
+ align:start position:0%
+higher energy than K Alpha for lithium
+ 
+
+ align:start position:0%
+higher energy than K Alpha for lithium
+like and so you may also then have
+
+ align:start position:0%
+like and so you may also then have
+ 
+
+ align:start position:0%
+like and so you may also then have
+the this is say these ones are the
+
+ align:start position:0%
+the this is say these ones are the
+ 
+
+ align:start position:0%
+the this is say these ones are the
+helium like and this is the K Alpha and
+
+ align:start position:0%
+helium like and this is the K Alpha and
+ 
+
+ align:start position:0%
+helium like and this is the K Alpha and
+the K beta the lithium like and then you
+
+ align:start position:0%
+the K beta the lithium like and then you
+ 
+
+ align:start position:0%
+the K beta the lithium like and then you
+can do your because you know exactly
+
+ align:start position:0%
+can do your because you know exactly
+ 
+
+ align:start position:0%
+can do your because you know exactly
+what these lines are because they're so
+
+ align:start position:0%
+what these lines are because they're so
+ 
+
+ align:start position:0%
+what these lines are because they're so
+specific you can do your line ratio
+
+ align:start position:0%
+specific you can do your line ratio
+ 
+
+ align:start position:0%
+specific you can do your line ratio
+trick that we used before and work out
+
+ align:start position:0%
+trick that we used before and work out
+ 
+
+ align:start position:0%
+trick that we used before and work out
+what the temperature is because you know
+
+ align:start position:0%
+what the temperature is because you know
+ 
+
+ align:start position:0%
+what the temperature is because you know
+this is a lower ionization State than
+
+ align:start position:0%
+this is a lower ionization State than
+ 
+
+ align:start position:0%
+this is a lower ionization State than
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+one yeah obviously if you are fully
+
+ align:start position:0%
+one yeah obviously if you are fully
+ 
+
+ align:start position:0%
+one yeah obviously if you are fully
+stripped if you have got to a
+
+ align:start position:0%
+stripped if you have got to a
+ 
+
+ align:start position:0%
+stripped if you have got to a
+temperature where there are no electrons
+
+ align:start position:0%
+temperature where there are no electrons
+ 
+
+ align:start position:0%
+temperature where there are no electrons
+left in your system you no longer have
+
+ align:start position:0%
+left in your system you no longer have
+ 
+
+ align:start position:0%
+left in your system you no longer have
+the line you would only get a line from
+
+ align:start position:0%
+the line you would only get a line from
+ 
+
+ align:start position:0%
+the line you would only get a line from
+recombination but the recombination has
+
+ align:start position:0%
+recombination but the recombination has
+ 
+
+ align:start position:0%
+recombination but the recombination has
+a spectrum as we talked about was an
+
+ align:start position:0%
+a spectrum as we talked about was an
+ 
+
+ align:start position:0%
+a spectrum as we talked about was an
+edge but still a spectrum
+
+ align:start position:0%
+edge but still a spectrum
+ 
+
+ align:start position:0%
+edge but still a spectrum
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no I believe that is
+
+ align:start position:0%
+no I believe that is
+ 
+
+ align:start position:0%
+no I believe that is
+separate yeah I I actually been a while
+
+ align:start position:0%
+separate yeah I I actually been a while
+ 
+
+ align:start position:0%
+separate yeah I I actually been a while
+since I reminded myself what lime Al was
+
+ align:start position:0%
+since I reminded myself what lime Al was
+ 
+
+ align:start position:0%
+since I reminded myself what lime Al was
+that's the one that's 121 n right oh
+
+ align:start position:0%
+that's the one that's 121 n right oh
+ 
+
+ align:start position:0%
+that's the one that's 121 n right oh
+okay any astrophysicist no okay yeah
+
+ align:start position:0%
+okay any astrophysicist no okay yeah
+ 
+
+ align:start position:0%
+okay any astrophysicist no okay yeah
+that's like a UV
+
+ align:start position:0%
+that's like a UV
+ 
+
+ align:start position:0%
+that's like a UV
+line is there a chance that it is
+
+ align:start position:0%
+line is there a chance that it is
+ 
+
+ align:start position:0%
+line is there a chance that it is
+related to these yeah I think it is an
+
+ align:start position:0%
+related to these yeah I think it is an
+ 
+
+ align:start position:0%
+related to these yeah I think it is an
+x-ray line but I can't remember the most
+
+ align:start position:0%
+x-ray line but I can't remember the most
+ 
+
+ align:start position:0%
+x-ray line but I can't remember the most
+common
+
+ align:start position:0%
+common
+ 
+
+ align:start position:0%
+common
+one makes me think it's y I thought it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called the Lyman Lyman series or lman
+
+ align:start position:0%
+called the Lyman Lyman series or lman
+ 
+
+ align:start position:0%
+called the Lyman Lyman series or lman
+that's a balma series what a Lyman
+
+ align:start position:0%
+that's a balma series what a Lyman
+ 
+
+ align:start position:0%
+that's a balma series what a Lyman
+series okay so maybe in hydrogen they
+
+ align:start position:0%
+series okay so maybe in hydrogen they
+ 
+
+ align:start position:0%
+series okay so maybe in hydrogen they
+have separate names that correspond to
+
+ align:start position:0%
+have separate names that correspond to
+ 
+
+ align:start position:0%
+have separate names that correspond to
+these um and I think historically right
+
+ align:start position:0%
+these um and I think historically right
+ 
+
+ align:start position:0%
+these um and I think historically right
+people were doing uh spectroscopy on
+
+ align:start position:0%
+people were doing uh spectroscopy on
+ 
+
+ align:start position:0%
+people were doing uh spectroscopy on
+astrophysical bodies which the first
+
+ align:start position:0%
+astrophysical bodies which the first
+ 
+
+ align:start position:0%
+astrophysical bodies which the first
+bodies we could look at that had these
+
+ align:start position:0%
+bodies we could look at that had these
+ 
+
+ align:start position:0%
+bodies we could look at that had these
+temperatures right so people were not
+
+ align:start position:0%
+temperatures right so people were not
+ 
+
+ align:start position:0%
+temperatures right so people were not
+doing spectroscopy on copper straight
+
+ align:start position:0%
+doing spectroscopy on copper straight
+ 
+
+ align:start position:0%
+doing spectroscopy on copper straight
+away but if you point your spectrometer
+
+ align:start position:0%
+away but if you point your spectrometer
+ 
+
+ align:start position:0%
+away but if you point your spectrometer
+at the sun then you can get these Alpha
+
+ align:start position:0%
+at the sun then you can get these Alpha
+ 
+
+ align:start position:0%
+at the sun then you can get these Alpha
+these Lyman ah Lyman series and balma
+
+ align:start position:0%
+these Lyman ah Lyman series and balma
+ 
+
+ align:start position:0%
+these Lyman ah Lyman series and balma
+series I'll look that up good question
+
+ align:start position:0%
+series I'll look that up good question
+ 
+
+ align:start position:0%
+series I'll look that up good question
+any questions online or comments if you
+
+ align:start position:0%
+any questions online or comments if you
+ 
+
+ align:start position:0%
+any questions online or comments if you
+know anything about Lyman series and
+
+ align:start position:0%
+know anything about Lyman series and
+ 
+
+ align:start position:0%
+know anything about Lyman series and
+balma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+series okay we can use this in Reverse
+
+ align:start position:0%
+series okay we can use this in Reverse
+ 
+
+ align:start position:0%
+series okay we can use this in Reverse
+to design filters for our x-ray systems
+
+ align:start position:0%
+to design filters for our x-ray systems
+ 
+
+ align:start position:0%
+to design filters for our x-ray systems
+so we often want to be able to measure
+
+ align:start position:0%
+so we often want to be able to measure
+ 
+
+ align:start position:0%
+so we often want to be able to measure
+just the light in a certain region here
+
+ align:start position:0%
+just the light in a certain region here
+ 
+
+ align:start position:0%
+just the light in a certain region here
+so this would be like taking a picture
+
+ align:start position:0%
+so this would be like taking a picture
+ 
+
+ align:start position:0%
+so this would be like taking a picture
+of just the X-rays and so we want to be
+
+ align:start position:0%
+of just the X-rays and so we want to be
+ 
+
+ align:start position:0%
+of just the X-rays and so we want to be
+able to filter out all the other light
+
+ align:start position:0%
+able to filter out all the other light
+ 
+
+ align:start position:0%
+able to filter out all the other light
+and just use uh the light in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region so this is looking at x-ray
+
+ align:start position:0%
+region so this is looking at x-ray
+ 
+
+ align:start position:0%
+region so this is looking at x-ray
+filters so a filter is a
+
+ align:start position:0%
+filters so a filter is a
+ 
+
+ align:start position:0%
+filters so a filter is a
+solid object it's usually a thin foil
+
+ align:start position:0%
+solid object it's usually a thin foil
+ 
+
+ align:start position:0%
+solid object it's usually a thin foil
+made out of some metal or or some
+
+ align:start position:0%
+made out of some metal or or some
+ 
+
+ align:start position:0%
+made out of some metal or or some
+nonmetal here um and the idea of the
+
+ align:start position:0%
+nonmetal here um and the idea of the
+ 
+
+ align:start position:0%
+nonmetal here um and the idea of the
+filters is that we still have these
+
+ align:start position:0%
+filters is that we still have these
+ 
+
+ align:start position:0%
+filters is that we still have these
+different energy levels here n equals 1
+
+ align:start position:0%
+different energy levels here n equals 1
+ 
+
+ align:start position:0%
+different energy levels here n equals 1
+Nal 2 nals 3 and four but now this is
+
+ align:start position:0%
+Nal 2 nals 3 and four but now this is
+ 
+
+ align:start position:0%
+Nal 2 nals 3 and four but now this is
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+um Z equals zero so this is for some
+
+ align:start position:0%
+um Z equals zero so this is for some
+ 
+
+ align:start position:0%
+um Z equals zero so this is for some
+solid like a lump of tungen or something
+
+ align:start position:0%
+solid like a lump of tungen or something
+ 
+
+ align:start position:0%
+solid like a lump of tungen or something
+like that and then if we have a photon
+
+ align:start position:0%
+like that and then if we have a photon
+ 
+
+ align:start position:0%
+like that and then if we have a photon
+coming in if there's a possibility that
+
+ align:start position:0%
+coming in if there's a possibility that
+ 
+
+ align:start position:0%
+coming in if there's a possibility that
+Photon has enough energy H bar Omega to
+
+ align:start position:0%
+Photon has enough energy H bar Omega to
+ 
+
+ align:start position:0%
+Photon has enough energy H bar Omega to
+excite an electron from one of the inner
+
+ align:start position:0%
+excite an electron from one of the inner
+ 
+
+ align:start position:0%
+excite an electron from one of the inner
+shells from one and two and three then
+
+ align:start position:0%
+shells from one and two and three then
+ 
+
+ align:start position:0%
+shells from one and two and three then
+that process is now favorable it's
+
+ align:start position:0%
+that process is now favorable it's
+ 
+
+ align:start position:0%
+that process is now favorable it's
+likely that that Photon will be absorbed
+
+ align:start position:0%
+likely that that Photon will be absorbed
+ 
+
+ align:start position:0%
+likely that that Photon will be absorbed
+if it doesn't match with any of these
+
+ align:start position:0%
+if it doesn't match with any of these
+ 
+
+ align:start position:0%
+if it doesn't match with any of these
+band gaps or any of these transitions
+
+ align:start position:0%
+band gaps or any of these transitions
+ 
+
+ align:start position:0%
+band gaps or any of these transitions
+then the photon will go through but if
+
+ align:start position:0%
+then the photon will go through but if
+ 
+
+ align:start position:0%
+then the photon will go through but if
+it does match then it will get
+
+ align:start position:0%
+it does match then it will get
+ 
+
+ align:start position:0%
+it does match then it will get
+absorbed so what we see in our
+
+ align:start position:0%
+absorbed so what we see in our
+ 
+
+ align:start position:0%
+absorbed so what we see in our
+absorption plot for a filter
+
+ align:start position:0%
+absorption plot for a filter
+ 
+
+ align:start position:0%
+absorption plot for a filter
+so this is that quantity Alpha the
+
+ align:start position:0%
+so this is that quantity Alpha the
+ 
+
+ align:start position:0%
+so this is that quantity Alpha the
+opacity as a function of
+
+ align:start position:0%
+opacity as a function of
+ 
+
+ align:start position:0%
+opacity as a function of
+frequency this we see a series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of what are called edges here so this is
+
+ align:start position:0%
+of what are called edges here so this is
+ 
+
+ align:start position:0%
+of what are called edges here so this is
+the L
+
+ align:start position:0%
+the L
+ 
+
+ align:start position:0%
+the L
+Edge and this is the K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Edge and um what you get is your lines
+
+ align:start position:0%
+Edge and um what you get is your lines
+ 
+
+ align:start position:0%
+Edge and um what you get is your lines
+corresponding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to your frequencies corresponding to K
+
+ align:start position:0%
+to your frequencies corresponding to K
+ 
+
+ align:start position:0%
+to your frequencies corresponding to K
+Alpha K beta all the way up to the
+
+ align:start position:0%
+Alpha K beta all the way up to the
+ 
+
+ align:start position:0%
+Alpha K beta all the way up to the
+highest K which is ionizing from
+
+ align:start position:0%
+highest K which is ionizing from
+ 
+
+ align:start position:0%
+highest K which is ionizing from
+whatever the highest occupied state is
+
+ align:start position:0%
+whatever the highest occupied state is
+ 
+
+ align:start position:0%
+whatever the highest occupied state is
+up into the Continuum and same here you
+
+ align:start position:0%
+up into the Continuum and same here you
+ 
+
+ align:start position:0%
+up into the Continuum and same here you
+get trying to space these
+
+ align:start position:0%
+get trying to space these
+ 
+
+ align:start position:0%
+get trying to space these
+parabolically L Alpha L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data so effectively you have a sudden
+
+ align:start position:0%
+data so effectively you have a sudden
+ 
+
+ align:start position:0%
+data so effectively you have a sudden
+increase in absorption whenever uh it is
+
+ align:start position:0%
+increase in absorption whenever uh it is
+ 
+
+ align:start position:0%
+increase in absorption whenever uh it is
+possible to do this ionization if you
+
+ align:start position:0%
+possible to do this ionization if you
+ 
+
+ align:start position:0%
+possible to do this ionization if you
+have done the homework yet and you've
+
+ align:start position:0%
+have done the homework yet and you've
+ 
+
+ align:start position:0%
+have done the homework yet and you've
+looked at some of the other filters you
+
+ align:start position:0%
+looked at some of the other filters you
+ 
+
+ align:start position:0%
+looked at some of the other filters you
+can generate on the hankki website you
+
+ align:start position:0%
+can generate on the hankki website you
+ 
+
+ align:start position:0%
+can generate on the hankki website you
+will have noticed these really weird
+
+ align:start position:0%
+will have noticed these really weird
+ 
+
+ align:start position:0%
+will have noticed these really weird
+absorption features hanky normally gives
+
+ align:start position:0%
+absorption features hanky normally gives
+ 
+
+ align:start position:0%
+absorption features hanky normally gives
+you transmission uh and so you will have
+
+ align:start position:0%
+you transmission uh and so you will have
+ 
+
+ align:start position:0%
+you transmission uh and so you will have
+seen one over this the absorption is one
+
+ align:start position:0%
+seen one over this the absorption is one
+ 
+
+ align:start position:0%
+seen one over this the absorption is one
+over the transmission but you will have
+
+ align:start position:0%
+over the transmission but you will have
+ 
+
+ align:start position:0%
+over the transmission but you will have
+noticed these really sharp edges that's
+
+ align:start position:0%
+noticed these really sharp edges that's
+ 
+
+ align:start position:0%
+noticed these really sharp edges that's
+not a numerical problem when you first
+
+ align:start position:0%
+not a numerical problem when you first
+ 
+
+ align:start position:0%
+not a numerical problem when you first
+see it you think oh the code is broken
+
+ align:start position:0%
+see it you think oh the code is broken
+ 
+
+ align:start position:0%
+see it you think oh the code is broken
+here no these are correspond to these
+
+ align:start position:0%
+here no these are correspond to these
+ 
+
+ align:start position:0%
+here no these are correspond to these
+very strong absorption edges here so if
+
+ align:start position:0%
+very strong absorption edges here so if
+ 
+
+ align:start position:0%
+very strong absorption edges here so if
+you have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectrum that has some lines in it and
+
+ align:start position:0%
+spectrum that has some lines in it and
+ 
+
+ align:start position:0%
+spectrum that has some lines in it and
+you put that Spectrum through this
+
+ align:start position:0%
+you put that Spectrum through this
+ 
+
+ align:start position:0%
+you put that Spectrum through this
+filter this filter would cut out for
+
+ align:start position:0%
+filter this filter would cut out for
+ 
+
+ align:start position:0%
+filter this filter would cut out for
+example this highest energy line here
+
+ align:start position:0%
+example this highest energy line here
+ 
+
+ align:start position:0%
+example this highest energy line here
+and You' just be left the Spectrum in
+
+ align:start position:0%
+and You' just be left the Spectrum in
+ 
+
+ align:start position:0%
+and You' just be left the Spectrum in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+region so this is how you use x-rays to
+
+ align:start position:0%
+region so this is how you use x-rays to
+ 
+
+ align:start position:0%
+region so this is how you use x-rays to
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+filtering oh
+
+ align:start position:0%
+filtering oh
+ 
+
+ align:start position:0%
+filtering oh
+okay fine questions on
+
+ align:start position:0%
+okay fine questions on
+ 
+
+ align:start position:0%
+okay fine questions on
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and the position of these edges depends
+
+ align:start position:0%
+and the position of these edges depends
+ 
+
+ align:start position:0%
+and the position of these edges depends
+on the element so if I use an aluminium
+
+ align:start position:0%
+on the element so if I use an aluminium
+ 
+
+ align:start position:0%
+on the element so if I use an aluminium
+filter or a Tungsten filter or a plastic
+
+ align:start position:0%
+filter or a Tungsten filter or a plastic
+ 
+
+ align:start position:0%
+filter or a Tungsten filter or a plastic
+filter it'll have edges in different
+
+ align:start position:0%
+filter it'll have edges in different
+ 
+
+ align:start position:0%
+filter it'll have edges in different
+places and so by using different filters
+
+ align:start position:0%
+places and so by using different filters
+ 
+
+ align:start position:0%
+places and so by using different filters
+I can image different parts of the
+
+ align:start position:0%
+I can image different parts of the
+ 
+
+ align:start position:0%
+I can image different parts of the
+spectrum so we'll talk about xray
+
+ align:start position:0%
+spectrum so we'll talk about xray
+ 
+
+ align:start position:0%
+spectrum so we'll talk about xray
+Imaging in a moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah not at all yeah just photo AB
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so that's a bit that does
+
+ align:start position:0%
+yeah yeah so that's a bit that does
+ 
+
+ align:start position:0%
+yeah yeah so that's a bit that does
+yeah yeah that's the sort of uh you need
+
+ align:start position:0%
+yeah yeah that's the sort of uh you need
+ 
+
+ align:start position:0%
+yeah yeah that's the sort of uh you need
+Quantum and treating the photon as a as
+
+ align:start position:0%
+Quantum and treating the photon as a as
+ 
+
+ align:start position:0%
+Quantum and treating the photon as a as
+a as a wave in order to get or you you
+
+ align:start position:0%
+a as a wave in order to get or you you
+ 
+
+ align:start position:0%
+a as a wave in order to get or you you
+need a Quantum treatment of it in order
+
+ align:start position:0%
+need a Quantum treatment of it in order
+ 
+
+ align:start position:0%
+need a Quantum treatment of it in order
+to get this roll off here yeah my
+
+ align:start position:0%
+to get this roll off here yeah my
+ 
+
+ align:start position:0%
+to get this roll off here yeah my
+explanation only covers why there's a
+
+ align:start position:0%
+explanation only covers why there's a
+ 
+
+ align:start position:0%
+explanation only covers why there's a
+sharp edge I haven't seen a nice
+
+ align:start position:0%
+sharp edge I haven't seen a nice
+ 
+
+ align:start position:0%
+sharp edge I haven't seen a nice
+intuitive explanation for this roll off
+
+ align:start position:0%
+intuitive explanation for this roll off
+ 
+
+ align:start position:0%
+intuitive explanation for this roll off
+after um but all all materials at high
+
+ align:start position:0%
+after um but all all materials at high
+ 
+
+ align:start position:0%
+after um but all all materials at high
+enough energies no matter what their
+
+ align:start position:0%
+enough energies no matter what their
+ 
+
+ align:start position:0%
+enough energies no matter what their
+absorption goes down to zero right so
+
+ align:start position:0%
+absorption goes down to zero right so
+ 
+
+ align:start position:0%
+absorption goes down to zero right so
+gamma rays will get through you know
+
+ align:start position:0%
+gamma rays will get through you know
+ 
+
+ align:start position:0%
+gamma rays will get through you know
+anything eventually yeah um
+
+ align:start position:0%
+anything eventually yeah um
+ 
+
+ align:start position:0%
+anything eventually yeah um
+Professor oh sorry I'm just gonna answer
+
+ align:start position:0%
+Professor oh sorry I'm just gonna answer
+ 
+
+ align:start position:0%
+Professor oh sorry I'm just gonna answer
+another question Jacob first and then
+
+ align:start position:0%
+another question Jacob first and then
+ 
+
+ align:start position:0%
+another question Jacob first and then
+I'll get back to you so the question was
+
+ align:start position:0%
+I'll get back to you so the question was
+ 
+
+ align:start position:0%
+I'll get back to you so the question was
+why the edges get taller and taller I
+
+ align:start position:0%
+why the edges get taller and taller I
+ 
+
+ align:start position:0%
+why the edges get taller and taller I
+think it's due to the likelihood of this
+
+ align:start position:0%
+think it's due to the likelihood of this
+ 
+
+ align:start position:0%
+think it's due to the likelihood of this
+interaction um but I'm not sure yeah
+
+ align:start position:0%
+interaction um but I'm not sure yeah
+ 
+
+ align:start position:0%
+interaction um but I'm not sure yeah
+sorry Jacob your
+
+ align:start position:0%
+sorry Jacob your
+ 
+
+ align:start position:0%
+sorry Jacob your
+question how do you design a material to
+
+ align:start position:0%
+question how do you design a material to
+ 
+
+ align:start position:0%
+question how do you design a material to
+uh specifically change out like take out
+
+ align:start position:0%
+uh specifically change out like take out
+ 
+
+ align:start position:0%
+uh specifically change out like take out
+a certain like the K Edge like or the L
+
+ align:start position:0%
+a certain like the K Edge like or the L
+ 
+
+ align:start position:0%
+a certain like the K Edge like or the L
+Edge you don't design a material you
+
+ align:start position:0%
+Edge you don't design a material you
+ 
+
+ align:start position:0%
+Edge you don't design a material you
+have a look and see what materials are
+
+ align:start position:0%
+have a look and see what materials are
+ 
+
+ align:start position:0%
+have a look and see what materials are
+available right yeah I mean how choose a
+
+ align:start position:0%
+available right yeah I mean how choose a
+ 
+
+ align:start position:0%
+available right yeah I mean how choose a
+material how do you choose a material
+
+ align:start position:0%
+material how do you choose a material
+ 
+
+ align:start position:0%
+material how do you choose a material
+well I I choose it by going on the hanky
+
+ align:start position:0%
+well I I choose it by going on the hanky
+ 
+
+ align:start position:0%
+well I I choose it by going on the hanky
+database and I generate these curves and
+
+ align:start position:0%
+database and I generate these curves and
+ 
+
+ align:start position:0%
+database and I generate these curves and
+I see what they are um so and I guess if
+
+ align:start position:0%
+I see what they are um so and I guess if
+ 
+
+ align:start position:0%
+I see what they are um so and I guess if
+you're very experienced you just know
+
+ align:start position:0%
+you're very experienced you just know
+ 
+
+ align:start position:0%
+you're very experienced you just know
+for example that this kedge is at 1.6 KV
+
+ align:start position:0%
+for example that this kedge is at 1.6 KV
+ 
+
+ align:start position:0%
+for example that this kedge is at 1.6 KV
+for aluminum and if you're trying to
+
+ align:start position:0%
+for aluminum and if you're trying to
+ 
+
+ align:start position:0%
+for aluminum and if you're trying to
+measure photons of energies below that
+
+ align:start position:0%
+measure photons of energies below that
+ 
+
+ align:start position:0%
+measure photons of energies below that
+then 1.6 this aluminum is quite a good
+
+ align:start position:0%
+then 1.6 this aluminum is quite a good
+ 
+
+ align:start position:0%
+then 1.6 this aluminum is quite a good
+filter um but you can't you can't
+
+ align:start position:0%
+filter um but you can't you can't
+ 
+
+ align:start position:0%
+filter um but you can't you can't
+engineer a material to have khes it's an
+
+ align:start position:0%
+engineer a material to have khes it's an
+ 
+
+ align:start position:0%
+engineer a material to have khes it's an
+atomic process so it really depends on
+
+ align:start position:0%
+atomic process so it really depends on
+ 
+
+ align:start position:0%
+atomic process so it really depends on
+the elements if for example you have a
+
+ align:start position:0%
+the elements if for example you have a
+ 
+
+ align:start position:0%
+the elements if for example you have a
+filter made out of a mixture of two
+
+ align:start position:0%
+filter made out of a mixture of two
+ 
+
+ align:start position:0%
+filter made out of a mixture of two
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+then it's just the combination of the
+
+ align:start position:0%
+then it's just the combination of the
+ 
+
+ align:start position:0%
+then it's just the combination of the
+absorption for those two different
+
+ align:start position:0%
+absorption for those two different
+ 
+
+ align:start position:0%
+absorption for those two different
+elements so yeah and you have to get the
+
+ align:start position:0%
+elements so yeah and you have to get the
+ 
+
+ align:start position:0%
+elements so yeah and you have to get the
+L Edge if you get the K Edge right or
+
+ align:start position:0%
+L Edge if you get the K Edge right or
+ 
+
+ align:start position:0%
+L Edge if you get the K Edge right or
+can you just get no no the L Edge will
+
+ align:start position:0%
+can you just get no no the L Edge will
+ 
+
+ align:start position:0%
+can you just get no no the L Edge will
+always be there as well and and the M
+
+ align:start position:0%
+always be there as well and and the M
+ 
+
+ align:start position:0%
+always be there as well and and the M
+Edge and so on but down to lower and
+
+ align:start position:0%
+Edge and so on but down to lower and
+ 
+
+ align:start position:0%
+Edge and so on but down to lower and
+lower energies right so they may not be
+
+ align:start position:0%
+lower energies right so they may not be
+ 
+
+ align:start position:0%
+lower energies right so they may not be
+interesting for your bit of the
+
+ align:start position:0%
+interesting for your bit of the
+ 
+
+ align:start position:0%
+interesting for your bit of the
+spectrum okay so you'll still see the
+
+ align:start position:0%
+spectrum okay so you'll still see the
+ 
+
+ align:start position:0%
+spectrum okay so you'll still see the
+bottom ones but you just know that
+
+ align:start position:0%
+bottom ones but you just know that
+ 
+
+ align:start position:0%
+bottom ones but you just know that
+they're too low of an energy to if you
+
+ align:start position:0%
+they're too low of an energy to if you
+ 
+
+ align:start position:0%
+they're too low of an energy to if you
+think your spectrum looks like this and
+
+ align:start position:0%
+think your spectrum looks like this and
+ 
+
+ align:start position:0%
+think your spectrum looks like this and
+you know that there's no interesting
+
+ align:start position:0%
+you know that there's no interesting
+ 
+
+ align:start position:0%
+you know that there's no interesting
+features down here it's just brm stong
+
+ align:start position:0%
+features down here it's just brm stong
+ 
+
+ align:start position:0%
+features down here it's just brm stong
+with very bright lines up at high
+
+ align:start position:0%
+with very bright lines up at high
+ 
+
+ align:start position:0%
+with very bright lines up at high
+energies then you don't really care what
+
+ align:start position:0%
+energies then you don't really care what
+ 
+
+ align:start position:0%
+energies then you don't really care what
+the structure is down here because when
+
+ align:start position:0%
+the structure is down here because when
+ 
+
+ align:start position:0%
+the structure is down here because when
+you multiply the transmission via your
+
+ align:start position:0%
+you multiply the transmission via your
+ 
+
+ align:start position:0%
+you multiply the transmission via your
+spectrum there'll be like little
+
+ align:start position:0%
+spectrum there'll be like little
+ 
+
+ align:start position:0%
+spectrum there'll be like little
+fluctuations down here but you don't
+
+ align:start position:0%
+fluctuations down here but you don't
+ 
+
+ align:start position:0%
+fluctuations down here but you don't
+care about them because your spectrum is
+
+ align:start position:0%
+care about them because your spectrum is
+ 
+
+ align:start position:0%
+care about them because your spectrum is
+going to be dominated by these lines you
+
+ align:start position:0%
+going to be dominated by these lines you
+ 
+
+ align:start position:0%
+going to be dominated by these lines you
+think okay makes
+
+ align:start position:0%
+think okay makes
+ 
+
+ align:start position:0%
+think okay makes
+sense other
+
+ align:start position:0%
+sense other
+ 
+
+ align:start position:0%
+sense other
+question okay let's talk about x-ray
+
+ align:start position:0%
+question okay let's talk about x-ray
+ 
+
+ align:start position:0%
+question okay let's talk about x-ray
+Imaging so why we might want to use a
+
+ align:start position:0%
+Imaging so why we might want to use a
+ 
+
+ align:start position:0%
+Imaging so why we might want to use a
+filter obviously if we're doing
+
+ align:start position:0%
+filter obviously if we're doing
+ 
+
+ align:start position:0%
+filter obviously if we're doing
+spectroscopy we don't care about the
+
+ align:start position:0%
+spectroscopy we don't care about the
+ 
+
+ align:start position:0%
+spectroscopy we don't care about the
+filters because we can just do
+
+ align:start position:0%
+filters because we can just do
+ 
+
+ align:start position:0%
+filters because we can just do
+spectroscopy and we can see where the
+
+ align:start position:0%
+spectroscopy and we can see where the
+ 
+
+ align:start position:0%
+spectroscopy and we can see where the
+lines are but if you don't want to do
+
+ align:start position:0%
+lines are but if you don't want to do
+ 
+
+ align:start position:0%
+lines are but if you don't want to do
+spectroscopy and you want to make an
+
+ align:start position:0%
+spectroscopy and you want to make an
+ 
+
+ align:start position:0%
+spectroscopy and you want to make an
+image you're going to need some of these
+
+ align:start position:0%
+image you're going to need some of these
+ 
+
+ align:start position:0%
+image you're going to need some of these
+filters so that you know what energies
+
+ align:start position:0%
+filters so that you know what energies
+ 
+
+ align:start position:0%
+filters so that you know what energies
+you're looking at so this is x-ray
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+image so one of the facts about x-ray
+
+ align:start position:0%
+image so one of the facts about x-ray
+ 
+
+ align:start position:0%
+image so one of the facts about x-ray
+Imaging is that there are no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lenses and that is a consequence of the
+
+ align:start position:0%
+lenses and that is a consequence of the
+ 
+
+ align:start position:0%
+lenses and that is a consequence of the
+fact that the refractive index is rough
+
+ align:start position:0%
+fact that the refractive index is rough
+ 
+
+ align:start position:0%
+fact that the refractive index is rough
+one for X-rays and lenses work on having
+
+ align:start position:0%
+one for X-rays and lenses work on having
+ 
+
+ align:start position:0%
+one for X-rays and lenses work on having
+a difference in refractive index from
+
+ align:start position:0%
+a difference in refractive index from
+ 
+
+ align:start position:0%
+a difference in refractive index from
+Air so if your refractive index of all
+
+ align:start position:0%
+Air so if your refractive index of all
+ 
+
+ align:start position:0%
+Air so if your refractive index of all
+your materials is about one you can no
+
+ align:start position:0%
+your materials is about one you can no
+ 
+
+ align:start position:0%
+your materials is about one you can no
+longer bend the Rays so the simplest
+
+ align:start position:0%
+longer bend the Rays so the simplest
+ 
+
+ align:start position:0%
+longer bend the Rays so the simplest
+thing that you can do for x-ray Imaging
+
+ align:start position:0%
+thing that you can do for x-ray Imaging
+ 
+
+ align:start position:0%
+thing that you can do for x-ray Imaging
+is called pinhole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Imaging pinhole Imaging is what the
+
+ align:start position:0%
+Imaging pinhole Imaging is what the
+ 
+
+ align:start position:0%
+Imaging pinhole Imaging is what the
+first cameras for visible light used as
+
+ align:start position:0%
+first cameras for visible light used as
+ 
+
+ align:start position:0%
+first cameras for visible light used as
+well you have your object which in this
+
+ align:start position:0%
+well you have your object which in this
+ 
+
+ align:start position:0%
+well you have your object which in this
+case I'm drawing as like a angle with
+
+ align:start position:0%
+case I'm drawing as like a angle with
+ 
+
+ align:start position:0%
+case I'm drawing as like a angle with
+very little symmetry for reasons that
+
+ align:start position:0%
+very little symmetry for reasons that
+ 
+
+ align:start position:0%
+very little symmetry for reasons that
+might become apparent later
+
+ align:start position:0%
+might become apparent later
+ 
+
+ align:start position:0%
+might become apparent later
+on you have your PIN hole which is a
+
+ align:start position:0%
+on you have your PIN hole which is a
+ 
+
+ align:start position:0%
+on you have your PIN hole which is a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+opening of diameter D in some plate
+
+ align:start position:0%
+opening of diameter D in some plate
+ 
+
+ align:start position:0%
+opening of diameter D in some plate
+which is otherwise completely
+
+ align:start position:0%
+which is otherwise completely
+ 
+
+ align:start position:0%
+which is otherwise completely
+absorbing and then this is just
+
+ align:start position:0%
+absorbing and then this is just
+ 
+
+ align:start position:0%
+absorbing and then this is just
+geometric optics so you trace the Rays
+
+ align:start position:0%
+geometric optics so you trace the Rays
+ 
+
+ align:start position:0%
+geometric optics so you trace the Rays
+of light from the corners of your
+
+ align:start position:0%
+of light from the corners of your
+ 
+
+ align:start position:0%
+of light from the corners of your
+object through the pin hole and if you
+
+ align:start position:0%
+object through the pin hole and if you
+ 
+
+ align:start position:0%
+object through the pin hole and if you
+get it right and I'm probably going to
+
+ align:start position:0%
+get it right and I'm probably going to
+ 
+
+ align:start position:0%
+get it right and I'm probably going to
+get it wrong you get an object which is
+
+ align:start position:0%
+get it wrong you get an object which is
+ 
+
+ align:start position:0%
+get it wrong you get an object which is
+inverted from the one that you started
+
+ align:start position:0%
+inverted from the one that you started
+ 
+
+ align:start position:0%
+inverted from the one that you started
+with so it's upside down and it's it's
+
+ align:start position:0%
+with so it's upside down and it's it's
+ 
+
+ align:start position:0%
+with so it's upside down and it's it's
+flipped up down and flipped left right
+
+ align:start position:0%
+flipped up down and flipped left right
+ 
+
+ align:start position:0%
+flipped up down and flipped left right
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+well that's not usually a big problem
+
+ align:start position:0%
+well that's not usually a big problem
+ 
+
+ align:start position:0%
+well that's not usually a big problem
+you can usually work
+
+ align:start position:0%
+you can usually work
+ 
+
+ align:start position:0%
+you can usually work
+out what's going on the object will also
+
+ align:start position:0%
+out what's going on the object will also
+ 
+
+ align:start position:0%
+out what's going on the object will also
+be magnified so there's some distance U
+
+ align:start position:0%
+be magnified so there's some distance U
+ 
+
+ align:start position:0%
+be magnified so there's some distance U
+between your object and your pinhole and
+
+ align:start position:0%
+between your object and your pinhole and
+ 
+
+ align:start position:0%
+between your object and your pinhole and
+some distance V between your pinhole and
+
+ align:start position:0%
+some distance V between your pinhole and
+ 
+
+ align:start position:0%
+some distance V between your pinhole and
+your detector could be film or some
+
+ align:start position:0%
+your detector could be film or some
+ 
+
+ align:start position:0%
+your detector could be film or some
+camera and so this is also
+
+ align:start position:0%
+camera and so this is also
+ 
+
+ align:start position:0%
+camera and so this is also
+magnified
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the ratio of V upon U and you can
+
+ align:start position:0%
+by the ratio of V upon U and you can
+ 
+
+ align:start position:0%
+by the ratio of V upon U and you can
+check that out by drawing some lines for
+
+ align:start position:0%
+check that out by drawing some lines for
+ 
+
+ align:start position:0%
+check that out by drawing some lines for
+yourself and you'll see very quickly
+
+ align:start position:0%
+yourself and you'll see very quickly
+ 
+
+ align:start position:0%
+yourself and you'll see very quickly
+from some geometric arguments and
+
+ align:start position:0%
+from some geometric arguments and
+ 
+
+ align:start position:0%
+from some geometric arguments and
+similarity of triangles that you get out
+
+ align:start position:0%
+similarity of triangles that you get out
+ 
+
+ align:start position:0%
+similarity of triangles that you get out
+this magnification here but this will
+
+ align:start position:0%
+this magnification here but this will
+ 
+
+ align:start position:0%
+this magnification here but this will
+also be blurred so you'll not get a
+
+ align:start position:0%
+also be blurred so you'll not get a
+ 
+
+ align:start position:0%
+also be blurred so you'll not get a
+perfect image and it will be blurred by
+
+ align:start position:0%
+perfect image and it will be blurred by
+ 
+
+ align:start position:0%
+perfect image and it will be blurred by
+two effects the first one is geometric
+
+ align:start position:0%
+two effects the first one is geometric
+ 
+
+ align:start position:0%
+two effects the first one is geometric
+blurring
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the geometric blurring is a function of
+
+ align:start position:0%
+the geometric blurring is a function of
+ 
+
+ align:start position:0%
+the geometric blurring is a function of
+the fact that you have to have some
+
+ align:start position:0%
+the fact that you have to have some
+ 
+
+ align:start position:0%
+the fact that you have to have some
+finite sized pin hole here ideally this
+
+ align:start position:0%
+finite sized pin hole here ideally this
+ 
+
+ align:start position:0%
+finite sized pin hole here ideally this
+pin hole would be infantes small and
+
+ align:start position:0%
+pin hole would be infantes small and
+ 
+
+ align:start position:0%
+pin hole would be infantes small and
+then all of your rays of light would
+
+ align:start position:0%
+then all of your rays of light would
+ 
+
+ align:start position:0%
+then all of your rays of light would
+have to go through the pinhole to make
+
+ align:start position:0%
+have to go through the pinhole to make
+ 
+
+ align:start position:0%
+have to go through the pinhole to make
+it to the detector in practice if your
+
+ align:start position:0%
+it to the detector in practice if your
+ 
+
+ align:start position:0%
+it to the detector in practice if your
+PIN hole is very very small then you
+
+ align:start position:0%
+PIN hole is very very small then you
+ 
+
+ align:start position:0%
+PIN hole is very very small then you
+don't get any light through at all and
+
+ align:start position:0%
+don't get any light through at all and
+ 
+
+ align:start position:0%
+don't get any light through at all and
+you don't get a very bright image so you
+
+ align:start position:0%
+you don't get a very bright image so you
+ 
+
+ align:start position:0%
+you don't get a very bright image so you
+have to increase the size of your
+
+ align:start position:0%
+have to increase the size of your
+ 
+
+ align:start position:0%
+have to increase the size of your
+pinhole to get enough light through to
+
+ align:start position:0%
+pinhole to get enough light through to
+ 
+
+ align:start position:0%
+pinhole to get enough light through to
+make an image the D trick blurring is
+
+ align:start position:0%
+make an image the D trick blurring is
+ 
+
+ align:start position:0%
+make an image the D trick blurring is
+effectively if you
+
+ align:start position:0%
+effectively if you
+ 
+
+ align:start position:0%
+effectively if you
+think that your object consists of two
+
+ align:start position:0%
+think that your object consists of two
+ 
+
+ align:start position:0%
+think that your object consists of two
+little right blobs like this so you're
+
+ align:start position:0%
+little right blobs like this so you're
+ 
+
+ align:start position:0%
+little right blobs like this so you're
+you're looking at it it's just two
+
+ align:start position:0%
+you're looking at it it's just two
+ 
+
+ align:start position:0%
+you're looking at it it's just two
+little LEDs like that the projection of
+
+ align:start position:0%
+little LEDs like that the projection of
+ 
+
+ align:start position:0%
+little LEDs like that the projection of
+those dots say a DOT here and a DOT here
+
+ align:start position:0%
+those dots say a DOT here and a DOT here
+ 
+
+ align:start position:0%
+those dots say a DOT here and a DOT here
+through the pin
+
+ align:start position:0%
+through the pin
+ 
+
+ align:start position:0%
+through the pin
+hole I draw one of
+
+ align:start position:0%
+hole I draw one of
+ 
+
+ align:start position:0%
+hole I draw one of
+these to the top side of the pin hole
+
+ align:start position:0%
+these to the top side of the pin hole
+ 
+
+ align:start position:0%
+these to the top side of the pin hole
+and one of them to the bottom side of
+
+ align:start position:0%
+and one of them to the bottom side of
+ 
+
+ align:start position:0%
+and one of them to the bottom side of
+the pin hole so if this is just a
+
+ align:start position:0%
+the pin hole so if this is just a
+ 
+
+ align:start position:0%
+the pin hole so if this is just a
+missing light uniformly in 4 Pi St
+
+ align:start position:0%
+missing light uniformly in 4 Pi St
+ 
+
+ align:start position:0%
+missing light uniformly in 4 Pi St
+radian then it will project a circle
+
+ align:start position:0%
+radian then it will project a circle
+ 
+
+ align:start position:0%
+radian then it will project a circle
+through here so we'll end up not with
+
+ align:start position:0%
+through here so we'll end up not with
+ 
+
+ align:start position:0%
+through here so we'll end up not with
+two dots but with two circles so this is
+
+ align:start position:0%
+two dots but with two circles so this is
+ 
+
+ align:start position:0%
+two dots but with two circles so this is
+purely geometric I'm just using Ray
+
+ align:start position:0%
+purely geometric I'm just using Ray
+ 
+
+ align:start position:0%
+purely geometric I'm just using Ray
+Optics here I don't need to think about
+
+ align:start position:0%
+Optics here I don't need to think about
+ 
+
+ align:start position:0%
+Optics here I don't need to think about
+waves whatsoever and the diameter of
+
+ align:start position:0%
+waves whatsoever and the diameter of
+ 
+
+ align:start position:0%
+waves whatsoever and the diameter of
+these circles here is going to be equal
+
+ align:start position:0%
+these circles here is going to be equal
+ 
+
+ align:start position:0%
+these circles here is going to be equal
+to m + one times the pin hole size so we
+
+ align:start position:0%
+to m + one times the pin hole size so we
+ 
+
+ align:start position:0%
+to m + one times the pin hole size so we
+can change how much this blur occurs by
+
+ align:start position:0%
+can change how much this blur occurs by
+ 
+
+ align:start position:0%
+can change how much this blur occurs by
+changing our magnification and also by
+
+ align:start position:0%
+changing our magnification and also by
+ 
+
+ align:start position:0%
+changing our magnification and also by
+changing the pinhole and in the limit
+
+ align:start position:0%
+changing the pinhole and in the limit
+ 
+
+ align:start position:0%
+changing the pinhole and in the limit
+but our pinhole size becomes very small
+
+ align:start position:0%
+but our pinhole size becomes very small
+ 
+
+ align:start position:0%
+but our pinhole size becomes very small
+our blur also becomes very small and we
+
+ align:start position:0%
+our blur also becomes very small and we
+ 
+
+ align:start position:0%
+our blur also becomes very small and we
+can resolve Point objects again but like
+
+ align:start position:0%
+can resolve Point objects again but like
+ 
+
+ align:start position:0%
+can resolve Point objects again but like
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+said we
+
+ align:start position:0%
+said we
+ 
+
+ align:start position:0%
+said we
+need well if we have a very small
+
+ align:start position:0%
+need well if we have a very small
+ 
+
+ align:start position:0%
+need well if we have a very small
+pinhole diameter then we have no
+
+ align:start position:0%
+pinhole diameter then we have no
+ 
+
+ align:start position:0%
+pinhole diameter then we have no
+light so there's a tradeoff here and if
+
+ align:start position:0%
+light so there's a tradeoff here and if
+ 
+
+ align:start position:0%
+light so there's a tradeoff here and if
+you do photography and you're aware of
+
+ align:start position:0%
+you do photography and you're aware of
+ 
+
+ align:start position:0%
+you do photography and you're aware of
+like f numbers and things like that some
+
+ align:start position:0%
+like f numbers and things like that some
+ 
+
+ align:start position:0%
+like f numbers and things like that some
+of this may be very familiar to you but
+
+ align:start position:0%
+of this may be very familiar to you but
+ 
+
+ align:start position:0%
+of this may be very familiar to you but
+for those of you who don't I think this
+
+ align:start position:0%
+for those of you who don't I think this
+ 
+
+ align:start position:0%
+for those of you who don't I think this
+treatment is valid there's another limit
+
+ align:start position:0%
+treatment is valid there's another limit
+ 
+
+ align:start position:0%
+treatment is valid there's another limit
+which is the defraction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit and this is where we need to take
+
+ align:start position:0%
+limit and this is where we need to take
+ 
+
+ align:start position:0%
+limit and this is where we need to take
+the wave nature of light into
+
+ align:start position:0%
+the wave nature of light into
+ 
+
+ align:start position:0%
+the wave nature of light into
+account so we have our little pin hole
+
+ align:start position:0%
+account so we have our little pin hole
+ 
+
+ align:start position:0%
+account so we have our little pin hole
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+here but we know from hen's principle if
+
+ align:start position:0%
+here but we know from hen's principle if
+ 
+
+ align:start position:0%
+here but we know from hen's principle if
+we got some wave fronts coming in like
+
+ align:start position:0%
+we got some wave fronts coming in like
+ 
+
+ align:start position:0%
+we got some wave fronts coming in like
+this every point on the wavefront is a
+
+ align:start position:0%
+this every point on the wavefront is a
+ 
+
+ align:start position:0%
+this every point on the wavefront is a
+source of thical wave
+
+ align:start position:0%
+source of thical wave
+ 
+
+ align:start position:0%
+source of thical wave
+fronts
+
+ align:start position:0%
+fronts
+ 
+
+ align:start position:0%
+fronts
+normally when there's no pin hole here
+
+ align:start position:0%
+normally when there's no pin hole here
+ 
+
+ align:start position:0%
+normally when there's no pin hole here
+that doesn't matter because our next
+
+ align:start position:0%
+that doesn't matter because our next
+ 
+
+ align:start position:0%
+that doesn't matter because our next
+wavefront is then made out of the sum of
+
+ align:start position:0%
+wavefront is then made out of the sum of
+ 
+
+ align:start position:0%
+wavefront is then made out of the sum of
+all of these little fical wavefronts but
+
+ align:start position:0%
+all of these little fical wavefronts but
+ 
+
+ align:start position:0%
+all of these little fical wavefronts but
+when we put our pinhole aperture in the
+
+ align:start position:0%
+when we put our pinhole aperture in the
+ 
+
+ align:start position:0%
+when we put our pinhole aperture in the
+way we block out some of those wave
+
+ align:start position:0%
+way we block out some of those wave
+ 
+
+ align:start position:0%
+way we block out some of those wave
+fronts and instead we start to get
+
+ align:start position:0%
+fronts and instead we start to get
+ 
+
+ align:start position:0%
+fronts and instead we start to get
+defraction so we start to get spherical
+
+ align:start position:0%
+defraction so we start to get spherical
+ 
+
+ align:start position:0%
+defraction so we start to get spherical
+waves coming out from this and so if we
+
+ align:start position:0%
+waves coming out from this and so if we
+ 
+
+ align:start position:0%
+waves coming out from this and so if we
+initially had a point source it's now
+
+ align:start position:0%
+initially had a point source it's now
+ 
+
+ align:start position:0%
+initially had a point source it's now
+going to be imaged into a blurry Source
+
+ align:start position:0%
+going to be imaged into a blurry Source
+ 
+
+ align:start position:0%
+going to be imaged into a blurry Source
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UHS okay I can't remember I think it's
+
+ align:start position:0%
+UHS okay I can't remember I think it's
+ 
+
+ align:start position:0%
+UHS okay I can't remember I think it's
+the rally criteria the rally criteria
+
+ align:start position:0%
+the rally criteria the rally criteria
+ 
+
+ align:start position:0%
+the rally criteria the rally criteria
+says that if you have two dots like
+
+ align:start position:0%
+says that if you have two dots like
+ 
+
+ align:start position:0%
+says that if you have two dots like
+this for
+
+ align:start position:0%
+this for
+ 
+
+ align:start position:0%
+this for
+example that are some distance apart
+
+ align:start position:0%
+example that are some distance apart
+ 
+
+ align:start position:0%
+example that are some distance apart
+then we can only distinguish them um if
+
+ align:start position:0%
+then we can only distinguish them um if
+ 
+
+ align:start position:0%
+then we can only distinguish them um if
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+blur is separated and this
+
+ align:start position:0%
+blur is separated and this
+ 
+
+ align:start position:0%
+blur is separated and this
+separation that sets a resolution is
+
+ align:start position:0%
+separation that sets a resolution is
+ 
+
+ align:start position:0%
+separation that sets a resolution is
+1.22 Lambda over
+
+ align:start position:0%
+1.22 Lambda over
+ 
+
+ align:start position:0%
+1.22 Lambda over
+D that's an angle space so I multiply it
+
+ align:start position:0%
+D that's an angle space so I multiply it
+ 
+
+ align:start position:0%
+D that's an angle space so I multiply it
+by V to bring that angle into a real uh
+
+ align:start position:0%
+by V to bring that angle into a real uh
+ 
+
+ align:start position:0%
+by V to bring that angle into a real uh
+position on our detector here so this
+
+ align:start position:0%
+position on our detector here so this
+ 
+
+ align:start position:0%
+position on our detector here so this
+1.22 comes from like zeros of the AR
+
+ align:start position:0%
+1.22 comes from like zeros of the AR
+ 
+
+ align:start position:0%
+1.22 comes from like zeros of the AR
+function these are actually like little
+
+ align:start position:0%
+function these are actually like little
+ 
+
+ align:start position:0%
+function these are actually like little
+syncs and we're trying to make sure that
+
+ align:start position:0%
+syncs and we're trying to make sure that
+ 
+
+ align:start position:0%
+syncs and we're trying to make sure that
+the first zeros are separated between
+
+ align:start position:0%
+the first zeros are separated between
+ 
+
+ align:start position:0%
+the first zeros are separated between
+these two here you may have seen this if
+
+ align:start position:0%
+these two here you may have seen this if
+ 
+
+ align:start position:0%
+these two here you may have seen this if
+you've done fraction Theory before so
+
+ align:start position:0%
+you've done fraction Theory before so
+ 
+
+ align:start position:0%
+you've done fraction Theory before so
+the geometric blur doesn't care about
+
+ align:start position:0%
+the geometric blur doesn't care about
+ 
+
+ align:start position:0%
+the geometric blur doesn't care about
+the wavelength of the light doesn't care
+
+ align:start position:0%
+the wavelength of the light doesn't care
+ 
+
+ align:start position:0%
+the wavelength of the light doesn't care
+about the energy of the photons the
+
+ align:start position:0%
+about the energy of the photons the
+ 
+
+ align:start position:0%
+about the energy of the photons the
+defraction blur does care about the
+
+ align:start position:0%
+defraction blur does care about the
+ 
+
+ align:start position:0%
+defraction blur does care about the
+wavelength of the light because it's a
+
+ align:start position:0%
+wavelength of the light because it's a
+ 
+
+ align:start position:0%
+wavelength of the light because it's a
+wave effect here and so we can make the
+
+ align:start position:0%
+wave effect here and so we can make the
+ 
+
+ align:start position:0%
+wave effect here and so we can make the
+refractive blur go away by having a
+
+ align:start position:0%
+refractive blur go away by having a
+ 
+
+ align:start position:0%
+refractive blur go away by having a
+bigger pinhole or by having a shorter
+
+ align:start position:0%
+bigger pinhole or by having a shorter
+ 
+
+ align:start position:0%
+bigger pinhole or by having a shorter
+wavelength so if we go to a bigger pin
+
+ align:start position:0%
+wavelength so if we go to a bigger pin
+ 
+
+ align:start position:0%
+wavelength so if we go to a bigger pin
+hole then our geometric blur will be
+
+ align:start position:0%
+hole then our geometric blur will be
+ 
+
+ align:start position:0%
+hole then our geometric blur will be
+worse and so there's actually a
+
+ align:start position:0%
+worse and so there's actually a
+ 
+
+ align:start position:0%
+worse and so there's actually a
+trade-off between these two there'll be
+
+ align:start position:0%
+trade-off between these two there'll be
+ 
+
+ align:start position:0%
+trade-off between these two there'll be
+a sweet spot that gives you the best
+
+ align:start position:0%
+a sweet spot that gives you the best
+ 
+
+ align:start position:0%
+a sweet spot that gives you the best
+resolution where you minimize the sum of
+
+ align:start position:0%
+resolution where you minimize the sum of
+ 
+
+ align:start position:0%
+resolution where you minimize the sum of
+the defraction and the geometric
+
+ align:start position:0%
+the defraction and the geometric
+ 
+
+ align:start position:0%
+the defraction and the geometric
+resolution but you need to think about
+
+ align:start position:0%
+resolution but you need to think about
+ 
+
+ align:start position:0%
+resolution but you need to think about
+this when you're designing pin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay oh the other thing about this is if
+
+ align:start position:0%
+okay oh the other thing about this is if
+ 
+
+ align:start position:0%
+okay oh the other thing about this is if
+you have a source that is emitting lots
+
+ align:start position:0%
+you have a source that is emitting lots
+ 
+
+ align:start position:0%
+you have a source that is emitting lots
+of light in lots of different
+
+ align:start position:0%
+of light in lots of different
+ 
+
+ align:start position:0%
+of light in lots of different
+wavelengths then the short wavelengths
+
+ align:start position:0%
+wavelengths then the short wavelengths
+ 
+
+ align:start position:0%
+wavelengths then the short wavelengths
+will be defract blurred and they'll be
+
+ align:start position:0%
+will be defract blurred and they'll be
+ 
+
+ align:start position:0%
+will be defract blurred and they'll be
+smeared out over your detector and the
+
+ align:start position:0%
+smeared out over your detector and the
+ 
+
+ align:start position:0%
+smeared out over your detector and the
+long wavelengths won't be but that means
+
+ align:start position:0%
+long wavelengths won't be but that means
+ 
+
+ align:start position:0%
+long wavelengths won't be but that means
+that you'll have this like blur over
+
+ align:start position:0%
+that you'll have this like blur over
+ 
+
+ align:start position:0%
+that you'll have this like blur over
+your whole detector from the short
+
+ align:start position:0%
+your whole detector from the short
+ 
+
+ align:start position:0%
+your whole detector from the short
+wavelengths uh which reduces your signal
+
+ align:start position:0%
+wavelengths uh which reduces your signal
+ 
+
+ align:start position:0%
+wavelengths uh which reduces your signal
+to noise and so this is especially where
+
+ align:start position:0%
+to noise and so this is especially where
+ 
+
+ align:start position:0%
+to noise and so this is especially where
+you want to have a
+
+ align:start position:0%
+you want to have a
+ 
+
+ align:start position:0%
+you want to have a
+filter so you want to filter out the low
+
+ align:start position:0%
+filter so you want to filter out the low
+ 
+
+ align:start position:0%
+filter so you want to filter out the low
+wavelengths so that they don't blur up
+
+ align:start position:0%
+wavelengths so that they don't blur up
+ 
+
+ align:start position:0%
+wavelengths so that they don't blur up
+uh out your image and you want to just
+
+ align:start position:0%
+uh out your image and you want to just
+ 
+
+ align:start position:0%
+uh out your image and you want to just
+have the high wavelengths like these
+
+ align:start position:0%
+have the high wavelengths like these
+ 
+
+ align:start position:0%
+have the high wavelengths like these
+ones here make an image just in like
+
+ align:start position:0%
+ones here make an image just in like
+ 
+
+ align:start position:0%
+ones here make an image just in like
+some of the K Alpha emission from the
+
+ align:start position:0%
+some of the K Alpha emission from the
+ 
+
+ align:start position:0%
+some of the K Alpha emission from the
+very hot parts of your
+
+ align:start position:0%
+very hot parts of your
+ 
+
+ align:start position:0%
+very hot parts of your
+plas okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes I'm not sure how that comes into
+
+ align:start position:0%
+yes yes I'm not sure how that comes into
+ 
+
+ align:start position:0%
+yes yes I'm not sure how that comes into
+this geometric optics framework
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+though okay I yeah I see where that's
+
+ align:start position:0%
+though okay I yeah I see where that's
+ 
+
+ align:start position:0%
+though okay I yeah I see where that's
+going for me this is for a pinhole it's
+
+ align:start position:0%
+going for me this is for a pinhole it's
+ 
+
+ align:start position:0%
+going for me this is for a pinhole it's
+always going to be inverted I guess
+
+ align:start position:0%
+always going to be inverted I guess
+ 
+
+ align:start position:0%
+always going to be inverted I guess
+theoretically you put two pin holes no
+
+ align:start position:0%
+theoretically you put two pin holes no
+ 
+
+ align:start position:0%
+theoretically you put two pin holes no
+that doesn't work well always inverted
+
+ align:start position:0%
+that doesn't work well always inverted
+ 
+
+ align:start position:0%
+that doesn't work well always inverted
+so yeah so maybe maybe it's negative in
+
+ align:start position:0%
+so yeah so maybe maybe it's negative in
+ 
+
+ align:start position:0%
+so yeah so maybe maybe it's negative in
+someone's sign convention but nothing in
+
+ align:start position:0%
+someone's sign convention but nothing in
+ 
+
+ align:start position:0%
+someone's sign convention but nothing in
+the one I'm using here because it's
+
+ align:start position:0%
+the one I'm using here because it's
+ 
+
+ align:start position:0%
+the one I'm using here because it's
+always true yeah good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question yeah well what I've missed out
+
+ align:start position:0%
+question yeah well what I've missed out
+ 
+
+ align:start position:0%
+question yeah well what I've missed out
+here is in fact that the transmission of
+
+ align:start position:0%
+here is in fact that the transmission of
+ 
+
+ align:start position:0%
+here is in fact that the transmission of
+as you know a thin bit of metal foil is
+
+ align:start position:0%
+as you know a thin bit of metal foil is
+ 
+
+ align:start position:0%
+as you know a thin bit of metal foil is
+actually opaque to visible light so if I
+
+ align:start position:0%
+actually opaque to visible light so if I
+ 
+
+ align:start position:0%
+actually opaque to visible light so if I
+put a very thin bit of aluminium foil in
+
+ align:start position:0%
+put a very thin bit of aluminium foil in
+ 
+
+ align:start position:0%
+put a very thin bit of aluminium foil in
+there I will definitely block out the
+
+ align:start position:0%
+there I will definitely block out the
+ 
+
+ align:start position:0%
+there I will definitely block out the
+light and you need like 200 nanometers
+
+ align:start position:0%
+light and you need like 200 nanometers
+ 
+
+ align:start position:0%
+light and you need like 200 nanometers
+so you can just deposit it on like some
+
+ align:start position:0%
+so you can just deposit it on like some
+ 
+
+ align:start position:0%
+so you can just deposit it on like some
+basically transparent plastic and then
+
+ align:start position:0%
+basically transparent plastic and then
+ 
+
+ align:start position:0%
+basically transparent plastic and then
+you'll also get the filtering from the
+
+ align:start position:0%
+you'll also get the filtering from the
+ 
+
+ align:start position:0%
+you'll also get the filtering from the
+aluminium k for example so yeah we
+
+ align:start position:0%
+aluminium k for example so yeah we
+ 
+
+ align:start position:0%
+aluminium k for example so yeah we
+haven't gone down to very low energies
+
+ align:start position:0%
+haven't gone down to very low energies
+ 
+
+ align:start position:0%
+haven't gone down to very low energies
+this is kind of like an x-ray regime
+
+ align:start position:0%
+this is kind of like an x-ray regime
+ 
+
+ align:start position:0%
+this is kind of like an x-ray regime
+treatment of it so of course you need
+
+ align:start position:0%
+treatment of it so of course you need
+ 
+
+ align:start position:0%
+treatment of it so of course you need
+x-ray photons in order to even get the
+
+ align:start position:0%
+x-ray photons in order to even get the
+ 
+
+ align:start position:0%
+x-ray photons in order to even get the
+the LH in reality this goes down and
+
+ align:start position:0%
+the LH in reality this goes down and
+ 
+
+ align:start position:0%
+the LH in reality this goes down and
+some other stuff happen down at this um
+
+ align:start position:0%
+some other stuff happen down at this um
+ 
+
+ align:start position:0%
+some other stuff happen down at this um
+visible wavelength yeah but anything any
+
+ align:start position:0%
+visible wavelength yeah but anything any
+ 
+
+ align:start position:0%
+visible wavelength yeah but anything any
+metal that is sufficiently thick and it
+
+ align:start position:0%
+metal that is sufficiently thick and it
+ 
+
+ align:start position:0%
+metal that is sufficiently thick and it
+doesn't need to be very thick will block
+
+ align:start position:0%
+doesn't need to be very thick will block
+ 
+
+ align:start position:0%
+doesn't need to be very thick will block
+all the visible light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+yes you're right I just constantly get
+
+ align:start position:0%
+yes you're right I just constantly get
+ 
+
+ align:start position:0%
+yes you're right I just constantly get
+confused between wavelength and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequency filter out long way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is visible light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generally okay good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question you can also do imaging and I'm
+
+ align:start position:0%
+question you can also do imaging and I'm
+ 
+
+ align:start position:0%
+question you can also do imaging and I'm
+not going to talk about length pinhole
+
+ align:start position:0%
+not going to talk about length pinhole
+ 
+
+ align:start position:0%
+not going to talk about length pinhole
+Imaging is quite limited um you can also
+
+ align:start position:0%
+Imaging is quite limited um you can also
+ 
+
+ align:start position:0%
+Imaging is quite limited um you can also
+do imaging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with vent
+
+ align:start position:0%
+with vent
+ 
+
+ align:start position:0%
+with vent
+crystals so if you've ever looked at
+
+ align:start position:0%
+crystals so if you've ever looked at
+ 
+
+ align:start position:0%
+crystals so if you've ever looked at
+uh defraction of x-rays from crystals
+
+ align:start position:0%
+uh defraction of x-rays from crystals
+ 
+
+ align:start position:0%
+uh defraction of x-rays from crystals
+you'll know that the uh crystals will
+
+ align:start position:0%
+you'll know that the uh crystals will
+ 
+
+ align:start position:0%
+you'll know that the uh crystals will
+defract light of certain wavelengths and
+
+ align:start position:0%
+defract light of certain wavelengths and
+ 
+
+ align:start position:0%
+defract light of certain wavelengths and
+if you have a bent Crystal you can also
+
+ align:start position:0%
+if you have a bent Crystal you can also
+ 
+
+ align:start position:0%
+if you have a bent Crystal you can also
+be focusing with it so people spend a
+
+ align:start position:0%
+be focusing with it so people spend a
+ 
+
+ align:start position:0%
+be focusing with it so people spend a
+lot of time very gently bending bits of
+
+ align:start position:0%
+lot of time very gently bending bits of
+ 
+
+ align:start position:0%
+lot of time very gently bending bits of
+Crystal and that makes a reflective lens
+
+ align:start position:0%
+Crystal and that makes a reflective lens
+ 
+
+ align:start position:0%
+Crystal and that makes a reflective lens
+so you can't have a transmissive lens
+
+ align:start position:0%
+so you can't have a transmissive lens
+ 
+
+ align:start position:0%
+so you can't have a transmissive lens
+but you can have a bent mirror
+
+ align:start position:0%
+but you can have a bent mirror
+ 
+
+ align:start position:0%
+but you can have a bent mirror
+effectively so there are you know two
+
+ align:start position:0%
+effectively so there are you know two
+ 
+
+ align:start position:0%
+effectively so there are you know two
+ways to focus light you can have a lens
+
+ align:start position:0%
+ways to focus light you can have a lens
+ 
+
+ align:start position:0%
+ways to focus light you can have a lens
+like this that your light goes through
+
+ align:start position:0%
+like this that your light goes through
+ 
+
+ align:start position:0%
+like this that your light goes through
+or equivalently you you can have a
+
+ align:start position:0%
+or equivalently you you can have a
+ 
+
+ align:start position:0%
+or equivalently you you can have a
+mirror like this that the light reflects
+
+ align:start position:0%
+mirror like this that the light reflects
+ 
+
+ align:start position:0%
+mirror like this that the light reflects
+off and because the mirror is
+
+ align:start position:0%
+off and because the mirror is
+ 
+
+ align:start position:0%
+off and because the mirror is
+bent it will get Focus to a different
+
+ align:start position:0%
+bent it will get Focus to a different
+ 
+
+ align:start position:0%
+bent it will get Focus to a different
+point and as you adjust this mirror it
+
+ align:start position:0%
+point and as you adjust this mirror it
+ 
+
+ align:start position:0%
+point and as you adjust this mirror it
+will depend where this gets focused on
+
+ align:start position:0%
+will depend where this gets focused on
+ 
+
+ align:start position:0%
+will depend where this gets focused on
+now even a crystal is not a mirror for
+
+ align:start position:0%
+now even a crystal is not a mirror for
+ 
+
+ align:start position:0%
+now even a crystal is not a mirror for
+x-rays it's a mirror for a certain
+
+ align:start position:0%
+x-rays it's a mirror for a certain
+ 
+
+ align:start position:0%
+x-rays it's a mirror for a certain
+wavelength of light and so if you put
+
+ align:start position:0%
+wavelength of light and so if you put
+ 
+
+ align:start position:0%
+wavelength of light and so if you put
+your detector here you might have the K
+
+ align:start position:0%
+your detector here you might have the K
+ 
+
+ align:start position:0%
+your detector here you might have the K
+Alpha focused onto your detector but for
+
+ align:start position:0%
+Alpha focused onto your detector but for
+ 
+
+ align:start position:0%
+Alpha focused onto your detector but for
+example the K beta which is coming in
+
+ align:start position:0%
+example the K beta which is coming in
+ 
+
+ align:start position:0%
+example the K beta which is coming in
+the same direction might get
+
+ align:start position:0%
+the same direction might get
+ 
+
+ align:start position:0%
+the same direction might get
+reflected or
+
+ align:start position:0%
+reflected or
+ 
+
+ align:start position:0%
+reflected or
+defract off to a different point which
+
+ align:start position:0%
+defract off to a different point which
+ 
+
+ align:start position:0%
+defract off to a different point which
+is off your detector so this is a way of
+
+ align:start position:0%
+is off your detector so this is a way of
+ 
+
+ align:start position:0%
+is off your detector so this is a way of
+doing monochromatic imag so effectively
+
+ align:start position:0%
+doing monochromatic imag so effectively
+ 
+
+ align:start position:0%
+doing monochromatic imag so effectively
+your Crystal here acts as both the
+
+ align:start position:0%
+your Crystal here acts as both the
+ 
+
+ align:start position:0%
+your Crystal here acts as both the
+filter and the focusing element so you
+
+ align:start position:0%
+filter and the focusing element so you
+ 
+
+ align:start position:0%
+filter and the focusing element so you
+can make beautiful images um you don't
+
+ align:start position:0%
+can make beautiful images um you don't
+ 
+
+ align:start position:0%
+can make beautiful images um you don't
+need to have a tiny pin hole so you can
+
+ align:start position:0%
+need to have a tiny pin hole so you can
+ 
+
+ align:start position:0%
+need to have a tiny pin hole so you can
+get lots and lots of light uh and you
+
+ align:start position:0%
+get lots and lots of light uh and you
+ 
+
+ align:start position:0%
+get lots and lots of light uh and you
+can get images with just a single
+
+ align:start position:0%
+can get images with just a single
+ 
+
+ align:start position:0%
+can get images with just a single
+wavelength which can be very powerful
+
+ align:start position:0%
+wavelength which can be very powerful
+ 
+
+ align:start position:0%
+wavelength which can be very powerful
+for saying like this is the very hot bit
+
+ align:start position:0%
+for saying like this is the very hot bit
+ 
+
+ align:start position:0%
+for saying like this is the very hot bit
+of my plasma that's producing K Alpha so
+
+ align:start position:0%
+of my plasma that's producing K Alpha so
+ 
+
+ align:start position:0%
+of my plasma that's producing K Alpha so
+B Crystal you can get what's called
+
+ align:start position:0%
+B Crystal you can get what's called
+ 
+
+ align:start position:0%
+B Crystal you can get what's called
+monochromatic Imaging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but bending bristles is extraordinarily
+
+ align:start position:0%
+but bending bristles is extraordinarily
+ 
+
+ align:start position:0%
+but bending bristles is extraordinarily
+expensive so pin holes are very very
+
+ align:start position:0%
+expensive so pin holes are very very
+ 
+
+ align:start position:0%
+expensive so pin holes are very very
+cheap and you'll find a lot of people
+
+ align:start position:0%
+cheap and you'll find a lot of people
+ 
+
+ align:start position:0%
+cheap and you'll find a lot of people
+using pinoles because they work pretty
+
+ align:start position:0%
+using pinoles because they work pretty
+ 
+
+ align:start position:0%
+using pinoles because they work pretty
+well and of course the bent crystals
+
+ align:start position:0%
+well and of course the bent crystals
+ 
+
+ align:start position:0%
+well and of course the bent crystals
+only work for individual energies and so
+
+ align:start position:0%
+only work for individual energies and so
+ 
+
+ align:start position:0%
+only work for individual energies and so
+if you want to like try and measure sort
+
+ align:start position:0%
+if you want to like try and measure sort
+ 
+
+ align:start position:0%
+if you want to like try and measure sort
+of more broadly what the radiation is
+
+ align:start position:0%
+of more broadly what the radiation is
+ 
+
+ align:start position:0%
+of more broadly what the radiation is
+from the plasma you'll miss out on that
+
+ align:start position:0%
+from the plasma you'll miss out on that
+ 
+
+ align:start position:0%
+from the plasma you'll miss out on that
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Laughter]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah my last last set of notes for today
+
+ align:start position:0%
+yeah my last last set of notes for today
+ 
+
+ align:start position:0%
+yeah my last last set of notes for today
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+promise sorry what
+
+ align:start position:0%
+promise sorry what
+ 
+
+ align:start position:0%
+promise sorry what
+yeah yeah diodes are pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good no no nice silicon 50 nmet stick
+
+ align:start position:0%
+good no no nice silicon 50 nmet stick
+ 
+
+ align:start position:0%
+good no no nice silicon 50 nmet stick
+perfectly good for x-rays up to about 10
+
+ align:start position:0%
+perfectly good for x-rays up to about 10
+ 
+
+ align:start position:0%
+perfectly good for x-rays up to about 10
+KV so um nothing wrong with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+di okay so a lot of these
+
+ align:start position:0%
+di okay so a lot of these
+ 
+
+ align:start position:0%
+di okay so a lot of these
+detectors are simply
+
+ align:start position:0%
+detectors are simply
+ 
+
+ align:start position:0%
+detectors are simply
+filled if you went to the dentist decade
+
+ align:start position:0%
+filled if you went to the dentist decade
+ 
+
+ align:start position:0%
+filled if you went to the dentist decade
+or so ago they would have used film in
+
+ align:start position:0%
+or so ago they would have used film in
+ 
+
+ align:start position:0%
+or so ago they would have used film in
+their x-ray things and in fact most of
+
+ align:start position:0%
+their x-ray things and in fact most of
+ 
+
+ align:start position:0%
+their x-ray things and in fact most of
+X-ray film was developed for medical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+applications and film is really good
+
+ align:start position:0%
+applications and film is really good
+ 
+
+ align:start position:0%
+applications and film is really good
+okay so film has a huge drawback it's
+
+ align:start position:0%
+okay so film has a huge drawback it's
+ 
+
+ align:start position:0%
+okay so film has a huge drawback it's
+time integrated so you have no sense of
+
+ align:start position:0%
+time integrated so you have no sense of
+ 
+
+ align:start position:0%
+time integrated so you have no sense of
+uh what the time is you have an integral
+
+ align:start position:0%
+uh what the time is you have an integral
+ 
+
+ align:start position:0%
+uh what the time is you have an integral
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intensity over time so if you have some
+
+ align:start position:0%
+intensity over time so if you have some
+ 
+
+ align:start position:0%
+intensity over time so if you have some
+filtering maybe you have still frequency
+
+ align:start position:0%
+filtering maybe you have still frequency
+ 
+
+ align:start position:0%
+filtering maybe you have still frequency
+information left in your image because
+
+ align:start position:0%
+information left in your image because
+ 
+
+ align:start position:0%
+information left in your image because
+you're like oh this is coming all from
+
+ align:start position:0%
+you're like oh this is coming all from
+ 
+
+ align:start position:0%
+you're like oh this is coming all from
+the K Alpha I got a special filter in
+
+ align:start position:0%
+the K Alpha I got a special filter in
+ 
+
+ align:start position:0%
+the K Alpha I got a special filter in
+but you don't have any time so that
+
+ align:start position:0%
+but you don't have any time so that
+ 
+
+ align:start position:0%
+but you don't have any time so that
+could be a really big problem if you're
+
+ align:start position:0%
+could be a really big problem if you're
+ 
+
+ align:start position:0%
+could be a really big problem if you're
+doing something with like a rapid
+
+ align:start position:0%
+doing something with like a rapid
+ 
+
+ align:start position:0%
+doing something with like a rapid
+implosion like in initial confin Fusion
+
+ align:start position:0%
+implosion like in initial confin Fusion
+ 
+
+ align:start position:0%
+implosion like in initial confin Fusion
+but it doesn't have to be a big problem
+
+ align:start position:0%
+but it doesn't have to be a big problem
+ 
+
+ align:start position:0%
+but it doesn't have to be a big problem
+for example if you've
+
+ align:start position:0%
+for example if you've
+ 
+
+ align:start position:0%
+for example if you've
+got uh a signal that is very bursty in
+
+ align:start position:0%
+got uh a signal that is very bursty in
+ 
+
+ align:start position:0%
+got uh a signal that is very bursty in
+time like an ICF so this could be you
+
+ align:start position:0%
+time like an ICF so this could be you
+ 
+
+ align:start position:0%
+time like an ICF so this could be you
+know a few hundred T seconds
+
+ align:start position:0%
+know a few hundred T seconds
+ 
+
+ align:start position:0%
+know a few hundred T seconds
+across and you have an x-ray diode
+
+ align:start position:0%
+across and you have an x-ray diode
+ 
+
+ align:start position:0%
+across and you have an x-ray diode
+looking at it and that iode has time
+
+ align:start position:0%
+looking at it and that iode has time
+ 
+
+ align:start position:0%
+looking at it and that iode has time
+resolution but no spatial resolution
+
+ align:start position:0%
+resolution but no spatial resolution
+ 
+
+ align:start position:0%
+resolution but no spatial resolution
+then you could use that di signal to say
+
+ align:start position:0%
+then you could use that di signal to say
+ 
+
+ align:start position:0%
+then you could use that di signal to say
+well all of my really bright x-rays REM
+
+ align:start position:0%
+well all of my really bright x-rays REM
+ 
+
+ align:start position:0%
+well all of my really bright x-rays REM
+missed 100 PCS so although this is time
+
+ align:start position:0%
+missed 100 PCS so although this is time
+ 
+
+ align:start position:0%
+missed 100 PCS so although this is time
+integrated I actually know that the time
+
+ align:start position:0%
+integrated I actually know that the time
+ 
+
+ align:start position:0%
+integrated I actually know that the time
+that this was integrating over was only
+
+ align:start position:0%
+that this was integrating over was only
+ 
+
+ align:start position:0%
+that this was integrating over was only
+T to t plus 100 PC so you can use a
+
+ align:start position:0%
+T to t plus 100 PC so you can use a
+ 
+
+ align:start position:0%
+T to t plus 100 PC so you can use a
+combination of Diagnostics to localize
+
+ align:start position:0%
+combination of Diagnostics to localize
+ 
+
+ align:start position:0%
+combination of Diagnostics to localize
+your signal in time that might be okay
+
+ align:start position:0%
+your signal in time that might be okay
+ 
+
+ align:start position:0%
+your signal in time that might be okay
+film is really high resolution um you
+
+ align:start position:0%
+film is really high resolution um you
+ 
+
+ align:start position:0%
+film is really high resolution um you
+know film grains are very small so it's
+
+ align:start position:0%
+know film grains are very small so it's
+ 
+
+ align:start position:0%
+know film grains are very small so it's
+can be much higher resolution than a
+
+ align:start position:0%
+can be much higher resolution than a
+ 
+
+ align:start position:0%
+can be much higher resolution than a
+detector um like something that has
+
+ align:start position:0%
+detector um like something that has
+ 
+
+ align:start position:0%
+detector um like something that has
+pixels uh you obviously don't have to
+
+ align:start position:0%
+pixels uh you obviously don't have to
+ 
+
+ align:start position:0%
+pixels uh you obviously don't have to
+scan it at very high resolution but we
+
+ align:start position:0%
+scan it at very high resolution but we
+ 
+
+ align:start position:0%
+scan it at very high resolution but we
+can do that it's also very well
+
+ align:start position:0%
+can do that it's also very well
+ 
+
+ align:start position:0%
+can do that it's also very well
+characterized so um although it may not
+
+ align:start position:0%
+characterized so um although it may not
+ 
+
+ align:start position:0%
+characterized so um although it may not
+be linear we know like this amount of
+
+ align:start position:0%
+be linear we know like this amount of
+ 
+
+ align:start position:0%
+be linear we know like this amount of
+Darkness corresponds to this much energy
+
+ align:start position:0%
+Darkness corresponds to this much energy
+ 
+
+ align:start position:0%
+Darkness corresponds to this much energy
+deposited so film is actually really
+
+ align:start position:0%
+deposited so film is actually really
+ 
+
+ align:start position:0%
+deposited so film is actually really
+precious and unfortunately a lot of of
+
+ align:start position:0%
+precious and unfortunately a lot of of
+ 
+
+ align:start position:0%
+precious and unfortunately a lot of of
+film manufacturers like Kodak have
+
+ align:start position:0%
+film manufacturers like Kodak have
+ 
+
+ align:start position:0%
+film manufacturers like Kodak have
+stopped making x-ray film because there
+
+ align:start position:0%
+stopped making x-ray film because there
+ 
+
+ align:start position:0%
+stopped making x-ray film because there
+isn't a market anymore I believe Omega
+
+ align:start position:0%
+isn't a market anymore I believe Omega
+ 
+
+ align:start position:0%
+isn't a market anymore I believe Omega
+has one of the large the Omega facility
+
+ align:start position:0%
+has one of the large the Omega facility
+ 
+
+ align:start position:0%
+has one of the large the Omega facility
+at rockchester has one of the largest
+
+ align:start position:0%
+at rockchester has one of the largest
+ 
+
+ align:start position:0%
+at rockchester has one of the largest
+stock piles of remaining medical film in
+
+ align:start position:0%
+stock piles of remaining medical film in
+ 
+
+ align:start position:0%
+stock piles of remaining medical film in
+a fridge because they can't buy it
+
+ align:start position:0%
+a fridge because they can't buy it
+ 
+
+ align:start position:0%
+a fridge because they can't buy it
+anymore and no one else is has any left
+
+ align:start position:0%
+anymore and no one else is has any left
+ 
+
+ align:start position:0%
+anymore and no one else is has any left
+so people keep begging Omega for some of
+
+ align:start position:0%
+so people keep begging Omega for some of
+ 
+
+ align:start position:0%
+so people keep begging Omega for some of
+their film from time to time so it's
+
+ align:start position:0%
+their film from time to time so it's
+ 
+
+ align:start position:0%
+their film from time to time so it's
+good stuff but a lot of people have now
+
+ align:start position:0%
+good stuff but a lot of people have now
+ 
+
+ align:start position:0%
+good stuff but a lot of people have now
+moved to something called image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plate image plate at first glance looks
+
+ align:start position:0%
+plate image plate at first glance looks
+ 
+
+ align:start position:0%
+plate image plate at first glance looks
+an awful lot light film it's a bit of
+
+ align:start position:0%
+an awful lot light film it's a bit of
+ 
+
+ align:start position:0%
+an awful lot light film it's a bit of
+plastic uh plastic looking stuff uh it's
+
+ align:start position:0%
+plastic uh plastic looking stuff uh it's
+ 
+
+ align:start position:0%
+plastic uh plastic looking stuff uh it's
+time integrating again there's no
+
+ align:start position:0%
+time integrating again there's no
+ 
+
+ align:start position:0%
+time integrating again there's no
+electronics to it what happens with
+
+ align:start position:0%
+electronics to it what happens with
+ 
+
+ align:start position:0%
+electronics to it what happens with
+image plate which is neat is the x-rays
+
+ align:start position:0%
+image plate which is neat is the x-rays
+ 
+
+ align:start position:0%
+image plate which is neat is the x-rays
+excited up to a meta stable state so you
+
+ align:start position:0%
+excited up to a meta stable state so you
+ 
+
+ align:start position:0%
+excited up to a meta stable state so you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+x-rays excite it up to this metastable
+
+ align:start position:0%
+x-rays excite it up to this metastable
+ 
+
+ align:start position:0%
+x-rays excite it up to this metastable
+state up here and because it's
+
+ align:start position:0%
+state up here and because it's
+ 
+
+ align:start position:0%
+state up here and because it's
+metastable it doesn't actually Decay
+
+ align:start position:0%
+metastable it doesn't actually Decay
+ 
+
+ align:start position:0%
+metastable it doesn't actually Decay
+straight away it's it's this is a you
+
+ align:start position:0%
+straight away it's it's this is a you
+ 
+
+ align:start position:0%
+straight away it's it's this is a you
+know this may be ah sorry yeah it
+
+ align:start position:0%
+know this may be ah sorry yeah it
+ 
+
+ align:start position:0%
+know this may be ah sorry yeah it
+doesn't make sense unless I do it like
+
+ align:start position:0%
+doesn't make sense unless I do it like
+ 
+
+ align:start position:0%
+doesn't make sense unless I do it like
+this the
+
+ align:start position:0%
+this the
+ 
+
+ align:start position:0%
+this the
+x-rays excite the the atoms in the
+
+ align:start position:0%
+x-rays excite the the atoms in the
+ 
+
+ align:start position:0%
+x-rays excite the the atoms in the
+plastic up to some Upper State and then
+
+ align:start position:0%
+plastic up to some Upper State and then
+ 
+
+ align:start position:0%
+plastic up to some Upper State and then
+via some non-radiated decays because of
+
+ align:start position:0%
+via some non-radiated decays because of
+ 
+
+ align:start position:0%
+via some non-radiated decays because of
+the peculiarity the plastic the system
+
+ align:start position:0%
+the peculiarity the plastic the system
+ 
+
+ align:start position:0%
+the peculiarity the plastic the system
+decays down to a metastable state and
+
+ align:start position:0%
+decays down to a metastable state and
+ 
+
+ align:start position:0%
+decays down to a metastable state and
+metastable in this case means that there
+
+ align:start position:0%
+metastable in this case means that there
+ 
+
+ align:start position:0%
+metastable in this case means that there
+is no permitted transition down this
+
+ align:start position:0%
+is no permitted transition down this
+ 
+
+ align:start position:0%
+is no permitted transition down this
+Lower State
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this doesn't happen um so this is a
+
+ align:start position:0%
+here this doesn't happen um so this is a
+ 
+
+ align:start position:0%
+here this doesn't happen um so this is a
+forbidden
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transition now even though the
+
+ align:start position:0%
+transition now even though the
+ 
+
+ align:start position:0%
+transition now even though the
+transition is forbidden there will be
+
+ align:start position:0%
+transition is forbidden there will be
+ 
+
+ align:start position:0%
+transition is forbidden there will be
+some other mechanism mostly to do as
+
+ align:start position:0%
+some other mechanism mostly to do as
+ 
+
+ align:start position:0%
+some other mechanism mostly to do as
+collisions which will eventually de
+
+ align:start position:0%
+collisions which will eventually de
+ 
+
+ align:start position:0%
+collisions which will eventually de
+excite the atoms in your detection
+
+ align:start position:0%
+excite the atoms in your detection
+ 
+
+ align:start position:0%
+excite the atoms in your detection
+again so You' got like a few hours to
+
+ align:start position:0%
+again so You' got like a few hours to
+ 
+
+ align:start position:0%
+again so You' got like a few hours to
+get this bit of image plate out and put
+
+ align:start position:0%
+get this bit of image plate out and put
+ 
+
+ align:start position:0%
+get this bit of image plate out and put
+it into a scanner and what the scanner
+
+ align:start position:0%
+it into a scanner and what the scanner
+ 
+
+ align:start position:0%
+it into a scanner and what the scanner
+does very cleverly is that it uses a
+
+ align:start position:0%
+does very cleverly is that it uses a
+ 
+
+ align:start position:0%
+does very cleverly is that it uses a
+laser to excite the image plate back up
+
+ align:start position:0%
+laser to excite the image plate back up
+ 
+
+ align:start position:0%
+laser to excite the image plate back up
+to some upper level and then it looks
+
+ align:start position:0%
+to some upper level and then it looks
+ 
+
+ align:start position:0%
+to some upper level and then it looks
+for the fluoresence as it decays back
+
+ align:start position:0%
+for the fluoresence as it decays back
+ 
+
+ align:start position:0%
+for the fluoresence as it decays back
+down again so you can read off the
+
+ align:start position:0%
+down again so you can read off the
+ 
+
+ align:start position:0%
+down again so you can read off the
+number of stored photons in each little
+
+ align:start position:0%
+number of stored photons in each little
+ 
+
+ align:start position:0%
+number of stored photons in each little
+bit of plastic using this little laser
+
+ align:start position:0%
+bit of plastic using this little laser
+ 
+
+ align:start position:0%
+bit of plastic using this little laser
+and do this scan and then you can reuse
+
+ align:start position:0%
+and do this scan and then you can reuse
+ 
+
+ align:start position:0%
+and do this scan and then you can reuse
+the image plate which you can't do as
+
+ align:start position:0%
+the image plate which you can't do as
+ 
+
+ align:start position:0%
+the image plate which you can't do as
+fill so image plate is like pretty nice
+
+ align:start position:0%
+fill so image plate is like pretty nice
+ 
+
+ align:start position:0%
+fill so image plate is like pretty nice
+um but you need an expensive scanner
+
+ align:start position:0%
+um but you need an expensive scanner
+ 
+
+ align:start position:0%
+um but you need an expensive scanner
+it has like a laser
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+readout so both of these are time
+
+ align:start position:0%
+readout so both of these are time
+ 
+
+ align:start position:0%
+readout so both of these are time
+integrated um you can get time gated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cameras so these are cameras for example
+
+ align:start position:0%
+cameras so these are cameras for example
+ 
+
+ align:start position:0%
+cameras so these are cameras for example
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+have some gate on them like this and
+
+ align:start position:0%
+have some gate on them like this and
+ 
+
+ align:start position:0%
+have some gate on them like this and
+maybe that gate is five NCS or something
+
+ align:start position:0%
+maybe that gate is five NCS or something
+ 
+
+ align:start position:0%
+maybe that gate is five NCS or something
+like that where you're really gating a
+
+ align:start position:0%
+like that where you're really gating a
+ 
+
+ align:start position:0%
+like that where you're really gating a
+very very fast burst of X-ray so that
+
+ align:start position:0%
+very very fast burst of X-ray so that
+ 
+
+ align:start position:0%
+very very fast burst of X-ray so that
+avoid this problem you know exactly when
+
+ align:start position:0%
+avoid this problem you know exactly when
+ 
+
+ align:start position:0%
+avoid this problem you know exactly when
+the x-rays were coming out but of course
+
+ align:start position:0%
+the x-rays were coming out but of course
+ 
+
+ align:start position:0%
+the x-rays were coming out but of course
+A Time gated camera is very expensive
+
+ align:start position:0%
+A Time gated camera is very expensive
+ 
+
+ align:start position:0%
+A Time gated camera is very expensive
+because now it's got lots of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electronics these are often things with
+
+ align:start position:0%
+electronics these are often things with
+ 
+
+ align:start position:0%
+electronics these are often things with
+names like hybrid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cosos these cameras can be very very
+
+ align:start position:0%
+cosos these cameras can be very very
+ 
+
+ align:start position:0%
+cosos these cameras can be very very
+expensive and they also may have
+
+ align:start position:0%
+expensive and they also may have
+ 
+
+ align:start position:0%
+expensive and they also may have
+relatively low
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resolution because each pi costs a lot
+
+ align:start position:0%
+resolution because each pi costs a lot
+ 
+
+ align:start position:0%
+resolution because each pi costs a lot
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+money so if you can get away with using
+
+ align:start position:0%
+money so if you can get away with using
+ 
+
+ align:start position:0%
+money so if you can get away with using
+film image plate you might be tempted to
+
+ align:start position:0%
+film image plate you might be tempted to
+ 
+
+ align:start position:0%
+film image plate you might be tempted to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+that finally there's something called a
+
+ align:start position:0%
+that finally there's something called a
+ 
+
+ align:start position:0%
+that finally there's something called a
+street
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+camera Street camera is a slightly odd
+
+ align:start position:0%
+camera Street camera is a slightly odd
+ 
+
+ align:start position:0%
+camera Street camera is a slightly odd
+device and when you first see a street
+
+ align:start position:0%
+device and when you first see a street
+ 
+
+ align:start position:0%
+device and when you first see a street
+camera image very hard to understand
+
+ align:start position:0%
+camera image very hard to understand
+ 
+
+ align:start position:0%
+camera image very hard to understand
+what's going on what you get out of your
+
+ align:start position:0%
+what's going on what you get out of your
+ 
+
+ align:start position:0%
+what's going on what you get out of your
+street camera is actually something
+
+ align:start position:0%
+street camera is actually something
+ 
+
+ align:start position:0%
+street camera is actually something
+that has got non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intensity position on one axis and time
+
+ align:start position:0%
+intensity position on one axis and time
+ 
+
+ align:start position:0%
+intensity position on one axis and time
+on the other axis so if you have
+
+ align:start position:0%
+on the other axis so if you have
+ 
+
+ align:start position:0%
+on the other axis so if you have
+something like an ICF capsule that is
+
+ align:start position:0%
+something like an ICF capsule that is
+ 
+
+ align:start position:0%
+something like an ICF capsule that is
+roughly circular and you put your streak
+
+ align:start position:0%
+roughly circular and you put your streak
+ 
+
+ align:start position:0%
+roughly circular and you put your streak
+slit here initially if this little
+
+ align:start position:0%
+slit here initially if this little
+ 
+
+ align:start position:0%
+slit here initially if this little
+circular blob is emitting nice and
+
+ align:start position:0%
+circular blob is emitting nice and
+ 
+
+ align:start position:0%
+circular blob is emitting nice and
+uniformly you would
+
+ align:start position:0%
+uniformly you would
+ 
+
+ align:start position:0%
+uniformly you would
+see nice uniform emission in all of X
+
+ align:start position:0%
+see nice uniform emission in all of X
+ 
+
+ align:start position:0%
+see nice uniform emission in all of X
+and as this ICF capsule gets
+
+ align:start position:0%
+and as this ICF capsule gets
+ 
+
+ align:start position:0%
+and as this ICF capsule gets
+smaller your slit stays the same and so
+
+ align:start position:0%
+smaller your slit stays the same and so
+ 
+
+ align:start position:0%
+smaller your slit stays the same and so
+the region that's being lit up on the
+
+ align:start position:0%
+the region that's being lit up on the
+ 
+
+ align:start position:0%
+the region that's being lit up on the
+slit gets smaller as well so you'd see a
+
+ align:start position:0%
+slit gets smaller as well so you'd see a
+ 
+
+ align:start position:0%
+slit gets smaller as well so you'd see a
+street image that looks like
+
+ align:start position:0%
+street image that looks like
+ 
+
+ align:start position:0%
+street image that looks like
+this where this is got more light on it
+
+ align:start position:0%
+this where this is got more light on it
+ 
+
+ align:start position:0%
+this where this is got more light on it
+and this region has no light so this is
+
+ align:start position:0%
+and this region has no light so this is
+ 
+
+ align:start position:0%
+and this region has no light so this is
+a very clever technique for monitoring
+
+ align:start position:0%
+a very clever technique for monitoring
+ 
+
+ align:start position:0%
+a very clever technique for monitoring
+like the evolution of a 1D profile of
+
+ align:start position:0%
+like the evolution of a 1D profile of
+ 
+
+ align:start position:0%
+like the evolution of a 1D profile of
+intensity in time and the reason these
+
+ align:start position:0%
+intensity in time and the reason these
+ 
+
+ align:start position:0%
+intensity in time and the reason these
+street cameras are so popular is that
+
+ align:start position:0%
+street cameras are so popular is that
+ 
+
+ align:start position:0%
+street cameras are so popular is that
+they're extremely fast and they're
+
+ align:start position:0%
+they're extremely fast and they're
+ 
+
+ align:start position:0%
+they're extremely fast and they're
+actually based on the same technology
+
+ align:start position:0%
+actually based on the same technology
+ 
+
+ align:start position:0%
+actually based on the same technology
+that a CRT television uh uses with like
+
+ align:start position:0%
+that a CRT television uh uses with like
+ 
+
+ align:start position:0%
+that a CRT television uh uses with like
+a beam of electrons being swept across
+
+ align:start position:0%
+a beam of electrons being swept across
+ 
+
+ align:start position:0%
+a beam of electrons being swept across
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so they are very old though so everyone
+
+ align:start position:0%
+so they are very old though so everyone
+ 
+
+ align:start position:0%
+so they are very old though so everyone
+who has one they keep breaking all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time okay any questions on
+
+ align:start position:0%
+time okay any questions on
+ 
+
+ align:start position:0%
+time okay any questions on
+detectors that's all I have for you
+
+ align:start position:0%
+detectors that's all I have for you
+ 
+
+ align:start position:0%
+detectors that's all I have for you
+today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes normally what you actually have is a
+
+ align:start position:0%
+yes normally what you actually have is a
+ 
+
+ align:start position:0%
+yes normally what you actually have is a
+bit of film that sits behind the street
+
+ align:start position:0%
+bit of film that sits behind the street
+ 
+
+ align:start position:0%
+bit of film that sits behind the street
+camera window and so the film gets
+
+ align:start position:0%
+camera window and so the film gets
+ 
+
+ align:start position:0%
+camera window and so the film gets
+exposed and it has this pattern on it
+
+ align:start position:0%
+exposed and it has this pattern on it
+ 
+
+ align:start position:0%
+exposed and it has this pattern on it
+and you'll have some timing dots from a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+laser that will tell you how to
+
+ align:start position:0%
+laser that will tell you how to
+ 
+
+ align:start position:0%
+laser that will tell you how to
+calibrate your time AIS and you might
+
+ align:start position:0%
+calibrate your time AIS and you might
+ 
+
+ align:start position:0%
+calibrate your time AIS and you might
+have some fiducial that tells you how to
+
+ align:start position:0%
+have some fiducial that tells you how to
+ 
+
+ align:start position:0%
+have some fiducial that tells you how to
+calibrate the spatial axis here but
+
+ align:start position:0%
+calibrate the spatial axis here but
+ 
+
+ align:start position:0%
+calibrate the spatial axis here but
+because it's something like film it does
+
+ align:start position:0%
+because it's something like film it does
+ 
+
+ align:start position:0%
+because it's something like film it does
+have a dependence on the intensity so
+
+ align:start position:0%
+have a dependence on the intensity so
+ 
+
+ align:start position:0%
+have a dependence on the intensity so
+it's not binary um but the intensity may
+
+ align:start position:0%
+it's not binary um but the intensity may
+ 
+
+ align:start position:0%
+it's not binary um but the intensity may
+be very nonlinear because to get this
+
+ align:start position:0%
+be very nonlinear because to get this
+ 
+
+ align:start position:0%
+be very nonlinear because to get this
+image you're like generating an electron
+
+ align:start position:0%
+image you're like generating an electron
+ 
+
+ align:start position:0%
+image you're like generating an electron
+beam and sweeping it and there's like
+
+ align:start position:0%
+beam and sweeping it and there's like
+ 
+
+ align:start position:0%
+beam and sweeping it and there's like
+magnets and electron bunching and all
+
+ align:start position:0%
+magnets and electron bunching and all
+ 
+
+ align:start position:0%
+magnets and electron bunching and all
+sorts of things like that so
+
+ align:start position:0%
+sorts of things like that so
+ 
+
+ align:start position:0%
+sorts of things like that so
+interpreting these in a very
+
+ align:start position:0%
+interpreting these in a very
+ 
+
+ align:start position:0%
+interpreting these in a very
+quantitative way can be very very
+
+ align:start position:0%
+quantitative way can be very very
+ 
+
+ align:start position:0%
+quantitative way can be very very
+hard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so there's something called a
+
+ align:start position:0%
+yeah yeah so there's something called a
+ 
+
+ align:start position:0%
+yeah yeah so there's something called a
+often something called like a
+
+ align:start position:0%
+often something called like a
+ 
+
+ align:start position:0%
+often something called like a
+microchannel plate which has some
+
+ align:start position:0%
+microchannel plate which has some
+ 
+
+ align:start position:0%
+microchannel plate which has some
+voltage across it when the uh photons
+
+ align:start position:0%
+voltage across it when the uh photons
+ 
+
+ align:start position:0%
+voltage across it when the uh photons
+come in they um ionize what's it
+
+ align:start position:0%
+come in they um ionize what's it
+ 
+
+ align:start position:0%
+come in they um ionize what's it
+photoelectric effect releasing electron
+
+ align:start position:0%
+photoelectric effect releasing electron
+ 
+
+ align:start position:0%
+photoelectric effect releasing electron
+from the surface that voltage sweeps the
+
+ align:start position:0%
+from the surface that voltage sweeps the
+ 
+
+ align:start position:0%
+from the surface that voltage sweeps the
+electron and accelerates it up there'll
+
+ align:start position:0%
+electron and accelerates it up there'll
+ 
+
+ align:start position:0%
+electron and accelerates it up there'll
+be magnets which bend the electron to a
+
+ align:start position:0%
+be magnets which bend the electron to a
+ 
+
+ align:start position:0%
+be magnets which bend the electron to a
+certain part of the time axis the
+
+ align:start position:0%
+certain part of the time axis the
+ 
+
+ align:start position:0%
+certain part of the time axis the
+electron will collide with a phosphor
+
+ align:start position:0%
+electron will collide with a phosphor
+ 
+
+ align:start position:0%
+electron will collide with a phosphor
+screen uh the electron excites the fosil
+
+ align:start position:0%
+screen uh the electron excites the fosil
+ 
+
+ align:start position:0%
+screen uh the electron excites the fosil
+the fosil decays and emits green light
+
+ align:start position:0%
+the fosil decays and emits green light
+ 
+
+ align:start position:0%
+the fosil decays and emits green light
+the green light is recorded
+
+ align:start position:0%
+the green light is recorded
+ 
+
+ align:start position:0%
+the green light is recorded
+by yeah so they're they're very fun uh
+
+ align:start position:0%
+by yeah so they're they're very fun uh
+ 
+
+ align:start position:0%
+by yeah so they're they're very fun uh
+but they are very complicated which is
+
+ align:start position:0%
+but they are very complicated which is
+ 
+
+ align:start position:0%
+but they are very complicated which is
+why you shouldn't like if you see a
+
+ align:start position:0%
+why you shouldn't like if you see a
+ 
+
+ align:start position:0%
+why you shouldn't like if you see a
+region that is twice as bright here than
+
+ align:start position:0%
+region that is twice as bright here than
+ 
+
+ align:start position:0%
+region that is twice as bright here than
+it is here that doesn't necessarily mean
+
+ align:start position:0%
+it is here that doesn't necessarily mean
+ 
+
+ align:start position:0%
+it is here that doesn't necessarily mean
+that it's emitting twice as many x-rays
+
+ align:start position:0%
+that it's emitting twice as many x-rays
+ 
+
+ align:start position:0%
+that it's emitting twice as many x-rays
+because it's very on Long linear and
+
+ align:start position:0%
+because it's very on Long linear and
+ 
+
+ align:start position:0%
+because it's very on Long linear and
+they're very sensitive to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+voltage yes it's a pulse magnetic field
+
+ align:start position:0%
+voltage yes it's a pulse magnetic field
+ 
+
+ align:start position:0%
+voltage yes it's a pulse magnetic field
+that's ramping up in time so as the
+
+ align:start position:0%
+that's ramping up in time so as the
+ 
+
+ align:start position:0%
+that's ramping up in time so as the
+magnetic field ramps up it sweeps
+
+ align:start position:0%
+magnetic field ramps up it sweeps
+ 
+
+ align:start position:0%
+magnetic field ramps up it sweeps
+electrons to different places that's
+
+ align:start position:0%
+electrons to different places that's
+ 
+
+ align:start position:0%
+electrons to different places that's
+exactly how cathode ray TV works and we
+
+ align:start position:0%
+exactly how cathode ray TV works and we
+ 
+
+ align:start position:0%
+exactly how cathode ray TV works and we
+were able to do cathode ray TVs to make
+
+ align:start position:0%
+were able to do cathode ray TVs to make
+ 
+
+ align:start position:0%
+were able to do cathode ray TVs to make
+moving images at 30 frames per second so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah but all the electrons from the
+
+ align:start position:0%
+yeah yeah but all the electrons from the
+ 
+
+ align:start position:0%
+yeah yeah but all the electrons from the
+photoelectric effect can be coming out
+
+ align:start position:0%
+photoelectric effect can be coming out
+ 
+
+ align:start position:0%
+photoelectric effect can be coming out
+with very similar energies and then
+
+ align:start position:0%
+with very similar energies and then
+ 
+
+ align:start position:0%
+with very similar energies and then
+they're accelerate so maybe they've got
+
+ align:start position:0%
+they're accelerate so maybe they've got
+ 
+
+ align:start position:0%
+they're accelerate so maybe they've got
+an energy range of a few EV but they're
+
+ align:start position:0%
+an energy range of a few EV but they're
+ 
+
+ align:start position:0%
+an energy range of a few EV but they're
+being accelerated over a killer electron
+
+ align:start position:0%
+being accelerated over a killer electron
+ 
+
+ align:start position:0%
+being accelerated over a killer electron
+volt which is also why you should not
+
+ align:start position:0%
+volt which is also why you should not
+ 
+
+ align:start position:0%
+volt which is also why you should not
+mess around with a crtv because inside
+
+ align:start position:0%
+mess around with a crtv because inside
+ 
+
+ align:start position:0%
+mess around with a crtv because inside
+it there is an electron beam that does
+
+ align:start position:0%
+it there is an electron beam that does
+ 
+
+ align:start position:0%
+it there is an electron beam that does
+Killer electron Vols
+
+ align:start position:0%
+Killer electron Vols
+ 
+
+ align:start position:0%
+Killer electron Vols
+yeah any other
+
+ align:start position:0%
+yeah any other
+ 
+
+ align:start position:0%
+yeah any other
+questions anyone online
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay next lecture we are going to talk
+
+ align:start position:0%
+okay next lecture we are going to talk
+ 
+
+ align:start position:0%
+okay next lecture we are going to talk
+about line broadening and we're going to
+
+ align:start position:0%
+about line broadening and we're going to
+ 
+
+ align:start position:0%
+about line broadening and we're going to
+finish off spectroscopy so see you on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tuesday
\ No newline at end of file
diff --git a/BZzkyqe6KD8.txt b/BZzkyqe6KD8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e060f2f303f4e552fce43b88c19728644e0affde
--- /dev/null
+++ b/BZzkyqe6KD8.txt
@@ -0,0 +1,8715 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so this is on oxidation
+
+ align:start position:0%
+ocw.mit.edu so this is on oxidation
+ 
+
+ align:start position:0%
+ocw.mit.edu so this is on oxidation
+reduction go okay so the demo uh
+
+ align:start position:0%
+reduction go okay so the demo uh
+ 
+
+ align:start position:0%
+reduction go okay so the demo uh
+involves a strip of magnesium and the
+
+ align:start position:0%
+involves a strip of magnesium and the
+ 
+
+ align:start position:0%
+involves a strip of magnesium and the
+Magnesium is a pretty reactive metal
+
+ align:start position:0%
+Magnesium is a pretty reactive metal
+ 
+
+ align:start position:0%
+Magnesium is a pretty reactive metal
+right now it's coated with magnesium
+
+ align:start position:0%
+right now it's coated with magnesium
+ 
+
+ align:start position:0%
+right now it's coated with magnesium
+oxide and what I'm going to do is I'm
+
+ align:start position:0%
+oxide and what I'm going to do is I'm
+ 
+
+ align:start position:0%
+oxide and what I'm going to do is I'm
+going to light it on fire when it gets
+
+ align:start position:0%
+going to light it on fire when it gets
+ 
+
+ align:start position:0%
+going to light it on fire when it gets
+lit uh it's going to Glow very very
+
+ align:start position:0%
+lit uh it's going to Glow very very
+ 
+
+ align:start position:0%
+lit uh it's going to Glow very very
+brightly and it's going to react with
+
+ align:start position:0%
+brightly and it's going to react with
+ 
+
+ align:start position:0%
+brightly and it's going to react with
+this block of carbon dioxide uh and
+
+ align:start position:0%
+this block of carbon dioxide uh and
+ 
+
+ align:start position:0%
+this block of carbon dioxide uh and
+magnesium oxide is what you have up
+
+ align:start position:0%
+magnesium oxide is what you have up
+ 
+
+ align:start position:0%
+magnesium oxide is what you have up
+there both of those magnesium oxide
+
+ align:start position:0%
+there both of those magnesium oxide
+ 
+
+ align:start position:0%
+there both of those magnesium oxide
+molecules will react with one molecule
+
+ align:start position:0%
+molecules will react with one molecule
+ 
+
+ align:start position:0%
+molecules will react with one molecule
+of carbon dioxide to form just graphine
+
+ align:start position:0%
+of carbon dioxide to form just graphine
+ 
+
+ align:start position:0%
+of carbon dioxide to form just graphine
+carbon as well as magnesium dioxide so
+
+ align:start position:0%
+carbon as well as magnesium dioxide so
+ 
+
+ align:start position:0%
+carbon as well as magnesium dioxide so
+you're going to get like a white and
+
+ align:start position:0%
+you're going to get like a white and
+ 
+
+ align:start position:0%
+you're going to get like a white and
+black powder inside of here and it's
+
+ align:start position:0%
+black powder inside of here and it's
+ 
+
+ align:start position:0%
+black powder inside of here and it's
+going to be really bright and really
+
+ align:start position:0%
+going to be really bright and really
+ 
+
+ align:start position:0%
+going to be really bright and really
+dangerous and can we lower the lights is
+
+ align:start position:0%
+dangerous and can we lower the lights is
+ 
+
+ align:start position:0%
+dangerous and can we lower the lights is
+that something we can do because that
+
+ align:start position:0%
+that something we can do because that
+ 
+
+ align:start position:0%
+that something we can do because that
+makes it a whole lot more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fun which which was two again two was
+
+ align:start position:0%
+fun which which was two again two was
+ 
+
+ align:start position:0%
+fun which which was two again two was
+the smiley the res one and three was EXC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going try it one more time okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right okay good
+
+ align:start position:0%
+right okay good
+ 
+
+ align:start position:0%
+right okay good
+try so oxidation reductions are really
+
+ align:start position:0%
+try so oxidation reductions are really
+ 
+
+ align:start position:0%
+try so oxidation reductions are really
+fun and so we're going to continue and
+
+ align:start position:0%
+fun and so we're going to continue and
+ 
+
+ align:start position:0%
+fun and so we're going to continue and
+tell you about those on Friday so
+
+ align:start position:0%
+tell you about those on Friday so
+ 
+
+ align:start position:0%
+tell you about those on Friday so
+oxidation reduction or redo so redo is
+
+ align:start position:0%
+oxidation reduction or redo so redo is
+ 
+
+ align:start position:0%
+oxidation reduction or redo so redo is
+the uh short hand for oxidation
+
+ align:start position:0%
+the uh short hand for oxidation
+ 
+
+ align:start position:0%
+the uh short hand for oxidation
+reduction um let's bring out your hands
+
+ align:start position:0%
+reduction um let's bring out your hands
+ 
+
+ align:start position:0%
+reduction um let's bring out your hands
+but let's bring the noise level down
+
+ align:start position:0%
+but let's bring the noise level down
+ 
+
+ align:start position:0%
+but let's bring the noise level down
+people have still been complaining about
+
+ align:start position:0%
+people have still been complaining about
+ 
+
+ align:start position:0%
+people have still been complaining about
+noise in class all right so um a Redux
+
+ align:start position:0%
+noise in class all right so um a Redux
+ 
+
+ align:start position:0%
+noise in class all right so um a Redux
+reaction chemical reaction that involves
+
+ align:start position:0%
+reaction chemical reaction that involves
+ 
+
+ align:start position:0%
+reaction chemical reaction that involves
+an exchange of electrons and so we saw
+
+ align:start position:0%
+an exchange of electrons and so we saw
+ 
+
+ align:start position:0%
+an exchange of electrons and so we saw
+uh what happens when we mix this with uh
+
+ align:start position:0%
+uh what happens when we mix this with uh
+ 
+
+ align:start position:0%
+uh what happens when we mix this with uh
+with uh some uh dry ice all right so
+
+ align:start position:0%
+with uh some uh dry ice all right so
+ 
+
+ align:start position:0%
+with uh some uh dry ice all right so
+let's do some definitions we always
+
+ align:start position:0%
+let's do some definitions we always
+ 
+
+ align:start position:0%
+let's do some definitions we always
+start units with definitions and most of
+
+ align:start position:0%
+start units with definitions and most of
+ 
+
+ align:start position:0%
+start units with definitions and most of
+you know some of these definitions
+
+ align:start position:0%
+you know some of these definitions
+ 
+
+ align:start position:0%
+you know some of these definitions
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+oxidation electron
+
+ align:start position:0%
+oxidation electron
+ 
+
+ align:start position:0%
+oxidation electron
+loss
+
+ align:start position:0%
+loss
+ 
+
+ align:start position:0%
+loss
+reduction electron are
+
+ align:start position:0%
+reduction electron are
+ 
+
+ align:start position:0%
+reduction electron are
+gained this one you may or may not be
+
+ align:start position:0%
+gained this one you may or may not be
+ 
+
+ align:start position:0%
+gained this one you may or may not be
+familiar with oxid oxidizing agent it
+
+ align:start position:0%
+familiar with oxid oxidizing agent it
+ 
+
+ align:start position:0%
+familiar with oxid oxidizing agent it
+accepts electrons so it oxidizes other
+
+ align:start position:0%
+accepts electrons so it oxidizes other
+ 
+
+ align:start position:0%
+accepts electrons so it oxidizes other
+things but it itself is
+
+ align:start position:0%
+things but it itself is
+ 
+
+ align:start position:0%
+things but it itself is
+reduced and reducing agent donates
+
+ align:start position:0%
+reduced and reducing agent donates
+ 
+
+ align:start position:0%
+reduced and reducing agent donates
+electrons it reduces other things it
+
+ align:start position:0%
+electrons it reduces other things it
+ 
+
+ align:start position:0%
+electrons it reduces other things it
+itself is oxidized and before you turn
+
+ align:start position:0%
+itself is oxidized and before you turn
+ 
+
+ align:start position:0%
+itself is oxidized and before you turn
+the page uh I just want to try to get
+
+ align:start position:0%
+the page uh I just want to try to get
+ 
+
+ align:start position:0%
+the page uh I just want to try to get
+you to remember these two terms so one
+
+ align:start position:0%
+you to remember these two terms so one
+ 
+
+ align:start position:0%
+you to remember these two terms so one
+way that I like to think about it is
+
+ align:start position:0%
+way that I like to think about it is
+ 
+
+ align:start position:0%
+way that I like to think about it is
+that a reducing agent might be somebody
+
+ align:start position:0%
+that a reducing agent might be somebody
+ 
+
+ align:start position:0%
+that a reducing agent might be somebody
+who is uh a little bit Shady they might
+
+ align:start position:0%
+who is uh a little bit Shady they might
+ 
+
+ align:start position:0%
+who is uh a little bit Shady they might
+walk up to someone and say in a crowded
+
+ align:start position:0%
+walk up to someone and say in a crowded
+ 
+
+ align:start position:0%
+walk up to someone and say in a crowded
+space don't look at me just
+
+ align:start position:0%
+space don't look at me just
+ 
+
+ align:start position:0%
+space don't look at me just
+listen did you want to buy an
+
+ align:start position:0%
+listen did you want to buy an
+ 
+
+ align:start position:0%
+listen did you want to buy an
+electron so that would be an agent of
+
+ align:start position:0%
+electron so that would be an agent of
+ 
+
+ align:start position:0%
+electron so that would be an agent of
+reduction going around now there could
+
+ align:start position:0%
+reduction going around now there could
+ 
+
+ align:start position:0%
+reduction going around now there could
+be ones that are a little bit Shady
+
+ align:start position:0%
+be ones that are a little bit Shady
+ 
+
+ align:start position:0%
+be ones that are a little bit Shady
+selling electrons to the highest bidder
+
+ align:start position:0%
+selling electrons to the highest bidder
+ 
+
+ align:start position:0%
+selling electrons to the highest bidder
+but there could also be agents of good
+
+ align:start position:0%
+but there could also be agents of good
+ 
+
+ align:start position:0%
+but there could also be agents of good
+I told you about free radical species
+
+ align:start position:0%
+I told you about free radical species
+ 
+
+ align:start position:0%
+I told you about free radical species
+there's a lot of free radicals in the
+
+ align:start position:0%
+there's a lot of free radicals in the
+ 
+
+ align:start position:0%
+there's a lot of free radicals in the
+universe they can be dangerous because
+
+ align:start position:0%
+universe they can be dangerous because
+ 
+
+ align:start position:0%
+universe they can be dangerous because
+they have a single unpaired electron
+
+ align:start position:0%
+they have a single unpaired electron
+ 
+
+ align:start position:0%
+they have a single unpaired electron
+which makes them really highly reactive
+
+ align:start position:0%
+which makes them really highly reactive
+ 
+
+ align:start position:0%
+which makes them really highly reactive
+so there might be an agent a secret
+
+ align:start position:0%
+so there might be an agent a secret
+ 
+
+ align:start position:0%
+so there might be an agent a secret
+agent of
+
+ align:start position:0%
+agent of
+ 
+
+ align:start position:0%
+agent of
+oxidation and it might want to Shield
+
+ align:start position:0%
+oxidation and it might want to Shield
+ 
+
+ align:start position:0%
+oxidation and it might want to Shield
+the universe from the power of free
+
+ align:start position:0%
+the universe from the power of free
+ 
+
+ align:start position:0%
+the universe from the power of free
+radicals and so it would go along and it
+
+ align:start position:0%
+radicals and so it would go along and it
+ 
+
+ align:start position:0%
+radicals and so it would go along and it
+would oxidize that give it give it take
+
+ align:start position:0%
+would oxidize that give it give it take
+ 
+
+ align:start position:0%
+would oxidize that give it give it take
+that that electron away and oxidize it
+
+ align:start position:0%
+that that electron away and oxidize it
+ 
+
+ align:start position:0%
+that that electron away and oxidize it
+and become reduced itself take that free
+
+ align:start position:0%
+and become reduced itself take that free
+ 
+
+ align:start position:0%
+and become reduced itself take that free
+radical away because the free radical
+
+ align:start position:0%
+radical away because the free radical
+ 
+
+ align:start position:0%
+radical away because the free radical
+species might not know how dangerous it
+
+ align:start position:0%
+species might not know how dangerous it
+ 
+
+ align:start position:0%
+species might not know how dangerous it
+is it's for everybody's good to Shield
+
+ align:start position:0%
+is it's for everybody's good to Shield
+ 
+
+ align:start position:0%
+is it's for everybody's good to Shield
+you from that power you might also have
+
+ align:start position:0%
+you from that power you might also have
+ 
+
+ align:start position:0%
+you from that power you might also have
+an agent of reduction that's a secret
+
+ align:start position:0%
+an agent of reduction that's a secret
+ 
+
+ align:start position:0%
+an agent of reduction that's a secret
+agent that might go up to the free
+
+ align:start position:0%
+agent that might go up to the free
+ 
+
+ align:start position:0%
+agent that might go up to the free
+radical species and give it an extra
+
+ align:start position:0%
+radical species and give it an extra
+ 
+
+ align:start position:0%
+radical species and give it an extra
+electron and then it has two and then
+
+ align:start position:0%
+electron and then it has two and then
+ 
+
+ align:start position:0%
+electron and then it has two and then
+it's more stable and less reactive so
+
+ align:start position:0%
+it's more stable and less reactive so
+ 
+
+ align:start position:0%
+it's more stable and less reactive so
+you might have these agents so that's
+
+ align:start position:0%
+you might have these agents so that's
+ 
+
+ align:start position:0%
+you might have these agents so that's
+how you should think about it think
+
+ align:start position:0%
+how you should think about it think
+ 
+
+ align:start position:0%
+how you should think about it think
+about an agent of oxidation it wants to
+
+ align:start position:0%
+about an agent of oxidation it wants to
+ 
+
+ align:start position:0%
+about an agent of oxidation it wants to
+go out and oxidize for the good of
+
+ align:start position:0%
+go out and oxidize for the good of
+ 
+
+ align:start position:0%
+go out and oxidize for the good of
+mankind or an agent of reduction that
+
+ align:start position:0%
+mankind or an agent of reduction that
+ 
+
+ align:start position:0%
+mankind or an agent of reduction that
+wants to go out and reduce other
+
+ align:start position:0%
+wants to go out and reduce other
+ 
+
+ align:start position:0%
+wants to go out and reduce other
+things so that might help you remember
+
+ align:start position:0%
+things so that might help you remember
+ 
+
+ align:start position:0%
+things so that might help you remember
+those those definitions we'll we'll hope
+
+ align:start position:0%
+those those definitions we'll we'll hope
+ 
+
+ align:start position:0%
+those those definitions we'll we'll hope
+so all right so let's take a look now we
+
+ align:start position:0%
+so all right so let's take a look now we
+ 
+
+ align:start position:0%
+so all right so let's take a look now we
+always start every unit with definitions
+
+ align:start position:0%
+always start every unit with definitions
+ 
+
+ align:start position:0%
+always start every unit with definitions
+and then we have a set of rules and
+
+ align:start position:0%
+and then we have a set of rules and
+ 
+
+ align:start position:0%
+and then we have a set of rules and
+guidelines so let's take a look at the
+
+ align:start position:0%
+guidelines so let's take a look at the
+ 
+
+ align:start position:0%
+guidelines so let's take a look at the
+guidelines luckily these guidelines are
+
+ align:start position:0%
+guidelines luckily these guidelines are
+ 
+
+ align:start position:0%
+guidelines luckily these guidelines are
+really pretty straightforward and you
+
+ align:start position:0%
+really pretty straightforward and you
+ 
+
+ align:start position:0%
+really pretty straightforward and you
+really shouldn't have a lot of
+
+ align:start position:0%
+really shouldn't have a lot of
+ 
+
+ align:start position:0%
+really shouldn't have a lot of
+difficulty keeping them in mind some of
+
+ align:start position:0%
+difficulty keeping them in mind some of
+ 
+
+ align:start position:0%
+difficulty keeping them in mind some of
+them we've really seen already we just
+
+ align:start position:0%
+them we've really seen already we just
+ 
+
+ align:start position:0%
+them we've really seen already we just
+didn't realize that they were going to
+
+ align:start position:0%
+didn't realize that they were going to
+ 
+
+ align:start position:0%
+didn't realize that they were going to
+be the guidelines that we would have so
+
+ align:start position:0%
+be the guidelines that we would have so
+ 
+
+ align:start position:0%
+be the guidelines that we would have so
+guidelines for assigning oxidation
+
+ align:start position:0%
+guidelines for assigning oxidation
+ 
+
+ align:start position:0%
+guidelines for assigning oxidation
+numbers in a free element every atom has
+
+ align:start position:0%
+numbers in a free element every atom has
+ 
+
+ align:start position:0%
+numbers in a free element every atom has
+an oxidation number of
+
+ align:start position:0%
+an oxidation number of
+ 
+
+ align:start position:0%
+an oxidation number of
+zero okay that seems pretty
+
+ align:start position:0%
+zero okay that seems pretty
+ 
+
+ align:start position:0%
+zero okay that seems pretty
+straightforward H2 oxidation number
+
+ align:start position:0%
+straightforward H2 oxidation number
+ 
+
+ align:start position:0%
+straightforward H2 oxidation number
+zero rule
+
+ align:start position:0%
+zero rule
+ 
+
+ align:start position:0%
+zero rule
+two ions composed of only one atom also
+
+ align:start position:0%
+two ions composed of only one atom also
+ 
+
+ align:start position:0%
+two ions composed of only one atom also
+called monatomic ions
+
+ align:start position:0%
+called monatomic ions
+ 
+
+ align:start position:0%
+called monatomic ions
+have an oxidation number that's equal to
+
+ align:start position:0%
+have an oxidation number that's equal to
+ 
+
+ align:start position:0%
+have an oxidation number that's equal to
+their charge if this wasn't true it
+
+ align:start position:0%
+their charge if this wasn't true it
+ 
+
+ align:start position:0%
+their charge if this wasn't true it
+would be deeply disturbing lithium plus
+
+ align:start position:0%
+would be deeply disturbing lithium plus
+ 
+
+ align:start position:0%
+would be deeply disturbing lithium plus
+one ions has an oxidation number of plus
+
+ align:start position:0%
+one ions has an oxidation number of plus
+ 
+
+ align:start position:0%
+one ions has an oxidation number of plus
+one I think we're good okay also in
+
+ align:start position:0%
+one I think we're good okay also in
+ 
+
+ align:start position:0%
+one I think we're good okay also in
+number two in forming compounds group
+
+ align:start position:0%
+number two in forming compounds group
+ 
+
+ align:start position:0%
+number two in forming compounds group
+one metals have an oxidation number of
+
+ align:start position:0%
+one metals have an oxidation number of
+ 
+
+ align:start position:0%
+one metals have an oxidation number of
+plus one lithium and all of its friends
+
+ align:start position:0%
+plus one lithium and all of its friends
+ 
+
+ align:start position:0%
+plus one lithium and all of its friends
+sodium Etc group two metals have an
+
+ align:start position:0%
+sodium Etc group two metals have an
+ 
+
+ align:start position:0%
+sodium Etc group two metals have an
+oxidation number of plus two calcium for
+
+ align:start position:0%
+oxidation number of plus two calcium for
+ 
+
+ align:start position:0%
+oxidation number of plus two calcium for
+example and aluminum is plus three in
+
+ align:start position:0%
+example and aluminum is plus three in
+ 
+
+ align:start position:0%
+example and aluminum is plus three in
+its compounds this is also something
+
+ align:start position:0%
+its compounds this is also something
+ 
+
+ align:start position:0%
+its compounds this is also something
+that we've seen before those group one
+
+ align:start position:0%
+that we've seen before those group one
+ 
+
+ align:start position:0%
+that we've seen before those group one
+and group two metals are not all that
+
+ align:start position:0%
+and group two metals are not all that
+ 
+
+ align:start position:0%
+and group two metals are not all that
+exciting they pretty much want to get
+
+ align:start position:0%
+exciting they pretty much want to get
+ 
+
+ align:start position:0%
+exciting they pretty much want to get
+their noble gas configuration and they
+
+ align:start position:0%
+their noble gas configuration and they
+ 
+
+ align:start position:0%
+their noble gas configuration and they
+want to lose either one if you're in
+
+ align:start position:0%
+want to lose either one if you're in
+ 
+
+ align:start position:0%
+want to lose either one if you're in
+group one or two electrons if you're in
+
+ align:start position:0%
+group one or two electrons if you're in
+ 
+
+ align:start position:0%
+group one or two electrons if you're in
+group two and so that's what they do
+
+ align:start position:0%
+group two and so that's what they do
+ 
+
+ align:start position:0%
+group two and so that's what they do
+here so this is good to keep in mind
+
+ align:start position:0%
+here so this is good to keep in mind
+ 
+
+ align:start position:0%
+here so this is good to keep in mind
+because it's going to help you with o
+
+ align:start position:0%
+because it's going to help you with o
+ 
+
+ align:start position:0%
+because it's going to help you with o
+figure out the oxidation number of other
+
+ align:start position:0%
+figure out the oxidation number of other
+ 
+
+ align:start position:0%
+figure out the oxidation number of other
+elements for which there are not such
+
+ align:start position:0%
+elements for which there are not such
+ 
+
+ align:start position:0%
+elements for which there are not such
+hard and fast rules
+
+ align:start position:0%
+hard and fast rules
+ 
+
+ align:start position:0%
+hard and fast rules
+number three
+
+ align:start position:0%
+number three
+ 
+
+ align:start position:0%
+number three
+oxygen oxygen in most compounds is
+
+ align:start position:0%
+oxygen oxygen in most compounds is
+ 
+
+ align:start position:0%
+oxygen oxygen in most compounds is
+min-2 again not that surprising that it
+
+ align:start position:0%
+min-2 again not that surprising that it
+ 
+
+ align:start position:0%
+min-2 again not that surprising that it
+would want to uh gain those two
+
+ align:start position:0%
+would want to uh gain those two
+ 
+
+ align:start position:0%
+would want to uh gain those two
+electrons however there's some
+
+ align:start position:0%
+electrons however there's some
+ 
+
+ align:start position:0%
+electrons however there's some
+exceptions oxygen is just an element
+
+ align:start position:0%
+exceptions oxygen is just an element
+ 
+
+ align:start position:0%
+exceptions oxygen is just an element
+full of exceptions um if it is in
+
+ align:start position:0%
+full of exceptions um if it is in
+ 
+
+ align:start position:0%
+full of exceptions um if it is in
+peroxides hydrogen peroxide o O2 2 minus
+
+ align:start position:0%
+peroxides hydrogen peroxide o O2 2 minus
+ 
+
+ align:start position:0%
+peroxides hydrogen peroxide o O2 2 minus
+then it's going to have an oxidation
+
+ align:start position:0%
+then it's going to have an oxidation
+ 
+
+ align:start position:0%
+then it's going to have an oxidation
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+minus1 so peroxides and later we'll see
+
+ align:start position:0%
+minus1 so peroxides and later we'll see
+ 
+
+ align:start position:0%
+minus1 so peroxides and later we'll see
+super oxides are exceptions but if it's
+
+ align:start position:0%
+super oxides are exceptions but if it's
+ 
+
+ align:start position:0%
+super oxides are exceptions but if it's
+not a peroxide or a super oxide it's
+
+ align:start position:0%
+not a peroxide or a super oxide it's
+ 
+
+ align:start position:0%
+not a peroxide or a super oxide it's
+going to be minus
+
+ align:start position:0%
+going to be minus
+ 
+
+ align:start position:0%
+going to be minus
+two all right rule number four
+
+ align:start position:0%
+two all right rule number four
+ 
+
+ align:start position:0%
+two all right rule number four
+hydrogen hydrogen is O mostly plus one
+
+ align:start position:0%
+hydrogen hydrogen is O mostly plus one
+ 
+
+ align:start position:0%
+hydrogen hydrogen is O mostly plus one
+we probably could guess that but there
+
+ align:start position:0%
+we probably could guess that but there
+ 
+
+ align:start position:0%
+we probably could guess that but there
+actually are some exceptions for this
+
+ align:start position:0%
+actually are some exceptions for this
+ 
+
+ align:start position:0%
+actually are some exceptions for this
+and you're going to see a lot of those
+
+ align:start position:0%
+and you're going to see a lot of those
+ 
+
+ align:start position:0%
+and you're going to see a lot of those
+exceptions in this unit and pretty much
+
+ align:start position:0%
+exceptions in this unit and pretty much
+ 
+
+ align:start position:0%
+exceptions in this unit and pretty much
+after this unit not so much ever again
+
+ align:start position:0%
+after this unit not so much ever again
+ 
+
+ align:start position:0%
+after this unit not so much ever again
+the exceptions are for the group one and
+
+ align:start position:0%
+the exceptions are for the group one and
+ 
+
+ align:start position:0%
+the exceptions are for the group one and
+the group two so the group one and group
+
+ align:start position:0%
+the group two so the group one and group
+ 
+
+ align:start position:0%
+the group two so the group one and group
+two rules supersede the fact that
+
+ align:start position:0%
+two rules supersede the fact that
+ 
+
+ align:start position:0%
+two rules supersede the fact that
+hydrogen is usually plus one so if you
+
+ align:start position:0%
+hydrogen is usually plus one so if you
+ 
+
+ align:start position:0%
+hydrogen is usually plus one so if you
+have hydrogen with lithium lithium is
+
+ align:start position:0%
+have hydrogen with lithium lithium is
+ 
+
+ align:start position:0%
+have hydrogen with lithium lithium is
+going to be plus one so hydrogen will be
+
+ align:start position:0%
+going to be plus one so hydrogen will be
+ 
+
+ align:start position:0%
+going to be plus one so hydrogen will be
+minus one sodium is is the same here and
+
+ align:start position:0%
+minus one sodium is is the same here and
+ 
+
+ align:start position:0%
+minus one sodium is is the same here and
+calcium that's group two again hydrogen
+
+ align:start position:0%
+calcium that's group two again hydrogen
+ 
+
+ align:start position:0%
+calcium that's group two again hydrogen
+would be minus one so group one group
+
+ align:start position:0%
+would be minus one so group one group
+ 
+
+ align:start position:0%
+would be minus one so group one group
+two rules supersede
+
+ align:start position:0%
+two rules supersede
+ 
+
+ align:start position:0%
+two rules supersede
+hydrogen all right what about our
+
+ align:start position:0%
+hydrogen all right what about our
+ 
+
+ align:start position:0%
+hydrogen all right what about our
+halides we have Florine it wants to be
+
+ align:start position:0%
+halides we have Florine it wants to be
+ 
+
+ align:start position:0%
+halides we have Florine it wants to be
+minus one other halogens chloride
+
+ align:start position:0%
+minus one other halogens chloride
+ 
+
+ align:start position:0%
+minus one other halogens chloride
+bromide iodide are negative when they
+
+ align:start position:0%
+bromide iodide are negative when they
+ 
+
+ align:start position:0%
+bromide iodide are negative when they
+are in
+
+ align:start position:0%
+are in
+ 
+
+ align:start position:0%
+are in
+salts um such as sodium chloride but if
+
+ align:start position:0%
+salts um such as sodium chloride but if
+ 
+
+ align:start position:0%
+salts um such as sodium chloride but if
+oxygen is there the oxygen rules are the
+
+ align:start position:0%
+oxygen is there the oxygen rules are the
+ 
+
+ align:start position:0%
+oxygen is there the oxygen rules are the
+ones that follow so here um if you have
+
+ align:start position:0%
+ones that follow so here um if you have
+ 
+
+ align:start position:0%
+ones that follow so here um if you have
+CL with oxygen then you're going to have
+
+ align:start position:0%
+CL with oxygen then you're going to have
+ 
+
+ align:start position:0%
+CL with oxygen then you're going to have
+a positive oxidation number for the
+
+ align:start position:0%
+a positive oxidation number for the
+ 
+
+ align:start position:0%
+a positive oxidation number for the
+chlorine because oxygen is going to be
+
+ align:start position:0%
+chlorine because oxygen is going to be
+ 
+
+ align:start position:0%
+chlorine because oxygen is going to be
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+two all right and and you'll see a
+
+ align:start position:0%
+two all right and and you'll see a
+ 
+
+ align:start position:0%
+two all right and and you'll see a
+number of these so-called oxy acids in
+
+ align:start position:0%
+number of these so-called oxy acids in
+ 
+
+ align:start position:0%
+number of these so-called oxy acids in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+unit all right
+
+ align:start position:0%
+unit all right
+ 
+
+ align:start position:0%
+unit all right
+six this one you probably already know
+
+ align:start position:0%
+six this one you probably already know
+ 
+
+ align:start position:0%
+six this one you probably already know
+but in a neutral mod molecule the sums
+
+ align:start position:0%
+but in a neutral mod molecule the sums
+ 
+
+ align:start position:0%
+but in a neutral mod molecule the sums
+of the oxidation numbers must equal zero
+
+ align:start position:0%
+of the oxidation numbers must equal zero
+ 
+
+ align:start position:0%
+of the oxidation numbers must equal zero
+so the sums must be neutral if the
+
+ align:start position:0%
+so the sums must be neutral if the
+ 
+
+ align:start position:0%
+so the sums must be neutral if the
+molecule is neutral and if you have
+
+ align:start position:0%
+molecule is neutral and if you have
+ 
+
+ align:start position:0%
+molecule is neutral and if you have
+something that is a polyatomic
+
+ align:start position:0%
+something that is a polyatomic
+ 
+
+ align:start position:0%
+something that is a polyatomic
+multi-atom ion the sum
+
+ align:start position:0%
+multi-atom ion the sum
+ 
+
+ align:start position:0%
+multi-atom ion the sum
+of the individual oxidation numbers
+
+ align:start position:0%
+of the individual oxidation numbers
+ 
+
+ align:start position:0%
+of the individual oxidation numbers
+needs to be equal to the overall charge
+
+ align:start position:0%
+needs to be equal to the overall charge
+ 
+
+ align:start position:0%
+needs to be equal to the overall charge
+on that ion so again we've seen things
+
+ align:start position:0%
+on that ion so again we've seen things
+ 
+
+ align:start position:0%
+on that ion so again we've seen things
+like this before um so we should have no
+
+ align:start position:0%
+like this before um so we should have no
+ 
+
+ align:start position:0%
+like this before um so we should have no
+trouble with these rules okay so let's
+
+ align:start position:0%
+trouble with these rules okay so let's
+ 
+
+ align:start position:0%
+trouble with these rules okay so let's
+just look an example of this suppose we
+
+ align:start position:0%
+just look an example of this suppose we
+ 
+
+ align:start position:0%
+just look an example of this suppose we
+have our friend
+
+ align:start position:0%
+have our friend
+ 
+
+ align:start position:0%
+have our friend
+nh4+ what is hydrogen's uh oxidation
+
+ align:start position:0%
+nh4+ what is hydrogen's uh oxidation
+ 
+
+ align:start position:0%
+nh4+ what is hydrogen's uh oxidation
+number going to be in this
+
+ align:start position:0%
+number going to be in this
+ 
+
+ align:start position:0%
+number going to be in this
+molecule it'll be+ one so it's not with
+
+ align:start position:0%
+molecule it'll be+ one so it's not with
+ 
+
+ align:start position:0%
+molecule it'll be+ one so it's not with
+a group one or group two
+
+ align:start position:0%
+a group one or group two
+ 
+
+ align:start position:0%
+a group one or group two
+um element so it's going to be plus
+
+ align:start position:0%
+um element so it's going to be plus
+ 
+
+ align:start position:0%
+um element so it's going to be plus
+one what about nitrogen there are no
+
+ align:start position:0%
+one what about nitrogen there are no
+ 
+
+ align:start position:0%
+one what about nitrogen there are no
+rules about nitrogen so we have to
+
+ align:start position:0%
+rules about nitrogen so we have to
+ 
+
+ align:start position:0%
+rules about nitrogen so we have to
+figure out based on the other rules what
+
+ align:start position:0%
+figure out based on the other rules what
+ 
+
+ align:start position:0%
+figure out based on the other rules what
+the oxidation number of nitrogen will be
+
+ align:start position:0%
+the oxidation number of nitrogen will be
+ 
+
+ align:start position:0%
+the oxidation number of nitrogen will be
+what is it going to be here it's going
+
+ align:start position:0%
+what is it going to be here it's going
+ 
+
+ align:start position:0%
+what is it going to be here it's going
+to be minus three and the reason for
+
+ align:start position:0%
+to be minus three and the reason for
+ 
+
+ align:start position:0%
+to be minus three and the reason for
+that is because of the rule we just
+
+ align:start position:0%
+that is because of the rule we just
+ 
+
+ align:start position:0%
+that is because of the rule we just
+talked about that the sum needs of the
+
+ align:start position:0%
+talked about that the sum needs of the
+ 
+
+ align:start position:0%
+talked about that the sum needs of the
+oxidation numbers needs to be equal to
+
+ align:start position:0%
+oxidation numbers needs to be equal to
+ 
+
+ align:start position:0%
+oxidation numbers needs to be equal to
+the charge on the molecule the charge is
+
+ align:start position:0%
+the charge on the molecule the charge is
+ 
+
+ align:start position:0%
+the charge on the molecule the charge is
+plus one so we have four hydrogens four
+
+ align:start position:0%
+plus one so we have four hydrogens four
+ 
+
+ align:start position:0%
+plus one so we have four hydrogens four
+plus plus 1 minus 3 is going to equal +
+
+ align:start position:0%
+plus plus 1 minus 3 is going to equal +
+ 
+
+ align:start position:0%
+plus plus 1 minus 3 is going to equal +
+one so nitrogen had to be minus three
+
+ align:start position:0%
+one so nitrogen had to be minus three
+ 
+
+ align:start position:0%
+one so nitrogen had to be minus three
+nitrogen can have a lot of different
+
+ align:start position:0%
+nitrogen can have a lot of different
+ 
+
+ align:start position:0%
+nitrogen can have a lot of different
+numbers so you want to pay attention to
+
+ align:start position:0%
+numbers so you want to pay attention to
+ 
+
+ align:start position:0%
+numbers so you want to pay attention to
+what's around it and whether they're
+
+ align:start position:0%
+what's around it and whether they're
+ 
+
+ align:start position:0%
+what's around it and whether they're
+rules or guidelines about those other
+
+ align:start position:0%
+rules or guidelines about those other
+ 
+
+ align:start position:0%
+rules or guidelines about those other
+elements all
+
+ align:start position:0%
+elements all
+ 
+
+ align:start position:0%
+elements all
+right seven oxidation numbers don't have
+
+ align:start position:0%
+right seven oxidation numbers don't have
+ 
+
+ align:start position:0%
+right seven oxidation numbers don't have
+to be integers they almost always are
+
+ align:start position:0%
+to be integers they almost always are
+ 
+
+ align:start position:0%
+to be integers they almost always are
+but there is one notable exception and
+
+ align:start position:0%
+but there is one notable exception and
+ 
+
+ align:start position:0%
+but there is one notable exception and
+it's from oxygen perhaps not a surprise
+
+ align:start position:0%
+it's from oxygen perhaps not a surprise
+ 
+
+ align:start position:0%
+it's from oxygen perhaps not a surprise
+oxygen is always causing trouble so in
+
+ align:start position:0%
+oxygen is always causing trouble so in
+ 
+
+ align:start position:0%
+oxygen is always causing trouble so in
+super oxide you have O2
+
+ align:start position:0%
+super oxide you have O2
+ 
+
+ align:start position:0%
+super oxide you have O2
+minus1 so what is the oxidation number
+
+ align:start position:0%
+minus1 so what is the oxidation number
+ 
+
+ align:start position:0%
+minus1 so what is the oxidation number
+on each oxygen in that O2 minus one
+
+ align:start position:0%
+on each oxygen in that O2 minus one
+ 
+
+ align:start position:0%
+on each oxygen in that O2 minus one
+molecule yep so it's minus
+
+ align:start position:0%
+molecule yep so it's minus
+ 
+
+ align:start position:0%
+molecule yep so it's minus
+one2 so oxygen is usually minus two
+
+ align:start position:0%
+one2 so oxygen is usually minus two
+ 
+
+ align:start position:0%
+one2 so oxygen is usually minus two
+except in peroxides and super
+
+ align:start position:0%
+except in peroxides and super
+ 
+
+ align:start position:0%
+except in peroxides and super
+oxides all right so let's take a look at
+
+ align:start position:0%
+oxides all right so let's take a look at
+ 
+
+ align:start position:0%
+oxides all right so let's take a look at
+some examples and I'll write some of
+
+ align:start position:0%
+some examples and I'll write some of
+ 
+
+ align:start position:0%
+some examples and I'll write some of
+these on the board and here are all of
+
+ align:start position:0%
+these on the board and here are all of
+ 
+
+ align:start position:0%
+these on the board and here are all of
+your rules so you can yell out what you
+
+ align:start position:0%
+your rules so you can yell out what you
+ 
+
+ align:start position:0%
+your rules so you can yell out what you
+think um I should be doing with these as
+
+ align:start position:0%
+think um I should be doing with these as
+ 
+
+ align:start position:0%
+think um I should be doing with these as
+we go
+
+ align:start position:0%
+we go
+ 
+
+ align:start position:0%
+we go
+along okay so we have lithium
+
+ align:start position:0%
+along okay so we have lithium
+ 
+
+ align:start position:0%
+along okay so we have lithium
+to oxide so here we know a lot about
+
+ align:start position:0%
+to oxide so here we know a lot about
+ 
+
+ align:start position:0%
+to oxide so here we know a lot about
+this what's the oxygen going to
+
+ align:start position:0%
+this what's the oxygen going to
+ 
+
+ align:start position:0%
+this what's the oxygen going to
+be minus two the overall charge on the
+
+ align:start position:0%
+be minus two the overall charge on the
+ 
+
+ align:start position:0%
+be minus two the overall charge on the
+molecule is zero and we have two
+
+ align:start position:0%
+molecule is zero and we have two
+ 
+
+ align:start position:0%
+molecule is zero and we have two
+lithiums and what's the charge on each
+
+ align:start position:0%
+lithiums and what's the charge on each
+ 
+
+ align:start position:0%
+lithiums and what's the charge on each
+one + one and so + 2 - 2 is zero
+
+ align:start position:0%
+one + one and so + 2 - 2 is zero
+ 
+
+ align:start position:0%
+one + one and so + 2 - 2 is zero
+great let's do another one we'll do
+
+ align:start position:0%
+great let's do another one we'll do
+ 
+
+ align:start position:0%
+great let's do another one we'll do
+PCL 5
+
+ align:start position:0%
+PCL 5
+ 
+
+ align:start position:0%
+PCL 5
+next so what do we know about CL what
+
+ align:start position:0%
+next so what do we know about CL what
+ 
+
+ align:start position:0%
+next so what do we know about CL what
+charge do we expect
+
+ align:start position:0%
+charge do we expect
+ 
+
+ align:start position:0%
+charge do we expect
+here minus one and there are five of
+
+ align:start position:0%
+here minus one and there are five of
+ 
+
+ align:start position:0%
+here minus one and there are five of
+those so chlorine likes to be minus1
+
+ align:start position:0%
+those so chlorine likes to be minus1
+ 
+
+ align:start position:0%
+those so chlorine likes to be minus1
+exception is with oxy o but it's not
+
+ align:start position:0%
+exception is with oxy o but it's not
+ 
+
+ align:start position:0%
+exception is with oxy o but it's not
+with oxygen here the overall charge is
+
+ align:start position:0%
+with oxygen here the overall charge is
+ 
+
+ align:start position:0%
+with oxygen here the overall charge is
+going to be zero because it's a neutral
+
+ align:start position:0%
+going to be zero because it's a neutral
+ 
+
+ align:start position:0%
+going to be zero because it's a neutral
+molecule so what does that mean about
+
+ align:start position:0%
+molecule so what does that mean about
+ 
+
+ align:start position:0%
+molecule so what does that mean about
+the charge on our
+
+ align:start position:0%
+the charge on our
+ 
+
+ align:start position:0%
+the charge on our
+phosphorus plus
+
+ align:start position:0%
+phosphorus plus
+ 
+
+ align:start position:0%
+phosphorus plus
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+right okay so now let's
+
+ align:start position:0%
+right okay so now let's
+ 
+
+ align:start position:0%
+right okay so now let's
+try
+
+ align:start position:0%
+try
+ 
+
+ align:start position:0%
+try
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+hno3 so let's do oxygen first what
+
+ align:start position:0%
+hno3 so let's do oxygen first what
+ 
+
+ align:start position:0%
+hno3 so let's do oxygen first what
+charge we expect on
+
+ align:start position:0%
+charge we expect on
+ 
+
+ align:start position:0%
+charge we expect on
+oxygen - two so we three of those minus
+
+ align:start position:0%
+oxygen - two so we three of those minus
+ 
+
+ align:start position:0%
+oxygen - two so we three of those minus
+2 overall this is going to be zero
+
+ align:start position:0%
+2 overall this is going to be zero
+ 
+
+ align:start position:0%
+2 overall this is going to be zero
+nitrogen can be varied so let's do
+
+ align:start position:0%
+nitrogen can be varied so let's do
+ 
+
+ align:start position:0%
+nitrogen can be varied so let's do
+hydrogen what do we expect hydrogen to
+
+ align:start position:0%
+hydrogen what do we expect hydrogen to
+ 
+
+ align:start position:0%
+hydrogen what do we expect hydrogen to
+be plus one right it's not with a group
+
+ align:start position:0%
+be plus one right it's not with a group
+ 
+
+ align:start position:0%
+be plus one right it's not with a group
+one or group two so what is that leave
+
+ align:start position:0%
+one or group two so what is that leave
+ 
+
+ align:start position:0%
+one or group two so what is that leave
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+nitrogen plus
+
+ align:start position:0%
+nitrogen plus
+ 
+
+ align:start position:0%
+nitrogen plus
+five so we have plus six then minus 6 is
+
+ align:start position:0%
+five so we have plus six then minus 6 is
+ 
+
+ align:start position:0%
+five so we have plus six then minus 6 is
+zero all right so why don't you try the
+
+ align:start position:0%
+zero all right so why don't you try the
+ 
+
+ align:start position:0%
+zero all right so why don't you try the
+next one as a clicker
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question all right 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep so oxygen is minus two it's not in a
+
+ align:start position:0%
+yep so oxygen is minus two it's not in a
+ 
+
+ align:start position:0%
+yep so oxygen is minus two it's not in a
+peroxide um or a super oxide the overall
+
+ align:start position:0%
+peroxide um or a super oxide the overall
+ 
+
+ align:start position:0%
+peroxide um or a super oxide the overall
+charge is zero so that means that each
+
+ align:start position:0%
+charge is zero so that means that each
+ 
+
+ align:start position:0%
+charge is zero so that means that each
+nitrogen must be+ one so we have plus
+
+ align:start position:0%
+nitrogen must be+ one so we have plus
+ 
+
+ align:start position:0%
+nitrogen must be+ one so we have plus
+two minus 2 is
+
+ align:start position:0%
+two minus 2 is
+ 
+
+ align:start position:0%
+two minus 2 is
+zero yeah what exactly a peroxide a
+
+ align:start position:0%
+zero yeah what exactly a peroxide a
+ 
+
+ align:start position:0%
+zero yeah what exactly a peroxide a
+peroxide so um they're really only those
+
+ align:start position:0%
+peroxide so um they're really only those
+ 
+
+ align:start position:0%
+peroxide so um they're really only those
+the hydrogen peroxide example so it'll
+
+ align:start position:0%
+the hydrogen peroxide example so it'll
+ 
+
+ align:start position:0%
+the hydrogen peroxide example so it'll
+it'll say that it's a peroxide so or a
+
+ align:start position:0%
+it'll say that it's a peroxide so or a
+ 
+
+ align:start position:0%
+it'll say that it's a peroxide so or a
+super oxide yeah so don't don't wor you
+
+ align:start position:0%
+super oxide yeah so don't don't wor you
+ 
+
+ align:start position:0%
+super oxide yeah so don't don't wor you
+don't have to worry about that it's
+
+ align:start position:0%
+don't have to worry about that it's
+ 
+
+ align:start position:0%
+don't have to worry about that it's
+going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clear okay good so
+
+ align:start position:0%
+clear okay good so
+ 
+
+ align:start position:0%
+clear okay good so
+now let's talk about some reactions that
+
+ align:start position:0%
+now let's talk about some reactions that
+ 
+
+ align:start position:0%
+now let's talk about some reactions that
+involve oxidations and reductions and to
+
+ align:start position:0%
+involve oxidations and reductions and to
+ 
+
+ align:start position:0%
+involve oxidations and reductions and to
+talk about these reactions you need to
+
+ align:start position:0%
+talk about these reactions you need to
+ 
+
+ align:start position:0%
+talk about these reactions you need to
+know how to do this and then we're going
+
+ align:start position:0%
+know how to do this and then we're going
+ 
+
+ align:start position:0%
+know how to do this and then we're going
+to talk about balancing reactions and
+
+ align:start position:0%
+to talk about balancing reactions and
+ 
+
+ align:start position:0%
+to talk about balancing reactions and
+you need all of these skills all right
+
+ align:start position:0%
+you need all of these skills all right
+ 
+
+ align:start position:0%
+you need all of these skills all right
+so first I just want to tell you about
+
+ align:start position:0%
+so first I just want to tell you about
+ 
+
+ align:start position:0%
+so first I just want to tell you about
+something called a disproportionation
+
+ align:start position:0%
+something called a disproportionation
+ 
+
+ align:start position:0%
+something called a disproportionation
+reaction where you have one element that
+
+ align:start position:0%
+reaction where you have one element that
+ 
+
+ align:start position:0%
+reaction where you have one element that
+is going to be both oxidized and reduced
+
+ align:start position:0%
+is going to be both oxidized and reduced
+ 
+
+ align:start position:0%
+is going to be both oxidized and reduced
+and this is a good example to allow us
+
+ align:start position:0%
+and this is a good example to allow us
+ 
+
+ align:start position:0%
+and this is a good example to allow us
+to think about what's happening in a
+
+ align:start position:0%
+to think about what's happening in a
+ 
+
+ align:start position:0%
+to think about what's happening in a
+different reaction so in this reaction
+
+ align:start position:0%
+different reaction so in this reaction
+ 
+
+ align:start position:0%
+different reaction so in this reaction
+um the element that is going to be both
+
+ align:start position:0%
+um the element that is going to be both
+ 
+
+ align:start position:0%
+um the element that is going to be both
+oxidized and reduced is CL um sodium is
+
+ align:start position:0%
+oxidized and reduced is CL um sodium is
+ 
+
+ align:start position:0%
+oxidized and reduced is CL um sodium is
+going to be a spectator ion and the
+
+ align:start position:0%
+going to be a spectator ion and the
+ 
+
+ align:start position:0%
+going to be a spectator ion and the
+oxygen is going to uh stay um in it
+
+ align:start position:0%
+oxygen is going to uh stay um in it
+ 
+
+ align:start position:0%
+oxygen is going to uh stay um in it
+min-2 form here and so we have chlorine
+
+ align:start position:0%
+min-2 form here and so we have chlorine
+ 
+
+ align:start position:0%
+min-2 form here and so we have chlorine
+going to chlorine in this compound and
+
+ align:start position:0%
+going to chlorine in this compound and
+ 
+
+ align:start position:0%
+going to chlorine in this compound and
+in this compound so we can break this
+
+ align:start position:0%
+in this compound so we can break this
+ 
+
+ align:start position:0%
+in this compound so we can break this
+down and think about what's happening
+
+ align:start position:0%
+down and think about what's happening
+ 
+
+ align:start position:0%
+down and think about what's happening
+with this species going to this and then
+
+ align:start position:0%
+with this species going to this and then
+ 
+
+ align:start position:0%
+with this species going to this and then
+also going to CL minus so let's think
+
+ align:start position:0%
+also going to CL minus so let's think
+ 
+
+ align:start position:0%
+also going to CL minus so let's think
+about what the oxidation number of
+
+ align:start position:0%
+about what the oxidation number of
+ 
+
+ align:start position:0%
+about what the oxidation number of
+chlorine is in CL minus so first oxygen
+
+ align:start position:0%
+chlorine is in CL minus so first oxygen
+ 
+
+ align:start position:0%
+chlorine is in CL minus so first oxygen
+I already told you is going to be minus
+
+ align:start position:0%
+I already told you is going to be minus
+ 
+
+ align:start position:0%
+I already told you is going to be minus
+two the overall charge on the molecule
+
+ align:start position:0%
+two the overall charge on the molecule
+ 
+
+ align:start position:0%
+two the overall charge on the molecule
+is minus1 so chlorine has to make this
+
+ align:start position:0%
+is minus1 so chlorine has to make this
+ 
+
+ align:start position:0%
+is minus1 so chlorine has to make this
+equation work so what is the oxidation
+
+ align:start position:0%
+equation work so what is the oxidation
+ 
+
+ align:start position:0%
+equation work so what is the oxidation
+number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cl plus one thank you so we have plus
+
+ align:start position:0%
+Cl plus one thank you so we have plus
+ 
+
+ align:start position:0%
+Cl plus one thank you so we have plus
+one here now let's take a look at this
+
+ align:start position:0%
+one here now let's take a look at this
+ 
+
+ align:start position:0%
+one here now let's take a look at this
+so oxygen we're going to have as min-2
+
+ align:start position:0%
+so oxygen we're going to have as min-2
+ 
+
+ align:start position:0%
+so oxygen we're going to have as min-2
+there are three of
+
+ align:start position:0%
+there are three of
+ 
+
+ align:start position:0%
+there are three of
+them that's going to equal overall
+
+ align:start position:0%
+them that's going to equal overall
+ 
+
+ align:start position:0%
+them that's going to equal overall
+minus1 so what's the oxidation number of
+
+ align:start position:0%
+minus1 so what's the oxidation number of
+ 
+
+ align:start position:0%
+minus1 so what's the oxidation number of
+chlorine
+
+ align:start position:0%
+chlorine
+ 
+
+ align:start position:0%
+chlorine
+here plus five right so we have a case
+
+ align:start position:0%
+here plus five right so we have a case
+ 
+
+ align:start position:0%
+here plus five right so we have a case
+now where we're going from + one to +
+
+ align:start position:0%
+now where we're going from + one to +
+ 
+
+ align:start position:0%
+now where we're going from + one to +
+5 is that an oxidation or a
+
+ align:start position:0%
+5 is that an oxidation or a
+ 
+
+ align:start position:0%
+5 is that an oxidation or a
+reduction that's an oxidation so we're
+
+ align:start position:0%
+reduction that's an oxidation so we're
+ 
+
+ align:start position:0%
+reduction that's an oxidation so we're
+increasing the number it is losing
+
+ align:start position:0%
+increasing the number it is losing
+ 
+
+ align:start position:0%
+increasing the number it is losing
+electrons it's becoming
+
+ align:start position:0%
+electrons it's becoming
+ 
+
+ align:start position:0%
+electrons it's becoming
+oxidized so down here we already have
+
+ align:start position:0%
+oxidized so down here we already have
+ 
+
+ align:start position:0%
+oxidized so down here we already have
+done all of our work and know that this
+
+ align:start position:0%
+done all of our work and know that this
+ 
+
+ align:start position:0%
+done all of our work and know that this
+is also going to be+ one
+
+ align:start position:0%
+is also going to be+ one
+ 
+
+ align:start position:0%
+is also going to be+ one
+so in this case we're going from + one
+
+ align:start position:0%
+so in this case we're going from + one
+ 
+
+ align:start position:0%
+so in this case we're going from + one
+to minus1 is that an oxidation or a
+
+ align:start position:0%
+to minus1 is that an oxidation or a
+ 
+
+ align:start position:0%
+to minus1 is that an oxidation or a
+reduction that's a reduction and that's
+
+ align:start position:0%
+reduction that's a reduction and that's
+ 
+
+ align:start position:0%
+reduction that's a reduction and that's
+good because it wouldn't be a very good
+
+ align:start position:0%
+good because it wouldn't be a very good
+ 
+
+ align:start position:0%
+good because it wouldn't be a very good
+disproportionation reaction otherwise
+
+ align:start position:0%
+disproportionation reaction otherwise
+ 
+
+ align:start position:0%
+disproportionation reaction otherwise
+something has to be oxidized same thing
+
+ align:start position:0%
+something has to be oxidized same thing
+ 
+
+ align:start position:0%
+something has to be oxidized same thing
+has to be oxidized and reduced so this
+
+ align:start position:0%
+has to be oxidized and reduced so this
+ 
+
+ align:start position:0%
+has to be oxidized and reduced so this
+is uh how you think about about this
+
+ align:start position:0%
+is uh how you think about about this
+ 
+
+ align:start position:0%
+is uh how you think about about this
+type of reaction so to consider whether
+
+ align:start position:0%
+type of reaction so to consider whether
+ 
+
+ align:start position:0%
+type of reaction so to consider whether
+something's being oxidized or reduced
+
+ align:start position:0%
+something's being oxidized or reduced
+ 
+
+ align:start position:0%
+something's being oxidized or reduced
+you need to be able to dissect out what
+
+ align:start position:0%
+you need to be able to dissect out what
+ 
+
+ align:start position:0%
+you need to be able to dissect out what
+the oxidation numbers
+
+ align:start position:0%
+the oxidation numbers
+ 
+
+ align:start position:0%
+the oxidation numbers
+are all right now we're going to balance
+
+ align:start position:0%
+are all right now we're going to balance
+ 
+
+ align:start position:0%
+are all right now we're going to balance
+so balancing is going to become very
+
+ align:start position:0%
+so balancing is going to become very
+ 
+
+ align:start position:0%
+so balancing is going to become very
+important for doing problems later on
+
+ align:start position:0%
+important for doing problems later on
+ 
+
+ align:start position:0%
+important for doing problems later on
+balancing redo reactions you balance
+
+ align:start position:0%
+balancing redo reactions you balance
+ 
+
+ align:start position:0%
+balancing redo reactions you balance
+differently if you're in acidic
+
+ align:start position:0%
+differently if you're in acidic
+ 
+
+ align:start position:0%
+differently if you're in acidic
+conditions versus basic conditions so
+
+ align:start position:0%
+conditions versus basic conditions so
+ 
+
+ align:start position:0%
+conditions versus basic conditions so
+we're first we're going to do acidic
+
+ align:start position:0%
+we're first we're going to do acidic
+ 
+
+ align:start position:0%
+we're first we're going to do acidic
+conditions and we're going to run
+
+ align:start position:0%
+conditions and we're going to run
+ 
+
+ align:start position:0%
+conditions and we're going to run
+through the steps for doing
+
+ align:start position:0%
+through the steps for doing
+ 
+
+ align:start position:0%
+through the steps for doing
+this first step is we're going to write
+
+ align:start position:0%
+this first step is we're going to write
+ 
+
+ align:start position:0%
+this first step is we're going to write
+two half reactions for for this so we
+
+ align:start position:0%
+two half reactions for for this so we
+ 
+
+ align:start position:0%
+two half reactions for for this so we
+have iron in here and we have chromium
+
+ align:start position:0%
+have iron in here and we have chromium
+ 
+
+ align:start position:0%
+have iron in here and we have chromium
+in here and we're going to separate
+
+ align:start position:0%
+in here and we're going to separate
+ 
+
+ align:start position:0%
+in here and we're going to separate
+those out because we're going to think
+
+ align:start position:0%
+those out because we're going to think
+ 
+
+ align:start position:0%
+those out because we're going to think
+about what iron is doing separately from
+
+ align:start position:0%
+about what iron is doing separately from
+ 
+
+ align:start position:0%
+about what iron is doing separately from
+what the chromium is doing so first um
+
+ align:start position:0%
+what the chromium is doing so first um
+ 
+
+ align:start position:0%
+what the chromium is doing so first um
+let's write out our chromium and think
+
+ align:start position:0%
+let's write out our chromium and think
+ 
+
+ align:start position:0%
+let's write out our chromium and think
+about what is happening to it here and
+
+ align:start position:0%
+about what is happening to it here and
+ 
+
+ align:start position:0%
+about what is happening to it here and
+that is a clicker question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right 10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds okay so let's take a look at why
+
+ align:start position:0%
+seconds okay so let's take a look at why
+ 
+
+ align:start position:0%
+seconds okay so let's take a look at why
+two is correct um for one thing you just
+
+ align:start position:0%
+two is correct um for one thing you just
+ 
+
+ align:start position:0%
+two is correct um for one thing you just
+have to remember the definitions um for
+
+ align:start position:0%
+have to remember the definitions um for
+ 
+
+ align:start position:0%
+have to remember the definitions um for
+another you have to recognize what's
+
+ align:start position:0%
+another you have to recognize what's
+ 
+
+ align:start position:0%
+another you have to recognize what's
+happening to the
+
+ align:start position:0%
+happening to the
+ 
+
+ align:start position:0%
+happening to the
+chromium so let's take a look at the
+
+ align:start position:0%
+chromium so let's take a look at the
+ 
+
+ align:start position:0%
+chromium so let's take a look at the
+chromium now so we have oxygen at minus
+
+ align:start position:0%
+chromium now so we have oxygen at minus
+ 
+
+ align:start position:0%
+chromium now so we have oxygen at minus
+2 there's seven of
+
+ align:start position:0%
+2 there's seven of
+ 
+
+ align:start position:0%
+2 there's seven of
+them and the overall charge of the
+
+ align:start position:0%
+them and the overall charge of the
+ 
+
+ align:start position:0%
+them and the overall charge of the
+molecule is minus
+
+ align:start position:0%
+molecule is minus
+ 
+
+ align:start position:0%
+molecule is minus
+two and so what does that mean for the
+
+ align:start position:0%
+two and so what does that mean for the
+ 
+
+ align:start position:0%
+two and so what does that mean for the
+oxidation number of this
+
+ align:start position:0%
+oxidation number of this
+ 
+
+ align:start position:0%
+oxidation number of this
+chromium it's going to be plus 6 is
+
+ align:start position:0%
+chromium it's going to be plus 6 is
+ 
+
+ align:start position:0%
+chromium it's going to be plus 6 is
+we're going to have 12 - 14 =
+
+ align:start position:0%
+we're going to have 12 - 14 =
+ 
+
+ align:start position:0%
+we're going to have 12 - 14 =
+-2 so we're going from plus 6 over here
+
+ align:start position:0%
+-2 so we're going from plus 6 over here
+ 
+
+ align:start position:0%
+-2 so we're going from plus 6 over here
+to+ three here so so is that an
+
+ align:start position:0%
+to+ three here so so is that an
+ 
+
+ align:start position:0%
+to+ three here so so is that an
+oxidation or
+
+ align:start position:0%
+oxidation or
+ 
+
+ align:start position:0%
+oxidation or
+reduction so that's the
+
+ align:start position:0%
+reduction so that's the
+ 
+
+ align:start position:0%
+reduction so that's the
+reduction so I kind of like this unit
+
+ align:start position:0%
+reduction so I kind of like this unit
+ 
+
+ align:start position:0%
+reduction so I kind of like this unit
+coming after acids and bases because a
+
+ align:start position:0%
+coming after acids and bases because a
+ 
+
+ align:start position:0%
+coming after acids and bases because a
+lot of those problems I think make
+
+ align:start position:0%
+lot of those problems I think make
+ 
+
+ align:start position:0%
+lot of those problems I think make
+people's brains hurt a little bit and
+
+ align:start position:0%
+people's brains hurt a little bit and
+ 
+
+ align:start position:0%
+people's brains hurt a little bit and
+you get here and it's like basic math so
+
+ align:start position:0%
+you get here and it's like basic math so
+ 
+
+ align:start position:0%
+you get here and it's like basic math so
+it's kind of exciting all right so the
+
+ align:start position:0%
+it's kind of exciting all right so the
+ 
+
+ align:start position:0%
+it's kind of exciting all right so the
+iron is even simpler we're going from
+
+ align:start position:0%
+iron is even simpler we're going from
+ 
+
+ align:start position:0%
+iron is even simpler we're going from
+plus two to plus3 so that's an oxidation
+
+ align:start position:0%
+plus two to plus3 so that's an oxidation
+ 
+
+ align:start position:0%
+plus two to plus3 so that's an oxidation
+so one thing is being reduced the other
+
+ align:start position:0%
+so one thing is being reduced the other
+ 
+
+ align:start position:0%
+so one thing is being reduced the other
+thing is is being oxidized that's what
+
+ align:start position:0%
+thing is is being oxidized that's what
+ 
+
+ align:start position:0%
+thing is is being oxidized that's what
+makes it a redo
+
+ align:start position:0%
+makes it a redo
+ 
+
+ align:start position:0%
+makes it a redo
+reaction all right so we know what's
+
+ align:start position:0%
+reaction all right so we know what's
+ 
+
+ align:start position:0%
+reaction all right so we know what's
+happening in terms of what's being
+
+ align:start position:0%
+happening in terms of what's being
+ 
+
+ align:start position:0%
+happening in terms of what's being
+oxidized what's being reduced now we'
+
+ align:start position:0%
+oxidized what's being reduced now we'
+ 
+
+ align:start position:0%
+oxidized what's being reduced now we'
+and we've broken these into two half
+
+ align:start position:0%
+and we've broken these into two half
+ 
+
+ align:start position:0%
+and we've broken these into two half
+reactions now we need to
+
+ align:start position:0%
+reactions now we need to
+ 
+
+ align:start position:0%
+reactions now we need to
+balance all right so the first thing
+
+ align:start position:0%
+balance all right so the first thing
+ 
+
+ align:start position:0%
+balance all right so the first thing
+we're going to do is we're going to
+
+ align:start position:0%
+we're going to do is we're going to
+ 
+
+ align:start position:0%
+we're going to do is we're going to
+balance our elements that are not oxygen
+
+ align:start position:0%
+balance our elements that are not oxygen
+ 
+
+ align:start position:0%
+balance our elements that are not oxygen
+and hydrogen so we're going to balance
+
+ align:start position:0%
+and hydrogen so we're going to balance
+ 
+
+ align:start position:0%
+and hydrogen so we're going to balance
+chromium and we're going to balance our
+
+ align:start position:0%
+chromium and we're going to balance our
+ 
+
+ align:start position:0%
+chromium and we're going to balance our
+iron what do we need to add to this top
+
+ align:start position:0%
+iron what do we need to add to this top
+ 
+
+ align:start position:0%
+iron what do we need to add to this top
+to balance
+
+ align:start position:0%
+to balance
+ 
+
+ align:start position:0%
+to balance
+chromium we need to add a
+
+ align:start position:0%
+chromium we need to add a
+ 
+
+ align:start position:0%
+chromium we need to add a
+two and we don't need to do anything to
+
+ align:start position:0%
+two and we don't need to do anything to
+ 
+
+ align:start position:0%
+two and we don't need to do anything to
+our iron we have one iron on one side
+
+ align:start position:0%
+our iron we have one iron on one side
+ 
+
+ align:start position:0%
+our iron we have one iron on one side
+one iron on the other side all right so
+
+ align:start position:0%
+one iron on the other side all right so
+ 
+
+ align:start position:0%
+one iron on the other side all right so
+all you need to do is insert the
+
+ align:start position:0%
+all you need to do is insert the
+ 
+
+ align:start position:0%
+all you need to do is insert the
+two Next Step we're going to add water
+
+ align:start position:0%
+two Next Step we're going to add water
+ 
+
+ align:start position:0%
+two Next Step we're going to add water
+to balance
+
+ align:start position:0%
+to balance
+ 
+
+ align:start position:0%
+to balance
+oxygen so how much water do we need to
+
+ align:start position:0%
+oxygen so how much water do we need to
+ 
+
+ align:start position:0%
+oxygen so how much water do we need to
+add to the top reaction to balance the
+
+ align:start position:0%
+add to the top reaction to balance the
+ 
+
+ align:start position:0%
+add to the top reaction to balance the
+oxygen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so here we're going to add seven
+
+ align:start position:0%
+so so here we're going to add seven
+ 
+
+ align:start position:0%
+so so here we're going to add seven
+Waters to balance the oxygen and again
+
+ align:start position:0%
+Waters to balance the oxygen and again
+ 
+
+ align:start position:0%
+Waters to balance the oxygen and again
+we have nothing to do down
+
+ align:start position:0%
+we have nothing to do down
+ 
+
+ align:start position:0%
+we have nothing to do down
+there all right so let's keep
+
+ align:start position:0%
+there all right so let's keep
+ 
+
+ align:start position:0%
+there all right so let's keep
+going next we want to balance the
+
+ align:start position:0%
+going next we want to balance the
+ 
+
+ align:start position:0%
+going next we want to balance the
+hydrogen we just added those Waters um
+
+ align:start position:0%
+hydrogen we just added those Waters um
+ 
+
+ align:start position:0%
+hydrogen we just added those Waters um
+and so now we have to balance hydrogen
+
+ align:start position:0%
+and so now we have to balance hydrogen
+ 
+
+ align:start position:0%
+and so now we have to balance hydrogen
+so we're going to balance the hydrogen
+
+ align:start position:0%
+so we're going to balance the hydrogen
+ 
+
+ align:start position:0%
+so we're going to balance the hydrogen
+by adding
+
+ align:start position:0%
+by adding
+ 
+
+ align:start position:0%
+by adding
+H+ some books have you Balan the
+
+ align:start position:0%
+H+ some books have you Balan the
+ 
+
+ align:start position:0%
+H+ some books have you Balan the
+hydrogen by adding a more correct
+
+ align:start position:0%
+hydrogen by adding a more correct
+ 
+
+ align:start position:0%
+hydrogen by adding a more correct
+species which is hydronium ion but when
+
+ align:start position:0%
+species which is hydronium ion but when
+ 
+
+ align:start position:0%
+species which is hydronium ion but when
+you do that you screw up your oxygens
+
+ align:start position:0%
+you do that you screw up your oxygens
+ 
+
+ align:start position:0%
+you do that you screw up your oxygens
+that you just balanced so that is
+
+ align:start position:0%
+that you just balanced so that is
+ 
+
+ align:start position:0%
+that you just balanced so that is
+infinitely harder to balance equations
+
+ align:start position:0%
+infinitely harder to balance equations
+ 
+
+ align:start position:0%
+infinitely harder to balance equations
+that way so I say let's not do that um
+
+ align:start position:0%
+that way so I say let's not do that um
+ 
+
+ align:start position:0%
+that way so I say let's not do that um
+so let's just use
+
+ align:start position:0%
+so let's just use
+ 
+
+ align:start position:0%
+so let's just use
+H+ so how many H+ do we need to add over
+
+ align:start position:0%
+H+ so how many H+ do we need to add over
+ 
+
+ align:start position:0%
+H+ so how many H+ do we need to add over
+here to balance the
+
+ align:start position:0%
+here to balance the
+ 
+
+ align:start position:0%
+here to balance the
+hydrogen 14 we've added 14 and again we
+
+ align:start position:0%
+hydrogen 14 we've added 14 and again we
+ 
+
+ align:start position:0%
+hydrogen 14 we've added 14 and again we
+don't have to do anything to the bottom
+
+ align:start position:0%
+don't have to do anything to the bottom
+ 
+
+ align:start position:0%
+don't have to do anything to the bottom
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+expression next we are going to balance
+
+ align:start position:0%
+expression next we are going to balance
+ 
+
+ align:start position:0%
+expression next we are going to balance
+the charge by inserting electrons so
+
+ align:start position:0%
+the charge by inserting electrons so
+ 
+
+ align:start position:0%
+the charge by inserting electrons so
+over here we have 14 - 2 + 12 and over
+
+ align:start position:0%
+over here we have 14 - 2 + 12 and over
+ 
+
+ align:start position:0%
+over here we have 14 - 2 + 12 and over
+here we have plus 6 so how many
+
+ align:start position:0%
+here we have plus 6 so how many
+ 
+
+ align:start position:0%
+here we have plus 6 so how many
+electrons are going are we going to need
+
+ align:start position:0%
+electrons are going are we going to need
+ 
+
+ align:start position:0%
+electrons are going are we going to need
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+add going to need to add six so we've
+
+ align:start position:0%
+add going to need to add six so we've
+ 
+
+ align:start position:0%
+add going to need to add six so we've
+added six over here so they have a
+
+ align:start position:0%
+added six over here so they have a
+ 
+
+ align:start position:0%
+added six over here so they have a
+negative charge so now we should be
+
+ align:start position:0%
+negative charge so now we should be
+ 
+
+ align:start position:0%
+negative charge so now we should be
+balanced on both sides and now we
+
+ align:start position:0%
+balanced on both sides and now we
+ 
+
+ align:start position:0%
+balanced on both sides and now we
+finally get to do something with a
+
+ align:start position:0%
+finally get to do something with a
+ 
+
+ align:start position:0%
+finally get to do something with a
+bottom expression and we can add an
+
+ align:start position:0%
+bottom expression and we can add an
+ 
+
+ align:start position:0%
+bottom expression and we can add an
+electron over here to balance the charge
+
+ align:start position:0%
+electron over here to balance the charge
+ 
+
+ align:start position:0%
+electron over here to balance the charge
+so plus two here plus two net on the
+
+ align:start position:0%
+so plus two here plus two net on the
+ 
+
+ align:start position:0%
+so plus two here plus two net on the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+side all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now we want to
+
+ align:start position:0%
+right now we want to
+ 
+
+ align:start position:0%
+right now we want to
+multiply so that the electrons are going
+
+ align:start position:0%
+multiply so that the electrons are going
+ 
+
+ align:start position:0%
+multiply so that the electrons are going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+cancel because this is an overall
+
+ align:start position:0%
+cancel because this is an overall
+ 
+
+ align:start position:0%
+cancel because this is an overall
+oxidation reduction reaction and our
+
+ align:start position:0%
+oxidation reduction reaction and our
+ 
+
+ align:start position:0%
+oxidation reduction reaction and our
+electrons should cancel
+
+ align:start position:0%
+electrons should cancel
+ 
+
+ align:start position:0%
+electrons should cancel
+so what do we need to multiply the
+
+ align:start position:0%
+so what do we need to multiply the
+ 
+
+ align:start position:0%
+so what do we need to multiply the
+bottom equation by
+
+ align:start position:0%
+bottom equation by
+ 
+
+ align:start position:0%
+bottom equation by
+six and there we go six here six here
+
+ align:start position:0%
+six and there we go six here six here
+ 
+
+ align:start position:0%
+six and there we go six here six here
+and six here now this is one of the
+
+ align:start position:0%
+and six here now this is one of the
+ 
+
+ align:start position:0%
+and six here now this is one of the
+places that people often in exams um
+
+ align:start position:0%
+places that people often in exams um
+ 
+
+ align:start position:0%
+places that people often in exams um
+make a mistake where they write six and
+
+ align:start position:0%
+make a mistake where they write six and
+ 
+
+ align:start position:0%
+make a mistake where they write six and
+then put um parentheses around it
+
+ align:start position:0%
+then put um parentheses around it
+ 
+
+ align:start position:0%
+then put um parentheses around it
+indicating that you're multiplying the
+
+ align:start position:0%
+indicating that you're multiplying the
+ 
+
+ align:start position:0%
+indicating that you're multiplying the
+whole thing by six which is fine but
+
+ align:start position:0%
+whole thing by six which is fine but
+ 
+
+ align:start position:0%
+whole thing by six which is fine but
+then they forget to actually carry that
+
+ align:start position:0%
+then they forget to actually carry that
+ 
+
+ align:start position:0%
+then they forget to actually carry that
+out on the next step so so when you
+
+ align:start position:0%
+out on the next step so so when you
+ 
+
+ align:start position:0%
+out on the next step so so when you
+multiply make sure that you continue um
+
+ align:start position:0%
+multiply make sure that you continue um
+ 
+
+ align:start position:0%
+multiply make sure that you continue um
+to if sometimes it's better just to
+
+ align:start position:0%
+to if sometimes it's better just to
+ 
+
+ align:start position:0%
+to if sometimes it's better just to
+write it all out because otherwise it's
+
+ align:start position:0%
+write it all out because otherwise it's
+ 
+
+ align:start position:0%
+write it all out because otherwise it's
+really easy to forget um and not
+
+ align:start position:0%
+really easy to forget um and not
+ 
+
+ align:start position:0%
+really easy to forget um and not
+multiply and then things won't make
+
+ align:start position:0%
+multiply and then things won't make
+ 
+
+ align:start position:0%
+multiply and then things won't make
+sense at the end all right so now we can
+
+ align:start position:0%
+sense at the end all right so now we can
+ 
+
+ align:start position:0%
+sense at the end all right so now we can
+add the half reactions and make the
+
+ align:start position:0%
+add the half reactions and make the
+ 
+
+ align:start position:0%
+add the half reactions and make the
+appropriate
+
+ align:start position:0%
+appropriate
+ 
+
+ align:start position:0%
+appropriate
+cancellations so we've now added it all
+
+ align:start position:0%
+cancellations so we've now added it all
+ 
+
+ align:start position:0%
+cancellations so we've now added it all
+together six electrons 14 H+ we have our
+
+ align:start position:0%
+together six electrons 14 H+ we have our
+ 
+
+ align:start position:0%
+together six electrons 14 H+ we have our
+chromium oxide compound we have now our
+
+ align:start position:0%
+chromium oxide compound we have now our
+ 
+
+ align:start position:0%
+chromium oxide compound we have now our
+six iron plus tws our two chromium plus
+
+ align:start position:0%
+six iron plus tws our two chromium plus
+ 
+
+ align:start position:0%
+six iron plus tws our two chromium plus
+3es our seven Waters our six iron plus
+
+ align:start position:0%
+3es our seven Waters our six iron plus
+ 
+
+ align:start position:0%
+3es our seven Waters our six iron plus
+3es and our six electrons and if we did
+
+ align:start position:0%
+3es and our six electrons and if we did
+ 
+
+ align:start position:0%
+3es and our six electrons and if we did
+everything right then the electrons um
+
+ align:start position:0%
+everything right then the electrons um
+ 
+
+ align:start position:0%
+everything right then the electrons um
+should cancel and we can double check
+
+ align:start position:0%
+should cancel and we can double check
+ 
+
+ align:start position:0%
+should cancel and we can double check
+it's always a good idea to double check
+
+ align:start position:0%
+it's always a good idea to double check
+ 
+
+ align:start position:0%
+it's always a good idea to double check
+that it's balanced so we have 14 H's
+
+ align:start position:0%
+that it's balanced so we have 14 H's
+ 
+
+ align:start position:0%
+that it's balanced so we have 14 H's
+here 14 H's there chromium 2 two oxygen
+
+ align:start position:0%
+here 14 H's there chromium 2 two oxygen
+ 
+
+ align:start position:0%
+here 14 H's there chromium 2 two oxygen
+7 7 iron 6 six this can catch a mistake
+
+ align:start position:0%
+7 7 iron 6 six this can catch a mistake
+ 
+
+ align:start position:0%
+7 7 iron 6 six this can catch a mistake
+that you might have made and then check
+
+ align:start position:0%
+that you might have made and then check
+ 
+
+ align:start position:0%
+that you might have made and then check
+the charge + 14 - 2 + 12 on one side
+
+ align:start position:0%
+the charge + 14 - 2 + 12 on one side
+ 
+
+ align:start position:0%
+the charge + 14 - 2 + 12 on one side
+plus um 6 + 18 so 24 on both
+
+ align:start position:0%
+plus um 6 + 18 so 24 on both
+ 
+
+ align:start position:0%
+plus um 6 + 18 so 24 on both
+sides it's pretty good right that's
+
+ align:start position:0%
+sides it's pretty good right that's
+ 
+
+ align:start position:0%
+sides it's pretty good right that's
+pretty simple so balancing that's in
+
+ align:start position:0%
+pretty simple so balancing that's in
+ 
+
+ align:start position:0%
+pretty simple so balancing that's in
+acidic solution we know it's an acidic
+
+ align:start position:0%
+acidic solution we know it's an acidic
+ 
+
+ align:start position:0%
+acidic solution we know it's an acidic
+because we have 14 H+ that feels quite
+
+ align:start position:0%
+because we have 14 H+ that feels quite
+ 
+
+ align:start position:0%
+because we have 14 H+ that feels quite
+acidic what do you do for basic solution
+
+ align:start position:0%
+acidic what do you do for basic solution
+ 
+
+ align:start position:0%
+acidic what do you do for basic solution
+now so for a basic solution what I
+
+ align:start position:0%
+now so for a basic solution what I
+ 
+
+ align:start position:0%
+now so for a basic solution what I
+recommend is just do the exact same
+
+ align:start position:0%
+recommend is just do the exact same
+ 
+
+ align:start position:0%
+recommend is just do the exact same
+thing that you did for your acidic
+
+ align:start position:0%
+thing that you did for your acidic
+ 
+
+ align:start position:0%
+thing that you did for your acidic
+solution and here again was the answer
+
+ align:start position:0%
+solution and here again was the answer
+ 
+
+ align:start position:0%
+solution and here again was the answer
+that we have and then quote neutralize
+
+ align:start position:0%
+that we have and then quote neutralize
+ 
+
+ align:start position:0%
+that we have and then quote neutralize
+um the acid um and make it basic adjust
+
+ align:start position:0%
+um the acid um and make it basic adjust
+ 
+
+ align:start position:0%
+um the acid um and make it basic adjust
+your pH by adding oh minus or hydroxide
+
+ align:start position:0%
+your pH by adding oh minus or hydroxide
+ 
+
+ align:start position:0%
+your pH by adding oh minus or hydroxide
+ion concentration to each side so if we
+
+ align:start position:0%
+ion concentration to each side so if we
+ 
+
+ align:start position:0%
+ion concentration to each side so if we
+do that now we're going to add 14 o o
+
+ align:start position:0%
+do that now we're going to add 14 o o
+ 
+
+ align:start position:0%
+do that now we're going to add 14 o o
+minus to this side and 14 oh minus to
+
+ align:start position:0%
+minus to this side and 14 oh minus to
+ 
+
+ align:start position:0%
+minus to this side and 14 oh minus to
+that side now 14 oh minus us+ 14 H+ are
+
+ align:start position:0%
+that side now 14 oh minus us+ 14 H+ are
+ 
+
+ align:start position:0%
+that side now 14 oh minus us+ 14 H+ are
+going to give us 14 water molecules over
+
+ align:start position:0%
+going to give us 14 water molecules over
+ 
+
+ align:start position:0%
+going to give us 14 water molecules over
+here and on this side we still have 14 o
+
+ align:start position:0%
+here and on this side we still have 14 o
+ 
+
+ align:start position:0%
+here and on this side we still have 14 o
+now we have this is not simplified
+
+ align:start position:0%
+now we have this is not simplified
+ 
+
+ align:start position:0%
+now we have this is not simplified
+because we have 14 waters on one side
+
+ align:start position:0%
+because we have 14 waters on one side
+ 
+
+ align:start position:0%
+because we have 14 waters on one side
+and seven on the other side so we can
+
+ align:start position:0%
+and seven on the other side so we can
+ 
+
+ align:start position:0%
+and seven on the other side so we can
+take that cancel out set these seven and
+
+ align:start position:0%
+take that cancel out set these seven and
+ 
+
+ align:start position:0%
+take that cancel out set these seven and
+we have seven left over here so we have
+
+ align:start position:0%
+we have seven left over here so we have
+ 
+
+ align:start position:0%
+we have seven left over here so we have
+seven Waters now on one side and 14
+
+ align:start position:0%
+seven Waters now on one side and 14
+ 
+
+ align:start position:0%
+seven Waters now on one side and 14
+hydroxides on the other so if we look at
+
+ align:start position:0%
+hydroxides on the other so if we look at
+ 
+
+ align:start position:0%
+hydroxides on the other so if we look at
+both of these expressions in acidic
+
+ align:start position:0%
+both of these expressions in acidic
+ 
+
+ align:start position:0%
+both of these expressions in acidic
+solution and in basic solution here in
+
+ align:start position:0%
+solution and in basic solution here in
+ 
+
+ align:start position:0%
+solution and in basic solution here in
+acidic solution we have 14 H+ on one
+
+ align:start position:0%
+acidic solution we have 14 H+ on one
+ 
+
+ align:start position:0%
+acidic solution we have 14 H+ on one
+side and seven waters on the other in
+
+ align:start position:0%
+side and seven waters on the other in
+ 
+
+ align:start position:0%
+side and seven waters on the other in
+basic we have seven waters on this side
+
+ align:start position:0%
+basic we have seven waters on this side
+ 
+
+ align:start position:0%
+basic we have seven waters on this side
+and 14 o minus on this side everything
+
+ align:start position:0%
+and 14 o minus on this side everything
+ 
+
+ align:start position:0%
+and 14 o minus on this side everything
+else should be the same and they should
+
+ align:start position:0%
+else should be the same and they should
+ 
+
+ align:start position:0%
+else should be the same and they should
+all add up all right so there we go that
+
+ align:start position:0%
+all add up all right so there we go that
+ 
+
+ align:start position:0%
+all add up all right so there we go that
+is balancing oxidation reductions it
+
+ align:start position:0%
+is balancing oxidation reductions it
+ 
+
+ align:start position:0%
+is balancing oxidation reductions it
+seems really straightforward um but it's
+
+ align:start position:0%
+seems really straightforward um but it's
+ 
+
+ align:start position:0%
+seems really straightforward um but it's
+very important we'll see next week that
+
+ align:start position:0%
+very important we'll see next week that
+ 
+
+ align:start position:0%
+very important we'll see next week that
+we need use this information to be able
+
+ align:start position:0%
+we need use this information to be able
+ 
+
+ align:start position:0%
+we need use this information to be able
+to do problems all right so end of 14
+
+ align:start position:0%
+to do problems all right so end of 14
+ 
+
+ align:start position:0%
+to do problems all right so end of 14
+now to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrochemistry so today's
+
+ align:start position:0%
+electrochemistry so today's
+ 
+
+ align:start position:0%
+electrochemistry so today's
+handout so we've been talking about
+
+ align:start position:0%
+handout so we've been talking about
+ 
+
+ align:start position:0%
+handout so we've been talking about
+oxidation reduction we're continuing
+
+ align:start position:0%
+oxidation reduction we're continuing
+ 
+
+ align:start position:0%
+oxidation reduction we're continuing
+talking about oxidation reduction I just
+
+ align:start position:0%
+talking about oxidation reduction I just
+ 
+
+ align:start position:0%
+talking about oxidation reduction I just
+want to remind you how really important
+
+ align:start position:0%
+want to remind you how really important
+ 
+
+ align:start position:0%
+want to remind you how really important
+oxidation reduction reactions are so
+
+ align:start position:0%
+oxidation reduction reactions are so
+ 
+
+ align:start position:0%
+oxidation reduction reactions are so
+we've talked about photosynthesis in
+
+ align:start position:0%
+we've talked about photosynthesis in
+ 
+
+ align:start position:0%
+we've talked about photosynthesis in
+this class we've talked about fuel cells
+
+ align:start position:0%
+this class we've talked about fuel cells
+ 
+
+ align:start position:0%
+this class we've talked about fuel cells
+all of these reactions that make energy
+
+ align:start position:0%
+all of these reactions that make energy
+ 
+
+ align:start position:0%
+all of these reactions that make energy
+in involve oxidation reduction loss of
+
+ align:start position:0%
+in involve oxidation reduction loss of
+ 
+
+ align:start position:0%
+in involve oxidation reduction loss of
+electrons gain of electrons basically
+
+ align:start position:0%
+electrons gain of electrons basically
+ 
+
+ align:start position:0%
+electrons gain of electrons basically
+the human body is a big battery we have
+
+ align:start position:0%
+the human body is a big battery we have
+ 
+
+ align:start position:0%
+the human body is a big battery we have
+lots of oxidation reduction reactions
+
+ align:start position:0%
+lots of oxidation reduction reactions
+ 
+
+ align:start position:0%
+lots of oxidation reduction reactions
+going on inside of us this is how we
+
+ align:start position:0%
+going on inside of us this is how we
+ 
+
+ align:start position:0%
+going on inside of us this is how we
+live this is how we make energy this is
+
+ align:start position:0%
+live this is how we make energy this is
+ 
+
+ align:start position:0%
+live this is how we make energy this is
+how we
+
+ align:start position:0%
+how we
+ 
+
+ align:start position:0%
+how we
+survive all right so electrochemistry is
+
+ align:start position:0%
+survive all right so electrochemistry is
+ 
+
+ align:start position:0%
+survive all right so electrochemistry is
+the study of Redux reactions usually um
+
+ align:start position:0%
+the study of Redux reactions usually um
+ 
+
+ align:start position:0%
+the study of Redux reactions usually um
+thinking about how they occur at an
+
+ align:start position:0%
+thinking about how they occur at an
+ 
+
+ align:start position:0%
+thinking about how they occur at an
+electrode so there are two types of
+
+ align:start position:0%
+electrode so there are two types of
+ 
+
+ align:start position:0%
+electrode so there are two types of
+reactions that you will be considering
+
+ align:start position:0%
+reactions that you will be considering
+ 
+
+ align:start position:0%
+reactions that you will be considering
+um you might be considering um a
+
+ align:start position:0%
+um you might be considering um a
+ 
+
+ align:start position:0%
+um you might be considering um a
+reaction that generates an electric
+
+ align:start position:0%
+reaction that generates an electric
+ 
+
+ align:start position:0%
+reaction that generates an electric
+current electron flow or electricity
+
+ align:start position:0%
+current electron flow or electricity
+ 
+
+ align:start position:0%
+current electron flow or electricity
+from a spontaneous reaction and you
+
+ align:start position:0%
+from a spontaneous reaction and you
+ 
+
+ align:start position:0%
+from a spontaneous reaction and you
+might consider one where you need to
+
+ align:start position:0%
+might consider one where you need to
+ 
+
+ align:start position:0%
+might consider one where you need to
+drive a reaction that is nonspontaneous
+
+ align:start position:0%
+drive a reaction that is nonspontaneous
+ 
+
+ align:start position:0%
+drive a reaction that is nonspontaneous
+using an electric current so a
+
+ align:start position:0%
+using an electric current so a
+ 
+
+ align:start position:0%
+using an electric current so a
+spontaneous reaction Delta G is what
+
+ align:start position:0%
+spontaneous reaction Delta G is what
+ 
+
+ align:start position:0%
+spontaneous reaction Delta G is what
+positive or negative negative right so
+
+ align:start position:0%
+positive or negative negative right so
+ 
+
+ align:start position:0%
+positive or negative negative right so
+spontaneous reaction Delta G is negative
+
+ align:start position:0%
+spontaneous reaction Delta G is negative
+ 
+
+ align:start position:0%
+spontaneous reaction Delta G is negative
+it's less than zero a nonspontaneous
+
+ align:start position:0%
+it's less than zero a nonspontaneous
+ 
+
+ align:start position:0%
+it's less than zero a nonspontaneous
+reaction is positive just a little
+
+ align:start position:0%
+reaction is positive just a little
+ 
+
+ align:start position:0%
+reaction is positive just a little
+review there uh for exam
+
+ align:start position:0%
+review there uh for exam
+ 
+
+ align:start position:0%
+review there uh for exam
+three all right so electrochemistry
+
+ align:start position:0%
+three all right so electrochemistry
+ 
+
+ align:start position:0%
+three all right so electrochemistry
+study of these Redux reactions
+
+ align:start position:0%
+study of these Redux reactions
+ 
+
+ align:start position:0%
+study of these Redux reactions
+electrochemical cells are devices where
+
+ align:start position:0%
+electrochemical cells are devices where
+ 
+
+ align:start position:0%
+electrochemical cells are devices where
+you generate electrons and they flow
+
+ align:start position:0%
+you generate electrons and they flow
+ 
+
+ align:start position:0%
+you generate electrons and they flow
+through the cell um and so you have the
+
+ align:start position:0%
+through the cell um and so you have the
+ 
+
+ align:start position:0%
+through the cell um and so you have the
+flow of electrons through a circuit and
+
+ align:start position:0%
+flow of electrons through a circuit and
+ 
+
+ align:start position:0%
+flow of electrons through a circuit and
+again that can be generated by a
+
+ align:start position:0%
+again that can be generated by a
+ 
+
+ align:start position:0%
+again that can be generated by a
+spontaneous reaction and if it is
+
+ align:start position:0%
+spontaneous reaction and if it is
+ 
+
+ align:start position:0%
+spontaneous reaction and if it is
+generated by a spontaneous reaction
+
+ align:start position:0%
+generated by a spontaneous reaction
+ 
+
+ align:start position:0%
+generated by a spontaneous reaction
+that's called a galvanic cell or you can
+
+ align:start position:0%
+that's called a galvanic cell or you can
+ 
+
+ align:start position:0%
+that's called a galvanic cell or you can
+use an electric current to force a
+
+ align:start position:0%
+use an electric current to force a
+ 
+
+ align:start position:0%
+use an electric current to force a
+non-spontaneous reaction to go and
+
+ align:start position:0%
+non-spontaneous reaction to go and
+ 
+
+ align:start position:0%
+non-spontaneous reaction to go and
+that's called an electrolytic cell and
+
+ align:start position:0%
+that's called an electrolytic cell and
+ 
+
+ align:start position:0%
+that's called an electrolytic cell and
+it's important to remember those
+
+ align:start position:0%
+it's important to remember those
+ 
+
+ align:start position:0%
+it's important to remember those
+definitions because a lot of problems
+
+ align:start position:0%
+definitions because a lot of problems
+ 
+
+ align:start position:0%
+definitions because a lot of problems
+tell you oh in this electrolytic cell
+
+ align:start position:0%
+tell you oh in this electrolytic cell
+ 
+
+ align:start position:0%
+tell you oh in this electrolytic cell
+and without that's telling you key
+
+ align:start position:0%
+and without that's telling you key
+ 
+
+ align:start position:0%
+and without that's telling you key
+information about what's going on in
+
+ align:start position:0%
+information about what's going on in
+ 
+
+ align:start position:0%
+information about what's going on in
+that problem so so if you uh don't have
+
+ align:start position:0%
+that problem so so if you uh don't have
+ 
+
+ align:start position:0%
+that problem so so if you uh don't have
+these uh committed to Memories you will
+
+ align:start position:0%
+these uh committed to Memories you will
+ 
+
+ align:start position:0%
+these uh committed to Memories you will
+uh find yourself in trouble but it's not
+
+ align:start position:0%
+uh find yourself in trouble but it's not
+ 
+
+ align:start position:0%
+uh find yourself in trouble but it's not
+too bad it's just two terms all right so
+
+ align:start position:0%
+too bad it's just two terms all right so
+ 
+
+ align:start position:0%
+too bad it's just two terms all right so
+a battery then so I have a uh a battery
+
+ align:start position:0%
+a battery then so I have a uh a battery
+ 
+
+ align:start position:0%
+a battery then so I have a uh a battery
+here a battery is a collection of
+
+ align:start position:0%
+here a battery is a collection of
+ 
+
+ align:start position:0%
+here a battery is a collection of
+galvanic cells um and it's going to give
+
+ align:start position:0%
+galvanic cells um and it's going to give
+ 
+
+ align:start position:0%
+galvanic cells um and it's going to give
+us it's going to use spontaneous
+
+ align:start position:0%
+us it's going to use spontaneous
+ 
+
+ align:start position:0%
+us it's going to use spontaneous
+reactions to give us an El electric
+
+ align:start position:0%
+reactions to give us an El electric
+ 
+
+ align:start position:0%
+reactions to give us an El electric
+current all right and again electrodes
+
+ align:start position:0%
+current all right and again electrodes
+ 
+
+ align:start position:0%
+current all right and again electrodes
+the definition for those they're just
+
+ align:start position:0%
+the definition for those they're just
+ 
+
+ align:start position:0%
+the definition for those they're just
+the conductors through which the
+
+ align:start position:0%
+the conductors through which the
+ 
+
+ align:start position:0%
+the conductors through which the
+electrons travel and they're two types
+
+ align:start position:0%
+electrons travel and they're two types
+ 
+
+ align:start position:0%
+electrons travel and they're two types
+let's quiet down again I hear the noise
+
+ align:start position:0%
+let's quiet down again I hear the noise
+ 
+
+ align:start position:0%
+let's quiet down again I hear the noise
+uh two types of electrodes we have
+
+ align:start position:0%
+uh two types of electrodes we have
+ 
+
+ align:start position:0%
+uh two types of electrodes we have
+anodes and
+
+ align:start position:0%
+anodes and
+ 
+
+ align:start position:0%
+anodes and
+cathodes all right so let's look at an
+
+ align:start position:0%
+cathodes all right so let's look at an
+ 
+
+ align:start position:0%
+cathodes all right so let's look at an
+electrochemical
+
+ align:start position:0%
+electrochemical
+ 
+
+ align:start position:0%
+electrochemical
+cell and consider again the anodes and
+
+ align:start position:0%
+cell and consider again the anodes and
+ 
+
+ align:start position:0%
+cell and consider again the anodes and
+the cathodes so this is my beautiful
+
+ align:start position:0%
+the cathodes so this is my beautiful
+ 
+
+ align:start position:0%
+the cathodes so this is my beautiful
+depiction of an El electrochemical cell
+
+ align:start position:0%
+depiction of an El electrochemical cell
+ 
+
+ align:start position:0%
+depiction of an El electrochemical cell
+this might be a better depiction of what
+
+ align:start position:0%
+this might be a better depiction of what
+ 
+
+ align:start position:0%
+this might be a better depiction of what
+it looks like but I think mine is not
+
+ align:start position:0%
+it looks like but I think mine is not
+ 
+
+ align:start position:0%
+it looks like but I think mine is not
+bad um just to help you out that's
+
+ align:start position:0%
+bad um just to help you out that's
+ 
+
+ align:start position:0%
+bad um just to help you out that's
+supposed to be a beaker that has fluid
+
+ align:start position:0%
+supposed to be a beaker that has fluid
+ 
+
+ align:start position:0%
+supposed to be a beaker that has fluid
+in it
+
+ align:start position:0%
+in it
+ 
+
+ align:start position:0%
+in it
+um this is also a beaker that has fluid
+
+ align:start position:0%
+um this is also a beaker that has fluid
+ 
+
+ align:start position:0%
+um this is also a beaker that has fluid
+in it and this is my uh electrode that
+
+ align:start position:0%
+in it and this is my uh electrode that
+ 
+
+ align:start position:0%
+in it and this is my uh electrode that
+is an anode in this case there is the uh
+
+ align:start position:0%
+is an anode in this case there is the uh
+ 
+
+ align:start position:0%
+is an anode in this case there is the uh
+anode there or the electrode there um
+
+ align:start position:0%
+anode there or the electrode there um
+ 
+
+ align:start position:0%
+anode there or the electrode there um
+here's another one that's the cathode
+
+ align:start position:0%
+here's another one that's the cathode
+ 
+
+ align:start position:0%
+here's another one that's the cathode
+another type of electrode it's over here
+
+ align:start position:0%
+another type of electrode it's over here
+ 
+
+ align:start position:0%
+another type of electrode it's over here
+this is my salt bridge the salt bridge
+
+ align:start position:0%
+this is my salt bridge the salt bridge
+ 
+
+ align:start position:0%
+this is my salt bridge the salt bridge
+here is this plastic tube and here I
+
+ align:start position:0%
+here is this plastic tube and here I
+ 
+
+ align:start position:0%
+here is this plastic tube and here I
+have a wire connecting my electrodes
+
+ align:start position:0%
+have a wire connecting my electrodes
+ 
+
+ align:start position:0%
+have a wire connecting my electrodes
+here you can't really see the wire but
+
+ align:start position:0%
+here you can't really see the wire but
+ 
+
+ align:start position:0%
+here you can't really see the wire but
+in both cases it goes through some kind
+
+ align:start position:0%
+in both cases it goes through some kind
+ 
+
+ align:start position:0%
+in both cases it goes through some kind
+of voltmeter that measures the electric
+
+ align:start position:0%
+of voltmeter that measures the electric
+ 
+
+ align:start position:0%
+of voltmeter that measures the electric
+electric current
+
+ align:start position:0%
+electric current
+ 
+
+ align:start position:0%
+electric current
+all right so now we'll get rid of this
+
+ align:start position:0%
+all right so now we'll get rid of this
+ 
+
+ align:start position:0%
+all right so now we'll get rid of this
+better picture but you can think about
+
+ align:start position:0%
+better picture but you can think about
+ 
+
+ align:start position:0%
+better picture but you can think about
+this picture as that picture if that
+
+ align:start position:0%
+this picture as that picture if that
+ 
+
+ align:start position:0%
+this picture as that picture if that
+helps and I always like to joke that you
+
+ align:start position:0%
+helps and I always like to joke that you
+ 
+
+ align:start position:0%
+helps and I always like to joke that you
+know you think you have it bad here at
+
+ align:start position:0%
+know you think you have it bad here at
+ 
+
+ align:start position:0%
+know you think you have it bad here at
+MIT in the old days um before you could
+
+ align:start position:0%
+MIT in the old days um before you could
+ 
+
+ align:start position:0%
+MIT in the old days um before you could
+do your problem set at 2 o'clock in the
+
+ align:start position:0%
+do your problem set at 2 o'clock in the
+ 
+
+ align:start position:0%
+do your problem set at 2 o'clock in the
+morning you had to build your own
+
+ align:start position:0%
+morning you had to build your own
+ 
+
+ align:start position:0%
+morning you had to build your own
+batteries um to be able to do it all
+
+ align:start position:0%
+batteries um to be able to do it all
+ 
+
+ align:start position:0%
+batteries um to be able to do it all
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+anode electrons are produced from
+
+ align:start position:0%
+anode electrons are produced from
+ 
+
+ align:start position:0%
+anode electrons are produced from
+oxidation at the anode so the electrons
+
+ align:start position:0%
+oxidation at the anode so the electrons
+ 
+
+ align:start position:0%
+oxidation at the anode so the electrons
+produced here flow out of the
+
+ align:start position:0%
+produced here flow out of the
+ 
+
+ align:start position:0%
+produced here flow out of the
+cell and in this particular type of
+
+ align:start position:0%
+cell and in this particular type of
+ 
+
+ align:start position:0%
+cell and in this particular type of
+electrochemical cell zinc solid is
+
+ align:start position:0%
+electrochemical cell zinc solid is
+ 
+
+ align:start position:0%
+electrochemical cell zinc solid is
+oxidized to zinc plus two so if we look
+
+ align:start position:0%
+oxidized to zinc plus two so if we look
+ 
+
+ align:start position:0%
+oxidized to zinc plus two so if we look
+at this over here this is my little
+
+ align:start position:0%
+at this over here this is my little
+ 
+
+ align:start position:0%
+at this over here this is my little
+beautiful uh depiction of the blow up of
+
+ align:start position:0%
+beautiful uh depiction of the blow up of
+ 
+
+ align:start position:0%
+beautiful uh depiction of the blow up of
+the of the electrode we have our zinc
+
+ align:start position:0%
+the of the electrode we have our zinc
+ 
+
+ align:start position:0%
+the of the electrode we have our zinc
+solid here and we have zinc plus two in
+
+ align:start position:0%
+solid here and we have zinc plus two in
+ 
+
+ align:start position:0%
+solid here and we have zinc plus two in
+aquous solution so when the electrons uh
+
+ align:start position:0%
+aquous solution so when the electrons uh
+ 
+
+ align:start position:0%
+aquous solution so when the electrons uh
+leave the zinc solid so that the zinc
+
+ align:start position:0%
+leave the zinc solid so that the zinc
+ 
+
+ align:start position:0%
+leave the zinc solid so that the zinc
+then uh leaves the electrode and goes
+
+ align:start position:0%
+then uh leaves the electrode and goes
+ 
+
+ align:start position:0%
+then uh leaves the electrode and goes
+into solution forming zinc plus two
+
+ align:start position:0%
+into solution forming zinc plus two
+ 
+
+ align:start position:0%
+into solution forming zinc plus two
+those electrons go out so the electrons
+
+ align:start position:0%
+those electrons go out so the electrons
+ 
+
+ align:start position:0%
+those electrons go out so the electrons
+will then go into the cathode and notice
+
+ align:start position:0%
+will then go into the cathode and notice
+ 
+
+ align:start position:0%
+will then go into the cathode and notice
+I had a typo in the handout I find this
+
+ align:start position:0%
+I had a typo in the handout I find this
+ 
+
+ align:start position:0%
+I had a typo in the handout I find this
+kind pretty funny I don't know if it's
+
+ align:start position:0%
+kind pretty funny I don't know if it's
+ 
+
+ align:start position:0%
+kind pretty funny I don't know if it's
+me or spell check right now I wrote
+
+ align:start position:0%
+me or spell check right now I wrote
+ 
+
+ align:start position:0%
+me or spell check right now I wrote
+elections are uh consumed oh man it's
+
+ align:start position:0%
+elections are uh consumed oh man it's
+ 
+
+ align:start position:0%
+elections are uh consumed oh man it's
+been a long week between the national
+
+ align:start position:0%
+been a long week between the national
+ 
+
+ align:start position:0%
+been a long week between the national
+elections and our t-shirt elections um
+
+ align:start position:0%
+elections and our t-shirt elections um
+ 
+
+ align:start position:0%
+elections and our t-shirt elections um
+anyway I didn't mean elections I meant
+
+ align:start position:0%
+anyway I didn't mean elections I meant
+ 
+
+ align:start position:0%
+anyway I didn't mean elections I meant
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+yes of course electrons are consumed by
+
+ align:start position:0%
+yes of course electrons are consumed by
+ 
+
+ align:start position:0%
+yes of course electrons are consumed by
+a reduction
+
+ align:start position:0%
+a reduction
+ 
+
+ align:start position:0%
+a reduction
+reaction of course I noticed that after
+
+ align:start position:0%
+reaction of course I noticed that after
+ 
+
+ align:start position:0%
+reaction of course I noticed that after
+I had printed hundreds of copies okay um
+
+ align:start position:0%
+I had printed hundreds of copies okay um
+ 
+
+ align:start position:0%
+I had printed hundreds of copies okay um
+and this particular reaction here copper
+
+ align:start position:0%
+and this particular reaction here copper
+ 
+
+ align:start position:0%
+and this particular reaction here copper
+plus two is reduced to Copper solid and
+
+ align:start position:0%
+plus two is reduced to Copper solid and
+ 
+
+ align:start position:0%
+plus two is reduced to Copper solid and
+if we look over here we have copper plus
+
+ align:start position:0%
+if we look over here we have copper plus
+ 
+
+ align:start position:0%
+if we look over here we have copper plus
+two in aquous solution when electrons
+
+ align:start position:0%
+two in aquous solution when electrons
+ 
+
+ align:start position:0%
+two in aquous solution when electrons
+two electrons come in those two
+
+ align:start position:0%
+two electrons come in those two
+ 
+
+ align:start position:0%
+two electrons come in those two
+electrons go to the Copper plus two and
+
+ align:start position:0%
+electrons go to the Copper plus two and
+ 
+
+ align:start position:0%
+electrons go to the Copper plus two and
+reduce it to copper solid and the copper
+
+ align:start position:0%
+reduce it to copper solid and the copper
+ 
+
+ align:start position:0%
+reduce it to copper solid and the copper
+solid actually plates on the
+
+ align:start position:0%
+solid actually plates on the
+ 
+
+ align:start position:0%
+solid actually plates on the
+electrode so we can measure the flow we
+
+ align:start position:0%
+electrode so we can measure the flow we
+ 
+
+ align:start position:0%
+electrode so we can measure the flow we
+can have a meter that measures the volts
+
+ align:start position:0%
+can have a meter that measures the volts
+ 
+
+ align:start position:0%
+can have a meter that measures the volts
+or the flow of electrons the electron
+
+ align:start position:0%
+or the flow of electrons the electron
+ 
+
+ align:start position:0%
+or the flow of electrons the electron
+current and also what's that salt bridge
+
+ align:start position:0%
+current and also what's that salt bridge
+ 
+
+ align:start position:0%
+current and also what's that salt bridge
+doing well the salt bridge can help
+
+ align:start position:0%
+doing well the salt bridge can help
+ 
+
+ align:start position:0%
+doing well the salt bridge can help
+maintain the neutrality in the system
+
+ align:start position:0%
+maintain the neutrality in the system
+ 
+
+ align:start position:0%
+maintain the neutrality in the system
+because over here we're generating plus
+
+ align:start position:0%
+because over here we're generating plus
+ 
+
+ align:start position:0%
+because over here we're generating plus
+charge and over here we're losing pris
+
+ align:start position:0%
+charge and over here we're losing pris
+ 
+
+ align:start position:0%
+charge and over here we're losing pris
+charge and so ions can flow through the
+
+ align:start position:0%
+charge and so ions can flow through the
+ 
+
+ align:start position:0%
+charge and so ions can flow through the
+salt bridge and keep the charges more
+
+ align:start position:0%
+salt bridge and keep the charges more
+ 
+
+ align:start position:0%
+salt bridge and keep the charges more
+similar in our two different
+
+ align:start position:0%
+similar in our two different
+ 
+
+ align:start position:0%
+similar in our two different
+beakers all right so I know my pictures
+
+ align:start position:0%
+beakers all right so I know my pictures
+ 
+
+ align:start position:0%
+beakers all right so I know my pictures
+are gorgeous but I have a little
+
+ align:start position:0%
+are gorgeous but I have a little
+ 
+
+ align:start position:0%
+are gorgeous but I have a little
+animation to show you um that um will
+
+ align:start position:0%
+animation to show you um that um will
+ 
+
+ align:start position:0%
+animation to show you um that um will
+also show you what I was talking about
+
+ align:start position:0%
+also show you what I was talking about
+ 
+
+ align:start position:0%
+also show you what I was talking about
+oxidation at the electrode so zinc um
+
+ align:start position:0%
+oxidation at the electrode so zinc um
+ 
+
+ align:start position:0%
+oxidation at the electrode so zinc um
+zinc solid is going to lose electrons
+
+ align:start position:0%
+zinc solid is going to lose electrons
+ 
+
+ align:start position:0%
+zinc solid is going to lose electrons
+and form zinc plus two and let me just
+
+ align:start position:0%
+and form zinc plus two and let me just
+ 
+
+ align:start position:0%
+and form zinc plus two and let me just
+show you that
+
+ align:start position:0%
+show you that
+ 
+
+ align:start position:0%
+show you that
+happening so there are the electrons
+
+ align:start position:0%
+happening so there are the electrons
+ 
+
+ align:start position:0%
+happening so there are the electrons
+going away and here is zinc popping off
+
+ align:start position:0%
+going away and here is zinc popping off
+ 
+
+ align:start position:0%
+going away and here is zinc popping off
+as zinc plus
+
+ align:start position:0%
+as zinc plus
+ 
+
+ align:start position:0%
+as zinc plus
+two and then the zinc plus two is going
+
+ align:start position:0%
+two and then the zinc plus two is going
+ 
+
+ align:start position:0%
+two and then the zinc plus two is going
+to be in solution so there are the
+
+ align:start position:0%
+to be in solution so there are the
+ 
+
+ align:start position:0%
+to be in solution so there are the
+electrons go again and the zinc solid
+
+ align:start position:0%
+electrons go again and the zinc solid
+ 
+
+ align:start position:0%
+electrons go again and the zinc solid
+pops off as zinc plus
+
+ align:start position:0%
+pops off as zinc plus
+ 
+
+ align:start position:0%
+pops off as zinc plus
+two all right so now let's consider
+
+ align:start position:0%
+two all right so now let's consider
+ 
+
+ align:start position:0%
+two all right so now let's consider
+reduction at the cathode so here we have
+
+ align:start position:0%
+reduction at the cathode so here we have
+ 
+
+ align:start position:0%
+reduction at the cathode so here we have
+our copper solid here we have a copper
+
+ align:start position:0%
+our copper solid here we have a copper
+ 
+
+ align:start position:0%
+our copper solid here we have a copper
+plus two and here the electrons are
+
+ align:start position:0%
+plus two and here the electrons are
+ 
+
+ align:start position:0%
+plus two and here the electrons are
+going to come in and um join up with our
+
+ align:start position:0%
+going to come in and um join up with our
+ 
+
+ align:start position:0%
+going to come in and um join up with our
+copper plus two and it's going to plate
+
+ align:start position:0%
+copper plus two and it's going to plate
+ 
+
+ align:start position:0%
+copper plus two and it's going to plate
+on to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrode there come the electrons there
+
+ align:start position:0%
+electrode there come the electrons there
+ 
+
+ align:start position:0%
+electrode there come the electrons there
+they come
+
+ align:start position:0%
+they come
+ 
+
+ align:start position:0%
+they come
+again and now we have added solid copper
+
+ align:start position:0%
+again and now we have added solid copper
+ 
+
+ align:start position:0%
+again and now we have added solid copper
+to our electrod and just one more time
+
+ align:start position:0%
+to our electrod and just one more time
+ 
+
+ align:start position:0%
+to our electrod and just one more time
+and I think it's so cool that we can
+
+ align:start position:0%
+and I think it's so cool that we can
+ 
+
+ align:start position:0%
+and I think it's so cool that we can
+just watch those electrons move like
+
+ align:start position:0%
+just watch those electrons move like
+ 
+
+ align:start position:0%
+just watch those electrons move like
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so there's our
+
+ align:start position:0%
+okay all right so there's our
+ 
+
+ align:start position:0%
+okay all right so there's our
+electrochemical cell where we have an
+
+ align:start position:0%
+electrochemical cell where we have an
+ 
+
+ align:start position:0%
+electrochemical cell where we have an
+oxidation and a reduction
+
+ align:start position:0%
+oxidation and a reduction
+ 
+
+ align:start position:0%
+oxidation and a reduction
+reaction um instead of drawing this
+
+ align:start position:0%
+reaction um instead of drawing this
+ 
+
+ align:start position:0%
+reaction um instead of drawing this
+admittedly beautiful picture every time
+
+ align:start position:0%
+admittedly beautiful picture every time
+ 
+
+ align:start position:0%
+admittedly beautiful picture every time
+we can have a shorthand representation
+
+ align:start position:0%
+we can have a shorthand representation
+ 
+
+ align:start position:0%
+we can have a shorthand representation
+for this so we can say um zinc solid and
+
+ align:start position:0%
+for this so we can say um zinc solid and
+ 
+
+ align:start position:0%
+for this so we can say um zinc solid and
+then we have a little line here that
+
+ align:start position:0%
+then we have a little line here that
+ 
+
+ align:start position:0%
+then we have a little line here that
+little line indicates we have a phase
+
+ align:start position:0%
+little line indicates we have a phase
+ 
+
+ align:start position:0%
+little line indicates we have a phase
+boundary so that means we're going from
+
+ align:start position:0%
+boundary so that means we're going from
+ 
+
+ align:start position:0%
+boundary so that means we're going from
+solid to a different phase and in this
+
+ align:start position:0%
+solid to a different phase and in this
+ 
+
+ align:start position:0%
+solid to a different phase and in this
+case we're going to aquous so solid zinc
+
+ align:start position:0%
+case we're going to aquous so solid zinc
+ 
+
+ align:start position:0%
+case we're going to aquous so solid zinc
+to zinc plus 2
+
+ align:start position:0%
+to zinc plus 2
+ 
+
+ align:start position:0%
+to zinc plus 2
+the two lines here indicate the salt
+
+ align:start position:0%
+the two lines here indicate the salt
+ 
+
+ align:start position:0%
+the two lines here indicate the salt
+bridge so this tells us that the
+
+ align:start position:0%
+bridge so this tells us that the
+ 
+
+ align:start position:0%
+bridge so this tells us that the
+reaction on this side is in one Beaker
+
+ align:start position:0%
+reaction on this side is in one Beaker
+ 
+
+ align:start position:0%
+reaction on this side is in one Beaker
+and the reaction on this side is in our
+
+ align:start position:0%
+and the reaction on this side is in our
+ 
+
+ align:start position:0%
+and the reaction on this side is in our
+other Beaker the reaction in the other
+
+ align:start position:0%
+other Beaker the reaction in the other
+ 
+
+ align:start position:0%
+other Beaker the reaction in the other
+side is copper plus two aquous a single
+
+ align:start position:0%
+side is copper plus two aquous a single
+ 
+
+ align:start position:0%
+side is copper plus two aquous a single
+line for phase boundary going to Copper
+
+ align:start position:0%
+line for phase boundary going to Copper
+ 
+
+ align:start position:0%
+line for phase boundary going to Copper
+solid now if we had say two aquous
+
+ align:start position:0%
+solid now if we had say two aquous
+ 
+
+ align:start position:0%
+solid now if we had say two aquous
+species we wouldn't have a phase
+
+ align:start position:0%
+species we wouldn't have a phase
+ 
+
+ align:start position:0%
+species we wouldn't have a phase
+boundary we' just have a comma but if
+
+ align:start position:0%
+boundary we' just have a comma but if
+ 
+
+ align:start position:0%
+boundary we' just have a comma but if
+you have a phase boundary you get the
+
+ align:start position:0%
+you have a phase boundary you get the
+ 
+
+ align:start position:0%
+you have a phase boundary you get the
+line all right so let's uh a click our
+
+ align:start position:0%
+line all right so let's uh a click our
+ 
+
+ align:start position:0%
+line all right so let's uh a click our
+comp I Let's uh consider another cell it
+
+ align:start position:0%
+comp I Let's uh consider another cell it
+ 
+
+ align:start position:0%
+comp I Let's uh consider another cell it
+still has zinc but now it has tin why
+
+ align:start position:0%
+still has zinc but now it has tin why
+ 
+
+ align:start position:0%
+still has zinc but now it has tin why
+don't you uh tell me which reaction is
+
+ align:start position:0%
+don't you uh tell me which reaction is
+ 
+
+ align:start position:0%
+don't you uh tell me which reaction is
+at the anode and which reaction is at
+
+ align:start position:0%
+at the anode and which reaction is at
+ 
+
+ align:start position:0%
+at the anode and which reaction is at
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cathode and also which of those is
+
+ align:start position:0%
+cathode and also which of those is
+ 
+
+ align:start position:0%
+cathode and also which of those is
+oxidations and which is reductions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right we'll just do 10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds great okay so uh some of these
+
+ align:start position:0%
+seconds great okay so uh some of these
+ 
+
+ align:start position:0%
+seconds great okay so uh some of these
+had parts of it right but there was a
+
+ align:start position:0%
+had parts of it right but there was a
+ 
+
+ align:start position:0%
+had parts of it right but there was a
+mistake we have an ox so that is wrong
+
+ align:start position:0%
+mistake we have an ox so that is wrong
+ 
+
+ align:start position:0%
+mistake we have an ox so that is wrong
+um so you have to pay attention to
+
+ align:start position:0%
+um so you have to pay attention to
+ 
+
+ align:start position:0%
+um so you have to pay attention to
+whether these match and then also that
+
+ align:start position:0%
+whether these match and then also that
+ 
+
+ align:start position:0%
+whether these match and then also that
+the reaction is written consistent with
+
+ align:start position:0%
+the reaction is written consistent with
+ 
+
+ align:start position:0%
+the reaction is written consistent with
+the word so only number two had all the
+
+ align:start position:0%
+the word so only number two had all the
+ 
+
+ align:start position:0%
+the word so only number two had all the
+various different parts right okay so we
+
+ align:start position:0%
+various different parts right okay so we
+ 
+
+ align:start position:0%
+various different parts right okay so we
+can come back here and you can enter so
+
+ align:start position:0%
+can come back here and you can enter so
+ 
+
+ align:start position:0%
+can come back here and you can enter so
+the reaction at the anode was the zinc
+
+ align:start position:0%
+the reaction at the anode was the zinc
+ 
+
+ align:start position:0%
+the reaction at the anode was the zinc
+reaction and that is an oxidation an ox
+
+ align:start position:0%
+reaction and that is an oxidation an ox
+ 
+
+ align:start position:0%
+reaction and that is an oxidation an ox
+the reaction at the cathode is the 10
+
+ align:start position:0%
+the reaction at the cathode is the 10
+ 
+
+ align:start position:0%
+the reaction at the cathode is the 10
+reaction um 10+ 4 two electrons 10 plus
+
+ align:start position:0%
+reaction um 10+ 4 two electrons 10 plus
+ 
+
+ align:start position:0%
+reaction um 10+ 4 two electrons 10 plus
+2 aquous and that's a reduction and
+
+ align:start position:0%
+2 aquous and that's a reduction and
+ 
+
+ align:start position:0%
+2 aquous and that's a reduction and
+while you have uh your clickers out why
+
+ align:start position:0%
+while you have uh your clickers out why
+ 
+
+ align:start position:0%
+while you have uh your clickers out why
+not don't you tell me how you would
+
+ align:start position:0%
+not don't you tell me how you would
+ 
+
+ align:start position:0%
+not don't you tell me how you would
+represent that electrochemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell all right let's just do 10 more
+
+ align:start position:0%
+cell all right let's just do 10 more
+ 
+
+ align:start position:0%
+cell all right let's just do 10 more
+seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M so right so I mentioned this very
+
+ align:start position:0%
+M so right so I mentioned this very
+ 
+
+ align:start position:0%
+M so right so I mentioned this very
+briefly this was my tricky clicker
+
+ align:start position:0%
+briefly this was my tricky clicker
+ 
+
+ align:start position:0%
+briefly this was my tricky clicker
+question because it's a
+
+ align:start position:0%
+question because it's a
+ 
+
+ align:start position:0%
+question because it's a
+competition so there's no phase
+
+ align:start position:0%
+competition so there's no phase
+ 
+
+ align:start position:0%
+competition so there's no phase
+transition here so you have a
+
+ align:start position:0%
+transition here so you have a
+ 
+
+ align:start position:0%
+transition here so you have a
+comma and the top one a few people put
+
+ align:start position:0%
+comma and the top one a few people put
+ 
+
+ align:start position:0%
+comma and the top one a few people put
+down but it's not it's not uh solid here
+
+ align:start position:0%
+down but it's not it's not uh solid here
+ 
+
+ align:start position:0%
+down but it's not it's not uh solid here
+so that one is is not correct okay so
+
+ align:start position:0%
+so that one is is not correct okay so
+ 
+
+ align:start position:0%
+so that one is is not correct okay so
+here you can write down in your notes
+
+ align:start position:0%
+here you can write down in your notes
+ 
+
+ align:start position:0%
+here you can write down in your notes
+you have the zinc um phase transition
+
+ align:start position:0%
+you have the zinc um phase transition
+ 
+
+ align:start position:0%
+you have the zinc um phase transition
+zinc plus two aquous and then we have
+
+ align:start position:0%
+zinc plus two aquous and then we have
+ 
+
+ align:start position:0%
+zinc plus two aquous and then we have
+our salt bridge zinc plus 4 aquous comma
+
+ align:start position:0%
+our salt bridge zinc plus 4 aquous comma
+ 
+
+ align:start position:0%
+our salt bridge zinc plus 4 aquous comma
+or SN 10 plus 4 comma 10 + 2 and now
+
+ align:start position:0%
+or SN 10 plus 4 comma 10 + 2 and now
+ 
+
+ align:start position:0%
+or SN 10 plus 4 comma 10 + 2 and now
+we're ready for
+
+ align:start position:0%
+we're ready for
+ 
+
+ align:start position:0%
+we're ready for
+winners we'll see if Sam's also ready to
+
+ align:start position:0%
+winners we'll see if Sam's also ready to
+ 
+
+ align:start position:0%
+winners we'll see if Sam's also ready to
+present the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+winners all
+
+ align:start position:0%
+winners all
+ 
+
+ align:start position:0%
+winners all
+right we need strategy to defeat Dan's
+
+ align:start position:0%
+right we need strategy to defeat Dan's
+ 
+
+ align:start position:0%
+right we need strategy to defeat Dan's
+recitation but we know what t-shirt
+
+ align:start position:0%
+recitation but we know what t-shirt
+ 
+
+ align:start position:0%
+recitation but we know what t-shirt
+we're playing for now all right have a
+
+ align:start position:0%
+we're playing for now all right have a
+ 
+
+ align:start position:0%
+we're playing for now all right have a
+great weekend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody all right let's just uh take
+
+ align:start position:0%
+everybody all right let's just uh take
+ 
+
+ align:start position:0%
+everybody all right let's just uh take
+10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right does someone want to tell me
+
+ align:start position:0%
+all right does someone want to tell me
+ 
+
+ align:start position:0%
+all right does someone want to tell me
+how they got the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep you know that your hydrogen will
+
+ align:start position:0%
+yep you know that your hydrogen will
+ 
+
+ align:start position:0%
+yep you know that your hydrogen will
+have a plus one charge and your oxygen
+
+ align:start position:0%
+have a plus one charge and your oxygen
+ 
+
+ align:start position:0%
+have a plus one charge and your oxygen
+will have a minus two charge because
+
+ align:start position:0%
+will have a minus two charge because
+ 
+
+ align:start position:0%
+will have a minus two charge because
+it's not a peroxide and you know your SU
+
+ align:start position:0%
+it's not a peroxide and you know your SU
+ 
+
+ align:start position:0%
+it's not a peroxide and you know your SU
+is going to be neutral so you add one
+
+ align:start position:0%
+is going to be neutral so you add one
+ 
+
+ align:start position:0%
+is going to be neutral so you add one
+yep that's right so this one um chlorine
+
+ align:start position:0%
+yep that's right so this one um chlorine
+ 
+
+ align:start position:0%
+yep that's right so this one um chlorine
+is usually minus one the exception is
+
+ align:start position:0%
+is usually minus one the exception is
+ 
+
+ align:start position:0%
+is usually minus one the exception is
+when it's with oxygen and so oxygen is
+
+ align:start position:0%
+when it's with oxygen and so oxygen is
+ 
+
+ align:start position:0%
+when it's with oxygen and so oxygen is
+always minus two unless it's in a
+
+ align:start position:0%
+always minus two unless it's in a
+ 
+
+ align:start position:0%
+always minus two unless it's in a
+peroxide or super oxide and hydrogen's
+
+ align:start position:0%
+peroxide or super oxide and hydrogen's
+ 
+
+ align:start position:0%
+peroxide or super oxide and hydrogen's
+always plus one except when it's with a
+
+ align:start position:0%
+always plus one except when it's with a
+ 
+
+ align:start position:0%
+always plus one except when it's with a
+metal like sodium um something group one
+
+ align:start position:0%
+metal like sodium um something group one
+ 
+
+ align:start position:0%
+metal like sodium um something group one
+or group two okay so today take out
+
+ align:start position:0%
+or group two okay so today take out
+ 
+
+ align:start position:0%
+or group two okay so today take out
+lecture 25 notes we're just going to
+
+ align:start position:0%
+lecture 25 notes we're just going to
+ 
+
+ align:start position:0%
+lecture 25 notes we're just going to
+wrap those notes up that shouldn't take
+
+ align:start position:0%
+wrap those notes up that shouldn't take
+ 
+
+ align:start position:0%
+wrap those notes up that shouldn't take
+too long and then keep going with
+
+ align:start position:0%
+too long and then keep going with
+ 
+
+ align:start position:0%
+too long and then keep going with
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+26 so we are talking about this cell and
+
+ align:start position:0%
+26 so we are talking about this cell and
+ 
+
+ align:start position:0%
+26 so we are talking about this cell and
+we're going to talk about this
+
+ align:start position:0%
+we're going to talk about this
+ 
+
+ align:start position:0%
+we're going to talk about this
+electrochemical cell a lot um so we had
+
+ align:start position:0%
+electrochemical cell a lot um so we had
+ 
+
+ align:start position:0%
+electrochemical cell a lot um so we had
+uh zinc on one side Zinc at the anode
+
+ align:start position:0%
+uh zinc on one side Zinc at the anode
+ 
+
+ align:start position:0%
+uh zinc on one side Zinc at the anode
+and the zinc was uh being oxidized
+
+ align:start position:0%
+and the zinc was uh being oxidized
+ 
+
+ align:start position:0%
+and the zinc was uh being oxidized
+generating electrons which come around
+
+ align:start position:0%
+generating electrons which come around
+ 
+
+ align:start position:0%
+generating electrons which come around
+to the copper and then the copper plus
+
+ align:start position:0%
+to the copper and then the copper plus
+ 
+
+ align:start position:0%
+to the copper and then the copper plus
+two ions were being reduced to Copper
+
+ align:start position:0%
+two ions were being reduced to Copper
+ 
+
+ align:start position:0%
+two ions were being reduced to Copper
+solid so the zinc um anode was being
+
+ align:start position:0%
+solid so the zinc um anode was being
+ 
+
+ align:start position:0%
+solid so the zinc um anode was being
+consumed and the copper cathode had
+
+ align:start position:0%
+consumed and the copper cathode had
+ 
+
+ align:start position:0%
+consumed and the copper cathode had
+copper solid being plated onto it so
+
+ align:start position:0%
+copper solid being plated onto it so
+ 
+
+ align:start position:0%
+copper solid being plated onto it so
+Faraday's law says that the amount at
+
+ align:start position:0%
+Faraday's law says that the amount at
+ 
+
+ align:start position:0%
+Faraday's law says that the amount at
+which an anode like the zinc anode is
+
+ align:start position:0%
+which an anode like the zinc anode is
+ 
+
+ align:start position:0%
+which an anode like the zinc anode is
+consumed and the amount of copper that
+
+ align:start position:0%
+consumed and the amount of copper that
+ 
+
+ align:start position:0%
+consumed and the amount of copper that
+gets plated on uh at the cathode is
+
+ align:start position:0%
+gets plated on uh at the cathode is
+ 
+
+ align:start position:0%
+gets plated on uh at the cathode is
+proportional to the charge that passes
+
+ align:start position:0%
+proportional to the charge that passes
+ 
+
+ align:start position:0%
+proportional to the charge that passes
+through the system so according to
+
+ align:start position:0%
+through the system so according to
+ 
+
+ align:start position:0%
+through the system so according to
+Faraday's law there's a proportionality
+
+ align:start position:0%
+Faraday's law there's a proportionality
+ 
+
+ align:start position:0%
+Faraday's law there's a proportionality
+between the consumption and uh also
+
+ align:start position:0%
+between the consumption and uh also
+ 
+
+ align:start position:0%
+between the consumption and uh also
+depositing of metal and the amount of
+
+ align:start position:0%
+depositing of metal and the amount of
+ 
+
+ align:start position:0%
+depositing of metal and the amount of
+charge going through the system so we
+
+ align:start position:0%
+charge going through the system so we
+ 
+
+ align:start position:0%
+charge going through the system so we
+can think about how much uh zinc is
+
+ align:start position:0%
+can think about how much uh zinc is
+ 
+
+ align:start position:0%
+can think about how much uh zinc is
+consumed and how much copper is
+
+ align:start position:0%
+consumed and how much copper is
+ 
+
+ align:start position:0%
+consumed and how much copper is
+deposited on its Ano on its cathode or
+
+ align:start position:0%
+deposited on its Ano on its cathode or
+ 
+
+ align:start position:0%
+deposited on its Ano on its cathode or
+its electrode um if the current if you
+
+ align:start position:0%
+its electrode um if the current if you
+ 
+
+ align:start position:0%
+its electrode um if the current if you
+have a current of one amp um flowing for
+
+ align:start position:0%
+have a current of one amp um flowing for
+ 
+
+ align:start position:0%
+have a current of one amp um flowing for
+one hour so let's just take a look at
+
+ align:start position:0%
+one hour so let's just take a look at
+ 
+
+ align:start position:0%
+one hour so let's just take a look at
+how we do a problem like this first step
+
+ align:start position:0%
+how we do a problem like this first step
+ 
+
+ align:start position:0%
+how we do a problem like this first step
+is we want to think about uh calculate
+
+ align:start position:0%
+is we want to think about uh calculate
+ 
+
+ align:start position:0%
+is we want to think about uh calculate
+the charge that's going through the the
+
+ align:start position:0%
+the charge that's going through the the
+ 
+
+ align:start position:0%
+the charge that's going through the the
+system and so Q here we have another q
+
+ align:start position:0%
+system and so Q here we have another q
+ 
+
+ align:start position:0%
+system and so Q here we have another q
+um not the reaction quotient but the
+
+ align:start position:0%
+um not the reaction quotient but the
+ 
+
+ align:start position:0%
+um not the reaction quotient but the
+magnitude of the charge and that's in
+
+ align:start position:0%
+magnitude of the charge and that's in
+ 
+
+ align:start position:0%
+magnitude of the charge and that's in
+kums and that's going to be equal to the
+
+ align:start position:0%
+kums and that's going to be equal to the
+ 
+
+ align:start position:0%
+kums and that's going to be equal to the
+current times the time so we have the
+
+ align:start position:0%
+current times the time so we have the
+ 
+
+ align:start position:0%
+current times the time so we have the
+current I and the current is in amps and
+
+ align:start position:0%
+current I and the current is in amps and
+ 
+
+ align:start position:0%
+current I and the current is in amps and
+T is in seconds and conveniently um amps
+
+ align:start position:0%
+T is in seconds and conveniently um amps
+ 
+
+ align:start position:0%
+T is in seconds and conveniently um amps
+equal kums per second so this equation
+
+ align:start position:0%
+equal kums per second so this equation
+ 
+
+ align:start position:0%
+equal kums per second so this equation
+works out our units uh will work out so
+
+ align:start position:0%
+works out our units uh will work out so
+ 
+
+ align:start position:0%
+works out our units uh will work out so
+Q is going to be equal to we have 1.08
+
+ align:start position:0%
+Q is going to be equal to we have 1.08
+ 
+
+ align:start position:0%
+Q is going to be equal to we have 1.08
+amps um and it was 1 hour so that's uh
+
+ align:start position:0%
+amps um and it was 1 hour so that's uh
+ 
+
+ align:start position:0%
+amps um and it was 1 hour so that's uh
+3,600 seconds or
+
+ align:start position:0%
+3,600 seconds or
+ 
+
+ align:start position:0%
+3,600 seconds or
+3,600 kums because we have an amp times
+
+ align:start position:0%
+3,600 kums because we have an amp times
+ 
+
+ align:start position:0%
+3,600 kums because we have an amp times
+second um and then here we have this
+
+ align:start position:0%
+second um and then here we have this
+ 
+
+ align:start position:0%
+second um and then here we have this
+number of kums and now we want to
+
+ align:start position:0%
+number of kums and now we want to
+ 
+
+ align:start position:0%
+number of kums and now we want to
+convert to the number of moles of
+
+ align:start position:0%
+convert to the number of moles of
+ 
+
+ align:start position:0%
+convert to the number of moles of
+electrons that that is equivalent to
+
+ align:start position:0%
+electrons that that is equivalent to
+ 
+
+ align:start position:0%
+electrons that that is equivalent to
+that that charge in koloms is equivalent
+
+ align:start position:0%
+that that charge in koloms is equivalent
+ 
+
+ align:start position:0%
+that that charge in koloms is equivalent
+to and here our Faraday constant is our
+
+ align:start position:0%
+to and here our Faraday constant is our
+ 
+
+ align:start position:0%
+to and here our Faraday constant is our
+conversion Factor so Faraday is constant
+
+ align:start position:0%
+conversion Factor so Faraday is constant
+ 
+
+ align:start position:0%
+conversion Factor so Faraday is constant
+we have um
+
+ align:start position:0%
+we have um
+ 
+
+ align:start position:0%
+we have um
+9648 kums per mole is one Faraday and
+
+ align:start position:0%
+9648 kums per mole is one Faraday and
+ 
+
+ align:start position:0%
+9648 kums per mole is one Faraday and
+it's this kind of funny looking F over
+
+ align:start position:0%
+it's this kind of funny looking F over
+ 
+
+ align:start position:0%
+it's this kind of funny looking F over
+here so we have our kums so we can use
+
+ align:start position:0%
+here so we have our kums so we can use
+ 
+
+ align:start position:0%
+here so we have our kums so we can use
+now the feraday constant to convert and
+
+ align:start position:0%
+now the feraday constant to convert and
+ 
+
+ align:start position:0%
+now the feraday constant to convert and
+we get
+
+ align:start position:0%
+we get
+ 
+
+ align:start position:0%
+we get
+0373 moles of electrons so that's the
+
+ align:start position:0%
+0373 moles of electrons so that's the
+ 
+
+ align:start position:0%
+0373 moles of electrons so that's the
+number of moles of electrons that would
+
+ align:start position:0%
+number of moles of electrons that would
+ 
+
+ align:start position:0%
+number of moles of electrons that would
+be going through our system that
+
+ align:start position:0%
+be going through our system that
+ 
+
+ align:start position:0%
+be going through our system that
+correspond to that amount of charge
+
+ align:start position:0%
+correspond to that amount of charge
+ 
+
+ align:start position:0%
+correspond to that amount of charge
+all right so now we need to relate this
+
+ align:start position:0%
+all right so now we need to relate this
+ 
+
+ align:start position:0%
+all right so now we need to relate this
+back to the zinc and the copper so step
+
+ align:start position:0%
+back to the zinc and the copper so step
+ 
+
+ align:start position:0%
+back to the zinc and the copper so step
+three we want to know first the number
+
+ align:start position:0%
+three we want to know first the number
+ 
+
+ align:start position:0%
+three we want to know first the number
+of moles of the zinc and copper involved
+
+ align:start position:0%
+of moles of the zinc and copper involved
+ 
+
+ align:start position:0%
+of moles of the zinc and copper involved
+and then convert that to grams because
+
+ align:start position:0%
+and then convert that to grams because
+ 
+
+ align:start position:0%
+and then convert that to grams because
+the problem ask us for
+
+ align:start position:0%
+the problem ask us for
+ 
+
+ align:start position:0%
+the problem ask us for
+grams so we have the number of moles of
+
+ align:start position:0%
+grams so we have the number of moles of
+ 
+
+ align:start position:0%
+grams so we have the number of moles of
+electrons that are going through the
+
+ align:start position:0%
+electrons that are going through the
+ 
+
+ align:start position:0%
+electrons that are going through the
+system and so for every one mole of zinc
+
+ align:start position:0%
+system and so for every one mole of zinc
+ 
+
+ align:start position:0%
+system and so for every one mole of zinc
+consumed how many electrons go into the
+
+ align:start position:0%
+consumed how many electrons go into the
+ 
+
+ align:start position:0%
+consumed how many electrons go into the
+system what's the ratio one two how many
+
+ align:start position:0%
+system what's the ratio one two how many
+ 
+
+ align:start position:0%
+system what's the ratio one two how many
+elect
+
+ align:start position:0%
+elect
+ 
+
+ align:start position:0%
+elect
+R so one zinc solid going to one zinc
+
+ align:start position:0%
+R so one zinc solid going to one zinc
+ 
+
+ align:start position:0%
+R so one zinc solid going to one zinc
+plus two so that's going to be two moles
+
+ align:start position:0%
+plus two so that's going to be two moles
+ 
+
+ align:start position:0%
+plus two so that's going to be two moles
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons and then we need to look up
+
+ align:start position:0%
+electrons and then we need to look up
+ 
+
+ align:start position:0%
+electrons and then we need to look up
+how are we going to convert our moles to
+
+ align:start position:0%
+how are we going to convert our moles to
+ 
+
+ align:start position:0%
+how are we going to convert our moles to
+grams what are we looking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up y m Mass molecular weight atomic mass
+
+ align:start position:0%
+up y m Mass molecular weight atomic mass
+ 
+
+ align:start position:0%
+up y m Mass molecular weight atomic mass
+um so we in our periodic table grams per
+
+ align:start position:0%
+um so we in our periodic table grams per
+ 
+
+ align:start position:0%
+um so we in our periodic table grams per
+mole and so we get 1.2 grams here when
+
+ align:start position:0%
+mole and so we get 1.2 grams here when
+ 
+
+ align:start position:0%
+mole and so we get 1.2 grams here when
+for this equation all right so for
+
+ align:start position:0%
+for this equation all right so for
+ 
+
+ align:start position:0%
+for this equation all right so for
+copper so we have the same number of
+
+ align:start position:0%
+copper so we have the same number of
+ 
+
+ align:start position:0%
+copper so we have the same number of
+moles of electrons that are going
+
+ align:start position:0%
+moles of electrons that are going
+ 
+
+ align:start position:0%
+moles of electrons that are going
+through the system so for every one mole
+
+ align:start position:0%
+through the system so for every one mole
+ 
+
+ align:start position:0%
+through the system so for every one mole
+of copper solid deposited on its
+
+ align:start position:0%
+of copper solid deposited on its
+ 
+
+ align:start position:0%
+of copper solid deposited on its
+electrode how many moles of electrons
+
+ align:start position:0%
+electrode how many moles of electrons
+ 
+
+ align:start position:0%
+electrode how many moles of electrons
+have to come into the
+
+ align:start position:0%
+have to come into the
+ 
+
+ align:start position:0%
+have to come into the
+system louder two yes so that's two as
+
+ align:start position:0%
+system louder two yes so that's two as
+ 
+
+ align:start position:0%
+system louder two yes so that's two as
+well and then we look up again in the
+
+ align:start position:0%
+well and then we look up again in the
+ 
+
+ align:start position:0%
+well and then we look up again in the
+periodic table the uh atomic weight
+
+ align:start position:0%
+periodic table the uh atomic weight
+ 
+
+ align:start position:0%
+periodic table the uh atomic weight
+molecular weight um and it's almost the
+
+ align:start position:0%
+molecular weight um and it's almost the
+ 
+
+ align:start position:0%
+molecular weight um and it's almost the
+same copper and zinc so to the number of
+
+ align:start position:0%
+same copper and zinc so to the number of
+ 
+
+ align:start position:0%
+same copper and zinc so to the number of
+significant figures it's the same amount
+
+ align:start position:0%
+significant figures it's the same amount
+ 
+
+ align:start position:0%
+significant figures it's the same amount
+of grams now this will not always be the
+
+ align:start position:0%
+of grams now this will not always be the
+ 
+
+ align:start position:0%
+of grams now this will not always be the
+case um they're just very close to each
+
+ align:start position:0%
+case um they're just very close to each
+ 
+
+ align:start position:0%
+case um they're just very close to each
+other in uh in their molecular or atomic
+
+ align:start position:0%
+other in uh in their molecular or atomic
+ 
+
+ align:start position:0%
+other in uh in their molecular or atomic
+weight okay so we have two significant
+
+ align:start position:0%
+weight okay so we have two significant
+ 
+
+ align:start position:0%
+weight okay so we have two significant
+figures also our current and time only
+
+ align:start position:0%
+figures also our current and time only
+ 
+
+ align:start position:0%
+figures also our current and time only
+had two two significant figures so we
+
+ align:start position:0%
+had two two significant figures so we
+ 
+
+ align:start position:0%
+had two two significant figures so we
+only have two significant figures um in
+
+ align:start position:0%
+only have two significant figures um in
+ 
+
+ align:start position:0%
+only have two significant figures um in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+problem all right so in this particular
+
+ align:start position:0%
+problem all right so in this particular
+ 
+
+ align:start position:0%
+problem all right so in this particular
+electrochemical cell again we had um our
+
+ align:start position:0%
+electrochemical cell again we had um our
+ 
+
+ align:start position:0%
+electrochemical cell again we had um our
+anode was being consumed and um the
+
+ align:start position:0%
+anode was being consumed and um the
+ 
+
+ align:start position:0%
+anode was being consumed and um the
+electrons that were generated um ended
+
+ align:start position:0%
+electrons that were generated um ended
+ 
+
+ align:start position:0%
+electrons that were generated um ended
+up plating the copper on sometimes
+
+ align:start position:0%
+up plating the copper on sometimes
+ 
+
+ align:start position:0%
+up plating the copper on sometimes
+you're not going to want to do that
+
+ align:start position:0%
+you're not going to want to do that
+ 
+
+ align:start position:0%
+you're not going to want to do that
+sometimes you're just going to want to
+
+ align:start position:0%
+sometimes you're just going to want to
+ 
+
+ align:start position:0%
+sometimes you're just going to want to
+actually plate um something with copper
+
+ align:start position:0%
+actually plate um something with copper
+ 
+
+ align:start position:0%
+actually plate um something with copper
+for example and so let's uh look at some
+
+ align:start position:0%
+for example and so let's uh look at some
+ 
+
+ align:start position:0%
+for example and so let's uh look at some
+of the uses for this kind of chemistry
+
+ align:start position:0%
+of the uses for this kind of chemistry
+ 
+
+ align:start position:0%
+of the uses for this kind of chemistry
+so here's some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electroplating this steel spoon will
+
+ align:start position:0%
+electroplating this steel spoon will
+ 
+
+ align:start position:0%
+electroplating this steel spoon will
+have a thin coating of copper deposited
+
+ align:start position:0%
+have a thin coating of copper deposited
+ 
+
+ align:start position:0%
+have a thin coating of copper deposited
+on it the cell consists of an anode of
+
+ align:start position:0%
+on it the cell consists of an anode of
+ 
+
+ align:start position:0%
+on it the cell consists of an anode of
+pure copper a solution of copper sulfate
+
+ align:start position:0%
+pure copper a solution of copper sulfate
+ 
+
+ align:start position:0%
+pure copper a solution of copper sulfate
+and as a cathode a spoon there is no net
+
+ align:start position:0%
+and as a cathode a spoon there is no net
+ 
+
+ align:start position:0%
+and as a cathode a spoon there is no net
+reaction but copper metal is transferred
+
+ align:start position:0%
+reaction but copper metal is transferred
+ 
+
+ align:start position:0%
+reaction but copper metal is transferred
+from the anode to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cathode it's pretty nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this kind of electroplating is
+
+ align:start position:0%
+okay so this kind of electroplating is
+ 
+
+ align:start position:0%
+okay so this kind of electroplating is
+pretty common um where you use these
+
+ align:start position:0%
+pretty common um where you use these
+ 
+
+ align:start position:0%
+pretty common um where you use these
+kind of reactions to get your copper
+
+ align:start position:0%
+kind of reactions to get your copper
+ 
+
+ align:start position:0%
+kind of reactions to get your copper
+which is in that solution to um to to
+
+ align:start position:0%
+which is in that solution to um to to
+ 
+
+ align:start position:0%
+which is in that solution to um to to
+plate as copper solid onto something so
+
+ align:start position:0%
+plate as copper solid onto something so
+ 
+
+ align:start position:0%
+plate as copper solid onto something so
+it could be a spoon it could be
+
+ align:start position:0%
+it could be a spoon it could be
+ 
+
+ align:start position:0%
+it could be a spoon it could be
+electrode yeah why is it dangerous why
+
+ align:start position:0%
+electrode yeah why is it dangerous why
+ 
+
+ align:start position:0%
+electrode yeah why is it dangerous why
+is it dangerous I you know I've seen
+
+ align:start position:0%
+is it dangerous I you know I've seen
+ 
+
+ align:start position:0%
+is it dangerous I you know I've seen
+these demos before so I'm not I'm not I
+
+ align:start position:0%
+these demos before so I'm not I'm not I
+ 
+
+ align:start position:0%
+these demos before so I'm not I'm not I
+think that they that's just like
+
+ align:start position:0%
+think that they that's just like
+ 
+
+ align:start position:0%
+think that they that's just like
+security regions to to say to say that I
+
+ align:start position:0%
+security regions to to say to say that I
+ 
+
+ align:start position:0%
+security regions to to say to say that I
+don't think it's like incred dangerous
+
+ align:start position:0%
+don't think it's like incred dangerous
+ 
+
+ align:start position:0%
+don't think it's like incred dangerous
+frankly but I probably shouldn't say
+
+ align:start position:0%
+frankly but I probably shouldn't say
+ 
+
+ align:start position:0%
+frankly but I probably shouldn't say
+that I'll get myself into all sorts of
+
+ align:start position:0%
+that I'll get myself into all sorts of
+ 
+
+ align:start position:0%
+that I'll get myself into all sorts of
+trouble don't try this at home I don't
+
+ align:start position:0%
+trouble don't try this at home I don't
+ 
+
+ align:start position:0%
+trouble don't try this at home I don't
+know why all right um usually when
+
+ align:start position:0%
+know why all right um usually when
+ 
+
+ align:start position:0%
+know why all right um usually when
+theuse
+
+ align:start position:0%
+theuse
+ 
+
+ align:start position:0%
+theuse
+are yeah but not like not that much
+
+ align:start position:0%
+are yeah but not like not that much
+ 
+
+ align:start position:0%
+are yeah but not like not that much
+worse than a lab stuff yeah Elena makes
+
+ align:start position:0%
+worse than a lab stuff yeah Elena makes
+ 
+
+ align:start position:0%
+worse than a lab stuff yeah Elena makes
+jewelry so she knows all about this but
+
+ align:start position:0%
+jewelry so she knows all about this but
+ 
+
+ align:start position:0%
+jewelry so she knows all about this but
+she doesn't she doesn't she does it very
+
+ align:start position:0%
+she doesn't she doesn't she does it very
+ 
+
+ align:start position:0%
+she doesn't she doesn't she does it very
+safely very safely okay all right so
+
+ align:start position:0%
+safely very safely okay all right so
+ 
+
+ align:start position:0%
+safely very safely okay all right so
+let's look at a couple other kinds of
+
+ align:start position:0%
+let's look at a couple other kinds of
+ 
+
+ align:start position:0%
+let's look at a couple other kinds of
+electrodes it is not always the case
+
+ align:start position:0%
+electrodes it is not always the case
+ 
+
+ align:start position:0%
+electrodes it is not always the case
+that electrode is consumed or that an
+
+ align:start position:0%
+that electrode is consumed or that an
+ 
+
+ align:start position:0%
+that electrode is consumed or that an
+electrode gets stuff deposited on it
+
+ align:start position:0%
+electrode gets stuff deposited on it
+ 
+
+ align:start position:0%
+electrode gets stuff deposited on it
+some electrodes are inert um an example
+
+ align:start position:0%
+some electrodes are inert um an example
+ 
+
+ align:start position:0%
+some electrodes are inert um an example
+for this is a platinum electrode it is
+
+ align:start position:0%
+for this is a platinum electrode it is
+ 
+
+ align:start position:0%
+for this is a platinum electrode it is
+inert so it doesn't get consumed and it
+
+ align:start position:0%
+inert so it doesn't get consumed and it
+ 
+
+ align:start position:0%
+inert so it doesn't get consumed and it
+doesn't get um reacted onto um during
+
+ align:start position:0%
+doesn't get um reacted onto um during
+ 
+
+ align:start position:0%
+doesn't get um reacted onto um during
+the reaction and so here's an example of
+
+ align:start position:0%
+the reaction and so here's an example of
+ 
+
+ align:start position:0%
+the reaction and so here's an example of
+a cell that uses this um so over here
+
+ align:start position:0%
+a cell that uses this um so over here
+ 
+
+ align:start position:0%
+a cell that uses this um so over here
+now we have still our copper system so
+
+ align:start position:0%
+now we have still our copper system so
+ 
+
+ align:start position:0%
+now we have still our copper system so
+this is our cathode again over here and
+
+ align:start position:0%
+this is our cathode again over here and
+ 
+
+ align:start position:0%
+this is our cathode again over here and
+a cathode does what oxidation or
+
+ align:start position:0%
+a cathode does what oxidation or
+ 
+
+ align:start position:0%
+a cathode does what oxidation or
+reduction where reduction and so this is
+
+ align:start position:0%
+reduction where reduction and so this is
+ 
+
+ align:start position:0%
+reduction where reduction and so this is
+our same reaction um copper plus two two
+
+ align:start position:0%
+our same reaction um copper plus two two
+ 
+
+ align:start position:0%
+our same reaction um copper plus two two
+electrodes code to Copper solid so this
+
+ align:start position:0%
+electrodes code to Copper solid so this
+ 
+
+ align:start position:0%
+electrodes code to Copper solid so this
+is doing the plating again but in this
+
+ align:start position:0%
+is doing the plating again but in this
+ 
+
+ align:start position:0%
+is doing the plating again but in this
+time it's different before we had the
+
+ align:start position:0%
+time it's different before we had the
+ 
+
+ align:start position:0%
+time it's different before we had the
+zinc um electrode that was being
+
+ align:start position:0%
+zinc um electrode that was being
+ 
+
+ align:start position:0%
+zinc um electrode that was being
+consumed but now we have this platinum
+
+ align:start position:0%
+consumed but now we have this platinum
+ 
+
+ align:start position:0%
+consumed but now we have this platinum
+and the reaction that happens at the
+
+ align:start position:0%
+and the reaction that happens at the
+ 
+
+ align:start position:0%
+and the reaction that happens at the
+anode it's still an oxidation always an
+
+ align:start position:0%
+anode it's still an oxidation always an
+ 
+
+ align:start position:0%
+anode it's still an oxidation always an
+oxidation at the anode but the oxidation
+
+ align:start position:0%
+oxidation at the anode but the oxidation
+ 
+
+ align:start position:0%
+oxidation at the anode but the oxidation
+reaction is chromium plus two going to
+
+ align:start position:0%
+reaction is chromium plus two going to
+ 
+
+ align:start position:0%
+reaction is chromium plus two going to
+chromium plus three in an electron so um
+
+ align:start position:0%
+chromium plus three in an electron so um
+ 
+
+ align:start position:0%
+chromium plus three in an electron so um
+here the electrode is inert and the
+
+ align:start position:0%
+here the electrode is inert and the
+ 
+
+ align:start position:0%
+here the electrode is inert and the
+reaction is all happening in the same
+
+ align:start position:0%
+reaction is all happening in the same
+ 
+
+ align:start position:0%
+reaction is all happening in the same
+phase all happening in
+
+ align:start position:0%
+phase all happening in
+ 
+
+ align:start position:0%
+phase all happening in
+solution so we can also write the uh not
+
+ align:start position:0%
+solution so we can also write the uh not
+ 
+
+ align:start position:0%
+solution so we can also write the uh not
+the notation for this kind of cell and
+
+ align:start position:0%
+the notation for this kind of cell and
+ 
+
+ align:start position:0%
+the notation for this kind of cell and
+so here we would have Platinum solid the
+
+ align:start position:0%
+so here we would have Platinum solid the
+ 
+
+ align:start position:0%
+so here we would have Platinum solid the
+single line which means the phase
+
+ align:start position:0%
+single line which means the phase
+ 
+
+ align:start position:0%
+single line which means the phase
+difference um chromium plus two aquous
+
+ align:start position:0%
+difference um chromium plus two aquous
+ 
+
+ align:start position:0%
+difference um chromium plus two aquous
+comma because now there's not a a phase
+
+ align:start position:0%
+comma because now there's not a a phase
+ 
+
+ align:start position:0%
+comma because now there's not a a phase
+transition between these a chromium plus
+
+ align:start position:0%
+transition between these a chromium plus
+ 
+
+ align:start position:0%
+transition between these a chromium plus
+three aquous the two lines that means
+
+ align:start position:0%
+three aquous the two lines that means
+ 
+
+ align:start position:0%
+three aquous the two lines that means
+what what do those mean
+
+ align:start position:0%
+what what do those mean
+ 
+
+ align:start position:0%
+what what do those mean
+again salt bridge so this indicates
+
+ align:start position:0%
+again salt bridge so this indicates
+ 
+
+ align:start position:0%
+again salt bridge so this indicates
+that's one Beaker this is the other
+
+ align:start position:0%
+that's one Beaker this is the other
+ 
+
+ align:start position:0%
+that's one Beaker this is the other
+Beaker and here we have the copper plus
+
+ align:start position:0%
+Beaker and here we have the copper plus
+ 
+
+ align:start position:0%
+Beaker and here we have the copper plus
+two Aqua single line for phase uh change
+
+ align:start position:0%
+two Aqua single line for phase uh change
+ 
+
+ align:start position:0%
+two Aqua single line for phase uh change
+and a copper solid so again our anode
+
+ align:start position:0%
+and a copper solid so again our anode
+ 
+
+ align:start position:0%
+and a copper solid so again our anode
+reaction and our cathode
+
+ align:start position:0%
+reaction and our cathode
+ 
+
+ align:start position:0%
+reaction and our cathode
+reaction all right so this is another
+
+ align:start position:0%
+reaction all right so this is another
+ 
+
+ align:start position:0%
+reaction all right so this is another
+kind um you can also use platinum
+
+ align:start position:0%
+kind um you can also use platinum
+ 
+
+ align:start position:0%
+kind um you can also use platinum
+electrodes in combination with what's
+
+ align:start position:0%
+electrodes in combination with what's
+ 
+
+ align:start position:0%
+electrodes in combination with what's
+known as a hydrogen electrode um so
+
+ align:start position:0%
+known as a hydrogen electrode um so
+ 
+
+ align:start position:0%
+known as a hydrogen electrode um so
+these are often together the Platinum
+
+ align:start position:0%
+these are often together the Platinum
+ 
+
+ align:start position:0%
+these are often together the Platinum
+with the hydrogen
+
+ align:start position:0%
+with the hydrogen
+ 
+
+ align:start position:0%
+with the hydrogen
+and many reduction potentials and when
+
+ align:start position:0%
+and many reduction potentials and when
+ 
+
+ align:start position:0%
+and many reduction potentials and when
+you get problem set 8 you're going to be
+
+ align:start position:0%
+you get problem set 8 you're going to be
+ 
+
+ align:start position:0%
+you get problem set 8 you're going to be
+looking up in your book a lot of
+
+ align:start position:0%
+looking up in your book a lot of
+ 
+
+ align:start position:0%
+looking up in your book a lot of
+standard reduction potentials and many
+
+ align:start position:0%
+standard reduction potentials and many
+ 
+
+ align:start position:0%
+standard reduction potentials and many
+of them will say measured against sh and
+
+ align:start position:0%
+of them will say measured against sh and
+ 
+
+ align:start position:0%
+of them will say measured against sh and
+a lot of people say like who is this she
+
+ align:start position:0%
+a lot of people say like who is this she
+ 
+
+ align:start position:0%
+a lot of people say like who is this she
+that measures all of these uh Potentials
+
+ align:start position:0%
+that measures all of these uh Potentials
+ 
+
+ align:start position:0%
+that measures all of these uh Potentials
+in the back of books and that she is the
+
+ align:start position:0%
+in the back of books and that she is the
+ 
+
+ align:start position:0%
+in the back of books and that she is the
+standard hydrogen electrode all right so
+
+ align:start position:0%
+standard hydrogen electrode all right so
+ 
+
+ align:start position:0%
+standard hydrogen electrode all right so
+let's think about how this electrode is
+
+ align:start position:0%
+let's think about how this electrode is
+ 
+
+ align:start position:0%
+let's think about how this electrode is
+being used so we when it's used used as
+
+ align:start position:0%
+being used so we when it's used used as
+ 
+
+ align:start position:0%
+being used so we when it's used used as
+a cathode we have um H+ aquous phase
+
+ align:start position:0%
+a cathode we have um H+ aquous phase
+ 
+
+ align:start position:0%
+a cathode we have um H+ aquous phase
+transition to H2 gas and then another
+
+ align:start position:0%
+transition to H2 gas and then another
+ 
+
+ align:start position:0%
+transition to H2 gas and then another
+phase transition to our solid Platinum
+
+ align:start position:0%
+phase transition to our solid Platinum
+ 
+
+ align:start position:0%
+phase transition to our solid Platinum
+inert electrode and here when it's used
+
+ align:start position:0%
+inert electrode and here when it's used
+ 
+
+ align:start position:0%
+inert electrode and here when it's used
+as a cathode H+ is being
+
+ align:start position:0%
+as a cathode H+ is being
+ 
+
+ align:start position:0%
+as a cathode H+ is being
+reduced but it can also be used as an
+
+ align:start position:0%
+reduced but it can also be used as an
+ 
+
+ align:start position:0%
+reduced but it can also be used as an
+anode and this is a clicker question why
+
+ align:start position:0%
+anode and this is a clicker question why
+ 
+
+ align:start position:0%
+anode and this is a clicker question why
+don't you tell me what would be
+
+ align:start position:0%
+don't you tell me what would be
+ 
+
+ align:start position:0%
+don't you tell me what would be
+happening when the hydrogen Platinum
+
+ align:start position:0%
+happening when the hydrogen Platinum
+ 
+
+ align:start position:0%
+happening when the hydrogen Platinum
+electrode is being used as an anode or
+
+ align:start position:0%
+electrode is being used as an anode or
+ 
+
+ align:start position:0%
+electrode is being used as an anode or
+reactions being used as an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anode 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds see if you can get 90% 89
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+89% oh
+
+ align:start position:0%
+89% oh
+ 
+
+ align:start position:0%
+89% oh
+far away okay that is the right answer
+
+ align:start position:0%
+far away okay that is the right answer
+ 
+
+ align:start position:0%
+far away okay that is the right answer
+though okay so some of these um the
+
+ align:start position:0%
+though okay so some of these um the
+ 
+
+ align:start position:0%
+though okay so some of these um the
+Platinum is inert so it's not doing
+
+ align:start position:0%
+Platinum is inert so it's not doing
+ 
+
+ align:start position:0%
+Platinum is inert so it's not doing
+anything um and it's over here so it's
+
+ align:start position:0%
+anything um and it's over here so it's
+ 
+
+ align:start position:0%
+anything um and it's over here so it's
+not doing anything so we can rule out
+
+ align:start position:0%
+not doing anything so we can rule out
+ 
+
+ align:start position:0%
+not doing anything so we can rule out
+all the things that Platinum are doing
+
+ align:start position:0%
+all the things that Platinum are doing
+ 
+
+ align:start position:0%
+all the things that Platinum are doing
+stuff all
+
+ align:start position:0%
+stuff all
+ 
+
+ align:start position:0%
+stuff all
+right H+ being oxidized you ever heard
+
+ align:start position:0%
+right H+ being oxidized you ever heard
+ 
+
+ align:start position:0%
+right H+ being oxidized you ever heard
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h2+ no so we don't want that we know at
+
+ align:start position:0%
+h2+ no so we don't want that we know at
+ 
+
+ align:start position:0%
+h2+ no so we don't want that we know at
+the anode it should be oxidized so we
+
+ align:start position:0%
+the anode it should be oxidized so we
+ 
+
+ align:start position:0%
+the anode it should be oxidized so we
+can eliminate all the ones that are
+
+ align:start position:0%
+can eliminate all the ones that are
+ 
+
+ align:start position:0%
+can eliminate all the ones that are
+reduced okay so we only have really kind
+
+ align:start position:0%
+reduced okay so we only have really kind
+ 
+
+ align:start position:0%
+reduced okay so we only have really kind
+of one good option if you say that the
+
+ align:start position:0%
+of one good option if you say that the
+ 
+
+ align:start position:0%
+of one good option if you say that the
+Platinum um is in Earth so H2 then gets
+
+ align:start position:0%
+Platinum um is in Earth so H2 then gets
+ 
+
+ align:start position:0%
+Platinum um is in Earth so H2 then gets
+oxidized in this case forming H+ all
+
+ align:start position:0%
+oxidized in this case forming H+ all
+ 
+
+ align:start position:0%
+oxidized in this case forming H+ all
+right so let's uh let's look at a let's
+
+ align:start position:0%
+right so let's uh let's look at a let's
+ 
+
+ align:start position:0%
+right so let's uh let's look at a let's
+look at a cell like this that uh uses
+
+ align:start position:0%
+look at a cell like this that uh uses
+ 
+
+ align:start position:0%
+look at a cell like this that uh uses
+the uh the hydrogen
+
+ align:start position:0%
+the uh the hydrogen
+ 
+
+ align:start position:0%
+the uh the hydrogen
+electrode so here's an example now on
+
+ align:start position:0%
+electrode so here's an example now on
+ 
+
+ align:start position:0%
+electrode so here's an example now on
+this side we have our regular zinc
+
+ align:start position:0%
+this side we have our regular zinc
+ 
+
+ align:start position:0%
+this side we have our regular zinc
+system system for our anode and so over
+
+ align:start position:0%
+system system for our anode and so over
+ 
+
+ align:start position:0%
+system system for our anode and so over
+here we're using as the cathode the
+
+ align:start position:0%
+here we're using as the cathode the
+ 
+
+ align:start position:0%
+here we're using as the cathode the
+hydrogen electrode and so here in this
+
+ align:start position:0%
+hydrogen electrode and so here in this
+ 
+
+ align:start position:0%
+hydrogen electrode and so here in this
+beautiful drawing that I made um we have
+
+ align:start position:0%
+beautiful drawing that I made um we have
+ 
+
+ align:start position:0%
+beautiful drawing that I made um we have
+a glass tube here where you're pumping
+
+ align:start position:0%
+a glass tube here where you're pumping
+ 
+
+ align:start position:0%
+a glass tube here where you're pumping
+H2 gas in at one atmosphere in the
+
+ align:start position:0%
+H2 gas in at one atmosphere in the
+ 
+
+ align:start position:0%
+H2 gas in at one atmosphere in the
+middle of the tube we have our inert
+
+ align:start position:0%
+middle of the tube we have our inert
+ 
+
+ align:start position:0%
+middle of the tube we have our inert
+Platinum uh electrode and then these are
+
+ align:start position:0%
+Platinum uh electrode and then these are
+ 
+
+ align:start position:0%
+Platinum uh electrode and then these are
+H2 gas bubbles down here and we have
+
+ align:start position:0%
+H2 gas bubbles down here and we have
+ 
+
+ align:start position:0%
+H2 gas bubbles down here and we have
+strong acid HCL which is our source of
+
+ align:start position:0%
+strong acid HCL which is our source of
+ 
+
+ align:start position:0%
+strong acid HCL which is our source of
+H+
+
+ align:start position:0%
+H+
+ 
+
+ align:start position:0%
+H+
+um in solution so over here again this
+
+ align:start position:0%
+um in solution so over here again this
+ 
+
+ align:start position:0%
+um in solution so over here again this
+is our cathode so we have a reduction at
+
+ align:start position:0%
+is our cathode so we have a reduction at
+ 
+
+ align:start position:0%
+is our cathode so we have a reduction at
+the cathode and we have H+ aquous phase
+
+ align:start position:0%
+the cathode and we have H+ aquous phase
+ 
+
+ align:start position:0%
+the cathode and we have H+ aquous phase
+transition H2 and gas and then another
+
+ align:start position:0%
+transition H2 and gas and then another
+ 
+
+ align:start position:0%
+transition H2 and gas and then another
+phase transition to our solid Platinum
+
+ align:start position:0%
+phase transition to our solid Platinum
+ 
+
+ align:start position:0%
+phase transition to our solid Platinum
+electrode and over here is our standard
+
+ align:start position:0%
+electrode and over here is our standard
+ 
+
+ align:start position:0%
+electrode and over here is our standard
+anode our oxidation that involves zinc
+
+ align:start position:0%
+anode our oxidation that involves zinc
+ 
+
+ align:start position:0%
+anode our oxidation that involves zinc
+and zinc plus two so we could also have
+
+ align:start position:0%
+and zinc plus two so we could also have
+ 
+
+ align:start position:0%
+and zinc plus two so we could also have
+had um the hydrogen electrode over here
+
+ align:start position:0%
+had um the hydrogen electrode over here
+ 
+
+ align:start position:0%
+had um the hydrogen electrode over here
+as well all right so that gives you a
+
+ align:start position:0%
+as well all right so that gives you a
+ 
+
+ align:start position:0%
+as well all right so that gives you a
+number of different examples of types of
+
+ align:start position:0%
+number of different examples of types of
+ 
+
+ align:start position:0%
+number of different examples of types of
+electrodes that you can have and types
+
+ align:start position:0%
+electrodes that you can have and types
+ 
+
+ align:start position:0%
+electrodes that you can have and types
+of cells that you can have um and uh and
+
+ align:start position:0%
+of cells that you can have um and uh and
+ 
+
+ align:start position:0%
+of cells that you can have um and uh and
+that is the end of this um
+
+ align:start position:0%
+that is the end of this um
+ 
+
+ align:start position:0%
+that is the end of this um
+today's our lecture 25 notes as soon as
+
+ align:start position:0%
+today's our lecture 25 notes as soon as
+ 
+
+ align:start position:0%
+today's our lecture 25 notes as soon as
+you finish writing that down we'll go
+
+ align:start position:0%
+you finish writing that down we'll go
+ 
+
+ align:start position:0%
+you finish writing that down we'll go
+and look at lecture 26 again we're
+
+ align:start position:0%
+and look at lecture 26 again we're
+ 
+
+ align:start position:0%
+and look at lecture 26 again we're
+continuing on the same theme and now
+
+ align:start position:0%
+continuing on the same theme and now
+ 
+
+ align:start position:0%
+continuing on the same theme and now
+we're going to talk about the potential
+
+ align:start position:0%
+we're going to talk about the potential
+ 
+
+ align:start position:0%
+we're going to talk about the potential
+of these cells so we've talked about the
+
+ align:start position:0%
+of these cells so we've talked about the
+ 
+
+ align:start position:0%
+of these cells so we've talked about the
+reactions happening at anodes and
+
+ align:start position:0%
+reactions happening at anodes and
+ 
+
+ align:start position:0%
+reactions happening at anodes and
+cathodes how to write them and now we're
+
+ align:start position:0%
+cathodes how to write them and now we're
+ 
+
+ align:start position:0%
+cathodes how to write them and now we're
+going to think about the change and
+
+ align:start position:0%
+going to think about the change and
+ 
+
+ align:start position:0%
+going to think about the change and
+potential that occurs when you run these
+
+ align:start position:0%
+potential that occurs when you run these
+ 
+
+ align:start position:0%
+potential that occurs when you run these
+reactions
\ No newline at end of file
diff --git a/CEbrxYGpfZY.txt b/CEbrxYGpfZY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e64451fd5193ab50551413b55012d167f6e48977
--- /dev/null
+++ b/CEbrxYGpfZY.txt
@@ -0,0 +1,6832 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi as I was getting myself prepared for
+
+ align:start position:0%
+hi as I was getting myself prepared for
+ 
+
+ align:start position:0%
+hi as I was getting myself prepared for
+the lecture an old Shaggy Dog science
+
+ align:start position:0%
+the lecture an old Shaggy Dog science
+ 
+
+ align:start position:0%
+the lecture an old Shaggy Dog science
+story came to mind that's usually told
+
+ align:start position:0%
+story came to mind that's usually told
+ 
+
+ align:start position:0%
+story came to mind that's usually told
+as a tribute to the German scientist
+
+ align:start position:0%
+as a tribute to the German scientist
+ 
+
+ align:start position:0%
+as a tribute to the German scientist
+thoroughness this was a story of when
+
+ align:start position:0%
+thoroughness this was a story of when
+ 
+
+ align:start position:0%
+thoroughness this was a story of when
+all the scientists of the world got
+
+ align:start position:0%
+all the scientists of the world got
+ 
+
+ align:start position:0%
+all the scientists of the world got
+together and decided for an annual
+
+ align:start position:0%
+together and decided for an annual
+ 
+
+ align:start position:0%
+together and decided for an annual
+project each country would study
+
+ align:start position:0%
+project each country would study
+ 
+
+ align:start position:0%
+project each country would study
+exhaustively a different animal and
+
+ align:start position:0%
+exhaustively a different animal and
+ 
+
+ align:start position:0%
+exhaustively a different animal and
+report at the end of a year as to what
+
+ align:start position:0%
+report at the end of a year as to what
+ 
+
+ align:start position:0%
+report at the end of a year as to what
+they had found out and at the end of the
+
+ align:start position:0%
+they had found out and at the end of the
+ 
+
+ align:start position:0%
+they had found out and at the end of the
+year every country but Germany had been
+
+ align:start position:0%
+year every country but Germany had been
+ 
+
+ align:start position:0%
+year every country but Germany had been
+heard from no one knew what had happened
+
+ align:start position:0%
+heard from no one knew what had happened
+ 
+
+ align:start position:0%
+heard from no one knew what had happened
+to the German scientists and 5 years
+
+ align:start position:0%
+to the German scientists and 5 years
+ 
+
+ align:start position:0%
+to the German scientists and 5 years
+later the German report came in a huge
+
+ align:start position:0%
+later the German report came in a huge
+ 
+
+ align:start position:0%
+later the German report came in a huge
+epitome and it was entitled Handbook of
+
+ align:start position:0%
+epitome and it was entitled Handbook of
+ 
+
+ align:start position:0%
+epitome and it was entitled Handbook of
+the elephant volume one and the reason
+
+ align:start position:0%
+the elephant volume one and the reason
+ 
+
+ align:start position:0%
+the elephant volume one and the reason
+that this story comes to mind is toold
+
+ align:start position:0%
+that this story comes to mind is toold
+ 
+
+ align:start position:0%
+that this story comes to mind is toold
+first of all the study of vector spaces
+
+ align:start position:0%
+first of all the study of vector spaces
+ 
+
+ align:start position:0%
+first of all the study of vector spaces
+has so many ramifications that to study
+
+ align:start position:0%
+has so many ramifications that to study
+ 
+
+ align:start position:0%
+has so many ramifications that to study
+the subject thoroughly should be a full
+
+ align:start position:0%
+the subject thoroughly should be a full
+ 
+
+ align:start position:0%
+the subject thoroughly should be a full
+Year's course by itself and secondly
+
+ align:start position:0%
+Year's course by itself and secondly
+ 
+
+ align:start position:0%
+Year's course by itself and secondly
+with respect ECT to the particular topic
+
+ align:start position:0%
+with respect ECT to the particular topic
+ 
+
+ align:start position:0%
+with respect ECT to the particular topic
+of basis vectors and spanning vectors
+
+ align:start position:0%
+of basis vectors and spanning vectors
+ 
+
+ align:start position:0%
+of basis vectors and spanning vectors
+and whether sub elements are linearly
+
+ align:start position:0%
+and whether sub elements are linearly
+ 
+
+ align:start position:0%
+and whether sub elements are linearly
+independent whereas we've invented a
+
+ align:start position:0%
+independent whereas we've invented a
+ 
+
+ align:start position:0%
+independent whereas we've invented a
+rather nice row reduced Matrix technique
+
+ align:start position:0%
+rather nice row reduced Matrix technique
+ 
+
+ align:start position:0%
+rather nice row reduced Matrix technique
+for finding out
+
+ align:start position:0%
+for finding out
+ 
+
+ align:start position:0%
+for finding out
+what space is Spann by a set of vectors
+
+ align:start position:0%
+what space is Spann by a set of vectors
+ 
+
+ align:start position:0%
+what space is Spann by a set of vectors
+and what a basis for that space is
+
+ align:start position:0%
+and what a basis for that space is
+ 
+
+ align:start position:0%
+and what a basis for that space is
+frequently we don't want that much
+
+ align:start position:0%
+frequently we don't want that much
+ 
+
+ align:start position:0%
+frequently we don't want that much
+information and what I'm leading up to
+
+ align:start position:0%
+information and what I'm leading up to
+ 
+
+ align:start position:0%
+information and what I'm leading up to
+is a topic which you've all had in a
+
+ align:start position:0%
+is a topic which you've all had in a
+ 
+
+ align:start position:0%
+is a topic which you've all had in a
+previous context it's called
+
+ align:start position:0%
+previous context it's called
+ 
+
+ align:start position:0%
+previous context it's called
+determinants and today what I would like
+
+ align:start position:0%
+determinants and today what I would like
+ 
+
+ align:start position:0%
+determinants and today what I would like
+to do is to study determinants within
+
+ align:start position:0%
+to do is to study determinants within
+ 
+
+ align:start position:0%
+to do is to study determinants within
+the framework of of vector spaces and
+
+ align:start position:0%
+the framework of of vector spaces and
+ 
+
+ align:start position:0%
+the framework of of vector spaces and
+the way it comes up is as follows
+
+ align:start position:0%
+the way it comes up is as follows
+ 
+
+ align:start position:0%
+the way it comes up is as follows
+suppose we have an N dimensional Vector
+
+ align:start position:0%
+suppose we have an N dimensional Vector
+ 
+
+ align:start position:0%
+suppose we have an N dimensional Vector
+space V and suppose that we pick a
+
+ align:start position:0%
+space V and suppose that we pick a
+ 
+
+ align:start position:0%
+space V and suppose that we pick a
+particular basis U1 up to unu n for V
+
+ align:start position:0%
+particular basis U1 up to unu n for V
+ 
+
+ align:start position:0%
+particular basis U1 up to unu n for V
+itself now the idea is this knowing that
+
+ align:start position:0%
+itself now the idea is this knowing that
+ 
+
+ align:start position:0%
+itself now the idea is this knowing that
+the dimension of V is n we immediately
+
+ align:start position:0%
+the dimension of V is n we immediately
+ 
+
+ align:start position:0%
+the dimension of V is n we immediately
+know that more than n vectors can't be a
+
+ align:start position:0%
+know that more than n vectors can't be a
+ 
+
+ align:start position:0%
+know that more than n vectors can't be a
+basis for V because they will be
+
+ align:start position:0%
+basis for V because they will be
+ 
+
+ align:start position:0%
+basis for V because they will be
+linearly dependent rather than linearly
+
+ align:start position:0%
+linearly dependent rather than linearly
+ 
+
+ align:start position:0%
+linearly dependent rather than linearly
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+fewer than n vectors of V cannot be a
+
+ align:start position:0%
+fewer than n vectors of V cannot be a
+ 
+
+ align:start position:0%
+fewer than n vectors of V cannot be a
+basis because fewer than n vectors since
+
+ align:start position:0%
+basis because fewer than n vectors since
+ 
+
+ align:start position:0%
+basis because fewer than n vectors since
+the dimension is n cannot span V
+
+ align:start position:0%
+the dimension is n cannot span V
+ 
+
+ align:start position:0%
+the dimension is n cannot span V
+consequently the only point of interest
+
+ align:start position:0%
+consequently the only point of interest
+ 
+
+ align:start position:0%
+consequently the only point of interest
+is what happens when we're given a set
+
+ align:start position:0%
+is what happens when we're given a set
+ 
+
+ align:start position:0%
+is what happens when we're given a set
+of n vectors in V namely given the N
+
+ align:start position:0%
+of n vectors in V namely given the N
+ 
+
+ align:start position:0%
+of n vectors in V namely given the N
+vectors Alpha One up to alpha n and
+
+ align:start position:0%
+vectors Alpha One up to alpha n and
+ 
+
+ align:start position:0%
+vectors Alpha One up to alpha n and
+V is this set a basis or isn't it and
+
+ align:start position:0%
+V is this set a basis or isn't it and
+ 
+
+ align:start position:0%
+V is this set a basis or isn't it and
+rather than to use the row reduced
+
+ align:start position:0%
+rather than to use the row reduced
+ 
+
+ align:start position:0%
+rather than to use the row reduced
+Matrix technique here what we're saying
+
+ align:start position:0%
+Matrix technique here what we're saying
+ 
+
+ align:start position:0%
+Matrix technique here what we're saying
+is we don't want for example in many
+
+ align:start position:0%
+is we don't want for example in many
+ 
+
+ align:start position:0%
+is we don't want for example in many
+cases to know what the betas look like
+
+ align:start position:0%
+cases to know what the betas look like
+ 
+
+ align:start position:0%
+cases to know what the betas look like
+that we talked about in our lecture on
+
+ align:start position:0%
+that we talked about in our lecture on
+ 
+
+ align:start position:0%
+that we talked about in our lecture on
+spanning vectors and the like all we
+
+ align:start position:0%
+spanning vectors and the like all we
+ 
+
+ align:start position:0%
+spanning vectors and the like all we
+want to know is are these vectors
+
+ align:start position:0%
+want to know is are these vectors
+ 
+
+ align:start position:0%
+want to know is are these vectors
+linearly independent or aren't they and
+
+ align:start position:0%
+linearly independent or aren't they and
+ 
+
+ align:start position:0%
+linearly independent or aren't they and
+so what we do is we essentially invent a
+
+ align:start position:0%
+so what we do is we essentially invent a
+ 
+
+ align:start position:0%
+so what we do is we essentially invent a
+function machine in other words what
+
+ align:start position:0%
+function machine in other words what
+ 
+
+ align:start position:0%
+function machine in other words what
+we're going to do is to construct a
+
+ align:start position:0%
+we're going to do is to construct a
+ 
+
+ align:start position:0%
+we're going to do is to construct a
+function in which given that the
+
+ align:start position:0%
+function in which given that the
+ 
+
+ align:start position:0%
+function in which given that the
+dimension of our space is n-dimensional
+
+ align:start position:0%
+dimension of our space is n-dimensional
+ 
+
+ align:start position:0%
+dimension of our space is n-dimensional
+the input of our function machine will
+
+ align:start position:0%
+the input of our function machine will
+ 
+
+ align:start position:0%
+the input of our function machine will
+be any set of n vectors from that space
+
+ align:start position:0%
+be any set of n vectors from that space
+ 
+
+ align:start position:0%
+be any set of n vectors from that space
+and the Machine will be programmed to
+
+ align:start position:0%
+and the Machine will be programmed to
+ 
+
+ align:start position:0%
+and the Machine will be programmed to
+give zero as an output if the vectors
+
+ align:start position:0%
+give zero as an output if the vectors
+ 
+
+ align:start position:0%
+give zero as an output if the vectors
+are linearly dependent in other words if
+
+ align:start position:0%
+are linearly dependent in other words if
+ 
+
+ align:start position:0%
+are linearly dependent in other words if
+they're not a basis and nonzero and I'll
+
+ align:start position:0%
+they're not a basis and nonzero and I'll
+ 
+
+ align:start position:0%
+they're not a basis and nonzero and I'll
+explain in more detail what nonzero why
+
+ align:start position:0%
+explain in more detail what nonzero why
+ 
+
+ align:start position:0%
+explain in more detail what nonzero why
+I pick nonzero rather than a specific
+
+ align:start position:0%
+I pick nonzero rather than a specific
+ 
+
+ align:start position:0%
+I pick nonzero rather than a specific
+nonzero number if the basis V if the N
+
+ align:start position:0%
+nonzero number if the basis V if the N
+ 
+
+ align:start position:0%
+nonzero number if the basis V if the N
+vectors do form a basis in other words I
+
+ align:start position:0%
+vectors do form a basis in other words I
+ 
+
+ align:start position:0%
+vectors do form a basis in other words I
+am going to invent a function D capital
+
+ align:start position:0%
+am going to invent a function D capital
+ 
+
+ align:start position:0%
+am going to invent a function D capital
+d to indicate the wood that determinant
+
+ align:start position:0%
+d to indicate the wood that determinant
+ 
+
+ align:start position:0%
+d to indicate the wood that determinant
+here such that D of the N vectors alpha
+
+ align:start position:0%
+here such that D of the N vectors alpha
+ 
+
+ align:start position:0%
+here such that D of the N vectors alpha
+1 up to alpha n will be zero if and only
+
+ align:start position:0%
+1 up to alpha n will be zero if and only
+ 
+
+ align:start position:0%
+1 up to alpha n will be zero if and only
+if the set of n vectors are linearly
+
+ align:start position:0%
+if the set of n vectors are linearly
+ 
+
+ align:start position:0%
+if the set of n vectors are linearly
+dependent now obviously a function
+
+ align:start position:0%
+dependent now obviously a function
+ 
+
+ align:start position:0%
+dependent now obviously a function
+machine can do nothing by itself we have
+
+ align:start position:0%
+machine can do nothing by itself we have
+ 
+
+ align:start position:0%
+machine can do nothing by itself we have
+to give and I hope this is well known by
+
+ align:start position:0%
+to give and I hope this is well known by
+ 
+
+ align:start position:0%
+to give and I hope this is well known by
+now in our course we have to endow any
+
+ align:start position:0%
+now in our course we have to endow any
+ 
+
+ align:start position:0%
+now in our course we have to endow any
+thing that we're working with with a
+
+ align:start position:0%
+thing that we're working with with a
+ 
+
+ align:start position:0%
+thing that we're working with with a
+particular structure so it feels free to
+
+ align:start position:0%
+particular structure so it feels free to
+ 
+
+ align:start position:0%
+particular structure so it feels free to
+work logically for us well among other
+
+ align:start position:0%
+work logically for us well among other
+ 
+
+ align:start position:0%
+work logically for us well among other
+things what do we know for sure is a set
+
+ align:start position:0%
+things what do we know for sure is a set
+ 
+
+ align:start position:0%
+things what do we know for sure is a set
+of n vectors which are a basis for V
+
+ align:start position:0%
+of n vectors which are a basis for V
+ 
+
+ align:start position:0%
+of n vectors which are a basis for V
+since we were given that the specific
+
+ align:start position:0%
+since we were given that the specific
+ 
+
+ align:start position:0%
+since we were given that the specific
+basis that V is being referred to with
+
+ align:start position:0%
+basis that V is being referred to with
+ 
+
+ align:start position:0%
+basis that V is being referred to with
+respect to uh U1 up to un then certainly
+
+ align:start position:0%
+respect to uh U1 up to un then certainly
+ 
+
+ align:start position:0%
+respect to uh U1 up to un then certainly
+if U1 up to un is the input of the D
+
+ align:start position:0%
+if U1 up to un is the input of the D
+ 
+
+ align:start position:0%
+if U1 up to un is the input of the D
+machine we want a nonzero output for the
+
+ align:start position:0%
+machine we want a nonzero output for the
+ 
+
+ align:start position:0%
+machine we want a nonzero output for the
+sake of just normalizing thing things
+
+ align:start position:0%
+sake of just normalizing thing things
+ 
+
+ align:start position:0%
+sake of just normalizing thing things
+let's program the machine so that D of
+
+ align:start position:0%
+let's program the machine so that D of
+ 
+
+ align:start position:0%
+let's program the machine so that D of
+U1 up to un will be
+
+ align:start position:0%
+U1 up to un will be
+ 
+
+ align:start position:0%
+U1 up to un will be
+one now notice by the way this only
+
+ align:start position:0%
+one now notice by the way this only
+ 
+
+ align:start position:0%
+one now notice by the way this only
+tells us one special basis there are
+
+ align:start position:0%
+tells us one special basis there are
+ 
+
+ align:start position:0%
+tells us one special basis there are
+many bases that I could have chosen for
+
+ align:start position:0%
+many bases that I could have chosen for
+ 
+
+ align:start position:0%
+many bases that I could have chosen for
+V and certainly condition one by itself
+
+ align:start position:0%
+V and certainly condition one by itself
+ 
+
+ align:start position:0%
+V and certainly condition one by itself
+isn't going to tell me any has no
+
+ align:start position:0%
+isn't going to tell me any has no
+ 
+
+ align:start position:0%
+isn't going to tell me any has no
+information programmed in it to tell me
+
+ align:start position:0%
+information programmed in it to tell me
+ 
+
+ align:start position:0%
+information programmed in it to tell me
+anything other than what it does to U1
+
+ align:start position:0%
+anything other than what it does to U1
+ 
+
+ align:start position:0%
+anything other than what it does to U1
+up to un as a second input to my D
+
+ align:start position:0%
+up to un as a second input to my D
+ 
+
+ align:start position:0%
+up to un as a second input to my D
+machine for programming it I certainly
+
+ align:start position:0%
+machine for programming it I certainly
+ 
+
+ align:start position:0%
+machine for programming it I certainly
+know that given the N vectors if any two
+
+ align:start position:0%
+know that given the N vectors if any two
+ 
+
+ align:start position:0%
+know that given the N vectors if any two
+of the vectors happen to be equal then
+
+ align:start position:0%
+of the vectors happen to be equal then
+ 
+
+ align:start position:0%
+of the vectors happen to be equal then
+those vectors are linearly dependent
+
+ align:start position:0%
+those vectors are linearly dependent
+ 
+
+ align:start position:0%
+those vectors are linearly dependent
+consequently I instruct my D machine
+
+ align:start position:0%
+consequently I instruct my D machine
+ 
+
+ align:start position:0%
+consequently I instruct my D machine
+that if the input is a set of vectors
+
+ align:start position:0%
+that if the input is a set of vectors
+ 
+
+ align:start position:0%
+that if the input is a set of vectors
+Alpha One up to alpha n and at least two
+
+ align:start position:0%
+Alpha One up to alpha n and at least two
+ 
+
+ align:start position:0%
+Alpha One up to alpha n and at least two
+of the alphas are equal and the way we
+
+ align:start position:0%
+of the alphas are equal and the way we
+ 
+
+ align:start position:0%
+of the alphas are equal and the way we
+say that mathematically is that Alpha I
+
+ align:start position:0%
+say that mathematically is that Alpha I
+ 
+
+ align:start position:0%
+say that mathematically is that Alpha I
+equals Alpha J for some I une equal to J
+
+ align:start position:0%
+equals Alpha J for some I une equal to J
+ 
+
+ align:start position:0%
+equals Alpha J for some I une equal to J
+that if two of the vectors in the set
+
+ align:start position:0%
+that if two of the vectors in the set
+ 
+
+ align:start position:0%
+that if two of the vectors in the set
+are equal we tell the machine to grind
+
+ align:start position:0%
+are equal we tell the machine to grind
+ 
+
+ align:start position:0%
+are equal we tell the machine to grind
+out zero as an output and by the way at
+
+ align:start position:0%
+out zero as an output and by the way at
+ 
+
+ align:start position:0%
+out zero as an output and by the way at
+this stage we should be very careful to
+
+ align:start position:0%
+this stage we should be very careful to
+ 
+
+ align:start position:0%
+this stage we should be very careful to
+recognize that this is not the only way
+
+ align:start position:0%
+recognize that this is not the only way
+ 
+
+ align:start position:0%
+recognize that this is not the only way
+in which a set of vectors can be
+
+ align:start position:0%
+in which a set of vectors can be
+ 
+
+ align:start position:0%
+in which a set of vectors can be
+linearly dependent there are many ways
+
+ align:start position:0%
+linearly dependent there are many ways
+ 
+
+ align:start position:0%
+linearly dependent there are many ways
+in which a set of vectors can be
+
+ align:start position:0%
+in which a set of vectors can be
+ 
+
+ align:start position:0%
+in which a set of vectors can be
+linearly dependent even if no two of the
+
+ align:start position:0%
+linearly dependent even if no two of the
+ 
+
+ align:start position:0%
+linearly dependent even if no two of the
+vectors are equal so consequently given
+
+ align:start position:0%
+vectors are equal so consequently given
+ 
+
+ align:start position:0%
+vectors are equal so consequently given
+a linearly dependent set of vectors in
+
+ align:start position:0%
+a linearly dependent set of vectors in
+ 
+
+ align:start position:0%
+a linearly dependent set of vectors in
+which no two are equal notice that
+
+ align:start position:0%
+which no two are equal notice that
+ 
+
+ align:start position:0%
+which no two are equal notice that
+condition two here will not work or do
+
+ align:start position:0%
+condition two here will not work or do
+ 
+
+ align:start position:0%
+condition two here will not work or do
+anything for me so all I have done by
+
+ align:start position:0%
+anything for me so all I have done by
+ 
+
+ align:start position:0%
+anything for me so all I have done by
+conditions one and two
+
+ align:start position:0%
+conditions one and two
+ 
+
+ align:start position:0%
+conditions one and two
+is I have endowed my D machine with two
+
+ align:start position:0%
+is I have endowed my D machine with two
+ 
+
+ align:start position:0%
+is I have endowed my D machine with two
+standards one particular case in which
+
+ align:start position:0%
+standards one particular case in which
+ 
+
+ align:start position:0%
+standards one particular case in which
+the output of the D machine will be the
+
+ align:start position:0%
+the output of the D machine will be the
+ 
+
+ align:start position:0%
+the output of the D machine will be the
+number one and a particular situation in
+
+ align:start position:0%
+number one and a particular situation in
+ 
+
+ align:start position:0%
+number one and a particular situation in
+which the output of the D machine will
+
+ align:start position:0%
+which the output of the D machine will
+ 
+
+ align:start position:0%
+which the output of the D machine will
+be zero but I have not solved the
+
+ align:start position:0%
+be zero but I have not solved the
+ 
+
+ align:start position:0%
+be zero but I have not solved the
+problem that I wanted so far namely to
+
+ align:start position:0%
+problem that I wanted so far namely to
+ 
+
+ align:start position:0%
+problem that I wanted so far namely to
+make sure that D grinds out zero if and
+
+ align:start position:0%
+make sure that D grinds out zero if and
+ 
+
+ align:start position:0%
+make sure that D grinds out zero if and
+only if the set of n vectors are
+
+ align:start position:0%
+only if the set of n vectors are
+ 
+
+ align:start position:0%
+only if the set of n vectors are
+linearly dependent let me now in Dow d
+
+ align:start position:0%
+linearly dependent let me now in Dow d
+ 
+
+ align:start position:0%
+linearly dependent let me now in Dow d
+with a third property it is a property
+
+ align:start position:0%
+with a third property it is a property
+ 
+
+ align:start position:0%
+with a third property it is a property
+that will suggest linearity to you and
+
+ align:start position:0%
+that will suggest linearity to you and
+ 
+
+ align:start position:0%
+that will suggest linearity to you and
+it's one which is amazingly powerful and
+
+ align:start position:0%
+it's one which is amazingly powerful and
+ 
+
+ align:start position:0%
+it's one which is amazingly powerful and
+what I mean by amazingly powerful
+
+ align:start position:0%
+what I mean by amazingly powerful
+ 
+
+ align:start position:0%
+what I mean by amazingly powerful
+hopefully will become clear in a few
+
+ align:start position:0%
+hopefully will become clear in a few
+ 
+
+ align:start position:0%
+hopefully will become clear in a few
+moments but the third property is this
+
+ align:start position:0%
+moments but the third property is this
+ 
+
+ align:start position:0%
+moments but the third property is this
+and rather than work with endles here to
+
+ align:start position:0%
+and rather than work with endles here to
+ 
+
+ align:start position:0%
+and rather than work with endles here to
+make things easier to read let me just
+
+ align:start position:0%
+make things easier to read let me just
+ 
+
+ align:start position:0%
+make things easier to read let me just
+take a three Tuple over here suppose I
+
+ align:start position:0%
+take a three Tuple over here suppose I
+ 
+
+ align:start position:0%
+take a three Tuple over here suppose I
+have a three-dimensional Vector space
+
+ align:start position:0%
+have a three-dimensional Vector space
+ 
+
+ align:start position:0%
+have a three-dimensional Vector space
+and I pick three vectors in that space
+
+ align:start position:0%
+and I pick three vectors in that space
+ 
+
+ align:start position:0%
+and I pick three vectors in that space
+suppose one of those vectors the way
+
+ align:start position:0%
+suppose one of those vectors the way
+ 
+
+ align:start position:0%
+suppose one of those vectors the way
+I've written it here it happens to be
+
+ align:start position:0%
+I've written it here it happens to be
+ 
+
+ align:start position:0%
+I've written it here it happens to be
+the second Vector suppose one of those
+
+ align:start position:0%
+the second Vector suppose one of those
+ 
+
+ align:start position:0%
+the second Vector suppose one of those
+vectors is itself written as the sum of
+
+ align:start position:0%
+vectors is itself written as the sum of
+ 
+
+ align:start position:0%
+vectors is itself written as the sum of
+two other vectors in the space then I
+
+ align:start position:0%
+two other vectors in the space then I
+ 
+
+ align:start position:0%
+two other vectors in the space then I
+tell the D machine to compute this as
+
+ align:start position:0%
+tell the D machine to compute this as
+ 
+
+ align:start position:0%
+tell the D machine to compute this as
+follows linearize this in other words
+
+ align:start position:0%
+follows linearize this in other words
+ 
+
+ align:start position:0%
+follows linearize this in other words
+compute this as if it were the sum of
+
+ align:start position:0%
+compute this as if it were the sum of
+ 
+
+ align:start position:0%
+compute this as if it were the sum of
+two separate determinants one of which
+
+ align:start position:0%
+two separate determinants one of which
+ 
+
+ align:start position:0%
+two separate determinants one of which
+had the Alpha 2 missing and the other of
+
+ align:start position:0%
+had the Alpha 2 missing and the other of
+ 
+
+ align:start position:0%
+had the Alpha 2 missing and the other of
+which had the beta 2 missing in other
+
+ align:start position:0%
+which had the beta 2 missing in other
+ 
+
+ align:start position:0%
+which had the beta 2 missing in other
+words what I do is is I endow the
+
+ align:start position:0%
+words what I do is is I endow the
+ 
+
+ align:start position:0%
+words what I do is is I endow the
+machine with the property that D of
+
+ align:start position:0%
+machine with the property that D of
+ 
+
+ align:start position:0%
+machine with the property that D of
+alpha 1 comma Alpha 2 + beta 2 comma
+
+ align:start position:0%
+alpha 1 comma Alpha 2 + beta 2 comma
+ 
+
+ align:start position:0%
+alpha 1 comma Alpha 2 + beta 2 comma
+Alpha 3 will be D of alpha 1 Alpha 2
+
+ align:start position:0%
+Alpha 3 will be D of alpha 1 Alpha 2
+ 
+
+ align:start position:0%
+Alpha 3 will be D of alpha 1 Alpha 2
+Alpha 3 plus d of alpha 1 beta 2 Alpha
+
+ align:start position:0%
+Alpha 3 plus d of alpha 1 beta 2 Alpha
+ 
+
+ align:start position:0%
+Alpha 3 plus d of alpha 1 beta 2 Alpha
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay and thirdly well thirdly I I don't
+
+ align:start position:0%
+okay and thirdly well thirdly I I don't
+ 
+
+ align:start position:0%
+okay and thirdly well thirdly I I don't
+mean thirdly I mean the other linear
+
+ align:start position:0%
+mean thirdly I mean the other linear
+ 
+
+ align:start position:0%
+mean thirdly I mean the other linear
+property if one of the input vectors is
+
+ align:start position:0%
+property if one of the input vectors is
+ 
+
+ align:start position:0%
+property if one of the input vectors is
+multiplied by a scalar I can Factor the
+
+ align:start position:0%
+multiplied by a scalar I can Factor the
+ 
+
+ align:start position:0%
+multiplied by a scalar I can Factor the
+Scala out in other words if the if the
+
+ align:start position:0%
+Scala out in other words if the if the
+ 
+
+ align:start position:0%
+Scala out in other words if the if the
+three vectors that are being tested in
+
+ align:start position:0%
+three vectors that are being tested in
+ 
+
+ align:start position:0%
+three vectors that are being tested in
+my three-dimensional space have the form
+
+ align:start position:0%
+my three-dimensional space have the form
+ 
+
+ align:start position:0%
+my three-dimensional space have the form
+alpha 1 C Alpha 2 and Alpha 3 D of alpha
+
+ align:start position:0%
+alpha 1 C Alpha 2 and Alpha 3 D of alpha
+ 
+
+ align:start position:0%
+alpha 1 C Alpha 2 and Alpha 3 D of alpha
+1 comma C Alpha 2 comma Alpha 3 will be
+
+ align:start position:0%
+1 comma C Alpha 2 comma Alpha 3 will be
+ 
+
+ align:start position:0%
+1 comma C Alpha 2 comma Alpha 3 will be
+C Factor the C out C * D of alpha 1
+
+ align:start position:0%
+C Factor the C out C * D of alpha 1
+ 
+
+ align:start position:0%
+C Factor the C out C * D of alpha 1
+Alpha 2 Alpha 3 and it's extremely
+
+ align:start position:0%
+Alpha 2 Alpha 3 and it's extremely
+ 
+
+ align:start position:0%
+Alpha 2 Alpha 3 and it's extremely
+important to notice that the C does not
+
+ align:start position:0%
+important to notice that the C does not
+ 
+
+ align:start position:0%
+important to notice that the C does not
+have to be a Scala multiple of all three
+
+ align:start position:0%
+have to be a Scala multiple of all three
+ 
+
+ align:start position:0%
+have to be a Scala multiple of all three
+vectors in the input notice that the
+
+ align:start position:0%
+vectors in the input notice that the
+ 
+
+ align:start position:0%
+vectors in the input notice that the
+fact that the C was multiplying one of
+
+ align:start position:0%
+fact that the C was multiplying one of
+ 
+
+ align:start position:0%
+fact that the C was multiplying one of
+the vectors is enough to factor the C
+
+ align:start position:0%
+the vectors is enough to factor the C
+ 
+
+ align:start position:0%
+the vectors is enough to factor the C
+out without belaboring this point all I
+
+ align:start position:0%
+out without belaboring this point all I
+ 
+
+ align:start position:0%
+out without belaboring this point all I
+want to say was that if the C were
+
+ align:start position:0%
+want to say was that if the C were
+ 
+
+ align:start position:0%
+want to say was that if the C were
+multiplying each of the alphas in other
+
+ align:start position:0%
+multiplying each of the alphas in other
+ 
+
+ align:start position:0%
+multiplying each of the alphas in other
+words If This Were D of C alpha 1 comma
+
+ align:start position:0%
+words If This Were D of C alpha 1 comma
+ 
+
+ align:start position:0%
+words If This Were D of C alpha 1 comma
+C Alpha 2 comma C Alpha 3 this would
+
+ align:start position:0%
+C Alpha 2 comma C Alpha 3 this would
+ 
+
+ align:start position:0%
+C Alpha 2 comma C Alpha 3 this would
+equal C cubed d alpha 1 Alpha 2 Alpha 3
+
+ align:start position:0%
+equal C cubed d alpha 1 Alpha 2 Alpha 3
+ 
+
+ align:start position:0%
+equal C cubed d alpha 1 Alpha 2 Alpha 3
+because we would factor out a c each
+
+ align:start position:0%
+because we would factor out a c each
+ 
+
+ align:start position:0%
+because we would factor out a c each
+time one for each Vector but let me
+
+ align:start position:0%
+time one for each Vector but let me
+ 
+
+ align:start position:0%
+time one for each Vector but let me
+illustrate this in terms of a 2x2
+
+ align:start position:0%
+illustrate this in terms of a 2x2
+ 
+
+ align:start position:0%
+illustrate this in terms of a 2x2
+uh a two-dimensional example for you
+
+ align:start position:0%
+uh a two-dimensional example for you
+ 
+
+ align:start position:0%
+uh a two-dimensional example for you
+suppose I'm dealing in two-dimensional
+
+ align:start position:0%
+suppose I'm dealing in two-dimensional
+ 
+
+ align:start position:0%
+suppose I'm dealing in two-dimensional
+space and I'm dealing with respect to a
+
+ align:start position:0%
+space and I'm dealing with respect to a
+ 
+
+ align:start position:0%
+space and I'm dealing with respect to a
+particular basis U1 and U2 and let's
+
+ align:start position:0%
+particular basis U1 and U2 and let's
+ 
+
+ align:start position:0%
+particular basis U1 and U2 and let's
+suppose that relative to that basis U1
+
+ align:start position:0%
+suppose that relative to that basis U1
+ 
+
+ align:start position:0%
+suppose that relative to that basis U1
+and U2 alpha 1 is the vector 3 comma 1
+
+ align:start position:0%
+and U2 alpha 1 is the vector 3 comma 1
+ 
+
+ align:start position:0%
+and U2 alpha 1 is the vector 3 comma 1
+beta 1 is the vector 6 comma 7 and beta
+
+ align:start position:0%
+beta 1 is the vector 6 comma 7 and beta
+ 
+
+ align:start position:0%
+beta 1 is the vector 6 comma 7 and beta
+2 is the vector 4 comma 5 let's use the
+
+ align:start position:0%
+2 is the vector 4 comma 5 let's use the
+ 
+
+ align:start position:0%
+2 is the vector 4 comma 5 let's use the
+let's recall the fact that one way or
+
+ align:start position:0%
+let's recall the fact that one way or
+ 
+
+ align:start position:0%
+let's recall the fact that one way or
+another we already know how to expand
+
+ align:start position:0%
+another we already know how to expand
+ 
+
+ align:start position:0%
+another we already know how to expand
+two by two determinants even though we
+
+ align:start position:0%
+two by two determinants even though we
+ 
+
+ align:start position:0%
+two by two determinants even though we
+may not know rigorously why the rules
+
+ align:start position:0%
+may not know rigorously why the rules
+ 
+
+ align:start position:0%
+may not know rigorously why the rules
+were chosen the idea is what would alpha
+
+ align:start position:0%
+were chosen the idea is what would alpha
+ 
+
+ align:start position:0%
+were chosen the idea is what would alpha
+1 plus beta 1 be it would be the two
+
+ align:start position:0%
+1 plus beta 1 be it would be the two
+ 
+
+ align:start position:0%
+1 plus beta 1 be it would be the two
+tppo whose first entry was 3 + 6 and
+
+ align:start position:0%
+tppo whose first entry was 3 + 6 and
+ 
+
+ align:start position:0%
+tppo whose first entry was 3 + 6 and
+whose second entry was 1 + 7 in other
+
+ align:start position:0%
+whose second entry was 1 + 7 in other
+ 
+
+ align:start position:0%
+whose second entry was 1 + 7 in other
+words the first row of the determinant
+
+ align:start position:0%
+words the first row of the determinant
+ 
+
+ align:start position:0%
+words the first row of the determinant
+that I'm going to be talking about has
+
+ align:start position:0%
+that I'm going to be talking about has
+ 
+
+ align:start position:0%
+that I'm going to be talking about has
+as its entries 3 + 6 and 1 + 7 beta 2
+
+ align:start position:0%
+as its entries 3 + 6 and 1 + 7 beta 2
+ 
+
+ align:start position:0%
+as its entries 3 + 6 and 1 + 7 beta 2
+which will make up the second row of my
+
+ align:start position:0%
+which will make up the second row of my
+ 
+
+ align:start position:0%
+which will make up the second row of my
+determinant has as its components four
+
+ align:start position:0%
+determinant has as its components four
+ 
+
+ align:start position:0%
+determinant has as its components four
+and five so the second row of my
+
+ align:start position:0%
+and five so the second row of my
+ 
+
+ align:start position:0%
+and five so the second row of my
+determinant is 4 five and using the
+
+ align:start position:0%
+determinant is 4 five and using the
+ 
+
+ align:start position:0%
+determinant is 4 five and using the
+usual rule for multiplying determinance
+
+ align:start position:0%
+usual rule for multiplying determinance
+ 
+
+ align:start position:0%
+usual rule for multiplying determinance
+this is 5 * 9 - 4 * 8 which is 13 and by
+
+ align:start position:0%
+this is 5 * 9 - 4 * 8 which is 13 and by
+ 
+
+ align:start position:0%
+this is 5 * 9 - 4 * 8 which is 13 and by
+the way just to refresh your memories
+
+ align:start position:0%
+the way just to refresh your memories
+ 
+
+ align:start position:0%
+the way just to refresh your memories
+here what have I computed in terms of my
+
+ align:start position:0%
+here what have I computed in terms of my
+ 
+
+ align:start position:0%
+here what have I computed in terms of my
+D language and the alpha 1 Alpha 2 and
+
+ align:start position:0%
+D language and the alpha 1 Alpha 2 and
+ 
+
+ align:start position:0%
+D language and the alpha 1 Alpha 2 and
+beta 2 is used here this is D of alpha 1
+
+ align:start position:0%
+beta 2 is used here this is D of alpha 1
+ 
+
+ align:start position:0%
+beta 2 is used here this is D of alpha 1
+plus beta 1 comma beta 2 all right on
+
+ align:start position:0%
+plus beta 1 comma beta 2 all right on
+ 
+
+ align:start position:0%
+plus beta 1 comma beta 2 all right on
+the other hand what would D of alpha 1
+
+ align:start position:0%
+the other hand what would D of alpha 1
+ 
+
+ align:start position:0%
+the other hand what would D of alpha 1
+beta 2 be D of alpha 1 beta 2 would be
+
+ align:start position:0%
+beta 2 be D of alpha 1 beta 2 would be
+ 
+
+ align:start position:0%
+beta 2 be D of alpha 1 beta 2 would be
+the 2x two determinant whose first row
+
+ align:start position:0%
+the 2x two determinant whose first row
+ 
+
+ align:start position:0%
+the 2x two determinant whose first row
+was 31 and whose second row was
+
+ align:start position:0%
+was 31 and whose second row was
+ 
+
+ align:start position:0%
+was 31 and whose second row was
+45 D of alpha 1 beta 2 would be the
+
+ align:start position:0%
+45 D of alpha 1 beta 2 would be the
+ 
+
+ align:start position:0%
+45 D of alpha 1 beta 2 would be the
+determinant
+
+ align:start position:0%
+determinant
+ 
+
+ align:start position:0%
+determinant
+whose first row I'm sorry D of beta 1
+
+ align:start position:0%
+whose first row I'm sorry D of beta 1
+ 
+
+ align:start position:0%
+whose first row I'm sorry D of beta 1
+comma beta 2 would be the determinant
+
+ align:start position:0%
+comma beta 2 would be the determinant
+ 
+
+ align:start position:0%
+comma beta 2 would be the determinant
+whose first row was 6 comma 67 and whose
+
+ align:start position:0%
+whose first row was 6 comma 67 and whose
+ 
+
+ align:start position:0%
+whose first row was 6 comma 67 and whose
+second row was 45 in other words these
+
+ align:start position:0%
+second row was 45 in other words these
+ 
+
+ align:start position:0%
+second row was 45 in other words these
+matrices here what is this again this is
+
+ align:start position:0%
+matrices here what is this again this is
+ 
+
+ align:start position:0%
+matrices here what is this again this is
+D of alpha 1 beta
+
+ align:start position:0%
+D of alpha 1 beta
+ 
+
+ align:start position:0%
+D of alpha 1 beta
+2 and this one
+
+ align:start position:0%
+2 and this one
+ 
+
+ align:start position:0%
+2 and this one
+here is D of beta 1 beta 2 and notice
+
+ align:start position:0%
+here is D of beta 1 beta 2 and notice
+ 
+
+ align:start position:0%
+here is D of beta 1 beta 2 and notice
+that this determinant by the traditional
+
+ align:start position:0%
+that this determinant by the traditional
+ 
+
+ align:start position:0%
+that this determinant by the traditional
+way of expanding is 11 this determinant
+
+ align:start position:0%
+way of expanding is 11 this determinant
+ 
+
+ align:start position:0%
+way of expanding is 11 this determinant
+is 30 - 28 which is 2 11 + 2 is 13 and
+
+ align:start position:0%
+is 30 - 28 which is 2 11 + 2 is 13 and
+ 
+
+ align:start position:0%
+is 30 - 28 which is 2 11 + 2 is 13 and
+we see that at least in this case D of
+
+ align:start position:0%
+we see that at least in this case D of
+ 
+
+ align:start position:0%
+we see that at least in this case D of
+alpha 1 + beta 1 comma beta 2 is the
+
+ align:start position:0%
+alpha 1 + beta 1 comma beta 2 is the
+ 
+
+ align:start position:0%
+alpha 1 + beta 1 comma beta 2 is the
+same as D of alpha 1 comma beta 2 plus d
+
+ align:start position:0%
+same as D of alpha 1 comma beta 2 plus d
+ 
+
+ align:start position:0%
+same as D of alpha 1 comma beta 2 plus d
+of beta 1 comma beta 2 so at least uh
+
+ align:start position:0%
+of beta 1 comma beta 2 so at least uh
+ 
+
+ align:start position:0%
+of beta 1 comma beta 2 so at least uh
+the first part of property 3 is obeyed
+
+ align:start position:0%
+the first part of property 3 is obeyed
+ 
+
+ align:start position:0%
+the first part of property 3 is obeyed
+in this particular example and to show
+
+ align:start position:0%
+in this particular example and to show
+ 
+
+ align:start position:0%
+in this particular example and to show
+what the second property is let's
+
+ align:start position:0%
+what the second property is let's
+ 
+
+ align:start position:0%
+what the second property is let's
+suppose Alpha 1 now I pick a new Alpha 1
+
+ align:start position:0%
+suppose Alpha 1 now I pick a new Alpha 1
+ 
+
+ align:start position:0%
+suppose Alpha 1 now I pick a new Alpha 1
+we'll call that 2 comma 6 suppose Alpha
+
+ align:start position:0%
+we'll call that 2 comma 6 suppose Alpha
+ 
+
+ align:start position:0%
+we'll call that 2 comma 6 suppose Alpha
+2 is 3 comma 4 then the determinant of
+
+ align:start position:0%
+2 is 3 comma 4 then the determinant of
+ 
+
+ align:start position:0%
+2 is 3 comma 4 then the determinant of
+alpha 1 and Alpha 2 would be what 26 34
+
+ align:start position:0%
+alpha 1 and Alpha 2 would be what 26 34
+ 
+
+ align:start position:0%
+alpha 1 and Alpha 2 would be what 26 34
+right and that's what 8 - 18 which is -
+
+ align:start position:0%
+right and that's what 8 - 18 which is -
+ 
+
+ align:start position:0%
+right and that's what 8 - 18 which is -
+10 on the other hand notice that a
+
+ align:start position:0%
+10 on the other hand notice that a
+ 
+
+ align:start position:0%
+10 on the other hand notice that a
+common that this Vector here could have
+
+ align:start position:0%
+common that this Vector here could have
+ 
+
+ align:start position:0%
+common that this Vector here could have
+been written as twice one comma three I
+
+ align:start position:0%
+been written as twice one comma three I
+ 
+
+ align:start position:0%
+been written as twice one comma three I
+can therefore factor out the two see
+
+ align:start position:0%
+can therefore factor out the two see
+ 
+
+ align:start position:0%
+can therefore factor out the two see
+notice this very carefully notice that
+
+ align:start position:0%
+notice this very carefully notice that
+ 
+
+ align:start position:0%
+notice this very carefully notice that
+the alphas which are written in a row
+
+ align:start position:0%
+the alphas which are written in a row
+ 
+
+ align:start position:0%
+the alphas which are written in a row
+here one row this way each Alpha forms a
+
+ align:start position:0%
+here one row this way each Alpha forms a
+ 
+
+ align:start position:0%
+here one row this way each Alpha forms a
+row when I I use the Matrix
+
+ align:start position:0%
+row when I I use the Matrix
+ 
+
+ align:start position:0%
+row when I I use the Matrix
+interpretation so what I'm saying is
+
+ align:start position:0%
+interpretation so what I'm saying is
+ 
+
+ align:start position:0%
+interpretation so what I'm saying is
+that 2 comma 6 is
+
+ align:start position:0%
+that 2 comma 6 is
+ 
+
+ align:start position:0%
+that 2 comma 6 is
+one vector it's a twole with respect to
+
+ align:start position:0%
+one vector it's a twole with respect to
+ 
+
+ align:start position:0%
+one vector it's a twole with respect to
+the bases U1 and U2 all I'm saying is
+
+ align:start position:0%
+the bases U1 and U2 all I'm saying is
+ 
+
+ align:start position:0%
+the bases U1 and U2 all I'm saying is
+factor out the two from the first row
+
+ align:start position:0%
+factor out the two from the first row
+ 
+
+ align:start position:0%
+factor out the two from the first row
+from the first Vector that leaves me
+
+ align:start position:0%
+from the first Vector that leaves me
+ 
+
+ align:start position:0%
+from the first Vector that leaves me
+with two outside 1 3 3 4 inside and
+
+ align:start position:0%
+with two outside 1 3 3 4 inside and
+ 
+
+ align:start position:0%
+with two outside 1 3 3 4 inside and
+notice that 4 * 4 - 9 is -5 * 2 is also
+
+ align:start position:0%
+notice that 4 * 4 - 9 is -5 * 2 is also
+ 
+
+ align:start position:0%
+notice that 4 * 4 - 9 is -5 * 2 is also
+-10 notice that these indeed are equal
+
+ align:start position:0%
+-10 notice that these indeed are equal
+ 
+
+ align:start position:0%
+-10 notice that these indeed are equal
+and not no that I could factor out the
+
+ align:start position:0%
+and not no that I could factor out the
+ 
+
+ align:start position:0%
+and not no that I could factor out the
+two simply by virtue of the fact that it
+
+ align:start position:0%
+two simply by virtue of the fact that it
+ 
+
+ align:start position:0%
+two simply by virtue of the fact that it
+was a common factor in one row it did
+
+ align:start position:0%
+was a common factor in one row it did
+ 
+
+ align:start position:0%
+was a common factor in one row it did
+not have to be a common factor in both
+
+ align:start position:0%
+not have to be a common factor in both
+ 
+
+ align:start position:0%
+not have to be a common factor in both
+rows in fact if it had been a common
+
+ align:start position:0%
+rows in fact if it had been a common
+ 
+
+ align:start position:0%
+rows in fact if it had been a common
+factor in both rows I would have had to
+
+ align:start position:0%
+factor in both rows I would have had to
+ 
+
+ align:start position:0%
+factor in both rows I would have had to
+factor out at two twice in other words a
+
+ align:start position:0%
+factor out at two twice in other words a
+ 
+
+ align:start position:0%
+factor out at two twice in other words a
+four over here now I can go on with
+
+ align:start position:0%
+four over here now I can go on with
+ 
+
+ align:start position:0%
+four over here now I can go on with
+things like this but again I want to
+
+ align:start position:0%
+things like this but again I want to
+ 
+
+ align:start position:0%
+things like this but again I want to
+stress the overview and the key point is
+
+ align:start position:0%
+stress the overview and the key point is
+ 
+
+ align:start position:0%
+stress the overview and the key point is
+that these three simple properties which
+
+ align:start position:0%
+that these three simple properties which
+ 
+
+ align:start position:0%
+that these three simple properties which
+I've just called simply one two and
+
+ align:start position:0%
+I've just called simply one two and
+ 
+
+ align:start position:0%
+I've just called simply one two and
+three those three properties that I've
+
+ align:start position:0%
+three those three properties that I've
+ 
+
+ align:start position:0%
+three those three properties that I've
+programmed the D machine with are enough
+
+ align:start position:0%
+programmed the D machine with are enough
+ 
+
+ align:start position:0%
+programmed the D machine with are enough
+to completely determine D in other words
+
+ align:start position:0%
+to completely determine D in other words
+ 
+
+ align:start position:0%
+to completely determine D in other words
+if I want to be dramatic over here the
+
+ align:start position:0%
+if I want to be dramatic over here the
+ 
+
+ align:start position:0%
+if I want to be dramatic over here the
+key point is that 1 two and three
+
+ align:start position:0%
+key point is that 1 two and three
+ 
+
+ align:start position:0%
+key point is that 1 two and three
+completely determine D I'll put an
+
+ align:start position:0%
+completely determine D I'll put an
+ 
+
+ align:start position:0%
+completely determine D I'll put an
+exclamation point down there because
+
+ align:start position:0%
+exclamation point down there because
+ 
+
+ align:start position:0%
+exclamation point down there because
+what I claim is that once these three
+
+ align:start position:0%
+what I claim is that once these three
+ 
+
+ align:start position:0%
+what I claim is that once these three
+properties are obeyed there is no
+
+ align:start position:0%
+properties are obeyed there is no
+ 
+
+ align:start position:0%
+properties are obeyed there is no
+possible way for D to behave other than
+
+ align:start position:0%
+possible way for D to behave other than
+ 
+
+ align:start position:0%
+possible way for D to behave other than
+in a very unique well-defined way that
+
+ align:start position:0%
+in a very unique well-defined way that
+ 
+
+ align:start position:0%
+in a very unique well-defined way that
+now has a perfectly well- defined
+
+ align:start position:0%
+now has a perfectly well- defined
+ 
+
+ align:start position:0%
+now has a perfectly well- defined
+structure let me give you some examples
+
+ align:start position:0%
+structure let me give you some examples
+ 
+
+ align:start position:0%
+structure let me give you some examples
+of that structure I'll just prove a
+
+ align:start position:0%
+of that structure I'll just prove a
+ 
+
+ align:start position:0%
+of that structure I'll just prove a
+couple of theorems I'll prove them in
+
+ align:start position:0%
+couple of theorems I'll prove them in
+ 
+
+ align:start position:0%
+couple of theorems I'll prove them in
+two dimensional space leaving it for the
+
+ align:start position:0%
+two dimensional space leaving it for the
+ 
+
+ align:start position:0%
+two dimensional space leaving it for the
+exercises to work in higher dimensional
+
+ align:start position:0%
+exercises to work in higher dimensional
+ 
+
+ align:start position:0%
+exercises to work in higher dimensional
+space but this doesn't get too cluttered
+
+ align:start position:0%
+space but this doesn't get too cluttered
+ 
+
+ align:start position:0%
+space but this doesn't get too cluttered
+first of all what I claim is that the D
+
+ align:start position:0%
+first of all what I claim is that the D
+ 
+
+ align:start position:0%
+first of all what I claim is that the D
+machine is so finicky that if you
+
+ align:start position:0%
+machine is so finicky that if you
+ 
+
+ align:start position:0%
+machine is so finicky that if you
+interchange the order in which the two
+
+ align:start position:0%
+interchange the order in which the two
+ 
+
+ align:start position:0%
+interchange the order in which the two
+vectors are
+
+ align:start position:0%
+vectors are
+ 
+
+ align:start position:0%
+vectors are
+given you change the sign of the
+
+ align:start position:0%
+given you change the sign of the
+ 
+
+ align:start position:0%
+given you change the sign of the
+output okay and in other words D of
+
+ align:start position:0%
+output okay and in other words D of
+ 
+
+ align:start position:0%
+output okay and in other words D of
+alpha 1 Alpha 2 in that order is the
+
+ align:start position:0%
+alpha 1 Alpha 2 in that order is the
+ 
+
+ align:start position:0%
+alpha 1 Alpha 2 in that order is the
+negative of D of Alpha 2 alpha 1 and the
+
+ align:start position:0%
+negative of D of Alpha 2 alpha 1 and the
+ 
+
+ align:start position:0%
+negative of D of Alpha 2 alpha 1 and the
+proof again follows very nicely in terms
+
+ align:start position:0%
+proof again follows very nicely in terms
+ 
+
+ align:start position:0%
+proof again follows very nicely in terms
+of our game structure the gimmick to
+
+ align:start position:0%
+of our game structure the gimmick to
+ 
+
+ align:start position:0%
+of our game structure the gimmick to
+begin with is that we must be clever
+
+ align:start position:0%
+begin with is that we must be clever
+ 
+
+ align:start position:0%
+begin with is that we must be clever
+enough to decide that we'll compute the
+
+ align:start position:0%
+enough to decide that we'll compute the
+ 
+
+ align:start position:0%
+enough to decide that we'll compute the
+determinant of alpha 1 + Alpha 2 comma
+
+ align:start position:0%
+determinant of alpha 1 + Alpha 2 comma
+ 
+
+ align:start position:0%
+determinant of alpha 1 + Alpha 2 comma
+alpha 1+ alpha 2 on the One Hand by our
+
+ align:start position:0%
+alpha 1+ alpha 2 on the One Hand by our
+ 
+
+ align:start position:0%
+alpha 1+ alpha 2 on the One Hand by our
+second property since two of the vectors
+
+ align:start position:0%
+second property since two of the vectors
+ 
+
+ align:start position:0%
+second property since two of the vectors
+making up the set being tested are equal
+
+ align:start position:0%
+making up the set being tested are equal
+ 
+
+ align:start position:0%
+making up the set being tested are equal
+it means that that determinant must be
+
+ align:start position:0%
+it means that that determinant must be
+ 
+
+ align:start position:0%
+it means that that determinant must be
+zero on the other hand by property three
+
+ align:start position:0%
+zero on the other hand by property three
+ 
+
+ align:start position:0%
+zero on the other hand by property three
+by linearity splitting this up as two
+
+ align:start position:0%
+by linearity splitting this up as two
+ 
+
+ align:start position:0%
+by linearity splitting this up as two
+terms notice that this is D of alpha 1
+
+ align:start position:0%
+terms notice that this is D of alpha 1
+ 
+
+ align:start position:0%
+terms notice that this is D of alpha 1
+comma alpha 1 + Alpha 2 plus d of Alpha
+
+ align:start position:0%
+comma alpha 1 + Alpha 2 plus d of Alpha
+ 
+
+ align:start position:0%
+comma alpha 1 + Alpha 2 plus d of Alpha
+2 comma alpha 1 + Alpha 2 in other words
+
+ align:start position:0%
+2 comma alpha 1 + Alpha 2 in other words
+ 
+
+ align:start position:0%
+2 comma alpha 1 + Alpha 2 in other words
+this result here now in
+
+ align:start position:0%
+this result here now in
+ 
+
+ align:start position:0%
+this result here now in
+turn noticing that these form of sum I
+
+ align:start position:0%
+turn noticing that these form of sum I
+ 
+
+ align:start position:0%
+turn noticing that these form of sum I
+can rewrite this one as what D of alpha
+
+ align:start position:0%
+can rewrite this one as what D of alpha
+ 
+
+ align:start position:0%
+can rewrite this one as what D of alpha
+1 comma Alpha 1 plus d of alpha 1 comma
+
+ align:start position:0%
+1 comma Alpha 1 plus d of alpha 1 comma
+ 
+
+ align:start position:0%
+1 comma Alpha 1 plus d of alpha 1 comma
+Alpha 2 this one is D of Alpha 2 comma
+
+ align:start position:0%
+Alpha 2 this one is D of Alpha 2 comma
+ 
+
+ align:start position:0%
+Alpha 2 this one is D of Alpha 2 comma
+alpha 1 plus d of Alpha 2 comma Alpha 2
+
+ align:start position:0%
+alpha 1 plus d of Alpha 2 comma Alpha 2
+ 
+
+ align:start position:0%
+alpha 1 plus d of Alpha 2 comma Alpha 2
+I've just written this whole thing out
+
+ align:start position:0%
+I've just written this whole thing out
+ 
+
+ align:start position:0%
+I've just written this whole thing out
+on this next line by Property 2 D of
+
+ align:start position:0%
+on this next line by Property 2 D of
+ 
+
+ align:start position:0%
+on this next line by Property 2 D of
+alpha 1 comma alpha 1 must be Zero D of
+
+ align:start position:0%
+alpha 1 comma alpha 1 must be Zero D of
+ 
+
+ align:start position:0%
+alpha 1 comma alpha 1 must be Zero D of
+Alpha 2 comma Alpha 2 must be zero
+
+ align:start position:0%
+Alpha 2 comma Alpha 2 must be zero
+ 
+
+ align:start position:0%
+Alpha 2 comma Alpha 2 must be zero
+because after all both you see two
+
+ align:start position:0%
+because after all both you see two
+ 
+
+ align:start position:0%
+because after all both you see two
+vectors are equal in
+
+ align:start position:0%
+vectors are equal in
+ 
+
+ align:start position:0%
+vectors are equal in
+this so what do I have left comparing
+
+ align:start position:0%
+this so what do I have left comparing
+ 
+
+ align:start position:0%
+this so what do I have left comparing
+this with this I have the D of alpha 1A
+
+ align:start position:0%
+this with this I have the D of alpha 1A
+ 
+
+ align:start position:0%
+this with this I have the D of alpha 1A
+Alpha 2 plus d of Alpha 2 comma alpha 1
+
+ align:start position:0%
+Alpha 2 plus d of Alpha 2 comma alpha 1
+ 
+
+ align:start position:0%
+Alpha 2 plus d of Alpha 2 comma alpha 1
+is zero and that means that the number
+
+ align:start position:0%
+is zero and that means that the number
+ 
+
+ align:start position:0%
+is zero and that means that the number
+and keep that in mind the determinant is
+
+ align:start position:0%
+and keep that in mind the determinant is
+ 
+
+ align:start position:0%
+and keep that in mind the determinant is
+a number it Maps the N vectors into a
+
+ align:start position:0%
+a number it Maps the N vectors into a
+ 
+
+ align:start position:0%
+a number it Maps the N vectors into a
+number which is either zero or nonzero
+
+ align:start position:0%
+number which is either zero or nonzero
+ 
+
+ align:start position:0%
+number which is either zero or nonzero
+but the determinant of alpha 1 comma
+
+ align:start position:0%
+but the determinant of alpha 1 comma
+ 
+
+ align:start position:0%
+but the determinant of alpha 1 comma
+Alpha 2 therefore must be the negative
+
+ align:start position:0%
+Alpha 2 therefore must be the negative
+ 
+
+ align:start position:0%
+Alpha 2 therefore must be the negative
+of the determinant of Alpha 2 Alpha 1
+
+ align:start position:0%
+of the determinant of Alpha 2 Alpha 1
+ 
+
+ align:start position:0%
+of the determinant of Alpha 2 Alpha 1
+because their sum is
+
+ align:start position:0%
+because their sum is
+ 
+
+ align:start position:0%
+because their sum is
+zero the second theorem and this is the
+
+ align:start position:0%
+zero the second theorem and this is the
+ 
+
+ align:start position:0%
+zero the second theorem and this is the
+one that relates determinants to
+
+ align:start position:0%
+one that relates determinants to
+ 
+
+ align:start position:0%
+one that relates determinants to
+matrices a very fantastic result
+
+ align:start position:0%
+matrices a very fantastic result
+ 
+
+ align:start position:0%
+matrices a very fantastic result
+one that has tremendous practical
+
+ align:start position:0%
+one that has tremendous practical
+ 
+
+ align:start position:0%
+one that has tremendous practical
+application that we'll also talk about
+
+ align:start position:0%
+application that we'll also talk about
+ 
+
+ align:start position:0%
+application that we'll also talk about
+later in the lecture and that is that if
+
+ align:start position:0%
+later in the lecture and that is that if
+ 
+
+ align:start position:0%
+later in the lecture and that is that if
+I take any one of my input vectors and
+
+ align:start position:0%
+I take any one of my input vectors and
+ 
+
+ align:start position:0%
+I take any one of my input vectors and
+replace it by itself plus a Scala
+
+ align:start position:0%
+replace it by itself plus a Scala
+ 
+
+ align:start position:0%
+replace it by itself plus a Scala
+multiple of
+
+ align:start position:0%
+multiple of
+ 
+
+ align:start position:0%
+multiple of
+another I do not change the determinant
+
+ align:start position:0%
+another I do not change the determinant
+ 
+
+ align:start position:0%
+another I do not change the determinant
+in other words for example if I replace
+
+ align:start position:0%
+in other words for example if I replace
+ 
+
+ align:start position:0%
+in other words for example if I replace
+alpha 1 by alpha 1 plus a Scala multiple
+
+ align:start position:0%
+alpha 1 by alpha 1 plus a Scala multiple
+ 
+
+ align:start position:0%
+alpha 1 by alpha 1 plus a Scala multiple
+of Alpha 2 and I leave Alpha 2 alone the
+
+ align:start position:0%
+of Alpha 2 and I leave Alpha 2 alone the
+ 
+
+ align:start position:0%
+of Alpha 2 and I leave Alpha 2 alone the
+the determinant of alpha 1 and Alpha 2
+
+ align:start position:0%
+the determinant of alpha 1 and Alpha 2
+ 
+
+ align:start position:0%
+the determinant of alpha 1 and Alpha 2
+will be the same as the determinant of
+
+ align:start position:0%
+will be the same as the determinant of
+ 
+
+ align:start position:0%
+will be the same as the determinant of
+alpha 1 plus C Alpha 2 comma Alpha 2 and
+
+ align:start position:0%
+alpha 1 plus C Alpha 2 comma Alpha 2 and
+ 
+
+ align:start position:0%
+alpha 1 plus C Alpha 2 comma Alpha 2 and
+again the proof is very easy namely look
+
+ align:start position:0%
+again the proof is very easy namely look
+ 
+
+ align:start position:0%
+again the proof is very easy namely look
+at the expression D of alpha 1 plus C
+
+ align:start position:0%
+at the expression D of alpha 1 plus C
+ 
+
+ align:start position:0%
+at the expression D of alpha 1 plus C
+Alpha 2 comma Alpha 2 use the linearity
+
+ align:start position:0%
+Alpha 2 comma Alpha 2 use the linearity
+ 
+
+ align:start position:0%
+Alpha 2 comma Alpha 2 use the linearity
+property that this is D of this is D of
+
+ align:start position:0%
+property that this is D of this is D of
+ 
+
+ align:start position:0%
+property that this is D of this is D of
+alpha 1 comma Alpha 2 plus d of C Alpha
+
+ align:start position:0%
+alpha 1 comma Alpha 2 plus d of C Alpha
+ 
+
+ align:start position:0%
+alpha 1 comma Alpha 2 plus d of C Alpha
+2 comma Alpha
+
+ align:start position:0%
+2 comma Alpha
+ 
+
+ align:start position:0%
+2 comma Alpha
+2 then use the the second part of the
+
+ align:start position:0%
+2 then use the the second part of the
+ 
+
+ align:start position:0%
+2 then use the the second part of the
+linearity property that the constant
+
+ align:start position:0%
+linearity property that the constant
+ 
+
+ align:start position:0%
+linearity property that the constant
+Factor C can be taken outside here so
+
+ align:start position:0%
+Factor C can be taken outside here so
+ 
+
+ align:start position:0%
+Factor C can be taken outside here so
+this becomes D of alpha 1 Alpha 2 plus C
+
+ align:start position:0%
+this becomes D of alpha 1 Alpha 2 plus C
+ 
+
+ align:start position:0%
+this becomes D of alpha 1 Alpha 2 plus C
+* D of Alpha 2 comma Alpha 2 and notice
+
+ align:start position:0%
+* D of Alpha 2 comma Alpha 2 and notice
+ 
+
+ align:start position:0%
+* D of Alpha 2 comma Alpha 2 and notice
+that since Alpha 2 is repeated here this
+
+ align:start position:0%
+that since Alpha 2 is repeated here this
+ 
+
+ align:start position:0%
+that since Alpha 2 is repeated here this
+determinant is zero and consequently
+
+ align:start position:0%
+determinant is zero and consequently
+ 
+
+ align:start position:0%
+determinant is zero and consequently
+what we've proven is that this is equal
+
+ align:start position:0%
+what we've proven is that this is equal
+ 
+
+ align:start position:0%
+what we've proven is that this is equal
+to this now I've just proven those two
+
+ align:start position:0%
+to this now I've just proven those two
+ 
+
+ align:start position:0%
+to this now I've just proven those two
+theorems because that's about all I need
+
+ align:start position:0%
+theorems because that's about all I need
+ 
+
+ align:start position:0%
+theorems because that's about all I need
+let me show you now that if I had never
+
+ align:start position:0%
+let me show you now that if I had never
+ 
+
+ align:start position:0%
+let me show you now that if I had never
+seen that shortcut method of expanding a
+
+ align:start position:0%
+seen that shortcut method of expanding a
+ 
+
+ align:start position:0%
+seen that shortcut method of expanding a
+2X two determinant as learned in high
+
+ align:start position:0%
+2X two determinant as learned in high
+ 
+
+ align:start position:0%
+2X two determinant as learned in high
+school how these three properties
+
+ align:start position:0%
+school how these three properties
+ 
+
+ align:start position:0%
+school how these three properties
+uniquely determine what D has to mean in
+
+ align:start position:0%
+uniquely determine what D has to mean in
+ 
+
+ align:start position:0%
+uniquely determine what D has to mean in
+other words why I said that these three
+
+ align:start position:0%
+other words why I said that these three
+ 
+
+ align:start position:0%
+other words why I said that these three
+properties uniquely determined d as an
+
+ align:start position:0%
+properties uniquely determined d as an
+ 
+
+ align:start position:0%
+properties uniquely determined d as an
+example let me take a two-dimensional
+
+ align:start position:0%
+example let me take a two-dimensional
+ 
+
+ align:start position:0%
+example let me take a two-dimensional
+Vector space again let me pick U1 and U2
+
+ align:start position:0%
+Vector space again let me pick U1 and U2
+ 
+
+ align:start position:0%
+Vector space again let me pick U1 and U2
+as a specific basis and that's important
+
+ align:start position:0%
+as a specific basis and that's important
+ 
+
+ align:start position:0%
+as a specific basis and that's important
+I've picked a specific basis U1 U2 now I
+
+ align:start position:0%
+I've picked a specific basis U1 U2 now I
+ 
+
+ align:start position:0%
+I've picked a specific basis U1 U2 now I
+pick any two vectors since V is a
+
+ align:start position:0%
+pick any two vectors since V is a
+ 
+
+ align:start position:0%
+pick any two vectors since V is a
+two-dimensional space I pick any two
+
+ align:start position:0%
+two-dimensional space I pick any two
+ 
+
+ align:start position:0%
+two-dimensional space I pick any two
+vectors Alpha 1 and Alpha 2
+
+ align:start position:0%
+vectors Alpha 1 and Alpha 2
+ 
+
+ align:start position:0%
+vectors Alpha 1 and Alpha 2
+and because of this notation this means
+
+ align:start position:0%
+and because of this notation this means
+ 
+
+ align:start position:0%
+and because of this notation this means
+that alpha 1 and Alpha 2 are both linear
+
+ align:start position:0%
+that alpha 1 and Alpha 2 are both linear
+ 
+
+ align:start position:0%
+that alpha 1 and Alpha 2 are both linear
+combinations of U1 and U2 say alpha 1 is
+
+ align:start position:0%
+combinations of U1 and U2 say alpha 1 is
+ 
+
+ align:start position:0%
+combinations of U1 and U2 say alpha 1 is
+this and Alpha 2 is this therefore what
+
+ align:start position:0%
+this and Alpha 2 is this therefore what
+ 
+
+ align:start position:0%
+this and Alpha 2 is this therefore what
+is D of alpha 1 comma Alpha 2 well by
+
+ align:start position:0%
+is D of alpha 1 comma Alpha 2 well by
+ 
+
+ align:start position:0%
+is D of alpha 1 comma Alpha 2 well by
+direct substitution D of alpha 1 Alpha
+
+ align:start position:0%
+direct substitution D of alpha 1 Alpha
+ 
+
+ align:start position:0%
+direct substitution D of alpha 1 Alpha
+2 just replace alpha 1 by what it's
+
+ align:start position:0%
+2 just replace alpha 1 by what it's
+ 
+
+ align:start position:0%
+2 just replace alpha 1 by what it's
+equal to here Alpha 2 by what it's equal
+
+ align:start position:0%
+equal to here Alpha 2 by what it's equal
+ 
+
+ align:start position:0%
+equal to here Alpha 2 by what it's equal
+to here and we get that D of alpha 1
+
+ align:start position:0%
+to here and we get that D of alpha 1
+ 
+
+ align:start position:0%
+to here and we get that D of alpha 1
+Alpha 2 is this expression
+
+ align:start position:0%
+Alpha 2 is this expression
+ 
+
+ align:start position:0%
+Alpha 2 is this expression
+now we use the linearity property we
+
+ align:start position:0%
+now we use the linearity property we
+ 
+
+ align:start position:0%
+now we use the linearity property we
+treat this as one number for the time
+
+ align:start position:0%
+treat this as one number for the time
+ 
+
+ align:start position:0%
+treat this as one number for the time
+being and split this up as a sum other
+
+ align:start position:0%
+being and split this up as a sum other
+ 
+
+ align:start position:0%
+being and split this up as a sum other
+words it's going to be D of this term
+
+ align:start position:0%
+words it's going to be D of this term
+ 
+
+ align:start position:0%
+words it's going to be D of this term
+comma this whole term plus d of this
+
+ align:start position:0%
+comma this whole term plus d of this
+ 
+
+ align:start position:0%
+comma this whole term plus d of this
+term comma this whole term in other
+
+ align:start position:0%
+term comma this whole term in other
+ 
+
+ align:start position:0%
+term comma this whole term in other
+words if I do that this breaks down to
+
+ align:start position:0%
+words if I do that this breaks down to
+ 
+
+ align:start position:0%
+words if I do that this breaks down to
+this now I notice that each of these two
+
+ align:start position:0%
+this now I notice that each of these two
+ 
+
+ align:start position:0%
+this now I notice that each of these two
+is a twole in which the second entry is
+
+ align:start position:0%
+is a twole in which the second entry is
+ 
+
+ align:start position:0%
+is a twole in which the second entry is
+a sum of two terms so I now split this
+
+ align:start position:0%
+a sum of two terms so I now split this
+ 
+
+ align:start position:0%
+a sum of two terms so I now split this
+up into what D of this comma this plus d
+
+ align:start position:0%
+up into what D of this comma this plus d
+ 
+
+ align:start position:0%
+up into what D of this comma this plus d
+of this comma This this term becomes D
+
+ align:start position:0%
+of this comma This this term becomes D
+ 
+
+ align:start position:0%
+of this comma This this term becomes D
+of this comma this term plus d of this
+
+ align:start position:0%
+of this comma this term plus d of this
+ 
+
+ align:start position:0%
+of this comma this term plus d of this
+comma this term and I hope it doesn't
+
+ align:start position:0%
+comma this term and I hope it doesn't
+ 
+
+ align:start position:0%
+comma this term and I hope it doesn't
+sound borish on my part to keep saying D
+
+ align:start position:0%
+sound borish on my part to keep saying D
+ 
+
+ align:start position:0%
+sound borish on my part to keep saying D
+of this comma this I prefer to say that
+
+ align:start position:0%
+of this comma this I prefer to say that
+ 
+
+ align:start position:0%
+of this comma this I prefer to say that
+for you so you can watch what I'm doing
+
+ align:start position:0%
+for you so you can watch what I'm doing
+ 
+
+ align:start position:0%
+for you so you can watch what I'm doing
+and then have you just be able
+
+ align:start position:0%
+and then have you just be able
+ 
+
+ align:start position:0%
+and then have you just be able
+afterwards to read what these things
+
+ align:start position:0%
+afterwards to read what these things
+ 
+
+ align:start position:0%
+afterwards to read what these things
+mean now when I'm down to here notice
+
+ align:start position:0%
+mean now when I'm down to here notice
+ 
+
+ align:start position:0%
+mean now when I'm down to here notice
+that by my second part of linearity I
+
+ align:start position:0%
+that by my second part of linearity I
+ 
+
+ align:start position:0%
+that by my second part of linearity I
+can factor out the a11 from here I can
+
+ align:start position:0%
+can factor out the a11 from here I can
+ 
+
+ align:start position:0%
+can factor out the a11 from here I can
+factor out the a21 because it's a common
+
+ align:start position:0%
+factor out the a21 because it's a common
+ 
+
+ align:start position:0%
+factor out the a21 because it's a common
+factor of this term in other words I can
+
+ align:start position:0%
+factor of this term in other words I can
+ 
+
+ align:start position:0%
+factor of this term in other words I can
+write this term as a11 a21 D of U1 comma
+
+ align:start position:0%
+write this term as a11 a21 D of U1 comma
+ 
+
+ align:start position:0%
+write this term as a11 a21 D of U1 comma
+U2 and again sparing you the details
+
+ align:start position:0%
+U2 and again sparing you the details
+ 
+
+ align:start position:0%
+U2 and again sparing you the details
+notice I can factor out an a11 A2 22
+
+ align:start position:0%
+notice I can factor out an a11 A2 22
+ 
+
+ align:start position:0%
+notice I can factor out an a11 A2 22
+from this term I can factor out an a12
+
+ align:start position:0%
+from this term I can factor out an a12
+ 
+
+ align:start position:0%
+from this term I can factor out an a12
+a21 from this term an a12 a22 from this
+
+ align:start position:0%
+a21 from this term an a12 a22 from this
+ 
+
+ align:start position:0%
+a21 from this term an a12 a22 from this
+term and that this now can be written in
+
+ align:start position:0%
+term and that this now can be written in
+ 
+
+ align:start position:0%
+term and that this now can be written in
+this particular way now what properties
+
+ align:start position:0%
+this particular way now what properties
+ 
+
+ align:start position:0%
+this particular way now what properties
+do I know that D is endowed with I know
+
+ align:start position:0%
+do I know that D is endowed with I know
+ 
+
+ align:start position:0%
+do I know that D is endowed with I know
+first of all that whenever D operates on
+
+ align:start position:0%
+first of all that whenever D operates on
+ 
+
+ align:start position:0%
+first of all that whenever D operates on
+a set of vectors where at least two of
+
+ align:start position:0%
+a set of vectors where at least two of
+ 
+
+ align:start position:0%
+a set of vectors where at least two of
+them are equal D must give zero as an
+
+ align:start position:0%
+them are equal D must give zero as an
+ 
+
+ align:start position:0%
+them are equal D must give zero as an
+output so D of U1 comma U1 is zero again
+
+ align:start position:0%
+output so D of U1 comma U1 is zero again
+ 
+
+ align:start position:0%
+output so D of U1 comma U1 is zero again
+U1 comma U2 is the particular basis with
+
+ align:start position:0%
+U1 comma U2 is the particular basis with
+ 
+
+ align:start position:0%
+U1 comma U2 is the particular basis with
+respect to which I Define V see
+
+ align:start position:0%
+respect to which I Define V see
+ 
+
+ align:start position:0%
+respect to which I Define V see
+therefore by property One D of U1 comma
+
+ align:start position:0%
+therefore by property One D of U1 comma
+ 
+
+ align:start position:0%
+therefore by property One D of U1 comma
+U2 must be
+
+ align:start position:0%
+U2 must be
+ 
+
+ align:start position:0%
+U2 must be
+one D of U2 comma U1 is just a the
+
+ align:start position:0%
+one D of U2 comma U1 is just a the
+ 
+
+ align:start position:0%
+one D of U2 comma U1 is just a the
+permuted order of U1 and U2 therefore by
+
+ align:start position:0%
+permuted order of U1 and U2 therefore by
+ 
+
+ align:start position:0%
+permuted order of U1 and U2 therefore by
+our first theorem that must be minus D
+
+ align:start position:0%
+our first theorem that must be minus D
+ 
+
+ align:start position:0%
+our first theorem that must be minus D
+of U1 U2 therefore it must be minus one
+
+ align:start position:0%
+of U1 U2 therefore it must be minus one
+ 
+
+ align:start position:0%
+of U1 U2 therefore it must be minus one
+and finally D of U2 comma U2 is zero and
+
+ align:start position:0%
+and finally D of U2 comma U2 is zero and
+ 
+
+ align:start position:0%
+and finally D of U2 comma U2 is zero and
+if I now collect everything that I have
+
+ align:start position:0%
+if I now collect everything that I have
+ 
+
+ align:start position:0%
+if I now collect everything that I have
+left here what do I have I have that D
+
+ align:start position:0%
+left here what do I have I have that D
+ 
+
+ align:start position:0%
+left here what do I have I have that D
+of alpha 1 comma Alpha
+
+ align:start position:0%
+of alpha 1 comma Alpha
+ 
+
+ align:start position:0%
+of alpha 1 comma Alpha
+2 is equal to what it's equal to a11 a22
+
+ align:start position:0%
+2 is equal to what it's equal to a11 a22
+ 
+
+ align:start position:0%
+2 is equal to what it's equal to a11 a22
+C * 1 minus a12 a21 in other words this
+
+ align:start position:0%
+C * 1 minus a12 a21 in other words this
+ 
+
+ align:start position:0%
+C * 1 minus a12 a21 in other words this
+is the determinant of alpha 1 comma
+
+ align:start position:0%
+is the determinant of alpha 1 comma
+ 
+
+ align:start position:0%
+is the determinant of alpha 1 comma
+Alpha 2 and let me again put an
+
+ align:start position:0%
+Alpha 2 and let me again put an
+ 
+
+ align:start position:0%
+Alpha 2 and let me again put an
+exclamation point here because if you
+
+ align:start position:0%
+exclamation point here because if you
+ 
+
+ align:start position:0%
+exclamation point here because if you
+now go back to the high school way of
+
+ align:start position:0%
+now go back to the high school way of
+ 
+
+ align:start position:0%
+now go back to the high school way of
+computing this determinant remember how
+
+ align:start position:0%
+computing this determinant remember how
+ 
+
+ align:start position:0%
+computing this determinant remember how
+we did it what would we have obtained
+
+ align:start position:0%
+we did it what would we have obtained
+ 
+
+ align:start position:0%
+we did it what would we have obtained
+and again let me just come back to this
+
+ align:start position:0%
+and again let me just come back to this
+ 
+
+ align:start position:0%
+and again let me just come back to this
+board for a second here remember how you
+
+ align:start position:0%
+board for a second here remember how you
+ 
+
+ align:start position:0%
+board for a second here remember how you
+use the Matrix of coefficients to take
+
+ align:start position:0%
+use the Matrix of coefficients to take
+ 
+
+ align:start position:0%
+use the Matrix of coefficients to take
+the determinant would be What a11 a22
+
+ align:start position:0%
+the determinant would be What a11 a22
+ 
+
+ align:start position:0%
+the determinant would be What a11 a22
+minus a12
+
+ align:start position:0%
+minus a12
+ 
+
+ align:start position:0%
+minus a12
+a21 see again notice two things that
+
+ align:start position:0%
+a21 see again notice two things that
+ 
+
+ align:start position:0%
+a21 see again notice two things that
+happen here first of all I get the same
+
+ align:start position:0%
+happen here first of all I get the same
+ 
+
+ align:start position:0%
+happen here first of all I get the same
+answer as I would have got the
+
+ align:start position:0%
+answer as I would have got the
+ 
+
+ align:start position:0%
+answer as I would have got the
+traditional way and second just as a
+
+ align:start position:0%
+traditional way and second just as a
+ 
+
+ align:start position:0%
+traditional way and second just as a
+minor aside that I'll emphasize more
+
+ align:start position:0%
+minor aside that I'll emphasize more
+ 
+
+ align:start position:0%
+minor aside that I'll emphasize more
+later in the lecture and also in the
+
+ align:start position:0%
+later in the lecture and also in the
+ 
+
+ align:start position:0%
+later in the lecture and also in the
+exercises notice that you can begin to
+
+ align:start position:0%
+exercises notice that you can begin to
+ 
+
+ align:start position:0%
+exercises notice that you can begin to
+suspect that the actual value of the
+
+ align:start position:0%
+suspect that the actual value of the
+ 
+
+ align:start position:0%
+suspect that the actual value of the
+determinant of alpha 1 and Alpha 2
+
+ align:start position:0%
+determinant of alpha 1 and Alpha 2
+ 
+
+ align:start position:0%
+determinant of alpha 1 and Alpha 2
+should depend on what basis was chosen
+
+ align:start position:0%
+should depend on what basis was chosen
+ 
+
+ align:start position:0%
+should depend on what basis was chosen
+because relative to a different basis
+
+ align:start position:0%
+because relative to a different basis
+ 
+
+ align:start position:0%
+because relative to a different basis
+notice that the coefficients might very
+
+ align:start position:0%
+notice that the coefficients might very
+ 
+
+ align:start position:0%
+notice that the coefficients might very
+well be different for Alpha 1 and Alpha
+
+ align:start position:0%
+well be different for Alpha 1 and Alpha
+ 
+
+ align:start position:0%
+well be different for Alpha 1 and Alpha
+2 but I don't want to mention that right
+
+ align:start position:0%
+2 but I don't want to mention that right
+ 
+
+ align:start position:0%
+2 but I don't want to mention that right
+now I think what as I say what the
+
+ align:start position:0%
+now I think what as I say what the
+ 
+
+ align:start position:0%
+now I think what as I say what the
+amazing result is that what I meant by
+
+ align:start position:0%
+amazing result is that what I meant by
+ 
+
+ align:start position:0%
+amazing result is that what I meant by
+saying that these three properties
+
+ align:start position:0%
+saying that these three properties
+ 
+
+ align:start position:0%
+saying that these three properties
+completely determined D is the fact that
+
+ align:start position:0%
+completely determined D is the fact that
+ 
+
+ align:start position:0%
+completely determined D is the fact that
+with these three properties the turned
+
+ align:start position:0%
+with these three properties the turned
+ 
+
+ align:start position:0%
+with these three properties the turned
+out that the high school
+
+ align:start position:0%
+out that the high school
+ 
+
+ align:start position:0%
+out that the high school
+definition was Ironclad meaning there
+
+ align:start position:0%
+definition was Ironclad meaning there
+ 
+
+ align:start position:0%
+definition was Ironclad meaning there
+was no other possible way to define what
+
+ align:start position:0%
+was no other possible way to define what
+ 
+
+ align:start position:0%
+was no other possible way to define what
+the determinant should be if you wanted
+
+ align:start position:0%
+the determinant should be if you wanted
+ 
+
+ align:start position:0%
+the determinant should be if you wanted
+these three properties to be obeyed by
+
+ align:start position:0%
+these three properties to be obeyed by
+ 
+
+ align:start position:0%
+these three properties to be obeyed by
+the way as some quick checks notice that
+
+ align:start position:0%
+the way as some quick checks notice that
+ 
+
+ align:start position:0%
+the way as some quick checks notice that
+relative to the basis U1 U2 U1 can be
+
+ align:start position:0%
+relative to the basis U1 U2 U1 can be
+ 
+
+ align:start position:0%
+relative to the basis U1 U2 U1 can be
+written this way U2 can be written this
+
+ align:start position:0%
+written this way U2 can be written this
+ 
+
+ align:start position:0%
+written this way U2 can be written this
+way we know that D of U1 U2 should be
+
+ align:start position:0%
+way we know that D of U1 U2 should be
+ 
+
+ align:start position:0%
+way we know that D of U1 U2 should be
+one and using the oldfashioned way for
+
+ align:start position:0%
+one and using the oldfashioned way for
+ 
+
+ align:start position:0%
+one and using the oldfashioned way for
+checking this what would the deter B it
+
+ align:start position:0%
+checking this what would the deter B it
+ 
+
+ align:start position:0%
+checking this what would the deter B it
+would be 1 * 1 - 0 * 0 which is 1
+
+ align:start position:0%
+would be 1 * 1 - 0 * 0 which is 1
+ 
+
+ align:start position:0%
+would be 1 * 1 - 0 * 0 which is 1
+secondly we also know that property two
+
+ align:start position:0%
+secondly we also know that property two
+ 
+
+ align:start position:0%
+secondly we also know that property two
+should yield zero as a determinant if
+
+ align:start position:0%
+should yield zero as a determinant if
+ 
+
+ align:start position:0%
+should yield zero as a determinant if
+the two vectors that were making up the
+
+ align:start position:0%
+the two vectors that were making up the
+ 
+
+ align:start position:0%
+the two vectors that were making up the
+input were equal let's call the vectors
+
+ align:start position:0%
+input were equal let's call the vectors
+ 
+
+ align:start position:0%
+input were equal let's call the vectors
+Au U1 bu U2 so the 2x two determinant I
+
+ align:start position:0%
+Au U1 bu U2 so the 2x two determinant I
+ 
+
+ align:start position:0%
+Au U1 bu U2 so the 2x two determinant I
+would get in this case is a b a b and if
+
+ align:start position:0%
+would get in this case is a b a b and if
+ 
+
+ align:start position:0%
+would get in this case is a b a b and if
+I expand that determinant it's what a *
+
+ align:start position:0%
+I expand that determinant it's what a *
+ 
+
+ align:start position:0%
+I expand that determinant it's what a *
+B minus a * B which is zero
+
+ align:start position:0%
+B minus a * B which is zero
+ 
+
+ align:start position:0%
+B minus a * B which is zero
+and now let me come back to that idea of
+
+ align:start position:0%
+and now let me come back to that idea of
+ 
+
+ align:start position:0%
+and now let me come back to that idea of
+what motivated the whole block of
+
+ align:start position:0%
+what motivated the whole block of
+ 
+
+ align:start position:0%
+what motivated the whole block of
+material here the trouble with writing
+
+ align:start position:0%
+material here the trouble with writing
+ 
+
+ align:start position:0%
+material here the trouble with writing
+vectors as endles that there really is
+
+ align:start position:0%
+vectors as endles that there really is
+ 
+
+ align:start position:0%
+vectors as endles that there really is
+something that requires Great care in
+
+ align:start position:0%
+something that requires Great care in
+ 
+
+ align:start position:0%
+something that requires Great care in
+advanced applications one must always be
+
+ align:start position:0%
+advanced applications one must always be
+ 
+
+ align:start position:0%
+advanced applications one must always be
+wary of this I am not going to give you
+
+ align:start position:0%
+wary of this I am not going to give you
+ 
+
+ align:start position:0%
+wary of this I am not going to give you
+the advanced applications here all I
+
+ align:start position:0%
+the advanced applications here all I
+ 
+
+ align:start position:0%
+the advanced applications here all I
+want you to do is to become prepared
+
+ align:start position:0%
+want you to do is to become prepared
+ 
+
+ align:start position:0%
+want you to do is to become prepared
+against the pitfalls and the thing is
+
+ align:start position:0%
+against the pitfalls and the thing is
+ 
+
+ align:start position:0%
+against the pitfalls and the thing is
+that in dealing with determinance as I
+
+ align:start position:0%
+that in dealing with determinance as I
+ 
+
+ align:start position:0%
+that in dealing with determinance as I
+said before you must be very very
+
+ align:start position:0%
+said before you must be very very
+ 
+
+ align:start position:0%
+said before you must be very very
+careful about what basis you're
+
+ align:start position:0%
+careful about what basis you're
+ 
+
+ align:start position:0%
+careful about what basis you're
+referring to for a given Vector space
+
+ align:start position:0%
+referring to for a given Vector space
+ 
+
+ align:start position:0%
+referring to for a given Vector space
+obviously the vectors do not depend on
+
+ align:start position:0%
+obviously the vectors do not depend on
+ 
+
+ align:start position:0%
+obviously the vectors do not depend on
+the basis but their representation does
+
+ align:start position:0%
+the basis but their representation does
+ 
+
+ align:start position:0%
+the basis but their representation does
+let me give you a for instance using V
+
+ align:start position:0%
+let me give you a for instance using V
+ 
+
+ align:start position:0%
+let me give you a for instance using V
+and U1 and U2 as in example number one
+
+ align:start position:0%
+and U1 and U2 as in example number one
+ 
+
+ align:start position:0%
+and U1 and U2 as in example number one
+suppose we let alpha 1 be the twole 3
+
+ align:start position:0%
+suppose we let alpha 1 be the twole 3
+ 
+
+ align:start position:0%
+suppose we let alpha 1 be the twole 3
+comma 4 in other words 3 U1 + 4 U2 and
+
+ align:start position:0%
+comma 4 in other words 3 U1 + 4 U2 and
+ 
+
+ align:start position:0%
+comma 4 in other words 3 U1 + 4 U2 and
+let Alpha 2 be 2 comma 5 then by what
+
+ align:start position:0%
+let Alpha 2 be 2 comma 5 then by what
+ 
+
+ align:start position:0%
+let Alpha 2 be 2 comma 5 then by what
+we've just proven the determinant of
+
+ align:start position:0%
+we've just proven the determinant of
+ 
+
+ align:start position:0%
+we've just proven the determinant of
+alpha 1 comma Alpha 2 must be the
+
+ align:start position:0%
+alpha 1 comma Alpha 2 must be the
+ 
+
+ align:start position:0%
+alpha 1 comma Alpha 2 must be the
+determinant of what Matrix the one whose
+
+ align:start position:0%
+determinant of what Matrix the one whose
+ 
+
+ align:start position:0%
+determinant of what Matrix the one whose
+first row is 3 comma four and whose
+
+ align:start position:0%
+first row is 3 comma four and whose
+ 
+
+ align:start position:0%
+first row is 3 comma four and whose
+second row is 2 comma 5 if I compute
+
+ align:start position:0%
+second row is 2 comma 5 if I compute
+ 
+
+ align:start position:0%
+second row is 2 comma 5 if I compute
+that determinant by the way notice now
+
+ align:start position:0%
+that determinant by the way notice now
+ 
+
+ align:start position:0%
+that determinant by the way notice now
+that I know that the shortcut way has to
+
+ align:start position:0%
+that I know that the shortcut way has to
+ 
+
+ align:start position:0%
+that I know that the shortcut way has to
+be the right answer I don't do this the
+
+ align:start position:0%
+be the right answer I don't do this the
+ 
+
+ align:start position:0%
+be the right answer I don't do this the
+long way anymore I just say Okay it's 3
+
+ align:start position:0%
+long way anymore I just say Okay it's 3
+ 
+
+ align:start position:0%
+long way anymore I just say Okay it's 3
+* 5 - 2 * 4 15 - 8 which is seven so the
+
+ align:start position:0%
+* 5 - 2 * 4 15 - 8 which is seven so the
+ 
+
+ align:start position:0%
+* 5 - 2 * 4 15 - 8 which is seven so the
+determinant of alpha 1 Alpha 2 is seven
+
+ align:start position:0%
+determinant of alpha 1 Alpha 2 is seven
+ 
+
+ align:start position:0%
+determinant of alpha 1 Alpha 2 is seven
+all right so far so good but let me
+
+ align:start position:0%
+all right so far so good but let me
+ 
+
+ align:start position:0%
+all right so far so good but let me
+point out the following thing notice
+
+ align:start position:0%
+point out the following thing notice
+ 
+
+ align:start position:0%
+point out the following thing notice
+that alpha 1 and Alpha 2 are also
+
+ align:start position:0%
+that alpha 1 and Alpha 2 are also
+ 
+
+ align:start position:0%
+that alpha 1 and Alpha 2 are also
+linearly independent namely 3 comma 4 is
+
+ align:start position:0%
+linearly independent namely 3 comma 4 is
+ 
+
+ align:start position:0%
+linearly independent namely 3 comma 4 is
+not a scalar multiple of 2 comma 5
+
+ align:start position:0%
+not a scalar multiple of 2 comma 5
+ 
+
+ align:start position:0%
+not a scalar multiple of 2 comma 5
+consequently since alpha 1 and Alpha 2
+
+ align:start position:0%
+consequently since alpha 1 and Alpha 2
+ 
+
+ align:start position:0%
+consequently since alpha 1 and Alpha 2
+are linearly independent and since V is
+
+ align:start position:0%
+are linearly independent and since V is
+ 
+
+ align:start position:0%
+are linearly independent and since V is
+a two-dimensional space it means that
+
+ align:start position:0%
+a two-dimensional space it means that
+ 
+
+ align:start position:0%
+a two-dimensional space it means that
+alpha 1 and Alpha 2 are themselves a
+
+ align:start position:0%
+alpha 1 and Alpha 2 are themselves a
+ 
+
+ align:start position:0%
+alpha 1 and Alpha 2 are themselves a
+basis for v in other words V is equal to
+
+ align:start position:0%
+basis for v in other words V is equal to
+ 
+
+ align:start position:0%
+basis for v in other words V is equal to
+the space span by Alpha 1 and Alpha 2 as
+
+ align:start position:0%
+the space span by Alpha 1 and Alpha 2 as
+ 
+
+ align:start position:0%
+the space span by Alpha 1 and Alpha 2 as
+a basis notice that relative to this new
+
+ align:start position:0%
+a basis notice that relative to this new
+ 
+
+ align:start position:0%
+a basis notice that relative to this new
+basis alpha 1 comma Alpha 2 alpha 1 is 1
+
+ align:start position:0%
+basis alpha 1 comma Alpha 2 alpha 1 is 1
+ 
+
+ align:start position:0%
+basis alpha 1 comma Alpha 2 alpha 1 is 1
+Alpha 1 + 0 Alpha 2 Alpha 2 is 0 alpha 1
+
+ align:start position:0%
+Alpha 1 + 0 Alpha 2 Alpha 2 is 0 alpha 1
+ 
+
+ align:start position:0%
+Alpha 1 + 0 Alpha 2 Alpha 2 is 0 alpha 1
++ 1 Alpha 2 and therefore using the
+
+ align:start position:0%
++ 1 Alpha 2 and therefore using the
+ 
+
+ align:start position:0%
++ 1 Alpha 2 and therefore using the
+traditional method of computing the
+
+ align:start position:0%
+traditional method of computing the
+ 
+
+ align:start position:0%
+traditional method of computing the
+determinant notice that the determinant
+
+ align:start position:0%
+determinant notice that the determinant
+ 
+
+ align:start position:0%
+determinant notice that the determinant
+of alpha 1 comma Alpha 2 relative to the
+
+ align:start position:0%
+of alpha 1 comma Alpha 2 relative to the
+ 
+
+ align:start position:0%
+of alpha 1 comma Alpha 2 relative to the
+basis alpha 1 and Alpha 2 would be what
+
+ align:start position:0%
+basis alpha 1 and Alpha 2 would be what
+ 
+
+ align:start position:0%
+basis alpha 1 and Alpha 2 would be what
+determinant it would be the determinant
+
+ align:start position:0%
+determinant it would be the determinant
+ 
+
+ align:start position:0%
+determinant it would be the determinant
+of the Matrix whose first row was one
+
+ align:start position:0%
+of the Matrix whose first row was one
+ 
+
+ align:start position:0%
+of the Matrix whose first row was one
+Zer and whose second row was 01 and that
+
+ align:start position:0%
+Zer and whose second row was 01 and that
+ 
+
+ align:start position:0%
+Zer and whose second row was 01 and that
+is one this looks like a contradiction
+
+ align:start position:0%
+is one this looks like a contradiction
+ 
+
+ align:start position:0%
+is one this looks like a contradiction
+you see on the one hand we have that D
+
+ align:start position:0%
+you see on the one hand we have that D
+ 
+
+ align:start position:0%
+you see on the one hand we have that D
+of alpha 1 Alpha 2 is one but down here
+
+ align:start position:0%
+of alpha 1 Alpha 2 is one but down here
+ 
+
+ align:start position:0%
+of alpha 1 Alpha 2 is one but down here
+we just
+
+ align:start position:0%
+we just
+ 
+
+ align:start position:0%
+we just
+saw that D of alpha 1 Alpha 2 was seven
+
+ align:start position:0%
+saw that D of alpha 1 Alpha 2 was seven
+ 
+
+ align:start position:0%
+saw that D of alpha 1 Alpha 2 was seven
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+correct well the answer is they're both
+
+ align:start position:0%
+correct well the answer is they're both
+ 
+
+ align:start position:0%
+correct well the answer is they're both
+correct that the first observation is
+
+ align:start position:0%
+correct that the first observation is
+ 
+
+ align:start position:0%
+correct that the first observation is
+that if the determinant of alpha 1 and
+
+ align:start position:0%
+that if the determinant of alpha 1 and
+ 
+
+ align:start position:0%
+that if the determinant of alpha 1 and
+Alpha 2 is not zero the value depends on
+
+ align:start position:0%
+Alpha 2 is not zero the value depends on
+ 
+
+ align:start position:0%
+Alpha 2 is not zero the value depends on
+the particular basis in other words if
+
+ align:start position:0%
+the particular basis in other words if
+ 
+
+ align:start position:0%
+the particular basis in other words if
+the determinant is zero it turns out
+
+ align:start position:0%
+the determinant is zero it turns out
+ 
+
+ align:start position:0%
+the determinant is zero it turns out
+that no matter what basis you use to
+
+ align:start position:0%
+that no matter what basis you use to
+ 
+
+ align:start position:0%
+that no matter what basis you use to
+represent the determinant of alpha 1 and
+
+ align:start position:0%
+represent the determinant of alpha 1 and
+ 
+
+ align:start position:0%
+represent the determinant of alpha 1 and
+Alpha 2 you will get zero once the
+
+ align:start position:0%
+Alpha 2 you will get zero once the
+ 
+
+ align:start position:0%
+Alpha 2 you will get zero once the
+determinant is zero in one basis and if
+
+ align:start position:0%
+determinant is zero in one basis and if
+ 
+
+ align:start position:0%
+determinant is zero in one basis and if
+the determinant is not zero with respect
+
+ align:start position:0%
+the determinant is not zero with respect
+ 
+
+ align:start position:0%
+the determinant is not zero with respect
+to a particular basis it will be non
+
+ align:start position:0%
+to a particular basis it will be non
+ 
+
+ align:start position:0%
+to a particular basis it will be non
+zero with respect to all bases but what
+
+ align:start position:0%
+zero with respect to all bases but what
+ 
+
+ align:start position:0%
+zero with respect to all bases but what
+nonzero number it will be does depend on
+
+ align:start position:0%
+nonzero number it will be does depend on
+ 
+
+ align:start position:0%
+nonzero number it will be does depend on
+the basis and that was why way back at
+
+ align:start position:0%
+the basis and that was why way back at
+ 
+
+ align:start position:0%
+the basis and that was why way back at
+the beginning we told the D machine
+
+ align:start position:0%
+the beginning we told the D machine
+ 
+
+ align:start position:0%
+the beginning we told the D machine
+simply to give a nonzero
+
+ align:start position:0%
+simply to give a nonzero
+ 
+
+ align:start position:0%
+simply to give a nonzero
+output if the the input was a set of n
+
+ align:start position:0%
+output if the the input was a set of n
+ 
+
+ align:start position:0%
+output if the the input was a set of n
+linearly independent vectors in summary
+
+ align:start position:0%
+linearly independent vectors in summary
+ 
+
+ align:start position:0%
+linearly independent vectors in summary
+when one says that the determinant of
+
+ align:start position:0%
+when one says that the determinant of
+ 
+
+ align:start position:0%
+when one says that the determinant of
+alpha 1 and Alpha 2 is seven it's
+
+ align:start position:0%
+alpha 1 and Alpha 2 is seven it's
+ 
+
+ align:start position:0%
+alpha 1 and Alpha 2 is seven it's
+tacitly assumed that D is being referred
+
+ align:start position:0%
+tacitly assumed that D is being referred
+ 
+
+ align:start position:0%
+tacitly assumed that D is being referred
+to with respect to the particular basis
+
+ align:start position:0%
+to with respect to the particular basis
+ 
+
+ align:start position:0%
+to with respect to the particular basis
+alpha 1 uh U1 U2 on the other hand when
+
+ align:start position:0%
+alpha 1 uh U1 U2 on the other hand when
+ 
+
+ align:start position:0%
+alpha 1 uh U1 U2 on the other hand when
+one says that D of alpha 1 Alpha 2 is 1
+
+ align:start position:0%
+one says that D of alpha 1 Alpha 2 is 1
+ 
+
+ align:start position:0%
+one says that D of alpha 1 Alpha 2 is 1
+it's tacitly assumed that the basis that
+
+ align:start position:0%
+it's tacitly assumed that the basis that
+ 
+
+ align:start position:0%
+it's tacitly assumed that the basis that
+we're using to express V is Alpha 1 and
+
+ align:start position:0%
+we're using to express V is Alpha 1 and
+ 
+
+ align:start position:0%
+we're using to express V is Alpha 1 and
+Alpha 2 again I'll drill that more in
+
+ align:start position:0%
+Alpha 2 again I'll drill that more in
+ 
+
+ align:start position:0%
+Alpha 2 again I'll drill that more in
+the exercises let me go on now to
+
+ align:start position:0%
+the exercises let me go on now to
+ 
+
+ align:start position:0%
+the exercises let me go on now to
+generalize what happens in n-dimensional
+
+ align:start position:0%
+generalize what happens in n-dimensional
+ 
+
+ align:start position:0%
+generalize what happens in n-dimensional
+space keeping in mind the fact that when
+
+ align:start position:0%
+space keeping in mind the fact that when
+ 
+
+ align:start position:0%
+space keeping in mind the fact that when
+we generalize what happens in
+
+ align:start position:0%
+we generalize what happens in
+ 
+
+ align:start position:0%
+we generalize what happens in
+n-dimensional Space the actual proofs
+
+ align:start position:0%
+n-dimensional Space the actual proofs
+ 
+
+ align:start position:0%
+n-dimensional Space the actual proofs
+become Messier but the theory remains
+
+ align:start position:0%
+become Messier but the theory remains
+ 
+
+ align:start position:0%
+become Messier but the theory remains
+very much the same I prefer to leave the
+
+ align:start position:0%
+very much the same I prefer to leave the
+ 
+
+ align:start position:0%
+very much the same I prefer to leave the
+messy details to the exercises either
+
+ align:start position:0%
+messy details to the exercises either
+ 
+
+ align:start position:0%
+messy details to the exercises either
+optional or required depending on how
+
+ align:start position:0%
+optional or required depending on how
+ 
+
+ align:start position:0%
+optional or required depending on how
+hard the exercises may be but let me
+
+ align:start position:0%
+hard the exercises may be but let me
+ 
+
+ align:start position:0%
+hard the exercises may be but let me
+summarize what the results are for any
+
+ align:start position:0%
+summarize what the results are for any
+ 
+
+ align:start position:0%
+summarize what the results are for any
+n-dimensional space keeping in mind
+
+ align:start position:0%
+n-dimensional space keeping in mind
+ 
+
+ align:start position:0%
+n-dimensional space keeping in mind
+we've proven the results rigorously for
+
+ align:start position:0%
+we've proven the results rigorously for
+ 
+
+ align:start position:0%
+we've proven the results rigorously for
+the case n equals 2 the generalization
+
+ align:start position:0%
+the case n equals 2 the generalization
+ 
+
+ align:start position:0%
+the case n equals 2 the generalization
+is this if I have an N dimensional
+
+ align:start position:0%
+is this if I have an N dimensional
+ 
+
+ align:start position:0%
+is this if I have an N dimensional
+Vector space V with respect to a
+
+ align:start position:0%
+Vector space V with respect to a
+ 
+
+ align:start position:0%
+Vector space V with respect to a
+particular basis U1 up to unu n and if
+
+ align:start position:0%
+particular basis U1 up to unu n and if
+ 
+
+ align:start position:0%
+particular basis U1 up to unu n and if
+alpha 1 up to alpha n are n vectors
+
+ align:start position:0%
+alpha 1 up to alpha n are n vectors
+ 
+
+ align:start position:0%
+alpha 1 up to alpha n are n vectors
+chosen from V so that they are linear
+
+ align:start position:0%
+chosen from V so that they are linear
+ 
+
+ align:start position:0%
+chosen from V so that they are linear
+combinations of the U's say in the
+
+ align:start position:0%
+combinations of the U's say in the
+ 
+
+ align:start position:0%
+combinations of the U's say in the
+traditional way that we've written these
+
+ align:start position:0%
+traditional way that we've written these
+ 
+
+ align:start position:0%
+traditional way that we've written these
+all the time it turns out the following
+
+ align:start position:0%
+all the time it turns out the following
+ 
+
+ align:start position:0%
+all the time it turns out the following
+that the determinant of alpha 1 up to
+
+ align:start position:0%
+that the determinant of alpha 1 up to
+ 
+
+ align:start position:0%
+that the determinant of alpha 1 up to
+Alpha
+
+ align:start position:0%
+Alpha
+ 
+
+ align:start position:0%
+Alpha
+n first of all it's conventional and
+
+ align:start position:0%
+n first of all it's conventional and
+ 
+
+ align:start position:0%
+n first of all it's conventional and
+convenient to write the determinant as
+
+ align:start position:0%
+convenient to write the determinant as
+ 
+
+ align:start position:0%
+convenient to write the determinant as
+if it were a matrix only replacing the
+
+ align:start position:0%
+if it were a matrix only replacing the
+ 
+
+ align:start position:0%
+if it were a matrix only replacing the
+square brackets by sort of absolute
+
+ align:start position:0%
+square brackets by sort of absolute
+ 
+
+ align:start position:0%
+square brackets by sort of absolute
+value signs vertical lines what we do is
+
+ align:start position:0%
+value signs vertical lines what we do is
+ 
+
+ align:start position:0%
+value signs vertical lines what we do is
+notice that alpha 1 is written as an
+
+ align:start position:0%
+notice that alpha 1 is written as an
+ 
+
+ align:start position:0%
+notice that alpha 1 is written as an
+nppo a11 up to a1n in other words the
+
+ align:start position:0%
+nppo a11 up to a1n in other words the
+ 
+
+ align:start position:0%
+nppo a11 up to a1n in other words the
+first row of the determinant represents
+
+ align:start position:0%
+first row of the determinant represents
+ 
+
+ align:start position:0%
+first row of the determinant represents
+alpha 1 as an nle Vector relative to the
+
+ align:start position:0%
+alpha 1 as an nle Vector relative to the
+ 
+
+ align:start position:0%
+alpha 1 as an nle Vector relative to the
+basis U1 up to unu n and a similar thing
+
+ align:start position:0%
+basis U1 up to unu n and a similar thing
+ 
+
+ align:start position:0%
+basis U1 up to unu n and a similar thing
+holds for Alpha 2 through alpha n and
+
+ align:start position:0%
+holds for Alpha 2 through alpha n and
+ 
+
+ align:start position:0%
+holds for Alpha 2 through alpha n and
+you may remember I told you what the
+
+ align:start position:0%
+you may remember I told you what the
+ 
+
+ align:start position:0%
+you may remember I told you what the
+recipe was when we were dealing with uh
+
+ align:start position:0%
+recipe was when we were dealing with uh
+ 
+
+ align:start position:0%
+recipe was when we were dealing with uh
+I told you what the re was when we were
+
+ align:start position:0%
+I told you what the re was when we were
+ 
+
+ align:start position:0%
+I told you what the re was when we were
+dealing with cross products and the like
+
+ align:start position:0%
+dealing with cross products and the like
+ 
+
+ align:start position:0%
+dealing with cross products and the like
+and the idea is simply this what you do
+
+ align:start position:0%
+and the idea is simply this what you do
+ 
+
+ align:start position:0%
+and the idea is simply this what you do
+is is you start in the upper left hand
+
+ align:start position:0%
+is is you start in the upper left hand
+ 
+
+ align:start position:0%
+is is you start in the upper left hand
+corner writing a plus sign then you
+
+ align:start position:0%
+corner writing a plus sign then you
+ 
+
+ align:start position:0%
+corner writing a plus sign then you
+alternate going along rows and columns
+
+ align:start position:0%
+alternate going along rows and columns
+ 
+
+ align:start position:0%
+alternate going along rows and columns
+in any order you want writing plus minus
+
+ align:start position:0%
+in any order you want writing plus minus
+ 
+
+ align:start position:0%
+in any order you want writing plus minus
+plus minus Etc plusus plus minus Etc
+
+ align:start position:0%
+plus minus Etc plusus plus minus Etc
+ 
+
+ align:start position:0%
+plus minus Etc plusus plus minus Etc
+pick any row or column that you want and
+
+ align:start position:0%
+pick any row or column that you want and
+ 
+
+ align:start position:0%
+pick any row or column that you want and
+then you go down that row or column
+
+ align:start position:0%
+then you go down that row or column
+ 
+
+ align:start position:0%
+then you go down that row or column
+factoring out a particular term the plus
+
+ align:start position:0%
+factoring out a particular term the plus
+ 
+
+ align:start position:0%
+factoring out a particular term the plus
+sign telling you to take out the term as
+
+ align:start position:0%
+sign telling you to take out the term as
+ 
+
+ align:start position:0%
+sign telling you to take out the term as
+it is the minus sign telling you to take
+
+ align:start position:0%
+it is the minus sign telling you to take
+ 
+
+ align:start position:0%
+it is the minus sign telling you to take
+out the term and change its sign and you
+
+ align:start position:0%
+out the term and change its sign and you
+ 
+
+ align:start position:0%
+out the term and change its sign and you
+multiply that term by the nus1 by nus1
+
+ align:start position:0%
+multiply that term by the nus1 by nus1
+ 
+
+ align:start position:0%
+multiply that term by the nus1 by nus1
+matrix that's left when you strike out
+
+ align:start position:0%
+matrix that's left when you strike out
+ 
+
+ align:start position:0%
+matrix that's left when you strike out
+the row and column in which that term
+
+ align:start position:0%
+the row and column in which that term
+ 
+
+ align:start position:0%
+the row and column in which that term
+occurs now if that still sounds like a
+
+ align:start position:0%
+occurs now if that still sounds like a
+ 
+
+ align:start position:0%
+occurs now if that still sounds like a
+tongue twister let's do this in terms of
+
+ align:start position:0%
+tongue twister let's do this in terms of
+ 
+
+ align:start position:0%
+tongue twister let's do this in terms of
+a specific semi-abstract semic concrete
+
+ align:start position:0%
+a specific semi-abstract semic concrete
+ 
+
+ align:start position:0%
+a specific semi-abstract semic concrete
+four-dimensional case namely let's
+
+ align:start position:0%
+four-dimensional case namely let's
+ 
+
+ align:start position:0%
+four-dimensional case namely let's
+suppose V is a four-dimensional vector
+
+ align:start position:0%
+suppose V is a four-dimensional vector
+ 
+
+ align:start position:0%
+suppose V is a four-dimensional vector
+space relative to a particular basis U1
+
+ align:start position:0%
+space relative to a particular basis U1
+ 
+
+ align:start position:0%
+space relative to a particular basis U1
+U2 u3 and u4 suppose alpha 1 Alpha 2
+
+ align:start position:0%
+U2 u3 and u4 suppose alpha 1 Alpha 2
+ 
+
+ align:start position:0%
+U2 u3 and u4 suppose alpha 1 Alpha 2
+Alpha 3 and Alpha 4 are these four
+
+ align:start position:0%
+Alpha 3 and Alpha 4 are these four
+ 
+
+ align:start position:0%
+Alpha 3 and Alpha 4 are these four
+specific vectors of v and again I can't
+
+ align:start position:0%
+specific vectors of v and again I can't
+ 
+
+ align:start position:0%
+specific vectors of v and again I can't
+keep emphasizing this too much even
+
+ align:start position:0%
+keep emphasizing this too much even
+ 
+
+ align:start position:0%
+keep emphasizing this too much even
+though I hope some of you are bored
+
+ align:start position:0%
+though I hope some of you are bored
+ 
+
+ align:start position:0%
+though I hope some of you are bored
+because you know it so well it's always
+
+ align:start position:0%
+because you know it so well it's always
+ 
+
+ align:start position:0%
+because you know it so well it's always
+understood when I write this that the
+
+ align:start position:0%
+understood when I write this that the
+ 
+
+ align:start position:0%
+understood when I write this that the
+components are relative to U1 U2 u3 u4
+
+ align:start position:0%
+components are relative to U1 U2 u3 u4
+ 
+
+ align:start position:0%
+components are relative to U1 U2 u3 u4
+for example this is 3u 1 + 5 U2 + 7 u3 +
+
+ align:start position:0%
+for example this is 3u 1 + 5 U2 + 7 u3 +
+ 
+
+ align:start position:0%
+for example this is 3u 1 + 5 U2 + 7 u3 +
+2 u4 now the traditional way of
+
+ align:start position:0%
+2 u4 now the traditional way of
+ 
+
+ align:start position:0%
+2 u4 now the traditional way of
+expanding this determinant is you write
+
+ align:start position:0%
+expanding this determinant is you write
+ 
+
+ align:start position:0%
+expanding this determinant is you write
+down the
+
+ align:start position:0%
+down the
+ 
+
+ align:start position:0%
+down the
+rows as the endle see you write down
+
+ align:start position:0%
+rows as the endle see you write down
+ 
+
+ align:start position:0%
+rows as the endle see you write down
+this is your first row second row third
+
+ align:start position:0%
+this is your first row second row third
+ 
+
+ align:start position:0%
+this is your first row second row third
+row fourth row see notice that
+
+ align:start position:0%
+row fourth row see notice that
+ 
+
+ align:start position:0%
+row fourth row see notice that
+the determinant is an N byn array of
+
+ align:start position:0%
+the determinant is an N byn array of
+ 
+
+ align:start position:0%
+the determinant is an N byn array of
+numbers that you have four vectors each
+
+ align:start position:0%
+numbers that you have four vectors each
+ 
+
+ align:start position:0%
+numbers that you have four vectors each
+Vector is a four tle and this is how you
+
+ align:start position:0%
+Vector is a four tle and this is how you
+ 
+
+ align:start position:0%
+Vector is a four tle and this is how you
+get this determinant now what do we do
+
+ align:start position:0%
+get this determinant now what do we do
+ 
+
+ align:start position:0%
+get this determinant now what do we do
+next next let's say for the sake of
+
+ align:start position:0%
+next next let's say for the sake of
+ 
+
+ align:start position:0%
+next next let's say for the sake of
+argument I elect to expand this
+
+ align:start position:0%
+argument I elect to expand this
+ 
+
+ align:start position:0%
+argument I elect to expand this
+determinant along the top row I first
+
+ align:start position:0%
+determinant along the top row I first
+ 
+
+ align:start position:0%
+determinant along the top row I first
+take the one out because it has a plus
+
+ align:start position:0%
+take the one out because it has a plus
+ 
+
+ align:start position:0%
+take the one out because it has a plus
+sign it comes out as one I multiply that
+
+ align:start position:0%
+sign it comes out as one I multiply that
+ 
+
+ align:start position:0%
+sign it comes out as one I multiply that
+by the 3X3 determinant that's left when
+
+ align:start position:0%
+by the 3X3 determinant that's left when
+ 
+
+ align:start position:0%
+by the 3X3 determinant that's left when
+I strike out the row and column in which
+
+ align:start position:0%
+I strike out the row and column in which
+ 
+
+ align:start position:0%
+I strike out the row and column in which
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+appears I take out two but make it a
+
+ align:start position:0%
+appears I take out two but make it a
+ 
+
+ align:start position:0%
+appears I take out two but make it a
+minus because of this signature here and
+
+ align:start position:0%
+minus because of this signature here and
+ 
+
+ align:start position:0%
+minus because of this signature here and
+multiply that by the 3X3 determinant
+
+ align:start position:0%
+multiply that by the 3X3 determinant
+ 
+
+ align:start position:0%
+multiply that by the 3X3 determinant
+that's left when I strike out the row
+
+ align:start position:0%
+that's left when I strike out the row
+ 
+
+ align:start position:0%
+that's left when I strike out the row
+and column in which two appears I factor
+
+ align:start position:0%
+and column in which two appears I factor
+ 
+
+ align:start position:0%
+and column in which two appears I factor
+out one as it is and multiply that by
+
+ align:start position:0%
+out one as it is and multiply that by
+ 
+
+ align:start position:0%
+out one as it is and multiply that by
+the 3X3 determinant that's left when I
+
+ align:start position:0%
+the 3X3 determinant that's left when I
+ 
+
+ align:start position:0%
+the 3X3 determinant that's left when I
+strike out the row and column in which
+
+ align:start position:0%
+strike out the row and column in which
+ 
+
+ align:start position:0%
+strike out the row and column in which
+this one appears and finally I take out
+
+ align:start position:0%
+this one appears and finally I take out
+ 
+
+ align:start position:0%
+this one appears and finally I take out
+this minus one and change its sign
+
+ align:start position:0%
+this minus one and change its sign
+ 
+
+ align:start position:0%
+this minus one and change its sign
+because of this minus code over here in
+
+ align:start position:0%
+because of this minus code over here in
+ 
+
+ align:start position:0%
+because of this minus code over here in
+other words comes out as a plus one
+
+ align:start position:0%
+other words comes out as a plus one
+ 
+
+ align:start position:0%
+other words comes out as a plus one
+multiplied by the 3X3 determinant that's
+
+ align:start position:0%
+multiplied by the 3X3 determinant that's
+ 
+
+ align:start position:0%
+multiplied by the 3X3 determinant that's
+left when I strike out the row and
+
+ align:start position:0%
+left when I strike out the row and
+ 
+
+ align:start position:0%
+left when I strike out the row and
+column in which minus one appears in and
+
+ align:start position:0%
+column in which minus one appears in and
+ 
+
+ align:start position:0%
+column in which minus one appears in and
+to make a long story short all we're
+
+ align:start position:0%
+to make a long story short all we're
+ 
+
+ align:start position:0%
+to make a long story short all we're
+saying is that this 4x4 determinant can
+
+ align:start position:0%
+saying is that this 4x4 determinant can
+ 
+
+ align:start position:0%
+saying is that this 4x4 determinant can
+be written as a sum of four 3x3
+
+ align:start position:0%
+be written as a sum of four 3x3
+ 
+
+ align:start position:0%
+be written as a sum of four 3x3
+determinants
+
+ align:start position:0%
+determinants
+ 
+
+ align:start position:0%
+determinants
+namely this which is precisely what I
+
+ align:start position:0%
+namely this which is precisely what I
+ 
+
+ align:start position:0%
+namely this which is precisely what I
+was saying the long way up here now what
+
+ align:start position:0%
+was saying the long way up here now what
+ 
+
+ align:start position:0%
+was saying the long way up here now what
+we say is each of these 3x 3s can be
+
+ align:start position:0%
+we say is each of these 3x 3s can be
+ 
+
+ align:start position:0%
+we say is each of these 3x 3s can be
+written as 3 2x2s namely I can factor
+
+ align:start position:0%
+written as 3 2x2s namely I can factor
+ 
+
+ align:start position:0%
+written as 3 2x2s namely I can factor
+out say again going across the top row I
+
+ align:start position:0%
+out say again going across the top row I
+ 
+
+ align:start position:0%
+out say again going across the top row I
+can pick any row or any column but let
+
+ align:start position:0%
+can pick any row or any column but let
+ 
+
+ align:start position:0%
+can pick any row or any column but let
+me stick to the top row like we did in i
+
+ align:start position:0%
+me stick to the top row like we did in i
+ 
+
+ align:start position:0%
+me stick to the top row like we did in i
+j and k for the time being but this
+
+ align:start position:0%
+j and k for the time being but this
+ 
+
+ align:start position:0%
+j and k for the time being but this
+becomes what 5 * this 2x two Matrix
+
+ align:start position:0%
+becomes what 5 * this 2x two Matrix
+ 
+
+ align:start position:0%
+becomes what 5 * this 2x two Matrix
+minus 3 3 * this 2x2 matrix plus 1 *
+
+ align:start position:0%
+minus 3 3 * this 2x2 matrix plus 1 *
+ 
+
+ align:start position:0%
+minus 3 3 * this 2x2 matrix plus 1 *
+this 2x2 matrix in other words this
+
+ align:start position:0%
+this 2x2 matrix in other words this
+ 
+
+ align:start position:0%
+this 2x2 matrix in other words this
+expression here I can now do that for
+
+ align:start position:0%
+expression here I can now do that for
+ 
+
+ align:start position:0%
+expression here I can now do that for
+each of these so each of the three by 3s
+
+ align:start position:0%
+each of these so each of the three by 3s
+ 
+
+ align:start position:0%
+each of these so each of the three by 3s
+give me 3 2x 2s so Al together I would
+
+ align:start position:0%
+give me 3 2x 2s so Al together I would
+ 
+
+ align:start position:0%
+give me 3 2x 2s so Al together I would
+have 12 2X tws and go through this whole
+
+ align:start position:0%
+have 12 2X tws and go through this whole
+ 
+
+ align:start position:0%
+have 12 2X tws and go through this whole
+mess to compute this thing and this can
+
+ align:start position:0%
+mess to compute this thing and this can
+ 
+
+ align:start position:0%
+mess to compute this thing and this can
+be a very very difficult sure this was
+
+ align:start position:0%
+be a very very difficult sure this was
+ 
+
+ align:start position:0%
+be a very very difficult sure this was
+only a four-dimensional case imagine
+
+ align:start position:0%
+only a four-dimensional case imagine
+ 
+
+ align:start position:0%
+only a four-dimensional case imagine
+trying to apply this technique for a
+
+ align:start position:0%
+trying to apply this technique for a
+ 
+
+ align:start position:0%
+trying to apply this technique for a
+uh a 10-dimensional vector space for the
+
+ align:start position:0%
+uh a 10-dimensional vector space for the
+ 
+
+ align:start position:0%
+uh a 10-dimensional vector space for the
+sake of argument it turns
+
+ align:start position:0%
+sake of argument it turns
+ 
+
+ align:start position:0%
+sake of argument it turns
+out that that
+
+ align:start position:0%
+out that that
+ 
+
+ align:start position:0%
+out that that
+recipe that we called theorem two gives
+
+ align:start position:0%
+recipe that we called theorem two gives
+ 
+
+ align:start position:0%
+recipe that we called theorem two gives
+us a tie-in between row reduced
+
+ align:start position:0%
+us a tie-in between row reduced
+ 
+
+ align:start position:0%
+us a tie-in between row reduced
+matrices and a quick way to compute
+
+ align:start position:0%
+matrices and a quick way to compute
+ 
+
+ align:start position:0%
+matrices and a quick way to compute
+determinants for example let's suppose
+
+ align:start position:0%
+determinants for example let's suppose
+ 
+
+ align:start position:0%
+determinants for example let's suppose
+we still wanted to compute the same
+
+ align:start position:0%
+we still wanted to compute the same
+ 
+
+ align:start position:0%
+we still wanted to compute the same
+determinant that we've written down over
+
+ align:start position:0%
+determinant that we've written down over
+ 
+
+ align:start position:0%
+determinant that we've written down over
+here let's call that let's write let's
+
+ align:start position:0%
+here let's call that let's write let's
+ 
+
+ align:start position:0%
+here let's call that let's write let's
+write it again over here what we already
+
+ align:start position:0%
+write it again over here what we already
+ 
+
+ align:start position:0%
+write it again over here what we already
+know is if I would to replace the second
+
+ align:start position:0%
+know is if I would to replace the second
+ 
+
+ align:start position:0%
+know is if I would to replace the second
+vector by the second minus twice the
+
+ align:start position:0%
+vector by the second minus twice the
+ 
+
+ align:start position:0%
+vector by the second minus twice the
+first the determinant does not change
+
+ align:start position:0%
+first the determinant does not change
+ 
+
+ align:start position:0%
+first the determinant does not change
+that's what theorem 2 said if you
+
+ align:start position:0%
+that's what theorem 2 said if you
+ 
+
+ align:start position:0%
+that's what theorem 2 said if you
+replace one vector by itself plus a
+
+ align:start position:0%
+replace one vector by itself plus a
+ 
+
+ align:start position:0%
+replace one vector by itself plus a
+Scala multiple of another you don't
+
+ align:start position:0%
+Scala multiple of another you don't
+ 
+
+ align:start position:0%
+Scala multiple of another you don't
+change the determinant similarly if I
+
+ align:start position:0%
+change the determinant similarly if I
+ 
+
+ align:start position:0%
+change the determinant similarly if I
+were to replace this vector by three
+
+ align:start position:0%
+were to replace this vector by three
+ 
+
+ align:start position:0%
+were to replace this vector by three
+times the first Vector I would still
+
+ align:start position:0%
+times the first Vector I would still
+ 
+
+ align:start position:0%
+times the first Vector I would still
+have the same determinant and finally if
+
+ align:start position:0%
+have the same determinant and finally if
+ 
+
+ align:start position:0%
+have the same determinant and finally if
+I were to replace this vector by three
+
+ align:start position:0%
+I were to replace this vector by three
+ 
+
+ align:start position:0%
+I were to replace this vector by three
+times the first Vector I would still
+
+ align:start position:0%
+times the first Vector I would still
+ 
+
+ align:start position:0%
+times the first Vector I would still
+have the same determinant I don't know
+
+ align:start position:0%
+have the same determinant I don't know
+ 
+
+ align:start position:0%
+have the same determinant I don't know
+if you've notice what I've been driving
+
+ align:start position:0%
+if you've notice what I've been driving
+ 
+
+ align:start position:0%
+if you've notice what I've been driving
+at but wasn't what I was saying here the
+
+ align:start position:0%
+at but wasn't what I was saying here the
+ 
+
+ align:start position:0%
+at but wasn't what I was saying here the
+same computational steps that one goes
+
+ align:start position:0%
+same computational steps that one goes
+ 
+
+ align:start position:0%
+same computational steps that one goes
+through in row reducing a matrix in
+
+ align:start position:0%
+through in row reducing a matrix in
+ 
+
+ align:start position:0%
+through in row reducing a matrix in
+other words let me row reduce this
+
+ align:start position:0%
+other words let me row reduce this
+ 
+
+ align:start position:0%
+other words let me row reduce this
+Matrix so that I get zeros every place
+
+ align:start position:0%
+Matrix so that I get zeros every place
+ 
+
+ align:start position:0%
+Matrix so that I get zeros every place
+say in My First
+
+ align:start position:0%
+say in My First
+ 
+
+ align:start position:0%
+say in My First
+Column except in the upper column by the
+
+ align:start position:0%
+Column except in the upper column by the
+ 
+
+ align:start position:0%
+Column except in the upper column by the
+way notice over here I always have the
+
+ align:start position:0%
+way notice over here I always have the
+ 
+
+ align:start position:0%
+way notice over here I always have the
+habit of putting a one in the upper left
+
+ align:start position:0%
+habit of putting a one in the upper left
+ 
+
+ align:start position:0%
+habit of putting a one in the upper left
+hand corner that's simply to uh
+
+ align:start position:0%
+hand corner that's simply to uh
+ 
+
+ align:start position:0%
+hand corner that's simply to uh
+facilitate the arithmetic I hope by this
+
+ align:start position:0%
+facilitate the arithmetic I hope by this
+ 
+
+ align:start position:0%
+facilitate the arithmetic I hope by this
+stage of the game you realize if this
+
+ align:start position:0%
+stage of the game you realize if this
+ 
+
+ align:start position:0%
+stage of the game you realize if this
+weren't a one I can always divide
+
+ align:start position:0%
+weren't a one I can always divide
+ 
+
+ align:start position:0%
+weren't a one I can always divide
+through by it or what have you and do
+
+ align:start position:0%
+through by it or what have you and do
+ 
+
+ align:start position:0%
+through by it or what have you and do
+the arithmetic another way I just do
+
+ align:start position:0%
+the arithmetic another way I just do
+ 
+
+ align:start position:0%
+the arithmetic another way I just do
+this thing for convenience but the
+
+ align:start position:0%
+this thing for convenience but the
+ 
+
+ align:start position:0%
+this thing for convenience but the
+important point is that this determinant
+
+ align:start position:0%
+important point is that this determinant
+ 
+
+ align:start position:0%
+important point is that this determinant
+is now equal to this determinant and be
+
+ align:start position:0%
+is now equal to this determinant and be
+ 
+
+ align:start position:0%
+is now equal to this determinant and be
+very careful notice if these had been
+
+ align:start position:0%
+very careful notice if these had been
+ 
+
+ align:start position:0%
+very careful notice if these had been
+matrices those if I put square brackets
+
+ align:start position:0%
+matrices those if I put square brackets
+ 
+
+ align:start position:0%
+matrices those if I put square brackets
+here and had made these matrices we
+
+ align:start position:0%
+here and had made these matrices we
+ 
+
+ align:start position:0%
+here and had made these matrices we
+would call the two matrices equivalent
+
+ align:start position:0%
+would call the two matrices equivalent
+ 
+
+ align:start position:0%
+would call the two matrices equivalent
+but different row equivalent but
+
+ align:start position:0%
+but different row equivalent but
+ 
+
+ align:start position:0%
+but different row equivalent but
+different matrices notice the
+
+ align:start position:0%
+different matrices notice the
+ 
+
+ align:start position:0%
+different matrices notice the
+determinant is a number and what we're
+
+ align:start position:0%
+determinant is a number and what we're
+ 
+
+ align:start position:0%
+determinant is a number and what we're
+saying saying is that the number named
+
+ align:start position:0%
+saying saying is that the number named
+ 
+
+ align:start position:0%
+saying saying is that the number named
+by this determinant is equal to the
+
+ align:start position:0%
+by this determinant is equal to the
+ 
+
+ align:start position:0%
+by this determinant is equal to the
+number named by this determinant all
+
+ align:start position:0%
+number named by this determinant all
+ 
+
+ align:start position:0%
+number named by this determinant all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+equal here's the key point I now notice
+
+ align:start position:0%
+equal here's the key point I now notice
+ 
+
+ align:start position:0%
+equal here's the key point I now notice
+that I have three zeros in the First
+
+ align:start position:0%
+that I have three zeros in the First
+ 
+
+ align:start position:0%
+that I have three zeros in the First
+Column I therefore elect to expand this
+
+ align:start position:0%
+Column I therefore elect to expand this
+ 
+
+ align:start position:0%
+Column I therefore elect to expand this
+determinant along the First Column why
+
+ align:start position:0%
+determinant along the First Column why
+ 
+
+ align:start position:0%
+determinant along the First Column why
+do I do this well let's take a look
+
+ align:start position:0%
+do I do this well let's take a look
+ 
+
+ align:start position:0%
+do I do this well let's take a look
+first of all I get a one multiplied by
+
+ align:start position:0%
+first of all I get a one multiplied by
+ 
+
+ align:start position:0%
+first of all I get a one multiplied by
+this 3x3 determinant that's left when I
+
+ align:start position:0%
+this 3x3 determinant that's left when I
+ 
+
+ align:start position:0%
+this 3x3 determinant that's left when I
+strike out the row and column in which
+
+ align:start position:0%
+strike out the row and column in which
+ 
+
+ align:start position:0%
+strike out the row and column in which
+one appears the beauty is that when I
+
+ align:start position:0%
+one appears the beauty is that when I
+ 
+
+ align:start position:0%
+one appears the beauty is that when I
+form the other three determinants 3x3
+
+ align:start position:0%
+form the other three determinants 3x3
+ 
+
+ align:start position:0%
+form the other three determinants 3x3
+determinants they're all going to be
+
+ align:start position:0%
+determinants they're all going to be
+ 
+
+ align:start position:0%
+determinants they're all going to be
+multiplied by zero for example over here
+
+ align:start position:0%
+multiplied by zero for example over here
+ 
+
+ align:start position:0%
+multiplied by zero for example over here
+I factor out well minus 0 which is still
+
+ align:start position:0%
+I factor out well minus 0 which is still
+ 
+
+ align:start position:0%
+I factor out well minus 0 which is still
+zero what do I multiply that by I
+
+ align:start position:0%
+zero what do I multiply that by I
+ 
+
+ align:start position:0%
+zero what do I multiply that by I
+multiply that by the 3X3 determinant
+
+ align:start position:0%
+multiply that by the 3X3 determinant
+ 
+
+ align:start position:0%
+multiply that by the 3X3 determinant
+that's left when I strike out the row
+
+ align:start position:0%
+that's left when I strike out the row
+ 
+
+ align:start position:0%
+that's left when I strike out the row
+and column that this zero appears in
+
+ align:start position:0%
+and column that this zero appears in
+ 
+
+ align:start position:0%
+and column that this zero appears in
+namely the 3X3 determinant 2 1 -1
+
+ align:start position:0%
+namely the 3X3 determinant 2 1 -1
+ 
+
+ align:start position:0%
+namely the 3X3 determinant 2 1 -1
+-145 2 3 4 but since that's being
+
+ align:start position:0%
+-145 2 3 4 but since that's being
+ 
+
+ align:start position:0%
+-145 2 3 4 but since that's being
+multiplied by zero the product will be
+
+ align:start position:0%
+multiplied by zero the product will be
+ 
+
+ align:start position:0%
+multiplied by zero the product will be
+zero to make a long story short to
+
+ align:start position:0%
+zero to make a long story short to
+ 
+
+ align:start position:0%
+zero to make a long story short to
+evaluate this determinant it's simply
+
+ align:start position:0%
+evaluate this determinant it's simply
+ 
+
+ align:start position:0%
+evaluate this determinant it's simply
+what + one times this 3x3 determinant I
+
+ align:start position:0%
+what + one times this 3x3 determinant I
+ 
+
+ align:start position:0%
+what + one times this 3x3 determinant I
+put the one in parenthesis here to
+
+ align:start position:0%
+put the one in parenthesis here to
+ 
+
+ align:start position:0%
+put the one in parenthesis here to
+indicate that I really factored that one
+
+ align:start position:0%
+indicate that I really factored that one
+ 
+
+ align:start position:0%
+indicate that I really factored that one
+out but really what we're saying is that
+
+ align:start position:0%
+out but really what we're saying is that
+ 
+
+ align:start position:0%
+out but really what we're saying is that
+this 4x4 determinant has the same value
+
+ align:start position:0%
+this 4x4 determinant has the same value
+ 
+
+ align:start position:0%
+this 4x4 determinant has the same value
+as this 3x3 determinant and now I R
+
+ align:start position:0%
+as this 3x3 determinant and now I R
+ 
+
+ align:start position:0%
+as this 3x3 determinant and now I R
+reduce this 3x3 determinant I replace
+
+ align:start position:0%
+reduce this 3x3 determinant I replace
+ 
+
+ align:start position:0%
+reduce this 3x3 determinant I replace
+the second Row in other words the second
+
+ align:start position:0%
+the second Row in other words the second
+ 
+
+ align:start position:0%
+the second Row in other words the second
+vector by the second plus the 1 the
+
+ align:start position:0%
+vector by the second plus the 1 the
+ 
+
+ align:start position:0%
+vector by the second plus the 1 the
+third by the third minus twice the 1 I
+
+ align:start position:0%
+third by the third minus twice the 1 I
+ 
+
+ align:start position:0%
+third by the third minus twice the 1 I
+now wind up with this 3x3 determinant
+
+ align:start position:0%
+now wind up with this 3x3 determinant
+ 
+
+ align:start position:0%
+now wind up with this 3x3 determinant
+since I don't change the value of the
+
+ align:start position:0%
+since I don't change the value of the
+ 
+
+ align:start position:0%
+since I don't change the value of the
+determinant when I replace one vector by
+
+ align:start position:0%
+determinant when I replace one vector by
+ 
+
+ align:start position:0%
+determinant when I replace one vector by
+itself plus a Scala multiple of another
+
+ align:start position:0%
+itself plus a Scala multiple of another
+ 
+
+ align:start position:0%
+itself plus a Scala multiple of another
+then notice very quickly that what
+
+ align:start position:0%
+then notice very quickly that what
+ 
+
+ align:start position:0%
+then notice very quickly that what
+happens over here is that these two
+
+ align:start position:0%
+happens over here is that these two
+ 
+
+ align:start position:0%
+happens over here is that these two
+determinants are equal again I elect to
+
+ align:start position:0%
+determinants are equal again I elect to
+ 
+
+ align:start position:0%
+determinants are equal again I elect to
+expand along the First Column factoring
+
+ align:start position:0%
+expand along the First Column factoring
+ 
+
+ align:start position:0%
+expand along the First Column factoring
+out the plus one being left with with
+
+ align:start position:0%
+out the plus one being left with with
+ 
+
+ align:start position:0%
+out the plus one being left with with
+the Matrix at the determinant whose
+
+ align:start position:0%
+the Matrix at the determinant whose
+ 
+
+ align:start position:0%
+the Matrix at the determinant whose
+entries are
+
+ align:start position:0%
+entries are
+ 
+
+ align:start position:0%
+entries are
+5811 and the other two terms contribute
+
+ align:start position:0%
+5811 and the other two terms contribute
+ 
+
+ align:start position:0%
+5811 and the other two terms contribute
+nothing because the coefficient is zero
+
+ align:start position:0%
+nothing because the coefficient is zero
+ 
+
+ align:start position:0%
+nothing because the coefficient is zero
+but I already know how to expand I've
+
+ align:start position:0%
+but I already know how to expand I've
+ 
+
+ align:start position:0%
+but I already know how to expand I've
+proven that how to expand a 2x2 matrix
+
+ align:start position:0%
+proven that how to expand a 2x2 matrix
+ 
+
+ align:start position:0%
+proven that how to expand a 2x2 matrix
+uh determinant that's just going to be
+
+ align:start position:0%
+uh determinant that's just going to be
+ 
+
+ align:start position:0%
+uh determinant that's just going to be
+what 5 - 8 or minus 3 and that's how the
+
+ align:start position:0%
+what 5 - 8 or minus 3 and that's how the
+ 
+
+ align:start position:0%
+what 5 - 8 or minus 3 and that's how the
+shortcut row reduction works much much
+
+ align:start position:0%
+shortcut row reduction works much much
+ 
+
+ align:start position:0%
+shortcut row reduction works much much
+more elegantly than the Brute Force
+
+ align:start position:0%
+more elegantly than the Brute Force
+ 
+
+ align:start position:0%
+more elegantly than the Brute Force
+technique and by the way this is the
+
+ align:start position:0%
+technique and by the way this is the
+ 
+
+ align:start position:0%
+technique and by the way this is the
+technique used in most if not all
+
+ align:start position:0%
+technique used in most if not all
+ 
+
+ align:start position:0%
+technique used in most if not all
+computers in determining the determinant
+
+ align:start position:0%
+computers in determining the determinant
+ 
+
+ align:start position:0%
+computers in determining the determinant
+of a set of n vectors in an
+
+ align:start position:0%
+of a set of n vectors in an
+ 
+
+ align:start position:0%
+of a set of n vectors in an
+n-dimensional Vector space well as I say
+
+ align:start position:0%
+n-dimensional Vector space well as I say
+ 
+
+ align:start position:0%
+n-dimensional Vector space well as I say
+this was meant as an overview I hope you
+
+ align:start position:0%
+this was meant as an overview I hope you
+ 
+
+ align:start position:0%
+this was meant as an overview I hope you
+now see the overall picture of what
+
+ align:start position:0%
+now see the overall picture of what
+ 
+
+ align:start position:0%
+now see the overall picture of what
+determinants are all about and in the
+
+ align:start position:0%
+determinants are all about and in the
+ 
+
+ align:start position:0%
+determinants are all about and in the
+excises I will try to give you some more
+
+ align:start position:0%
+excises I will try to give you some more
+ 
+
+ align:start position:0%
+excises I will try to give you some more
+sophisticated and elaborate
+
+ align:start position:0%
+sophisticated and elaborate
+ 
+
+ align:start position:0%
+sophisticated and elaborate
+details next time what we will do is
+
+ align:start position:0%
+details next time what we will do is
+ 
+
+ align:start position:0%
+details next time what we will do is
+talk about an application of how
+
+ align:start position:0%
+talk about an application of how
+ 
+
+ align:start position:0%
+talk about an application of how
+determinants are used in certain aspects
+
+ align:start position:0%
+determinants are used in certain aspects
+ 
+
+ align:start position:0%
+determinants are used in certain aspects
+ects of vector spaces in particular
+
+ align:start position:0%
+ects of vector spaces in particular
+ 
+
+ align:start position:0%
+ects of vector spaces in particular
+we're going to talk about something
+
+ align:start position:0%
+we're going to talk about something
+ 
+
+ align:start position:0%
+we're going to talk about something
+called uh igen values or igen vectors
+
+ align:start position:0%
+called uh igen values or igen vectors
+ 
+
+ align:start position:0%
+called uh igen values or igen vectors
+but more about that next time until next
+
+ align:start position:0%
+but more about that next time until next
+ 
+
+ align:start position:0%
+but more about that next time until next
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+goodbye funding for the publication of
+
+ align:start position:0%
+goodbye funding for the publication of
+ 
+
+ align:start position:0%
+goodbye funding for the publication of
+this video was provided by the Gabriella
+
+ align:start position:0%
+this video was provided by the Gabriella
+ 
+
+ align:start position:0%
+this video was provided by the Gabriella
+and Paul rosenbom
+
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+and Paul rosenbom
+ 
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+and Paul rosenbom
+foundation help ocw continue to provide
+
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\ No newline at end of file
diff --git a/D3bblng-Kcc.txt b/D3bblng-Kcc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7bda797b52803f8f64458408917da6081d871751
--- /dev/null
+++ b/D3bblng-Kcc.txt
@@ -0,0 +1,1530 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+[MUSIC PLAYING]
+
+PROFESSOR: Last time, we began
+a discussion of feedback.
+
+And I briefly introduced a
+number of applications.
+
+For example, the use of feedback
+in compensating for
+
+non-ideal elements
+in a system.
+
+And also, as another example,
+the use of feedback in
+
+stabilizing unstable systems.
+
+In this final lecture, what
+I'd like to do is focus in
+
+more detail on the use
+of feedback to
+
+stabilize unstable systems.
+
+And the specific context in
+which I'd like to do that is
+
+in the context of the
+inverted pendulum.
+
+Now, I've referred to the
+inverted pendulum in several
+
+past lectures.
+
+And, basically, as everyone
+realizes, a pendulum is
+
+essentially a rod with a
+weight on the bottom.
+
+And, naturally, an inverted
+pendulum is just
+
+that, upside down.
+
+And so it's essentially a
+rod that's top-heavy.
+
+And the idea with the inverted
+pendulum is, although by
+
+itself it's unstable around a
+pivot point at the bottom, the
+
+idea is to apply an external
+input, an acceleration,
+
+essentially to keep
+it balanced.
+
+And we've all probably done
+this type of thing at some
+
+point in our lives, either
+childhood or not.
+
+And so that's the system that
+I'd like to analyze and then
+
+illustrate in this lecture.
+
+Now, the context in which we'll
+do that is not with my
+
+son's horse, but actually with
+an inverted pendulum which is
+
+mounted on a cart.
+
+And first I'd like to go through
+an analysis of it, and
+
+then we'll actually see
+how the system works.
+
+So basically, then, the system
+that we're talking about is
+
+going to be a system which
+is a movable cart.
+
+Mounted on the cart is a rod
+with a weight on the top.
+
+And this then becomes the
+inverted pendulum.
+
+And the cart has an external
+acceleration applied to it,
+
+which is the input that we
+can apply to the system.
+
+And then, in general, we can
+expect some disturbances.
+
+And I'm going to represent the
+disturbances in terms of an
+
+angular acceleration, which
+shows up around the weight at
+
+the top of the rod.
+
+So if we look at the system,
+then, as I've kind of
+
+indicated it here, basically
+we have two inputs.
+
+We have an input, which are
+the external disturbances,
+
+which we can assume that we
+have no control over.
+
+And then there is the
+acceleration that's apply to
+
+the cart externally, or in the
+case of balancing my son's
+
+horse, it's the movement
+of my hand.
+
+And then, through the system
+dynamics, that ends up
+
+influencing the angle
+of the rod.
+
+And we'll think of the
+angle of the rod
+
+as the system output.
+
+And basically the idea, then,
+is to try to keep that angle
+
+at 0 by applying the appropriate
+acceleration.
+
+Now, as I've mentioned several
+times previously, if we know
+
+exactly what the system dynamics
+are, and if we know
+
+exactly what the external
+disturbances are, then
+
+theoretically we can choose an
+acceleration for the cart
+
+which will exactly balance the
+system, or balance the rod.
+
+However, since the system is
+inherently unstable, any
+
+deviation from that model-- in
+particular, any unanticipated
+
+external disturbances--
+
+will excite the instability.
+
+And what that means is that
+the rod will fall.
+
+So the idea, then, is, as we'll
+see, to stabilize the
+
+system by placing feedback
+around it.
+
+In particular through a
+measurement of the output
+
+angle, processed through some
+appropriate feedback dynamics,
+
+using that to control the
+acceleration of the cart.
+
+And if we choose the feedback
+dynamics correctly, then, in
+
+fact, we can end up with a
+stable system, even though the
+
+open-loop system is unstable.
+
+Well, as a first step, let's
+analyze the system in its
+
+open-loop form.
+
+In particular, let's analyze the
+system without feedback,
+
+demonstrate that, indeed, it is
+unstable, and then see how
+
+we can stabilize it
+using feedback.
+
+So the system, then, is--
+
+as we've indicated, the
+variables involved are the
+
+measured angle, which represents
+the output, the
+
+angular acceleration due to
+external disturbances, and
+
+then there is the
+applied external
+
+acceleration on the cart.
+
+So these represent the
+variables, with L representing
+
+the length of the rod, and s of
+t I indicate here, which we
+
+won't really be paying attention
+to, as the position
+
+of the cart.
+
+And without going into the
+details specifically, what
+
+we'll do is set up the equation,
+or write the
+
+equation, in terms of balancing
+the acceleration.
+
+And if you go through that
+process, then the basic
+
+equation that you end up with
+is the equation that I
+
+indicate here.
+
+And this equation, then, tells
+us how the basic forces, or
+
+accelerations, are balanced,
+where this is the second
+
+derivative of the angle.
+
+And then we have the
+acceleration due to gravity,
+
+reflected through the angular
+acceleration times the sine of
+
+the angle, the angular
+acceleration due to the
+
+external disturbances, and
+finally, the angular
+
+acceleration due to the
+motion of the cart.
+
+Now, this equation, as it's
+written here, is a nonlinear
+
+equation in the angle
+theta of t.
+
+And what we'd like to do is
+linearize the equation.
+
+And we'll linearize the
+equation by making the
+
+assumption that the angle is
+very small, close to 0.
+
+In other words, what we'll
+assume is that we're able to
+
+keep the rod relatively
+vertical.
+
+And our analysis, because
+we're linearizing the
+
+equations, will obviously
+depend on that.
+
+So making the assumption that
+the angle is small, we then
+
+assume that the sine of the
+angle is approximately equal
+
+to the angle, and the cosine of
+the angle is approximately
+
+equal to 1.
+
+That will then linearize
+this equation.
+
+And the resulting equation,
+then, in its linearized form,
+
+is the one that I
+indicate here.
+
+So we have an equation of
+motion, which linearizes the
+
+balance of the accelerations.
+
+And what we see on the
+right-hand side of the
+
+equation is the combined inputs
+due to the angular
+
+acceleration of the rod and the
+acceleration of the cart.
+
+And on the left-hand side of
+the equation, we have the
+
+other forces due to the
+change in the angle.
+
+So this is, then, the
+differential equation
+
+associated with the open-loop
+system, the basic dynamics of
+
+the system.
+
+And if we apply the Laplace
+transform to this equation and
+
+solve for the system function,
+then the basic equation that
+
+we're left with expresses the
+Laplace transform of the
+
+angle, equal to the system
+function, the open-loop system
+
+function, times the Laplace
+transform of
+
+the combined inputs.
+
+And I remind you again that our
+assumption is that this is
+
+an input that we have
+no control over.
+
+This is the input that
+we can control.
+
+And the two together,
+of course, form
+
+the combined input.
+
+Now, we can, of course, solve
+for the poles and 0's.
+
+There are no 0's.
+
+And there are two poles, since
+this is a second-order
+
+denominator.
+
+And looking at the poles in the
+s-plane then, we see that
+
+we have a pair of poles, one at
+minus the square root of g
+
+over L, and one at plus the
+square root of g over L.
+
+And the important observation,
+then, is that while this pole
+
+represents a stable pole, the
+right half-plane pole
+
+represents an unstable pole.
+
+And so this system, in fact,
+is an unstable system.
+
+It's unstable because what we
+have is a pole in the right
+
+half-plane for the
+open-loop system.
+
+Now, before we see how to
+stabilize the system, let's,
+
+in fact, look at the mechanical
+setup, which we
+
+won't turn on for now, and just
+see essentially what this
+
+instability means and what the
+physical orientation of the
+
+equipment is.
+
+So what we have, which you just
+saw a caricature of in
+
+the view graph, is an
+inverted pendulum.
+
+This represents the pendulum.
+
+And it's mounted with the pivot
+point at the bottom.
+
+It's mounted on a cart.
+
+And here we have the cart.
+
+And this is a pivot point.
+
+And, as you can see, the
+cart can move back
+
+and forth on a track.
+
+And the external acceleration,
+which is applied to the cart,
+
+is applied through this cable.
+
+And that cable is controlled
+by a motor.
+
+And we have the motor at
+this end of the track.
+
+And so as the motor turns,
+then the cart will
+
+move back and forth.
+
+OK.
+
+Now, since the system
+is not turned on
+
+and there's no feedback--
+
+in fact, the system, as we just
+saw in the transparency,
+
+is an unstable system.
+
+And what that instability means
+is that, for example, if
+
+I set the angle to 0 and then
+let it go, then as soon as
+
+there's a slight external
+disturbance, it
+
+will start to fall.
+
+Now, you can imagine that not
+only is the system unstable as
+
+it is, but certainly can't
+accommodate changes in the
+
+system dynamics.
+
+For example, if we change,
+let's say, the
+
+weight of the pendulum.
+
+So if we thought, for example,
+of changing the weight by,
+
+let's say, putting something
+like a glass with something in
+
+it on top, and I think about
+trying to balance it by
+
+itself, obviously that's hard.
+
+In fact, I would say, without
+turning the system on,
+
+guaranteed to be impossible.
+
+So the basic system, as we've
+just analyzed it, is
+
+inherently an unstable system.
+
+The instability reflecting in
+the fact that the pendulum,
+
+following its own natural
+forces, will tend to fall.
+
+And now what we want to look at
+is how, through the use of
+
+feedback, we can, in fact,
+stabilize the system.
+
+So let's first, once again, look
+at the open-loop system.
+
+And the open-loop system
+function that we saw was a
+
+system function of this form, 1
+over Ls squared minus g, and
+
+that represents the system
+function associated with the
+
+two inputs, one being the
+external disturbances, the
+
+other being the externally
+applied acceleration.
+
+And the system function here
+
+represents the system dynamics.
+
+And the resulting output
+is the angle.
+
+Now, the feedback, the basic
+strategy behind the feedback,
+
+is to in some way use the
+measured angle, make a
+
+measurement of the angle, and
+use that through appropriate
+
+feedback dynamics to stabilize
+the system.
+
+And so with feedback applied
+around the system then, there
+
+would be some measurement of
+the angle through some
+
+appropriately chosen
+feedback dynamics.
+
+And that then would determine
+for us the applied external
+
+acceleration corresponding to
+what the motor does by pulling
+
+the cable back and forth.
+
+And we would like to choose
+G of s so that the overall
+
+system is stable.
+
+Now, as you recall from the
+lecture last time, with the
+
+feedback around the system and
+expressed here in terms of
+
+negative feedback, the overall
+transfer function then is the
+
+transfer function associated
+with the basic feedback loop,
+
+where H of s is the open-loop
+system and G of s corresponds
+
+to the feedback dynamics.
+
+Now, that's the basic
+strategy.
+
+We haven't decided yet how to
+choose the feedback dynamics.
+
+And that becomes
+the next step.
+
+And we want to choose the
+dynamics in such a way that
+
+the system ends up
+being stabilized.
+
+Well, I think the thing to do is
+just simply begin with what
+
+would seem to be the most
+obvious, which is a simple
+
+measurement of the angle.
+
+Let's take the angular
+measurements, feed that back,
+
+let's say through a
+potentiometer and perhaps an
+
+amplifier, so that there's some
+gain, and see if we can
+
+stabilize the system simply
+through feedback which is
+
+proportional to a measurement
+of the angle, what.
+
+Is typically referred to as
+"proportional feedback." Well,
+
+let's analyze the results
+of doing that.
+
+Once again we have the basic
+feedback equation, where the
+
+open-loop transfer function
+is what we had developed
+
+previously, given by the
+second-order expression.
+
+Now, using proportional
+feedback, we choose the
+
+acceleration a of t to be
+directly proportional through
+
+a gain constant or attenuation
+constant K1, directly
+
+proportional to the measured
+angle theta of t.
+
+And consequently the system
+function in the feedback path
+
+is just simply a gain
+or attenuate K1.
+
+So this, then, is the
+system function for
+
+the feedback path.
+
+Well, substituting this into
+the closed-loop expression,
+
+then the overall expression for
+the Laplace transform of
+
+the output angle is, as I
+indicate here, namely that
+
+theta of s is proportional
+through this system function.
+
+So the Laplace transform of the
+input X of t-- and let me
+
+remind you that X of t, the
+external disturbances, now
+
+represent the only input,
+since the other input
+
+corresponding to the applied
+acceleration to the cart is
+
+now controlled only through
+the feedback loop.
+
+So we have this system function,
+then, for the
+
+closed-loop system.
+
+We recognize this once again
+as a second-order system.
+
+And the poles of this
+second-order system are then
+
+given by plus and minus the
+square root of g minus K1,
+
+divided by L. So K1, the
+feedback constant, clearly
+
+influences the position
+of the poles.
+
+And let's look, in fact,
+at where the
+
+poles are in the s-plane.
+
+Well, first of all, with K1
+equal to 0, which, of course,
+
+is no feedback and corresponds
+to the open-loop system, we
+
+have the poles where they
+were previously.
+
+And if we now choose K1, let's
+say less than 0, then what
+
+will happen as K1 becomes more
+and more negative, so that
+
+this term is more and more
+positive, is that the left
+
+half-plane pole will move
+further into the left
+
+half-plane, the right half-plane
+pole will move
+
+further into the right
+half-plane.
+
+So clearly with K1 negative,
+this pole, which represents an
+
+instability, becomes
+even more unstable.
+
+Well, instead of K1 negative,
+let's try K1 positive and see
+
+what happens.
+
+And with K1 positive, what
+happens in this case is that
+
+the left half-plane pole moves
+closer to the origin, the
+
+right half-plane pole moves
+closer to the origin.
+
+What one would hope is that they
+both end up in the left
+
+half-plane at some point.
+
+But, in fact, they don't.
+
+What happens is that eventually
+they both reach the
+
+origin, split at that point,
+and travel along the
+
+j-omega-axis.
+
+Now, this movement of the poles,
+as we vary K1 either
+
+positive or negative, what we
+see is that with the open-loop
+
+system, as we introduce
+feedback, those basic poles
+
+move in the s-plane, either this
+way, as K1 becomes more
+
+negative, or for this particular
+case, if K1 is
+
+positive, they move in together,
+split, and move
+
+along the j-omega-axis.
+
+And that locus of the poles,
+in fact, is referred to in
+
+feedback terminology as the
+"root locus." And as is
+
+discussed in much more detail in
+the text, there are lots of
+
+ways of determining the root
+locus for feedback systems
+
+without explicitly solving
+for the roots.
+
+For this particular example, in
+fact, we can determine the
+
+root locus in the most
+straightforward way simply by
+
+solving for the roots
+of the denominator
+
+of the system function.
+
+Now, notice that in this case,
+these poles, with K1 positive,
+
+have moved together.
+
+They move along the
+j-omega-axis.
+
+And before they come
+together, the
+
+system is clearly unstable.
+
+Even when they come together
+and split, the system is
+
+marginally stable, because,
+in fact, the system
+
+would tend to oscillate.
+
+And what that oscillation
+means is that with the
+
+measurement of the angles,
+essentially if the poles are
+
+operating on the j-omega-axis,
+what will happen is that
+
+things will oscillate
+back and forth.
+
+Perhaps with the cart moving
+back and forth trying to
+
+compensate, and the rod
+sort of moving in
+
+the opposite direction.
+
+In any case, what's happened
+is, with just proportional
+
+feedback, we apparently
+are unable to
+
+stabilize the system.
+
+Well, you could think that the
+reason, perhaps, is that we're
+
+not responding fast enough.
+
+For example, if the angle starts
+to change, perhaps, in
+
+fact, we should make the
+feedback proportional to the
+
+rate of change of angles,
+rather than
+
+to the angle itself.
+
+And so we could examine the
+possibility of using what's
+
+referred to as "derivative
+feedback."
+
+In derivative feedback, what we
+would do is to choose, for
+
+the feedback equation, or for
+the feedback system function,
+
+something reflecting a
+measurement of the derivative
+
+of the angle.
+
+And so here again, once again,
+we have the open-loop system
+
+function with derivative
+feedback.
+
+We'll attempt to--
+
+or we will use this feedback.
+
+And acceleration, which instead
+of being proportional
+
+to the angle, as it was in the
+previous case, an acceleration
+
+which is proportional to the
+derivative of the angle.
+
+And so the basic feedback
+dynamics, or feedback system
+
+function, is then G of s
+is equal to K2 times s.
+
+The multiplication by s
+reflecting the fact that in
+
+the time domain it's measuring
+the derivative of the angle.
+
+The associated system function
+is then indicated here.
+
+And if we solve again this
+second-order equation for its
+
+roots, that tells us that the
+location of the poles are
+
+given by this equation.
+
+And so now what we would want to
+look at is how these poles
+
+move as we vary the derivative
+feedback constant K2.
+
+So let's look at the root
+locus for that case.
+
+And first, once again, we have
+the basic open-loop poles.
+
+And the open-loop poles consist
+of a pole on the left
+
+half-plane and a pole on
+the right half-plane,
+
+corresponding in this equation
+to K2 equal to 0.
+
+That is, no feedback
+in the system.
+
+If K2 is negative, then what you
+can see is that this real
+
+part will become
+more negative.
+
+Since K2 is squared here, this
+is still a positive quantity.
+
+And, in fact, then with K2 less
+than 0, the root locus
+
+that we get is indicated
+by this.
+
+Now, notice, then, that this
+right half-plane pole is
+
+becoming more unstable.
+
+And the left half-plane
+pole likewise is
+
+becoming more unstable.
+
+And this point, by the way,
+corresponds to where this pole
+
+ends up, or where the root
+locus ends up, when K2
+
+eventually becomes infinite.
+
+So clearly K2 negative is not
+going to stabilize the system.
+
+Let's try K2 positive.
+
+And the root locus dictated by
+this equation, then, is what I
+
+indicate here.
+
+The left half-plane pole moves
+further into the left
+
+half-plane.
+
+That's good.
+
+That's getting more stable.
+
+The right half-plane pole is
+moving closer to the left
+
+half-plane, but unfortunately
+never gets there.
+
+And, in fact, it's when K2
+eventually becomes infinite
+
+that this pole just gets to
+the point where the system
+
+becomes marginally stable.
+
+So what we found is that with
+proportional feedback, we
+
+can't stabilize the system, with
+the derivative feedback,
+
+we can't stabilize the system,
+by themselves.
+
+And a logical next choice is to
+see if we can stabilize the
+
+system by both measuring the
+angle and at the same time
+
+being careful to be responsive
+to how fast that angle is
+
+changing, so that if it's
+changing too fast, we can move
+
+the cart or our hand
+under the inverted
+
+pendulum more quickly.
+
+Well, now then what we want
+to examine is the use of
+
+proportional plus derivative
+feedback.
+
+And in that case, we then have a
+choice for the acceleration,
+
+which is proportional with one
+constant to the angle and
+
+proportional with another
+constant to the
+
+derivative of the angle.
+
+And so the basic system
+function, then, with
+
+proportional plus derivative
+feedback, is a system function
+
+which is K1 plus K2 times s.
+
+We then have an overall
+closed-loop system function,
+
+theta of s, which is given
+by this equation.
+
+And so the roots of this
+equation then represent the
+
+poles of the closed-loop
+system.
+
+And those poles involve
+two parameters.
+
+They involve the parameter K2,
+which is proportional to the
+
+derivative of the angle, and
+the constant K1, which is
+
+proportional to the angle.
+
+And we'll, first of all, examine
+this just with K2
+
+positive, because what we can
+see is that as we vary K1, if
+
+K2 were negative, that would,
+more or less immediately, put
+
+poles into the right
+half-plane.
+
+And the more negative K2
+got, the larger this
+
+term is going to get.
+
+So, in fact, as it will turn
+out, we can stabilize the
+
+system, provided that
+we choose K2 to be
+
+greater than 0.
+
+All right.
+
+Now, with K2 greater than 0,
+what happens in the location
+
+of the poles is that if K2 is
+greater than 0, and we choose
+
+K1 greater than 0--
+
+I'm sorry.
+
+We choose K1 equal to 0, then in
+effect the influence of K2
+
+is to shift the poles of the
+open-loop system slightly.
+
+And so with K2 greater than 0
+and K1 equal to 0, we have a
+
+set of poles, which are
+indicated here, and so this is
+
+just a shift, slight shift, to
+the left, depending on the
+
+value of K2, a shift to the left
+of the open-loop poles.
+
+Now, as we vary K1, and in
+particular we're going to
+
+choose K1 greater than 0, what
+happens is that the poles will
+
+begin to move together, as they
+did previously when we
+
+looked at the variation of K1.
+
+The poles will move together,
+reach a point where we have a
+
+second-order pole, and then
+those poles will split and
+
+move parallel to the
+j-omega-axis.
+
+So what's indicated here
+is the root locus.
+
+And what this represents, then,
+as long as we make K1
+
+large enough so that this poles
+moves into the left
+
+half-plane, is that
+it represents
+
+now a stable system.
+
+OK.
+
+So what we've seen is that
+proportional feedback by
+
+itself or derivative feedback by
+itself won't stabilize the
+
+system, whereas with the right
+choice of feedback constants,
+
+proportional plus derivative
+feedback will.
+
+And we saw that basically by
+examining the root locus in
+
+the s-plane.
+
+All right.
+
+Well, let's actually watch
+the system in action.
+
+And I described it to
+you previously.
+
+Basically, an inverted
+pendulum on a cart.
+
+And so I still have it off.
+
+And, of course, we have
+the pendulum.
+
+And as I indicated, it's
+pivoted at the base.
+
+And the angle is measured by a
+potentiometer that we have
+
+attached to the pivot point.
+
+And the measurement of the angle
+is fed back through this
+
+wire to a motor that we have at
+the other end of the table.
+
+And then that motor basically
+is used to provide the
+
+acceleration to drive
+the cart.
+
+OK.
+
+Well, let's turn it on.
+
+And when we turn it on,
+it'll take just
+
+an instant to stabilize.
+
+And fortunately we have the
+constants set right, and there
+
+we have now the stabilization
+of an unstable system.
+
+Remember that with the feedback
+off, the system is
+
+unstable because the pendulum
+will fall, whereas now it's
+
+stabilized.
+
+Now, also, as you can see, not
+only have we stabilized it,
+
+but we're able to compensate
+through the feedback to
+
+changes in the external
+disturbances.
+
+For example, by tapping it,
+because of the feedback and
+
+the measurement of the angle,
+it will more or less
+
+automatically stabilize.
+
+Now, in addition to being stable
+in the presence of
+
+external disturbances, it also
+remains stable and remains
+
+balanced even if we were to
+change the system dynamics.
+
+And let me just illustrate that
+with the glass that we've
+
+talked about before.
+
+Let's first not be too bold, and
+we'll take the liquid out
+
+of the glass.
+
+And presumably if it can adjust
+to changes in the
+
+system dynamics, then if I put
+the glass on, in fact, it will
+
+remain balanced.
+
+And indeed it does.
+
+And let me point out, by the
+way, that I don't have to be
+
+very careful about exactly where
+I position the glass.
+
+And furthermore, I can change
+the overall system even
+
+further by, let's say for
+example, pouring a liquid in.
+
+And now let me also comment that
+I've changed the physics
+
+of it a little bit.
+
+Because the liquid can slosh
+around a little bit, it
+
+becomes a little more
+complicated a system.
+
+But as you can see, it still
+remains balanced.
+
+Now, if we really don't want to
+be too conservative at all,
+
+we could wonder whether, with
+the feedback constants we
+
+have, we could, in
+fact, balance the
+
+pitcher on the top.
+
+And, well, I guess we may
+as well give that a try.
+
+And so now we're changing the
+mass at the top of the
+
+pendulum by a considerable
+amount.
+
+And, again, the system basically
+can respond to it.
+
+Now, this is a fairly
+complicated system.
+
+The liquid is sloshing around.
+
+We, in fact, as you can see,
+have an instability right now,
+
+although it's controlled.
+
+And that's because the physics
+of the dynamics has changed.
+
+And we can put a little bit more
+mass into the system, and
+
+maybe or maybe not that will cut
+down on the instability.
+
+OK.
+
+Well, in fact, what happened
+there is that we increased the
+
+mass at the top of the
+pendulum slightly.
+
+And that provided just
+enough damping to
+
+stabilize the system.
+
+OK.
+
+Well, with this lecture and
+this demonstration, this
+
+concludes this entire
+set of lectures.
+
+It concludes it especially if
+the pitcher happens to fall.
+
+But, seriously, this concludes
+the set of lectures as we have
+
+put them together.
+
+And let me just comment that,
+as a professor of mine once
+
+said, and which I've never
+forgotten, the purpose of a
+
+set of lectures, or of a course,
+or, for that matter
+
+anything that you study, is not
+really to cover a subject,
+
+but to uncover the subject.
+
+And I hope that, at least to
+some degree, we were able to
+
+uncover the topic of signals
+and systems through this
+
+series of lectures.
+
+There are a lot of topics that
+we got only a very brief
+
+glimpse into.
+
+And I hope that at least what
+we've been able to do is get
+
+you interested enough in them so
+that you'll pursue some of
+
+these on your own.
+
+And so I'd like to conclude by
+thanking you, both for your
+
+patience and your interest.
+
+And I hope that you have enough
+interest to pursue some
+
+of these topics further.
+
+Thank you.
+
+FILMING DIRECTOR: Okay.
+
+That's a wrap.
\ No newline at end of file
diff --git a/EYANqW4zwwo.txt b/EYANqW4zwwo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..37cb76087e9f219423bfb7ce8cc4d46956bfcd01
--- /dev/null
+++ b/EYANqW4zwwo.txt
@@ -0,0 +1,4276 @@
+ANNOUNCER: The following content
+is provided under a
+
+Creative Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+MICHAEL KREMER: So I understand
+that in the session
+
+that you just had, you went
+through the deworming case.
+
+And I was just talking to some
+people in the break, and they
+
+were saying that everything's
+been very focused on methods,
+
+which is understandable.
+
+That's what the purpose
+of the course is.
+
+But it sounded like people were
+interested in hearing a
+
+little bit about the substantive
+results.
+
+So I just thought before I
+launched into this lecture,
+
+I'd say a little
+bit about that.
+
+And maybe this is also a way
+to give you a little bit of
+
+background on where
+I'm coming from.
+
+So I taught secondary school in
+Kenya right after college
+
+and then went to grad school.
+
+And then I went back after
+graduating, from getting my
+
+Ph.D. and getting a real job
+and having some money.
+
+I eventually went back to
+visit some friends.
+
+And one of them was working
+for an NGO, which was just
+
+starting work in
+western Kenya.
+
+And his job was to find seven
+schools to start a program in.
+
+And I said to him, not really
+thinking this was something
+
+that he would do, "Why don't
+you pick twice as many and
+
+choose the seven randomly, at
+least where you're going to
+
+start?" And much to my surprise,
+he was interested.
+
+And then he went to his boss,
+and his boss actually did it.
+
+So that's, in part, how this
+wave of randomized evaluations
+
+with NGOs got going.
+
+This NGO worked a lot
+on education.
+
+And over the years, we tried a
+number of things to try to get
+
+more kids in school and stop
+kids from dropping out.
+
+But eventually, they tried
+treating kids for worms.
+
+And part of this was based on
+reading the literature which
+
+suggested that this is an
+important health intervention.
+
+There was a question, would
+it have education effects.
+
+So it turned out, of all the
+various things that we looked
+
+at, we calculated what was the
+cost per additional year of
+
+schooling generated.
+
+So we're comparing a bunch
+of things in that same
+
+environment in western Kenya.
+
+And deworming came out an order
+of magnitude better than
+
+anything else.
+
+So this was a really
+striking result.
+
+If you spent $3.50, you could
+generate an additional year of
+
+education for a child.
+
+It was just much cheaper than
+any of the other alternatives.
+
+So we had that academic
+result.
+
+There were people at the World
+Bank who were very
+
+interested in this.
+
+There's a lot of heterogeneity
+in the Bank, but a lot of
+
+people there who are very
+interested in and understand
+
+evidence or are interested
+in or responsive to it.
+
+And the particular people who
+are working on health and
+
+education sector in the Bank
+in Kenya, that very much
+
+applies to.
+
+So they then took it to the
+Ministry of Education and
+
+brought us in to talk
+to the people in
+
+the Ministry of Education.
+
+This process took quite
+a lot of time.
+
+I don't want to underestimate
+this.
+
+Took a lot of time.
+
+The first time, they said, these
+results are interesting,
+
+then, yes, we should
+pursue them.
+
+But there's a lot going on
+inside the Ministry of
+
+Education, lots of
+other priorities.
+
+There are teacher strikes.
+
+There's all sorts of
+things that have
+
+to take higher priority.
+
+But both externally, outside
+in international fora and
+
+academic fora, and internally
+inside Kenya, we kept
+
+bringing this up.
+
+And eventually, the permanent
+secretary, who's very strong,
+
+the permanent secretary of the
+Ministry of Education said,
+
+let's do this.
+
+And he brought in
+various people.
+
+And they decided they were
+going to try to implement
+
+this, have a national
+scale up of this.
+
+And there was both that internal
+persuasion of people
+
+within the Ministry
+of Education.
+
+And then, of course, there's
+the question of
+
+getting budget for it.
+
+Obviously, having the World Bank
+on side helped on that.
+
+The other thing that
+we did was--
+
+so Esther and I were both
+involved in an event the World
+
+Economic Forum put
+on in Davos.
+
+And working with that group,
+we were able to arrange for
+
+there to be an event in Davos
+on this issue of deworming.
+
+And we helped start an
+organization called Deworm the
+
+World which was designed
+to promote this.
+
+And we invited the
+prime minister of
+
+Kenya to come speak.
+
+And he made this announcement.
+
+And I think that helped drive
+this forward a lot.
+
+Because once you got a public
+announcement by a politician,
+
+then it's really going
+to happen in a way.
+
+So between the support
+internally within the ministry
+
+and this higher level political
+support, Kenya has,
+
+just as we speak, just in the
+past few months, dewormed
+
+almost 3 million children.
+
+So this is an example of how, if
+you can identify successful
+
+intervention, it can really help
+promote scale-up of the
+
+successful interventions.
+
+Ultimately, that's the purpose
+of what we're doing is trying
+
+to improve policy.
+
+So I just wanted to give you
+that tie-in to reality before
+
+plunging back into
+econometrics.
+
+Any comments or questions
+on that?
+
+AUDIENCE: I thought it was
+really interesting.
+
+Could you just give
+us a couple of the
+
+year points in that?
+
+You talked about things
+taking a long time.
+
+Can you give more concrete
+evidence?
+
+MICHAEL KREMER: Our article
+appeared, and publishing the
+
+article takes a long time too.
+
+Our article appeared
+in 2004, I believe.
+
+It's now 2009, and this
+is happening now.
+
+The NGO responded much
+more quickly.
+
+Although eventually,
+they changed
+
+their strategy as well.
+
+So the NGO scaled up.
+
+But to get the national
+government to scale up, I
+
+think that took a
+
+constellation of various people.
+
+It took some time for this to
+get in the media, to get in
+
+the academic world, to get out
+to the media, to get out to
+
+opinion leaders, both
+internationally.
+
+And then it took time for the
+right set of people to be
+
+available and the money to
+be available to do it.
+
+Yes?
+
+AUDIENCE: Just kind of
+following up on that.
+
+This is a issue that is
+obviously quite concerning,
+
+the bridge between academia
+and the policy world.
+
+And the fact that this research
+is absolutely
+
+fabulous, but then, at
+the end of the day,
+
+it stays in a textbook.
+
+And what use is it
+to beneficiaries?
+
+This example is, again,
+fabulous.
+
+But what sort of actions or
+roles are there to extend
+
+findings into the policy
+world and into
+
+the development world?
+
+I'm sure that's a big topic.
+
+But just very briefly, is J-PAL
+or sister organizations
+
+doing that sort of extension?
+
+MICHAEL KREMER: In this
+particular case, I would say
+
+that I spent a fair amount of
+time afterwards trying to
+
+disseminate this.
+
+And J-PAL has been very
+important in starting to
+
+deworm the world.
+
+I think this requires effort at
+a variety of levels, both
+
+in trying to get the prime
+minister on board, but also in
+
+trying to do tasks like, well,
+you need a spreadsheet of
+
+where are all the schools in the
+country, and which ones of
+
+them are in areas where we think
+that there's worms, and
+
+working out a bunch of logistics
+of, well, how many
+
+trainers do you need,
+and so on.
+
+Now I think in different
+settings, they'll be--
+
+in this one, people who are
+at J-PAL and IPA have been
+
+involved in even down to
+that spreadsheet level.
+
+That may not be the
+case all the time.
+
+I think it depends a lot on
+the particular government.
+
+I think, obviously, J-PAL
+is primarily a academic
+
+organization.
+
+And so it's not the right
+organization to manage the
+
+actual roll out.
+
+But where you draw the line,
+it's a difficult question.
+
+But I also--
+
+Yes.
+
+AUDIENCE: [INAUDIBLE].
+
+MICHAEL KREMER: No, go ahead.
+
+AUDIENCE: So it seems like that
+the deworming medication
+
+is really cheap, and it's
+a very easy treatment.
+
+Have you looked at other types
+of diseases and using the
+
+school system to try
+and manage it?
+
+MICHAEL KREMER: Yeah.
+
+So there are other things which
+could be done in the
+
+school health area
+and perhaps with
+
+micronutrients, et cetera.
+
+I don't want to go too far there
+both because I want to
+
+get back to the econometrics and
+because I know more about
+
+worms than I do other things.
+
+But I think there are
+micronutrients and other
+
+things that could be
+delivered that way.
+
+There's some work that's been
+done on presumptive treatment
+
+for malaria that is very
+intriguing and suggests that
+
+might work.
+
+There's also things you can
+do on education, HIV/AIDS
+
+education, and so on.
+
+Pascaline Dupas does some
+very nice work on that.
+
+And then Esther and Pascaline
+and Samuel Sinei and I have
+
+some joint work on
+that as well.
+
+OK.
+
+Well, let me turn to the topic
+of this lecture, which is--
+
+and I'm happy if there's time
+at the end or in the break,
+
+I'm happy to follow up
+on these issues--
+
+which is managing threats to
+
+evaluation and to data analysis.
+
+So I think in the previous
+discussion, there's been
+
+things about how do you set up
+your sample size, how do you
+
+actually randomize.
+
+Doing those things is obviously
+critical, but it
+
+might not be sufficient.
+
+Because there can still be
+problems with impact
+
+measurement and analysis.
+
+Some of those, you can try to
+minimize ahead of time.
+
+I'm going to focus mostly
+on what can be
+
+done ahead of time.
+
+And then Shawn's going to talk
+about what can be done in the
+
+analysis stage to try and deal
+with problems that did come
+
+up, and what inferences you can
+make, and what inferences
+
+you can't make.
+
+I'm going to do a small,
+semi-randomized trial here,
+
+quasi-randomized trial,
+I guess should say.
+
+I'm going to consider a program
+which is giving people
+
+money as a social, anti-poverty
+program.
+
+I think, rather than do
+full randomization--
+
+you can actually leave that
+down for awhile--
+
+I'll come back to the
+evaluation of
+
+this program later.
+
+Now I'm going to do the
+randomization and the
+
+implementation.
+
+And we can do the--
+
+AUDIENCE: Too late.
+
+MICHAEL KREMER: OK.
+
+Too late?
+
+OK, that's fine.
+
+We could count off people, one,
+two, one, two, and then
+
+just give all the ones $500
+and the twos nothing.
+
+AUDIENCE: It really does
+feel bad when you're
+
+in the control group.
+
+AUDIENCE: No sharing.
+
+[UNINTELLIGIBLE].
+
+AUDIENCE: This is real
+money or this--
+
+MICHAEL KREMER: Don't worry.
+
+Well, you shouldn't feel
+too bad if you're
+
+in the control group.
+
+AUDIENCE: I meant
+cash or money?
+
+MICHAEL KREMER: You've got
+the money now, yeah?
+
+AUDIENCE: [UNINTELLIGIBLE]
+cash?
+
+MICHAEL KREMER: Yeah, they'll
+be opportunities later on.
+
+OK, here are the problems
+I want to discuss.
+
+The first one is--
+
+so hang on to this money, we'll
+deal with it later on--
+
+the first one is attrition.
+
+The second is externalities.
+
+And the third one is
+partial compliance.
+
+So the first one is attrition.
+
+Some people you're not able to
+collect follow up data on.
+
+You try, but you're
+not able to.
+
+The second one, externalities.
+
+What happens if your program,
+as in the case of deworming,
+
+winds up affecting the
+comparison group as well as
+
+the treatment group?
+
+And the third one is
+partial compliance.
+
+You want to implement in certain
+places, but some
+
+places, they don't actually
+implement it.
+
+Maybe some of your
+comparison group
+
+accidentally gets treated.
+
+What do you do in that case?
+
+All of these things are really
+about internal validity.
+
+So there's important questions
+of external validity and
+
+interpretation.
+
+And Shawn's going to talk
+to some about those.
+
+But I'm going to just
+focus on the
+
+internal validity of these.
+
+So the first question with
+attrition is is it going to be
+
+a problem if some of the people
+disappear before you
+
+can collect the data.
+
+And this can be a real problem
+in Kenya for example.
+
+Kids often change their name.
+
+So it's just a part
+of the culture.
+
+You change your name
+at some point.
+
+That's going to make it
+difficult to find everybody
+
+afterwards.
+
+So a first question-- oh gosh,
+I thought this was going to
+
+come up bit by bit.
+
+Well, OK.
+
+We got the whole slide.
+
+So is it a problem if the type
+of person who disappears is
+
+correlated with the treatment?
+
+And does anybody want to
+answer that even though
+
+there's some answer there?
+
+This says the name of it,
+but it's not saying
+
+what the issue is.
+
+Does anybody want to
+comment on that?
+
+Yes.
+
+AUDIENCE: So if the attrition
+is quantited with treatment,
+
+then you're going to end up
+with underestimated or
+
+overestimated effect depending
+on what the correlation is.
+
+MICHAEL KREMER: OK.
+
+That's great.
+
+Can you say more about that?
+
+AUDIENCE: So if the correlation
+is that the people
+
+who disappear are people who
+didn't get the treatment, who
+
+most needed the treatment, then
+what you're left with in
+
+the control group is stronger
+people, the people who maybe
+
+didn't need the treatment as
+much or maybe had other
+
+reasons that they were
+doing just fine.
+
+And so it's going to look like
+the treatment effect is less
+
+because you have a strong
+control treatment group
+
+compared to a randomized
+treatment group.
+
+MICHAEL KREMER: Right.
+
+OK.
+
+So that's great.
+
+So let's go through an example
+where we can potentially see
+
+that sort of thing happening.
+
+So let's think about a problem
+where there's some kids who
+
+don't come to school because
+they're too weak, they're
+
+undernourished.
+
+So imagine that's the context.
+
+And imagine you start a school
+feeding program, and you want
+
+to do an evaluation of the
+impact of this on school
+
+attendance.
+
+So this, in fact, was something
+we wanted to do.
+
+And imagine you're interested
+both in the impact on
+
+enrollment, but also on
+children's nutrition, which
+
+you measure by their weight.
+
+And imagine that the real effect
+of this program is that
+
+the weak, stunted children
+actually go to school more if
+
+they're near a treatment
+school.
+
+So if you go to all the schools
+and you measure
+
+everyone who's in school on a
+given day, in that case, are
+
+you going to see the treatment
+and control difference in
+
+weight overstated
+or understated?
+
+AUDIENCE: Overstated.
+
+MICHAEL KREMER: Overstated.
+
+So what's the story for why
+it would be overstated?
+
+AUDIENCE: Because in the
+treatment schools, a lot of
+
+kids who really need
+the nutrition
+
+would start going in.
+
+Whereas, in the control group,
+they have no incentive to go.
+
+So they're not being
+included in it.
+
+MICHAEL KREMER: That's
+interesting.
+
+That's interesting.
+
+OK, OK.
+
+In fact, the example is going
+to be the opposite.
+
+But I think it's true, you could
+tell a story where this
+
+could go either way.
+
+And you just told a story where
+it would go that way.
+
+Let's show you a hypothetical
+numerical example.
+
+And if you can actually
+work through this,
+
+that would be useful.
+
+Imagine there's just three
+kids in each of these
+
+communities.
+
+So imagine that before
+treatment, the distribution
+
+looked identical.
+
+So there was one kid who weighed
+30 kilos, another at
+
+35, another at 40.
+
+And after treatment, let's say
+it's a successful program, and
+
+it gets everybody up
+by two pounds--
+
+I guess we should do this in
+pounds given these numbers--
+
+moves everybody up
+by two pounds.
+
+In the comparison group,
+everybody stays the same.
+
+So when you calculate, the
+average here is going to be
+
+35, and here it's
+going to be 35.
+
+So there's going to be no
+difference at baseline.
+
+If you look afterwards, if you
+didn't have any attrition and
+
+you managed to follow all
+these kids, you would
+
+correctly measure the impact
+of this program.
+
+You would say that it's added
+two pounds to people's weight.
+
+Now here's one possible
+pattern of attrition.
+
+Suppose you go on a given day,
+but not all of the kids are
+
+there that day.
+
+So in particular, imagine that
+the weaker kids are less
+
+likely to be there.
+
+So suppose only children who
+are more than 30 kilograms
+
+come to school.
+
+Imagine the kids who are less
+than 30 kilograms are only
+
+there half the time
+or something.
+
+And you happen to show up on a
+day when kids who are only
+
+over 30 kilograms
+come to school.
+
+Well, then the person who is
+still at 30 kilograms in the
+
+comparison group isn't going
+to be there at all.
+
+You'll measure the average
+here at 37 and a half.
+
+So you'll see no difference
+beforehand.
+
+Afterwards, can you compute what
+you're going to estimate
+
+the impact of the
+treatment to be?
+
+Yeah.
+
+AUDIENCE: It's negative
+half a pound.
+
+MICHAEL KREMER: Negative
+half a pound, right.
+
+So in this case, for this
+particular set of assumptions,
+
+you'll underestimate
+the impact.
+
+It's not necessarily the case
+that attrition differences
+
+between the groups always
+lead to underestimates.
+
+It can be the opposite.
+
+So we happened to pick a case
+here where it worked this way.
+
+But here's another example.
+
+Let's put that other
+context behind us.
+
+Think about a different
+context.
+
+Think about the context
+of we're just
+
+trying to improve learning.
+
+And we've got a new
+math course.
+
+And it's a hard course.
+
+For example, in the state of
+Massachusetts, there are now
+
+graduation requirements.
+
+Used to be that it was very
+easy to graduate from
+
+secondary school.
+
+They put in requirements to
+make this much tougher.
+
+You have to pass an exam.
+
+And the proponents of this
+argue, well, it's a good thing
+
+because it forces the kids to
+study more, it forces the
+
+teachers to really
+prepare them.
+
+And they're probably right.
+
+The opponents argue that, well,
+the kids who figure
+
+they're not going to be able
+to pass just drop out.
+
+They may be right as well.
+
+So if you're trying
+to evaluate the
+
+impact of this program--
+
+and imagine that we randomized
+across states in the US, and
+
+some states implemented,
+and some didn't--
+
+if you looked at the average
+score among those who got
+
+through, well, you might
+see it's better in
+
+the treatment group.
+
+But would that be the right
+conclusion about the impact of
+
+the program?
+
+It might not be.
+
+So let me keep going
+with this.
+
+So we've got this
+harder course.
+
+Imagine those who can't
+handle it drop out.
+
+You give the same
+math test in the
+
+treatment and control schools.
+
+But you only have data on those
+who didn't drop out
+
+because you go to the school
+and you get everybody who's
+
+there in the school.
+
+So what's the direction
+the bias is going
+
+to be in that case?
+
+AUDIENCE: It'll overstate
+the effect.
+
+You'll only see the strongest.
+
+MICHAEL KREMER: Exactly,
+exactly.
+
+In the treatment group, you'll
+only see the strong students.
+
+In the comparison group,
+you'll have the mix.
+
+So that's an example of
+the case that you
+
+were talking about.
+
+In the deworming program with
+testing, what was the natural
+
+concern with attrition
+bias there?
+
+AUDIENCE: The weakest, the
+ones with the most worms
+
+weren't going to be--
+
+MICHAEL KREMER: Exactly,
+you get them to stay.
+
+The kid's pretty weak because
+they've had lots of worms.
+
+You cut off the worms,
+they come to school.
+
+So the treatment group would
+then be adding in these kids
+
+who are weaker in some way.
+
+So that would be the concern.
+
+How do you deal with it?
+
+Well, one way is you can try
+to follow everybody up.
+
+And this is the first thing
+you should do is the brute
+
+force approach, which is to try
+and follow everybody up.
+
+And that means if it's a school
+program, maybe you
+
+don't just test the kids in
+the school, the ones who
+
+dropped out, you try and find
+them and test them anyway.
+
+Now that's expensive.
+
+And it's very difficult to find
+people, and it may be
+
+difficult to get them
+to take the exam.
+
+But if you think that the
+program is going seriously
+
+affect dropout rates, then that
+can be a very important
+
+thing to do.
+
+To do that, you have to pick a
+sample of those who are going
+
+to be tested before the
+treatment, and you have to
+
+follow those people.
+
+So if you hadn't done a
+baseline, then this is going
+
+to be especially hard because
+you don't even know who
+
+dropped out.
+
+They might not have records
+of those kids.
+
+There's sometimes questions.
+
+Should you do a baseline,
+or should you not?
+
+In theory, you could do a
+randomized evaluation without
+
+a baseline.
+
+Almost always, it's much better
+to have the baseline.
+
+And this is one of them, which
+is if the program might affect
+
+dropout, you want to measure the
+effect of the program by
+
+looking at the people who were
+initially in the program.
+
+So then imagine that you do
+that, but the truth is it's
+
+just hard to find all these
+kids who dropped out.
+
+Some of them have moved, or
+they're not home, or whatever,
+
+or they don't want to
+come take the test.
+
+So imagine that you've done
+this, and the treatment group
+
+has 20% attrition,
+the comparison
+
+group has 20% attrition.
+
+Are you then OK?
+
+OK.
+
+I'm seeing the answer, no.
+
+Does anybody want to say
+what the potential
+
+problem might be?
+
+Yeah.
+
+AUDIENCE: Well, if it's not
+random as to who drops out,
+
+then we're just still going to
+have to [UNINTELLIGIBLE]
+
+facts.
+
+If there's still a correlation
+between who's dropping out in
+
+the control group versus who's
+dropping out in the treatment
+
+group, that's still going
+to affect the outcomes.
+
+MICHAEL KREMER: Yeah.
+
+That's exactly right.
+
+I'm trying to think
+of this myself.
+
+Can anybody come up with a
+hypothetical, but concrete
+
+example, where you could have
+the same attrition rate in the
+
+two groups, but your estimate
+would still be messed up or
+
+biased, to use the
+technical term?
+
+Yeah.
+
+AUDIENCE: For example, if the
+treatment group is only the
+
+[UNINTELLIGIBLE]
+
+could drop off and then
+the control group is
+
+[? losing flow ?]
+
+would drop off, it's not going
+to [UNINTELLIGIBLE].
+
+MICHAEL KREMER: Exactly,
+exactly.
+
+So if, in each case, you lose
+20%, but in the treatment
+
+group, you're losing the top 20%
+and the comparison group,
+
+you're losing the bottom 20%,
+and you only measure those who
+
+remain, you're going
+to be biased.
+
+So here's an example of
+something that could do that.
+
+Imagine that you put in a
+remedial education program.
+
+Imagine you lower the levels
+of the curriculum.
+
+Well, then maybe the kids in the
+treatment group, maybe the
+
+kids who are at the top of the
+distribution say, I don't want
+
+to be in this school, I'm
+switching to another school,
+
+because they don't want the
+lower level curriculum.
+
+So you lose 20%.
+
+In the comparison school, the
+20% at the top don't drop out,
+
+but the 20% at the bottom drop
+out because they didn't have
+
+this special attention.
+
+So in each case, you've got
+20% attrition, but the
+
+estimate of the impact of the
+program is going to be very
+
+seriously biased.
+
+So how can you deal with that?
+
+Well, what you should do
+is you should check
+
+whether you have a--
+
+imagine you had pre-test
+scores for the kids.
+
+Well, then you could see what's
+the predictors of drop
+
+out in the treatment group and
+in the comparison group.
+
+And ideally, you'd find the
+predictors are the same.
+
+And then you're somewhat
+reassured.
+
+You're not completely,
+completely safe because maybe
+
+your initial test scores aren't
+really a good measure
+
+of their true eventual
+test score.
+
+But it helps a lot.
+
+The other thing you can do is
+you can try to bound the
+
+extent of the bias.
+
+So we go through an exercise
+like this in
+
+the deworming paper.
+
+So suppose everyone who dropped
+out of the treatment
+
+got the lowest test score
+that you got.
+
+So what you can do is you can
+say, we're going to put those
+
+people for whom we don't have
+outcome data, we're going to
+
+create an artificial data set,
+where we put them back in the
+
+data, but we artificially
+assign them the lowest
+
+conceivable score.
+
+And then suppose everybody who
+dropped out of the control
+
+group got the highest score
+that anybody could get.
+
+So if you artificially give
+everybody who dropped out of
+
+treatment the lowest possible
+score, and you artificially
+
+give everybody who dropped out
+of the control group the
+
+highest possible score, well,
+then you're bending over
+
+backwards to say, how bad
+could the program
+
+potentially have been.
+
+And if you do this exercise and
+you find that even when
+
+you do this, it looks like the
+program is good, then you can
+
+be pretty confident the
+program's good.
+
+So this is what's called
+constructing the lower bound.
+
+And similarly, you can construct
+an upper bound on
+
+how well the program did.
+
+And if you have a high dropout
+rate, your lower bound and
+
+your upper bound are going
+to be very far
+
+apart from each other.
+
+You're not going to be able to
+say that much about what the
+
+impact of the program is.
+
+But if you have a low dropout
+rate, it might be that your
+
+bounds are very close
+together.
+
+AUDIENCE: And cheaper.
+
+MICHAEL KREMER: It's cheaper
+than fighting everybody, yeah.
+
+I think a lot depends on
+the particular context.
+
+And there's also various
+bounds you can do.
+
+So let me not go into the
+full detail on that.
+
+But you can have bounds that
+are very conservative.
+
+This would be an example of
+them, where this is very much
+
+a worst case scenario.
+
+You can imagine other scenarios
+that are not the
+
+very worst case scenario, but
+are pretty bad case scenarios,
+
+and say, even in that case, the
+program would have worked.
+
+The next topic is going
+to be externalities.
+
+But before I go on to that, do
+people have questions on
+
+attrition or comments on it?
+
+Or questions about
+this in practice?
+
+OK, let me move on
+to externalities.
+
+So first, I want to create
+some externalities.
+
+So everybody who got
+some money--
+
+I heard a suggestion of
+sharing some money.
+
+So why don't we implement
+that?
+
+So why don't you turn to your
+neighbor, and why don't you
+
+share some of the money
+with your neighbor?
+
+I'll let you decide how generous
+you want to be.
+
+It is fake money after all.
+
+AUDIENCE: Can we give to
+multiple neighbors?
+
+MICHAEL KREMER: Do whatever
+you like, do
+
+whatever you like.
+
+And by the way, what you guys
+just did, there are a lot of
+
+theories of development--
+
+I don't know whether this is
+practice or not-- which would
+
+say that that sort of thing
+might happen, a lot of
+
+theories about risk sharing
+within communities, and so on.
+
+Maybe that's all propaganda,
+I don't know.
+
+But anyway, some people would
+claim that that sort of thing
+
+can happen.
+
+So now what I want to talk about
+though is what's the
+
+impact on our program
+evaluation.
+
+What I'd like to do is to do a
+program evaluation now of what
+
+was the impact of this
+program, where
+
+you're all a village.
+
+I gave half the people
+in the village $500.
+
+So how did we do that?
+
+Well, we pseudo-randomized the
+program, reasonably close,
+
+counting off one, two.
+
+What's the impact
+of the program?
+
+Well, let's figure out how much
+money our treatment group
+
+people have and our comparison
+group people have.
+
+So if you can look in your
+wallet, figure out how much
+
+money you have there, add in
+the fake money, and come up
+
+with a total.
+
+And then we'll try
+and do some--
+
+I'll do some data collection.
+
+So let me put this up here.
+
+AUDIENCE: Our actual money?
+
+MICHAEL KREMER: Yeah, add in
+your actual money and your
+
+fake money, and we'll see.
+
+So are you a treatment
+group person?
+
+AUDIENCE: Yes.
+
+MICHAEL KREMER: OK.
+
+So how much money do you have,
+including everything?
+
+AUDIENCE: $784.
+
+MICHAEL KREMER: $784, OK.
+
+I hope there's no thieves
+around here that I'm
+
+revealing things to.
+
+AUDIENCE: $784?
+
+AUDIENCE: Including this.
+
+AUDIENCE: Because I'm
+a control group.
+
+MICHAEL KREMER: You're
+a control group.
+
+AUDIENCE: I have $300.
+
+MICHAEL KREMER: $300.
+
+AUDIENCE: [? Only money ?]
+pounds [? away ?].
+
+AUDIENCE: But these guys
+gave it to you.
+
+AUDIENCE: It was on your Charlie
+card or whatever.
+
+MICHAEL KREMER: So how
+much do you have?
+
+AUDIENCE: $407.
+
+MICHAEL KREMER: $407.
+
+And you're a treatment, right?
+
+AUDIENCE: I got $14 and
+$1 on my Charlie card.
+
+MICHAEL KREMER: OK.
+
+So $15, we'll call it.
+
+AUDIENCE: $550.
+
+MICHAEL KREMER: $550.
+
+Maybe the second row
+should just come up
+
+and write on here.
+
+AUDIENCE: $140.
+
+MICHAEL KREMER: Sorry?
+
+AUDIENCE: $140.
+
+MICHAEL KREMER: $140.
+
+AUDIENCE: $428.
+
+MICHAEL KREMER: $428.
+
+AUDIENCE: $318.
+
+MICHAEL KREMER: $318.
+
+AUDIENCE: $698.
+
+MICHAEL KREMER: I'll
+put this here.
+
+AUDIENCE: $263.
+
+MICHAEL KREMER: And are
+you a one or a two?
+
+AUDIENCE: I'm $500, I
+don't know what--
+
+MICHAEL KREMER: So
+you're group one.
+
+And sorry, what was
+the number again?
+
+AUDIENCE: $263.
+
+MICHAEL KREMER: $263.
+
+You're a very generous guy at
+least with fake money, right?
+
+AUDIENCE: $270.
+
+MICHAEL KREMER: Oh, $270.
+
+Looks like the program was
+
+counterproductive in your case.
+
+We had a negative seven
+effect on income.
+
+AUDIENCE: I have $227.
+
+MICHAEL KREMER: $227.
+
+AUDIENCE: $500.
+
+MICHAEL KREMER: $500.
+
+You know what?
+
+We could go and do the full
+sample, but maybe we should--
+
+well, we'll take two more.
+
+AUDIENCE: $700.
+
+MICHAEL KREMER: I'm sorry,
+which group are you?
+
+AUDIENCE: Treatment.
+
+MICHAEL KREMER: $700, OK.
+
+AUDIENCE: I'm control,
+and I have $200.
+
+MICHAEL KREMER: $200?
+
+Oh, so that got the--
+
+We'll just take a partial sample
+rather keep going.
+
+Let's try and get the average in
+the treatment group and the
+
+average in the comparison
+group.
+
+AUDIENCE: The average in the
+treatment group is 507 or 8.
+
+MICHAEL KREMER: 508.
+
+AUDIENCE: And the average in
+the control group is 249.
+
+MICHAEL KREMER: 249.
+
+So now we do our evaluation.
+
+And we go through, and
+we say, OK, we
+
+gave out $500 to people.
+
+Now we've gone back to see how
+they're doing, compare them to
+
+the comparison group.
+
+And it looks like they're
+$259 richer.
+
+So did the program work?
+
+Well, the program worked.
+
+But was it cost effective?
+
+Not really.
+
+Because we gave them $500.
+
+They're only $250 approximately
+richer.
+
+This really wasn't
+a big success.
+
+AUDIENCE: Well--
+
+MICHAEL KREMER: Go ahead.
+
+AUDIENCE: That's only one way
+of looking at it, right?
+
+MICHAEL KREMER: Exactly.
+
+That's one way of
+looking at it.
+
+If you came with that
+conclusion, you'd be missing a
+
+really important dimension
+of what the impact
+
+of the program is.
+
+Certainly, if you're a policy
+maker who's mostly concerned
+
+about what's the impact on the
+community, not what's the
+
+impact on the particular
+individual I gave it to, then
+
+you'd basically have a very
+misleading answer.
+
+So that's the danger.
+
+The topic of this lecture
+is what are threats.
+
+And this is a threat.
+
+You misunderstand the impact
+of the program because you
+
+haven't adequately accounted
+for the externality.
+
+That's the problem.
+
+Let me now talk about what can
+you do about that problem.
+
+So let me look at this in the
+context of deworming.
+
+Then maybe we can come back
+to this example again.
+
+So in the case of deworming,
+a lot of the earlier work
+
+randomized deworming treatment
+within schools.
+
+So the problem is that when
+you are dewormed, that may
+
+interfere with the transmission
+of the disease.
+
+If the treatment kills the worms
+in your body, that means
+
+the worms are no longer laying
+eggs, they're no longer being
+
+spread in the community
+as much.
+
+So what's the problem that
+that's going to create for the
+
+evaluation?
+
+AUDIENCE: You're going to see
+benefits in the control group.
+
+MICHAEL KREMER: Right.
+
+You could see benefits in the
+control group, just as this
+
+cash example.
+
+In this particular case, we
+argue that those benefits
+
+might not just have affected
+kids who go to that school,
+
+but might have also affected
+neighboring schools as well.
+
+But let's start out with the
+analytically simpler case.
+
+Suppose the benefits
+are local.
+
+So suppose you only shared money
+with your neighbors, but
+
+you don't share money with
+people in another classroom in
+
+engineering or something
+like that.
+
+And how can you measure the
+total impact, the impact on
+
+the community as a whole
+of the program?
+
+What could you do
+in that case?
+
+AUDIENCE: You could phase in at
+different rates to try and
+
+evaluate what would be the
+impact of just having a
+
+peer-controlled peer treatment
+and then try and figure out
+
+from the phase-in what
+the impact of the
+
+externality would be.
+
+MICHAEL KREMER: So you
+could phase it in.
+
+In this case, if the
+externalities were local
+
+within a school or within a
+classroom, in the case of this
+
+money example, you could phase
+it in at the level of schools
+
+or of classrooms.
+
+And say, we're going to do
+20% of the people in that
+
+classroom, 40% of the people in
+this classroom, 60% of the
+
+people in that classroom.
+
+By the way, before I go further
+with this, so there's
+
+an advantage of this-- well,
+let me come back to this.
+
+I'm going to immediately assess
+the advantage of this,
+
+but there's also
+a disadvantage.
+
+So let's take this case where's
+there's externalities
+
+within a school.
+
+So if we think about this
+particular case, so imagine
+
+that there's no externalities.
+
+Pupil one is treated,
+and the outcome is
+
+they don't have worms.
+
+Pupil two is not treated, but
+they still don't have worms.
+
+Some people just don't
+get the worms.
+
+Pupil three is treated.
+
+They don't have worms because
+the medicine worked.
+
+Pupil four is not treated,
+and they do have worms.
+
+Pupil five is treated, and
+they don't have worms.
+
+Pupil six isn't treated,
+and they do have worms.
+
+So in this case, where there's
+no externalities going on,
+
+what's going to be the estimate
+of the treatment
+
+effect here?
+
+AUDIENCE: 100% [INAUDIBLE].
+
+MICHAEL KREMER: I'm sorry.
+
+You said 100%?
+
+Do you want to go through
+the reasoning you're
+
+thinking up on that?
+
+AUDIENCE: [INAUDIBLE].
+
+MICHAEL KREMER: So it's true
+that nobody who is treated has
+
+worms because the
+medicine works.
+
+So the total people in worms and
+the treatment group with
+
+worms is going to be 0.
+
+So in that sense, you've
+eliminated 100% of the group
+
+that does have worms.
+
+How many in the control group
+are going to have worms?
+
+AUDIENCE: Three.
+
+MICHAEL KREMER: Three.
+
+So it depends how you define--
+
+this is a big distinction
+that people--
+
+it's tedious, but it's important
+to make when you
+
+write things up is percentage
+effect versus
+
+percentage point effect.
+
+So percentage point is
+the absolute value.
+
+So let me first do the
+percentage point and then come
+
+back to the percent.
+
+So we have 0 people having it
+in the treatment group.
+
+The total in the control with
+worms, was that three if I
+
+remember right?
+
+OK.
+
+So 50% of people have it in the
+control group, 0 have it
+
+in the comparison group.
+
+So it's a 50 percentage
+point difference.
+
+The difference between 50
+percentage points and 0
+
+percentage points.
+
+So one accurate way to write
+this up would be say we had a
+
+50 percentage point
+difference.
+
+Another way would be to say,
+we eliminated 100% of the
+
+initial level.
+
+They're both accurate.
+
+It's just different ways
+of expressing it.
+
+When you write things up,
+the convention is to use
+
+percentage point for
+the absolute value.
+
+So the treatment effect
+would be 50
+
+percentage points or 100%.
+
+But now suppose that you
+actually do have
+
+externalities.
+
+So some children are not
+reinfected with worms.
+
+So these worms have a life
+cycle, so eventually the worms
+
+in you die.
+
+You have a high wormload because
+you're continually
+
+being reinfected.
+
+So think about this example,
+where some of the kids in the
+
+comparison group don't
+get reinfected.
+
+Let's just think about the
+percentage point effect for
+
+comparison.
+
+What are you going to estimate
+the impact being in this case?
+
+AUDIENCE: 53?
+
+MICHAEL KREMER: Right.
+
+Did I just--
+
+let's see this thing.
+
+Let me just do the--
+
+I'm sorry.
+
+We didn't--
+
+I think this other thing,
+did we do the counting
+
+right in that one?
+
+AUDIENCE: Well, you said there
+was 50% control with worms.
+
+And unless I'm misunderstanding
+it, it looks
+
+like it's 100%.
+
+MICHAEL KREMER: Yeah,
+that's right.
+
+Somebody had said 50,
+and I didn't look.
+
+I just assumed that was
+the right number.
+
+Let me just look at the nos.
+
+Yes, that's right.
+
+I'm sorry.
+
+It's 100% who have worms.
+
+Sorry, that was very
+confusing.
+
+So now I see why you said-- it's
+100% either way whether
+
+it's percentage points
+or percent.
+
+You would have reached
+that same conclusion.
+
+Let me just go back here just
+to repeat, in case it wasn't
+
+clear to others like it
+wasn't clear to me.
+
+So if the total in the treatment
+with worms is 100%
+
+in this example, total in the
+control with worms is 0.
+
+I think I must've got confused
+in reading it in horizontal
+
+lines there.
+
+So in this case, the total
+in the treatment
+
+group with worms is--
+
+we still have 0 in the treatment
+group with worms.
+
+And in the comparison group,
+we've got 67%, 67%.
+
+So we're going to estimate
+the treatment effect in
+
+this case being 67%.
+
+Now notice that this--
+
+AUDIENCE: 130?
+
+Why?
+
+Oh, because it's
+the difference.
+
+MICHAEL KREMER: The
+difference, yeah.
+
+The difference between
+100 and 67.
+
+Sorry, the hundred and--
+
+see if we got this--
+
+the hundred--
+
+AUDIENCE: It's the total
+[UNINTELLIGIBLE]
+
+0.
+
+MICHAEL KREMER: This is
+0, and this is 67.
+
+So we've estimated 67% effect.
+
+So the thing to take away from
+this is that if there were no
+
+externalities, we would have
+estimated this correctly at
+
+100%, the effect
+of the program.
+
+Now we say, suppose there are
+externalities to this.
+
+So now that makes the program
+actually better because more
+
+people are being cured of worms
+through this program.
+
+But we're going to estimate the
+effect of the program is
+
+actually lower.
+
+Instead of estimating the 100%
+benefit, we'll estimate only a
+
+67% benefit.
+
+So how do you deal with that?
+
+Well, if you design the unit
+of the randomization, so it
+
+encompasses all those
+spillovers, that's one way to
+
+address this problem.
+
+So if you expected all the
+externalities are within
+
+school, you can just randomize
+at the level of the school.
+
+So here's another approach.
+
+And this is the actual data
+from the program.
+
+The percentage of children
+with a moderate or heavy
+
+infection in the treatment
+schools was 27%.
+
+It was 52% in the comparison
+schools.
+
+So the program reduced
+moderate to heavy
+
+infections by 25%.
+
+This medicine probably affected
+more kids initially.
+
+But if you go back and measure
+a year later, some of them
+
+have been reinfected.
+
+You also got a reduction in the
+number of kids who were
+
+sick and who are anemic.
+
+This is comparing one school
+to another school.
+
+So we will have accounted for
+the total impact of the
+
+program within schools if
+there's within school
+
+spillovers.
+
+Suppose you wanted to actually
+measure the spillovers.
+
+Suppose you were interested in
+the spillovers themselves and
+
+not just the total impact.
+
+And you might well be.
+
+Imagine you are interested in
+the question of do we really
+
+need to incentivize people to
+take this, or could we charge
+
+them for the medicine.
+
+Well, if you thought that
+everybody benefited from the
+
+medicine pretty much equally,
+whether you took it or not,
+
+because most of the impact was
+on the transmission of the
+
+disease, then you might need
+to subsidize it more.
+
+You might want to subsidize it
+more than if you thought the
+
+individual got all
+the benefit.
+
+So if you actually want to
+measure the spillovers, here's
+
+one of the things we did in
+the paper on deworming.
+
+So at the time--
+
+this is no longer the case, I
+want to emphasize-- but at the
+
+time, there was concern that the
+official guidelines were
+
+not to treat girls over 12
+unless you knew they had
+
+worms, they shouldn't be treated
+presumptively in case
+
+the medicine caused birth
+defects and in case the girls
+
+were pregnant.
+
+Turns out, that they've now
+given this widely enough that
+
+WHO guidance is there's no
+evidence it causes birth
+
+defects, and you can give
+it to everybody.
+
+But at the time, they weren't
+giving it to girls above 12.
+
+So imagine you compared girls
+above 12 in the treatments
+
+schools to girls above 12 in
+the comparison schools.
+
+There are some other
+things we can do.
+
+So there are some other sources
+of who wasn't treated.
+
+This comparison I'm going
+to show you is a little
+
+bit more than that.
+
+But you can compare the treated
+students in treatment
+
+schools to the comparable
+students in
+
+the comparison schools.
+
+So kids who looked comparable
+on a variety of observable
+
+dimensions or who wound up
+taking this when they became
+
+eligible to take it.
+
+We saw a very big gap
+in prevalence
+
+among those two groups.
+
+So this is much more
+of a straight
+
+treatment comparison look.
+
+Here, we're looking at the
+untreated students in the
+
+treatment schools and trying to
+find comparable students in
+
+the comparison schools.
+
+I should emphasize this isn't
+quite as pure as a standard
+
+randomized design.
+
+This program was phased
+in over time.
+
+These are the people that when
+their school was phased in,
+
+they wound up not
+getting treated.
+
+So maybe there were differences
+between years, but
+
+that's a caveat or a footnote.
+
+So none of these guys were
+treated, but these people were
+
+in a school where their
+classmates were treated.
+
+So they have much lower levels
+of infection than these people
+
+who were also not treated,
+but whose
+
+classmates were not treated.
+
+Now what if you expect
+externalities across--
+
+so actually, before I go on to
+this further challenge of what
+
+if there are externalities
+across schools, just sticking
+
+with this question of
+externalities within schools,
+
+talked about one way of dealing
+with that was to do
+
+the randomization at the
+level of the school.
+
+So what's the disadvantage of
+doing the randomization at the
+
+level of the school?
+
+AUDIENCE: Assuming that
+everybody in the same school
+
+is at the same level.
+
+MICHAEL KREMER: So you could
+still have some differences
+
+within the school.
+
+But there is a sense in which
+you're going to have less
+
+information if you're
+randomizing at the level of
+
+the school.
+
+Yes.
+
+AUDIENCE: You'd need
+more schools.
+
+MICHAEL KREMER: Yeah, right.
+
+The crudest way of putting this
+is if there's 400 kids in
+
+a school and you have 100
+schools and you're randomizing
+
+at the level of the individual,
+then you've got
+
+40,000 observations.
+
+And if you've got 200 schools
+you're randomizing and you're
+
+randomizing at the level of
+the school, you've got 100
+
+treatment schools and 100
+comparison schools.
+
+Much smaller sample size,
+much less power.
+
+That particular calculation I
+just did is overstating the
+
+difference.
+
+You've learned about clustering
+
+standard errors before.
+
+But since there's a
+lot of variation--
+
+to come back to the way you
+were putting it-- since
+
+there's a lot of random
+variation between schools--
+
+some schools have good
+headmasters, some schools have
+
+bad headmasters, et cetera--
+
+there's a lot of background
+noise.
+
+And it's going to make it harder
+to estimate precisely
+
+the impact of the program.
+
+So you really have to think
+about your particular context.
+
+When you're thinking about what
+level to randomize at,
+
+think about, in your context, do
+you think spillovers are a
+
+real issue.
+
+If you think spillovers are a
+real issue, then you better
+
+randomize at a higher level.
+
+But if you think, in this
+particular context, I don't
+
+need to worry about it, if this
+were a cancer drug rather
+
+than a worm drug, then you
+wouldn't need to worry about
+
+it, and you're much better
+off randomizing at
+
+the individual level.
+
+There might also be-- yes.
+
+AUDIENCE: So this might be a
+little too [INAUDIBLE], but if
+
+you're worried about attrition,
+would randomizing
+
+at a higher level make that
+less of an issue as well
+
+because now you're looking
+at a higher [INAUDIBLE]?
+
+So if you lose individuals
+within that,
+
+it's still an issue.
+
+MICHAEL KREMER: It would
+still be an issue.
+
+Yeah, it's still an issue.
+
+So let's say that we've decided
+
+we're going to randomize.
+
+Take this worm example.
+
+And we think that most of the
+externalities are within
+
+schools, so we're going to
+randomize within schools.
+
+We know that there might be
+some externalities across
+
+schools because this is an
+environment where everybody
+
+lives on their own
+farm basically.
+
+So you might have two kids
+living next to each other, one
+
+of whom goes to one
+school and another
+
+goes to another school.
+
+That's not that uncommon.
+
+So you could have some
+externalities across schools.
+
+But randomizing at the level of
+a district would really not
+
+logistically be very possible.
+
+You'd have no sample
+size left.
+
+So you know there might be
+some externalities across
+
+schools as well as those
+within them.
+
+But you've already made the
+decision to randomize at the
+
+level of schools.
+
+So what do you do?
+
+Well, what you can try and do is
+use random variation in the
+
+density of treatment nearby.
+
+So if you pick the schools
+randomly that were going to be
+
+treatment schools and the ones
+that are going to be
+
+comparison schools, there will
+be some comparison schools
+
+that happen to be completely
+surrounded
+
+by treatment schools.
+
+There will be other comparison
+schools that don't have any
+
+treatment schools nearby.
+
+So you can use that to try
+to pick up how big the
+
+externality is.
+
+So that's what we tried
+to do in this paper.
+
+So here's a map.
+
+So the ones are group
+one schools.
+
+They've been treated.
+
+The twos are group two
+schools, treated
+
+in the second way.
+
+Threes are group three
+schools, now treated
+
+to the third way.
+
+Here's a school that's in the
+middle of the lake which I
+
+think is actually
+on an island.
+
+These schools in Uganda are
+not really in Uganda.
+
+GPS used to be intentionally
+degraded because people were
+
+wanting to use it for military--
+it was developed by
+
+the military, I guess--
+
+they didn't want foreign
+militaries to have it.
+
+There are measured
+with some error.
+
+So we've got these schools.
+
+So we can see there are some
+schools that are near
+
+treatment schools.
+
+Other schools aren't near
+treatment schools.
+
+By the way, the treatment
+schools in this example I just
+
+did here, the ones shared
+with the twos.
+
+But you could imagine the ones
+might share with other ones.
+
+So there could be externalities
+on other
+
+treatment schools.
+
+Here's a group three school
+that's all by itself and
+
+doesn't have any neighbors
+who were treated.
+
+Here is a group three school
+that has three group one
+
+schools that are treated.
+
+So would you want to compare
+those to estimate what the
+
+effect of the deworming
+program is?
+
+AUDIENCE: Wouldn't you use it to
+estimate the impact of the
+
+spillovers?
+
+MICHAEL KREMER: Yeah, suppose
+you were interested in
+
+estimating the impact of the
+spillovers, the medical
+
+spillovers of treatment.
+
+Could you compare those
+two schools?
+
+What might make that comparison
+invalid if you're
+
+trying to estimate the
+impact of spillovers?
+
+AUDIENCE: [INAUDIBLE].
+
+MICHAEL KREMER: I'm sorry.
+
+One means a treatment school.
+
+Three means a comparison
+school.
+
+AUDIENCE: [INAUDIBLE].
+
+MICHAEL KREMER: So
+one's more rural.
+
+Exactly.
+
+This one is obviously in
+a less densely settled
+
+population.
+
+This one, turns out these are
+all rural, but this is
+
+obviously much more
+densely settled.
+
+That's why they've got all these
+schools around there.
+
+So now in this particular
+setting, why
+
+might that be a problem?
+
+Yeah.
+
+AUDIENCE: Because that area
+might be internally different
+
+from the [INAUDIBLE].
+
+MICHAEL KREMER: Yeah.
+
+So this is a disease.
+
+I probably should
+have said more
+
+about this in the beginning.
+
+So these worms affect one out of
+every three or four people
+
+in the world.
+
+And they're spread through
+fecal-oral routes.
+
+They're spread through
+fecal matter.
+
+What are the odds that you're
+going to get contaminated with
+
+fecal matter?
+
+It depends how many other people
+are depositing fecal
+
+matter in the environment.
+
+Clearly, over here, there's a
+lot of people nearby you who
+
+might be depositing fecal matter
+in the environment.
+
+Over here, there
+aren't so many.
+
+So you might think that that's
+how densely settled the
+
+population is.
+
+We don't think of Alaska or
+the middle of the desert
+
+somewhere being very diseased
+environments.
+
+But you think of a highly
+concentrated place having a
+
+lot more disease.
+
+There's reasons to think that
+sparsely settled places will
+
+have different prevalence of
+the disease than heavily
+
+settled places.
+
+So what we did because of that,
+we didn't want to just
+
+look at the number of treatment
+school nearby.
+
+We just talked about why that
+would be a problem.
+
+But we want to do that
+controlling for the total
+
+number of schools nearby.
+
+So we control for the total
+density in the area, total
+
+number of schools within a
+certain distance or pupils
+
+within a certain distance, and
+see what's the effect of those
+
+schools being treatment schools
+as opposed to being
+
+comparison schools.
+
+Oops, did I skip a--
+
+OK.
+
+So controlling for density,
+what we find is that the
+
+infection rates are 26
+percentage points lower per
+
+1,000 pupils in treatment
+schools within 3 kilometers.
+
+And then if you go further out,
+there are 14 percentage
+
+points per treatment schools
+that are 3 to
+
+6 kilometers away.
+
+So this is controlling for the
+overall density in the area.
+
+So hopefully, we're abstracting
+from that
+
+particular problem.
+
+So now suppose we want to
+estimate the overall effects.
+
+So let me come back
+to this problem.
+
+Clearly, we've incorrectly
+estimated.
+
+We estimated that only $250
+of benefit went through.
+
+But we think that the true
+effect should include the
+
+effect on the comparison.
+
+In this previous case, we were
+able to estimate the increase
+
+in school participation in the
+treatment group and then also
+
+in the comparison group through
+this technique that I
+
+just outlined.
+
+So we know in the comparison
+schools, there's a 1.5
+
+percentage point increase
+in school participation.
+
+There are three pupils in
+control schools for every
+
+treated child.
+
+And in the treatment schools,
+there was a 7 percentage point
+
+increase in school participation
+for all
+
+children, but you only needed to
+treat 2/3 of the children.
+
+So you can then calculate what
+the overall effect is of
+
+treating one child.
+
+So if you treat one child, you
+pick up three children in
+
+comparison schools, each of whom
+gets a benefit of 0.015
+
+additional years of education.
+
+Then you pick up this is the
+effect on children in the same
+
+school, and you get an
+overall effect of
+
+0.15 years of education.
+
+So treating a child costs
+about $0.50--
+
+in fact, it's probably cheaper
+than that when done at scale--
+
+but the impact that you're going
+to get is if each child,
+
+you get an extra 0.15 years of
+education, if you treat seven
+
+children, you'll get about an
+extra year of education.
+
+7 times $0.50 is $3.50.
+
+You spend $3.50 on deworming,
+and you get an
+
+extra year of education.
+
+Let me pause again here, and
+I'll go on and discuss some
+
+issues on partial compliance
+and sample selection bias.
+
+I'll get partway through that
+topic, and then Shawn's going
+
+to take up where I leave off.
+
+But are there any questions on
+externalities before I go on?
+
+OK.
+
+So you might think if you
+randomize where the treatment
+
+is, you're going to get rid
+of sample selection bias.
+
+That's not necessarily
+the case.
+
+So let me show an example.
+
+So where you randomize where
+you want the program to be,
+
+that's not necessarily the
+sole determinant of which
+
+places actually get treated.
+
+So let me talk about why.
+
+So one example would be people
+who are assigned to the
+
+comparison group might try to
+move into the treatment group.
+
+I don't think this happened, but
+parents could try and move
+
+their children from the
+comparison school to the
+
+treatment school.
+
+It's at least hypothetically
+possible.
+
+What are other possible reasons
+why you might not get
+
+this match between the initial
+assignment and where people
+
+wound up, where the people
+wound up treated?
+
+Yeah.
+
+AUDIENCE: So you might get
+somebody treated, and they
+
+don't want to take
+the medication.
+
+MICHAEL KREMER: Sure, exactly.
+
+In the case of deworming, there
+were some people who
+
+either didn't want to take the
+medication or who maybe they
+
+wanted to, but they weren't
+able to get the permission
+
+slip to do it.
+
+So that's one great example.
+
+What are other possible
+examples?
+
+If you think about
+your concrete
+
+experience, imagine that--
+
+I'll tell you a story
+from our experience.
+
+When this NGO was trying to
+get started and they were
+
+trying to pick the seven schools
+where they were going
+
+to work, they picked the
+schools, and they had to go to
+
+the government for permission
+to start working.
+
+And permission was slow.
+
+It kept being slow and slow.
+
+And they didn't realize
+what was going on.
+
+And it turned out, eventually,
+that there was a politician
+
+who was upset.
+
+The NGO didn't understand why
+the politician was upset.
+
+Because one of the schools was
+in his constituency, where
+
+they were going to
+start working.
+
+Well, it turned out it was in
+the part of his constituency
+
+that voted for his opponent.
+
+So in that sort of a situation,
+what the--
+
+I don't remember exactly the
+timing of this, but what the
+
+eventual resolution of this was
+they started working in
+
+the other part of his
+constituency, where his
+
+supporters lived as well.
+
+So they're all sorts of cases
+where you're going to want to
+
+randomize, but you may
+not be able to
+
+have that happen perfectly.
+
+In this case, it wasn't a,
+quote, "legitimate" reason.
+
+But there are other cases
+where there'd be very
+
+legitimate reasons why.
+
+Maybe the need is very intense
+in some area, and so the NGO
+
+or the organization feels
+it's very important to
+
+work in that area.
+
+So there may be lots of reasons
+why some people in the
+
+comparison group wind
+up getting treated.
+
+So there are cases like we
+just heard about where
+
+individuals allocated
+to treatment
+
+might not get treatment.
+
+And there are cases where
+people who are in the
+
+comparison group
+do get treated.
+
+So in the case of deworming,
+78% of those assigned to
+
+receive treatment got
+some treatment.
+
+And the main reason they weren't
+treated is they just
+
+happened to be absent from
+school the day that the
+
+treatment was given.
+
+Some students in the comparison
+group were treated
+
+because they went out and got
+the treatment on their own
+
+through clinics.
+
+So what do you do?
+
+Suppose this has already
+happened.
+
+So imagine you have data on
+everybody, so attrition isn't
+
+the problem, but
+just the actual
+
+assignment to treatment.
+
+The assignment to treatment
+and actual treatment don't
+
+correspond.
+
+So first, what's the problem
+if you just do a straight
+
+comparison, and what might
+you do about it?
+
+AUDIENCE: In this
+[UNINTELLIGIBLE], say they
+
+[UNINTELLIGIBLE] the students
+who were absent just by
+
+[UNINTELLIGIBLE] to their homes
+and [UNINTELLIGIBLE]?
+
+MICHAEL KREMER: No, so the
+program didn't do that.
+
+So we talked about in the case
+of the evaluation, when you're
+
+trying to measure the test
+scores or the impact on
+
+attendance, you could-- well,
+impact on attendance,
+
+obviously, you find out whether
+they're there or not
+
+by visiting the school.
+
+Unless you wanted to
+do test scores, you
+
+could track them home.
+
+But the way the program was
+implemented, those kids who
+
+weren't at school that day
+when they gave out the
+
+deworming pills, they just
+didn't get treated.
+
+Maybe the program shouldn't have
+been run that way, but
+
+that's how it was run.
+
+And there are reasons
+why maybe it
+
+should be run that way.
+
+AUDIENCE: In the end, you
+wouldn't be considering the
+
+effect of actually
+treating people?
+
+You'd be comparing the effect of
+intending to treat people.
+
+MICHAEL KREMER: This is exactly
+where we're going to
+
+go, and it's where I'm going to
+wind up and where Shawn's
+
+going to be taking over.
+
+Imagine you are interested in
+the impact of this program on
+
+test scores.
+
+So one thing you might think
+would be the right thing to do
+
+would be to just look at the
+people who actually were
+
+treated and compare
+them to people who
+
+actually weren't treated.
+
+That's going to be problematic
+for reasons that
+
+we'll explain later.
+
+But let me follow up on your
+suggestion which is if you're
+
+a policy maker, there are
+questions beyond this you'd be
+
+interested in.
+
+But you raised the idea of
+saying, well, what's the
+
+impact of the intent
+to treat somebody.
+
+And that is going
+to be the right
+
+answer to some questions.
+
+So let me start with that
+question, the relatively
+
+easier question.
+
+I'll let Shawn handle the
+harder questions.
+
+Suppose you're a policy maker,
+and you're saying, look,
+
+what's the impact of
+putting in this
+
+school-based deworming program?
+
+Well, if you're interested
+in what's the impact of a
+
+school-based deworming program,
+well, you know in
+
+reality, it's a true thing that
+you want to get at that
+
+some people are not
+going to get it.
+
+If this is a school-based
+program and you hand out the
+
+pills at the school, tracking
+kids to their houses who are
+
+absent that day, that's
+expensive.
+
+That's hard to implement.
+
+It uses too much
+teachers' time.
+
+You're probably not
+going to find that
+
+many of the kids anyway.
+
+So you wouldn't actually
+implement it that way.
+
+If you're a scientist,
+you do care.
+
+But if you're the policy maker,
+you might say, no, the
+
+true effect of this program is
+that I'm only going to be able
+
+to get 78% of the pupils because
+22% of the pupils
+
+aren't there.
+
+And if some kids don't
+want worms--
+
+don't want the medicine-- sorry,
+if they don't want--
+
+or maybe they do want the worms,
+or they don't want the
+
+worms, but they don't want
+the medicine either.
+
+Anyway, if some kids aren't
+going to take it, then those
+
+kids aren't going to take it.
+
+So you might think, well, I want
+to measure the impact of
+
+this program in realistic
+conditions.
+
+And realistic conditions are
+that not everybody's going to
+
+be able to get it.
+
+So let's suppose that you're
+a policy maker.
+
+Then what you could do is you
+could look at what's called
+
+the intention to treat estimate,
+which is what's the
+
+effect of the school having the
+program or being assigned
+
+to the program.
+
+This comes up in medical
+trials a lot with, say,
+
+chemotherapy.
+
+So some people who start
+chemotherapy don't finish it
+
+because it's just too
+painful for them.
+
+Or they're not able to
+handle it medically.
+
+Again, do want to measure the
+impact of chemotherapy on
+
+those people who managed to
+get all the way through?
+
+Well, not necessarily.
+
+Maybe what you're interested
+in is what's the effect of
+
+being in this group
+that tries it.
+
+Yes.
+
+AUDIENCE: Do you think it
+actually happened in 1997?
+
+MICHAEL KREMER: So yeah,
+I guess that actually
+
+helps on the dates.
+
+AUDIENCE: So it actually
+is 10 years on the--
+
+MICHAEL KREMER: That's right.
+
+So it's 10 years.
+
+It's 10 years before this was
+rolled out nationally.
+
+So yes, some things happened
+before that, but this is a
+
+long delay.
+
+Yeah, so that first delay
+of publication
+
+took quite a while.
+
+And then there was a second
+delay after it.
+
+Unfortunately, there's often a
+long delay in these things.
+
+Let me see where we are.
+
+So what you can do is you use
+the original assignment, and
+
+then you're winding up with
+what's called an intention to
+
+treat estimate.
+
+So what intention to treat
+measures is what happened to
+
+the average child who was in
+a treated school in the
+
+population.
+
+So it's not saying, what
+happens to the kids who
+
+actually got the medicine.
+
+It's saying, what happened to
+the average child who is in a
+
+treated school.
+
+So that's the correct
+interpretation of that.
+
+Now is that the right
+number to look for?
+
+I talked about some purposes
+where that might be the right
+
+number to look for.
+
+What would be some reasons why
+you might be interested in
+
+other questions other than the
+answer to that question of
+
+what happened to the average
+child in a treated school?
+
+AUDIENCE: You were thinking of
+having a mandatory deworming
+
+program in Kenya.
+
+And then you want to know what
+would be the impact if
+
+everybody was forced to treat.
+
+MICHAEL KREMER: Exactly.
+
+So in this particular case, this
+was a program where it
+
+was designed in such
+a way that not
+
+everybody had to be treated.
+
+It wasn't that you can't come to
+school unless you show your
+
+certificate showing you've
+been treated.
+
+But you might well be interested
+in, well, what if
+
+we went a step further.
+
+And we said, we're going to keep
+a supply of medicine at
+
+the school, and if you are gone
+that particular day, then
+
+you get it the next day.
+
+And we don't let you come
+back to school unless
+
+you take the medicine.
+
+Well, you wouldn't
+be measuring the
+
+impact of that program.
+
+Intention to treat is very good
+if you're interested in
+
+the narrow question of
+what's the impact
+
+of this exact program.
+
+But if you're trying to go
+beyond what's the impact of
+
+this exact program, you're
+trying to start to think about
+
+generalization, then maybe you
+want to understand some of the
+
+underlying parameters.
+
+And in this case, the underlying
+parameter is what's
+
+the effect on school attendance
+of a kid who had
+
+worms or a particular level of
+worms no longer having that.
+
+And then it's using that
+underlying parameter that you
+
+might be able to generalize what
+would be the effect of
+
+everybody getting treated, what
+would be the effect of
+
+only some people getting
+treated.
+
+So to do that, Shawn's going to
+talk a little bit about how
+
+you would do that.
+
+Let's do this example, where
+we're trying to get the--
+
+I'm wondering whether to skip
+this example or not.
+
+I'll do it.
+
+I'll go through it.
+
+In this example, if you look
+at the people who were--
+
+here's the intent, whether
+there was an intention to
+
+treat them.
+
+So all school one, you tried to
+treat everybody, but only
+
+some of them got treated.
+
+In school two, the intent
+was not to treat that.
+
+They were assigned to the
+comparison group.
+
+But a few people got
+treated anyway.
+
+And this is the change in weight
+for each individual.
+
+So then if we average the change
+in weight, the average
+
+change in school one--
+
+I don't know if people want to
+figure that out for a second--
+
+AUDIENCE: [INAUDIBLE]?
+
+MICHAEL KREMER: Sorry?
+
+AUDIENCE: [INAUDIBLE]?
+
+MICHAEL KREMER: So
+it's 1.3, right?
+
+And the average change
+in school two is 0.9.
+
+So the intention to treat effect
+would be comparing the
+
+1.3 to the 0.9.
+
+Now when is that useful?
+
+Well, that's what I'm saying,
+for an actual program.
+
+But you're not measuring this
+medical effect that you'd want
+
+for generalization.
+
+Here is an example where it's a
+malaria prevention program,
+
+but there's political
+pressures to treat.
+
+And so you add.
+
+Again, you can measure this
+impact, this intention to
+
+treat measure.
+
+Let me--
+
+I'm wondering whether
+I should--
+
+let me go back here and say--
+
+Initially, the blue circles
+were the ones that were
+
+supposed to be treated.
+
+I want to talk about why you
+can't do what the apparently
+
+obvious thing of just comparing
+the guys who were
+
+treated to the ones
+who weren't.
+
+You've got this malaria
+prevention program.
+
+40 villages are sampled.
+
+20 were assigned to get the
+treatment the first year.
+
+20 were assigned to
+be the comparison.
+
+But some of the comparison
+villages object to this, and
+
+they say, we want to
+be treated too.
+
+And the program manager says,
+look, we just have to go ahead
+
+and treat this.
+
+So if the program only gets
+implemented in 15 villages, as
+
+well as in 2 villages that
+were supposed to be
+
+comparison, so what do
+you do to measure the
+
+impact of the program?
+
+So by the way, in the previous
+case I mentioned with the
+
+politician in Kenya, the extra
+school was neither treatment
+
+or comparison, so really, in
+that case, there was no
+
+problem because it was just
+out of the sample frame
+
+altogether, the extra school
+that got treated.
+
+In this case, some of the
+comparison schools wind up
+
+getting treated.
+
+So how do you measure it?
+
+Well, here's the problem with
+what would happen if you just
+
+did the naive thing and said,
+we're going to compare all the
+
+guys who actually got treated
+to the comparison schools.
+
+So we've got the blue schools
+are the ones that were
+
+supposed to be treated that
+are in the sample.
+
+The white schools are
+other villages.
+
+So T is the original
+treatment group.
+
+The T's are supposed
+to be treated.
+
+The blues without T's in them
+are supposed to be the
+
+comparison.
+
+Now the actual treatment
+are the green circles.
+
+So you can't compare the
+green circle villages
+
+with the blue dots.
+
+The green circles are the ones
+that were actually treated.
+
+And the blue dots are
+the comparison.
+
+Why can't you make
+that comparison?
+
+AUDIENCE: They're not
+randomly assigned
+
+from the very beginning.
+
+MICHAEL KREMER: They're not
+randomly assigned from the
+
+very beginning.
+
+And can you be more specific
+about what your hypothesis
+
+might be on the difference?
+
+AUDIENCE: [UNINTELLIGIBLE]
+that fought to get the
+
+treatment would prefer some
+help from the schools or
+
+villages that were initially
+selected randomly.
+
+MICHAEL KREMER: Exactly,
+exactly.
+
+The guys who fought to get the
+treatment might differ from
+
+the ones that are initially
+selected randomly.
+
+They might have particularly
+capable leaders, for example,
+
+or influential leaders.
+
+And those influential leaders--
+this politician who
+
+managed to get the NGO program
+assigned to his area, he might
+
+have fought to get lots of other
+programs assigned there.
+
+So we don't know whether we're
+measuring the impact of this
+
+program, or we're measuring
+the fact that they're just
+
+able to use their political
+influence to get everything
+
+assigned there.
+
+And similarly, if you
+leave out the--
+
+So this is basically
+just making the
+
+point that you said.
+
+The other thing that you could
+think about doing is comparing
+
+the villages that were assigned
+to be a treatment
+
+group and actually got treated
+with the ones that were
+
+supposed to be a comparison
+group.
+
+So what's the problem
+with that?
+
+AUDIENCE: Attrition.
+
+It's kind of like attrition.
+
+MICHAEL KREMER: Exactly, it's
+the same principle, which is
+
+you'd be leaving out a group
+that is the ones who were
+
+assigned to be treated,
+but didn't
+
+wind up getting treated.
+
+Well, the ones who were assigned
+to be treated and,
+
+nonetheless, didn't get treated,
+those might be the
+
+ones-- so for example, imagine
+there's violence in some of
+
+these areas.
+
+And your field workers can't go
+there, so they never wound
+
+up getting treated.
+
+Well, the violence itself might
+have had an impact on
+
+development outcomes.
+
+So you may be measuring the
+impact of the violence or of
+
+particularly bad leaders who,
+despite being in the treatment
+
+group, still can't get their
+village treated.
+
+So that's not going to be a
+valid comparison either.
+
+So one thing you can do is the
+intention to treat estimator.
+
+You can do that again
+in this case.
+
+So compare the initial 20
+treatment villages with the
+
+initial 20 comparison
+villages.
+
+And then you've got
+the ITT estimator.
+
+Now before I argued that the ITT
+estimator, in the case of
+
+the deworming program, that
+arguably might be a very good
+
+measure of some things.
+
+You might not be able to do some
+other things with it, but
+
+it was still a useful measure.
+
+But in this case, suppose we
+want to actually understand
+
+what the impact of the malaria
+treatment program.
+
+And we know that what's the
+impact of it if you're able to
+
+implement it.
+
+Well, the intention to
+treat estimator isn't
+
+really telling you that.
+
+It's telling you what's the
+effect of being assigned to
+
+the treatment.
+
+But it's not saying what's the
+effect of the program in the
+
+cases where you're able
+to implement it.
+
+So that's a problem.
+
+And that's where I'm going to
+leave you with that problem.
+
+And then Shawn's going to
+tell you, at least,
+
+a solution to it.
\ No newline at end of file
diff --git a/FcNUJpbvTy8.txt b/FcNUJpbvTy8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1f8bd4bb5fcfb8c80da29196bcf8fae03bad9cfb
--- /dev/null
+++ b/FcNUJpbvTy8.txt
@@ -0,0 +1,11373 @@
+align:start position:0%
+ 
+all right we're beginning the uh lecture
+
+ align:start position:0%
+all right we're beginning the uh lecture
+ 
+
+ align:start position:0%
+all right we're beginning the uh lecture
+on handout number 15 this is um the
+
+ align:start position:0%
+on handout number 15 this is um the
+ 
+
+ align:start position:0%
+on handout number 15 this is um the
+second lecture on uh dopent diffusion
+
+ align:start position:0%
+second lecture on uh dopent diffusion
+ 
+
+ align:start position:0%
+second lecture on uh dopent diffusion
+and profile measurement and we're uh
+
+ align:start position:0%
+and profile measurement and we're uh
+ 
+
+ align:start position:0%
+and profile measurement and we're uh
+working on chapter seven of your
+
+ align:start position:0%
+working on chapter seven of your
+ 
+
+ align:start position:0%
+working on chapter seven of your
+text so last time we introduced some of
+
+ align:start position:0%
+text so last time we introduced some of
+ 
+
+ align:start position:0%
+text so last time we introduced some of
+the basics of dop and diffusion we
+
+ align:start position:0%
+the basics of dop and diffusion we
+ 
+
+ align:start position:0%
+the basics of dop and diffusion we
+talked about uh basic definition of
+
+ align:start position:0%
+talked about uh basic definition of
+ 
+
+ align:start position:0%
+talked about uh basic definition of
+sheet resistance and the scaling
+
+ align:start position:0%
+sheet resistance and the scaling
+ 
+
+ align:start position:0%
+sheet resistance and the scaling
+requires PR L and we pointed out there's
+
+ align:start position:0%
+requires PR L and we pointed out there's
+ 
+
+ align:start position:0%
+requires PR L and we pointed out there's
+a conflict between the need for smaller
+
+ align:start position:0%
+a conflict between the need for smaller
+ 
+
+ align:start position:0%
+a conflict between the need for smaller
+serious resistance and the need to
+
+ align:start position:0%
+serious resistance and the need to
+ 
+
+ align:start position:0%
+serious resistance and the need to
+decrease function depths to improve
+
+ align:start position:0%
+decrease function depths to improve
+ 
+
+ align:start position:0%
+decrease function depths to improve
+control on the channel charge we also
+
+ align:start position:0%
+control on the channel charge we also
+ 
+
+ align:start position:0%
+control on the channel charge we also
+talked about short Channel effects and
+
+ align:start position:0%
+talked about short Channel effects and
+ 
+
+ align:start position:0%
+talked about short Channel effects and
+how BT decreases as L uh goes
+
+ align:start position:0%
+how BT decreases as L uh goes
+ 
+
+ align:start position:0%
+how BT decreases as L uh goes
+down we mentioned the use of
+
+ align:start position:0%
+down we mentioned the use of
+ 
+
+ align:start position:0%
+down we mentioned the use of
+predeposition uh either in the gas phase
+
+ align:start position:0%
+predeposition uh either in the gas phase
+ 
+
+ align:start position:0%
+predeposition uh either in the gas phase
+or byon implantation and then the use of
+
+ align:start position:0%
+or byon implantation and then the use of
+ 
+
+ align:start position:0%
+or byon implantation and then the use of
+subsequent Drive-In of dopents to create
+
+ align:start position:0%
+subsequent Drive-In of dopents to create
+ 
+
+ align:start position:0%
+subsequent Drive-In of dopents to create
+doped
+
+ align:start position:0%
+doped
+ 
+
+ align:start position:0%
+doped
+regions we spoke about macroscopic
+
+ align:start position:0%
+regions we spoke about macroscopic
+ 
+
+ align:start position:0%
+regions we spoke about macroscopic
+diffusion from the point of fixed first
+
+ align:start position:0%
+diffusion from the point of fixed first
+ 
+
+ align:start position:0%
+diffusion from the point of fixed first
+and second laws and gave a few cases
+
+ align:start position:0%
+and second laws and gave a few cases
+ 
+
+ align:start position:0%
+and second laws and gave a few cases
+there were only about three or four
+
+ align:start position:0%
+there were only about three or four
+ 
+
+ align:start position:0%
+there were only about three or four
+cases where there are simp analytic
+
+ align:start position:0%
+cases where there are simp analytic
+ 
+
+ align:start position:0%
+cases where there are simp analytic
+solutions to the diffusion
+
+ align:start position:0%
+solutions to the diffusion
+ 
+
+ align:start position:0%
+solutions to the diffusion
+equation today I want to just briefly
+
+ align:start position:0%
+equation today I want to just briefly
+ 
+
+ align:start position:0%
+equation today I want to just briefly
+review those analytic solution
+
+ align:start position:0%
+review those analytic solution
+ 
+
+ align:start position:0%
+review those analytic solution
+examples and then um talk about uh a
+
+ align:start position:0%
+examples and then um talk about uh a
+ 
+
+ align:start position:0%
+examples and then um talk about uh a
+brief introduction to numerical
+
+ align:start position:0%
+brief introduction to numerical
+ 
+
+ align:start position:0%
+brief introduction to numerical
+solutions to diffusion
+
+ align:start position:0%
+solutions to diffusion
+ 
+
+ align:start position:0%
+solutions to diffusion
+equation then we'll talk about uh design
+
+ align:start position:0%
+equation then we'll talk about uh design
+ 
+
+ align:start position:0%
+equation then we'll talk about uh design
+of diffused layers based upon certain
+
+ align:start position:0%
+of diffused layers based upon certain
+ 
+
+ align:start position:0%
+of diffused layers based upon certain
+device requirements such as the sheet
+
+ align:start position:0%
+device requirements such as the sheet
+ 
+
+ align:start position:0%
+device requirements such as the sheet
+resistance and uh our first deviation
+
+ align:start position:0%
+resistance and uh our first deviation
+ 
+
+ align:start position:0%
+resistance and uh our first deviation
+from fii and diffusion we'll we'll
+
+ align:start position:0%
+from fii and diffusion we'll we'll
+ 
+
+ align:start position:0%
+from fii and diffusion we'll we'll
+discuss electric field effects on dop
+
+ align:start position:0%
+discuss electric field effects on dop
+ 
+
+ align:start position:0%
+discuss electric field effects on dop
+and diffusion
+
+ align:start position:0%
+and diffusion
+ 
+
+ align:start position:0%
+and diffusion
+so let's go on on to slide number two
+
+ align:start position:0%
+so let's go on on to slide number two
+ 
+
+ align:start position:0%
+so let's go on on to slide number two
+and just review from last time uh this
+
+ align:start position:0%
+and just review from last time uh this
+ 
+
+ align:start position:0%
+and just review from last time uh this
+pictorial um view of fixed Second Law
+
+ align:start position:0%
+pictorial um view of fixed Second Law
+ 
+
+ align:start position:0%
+pictorial um view of fixed Second Law
+what I'm showing here is a volume
+
+ align:start position:0%
+what I'm showing here is a volume
+ 
+
+ align:start position:0%
+what I'm showing here is a volume
+element um that is uh shown by the blue
+
+ align:start position:0%
+element um that is uh shown by the blue
+ 
+
+ align:start position:0%
+element um that is uh shown by the blue
+sort of rectangular uh element and there
+
+ align:start position:0%
+sort of rectangular uh element and there
+ 
+
+ align:start position:0%
+sort of rectangular uh element and there
+is a flux F Sub in going in the left
+
+ align:start position:0%
+is a flux F Sub in going in the left
+ 
+
+ align:start position:0%
+is a flux F Sub in going in the left
+hand face and a flux F sub out uh going
+
+ align:start position:0%
+hand face and a flux F sub out uh going
+ 
+
+ align:start position:0%
+hand face and a flux F sub out uh going
+out in the right hand face remember
+
+ align:start position:0%
+out in the right hand face remember
+ 
+
+ align:start position:0%
+out in the right hand face remember
+again our basic definition of flux is
+
+ align:start position:0%
+again our basic definition of flux is
+ 
+
+ align:start position:0%
+again our basic definition of flux is
+it's a number of atoms or particles per
+
+ align:start position:0%
+it's a number of atoms or particles per
+ 
+
+ align:start position:0%
+it's a number of atoms or particles per
+unit time per unit area so looking at
+
+ align:start position:0%
+unit time per unit area so looking at
+ 
+
+ align:start position:0%
+unit time per unit area so looking at
+this uh in this Cube we can uh calculate
+
+ align:start position:0%
+this uh in this Cube we can uh calculate
+ 
+
+ align:start position:0%
+this uh in this Cube we can uh calculate
+the net flow of atoms into this volume
+
+ align:start position:0%
+the net flow of atoms into this volume
+ 
+
+ align:start position:0%
+the net flow of atoms into this volume
+uh into that small volume as shown in
+
+ align:start position:0%
+uh into that small volume as shown in
+ 
+
+ align:start position:0%
+uh into that small volume as shown in
+the upper left uh corner is equal to the
+
+ align:start position:0%
+the upper left uh corner is equal to the
+ 
+
+ align:start position:0%
+the upper left uh corner is equal to the
+area a of one of those faces times the
+
+ align:start position:0%
+area a of one of those faces times the
+ 
+
+ align:start position:0%
+area a of one of those faces times the
+difference between F out minus
+
+ align:start position:0%
+difference between F out minus
+ 
+
+ align:start position:0%
+difference between F out minus
+FN so that's the net flow of atoms and
+
+ align:start position:0%
+FN so that's the net flow of atoms and
+ 
+
+ align:start position:0%
+FN so that's the net flow of atoms and
+we can write that as a times and just
+
+ align:start position:0%
+we can write that as a times and just
+ 
+
+ align:start position:0%
+we can write that as a times and just
+looking at uh sort of the geometry it's
+
+ align:start position:0%
+looking at uh sort of the geometry it's
+ 
+
+ align:start position:0%
+looking at uh sort of the geometry it's
+Delta x times the the uh change in
+
+ align:start position:0%
+Delta x times the the uh change in
+ 
+
+ align:start position:0%
+Delta x times the the uh change in
+concentration Delta C divided Delta time
+
+ align:start position:0%
+concentration Delta C divided Delta time
+ 
+
+ align:start position:0%
+concentration Delta C divided Delta time
+uh delta T so we're can just rearrange
+
+ align:start position:0%
+uh delta T so we're can just rearrange
+ 
+
+ align:start position:0%
+uh delta T so we're can just rearrange
+just a little bit the A's go out and
+
+ align:start position:0%
+just a little bit the A's go out and
+ 
+
+ align:start position:0%
+just a little bit the A's go out and
+what we see is that the first derivative
+
+ align:start position:0%
+what we see is that the first derivative
+ 
+
+ align:start position:0%
+what we see is that the first derivative
+of the flux Delta F over Delta X is
+
+ align:start position:0%
+of the flux Delta F over Delta X is
+ 
+
+ align:start position:0%
+of the flux Delta F over Delta X is
+equal to the time change Delta C over
+
+ align:start position:0%
+equal to the time change Delta C over
+ 
+
+ align:start position:0%
+equal to the time change Delta C over
+delta T um so mathematically if we want
+
+ align:start position:0%
+delta T um so mathematically if we want
+ 
+
+ align:start position:0%
+delta T um so mathematically if we want
+to write this uh not in terms of Deltas
+
+ align:start position:0%
+to write this uh not in terms of Deltas
+ 
+
+ align:start position:0%
+to write this uh not in terms of Deltas
+or differences but in terms of um
+
+ align:start position:0%
+or differences but in terms of um
+ 
+
+ align:start position:0%
+or differences but in terms of um
+differentials what we see is a Time rate
+
+ align:start position:0%
+differentials what we see is a Time rate
+ 
+
+ align:start position:0%
+differentials what we see is a Time rate
+of change of the of the concentration in
+
+ align:start position:0%
+of change of the of the concentration in
+ 
+
+ align:start position:0%
+of change of the of the concentration in
+the Box partial C partial T is equal to
+
+ align:start position:0%
+the Box partial C partial T is equal to
+ 
+
+ align:start position:0%
+the Box partial C partial T is equal to
+the first derivative of the flux partial
+
+ align:start position:0%
+the first derivative of the flux partial
+ 
+
+ align:start position:0%
+the first derivative of the flux partial
+partial
+
+ align:start position:0%
+partial
+ 
+
+ align:start position:0%
+partial
+X and then we can substitute in the
+
+ align:start position:0%
+X and then we can substitute in the
+ 
+
+ align:start position:0%
+X and then we can substitute in the
+equation on the center of the page for
+
+ align:start position:0%
+equation on the center of the page for
+ 
+
+ align:start position:0%
+equation on the center of the page for
+the flux we know from fixed first law
+
+ align:start position:0%
+the flux we know from fixed first law
+ 
+
+ align:start position:0%
+the flux we know from fixed first law
+that f is equal to D partial C partial X
+
+ align:start position:0%
+that f is equal to D partial C partial X
+ 
+
+ align:start position:0%
+that f is equal to D partial C partial X
+so that is indeed um a way of deriving
+
+ align:start position:0%
+so that is indeed um a way of deriving
+ 
+
+ align:start position:0%
+so that is indeed um a way of deriving
+uh just sort of bookkeep of deriving
+
+ align:start position:0%
+uh just sort of bookkeep of deriving
+ 
+
+ align:start position:0%
+uh just sort of bookkeep of deriving
+fixed Second
+
+ align:start position:0%
+fixed Second
+ 
+
+ align:start position:0%
+fixed Second
+Law now uh the equation in the center of
+
+ align:start position:0%
+Law now uh the equation in the center of
+ 
+
+ align:start position:0%
+Law now uh the equation in the center of
+the page can be simplified somewhat if
+
+ align:start position:0%
+the page can be simplified somewhat if
+ 
+
+ align:start position:0%
+the page can be simplified somewhat if
+uh we have a special case where the
+
+ align:start position:0%
+uh we have a special case where the
+ 
+
+ align:start position:0%
+uh we have a special case where the
+diffusivity is a constant where it
+
+ align:start position:0%
+diffusivity is a constant where it
+ 
+
+ align:start position:0%
+diffusivity is a constant where it
+doesn't vary in space I can pull the D
+
+ align:start position:0%
+doesn't vary in space I can pull the D
+ 
+
+ align:start position:0%
+doesn't vary in space I can pull the D
+out of the partial deriva with respect
+
+ align:start position:0%
+out of the partial deriva with respect
+ 
+
+ align:start position:0%
+out of the partial deriva with respect
+to X and we just get um partial C
+
+ align:start position:0%
+to X and we just get um partial C
+ 
+
+ align:start position:0%
+to X and we just get um partial C
+partial T so the time rate of change uh
+
+ align:start position:0%
+partial T so the time rate of change uh
+ 
+
+ align:start position:0%
+partial T so the time rate of change uh
+of the concentration is equal to a
+
+ align:start position:0%
+of the concentration is equal to a
+ 
+
+ align:start position:0%
+of the concentration is equal to a
+constant diffusivity it's a number times
+
+ align:start position:0%
+constant diffusivity it's a number times
+ 
+
+ align:start position:0%
+constant diffusivity it's a number times
+the second derivative of the
+
+ align:start position:0%
+the second derivative of the
+ 
+
+ align:start position:0%
+the second derivative of the
+concentration with respect to X so that
+
+ align:start position:0%
+concentration with respect to X so that
+ 
+
+ align:start position:0%
+concentration with respect to X so that
+is uh at the bottom of the page would be
+
+ align:start position:0%
+is uh at the bottom of the page would be
+ 
+
+ align:start position:0%
+is uh at the bottom of the page would be
+then the special case of fixed second
+
+ align:start position:0%
+then the special case of fixed second
+ 
+
+ align:start position:0%
+then the special case of fixed second
+law when the diffusivity is a
+
+ align:start position:0%
+law when the diffusivity is a
+ 
+
+ align:start position:0%
+law when the diffusivity is a
+constant so let's go on to slide number
+
+ align:start position:0%
+constant so let's go on to slide number
+ 
+
+ align:start position:0%
+constant so let's go on to slide number
+three uh and these are um a couple of
+
+ align:start position:0%
+three uh and these are um a couple of
+ 
+
+ align:start position:0%
+three uh and these are um a couple of
+cases we solved last time where we we
+
+ align:start position:0%
+cases we solved last time where we we
+ 
+
+ align:start position:0%
+cases we solved last time where we we
+wrote down the solutions last time for
+
+ align:start position:0%
+wrote down the solutions last time for
+ 
+
+ align:start position:0%
+wrote down the solutions last time for
+two cases which are commonly encountered
+
+ align:start position:0%
+two cases which are commonly encountered
+ 
+
+ align:start position:0%
+two cases which are commonly encountered
+and which for which analytic Solutions
+
+ align:start position:0%
+and which for which analytic Solutions
+ 
+
+ align:start position:0%
+and which for which analytic Solutions
+are available on the left hand side and
+
+ align:start position:0%
+are available on the left hand side and
+ 
+
+ align:start position:0%
+are available on the left hand side and
+reviewing the case of a predeposition
+
+ align:start position:0%
+reviewing the case of a predeposition
+ 
+
+ align:start position:0%
+reviewing the case of a predeposition
+and again by sort of by definition in
+
+ align:start position:0%
+and again by sort of by definition in
+ 
+
+ align:start position:0%
+and again by sort of by definition in
+this case we are assuming that there is
+
+ align:start position:0%
+this case we are assuming that there is
+ 
+
+ align:start position:0%
+this case we are assuming that there is
+a supply of do of of dopent or atoms
+
+ align:start position:0%
+a supply of do of of dopent or atoms
+ 
+
+ align:start position:0%
+a supply of do of of dopent or atoms
+that are diffusing that holds the
+
+ align:start position:0%
+that are diffusing that holds the
+ 
+
+ align:start position:0%
+that are diffusing that holds the
+surface concentration at a constant
+
+ align:start position:0%
+surface concentration at a constant
+ 
+
+ align:start position:0%
+surface concentration at a constant
+value C subs and number is fixed and we
+
+ align:start position:0%
+value C subs and number is fixed and we
+ 
+
+ align:start position:0%
+value C subs and number is fixed and we
+said in this case that the shape of the
+
+ align:start position:0%
+said in this case that the shape of the
+ 
+
+ align:start position:0%
+said in this case that the shape of the
+profile c as a function of depth X and
+
+ align:start position:0%
+profile c as a function of depth X and
+ 
+
+ align:start position:0%
+profile c as a function of depth X and
+time is given by this surface
+
+ align:start position:0%
+time is given by this surface
+ 
+
+ align:start position:0%
+time is given by this surface
+concentration C Subs times the
+
+ align:start position:0%
+concentration C Subs times the
+ 
+
+ align:start position:0%
+concentration C Subs times the
+complimentary error function of X over
+
+ align:start position:0%
+complimentary error function of X over
+ 
+
+ align:start position:0%
+complimentary error function of X over
+2un DT so that is the actual analytic
+
+ align:start position:0%
+2un DT so that is the actual analytic
+ 
+
+ align:start position:0%
+2un DT so that is the actual analytic
+solution to fix second law for a
+
+ align:start position:0%
+solution to fix second law for a
+ 
+
+ align:start position:0%
+solution to fix second law for a
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+diffusivity and uh we also know that the
+
+ align:start position:0%
+diffusivity and uh we also know that the
+ 
+
+ align:start position:0%
+diffusivity and uh we also know that the
+integral of that uh that function uh
+
+ align:start position:0%
+integral of that uh that function uh
+ 
+
+ align:start position:0%
+integral of that uh that function uh
+integrated over over space or throughout
+
+ align:start position:0%
+integrated over over space or throughout
+ 
+
+ align:start position:0%
+integrated over over space or throughout
+the the Silicon uh has a value Q that's
+
+ align:start position:0%
+the the Silicon uh has a value Q that's
+ 
+
+ align:start position:0%
+the the Silicon uh has a value Q that's
+the do so the area under the curve and
+
+ align:start position:0%
+the do so the area under the curve and
+ 
+
+ align:start position:0%
+the do so the area under the curve and
+that can be solved for and it turns out
+
+ align:start position:0%
+that can be solved for and it turns out
+ 
+
+ align:start position:0%
+that can be solved for and it turns out
+to be 2 CS overun of Pi *
+
+ align:start position:0%
+to be 2 CS overun of Pi *
+ 
+
+ align:start position:0%
+to be 2 CS overun of Pi *
+DT um so this is a particular case and
+
+ align:start position:0%
+DT um so this is a particular case and
+ 
+
+ align:start position:0%
+DT um so this is a particular case and
+we in fact showing a plot um on the
+
+ align:start position:0%
+we in fact showing a plot um on the
+ 
+
+ align:start position:0%
+we in fact showing a plot um on the
+vertical axis of C over c s as a
+
+ align:start position:0%
+vertical axis of C over c s as a
+ 
+
+ align:start position:0%
+vertical axis of C over c s as a
+function of depth
+
+ align:start position:0%
+function of depth
+ 
+
+ align:start position:0%
+function of depth
+for uh several different uh times there
+
+ align:start position:0%
+for uh several different uh times there
+ 
+
+ align:start position:0%
+for uh several different uh times there
+are three curves here shown where the
+
+ align:start position:0%
+are three curves here shown where the
+ 
+
+ align:start position:0%
+are three curves here shown where the
+square of DT or two times the square of
+
+ align:start position:0%
+square of DT or two times the square of
+ 
+
+ align:start position:0%
+square of DT or two times the square of
+DT is being varied from 0.1 Micron all
+
+ align:start position:0%
+DT is being varied from 0.1 Micron all
+ 
+
+ align:start position:0%
+DT is being varied from 0.1 Micron all
+the way up to one micron you get a feel
+
+ align:start position:0%
+the way up to one micron you get a feel
+ 
+
+ align:start position:0%
+the way up to one micron you get a feel
+for how the shape of the comp
+
+ align:start position:0%
+for how the shape of the comp
+ 
+
+ align:start position:0%
+for how the shape of the comp
+complimentary airor function evolves
+
+ align:start position:0%
+complimentary airor function evolves
+ 
+
+ align:start position:0%
+complimentary airor function evolves
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+time um in contrast on the right hand
+
+ align:start position:0%
+time um in contrast on the right hand
+ 
+
+ align:start position:0%
+time um in contrast on the right hand
+side we're showing the case of a
+
+ align:start position:0%
+side we're showing the case of a
+ 
+
+ align:start position:0%
+side we're showing the case of a
+drive-in that would typically be done
+
+ align:start position:0%
+drive-in that would typically be done
+ 
+
+ align:start position:0%
+drive-in that would typically be done
+after prep and driving takes place uh
+
+ align:start position:0%
+after prep and driving takes place uh
+ 
+
+ align:start position:0%
+after prep and driving takes place uh
+usually under the assumption of a
+
+ align:start position:0%
+usually under the assumption of a
+ 
+
+ align:start position:0%
+usually under the assumption of a
+constant dose Q so the con area under
+
+ align:start position:0%
+constant dose Q so the con area under
+ 
+
+ align:start position:0%
+constant dose Q so the con area under
+the curve and what's happening as a
+
+ align:start position:0%
+the curve and what's happening as a
+ 
+
+ align:start position:0%
+the curve and what's happening as a
+function of time then um is the the
+
+ align:start position:0%
+function of time then um is the the
+ 
+
+ align:start position:0%
+function of time then um is the the
+shape of the curve is changing and it
+
+ align:start position:0%
+shape of the curve is changing and it
+ 
+
+ align:start position:0%
+shape of the curve is changing and it
+it's um we know the solution is a gausin
+
+ align:start position:0%
+it's um we know the solution is a gausin
+ 
+
+ align:start position:0%
+it's um we know the solution is a gausin
+uh the solution to fix Second
+
+ align:start position:0%
+uh the solution to fix Second
+ 
+
+ align:start position:0%
+uh the solution to fix Second
+Law um and in fact if you look at this
+
+ align:start position:0%
+Law um and in fact if you look at this
+ 
+
+ align:start position:0%
+Law um and in fact if you look at this
+equation as a function of time you'll
+
+ align:start position:0%
+equation as a function of time you'll
+ 
+
+ align:start position:0%
+equation as a function of time you'll
+see that the the concentration of the
+
+ align:start position:0%
+see that the the concentration of the
+ 
+
+ align:start position:0%
+see that the the concentration of the
+surface is dropping as a function of
+
+ align:start position:0%
+surface is dropping as a function of
+ 
+
+ align:start position:0%
+surface is dropping as a function of
+time according to 1 over the of
+
+ align:start position:0%
+time according to 1 over the of
+ 
+
+ align:start position:0%
+time according to 1 over the of
+DT and uh the P profile is it's
+
+ align:start position:0%
+DT and uh the P profile is it's
+ 
+
+ align:start position:0%
+DT and uh the P profile is it's
+broadening it's width or standard
+
+ align:start position:0%
+broadening it's width or standard
+ 
+
+ align:start position:0%
+broadening it's width or standard
+deviation is in inreasing according to
+
+ align:start position:0%
+deviation is in inreasing according to
+ 
+
+ align:start position:0%
+deviation is in inreasing according to
+DT and U there are a couple different
+
+ align:start position:0%
+DT and U there are a couple different
+ 
+
+ align:start position:0%
+DT and U there are a couple different
+cases shown on the light um so these
+
+ align:start position:0%
+cases shown on the light um so these
+ 
+
+ align:start position:0%
+cases shown on the light um so these
+Solutions are valid under this
+
+ align:start position:0%
+Solutions are valid under this
+ 
+
+ align:start position:0%
+Solutions are valid under this
+particular case where the concentration
+
+ align:start position:0%
+particular case where the concentration
+ 
+
+ align:start position:0%
+particular case where the concentration
+of a diffusing dopen is less than inabi
+
+ align:start position:0%
+of a diffusing dopen is less than inabi
+ 
+
+ align:start position:0%
+of a diffusing dopen is less than inabi
+and that that implies uh in that case
+
+ align:start position:0%
+and that that implies uh in that case
+ 
+
+ align:start position:0%
+and that that implies uh in that case
+that the diffusivity is a constant it
+
+ align:start position:0%
+that the diffusivity is a constant it
+ 
+
+ align:start position:0%
+that the diffusivity is a constant it
+doesn't vary in space we'll talk in
+
+ align:start position:0%
+doesn't vary in space we'll talk in
+ 
+
+ align:start position:0%
+doesn't vary in space we'll talk in
+subsequent lectures about the case when
+
+ align:start position:0%
+subsequent lectures about the case when
+ 
+
+ align:start position:0%
+subsequent lectures about the case when
+that uh the concentration is quite high
+
+ align:start position:0%
+that uh the concentration is quite high
+ 
+
+ align:start position:0%
+that uh the concentration is quite high
+or higher than
+
+ align:start position:0%
+or higher than
+ 
+
+ align:start position:0%
+or higher than
+nly so let's go on to slide number four
+
+ align:start position:0%
+nly so let's go on to slide number four
+ 
+
+ align:start position:0%
+nly so let's go on to slide number four
+and uh this reviews from last time what
+
+ align:start position:0%
+and uh this reviews from last time what
+ 
+
+ align:start position:0%
+and uh this reviews from last time what
+we showed is an arous plot of the
+
+ align:start position:0%
+we showed is an arous plot of the
+ 
+
+ align:start position:0%
+we showed is an arous plot of the
+intrinsic diffusion coefficients of some
+
+ align:start position:0%
+intrinsic diffusion coefficients of some
+ 
+
+ align:start position:0%
+intrinsic diffusion coefficients of some
+common delins and silicon and what we're
+
+ align:start position:0%
+common delins and silicon and what we're
+ 
+
+ align:start position:0%
+common delins and silicon and what we're
+showing on the left axis uh on a log
+
+ align:start position:0%
+showing on the left axis uh on a log
+ 
+
+ align:start position:0%
+showing on the left axis uh on a log
+scale is a diffusivity in units of C
+
+ align:start position:0%
+scale is a diffusivity in units of C
+ 
+
+ align:start position:0%
+scale is a diffusivity in units of C
+centimet squar per second and the x-axis
+
+ align:start position:0%
+centimet squar per second and the x-axis
+ 
+
+ align:start position:0%
+centimet squar per second and the x-axis
+is uh 1,000 over temperature in
+
+ align:start position:0%
+is uh 1,000 over temperature in
+ 
+
+ align:start position:0%
+is uh 1,000 over temperature in
+Kelvin the lower x-axis the upper x-axis
+
+ align:start position:0%
+Kelvin the lower x-axis the upper x-axis
+ 
+
+ align:start position:0%
+Kelvin the lower x-axis the upper x-axis
+actually has the temperatures uh uh
+
+ align:start position:0%
+actually has the temperatures uh uh
+ 
+
+ align:start position:0%
+actually has the temperatures uh uh
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+indicated so um we are intrinsic
+
+ align:start position:0%
+indicated so um we are intrinsic
+ 
+
+ align:start position:0%
+indicated so um we are intrinsic
+diffusivities so they apply when in the
+
+ align:start position:0%
+diffusivities so they apply when in the
+ 
+
+ align:start position:0%
+diffusivities so they apply when in the
+carrier concent the um concentration of
+
+ align:start position:0%
+carrier concent the um concentration of
+ 
+
+ align:start position:0%
+carrier concent the um concentration of
+the dope and is less than ni uh at the
+
+ align:start position:0%
+the dope and is less than ni uh at the
+ 
+
+ align:start position:0%
+the dope and is less than ni uh at the
+diffusion temperature one thing you can
+
+ align:start position:0%
+diffusion temperature one thing you can
+ 
+
+ align:start position:0%
+diffusion temperature one thing you can
+notice right off the bat is there there
+
+ align:start position:0%
+notice right off the bat is there there
+ 
+
+ align:start position:0%
+notice right off the bat is there there
+are some fast diffusers in Silicon such
+
+ align:start position:0%
+are some fast diffusers in Silicon such
+ 
+
+ align:start position:0%
+are some fast diffusers in Silicon such
+as Bond fos vering Indian they the upper
+
+ align:start position:0%
+as Bond fos vering Indian they the upper
+ 
+
+ align:start position:0%
+as Bond fos vering Indian they the upper
+three curves and the slower diffusers
+
+ align:start position:0%
+three curves and the slower diffusers
+ 
+
+ align:start position:0%
+three curves and the slower diffusers
+are Arsenic and anamor silic uh it turns
+
+ align:start position:0%
+are Arsenic and anamor silic uh it turns
+ 
+
+ align:start position:0%
+are Arsenic and anamor silic uh it turns
+out just for practical reasons because
+
+ align:start position:0%
+out just for practical reasons because
+ 
+
+ align:start position:0%
+out just for practical reasons because
+of their High electrical solubility that
+
+ align:start position:0%
+of their High electrical solubility that
+ 
+
+ align:start position:0%
+of their High electrical solubility that
+Boron is often the um ptype doener
+
+ align:start position:0%
+Boron is often the um ptype doener
+ 
+
+ align:start position:0%
+Boron is often the um ptype doener
+Choice it pretty much is and arsenic uh
+
+ align:start position:0%
+Choice it pretty much is and arsenic uh
+ 
+
+ align:start position:0%
+Choice it pretty much is and arsenic uh
+in N type dopers you can choose arsenic
+
+ align:start position:0%
+in N type dopers you can choose arsenic
+ 
+
+ align:start position:0%
+in N type dopers you can choose arsenic
+or phosis but arsenic is usually chosen
+
+ align:start position:0%
+or phosis but arsenic is usually chosen
+ 
+
+ align:start position:0%
+or phosis but arsenic is usually chosen
+uh because of its higher electrical
+
+ align:start position:0%
+uh because of its higher electrical
+ 
+
+ align:start position:0%
+uh because of its higher electrical
+solubility and uh also sometimes it's
+
+ align:start position:0%
+solubility and uh also sometimes it's
+ 
+
+ align:start position:0%
+solubility and uh also sometimes it's
+lower diffusion coefficient it's easier
+
+ align:start position:0%
+lower diffusion coefficient it's easier
+ 
+
+ align:start position:0%
+lower diffusion coefficient it's easier
+to control
+
+ align:start position:0%
+to control
+ 
+
+ align:start position:0%
+to control
+profiles so what typically we're going
+
+ align:start position:0%
+profiles so what typically we're going
+ 
+
+ align:start position:0%
+profiles so what typically we're going
+to have issues with controlling
+
+ align:start position:0%
+to have issues with controlling
+ 
+
+ align:start position:0%
+to have issues with controlling
+diffusion in the pp regions because Bond
+
+ align:start position:0%
+diffusion in the pp regions because Bond
+ 
+
+ align:start position:0%
+diffusion in the pp regions because Bond
+uh is diffusing at any given temperature
+
+ align:start position:0%
+uh is diffusing at any given temperature
+ 
+
+ align:start position:0%
+uh is diffusing at any given temperature
+almost in order of magnitude uh higher
+
+ align:start position:0%
+almost in order of magnitude uh higher
+ 
+
+ align:start position:0%
+almost in order of magnitude uh higher
+diffusivity than the case of
+
+ align:start position:0%
+diffusivity than the case of
+ 
+
+ align:start position:0%
+diffusivity than the case of
+arsenic all right let's go on to slide
+
+ align:start position:0%
+arsenic all right let's go on to slide
+ 
+
+ align:start position:0%
+arsenic all right let's go on to slide
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+five and um here what we are trying to
+
+ align:start position:0%
+five and um here what we are trying to
+ 
+
+ align:start position:0%
+five and um here what we are trying to
+talk about is uh the effect of
+
+ align:start position:0%
+talk about is uh the effect of
+ 
+
+ align:start position:0%
+talk about is uh the effect of
+successive diffusions in say a moss
+
+ align:start position:0%
+successive diffusions in say a moss
+ 
+
+ align:start position:0%
+successive diffusions in say a moss
+process flow um uh on the on the doping
+
+ align:start position:0%
+process flow um uh on the on the doping
+ 
+
+ align:start position:0%
+process flow um uh on the on the doping
+profiles you remember from the first
+
+ align:start position:0%
+profiles you remember from the first
+ 
+
+ align:start position:0%
+profiles you remember from the first
+lecture of this course we talked uh we
+
+ align:start position:0%
+lecture of this course we talked uh we
+ 
+
+ align:start position:0%
+lecture of this course we talked uh we
+kind of walked through uh an example of
+
+ align:start position:0%
+kind of walked through uh an example of
+ 
+
+ align:start position:0%
+kind of walked through uh an example of
+NR circuit bation process and you know
+
+ align:start position:0%
+NR circuit bation process and you know
+ 
+
+ align:start position:0%
+NR circuit bation process and you know
+that they involve a large number of
+
+ align:start position:0%
+that they involve a large number of
+ 
+
+ align:start position:0%
+that they involve a large number of
+different steps at various temperatures
+
+ align:start position:0%
+different steps at various temperatures
+ 
+
+ align:start position:0%
+different steps at various temperatures
+we don't just simply do a pre-ip and
+
+ align:start position:0%
+we don't just simply do a pre-ip and
+ 
+
+ align:start position:0%
+we don't just simply do a pre-ip and
+then a drive-in and then it's done that
+
+ align:start position:0%
+then a drive-in and then it's done that
+ 
+
+ align:start position:0%
+then a drive-in and then it's done that
+could be oxidations it could be uh other
+
+ align:start position:0%
+could be oxidations it could be uh other
+ 
+
+ align:start position:0%
+could be oxidations it could be uh other
+uh high temperature steps in which uh
+
+ align:start position:0%
+uh high temperature steps in which uh
+ 
+
+ align:start position:0%
+uh high temperature steps in which uh
+the doens are going to move so if you
+
+ align:start position:0%
+the doens are going to move so if you
+ 
+
+ align:start position:0%
+the doens are going to move so if you
+have a whole series of steps what's the
+
+ align:start position:0%
+have a whole series of steps what's the
+ 
+
+ align:start position:0%
+have a whole series of steps what's the
+question is what is the uh actual final
+
+ align:start position:0%
+question is what is the uh actual final
+ 
+
+ align:start position:0%
+question is what is the uh actual final
+profile and how can we approximated well
+
+ align:start position:0%
+profile and how can we approximated well
+ 
+
+ align:start position:0%
+profile and how can we approximated well
+it turns out in the case of gine
+
+ align:start position:0%
+it turns out in the case of gine
+ 
+
+ align:start position:0%
+it turns out in the case of gine
+diffusion that uh we can write the total
+
+ align:start position:0%
+diffusion that uh we can write the total
+ 
+
+ align:start position:0%
+diffusion that uh we can write the total
+effective D2
+
+ align:start position:0%
+effective D2
+ 
+
+ align:start position:0%
+effective D2
+product uh as being a measure of a
+
+ align:start position:0%
+product uh as being a measure of a
+ 
+
+ align:start position:0%
+product uh as being a measure of a
+thermal budget that's used in that
+
+ align:start position:0%
+thermal budget that's used in that
+ 
+
+ align:start position:0%
+thermal budget that's used in that
+process and for ging diffusion we can
+
+ align:start position:0%
+process and for ging diffusion we can
+ 
+
+ align:start position:0%
+process and for ging diffusion we can
+actually sum up the products of the
+
+ align:start position:0%
+actually sum up the products of the
+ 
+
+ align:start position:0%
+actually sum up the products of the
+diffusivity in any given time step times
+
+ align:start position:0%
+diffusivity in any given time step times
+ 
+
+ align:start position:0%
+diffusivity in any given time step times
+the length of that time step D * T we
+
+ align:start position:0%
+the length of that time step D * T we
+ 
+
+ align:start position:0%
+the length of that time step D * T we
+can sum up those DT products add them up
+
+ align:start position:0%
+can sum up those DT products add them up
+ 
+
+ align:start position:0%
+can sum up those DT products add them up
+and uh end up with an effective DT for
+
+ align:start position:0%
+and uh end up with an effective DT for
+ 
+
+ align:start position:0%
+and uh end up with an effective DT for
+the entire process again assuming that
+
+ align:start position:0%
+the entire process again assuming that
+ 
+
+ align:start position:0%
+the entire process again assuming that
+in each case the the diffusion satisfies
+
+ align:start position:0%
+in each case the the diffusion satisfies
+ 
+
+ align:start position:0%
+in each case the the diffusion satisfies
+the the gaussing
+
+ align:start position:0%
+the the gaussing
+ 
+
+ align:start position:0%
+the the gaussing
+assumptions what we'll typically find as
+
+ align:start position:0%
+assumptions what we'll typically find as
+ 
+
+ align:start position:0%
+assumptions what we'll typically find as
+you go through a whole process is that
+
+ align:start position:0%
+you go through a whole process is that
+ 
+
+ align:start position:0%
+you go through a whole process is that
+the some of the processing steps may be
+
+ align:start position:0%
+the some of the processing steps may be
+ 
+
+ align:start position:0%
+the some of the processing steps may be
+negligible and that's because the
+
+ align:start position:0%
+negligible and that's because the
+ 
+
+ align:start position:0%
+negligible and that's because the
+diffusion coefficient in this formula is
+
+ align:start position:0%
+diffusion coefficient in this formula is
+ 
+
+ align:start position:0%
+diffusion coefficient in this formula is
+exponentially activated uh or it varies
+
+ align:start position:0%
+exponentially activated uh or it varies
+ 
+
+ align:start position:0%
+exponentially activated uh or it varies
+with temperature exponential so the
+
+ align:start position:0%
+with temperature exponential so the
+ 
+
+ align:start position:0%
+with temperature exponential so the
+highest temperature steps in the process
+
+ align:start position:0%
+highest temperature steps in the process
+ 
+
+ align:start position:0%
+highest temperature steps in the process
+typically dominate um it's not always
+
+ align:start position:0%
+typically dominate um it's not always
+ 
+
+ align:start position:0%
+typically dominate um it's not always
+the case for example when we talk about
+
+ align:start position:0%
+the case for example when we talk about
+ 
+
+ align:start position:0%
+the case for example when we talk about
+trans enhanced diffusion uh we see
+
+ align:start position:0%
+trans enhanced diffusion uh we see
+ 
+
+ align:start position:0%
+trans enhanced diffusion uh we see
+that's not the case but for normal
+
+ align:start position:0%
+that's not the case but for normal
+ 
+
+ align:start position:0%
+that's not the case but for normal
+diffusion you expect the highest
+
+ align:start position:0%
+diffusion you expect the highest
+ 
+
+ align:start position:0%
+diffusion you expect the highest
+temperature steps to dominate this
+
+ align:start position:0%
+temperature steps to dominate this
+ 
+
+ align:start position:0%
+temperature steps to dominate this
+equation and so you can usually zoom in
+
+ align:start position:0%
+equation and so you can usually zoom in
+ 
+
+ align:start position:0%
+equation and so you can usually zoom in
+on those as being the ones that that
+
+ align:start position:0%
+on those as being the ones that that
+ 
+
+ align:start position:0%
+on those as being the ones that that
+primarily determine the DT product and
+
+ align:start position:0%
+primarily determine the DT product and
+ 
+
+ align:start position:0%
+primarily determine the DT product and
+therefore the shape of the
+
+ align:start position:0%
+therefore the shape of the
+ 
+
+ align:start position:0%
+therefore the shape of the
+profile one thing you have we have to be
+
+ align:start position:0%
+profile one thing you have we have to be
+ 
+
+ align:start position:0%
+profile one thing you have we have to be
+aware of is that this uh gaussian
+
+ align:start position:0%
+aware of is that this uh gaussian
+ 
+
+ align:start position:0%
+aware of is that this uh gaussian
+solution we've been talking about only
+
+ align:start position:0%
+solution we've been talking about only
+ 
+
+ align:start position:0%
+solution we've been talking about only
+holds if the Delta function
+
+ align:start position:0%
+holds if the Delta function
+ 
+
+ align:start position:0%
+holds if the Delta function
+approximation for the initial profile is
+
+ align:start position:0%
+approximation for the initial profile is
+ 
+
+ align:start position:0%
+approximation for the initial profile is
+reasonable we talked about this last
+
+ align:start position:0%
+reasonable we talked about this last
+ 
+
+ align:start position:0%
+reasonable we talked about this last
+time so it holds in the case where the
+
+ align:start position:0%
+time so it holds in the case where the
+ 
+
+ align:start position:0%
+time so it holds in the case where the
+width of the profile um initially when
+
+ align:start position:0%
+width of the profile um initially when
+ 
+
+ align:start position:0%
+width of the profile um initially when
+you start is small compared to the the
+
+ align:start position:0%
+you start is small compared to the the
+ 
+
+ align:start position:0%
+you start is small compared to the the
+final width or compared to the total um
+
+ align:start position:0%
+final width or compared to the total um
+ 
+
+ align:start position:0%
+final width or compared to the total um
+DT if that uh assumption is is not valid
+
+ align:start position:0%
+DT if that uh assumption is is not valid
+ 
+
+ align:start position:0%
+DT if that uh assumption is is not valid
+then and we don't have a simple uh uh
+
+ align:start position:0%
+then and we don't have a simple uh uh
+ 
+
+ align:start position:0%
+then and we don't have a simple uh uh
+ging solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+necessarily okay let's go on to slide
+
+ align:start position:0%
+necessarily okay let's go on to slide
+ 
+
+ align:start position:0%
+necessarily okay let's go on to slide
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+six and uh here we're going to go
+
+ align:start position:0%
+six and uh here we're going to go
+ 
+
+ align:start position:0%
+six and uh here we're going to go
+through um some principles and examples
+
+ align:start position:0%
+through um some principles and examples
+ 
+
+ align:start position:0%
+through um some principles and examples
+of the design of diffuse layers so what
+
+ align:start position:0%
+of the design of diffuse layers so what
+ 
+
+ align:start position:0%
+of the design of diffuse layers so what
+we want to do is as as an engineer uh
+
+ align:start position:0%
+we want to do is as as an engineer uh
+ 
+
+ align:start position:0%
+we want to do is as as an engineer uh
+process engineer or working with Device
+
+ align:start position:0%
+process engineer or working with Device
+ 
+
+ align:start position:0%
+process engineer or working with Device
+engineers we want to uh typically design
+
+ align:start position:0%
+engineers we want to uh typically design
+ 
+
+ align:start position:0%
+engineers we want to uh typically design
+a diffusion process um or a prep in
+
+ align:start position:0%
+a diffusion process um or a prep in
+ 
+
+ align:start position:0%
+a diffusion process um or a prep in
+diffusion in a driving process so that
+
+ align:start position:0%
+diffusion in a driving process so that
+ 
+
+ align:start position:0%
+diffusion in a driving process so that
+we end up with a certain sheet
+
+ align:start position:0%
+we end up with a certain sheet
+ 
+
+ align:start position:0%
+we end up with a certain sheet
+resistance that's required electrically
+
+ align:start position:0%
+resistance that's required electrically
+ 
+
+ align:start position:0%
+resistance that's required electrically
+um by the uh by the
+
+ align:start position:0%
+um by the uh by the
+ 
+
+ align:start position:0%
+um by the uh by the
+device so that's that's sort of the uh
+
+ align:start position:0%
+device so that's that's sort of the uh
+ 
+
+ align:start position:0%
+device so that's that's sort of the uh
+the goal of uh of this section and I'm
+
+ align:start position:0%
+the goal of uh of this section and I'm
+ 
+
+ align:start position:0%
+the goal of uh of this section and I'm
+showing on the le- hand side just the
+
+ align:start position:0%
+showing on the le- hand side just the
+ 
+
+ align:start position:0%
+showing on the le- hand side just the
+example of um a cube of silicon where
+
+ align:start position:0%
+example of um a cube of silicon where
+ 
+
+ align:start position:0%
+example of um a cube of silicon where
+the top region is colored in Orange and
+
+ align:start position:0%
+the top region is colored in Orange and
+ 
+
+ align:start position:0%
+the top region is colored in Orange and
+that is the little sheet uh through
+
+ align:start position:0%
+that is the little sheet uh through
+ 
+
+ align:start position:0%
+that is the little sheet uh through
+which we're going to be passing uh a
+
+ align:start position:0%
+which we're going to be passing uh a
+ 
+
+ align:start position:0%
+which we're going to be passing uh a
+current and measuring the voltage and uh
+
+ align:start position:0%
+current and measuring the voltage and uh
+ 
+
+ align:start position:0%
+current and measuring the voltage and uh
+the uh this little uh she has a
+
+ align:start position:0%
+the uh this little uh she has a
+ 
+
+ align:start position:0%
+the uh this little uh she has a
+particular geometry what we're going to
+
+ align:start position:0%
+particular geometry what we're going to
+ 
+
+ align:start position:0%
+particular geometry what we're going to
+consider is the case where the uh
+
+ align:start position:0%
+consider is the case where the uh
+ 
+
+ align:start position:0%
+consider is the case where the uh
+length of this resistor um is actually
+
+ align:start position:0%
+length of this resistor um is actually
+ 
+
+ align:start position:0%
+length of this resistor um is actually
+equal to its its width so it's uh it's a
+
+ align:start position:0%
+equal to its its width so it's uh it's a
+ 
+
+ align:start position:0%
+equal to its its width so it's uh it's a
+square and it has Dimension W by
+
+ align:start position:0%
+square and it has Dimension W by
+ 
+
+ align:start position:0%
+square and it has Dimension W by
+W um and so we're going to define the
+
+ align:start position:0%
+W um and so we're going to define the
+ 
+
+ align:start position:0%
+W um and so we're going to define the
+sheet resistance uh of this function
+
+ align:start position:0%
+sheet resistance uh of this function
+ 
+
+ align:start position:0%
+sheet resistance uh of this function
+last time we talked about it um as being
+
+ align:start position:0%
+last time we talked about it um as being
+ 
+
+ align:start position:0%
+last time we talked about it um as being
+the resistivity which is an intrinsic
+
+ align:start position:0%
+the resistivity which is an intrinsic
+ 
+
+ align:start position:0%
+the resistivity which is an intrinsic
+property of the material depending on
+
+ align:start position:0%
+property of the material depending on
+ 
+
+ align:start position:0%
+property of the material depending on
+how it's doped in BRS divided by XJ The
+
+ align:start position:0%
+how it's doped in BRS divided by XJ The
+ 
+
+ align:start position:0%
+how it's doped in BRS divided by XJ The
+Junction depth you can see XJ and Mark
+
+ align:start position:0%
+Junction depth you can see XJ and Mark
+ 
+
+ align:start position:0%
+Junction depth you can see XJ and Mark
+on the left left hand side and the units
+
+ align:start position:0%
+on the left left hand side and the units
+ 
+
+ align:start position:0%
+on the left left hand side and the units
+of that sheet resistance then are um
+
+ align:start position:0%
+of that sheet resistance then are um
+ 
+
+ align:start position:0%
+of that sheet resistance then are um
+given it to be ohms per
+
+ align:start position:0%
+given it to be ohms per
+ 
+
+ align:start position:0%
+given it to be ohms per
+square so so the sheet resistance is
+
+ align:start position:0%
+square so so the sheet resistance is
+ 
+
+ align:start position:0%
+square so so the sheet resistance is
+indeed the resistance r that you would
+
+ align:start position:0%
+indeed the resistance r that you would
+ 
+
+ align:start position:0%
+indeed the resistance r that you would
+get in a resistor made of one square
+
+ align:start position:0%
+get in a resistor made of one square
+ 
+
+ align:start position:0%
+get in a resistor made of one square
+uh of this material and we you can
+
+ align:start position:0%
+uh of this material and we you can
+ 
+
+ align:start position:0%
+uh of this material and we you can
+easily write it as uh Roman R subs or uh
+
+ align:start position:0%
+easily write it as uh Roman R subs or uh
+ 
+
+ align:start position:0%
+easily write it as uh Roman R subs or uh
+row Greek the Greek letter row SS and uh
+
+ align:start position:0%
+row Greek the Greek letter row SS and uh
+ 
+
+ align:start position:0%
+row Greek the Greek letter row SS and uh
+uh the S indicating is for Sheet the
+
+ align:start position:0%
+uh the S indicating is for Sheet the
+ 
+
+ align:start position:0%
+uh the S indicating is for Sheet the
+resistivity row remember is given by one
+
+ align:start position:0%
+resistivity row remember is given by one
+ 
+
+ align:start position:0%
+resistivity row remember is given by one
+over Q electronic charge times the car
+
+ align:start position:0%
+over Q electronic charge times the car
+ 
+
+ align:start position:0%
+over Q electronic charge times the car
+concentration n times Mobility which is
+
+ align:start position:0%
+concentration n times Mobility which is
+ 
+
+ align:start position:0%
+concentration n times Mobility which is
+in general a function of N and the
+
+ align:start position:0%
+in general a function of N and the
+ 
+
+ align:start position:0%
+in general a function of N and the
+resistivity has units of on centimeter
+
+ align:start position:0%
+resistivity has units of on centimeter
+ 
+
+ align:start position:0%
+resistivity has units of on centimeter
+XJ has units of centimeter they cancel
+
+ align:start position:0%
+XJ has units of centimeter they cancel
+ 
+
+ align:start position:0%
+XJ has units of centimeter they cancel
+out with a sheet resistance in ohms per
+
+ align:start position:0%
+out with a sheet resistance in ohms per
+ 
+
+ align:start position:0%
+out with a sheet resistance in ohms per
+square um that's all
+
+ align:start position:0%
+square um that's all
+ 
+
+ align:start position:0%
+square um that's all
+reasonably uh intuitive in assuming you
+
+ align:start position:0%
+reasonably uh intuitive in assuming you
+ 
+
+ align:start position:0%
+reasonably uh intuitive in assuming you
+have a constantly doped a constant doped
+
+ align:start position:0%
+have a constantly doped a constant doped
+ 
+
+ align:start position:0%
+have a constantly doped a constant doped
+um layer for if a layer is non-uniformly
+
+ align:start position:0%
+um layer for if a layer is non-uniformly
+ 
+
+ align:start position:0%
+um layer for if a layer is non-uniformly
+doped you need to integrate uh the uh
+
+ align:start position:0%
+doped you need to integrate uh the uh
+ 
+
+ align:start position:0%
+doped you need to integrate uh the uh
+the doping uh profile times the the
+
+ align:start position:0%
+the doping uh profile times the the
+ 
+
+ align:start position:0%
+the doping uh profile times the the
+mobility in order to calculate the sheet
+
+ align:start position:0%
+mobility in order to calculate the sheet
+ 
+
+ align:start position:0%
+mobility in order to calculate the sheet
+resistance so the equation shown in near
+
+ align:start position:0%
+resistance so the equation shown in near
+ 
+
+ align:start position:0%
+resistance so the equation shown in near
+the bottom of the slide say sheet
+
+ align:start position:0%
+the bottom of the slide say sheet
+ 
+
+ align:start position:0%
+the bottom of the slide say sheet
+resistance uh can be obtained by one
+
+ align:start position:0%
+resistance uh can be obtained by one
+ 
+
+ align:start position:0%
+resistance uh can be obtained by one
+over the integral Q * the integral from
+
+ align:start position:0%
+over the integral Q * the integral from
+ 
+
+ align:start position:0%
+over the integral Q * the integral from
+zero to the junction depth of a doping
+
+ align:start position:0%
+zero to the junction depth of a doping
+ 
+
+ align:start position:0%
+zero to the junction depth of a doping
+of the car concentration profile n of X
+
+ align:start position:0%
+of the car concentration profile n of X
+ 
+
+ align:start position:0%
+of the car concentration profile n of X
+or the doping profile minus NB or NB is
+
+ align:start position:0%
+or the doping profile minus NB or NB is
+ 
+
+ align:start position:0%
+or the doping profile minus NB or NB is
+the background concentration that tells
+
+ align:start position:0%
+the background concentration that tells
+ 
+
+ align:start position:0%
+the background concentration that tells
+you where uh when you cut off the
+
+ align:start position:0%
+you where uh when you cut off the
+ 
+
+ align:start position:0%
+you where uh when you cut off the
+electron concentration that quantity uh
+
+ align:start position:0%
+electron concentration that quantity uh
+ 
+
+ align:start position:0%
+electron concentration that quantity uh
+times the mobility which is in general
+
+ align:start position:0%
+times the mobility which is in general
+ 
+
+ align:start position:0%
+times the mobility which is in general
+function of of of n uh DX
+
+ align:start position:0%
+function of of of n uh DX
+ 
+
+ align:start position:0%
+function of of of n uh DX
+integrated um so that's what you would
+
+ align:start position:0%
+integrated um so that's what you would
+ 
+
+ align:start position:0%
+integrated um so that's what you would
+do in the case of a non-uniformly doped
+
+ align:start position:0%
+do in the case of a non-uniformly doped
+ 
+
+ align:start position:0%
+do in the case of a non-uniformly doped
+layer with the dope and concentrations
+
+ align:start position:0%
+layer with the dope and concentrations
+ 
+
+ align:start position:0%
+layer with the dope and concentrations
+varying in
+
+ align:start position:0%
+varying in
+ 
+
+ align:start position:0%
+varying in
+thickness uh now it turns out this
+
+ align:start position:0%
+thickness uh now it turns out this
+ 
+
+ align:start position:0%
+thickness uh now it turns out this
+equation uh you can solve it yourself
+
+ align:start position:0%
+equation uh you can solve it yourself
+ 
+
+ align:start position:0%
+equation uh you can solve it yourself
+but this equation has already been
+
+ align:start position:0%
+but this equation has already been
+ 
+
+ align:start position:0%
+but this equation has already been
+numerically integrated uh by Irwin for
+
+ align:start position:0%
+numerically integrated uh by Irwin for
+ 
+
+ align:start position:0%
+numerically integrated uh by Irwin for
+um a couple of different analytical
+
+ align:start position:0%
+um a couple of different analytical
+ 
+
+ align:start position:0%
+um a couple of different analytical
+profiles in particular the case of the
+
+ align:start position:0%
+profiles in particular the case of the
+ 
+
+ align:start position:0%
+profiles in particular the case of the
+ging and the complimentary error
+
+ align:start position:0%
+ging and the complimentary error
+ 
+
+ align:start position:0%
+ging and the complimentary error
+function profiles and those uh the
+
+ align:start position:0%
+function profiles and those uh the
+ 
+
+ align:start position:0%
+function profiles and those uh the
+solutions to those integrals are given
+
+ align:start position:0%
+solutions to those integrals are given
+ 
+
+ align:start position:0%
+solutions to those integrals are given
+in your text uh either in chapter 7even
+
+ align:start position:0%
+in your text uh either in chapter 7even
+ 
+
+ align:start position:0%
+in your text uh either in chapter 7even
+or there's also an appendix where the
+
+ align:start position:0%
+or there's also an appendix where the
+ 
+
+ align:start position:0%
+or there's also an appendix where the
+solutions are given so let's go on to uh
+
+ align:start position:0%
+solutions are given so let's go on to uh
+ 
+
+ align:start position:0%
+solutions are given so let's go on to uh
+slide number
+
+ align:start position:0%
+slide number
+ 
+
+ align:start position:0%
+slide number
+seven and at the top of the slide we're
+
+ align:start position:0%
+seven and at the top of the slide we're
+ 
+
+ align:start position:0%
+seven and at the top of the slide we're
+showing an example of our wind curves
+
+ align:start position:0%
+showing an example of our wind curves
+ 
+
+ align:start position:0%
+showing an example of our wind curves
+for the particular case of the
+
+ align:start position:0%
+for the particular case of the
+ 
+
+ align:start position:0%
+for the particular case of the
+pype uh Gan profiles in an end type
+
+ align:start position:0%
+pype uh Gan profiles in an end type
+ 
+
+ align:start position:0%
+pype uh Gan profiles in an end type
+background and what you see uh in these
+
+ align:start position:0%
+background and what you see uh in these
+ 
+
+ align:start position:0%
+background and what you see uh in these
+curves on the uh Y axis is a Surface
+
+ align:start position:0%
+curves on the uh Y axis is a Surface
+ 
+
+ align:start position:0%
+curves on the uh Y axis is a Surface
+concentration so that would be C subs
+
+ align:start position:0%
+concentration so that would be C subs
+ 
+
+ align:start position:0%
+concentration so that would be C subs
+and adoms P centimeter the xaxis now is
+
+ align:start position:0%
+and adoms P centimeter the xaxis now is
+ 
+
+ align:start position:0%
+and adoms P centimeter the xaxis now is
+effective conductivity and it has units
+
+ align:start position:0%
+effective conductivity and it has units
+ 
+
+ align:start position:0%
+effective conductivity and it has units
+of uh ohm centimeter the minus
+
+ align:start position:0%
+of uh ohm centimeter the minus
+ 
+
+ align:start position:0%
+of uh ohm centimeter the minus
+one um so that's the FX axis if you just
+
+ align:start position:0%
+one um so that's the FX axis if you just
+ 
+
+ align:start position:0%
+one um so that's the FX axis if you just
+go to the bottom of the slide uh
+
+ align:start position:0%
+go to the bottom of the slide uh
+ 
+
+ align:start position:0%
+go to the bottom of the slide uh
+thinking about it that is the effective
+
+ align:start position:0%
+thinking about it that is the effective
+ 
+
+ align:start position:0%
+thinking about it that is the effective
+average conductivity the inverse of the
+
+ align:start position:0%
+average conductivity the inverse of the
+ 
+
+ align:start position:0%
+average conductivity the inverse of the
+average resistivity so we can write this
+
+ align:start position:0%
+average resistivity so we can write this
+ 
+
+ align:start position:0%
+average resistivity so we can write this
+as a sigma bar and it's equal to a one
+
+ align:start position:0%
+as a sigma bar and it's equal to a one
+ 
+
+ align:start position:0%
+as a sigma bar and it's equal to a one
+over the product of row sub s times uh
+
+ align:start position:0%
+over the product of row sub s times uh
+ 
+
+ align:start position:0%
+over the product of row sub s times uh
+XJ so it's one over the sheet the
+
+ align:start position:0%
+XJ so it's one over the sheet the
+ 
+
+ align:start position:0%
+XJ so it's one over the sheet the
+product the sheet resistance times the
+
+ align:start position:0%
+product the sheet resistance times the
+ 
+
+ align:start position:0%
+product the sheet resistance times the
+junction deck um so there are kind of
+
+ align:start position:0%
+junction deck um so there are kind of
+ 
+
+ align:start position:0%
+junction deck um so there are kind of
+three key parameters we need to identify
+
+ align:start position:0%
+three key parameters we need to identify
+ 
+
+ align:start position:0%
+three key parameters we need to identify
+and using these curves there's a surface
+
+ align:start position:0%
+and using these curves there's a surface
+ 
+
+ align:start position:0%
+and using these curves there's a surface
+concentration which is the y-
+
+ align:start position:0%
+concentration which is the y-
+ 
+
+ align:start position:0%
+concentration which is the y-
+axis uh in the profile there is again
+
+ align:start position:0%
+axis uh in the profile there is again
+ 
+
+ align:start position:0%
+axis uh in the profile there is again
+this is for a particular type this for a
+
+ align:start position:0%
+this is for a particular type this for a
+ 
+
+ align:start position:0%
+this is for a particular type this for a
+gum profile there is the sheet
+
+ align:start position:0%
+gum profile there is the sheet
+ 
+
+ align:start position:0%
+gum profile there is the sheet
+resistance um which is uh coming into
+
+ align:start position:0%
+resistance um which is uh coming into
+ 
+
+ align:start position:0%
+resistance um which is uh coming into
+this effective conductivity that's
+
+ align:start position:0%
+this effective conductivity that's
+ 
+
+ align:start position:0%
+this effective conductivity that's
+really part of the x-axis and there's
+
+ align:start position:0%
+really part of the x-axis and there's
+ 
+
+ align:start position:0%
+really part of the x-axis and there's
+the junction depth so the x-axis has
+
+ align:start position:0%
+the junction depth so the x-axis has
+ 
+
+ align:start position:0%
+the junction depth so the x-axis has
+sheet resistance and Junction depth um
+
+ align:start position:0%
+sheet resistance and Junction depth um
+ 
+
+ align:start position:0%
+sheet resistance and Junction depth um
+built into it the uh and now the
+
+ align:start position:0%
+built into it the uh and now the
+ 
+
+ align:start position:0%
+built into it the uh and now the
+metallurgical Junction is the place the
+
+ align:start position:0%
+metallurgical Junction is the place the
+ 
+
+ align:start position:0%
+metallurgical Junction is the place the
+point in depth where the Cal
+
+ align:start position:0%
+point in depth where the Cal
+ 
+
+ align:start position:0%
+point in depth where the Cal
+concentration in of the uh in the
+
+ align:start position:0%
+concentration in of the uh in the
+ 
+
+ align:start position:0%
+concentration in of the uh in the
+diffused region of the diffused dopin
+
+ align:start position:0%
+diffused region of the diffused dopin
+ 
+
+ align:start position:0%
+diffused region of the diffused dopin
+equals the background concentration
+
+ align:start position:0%
+equals the background concentration
+ 
+
+ align:start position:0%
+equals the background concentration
+CB and we'll do an example shortly after
+
+ align:start position:0%
+CB and we'll do an example shortly after
+ 
+
+ align:start position:0%
+CB and we'll do an example shortly after
+this um where you can see how these uh
+
+ align:start position:0%
+this um where you can see how these uh
+ 
+
+ align:start position:0%
+this um where you can see how these uh
+curves are used but each curve different
+
+ align:start position:0%
+curves are used but each curve different
+ 
+
+ align:start position:0%
+curves are used but each curve different
+color is for a different background uh
+
+ align:start position:0%
+color is for a different background uh
+ 
+
+ align:start position:0%
+color is for a different background uh
+concentration uh so this basically tells
+
+ align:start position:0%
+concentration uh so this basically tells
+ 
+
+ align:start position:0%
+concentration uh so this basically tells
+you that you can take these three key
+
+ align:start position:0%
+you that you can take these three key
+ 
+
+ align:start position:0%
+you that you can take these three key
+parameters and uh uh they have a unique
+
+ align:start position:0%
+parameters and uh uh they have a unique
+ 
+
+ align:start position:0%
+parameters and uh uh they have a unique
+relationship among themselves for the
+
+ align:start position:0%
+relationship among themselves for the
+ 
+
+ align:start position:0%
+relationship among themselves for the
+particular case uh where the shape of
+
+ align:start position:0%
+particular case uh where the shape of
+ 
+
+ align:start position:0%
+particular case uh where the shape of
+the profile is known in this case it's
+
+ align:start position:0%
+the profile is known in this case it's
+ 
+
+ align:start position:0%
+the profile is known in this case it's
+gum so in fact let's go on to slide
+
+ align:start position:0%
+gum so in fact let's go on to slide
+ 
+
+ align:start position:0%
+gum so in fact let's go on to slide
+number eight we're going to walk through
+
+ align:start position:0%
+number eight we're going to walk through
+ 
+
+ align:start position:0%
+number eight we're going to walk through
+the best way to uh understand these ear
+
+ align:start position:0%
+the best way to uh understand these ear
+ 
+
+ align:start position:0%
+the best way to uh understand these ear
+WIS curves is go do an
+
+ align:start position:0%
+WIS curves is go do an
+ 
+
+ align:start position:0%
+WIS curves is go do an
+example and what we're asked to do in
+
+ align:start position:0%
+example and what we're asked to do in
+ 
+
+ align:start position:0%
+example and what we're asked to do in
+this example is to calculate the
+
+ align:start position:0%
+this example is to calculate the
+ 
+
+ align:start position:0%
+this example is to calculate the
+drive-in conditions which means the
+
+ align:start position:0%
+drive-in conditions which means the
+ 
+
+ align:start position:0%
+drive-in conditions which means the
+temperature uh and the time to produce a
+
+ align:start position:0%
+temperature uh and the time to produce a
+ 
+
+ align:start position:0%
+temperature uh and the time to produce a
+seamoss uh P well so it's a p type a
+
+ align:start position:0%
+seamoss uh P well so it's a p type a
+ 
+
+ align:start position:0%
+seamoss uh P well so it's a p type a
+region it's called a p well of a certain
+
+ align:start position:0%
+region it's called a p well of a certain
+ 
+
+ align:start position:0%
+region it's called a p well of a certain
+thickness and and um uh what we want to
+
+ align:start position:0%
+thickness and and um uh what we want to
+ 
+
+ align:start position:0%
+thickness and and um uh what we want to
+do we're told that the constraint is the
+
+ align:start position:0%
+do we're told that the constraint is the
+ 
+
+ align:start position:0%
+do we're told that the constraint is the
+KET resistance of that P well shouldn't
+
+ align:start position:0%
+KET resistance of that P well shouldn't
+ 
+
+ align:start position:0%
+KET resistance of that P well shouldn't
+be 900 ohms per
+
+ align:start position:0%
+be 900 ohms per
+ 
+
+ align:start position:0%
+be 900 ohms per
+square okay and it has to have a certain
+
+ align:start position:0%
+square okay and it has to have a certain
+ 
+
+ align:start position:0%
+square okay and it has to have a certain
+Junction depth which is shown
+
+ align:start position:0%
+Junction depth which is shown
+ 
+
+ align:start position:0%
+Junction depth which is shown
+schematically in the figure XJ to be
+
+ align:start position:0%
+schematically in the figure XJ to be
+ 
+
+ align:start position:0%
+schematically in the figure XJ to be
+three microns uh and that XJ again is
+
+ align:start position:0%
+three microns uh and that XJ again is
+ 
+
+ align:start position:0%
+three microns uh and that XJ again is
+the point where the brwn concentration
+
+ align:start position:0%
+the point where the brwn concentration
+ 
+
+ align:start position:0%
+the point where the brwn concentration
+then will reach the background
+
+ align:start position:0%
+then will reach the background
+ 
+
+ align:start position:0%
+then will reach the background
+concentration which is um uh given by uh
+
+ align:start position:0%
+concentration which is um uh given by uh
+ 
+
+ align:start position:0%
+concentration which is um uh given by uh
+10 15 cubic cm here so again we're
+
+ align:start position:0%
+10 15 cubic cm here so again we're
+ 
+
+ align:start position:0%
+10 15 cubic cm here so again we're
+informing a PO by ion implanting
+
+ align:start position:0%
+informing a PO by ion implanting
+ 
+
+ align:start position:0%
+informing a PO by ion implanting
+Bond um into this uh into the region
+
+ align:start position:0%
+Bond um into this uh into the region
+ 
+
+ align:start position:0%
+Bond um into this uh into the region
+onto the wafer and the region on the
+
+ align:start position:0%
+onto the wafer and the region on the
+ 
+
+ align:start position:0%
+onto the wafer and the region on the
+left is blocked so we're just being in
+
+ align:start position:0%
+left is blocked so we're just being in
+ 
+
+ align:start position:0%
+left is blocked so we're just being in
+one region and typically you would
+
+ align:start position:0%
+one region and typically you would
+ 
+
+ align:start position:0%
+one region and typically you would
+implant um Boron at a certain dose say
+
+ align:start position:0%
+implant um Boron at a certain dose say
+ 
+
+ align:start position:0%
+implant um Boron at a certain dose say
+10 of the 13th and energy and then we
+
+ align:start position:0%
+10 of the 13th and energy and then we
+ 
+
+ align:start position:0%
+10 of the 13th and energy and then we
+want to drive that in and we're
+
+ align:start position:0%
+want to drive that in and we're
+ 
+
+ align:start position:0%
+want to drive that in and we're
+interested in the driving conditions
+
+ align:start position:0%
+interested in the driving conditions
+ 
+
+ align:start position:0%
+interested in the driving conditions
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+temperature in time will we need to get
+
+ align:start position:0%
+temperature in time will we need to get
+ 
+
+ align:start position:0%
+temperature in time will we need to get
+it to go that far and to have a
+
+ align:start position:0%
+it to go that far and to have a
+ 
+
+ align:start position:0%
+it to go that far and to have a
+particular um sheet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resistance uh and we're going to use
+
+ align:start position:0%
+resistance uh and we're going to use
+ 
+
+ align:start position:0%
+resistance uh and we're going to use
+Irwin's curves to do your so let's look
+
+ align:start position:0%
+Irwin's curves to do your so let's look
+ 
+
+ align:start position:0%
+Irwin's curves to do your so let's look
+on slide number uh
+
+ align:start position:0%
+on slide number uh
+ 
+
+ align:start position:0%
+on slide number uh
+nine um so these are the constraints
+
+ align:start position:0%
+nine um so these are the constraints
+ 
+
+ align:start position:0%
+nine um so these are the constraints
+again repeated the sheet resistance is
+
+ align:start position:0%
+again repeated the sheet resistance is
+ 
+
+ align:start position:0%
+again repeated the sheet resistance is
+900 ohms per square The Junction depth
+
+ align:start position:0%
+900 ohms per square The Junction depth
+ 
+
+ align:start position:0%
+900 ohms per square The Junction depth
+has to be three microns and the
+
+ align:start position:0%
+has to be three microns and the
+ 
+
+ align:start position:0%
+has to be three microns and the
+background concentration either NB or uh
+
+ align:start position:0%
+background concentration either NB or uh
+ 
+
+ align:start position:0%
+background concentration either NB or uh
+substrate concentration maybe WR NBC is
+
+ align:start position:0%
+substrate concentration maybe WR NBC is
+ 
+
+ align:start position:0%
+substrate concentration maybe WR NBC is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+15th so given the requirements that we
+
+ align:start position:0%
+15th so given the requirements that we
+ 
+
+ align:start position:0%
+15th so given the requirements that we
+have been uh told I can actually
+
+ align:start position:0%
+have been uh told I can actually
+ 
+
+ align:start position:0%
+have been uh told I can actually
+immediately find the x-axis on the urban
+
+ align:start position:0%
+immediately find the x-axis on the urban
+ 
+
+ align:start position:0%
+immediately find the x-axis on the urban
+curve with the average connectivity
+
+ align:start position:0%
+curve with the average connectivity
+ 
+
+ align:start position:0%
+curve with the average connectivity
+layer it's just one over the shapeless
+
+ align:start position:0%
+layer it's just one over the shapeless
+ 
+
+ align:start position:0%
+layer it's just one over the shapeless
+distance times
+
+ align:start position:0%
+distance times
+ 
+
+ align:start position:0%
+distance times
+XJ so the average connectivity
+
+ align:start position:0%
+XJ so the average connectivity
+ 
+
+ align:start position:0%
+XJ so the average connectivity
+calculates out to the 3.7 ohm cim minus
+
+ align:start position:0%
+calculates out to the 3.7 ohm cim minus
+ 
+
+ align:start position:0%
+calculates out to the 3.7 ohm cim minus
+one um we can now from Irwin's curve we
+
+ align:start position:0%
+one um we can now from Irwin's curve we
+ 
+
+ align:start position:0%
+one um we can now from Irwin's curve we
+can obtain assuming this the galy uh
+
+ align:start position:0%
+can obtain assuming this the galy uh
+ 
+
+ align:start position:0%
+can obtain assuming this the galy uh
+that's assumption we we need to make at
+
+ align:start position:0%
+that's assumption we we need to make at
+ 
+
+ align:start position:0%
+that's assumption we we need to make at
+this point which we'll show is
+
+ align:start position:0%
+this point which we'll show is
+ 
+
+ align:start position:0%
+this point which we'll show is
+reasonable later we can then obtain the
+
+ align:start position:0%
+reasonable later we can then obtain the
+ 
+
+ align:start position:0%
+reasonable later we can then obtain the
+surface concentration so if in order for
+
+ align:start position:0%
+surface concentration so if in order for
+ 
+
+ align:start position:0%
+surface concentration so if in order for
+me knowing the shape of the Gan
+
+ align:start position:0%
+me knowing the shape of the Gan
+ 
+
+ align:start position:0%
+me knowing the shape of the Gan
+basically IR intervals tells us that the
+
+ align:start position:0%
+basically IR intervals tells us that the
+ 
+
+ align:start position:0%
+basically IR intervals tells us that the
+service concentration has to be about 4
+
+ align:start position:0%
+service concentration has to be about 4
+ 
+
+ align:start position:0%
+service concentration has to be about 4
+* 10 17th per cubic
+
+ align:start position:0%
+* 10 17th per cubic
+ 
+
+ align:start position:0%
+* 10 17th per cubic
+cm in order to achieve an average
+
+ align:start position:0%
+cm in order to achieve an average
+ 
+
+ align:start position:0%
+cm in order to achieve an average
+conductivity that has been specified of
+
+ align:start position:0%
+conductivity that has been specified of
+ 
+
+ align:start position:0%
+conductivity that has been specified of
+3.7 um uh assuming the junction depth is
+
+ align:start position:0%
+3.7 um uh assuming the junction depth is
+ 
+
+ align:start position:0%
+3.7 um uh assuming the junction depth is
+three microns so that's and if you can
+
+ align:start position:0%
+three microns so that's and if you can
+ 
+
+ align:start position:0%
+three microns so that's and if you can
+you want to see that how we actually do
+
+ align:start position:0%
+you want to see that how we actually do
+ 
+
+ align:start position:0%
+you want to see that how we actually do
+that you can go on to slide number 10
+
+ align:start position:0%
+that you can go on to slide number 10
+ 
+
+ align:start position:0%
+that you can go on to slide number 10
+and this actually shows how the curve we
+
+ align:start position:0%
+and this actually shows how the curve we
+ 
+
+ align:start position:0%
+and this actually shows how the curve we
+used um again this is for a ptype
+
+ align:start position:0%
+used um again this is for a ptype
+ 
+
+ align:start position:0%
+used um again this is for a ptype
+gussian profile and all we've done is is
+
+ align:start position:0%
+gussian profile and all we've done is is
+ 
+
+ align:start position:0%
+gussian profile and all we've done is is
+uh on the x-axis picked out it's a
+
+ align:start position:0%
+uh on the x-axis picked out it's a
+ 
+
+ align:start position:0%
+uh on the x-axis picked out it's a
+little hard because this is a log long
+
+ align:start position:0%
+little hard because this is a log long
+ 
+
+ align:start position:0%
+little hard because this is a log long
+plot on the x-axis picked out the
+
+ align:start position:0%
+plot on the x-axis picked out the
+ 
+
+ align:start position:0%
+plot on the x-axis picked out the
+average conductivity to be
+
+ align:start position:0%
+average conductivity to be
+ 
+
+ align:start position:0%
+average conductivity to be
+3.7 and it's a little tricky to find
+
+ align:start position:0%
+3.7 and it's a little tricky to find
+ 
+
+ align:start position:0%
+3.7 and it's a little tricky to find
+that but uh you can and then you see you
+
+ align:start position:0%
+that but uh you can and then you see you
+ 
+
+ align:start position:0%
+that but uh you can and then you see you
+read off the y- AIS as shown by that uh
+
+ align:start position:0%
+read off the y- AIS as shown by that uh
+ 
+
+ align:start position:0%
+read off the y- AIS as shown by that uh
+horizontal line surface concentration
+
+ align:start position:0%
+horizontal line surface concentration
+ 
+
+ align:start position:0%
+horizontal line surface concentration
+about four * 10 the 17th and again we
+
+ align:start position:0%
+about four * 10 the 17th and again we
+ 
+
+ align:start position:0%
+about four * 10 the 17th and again we
+have multiple curves we can choose I
+
+ align:start position:0%
+have multiple curves we can choose I
+ 
+
+ align:start position:0%
+have multiple curves we can choose I
+choose to use the orange
+
+ align:start position:0%
+choose to use the orange
+ 
+
+ align:start position:0%
+choose to use the orange
+curve uh which is for the case of a
+
+ align:start position:0%
+curve uh which is for the case of a
+ 
+
+ align:start position:0%
+curve uh which is for the case of a
+background concentration in this example
+
+ align:start position:0%
+background concentration in this example
+ 
+
+ align:start position:0%
+background concentration in this example
+of 10 the
+
+ align:start position:0%
+of 10 the
+ 
+
+ align:start position:0%
+of 10 the
+15th uh if the background concentration
+
+ align:start position:0%
+15th uh if the background concentration
+ 
+
+ align:start position:0%
+15th uh if the background concentration
+say had been uh a little bit higher say
+
+ align:start position:0%
+say had been uh a little bit higher say
+ 
+
+ align:start position:0%
+say had been uh a little bit higher say
+10 the 16th or um 10 the 17th what you
+
+ align:start position:0%
+10 the 16th or um 10 the 17th what you
+ 
+
+ align:start position:0%
+10 the 16th or um 10 the 17th what you
+see would have happened um is that the
+
+ align:start position:0%
+see would have happened um is that the
+ 
+
+ align:start position:0%
+see would have happened um is that the
+uh the surface concentration would have
+
+ align:start position:0%
+uh the surface concentration would have
+ 
+
+ align:start position:0%
+uh the surface concentration would have
+actually moved down a little bit uh on
+
+ align:start position:0%
+actually moved down a little bit uh on
+ 
+
+ align:start position:0%
+actually moved down a little bit uh on
+the y- AIS it would have be intersect a
+
+ align:start position:0%
+the y- AIS it would have be intersect a
+ 
+
+ align:start position:0%
+the y- AIS it would have be intersect a
+slightly different
+
+ align:start position:0%
+slightly different
+ 
+
+ align:start position:0%
+slightly different
+curve okay so that's how we come up with
+
+ align:start position:0%
+curve okay so that's how we come up with
+ 
+
+ align:start position:0%
+curve okay so that's how we come up with
+the um the surface
+
+ align:start position:0%
+the um the surface
+ 
+
+ align:start position:0%
+the um the surface
+concentration
+
+ align:start position:0%
+concentration
+ 
+
+ align:start position:0%
+concentration
+so let's go on to uh slide 11 and
+
+ align:start position:0%
+so let's go on to uh slide 11 and
+ 
+
+ align:start position:0%
+so let's go on to uh slide 11 and
+thinking about that surface
+
+ align:start position:0%
+thinking about that surface
+ 
+
+ align:start position:0%
+thinking about that surface
+concentration C Subs we know it's well
+
+ align:start position:0%
+concentration C Subs we know it's well
+ 
+
+ align:start position:0%
+concentration C Subs we know it's well
+below the solent solubility of B and
+
+ align:start position:0%
+below the solent solubility of B and
+ 
+
+ align:start position:0%
+below the solent solubility of B and
+silicon it's only 410 and the
+
+ align:start position:0%
+silicon it's only 410 and the
+ 
+
+ align:start position:0%
+silicon it's only 410 and the
+17th and it's probably likely below the
+
+ align:start position:0%
+17th and it's probably likely below the
+ 
+
+ align:start position:0%
+17th and it's probably likely below the
+value of n subi at the diffusion
+
+ align:start position:0%
+value of n subi at the diffusion
+ 
+
+ align:start position:0%
+value of n subi at the diffusion
+temperature again at a th000 degrees
+
+ align:start position:0%
+temperature again at a th000 degrees
+ 
+
+ align:start position:0%
+temperature again at a th000 degrees
+which is probably somewhere near or a
+
+ align:start position:0%
+which is probably somewhere near or a
+ 
+
+ align:start position:0%
+which is probably somewhere near or a
+minimum temperature you'll be using to
+
+ align:start position:0%
+minimum temperature you'll be using to
+ 
+
+ align:start position:0%
+minimum temperature you'll be using to
+drive this in Andi is about mid 10 to
+
+ align:start position:0%
+drive this in Andi is about mid 10 to
+ 
+
+ align:start position:0%
+drive this in Andi is about mid 10 to
+the 18th and so mid10 to the 17th is
+
+ align:start position:0%
+the 18th and so mid10 to the 17th is
+ 
+
+ align:start position:0%
+the 18th and so mid10 to the 17th is
+well below that so it's it's probably
+
+ align:start position:0%
+well below that so it's it's probably
+ 
+
+ align:start position:0%
+well below that so it's it's probably
+valid then to
+
+ align:start position:0%
+valid then to
+ 
+
+ align:start position:0%
+valid then to
+say that the profile is galxy it's
+
+ align:start position:0%
+say that the profile is galxy it's
+ 
+
+ align:start position:0%
+say that the profile is galxy it's
+probably valid to say that uh it is a
+
+ align:start position:0%
+probably valid to say that uh it is a
+ 
+
+ align:start position:0%
+probably valid to say that uh it is a
+constant diffusivity
+
+ align:start position:0%
+constant diffusivity
+ 
+
+ align:start position:0%
+constant diffusivity
+d uh and therefore we can assume this a
+
+ align:start position:0%
+d uh and therefore we can assume this a
+ 
+
+ align:start position:0%
+d uh and therefore we can assume this a
+gan uh type of solution because it's a
+
+ align:start position:0%
+gan uh type of solution because it's a
+ 
+
+ align:start position:0%
+gan uh type of solution because it's a
+driving so we so we can write down sort
+
+ align:start position:0%
+driving so we so we can write down sort
+ 
+
+ align:start position:0%
+driving so we so we can write down sort
+of by inspection the equation in the
+
+ align:start position:0%
+of by inspection the equation in the
+ 
+
+ align:start position:0%
+of by inspection the equation in the
+center of the the slide which is the Gin
+
+ align:start position:0%
+center of the the slide which is the Gin
+ 
+
+ align:start position:0%
+center of the the slide which is the Gin
+equation um uh and then uh we know that
+
+ align:start position:0%
+equation um uh and then uh we know that
+ 
+
+ align:start position:0%
+equation um uh and then uh we know that
+uh at the point where xal XJ the uh car
+
+ align:start position:0%
+uh at the point where xal XJ the uh car
+ 
+
+ align:start position:0%
+uh at the point where xal XJ the uh car
+concentration or the doping
+
+ align:start position:0%
+concentration or the doping
+ 
+
+ align:start position:0%
+concentration or the doping
+concentration Cen of the Boron reaches
+
+ align:start position:0%
+concentration Cen of the Boron reaches
+ 
+
+ align:start position:0%
+concentration Cen of the Boron reaches
+that of the background that's a
+
+ align:start position:0%
+that of the background that's a
+ 
+
+ align:start position:0%
+that of the background that's a
+definitional exj so if you look in the
+
+ align:start position:0%
+definitional exj so if you look in the
+ 
+
+ align:start position:0%
+definitional exj so if you look in the
+middle of this slide we're saying uh the
+
+ align:start position:0%
+middle of this slide we're saying uh the
+ 
+
+ align:start position:0%
+middle of this slide we're saying uh the
+background open Con background
+
+ align:start position:0%
+background open Con background
+ 
+
+ align:start position:0%
+background open Con background
+concentration CBC is equal to the
+
+ align:start position:0%
+concentration CBC is equal to the
+ 
+
+ align:start position:0%
+concentration CBC is equal to the
+surface concentration C sub s which we
+
+ align:start position:0%
+surface concentration C sub s which we
+ 
+
+ align:start position:0%
+surface concentration C sub s which we
+just located which is fam times
+
+ align:start position:0%
+just located which is fam times
+ 
+
+ align:start position:0%
+just located which is fam times
+exponential of the minus XJ S 4 DT
+
+ align:start position:0%
+exponential of the minus XJ S 4 DT
+ 
+
+ align:start position:0%
+exponential of the minus XJ S 4 DT
+that's the definition of
+
+ align:start position:0%
+that's the definition of
+ 
+
+ align:start position:0%
+that's the definition of
+XJ so we know XJ in this equation we
+
+ align:start position:0%
+XJ so we know XJ in this equation we
+ 
+
+ align:start position:0%
+XJ so we know XJ in this equation we
+just found c s we know the background
+
+ align:start position:0%
+just found c s we know the background
+ 
+
+ align:start position:0%
+just found c s we know the background
+open concentration the only thing we
+
+ align:start position:0%
+open concentration the only thing we
+ 
+
+ align:start position:0%
+open concentration the only thing we
+don't know is DT so we can invert that
+
+ align:start position:0%
+don't know is DT so we can invert that
+ 
+
+ align:start position:0%
+don't know is DT so we can invert that
+equation and solve for DT plug in all
+
+ align:start position:0%
+equation and solve for DT plug in all
+ 
+
+ align:start position:0%
+equation and solve for DT plug in all
+the numbers and you get um a DT product
+
+ align:start position:0%
+the numbers and you get um a DT product
+ 
+
+ align:start position:0%
+the numbers and you get um a DT product
+uh in order to obtain this scalan of 3.7
+
+ align:start position:0%
+uh in order to obtain this scalan of 3.7
+ 
+
+ align:start position:0%
+uh in order to obtain this scalan of 3.7
+* 10us 9 cm
+
+ align:start position:0%
+* 10us 9 cm
+ 
+
+ align:start position:0%
+* 10us 9 cm
+s that's the DT product the so-call if
+
+ align:start position:0%
+s that's the DT product the so-call if
+ 
+
+ align:start position:0%
+s that's the DT product the so-call if
+you would like to use the term thermal
+
+ align:start position:0%
+you would like to use the term thermal
+ 
+
+ align:start position:0%
+you would like to use the term thermal
+budget for the drive-in process um so
+
+ align:start position:0%
+budget for the drive-in process um so
+ 
+
+ align:start position:0%
+budget for the drive-in process um so
+that gives us an idea and we don't know
+
+ align:start position:0%
+that gives us an idea and we don't know
+ 
+
+ align:start position:0%
+that gives us an idea and we don't know
+what D is or what T is but we're going
+
+ align:start position:0%
+what D is or what T is but we're going
+ 
+
+ align:start position:0%
+what D is or what T is but we're going
+to design uh a certain
+
+ align:start position:0%
+to design uh a certain
+ 
+
+ align:start position:0%
+to design uh a certain
+temperature and time so we constrain to
+
+ align:start position:0%
+temperature and time so we constrain to
+ 
+
+ align:start position:0%
+temperature and time so we constrain to
+the fact that the D product will be this
+
+ align:start position:0%
+the fact that the D product will be this
+ 
+
+ align:start position:0%
+the fact that the D product will be this
+number so let's go on slide number uh
+
+ align:start position:0%
+number so let's go on slide number uh
+ 
+
+ align:start position:0%
+number so let's go on slide number uh
+number 12 and again I'm repeating the DT
+
+ align:start position:0%
+number 12 and again I'm repeating the DT
+ 
+
+ align:start position:0%
+number 12 and again I'm repeating the DT
+product from the top 3.9 * m minus 9
+
+ align:start position:0%
+product from the top 3.9 * m minus 9
+ 
+
+ align:start position:0%
+product from the top 3.9 * m minus 9
+3.7 uh let's just assume a temperature
+
+ align:start position:0%
+3.7 uh let's just assume a temperature
+ 
+
+ align:start position:0%
+3.7 uh let's just assume a temperature
+and see what happen see what time is
+
+ align:start position:0%
+and see what happen see what time is
+ 
+
+ align:start position:0%
+and see what happen see what time is
+associated with that if it's a
+
+ align:start position:0%
+associated with that if it's a
+ 
+
+ align:start position:0%
+associated with that if it's a
+reasonable amount of time so say uh we
+
+ align:start position:0%
+reasonable amount of time so say uh we
+ 
+
+ align:start position:0%
+reasonable amount of time so say uh we
+know we're diffusing pretty deep down to
+
+ align:start position:0%
+know we're diffusing pretty deep down to
+ 
+
+ align:start position:0%
+know we're diffusing pretty deep down to
+three microns so let's just say we
+
+ align:start position:0%
+three microns so let's just say we
+ 
+
+ align:start position:0%
+three microns so let's just say we
+assume we drive in at 1100 cenade and
+
+ align:start position:0%
+assume we drive in at 1100 cenade and
+ 
+
+ align:start position:0%
+assume we drive in at 1100 cenade and
+then you can look
+
+ align:start position:0%
+then you can look
+ 
+
+ align:start position:0%
+then you can look
+up uh from your plots or you can
+
+ align:start position:0%
+up uh from your plots or you can
+ 
+
+ align:start position:0%
+up uh from your plots or you can
+calculate diffusivity of B 1100 it's
+
+ align:start position:0%
+calculate diffusivity of B 1100 it's
+ 
+
+ align:start position:0%
+calculate diffusivity of B 1100 it's
+about 1.5 * 10- 13 7 Square per second
+
+ align:start position:0%
+about 1.5 * 10- 13 7 Square per second
+ 
+
+ align:start position:0%
+about 1.5 * 10- 13 7 Square per second
+and so then you can solve for time the
+
+ align:start position:0%
+and so then you can solve for time the
+ 
+
+ align:start position:0%
+and so then you can solve for time the
+drive in time calculate that out you get
+
+ align:start position:0%
+drive in time calculate that out you get
+ 
+
+ align:start position:0%
+drive in time calculate that out you get
+about 6.7 hours it's plenty long that
+
+ align:start position:0%
+about 6.7 hours it's plenty long that
+ 
+
+ align:start position:0%
+about 6.7 hours it's plenty long that
+tells you probably from a practical
+
+ align:start position:0%
+tells you probably from a practical
+ 
+
+ align:start position:0%
+tells you probably from a practical
+point of view you would not want to do
+
+ align:start position:0%
+point of view you would not want to do
+ 
+
+ align:start position:0%
+point of view you would not want to do
+this driving any lower temperature
+
+ align:start position:0%
+this driving any lower temperature
+ 
+
+ align:start position:0%
+this driving any lower temperature
+because it would just take two them
+
+ align:start position:0%
+because it would just take two them
+ 
+
+ align:start position:0%
+because it would just take two them
+off okay so um
+
+ align:start position:0%
+off okay so um
+ 
+
+ align:start position:0%
+off okay so um
+now one thing we'd like to to calculate
+
+ align:start position:0%
+now one thing we'd like to to calculate
+ 
+
+ align:start position:0%
+now one thing we'd like to to calculate
+we we have um figured out the surface
+
+ align:start position:0%
+we we have um figured out the surface
+ 
+
+ align:start position:0%
+we we have um figured out the surface
+concentration 's curves and we have the
+
+ align:start position:0%
+concentration 's curves and we have the
+ 
+
+ align:start position:0%
+concentration 's curves and we have the
+DK product it will be interesting to
+
+ align:start position:0%
+DK product it will be interesting to
+ 
+
+ align:start position:0%
+DK product it will be interesting to
+calculate the initial dose or the dose
+
+ align:start position:0%
+calculate the initial dose or the dose
+ 
+
+ align:start position:0%
+calculate the initial dose or the dose
+the area and the curve for the Gan
+
+ align:start position:0%
+the area and the curve for the Gan
+ 
+
+ align:start position:0%
+the area and the curve for the Gan
+profile we have everything we need again
+
+ align:start position:0%
+profile we have everything we need again
+ 
+
+ align:start position:0%
+profile we have everything we need again
+we know the dose Q is the surface
+
+ align:start position:0%
+we know the dose Q is the surface
+ 
+
+ align:start position:0%
+we know the dose Q is the surface
+concentration C sub stimes theun of Pi
+
+ align:start position:0%
+concentration C sub stimes theun of Pi
+ 
+
+ align:start position:0%
+concentration C sub stimes theun of Pi
+DT and we have all those quantities we
+
+ align:start position:0%
+DT and we have all those quantities we
+ 
+
+ align:start position:0%
+DT and we have all those quantities we
+can plug them in and we get Q = to 4.3 *
+
+ align:start position:0%
+can plug them in and we get Q = to 4.3 *
+ 
+
+ align:start position:0%
+can plug them in and we get Q = to 4.3 *
+10 13 that's the end on the
+
+ align:start position:0%
+10 13 that's the end on the
+ 
+
+ align:start position:0%
+10 13 that's the end on the
+gasi uh it's a relatively low dose
+
+ align:start position:0%
+gasi uh it's a relatively low dose
+ 
+
+ align:start position:0%
+gasi uh it's a relatively low dose
+compared to uh implant range so it it's
+
+ align:start position:0%
+compared to uh implant range so it it's
+ 
+
+ align:start position:0%
+compared to uh implant range so it it's
+um they can be implanted so this dose
+
+ align:start position:0%
+um they can be implanted so this dose
+ 
+
+ align:start position:0%
+um they can be implanted so this dose
+can easily be implanted into a very
+
+ align:start position:0%
+can easily be implanted into a very
+ 
+
+ align:start position:0%
+can easily be implanted into a very
+narrow layer close to the surface which
+
+ align:start position:0%
+narrow layer close to the surface which
+ 
+
+ align:start position:0%
+narrow layer close to the surface which
+justifies implicitly that narrow layer
+
+ align:start position:0%
+justifies implicitly that narrow layer
+ 
+
+ align:start position:0%
+justifies implicitly that narrow layer
+might only be a th ACS deep it justifies
+
+ align:start position:0%
+might only be a th ACS deep it justifies
+ 
+
+ align:start position:0%
+might only be a th ACS deep it justifies
+our implicit assumption in using a gin
+
+ align:start position:0%
+our implicit assumption in using a gin
+ 
+
+ align:start position:0%
+our implicit assumption in using a gin
+Pro profile that the initial
+
+ align:start position:0%
+Pro profile that the initial
+ 
+
+ align:start position:0%
+Pro profile that the initial
+distribution would be a Delta function
+
+ align:start position:0%
+distribution would be a Delta function
+ 
+
+ align:start position:0%
+distribution would be a Delta function
+maybe only again few th000 ANS deep and
+
+ align:start position:0%
+maybe only again few th000 ANS deep and
+ 
+
+ align:start position:0%
+maybe only again few th000 ANS deep and
+you're going to a final Junction depth
+
+ align:start position:0%
+you're going to a final Junction depth
+ 
+
+ align:start position:0%
+you're going to a final Junction depth
+that is uh three microns and um
+
+ align:start position:0%
+that is uh three microns and um
+ 
+
+ align:start position:0%
+that is uh three microns and um
+certainly um uh that that scene is
+
+ align:start position:0%
+certainly um uh that that scene is
+ 
+
+ align:start position:0%
+certainly um uh that that scene is
+Justified using the Gan
+
+ align:start position:0%
+Justified using the Gan
+ 
+
+ align:start position:0%
+Justified using the Gan
+profile okay let's go on to uh slide
+
+ align:start position:0%
+profile okay let's go on to uh slide
+ 
+
+ align:start position:0%
+profile okay let's go on to uh slide
+number 13 and now that that was the case
+
+ align:start position:0%
+number 13 and now that that was the case
+ 
+
+ align:start position:0%
+number 13 and now that that was the case
+we just talked aboutum we had implanted
+
+ align:start position:0%
+we just talked aboutum we had implanted
+ 
+
+ align:start position:0%
+we just talked aboutum we had implanted
+the dose let's just take the case where
+
+ align:start position:0%
+the dose let's just take the case where
+ 
+
+ align:start position:0%
+the dose let's just take the case where
+if we used a gas um phase uh uh prep uh
+
+ align:start position:0%
+if we used a gas um phase uh uh prep uh
+ 
+
+ align:start position:0%
+if we used a gas um phase uh uh prep uh
+step as an example to get the uh born
+
+ align:start position:0%
+step as an example to get the uh born
+ 
+
+ align:start position:0%
+step as an example to get the uh born
+initially uh into the wafer and say that
+
+ align:start position:0%
+initially uh into the wafer and say that
+ 
+
+ align:start position:0%
+initially uh into the wafer and say that
+was done at 950 you can then use the
+
+ align:start position:0%
+was done at 950 you can then use the
+ 
+
+ align:start position:0%
+was done at 950 you can then use the
+charts in your book or in the handouts
+
+ align:start position:0%
+charts in your book or in the handouts
+ 
+
+ align:start position:0%
+charts in your book or in the handouts
+to look up the Sol solubility of born at
+
+ align:start position:0%
+to look up the Sol solubility of born at
+ 
+
+ align:start position:0%
+to look up the Sol solubility of born at
+950 and you'll see it's pretty high it's
+
+ align:start position:0%
+950 and you'll see it's pretty high it's
+ 
+
+ align:start position:0%
+950 and you'll see it's pretty high it's
+2.51
+
+ align:start position:0%
+2.51
+ 
+
+ align:start position:0%
+2.51
+20 at that temperature then we can also
+
+ align:start position:0%
+20 at that temperature then we can also
+ 
+
+ align:start position:0%
+20 at that temperature then we can also
+look up the deity it's about 41 Theus
+
+ align:start position:0%
+look up the deity it's about 41 Theus
+ 
+
+ align:start position:0%
+look up the deity it's about 41 Theus
+15 so you can solve for the dose in the
+
+ align:start position:0%
+15 so you can solve for the dose in the
+ 
+
+ align:start position:0%
+15 so you can solve for the dose in the
+complimentary error function profile q
+
+ align:start position:0%
+complimentary error function profile q
+ 
+
+ align:start position:0%
+complimentary error function profile q
+and you have everything you need in that
+
+ align:start position:0%
+and you have everything you need in that
+ 
+
+ align:start position:0%
+and you have everything you need in that
+um equation 2 C Subs overun of Pi of KT
+
+ align:start position:0%
+um equation 2 C Subs overun of Pi of KT
+ 
+
+ align:start position:0%
+um equation 2 C Subs overun of Pi of KT
+and so the time that you were required
+
+ align:start position:0%
+and so the time that you were required
+ 
+
+ align:start position:0%
+and so the time that you were required
+to deposit that dose into the wafer T of
+
+ align:start position:0%
+to deposit that dose into the wafer T of
+ 
+
+ align:start position:0%
+to deposit that dose into the wafer T of
+the prep can be solved and you find
+
+ align:start position:0%
+the prep can be solved and you find
+ 
+
+ align:start position:0%
+the prep can be solved and you find
+about 5.5
+
+ align:start position:0%
+about 5.5
+ 
+
+ align:start position:0%
+about 5.5
+seconds so you now see that the uh DT
+
+ align:start position:0%
+seconds so you now see that the uh DT
+ 
+
+ align:start position:0%
+seconds so you now see that the uh DT
+product of the predi which you can
+
+ align:start position:0%
+product of the predi which you can
+ 
+
+ align:start position:0%
+product of the predi which you can
+calculate it's 5.5 seconds times the
+
+ align:start position:0%
+calculate it's 5.5 seconds times the
+ 
+
+ align:start position:0%
+calculate it's 5.5 seconds times the
+diffusivity at 950 which we see from
+
+ align:start position:0%
+diffusivity at 950 which we see from
+ 
+
+ align:start position:0%
+diffusivity at 950 which we see from
+regardless 4 10us
+
+ align:start position:0%
+regardless 4 10us
+ 
+
+ align:start position:0%
+regardless 4 10us
+so that DT prep is about 2 * 10us
+
+ align:start position:0%
+so that DT prep is about 2 * 10us
+ 
+
+ align:start position:0%
+so that DT prep is about 2 * 10us
+14th uh and comparing that to the DT of
+
+ align:start position:0%
+14th uh and comparing that to the DT of
+ 
+
+ align:start position:0%
+14th uh and comparing that to the DT of
+the drivein which was solved for earlier
+
+ align:start position:0%
+the drivein which was solved for earlier
+ 
+
+ align:start position:0%
+the drivein which was solved for earlier
+which is about 1 and a half time 10us 13
+
+ align:start position:0%
+which is about 1 and a half time 10us 13
+ 
+
+ align:start position:0%
+which is about 1 and a half time 10us 13
+so you know order of magnitude uh
+
+ align:start position:0%
+so you know order of magnitude uh
+ 
+
+ align:start position:0%
+so you know order of magnitude uh
+difference there again this tells that
+
+ align:start position:0%
+difference there again this tells that
+ 
+
+ align:start position:0%
+difference there again this tells that
+the Assumption of gine diffusions is
+
+ align:start position:0%
+the Assumption of gine diffusions is
+ 
+
+ align:start position:0%
+the Assumption of gine diffusions is
+Justified whe even if we done a solid
+
+ align:start position:0%
+Justified whe even if we done a solid
+ 
+
+ align:start position:0%
+Justified whe even if we done a solid
+phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prep okay so that's uh the end of slide
+
+ align:start position:0%
+prep okay so that's uh the end of slide
+ 
+
+ align:start position:0%
+prep okay so that's uh the end of slide
+13 that sort of gives you an idea of how
+
+ align:start position:0%
+13 that sort of gives you an idea of how
+ 
+
+ align:start position:0%
+13 that sort of gives you an idea of how
+these herban curves can be used to
+
+ align:start position:0%
+these herban curves can be used to
+ 
+
+ align:start position:0%
+these herban curves can be used to
+design a process the alternative you
+
+ align:start position:0%
+design a process the alternative you
+ 
+
+ align:start position:0%
+design a process the alternative you
+could use them is to uh to read off uh
+
+ align:start position:0%
+could use them is to uh to read off uh
+ 
+
+ align:start position:0%
+could use them is to uh to read off uh
+if you go back to just momentarily uh
+
+ align:start position:0%
+if you go back to just momentarily uh
+ 
+
+ align:start position:0%
+if you go back to just momentarily uh
+slide 10 you might the problem might be
+
+ align:start position:0%
+slide 10 you might the problem might be
+ 
+
+ align:start position:0%
+slide 10 you might the problem might be
+specified differently you might be
+
+ align:start position:0%
+specified differently you might be
+ 
+
+ align:start position:0%
+specified differently you might be
+given um you know uh some kind of
+
+ align:start position:0%
+given um you know uh some kind of
+ 
+
+ align:start position:0%
+given um you know uh some kind of
+surface concentration and uh background
+
+ align:start position:0%
+surface concentration and uh background
+ 
+
+ align:start position:0%
+surface concentration and uh background
+concentration have to back out um uh
+
+ align:start position:0%
+concentration have to back out um uh
+ 
+
+ align:start position:0%
+concentration have to back out um uh
+what the effective connectivity of the
+
+ align:start position:0%
+what the effective connectivity of the
+ 
+
+ align:start position:0%
+what the effective connectivity of the
+layer might be so the different ways
+
+ align:start position:0%
+layer might be so the different ways
+ 
+
+ align:start position:0%
+layer might be so the different ways
+that get in with
+
+ align:start position:0%
+that get in with
+ 
+
+ align:start position:0%
+that get in with
+curbs so let's go on now to um slide
+
+ align:start position:0%
+curbs so let's go on now to um slide
+ 
+
+ align:start position:0%
+curbs so let's go on now to um slide
+number 14 and I want to shift gears a
+
+ align:start position:0%
+number 14 and I want to shift gears a
+ 
+
+ align:start position:0%
+number 14 and I want to shift gears a
+little bit because um we have more or
+
+ align:start position:0%
+little bit because um we have more or
+ 
+
+ align:start position:0%
+little bit because um we have more or
+less covered the a few cases for which
+
+ align:start position:0%
+less covered the a few cases for which
+ 
+
+ align:start position:0%
+less covered the a few cases for which
+the um analytic Solutions can be obtain
+
+ align:start position:0%
+the um analytic Solutions can be obtain
+ 
+
+ align:start position:0%
+the um analytic Solutions can be obtain
+and those are important cases but
+
+ align:start position:0%
+and those are important cases but
+ 
+
+ align:start position:0%
+and those are important cases but
+primarily when the dope in concentration
+
+ align:start position:0%
+primarily when the dope in concentration
+ 
+
+ align:start position:0%
+primarily when the dope in concentration
+is low or uh satisfying certain special
+
+ align:start position:0%
+is low or uh satisfying certain special
+ 
+
+ align:start position:0%
+is low or uh satisfying certain special
+conditions like during
+
+ align:start position:0%
+conditions like during
+ 
+
+ align:start position:0%
+conditions like during
+preps it turn it'll turn out there's
+
+ align:start position:0%
+preps it turn it'll turn out there's
+ 
+
+ align:start position:0%
+preps it turn it'll turn out there's
+most cases we cannot solve analytically
+
+ align:start position:0%
+most cases we cannot solve analytically
+ 
+
+ align:start position:0%
+most cases we cannot solve analytically
+so these Solutions have to be obtained
+
+ align:start position:0%
+so these Solutions have to be obtained
+ 
+
+ align:start position:0%
+so these Solutions have to be obtained
+by using computers using numerical
+
+ align:start position:0%
+by using computers using numerical
+ 
+
+ align:start position:0%
+by using computers using numerical
+methods and um so I wanted to introduce
+
+ align:start position:0%
+methods and um so I wanted to introduce
+ 
+
+ align:start position:0%
+methods and um so I wanted to introduce
+you in the next few slides to uh some of
+
+ align:start position:0%
+you in the next few slides to uh some of
+ 
+
+ align:start position:0%
+you in the next few slides to uh some of
+the simplest tight CH numerical methods
+
+ align:start position:0%
+the simplest tight CH numerical methods
+ 
+
+ align:start position:0%
+the simplest tight CH numerical methods
+so you have an idea or a feel for how
+
+ align:start position:0%
+so you have an idea or a feel for how
+ 
+
+ align:start position:0%
+so you have an idea or a feel for how
+you yourself could Implement these
+
+ align:start position:0%
+you yourself could Implement these
+ 
+
+ align:start position:0%
+you yourself could Implement these
+numerical techniques if you need to do
+
+ align:start position:0%
+numerical techniques if you need to do
+ 
+
+ align:start position:0%
+numerical techniques if you need to do
+it and there are uh textbooks on this
+
+ align:start position:0%
+it and there are uh textbooks on this
+ 
+
+ align:start position:0%
+it and there are uh textbooks on this
+topic um in particular if you want to
+
+ align:start position:0%
+topic um in particular if you want to
+ 
+
+ align:start position:0%
+topic um in particular if you want to
+look at more detailed information on
+
+ align:start position:0%
+look at more detailed information on
+ 
+
+ align:start position:0%
+look at more detailed information on
+numerical Solutions of the Fusion
+
+ align:start position:0%
+numerical Solutions of the Fusion
+ 
+
+ align:start position:0%
+numerical Solutions of the Fusion
+equation there's a uh a book by Jay
+
+ align:start position:0%
+equation there's a uh a book by Jay
+ 
+
+ align:start position:0%
+equation there's a uh a book by Jay
+crank called the mathematics and
+
+ align:start position:0%
+crank called the mathematics and
+ 
+
+ align:start position:0%
+crank called the mathematics and
+diffusion has a chapter on numerical
+
+ align:start position:0%
+diffusion has a chapter on numerical
+ 
+
+ align:start position:0%
+diffusion has a chapter on numerical
+methods uh for this particular
+
+ align:start position:0%
+methods uh for this particular
+ 
+
+ align:start position:0%
+methods uh for this particular
+equation the nice thing about numerical
+
+ align:start position:0%
+equation the nice thing about numerical
+ 
+
+ align:start position:0%
+equation the nice thing about numerical
+methods they can be used to solve for
+
+ align:start position:0%
+methods they can be used to solve for
+ 
+
+ align:start position:0%
+methods they can be used to solve for
+arbitrary initial starting profiles so
+
+ align:start position:0%
+arbitrary initial starting profiles so
+ 
+
+ align:start position:0%
+arbitrary initial starting profiles so
+you don't have to make any detailed
+
+ align:start position:0%
+you don't have to make any detailed
+ 
+
+ align:start position:0%
+you don't have to make any detailed
+assumptions arbitrary boundary
+
+ align:start position:0%
+assumptions arbitrary boundary
+ 
+
+ align:start position:0%
+assumptions arbitrary boundary
+conditions and in the case where the
+
+ align:start position:0%
+conditions and in the case where the
+ 
+
+ align:start position:0%
+conditions and in the case where the
+diffusivity varies in space so if you
+
+ align:start position:0%
+diffusivity varies in space so if you
+ 
+
+ align:start position:0%
+diffusivity varies in space so if you
+have a concentration dependent
+
+ align:start position:0%
+have a concentration dependent
+ 
+
+ align:start position:0%
+have a concentration dependent
+diffusivity which will be the case uh
+
+ align:start position:0%
+diffusivity which will be the case uh
+ 
+
+ align:start position:0%
+diffusivity which will be the case uh
+we'll talk about in in later lectures
+
+ align:start position:0%
+we'll talk about in in later lectures
+ 
+
+ align:start position:0%
+we'll talk about in in later lectures
+when the uh car when the dopin
+
+ align:start position:0%
+when the uh car when the dopin
+ 
+
+ align:start position:0%
+when the uh car when the dopin
+concentration is quite high and you can
+
+ align:start position:0%
+concentration is quite high and you can
+ 
+
+ align:start position:0%
+concentration is quite high and you can
+use numerical
+
+ align:start position:0%
+use numerical
+ 
+
+ align:start position:0%
+use numerical
+methods so what I'm picturing here on
+
+ align:start position:0%
+methods so what I'm picturing here on
+ 
+
+ align:start position:0%
+methods so what I'm picturing here on
+slide number 14 is a very schematic
+
+ align:start position:0%
+slide number 14 is a very schematic
+ 
+
+ align:start position:0%
+slide number 14 is a very schematic
+picture of uh atoms moving around
+
+ align:start position:0%
+picture of uh atoms moving around
+ 
+
+ align:start position:0%
+picture of uh atoms moving around
+between planes in a lattice and so uh
+
+ align:start position:0%
+between planes in a lattice and so uh
+ 
+
+ align:start position:0%
+between planes in a lattice and so uh
+let's use this picture to get some
+
+ align:start position:0%
+let's use this picture to get some
+ 
+
+ align:start position:0%
+let's use this picture to get some
+physical insight into the diffusion
+
+ align:start position:0%
+physical insight into the diffusion
+ 
+
+ align:start position:0%
+physical insight into the diffusion
+process so each plane here is sort of
+
+ align:start position:0%
+process so each plane here is sort of
+ 
+
+ align:start position:0%
+process so each plane here is sort of
+indicated by a vertical bar and 0 1 2 3
+
+ align:start position:0%
+indicated by a vertical bar and 0 1 2 3
+ 
+
+ align:start position:0%
+indicated by a vertical bar and 0 1 2 3
+4 and the distance between these planes
+
+ align:start position:0%
+4 and the distance between these planes
+ 
+
+ align:start position:0%
+4 and the distance between these planes
+is given by the distance Delta X as
+
+ align:start position:0%
+is given by the distance Delta X as
+ 
+
+ align:start position:0%
+is given by the distance Delta X as
+units of
+
+ align:start position:0%
+units of
+ 
+
+ align:start position:0%
+units of
+length and uh in subi here so n0 N1 and
+
+ align:start position:0%
+length and uh in subi here so n0 N1 and
+ 
+
+ align:start position:0%
+length and uh in subi here so n0 N1 and
+two is the planer Atomic density uh of
+
+ align:start position:0%
+two is the planer Atomic density uh of
+ 
+
+ align:start position:0%
+two is the planer Atomic density uh of
+the I plant so it's the number of atoms
+
+ align:start position:0%
+the I plant so it's the number of atoms
+ 
+
+ align:start position:0%
+the I plant so it's the number of atoms
+per square centimeter um in in a given
+
+ align:start position:0%
+per square centimeter um in in a given
+ 
+
+ align:start position:0%
+per square centimeter um in in a given
+plane and um
+
+ align:start position:0%
+plane and um
+ 
+
+ align:start position:0%
+plane and um
+cabi uh has volume concentration you
+
+ align:start position:0%
+cabi uh has volume concentration you
+ 
+
+ align:start position:0%
+cabi uh has volume concentration you
+it's it's the average volume
+
+ align:start position:0%
+it's it's the average volume
+ 
+
+ align:start position:0%
+it's it's the average volume
+concentration at any point so you can
+
+ align:start position:0%
+concentration at any point so you can
+ 
+
+ align:start position:0%
+concentration at any point so you can
+calculate you can get between the two c
+
+ align:start position:0%
+calculate you can get between the two c
+ 
+
+ align:start position:0%
+calculate you can get between the two c
+is just n subi over Delta X or n subi is
+
+ align:start position:0%
+is just n subi over Delta X or n subi is
+ 
+
+ align:start position:0%
+is just n subi over Delta X or n subi is
+just C subi * Delta
+
+ align:start position:0%
+just C subi * Delta
+ 
+
+ align:start position:0%
+just C subi * Delta
+X okay so let's go on to slide 15 or at
+
+ align:start position:0%
+X okay so let's go on to slide 15 or at
+ 
+
+ align:start position:0%
+X okay so let's go on to slide 15 or at
+the top I just reproduced that picture
+
+ align:start position:0%
+the top I just reproduced that picture
+ 
+
+ align:start position:0%
+the top I just reproduced that picture
+soly smaller version of it um and just
+
+ align:start position:0%
+soly smaller version of it um and just
+ 
+
+ align:start position:0%
+soly smaller version of it um and just
+reminding ourselves the the relationship
+
+ align:start position:0%
+reminding ourselves the the relationship
+ 
+
+ align:start position:0%
+reminding ourselves the the relationship
+between CI and
+
+ align:start position:0%
+between CI and
+ 
+
+ align:start position:0%
+between CI and
+ni now as we're looking at this lattice
+
+ align:start position:0%
+ni now as we're looking at this lattice
+ 
+
+ align:start position:0%
+ni now as we're looking at this lattice
+we know that the atoms are relatively
+
+ align:start position:0%
+we know that the atoms are relatively
+ 
+
+ align:start position:0%
+we know that the atoms are relatively
+fixed in the lattice but they do vibrate
+
+ align:start position:0%
+fixed in the lattice but they do vibrate
+ 
+
+ align:start position:0%
+fixed in the lattice but they do vibrate
+about their average position in a plane
+
+ align:start position:0%
+about their average position in a plane
+ 
+
+ align:start position:0%
+about their average position in a plane
+where average position and they're
+
+ align:start position:0%
+where average position and they're
+ 
+
+ align:start position:0%
+where average position and they're
+vibrating at some frequency V subd which
+
+ align:start position:0%
+vibrating at some frequency V subd which
+ 
+
+ align:start position:0%
+vibrating at some frequency V subd which
+is called the uh Debby frequency and
+
+ align:start position:0%
+is called the uh Debby frequency and
+ 
+
+ align:start position:0%
+is called the uh Debby frequency and
+that's that
+
+ align:start position:0%
+that's that
+ 
+
+ align:start position:0%
+that's that
+number is typically on the a of about 10
+
+ align:start position:0%
+number is typically on the a of about 10
+ 
+
+ align:start position:0%
+number is typically on the a of about 10
+to 13th uh per second so it's pretty
+
+ align:start position:0%
+to 13th uh per second so it's pretty
+ 
+
+ align:start position:0%
+to 13th uh per second so it's pretty
+high frequency they're vibrating about
+
+ align:start position:0%
+high frequency they're vibrating about
+ 
+
+ align:start position:0%
+high frequency they're vibrating about
+their average blatus positions at a
+
+ align:start position:0%
+their average blatus positions at a
+ 
+
+ align:start position:0%
+their average blatus positions at a
+finite
+
+ align:start position:0%
+finite
+ 
+
+ align:start position:0%
+finite
+temperature uh now sometimes in during
+
+ align:start position:0%
+temperature uh now sometimes in during
+ 
+
+ align:start position:0%
+temperature uh now sometimes in during
+this vibration an atom will actually be
+
+ align:start position:0%
+this vibration an atom will actually be
+ 
+
+ align:start position:0%
+this vibration an atom will actually be
+able to surmount the energy barrier uh
+
+ align:start position:0%
+able to surmount the energy barrier uh
+ 
+
+ align:start position:0%
+able to surmount the energy barrier uh
+that exists in going from one last
+
+ align:start position:0%
+that exists in going from one last
+ 
+
+ align:start position:0%
+that exists in going from one last
+position to the next or one plane to the
+
+ align:start position:0%
+position to the next or one plane to the
+ 
+
+ align:start position:0%
+position to the next or one plane to the
+next so and it will actually be able to
+
+ align:start position:0%
+next so and it will actually be able to
+ 
+
+ align:start position:0%
+next so and it will actually be able to
+hop to an adjacent plane and there's an
+
+ align:start position:0%
+hop to an adjacent plane and there's an
+ 
+
+ align:start position:0%
+hop to an adjacent plane and there's an
+energy barrier which we'll call an Isa B
+
+ align:start position:0%
+energy barrier which we'll call an Isa B
+ 
+
+ align:start position:0%
+energy barrier which we'll call an Isa B
+uh to get from one plane to the
+
+ align:start position:0%
+uh to get from one plane to the
+ 
+
+ align:start position:0%
+uh to get from one plane to the
+next and uh this hopping frequency we
+
+ align:start position:0%
+next and uh this hopping frequency we
+ 
+
+ align:start position:0%
+next and uh this hopping frequency we
+call um
+
+ align:start position:0%
+call um
+ 
+
+ align:start position:0%
+call um
+BNB uh which is just a duy frequency VD
+
+ align:start position:0%
+BNB uh which is just a duy frequency VD
+ 
+
+ align:start position:0%
+BNB uh which is just a duy frequency VD
+that's the vibration frequency times a
+
+ align:start position:0%
+that's the vibration frequency times a
+ 
+
+ align:start position:0%
+that's the vibration frequency times a
+boltman factor exponential the minus uh
+
+ align:start position:0%
+boltman factor exponential the minus uh
+ 
+
+ align:start position:0%
+boltman factor exponential the minus uh
+e that's the energy barrier over
+
+ align:start position:0%
+e that's the energy barrier over
+ 
+
+ align:start position:0%
+e that's the energy barrier over
+KT so this V subb small V subb gives us
+
+ align:start position:0%
+KT so this V subb small V subb gives us
+ 
+
+ align:start position:0%
+KT so this V subb small V subb gives us
+an idea of the frequency of hopping from
+
+ align:start position:0%
+an idea of the frequency of hopping from
+ 
+
+ align:start position:0%
+an idea of the frequency of hopping from
+atoms from one plane to the next and
+
+ align:start position:0%
+atoms from one plane to the next and
+ 
+
+ align:start position:0%
+atoms from one plane to the next and
+what we assume in this derivation is
+
+ align:start position:0%
+what we assume in this derivation is
+ 
+
+ align:start position:0%
+what we assume in this derivation is
+that there's equal probability of
+
+ align:start position:0%
+that there's equal probability of
+ 
+
+ align:start position:0%
+that there's equal probability of
+jumping right or left because this is a
+
+ align:start position:0%
+jumping right or left because this is a
+ 
+
+ align:start position:0%
+jumping right or left because this is a
+random process um so if we look at any
+
+ align:start position:0%
+random process um so if we look at any
+ 
+
+ align:start position:0%
+random process um so if we look at any
+given plane we can say um the number of
+
+ align:start position:0%
+given plane we can say um the number of
+ 
+
+ align:start position:0%
+given plane we can say um the number of
+atoms jumping to the right of that plane
+
+ align:start position:0%
+atoms jumping to the right of that plane
+ 
+
+ align:start position:0%
+atoms jumping to the right of that plane
+per unit time is just VB over two times
+
+ align:start position:0%
+per unit time is just VB over two times
+ 
+
+ align:start position:0%
+per unit time is just VB over two times
+the number of atoms in that plane and
+
+ align:start position:0%
+the number of atoms in that plane and
+ 
+
+ align:start position:0%
+the number of atoms in that plane and
+half going go right number jumping left
+
+ align:start position:0%
+half going go right number jumping left
+ 
+
+ align:start position:0%
+half going go right number jumping left
+per unit time is just BB over two times
+
+ align:start position:0%
+per unit time is just BB over two times
+ 
+
+ align:start position:0%
+per unit time is just BB over two times
+the number in PL n so those two are
+
+ align:start position:0%
+the number in PL n so those two are
+ 
+
+ align:start position:0%
+the number in PL n so those two are
+equal um now if we do the bookkeeping
+
+ align:start position:0%
+equal um now if we do the bookkeeping
+ 
+
+ align:start position:0%
+equal um now if we do the bookkeeping
+and say look at the number of atoms
+
+ align:start position:0%
+and say look at the number of atoms
+ 
+
+ align:start position:0%
+and say look at the number of atoms
+crossing a plane uh the particular plane
+
+ align:start position:0%
+crossing a plane uh the particular plane
+ 
+
+ align:start position:0%
+crossing a plane uh the particular plane
+at I equals 2 in the above diagram so
+
+ align:start position:0%
+at I equals 2 in the above diagram so
+ 
+
+ align:start position:0%
+at I equals 2 in the above diagram so
+the plane labeled two uh number of atoms
+
+ align:start position:0%
+the plane labeled two uh number of atoms
+ 
+
+ align:start position:0%
+the plane labeled two uh number of atoms
+Crossing that plane per unit time well
+
+ align:start position:0%
+Crossing that plane per unit time well
+ 
+
+ align:start position:0%
+Crossing that plane per unit time well
+we can just uh write that as a
+
+ align:start position:0%
+we can just uh write that as a
+ 
+
+ align:start position:0%
+we can just uh write that as a
+flux and F an equation the bottom well
+
+ align:start position:0%
+flux and F an equation the bottom well
+ 
+
+ align:start position:0%
+flux and F an equation the bottom well
+that's just going to be uh the number of
+
+ align:start position:0%
+that's just going to be uh the number of
+ 
+
+ align:start position:0%
+that's just going to be uh the number of
+atoms um basically per unit time uh
+
+ align:start position:0%
+atoms um basically per unit time uh
+ 
+
+ align:start position:0%
+atoms um basically per unit time uh
+jumping to the right minus those uh
+
+ align:start position:0%
+jumping to the right minus those uh
+ 
+
+ align:start position:0%
+jumping to the right minus those uh
+jumping to the left uh so you write that
+
+ align:start position:0%
+jumping to the left uh so you write that
+ 
+
+ align:start position:0%
+jumping to the left uh so you write that
+as V minus VB over 2 N2 minus
+
+ align:start position:0%
+as V minus VB over 2 N2 minus
+ 
+
+ align:start position:0%
+as V minus VB over 2 N2 minus
+N1 again assuming equal probability
+
+ align:start position:0%
+N1 again assuming equal probability
+ 
+
+ align:start position:0%
+N1 again assuming equal probability
+going uh either way um so uh and then
+
+ align:start position:0%
+going uh either way um so uh and then
+ 
+
+ align:start position:0%
+going uh either way um so uh and then
+you can convert that the difference
+
+ align:start position:0%
+you can convert that the difference
+ 
+
+ align:start position:0%
+you can convert that the difference
+between uh Atomic uh density and uh
+
+ align:start position:0%
+between uh Atomic uh density and uh
+ 
+
+ align:start position:0%
+between uh Atomic uh density and uh
+numbered adoms per cubic centimeter just
+
+ align:start position:0%
+numbered adoms per cubic centimeter just
+ 
+
+ align:start position:0%
+numbered adoms per cubic centimeter just
+by multiplying using the definition of n
+
+ align:start position:0%
+by multiplying using the definition of n
+ 
+
+ align:start position:0%
+by multiplying using the definition of n
+is equal to Delta x *
+
+ align:start position:0%
+is equal to Delta x *
+ 
+
+ align:start position:0%
+is equal to Delta x *
+concentration you have then expression
+
+ align:start position:0%
+concentration you have then expression
+ 
+
+ align:start position:0%
+concentration you have then expression
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+flux um Crossing plane IAL
+
+ align:start position:0%
+flux um Crossing plane IAL
+ 
+
+ align:start position:0%
+flux um Crossing plane IAL
+2 and then you multiply and divide by
+
+ align:start position:0%
+2 and then you multiply and divide by
+ 
+
+ align:start position:0%
+2 and then you multiply and divide by
+Delta X and you end up with this
+
+ align:start position:0%
+Delta X and you end up with this
+ 
+
+ align:start position:0%
+Delta X and you end up with this
+equation that this flux is equal to
+
+ align:start position:0%
+equation that this flux is equal to
+ 
+
+ align:start position:0%
+equation that this flux is equal to
+looking the right hand side minus bb/ 2
+
+ align:start position:0%
+looking the right hand side minus bb/ 2
+ 
+
+ align:start position:0%
+looking the right hand side minus bb/ 2
+Delta x^2 times the the uh Delta C over
+
+ align:start position:0%
+Delta x^2 times the the uh Delta C over
+ 
+
+ align:start position:0%
+Delta x^2 times the the uh Delta C over
+Delta X something that's starting to
+
+ align:start position:0%
+Delta X something that's starting to
+ 
+
+ align:start position:0%
+Delta X something that's starting to
+look like uh a slope so we immediately
+
+ align:start position:0%
+look like uh a slope so we immediately
+ 
+
+ align:start position:0%
+look like uh a slope so we immediately
+see some kind of fix law fix law here
+
+ align:start position:0%
+see some kind of fix law fix law here
+ 
+
+ align:start position:0%
+see some kind of fix law fix law here
+where a flux is related to a slope times
+
+ align:start position:0%
+where a flux is related to a slope times
+ 
+
+ align:start position:0%
+where a flux is related to a slope times
+something out in front that that is a
+
+ align:start position:0%
+something out in front that that is a
+ 
+
+ align:start position:0%
+something out in front that that is a
+constant so that's at the bottom of
+
+ align:start position:0%
+constant so that's at the bottom of
+ 
+
+ align:start position:0%
+constant so that's at the bottom of
+slide 15 let's go on to slide 16 and
+
+ align:start position:0%
+slide 15 let's go on to slide 16 and
+ 
+
+ align:start position:0%
+slide 15 let's go on to slide 16 and
+I've just repeated that equation that we
+
+ align:start position:0%
+I've just repeated that equation that we
+ 
+
+ align:start position:0%
+I've just repeated that equation that we
+just had but I added one more uh thing
+
+ align:start position:0%
+just had but I added one more uh thing
+ 
+
+ align:start position:0%
+just had but I added one more uh thing
+on the right uh one more equality and we
+
+ align:start position:0%
+on the right uh one more equality and we
+ 
+
+ align:start position:0%
+on the right uh one more equality and we
+set that flux equal to diffusivity a
+
+ align:start position:0%
+set that flux equal to diffusivity a
+ 
+
+ align:start position:0%
+set that flux equal to diffusivity a
+number D times the slope Delta C over
+
+ align:start position:0%
+number D times the slope Delta C over
+ 
+
+ align:start position:0%
+number D times the slope Delta C over
+Delta X where we Define the diusivity in
+
+ align:start position:0%
+Delta X where we Define the diusivity in
+ 
+
+ align:start position:0%
+Delta X where we Define the diusivity in
+this particular equation to be equal to
+
+ align:start position:0%
+this particular equation to be equal to
+ 
+
+ align:start position:0%
+this particular equation to be equal to
+uh the VB over 2 * Delta
+
+ align:start position:0%
+uh the VB over 2 * Delta
+ 
+
+ align:start position:0%
+uh the VB over 2 * Delta
+x^2 so there is fixed fixed first law
+
+ align:start position:0%
+x^2 so there is fixed fixed first law
+ 
+
+ align:start position:0%
+x^2 so there is fixed fixed first law
+the flux is equal to minus a diffusivity
+
+ align:start position:0%
+the flux is equal to minus a diffusivity
+ 
+
+ align:start position:0%
+the flux is equal to minus a diffusivity
+a constant number times Delta C over
+
+ align:start position:0%
+a constant number times Delta C over
+ 
+
+ align:start position:0%
+a constant number times Delta C over
+Delta X and the diffusivity has some
+
+ align:start position:0%
+Delta X and the diffusivity has some
+ 
+
+ align:start position:0%
+Delta X and the diffusivity has some
+atonic
+
+ align:start position:0%
+atonic
+ 
+
+ align:start position:0%
+atonic
+scale um mechanisms view to it in fact
+
+ align:start position:0%
+scale um mechanisms view to it in fact
+ 
+
+ align:start position:0%
+scale um mechanisms view to it in fact
+it's uh proportional to the jump
+
+ align:start position:0%
+it's uh proportional to the jump
+ 
+
+ align:start position:0%
+it's uh proportional to the jump
+frequency uh V subd uh and therefore
+
+ align:start position:0%
+frequency uh V subd uh and therefore
+ 
+
+ align:start position:0%
+frequency uh V subd uh and therefore
+proportional being related to the energy
+
+ align:start position:0%
+proportional being related to the energy
+ 
+
+ align:start position:0%
+proportional being related to the energy
+bar
+
+ align:start position:0%
+bar
+ 
+
+ align:start position:0%
+bar
+to hop between adjacent positions or
+
+ align:start position:0%
+to hop between adjacent positions or
+ 
+
+ align:start position:0%
+to hop between adjacent positions or
+adjacent clients uh so gives you some
+
+ align:start position:0%
+adjacent clients uh so gives you some
+ 
+
+ align:start position:0%
+adjacent clients uh so gives you some
+idea of what at the atomic scale what
+
+ align:start position:0%
+idea of what at the atomic scale what
+ 
+
+ align:start position:0%
+idea of what at the atomic scale what
+goes into to determining the diffusivity
+
+ align:start position:0%
+goes into to determining the diffusivity
+ 
+
+ align:start position:0%
+goes into to determining the diffusivity
+view okay in addition to giving us an
+
+ align:start position:0%
+view okay in addition to giving us an
+ 
+
+ align:start position:0%
+view okay in addition to giving us an
+atomic scale view we can actually use
+
+ align:start position:0%
+atomic scale view we can actually use
+ 
+
+ align:start position:0%
+atomic scale view we can actually use
+this type of formalism to go ahead and
+
+ align:start position:0%
+this type of formalism to go ahead and
+ 
+
+ align:start position:0%
+this type of formalism to go ahead and
+derive uh a numerical solution to uh fix
+
+ align:start position:0%
+derive uh a numerical solution to uh fix
+ 
+
+ align:start position:0%
+derive uh a numerical solution to uh fix
+equation so let's go on to to do that
+
+ align:start position:0%
+equation so let's go on to to do that
+ 
+
+ align:start position:0%
+equation so let's go on to to do that
+we'll go on to slide number 17 which um
+
+ align:start position:0%
+we'll go on to slide number 17 which um
+ 
+
+ align:start position:0%
+we'll go on to slide number 17 which um
+a slightly different sketch but the the
+
+ align:start position:0%
+a slightly different sketch but the the
+ 
+
+ align:start position:0%
+a slightly different sketch but the the
+exact same ideas of what we're going to
+
+ align:start position:0%
+exact same ideas of what we're going to
+ 
+
+ align:start position:0%
+exact same ideas of what we're going to
+be going through uh and what I'm showing
+
+ align:start position:0%
+be going through uh and what I'm showing
+ 
+
+ align:start position:0%
+be going through uh and what I'm showing
+uh on the left- hand side in the bottom
+
+ align:start position:0%
+uh on the left- hand side in the bottom
+ 
+
+ align:start position:0%
+uh on the left- hand side in the bottom
+is a plot of concentration as a function
+
+ align:start position:0%
+is a plot of concentration as a function
+ 
+
+ align:start position:0%
+is a plot of concentration as a function
+of X so distance and let's say has some
+
+ align:start position:0%
+of X so distance and let's say has some
+ 
+
+ align:start position:0%
+of X so distance and let's say has some
+shape this dark uh dark decreasing uh
+
+ align:start position:0%
+shape this dark uh dark decreasing uh
+ 
+
+ align:start position:0%
+shape this dark uh dark decreasing uh
+black line and it's decreasing uh from
+
+ align:start position:0%
+black line and it's decreasing uh from
+ 
+
+ align:start position:0%
+black line and it's decreasing uh from
+left to to right and what we're going to
+
+ align:start position:0%
+left to to right and what we're going to
+ 
+
+ align:start position:0%
+left to to right and what we're going to
+do is we're going to discretize this let
+
+ align:start position:0%
+do is we're going to discretize this let
+ 
+
+ align:start position:0%
+do is we're going to discretize this let
+me look at discrete uh positions in
+
+ align:start position:0%
+me look at discrete uh positions in
+ 
+
+ align:start position:0%
+me look at discrete uh positions in
+Space X and the concentration C 0 C1 and
+
+ align:start position:0%
+Space X and the concentration C 0 C1 and
+ 
+
+ align:start position:0%
+Space X and the concentration C 0 C1 and
+C2 and the spacing between those planes
+
+ align:start position:0%
+C2 and the spacing between those planes
+ 
+
+ align:start position:0%
+C2 and the spacing between those planes
+is going to be a constant just like we
+
+ align:start position:0%
+is going to be a constant just like we
+ 
+
+ align:start position:0%
+is going to be a constant just like we
+used before uh Delta
+
+ align:start position:0%
+used before uh Delta
+ 
+
+ align:start position:0%
+used before uh Delta
+X and so what we're going to look at uh
+
+ align:start position:0%
+X and so what we're going to look at uh
+ 
+
+ align:start position:0%
+X and so what we're going to look at uh
+is in the time interval delta T a
+
+ align:start position:0%
+is in the time interval delta T a
+ 
+
+ align:start position:0%
+is in the time interval delta T a
+certain time interval Delta 2 uh what is
+
+ align:start position:0%
+certain time interval Delta 2 uh what is
+ 
+
+ align:start position:0%
+certain time interval Delta 2 uh what is
+the number of atoms crossing a certain
+
+ align:start position:0%
+the number of atoms crossing a certain
+ 
+
+ align:start position:0%
+the number of atoms crossing a certain
+plane per unit area and we call that to
+
+ align:start position:0%
+plane per unit area and we call that to
+ 
+
+ align:start position:0%
+plane per unit area and we call that to
+the plane R which we had labeled R above
+
+ align:start position:0%
+the plane R which we had labeled R above
+ 
+
+ align:start position:0%
+the plane R which we had labeled R above
+Q subr it's just the flux F subr time
+
+ align:start position:0%
+Q subr it's just the flux F subr time
+ 
+
+ align:start position:0%
+Q subr it's just the flux F subr time
+delta T that's the number of atoms
+
+ align:start position:0%
+delta T that's the number of atoms
+ 
+
+ align:start position:0%
+delta T that's the number of atoms
+crossing the unit area in a given uh
+
+ align:start position:0%
+crossing the unit area in a given uh
+ 
+
+ align:start position:0%
+crossing the unit area in a given uh
+time interval that just basically is
+
+ align:start position:0%
+time interval that just basically is
+ 
+
+ align:start position:0%
+time interval that just basically is
+comes from the definition of what flux
+
+ align:start position:0%
+comes from the definition of what flux
+ 
+
+ align:start position:0%
+comes from the definition of what flux
+is and um we then can write in for the
+
+ align:start position:0%
+is and um we then can write in for the
+ 
+
+ align:start position:0%
+is and um we then can write in for the
+flux uh the flux is just the diffusivity
+
+ align:start position:0%
+flux uh the flux is just the diffusivity
+ 
+
+ align:start position:0%
+flux uh the flux is just the diffusivity
+of D times the concentration difference
+
+ align:start position:0%
+of D times the concentration difference
+ 
+
+ align:start position:0%
+of D times the concentration difference
+across that
+
+ align:start position:0%
+across that
+ 
+
+ align:start position:0%
+across that
+plane across plane R well the
+
+ align:start position:0%
+plane across plane R well the
+ 
+
+ align:start position:0%
+plane across plane R well the
+concentration difference across plane R
+
+ align:start position:0%
+concentration difference across plane R
+ 
+
+ align:start position:0%
+concentration difference across plane R
+is C1 minus C / Delta X so we can uh
+
+ align:start position:0%
+is C1 minus C / Delta X so we can uh
+ 
+
+ align:start position:0%
+is C1 minus C / Delta X so we can uh
+approximate that way the flux Crossing
+
+ align:start position:0%
+approximate that way the flux Crossing
+ 
+
+ align:start position:0%
+approximate that way the flux Crossing
+plane R what's the flux Crossing plane s
+
+ align:start position:0%
+plane R what's the flux Crossing plane s
+ 
+
+ align:start position:0%
+plane R what's the flux Crossing plane s
+well we do the exact same thing or the
+
+ align:start position:0%
+well we do the exact same thing or the
+ 
+
+ align:start position:0%
+well we do the exact same thing or the
+number of atoms Crossing plane s it's
+
+ align:start position:0%
+number of atoms Crossing plane s it's
+ 
+
+ align:start position:0%
+number of atoms Crossing plane s it's
+just the diffusivity times Delta P times
+
+ align:start position:0%
+just the diffusivity times Delta P times
+ 
+
+ align:start position:0%
+just the diffusivity times Delta P times
+this time we subtract C2 minus C1 over
+
+ align:start position:0%
+this time we subtract C2 minus C1 over
+ 
+
+ align:start position:0%
+this time we subtract C2 minus C1 over
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+X so we can then do some bookkeeping and
+
+ align:start position:0%
+X so we can then do some bookkeeping and
+ 
+
+ align:start position:0%
+X so we can then do some bookkeeping and
+calculate the knit number of atoms
+
+ align:start position:0%
+calculate the knit number of atoms
+ 
+
+ align:start position:0%
+calculate the knit number of atoms
+accumulated in that shaded region
+
+ align:start position:0%
+accumulated in that shaded region
+ 
+
+ align:start position:0%
+accumulated in that shaded region
+between plain R and plain s in the K in
+
+ align:start position:0%
+between plain R and plain s in the K in
+ 
+
+ align:start position:0%
+between plain R and plain s in the K in
+delta T it's just um uh QR minus Qs and
+
+ align:start position:0%
+delta T it's just um uh QR minus Qs and
+ 
+
+ align:start position:0%
+delta T it's just um uh QR minus Qs and
+we just subtract these two expressions
+
+ align:start position:0%
+we just subtract these two expressions
+ 
+
+ align:start position:0%
+we just subtract these two expressions
+and you see what you end up with is is
+
+ align:start position:0%
+and you see what you end up with is is
+ 
+
+ align:start position:0%
+and you see what you end up with is is
+equal to a
+
+ align:start position:0%
+equal to a
+ 
+
+ align:start position:0%
+equal to a
+diff time the time interval delta T
+
+ align:start position:0%
+diff time the time interval delta T
+ 
+
+ align:start position:0%
+diff time the time interval delta T
+times in parentheses the C - 2 C1 + C2
+
+ align:start position:0%
+times in parentheses the C - 2 C1 + C2
+ 
+
+ align:start position:0%
+times in parentheses the C - 2 C1 + C2
+that whole same quantity over Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X now if we divide that those that net
+
+ align:start position:0%
+X now if we divide that those that net
+ 
+
+ align:start position:0%
+X now if we divide that those that net
+gain in the number of atoms divided by
+
+ align:start position:0%
+gain in the number of atoms divided by
+ 
+
+ align:start position:0%
+gain in the number of atoms divided by
+Delta X is shown below that is the net
+
+ align:start position:0%
+Delta X is shown below that is the net
+ 
+
+ align:start position:0%
+Delta X is shown below that is the net
+gain in the concentration in that shaded
+
+ align:start position:0%
+gain in the concentration in that shaded
+ 
+
+ align:start position:0%
+gain in the concentration in that shaded
+region that's Delta C and that's just QR
+
+ align:start position:0%
+region that's Delta C and that's just QR
+ 
+
+ align:start position:0%
+region that's Delta C and that's just QR
+minus Qs that quantity divided by Delta
+
+ align:start position:0%
+minus Qs that quantity divided by Delta
+ 
+
+ align:start position:0%
+minus Qs that quantity divided by Delta
+x uh so I can uh substituting in QR
+
+ align:start position:0%
+x uh so I can uh substituting in QR
+ 
+
+ align:start position:0%
+x uh so I can uh substituting in QR
+minus Qs and you end up with the
+
+ align:start position:0%
+minus Qs and you end up with the
+ 
+
+ align:start position:0%
+minus Qs and you end up with the
+equation near the bottom which just says
+
+ align:start position:0%
+equation near the bottom which just says
+ 
+
+ align:start position:0%
+equation near the bottom which just says
+the net gain in the concentration Delta
+
+ align:start position:0%
+the net gain in the concentration Delta
+ 
+
+ align:start position:0%
+the net gain in the concentration Delta
+C in this shaded region is just
+
+ align:start position:0%
+C in this shaded region is just
+ 
+
+ align:start position:0%
+C in this shaded region is just
+diffusivity D time delta T times this
+
+ align:start position:0%
+diffusivity D time delta T times this
+ 
+
+ align:start position:0%
+diffusivity D time delta T times this
+quantity and parentheses which is
+
+ align:start position:0%
+quantity and parentheses which is
+ 
+
+ align:start position:0%
+quantity and parentheses which is
+related to the concentrations in those
+
+ align:start position:0%
+related to the concentrations in those
+ 
+
+ align:start position:0%
+related to the concentrations in those
+three regions divided by Delta
+
+ align:start position:0%
+three regions divided by Delta
+ 
+
+ align:start position:0%
+three regions divided by Delta
+x^2 so what it says is at a given point
+
+ align:start position:0%
+x^2 so what it says is at a given point
+ 
+
+ align:start position:0%
+x^2 so what it says is at a given point
+C1 in this Cur if I know the
+
+ align:start position:0%
+C1 in this Cur if I know the
+ 
+
+ align:start position:0%
+C1 in this Cur if I know the
+concentrations of the neighboring points
+
+ align:start position:0%
+concentrations of the neighboring points
+ 
+
+ align:start position:0%
+concentrations of the neighboring points
+so I know its neighbors I know the
+
+ align:start position:0%
+so I know its neighbors I know the
+ 
+
+ align:start position:0%
+so I know its neighbors I know the
+concentration at uh c0 and it's C2 you
+
+ align:start position:0%
+concentration at uh c0 and it's C2 you
+ 
+
+ align:start position:0%
+concentration at uh c0 and it's C2 you
+can calculate a new concentration after
+
+ align:start position:0%
+can calculate a new concentration after
+ 
+
+ align:start position:0%
+can calculate a new concentration after
+a certain time step delta T at C1 um
+
+ align:start position:0%
+a certain time step delta T at C1 um
+ 
+
+ align:start position:0%
+a certain time step delta T at C1 um
+just by knowing its neighbors um at this
+
+ align:start position:0%
+just by knowing its neighbors um at this
+ 
+
+ align:start position:0%
+just by knowing its neighbors um at this
+time step the concentration of its
+
+ align:start position:0%
+time step the concentration of its
+ 
+
+ align:start position:0%
+time step the concentration of its
+neighbors um so uh if we go on to slide
+
+ align:start position:0%
+neighbors um so uh if we go on to slide
+ 
+
+ align:start position:0%
+neighbors um so uh if we go on to slide
+number 18 we can then use that
+
+ align:start position:0%
+number 18 we can then use that
+ 
+
+ align:start position:0%
+number 18 we can then use that
+information to come up with something
+
+ align:start position:0%
+information to come up with something
+ 
+
+ align:start position:0%
+information to come up with something
+called an explicit finite difference
+
+ align:start position:0%
+called an explicit finite difference
+ 
+
+ align:start position:0%
+called an explicit finite difference
+formula that's what the equation being
+
+ align:start position:0%
+formula that's what the equation being
+ 
+
+ align:start position:0%
+formula that's what the equation being
+shown near the top of of the slide 18 uh
+
+ align:start position:0%
+shown near the top of of the slide 18 uh
+ 
+
+ align:start position:0%
+shown near the top of of the slide 18 uh
+what you're saying is that the
+
+ align:start position:0%
+what you're saying is that the
+ 
+
+ align:start position:0%
+what you're saying is that the
+concentration at any given point I in in
+
+ align:start position:0%
+concentration at any given point I in in
+ 
+
+ align:start position:0%
+concentration at any given point I in in
+one of these
+
+ align:start position:0%
+one of these
+ 
+
+ align:start position:0%
+one of these
+slabs at a new time t plus delta T so
+
+ align:start position:0%
+slabs at a new time t plus delta T so
+ 
+
+ align:start position:0%
+slabs at a new time t plus delta T so
+we're going to evolve this profile over
+
+ align:start position:0%
+we're going to evolve this profile over
+ 
+
+ align:start position:0%
+we're going to evolve this profile over
+time so C plus on the leftand
+
+ align:start position:0%
+time so C plus on the leftand
+ 
+
+ align:start position:0%
+time so C plus on the leftand
+side uh is equal to the concentration at
+
+ align:start position:0%
+side uh is equal to the concentration at
+ 
+
+ align:start position:0%
+side uh is equal to the concentration at
+time T so one interval below before that
+
+ align:start position:0%
+time T so one interval below before that
+ 
+
+ align:start position:0%
+time T so one interval below before that
+whatever it was before plus we add in
+
+ align:start position:0%
+whatever it was before plus we add in
+ 
+
+ align:start position:0%
+whatever it was before plus we add in
+this uh this difference this term on the
+
+ align:start position:0%
+this uh this difference this term on the
+ 
+
+ align:start position:0%
+this uh this difference this term on the
+right that gives a change in the
+
+ align:start position:0%
+right that gives a change in the
+ 
+
+ align:start position:0%
+right that gives a change in the
+concentration in the I slab after a Time
+
+ align:start position:0%
+concentration in the I slab after a Time
+ 
+
+ align:start position:0%
+concentration in the I slab after a Time
+step delta T and that term is just D the
+
+ align:start position:0%
+step delta T and that term is just D the
+ 
+
+ align:start position:0%
+step delta T and that term is just D the
+diffusivity delta T / Delta f^ 2times
+
+ align:start position:0%
+diffusivity delta T / Delta f^ 2times
+ 
+
+ align:start position:0%
+diffusivity delta T / Delta f^ 2times
+the quantity parentheses where again the
+
+ align:start position:0%
+the quantity parentheses where again the
+ 
+
+ align:start position:0%
+the quantity parentheses where again the
+quantity parentheses in order evaluated
+
+ align:start position:0%
+quantity parentheses in order evaluated
+ 
+
+ align:start position:0%
+quantity parentheses in order evaluated
+at any point C all I need to know is the
+
+ align:start position:0%
+at any point C all I need to know is the
+ 
+
+ align:start position:0%
+at any point C all I need to know is the
+concentration at that point and the
+
+ align:start position:0%
+concentration at that point and the
+ 
+
+ align:start position:0%
+concentration at that point and the
+concentration it's two nearest
+
+ align:start position:0%
+concentration it's two nearest
+ 
+
+ align:start position:0%
+concentration it's two nearest
+Neighbors in in whatever way that we've
+
+ align:start position:0%
+Neighbors in in whatever way that we've
+ 
+
+ align:start position:0%
+Neighbors in in whatever way that we've
+discretized we've discretized this
+
+ align:start position:0%
+discretized we've discretized this
+ 
+
+ align:start position:0%
+discretized we've discretized this
+continuous function into uh little
+
+ align:start position:0%
+continuous function into uh little
+ 
+
+ align:start position:0%
+continuous function into uh little
+intervals Delta
+
+ align:start position:0%
+intervals Delta
+ 
+
+ align:start position:0%
+intervals Delta
+X so that is a an explicit formula you
+
+ align:start position:0%
+X so that is a an explicit formula you
+ 
+
+ align:start position:0%
+X so that is a an explicit formula you
+can use to evolve a a concentration
+
+ align:start position:0%
+can use to evolve a a concentration
+ 
+
+ align:start position:0%
+can use to evolve a a concentration
+profile um in shape over time and if you
+
+ align:start position:0%
+profile um in shape over time and if you
+ 
+
+ align:start position:0%
+profile um in shape over time and if you
+look at it for a few minutes you can
+
+ align:start position:0%
+look at it for a few minutes you can
+ 
+
+ align:start position:0%
+look at it for a few minutes you can
+notice the similarity of that difference
+
+ align:start position:0%
+notice the similarity of that difference
+ 
+
+ align:start position:0%
+notice the similarity of that difference
+formula to the differential equation for
+
+ align:start position:0%
+formula to the differential equation for
+ 
+
+ align:start position:0%
+formula to the differential equation for
+diffusion which uh if you take the the
+
+ align:start position:0%
+diffusion which uh if you take the the
+ 
+
+ align:start position:0%
+diffusion which uh if you take the the
+partial uh partial G on this equation
+
+ align:start position:0%
+partial uh partial G on this equation
+ 
+
+ align:start position:0%
+partial uh partial G on this equation
+shown in the center and lo it over the
+
+ align:start position:0%
+shown in the center and lo it over the
+ 
+
+ align:start position:0%
+shown in the center and lo it over the
+right hand side you can see that partial
+
+ align:start position:0%
+right hand side you can see that partial
+ 
+
+ align:start position:0%
+right hand side you can see that partial
+C is equal to some constant D times a
+
+ align:start position:0%
+C is equal to some constant D times a
+ 
+
+ align:start position:0%
+C is equal to some constant D times a
+second derivative of concentration with
+
+ align:start position:0%
+second derivative of concentration with
+ 
+
+ align:start position:0%
+second derivative of concentration with
+respect to X and in fact this partial um
+
+ align:start position:0%
+respect to X and in fact this partial um
+ 
+
+ align:start position:0%
+respect to X and in fact this partial um
+second derivative of C with respect to X
+
+ align:start position:0%
+second derivative of C with respect to X
+ 
+
+ align:start position:0%
+second derivative of C with respect to X
+it can be numerically evaluated as the
+
+ align:start position:0%
+it can be numerically evaluated as the
+ 
+
+ align:start position:0%
+it can be numerically evaluated as the
+term in the first equation on on on
+
+ align:start position:0%
+term in the first equation on on on
+ 
+
+ align:start position:0%
+term in the first equation on on on
+slide 18 on the right hand side that is
+
+ align:start position:0%
+slide 18 on the right hand side that is
+ 
+
+ align:start position:0%
+slide 18 on the right hand side that is
+a numerical solution to that
+
+ align:start position:0%
+a numerical solution to that
+ 
+
+ align:start position:0%
+a numerical solution to that
+differential
+
+ align:start position:0%
+differential
+ 
+
+ align:start position:0%
+differential
+equation and um I won't derive it here
+
+ align:start position:0%
+equation and um I won't derive it here
+ 
+
+ align:start position:0%
+equation and um I won't derive it here
+if you go back to crank's book or any of
+
+ align:start position:0%
+if you go back to crank's book or any of
+ 
+
+ align:start position:0%
+if you go back to crank's book or any of
+the books on uh uh numerical methods and
+
+ align:start position:0%
+the books on uh uh numerical methods and
+ 
+
+ align:start position:0%
+the books on uh uh numerical methods and
+you find that uh the method is
+
+ align:start position:0%
+you find that uh the method is
+ 
+
+ align:start position:0%
+you find that uh the method is
+numerically stable so it works from a
+
+ align:start position:0%
+numerically stable so it works from a
+ 
+
+ align:start position:0%
+numerically stable so it works from a
+numerical point of view it gives
+
+ align:start position:0%
+numerical point of view it gives
+ 
+
+ align:start position:0%
+numerical point of view it gives
+reasonable
+
+ align:start position:0%
+reasonable
+ 
+
+ align:start position:0%
+reasonable
+answers for a particular condition we
+
+ align:start position:0%
+answers for a particular condition we
+ 
+
+ align:start position:0%
+answers for a particular condition we
+have when we're doing the solution we
+
+ align:start position:0%
+have when we're doing the solution we
+ 
+
+ align:start position:0%
+have when we're doing the solution we
+have a condition on a quantity R where
+
+ align:start position:0%
+have a condition on a quantity R where
+ 
+
+ align:start position:0%
+have a condition on a quantity R where
+this quantity R is is is what mult the
+
+ align:start position:0%
+this quantity R is is is what mult the
+ 
+
+ align:start position:0%
+this quantity R is is is what mult the
+plus uh the concentration change in a in
+
+ align:start position:0%
+plus uh the concentration change in a in
+ 
+
+ align:start position:0%
+plus uh the concentration change in a in
+in a slab at certain time step delta T
+
+ align:start position:0%
+in a slab at certain time step delta T
+ 
+
+ align:start position:0%
+in a slab at certain time step delta T
+that D delta T over Delta x^2 that
+
+ align:start position:0%
+that D delta T over Delta x^2 that
+ 
+
+ align:start position:0%
+that D delta T over Delta x^2 that
+multiplier has to be less than or equal
+
+ align:start position:0%
+multiplier has to be less than or equal
+ 
+
+ align:start position:0%
+multiplier has to be less than or equal
+to 1 12 if that multiplier gets too
+
+ align:start position:0%
+to 1 12 if that multiplier gets too
+ 
+
+ align:start position:0%
+to 1 12 if that multiplier gets too
+large the meth the whole method breaks
+
+ align:start position:0%
+large the meth the whole method breaks
+ 
+
+ align:start position:0%
+large the meth the whole method breaks
+down become unstable and you get
+
+ align:start position:0%
+down become unstable and you get
+ 
+
+ align:start position:0%
+down become unstable and you get
+nonsense Absolut um totally unmeaningful
+
+ align:start position:0%
+nonsense Absolut um totally unmeaningful
+ 
+
+ align:start position:0%
+nonsense Absolut um totally unmeaningful
+um Solutions so you need to keep need to
+
+ align:start position:0%
+um Solutions so you need to keep need to
+ 
+
+ align:start position:0%
+um Solutions so you need to keep need to
+adjust if you're doing this numerical
+
+ align:start position:0%
+adjust if you're doing this numerical
+ 
+
+ align:start position:0%
+adjust if you're doing this numerical
+make sure you adjust your time steps
+
+ align:start position:0%
+make sure you adjust your time steps
+ 
+
+ align:start position:0%
+make sure you adjust your time steps
+delta T to be small enough enough so
+
+ align:start position:0%
+delta T to be small enough enough so
+ 
+
+ align:start position:0%
+delta T to be small enough enough so
+that this
+
+ align:start position:0%
+that this
+ 
+
+ align:start position:0%
+that this
+holds um and uh your Delta X um to be be
+
+ align:start position:0%
+holds um and uh your Delta X um to be be
+ 
+
+ align:start position:0%
+holds um and uh your Delta X um to be be
+of appropriate size in delta T um so
+
+ align:start position:0%
+of appropriate size in delta T um so
+ 
+
+ align:start position:0%
+of appropriate size in delta T um so
+that you don't get yourself out of the
+
+ align:start position:0%
+that you don't get yourself out of the
+ 
+
+ align:start position:0%
+that you don't get yourself out of the
+um out of the
+
+ align:start position:0%
+um out of the
+ 
+
+ align:start position:0%
+um out of the
+physically um out of the numerically
+
+ align:start position:0%
+physically um out of the numerically
+ 
+
+ align:start position:0%
+physically um out of the numerically
+stable uh solution it's a very powerful
+
+ align:start position:0%
+stable uh solution it's a very powerful
+ 
+
+ align:start position:0%
+stable uh solution it's a very powerful
+technique it's very simple that's one of
+
+ align:start position:0%
+technique it's very simple that's one of
+ 
+
+ align:start position:0%
+technique it's very simple that's one of
+the nice things about it um and it's
+
+ align:start position:0%
+the nice things about it um and it's
+ 
+
+ align:start position:0%
+the nice things about it um and it's
+certainly going to be required to use
+
+ align:start position:0%
+certainly going to be required to use
+ 
+
+ align:start position:0%
+certainly going to be required to use
+some method numerical method uh when the
+
+ align:start position:0%
+some method numerical method uh when the
+ 
+
+ align:start position:0%
+some method numerical method uh when the
+diffusivity is not not a constant um
+
+ align:start position:0%
+diffusivity is not not a constant um
+ 
+
+ align:start position:0%
+diffusivity is not not a constant um
+um if you were to sit down you could
+
+ align:start position:0%
+um if you were to sit down you could
+ 
+
+ align:start position:0%
+um if you were to sit down you could
+write your own simple simulator using
+
+ align:start position:0%
+write your own simple simulator using
+ 
+
+ align:start position:0%
+write your own simple simulator using
+this very uh relatably uh easy to use a
+
+ align:start position:0%
+this very uh relatably uh easy to use a
+ 
+
+ align:start position:0%
+this very uh relatably uh easy to use a
+finite difference one um it is not the
+
+ align:start position:0%
+finite difference one um it is not the
+ 
+
+ align:start position:0%
+finite difference one um it is not the
+particular type of numerical method
+
+ align:start position:0%
+particular type of numerical method
+ 
+
+ align:start position:0%
+particular type of numerical method
+that's been that is being used in
+
+ align:start position:0%
+that's been that is being used in
+ 
+
+ align:start position:0%
+that's been that is being used in
+Supreme 4 Supreme 4 has a more
+
+ align:start position:0%
+Supreme 4 Supreme 4 has a more
+ 
+
+ align:start position:0%
+Supreme 4 Supreme 4 has a more
+sophisticated numerical solution method
+
+ align:start position:0%
+sophisticated numerical solution method
+ 
+
+ align:start position:0%
+sophisticated numerical solution method
+for diffusion equation um this is much
+
+ align:start position:0%
+for diffusion equation um this is much
+ 
+
+ align:start position:0%
+for diffusion equation um this is much
+more simplified this particular method
+
+ align:start position:0%
+more simplified this particular method
+ 
+
+ align:start position:0%
+more simplified this particular method
+it can be slow it has all of its own
+
+ align:start position:0%
+it can be slow it has all of its own
+ 
+
+ align:start position:0%
+it can be slow it has all of its own
+problems but the beauty of it is the
+
+ align:start position:0%
+problems but the beauty of it is the
+ 
+
+ align:start position:0%
+problems but the beauty of it is the
+Simplicity and just to give you an idea
+
+ align:start position:0%
+Simplicity and just to give you an idea
+ 
+
+ align:start position:0%
+Simplicity and just to give you an idea
+a of how one would would might use
+
+ align:start position:0%
+a of how one would would might use
+ 
+
+ align:start position:0%
+a of how one would would might use
+numerical Solutions uh to obtain num
+
+ align:start position:0%
+numerical Solutions uh to obtain num
+ 
+
+ align:start position:0%
+numerical Solutions uh to obtain num
+numerical methods to obtain Solutions of
+
+ align:start position:0%
+numerical methods to obtain Solutions of
+ 
+
+ align:start position:0%
+numerical methods to obtain Solutions of
+diffusion
+
+ align:start position:0%
+diffusion
+ 
+
+ align:start position:0%
+diffusion
+equos okay let's go on now to
+
+ align:start position:0%
+equos okay let's go on now to
+ 
+
+ align:start position:0%
+equos okay let's go on now to
+um uh slide number 19 what what I want
+
+ align:start position:0%
+um uh slide number 19 what what I want
+ 
+
+ align:start position:0%
+um uh slide number 19 what what I want
+to talk about at this point are from now
+
+ align:start position:0%
+to talk about at this point are from now
+ 
+
+ align:start position:0%
+to talk about at this point are from now
+on and this the rest of this lecture and
+
+ align:start position:0%
+on and this the rest of this lecture and
+ 
+
+ align:start position:0%
+on and this the rest of this lecture and
+the next couple of lectures will be the
+
+ align:start position:0%
+the next couple of lectures will be the
+ 
+
+ align:start position:0%
+the next couple of lectures will be the
+uh so-called mod modifications of pixel
+
+ align:start position:0%
+uh so-called mod modifications of pixel
+ 
+
+ align:start position:0%
+uh so-called mod modifications of pixel
+laws fix laws are introduced in a lot of
+
+ align:start position:0%
+laws fix laws are introduced in a lot of
+ 
+
+ align:start position:0%
+laws fix laws are introduced in a lot of
+basic courses um Material Science or or
+
+ align:start position:0%
+basic courses um Material Science or or
+ 
+
+ align:start position:0%
+basic courses um Material Science or or
+or physics um and uh when we are
+
+ align:start position:0%
+or physics um and uh when we are
+ 
+
+ align:start position:0%
+or physics um and uh when we are
+diffusing uh dolance in semiconductors
+
+ align:start position:0%
+diffusing uh dolance in semiconductors
+ 
+
+ align:start position:0%
+diffusing uh dolance in semiconductors
+in Practical
+
+ align:start position:0%
+in Practical
+ 
+
+ align:start position:0%
+in Practical
+cases there are a few a number of cases
+
+ align:start position:0%
+cases there are a few a number of cases
+ 
+
+ align:start position:0%
+cases there are a few a number of cases
+where uh fixed laws need to be modified
+
+ align:start position:0%
+where uh fixed laws need to be modified
+ 
+
+ align:start position:0%
+where uh fixed laws need to be modified
+to take into account uh the things that
+
+ align:start position:0%
+to take into account uh the things that
+ 
+
+ align:start position:0%
+to take into account uh the things that
+are really going on in semor processing
+
+ align:start position:0%
+are really going on in semor processing
+ 
+
+ align:start position:0%
+are really going on in semor processing
+and the first thing that we'll talk
+
+ align:start position:0%
+and the first thing that we'll talk
+ 
+
+ align:start position:0%
+and the first thing that we'll talk
+about here on slide 19 is so-called
+
+ align:start position:0%
+about here on slide 19 is so-called
+ 
+
+ align:start position:0%
+about here on slide 19 is so-called
+electric field effect
+
+ align:start position:0%
+electric field effect
+ 
+
+ align:start position:0%
+electric field effect
+and this occurs in the case when the
+
+ align:start position:0%
+and this occurs in the case when the
+ 
+
+ align:start position:0%
+and this occurs in the case when the
+doping
+
+ align:start position:0%
+doping
+ 
+
+ align:start position:0%
+doping
+concentration uh is uh is higher than
+
+ align:start position:0%
+concentration uh is uh is higher than
+ 
+
+ align:start position:0%
+concentration uh is uh is higher than
+insabi so uh insabi is intrinsic carrier
+
+ align:start position:0%
+insabi so uh insabi is intrinsic carrier
+ 
+
+ align:start position:0%
+insabi so uh insabi is intrinsic carrier
+concentration at a diffusion temperature
+
+ align:start position:0%
+concentration at a diffusion temperature
+ 
+
+ align:start position:0%
+concentration at a diffusion temperature
+again of a th inbi is close to mid10 to
+
+ align:start position:0%
+again of a th inbi is close to mid10 to
+ 
+
+ align:start position:0%
+again of a th inbi is close to mid10 to
+the 18th or so um if the doe
+
+ align:start position:0%
+the 18th or so um if the doe
+ 
+
+ align:start position:0%
+the 18th or so um if the doe
+concentration gets higher than that you
+
+ align:start position:0%
+concentration gets higher than that you
+ 
+
+ align:start position:0%
+concentration gets higher than that you
+can start to have um uh a
+
+ align:start position:0%
+can start to have um uh a
+ 
+
+ align:start position:0%
+can start to have um uh a
+non-uniformity in the um in the charge
+
+ align:start position:0%
+non-uniformity in the um in the charge
+ 
+
+ align:start position:0%
+non-uniformity in the um in the charge
+distribution in the semiconductor and
+
+ align:start position:0%
+distribution in the semiconductor and
+ 
+
+ align:start position:0%
+distribution in the semiconductor and
+electric field effects can become
+
+ align:start position:0%
+electric field effects can become
+ 
+
+ align:start position:0%
+electric field effects can become
+important and this is a a schematic
+
+ align:start position:0%
+important and this is a a schematic
+ 
+
+ align:start position:0%
+important and this is a a schematic
+demonstration of how electric Fields can
+
+ align:start position:0%
+demonstration of how electric Fields can
+ 
+
+ align:start position:0%
+demonstration of how electric Fields can
+arise when dope and are diffusing and
+
+ align:start position:0%
+arise when dope and are diffusing and
+ 
+
+ align:start position:0%
+arise when dope and are diffusing and
+silic and there's a plot of
+
+ align:start position:0%
+silic and there's a plot of
+ 
+
+ align:start position:0%
+silic and there's a plot of
+concentration schematically versus dep
+
+ align:start position:0%
+concentration schematically versus dep
+ 
+
+ align:start position:0%
+concentration schematically versus dep
+and the um the red uh the red line is
+
+ align:start position:0%
+and the um the red uh the red line is
+ 
+
+ align:start position:0%
+and the um the red uh the red line is
+supposed to represent the profile at any
+
+ align:start position:0%
+supposed to represent the profile at any
+ 
+
+ align:start position:0%
+supposed to represent the profile at any
+given point in time for say arsenic
+
+ align:start position:0%
+given point in time for say arsenic
+ 
+
+ align:start position:0%
+given point in time for say arsenic
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+diffusing and arsenic is a donor if has
+
+ align:start position:0%
+diffusing and arsenic is a donor if has
+ 
+
+ align:start position:0%
+diffusing and arsenic is a donor if has
+one extra electron floating around it um
+
+ align:start position:0%
+one extra electron floating around it um
+ 
+
+ align:start position:0%
+one extra electron floating around it um
+and but the atom itself uh in the
+
+ align:start position:0%
+and but the atom itself uh in the
+ 
+
+ align:start position:0%
+and but the atom itself uh in the
+absence this electron this extra gance
+
+ align:start position:0%
+absence this electron this extra gance
+ 
+
+ align:start position:0%
+absence this electron this extra gance
+electron um is the donor itself is
+
+ align:start position:0%
+electron um is the donor itself is
+ 
+
+ align:start position:0%
+electron um is the donor itself is
+positively charged as an ion this arsic
+
+ align:start position:0%
+positively charged as an ion this arsic
+ 
+
+ align:start position:0%
+positively charged as an ion this arsic
+diffusing and uh there are the electrons
+
+ align:start position:0%
+diffusing and uh there are the electrons
+ 
+
+ align:start position:0%
+diffusing and uh there are the electrons
+um associated with this heavily dope
+
+ align:start position:0%
+um associated with this heavily dope
+ 
+
+ align:start position:0%
+um associated with this heavily dope
+Arion can diffuse ahead of the dopin and
+
+ align:start position:0%
+Arion can diffuse ahead of the dopin and
+ 
+
+ align:start position:0%
+Arion can diffuse ahead of the dopin and
+so this blue line is meant to represent
+
+ align:start position:0%
+so this blue line is meant to represent
+ 
+
+ align:start position:0%
+so this blue line is meant to represent
+the distribution or the diffusion
+
+ align:start position:0%
+the distribution or the diffusion
+ 
+
+ align:start position:0%
+the distribution or the diffusion
+profile of electrons let's
+
+ align:start position:0%
+profile of electrons let's
+ 
+
+ align:start position:0%
+profile of electrons let's
+say so the electrons uh diffuse and
+
+ align:start position:0%
+say so the electrons uh diffuse and
+ 
+
+ align:start position:0%
+say so the electrons uh diffuse and
+holes diffuse more rapidly than their
+
+ align:start position:0%
+holes diffuse more rapidly than their
+ 
+
+ align:start position:0%
+holes diffuse more rapidly than their
+Associated donors and
+
+ align:start position:0%
+Associated donors and
+ 
+
+ align:start position:0%
+Associated donors and
+acceptors because of that more rapid
+
+ align:start position:0%
+acceptors because of that more rapid
+ 
+
+ align:start position:0%
+acceptors because of that more rapid
+diffusion um they they'll diffuse sort
+
+ align:start position:0%
+diffusion um they they'll diffuse sort
+ 
+
+ align:start position:0%
+diffusion um they they'll diffuse sort
+the profile for electrons will be a
+
+ align:start position:0%
+the profile for electrons will be a
+ 
+
+ align:start position:0%
+the profile for electrons will be a
+little bit deeper diffuse s of ahead um
+
+ align:start position:0%
+little bit deeper diffuse s of ahead um
+ 
+
+ align:start position:0%
+little bit deeper diffuse s of ahead um
+being do that they're associated with
+
+ align:start position:0%
+being do that they're associated with
+ 
+
+ align:start position:0%
+being do that they're associated with
+until they reach some steady state
+
+ align:start position:0%
+until they reach some steady state
+ 
+
+ align:start position:0%
+until they reach some steady state
+condition where um the the drift flux uh
+
+ align:start position:0%
+condition where um the the drift flux uh
+ 
+
+ align:start position:0%
+condition where um the the drift flux uh
+from the internal electric field
+
+ align:start position:0%
+from the internal electric field
+ 
+
+ align:start position:0%
+from the internal electric field
+uh it's going to balance the diffusion
+
+ align:start position:0%
+uh it's going to balance the diffusion
+ 
+
+ align:start position:0%
+uh it's going to balance the diffusion
+uh the diffusion
+
+ align:start position:0%
+uh the diffusion
+ 
+
+ align:start position:0%
+uh the diffusion
+flux and and so what we look at here is
+
+ align:start position:0%
+flux and and so what we look at here is
+ 
+
+ align:start position:0%
+flux and and so what we look at here is
+there if you just look at this uh this
+
+ align:start position:0%
+there if you just look at this uh this
+ 
+
+ align:start position:0%
+there if you just look at this uh this
+schematic picture you'll see there is
+
+ align:start position:0%
+schematic picture you'll see there is
+ 
+
+ align:start position:0%
+schematic picture you'll see there is
+indeed from your Elementary um
+
+ align:start position:0%
+indeed from your Elementary um
+ 
+
+ align:start position:0%
+indeed from your Elementary um
+Electronics or solid state physics there
+
+ align:start position:0%
+Electronics or solid state physics there
+ 
+
+ align:start position:0%
+Electronics or solid state physics there
+is an electric field induced by this the
+
+ align:start position:0%
+is an electric field induced by this the
+ 
+
+ align:start position:0%
+is an electric field induced by this the
+fact that there's a net positive charge
+
+ align:start position:0%
+fact that there's a net positive charge
+ 
+
+ align:start position:0%
+fact that there's a net positive charge
+on the left region that is if you
+
+ align:start position:0%
+on the left region that is if you
+ 
+
+ align:start position:0%
+on the left region that is if you
+subtract all the Arsenic doners you
+
+ align:start position:0%
+subtract all the Arsenic doners you
+ 
+
+ align:start position:0%
+subtract all the Arsenic doners you
+subract the electron concentration there
+
+ align:start position:0%
+subract the electron concentration there
+ 
+
+ align:start position:0%
+subract the electron concentration there
+there's a net positive charge on the
+
+ align:start position:0%
+there's a net positive charge on the
+ 
+
+ align:start position:0%
+there's a net positive charge on the
+left there's a little bit of net
+
+ align:start position:0%
+left there's a little bit of net
+ 
+
+ align:start position:0%
+left there's a little bit of net
+negative charge on the right that
+
+ align:start position:0%
+negative charge on the right that
+ 
+
+ align:start position:0%
+negative charge on the right that
+produces an electric field pointing from
+
+ align:start position:0%
+produces an electric field pointing from
+ 
+
+ align:start position:0%
+produces an electric field pointing from
+left to right um so um that electric
+
+ align:start position:0%
+left to right um so um that electric
+ 
+
+ align:start position:0%
+left to right um so um that electric
+field then tends to cause electrons to
+
+ align:start position:0%
+field then tends to cause electrons to
+ 
+
+ align:start position:0%
+field then tends to cause electrons to
+drift from right to left right because
+
+ align:start position:0%
+drift from right to left right because
+ 
+
+ align:start position:0%
+drift from right to left right because
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+drift um against the field um so they're
+
+ align:start position:0%
+drift um against the field um so they're
+ 
+
+ align:start position:0%
+drift um against the field um so they're
+going to be drifting from right to left
+
+ align:start position:0%
+going to be drifting from right to left
+ 
+
+ align:start position:0%
+going to be drifting from right to left
+while they're diffusing from left to
+
+ align:start position:0%
+while they're diffusing from left to
+ 
+
+ align:start position:0%
+while they're diffusing from left to
+right because there's a concentration
+
+ align:start position:0%
+right because there's a concentration
+ 
+
+ align:start position:0%
+right because there's a concentration
+gradient so the electric field will
+
+ align:start position:0%
+gradient so the electric field will
+ 
+
+ align:start position:0%
+gradient so the electric field will
+build up to the point where there's
+
+ align:start position:0%
+build up to the point where there's
+ 
+
+ align:start position:0%
+build up to the point where there's
+steady state where that drift uh flux
+
+ align:start position:0%
+steady state where that drift uh flux
+ 
+
+ align:start position:0%
+steady state where that drift uh flux
+just balances the diffusion flux uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons and again the physical orig
+
+ align:start position:0%
+electrons and again the physical orig
+ 
+
+ align:start position:0%
+electrons and again the physical orig
+this electric field is AFF that well
+
+ align:start position:0%
+this electric field is AFF that well
+ 
+
+ align:start position:0%
+this electric field is AFF that well
+electrons are are charged and holes and
+
+ align:start position:0%
+electrons are are charged and holes and
+ 
+
+ align:start position:0%
+electrons are are charged and holes and
+they have somewhat higher Mobility they
+
+ align:start position:0%
+they have somewhat higher Mobility they
+ 
+
+ align:start position:0%
+they have somewhat higher Mobility they
+can move around the wse much more
+
+ align:start position:0%
+can move around the wse much more
+ 
+
+ align:start position:0%
+can move around the wse much more
+readily than the dopen ions um
+
+ align:start position:0%
+readily than the dopen ions um
+ 
+
+ align:start position:0%
+readily than the dopen ions um
+themselves okay and again this is only
+
+ align:start position:0%
+themselves okay and again this is only
+ 
+
+ align:start position:0%
+themselves okay and again this is only
+going to happen in the particular case
+
+ align:start position:0%
+going to happen in the particular case
+ 
+
+ align:start position:0%
+going to happen in the particular case
+where the concentration of the doping is
+
+ align:start position:0%
+where the concentration of the doping is
+ 
+
+ align:start position:0%
+where the concentration of the doping is
+higher than in otherwise the uh the uh
+
+ align:start position:0%
+higher than in otherwise the uh the uh
+ 
+
+ align:start position:0%
+higher than in otherwise the uh the uh
+the background electron concentration is
+
+ align:start position:0%
+the background electron concentration is
+ 
+
+ align:start position:0%
+the background electron concentration is
+set by the temperature sure it's just a
+
+ align:start position:0%
+set by the temperature sure it's just a
+ 
+
+ align:start position:0%
+set by the temperature sure it's just a
+constant through uh throughout
+
+ align:start position:0%
+constant through uh throughout
+ 
+
+ align:start position:0%
+constant through uh throughout
+space so the electric field would not
+
+ align:start position:0%
+space so the electric field would not
+ 
+
+ align:start position:0%
+space so the electric field would not
+would not develop right at the edge of
+
+ align:start position:0%
+would not develop right at the edge of
+ 
+
+ align:start position:0%
+would not develop right at the edge of
+this diffusion
+
+ align:start position:0%
+this diffusion
+ 
+
+ align:start position:0%
+this diffusion
+profile let's go on to slide number 20
+
+ align:start position:0%
+profile let's go on to slide number 20
+ 
+
+ align:start position:0%
+profile let's go on to slide number 20
+and so what we do is we modify pick's
+
+ align:start position:0%
+and so what we do is we modify pick's
+ 
+
+ align:start position:0%
+and so what we do is we modify pick's
+first law and we modify in a way that's
+
+ align:start position:0%
+first law and we modify in a way that's
+ 
+
+ align:start position:0%
+first law and we modify in a way that's
+that's very similar and and pretty much
+
+ align:start position:0%
+that's very similar and and pretty much
+ 
+
+ align:start position:0%
+that's very similar and and pretty much
+almost identical to what we do in our uh
+
+ align:start position:0%
+almost identical to what we do in our uh
+ 
+
+ align:start position:0%
+almost identical to what we do in our uh
+uh electronics or Sol State because
+
+ align:start position:0%
+uh electronics or Sol State because
+ 
+
+ align:start position:0%
+uh electronics or Sol State because
+classes we say that the total impurity
+
+ align:start position:0%
+classes we say that the total impurity
+ 
+
+ align:start position:0%
+classes we say that the total impurity
+atom flux and the presence of both a
+
+ align:start position:0%
+atom flux and the presence of both a
+ 
+
+ align:start position:0%
+atom flux and the presence of both a
+concentration gradient and an electric
+
+ align:start position:0%
+concentration gradient and an electric
+ 
+
+ align:start position:0%
+concentration gradient and an electric
+field can be written down as the sum of
+
+ align:start position:0%
+field can be written down as the sum of
+ 
+
+ align:start position:0%
+field can be written down as the sum of
+two fluxes one is f which is the normal
+
+ align:start position:0%
+two fluxes one is f which is the normal
+ 
+
+ align:start position:0%
+two fluxes one is f which is the normal
+fickin diffusion flux which is given by
+
+ align:start position:0%
+fickin diffusion flux which is given by
+ 
+
+ align:start position:0%
+fickin diffusion flux which is given by
+minus D partial C partial X Plus F Prime
+
+ align:start position:0%
+minus D partial C partial X Plus F Prime
+ 
+
+ align:start position:0%
+minus D partial C partial X Plus F Prime
+where F Prime is now the drift flux due
+
+ align:start position:0%
+where F Prime is now the drift flux due
+ 
+
+ align:start position:0%
+where F Prime is now the drift flux due
+to the electric field and for the drift
+
+ align:start position:0%
+to the electric field and for the drift
+ 
+
+ align:start position:0%
+to the electric field and for the drift
+flux I wrote down Z which is the the
+
+ align:start position:0%
+flux I wrote down Z which is the the
+ 
+
+ align:start position:0%
+flux I wrote down Z which is the the
+charge uh the charge number Z would be
+
+ align:start position:0%
+charge uh the charge number Z would be
+ 
+
+ align:start position:0%
+charge uh the charge number Z would be
+one uh you know for electron depends on
+
+ align:start position:0%
+one uh you know for electron depends on
+ 
+
+ align:start position:0%
+one uh you know for electron depends on
+the number of electronic charges
+
+ align:start position:0%
+the number of electronic charges
+ 
+
+ align:start position:0%
+the number of electronic charges
+associated with whatever is uh drifting
+
+ align:start position:0%
+associated with whatever is uh drifting
+ 
+
+ align:start position:0%
+associated with whatever is uh drifting
+times the mobility
+
+ align:start position:0%
+times the mobility
+ 
+
+ align:start position:0%
+times the mobility
+mu times the concentration c times the
+
+ align:start position:0%
+mu times the concentration c times the
+ 
+
+ align:start position:0%
+mu times the concentration c times the
+electric field that is uh the flux to
+
+ align:start position:0%
+electric field that is uh the flux to
+ 
+
+ align:start position:0%
+electric field that is uh the flux to
+the drift again that's not a diffusion
+
+ align:start position:0%
+the drift again that's not a diffusion
+ 
+
+ align:start position:0%
+the drift again that's not a diffusion
+process that's that's the drift process
+
+ align:start position:0%
+process that's that's the drift process
+ 
+
+ align:start position:0%
+process that's that's the drift process
+it's different physical process we going
+
+ align:start position:0%
+it's different physical process we going
+ 
+
+ align:start position:0%
+it's different physical process we going
+to add these two together now right then
+
+ align:start position:0%
+to add these two together now right then
+ 
+
+ align:start position:0%
+to add these two together now right then
+is the total flux so we have a non-fan
+
+ align:start position:0%
+is the total flux so we have a non-fan
+ 
+
+ align:start position:0%
+is the total flux so we have a non-fan
+term on the
+
+ align:start position:0%
+term on the
+ 
+
+ align:start position:0%
+term on the
+right um but because of the Einstein
+
+ align:start position:0%
+right um but because of the Einstein
+ 
+
+ align:start position:0%
+right um but because of the Einstein
+relation we can actually when we're
+
+ align:start position:0%
+relation we can actually when we're
+ 
+
+ align:start position:0%
+relation we can actually when we're
+talking about the diffusion of carriers
+
+ align:start position:0%
+talking about the diffusion of carriers
+ 
+
+ align:start position:0%
+talking about the diffusion of carriers
+like electrons and holes we know that
+
+ align:start position:0%
+like electrons and holes we know that
+ 
+
+ align:start position:0%
+like electrons and holes we know that
+their Mobility is directly proportional
+
+ align:start position:0%
+their Mobility is directly proportional
+ 
+
+ align:start position:0%
+their Mobility is directly proportional
+to the diffusivity and the
+
+ align:start position:0%
+to the diffusivity and the
+ 
+
+ align:start position:0%
+to the diffusivity and the
+proportionality constant is Q over KT so
+
+ align:start position:0%
+proportionality constant is Q over KT so
+ 
+
+ align:start position:0%
+proportionality constant is Q over KT so
+mu is equal to um D * Q over KT so I we
+
+ align:start position:0%
+mu is equal to um D * Q over KT so I we
+ 
+
+ align:start position:0%
+mu is equal to um D * Q over KT so I we
+can substitute in for the mobility in
+
+ align:start position:0%
+can substitute in for the mobility in
+ 
+
+ align:start position:0%
+can substitute in for the mobility in
+the upper right hand or equation with
+
+ align:start position:0%
+the upper right hand or equation with
+ 
+
+ align:start position:0%
+the upper right hand or equation with
+the substitute in uh Q over KT *
+
+ align:start position:0%
+the substitute in uh Q over KT *
+ 
+
+ align:start position:0%
+the substitute in uh Q over KT *
+D I can also substitute in the fact
+
+ align:start position:0%
+D I can also substitute in the fact
+ 
+
+ align:start position:0%
+D I can also substitute in the fact
+electric field e is degrading to the
+
+ align:start position:0%
+electric field e is degrading to the
+ 
+
+ align:start position:0%
+electric field e is degrading to the
+potential where the potential s uh can
+
+ align:start position:0%
+potential where the potential s uh can
+ 
+
+ align:start position:0%
+potential where the potential s uh can
+be related to the car concentration n uh
+
+ align:start position:0%
+be related to the car concentration n uh
+ 
+
+ align:start position:0%
+be related to the car concentration n uh
+as minus k T times the L of n over n
+
+ align:start position:0%
+as minus k T times the L of n over n
+ 
+
+ align:start position:0%
+as minus k T times the L of n over n
+i so basically by substituting in uh the
+
+ align:start position:0%
+i so basically by substituting in uh the
+ 
+
+ align:start position:0%
+i so basically by substituting in uh the
+expression proportional diffusivity for
+
+ align:start position:0%
+expression proportional diffusivity for
+ 
+
+ align:start position:0%
+expression proportional diffusivity for
+mu and substituting in for the electric
+
+ align:start position:0%
+mu and substituting in for the electric
+ 
+
+ align:start position:0%
+mu and substituting in for the electric
+field how it relates to the potential
+
+ align:start position:0%
+field how it relates to the potential
+ 
+
+ align:start position:0%
+field how it relates to the potential
+and therefore to n/ n i we get the
+
+ align:start position:0%
+and therefore to n/ n i we get the
+ 
+
+ align:start position:0%
+and therefore to n/ n i we get the
+equation um near the bottom for the flux
+
+ align:start position:0%
+equation um near the bottom for the flux
+ 
+
+ align:start position:0%
+equation um near the bottom for the flux
+F that's just the usual F minus D *
+
+ align:start position:0%
+F that's just the usual F minus D *
+ 
+
+ align:start position:0%
+F that's just the usual F minus D *
+partial C partial x * minus D time the
+
+ align:start position:0%
+partial C partial x * minus D time the
+ 
+
+ align:start position:0%
+partial C partial x * minus D time the
+concentration C time now we've come up
+
+ align:start position:0%
+concentration C time now we've come up
+ 
+
+ align:start position:0%
+concentration C time now we've come up
+with this um this s uh term partial
+
+ align:start position:0%
+with this um this s uh term partial
+ 
+
+ align:start position:0%
+with this um this s uh term partial
+partial x uh of me potential um then n
+
+ align:start position:0%
+partial x uh of me potential um then n
+ 
+
+ align:start position:0%
+partial x uh of me potential um then n
+Over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N um so now this is a new um flux uh
+
+ align:start position:0%
+N um so now this is a new um flux uh
+ 
+
+ align:start position:0%
+N um so now this is a new um flux uh
+flux
+
+ align:start position:0%
+flux
+ 
+
+ align:start position:0%
+flux
+equation and um we can now we use for
+
+ align:start position:0%
+equation and um we can now we use for
+ 
+
+ align:start position:0%
+equation and um we can now we use for
+the car concentration n you have to be
+
+ align:start position:0%
+the car concentration n you have to be
+ 
+
+ align:start position:0%
+the car concentration n you have to be
+careful it's not just equal to ND
+
+ align:start position:0%
+careful it's not just equal to ND
+ 
+
+ align:start position:0%
+careful it's not just equal to ND
+because ni can be a order ND and so we
+
+ align:start position:0%
+because ni can be a order ND and so we
+ 
+
+ align:start position:0%
+because ni can be a order ND and so we
+need to make sure we use the full
+
+ align:start position:0%
+need to make sure we use the full
+ 
+
+ align:start position:0%
+need to make sure we use the full
+expression for the carer concentration
+
+ align:start position:0%
+expression for the carer concentration
+ 
+
+ align:start position:0%
+expression for the carer concentration
+and it's 1/2 this uh at the bottom
+
+ align:start position:0%
+and it's 1/2 this uh at the bottom
+ 
+
+ align:start position:0%
+and it's 1/2 this uh at the bottom
+equation here it's 1/2 times the
+
+ align:start position:0%
+equation here it's 1/2 times the
+ 
+
+ align:start position:0%
+equation here it's 1/2 times the
+quantity squ OT of nd2 + 4 n i s plus N
+
+ align:start position:0%
+quantity squ OT of nd2 + 4 n i s plus N
+ 
+
+ align:start position:0%
+quantity squ OT of nd2 + 4 n i s plus N
+D um that comes from charge
+
+ align:start position:0%
+D um that comes from charge
+ 
+
+ align:start position:0%
+D um that comes from charge
+neutrality um given that we there's
+
+ align:start position:0%
+neutrality um given that we there's
+ 
+
+ align:start position:0%
+neutrality um given that we there's
+there therefore there's a relationship
+
+ align:start position:0%
+there therefore there's a relationship
+ 
+
+ align:start position:0%
+there therefore there's a relationship
+between n the car concentration and um
+
+ align:start position:0%
+between n the car concentration and um
+ 
+
+ align:start position:0%
+between n the car concentration and um
+the concentration of the dopent C
+
+ align:start position:0%
+the concentration of the dopent C
+ 
+
+ align:start position:0%
+the concentration of the dopent C
+because again uh the the concentration C
+
+ align:start position:0%
+because again uh the the concentration C
+ 
+
+ align:start position:0%
+because again uh the the concentration C
+it's just NB minus
+
+ align:start position:0%
+it's just NB minus
+ 
+
+ align:start position:0%
+it's just NB minus
+na um so it's the net concentration so
+
+ align:start position:0%
+na um so it's the net concentration so
+ 
+
+ align:start position:0%
+na um so it's the net concentration so
+we have a relationship between n and C
+
+ align:start position:0%
+we have a relationship between n and C
+ 
+
+ align:start position:0%
+we have a relationship between n and C
+we use that to make this flux equation F
+
+ align:start position:0%
+we use that to make this flux equation F
+ 
+
+ align:start position:0%
+we use that to make this flux equation F
+to be written only in terms of the
+
+ align:start position:0%
+to be written only in terms of the
+ 
+
+ align:start position:0%
+to be written only in terms of the
+concentration C so with L of the next
+
+ align:start position:0%
+concentration C so with L of the next
+ 
+
+ align:start position:0%
+concentration C so with L of the next
+page slide
+
+ align:start position:0%
+page slide
+ 
+
+ align:start position:0%
+page slide
+21 what we find is that uh we can do
+
+ align:start position:0%
+21 what we find is that uh we can do
+ 
+
+ align:start position:0%
+21 what we find is that uh we can do
+this compression of this equation and we
+
+ align:start position:0%
+this compression of this equation and we
+ 
+
+ align:start position:0%
+this compression of this equation and we
+find that the total flux now f is
+
+ align:start position:0%
+find that the total flux now f is
+ 
+
+ align:start position:0%
+find that the total flux now f is
+written by as something called minus H *
+
+ align:start position:0%
+written by as something called minus H *
+ 
+
+ align:start position:0%
+written by as something called minus H *
+the diffusivity of a dop d sub a partial
+
+ align:start position:0%
+the diffusivity of a dop d sub a partial
+ 
+
+ align:start position:0%
+the diffusivity of a dop d sub a partial
+C partial X so we've been able to
+
+ align:start position:0%
+C partial X so we've been able to
+ 
+
+ align:start position:0%
+C partial X so we've been able to
+actually write down an equation looks
+
+ align:start position:0%
+actually write down an equation looks
+ 
+
+ align:start position:0%
+actually write down an equation looks
+just like um fixed first law but there's
+
+ align:start position:0%
+just like um fixed first law but there's
+ 
+
+ align:start position:0%
+just like um fixed first law but there's
+an h factor multiplying it and this h
+
+ align:start position:0%
+an h factor multiplying it and this h
+ 
+
+ align:start position:0%
+an h factor multiplying it and this h
+factor turns out to be equal to 1 plus
+
+ align:start position:0%
+factor turns out to be equal to 1 plus
+ 
+
+ align:start position:0%
+factor turns out to be equal to 1 plus
+uh C / the quantity squ of c^2 + 4 and
+
+ align:start position:0%
+uh C / the quantity squ of c^2 + 4 and
+ 
+
+ align:start position:0%
+uh C / the quantity squ of c^2 + 4 and
+i^
+
+ align:start position:0%
+i^
+ 
+
+ align:start position:0%
+i^
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+um so basically uh it looks this in the
+
+ align:start position:0%
+um so basically uh it looks this in the
+ 
+
+ align:start position:0%
+um so basically uh it looks this in the
+in the presence of an electric field it
+
+ align:start position:0%
+in the presence of an electric field it
+ 
+
+ align:start position:0%
+in the presence of an electric field it
+looks just like we have an enhancement
+
+ align:start position:0%
+looks just like we have an enhancement
+ 
+
+ align:start position:0%
+looks just like we have an enhancement
+in the diusivity of the dopin by a
+
+ align:start position:0%
+in the diusivity of the dopin by a
+ 
+
+ align:start position:0%
+in the diusivity of the dopin by a
+factor called H you can you can we just
+
+ align:start position:0%
+factor called H you can you can we just
+ 
+
+ align:start position:0%
+factor called H you can you can we just
+work that out so uh interestingly we see
+
+ align:start position:0%
+work that out so uh interestingly we see
+ 
+
+ align:start position:0%
+work that out so uh interestingly we see
+that it electric field effect uh on a
+
+ align:start position:0%
+that it electric field effect uh on a
+ 
+
+ align:start position:0%
+that it electric field effect uh on a
+dopant that is creating the field on
+
+ align:start position:0%
+dopant that is creating the field on
+ 
+
+ align:start position:0%
+dopant that is creating the field on
+that buin itself it enhances theity and
+
+ align:start position:0%
+that buin itself it enhances theity and
+ 
+
+ align:start position:0%
+that buin itself it enhances theity and
+it turns out H has an upper bound of
+
+ align:start position:0%
+it turns out H has an upper bound of
+ 
+
+ align:start position:0%
+it turns out H has an upper bound of
+two so H is not going to be any larger
+
+ align:start position:0%
+two so H is not going to be any larger
+ 
+
+ align:start position:0%
+two so H is not going to be any larger
+than two and that means that the
+
+ align:start position:0%
+than two and that means that the
+ 
+
+ align:start position:0%
+than two and that means that the
+electric field enhancement term can
+
+ align:start position:0%
+electric field enhancement term can
+ 
+
+ align:start position:0%
+electric field enhancement term can
+enhance the diffusivity the doping that
+
+ align:start position:0%
+enhance the diffusivity the doping that
+ 
+
+ align:start position:0%
+enhance the diffusivity the doping that
+causes the field by as much as or a
+
+ align:start position:0%
+causes the field by as much as or a
+ 
+
+ align:start position:0%
+causes the field by as much as or a
+maximum Lim factor of
+
+ align:start position:0%
+maximum Lim factor of
+ 
+
+ align:start position:0%
+maximum Lim factor of
+two and this happens when the doping
+
+ align:start position:0%
+two and this happens when the doping
+ 
+
+ align:start position:0%
+two and this happens when the doping
+concentration term uh or C is much much
+
+ align:start position:0%
+concentration term uh or C is much much
+ 
+
+ align:start position:0%
+concentration term uh or C is much much
+greater than uh ni and you can see that
+
+ align:start position:0%
+greater than uh ni and you can see that
+ 
+
+ align:start position:0%
+greater than uh ni and you can see that
+by substituting in um and calculating
+
+ align:start position:0%
+by substituting in um and calculating
+ 
+
+ align:start position:0%
+by substituting in um and calculating
+out what H is in certain
+
+ align:start position:0%
+out what H is in certain
+ 
+
+ align:start position:0%
+out what H is in certain
+conditions uh when in the special case
+
+ align:start position:0%
+conditions uh when in the special case
+ 
+
+ align:start position:0%
+conditions uh when in the special case
+where um you know C is NI then uh H goes
+
+ align:start position:0%
+where um you know C is NI then uh H goes
+ 
+
+ align:start position:0%
+where um you know C is NI then uh H goes
+back to being
+
+ align:start position:0%
+back to being
+ 
+
+ align:start position:0%
+back to being
+to so uh how do we get to this equation
+
+ align:start position:0%
+to so uh how do we get to this equation
+ 
+
+ align:start position:0%
+to so uh how do we get to this equation
+where the simplified age Factor well if
+
+ align:start position:0%
+where the simplified age Factor well if
+ 
+
+ align:start position:0%
+where the simplified age Factor well if
+you go on uh onto slide number 22
+
+ align:start position:0%
+you go on uh onto slide number 22
+ 
+
+ align:start position:0%
+you go on uh onto slide number 22
+actually I'm not going to go through all
+
+ align:start position:0%
+actually I'm not going to go through all
+ 
+
+ align:start position:0%
+actually I'm not going to go through all
+the algebra but basically uh what we did
+
+ align:start position:0%
+the algebra but basically uh what we did
+ 
+
+ align:start position:0%
+the algebra but basically uh what we did
+was we um used a particular fact which
+
+ align:start position:0%
+was we um used a particular fact which
+ 
+
+ align:start position:0%
+was we um used a particular fact which
+is that on the top of slide 22 partial
+
+ align:start position:0%
+is that on the top of slide 22 partial
+ 
+
+ align:start position:0%
+is that on the top of slide 22 partial
+partial X on the logarithm of X is equal
+
+ align:start position:0%
+partial X on the logarithm of X is equal
+ 
+
+ align:start position:0%
+partial X on the logarithm of X is equal
+to 1 /x and uh uh what we needed to find
+
+ align:start position:0%
+to 1 /x and uh uh what we needed to find
+ 
+
+ align:start position:0%
+to 1 /x and uh uh what we needed to find
+in that earlier defusion um and that
+
+ align:start position:0%
+in that earlier defusion um and that
+ 
+
+ align:start position:0%
+in that earlier defusion um and that
+earlier drift term there was a term that
+
+ align:start position:0%
+earlier drift term there was a term that
+ 
+
+ align:start position:0%
+earlier drift term there was a term that
+went partial partial X
+
+ align:start position:0%
+went partial partial X
+ 
+
+ align:start position:0%
+went partial partial X
+when um of hando the
+
+ align:start position:0%
+when um of hando the
+ 
+
+ align:start position:0%
+when um of hando the
+n and so just by going to the algebra
+
+ align:start position:0%
+n and so just by going to the algebra
+ 
+
+ align:start position:0%
+n and so just by going to the algebra
+shown on on uh we can substit on slide
+
+ align:start position:0%
+shown on on uh we can substit on slide
+ 
+
+ align:start position:0%
+shown on on uh we can substit on slide
+22 we can substitute for the car
+
+ align:start position:0%
+22 we can substitute for the car
+ 
+
+ align:start position:0%
+22 we can substitute for the car
+concentration n and we can find uh an
+
+ align:start position:0%
+concentration n and we can find uh an
+ 
+
+ align:start position:0%
+concentration n and we can find uh an
+expression for partial partial X of Len
+
+ align:start position:0%
+expression for partial partial X of Len
+ 
+
+ align:start position:0%
+expression for partial partial X of Len
+of n over n i and you see that in the
+
+ align:start position:0%
+of n over n i and you see that in the
+ 
+
+ align:start position:0%
+of n over n i and you see that in the
+middle of the of the slide and then we
+
+ align:start position:0%
+middle of the of the slide and then we
+ 
+
+ align:start position:0%
+middle of the of the slide and then we
+substitute in the dopin concentration in
+
+ align:start position:0%
+substitute in the dopin concentration in
+ 
+
+ align:start position:0%
+substitute in the dopin concentration in
+D is equal to C and we're able to see
+
+ align:start position:0%
+D is equal to C and we're able to see
+ 
+
+ align:start position:0%
+D is equal to C and we're able to see
+that the flux the total flux is the
+
+ align:start position:0%
+that the flux the total flux is the
+ 
+
+ align:start position:0%
+that the flux the total flux is the
+usual fickian term D minus D * partial C
+
+ align:start position:0%
+usual fickian term D minus D * partial C
+ 
+
+ align:start position:0%
+usual fickian term D minus D * partial C
+partial x minus this other term which
+
+ align:start position:0%
+partial x minus this other term which
+ 
+
+ align:start position:0%
+partial x minus this other term which
+ends up being able to be written um just
+
+ align:start position:0%
+ends up being able to be written um just
+ 
+
+ align:start position:0%
+ends up being able to be written um just
+like partial C partial X in terms of
+
+ align:start position:0%
+like partial C partial X in terms of
+ 
+
+ align:start position:0%
+like partial C partial X in terms of
+partial C partial x times the h
+
+ align:start position:0%
+partial C partial x times the h
+ 
+
+ align:start position:0%
+partial C partial x times the h
+factor where H was uh is equal to as it
+
+ align:start position:0%
+factor where H was uh is equal to as it
+ 
+
+ align:start position:0%
+factor where H was uh is equal to as it
+sh on the bottom 1 plus C over the
+
+ align:start position:0%
+sh on the bottom 1 plus C over the
+ 
+
+ align:start position:0%
+sh on the bottom 1 plus C over the
+square c^2 + 4 and I S so that's just
+
+ align:start position:0%
+square c^2 + 4 and I S so that's just
+ 
+
+ align:start position:0%
+square c^2 + 4 and I S so that's just
+justifies the derivation of each factor
+
+ align:start position:0%
+justifies the derivation of each factor
+ 
+
+ align:start position:0%
+justifies the derivation of each factor
+uh on slide 22
+
+ align:start position:0%
+uh on slide 22
+ 
+
+ align:start position:0%
+uh on slide 22
+okay so just go back to SL 21 for one
+
+ align:start position:0%
+okay so just go back to SL 21 for one
+ 
+
+ align:start position:0%
+okay so just go back to SL 21 for one
+second and just want to remind ourselves
+
+ align:start position:0%
+second and just want to remind ourselves
+ 
+
+ align:start position:0%
+second and just want to remind ourselves
+that the uh total flux F now in the
+
+ align:start position:0%
+that the uh total flux F now in the
+ 
+
+ align:start position:0%
+that the uh total flux F now in the
+presence of a High car concentration can
+
+ align:start position:0%
+presence of a High car concentration can
+ 
+
+ align:start position:0%
+presence of a High car concentration can
+be written just like the fing diffusion
+
+ align:start position:0%
+be written just like the fing diffusion
+ 
+
+ align:start position:0%
+be written just like the fing diffusion
+but the H there's a multiplier H from
+
+ align:start position:0%
+but the H there's a multiplier H from
+ 
+
+ align:start position:0%
+but the H there's a multiplier H from
+the bity of the Dober atom
+
+ align:start position:0%
+the bity of the Dober atom
+ 
+
+ align:start position:0%
+the bity of the Dober atom
+a let's skip on to slide 23 now uh
+
+ align:start position:0%
+a let's skip on to slide 23 now uh
+ 
+
+ align:start position:0%
+a let's skip on to slide 23 now uh
+however so that's when we're talking
+
+ align:start position:0%
+however so that's when we're talking
+ 
+
+ align:start position:0%
+however so that's when we're talking
+about um the amount of enhancement you
+
+ align:start position:0%
+about um the amount of enhancement you
+ 
+
+ align:start position:0%
+about um the amount of enhancement you
+might get in the high concentration
+
+ align:start position:0%
+might get in the high concentration
+ 
+
+ align:start position:0%
+might get in the high concentration
+species
+
+ align:start position:0%
+species
+ 
+
+ align:start position:0%
+species
+um but you may have two different
+
+ align:start position:0%
+um but you may have two different
+ 
+
+ align:start position:0%
+um but you may have two different
+species diffusing and in the case where
+
+ align:start position:0%
+species diffusing and in the case where
+ 
+
+ align:start position:0%
+species diffusing and in the case where
+the species are at different
+
+ align:start position:0%
+the species are at different
+ 
+
+ align:start position:0%
+the species are at different
+concentrations the electric field term
+
+ align:start position:0%
+concentrations the electric field term
+ 
+
+ align:start position:0%
+concentrations the electric field term
+can actually cause an even larger change
+
+ align:start position:0%
+can actually cause an even larger change
+ 
+
+ align:start position:0%
+can actually cause an even larger change
+in the diffusivity of the low
+
+ align:start position:0%
+in the diffusivity of the low
+ 
+
+ align:start position:0%
+in the diffusivity of the low
+concentration building so let's look at
+
+ align:start position:0%
+concentration building so let's look at
+ 
+
+ align:start position:0%
+concentration building so let's look at
+a particular example uh shown on slide
+
+ align:start position:0%
+a particular example uh shown on slide
+ 
+
+ align:start position:0%
+a particular example uh shown on slide
+23 and uh what we're we're showing here
+
+ align:start position:0%
+23 and uh what we're we're showing here
+ 
+
+ align:start position:0%
+23 and uh what we're we're showing here
+is concentration is a function of depth
+
+ align:start position:0%
+is concentration is a function of depth
+ 
+
+ align:start position:0%
+is concentration is a function of depth
+and the red curve in high concentration
+
+ align:start position:0%
+and the red curve in high concentration
+ 
+
+ align:start position:0%
+and the red curve in high concentration
+let's say a high concentration arsenic
+
+ align:start position:0%
+let's say a high concentration arsenic
+ 
+
+ align:start position:0%
+let's say a high concentration arsenic
+profile um the initial arsenic profile
+
+ align:start position:0%
+profile um the initial arsenic profile
+ 
+
+ align:start position:0%
+profile um the initial arsenic profile
+looks it was I a plet or something it
+
+ align:start position:0%
+looks it was I a plet or something it
+ 
+
+ align:start position:0%
+looks it was I a plet or something it
+looks like this as shown in the solid
+
+ align:start position:0%
+looks like this as shown in the solid
+ 
+
+ align:start position:0%
+looks like this as shown in the solid
+red curve um the background building is
+
+ align:start position:0%
+red curve um the background building is
+ 
+
+ align:start position:0%
+red curve um the background building is
+initially all constant it's p typ so
+
+ align:start position:0%
+initially all constant it's p typ so
+ 
+
+ align:start position:0%
+initially all constant it's p typ so
+this is boron is shown by the solid um
+
+ align:start position:0%
+this is boron is shown by the solid um
+ 
+
+ align:start position:0%
+this is boron is shown by the solid um
+blue
+
+ align:start position:0%
+blue
+ 
+
+ align:start position:0%
+blue
+line now we're going to simulate uh
+
+ align:start position:0%
+line now we're going to simulate uh
+ 
+
+ align:start position:0%
+line now we're going to simulate uh
+including electric field effects at a
+
+ align:start position:0%
+including electric field effects at a
+ 
+
+ align:start position:0%
+including electric field effects at a
+th000 degrees the diffusion of the arsic
+
+ align:start position:0%
+th000 degrees the diffusion of the arsic
+ 
+
+ align:start position:0%
+th000 degrees the diffusion of the arsic
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+Boron U well it turns out the Arsenic
+
+ align:start position:0%
+Boron U well it turns out the Arsenic
+ 
+
+ align:start position:0%
+Boron U well it turns out the Arsenic
+does in diffuse as shown by the dash
+
+ align:start position:0%
+does in diffuse as shown by the dash
+ 
+
+ align:start position:0%
+does in diffuse as shown by the dash
+line but that the electric field that it
+
+ align:start position:0%
+line but that the electric field that it
+ 
+
+ align:start position:0%
+line but that the electric field that it
+produces right near its um the slope
+
+ align:start position:0%
+produces right near its um the slope
+ 
+
+ align:start position:0%
+produces right near its um the slope
+right near the edge of its profile
+
+ align:start position:0%
+right near the edge of its profile
+ 
+
+ align:start position:0%
+right near the edge of its profile
+actually that electric field can cause a
+
+ align:start position:0%
+actually that electric field can cause a
+ 
+
+ align:start position:0%
+actually that electric field can cause a
+flux of of boron ions ions which can
+
+ align:start position:0%
+flux of of boron ions ions which can
+ 
+
+ align:start position:0%
+flux of of boron ions ions which can
+cause the Bon to uh itself to move so
+
+ align:start position:0%
+cause the Bon to uh itself to move so
+ 
+
+ align:start position:0%
+cause the Bon to uh itself to move so
+the final Boron profile uh now is is
+
+ align:start position:0%
+the final Boron profile uh now is is
+ 
+
+ align:start position:0%
+the final Boron profile uh now is is
+shown by the blue dash line has this
+
+ align:start position:0%
+shown by the blue dash line has this
+ 
+
+ align:start position:0%
+shown by the blue dash line has this
+little um hump in it and then a dip and
+
+ align:start position:0%
+little um hump in it and then a dip and
+ 
+
+ align:start position:0%
+little um hump in it and then a dip and
+that that little dip occurs right near
+
+ align:start position:0%
+that that little dip occurs right near
+ 
+
+ align:start position:0%
+that that little dip occurs right near
+where the the junction is right where is
+
+ align:start position:0%
+where the the junction is right where is
+ 
+
+ align:start position:0%
+where the the junction is right where is
+a blonde the arch and the blonde cross
+
+ align:start position:0%
+a blonde the arch and the blonde cross
+ 
+
+ align:start position:0%
+a blonde the arch and the blonde cross
+and there's no way by ficking in
+
+ align:start position:0%
+and there's no way by ficking in
+ 
+
+ align:start position:0%
+and there's no way by ficking in
+diffusion he would ever predict that a
+
+ align:start position:0%
+diffusion he would ever predict that a
+ 
+
+ align:start position:0%
+diffusion he would ever predict that a
+constant profile of Bon would end up
+
+ align:start position:0%
+constant profile of Bon would end up
+ 
+
+ align:start position:0%
+constant profile of Bon would end up
+being looking the way it does uh in this
+
+ align:start position:0%
+being looking the way it does uh in this
+ 
+
+ align:start position:0%
+being looking the way it does uh in this
+particular plot again that's because of
+
+ align:start position:0%
+particular plot again that's because of
+ 
+
+ align:start position:0%
+particular plot again that's because of
+the second term the electric field term
+
+ align:start position:0%
+the second term the electric field term
+ 
+
+ align:start position:0%
+the second term the electric field term
+that non-fickian
+
+ align:start position:0%
+that non-fickian
+ 
+
+ align:start position:0%
+that non-fickian
+term so and when you want to think about
+
+ align:start position:0%
+term so and when you want to think about
+ 
+
+ align:start position:0%
+term so and when you want to think about
+that how that occurred look at the
+
+ align:start position:0%
+that how that occurred look at the
+ 
+
+ align:start position:0%
+that how that occurred look at the
+electric field Arrow drawn from left to
+
+ align:start position:0%
+electric field Arrow drawn from left to
+ 
+
+ align:start position:0%
+electric field Arrow drawn from left to
+right uh again drawing from positive net
+
+ align:start position:0%
+right uh again drawing from positive net
+ 
+
+ align:start position:0%
+right uh again drawing from positive net
+positive to net negative charge that
+
+ align:start position:0%
+positive to net negative charge that
+ 
+
+ align:start position:0%
+positive to net negative charge that
+direction of e pulls the the born again
+
+ align:start position:0%
+direction of e pulls the the born again
+ 
+
+ align:start position:0%
+direction of e pulls the the born again
+remember the born ions as they diffuse
+
+ align:start position:0%
+remember the born ions as they diffuse
+ 
+
+ align:start position:0%
+remember the born ions as they diffuse
+their B minus these acceptors andit
+
+ align:start position:0%
+their B minus these acceptors andit
+ 
+
+ align:start position:0%
+their B minus these acceptors andit
+negative charge so they're going to be
+
+ align:start position:0%
+negative charge so they're going to be
+ 
+
+ align:start position:0%
+negative charge so they're going to be
+pulled in they're going to move to the
+
+ align:start position:0%
+pulled in they're going to move to the
+ 
+
+ align:start position:0%
+pulled in they're going to move to the
+left the by the electric field they'll
+
+ align:start position:0%
+left the by the electric field they'll
+ 
+
+ align:start position:0%
+left the by the electric field they'll
+be pulled into the npl region and
+
+ align:start position:0%
+be pulled into the npl region and
+ 
+
+ align:start position:0%
+be pulled into the npl region and
+deplete some of the blond uh in the
+
+ align:start position:0%
+deplete some of the blond uh in the
+ 
+
+ align:start position:0%
+deplete some of the blond uh in the
+region past the junction and you end up
+
+ align:start position:0%
+region past the junction and you end up
+ 
+
+ align:start position:0%
+region past the junction and you end up
+with this sort of hump and dip uh which
+
+ align:start position:0%
+with this sort of hump and dip uh which
+ 
+
+ align:start position:0%
+with this sort of hump and dip uh which
+is a non- ficking type of of motion but
+
+ align:start position:0%
+is a non- ficking type of of motion but
+ 
+
+ align:start position:0%
+is a non- ficking type of of motion but
+induced by uh the electric field created
+
+ align:start position:0%
+induced by uh the electric field created
+ 
+
+ align:start position:0%
+induced by uh the electric field created
+by the higher concentration arsenic uh
+
+ align:start position:0%
+by the higher concentration arsenic uh
+ 
+
+ align:start position:0%
+by the higher concentration arsenic uh
+species so this can have quite a bit uh
+
+ align:start position:0%
+species so this can have quite a bit uh
+ 
+
+ align:start position:0%
+species so this can have quite a bit uh
+of an effect on the the diffusion
+
+ align:start position:0%
+of an effect on the the diffusion
+ 
+
+ align:start position:0%
+of an effect on the the diffusion
+profiles uh near a junction and we see
+
+ align:start position:0%
+profiles uh near a junction and we see
+ 
+
+ align:start position:0%
+profiles uh near a junction and we see
+this all the time in our devices in fact
+
+ align:start position:0%
+this all the time in our devices in fact
+ 
+
+ align:start position:0%
+this all the time in our devices in fact
+you go on to slide number
+
+ align:start position:0%
+you go on to slide number
+ 
+
+ align:start position:0%
+you go on to slide number
+23 showing uh a simulation example of an
+
+ align:start position:0%
+23 showing uh a simulation example of an
+ 
+
+ align:start position:0%
+23 showing uh a simulation example of an
+in mosfet this is these are two supreme
+
+ align:start position:0%
+in mosfet this is these are two supreme
+ 
+
+ align:start position:0%
+in mosfet this is these are two supreme
+simulations both 5,000 de uh for mosfets
+
+ align:start position:0%
+simulations both 5,000 de uh for mosfets
+ 
+
+ align:start position:0%
+simulations both 5,000 de uh for mosfets
+you'll recognize the poly silic gate
+
+ align:start position:0%
+you'll recognize the poly silic gate
+ 
+
+ align:start position:0%
+you'll recognize the poly silic gate
+here in the
+
+ align:start position:0%
+here in the
+ 
+
+ align:start position:0%
+here in the
+magenta um and the source and drains uh
+
+ align:start position:0%
+magenta um and the source and drains uh
+ 
+
+ align:start position:0%
+magenta um and the source and drains uh
+regions are Arsenic and they are shown
+
+ align:start position:0%
+regions are Arsenic and they are shown
+ 
+
+ align:start position:0%
+regions are Arsenic and they are shown
+in black um if you look first at the
+
+ align:start position:0%
+in black um if you look first at the
+ 
+
+ align:start position:0%
+in black um if you look first at the
+left in the case of no electric field um
+
+ align:start position:0%
+left in the case of no electric field um
+ 
+
+ align:start position:0%
+left in the case of no electric field um
+you see uh these these different
+
+ align:start position:0%
+you see uh these these different
+ 
+
+ align:start position:0%
+you see uh these these different
+Contours the green yellow uh sort of
+
+ align:start position:0%
+Contours the green yellow uh sort of
+ 
+
+ align:start position:0%
+Contours the green yellow uh sort of
+light orange and then dark orange or red
+
+ align:start position:0%
+light orange and then dark orange or red
+ 
+
+ align:start position:0%
+light orange and then dark orange or red
+um we see the Boron sort of uniformly
+
+ align:start position:0%
+um we see the Boron sort of uniformly
+ 
+
+ align:start position:0%
+um we see the Boron sort of uniformly
+doped and um its Contours are shown by
+
+ align:start position:0%
+doped and um its Contours are shown by
+ 
+
+ align:start position:0%
+doped and um its Contours are shown by
+the different
+
+ align:start position:0%
+the different
+ 
+
+ align:start position:0%
+the different
+colors uh and now what happens on the
+
+ align:start position:0%
+colors uh and now what happens on the
+ 
+
+ align:start position:0%
+colors uh and now what happens on the
+right in the presence of electric field
+
+ align:start position:0%
+right in the presence of electric field
+ 
+
+ align:start position:0%
+right in the presence of electric field
+instead of these sort of uniform lateral
+
+ align:start position:0%
+instead of these sort of uniform lateral
+ 
+
+ align:start position:0%
+instead of these sort of uniform lateral
+doping Contours full of L you see uh
+
+ align:start position:0%
+doping Contours full of L you see uh
+ 
+
+ align:start position:0%
+doping Contours full of L you see uh
+they there's a um electric field that
+
+ align:start position:0%
+they there's a um electric field that
+ 
+
+ align:start position:0%
+they there's a um electric field that
+sort of Acts on the blor and and L
+
+ align:start position:0%
+sort of Acts on the blor and and L
+ 
+
+ align:start position:0%
+sort of Acts on the blor and and L
+changes uh the dop and distribution in
+
+ align:start position:0%
+changes uh the dop and distribution in
+ 
+
+ align:start position:0%
+changes uh the dop and distribution in
+its shape in fact they Dom it dominates
+
+ align:start position:0%
+its shape in fact they Dom it dominates
+ 
+
+ align:start position:0%
+its shape in fact they Dom it dominates
+the shape of the blonde distribution
+
+ align:start position:0%
+the shape of the blonde distribution
+ 
+
+ align:start position:0%
+the shape of the blonde distribution
+particularly near the source drain
+
+ align:start position:0%
+particularly near the source drain
+ 
+
+ align:start position:0%
+particularly near the source drain
+Junctions of a mosfet device the blonde
+
+ align:start position:0%
+Junctions of a mosfet device the blonde
+ 
+
+ align:start position:0%
+Junctions of a mosfet device the blonde
+basically gets pulled in to underneath
+
+ align:start position:0%
+basically gets pulled in to underneath
+ 
+
+ align:start position:0%
+basically gets pulled in to underneath
+the source and drains and there's quite
+
+ align:start position:0%
+the source and drains and there's quite
+ 
+
+ align:start position:0%
+the source and drains and there's quite
+a bit of loss of blond from the channel
+
+ align:start position:0%
+a bit of loss of blond from the channel
+ 
+
+ align:start position:0%
+a bit of loss of blond from the channel
+into the source drains uh that do
+
+ align:start position:0%
+into the source drains uh that do
+ 
+
+ align:start position:0%
+into the source drains uh that do
+electric field effect it's not predicted
+
+ align:start position:0%
+electric field effect it's not predicted
+ 
+
+ align:start position:0%
+electric field effect it's not predicted
+on the on the left hand side so even
+
+ align:start position:0%
+on the on the left hand side so even
+ 
+
+ align:start position:0%
+on the on the left hand side so even
+though H the h factor the enhancement in
+
+ align:start position:0%
+though H the h factor the enhancement in
+ 
+
+ align:start position:0%
+though H the h factor the enhancement in
+the Arsenic diffusivity is limited to uh
+
+ align:start position:0%
+the Arsenic diffusivity is limited to uh
+ 
+
+ align:start position:0%
+the Arsenic diffusivity is limited to uh
+at most a factor to so there's not too
+
+ align:start position:0%
+at most a factor to so there's not too
+ 
+
+ align:start position:0%
+at most a factor to so there's not too
+much effect on the Junction in the ARs
+
+ align:start position:0%
+much effect on the Junction in the ARs
+ 
+
+ align:start position:0%
+much effect on the Junction in the ARs
+this in the black
+
+ align:start position:0%
+this in the black
+ 
+
+ align:start position:0%
+this in the black
+Junctions uh RS don't change that
+
+ align:start position:0%
+Junctions uh RS don't change that
+ 
+
+ align:start position:0%
+Junctions uh RS don't change that
+significantly but it dominates the
+
+ align:start position:0%
+significantly but it dominates the
+ 
+
+ align:start position:0%
+significantly but it dominates the
+diffusion of the Boron
+
+ align:start position:0%
+diffusion of the Boron
+ 
+
+ align:start position:0%
+diffusion of the Boron
+underneath or at a lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concentration so let's go on to slide
+
+ align:start position:0%
+concentration so let's go on to slide
+ 
+
+ align:start position:0%
+concentration so let's go on to slide
+number 25 I just want to summarize uh
+
+ align:start position:0%
+number 25 I just want to summarize uh
+ 
+
+ align:start position:0%
+number 25 I just want to summarize uh
+this second lecture on diffusion we
+
+ align:start position:0%
+this second lecture on diffusion we
+ 
+
+ align:start position:0%
+this second lecture on diffusion we
+reviewed uh a few cases of simple
+
+ align:start position:0%
+reviewed uh a few cases of simple
+ 
+
+ align:start position:0%
+reviewed uh a few cases of simple
+constant diusivity um these generally
+
+ align:start position:0%
+constant diusivity um these generally
+ 
+
+ align:start position:0%
+constant diusivity um these generally
+apply well uh to uh the case of low
+
+ align:start position:0%
+apply well uh to uh the case of low
+ 
+
+ align:start position:0%
+apply well uh to uh the case of low
+doping concentrations uh in a seamless
+
+ align:start position:0%
+doping concentrations uh in a seamless
+ 
+
+ align:start position:0%
+doping concentrations uh in a seamless
+process flow that usually lean to
+
+ align:start position:0%
+process flow that usually lean to
+ 
+
+ align:start position:0%
+process flow that usually lean to
+diffusion of the seamless Wells which
+
+ align:start position:0%
+diffusion of the seamless Wells which
+ 
+
+ align:start position:0%
+diffusion of the seamless Wells which
+are fairly lightly doped uh say below
+
+ align:start position:0%
+are fairly lightly doped uh say below
+ 
+
+ align:start position:0%
+are fairly lightly doped uh say below
+mid 10 the 17th or below 10 to the 18th
+
+ align:start position:0%
+mid 10 the 17th or below 10 to the 18th
+ 
+
+ align:start position:0%
+mid 10 the 17th or below 10 to the 18th
+they usually diffused in at very high
+
+ align:start position:0%
+they usually diffused in at very high
+ 
+
+ align:start position:0%
+they usually diffused in at very high
+temperatures and subi is large and they
+
+ align:start position:0%
+temperatures and subi is large and they
+ 
+
+ align:start position:0%
+temperatures and subi is large and they
+satisfy the fact that the the dop and
+
+ align:start position:0%
+satisfy the fact that the the dop and
+ 
+
+ align:start position:0%
+satisfy the fact that the the dop and
+conentration is less than an I so you
+
+ align:start position:0%
+conentration is less than an I so you
+ 
+
+ align:start position:0%
+conentration is less than an I so you
+have constant diffusivities
+
+ align:start position:0%
+have constant diffusivities
+ 
+
+ align:start position:0%
+have constant diffusivities
+but beyond that case there uh turns out
+
+ align:start position:0%
+but beyond that case there uh turns out
+ 
+
+ align:start position:0%
+but beyond that case there uh turns out
+most diffusion problems in uh in devices
+
+ align:start position:0%
+most diffusion problems in uh in devices
+ 
+
+ align:start position:0%
+most diffusion problems in uh in devices
+need to be solved
+
+ align:start position:0%
+need to be solved
+ 
+
+ align:start position:0%
+need to be solved
+numerically and we introduced a very
+
+ align:start position:0%
+numerically and we introduced a very
+ 
+
+ align:start position:0%
+numerically and we introduced a very
+simple but uh powerful method for a
+
+ align:start position:0%
+simple but uh powerful method for a
+ 
+
+ align:start position:0%
+simple but uh powerful method for a
+numerical solution with the fusion
+
+ align:start position:0%
+numerical solution with the fusion
+ 
+
+ align:start position:0%
+numerical solution with the fusion
+equation and it actually was a finite
+
+ align:start position:0%
+equation and it actually was a finite
+ 
+
+ align:start position:0%
+equation and it actually was a finite
+difference formula formula it's not it's
+
+ align:start position:0%
+difference formula formula it's not it's
+ 
+
+ align:start position:0%
+difference formula formula it's not it's
+not that sophisticated and it's not
+
+ align:start position:0%
+not that sophisticated and it's not
+ 
+
+ align:start position:0%
+not that sophisticated and it's not
+actually the formulation that use is
+
+ align:start position:0%
+actually the formulation that use is
+ 
+
+ align:start position:0%
+actually the formulation that use is
+using Supreme for but gives you an idea
+
+ align:start position:0%
+using Supreme for but gives you an idea
+ 
+
+ align:start position:0%
+using Supreme for but gives you an idea
+if you needed to write your own simple
+
+ align:start position:0%
+if you needed to write your own simple
+ 
+
+ align:start position:0%
+if you needed to write your own simple
+uh method
+
+ align:start position:0%
+uh method
+ 
+
+ align:start position:0%
+uh method
+um the uh we talked about the first type
+
+ align:start position:0%
+um the uh we talked about the first type
+ 
+
+ align:start position:0%
+um the uh we talked about the first type
+of modification we need to make to fix
+
+ align:start position:0%
+of modification we need to make to fix
+ 
+
+ align:start position:0%
+of modification we need to make to fix
+uh first law and that was for electric
+
+ align:start position:0%
+uh first law and that was for electric
+ 
+
+ align:start position:0%
+uh first law and that was for electric
+field effects which can enhance the
+
+ align:start position:0%
+field effects which can enhance the
+ 
+
+ align:start position:0%
+field effects which can enhance the
+diffusivity of a high concentration
+
+ align:start position:0%
+diffusivity of a high concentration
+ 
+
+ align:start position:0%
+diffusivity of a high concentration
+species uh up to a factor two but can
+
+ align:start position:0%
+species uh up to a factor two but can
+ 
+
+ align:start position:0%
+species uh up to a factor two but can
+dramatically impact the motion of
+
+ align:start position:0%
+dramatically impact the motion of
+ 
+
+ align:start position:0%
+dramatically impact the motion of
+species at lower
+
+ align:start position:0%
+species at lower
+ 
+
+ align:start position:0%
+species at lower
+concentrations and what we're going to
+
+ align:start position:0%
+concentrations and what we're going to
+ 
+
+ align:start position:0%
+concentrations and what we're going to
+talk about next time are further um sort
+
+ align:start position:0%
+talk about next time are further um sort
+ 
+
+ align:start position:0%
+talk about next time are further um sort
+of Corrections to the simple uh uh piing
+
+ align:start position:0%
+of Corrections to the simple uh uh piing
+ 
+
+ align:start position:0%
+of Corrections to the simple uh uh piing
+diffusion that we've been talking about
+
+ align:start position:0%
+diffusion that we've been talking about
+ 
+
+ align:start position:0%
+diffusion that we've been talking about
+and more realistic doping profiles such
+
+ align:start position:0%
+and more realistic doping profiles such
+ 
+
+ align:start position:0%
+and more realistic doping profiles such
+as the case uh when we have
+
+ align:start position:0%
+as the case uh when we have
+ 
+
+ align:start position:0%
+as the case uh when we have
+concentration dependent dependent defic
+
+ align:start position:0%
+concentration dependent dependent defic
+ 
+
+ align:start position:0%
+concentration dependent dependent defic
+okay that's all I have for today and
+
+ align:start position:0%
+okay that's all I have for today and
+ 
+
+ align:start position:0%
+okay that's all I have for today and
+thanks very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much
\ No newline at end of file
diff --git a/FdwTROVfEPE.txt b/FdwTROVfEPE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b62c6ae079e16d295f2d7987cd35ca9725cda3b3
--- /dev/null
+++ b/FdwTROVfEPE.txt
@@ -0,0 +1,1941 @@
+The following content is
+provided under a Creative
+
+Commons License.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation, or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Hi.
+
+Today's lesson, well, I
+settled for the title,
+
+"Circular Functions." But I
+guess it could have been
+
+called a lot of different
+things.
+
+It could've been called
+'Trigonometry without
+
+Triangles'.
+
+It could have been called
+'Trigonometry Revisited'.
+
+And the whole point is that much
+of what today's lecture
+
+hinges on is a hang-up that
+bothered me, and which I think
+
+may bother you and is worthwhile
+discussing.
+
+I remember, when I was in
+high school, I asked my
+
+trigonometry teacher, why
+would I have to know
+
+trigonometry?
+
+And his answer was,
+surveyors use it.
+
+And at that particular time, I
+didn't know what I was going
+
+to be, but I knew what
+I wasn't going to be.
+
+I wasn't going to
+be a surveyor.
+
+And I kind of took the course
+kind of lightly, and really
+
+got clobbered a year or two
+later when I got into calculus
+
+and physics courses.
+
+So what I would like to do
+today is to introduce the
+
+notion of what we call circular
+functions, and point
+
+out what the connection is
+between these and the
+
+trigonometric functions that we
+learned when we studied the
+
+subject that we call
+trigonometry, and which might
+
+better have been called
+numerical geometry.
+
+Let me get to the point
+right away.
+
+Let's imagine that I say
+circular functions to you.
+
+I think it's rather natural
+that, as soon as I say that,
+
+you think of a circle.
+
+And because you think of a
+circle, let me draw a circle
+
+here, and let me assume that the
+radius of the circle is 1.
+
+In other words, I have the
+circle here, 'x squared' plus
+
+'y squared' equals 1.
+
+Now, the thing is this.
+
+When I talk about--
+
+And I'm assuming now that you
+are familiar with the
+
+trigonometric functions in
+the traditional sense.
+
+And in fact, the first section
+of our supplementary notes in
+
+the reading material that goes
+with the present lecture takes
+
+care of the fact that, if you
+don't recall some of these
+
+things too well, there's ample
+opportunity for refreshing
+
+your minds and getting
+some review in here.
+
+But the idea is something
+like this.
+
+When we're talking about
+calculus, we talk about
+
+functions of a real variable.
+
+We are assuming that our
+functions have the property
+
+that the domain is a set of
+suitably chosen real numbers,
+
+and the image is a suitably
+chosen set of real numbers.
+
+We do not think of inputs
+as being angles and
+
+things of this type.
+
+And so the question is, how can
+we define, for example--
+
+let's call it the
+'sine machine'.
+
+Let me come down here.
+
+I'll call it the
+'sine machine'.
+
+If the input is the number 't',
+I want the output, say,
+
+to be 'sine t'.
+
+But you see, now I'm talking
+about a number, not an angle.
+
+Well, one way of doing this
+thing visually is the old idea
+
+of the number line.
+
+Let us think of a number as
+being a length, the same as we
+
+do in coordinate geometry.
+
+We knock off lengths along the
+x-axis and the y-axis.
+
+Let me think of 't'
+as being a length.
+
+As such, I can take 't' and lay
+it off along my circle in
+
+such a way that the length
+originates at 'S' and
+
+terminates, shall we say,
+at some point 'P' whose
+
+coordinates are 'x' and 'y'.
+
+Now, notice what I'm
+saying here.
+
+I lay the length off along
+the circumference.
+
+I'll talk more about that
+a little bit later.
+
+Now, so far, so good.
+
+No mention of the word "angle"
+here or anything like this.
+
+Now, wherever t terminates-- and
+again, conventions here,
+
+if 't' is positive, I lay if
+off along the circle in the
+
+so-called positive direction,
+namely, what?
+
+Counter-clockwise.
+
+If 't' is negative, I'll lay
+it off in the clockwise
+
+direction, et cetera.
+
+The usual trigonometric
+conventions.
+
+Now what I do is is, at the
+point 'P', I drop a
+
+perpendicular.
+
+And I define the sine of 't'
+to be the length, 'PR', and
+
+the cosine of 'P' to be
+the length, 'OR'.
+
+In other words, I could
+write that like this.
+
+I could write down that I'm
+defining 'sine t' to be the
+
+length of 'RP' in that
+direction, meaning, of course,
+
+that this is just a fancy way of
+saying that the sine of 't'
+
+will just be the y-coordinate
+of the point at which the
+
+length 't' terminates
+on the circle.
+
+And in a similar way, 'cosine t'
+will be the directed length
+
+from 'O' to 'R', or more
+conventionally, the
+
+x-coordinate.
+
+Now, notice I can do this
+with any length.
+
+Whatever length I'm given, I
+just mark this length off.
+
+It's a finite length.
+
+Eventually, it has
+to terminate some
+
+place on the circle.
+
+Wherever it terminates, the
+x-coordinate of the point of
+
+termination is called the
+cosine of 't', and the
+
+y-coordinate is called
+the sine of 't'.
+
+And notice that, in this way,
+both the sine and the cosine
+
+are functions which map real
+numbers into real numbers.
+
+So that part, I hope,
+is clear.
+
+Notice again, I can mimic
+the usual traditional
+
+trigonometry.
+
+I can define the tangent of t
+to be the number 'sine t',
+
+divided by the number 'cosine
+t', et cetera.
+
+And I'll leave those details
+to the reading material.
+
+I can ascertain rather
+interesting results the same
+
+way as I could in regular
+traditional trigonometry.
+
+In fact, I can get some certain
+results very nicely.
+
+I remember, for example--
+
+Well, I won't even
+go into these.
+
+But how did you talk about the
+sine of 0 when one talked
+
+about traditional
+trigonometry?
+
+How did you embed a 0-degree
+angle into a triangle, and
+
+things of this type.
+
+Notice that in terms of
+my tradition here--
+
+and we'll summarize these
+results in a minute-- but
+
+notice, for example, that the
+sine of 0 comes out to be 0
+
+very nicely, because when
+'t' is 0, the length 0
+
+terminates at 'S'.
+
+'S' is on the x-axis.
+
+That makes, what?
+'y' equal to 0.
+
+Notice also that, if the radius
+of my circle is 1, the
+
+circumference is 2 pi.
+
+So for example, what I usually
+think of a 90-degree angle
+
+would be the length pi/2.
+
+And without making any fuss over
+this, again, leaving most
+
+of the details to the reading
+and to the simplicity of just
+
+plugging these things in, we
+arrive at these rather
+
+familiar results.
+
+We also get, very quickly, in
+addition to these results,
+
+things like the fundamental
+result that we always like
+
+with trigonometric functions.
+
+That's 'sine squared t' plus
+'cosine squared t' is 1.
+
+And how do we know that?
+
+Remember that 'cosine t' was
+just another name for the
+
+x-coordinate at which the point
+
+terminated on the circle.
+
+In other words, notice
+that 'cosine
+
+squared t' is 'x squared'.
+
+'Sine squared t'
+is 'y squared'.
+
+The x-coordinate and the
+y-coordinate are related by
+
+the fact that, what?
+
+The sum of the squares to be on
+the circle is equal to 1.
+
+We could even graph 'sine t'
+without any problem at all.
+
+Namely, we observe that when
+'t' is 0, 'sine t' is 0.
+
+Notice that as we go along the
+circle, the sine increases up
+
+until we get to pi/2, at which
+it peaks at 1, then decreases
+
+at pi, back down to 0.
+
+And if that's giving you trouble
+to follow, let's
+
+simply come back to our diagram
+to make sure that we
+
+understand this.
+
+In other words, all we're saying
+is, as 't' gets longer,
+
+its y-coordinate increases from
+0 to a maximum of 1, when
+
+the particle was over here.
+
+Then, as 't' goes from to pi/2
+to pi, the length of the
+
+y-coordinate decreases until
+it again becomes 0.
+
+And again, without making much
+more ado over this, we get the
+
+usual curve that we associate
+with the sine function even
+
+when we thought of it
+as a traditional
+
+trigonometric problem.
+
+But the major point that I want
+you to see right now--
+
+and we won't worry about
+why I want to do this--
+
+I can define the trigonometric
+functions in such a way that
+
+their domains are real numbers
+rather than angles.
+
+And in fact, this is the main
+reason why people invented the
+
+notion of radian measure.
+
+Let me see if I can't make that
+a little bit clearer,
+
+once and for all.
+
+You see, the question is this.
+
+Let's suppose I'm talking--
+
+Oh, let me give you some
+letters over here.
+
+We'll put a 'Q' over here.
+
+Let's talk about angle, 'QOS'.
+
+That's a right angle.
+
+It's 1/4 of a rotation
+of the circle.
+
+Now, the question that I have
+in mind is, if something is
+
+1/4 of a rotation, why do you
+need two different ways of
+
+saying that?
+
+Why do we have to say it's 90
+degrees or pi/2 radians, and
+
+bring in a new measure when we
+already have another way of
+
+measuring circles, angles
+of circles?
+
+The idea is something
+like this.
+
+Let's again mimic the idea of
+taking the length 't' and
+
+laying it off along the
+circle like this.
+
+Now, here's the idea.
+
+Remember, the radius of
+this circle is 1.
+
+So notice that 'PR', in other
+words, this y-coordinate, is
+
+what we call, by definition,
+the sine of 't'.
+
+In other words, just above we
+said that 'sine t' was the
+
+length 'R' to 'P' in
+that direction.
+
+Now, the point is, I said
+disregard traditional
+
+trigonometry, but we can't
+really disregard it.
+
+It exists.
+
+For the person who's had
+traditional trigonometry, how
+
+would he tend to look at this
+length divided by this length?
+
+He would think of that
+as being what?
+
+It's side opposite
+over hypotenuse.
+
+That also suggests sine.
+
+And the sine of what?
+
+Well, the sine of what
+angle this is.
+
+Now, the thing is this.
+
+Somehow or other, to avoid
+ambiguity, if we could have
+
+called whatever measure this
+angle was measured in terms
+
+of, if we could have called
+that unit 't', then notice
+
+that the sine of the angle 't'
+would have been numerically
+
+the same as the sine
+of the number 't'.
+
+And again, if this seems like a
+hard point to understand, we
+
+explore this in great
+detail in our notes.
+
+But the idea is this.
+
+You see, somehow or other, if
+'sine t' is going to have two
+
+different meanings, we would
+like to make sure that we pick
+
+the kind of a unit where it
+makes no difference whether
+
+you're thinking of 't' as being
+a number or thinking of
+
+'t' as being a length.
+
+For example, suppose I now
+invent the word "radian" to
+
+mean the following.
+
+An angle is said to
+have 't' radians.
+
+If, when made the central angle
+of a unit circle, a
+
+circle whose radius is 1, it
+subtends an arc whose length
+
+is 't' units of length.
+
+See, in other words, I would
+define the measure called
+
+radians so that an angle of
+'t' radians intercepts the
+
+length 't' over here.
+
+In that way, 'sine t' is
+unambiguous whether you're
+
+talking about an angle
+or a length.
+
+For example, when I say
+the sine of pi/1
+
+radians, what do I mean?
+
+I mean the angle which is the
+sine of the angle which
+
+intercepts a length, an
+arc, pi/2 units long.
+
+Well, see, pi/2 is
+this length.
+
+I'm now talking about
+this angle here.
+
+And the sine, therefore, of
+pi/2 radians, in terms of
+
+classical trigonometry, is 1.
+
+But that's also what the sine
+of a number pi/2 was.
+
+This explains the convention
+that one says when one uses
+
+radians, you can leave
+the label off.
+
+All we're saying is that, if
+we had used degrees, there
+
+would have been an ambiguity.
+
+Certainly, the sine of 3
+degrees is not the same
+
+as the sine of 3.
+
+You see, 3 degrees is a
+rather small angle.
+
+But 3 is a rather great length
+when you're talking about the
+
+arc of the unit circle here.
+
+Remember, 1/2 circle is pi units
+long, so 3 would be just
+
+about this long.
+
+In other words, notice that 3
+radians and 3 degrees are
+
+entirely different things.
+
+But the beauty is what?
+
+That if we agreed to use radian
+measure, then we have
+
+no ambiguity when we talk
+about the sine.
+
+The sine of the number 't' will
+equal the sine of the
+
+angle 't' radians.
+
+The cosine of a number 't' will
+equal the cosine of the
+
+angle 't' radians.
+
+In a certain sense, it was
+analogous to when we talked
+
+about the derivative 'dy/dx',
+then wanted to define
+
+differentials 'dy' and 'dx'
+separately, so that 'dy'
+
+divided by 'dx' would be the
+same as 'dy/dx', that we
+
+wanted to avoid any ambiguity
+where the same symbol could be
+
+interpreted in two different
+ways to give
+
+two different answers.
+
+By the way, again, there is
+nothing sacred about our
+
+choice of why we pick
+circular functions.
+
+We could have picked hyperbolic
+functions.
+
+Namely, why couldn't we have
+started, say, with one branch
+
+of the hyperbola, 'x squared'
+minus 'y squared' equals 1.
+
+Given a length 't', why couldn't
+we have measured 't'
+
+off along the hyperbola?
+
+Say this way if 't' is positive,
+the other way if 't'
+
+is negative.
+
+And then what we could
+have done is drop the
+
+perpendicular again.
+
+And we could have
+defined what?
+
+The y-coordinate to
+be the hyperbolic.
+
+Well, we couldn't call it cosine
+anymore because it
+
+would be confused with the
+circular functions.
+
+We could have invented a name,
+as we later will, called the
+
+'hyperbolic cosine'.
+
+I won't go into any more
+detail on this.
+
+See, this is an abbreviation
+for hyperbolic
+
+cosine, meaning this--
+
+I'm sorry, I got
+this backwards.
+
+Call the x-coordinate the
+hyperbolic cosine, the
+
+y-coordinate the hyperbolic
+sine.
+
+You don't have to know anything
+about advanced
+
+mathematics to see this.
+
+All I'm saying is, I could just
+as easily have taken any
+
+geometric figure, marked off
+lengths along it, taken the
+
+x-coordinates and the
+y-coordinates, and seen what
+
+relationships they obey.
+
+You see, as such, there's
+nothing sacred about working
+
+on a circle.
+
+Not only that, but even after
+you agree to work on the
+
+circle, there are many
+other ways that one
+
+could have done this.
+
+For example, someone might have
+said, look it, when you
+
+take this length called 't', why
+did you elect to mark it
+
+off along the circle?
+
+Why couldn't you have taken a
+radius equal to 't', taken 'S'
+
+as a center, and swung an arc
+that met the circle, and call
+
+this length 't'?
+
+You see, instead of measuring
+along the circle, measure
+
+along the straight line.
+
+Again, you could have done
+this if you wanted to.
+
+Why you would've wanted
+to do this?
+
+Well, you have the same
+right to do this
+
+as I had to do mine.
+
+Of course, you have to be
+a little bit careful.
+
+For example, in this particular
+configuration,
+
+notice that, if this is how
+you're going to define your
+
+trigonometric function, your
+input, your domain, has to be
+
+somewhere between 0 and 2.
+
+In other words, you cannot have
+a length longer than 2,
+
+because notice that the
+diameter of the
+
+circle is only 2.
+
+And therefore, if 't' were
+greater than 2, when you swung
+
+an arc from the point 'S',
+it wouldn't meet
+
+the circle at all.
+
+Well, that's no great
+handicap.
+
+It's no great disaster.
+
+You still have the right
+to make up whatever
+
+functions you want.
+
+I will try to make it clearer
+why we chose these circular
+
+functions from a physical point
+of view as we go along.
+
+What I thought I'd like to do
+now is, having motivated, that
+
+we can invent the trigonometric
+functions in
+
+terms of numbers definitions
+along this circle.
+
+And coupled with the fact that,
+in radian measure, you
+
+can have a very nice
+identification between what's
+
+happening pictorially and what's
+happening analytically,
+
+to show, for example, that in
+terms of our subject called
+
+calculus, that we're pretty much
+home free once we learn
+
+these basic ideas.
+
+You see, the important point
+is that, in a manner of
+
+speaking, we have finished
+differential calculus.
+
+We know what all the recipes
+are We know what properties
+
+things have.
+
+So all of the rules that we
+learned will apply to any
+
+particular type of function
+that we're talking about.
+
+For example, let's suppose
+we define 'f of
+
+x' to be 'sine x'.
+
+And we want to find the
+derivative of 'sine x'.
+
+Notice that 'f prime of x'
+evaluated at any number 'x1'
+
+has already been
+defined for us.
+
+It's the limit as 'delta x'
+approaches 0, 'f of 'x1 plus
+
+delta x'', minus 'f of
+x1' over 'delta x'.
+
+This is true for any
+function 'f'.
+
+In particular, if 'f of x' is
+'sine x', all we get is what?
+
+That the derivative is the limit
+as 'delta x' approaches
+
+0, sine of 'x1 plus delta
+x' minus sine of
+
+'x1' over 'delta x'.
+
+Now you see, on this
+particular score,
+
+nobody can fault us.
+
+This is still the basic
+definition.
+
+All that happens computationally
+is that, if
+
+we're not familiar with our
+new functions called the
+
+trigonometric functions, we
+might not know how to express
+
+sine of 'x1 plus delta x' in
+a more convenient form.
+
+What do we mean by a more
+convenient form?
+
+Well, notice again, as is always
+the case when we take a
+
+derivative, as delta x
+approaches 0, our numerator
+
+becomes 'sine x1' minus 'sine
+x1', which is 0/0.
+
+And we're back to our familiar
+taboo form of 0/0.
+
+Somehow or other, we're going
+to have to make a refinement
+
+on our numerator that
+will allow us to get
+
+rid of a 0/0 form.
+
+Well, to make a long story
+short, if we happen to know
+
+the addition formula
+for the sine--
+
+in other words, 'sine 'x1 plus
+delta x'' is ''sine x1'
+
+'cosine delta x'', plus ''sine
+delta x' 'cosine x1''--
+
+then we subtract off 'sine x1'
+and divide by 'delta x', and
+
+then we factor and
+collect terms.
+
+We see what?
+
+Without any knowledge
+of calculus at
+
+all, but just what?
+
+By our definition of derivative,
+just by our
+
+definition, coupled with
+properties of the
+
+trigonometric functions, we wind
+up with the fact that 'f
+
+prime of x1' is this
+particular limit.
+
+Now certainly, our limit
+theorems don't change.
+
+The limit of a sum is
+still going to be
+
+the sum of the limits.
+
+The limit of a product
+will still be the
+
+product of the limits.
+
+So all in all, what we have to
+sort of do is figure out what
+
+these limits will be.
+
+Certainly, as 'delta x'
+approaches 0, this will stay
+
+'cosine x1'.
+
+Certainly this will stay 'sine
+x1', because 'x1' is a fixed
+
+number that doesn't depend
+on 'delta x'.
+
+But notice, rather
+interestingly, that both of my
+
+expressions in parentheses
+happen to take on that 0/0
+
+form if we're not careful.
+
+Namely, if you replace 'delta
+x' by 0, sine 0 is 0, 0/0 is
+
+0, and we run into trouble here
+if we replace 'delta x'
+
+by 0, which of course
+we can't do.
+
+This is the same definition
+of limit as we had before.
+
+'Delta x' gets arbitrarily
+close to 0, but never is
+
+allowed to get there.
+
+Well, you see, if nothing else,
+this motivates why we
+
+would like to learn this
+particular type of limit.
+
+In other words, what we would
+like to know is, how do you--
+
+the 'delta x' symbol here
+isn't that important.
+
+'Delta x' just stands
+for any number.
+
+Notice that what we would like
+to know is, if you take the
+
+sine of something over that same
+something, and take the
+
+limit as that same something
+goes to 0, we would like to
+
+know what that becomes.
+
+In a similar way, we would like
+to know how to handle
+
+this quotient here, because
+notice that when 'delta x' is
+
+0, cosine 0 is 1.
+
+This is 1 minus 1 over 0.
+
+It's another 0/0 form.
+
+So the problem that we're
+confronted with is that, what
+
+we would like to do is to figure
+out how to handle the
+
+limit of 'sine t' over 't'
+as 't' approaches 0.
+
+Now, what's 't' here?
+'t' is a number.
+
+Remember that.
+
+This is the big pitch
+I've been making.
+
+We're thinking of
+'t' as a number.
+
+If, on the other hand, you feel
+more comfortable thinking
+
+in terms of traditional
+trigonometry--
+
+and let's face it, the more
+background you've had in
+
+traditional trigonometry, the
+more comfortable you're going
+
+to feel using it.
+
+Let's simply agree to do this,
+that if it bothers you to
+
+think of this as a length
+divided by a length, et
+
+cetera, and that this is a
+length or a number, let's
+
+agree that we will go back to
+angles but use radian measure.
+
+Why?
+
+Because if the angle is measured
+in radians, the sine
+
+of the angle 't' radians is the
+same as the number, the
+
+sine, of the number 't'.
+
+Well again, here's how this
+problem is tackled.
+
+What we do is we mark off the
+angle of 't' radians.
+
+Remember that we have
+the unit circle.
+
+And what we very cleverly do
+is we catch our wedge, our
+
+circular wedge, between
+two right triangles.
+
+Again, without making a big
+issue over this, notice that
+
+this length is 'sine t', this
+length is 'cosine t', so the
+
+area of the small triangle
+is 'sine t' times
+
+'cosine t' over 2.
+
+See, 'sine t' times
+'cosine t' over 2.
+
+Now, on the other hand, since
+that's caught in our wedge,
+
+what is the area of our wedge?
+
+Well, since the area of the
+entire circle is pi-- see, pi
+
+'R squared' and 'R' is 1--
+
+since the area of the entire
+circle is pi--
+
+and we're taking what?
+
+'t' of the 2pi.
+
+So there are two pi radians
+in a circle.
+
+So the sector of the circle that
+we have, it's 't/2pi' of
+
+the entire circle.
+
+And by the way, this is done
+more rigorously and carried
+
+out in detail in the notes.
+
+Let me point out that, if we
+insisted on working with
+
+degrees, instead of
+'t/2pi', we just
+
+would have had 't/360'.
+
+Because, you see, if we're
+dealing with degrees, the
+
+entire angle and measure of the
+circle is 360 degrees, and
+
+we would have had 't/360'.
+
+But here we've used the
+fact that we're
+
+dealing with radians.
+
+And finally, the bigger
+triangle, which includes the
+
+wedge, has, as its base, 1,
+so that's the radius.
+
+And since the tangent is side
+opposite over side adjacent,
+
+this length is 'tangent t'.
+
+And so what we have is what?
+
+That ''sine t' 'cosine t/2' must
+be less than this, which
+
+in turn must be less than this,
+multiplying through by 2
+
+and dividing through
+by 'sine t'.
+
+And by the way, this hinges on
+the fact that 't' is positive.
+
+Again, in our notes, we treat
+the case where 't' is negative
+
+to arrive at the same result.
+
+Remembering that 'tan t' is
+'sine t' over 'cosine t', we
+
+wind up with this result.
+
+And now, observing that
+as 't' approaches 0,
+
+this approaches 1.
+
+This also approaches 1.
+
+And 't' over 'sine t' is caught
+between these two.
+
+We get that the limit of 't'
+over 'sine t' as 't'
+
+approaches 0 is 1.
+
+Now of course, since this limit
+is 1, the limit of the
+
+reciprocal of this will be
+the reciprocal of this.
+
+But what's very nice about the
+number 1 is that it's equal to
+
+its own reciprocal.
+
+In other words, what we've now
+shown is that the limit of
+
+'sine t' over 't' as 't'
+approaches 0 is 1.
+
+That, as I said before,
+is done in the text.
+
+We do it in our notes.
+
+But the thing that I hope this
+motivates is why we want to do
+
+this in the first place.
+
+Notice that this was a limit
+that we had to compute if we
+
+wanted to compute the derivative
+of the sine.
+
+Now, the next thing was, how
+do we handle '1 - cosine t'
+
+over 't' as 't' approaches 0?
+
+Again, leaving the details to
+you to sketch in as you see
+
+fit, let me point out simply
+what the mathematics
+
+involved here is.
+
+You see, what we can handle
+is 'sine t' over 't'.
+
+That means that what we would
+like to do is, whenever we're
+
+given an alien form, we would
+somehow or other like to
+
+figure some way of factoring
+a sine t over
+
+t out of this thing.
+
+When you look at '1 - cosine
+t', the identity, 'sine
+
+squared' equals '1 - 'cosine
+squared t'',
+
+should suggest itself.
+
+Now, how do you get from '1 -
+cosine t' to '1 - 'cosine
+
+squared t''?
+
+You have to multiply
+by '1 + cosine t'.
+
+And if you multiply by '1 +
+cosine t' upstairs, you must
+
+multiply by '1 + cosine
+t' downstairs.
+
+By the way, the only time you
+can't multiply by something is
+
+when the thing is 0.
+
+You can't put that into
+the denominator.
+
+Notice that 'cosine t' is
+not 0 in a neighborhood
+
+of 't' equals 0.
+
+See, 'cosine t' behaves like 1
+when 't' is near 0, so this is
+
+a permissible step in this
+particular problem.
+
+The point is, we now factor '1 -
+'cosine squared t'' as 'sine
+
+t' times 'sine t'.
+
+See, that's 'sine squared t'.
+
+We break up our 't' times
+'1 + cosine t' this way.
+
+Now we know that the limit of
+a product is the product of
+
+the limits.
+
+This we already know
+goes to 1.
+
+And as 't' approaches 0, from
+our previous limit work on the
+
+like, notice here, the limit of
+a quotient is the quotient
+
+of the limits, the numerator
+goes to 0, the denominator
+
+goes to 2, because as t
+approaches 0, cosine 0 is 1.
+
+At any rate, that's
+0/2, which is 0.
+
+And so this limit is 0.
+
+Now, at the risk of giving you
+a slight headache as I take
+
+the board down here, let
+me just review what
+
+it was that we did.
+
+You see, notice that, without
+any knowledge of these limits
+
+at all, we were able to show
+that whatever the derivative
+
+of 'sine x' was, it was this
+particular thing here.
+
+Now what we've done is we've
+shown that this is 1, and
+
+we've shown that this is 0.
+
+And using our limit theorems,
+what we now see is what?
+
+That if 'f of x' is 'sine x', 'f
+prime of x' is 'cosine x'.
+
+Let me just write that down over
+here, that if 'y' equals
+
+'sine x', 'dy/dx'
+is 'cosine x'.
+
+And again, notice how much of
+the calculus involved here was
+
+nothing new.
+
+It goes back to the so-called
+baby chapter that nobody
+
+likes, where we go back to
+epsilons, deltas, you see
+
+derivatives by 'delta
+x', et cetera.
+
+See, those recipes always
+remain the same.
+
+What happens is, as you invent
+new functions, you need a
+
+different degree of
+computational sophistication
+
+to find the desired limits.
+
+By the way, once you get over
+these hurdles, everything
+
+again starts to go smoothly
+as before.
+
+For example, our chain rule.
+
+Suppose we have now that 'y'
+equals 'sine u', where 'u' is
+
+some differentiable
+function of 'x'.
+
+And we now want to
+find the 'dy/dx'.
+
+Well, you see, the point is
+that we know that the
+
+derivative of 'sine u' with
+respect to 'u' would be
+
+'cosine u'.
+
+What we want is the derivative
+of 'sine u'
+
+with respect to 'x'.
+
+And we motivate the chain rule
+the same way as we did before.
+
+It happens to be that we're
+dealing with the specific
+
+value called sine,
+but it could've
+
+been any old function.
+
+How would you differentiate 'f
+of u' with respect to 'x' if
+
+you know how to differentiate 'f
+of u' with respect to 'u'?
+
+And the answer is, you would
+just differentiate with
+
+respect to 'u', and multiply
+that by a derivative of 'u'
+
+with respect to 'x'.
+
+In other words, we get
+the result what?
+
+That since 'dy/du' is 'cosine
+u', we get that the derivative
+
+of 'sine u' with respect
+to 'x' is
+
+'cosine u' times 'du/dx'.
+
+And by the way, one rather nice
+application of this is
+
+that it gives us a very quick
+way of getting the derivative
+
+of 'cosine x'.
+
+After all, our basic identity
+is that 'cosine x' is sine
+
+pi/2 minus 'x'.
+
+Again, a number or an
+angle, either way.
+
+As long as the measurement is
+in radians, it makes no
+
+difference whether you think of
+this as being an angle or
+
+being a number.
+
+The answer will be the same.
+
+The idea is this.
+
+To take the derivative of
+'cosine x' with respect to
+
+'x', all I have to differentiate
+is sine pi/2
+
+minus 'x' with respect to 'x'.
+
+But I know how to do that.
+
+Namely, the derivative of sine
+pi/2 minus 'x' is cosine pi/2
+
+minus 'x,' and by the chain
+rule, times the derivative of
+
+this with respect to 'x'.
+
+Well, pi/2 is a constant.
+
+The derivative of 'minus
+x' is minus 1.
+
+And then, remembering that the
+cosine of pi/2 minus 'x' is
+
+'sine x', I now have the result
+that the derivative of
+
+the cosine is minus the sine.
+
+And again, I can do all sorts
+of things this way.
+
+If I want the derivative of a
+tangent, I could write tangent
+
+as sine over cosine.
+
+Use the quotient rule.
+
+You see, as soon as I make one
+breakthrough, all of the
+
+previous body of calculus
+comes to my
+
+rescue, so to speak.
+
+By the way, what I'd like to do
+now is point out why, from
+
+a physical point of view, we
+like circular functions to be
+
+independent of angles
+and the like.
+
+With the results that we've
+derived so far, it's rather
+
+easy to derive one
+more result.
+
+Namely, let's assume
+that a particle is
+
+moving along the x-axis--
+
+I'm going to start with the
+answer, sort of, and work
+
+backwards--
+
+according to the rule, 'x'
+equals 'sine kt', where 't' is
+
+time and 'k' is a constant.
+
+Then its speed, 'dx/dt',
+is what?
+
+It's the derivative of 'sine
+kt', which is 'cosine kt',
+
+times the derivative of what's
+inside with respect to 't'.
+
+In other words, it's
+'k cosine kt'.
+
+The second derivative of 'x'
+with respect to 't', namely,
+
+the acceleration is what?
+
+How do you differentiate
+the cosine?
+
+The derivative of the cosine
+is minus the sine.
+
+By the chain rule, I must
+multiply by the derivative of
+
+'kt' with respect to 't', which
+gives me another factor
+
+of 't' over here.
+
+Remembering that 'x' equals
+'sine kt', I arrive at this
+
+particular so-called
+differential equation.
+
+And what does this say?
+
+It says that 'd2x/ dt squared',
+the acceleration, is
+
+proportional to the
+displacement, the distance
+
+traveled, but in the
+opposite direction.
+
+You see, 'k squared' can't
+be negative, so 'minus 'k
+
+squared'' can't be positive.
+
+This says what?
+
+The acceleration is proportional
+to the
+
+displacement, but in the
+opposite direction.
+
+Does that problem require any
+knowledge of angles to solve?
+
+Notice that this is a perfectly
+
+good physical problem.
+
+It's known as simple
+harmonic motion.
+
+And all I'm trying to have you
+see is that, by inventing the
+
+circular functions in the proper
+way, not only can we do
+
+their calculus, but even more
+importantly, if we reverse
+
+these steps, for example, we
+can show that, to solve the
+
+physical problem of simple
+harmonic motion, we have to
+
+know the so-called circular
+trigonometric functions.
+
+And this is a far cry, you see,
+from using trigonometry
+
+in the sense that the surveyor
+uses trigonometry.
+
+You see, this ties up with my
+initial hang-up that I was
+
+telling you about at the
+beginning of the program.
+
+By the way, in closing, I should
+also make reference to
+
+something that we pointed out
+in our last lecture, namely,
+
+inverse differentiation.
+
+Keep in mind, also, that as you
+read the calculus of the
+
+trigonometric functions, that
+the fact that we know that the
+
+derivative of sine u with
+respect to 'u' was 'cosine u'
+
+gives us, with a switch in
+emphasis, the result that the
+
+integral 'cosine u', 'du' is
+'sine u' plus a constant.
+
+And in a similar way, since the
+derivative of cosine is
+
+minus the sine, the integral
+of 'sine u' with respect to
+
+'u' is 'minus cosine
+u' plus a constant.
+
+Be careful.
+
+Notice how the sines
+can screw you up.
+
+Namely, they're in the opposite
+sense when you're
+
+integrating as when you
+were differentiating.
+
+But again, these are the details
+which I expect you can
+
+have come out in the
+wash rather nicely.
+
+We can continue on this way,
+from knowing how to
+
+differentiate 'sine x'
+to the nth power.
+
+Namely, it's 'n - 1' 'x', times
+the derivative of 'sine
+
+x', which is 'cosine x'.
+
+We don't want this in here.
+
+That's a differential form.
+
+Without going into any detail
+here, notice that a
+
+modification of this shows us
+that, if we differentiate
+
+this, we wind up with this.
+
+We could now take the time, if
+this were the proper place, to
+
+develop all sorts of derivative
+formulas and
+
+integral formulas.
+
+As you study your study guide,
+you will notice that the
+
+lesson after this is concerned
+with the calculus of the
+
+circular functions.
+
+My feeling is is that, with
+this as background, a very
+
+good review of the previous part
+of the course will be to
+
+see how much of this you can
+apply on your own to these new
+
+functions called the
+circular functions.
+
+Next time, we will talk, as
+you may be able to guess,
+
+about the inverse circular
+functions
+
+and why they're important.
+
+But until next time, goodbye.
+
+Funding for the publication of
+this video was provided by the
+
+Gabriella and Paul Rosenbaum
+Foundation.
+
+Help OCW continue to provide
+free and open access to MIT
+
+courses by making a donation
+at ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/FkfsmwAtDdY.txt b/FkfsmwAtDdY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cb923c4f9f820e5ab76ee759d41cbf782e264759
--- /dev/null
+++ b/FkfsmwAtDdY.txt
@@ -0,0 +1,4176 @@
+align:start position:0%
+ 
+you've seen a lot of functions in
+
+ align:start position:0%
+you've seen a lot of functions in
+ 
+
+ align:start position:0%
+you've seen a lot of functions in
+introductory calculus trig functions
+
+ align:start position:0%
+introductory calculus trig functions
+ 
+
+ align:start position:0%
+introductory calculus trig functions
+rational functions exponentials logs and
+
+ align:start position:0%
+rational functions exponentials logs and
+ 
+
+ align:start position:0%
+rational functions exponentials logs and
+so on I don't know whether your calculus
+
+ align:start position:0%
+so on I don't know whether your calculus
+ 
+
+ align:start position:0%
+so on I don't know whether your calculus
+course has included a general discussion
+
+ align:start position:0%
+course has included a general discussion
+ 
+
+ align:start position:0%
+course has included a general discussion
+of functions uh the old-fashioned ones
+
+ align:start position:0%
+of functions uh the old-fashioned ones
+ 
+
+ align:start position:0%
+of functions uh the old-fashioned ones
+didn't and we will go into that now in
+
+ align:start position:0%
+didn't and we will go into that now in
+ 
+
+ align:start position:0%
+didn't and we will go into that now in
+this segment and we're going to be
+
+ align:start position:0%
+this segment and we're going to be
+ 
+
+ align:start position:0%
+this segment and we're going to be
+interpreting functions as a special case
+
+ align:start position:0%
+interpreting functions as a special case
+ 
+
+ align:start position:0%
+interpreting functions as a special case
+of binary relations so let's just say
+
+ align:start position:0%
+of binary relations so let's just say
+ 
+
+ align:start position:0%
+of binary relations so let's just say
+what a binary relation is a binary
+
+ align:start position:0%
+what a binary relation is a binary
+ 
+
+ align:start position:0%
+what a binary relation is a binary
+relation is a mathematical object that
+
+ align:start position:0%
+relation is a mathematical object that
+ 
+
+ align:start position:0%
+relation is a mathematical object that
+Associates elements of one set called
+
+ align:start position:0%
+Associates elements of one set called
+ 
+
+ align:start position:0%
+Associates elements of one set called
+The Domain with elements of another set
+
+ align:start position:0%
+The Domain with elements of another set
+ 
+
+ align:start position:0%
+The Domain with elements of another set
+called the co-domain and I'm going to
+
+ align:start position:0%
+called the co-domain and I'm going to
+ 
+
+ align:start position:0%
+called the co-domain and I'm going to
+give you a bunch of examples of binary
+
+ align:start position:0%
+give you a bunch of examples of binary
+ 
+
+ align:start position:0%
+give you a bunch of examples of binary
+relations in a in a short moment but
+
+ align:start position:0%
+relations in a in a short moment but
+ 
+
+ align:start position:0%
+relations in a in a short moment but
+let's just talk about uh what they're
+
+ align:start position:0%
+let's just talk about uh what they're
+ 
+
+ align:start position:0%
+let's just talk about uh what they're
+for and what their role is so they may
+
+ align:start position:0%
+for and what their role is so they may
+ 
+
+ align:start position:0%
+for and what their role is so they may
+be familiar to you as computer
+
+ align:start position:0%
+be familiar to you as computer
+ 
+
+ align:start position:0%
+be familiar to you as computer
+scientists if you've worked with any
+
+ align:start position:0%
+scientists if you've worked with any
+ 
+
+ align:start position:0%
+scientists if you've worked with any
+relational databases like SQL or MySQL
+
+ align:start position:0%
+relational databases like SQL or MySQL
+ 
+
+ align:start position:0%
+relational databases like SQL or MySQL
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+SQL uh and we'll see an example that
+
+ align:start position:0%
+SQL uh and we'll see an example that
+ 
+
+ align:start position:0%
+SQL uh and we'll see an example that
+indicates where the original ideas
+
+ align:start position:0%
+indicates where the original ideas
+ 
+
+ align:start position:0%
+indicates where the original ideas
+behind uh those relational databases
+
+ align:start position:0%
+behind uh those relational databases
+ 
+
+ align:start position:0%
+behind uh those relational databases
+came from but even more fundamental
+
+ align:start position:0%
+came from but even more fundamental
+ 
+
+ align:start position:0%
+came from but even more fundamental
+relations are one of the most basic
+
+ align:start position:0%
+relations are one of the most basic
+ 
+
+ align:start position:0%
+relations are one of the most basic
+mathematical abstractions right after
+
+ align:start position:0%
+mathematical abstractions right after
+ 
+
+ align:start position:0%
+mathematical abstractions right after
+sets and they uh play a role everywhere
+
+ align:start position:0%
+sets and they uh play a role everywhere
+ 
+
+ align:start position:0%
+sets and they uh play a role everywhere
+uh we're going to be looking in later
+
+ align:start position:0%
+uh we're going to be looking in later
+ 
+
+ align:start position:0%
+uh we're going to be looking in later
+lectures at special kinds of binary
+
+ align:start position:0%
+lectures at special kinds of binary
+ 
+
+ align:start position:0%
+lectures at special kinds of binary
+relations like equivalence relations and
+
+ align:start position:0%
+relations like equivalence relations and
+ 
+
+ align:start position:0%
+relations like equivalence relations and
+partial orders uh and uh numerical
+
+ align:start position:0%
+partial orders uh and uh numerical
+ 
+
+ align:start position:0%
+partial orders uh and uh numerical
+congruences
+
+ align:start position:0%
+congruences
+ 
+
+ align:start position:0%
+congruences
+but today we're going to set up the
+
+ align:start position:0%
+but today we're going to set up the
+ 
+
+ align:start position:0%
+but today we're going to set up the
+Machinery to be using binary relations
+
+ align:start position:0%
+Machinery to be using binary relations
+ 
+
+ align:start position:0%
+Machinery to be using binary relations
+for counting which will be another
+
+ align:start position:0%
+for counting which will be another
+ 
+
+ align:start position:0%
+for counting which will be another
+important application uh in this class
+
+ align:start position:0%
+important application uh in this class
+ 
+
+ align:start position:0%
+important application uh in this class
+so let's look at an
+
+ align:start position:0%
+so let's look at an
+ 
+
+ align:start position:0%
+so let's look at an
+example um and I'm going to take one
+
+ align:start position:0%
+example um and I'm going to take one
+ 
+
+ align:start position:0%
+example um and I'm going to take one
+that's close to home the registered for
+
+ align:start position:0%
+that's close to home the registered for
+ 
+
+ align:start position:0%
+that's close to home the registered for
+relation which is a relation between
+
+ align:start position:0%
+relation which is a relation between
+ 
+
+ align:start position:0%
+relation which is a relation between
+students that's going to be the domain
+
+ align:start position:0%
+students that's going to be the domain
+ 
+
+ align:start position:0%
+students that's going to be the domain
+uh in this case four students Jason Joan
+
+ align:start position:0%
+uh in this case four students Jason Joan
+ 
+
+ align:start position:0%
+uh in this case four students Jason Joan
+eway and Adam and
+
+ align:start position:0%
+eway and Adam and
+ 
+
+ align:start position:0%
+eway and Adam and
+subjects uh for subjects as a
+
+ align:start position:0%
+subjects uh for subjects as a
+ 
+
+ align:start position:0%
+subjects uh for subjects as a
+coincidence
+
+ align:start position:0%
+coincidence
+ 
+
+ align:start position:0%
+coincidence
+60423 012
+
+ align:start position:0%
+60423 012
+ 
+
+ align:start position:0%
+60423 012
+and4 and the relation R is going to be
+
+ align:start position:0%
+and4 and the relation R is going to be
+ 
+
+ align:start position:0%
+and4 and the relation R is going to be
+indicated by arrows which show just
+
+ align:start position:0%
+indicated by arrows which show just
+ 
+
+ align:start position:0%
+indicated by arrows which show just
+which students are associated with which
+
+ align:start position:0%
+which students are associated with which
+ 
+
+ align:start position:0%
+which students are associated with which
+subjects meaning that they're registered
+
+ align:start position:0%
+subjects meaning that they're registered
+ 
+
+ align:start position:0%
+subjects meaning that they're registered
+for that subject so if we look at
+
+ align:start position:0%
+for that subject so if we look at
+ 
+
+ align:start position:0%
+for that subject so if we look at
+Jason uh we can see that there there's a
+
+ align:start position:0%
+Jason uh we can see that there there's a
+ 
+
+ align:start position:0%
+Jason uh we can see that there there's a
+particular Arrow connecting Jason and 60
+
+ align:start position:0%
+particular Arrow connecting Jason and 60
+ 
+
+ align:start position:0%
+particular Arrow connecting Jason and 60
+42 and what that tells us is that Jason
+
+ align:start position:0%
+42 and what that tells us is that Jason
+ 
+
+ align:start position:0%
+42 and what that tells us is that Jason
+is registered for
+
+ align:start position:0%
+is registered for
+ 
+
+ align:start position:0%
+is registered for
+6042 now there's a bunch of notations
+
+ align:start position:0%
+6042 now there's a bunch of notations
+ 
+
+ align:start position:0%
+6042 now there's a bunch of notations
+that are used uh with respect to Binary
+
+ align:start position:0%
+that are used uh with respect to Binary
+ 
+
+ align:start position:0%
+that are used uh with respect to Binary
+relations so let's look at some
+
+ align:start position:0%
+relations so let's look at some
+ 
+
+ align:start position:0%
+relations so let's look at some
+um one way to write it is if you think
+
+ align:start position:0%
+um one way to write it is if you think
+ 
+
+ align:start position:0%
+um one way to write it is if you think
+of the relation r as like an equality
+
+ align:start position:0%
+of the relation r as like an equality
+ 
+
+ align:start position:0%
+of the relation r as like an equality
+sign or a less than sign where it's
+
+ align:start position:0%
+sign or a less than sign where it's
+ 
+
+ align:start position:0%
+sign or a less than sign where it's
+normally written in the middle of the
+
+ align:start position:0%
+normally written in the middle of the
+ 
+
+ align:start position:0%
+normally written in the middle of the
+two things that it's connecting as in
+
+ align:start position:0%
+two things that it's connecting as in
+ 
+
+ align:start position:0%
+two things that it's connecting as in
+this example Json R 6042 that would be
+
+ align:start position:0%
+this example Json R 6042 that would be
+ 
+
+ align:start position:0%
+this example Json R 6042 that would be
+called infix not
+
+ align:start position:0%
+called infix not
+ 
+
+ align:start position:0%
+called infix not
+ation um sometimes it's written as a
+
+ align:start position:0%
+ation um sometimes it's written as a
+ 
+
+ align:start position:0%
+ation um sometimes it's written as a
+binary predicate R of Json comma
+
+ align:start position:0%
+binary predicate R of Json comma
+ 
+
+ align:start position:0%
+binary predicate R of Json comma
+6042 that would be kind of prefix
+
+ align:start position:0%
+6042 that would be kind of prefix
+ 
+
+ align:start position:0%
+6042 that would be kind of prefix
+notation where the relation or operator
+
+ align:start position:0%
+notation where the relation or operator
+ 
+
+ align:start position:0%
+notation where the relation or operator
+comes first uh and then uh if you start
+
+ align:start position:0%
+comes first uh and then uh if you start
+ 
+
+ align:start position:0%
+comes first uh and then uh if you start
+being a little closer to the formal
+
+ align:start position:0%
+being a little closer to the formal
+ 
+
+ align:start position:0%
+being a little closer to the formal
+definition of what a binary relation is
+
+ align:start position:0%
+definition of what a binary relation is
+ 
+
+ align:start position:0%
+definition of what a binary relation is
+you could say that the ordered pair Json
+
+ align:start position:0%
+you could say that the ordered pair Json
+ 
+
+ align:start position:0%
+you could say that the ordered pair Json
+6042 is a member of the relation if you
+
+ align:start position:0%
+6042 is a member of the relation if you
+ 
+
+ align:start position:0%
+6042 is a member of the relation if you
+wanted to be really precise you would
+
+ align:start position:0%
+wanted to be really precise you would
+ 
+
+ align:start position:0%
+wanted to be really precise you would
+say that it was a member of the graph of
+
+ align:start position:0%
+say that it was a member of the graph of
+ 
+
+ align:start position:0%
+say that it was a member of the graph of
+the relation and I'll come back and
+
+ align:start position:0%
+the relation and I'll come back and
+ 
+
+ align:start position:0%
+the relation and I'll come back and
+elaborate further on what the graph of a
+
+ align:start position:0%
+elaborate further on what the graph of a
+ 
+
+ align:start position:0%
+elaborate further on what the graph of a
+relation is and uh uh and what this
+
+ align:start position:0%
+relation is and uh uh and what this
+ 
+
+ align:start position:0%
+relation is and uh uh and what this
+ordered pairs business
+
+ align:start position:0%
+ordered pairs business
+ 
+
+ align:start position:0%
+ordered pairs business
+is but for now just let's continue with
+
+ align:start position:0%
+is but for now just let's continue with
+ 
+
+ align:start position:0%
+is but for now just let's continue with
+this example and a basic concept with
+
+ align:start position:0%
+this example and a basic concept with
+ 
+
+ align:start position:0%
+this example and a basic concept with
+relations is the idea of the image of a
+
+ align:start position:0%
+relations is the idea of the image of a
+ 
+
+ align:start position:0%
+relations is the idea of the image of a
+bunch of domain elements under the
+
+ align:start position:0%
+bunch of domain elements under the
+ 
+
+ align:start position:0%
+bunch of domain elements under the
+relation so you can think of the
+
+ align:start position:0%
+relation so you can think of the
+ 
+
+ align:start position:0%
+relation so you can think of the
+relation as an operator that applies to
+
+ align:start position:0%
+relation as an operator that applies to
+ 
+
+ align:start position:0%
+relation as an operator that applies to
+domain elements or even sets of domain
+
+ align:start position:0%
+domain elements or even sets of domain
+ 
+
+ align:start position:0%
+domain elements or even sets of domain
+element elements so if I write R of Json
+
+ align:start position:0%
+element elements so if I write R of Json
+ 
+
+ align:start position:0%
+element elements so if I write R of Json
+that defines the subjects that Json is
+
+ align:start position:0%
+that defines the subjects that Json is
+ 
+
+ align:start position:0%
+that defines the subjects that Json is
+registered for so looking at the picture
+
+ align:start position:0%
+registered for so looking at the picture
+ 
+
+ align:start position:0%
+registered for so looking at the picture
+R is not a function so that there may be
+
+ align:start position:0%
+R is not a function so that there may be
+ 
+
+ align:start position:0%
+R is not a function so that there may be
+more than one subject as is you'd expect
+
+ align:start position:0%
+more than one subject as is you'd expect
+ 
+
+ align:start position:0%
+more than one subject as is you'd expect
+for a student to be registered for
+
+ align:start position:0%
+for a student to be registered for
+ 
+
+ align:start position:0%
+for a student to be registered for
+multiple courses at MIT uh so Jason in
+
+ align:start position:0%
+multiple courses at MIT uh so Jason in
+ 
+
+ align:start position:0%
+multiple courses at MIT uh so Jason in
+this diagram is registered for 6042 and
+
+ align:start position:0%
+this diagram is registered for 6042 and
+ 
+
+ align:start position:0%
+this diagram is registered for 6042 and
+6012 as indicated by the highlighted two
+
+ align:start position:0%
+6012 as indicated by the highlighted two
+ 
+
+ align:start position:0%
+6012 as indicated by the highlighted two
+uh connection app arrows which we've
+
+ align:start position:0%
+uh connection app arrows which we've
+ 
+
+ align:start position:0%
+uh connection app arrows which we've
+made
+
+ align:start position:0%
+made
+ 
+
+ align:start position:0%
+made
+red uh which means that R of Json is
+
+ align:start position:0%
+red uh which means that R of Json is
+ 
+
+ align:start position:0%
+red uh which means that R of Json is
+that set of two courses that he's
+
+ align:start position:0%
+that set of two courses that he's
+ 
+
+ align:start position:0%
+that set of two courses that he's
+Associated there that he's associated
+
+ align:start position:0%
+Associated there that he's associated
+ 
+
+ align:start position:0%
+Associated there that he's associated
+with or that are associated with him
+
+ align:start position:0%
+with or that are associated with him
+ 
+
+ align:start position:0%
+with or that are associated with him
+that he's registered for 6042 and
+
+ align:start position:0%
+that he's registered for 6042 and
+ 
+
+ align:start position:0%
+that he's registered for 6042 and
+6012 so at this point we've applied R to
+
+ align:start position:0%
+6012 so at this point we've applied R to
+ 
+
+ align:start position:0%
+6012 so at this point we've applied R to
+one domain element one student Json but
+
+ align:start position:0%
+one domain element one student Json but
+ 
+
+ align:start position:0%
+one domain element one student Json but
+the interesting case is when you apply R
+
+ align:start position:0%
+the interesting case is when you apply R
+ 
+
+ align:start position:0%
+the interesting case is when you apply R
+to a bunch of students so the general
+
+ align:start position:0%
+to a bunch of students so the general
+ 
+
+ align:start position:0%
+to a bunch of students so the general
+setup is that if x is a set of students
+
+ align:start position:0%
+setup is that if x is a set of students
+ 
+
+ align:start position:0%
+setup is that if x is a set of students
+students a subset of the domain which
+
+ align:start position:0%
+students a subset of the domain which
+ 
+
+ align:start position:0%
+students a subset of the domain which
+we've been showing in green then if I
+
+ align:start position:0%
+we've been showing in green then if I
+ 
+
+ align:start position:0%
+we've been showing in green then if I
+apply R to X it gives me all the
+
+ align:start position:0%
+apply R to X it gives me all the
+ 
+
+ align:start position:0%
+apply R to X it gives me all the
+subjects that they're taking among them
+
+ align:start position:0%
+subjects that they're taking among them
+ 
+
+ align:start position:0%
+subjects that they're taking among them
+all the subjects that any one of them is
+
+ align:start position:0%
+all the subjects that any one of them is
+ 
+
+ align:start position:0%
+all the subjects that any one of them is
+taken let's take a look at an example um
+
+ align:start position:0%
+taken let's take a look at an example um
+ 
+
+ align:start position:0%
+taken let's take a look at an example um
+well another way to say it I guess is
+
+ align:start position:0%
+well another way to say it I guess is
+ 
+
+ align:start position:0%
+well another way to say it I guess is
+that R ofx is everything in r that
+
+ align:start position:0%
+that R ofx is everything in r that
+ 
+
+ align:start position:0%
+that R ofx is everything in r that
+relates to things in
+
+ align:start position:0%
+relates to things in
+ 
+
+ align:start position:0%
+relates to things in
+X um so if I look at Jason and
+
+ align:start position:0%
+X um so if I look at Jason and
+ 
+
+ align:start position:0%
+X um so if I look at Jason and
+eway and I want to know what are they
+
+ align:start position:0%
+eway and I want to know what are they
+ 
+
+ align:start position:0%
+eway and I want to know what are they
+connected what are what do they connect
+
+ align:start position:0%
+connected what are what do they connect
+ 
+
+ align:start position:0%
+connected what are what do they connect
+to under R these are the subjects that
+
+ align:start position:0%
+to under R these are the subjects that
+ 
+
+ align:start position:0%
+to under R these are the subjects that
+Jason or eway is registered for the way
+
+ align:start position:0%
+Jason or eway is registered for the way
+ 
+
+ align:start position:0%
+Jason or eway is registered for the way
+I'd find that is by looking at the arrow
+
+ align:start position:0%
+I'd find that is by looking at the arrow
+ 
+
+ align:start position:0%
+I'd find that is by looking at the arrow
+diagram and I'd find that Jason is
+
+ align:start position:0%
+diagram and I'd find that Jason is
+ 
+
+ align:start position:0%
+diagram and I'd find that Jason is
+taking 042 and 012 and eway is taking
+
+ align:start position:0%
+taking 042 and 012 and eway is taking
+ 
+
+ align:start position:0%
+taking 042 and 012 and eway is taking
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and4 so between them they're taking
+
+ align:start position:0%
+and4 so between them they're taking
+ 
+
+ align:start position:0%
+and4 so between them they're taking
+three courses so R of Jason and eway is
+
+ align:start position:0%
+three courses so R of Jason and eway is
+ 
+
+ align:start position:0%
+three courses so R of Jason and eway is
+in fact 042 012 and4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so another way to understand this idea
+
+ align:start position:0%
+so another way to understand this idea
+ 
+
+ align:start position:0%
+so another way to understand this idea
+of the image of a set R ofx is that X is
+
+ align:start position:0%
+of the image of a set R ofx is that X is
+ 
+
+ align:start position:0%
+of the image of a set R ofx is that X is
+a set of points in the set that you're
+
+ align:start position:0%
+a set of points in the set that you're
+ 
+
+ align:start position:0%
+a set of points in the set that you're
+starting with called The Domain uh and R
+
+ align:start position:0%
+starting with called The Domain uh and R
+ 
+
+ align:start position:0%
+starting with called The Domain uh and R
+ofx is going to be all of the end points
+
+ align:start position:0%
+ofx is going to be all of the end points
+ 
+
+ align:start position:0%
+ofx is going to be all of the end points
+in the other set the code domain that
+
+ align:start position:0%
+in the other set the code domain that
+ 
+
+ align:start position:0%
+in the other set the code domain that
+start at X if I said that as a statement
+
+ align:start position:0%
+start at X if I said that as a statement
+ 
+
+ align:start position:0%
+start at X if I said that as a statement
+in formal logic or in set theory with
+
+ align:start position:0%
+in formal logic or in set theory with
+ 
+
+ align:start position:0%
+in formal logic or in set theory with
+logical notation I would say that r ofx
+
+ align:start position:0%
+logical notation I would say that r ofx
+ 
+
+ align:start position:0%
+logical notation I would say that r ofx
+is the set of J in subjects such that
+
+ align:start position:0%
+is the set of J in subjects such that
+ 
+
+ align:start position:0%
+is the set of J in subjects such that
+there is a D in
+
+ align:start position:0%
+there is a D in
+ 
+
+ align:start position:0%
+there is a D in
+X such that
+
+ align:start position:0%
+X such that
+ 
+
+ align:start position:0%
+X such that
+drj so what that that's exactly saying
+
+ align:start position:0%
+drj so what that that's exactly saying
+ 
+
+ align:start position:0%
+drj so what that that's exactly saying
+that um drj says that D is the starting
+
+ align:start position:0%
+that um drj says that D is the starting
+ 
+
+ align:start position:0%
+that um drj says that D is the starting
+point in the domain D is a student um J
+
+ align:start position:0%
+point in the domain D is a student um J
+ 
+
+ align:start position:0%
+point in the domain D is a student um J
+is a subject drj means there's an arrow
+
+ align:start position:0%
+is a subject drj means there's an arrow
+ 
+
+ align:start position:0%
+is a subject drj means there's an arrow
+that goes from student D to subject
+
+ align:start position:0%
+that goes from student D to subject
+ 
+
+ align:start position:0%
+that goes from student D to subject
+object J and we're collecting the set of
+
+ align:start position:0%
+object J and we're collecting the set of
+ 
+
+ align:start position:0%
+object J and we're collecting the set of
+those JS that start at some D so and
+
+ align:start position:0%
+those JS that start at some D so and
+ 
+
+ align:start position:0%
+those JS that start at some D so and
+arrow from X goes to J is what exists a
+
+ align:start position:0%
+arrow from X goes to J is what exists a
+ 
+
+ align:start position:0%
+arrow from X goes to J is what exists a
+D in X drj means uh written in logic
+
+ align:start position:0%
+D in X drj means uh written in logic
+ 
+
+ align:start position:0%
+D in X drj means uh written in logic
+notation it's really talking about the
+
+ align:start position:0%
+notation it's really talking about the
+ 
+
+ align:start position:0%
+notation it's really talking about the
+end points of arrows and that's a nice
+
+ align:start position:0%
+end points of arrows and that's a nice
+ 
+
+ align:start position:0%
+end points of arrows and that's a nice
+way to think about it but you ought to
+
+ align:start position:0%
+way to think about it but you ought to
+ 
+
+ align:start position:0%
+way to think about it but you ought to
+be able also to retreat to give a nice
+
+ align:start position:0%
+be able also to retreat to give a nice
+ 
+
+ align:start position:0%
+be able also to retreat to give a nice
+crisp set theoretic definition without
+
+ align:start position:0%
+crisp set theoretic definition without
+ 
+
+ align:start position:0%
+crisp set theoretic definition without
+reference to pictures
+
+ align:start position:0%
+reference to pictures
+ 
+
+ align:start position:0%
+reference to pictures
+um if need be so that's an official
+
+ align:start position:0%
+um if need be so that's an official
+ 
+
+ align:start position:0%
+um if need be so that's an official
+definition of the image under
+
+ align:start position:0%
+definition of the image under
+ 
+
+ align:start position:0%
+definition of the image under
+R Let's uh turn now to uh an operation
+
+ align:start position:0%
+R Let's uh turn now to uh an operation
+ 
+
+ align:start position:0%
+R Let's uh turn now to uh an operation
+on relations which converts one relation
+
+ align:start position:0%
+on relations which converts one relation
+ 
+
+ align:start position:0%
+on relations which converts one relation
+into another relation called the inverse
+
+ align:start position:0%
+into another relation called the inverse
+ 
+
+ align:start position:0%
+into another relation called the inverse
+of R and the inverse of R Is What You
+
+ align:start position:0%
+of R and the inverse of R Is What You
+ 
+
+ align:start position:0%
+of R and the inverse of R Is What You
+Get by turning the arrows around so
+
+ align:start position:0%
+Get by turning the arrows around so
+ 
+
+ align:start position:0%
+Get by turning the arrows around so
+let's look at the relation R which is
+
+ align:start position:0%
+let's look at the relation R which is
+ 
+
+ align:start position:0%
+let's look at the relation R which is
+the registered for relation going from D
+
+ align:start position:0%
+the registered for relation going from D
+ 
+
+ align:start position:0%
+the registered for relation going from D
+students to J subjects and then if I
+
+ align:start position:0%
+students to J subjects and then if I
+ 
+
+ align:start position:0%
+students to J subjects and then if I
+look at r inverse R inverse I could
+
+ align:start position:0%
+look at r inverse R inverse I could
+ 
+
+ align:start position:0%
+look at r inverse R inverse I could
+think of as the registers relation 6042
+
+ align:start position:0%
+think of as the registers relation 6042
+ 
+
+ align:start position:0%
+think of as the registers relation 6042
+registers Jason and and 6012 registers
+
+ align:start position:0%
+registers Jason and and 6012 registers
+ 
+
+ align:start position:0%
+registers Jason and and 6012 registers
+Jason and eway it's a funny usage of the
+
+ align:start position:0%
+Jason and eway it's a funny usage of the
+ 
+
+ align:start position:0%
+Jason and eway it's a funny usage of the
+word but I needed something short that
+
+ align:start position:0%
+word but I needed something short that
+ 
+
+ align:start position:0%
+word but I needed something short that
+would fit on the slide so registers is
+
+ align:start position:0%
+would fit on the slide so registers is
+ 
+
+ align:start position:0%
+would fit on the slide so registers is
+basically turning the arrows backwards
+
+ align:start position:0%
+basically turning the arrows backwards
+ 
+
+ align:start position:0%
+basically turning the arrows backwards
+of uh is registered
+
+ align:start position:0%
+of uh is registered
+ 
+
+ align:start position:0%
+of uh is registered
+for and now I can apply the definition
+
+ align:start position:0%
+for and now I can apply the definition
+ 
+
+ align:start position:0%
+for and now I can apply the definition
+of image to our inverse in a useful way
+
+ align:start position:0%
+of image to our inverse in a useful way
+ 
+
+ align:start position:0%
+of image to our inverse in a useful way
+but just to be crisp about what we're
+
+ align:start position:0%
+but just to be crisp about what we're
+ 
+
+ align:start position:0%
+but just to be crisp about what we're
+doing here is formally our inverse is
+
+ align:start position:0%
+doing here is formally our inverse is
+ 
+
+ align:start position:0%
+doing here is formally our inverse is
+gotten by flipping the role of the
+
+ align:start position:0%
+gotten by flipping the role of the
+ 
+
+ align:start position:0%
+gotten by flipping the role of the
+domain and the code domain so we have
+
+ align:start position:0%
+domain and the code domain so we have
+ 
+
+ align:start position:0%
+domain and the code domain so we have
+that drj if and only if J R inverse
+
+ align:start position:0%
+that drj if and only if J R inverse
+ 
+
+ align:start position:0%
+that drj if and only if J R inverse
+D so let's look at R inverse of 6012
+
+ align:start position:0%
+D so let's look at R inverse of 6012
+ 
+
+ align:start position:0%
+D so let's look at R inverse of 6012
+what that's going to mean is all the
+
+ align:start position:0%
+what that's going to mean is all the
+ 
+
+ align:start position:0%
+what that's going to mean is all the
+students that are taking
+
+ align:start position:0%
+students that are taking
+ 
+
+ align:start position:0%
+students that are taking
+6012 so we start off at 6012 and we go
+
+ align:start position:0%
+6012 so we start off at 6012 and we go
+ 
+
+ align:start position:0%
+6012 so we start off at 6012 and we go
+back to all the students that are
+
+ align:start position:0%
+back to all the students that are
+ 
+
+ align:start position:0%
+back to all the students that are
+registered for it it's Jason and eway
+
+ align:start position:0%
+registered for it it's Jason and eway
+ 
+
+ align:start position:0%
+registered for it it's Jason and eway
+again and so R inverse of 6012 is Jason
+
+ align:start position:0%
+again and so R inverse of 6012 is Jason
+ 
+
+ align:start position:0%
+again and so R inverse of 6012 is Jason
+and eay R inverse of 6012 and 63 well
+
+ align:start position:0%
+and eay R inverse of 6012 and 63 well
+ 
+
+ align:start position:0%
+and eay R inverse of 6012 and 63 well
+same deal let's look at
+
+ align:start position:0%
+same deal let's look at
+ 
+
+ align:start position:0%
+same deal let's look at
+63 and 6012 and look at all the students
+
+ align:start position:0%
+63 and 6012 and look at all the students
+ 
+
+ align:start position:0%
+63 and 6012 and look at all the students
+that are registered for either one of
+
+ align:start position:0%
+that are registered for either one of
+ 
+
+ align:start position:0%
+that are registered for either one of
+them now it's Jason Joan and eway shown
+
+ align:start position:0%
+them now it's Jason Joan and eway shown
+ 
+
+ align:start position:0%
+them now it's Jason Joan and eway shown
+by those red arrows those all the arrows
+
+ align:start position:0%
+by those red arrows those all the arrows
+ 
+
+ align:start position:0%
+by those red arrows those all the arrows
+coming out of those two courses 03 and
+
+ align:start position:0%
+coming out of those two courses 03 and
+ 
+
+ align:start position:0%
+coming out of those two courses 03 and
+012 and so our inverse
+
+ align:start position:0%
+012 and so our inverse
+ 
+
+ align:start position:0%
+012 and so our inverse
+of3 and 012 is that set of three
+
+ align:start position:0%
+of3 and 012 is that set of three
+ 
+
+ align:start position:0%
+of3 and 012 is that set of three
+students Jon Joan and
+
+ align:start position:0%
+students Jon Joan and
+ 
+
+ align:start position:0%
+students Jon Joan and
+eway and in general when you start off
+
+ align:start position:0%
+eway and in general when you start off
+ 
+
+ align:start position:0%
+eway and in general when you start off
+with a bunch of subjects a bunch of
+
+ align:start position:0%
+with a bunch of subjects a bunch of
+ 
+
+ align:start position:0%
+with a bunch of subjects a bunch of
+elements of the codomain and you apply R
+
+ align:start position:0%
+elements of the codomain and you apply R
+ 
+
+ align:start position:0%
+elements of the codomain and you apply R
+inverse to it it's called the inverse
+
+ align:start position:0%
+inverse to it it's called the inverse
+ 
+
+ align:start position:0%
+inverse to it it's called the inverse
+image of Y under
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R well let's look at the set J of all
+
+ align:start position:0%
+R well let's look at the set J of all
+ 
+
+ align:start position:0%
+R well let's look at the set J of all
+the subjects and think about what is r
+
+ align:start position:0%
+the subjects and think about what is r
+ 
+
+ align:start position:0%
+the subjects and think about what is r
+inverse of J what does it mean well R
+
+ align:start position:0%
+inverse of J what does it mean well R
+ 
+
+ align:start position:0%
+inverse of J what does it mean well R
+inverse of J is all the students that
+
+ align:start position:0%
+inverse of J is all the students that
+ 
+
+ align:start position:0%
+inverse of J is all the students that
+are registered for some subject at
+
+ align:start position:0%
+are registered for some subject at
+ 
+
+ align:start position:0%
+are registered for some subject at
+all um which is a good thing to have so
+
+ align:start position:0%
+all um which is a good thing to have so
+ 
+
+ align:start position:0%
+all um which is a good thing to have so
+now I can start using these sets to make
+
+ align:start position:0%
+now I can start using these sets to make
+ 
+
+ align:start position:0%
+now I can start using these sets to make
+to make assertions about my database
+
+ align:start position:0%
+to make assertions about my database
+ 
+
+ align:start position:0%
+to make assertions about my database
+that can be useful to know so for
+
+ align:start position:0%
+that can be useful to know so for
+ 
+
+ align:start position:0%
+that can be useful to know so for
+example if I want to say that every
+
+ align:start position:0%
+example if I want to say that every
+ 
+
+ align:start position:0%
+example if I want to say that every
+student is registered for some
+
+ align:start position:0%
+student is registered for some
+ 
+
+ align:start position:0%
+student is registered for some
+subject which of course they are uh what
+
+ align:start position:0%
+subject which of course they are uh what
+ 
+
+ align:start position:0%
+subject which of course they are uh what
+I would say is that D the set of all
+
+ align:start position:0%
+I would say is that D the set of all
+ 
+
+ align:start position:0%
+I would say is that D the set of all
+students is a subset of R inverse of J
+
+ align:start position:0%
+students is a subset of R inverse of J
+ 
+
+ align:start position:0%
+students is a subset of R inverse of J
+so this concise set theoretic and uh
+
+ align:start position:0%
+so this concise set theoretic and uh
+ 
+
+ align:start position:0%
+so this concise set theoretic and uh
+containment uh statement D is a subset
+
+ align:start position:0%
+containment uh statement D is a subset
+ 
+
+ align:start position:0%
+containment uh statement D is a subset
+of R inverse of J is a slick way of
+
+ align:start position:0%
+of R inverse of J is a slick way of
+ 
+
+ align:start position:0%
+of R inverse of J is a slick way of
+writing the precise statement that says
+
+ align:start position:0%
+writing the precise statement that says
+ 
+
+ align:start position:0%
+writing the precise statement that says
+that um uh all the students are
+
+ align:start position:0%
+that um uh all the students are
+ 
+
+ align:start position:0%
+that um uh all the students are
+registered for some
+
+ align:start position:0%
+registered for some
+ 
+
+ align:start position:0%
+registered for some
+subject now it happens not to be true by
+
+ align:start position:0%
+subject now it happens not to be true by
+ 
+
+ align:start position:0%
+subject now it happens not to be true by
+the way because if you looked back at
+
+ align:start position:0%
+the way because if you looked back at
+ 
+
+ align:start position:0%
+the way because if you looked back at
+that example Adam was not registered for
+
+ align:start position:0%
+that example Adam was not registered for
+ 
+
+ align:start position:0%
+that example Adam was not registered for
+a subject so we're not claiming that
+
+ align:start position:0%
+a subject so we're not claiming that
+ 
+
+ align:start position:0%
+a subject so we're not claiming that
+this is true but simply that uh there
+
+ align:start position:0%
+this is true but simply that uh there
+ 
+
+ align:start position:0%
+this is true but simply that uh there
+there's a nice way to express it using
+
+ align:start position:0%
+there's a nice way to express it using
+ 
+
+ align:start position:0%
+there's a nice way to express it using
+images and
+
+ align:start position:0%
+images and
+ 
+
+ align:start position:0%
+images and
+containment let's look at a different
+
+ align:start position:0%
+containment let's look at a different
+ 
+
+ align:start position:0%
+containment let's look at a different
+relation that we could call the advisor
+
+ align:start position:0%
+relation that we could call the advisor
+ 
+
+ align:start position:0%
+relation that we could call the advisor
+relation so the advisor relation is
+
+ align:start position:0%
+relation so the advisor relation is
+ 
+
+ align:start position:0%
+relation so the advisor relation is
+going to have co- domain the same set of
+
+ align:start position:0%
+going to have co- domain the same set of
+ 
+
+ align:start position:0%
+going to have co- domain the same set of
+students D but it's going to have as a
+
+ align:start position:0%
+students D but it's going to have as a
+ 
+
+ align:start position:0%
+students D but it's going to have as a
+domain the set of professors and I've
+
+ align:start position:0%
+domain the set of professors and I've
+ 
+
+ align:start position:0%
+domain the set of professors and I've
+written down the initials of five
+
+ align:start position:0%
+written down the initials of five
+ 
+
+ align:start position:0%
+written down the initials of five
+prominent professors uh mine is at the
+
+ align:start position:0%
+prominent professors uh mine is at the
+ 
+
+ align:start position:0%
+prominent professors uh mine is at the
+top and you may recognize some of the
+
+ align:start position:0%
+top and you may recognize some of the
+ 
+
+ align:start position:0%
+top and you may recognize some of the
+others but it doesn't really matter if
+
+ align:start position:0%
+others but it doesn't really matter if
+ 
+
+ align:start position:0%
+others but it doesn't really matter if
+you don't um and the advises Rel V is
+
+ align:start position:0%
+you don't um and the advises Rel V is
+ 
+
+ align:start position:0%
+you don't um and the advises Rel V is
+going to be indicated by those arrows so
+
+ align:start position:0%
+going to be indicated by those arrows so
+ 
+
+ align:start position:0%
+going to be indicated by those arrows so
+in particular it shows that armm is the
+
+ align:start position:0%
+in particular it shows that armm is the
+ 
+
+ align:start position:0%
+in particular it shows that armm is the
+adviser of Jason Joan eway and Adam
+
+ align:start position:0%
+adviser of Jason Joan eway and Adam
+ 
+
+ align:start position:0%
+adviser of Jason Joan eway and Adam
+which he happens to be um FTL is an
+
+ align:start position:0%
+which he happens to be um FTL is an
+ 
+
+ align:start position:0%
+which he happens to be um FTL is an
+advisor of Joan and eway so Joan has two
+
+ align:start position:0%
+advisor of Joan and eway so Joan has two
+ 
+
+ align:start position:0%
+advisor of Joan and eway so Joan has two
+advisor because she's a double major um
+
+ align:start position:0%
+advisor because she's a double major um
+ 
+
+ align:start position:0%
+advisor because she's a double major um
+eway does as well uh and Adam does as
+
+ align:start position:0%
+eway does as well uh and Adam does as
+ 
+
+ align:start position:0%
+eway does as well uh and Adam does as
+well now that I look at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example so if I look at in particular
+
+ align:start position:0%
+example so if I look at in particular
+ 
+
+ align:start position:0%
+example so if I look at in particular
+now the advisees of FTL or TLP I'm
+
+ align:start position:0%
+now the advisees of FTL or TLP I'm
+ 
+
+ align:start position:0%
+now the advisees of FTL or TLP I'm
+looking at V of the set consisting of
+
+ align:start position:0%
+looking at V of the set consisting of
+ 
+
+ align:start position:0%
+looking at V of the set consisting of
+FTL and TLP and it's going to be Joan
+
+ align:start position:0%
+FTL and TLP and it's going to be Joan
+ 
+
+ align:start position:0%
+FTL and TLP and it's going to be Joan
+eway and Adam so taking the image of FTL
+
+ align:start position:0%
+eway and Adam so taking the image of FTL
+ 
+
+ align:start position:0%
+eway and Adam so taking the image of FTL
+and TLP that that's the set of advisees
+
+ align:start position:0%
+and TLP that that's the set of advisees
+ 
+
+ align:start position:0%
+and TLP that that's the set of advisees
+of either of those two professors I get
+
+ align:start position:0%
+of either of those two professors I get
+ 
+
+ align:start position:0%
+of either of those two professors I get
+this set of three students Joan eway and
+
+ align:start position:0%
+this set of three students Joan eway and
+ 
+
+ align:start position:0%
+this set of three students Joan eway and
+Adam well that's a set of students and
+
+ align:start position:0%
+Adam well that's a set of students and
+ 
+
+ align:start position:0%
+Adam well that's a set of students and
+the registered relation applies to a set
+
+ align:start position:0%
+the registered relation applies to a set
+ 
+
+ align:start position:0%
+the registered relation applies to a set
+of students so let's do that if I now
+
+ align:start position:0%
+of students so let's do that if I now
+ 
+
+ align:start position:0%
+of students so let's do that if I now
+apply R to Joan and eway and Adam what
+
+ align:start position:0%
+apply R to Joan and eway and Adam what
+ 
+
+ align:start position:0%
+apply R to Joan and eway and Adam what
+I'm getting is the subjects that they're
+
+ align:start position:0%
+I'm getting is the subjects that they're
+ 
+
+ align:start position:0%
+I'm getting is the subjects that they're
+registered
+
+ align:start position:0%
+registered
+ 
+
+ align:start position:0%
+registered
+for um so this is called composing r and
+
+ align:start position:0%
+for um so this is called composing r and
+ 
+
+ align:start position:0%
+for um so this is called composing r and
+v I've applied V and then I'm applying R
+
+ align:start position:0%
+v I've applied V and then I'm applying R
+ 
+
+ align:start position:0%
+v I've applied V and then I'm applying R
+to the result in this case um R of V of
+
+ align:start position:0%
+to the result in this case um R of V of
+ 
+
+ align:start position:0%
+to the result in this case um R of V of
+FTL and TLP is the same as R of Joan ehu
+
+ align:start position:0%
+FTL and TLP is the same as R of Joan ehu
+ 
+
+ align:start position:0%
+FTL and TLP is the same as R of Joan ehu
+and atom it's the courses that any of
+
+ align:start position:0%
+and atom it's the courses that any of
+ 
+
+ align:start position:0%
+and atom it's the courses that any of
+them are taken taking and it's 0312
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and4 so the way to understand this R of
+
+ align:start position:0%
+and4 so the way to understand this R of
+ 
+
+ align:start position:0%
+and4 so the way to understand this R of
+v in general is you start off with any
+
+ align:start position:0%
+v in general is you start off with any
+ 
+
+ align:start position:0%
+v in general is you start off with any
+set X of professors in the domain you
+
+ align:start position:0%
+set X of professors in the domain you
+ 
+
+ align:start position:0%
+set X of professors in the domain you
+take V ofx are the uh advisees that they
+
+ align:start position:0%
+take V ofx are the uh advisees that they
+ 
+
+ align:start position:0%
+take V ofx are the uh advisees that they
+have and then you take R of the advisees
+
+ align:start position:0%
+have and then you take R of the advisees
+ 
+
+ align:start position:0%
+have and then you take R of the advisees
+and you get the subjects that the
+
+ align:start position:0%
+and you get the subjects that the
+ 
+
+ align:start position:0%
+and you get the subjects that the
+advises are taken so R of V ofx is the
+
+ align:start position:0%
+advises are taken so R of V ofx is the
+ 
+
+ align:start position:0%
+advises are taken so R of V ofx is the
+subjects that advise es of X are taken
+
+ align:start position:0%
+subjects that advise es of X are taken
+ 
+
+ align:start position:0%
+subjects that advise es of X are taken
+are registered
+
+ align:start position:0%
+are registered
+ 
+
+ align:start position:0%
+are registered
+for well we can abstract that out and
+
+ align:start position:0%
+for well we can abstract that out and
+ 
+
+ align:start position:0%
+for well we can abstract that out and
+call this the composition of r and v
+
+ align:start position:0%
+call this the composition of r and v
+ 
+
+ align:start position:0%
+call this the composition of r and v
+it's defined the same way that
+
+ align:start position:0%
+it's defined the same way that
+ 
+
+ align:start position:0%
+it's defined the same way that
+functional composition is so R of V uh
+
+ align:start position:0%
+functional composition is so R of V uh
+ 
+
+ align:start position:0%
+functional composition is so R of V uh
+is the relation and the images of that
+
+ align:start position:0%
+is the relation and the images of that
+ 
+
+ align:start position:0%
+is the relation and the images of that
+relation the images of a set of
+
+ align:start position:0%
+relation the images of a set of
+ 
+
+ align:start position:0%
+relation the images of a set of
+professors under R of V is defined to be
+
+ align:start position:0%
+professors under R of V is defined to be
+ 
+
+ align:start position:0%
+professors under R of V is defined to be
+apply V to X and then apply R to V of
+
+ align:start position:0%
+apply V to X and then apply R to V of
+ 
+
+ align:start position:0%
+apply V to X and then apply R to V of
+x uh and it's again called the
+
+ align:start position:0%
+x uh and it's again called the
+ 
+
+ align:start position:0%
+x uh and it's again called the
+composition of r and v
+
+ align:start position:0%
+composition of r and v
+ 
+
+ align:start position:0%
+composition of r and v
+what it means now is that two things are
+
+ align:start position:0%
+what it means now is that two things are
+ 
+
+ align:start position:0%
+what it means now is that two things are
+related by R of v it relates professors
+
+ align:start position:0%
+related by R of v it relates professors
+ 
+
+ align:start position:0%
+related by R of v it relates professors
+and subjects and it says that a
+
+ align:start position:0%
+and subjects and it says that a
+ 
+
+ align:start position:0%
+and subjects and it says that a
+professor and a subject are related if
+
+ align:start position:0%
+professor and a subject are related if
+ 
+
+ align:start position:0%
+professor and a subject are related if
+the professor has an advise some advise
+
+ align:start position:0%
+the professor has an advise some advise
+ 
+
+ align:start position:0%
+the professor has an advise some advise
+in that subject P for a professor
+
+ align:start position:0%
+in that subject P for a professor
+ 
+
+ align:start position:0%
+in that subject P for a professor
+composition of r with v j for a subject
+
+ align:start position:0%
+composition of r with v j for a subject
+ 
+
+ align:start position:0%
+composition of r with v j for a subject
+holds if and only if Professor P has an
+
+ align:start position:0%
+holds if and only if Professor P has an
+ 
+
+ align:start position:0%
+holds if and only if Professor P has an
+advise Z registered in subject
+
+ align:start position:0%
+advise Z registered in subject
+ 
+
+ align:start position:0%
+advise Z registered in subject
+J let's see how you figure that kind of
+
+ align:start position:0%
+J let's see how you figure that kind of
+ 
+
+ align:start position:0%
+J let's see how you figure that kind of
+thing out so um I'm going to draw the V
+
+ align:start position:0%
+thing out so um I'm going to draw the V
+ 
+
+ align:start position:0%
+thing out so um I'm going to draw the V
+relation which goes from P professors to
+
+ align:start position:0%
+relation which goes from P professors to
+ 
+
+ align:start position:0%
+relation which goes from P professors to
+D students and then the r relation that
+
+ align:start position:0%
+D students and then the r relation that
+ 
+
+ align:start position:0%
+D students and then the r relation that
+goes from D students to J subjects uh
+
+ align:start position:0%
+goes from D students to J subjects uh
+ 
+
+ align:start position:0%
+goes from D students to J subjects uh
+and by showing them in this way I can
+
+ align:start position:0%
+and by showing them in this way I can
+ 
+
+ align:start position:0%
+and by showing them in this way I can
+understand the composition of r and v as
+
+ align:start position:0%
+understand the composition of r and v as
+ 
+
+ align:start position:0%
+understand the composition of r and v as
+following two arrows you start off say
+
+ align:start position:0%
+following two arrows you start off say
+ 
+
+ align:start position:0%
+following two arrows you start off say
+at armm and you follow a v Arrow from
+
+ align:start position:0%
+at armm and you follow a v Arrow from
+ 
+
+ align:start position:0%
+at armm and you follow a v Arrow from
+armm to his advisor y z
+
+ align:start position:0%
+armm to his advisor y z
+ 
+
+ align:start position:0%
+armm to his advisor y z
+eway then you follow another arrow from
+
+ align:start position:0%
+eway then you follow another arrow from
+ 
+
+ align:start position:0%
+eway then you follow another arrow from
+eway to 6012 and you discover hey armm
+
+ align:start position:0%
+eway to 6012 and you discover hey armm
+ 
+
+ align:start position:0%
+eway to 6012 and you discover hey armm
+has an advise Z in so now we can say
+
+ align:start position:0%
+has an advise Z in so now we can say
+ 
+
+ align:start position:0%
+has an advise Z in so now we can say
+that Professor armm is in the relation R
+
+ align:start position:0%
+that Professor armm is in the relation R
+ 
+
+ align:start position:0%
+that Professor armm is in the relation R
+composed with V with
+
+ align:start position:0%
+composed with V with
+ 
+
+ align:start position:0%
+composed with V with
+6012 because of this path armm has e as
+
+ align:start position:0%
+6012 because of this path armm has e as
+ 
+
+ align:start position:0%
+6012 because of this path armm has e as
+an advise e and eway is registered for
+
+ align:start position:0%
+an advise e and eway is registered for
+ 
+
+ align:start position:0%
+an advise e and eway is registered for
+6012 and this relation r V we figured
+
+ align:start position:0%
+6012 and this relation r V we figured
+ 
+
+ align:start position:0%
+6012 and this relation r V we figured
+out is the relation that the professor
+
+ align:start position:0%
+out is the relation that the professor
+ 
+
+ align:start position:0%
+out is the relation that the professor
+has an advise e in the subject so in
+
+ align:start position:0%
+has an advise e in the subject so in
+ 
+
+ align:start position:0%
+has an advise e in the subject so in
+general what we can say is that a
+
+ align:start position:0%
+general what we can say is that a
+ 
+
+ align:start position:0%
+general what we can say is that a
+professor p is in the ROV relation to J
+
+ align:start position:0%
+professor p is in the ROV relation to J
+ 
+
+ align:start position:0%
+professor p is in the ROV relation to J
+if and only if and here we're going to
+
+ align:start position:0%
+if and only if and here we're going to
+ 
+
+ align:start position:0%
+if and only if and here we're going to
+State it in formal logical notation
+
+ align:start position:0%
+State it in formal logical notation
+ 
+
+ align:start position:0%
+State it in formal logical notation
+which really applies in general not just
+
+ align:start position:0%
+which really applies in general not just
+ 
+
+ align:start position:0%
+which really applies in general not just
+to this particular example so the
+
+ align:start position:0%
+to this particular example so the
+ 
+
+ align:start position:0%
+to this particular example so the
+definition of R composed with v is that
+
+ align:start position:0%
+definition of R composed with v is that
+ 
+
+ align:start position:0%
+definition of R composed with v is that
+p r composed with VJ means there's a d
+
+ align:start position:0%
+p r composed with VJ means there's a d
+ 
+
+ align:start position:0%
+p r composed with VJ means there's a d
+that connects p and J through V and D in
+
+ align:start position:0%
+that connects p and J through V and D in
+ 
+
+ align:start position:0%
+that connects p and J through V and D in
+particular uh that there's a d such that
+
+ align:start position:0%
+particular uh that there's a d such that
+ 
+
+ align:start position:0%
+particular uh that there's a d such that
+PV D which means there's an arrow a v
+
+ align:start position:0%
+PV D which means there's an arrow a v
+ 
+
+ align:start position:0%
+PV D which means there's an arrow a v
+Arrow from P to D and D RJ there's an R
+
+ align:start position:0%
+Arrow from P to D and D RJ there's an R
+ 
+
+ align:start position:0%
+Arrow from P to D and D RJ there's an R
+Arrow from D to J for some
+
+ align:start position:0%
+Arrow from D to J for some
+ 
+
+ align:start position:0%
+Arrow from D to J for some
+d by the way there's a technicality here
+
+ align:start position:0%
+d by the way there's a technicality here
+ 
+
+ align:start position:0%
+d by the way there's a technicality here
+that um when you write the formula uh
+
+ align:start position:0%
+that um when you write the formula uh
+ 
+
+ align:start position:0%
+that um when you write the formula uh
+PVD and
+
+ align:start position:0%
+PVD and
+ 
+
+ align:start position:0%
+PVD and
+drj um following the diagram where you
+
+ align:start position:0%
+drj um following the diagram where you
+ 
+
+ align:start position:0%
+drj um following the diagram where you
+start with V on the left and follow a v
+
+ align:start position:0%
+start with V on the left and follow a v
+ 
+
+ align:start position:0%
+start with V on the left and follow a v
+arrow and then an R Arrow it's natural
+
+ align:start position:0%
+arrow and then an R Arrow it's natural
+ 
+
+ align:start position:0%
+arrow and then an R Arrow it's natural
+to think of them as written in left to
+
+ align:start position:0%
+to think of them as written in left to
+ 
+
+ align:start position:0%
+to think of them as written in left to
+right order of what you apply first VR
+
+ align:start position:0%
+right order of what you apply first VR
+ 
+
+ align:start position:0%
+right order of what you apply first VR
+but of course that's not the way
+
+ align:start position:0%
+but of course that's not the way
+ 
+
+ align:start position:0%
+but of course that's not the way
+composition works when you apply one
+
+ align:start position:0%
+composition works when you apply one
+ 
+
+ align:start position:0%
+composition works when you apply one
+function R to V to something you're
+
+ align:start position:0%
+function R to V to something you're
+ 
+
+ align:start position:0%
+function R to V to something you're
+applying V first and you write it on the
+
+ align:start position:0%
+applying V first and you write it on the
+ 
+
+ align:start position:0%
+applying V first and you write it on the
+right so R oov is written like function
+
+ align:start position:0%
+right so R oov is written like function
+ 
+
+ align:start position:0%
+right so R oov is written like function
+composition where V applies first but
+
+ align:start position:0%
+composition where V applies first but
+ 
+
+ align:start position:0%
+composition where V applies first but
+the logical statement um uh the natural
+
+ align:start position:0%
+the logical statement um uh the natural
+ 
+
+ align:start position:0%
+the logical statement um uh the natural
+way to write it is to follow the way the
+
+ align:start position:0%
+way to write it is to follow the way the
+ 
+
+ align:start position:0%
+way to write it is to follow the way the
+picture works and the v's and rs get
+
+ align:start position:0%
+picture works and the v's and rs get
+ 
+
+ align:start position:0%
+picture works and the v's and rs get
+reversed so watch out for that
+
+ align:start position:0%
+reversed so watch out for that
+ 
+
+ align:start position:0%
+reversed so watch out for that
+confusion well I want to introduce one
+
+ align:start position:0%
+confusion well I want to introduce one
+ 
+
+ align:start position:0%
+confusion well I want to introduce one
+more relation to flesh out this example
+
+ align:start position:0%
+more relation to flesh out this example
+ 
+
+ align:start position:0%
+more relation to flesh out this example
+and that'll be the teach's relation so
+
+ align:start position:0%
+and that'll be the teach's relation so
+ 
+
+ align:start position:0%
+and that'll be the teach's relation so
+the teach's relation is going to have as
+
+ align:start position:0%
+the teach's relation is going to have as
+ 
+
+ align:start position:0%
+the teach's relation is going to have as
+domain professors again uh and as
+
+ align:start position:0%
+domain professors again uh and as
+ 
+
+ align:start position:0%
+domain professors again uh and as
+codomain subjects and it's simply going
+
+ align:start position:0%
+codomain subjects and it's simply going
+ 
+
+ align:start position:0%
+codomain subjects and it's simply going
+to tell us who's teaching what so here
+
+ align:start position:0%
+to tell us who's teaching what so here
+ 
+
+ align:start position:0%
+to tell us who's teaching what so here
+we're going to see that um armm is
+
+ align:start position:0%
+we're going to see that um armm is
+ 
+
+ align:start position:0%
+we're going to see that um armm is
+teaching 6042 as you well know and ft is
+
+ align:start position:0%
+teaching 6042 as you well know and ft is
+ 
+
+ align:start position:0%
+teaching 6042 as you well know and ft is
+teaching 6042 which he does frequently
+
+ align:start position:0%
+teaching 6042 which he does frequently
+ 
+
+ align:start position:0%
+teaching 6042 which he does frequently
+but not this
+
+ align:start position:0%
+but not this
+ 
+
+ align:start position:0%
+but not this
+term um and now I can again use my
+
+ align:start position:0%
+term um and now I can again use my
+ 
+
+ align:start position:0%
+term um and now I can again use my
+relational operators to start making
+
+ align:start position:0%
+relational operators to start making
+ 
+
+ align:start position:0%
+relational operators to start making
+assertions about this about these people
+
+ align:start position:0%
+assertions about this about these people
+ 
+
+ align:start position:0%
+assertions about this about these people
+and relations involving teaching and
+
+ align:start position:0%
+and relations involving teaching and
+ 
+
+ align:start position:0%
+and relations involving teaching and
+advisees so I and the useful way to do
+
+ align:start position:0%
+advisees so I and the useful way to do
+ 
+
+ align:start position:0%
+advisees so I and the useful way to do
+that is by applying set operations to
+
+ align:start position:0%
+that is by applying set operations to
+ 
+
+ align:start position:0%
+that is by applying set operations to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+relations um because I can think of the
+
+ align:start position:0%
+relations um because I can think of the
+ 
+
+ align:start position:0%
+relations um because I can think of the
+relations as being that set of arrows so
+
+ align:start position:0%
+relations as being that set of arrows so
+ 
+
+ align:start position:0%
+relations as being that set of arrows so
+suppose I wanted to make some statement
+
+ align:start position:0%
+suppose I wanted to make some statement
+ 
+
+ align:start position:0%
+suppose I wanted to make some statement
+that a professor should not teach their
+
+ align:start position:0%
+that a professor should not teach their
+ 
+
+ align:start position:0%
+that a professor should not teach their
+own advise Z because uh it's too much
+
+ align:start position:0%
+own advise Z because uh it's too much
+ 
+
+ align:start position:0%
+own advise Z because uh it's too much
+power for one person to have over a
+
+ align:start position:0%
+power for one person to have over a
+ 
+
+ align:start position:0%
+power for one person to have over a
+student um this is not true by the way
+
+ align:start position:0%
+student um this is not true by the way
+ 
+
+ align:start position:0%
+student um this is not true by the way
+it's common for professors to teach
+
+ align:start position:0%
+it's common for professors to teach
+ 
+
+ align:start position:0%
+it's common for professors to teach
+advises but there are other kinds of
+
+ align:start position:0%
+advises but there are other kinds of
+ 
+
+ align:start position:0%
+advises but there are other kinds of
+rules about uh dual relationships uh
+
+ align:start position:0%
+rules about uh dual relationships uh
+ 
+
+ align:start position:0%
+rules about uh dual relationships uh
+between Su uh supervisory relationships
+
+ align:start position:0%
+between Su uh supervisory relationships
+ 
+
+ align:start position:0%
+between Su uh supervisory relationships
+and personal relationships but anyway
+
+ align:start position:0%
+and personal relationships but anyway
+ 
+
+ align:start position:0%
+and personal relationships but anyway
+let's say if we can say that profs
+
+ align:start position:0%
+let's say if we can say that profs
+ 
+
+ align:start position:0%
+let's say if we can say that profs
+should not supervise or should not teach
+
+ align:start position:0%
+should not supervise or should not teach
+ 
+
+ align:start position:0%
+should not supervise or should not teach
+any one that they're advising well um if
+
+ align:start position:0%
+any one that they're advising well um if
+ 
+
+ align:start position:0%
+any one that they're advising well um if
+we were saying that in logical notation
+
+ align:start position:0%
+we were saying that in logical notation
+ 
+
+ align:start position:0%
+we were saying that in logical notation
+what we would say is that for every
+
+ align:start position:0%
+what we would say is that for every
+ 
+
+ align:start position:0%
+what we would say is that for every
+professor and subject it's not the case
+
+ align:start position:0%
+professor and subject it's not the case
+ 
+
+ align:start position:0%
+professor and subject it's not the case
+that uh the professor has an advise Z in
+
+ align:start position:0%
+that uh the professor has an advise Z in
+ 
+
+ align:start position:0%
+that uh the professor has an advise Z in
+subject J and the professor is teaching
+
+ align:start position:0%
+subject J and the professor is teaching
+ 
+
+ align:start position:0%
+subject J and the professor is teaching
+subject J so that's how you say it in
+
+ align:start position:0%
+subject J so that's how you say it in
+ 
+
+ align:start position:0%
+subject J so that's how you say it in
+logic but there's a very slick way to
+
+ align:start position:0%
+logic but there's a very slick way to
+ 
+
+ align:start position:0%
+logic but there's a very slick way to
+say it without all the formulas in the
+
+ align:start position:0%
+say it without all the formulas in the
+ 
+
+ align:start position:0%
+say it without all the formulas in the
+quantifiers I could just say that t the
+
+ align:start position:0%
+quantifiers I could just say that t the
+ 
+
+ align:start position:0%
+quantifiers I could just say that t the
+relationship of his teaching
+
+ align:start position:0%
+relationship of his teaching
+ 
+
+ align:start position:0%
+relationship of his teaching
+intersected with the relationship of has
+
+ align:start position:0%
+intersected with the relationship of has
+ 
+
+ align:start position:0%
+intersected with the relationship of has
+an advise Z in the subject is empty
+
+ align:start position:0%
+an advise Z in the subject is empty
+ 
+
+ align:start position:0%
+an advise Z in the subject is empty
+there is no pair of Professor and
+
+ align:start position:0%
+there is no pair of Professor and
+ 
+
+ align:start position:0%
+there is no pair of Professor and
+subject that is in both T and in R of v
+
+ align:start position:0%
+subject that is in both T and in R of v
+ 
+
+ align:start position:0%
+subject that is in both T and in R of v
+um and this bottom expression here gives
+
+ align:start position:0%
+um and this bottom expression here gives
+ 
+
+ align:start position:0%
+um and this bottom expression here gives
+you a a sense of the concise way that
+
+ align:start position:0%
+you a a sense of the concise way that
+ 
+
+ align:start position:0%
+you a a sense of the concise way that
+you can express queries and assertions
+
+ align:start position:0%
+you can express queries and assertions
+ 
+
+ align:start position:0%
+you can express queries and assertions
+about the database using a combination
+
+ align:start position:0%
+about the database using a combination
+ 
+
+ align:start position:0%
+about the database using a combination
+of relational operators and set
+
+ align:start position:0%
+of relational operators and set
+ 
+
+ align:start position:0%
+of relational operators and set
+operators another way to say it by the
+
+ align:start position:0%
+operators another way to say it by the
+ 
+
+ align:start position:0%
+operators another way to say it by the
+way this is a general set theoretic fact
+
+ align:start position:0%
+way this is a general set theoretic fact
+ 
+
+ align:start position:0%
+way this is a general set theoretic fact
+is the way to say that T and R of V
+
+ align:start position:0%
+is the way to say that T and R of V
+ 
+
+ align:start position:0%
+is the way to say that T and R of V
+intersected is empty is to say that they
+
+ align:start position:0%
+intersected is empty is to say that they
+ 
+
+ align:start position:0%
+intersected is empty is to say that they
+that the set T and the set R of V
+
+ align:start position:0%
+that the set T and the set R of V
+ 
+
+ align:start position:0%
+that the set T and the set R of V
+whatever they are have no points in
+
+ align:start position:0%
+whatever they are have no points in
+ 
+
+ align:start position:0%
+whatever they are have no points in
+common uh an equivalent way to say that
+
+ align:start position:0%
+common uh an equivalent way to say that
+ 
+
+ align:start position:0%
+common uh an equivalent way to say that
+is that one set is contained in the
+
+ align:start position:0%
+is that one set is contained in the
+ 
+
+ align:start position:0%
+is that one set is contained in the
+complement of the other set so I could
+
+ align:start position:0%
+complement of the other set so I could
+ 
+
+ align:start position:0%
+complement of the other set so I could
+equally well have said this as R
+
+ align:start position:0%
+equally well have said this as R
+ 
+
+ align:start position:0%
+equally well have said this as R
+composed with v is a subset of of not
+
+ align:start position:0%
+composed with v is a subset of of not
+ 
+
+ align:start position:0%
+composed with v is a subset of of not
+t well let's step back now and summarize
+
+ align:start position:0%
+t well let's step back now and summarize
+ 
+
+ align:start position:0%
+t well let's step back now and summarize
+what we've done by example and and say a
+
+ align:start position:0%
+what we've done by example and and say a
+ 
+
+ align:start position:0%
+what we've done by example and and say a
+little bit about what it how it works in
+
+ align:start position:0%
+little bit about what it how it works in
+ 
+
+ align:start position:0%
+little bit about what it how it works in
+general so as I said a binary relation
+
+ align:start position:0%
+general so as I said a binary relation
+ 
+
+ align:start position:0%
+general so as I said a binary relation
+um and we'll start to be slightly more
+
+ align:start position:0%
+um and we'll start to be slightly more
+ 
+
+ align:start position:0%
+um and we'll start to be slightly more
+formal now a binary relation R from a
+
+ align:start position:0%
+formal now a binary relation R from a
+ 
+
+ align:start position:0%
+formal now a binary relation R from a
+set a to a set B Associates elements of
+
+ align:start position:0%
+set a to a set B Associates elements of
+ 
+
+ align:start position:0%
+set a to a set B Associates elements of
+a with elements of B and um there's a
+
+ align:start position:0%
+a with elements of B and um there's a
+ 
+
+ align:start position:0%
+a with elements of B and um there's a
+picture of a general set a called The
+
+ align:start position:0%
+picture of a general set a called The
+ 
+
+ align:start position:0%
+picture of a general set a called The
+Domain and a general set B called the
+
+ align:start position:0%
+Domain and a general set B called the
+ 
+
+ align:start position:0%
+Domain and a general set B called the
+codomain
+
+ align:start position:0%
+codomain
+ 
+
+ align:start position:0%
+codomain
+and R is given by those arrows well what
+
+ align:start position:0%
+and R is given by those arrows well what
+ 
+
+ align:start position:0%
+and R is given by those arrows well what
+exactly are arrows well if you're going
+
+ align:start position:0%
+exactly are arrows well if you're going
+ 
+
+ align:start position:0%
+exactly are arrows well if you're going
+to formalize arrows um the set of them
+
+ align:start position:0%
+to formalize arrows um the set of them
+ 
+
+ align:start position:0%
+to formalize arrows um the set of them
+is What's called the graph of R so
+
+ align:start position:0%
+is What's called the graph of R so
+ 
+
+ align:start position:0%
+is What's called the graph of R so
+technically a relation really has three
+
+ align:start position:0%
+technically a relation really has three
+ 
+
+ align:start position:0%
+technically a relation really has three
+parts it's not to be identified with
+
+ align:start position:0%
+parts it's not to be identified with
+ 
+
+ align:start position:0%
+parts it's not to be identified with
+just its arrows a relation has a domain
+
+ align:start position:0%
+just its arrows a relation has a domain
+ 
+
+ align:start position:0%
+just its arrows a relation has a domain
+and a co-domain and some bunch of arrows
+
+ align:start position:0%
+and a co-domain and some bunch of arrows
+ 
+
+ align:start position:0%
+and a co-domain and some bunch of arrows
+going from the domain to the co- domain
+
+ align:start position:0%
+going from the domain to the co- domain
+ 
+
+ align:start position:0%
+going from the domain to the co- domain
+um uh the arrow can be formalized by
+
+ align:start position:0%
+um uh the arrow can be formalized by
+ 
+
+ align:start position:0%
+um uh the arrow can be formalized by
+saying all that matters about an arrow
+
+ align:start position:0%
+saying all that matters about an arrow
+ 
+
+ align:start position:0%
+saying all that matters about an arrow
+is where it begins and where it ends
+
+ align:start position:0%
+is where it begins and where it ends
+ 
+
+ align:start position:0%
+is where it begins and where it ends
+because it's just designed to reflect an
+
+ align:start position:0%
+because it's just designed to reflect an
+ 
+
+ align:start position:0%
+because it's just designed to reflect an
+association between an element of the
+
+ align:start position:0%
+association between an element of the
+ 
+
+ align:start position:0%
+association between an element of the
+domain and an element of the co-domain
+
+ align:start position:0%
+domain and an element of the co-domain
+ 
+
+ align:start position:0%
+domain and an element of the co-domain
+so technically the arrows are just
+
+ align:start position:0%
+so technically the arrows are just
+ 
+
+ align:start position:0%
+so technically the arrows are just
+ordered pairs and in this case there are
+
+ align:start position:0%
+ordered pairs and in this case there are
+ 
+
+ align:start position:0%
+ordered pairs and in this case there are
+three arrows one from a to B2 and so you
+
+ align:start position:0%
+three arrows one from a to B2 and so you
+ 
+
+ align:start position:0%
+three arrows one from a to B2 and so you
+see at the bottom of the slide um uh an
+
+ align:start position:0%
+see at the bottom of the slide um uh an
+ 
+
+ align:start position:0%
+see at the bottom of the slide um uh an
+ordered pair A1 B2 um another arrow goes
+
+ align:start position:0%
+ordered pair A1 B2 um another arrow goes
+ 
+
+ align:start position:0%
+ordered pair A1 B2 um another arrow goes
+from A1 to B4 so you see the ordered
+
+ align:start position:0%
+from A1 to B4 so you see the ordered
+ 
+
+ align:start position:0%
+from A1 to B4 so you see the ordered
+pair A1 B4 and the final arrow is A3 B4
+
+ align:start position:0%
+pair A1 B4 and the final arrow is A3 B4
+ 
+
+ align:start position:0%
+pair A1 B4 and the final arrow is A3 B4
+and you see that pair so all the
+
+ align:start position:0%
+and you see that pair so all the
+ 
+
+ align:start position:0%
+and you see that pair so all the
+language about arrows is really talking
+
+ align:start position:0%
+language about arrows is really talking
+ 
+
+ align:start position:0%
+language about arrows is really talking
+about ordered pairs um uh it's just that
+
+ align:start position:0%
+about ordered pairs um uh it's just that
+ 
+
+ align:start position:0%
+about ordered pairs um uh it's just that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+geometric uh Vision uh image of these
+
+ align:start position:0%
+geometric uh Vision uh image of these
+ 
+
+ align:start position:0%
+geometric uh Vision uh image of these
+diagrams with their arrows makes a lot
+
+ align:start position:0%
+diagrams with their arrows makes a lot
+ 
+
+ align:start position:0%
+diagrams with their arrows makes a lot
+of properties much
+
+ align:start position:0%
+of properties much
+ 
+
+ align:start position:0%
+of properties much
+clearer so the range of R is a important
+
+ align:start position:0%
+clearer so the range of R is a important
+ 
+
+ align:start position:0%
+clearer so the range of R is a important
+concept um that comes up regularly and
+
+ align:start position:0%
+concept um that comes up regularly and
+ 
+
+ align:start position:0%
+concept um that comes up regularly and
+tends to be a little confusing for
+
+ align:start position:0%
+tends to be a little confusing for
+ 
+
+ align:start position:0%
+tends to be a little confusing for
+people the range of R is simply the
+
+ align:start position:0%
+people the range of R is simply the
+ 
+
+ align:start position:0%
+people the range of R is simply the
+elements with arrows coming in from
+
+ align:start position:0%
+elements with arrows coming in from
+ 
+
+ align:start position:0%
+elements with arrows coming in from
+R uh it's all of the elements that are
+
+ align:start position:0%
+R uh it's all of the elements that are
+ 
+
+ align:start position:0%
+R uh it's all of the elements that are
+hit by uh an arrow that starts in the
+
+ align:start position:0%
+hit by uh an arrow that starts in the
+ 
+
+ align:start position:0%
+hit by uh an arrow that starts in the
+domain so it's really R of the domain is
+
+ align:start position:0%
+domain so it's really R of the domain is
+ 
+
+ align:start position:0%
+domain so it's really R of the domain is
+the range of R now notice that this is
+
+ align:start position:0%
+the range of R now notice that this is
+ 
+
+ align:start position:0%
+the range of R now notice that this is
+typically not equal to the whole co-
+
+ align:start position:0%
+typically not equal to the whole co-
+ 
+
+ align:start position:0%
+typically not equal to the whole co-
+domain let's look at this example here
+
+ align:start position:0%
+domain let's look at this example here
+ 
+
+ align:start position:0%
+domain let's look at this example here
+the range of R are the hit the points
+
+ align:start position:0%
+the range of R are the hit the points
+ 
+
+ align:start position:0%
+the range of R are the hit the points
+that are hit by elements of a under R
+
+ align:start position:0%
+that are hit by elements of a under R
+ 
+
+ align:start position:0%
+that are hit by elements of a under R
+namely just B2 and
+
+ align:start position:0%
+namely just B2 and
+ 
+
+ align:start position:0%
+namely just B2 and
+B4 uh the co- domain has elements B1 and
+
+ align:start position:0%
+B4 uh the co- domain has elements B1 and
+ 
+
+ align:start position:0%
+B4 uh the co- domain has elements B1 and
+B3 that are missing and that are not in
+
+ align:start position:0%
+B3 that are missing and that are not in
+ 
+
+ align:start position:0%
+B3 that are missing and that are not in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+range well as I said functions are a
+
+ align:start position:0%
+range well as I said functions are a
+ 
+
+ align:start position:0%
+range well as I said functions are a
+special case of relation so let's just
+
+ align:start position:0%
+special case of relation so let's just
+ 
+
+ align:start position:0%
+special case of relation so let's just
+look at that um a function uh F from a
+
+ align:start position:0%
+look at that um a function uh F from a
+ 
+
+ align:start position:0%
+look at that um a function uh F from a
+set a to a set B is a relation which
+
+ align:start position:0%
+set a to a set B is a relation which
+ 
+
+ align:start position:0%
+set a to a set B is a relation which
+Associates with each element in the
+
+ align:start position:0%
+Associates with each element in the
+ 
+
+ align:start position:0%
+Associates with each element in the
+domain each element little a in the
+
+ align:start position:0%
+domain each element little a in the
+ 
+
+ align:start position:0%
+domain each element little a in the
+domain capital A with most one element
+
+ align:start position:0%
+domain capital A with most one element
+ 
+
+ align:start position:0%
+domain capital A with most one element
+of the codomain
+
+ align:start position:0%
+of the codomain
+ 
+
+ align:start position:0%
+of the codomain
+B so this one element if it exists is
+
+ align:start position:0%
+B so this one element if it exists is
+ 
+
+ align:start position:0%
+B so this one element if it exists is
+called f of a it's the image of the
+
+ align:start position:0%
+called f of a it's the image of the
+ 
+
+ align:start position:0%
+called f of a it's the image of the
+element a under the relation F but
+
+ align:start position:0%
+element a under the relation F but
+ 
+
+ align:start position:0%
+element a under the relation F but
+what's special about it is that F of a
+
+ align:start position:0%
+what's special about it is that F of a
+ 
+
+ align:start position:0%
+what's special about it is that F of a
+contains at most one element so let's
+
+ align:start position:0%
+contains at most one element so let's
+ 
+
+ align:start position:0%
+contains at most one element so let's
+just look at an example again um a way
+
+ align:start position:0%
+just look at an example again um a way
+ 
+
+ align:start position:0%
+just look at an example again um a way
+to say that that a relation is a
+
+ align:start position:0%
+to say that that a relation is a
+ 
+
+ align:start position:0%
+to say that that a relation is a
+function is to look at all of the points
+
+ align:start position:0%
+function is to look at all of the points
+ 
+
+ align:start position:0%
+function is to look at all of the points
+on the left in the in the domain and
+
+ align:start position:0%
+on the left in the in the domain and
+ 
+
+ align:start position:0%
+on the left in the in the domain and
+make sure that none of them have more
+
+ align:start position:0%
+make sure that none of them have more
+ 
+
+ align:start position:0%
+make sure that none of them have more
+than one Arrow coming out well in this
+
+ align:start position:0%
+than one Arrow coming out well in this
+ 
+
+ align:start position:0%
+than one Arrow coming out well in this
+picture there are a couple of violations
+
+ align:start position:0%
+picture there are a couple of violations
+ 
+
+ align:start position:0%
+picture there are a couple of violations
+about that of that there are a couple of
+
+ align:start position:0%
+about that of that there are a couple of
+ 
+
+ align:start position:0%
+about that of that there are a couple of
+points on the left in a that have more
+
+ align:start position:0%
+points on the left in a that have more
+ 
+
+ align:start position:0%
+points on the left in a that have more
+than one Arrow coming out there's are
+
+ align:start position:0%
+than one Arrow coming out there's are
+ 
+
+ align:start position:0%
+than one Arrow coming out there's are
+two bad edges but if I erase those now
+
+ align:start position:0%
+two bad edges but if I erase those now
+ 
+
+ align:start position:0%
+two bad edges but if I erase those now
+I'm left with a function and sure enough
+
+ align:start position:0%
+I'm left with a function and sure enough
+ 
+
+ align:start position:0%
+I'm left with a function and sure enough
+there's at most one Arrow coming out of
+
+ align:start position:0%
+there's at most one Arrow coming out of
+ 
+
+ align:start position:0%
+there's at most one Arrow coming out of
+each of the points on the left in a some
+
+ align:start position:0%
+each of the points on the left in a some
+ 
+
+ align:start position:0%
+each of the points on the left in a some
+of the points have no arrows coming out
+
+ align:start position:0%
+of the points have no arrows coming out
+ 
+
+ align:start position:0%
+of the points have no arrows coming out
+that's fine um and so so for those green
+
+ align:start position:0%
+that's fine um and so so for those green
+ 
+
+ align:start position:0%
+that's fine um and so so for those green
+points with an arrow out there's a
+
+ align:start position:0%
+points with an arrow out there's a
+ 
+
+ align:start position:0%
+points with an arrow out there's a
+unique F of the Green Point equal to a
+
+ align:start position:0%
+unique F of the Green Point equal to a
+ 
+
+ align:start position:0%
+unique F of the Green Point equal to a
+magenta point in B that's uniquely
+
+ align:start position:0%
+magenta point in B that's uniquely
+ 
+
+ align:start position:0%
+magenta point in B that's uniquely
+determined by the functional relation F
+
+ align:start position:0%
+determined by the functional relation F
+ 
+
+ align:start position:0%
+determined by the functional relation F
+which may not be defined for all of the
+
+ align:start position:0%
+which may not be defined for all of the
+ 
+
+ align:start position:0%
+which may not be defined for all of the
+green points if they don't have any
+
+ align:start position:0%
+green points if they don't have any
+ 
+
+ align:start position:0%
+green points if they don't have any
+Arrow coming out of them so function
+
+ align:start position:0%
+Arrow coming out of them so function
+ 
+
+ align:start position:0%
+Arrow coming out of them so function
+means less than or equal to one Arrow
+
+ align:start position:0%
+means less than or equal to one Arrow
+ 
+
+ align:start position:0%
+means less than or equal to one Arrow
+coming
+
+ align:start position:0%
+coming
+ 
+
+ align:start position:0%
+coming
+out um so if we said this formally
+
+ align:start position:0%
+out um so if we said this formally
+ 
+
+ align:start position:0%
+out um so if we said this formally
+without talking about the arrows one way
+
+ align:start position:0%
+without talking about the arrows one way
+ 
+
+ align:start position:0%
+without talking about the arrows one way
+is simply to say that uh that a relation
+
+ align:start position:0%
+is simply to say that uh that a relation
+ 
+
+ align:start position:0%
+is simply to say that uh that a relation
+is a function if F of little a is if the
+
+ align:start position:0%
+is a function if F of little a is if the
+ 
+
+ align:start position:0%
+is a function if F of little a is if the
+size of f of little a is less than or
+
+ align:start position:0%
+size of f of little a is less than or
+ 
+
+ align:start position:0%
+size of f of little a is less than or
+equal to one for all of the domain
+
+ align:start position:0%
+equal to one for all of the domain
+ 
+
+ align:start position:0%
+equal to one for all of the domain
+elements a um and a more Elementary way
+
+ align:start position:0%
+elements a um and a more Elementary way
+ 
+
+ align:start position:0%
+elements a um and a more Elementary way
+to say it um using just the language of
+
+ align:start position:0%
+to say it um using just the language of
+ 
+
+ align:start position:0%
+to say it um using just the language of
+relations and equality and buole and
+
+ align:start position:0%
+relations and equality and buole and
+ 
+
+ align:start position:0%
+relations and equality and buole and
+connectives is to say that if a is
+
+ align:start position:0%
+connectives is to say that if a is
+ 
+
+ align:start position:0%
+connectives is to say that if a is
+connected to two things by f if AF FB
+
+ align:start position:0%
+connected to two things by f if AF FB
+ 
+
+ align:start position:0%
+connected to two things by f if AF FB
+and AF FB Prime then in fact B is equal
+
+ align:start position:0%
+and AF FB Prime then in fact B is equal
+ 
+
+ align:start position:0%
+and AF FB Prime then in fact B is equal
+to B
+
+ align:start position:0%
+to B
+ 
+
+ align:start position:0%
+to B
+Prime and that wraps up functions
\ No newline at end of file
diff --git a/Fo8v7juSgRw.txt b/Fo8v7juSgRw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9f77d9e6ad98ac7e285c067c85e4f95b40fe7b81
--- /dev/null
+++ b/Fo8v7juSgRw.txt
@@ -0,0 +1,20455 @@
+align:start position:0%
+ 
+welcome everybody um we
+
+ align:start position:0%
+welcome everybody um we
+ 
+
+ align:start position:0%
+welcome everybody um we
+are extremely fortunate and proud to
+
+ align:start position:0%
+are extremely fortunate and proud to
+ 
+
+ align:start position:0%
+are extremely fortunate and proud to
+have with us today Christopher craft
+
+ align:start position:0%
+have with us today Christopher craft
+ 
+
+ align:start position:0%
+have with us today Christopher craft
+actually Christopher craft Jr he told us
+
+ align:start position:0%
+actually Christopher craft Jr he told us
+ 
+
+ align:start position:0%
+actually Christopher craft Jr he told us
+last night that his father Christopher
+
+ align:start position:0%
+last night that his father Christopher
+ 
+
+ align:start position:0%
+last night that his father Christopher
+craft was born within about a block of
+
+ align:start position:0%
+craft was born within about a block of
+ 
+
+ align:start position:0%
+craft was born within about a block of
+Columbus Circle and that's how he picked
+
+ align:start position:0%
+Columbus Circle and that's how he picked
+ 
+
+ align:start position:0%
+Columbus Circle and that's how he picked
+up the name Christopher Columbus craft
+
+ align:start position:0%
+up the name Christopher Columbus craft
+ 
+
+ align:start position:0%
+up the name Christopher Columbus craft
+which was passed on to Chris Craft Jr um
+
+ align:start position:0%
+which was passed on to Chris Craft Jr um
+ 
+
+ align:start position:0%
+which was passed on to Chris Craft Jr um
+I don't really need to say very much by
+
+ align:start position:0%
+I don't really need to say very much by
+ 
+
+ align:start position:0%
+I don't really need to say very much by
+means of uh introduction because Chris
+
+ align:start position:0%
+means of uh introduction because Chris
+ 
+
+ align:start position:0%
+means of uh introduction because Chris
+Craft is a name that has been associated
+
+ align:start position:0%
+Craft is a name that has been associated
+ 
+
+ align:start position:0%
+Craft is a name that has been associated
+with America's Space Program since the
+
+ align:start position:0%
+with America's Space Program since the
+ 
+
+ align:start position:0%
+with America's Space Program since the
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+beginning uh and actually from the very
+
+ align:start position:0%
+beginning uh and actually from the very
+ 
+
+ align:start position:0%
+beginning uh and actually from the very
+beginning of his career right after he
+
+ align:start position:0%
+beginning of his career right after he
+ 
+
+ align:start position:0%
+beginning of his career right after he
+uh graduated from um university in
+
+ align:start position:0%
+uh graduated from um university in
+ 
+
+ align:start position:0%
+uh graduated from um university in
+Virginia he went to work for the old
+
+ align:start position:0%
+Virginia he went to work for the old
+ 
+
+ align:start position:0%
+Virginia he went to work for the old
+nacka the national uh Commission on a
+
+ align:start position:0%
+nacka the national uh Commission on a
+ 
+
+ align:start position:0%
+nacka the national uh Commission on a
+itics and that of course became
+
+ align:start position:0%
+itics and that of course became
+ 
+
+ align:start position:0%
+itics and that of course became
+eventually NASA so Chris Craft is a
+
+ align:start position:0%
+eventually NASA so Chris Craft is a
+ 
+
+ align:start position:0%
+eventually NASA so Chris Craft is a
+person who has grown up uh with the
+
+ align:start position:0%
+person who has grown up uh with the
+ 
+
+ align:start position:0%
+person who has grown up uh with the
+space program and in fact uh was
+
+ align:start position:0%
+space program and in fact uh was
+ 
+
+ align:start position:0%
+space program and in fact uh was
+responsible for making the Space Program
+
+ align:start position:0%
+responsible for making the Space Program
+ 
+
+ align:start position:0%
+responsible for making the Space Program
+grow up he was instrumental essentially
+
+ align:start position:0%
+grow up he was instrumental essentially
+ 
+
+ align:start position:0%
+grow up he was instrumental essentially
+in inventing the concept of Mission
+
+ align:start position:0%
+in inventing the concept of Mission
+ 
+
+ align:start position:0%
+in inventing the concept of Mission
+Control and uh became after being a
+
+ align:start position:0%
+Control and uh became after being a
+ 
+
+ align:start position:0%
+Control and uh became after being a
+flight director for some of the early
+
+ align:start position:0%
+flight director for some of the early
+ 
+
+ align:start position:0%
+flight director for some of the early
+flights became the head of uh flight
+
+ align:start position:0%
+flights became the head of uh flight
+ 
+
+ align:start position:0%
+flights became the head of uh flight
+operations and eventually the director
+
+ align:start position:0%
+operations and eventually the director
+ 
+
+ align:start position:0%
+operations and eventually the director
+of the Johnson Space Center uh which is
+
+ align:start position:0%
+of the Johnson Space Center uh which is
+ 
+
+ align:start position:0%
+of the Johnson Space Center uh which is
+the home of human space flight in this
+
+ align:start position:0%
+the home of human space flight in this
+ 
+
+ align:start position:0%
+the home of human space flight in this
+country he uh had that position through
+
+ align:start position:0%
+country he uh had that position through
+ 
+
+ align:start position:0%
+country he uh had that position through
+1982 which was the uh the end of the uh
+
+ align:start position:0%
+1982 which was the uh the end of the uh
+ 
+
+ align:start position:0%
+1982 which was the uh the end of the uh
+original orbital flight test phase of
+
+ align:start position:0%
+original orbital flight test phase of
+ 
+
+ align:start position:0%
+original orbital flight test phase of
+the Orbiter so he really was uh in
+
+ align:start position:0%
+the Orbiter so he really was uh in
+ 
+
+ align:start position:0%
+the Orbiter so he really was uh in
+charge of the Space Center when the
+
+ align:start position:0%
+charge of the Space Center when the
+ 
+
+ align:start position:0%
+charge of the Space Center when the
+space shuttle was being developed and of
+
+ align:start position:0%
+space shuttle was being developed and of
+ 
+
+ align:start position:0%
+space shuttle was being developed and of
+course this uh this course is a course
+
+ align:start position:0%
+course this uh this course is a course
+ 
+
+ align:start position:0%
+course this uh this course is a course
+in the systems engineering of the Space
+
+ align:start position:0%
+in the systems engineering of the Space
+ 
+
+ align:start position:0%
+in the systems engineering of the Space
+Shuttle um I just want uh in in public
+
+ align:start position:0%
+Shuttle um I just want uh in in public
+ 
+
+ align:start position:0%
+Shuttle um I just want uh in in public
+here to acknowledge uh that there have
+
+ align:start position:0%
+here to acknowledge uh that there have
+ 
+
+ align:start position:0%
+here to acknowledge uh that there have
+been uh expenses involved in bringing
+
+ align:start position:0%
+been uh expenses involved in bringing
+ 
+
+ align:start position:0%
+been uh expenses involved in bringing
+all of the special lectures that we've
+
+ align:start position:0%
+all of the special lectures that we've
+ 
+
+ align:start position:0%
+all of the special lectures that we've
+had who have participated in this course
+
+ align:start position:0%
+had who have participated in this course
+ 
+
+ align:start position:0%
+had who have participated in this course
+and it would not have been possible
+
+ align:start position:0%
+and it would not have been possible
+ 
+
+ align:start position:0%
+and it would not have been possible
+without the support of the rper
+
+ align:start position:0%
+without the support of the rper
+ 
+
+ align:start position:0%
+without the support of the rper
+laboratory and we thank Dr Ellie guy who
+
+ align:start position:0%
+laboratory and we thank Dr Ellie guy who
+ 
+
+ align:start position:0%
+laboratory and we thank Dr Ellie guy who
+uh has provided that support we we
+
+ align:start position:0%
+uh has provided that support we we
+ 
+
+ align:start position:0%
+uh has provided that support we we
+couldn't have done it without you and we
+
+ align:start position:0%
+couldn't have done it without you and we
+ 
+
+ align:start position:0%
+couldn't have done it without you and we
+really appreciate it that's enough for
+
+ align:start position:0%
+really appreciate it that's enough for
+ 
+
+ align:start position:0%
+really appreciate it that's enough for
+me uh we all came here to hear Chris
+
+ align:start position:0%
+me uh we all came here to hear Chris
+ 
+
+ align:start position:0%
+me uh we all came here to hear Chris
+Kraft talk about uh the development
+
+ align:start position:0%
+Kraft talk about uh the development
+ 
+
+ align:start position:0%
+Kraft talk about uh the development
+invention and development of Mission
+
+ align:start position:0%
+invention and development of Mission
+ 
+
+ align:start position:0%
+invention and development of Mission
+Control and the uh systems engineering
+
+ align:start position:0%
+Control and the uh systems engineering
+ 
+
+ align:start position:0%
+Control and the uh systems engineering
+and development of the Space Shuttle I
+
+ align:start position:0%
+and development of the Space Shuttle I
+ 
+
+ align:start position:0%
+and development of the Space Shuttle I
+will tell you that uh Chris Craft is
+
+ align:start position:0%
+will tell you that uh Chris Craft is
+ 
+
+ align:start position:0%
+will tell you that uh Chris Craft is
+somebody who's not afraid to express his
+
+ align:start position:0%
+somebody who's not afraid to express his
+ 
+
+ align:start position:0%
+somebody who's not afraid to express his
+opinion I and we're looking forward to
+
+ align:start position:0%
+opinion I and we're looking forward to
+ 
+
+ align:start position:0%
+opinion I and we're looking forward to
+hearing them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chris good
+
+ align:start position:0%
+Chris good
+ 
+
+ align:start position:0%
+Chris good
+morning
+
+ align:start position:0%
+morning
+ 
+
+ align:start position:0%
+morning
+uh it's
+
+ align:start position:0%
+uh it's
+ 
+
+ align:start position:0%
+uh it's
+it's not hard but uh sometimes difficult
+
+ align:start position:0%
+it's not hard but uh sometimes difficult
+ 
+
+ align:start position:0%
+it's not hard but uh sometimes difficult
+to uh return to uh MIT where
+
+ align:start position:0%
+to uh return to uh MIT where
+ 
+
+ align:start position:0%
+to uh return to uh MIT where
+I uh have a lot of friends who came this
+
+ align:start position:0%
+I uh have a lot of friends who came this
+ 
+
+ align:start position:0%
+I uh have a lot of friends who came this
+morning
+
+ align:start position:0%
+morning
+ 
+
+ align:start position:0%
+morning
+uh they they sort of overwhelmed me then
+
+ align:start position:0%
+uh they they sort of overwhelmed me then
+ 
+
+ align:start position:0%
+uh they they sort of overwhelmed me then
+and uh I'm sure they would overwhelm me
+
+ align:start position:0%
+and uh I'm sure they would overwhelm me
+ 
+
+ align:start position:0%
+and uh I'm sure they would overwhelm me
+now if uh we got into some deep
+
+ align:start position:0%
+now if uh we got into some deep
+ 
+
+ align:start position:0%
+now if uh we got into some deep
+technical subject about which I knew
+
+ align:start position:0%
+technical subject about which I knew
+ 
+
+ align:start position:0%
+technical subject about which I knew
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+little at the time uh I'll say a little
+
+ align:start position:0%
+little at the time uh I'll say a little
+ 
+
+ align:start position:0%
+little at the time uh I'll say a little
+bit more about that what I what I did
+
+ align:start position:0%
+bit more about that what I what I did
+ 
+
+ align:start position:0%
+bit more about that what I what I did
+want to say though
+
+ align:start position:0%
+want to say though
+ 
+
+ align:start position:0%
+want to say though
+that uh the people that preceded me in
+
+ align:start position:0%
+that uh the people that preceded me in
+ 
+
+ align:start position:0%
+that uh the people that preceded me in
+lecturing to
+
+ align:start position:0%
+lecturing to
+ 
+
+ align:start position:0%
+lecturing to
+you uh you've been very fortunate
+
+ align:start position:0%
+you uh you've been very fortunate
+ 
+
+ align:start position:0%
+you uh you've been very fortunate
+because uh uh they indeed are uh the
+
+ align:start position:0%
+because uh uh they indeed are uh the
+ 
+
+ align:start position:0%
+because uh uh they indeed are uh the
+stars of the Space Shuttle they did a
+
+ align:start position:0%
+stars of the Space Shuttle they did a
+ 
+
+ align:start position:0%
+stars of the Space Shuttle they did a
+fantastic job and I hope you got that
+
+ align:start position:0%
+fantastic job and I hope you got that
+ 
+
+ align:start position:0%
+fantastic job and I hope you got that
+sense from them as they spoke to you
+
+ align:start position:0%
+sense from them as they spoke to you
+ 
+
+ align:start position:0%
+sense from them as they spoke to you
+they are the best and if uh if I were if
+
+ align:start position:0%
+they are the best and if uh if I were if
+ 
+
+ align:start position:0%
+they are the best and if uh if I were if
+I were going to say two things about U
+
+ align:start position:0%
+I were going to say two things about U
+ 
+
+ align:start position:0%
+I were going to say two things about U
+management that I have learned in my
+
+ align:start position:0%
+management that I have learned in my
+ 
+
+ align:start position:0%
+management that I have learned in my
+lifetime uh the first would be uh you're
+
+ align:start position:0%
+lifetime uh the first would be uh you're
+ 
+
+ align:start position:0%
+lifetime uh the first would be uh you're
+absolutely no better than the people
+
+ align:start position:0%
+absolutely no better than the people
+ 
+
+ align:start position:0%
+absolutely no better than the people
+around you
+
+ align:start position:0%
+around you
+ 
+
+ align:start position:0%
+around you
+without uh a lot of great brains around
+
+ align:start position:0%
+without uh a lot of great brains around
+ 
+
+ align:start position:0%
+without uh a lot of great brains around
+you you're not very good no matter if
+
+ align:start position:0%
+you you're not very good no matter if
+ 
+
+ align:start position:0%
+you you're not very good no matter if
+you're the best person in the world and
+
+ align:start position:0%
+you're the best person in the world and
+ 
+
+ align:start position:0%
+you're the best person in the world and
+too many people have learned that the
+
+ align:start position:0%
+too many people have learned that the
+ 
+
+ align:start position:0%
+too many people have learned that the
+hard way and not recognize that fact
+
+ align:start position:0%
+hard way and not recognize that fact
+ 
+
+ align:start position:0%
+hard way and not recognize that fact
+second thing we talked about last night
+
+ align:start position:0%
+second thing we talked about last night
+ 
+
+ align:start position:0%
+second thing we talked about last night
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+dinner and that was uh the second thing
+
+ align:start position:0%
+dinner and that was uh the second thing
+ 
+
+ align:start position:0%
+dinner and that was uh the second thing
+you learn as a engineering manager
+
+ align:start position:0%
+you learn as a engineering manager
+ 
+
+ align:start position:0%
+you learn as a engineering manager
+is that it every day is a compromise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh everything you do you you have this
+
+ align:start position:0%
+uh everything you do you you have this
+ 
+
+ align:start position:0%
+uh everything you do you you have this
+idealistic view of doing it the best way
+
+ align:start position:0%
+idealistic view of doing it the best way
+ 
+
+ align:start position:0%
+idealistic view of doing it the best way
+possible doing it better every day doing
+
+ align:start position:0%
+possible doing it better every day doing
+ 
+
+ align:start position:0%
+possible doing it better every day doing
+it uh without worrying too much about
+
+ align:start position:0%
+it uh without worrying too much about
+ 
+
+ align:start position:0%
+it uh without worrying too much about
+the cost too much about the
+
+ align:start position:0%
+the cost too much about the
+ 
+
+ align:start position:0%
+the cost too much about the
+budget too much about the schedule uh
+
+ align:start position:0%
+budget too much about the schedule uh
+ 
+
+ align:start position:0%
+budget too much about the schedule uh
+you go in with that idea but those
+
+ align:start position:0%
+you go in with that idea but those
+ 
+
+ align:start position:0%
+you go in with that idea but those
+things you have to face every day and so
+
+ align:start position:0%
+things you have to face every day and so
+ 
+
+ align:start position:0%
+things you have to face every day and so
+managers has become great
+
+ align:start position:0%
+managers has become great
+ 
+
+ align:start position:0%
+managers has become great
+compromisers and the systems you end up
+
+ align:start position:0%
+compromisers and the systems you end up
+ 
+
+ align:start position:0%
+compromisers and the systems you end up
+with are not what you really
+
+ align:start position:0%
+with are not what you really
+ 
+
+ align:start position:0%
+with are not what you really
+wanted but if you're smart they do the
+
+ align:start position:0%
+wanted but if you're smart they do the
+ 
+
+ align:start position:0%
+wanted but if you're smart they do the
+job so if I were going to add two things
+
+ align:start position:0%
+job so if I were going to add two things
+ 
+
+ align:start position:0%
+job so if I were going to add two things
+to your education at MIT that's where I
+
+ align:start position:0%
+to your education at MIT that's where I
+ 
+
+ align:start position:0%
+to your education at MIT that's where I
+would come
+
+ align:start position:0%
+would come
+ 
+
+ align:start position:0%
+would come
+from uh the third thing I would say is
+
+ align:start position:0%
+from uh the third thing I would say is
+ 
+
+ align:start position:0%
+from uh the third thing I would say is
+that whether you like it or not you
+
+ align:start position:0%
+that whether you like it or not you
+ 
+
+ align:start position:0%
+that whether you like it or not you
+people sitting here not you oldheads
+
+ align:start position:0%
+people sitting here not you oldheads
+ 
+
+ align:start position:0%
+people sitting here not you oldheads
+but you people sitting here are the
+
+ align:start position:0%
+but you people sitting here are the
+ 
+
+ align:start position:0%
+but you people sitting here are the
+people that are going to do the next
+
+ align:start position:0%
+people that are going to do the next
+ 
+
+ align:start position:0%
+people that are going to do the next
+Space
+
+ align:start position:0%
+Space
+ 
+
+ align:start position:0%
+Space
+Program you are the ones that are going
+
+ align:start position:0%
+Program you are the ones that are going
+ 
+
+ align:start position:0%
+Program you are the ones that are going
+to take us back to the Moon if and when
+
+ align:start position:0%
+to take us back to the Moon if and when
+ 
+
+ align:start position:0%
+to take us back to the Moon if and when
+we get there it's going to be up to you
+
+ align:start position:0%
+we get there it's going to be up to you
+ 
+
+ align:start position:0%
+we get there it's going to be up to you
+to do the
+
+ align:start position:0%
+to do the
+ 
+
+ align:start position:0%
+to do the
+job uh in
+
+ align:start position:0%
+job uh in
+ 
+
+ align:start position:0%
+job uh in
+1968 the average age of my organization
+
+ align:start position:0%
+1968 the average age of my organization
+ 
+
+ align:start position:0%
+1968 the average age of my organization
+and I think I was 44 was
+
+ align:start position:0%
+and I think I was 44 was
+ 
+
+ align:start position:0%
+and I think I was 44 was
+26 so we
+
+ align:start position:0%
+26 so we
+ 
+
+ align:start position:0%
+26 so we
+had an awful lot of young people who did
+
+ align:start position:0%
+had an awful lot of young people who did
+ 
+
+ align:start position:0%
+had an awful lot of young people who did
+the job and did it extremely
+
+ align:start position:0%
+the job and did it extremely
+ 
+
+ align:start position:0%
+the job and did it extremely
+well uh the guy sitting there on Apollo
+
+ align:start position:0%
+well uh the guy sitting there on Apollo
+ 
+
+ align:start position:0%
+well uh the guy sitting there on Apollo
+11 uh screaming into them into his
+
+ align:start position:0%
+11 uh screaming into them into his
+ 
+
+ align:start position:0%
+11 uh screaming into them into his
+headset that it was still go I think was
+
+ align:start position:0%
+headset that it was still go I think was
+ 
+
+ align:start position:0%
+headset that it was still go I think was
+25 years old at the time and he was a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+veteran and if he hadn't been a veteran
+
+ align:start position:0%
+veteran and if he hadn't been a veteran
+ 
+
+ align:start position:0%
+veteran and if he hadn't been a veteran
+he sure in hell was
+
+ align:start position:0%
+he sure in hell was
+ 
+
+ align:start position:0%
+he sure in hell was
+a few minutes after he kept yelling into
+
+ align:start position:0%
+a few minutes after he kept yelling into
+ 
+
+ align:start position:0%
+a few minutes after he kept yelling into
+that microphone that it was go and if
+
+ align:start position:0%
+that microphone that it was go and if
+ 
+
+ align:start position:0%
+that microphone that it was go and if
+you I hope you've seen that on
+
+ align:start position:0%
+you I hope you've seen that on
+ 
+
+ align:start position:0%
+you I hope you've seen that on
+television if you haven't it's a really
+
+ align:start position:0%
+television if you haven't it's a really
+ 
+
+ align:start position:0%
+television if you haven't it's a really
+great moment in
+
+ align:start position:0%
+great moment in
+ 
+
+ align:start position:0%
+great moment in
+Apollo uh let me start from
+
+ align:start position:0%
+Apollo uh let me start from
+ 
+
+ align:start position:0%
+Apollo uh let me start from
+uh the
+
+ align:start position:0%
+uh the
+ 
+
+ align:start position:0%
+uh the
+beginning uh in Project
+
+ align:start position:0%
+beginning uh in Project
+ 
+
+ align:start position:0%
+beginning uh in Project
+Mercury uh we started with a space task
+
+ align:start position:0%
+Mercury uh we started with a space task
+ 
+
+ align:start position:0%
+Mercury uh we started with a space task
+group of 35 people eight of which were
+
+ align:start position:0%
+group of 35 people eight of which were
+ 
+
+ align:start position:0%
+group of 35 people eight of which were
+secretaries and those of us that came
+
+ align:start position:0%
+secretaries and those of us that came
+ 
+
+ align:start position:0%
+secretaries and those of us that came
+out of the NACA the National advisory
+
+ align:start position:0%
+out of the NACA the National advisory
+ 
+
+ align:start position:0%
+out of the NACA the National advisory
+committee for
+
+ align:start position:0%
+committee for
+ 
+
+ align:start position:0%
+committee for
+Aeronautics uh was um where we were
+
+ align:start position:0%
+Aeronautics uh was um where we were
+ 
+
+ align:start position:0%
+Aeronautics uh was um where we were
+smart guys we were very capable people
+
+ align:start position:0%
+smart guys we were very capable people
+ 
+
+ align:start position:0%
+smart guys we were very capable people
+but we didn't know a damn thing about
+
+ align:start position:0%
+but we didn't know a damn thing about
+ 
+
+ align:start position:0%
+but we didn't know a damn thing about
+how to fly in space believe me if you
+
+ align:start position:0%
+how to fly in space believe me if you
+ 
+
+ align:start position:0%
+how to fly in space believe me if you
+had asked us at the time how do you get
+
+ align:start position:0%
+had asked us at the time how do you get
+ 
+
+ align:start position:0%
+had asked us at the time how do you get
+fluid out of a tank at zero
+
+ align:start position:0%
+fluid out of a tank at zero
+ 
+
+ align:start position:0%
+fluid out of a tank at zero
+g i don't believe you'd gotten the right
+
+ align:start position:0%
+g i don't believe you'd gotten the right
+ 
+
+ align:start position:0%
+g i don't believe you'd gotten the right
+answer from more than two guys maybe Max
+
+ align:start position:0%
+answer from more than two guys maybe Max
+ 
+
+ align:start position:0%
+answer from more than two guys maybe Max
+V would have said well you got to put a
+
+ align:start position:0%
+V would have said well you got to put a
+ 
+
+ align:start position:0%
+V would have said well you got to put a
+bladder in there and put pressure behind
+
+ align:start position:0%
+bladder in there and put pressure behind
+ 
+
+ align:start position:0%
+bladder in there and put pressure behind
+it and squeeze the stuff out because
+
+ align:start position:0%
+it and squeeze the stuff out because
+ 
+
+ align:start position:0%
+it and squeeze the stuff out because
+when we Flo it you don't know where it
+
+ align:start position:0%
+when we Flo it you don't know where it
+ 
+
+ align:start position:0%
+when we Flo it you don't know where it
+is in the tank and secondly how much
+
+ align:start position:0%
+is in the tank and secondly how much
+ 
+
+ align:start position:0%
+is in the tank and secondly how much
+have you got
+
+ align:start position:0%
+have you got
+ 
+
+ align:start position:0%
+have you got
+left in a tank kind of an interesting
+
+ align:start position:0%
+left in a tank kind of an interesting
+ 
+
+ align:start position:0%
+left in a tank kind of an interesting
+project if you don't know what Zer G is
+
+ align:start position:0%
+project if you don't know what Zer G is
+ 
+
+ align:start position:0%
+project if you don't know what Zer G is
+all about so when we
+
+ align:start position:0%
+all about so when we
+ 
+
+ align:start position:0%
+all about so when we
+started in Project Mercury we didn't
+
+ align:start position:0%
+started in Project Mercury we didn't
+ 
+
+ align:start position:0%
+started in Project Mercury we didn't
+know much about systems designed for
+
+ align:start position:0%
+know much about systems designed for
+ 
+
+ align:start position:0%
+know much about systems designed for
+space we certainly had high questions
+
+ align:start position:0%
+space we certainly had high questions
+ 
+
+ align:start position:0%
+space we certainly had high questions
+about man capability to perform a task
+
+ align:start position:0%
+about man capability to perform a task
+ 
+
+ align:start position:0%
+about man capability to perform a task
+in space and I'd say 98 to 99% of the
+
+ align:start position:0%
+in space and I'd say 98 to 99% of the
+ 
+
+ align:start position:0%
+in space and I'd say 98 to 99% of the
+medical community in the United States
+
+ align:start position:0%
+medical community in the United States
+ 
+
+ align:start position:0%
+medical community in the United States
+thought that the astronaut when he got
+
+ align:start position:0%
+thought that the astronaut when he got
+ 
+
+ align:start position:0%
+thought that the astronaut when he got
+there would be a blithering
+
+ align:start position:0%
+there would be a blithering
+ 
+
+ align:start position:0%
+there would be a blithering
+idiot that he would probably swallow his
+
+ align:start position:0%
+idiot that he would probably swallow his
+ 
+
+ align:start position:0%
+idiot that he would probably swallow his
+tongue that he couldn't see because his
+
+ align:start position:0%
+tongue that he couldn't see because his
+ 
+
+ align:start position:0%
+tongue that he couldn't see because his
+eyeballs were bulging at it or that
+
+ align:start position:0%
+eyeballs were bulging at it or that
+ 
+
+ align:start position:0%
+eyeballs were bulging at it or that
+because of the worry he was going
+
+ align:start position:0%
+because of the worry he was going
+ 
+
+ align:start position:0%
+because of the worry he was going
+through he would have a 24 24hour ulcer
+
+ align:start position:0%
+through he would have a 24 24hour ulcer
+ 
+
+ align:start position:0%
+through he would have a 24 24hour ulcer
+sitting on the pad and he and they would
+
+ align:start position:0%
+sitting on the pad and he and they would
+ 
+
+ align:start position:0%
+sitting on the pad and he and they would
+suddenly have to be at his side the
+
+ align:start position:0%
+suddenly have to be at his side the
+ 
+
+ align:start position:0%
+suddenly have to be at his side the
+medical community thought so that's
+
+ align:start position:0%
+medical community thought so that's
+ 
+
+ align:start position:0%
+medical community thought so that's
+where we were coming
+
+ align:start position:0%
+where we were coming
+ 
+
+ align:start position:0%
+where we were coming
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+and so we decided we're going to put man
+
+ align:start position:0%
+and so we decided we're going to put man
+ 
+
+ align:start position:0%
+and so we decided we're going to put man
+in space and thank you very
+
+ align:start position:0%
+in space and thank you very
+ 
+
+ align:start position:0%
+in space and thank you very
+much uh it was a daunting task but one
+
+ align:start position:0%
+much uh it was a daunting task but one
+ 
+
+ align:start position:0%
+much uh it was a daunting task but one
+which most of us realized from the getg
+
+ align:start position:0%
+which most of us realized from the getg
+ 
+
+ align:start position:0%
+which most of us realized from the getg
+go that we were in the middle of
+
+ align:start position:0%
+go that we were in the middle of
+ 
+
+ align:start position:0%
+go that we were in the middle of
+probably man's Greatest
+
+ align:start position:0%
+probably man's Greatest
+ 
+
+ align:start position:0%
+probably man's Greatest
+Adventure believe me we did know that I
+
+ align:start position:0%
+Adventure believe me we did know that I
+ 
+
+ align:start position:0%
+Adventure believe me we did know that I
+felt it and I think everybody felt it it
+
+ align:start position:0%
+felt it and I think everybody felt it it
+ 
+
+ align:start position:0%
+felt it and I think everybody felt it it
+was a it was sort of a uh
+
+ align:start position:0%
+was a it was sort of a uh
+ 
+
+ align:start position:0%
+was a it was sort of a uh
+Euphoria and in we were in what you
+
+ align:start position:0%
+Euphoria and in we were in what you
+ 
+
+ align:start position:0%
+Euphoria and in we were in what you
+would might call engineering Euphoria
+
+ align:start position:0%
+would might call engineering Euphoria
+ 
+
+ align:start position:0%
+would might call engineering Euphoria
+like Ed White was on GED 4 he was
+
+ align:start position:0%
+like Ed White was on GED 4 he was
+ 
+
+ align:start position:0%
+like Ed White was on GED 4 he was
+certain when he was outside the
+
+ align:start position:0%
+certain when he was outside the
+ 
+
+ align:start position:0%
+certain when he was outside the
+spacecraft I'm absolutely certain he was
+
+ align:start position:0%
+spacecraft I'm absolutely certain he was
+ 
+
+ align:start position:0%
+spacecraft I'm absolutely certain he was
+euphoric the Press that he must have
+
+ align:start position:0%
+euphoric the Press that he must have
+ 
+
+ align:start position:0%
+euphoric the Press that he must have
+been euphoric and I said oh no he was
+
+ align:start position:0%
+been euphoric and I said oh no he was
+ 
+
+ align:start position:0%
+been euphoric and I said oh no he was
+worried about what doing the right
+
+ align:start position:0%
+worried about what doing the right
+ 
+
+ align:start position:0%
+worried about what doing the right
+things and doing all the right things at
+
+ align:start position:0%
+things and doing all the right things at
+ 
+
+ align:start position:0%
+things and doing all the right things at
+the right time he was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+euphoric again and if you you don't
+
+ align:start position:0%
+euphoric again and if you you don't
+ 
+
+ align:start position:0%
+euphoric again and if you you don't
+recall but they said something finally
+
+ align:start position:0%
+recall but they said something finally
+ 
+
+ align:start position:0%
+recall but they said something finally
+at the end of that and said what does
+
+ align:start position:0%
+at the end of that and said what does
+ 
+
+ align:start position:0%
+at the end of that and said what does
+the flight director have to say and I
+
+ align:start position:0%
+the flight director have to say and I
+ 
+
+ align:start position:0%
+the flight director have to say and I
+said get him back in the
+
+ align:start position:0%
+said get him back in the
+ 
+
+ align:start position:0%
+said get him back in the
+spacecraft as loud as I could see I
+
+ align:start position:0%
+spacecraft as loud as I could see I
+ 
+
+ align:start position:0%
+spacecraft as loud as I could see I
+think one of the few times I've ever
+
+ align:start position:0%
+think one of the few times I've ever
+ 
+
+ align:start position:0%
+think one of the few times I've ever
+spoken on the air on the air
+
+ align:start position:0%
+spoken on the air on the air
+ 
+
+ align:start position:0%
+spoken on the air on the air
+ground so we were were faced with
+
+ align:start position:0%
+ground so we were were faced with
+ 
+
+ align:start position:0%
+ground so we were were faced with
+putting somebody into this new
+
+ align:start position:0%
+putting somebody into this new
+ 
+
+ align:start position:0%
+putting somebody into this new
+environment for the first time and how
+
+ align:start position:0%
+environment for the first time and how
+ 
+
+ align:start position:0%
+environment for the first time and how
+do you do that what are the problems
+
+ align:start position:0%
+do you do that what are the problems
+ 
+
+ align:start position:0%
+do you do that what are the problems
+you're fa
+
+ align:start position:0%
+you're fa
+ 
+
+ align:start position:0%
+you're fa
+with when we began to think about uh how
+
+ align:start position:0%
+with when we began to think about uh how
+ 
+
+ align:start position:0%
+with when we began to think about uh how
+we did flight tests in airplanes you
+
+ align:start position:0%
+we did flight tests in airplanes you
+ 
+
+ align:start position:0%
+we did flight tests in airplanes you
+would sit on the ground and you would
+
+ align:start position:0%
+would sit on the ground and you would
+ 
+
+ align:start position:0%
+would sit on the ground and you would
+write a flight test requirements a set
+
+ align:start position:0%
+write a flight test requirements a set
+ 
+
+ align:start position:0%
+write a flight test requirements a set
+of things you wanted him to do on a
+
+ align:start position:0%
+of things you wanted him to do on a
+ 
+
+ align:start position:0%
+of things you wanted him to do on a
+flight you'd sit on the ground hold a
+
+ align:start position:0%
+flight you'd sit on the ground hold a
+ 
+
+ align:start position:0%
+flight you'd sit on the ground hold a
+microphone and and talk to him and he'd
+
+ align:start position:0%
+microphone and and talk to him and he'd
+ 
+
+ align:start position:0%
+microphone and and talk to him and he'd
+say I just did so and so and if he was
+
+ align:start position:0%
+say I just did so and so and if he was
+ 
+
+ align:start position:0%
+say I just did so and so and if he was
+one of the best test Pils he probably
+
+ align:start position:0%
+one of the best test Pils he probably
+ 
+
+ align:start position:0%
+one of the best test Pils he probably
+didn't tell you damn thing they just
+
+ align:start position:0%
+didn't tell you damn thing they just
+ 
+
+ align:start position:0%
+didn't tell you damn thing they just
+kept quiet like Neil armstr dong did
+
+ align:start position:0%
+kept quiet like Neil armstr dong did
+ 
+
+ align:start position:0%
+kept quiet like Neil armstr dong did
+most of the time you just kept quiet you
+
+ align:start position:0%
+most of the time you just kept quiet you
+ 
+
+ align:start position:0%
+most of the time you just kept quiet you
+kept having to prompt them to tell you
+
+ align:start position:0%
+kept having to prompt them to tell you
+ 
+
+ align:start position:0%
+kept having to prompt them to tell you
+what they were doing so that's where we
+
+ align:start position:0%
+what they were doing so that's where we
+ 
+
+ align:start position:0%
+what they were doing so that's where we
+were coming from we had
+
+ align:start position:0%
+were coming from we had
+ 
+
+ align:start position:0%
+were coming from we had
+instrumentation we had been de
+
+ align:start position:0%
+instrumentation we had been de
+ 
+
+ align:start position:0%
+instrumentation we had been de
+developing Telemetry from the bomb drop
+
+ align:start position:0%
+developing Telemetry from the bomb drop
+ 
+
+ align:start position:0%
+developing Telemetry from the bomb drop
+test that we had made at Langley so we
+
+ align:start position:0%
+test that we had made at Langley so we
+ 
+
+ align:start position:0%
+test that we had made at Langley so we
+knew quite a bit about Telemetry we
+
+ align:start position:0%
+knew quite a bit about Telemetry we
+ 
+
+ align:start position:0%
+knew quite a bit about Telemetry we
+didn't know very little about air to
+
+ align:start position:0%
+didn't know very little about air to
+ 
+
+ align:start position:0%
+didn't know very little about air to
+ground we knew that we would like to
+
+ align:start position:0%
+ground we knew that we would like to
+ 
+
+ align:start position:0%
+ground we knew that we would like to
+talk to this guy about every 15 minutes
+
+ align:start position:0%
+talk to this guy about every 15 minutes
+ 
+
+ align:start position:0%
+talk to this guy about every 15 minutes
+or so
+
+ align:start position:0%
+or so
+ 
+
+ align:start position:0%
+or so
+what you did when you went across the
+
+ align:start position:0%
+what you did when you went across the
+ 
+
+ align:start position:0%
+what you did when you went across the
+country as an airplane P so if you're
+
+ align:start position:0%
+country as an airplane P so if you're
+ 
+
+ align:start position:0%
+country as an airplane P so if you're
+going around the world I like to talk to
+
+ align:start position:0%
+going around the world I like to talk to
+ 
+
+ align:start position:0%
+going around the world I like to talk to
+them about every 15 minutes and so we
+
+ align:start position:0%
+them about every 15 minutes and so we
+ 
+
+ align:start position:0%
+them about every 15 minutes and so we
+got out the geography books and said
+
+ align:start position:0%
+got out the geography books and said
+ 
+
+ align:start position:0%
+got out the geography books and said
+well we're going to fly around this
+
+ align:start position:0%
+well we're going to fly around this
+ 
+
+ align:start position:0%
+well we're going to fly around this
+thing and here's what this Chinese
+
+ align:start position:0%
+thing and here's what this Chinese
+ 
+
+ align:start position:0%
+thing and here's what this Chinese
+finger puzzle looks like as it goes
+
+ align:start position:0%
+finger puzzle looks like as it goes
+ 
+
+ align:start position:0%
+finger puzzle looks like as it goes
+around the earth and we're going to be
+
+ align:start position:0%
+around the earth and we're going to be
+ 
+
+ align:start position:0%
+around the earth and we're going to be
+over this part of the earth and this is
+
+ align:start position:0%
+over this part of the earth and this is
+ 
+
+ align:start position:0%
+over this part of the earth and this is
+where insertion is going to take place
+
+ align:start position:0%
+where insertion is going to take place
+ 
+
+ align:start position:0%
+where insertion is going to take place
+and this is where we're going to do
+
+ align:start position:0%
+and this is where we're going to do
+ 
+
+ align:start position:0%
+and this is where we're going to do
+orbit determination and this is where
+
+ align:start position:0%
+orbit determination and this is where
+ 
+
+ align:start position:0%
+orbit determination and this is where
+we're going to do
+
+ align:start position:0%
+we're going to do
+ 
+
+ align:start position:0%
+we're going to do
+retrofire and we're going to we are
+
+ align:start position:0%
+retrofire and we're going to we are
+ 
+
+ align:start position:0%
+retrofire and we're going to we are
+going to be up there going around this
+
+ align:start position:0%
+going to be up there going around this
+ 
+
+ align:start position:0%
+going to be up there going around this
+particular section of the earth and you
+
+ align:start position:0%
+particular section of the earth and you
+ 
+
+ align:start position:0%
+particular section of the earth and you
+looked at the geography and said well
+
+ align:start position:0%
+looked at the geography and said well
+ 
+
+ align:start position:0%
+looked at the geography and said well
+we've got a tracking range in Cape
+
+ align:start position:0%
+we've got a tracking range in Cape
+ 
+
+ align:start position:0%
+we've got a tracking range in Cape
+canaval we've got tracking range on the
+
+ align:start position:0%
+canaval we've got tracking range on the
+ 
+
+ align:start position:0%
+canaval we've got tracking range on the
+west coast we got a few Radars in in uh
+
+ align:start position:0%
+west coast we got a few Radars in in uh
+ 
+
+ align:start position:0%
+west coast we got a few Radars in in uh
+Australia but in between this if we're
+
+ align:start position:0%
+Australia but in between this if we're
+ 
+
+ align:start position:0%
+Australia but in between this if we're
+going to speak to them every 15 minutes
+
+ align:start position:0%
+going to speak to them every 15 minutes
+ 
+
+ align:start position:0%
+going to speak to them every 15 minutes
+this is where we'd like to be and so we
+
+ align:start position:0%
+this is where we'd like to be and so we
+ 
+
+ align:start position:0%
+this is where we'd like to be and so we
+end up saying well there's the Canary
+
+ align:start position:0%
+end up saying well there's the Canary
+ 
+
+ align:start position:0%
+end up saying well there's the Canary
+Islands there's cono there's zanar
+
+ align:start position:0%
+Islands there's cono there's zanar
+ 
+
+ align:start position:0%
+Islands there's cono there's zanar
+there's m in austral and so on and
+
+ align:start position:0%
+there's m in austral and so on and
+ 
+
+ align:start position:0%
+there's m in austral and so on and
+immediately said well if we're going to
+
+ align:start position:0%
+immediately said well if we're going to
+ 
+
+ align:start position:0%
+immediately said well if we're going to
+have to talk to them we're going to have
+
+ align:start position:0%
+have to talk to them we're going to have
+ 
+
+ align:start position:0%
+have to talk to them we're going to have
+to have reception there so we're going
+
+ align:start position:0%
+to have reception there so we're going
+ 
+
+ align:start position:0%
+to have reception there so we're going
+to have to build a station at each one
+
+ align:start position:0%
+to have to build a station at each one
+ 
+
+ align:start position:0%
+to have to build a station at each one
+of those locations and we're going to
+
+ align:start position:0%
+of those locations and we're going to
+ 
+
+ align:start position:0%
+of those locations and we're going to
+have to tie them all
+
+ align:start position:0%
+have to tie them all
+ 
+
+ align:start position:0%
+have to tie them all
+together and Lord have mercy here we are
+
+ align:start position:0%
+together and Lord have mercy here we are
+ 
+
+ align:start position:0%
+together and Lord have mercy here we are
+with a whole requirement to build a
+
+ align:start position:0%
+with a whole requirement to build a
+ 
+
+ align:start position:0%
+with a whole requirement to build a
+worldwide
+
+ align:start position:0%
+worldwide
+ 
+
+ align:start position:0%
+worldwide
+Network and nobody to do it with 35
+
+ align:start position:0%
+Network and nobody to do it with 35
+ 
+
+ align:start position:0%
+Network and nobody to do it with 35
+people to do it with and so we
+
+ align:start position:0%
+people to do it with and so we
+ 
+
+ align:start position:0%
+people to do it with and so we
+immediately got a group together got
+
+ align:start position:0%
+immediately got a group together got
+ 
+
+ align:start position:0%
+immediately got a group together got
+westing house westing house Westing
+
+ align:start position:0%
+westing house westing house Westing
+ 
+
+ align:start position:0%
+westing house westing house Westing
+Electric Western elect I can't say that
+
+ align:start position:0%
+Electric Western elect I can't say that
+ 
+
+ align:start position:0%
+Electric Western elect I can't say that
+this morning Western
+
+ align:start position:0%
+this morning Western
+ 
+
+ align:start position:0%
+this morning Western
+Electric and Bell labs and bunch of
+
+ align:start position:0%
+Electric and Bell labs and bunch of
+ 
+
+ align:start position:0%
+Electric and Bell labs and bunch of
+people like that and started building
+
+ align:start position:0%
+people like that and started building
+ 
+
+ align:start position:0%
+people like that and started building
+the worldwide
+
+ align:start position:0%
+the worldwide
+ 
+
+ align:start position:0%
+the worldwide
+network uh that was a heck of a project
+
+ align:start position:0%
+network uh that was a heck of a project
+ 
+
+ align:start position:0%
+network uh that was a heck of a project
+to to to do at that point in time and
+
+ align:start position:0%
+to to to do at that point in time and
+ 
+
+ align:start position:0%
+to to to do at that point in time and
+the diplomacy just the Diplomatic
+
+ align:start position:0%
+the diplomacy just the Diplomatic
+ 
+
+ align:start position:0%
+the diplomacy just the Diplomatic
+requirements in the State uh all the
+
+ align:start position:0%
+requirements in the State uh all the
+ 
+
+ align:start position:0%
+requirements in the State uh all the
+states that we had to deal with around
+
+ align:start position:0%
+states that we had to deal with around
+ 
+
+ align:start position:0%
+states that we had to deal with around
+the world was a project in itself
+
+ align:start position:0%
+the world was a project in itself
+ 
+
+ align:start position:0%
+the world was a project in itself
+so having done that we just said how
+
+ align:start position:0%
+so having done that we just said how
+ 
+
+ align:start position:0%
+so having done that we just said how
+many times would we how many times
+
+ align:start position:0%
+many times would we how many times
+ 
+
+ align:start position:0%
+many times would we how many times
+around the earth do you think we'd like
+
+ align:start position:0%
+around the earth do you think we'd like
+ 
+
+ align:start position:0%
+around the earth do you think we'd like
+to go or need to go on the first flight
+
+ align:start position:0%
+to go or need to go on the first flight
+ 
+
+ align:start position:0%
+to go or need to go on the first flight
+and what do you think would determine
+
+ align:start position:0%
+and what do you think would determine
+ 
+
+ align:start position:0%
+and what do you think would determine
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+well in 19
+
+ align:start position:0%
+well in 19
+ 
+
+ align:start position:0%
+well in 19
+59 if you put a a spacecraft up from
+
+ align:start position:0%
+59 if you put a a spacecraft up from
+ 
+
+ align:start position:0%
+59 if you put a a spacecraft up from
+Cape canaval or from vandenbberg Air
+
+ align:start position:0%
+Cape canaval or from vandenbberg Air
+ 
+
+ align:start position:0%
+Cape canaval or from vandenbberg Air
+Force
+
+ align:start position:0%
+Force
+ 
+
+ align:start position:0%
+Force
+Base and you asked is it in orbit of the
+
+ align:start position:0%
+Base and you asked is it in orbit of the
+ 
+
+ align:start position:0%
+Base and you asked is it in orbit of the
+then flight director he would
+
+ align:start position:0%
+then flight director he would
+ 
+
+ align:start position:0%
+then flight director he would
+say I don't know I'll tell you when it
+
+ align:start position:0%
+say I don't know I'll tell you when it
+ 
+
+ align:start position:0%
+say I don't know I'll tell you when it
+comes over up comes up over Kodiak
+
+ align:start position:0%
+comes over up comes up over Kodiak
+ 
+
+ align:start position:0%
+comes over up comes up over Kodiak
+Alaska 45 minutes from
+
+ align:start position:0%
+Alaska 45 minutes from
+ 
+
+ align:start position:0%
+Alaska 45 minutes from
+now and I'm saying to myself well if
+
+ align:start position:0%
+now and I'm saying to myself well if
+ 
+
+ align:start position:0%
+now and I'm saying to myself well if
+this thing isn't in orbit and I want to
+
+ align:start position:0%
+this thing isn't in orbit and I want to
+ 
+
+ align:start position:0%
+this thing isn't in orbit and I want to
+bring it down in the water before it
+
+ align:start position:0%
+bring it down in the water before it
+ 
+
+ align:start position:0%
+bring it down in the water before it
+hits the coast of Africa I've got to
+
+ align:start position:0%
+hits the coast of Africa I've got to
+ 
+
+ align:start position:0%
+hits the coast of Africa I've got to
+know when to fire turn that spacecraft
+
+ align:start position:0%
+know when to fire turn that spacecraft
+ 
+
+ align:start position:0%
+know when to fire turn that spacecraft
+or and fire the Retro Rockets So i' have
+
+ align:start position:0%
+or and fire the Retro Rockets So i' have
+ 
+
+ align:start position:0%
+or and fire the Retro Rockets So i' have
+to know
+
+ align:start position:0%
+to know
+ 
+
+ align:start position:0%
+to know
+immediately or at least within two or
+
+ align:start position:0%
+immediately or at least within two or
+ 
+
+ align:start position:0%
+immediately or at least within two or
+three minutes to turn a spacecraft
+
+ align:start position:0%
+three minutes to turn a spacecraft
+ 
+
+ align:start position:0%
+three minutes to turn a spacecraft
+around and fire the Retro Rockets what
+
+ align:start position:0%
+around and fire the Retro Rockets what
+ 
+
+ align:start position:0%
+around and fire the Retro Rockets what
+the orbit is because if I don't I don't
+
+ align:start position:0%
+the orbit is because if I don't I don't
+ 
+
+ align:start position:0%
+the orbit is because if I don't I don't
+know where it's coming down and I don't
+
+ align:start position:0%
+know where it's coming down and I don't
+ 
+
+ align:start position:0%
+know where it's coming down and I don't
+know where to send the ships to pick
+
+ align:start position:0%
+know where to send the ships to pick
+ 
+
+ align:start position:0%
+know where to send the ships to pick
+that young astronaut up so realized that
+
+ align:start position:0%
+that young astronaut up so realized that
+ 
+
+ align:start position:0%
+that young astronaut up so realized that
+in 1959 nobody knew what a short Arc
+
+ align:start position:0%
+in 1959 nobody knew what a short Arc
+ 
+
+ align:start position:0%
+in 1959 nobody knew what a short Arc
+solution was from a cand radar in 30
+
+ align:start position:0%
+solution was from a cand radar in 30
+ 
+
+ align:start position:0%
+solution was from a cand radar in 30
+seconds of data furthermore they didn't
+
+ align:start position:0%
+seconds of data furthermore they didn't
+ 
+
+ align:start position:0%
+seconds of data furthermore they didn't
+have a computer to do it
+
+ align:start position:0%
+have a computer to do it
+ 
+
+ align:start position:0%
+have a computer to do it
+with you know we we were we were slide
+
+ align:start position:0%
+with you know we we were we were slide
+ 
+
+ align:start position:0%
+with you know we we were we were slide
+group people Marshon and computers crank
+
+ align:start position:0%
+group people Marshon and computers crank
+ 
+
+ align:start position:0%
+group people Marshon and computers crank
+computers and you're suddenly faced with
+
+ align:start position:0%
+computers and you're suddenly faced with
+ 
+
+ align:start position:0%
+computers and you're suddenly faced with
+the fact that you got to build a
+
+ align:start position:0%
+the fact that you got to build a
+ 
+
+ align:start position:0%
+the fact that you got to build a
+computer system to take radar data from
+
+ align:start position:0%
+computer system to take radar data from
+ 
+
+ align:start position:0%
+computer system to take radar data from
+Cape kaval and Bermuda do massage that
+
+ align:start position:0%
+Cape kaval and Bermuda do massage that
+ 
+
+ align:start position:0%
+Cape kaval and Bermuda do massage that
+data and within 30 seconds of a short
+
+ align:start position:0%
+data and within 30 seconds of a short
+ 
+
+ align:start position:0%
+data and within 30 seconds of a short
+Arc solution tell the people that have
+
+ align:start position:0%
+Arc solution tell the people that have
+ 
+
+ align:start position:0%
+Arc solution tell the people that have
+got to turn that spacecraft around and
+
+ align:start position:0%
+got to turn that spacecraft around and
+ 
+
+ align:start position:0%
+got to turn that spacecraft around and
+fire the Retro rockets in two
+
+ align:start position:0%
+fire the Retro rockets in two
+ 
+
+ align:start position:0%
+fire the Retro rockets in two
+minutes today that's
+
+ align:start position:0%
+minutes today that's
+ 
+
+ align:start position:0%
+minutes today that's
+sounds
+
+ align:start position:0%
+sounds
+ 
+
+ align:start position:0%
+sounds
+unbelievable when you talk about uh air
+
+ align:start position:0%
+unbelievable when you talk about uh air
+ 
+
+ align:start position:0%
+unbelievable when you talk about uh air
+to ground Communications or ground to
+
+ align:start position:0%
+to ground Communications or ground to
+ 
+
+ align:start position:0%
+to ground Communications or ground to
+ground Communications in
+
+ align:start position:0%
+ground Communications in
+ 
+
+ align:start position:0%
+ground Communications in
+Africa the best you had was 20 words of
+
+ align:start position:0%
+Africa the best you had was 20 words of
+ 
+
+ align:start position:0%
+Africa the best you had was 20 words of
+teletype per
+
+ align:start position:0%
+teletype per
+ 
+
+ align:start position:0%
+teletype per
+minute now so if you're going to know
+
+ align:start position:0%
+minute now so if you're going to know
+ 
+
+ align:start position:0%
+minute now so if you're going to know
+what's going on in the spacecraft or
+
+ align:start position:0%
+what's going on in the spacecraft or
+ 
+
+ align:start position:0%
+what's going on in the spacecraft or
+what the astronaut said as he flew over
+
+ align:start position:0%
+what the astronaut said as he flew over
+ 
+
+ align:start position:0%
+what the astronaut said as he flew over
+Kano Nigeria you were going to get it
+
+ align:start position:0%
+Kano Nigeria you were going to get it
+ 
+
+ align:start position:0%
+Kano Nigeria you were going to get it
+back in 20 words of t
+
+ align:start position:0%
+back in 20 words of t
+ 
+
+ align:start position:0%
+back in 20 words of t
+type so how do you make real time
+
+ align:start position:0%
+type so how do you make real time
+ 
+
+ align:start position:0%
+type so how do you make real time
+decisions under those circumstances what
+
+ align:start position:0%
+decisions under those circumstances what
+ 
+
+ align:start position:0%
+decisions under those circumstances what
+is a real time
+
+ align:start position:0%
+is a real time
+ 
+
+ align:start position:0%
+is a real time
+decision where are you going to make it
+
+ align:start position:0%
+decision where are you going to make it
+ 
+
+ align:start position:0%
+decision where are you going to make it
+a decision do you need some Central
+
+ align:start position:0%
+a decision do you need some Central
+ 
+
+ align:start position:0%
+a decision do you need some Central
+facility which invented mission
+
+ align:start position:0%
+facility which invented mission
+ 
+
+ align:start position:0%
+facility which invented mission
+control and suddenly then if we're going
+
+ align:start position:0%
+control and suddenly then if we're going
+ 
+
+ align:start position:0%
+control and suddenly then if we're going
+to do this job and we're going to have
+
+ align:start position:0%
+to do this job and we're going to have
+ 
+
+ align:start position:0%
+to do this job and we're going to have
+uh people looking at this data we've got
+
+ align:start position:0%
+uh people looking at this data we've got
+ 
+
+ align:start position:0%
+uh people looking at this data we've got
+to train a group of people to go to all
+
+ align:start position:0%
+to train a group of people to go to all
+ 
+
+ align:start position:0%
+to train a group of people to go to all
+these locations around the world and if
+
+ align:start position:0%
+these locations around the world and if
+ 
+
+ align:start position:0%
+these locations around the world and if
+you're going to make decisions in a
+
+ align:start position:0%
+you're going to make decisions in a
+ 
+
+ align:start position:0%
+you're going to make decisions in a
+central
+
+ align:start position:0%
+central
+ 
+
+ align:start position:0%
+central
+location then you've got to have some
+
+ align:start position:0%
+location then you've got to have some
+ 
+
+ align:start position:0%
+location then you've got to have some
+means of getting that data back to them
+
+ align:start position:0%
+means of getting that data back to them
+ 
+
+ align:start position:0%
+means of getting that data back to them
+of massaging that data letting people
+
+ align:start position:0%
+of massaging that data letting people
+ 
+
+ align:start position:0%
+of massaging that data letting people
+know outside the the limits of that
+
+ align:start position:0%
+know outside the the limits of that
+ 
+
+ align:start position:0%
+know outside the the limits of that
+control facility what is going on so
+
+ align:start position:0%
+control facility what is going on so
+ 
+
+ align:start position:0%
+control facility what is going on so
+they can interrelate with each other
+
+ align:start position:0%
+they can interrelate with each other
+ 
+
+ align:start position:0%
+they can interrelate with each other
+nobody had ever done that before and the
+
+ align:start position:0%
+nobody had ever done that before and the
+ 
+
+ align:start position:0%
+nobody had ever done that before and the
+first time we cranked ourselves up in a
+
+ align:start position:0%
+first time we cranked ourselves up in a
+ 
+
+ align:start position:0%
+first time we cranked ourselves up in a
+bunch of small kobby holds in a old
+
+ align:start position:0%
+bunch of small kobby holds in a old
+ 
+
+ align:start position:0%
+bunch of small kobby holds in a old
+flight wind tunnel building in lley
+
+ align:start position:0%
+flight wind tunnel building in lley
+ 
+
+ align:start position:0%
+flight wind tunnel building in lley
+field Virginia and started doing what we
+
+ align:start position:0%
+field Virginia and started doing what we
+ 
+
+ align:start position:0%
+field Virginia and started doing what we
+would call the initial simulations we
+
+ align:start position:0%
+would call the initial simulations we
+ 
+
+ align:start position:0%
+would call the initial simulations we
+found out we didn't even know how to
+
+ align:start position:0%
+found out we didn't even know how to
+ 
+
+ align:start position:0%
+found out we didn't even know how to
+talk with each other and everybody was
+
+ align:start position:0%
+talk with each other and everybody was
+ 
+
+ align:start position:0%
+talk with each other and everybody was
+talking at
+
+ align:start position:0%
+talking at
+ 
+
+ align:start position:0%
+talking at
+once so we had to invent a whole new
+
+ align:start position:0%
+once so we had to invent a whole new
+ 
+
+ align:start position:0%
+once so we had to invent a whole new
+language had to have negative reporting
+
+ align:start position:0%
+language had to have negative reporting
+ 
+
+ align:start position:0%
+language had to have negative reporting
+and things like that which people had
+
+ align:start position:0%
+and things like that which people had
+ 
+
+ align:start position:0%
+and things like that which people had
+never heard of
+
+ align:start position:0%
+never heard of
+ 
+
+ align:start position:0%
+never heard of
+before and rapidly then we began to
+
+ align:start position:0%
+before and rapidly then we began to
+ 
+
+ align:start position:0%
+before and rapidly then we began to
+realize we had a big task in front of us
+
+ align:start position:0%
+realize we had a big task in front of us
+ 
+
+ align:start position:0%
+realize we had a big task in front of us
+if you're going to recover this
+
+ align:start position:0%
+if you're going to recover this
+ 
+
+ align:start position:0%
+if you're going to recover this
+gentleman uh at the end of the flight
+
+ align:start position:0%
+gentleman uh at the end of the flight
+ 
+
+ align:start position:0%
+gentleman uh at the end of the flight
+that's not too hard we can send a few
+
+ align:start position:0%
+that's not too hard we can send a few
+ 
+
+ align:start position:0%
+that's not too hard we can send a few
+ships out there and we probably ought to
+
+ align:start position:0%
+ships out there and we probably ought to
+ 
+
+ align:start position:0%
+ships out there and we probably ought to
+have a helicopter there to pick them up
+
+ align:start position:0%
+have a helicopter there to pick them up
+ 
+
+ align:start position:0%
+have a helicopter there to pick them up
+and maybe we can have one of these light
+
+ align:start position:0%
+and maybe we can have one of these light
+ 
+
+ align:start position:0%
+and maybe we can have one of these light
+carriers but if the doctors are right we
+
+ align:start position:0%
+carriers but if the doctors are right we
+ 
+
+ align:start position:0%
+carriers but if the doctors are right we
+might have to come down
+
+ align:start position:0%
+might have to come down
+ 
+
+ align:start position:0%
+might have to come down
+anywhere anywhere in the 360 degrees on
+
+ align:start position:0%
+anywhere anywhere in the 360 degrees on
+ 
+
+ align:start position:0%
+anywhere anywhere in the 360 degrees on
+those three revolutions now who are we
+
+ align:start position:0%
+those three revolutions now who are we
+ 
+
+ align:start position:0%
+those three revolutions now who are we
+talking to we're talking about talking
+
+ align:start position:0%
+talking to we're talking about talking
+ 
+
+ align:start position:0%
+talking to we're talking about talking
+to the search and rescue people we're
+
+ align:start position:0%
+to the search and rescue people we're
+ 
+
+ align:start position:0%
+to the search and rescue people we're
+talking to Destroyer captains we're
+
+ align:start position:0%
+talking to Destroyer captains we're
+ 
+
+ align:start position:0%
+talking to Destroyer captains we're
+talking to people that have got to fish
+
+ align:start position:0%
+talking to people that have got to fish
+ 
+
+ align:start position:0%
+talking to people that have got to fish
+this thing out of the sea and how did
+
+ align:start position:0%
+this thing out of the sea and how did
+ 
+
+ align:start position:0%
+this thing out of the sea and how did
+they do that and how do they not get
+
+ align:start position:0%
+they do that and how do they not get
+ 
+
+ align:start position:0%
+they do that and how do they not get
+burned with the fuel that might be
+
+ align:start position:0%
+burned with the fuel that might be
+ 
+
+ align:start position:0%
+burned with the fuel that might be
+running out of the spacecraft and
+
+ align:start position:0%
+running out of the spacecraft and
+ 
+
+ align:start position:0%
+running out of the spacecraft and
+suddenly we have to train probably
+
+ align:start position:0%
+suddenly we have to train probably
+ 
+
+ align:start position:0%
+suddenly we have to train probably
+10,000
+
+ align:start position:0%
+10,000
+ 
+
+ align:start position:0%
+10,000
+people and how to recover this machine
+
+ align:start position:0%
+people and how to recover this machine
+ 
+
+ align:start position:0%
+people and how to recover this machine
+or how do you if this if the spacecraft
+
+ align:start position:0%
+or how do you if this if the spacecraft
+ 
+
+ align:start position:0%
+or how do you if this if the spacecraft
+is sitting in the water we've got to
+
+ align:start position:0%
+is sitting in the water we've got to
+ 
+
+ align:start position:0%
+is sitting in the water we've got to
+train several hundred frog men how to
+
+ align:start position:0%
+train several hundred frog men how to
+ 
+
+ align:start position:0%
+train several hundred frog men how to
+jump out of an airplane with tools to
+
+ align:start position:0%
+jump out of an airplane with tools to
+ 
+
+ align:start position:0%
+jump out of an airplane with tools to
+get to the
+
+ align:start position:0%
+get to the
+ 
+
+ align:start position:0%
+get to the
+astronaut so it it was a tremendous task
+
+ align:start position:0%
+astronaut so it it was a tremendous task
+ 
+
+ align:start position:0%
+astronaut so it it was a tremendous task
+for a group of people who had never done
+
+ align:start position:0%
+for a group of people who had never done
+ 
+
+ align:start position:0%
+for a group of people who had never done
+much but do wind tunnel tests or flight
+
+ align:start position:0%
+much but do wind tunnel tests or flight
+ 
+
+ align:start position:0%
+much but do wind tunnel tests or flight
+tests at L
+
+ align:start position:0%
+tests at L
+ 
+
+ align:start position:0%
+tests at L
+field so the early days we had to to
+
+ align:start position:0%
+field so the early days we had to to
+ 
+
+ align:start position:0%
+field so the early days we had to to
+come up with orbit
+
+ align:start position:0%
+come up with orbit
+ 
+
+ align:start position:0%
+come up with orbit
+determination how to look at the
+
+ align:start position:0%
+determination how to look at the
+ 
+
+ align:start position:0%
+determination how to look at the
+astronaut's Health how do we get
+
+ align:start position:0%
+astronaut's Health how do we get
+ 
+
+ align:start position:0%
+astronaut's Health how do we get
+something down that we can look at can
+
+ align:start position:0%
+something down that we can look at can
+ 
+
+ align:start position:0%
+something down that we can look at can
+we get an e G down can we get his his
+
+ align:start position:0%
+we get an e G down can we get his his
+ 
+
+ align:start position:0%
+we get an e G down can we get his his
+breath rate down to the each one of
+
+ align:start position:0%
+breath rate down to the each one of
+ 
+
+ align:start position:0%
+breath rate down to the each one of
+these stations so we know what the man's
+
+ align:start position:0%
+these stations so we know what the man's
+ 
+
+ align:start position:0%
+these stations so we know what the man's
+health is an interesting story what we
+
+ align:start position:0%
+health is an interesting story what we
+ 
+
+ align:start position:0%
+health is an interesting story what we
+did eventually build a a a simulator to
+
+ align:start position:0%
+did eventually build a a a simulator to
+ 
+
+ align:start position:0%
+did eventually build a a a simulator to
+train the
+
+ align:start position:0%
+train the
+ 
+
+ align:start position:0%
+train the
+astronauts and we had no way of getting
+
+ align:start position:0%
+astronauts and we had no way of getting
+ 
+
+ align:start position:0%
+astronauts and we had no way of getting
+data to each one of these sites around
+
+ align:start position:0%
+data to each one of these sites around
+ 
+
+ align:start position:0%
+data to each one of these sites around
+the world that would allow us to run a
+
+ align:start position:0%
+the world that would allow us to run a
+ 
+
+ align:start position:0%
+the world that would allow us to run a
+full-fledged worldwide simulation in
+
+ align:start position:0%
+full-fledged worldwide simulation in
+ 
+
+ align:start position:0%
+full-fledged worldwide simulation in
+real time so we would put it on tape cut
+
+ align:start position:0%
+real time so we would put it on tape cut
+ 
+
+ align:start position:0%
+real time so we would put it on tape cut
+it up in
+
+ align:start position:0%
+it up in
+ 
+
+ align:start position:0%
+it up in
+sections send out a
+
+ align:start position:0%
+sections send out a
+ 
+
+ align:start position:0%
+sections send out a
+script of what the astronaut was going
+
+ align:start position:0%
+script of what the astronaut was going
+ 
+
+ align:start position:0%
+script of what the astronaut was going
+to say and do and play this six or eight
+
+ align:start position:0%
+to say and do and play this six or eight
+ 
+
+ align:start position:0%
+to say and do and play this six or eight
+minutes of a tape as that's what they
+
+ align:start position:0%
+minutes of a tape as that's what they
+ 
+
+ align:start position:0%
+minutes of a tape as that's what they
+would see as the spacecraft appeared
+
+ align:start position:0%
+would see as the spacecraft appeared
+ 
+
+ align:start position:0%
+would see as the spacecraft appeared
+over their station and when we said well
+
+ align:start position:0%
+over their station and when we said well
+ 
+
+ align:start position:0%
+over their station and when we said well
+we got to train a bunch of
+
+ align:start position:0%
+we got to train a bunch of
+ 
+
+ align:start position:0%
+we got to train a bunch of
+doctors an interesting story was we went
+
+ align:start position:0%
+doctors an interesting story was we went
+ 
+
+ align:start position:0%
+doctors an interesting story was we went
+down to the Veterans Administration in
+
+ align:start position:0%
+down to the Veterans Administration in
+ 
+
+ align:start position:0%
+down to the Veterans Administration in
+uh Houston and said well we we'd like to
+
+ align:start position:0%
+uh Houston and said well we we'd like to
+ 
+
+ align:start position:0%
+uh Houston and said well we we'd like to
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+put some instruments that we were
+
+ align:start position:0%
+put some instruments that we were
+ 
+
+ align:start position:0%
+put some instruments that we were
+developing on people that are sick here
+
+ align:start position:0%
+developing on people that are sick here
+ 
+
+ align:start position:0%
+developing on people that are sick here
+and so as they come in various types of
+
+ align:start position:0%
+and so as they come in various types of
+ 
+
+ align:start position:0%
+and so as they come in various types of
+diseases and fortunately one day we had
+
+ align:start position:0%
+diseases and fortunately one day we had
+ 
+
+ align:start position:0%
+diseases and fortunately one day we had
+a guy instrumented and he had a heart
+
+ align:start position:0%
+a guy instrumented and he had a heart
+ 
+
+ align:start position:0%
+a guy instrumented and he had a heart
+attack so we were able to record all
+
+ align:start position:0%
+attack so we were able to record all
+ 
+
+ align:start position:0%
+attack so we were able to record all
+these things that were going on in this
+
+ align:start position:0%
+these things that were going on in this
+ 
+
+ align:start position:0%
+these things that were going on in this
+gentleman his temperature is his EKG his
+
+ align:start position:0%
+gentleman his temperature is his EKG his
+ 
+
+ align:start position:0%
+gentleman his temperature is his EKG his
+breath rate and what his blood pressure
+
+ align:start position:0%
+breath rate and what his blood pressure
+ 
+
+ align:start position:0%
+breath rate and what his blood pressure
+was and so
+
+ align:start position:0%
+was and so
+ 
+
+ align:start position:0%
+was and so
+on and put all that on the
+
+ align:start position:0%
+on and put all that on the
+ 
+
+ align:start position:0%
+on and put all that on the
+tape sent that out to the remote sites
+
+ align:start position:0%
+tape sent that out to the remote sites
+ 
+
+ align:start position:0%
+tape sent that out to the remote sites
+and then had each of the sites as this
+
+ align:start position:0%
+and then had each of the sites as this
+ 
+
+ align:start position:0%
+and then had each of the sites as this
+occurred have the doctors
+
+ align:start position:0%
+occurred have the doctors
+ 
+
+ align:start position:0%
+occurred have the doctors
+diagnose what was wrong with the
+
+ align:start position:0%
+diagnose what was wrong with the
+ 
+
+ align:start position:0%
+diagnose what was wrong with the
+astronaut I don't believe in any one of
+
+ align:start position:0%
+astronaut I don't believe in any one of
+ 
+
+ align:start position:0%
+astronaut I don't believe in any one of
+the 17 stations we had anybody diagnosed
+
+ align:start position:0%
+the 17 stations we had anybody diagnosed
+ 
+
+ align:start position:0%
+the 17 stations we had anybody diagnosed
+it as a heart
+
+ align:start position:0%
+it as a heart
+ 
+
+ align:start position:0%
+it as a heart
+attack they all said he had appendicitis
+
+ align:start position:0%
+attack they all said he had appendicitis
+ 
+
+ align:start position:0%
+attack they all said he had appendicitis
+or he was having
+
+ align:start position:0%
+or he was having
+ 
+
+ align:start position:0%
+or he was having
+a some kind of shock take place to him
+
+ align:start position:0%
+a some kind of shock take place to him
+ 
+
+ align:start position:0%
+a some kind of shock take place to him
+because he was frightened to death or
+
+ align:start position:0%
+because he was frightened to death or
+ 
+
+ align:start position:0%
+because he was frightened to death or
+any anything but a heart attack so that
+
+ align:start position:0%
+any anything but a heart attack so that
+ 
+
+ align:start position:0%
+any anything but a heart attack so that
+was sort of classical of the things we
+
+ align:start position:0%
+was sort of classical of the things we
+ 
+
+ align:start position:0%
+was sort of classical of the things we
+did and improvised in order
+
+ align:start position:0%
+did and improvised in order
+ 
+
+ align:start position:0%
+did and improvised in order
+to get ourselves capable of running a
+
+ align:start position:0%
+to get ourselves capable of running a
+ 
+
+ align:start position:0%
+to get ourselves capable of running a
+worldwide operation which allowed us to
+
+ align:start position:0%
+worldwide operation which allowed us to
+ 
+
+ align:start position:0%
+worldwide operation which allowed us to
+make decisions in real time now the
+
+ align:start position:0%
+make decisions in real time now the
+ 
+
+ align:start position:0%
+make decisions in real time now the
+other thing that we invented at that
+
+ align:start position:0%
+other thing that we invented at that
+ 
+
+ align:start position:0%
+other thing that we invented at that
+time I say invented it just came about
+
+ align:start position:0%
+time I say invented it just came about
+ 
+
+ align:start position:0%
+time I say invented it just came about
+by Evolution was the book called Mission
+
+ align:start position:0%
+by Evolution was the book called Mission
+ 
+
+ align:start position:0%
+by Evolution was the book called Mission
+rules and that was probably the smartest
+
+ align:start position:0%
+rules and that was probably the smartest
+ 
+
+ align:start position:0%
+rules and that was probably the smartest
+thing we ever did as we began to look at
+
+ align:start position:0%
+thing we ever did as we began to look at
+ 
+
+ align:start position:0%
+thing we ever did as we began to look at
+the spacecraft system
+
+ align:start position:0%
+the spacecraft system
+ 
+
+ align:start position:0%
+the spacecraft system
+we started asking questions well if this
+
+ align:start position:0%
+we started asking questions well if this
+ 
+
+ align:start position:0%
+we started asking questions well if this
+system is
+
+ align:start position:0%
+system is
+ 
+
+ align:start position:0%
+system is
+failing what are the measurements that
+
+ align:start position:0%
+failing what are the measurements that
+ 
+
+ align:start position:0%
+failing what are the measurements that
+we're going to have there and and if it
+
+ align:start position:0%
+we're going to have there and and if it
+ 
+
+ align:start position:0%
+we're going to have there and and if it
+is failing what and it isn't operating
+
+ align:start position:0%
+is failing what and it isn't operating
+ 
+
+ align:start position:0%
+is failing what and it isn't operating
+at the right temperature at the right
+
+ align:start position:0%
+at the right temperature at the right
+ 
+
+ align:start position:0%
+at the right temperature at the right
+pressure and it's off nominal what will
+
+ align:start position:0%
+pressure and it's off nominal what will
+ 
+
+ align:start position:0%
+pressure and it's off nominal what will
+the system do and how do we measure that
+
+ align:start position:0%
+the system do and how do we measure that
+ 
+
+ align:start position:0%
+the system do and how do we measure that
+on the ground how we detect it where is
+
+ align:start position:0%
+on the ground how we detect it where is
+ 
+
+ align:start position:0%
+on the ground how we detect it where is
+the instrument located on the system
+
+ align:start position:0%
+the instrument located on the system
+ 
+
+ align:start position:0%
+the instrument located on the system
+because it might be affected by the
+
+ align:start position:0%
+because it might be affected by the
+ 
+
+ align:start position:0%
+because it might be affected by the
+position it's located in the spacecraft
+
+ align:start position:0%
+position it's located in the spacecraft
+ 
+
+ align:start position:0%
+position it's located in the spacecraft
+it might be hot might be cold might be
+
+ align:start position:0%
+it might be hot might be cold might be
+ 
+
+ align:start position:0%
+it might be hot might be cold might be
+suffering different kinds of pressures
+
+ align:start position:0%
+suffering different kinds of pressures
+ 
+
+ align:start position:0%
+suffering different kinds of pressures
+than it was measured on the ground and
+
+ align:start position:0%
+than it was measured on the ground and
+ 
+
+ align:start position:0%
+than it was measured on the ground and
+as we began to ask those questions of
+
+ align:start position:0%
+as we began to ask those questions of
+ 
+
+ align:start position:0%
+as we began to ask those questions of
+the systems
+
+ align:start position:0%
+the systems
+ 
+
+ align:start position:0%
+the systems
+engineer the system engineer not systems
+
+ align:start position:0%
+engineer the system engineer not systems
+ 
+
+ align:start position:0%
+engineer the system engineer not systems
+Engineers because I don't think we had
+
+ align:start position:0%
+Engineers because I don't think we had
+ 
+
+ align:start position:0%
+Engineers because I don't think we had
+any at the
+
+ align:start position:0%
+any at the
+ 
+
+ align:start position:0%
+any at the
+time and you began and they would say
+
+ align:start position:0%
+time and you began and they would say
+ 
+
+ align:start position:0%
+time and you began and they would say
+why the hell do you want to know that
+
+ align:start position:0%
+why the hell do you want to know that
+ 
+
+ align:start position:0%
+why the hell do you want to know that
+the system is either working or it ain't
+
+ align:start position:0%
+the system is either working or it ain't
+ 
+
+ align:start position:0%
+the system is either working or it ain't
+working and we said yes that's a good
+
+ align:start position:0%
+working and we said yes that's a good
+ 
+
+ align:start position:0%
+working and we said yes that's a good
+answer except that now we've got this
+
+ align:start position:0%
+answer except that now we've got this
+ 
+
+ align:start position:0%
+answer except that now we've got this
+system in space and if we want to
+
+ align:start position:0%
+system in space and if we want to
+ 
+
+ align:start position:0%
+system in space and if we want to
+continue this flight and not have a
+
+ align:start position:0%
+continue this flight and not have a
+ 
+
+ align:start position:0%
+continue this flight and not have a
+contingency operation we'd like to know
+
+ align:start position:0%
+contingency operation we'd like to know
+ 
+
+ align:start position:0%
+contingency operation we'd like to know
+how how long the system is going to last
+
+ align:start position:0%
+how how long the system is going to last
+ 
+
+ align:start position:0%
+how how long the system is going to last
+if it isn't operating under normal
+
+ align:start position:0%
+if it isn't operating under normal
+ 
+
+ align:start position:0%
+if it isn't operating under normal
+conditions so that prompted us then to
+
+ align:start position:0%
+conditions so that prompted us then to
+ 
+
+ align:start position:0%
+conditions so that prompted us then to
+start thinking about how the system
+
+ align:start position:0%
+start thinking about how the system
+ 
+
+ align:start position:0%
+start thinking about how the system
+failed and what we were going to do
+
+ align:start position:0%
+failed and what we were going to do
+ 
+
+ align:start position:0%
+failed and what we were going to do
+about it if the if the thermal system
+
+ align:start position:0%
+about it if the if the thermal system
+ 
+
+ align:start position:0%
+about it if the if the thermal system
+that kept the astronaut from getting hot
+
+ align:start position:0%
+that kept the astronaut from getting hot
+ 
+
+ align:start position:0%
+that kept the astronaut from getting hot
+or getting too cold wasn't functioning
+
+ align:start position:0%
+or getting too cold wasn't functioning
+ 
+
+ align:start position:0%
+or getting too cold wasn't functioning
+properly what could we do about it how
+
+ align:start position:0%
+properly what could we do about it how
+ 
+
+ align:start position:0%
+properly what could we do about it how
+long could he stand being at a
+
+ align:start position:0%
+long could he stand being at a
+ 
+
+ align:start position:0%
+long could he stand being at a
+temperature of 85 degrees inside his
+
+ align:start position:0%
+temperature of 85 degrees inside his
+ 
+
+ align:start position:0%
+temperature of 85 degrees inside his
+space suit and and then that said well
+
+ align:start position:0%
+space suit and and then that said well
+ 
+
+ align:start position:0%
+space suit and and then that said well
+if it stays there and we can only go X
+
+ align:start position:0%
+if it stays there and we can only go X
+ 
+
+ align:start position:0%
+if it stays there and we can only go X
+number of minutes what are we going to
+
+ align:start position:0%
+number of minutes what are we going to
+ 
+
+ align:start position:0%
+number of minutes what are we going to
+do about it what is the the rule of the
+
+ align:start position:0%
+do about it what is the the rule of the
+ 
+
+ align:start position:0%
+do about it what is the the rule of the
+game that says we should re-enter or not
+
+ align:start position:0%
+game that says we should re-enter or not
+ 
+
+ align:start position:0%
+game that says we should re-enter or not
+reenter or go to the next primary
+
+ align:start position:0%
+reenter or go to the next primary
+ 
+
+ align:start position:0%
+reenter or go to the next primary
+recovery area Etc and it allowed us then
+
+ align:start position:0%
+recovery area Etc and it allowed us then
+ 
+
+ align:start position:0%
+recovery area Etc and it allowed us then
+to write down for almost every for every
+
+ align:start position:0%
+to write down for almost every for every
+ 
+
+ align:start position:0%
+to write down for almost every for every
+system and the man
+
+ align:start position:0%
+system and the man
+ 
+
+ align:start position:0%
+system and the man
+what we would do under certain
+
+ align:start position:0%
+what we would do under certain
+ 
+
+ align:start position:0%
+what we would do under certain
+circumstances call those a set of
+
+ align:start position:0%
+circumstances call those a set of
+ 
+
+ align:start position:0%
+circumstances call those a set of
+mission rules and that prompted us to
+
+ align:start position:0%
+mission rules and that prompted us to
+ 
+
+ align:start position:0%
+mission rules and that prompted us to
+develop a bunch of
+
+ align:start position:0%
+develop a bunch of
+ 
+
+ align:start position:0%
+develop a bunch of
+malfunction uh criteria what what
+
+ align:start position:0%
+malfunction uh criteria what what
+ 
+
+ align:start position:0%
+malfunction uh criteria what what
+malfunction procedures do you are you
+
+ align:start position:0%
+malfunction procedures do you are you
+ 
+
+ align:start position:0%
+malfunction procedures do you are you
+going to go through and then that
+
+ align:start position:0%
+going to go through and then that
+ 
+
+ align:start position:0%
+going to go through and then that
+prompted us to ask the contractor and
+
+ align:start position:0%
+prompted us to ask the contractor and
+ 
+
+ align:start position:0%
+prompted us to ask the contractor and
+the manufacturer of the systems and that
+
+ align:start position:0%
+the manufacturer of the systems and that
+ 
+
+ align:start position:0%
+the manufacturer of the systems and that
+developed a whole new set of schematics
+
+ align:start position:0%
+developed a whole new set of schematics
+ 
+
+ align:start position:0%
+developed a whole new set of schematics
+that they hadn't been used to cost us a
+
+ align:start position:0%
+that they hadn't been used to cost us a
+ 
+
+ align:start position:0%
+that they hadn't been used to cost us a
+lot of money to do that they didn't want
+
+ align:start position:0%
+lot of money to do that they didn't want
+ 
+
+ align:start position:0%
+lot of money to do that they didn't want
+to do it they didn't know why we wanted
+
+ align:start position:0%
+to do it they didn't know why we wanted
+ 
+
+ align:start position:0%
+to do it they didn't know why we wanted
+to do it but as they began to see the
+
+ align:start position:0%
+to do it but as they began to see the
+ 
+
+ align:start position:0%
+to do it but as they began to see the
+mission rules and we got those out in
+
+ align:start position:0%
+mission rules and we got those out in
+ 
+
+ align:start position:0%
+mission rules and we got those out in
+front of them and said we're going to do
+
+ align:start position:0%
+front of them and said we're going to do
+ 
+
+ align:start position:0%
+front of them and said we're going to do
+this with your spacecraft and your
+
+ align:start position:0%
+this with your spacecraft and your
+ 
+
+ align:start position:0%
+this with your spacecraft and your
+system then they began to realize they
+
+ align:start position:0%
+system then they began to realize they
+ 
+
+ align:start position:0%
+system then they began to realize they
+better start thinking about those things
+
+ align:start position:0%
+better start thinking about those things
+ 
+
+ align:start position:0%
+better start thinking about those things
+and that's what brought in my mind a
+
+ align:start position:0%
+and that's what brought in my mind a
+ 
+
+ align:start position:0%
+and that's what brought in my mind a
+group of people together in systems
+
+ align:start position:0%
+group of people together in systems
+ 
+
+ align:start position:0%
+group of people together in systems
+engineer because you began to find out
+
+ align:start position:0%
+engineer because you began to find out
+ 
+
+ align:start position:0%
+engineer because you began to find out
+how the systems reacted with each
+
+ align:start position:0%
+how the systems reacted with each
+ 
+
+ align:start position:0%
+how the systems reacted with each
+other and that was a question that most
+
+ align:start position:0%
+other and that was a question that most
+ 
+
+ align:start position:0%
+other and that was a question that most
+Engineers didn't think about if if the
+
+ align:start position:0%
+Engineers didn't think about if if the
+ 
+
+ align:start position:0%
+Engineers didn't think about if if the
+ther control system is not functioning
+
+ align:start position:0%
+ther control system is not functioning
+ 
+
+ align:start position:0%
+ther control system is not functioning
+properly what does it do to the reaction
+
+ align:start position:0%
+properly what does it do to the reaction
+ 
+
+ align:start position:0%
+properly what does it do to the reaction
+control system or as we had on one of
+
+ align:start position:0%
+control system or as we had on one of
+ 
+
+ align:start position:0%
+control system or as we had on one of
+our first orbital flights the the seats
+
+ align:start position:0%
+our first orbital flights the the seats
+ 
+
+ align:start position:0%
+our first orbital flights the the seats
+on the small thrusters that were using
+
+ align:start position:0%
+on the small thrusters that were using
+ 
+
+ align:start position:0%
+on the small thrusters that were using
+for attitude control were not seating
+
+ align:start position:0%
+for attitude control were not seating
+ 
+
+ align:start position:0%
+for attitude control were not seating
+properly and the experts said it's
+
+ align:start position:0%
+properly and the experts said it's
+ 
+
+ align:start position:0%
+properly and the experts said it's
+freezing it's getting slush in the
+
+ align:start position:0%
+freezing it's getting slush in the
+ 
+
+ align:start position:0%
+freezing it's getting slush in the
+system and it's causing the valves to
+
+ align:start position:0%
+system and it's causing the valves to
+ 
+
+ align:start position:0%
+system and it's causing the valves to
+stay open and they're not getting a
+
+ align:start position:0%
+stay open and they're not getting a
+ 
+
+ align:start position:0%
+stay open and they're not getting a
+proper fluid to it so we put a thermost
+
+ align:start position:0%
+proper fluid to it so we put a thermost
+ 
+
+ align:start position:0%
+proper fluid to it so we put a thermost
+on the next spacecraft and it was
+
+ align:start position:0%
+on the next spacecraft and it was
+ 
+
+ align:start position:0%
+on the next spacecraft and it was
+freezing it was getting hot because the
+
+ align:start position:0%
+freezing it was getting hot because the
+ 
+
+ align:start position:0%
+freezing it was getting hot because the
+feedback from the Thruster was getting
+
+ align:start position:0%
+feedback from the Thruster was getting
+ 
+
+ align:start position:0%
+feedback from the Thruster was getting
+on the lines and causing the seats to
+
+ align:start position:0%
+on the lines and causing the seats to
+ 
+
+ align:start position:0%
+on the lines and causing the seats to
+war and it was sitting there dribbling
+
+ align:start position:0%
+war and it was sitting there dribbling
+ 
+
+ align:start position:0%
+war and it was sitting there dribbling
+out and causing the attitude to be
+
+ align:start position:0%
+out and causing the attitude to be
+ 
+
+ align:start position:0%
+out and causing the attitude to be
+sloppy and jump around and as a matter
+
+ align:start position:0%
+sloppy and jump around and as a matter
+ 
+
+ align:start position:0%
+sloppy and jump around and as a matter
+of fact on one flight we had to reenter
+
+ align:start position:0%
+of fact on one flight we had to reenter
+ 
+
+ align:start position:0%
+of fact on one flight we had to reenter
+early with the first chimpanzee flight
+
+ align:start position:0%
+early with the first chimpanzee flight
+ 
+
+ align:start position:0%
+early with the first chimpanzee flight
+because the machine was running out of
+
+ align:start position:0%
+because the machine was running out of
+ 
+
+ align:start position:0%
+because the machine was running out of
+propellant so it began to have everybody
+
+ align:start position:0%
+propellant so it began to have everybody
+ 
+
+ align:start position:0%
+propellant so it began to have everybody
+start thinking about how does my system
+
+ align:start position:0%
+start thinking about how does my system
+ 
+
+ align:start position:0%
+start thinking about how does my system
+fit with everybody else's system how
+
+ align:start position:0%
+fit with everybody else's system how
+ 
+
+ align:start position:0%
+fit with everybody else's system how
+does that fit with the game plan that
+
+ align:start position:0%
+does that fit with the game plan that
+ 
+
+ align:start position:0%
+does that fit with the game plan that
+we're trying to come up
+
+ align:start position:0%
+we're trying to come up
+ 
+
+ align:start position:0%
+we're trying to come up
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+and at the same
+
+ align:start position:0%
+and at the same
+ 
+
+ align:start position:0%
+and at the same
+time uh the organization then was able
+
+ align:start position:0%
+time uh the organization then was able
+ 
+
+ align:start position:0%
+time uh the organization then was able
+to look at all of these things that we
+
+ align:start position:0%
+to look at all of these things that we
+ 
+
+ align:start position:0%
+to look at all of these things that we
+said we were going to do and became a
+
+ align:start position:0%
+said we were going to do and became a
+ 
+
+ align:start position:0%
+said we were going to do and became a
+heck of a management tool I remember
+
+ align:start position:0%
+heck of a management tool I remember
+ 
+
+ align:start position:0%
+heck of a management tool I remember
+James web used I used to come down
+
+ align:start position:0%
+James web used I used to come down
+ 
+
+ align:start position:0%
+James web used I used to come down
+administrator mass at the time and I
+
+ align:start position:0%
+administrator mass at the time and I
+ 
+
+ align:start position:0%
+administrator mass at the time and I
+would show him in the control center how
+
+ align:start position:0%
+would show him in the control center how
+ 
+
+ align:start position:0%
+would show him in the control center how
+we ran an operation and how we made
+
+ align:start position:0%
+we ran an operation and how we made
+ 
+
+ align:start position:0%
+we ran an operation and how we made
+decisions and he was absolutely
+
+ align:start position:0%
+decisions and he was absolutely
+ 
+
+ align:start position:0%
+decisions and he was absolutely
+livid about that because he said that's
+
+ align:start position:0%
+livid about that because he said that's
+ 
+
+ align:start position:0%
+livid about that because he said that's
+what I want in
+
+ align:start position:0%
+what I want in
+ 
+
+ align:start position:0%
+what I want in
+Washington I want to be able to have
+
+ align:start position:0%
+Washington I want to be able to have
+ 
+
+ align:start position:0%
+Washington I want to be able to have
+those kinds of things put in front of me
+
+ align:start position:0%
+those kinds of things put in front of me
+ 
+
+ align:start position:0%
+those kinds of things put in front of me
+so I got all these things so I can make
+
+ align:start position:0%
+so I got all these things so I can make
+ 
+
+ align:start position:0%
+so I got all these things so I can make
+a decision I need you in Wasing I want
+
+ align:start position:0%
+a decision I need you in Wasing I want
+ 
+
+ align:start position:0%
+a decision I need you in Wasing I want
+you to come up here and fix tell me how
+
+ align:start position:0%
+you to come up here and fix tell me how
+ 
+
+ align:start position:0%
+you to come up here and fix tell me how
+to build a system like that to do
+
+ align:start position:0%
+to build a system like that to do
+ 
+
+ align:start position:0%
+to build a system like that to do
+management I must say that I've never
+
+ align:start position:0%
+management I must say that I've never
+ 
+
+ align:start position:0%
+management I must say that I've never
+been able to do that but
+
+ align:start position:0%
+been able to do that but
+ 
+
+ align:start position:0%
+been able to do that but
+was very emphatic about wanting to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh jump to the conclusion of
+
+ align:start position:0%
+that uh jump to the conclusion of
+ 
+
+ align:start position:0%
+that uh jump to the conclusion of
+mercury I think we learned an awful lot
+
+ align:start position:0%
+mercury I think we learned an awful lot
+ 
+
+ align:start position:0%
+mercury I think we learned an awful lot
+from that program we learned that man
+
+ align:start position:0%
+from that program we learned that man
+ 
+
+ align:start position:0%
+from that program we learned that man
+could do a a job he could do it just as
+
+ align:start position:0%
+could do a a job he could do it just as
+ 
+
+ align:start position:0%
+could do a a job he could do it just as
+well at zero gravity and particularly in
+
+ align:start position:0%
+well at zero gravity and particularly in
+ 
+
+ align:start position:0%
+well at zero gravity and particularly in
+Mercury where he couldn't move around he
+
+ align:start position:0%
+Mercury where he couldn't move around he
+ 
+
+ align:start position:0%
+Mercury where he couldn't move around he
+didn't get sick fortunately as he did
+
+ align:start position:0%
+didn't get sick fortunately as he did
+ 
+
+ align:start position:0%
+didn't get sick fortunately as he did
+eventually in some of our spacecraft but
+
+ align:start position:0%
+eventually in some of our spacecraft but
+ 
+
+ align:start position:0%
+eventually in some of our spacecraft but
+certainly man could do the job in space
+
+ align:start position:0%
+certainly man could do the job in space
+ 
+
+ align:start position:0%
+certainly man could do the job in space
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+up there as you could in a fighter
+
+ align:start position:0%
+up there as you could in a fighter
+ 
+
+ align:start position:0%
+up there as you could in a fighter
+airplane on the
+
+ align:start position:0%
+airplane on the
+ 
+
+ align:start position:0%
+airplane on the
+earth uh but it was Child's
+
+ align:start position:0%
+earth uh but it was Child's
+ 
+
+ align:start position:0%
+earth uh but it was Child's
+Play Mercury was Child's Play we put it
+
+ align:start position:0%
+Play Mercury was Child's Play we put it
+ 
+
+ align:start position:0%
+Play Mercury was Child's Play we put it
+up there we fired the Retro rockets and
+
+ align:start position:0%
+up there we fired the Retro rockets and
+ 
+
+ align:start position:0%
+up there we fired the Retro rockets and
+it landed and we picked them
+
+ align:start position:0%
+it landed and we picked them
+ 
+
+ align:start position:0%
+it landed and we picked them
+up a hell of a job at that time but it
+
+ align:start position:0%
+up a hell of a job at that time but it
+ 
+
+ align:start position:0%
+up a hell of a job at that time but it
+was Child's Play and
+
+ align:start position:0%
+was Child's Play and
+ 
+
+ align:start position:0%
+was Child's Play and
+so Mr Kennedy and his great
+
+ align:start position:0%
+so Mr Kennedy and his great
+ 
+
+ align:start position:0%
+so Mr Kennedy and his great
+wisdom in April of 1962
+
+ align:start position:0%
+wisdom in April of 1962
+ 
+
+ align:start position:0%
+wisdom in April of 1962
+uh excuse me 61 when he saw the reaction
+
+ align:start position:0%
+uh excuse me 61 when he saw the reaction
+ 
+
+ align:start position:0%
+uh excuse me 61 when he saw the reaction
+of the world to Alan Shephard's First
+
+ align:start position:0%
+of the world to Alan Shephard's First
+ 
+
+ align:start position:0%
+of the world to Alan Shephard's First
+Flight asked NASA well what what can we
+
+ align:start position:0%
+Flight asked NASA well what what can we
+ 
+
+ align:start position:0%
+Flight asked NASA well what what can we
+do to Ace the
+
+ align:start position:0%
+do to Ace the
+ 
+
+ align:start position:0%
+do to Ace the
+Russians and NASA in its great wisdom
+
+ align:start position:0%
+Russians and NASA in its great wisdom
+ 
+
+ align:start position:0%
+Russians and NASA in its great wisdom
+said well probably in about 10 years we
+
+ align:start position:0%
+said well probably in about 10 years we
+ 
+
+ align:start position:0%
+said well probably in about 10 years we
+can go around the
+
+ align:start position:0%
+can go around the
+ 
+
+ align:start position:0%
+can go around the
+Moon George low and others in Washington
+
+ align:start position:0%
+Moon George low and others in Washington
+ 
+
+ align:start position:0%
+Moon George low and others in Washington
+had been doing some work on on lunar
+
+ align:start position:0%
+had been doing some work on on lunar
+ 
+
+ align:start position:0%
+had been doing some work on on lunar
+spacecraft
+
+ align:start position:0%
+spacecraft
+ 
+
+ align:start position:0%
+spacecraft
+and in the great wisdom of whoever made
+
+ align:start position:0%
+and in the great wisdom of whoever made
+ 
+
+ align:start position:0%
+and in the great wisdom of whoever made
+such a decision the president asked why
+
+ align:start position:0%
+such a decision the president asked why
+ 
+
+ align:start position:0%
+such a decision the president asked why
+don't why can't you land on the
+
+ align:start position:0%
+don't why can't you land on the
+ 
+
+ align:start position:0%
+don't why can't you land on the
+Move now I want you to know that that
+
+ align:start position:0%
+Move now I want you to know that that
+ 
+
+ align:start position:0%
+Move now I want you to know that that
+was 1961 and Chris Kraft did not know
+
+ align:start position:0%
+was 1961 and Chris Kraft did not know
+ 
+
+ align:start position:0%
+was 1961 and Chris Kraft did not know
+how to
+
+ align:start position:0%
+how to
+ 
+
+ align:start position:0%
+how to
+determine orbital mechanics from 30
+
+ align:start position:0%
+determine orbital mechanics from 30
+ 
+
+ align:start position:0%
+determine orbital mechanics from 30
+seconds of radar at C
+
+ align:start position:0%
+seconds of radar at C
+ 
+
+ align:start position:0%
+seconds of radar at C
+canaval and this man in 1961 says we're
+
+ align:start position:0%
+canaval and this man in 1961 says we're
+ 
+
+ align:start position:0%
+canaval and this man in 1961 says we're
+going to the Moon in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decade and I thought he was a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+daed I must say I thought he was a
+
+ align:start position:0%
+daed I must say I thought he was a
+ 
+
+ align:start position:0%
+daed I must say I thought he was a
+little D the second
+
+ align:start position:0%
+little D the second
+ 
+
+ align:start position:0%
+little D the second
+day
+
+ align:start position:0%
+day
+ 
+
+ align:start position:0%
+day
+I uh thought a little bit better of it
+
+ align:start position:0%
+I uh thought a little bit better of it
+ 
+
+ align:start position:0%
+I uh thought a little bit better of it
+and then about three months later when
+
+ align:start position:0%
+and then about three months later when
+ 
+
+ align:start position:0%
+and then about three months later when
+he came to make that famous
+
+ align:start position:0%
+he came to make that famous
+ 
+
+ align:start position:0%
+he came to make that famous
+speech in
+
+ align:start position:0%
+speech in
+ 
+
+ align:start position:0%
+speech in
+uh uh rice Stadium
+
+ align:start position:0%
+uh uh rice Stadium
+ 
+
+ align:start position:0%
+uh uh rice Stadium
+I was called back from Cape canaval to
+
+ align:start position:0%
+I was called back from Cape canaval to
+ 
+
+ align:start position:0%
+I was called back from Cape canaval to
+tell him how we were going to go to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moon and I'm telling you I did not know
+
+ align:start position:0%
+moon and I'm telling you I did not know
+ 
+
+ align:start position:0%
+moon and I'm telling you I did not know
+a damn thing about how to go to the bo
+
+ align:start position:0%
+a damn thing about how to go to the bo
+ 
+
+ align:start position:0%
+a damn thing about how to go to the bo
+you know if you had
+
+ align:start position:0%
+you know if you had
+ 
+
+ align:start position:0%
+you know if you had
+said free return trajectory to me God
+
+ align:start position:0%
+said free return trajectory to me God
+ 
+
+ align:start position:0%
+said free return trajectory to me God
+I'd have thought it was a pass to the
+
+ align:start position:0%
+I'd have thought it was a pass to the
+ 
+
+ align:start position:0%
+I'd have thought it was a pass to the
+Astros baseball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game but here I was faced with the fact
+
+ align:start position:0%
+game but here I was faced with the fact
+ 
+
+ align:start position:0%
+game but here I was faced with the fact
+I've got to stand up in front of the
+
+ align:start position:0%
+I've got to stand up in front of the
+ 
+
+ align:start position:0%
+I've got to stand up in front of the
+president of the United States in a room
+
+ align:start position:0%
+president of the United States in a room
+ 
+
+ align:start position:0%
+president of the United States in a room
+much like this one only with about only
+
+ align:start position:0%
+much like this one only with about only
+ 
+
+ align:start position:0%
+much like this one only with about only
+10 or 12 people in it and tell that
+
+ align:start position:0%
+10 or 12 people in it and tell that
+ 
+
+ align:start position:0%
+10 or 12 people in it and tell that
+gentleman how you going to go to the
+
+ align:start position:0%
+gentleman how you going to go to the
+ 
+
+ align:start position:0%
+gentleman how you going to go to the
+moon and that was I I was a quick learn
+
+ align:start position:0%
+moon and that was I I was a quick learn
+ 
+
+ align:start position:0%
+moon and that was I I was a quick learn
+I'm telling you a really quick learn
+
+ align:start position:0%
+I'm telling you a really quick learn
+ 
+
+ align:start position:0%
+I'm telling you a really quick learn
+from people like these guys know John
+
+ align:start position:0%
+from people like these guys know John
+ 
+
+ align:start position:0%
+from people like these guys know John
+Mayor and Bill Tindle taught me in a few
+
+ align:start position:0%
+Mayor and Bill Tindle taught me in a few
+ 
+
+ align:start position:0%
+Mayor and Bill Tindle taught me in a few
+hours how to do the orbital mechanics to
+
+ align:start position:0%
+hours how to do the orbital mechanics to
+ 
+
+ align:start position:0%
+hours how to do the orbital mechanics to
+go to the Moon not how to do it but what
+
+ align:start position:0%
+go to the Moon not how to do it but what
+ 
+
+ align:start position:0%
+go to the Moon not how to do it but what
+took place so
+
+ align:start position:0%
+took place so
+ 
+
+ align:start position:0%
+took place so
+here we were at the end of mercury and
+
+ align:start position:0%
+here we were at the end of mercury and
+ 
+
+ align:start position:0%
+here we were at the end of mercury and
+we're going to then have to go go to the
+
+ align:start position:0%
+we're going to then have to go go to the
+ 
+
+ align:start position:0%
+we're going to then have to go go to the
+moon on how are we going to get there
+
+ align:start position:0%
+moon on how are we going to get there
+ 
+
+ align:start position:0%
+moon on how are we going to get there
+and how we going to train ourselves what
+
+ align:start position:0%
+and how we going to train ourselves what
+ 
+
+ align:start position:0%
+and how we going to train ourselves what
+are the systems we need to do the job
+
+ align:start position:0%
+are the systems we need to do the job
+ 
+
+ align:start position:0%
+are the systems we need to do the job
+what new control center do we need what
+
+ align:start position:0%
+what new control center do we need what
+ 
+
+ align:start position:0%
+what new control center do we need what
+kind of operations do we need to think
+
+ align:start position:0%
+kind of operations do we need to think
+ 
+
+ align:start position:0%
+kind of operations do we need to think
+about what kind of trajectory analysis
+
+ align:start position:0%
+about what kind of trajectory analysis
+ 
+
+ align:start position:0%
+about what kind of trajectory analysis
+do we need and what kind of computers do
+
+ align:start position:0%
+do we need and what kind of computers do
+ 
+
+ align:start position:0%
+do we need and what kind of computers do
+we need and what kind of communications
+
+ align:start position:0%
+we need and what kind of communications
+ 
+
+ align:start position:0%
+we need and what kind of communications
+do we need suddenly we've got a whole
+
+ align:start position:0%
+do we need suddenly we've got a whole
+ 
+
+ align:start position:0%
+do we need suddenly we've got a whole
+new set of problems we've got to if
+
+ align:start position:0%
+new set of problems we've got to if
+ 
+
+ align:start position:0%
+new set of problems we've got to if
+we're going to do Rendevous at the Moon
+
+ align:start position:0%
+we're going to do Rendevous at the Moon
+ 
+
+ align:start position:0%
+we're going to do Rendevous at the Moon
+we've got to teach ourselves how to do
+
+ align:start position:0%
+we've got to teach ourselves how to do
+ 
+
+ align:start position:0%
+we've got to teach ourselves how to do
+Rend at the Earth
+
+ align:start position:0%
+Rend at the Earth
+ 
+
+ align:start position:0%
+Rend at the Earth
+uh if we're going to send something
+
+ align:start position:0%
+uh if we're going to send something
+ 
+
+ align:start position:0%
+uh if we're going to send something
+around the Moon we better have a heck of
+
+ align:start position:0%
+around the Moon we better have a heck of
+ 
+
+ align:start position:0%
+around the Moon we better have a heck of
+a system to determine whether we are
+
+ align:start position:0%
+a system to determine whether we are
+ 
+
+ align:start position:0%
+a system to determine whether we are
+truly aiming at the moon or whether
+
+ align:start position:0%
+truly aiming at the moon or whether
+ 
+
+ align:start position:0%
+truly aiming at the moon or whether
+we're going to hit the moon and in fact
+
+ align:start position:0%
+we're going to hit the moon and in fact
+ 
+
+ align:start position:0%
+we're going to hit the moon and in fact
+on Apollo 8 I wasn't sure that George
+
+ align:start position:0%
+on Apollo 8 I wasn't sure that George
+ 
+
+ align:start position:0%
+on Apollo 8 I wasn't sure that George
+Miller who was ahead of man space flight
+
+ align:start position:0%
+Miller who was ahead of man space flight
+ 
+
+ align:start position:0%
+Miller who was ahead of man space flight
+was sure we weren't going to hit the
+
+ align:start position:0%
+was sure we weren't going to hit the
+ 
+
+ align:start position:0%
+was sure we weren't going to hit the
+moon when we told him that we wanted to
+
+ align:start position:0%
+moon when we told him that we wanted to
+ 
+
+ align:start position:0%
+moon when we told him that we wanted to
+repeat we wanted to do the trajectory as
+
+ align:start position:0%
+repeat we wanted to do the trajectory as
+ 
+
+ align:start position:0%
+repeat we wanted to do the trajectory as
+we were going to do it landed then you
+
+ align:start position:0%
+we were going to do it landed then you
+ 
+
+ align:start position:0%
+we were going to do it landed then you
+ended up being 60 miles above the lunar
+
+ align:start position:0%
+ended up being 60 miles above the lunar
+ 
+
+ align:start position:0%
+ended up being 60 miles above the lunar
+surface as you entered orbit around the
+
+ align:start position:0%
+surface as you entered orbit around the
+ 
+
+ align:start position:0%
+surface as you entered orbit around the
+moon
+
+ align:start position:0%
+moon
+ 
+
+ align:start position:0%
+moon
+and can you really tell me that 270,000
+
+ align:start position:0%
+and can you really tell me that 270,000
+ 
+
+ align:start position:0%
+and can you really tell me that 270,000
+miles away whether the spacecraft is
+
+ align:start position:0%
+miles away whether the spacecraft is
+ 
+
+ align:start position:0%
+miles away whether the spacecraft is
+going to hit the moon when you're 10
+
+ align:start position:0%
+going to hit the moon when you're 10
+ 
+
+ align:start position:0%
+going to hit the moon when you're 10
+hours away or is it going to go around
+
+ align:start position:0%
+hours away or is it going to go around
+ 
+
+ align:start position:0%
+hours away or is it going to go around
+in so we we're faced with all those new
+
+ align:start position:0%
+in so we we're faced with all those new
+ 
+
+ align:start position:0%
+in so we we're faced with all those new
+problems that's what got us to the gmany
+
+ align:start position:0%
+problems that's what got us to the gmany
+ 
+
+ align:start position:0%
+problems that's what got us to the gmany
+program we wanted to be able to build a
+
+ align:start position:0%
+program we wanted to be able to build a
+ 
+
+ align:start position:0%
+program we wanted to be able to build a
+spaceship that would allow us to do
+
+ align:start position:0%
+spaceship that would allow us to do
+ 
+
+ align:start position:0%
+spaceship that would allow us to do
+maneuvering in in orbit that would allow
+
+ align:start position:0%
+maneuvering in in orbit that would allow
+ 
+
+ align:start position:0%
+maneuvering in in orbit that would allow
+us to stay up there 14 days which is how
+
+ align:start position:0%
+us to stay up there 14 days which is how
+ 
+
+ align:start position:0%
+us to stay up there 14 days which is how
+long the spacecraft flight to the moon
+
+ align:start position:0%
+long the spacecraft flight to the moon
+ 
+
+ align:start position:0%
+long the spacecraft flight to the moon
+and back would be that would allow us to
+
+ align:start position:0%
+and back would be that would allow us to
+ 
+
+ align:start position:0%
+and back would be that would allow us to
+do uh re-entry guidance using yellow a d
+
+ align:start position:0%
+do uh re-entry guidance using yellow a d
+ 
+
+ align:start position:0%
+do uh re-entry guidance using yellow a d
+of a blunt body enough
+
+ align:start position:0%
+of a blunt body enough
+ 
+
+ align:start position:0%
+of a blunt body enough
+to uh skip it out as you came back to
+
+ align:start position:0%
+to uh skip it out as you came back to
+ 
+
+ align:start position:0%
+to uh skip it out as you came back to
+Earth and then go back up and then re
+
+ align:start position:0%
+Earth and then go back up and then re
+ 
+
+ align:start position:0%
+Earth and then go back up and then re
+enter at a at a much lower velocity so
+
+ align:start position:0%
+enter at a at a much lower velocity so
+ 
+
+ align:start position:0%
+enter at a at a much lower velocity so
+you wouldn't burn up spacecraft those
+
+ align:start position:0%
+you wouldn't burn up spacecraft those
+ 
+
+ align:start position:0%
+you wouldn't burn up spacecraft those
+are the kind of things we were suddenly
+
+ align:start position:0%
+are the kind of things we were suddenly
+ 
+
+ align:start position:0%
+are the kind of things we were suddenly
+thinking about as we built the germanes
+
+ align:start position:0%
+thinking about as we built the germanes
+ 
+
+ align:start position:0%
+thinking about as we built the germanes
+spacecraft we needed an onboard computer
+
+ align:start position:0%
+spacecraft we needed an onboard computer
+ 
+
+ align:start position:0%
+spacecraft we needed an onboard computer
+unheard
+
+ align:start position:0%
+unheard
+ 
+
+ align:start position:0%
+unheard
+of in that time period the Air Force had
+
+ align:start position:0%
+of in that time period the Air Force had
+ 
+
+ align:start position:0%
+of in that time period the Air Force had
+been putting some on airplanes but never
+
+ align:start position:0%
+been putting some on airplanes but never
+ 
+
+ align:start position:0%
+been putting some on airplanes but never
+had we had one on board a
+
+ align:start position:0%
+had we had one on board a
+ 
+
+ align:start position:0%
+had we had one on board a
+spacecraft so gmany was designed to be a
+
+ align:start position:0%
+spacecraft so gmany was designed to be a
+ 
+
+ align:start position:0%
+spacecraft so gmany was designed to be a
+maneuvering capable Onan space to
+
+ align:start position:0%
+maneuvering capable Onan space to
+ 
+
+ align:start position:0%
+maneuvering capable Onan space to
+Rendevous and dock with a Target to uh
+
+ align:start position:0%
+Rendevous and dock with a Target to uh
+ 
+
+ align:start position:0%
+Rendevous and dock with a Target to uh
+determine the capability of man to
+
+ align:start position:0%
+determine the capability of man to
+ 
+
+ align:start position:0%
+determine the capability of man to
+survive for 14 days to do
+
+ align:start position:0%
+survive for 14 days to do
+ 
+
+ align:start position:0%
+survive for 14 days to do
+a a heat shield which was much more
+
+ align:start position:0%
+a a heat shield which was much more
+ 
+
+ align:start position:0%
+a a heat shield which was much more
+flexible and
+
+ align:start position:0%
+flexible and
+ 
+
+ align:start position:0%
+flexible and
+reusable and to build a maneuvering
+
+ align:start position:0%
+reusable and to build a maneuvering
+ 
+
+ align:start position:0%
+reusable and to build a maneuvering
+system and finally to do guidance and
+
+ align:start position:0%
+system and finally to do guidance and
+ 
+
+ align:start position:0%
+system and finally to do guidance and
+control for landing Point control and
+
+ align:start position:0%
+control for landing Point control and
+ 
+
+ align:start position:0%
+control for landing Point control and
+develop a
+
+ align:start position:0%
+develop a
+ 
+
+ align:start position:0%
+develop a
+footprint on the earth for geminy which
+
+ align:start position:0%
+footprint on the earth for geminy which
+ 
+
+ align:start position:0%
+footprint on the earth for geminy which
+is what we were going to have to do on
+
+ align:start position:0%
+is what we were going to have to do on
+ 
+
+ align:start position:0%
+is what we were going to have to do on
+Apollo geminy was a very successful
+
+ align:start position:0%
+Apollo geminy was a very successful
+ 
+
+ align:start position:0%
+Apollo geminy was a very successful
+program without it we could never have
+
+ align:start position:0%
+program without it we could never have
+ 
+
+ align:start position:0%
+program without it we could never have
+gone to the Moon we learned how to
+
+ align:start position:0%
+gone to the Moon we learned how to
+ 
+
+ align:start position:0%
+gone to the Moon we learned how to
+operate in space how to maneuvering
+
+ align:start position:0%
+operate in space how to maneuvering
+ 
+
+ align:start position:0%
+operate in space how to maneuvering
+space we learned how to do Eva which was
+
+ align:start position:0%
+space we learned how to do Eva which was
+ 
+
+ align:start position:0%
+space we learned how to do Eva which was
+a total disaster as we flew in Germany I
+
+ align:start position:0%
+a total disaster as we flew in Germany I
+ 
+
+ align:start position:0%
+a total disaster as we flew in Germany I
+don't think we even even by doing doing
+
+ align:start position:0%
+don't think we even even by doing doing
+ 
+
+ align:start position:0%
+don't think we even even by doing doing
+it five or six times in uh on the final
+
+ align:start position:0%
+it five or six times in uh on the final
+ 
+
+ align:start position:0%
+it five or six times in uh on the final
+flight of Germany 12 Buzz aldr was able
+
+ align:start position:0%
+flight of Germany 12 Buzz aldr was able
+ 
+
+ align:start position:0%
+flight of Germany 12 Buzz aldr was able
+to do uh a ra a reasonable job in extra
+
+ align:start position:0%
+to do uh a ra a reasonable job in extra
+ 
+
+ align:start position:0%
+to do uh a ra a reasonable job in extra
+vehicular activity we had to build a
+
+ align:start position:0%
+vehicular activity we had to build a
+ 
+
+ align:start position:0%
+vehicular activity we had to build a
+suit that was flexible to be able to
+
+ align:start position:0%
+suit that was flexible to be able to
+ 
+
+ align:start position:0%
+suit that was flexible to be able to
+walk on the moon we had to build a
+
+ align:start position:0%
+walk on the moon we had to build a
+ 
+
+ align:start position:0%
+walk on the moon we had to build a
+backpack which would in truth was
+
+ align:start position:0%
+backpack which would in truth was
+ 
+
+ align:start position:0%
+backpack which would in truth was
+another spacecraft
+
+ align:start position:0%
+another spacecraft
+ 
+
+ align:start position:0%
+another spacecraft
+to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Apollo uh we had to build a new control
+
+ align:start position:0%
+Apollo uh we had to build a new control
+ 
+
+ align:start position:0%
+Apollo uh we had to build a new control
+center because we had a a a computer
+
+ align:start position:0%
+center because we had a a a computer
+ 
+
+ align:start position:0%
+center because we had a a a computer
+which we actually doubled the storage
+
+ align:start position:0%
+which we actually doubled the storage
+ 
+
+ align:start position:0%
+which we actually doubled the storage
+capacity on Mercury and then gave it
+
+ align:start position:0%
+capacity on Mercury and then gave it
+ 
+
+ align:start position:0%
+capacity on Mercury and then gave it
+60,000 64,000
+
+ align:start position:0%
+60,000 64,000
+ 
+
+ align:start position:0%
+60,000 64,000
+words today you have that in some kids
+
+ align:start position:0%
+words today you have that in some kids
+ 
+
+ align:start position:0%
+words today you have that in some kids
+thing that he carries on his airplane
+
+ align:start position:0%
+thing that he carries on his airplane
+ 
+
+ align:start position:0%
+thing that he carries on his airplane
+and one touch of his throat but 64,000
+
+ align:start position:0%
+and one touch of his throat but 64,000
+ 
+
+ align:start position:0%
+and one touch of his throat but 64,000
+words was all we had then when we flew
+
+ align:start position:0%
+words was all we had then when we flew
+ 
+
+ align:start position:0%
+words was all we had then when we flew
+Germany we had a million words when we
+
+ align:start position:0%
+Germany we had a million words when we
+ 
+
+ align:start position:0%
+Germany we had a million words when we
+flew Apollo we had five and a half
+
+ align:start position:0%
+flew Apollo we had five and a half
+ 
+
+ align:start position:0%
+flew Apollo we had five and a half
+million words so the computer complex
+
+ align:start position:0%
+million words so the computer complex
+ 
+
+ align:start position:0%
+million words so the computer complex
+was changing on as continuously when we
+
+ align:start position:0%
+was changing on as continuously when we
+ 
+
+ align:start position:0%
+was changing on as continuously when we
+did Mercury we used a grease pencil to
+
+ align:start position:0%
+did Mercury we used a grease pencil to
+ 
+
+ align:start position:0%
+did Mercury we used a grease pencil to
+write down the numbers as they came back
+
+ align:start position:0%
+write down the numbers as they came back
+ 
+
+ align:start position:0%
+write down the numbers as they came back
+from cono Nigerian 20 words of teletype
+
+ align:start position:0%
+from cono Nigerian 20 words of teletype
+ 
+
+ align:start position:0%
+from cono Nigerian 20 words of teletype
+we had to build a new display system and
+
+ align:start position:0%
+we had to build a new display system and
+ 
+
+ align:start position:0%
+we had to build a new display system and
+a digital display system with a computer
+
+ align:start position:0%
+a digital display system with a computer
+ 
+
+ align:start position:0%
+a digital display system with a computer
+and the first digital display system was
+
+ align:start position:0%
+and the first digital display system was
+ 
+
+ align:start position:0%
+and the first digital display system was
+not graphics at all what we did was
+
+ align:start position:0%
+not graphics at all what we did was
+ 
+
+ align:start position:0%
+not graphics at all what we did was
+build a a
+
+ align:start position:0%
+build a a
+ 
+
+ align:start position:0%
+build a a
+slide that was the background for the
+
+ align:start position:0%
+slide that was the background for the
+ 
+
+ align:start position:0%
+slide that was the background for the
+for the uh display that you wanted we
+
+ align:start position:0%
+for the uh display that you wanted we
+ 
+
+ align:start position:0%
+for the uh display that you wanted we
+had a set of you of uh 4 and a half inch
+
+ align:start position:0%
+had a set of you of uh 4 and a half inch
+ 
+
+ align:start position:0%
+had a set of you of uh 4 and a half inch
+Lantern slides a bank of 100 for each
+
+ align:start position:0%
+Lantern slides a bank of 100 for each
+ 
+
+ align:start position:0%
+Lantern slides a bank of 100 for each
+space each station in the control center
+
+ align:start position:0%
+space each station in the control center
+ 
+
+ align:start position:0%
+space each station in the control center
+and then the computer filled in the
+
+ align:start position:0%
+and then the computer filled in the
+ 
+
+ align:start position:0%
+and then the computer filled in the
+numbers now that's that's in 1964 65 66
+
+ align:start position:0%
+numbers now that's that's in 1964 65 66
+ 
+
+ align:start position:0%
+numbers now that's that's in 1964 65 66
+it wasn't until we got to the latter
+
+ align:start position:0%
+it wasn't until we got to the latter
+ 
+
+ align:start position:0%
+it wasn't until we got to the latter
+stages of Follow that we had computer
+
+ align:start position:0%
+stages of Follow that we had computer
+ 
+
+ align:start position:0%
+stages of Follow that we had computer
+Graphics I don't know whether you can
+
+ align:start position:0%
+Graphics I don't know whether you can
+ 
+
+ align:start position:0%
+Graphics I don't know whether you can
+realize it that or not that's you know
+
+ align:start position:0%
+realize it that or not that's you know
+ 
+
+ align:start position:0%
+realize it that or not that's you know
+computer Graphics today is go football
+
+ align:start position:0%
+computer Graphics today is go football
+ 
+
+ align:start position:0%
+computer Graphics today is go football
+games on computer Graphics but then we
+
+ align:start position:0%
+games on computer Graphics but then we
+ 
+
+ align:start position:0%
+games on computer Graphics but then we
+didn't have it so we had to redesign a
+
+ align:start position:0%
+didn't have it so we had to redesign a
+ 
+
+ align:start position:0%
+didn't have it so we had to redesign a
+Control Center and continuously redesign
+
+ align:start position:0%
+Control Center and continuously redesign
+ 
+
+ align:start position:0%
+Control Center and continuously redesign
+a control center we had to have a
+
+ align:start position:0%
+a control center we had to have a
+ 
+
+ align:start position:0%
+a control center we had to have a
+computer control Communication
+
+ align:start position:0%
+computer control Communication
+ 
+
+ align:start position:0%
+computer control Communication
+System all of those things were built we
+
+ align:start position:0%
+System all of those things were built we
+ 
+
+ align:start position:0%
+System all of those things were built we
+had to utilize and build in NASA the
+
+ align:start position:0%
+had to utilize and build in NASA the
+ 
+
+ align:start position:0%
+had to utilize and build in NASA the
+first commun
+
+ align:start position:0%
+first commun
+ 
+
+ align:start position:0%
+first commun
+satellite from which came the revolution
+
+ align:start position:0%
+satellite from which came the revolution
+ 
+
+ align:start position:0%
+satellite from which came the revolution
+in the world in my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+opinion uh I want to I want to get
+
+ align:start position:0%
+opinion uh I want to I want to get
+ 
+
+ align:start position:0%
+opinion uh I want to I want to get
+to uh I could go through Apollo and
+
+ align:start position:0%
+to uh I could go through Apollo and
+ 
+
+ align:start position:0%
+to uh I could go through Apollo and
+things like TR trans lunar trajectories
+
+ align:start position:0%
+things like TR trans lunar trajectories
+ 
+
+ align:start position:0%
+things like TR trans lunar trajectories
+and free return trajectories and what H
+
+ align:start position:0%
+and free return trajectories and what H
+ 
+
+ align:start position:0%
+and free return trajectories and what H
+what might happen if you were off by a
+
+ align:start position:0%
+what might happen if you were off by a
+ 
+
+ align:start position:0%
+what might happen if you were off by a
+few feet per second or a few tents of a
+
+ align:start position:0%
+few feet per second or a few tents of a
+ 
+
+ align:start position:0%
+few feet per second or a few tents of a
+degree when you fired your
+
+ align:start position:0%
+degree when you fired your
+ 
+
+ align:start position:0%
+degree when you fired your
+uh uh orbital the the orbital
+
+ align:start position:0%
+uh uh orbital the the orbital
+ 
+
+ align:start position:0%
+uh uh orbital the the orbital
+maneuvering system of the APO on the
+
+ align:start position:0%
+maneuvering system of the APO on the
+ 
+
+ align:start position:0%
+maneuvering system of the APO on the
+back side of the moon which is where you
+
+ align:start position:0%
+back side of the moon which is where you
+ 
+
+ align:start position:0%
+back side of the moon which is where you
+had to do it for Optimum performance
+
+ align:start position:0%
+had to do it for Optimum performance
+ 
+
+ align:start position:0%
+had to do it for Optimum performance
+characteristics and when the thing
+
+ align:start position:0%
+characteristics and when the thing
+ 
+
+ align:start position:0%
+characteristics and when the thing
+showed up on the as it came out and view
+
+ align:start position:0%
+showed up on the as it came out and view
+ 
+
+ align:start position:0%
+showed up on the as it came out and view
+on the front side of the moon and it was
+
+ align:start position:0%
+on the front side of the moon and it was
+ 
+
+ align:start position:0%
+on the front side of the moon and it was
+right not in the right trajectory what
+
+ align:start position:0%
+right not in the right trajectory what
+ 
+
+ align:start position:0%
+right not in the right trajectory what
+the hell are you going to do about
+
+ align:start position:0%
+the hell are you going to do about
+ 
+
+ align:start position:0%
+the hell are you going to do about
+it where is it going is it going around
+
+ align:start position:0%
+it where is it going is it going around
+ 
+
+ align:start position:0%
+it where is it going is it going around
+the Sun
+
+ align:start position:0%
+the Sun
+ 
+
+ align:start position:0%
+the Sun
+is it coming back to Earth is it going
+
+ align:start position:0%
+is it coming back to Earth is it going
+ 
+
+ align:start position:0%
+is it coming back to Earth is it going
+to hit the
+
+ align:start position:0%
+to hit the
+ 
+
+ align:start position:0%
+to hit the
+Moon and what am I going to do about it
+
+ align:start position:0%
+Moon and what am I going to do about it
+ 
+
+ align:start position:0%
+Moon and what am I going to do about it
+if it is on one of those paths and my
+
+ align:start position:0%
+if it is on one of those paths and my
+ 
+
+ align:start position:0%
+if it is on one of those paths and my
+orbital my my maneuvering engine which
+
+ align:start position:0%
+orbital my my maneuvering engine which
+ 
+
+ align:start position:0%
+orbital my my maneuvering engine which
+has 10,000 PS of thrust is not working
+
+ align:start position:0%
+has 10,000 PS of thrust is not working
+ 
+
+ align:start position:0%
+has 10,000 PS of thrust is not working
+or not working properly or it wasn't
+
+ align:start position:0%
+or not working properly or it wasn't
+ 
+
+ align:start position:0%
+or not working properly or it wasn't
+pointed in the right direction you had
+
+ align:start position:0%
+pointed in the right direction you had
+ 
+
+ align:start position:0%
+pointed in the right direction you had
+to be prepared to think about those
+
+ align:start position:0%
+to be prepared to think about those
+ 
+
+ align:start position:0%
+to be prepared to think about those
+problems and make a real time
+
+ align:start position:0%
+problems and make a real time
+ 
+
+ align:start position:0%
+problems and make a real time
+decision as to what to do
+
+ align:start position:0%
+decision as to what to do
+ 
+
+ align:start position:0%
+decision as to what to do
+I hope I'm impressing you with that
+
+ align:start position:0%
+I hope I'm impressing you with that
+ 
+
+ align:start position:0%
+I hope I'm impressing you with that
+because that's what you guys are faced
+
+ align:start position:0%
+because that's what you guys are faced
+ 
+
+ align:start position:0%
+because that's what you guys are faced
+with in going back to the
+
+ align:start position:0%
+with in going back to the
+ 
+
+ align:start position:0%
+with in going back to the
+Moon you know it isn't just a simple
+
+ align:start position:0%
+Moon you know it isn't just a simple
+ 
+
+ align:start position:0%
+Moon you know it isn't just a simple
+problem of orbital mechanics it's a
+
+ align:start position:0%
+problem of orbital mechanics it's a
+ 
+
+ align:start position:0%
+problem of orbital mechanics it's a
+problem of what are you going to do if
+
+ align:start position:0%
+problem of what are you going to do if
+ 
+
+ align:start position:0%
+problem of what are you going to do if
+it isn't correct if it isn't on the
+
+ align:start position:0%
+it isn't correct if it isn't on the
+ 
+
+ align:start position:0%
+it isn't correct if it isn't on the
+right path if the system isn't working
+
+ align:start position:0%
+right path if the system isn't working
+ 
+
+ align:start position:0%
+right path if the system isn't working
+properly can you
+
+ align:start position:0%
+properly can you
+ 
+
+ align:start position:0%
+properly can you
+land those things have to be thought out
+
+ align:start position:0%
+land those things have to be thought out
+ 
+
+ align:start position:0%
+land those things have to be thought out
+and thought out carefully before for the
+
+ align:start position:0%
+and thought out carefully before for the
+ 
+
+ align:start position:0%
+and thought out carefully before for the
+fact not in real time you can make all
+
+ align:start position:0%
+fact not in real time you can make all
+ 
+
+ align:start position:0%
+fact not in real time you can make all
+of the decisions in the computer which
+
+ align:start position:0%
+of the decisions in the computer which
+ 
+
+ align:start position:0%
+of the decisions in the computer which
+you would have made after you thought
+
+ align:start position:0%
+you would have made after you thought
+ 
+
+ align:start position:0%
+you would have made after you thought
+about it in real time but think of the
+
+ align:start position:0%
+about it in real time but think of the
+ 
+
+ align:start position:0%
+about it in real time but think of the
+orbital mechanics problems associated
+
+ align:start position:0%
+orbital mechanics problems associated
+ 
+
+ align:start position:0%
+orbital mechanics problems associated
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+that in real time and the back
+
+ align:start position:0%
+that in real time and the back
+ 
+
+ align:start position:0%
+that in real time and the back
+background then of the math and the
+
+ align:start position:0%
+background then of the math and the
+ 
+
+ align:start position:0%
+background then of the math and the
+thought processes that have to go into
+
+ align:start position:0%
+thought processes that have to go into
+ 
+
+ align:start position:0%
+thought processes that have to go into
+making those
+
+ align:start position:0%
+making those
+ 
+
+ align:start position:0%
+making those
+decisions you're descending to the moon
+
+ align:start position:0%
+decisions you're descending to the moon
+ 
+
+ align:start position:0%
+decisions you're descending to the moon
+and there one of these gentlemen sitting
+
+ align:start position:0%
+and there one of these gentlemen sitting
+ 
+
+ align:start position:0%
+and there one of these gentlemen sitting
+here you start to do the uh the
+
+ align:start position:0%
+here you start to do the uh the
+ 
+
+ align:start position:0%
+here you start to do the uh the
+uh descent to the
+
+ align:start position:0%
+uh descent to the
+ 
+
+ align:start position:0%
+uh descent to the
+moon and lo and behold you bring up the
+
+ align:start position:0%
+moon and lo and behold you bring up the
+ 
+
+ align:start position:0%
+moon and lo and behold you bring up the
+system on the limb and the abort light
+
+ align:start position:0%
+system on the limb and the abort light
+ 
+
+ align:start position:0%
+system on the limb and the abort light
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+on and what the hell does that mean well
+
+ align:start position:0%
+on and what the hell does that mean well
+ 
+
+ align:start position:0%
+on and what the hell does that mean well
+it means if you start the engine right
+
+ align:start position:0%
+it means if you start the engine right
+ 
+
+ align:start position:0%
+it means if you start the engine right
+now it's going to start doing a randev
+
+ align:start position:0%
+now it's going to start doing a randev
+ 
+
+ align:start position:0%
+now it's going to start doing a randev
+back with the Command Module it's not
+
+ align:start position:0%
+back with the Command Module it's not
+ 
+
+ align:start position:0%
+back with the Command Module it's not
+going to land on the lunar
+
+ align:start position:0%
+going to land on the lunar
+ 
+
+ align:start position:0%
+going to land on the lunar
+surface and I've got a computer program
+
+ align:start position:0%
+surface and I've got a computer program
+ 
+
+ align:start position:0%
+surface and I've got a computer program
+that's hard
+
+ align:start position:0%
+that's hard
+ 
+
+ align:start position:0%
+that's hard
+wired to do that job with I don't have
+
+ align:start position:0%
+wired to do that job with I don't have
+ 
+
+ align:start position:0%
+wired to do that job with I don't have
+the capability of reprogramming it like
+
+ align:start position:0%
+the capability of reprogramming it like
+ 
+
+ align:start position:0%
+the capability of reprogramming it like
+you have by just sending up a whole new
+
+ align:start position:0%
+you have by just sending up a whole new
+ 
+
+ align:start position:0%
+you have by just sending up a whole new
+set of software how am I going to figure
+
+ align:start position:0%
+set of software how am I going to figure
+ 
+
+ align:start position:0%
+set of software how am I going to figure
+that damn thing out I've got a thir
+
+ align:start position:0%
+that damn thing out I've got a thir
+ 
+
+ align:start position:0%
+that damn thing out I've got a thir
+thousand words of pad in this
+
+ align:start position:0%
+thousand words of pad in this
+ 
+
+ align:start position:0%
+thousand words of pad in this
+computer is it possible
+
+ align:start position:0%
+computer is it possible
+ 
+
+ align:start position:0%
+computer is it possible
+in real time to obviate that abort
+
+ align:start position:0%
+in real time to obviate that abort
+ 
+
+ align:start position:0%
+in real time to obviate that abort
+signal and still land on the
+
+ align:start position:0%
+signal and still land on the
+ 
+
+ align:start position:0%
+signal and still land on the
+moon and this gentleman sitting over
+
+ align:start position:0%
+moon and this gentleman sitting over
+ 
+
+ align:start position:0%
+moon and this gentleman sitting over
+here figured that
+
+ align:start position:0%
+here figured that
+ 
+
+ align:start position:0%
+here figured that
+out he's figured out how to tell the
+
+ align:start position:0%
+out he's figured out how to tell the
+ 
+
+ align:start position:0%
+out he's figured out how to tell the
+computer ignore that
+
+ align:start position:0%
+computer ignore that
+ 
+
+ align:start position:0%
+computer ignore that
+signal by going into the certain places
+
+ align:start position:0%
+signal by going into the certain places
+ 
+
+ align:start position:0%
+signal by going into the certain places
+in the software in that hardwired
+
+ align:start position:0%
+in the software in that hardwired
+ 
+
+ align:start position:0%
+in the software in that hardwired
+software and saying don't listen to the
+
+ align:start position:0%
+software and saying don't listen to the
+ 
+
+ align:start position:0%
+software and saying don't listen to the
+abort signal for a
+
+ align:start position:0%
+abort signal for a
+ 
+
+ align:start position:0%
+abort signal for a
+while don't listen to it but if I need
+
+ align:start position:0%
+while don't listen to it but if I need
+ 
+
+ align:start position:0%
+while don't listen to it but if I need
+to listen to it on the way down then
+
+ align:start position:0%
+to listen to it on the way down then
+ 
+
+ align:start position:0%
+to listen to it on the way down then
+listen to it and you got to do that with
+
+ align:start position:0%
+listen to it and you got to do that with
+ 
+
+ align:start position:0%
+listen to it and you got to do that with
+a thousand words that's pretty tough
+
+ align:start position:0%
+a thousand words that's pretty tough
+ 
+
+ align:start position:0%
+a thousand words that's pretty tough
+problem in real time one which nobody
+
+ align:start position:0%
+problem in real time one which nobody
+ 
+
+ align:start position:0%
+problem in real time one which nobody
+had thought about
+
+ align:start position:0%
+had thought about
+ 
+
+ align:start position:0%
+had thought about
+before until it
+
+ align:start position:0%
+before until it
+ 
+
+ align:start position:0%
+before until it
+happened or as I said this 25 year old
+
+ align:start position:0%
+happened or as I said this 25 year old
+ 
+
+ align:start position:0%
+happened or as I said this 25 year old
+young man on Apollo 11 and the vehicles
+
+ align:start position:0%
+young man on Apollo 11 and the vehicles
+ 
+
+ align:start position:0%
+young man on Apollo 11 and the vehicles
+are descending to the moon and he's
+
+ align:start position:0%
+are descending to the moon and he's
+ 
+
+ align:start position:0%
+are descending to the moon and he's
+getting all these signals back that says
+
+ align:start position:0%
+getting all these signals back that says
+ 
+
+ align:start position:0%
+getting all these signals back that says
+the computer is over loaded and it's
+
+ align:start position:0%
+the computer is over loaded and it's
+ 
+
+ align:start position:0%
+the computer is over loaded and it's
+doing so many tasks and
+
+ align:start position:0%
+doing so many tasks and
+ 
+
+ align:start position:0%
+doing so many tasks and
+stopping why is it doing that we've done
+
+ align:start position:0%
+stopping why is it doing that we've done
+ 
+
+ align:start position:0%
+stopping why is it doing that we've done
+it on Apollo a 10 when we started down
+
+ align:start position:0%
+it on Apollo a 10 when we started down
+ 
+
+ align:start position:0%
+it on Apollo a 10 when we started down
+to the moon and worked fine and we did a
+
+ align:start position:0%
+to the moon and worked fine and we did a
+ 
+
+ align:start position:0%
+to the moon and worked fine and we did a
+Rendevous from it but we had to radar
+
+ align:start position:0%
+Rendevous from it but we had to radar
+ 
+
+ align:start position:0%
+Rendevous from it but we had to radar
+on and going down to the Moon we didn't
+
+ align:start position:0%
+on and going down to the Moon we didn't
+ 
+
+ align:start position:0%
+on and going down to the Moon we didn't
+need the radar on and that radar was
+
+ align:start position:0%
+need the radar on and that radar was
+ 
+
+ align:start position:0%
+need the radar on and that radar was
+going into the computer was flooding the
+
+ align:start position:0%
+going into the computer was flooding the
+ 
+
+ align:start position:0%
+going into the computer was flooding the
+computer with data but these guys didn't
+
+ align:start position:0%
+computer with data but these guys didn't
+ 
+
+ align:start position:0%
+computer with data but these guys didn't
+know that they had to figure out how to
+
+ align:start position:0%
+know that they had to figure out how to
+ 
+
+ align:start position:0%
+know that they had to figure out how to
+get around that signal
+
+ align:start position:0%
+get around that signal
+ 
+
+ align:start position:0%
+get around that signal
+if I if I sound like that's a big
+
+ align:start position:0%
+if I if I sound like that's a big
+ 
+
+ align:start position:0%
+if I if I sound like that's a big
+problem it is a big
+
+ align:start position:0%
+problem it is a big
+ 
+
+ align:start position:0%
+problem it is a big
+problem and it's going to get bigger the
+
+ align:start position:0%
+problem and it's going to get bigger the
+ 
+
+ align:start position:0%
+problem and it's going to get bigger the
+spacecraft are going to get more
+
+ align:start position:0%
+spacecraft are going to get more
+ 
+
+ align:start position:0%
+spacecraft are going to get more
+complex with each passing day and you're
+
+ align:start position:0%
+complex with each passing day and you're
+ 
+
+ align:start position:0%
+complex with each passing day and you're
+going to have to figure out how to do
+
+ align:start position:0%
+going to have to figure out how to do
+ 
+
+ align:start position:0%
+going to have to figure out how to do
+that stuff in real time and that's what
+
+ align:start position:0%
+that stuff in real time and that's what
+ 
+
+ align:start position:0%
+that stuff in real time and that's what
+you the flight operations people and the
+
+ align:start position:0%
+you the flight operations people and the
+ 
+
+ align:start position:0%
+you the flight operations people and the
+designers of Tomorrow are going to be
+
+ align:start position:0%
+designers of Tomorrow are going to be
+ 
+
+ align:start position:0%
+designers of Tomorrow are going to be
+and that's what you're going to be fac
+
+ align:start position:0%
+and that's what you're going to be fac
+ 
+
+ align:start position:0%
+and that's what you're going to be fac
+with uh I know you're
+
+ align:start position:0%
+with uh I know you're
+ 
+
+ align:start position:0%
+with uh I know you're
+I'm working on the
+
+ align:start position:0%
+I'm working on the
+ 
+
+ align:start position:0%
+I'm working on the
+uh space shuttle try to make it better
+
+ align:start position:0%
+uh space shuttle try to make it better
+ 
+
+ align:start position:0%
+uh space shuttle try to make it better
+that's what your task is in this
+
+ align:start position:0%
+that's what your task is in this
+ 
+
+ align:start position:0%
+that's what your task is in this
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+uh we should have had you around for the
+
+ align:start position:0%
+uh we should have had you around for the
+ 
+
+ align:start position:0%
+uh we should have had you around for the
+last 25
+
+ align:start position:0%
+last 25
+ 
+
+ align:start position:0%
+last 25
+years because it needs to be made
+
+ align:start position:0%
+years because it needs to be made
+ 
+
+ align:start position:0%
+years because it needs to be made
+better and it's a travesty I use a I'll
+
+ align:start position:0%
+better and it's a travesty I use a I'll
+ 
+
+ align:start position:0%
+better and it's a travesty I use a I'll
+use that word again it's a travesty that
+
+ align:start position:0%
+use that word again it's a travesty that
+ 
+
+ align:start position:0%
+use that word again it's a travesty that
+we haven't been making it better
+
+ align:start position:0%
+we haven't been making it better
+ 
+
+ align:start position:0%
+we haven't been making it better
+and making it less costly to
+
+ align:start position:0%
+and making it less costly to
+ 
+
+ align:start position:0%
+and making it less costly to
+fly we should have been doing that so
+
+ align:start position:0%
+fly we should have been doing that so
+ 
+
+ align:start position:0%
+fly we should have been doing that so
+let me start into the space shuttle a
+
+ align:start position:0%
+let me start into the space shuttle a
+ 
+
+ align:start position:0%
+let me start into the space shuttle a
+little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh one one of the questions that Jeff
+
+ align:start position:0%
+uh one one of the questions that Jeff
+ 
+
+ align:start position:0%
+uh one one of the questions that Jeff
+asked me that these people will be
+
+ align:start position:0%
+asked me that these people will be
+ 
+
+ align:start position:0%
+asked me that these people will be
+interested in uh in hearing is uh how
+
+ align:start position:0%
+interested in uh in hearing is uh how
+ 
+
+ align:start position:0%
+interested in uh in hearing is uh how
+did you decide to do it Mann as opposed
+
+ align:start position:0%
+did you decide to do it Mann as opposed
+ 
+
+ align:start position:0%
+did you decide to do it Mann as opposed
+to unmanned on the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flight
+
+ align:start position:0%
+flight
+ 
+
+ align:start position:0%
+flight
+uh sort of out of necessity I guess you
+
+ align:start position:0%
+uh sort of out of necessity I guess you
+ 
+
+ align:start position:0%
+uh sort of out of necessity I guess you
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+say we the more we looked at the systems
+
+ align:start position:0%
+say we the more we looked at the systems
+ 
+
+ align:start position:0%
+say we the more we looked at the systems
+the we the more we looked at the Space
+
+ align:start position:0%
+the we the more we looked at the Space
+ 
+
+ align:start position:0%
+the we the more we looked at the Space
+Shuttle more we realized that the man
+
+ align:start position:0%
+Shuttle more we realized that the man
+ 
+
+ align:start position:0%
+Shuttle more we realized that the man
+could furnish us a certain amount of
+
+ align:start position:0%
+could furnish us a certain amount of
+ 
+
+ align:start position:0%
+could furnish us a certain amount of
+reliability in space operations and in
+
+ align:start position:0%
+reliability in space operations and in
+ 
+
+ align:start position:0%
+reliability in space operations and in
+Bas systems and choosing
+
+ align:start position:0%
+Bas systems and choosing
+ 
+
+ align:start position:0%
+Bas systems and choosing
+systems the the more reliable the
+
+ align:start position:0%
+systems the the more reliable the
+ 
+
+ align:start position:0%
+systems the the more reliable the
+machine would become but we had to
+
+ align:start position:0%
+machine would become but we had to
+ 
+
+ align:start position:0%
+machine would become but we had to
+convince ourselves that that was a
+
+ align:start position:0%
+convince ourselves that that was a
+ 
+
+ align:start position:0%
+convince ourselves that that was a
+rational thing to do now let's let's go
+
+ align:start position:0%
+rational thing to do now let's let's go
+ 
+
+ align:start position:0%
+rational thing to do now let's let's go
+back and and give you some thought
+
+ align:start position:0%
+back and and give you some thought
+ 
+
+ align:start position:0%
+back and and give you some thought
+process about the space shuttle
+
+ align:start position:0%
+process about the space shuttle
+ 
+
+ align:start position:0%
+process about the space shuttle
+design as we did the initial design we
+
+ align:start position:0%
+design as we did the initial design we
+ 
+
+ align:start position:0%
+design as we did the initial design we
+wanted an escape
+
+ align:start position:0%
+wanted an escape
+ 
+
+ align:start position:0%
+wanted an escape
+system we wanted to build a pod
+
+ align:start position:0%
+system we wanted to build a pod
+ 
+
+ align:start position:0%
+system we wanted to build a pod
+into the uh cockpit to allow the
+
+ align:start position:0%
+into the uh cockpit to allow the
+ 
+
+ align:start position:0%
+into the uh cockpit to allow the
+astronauts to escape if we had problems
+
+ align:start position:0%
+astronauts to escape if we had problems
+ 
+
+ align:start position:0%
+astronauts to escape if we had problems
+and because the building the sh space
+
+ align:start position:0%
+and because the building the sh space
+ 
+
+ align:start position:0%
+and because the building the sh space
+shuttle main engine was very
+
+ align:start position:0%
+shuttle main engine was very
+ 
+
+ align:start position:0%
+shuttle main engine was very
+difficult these people know about subn
+
+ align:start position:0%
+difficult these people know about subn
+ 
+
+ align:start position:0%
+difficult these people know about subn
+Subs synchronous
+
+ align:start position:0%
+Subs synchronous
+ 
+
+ align:start position:0%
+Subs synchronous
+world uh you couldn't we couldn't find
+
+ align:start position:0%
+world uh you couldn't we couldn't find
+ 
+
+ align:start position:0%
+world uh you couldn't we couldn't find
+any berries in the world that would
+
+ align:start position:0%
+any berries in the world that would
+ 
+
+ align:start position:0%
+any berries in the world that would
+withstand that load they were they were
+
+ align:start position:0%
+withstand that load they were they were
+ 
+
+ align:start position:0%
+withstand that load they were they were
+failing and you didn't know when they
+
+ align:start position:0%
+failing and you didn't know when they
+ 
+
+ align:start position:0%
+failing and you didn't know when they
+were going to fail so we had we built a
+
+ align:start position:0%
+were going to fail so we had we built a
+ 
+
+ align:start position:0%
+were going to fail so we had we built a
+uh automatic shutdown system into the uh
+
+ align:start position:0%
+uh automatic shutdown system into the uh
+ 
+
+ align:start position:0%
+uh automatic shutdown system into the uh
+engine and the auto that's eron and I
+
+ align:start position:0%
+engine and the auto that's eron and I
+ 
+
+ align:start position:0%
+engine and the auto that's eron and I
+were talking about that this morning Mr
+
+ align:start position:0%
+were talking about that this morning Mr
+ 
+
+ align:start position:0%
+were talking about that this morning Mr
+Cen Professor Cohen and uh you know that
+
+ align:start position:0%
+Cen Professor Cohen and uh you know that
+ 
+
+ align:start position:0%
+Cen Professor Cohen and uh you know that
+that sounds well we'll just figure out
+
+ align:start position:0%
+that sounds well we'll just figure out
+ 
+
+ align:start position:0%
+that sounds well we'll just figure out
+what all the parameters are that tell
+
+ align:start position:0%
+what all the parameters are that tell
+ 
+
+ align:start position:0%
+what all the parameters are that tell
+you when the engine is malfunctioning
+
+ align:start position:0%
+you when the engine is malfunctioning
+ 
+
+ align:start position:0%
+you when the engine is malfunctioning
+and shut it down because we don't want
+
+ align:start position:0%
+and shut it down because we don't want
+ 
+
+ align:start position:0%
+and shut it down because we don't want
+it to blow up so we're going to look at
+
+ align:start position:0%
+it to blow up so we're going to look at
+ 
+
+ align:start position:0%
+it to blow up so we're going to look at
+RPM of the pumps and we're going to look
+
+ align:start position:0%
+RPM of the pumps and we're going to look
+ 
+
+ align:start position:0%
+RPM of the pumps and we're going to look
+at temperature in the so going to look
+
+ align:start position:0%
+at temperature in the so going to look
+ 
+
+ align:start position:0%
+at temperature in the so going to look
+at the pressure in the in the in the
+
+ align:start position:0%
+at the pressure in the in the in the
+ 
+
+ align:start position:0%
+at the pressure in the in the in the
+engine head and we're going to look at
+
+ align:start position:0%
+engine head and we're going to look at
+ 
+
+ align:start position:0%
+engine head and we're going to look at
+the fuel flow rates etc etc that sounds
+
+ align:start position:0%
+the fuel flow rates etc etc that sounds
+ 
+
+ align:start position:0%
+the fuel flow rates etc etc that sounds
+like well we could do that but how do
+
+ align:start position:0%
+like well we could do that but how do
+ 
+
+ align:start position:0%
+like well we could do that but how do
+you know it's
+
+ align:start position:0%
+you know it's
+ 
+
+ align:start position:0%
+you know it's
+right how do you know you're not
+
+ align:start position:0%
+right how do you know you're not
+ 
+
+ align:start position:0%
+right how do you know you're not
+shutting down a good engine and the
+
+ align:start position:0%
+shutting down a good engine and the
+ 
+
+ align:start position:0%
+shutting down a good engine and the
+point I'm making there is the
+
+ align:start position:0%
+point I'm making there is the
+ 
+
+ align:start position:0%
+point I'm making there is the
+reliability of the instrument becomes
+
+ align:start position:0%
+reliability of the instrument becomes
+ 
+
+ align:start position:0%
+reliability of the instrument becomes
+more important than the
+
+ align:start position:0%
+more important than the
+ 
+
+ align:start position:0%
+more important than the
+engine think about that so you can well
+
+ align:start position:0%
+engine think about that so you can well
+ 
+
+ align:start position:0%
+engine think about that so you can well
+I'll have I'll have an automatic shut
+
+ align:start position:0%
+I'll have I'll have an automatic shut
+ 
+
+ align:start position:0%
+I'll have I'll have an automatic shut
+down have the automatic abort get it get
+
+ align:start position:0%
+down have the automatic abort get it get
+ 
+
+ align:start position:0%
+down have the automatic abort get it get
+the astronaut away but you got to some
+
+ align:start position:0%
+the astronaut away but you got to some
+ 
+
+ align:start position:0%
+the astronaut away but you got to some
+something's got to make that decision
+
+ align:start position:0%
+something's got to make that decision
+ 
+
+ align:start position:0%
+something's got to make that decision
+nobody on the ground can do it fast
+
+ align:start position:0%
+nobody on the ground can do it fast
+ 
+
+ align:start position:0%
+nobody on the ground can do it fast
+enough Dr if the engine's going to blow
+
+ align:start position:0%
+enough Dr if the engine's going to blow
+ 
+
+ align:start position:0%
+enough Dr if the engine's going to blow
+up astronaut can't do it his reaction
+
+ align:start position:0%
+up astronaut can't do it his reaction
+ 
+
+ align:start position:0%
+up astronaut can't do it his reaction
+time is about one and a half seconds no
+
+ align:start position:0%
+time is about one and a half seconds no
+ 
+
+ align:start position:0%
+time is about one and a half seconds no
+matter how much data you give him or how
+
+ align:start position:0%
+matter how much data you give him or how
+ 
+
+ align:start position:0%
+matter how much data you give him or how
+good the data is so it's got to be
+
+ align:start position:0%
+good the data is so it's got to be
+ 
+
+ align:start position:0%
+good the data is so it's got to be
+automatic and that's a that's a very
+
+ align:start position:0%
+automatic and that's a that's a very
+ 
+
+ align:start position:0%
+automatic and that's a that's a very
+difficult task for an engineer he can
+
+ align:start position:0%
+difficult task for an engineer he can
+ 
+
+ align:start position:0%
+difficult task for an engineer he can
+make the system work
+
+ align:start position:0%
+make the system work
+ 
+
+ align:start position:0%
+make the system work
+but he can't tell you very
+
+ align:start position:0%
+but he can't tell you very
+ 
+
+ align:start position:0%
+but he can't tell you very
+rapidly when it's going to
+
+ align:start position:0%
+rapidly when it's going to
+ 
+
+ align:start position:0%
+rapidly when it's going to
+fail and and Rocket engines have a bad
+
+ align:start position:0%
+fail and and Rocket engines have a bad
+ 
+
+ align:start position:0%
+fail and and Rocket engines have a bad
+nasty habit of going like that and it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gone you got to figure out when that's
+
+ align:start position:0%
+gone you got to figure out when that's
+ 
+
+ align:start position:0%
+gone you got to figure out when that's
+going to happen so designing
+
+ align:start position:0%
+going to happen so designing
+ 
+
+ align:start position:0%
+going to happen so designing
+instrumentation to do that we then
+
+ align:start position:0%
+instrumentation to do that we then
+ 
+
+ align:start position:0%
+instrumentation to do that we then
+started thinking about that in
+
+ align:start position:0%
+started thinking about that in
+ 
+
+ align:start position:0%
+started thinking about that in
+application to the Space
+
+ align:start position:0%
+application to the Space
+ 
+
+ align:start position:0%
+application to the Space
+Shuttle and as our our experience with
+
+ align:start position:0%
+Shuttle and as our our experience with
+ 
+
+ align:start position:0%
+Shuttle and as our our experience with
+redundancy reliability numbers thinking
+
+ align:start position:0%
+redundancy reliability numbers thinking
+ 
+
+ align:start position:0%
+redundancy reliability numbers thinking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that we said we want a system in the
+
+ align:start position:0%
+that we said we want a system in the
+ 
+
+ align:start position:0%
+that we said we want a system in the
+shuttle that's going to be fail
+
+ align:start position:0%
+shuttle that's going to be fail
+ 
+
+ align:start position:0%
+shuttle that's going to be fail
+operational fail
+
+ align:start position:0%
+operational fail
+ 
+
+ align:start position:0%
+operational fail
+operational fail
+
+ align:start position:0%
+operational fail
+ 
+
+ align:start position:0%
+operational fail
+safe that's quad
+
+ align:start position:0%
+safe that's quad
+ 
+
+ align:start position:0%
+safe that's quad
+redundancy so every critical
+
+ align:start position:0%
+redundancy so every critical
+ 
+
+ align:start position:0%
+redundancy so every critical
+system has quad redundancy in the space
+
+ align:start position:0%
+system has quad redundancy in the space
+ 
+
+ align:start position:0%
+system has quad redundancy in the space
+shuttle that sounds like a good idea
+
+ align:start position:0%
+shuttle that sounds like a good idea
+ 
+
+ align:start position:0%
+shuttle that sounds like a good idea
+doesn't it come back to that in a
+
+ align:start position:0%
+doesn't it come back to that in a
+ 
+
+ align:start position:0%
+doesn't it come back to that in a
+minute we said we would like to have a
+
+ align:start position:0%
+minute we said we would like to have a
+ 
+
+ align:start position:0%
+minute we said we would like to have a
+Escape
+
+ align:start position:0%
+Escape
+ 
+
+ align:start position:0%
+Escape
+pod but the Escape pod has got to have a
+
+ align:start position:0%
+pod but the Escape pod has got to have a
+ 
+
+ align:start position:0%
+pod but the Escape pod has got to have a
+stability and control system it's got to
+
+ align:start position:0%
+stability and control system it's got to
+ 
+
+ align:start position:0%
+stability and control system it's got to
+have a control system because it's going
+
+ align:start position:0%
+have a control system because it's going
+ 
+
+ align:start position:0%
+have a control system because it's going
+to be a spacecraft when is it going to
+
+ align:start position:0%
+to be a spacecraft when is it going to
+ 
+
+ align:start position:0%
+to be a spacecraft when is it going to
+use the Pod is the Pod going to be used
+
+ align:start position:0%
+use the Pod is the Pod going to be used
+ 
+
+ align:start position:0%
+use the Pod is the Pod going to be used
+at 100 feet off the pad 100,000 ft off
+
+ align:start position:0%
+at 100 feet off the pad 100,000 ft off
+ 
+
+ align:start position:0%
+at 100 feet off the pad 100,000 ft off
+the pad
+
+ align:start position:0%
+the pad
+ 
+
+ align:start position:0%
+the pad
+500,000 ft off the
+
+ align:start position:0%
+500,000 ft off the
+ 
+
+ align:start position:0%
+500,000 ft off the
+path and if this thing is descending
+
+ align:start position:0%
+path and if this thing is descending
+ 
+
+ align:start position:0%
+path and if this thing is descending
+from any one of those altitudes how are
+
+ align:start position:0%
+from any one of those altitudes how are
+ 
+
+ align:start position:0%
+from any one of those altitudes how are
+you going to control
+
+ align:start position:0%
+you going to control
+ 
+
+ align:start position:0%
+you going to control
+it very rapidly that's another
+
+ align:start position:0%
+it very rapidly that's another
+ 
+
+ align:start position:0%
+it very rapidly that's another
+spacecraft it's probably a bigger job in
+
+ align:start position:0%
+spacecraft it's probably a bigger job in
+ 
+
+ align:start position:0%
+spacecraft it's probably a bigger job in
+building that spacecraft than building
+
+ align:start position:0%
+building that spacecraft than building
+ 
+
+ align:start position:0%
+building that spacecraft than building
+the space shuttle
+
+ align:start position:0%
+the space shuttle
+ 
+
+ align:start position:0%
+the space shuttle
+itself so you can see why we didn't do
+
+ align:start position:0%
+itself so you can see why we didn't do
+ 
+
+ align:start position:0%
+itself so you can see why we didn't do
+it too tough too big a
+
+ align:start position:0%
+it too tough too big a
+ 
+
+ align:start position:0%
+it too tough too big a
+job we said we'd like to have a go round
+
+ align:start position:0%
+job we said we'd like to have a go round
+ 
+
+ align:start position:0%
+job we said we'd like to have a go round
+capability on this
+
+ align:start position:0%
+capability on this
+ 
+
+ align:start position:0%
+capability on this
+machine uh it's going to have a l of
+
+ align:start position:0%
+machine uh it's going to have a l of
+ 
+
+ align:start position:0%
+machine uh it's going to have a l of
+about four to five at the at best and
+
+ align:start position:0%
+about four to five at the at best and
+ 
+
+ align:start position:0%
+about four to five at the at best and
+The Descent angle that you come that you
+
+ align:start position:0%
+The Descent angle that you come that you
+ 
+
+ align:start position:0%
+The Descent angle that you come that you
+come down to land is 23
+
+ align:start position:0%
+come down to land is 23
+ 
+
+ align:start position:0%
+come down to land is 23
+degrees let me tell you something I have
+
+ align:start position:0%
+degrees let me tell you something I have
+ 
+
+ align:start position:0%
+degrees let me tell you something I have
+flown in a Gulf Stream 2 on a 23 degree
+
+ align:start position:0%
+flown in a Gulf Stream 2 on a 23 degree
+ 
+
+ align:start position:0%
+flown in a Gulf Stream 2 on a 23 degree
+descent trajectory and that is scary as
+
+ align:start position:0%
+descent trajectory and that is scary as
+ 
+
+ align:start position:0%
+descent trajectory and that is scary as
+hell you're flying a
+
+ align:start position:0%
+hell you're flying a
+ 
+
+ align:start position:0%
+hell you're flying a
+that machine is coming down like that
+
+ align:start position:0%
+that machine is coming down like that
+ 
+
+ align:start position:0%
+that machine is coming down like that
+and you're you've got you're hanging on
+
+ align:start position:0%
+and you're you've got you're hanging on
+ 
+
+ align:start position:0%
+and you're you've got you're hanging on
+your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+straps so we'd like to be able to have a
+
+ align:start position:0%
+straps so we'd like to be able to have a
+ 
+
+ align:start position:0%
+straps so we'd like to be able to have a
+go around capability so okay we'll put
+
+ align:start position:0%
+go around capability so okay we'll put
+ 
+
+ align:start position:0%
+go around capability so okay we'll put
+some jet engines on it it's got to have
+
+ align:start position:0%
+some jet engines on it it's got to have
+ 
+
+ align:start position:0%
+some jet engines on it it's got to have
+fuel it's got to have a tank I got a
+
+ align:start position:0%
+fuel it's got to have a tank I got a
+ 
+
+ align:start position:0%
+fuel it's got to have a tank I got a
+lines on it got to have a certain amount
+
+ align:start position:0%
+lines on it got to have a certain amount
+ 
+
+ align:start position:0%
+lines on it got to have a certain amount
+of redundancy with it certain amount of
+
+ align:start position:0%
+of redundancy with it certain amount of
+ 
+
+ align:start position:0%
+of redundancy with it certain amount of
+power it's got to be absorbed into the
+
+ align:start position:0%
+power it's got to be absorbed into the
+ 
+
+ align:start position:0%
+power it's got to be absorbed into the
+thermal protection system and come out
+
+ align:start position:0%
+thermal protection system and come out
+ 
+
+ align:start position:0%
+thermal protection system and come out
+extend when I want to do this go around
+
+ align:start position:0%
+extend when I want to do this go around
+ 
+
+ align:start position:0%
+extend when I want to do this go around
+as I'm reentering some space so I can go
+
+ align:start position:0%
+as I'm reentering some space so I can go
+ 
+
+ align:start position:0%
+as I'm reentering some space so I can go
+once around the the runway and
+
+ align:start position:0%
+once around the the runway and
+ 
+
+ align:start position:0%
+once around the the runway and
+land it didn't take us long to figure
+
+ align:start position:0%
+land it didn't take us long to figure
+ 
+
+ align:start position:0%
+land it didn't take us long to figure
+out if we built that system we couldn't
+
+ align:start position:0%
+out if we built that system we couldn't
+ 
+
+ align:start position:0%
+out if we built that system we couldn't
+carry a damn pound into
+
+ align:start position:0%
+carry a damn pound into
+ 
+
+ align:start position:0%
+carry a damn pound into
+orbit there went our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+payload and we very rapidly started
+
+ align:start position:0%
+payload and we very rapidly started
+ 
+
+ align:start position:0%
+payload and we very rapidly started
+figuring how to do Ted Dead stick
+
+ align:start position:0%
+figuring how to do Ted Dead stick
+ 
+
+ align:start position:0%
+figuring how to do Ted Dead stick
+Landings and how to preserve the energy
+
+ align:start position:0%
+Landings and how to preserve the energy
+ 
+
+ align:start position:0%
+Landings and how to preserve the energy
+and how to get this machine lined up on
+
+ align:start position:0%
+and how to get this machine lined up on
+ 
+
+ align:start position:0%
+and how to get this machine lined up on
+the runway at way high altitudes and etc
+
+ align:start position:0%
+the runway at way high altitudes and etc
+ 
+
+ align:start position:0%
+the runway at way high altitudes and etc
+etc so we did away with the gound
+
+ align:start position:0%
+etc so we did away with the gound
+ 
+
+ align:start position:0%
+etc so we did away with the gound
+capability we've done away with the Pod
+
+ align:start position:0%
+capability we've done away with the Pod
+ 
+
+ align:start position:0%
+capability we've done away with the Pod
+done away with the go around capability
+
+ align:start position:0%
+done away with the go around capability
+ 
+
+ align:start position:0%
+done away with the go around capability
+now we don't have an escape
+
+ align:start position:0%
+now we don't have an escape
+ 
+
+ align:start position:0%
+now we don't have an escape
+system what is your Escape system on the
+
+ align:start position:0%
+system what is your Escape system on the
+ 
+
+ align:start position:0%
+system what is your Escape system on the
+shuttle well on Mercury and Apollo the
+
+ align:start position:0%
+shuttle well on Mercury and Apollo the
+ 
+
+ align:start position:0%
+shuttle well on Mercury and Apollo the
+Escape system is a solid rocket
+
+ align:start position:0%
+Escape system is a solid rocket
+ 
+
+ align:start position:0%
+Escape system is a solid rocket
+solid Rockets
+
+ align:start position:0%
+solid Rockets
+ 
+
+ align:start position:0%
+solid Rockets
+have close to 100% reliability as you
+
+ align:start position:0%
+have close to 100% reliability as you
+ 
+
+ align:start position:0%
+have close to 100% reliability as you
+can get usually if you if it lights it
+
+ align:start position:0%
+can get usually if you if it lights it
+ 
+
+ align:start position:0%
+can get usually if you if it lights it
+burns and it
+
+ align:start position:0%
+burns and it
+ 
+
+ align:start position:0%
+burns and it
+goes God we got two solid rockets on the
+
+ align:start position:0%
+goes God we got two solid rockets on the
+ 
+
+ align:start position:0%
+goes God we got two solid rockets on the
+shuttle why aren't they our Escape
+
+ align:start position:0%
+shuttle why aren't they our Escape
+ 
+
+ align:start position:0%
+shuttle why aren't they our Escape
+system because if we can get this thing
+
+ align:start position:0%
+system because if we can get this thing
+ 
+
+ align:start position:0%
+system because if we can get this thing
+to 200,000 ft it'll
+
+ align:start position:0%
+to 200,000 ft it'll
+ 
+
+ align:start position:0%
+to 200,000 ft it'll
+fly so we can return to the launch site
+
+ align:start position:0%
+fly so we can return to the launch site
+ 
+
+ align:start position:0%
+fly so we can return to the launch site
+and land from 200,000 feet because you
+
+ align:start position:0%
+and land from 200,000 feet because you
+ 
+
+ align:start position:0%
+and land from 200,000 feet because you
+very far down range at 200,000 ft God
+
+ align:start position:0%
+very far down range at 200,000 ft God
+ 
+
+ align:start position:0%
+very far down range at 200,000 ft God
+that's a good
+
+ align:start position:0%
+that's a good
+ 
+
+ align:start position:0%
+that's a good
+idea great
+
+ align:start position:0%
+idea great
+ 
+
+ align:start position:0%
+idea great
+idea but the Rockets have to be 100%
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reliable wasn't 100% reliable on the
+
+ align:start position:0%
+reliable wasn't 100% reliable on the
+ 
+
+ align:start position:0%
+reliable wasn't 100% reliable on the
+Challenger
+
+ align:start position:0%
+Challenger
+ 
+
+ align:start position:0%
+Challenger
+accident I can't account I can't
+
+ align:start position:0%
+accident I can't account I can't
+ 
+
+ align:start position:0%
+accident I can't account I can't
+account unfortunately I cannot account
+
+ align:start position:0%
+account unfortunately I cannot account
+ 
+
+ align:start position:0%
+account unfortunately I cannot account
+for the fallacies of man
+
+ align:start position:0%
+for the fallacies of man
+ 
+
+ align:start position:0%
+for the fallacies of man
+I'll come back to that if you want me to
+
+ align:start position:0%
+I'll come back to that if you want me to
+ 
+
+ align:start position:0%
+I'll come back to that if you want me to
+talk about the Char tracks but we built
+
+ align:start position:0%
+talk about the Char tracks but we built
+ 
+
+ align:start position:0%
+talk about the Char tracks but we built
+the solid Rockets to have 100%
+
+ align:start position:0%
+the solid Rockets to have 100%
+ 
+
+ align:start position:0%
+the solid Rockets to have 100%
+reliability and they were our Escape
+
+ align:start position:0%
+reliability and they were our Escape
+ 
+
+ align:start position:0%
+reliability and they were our Escape
+rocket so we've got quad
+
+ align:start position:0%
+rocket so we've got quad
+ 
+
+ align:start position:0%
+rocket so we've got quad
+redundancy we've
+
+ align:start position:0%
+redundancy we've
+ 
+
+ align:start position:0%
+redundancy we've
+got uh engines that will perform to the
+
+ align:start position:0%
+got uh engines that will perform to the
+ 
+
+ align:start position:0%
+got uh engines that will perform to the
+best of our ability and shut down if
+
+ align:start position:0%
+best of our ability and shut down if
+ 
+
+ align:start position:0%
+best of our ability and shut down if
+they are going to explode we got solid
+
+ align:start position:0%
+they are going to explode we got solid
+ 
+
+ align:start position:0%
+they are going to explode we got solid
+Rockets as a as a Escape system
+
+ align:start position:0%
+Rockets as a as a Escape system
+ 
+
+ align:start position:0%
+Rockets as a as a Escape system
+and we will teach the pilots with the
+
+ align:start position:0%
+and we will teach the pilots with the
+ 
+
+ align:start position:0%
+and we will teach the pilots with the
+best control system we can come up with
+
+ align:start position:0%
+best control system we can come up with
+ 
+
+ align:start position:0%
+best control system we can come up with
+to land this machine Dead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stick now we got to convince ourselves
+
+ align:start position:0%
+stick now we got to convince ourselves
+ 
+
+ align:start position:0%
+stick now we got to convince ourselves
+and the management that the best way to
+
+ align:start position:0%
+and the management that the best way to
+ 
+
+ align:start position:0%
+and the management that the best way to
+fly this thing is
+
+ align:start position:0%
+fly this thing is
+ 
+
+ align:start position:0%
+fly this thing is
+unmaned or manned on the first
+
+ align:start position:0%
+unmaned or manned on the first
+ 
+
+ align:start position:0%
+unmaned or manned on the first
+flight and we looked at flying unmanned
+
+ align:start position:0%
+flight and we looked at flying unmanned
+ 
+
+ align:start position:0%
+flight and we looked at flying unmanned
+we could have done that we could have
+
+ align:start position:0%
+we could have done that we could have
+ 
+
+ align:start position:0%
+we could have done that we could have
+put an automatic control system in to
+
+ align:start position:0%
+put an automatic control system in to
+ 
+
+ align:start position:0%
+put an automatic control system in to
+take the place of the man and these
+
+ align:start position:0%
+take the place of the man and these
+ 
+
+ align:start position:0%
+take the place of the man and these
+Pilots that tell
+
+ align:start position:0%
+Pilots that tell
+ 
+
+ align:start position:0%
+Pilots that tell
+you they do manual control during
+
+ align:start position:0%
+you they do manual control during
+ 
+
+ align:start position:0%
+you they do manual control during
+re-entry in the
+
+ align:start position:0%
+re-entry in the
+ 
+
+ align:start position:0%
+re-entry in the
+shuttle
+
+ align:start position:0%
+shuttle
+ 
+
+ align:start position:0%
+shuttle
+hogwash pure hogwash the shuttle will
+
+ align:start position:0%
+hogwash pure hogwash the shuttle will
+ 
+
+ align:start position:0%
+hogwash pure hogwash the shuttle will
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+fly without the automatic control system
+
+ align:start position:0%
+fly without the automatic control system
+ 
+
+ align:start position:0%
+fly without the automatic control system
+the pilots are flying the Outer
+
+ align:start position:0%
+the pilots are flying the Outer
+ 
+
+ align:start position:0%
+the pilots are flying the Outer
+Loop I can fly it I have flown it in the
+
+ align:start position:0%
+Loop I can fly it I have flown it in the
+ 
+
+ align:start position:0%
+Loop I can fly it I have flown it in the
+simulator you know how I do it I don't
+
+ align:start position:0%
+simulator you know how I do it I don't
+ 
+
+ align:start position:0%
+simulator you know how I do it I don't
+touch the damn thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I set you know you set the damn end of
+
+ align:start position:0%
+I set you know you set the damn end of
+ 
+
+ align:start position:0%
+I set you know you set the damn end of
+the runway into the
+
+ align:start position:0%
+the runway into the
+ 
+
+ align:start position:0%
+the runway into the
+computer right down and that's the way
+
+ align:start position:0%
+computer right down and that's the way
+ 
+
+ align:start position:0%
+computer right down and that's the way
+95% of the airliners land today is on
+
+ align:start position:0%
+95% of the airliners land today is on
+ 
+
+ align:start position:0%
+95% of the airliners land today is on
+automatic control and frankly that's how
+
+ align:start position:0%
+automatic control and frankly that's how
+ 
+
+ align:start position:0%
+automatic control and frankly that's how
+the astronauts ought to do it haven't
+
+ align:start position:0%
+the astronauts ought to do it haven't
+ 
+
+ align:start position:0%
+the astronauts ought to do it haven't
+done it yet they keep telling me what
+
+ align:start position:0%
+done it yet they keep telling me what
+ 
+
+ align:start position:0%
+done it yet they keep telling me what
+are we going to do if the system fails
+
+ align:start position:0%
+are we going to do if the system fails
+ 
+
+ align:start position:0%
+are we going to do if the system fails
+and I say to you're going to wind your
+
+ align:start position:0%
+and I say to you're going to wind your
+ 
+
+ align:start position:0%
+and I say to you're going to wind your
+damn clock because that system fails the
+
+ align:start position:0%
+damn clock because that system fails the
+ 
+
+ align:start position:0%
+damn clock because that system fails the
+thing is gone it's an unstable
+
+ align:start position:0%
+thing is gone it's an unstable
+ 
+
+ align:start position:0%
+thing is gone it's an unstable
+machine from Mach
+
+ align:start position:0%
+machine from Mach
+ 
+
+ align:start position:0%
+machine from Mach
+25 to touchdown it's an unstable
+
+ align:start position:0%
+25 to touchdown it's an unstable
+ 
+
+ align:start position:0%
+25 to touchdown it's an unstable
+machine if it diverges it's
+
+ align:start position:0%
+machine if it diverges it's
+ 
+
+ align:start position:0%
+machine if it diverges it's
+gone so probably tell you they doing
+
+ align:start position:0%
+gone so probably tell you they doing
+ 
+
+ align:start position:0%
+gone so probably tell you they doing
+manual entry on the space shuttle I
+
+ align:start position:0%
+manual entry on the space shuttle I
+ 
+
+ align:start position:0%
+manual entry on the space shuttle I
+repeat that statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hogwash can be
+
+ align:start position:0%
+hogwash can be
+ 
+
+ align:start position:0%
+hogwash can be
+done now can teach them however by
+
+ align:start position:0%
+done now can teach them however by
+ 
+
+ align:start position:0%
+done now can teach them however by
+building a Gulf Stream two
+
+ align:start position:0%
+building a Gulf Stream two
+ 
+
+ align:start position:0%
+building a Gulf Stream two
+into a space shuttle like vehicle I can
+
+ align:start position:0%
+into a space shuttle like vehicle I can
+ 
+
+ align:start position:0%
+into a space shuttle like vehicle I can
+put the control system that they've got
+
+ align:start position:0%
+put the control system that they've got
+ 
+
+ align:start position:0%
+put the control system that they've got
+in there I can repeat that I can make it
+
+ align:start position:0%
+in there I can repeat that I can make it
+ 
+
+ align:start position:0%
+in there I can repeat that I can make it
+come down I can put reverse thrust you
+
+ align:start position:0%
+come down I can put reverse thrust you
+ 
+
+ align:start position:0%
+come down I can put reverse thrust you
+believe on both engines and a G2 and
+
+ align:start position:0%
+believe on both engines and a G2 and
+ 
+
+ align:start position:0%
+believe on both engines and a G2 and
+you're descending and you got both those
+
+ align:start position:0%
+you're descending and you got both those
+ 
+
+ align:start position:0%
+you're descending and you got both those
+damn engines back there going like that
+
+ align:start position:0%
+damn engines back there going like that
+ 
+
+ align:start position:0%
+damn engines back there going like that
+as it does its reverse thrust to match
+
+ align:start position:0%
+as it does its reverse thrust to match
+ 
+
+ align:start position:0%
+as it does its reverse thrust to match
+the drag of the shuttle entry but I can
+
+ align:start position:0%
+the drag of the shuttle entry but I can
+ 
+
+ align:start position:0%
+the drag of the shuttle entry but I can
+teach them pretty well how to do Dead
+
+ align:start position:0%
+teach them pretty well how to do Dead
+ 
+
+ align:start position:0%
+teach them pretty well how to do Dead
+stick Landings and so I put all that
+
+ align:start position:0%
+stick Landings and so I put all that
+ 
+
+ align:start position:0%
+stick Landings and so I put all that
+together and Mr Cohen and Professor
+
+ align:start position:0%
+together and Mr Cohen and Professor
+ 
+
+ align:start position:0%
+together and Mr Cohen and Professor
+Cohen and uh myself and a few others go
+
+ align:start position:0%
+Cohen and uh myself and a few others go
+ 
+
+ align:start position:0%
+Cohen and uh myself and a few others go
+to Washington to convinc the powers that
+
+ align:start position:0%
+to Washington to convinc the powers that
+ 
+
+ align:start position:0%
+to Washington to convinc the powers that
+be that we can fly this machine man on
+
+ align:start position:0%
+be that we can fly this machine man on
+ 
+
+ align:start position:0%
+be that we can fly this machine man on
+the first flight because it is the most
+
+ align:start position:0%
+the first flight because it is the most
+ 
+
+ align:start position:0%
+the first flight because it is the most
+reliable way to fly machine and we
+
+ align:start position:0%
+reliable way to fly machine and we
+ 
+
+ align:start position:0%
+reliable way to fly machine and we
+convinced them it took a little
+
+ align:start position:0%
+convinced them it took a little
+ 
+
+ align:start position:0%
+convinced them it took a little
+doing a lot fancy talking I guess but
+
+ align:start position:0%
+doing a lot fancy talking I guess but
+ 
+
+ align:start position:0%
+doing a lot fancy talking I guess but
+that's what we decided to do and I think
+
+ align:start position:0%
+that's what we decided to do and I think
+ 
+
+ align:start position:0%
+that's what we decided to do and I think
+it was a good decision in
+
+ align:start position:0%
+it was a good decision in
+ 
+
+ align:start position:0%
+it was a good decision in
+retrospect it was a lousy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decision
+
+ align:start position:0%
+decision
+ 
+
+ align:start position:0%
+decision
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+because if we had had unmanned flying
+
+ align:start position:0%
+because if we had had unmanned flying
+ 
+
+ align:start position:0%
+because if we had had unmanned flying
+capability on the orbit and we had to
+
+ align:start position:0%
+capability on the orbit and we had to
+ 
+
+ align:start position:0%
+capability on the orbit and we had to
+challenge your
+
+ align:start position:0%
+challenge your
+ 
+
+ align:start position:0%
+challenge your
+accident we could have flown it again
+
+ align:start position:0%
+accident we could have flown it again
+ 
+
+ align:start position:0%
+accident we could have flown it again
+the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+day with an unmaned control
+
+ align:start position:0%
+day with an unmaned control
+ 
+
+ align:start position:0%
+day with an unmaned control
+system and
+
+ align:start position:0%
+system and
+ 
+
+ align:start position:0%
+system and
+proved that it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but we didn't have that
+
+ align:start position:0%
+okay but we didn't have that
+ 
+
+ align:start position:0%
+okay but we didn't have that
+capability and when you get into the
+
+ align:start position:0%
+capability and when you get into the
+ 
+
+ align:start position:0%
+capability and when you get into the
+politics of flying men in space in this
+
+ align:start position:0%
+politics of flying men in space in this
+ 
+
+ align:start position:0%
+politics of flying men in space in this
+country rational thinking does not carry
+
+ align:start position:0%
+country rational thinking does not carry
+ 
+
+ align:start position:0%
+country rational thinking does not carry
+the day political thinking carries the
+
+ align:start position:0%
+the day political thinking carries the
+ 
+
+ align:start position:0%
+the day political thinking carries the
+day even in nass you'll find that out as
+
+ align:start position:0%
+day even in nass you'll find that out as
+ 
+
+ align:start position:0%
+day even in nass you'll find that out as
+young Engineers also
+
+ align:start position:0%
+young Engineers also
+ 
+
+ align:start position:0%
+young Engineers also
+that you not only have to be an engineer
+
+ align:start position:0%
+that you not only have to be an engineer
+ 
+
+ align:start position:0%
+that you not only have to be an engineer
+you do have to be somewhat of a
+
+ align:start position:0%
+you do have to be somewhat of a
+ 
+
+ align:start position:0%
+you do have to be somewhat of a
+politician in order to sell your
+
+ align:start position:0%
+politician in order to sell your
+ 
+
+ align:start position:0%
+politician in order to sell your
+programs
+
+ align:start position:0%
+programs
+ 
+
+ align:start position:0%
+programs
+so we convinced
+
+ align:start position:0%
+so we convinced
+ 
+
+ align:start position:0%
+so we convinced
+ourselves
+
+ align:start position:0%
+ourselves
+ 
+
+ align:start position:0%
+ourselves
+that it was the best thing to do at that
+
+ align:start position:0%
+that it was the best thing to do at that
+ 
+
+ align:start position:0%
+that it was the best thing to do at that
+time to fly man on the first flight
+
+ align:start position:0%
+time to fly man on the first flight
+ 
+
+ align:start position:0%
+time to fly man on the first flight
+uh because it's in my head and it comes
+
+ align:start position:0%
+uh because it's in my head and it comes
+ 
+
+ align:start position:0%
+uh because it's in my head and it comes
+out I I want to say a little bit about
+
+ align:start position:0%
+out I I want to say a little bit about
+ 
+
+ align:start position:0%
+out I I want to say a little bit about
+the problems that they face
+
+ align:start position:0%
+the problems that they face
+ 
+
+ align:start position:0%
+the problems that they face
+today or the way in which they use the
+
+ align:start position:0%
+today or the way in which they use the
+ 
+
+ align:start position:0%
+today or the way in which they use the
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+shuttle today is
+
+ align:start position:0%
+shuttle today is
+ 
+
+ align:start position:0%
+shuttle today is
+frankly not how we intended the machine
+
+ align:start position:0%
+frankly not how we intended the machine
+ 
+
+ align:start position:0%
+frankly not how we intended the machine
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+fly we have quad
+
+ align:start position:0%
+fly we have quad
+ 
+
+ align:start position:0%
+fly we have quad
+redundancy and the way Nasa uses it
+
+ align:start position:0%
+redundancy and the way Nasa uses it
+ 
+
+ align:start position:0%
+redundancy and the way Nasa uses it
+makes it less
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reliable than if we had just had a damn
+
+ align:start position:0%
+reliable than if we had just had a damn
+ 
+
+ align:start position:0%
+reliable than if we had just had a damn
+single string system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why because they have to have all quad
+
+ align:start position:0%
+why because they have to have all quad
+ 
+
+ align:start position:0%
+why because they have to have all quad
+redundant systems working at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+liftoff so all four systems have to be
+
+ align:start position:0%
+liftoff so all four systems have to be
+ 
+
+ align:start position:0%
+liftoff so all four systems have to be
+operating at lift off that's
+
+ align:start position:0%
+operating at lift off that's
+ 
+
+ align:start position:0%
+operating at lift off that's
+hard it's hard enough to have one
+
+ align:start position:0%
+hard it's hard enough to have one
+ 
+
+ align:start position:0%
+hard it's hard enough to have one
+operating properly now you have to have
+
+ align:start position:0%
+operating properly now you have to have
+ 
+
+ align:start position:0%
+operating properly now you have to have
+all four in all of the places where you
+
+ align:start position:0%
+all four in all of the places where you
+ 
+
+ align:start position:0%
+all four in all of the places where you
+have quad
+
+ align:start position:0%
+have quad
+ 
+
+ align:start position:0%
+have quad
+redundancy that isn't how we intended it
+
+ align:start position:0%
+redundancy that isn't how we intended it
+ 
+
+ align:start position:0%
+redundancy that isn't how we intended it
+to to work what we intended to do was
+
+ align:start position:0%
+to to work what we intended to do was
+ 
+
+ align:start position:0%
+to to work what we intended to do was
+you to the pad and get ready to launch
+
+ align:start position:0%
+you to the pad and get ready to launch
+ 
+
+ align:start position:0%
+you to the pad and get ready to launch
+and one system fails you keep right on
+
+ align:start position:0%
+and one system fails you keep right on
+ 
+
+ align:start position:0%
+and one system fails you keep right on
+going if you have two fail you keep
+
+ align:start position:0%
+going if you have two fail you keep
+ 
+
+ align:start position:0%
+going if you have two fail you keep
+right on
+
+ align:start position:0%
+right on
+ 
+
+ align:start position:0%
+right on
+going that's the way we intended it to
+
+ align:start position:0%
+going that's the way we intended it to
+ 
+
+ align:start position:0%
+going that's the way we intended it to
+be because we wanted it to be a reusable
+
+ align:start position:0%
+be because we wanted it to be a reusable
+ 
+
+ align:start position:0%
+be because we wanted it to be a reusable
+system with quick
+
+ align:start position:0%
+system with quick
+ 
+
+ align:start position:0%
+system with quick
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+turnaround two weeks we want to be able
+
+ align:start position:0%
+turnaround two weeks we want to be able
+ 
+
+ align:start position:0%
+turnaround two weeks we want to be able
+to turn that machine
+
+ align:start position:0%
+to turn that machine
+ 
+
+ align:start position:0%
+to turn that machine
+around and you could do that
+
+ align:start position:0%
+around and you could do that
+ 
+
+ align:start position:0%
+around and you could do that
+today because God they've flown at 10
+
+ align:start position:0%
+today because God they've flown at 10
+ 
+
+ align:start position:0%
+today because God they've flown at 10
+some time they know that machine they
+
+ align:start position:0%
+some time they know that machine they
+ 
+
+ align:start position:0%
+some time they know that machine they
+know it well they know how the systems
+
+ align:start position:0%
+know it well they know how the systems
+ 
+
+ align:start position:0%
+know it well they know how the systems
+perform you can look at the Telemetry
+
+ align:start position:0%
+perform you can look at the Telemetry
+ 
+
+ align:start position:0%
+perform you can look at the Telemetry
+when it lands and say all three of the
+
+ align:start position:0%
+when it lands and say all three of the
+ 
+
+ align:start position:0%
+when it lands and say all three of the
+three of the four were working and I got
+
+ align:start position:0%
+three of the four were working and I got
+ 
+
+ align:start position:0%
+three of the four were working and I got
+a thing over here I can fix that in 10
+
+ align:start position:0%
+a thing over here I can fix that in 10
+ 
+
+ align:start position:0%
+a thing over here I can fix that in 10
+minutes I'm ready to go they put more
+
+ align:start position:0%
+minutes I'm ready to go they put more
+ 
+
+ align:start position:0%
+minutes I'm ready to go they put more
+time on the systems on the ground than
+
+ align:start position:0%
+time on the systems on the ground than
+ 
+
+ align:start position:0%
+time on the systems on the ground than
+they do in
+
+ align:start position:0%
+they do in
+ 
+
+ align:start position:0%
+they do in
+Flight testing the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+machine is that
+
+ align:start position:0%
+machine is that
+ 
+
+ align:start position:0%
+machine is that
+expensive my God that's the reason it
+
+ align:start position:0%
+expensive my God that's the reason it
+ 
+
+ align:start position:0%
+expensive my God that's the reason it
+costs $4 billion dollar a year to keep
+
+ align:start position:0%
+costs $4 billion dollar a year to keep
+ 
+
+ align:start position:0%
+costs $4 billion dollar a year to keep
+all those running standing army at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capear if you're going to build
+
+ align:start position:0%
+capear if you're going to build
+ 
+
+ align:start position:0%
+capear if you're going to build
+redundancy in in the future you guys
+
+ align:start position:0%
+redundancy in in the future you guys
+ 
+
+ align:start position:0%
+redundancy in in the future you guys
+you're going to put redundancy in this
+
+ align:start position:0%
+you're going to put redundancy in this
+ 
+
+ align:start position:0%
+you're going to put redundancy in this
+machine don't tell them about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it now that may sound funny but that's
+
+ align:start position:0%
+it now that may sound funny but that's
+ 
+
+ align:start position:0%
+it now that may sound funny but that's
+how your computer is designed
+
+ align:start position:0%
+how your computer is designed
+ 
+
+ align:start position:0%
+how your computer is designed
+you don't have bike in your computer
+
+ align:start position:0%
+you don't have bike in your computer
+ 
+
+ align:start position:0%
+you don't have bike in your computer
+anymore built in test equipment you know
+
+ align:start position:0%
+anymore built in test equipment you know
+ 
+
+ align:start position:0%
+anymore built in test equipment you know
+why because the damn Engineers kept
+
+ align:start position:0%
+why because the damn Engineers kept
+ 
+
+ align:start position:0%
+why because the damn Engineers kept
+using it so now the computer pillers
+
+ align:start position:0%
+using it so now the computer pillers
+ 
+
+ align:start position:0%
+using it so now the computer pillers
+build in the test equipment but they
+
+ align:start position:0%
+build in the test equipment but they
+ 
+
+ align:start position:0%
+build in the test equipment but they
+don't tell you it's there the redundancy
+
+ align:start position:0%
+don't tell you it's there the redundancy
+ 
+
+ align:start position:0%
+don't tell you it's there the redundancy
+Works
+
+ align:start position:0%
+Works
+ 
+
+ align:start position:0%
+Works
+automatically probably got three or four
+
+ align:start position:0%
+automatically probably got three or four
+ 
+
+ align:start position:0%
+automatically probably got three or four
+in there just like we do in the shuttle
+
+ align:start position:0%
+in there just like we do in the shuttle
+ 
+
+ align:start position:0%
+in there just like we do in the shuttle
+but your computer keeps work it might be
+
+ align:start position:0%
+but your computer keeps work it might be
+ 
+
+ align:start position:0%
+but your computer keeps work it might be
+a little
+
+ align:start position:0%
+a little
+ 
+
+ align:start position:0%
+a little
+slower sometimes it get you mad as hell
+
+ align:start position:0%
+slower sometimes it get you mad as hell
+ 
+
+ align:start position:0%
+slower sometimes it get you mad as hell
+but they don't tell you about it so my
+
+ align:start position:0%
+but they don't tell you about it so my
+ 
+
+ align:start position:0%
+but they don't tell you about it so my
+advice is don't tell the people about it
+
+ align:start position:0%
+advice is don't tell the people about it
+ 
+
+ align:start position:0%
+advice is don't tell the people about it
+the next time don't tell the people the
+
+ align:start position:0%
+the next time don't tell the people the
+ 
+
+ align:start position:0%
+the next time don't tell the people the
+cape this's got quadr dcy and that
+
+ align:start position:0%
+cape this's got quadr dcy and that
+ 
+
+ align:start position:0%
+cape this's got quadr dcy and that
+sounds that's probably somewhat
+
+ align:start position:0%
+sounds that's probably somewhat
+ 
+
+ align:start position:0%
+sounds that's probably somewhat
+foolishness but I guarantee that if I
+
+ align:start position:0%
+foolishness but I guarantee that if I
+ 
+
+ align:start position:0%
+foolishness but I guarantee that if I
+had anything to do about it and the next
+
+ align:start position:0%
+had anything to do about it and the next
+ 
+
+ align:start position:0%
+had anything to do about it and the next
+time I might very well do it that
+
+ align:start position:0%
+time I might very well do it that
+ 
+
+ align:start position:0%
+time I might very well do it that
+way because it's not the right way to
+
+ align:start position:0%
+way because it's not the right way to
+ 
+
+ align:start position:0%
+way because it's not the right way to
+think about this machine the machine is
+
+ align:start position:0%
+think about this machine the machine is
+ 
+
+ align:start position:0%
+think about this machine the machine is
+a beautiful
+
+ align:start position:0%
+a beautiful
+ 
+
+ align:start position:0%
+a beautiful
+wonderful piece of hardware
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Orbiter system the most complex system
+
+ align:start position:0%
+Orbiter system the most complex system
+ 
+
+ align:start position:0%
+Orbiter system the most complex system
+ever built by man to fly has
+
+ align:start position:0%
+ever built by man to fly has
+ 
+
+ align:start position:0%
+ever built by man to fly has
+never I was talking to some co-ops a few
+
+ align:start position:0%
+never I was talking to some co-ops a few
+ 
+
+ align:start position:0%
+never I was talking to some co-ops a few
+days ago I said that word 14 times it's
+
+ align:start position:0%
+days ago I said that word 14 times it's
+ 
+
+ align:start position:0%
+days ago I said that word 14 times it's
+never had a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+failure the Orbiter has never had a
+
+ align:start position:0%
+failure the Orbiter has never had a
+ 
+
+ align:start position:0%
+failure the Orbiter has never had a
+failure that would have prevented that
+
+ align:start position:0%
+failure that would have prevented that
+ 
+
+ align:start position:0%
+failure that would have prevented that
+machine from Landing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+safely n is now going to use however all
+
+ align:start position:0%
+safely n is now going to use however all
+ 
+
+ align:start position:0%
+safely n is now going to use however all
+the components that have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+failed they're going to use the solid
+
+ align:start position:0%
+failed they're going to use the solid
+ 
+
+ align:start position:0%
+failed they're going to use the solid
+rocket you're going to put a command
+
+ align:start position:0%
+rocket you're going to put a command
+ 
+
+ align:start position:0%
+rocket you're going to put a command
+like service module on top of it with an
+
+ align:start position:0%
+like service module on top of it with an
+ 
+
+ align:start position:0%
+like service module on top of it with an
+escape
+
+ align:start position:0%
+escape
+ 
+
+ align:start position:0%
+escape
+rocket and fly it that system has
+
+ align:start position:0%
+rocket and fly it that system has
+ 
+
+ align:start position:0%
+rocket and fly it that system has
+failed they're going to use the
+
+ align:start position:0%
+failed they're going to use the
+ 
+
+ align:start position:0%
+failed they're going to use the
+tank can't figure out Engineers this day
+
+ align:start position:0%
+tank can't figure out Engineers this day
+ 
+
+ align:start position:0%
+tank can't figure out Engineers this day
+in time can't figure out to put how to
+
+ align:start position:0%
+in time can't figure out to put how to
+ 
+
+ align:start position:0%
+in time can't figure out to put how to
+put insulation on a tank
+
+ align:start position:0%
+put insulation on a tank
+ 
+
+ align:start position:0%
+put insulation on a tank
+ridiculous not only ridiculous
+
+ align:start position:0%
+ridiculous not only ridiculous
+ 
+
+ align:start position:0%
+ridiculous not only ridiculous
+ludicrous you mean to tell me at the AR
+
+ align:start position:0%
+ludicrous you mean to tell me at the AR
+ 
+
+ align:start position:0%
+ludicrous you mean to tell me at the AR
+a design engineer sitting in this room
+
+ align:start position:0%
+a design engineer sitting in this room
+ 
+
+ align:start position:0%
+a design engineer sitting in this room
+that can't tell you how to keep the foam
+
+ align:start position:0%
+that can't tell you how to keep the foam
+ 
+
+ align:start position:0%
+that can't tell you how to keep the foam
+insulation on that tank hell my son
+
+ align:start position:0%
+insulation on that tank hell my son
+ 
+
+ align:start position:0%
+insulation on that tank hell my son
+could do it in fact my grandson could
+
+ align:start position:0%
+could do it in fact my grandson could
+ 
+
+ align:start position:0%
+could do it in fact my grandson could
+probably do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the engines the space shuttle main
+
+ align:start position:0%
+the engines the space shuttle main
+ 
+
+ align:start position:0%
+the engines the space shuttle main
+engines that is a damn tough piece of
+
+ align:start position:0%
+engines that is a damn tough piece of
+ 
+
+ align:start position:0%
+engines that is a damn tough piece of
+Hardware that's what we're going to use
+
+ align:start position:0%
+Hardware that's what we're going to use
+ 
+
+ align:start position:0%
+Hardware that's what we're going to use
+that's what we're going to put in orbit
+
+ align:start position:0%
+that's what we're going to put in orbit
+ 
+
+ align:start position:0%
+that's what we're going to put in orbit
+and use it as a MCH as a as a propulsion
+
+ align:start position:0%
+and use it as a MCH as a as a propulsion
+ 
+
+ align:start position:0%
+and use it as a MCH as a as a propulsion
+system to send you to the moon now they
+
+ align:start position:0%
+system to send you to the moon now they
+ 
+
+ align:start position:0%
+system to send you to the moon now they
+say oh we're going to make some changes
+
+ align:start position:0%
+say oh we're going to make some changes
+ 
+
+ align:start position:0%
+say oh we're going to make some changes
+to it make it
+
+ align:start position:0%
+to it make it
+ 
+
+ align:start position:0%
+to it make it
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+H I'll probably be dead gone but I'd
+
+ align:start position:0%
+H I'll probably be dead gone but I'd
+ 
+
+ align:start position:0%
+H I'll probably be dead gone but I'd
+like to see it
+
+ align:start position:0%
+like to see it
+ 
+
+ align:start position:0%
+like to see it
+that thing is designed right up to the
+
+ align:start position:0%
+that thing is designed right up to the
+ 
+
+ align:start position:0%
+that thing is designed right up to the
+teeth maximum power you can get out of
+
+ align:start position:0%
+teeth maximum power you can get out of
+ 
+
+ align:start position:0%
+teeth maximum power you can get out of
+hydrogen and oxygen has an ISP of above
+
+ align:start position:0%
+hydrogen and oxygen has an ISP of above
+ 
+
+ align:start position:0%
+hydrogen and oxygen has an ISP of above
+460 and the engine on the shuttle is
+
+ align:start position:0%
+460 and the engine on the shuttle is
+ 
+
+ align:start position:0%
+460 and the engine on the shuttle is
+458 I don't know how you can get much
+
+ align:start position:0%
+458 I don't know how you can get much
+ 
+
+ align:start position:0%
+458 I don't know how you can get much
+more efficient than that but that really
+
+ align:start position:0%
+more efficient than that but that really
+ 
+
+ align:start position:0%
+more efficient than that but that really
+is a tough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+engine continuously changing components
+
+ align:start position:0%
+engine continuously changing components
+ 
+
+ align:start position:0%
+engine continuously changing components
+but those are the three components NES
+
+ align:start position:0%
+but those are the three components NES
+ 
+
+ align:start position:0%
+but those are the three components NES
+when use those to go or the moon but I
+
+ align:start position:0%
+when use those to go or the moon but I
+ 
+
+ align:start position:0%
+when use those to go or the moon but I
+would throw the Orbiter
+
+ align:start position:0%
+would throw the Orbiter
+ 
+
+ align:start position:0%
+would throw the Orbiter
+away never had a failure on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Orbiter
+
+ align:start position:0%
+Orbiter
+ 
+
+ align:start position:0%
+Orbiter
+uh talk a little bit about rtls we
+
+ align:start position:0%
+uh talk a little bit about rtls we
+ 
+
+ align:start position:0%
+uh talk a little bit about rtls we
+turned the laite that sounds like
+
+ align:start position:0%
+turned the laite that sounds like
+ 
+
+ align:start position:0%
+turned the laite that sounds like
+something easy to do but think about the
+
+ align:start position:0%
+something easy to do but think about the
+ 
+
+ align:start position:0%
+something easy to do but think about the
+software involved in that little dude
+
+ align:start position:0%
+software involved in that little dude
+ 
+
+ align:start position:0%
+software involved in that little dude
+and figuring out how to do
+
+ align:start position:0%
+and figuring out how to do
+ 
+
+ align:start position:0%
+and figuring out how to do
+it how to re how to take that machine
+
+ align:start position:0%
+it how to re how to take that machine
+ 
+
+ align:start position:0%
+it how to re how to take that machine
+back to land at Cape canaval if you do
+
+ align:start position:0%
+back to land at Cape canaval if you do
+ 
+
+ align:start position:0%
+back to land at Cape canaval if you do
+have an abort think about the software
+
+ align:start position:0%
+have an abort think about the software
+ 
+
+ align:start position:0%
+have an abort think about the software
+involved in that think about the
+
+ align:start position:0%
+involved in that think about the
+ 
+
+ align:start position:0%
+involved in that think about the
+possibilities think about the cut off
+
+ align:start position:0%
+possibilities think about the cut off
+ 
+
+ align:start position:0%
+possibilities think about the cut off
+conditions think about the mck number
+
+ align:start position:0%
+conditions think about the mck number
+ 
+
+ align:start position:0%
+conditions think about the mck number
+range you're going to have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fly
+
+ align:start position:0%
+fly
+ 
+
+ align:start position:0%
+fly
+so return to launch site was part of our
+
+ align:start position:0%
+so return to launch site was part of our
+ 
+
+ align:start position:0%
+so return to launch site was part of our
+philosophy of not having an escape
+
+ align:start position:0%
+philosophy of not having an escape
+ 
+
+ align:start position:0%
+philosophy of not having an escape
+system per
+
+ align:start position:0%
+system per
+ 
+
+ align:start position:0%
+system per
+se on the
+
+ align:start position:0%
+se on the
+ 
+
+ align:start position:0%
+se on the
+shuttle I'd like to also
+
+ align:start position:0%
+shuttle I'd like to also
+ 
+
+ align:start position:0%
+shuttle I'd like to also
+I know we have some navigation guidance
+
+ align:start position:0%
+I know we have some navigation guidance
+ 
+
+ align:start position:0%
+I know we have some navigation guidance
+people in this
+
+ align:start position:0%
+people in this
+ 
+
+ align:start position:0%
+people in this
+audience how then did we decide Jeff
+
+ align:start position:0%
+audience how then did we decide Jeff
+ 
+
+ align:start position:0%
+audience how then did we decide Jeff
+asked me to fly the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time that was tough very difficult we
+
+ align:start position:0%
+time that was tough very difficult we
+ 
+
+ align:start position:0%
+time that was tough very difficult we
+had some of the best experts in the
+
+ align:start position:0%
+had some of the best experts in the
+ 
+
+ align:start position:0%
+had some of the best experts in the
+world come review what we were doing
+
+ align:start position:0%
+world come review what we were doing
+ 
+
+ align:start position:0%
+world come review what we were doing
+look at all the systems the one thing
+
+ align:start position:0%
+look at all the systems the one thing
+ 
+
+ align:start position:0%
+look at all the systems the one thing
+that two things really that they had the
+
+ align:start position:0%
+that two things really that they had the
+ 
+
+ align:start position:0%
+that two things really that they had the
+most trouble with
+
+ align:start position:0%
+most trouble with
+ 
+
+ align:start position:0%
+most trouble with
+in in making sure we knew what we were
+
+ align:start position:0%
+in in making sure we knew what we were
+ 
+
+ align:start position:0%
+in in making sure we knew what we were
+doing first with the thermal protection
+
+ align:start position:0%
+doing first with the thermal protection
+ 
+
+ align:start position:0%
+doing first with the thermal protection
+system and we never really convinced the
+
+ align:start position:0%
+system and we never really convinced the
+ 
+
+ align:start position:0%
+system and we never really convinced the
+experts that we did have a thermal
+
+ align:start position:0%
+experts that we did have a thermal
+ 
+
+ align:start position:0%
+experts that we did have a thermal
+protection system that work that would
+
+ align:start position:0%
+protection system that work that would
+ 
+
+ align:start position:0%
+protection system that work that would
+work as a matter of fact the man who
+
+ align:start position:0%
+work as a matter of fact the man who
+ 
+
+ align:start position:0%
+work as a matter of fact the man who
+invented lunar orbit rodo at least sold
+
+ align:start position:0%
+invented lunar orbit rodo at least sold
+ 
+
+ align:start position:0%
+invented lunar orbit rodo at least sold
+the day he didn't invent it but he sold
+
+ align:start position:0%
+the day he didn't invent it but he sold
+ 
+
+ align:start position:0%
+the day he didn't invent it but he sold
+the day in using lunar Robert Rond
+
+ align:start position:0%
+the day in using lunar Robert Rond
+ 
+
+ align:start position:0%
+the day in using lunar Robert Rond
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+chief structures engineer in the United
+
+ align:start position:0%
+chief structures engineer in the United
+ 
+
+ align:start position:0%
+chief structures engineer in the United
+States that's probably a stretch but one
+
+ align:start position:0%
+States that's probably a stretch but one
+ 
+
+ align:start position:0%
+States that's probably a stretch but one
+of them at
+
+ align:start position:0%
+of them at
+ 
+
+ align:start position:0%
+of them at
+Stanford wrote me a cosign
+
+ align:start position:0%
+Stanford wrote me a cosign
+ 
+
+ align:start position:0%
+Stanford wrote me a cosign
+letter on T minus one month after we had
+
+ align:start position:0%
+letter on T minus one month after we had
+ 
+
+ align:start position:0%
+letter on T minus one month after we had
+reviewed this system we had done
+
+ align:start position:0%
+reviewed this system we had done
+ 
+
+ align:start position:0%
+reviewed this system we had done
+everything they asked us to do we ran
+
+ align:start position:0%
+everything they asked us to do we ran
+ 
+
+ align:start position:0%
+everything they asked us to do we ran
+combined loads tests we were ran worse
+
+ align:start position:0%
+combined loads tests we were ran worse
+ 
+
+ align:start position:0%
+combined loads tests we were ran worse
+loads tests we ran combined worse loads
+
+ align:start position:0%
+loads tests we ran combined worse loads
+ 
+
+ align:start position:0%
+loads tests we ran combined worse loads
+tests to prove to ourselves that the
+
+ align:start position:0%
+tests to prove to ourselves that the
+ 
+
+ align:start position:0%
+tests to prove to ourselves that the
+thermal protection system wouldn't fail
+
+ align:start position:0%
+thermal protection system wouldn't fail
+ 
+
+ align:start position:0%
+thermal protection system wouldn't fail
+I got this letter at T minus one
+
+ align:start position:0%
+I got this letter at T minus one
+ 
+
+ align:start position:0%
+I got this letter at T minus one
+month now in my effects at Virginia Tech
+
+ align:start position:0%
+month now in my effects at Virginia Tech
+ 
+
+ align:start position:0%
+month now in my effects at Virginia Tech
+as a matter of fact Virginia Tech said
+
+ align:start position:0%
+as a matter of fact Virginia Tech said
+ 
+
+ align:start position:0%
+as a matter of fact Virginia Tech said
+are you sure you want this
+
+ align:start position:0%
+are you sure you want this
+ 
+
+ align:start position:0%
+are you sure you want this
+letter in your in your files I said oh
+
+ align:start position:0%
+letter in your in your files I said oh
+ 
+
+ align:start position:0%
+letter in your in your files I said oh
+yes I want that letter in my fil it's
+
+ align:start position:0%
+yes I want that letter in my fil it's
+ 
+
+ align:start position:0%
+yes I want that letter in my fil it's
+probably the most important letter
+
+ align:start position:0%
+probably the most important letter
+ 
+
+ align:start position:0%
+probably the most important letter
+you'll ever have in my files but these
+
+ align:start position:0%
+you'll ever have in my files but these
+ 
+
+ align:start position:0%
+you'll ever have in my files but these
+two gentlemen said we implore
+
+ align:start position:0%
+two gentlemen said we implore
+ 
+
+ align:start position:0%
+two gentlemen said we implore
+you not to fly the SP
+
+ align:start position:0%
+you not to fly the SP
+ 
+
+ align:start position:0%
+you not to fly the SP
+shut Orbiter about fly the or
+
+ align:start position:0%
+shut Orbiter about fly the or
+ 
+
+ align:start position:0%
+shut Orbiter about fly the or
+because the tiles are going to come off
+
+ align:start position:0%
+because the tiles are going to come off
+ 
+
+ align:start position:0%
+because the tiles are going to come off
+it may not come off while you're at the
+
+ align:start position:0%
+it may not come off while you're at the
+ 
+
+ align:start position:0%
+it may not come off while you're at the
+max heating pulse but by the time you
+
+ align:start position:0%
+max heating pulse but by the time you
+ 
+
+ align:start position:0%
+max heating pulse but by the time you
+get ready to land NASA is going to be
+
+ align:start position:0%
+get ready to land NASA is going to be
+ 
+
+ align:start position:0%
+get ready to land NASA is going to be
+totally embarrassed because all the
+
+ align:start position:0%
+totally embarrassed because all the
+ 
+
+ align:start position:0%
+totally embarrassed because all the
+tiles are going to fall
+
+ align:start position:0%
+tiles are going to fall
+ 
+
+ align:start position:0%
+tiles are going to fall
+off and we would ask you to put a steel
+
+ align:start position:0%
+off and we would ask you to put a steel
+ 
+
+ align:start position:0%
+off and we would ask you to put a steel
+net around this vehicle so that they
+
+ align:start position:0%
+net around this vehicle so that they
+ 
+
+ align:start position:0%
+net around this vehicle so that they
+won't fall off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm I'm still a
+
+ align:start position:0%
+I'm I'm still a
+ 
+
+ align:start position:0%
+I'm I'm still a
+gas at that letter because I don't know
+
+ align:start position:0%
+gas at that letter because I don't know
+ 
+
+ align:start position:0%
+gas at that letter because I don't know
+what we else we could have done to
+
+ align:start position:0%
+what we else we could have done to
+ 
+
+ align:start position:0%
+what we else we could have done to
+satisfy them that we had done everything
+
+ align:start position:0%
+satisfy them that we had done everything
+ 
+
+ align:start position:0%
+satisfy them that we had done everything
+they asked us we they were concerned
+
+ align:start position:0%
+they asked us we they were concerned
+ 
+
+ align:start position:0%
+they asked us we they were concerned
+that the that the strain isolation pad
+
+ align:start position:0%
+that the that the strain isolation pad
+ 
+
+ align:start position:0%
+that the that the strain isolation pad
+which is what the tile sits on and you
+
+ align:start position:0%
+which is what the tile sits on and you
+ 
+
+ align:start position:0%
+which is what the tile sits on and you
+you've had that explanation they were
+
+ align:start position:0%
+you've had that explanation they were
+ 
+
+ align:start position:0%
+you've had that explanation they were
+they were concerned that combined
+
+ align:start position:0%
+they were concerned that combined
+ 
+
+ align:start position:0%
+they were concerned that combined
+vibrations and aerodynamic loads would
+
+ align:start position:0%
+vibrations and aerodynamic loads would
+ 
+
+ align:start position:0%
+vibrations and aerodynamic loads would
+cause a failure in this sip or at least
+
+ align:start position:0%
+cause a failure in this sip or at least
+ 
+
+ align:start position:0%
+cause a failure in this sip or at least
+at the glue J and and that indeed all
+
+ align:start position:0%
+at the glue J and and that indeed all
+ 
+
+ align:start position:0%
+at the glue J and and that indeed all
+the major tiles that had gone through
+
+ align:start position:0%
+the major tiles that had gone through
+ 
+
+ align:start position:0%
+the major tiles that had gone through
+the large heat PS would fall off Mr Cen
+
+ align:start position:0%
+the large heat PS would fall off Mr Cen
+ 
+
+ align:start position:0%
+the large heat PS would fall off Mr Cen
+Professor Co I'll keep calling you Mr
+
+ align:start position:0%
+Professor Co I'll keep calling you Mr
+ 
+
+ align:start position:0%
+Professor Co I'll keep calling you Mr
+Cohen Professor
+
+ align:start position:0%
+Cohen Professor
+ 
+
+ align:start position:0%
+Cohen Professor
+Cohen and I met them on the queen
+
+ align:start position:0%
+Cohen and I met them on the queen
+ 
+
+ align:start position:0%
+Cohen and I met them on the queen
+maray at an AI meeting that that
+
+ align:start position:0%
+maray at an AI meeting that that
+ 
+
+ align:start position:0%
+maray at an AI meeting that that
+uh after the first
+
+ align:start position:0%
+uh after the first
+ 
+
+ align:start position:0%
+uh after the first
+flight had taken place was satisfactory
+
+ align:start position:0%
+flight had taken place was satisfactory
+ 
+
+ align:start position:0%
+flight had taken place was satisfactory
+well FW
+
+ align:start position:0%
+well FW
+ 
+
+ align:start position:0%
+well FW
+beautifully they came those two
+
+ align:start position:0%
+beautifully they came those two
+ 
+
+ align:start position:0%
+beautifully they came those two
+gentlemen came running out and I asked
+
+ align:start position:0%
+gentlemen came running out and I asked
+ 
+
+ align:start position:0%
+gentlemen came running out and I asked
+Aaron if we would come and sit down and
+
+ align:start position:0%
+Aaron if we would come and sit down and
+ 
+
+ align:start position:0%
+Aaron if we would come and sit down and
+have a drink with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them and we said hell no and walked away
+
+ align:start position:0%
+them and we said hell no and walked away
+ 
+
+ align:start position:0%
+them and we said hell no and walked away
+from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so that's what I thought of that
+
+ align:start position:0%
+them so that's what I thought of that
+ 
+
+ align:start position:0%
+them so that's what I thought of that
+letter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh now the the other thing I want to
+
+ align:start position:0%
+uh now the the other thing I want to
+ 
+
+ align:start position:0%
+uh now the the other thing I want to
+talk about is the control system of the
+
+ align:start position:0%
+talk about is the control system of the
+ 
+
+ align:start position:0%
+talk about is the control system of the
+shuttle we had several
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gentlemen
+
+ align:start position:0%
+gentlemen
+ 
+
+ align:start position:0%
+gentlemen
+did the public affairs officer said we
+
+ align:start position:0%
+did the public affairs officer said we
+ 
+
+ align:start position:0%
+did the public affairs officer said we
+have we need a comment from you after
+
+ align:start position:0%
+have we need a comment from you after
+ 
+
+ align:start position:0%
+have we need a comment from you after
+the after the machine had landed on what
+
+ align:start position:0%
+the after the machine had landed on what
+ 
+
+ align:start position:0%
+the after the machine had landed on what
+what you think of this flight and I said
+
+ align:start position:0%
+what you think of this flight and I said
+ 
+
+ align:start position:0%
+what you think of this flight and I said
+I said we have just become infinitely
+
+ align:start position:0%
+I said we have just become infinitely
+ 
+
+ align:start position:0%
+I said we have just become infinitely
+smarter
+
+ align:start position:0%
+smarter
+ 
+
+ align:start position:0%
+smarter
+uh not so much about the tile where we
+
+ align:start position:0%
+uh not so much about the tile where we
+ 
+
+ align:start position:0%
+uh not so much about the tile where we
+in the story I'm about to tell the
+
+ align:start position:0%
+in the story I'm about to tell the
+ 
+
+ align:start position:0%
+in the story I'm about to tell the
+automatic control
+
+ align:start position:0%
+automatic control
+ 
+
+ align:start position:0%
+automatic control
+system there there in terms of the the
+
+ align:start position:0%
+system there there in terms of the the
+ 
+
+ align:start position:0%
+system there there in terms of the the
+the aerodynamic parameters that it has
+
+ align:start position:0%
+the aerodynamic parameters that it has
+ 
+
+ align:start position:0%
+the aerodynamic parameters that it has
+to deal
+
+ align:start position:0%
+to deal
+ 
+
+ align:start position:0%
+to deal
+with there are there are roughly
+
+ align:start position:0%
+with there are there are roughly
+ 
+
+ align:start position:0%
+with there are there are roughly
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+variables in the aerodynamics of the
+
+ align:start position:0%
+variables in the aerodynamics of the
+ 
+
+ align:start position:0%
+variables in the aerodynamics of the
+machine all the way from products of
+
+ align:start position:0%
+machine all the way from products of
+ 
+
+ align:start position:0%
+machine all the way from products of
+inertia to CN
+
+ align:start position:0%
+inertia to CN
+ 
+
+ align:start position:0%
+inertia to CN
+beta know CN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta CN beta know the young man knows
+
+ align:start position:0%
+beta CN beta know the young man knows
+ 
+
+ align:start position:0%
+beta CN beta know the young man knows
+what CN beta that's the capability of
+
+ align:start position:0%
+what CN beta that's the capability of
+ 
+
+ align:start position:0%
+what CN beta that's the capability of
+the rudder to stabilize the
+
+ align:start position:0%
+the rudder to stabilize the
+ 
+
+ align:start position:0%
+the rudder to stabilize the
+machine was is it going moment do the
+
+ align:start position:0%
+machine was is it going moment do the
+ 
+
+ align:start position:0%
+machine was is it going moment do the
+side I still still do remember a little
+
+ align:start position:0%
+side I still still do remember a little
+ 
+
+ align:start position:0%
+side I still still do remember a little
+bit of it than that anyway there the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+airplane is there is no facili in the
+
+ align:start position:0%
+airplane is there is no facili in the
+ 
+
+ align:start position:0%
+airplane is there is no facili in the
+world to measure the aerodynamic those
+
+ align:start position:0%
+world to measure the aerodynamic those
+ 
+
+ align:start position:0%
+world to measure the aerodynamic those
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+parameters uh uh very accurately
+
+ align:start position:0%
+parameters uh uh very accurately
+ 
+
+ align:start position:0%
+parameters uh uh very accurately
+anyway uh in the in that would tell you
+
+ align:start position:0%
+anyway uh in the in that would tell you
+ 
+
+ align:start position:0%
+anyway uh in the in that would tell you
+what to design the automatic control
+
+ align:start position:0%
+what to design the automatic control
+ 
+
+ align:start position:0%
+what to design the automatic control
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+to uh particularly it's not it's not not
+
+ align:start position:0%
+to uh particularly it's not it's not not
+ 
+
+ align:start position:0%
+to uh particularly it's not it's not not
+so difficult at High mock numbers above
+
+ align:start position:0%
+so difficult at High mock numbers above
+ 
+
+ align:start position:0%
+so difficult at High mock numbers above
+say 10 you can use uh what do you call
+
+ align:start position:0%
+say 10 you can use uh what do you call
+ 
+
+ align:start position:0%
+say 10 you can use uh what do you call
+it Newtonian flow and and uh you as you
+
+ align:start position:0%
+it Newtonian flow and and uh you as you
+ 
+
+ align:start position:0%
+it Newtonian flow and and uh you as you
+well know you use the aerodynamic
+
+ align:start position:0%
+well know you use the aerodynamic
+ 
+
+ align:start position:0%
+well know you use the aerodynamic
+controls when you can you use the
+
+ align:start position:0%
+controls when you can you use the
+ 
+
+ align:start position:0%
+controls when you can you use the
+thrusters when you can and you combine
+
+ align:start position:0%
+thrusters when you can and you combine
+ 
+
+ align:start position:0%
+thrusters when you can and you combine
+the two as you trans
+
+ align:start position:0%
+the two as you trans
+ 
+
+ align:start position:0%
+the two as you trans
+transfer from one to the other in the
+
+ align:start position:0%
+transfer from one to the other in the
+ 
+
+ align:start position:0%
+transfer from one to the other in the
+range of flight or in the flight
+
+ align:start position:0%
+range of flight or in the flight
+ 
+
+ align:start position:0%
+range of flight or in the flight
+reges but
+
+ align:start position:0%
+reges but
+ 
+
+ align:start position:0%
+reges but
+actually it's a guess we looked at all
+
+ align:start position:0%
+actually it's a guess we looked at all
+ 
+
+ align:start position:0%
+actually it's a guess we looked at all
+of the possibilities of that had been
+
+ align:start position:0%
+of the possibilities of that had been
+ 
+
+ align:start position:0%
+of the possibilities of that had been
+done at uh on the X15 had been done on
+
+ align:start position:0%
+done at uh on the X15 had been done on
+ 
+
+ align:start position:0%
+done at uh on the X15 had been done on
+the Dinos program had been done in Wind
+
+ align:start position:0%
+the Dinos program had been done in Wind
+ 
+
+ align:start position:0%
+the Dinos program had been done in Wind
+Tunnel tests of almost every
+
+ align:start position:0%
+Tunnel tests of almost every
+ 
+
+ align:start position:0%
+Tunnel tests of almost every
+configuration for Hypersonic flow and
+
+ align:start position:0%
+configuration for Hypersonic flow and
+ 
+
+ align:start position:0%
+configuration for Hypersonic flow and
+you just could nail down what those 35
+
+ align:start position:0%
+you just could nail down what those 35
+ 
+
+ align:start position:0%
+you just could nail down what those 35
+parameters were so what we did was we
+
+ align:start position:0%
+parameters were so what we did was we
+ 
+
+ align:start position:0%
+parameters were so what we did was we
+said here's what we think it is here's a
+
+ align:start position:0%
+said here's what we think it is here's a
+ 
+
+ align:start position:0%
+said here's what we think it is here's a
+variation on top of
+
+ align:start position:0%
+variation on top of
+ 
+
+ align:start position:0%
+variation on top of
+that and here's a deviation on top of
+
+ align:start position:0%
+that and here's a deviation on top of
+ 
+
+ align:start position:0%
+that and here's a deviation on top of
+that and here's those 35 parameters
+
+ align:start position:0%
+that and here's those 35 parameters
+ 
+
+ align:start position:0%
+that and here's those 35 parameters
+throughout the total marck range and and
+
+ align:start position:0%
+throughout the total marck range and and
+ 
+
+ align:start position:0%
+throughout the total marck range and and
+we're going to do a Monte Carlo
+
+ align:start position:0%
+we're going to do a Monte Carlo
+ 
+
+ align:start position:0%
+we're going to do a Monte Carlo
+analysis at every tenth of a mock
+
+ align:start position:0%
+analysis at every tenth of a mock
+ 
+
+ align:start position:0%
+analysis at every tenth of a mock
+number from
+
+ align:start position:0%
+number from
+ 
+
+ align:start position:0%
+number from
+25 to
+
+ align:start position:0%
+25 to
+ 
+
+ align:start position:0%
+25 to
+touchdown and have no failures and if we
+
+ align:start position:0%
+touchdown and have no failures and if we
+ 
+
+ align:start position:0%
+touchdown and have no failures and if we
+have a failure have to change the gains
+
+ align:start position:0%
+have a failure have to change the gains
+ 
+
+ align:start position:0%
+have a failure have to change the gains
+go back and run it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again I don't know about you that sure
+
+ align:start position:0%
+again I don't know about you that sure
+ 
+
+ align:start position:0%
+again I don't know about you that sure
+convinced me that that machine would
+
+ align:start position:0%
+convinced me that that machine would
+ 
+
+ align:start position:0%
+convinced me that that machine would
+apply
+
+ align:start position:0%
+apply
+ 
+
+ align:start position:0%
+apply
+but I still
+
+ align:start position:0%
+but I still
+ 
+
+ align:start position:0%
+but I still
+said we just became infinitely
+
+ align:start position:0%
+said we just became infinitely
+ 
+
+ align:start position:0%
+said we just became infinitely
+smarter I I said before we
+
+ align:start position:0%
+smarter I I said before we
+ 
+
+ align:start position:0%
+smarter I I said before we
+flew we will certainly have to change
+
+ align:start position:0%
+flew we will certainly have to change
+ 
+
+ align:start position:0%
+flew we will certainly have to change
+the gains because there will be regions
+
+ align:start position:0%
+the gains because there will be regions
+ 
+
+ align:start position:0%
+the gains because there will be regions
+where the machine is is oscillatory
+
+ align:start position:0%
+where the machine is is oscillatory
+ 
+
+ align:start position:0%
+where the machine is is oscillatory
+coming down and might might frighten
+
+ align:start position:0%
+coming down and might might frighten
+ 
+
+ align:start position:0%
+coming down and might might frighten
+somebody even if they even if they were
+
+ align:start position:0%
+somebody even if they even if they were
+ 
+
+ align:start position:0%
+somebody even if they even if they were
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+damp that was post flight I
+
+ align:start position:0%
+damp that was post flight I
+ 
+
+ align:start position:0%
+damp that was post flight I
+said I don't ever want to change the
+
+ align:start position:0%
+said I don't ever want to change the
+ 
+
+ align:start position:0%
+said I don't ever want to change the
+games the damn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+worked so those two J those two problems
+
+ align:start position:0%
+worked so those two J those two problems
+ 
+
+ align:start position:0%
+worked so those two J those two problems
+were the fundamentally hardest problems
+
+ align:start position:0%
+were the fundamentally hardest problems
+ 
+
+ align:start position:0%
+were the fundamentally hardest problems
+to build and test and assure yourself
+
+ align:start position:0%
+to build and test and assure yourself
+ 
+
+ align:start position:0%
+to build and test and assure yourself
+that you were ready to fly but in the
+
+ align:start position:0%
+that you were ready to fly but in the
+ 
+
+ align:start position:0%
+that you were ready to fly but in the
+end how did we decide to
+
+ align:start position:0%
+end how did we decide to
+ 
+
+ align:start position:0%
+end how did we decide to
+fly frankly I didn't know what else to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do I in my mind Professor cen's mind
+
+ align:start position:0%
+do I in my mind Professor cen's mind
+ 
+
+ align:start position:0%
+do I in my mind Professor cen's mind
+John mind who was the head of man space
+
+ align:start position:0%
+John mind who was the head of man space
+ 
+
+ align:start position:0%
+John mind who was the head of man space
+PL these gentleman sitting in front of
+
+ align:start position:0%
+PL these gentleman sitting in front of
+ 
+
+ align:start position:0%
+PL these gentleman sitting in front of
+me that worked on the automatic control
+
+ align:start position:0%
+me that worked on the automatic control
+ 
+
+ align:start position:0%
+me that worked on the automatic control
+system we didn't know what else to do
+
+ align:start position:0%
+system we didn't know what else to do
+ 
+
+ align:start position:0%
+system we didn't know what else to do
+we've done everything we could think of
+
+ align:start position:0%
+we've done everything we could think of
+ 
+
+ align:start position:0%
+we've done everything we could think of
+we suspected there were some unknown
+
+ align:start position:0%
+we suspected there were some unknown
+ 
+
+ align:start position:0%
+we suspected there were some unknown
+unknowns good old NASA term unknown
+
+ align:start position:0%
+unknowns good old NASA term unknown
+ 
+
+ align:start position:0%
+unknowns good old NASA term unknown
+unknowns but we didn't know what they
+
+ align:start position:0%
+unknowns but we didn't know what they
+ 
+
+ align:start position:0%
+unknowns but we didn't know what they
+were we didn't know where to test we
+
+ align:start position:0%
+were we didn't know where to test we
+ 
+
+ align:start position:0%
+were we didn't know where to test we
+didn't know how to test it so got to go
+
+ align:start position:0%
+didn't know how to test it so got to go
+ 
+
+ align:start position:0%
+didn't know how to test it so got to go
+light the torch and do it
+
+ align:start position:0%
+light the torch and do it
+ 
+
+ align:start position:0%
+light the torch and do it
+I don't think it took a lot
+
+ align:start position:0%
+I don't think it took a lot
+ 
+
+ align:start position:0%
+I don't think it took a lot
+of guts or neres I think it we I think
+
+ align:start position:0%
+of guts or neres I think it we I think
+ 
+
+ align:start position:0%
+of guts or neres I think it we I think
+we were pretty sure of
+
+ align:start position:0%
+we were pretty sure of
+ 
+
+ align:start position:0%
+we were pretty sure of
+ourselves now the Challenger accident
+
+ align:start position:0%
+ourselves now the Challenger accident
+ 
+
+ align:start position:0%
+ourselves now the Challenger accident
+and the Columbia accident are
+
+ align:start position:0%
+and the Columbia accident are
+ 
+
+ align:start position:0%
+and the Columbia accident are
+horrible tragedy there's no question
+
+ align:start position:0%
+horrible tragedy there's no question
+ 
+
+ align:start position:0%
+horrible tragedy there's no question
+about that but they shouldn't have
+
+ align:start position:0%
+about that but they shouldn't have
+ 
+
+ align:start position:0%
+about that but they shouldn't have
+happened and they they could have been
+
+ align:start position:0%
+happened and they they could have been
+ 
+
+ align:start position:0%
+happened and they they could have been
+prevented and that's the other thing you
+
+ align:start position:0%
+prevented and that's the other thing you
+ 
+
+ align:start position:0%
+prevented and that's the other thing you
+have to remember when you get into this
+
+ align:start position:0%
+have to remember when you get into this
+ 
+
+ align:start position:0%
+have to remember when you get into this
+business some of you if not all of you
+
+ align:start position:0%
+business some of you if not all of you
+ 
+
+ align:start position:0%
+business some of you if not all of you
+are going to be responsible for the
+
+ align:start position:0%
+are going to be responsible for the
+ 
+
+ align:start position:0%
+are going to be responsible for the
+lives of the people that are
+
+ align:start position:0%
+lives of the people that are
+ 
+
+ align:start position:0%
+lives of the people that are
+flying and the responsibility of the
+
+ align:start position:0%
+flying and the responsibility of the
+ 
+
+ align:start position:0%
+flying and the responsibility of the
+program because it may very well be
+
+ align:start position:0%
+program because it may very well be
+ 
+
+ align:start position:0%
+program because it may very well be
+something that just causes the space
+
+ align:start position:0%
+something that just causes the space
+ 
+
+ align:start position:0%
+something that just causes the space
+program to collapse in the United
+
+ align:start position:0%
+program to collapse in the United
+ 
+
+ align:start position:0%
+program to collapse in the United
+States and that is a tough
+
+ align:start position:0%
+States and that is a tough
+ 
+
+ align:start position:0%
+States and that is a tough
+task you don't learn that overnight you
+
+ align:start position:0%
+task you don't learn that overnight you
+ 
+
+ align:start position:0%
+task you don't learn that overnight you
+don't you just sort of have to learn to
+
+ align:start position:0%
+don't you just sort of have to learn to
+ 
+
+ align:start position:0%
+don't you just sort of have to learn to
+live with it
+
+ align:start position:0%
+live with it
+ 
+
+ align:start position:0%
+live with it
+and frankly you have to like
+
+ align:start position:0%
+and frankly you have to like
+ 
+
+ align:start position:0%
+and frankly you have to like
+it you have to like being in that
+
+ align:start position:0%
+it you have to like being in that
+ 
+
+ align:start position:0%
+it you have to like being in that
+position I had one of my flight
+
+ align:start position:0%
+position I had one of my flight
+ 
+
+ align:start position:0%
+position I had one of my flight
+directors who became very much affected
+
+ align:start position:0%
+directors who became very much affected
+ 
+
+ align:start position:0%
+directors who became very much affected
+by it
+
+ align:start position:0%
+by it
+ 
+
+ align:start position:0%
+by it
+mentally so so affected that he quit
+
+ align:start position:0%
+mentally so so affected that he quit
+ 
+
+ align:start position:0%
+mentally so so affected that he quit
+went became a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+psychiatrist didn't ever didn't ever
+
+ align:start position:0%
+psychiatrist didn't ever didn't ever
+ 
+
+ align:start position:0%
+psychiatrist didn't ever didn't ever
+form as a psychiatrist we got a got his
+
+ align:start position:0%
+form as a psychiatrist we got a got his
+ 
+
+ align:start position:0%
+form as a psychiatrist we got a got his
+degree in
+
+ align:start position:0%
+degree in
+ 
+
+ align:start position:0%
+degree in
+Psychiatry bill
+
+ align:start position:0%
+Psychiatry bill
+ 
+
+ align:start position:0%
+Psychiatry bill
+shacker you know one of my very closest
+
+ align:start position:0%
+shacker you know one of my very closest
+ 
+
+ align:start position:0%
+shacker you know one of my very closest
+friends now making me kind of Rich
+
+ align:start position:0%
+friends now making me kind of Rich
+ 
+
+ align:start position:0%
+friends now making me kind of Rich
+because we ow a lot of oil wells in
+
+ align:start position:0%
+because we ow a lot of oil wells in
+ 
+
+ align:start position:0%
+because we ow a lot of oil wells in
+Oklahoma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together but it is it is a tough job but
+
+ align:start position:0%
+together but it is it is a tough job but
+ 
+
+ align:start position:0%
+together but it is it is a tough job but
+it is a marvelous
+
+ align:start position:0%
+it is a marvelous
+ 
+
+ align:start position:0%
+it is a marvelous
+job there is nothing I can think of
+
+ align:start position:0%
+job there is nothing I can think of
+ 
+
+ align:start position:0%
+job there is nothing I can think of
+including pitching in the World Series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or winning the US
+
+ align:start position:0%
+or winning the US
+ 
+
+ align:start position:0%
+or winning the US
+Open it comes close to being in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+business every day is a
+
+ align:start position:0%
+business every day is a
+ 
+
+ align:start position:0%
+business every day is a
+challenge every day is is hell and every
+
+ align:start position:0%
+challenge every day is is hell and every
+ 
+
+ align:start position:0%
+challenge every day is is hell and every
+day the best feeling you've ever had in
+
+ align:start position:0%
+day the best feeling you've ever had in
+ 
+
+ align:start position:0%
+day the best feeling you've ever had in
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+life it's how you feel every day you go
+
+ align:start position:0%
+life it's how you feel every day you go
+ 
+
+ align:start position:0%
+life it's how you feel every day you go
+through those you go through those
+
+ align:start position:0%
+through those you go through those
+ 
+
+ align:start position:0%
+through those you go through those
+trents almost every
+
+ align:start position:0%
+trents almost every
+ 
+
+ align:start position:0%
+trents almost every
+day so I highly recommend it to
+
+ align:start position:0%
+day so I highly recommend it to
+ 
+
+ align:start position:0%
+day so I highly recommend it to
+you I don't think you'll get
+
+ align:start position:0%
+you I don't think you'll get
+ 
+
+ align:start position:0%
+you I don't think you'll get
+rich till you retire and become a board
+
+ align:start position:0%
+rich till you retire and become a board
+ 
+
+ align:start position:0%
+rich till you retire and become a board
+member like some of us
+
+ align:start position:0%
+member like some of us
+ 
+
+ align:start position:0%
+member like some of us
+have uh but but before that uh you're
+
+ align:start position:0%
+have uh but but before that uh you're
+ 
+
+ align:start position:0%
+have uh but but before that uh you're
+not going to get rich but you're going
+
+ align:start position:0%
+not going to get rich but you're going
+ 
+
+ align:start position:0%
+not going to get rich but you're going
+to be happy every day and you're going
+
+ align:start position:0%
+to be happy every day and you're going
+ 
+
+ align:start position:0%
+to be happy every day and you're going
+to feel like you contributed every
+
+ align:start position:0%
+to feel like you contributed every
+ 
+
+ align:start position:0%
+to feel like you contributed every
+day and I don't know at least in our
+
+ align:start position:0%
+day and I don't know at least in our
+ 
+
+ align:start position:0%
+day and I don't know at least in our
+business anything better than that
+
+ align:start position:0%
+business anything better than that
+ 
+
+ align:start position:0%
+business anything better than that
+gentlemen all sitting here in front of
+
+ align:start position:0%
+gentlemen all sitting here in front of
+ 
+
+ align:start position:0%
+gentlemen all sitting here in front of
+me will will attest to that it's a great
+
+ align:start position:0%
+me will will attest to that it's a great
+ 
+
+ align:start position:0%
+me will will attest to that it's a great
+life with that I'll stop and take your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I turn
+
+ align:start position:0%
+I turn
+ 
+
+ align:start position:0%
+I turn
+hav turn any off where is the this is
+
+ align:start position:0%
+hav turn any off where is the this is
+ 
+
+ align:start position:0%
+hav turn any off where is the this is
+this is your chance uh pull a plug
+
+ align:start position:0%
+this is your chance uh pull a plug
+ 
+
+ align:start position:0%
+this is your chance uh pull a plug
+where's the
+
+ align:start position:0%
+where's the
+ 
+
+ align:start position:0%
+where's the
+plug get
+
+ align:start position:0%
+plug get
+ 
+
+ align:start position:0%
+plug get
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than can you can you stand
+
+ align:start position:0%
+than can you can you stand
+ 
+
+ align:start position:0%
+than can you can you stand
+up would be the systems that you would
+
+ align:start position:0%
+up would be the systems that you would
+ 
+
+ align:start position:0%
+up would be the systems that you would
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+could use most Improvement on the
+
+ align:start position:0%
+could use most Improvement on the
+ 
+
+ align:start position:0%
+could use most Improvement on the
+shut with today's
+
+ align:start position:0%
+shut with today's
+ 
+
+ align:start position:0%
+shut with today's
+technology and as you see things what
+
+ align:start position:0%
+technology and as you see things what
+ 
+
+ align:start position:0%
+technology and as you see things what
+would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the my answer would my first answer
+
+ align:start position:0%
+the my answer would my first answer
+ 
+
+ align:start position:0%
+the my answer would my first answer
+would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+political I improveed I'd improved the
+
+ align:start position:0%
+political I improveed I'd improved the
+ 
+
+ align:start position:0%
+political I improveed I'd improved the
+thermal protection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system I don't think it has to be
+
+ align:start position:0%
+system I don't think it has to be
+ 
+
+ align:start position:0%
+system I don't think it has to be
+improved very much
+
+ align:start position:0%
+improved very much
+ 
+
+ align:start position:0%
+improved very much
+but it would sure get a lot of people
+
+ align:start position:0%
+but it would sure get a lot of people
+ 
+
+ align:start position:0%
+but it would sure get a lot of people
+off our backs if we improve the thermal
+
+ align:start position:0%
+off our backs if we improve the thermal
+ 
+
+ align:start position:0%
+off our backs if we improve the thermal
+protection system and and there are ways
+
+ align:start position:0%
+protection system and and there are ways
+ 
+
+ align:start position:0%
+protection system and and there are ways
+of doing that today you could you could
+
+ align:start position:0%
+of doing that today you could you could
+ 
+
+ align:start position:0%
+of doing that today you could you could
+take there some advancements in the
+
+ align:start position:0%
+take there some advancements in the
+ 
+
+ align:start position:0%
+take there some advancements in the
+state-of-the-art of materials probably
+
+ align:start position:0%
+state-of-the-art of materials probably
+ 
+
+ align:start position:0%
+state-of-the-art of materials probably
+in the way you attach to the the child
+
+ align:start position:0%
+in the way you attach to the the child
+ 
+
+ align:start position:0%
+in the way you attach to the the child
+to the machine probably the way you
+
+ align:start position:0%
+to the machine probably the way you
+ 
+
+ align:start position:0%
+to the machine probably the way you
+proof test it all those things I think
+
+ align:start position:0%
+proof test it all those things I think
+ 
+
+ align:start position:0%
+proof test it all those things I think
+would be where I would go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first uh I'd put an El system
+
+ align:start position:0%
+first uh I'd put an El system
+ 
+
+ align:start position:0%
+first uh I'd put an El system
+in secondly as
+
+ align:start position:0%
+in secondly as
+ 
+
+ align:start position:0%
+in secondly as
+opposed and get rid of the
+
+ align:start position:0%
+opposed and get rid of the
+ 
+
+ align:start position:0%
+opposed and get rid of the
+Hydraulics because I think that's
+
+ align:start position:0%
+Hydraulics because I think that's
+ 
+
+ align:start position:0%
+Hydraulics because I think that's
+a uh a maintenance problem and I think
+
+ align:start position:0%
+a uh a maintenance problem and I think
+ 
+
+ align:start position:0%
+a uh a maintenance problem and I think
+that the apus are always going to be a
+
+ align:start position:0%
+that the apus are always going to be a
+ 
+
+ align:start position:0%
+that the apus are always going to be a
+problem because you're you got something
+
+ align:start position:0%
+problem because you're you got something
+ 
+
+ align:start position:0%
+problem because you're you got something
+that's turning up at 40,000 RPM a rotor
+
+ align:start position:0%
+that's turning up at 40,000 RPM a rotor
+ 
+
+ align:start position:0%
+that's turning up at 40,000 RPM a rotor
+that's about that big turning up 40,000
+
+ align:start position:0%
+that's about that big turning up 40,000
+ 
+
+ align:start position:0%
+that's about that big turning up 40,000
+RPM and that because that 40,000 RPM
+
+ align:start position:0%
+RPM and that because that 40,000 RPM
+ 
+
+ align:start position:0%
+RPM and that because that 40,000 RPM
+actually instead of this diameter is now
+
+ align:start position:0%
+actually instead of this diameter is now
+ 
+
+ align:start position:0%
+actually instead of this diameter is now
+an eigh to quarter of an inch bigger
+
+ align:start position:0%
+an eigh to quarter of an inch bigger
+ 
+
+ align:start position:0%
+an eigh to quarter of an inch bigger
+because the metal is stretching under
+
+ align:start position:0%
+because the metal is stretching under
+ 
+
+ align:start position:0%
+because the metal is stretching under
+those conditions the valves we've had
+
+ align:start position:0%
+those conditions the valves we've had
+ 
+
+ align:start position:0%
+those conditions the valves we've had
+trouble with as you well know this the
+
+ align:start position:0%
+trouble with as you well know this the
+ 
+
+ align:start position:0%
+trouble with as you well know this the
+material where this thing is pulsing so
+
+ align:start position:0%
+material where this thing is pulsing so
+ 
+
+ align:start position:0%
+material where this thing is pulsing so
+i' I'd go to and and that's been these
+
+ align:start position:0%
+i' I'd go to and and that's been these
+ 
+
+ align:start position:0%
+i' I'd go to and and that's been these
+are nothing new there are designs there
+
+ align:start position:0%
+are nothing new there are designs there
+ 
+
+ align:start position:0%
+are nothing new there are designs there
+are electric motors there are Power
+
+ align:start position:0%
+are electric motors there are Power
+ 
+
+ align:start position:0%
+are electric motors there are Power
+Systems that would do it much better
+
+ align:start position:0%
+Systems that would do it much better
+ 
+
+ align:start position:0%
+Systems that would do it much better
+than the a than a hydraulic
+
+ align:start position:0%
+than the a than a hydraulic
+ 
+
+ align:start position:0%
+than the a than a hydraulic
+system uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those two systems I think are are
+
+ align:start position:0%
+those two systems I think are are
+ 
+
+ align:start position:0%
+those two systems I think are are
+primary
+
+ align:start position:0%
+primary
+ 
+
+ align:start position:0%
+primary
+now the other thing is you have to keep
+
+ align:start position:0%
+now the other thing is you have to keep
+ 
+
+ align:start position:0%
+now the other thing is you have to keep
+up with the stateof thee art and the
+
+ align:start position:0%
+up with the stateof thee art and the
+ 
+
+ align:start position:0%
+up with the stateof thee art and the
+problem you have one of the biggest
+
+ align:start position:0%
+problem you have one of the biggest
+ 
+
+ align:start position:0%
+problem you have one of the biggest
+problems you have in the shle today
+
+ align:start position:0%
+problems you have in the shle today
+ 
+
+ align:start position:0%
+problems you have in the shle today
+nobody builds the parts anymore you go
+
+ align:start position:0%
+nobody builds the parts anymore you go
+ 
+
+ align:start position:0%
+nobody builds the parts anymore you go
+to the manufacturers and they say oh
+
+ align:start position:0%
+to the manufacturers and they say oh
+ 
+
+ align:start position:0%
+to the manufacturers and they say oh
+stopped building that system 10 years
+
+ align:start position:0%
+stopped building that system 10 years
+ 
+
+ align:start position:0%
+stopped building that system 10 years
+ago so all the circuit boards everything
+
+ align:start position:0%
+ago so all the circuit boards everything
+ 
+
+ align:start position:0%
+ago so all the circuit boards everything
+is pass a and that sounds like well we
+
+ align:start position:0%
+is pass a and that sounds like well we
+ 
+
+ align:start position:0%
+is pass a and that sounds like well we
+just change the circuit board well
+
+ align:start position:0%
+just change the circuit board well
+ 
+
+ align:start position:0%
+just change the circuit board well
+that's that is a problem because the
+
+ align:start position:0%
+that's that is a problem because the
+ 
+
+ align:start position:0%
+that's that is a problem because the
+process specs are got to be looked at
+
+ align:start position:0%
+process specs are got to be looked at
+ 
+
+ align:start position:0%
+process specs are got to be looked at
+the uh sneak
+
+ align:start position:0%
+the uh sneak
+ 
+
+ align:start position:0%
+the uh sneak
+circuitry the sleak pths it got to be
+
+ align:start position:0%
+circuitry the sleak pths it got to be
+ 
+
+ align:start position:0%
+circuitry the sleak pths it got to be
+looked at because that was the thing
+
+ align:start position:0%
+looked at because that was the thing
+ 
+
+ align:start position:0%
+looked at because that was the thing
+that always got to us and bace flight
+
+ align:start position:0%
+that always got to us and bace flight
+ 
+
+ align:start position:0%
+that always got to us and bace flight
+was everything works fine in an noral
+
+ align:start position:0%
+was everything works fine in an noral
+ 
+
+ align:start position:0%
+was everything works fine in an noral
+thing but someday somebody turned
+
+ align:start position:0%
+thing but someday somebody turned
+ 
+
+ align:start position:0%
+thing but someday somebody turned
+something off and the thing glitched and
+
+ align:start position:0%
+something off and the thing glitched and
+ 
+
+ align:start position:0%
+something off and the thing glitched and
+you know it fired the retro rocket or
+
+ align:start position:0%
+you know it fired the retro rocket or
+ 
+
+ align:start position:0%
+you know it fired the retro rocket or
+something like that and uh so you have
+
+ align:start position:0%
+something like that and uh so you have
+ 
+
+ align:start position:0%
+something like that and uh so you have
+to be sure that when you do redesign the
+
+ align:start position:0%
+to be sure that when you do redesign the
+ 
+
+ align:start position:0%
+to be sure that when you do redesign the
+circuitry into the modern world all that
+
+ align:start position:0%
+circuitry into the modern world all that
+ 
+
+ align:start position:0%
+circuitry into the modern world all that
+it's properly
+
+ align:start position:0%
+it's properly
+ 
+
+ align:start position:0%
+it's properly
+done uh a lot of things you don't need
+
+ align:start position:0%
+done uh a lot of things you don't need
+ 
+
+ align:start position:0%
+done uh a lot of things you don't need
+on Space Shuttle problem you don't need
+
+ align:start position:0%
+on Space Shuttle problem you don't need
+ 
+
+ align:start position:0%
+on Space Shuttle problem you don't need
+the backup flight control system which
+
+ align:start position:0%
+the backup flight control system which
+ 
+
+ align:start position:0%
+the backup flight control system which
+is cost a lot of
+
+ align:start position:0%
+is cost a lot of
+ 
+
+ align:start position:0%
+is cost a lot of
+money uh and and then I think I the
+
+ align:start position:0%
+money uh and and then I think I the
+ 
+
+ align:start position:0%
+money uh and and then I think I the
+biggest thing I would do is force the
+
+ align:start position:0%
+biggest thing I would do is force the
+ 
+
+ align:start position:0%
+biggest thing I would do is force the
+system to use automated
+
+ align:start position:0%
+system to use automated
+ 
+
+ align:start position:0%
+system to use automated
+checkup that's where the money is I
+
+ align:start position:0%
+checkup that's where the money is I
+ 
+
+ align:start position:0%
+checkup that's where the money is I
+think in uh maintaining the Machining is
+
+ align:start position:0%
+think in uh maintaining the Machining is
+ 
+
+ align:start position:0%
+think in uh maintaining the Machining is
+the uh nobody is willing to use
+
+ align:start position:0%
+the uh nobody is willing to use
+ 
+
+ align:start position:0%
+the uh nobody is willing to use
+automatic checkup it's
+
+ align:start position:0%
+automatic checkup it's
+ 
+
+ align:start position:0%
+automatic checkup it's
+there and you could do it very easily
+
+ align:start position:0%
+there and you could do it very easily
+ 
+
+ align:start position:0%
+there and you could do it very easily
+but people who take nille are they need
+
+ align:start position:0%
+but people who take nille are they need
+ 
+
+ align:start position:0%
+but people who take nille are they need
+to be flight
+
+ align:start position:0%
+to be flight
+ 
+
+ align:start position:0%
+to be flight
+controllers uh what I mean by that
+
+ align:start position:0%
+controllers uh what I mean by that
+ 
+
+ align:start position:0%
+controllers uh what I mean by that
+is the people like C canav who who
+
+ align:start position:0%
+is the people like C canav who who
+ 
+
+ align:start position:0%
+is the people like C canav who who
+prepare and maintain the machine have a
+
+ align:start position:0%
+prepare and maintain the machine have a
+ 
+
+ align:start position:0%
+prepare and maintain the machine have a
+totally different approach to the space
+
+ align:start position:0%
+totally different approach to the space
+ 
+
+ align:start position:0%
+totally different approach to the space
+machine than the FL controllers do the
+
+ align:start position:0%
+machine than the FL controllers do the
+ 
+
+ align:start position:0%
+machine than the FL controllers do the
+people at DEC want it to be perfect when
+
+ align:start position:0%
+people at DEC want it to be perfect when
+ 
+
+ align:start position:0%
+people at DEC want it to be perfect when
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+launched so when they do the checkout
+
+ align:start position:0%
+launched so when they do the checkout
+ 
+
+ align:start position:0%
+launched so when they do the checkout
+and it doesn't work right they go plug a
+
+ align:start position:0%
+and it doesn't work right they go plug a
+ 
+
+ align:start position:0%
+and it doesn't work right they go plug a
+new board in or they go put a new system
+
+ align:start position:0%
+new board in or they go put a new system
+ 
+
+ align:start position:0%
+new board in or they go put a new system
+in or change out the fuel cell a flight
+
+ align:start position:0%
+in or change out the fuel cell a flight
+ 
+
+ align:start position:0%
+in or change out the fuel cell a flight
+controller does not have that
+
+ align:start position:0%
+controller does not have that
+ 
+
+ align:start position:0%
+controller does not have that
+prerogative he's got to figure out how
+
+ align:start position:0%
+prerogative he's got to figure out how
+ 
+
+ align:start position:0%
+prerogative he's got to figure out how
+how do I live with what I've got and
+
+ align:start position:0%
+how do I live with what I've got and
+ 
+
+ align:start position:0%
+how do I live with what I've got and
+make the best of
+
+ align:start position:0%
+make the best of
+ 
+
+ align:start position:0%
+make the best of
+it I think that's the best attitude and
+
+ align:start position:0%
+it I think that's the best attitude and
+ 
+
+ align:start position:0%
+it I think that's the best attitude and
+you need more of that in the maintenance
+
+ align:start position:0%
+you need more of that in the maintenance
+ 
+
+ align:start position:0%
+you need more of that in the maintenance
+side of the of the things that I think
+
+ align:start position:0%
+side of the of the things that I think
+ 
+
+ align:start position:0%
+side of the of the things that I think
+the biggest that's where the biggest
+
+ align:start position:0%
+the biggest that's where the biggest
+ 
+
+ align:start position:0%
+the biggest that's where the biggest
+savings the biggest Improvement could be
+
+ align:start position:0%
+savings the biggest Improvement could be
+ 
+
+ align:start position:0%
+savings the biggest Improvement could be
+made in space
+
+ align:start position:0%
+made in space
+ 
+
+ align:start position:0%
+made in space
+shuttle the other thing I think about is
+
+ align:start position:0%
+shuttle the other thing I think about is
+ 
+
+ align:start position:0%
+shuttle the other thing I think about is
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+engine
+
+ align:start position:0%
+engine
+ 
+
+ align:start position:0%
+engine
+ssme I think if you derated the ssme so
+
+ align:start position:0%
+ssme I think if you derated the ssme so
+ 
+
+ align:start position:0%
+ssme I think if you derated the ssme so
+that the turnaround time on the engine
+
+ align:start position:0%
+that the turnaround time on the engine
+ 
+
+ align:start position:0%
+that the turnaround time on the engine
+and the reliability of the engine would
+
+ align:start position:0%
+and the reliability of the engine would
+ 
+
+ align:start position:0%
+and the reliability of the engine would
+go up
+
+ align:start position:0%
+go up
+ 
+
+ align:start position:0%
+go up
+significantly significantly if you
+
+ align:start position:0%
+significantly significantly if you
+ 
+
+ align:start position:0%
+significantly significantly if you
+derated the engine IE instead of asking
+
+ align:start position:0%
+derated the engine IE instead of asking
+ 
+
+ align:start position:0%
+derated the engine IE instead of asking
+it to put out8 every time you go to the
+
+ align:start position:0%
+it to put out8 every time you go to the
+ 
+
+ align:start position:0%
+it to put out8 every time you go to the
+space station because you're going up to
+
+ align:start position:0%
+space station because you're going up to
+ 
+
+ align:start position:0%
+space station because you're going up to
+the higher
+
+ align:start position:0%
+the higher
+ 
+
+ align:start position:0%
+the higher
+inclinations you just put a bigger and
+
+ align:start position:0%
+inclinations you just put a bigger and
+ 
+
+ align:start position:0%
+inclinations you just put a bigger and
+bigger head in it or whatever it is what
+
+ align:start position:0%
+bigger head in it or whatever it is what
+ 
+
+ align:start position:0%
+bigger head in it or whatever it is what
+it take whatever it takes to derate the
+
+ align:start position:0%
+it take whatever it takes to derate the
+ 
+
+ align:start position:0%
+it take whatever it takes to derate the
+engine make it run at 95% power was the
+
+ align:start position:0%
+engine make it run at 95% power was the
+ 
+
+ align:start position:0%
+engine make it run at 95% power was the
+thing to last forever to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that mention
+
+ align:start position:0%
+that mention
+ 
+
+ align:start position:0%
+that mention
+uh talk about going back to the and I
+
+ align:start position:0%
+uh talk about going back to the and I
+ 
+
+ align:start position:0%
+uh talk about going back to the and I
+was going to ask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you couple of parts of the question one
+
+ align:start position:0%
+you couple of parts of the question one
+ 
+
+ align:start position:0%
+you couple of parts of the question one
+is what for two is it to go to the moon
+
+ align:start position:0%
+is what for two is it to go to the moon
+ 
+
+ align:start position:0%
+is what for two is it to go to the moon
+or is a stepping stone to do something
+
+ align:start position:0%
+or is a stepping stone to do something
+ 
+
+ align:start position:0%
+or is a stepping stone to do something
+else and then perhaps you could comment
+
+ align:start position:0%
+else and then perhaps you could comment
+ 
+
+ align:start position:0%
+else and then perhaps you could comment
+on what your prediction is for the Space
+
+ align:start position:0%
+on what your prediction is for the Space
+ 
+
+ align:start position:0%
+on what your prediction is for the Space
+Program in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+future I go back to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Boon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh well I think that there are enough
+
+ align:start position:0%
+uh well I think that there are enough
+ 
+
+ align:start position:0%
+uh well I think that there are enough
+resources on the
+
+ align:start position:0%
+resources on the
+ 
+
+ align:start position:0%
+resources on the
+moon to make it economically viable
+
+ align:start position:0%
+moon to make it economically viable
+ 
+
+ align:start position:0%
+moon to make it economically viable
+number one number two I think you
+
+ align:start position:0%
+number one number two I think you
+ 
+
+ align:start position:0%
+number one number two I think you
+could uh develop enough electrical power
+
+ align:start position:0%
+could uh develop enough electrical power
+ 
+
+ align:start position:0%
+could uh develop enough electrical power
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+moon to provide a
+
+ align:start position:0%
+moon to provide a
+ 
+
+ align:start position:0%
+moon to provide a
+uh enough power for the people that were
+
+ align:start position:0%
+uh enough power for the people that were
+ 
+
+ align:start position:0%
+uh enough power for the people that were
+going to live there and be stationed
+
+ align:start position:0%
+going to live there and be stationed
+ 
+
+ align:start position:0%
+going to live there and be stationed
+there permanently and it and you would
+
+ align:start position:0%
+there permanently and it and you would
+ 
+
+ align:start position:0%
+there permanently and it and you would
+do it on the back side by the way not on
+
+ align:start position:0%
+do it on the back side by the way not on
+ 
+
+ align:start position:0%
+do it on the back side by the way not on
+the front side because that's where you
+
+ align:start position:0%
+the front side because that's where you
+ 
+
+ align:start position:0%
+the front side because that's where you
+want it you would want your permanent
+
+ align:start position:0%
+want it you would want your permanent
+ 
+
+ align:start position:0%
+want it you would want your permanent
+base on the moon to be on the back side
+
+ align:start position:0%
+base on the moon to be on the back side
+ 
+
+ align:start position:0%
+base on the moon to be on the back side
+because it would be shielded from all
+
+ align:start position:0%
+because it would be shielded from all
+ 
+
+ align:start position:0%
+because it would be shielded from all
+the electronic signals from the earth so
+
+ align:start position:0%
+the electronic signals from the earth so
+ 
+
+ align:start position:0%
+the electronic signals from the earth so
+it's the best place in the world to look
+
+ align:start position:0%
+it's the best place in the world to look
+ 
+
+ align:start position:0%
+it's the best place in the world to look
+at the rest of the
+
+ align:start position:0%
+at the rest of the
+ 
+
+ align:start position:0%
+at the rest of the
+universe so I build my Bas bace on the
+
+ align:start position:0%
+universe so I build my Bas bace on the
+ 
+
+ align:start position:0%
+universe so I build my Bas bace on the
+back side of the moon
+
+ align:start position:0%
+back side of the moon
+ 
+
+ align:start position:0%
+back side of the moon
+and then I I believe there
+
+ align:start position:0%
+and then I I believe there
+ 
+
+ align:start position:0%
+and then I I believe there
+are possibilities although it's not
+
+ align:start position:0%
+are possibilities although it's not
+ 
+
+ align:start position:0%
+are possibilities although it's not
+technically sound yet but I believe
+
+ align:start position:0%
+technically sound yet but I believe
+ 
+
+ align:start position:0%
+technically sound yet but I believe
+there are possibilities of pro of
+
+ align:start position:0%
+there are possibilities of pro of
+ 
+
+ align:start position:0%
+there are possibilities of pro of
+providing enough electrical
+
+ align:start position:0%
+providing enough electrical
+ 
+
+ align:start position:0%
+providing enough electrical
+power to the Earth from the Moon that
+
+ align:start position:0%
+power to the Earth from the Moon that
+ 
+
+ align:start position:0%
+power to the Earth from the Moon that
+you could shut down every Power Plant in
+
+ align:start position:0%
+you could shut down every Power Plant in
+ 
+
+ align:start position:0%
+you could shut down every Power Plant in
+Europe you get that much electrical
+
+ align:start position:0%
+Europe you get that much electrical
+ 
+
+ align:start position:0%
+Europe you get that much electrical
+energy from the Moon and that would
+
+ align:start position:0%
+energy from the Moon and that would
+ 
+
+ align:start position:0%
+energy from the Moon and that would
+certainly
+
+ align:start position:0%
+certainly
+ 
+
+ align:start position:0%
+certainly
+offload the power requirements on the
+
+ align:start position:0%
+offload the power requirements on the
+ 
+
+ align:start position:0%
+offload the power requirements on the
+earth which are
+
+ align:start position:0%
+earth which are
+ 
+
+ align:start position:0%
+earth which are
+almost logarithmic aren't
+
+ align:start position:0%
+almost logarithmic aren't
+ 
+
+ align:start position:0%
+almost logarithmic aren't
+they uh China end up using more
+
+ align:start position:0%
+they uh China end up using more
+ 
+
+ align:start position:0%
+they uh China end up using more
+electrical to and we do shortly so we
+
+ align:start position:0%
+electrical to and we do shortly so we
+ 
+
+ align:start position:0%
+electrical to and we do shortly so we
+need electrical power and I think you
+
+ align:start position:0%
+need electrical power and I think you
+ 
+
+ align:start position:0%
+need electrical power and I think you
+could get that from the moon plus I
+
+ align:start position:0%
+could get that from the moon plus I
+ 
+
+ align:start position:0%
+could get that from the moon plus I
+think that
+
+ align:start position:0%
+think that
+ 
+
+ align:start position:0%
+think that
+the geophysicist and the
+
+ align:start position:0%
+the geophysicist and the
+ 
+
+ align:start position:0%
+the geophysicist and the
+geologists astrophysicists all can give
+
+ align:start position:0%
+geologists astrophysicists all can give
+ 
+
+ align:start position:0%
+geologists astrophysicists all can give
+you a thousand reasons why you should go
+
+ align:start position:0%
+you a thousand reasons why you should go
+ 
+
+ align:start position:0%
+you a thousand reasons why you should go
+back to the Moon because it's still they
+
+ align:start position:0%
+back to the Moon because it's still they
+ 
+
+ align:start position:0%
+back to the Moon because it's still they
+what what
+
+ align:start position:0%
+what what
+ 
+
+ align:start position:0%
+what what
+uh L Yuri what you Mr what Professor
+
+ align:start position:0%
+uh L Yuri what you Mr what Professor
+ 
+
+ align:start position:0%
+uh L Yuri what you Mr what Professor
+Yuri said it is the Ros Rosetta Stone of
+
+ align:start position:0%
+Yuri said it is the Ros Rosetta Stone of
+ 
+
+ align:start position:0%
+Yuri said it is the Ros Rosetta Stone of
+the universe there's more to be known
+
+ align:start position:0%
+the universe there's more to be known
+ 
+
+ align:start position:0%
+the universe there's more to be known
+from the Moon about the
+
+ align:start position:0%
+from the Moon about the
+ 
+
+ align:start position:0%
+from the Moon about the
+Earth than you can ever get out of the
+
+ align:start position:0%
+Earth than you can ever get out of the
+ 
+
+ align:start position:0%
+Earth than you can ever get out of the
+earth so it's still very useful to go
+
+ align:start position:0%
+earth so it's still very useful to go
+ 
+
+ align:start position:0%
+earth so it's still very useful to go
+back there from the scientific point of
+
+ align:start position:0%
+back there from the scientific point of
+ 
+
+ align:start position:0%
+back there from the scientific point of
+view plus the engineering and economics
+
+ align:start position:0%
+view plus the engineering and economics
+ 
+
+ align:start position:0%
+view plus the engineering and economics
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+it uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think it's I I didn't say it but I
+
+ align:start position:0%
+I think it's I I didn't say it but I
+ 
+
+ align:start position:0%
+I think it's I I didn't say it but I
+think because I'm wasn't sure you wanted
+
+ align:start position:0%
+think because I'm wasn't sure you wanted
+ 
+
+ align:start position:0%
+think because I'm wasn't sure you wanted
+to have such discussion but uh I will I
+
+ align:start position:0%
+to have such discussion but uh I will I
+ 
+
+ align:start position:0%
+to have such discussion but uh I will I
+think it's a travesty that we aren't
+
+ align:start position:0%
+think it's a travesty that we aren't
+ 
+
+ align:start position:0%
+think it's a travesty that we aren't
+doing it with the space shuttle and the
+
+ align:start position:0%
+doing it with the space shuttle and the
+ 
+
+ align:start position:0%
+doing it with the space shuttle and the
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+station to go back to the moon or to go
+
+ align:start position:0%
+station to go back to the moon or to go
+ 
+
+ align:start position:0%
+station to go back to the moon or to go
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Mars why do I think that
+
+ align:start position:0%
+Mars why do I think that
+ 
+
+ align:start position:0%
+Mars why do I think that
+because if you go to either case I I
+
+ align:start position:0%
+because if you go to either case I I
+ 
+
+ align:start position:0%
+because if you go to either case I I
+don't understand why you want to build
+
+ align:start position:0%
+don't understand why you want to build
+ 
+
+ align:start position:0%
+don't understand why you want to build
+an earth entering vehicle
+
+ align:start position:0%
+an earth entering vehicle
+ 
+
+ align:start position:0%
+an earth entering vehicle
+to go to the moon what you want is an
+
+ align:start position:0%
+to go to the moon what you want is an
+ 
+
+ align:start position:0%
+to go to the moon what you want is an
+inter inter interplanetary
+
+ align:start position:0%
+inter inter interplanetary
+ 
+
+ align:start position:0%
+inter inter interplanetary
+spacecraft why does it have to have a
+
+ align:start position:0%
+spacecraft why does it have to have a
+ 
+
+ align:start position:0%
+spacecraft why does it have to have a
+heat shield why does it have to have
+
+ align:start position:0%
+heat shield why does it have to have
+ 
+
+ align:start position:0%
+heat shield why does it have to have
+parachutes why does it have or some kind
+
+ align:start position:0%
+parachutes why does it have or some kind
+ 
+
+ align:start position:0%
+parachutes why does it have or some kind
+of Landing capability why not just go to
+
+ align:start position:0%
+of Landing capability why not just go to
+ 
+
+ align:start position:0%
+of Landing capability why not just go to
+and from Earth orbit and the space
+
+ align:start position:0%
+and from Earth orbit and the space
+ 
+
+ align:start position:0%
+and from Earth orbit and the space
+shuttle the
+
+ align:start position:0%
+shuttle the
+ 
+
+ align:start position:0%
+shuttle the
+greatest machine for carrying things to
+
+ align:start position:0%
+greatest machine for carrying things to
+ 
+
+ align:start position:0%
+greatest machine for carrying things to
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+from orbit that's ever been thought of
+
+ align:start position:0%
+from orbit that's ever been thought of
+ 
+
+ align:start position:0%
+from orbit that's ever been thought of
+and the one they're going to build
+
+ align:start position:0%
+and the one they're going to build
+ 
+
+ align:start position:0%
+and the one they're going to build
+is even if it's an unmanned vehicle it's
+
+ align:start position:0%
+is even if it's an unmanned vehicle it's
+ 
+
+ align:start position:0%
+is even if it's an unmanned vehicle it's
+still going to have awful lot of
+
+ align:start position:0%
+still going to have awful lot of
+ 
+
+ align:start position:0%
+still going to have awful lot of
+complexity to it so I and I think that
+
+ align:start position:0%
+complexity to it so I and I think that
+ 
+
+ align:start position:0%
+complexity to it so I and I think that
+you've made the space shuttle
+
+ align:start position:0%
+you've made the space shuttle
+ 
+
+ align:start position:0%
+you've made the space shuttle
+economically viable which nobody thinks
+
+ align:start position:0%
+economically viable which nobody thinks
+ 
+
+ align:start position:0%
+economically viable which nobody thinks
+you can and maybe Chris Craft is the
+
+ align:start position:0%
+you can and maybe Chris Craft is the
+ 
+
+ align:start position:0%
+you can and maybe Chris Craft is the
+only one that thinks you can and you
+
+ align:start position:0%
+only one that thinks you can and you
+ 
+
+ align:start position:0%
+only one that thinks you can and you
+know that's if that's true that's true I
+
+ align:start position:0%
+know that's if that's true that's true I
+ 
+
+ align:start position:0%
+know that's if that's true that's true I
+don't think that way I think the space
+
+ align:start position:0%
+don't think that way I think the space
+ 
+
+ align:start position:0%
+don't think that way I think the space
+shuttle is an an economically viable
+
+ align:start position:0%
+shuttle is an an economically viable
+ 
+
+ align:start position:0%
+shuttle is an an economically viable
+machine and I so it's a travesty to me
+
+ align:start position:0%
+machine and I so it's a travesty to me
+ 
+
+ align:start position:0%
+machine and I so it's a travesty to me
+to throw it away
+
+ align:start position:0%
+to throw it away
+ 
+
+ align:start position:0%
+to throw it away
+and the space station could be used as
+
+ align:start position:0%
+and the space station could be used as
+ 
+
+ align:start position:0%
+and the space station could be used as
+the place where you assemble all this
+
+ align:start position:0%
+the place where you assemble all this
+ 
+
+ align:start position:0%
+the place where you assemble all this
+stuff and everybody says well it's up
+
+ align:start position:0%
+stuff and everybody says well it's up
+ 
+
+ align:start position:0%
+stuff and everybody says well it's up
+it's at the wrong inclination yes it is
+
+ align:start position:0%
+it's at the wrong inclination yes it is
+ 
+
+ align:start position:0%
+it's at the wrong inclination yes it is
+at the wrong inclination we were foolish
+
+ align:start position:0%
+at the wrong inclination we were foolish
+ 
+
+ align:start position:0%
+at the wrong inclination we were foolish
+to put it there in the first place but
+
+ align:start position:0%
+to put it there in the first place but
+ 
+
+ align:start position:0%
+to put it there in the first place but
+that's where it is
+
+ align:start position:0%
+that's where it is
+ 
+
+ align:start position:0%
+that's where it is
+but uh every time I had a little bit of
+
+ align:start position:0%
+but uh every time I had a little bit of
+ 
+
+ align:start position:0%
+but uh every time I had a little bit of
+fuel left over I inch it down a little
+
+ align:start position:0%
+fuel left over I inch it down a little
+ 
+
+ align:start position:0%
+fuel left over I inch it down a little
+bit you know and the first thing you
+
+ align:start position:0%
+bit you know and the first thing you
+ 
+
+ align:start position:0%
+bit you know and the first thing you
+know it'd be down to 28 and a half
+
+ align:start position:0%
+know it'd be down to 28 and a half
+ 
+
+ align:start position:0%
+know it'd be down to 28 and a half
+degrees and it wouldn't cost today it
+
+ align:start position:0%
+degrees and it wouldn't cost today it
+ 
+
+ align:start position:0%
+degrees and it wouldn't cost today it
+cost you 15,000
+
+ align:start position:0%
+cost you 15,000
+ 
+
+ align:start position:0%
+cost you 15,000
+of payload to go to the space station
+
+ align:start position:0%
+of payload to go to the space station
+ 
+
+ align:start position:0%
+of payload to go to the space station
+and that's a travesty too so you would
+
+ align:start position:0%
+and that's a travesty too so you would
+ 
+
+ align:start position:0%
+and that's a travesty too so you would
+want to do that continuously but uh so
+
+ align:start position:0%
+want to do that continuously but uh so
+ 
+
+ align:start position:0%
+want to do that continuously but uh so
+i' I'd use the space station as my
+
+ align:start position:0%
+i' I'd use the space station as my
+ 
+
+ align:start position:0%
+i' I'd use the space station as my
+assembly point and I'd use the space sh
+
+ align:start position:0%
+assembly point and I'd use the space sh
+ 
+
+ align:start position:0%
+assembly point and I'd use the space sh
+shuttle as the machine to go there and
+
+ align:start position:0%
+shuttle as the machine to go there and
+ 
+
+ align:start position:0%
+shuttle as the machine to go there and
+then I'd build myself a bunch of
+
+ align:start position:0%
+then I'd build myself a bunch of
+ 
+
+ align:start position:0%
+then I'd build myself a bunch of
+interplanetary spacecraft to go to and
+
+ align:start position:0%
+interplanetary spacecraft to go to and
+ 
+
+ align:start position:0%
+interplanetary spacecraft to go to and
+from the the moon and Mars and when I
+
+ align:start position:0%
+from the the moon and Mars and when I
+ 
+
+ align:start position:0%
+from the the moon and Mars and when I
+did that uh I'd be smart enough to build
+
+ align:start position:0%
+did that uh I'd be smart enough to build
+ 
+
+ align:start position:0%
+did that uh I'd be smart enough to build
+all these new fangles
+
+ align:start position:0%
+all these new fangles
+ 
+
+ align:start position:0%
+all these new fangles
+structures inflatable structures Etc
+
+ align:start position:0%
+structures inflatable structures Etc
+ 
+
+ align:start position:0%
+structures inflatable structures Etc
+which you could use not only as the in
+
+ align:start position:0%
+which you could use not only as the in
+ 
+
+ align:start position:0%
+which you could use not only as the in
+prioritary spacecraft but you use that
+
+ align:start position:0%
+prioritary spacecraft but you use that
+ 
+
+ align:start position:0%
+prioritary spacecraft but you use that
+place where you would live on the moon
+
+ align:start position:0%
+place where you would live on the moon
+ 
+
+ align:start position:0%
+place where you would live on the moon
+so I I think it has a better approach
+
+ align:start position:0%
+so I I think it has a better approach
+ 
+
+ align:start position:0%
+so I I think it has a better approach
+from an engineering point of
+
+ align:start position:0%
+from an engineering point of
+ 
+
+ align:start position:0%
+from an engineering point of
+view whether that's the
+
+ align:start position:0%
+view whether that's the
+ 
+
+ align:start position:0%
+view whether that's the
+political way to sell the program Mr
+
+ align:start position:0%
+political way to sell the program Mr
+ 
+
+ align:start position:0%
+political way to sell the program Mr
+Griffin has got to do that I mean that's
+
+ align:start position:0%
+Griffin has got to do that I mean that's
+ 
+
+ align:start position:0%
+Griffin has got to do that I mean that's
+what his job is fortunately it's not
+
+ align:start position:0%
+what his job is fortunately it's not
+ 
+
+ align:start position:0%
+what his job is fortunately it's not
+mine I was to be the Deputy
+
+ align:start position:0%
+mine I was to be the Deputy
+ 
+
+ align:start position:0%
+mine I was to be the Deputy
+Administrator and the administrator of
+
+ align:start position:0%
+Administrator and the administrator of
+ 
+
+ align:start position:0%
+Administrator and the administrator of
+NASA several
+
+ align:start position:0%
+NASA several
+ 
+
+ align:start position:0%
+NASA several
+times and you can hear the way I talk
+
+ align:start position:0%
+times and you can hear the way I talk
+ 
+
+ align:start position:0%
+times and you can hear the way I talk
+here I to last about six days to six
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+months uh what do I think about
+
+ align:start position:0%
+months uh what do I think about
+ 
+
+ align:start position:0%
+months uh what do I think about
+tomorrow's what do I think about the
+
+ align:start position:0%
+tomorrow's what do I think about the
+ 
+
+ align:start position:0%
+tomorrow's what do I think about the
+possibilities of today's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plans hate to say this but I think it's
+
+ align:start position:0%
+plans hate to say this but I think it's
+ 
+
+ align:start position:0%
+plans hate to say this but I think it's
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+fail I don't think it'll work
+
+ align:start position:0%
+fail I don't think it'll work
+ 
+
+ align:start position:0%
+fail I don't think it'll work
+I don't think the program
+
+ align:start position:0%
+I don't think the program
+ 
+
+ align:start position:0%
+I don't think the program
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+uh stipulated today is the way to do
+
+ align:start position:0%
+uh stipulated today is the way to do
+ 
+
+ align:start position:0%
+uh stipulated today is the way to do
+it and I don't think the political
+
+ align:start position:0%
+it and I don't think the political
+ 
+
+ align:start position:0%
+it and I don't think the political
+climate is such that the budgetary
+
+ align:start position:0%
+climate is such that the budgetary
+ 
+
+ align:start position:0%
+climate is such that the budgetary
+support will be
+
+ align:start position:0%
+support will be
+ 
+
+ align:start position:0%
+support will be
+provided and I hope I'm
+
+ align:start position:0%
+provided and I hope I'm
+ 
+
+ align:start position:0%
+provided and I hope I'm
+wrong I don't think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I pardon
+
+ align:start position:0%
+I pardon
+ 
+
+ align:start position:0%
+I pardon
+now hell Chinese are 50 years from the
+
+ align:start position:0%
+now hell Chinese are 50 years from the
+ 
+
+ align:start position:0%
+now hell Chinese are 50 years from the
+going to the Moon they can't buy it from
+
+ align:start position:0%
+going to the Moon they can't buy it from
+ 
+
+ align:start position:0%
+going to the Moon they can't buy it from
+Russia that's what they're doing today
+
+ align:start position:0%
+Russia that's what they're doing today
+ 
+
+ align:start position:0%
+Russia that's what they're doing today
+they're buying all the technology to put
+
+ align:start position:0%
+they're buying all the technology to put
+ 
+
+ align:start position:0%
+they're buying all the technology to put
+man in space from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Russia you know the thought that makes
+
+ align:start position:0%
+Russia you know the thought that makes
+ 
+
+ align:start position:0%
+Russia you know the thought that makes
+me think well the Russians still using
+
+ align:start position:0%
+me think well the Russians still using
+ 
+
+ align:start position:0%
+me think well the Russians still using
+the same spacecraft with slight
+
+ align:start position:0%
+the same spacecraft with slight
+ 
+
+ align:start position:0%
+the same spacecraft with slight
+variation that they put gagaran up in
+
+ align:start position:0%
+variation that they put gagaran up in
+ 
+
+ align:start position:0%
+variation that they put gagaran up in
+19 61 literally it's pretty close to it
+
+ align:start position:0%
+19 61 literally it's pretty close to it
+ 
+
+ align:start position:0%
+19 61 literally it's pretty close to it
+I've sat in it have you sat in it
+
+ align:start position:0%
+I've sat in it have you sat in it
+ 
+
+ align:start position:0%
+I've sat in it have you sat in it
+FR sit in it like
+
+ align:start position:0%
+FR sit in it like
+ 
+
+ align:start position:0%
+FR sit in it like
+this uh but they used it over and over
+
+ align:start position:0%
+this uh but they used it over and over
+ 
+
+ align:start position:0%
+this uh but they used it over and over
+and over and over again the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B52 been used over and over again it's
+
+ align:start position:0%
+B52 been used over and over again it's
+ 
+
+ align:start position:0%
+B52 been used over and over again it's
+got a new Wing got new electronics got
+
+ align:start position:0%
+got a new Wing got new electronics got
+ 
+
+ align:start position:0%
+got a new Wing got new electronics got
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+bombs got new everything on it the only
+
+ align:start position:0%
+bombs got new everything on it the only
+ 
+
+ align:start position:0%
+bombs got new everything on it the only
+thing that's the same is the
+
+ align:start position:0%
+thing that's the same is the
+ 
+
+ align:start position:0%
+thing that's the same is the
+configuration got new engines had new
+
+ align:start position:0%
+configuration got new engines had new
+ 
+
+ align:start position:0%
+configuration got new engines had new
+engines probably five times in it's
+
+ align:start position:0%
+engines probably five times in it's
+ 
+
+ align:start position:0%
+engines probably five times in it's
+lifetime that's what we ought to be
+
+ align:start position:0%
+lifetime that's what we ought to be
+ 
+
+ align:start position:0%
+lifetime that's what we ought to be
+doing with the
+
+ align:start position:0%
+doing with the
+ 
+
+ align:start position:0%
+doing with the
+shuttle isn't it why we seem to have
+
+ align:start position:0%
+shuttle isn't it why we seem to have
+ 
+
+ align:start position:0%
+shuttle isn't it why we seem to have
+this great propensity in this country
+
+ align:start position:0%
+this great propensity in this country
+ 
+
+ align:start position:0%
+this great propensity in this country
+for building something wonderful and
+
+ align:start position:0%
+for building something wonderful and
+ 
+
+ align:start position:0%
+for building something wonderful and
+great and high performance and then
+
+ align:start position:0%
+great and high performance and then
+ 
+
+ align:start position:0%
+great and high performance and then
+throwing it
+
+ align:start position:0%
+throwing it
+ 
+
+ align:start position:0%
+throwing it
+away you know we put up the sky lab
+
+ align:start position:0%
+away you know we put up the sky lab
+ 
+
+ align:start position:0%
+away you know we put up the sky lab
+wonderful throw it away don't build
+
+ align:start position:0%
+wonderful throw it away don't build
+ 
+
+ align:start position:0%
+wonderful throw it away don't build
+anymore build a Saturn five
+
+ align:start position:0%
+anymore build a Saturn five
+ 
+
+ align:start position:0%
+anymore build a Saturn five
+will it put 200,000 lbs on
+
+ align:start position:0%
+will it put 200,000 lbs on
+ 
+
+ align:start position:0%
+will it put 200,000 lbs on
+it to the moon it's rotting away at say
+
+ align:start position:0%
+it to the moon it's rotting away at say
+ 
+
+ align:start position:0%
+it to the moon it's rotting away at say
+Johnson space c they got so mad at
+
+ align:start position:0%
+Johnson space c they got so mad at
+ 
+
+ align:start position:0%
+Johnson space c they got so mad at
+people the the trekkies in the country
+
+ align:start position:0%
+people the the trekkies in the country
+ 
+
+ align:start position:0%
+people the the trekkies in the country
+got so mad you at the Johnson Space
+
+ align:start position:0%
+got so mad you at the Johnson Space
+ 
+
+ align:start position:0%
+got so mad you at the Johnson Space
+Center and made them build a hanger to
+
+ align:start position:0%
+Center and made them build a hanger to
+ 
+
+ align:start position:0%
+Center and made them build a hanger to
+put it in so it wouldn't brought
+
+ align:start position:0%
+put it in so it wouldn't brought
+ 
+
+ align:start position:0%
+put it in so it wouldn't brought
+anymore we build a space station we're
+
+ align:start position:0%
+anymore we build a space station we're
+ 
+
+ align:start position:0%
+anymore we build a space station we're
+throwing it away we build a space
+
+ align:start position:0%
+throwing it away we build a space
+ 
+
+ align:start position:0%
+throwing it away we build a space
+shuttle we're throwing it
+
+ align:start position:0%
+shuttle we're throwing it
+ 
+
+ align:start position:0%
+shuttle we're throwing it
+away golly my mother would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bananas we had leftovers at almost every
+
+ align:start position:0%
+bananas we had leftovers at almost every
+ 
+
+ align:start position:0%
+bananas we had leftovers at almost every
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+meal I know that's TR but don't you
+
+ align:start position:0%
+meal I know that's TR but don't you
+ 
+
+ align:start position:0%
+meal I know that's TR but don't you
+think that's
+
+ align:start position:0%
+think that's
+ 
+
+ align:start position:0%
+think that's
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+foolishness do things that way I think
+
+ align:start position:0%
+foolishness do things that way I think
+ 
+
+ align:start position:0%
+foolishness do things that way I think
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+is that you know we did learn from from
+
+ align:start position:0%
+is that you know we did learn from from
+ 
+
+ align:start position:0%
+is that you know we did learn from from
+space FL that everybody seemed to learn
+
+ align:start position:0%
+space FL that everybody seemed to learn
+ 
+
+ align:start position:0%
+space FL that everybody seemed to learn
+from everybody else's experiences that
+
+ align:start position:0%
+from everybody else's experiences that
+ 
+
+ align:start position:0%
+from everybody else's experiences that
+was an amazing fact than me in the early
+
+ align:start position:0%
+was an amazing fact than me in the early
+ 
+
+ align:start position:0%
+was an amazing fact than me in the early
+days particularly the astronauts
+
+ align:start position:0%
+days particularly the astronauts
+ 
+
+ align:start position:0%
+days particularly the astronauts
+would each one that flew was so much
+
+ align:start position:0%
+would each one that flew was so much
+ 
+
+ align:start position:0%
+would each one that flew was so much
+better than the one before knew how to
+
+ align:start position:0%
+better than the one before knew how to
+ 
+
+ align:start position:0%
+better than the one before knew how to
+do the job better than the one before
+
+ align:start position:0%
+do the job better than the one before
+ 
+
+ align:start position:0%
+do the job better than the one before
+and made it so much easier for them and
+
+ align:start position:0%
+and made it so much easier for them and
+ 
+
+ align:start position:0%
+and made it so much easier for them and
+they you know all of those things were
+
+ align:start position:0%
+they you know all of those things were
+ 
+
+ align:start position:0%
+they you know all of those things were
+you could see yourself advancing and
+
+ align:start position:0%
+you could see yourself advancing and
+ 
+
+ align:start position:0%
+you could see yourself advancing and
+it's they just built on this experience
+
+ align:start position:0%
+it's they just built on this experience
+ 
+
+ align:start position:0%
+it's they just built on this experience
+of each man and I don't know how they
+
+ align:start position:0%
+of each man and I don't know how they
+ 
+
+ align:start position:0%
+of each man and I don't know how they
+transmitted that to each other they
+
+ align:start position:0%
+transmitted that to each other they
+ 
+
+ align:start position:0%
+transmitted that to each other they
+didn't obviously because they didn't
+
+ align:start position:0%
+didn't obviously because they didn't
+ 
+
+ align:start position:0%
+didn't obviously because they didn't
+have a brain connection but
+
+ align:start position:0%
+have a brain connection but
+ 
+
+ align:start position:0%
+have a brain connection but
+that's the way we ought to be doing here
+
+ align:start position:0%
+that's the way we ought to be doing here
+ 
+
+ align:start position:0%
+that's the way we ought to be doing here
+we got all these things that we we build
+
+ align:start position:0%
+we got all these things that we we build
+ 
+
+ align:start position:0%
+we got all these things that we we build
+and then throw away and don't take
+
+ align:start position:0%
+and then throw away and don't take
+ 
+
+ align:start position:0%
+and then throw away and don't take
+advantage of that doesn't make a lot of
+
+ align:start position:0%
+advantage of that doesn't make a lot of
+ 
+
+ align:start position:0%
+advantage of that doesn't make a lot of
+sense to me now I know there are
+
+ align:start position:0%
+sense to me now I know there are
+ 
+
+ align:start position:0%
+sense to me now I know there are
+politics involved and that's the reason
+
+ align:start position:0%
+politics involved and that's the reason
+ 
+
+ align:start position:0%
+politics involved and that's the reason
+I said you have to take into account of
+
+ align:start position:0%
+I said you have to take into account of
+ 
+
+ align:start position:0%
+I said you have to take into account of
+politics when can you get the money how
+
+ align:start position:0%
+politics when can you get the money how
+ 
+
+ align:start position:0%
+politics when can you get the money how
+do you convince people that you need to
+
+ align:start position:0%
+do you convince people that you need to
+ 
+
+ align:start position:0%
+do you convince people that you need to
+do things what does it do to the jobs
+
+ align:start position:0%
+do things what does it do to the jobs
+ 
+
+ align:start position:0%
+do things what does it do to the jobs
+situation how does it affect each
+
+ align:start position:0%
+situation how does it affect each
+ 
+
+ align:start position:0%
+situation how does it affect each
+senators and each congressman state in
+
+ align:start position:0%
+senators and each congressman state in
+ 
+
+ align:start position:0%
+senators and each congressman state in
+terms of the money that you bring into
+
+ align:start position:0%
+terms of the money that you bring into
+ 
+
+ align:start position:0%
+terms of the money that you bring into
+that area and that so etc etc we built
+
+ align:start position:0%
+that area and that so etc etc we built
+ 
+
+ align:start position:0%
+that area and that so etc etc we built
+we built the Space Shuttle we had a
+
+ align:start position:0%
+we built the Space Shuttle we had a
+ 
+
+ align:start position:0%
+we built the Space Shuttle we had a
+contract in every state in the Union
+
+ align:start position:0%
+contract in every state in the Union
+ 
+
+ align:start position:0%
+contract in every state in the Union
+except
+
+ align:start position:0%
+except
+ 
+
+ align:start position:0%
+except
+Alaska and we did that on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+purpose I just have to go to all a Aon
+
+ align:start position:0%
+purpose I just have to go to all a Aon
+ 
+
+ align:start position:0%
+purpose I just have to go to all a Aon
+and I flew to every one of those there
+
+ align:start position:0%
+and I flew to every one of those there
+ 
+
+ align:start position:0%
+and I flew to every one of those there
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+major subcontractors in the shuttle and
+
+ align:start position:0%
+major subcontractors in the shuttle and
+ 
+
+ align:start position:0%
+major subcontractors in the shuttle and
+they were all over the country and we go
+
+ align:start position:0%
+they were all over the country and we go
+ 
+
+ align:start position:0%
+they were all over the country and we go
+visit them at least three or four times
+
+ align:start position:0%
+visit them at least three or four times
+ 
+
+ align:start position:0%
+visit them at least three or four times
+in a couple
+
+ align:start position:0%
+in a couple
+ 
+
+ align:start position:0%
+in a couple
+years so the politics has to be there we
+
+ align:start position:0%
+years so the politics has to be there we
+ 
+
+ align:start position:0%
+years so the politics has to be there we
+were lucky in Apollo the I call it the
+
+ align:start position:0%
+were lucky in Apollo the I call it the
+ 
+
+ align:start position:0%
+were lucky in Apollo the I call it the
+conjunction of the stars and the
+
+ align:start position:0%
+conjunction of the stars and the
+ 
+
+ align:start position:0%
+conjunction of the stars and the
+conjunction of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+politics I want I want to tell you
+
+ align:start position:0%
+politics I want I want to tell you
+ 
+
+ align:start position:0%
+politics I want I want to tell you
+that's a story I've meant to
+
+ align:start position:0%
+that's a story I've meant to
+ 
+
+ align:start position:0%
+that's a story I've meant to
+tell uh in about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1978 we 77
+
+ align:start position:0%
+1978 we 77
+ 
+
+ align:start position:0%
+1978 we 77
+may we were really behind the power
+
+ align:start position:0%
+may we were really behind the power
+ 
+
+ align:start position:0%
+may we were really behind the power
+curve on the budget for the
+
+ align:start position:0%
+curve on the budget for the
+ 
+
+ align:start position:0%
+curve on the budget for the
+shuttle we had been pushing a bow wave
+
+ align:start position:0%
+shuttle we had been pushing a bow wave
+ 
+
+ align:start position:0%
+shuttle we had been pushing a bow wave
+of about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10% less funds than we needed each year
+
+ align:start position:0%
+10% less funds than we needed each year
+ 
+
+ align:start position:0%
+10% less funds than we needed each year
+so that in about that time period we
+
+ align:start position:0%
+so that in about that time period we
+ 
+
+ align:start position:0%
+so that in about that time period we
+needed if we were going to have any
+
+ align:start position:0%
+needed if we were going to have any
+ 
+
+ align:start position:0%
+needed if we were going to have any
+semblance of making a
+
+ align:start position:0%
+semblance of making a
+ 
+
+ align:start position:0%
+semblance of making a
+1980 or 81 First Flight we needed $600
+
+ align:start position:0%
+1980 or 81 First Flight we needed $600
+ 
+
+ align:start position:0%
+1980 or 81 First Flight we needed $600
+million doll
+
+ align:start position:0%
+million doll
+ 
+
+ align:start position:0%
+million doll
+supplement and about that much per year
+
+ align:start position:0%
+supplement and about that much per year
+ 
+
+ align:start position:0%
+supplement and about that much per year
+more than we were
+
+ align:start position:0%
+more than we were
+ 
+
+ align:start position:0%
+more than we were
+getting and NASA had this big meeting uh
+
+ align:start position:0%
+getting and NASA had this big meeting uh
+ 
+
+ align:start position:0%
+getting and NASA had this big meeting uh
+down at the Johnson Space Center and we
+
+ align:start position:0%
+down at the Johnson Space Center and we
+ 
+
+ align:start position:0%
+down at the Johnson Space Center and we
+all talked about what the problems were
+
+ align:start position:0%
+all talked about what the problems were
+ 
+
+ align:start position:0%
+all talked about what the problems were
+and how we going to meet that and
+
+ align:start position:0%
+and how we going to meet that and
+ 
+
+ align:start position:0%
+and how we going to meet that and
+everybody absolutely all the politics
+
+ align:start position:0%
+everybody absolutely all the politics
+ 
+
+ align:start position:0%
+everybody absolutely all the politics
+said you can't go ask for a supplement
+
+ align:start position:0%
+said you can't go ask for a supplement
+ 
+
+ align:start position:0%
+said you can't go ask for a supplement
+you can't go ask the Congress for any
+
+ align:start position:0%
+you can't go ask the Congress for any
+ 
+
+ align:start position:0%
+you can't go ask the Congress for any
+more you can't go to the White House and
+
+ align:start position:0%
+more you can't go to the White House and
+ 
+
+ align:start position:0%
+more you can't go to the White House and
+say we need more money so you may just
+
+ align:start position:0%
+say we need more money so you may just
+ 
+
+ align:start position:0%
+say we need more money so you may just
+have to turn this thing into an X15
+
+ align:start position:0%
+have to turn this thing into an X15
+ 
+
+ align:start position:0%
+have to turn this thing into an X15
+project a research project project first
+
+ align:start position:0%
+project a research project project first
+ 
+
+ align:start position:0%
+project a research project project first
+shuttle flight will be whenever we can
+
+ align:start position:0%
+shuttle flight will be whenever we can
+ 
+
+ align:start position:0%
+shuttle flight will be whenever we can
+build it and it'll just be a test
+
+ align:start position:0%
+build it and it'll just be a test
+ 
+
+ align:start position:0%
+build it and it'll just be a test
+vehicle so we were all very downhearted
+
+ align:start position:0%
+vehicle so we were all very downhearted
+ 
+
+ align:start position:0%
+vehicle so we were all very downhearted
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that Mr Frost who was then the
+
+ align:start position:0%
+that Mr Frost who was then the
+ 
+
+ align:start position:0%
+that Mr Frost who was then the
+administrator Dr Frost who was then the
+
+ align:start position:0%
+administrator Dr Frost who was then the
+ 
+
+ align:start position:0%
+administrator Dr Frost who was then the
+administrator went up to the White House
+
+ align:start position:0%
+administrator went up to the White House
+ 
+
+ align:start position:0%
+administrator went up to the White House
+about three days later and Carter who
+
+ align:start position:0%
+about three days later and Carter who
+ 
+
+ align:start position:0%
+about three days later and Carter who
+was the president called him in and he
+
+ align:start position:0%
+was the president called him in and he
+ 
+
+ align:start position:0%
+was the president called him in and he
+said I want to tell you how wonderful
+
+ align:start position:0%
+said I want to tell you how wonderful
+ 
+
+ align:start position:0%
+said I want to tell you how wonderful
+that space shuttle
+
+ align:start position:0%
+that space shuttle
+ 
+
+ align:start position:0%
+that space shuttle
+is and frost
+
+ align:start position:0%
+is and frost
+ 
+
+ align:start position:0%
+is and frost
+you know he he said I could feel myself
+
+ align:start position:0%
+you know he he said I could feel myself
+ 
+
+ align:start position:0%
+you know he he said I could feel myself
+tightened up and he said you know I just
+
+ align:start position:0%
+tightened up and he said you know I just
+ 
+
+ align:start position:0%
+tightened up and he said you know I just
+had this meeting with the Russians at
+
+ align:start position:0%
+had this meeting with the Russians at
+ 
+
+ align:start position:0%
+had this meeting with the Russians at
+the salt
+
+ align:start position:0%
+the salt
+ 
+
+ align:start position:0%
+the salt
+talks what it whatever salt
+
+ align:start position:0%
+talks what it whatever salt
+ 
+
+ align:start position:0%
+talks what it whatever salt
+meant and I was pointing out to them
+
+ align:start position:0%
+meant and I was pointing out to them
+ 
+
+ align:start position:0%
+meant and I was pointing out to them
+that we were building this marvelous new
+
+ align:start position:0%
+that we were building this marvelous new
+ 
+
+ align:start position:0%
+that we were building this marvelous new
+space machine and we were going to do
+
+ align:start position:0%
+space machine and we were going to do
+ 
+
+ align:start position:0%
+space machine and we were going to do
+all be able to do all kinds of things
+
+ align:start position:0%
+all be able to do all kinds of things
+ 
+
+ align:start position:0%
+all be able to do all kinds of things
+with it we're going to be able to fly
+
+ align:start position:0%
+with it we're going to be able to fly
+ 
+
+ align:start position:0%
+with it we're going to be able to fly
+over Russia look at the
+
+ align:start position:0%
+over Russia look at the
+ 
+
+ align:start position:0%
+over Russia look at the
+world and uh he said it carried the
+
+ align:start position:0%
+world and uh he said it carried the
+ 
+
+ align:start position:0%
+world and uh he said it carried the
+day in Fr says oh my
+
+ align:start position:0%
+day in Fr says oh my
+ 
+
+ align:start position:0%
+day in Fr says oh my
+God what is NASA going to do about that
+
+ align:start position:0%
+God what is NASA going to do about that
+ 
+
+ align:start position:0%
+God what is NASA going to do about that
+came back thought about it a few days
+
+ align:start position:0%
+came back thought about it a few days
+ 
+
+ align:start position:0%
+came back thought about it a few days
+and he went back to see the
+
+ align:start position:0%
+and he went back to see the
+ 
+
+ align:start position:0%
+and he went back to see the
+president he said Mr President I have to
+
+ align:start position:0%
+president he said Mr President I have to
+ 
+
+ align:start position:0%
+president he said Mr President I have to
+tell you this shuttle is in trouble we
+
+ align:start position:0%
+tell you this shuttle is in trouble we
+ 
+
+ align:start position:0%
+tell you this shuttle is in trouble we
+don't have the money we're not going to
+
+ align:start position:0%
+don't have the money we're not going to
+ 
+
+ align:start position:0%
+don't have the money we're not going to
+make the launch dates it's questionable
+
+ align:start position:0%
+make the launch dates it's questionable
+ 
+
+ align:start position:0%
+make the launch dates it's questionable
+whether we can even build a machine at
+
+ align:start position:0%
+whether we can even build a machine at
+ 
+
+ align:start position:0%
+whether we can even build a machine at
+this point in time because we haven't
+
+ align:start position:0%
+this point in time because we haven't
+ 
+
+ align:start position:0%
+this point in time because we haven't
+built the thermal protection since we
+
+ align:start position:0%
+built the thermal protection since we
+ 
+
+ align:start position:0%
+built the thermal protection since we
+didn't had the factory built yet to
+
+ align:start position:0%
+didn't had the factory built yet to
+ 
+
+ align:start position:0%
+didn't had the factory built yet to
+build the tiles
+
+ align:start position:0%
+build the tiles
+ 
+
+ align:start position:0%
+build the tiles
+Mr car said how much do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need how much do you
+
+ align:start position:0%
+need how much do you
+ 
+
+ align:start position:0%
+need how much do you
+need and he said well I think we need
+
+ align:start position:0%
+need and he said well I think we need
+ 
+
+ align:start position:0%
+need and he said well I think we need
+about $600 million this year
+
+ align:start position:0%
+about $600 million this year
+ 
+
+ align:start position:0%
+about $600 million this year
+and uh I think we'll need about $400
+
+ align:start position:0%
+and uh I think we'll need about $400
+ 
+
+ align:start position:0%
+and uh I think we'll need about $400
+million a year that was a wild get that
+
+ align:start position:0%
+million a year that was a wild get that
+ 
+
+ align:start position:0%
+million a year that was a wild get that
+was a wag on Dr fr's part and the
+
+ align:start position:0%
+was a wag on Dr fr's part and the
+ 
+
+ align:start position:0%
+was a wag on Dr fr's part and the
+President says you'll get it
+
+ align:start position:0%
+President says you'll get it
+ 
+
+ align:start position:0%
+President says you'll get it
+so that's how close we
+
+ align:start position:0%
+so that's how close we
+ 
+
+ align:start position:0%
+so that's how close we
+were to the shuttle
+
+ align:start position:0%
+were to the shuttle
+ 
+
+ align:start position:0%
+were to the shuttle
+failing in a from a
+
+ align:start position:0%
+failing in a from a
+ 
+
+ align:start position:0%
+failing in a from a
+political point of
+
+ align:start position:0%
+political point of
+ 
+
+ align:start position:0%
+political point of
+view
+
+ align:start position:0%
+view
+ 
+
+ align:start position:0%
+view
+so I don't know what the politics of
+
+ align:start position:0%
+so I don't know what the politics of
+ 
+
+ align:start position:0%
+so I don't know what the politics of
+Tomorrow is that might change our mind
+
+ align:start position:0%
+Tomorrow is that might change our mind
+ 
+
+ align:start position:0%
+Tomorrow is that might change our mind
+it would be wonderful if the Chinese
+
+ align:start position:0%
+it would be wonderful if the Chinese
+ 
+
+ align:start position:0%
+it would be wonderful if the Chinese
+were laying on the moon
+
+ align:start position:0%
+were laying on the moon
+ 
+
+ align:start position:0%
+were laying on the moon
+tomorrow that might get the Congress
+
+ align:start position:0%
+tomorrow that might get the Congress
+ 
+
+ align:start position:0%
+tomorrow that might get the Congress
+back in
+
+ align:start position:0%
+back in
+ 
+
+ align:start position:0%
+back in
+action but I just can't see can you see
+
+ align:start position:0%
+action but I just can't see can you see
+ 
+
+ align:start position:0%
+action but I just can't see can you see
+the Congress
+
+ align:start position:0%
+the Congress
+ 
+
+ align:start position:0%
+the Congress
+in the face of what's happened to katri
+
+ align:start position:0%
+in the face of what's happened to katri
+ 
+
+ align:start position:0%
+in the face of what's happened to katri
+and Rita
+
+ align:start position:0%
+and Rita
+ 
+
+ align:start position:0%
+and Rita
+and and a few other things that happened
+
+ align:start position:0%
+and and a few other things that happened
+ 
+
+ align:start position:0%
+and and a few other things that happened
+in the United States and the Iraq Iraqi
+
+ align:start position:0%
+in the United States and the Iraq Iraqi
+ 
+
+ align:start position:0%
+in the United States and the Iraq Iraqi
+Iraqi War the budgetary problem they
+
+ align:start position:0%
+Iraqi War the budgetary problem they
+ 
+
+ align:start position:0%
+Iraqi War the budgetary problem they
+face I can't see them give a mass of the
+
+ align:start position:0%
+face I can't see them give a mass of the
+ 
+
+ align:start position:0%
+face I can't see them give a mass of the
+money they need to do the program and
+
+ align:start position:0%
+money they need to do the program and
+ 
+
+ align:start position:0%
+money they need to do the program and
+NASA says they can go back to the
+
+ align:start position:0%
+NASA says they can go back to the
+ 
+
+ align:start position:0%
+NASA says they can go back to the
+Moon uh between now and and N what is it
+
+ align:start position:0%
+Moon uh between now and and N what is it
+ 
+
+ align:start position:0%
+Moon uh between now and and N what is it
+2018 for 106 billion
+
+ align:start position:0%
+2018 for 106 billion
+ 
+
+ align:start position:0%
+2018 for 106 billion
+dollar you know
+
+ align:start position:0%
+dollar you know
+ 
+
+ align:start position:0%
+dollar you know
+Mr Webb doubled the price you know we
+
+ align:start position:0%
+Mr Webb doubled the price you know we
+ 
+
+ align:start position:0%
+Mr Webb doubled the price you know we
+all all us great cost estimators
+
+ align:start position:0%
+all all us great cost estimators
+ 
+
+ align:start position:0%
+all all us great cost estimators
+estimated the cost of the shuttle and
+
+ align:start position:0%
+estimated the cost of the shuttle and
+ 
+
+ align:start position:0%
+estimated the cost of the shuttle and
+Jim Web got it and multiplied it by
+
+ align:start position:0%
+Jim Web got it and multiplied it by
+ 
+
+ align:start position:0%
+Jim Web got it and multiplied it by
+two today I'd say you have to multiply
+
+ align:start position:0%
+two today I'd say you have to multiply
+ 
+
+ align:start position:0%
+two today I'd say you have to multiply
+that by
+
+ align:start position:0%
+that by
+ 
+
+ align:start position:0%
+that by
+10 if you think you going back to the
+
+ align:start position:0%
+10 if you think you going back to the
+ 
+
+ align:start position:0%
+10 if you think you going back to the
+moon and I can't
+
+ align:start position:0%
+moon and I can't
+ 
+
+ align:start position:0%
+moon and I can't
+imagine Aaron and I worked on a program
+
+ align:start position:0%
+imagine Aaron and I worked on a program
+ 
+
+ align:start position:0%
+imagine Aaron and I worked on a program
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+uh 19 what
+
+ align:start position:0%
+uh 19 what
+ 
+
+ align:start position:0%
+uh 19 what
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+98 when when did we do the lunar study
+
+ align:start position:0%
+98 when when did we do the lunar study
+ 
+
+ align:start position:0%
+98 when when did we do the lunar study
+going back going back to the I mean
+
+ align:start position:0%
+going back going back to the I mean
+ 
+
+ align:start position:0%
+going back going back to the I mean
+excuse me the Mars
+
+ align:start position:0%
+excuse me the Mars
+ 
+
+ align:start position:0%
+excuse me the Mars
+study 89 we estimated the cost of $1
+
+ align:start position:0%
+study 89 we estimated the cost of $1
+ 
+
+ align:start position:0%
+study 89 we estimated the cost of $1
+1989 to go to Mars at400 billion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dollar and I think we were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+low so I I know I have I keep have to
+
+ align:start position:0%
+low so I I know I have I keep have to
+ 
+
+ align:start position:0%
+low so I I know I have I keep have to
+catch myself I know it's a
+
+ align:start position:0%
+catch myself I know it's a
+ 
+
+ align:start position:0%
+catch myself I know it's a
+politics you have to be concerned about
+
+ align:start position:0%
+politics you have to be concerned about
+ 
+
+ align:start position:0%
+politics you have to be concerned about
+it you know if you told them that it was
+
+ align:start position:0%
+it you know if you told them that it was
+ 
+
+ align:start position:0%
+it you know if you told them that it was
+going to cost $400 billion then for sure
+
+ align:start position:0%
+going to cost $400 billion then for sure
+ 
+
+ align:start position:0%
+going to cost $400 billion then for sure
+it would be cancelled
+
+ align:start position:0%
+it would be cancelled
+ 
+
+ align:start position:0%
+it would be cancelled
+right but so you got to tell them
+
+ align:start position:0%
+right but so you got to tell them
+ 
+
+ align:start position:0%
+right but so you got to tell them
+something that's rational but I don't
+
+ align:start position:0%
+something that's rational but I don't
+ 
+
+ align:start position:0%
+something that's rational but I don't
+think they'll get supported even this
+
+ align:start position:0%
+think they'll get supported even this
+ 
+
+ align:start position:0%
+think they'll get supported even this
+even with the mount somebody they say
+
+ align:start position:0%
+even with the mount somebody they say
+ 
+
+ align:start position:0%
+even with the mount somebody they say
+it's what it cost I hope I am a
+
+ align:start position:0%
+it's what it cost I hope I am a
+ 
+
+ align:start position:0%
+it's what it cost I hope I am a
+pessimist just I have two separate
+
+ align:start position:0%
+pessimist just I have two separate
+ 
+
+ align:start position:0%
+pessimist just I have two separate
+questions uh one is I was wondering if
+
+ align:start position:0%
+questions uh one is I was wondering if
+ 
+
+ align:start position:0%
+questions uh one is I was wondering if
+with the improvements you said were made
+
+ align:start position:0%
+with the improvements you said were made
+ 
+
+ align:start position:0%
+with the improvements you said were made
+in uh in Computing capability from
+
+ align:start position:0%
+in uh in Computing capability from
+ 
+
+ align:start position:0%
+in uh in Computing capability from
+Mercury through uh the shuttle I was
+
+ align:start position:0%
+Mercury through uh the shuttle I was
+ 
+
+ align:start position:0%
+Mercury through uh the shuttle I was
+wondering if there was any thought into
+
+ align:start position:0%
+wondering if there was any thought into
+ 
+
+ align:start position:0%
+wondering if there was any thought into
+making the computer systems on the
+
+ align:start position:0%
+making the computer systems on the
+ 
+
+ align:start position:0%
+making the computer systems on the
+shuttle more upgradable and if it if it
+
+ align:start position:0%
+shuttle more upgradable and if it if it
+ 
+
+ align:start position:0%
+shuttle more upgradable and if it if it
+was would there have been any value
+
+ align:start position:0%
+was would there have been any value
+ 
+
+ align:start position:0%
+was would there have been any value
+using modern systems um and then the
+
+ align:start position:0%
+using modern systems um and then the
+ 
+
+ align:start position:0%
+using modern systems um and then the
+second question is related to the um the
+
+ align:start position:0%
+second question is related to the um the
+ 
+
+ align:start position:0%
+second question is related to the um the
+comment you made about if the uh if the
+
+ align:start position:0%
+comment you made about if the uh if the
+ 
+
+ align:start position:0%
+comment you made about if the uh if the
+shuttle is designed to fly automatically
+
+ align:start position:0%
+shuttle is designed to fly automatically
+ 
+
+ align:start position:0%
+shuttle is designed to fly automatically
+after the Challenger accident could just
+
+ align:start position:0%
+after the Challenger accident could just
+ 
+
+ align:start position:0%
+after the Challenger accident could just
+flown again the next day and I wasn't
+
+ align:start position:0%
+flown again the next day and I wasn't
+ 
+
+ align:start position:0%
+flown again the next day and I wasn't
+really sure what you Me by that so I was
+
+ align:start position:0%
+really sure what you Me by that so I was
+ 
+
+ align:start position:0%
+really sure what you Me by that so I was
+hoping you could elaborate on it a bit
+
+ align:start position:0%
+hoping you could elaborate on it a bit
+ 
+
+ align:start position:0%
+hoping you could elaborate on it a bit
+uh let me go to your first question uh
+
+ align:start position:0%
+uh let me go to your first question uh
+ 
+
+ align:start position:0%
+uh let me go to your first question uh
+it isn't a hardware it's a software and
+
+ align:start position:0%
+it isn't a hardware it's a software and
+ 
+
+ align:start position:0%
+it isn't a hardware it's a software and
+it's a software checkout and it's a
+
+ align:start position:0%
+it's a software checkout and it's a
+ 
+
+ align:start position:0%
+it's a software checkout and it's a
+software
+
+ align:start position:0%
+software
+ 
+
+ align:start position:0%
+software
+validation that you have to worry about
+
+ align:start position:0%
+validation that you have to worry about
+ 
+
+ align:start position:0%
+validation that you have to worry about
+on the on the Orbiter when you you have
+
+ align:start position:0%
+on the on the Orbiter when you you have
+ 
+
+ align:start position:0%
+on the on the Orbiter when you you have
+four systems that are operating on a 40
+
+ align:start position:0%
+four systems that are operating on a 40
+ 
+
+ align:start position:0%
+four systems that are operating on a 40
+m second time cycle and checking with
+
+ align:start position:0%
+m second time cycle and checking with
+ 
+
+ align:start position:0%
+m second time cycle and checking with
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+other uh at the end of that cycle
+
+ align:start position:0%
+other uh at the end of that cycle
+ 
+
+ align:start position:0%
+other uh at the end of that cycle
+they're all in in lock
+
+ align:start position:0%
+they're all in in lock
+ 
+
+ align:start position:0%
+they're all in in lock
+step John is looking at me saying my God
+
+ align:start position:0%
+step John is looking at me saying my God
+ 
+
+ align:start position:0%
+step John is looking at me saying my God
+how did we ever do that and I don't know
+
+ align:start position:0%
+how did we ever do that and I don't know
+ 
+
+ align:start position:0%
+how did we ever do that and I don't know
+how we ever did it but we did it but
+
+ align:start position:0%
+how we ever did it but we did it but
+ 
+
+ align:start position:0%
+how we ever did it but we did it but
+that it's the software not the hardware
+
+ align:start position:0%
+that it's the software not the hardware
+ 
+
+ align:start position:0%
+that it's the software not the hardware
+so when you build a new replace have an
+
+ align:start position:0%
+so when you build a new replace have an
+ 
+
+ align:start position:0%
+so when you build a new replace have an
+update computer which you should have
+
+ align:start position:0%
+update computer which you should have
+ 
+
+ align:start position:0%
+update computer which you should have
+and will have it's the software that's
+
+ align:start position:0%
+and will have it's the software that's
+ 
+
+ align:start position:0%
+and will have it's the software that's
+the problem not the hardware always
+
+ align:start position:0%
+the problem not the hardware always
+ 
+
+ align:start position:0%
+the problem not the hardware always
+that's always been the
+
+ align:start position:0%
+that's always been the
+ 
+
+ align:start position:0%
+that's always been the
+case yeah trying to make trying to make
+
+ align:start position:0%
+case yeah trying to make trying to make
+ 
+
+ align:start position:0%
+case yeah trying to make trying to make
+the software fit into the new
+
+ align:start position:0%
+the software fit into the new
+ 
+
+ align:start position:0%
+the software fit into the new
+computer the way the hooks are in this
+
+ align:start position:0%
+computer the way the hooks are in this
+ 
+
+ align:start position:0%
+computer the way the hooks are in this
+system uh it's just totally different
+
+ align:start position:0%
+system uh it's just totally different
+ 
+
+ align:start position:0%
+system uh it's just totally different
+and therefore the
+
+ align:start position:0%
+and therefore the
+ 
+
+ align:start position:0%
+and therefore the
+guarantee that the system doesn't have a
+
+ align:start position:0%
+guarantee that the system doesn't have a
+ 
+
+ align:start position:0%
+guarantee that the system doesn't have a
+bunch of uh glitches in
+
+ align:start position:0%
+bunch of uh glitches in
+ 
+
+ align:start position:0%
+bunch of uh glitches in
+it uh that are going to get to you you
+
+ align:start position:0%
+it uh that are going to get to you you
+ 
+
+ align:start position:0%
+it uh that are going to get to you you
+know when we when we flew to the moon on
+
+ align:start position:0%
+know when we when we flew to the moon on
+ 
+
+ align:start position:0%
+know when we when we flew to the moon on
+Apollo 11 we had a book about that thick
+
+ align:start position:0%
+Apollo 11 we had a book about that thick
+ 
+
+ align:start position:0%
+Apollo 11 we had a book about that thick
+with computer anomalies in
+
+ align:start position:0%
+with computer anomalies in
+ 
+
+ align:start position:0%
+with computer anomalies in
+it we understood them all but that's how
+
+ align:start position:0%
+it we understood them all but that's how
+ 
+
+ align:start position:0%
+it we understood them all but that's how
+many software fixes we needed to make we
+
+ align:start position:0%
+many software fixes we needed to make we
+ 
+
+ align:start position:0%
+many software fixes we needed to make we
+just didn't make them because we didn't
+
+ align:start position:0%
+just didn't make them because we didn't
+ 
+
+ align:start position:0%
+just didn't make them because we didn't
+want to or nor have the time to do
+
+ align:start position:0%
+want to or nor have the time to do
+ 
+
+ align:start position:0%
+want to or nor have the time to do
+it uh what I meant by flying the uh an
+
+ align:start position:0%
+it uh what I meant by flying the uh an
+ 
+
+ align:start position:0%
+it uh what I meant by flying the uh an
+unmanned shuttle was that you couldn't
+
+ align:start position:0%
+unmanned shuttle was that you couldn't
+ 
+
+ align:start position:0%
+unmanned shuttle was that you couldn't
+convince the politicians
+
+ align:start position:0%
+convince the politicians
+ 
+
+ align:start position:0%
+convince the politicians
+or the poers that be whoever they are
+
+ align:start position:0%
+or the poers that be whoever they are
+ 
+
+ align:start position:0%
+or the poers that be whoever they are
+that you could fly the shuttle the next
+
+ align:start position:0%
+that you could fly the shuttle the next
+ 
+
+ align:start position:0%
+that you could fly the shuttle the next
+day un a man but if you didn't have a
+
+ align:start position:0%
+day un a man but if you didn't have a
+ 
+
+ align:start position:0%
+day un a man but if you didn't have a
+man in it who would have cared and so
+
+ align:start position:0%
+man in it who would have cared and so
+ 
+
+ align:start position:0%
+man in it who would have cared and so
+you could have flown it the next day and
+
+ align:start position:0%
+you could have flown it the next day and
+ 
+
+ align:start position:0%
+you could have flown it the next day and
+it would have worked perfectly because
+
+ align:start position:0%
+it would have worked perfectly because
+ 
+
+ align:start position:0%
+it would have worked perfectly because
+it was warmer at the
+
+ align:start position:0%
+it was warmer at the
+ 
+
+ align:start position:0%
+it was warmer at the
+cake you know do you know what the
+
+ align:start position:0%
+cake you know do you know what the
+ 
+
+ align:start position:0%
+cake you know do you know what the
+condition on the pad was the morning
+
+ align:start position:0%
+condition on the pad was the morning
+ 
+
+ align:start position:0%
+condition on the pad was the morning
+they launched
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+challenger no there were icicles hanging
+
+ align:start position:0%
+challenger no there were icicles hanging
+ 
+
+ align:start position:0%
+challenger no there were icicles hanging
+off the Gantry that
+
+ align:start position:0%
+off the Gantry that
+ 
+
+ align:start position:0%
+off the Gantry that
+long and that big
+
+ align:start position:0%
+long and that big
+ 
+
+ align:start position:0%
+long and that big
+around at Cape
+
+ align:start position:0%
+around at Cape
+ 
+
+ align:start position:0%
+around at Cape
+canabra let me tell you something they
+
+ align:start position:0%
+canabra let me tell you something they
+ 
+
+ align:start position:0%
+canabra let me tell you something they
+did you know why they got there they did
+
+ align:start position:0%
+did you know why they got there they did
+ 
+
+ align:start position:0%
+did you know why they got there they did
+what we did in
+
+ align:start position:0%
+what we did in
+ 
+
+ align:start position:0%
+what we did in
+1920 turn the water on let it run all
+
+ align:start position:0%
+1920 turn the water on let it run all
+ 
+
+ align:start position:0%
+1920 turn the water on let it run all
+night because they were afraid that the
+
+ align:start position:0%
+night because they were afraid that the
+ 
+
+ align:start position:0%
+night because they were afraid that the
+the uh fire suppression system on the
+
+ align:start position:0%
+the uh fire suppression system on the
+ 
+
+ align:start position:0%
+the uh fire suppression system on the
+pad was going to
+
+ align:start position:0%
+pad was going to
+ 
+
+ align:start position:0%
+pad was going to
+freeze and not be able to be turned on
+
+ align:start position:0%
+freeze and not be able to be turned on
+ 
+
+ align:start position:0%
+freeze and not be able to be turned on
+when they launched so they let it drip
+
+ align:start position:0%
+when they launched so they let it drip
+ 
+
+ align:start position:0%
+when they launched so they let it drip
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+night and I'm sitting there saying that
+
+ align:start position:0%
+night and I'm sitting there saying that
+ 
+
+ align:start position:0%
+night and I'm sitting there saying that
+solid rocket has not been qualif for
+
+ align:start position:0%
+solid rocket has not been qualif for
+ 
+
+ align:start position:0%
+solid rocket has not been qualif for
+temperatures below 47 degrees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F and they're convincing themselves that
+
+ align:start position:0%
+F and they're convincing themselves that
+ 
+
+ align:start position:0%
+F and they're convincing themselves that
+the core temperature of the
+
+ align:start position:0%
+the core temperature of the
+ 
+
+ align:start position:0%
+the core temperature of the
+solids is much higher than that because
+
+ align:start position:0%
+solids is much higher than that because
+ 
+
+ align:start position:0%
+solids is much higher than that because
+it's been sitting in the sun for the
+
+ align:start position:0%
+it's been sitting in the sun for the
+ 
+
+ align:start position:0%
+it's been sitting in the sun for the
+last two months and the temperature is
+
+ align:start position:0%
+last two months and the temperature is
+ 
+
+ align:start position:0%
+last two months and the temperature is
+so and so but they didn't think about
+
+ align:start position:0%
+so and so but they didn't think about
+ 
+
+ align:start position:0%
+so and so but they didn't think about
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seals you remember that Professor
+
+ align:start position:0%
+seals you remember that Professor
+ 
+
+ align:start position:0%
+seals you remember that Professor
+sticking a seal in the ice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what I meant by you could the
+
+ align:start position:0%
+that's what I meant by you could the
+ 
+
+ align:start position:0%
+that's what I meant by you could the
+next day the temperature would have been
+
+ align:start position:0%
+next day the temperature would have been
+ 
+
+ align:start position:0%
+next day the temperature would have been
+warmer new rockets on Max F said the
+
+ align:start position:0%
+warmer new rockets on Max F said the
+ 
+
+ align:start position:0%
+warmer new rockets on Max F said the
+next day why don't you just put a belly
+
+ align:start position:0%
+next day why don't you just put a belly
+ 
+
+ align:start position:0%
+next day why don't you just put a belly
+band and a heater put a heater around
+
+ align:start position:0%
+band and a heater put a heater around
+ 
+
+ align:start position:0%
+band and a heater put a heater around
+the joint and put a belly band over top
+
+ align:start position:0%
+the joint and put a belly band over top
+ 
+
+ align:start position:0%
+the joint and put a belly band over top
+of it and
+
+ align:start position:0%
+of it and
+ 
+
+ align:start position:0%
+of it and
+fly damn good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea yes
+
+ align:start position:0%
+idea yes
+ 
+
+ align:start position:0%
+idea yes
+sir uh you mentioned that the one of the
+
+ align:start position:0%
+sir uh you mentioned that the one of the
+ 
+
+ align:start position:0%
+sir uh you mentioned that the one of the
+reasons the shuttle is so expensive
+
+ align:start position:0%
+reasons the shuttle is so expensive
+ 
+
+ align:start position:0%
+reasons the shuttle is so expensive
+because you have many redundant systems
+
+ align:start position:0%
+because you have many redundant systems
+ 
+
+ align:start position:0%
+because you have many redundant systems
+on board now what what would be your
+
+ align:start position:0%
+on board now what what would be your
+ 
+
+ align:start position:0%
+on board now what what would be your
+solution not to have them on board or
+
+ align:start position:0%
+solution not to have them on board or
+ 
+
+ align:start position:0%
+solution not to have them on board or
+just to uh not to have them all
+
+ align:start position:0%
+just to uh not to have them all
+ 
+
+ align:start position:0%
+just to uh not to have them all
+operating at launch no you got the wrong
+
+ align:start position:0%
+operating at launch no you got the wrong
+ 
+
+ align:start position:0%
+operating at launch no you got the wrong
+you got the wrong implication there it's
+
+ align:start position:0%
+you got the wrong implication there it's
+ 
+
+ align:start position:0%
+you got the wrong implication there it's
+expensive because they insist on having
+
+ align:start position:0%
+expensive because they insist on having
+ 
+
+ align:start position:0%
+expensive because they insist on having
+them operating at the time of launch
+
+ align:start position:0%
+them operating at the time of launch
+ 
+
+ align:start position:0%
+them operating at the time of launch
+it's not the
+
+ align:start position:0%
+it's not the
+ 
+
+ align:start position:0%
+it's not the
+redundancy that makes it more expensive
+
+ align:start position:0%
+redundancy that makes it more expensive
+ 
+
+ align:start position:0%
+redundancy that makes it more expensive
+it's the check out and the testing the
+
+ align:start position:0%
+it's the check out and the testing the
+ 
+
+ align:start position:0%
+it's the check out and the testing the
+proof that it's there and the
+
+ align:start position:0%
+proof that it's there and the
+ 
+
+ align:start position:0%
+proof that it's there and the
+replacement of the system
+
+ align:start position:0%
+replacement of the system
+ 
+
+ align:start position:0%
+replacement of the system
+and the use of the system that makes it
+
+ align:start position:0%
+and the use of the system that makes it
+ 
+
+ align:start position:0%
+and the use of the system that makes it
+more expensive but what makes the
+
+ align:start position:0%
+more expensive but what makes the
+ 
+
+ align:start position:0%
+more expensive but what makes the
+shuttle so expensive is the numbers of
+
+ align:start position:0%
+shuttle so expensive is the numbers of
+ 
+
+ align:start position:0%
+shuttle so expensive is the numbers of
+people involved in preparing
+
+ align:start position:0%
+people involved in preparing
+ 
+
+ align:start position:0%
+people involved in preparing
+it there are roughly 10,000 people
+
+ align:start position:0%
+it there are roughly 10,000 people
+ 
+
+ align:start position:0%
+it there are roughly 10,000 people
+involved in that
+
+ align:start position:0%
+involved in that
+ 
+
+ align:start position:0%
+involved in that
+operation who make X number of dollars
+
+ align:start position:0%
+operation who make X number of dollars
+ 
+
+ align:start position:0%
+operation who make X number of dollars
+per hour or day and cost it cost in
+
+ align:start position:0%
+per hour or day and cost it cost in
+ 
+
+ align:start position:0%
+per hour or day and cost it cost in
+today's money about
+
+ align:start position:0%
+today's money about
+ 
+
+ align:start position:0%
+today's money about
+a year to fly the shuttle seven
+
+ align:start position:0%
+a year to fly the shuttle seven
+ 
+
+ align:start position:0%
+a year to fly the shuttle seven
+times probably cost5 billion a year to
+
+ align:start position:0%
+times probably cost5 billion a year to
+ 
+
+ align:start position:0%
+times probably cost5 billion a year to
+fly 30 times not much different maybe
+
+ align:start position:0%
+fly 30 times not much different maybe
+ 
+
+ align:start position:0%
+fly 30 times not much different maybe
+5.5 million so it's the people you got
+
+ align:start position:0%
+5.5 million so it's the people you got
+ 
+
+ align:start position:0%
+5.5 million so it's the people you got
+to get rid of the people and that's
+
+ align:start position:0%
+to get rid of the people and that's
+ 
+
+ align:start position:0%
+to get rid of the people and that's
+that's what people have been trying to
+
+ align:start position:0%
+that's what people have been trying to
+ 
+
+ align:start position:0%
+that's what people have been trying to
+do that ever since
+
+ align:start position:0%
+do that ever since
+ 
+
+ align:start position:0%
+do that ever since
+Mercury get rid of the amount of people
+
+ align:start position:0%
+Mercury get rid of the amount of people
+ 
+
+ align:start position:0%
+Mercury get rid of the amount of people
+and they they try and they put in the
+
+ align:start position:0%
+and they they try and they put in the
+ 
+
+ align:start position:0%
+and they they try and they put in the
+automaticity and the automatic check
+
+ align:start position:0%
+automaticity and the automatic check
+ 
+
+ align:start position:0%
+automaticity and the automatic check
+out and then don't use
+
+ align:start position:0%
+out and then don't use
+ 
+
+ align:start position:0%
+out and then don't use
+it check it you know as I said they put
+
+ align:start position:0%
+it check it you know as I said they put
+ 
+
+ align:start position:0%
+it check it you know as I said they put
+more hours on it in the hanger than they
+
+ align:start position:0%
+more hours on it in the hanger than they
+ 
+
+ align:start position:0%
+more hours on it in the hanger than they
+do in
+
+ align:start position:0%
+do in
+ 
+
+ align:start position:0%
+do in
+space where at the system check of you
+
+ align:start position:0%
+space where at the system check of you
+ 
+
+ align:start position:0%
+space where at the system check of you
+and it takes people to do
+
+ align:start position:0%
+and it takes people to do
+ 
+
+ align:start position:0%
+and it takes people to do
+that so it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people uh I think you have to have some
+
+ align:start position:0%
+people uh I think you have to have some
+ 
+
+ align:start position:0%
+people uh I think you have to have some
+hard-nosed
+
+ align:start position:0%
+hard-nosed
+ 
+
+ align:start position:0%
+hard-nosed
+SOB that says I'm GNA get rid of the
+
+ align:start position:0%
+SOB that says I'm GNA get rid of the
+ 
+
+ align:start position:0%
+SOB that says I'm GNA get rid of the
+people and you do it with
+
+ align:start position:0%
+people and you do it with
+ 
+
+ align:start position:0%
+people and you do it with
+automaticity automatic checkup automatic
+
+ align:start position:0%
+automaticity automatic checkup automatic
+ 
+
+ align:start position:0%
+automaticity automatic checkup automatic
+everything in today's world why would
+
+ align:start position:0%
+everything in today's world why would
+ 
+
+ align:start position:0%
+everything in today's world why would
+you do it any other way give you another
+
+ align:start position:0%
+you do it any other way give you another
+ 
+
+ align:start position:0%
+you do it any other way give you another
+example when we built the caution and
+
+ align:start position:0%
+example when we built the caution and
+ 
+
+ align:start position:0%
+example when we built the caution and
+warning
+
+ align:start position:0%
+warning
+ 
+
+ align:start position:0%
+warning
+system on the space
+
+ align:start position:0%
+system on the space
+ 
+
+ align:start position:0%
+system on the space
+shuttle this the uh safety and
+
+ align:start position:0%
+shuttle this the uh safety and
+ 
+
+ align:start position:0%
+shuttle this the uh safety and
+reliability people said it has to be
+
+ align:start position:0%
+reliability people said it has to be
+ 
+
+ align:start position:0%
+reliability people said it has to be
+hardwired can you imagine
+
+ align:start position:0%
+hardwired can you imagine
+ 
+
+ align:start position:0%
+hardwired can you imagine
+that why would use
+
+ align:start position:0%
+that why would use
+ 
+
+ align:start position:0%
+that why would use
+bits instead of hard wire oh but it's a
+
+ align:start position:0%
+bits instead of hard wire oh but it's a
+ 
+
+ align:start position:0%
+bits instead of hard wire oh but it's a
+lot safer lot
+
+ align:start position:0%
+lot safer lot
+ 
+
+ align:start position:0%
+lot safer lot
+reliable use my same word hogwash it's a
+
+ align:start position:0%
+reliable use my same word hogwash it's a
+ 
+
+ align:start position:0%
+reliable use my same word hogwash it's a
+lot safer and more reliable with
+
+ align:start position:0%
+lot safer and more reliable with
+ 
+
+ align:start position:0%
+lot safer and more reliable with
+bits but that's the
+
+ align:start position:0%
+bits but that's the
+ 
+
+ align:start position:0%
+bits but that's the
+system you got to change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+and two of us have tried see us flying
+
+ align:start position:0%
+and two of us have tried see us flying
+ 
+
+ align:start position:0%
+and two of us have tried see us flying
+down in flames almost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everywhere yes
+
+ align:start position:0%
+everywhere yes
+ 
+
+ align:start position:0%
+everywhere yes
+sir as young here a lot of us you know
+
+ align:start position:0%
+sir as young here a lot of us you know
+ 
+
+ align:start position:0%
+sir as young here a lot of us you know
+hear all about the AP and a lot of us
+
+ align:start position:0%
+hear all about the AP and a lot of us
+ 
+
+ align:start position:0%
+hear all about the AP and a lot of us
+even talk about the old good old days
+
+ align:start position:0%
+even talk about the old good old days
+ 
+
+ align:start position:0%
+even talk about the old good old days
+where you know we wish we were live in
+
+ align:start position:0%
+where you know we wish we were live in
+ 
+
+ align:start position:0%
+where you know we wish we were live in
+the days of you know engineering by the
+
+ align:start position:0%
+the days of you know engineering by the
+ 
+
+ align:start position:0%
+the days of you know engineering by the
+your pants is is that type of job and
+
+ align:start position:0%
+your pants is is that type of job and
+ 
+
+ align:start position:0%
+your pants is is that type of job and
+that type of excitement of an
+
+ align:start position:0%
+that type of excitement of an
+ 
+
+ align:start position:0%
+that type of excitement of an
+engineering possible in N environment
+
+ align:start position:0%
+engineering possible in N environment
+ 
+
+ align:start position:0%
+engineering possible in N environment
+today or should we look elsewhere like
+
+ align:start position:0%
+today or should we look elsewhere like
+ 
+
+ align:start position:0%
+today or should we look elsewhere like
+towards private Enterprises or or can we
+
+ align:start position:0%
+towards private Enterprises or or can we
+ 
+
+ align:start position:0%
+towards private Enterprises or or can we
+find the type of job we hear about
+
+ align:start position:0%
+find the type of job we hear about
+ 
+
+ align:start position:0%
+find the type of job we hear about
+holidays in NASA these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+days have to be careful how I answer
+
+ align:start position:0%
+days have to be careful how I answer
+ 
+
+ align:start position:0%
+days have to be careful how I answer
+that I want you in NASA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it's important that you guys be a
+
+ align:start position:0%
+uh it's important that you guys be a
+ 
+
+ align:start position:0%
+uh it's important that you guys be a
+Daner or at least in the space program
+
+ align:start position:0%
+Daner or at least in the space program
+ 
+
+ align:start position:0%
+Daner or at least in the space program
+working in the industry because you are
+
+ align:start position:0%
+working in the industry because you are
+ 
+
+ align:start position:0%
+working in the industry because you are
+tomorrow's
+
+ align:start position:0%
+tomorrow's
+ 
+
+ align:start position:0%
+tomorrow's
+opportunity you don't want to do just
+
+ align:start position:0%
+opportunity you don't want to do just
+ 
+
+ align:start position:0%
+opportunity you don't want to do just
+because you hear Chris CRA say things
+
+ align:start position:0%
+because you hear Chris CRA say things
+ 
+
+ align:start position:0%
+because you hear Chris CRA say things
+that doesn't mean a damn thing tomorrow
+
+ align:start position:0%
+that doesn't mean a damn thing tomorrow
+ 
+
+ align:start position:0%
+that doesn't mean a damn thing tomorrow
+you have to do it yourself and you have
+
+ align:start position:0%
+you have to do it yourself and you have
+ 
+
+ align:start position:0%
+you have to do it yourself and you have
+to want to do it yourself and you have
+
+ align:start position:0%
+to want to do it yourself and you have
+ 
+
+ align:start position:0%
+to want to do it yourself and you have
+to bring the IDE
+
+ align:start position:0%
+to bring the IDE
+ 
+
+ align:start position:0%
+to bring the IDE
+is to the program and you have to be
+
+ align:start position:0%
+is to the program and you have to be
+ 
+
+ align:start position:0%
+is to the program and you have to be
+willing to do that and it's a
+
+ align:start position:0%
+willing to do that and it's a
+ 
+
+ align:start position:0%
+willing to do that and it's a
+willingness to take on the the things
+
+ align:start position:0%
+willingness to take on the the things
+ 
+
+ align:start position:0%
+willingness to take on the the things
+that must be taken on in order to get
+
+ align:start position:0%
+that must be taken on in order to get
+ 
+
+ align:start position:0%
+that must be taken on in order to get
+the job
+
+ align:start position:0%
+the job
+ 
+
+ align:start position:0%
+the job
+done so your question about seed of the
+
+ align:start position:0%
+done so your question about seed of the
+ 
+
+ align:start position:0%
+done so your question about seed of the
+pants Etc sure we did a lot of things
+
+ align:start position:0%
+pants Etc sure we did a lot of things
+ 
+
+ align:start position:0%
+pants Etc sure we did a lot of things
+when we first started by seed of the
+
+ align:start position:0%
+when we first started by seed of the
+ 
+
+ align:start position:0%
+when we first started by seed of the
+pants because we didn't
+
+ align:start position:0%
+pants because we didn't
+ 
+
+ align:start position:0%
+pants because we didn't
+know any other way to do it we had to we
+
+ align:start position:0%
+know any other way to do it we had to we
+ 
+
+ align:start position:0%
+know any other way to do it we had to we
+did it by fi we did it by last
+
+ align:start position:0%
+did it by fi we did it by last
+ 
+
+ align:start position:0%
+did it by fi we did it by last
+experience most of us had been in the
+
+ align:start position:0%
+experience most of us had been in the
+ 
+
+ align:start position:0%
+experience most of us had been in the
+not a lot of us had been in the flight
+
+ align:start position:0%
+not a lot of us had been in the flight
+ 
+
+ align:start position:0%
+not a lot of us had been in the flight
+test World airplane flight test world so
+
+ align:start position:0%
+test World airplane flight test world so
+ 
+
+ align:start position:0%
+test World airplane flight test world so
+we did it by having seen the past having
+
+ align:start position:0%
+we did it by having seen the past having
+ 
+
+ align:start position:0%
+we did it by having seen the past having
+doing things the right way that was our
+
+ align:start position:0%
+doing things the right way that was our
+ 
+
+ align:start position:0%
+doing things the right way that was our
+seat of the pants so our seat of the
+
+ align:start position:0%
+seat of the pants so our seat of the
+ 
+
+ align:start position:0%
+seat of the pants so our seat of the
+pants wasn't just a scarf around our
+
+ align:start position:0%
+pants wasn't just a scarf around our
+ 
+
+ align:start position:0%
+pants wasn't just a scarf around our
+neck so to
+
+ align:start position:0%
+neck so to
+ 
+
+ align:start position:0%
+neck so to
+speak it was done it was an educated
+
+ align:start position:0%
+speak it was done it was an educated
+ 
+
+ align:start position:0%
+speak it was done it was an educated
+seat of the pants and that's what you
+
+ align:start position:0%
+seat of the pants and that's what you
+ 
+
+ align:start position:0%
+seat of the pants and that's what you
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+in the end it will take a lot of the
+
+ align:start position:0%
+in the end it will take a lot of the
+ 
+
+ align:start position:0%
+in the end it will take a lot of the
+seed of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pains I think the
+
+ align:start position:0%
+pains I think the
+ 
+
+ align:start position:0%
+pains I think the
+way I know Aon and I have done it was
+
+ align:start position:0%
+way I know Aon and I have done it was
+ 
+
+ align:start position:0%
+way I know Aon and I have done it was
+to believe in the people you have you
+
+ align:start position:0%
+to believe in the people you have you
+ 
+
+ align:start position:0%
+to believe in the people you have you
+have to learn how to find out who the
+
+ align:start position:0%
+have to learn how to find out who the
+ 
+
+ align:start position:0%
+have to learn how to find out who the
+guys that are that know what they're
+
+ align:start position:0%
+guys that are that know what they're
+ 
+
+ align:start position:0%
+guys that are that know what they're
+talking about and trust them have put
+
+ align:start position:0%
+talking about and trust them have put
+ 
+
+ align:start position:0%
+talking about and trust them have put
+them in the job give them responsibility
+
+ align:start position:0%
+them in the job give them responsibility
+ 
+
+ align:start position:0%
+them in the job give them responsibility
+and authority to do it and then trust
+
+ align:start position:0%
+and authority to do it and then trust
+ 
+
+ align:start position:0%
+and authority to do it and then trust
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+and you have to build
+
+ align:start position:0%
+and you have to build
+ 
+
+ align:start position:0%
+and you have to build
+them that the biggest problem that you
+
+ align:start position:0%
+them that the biggest problem that you
+ 
+
+ align:start position:0%
+them that the biggest problem that you
+have today that NASA has today and the
+
+ align:start position:0%
+have today that NASA has today and the
+ 
+
+ align:start position:0%
+have today that NASA has today and the
+Aerospace industry has today biggest
+
+ align:start position:0%
+Aerospace industry has today biggest
+ 
+
+ align:start position:0%
+Aerospace industry has today biggest
+problem can't say that too strong is
+
+ align:start position:0%
+problem can't say that too strong is
+ 
+
+ align:start position:0%
+problem can't say that too strong is
+that they have not built anything in 25
+
+ align:start position:0%
+that they have not built anything in 25
+ 
+
+ align:start position:0%
+that they have not built anything in 25
+years and so they've forgotten what it
+
+ align:start position:0%
+years and so they've forgotten what it
+ 
+
+ align:start position:0%
+years and so they've forgotten what it
+takes to do
+
+ align:start position:0%
+takes to do
+ 
+
+ align:start position:0%
+takes to do
+it you don't know how to do it but if I
+
+ align:start position:0%
+it you don't know how to do it but if I
+ 
+
+ align:start position:0%
+it you don't know how to do it but if I
+put you on the job and put you in the
+
+ align:start position:0%
+put you on the job and put you in the
+ 
+
+ align:start position:0%
+put you on the job and put you in the
+give you the authority to do it you
+
+ align:start position:0%
+give you the authority to do it you
+ 
+
+ align:start position:0%
+give you the authority to do it you
+could do it in three or four years you
+
+ align:start position:0%
+could do it in three or four years you
+ 
+
+ align:start position:0%
+could do it in three or four years you
+need my help and guys like me to tell
+
+ align:start position:0%
+need my help and guys like me to tell
+ 
+
+ align:start position:0%
+need my help and guys like me to tell
+you where the bumps in the road
+
+ align:start position:0%
+you where the bumps in the road
+ 
+
+ align:start position:0%
+you where the bumps in the road
+are but you're going to do it a hell of
+
+ align:start position:0%
+are but you're going to do it a hell of
+ 
+
+ align:start position:0%
+are but you're going to do it a hell of
+a lot better than I
+
+ align:start position:0%
+a lot better than I
+ 
+
+ align:start position:0%
+a lot better than I
+did given the opportunity to do
+
+ align:start position:0%
+did given the opportunity to do
+ 
+
+ align:start position:0%
+did given the opportunity to do
+it that answer your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question I
+
+ align:start position:0%
+question I
+ 
+
+ align:start position:0%
+question I
+you might have to help
+
+ align:start position:0%
+you might have to help
+ 
+
+ align:start position:0%
+you might have to help
+it you have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vote I say that only I was hoping when I
+
+ align:start position:0%
+vote I say that only I was hoping when I
+ 
+
+ align:start position:0%
+vote I say that only I was hoping when I
+in the 60s I was hoping that all these
+
+ align:start position:0%
+in the 60s I was hoping that all these
+ 
+
+ align:start position:0%
+in the 60s I was hoping that all these
+Space Cadets all these trekkies all
+
+ align:start position:0%
+Space Cadets all these trekkies all
+ 
+
+ align:start position:0%
+Space Cadets all these trekkies all
+those guys would now be in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Congress and and that they would vote
+
+ align:start position:0%
+Congress and and that they would vote
+ 
+
+ align:start position:0%
+Congress and and that they would vote
+for the Space Program boy was I ever
+
+ align:start position:0%
+for the Space Program boy was I ever
+ 
+
+ align:start position:0%
+for the Space Program boy was I ever
+dead wrong
+
+ align:start position:0%
+dead wrong
+ 
+
+ align:start position:0%
+dead wrong
+you know uh there aren't enough Grateful
+
+ align:start position:0%
+you know uh there aren't enough Grateful
+ 
+
+ align:start position:0%
+you know uh there aren't enough Grateful
+Dead fans
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around yes sir think sucess of the was
+
+ align:start position:0%
+around yes sir think sucess of the was
+ 
+
+ align:start position:0%
+around yes sir think sucess of the was
+in some way link to the F that was
+
+ align:start position:0%
+in some way link to the F that was
+ 
+
+ align:start position:0%
+in some way link to the F that was
+taking place in the
+
+ align:start position:0%
+taking place in the
+ 
+
+ align:start position:0%
+taking place in the
+60s oh
+
+ align:start position:0%
+60s oh
+ 
+
+ align:start position:0%
+60s oh
+absolutely I think that
+
+ align:start position:0%
+absolutely I think that
+ 
+
+ align:start position:0%
+absolutely I think that
+uh Lord you know we had an
+
+ align:start position:0%
+uh Lord you know we had an
+ 
+
+ align:start position:0%
+uh Lord you know we had an
+enthusiasm at the
+
+ align:start position:0%
+enthusiasm at the
+ 
+
+ align:start position:0%
+enthusiasm at the
+time that is is probably
+
+ align:start position:0%
+time that is is probably
+ 
+
+ align:start position:0%
+time that is is probably
+unparalleled in
+
+ align:start position:0%
+unparalleled in
+ 
+
+ align:start position:0%
+unparalleled in
+engineering circles now we had the
+
+ align:start position:0%
+engineering circles now we had the
+ 
+
+ align:start position:0%
+engineering circles now we had the
+Manhattan Project to build a nuclear
+
+ align:start position:0%
+Manhattan Project to build a nuclear
+ 
+
+ align:start position:0%
+Manhattan Project to build a nuclear
+bomb uh Draper had the project to build
+
+ align:start position:0%
+bomb uh Draper had the project to build
+ 
+
+ align:start position:0%
+bomb uh Draper had the project to build
+a PO submarine but it was it was close
+
+ align:start position:0%
+a PO submarine but it was it was close
+ 
+
+ align:start position:0%
+a PO submarine but it was it was close
+clustered clustered what is that
+
+ align:start position:0%
+clustered clustered what is that
+ 
+
+ align:start position:0%
+clustered clustered what is that
+word yeah and and
+
+ align:start position:0%
+word yeah and and
+ 
+
+ align:start position:0%
+word yeah and and
+uh it wasn't it wasn't seen as we
+
+ align:start position:0%
+uh it wasn't it wasn't seen as we
+ 
+
+ align:start position:0%
+uh it wasn't it wasn't seen as we
+brought it to the four it wasn't a
+
+ align:start position:0%
+brought it to the four it wasn't a
+ 
+
+ align:start position:0%
+brought it to the four it wasn't a
+national program it wasn't National
+
+ align:start position:0%
+national program it wasn't National
+ 
+
+ align:start position:0%
+national program it wasn't National
+priority it wasn't national pride those
+
+ align:start position:0%
+priority it wasn't national pride those
+ 
+
+ align:start position:0%
+priority it wasn't national pride those
+you know that nobody knew about it
+
+ align:start position:0%
+you know that nobody knew about it
+ 
+
+ align:start position:0%
+you know that nobody knew about it
+everybody knew about
+
+ align:start position:0%
+everybody knew about
+ 
+
+ align:start position:0%
+everybody knew about
+Apollo you know I was damn proud to walk
+
+ align:start position:0%
+Apollo you know I was damn proud to walk
+ 
+
+ align:start position:0%
+Apollo you know I was damn proud to walk
+into any room where I ever
+
+ align:start position:0%
+into any room where I ever
+ 
+
+ align:start position:0%
+into any room where I ever
+went to say I want worked on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Apollo you know God that reminds me of a
+
+ align:start position:0%
+Apollo you know God that reminds me of a
+ 
+
+ align:start position:0%
+Apollo you know God that reminds me of a
+horrible to make my point uh reminds me
+
+ align:start position:0%
+horrible to make my point uh reminds me
+ 
+
+ align:start position:0%
+horrible to make my point uh reminds me
+of a horrible cartoon I was in Austin is
+
+ align:start position:0%
+of a horrible cartoon I was in Austin is
+ 
+
+ align:start position:0%
+of a horrible cartoon I was in Austin is
+about well following the Challenger
+
+ align:start position:0%
+about well following the Challenger
+ 
+
+ align:start position:0%
+about well following the Challenger
+accident and here I am one of the
+
+ align:start position:0%
+accident and here I am one of the
+ 
+
+ align:start position:0%
+accident and here I am one of the
+proudest people ever be in
+
+ align:start position:0%
+proudest people ever be in
+ 
+
+ align:start position:0%
+proudest people ever be in
+NASA the cartoon in the paper where I
+
+ align:start position:0%
+NASA the cartoon in the paper where I
+ 
+
+ align:start position:0%
+NASA the cartoon in the paper where I
+got up that morning was the
+
+ align:start position:0%
+got up that morning was the
+ 
+
+ align:start position:0%
+got up that morning was the
+following showed these kids playing with
+
+ align:start position:0%
+following showed these kids playing with
+ 
+
+ align:start position:0%
+following showed these kids playing with
+a what's the circle
+
+ align:start position:0%
+a what's the circle
+ 
+
+ align:start position:0%
+a what's the circle
+thing frisbee two kids playing with a
+
+ align:start position:0%
+thing frisbee two kids playing with a
+ 
+
+ align:start position:0%
+thing frisbee two kids playing with a
+frisbee first one he throws it over here
+
+ align:start position:0%
+frisbee first one he throws it over here
+ 
+
+ align:start position:0%
+frisbee first one he throws it over here
+this guy second second one he throws it
+
+ align:start position:0%
+this guy second second one he throws it
+ 
+
+ align:start position:0%
+this guy second second one he throws it
+back third one the damn thing explodes
+
+ align:start position:0%
+back third one the damn thing explodes
+ 
+
+ align:start position:0%
+back third one the damn thing explodes
+in his
+
+ align:start position:0%
+in his
+ 
+
+ align:start position:0%
+in his
+face fourth one says his father works
+
+ align:start position:0%
+face fourth one says his father works
+ 
+
+ align:start position:0%
+face fourth one says his father works
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+NASA well that brings it home to you
+
+ align:start position:0%
+NASA well that brings it home to you
+ 
+
+ align:start position:0%
+NASA well that brings it home to you
+pretty damn fast doesn't
+
+ align:start position:0%
+pretty damn fast doesn't
+ 
+
+ align:start position:0%
+pretty damn fast doesn't
+it nobody would nobody in in
+
+ align:start position:0%
+it nobody would nobody in in
+ 
+
+ align:start position:0%
+it nobody would nobody in in
+1967 68 69 nobody would have dared put
+
+ align:start position:0%
+1967 68 69 nobody would have dared put
+ 
+
+ align:start position:0%
+1967 68 69 nobody would have dared put
+that cartoon in the paper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by having new people in a space program
+
+ align:start position:0%
+by having new people in a space program
+ 
+
+ align:start position:0%
+by having new people in a space program
+there's always this lack of experience
+
+ align:start position:0%
+there's always this lack of experience
+ 
+
+ align:start position:0%
+there's always this lack of experience
+which you have to trade just to have how
+
+ align:start position:0%
+which you have to trade just to have how
+ 
+
+ align:start position:0%
+which you have to trade just to have how
+do you transmit that
+
+ align:start position:0%
+do you transmit that
+ 
+
+ align:start position:0%
+do you transmit that
+experience to new people you intermingle
+
+ align:start position:0%
+experience to new people you intermingle
+ 
+
+ align:start position:0%
+experience to new people you intermingle
+you intermingle the young with the
+
+ align:start position:0%
+you intermingle the young with the
+ 
+
+ align:start position:0%
+you intermingle the young with the
+old you bring you bring the uh elderly
+
+ align:start position:0%
+old you bring you bring the uh elderly
+ 
+
+ align:start position:0%
+old you bring you bring the uh elderly
+Engineers into the
+
+ align:start position:0%
+Engineers into the
+ 
+
+ align:start position:0%
+Engineers into the
+system and make you responsible for
+
+ align:start position:0%
+system and make you responsible for
+ 
+
+ align:start position:0%
+system and make you responsible for
+Designing the system but have me your
+
+ align:start position:0%
+Designing the system but have me your
+ 
+
+ align:start position:0%
+Designing the system but have me your
+hip
+
+ align:start position:0%
+hip
+ 
+
+ align:start position:0%
+hip
+pocket but after six months after two
+
+ align:start position:0%
+pocket but after six months after two
+ 
+
+ align:start position:0%
+pocket but after six months after two
+years you don't need me in your hip
+
+ align:start position:0%
+years you don't need me in your hip
+ 
+
+ align:start position:0%
+years you don't need me in your hip
+pocket
+
+ align:start position:0%
+pocket
+ 
+
+ align:start position:0%
+pocket
+anymore because you would have learned
+
+ align:start position:0%
+anymore because you would have learned
+ 
+
+ align:start position:0%
+anymore because you would have learned
+all those things and learned them better
+
+ align:start position:0%
+all those things and learned them better
+ 
+
+ align:start position:0%
+all those things and learned them better
+and done them
+
+ align:start position:0%
+and done them
+ 
+
+ align:start position:0%
+and done them
+better so you have to mix
+
+ align:start position:0%
+better so you have to mix
+ 
+
+ align:start position:0%
+better so you have to mix
+the you know the ingredients for the pie
+
+ align:start position:0%
+the you know the ingredients for the pie
+ 
+
+ align:start position:0%
+the you know the ingredients for the pie
+and the cake have to be there and that's
+
+ align:start position:0%
+and the cake have to be there and that's
+ 
+
+ align:start position:0%
+and the cake have to be there and that's
+part of the
+
+ align:start position:0%
+part of the
+ 
+
+ align:start position:0%
+part of the
+ingredient and that's what why hasn't
+
+ align:start position:0%
+ingredient and that's what why hasn't
+ 
+
+ align:start position:0%
+ingredient and that's what why hasn't
+that taken place because two reasons
+
+ align:start position:0%
+that taken place because two reasons
+ 
+
+ align:start position:0%
+that taken place because two reasons
+uh NASA hasn't done anything in terms of
+
+ align:start position:0%
+uh NASA hasn't done anything in terms of
+ 
+
+ align:start position:0%
+uh NASA hasn't done anything in terms of
+building new hardware other than the
+
+ align:start position:0%
+building new hardware other than the
+ 
+
+ align:start position:0%
+building new hardware other than the
+space station which is really not wasn't
+
+ align:start position:0%
+space station which is really not wasn't
+ 
+
+ align:start position:0%
+space station which is really not wasn't
+testing the state-ofthe-art it was a
+
+ align:start position:0%
+testing the state-ofthe-art it was a
+ 
+
+ align:start position:0%
+testing the state-ofthe-art it was a
+great program it didn't test the State
+
+ align:start position:0%
+great program it didn't test the State
+ 
+
+ align:start position:0%
+great program it didn't test the State
+ofthe art but the
+
+ align:start position:0%
+ofthe art but the
+ 
+
+ align:start position:0%
+ofthe art but the
+industry has been doing the same thing
+
+ align:start position:0%
+industry has been doing the same thing
+ 
+
+ align:start position:0%
+industry has been doing the same thing
+the industry has been building airplanes
+
+ align:start position:0%
+the industry has been building airplanes
+ 
+
+ align:start position:0%
+the industry has been building airplanes
+but they haven't been building any
+
+ align:start position:0%
+but they haven't been building any
+ 
+
+ align:start position:0%
+but they haven't been building any
+spaceships so they've lost that
+
+ align:start position:0%
+spaceships so they've lost that
+ 
+
+ align:start position:0%
+spaceships so they've lost that
+capability also that's the travesty too
+
+ align:start position:0%
+capability also that's the travesty too
+ 
+
+ align:start position:0%
+capability also that's the travesty too
+you got to rebuild them both at the same
+
+ align:start position:0%
+you got to rebuild them both at the same
+ 
+
+ align:start position:0%
+you got to rebuild them both at the same
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+but it only happens by
+
+ align:start position:0%
+but it only happens by
+ 
+
+ align:start position:0%
+but it only happens by
+experience I can't take what Mr
+
+ align:start position:0%
+experience I can't take what Mr
+ 
+
+ align:start position:0%
+experience I can't take what Mr
+Professor Coen I knows or what I know
+
+ align:start position:0%
+Professor Coen I knows or what I know
+ 
+
+ align:start position:0%
+Professor Coen I knows or what I know
+and put it in your
+
+ align:start position:0%
+and put it in your
+ 
+
+ align:start position:0%
+and put it in your
+head you have to you have to
+
+ align:start position:0%
+head you have to you have to
+ 
+
+ align:start position:0%
+head you have to you have to
+fail a few times it's only by the
+
+ align:start position:0%
+fail a few times it's only by the
+ 
+
+ align:start position:0%
+fail a few times it's only by the
+failures that you're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+learn you know I once heard a sermon
+
+ align:start position:0%
+learn you know I once heard a sermon
+ 
+
+ align:start position:0%
+learn you know I once heard a sermon
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+said um when you're a young Christian or
+
+ align:start position:0%
+said um when you're a young Christian or
+ 
+
+ align:start position:0%
+said um when you're a young Christian or
+Hebrew walking down the the aisle all
+
+ align:start position:0%
+Hebrew walking down the the aisle all
+ 
+
+ align:start position:0%
+Hebrew walking down the the aisle all
+the doors are
+
+ align:start position:0%
+the doors are
+ 
+
+ align:start position:0%
+the doors are
+open your doors are all open I'm walking
+
+ align:start position:0%
+open your doors are all open I'm walking
+ 
+
+ align:start position:0%
+open your doors are all open I'm walking
+down the aisle and I'm pretty close to
+
+ align:start position:0%
+down the aisle and I'm pretty close to
+ 
+
+ align:start position:0%
+down the aisle and I'm pretty close to
+the end and they're all the ones behind
+
+ align:start position:0%
+the end and they're all the ones behind
+ 
+
+ align:start position:0%
+the end and they're all the ones behind
+me are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shut you're willing
+
+ align:start position:0%
+shut you're willing
+ 
+
+ align:start position:0%
+shut you're willing
+to go into all those doors I'm
+
+ align:start position:0%
+to go into all those doors I'm
+ 
+
+ align:start position:0%
+to go into all those doors I'm
+frightened to death to go in those damn
+
+ align:start position:0%
+frightened to death to go in those damn
+ 
+
+ align:start position:0%
+frightened to death to go in those damn
+doors so we need need you and you need
+
+ align:start position:0%
+doors so we need need you and you need
+ 
+
+ align:start position:0%
+doors so we need need you and you need
+me but you don't need me very long till
+
+ align:start position:0%
+me but you don't need me very long till
+ 
+
+ align:start position:0%
+me but you don't need me very long till
+you get up to speed so don't be
+
+ align:start position:0%
+you get up to speed so don't be
+ 
+
+ align:start position:0%
+you get up to speed so don't be
+frightened of it go do it and don't be
+
+ align:start position:0%
+frightened of it go do it and don't be
+ 
+
+ align:start position:0%
+frightened of it go do it and don't be
+afraid to
+
+ align:start position:0%
+afraid to
+ 
+
+ align:start position:0%
+afraid to
+fail we learn much more from our
+
+ align:start position:0%
+fail we learn much more from our
+ 
+
+ align:start position:0%
+fail we learn much more from our
+failures than we ever learn from our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+successes back
+
+ align:start position:0%
+successes back
+ 
+
+ align:start position:0%
+successes back
+there've seen over the you thinkal
+
+ align:start position:0%
+there've seen over the you thinkal
+ 
+
+ align:start position:0%
+there've seen over the you thinkal
+access SP not necessarily going now but
+
+ align:start position:0%
+access SP not necessarily going now but
+ 
+
+ align:start position:0%
+access SP not necessarily going now but
+also in the
+
+ align:start position:0%
+also in the
+ 
+
+ align:start position:0%
+also in the
+future we have that ability
+
+ align:start position:0%
+future we have that ability
+ 
+
+ align:start position:0%
+future we have that ability
+toass framework with all the know issues
+
+ align:start position:0%
+toass framework with all the know issues
+ 
+
+ align:start position:0%
+toass framework with all the know issues
+with bureaucracy issues know is that a
+
+ align:start position:0%
+with bureaucracy issues know is that a
+ 
+
+ align:start position:0%
+with bureaucracy issues know is that a
+possible way for us to continue well I
+
+ align:start position:0%
+possible way for us to continue well I
+ 
+
+ align:start position:0%
+possible way for us to continue well I
+think it's very possible but the problem
+
+ align:start position:0%
+think it's very possible but the problem
+ 
+
+ align:start position:0%
+think it's very possible but the problem
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+money problem is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+investment you
+
+ align:start position:0%
+investment you
+ 
+
+ align:start position:0%
+investment you
+know investment specialist say if you
+
+ align:start position:0%
+know investment specialist say if you
+ 
+
+ align:start position:0%
+know investment specialist say if you
+can't give me a return on investment in
+
+ align:start position:0%
+can't give me a return on investment in
+ 
+
+ align:start position:0%
+can't give me a return on investment in
+three years maximum five years I don't I
+
+ align:start position:0%
+three years maximum five years I don't I
+ 
+
+ align:start position:0%
+three years maximum five years I don't I
+won't invest in it and the Aerospace
+
+ align:start position:0%
+won't invest in it and the Aerospace
+ 
+
+ align:start position:0%
+won't invest in it and the Aerospace
+industry is worse than that they don't
+
+ align:start position:0%
+industry is worse than that they don't
+ 
+
+ align:start position:0%
+industry is worse than that they don't
+have any money so they don't they aren't
+
+ align:start position:0%
+have any money so they don't they aren't
+ 
+
+ align:start position:0%
+have any money so they don't they aren't
+willing to make an investment in the
+
+ align:start position:0%
+willing to make an investment in the
+ 
+
+ align:start position:0%
+willing to make an investment in the
+future so the investors who have the
+
+ align:start position:0%
+future so the investors who have the
+ 
+
+ align:start position:0%
+future so the investors who have the
+money want to
+
+ align:start position:0%
+money want to
+ 
+
+ align:start position:0%
+money want to
+return the guys that have the capability
+
+ align:start position:0%
+return the guys that have the capability
+ 
+
+ align:start position:0%
+return the guys that have the capability
+to do it don't have the money to
+
+ align:start position:0%
+to do it don't have the money to
+ 
+
+ align:start position:0%
+to do it don't have the money to
+invest so until it gets to the point
+
+ align:start position:0%
+invest so until it gets to the point
+ 
+
+ align:start position:0%
+invest so until it gets to the point
+where it's a little more realistic from
+
+ align:start position:0%
+where it's a little more realistic from
+ 
+
+ align:start position:0%
+where it's a little more realistic from
+a return on investment it's not going to
+
+ align:start position:0%
+a return on investment it's not going to
+ 
+
+ align:start position:0%
+a return on investment it's not going to
+get to the point where commercial
+
+ align:start position:0%
+get to the point where commercial
+ 
+
+ align:start position:0%
+get to the point where commercial
+Ventures are willing to do it because
+
+ align:start position:0%
+Ventures are willing to do it because
+ 
+
+ align:start position:0%
+Ventures are willing to do it because
+it's just too expensive and the the prob
+
+ align:start position:0%
+it's just too expensive and the the prob
+ 
+
+ align:start position:0%
+it's just too expensive and the the prob
+the the probability of failure so high
+
+ align:start position:0%
+the the probability of failure so high
+ 
+
+ align:start position:0%
+the the probability of failure so high
+in our
+
+ align:start position:0%
+in our
+ 
+
+ align:start position:0%
+in our
+business that investors shy away from
+
+ align:start position:0%
+business that investors shy away from
+ 
+
+ align:start position:0%
+business that investors shy away from
+it so I think it will come to that
+
+ align:start position:0%
+it so I think it will come to that
+ 
+
+ align:start position:0%
+it so I think it will come to that
+but I don't think it's going to come
+
+ align:start position:0%
+but I don't think it's going to come
+ 
+
+ align:start position:0%
+but I don't think it's going to come
+very rapidly as it did in for instance
+
+ align:start position:0%
+very rapidly as it did in for instance
+ 
+
+ align:start position:0%
+very rapidly as it did in for instance
+in the airplane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bu I mean even
+
+ align:start position:0%
+bu I mean even
+ 
+
+ align:start position:0%
+bu I mean even
+today we wouldn't be
+
+ align:start position:0%
+today we wouldn't be
+ 
+
+ align:start position:0%
+today we wouldn't be
+flying the transports we have or the
+
+ align:start position:0%
+flying the transports we have or the
+ 
+
+ align:start position:0%
+flying the transports we have or the
+supersonic airplanes that we have
+
+ align:start position:0%
+supersonic airplanes that we have
+ 
+
+ align:start position:0%
+supersonic airplanes that we have
+without the in government having made
+
+ align:start position:0%
+without the in government having made
+ 
+
+ align:start position:0%
+without the in government having made
+that investment at the
+
+ align:start position:0%
+that investment at the
+ 
+
+ align:start position:0%
+that investment at the
+time you know the the 707 first big
+
+ align:start position:0%
+time you know the the 707 first big
+ 
+
+ align:start position:0%
+time you know the the 707 first big
+really good jet transport was totally
+
+ align:start position:0%
+really good jet transport was totally
+ 
+
+ align:start position:0%
+really good jet transport was totally
+dependent upon the
+
+ align:start position:0%
+dependent upon the
+ 
+
+ align:start position:0%
+dependent upon the
+b47
+
+ align:start position:0%
+b47
+ 
+
+ align:start position:0%
+b47
+airport which is built by the same
+
+ align:start position:0%
+airport which is built by the same
+ 
+
+ align:start position:0%
+airport which is built by the same
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+right and so it was the government
+
+ align:start position:0%
+right and so it was the government
+ 
+
+ align:start position:0%
+right and so it was the government
+investment you know everybody say well
+
+ align:start position:0%
+investment you know everybody say well
+ 
+
+ align:start position:0%
+investment you know everybody say well
+we did in the airplane business to a
+
+ align:start position:0%
+we did in the airplane business to a
+ 
+
+ align:start position:0%
+we did in the airplane business to a
+certain extent but nowhere near as much
+
+ align:start position:0%
+certain extent but nowhere near as much
+ 
+
+ align:start position:0%
+certain extent but nowhere near as much
+as people think because it was all of
+
+ align:start position:0%
+as people think because it was all of
+ 
+
+ align:start position:0%
+as people think because it was all of
+the technology was done by the in
+
+ align:start position:0%
+the technology was done by the in
+ 
+
+ align:start position:0%
+the technology was done by the in
+government investment in the airport
+
+ align:start position:0%
+government investment in the airport
+ 
+
+ align:start position:0%
+government investment in the airport
+and you know the next step the
+
+ align:start position:0%
+and you know the next step the
+ 
+
+ align:start position:0%
+and you know the next step the
+supersonic bomber or excuse me
+
+ align:start position:0%
+supersonic bomber or excuse me
+ 
+
+ align:start position:0%
+supersonic bomber or excuse me
+supersonic transport which we ought to
+
+ align:start position:0%
+supersonic transport which we ought to
+ 
+
+ align:start position:0%
+supersonic transport which we ought to
+have it's a that's another travesty that
+
+ align:start position:0%
+have it's a that's another travesty that
+ 
+
+ align:start position:0%
+have it's a that's another travesty that
+we don't have a supersonic
+
+ align:start position:0%
+we don't have a supersonic
+ 
+
+ align:start position:0%
+we don't have a supersonic
+trans
+
+ align:start position:0%
+trans
+ 
+
+ align:start position:0%
+trans
+uh that hasn't been done by Boeing or
+
+ align:start position:0%
+uh that hasn't been done by Boeing or
+ 
+
+ align:start position:0%
+uh that hasn't been done by Boeing or
+locky
+
+ align:start position:0%
+locky
+ 
+
+ align:start position:0%
+locky
+because they don't have the they aren't
+
+ align:start position:0%
+because they don't have the they aren't
+ 
+
+ align:start position:0%
+because they don't have the they aren't
+willing to
+
+ align:start position:0%
+willing to
+ 
+
+ align:start position:0%
+willing to
+invest that kind of money on their own
+
+ align:start position:0%
+invest that kind of money on their own
+ 
+
+ align:start position:0%
+invest that kind of money on their own
+so they take
+
+ align:start position:0%
+so they take
+ 
+
+ align:start position:0%
+so they take
+the the investment of the Govern govern
+
+ align:start position:0%
+the the investment of the Govern govern
+ 
+
+ align:start position:0%
+the the investment of the Govern govern
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+supersonic aerodynamics and engines and
+
+ align:start position:0%
+supersonic aerodynamics and engines and
+ 
+
+ align:start position:0%
+supersonic aerodynamics and engines and
+structure and use it in a supersonic
+
+ align:start position:0%
+structure and use it in a supersonic
+ 
+
+ align:start position:0%
+structure and use it in a supersonic
+airport so I I think it's a ways off a
+
+ align:start position:0%
+airport so I I think it's a ways off a
+ 
+
+ align:start position:0%
+airport so I I think it's a ways off a
+lot of people have tried
+
+ align:start position:0%
+lot of people have tried
+ 
+
+ align:start position:0%
+lot of people have tried
+it most notable being kler
+
+ align:start position:0%
+it most notable being kler
+ 
+
+ align:start position:0%
+it most notable being kler
+recently and have
+
+ align:start position:0%
+recently and have
+ 
+
+ align:start position:0%
+recently and have
+failed I think it can be done pro and
+
+ align:start position:0%
+failed I think it can be done pro and
+ 
+
+ align:start position:0%
+failed I think it can be done pro and
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+better you can do it better outside of
+
+ align:start position:0%
+better you can do it better outside of
+ 
+
+ align:start position:0%
+better you can do it better outside of
+the government because you don't have
+
+ align:start position:0%
+the government because you don't have
+ 
+
+ align:start position:0%
+the government because you don't have
+all those regulations to contend with
+
+ align:start position:0%
+all those regulations to contend with
+ 
+
+ align:start position:0%
+all those regulations to contend with
+and all the gaos on top of
+
+ align:start position:0%
+and all the gaos on top of
+ 
+
+ align:start position:0%
+and all the gaos on top of
+you just going to take a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l uh I hesitate to say this but I will
+
+ align:start position:0%
+l uh I hesitate to say this but I will
+ 
+
+ align:start position:0%
+l uh I hesitate to say this but I will
+uh programs like the
+
+ align:start position:0%
+uh programs like the
+ 
+
+ align:start position:0%
+uh programs like the
+uh what's the name of Ran's
+
+ align:start position:0%
+uh what's the name of Ran's
+ 
+
+ align:start position:0%
+uh what's the name of Ran's
+vehicle big
+
+ align:start position:0%
+vehicle big
+ 
+
+ align:start position:0%
+vehicle big
+hard spaceship
+
+ align:start position:0%
+hard spaceship
+ 
+
+ align:start position:0%
+hard spaceship
+one that's trickery
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's Child's Play what he's
+
+ align:start position:0%
+that's Child's Play what he's
+ 
+
+ align:start position:0%
+that's Child's Play what he's
+doing Wy tries to go to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbit that's his next
+
+ align:start position:0%
+orbit that's his next
+ 
+
+ align:start position:0%
+orbit that's his next
+step tell me when that's going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen I you know he's he's kidding the
+
+ align:start position:0%
+happen I you know he's he's kidding the
+ 
+
+ align:start position:0%
+happen I you know he's he's kidding the
+world at the moment Chris Craft say
+
+ align:start position:0%
+world at the moment Chris Craft say
+ 
+
+ align:start position:0%
+world at the moment Chris Craft say
+it I I want you to remember that because
+
+ align:start position:0%
+it I I want you to remember that because
+ 
+
+ align:start position:0%
+it I I want you to remember that because
+I I could be dead wrong so but that's my
+
+ align:start position:0%
+I I could be dead wrong so but that's my
+ 
+
+ align:start position:0%
+I I could be dead wrong so but that's my
+opinion it's just child's
+
+ align:start position:0%
+opinion it's just child's
+ 
+
+ align:start position:0%
+opinion it's just child's
+prti you know we did we did the X1 in
+
+ align:start position:0%
+prti you know we did we did the X1 in
+ 
+
+ align:start position:0%
+prti you know we did we did the X1 in
+1946 and we didn't have any buckling in
+
+ align:start position:0%
+1946 and we didn't have any buckling in
+ 
+
+ align:start position:0%
+1946 and we didn't have any buckling in
+the structure either which he had where
+
+ align:start position:0%
+the structure either which he had where
+ 
+
+ align:start position:0%
+the structure either which he had where
+do you think that buckling came
+
+ align:start position:0%
+do you think that buckling came
+ 
+
+ align:start position:0%
+do you think that buckling came
+from what do you think happened
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there where' it come fromp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's great
+
+ align:start position:0%
+it's great
+ 
+
+ align:start position:0%
+it's great
+absolutely but don't kid yourself that
+
+ align:start position:0%
+absolutely but don't kid yourself that
+ 
+
+ align:start position:0%
+absolutely but don't kid yourself that
+you know that the next step is flying a
+
+ align:start position:0%
+you know that the next step is flying a
+ 
+
+ align:start position:0%
+you know that the next step is flying a
+machine to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbit yeah I I'm I'm in fault for being
+
+ align:start position:0%
+orbit yeah I I'm I'm in fault for being
+ 
+
+ align:start position:0%
+orbit yeah I I'm I'm in fault for being
+so negative about it but because you're
+
+ align:start position:0%
+so negative about it but because you're
+ 
+
+ align:start position:0%
+so negative about it but because you're
+right I think it does inspire the young
+
+ align:start position:0%
+right I think it does inspire the young
+ 
+
+ align:start position:0%
+right I think it does inspire the young
+to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it as much as I hate to cut us off it is
+
+ align:start position:0%
+it as much as I hate to cut us off it is
+ 
+
+ align:start position:0%
+it as much as I hate to cut us off it is
+11:00 uh class is over students again
+
+ align:start position:0%
+11:00 uh class is over students again
+ 
+
+ align:start position:0%
+11:00 uh class is over students again
+remember to pick up your papers but uh
+
+ align:start position:0%
+remember to pick up your papers but uh
+ 
+
+ align:start position:0%
+remember to pick up your papers but uh
+Chris this has been just an
+
+ align:start position:0%
+Chris this has been just an
+ 
+
+ align:start position:0%
+Chris this has been just an
+extraordinary opportunity and an
+
+ align:start position:0%
+extraordinary opportunity and an
+ 
+
+ align:start position:0%
+extraordinary opportunity and an
+experience for all of us and once more
+
+ align:start position:0%
+experience for all of us and once more
+ 
+
+ align:start position:0%
+experience for all of us and once more
+we're very appreciative appreciative we
+
+ align:start position:0%
+we're very appreciative appreciative we
+ 
+
+ align:start position:0%
+we're very appreciative appreciative we
+know you don't give very many public
+
+ align:start position:0%
+know you don't give very many public
+ 
+
+ align:start position:0%
+know you don't give very many public
+lectures these days uh and that that you
+
+ align:start position:0%
+lectures these days uh and that that you
+ 
+
+ align:start position:0%
+lectures these days uh and that that you
+chose to come here and talk to everybody
+
+ align:start position:0%
+chose to come here and talk to everybody
+ 
+
+ align:start position:0%
+chose to come here and talk to everybody
+uh at MIT we we truly appreciate and
+
+ align:start position:0%
+uh at MIT we we truly appreciate and
+ 
+
+ align:start position:0%
+uh at MIT we we truly appreciate and
+we'd like to thank you again
+
+ align:start position:0%
+we'd like to thank you again
+ 
+
+ align:start position:0%
+we'd like to thank you again
+[Applause]
\ No newline at end of file
diff --git a/Fp7usgx_CvM.txt b/Fp7usgx_CvM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..95dbf9aa82f4c61e85c212ad21cffe358a1faeed
--- /dev/null
+++ b/Fp7usgx_CvM.txt
@@ -0,0 +1,8291 @@
+align:start position:0%
+ 
+let's get started
+
+ align:start position:0%
+let's get started
+ 
+
+ align:start position:0%
+let's get started
+so today we're gonna look at one of my
+
+ align:start position:0%
+so today we're gonna look at one of my
+ 
+
+ align:start position:0%
+so today we're gonna look at one of my
+favorite puzzles I'll say right at the
+
+ align:start position:0%
+favorite puzzles I'll say right at the
+ 
+
+ align:start position:0%
+favorite puzzles I'll say right at the
+beginning that the coding associated
+
+ align:start position:0%
+beginning that the coding associated
+ 
+
+ align:start position:0%
+beginning that the coding associated
+with the puzzle is fairly
+
+ align:start position:0%
+with the puzzle is fairly
+ 
+
+ align:start position:0%
+with the puzzle is fairly
+straightforward but the analysis
+
+ align:start position:0%
+straightforward but the analysis
+ 
+
+ align:start position:0%
+straightforward but the analysis
+associated with this puzzle is quite
+
+ align:start position:0%
+associated with this puzzle is quite
+ 
+
+ align:start position:0%
+associated with this puzzle is quite
+intricate and in particular if you're
+
+ align:start position:0%
+intricate and in particular if you're
+ 
+
+ align:start position:0%
+intricate and in particular if you're
+gonna have to do worst-case analysis
+
+ align:start position:0%
+gonna have to do worst-case analysis
+ 
+
+ align:start position:0%
+gonna have to do worst-case analysis
+which is really a good thing to for you
+
+ align:start position:0%
+which is really a good thing to for you
+ 
+
+ align:start position:0%
+which is really a good thing to for you
+to learn about because asymptotic
+
+ align:start position:0%
+to learn about because asymptotic
+ 
+
+ align:start position:0%
+to learn about because asymptotic
+analysis in algorithms is all about
+
+ align:start position:0%
+analysis in algorithms is all about
+ 
+
+ align:start position:0%
+analysis in algorithms is all about
+worst case alright so keep that in mind
+
+ align:start position:0%
+worst case alright so keep that in mind
+ 
+
+ align:start position:0%
+worst case alright so keep that in mind
+when you try to come up with answers to
+
+ align:start position:0%
+when you try to come up with answers to
+ 
+
+ align:start position:0%
+when you try to come up with answers to
+my questions always keep in mind that
+
+ align:start position:0%
+my questions always keep in mind that
+ 
+
+ align:start position:0%
+my questions always keep in mind that
+I'm going to be asking for what happens
+
+ align:start position:0%
+I'm going to be asking for what happens
+ 
+
+ align:start position:0%
+I'm going to be asking for what happens
+in the worst case know in the context of
+
+ align:start position:0%
+in the worst case know in the context of
+ 
+
+ align:start position:0%
+in the worst case know in the context of
+our puzzle which is is called the
+
+ align:start position:0%
+our puzzle which is is called the
+ 
+
+ align:start position:0%
+our puzzle which is is called the
+crystal ball puzzle and it's fairly
+
+ align:start position:0%
+crystal ball puzzle and it's fairly
+ 
+
+ align:start position:0%
+crystal ball puzzle and it's fairly
+popular in the literature though I've
+
+ align:start position:0%
+popular in the literature though I've
+ 
+
+ align:start position:0%
+popular in the literature though I've
+generalized it a little bit you have the
+
+ align:start position:0%
+generalized it a little bit you have the
+ 
+
+ align:start position:0%
+generalized it a little bit you have the
+situation where you're supposed to
+
+ align:start position:0%
+situation where you're supposed to
+ 
+
+ align:start position:0%
+situation where you're supposed to
+figure out the hardness coefficient of a
+
+ align:start position:0%
+figure out the hardness coefficient of a
+ 
+
+ align:start position:0%
+figure out the hardness coefficient of a
+crystal ball and in the generalized
+
+ align:start position:0%
+crystal ball and in the generalized
+ 
+
+ align:start position:0%
+crystal ball and in the generalized
+version you have a set of identical
+
+ align:start position:0%
+version you have a set of identical
+ 
+
+ align:start position:0%
+version you have a set of identical
+crystal balls right so how do you find
+
+ align:start position:0%
+crystal balls right so how do you find
+ 
+
+ align:start position:0%
+crystal balls right so how do you find
+this hardness coefficient well you go up
+
+ align:start position:0%
+this hardness coefficient well you go up
+ 
+
+ align:start position:0%
+this hardness coefficient well you go up
+to this Shanghai tower that has 128
+
+ align:start position:0%
+to this Shanghai tower that has 128
+ 
+
+ align:start position:0%
+to this Shanghai tower that has 128
+floors one through 128 and you drop this
+
+ align:start position:0%
+floors one through 128 and you drop this
+ 
+
+ align:start position:0%
+floors one through 128 and you drop this
+ball from say floor one so just you're
+
+ align:start position:0%
+ball from say floor one so just you're
+ 
+
+ align:start position:0%
+ball from say floor one so just you're
+standing here and let's say you just
+
+ align:start position:0%
+standing here and let's say you just
+ 
+
+ align:start position:0%
+standing here and let's say you just
+drop it from there or you go up to floor
+
+ align:start position:0%
+drop it from there or you go up to floor
+ 
+
+ align:start position:0%
+drop it from there or you go up to floor
+to and you drop the ball and the
+
+ align:start position:0%
+to and you drop the ball and the
+ 
+
+ align:start position:0%
+to and you drop the ball and the
+hardness coefficient is defined as the
+
+ align:start position:0%
+hardness coefficient is defined as the
+ 
+
+ align:start position:0%
+hardness coefficient is defined as the
+highest floor from which you can drop
+
+ align:start position:0%
+highest floor from which you can drop
+ 
+
+ align:start position:0%
+highest floor from which you can drop
+the ball and the ball does not break
+
+ align:start position:0%
+the ball and the ball does not break
+ 
+
+ align:start position:0%
+the ball and the ball does not break
+okay so what this means is if floor F
+
+ align:start position:0%
+okay so what this means is if floor F
+ 
+
+ align:start position:0%
+okay so what this means is if floor F
+the ball doesn't break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it breaks at f+ 1 then the hardness
+
+ align:start position:0%
+and it breaks at f+ 1 then the hardness
+ 
+
+ align:start position:0%
+and it breaks at f+ 1 then the hardness
+coefficient is F and you can assume a
+
+ align:start position:0%
+coefficient is F and you can assume a
+ 
+
+ align:start position:0%
+coefficient is F and you can assume a
+monotone a city properly that says that
+
+ align:start position:0%
+monotone a city properly that says that
+ 
+
+ align:start position:0%
+monotone a city properly that says that
+if it did not break at floor F then it
+
+ align:start position:0%
+if it did not break at floor F then it
+ 
+
+ align:start position:0%
+if it did not break at floor F then it
+won't break this implies that it won't
+
+ align:start position:0%
+won't break this implies that it won't
+ 
+
+ align:start position:0%
+won't break this implies that it won't
+break it at any floor less than or equal
+
+ align:start position:0%
+break it at any floor less than or equal
+ 
+
+ align:start position:0%
+break it at any floor less than or equal
+to F okay which makes sense right
+
+ align:start position:0%
+to F okay which makes sense right
+ 
+
+ align:start position:0%
+to F okay which makes sense right
+I'm not otherwise it would be kind of
+
+ align:start position:0%
+I'm not otherwise it would be kind of
+ 
+
+ align:start position:0%
+I'm not otherwise it would be kind of
+complicated it would be random and
+
+ align:start position:0%
+complicated it would be random and
+ 
+
+ align:start position:0%
+complicated it would be random and
+everyone be able to do any interesting
+
+ align:start position:0%
+everyone be able to do any interesting
+ 
+
+ align:start position:0%
+everyone be able to do any interesting
+analysis um so the easy a version of the
+
+ align:start position:0%
+analysis um so the easy a version of the
+ 
+
+ align:start position:0%
+analysis um so the easy a version of the
+puzzle of course which is not
+
+ align:start position:0%
+puzzle of course which is not
+ 
+
+ align:start position:0%
+puzzle of course which is not
+particularly interesting is if you need
+
+ align:start position:0%
+particularly interesting is if you need
+ 
+
+ align:start position:0%
+particularly interesting is if you need
+it to get this this exactly right so
+
+ align:start position:0%
+it to get this this exactly right so
+ 
+
+ align:start position:0%
+it to get this this exactly right so
+your job depends on getting that number
+
+ align:start position:0%
+your job depends on getting that number
+ 
+
+ align:start position:0%
+your job depends on getting that number
+exactly right so there's no shortcuts
+
+ align:start position:0%
+exactly right so there's no shortcuts
+ 
+
+ align:start position:0%
+exactly right so there's no shortcuts
+you got to get it right you can't be off
+
+ align:start position:0%
+you got to get it right you can't be off
+ 
+
+ align:start position:0%
+you got to get it right you can't be off
+by one either way and I you I have only
+
+ align:start position:0%
+by one either way and I you I have only
+ 
+
+ align:start position:0%
+by one either way and I you I have only
+one ball right so you only have one ball
+
+ align:start position:0%
+one ball right so you only have one ball
+ 
+
+ align:start position:0%
+one ball right so you only have one ball
+so so what can you do if you only have
+
+ align:start position:0%
+so so what can you do if you only have
+ 
+
+ align:start position:0%
+so so what can you do if you only have
+one ball and you have to get it exactly
+
+ align:start position:0%
+one ball and you have to get it exactly
+ 
+
+ align:start position:0%
+one ball and you have to get it exactly
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+try every floor right and and but more
+
+ align:start position:0%
+try every floor right and and but more
+ 
+
+ align:start position:0%
+try every floor right and and but more
+important I try from lower floors to
+
+ align:start position:0%
+important I try from lower floors to
+ 
+
+ align:start position:0%
+important I try from lower floors to
+higher floors right so you drop it at
+
+ align:start position:0%
+higher floors right so you drop it at
+ 
+
+ align:start position:0%
+higher floors right so you drop it at
+floor one I saw one ball you drop from
+
+ align:start position:0%
+floor one I saw one ball you drop from
+ 
+
+ align:start position:0%
+floor one I saw one ball you drop from
+floor one and if it in and if it breaks
+
+ align:start position:0%
+floor one and if it in and if it breaks
+ 
+
+ align:start position:0%
+floor one and if it in and if it breaks
+then your hardness coefficient is is you
+
+ align:start position:0%
+then your hardness coefficient is is you
+ 
+
+ align:start position:0%
+then your hardness coefficient is is you
+return zero but then if you keep going
+
+ align:start position:0%
+return zero but then if you keep going
+ 
+
+ align:start position:0%
+return zero but then if you keep going
+and it and it let's say you drop I've
+
+ align:start position:0%
+and it and it let's say you drop I've
+ 
+
+ align:start position:0%
+and it and it let's say you drop I've
+got a dot from floor 65 and it breaks
+
+ align:start position:0%
+got a dot from floor 65 and it breaks
+ 
+
+ align:start position:0%
+got a dot from floor 65 and it breaks
+and you've gone in order then the
+
+ align:start position:0%
+and you've gone in order then the
+ 
+
+ align:start position:0%
+and you've gone in order then the
+hardness coefficient is 64 okay right so
+
+ align:start position:0%
+hardness coefficient is 64 okay right so
+ 
+
+ align:start position:0%
+hardness coefficient is 64 okay right so
+that's easy enough there's there's no
+
+ align:start position:0%
+that's easy enough there's there's no
+ 
+
+ align:start position:0%
+that's easy enough there's there's no
+optimization here it's the only thing
+
+ align:start position:0%
+optimization here it's the only thing
+ 
+
+ align:start position:0%
+optimization here it's the only thing
+you can do so that's why it's not
+
+ align:start position:0%
+you can do so that's why it's not
+ 
+
+ align:start position:0%
+you can do so that's why it's not
+particularly interesting now if you have
+
+ align:start position:0%
+particularly interesting now if you have
+ 
+
+ align:start position:0%
+particularly interesting now if you have
+identical crystal balls that are
+
+ align:start position:0%
+identical crystal balls that are
+ 
+
+ align:start position:0%
+identical crystal balls that are
+guaranteed
+
+ align:start position:0%
+guaranteed
+ 
+
+ align:start position:0%
+guaranteed
+they were manufactured in exactly the
+
+ align:start position:0%
+they were manufactured in exactly the
+ 
+
+ align:start position:0%
+they were manufactured in exactly the
+same way
+
+ align:start position:0%
+same way
+ 
+
+ align:start position:0%
+same way
+etc etc then obviously things get a lot
+
+ align:start position:0%
+etc etc then obviously things get a lot
+ 
+
+ align:start position:0%
+etc etc then obviously things get a lot
+more interesting because you can try to
+
+ align:start position:0%
+more interesting because you can try to
+ 
+
+ align:start position:0%
+more interesting because you can try to
+minimize something and I'm gonna write
+
+ align:start position:0%
+minimize something and I'm gonna write
+ 
+
+ align:start position:0%
+minimize something and I'm gonna write
+it over here because I want you to keep
+
+ align:start position:0%
+it over here because I want you to keep
+ 
+
+ align:start position:0%
+it over here because I want you to keep
+this in mind throughout the lecture our
+
+ align:start position:0%
+this in mind throughout the lecture our
+ 
+
+ align:start position:0%
+this in mind throughout the lecture our
+goal here is to minimize the worst case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number of drops for our problem and if
+
+ align:start position:0%
+number of drops for our problem and if
+ 
+
+ align:start position:0%
+number of drops for our problem and if
+we want to we want to solve the problem
+
+ align:start position:0%
+we want to we want to solve the problem
+ 
+
+ align:start position:0%
+we want to we want to solve the problem
+in the general case with the balls and I
+
+ align:start position:0%
+in the general case with the balls and I
+ 
+
+ align:start position:0%
+in the general case with the balls and I
+should say D identical balls but more
+
+ align:start position:0%
+should say D identical balls but more
+ 
+
+ align:start position:0%
+should say D identical balls but more
+important the reason I'm writing this up
+
+ align:start position:0%
+important the reason I'm writing this up
+ 
+
+ align:start position:0%
+important the reason I'm writing this up
+is as I said before we need to focus on
+
+ align:start position:0%
+is as I said before we need to focus on
+ 
+
+ align:start position:0%
+is as I said before we need to focus on
+the worst case right so it may be the
+
+ align:start position:0%
+the worst case right so it may be the
+ 
+
+ align:start position:0%
+the worst case right so it may be the
+case that for a given set of balls your
+
+ align:start position:0%
+case that for a given set of balls your
+ 
+
+ align:start position:0%
+case that for a given set of balls your
+algorithm does very well I in in in the
+
+ align:start position:0%
+algorithm does very well I in in in the
+ 
+
+ align:start position:0%
+algorithm does very well I in in in the
+sense that the hardness coefficient
+
+ align:start position:0%
+sense that the hardness coefficient
+ 
+
+ align:start position:0%
+sense that the hardness coefficient
+happened to be 42 and you you picked the
+
+ align:start position:0%
+happened to be 42 and you you picked the
+ 
+
+ align:start position:0%
+happened to be 42 and you you picked the
+floor as as of 41 to begin with and so
+
+ align:start position:0%
+floor as as of 41 to begin with and so
+ 
+
+ align:start position:0%
+floor as as of 41 to begin with and so
+you drop from 41 and it doesn't break
+
+ align:start position:0%
+you drop from 41 and it doesn't break
+ 
+
+ align:start position:0%
+you drop from 41 and it doesn't break
+and then you go to 42 and it doesn't
+
+ align:start position:0%
+and then you go to 42 and it doesn't
+ 
+
+ align:start position:0%
+and then you go to 42 and it doesn't
+break and you go to 43 and it doesn't M
+
+ align:start position:0%
+break and you go to 43 and it doesn't M
+ 
+
+ align:start position:0%
+break and you go to 43 and it doesn't M
+it breaks and you go oh I only needed
+
+ align:start position:0%
+it breaks and you go oh I only needed
+ 
+
+ align:start position:0%
+it breaks and you go oh I only needed
+two drops for this particular problem
+
+ align:start position:0%
+two drops for this particular problem
+ 
+
+ align:start position:0%
+two drops for this particular problem
+but but if you but if the hardness
+
+ align:start position:0%
+but but if you but if the hardness
+ 
+
+ align:start position:0%
+but but if you but if the hardness
+coefficient happened to be a 65 and you
+
+ align:start position:0%
+coefficient happened to be a 65 and you
+ 
+
+ align:start position:0%
+coefficient happened to be a 65 and you
+started from floor 41 I mean you need 20
+
+ align:start position:0%
+started from floor 41 I mean you need 20
+ 
+
+ align:start position:0%
+started from floor 41 I mean you need 20
+odd number of drops right so you have to
+
+ align:start position:0%
+odd number of drops right so you have to
+ 
+
+ align:start position:0%
+odd number of drops right so you have to
+be careful I in that you have to analyze
+
+ align:start position:0%
+be careful I in that you have to analyze
+ 
+
+ align:start position:0%
+be careful I in that you have to analyze
+whatever strategy you come up with I in
+
+ align:start position:0%
+whatever strategy you come up with I in
+ 
+
+ align:start position:0%
+whatever strategy you come up with I in
+the case where the hardness coefficient
+
+ align:start position:0%
+the case where the hardness coefficient
+ 
+
+ align:start position:0%
+the case where the hardness coefficient
+could be pretty much anything I mean it
+
+ align:start position:0%
+could be pretty much anything I mean it
+ 
+
+ align:start position:0%
+could be pretty much anything I mean it
+could be zero or it could be 128 all
+
+ align:start position:0%
+could be zero or it could be 128 all
+ 
+
+ align:start position:0%
+could be zero or it could be 128 all
+right I'm not a Shanghai Tower example
+
+ align:start position:0%
+right I'm not a Shanghai Tower example
+ 
+
+ align:start position:0%
+right I'm not a Shanghai Tower example
+all right so the first interesting
+
+ align:start position:0%
+all right so the first interesting
+ 
+
+ align:start position:0%
+all right so the first interesting
+question is what happens when I have two
+
+ align:start position:0%
+question is what happens when I have two
+ 
+
+ align:start position:0%
+question is what happens when I have two
+identical balls right so oh before we do
+
+ align:start position:0%
+identical balls right so oh before we do
+ 
+
+ align:start position:0%
+identical balls right so oh before we do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+according to according to my metric here
+
+ align:start position:0%
+according to according to my metric here
+ 
+
+ align:start position:0%
+according to according to my metric here
+what is the worst case
+
+ align:start position:0%
+what is the worst case
+ 
+
+ align:start position:0%
+what is the worst case
+number of drops for one ball what is the
+
+ align:start position:0%
+number of drops for one ball what is the
+ 
+
+ align:start position:0%
+number of drops for one ball what is the
+worst case number of drops for one ball
+
+ align:start position:0%
+worst case number of drops for one ball
+ 
+
+ align:start position:0%
+worst case number of drops for one ball
+give me a number
+
+ align:start position:0%
+give me a number
+ 
+
+ align:start position:0%
+give me a number
+someone else yeah back there 128 exactly
+
+ align:start position:0%
+someone else yeah back there 128 exactly
+ 
+
+ align:start position:0%
+someone else yeah back there 128 exactly
+right so it's it's 128 because I could
+
+ align:start position:0%
+right so it's it's 128 because I could
+ 
+
+ align:start position:0%
+right so it's it's 128 because I could
+have had a ball that doesn't break from
+
+ align:start position:0%
+have had a ball that doesn't break from
+ 
+
+ align:start position:0%
+have had a ball that doesn't break from
+the 128 floor I don't know that to begin
+
+ align:start position:0%
+the 128 floor I don't know that to begin
+ 
+
+ align:start position:0%
+the 128 floor I don't know that to begin
+with I have to start with floor 1 and I
+
+ align:start position:0%
+with I have to start with floor 1 and I
+ 
+
+ align:start position:0%
+with I have to start with floor 1 and I
+gotta go 1 2 3 4 etc right so the worst
+
+ align:start position:0%
+gotta go 1 2 3 4 etc right so the worst
+ 
+
+ align:start position:0%
+gotta go 1 2 3 4 etc right so the worst
+case for one ball is 128 and then you
+
+ align:start position:0%
+case for one ball is 128 and then you
+ 
+
+ align:start position:0%
+case for one ball is 128 and then you
+can't do better than that alright it but
+
+ align:start position:0%
+can't do better than that alright it but
+ 
+
+ align:start position:0%
+can't do better than that alright it but
+of course it gets more interesting when
+
+ align:start position:0%
+of course it gets more interesting when
+ 
+
+ align:start position:0%
+of course it gets more interesting when
+D is large right so so our goal now is
+
+ align:start position:0%
+D is large right so so our goal now is
+ 
+
+ align:start position:0%
+D is large right so so our goal now is
+to discover an algorithm that is going
+
+ align:start position:0%
+to discover an algorithm that is going
+ 
+
+ align:start position:0%
+to discover an algorithm that is going
+to minimize the worst case number of
+
+ align:start position:0%
+to minimize the worst case number of
+ 
+
+ align:start position:0%
+to minimize the worst case number of
+drops for D equals 2 okay that's that's
+
+ align:start position:0%
+drops for D equals 2 okay that's that's
+ 
+
+ align:start position:0%
+drops for D equals 2 okay that's that's
+our that's our current goal right and
+
+ align:start position:0%
+our that's our current goal right and
+ 
+
+ align:start position:0%
+our that's our current goal right and
+then we'll look at more even more
+
+ align:start position:0%
+then we'll look at more even more
+ 
+
+ align:start position:0%
+then we'll look at more even more
+general things so how would you do if
+
+ align:start position:0%
+general things so how would you do if
+ 
+
+ align:start position:0%
+general things so how would you do if
+thinks if you had D equals 2 right it
+
+ align:start position:0%
+thinks if you had D equals 2 right it
+ 
+
+ align:start position:0%
+thinks if you had D equals 2 right it
+just it doesn't matter if you don't get
+
+ align:start position:0%
+just it doesn't matter if you don't get
+ 
+
+ align:start position:0%
+just it doesn't matter if you don't get
+the algorithm right I'll let me analyze
+
+ align:start position:0%
+the algorithm right I'll let me analyze
+ 
+
+ align:start position:0%
+the algorithm right I'll let me analyze
+it you propose something you'll analyze
+
+ align:start position:0%
+it you propose something you'll analyze
+ 
+
+ align:start position:0%
+it you propose something you'll analyze
+it and then we'll decide if we can do
+
+ align:start position:0%
+it and then we'll decide if we can do
+ 
+
+ align:start position:0%
+it and then we'll decide if we can do
+better or not yeah go ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh use the bottom half excellent what's
+
+ align:start position:0%
+Oh use the bottom half excellent what's
+ 
+
+ align:start position:0%
+Oh use the bottom half excellent what's
+your name sorry Domon um and so so so
+
+ align:start position:0%
+your name sorry Domon um and so so so
+ 
+
+ align:start position:0%
+your name sorry Domon um and so so so
+Domon says that we should do binary
+
+ align:start position:0%
+Domon says that we should do binary
+ 
+
+ align:start position:0%
+Domon says that we should do binary
+search right which is very intuitive and
+
+ align:start position:0%
+search right which is very intuitive and
+ 
+
+ align:start position:0%
+search right which is very intuitive and
+kind of make sense in a lot of context
+
+ align:start position:0%
+kind of make sense in a lot of context
+ 
+
+ align:start position:0%
+kind of make sense in a lot of context
+including this one and so let's drop
+
+ align:start position:0%
+including this one and so let's drop
+ 
+
+ align:start position:0%
+including this one and so let's drop
+from sorry from 64 and the reason she
+
+ align:start position:0%
+from sorry from 64 and the reason she
+ 
+
+ align:start position:0%
+from sorry from 64 and the reason she
+picked that is because 128 divided by 2
+
+ align:start position:0%
+picked that is because 128 divided by 2
+ 
+
+ align:start position:0%
+picked that is because 128 divided by 2
+is 64 and if it breaks then I you need
+
+ align:start position:0%
+is 64 and if it breaks then I you need
+ 
+
+ align:start position:0%
+is 64 and if it breaks then I you need
+to look at the interval 1 comma 63 right
+
+ align:start position:0%
+to look at the interval 1 comma 63 right
+ 
+
+ align:start position:0%
+to look at the interval 1 comma 63 right
+because it if it I'm sorry if it yeah
+
+ align:start position:0%
+because it if it I'm sorry if it yeah
+ 
+
+ align:start position:0%
+because it if it I'm sorry if it yeah
+that's right if it if it breaks you you
+
+ align:start position:0%
+that's right if it if it breaks you you
+ 
+
+ align:start position:0%
+that's right if it if it breaks you you
+need to look at the interval 1 comma 63
+
+ align:start position:0%
+need to look at the interval 1 comma 63
+ 
+
+ align:start position:0%
+need to look at the interval 1 comma 63
+with the second ball I mean that that
+
+ align:start position:0%
+with the second ball I mean that that
+ 
+
+ align:start position:0%
+with the second ball I mean that that
+first ball is gone okay it shards of
+
+ align:start position:0%
+first ball is gone okay it shards of
+ 
+
+ align:start position:0%
+first ball is gone okay it shards of
+crystal or whatever you want to call it
+
+ align:start position:0%
+crystal or whatever you want to call it
+ 
+
+ align:start position:0%
+crystal or whatever you want to call it
+um so so you just have the second ball
+
+ align:start position:0%
+um so so you just have the second ball
+ 
+
+ align:start position:0%
+um so so you just have the second ball
+and so now at this point you have no
+
+ align:start position:0%
+and so now at this point you have no
+ 
+
+ align:start position:0%
+and so now at this point you have no
+choice
+
+ align:start position:0%
+choice
+ 
+
+ align:start position:0%
+choice
+alright you only have one ball left
+
+ align:start position:0%
+alright you only have one ball left
+ 
+
+ align:start position:0%
+alright you only have one ball left
+right as I mentioned your job depends on
+
+ align:start position:0%
+right as I mentioned your job depends on
+ 
+
+ align:start position:0%
+right as I mentioned your job depends on
+getting that hardness coefficient right
+
+ align:start position:0%
+getting that hardness coefficient right
+ 
+
+ align:start position:0%
+getting that hardness coefficient right
+so you can only use that first algorithm
+
+ align:start position:0%
+so you can only use that first algorithm
+ 
+
+ align:start position:0%
+so you can only use that first algorithm
+in terms of starting from 1 and going
+
+ align:start position:0%
+in terms of starting from 1 and going
+ 
+
+ align:start position:0%
+in terms of starting from 1 and going
+all the way to 63 and so what is the
+
+ align:start position:0%
+all the way to 63 and so what is the
+ 
+
+ align:start position:0%
+all the way to 63 and so what is the
+worst case number of drops given that
+
+ align:start position:0%
+worst case number of drops given that
+ 
+
+ align:start position:0%
+worst case number of drops given that
+diamond picked the midpoint for this
+
+ align:start position:0%
+diamond picked the midpoint for this
+ 
+
+ align:start position:0%
+diamond picked the midpoint for this
+algorithm someone else yeah go ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's succeed 63
+
+ align:start position:0%
+it's succeed 63
+ 
+
+ align:start position:0%
+it's succeed 63
+no actually it's you're off by one
+
+ align:start position:0%
+no actually it's you're off by one
+ 
+
+ align:start position:0%
+no actually it's you're off by one
+because I did drop the ball here right
+
+ align:start position:0%
+because I did drop the ball here right
+ 
+
+ align:start position:0%
+because I did drop the ball here right
+so so close so I first ball I was
+
+ align:start position:0%
+so so close so I first ball I was
+ 
+
+ align:start position:0%
+so so close so I first ball I was
+dropped once one drop and at this one if
+
+ align:start position:0%
+dropped once one drop and at this one if
+ 
+
+ align:start position:0%
+dropped once one drop and at this one if
+in fact you at the hardness coefficient
+
+ align:start position:0%
+in fact you at the hardness coefficient
+ 
+
+ align:start position:0%
+in fact you at the hardness coefficient
+was 64 you drop the second ball 62 63
+
+ align:start position:0%
+was 64 you drop the second ball 62 63
+ 
+
+ align:start position:0%
+was 64 you drop the second ball 62 63
+times and that would be the worst case
+
+ align:start position:0%
+times and that would be the worst case
+ 
+
+ align:start position:0%
+times and that would be the worst case
+in the in this instance now I've skipped
+
+ align:start position:0%
+in the in this instance now I've skipped
+ 
+
+ align:start position:0%
+in the in this instance now I've skipped
+over one little thing at the fact that
+
+ align:start position:0%
+over one little thing at the fact that
+ 
+
+ align:start position:0%
+over one little thing at the fact that
+this is the midpoint implies that this
+
+ align:start position:0%
+this is the midpoint implies that this
+ 
+
+ align:start position:0%
+this is the midpoint implies that this
+is in fact the correct answer but we do
+
+ align:start position:0%
+is in fact the correct answer but we do
+ 
+
+ align:start position:0%
+is in fact the correct answer but we do
+have to analyze I mean remember you know
+
+ align:start position:0%
+have to analyze I mean remember you know
+ 
+
+ align:start position:0%
+have to analyze I mean remember you know
+when you do analysis you do have to
+
+ align:start position:0%
+when you do analysis you do have to
+ 
+
+ align:start position:0%
+when you do analysis you do have to
+cover the entire spectrum here so you do
+
+ align:start position:0%
+cover the entire spectrum here so you do
+ 
+
+ align:start position:0%
+cover the entire spectrum here so you do
+have to Kate it look at the case where
+
+ align:start position:0%
+have to Kate it look at the case where
+ 
+
+ align:start position:0%
+have to Kate it look at the case where
+the drop from 64 it does not break okay
+
+ align:start position:0%
+the drop from 64 it does not break okay
+ 
+
+ align:start position:0%
+the drop from 64 it does not break okay
+and in that case you're looking at
+
+ align:start position:0%
+and in that case you're looking at
+ 
+
+ align:start position:0%
+and in that case you're looking at
+looking at 65 through 128 but you do
+
+ align:start position:0%
+looking at 65 through 128 but you do
+ 
+
+ align:start position:0%
+looking at 65 through 128 but you do
+have two balls for this right it didn't
+
+ align:start position:0%
+have two balls for this right it didn't
+ 
+
+ align:start position:0%
+have two balls for this right it didn't
+break so you still have two balls for
+
+ align:start position:0%
+break so you still have two balls for
+ 
+
+ align:start position:0%
+break so you still have two balls for
+that right and so you can imagine that
+
+ align:start position:0%
+that right and so you can imagine that
+ 
+
+ align:start position:0%
+that right and so you can imagine that
+now that you have two balls and you have
+
+ align:start position:0%
+now that you have two balls and you have
+ 
+
+ align:start position:0%
+now that you have two balls and you have
+a small interval that you're going to be
+
+ align:start position:0%
+a small interval that you're going to be
+ 
+
+ align:start position:0%
+a small interval that you're going to be
+able to do something like 32 for that
+
+ align:start position:0%
+able to do something like 32 for that
+ 
+
+ align:start position:0%
+able to do something like 32 for that
+the bottom line is you don't even need
+
+ align:start position:0%
+the bottom line is you don't even need
+ 
+
+ align:start position:0%
+the bottom line is you don't even need
+you can get a little bit lazy here you
+
+ align:start position:0%
+you can get a little bit lazy here you
+ 
+
+ align:start position:0%
+you can get a little bit lazy here you
+don't really need to analyze what the
+
+ align:start position:0%
+don't really need to analyze what the
+ 
+
+ align:start position:0%
+don't really need to analyze what the
+number is because you know that this
+
+ align:start position:0%
+number is because you know that this
+ 
+
+ align:start position:0%
+number is because you know that this
+number 63 plus 1is is larger than that
+
+ align:start position:0%
+number 63 plus 1is is larger than that
+ 
+
+ align:start position:0%
+number 63 plus 1is is larger than that
+right because you want it worst case
+
+ align:start position:0%
+right because you want it worst case
+ 
+
+ align:start position:0%
+right because you want it worst case
+right so this is the kind of thing that
+
+ align:start position:0%
+right so this is the kind of thing that
+ 
+
+ align:start position:0%
+right so this is the kind of thing that
+you have to do when you do algorithmic
+
+ align:start position:0%
+you have to do when you do algorithmic
+ 
+
+ align:start position:0%
+you have to do when you do algorithmic
+analysis maybe not exactly if I in in a
+
+ align:start position:0%
+analysis maybe not exactly if I in in a
+ 
+
+ align:start position:0%
+analysis maybe not exactly if I in in a
+puzzle situation like this but you have
+
+ align:start position:0%
+puzzle situation like this but you have
+ 
+
+ align:start position:0%
+puzzle situation like this but you have
+to look at all the cases right then you
+
+ align:start position:0%
+to look at all the cases right then you
+ 
+
+ align:start position:0%
+to look at all the cases right then you
+have to find kind of the max of all the
+
+ align:start position:0%
+have to find kind of the max of all the
+ 
+
+ align:start position:0%
+have to find kind of the max of all the
+cases right so is this the best you can
+
+ align:start position:0%
+cases right so is this the best you can
+ 
+
+ align:start position:0%
+cases right so is this the best you can
+do yeah go ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every 16
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+30 seconds you have to only test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's correct yeah I mean this is
+
+ align:start position:0%
+that's correct yeah I mean this is
+ 
+
+ align:start position:0%
+that's correct yeah I mean this is
+obviously there's not gonna be a whole
+
+ align:start position:0%
+obviously there's not gonna be a whole
+ 
+
+ align:start position:0%
+obviously there's not gonna be a whole
+lot of optimization here but V equals
+
+ align:start position:0%
+lot of optimization here but V equals
+ 
+
+ align:start position:0%
+lot of optimization here but V equals
+two but you'd be surprised as to how
+
+ align:start position:0%
+two but you'd be surprised as to how
+ 
+
+ align:start position:0%
+two but you'd be surprised as to how
+much better you can do then 64 which is
+
+ align:start position:0%
+much better you can do then 64 which is
+ 
+
+ align:start position:0%
+much better you can do then 64 which is
+obviously a big step forward from 128
+
+ align:start position:0%
+obviously a big step forward from 128
+ 
+
+ align:start position:0%
+obviously a big step forward from 128
+but you can you can go a few more steps
+
+ align:start position:0%
+but you can you can go a few more steps
+ 
+
+ align:start position:0%
+but you can you can go a few more steps
+as well and so what was your name Lucy
+
+ align:start position:0%
+as well and so what was your name Lucy
+ 
+
+ align:start position:0%
+as well and so what was your name Lucy
+so Lucy has it right you it's it's a
+
+ align:start position:0%
+so Lucy has it right you it's it's a
+ 
+
+ align:start position:0%
+so Lucy has it right you it's it's a
+similar idea except you don't
+
+ align:start position:0%
+similar idea except you don't
+ 
+
+ align:start position:0%
+similar idea except you don't
+necessarily need to do the intuitive
+
+ align:start position:0%
+necessarily need to do the intuitive
+ 
+
+ align:start position:0%
+necessarily need to do the intuitive
+binary search it's actually kind of
+
+ align:start position:0%
+binary search it's actually kind of
+ 
+
+ align:start position:0%
+binary search it's actually kind of
+different from that because of the way
+
+ align:start position:0%
+different from that because of the way
+ 
+
+ align:start position:0%
+different from that because of the way
+this problem is structured and what her
+
+ align:start position:0%
+this problem is structured and what her
+ 
+
+ align:start position:0%
+this problem is structured and what her
+idea is is that we'll we look at
+
+ align:start position:0%
+idea is is that we'll we look at
+ 
+
+ align:start position:0%
+idea is is that we'll we look at
+something smaller a smaller interval
+
+ align:start position:0%
+something smaller a smaller interval
+ 
+
+ align:start position:0%
+something smaller a smaller interval
+okay and that she picks 16 so let's go
+
+ align:start position:0%
+okay and that she picks 16 so let's go
+ 
+
+ align:start position:0%
+okay and that she picks 16 so let's go
+1632 sour algorithm is something that
+
+ align:start position:0%
+1632 sour algorithm is something that
+ 
+
+ align:start position:0%
+1632 sour algorithm is something that
+goes 16 32 48 64 that a dot and you know
+
+ align:start position:0%
+goes 16 32 48 64 that a dot and you know
+ 
+
+ align:start position:0%
+goes 16 32 48 64 that a dot and you know
+maybe gets up all the way to I guess six
+
+ align:start position:0%
+maybe gets up all the way to I guess six
+ 
+
+ align:start position:0%
+maybe gets up all the way to I guess six
+yeah 128 and 16 16 is a it's 128 is a
+
+ align:start position:0%
+yeah 128 and 16 16 is a it's 128 is a
+ 
+
+ align:start position:0%
+yeah 128 and 16 16 is a it's 128 is a
+multiple of 16 right some some math
+
+ align:start position:0%
+multiple of 16 right some some math
+ 
+
+ align:start position:0%
+multiple of 16 right some some math
+person tell make sure I'm right so so
+
+ align:start position:0%
+person tell make sure I'm right so so
+ 
+
+ align:start position:0%
+person tell make sure I'm right so so
+you have so what happens here so let's
+
+ align:start position:0%
+you have so what happens here so let's
+ 
+
+ align:start position:0%
+you have so what happens here so let's
+analyze this and to make sure that we're
+
+ align:start position:0%
+analyze this and to make sure that we're
+ 
+
+ align:start position:0%
+analyze this and to make sure that we're
+good in terms of an improvement right we
+
+ align:start position:0%
+good in terms of an improvement right we
+ 
+
+ align:start position:0%
+good in terms of an improvement right we
+have to be careful so let's just
+
+ align:start position:0%
+have to be careful so let's just
+ 
+
+ align:start position:0%
+have to be careful so let's just
+arbitrarily say that it broke it's 64
+
+ align:start position:0%
+arbitrarily say that it broke it's 64
+ 
+
+ align:start position:0%
+arbitrarily say that it broke it's 64
+okay because that's kind of what
+
+ align:start position:0%
+okay because that's kind of what
+ 
+
+ align:start position:0%
+okay because that's kind of what
+happened over in that previous algorithm
+
+ align:start position:0%
+happened over in that previous algorithm
+ 
+
+ align:start position:0%
+happened over in that previous algorithm
+to so that means I've done four drops
+
+ align:start position:0%
+to so that means I've done four drops
+ 
+
+ align:start position:0%
+to so that means I've done four drops
+without a break right I'm sorry four
+
+ align:start position:0%
+without a break right I'm sorry four
+ 
+
+ align:start position:0%
+without a break right I'm sorry four
+drops three drops without a break and
+
+ align:start position:0%
+drops three drops without a break and
+ 
+
+ align:start position:0%
+drops three drops without a break and
+four drops total right um so I've done
+
+ align:start position:0%
+four drops total right um so I've done
+ 
+
+ align:start position:0%
+four drops total right um so I've done
+four drops but now the cool thing is I
+
+ align:start position:0%
+four drops but now the cool thing is I
+ 
+
+ align:start position:0%
+four drops but now the cool thing is I
+don't have to start from 16 I can Stein
+
+ align:start position:0%
+don't have to start from 16 I can Stein
+ 
+
+ align:start position:0%
+don't have to start from 16 I can Stein
+oh it didn't break at 48 right so so I
+
+ align:start position:0%
+oh it didn't break at 48 right so so I
+ 
+
+ align:start position:0%
+oh it didn't break at 48 right so so I
+can I can now look at 4 drop still break
+
+ align:start position:0%
+can I can now look at 4 drop still break
+ 
+
+ align:start position:0%
+can I can now look at 4 drop still break
+a first-ball
+
+ align:start position:0%
+a first-ball
+ 
+
+ align:start position:0%
+a first-ball
+that is what I wanted to say and now I
+
+ align:start position:0%
+that is what I wanted to say and now I
+ 
+
+ align:start position:0%
+that is what I wanted to say and now I
+need I can look at the interval 48 49
+
+ align:start position:0%
+need I can look at the interval 48 49
+ 
+
+ align:start position:0%
+need I can look at the interval 48 49
+because 48 it did not break right 49 to
+
+ align:start position:0%
+because 48 it did not break right 49 to
+ 
+
+ align:start position:0%
+because 48 it did not break right 49 to
+63 inclusive right and so if you do that
+
+ align:start position:0%
+63 inclusive right and so if you do that
+ 
+
+ align:start position:0%
+63 inclusive right and so if you do that
+that's 15 it's 15
+
+ align:start position:0%
+that's 15 it's 15
+ 
+
+ align:start position:0%
+that's 15 it's 15
+the difference is 14 but it's inclusive
+
+ align:start position:0%
+the difference is 14 but it's inclusive
+ 
+
+ align:start position:0%
+the difference is 14 but it's inclusive
+so it's 15 so 15 plus 4 right there is
+
+ align:start position:0%
+so it's 15 so 15 plus 4 right there is
+ 
+
+ align:start position:0%
+so it's 15 so 15 plus 4 right there is
+19 drops all right
+
+ align:start position:0%
+19 drops all right
+ 
+
+ align:start position:0%
+19 drops all right
+yeah yes that's absolutely correct so so
+
+ align:start position:0%
+yeah yes that's absolutely correct so so
+ 
+
+ align:start position:0%
+yeah yes that's absolutely correct so so
+19 is not the worst case I mean it is
+
+ align:start position:0%
+19 is not the worst case I mean it is
+ 
+
+ align:start position:0%
+19 is not the worst case I mean it is
+looking good but this was exactly the
+
+ align:start position:0%
+looking good but this was exactly the
+ 
+
+ align:start position:0%
+looking good but this was exactly the
+point I was trying to make right from
+
+ align:start position:0%
+point I was trying to make right from
+ 
+
+ align:start position:0%
+point I was trying to make right from
+the beginning you're not done yet I mean
+
+ align:start position:0%
+the beginning you're not done yet I mean
+ 
+
+ align:start position:0%
+the beginning you're not done yet I mean
+you cannot just go off and say that 19
+
+ align:start position:0%
+you cannot just go off and say that 19
+ 
+
+ align:start position:0%
+you cannot just go off and say that 19
+is the worst case for this algorithm the
+
+ align:start position:0%
+is the worst case for this algorithm the
+ 
+
+ align:start position:0%
+is the worst case for this algorithm the
+worst case for this out this particular
+
+ align:start position:0%
+worst case for this out this particular
+ 
+
+ align:start position:0%
+worst case for this out this particular
+algorithm occurs at a different point
+
+ align:start position:0%
+algorithm occurs at a different point
+ 
+
+ align:start position:0%
+algorithm occurs at a different point
+from the original algorithm that went
+
+ align:start position:0%
+from the original algorithm that went
+ 
+
+ align:start position:0%
+from the original algorithm that went
+Midway right every algorithm is
+
+ align:start position:0%
+Midway right every algorithm is
+ 
+
+ align:start position:0%
+Midway right every algorithm is
+different the parameters are are
+
+ align:start position:0%
+different the parameters are are
+ 
+
+ align:start position:0%
+different the parameters are are
+different here and so I'm just calling
+
+ align:start position:0%
+different here and so I'm just calling
+ 
+
+ align:start position:0%
+different here and so I'm just calling
+it a different algorithm but the the
+
+ align:start position:0%
+it a different algorithm but the the
+ 
+
+ align:start position:0%
+it a different algorithm but the the
+case that would happen is I guess you'd
+
+ align:start position:0%
+case that would happen is I guess you'd
+ 
+
+ align:start position:0%
+case that would happen is I guess you'd
+have 112 here and then you'd go 1 2 so
+
+ align:start position:0%
+have 112 here and then you'd go 1 2 so
+ 
+
+ align:start position:0%
+have 112 here and then you'd go 1 2 so
+how many so let's say it gets to 128 and
+
+ align:start position:0%
+how many so let's say it gets to 128 and
+ 
+
+ align:start position:0%
+how many so let's say it gets to 128 and
+if it doesn't break then you're clearly
+
+ align:start position:0%
+if it doesn't break then you're clearly
+ 
+
+ align:start position:0%
+if it doesn't break then you're clearly
+done so that's not the worst case right
+
+ align:start position:0%
+done so that's not the worst case right
+ 
+
+ align:start position:0%
+done so that's not the worst case right
+so if it gets to 128 and it and it
+
+ align:start position:0%
+so if it gets to 128 and it and it
+ 
+
+ align:start position:0%
+so if it gets to 128 and it and it
+breaks then so how many drops have we
+
+ align:start position:0%
+breaks then so how many drops have we
+ 
+
+ align:start position:0%
+breaks then so how many drops have we
+done 128 divided by 16 is what is 8 are
+
+ align:start position:0%
+done 128 divided by 16 is what is 8 are
+ 
+
+ align:start position:0%
+done 128 divided by 16 is what is 8 are
+you sure you're all sure ok then I'm
+
+ align:start position:0%
+you sure you're all sure ok then I'm
+ 
+
+ align:start position:0%
+you sure you're all sure ok then I'm
+sure so that's 8 drops and now you need
+
+ align:start position:0%
+sure so that's 8 drops and now you need
+ 
+
+ align:start position:0%
+sure so that's 8 drops and now you need
+to do 113 to 127 and that we know is 15
+
+ align:start position:0%
+to do 113 to 127 and that we know is 15
+ 
+
+ align:start position:0%
+to do 113 to 127 and that we know is 15
+so that's 23 all right so so the best
+
+ align:start position:0%
+so that's 23 all right so so the best
+ 
+
+ align:start position:0%
+so that's 23 all right so so the best
+you've done here is it's 23 right but
+
+ align:start position:0%
+you've done here is it's 23 right but
+ 
+
+ align:start position:0%
+you've done here is it's 23 right but
+I'll be satisfied we're never satisfied
+
+ align:start position:0%
+I'll be satisfied we're never satisfied
+ 
+
+ align:start position:0%
+I'll be satisfied we're never satisfied
+right you always want to do a little bit
+
+ align:start position:0%
+right you always want to do a little bit
+ 
+
+ align:start position:0%
+right you always want to do a little bit
+better okay so so how did she pick 16
+
+ align:start position:0%
+better okay so so how did she pick 16
+ 
+
+ align:start position:0%
+better okay so so how did she pick 16
+why did you come up with 16 losing it
+
+ align:start position:0%
+why did you come up with 16 losing it
+ 
+
+ align:start position:0%
+why did you come up with 16 losing it
+looked like a nice number
+
+ align:start position:0%
+looked like a nice number
+ 
+
+ align:start position:0%
+looked like a nice number
+you just figured oh nice okay so so so
+
+ align:start position:0%
+you just figured oh nice okay so so so
+ 
+
+ align:start position:0%
+you just figured oh nice okay so so so
+if you had 17 then we would have real
+
+ align:start position:0%
+if you had 17 then we would have real
+ 
+
+ align:start position:0%
+if you had 17 then we would have real
+trouble right with all these numbers
+
+ align:start position:0%
+trouble right with all these numbers
+ 
+
+ align:start position:0%
+trouble right with all these numbers
+yeah go ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beautiful beautiful I love you guys
+
+ align:start position:0%
+beautiful beautiful I love you guys
+ 
+
+ align:start position:0%
+beautiful beautiful I love you guys
+you guys make it so easy so that's the
+
+ align:start position:0%
+you guys make it so easy so that's the
+ 
+
+ align:start position:0%
+you guys make it so easy so that's the
+next thing I was going to try and pry
+
+ align:start position:0%
+next thing I was going to try and pry
+ 
+
+ align:start position:0%
+next thing I was going to try and pry
+out of you but you got it out without
+
+ align:start position:0%
+out of you but you got it out without
+ 
+
+ align:start position:0%
+out of you but you got it out without
+much effort from me so you can you can
+
+ align:start position:0%
+much effort from me so you can you can
+ 
+
+ align:start position:0%
+much effort from me so you can you can
+kind of get analytical here as opposed
+
+ align:start position:0%
+kind of get analytical here as opposed
+ 
+
+ align:start position:0%
+kind of get analytical here as opposed
+to doing things and particularly which
+
+ align:start position:0%
+to doing things and particularly which
+ 
+
+ align:start position:0%
+to doing things and particularly which
+was you know try a number and figure out
+
+ align:start position:0%
+was you know try a number and figure out
+ 
+
+ align:start position:0%
+was you know try a number and figure out
+what happened which is kind of what we
+
+ align:start position:0%
+what happened which is kind of what we
+ 
+
+ align:start position:0%
+what happened which is kind of what we
+did and you can be a little more
+
+ align:start position:0%
+did and you can be a little more
+ 
+
+ align:start position:0%
+did and you can be a little more
+analytical about this and you could say
+
+ align:start position:0%
+analytical about this and you could say
+ 
+
+ align:start position:0%
+analytical about this and you could say
+hey I'm suppose I want to find this
+
+ align:start position:0%
+hey I'm suppose I want to find this
+ 
+
+ align:start position:0%
+hey I'm suppose I want to find this
+number K which is kind of the 64 started
+
+ align:start position:0%
+number K which is kind of the 64 started
+ 
+
+ align:start position:0%
+number K which is kind of the 64 started
+with 64 went to 16 and now we're
+
+ align:start position:0%
+with 64 went to 16 and now we're
+ 
+
+ align:start position:0%
+with 64 went to 16 and now we're
+thinking we can do better than 16 even
+
+ align:start position:0%
+thinking we can do better than 16 even
+ 
+
+ align:start position:0%
+thinking we can do better than 16 even
+and we start dropping things at K 2 K 3
+
+ align:start position:0%
+and we start dropping things at K 2 K 3
+ 
+
+ align:start position:0%
+and we start dropping things at K 2 K 3
+K and I want to get this exactly right
+
+ align:start position:0%
+K and I want to get this exactly right
+ 
+
+ align:start position:0%
+K and I want to get this exactly right
+so let me look at my notes and you go
+
+ align:start position:0%
+so let me look at my notes and you go
+ 
+
+ align:start position:0%
+so let me look at my notes and you go
+dot a dot n divided by K minus 1 times K
+
+ align:start position:0%
+dot a dot n divided by K minus 1 times K
+ 
+
+ align:start position:0%
+dot a dot n divided by K minus 1 times K
+and n divided by K times K which is
+
+ align:start position:0%
+and n divided by K times K which is
+ 
+
+ align:start position:0%
+and n divided by K times K which is
+obviously M and so I I'm trying to I'm
+
+ align:start position:0%
+obviously M and so I I'm trying to I'm
+ 
+
+ align:start position:0%
+obviously M and so I I'm trying to I'm
+trying to write it and I'm trying to get
+
+ align:start position:0%
+trying to write it and I'm trying to get
+ 
+
+ align:start position:0%
+trying to write it and I'm trying to get
+this K I want to write something I want
+
+ align:start position:0%
+this K I want to write something I want
+ 
+
+ align:start position:0%
+this K I want to write something I want
+to minimize some quantity and discover
+
+ align:start position:0%
+to minimize some quantity and discover
+ 
+
+ align:start position:0%
+to minimize some quantity and discover
+the K that is going to give me my best
+
+ align:start position:0%
+the K that is going to give me my best
+ 
+
+ align:start position:0%
+the K that is going to give me my best
+case in the worst case okay minimize the
+
+ align:start position:0%
+case in the worst case okay minimize the
+ 
+
+ align:start position:0%
+case in the worst case okay minimize the
+worst case right so that's that's really
+
+ align:start position:0%
+worst case right so that's that's really
+ 
+
+ align:start position:0%
+worst case right so that's that's really
+what I want so so if you look at what
+
+ align:start position:0%
+what I want so so if you look at what
+ 
+
+ align:start position:0%
+what I want so so if you look at what
+what happens here you're you're in a
+
+ align:start position:0%
+what happens here you're you're in a
+ 
+
+ align:start position:0%
+what happens here you're you're in a
+situation where you have to now you have
+
+ align:start position:0%
+situation where you have to now you have
+ 
+
+ align:start position:0%
+situation where you have to now you have
+to count right I mean what do you want
+
+ align:start position:0%
+to count right I mean what do you want
+ 
+
+ align:start position:0%
+to count right I mean what do you want
+to I decided that that K is this general
+
+ align:start position:0%
+to I decided that that K is this general
+ 
+
+ align:start position:0%
+to I decided that that K is this general
+strategy and we don't quite know what K
+
+ align:start position:0%
+strategy and we don't quite know what K
+ 
+
+ align:start position:0%
+strategy and we don't quite know what K
+is and we have to do some analysis of
+
+ align:start position:0%
+is and we have to do some analysis of
+ 
+
+ align:start position:0%
+is and we have to do some analysis of
+the worst-case situation in order to
+
+ align:start position:0%
+the worst-case situation in order to
+ 
+
+ align:start position:0%
+the worst-case situation in order to
+find the K that would work well for us
+
+ align:start position:0%
+find the K that would work well for us
+ 
+
+ align:start position:0%
+find the K that would work well for us
+and so the way you do this is by
+
+ align:start position:0%
+and so the way you do this is by
+ 
+
+ align:start position:0%
+and so the way you do this is by
+essentially the analysis we've done so
+
+ align:start position:0%
+essentially the analysis we've done so
+ 
+
+ align:start position:0%
+essentially the analysis we've done so
+far and
+
+ align:start position:0%
+far and
+ 
+
+ align:start position:0%
+far and
+kind of we have a nice the the the point
+
+ align:start position:0%
+kind of we have a nice the the the point
+ 
+
+ align:start position:0%
+kind of we have a nice the the the point
+that was made here I think was it was
+
+ align:start position:0%
+that was made here I think was it was
+ 
+
+ align:start position:0%
+that was made here I think was it was
+Kevin who said we have to go to the last
+
+ align:start position:0%
+Kevin who said we have to go to the last
+ 
+
+ align:start position:0%
+Kevin who said we have to go to the last
+drop because that's kind of the the case
+
+ align:start position:0%
+drop because that's kind of the the case
+ 
+
+ align:start position:0%
+drop because that's kind of the the case
+where I it's the worst case and that's
+
+ align:start position:0%
+where I it's the worst case and that's
+ 
+
+ align:start position:0%
+where I it's the worst case and that's
+similar here as well because if you go
+
+ align:start position:0%
+similar here as well because if you go
+ 
+
+ align:start position:0%
+similar here as well because if you go
+up all the way here and then it breaks
+
+ align:start position:0%
+up all the way here and then it breaks
+ 
+
+ align:start position:0%
+up all the way here and then it breaks
+if it doesn't break here you're done
+
+ align:start position:0%
+if it doesn't break here you're done
+ 
+
+ align:start position:0%
+if it doesn't break here you're done
+if it breaks here then you've got you've
+
+ align:start position:0%
+if it breaks here then you've got you've
+ 
+
+ align:start position:0%
+if it breaks here then you've got you've
+done a lot of drops before it broke that
+
+ align:start position:0%
+done a lot of drops before it broke that
+ 
+
+ align:start position:0%
+done a lot of drops before it broke that
+first ball and so that's at the
+
+ align:start position:0%
+first ball and so that's at the
+ 
+
+ align:start position:0%
+first ball and so that's at the
+situation which you can pull them as
+
+ align:start position:0%
+situation which you can pull them as
+ 
+
+ align:start position:0%
+situation which you can pull them as
+your worst case situation right so
+
+ align:start position:0%
+your worst case situation right so
+ 
+
+ align:start position:0%
+your worst case situation right so
+that's exactly what we did before and so
+
+ align:start position:0%
+that's exactly what we did before and so
+ 
+
+ align:start position:0%
+that's exactly what we did before and so
+so if you really think about it the
+
+ align:start position:0%
+so if you really think about it the
+ 
+
+ align:start position:0%
+so if you really think about it the
+assumed first ball doesn't break till
+
+ align:start position:0%
+assumed first ball doesn't break till
+ 
+
+ align:start position:0%
+assumed first ball doesn't break till
+the last draw is the is the worst-case
+
+ align:start position:0%
+the last draw is the is the worst-case
+ 
+
+ align:start position:0%
+the last draw is the is the worst-case
+situation right and so what does that
+
+ align:start position:0%
+situation right and so what does that
+ 
+
+ align:start position:0%
+situation right and so what does that
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+from a symbolic standpoint with respect
+
+ align:start position:0%
+from a symbolic standpoint with respect
+ 
+
+ align:start position:0%
+from a symbolic standpoint with respect
+to the number of drops of so so the
+
+ align:start position:0%
+to the number of drops of so so the
+ 
+
+ align:start position:0%
+to the number of drops of so so the
+number of drops in this case of the
+
+ align:start position:0%
+number of drops in this case of the
+ 
+
+ align:start position:0%
+number of drops in this case of the
+first ball can someone give me an
+
+ align:start position:0%
+first ball can someone give me an
+ 
+
+ align:start position:0%
+first ball can someone give me an
+equation for it yeah okay you're Kevin -
+
+ align:start position:0%
+equation for it yeah okay you're Kevin -
+ 
+
+ align:start position:0%
+equation for it yeah okay you're Kevin -
+yeah okay so so n over K right so so
+
+ align:start position:0%
+yeah okay so so n over K right so so
+ 
+
+ align:start position:0%
+yeah okay so so n over K right so so
+that's the that's what happened there
+
+ align:start position:0%
+that's the that's what happened there
+ 
+
+ align:start position:0%
+that's the that's what happened there
+now well it broke right that's what we
+
+ align:start position:0%
+now well it broke right that's what we
+ 
+
+ align:start position:0%
+now well it broke right that's what we
+decided here and so now you need to
+
+ align:start position:0%
+decided here and so now you need to
+ 
+
+ align:start position:0%
+decided here and so now you need to
+search and K plus 1 right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+- I bet you got to go all the way there
+
+ align:start position:0%
+- I bet you got to go all the way there
+ 
+
+ align:start position:0%
+- I bet you got to go all the way there
+I'm sorry it broke there so you got to
+
+ align:start position:0%
+I'm sorry it broke there so you got to
+ 
+
+ align:start position:0%
+I'm sorry it broke there so you got to
+go n minus 1 is the same as what I wrote
+
+ align:start position:0%
+go n minus 1 is the same as what I wrote
+ 
+
+ align:start position:0%
+go n minus 1 is the same as what I wrote
+before in but it's just that I had
+
+ align:start position:0%
+before in but it's just that I had
+ 
+
+ align:start position:0%
+before in but it's just that I had
+numbers and it was kind of easier to
+
+ align:start position:0%
+numbers and it was kind of easier to
+ 
+
+ align:start position:0%
+numbers and it was kind of easier to
+write numbers then write these symbols
+
+ align:start position:0%
+write numbers then write these symbols
+ 
+
+ align:start position:0%
+write numbers then write these symbols
+but we have to do this because we don't
+
+ align:start position:0%
+but we have to do this because we don't
+ 
+
+ align:start position:0%
+but we have to do this because we don't
+know what K is okay so the if you look
+
+ align:start position:0%
+know what K is okay so the if you look
+ 
+
+ align:start position:0%
+know what K is okay so the if you look
+at the how many
+
+ align:start position:0%
+at the how many
+ 
+
+ align:start position:0%
+at the how many
+drops are and if you guys can do this
+
+ align:start position:0%
+drops are and if you guys can do this
+ 
+
+ align:start position:0%
+drops are and if you guys can do this
+you get a if you notice this gets
+
+ align:start position:0%
+you get a if you notice this gets
+ 
+
+ align:start position:0%
+you get a if you notice this gets
+simplified to and yeah so this is n then
+
+ align:start position:0%
+simplified to and yeah so this is n then
+ 
+
+ align:start position:0%
+simplified to and yeah so this is n then
+you have minus k plus 1 all the way to n
+
+ align:start position:0%
+you have minus k plus 1 all the way to n
+ 
+
+ align:start position:0%
+you have minus k plus 1 all the way to n
+minus 1 right so if you subtract and
+
+ align:start position:0%
+minus 1 right so if you subtract and
+ 
+
+ align:start position:0%
+minus 1 right so if you subtract and
+this is a plus 1 here boy
+
+ align:start position:0%
+this is a plus 1 here boy
+ 
+
+ align:start position:0%
+this is a plus 1 here boy
+this is confusing I'm not good at math
+
+ align:start position:0%
+this is confusing I'm not good at math
+ 
+
+ align:start position:0%
+this is confusing I'm not good at math
+I'm definitely not good at math so this
+
+ align:start position:0%
+I'm definitely not good at math so this
+ 
+
+ align:start position:0%
+I'm definitely not good at math so this
+is K minus 1 drops in the worst case
+
+ align:start position:0%
+is K minus 1 drops in the worst case
+ 
+
+ align:start position:0%
+is K minus 1 drops in the worst case
+alright so you now need to add these two
+
+ align:start position:0%
+alright so you now need to add these two
+ 
+
+ align:start position:0%
+alright so you now need to add these two
+things together so what we'd like to do
+
+ align:start position:0%
+things together so what we'd like to do
+ 
+
+ align:start position:0%
+things together so what we'd like to do
+is minimize and my n divided by K which
+
+ align:start position:0%
+is minimize and my n divided by K which
+ 
+
+ align:start position:0%
+is minimize and my n divided by K which
+is this Plus that right we want to
+
+ align:start position:0%
+is this Plus that right we want to
+ 
+
+ align:start position:0%
+is this Plus that right we want to
+minimize this function right n its
+
+ align:start position:0%
+minimize this function right n its
+ 
+
+ align:start position:0%
+minimize this function right n its
+constant K is a variable right and we
+
+ align:start position:0%
+constant K is a variable right and we
+ 
+
+ align:start position:0%
+constant K is a variable right and we
+know for a given n we want to discover
+
+ align:start position:0%
+know for a given n we want to discover
+ 
+
+ align:start position:0%
+know for a given n we want to discover
+the K that minimizes this quantity and
+
+ align:start position:0%
+the K that minimizes this quantity and
+ 
+
+ align:start position:0%
+the K that minimizes this quantity and
+it goes back to the intuition that that
+
+ align:start position:0%
+it goes back to the intuition that that
+ 
+
+ align:start position:0%
+it goes back to the intuition that that
+I think Josh had about the square root
+
+ align:start position:0%
+I think Josh had about the square root
+ 
+
+ align:start position:0%
+I think Josh had about the square root
+of n right
+
+ align:start position:0%
+of n right
+ 
+
+ align:start position:0%
+of n right
+so again high school calculus here which
+
+ align:start position:0%
+so again high school calculus here which
+ 
+
+ align:start position:0%
+so again high school calculus here which
+I've forgotten is hopefully you haven't
+
+ align:start position:0%
+I've forgotten is hopefully you haven't
+ 
+
+ align:start position:0%
+I've forgotten is hopefully you haven't
+because you still need it I don't and
+
+ align:start position:0%
+because you still need it I don't and
+ 
+
+ align:start position:0%
+because you still need it I don't and
+you end up essentially saying you can
+
+ align:start position:0%
+you end up essentially saying you can
+ 
+
+ align:start position:0%
+you end up essentially saying you can
+turn this into 2 raised to square root
+
+ align:start position:0%
+turn this into 2 raised to square root
+ 
+
+ align:start position:0%
+turn this into 2 raised to square root
+of n minus 1 drops in the worst case all
+
+ align:start position:0%
+of n minus 1 drops in the worst case all
+ 
+
+ align:start position:0%
+of n minus 1 drops in the worst case all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so 4 so you can take that the floor of
+
+ align:start position:0%
+so 4 so you can take that the floor of
+ 
+
+ align:start position:0%
+so 4 so you can take that the floor of
+that and that's that's 11 okay so so
+
+ align:start position:0%
+that and that's that's 11 okay so so
+ 
+
+ align:start position:0%
+that and that's that's 11 okay so so
+that's the square root of n so 2 times
+
+ align:start position:0%
+that's the square root of n so 2 times
+ 
+
+ align:start position:0%
+that's the square root of n so 2 times
+11 minus 1 is 21 so you can do 21
+
+ align:start position:0%
+11 minus 1 is 21 so you can do 21
+ 
+
+ align:start position:0%
+11 minus 1 is 21 so you can do 21
+so you think 21 is the optimum yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes you can you can do a little bit
+
+ align:start position:0%
+yes yes you can you can do a little bit
+ 
+
+ align:start position:0%
+yes yes you can you can do a little bit
+better I don't want to do this yes yet
+
+ align:start position:0%
+better I don't want to do this yes yet
+ 
+
+ align:start position:0%
+better I don't want to do this yes yet
+hopefully we'll have time we'll get to
+
+ align:start position:0%
+hopefully we'll have time we'll get to
+ 
+
+ align:start position:0%
+hopefully we'll have time we'll get to
+that because I want to go to the the D
+
+ align:start position:0%
+that because I want to go to the the D
+ 
+
+ align:start position:0%
+that because I want to go to the the D
+greater than two case but you're
+
+ align:start position:0%
+greater than two case but you're
+ 
+
+ align:start position:0%
+greater than two case but you're
+absolutely right it turns out you can do
+
+ align:start position:0%
+absolutely right it turns out you can do
+ 
+
+ align:start position:0%
+absolutely right it turns out you can do
+this would this would give you 21 as I
+
+ align:start position:0%
+this would this would give you 21 as I
+ 
+
+ align:start position:0%
+this would this would give you 21 as I
+mentioned at 22 minus one I tell thought
+
+ align:start position:0%
+mentioned at 22 minus one I tell thought
+ 
+
+ align:start position:0%
+mentioned at 22 minus one I tell thought
+you can do better by a few drops and the
+
+ align:start position:0%
+you can do better by a few drops and the
+ 
+
+ align:start position:0%
+you can do better by a few drops and the
+assumption we made here
+
+ align:start position:0%
+assumption we made here
+ 
+
+ align:start position:0%
+assumption we made here
+what is the assumption that we made here
+
+ align:start position:0%
+what is the assumption that we made here
+ 
+
+ align:start position:0%
+what is the assumption that we made here
+but I wrote this what assumption did I
+
+ align:start position:0%
+but I wrote this what assumption did I
+ 
+
+ align:start position:0%
+but I wrote this what assumption did I
+make which is kind of similar to what
+
+ align:start position:0%
+make which is kind of similar to what
+ 
+
+ align:start position:0%
+make which is kind of similar to what
+Kevin just said but not exactly right
+
+ align:start position:0%
+Kevin just said but not exactly right
+ 
+
+ align:start position:0%
+Kevin just said but not exactly right
+but someone point out the assumption
+
+ align:start position:0%
+but someone point out the assumption
+ 
+
+ align:start position:0%
+but someone point out the assumption
+that was made here not you someone else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right go for it
+
+ align:start position:0%
+all right go for it
+ 
+
+ align:start position:0%
+all right go for it
+yeah the intervals are equal right so so
+
+ align:start position:0%
+yeah the intervals are equal right so so
+ 
+
+ align:start position:0%
+yeah the intervals are equal right so so
+so I this look it's it's a different
+
+ align:start position:0%
+so I this look it's it's a different
+ 
+
+ align:start position:0%
+so I this look it's it's a different
+problem if it didn't break here then I
+
+ align:start position:0%
+problem if it didn't break here then I
+ 
+
+ align:start position:0%
+problem if it didn't break here then I
+got a smaller I have two balls and I had
+
+ align:start position:0%
+got a smaller I have two balls and I had
+ 
+
+ align:start position:0%
+got a smaller I have two balls and I had
+a smaller problem so why would I use the
+
+ align:start position:0%
+a smaller problem so why would I use the
+ 
+
+ align:start position:0%
+a smaller problem so why would I use the
+same K right I mean that kind of makes
+
+ align:start position:0%
+same K right I mean that kind of makes
+ 
+
+ align:start position:0%
+same K right I mean that kind of makes
+sense right so now it's more complicated
+
+ align:start position:0%
+sense right so now it's more complicated
+ 
+
+ align:start position:0%
+sense right so now it's more complicated
+and I hopefully will get to that but I
+
+ align:start position:0%
+and I hopefully will get to that but I
+ 
+
+ align:start position:0%
+and I hopefully will get to that but I
+want to do other things first
+
+ align:start position:0%
+want to do other things first
+ 
+
+ align:start position:0%
+want to do other things first
+so that's the reason so at least you
+
+ align:start position:0%
+so that's the reason so at least you
+ 
+
+ align:start position:0%
+so that's the reason so at least you
+know why 21 isn't optimal right it's
+
+ align:start position:0%
+know why 21 isn't optimal right it's
+ 
+
+ align:start position:0%
+know why 21 isn't optimal right it's
+because of this constraint that we
+
+ align:start position:0%
+because of this constraint that we
+ 
+
+ align:start position:0%
+because of this constraint that we
+placed on ourselves in order to do this
+
+ align:start position:0%
+placed on ourselves in order to do this
+ 
+
+ align:start position:0%
+placed on ourselves in order to do this
+analysis to get to the point where we
+
+ align:start position:0%
+analysis to get to the point where we
+ 
+
+ align:start position:0%
+analysis to get to the point where we
+had two times square root of n minus one
+
+ align:start position:0%
+had two times square root of n minus one
+ 
+
+ align:start position:0%
+had two times square root of n minus one
+that that corresponds to the equally
+
+ align:start position:0%
+that that corresponds to the equally
+ 
+
+ align:start position:0%
+that that corresponds to the equally
+level constraint okay all right so good
+
+ align:start position:0%
+level constraint okay all right so good
+ 
+
+ align:start position:0%
+level constraint okay all right so good
+all right any questions about this so as
+
+ align:start position:0%
+all right any questions about this so as
+ 
+
+ align:start position:0%
+all right any questions about this so as
+you can imagine I'm not going to show
+
+ align:start position:0%
+you can imagine I'm not going to show
+ 
+
+ align:start position:0%
+you can imagine I'm not going to show
+you code that computes two times square
+
+ align:start position:0%
+you code that computes two times square
+ 
+
+ align:start position:0%
+you code that computes two times square
+root of n minus 1 right I said that that
+
+ align:start position:0%
+root of n minus 1 right I said that that
+ 
+
+ align:start position:0%
+root of n minus 1 right I said that that
+doesn't make sense but we do have code
+
+ align:start position:0%
+doesn't make sense but we do have code
+ 
+
+ align:start position:0%
+doesn't make sense but we do have code
+to look at that corresponds to at the
+
+ align:start position:0%
+to look at that corresponds to at the
+ 
+
+ align:start position:0%
+to look at that corresponds to at the
+case where a D could be 3 D could be 4
+
+ align:start position:0%
+case where a D could be 3 D could be 4
+ 
+
+ align:start position:0%
+case where a D could be 3 D could be 4
+and and then obviously it gets more
+
+ align:start position:0%
+and and then obviously it gets more
+ 
+
+ align:start position:0%
+and and then obviously it gets more
+interesting in terms of what your
+
+ align:start position:0%
+interesting in terms of what your
+ 
+
+ align:start position:0%
+interesting in terms of what your
+strategy is and we won't go with
+
+ align:start position:0%
+strategy is and we won't go with
+ 
+
+ align:start position:0%
+strategy is and we won't go with
+optimizing in fact it's an open problem
+
+ align:start position:0%
+optimizing in fact it's an open problem
+ 
+
+ align:start position:0%
+optimizing in fact it's an open problem
+as to what the optimum strategy would be
+
+ align:start position:0%
+as to what the optimum strategy would be
+ 
+
+ align:start position:0%
+as to what the optimum strategy would be
+for arbitrary D in the D meaning the
+
+ align:start position:0%
+for arbitrary D in the D meaning the
+ 
+
+ align:start position:0%
+for arbitrary D in the D meaning the
+number of balls if it's 5 6 whatever
+
+ align:start position:0%
+number of balls if it's 5 6 whatever
+ 
+
+ align:start position:0%
+number of balls if it's 5 6 whatever
+partly because of what I just talked
+
+ align:start position:0%
+partly because of what I just talked
+ 
+
+ align:start position:0%
+partly because of what I just talked
+about with respect to you need to
+
+ align:start position:0%
+about with respect to you need to
+ 
+
+ align:start position:0%
+about with respect to you need to
+utilize unequal intervals but the
+
+ align:start position:0%
+utilize unequal intervals but the
+ 
+
+ align:start position:0%
+utilize unequal intervals but the
+natural thing to do now is to move to D
+
+ align:start position:0%
+natural thing to do now is to move to D
+ 
+
+ align:start position:0%
+natural thing to do now is to move to D
+equals arbitrary number of balls and
+
+ align:start position:0%
+equals arbitrary number of balls and
+ 
+
+ align:start position:0%
+equals arbitrary number of balls and
+stick with kind of the same algorithmic
+
+ align:start position:0%
+stick with kind of the same algorithmic
+ 
+
+ align:start position:0%
+stick with kind of the same algorithmic
+approach of having equal intervals right
+
+ align:start position:0%
+approach of having equal intervals right
+ 
+
+ align:start position:0%
+approach of having equal intervals right
+and but the question is you know what
+
+ align:start position:0%
+and but the question is you know what
+ 
+
+ align:start position:0%
+and but the question is you know what
+are these intervals what and how would
+
+ align:start position:0%
+are these intervals what and how would
+ 
+
+ align:start position:0%
+are these intervals what and how would
+we find the size of these intervals
+
+ align:start position:0%
+we find the size of these intervals
+ 
+
+ align:start position:0%
+we find the size of these intervals
+right because it's kind of not
+
+ align:start position:0%
+right because it's kind of not
+ 
+
+ align:start position:0%
+right because it's kind of not
+immediately obvious if I told you D was
+
+ align:start position:0%
+immediately obvious if I told you D was
+ 
+
+ align:start position:0%
+immediately obvious if I told you D was
+5 and you don't want to just keep the 3
+
+ align:start position:0%
+5 and you don't want to just keep the 3
+ 
+
+ align:start position:0%
+5 and you don't want to just keep the 3
+balls away and you know sell them later
+
+ align:start position:0%
+balls away and you know sell them later
+ 
+
+ align:start position:0%
+balls away and you know sell them later
+and just use the 2 right that doesn't
+
+ align:start position:0%
+and just use the 2 right that doesn't
+ 
+
+ align:start position:0%
+and just use the 2 right that doesn't
+give you your minimum doesn't minimize
+
+ align:start position:0%
+give you your minimum doesn't minimize
+ 
+
+ align:start position:0%
+give you your minimum doesn't minimize
+your worst case you want to use these
+
+ align:start position:0%
+your worst case you want to use these
+ 
+
+ align:start position:0%
+your worst case you want to use these
+you use these balls cool all right so
+
+ align:start position:0%
+you use these balls cool all right so
+ 
+
+ align:start position:0%
+you use these balls cool all right so
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+let's talk a little bit about if I had d
+
+ align:start position:0%
+let's talk a little bit about if I had d
+ 
+
+ align:start position:0%
+let's talk a little bit about if I had d
+equals 3 I mean again gonna use your
+
+ align:start position:0%
+equals 3 I mean again gonna use your
+ 
+
+ align:start position:0%
+equals 3 I mean again gonna use your
+intuition what do you think we should do
+
+ align:start position:0%
+intuition what do you think we should do
+ 
+
+ align:start position:0%
+intuition what do you think we should do
+what happened for D equals 2 with
+
+ align:start position:0%
+what happened for D equals 2 with
+ 
+
+ align:start position:0%
+what happened for D equals 2 with
+respect to that interval and how is it
+
+ align:start position:0%
+respect to that interval and how is it
+ 
+
+ align:start position:0%
+respect to that interval and how is it
+related to n right so what do you think
+
+ align:start position:0%
+related to n right so what do you think
+ 
+
+ align:start position:0%
+related to n right so what do you think
+I just wild guess maybe even what do you
+
+ align:start position:0%
+I just wild guess maybe even what do you
+ 
+
+ align:start position:0%
+I just wild guess maybe even what do you
+think we need to do if he had d equals 3
+
+ align:start position:0%
+think we need to do if he had d equals 3
+ 
+
+ align:start position:0%
+think we need to do if he had d equals 3
+for that very first ball in terms of
+
+ align:start position:0%
+for that very first ball in terms of
+ 
+
+ align:start position:0%
+for that very first ball in terms of
+what we need to look at in relation to
+
+ align:start position:0%
+what we need to look at in relation to
+ 
+
+ align:start position:0%
+what we need to look at in relation to
+the interval sighs yeah back there
+
+ align:start position:0%
+the interval sighs yeah back there
+ 
+
+ align:start position:0%
+the interval sighs yeah back there
+ah-ha cube root cube root what what's
+
+ align:start position:0%
+ah-ha cube root cube root what what's
+ 
+
+ align:start position:0%
+ah-ha cube root cube root what what's
+your name Ryan so Ryan says you know
+
+ align:start position:0%
+your name Ryan so Ryan says you know
+ 
+
+ align:start position:0%
+your name Ryan so Ryan says you know
+cube root and yeah that that's the
+
+ align:start position:0%
+cube root and yeah that that's the
+ 
+
+ align:start position:0%
+cube root and yeah that that's the
+correct intuition it's a little bit
+
+ align:start position:0%
+correct intuition it's a little bit
+ 
+
+ align:start position:0%
+correct intuition it's a little bit
+unclear you know what happens you know
+
+ align:start position:0%
+unclear you know what happens you know
+ 
+
+ align:start position:0%
+unclear you know what happens you know
+so they do cube roots and maybe you have
+
+ align:start position:0%
+so they do cube roots and maybe you have
+ 
+
+ align:start position:0%
+so they do cube roots and maybe you have
+you know what's the cube root of 128 5
+
+ align:start position:0%
+you know what's the cube root of 128 5
+ 
+
+ align:start position:0%
+you know what's the cube root of 128 5
+you know yeah that's right I think it's
+
+ align:start position:0%
+you know yeah that's right I think it's
+ 
+
+ align:start position:0%
+you know yeah that's right I think it's
+5 ok it's close to 5 you know it's it's
+
+ align:start position:0%
+5 ok it's close to 5 you know it's it's
+ 
+
+ align:start position:0%
+5 ok it's close to 5 you know it's it's
+say six or five or six right and and so
+
+ align:start position:0%
+say six or five or six right and and so
+ 
+
+ align:start position:0%
+say six or five or six right and and so
+maybe I do six and then I do 12 and it's
+
+ align:start position:0%
+maybe I do six and then I do 12 and it's
+ 
+
+ align:start position:0%
+maybe I do six and then I do 12 and it's
+that is it's a little bit strange so it
+
+ align:start position:0%
+that is it's a little bit strange so it
+ 
+
+ align:start position:0%
+that is it's a little bit strange so it
+turns out it's actually the six in 12
+
+ align:start position:0%
+turns out it's actually the six in 12
+ 
+
+ align:start position:0%
+turns out it's actually the six in 12
+when you start with 128 when you have
+
+ align:start position:0%
+when you start with 128 when you have
+ 
+
+ align:start position:0%
+when you start with 128 when you have
+three balls doesn't seem like it's gonna
+
+ align:start position:0%
+three balls doesn't seem like it's gonna
+ 
+
+ align:start position:0%
+three balls doesn't seem like it's gonna
+give you the worst case right right
+
+ align:start position:0%
+give you the worst case right right
+ 
+
+ align:start position:0%
+give you the worst case right right
+because you know like in the worst case
+
+ align:start position:0%
+because you know like in the worst case
+ 
+
+ align:start position:0%
+because you know like in the worst case
+you might be dropping the ball six 12 18
+
+ align:start position:0%
+you might be dropping the ball six 12 18
+ 
+
+ align:start position:0%
+you might be dropping the ball six 12 18
+24 etcetera etcetera right um so cube
+
+ align:start position:0%
+24 etcetera etcetera right um so cube
+ 
+
+ align:start position:0%
+24 etcetera etcetera right um so cube
+root is right but it's something a
+
+ align:start position:0%
+root is right but it's something a
+ 
+
+ align:start position:0%
+root is right but it's something a
+little bit different because it gave us
+
+ align:start position:0%
+little bit different because it gave us
+ 
+
+ align:start position:0%
+little bit different because it gave us
+this interval that was kind of too small
+
+ align:start position:0%
+this interval that was kind of too small
+ 
+
+ align:start position:0%
+this interval that was kind of too small
+so how would I get something that's
+
+ align:start position:0%
+so how would I get something that's
+ 
+
+ align:start position:0%
+so how would I get something that's
+bigger you'd want things that are a
+
+ align:start position:0%
+bigger you'd want things that are a
+ 
+
+ align:start position:0%
+bigger you'd want things that are a
+little bit bigger right I mean yeah I
+
+ align:start position:0%
+little bit bigger right I mean yeah I
+ 
+
+ align:start position:0%
+little bit bigger right I mean yeah I
+think you're going to the right
+
+ align:start position:0%
+think you're going to the right
+ 
+
+ align:start position:0%
+think you're going to the right
+direction but I don't want six and
+
+ align:start position:0%
+direction but I don't want six and
+ 
+
+ align:start position:0%
+direction but I don't want six and
+twelve and eighteen
+
+ align:start position:0%
+twelve and eighteen
+ 
+
+ align:start position:0%
+twelve and eighteen
+I mean clearly that's going to give me
+
+ align:start position:0%
+I mean clearly that's going to give me
+ 
+
+ align:start position:0%
+I mean clearly that's going to give me
+like 25 drops and that's even worse than
+
+ align:start position:0%
+like 25 drops and that's even worse than
+ 
+
+ align:start position:0%
+like 25 drops and that's even worse than
+then then the two ball case which really
+
+ align:start position:0%
+then then the two ball case which really
+ 
+
+ align:start position:0%
+then then the two ball case which really
+means you should lose your job and never
+
+ align:start position:0%
+means you should lose your job and never
+ 
+
+ align:start position:0%
+means you should lose your job and never
+get another one right so if you do
+
+ align:start position:0%
+get another one right so if you do
+ 
+
+ align:start position:0%
+get another one right so if you do
+something that bad right so so that
+
+ align:start position:0%
+something that bad right so so that
+ 
+
+ align:start position:0%
+something that bad right so so that
+that's up to what what would you do
+
+ align:start position:0%
+that's up to what what would you do
+ 
+
+ align:start position:0%
+that's up to what what would you do
+that's you know kind of different from
+
+ align:start position:0%
+that's you know kind of different from
+ 
+
+ align:start position:0%
+that's you know kind of different from
+cube root but related to cube root right
+
+ align:start position:0%
+cube root but related to cube root right
+ 
+
+ align:start position:0%
+cube root but related to cube root right
+yeah go ahead fun
+
+ align:start position:0%
+yeah go ahead fun
+ 
+
+ align:start position:0%
+yeah go ahead fun
+yeah so what you want to do is you want
+
+ align:start position:0%
+yeah so what you want to do is you want
+ 
+
+ align:start position:0%
+yeah so what you want to do is you want
+to start it makes sense that when you
+
+ align:start position:0%
+to start it makes sense that when you
+ 
+
+ align:start position:0%
+to start it makes sense that when you
+have lots of balls in terms of being
+
+ align:start position:0%
+have lots of balls in terms of being
+ 
+
+ align:start position:0%
+have lots of balls in terms of being
+able to use them that you start with
+
+ align:start position:0%
+able to use them that you start with
+ 
+
+ align:start position:0%
+able to use them that you start with
+larger intervals and you shrink them
+
+ align:start position:0%
+larger intervals and you shrink them
+ 
+
+ align:start position:0%
+larger intervals and you shrink them
+right that's exactly what happened with
+
+ align:start position:0%
+right that's exactly what happened with
+ 
+
+ align:start position:0%
+right that's exactly what happened with
+two balls
+
+ align:start position:0%
+two balls
+ 
+
+ align:start position:0%
+two balls
+you started with K I in in the case
+
+ align:start position:0%
+you started with K I in in the case
+ 
+
+ align:start position:0%
+you started with K I in in the case
+where we had two balls and then we're
+
+ align:start position:0%
+where we had two balls and then we're
+ 
+
+ align:start position:0%
+where we had two balls and then we're
+down to one when we have one ball right
+
+ align:start position:0%
+down to one when we have one ball right
+ 
+
+ align:start position:0%
+down to one when we have one ball right
+so that's really what you're doing when
+
+ align:start position:0%
+so that's really what you're doing when
+ 
+
+ align:start position:0%
+so that's really what you're doing when
+you have one ball all you can do is go
+
+ align:start position:0%
+you have one ball all you can do is go
+ 
+
+ align:start position:0%
+you have one ball all you can do is go
+one floor at a time when you have when
+
+ align:start position:0%
+one floor at a time when you have when
+ 
+
+ align:start position:0%
+one floor at a time when you have when
+you have two balls you go K where K
+
+ align:start position:0%
+you have two balls you go K where K
+ 
+
+ align:start position:0%
+you have two balls you go K where K
+happened to be square root of n and then
+
+ align:start position:0%
+happened to be square root of n and then
+ 
+
+ align:start position:0%
+happened to be square root of n and then
+we had three balls you kind of want to
+
+ align:start position:0%
+we had three balls you kind of want to
+ 
+
+ align:start position:0%
+we had three balls you kind of want to
+start with with like n raised to 2/3 in
+
+ align:start position:0%
+start with with like n raised to 2/3 in
+ 
+
+ align:start position:0%
+start with with like n raised to 2/3 in
+terms of the in terms of the interval
+
+ align:start position:0%
+terms of the in terms of the interval
+ 
+
+ align:start position:0%
+terms of the in terms of the interval
+right and then if I had four balls the
+
+ align:start position:0%
+right and then if I had four balls the
+ 
+
+ align:start position:0%
+right and then if I had four balls the
+argument would be that I would start
+
+ align:start position:0%
+argument would be that I would start
+ 
+
+ align:start position:0%
+argument would be that I would start
+with n raised to three three quarters
+
+ align:start position:0%
+with n raised to three three quarters
+ 
+
+ align:start position:0%
+with n raised to three three quarters
+and then I'll go to square root of N and
+
+ align:start position:0%
+and then I'll go to square root of N and
+ 
+
+ align:start position:0%
+and then I'll go to square root of N and
+then I'll go so on and so forth and what
+
+ align:start position:0%
+then I'll go so on and so forth and what
+ 
+
+ align:start position:0%
+then I'll go so on and so forth and what
+is that reminding you of well what is
+
+ align:start position:0%
+is that reminding you of well what is
+ 
+
+ align:start position:0%
+is that reminding you of well what is
+what is this in terms of these powers
+
+ align:start position:0%
+what is this in terms of these powers
+ 
+
+ align:start position:0%
+what is this in terms of these powers
+and you know getting up to not quite n
+
+ align:start position:0%
+and you know getting up to not quite n
+ 
+
+ align:start position:0%
+and you know getting up to not quite n
+but five six N and so on what is that
+
+ align:start position:0%
+but five six N and so on what is that
+ 
+
+ align:start position:0%
+but five six N and so on what is that
+reminding you of from number number
+
+ align:start position:0%
+reminding you of from number number
+ 
+
+ align:start position:0%
+reminding you of from number number
+theory or just sort of regular
+
+ align:start position:0%
+theory or just sort of regular
+ 
+
+ align:start position:0%
+theory or just sort of regular
+arithmetic yeah different bases it's
+
+ align:start position:0%
+arithmetic yeah different bases it's
+ 
+
+ align:start position:0%
+arithmetic yeah different bases it's
+different different radix arithmetic
+
+ align:start position:0%
+different different radix arithmetic
+ 
+
+ align:start position:0%
+different different radix arithmetic
+right so it turns out the way you want
+
+ align:start position:0%
+right so it turns out the way you want
+ 
+
+ align:start position:0%
+right so it turns out the way you want
+to solve this problem and and this is in
+
+ align:start position:0%
+to solve this problem and and this is in
+ 
+
+ align:start position:0%
+to solve this problem and and this is in
+keeping with the intuition you have you
+
+ align:start position:0%
+keeping with the intuition you have you
+ 
+
+ align:start position:0%
+keeping with the intuition you have you
+you have with respect to the cube roots
+
+ align:start position:0%
+you have with respect to the cube roots
+ 
+
+ align:start position:0%
+you have with respect to the cube roots
+and so on and so forth the way we want
+
+ align:start position:0%
+and so on and so forth the way we want
+ 
+
+ align:start position:0%
+and so on and so forth the way we want
+to do this is we want to think about D
+
+ align:start position:0%
+to do this is we want to think about D
+ 
+
+ align:start position:0%
+to do this is we want to think about D
+digit numbers and at the numbers
+
+ align:start position:0%
+digit numbers and at the numbers
+ 
+
+ align:start position:0%
+digit numbers and at the numbers
+themselves and D is the number of balls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so that's that D digits but what
+
+ align:start position:0%
+and so that's that D digits but what
+ 
+
+ align:start position:0%
+and so that's that D digits but what
+what is the Vedic sub these numbers okay
+
+ align:start position:0%
+what is the Vedic sub these numbers okay
+ 
+
+ align:start position:0%
+what is the Vedic sub these numbers okay
+the the radix of these numbers are going
+
+ align:start position:0%
+the the radix of these numbers are going
+ 
+
+ align:start position:0%
+the the radix of these numbers are going
+to be related to that to the K to the
+
+ align:start position:0%
+to be related to that to the K to the
+ 
+
+ align:start position:0%
+to be related to that to the K to the
+intervals right so you you you
+
+ align:start position:0%
+intervals right so you you you
+ 
+
+ align:start position:0%
+intervals right so you you you
+essentially want to say you know I'm
+
+ align:start position:0%
+essentially want to say you know I'm
+ 
+
+ align:start position:0%
+essentially want to say you know I'm
+counting in multiples of K right you
+
+ align:start position:0%
+counting in multiples of K right you
+ 
+
+ align:start position:0%
+counting in multiples of K right you
+know I went K 2 K 3 K etcetera so if I
+
+ align:start position:0%
+know I went K 2 K 3 K etcetera so if I
+ 
+
+ align:start position:0%
+know I went K 2 K 3 K etcetera so if I
+had like radix K that means I'm just
+
+ align:start position:0%
+had like radix K that means I'm just
+ 
+
+ align:start position:0%
+had like radix K that means I'm just
+incrementing that particular particular
+
+ align:start position:0%
+incrementing that particular particular
+ 
+
+ align:start position:0%
+incrementing that particular particular
+digit right you know 5 if I go if I had
+
+ align:start position:0%
+digit right you know 5 if I go if I had
+ 
+
+ align:start position:0%
+digit right you know 5 if I go if I had
+radix 12 and
+
+ align:start position:0%
+radix 12 and
+ 
+
+ align:start position:0%
+radix 12 and
+and I had one zero in radix 12 right
+
+ align:start position:0%
+and I had one zero in radix 12 right
+ 
+
+ align:start position:0%
+and I had one zero in radix 12 right
+then you know this this this would be so
+
+ align:start position:0%
+then you know this this this would be so
+ 
+
+ align:start position:0%
+then you know this this this would be so
+when I go to zero then at the the most
+
+ align:start position:0%
+when I go to zero then at the the most
+ 
+
+ align:start position:0%
+when I go to zero then at the the most
+significant digit
+
+ align:start position:0%
+significant digit
+ 
+
+ align:start position:0%
+significant digit
+I got incremented and so this this is
+
+ align:start position:0%
+I got incremented and so this this is
+ 
+
+ align:start position:0%
+I got incremented and so this this is
+plus 12 this is 12 times larger I'm
+
+ align:start position:0%
+plus 12 this is 12 times larger I'm
+ 
+
+ align:start position:0%
+plus 12 this is 12 times larger I'm
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+12 larger then 2 0 is 12 larger than 1 0
+
+ align:start position:0%
+12 larger then 2 0 is 12 larger than 1 0
+ 
+
+ align:start position:0%
+12 larger then 2 0 is 12 larger than 1 0
+in in in radix 12 right make sense just
+
+ align:start position:0%
+in in in radix 12 right make sense just
+ 
+
+ align:start position:0%
+in in in radix 12 right make sense just
+like 20 is 10 larger than 10 10 in in
+
+ align:start position:0%
+like 20 is 10 larger than 10 10 in in
+ 
+
+ align:start position:0%
+like 20 is 10 larger than 10 10 in in
+decimal right so so that's that's the
+
+ align:start position:0%
+decimal right so so that's that's the
+ 
+
+ align:start position:0%
+decimal right so so that's that's the
+way you want to think about this and so
+
+ align:start position:0%
+way you want to think about this and so
+ 
+
+ align:start position:0%
+way you want to think about this and so
+I you're gonna do our Airy numbers and
+
+ align:start position:0%
+I you're gonna do our Airy numbers and
+ 
+
+ align:start position:0%
+I you're gonna do our Airy numbers and
+the first thing that you need to do is
+
+ align:start position:0%
+the first thing that you need to do is
+ 
+
+ align:start position:0%
+the first thing that you need to do is
+you need to figure out based on the
+
+ align:start position:0%
+you need to figure out based on the
+ 
+
+ align:start position:0%
+you need to figure out based on the
+number of floors that you have figure
+
+ align:start position:0%
+number of floors that you have figure
+ 
+
+ align:start position:0%
+number of floors that you have figure
+out your given D you're given n the
+
+ align:start position:0%
+out your given D you're given n the
+ 
+
+ align:start position:0%
+out your given D you're given n the
+number of floors and you're given the
+
+ align:start position:0%
+number of floors and you're given the
+ 
+
+ align:start position:0%
+number of floors and you're given the
+number of balls you got to figure out
+
+ align:start position:0%
+number of balls you got to figure out
+ 
+
+ align:start position:0%
+number of balls you got to figure out
+what radix you're working in and this is
+
+ align:start position:0%
+what radix you're working in and this is
+ 
+
+ align:start position:0%
+what radix you're working in and this is
+going to be a generalization of the
+
+ align:start position:0%
+going to be a generalization of the
+ 
+
+ align:start position:0%
+going to be a generalization of the
+square root of n as you'll see we we
+
+ align:start position:0%
+square root of n as you'll see we we
+ 
+
+ align:start position:0%
+square root of n as you'll see we we
+want to choose the radix such that R
+
+ align:start position:0%
+want to choose the radix such that R
+ 
+
+ align:start position:0%
+want to choose the radix such that R
+raised to D is greater than n I choose R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that R raised to D is greater than
+
+ align:start position:0%
+such that R raised to D is greater than
+ 
+
+ align:start position:0%
+such that R raised to D is greater than
+n right and so that comes back to
+
+ align:start position:0%
+n right and so that comes back to
+ 
+
+ align:start position:0%
+n right and so that comes back to
+obviously if you need it if D where 2
+
+ align:start position:0%
+obviously if you need it if D where 2
+ 
+
+ align:start position:0%
+obviously if you need it if D where 2
+then it makes sense that our would be
+
+ align:start position:0%
+then it makes sense that our would be
+ 
+
+ align:start position:0%
+then it makes sense that our would be
+square root of M right which is in
+
+ align:start position:0%
+square root of M right which is in
+ 
+
+ align:start position:0%
+square root of M right which is in
+keeping with what we talked about right
+
+ align:start position:0%
+keeping with what we talked about right
+ 
+
+ align:start position:0%
+keeping with what we talked about right
+but if if D is 3 then that radix not
+
+ align:start position:0%
+but if if D is 3 then that radix not
+ 
+
+ align:start position:0%
+but if if D is 3 then that radix not
+necessarily the interval that we choose
+
+ align:start position:0%
+necessarily the interval that we choose
+ 
+
+ align:start position:0%
+necessarily the interval that we choose
+because the intervals are going to be
+
+ align:start position:0%
+because the intervals are going to be
+ 
+
+ align:start position:0%
+because the intervals are going to be
+different it's going to be more like the
+
+ align:start position:0%
+different it's going to be more like the
+ 
+
+ align:start position:0%
+different it's going to be more like the
+cube root of n which is also proposed
+
+ align:start position:0%
+cube root of n which is also proposed
+ 
+
+ align:start position:0%
+cube root of n which is also proposed
+right Brian mentioned that and so so in
+
+ align:start position:0%
+right Brian mentioned that and so so in
+ 
+
+ align:start position:0%
+right Brian mentioned that and so so in
+this case let's say that n were 128 and
+
+ align:start position:0%
+this case let's say that n were 128 and
+ 
+
+ align:start position:0%
+this case let's say that n were 128 and
+D equals 4 then we would choose R equals
+
+ align:start position:0%
+D equals 4 then we would choose R equals
+ 
+
+ align:start position:0%
+D equals 4 then we would choose R equals
+4 because 4 raised to 4 is 256 which is
+
+ align:start position:0%
+4 because 4 raised to 4 is 256 which is
+ 
+
+ align:start position:0%
+4 because 4 raised to 4 is 256 which is
+greater than 128 and we can't use 3
+
+ align:start position:0%
+greater than 128 and we can't use 3
+ 
+
+ align:start position:0%
+greater than 128 and we can't use 3
+because 3
+
+ align:start position:0%
+because 3
+ 
+
+ align:start position:0%
+because 3
+raise to4 is only 81 and 81 isn't
+
+ align:start position:0%
+raise to4 is only 81 and 81 isn't
+ 
+
+ align:start position:0%
+raise to4 is only 81 and 81 isn't
+greater than 128 right so you'd have to
+
+ align:start position:0%
+greater than 128 right so you'd have to
+ 
+
+ align:start position:0%
+greater than 128 right so you'd have to
+choose four so so what we are now saying
+
+ align:start position:0%
+choose four so so what we are now saying
+ 
+
+ align:start position:0%
+choose four so so what we are now saying
+is we want to somehow figure out if
+
+ align:start position:0%
+is we want to somehow figure out if
+ 
+
+ align:start position:0%
+is we want to somehow figure out if
+you're not quite there at an algorithm
+
+ align:start position:0%
+you're not quite there at an algorithm
+ 
+
+ align:start position:0%
+you're not quite there at an algorithm
+yet but we have a kind of a path forward
+
+ align:start position:0%
+yet but we have a kind of a path forward
+ 
+
+ align:start position:0%
+yet but we have a kind of a path forward
+I in that we want to look at the
+
+ align:start position:0%
+I in that we want to look at the
+ 
+
+ align:start position:0%
+I in that we want to look at the
+representation that our airy
+
+ align:start position:0%
+representation that our airy
+ 
+
+ align:start position:0%
+representation that our airy
+representation of these digital numbers
+
+ align:start position:0%
+representation of these digital numbers
+ 
+
+ align:start position:0%
+representation of these digital numbers
+and we're going to essentially I
+
+ align:start position:0%
+and we're going to essentially I
+ 
+
+ align:start position:0%
+and we're going to essentially I
+increment and so with our goal
+
+ align:start position:0%
+increment and so with our goal
+ 
+
+ align:start position:0%
+increment and so with our goal
+roughly speaking we're going to go with
+
+ align:start position:0%
+roughly speaking we're going to go with
+ 
+
+ align:start position:0%
+roughly speaking we're going to go with
+this representation and we're going to
+
+ align:start position:0%
+this representation and we're going to
+ 
+
+ align:start position:0%
+this representation and we're going to
+start incrementing digits so we just go
+
+ align:start position:0%
+start incrementing digits so we just go
+ 
+
+ align:start position:0%
+start incrementing digits so we just go
+0 1 2 in terms of the digits but but
+
+ align:start position:0%
+0 1 2 in terms of the digits but but
+ 
+
+ align:start position:0%
+0 1 2 in terms of the digits but but
+because the representation is our airy
+
+ align:start position:0%
+because the representation is our airy
+ 
+
+ align:start position:0%
+because the representation is our airy
+that means something different in terms
+
+ align:start position:0%
+that means something different in terms
+ 
+
+ align:start position:0%
+that means something different in terms
+of the number of floors depending on
+
+ align:start position:0%
+of the number of floors depending on
+ 
+
+ align:start position:0%
+of the number of floors depending on
+what R is right I mean just like I said
+
+ align:start position:0%
+what R is right I mean just like I said
+ 
+
+ align:start position:0%
+what R is right I mean just like I said
+um if this were if this were ternary a
+
+ align:start position:0%
+um if this were if this were ternary a
+ 
+
+ align:start position:0%
+um if this were if this were ternary a
+ternary representation then then in
+
+ align:start position:0%
+ternary representation then then in
+ 
+
+ align:start position:0%
+ternary representation then then in
+terms of floors this is only you know
+
+ align:start position:0%
+terms of floors this is only you know
+ 
+
+ align:start position:0%
+terms of floors this is only you know
+this would be a 4 ternary this would be
+
+ align:start position:0%
+this would be a 4 ternary this would be
+ 
+
+ align:start position:0%
+this would be a 4 ternary this would be
+3 floors to 0 the in to 0 would be 3
+
+ align:start position:0%
+3 floors to 0 the in to 0 would be 3
+ 
+
+ align:start position:0%
+3 floors to 0 the in to 0 would be 3
+floors away from 1 0 right in decimal to
+
+ align:start position:0%
+floors away from 1 0 right in decimal to
+ 
+
+ align:start position:0%
+floors away from 1 0 right in decimal to
+0 is 10 floors away from 1 0 and so on
+
+ align:start position:0%
+0 is 10 floors away from 1 0 and so on
+ 
+
+ align:start position:0%
+0 is 10 floors away from 1 0 and so on
+and so forth that makes sense yeah ask
+
+ align:start position:0%
+and so forth that makes sense yeah ask
+ 
+
+ align:start position:0%
+and so forth that makes sense yeah ask
+me questions if if you're confused um so
+
+ align:start position:0%
+me questions if if you're confused um so
+ 
+
+ align:start position:0%
+me questions if if you're confused um so
+let's take an example so and then we'll
+
+ align:start position:0%
+let's take an example so and then we'll
+ 
+
+ align:start position:0%
+let's take an example so and then we'll
+we'll look at that we look at code that
+
+ align:start position:0%
+we'll look at that we look at code that
+ 
+
+ align:start position:0%
+we'll look at that we look at code that
+actually builds this algorithm from from
+
+ align:start position:0%
+actually builds this algorithm from from
+ 
+
+ align:start position:0%
+actually builds this algorithm from from
+scratch so if we take our example of D
+
+ align:start position:0%
+scratch so if we take our example of D
+ 
+
+ align:start position:0%
+scratch so if we take our example of D
+equals 4 for our canonical one 28th
+
+ align:start position:0%
+equals 4 for our canonical one 28th
+ 
+
+ align:start position:0%
+equals 4 for our canonical one 28th
+floor Shanghai Tower because you do want
+
+ align:start position:0%
+floor Shanghai Tower because you do want
+ 
+
+ align:start position:0%
+floor Shanghai Tower because you do want
+to get a sense of how things improve we
+
+ align:start position:0%
+to get a sense of how things improve we
+ 
+
+ align:start position:0%
+to get a sense of how things improve we
+did improve from obviously D equals 1
+
+ align:start position:0%
+did improve from obviously D equals 1
+ 
+
+ align:start position:0%
+did improve from obviously D equals 1
+through D equals 2 with the equal
+
+ align:start position:0%
+through D equals 2 with the equal
+ 
+
+ align:start position:0%
+through D equals 2 with the equal
+interval assumption but with this radix
+
+ align:start position:0%
+interval assumption but with this radix
+ 
+
+ align:start position:0%
+interval assumption but with this radix
+idea we'd like to see how much better we
+
+ align:start position:0%
+idea we'd like to see how much better we
+ 
+
+ align:start position:0%
+idea we'd like to see how much better we
+can do right with D equals 4 and we
+
+ align:start position:0%
+can do right with D equals 4 and we
+ 
+
+ align:start position:0%
+can do right with D equals 4 and we
+wanted is substantially better than then
+
+ align:start position:0%
+wanted is substantially better than then
+ 
+
+ align:start position:0%
+wanted is substantially better than then
+21 drops or whatever we had back there
+
+ align:start position:0%
+21 drops or whatever we had back there
+ 
+
+ align:start position:0%
+21 drops or whatever we had back there
+so so R is 4 D is 4 I'm sorry D is 4
+
+ align:start position:0%
+so so R is 4 D is 4 I'm sorry D is 4
+ 
+
+ align:start position:0%
+so so R is 4 D is 4 I'm sorry D is 4
+n equals 128 and what we're going to do
+
+ align:start position:0%
+n equals 128 and what we're going to do
+ 
+
+ align:start position:0%
+n equals 128 and what we're going to do
+is the smallest number is zero zero zero
+
+ align:start position:0%
+is the smallest number is zero zero zero
+ 
+
+ align:start position:0%
+is the smallest number is zero zero zero
+zero and in in brackets I'm gonna write
+
+ align:start position:0%
+zero and in in brackets I'm gonna write
+ 
+
+ align:start position:0%
+zero and in in brackets I'm gonna write
+you know what that decimal
+
+ align:start position:0%
+you know what that decimal
+ 
+
+ align:start position:0%
+you know what that decimal
+representation is because I think that
+
+ align:start position:0%
+representation is because I think that
+ 
+
+ align:start position:0%
+representation is because I think that
+does give you some intuition and you get
+
+ align:start position:0%
+does give you some intuition and you get
+ 
+
+ align:start position:0%
+does give you some intuition and you get
+a sense of how this translates into into
+
+ align:start position:0%
+a sense of how this translates into into
+ 
+
+ align:start position:0%
+a sense of how this translates into into
+floors and after after a while if you're
+
+ align:start position:0%
+floors and after after a while if you're
+ 
+
+ align:start position:0%
+floors and after after a while if you're
+going to tell someone to do this you
+
+ align:start position:0%
+going to tell someone to do this you
+ 
+
+ align:start position:0%
+going to tell someone to do this you
+want to give them floor numbers in
+
+ align:start position:0%
+want to give them floor numbers in
+ 
+
+ align:start position:0%
+want to give them floor numbers in
+decimal because Shangai tower doesn't
+
+ align:start position:0%
+decimal because Shangai tower doesn't
+ 
+
+ align:start position:0%
+decimal because Shangai tower doesn't
+have some weird
+
+ align:start position:0%
+have some weird
+ 
+
+ align:start position:0%
+have some weird
+representation for the floors when you
+
+ align:start position:0%
+representation for the floors when you
+ 
+
+ align:start position:0%
+representation for the floors when you
+get into an elevator or anything like
+
+ align:start position:0%
+get into an elevator or anything like
+ 
+
+ align:start position:0%
+get into an elevator or anything like
+that so so this is floor zero and now
+
+ align:start position:0%
+that so so this is floor zero and now
+ 
+
+ align:start position:0%
+that so so this is floor zero and now
+the highest number is 3 3 3 3 which
+
+ align:start position:0%
+the highest number is 3 3 3 3 which
+ 
+
+ align:start position:0%
+the highest number is 3 3 3 3 which
+happens to be 255 I'm not gonna write
+
+ align:start position:0%
+happens to be 255 I'm not gonna write
+ 
+
+ align:start position:0%
+happens to be 255 I'm not gonna write
+floor each time but when I put things in
+
+ align:start position:0%
+floor each time but when I put things in
+ 
+
+ align:start position:0%
+floor each time but when I put things in
+brackets here that's the decimal
+
+ align:start position:0%
+brackets here that's the decimal
+ 
+
+ align:start position:0%
+brackets here that's the decimal
+representation okay so that's 255 so
+
+ align:start position:0%
+representation okay so that's 255 so
+ 
+
+ align:start position:0%
+representation okay so that's 255 so
+that's obviously too big we don't need
+
+ align:start position:0%
+that's obviously too big we don't need
+ 
+
+ align:start position:0%
+that's obviously too big we don't need
+that but we're stuck with having to
+
+ align:start position:0%
+that but we're stuck with having to
+ 
+
+ align:start position:0%
+that but we're stuck with having to
+choose r equals 4 for the reasons I
+
+ align:start position:0%
+choose r equals 4 for the reasons I
+ 
+
+ align:start position:0%
+choose r equals 4 for the reasons I
+described to you before right so so
+
+ align:start position:0%
+described to you before right so so
+ 
+
+ align:start position:0%
+described to you before right so so
+there's somewhere in here there's a
+
+ align:start position:0%
+there's somewhere in here there's a
+ 
+
+ align:start position:0%
+there's somewhere in here there's a
+there's a 128 and I can't I don't have
+
+ align:start position:0%
+there's a 128 and I can't I don't have
+ 
+
+ align:start position:0%
+there's a 128 and I can't I don't have
+it right up in front of me as to what
+
+ align:start position:0%
+it right up in front of me as to what
+ 
+
+ align:start position:0%
+it right up in front of me as to what
+what 128 would correspond to but 1 2 3 3
+
+ align:start position:0%
+what 128 would correspond to but 1 2 3 3
+ 
+
+ align:start position:0%
+what 128 would correspond to but 1 2 3 3
+for example would be floor 1 1 1 alright
+
+ align:start position:0%
+for example would be floor 1 1 1 alright
+ 
+
+ align:start position:0%
+for example would be floor 1 1 1 alright
+so so the way this works and you all
+
+ align:start position:0%
+so so the way this works and you all
+ 
+
+ align:start position:0%
+so so the way this works and you all
+know you're radix arithmetic it's a 3
+
+ align:start position:0%
+know you're radix arithmetic it's a 3
+ 
+
+ align:start position:0%
+know you're radix arithmetic it's a 3
+times 1 plus 3 3 times 4 plus 2 times 4
+
+ align:start position:0%
+times 1 plus 3 3 times 4 plus 2 times 4
+ 
+
+ align:start position:0%
+times 1 plus 3 3 times 4 plus 2 times 4
+square plus 1 times 4 cubed right that's
+
+ align:start position:0%
+square plus 1 times 4 cubed right that's
+ 
+
+ align:start position:0%
+square plus 1 times 4 cubed right that's
+that's what you have and that's how you
+
+ align:start position:0%
+that's what you have and that's how you
+ 
+
+ align:start position:0%
+that's what you have and that's how you
+get 1 1 1 so all what you have to do in
+
+ align:start position:0%
+get 1 1 1 so all what you have to do in
+ 
+
+ align:start position:0%
+get 1 1 1 so all what you have to do in
+order to do this right is is to start
+
+ align:start position:0%
+order to do this right is is to start
+ 
+
+ align:start position:0%
+order to do this right is is to start
+with the most significant digit which is
+
+ align:start position:0%
+with the most significant digit which is
+ 
+
+ align:start position:0%
+with the most significant digit which is
+the leftmost digit and that makes sense
+
+ align:start position:0%
+the leftmost digit and that makes sense
+ 
+
+ align:start position:0%
+the leftmost digit and that makes sense
+because we want our intervals when we
+
+ align:start position:0%
+because we want our intervals when we
+ 
+
+ align:start position:0%
+because we want our intervals when we
+have lots of balls to be large and that
+
+ align:start position:0%
+have lots of balls to be large and that
+ 
+
+ align:start position:0%
+have lots of balls to be large and that
+as you move and the balls break you're
+
+ align:start position:0%
+as you move and the balls break you're
+ 
+
+ align:start position:0%
+as you move and the balls break you're
+going to start shifting rightward and
+
+ align:start position:0%
+going to start shifting rightward and
+ 
+
+ align:start position:0%
+going to start shifting rightward and
+you're going to be incrementing
+
+ align:start position:0%
+you're going to be incrementing
+ 
+
+ align:start position:0%
+you're going to be incrementing
+different things right and that's
+
+ align:start position:0%
+different things right and that's
+ 
+
+ align:start position:0%
+different things right and that's
+essentially going to give us give us our
+
+ align:start position:0%
+essentially going to give us give us our
+ 
+
+ align:start position:0%
+essentially going to give us give us our
+give us a round with them and so we'll
+
+ align:start position:0%
+give us a round with them and so we'll
+ 
+
+ align:start position:0%
+give us a round with them and so we'll
+talk about let me just give you an
+
+ align:start position:0%
+talk about let me just give you an
+ 
+
+ align:start position:0%
+talk about let me just give you an
+example of the algorithm
+
+ align:start position:0%
+example of the algorithm
+ 
+
+ align:start position:0%
+example of the algorithm
+we'll if you look at we look at how the
+
+ align:start position:0%
+we'll if you look at we look at how the
+ 
+
+ align:start position:0%
+we'll if you look at we look at how the
+algorithm is implemented as I mentioned
+
+ align:start position:0%
+algorithm is implemented as I mentioned
+ 
+
+ align:start position:0%
+algorithm is implemented as I mentioned
+this it turns it into 10 lines of code
+
+ align:start position:0%
+this it turns it into 10 lines of code
+ 
+
+ align:start position:0%
+this it turns it into 10 lines of code
+because all you're doing is translating
+
+ align:start position:0%
+because all you're doing is translating
+ 
+
+ align:start position:0%
+because all you're doing is translating
+into this representation and you're just
+
+ align:start position:0%
+into this representation and you're just
+ 
+
+ align:start position:0%
+into this representation and you're just
+incrementing bits of the representation
+
+ align:start position:0%
+incrementing bits of the representation
+ 
+
+ align:start position:0%
+incrementing bits of the representation
+and it's interactive you can play with
+
+ align:start position:0%
+and it's interactive you can play with
+ 
+
+ align:start position:0%
+and it's interactive you can play with
+it later today or whenever I ate and you
+
+ align:start position:0%
+it later today or whenever I ate and you
+ 
+
+ align:start position:0%
+it later today or whenever I ate and you
+can't think of a hardness coefficients
+
+ align:start position:0%
+can't think of a hardness coefficients
+ 
+
+ align:start position:0%
+can't think of a hardness coefficients
+in your head and see how things work out
+
+ align:start position:0%
+in your head and see how things work out
+ 
+
+ align:start position:0%
+in your head and see how things work out
+but before we end we obviously have to
+
+ align:start position:0%
+but before we end we obviously have to
+ 
+
+ align:start position:0%
+but before we end we obviously have to
+do a worst-case analysis of this of this
+
+ align:start position:0%
+do a worst-case analysis of this of this
+ 
+
+ align:start position:0%
+do a worst-case analysis of this of this
+algorithm because that's the whole point
+
+ align:start position:0%
+algorithm because that's the whole point
+ 
+
+ align:start position:0%
+algorithm because that's the whole point
+of this exercise so let's so so in this
+
+ align:start position:0%
+of this exercise so let's so so in this
+ 
+
+ align:start position:0%
+of this exercise so let's so so in this
+case where do you think I should so I
+
+ align:start position:0%
+case where do you think I should so I
+ 
+
+ align:start position:0%
+case where do you think I should so I
+don't want to drop obviously at floor
+
+ align:start position:0%
+don't want to drop obviously at floor
+ 
+
+ align:start position:0%
+don't want to drop obviously at floor
+zero I mean that there's no notion of
+
+ align:start position:0%
+zero I mean that there's no notion of
+ 
+
+ align:start position:0%
+zero I mean that there's no notion of
+that so very wide drop out at the
+
+ align:start position:0%
+that so very wide drop out at the
+ 
+
+ align:start position:0%
+that so very wide drop out at the
+beginning the first drop is that given
+
+ align:start position:0%
+beginning the first drop is that given
+ 
+
+ align:start position:0%
+beginning the first drop is that given
+what I told you you can tell me in any
+
+ align:start position:0%
+what I told you you can tell me in any
+ 
+
+ align:start position:0%
+what I told you you can tell me in any
+any representation where would I drop
+
+ align:start position:0%
+any representation where would I drop
+ 
+
+ align:start position:0%
+any representation where would I drop
+the first ball if I have four balls at
+
+ align:start position:0%
+the first ball if I have four balls at
+ 
+
+ align:start position:0%
+the first ball if I have four balls at
+128 floors I said I want to start with
+
+ align:start position:0%
+128 floors I said I want to start with
+ 
+
+ align:start position:0%
+128 floors I said I want to start with
+it's something that that obviously
+
+ align:start position:0%
+it's something that that obviously
+ 
+
+ align:start position:0%
+it's something that that obviously
+there's some large interval here and I
+
+ align:start position:0%
+there's some large interval here and I
+ 
+
+ align:start position:0%
+there's some large interval here and I
+want to I I want to start in the left
+
+ align:start position:0%
+want to I I want to start in the left
+ 
+
+ align:start position:0%
+want to I I want to start in the left
+hand side and I want to increment the
+
+ align:start position:0%
+hand side and I want to increment the
+ 
+
+ align:start position:0%
+hand side and I want to increment the
+leftmost bit which is the most
+
+ align:start position:0%
+leftmost bit which is the most
+ 
+
+ align:start position:0%
+leftmost bit which is the most
+significant bit right so I would start
+
+ align:start position:0%
+significant bit right so I would start
+ 
+
+ align:start position:0%
+significant bit right so I would start
+with 1 0 0 0 ok so the first drop is at
+
+ align:start position:0%
+with 1 0 0 0 ok so the first drop is at
+ 
+
+ align:start position:0%
+with 1 0 0 0 ok so the first drop is at
+1 0 0 0 which is at floor 64 ok that's
+
+ align:start position:0%
+1 0 0 0 which is at floor 64 ok that's
+ 
+
+ align:start position:0%
+1 0 0 0 which is at floor 64 ok that's
+the first row now if if in fact on this
+
+ align:start position:0%
+the first row now if if in fact on this
+ 
+
+ align:start position:0%
+the first row now if if in fact on this
+this eye does not break all right so
+
+ align:start position:0%
+this eye does not break all right so
+ 
+
+ align:start position:0%
+this eye does not break all right so
+let's assume that this does not break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then what do I do next
+
+ align:start position:0%
+then what do I do next
+ 
+
+ align:start position:0%
+then what do I do next
+to 0 0 0 right and this would be 128
+
+ align:start position:0%
+to 0 0 0 right and this would be 128
+ 
+
+ align:start position:0%
+to 0 0 0 right and this would be 128
+right ok let's assume that this breaks
+
+ align:start position:0%
+right ok let's assume that this breaks
+ 
+
+ align:start position:0%
+right ok let's assume that this breaks
+here all right
+
+ align:start position:0%
+here all right
+ 
+
+ align:start position:0%
+here all right
+so now what do I do it broke I lost a
+
+ align:start position:0%
+so now what do I do it broke I lost a
+ 
+
+ align:start position:0%
+so now what do I do it broke I lost a
+ball now I have three balls left still
+
+ align:start position:0%
+ball now I have three balls left still
+ 
+
+ align:start position:0%
+ball now I have three balls left still
+that's the good news and harmony so what
+
+ align:start position:0%
+that's the good news and harmony so what
+ 
+
+ align:start position:0%
+that's the good news and harmony so what
+do I need where do I need to move if I
+
+ align:start position:0%
+do I need where do I need to move if I
+ 
+
+ align:start position:0%
+do I need where do I need to move if I
+have 3 balls left I need to be in a
+
+ align:start position:0%
+have 3 balls left I need to be in a
+ 
+
+ align:start position:0%
+have 3 balls left I need to be in a
+representation that has how many
+
+ align:start position:0%
+representation that has how many
+ 
+
+ align:start position:0%
+representation that has how many
+digits three digits right so I need to
+
+ align:start position:0%
+digits three digits right so I need to
+ 
+
+ align:start position:0%
+digits three digits right so I need to
+move III a broker mm so I know that it's
+
+ align:start position:0%
+move III a broker mm so I know that it's
+ 
+
+ align:start position:0%
+move III a broker mm so I know that it's
+less than 2000 so I need to go back to
+
+ align:start position:0%
+less than 2000 so I need to go back to
+ 
+
+ align:start position:0%
+less than 2000 so I need to go back to
+this because this is the this is the
+
+ align:start position:0%
+this because this is the this is the
+ 
+
+ align:start position:0%
+this because this is the this is the
+highest floor in general whenever things
+
+ align:start position:0%
+highest floor in general whenever things
+ 
+
+ align:start position:0%
+highest floor in general whenever things
+break you you go back to the highest
+
+ align:start position:0%
+break you you go back to the highest
+ 
+
+ align:start position:0%
+break you you go back to the highest
+floor that you know that the ball been
+
+ align:start position:0%
+floor that you know that the ball been
+ 
+
+ align:start position:0%
+floor that you know that the ball been
+break right I mean that's the canonical
+
+ align:start position:0%
+break right I mean that's the canonical
+ 
+
+ align:start position:0%
+break right I mean that's the canonical
+strategy that we followed all through
+
+ align:start position:0%
+strategy that we followed all through
+ 
+
+ align:start position:0%
+strategy that we followed all through
+when something when the ball breaks you
+
+ align:start position:0%
+when something when the ball breaks you
+ 
+
+ align:start position:0%
+when something when the ball breaks you
+go back and say oh but I do know that
+
+ align:start position:0%
+go back and say oh but I do know that
+ 
+
+ align:start position:0%
+go back and say oh but I do know that
+there was a highest floor in which the
+
+ align:start position:0%
+there was a highest floor in which the
+ 
+
+ align:start position:0%
+there was a highest floor in which the
+ball did not break and I have to start
+
+ align:start position:0%
+ball did not break and I have to start
+ 
+
+ align:start position:0%
+ball did not break and I have to start
+with one plus that right so so so what
+
+ align:start position:0%
+with one plus that right so so so what
+ 
+
+ align:start position:0%
+with one plus that right so so so what
+I'm going to do here is I need to go up
+
+ align:start position:0%
+I'm going to do here is I need to go up
+ 
+
+ align:start position:0%
+I'm going to do here is I need to go up
+and yeah because it broke I need to look
+
+ align:start position:0%
+and yeah because it broke I need to look
+ 
+
+ align:start position:0%
+and yeah because it broke I need to look
+at one zero zero one
+
+ align:start position:0%
+at one zero zero one
+ 
+
+ align:start position:0%
+at one zero zero one
+right the interval that I need to look
+
+ align:start position:0%
+right the interval that I need to look
+ 
+
+ align:start position:0%
+right the interval that I need to look
+at is 1 0 0 1 right because it's one
+
+ align:start position:0%
+at is 1 0 0 1 right because it's one
+ 
+
+ align:start position:0%
+at is 1 0 0 1 right because it's one
+more than that and all the way to 1 3 3
+
+ align:start position:0%
+more than that and all the way to 1 3 3
+ 
+
+ align:start position:0%
+more than that and all the way to 1 3 3
+3 which is 1 less than that ok so and
+
+ align:start position:0%
+3 which is 1 less than that ok so and
+ 
+
+ align:start position:0%
+3 which is 1 less than that ok so and
+this if this is you may feel a little
+
+ align:start position:0%
+this if this is you may feel a little
+ 
+
+ align:start position:0%
+this if this is you may feel a little
+bit better looking at this in decimal I
+
+ align:start position:0%
+bit better looking at this in decimal I
+ 
+
+ align:start position:0%
+bit better looking at this in decimal I
+certainly do it's 65 127 which makes
+
+ align:start position:0%
+certainly do it's 65 127 which makes
+ 
+
+ align:start position:0%
+certainly do it's 65 127 which makes
+perfect sense so far we've played around
+
+ align:start position:0%
+perfect sense so far we've played around
+ 
+
+ align:start position:0%
+perfect sense so far we've played around
+with with with the balls the first two
+
+ align:start position:0%
+with with with the balls the first two
+ 
+
+ align:start position:0%
+with with with the balls the first two
+balls and so we haven't really seen
+
+ align:start position:0%
+balls and so we haven't really seen
+ 
+
+ align:start position:0%
+balls and so we haven't really seen
+anything very dramatically different
+
+ align:start position:0%
+anything very dramatically different
+ 
+
+ align:start position:0%
+anything very dramatically different
+from the the 2 ball case but more more
+
+ align:start position:0%
+from the the 2 ball case but more more
+ 
+
+ align:start position:0%
+from the the 2 ball case but more more
+is coming right let's say this does not
+
+ align:start position:0%
+is coming right let's say this does not
+ 
+
+ align:start position:0%
+is coming right let's say this does not
+break if this does not break then what
+
+ align:start position:0%
+break if this does not break then what
+ 
+
+ align:start position:0%
+break if this does not break then what
+would I do now if it does not break I'm
+
+ align:start position:0%
+would I do now if it does not break I'm
+ 
+
+ align:start position:0%
+would I do now if it does not break I'm
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my bad my bad
+
+ align:start position:0%
+my bad my bad
+ 
+
+ align:start position:0%
+my bad my bad
+take I haven't even actually told you
+
+ align:start position:0%
+take I haven't even actually told you
+ 
+
+ align:start position:0%
+take I haven't even actually told you
+I've just talked about the interval and
+
+ align:start position:0%
+I've just talked about the interval and
+ 
+
+ align:start position:0%
+I've just talked about the interval and
+I haven't said what drop you need to
+
+ align:start position:0%
+I haven't said what drop you need to
+ 
+
+ align:start position:0%
+I haven't said what drop you need to
+make right so so ignore what I said
+
+ align:start position:0%
+make right so so ignore what I said
+ 
+
+ align:start position:0%
+make right so so ignore what I said
+right just now I think that the the next
+
+ align:start position:0%
+right just now I think that the the next
+ 
+
+ align:start position:0%
+right just now I think that the the next
+question is the ball broke and I have a
+
+ align:start position:0%
+question is the ball broke and I have a
+ 
+
+ align:start position:0%
+question is the ball broke and I have a
+second ball and I want the first drop of
+
+ align:start position:0%
+second ball and I want the first drop of
+ 
+
+ align:start position:0%
+second ball and I want the first drop of
+the second ball all right
+
+ align:start position:0%
+the second ball all right
+ 
+
+ align:start position:0%
+the second ball all right
+and I I want to look at this I want to
+
+ align:start position:0%
+and I I want to look at this I want to
+ 
+
+ align:start position:0%
+and I I want to look at this I want to
+look at this interval and it has to be
+
+ align:start position:0%
+look at this interval and it has to be
+ 
+
+ align:start position:0%
+look at this interval and it has to be
+we're inside this interval but it's not
+
+ align:start position:0%
+we're inside this interval but it's not
+ 
+
+ align:start position:0%
+we're inside this interval but it's not
+going to be I'm not I'm not gonna drop
+
+ align:start position:0%
+going to be I'm not I'm not gonna drop
+ 
+
+ align:start position:0%
+going to be I'm not I'm not gonna drop
+this at this floor sixty-five or one
+
+ align:start position:0%
+this at this floor sixty-five or one
+ 
+
+ align:start position:0%
+this at this floor sixty-five or one
+three three three I want to I want to
+
+ align:start position:0%
+three three three I want to I want to
+ 
+
+ align:start position:0%
+three three three I want to I want to
+pick something in between right and so
+
+ align:start position:0%
+pick something in between right and so
+ 
+
+ align:start position:0%
+pick something in between right and so
+now looking at this
+
+ align:start position:0%
+now looking at this
+ 
+
+ align:start position:0%
+now looking at this
+tell me according to what you know so
+
+ align:start position:0%
+tell me according to what you know so
+ 
+
+ align:start position:0%
+tell me according to what you know so
+far where do you think I should drop the
+
+ align:start position:0%
+far where do you think I should drop the
+ 
+
+ align:start position:0%
+far where do you think I should drop the
+second ball for the first time go ahead
+
+ align:start position:0%
+second ball for the first time go ahead
+ 
+
+ align:start position:0%
+second ball for the first time go ahead
+96 and how did you get that you and you
+
+ align:start position:0%
+96 and how did you get that you and you
+ 
+
+ align:start position:0%
+96 and how did you get that you and you
+put one one zero zero perfect
+
+ align:start position:0%
+put one one zero zero perfect
+ 
+
+ align:start position:0%
+put one one zero zero perfect
+what's your name Evan so Evan says 96 I
+
+ align:start position:0%
+what's your name Evan so Evan says 96 I
+ 
+
+ align:start position:0%
+what's your name Evan so Evan says 96 I
+guess he thinks in decimal you know
+
+ align:start position:0%
+guess he thinks in decimal you know
+ 
+
+ align:start position:0%
+guess he thinks in decimal you know
+naturally like most of us but the the
+
+ align:start position:0%
+naturally like most of us but the the
+ 
+
+ align:start position:0%
+naturally like most of us but the the
+way you would code this by the way is by
+
+ align:start position:0%
+way you would code this by the way is by
+ 
+
+ align:start position:0%
+way you would code this by the way is by
+incrementing this digit okay and you'd
+
+ align:start position:0%
+incrementing this digit okay and you'd
+ 
+
+ align:start position:0%
+incrementing this digit okay and you'd
+get one one zero one one zero zero and
+
+ align:start position:0%
+get one one zero one one zero zero and
+ 
+
+ align:start position:0%
+get one one zero one one zero zero and
+in this case let's say it does not break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I where you go Evan yeah after 96
+
+ align:start position:0%
+then I where you go Evan yeah after 96
+ 
+
+ align:start position:0%
+then I where you go Evan yeah after 96
+it doesn't break what would you do well
+
+ align:start position:0%
+it doesn't break what would you do well
+ 
+
+ align:start position:0%
+it doesn't break what would you do well
+it's in now in and in this
+
+ align:start position:0%
+it's in now in and in this
+ 
+
+ align:start position:0%
+it's in now in and in this
+representation they did an easy it
+
+ align:start position:0%
+representation they did an easy it
+ 
+
+ align:start position:0%
+representation they did an easy it
+whatever is easier for you perfect one
+
+ align:start position:0%
+whatever is easier for you perfect one
+ 
+
+ align:start position:0%
+whatever is easier for you perfect one
+to zero zero which happens to be I think
+
+ align:start position:0%
+to zero zero which happens to be I think
+ 
+
+ align:start position:0%
+to zero zero which happens to be I think
+112 so you go to floor 112 this was 96
+
+ align:start position:0%
+112 so you go to floor 112 this was 96
+ 
+
+ align:start position:0%
+112 so you go to floor 112 this was 96
+all right and then you need to add
+
+ align:start position:0%
+all right and then you need to add
+ 
+
+ align:start position:0%
+all right and then you need to add
+another 16 to that yep 112 and so on
+
+ align:start position:0%
+another 16 to that yep 112 and so on
+ 
+
+ align:start position:0%
+another 16 to that yep 112 and so on
+right so I want I won't bore you with
+
+ align:start position:0%
+right so I want I won't bore you with
+ 
+
+ align:start position:0%
+right so I want I won't bore you with
+this you get a sense of what's what's
+
+ align:start position:0%
+this you get a sense of what's what's
+ 
+
+ align:start position:0%
+this you get a sense of what's what's
+going on here and obviously with these
+
+ align:start position:0%
+going on here and obviously with these
+ 
+
+ align:start position:0%
+going on here and obviously with these
+things you can wave your hands and you
+
+ align:start position:0%
+things you can wave your hands and you
+ 
+
+ align:start position:0%
+things you can wave your hands and you
+get a sense of what's going on but
+
+ align:start position:0%
+get a sense of what's going on but
+ 
+
+ align:start position:0%
+get a sense of what's going on but
+ultimately you know what's great about
+
+ align:start position:0%
+ultimately you know what's great about
+ 
+
+ align:start position:0%
+ultimately you know what's great about
+computer science and programming is
+
+ align:start position:0%
+computer science and programming is
+ 
+
+ align:start position:0%
+computer science and programming is
+there's you got to teach the dumb
+
+ align:start position:0%
+there's you got to teach the dumb
+ 
+
+ align:start position:0%
+there's you got to teach the dumb
+computer to do exactly the right thing
+
+ align:start position:0%
+computer to do exactly the right thing
+ 
+
+ align:start position:0%
+computer to do exactly the right thing
+and there's no two things about it in
+
+ align:start position:0%
+and there's no two things about it in
+ 
+
+ align:start position:0%
+and there's no two things about it in
+terms of you understand this algorithm I
+
+ align:start position:0%
+terms of you understand this algorithm I
+ 
+
+ align:start position:0%
+terms of you understand this algorithm I
+didn't understand this algorithm until I
+
+ align:start position:0%
+didn't understand this algorithm until I
+ 
+
+ align:start position:0%
+didn't understand this algorithm until I
+coded it fully right I mean maybe I
+
+ align:start position:0%
+coded it fully right I mean maybe I
+ 
+
+ align:start position:0%
+coded it fully right I mean maybe I
+still don't understand it considering
+
+ align:start position:0%
+still don't understand it considering
+ 
+
+ align:start position:0%
+still don't understand it considering
+the mistakes I'm making but this is
+
+ align:start position:0%
+the mistakes I'm making but this is
+ 
+
+ align:start position:0%
+the mistakes I'm making but this is
+because I've lost a bunch of gray cells
+
+ align:start position:0%
+because I've lost a bunch of gray cells
+ 
+
+ align:start position:0%
+because I've lost a bunch of gray cells
+so so let me let me show you what the
+
+ align:start position:0%
+so so let me let me show you what the
+ 
+
+ align:start position:0%
+so so let me let me show you what the
+code looks like it's 15 lines of code
+
+ align:start position:0%
+code looks like it's 15 lines of code
+ 
+
+ align:start position:0%
+code looks like it's 15 lines of code
+right it's not that much and as you can
+
+ align:start position:0%
+right it's not that much and as you can
+ 
+
+ align:start position:0%
+right it's not that much and as you can
+imagine the the the representation is I
+
+ align:start position:0%
+imagine the the the representation is I
+ 
+
+ align:start position:0%
+imagine the the the representation is I
+could have used many things I just used
+
+ align:start position:0%
+could have used many things I just used
+ 
+
+ align:start position:0%
+could have used many things I just used
+a list for each of these digits I'm
+
+ align:start position:0%
+a list for each of these digits I'm
+ 
+
+ align:start position:0%
+a list for each of these digits I'm
+incrementing these these digits and will
+
+ align:start position:0%
+incrementing these these digits and will
+ 
+
+ align:start position:0%
+incrementing these these digits and will
+I want to spend a whole lot of time on
+
+ align:start position:0%
+I want to spend a whole lot of time on
+ 
+
+ align:start position:0%
+I want to spend a whole lot of time on
+the code but what I want to do before we
+
+ align:start position:0%
+the code but what I want to do before we
+ 
+
+ align:start position:0%
+the code but what I want to do before we
+end here is talk about actually let me
+
+ align:start position:0%
+end here is talk about actually let me
+ 
+
+ align:start position:0%
+end here is talk about actually let me
+do that first before we we go to the
+
+ align:start position:0%
+do that first before we we go to the
+ 
+
+ align:start position:0%
+do that first before we we go to the
+code I want to talk about the worst case
+
+ align:start position:0%
+code I want to talk about the worst case
+ 
+
+ align:start position:0%
+code I want to talk about the worst case
+here right because that's all that's
+
+ align:start position:0%
+here right because that's all that's
+ 
+
+ align:start position:0%
+here right because that's all that's
+what this is all about I want to get an
+
+ align:start position:0%
+what this is all about I want to get an
+ 
+
+ align:start position:0%
+what this is all about I want to get an
+equation just like we did for two times
+
+ align:start position:0%
+equation just like we did for two times
+ 
+
+ align:start position:0%
+equation just like we did for two times
+square root of n minus one and all of
+
+ align:start position:0%
+square root of n minus one and all of
+ 
+
+ align:start position:0%
+square root of n minus one and all of
+these different things I want to get an
+
+ align:start position:0%
+these different things I want to get an
+ 
+
+ align:start position:0%
+these different things I want to get an
+equation for the worst case in terms of
+
+ align:start position:0%
+equation for the worst case in terms of
+ 
+
+ align:start position:0%
+equation for the worst case in terms of
+the number of drops in relation to R and
+
+ align:start position:0%
+the number of drops in relation to R and
+ 
+
+ align:start position:0%
+the number of drops in relation to R and
+D which are obviously related to n right
+
+ align:start position:0%
+D which are obviously related to n right
+ 
+
+ align:start position:0%
+D which are obviously related to n right
+because our raise to D has to be greater
+
+ align:start position:0%
+because our raise to D has to be greater
+ 
+
+ align:start position:0%
+because our raise to D has to be greater
+than n right so if you kind of look at
+
+ align:start position:0%
+than n right so if you kind of look at
+ 
+
+ align:start position:0%
+than n right so if you kind of look at
+this and it turns out this is not a
+
+ align:start position:0%
+this and it turns out this is not a
+ 
+
+ align:start position:0%
+this and it turns out this is not a
+difficult analysis right if you if you
+
+ align:start position:0%
+difficult analysis right if you if you
+ 
+
+ align:start position:0%
+difficult analysis right if you if you
+think if you think about it and you
+
+ align:start position:0%
+think if you think about it and you
+ 
+
+ align:start position:0%
+think if you think about it and you
+start thinking about worst case and you
+
+ align:start position:0%
+start thinking about worst case and you
+ 
+
+ align:start position:0%
+start thinking about worst case and you
+think about how we are incrementing
+
+ align:start position:0%
+think about how we are incrementing
+ 
+
+ align:start position:0%
+think about how we are incrementing
+these things um these phases and if you
+
+ align:start position:0%
+these things um these phases and if you
+ 
+
+ align:start position:0%
+these things um these phases and if you
+can think about a phase as as when a
+
+ align:start position:0%
+can think about a phase as as when a
+ 
+
+ align:start position:0%
+can think about a phase as as when a
+better ball breaks you know that's when
+
+ align:start position:0%
+better ball breaks you know that's when
+ 
+
+ align:start position:0%
+better ball breaks you know that's when
+a phase is done and you move to the
+
+ align:start position:0%
+a phase is done and you move to the
+ 
+
+ align:start position:0%
+a phase is done and you move to the
+second phase right tell me I what how
+
+ align:start position:0%
+second phase right tell me I what how
+ 
+
+ align:start position:0%
+second phase right tell me I what how
+many drops I have you break break it up
+
+ align:start position:0%
+many drops I have you break break it up
+ 
+
+ align:start position:0%
+many drops I have you break break it up
+in terms of the number of phases right
+
+ align:start position:0%
+in terms of the number of phases right
+ 
+
+ align:start position:0%
+in terms of the number of phases right
+or the number of balls whichever way you
+
+ align:start position:0%
+or the number of balls whichever way you
+ 
+
+ align:start position:0%
+or the number of balls whichever way you
+want to think about it and use the same
+
+ align:start position:0%
+want to think about it and use the same
+ 
+
+ align:start position:0%
+want to think about it and use the same
+kind of worst-case analysis we've done
+
+ align:start position:0%
+kind of worst-case analysis we've done
+ 
+
+ align:start position:0%
+kind of worst-case analysis we've done
+with respect to what happens what
+
+ align:start position:0%
+with respect to what happens what
+ 
+
+ align:start position:0%
+with respect to what happens what
+happens in the in the worst case you
+
+ align:start position:0%
+happens in the in the worst case you
+ 
+
+ align:start position:0%
+happens in the in the worst case you
+have to keep you know doing a bunch of
+
+ align:start position:0%
+have to keep you know doing a bunch of
+ 
+
+ align:start position:0%
+have to keep you know doing a bunch of
+drops and in really for these algorithms
+
+ align:start position:0%
+drops and in really for these algorithms
+ 
+
+ align:start position:0%
+drops and in really for these algorithms
+the floor 127 the hardness coefficient
+
+ align:start position:0%
+the floor 127 the hardness coefficient
+ 
+
+ align:start position:0%
+the floor 127 the hardness coefficient
+of of actually the hardness coefficient
+
+ align:start position:0%
+of of actually the hardness coefficient
+ 
+
+ align:start position:0%
+of of actually the hardness coefficient
+of 127 was is this the hard one right
+
+ align:start position:0%
+of 127 was is this the hard one right
+ 
+
+ align:start position:0%
+of 127 was is this the hard one right
+it's it's a difficult one because you
+
+ align:start position:0%
+it's it's a difficult one because you
+ 
+
+ align:start position:0%
+it's it's a difficult one because you
+kind of go through and you go all the
+
+ align:start position:0%
+kind of go through and you go all the
+ 
+
+ align:start position:0%
+kind of go through and you go all the
+way there and you do all of these things
+
+ align:start position:0%
+way there and you do all of these things
+ 
+
+ align:start position:0%
+way there and you do all of these things
+before you drop a ball a lot of times
+
+ align:start position:0%
+before you drop a ball a lot of times
+ 
+
+ align:start position:0%
+before you drop a ball a lot of times
+before it breaks and you do that for
+
+ align:start position:0%
+before it breaks and you do that for
+ 
+
+ align:start position:0%
+before it breaks and you do that for
+every ball right that would be the worst
+
+ align:start position:0%
+every ball right that would be the worst
+ 
+
+ align:start position:0%
+every ball right that would be the worst
+case right so that's kind of where
+
+ align:start position:0%
+case right so that's kind of where
+ 
+
+ align:start position:0%
+case right so that's kind of where
+things are at so from a symbolic
+
+ align:start position:0%
+things are at so from a symbolic
+ 
+
+ align:start position:0%
+things are at so from a symbolic
+standpoint what is the worst case in the
+
+ align:start position:0%
+standpoint what is the worst case in the
+ 
+
+ align:start position:0%
+standpoint what is the worst case in the
+first phase in terms of the number of
+
+ align:start position:0%
+first phase in terms of the number of
+ 
+
+ align:start position:0%
+first phase in terms of the number of
+of the first ball from a symbolic
+
+ align:start position:0%
+of the first ball from a symbolic
+ 
+
+ align:start position:0%
+of the first ball from a symbolic
+standpoint right it's the first digit
+
+ align:start position:0%
+standpoint right it's the first digit
+ 
+
+ align:start position:0%
+standpoint right it's the first digit
+I'm talking about it's the first ball
+
+ align:start position:0%
+I'm talking about it's the first ball
+ 
+
+ align:start position:0%
+I'm talking about it's the first ball
+I'm talking about and I'm dropping this
+
+ align:start position:0%
+I'm talking about and I'm dropping this
+ 
+
+ align:start position:0%
+I'm talking about and I'm dropping this
+ball as you can see at these different
+
+ align:start position:0%
+ball as you can see at these different
+ 
+
+ align:start position:0%
+ball as you can see at these different
+points so in general how many drops
+
+ align:start position:0%
+points so in general how many drops
+ 
+
+ align:start position:0%
+points so in general how many drops
+would I have
+
+ align:start position:0%
+would I have
+ 
+
+ align:start position:0%
+would I have
+Minoo either I may be done completely
+
+ align:start position:0%
+Minoo either I may be done completely
+ 
+
+ align:start position:0%
+Minoo either I may be done completely
+because it I know it doesn't break it
+
+ align:start position:0%
+because it I know it doesn't break it
+ 
+
+ align:start position:0%
+because it I know it doesn't break it
+floor 128 or what I have you but what is
+
+ align:start position:0%
+floor 128 or what I have you but what is
+ 
+
+ align:start position:0%
+floor 128 or what I have you but what is
+what is the worst case when that ball
+
+ align:start position:0%
+what is the worst case when that ball
+ 
+
+ align:start position:0%
+what is the worst case when that ball
+breaks give me an equation someone
+
+ align:start position:0%
+breaks give me an equation someone
+ 
+
+ align:start position:0%
+breaks give me an equation someone
+what's so I drop it once I drop it twice
+
+ align:start position:0%
+what's so I drop it once I drop it twice
+ 
+
+ align:start position:0%
+what's so I drop it once I drop it twice
+and I am I going to drop it like like if
+
+ align:start position:0%
+and I am I going to drop it like like if
+ 
+
+ align:start position:0%
+and I am I going to drop it like like if
+R is five am I gonna drop it ten times
+
+ align:start position:0%
+R is five am I gonna drop it ten times
+ 
+
+ align:start position:0%
+R is five am I gonna drop it ten times
+I'm what am i doing in terms of the what
+
+ align:start position:0%
+I'm what am i doing in terms of the what
+ 
+
+ align:start position:0%
+I'm what am i doing in terms of the what
+is the upper limit in terms of this this
+
+ align:start position:0%
+is the upper limit in terms of this this
+ 
+
+ align:start position:0%
+is the upper limit in terms of this this
+digit our minus one and where am i
+
+ align:start position:0%
+digit our minus one and where am i
+ 
+
+ align:start position:0%
+digit our minus one and where am i
+starting from one right so there you go
+
+ align:start position:0%
+starting from one right so there you go
+ 
+
+ align:start position:0%
+starting from one right so there you go
+what's enough course answer our minus 1
+
+ align:start position:0%
+what's enough course answer our minus 1
+ 
+
+ align:start position:0%
+what's enough course answer our minus 1
+right so that's it so it turns out that
+
+ align:start position:0%
+right so that's it so it turns out that
+ 
+
+ align:start position:0%
+right so that's it so it turns out that
+I have R minus 1 drops in the worst case
+
+ align:start position:0%
+I have R minus 1 drops in the worst case
+ 
+
+ align:start position:0%
+I have R minus 1 drops in the worst case
+for the first ball and I mean it's a
+
+ align:start position:0%
+for the first ball and I mean it's a
+ 
+
+ align:start position:0%
+for the first ball and I mean it's a
+same representation every digit is the
+
+ align:start position:0%
+same representation every digit is the
+ 
+
+ align:start position:0%
+same representation every digit is the
+same radix obviously right and now that
+
+ align:start position:0%
+same radix obviously right and now that
+ 
+
+ align:start position:0%
+same radix obviously right and now that
+that ball broke and I moved to that to
+
+ align:start position:0%
+that ball broke and I moved to that to
+ 
+
+ align:start position:0%
+that ball broke and I moved to that to
+the second digit with the second ball
+
+ align:start position:0%
+the second digit with the second ball
+ 
+
+ align:start position:0%
+the second digit with the second ball
+and I'm gonna start again and in the
+
+ align:start position:0%
+and I'm gonna start again and in the
+ 
+
+ align:start position:0%
+and I'm gonna start again and in the
+worst case I could have R minus 1 drops
+
+ align:start position:0%
+worst case I could have R minus 1 drops
+ 
+
+ align:start position:0%
+worst case I could have R minus 1 drops
+with that as well right because I'm
+
+ align:start position:0%
+with that as well right because I'm
+ 
+
+ align:start position:0%
+with that as well right because I'm
+gonna go increment from 0 the first one
+
+ align:start position:0%
+gonna go increment from 0 the first one
+ 
+
+ align:start position:0%
+gonna go increment from 0 the first one
+I'm going to do is a 1 and then I'm
+
+ align:start position:0%
+I'm going to do is a 1 and then I'm
+ 
+
+ align:start position:0%
+I'm going to do is a 1 and then I'm
+gonna do a two and all the way to R
+
+ align:start position:0%
+gonna do a two and all the way to R
+ 
+
+ align:start position:0%
+gonna do a two and all the way to R
+minus 1 right so our minus 1 drops for
+
+ align:start position:0%
+minus 1 right so our minus 1 drops for
+ 
+
+ align:start position:0%
+minus 1 right so our minus 1 drops for
+the second ball and then I go all the
+
+ align:start position:0%
+the second ball and then I go all the
+ 
+
+ align:start position:0%
+the second ball and then I go all the
+way to D balls so so my answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah go ahead yes you're absolutely
+
+ align:start position:0%
+yeah go ahead yes you're absolutely
+ 
+
+ align:start position:0%
+yeah go ahead yes you're absolutely
+right that but if the if the number were
+
+ align:start position:0%
+right that but if the if the number were
+ 
+
+ align:start position:0%
+right that but if the if the number were
+255 so one of the things that's
+
+ align:start position:0%
+255 so one of the things that's
+ 
+
+ align:start position:0%
+255 so one of the things that's
+happening here is we have lost some
+
+ align:start position:0%
+happening here is we have lost some
+ 
+
+ align:start position:0%
+happening here is we have lost some
+precision because our raise to D needed
+
+ align:start position:0%
+precision because our raise to D needed
+ 
+
+ align:start position:0%
+precision because our raise to D needed
+to be this large number of 255 and this
+
+ align:start position:0%
+to be this large number of 255 and this
+ 
+
+ align:start position:0%
+to be this large number of 255 and this
+algorithm is actually going to work for
+
+ align:start position:0%
+algorithm is actually going to work for
+ 
+
+ align:start position:0%
+algorithm is actually going to work for
+255 floors all right
+
+ align:start position:0%
+255 floors all right
+ 
+
+ align:start position:0%
+255 floors all right
+yeah because of em so so so it's not
+
+ align:start position:0%
+yeah because of em so so so it's not
+ 
+
+ align:start position:0%
+yeah because of em so so so it's not
+yeah so that's kind of you know the it's
+
+ align:start position:0%
+yeah so that's kind of you know the it's
+ 
+
+ align:start position:0%
+yeah so that's kind of you know the it's
+a good question you asked but
+
+ align:start position:0%
+a good question you asked but
+ 
+
+ align:start position:0%
+a good question you asked but
+unfortunately you kind of want to choose
+
+ align:start position:0%
+unfortunately you kind of want to choose
+ 
+
+ align:start position:0%
+unfortunately you kind of want to choose
+a case where you you have perfect
+
+ align:start position:0%
+a case where you you have perfect
+ 
+
+ align:start position:0%
+a case where you you have perfect
+precision in terms of R raised to D is
+
+ align:start position:0%
+precision in terms of R raised to D is
+ 
+
+ align:start position:0%
+precision in terms of R raised to D is
+exactly what you need it to be and in
+
+ align:start position:0%
+exactly what you need it to be and in
+ 
+
+ align:start position:0%
+exactly what you need it to be and in
+that case this analysis works right yeah
+
+ align:start position:0%
+that case this analysis works right yeah
+ 
+
+ align:start position:0%
+that case this analysis works right yeah
+that's the max n that does exactly right
+
+ align:start position:0%
+that's the max n that does exactly right
+ 
+
+ align:start position:0%
+that's the max n that does exactly right
+so I mean 255 is substantially larger
+
+ align:start position:0%
+so I mean 255 is substantially larger
+ 
+
+ align:start position:0%
+so I mean 255 is substantially larger
+than 128 so it kind of makes sense that
+
+ align:start position:0%
+than 128 so it kind of makes sense that
+ 
+
+ align:start position:0%
+than 128 so it kind of makes sense that
+that as you said that you would be able
+
+ align:start position:0%
+that as you said that you would be able
+ 
+
+ align:start position:0%
+that as you said that you would be able
+to shave off certain things right and so
+
+ align:start position:0%
+to shave off certain things right and so
+ 
+
+ align:start position:0%
+to shave off certain things right and so
+you can kind of do that but it's a
+
+ align:start position:0%
+you can kind of do that but it's a
+ 
+
+ align:start position:0%
+you can kind of do that but it's a
+little more involved but I think the the
+
+ align:start position:0%
+little more involved but I think the the
+ 
+
+ align:start position:0%
+little more involved but I think the the
+intuition is important and the intuition
+
+ align:start position:0%
+intuition is important and the intuition
+ 
+
+ align:start position:0%
+intuition is important and the intuition
+is simply that your worst case number of
+
+ align:start position:0%
+is simply that your worst case number of
+ 
+
+ align:start position:0%
+is simply that your worst case number of
+drops assuming you're being a little bit
+
+ align:start position:0%
+drops assuming you're being a little bit
+ 
+
+ align:start position:0%
+drops assuming you're being a little bit
+imprecise would simply be R minus 1
+
+ align:start position:0%
+imprecise would simply be R minus 1
+ 
+
+ align:start position:0%
+imprecise would simply be R minus 1
+times D in the in the worst case and
+
+ align:start position:0%
+times D in the in the worst case and
+ 
+
+ align:start position:0%
+times D in the in the worst case and
+this would be true for all n which is
+
+ align:start position:0%
+this would be true for all n which is
+ 
+
+ align:start position:0%
+this would be true for all n which is
+less than R raised to D you know for all
+
+ align:start position:0%
+less than R raised to D you know for all
+ 
+
+ align:start position:0%
+less than R raised to D you know for all
+n all right so it's a so now just in
+
+ align:start position:0%
+n all right so it's a so now just in
+ 
+
+ align:start position:0%
+n all right so it's a so now just in
+terms of numbers I had R equals 4 and D
+
+ align:start position:0%
+terms of numbers I had R equals 4 and D
+ 
+
+ align:start position:0%
+terms of numbers I had R equals 4 and D
+equals 4 and so you end up getting 12
+
+ align:start position:0%
+equals 4 and so you end up getting 12
+ 
+
+ align:start position:0%
+equals 4 and so you end up getting 12
+drops for the 128th case all the way do
+
+ align:start position:0%
+drops for the 128th case all the way do
+ 
+
+ align:start position:0%
+drops for the 128th case all the way do
+you know 255 as well
+
+ align:start position:0%
+you know 255 as well
+ 
+
+ align:start position:0%
+you know 255 as well
+you need you need 12 drops in the worst
+
+ align:start position:0%
+you need you need 12 drops in the worst
+ 
+
+ align:start position:0%
+you need you need 12 drops in the worst
+case even for 255 floors right which
+
+ align:start position:0%
+case even for 255 floors right which
+ 
+
+ align:start position:0%
+case even for 255 floors right which
+which is really what you were asking
+
+ align:start position:0%
+which is really what you were asking
+ 
+
+ align:start position:0%
+which is really what you were asking
+right so good all right that makes sense
+
+ align:start position:0%
+right so good all right that makes sense
+ 
+
+ align:start position:0%
+right so good all right that makes sense
+yeah so I'm not gonna spend a whole lot
+
+ align:start position:0%
+yeah so I'm not gonna spend a whole lot
+ 
+
+ align:start position:0%
+yeah so I'm not gonna spend a whole lot
+of time on this code but that's it
+
+ align:start position:0%
+of time on this code but that's it
+ 
+
+ align:start position:0%
+of time on this code but that's it
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+converting I could have used a Python
+
+ align:start position:0%
+converting I could have used a Python
+ 
+
+ align:start position:0%
+converting I could have used a Python
+library function for that but that's
+
+ align:start position:0%
+library function for that but that's
+ 
+
+ align:start position:0%
+library function for that but that's
+simply a conversion because I wanted to
+
+ align:start position:0%
+simply a conversion because I wanted to
+ 
+
+ align:start position:0%
+simply a conversion because I wanted to
+print things out I don't even need that
+
+ align:start position:0%
+print things out I don't even need that
+ 
+
+ align:start position:0%
+print things out I don't even need that
+this particular subroutine which is
+
+ align:start position:0%
+this particular subroutine which is
+ 
+
+ align:start position:0%
+this particular subroutine which is
+essentially something that is doing
+
+ align:start position:0%
+essentially something that is doing
+ 
+
+ align:start position:0%
+essentially something that is doing
+conversion from a decimal to do to our
+
+ align:start position:0%
+conversion from a decimal to do to our
+ 
+
+ align:start position:0%
+conversion from a decimal to do to our
+arithmetic and as you can see you see a
+
+ align:start position:0%
+arithmetic and as you can see you see a
+ 
+
+ align:start position:0%
+arithmetic and as you can see you see a
+subtract in and and adding the the the
+
+ align:start position:0%
+subtract in and and adding the the the
+ 
+
+ align:start position:0%
+subtract in and and adding the the the
+adding is is the incrementation that I
+
+ align:start position:0%
+adding is is the incrementation that I
+ 
+
+ align:start position:0%
+adding is is the incrementation that I
+just erased but you do see it up there
+
+ align:start position:0%
+just erased but you do see it up there
+ 
+
+ align:start position:0%
+just erased but you do see it up there
+from 1 0 to 2 0 that's why you add
+
+ align:start position:0%
+from 1 0 to 2 0 that's why you add
+ 
+
+ align:start position:0%
+from 1 0 to 2 0 that's why you add
+sometimes you need to subtract because
+
+ align:start position:0%
+sometimes you need to subtract because
+ 
+
+ align:start position:0%
+sometimes you need to subtract because
+things break and when things break you
+
+ align:start position:0%
+things break and when things break you
+ 
+
+ align:start position:0%
+things break and when things break you
+you need to go back to the to the
+
+ align:start position:0%
+you need to go back to the to the
+ 
+
+ align:start position:0%
+you need to go back to the to the
+highest floor where the ball didn't
+
+ align:start position:0%
+highest floor where the ball didn't
+ 
+
+ align:start position:0%
+highest floor where the ball didn't
+break right so that's where you you you
+
+ align:start position:0%
+break right so that's where you you you
+ 
+
+ align:start position:0%
+break right so that's where you you you
+have you do the subtraction and so this
+
+ align:start position:0%
+have you do the subtraction and so this
+ 
+
+ align:start position:0%
+have you do the subtraction and so this
+is how if you ran this this it's not the
+
+ align:start position:0%
+is how if you ran this this it's not the
+ 
+
+ align:start position:0%
+is how if you ran this this it's not the
+greatest user user interface I'll admit
+
+ align:start position:0%
+greatest user user interface I'll admit
+ 
+
+ align:start position:0%
+greatest user user interface I'll admit
+but that's not the point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm gonna do 128 and 4 which is our
+
+ align:start position:0%
+so I'm gonna do 128 and 4 which is our
+ 
+
+ align:start position:0%
+so I'm gonna do 128 and 4 which is our
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+and he says radix shows in his ball 4
+
+ align:start position:0%
+and he says radix shows in his ball 4
+ 
+
+ align:start position:0%
+and he says radix shows in his ball 4
+did the ball break I say no and then I
+
+ align:start position:0%
+did the ball break I say no and then I
+ 
+
+ align:start position:0%
+did the ball break I say no and then I
+you know did they drop the ball did the
+
+ align:start position:0%
+you know did they drop the ball did the
+ 
+
+ align:start position:0%
+you know did they drop the ball did the
+ball break if I say no here then I'm
+
+ align:start position:0%
+ball break if I say no here then I'm
+ 
+
+ align:start position:0%
+ball break if I say no here then I'm
+done right so I'm gonna go ahead and say
+
+ align:start position:0%
+done right so I'm gonna go ahead and say
+ 
+
+ align:start position:0%
+done right so I'm gonna go ahead and say
+yes and then I'm gonna say no and then
+
+ align:start position:0%
+yes and then I'm gonna say no and then
+ 
+
+ align:start position:0%
+yes and then I'm gonna say no and then
+no I'm gonna keep going no no no because
+
+ align:start position:0%
+no I'm gonna keep going no no no because
+ 
+
+ align:start position:0%
+no I'm gonna keep going no no no because
+this is the worst case and I got 11
+
+ align:start position:0%
+this is the worst case and I got 11
+ 
+
+ align:start position:0%
+this is the worst case and I got 11
+right in this case so you do get closed
+
+ align:start position:0%
+right in this case so you do get closed
+ 
+
+ align:start position:0%
+right in this case so you do get closed
+in in the sense that grata was asking
+
+ align:start position:0%
+in in the sense that grata was asking
+ 
+
+ align:start position:0%
+in in the sense that grata was asking
+you know could you shave off you only
+
+ align:start position:0%
+you know could you shave off you only
+ 
+
+ align:start position:0%
+you know could you shave off you only
+shaved off one because of the
+
+ align:start position:0%
+shaved off one because of the
+ 
+
+ align:start position:0%
+shaved off one because of the
+imprecision so there is a case where
+
+ align:start position:0%
+imprecision so there is a case where
+ 
+
+ align:start position:0%
+imprecision so there is a case where
+even though you would only get 12 for
+
+ align:start position:0%
+even though you would only get 12 for
+ 
+
+ align:start position:0%
+even though you would only get 12 for
+255 but you do get 11 for 128 okay all
+
+ align:start position:0%
+255 but you do get 11 for 128 okay all
+ 
+
+ align:start position:0%
+255 but you do get 11 for 128 okay all
+right cool
+
+ align:start position:0%
+right cool
+ 
+
+ align:start position:0%
+right cool
+good so I'll let you look at the code if
+
+ align:start position:0%
+good so I'll let you look at the code if
+ 
+
+ align:start position:0%
+good so I'll let you look at the code if
+you guys can again can leave anytime you
+
+ align:start position:0%
+you guys can again can leave anytime you
+ 
+
+ align:start position:0%
+you guys can again can leave anytime you
+want I just wanted to mention I want to
+
+ align:start position:0%
+want I just wanted to mention I want to
+ 
+
+ align:start position:0%
+want I just wanted to mention I want to
+go back to the one thing that I didn't
+
+ align:start position:0%
+go back to the one thing that I didn't
+ 
+
+ align:start position:0%
+go back to the one thing that I didn't
+get that I mentioned but I haven't
+
+ align:start position:0%
+get that I mentioned but I haven't
+ 
+
+ align:start position:0%
+get that I mentioned but I haven't
+gotten to which is this is still you can
+
+ align:start position:0%
+gotten to which is this is still you can
+ 
+
+ align:start position:0%
+gotten to which is this is still you can
+still do better right you can still do
+
+ align:start position:0%
+still do better right you can still do
+ 
+
+ align:start position:0%
+still do better right you can still do
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+not because of what guna Tara mentioned
+
+ align:start position:0%
+not because of what guna Tara mentioned
+ 
+
+ align:start position:0%
+not because of what guna Tara mentioned
+you know that's just that imprecision
+
+ align:start position:0%
+you know that's just that imprecision
+ 
+
+ align:start position:0%
+you know that's just that imprecision
+thing but assuming even that was taken
+
+ align:start position:0%
+thing but assuming even that was taken
+ 
+
+ align:start position:0%
+thing but assuming even that was taken
+care of because the numbers worked out
+
+ align:start position:0%
+care of because the numbers worked out
+ 
+
+ align:start position:0%
+care of because the numbers worked out
+you can do better because K can be made
+
+ align:start position:0%
+you can do better because K can be made
+ 
+
+ align:start position:0%
+you can do better because K can be made
+different you could do unequal intervals
+
+ align:start position:0%
+different you could do unequal intervals
+ 
+
+ align:start position:0%
+different you could do unequal intervals
+right so let me put that into the in the
+
+ align:start position:0%
+right so let me put that into the in the
+ 
+
+ align:start position:0%
+right so let me put that into the in the
+notes and you can read it by yourself
+
+ align:start position:0%
+notes and you can read it by yourself
+ 
+
+ align:start position:0%
+notes and you can read it by yourself
+you had a question not even start asking
+
+ align:start position:0%
+you had a question not even start asking
+ 
+
+ align:start position:0%
+you had a question not even start asking
+you or why did I start telling you where
+
+ align:start position:0%
+you or why did I start telling you where
+ 
+
+ align:start position:0%
+you or why did I start telling you where
+like put a next ball drop because it
+
+ align:start position:0%
+like put a next ball drop because it
+ 
+
+ align:start position:0%
+like put a next ball drop because it
+went one two and
+
+ align:start position:0%
+went one two and
+ 
+
+ align:start position:0%
+went one two and
+and went also to ball three and ball
+
+ align:start position:0%
+and went also to ball three and ball
+ 
+
+ align:start position:0%
+and went also to ball three and ball
+four I'm gonna just state ball - that's
+
+ align:start position:0%
+four I'm gonna just state ball - that's
+ 
+
+ align:start position:0%
+four I'm gonna just state ball - that's
+that's because I'm lazy yeah
+
+ align:start position:0%
+that's because I'm lazy yeah
+ 
+
+ align:start position:0%
+that's because I'm lazy yeah
+so it'd be a fine exercise to fix that I
+
+ align:start position:0%
+so it'd be a fine exercise to fix that I
+ 
+
+ align:start position:0%
+so it'd be a fine exercise to fix that I
+mean it's not one of the it's not one of
+
+ align:start position:0%
+mean it's not one of the it's not one of
+ 
+
+ align:start position:0%
+mean it's not one of the it's not one of
+the exercises that's how you turn you
+
+ align:start position:0%
+the exercises that's how you turn you
+ 
+
+ align:start position:0%
+the exercises that's how you turn you
+know after 30 years of teaching whenever
+
+ align:start position:0%
+know after 30 years of teaching whenever
+ 
+
+ align:start position:0%
+know after 30 years of teaching whenever
+I get a question I turn it into an
+
+ align:start position:0%
+I get a question I turn it into an
+ 
+
+ align:start position:0%
+I get a question I turn it into an
+opportunity you know for homework okay
+
+ align:start position:0%
+opportunity you know for homework okay
+ 
+
+ align:start position:0%
+opportunity you know for homework okay
+all right that's how it works
+
+ align:start position:0%
+all right that's how it works
+ 
+
+ align:start position:0%
+all right that's how it works
+all right good see you guys next time
\ No newline at end of file
diff --git a/FqiB9tmtdSc.txt b/FqiB9tmtdSc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b04b460fa5521c154b90453faf32fd91738558be
--- /dev/null
+++ b/FqiB9tmtdSc.txt
@@ -0,0 +1,1219 @@
+align:start position:0%
+ 
+preprocessing the data can be difficult
+
+ align:start position:0%
+preprocessing the data can be difficult
+ 
+
+ align:start position:0%
+preprocessing the data can be difficult
+but luckily ours packages provide
+
+ align:start position:0%
+but luckily ours packages provide
+ 
+
+ align:start position:0%
+but luckily ours packages provide
+easy-to-use functions for the most
+
+ align:start position:0%
+easy-to-use functions for the most
+ 
+
+ align:start position:0%
+easy-to-use functions for the most
+common tasks in this video will load and
+
+ align:start position:0%
+common tasks in this video will load and
+ 
+
+ align:start position:0%
+common tasks in this video will load and
+process our data in our in your our
+
+ align:start position:0%
+process our data in our in your our
+ 
+
+ align:start position:0%
+process our data in our in your our
+console let's load the data set
+
+ align:start position:0%
+console let's load the data set
+ 
+
+ align:start position:0%
+console let's load the data set
+tweets dot csv with the read csv
+
+ align:start position:0%
+tweets dot csv with the read csv
+ 
+
+ align:start position:0%
+tweets dot csv with the read csv
+function but since we're working with
+
+ align:start position:0%
+function but since we're working with
+ 
+
+ align:start position:0%
+function but since we're working with
+text data here we need one extra
+
+ align:start position:0%
+text data here we need one extra
+ 
+
+ align:start position:0%
+text data here we need one extra
+argument which is strings as factors
+
+ align:start position:0%
+argument which is strings as factors
+ 
+
+ align:start position:0%
+argument which is strings as factors
+equals false so we'll call our data set
+
+ align:start position:0%
+equals false so we'll call our data set
+ 
+
+ align:start position:0%
+equals false so we'll call our data set
+tweets and we'll use the read csv
+
+ align:start position:0%
+tweets and we'll use the read csv
+ 
+
+ align:start position:0%
+tweets and we'll use the read csv
+function to read in the data file tweets
+
+ align:start position:0%
+function to read in the data file tweets
+ 
+
+ align:start position:0%
+function to read in the data file tweets
+dot csv but then we'll add the extra
+
+ align:start position:0%
+dot csv but then we'll add the extra
+ 
+
+ align:start position:0%
+dot csv but then we'll add the extra
+argument strings as factors equals false
+
+ align:start position:0%
+argument strings as factors equals false
+ 
+
+ align:start position:0%
+argument strings as factors equals false
+you'll always need to add this extra
+
+ align:start position:0%
+you'll always need to add this extra
+ 
+
+ align:start position:0%
+you'll always need to add this extra
+argument when working on a text
+
+ align:start position:0%
+argument when working on a text
+ 
+
+ align:start position:0%
+argument when working on a text
+analytics problem so that the text is
+
+ align:start position:0%
+analytics problem so that the text is
+ 
+
+ align:start position:0%
+analytics problem so that the text is
+read in properly now let's take a look
+
+ align:start position:0%
+read in properly now let's take a look
+ 
+
+ align:start position:0%
+read in properly now let's take a look
+at the structure of our data with the
+
+ align:start position:0%
+at the structure of our data with the
+ 
+
+ align:start position:0%
+at the structure of our data with the
+STR function we can see that we have one
+
+ align:start position:0%
+STR function we can see that we have one
+ 
+
+ align:start position:0%
+STR function we can see that we have one
+thousand one hundred and eighty-one
+
+ align:start position:0%
+thousand one hundred and eighty-one
+ 
+
+ align:start position:0%
+thousand one hundred and eighty-one
+observations of two variables the text
+
+ align:start position:0%
+observations of two variables the text
+ 
+
+ align:start position:0%
+observations of two variables the text
+of the tweet called tweet and the
+
+ align:start position:0%
+of the tweet called tweet and the
+ 
+
+ align:start position:0%
+of the tweet called tweet and the
+average sentiment score called AVG for
+
+ align:start position:0%
+average sentiment score called AVG for
+ 
+
+ align:start position:0%
+average sentiment score called AVG for
+average the tweet texts are real tweets
+
+ align:start position:0%
+average the tweet texts are real tweets
+ 
+
+ align:start position:0%
+average the tweet texts are real tweets
+that we found on the internet directed
+
+ align:start position:0%
+that we found on the internet directed
+ 
+
+ align:start position:0%
+that we found on the internet directed
+to apple with a few cleaned up words
+
+ align:start position:0%
+to apple with a few cleaned up words
+ 
+
+ align:start position:0%
+to apple with a few cleaned up words
+we're more interested in being able to
+
+ align:start position:0%
+we're more interested in being able to
+ 
+
+ align:start position:0%
+we're more interested in being able to
+detect the tweets with clear negative
+
+ align:start position:0%
+detect the tweets with clear negative
+ 
+
+ align:start position:0%
+detect the tweets with clear negative
+sentiment so let's define a new variable
+
+ align:start position:0%
+sentiment so let's define a new variable
+ 
+
+ align:start position:0%
+sentiment so let's define a new variable
+in our data set tweets called negative
+
+ align:start position:0%
+in our data set tweets called negative
+ 
+
+ align:start position:0%
+in our data set tweets called negative
+and we'll set this equal to AZ dot
+
+ align:start position:0%
+and we'll set this equal to AZ dot
+ 
+
+ align:start position:0%
+and we'll set this equal to AZ dot
+factor tweets dollar sign AVG for
+
+ align:start position:0%
+factor tweets dollar sign AVG for
+ 
+
+ align:start position:0%
+factor tweets dollar sign AVG for
+average less than or equal to negative
+
+ align:start position:0%
+average less than or equal to negative
+ 
+
+ align:start position:0%
+average less than or equal to negative
+one this will set tweets negative equal
+
+ align:start position:0%
+one this will set tweets negative equal
+ 
+
+ align:start position:0%
+one this will set tweets negative equal
+to true if the average sentiment score
+
+ align:start position:0%
+to true if the average sentiment score
+ 
+
+ align:start position:0%
+to true if the average sentiment score
+is less than or equal to negative one
+
+ align:start position:0%
+is less than or equal to negative one
+ 
+
+ align:start position:0%
+is less than or equal to negative one
+and we'll set tweets negative equal to
+
+ align:start position:0%
+and we'll set tweets negative equal to
+ 
+
+ align:start position:0%
+and we'll set tweets negative equal to
+false if the average sentiment score is
+
+ align:start position:0%
+false if the average sentiment score is
+ 
+
+ align:start position:0%
+false if the average sentiment score is
+greater than negative one let's look at
+
+ align:start position:0%
+greater than negative one let's look at
+ 
+
+ align:start position:0%
+greater than negative one let's look at
+a table of this new variable negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can see that 182 of the 1181 tweets
+
+ align:start position:0%
+we can see that 182 of the 1181 tweets
+ 
+
+ align:start position:0%
+we can see that 182 of the 1181 tweets
+or about 15% are negative now to
+
+ align:start position:0%
+or about 15% are negative now to
+ 
+
+ align:start position:0%
+or about 15% are negative now to
+pre-process our text a test that we can
+
+ align:start position:0%
+pre-process our text a test that we can
+ 
+
+ align:start position:0%
+pre-process our text a test that we can
+use the bag-of-words approach will be
+
+ align:start position:0%
+use the bag-of-words approach will be
+ 
+
+ align:start position:0%
+use the bag-of-words approach will be
+using the TM text mining package we'll
+
+ align:start position:0%
+using the TM text mining package we'll
+ 
+
+ align:start position:0%
+using the TM text mining package we'll
+need to install and load two packages to
+
+ align:start position:0%
+need to install and load two packages to
+ 
+
+ align:start position:0%
+need to install and load two packages to
+do this first let's install the package
+
+ align:start position:0%
+do this first let's install the package
+ 
+
+ align:start position:0%
+do this first let's install the package
+TM and go ahead and select a Korean Muir
+
+ align:start position:0%
+TM and go ahead and select a Korean Muir
+ 
+
+ align:start position:0%
+TM and go ahead and select a Korean Muir
+near you as soon as that package is done
+
+ align:start position:0%
+near you as soon as that package is done
+ 
+
+ align:start position:0%
+near you as soon as that package is done
+installing in your back at the blinking
+
+ align:start position:0%
+installing in your back at the blinking
+ 
+
+ align:start position:0%
+installing in your back at the blinking
+cursor go ahead and load that package
+
+ align:start position:0%
+cursor go ahead and load that package
+ 
+
+ align:start position:0%
+cursor go ahead and load that package
+with the library command then we also
+
+ align:start position:0%
+with the library command then we also
+ 
+
+ align:start position:0%
+with the library command then we also
+need to install the package snowball see
+
+ align:start position:0%
+need to install the package snowball see
+ 
+
+ align:start position:0%
+need to install the package snowball see
+this package helps us use the TM package
+
+ align:start position:0%
+this package helps us use the TM package
+ 
+
+ align:start position:0%
+this package helps us use the TM package
+and go ahead and load the snowball
+
+ align:start position:0%
+and go ahead and load the snowball
+ 
+
+ align:start position:0%
+and go ahead and load the snowball
+package as well one of the concepts
+
+ align:start position:0%
+package as well one of the concepts
+ 
+
+ align:start position:0%
+package as well one of the concepts
+introduced by the TM package is that of
+
+ align:start position:0%
+introduced by the TM package is that of
+ 
+
+ align:start position:0%
+introduced by the TM package is that of
+a corpus a corpus is a collection of
+
+ align:start position:0%
+a corpus a corpus is a collection of
+ 
+
+ align:start position:0%
+a corpus a corpus is a collection of
+documents we'll need to convert our
+
+ align:start position:0%
+documents we'll need to convert our
+ 
+
+ align:start position:0%
+documents we'll need to convert our
+tweets to a corpus for pre-processing TM
+
+ align:start position:0%
+tweets to a corpus for pre-processing TM
+ 
+
+ align:start position:0%
+tweets to a corpus for pre-processing TM
+can create a corpus in many different
+
+ align:start position:0%
+can create a corpus in many different
+ 
+
+ align:start position:0%
+can create a corpus in many different
+ways but we'll create it from the tweet
+
+ align:start position:0%
+ways but we'll create it from the tweet
+ 
+
+ align:start position:0%
+ways but we'll create it from the tweet
+column of our data frame using two
+
+ align:start position:0%
+column of our data frame using two
+ 
+
+ align:start position:0%
+column of our data frame using two
+functions corpus and vector source we'll
+
+ align:start position:0%
+functions corpus and vector source we'll
+ 
+
+ align:start position:0%
+functions corpus and vector source we'll
+call our corpus corpus and then use the
+
+ align:start position:0%
+call our corpus corpus and then use the
+ 
+
+ align:start position:0%
+call our corpus corpus and then use the
+corpus and the vector source functions
+
+ align:start position:0%
+corpus and the vector source functions
+ 
+
+ align:start position:0%
+corpus and the vector source functions
+calls on our tweets variable of our
+
+ align:start position:0%
+calls on our tweets variable of our
+ 
+
+ align:start position:0%
+calls on our tweets variable of our
+tweets dataset
+
+ align:start position:0%
+tweets dataset
+ 
+
+ align:start position:0%
+tweets dataset
+so that's tweets dollar sign tweet we
+
+ align:start position:0%
+so that's tweets dollar sign tweet we
+ 
+
+ align:start position:0%
+so that's tweets dollar sign tweet we
+can check that this has worked by typing
+
+ align:start position:0%
+can check that this has worked by typing
+ 
+
+ align:start position:0%
+can check that this has worked by typing
+corpus and seeing that our corpus has
+
+ align:start position:0%
+corpus and seeing that our corpus has
+ 
+
+ align:start position:0%
+corpus and seeing that our corpus has
+1181 text documents and we can check
+
+ align:start position:0%
+1181 text documents and we can check
+ 
+
+ align:start position:0%
+1181 text documents and we can check
+that the documents match our tweets by
+
+ align:start position:0%
+that the documents match our tweets by
+ 
+
+ align:start position:0%
+that the documents match our tweets by
+using double brackets so type corpus -
+
+ align:start position:0%
+using double brackets so type corpus -
+ 
+
+ align:start position:0%
+using double brackets so type corpus -
+left square brackets the number one and
+
+ align:start position:0%
+left square brackets the number one and
+ 
+
+ align:start position:0%
+left square brackets the number one and
+two right square brackets this shows us
+
+ align:start position:0%
+two right square brackets this shows us
+ 
+
+ align:start position:0%
+two right square brackets this shows us
+the first tweet in our corpus now we're
+
+ align:start position:0%
+the first tweet in our corpus now we're
+ 
+
+ align:start position:0%
+the first tweet in our corpus now we're
+ready to start pre-processing our data
+
+ align:start position:0%
+ready to start pre-processing our data
+ 
+
+ align:start position:0%
+ready to start pre-processing our data
+pre-processing is easy in TN each
+
+ align:start position:0%
+pre-processing is easy in TN each
+ 
+
+ align:start position:0%
+pre-processing is easy in TN each
+operation
+
+ align:start position:0%
+operation
+ 
+
+ align:start position:0%
+operation
+stemming or removing stop words can be
+
+ align:start position:0%
+stemming or removing stop words can be
+ 
+
+ align:start position:0%
+stemming or removing stop words can be
+done with one line in our where we use
+
+ align:start position:0%
+done with one line in our where we use
+ 
+
+ align:start position:0%
+done with one line in our where we use
+the TM map function let's try it out by
+
+ align:start position:0%
+the TM map function let's try it out by
+ 
+
+ align:start position:0%
+the TM map function let's try it out by
+changing all of the text in our tweets
+
+ align:start position:0%
+changing all of the text in our tweets
+ 
+
+ align:start position:0%
+changing all of the text in our tweets
+to lowercase to do that will replace our
+
+ align:start position:0%
+to lowercase to do that will replace our
+ 
+
+ align:start position:0%
+to lowercase to do that will replace our
+corpus with the output of the TM
+
+ align:start position:0%
+corpus with the output of the TM
+ 
+
+ align:start position:0%
+corpus with the output of the TM
+underscore map function where the first
+
+ align:start position:0%
+underscore map function where the first
+ 
+
+ align:start position:0%
+underscore map function where the first
+argument is the name of our corpus and
+
+ align:start position:0%
+argument is the name of our corpus and
+ 
+
+ align:start position:0%
+argument is the name of our corpus and
+the second argument is what we want to
+
+ align:start position:0%
+the second argument is what we want to
+ 
+
+ align:start position:0%
+the second argument is what we want to
+do in this case - lower - lower is a
+
+ align:start position:0%
+do in this case - lower - lower is a
+ 
+
+ align:start position:0%
+do in this case - lower - lower is a
+standard function in our and this is
+
+ align:start position:0%
+standard function in our and this is
+ 
+
+ align:start position:0%
+standard function in our and this is
+like when we pass mean to the T apply
+
+ align:start position:0%
+like when we pass mean to the T apply
+ 
+
+ align:start position:0%
+like when we pass mean to the T apply
+function we're passing the TM map
+
+ align:start position:0%
+function we're passing the TM map
+ 
+
+ align:start position:0%
+function we're passing the TM map
+function a function to use on our corpus
+
+ align:start position:0%
+function a function to use on our corpus
+ 
+
+ align:start position:0%
+function a function to use on our corpus
+let's see what that did by looking at
+
+ align:start position:0%
+let's see what that did by looking at
+ 
+
+ align:start position:0%
+let's see what that did by looking at
+our first tweet again go ahead and hit
+
+ align:start position:0%
+our first tweet again go ahead and hit
+ 
+
+ align:start position:0%
+our first tweet again go ahead and hit
+the up arrow twice to get back to corpus
+
+ align:start position:0%
+the up arrow twice to get back to corpus
+ 
+
+ align:start position:0%
+the up arrow twice to get back to corpus
+1 and now we can see that all of our
+
+ align:start position:0%
+1 and now we can see that all of our
+ 
+
+ align:start position:0%
+1 and now we can see that all of our
+letters are lowercase now let's remove
+
+ align:start position:0%
+letters are lowercase now let's remove
+ 
+
+ align:start position:0%
+letters are lowercase now let's remove
+all punctuation this is done in a very
+
+ align:start position:0%
+all punctuation this is done in a very
+ 
+
+ align:start position:0%
+all punctuation this is done in a very
+similar way except this time we give the
+
+ align:start position:0%
+similar way except this time we give the
+ 
+
+ align:start position:0%
+similar way except this time we give the
+argument remove punctuation instead of
+
+ align:start position:0%
+argument remove punctuation instead of
+ 
+
+ align:start position:0%
+argument remove punctuation instead of
+to lower hit the up arrow twice and in
+
+ align:start position:0%
+to lower hit the up arrow twice and in
+ 
+
+ align:start position:0%
+to lower hit the up arrow twice and in
+the TM map function delete to lower and
+
+ align:start position:0%
+the TM map function delete to lower and
+ 
+
+ align:start position:0%
+the TM map function delete to lower and
+type remove punctuation let's see what
+
+ align:start position:0%
+type remove punctuation let's see what
+ 
+
+ align:start position:0%
+type remove punctuation let's see what
+this did to our first tweet again now
+
+ align:start position:0%
+this did to our first tweet again now
+ 
+
+ align:start position:0%
+this did to our first tweet again now
+the comma after say the exclamation
+
+ align:start position:0%
+the comma after say the exclamation
+ 
+
+ align:start position:0%
+the comma after say the exclamation
+point after received and the @ symbols
+
+ align:start position:0%
+point after received and the @ symbols
+ 
+
+ align:start position:0%
+point after received and the @ symbols
+before Apple are all gone now we want to
+
+ align:start position:0%
+before Apple are all gone now we want to
+ 
+
+ align:start position:0%
+before Apple are all gone now we want to
+remove the stop words in our tweets TM
+
+ align:start position:0%
+remove the stop words in our tweets TM
+ 
+
+ align:start position:0%
+remove the stop words in our tweets TM
+provides a list of stop words for the
+
+ align:start position:0%
+provides a list of stop words for the
+ 
+
+ align:start position:0%
+provides a list of stop words for the
+English language we can check it out by
+
+ align:start position:0%
+English language we can check it out by
+ 
+
+ align:start position:0%
+English language we can check it out by
+typing stop words and then in
+
+ align:start position:0%
+typing stop words and then in
+ 
+
+ align:start position:0%
+typing stop words and then in
+parenthesis in quotes English and then
+
+ align:start position:0%
+parenthesis in quotes English and then
+ 
+
+ align:start position:0%
+parenthesis in quotes English and then
+we'll look at the 1st through the 10th
+
+ align:start position:0%
+we'll look at the 1st through the 10th
+ 
+
+ align:start position:0%
+we'll look at the 1st through the 10th
+stop words we see that these are words
+
+ align:start position:0%
+stop words we see that these are words
+ 
+
+ align:start position:0%
+stop words we see that these are words
+like I me my myself etc removing words
+
+ align:start position:0%
+like I me my myself etc removing words
+ 
+
+ align:start position:0%
+like I me my myself etc removing words
+can be done with a remove words argument
+
+ align:start position:0%
+can be done with a remove words argument
+ 
+
+ align:start position:0%
+can be done with a remove words argument
+to the TM map function but we need one
+
+ align:start position:0%
+to the TM map function but we need one
+ 
+
+ align:start position:0%
+to the TM map function but we need one
+extra argument this time what the stop
+
+ align:start position:0%
+extra argument this time what the stop
+ 
+
+ align:start position:0%
+extra argument this time what the stop
+words are that we want to remove will
+
+ align:start position:0%
+words are that we want to remove will
+ 
+
+ align:start position:0%
+words are that we want to remove will
+remove all of these English stop words
+
+ align:start position:0%
+remove all of these English stop words
+ 
+
+ align:start position:0%
+remove all of these English stop words
+but will also remove the word Apple
+
+ align:start position:0%
+but will also remove the word Apple
+ 
+
+ align:start position:0%
+but will also remove the word Apple
+since all of these tweets have the word
+
+ align:start position:0%
+since all of these tweets have the word
+ 
+
+ align:start position:0%
+since all of these tweets have the word
+Apple and it probably won't be very
+
+ align:start position:0%
+Apple and it probably won't be very
+ 
+
+ align:start position:0%
+Apple and it probably won't be very
+useful in our prediction problem
+
+ align:start position:0%
+useful in our prediction problem
+ 
+
+ align:start position:0%
+useful in our prediction problem
+so go ahead and hit the up arrow to get
+
+ align:start position:0%
+so go ahead and hit the up arrow to get
+ 
+
+ align:start position:0%
+so go ahead and hit the up arrow to get
+back to the TMF function delete remove
+
+ align:start position:0%
+back to the TMF function delete remove
+ 
+
+ align:start position:0%
+back to the TMF function delete remove
+punctuation and instead type remove
+
+ align:start position:0%
+punctuation and instead type remove
+ 
+
+ align:start position:0%
+punctuation and instead type remove
+words then we need to add one extra
+
+ align:start position:0%
+words then we need to add one extra
+ 
+
+ align:start position:0%
+words then we need to add one extra
+argument C and then in parenthesis and
+
+ align:start position:0%
+argument C and then in parenthesis and
+ 
+
+ align:start position:0%
+argument C and then in parenthesis and
+in quotes Apple this is us removing the
+
+ align:start position:0%
+in quotes Apple this is us removing the
+ 
+
+ align:start position:0%
+in quotes Apple this is us removing the
+word Apple and then stop words
+
+ align:start position:0%
+word Apple and then stop words
+ 
+
+ align:start position:0%
+word Apple and then stop words
+parenthesis in quotes English so this
+
+ align:start position:0%
+parenthesis in quotes English so this
+ 
+
+ align:start position:0%
+parenthesis in quotes English so this
+will remove the word Apple and all of
+
+ align:start position:0%
+will remove the word Apple and all of
+ 
+
+ align:start position:0%
+will remove the word Apple and all of
+the English stop words let's take a look
+
+ align:start position:0%
+the English stop words let's take a look
+ 
+
+ align:start position:0%
+the English stop words let's take a look
+at our first tweet again to see what
+
+ align:start position:0%
+at our first tweet again to see what
+ 
+
+ align:start position:0%
+at our first tweet again to see what
+happened now we can see that we have
+
+ align:start position:0%
+happened now we can see that we have
+ 
+
+ align:start position:0%
+happened now we can see that we have
+significantly fewer words only the words
+
+ align:start position:0%
+significantly fewer words only the words
+ 
+
+ align:start position:0%
+significantly fewer words only the words
+that are not stop words lastly we want
+
+ align:start position:0%
+that are not stop words lastly we want
+ 
+
+ align:start position:0%
+that are not stop words lastly we want
+to stim our document with the stim
+
+ align:start position:0%
+to stim our document with the stim
+ 
+
+ align:start position:0%
+to stim our document with the stim
+document argument go ahead and scroll
+
+ align:start position:0%
+document argument go ahead and scroll
+ 
+
+ align:start position:0%
+document argument go ahead and scroll
+back up to the remove punctuation delete
+
+ align:start position:0%
+back up to the remove punctuation delete
+ 
+
+ align:start position:0%
+back up to the remove punctuation delete
+remove punctuation and type stim
+
+ align:start position:0%
+remove punctuation and type stim
+ 
+
+ align:start position:0%
+remove punctuation and type stim
+document if you hit enter and then look
+
+ align:start position:0%
+document if you hit enter and then look
+ 
+
+ align:start position:0%
+document if you hit enter and then look
+at the first tweet again we can see that
+
+ align:start position:0%
+at the first tweet again we can see that
+ 
+
+ align:start position:0%
+at the first tweet again we can see that
+this took off the ending of customer
+
+ align:start position:0%
+this took off the ending of customer
+ 
+
+ align:start position:0%
+this took off the ending of customer
+service received an app store in the
+
+ align:start position:0%
+service received an app store in the
+ 
+
+ align:start position:0%
+service received an app store in the
+next video we'll investigate our corpus
+
+ align:start position:0%
+next video we'll investigate our corpus
+ 
+
+ align:start position:0%
+next video we'll investigate our corpus
+and prepare it for our prediction
+
+ align:start position:0%
+and prepare it for our prediction
+ 
+
+ align:start position:0%
+and prepare it for our prediction
+problem
\ No newline at end of file
diff --git a/G0iYkb9YiRg.txt b/G0iYkb9YiRg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..56c429d8b3d159e1d7cee754499869cd348cc48d
--- /dev/null
+++ b/G0iYkb9YiRg.txt
@@ -0,0 +1,1478 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So I will go into a
+little about what the class
+
+is, and what you're
+going to do.
+
+I'll just put one slide about
+requirements and outcomes.
+
+So what are the requirements?
+
+We require you to be a good
+programmer with a lot of
+
+programming experience.
+
+As I said, we are going down
+to very bare metal.
+
+And there won't be any
+niceties of just
+
+writing Java code.
+
+So you're going to run into a
+lot of these kind of issues.
+
+Fluent in C is --
+
+I wouldn't call it a 100%
+requirement, but it really
+
+helps if you're fluent in C.
+If not, you'll have to
+
+probably spend a lot of time
+trying to understand C, C++.
+
+And in this class that means --
+just start doing it today,
+
+just get a C book and then
+try to understand.
+
+If you run a lot of Java it
+might be an easy transition.
+
+But get to the transition
+fast, don't wait.
+
+What are we expecting
+at the end?
+
+We expect at the end
+for you to know --
+
+AUDIENCE: I have to go.
+
+Thank you very much
+[INAUDIBLE]
+
+PROFESSOR: So what
+do we expect?
+
+We expect at the end you'll
+probably understand a lot of
+
+fundamentals and concepts of
+parallel programming --
+
+both hardware and software.
+
+Because the nice
+thing about --
+
+or the nice thing or the
+bad thing about Cell --
+
+is a lot of hardware conceptuals
+to expose.
+
+There's no nice abstraction
+layers in there.
+
+You'll understand a lot of
+issues about parallel
+
+performance.
+
+We started here, you write a
+program, compile -- it's not
+
+just order n you're
+looking for.
+
+You're looking for all
+these constants.
+
+All these things matter,
+basically.
+
+You should be able to synthesize
+a fairly complex
+
+parallel program by the end,
+because that's what your group
+
+project's going to be.
+
+And you'll get a lot of hands-on
+experience with the
+
+Cell processor, so we'll
+understand this one
+
+instance very well.
+
+So that is what we are expecting
+will happen at the
+
+end of this 3.5 weeks.
+
+So the project.
+
+You proposed the projects, we
+did something different.
+
+So it's all your ideas that
+we are going to do.
+
+We selected seven groups out
+of these -- there are seven
+
+projects in there --
+
+mainly based on the strength
+of the project proposals.
+
+And I was pretty impressed with
+the height of things you
+
+guys proposed.
+
+So here are the seven
+projects.
+
+Let's actually try to figure
+out who's who.
+
+Who's doing distributed
+real-time ray tracer?
+
+OK, that's not true.
+
+OK, how about the global
+illumination?
+
+OK.
+
+Linear algebra pack?
+
+OK, good.
+
+Molecular dynamics?
+
+OK.
+
+Speech synthesizer?
+
+OK.
+
+Soft radio?
+
+OK.
+
+Backgammon tutor?
+
+OK.
+
+And there are some people who
+are, I think, in this class
+
+thinking that they
+can join a group.
+
+So at the end, there are a few
+groups that only have one
+
+member, so probably go ahead
+and talk to them and see
+
+whether they are willing
+to work with people.
+
+So I'll give you a little bit of
+time, because I'm going to
+
+finish early.
+
+OK, let's ask -- who are
+the people who are
+
+hoping to join a group?
+
+Is there anybody who came?
+
+I got a few emails, I don't
+know that anybody's here.
+
+Oh good.
+
+So it's not going
+to be a problem.
+
+So I did the project
+characteristics.
+
+You can see that they are
+ambitious projects, but
+
+accomplishable.
+
+I was worried that people would
+say, "I'm going to build
+
+this entire thing", and it's
+going to take a year.
+
+But I think most of the projects
+that they proposed
+
+are doable.
+
+Another thing is important
+and relevant things.
+
+I think for a lot of these
+things, if the code is done
+
+right other people might
+even use it.
+
+I think this can start
+something, it's not just going
+
+to be this project.
+
+And there's a lot of opportunity
+to sizzle.
+
+I think some people will come
+up with these things that I
+
+think at the end will
+be so amazing.
+
+And that's what got
+me excited.
+
+But get them started as soon as
+possible, because this is
+
+not a semester course, this is
+going to run so fast. There's
+
+only a few all nighters
+you can pull,
+
+basically is what it is.
+
+So there's a note of caution.
+
+Cell processor is very new.
+
+We heard about that today.
+
+I mean this is a really
+cool thing, but it has
+
+its problems in there.
+
+It's not an easy architecture
+to work with.
+
+There is though this
+nice abstraction.
+
+So it's just then from this
+being completely abstracted
+
+out, writing Java code, to
+all the way to metal.
+
+So it's just almost a jump
+from going to a higher
+
+language of assembly.
+
+So there's a huge, big gap in
+there, and that's going to be
+
+a lot of issues in there.
+
+The tool chain is very
+thin and brittle.
+
+So my pointing out all those
+things, you wish there's a
+
+tool, but there's nothing.
+
+And even the existing tools --
+
+we just got the SDK 2.0 into
+working I think this morning
+
+-- and so there might
+be issues in there.
+
+Most of the staff have
+limited experience.
+
+For example, SDK 2.0.
+
+We just got it working, so we
+haven't used it yet in there.
+
+So that can create problems,
+especially in
+
+a fast moving course.
+
+The projects you are doing
+are of your own making.
+
+Most of the classes --
+
+if you need to [UNINTELLIGIBLE]
+
+classes, we actually come up
+with the projects, TAs go and
+
+implement it once, we know
+all the gotchas.
+
+And then when you get the
+project we know there's an
+
+existence proof that
+it's doable, it
+
+works, the tools work.
+
+We know at least there's
+one path through it.
+
+There's nothing like
+that here.
+
+Everybody's kind of just jumping
+at it head on, and
+
+hoping that we can read them.
+
+And we might find issues that
+are very hard, and that's why
+
+we actually have very
+close contact with
+
+those guys at IBM.
+
+So if things happen, we'll call
+them and they will be
+
+available to help us.
+
+But it's not something you can
+say -- oh yeah, I know, just
+
+go do that.
+
+Or -- here's the way out.
+
+So there might be issues like
+that, so we have to be very
+
+careful of that.
+
+And you will face these kinds of
+problems. That's more given
+
+than anything else, so
+be ready for that.
+
+This is not just writing some
+high level code and getting
+
+away with it.
+
+And you're all in
+this together.
+
+So the staff, you,
+me, everybody --
+
+we're just doing it for the
+first time in some sense.
+
+And that's the fun part about
+it, because as you pointed
+
+out, there might be some stuff
+that you guys come out with
+
+that will become more like
+folklore and the basis for the
+
+things people do.
+
+Because you might say --
+hey, there's a neat
+
+way of doing that.
+
+You will be the first to
+do this kind of thing.
+
+So there's that time, but on
+planning the three week course
+
+it's a large chunk to bite.
+
+If it is more for a PhD,
+then you can say --
+
+OK, spend three months
+figuring it out.
+
+There's no other time limit.
+
+So we will try to manage this
+process, but you need to try
+
+to -- expectations of what you
+are trying to get done, and
+
+then be able to get it done.
+
+So you have to always
+balance this out.
+
+If you're running into issues,
+get to us very fast. Because
+
+we need to figure it out.
+
+And we might have to actually
+also figure it out from
+
+somebody else, so we can
+escalate it up and get the
+
+information.
+
+Because three weeks are
+going to go so fast.
+
+How many people are taking
+the class for a grade?
+
+So people who are taking it for
+a grade, here is what we
+
+are going to do.
+
+The first thing, what I call
+mini quizzes, is just a prop
+
+so you will come into class.
+
+So the way I am going to do that
+is, at the beginning of
+
+the class I am going to give you
+a piece of paper with two
+
+questions from the
+previous lecture.
+
+You can do anything you
+want to answer it.
+
+You can talk to people,
+look it up, whatever.
+
+And then at the end
+of the class
+
+basically we want it back.
+
+And the only requirement is, you
+have to come individually
+
+to pick your thing up, and you
+have to come individually to
+
+hand it in, and you can't write
+somebody else's anwers
+
+physically, but you can
+talk to each other.
+
+So we'll try to make it a little
+bit entertaining, and a
+
+little bit thought-provoking,
+but nothing like you have to
+
+spend hours doing it.
+
+It'll be probably
+five minutes.
+
+Normally we will do a break
+inbetween, so you probably can
+
+talk to each other and come up
+with some of the answers.
+
+So this is just the fact that
+the people who are actually
+
+getting the grades will be
+coming to class, more than
+
+anything else I'll be testing.
+
+And then we have these lab
+projects at the beginning,
+
+that will get some grade.
+
+And the final group project.
+
+And then we have a final
+competition.
+
+So since everybody's not doing
+the same project, we are going
+
+to decide on performance --
+
+so how well your code ran, how
+much MIPS or [? GOPs ?] you
+
+were able to get from that.
+
+And how raw performance
+is in there.
+
+And then we will also
+look at it from a
+
+complexity point of view.
+
+So for example, as I pointed
+out, if you do matrix
+
+multiplier you get certain
+performance, so if you do
+
+[? FF3, ?] you get certain
+performance.
+
+So just absolute numbers is not
+what matters, but how far
+
+you can get hard
+algorithm too.
+
+Completeness.
+
+So were you able to get
+your project through?
+
+How much do you actually have a
+compete solution at the end
+
+that something works?
+
+That's important.
+
+Algorithmic complexity -- how
+much of a complexity did you
+
+bite in, both from more of a
+pure algorithm point of view,
+
+and also implementing some
+shared complexity in there.
+
+And demo and presentation.
+
+So OK, those two.
+
+So we are going to select
+a winning team.
+
+We haven't figured exactly what,
+but we'll give everybody
+
+a gift set depending on --
+
+this is what we are aiming
+at right now.
+
+Also we are going to invite the
+winning team to spend a
+
+day at IBM TJ Watson.
+
+You get to give a presentation
+to a bunch of people there,
+
+and probably go see what
+they are doing.
+
+That should be a fun
+day to spend.
+
+We haven't scheduled a day,
+depending on the class
+
+schedule and stuff like that,
+the winning team will go spend
+
+a day out in there.
+
+That will be a fun thing to
+do, there's a lot of cool
+
+stuff going on there.
+
+They will get to actually
+interact with some
+
+researchers, see what they
+do, as well as present
+
+this work to them.
+
+And since this is new
+everybody's excited.
+
+I think hopefully we'll come
+up with a team that will do
+
+things that other people will be
+interested in and will use.
+
+So these kind of come from
+backward because I wanted to
+
+get Mike Perrone first.
+So my name is Saman --
+
+Saman Amarasinghe --
+
+I live in CSAIL.
+
+I have had a lot of
+interest in --
+
+[LAUGHTER]
+
+Not as much as you
+guys probably.
+
+I have a lot of interest in
+languages, compilers, and
+
+computer architecture.
+
+So if you have been at this game
+for a long time, in the
+
+early 1990s there was a huge
+surge in parallel performance,
+
+work on parallelism, and at
+that time I did the SUIF
+
+parallelizing compiler
+in there.
+
+And then, everybody says -- hey,
+there's this Moore slope
+
+of performance, who cares
+about parallelism?
+
+So there was this decade
+when this paralellism
+
+kind of died down.
+
+I kind of hid under the radar
+and kind of survived through
+
+that thing, and then again I
+think parallelism coming up.
+
+So we are doing a bunch of
+parallel work in here.
+
+So I probably have a perspective
+that goes
+
+somewhere old, and
+then coming up.
+
+Probably Aaron can also
+relate to that.
+
+Aaron: There's one of
+us who did that.
+
+PROFESSOR: Yeah exactly.
+
+Going through that, kind
+of survived in that.
+
+And Rodric is sitting there.
+
+So Rodric is right now at IBM
+PJ Watson, but he's probably
+
+going to live at CSAIL next
+month, so he's going to be
+
+here more than me in fact.
+
+He was actually in the lab until
+a few months ago, as a
+
+research scientist. He's also
+interested in a lot of these
+
+kinds of things -- compilers,
+architecture, parallel
+
+architecture, and
+FPGA type work.
+
+And then we have two TAs.
+
+Where's David and Phil?
+
+OK, get up.
+
+So they actually have
+some experience.
+
+Probably they are about a week
+ahead of you on understanding
+
+Cell, not too much.
+
+They are going to lead the
+recitations and be available
+
+to help you in there.
+
+So really use those resources
+as much as possible.
+
+And then we are going to have
+a huge amount of guest
+
+lecturers, and I was pretty
+happy with the
+
+kind of list we got.
+
+Mike Perrone just came and gave
+you the lecture, and Alan
+
+is going to talk
+in a few weeks.
+
+And Professor Arvind, Brad
+Kuszmaul, Mike Acton -- that
+
+Mike Perrone talk about is
+going to come at the end.
+
+And Bill Thies, who was one
+of the PhD students in the
+
+Streamit group, is going
+to talk about
+
+the Streamit language.
+
+So the way we have kind of
+structured the class is, how
+
+do you go about extracting
+parallelism.
+
+There's implicit parallelism.
+
+And sometimes the
+current way of
+
+everything done by hardware.
+
+In the next lecture, I will just
+touch upon superscalar
+
+hardware, what it is and
+what its problems are.
+
+Implicit parallelism means
+you can do by compiler.
+
+So you write a C program, and
+let the compiler deal with the
+
+parallelism.
+
+For as long as you are a
+programmer, you don't have to
+
+deal with that thing.
+
+In lectures 11 and 12
+I will talk about
+
+parallelizing compilers.
+
+So we'll cover how you can
+do that [? in C. ?]
+
+So that means kind of abstract
+it out, and leaving it out of
+
+the end programmer.
+
+So the hardware exposes it, but
+we put a software layer.
+
+And then the other end is
+explicit parallelism.
+
+That's where, I think, we are
+going to spend most of the
+
+time in this class.
+
+So in the first part of explicit
+parallelism is the
+
+library approach.
+
+What that means is you are using
+MPI type things, so you
+
+are basically at the metal
+dealing with this parallelism.
+
+I am going to do lecture
+4 on concurrency.
+
+How many people took 6.170 last
+year when I was teaching?
+
+OK.
+
+I did a lecture on concurrency
+there, so something very
+
+similar I'm going to do in here
+-- to get the basics of
+
+parallelism.
+
+In order to write a parallel
+program, the program has to
+
+run concurrently.
+
+There's a lot of issues for
+writing concurrent programs.
+
+It is necessary to get parallel,
+it's not sufficient.
+
+There are a lot more other
+things to worry about.
+
+But let's deal with those
+kind of issues --
+
+deal with things like
+synchronization, deadlocks,
+
+and issues like that.
+
+So I'm going to give that, and
+then Rodric is going to have a
+
+few lecture on design
+patterns.
+
+So if you want to write a
+parallel program, how do you
+
+look at it?
+
+Different algorithms will
+have different ways of
+
+parallelizing.
+
+So he's going to go about
+looking at these kind of
+
+parallel patterns.
+
+If you have this kind of
+program, here is a
+
+way to look at it.
+
+Here's another way
+to look at it.
+
+So kind of go through
+that in there.
+
+And in concurrency we work
+with a lot more abstract
+
+parallel model, and get slowly
+down to all the realism needed
+
+in dealing with Cell.
+
+And then we are going to have
+a bunch of guest lectures,
+
+mainly dealing with other ways
+of doing parallelism.
+
+So this is one way.
+
+We are going to have a lecture
+on Streamit, because you might
+
+be able to use that also
+as a way on Cell.
+
+So a little bit of high
+abstraction, we are trying to
+
+make that available on Cell.
+
+So if that comes to, then you
+might be able to even have
+
+that as a part of your
+toolbox in there.
+
+The other three talks are
+about very different
+
+approaches for parallelism.
+
+I think they will give you a
+big picture view, it's not
+
+that you're just going
+through one
+
+parallelling down in there.
+
+I think at the end of to the day
+you'll understand not only
+
+how to deal with Cell, but
+kind of a general way of
+
+looking at parallelism, and
+maybe from that approach
+
+[UNINTELLIGIBLE] parallelism
+in there.
+
+So the lectures are organized
+as follows.
+
+We are now at the end
+of the day here.
+
+Tomorrow we'll have
+a recitation on
+
+getting to know Cell.
+
+We are trying to figure out a
+good room, so just check your
+
+email to figure out exactly
+where we are going to have it,
+
+because we are trying
+to figure it out.
+
+We want to find a room with
+machines so everybody can
+
+actualy get hands-on experience
+in kind of a
+
+lecture format.
+
+And then we will have the
+architecture, just general
+
+parallel architecture, and an
+introduction to concurrent
+
+programming.
+
+And then Rodric is going to
+have individual meets with
+
+individual groups,
+trying to get the
+
+groups' projects going.
+
+So at that point kind of figure
+out how we are doing
+
+it, have some early ideas about
+it so you can start
+
+thinking and start the process
+of doing that.
+
+You can start working on Cell
+probably from tomorrow, but
+
+really get a day to kind of
+get familiarized, and then
+
+here start the project.
+
+And then we will have
+some lectures on
+
+design patterns in here.
+
+And as we go we'll have more
+hands-on experience also.
+
+Then we'll have a lecture
+on Streamit.
+
+So if you are using Streamit for
+a part of the run program,
+
+you'll be able to understand
+what's going on.
+
+And we'll get to some debugging
+tools, hopefully we
+
+will have to deal with these
+things before that, but here's
+
+something that if you're really
+stuck, to get a breadth
+
+of tools available in here.
+
+And then we'll talk in general
+about debugging and
+
+performance monitoring and
+performance optimization.
+
+So at this point hopefully you
+have done the first cart, you
+
+have figured out what problems,
+and start optimizing
+
+things in here.
+
+And then we'll going into a
+little bit more breadth,
+
+things like traffic paralleizing
+compilers that I
+
+talk about, getting implicit
+parallelism in here.
+
+And then we will have a bunch of
+guest lecturers coming in.
+
+And we'll talk about some
+hardware and the future,
+
+because we are just starting
+this very new phase in
+
+programming that might change
+almost everybody.
+
+Five years, ten years down the
+line if you go through
+
+computer science, you might have
+a very different flavor,
+
+if what people think of
+parallelism takes hold.
+
+So let's look at some future,
+and talk about that.
+
+And it's a nice way to
+finish the lectures.
+
+A few more days and then
+we'll have group
+
+presentations in here.
+
+So each group will get about
+15 minutes time to present
+
+what they have done and give
+a little bit of a demo.
+
+And then finally on
+Friday we will
+
+have awards and reception.
+
+So this is what we got.
+
+Any questions?
+
+AUDIENCE: For recitations, if
+we're not in a room with
+
+machines should we
+bring laptops?
+
+PROFESSOR: So that's
+a good question.
+
+Who doesn't have a laptop
+they can bring?
+
+OK.
+
+If that is the case, we can have
+it in any room we want,
+
+and have the network.
+
+And we might have one or two
+additional machines for people
+
+who don't have a laptop.
+
+And that actually will work
+much better than everybody
+
+marching into some kind of a
+computer room that's not
+
+structured properly
+for doing a class.
+
+OK, that actually helps a lot.
+
+That's a good point, I think
+that helps a lot.
+
+OK, we'll do that
+that way then.
+
+AUDIENCE: How do we get access
+to these machines?
+
+PROFESSOR: OK.
+
+Rodric, you --
+
+RODRIC RABBAH: Every room has
+a PS3 dedicated to them.
+
+And every group has accounts
+on their dedicated PS3.
+
+I have your usernames
+and passwords.
+
+I will pass them out tomorrow,
+because I'm going to propagate
+
+the new SDK to all the PS3's --
+to sort of test it with one
+
+and make sure everything's
+working.
+
+So you'll get them at the first
+recitation tomorrow.
+
+Unless you really want them
+today, then come talk to me or
+
+send me email.
+
+PROFESSOR: You'll get
+to take home --
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yes.
+
+RODRIC RABBAH: Yes.
+
+PROFESSOR: We couldn't even put
+it in the machine room,
+
+because they were scared
+somebody was going
+
+to take them home.
+
+So we actually have it in a
+different room -- closed,
+
+nicely locked --
+
+or on the network.
+
+So I have been a very popular
+person lately, a lot of people
+
+have tried to bribe me
+to get access to
+
+one of these masters.
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+AUDIENCE: How much does
+the PS3 cost?
+
+PROFESSOR: Officially $600, but
+then eBay's going up to
+
+like $2,500 these days.
+
+AUDIENCE: No.
+
+PROFESSOR: That's gone down?
+
+AUDIENCE: They're down between
+$400 and $500.
+
+PROFESSOR: Oh, OK.
+
+AUDIENCE: They tried
+[? to rope me in. ?]
+
+[LAUGHTER]
+
+PROFESSOR: OK.
+
+But during Christmas
+it was down for --
+
+a few desperate payers who
+were trying to bribe me.
+
+[LAUGHTER]
+
+So I guess their volume
+has caught up to --
+
+AUDIENCE: No, the demand
+has dropped.
+
+PROFESSOR: OK.
+
+AUDIENCE: [INAUDIBLE]
+
+AUDIENCE: Will we get to
+see the Playstation?
+
+PROFESSOR: Tomorrow we
+can bring one --
+
+AUDIENCE: I can bring
+one [INAUDIBLE]
+
+PROFESSOR: If you put
+a game in it's fun.
+
+You can put a game in and play
+it, but this is going to be
+
+Linux so it's a little
+bit boring.
+
+[LAUGHTER]
+
+AUDIENCE: So these are
+things that actually
+
+cannot play the games.
+
+PROFESSOR: It can.
+
+Interestingly, mostly these
+game machines are sold for
+
+less than production value.
+
+So Microsoft, Nintendo, and
+Sony before made sure that
+
+nobody can run anything other
+than the published games that
+
+they've charged $25 per pop to
+
+recover the cost. Huh?
+
+No, $60 for the game.
+
+I think they are charging $25
+from the game maker just for
+
+the privilege of running
+the game.
+
+That's how they make
+their money.
+
+But, [UNINTELLIGIBLE]
+
+when they made PS3 bootable
+by Linux.
+
+So in fact, it's much cheaper,
+you get a Blu-Ray player, and
+
+this Cell processor for a lot
+less than the production cost.
+
+AUDIENCE: Does Linux on
+the PS3 run on top
+
+of the PS3 OS though?
+
+PROFESSOR: No.
+
+It just boots up PS3.
+
+What it does is in fact --
+
+right now, you don't get
+access to the graphics
+
+processor properly.
+
+So you can run open G11.
+
+You have framebuffer access,
+but you don't get the full
+
+graphics access out of that.
+
+AUDIENCE: Which distribution
+are we using?
+
+PROFESSOR: Which one?
+
+AUDIENCE: We're using
+Yellow Dog.
+
+AUDIENCE: So in other words,
+Mario and Luigi are
+
+subsidizing what we're
+going to do.
+
+[LAUGHTER]
+
+PROFESSOR: Yeah, exactly.
+
+All those shoot them up games
+are basically what subsidizes.
+
+Actually he said, in one sense,
+you get the processor
+
+down to $200 because they are
+selling all the other things.
+
+And the other thing, actually
+if you want to build a high
+
+performance Cell farm, it's
+probably cheaper because I
+
+think that the Cell blend
+would be $2,000.
+
+It should be cheaper to
+buy a bunch of PS3's,
+
+connect them together.
+
+But there might be issues about
+things like network
+
+access, file access, because as
+you pointed out, the board
+
+access is pretty primitive.
+
+Because for games you don't
+need this high bandwidth
+
+connection, you just need
+to download it once.
+
+So there might be issues
+using it for cluster.
+
+OK.
+
+Anything else?
+
+OK, good.
\ No newline at end of file
diff --git a/G6bUKW3S_Us.txt b/G6bUKW3S_Us.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3a2fb1a0c4517fe6a9f1852c18ff6828b38a14ec
--- /dev/null
+++ b/G6bUKW3S_Us.txt
@@ -0,0 +1,17259 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we spent a lot of
+
+ align:start position:0%
+we spent a lot of
+ 
+
+ align:start position:0%
+we spent a lot of
+the last few lectures going through some
+
+ align:start position:0%
+the last few lectures going through some
+ 
+
+ align:start position:0%
+the last few lectures going through some
+substancing but also going to a lot of
+
+ align:start position:0%
+substancing but also going to a lot of
+ 
+
+ align:start position:0%
+substancing but also going to a lot of
+methodology
+
+ align:start position:0%
+methodology
+ 
+
+ align:start position:0%
+methodology
+so I thought that today we have kind of
+
+ align:start position:0%
+so I thought that today we have kind of
+ 
+
+ align:start position:0%
+so I thought that today we have kind of
+on the right to uh go to be deep longer
+
+ align:start position:0%
+on the right to uh go to be deep longer
+ 
+
+ align:start position:0%
+on the right to uh go to be deep longer
+on substance and shorter on methodology
+
+ align:start position:0%
+on substance and shorter on methodology
+ 
+
+ align:start position:0%
+on substance and shorter on methodology
+so what I'm going to do is a bit of an
+
+ align:start position:0%
+so what I'm going to do is a bit of an
+ 
+
+ align:start position:0%
+so what I'm going to do is a bit of an
+overview
+
+ align:start position:0%
+overview
+ 
+
+ align:start position:0%
+overview
+of what we have learned over the years
+
+ align:start position:0%
+of what we have learned over the years
+ 
+
+ align:start position:0%
+of what we have learned over the years
+and on
+
+ align:start position:0%
+and on
+ 
+
+ align:start position:0%
+and on
+the education systems and you know what
+
+ align:start position:0%
+the education systems and you know what
+ 
+
+ align:start position:0%
+the education systems and you know what
+is wrong with them if you remember in
+
+ align:start position:0%
+is wrong with them if you remember in
+ 
+
+ align:start position:0%
+is wrong with them if you remember in
+our first lecture I showed you some
+
+ align:start position:0%
+our first lecture I showed you some
+ 
+
+ align:start position:0%
+our first lecture I showed you some
+some numbers on what kids know and
+
+ align:start position:0%
+some numbers on what kids know and
+ 
+
+ align:start position:0%
+some numbers on what kids know and
+basically that's kind of the central
+
+ align:start position:0%
+basically that's kind of the central
+ 
+
+ align:start position:0%
+basically that's kind of the central
+puzzle I'm going to to study today so
+
+ align:start position:0%
+puzzle I'm going to to study today so
+ 
+
+ align:start position:0%
+puzzle I'm going to to study today so
+there is a lot because
+
+ align:start position:0%
+there is a lot because
+ 
+
+ align:start position:0%
+there is a lot because
+I think for
+
+ align:start position:0%
+I think for
+ 
+
+ align:start position:0%
+I think for
+practical reasons it turns out that it's
+
+ align:start position:0%
+practical reasons it turns out that it's
+ 
+
+ align:start position:0%
+practical reasons it turns out that it's
+relatively easy to experiment on kids
+
+ align:start position:0%
+relatively easy to experiment on kids
+ 
+
+ align:start position:0%
+relatively easy to experiment on kids
+because they are your captive audience
+
+ align:start position:0%
+because they are your captive audience
+ 
+
+ align:start position:0%
+because they are your captive audience
+and classrooms so a lot of the movement
+
+ align:start position:0%
+and classrooms so a lot of the movement
+ 
+
+ align:start position:0%
+and classrooms so a lot of the movement
+of running randomized control trials
+
+ align:start position:0%
+of running randomized control trials
+ 
+
+ align:start position:0%
+of running randomized control trials
+started on school on on asking questions
+
+ align:start position:0%
+started on school on on asking questions
+ 
+
+ align:start position:0%
+started on school on on asking questions
+on school quality
+
+ align:start position:0%
+on school quality
+ 
+
+ align:start position:0%
+on school quality
+so this is really one area where you can
+
+ align:start position:0%
+so this is really one area where you can
+ 
+
+ align:start position:0%
+so this is really one area where you can
+go beyond a single well-identified study
+
+ align:start position:0%
+go beyond a single well-identified study
+ 
+
+ align:start position:0%
+go beyond a single well-identified study
+tells you a thing to step back and think
+
+ align:start position:0%
+tells you a thing to step back and think
+ 
+
+ align:start position:0%
+tells you a thing to step back and think
+you know how does the whole picture look
+
+ align:start position:0%
+you know how does the whole picture look
+ 
+
+ align:start position:0%
+you know how does the whole picture look
+like and where issues of
+
+ align:start position:0%
+like and where issues of
+ 
+
+ align:start position:0%
+like and where issues of
+external validity and this data and the
+
+ align:start position:0%
+external validity and this data and the
+ 
+
+ align:start position:0%
+external validity and this data and the
+other applies less because it's not that
+
+ align:start position:0%
+other applies less because it's not that
+ 
+
+ align:start position:0%
+other applies less because it's not that
+you're interested in each of the points
+
+ align:start position:0%
+you're interested in each of the points
+ 
+
+ align:start position:0%
+you're interested in each of the points
+specifically because how the whole
+
+ align:start position:0%
+specifically because how the whole
+ 
+
+ align:start position:0%
+specifically because how the whole
+picture fits together and in some
+
+ align:start position:0%
+picture fits together and in some
+ 
+
+ align:start position:0%
+picture fits together and in some
+areas we we are not at this point yet we
+
+ align:start position:0%
+areas we we are not at this point yet we
+ 
+
+ align:start position:0%
+areas we we are not at this point yet we
+are kind of we have a disparate sets of
+
+ align:start position:0%
+are kind of we have a disparate sets of
+ 
+
+ align:start position:0%
+are kind of we have a disparate sets of
+facts I think the economics of a family
+
+ align:start position:0%
+facts I think the economics of a family
+ 
+
+ align:start position:0%
+facts I think the economics of a family
+gender is a little bit like that where
+
+ align:start position:0%
+gender is a little bit like that where
+ 
+
+ align:start position:0%
+gender is a little bit like that where
+we are still trying trying to feel our
+
+ align:start position:0%
+we are still trying trying to feel our
+ 
+
+ align:start position:0%
+we are still trying trying to feel our
+way around uh by uh looking at various
+
+ align:start position:0%
+way around uh by uh looking at various
+ 
+
+ align:start position:0%
+way around uh by uh looking at various
+case studying various things but the
+
+ align:start position:0%
+case studying various things but the
+ 
+
+ align:start position:0%
+case studying various things but the
+education one is one education Supply
+
+ align:start position:0%
+education one is one education Supply
+ 
+
+ align:start position:0%
+education one is one education Supply
+the quality of education is really where
+
+ align:start position:0%
+the quality of education is really where
+ 
+
+ align:start position:0%
+the quality of education is really where
+one place where we have mercy
+
+ align:start position:0%
+one place where we have mercy
+ 
+
+ align:start position:0%
+one place where we have mercy
+so I thought I would take advantage of
+
+ align:start position:0%
+so I thought I would take advantage of
+ 
+
+ align:start position:0%
+so I thought I would take advantage of
+that to to to do one more of these
+
+ align:start position:0%
+that to to to do one more of these
+ 
+
+ align:start position:0%
+that to to to do one more of these
+overview lectures instead of drilling
+
+ align:start position:0%
+overview lectures instead of drilling
+ 
+
+ align:start position:0%
+overview lectures instead of drilling
+down in details on
+
+ align:start position:0%
+down in details on
+ 
+
+ align:start position:0%
+down in details on
+what would have been for today which is
+
+ align:start position:0%
+what would have been for today which is
+ 
+
+ align:start position:0%
+what would have been for today which is
+uh some regression discontinuity design
+
+ align:start position:0%
+uh some regression discontinuity design
+ 
+
+ align:start position:0%
+uh some regression discontinuity design
+so we'll have to find another time to uh
+
+ align:start position:0%
+so we'll have to find another time to uh
+ 
+
+ align:start position:0%
+so we'll have to find another time to uh
+for an example on rdd or maybe do it in
+
+ align:start position:0%
+for an example on rdd or maybe do it in
+ 
+
+ align:start position:0%
+for an example on rdd or maybe do it in
+restitution
+
+ align:start position:0%
+restitution
+ 
+
+ align:start position:0%
+restitution
+uh so obviously it's useful to put that
+
+ align:start position:0%
+uh so obviously it's useful to put that
+ 
+
+ align:start position:0%
+uh so obviously it's useful to put that
+in context of the covid-19 pandemic
+
+ align:start position:0%
+in context of the covid-19 pandemic
+ 
+
+ align:start position:0%
+in context of the covid-19 pandemic
+because it's a real like it's a total
+
+ align:start position:0%
+because it's a real like it's a total
+ 
+
+ align:start position:0%
+because it's a real like it's a total
+tsunami on the education system in
+
+ align:start position:0%
+tsunami on the education system in
+ 
+
+ align:start position:0%
+tsunami on the education system in
+developing countries in developed
+
+ align:start position:0%
+developing countries in developed
+ 
+
+ align:start position:0%
+developing countries in developed
+countries as well obviously in the U.S a
+
+ align:start position:0%
+countries as well obviously in the U.S a
+ 
+
+ align:start position:0%
+countries as well obviously in the U.S a
+lot of kids stayed out of school for
+
+ align:start position:0%
+lot of kids stayed out of school for
+ 
+
+ align:start position:0%
+lot of kids stayed out of school for
+more than a year but
+
+ align:start position:0%
+more than a year but
+ 
+
+ align:start position:0%
+more than a year but
+worldwide 300 million children have been
+
+ align:start position:0%
+worldwide 300 million children have been
+ 
+
+ align:start position:0%
+worldwide 300 million children have been
+affected by school closures
+
+ align:start position:0%
+affected by school closures
+ 
+
+ align:start position:0%
+affected by school closures
+and in many countries the schools are
+
+ align:start position:0%
+and in many countries the schools are
+ 
+
+ align:start position:0%
+and in many countries the schools are
+yet to reopen in India for example it's
+
+ align:start position:0%
+yet to reopen in India for example it's
+ 
+
+ align:start position:0%
+yet to reopen in India for example it's
+mostly not reopened so as of today as
+
+ align:start position:0%
+mostly not reopened so as of today as
+ 
+
+ align:start position:0%
+mostly not reopened so as of today as
+most of the kids know in which countries
+
+ align:start position:0%
+most of the kids know in which countries
+ 
+
+ align:start position:0%
+most of the kids know in which countries
+are back in schools they are still 128
+
+ align:start position:0%
+are back in schools they are still 128
+ 
+
+ align:start position:0%
+are back in schools they are still 128
+millions of the kids who are still
+
+ align:start position:0%
+millions of the kids who are still
+ 
+
+ align:start position:0%
+millions of the kids who are still
+affected that should be the end of
+
+ align:start position:0%
+affected that should be the end of
+ 
+
+ align:start position:0%
+affected that should be the end of
+September of 2021
+
+ align:start position:0%
+September of 2021
+ 
+
+ align:start position:0%
+September of 2021
+who have not gone back to school and
+
+ align:start position:0%
+who have not gone back to school and
+ 
+
+ align:start position:0%
+who have not gone back to school and
+they are now all in in poor countries
+
+ align:start position:0%
+they are now all in in poor countries
+ 
+
+ align:start position:0%
+they are now all in in poor countries
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um that's a big
+
+ align:start position:0%
+um that's a big
+ 
+
+ align:start position:0%
+um that's a big
+and perhaps not surprisingly but it's
+
+ align:start position:0%
+and perhaps not surprisingly but it's
+ 
+
+ align:start position:0%
+and perhaps not surprisingly but it's
+been actually immersion it has
+
+ align:start position:0%
+been actually immersion it has
+ 
+
+ align:start position:0%
+been actually immersion it has
+catastrophic impact on on learning
+
+ align:start position:0%
+catastrophic impact on on learning
+ 
+
+ align:start position:0%
+catastrophic impact on on learning
+levels
+
+ align:start position:0%
+levels
+ 
+
+ align:start position:0%
+levels
+even in the short run what you can see
+
+ align:start position:0%
+even in the short run what you can see
+ 
+
+ align:start position:0%
+even in the short run what you can see
+is that for example so this is the data
+
+ align:start position:0%
+is that for example so this is the data
+ 
+
+ align:start position:0%
+is that for example so this is the data
+from Pata that looks at
+
+ align:start position:0%
+from Pata that looks at
+ 
+
+ align:start position:0%
+from Pata that looks at
+that uses their simple assert test to
+
+ align:start position:0%
+that uses their simple assert test to
+ 
+
+ align:start position:0%
+that uses their simple assert test to
+the simple measure tool for measuring
+
+ align:start position:0%
+the simple measure tool for measuring
+ 
+
+ align:start position:0%
+the simple measure tool for measuring
+reading and Mathematics ability looking
+
+ align:start position:0%
+reading and Mathematics ability looking
+ 
+
+ align:start position:0%
+reading and Mathematics ability looking
+at arithmetic and I'll show you the
+
+ align:start position:0%
+at arithmetic and I'll show you the
+ 
+
+ align:start position:0%
+at arithmetic and I'll show you the
+reading in the next time uh so in 2018
+
+ align:start position:0%
+reading in the next time uh so in 2018
+ 
+
+ align:start position:0%
+reading in the next time uh so in 2018
+and into 2021 a sample of about 28 20
+
+ align:start position:0%
+and into 2021 a sample of about 28 20
+ 
+
+ align:start position:0%
+and into 2021 a sample of about 28 20
+000 kids that they had done in in 2018
+
+ align:start position:0%
+000 kids that they had done in in 2018
+ 
+
+ align:start position:0%
+000 kids that they had done in in 2018
+were able to follow in 2021
+
+ align:start position:0%
+were able to follow in 2021
+ 
+
+ align:start position:0%
+were able to follow in 2021
+and what we have here is uh already in
+
+ align:start position:0%
+and what we have here is uh already in
+ 
+
+ align:start position:0%
+and what we have here is uh already in
+the best of time it's not that good if
+
+ align:start position:0%
+the best of time it's not that good if
+ 
+
+ align:start position:0%
+the best of time it's not that good if
+you take this the kids in standard five
+
+ align:start position:0%
+you take this the kids in standard five
+ 
+
+ align:start position:0%
+you take this the kids in standard five
+for example uh the only uh 34 percent of
+
+ align:start position:0%
+for example uh the only uh 34 percent of
+ 
+
+ align:start position:0%
+for example uh the only uh 34 percent of
+them can do a division okay just a
+
+ align:start position:0%
+them can do a division okay just a
+ 
+
+ align:start position:0%
+them can do a division okay just a
+division at that at the division level
+
+ align:start position:0%
+division at that at the division level
+ 
+
+ align:start position:0%
+division at that at the division level
+so another 20 percent are one level
+
+ align:start position:0%
+so another 20 percent are one level
+ 
+
+ align:start position:0%
+so another 20 percent are one level
+above so about half of the kids can do
+
+ align:start position:0%
+above so about half of the kids can do
+ 
+
+ align:start position:0%
+above so about half of the kids can do
+so half of the kids little more than
+
+ align:start position:0%
+so half of the kids little more than
+ 
+
+ align:start position:0%
+so half of the kids little more than
+half of the kid can do at least a
+
+ align:start position:0%
+half of the kid can do at least a
+ 
+
+ align:start position:0%
+half of the kid can do at least a
+subtraction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in in standard five a little less than
+
+ align:start position:0%
+in in standard five a little less than
+ 
+
+ align:start position:0%
+in in standard five a little less than
+half of the kid could do at least a
+
+ align:start position:0%
+half of the kid could do at least a
+ 
+
+ align:start position:0%
+half of the kid could do at least a
+subtraction in uh in standard four and
+
+ align:start position:0%
+subtraction in uh in standard four and
+ 
+
+ align:start position:0%
+subtraction in uh in standard four and
+it's an easy subtraction it's like a two
+
+ align:start position:0%
+it's an easy subtraction it's like a two
+ 
+
+ align:start position:0%
+it's an easy subtraction it's like a two
+digit minus two digit with carryover
+
+ align:start position:0%
+digit minus two digit with carryover
+ 
+
+ align:start position:0%
+digit minus two digit with carryover
+but then if we are looking at uh at this
+
+ align:start position:0%
+but then if we are looking at uh at this
+ 
+
+ align:start position:0%
+but then if we are looking at uh at this
+one now
+
+ align:start position:0%
+one now
+ 
+
+ align:start position:0%
+one now
+basically the standard five kids are now
+
+ align:start position:0%
+basically the standard five kids are now
+ 
+
+ align:start position:0%
+basically the standard five kids are now
+below 50 percent
+
+ align:start position:0%
+below 50 percent
+ 
+
+ align:start position:0%
+below 50 percent
+understand that four kids basically none
+
+ align:start position:0%
+understand that four kids basically none
+ 
+
+ align:start position:0%
+understand that four kids basically none
+of them are at division level almost so
+
+ align:start position:0%
+of them are at division level almost so
+ 
+
+ align:start position:0%
+of them are at division level almost so
+about a quarter of the key that's
+
+ align:start position:0%
+about a quarter of the key that's
+ 
+
+ align:start position:0%
+about a quarter of the key that's
+abstraction or above
+
+ align:start position:0%
+abstraction or above
+ 
+
+ align:start position:0%
+abstraction or above
+so we started from a low level and with
+
+ align:start position:0%
+so we started from a low level and with
+ 
+
+ align:start position:0%
+so we started from a low level and with
+the pandemic we have a catastrophically
+
+ align:start position:0%
+the pandemic we have a catastrophically
+ 
+
+ align:start position:0%
+the pandemic we have a catastrophically
+low level
+
+ align:start position:0%
+low level
+ 
+
+ align:start position:0%
+low level
+and of course we don't know how people
+
+ align:start position:0%
+and of course we don't know how people
+ 
+
+ align:start position:0%
+and of course we don't know how people
+will catch up but
+
+ align:start position:0%
+will catch up but
+ 
+
+ align:start position:0%
+will catch up but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it has been so slow any progress on
+
+ align:start position:0%
+it has been so slow any progress on
+ 
+
+ align:start position:0%
+it has been so slow any progress on
+quality of Education over the years has
+
+ align:start position:0%
+quality of Education over the years has
+ 
+
+ align:start position:0%
+quality of Education over the years has
+been so slow that a decline like that is
+
+ align:start position:0%
+been so slow that a decline like that is
+ 
+
+ align:start position:0%
+been so slow that a decline like that is
+going to be a big thing to to recover
+
+ align:start position:0%
+going to be a big thing to to recover
+ 
+
+ align:start position:0%
+going to be a big thing to to recover
+something in Reading so if you're
+
+ align:start position:0%
+something in Reading so if you're
+ 
+
+ align:start position:0%
+something in Reading so if you're
+looking for example at the the fraction
+
+ align:start position:0%
+looking for example at the the fraction
+ 
+
+ align:start position:0%
+looking for example at the the fraction
+of kids in in standard five uh who were
+
+ align:start position:0%
+of kids in in standard five uh who were
+ 
+
+ align:start position:0%
+of kids in in standard five uh who were
+at standard two level it was 46 percent
+
+ align:start position:0%
+at standard two level it was 46 percent
+ 
+
+ align:start position:0%
+at standard two level it was 46 percent
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+before the pandemic and it's at 34
+
+ align:start position:0%
+before the pandemic and it's at 34
+ 
+
+ align:start position:0%
+before the pandemic and it's at 34
+percent
+
+ align:start position:0%
+percent
+ 
+
+ align:start position:0%
+percent
+at the time they did the server and
+
+ align:start position:0%
+at the time they did the server and
+ 
+
+ align:start position:0%
+at the time they did the server and
+since then these kids in Karnataka are
+
+ align:start position:0%
+since then these kids in Karnataka are
+ 
+
+ align:start position:0%
+since then these kids in Karnataka are
+still not in back in school
+
+ align:start position:0%
+still not in back in school
+ 
+
+ align:start position:0%
+still not in back in school
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is still a snapshot we don't know
+
+ align:start position:0%
+this is still a snapshot we don't know
+ 
+
+ align:start position:0%
+this is still a snapshot we don't know
+what's going to happen in the future as
+
+ align:start position:0%
+what's going to happen in the future as
+ 
+
+ align:start position:0%
+what's going to happen in the future as
+they go back to school but there are two
+
+ align:start position:0%
+they go back to school but there are two
+ 
+
+ align:start position:0%
+they go back to school but there are two
+things that are
+
+ align:start position:0%
+things that are
+ 
+
+ align:start position:0%
+things that are
+probably going to happen on the one hand
+
+ align:start position:0%
+probably going to happen on the one hand
+ 
+
+ align:start position:0%
+probably going to happen on the one hand
+a lot of the kids the older kids are
+
+ align:start position:0%
+a lot of the kids the older kids are
+ 
+
+ align:start position:0%
+a lot of the kids the older kids are
+just not going to go back at all
+
+ align:start position:0%
+just not going to go back at all
+ 
+
+ align:start position:0%
+just not going to go back at all
+to the reenoldment of teenagers
+
+ align:start position:0%
+to the reenoldment of teenagers
+ 
+
+ align:start position:0%
+to the reenoldment of teenagers
+presumably is going to be uh to be quite
+
+ align:start position:0%
+presumably is going to be uh to be quite
+ 
+
+ align:start position:0%
+presumably is going to be uh to be quite
+low so it's a you know it's a generation
+
+ align:start position:0%
+low so it's a you know it's a generation
+ 
+
+ align:start position:0%
+low so it's a you know it's a generation
+that is going to suffer an enormous
+
+ align:start position:0%
+that is going to suffer an enormous
+ 
+
+ align:start position:0%
+that is going to suffer an enormous
+amount I was talking to David Atkin who
+
+ align:start position:0%
+amount I was talking to David Atkin who
+ 
+
+ align:start position:0%
+amount I was talking to David Atkin who
+pointed out you know maybe the other it
+
+ align:start position:0%
+pointed out you know maybe the other it
+ 
+
+ align:start position:0%
+pointed out you know maybe the other it
+will kind of even out the other
+
+ align:start position:0%
+will kind of even out the other
+ 
+
+ align:start position:0%
+will kind of even out the other
+generation will be more educated so it's
+
+ align:start position:0%
+generation will be more educated so it's
+ 
+
+ align:start position:0%
+generation will be more educated so it's
+just this one generation maybe it's not
+
+ align:start position:0%
+just this one generation maybe it's not
+ 
+
+ align:start position:0%
+just this one generation maybe it's not
+that bad on aggregate that's going back
+
+ align:start position:0%
+that bad on aggregate that's going back
+ 
+
+ align:start position:0%
+that bad on aggregate that's going back
+to this equilibrium impact but for that
+
+ align:start position:0%
+to this equilibrium impact but for that
+ 
+
+ align:start position:0%
+to this equilibrium impact but for that
+generation it's certainly a disaster
+
+ align:start position:0%
+generation it's certainly a disaster
+ 
+
+ align:start position:0%
+generation it's certainly a disaster
+and then the other thing is that
+
+ align:start position:0%
+and then the other thing is that
+ 
+
+ align:start position:0%
+and then the other thing is that
+for the kids who will go back to school
+
+ align:start position:0%
+for the kids who will go back to school
+ 
+
+ align:start position:0%
+for the kids who will go back to school
+they will go back to school with a very
+
+ align:start position:0%
+they will go back to school with a very
+ 
+
+ align:start position:0%
+they will go back to school with a very
+different experiences
+
+ align:start position:0%
+different experiences
+ 
+
+ align:start position:0%
+different experiences
+with even more heterogeneity in levels
+
+ align:start position:0%
+with even more heterogeneity in levels
+ 
+
+ align:start position:0%
+with even more heterogeneity in levels
+that they started from
+
+ align:start position:0%
+that they started from
+ 
+
+ align:start position:0%
+that they started from
+because another thing of this that you
+
+ align:start position:0%
+because another thing of this that you
+ 
+
+ align:start position:0%
+because another thing of this that you
+see even from this simple test is not
+
+ align:start position:0%
+see even from this simple test is not
+ 
+
+ align:start position:0%
+see even from this simple test is not
+only the levels are low but the kids are
+
+ align:start position:0%
+only the levels are low but the kids are
+ 
+
+ align:start position:0%
+only the levels are low but the kids are
+all over the place
+
+ align:start position:0%
+all over the place
+ 
+
+ align:start position:0%
+all over the place
+some kids in standard one can read at
+
+ align:start position:0%
+some kids in standard one can read at
+ 
+
+ align:start position:0%
+some kids in standard one can read at
+standard two that very many a lot cannot
+
+ align:start position:0%
+standard two that very many a lot cannot
+ 
+
+ align:start position:0%
+standard two that very many a lot cannot
+even recognize the letters that's in
+
+ align:start position:0%
+even recognize the letters that's in
+ 
+
+ align:start position:0%
+even recognize the letters that's in
+normal time
+
+ align:start position:0%
+normal time
+ 
+
+ align:start position:0%
+normal time
+uh and then in in the after the pandemic
+
+ align:start position:0%
+uh and then in in the after the pandemic
+ 
+
+ align:start position:0%
+uh and then in in the after the pandemic
+that there is even more that cannot
+
+ align:start position:0%
+that there is even more that cannot
+ 
+
+ align:start position:0%
+that there is even more that cannot
+recognize the letters but there is still
+
+ align:start position:0%
+recognize the letters but there is still
+ 
+
+ align:start position:0%
+recognize the letters but there is still
+it's not kind of neatly organized around
+
+ align:start position:0%
+it's not kind of neatly organized around
+ 
+
+ align:start position:0%
+it's not kind of neatly organized around
+the diagonal so kids of the same age are
+
+ align:start position:0%
+the diagonal so kids of the same age are
+ 
+
+ align:start position:0%
+the diagonal so kids of the same age are
+very different uh arrive at different
+
+ align:start position:0%
+very different uh arrive at different
+ 
+
+ align:start position:0%
+very different uh arrive at different
+levels and that's uh that's true in 2018
+
+ align:start position:0%
+levels and that's uh that's true in 2018
+ 
+
+ align:start position:0%
+levels and that's uh that's true in 2018
+that's even more true in 2021 and so
+
+ align:start position:0%
+that's even more true in 2021 and so
+ 
+
+ align:start position:0%
+that's even more true in 2021 and so
+that's something the school system will
+
+ align:start position:0%
+that's something the school system will
+ 
+
+ align:start position:0%
+that's something the school system will
+have to Grapple with
+
+ align:start position:0%
+have to Grapple with
+ 
+
+ align:start position:0%
+have to Grapple with
+but in some sense uh although I think
+
+ align:start position:0%
+but in some sense uh although I think
+ 
+
+ align:start position:0%
+but in some sense uh although I think
+this is a catastrophe and something that
+
+ align:start position:0%
+this is a catastrophe and something that
+ 
+
+ align:start position:0%
+this is a catastrophe and something that
+probably you guys some of you guys will
+
+ align:start position:0%
+probably you guys some of you guys will
+ 
+
+ align:start position:0%
+probably you guys some of you guys will
+want to study uh Salome is already kind
+
+ align:start position:0%
+want to study uh Salome is already kind
+ 
+
+ align:start position:0%
+want to study uh Salome is already kind
+of working on it in Mexico in the in the
+
+ align:start position:0%
+of working on it in Mexico in the in the
+ 
+
+ align:start position:0%
+of working on it in Mexico in the in the
+present but in the future as the
+
+ align:start position:0%
+present but in the future as the
+ 
+
+ align:start position:0%
+present but in the future as the
+pandemics subsides the question of how
+
+ align:start position:0%
+pandemics subsides the question of how
+ 
+
+ align:start position:0%
+pandemics subsides the question of how
+the vientry will takes place will will
+
+ align:start position:0%
+the vientry will takes place will will
+ 
+
+ align:start position:0%
+the vientry will takes place will will
+be pretty Central
+
+ align:start position:0%
+be pretty Central
+ 
+
+ align:start position:0%
+be pretty Central
+but but in some sense it's not new like
+
+ align:start position:0%
+but but in some sense it's not new like
+ 
+
+ align:start position:0%
+but but in some sense it's not new like
+in the U.S the the very much like in the
+
+ align:start position:0%
+in the U.S the the very much like in the
+ 
+
+ align:start position:0%
+in the U.S the the very much like in the
+U.S the the racial discrepancy in the
+
+ align:start position:0%
+U.S the the racial discrepancy in the
+ 
+
+ align:start position:0%
+U.S the the racial discrepancy in the
+burden of disease
+
+ align:start position:0%
+burden of disease
+ 
+
+ align:start position:0%
+burden of disease
+kind of put a magnifier on existing uh
+
+ align:start position:0%
+kind of put a magnifier on existing uh
+ 
+
+ align:start position:0%
+kind of put a magnifier on existing uh
+uh racial discrimination across any
+
+ align:start position:0%
+uh racial discrimination across any
+ 
+
+ align:start position:0%
+uh racial discrimination across any
+number of Dimensions that sort of
+
+ align:start position:0%
+number of Dimensions that sort of
+ 
+
+ align:start position:0%
+number of Dimensions that sort of
+collapsed in other coalescing to produce
+
+ align:start position:0%
+collapsed in other coalescing to produce
+ 
+
+ align:start position:0%
+collapsed in other coalescing to produce
+that outcome similarly this
+
+ align:start position:0%
+that outcome similarly this
+ 
+
+ align:start position:0%
+that outcome similarly this
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+drop in the level combined with
+
+ align:start position:0%
+drop in the level combined with
+ 
+
+ align:start position:0%
+drop in the level combined with
+increasing heterogeneity of experiences
+
+ align:start position:0%
+increasing heterogeneity of experiences
+ 
+
+ align:start position:0%
+increasing heterogeneity of experiences
+exacerbate existing trends
+
+ align:start position:0%
+exacerbate existing trends
+ 
+
+ align:start position:0%
+exacerbate existing trends
+and to China basically that you you find
+
+ align:start position:0%
+and to China basically that you you find
+ 
+
+ align:start position:0%
+and to China basically that you you find
+very high enrollment rates but a lot of
+
+ align:start position:0%
+very high enrollment rates but a lot of
+ 
+
+ align:start position:0%
+very high enrollment rates but a lot of
+absenteeism
+
+ align:start position:0%
+absenteeism
+ 
+
+ align:start position:0%
+absenteeism
+and very low learning levels
+
+ align:start position:0%
+and very low learning levels
+ 
+
+ align:start position:0%
+and very low learning levels
+so this is for India and then I'll show
+
+ align:start position:0%
+so this is for India and then I'll show
+ 
+
+ align:start position:0%
+so this is for India and then I'll show
+you the the world in the in the next
+
+ align:start position:0%
+you the the world in the in the next
+ 
+
+ align:start position:0%
+you the the world in the in the next
+slide this is a picture from 2014 but it
+
+ align:start position:0%
+slide this is a picture from 2014 but it
+ 
+
+ align:start position:0%
+slide this is a picture from 2014 but it
+you know post until the pandemic it was
+
+ align:start position:0%
+you know post until the pandemic it was
+ 
+
+ align:start position:0%
+you know post until the pandemic it was
+more or less correct most of the kids
+
+ align:start position:0%
+more or less correct most of the kids
+ 
+
+ align:start position:0%
+more or less correct most of the kids
+are on hold so 2014 you are 20 97
+
+ align:start position:0%
+are on hold so 2014 you are 20 97
+ 
+
+ align:start position:0%
+are on hold so 2014 you are 20 97
+percent of kids enrolled in school
+
+ align:start position:0%
+percent of kids enrolled in school
+ 
+
+ align:start position:0%
+percent of kids enrolled in school
+this was the the sixth year in a row
+
+ align:start position:0%
+this was the the sixth year in a row
+ 
+
+ align:start position:0%
+this was the the sixth year in a row
+that enrollment had been at 96 or above
+
+ align:start position:0%
+that enrollment had been at 96 or above
+ 
+
+ align:start position:0%
+that enrollment had been at 96 or above
+so that's great but the attendance is
+
+ align:start position:0%
+so that's great but the attendance is
+ 
+
+ align:start position:0%
+so that's great but the attendance is
+not very good if you show up on any
+
+ align:start position:0%
+not very good if you show up on any
+ 
+
+ align:start position:0%
+not very good if you show up on any
+random day uh you find 71 percent of the
+
+ align:start position:0%
+random day uh you find 71 percent of the
+ 
+
+ align:start position:0%
+random day uh you find 71 percent of the
+children actually present and it's not
+
+ align:start position:0%
+children actually present and it's not
+ 
+
+ align:start position:0%
+children actually present and it's not
+always the same 71 percent so it means
+
+ align:start position:0%
+always the same 71 percent so it means
+ 
+
+ align:start position:0%
+always the same 71 percent so it means
+that like the the kids get between their
+
+ align:start position:0%
+that like the the kids get between their
+ 
+
+ align:start position:0%
+that like the the kids get between their
+own absences and the absences of the
+
+ align:start position:0%
+own absences and the absences of the
+ 
+
+ align:start position:0%
+own absences and the absences of the
+teachers they miss maybe about half of
+
+ align:start position:0%
+teachers they miss maybe about half of
+ 
+
+ align:start position:0%
+teachers they miss maybe about half of
+the school that they should have and
+
+ align:start position:0%
+the school that they should have and
+ 
+
+ align:start position:0%
+the school that they should have and
+they go one day they come back the next
+
+ align:start position:0%
+they go one day they come back the next
+ 
+
+ align:start position:0%
+they go one day they come back the next
+day they go one day they come back to
+
+ align:start position:0%
+day they go one day they come back to
+ 
+
+ align:start position:0%
+day they go one day they come back to
+the absent their presence pattern is
+
+ align:start position:0%
+the absent their presence pattern is
+ 
+
+ align:start position:0%
+the absent their presence pattern is
+extremely regular
+
+ align:start position:0%
+extremely regular
+ 
+
+ align:start position:0%
+extremely regular
+and then this is not equal across the
+
+ align:start position:0%
+and then this is not equal across the
+ 
+
+ align:start position:0%
+and then this is not equal across the
+country so in the North in Utah West
+
+ align:start position:0%
+country so in the North in Utah West
+ 
+
+ align:start position:0%
+country so in the North in Utah West
+Bengal absence rates are even lower with
+
+ align:start position:0%
+Bengal absence rates are even lower with
+ 
+
+ align:start position:0%
+Bengal absence rates are even lower with
+about 50 presence and it's better in the
+
+ align:start position:0%
+about 50 presence and it's better in the
+ 
+
+ align:start position:0%
+about 50 presence and it's better in the
+South like many of the social patterns
+
+ align:start position:0%
+South like many of the social patterns
+ 
+
+ align:start position:0%
+South like many of the social patterns
+uh if you're looking at the the world as
+
+ align:start position:0%
+uh if you're looking at the the world as
+ 
+
+ align:start position:0%
+uh if you're looking at the the world as
+a whole we don't have perfect data for
+
+ align:start position:0%
+a whole we don't have perfect data for
+ 
+
+ align:start position:0%
+a whole we don't have perfect data for
+the world as a whole but
+
+ align:start position:0%
+the world as a whole but
+ 
+
+ align:start position:0%
+the world as a whole but
+this is a
+
+ align:start position:0%
+this is a
+ 
+
+ align:start position:0%
+this is a
+enrollment with a darker the better so
+
+ align:start position:0%
+enrollment with a darker the better so
+ 
+
+ align:start position:0%
+enrollment with a darker the better so
+basically most countries now this is
+
+ align:start position:0%
+basically most countries now this is
+ 
+
+ align:start position:0%
+basically most countries now this is
+again pre-pandemic most countries were
+
+ align:start position:0%
+again pre-pandemic most countries were
+ 
+
+ align:start position:0%
+again pre-pandemic most countries were
+at that where data was measured were
+
+ align:start position:0%
+at that where data was measured were
+ 
+
+ align:start position:0%
+at that where data was measured were
+above 90 percent you know with some
+
+ align:start position:0%
+above 90 percent you know with some
+ 
+
+ align:start position:0%
+above 90 percent you know with some
+exception and basically the only
+
+ align:start position:0%
+exception and basically the only
+ 
+
+ align:start position:0%
+exception and basically the only
+exception being the sale countries
+
+ align:start position:0%
+exception being the sale countries
+ 
+
+ align:start position:0%
+exception being the sale countries
+which have lower lower
+
+ align:start position:0%
+which have lower lower
+ 
+
+ align:start position:0%
+which have lower lower
+annulments
+
+ align:start position:0%
+annulments
+ 
+
+ align:start position:0%
+annulments
+but other than this band where
+
+ align:start position:0%
+but other than this band where
+ 
+
+ align:start position:0%
+but other than this band where
+enrollment remaining issue the question
+
+ align:start position:0%
+enrollment remaining issue the question
+ 
+
+ align:start position:0%
+enrollment remaining issue the question
+of an element has somehow been had been
+
+ align:start position:0%
+of an element has somehow been had been
+ 
+
+ align:start position:0%
+of an element has somehow been had been
+solved
+
+ align:start position:0%
+solved
+ 
+
+ align:start position:0%
+solved
+by the way during the pandemic most of
+
+ align:start position:0%
+by the way during the pandemic most of
+ 
+
+ align:start position:0%
+by the way during the pandemic most of
+the kids stayed in the world because
+
+ align:start position:0%
+the kids stayed in the world because
+ 
+
+ align:start position:0%
+the kids stayed in the world because
+nobody bothered to take them off the
+
+ align:start position:0%
+nobody bothered to take them off the
+ 
+
+ align:start position:0%
+nobody bothered to take them off the
+role but that doesn't mean they're
+
+ align:start position:0%
+role but that doesn't mean they're
+ 
+
+ align:start position:0%
+role but that doesn't mean they're
+really there
+
+ align:start position:0%
+really there
+ 
+
+ align:start position:0%
+really there
+but the absence of course is even is
+
+ align:start position:0%
+but the absence of course is even is
+ 
+
+ align:start position:0%
+but the absence of course is even is
+is mostly much less good so here the
+
+ align:start position:0%
+is mostly much less good so here the
+ 
+
+ align:start position:0%
+is mostly much less good so here the
+there are much fewer countries in dark
+
+ align:start position:0%
+there are much fewer countries in dark
+ 
+
+ align:start position:0%
+there are much fewer countries in dark
+blue uh
+
+ align:start position:0%
+blue uh
+ 
+
+ align:start position:0%
+blue uh
+quite a few countries solid blue and but
+
+ align:start position:0%
+quite a few countries solid blue and but
+ 
+
+ align:start position:0%
+quite a few countries solid blue and but
+we see countries are appearing in in
+
+ align:start position:0%
+we see countries are appearing in in
+ 
+
+ align:start position:0%
+we see countries are appearing in in
+light blue so this is India between 70
+
+ align:start position:0%
+light blue so this is India between 70
+ 
+
+ align:start position:0%
+light blue so this is India between 70
+and 80 percent happy to see that the two
+
+ align:start position:0%
+and 80 percent happy to see that the two
+ 
+
+ align:start position:0%
+and 80 percent happy to see that the two
+sources coincide
+
+ align:start position:0%
+sources coincide
+ 
+
+ align:start position:0%
+sources coincide
+and then uh we still have our sale
+
+ align:start position:0%
+and then uh we still have our sale
+ 
+
+ align:start position:0%
+and then uh we still have our sale
+country where not only they are not
+
+ align:start position:0%
+country where not only they are not
+ 
+
+ align:start position:0%
+country where not only they are not
+enrolled but in addition they don't go
+
+ align:start position:0%
+enrolled but in addition they don't go
+ 
+
+ align:start position:0%
+enrolled but in addition they don't go
+uh and and other countries where it's in
+
+ align:start position:0%
+uh and and other countries where it's in
+ 
+
+ align:start position:0%
+uh and and other countries where it's in
+the you know Pakistan Etc where it goes
+
+ align:start position:0%
+the you know Pakistan Etc where it goes
+ 
+
+ align:start position:0%
+the you know Pakistan Etc where it goes
+into the red and yellow so people don't
+
+ align:start position:0%
+into the red and yellow so people don't
+ 
+
+ align:start position:0%
+into the red and yellow so people don't
+show up that much
+
+ align:start position:0%
+show up that much
+ 
+
+ align:start position:0%
+show up that much
+and then as we already saw that they
+
+ align:start position:0%
+and then as we already saw that they
+ 
+
+ align:start position:0%
+and then as we already saw that they
+don't learn that much again that's data
+
+ align:start position:0%
+don't learn that much again that's data
+ 
+
+ align:start position:0%
+don't learn that much again that's data
+from from India
+
+ align:start position:0%
+from from India
+ 
+
+ align:start position:0%
+from from India
+uh uh since until
+
+ align:start position:0%
+uh uh since until
+ 
+
+ align:start position:0%
+uh uh since until
+1916 it's continued similarly the
+
+ align:start position:0%
+1916 it's continued similarly the
+ 
+
+ align:start position:0%
+1916 it's continued similarly the
+fraction of standard two kids who can
+
+ align:start position:0%
+fraction of standard two kids who can
+ 
+
+ align:start position:0%
+fraction of standard two kids who can
+who can read standard five kids who can
+
+ align:start position:0%
+who can read standard five kids who can
+ 
+
+ align:start position:0%
+who can read standard five kids who can
+read the stand up to text so like a
+
+ align:start position:0%
+read the stand up to text so like a
+ 
+
+ align:start position:0%
+read the stand up to text so like a
+paragraph basically and it's you know
+
+ align:start position:0%
+paragraph basically and it's you know
+ 
+
+ align:start position:0%
+paragraph basically and it's you know
+less than half not really going anywhere
+
+ align:start position:0%
+less than half not really going anywhere
+ 
+
+ align:start position:0%
+less than half not really going anywhere
+until it collapsed in in 2021.
+
+ align:start position:0%
+until it collapsed in in 2021.
+ 
+
+ align:start position:0%
+until it collapsed in in 2021.
+if anything in math it's a bit worse so
+
+ align:start position:0%
+if anything in math it's a bit worse so
+ 
+
+ align:start position:0%
+if anything in math it's a bit worse so
+that's the type of problems that they
+
+ align:start position:0%
+that's the type of problems that they
+ 
+
+ align:start position:0%
+that's the type of problems that they
+solve uh all that they are required to
+
+ align:start position:0%
+solve uh all that they are required to
+ 
+
+ align:start position:0%
+solve uh all that they are required to
+solve and the way the test works is that
+
+ align:start position:0%
+solve and the way the test works is that
+ 
+
+ align:start position:0%
+solve and the way the test works is that
+they're first shown the two-digit
+
+ align:start position:0%
+they're first shown the two-digit
+ 
+
+ align:start position:0%
+they're first shown the two-digit
+subtraction if they can do it they'll
+
+ align:start position:0%
+subtraction if they can do it they'll
+ 
+
+ align:start position:0%
+subtraction if they can do it they'll
+ask for a division if they cannot do it
+
+ align:start position:0%
+ask for a division if they cannot do it
+ 
+
+ align:start position:0%
+ask for a division if they cannot do it
+they are asked to recognize the numbers
+
+ align:start position:0%
+they are asked to recognize the numbers
+ 
+
+ align:start position:0%
+they are asked to recognize the numbers
+two digit number and then one digit
+
+ align:start position:0%
+two digit number and then one digit
+ 
+
+ align:start position:0%
+two digit number and then one digit
+number so that's how you have this level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so who can do a subtraction uh so we
+
+ align:start position:0%
+um so who can do a subtraction uh so we
+ 
+
+ align:start position:0%
+um so who can do a subtraction uh so we
+already saw these type of numbers but in
+
+ align:start position:0%
+already saw these type of numbers but in
+ 
+
+ align:start position:0%
+already saw these type of numbers but in
+standard five only half of the kids
+
+ align:start position:0%
+standard five only half of the kids
+ 
+
+ align:start position:0%
+standard five only half of the kids
+could do a subtraction in 2014.
+
+ align:start position:0%
+could do a subtraction in 2014.
+ 
+
+ align:start position:0%
+could do a subtraction in 2014.
+and in standard 8 only 44 percent of the
+
+ align:start position:0%
+and in standard 8 only 44 percent of the
+ 
+
+ align:start position:0%
+and in standard 8 only 44 percent of the
+kid could do this division
+
+ align:start position:0%
+kid could do this division
+ 
+
+ align:start position:0%
+kid could do this division
+so this in a sense was the well-known
+
+ align:start position:0%
+so this in a sense was the well-known
+ 
+
+ align:start position:0%
+so this in a sense was the well-known
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+maybe it was known to you maybe it was
+
+ align:start position:0%
+maybe it was known to you maybe it was
+ 
+
+ align:start position:0%
+maybe it was known to you maybe it was
+not not known to you but it was well
+
+ align:start position:0%
+not not known to you but it was well
+ 
+
+ align:start position:0%
+not not known to you but it was well
+known to uh
+
+ align:start position:0%
+known to uh
+ 
+
+ align:start position:0%
+known to uh
+say the general education establishment
+
+ align:start position:0%
+say the general education establishment
+ 
+
+ align:start position:0%
+say the general education establishment
+uh this is something that again is not
+
+ align:start position:0%
+uh this is something that again is not
+ 
+
+ align:start position:0%
+uh this is something that again is not
+specific to India for a while we've
+
+ align:start position:0%
+specific to India for a while we've
+ 
+
+ align:start position:0%
+specific to India for a while we've
+known it mostly for India because every
+
+ align:start position:0%
+known it mostly for India because every
+ 
+
+ align:start position:0%
+known it mostly for India because every
+year this asset survey where they went
+
+ align:start position:0%
+year this asset survey where they went
+ 
+
+ align:start position:0%
+year this asset survey where they went
+to every single district and surveyed a
+
+ align:start position:0%
+to every single district and surveyed a
+ 
+
+ align:start position:0%
+to every single district and surveyed a
+representative sample of kids regardless
+
+ align:start position:0%
+representative sample of kids regardless
+ 
+
+ align:start position:0%
+representative sample of kids regardless
+of their annulment status
+
+ align:start position:0%
+of their annulment status
+ 
+
+ align:start position:0%
+of their annulment status
+uh since then the World Bank has done
+
+ align:start position:0%
+uh since then the World Bank has done
+ 
+
+ align:start position:0%
+uh since then the World Bank has done
+and then after the pandemic for the sort
+
+ align:start position:0%
+and then after the pandemic for the sort
+ 
+
+ align:start position:0%
+and then after the pandemic for the sort
+of expanded in other places and then we
+
+ align:start position:0%
+of expanded in other places and then we
+ 
+
+ align:start position:0%
+of expanded in other places and then we
+also have those big standardized tests
+
+ align:start position:0%
+also have those big standardized tests
+ 
+
+ align:start position:0%
+also have those big standardized tests
+like the Pisa which are used mostly in
+
+ align:start position:0%
+like the Pisa which are used mostly in
+ 
+
+ align:start position:0%
+like the Pisa which are used mostly in
+the Richer countries uh and then
+
+ align:start position:0%
+the Richer countries uh and then
+ 
+
+ align:start position:0%
+the Richer countries uh and then
+different countries started running
+
+ align:start position:0%
+different countries started running
+ 
+
+ align:start position:0%
+different countries started running
+their pattern there are third types
+
+ align:start position:0%
+their pattern there are third types
+ 
+
+ align:start position:0%
+their pattern there are third types
+tests so
+
+ align:start position:0%
+tests so
+ 
+
+ align:start position:0%
+tests so
+there was a little bit of uh kind of
+
+ align:start position:0%
+there was a little bit of uh kind of
+ 
+
+ align:start position:0%
+there was a little bit of uh kind of
+impressionistic data flowy floating all
+
+ align:start position:0%
+impressionistic data flowy floating all
+ 
+
+ align:start position:0%
+impressionistic data flowy floating all
+over the place and underpany Goldberg
+
+ align:start position:0%
+over the place and underpany Goldberg
+ 
+
+ align:start position:0%
+over the place and underpany Goldberg
+when she was Chief Economist and with
+
+ align:start position:0%
+when she was Chief Economist and with
+ 
+
+ align:start position:0%
+when she was Chief Economist and with
+the huge effort of Noam ungrast that
+
+ align:start position:0%
+the huge effort of Noam ungrast that
+ 
+
+ align:start position:0%
+the huge effort of Noam ungrast that
+would be Josh's son uh they made an
+
+ align:start position:0%
+would be Josh's son uh they made an
+ 
+
+ align:start position:0%
+would be Josh's son uh they made an
+effort to uh harmonize
+
+ align:start position:0%
+effort to uh harmonize
+ 
+
+ align:start position:0%
+effort to uh harmonize
+the learning levels across
+
+ align:start position:0%
+the learning levels across
+ 
+
+ align:start position:0%
+the learning levels across
+across countries basically by linking
+
+ align:start position:0%
+across countries basically by linking
+ 
+
+ align:start position:0%
+across countries basically by linking
+them back to an uh to to an essay like
+
+ align:start position:0%
+them back to an uh to to an essay like
+ 
+
+ align:start position:0%
+them back to an uh to to an essay like
+skill so it's a skin in 600 but uh
+
+ align:start position:0%
+skill so it's a skin in 600 but uh
+ 
+
+ align:start position:0%
+skill so it's a skin in 600 but uh
+basically using countries like India for
+
+ align:start position:0%
+basically using countries like India for
+ 
+
+ align:start position:0%
+basically using countries like India for
+example that have both a pizza-like test
+
+ align:start position:0%
+example that have both a pizza-like test
+ 
+
+ align:start position:0%
+example that have both a pizza-like test
+and a simple instrument and then to
+
+ align:start position:0%
+and a simple instrument and then to
+ 
+
+ align:start position:0%
+and a simple instrument and then to
+create a sort of a crossover so every
+
+ align:start position:0%
+create a sort of a crossover so every
+ 
+
+ align:start position:0%
+create a sort of a crossover so every
+country that has the two tests can be
+
+ align:start position:0%
+country that has the two tests can be
+ 
+
+ align:start position:0%
+country that has the two tests can be
+used to create a crossover between the
+
+ align:start position:0%
+used to create a crossover between the
+ 
+
+ align:start position:0%
+used to create a crossover between the
+different tests and in this way you can
+
+ align:start position:0%
+different tests and in this way you can
+ 
+
+ align:start position:0%
+different tests and in this way you can
+move from you know to put on a common
+
+ align:start position:0%
+move from you know to put on a common
+ 
+
+ align:start position:0%
+move from you know to put on a common
+scale countries that don't have a tool
+
+ align:start position:0%
+scale countries that don't have a tool
+ 
+
+ align:start position:0%
+scale countries that don't have a tool
+or common test to it's kind of a chain
+
+ align:start position:0%
+or common test to it's kind of a chain
+ 
+
+ align:start position:0%
+or common test to it's kind of a chain
+of things
+
+ align:start position:0%
+of things
+ 
+
+ align:start position:0%
+of things
+so it's a little bit impressionistic but
+
+ align:start position:0%
+so it's a little bit impressionistic but
+ 
+
+ align:start position:0%
+so it's a little bit impressionistic but
+it's it's a nice database it's publicly
+
+ align:start position:0%
+it's it's a nice database it's publicly
+ 
+
+ align:start position:0%
+it's it's a nice database it's publicly
+available the published a small
+
+ align:start position:0%
+available the published a small
+ 
+
+ align:start position:0%
+available the published a small
+descriptive paper on it in nature
+
+ align:start position:0%
+descriptive paper on it in nature
+ 
+
+ align:start position:0%
+descriptive paper on it in nature
+presently and the data is available so
+
+ align:start position:0%
+presently and the data is available so
+ 
+
+ align:start position:0%
+presently and the data is available so
+that's something interesting to to play
+
+ align:start position:0%
+that's something interesting to to play
+ 
+
+ align:start position:0%
+that's something interesting to to play
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+and this is one of the descriptive
+
+ align:start position:0%
+and this is one of the descriptive
+ 
+
+ align:start position:0%
+and this is one of the descriptive
+things so it's kind of hard to interpret
+
+ align:start position:0%
+things so it's kind of hard to interpret
+ 
+
+ align:start position:0%
+things so it's kind of hard to interpret
+the scale of course it's 600 whatever
+
+ align:start position:0%
+the scale of course it's 600 whatever
+ 
+
+ align:start position:0%
+the scale of course it's 600 whatever
+that means but for example you have
+
+ align:start position:0%
+that means but for example you have
+ 
+
+ align:start position:0%
+that means but for example you have
+Singapore here the U.S here and the
+
+ align:start position:0%
+Singapore here the U.S here and the
+ 
+
+ align:start position:0%
+Singapore here the U.S here and the
+worst countries like way below so there
+
+ align:start position:0%
+worst countries like way below so there
+ 
+
+ align:start position:0%
+worst countries like way below so there
+is vast differences in the in in what
+
+ align:start position:0%
+is vast differences in the in in what
+ 
+
+ align:start position:0%
+is vast differences in the in in what
+people learn uh
+
+ align:start position:0%
+people learn uh
+ 
+
+ align:start position:0%
+people learn uh
+you know you know in what people do
+
+ align:start position:0%
+you know you know in what people do
+ 
+
+ align:start position:0%
+you know you know in what people do
+let's say from this learning test and
+
+ align:start position:0%
+let's say from this learning test and
+ 
+
+ align:start position:0%
+let's say from this learning test and
+generally it's pretty correlated with
+
+ align:start position:0%
+generally it's pretty correlated with
+ 
+
+ align:start position:0%
+generally it's pretty correlated with
+income levels
+
+ align:start position:0%
+income levels
+ 
+
+ align:start position:0%
+income levels
+where poor countries
+
+ align:start position:0%
+where poor countries
+ 
+
+ align:start position:0%
+where poor countries
+I think this kind of the cluster of
+
+ align:start position:0%
+I think this kind of the cluster of
+ 
+
+ align:start position:0%
+I think this kind of the cluster of
+African country here that does pretty
+
+ align:start position:0%
+African country here that does pretty
+ 
+
+ align:start position:0%
+African country here that does pretty
+badly uh India just to tell you that
+
+ align:start position:0%
+badly uh India just to tell you that
+ 
+
+ align:start position:0%
+badly uh India just to tell you that
+India that we that we've talked a lot
+
+ align:start position:0%
+India that we that we've talked a lot
+ 
+
+ align:start position:0%
+India that we that we've talked a lot
+about India and we are going to talk a
+
+ align:start position:0%
+about India and we are going to talk a
+ 
+
+ align:start position:0%
+about India and we are going to talk a
+fair amount about India you might think
+
+ align:start position:0%
+fair amount about India you might think
+ 
+
+ align:start position:0%
+fair amount about India you might think
+well in something specific about India
+
+ align:start position:0%
+well in something specific about India
+ 
+
+ align:start position:0%
+well in something specific about India
+it's not it's terrible but India is
+
+ align:start position:0%
+it's not it's terrible but India is
+ 
+
+ align:start position:0%
+it's not it's terrible but India is
+actually not that you know
+
+ align:start position:0%
+actually not that you know
+ 
+
+ align:start position:0%
+actually not that you know
+it's out of where it should be on the on
+
+ align:start position:0%
+it's out of where it should be on the on
+ 
+
+ align:start position:0%
+it's out of where it should be on the on
+the line so it's relatively specific uh
+
+ align:start position:0%
+the line so it's relatively specific uh
+ 
+
+ align:start position:0%
+the line so it's relatively specific uh
+relatively representative of what's
+
+ align:start position:0%
+relatively representative of what's
+ 
+
+ align:start position:0%
+relatively representative of what's
+going on in the world
+
+ align:start position:0%
+going on in the world
+ 
+
+ align:start position:0%
+going on in the world
+so that's the part that I would say is
+
+ align:start position:0%
+so that's the part that I would say is
+ 
+
+ align:start position:0%
+so that's the part that I would say is
+noon was noon and to start with it's a
+
+ align:start position:0%
+noon was noon and to start with it's a
+ 
+
+ align:start position:0%
+noon was noon and to start with it's a
+big problem that kids everyone's going
+
+ align:start position:0%
+big problem that kids everyone's going
+ 
+
+ align:start position:0%
+big problem that kids everyone's going
+to school they spend a lot of time in
+
+ align:start position:0%
+to school they spend a lot of time in
+ 
+
+ align:start position:0%
+to school they spend a lot of time in
+school and then alone
+
+ align:start position:0%
+school and then alone
+ 
+
+ align:start position:0%
+school and then alone
+very little seems to be a big waste of
+
+ align:start position:0%
+very little seems to be a big waste of
+ 
+
+ align:start position:0%
+very little seems to be a big waste of
+time for everyone involved
+
+ align:start position:0%
+time for everyone involved
+ 
+
+ align:start position:0%
+time for everyone involved
+and and a problem because
+
+ align:start position:0%
+and and a problem because
+ 
+
+ align:start position:0%
+and and a problem because
+it would be nice if people learned more
+
+ align:start position:0%
+it would be nice if people learned more
+ 
+
+ align:start position:0%
+it would be nice if people learned more
+but in some sense I've come to uh to
+
+ align:start position:0%
+but in some sense I've come to uh to
+ 
+
+ align:start position:0%
+but in some sense I've come to uh to
+realize that that might not be the worst
+
+ align:start position:0%
+realize that that might not be the worst
+ 
+
+ align:start position:0%
+realize that that might not be the worst
+problem that that schools are worse than
+
+ align:start position:0%
+problem that that schools are worse than
+ 
+
+ align:start position:0%
+problem that that schools are worse than
+that they are worse than
+
+ align:start position:0%
+that they are worse than
+ 
+
+ align:start position:0%
+that they are worse than
+not being a very effective production
+
+ align:start position:0%
+not being a very effective production
+ 
+
+ align:start position:0%
+not being a very effective production
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+and that in our focus on production
+
+ align:start position:0%
+and that in our focus on production
+ 
+
+ align:start position:0%
+and that in our focus on production
+function we are missing uh a couple of
+
+ align:start position:0%
+function we are missing uh a couple of
+ 
+
+ align:start position:0%
+function we are missing uh a couple of
+things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first one the the
+
+ align:start position:0%
+the first one the the
+ 
+
+ align:start position:0%
+the first one the the
+and the perhaps the most important thing
+
+ align:start position:0%
+and the perhaps the most important thing
+ 
+
+ align:start position:0%
+and the perhaps the most important thing
+which I want to uh which I want to
+
+ align:start position:0%
+which I want to uh which I want to
+ 
+
+ align:start position:0%
+which I want to uh which I want to
+convey is that schools are not only they
+
+ align:start position:0%
+convey is that schools are not only they
+ 
+
+ align:start position:0%
+convey is that schools are not only they
+are unable to teach anything but they
+
+ align:start position:0%
+are unable to teach anything but they
+ 
+
+ align:start position:0%
+are unable to teach anything but they
+are unable to leverage and to
+
+ align:start position:0%
+are unable to leverage and to
+ 
+
+ align:start position:0%
+are unable to leverage and to
+acknowledge the skills that already
+
+ align:start position:0%
+acknowledge the skills that already
+ 
+
+ align:start position:0%
+acknowledge the skills that already
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+uh so in fact they don't teach but they
+
+ align:start position:0%
+uh so in fact they don't teach but they
+ 
+
+ align:start position:0%
+uh so in fact they don't teach but they
+also have a role of certification and
+
+ align:start position:0%
+also have a role of certification and
+ 
+
+ align:start position:0%
+also have a role of certification and
+they also should you know leverage
+
+ align:start position:0%
+they also should you know leverage
+ 
+
+ align:start position:0%
+they also should you know leverage
+what's there and kind of transform it so
+
+ align:start position:0%
+what's there and kind of transform it so
+ 
+
+ align:start position:0%
+what's there and kind of transform it so
+that kids can learn more and they are
+
+ align:start position:0%
+that kids can learn more and they are
+ 
+
+ align:start position:0%
+that kids can learn more and they are
+completely unable to do that
+
+ align:start position:0%
+completely unable to do that
+ 
+
+ align:start position:0%
+completely unable to do that
+so not only they don't teach but they
+
+ align:start position:0%
+so not only they don't teach but they
+ 
+
+ align:start position:0%
+so not only they don't teach but they
+also don't certified knowledge that they
+
+ align:start position:0%
+also don't certified knowledge that they
+ 
+
+ align:start position:0%
+also don't certified knowledge that they
+that's already there so they are missing
+
+ align:start position:0%
+that's already there so they are missing
+ 
+
+ align:start position:0%
+that's already there so they are missing
+at their second task which is pretty
+
+ align:start position:0%
+at their second task which is pretty
+ 
+
+ align:start position:0%
+at their second task which is pretty
+important because that's what people
+
+ align:start position:0%
+important because that's what people
+ 
+
+ align:start position:0%
+important because that's what people
+you know are able usually to take to the
+
+ align:start position:0%
+you know are able usually to take to the
+ 
+
+ align:start position:0%
+you know are able usually to take to the
+labor market is a diploma
+
+ align:start position:0%
+labor market is a diploma
+ 
+
+ align:start position:0%
+labor market is a diploma
+if the school stood nothing at least
+
+ align:start position:0%
+if the school stood nothing at least
+ 
+
+ align:start position:0%
+if the school stood nothing at least
+they should be able to administers
+
+ align:start position:0%
+they should be able to administers
+ 
+
+ align:start position:0%
+they should be able to administers
+diploma that if you have the skills you
+
+ align:start position:0%
+diploma that if you have the skills you
+ 
+
+ align:start position:0%
+diploma that if you have the skills you
+should be able to to get the parchment
+
+ align:start position:0%
+should be able to to get the parchment
+ 
+
+ align:start position:0%
+should be able to to get the parchment
+paper that goes with it
+
+ align:start position:0%
+paper that goes with it
+ 
+
+ align:start position:0%
+paper that goes with it
+uh so why do I think that school are
+
+ align:start position:0%
+uh so why do I think that school are
+ 
+
+ align:start position:0%
+uh so why do I think that school are
+unable to
+
+ align:start position:0%
+unable to
+ 
+
+ align:start position:0%
+unable to
+to boost leverage and recognize the
+
+ align:start position:0%
+to boost leverage and recognize the
+ 
+
+ align:start position:0%
+to boost leverage and recognize the
+knowledge that's there
+
+ align:start position:0%
+knowledge that's there
+ 
+
+ align:start position:0%
+knowledge that's there
+so I'll give you two uh two examples
+
+ align:start position:0%
+so I'll give you two uh two examples
+ 
+
+ align:start position:0%
+so I'll give you two uh two examples
+where that's pretty egregious uh both
+
+ align:start position:0%
+where that's pretty egregious uh both
+ 
+
+ align:start position:0%
+where that's pretty egregious uh both
+I'm involved with uh one is a set of
+
+ align:start position:0%
+I'm involved with uh one is a set of
+ 
+
+ align:start position:0%
+I'm involved with uh one is a set of
+studies that I've done with a
+
+ align:start position:0%
+studies that I've done with a
+ 
+
+ align:start position:0%
+studies that I've done with a
+psychologist at Harvard uh Liz pelke who
+
+ align:start position:0%
+psychologist at Harvard uh Liz pelke who
+ 
+
+ align:start position:0%
+psychologist at Harvard uh Liz pelke who
+is a specialist of math
+
+ align:start position:0%
+is a specialist of math
+ 
+
+ align:start position:0%
+is a specialist of math
+Master Early Childhood Mass education
+
+ align:start position:0%
+Master Early Childhood Mass education
+ 
+
+ align:start position:0%
+Master Early Childhood Mass education
+and Justin who was then students here is
+
+ align:start position:0%
+and Justin who was then students here is
+ 
+
+ align:start position:0%
+and Justin who was then students here is
+now at Chicago
+
+ align:start position:0%
+now at Chicago
+ 
+
+ align:start position:0%
+now at Chicago
+and and a student of of Liz who is now
+
+ align:start position:0%
+and and a student of of Liz who is now
+ 
+
+ align:start position:0%
+and and a student of of Liz who is now
+at NYU in the psychology department
+
+ align:start position:0%
+at NYU in the psychology department
+ 
+
+ align:start position:0%
+at NYU in the psychology department
+uh so what we did is that so the
+
+ align:start position:0%
+uh so what we did is that so the
+ 
+
+ align:start position:0%
+uh so what we did is that so the
+objective of this work and the reason
+
+ align:start position:0%
+objective of this work and the reason
+ 
+
+ align:start position:0%
+objective of this work and the reason
+why I came to sort of came to see her
+
+ align:start position:0%
+why I came to sort of came to see her
+ 
+
+ align:start position:0%
+why I came to sort of came to see her
+and to ask her to work with me
+
+ align:start position:0%
+and to ask her to work with me
+ 
+
+ align:start position:0%
+and to ask her to work with me
+uh is going to come back in uh towards
+
+ align:start position:0%
+uh is going to come back in uh towards
+ 
+
+ align:start position:0%
+uh is going to come back in uh towards
+the end of this lecture where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I had been working with primary school
+
+ align:start position:0%
+I had been working with primary school
+ 
+
+ align:start position:0%
+I had been working with primary school
+and trying to improve the quality of
+
+ align:start position:0%
+and trying to improve the quality of
+ 
+
+ align:start position:0%
+and trying to improve the quality of
+primary school for a long time
+
+ align:start position:0%
+primary school for a long time
+ 
+
+ align:start position:0%
+primary school for a long time
+and found it very difficult because even
+
+ align:start position:0%
+and found it very difficult because even
+ 
+
+ align:start position:0%
+and found it very difficult because even
+though we have intervention that we know
+
+ align:start position:0%
+though we have intervention that we know
+ 
+
+ align:start position:0%
+though we have intervention that we know
+work it's like pulling teeth to get them
+
+ align:start position:0%
+work it's like pulling teeth to get them
+ 
+
+ align:start position:0%
+work it's like pulling teeth to get them
+adopted so we'll go back one of the
+
+ align:start position:0%
+adopted so we'll go back one of the
+ 
+
+ align:start position:0%
+adopted so we'll go back one of the
+things I want to discuss today is why
+
+ align:start position:0%
+things I want to discuss today is why
+ 
+
+ align:start position:0%
+things I want to discuss today is why
+that's the case but for now take that
+
+ align:start position:0%
+that's the case but for now take that
+ 
+
+ align:start position:0%
+that's the case but for now take that
+for a fact
+
+ align:start position:0%
+for a fact
+ 
+
+ align:start position:0%
+for a fact
+we have ideas of what what works but
+
+ align:start position:0%
+we have ideas of what what works but
+ 
+
+ align:start position:0%
+we have ideas of what what works but
+nobody is interested in it okay so I
+
+ align:start position:0%
+nobody is interested in it okay so I
+ 
+
+ align:start position:0%
+nobody is interested in it okay so I
+felt but at the same time more and more
+
+ align:start position:0%
+felt but at the same time more and more
+ 
+
+ align:start position:0%
+felt but at the same time more and more
+kids go to preschools
+
+ align:start position:0%
+kids go to preschools
+ 
+
+ align:start position:0%
+kids go to preschools
+and there nobody cares what they do in
+
+ align:start position:0%
+and there nobody cares what they do in
+ 
+
+ align:start position:0%
+and there nobody cares what they do in
+preschool
+
+ align:start position:0%
+preschool
+ 
+
+ align:start position:0%
+preschool
+oh it could be singing or mopping the
+
+ align:start position:0%
+oh it could be singing or mopping the
+ 
+
+ align:start position:0%
+oh it could be singing or mopping the
+floor or whatever it doesn't really
+
+ align:start position:0%
+floor or whatever it doesn't really
+ 
+
+ align:start position:0%
+floor or whatever it doesn't really
+matter it's child care so no one has
+
+ align:start position:0%
+matter it's child care so no one has
+ 
+
+ align:start position:0%
+matter it's child care so no one has
+much of a view
+
+ align:start position:0%
+much of a view
+ 
+
+ align:start position:0%
+much of a view
+so I thought well that's like a margin
+
+ align:start position:0%
+so I thought well that's like a margin
+ 
+
+ align:start position:0%
+so I thought well that's like a margin
+of action
+
+ align:start position:0%
+of action
+ 
+
+ align:start position:0%
+of action
+we should try and act in preschool to
+
+ align:start position:0%
+we should try and act in preschool to
+ 
+
+ align:start position:0%
+we should try and act in preschool to
+make the poor kids ready for school
+
+ align:start position:0%
+make the poor kids ready for school
+ 
+
+ align:start position:0%
+make the poor kids ready for school
+rather than try to fix the problem once
+
+ align:start position:0%
+rather than try to fix the problem once
+ 
+
+ align:start position:0%
+rather than try to fix the problem once
+they are in school
+
+ align:start position:0%
+they are in school
+ 
+
+ align:start position:0%
+they are in school
+and since Liz was working on on Early
+
+ align:start position:0%
+and since Liz was working on on Early
+ 
+
+ align:start position:0%
+and since Liz was working on on Early
+Childhood acquisition of math I thought
+
+ align:start position:0%
+Childhood acquisition of math I thought
+ 
+
+ align:start position:0%
+Childhood acquisition of math I thought
+maybe she knows something about or can
+
+ align:start position:0%
+maybe she knows something about or can
+ 
+
+ align:start position:0%
+maybe she knows something about or can
+develop something about that that we can
+
+ align:start position:0%
+develop something about that that we can
+ 
+
+ align:start position:0%
+develop something about that that we can
+Implement in in preschools to make the
+
+ align:start position:0%
+Implement in in preschools to make the
+ 
+
+ align:start position:0%
+Implement in in preschools to make the
+kids in preschool ahead of the game and
+
+ align:start position:0%
+kids in preschool ahead of the game and
+ 
+
+ align:start position:0%
+kids in preschool ahead of the game and
+able to understand better what's going
+
+ align:start position:0%
+able to understand better what's going
+ 
+
+ align:start position:0%
+able to understand better what's going
+on in school
+
+ align:start position:0%
+on in school
+ 
+
+ align:start position:0%
+on in school
+so uh so she was super interested in
+
+ align:start position:0%
+so uh so she was super interested in
+ 
+
+ align:start position:0%
+so uh so she was super interested in
+doing that so we started with a small
+
+ align:start position:0%
+doing that so we started with a small
+ 
+
+ align:start position:0%
+doing that so we started with a small
+experiment about 1500 kids in uh
+
+ align:start position:0%
+experiment about 1500 kids in uh
+ 
+
+ align:start position:0%
+experiment about 1500 kids in uh
+in preschool preschool classes operated
+
+ align:start position:0%
+in preschool preschool classes operated
+ 
+
+ align:start position:0%
+in preschool preschool classes operated
+by pratam in Delhi so this is kind of a
+
+ align:start position:0%
+by pratam in Delhi so this is kind of a
+ 
+
+ align:start position:0%
+by pratam in Delhi so this is kind of a
+class which is on a porch like a few
+
+ align:start position:0%
+class which is on a porch like a few
+ 
+
+ align:start position:0%
+class which is on a porch like a few
+kids and a young woman that's your class
+
+ align:start position:0%
+kids and a young woman that's your class
+ 
+
+ align:start position:0%
+kids and a young woman that's your class
+and they are playing one of our games so
+
+ align:start position:0%
+and they are playing one of our games so
+ 
+
+ align:start position:0%
+and they are playing one of our games so
+we are three condition
+
+ align:start position:0%
+we are three condition
+ 
+
+ align:start position:0%
+we are three condition
+one is math games where they played a
+
+ align:start position:0%
+one is math games where they played a
+ 
+
+ align:start position:0%
+one is math games where they played a
+curricula for a few weeks a whole
+
+ align:start position:0%
+curricula for a few weeks a whole
+ 
+
+ align:start position:0%
+curricula for a few weeks a whole
+curriculum on
+
+ align:start position:0%
+curriculum on
+ 
+
+ align:start position:0%
+curriculum on
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+kind of building
+
+ align:start position:0%
+kind of building
+ 
+
+ align:start position:0%
+kind of building
+non-symbolic math skills I'll tell you
+
+ align:start position:0%
+non-symbolic math skills I'll tell you
+ 
+
+ align:start position:0%
+non-symbolic math skills I'll tell you
+what it is in a second how it works then
+
+ align:start position:0%
+what it is in a second how it works then
+ 
+
+ align:start position:0%
+what it is in a second how it works then
+we had a sort of active control
+
+ align:start position:0%
+we had a sort of active control
+ 
+
+ align:start position:0%
+we had a sort of active control
+condition which is playing very similar
+
+ align:start position:0%
+condition which is playing very similar
+ 
+
+ align:start position:0%
+condition which is playing very similar
+games but to teach social skills instead
+
+ align:start position:0%
+games but to teach social skills instead
+ 
+
+ align:start position:0%
+games but to teach social skills instead
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+math the idea was not so much to teach
+
+ align:start position:0%
+math the idea was not so much to teach
+ 
+
+ align:start position:0%
+math the idea was not so much to teach
+social skills although why not it
+
+ align:start position:0%
+social skills although why not it
+ 
+
+ align:start position:0%
+social skills although why not it
+doesn't hurt but mainly to have a
+
+ align:start position:0%
+doesn't hurt but mainly to have a
+ 
+
+ align:start position:0%
+doesn't hurt but mainly to have a
+because not much is happens in those
+
+ align:start position:0%
+because not much is happens in those
+ 
+
+ align:start position:0%
+because not much is happens in those
+schools at all in general so we didn't
+
+ align:start position:0%
+schools at all in general so we didn't
+ 
+
+ align:start position:0%
+schools at all in general so we didn't
+want to say that they're learning better
+
+ align:start position:0%
+want to say that they're learning better
+ 
+
+ align:start position:0%
+want to say that they're learning better
+because someone is finally talking to
+
+ align:start position:0%
+because someone is finally talking to
+ 
+
+ align:start position:0%
+because someone is finally talking to
+them but they could be talking to them
+
+ align:start position:0%
+them but they could be talking to them
+ 
+
+ align:start position:0%
+them but they could be talking to them
+about something totally different so
+
+ align:start position:0%
+about something totally different so
+ 
+
+ align:start position:0%
+about something totally different so
+that's our active control and then a
+
+ align:start position:0%
+that's our active control and then a
+ 
+
+ align:start position:0%
+that's our active control and then a
+normal curriculum
+
+ align:start position:0%
+normal curriculum
+ 
+
+ align:start position:0%
+normal curriculum
+uh so we did some pretest and the games
+
+ align:start position:0%
+uh so we did some pretest and the games
+ 
+
+ align:start position:0%
+uh so we did some pretest and the games
+uh for three months and then a first
+
+ align:start position:0%
+uh for three months and then a first
+ 
+
+ align:start position:0%
+uh for three months and then a first
+post test and then we continued tracking
+
+ align:start position:0%
+post test and then we continued tracking
+ 
+
+ align:start position:0%
+post test and then we continued tracking
+the kids after they've reached school so
+
+ align:start position:0%
+the kids after they've reached school so
+ 
+
+ align:start position:0%
+the kids after they've reached school so
+long time after we have anything to do
+
+ align:start position:0%
+long time after we have anything to do
+ 
+
+ align:start position:0%
+long time after we have anything to do
+with them and in a sense that's the key
+
+ align:start position:0%
+with them and in a sense that's the key
+ 
+
+ align:start position:0%
+with them and in a sense that's the key
+is um
+
+ align:start position:0%
+is um
+ 
+
+ align:start position:0%
+is um
+so that's sort of that's the the game so
+
+ align:start position:0%
+so that's sort of that's the the game so
+ 
+
+ align:start position:0%
+so that's sort of that's the the game so
+this is based on this idea that uh um
+
+ align:start position:0%
+this is based on this idea that uh um
+ 
+
+ align:start position:0%
+this is based on this idea that uh um
+this cognitive scientists developed that
+
+ align:start position:0%
+this cognitive scientists developed that
+ 
+
+ align:start position:0%
+this cognitive scientists developed that
+before uh humans or in fact animals
+
+ align:start position:0%
+before uh humans or in fact animals
+ 
+
+ align:start position:0%
+before uh humans or in fact animals
+develop any notion of symbolic
+
+ align:start position:0%
+develop any notion of symbolic
+ 
+
+ align:start position:0%
+develop any notion of symbolic
+mathematics so understand numbers for
+
+ align:start position:0%
+mathematics so understand numbers for
+ 
+
+ align:start position:0%
+mathematics so understand numbers for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+we already have a sense of some basic
+
+ align:start position:0%
+we already have a sense of some basic
+ 
+
+ align:start position:0%
+we already have a sense of some basic
+sense of mathematics for example what is
+
+ align:start position:0%
+sense of mathematics for example what is
+ 
+
+ align:start position:0%
+sense of mathematics for example what is
+bigger and what is smaller
+
+ align:start position:0%
+bigger and what is smaller
+ 
+
+ align:start position:0%
+bigger and what is smaller
+and bearing extreme disability everyone
+
+ align:start position:0%
+and bearing extreme disability everyone
+ 
+
+ align:start position:0%
+and bearing extreme disability everyone
+has that
+
+ align:start position:0%
+has that
+ 
+
+ align:start position:0%
+has that
+and it can be trained you can become
+
+ align:start position:0%
+and it can be trained you can become
+ 
+
+ align:start position:0%
+and it can be trained you can become
+better at it
+
+ align:start position:0%
+better at it
+ 
+
+ align:start position:0%
+better at it
+and uh from a purely correlational point
+
+ align:start position:0%
+and uh from a purely correlational point
+ 
+
+ align:start position:0%
+and uh from a purely correlational point
+of view kids who were better at this
+
+ align:start position:0%
+of view kids who were better at this
+ 
+
+ align:start position:0%
+of view kids who were better at this
+type of test when they were five
+
+ align:start position:0%
+type of test when they were five
+ 
+
+ align:start position:0%
+type of test when they were five
+are doing better at Pisa mathematics at
+
+ align:start position:0%
+are doing better at Pisa mathematics at
+ 
+
+ align:start position:0%
+are doing better at Pisa mathematics at
+15.
+
+ align:start position:0%
+15.
+ 
+
+ align:start position:0%
+15.
+of course what we don't know is that it
+
+ align:start position:0%
+of course what we don't know is that it
+ 
+
+ align:start position:0%
+of course what we don't know is that it
+means they have an underlying ability
+
+ align:start position:0%
+means they have an underlying ability
+ 
+
+ align:start position:0%
+means they have an underlying ability
+that makes them good at all sorts of
+
+ align:start position:0%
+that makes them good at all sorts of
+ 
+
+ align:start position:0%
+that makes them good at all sorts of
+math or whether this is that
+
+ align:start position:0%
+math or whether this is that
+ 
+
+ align:start position:0%
+math or whether this is that
+non-symbolic skills that kind of they
+
+ align:start position:0%
+non-symbolic skills that kind of they
+ 
+
+ align:start position:0%
+non-symbolic skills that kind of they
+built on more effectively to learn math
+
+ align:start position:0%
+built on more effectively to learn math
+ 
+
+ align:start position:0%
+built on more effectively to learn math
+through that there toward their career
+
+ align:start position:0%
+through that there toward their career
+ 
+
+ align:start position:0%
+through that there toward their career
+uh but what she what what they certainly
+
+ align:start position:0%
+uh but what she what what they certainly
+ 
+
+ align:start position:0%
+uh but what she what what they certainly
+hoped is that that was the case and
+
+ align:start position:0%
+hoped is that that was the case and
+ 
+
+ align:start position:0%
+hoped is that that was the case and
+therefore our the idea of our curriculum
+
+ align:start position:0%
+therefore our the idea of our curriculum
+ 
+
+ align:start position:0%
+therefore our the idea of our curriculum
+was initially to train non-symbolic math
+
+ align:start position:0%
+was initially to train non-symbolic math
+ 
+
+ align:start position:0%
+was initially to train non-symbolic math
+skills only
+
+ align:start position:0%
+skills only
+ 
+
+ align:start position:0%
+skills only
+and to see whether there is a
+
+ align:start position:0%
+and to see whether there is a
+ 
+
+ align:start position:0%
+and to see whether there is a
+translation of this impossible whether
+
+ align:start position:0%
+translation of this impossible whether
+ 
+
+ align:start position:0%
+translation of this impossible whether
+that can be trained and second of all
+
+ align:start position:0%
+that can be trained and second of all
+ 
+
+ align:start position:0%
+that can be trained and second of all
+whether if we manage to train them
+
+ align:start position:0%
+whether if we manage to train them
+ 
+
+ align:start position:0%
+whether if we manage to train them
+whether there is a translation in
+
+ align:start position:0%
+whether there is a translation in
+ 
+
+ align:start position:0%
+whether there is a translation in
+symbolic muskets down the line
+
+ align:start position:0%
+symbolic muskets down the line
+ 
+
+ align:start position:0%
+symbolic muskets down the line
+so that's an example of a game you have
+
+ align:start position:0%
+so that's an example of a game you have
+ 
+
+ align:start position:0%
+so that's an example of a game you have
+a card you do one has more dots than the
+
+ align:start position:0%
+a card you do one has more dots than the
+ 
+
+ align:start position:0%
+a card you do one has more dots than the
+other I think you can guess without
+
+ align:start position:0%
+other I think you can guess without
+ 
+
+ align:start position:0%
+other I think you can guess without
+counting and so the kids move the one
+
+ align:start position:0%
+counting and so the kids move the one
+ 
+
+ align:start position:0%
+counting and so the kids move the one
+that has murdered towards the the red
+
+ align:start position:0%
+that has murdered towards the the red
+ 
+
+ align:start position:0%
+that has murdered towards the the red
+bar this turn that's the hardest one
+
+ align:start position:0%
+bar this turn that's the hardest one
+ 
+
+ align:start position:0%
+bar this turn that's the hardest one
+because there are more points so young
+
+ align:start position:0%
+because there are more points so young
+ 
+
+ align:start position:0%
+because there are more points so young
+kids cannot do the many points and then
+
+ align:start position:0%
+kids cannot do the many points and then
+ 
+
+ align:start position:0%
+kids cannot do the many points and then
+as you get older and you can practice
+
+ align:start position:0%
+as you get older and you can practice
+ 
+
+ align:start position:0%
+as you get older and you can practice
+with that and then you become better as
+
+ align:start position:0%
+with that and then you become better as
+ 
+
+ align:start position:0%
+with that and then you become better as
+you practice then when they turn the
+
+ align:start position:0%
+you practice then when they turn the
+ 
+
+ align:start position:0%
+you practice then when they turn the
+count it actually gives them some
+
+ align:start position:0%
+count it actually gives them some
+ 
+
+ align:start position:0%
+count it actually gives them some
+her presentation including symbols so
+
+ align:start position:0%
+her presentation including symbols so
+ 
+
+ align:start position:0%
+her presentation including symbols so
+that introduces a little bit of the
+
+ align:start position:0%
+that introduces a little bit of the
+ 
+
+ align:start position:0%
+that introduces a little bit of the
+translation
+
+ align:start position:0%
+translation
+ 
+
+ align:start position:0%
+translation
+one can one thing kids are also
+
+ align:start position:0%
+one can one thing kids are also
+ 
+
+ align:start position:0%
+one can one thing kids are also
+surprisingly good is visual form
+
+ align:start position:0%
+surprisingly good is visual form
+ 
+
+ align:start position:0%
+surprisingly good is visual form
+analysis so here it's like there's one
+
+ align:start position:0%
+analysis so here it's like there's one
+ 
+
+ align:start position:0%
+analysis so here it's like there's one
+car that's not the same as the other
+
+ align:start position:0%
+car that's not the same as the other
+ 
+
+ align:start position:0%
+car that's not the same as the other
+uh what's the card that's different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the one that had the floating point so
+
+ align:start position:0%
+the one that had the floating point so
+ 
+
+ align:start position:0%
+the one that had the floating point so
+they choose these are Plastics and they
+
+ align:start position:0%
+they choose these are Plastics and they
+ 
+
+ align:start position:0%
+they choose these are Plastics and they
+choose oh that was the wrong one that's
+
+ align:start position:0%
+choose oh that was the wrong one that's
+ 
+
+ align:start position:0%
+choose oh that was the wrong one that's
+the right one
+
+ align:start position:0%
+the right one
+ 
+
+ align:start position:0%
+the right one
+uh and then we had very very similar
+
+ align:start position:0%
+uh and then we had very very similar
+ 
+
+ align:start position:0%
+uh and then we had very very similar
+things for uh various structures same
+
+ align:start position:0%
+things for uh various structures same
+ 
+
+ align:start position:0%
+things for uh various structures same
+rules to learn
+
+ align:start position:0%
+rules to learn
+ 
+
+ align:start position:0%
+rules to learn
+emotion and gaze so for example this is
+
+ align:start position:0%
+emotion and gaze so for example this is
+ 
+
+ align:start position:0%
+emotion and gaze so for example this is
+the odd one out all of these are
+
+ align:start position:0%
+the odd one out all of these are
+ 
+
+ align:start position:0%
+the odd one out all of these are
+reasonably happy this one is so that's
+
+ align:start position:0%
+reasonably happy this one is so that's
+ 
+
+ align:start position:0%
+reasonably happy this one is so that's
+the equivalent for social games so we
+
+ align:start position:0%
+the equivalent for social games so we
+ 
+
+ align:start position:0%
+the equivalent for social games so we
+kind of constructed games that were
+
+ align:start position:0%
+kind of constructed games that were
+ 
+
+ align:start position:0%
+kind of constructed games that were
+precisely the same but
+
+ align:start position:0%
+precisely the same but
+ 
+
+ align:start position:0%
+precisely the same but
+in that sense working with psychologist
+
+ align:start position:0%
+in that sense working with psychologist
+ 
+
+ align:start position:0%
+in that sense working with psychologist
+is interesting because they really get
+
+ align:start position:0%
+is interesting because they really get
+ 
+
+ align:start position:0%
+is interesting because they really get
+into the details of things more than we
+
+ align:start position:0%
+into the details of things more than we
+ 
+
+ align:start position:0%
+into the details of things more than we
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+okay what do we find so the first
+
+ align:start position:0%
+okay what do we find so the first
+ 
+
+ align:start position:0%
+okay what do we find so the first
+finding and I want you to keep that and
+
+ align:start position:0%
+finding and I want you to keep that and
+ 
+
+ align:start position:0%
+finding and I want you to keep that and
+hold that suit because that's going to
+
+ align:start position:0%
+hold that suit because that's going to
+ 
+
+ align:start position:0%
+hold that suit because that's going to
+come
+
+ align:start position:0%
+come
+ 
+
+ align:start position:0%
+come
+handy in a little while
+
+ align:start position:0%
+handy in a little while
+ 
+
+ align:start position:0%
+handy in a little while
+is that the kids so this test these
+
+ align:start position:0%
+is that the kids so this test these
+ 
+
+ align:start position:0%
+is that the kids so this test these
+games were developed in Harvard in
+
+ align:start position:0%
+games were developed in Harvard in
+ 
+
+ align:start position:0%
+games were developed in Harvard in
+Lisa's Lab at Harvard
+
+ align:start position:0%
+Lisa's Lab at Harvard
+ 
+
+ align:start position:0%
+Lisa's Lab at Harvard
+and tested in Cambridge with whoever
+
+ align:start position:0%
+and tested in Cambridge with whoever
+ 
+
+ align:start position:0%
+and tested in Cambridge with whoever
+rather his volunteer if you have kids
+
+ align:start position:0%
+rather his volunteer if you have kids
+ 
+
+ align:start position:0%
+rather his volunteer if you have kids
+you can go from infant to uh to 10 I've
+
+ align:start position:0%
+you can go from infant to uh to 10 I've
+ 
+
+ align:start position:0%
+you can go from infant to uh to 10 I've
+taken my own kids it's quite fun they
+
+ align:start position:0%
+taken my own kids it's quite fun they
+ 
+
+ align:start position:0%
+taken my own kids it's quite fun they
+make them play all sorts of experiment
+
+ align:start position:0%
+make them play all sorts of experiment
+ 
+
+ align:start position:0%
+make them play all sorts of experiment
+and then in particular they came and
+
+ align:start position:0%
+and then in particular they came and
+ 
+
+ align:start position:0%
+and then in particular they came and
+played our
+
+ align:start position:0%
+played our
+ 
+
+ align:start position:0%
+played our
+they came and played out our games so we
+
+ align:start position:0%
+they came and played out our games so we
+ 
+
+ align:start position:0%
+they came and played out our games so we
+have observations from the kids mostly
+
+ align:start position:0%
+have observations from the kids mostly
+ 
+
+ align:start position:0%
+have observations from the kids mostly
+of postdoctoral students and assistant
+
+ align:start position:0%
+of postdoctoral students and assistant
+ 
+
+ align:start position:0%
+of postdoctoral students and assistant
+professors and that kind of things in
+
+ align:start position:0%
+professors and that kind of things in
+ 
+
+ align:start position:0%
+professors and that kind of things in
+Cambridge and and then we did the exact
+
+ align:start position:0%
+Cambridge and and then we did the exact
+ 
+
+ align:start position:0%
+Cambridge and and then we did the exact
+same you know we have the exact same
+
+ align:start position:0%
+same you know we have the exact same
+ 
+
+ align:start position:0%
+same you know we have the exact same
+measurement for these Indian kids who
+
+ align:start position:0%
+measurement for these Indian kids who
+ 
+
+ align:start position:0%
+measurement for these Indian kids who
+are living in slums in Delhi
+
+ align:start position:0%
+are living in slums in Delhi
+ 
+
+ align:start position:0%
+are living in slums in Delhi
+and they are just as good at playing
+
+ align:start position:0%
+and they are just as good at playing
+ 
+
+ align:start position:0%
+and they are just as good at playing
+these games they learn the rules they
+
+ align:start position:0%
+these games they learn the rules they
+ 
+
+ align:start position:0%
+these games they learn the rules they
+are able to learn quickly they progress
+
+ align:start position:0%
+are able to learn quickly they progress
+ 
+
+ align:start position:0%
+are able to learn quickly they progress
+fast
+
+ align:start position:0%
+fast
+ 
+
+ align:start position:0%
+fast
+they have just as much of these poor
+
+ align:start position:0%
+they have just as much of these poor
+ 
+
+ align:start position:0%
+they have just as much of these poor
+Indian kids have just as much an
+
+ align:start position:0%
+Indian kids have just as much an
+ 
+
+ align:start position:0%
+Indian kids have just as much an
+intuitive grasp and interesting number
+
+ align:start position:0%
+intuitive grasp and interesting number
+ 
+
+ align:start position:0%
+intuitive grasp and interesting number
+and geometry as the kids of uh of uh you
+
+ align:start position:0%
+and geometry as the kids of uh of uh you
+ 
+
+ align:start position:0%
+and geometry as the kids of uh of uh you
+know the faculty brats in in the in
+
+ align:start position:0%
+know the faculty brats in in the in
+ 
+
+ align:start position:0%
+know the faculty brats in in the in
+in Cambridge
+
+ align:start position:0%
+in Cambridge
+ 
+
+ align:start position:0%
+in Cambridge
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+kind of descriptive nothing to do with
+
+ align:start position:0%
+kind of descriptive nothing to do with
+ 
+
+ align:start position:0%
+kind of descriptive nothing to do with
+the intervention but it's interesting
+
+ align:start position:0%
+the intervention but it's interesting
+ 
+
+ align:start position:0%
+the intervention but it's interesting
+the second thing is that you can
+
+ align:start position:0%
+the second thing is that you can
+ 
+
+ align:start position:0%
+the second thing is that you can
+definitely train those these
+
+ align:start position:0%
+definitely train those these
+ 
+
+ align:start position:0%
+definitely train those these
+non-symbolic Mass test uh this bar is
+
+ align:start position:0%
+non-symbolic Mass test uh this bar is
+ 
+
+ align:start position:0%
+non-symbolic Mass test uh this bar is
+simply the difference between a
+
+ align:start position:0%
+simply the difference between a
+ 
+
+ align:start position:0%
+simply the difference between a
+treatment and the control control and
+
+ align:start position:0%
+treatment and the control control and
+ 
+
+ align:start position:0%
+treatment and the control control and
+then for the for the symbolic for the
+
+ align:start position:0%
+then for the for the symbolic for the
+ 
+
+ align:start position:0%
+then for the for the symbolic for the
+math games and that for the social games
+
+ align:start position:0%
+math games and that for the social games
+ 
+
+ align:start position:0%
+math games and that for the social games
+you can see that even with the social
+
+ align:start position:0%
+you can see that even with the social
+ 
+
+ align:start position:0%
+you can see that even with the social
+games they make progress so that's the
+
+ align:start position:0%
+games they make progress so that's the
+ 
+
+ align:start position:0%
+games they make progress so that's the
+fact that someone is you know teaching
+
+ align:start position:0%
+fact that someone is you know teaching
+ 
+
+ align:start position:0%
+fact that someone is you know teaching
+them to play games and all that that's
+
+ align:start position:0%
+them to play games and all that that's
+ 
+
+ align:start position:0%
+them to play games and all that that's
+probably not related to their ability to
+
+ align:start position:0%
+probably not related to their ability to
+ 
+
+ align:start position:0%
+probably not related to their ability to
+do the the tests uh so these tests are
+
+ align:start position:0%
+do the the tests uh so these tests are
+ 
+
+ align:start position:0%
+do the the tests uh so these tests are
+now presented in a completely
+
+ align:start position:0%
+now presented in a completely
+ 
+
+ align:start position:0%
+now presented in a completely
+non-gamified way but it's still the same
+
+ align:start position:0%
+non-gamified way but it's still the same
+ 
+
+ align:start position:0%
+non-gamified way but it's still the same
+type of things and they are much better
+
+ align:start position:0%
+type of things and they are much better
+ 
+
+ align:start position:0%
+type of things and they are much better
+at it
+
+ align:start position:0%
+at it
+ 
+
+ align:start position:0%
+at it
+much better even than the social games
+
+ align:start position:0%
+much better even than the social games
+ 
+
+ align:start position:0%
+much better even than the social games
+so that's one
+
+ align:start position:0%
+so that's one
+ 
+
+ align:start position:0%
+so that's one
+the second finding is that that's this
+
+ align:start position:0%
+the second finding is that that's this
+ 
+
+ align:start position:0%
+the second finding is that that's this
+this impact in particular the difference
+
+ align:start position:0%
+this impact in particular the difference
+ 
+
+ align:start position:0%
+this impact in particular the difference
+between math and social which is a true
+
+ align:start position:0%
+between math and social which is a true
+ 
+
+ align:start position:0%
+between math and social which is a true
+effect of learning the math it is it's
+
+ align:start position:0%
+effect of learning the math it is it's
+ 
+
+ align:start position:0%
+effect of learning the math it is it's
+remarkably stable
+
+ align:start position:0%
+remarkably stable
+ 
+
+ align:start position:0%
+remarkably stable
+uh you know what 18 months later they
+
+ align:start position:0%
+uh you know what 18 months later they
+ 
+
+ align:start position:0%
+uh you know what 18 months later they
+are still just as much better at it so
+
+ align:start position:0%
+are still just as much better at it so
+ 
+
+ align:start position:0%
+are still just as much better at it so
+it's not just that you know temporarily
+
+ align:start position:0%
+it's not just that you know temporarily
+ 
+
+ align:start position:0%
+it's not just that you know temporarily
+they got a weekend and that's striking
+
+ align:start position:0%
+they got a weekend and that's striking
+ 
+
+ align:start position:0%
+they got a weekend and that's striking
+because most educational intervention
+
+ align:start position:0%
+because most educational intervention
+ 
+
+ align:start position:0%
+because most educational intervention
+have impacted the advantage over time so
+
+ align:start position:0%
+have impacted the advantage over time so
+ 
+
+ align:start position:0%
+have impacted the advantage over time so
+usually you find an effect and then it
+
+ align:start position:0%
+usually you find an effect and then it
+ 
+
+ align:start position:0%
+usually you find an effect and then it
+goes away as you know life occurs
+
+ align:start position:0%
+goes away as you know life occurs
+ 
+
+ align:start position:0%
+goes away as you know life occurs
+interestingly We are following these
+
+ align:start position:0%
+interestingly We are following these
+ 
+
+ align:start position:0%
+interestingly We are following these
+kids now so this is like now they are in
+
+ align:start position:0%
+kids now so this is like now they are in
+ 
+
+ align:start position:0%
+kids now so this is like now they are in
+middle school so we are kind of
+
+ align:start position:0%
+middle school so we are kind of
+ 
+
+ align:start position:0%
+middle school so we are kind of
+interested to see whether it's still
+
+ align:start position:0%
+interested to see whether it's still
+ 
+
+ align:start position:0%
+interested to see whether it's still
+there but you know 18 months later it's
+
+ align:start position:0%
+there but you know 18 months later it's
+ 
+
+ align:start position:0%
+there but you know 18 months later it's
+still there
+
+ align:start position:0%
+still there
+ 
+
+ align:start position:0%
+still there
+third finding
+
+ align:start position:0%
+third finding
+ 
+
+ align:start position:0%
+third finding
+ah at end line one they are still with
+
+ align:start position:0%
+ah at end line one they are still with
+ 
+
+ align:start position:0%
+ah at end line one they are still with
+us they are still in the in the pattern
+
+ align:start position:0%
+us they are still in the in the pattern
+ 
+
+ align:start position:0%
+us they are still in the in the pattern
+preschool and pardon preschool does
+
+ align:start position:0%
+preschool and pardon preschool does
+ 
+
+ align:start position:0%
+preschool and pardon preschool does
+start introducing numbers and that type
+
+ align:start position:0%
+start introducing numbers and that type
+ 
+
+ align:start position:0%
+start introducing numbers and that type
+of things
+
+ align:start position:0%
+of things
+ 
+
+ align:start position:0%
+of things
+and at this point the effect is smaller
+
+ align:start position:0%
+and at this point the effect is smaller
+ 
+
+ align:start position:0%
+and at this point the effect is smaller
+so we can also test them on whether they
+
+ align:start position:0%
+so we can also test them on whether they
+ 
+
+ align:start position:0%
+so we can also test them on whether they
+can recognize numbers and shape and you
+
+ align:start position:0%
+can recognize numbers and shape and you
+ 
+
+ align:start position:0%
+can recognize numbers and shape and you
+know do you know that this is a this is
+
+ align:start position:0%
+know do you know that this is a this is
+ 
+
+ align:start position:0%
+know do you know that this is a this is
+a circle this is a rhombus Etc or the
+
+ align:start position:0%
+a circle this is a rhombus Etc or the
+ 
+
+ align:start position:0%
+a circle this is a rhombus Etc or the
+other numbers and they are somewhat
+
+ align:start position:0%
+other numbers and they are somewhat
+ 
+
+ align:start position:0%
+other numbers and they are somewhat
+better at it
+
+ align:start position:0%
+better at it
+ 
+
+ align:start position:0%
+better at it
+at inline one
+
+ align:start position:0%
+at inline one
+ 
+
+ align:start position:0%
+at inline one
+but then that difference entirely goes
+
+ align:start position:0%
+but then that difference entirely goes
+ 
+
+ align:start position:0%
+but then that difference entirely goes
+away as soon as I reach School
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so initiate so they start with them you
+
+ align:start position:0%
+so initiate so they start with them you
+ 
+
+ align:start position:0%
+so initiate so they start with them you
+know they arrive at school with a much
+
+ align:start position:0%
+know they arrive at school with a much
+ 
+
+ align:start position:0%
+know they arrive at school with a much
+greater sense of abstract mathematics
+
+ align:start position:0%
+greater sense of abstract mathematics
+ 
+
+ align:start position:0%
+greater sense of abstract mathematics
+as long as they were in the part-time
+
+ align:start position:0%
+as long as they were in the part-time
+ 
+
+ align:start position:0%
+as long as they were in the part-time
+environment there were some translation
+
+ align:start position:0%
+environment there were some translation
+ 
+
+ align:start position:0%
+environment there were some translation
+of that sense of abstract mathematics to
+
+ align:start position:0%
+of that sense of abstract mathematics to
+ 
+
+ align:start position:0%
+of that sense of abstract mathematics to
+not non-abstract mathematics but as soon
+
+ align:start position:0%
+not non-abstract mathematics but as soon
+ 
+
+ align:start position:0%
+not non-abstract mathematics but as soon
+as they leave school the rich school
+
+ align:start position:0%
+as they leave school the rich school
+ 
+
+ align:start position:0%
+as they leave school the rich school
+this is gone
+
+ align:start position:0%
+this is gone
+ 
+
+ align:start position:0%
+this is gone
+and uh so that's that's the result I
+
+ align:start position:0%
+and uh so that's that's the result I
+ 
+
+ align:start position:0%
+and uh so that's that's the result I
+want to this means this is a failure as
+
+ align:start position:0%
+want to this means this is a failure as
+ 
+
+ align:start position:0%
+want to this means this is a failure as
+an intervention for my from my objective
+
+ align:start position:0%
+an intervention for my from my objective
+ 
+
+ align:start position:0%
+an intervention for my from my objective
+but it's still an important result
+
+ align:start position:0%
+but it's still an important result
+ 
+
+ align:start position:0%
+but it's still an important result
+because what is telling us is that
+
+ align:start position:0%
+because what is telling us is that
+ 
+
+ align:start position:0%
+because what is telling us is that
+these kids have acquired these kids have
+
+ align:start position:0%
+these kids have acquired these kids have
+ 
+
+ align:start position:0%
+these kids have acquired these kids have
+acquired some skills that in the proper
+
+ align:start position:0%
+acquired some skills that in the proper
+ 
+
+ align:start position:0%
+acquired some skills that in the proper
+environment could be translated into
+
+ align:start position:0%
+environment could be translated into
+ 
+
+ align:start position:0%
+environment could be translated into
+learning to do numbers but the schools
+
+ align:start position:0%
+learning to do numbers but the schools
+ 
+
+ align:start position:0%
+learning to do numbers but the schools
+are totally unable to use it
+
+ align:start position:0%
+are totally unable to use it
+ 
+
+ align:start position:0%
+are totally unable to use it
+and you know it's not entirely
+
+ align:start position:0%
+and you know it's not entirely
+ 
+
+ align:start position:0%
+and you know it's not entirely
+surprising because they go to school and
+
+ align:start position:0%
+surprising because they go to school and
+ 
+
+ align:start position:0%
+surprising because they go to school and
+they start learning multiplication table
+
+ align:start position:0%
+they start learning multiplication table
+ 
+
+ align:start position:0%
+they start learning multiplication table
+and singing songs and so at very early
+
+ align:start position:0%
+and singing songs and so at very early
+ 
+
+ align:start position:0%
+and singing songs and so at very early
+grade mathematics in Indian primary
+
+ align:start position:0%
+grade mathematics in Indian primary
+ 
+
+ align:start position:0%
+grade mathematics in Indian primary
+school is more akin to poetry than to
+
+ align:start position:0%
+school is more akin to poetry than to
+ 
+
+ align:start position:0%
+school is more akin to poetry than to
+math
+
+ align:start position:0%
+math
+ 
+
+ align:start position:0%
+math
+um but uh this is so I'm not surprised
+
+ align:start position:0%
+um but uh this is so I'm not surprised
+ 
+
+ align:start position:0%
+um but uh this is so I'm not surprised
+by this result although I'm a bit sad
+
+ align:start position:0%
+by this result although I'm a bit sad
+ 
+
+ align:start position:0%
+by this result although I'm a bit sad
+but I um but I think this kind of shows
+
+ align:start position:0%
+but I um but I think this kind of shows
+ 
+
+ align:start position:0%
+but I um but I think this kind of shows
+like we handed you kids who were able to
+
+ align:start position:0%
+like we handed you kids who were able to
+ 
+
+ align:start position:0%
+like we handed you kids who were able to
+do math and you just uh erase that for
+
+ align:start position:0%
+do math and you just uh erase that for
+ 
+
+ align:start position:0%
+do math and you just uh erase that for
+them without by the way raising their
+
+ align:start position:0%
+them without by the way raising their
+ 
+
+ align:start position:0%
+them without by the way raising their
+their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non-symbolic sense of math
+
+ align:start position:0%
+non-symbolic sense of math
+ 
+
+ align:start position:0%
+non-symbolic sense of math
+yeah actually interpret the magnets
+
+ align:start position:0%
+yeah actually interpret the magnets
+ 
+
+ align:start position:0%
+yeah actually interpret the magnets
+which is that like standard deviation
+
+ align:start position:0%
+which is that like standard deviation
+ 
+
+ align:start position:0%
+which is that like standard deviation
+the standard deviation like in most
+
+ align:start position:0%
+the standard deviation like in most
+ 
+
+ align:start position:0%
+the standard deviation like in most
+things so uh so they were uh so there
+
+ align:start position:0%
+things so uh so they were uh so there
+ 
+
+ align:start position:0%
+things so uh so they were uh so there
+were 0.13 celebration
+
+ align:start position:0%
+were 0.13 celebration
+ 
+
+ align:start position:0%
+were 0.13 celebration
+higher in the in the
+
+ align:start position:0%
+higher in the in the
+ 
+
+ align:start position:0%
+higher in the in the
+symbolic Mass which they had not learned
+
+ align:start position:0%
+symbolic Mass which they had not learned
+ 
+
+ align:start position:0%
+symbolic Mass which they had not learned
+in the in the games in the first end
+
+ align:start position:0%
+in the in the games in the first end
+ 
+
+ align:start position:0%
+in the in the games in the first end
+line and then
+
+ align:start position:0%
+line and then
+ 
+
+ align:start position:0%
+line and then
+0.025 which means zero basically uh down
+
+ align:start position:0%
+0.025 which means zero basically uh down
+ 
+
+ align:start position:0%
+0.025 which means zero basically uh down
+the line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means that school are not able
+
+ align:start position:0%
+so that means that school are not able
+ 
+
+ align:start position:0%
+so that means that school are not able
+to Leverage The increased mathematical
+
+ align:start position:0%
+to Leverage The increased mathematical
+ 
+
+ align:start position:0%
+to Leverage The increased mathematical
+ability for so for us what does this
+
+ align:start position:0%
+ability for so for us what does this
+ 
+
+ align:start position:0%
+ability for so for us what does this
+mean is we have to go back to the
+
+ align:start position:0%
+mean is we have to go back to the
+ 
+
+ align:start position:0%
+mean is we have to go back to the
+drawing board to do that ourselves
+
+ align:start position:0%
+drawing board to do that ourselves
+ 
+
+ align:start position:0%
+drawing board to do that ourselves
+I'll go back to that in a bit but for
+
+ align:start position:0%
+I'll go back to that in a bit but for
+ 
+
+ align:start position:0%
+I'll go back to that in a bit but for
+kind of understanding schools that's the
+
+ align:start position:0%
+kind of understanding schools that's the
+ 
+
+ align:start position:0%
+kind of understanding schools that's the
+first point I want to make is that
+
+ align:start position:0%
+first point I want to make is that
+ 
+
+ align:start position:0%
+first point I want to make is that
+they were on the grade one were unable
+
+ align:start position:0%
+they were on the grade one were unable
+ 
+
+ align:start position:0%
+they were on the grade one were unable
+to do that no
+
+ align:start position:0%
+to do that no
+ 
+
+ align:start position:0%
+to do that no
+just maybe this is a bit special they
+
+ align:start position:0%
+just maybe this is a bit special they
+ 
+
+ align:start position:0%
+just maybe this is a bit special they
+don't they're not set up to uh their
+
+ align:start position:0%
+don't they're not set up to uh their
+ 
+
+ align:start position:0%
+don't they're not set up to uh their
+curriculum is is rigid the curriculum is
+
+ align:start position:0%
+curriculum is is rigid the curriculum is
+ 
+
+ align:start position:0%
+curriculum is is rigid the curriculum is
+is based first on and just you know
+
+ align:start position:0%
+is based first on and just you know
+ 
+
+ align:start position:0%
+is based first on and just you know
+learning the multiplication table they
+
+ align:start position:0%
+learning the multiplication table they
+ 
+
+ align:start position:0%
+learning the multiplication table they
+can't switch
+
+ align:start position:0%
+can't switch
+ 
+
+ align:start position:0%
+can't switch
+so here's another example of the fact
+
+ align:start position:0%
+so here's another example of the fact
+ 
+
+ align:start position:0%
+so here's another example of the fact
+that there is a lot of skill out there
+
+ align:start position:0%
+that there is a lot of skill out there
+ 
+
+ align:start position:0%
+that there is a lot of skill out there
+that the the schools are not able to uh
+
+ align:start position:0%
+that the the schools are not able to uh
+ 
+
+ align:start position:0%
+that the the schools are not able to uh
+to pick up
+
+ align:start position:0%
+to pick up
+ 
+
+ align:start position:0%
+to pick up
+and that studies that we did with the
+
+ align:start position:0%
+and that studies that we did with the
+ 
+
+ align:start position:0%
+and that studies that we did with the
+same basically coup
+
+ align:start position:0%
+same basically coup
+ 
+
+ align:start position:0%
+same basically coup
+on which is purely an observational
+
+ align:start position:0%
+on which is purely an observational
+ 
+
+ align:start position:0%
+on which is purely an observational
+study descriptive study of kids who sell
+
+ align:start position:0%
+study descriptive study of kids who sell
+ 
+
+ align:start position:0%
+study descriptive study of kids who sell
+in markets so I'm sure you've seen them
+
+ align:start position:0%
+in markets so I'm sure you've seen them
+ 
+
+ align:start position:0%
+in markets so I'm sure you've seen them
+uh in the eight countries you grew up
+
+ align:start position:0%
+uh in the eight countries you grew up
+ 
+
+ align:start position:0%
+uh in the eight countries you grew up
+with these kids selling in markets uh
+
+ align:start position:0%
+with these kids selling in markets uh
+ 
+
+ align:start position:0%
+with these kids selling in markets uh
+and they do a ton of math in there in
+
+ align:start position:0%
+and they do a ton of math in there in
+ 
+
+ align:start position:0%
+and they do a ton of math in there in
+the head at least in Indian market they
+
+ align:start position:0%
+the head at least in Indian market they
+ 
+
+ align:start position:0%
+the head at least in Indian market they
+just are so fast
+
+ align:start position:0%
+just are so fast
+ 
+
+ align:start position:0%
+just are so fast
+and this is something that has always
+
+ align:start position:0%
+and this is something that has always
+ 
+
+ align:start position:0%
+and this is something that has always
+struck a budget and Me
+
+ align:start position:0%
+struck a budget and Me
+ 
+
+ align:start position:0%
+struck a budget and Me
+Odd about the Acer test
+
+ align:start position:0%
+Odd about the Acer test
+ 
+
+ align:start position:0%
+Odd about the Acer test
+which is how come the kids cannot do the
+
+ align:start position:0%
+which is how come the kids cannot do the
+ 
+
+ align:start position:0%
+which is how come the kids cannot do the
+other test when they are doing things
+
+ align:start position:0%
+other test when they are doing things
+ 
+
+ align:start position:0%
+other test when they are doing things
+that are so much harder uh you know on a
+
+ align:start position:0%
+that are so much harder uh you know on a
+ 
+
+ align:start position:0%
+that are so much harder uh you know on a
+routine basis in their shop like what's
+
+ align:start position:0%
+routine basis in their shop like what's
+ 
+
+ align:start position:0%
+routine basis in their shop like what's
+the that
+
+ align:start position:0%
+the that
+ 
+
+ align:start position:0%
+the that
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's kind of the puzzle and so you
+
+ align:start position:0%
+that's kind of the puzzle and so you
+ 
+
+ align:start position:0%
+that's kind of the puzzle and so you
+might think well one reason is that it's
+
+ align:start position:0%
+might think well one reason is that it's
+ 
+
+ align:start position:0%
+might think well one reason is that it's
+only the kids after all there are not so
+
+ align:start position:0%
+only the kids after all there are not so
+ 
+
+ align:start position:0%
+only the kids after all there are not so
+many Market children and it's only the
+
+ align:start position:0%
+many Market children and it's only the
+ 
+
+ align:start position:0%
+many Market children and it's only the
+kids who are super good at math who are
+
+ align:start position:0%
+kids who are super good at math who are
+ 
+
+ align:start position:0%
+kids who are super good at math who are
+selected to to be Market seller and the
+
+ align:start position:0%
+selected to to be Market seller and the
+ 
+
+ align:start position:0%
+selected to to be Market seller and the
+other one to do other kind of things
+
+ align:start position:0%
+other one to do other kind of things
+ 
+
+ align:start position:0%
+other one to do other kind of things
+or it could be that the SR test is not
+
+ align:start position:0%
+or it could be that the SR test is not
+ 
+
+ align:start position:0%
+or it could be that the SR test is not
+incentivized no one cares they don't do
+
+ align:start position:0%
+incentivized no one cares they don't do
+ 
+
+ align:start position:0%
+incentivized no one cares they don't do
+it you know whatever or
+
+ align:start position:0%
+it you know whatever or
+ 
+
+ align:start position:0%
+it you know whatever or
+it could be that they knew how to do
+
+ align:start position:0%
+it could be that they knew how to do
+ 
+
+ align:start position:0%
+it could be that they knew how to do
+that in their head but they can't write
+
+ align:start position:0%
+that in their head but they can't write
+ 
+
+ align:start position:0%
+that in their head but they can't write
+and so they are completely baffled by
+
+ align:start position:0%
+and so they are completely baffled by
+ 
+
+ align:start position:0%
+and so they are completely baffled by
+the physical form of the test
+
+ align:start position:0%
+the physical form of the test
+ 
+
+ align:start position:0%
+the physical form of the test
+so we kind of were interested in in
+
+ align:start position:0%
+so we kind of were interested in in
+ 
+
+ align:start position:0%
+so we kind of were interested in in
+testing all these things
+
+ align:start position:0%
+testing all these things
+ 
+
+ align:start position:0%
+testing all these things
+so what we did is that we run to study
+
+ align:start position:0%
+so what we did is that we run to study
+ 
+
+ align:start position:0%
+so what we did is that we run to study
+one in Kolkata or in Delhi
+
+ align:start position:0%
+one in Kolkata or in Delhi
+ 
+
+ align:start position:0%
+one in Kolkata or in Delhi
+where we sent mystery shoppers to to the
+
+ align:start position:0%
+where we sent mystery shoppers to to the
+ 
+
+ align:start position:0%
+where we sent mystery shoppers to to the
+shops uh to buy some fruits and
+
+ align:start position:0%
+shops uh to buy some fruits and
+ 
+
+ align:start position:0%
+shops uh to buy some fruits and
+vegetables from the kids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the way they did it is that they put at
+
+ align:start position:0%
+the way they did it is that they put at
+ 
+
+ align:start position:0%
+the way they did it is that they put at
+least two things say eggplant and
+
+ align:start position:0%
+least two things say eggplant and
+ 
+
+ align:start position:0%
+least two things say eggplant and
+tomatoes
+
+ align:start position:0%
+tomatoes
+ 
+
+ align:start position:0%
+tomatoes
+they bought a funny quantity so not half
+
+ align:start position:0%
+they bought a funny quantity so not half
+ 
+
+ align:start position:0%
+they bought a funny quantity so not half
+kg So when you buy when you go to the
+
+ align:start position:0%
+kg So when you buy when you go to the
+ 
+
+ align:start position:0%
+kg So when you buy when you go to the
+market you can either say give me half
+
+ align:start position:0%
+market you can either say give me half
+ 
+
+ align:start position:0%
+market you can either say give me half
+kg of tomatoes or you can take the
+
+ align:start position:0%
+kg of tomatoes or you can take the
+ 
+
+ align:start position:0%
+kg of tomatoes or you can take the
+tomatoes in a basket and you you get
+
+ align:start position:0%
+tomatoes in a basket and you you get
+ 
+
+ align:start position:0%
+tomatoes in a basket and you you get
+them weight so then you get like 323
+
+ align:start position:0%
+them weight so then you get like 323
+ 
+
+ align:start position:0%
+them weight so then you get like 323
+grams
+
+ align:start position:0%
+grams
+ 
+
+ align:start position:0%
+grams
+so it doesn't get grounded up
+
+ align:start position:0%
+so it doesn't get grounded up
+ 
+
+ align:start position:0%
+so it doesn't get grounded up
+necessarily so they they got they got
+
+ align:start position:0%
+necessarily so they they got they got
+ 
+
+ align:start position:0%
+necessarily so they they got they got
+tomato and eggplant
+
+ align:start position:0%
+tomato and eggplant
+ 
+
+ align:start position:0%
+tomato and eggplant
+and then they handed a bill to the
+
+ align:start position:0%
+and then they handed a bill to the
+ 
+
+ align:start position:0%
+and then they handed a bill to the
+person to the kid who gave them change
+
+ align:start position:0%
+person to the kid who gave them change
+ 
+
+ align:start position:0%
+person to the kid who gave them change
+so the oppression involves a complicated
+
+ align:start position:0%
+so the oppression involves a complicated
+ 
+
+ align:start position:0%
+so the oppression involves a complicated
+multiplication uh the addition and then
+
+ align:start position:0%
+multiplication uh the addition and then
+ 
+
+ align:start position:0%
+multiplication uh the addition and then
+the subtraction
+
+ align:start position:0%
+the subtraction
+ 
+
+ align:start position:0%
+the subtraction
+and then they kind of challenged the kid
+
+ align:start position:0%
+and then they kind of challenged the kid
+ 
+
+ align:start position:0%
+and then they kind of challenged the kid
+on saying are you sure this is the right
+
+ align:start position:0%
+on saying are you sure this is the right
+ 
+
+ align:start position:0%
+on saying are you sure this is the right
+amount you give me and the key that to
+
+ align:start position:0%
+amount you give me and the key that to
+ 
+
+ align:start position:0%
+amount you give me and the key that to
+explain you know yes you take this
+
+ align:start position:0%
+explain you know yes you take this
+ 
+
+ align:start position:0%
+explain you know yes you take this
+multiplied by this this is this so you
+
+ align:start position:0%
+multiplied by this this is this so you
+ 
+
+ align:start position:0%
+multiplied by this this is this so you
+you know I'm right
+
+ align:start position:0%
+you know I'm right
+ 
+
+ align:start position:0%
+you know I'm right
+uh so we did that in Calcutta in Delhi
+
+ align:start position:0%
+uh so we did that in Calcutta in Delhi
+ 
+
+ align:start position:0%
+uh so we did that in Calcutta in Delhi
+and then we took the kids apart the last
+
+ align:start position:0%
+and then we took the kids apart the last
+ 
+
+ align:start position:0%
+and then we took the kids apart the last
+pair who went to do their shopping asked
+
+ align:start position:0%
+pair who went to do their shopping asked
+ 
+
+ align:start position:0%
+pair who went to do their shopping asked
+the parents if we could borrow the kids
+
+ align:start position:0%
+the parents if we could borrow the kids
+ 
+
+ align:start position:0%
+the parents if we could borrow the kids
+to do some math with them
+
+ align:start position:0%
+to do some math with them
+ 
+
+ align:start position:0%
+to do some math with them
+and uh and they did usually they agreed
+
+ align:start position:0%
+and uh and they did usually they agreed
+ 
+
+ align:start position:0%
+and uh and they did usually they agreed
+I came and did some maths with some math
+
+ align:start position:0%
+I came and did some maths with some math
+ 
+
+ align:start position:0%
+I came and did some maths with some math
+and then there we gave them
+
+ align:start position:0%
+and then there we gave them
+ 
+
+ align:start position:0%
+and then there we gave them
+problems of increasing level of
+
+ align:start position:0%
+problems of increasing level of
+ 
+
+ align:start position:0%
+problems of increasing level of
+abstraction so it's like an increasing
+
+ align:start position:0%
+abstraction so it's like an increasing
+ 
+
+ align:start position:0%
+abstraction so it's like an increasing
+level of far away it is so see if the
+
+ align:start position:0%
+level of far away it is so see if the
+ 
+
+ align:start position:0%
+level of far away it is so see if the
+guy is selling Tomatoes we are like so
+
+ align:start position:0%
+guy is selling Tomatoes we are like so
+ 
+
+ align:start position:0%
+guy is selling Tomatoes we are like so
+suppose the price of tomatoes is now 23
+
+ align:start position:0%
+suppose the price of tomatoes is now 23
+ 
+
+ align:start position:0%
+suppose the price of tomatoes is now 23
+rupees instead of 20
+
+ align:start position:0%
+rupees instead of 20
+ 
+
+ align:start position:0%
+rupees instead of 20
+uh how much would I pay you for half a
+
+ align:start position:0%
+uh how much would I pay you for half a
+ 
+
+ align:start position:0%
+uh how much would I pay you for half a
+kg of tomatoes and then when you replace
+
+ align:start position:0%
+kg of tomatoes and then when you replace
+ 
+
+ align:start position:0%
+kg of tomatoes and then when you replace
+the tomatoes by eggplant and then the
+
+ align:start position:0%
+the tomatoes by eggplant and then the
+ 
+
+ align:start position:0%
+the tomatoes by eggplant and then the
+eggplant by pens we are sell by units
+
+ align:start position:0%
+eggplant by pens we are sell by units
+ 
+
+ align:start position:0%
+eggplant by pens we are sell by units
+and not by and not by kilo so that
+
+ align:start position:0%
+and not by and not by kilo so that
+ 
+
+ align:start position:0%
+and not by and not by kilo so that
+changed the operation so increasing
+
+ align:start position:0%
+changed the operation so increasing
+ 
+
+ align:start position:0%
+changed the operation so increasing
+level of diff different from what you do
+
+ align:start position:0%
+level of diff different from what you do
+ 
+
+ align:start position:0%
+level of diff different from what you do
+in a normal in a day-to-day basis and
+
+ align:start position:0%
+in a normal in a day-to-day basis and
+ 
+
+ align:start position:0%
+in a normal in a day-to-day basis and
+then abstraction what is a
+
+ align:start position:0%
+then abstraction what is a
+ 
+
+ align:start position:0%
+then abstraction what is a
+55 times 7 and basically the SR test
+
+ align:start position:0%
+55 times 7 and basically the SR test
+ 
+
+ align:start position:0%
+55 times 7 and basically the SR test
+uh and done so that's what and then in
+
+ align:start position:0%
+uh and done so that's what and then in
+ 
+
+ align:start position:0%
+uh and done so that's what and then in
+Delhi we did the opposite which is we
+
+ align:start position:0%
+Delhi we did the opposite which is we
+ 
+
+ align:start position:0%
+Delhi we did the opposite which is we
+went to schools in this very
+
+ align:start position:0%
+went to schools in this very
+ 
+
+ align:start position:0%
+went to schools in this very
+neighborhoods by the way a lot of the
+
+ align:start position:0%
+neighborhoods by the way a lot of the
+ 
+
+ align:start position:0%
+neighborhoods by the way a lot of the
+kids who are in markets are also in
+
+ align:start position:0%
+kids who are in markets are also in
+ 
+
+ align:start position:0%
+kids who are in markets are also in
+school but not all of them and then so
+
+ align:start position:0%
+school but not all of them and then so
+ 
+
+ align:start position:0%
+school but not all of them and then so
+we went to schools where most kids are
+
+ align:start position:0%
+we went to schools where most kids are
+ 
+
+ align:start position:0%
+we went to schools where most kids are
+not working in markets but they are very
+
+ align:start position:0%
+not working in markets but they are very
+ 
+
+ align:start position:0%
+not working in markets but they are very
+similar um
+
+ align:start position:0%
+similar um
+ 
+
+ align:start position:0%
+similar um
+neighborhoods social status Etc
+
+ align:start position:0%
+neighborhoods social status Etc
+ 
+
+ align:start position:0%
+neighborhoods social status Etc
+and we had them do the same tests plus
+
+ align:start position:0%
+and we had them do the same tests plus
+ 
+
+ align:start position:0%
+and we had them do the same tests plus
+uh sell items
+
+ align:start position:0%
+uh sell items
+ 
+
+ align:start position:0%
+uh sell items
+so they set up a little market and they
+
+ align:start position:0%
+so they set up a little market and they
+ 
+
+ align:start position:0%
+so they set up a little market and they
+are selling the selling selling the
+
+ align:start position:0%
+are selling the selling selling the
+ 
+
+ align:start position:0%
+are selling the selling selling the
+items
+
+ align:start position:0%
+items
+ 
+
+ align:start position:0%
+items
+so that's the project there was a
+
+ align:start position:0%
+so that's the project there was a
+ 
+
+ align:start position:0%
+so that's the project there was a
+descriptive
+
+ align:start position:0%
+descriptive
+ 
+
+ align:start position:0%
+descriptive
+um very fun study to do
+
+ align:start position:0%
+um very fun study to do
+ 
+
+ align:start position:0%
+um very fun study to do
+and here's what we found so uh the first
+
+ align:start position:0%
+and here's what we found so uh the first
+ 
+
+ align:start position:0%
+and here's what we found so uh the first
+thing we found is that our sort of
+
+ align:start position:0%
+thing we found is that our sort of
+ 
+
+ align:start position:0%
+thing we found is that our sort of
+impressionistic impression that
+
+ align:start position:0%
+impressionistic impression that
+ 
+
+ align:start position:0%
+impressionistic impression that
+impersonating impression makes it a bit
+
+ align:start position:0%
+impersonating impression makes it a bit
+ 
+
+ align:start position:0%
+impersonating impression makes it a bit
+over determined our filling observations
+
+ align:start position:0%
+over determined our filling observations
+ 
+
+ align:start position:0%
+over determined our filling observations
+that the kids are really good at doing
+
+ align:start position:0%
+that the kids are really good at doing
+ 
+
+ align:start position:0%
+that the kids are really good at doing
+this math seems to really hold true so
+
+ align:start position:0%
+this math seems to really hold true so
+ 
+
+ align:start position:0%
+this math seems to really hold true so
+in Kolkata they are above there are
+
+ align:start position:0%
+in Kolkata they are above there are
+ 
+
+ align:start position:0%
+in Kolkata they are above there are
+around 90 percent uh right the first
+
+ align:start position:0%
+around 90 percent uh right the first
+ 
+
+ align:start position:0%
+around 90 percent uh right the first
+time and then if they were wrong since
+
+ align:start position:0%
+time and then if they were wrong since
+ 
+
+ align:start position:0%
+time and then if they were wrong since
+they were challenged they had a chance
+
+ align:start position:0%
+they were challenged they had a chance
+ 
+
+ align:start position:0%
+they were challenged they had a chance
+to correct and then with correction
+
+ align:start position:0%
+to correct and then with correction
+ 
+
+ align:start position:0%
+to correct and then with correction
+there are like 95 98 percent
+
+ align:start position:0%
+there are like 95 98 percent
+ 
+
+ align:start position:0%
+there are like 95 98 percent
+uh on in their
+
+ align:start position:0%
+uh on in their
+ 
+
+ align:start position:0%
+uh on in their
+in the this uh
+
+ align:start position:0%
+in the this uh
+ 
+
+ align:start position:0%
+in the this uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+real transactions
+
+ align:start position:0%
+real transactions
+ 
+
+ align:start position:0%
+real transactions
+in Delhi the first one was a little
+
+ align:start position:0%
+in Delhi the first one was a little
+ 
+
+ align:start position:0%
+in Delhi the first one was a little
+lower uh I think that's because those
+
+ align:start position:0%
+lower uh I think that's because those
+ 
+
+ align:start position:0%
+lower uh I think that's because those
+were relatively unusual for Market
+
+ align:start position:0%
+were relatively unusual for Market
+ 
+
+ align:start position:0%
+were relatively unusual for Market
+transactions to ask you two goods in
+
+ align:start position:0%
+transactions to ask you two goods in
+ 
+
+ align:start position:0%
+transactions to ask you two goods in
+unusual quantity but then when the
+
+ align:start position:0%
+unusual quantity but then when the
+ 
+
+ align:start position:0%
+unusual quantity but then when the
+second times got around second person
+
+ align:start position:0%
+second times got around second person
+ 
+
+ align:start position:0%
+second times got around second person
+got around the data their brain were
+
+ align:start position:0%
+got around the data their brain were
+ 
+
+ align:start position:0%
+got around the data their brain were
+awake and they were they also with like
+
+ align:start position:0%
+awake and they were they also with like
+ 
+
+ align:start position:0%
+awake and they were they also with like
+94 95 accuracy
+
+ align:start position:0%
+94 95 accuracy
+ 
+
+ align:start position:0%
+94 95 accuracy
+and then you comprehend the school
+
+ align:start position:0%
+and then you comprehend the school
+ 
+
+ align:start position:0%
+and then you comprehend the school
+children doing the same exercise and
+
+ align:start position:0%
+children doing the same exercise and
+ 
+
+ align:start position:0%
+children doing the same exercise and
+they are much worse
+
+ align:start position:0%
+they are much worse
+ 
+
+ align:start position:0%
+they are much worse
+so uh so that's the first thing that
+
+ align:start position:0%
+so uh so that's the first thing that
+ 
+
+ align:start position:0%
+so uh so that's the first thing that
+they are very good at doing that are
+
+ align:start position:0%
+they are very good at doing that are
+ 
+
+ align:start position:0%
+they are very good at doing that are
+indeed very good at Market arithmetics
+
+ align:start position:0%
+indeed very good at Market arithmetics
+ 
+
+ align:start position:0%
+indeed very good at Market arithmetics
+much better than school children
+
+ align:start position:0%
+much better than school children
+ 
+
+ align:start position:0%
+much better than school children
+so you could think it's just selection
+
+ align:start position:0%
+so you could think it's just selection
+ 
+
+ align:start position:0%
+so you could think it's just selection
+so it's it's the kids the best kids at
+
+ align:start position:0%
+so it's it's the kids the best kids at
+ 
+
+ align:start position:0%
+so it's it's the kids the best kids at
+math are in working in the market
+
+ align:start position:0%
+math are in working in the market
+ 
+
+ align:start position:0%
+math are in working in the market
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so we can look at so oh you could say
+
+ align:start position:0%
+so we can look at so oh you could say
+ 
+
+ align:start position:0%
+so we can look at so oh you could say
+well there might be other reason for
+
+ align:start position:0%
+well there might be other reason for
+ 
+
+ align:start position:0%
+well there might be other reason for
+example they know everything by heart
+
+ align:start position:0%
+example they know everything by heart
+ 
+
+ align:start position:0%
+example they know everything by heart
+they just have a table in the back of
+
+ align:start position:0%
+they just have a table in the back of
+ 
+
+ align:start position:0%
+they just have a table in the back of
+their mind that that tells them how much
+
+ align:start position:0%
+their mind that that tells them how much
+ 
+
+ align:start position:0%
+their mind that that tells them how much
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+um things cost
+
+ align:start position:0%
+um things cost
+ 
+
+ align:start position:0%
+um things cost
+so here we can look at the people's
+
+ align:start position:0%
+so here we can look at the people's
+ 
+
+ align:start position:0%
+so here we can look at the people's
+ability to uh to do other to do other
+
+ align:start position:0%
+ability to uh to do other to do other
+ 
+
+ align:start position:0%
+ability to uh to do other to do other
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+uh so in Kolkata we just had one
+
+ align:start position:0%
+uh so in Kolkata we just had one
+ 
+
+ align:start position:0%
+uh so in Kolkata we just had one
+hypothetical transaction that was quite
+
+ align:start position:0%
+hypothetical transaction that was quite
+ 
+
+ align:start position:0%
+hypothetical transaction that was quite
+removed to what they were doing usually
+
+ align:start position:0%
+removed to what they were doing usually
+ 
+
+ align:start position:0%
+removed to what they were doing usually
+and we saw that they were not doing that
+
+ align:start position:0%
+and we saw that they were not doing that
+ 
+
+ align:start position:0%
+and we saw that they were not doing that
+great on it
+
+ align:start position:0%
+great on it
+ 
+
+ align:start position:0%
+great on it
+uh so now in delhi what we did is we
+
+ align:start position:0%
+uh so now in delhi what we did is we
+ 
+
+ align:start position:0%
+uh so now in delhi what we did is we
+progressed as I was saying by level of
+
+ align:start position:0%
+progressed as I was saying by level of
+ 
+
+ align:start position:0%
+progressed as I was saying by level of
+how far it is and so the further it is
+
+ align:start position:0%
+how far it is and so the further it is
+ 
+
+ align:start position:0%
+how far it is and so the further it is
+the more difficult it is
+
+ align:start position:0%
+the more difficult it is
+ 
+
+ align:start position:0%
+the more difficult it is
+so if it's the same type of goods it's
+
+ align:start position:0%
+so if it's the same type of goods it's
+ 
+
+ align:start position:0%
+so if it's the same type of goods it's
+better if it's at least in the same unit
+
+ align:start position:0%
+better if it's at least in the same unit
+ 
+
+ align:start position:0%
+better if it's at least in the same unit
+it's better or if it's and so there is
+
+ align:start position:0%
+it's better or if it's and so there is
+ 
+
+ align:start position:0%
+it's better or if it's and so there is
+some flexibility within my within Market
+
+ align:start position:0%
+some flexibility within my within Market
+ 
+
+ align:start position:0%
+some flexibility within my within Market
+transaction they can do other ones and
+
+ align:start position:0%
+transaction they can do other ones and
+ 
+
+ align:start position:0%
+transaction they can do other ones and
+then the more but there's a limit to
+
+ align:start position:0%
+then the more but there's a limit to
+ 
+
+ align:start position:0%
+then the more but there's a limit to
+this flexibility there there are so they
+
+ align:start position:0%
+this flexibility there there are so they
+ 
+
+ align:start position:0%
+this flexibility there there are so they
+are not it's not by road because you can
+
+ align:start position:0%
+are not it's not by road because you can
+ 
+
+ align:start position:0%
+are not it's not by road because you can
+change the number on them but there is
+
+ align:start position:0%
+change the number on them but there is
+ 
+
+ align:start position:0%
+change the number on them but there is
+some limit to this to this you know how
+
+ align:start position:0%
+some limit to this to this you know how
+ 
+
+ align:start position:0%
+some limit to this to this you know how
+well they can adapt to other things so
+
+ align:start position:0%
+well they can adapt to other things so
+ 
+
+ align:start position:0%
+well they can adapt to other things so
+they are not like that spectacular at
+
+ align:start position:0%
+they are not like that spectacular at
+ 
+
+ align:start position:0%
+they are not like that spectacular at
+math once you remove
+
+ align:start position:0%
+math once you remove
+ 
+
+ align:start position:0%
+math once you remove
+and where are they really have a problem
+
+ align:start position:0%
+and where are they really have a problem
+ 
+
+ align:start position:0%
+and where are they really have a problem
+and again this is what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observation is that they are really
+
+ align:start position:0%
+observation is that they are really
+ 
+
+ align:start position:0%
+observation is that they are really
+terrible at the pattern at the pattern
+
+ align:start position:0%
+terrible at the pattern at the pattern
+ 
+
+ align:start position:0%
+terrible at the pattern at the pattern
+type tests are only 32 percent of them
+
+ align:start position:0%
+type tests are only 32 percent of them
+ 
+
+ align:start position:0%
+type tests are only 32 percent of them
+can do a division in Kolkata 15 percent
+
+ align:start position:0%
+can do a division in Kolkata 15 percent
+ 
+
+ align:start position:0%
+can do a division in Kolkata 15 percent
+in uh in in Delhi only about half can do
+
+ align:start position:0%
+in uh in in Delhi only about half can do
+ 
+
+ align:start position:0%
+in uh in in Delhi only about half can do
+a subtraction uh so similar to the
+
+ align:start position:0%
+a subtraction uh so similar to the
+ 
+
+ align:start position:0%
+a subtraction uh so similar to the
+Karnataka level for example
+
+ align:start position:0%
+Karnataka level for example
+ 
+
+ align:start position:0%
+Karnataka level for example
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and there the daily school children are
+
+ align:start position:0%
+and there the daily school children are
+ 
+
+ align:start position:0%
+and there the daily school children are
+much better than they are
+
+ align:start position:0%
+much better than they are
+ 
+
+ align:start position:0%
+much better than they are
+so it's so it was not like just
+
+ align:start position:0%
+so it's so it was not like just
+ 
+
+ align:start position:0%
+so it's so it was not like just
+selection the best mathematician end up
+
+ align:start position:0%
+selection the best mathematician end up
+ 
+
+ align:start position:0%
+selection the best mathematician end up
+in the class the best mathematician can
+
+ align:start position:0%
+in the class the best mathematician can
+ 
+
+ align:start position:0%
+in the class the best mathematician can
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+Market Mass
+
+ align:start position:0%
+Market Mass
+ 
+
+ align:start position:0%
+Market Mass
+uh not spectacularly because they can't
+
+ align:start position:0%
+uh not spectacularly because they can't
+ 
+
+ align:start position:0%
+uh not spectacularly because they can't
+go away spectacularly for their own job
+
+ align:start position:0%
+go away spectacularly for their own job
+ 
+
+ align:start position:0%
+go away spectacularly for their own job
+but they they don't have the kind of
+
+ align:start position:0%
+but they they don't have the kind of
+ 
+
+ align:start position:0%
+but they they don't have the kind of
+mental gymnastics to go to other things
+
+ align:start position:0%
+mental gymnastics to go to other things
+ 
+
+ align:start position:0%
+mental gymnastics to go to other things
+but they really can't go to the to uh to
+
+ align:start position:0%
+but they really can't go to the to uh to
+ 
+
+ align:start position:0%
+but they really can't go to the to uh to
+the Acer test and they do worse than the
+
+ align:start position:0%
+the Acer test and they do worse than the
+ 
+
+ align:start position:0%
+the Acer test and they do worse than the
+delicate
+
+ align:start position:0%
+delicate
+ 
+
+ align:start position:0%
+delicate
+so the delicates can do the SR test
+
+ align:start position:0%
+so the delicates can do the SR test
+ 
+
+ align:start position:0%
+so the delicates can do the SR test
+quite well in fact when you compare to
+
+ align:start position:0%
+quite well in fact when you compare to
+ 
+
+ align:start position:0%
+quite well in fact when you compare to
+the rest of India but they cannot do a
+
+ align:start position:0%
+the rest of India but they cannot do a
+ 
+
+ align:start position:0%
+the rest of India but they cannot do a
+hypothetical transaction the market kids
+
+ align:start position:0%
+hypothetical transaction the market kids
+ 
+
+ align:start position:0%
+hypothetical transaction the market kids
+can do the market transaction but it
+
+ align:start position:0%
+can do the market transaction but it
+ 
+
+ align:start position:0%
+can do the market transaction but it
+cannot cannot do the daily test
+
+ align:start position:0%
+cannot cannot do the daily test
+ 
+
+ align:start position:0%
+cannot cannot do the daily test
+and one of the things that really trips
+
+ align:start position:0%
+and one of the things that really trips
+ 
+
+ align:start position:0%
+and one of the things that really trips
+the market kids is uh the where you
+
+ align:start position:0%
+the market kids is uh the where you
+ 
+
+ align:start position:0%
+the market kids is uh the where you
+really have a huge drop off
+
+ align:start position:0%
+really have a huge drop off
+ 
+
+ align:start position:0%
+really have a huge drop off
+is when things are presented in abstract
+
+ align:start position:0%
+is when things are presented in abstract
+ 
+
+ align:start position:0%
+is when things are presented in abstract
+term as opposed to uncut them
+
+ align:start position:0%
+term as opposed to uncut them
+ 
+
+ align:start position:0%
+term as opposed to uncut them
+so the same kid can do uh can you give
+
+ align:start position:0%
+so the same kid can do uh can you give
+ 
+
+ align:start position:0%
+so the same kid can do uh can you give
+me uh the price of one pen if a five Pen
+
+ align:start position:0%
+me uh the price of one pen if a five Pen
+ 
+
+ align:start position:0%
+me uh the price of one pen if a five Pen
+cost 20 cents and cannot do uh 20
+
+ align:start position:0%
+cost 20 cents and cannot do uh 20
+ 
+
+ align:start position:0%
+cost 20 cents and cannot do uh 20
+divided by 5.
+
+ align:start position:0%
+divided by 5.
+ 
+
+ align:start position:0%
+divided by 5.
+the basically this is what this says
+
+ align:start position:0%
+the basically this is what this says
+ 
+
+ align:start position:0%
+the basically this is what this says
+this is what this comparison here
+
+ align:start position:0%
+this is what this comparison here
+ 
+
+ align:start position:0%
+this is what this comparison here
+similarly for for those kids so going to
+
+ align:start position:0%
+similarly for for those kids so going to
+ 
+
+ align:start position:0%
+similarly for for those kids so going to
+abstraction is what makes it even if
+
+ align:start position:0%
+abstraction is what makes it even if
+ 
+
+ align:start position:0%
+abstraction is what makes it even if
+it's the exact same problem
+
+ align:start position:0%
+it's the exact same problem
+ 
+
+ align:start position:0%
+it's the exact same problem
+uh removing the the anchoring to a real
+
+ align:start position:0%
+uh removing the the anchoring to a real
+ 
+
+ align:start position:0%
+uh removing the the anchoring to a real
+items is very difficult for them
+
+ align:start position:0%
+items is very difficult for them
+ 
+
+ align:start position:0%
+items is very difficult for them
+with one exception
+
+ align:start position:0%
+with one exception
+ 
+
+ align:start position:0%
+with one exception
+when it is possible to round things up
+
+ align:start position:0%
+when it is possible to round things up
+ 
+
+ align:start position:0%
+when it is possible to round things up
+for example if the problem is 31 times 7
+
+ align:start position:0%
+for example if the problem is 31 times 7
+ 
+
+ align:start position:0%
+for example if the problem is 31 times 7
+which you can do as 30 times 7 plus 7
+
+ align:start position:0%
+which you can do as 30 times 7 plus 7
+ 
+
+ align:start position:0%
+which you can do as 30 times 7 plus 7
+they are they are good at that they are
+
+ align:start position:0%
+they are they are good at that they are
+ 
+
+ align:start position:0%
+they are they are good at that they are
+good at simplifying problems even when
+
+ align:start position:0%
+good at simplifying problems even when
+ 
+
+ align:start position:0%
+good at simplifying problems even when
+they are abstract
+
+ align:start position:0%
+they are abstract
+ 
+
+ align:start position:0%
+they are abstract
+so uh when they are um so this is a
+
+ align:start position:0%
+so uh when they are um so this is a
+ 
+
+ align:start position:0%
+so uh when they are um so this is a
+subtraction we didn't do it for division
+
+ align:start position:0%
+subtraction we didn't do it for division
+ 
+
+ align:start position:0%
+subtraction we didn't do it for division
+but for a non-readable abstract
+
+ align:start position:0%
+but for a non-readable abstract
+ 
+
+ align:start position:0%
+but for a non-readable abstract
+subtraction even after correction if
+
+ align:start position:0%
+subtraction even after correction if
+ 
+
+ align:start position:0%
+subtraction even after correction if
+they finally get it 65 percent of the
+
+ align:start position:0%
+they finally get it 65 percent of the
+ 
+
+ align:start position:0%
+they finally get it 65 percent of the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+if it's surroundable they get it 85
+
+ align:start position:0%
+if it's surroundable they get it 85
+ 
+
+ align:start position:0%
+if it's surroundable they get it 85
+percent of the time
+
+ align:start position:0%
+percent of the time
+ 
+
+ align:start position:0%
+percent of the time
+in an abstract form
+
+ align:start position:0%
+in an abstract form
+ 
+
+ align:start position:0%
+in an abstract form
+if it's uncut they do better to start
+
+ align:start position:0%
+if it's uncut they do better to start
+ 
+
+ align:start position:0%
+if it's uncut they do better to start
+with that's what we saw in the previous
+
+ align:start position:0%
+with that's what we saw in the previous
+ 
+
+ align:start position:0%
+with that's what we saw in the previous
+graph that the the abstraction tripped
+
+ align:start position:0%
+graph that the the abstraction tripped
+ 
+
+ align:start position:0%
+graph that the the abstraction tripped
+them up but and then rounded 100 and on
+
+ align:start position:0%
+them up but and then rounded 100 and on
+ 
+
+ align:start position:0%
+them up but and then rounded 100 and on
+the button on car they are you know as
+
+ align:start position:0%
+the button on car they are you know as
+ 
+
+ align:start position:0%
+the button on car they are you know as
+good as they are in the market they
+
+ align:start position:0%
+good as they are in the market they
+ 
+
+ align:start position:0%
+good as they are in the market they
+reach 290 so they are very good at
+
+ align:start position:0%
+reach 290 so they are very good at
+ 
+
+ align:start position:0%
+reach 290 so they are very good at
+rounding
+
+ align:start position:0%
+rounding
+ 
+
+ align:start position:0%
+rounding
+and the by cons by comparison the daily
+
+ align:start position:0%
+and the by cons by comparison the daily
+ 
+
+ align:start position:0%
+and the by cons by comparison the daily
+school children don't get uh much as
+
+ align:start position:0%
+school children don't get uh much as
+ 
+
+ align:start position:0%
+school children don't get uh much as
+much as a boost
+
+ align:start position:0%
+much as a boost
+ 
+
+ align:start position:0%
+much as a boost
+on rounding as the daily as as the daily
+
+ align:start position:0%
+on rounding as the daily as as the daily
+ 
+
+ align:start position:0%
+on rounding as the daily as as the daily
+Market children and the reason is that
+
+ align:start position:0%
+Market children and the reason is that
+ 
+
+ align:start position:0%
+Market children and the reason is that
+there is school children don't use
+
+ align:start position:0%
+there is school children don't use
+ 
+
+ align:start position:0%
+there is school children don't use
+this strategy at all so they have
+
+ align:start position:0%
+this strategy at all so they have
+ 
+
+ align:start position:0%
+this strategy at all so they have
+uh this is what the
+
+ align:start position:0%
+uh this is what the
+ 
+
+ align:start position:0%
+uh this is what the
+what they write up
+
+ align:start position:0%
+what they write up
+ 
+
+ align:start position:0%
+what they write up
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know how much how much do they write
+
+ align:start position:0%
+you know how much how much do they write
+ 
+
+ align:start position:0%
+you know how much how much do they write
+on a piece of paper to solve the problem
+
+ align:start position:0%
+on a piece of paper to solve the problem
+ 
+
+ align:start position:0%
+on a piece of paper to solve the problem
+and so this is a number of tally marks
+
+ align:start position:0%
+and so this is a number of tally marks
+ 
+
+ align:start position:0%
+and so this is a number of tally marks
+that they are making
+
+ align:start position:0%
+that they are making
+ 
+
+ align:start position:0%
+that they are making
+and so the
+
+ align:start position:0%
+and so the
+ 
+
+ align:start position:0%
+and so the
+the kids in Market basically do
+
+ align:start position:0%
+the kids in Market basically do
+ 
+
+ align:start position:0%
+the kids in Market basically do
+everything in their head
+
+ align:start position:0%
+everything in their head
+ 
+
+ align:start position:0%
+everything in their head
+the kid is in Delhi do everything uh
+
+ align:start position:0%
+the kid is in Delhi do everything uh
+ 
+
+ align:start position:0%
+the kid is in Delhi do everything uh
+written up the right Million numbers and
+
+ align:start position:0%
+written up the right Million numbers and
+ 
+
+ align:start position:0%
+written up the right Million numbers and
+I realize that I'm not showing I'm
+
+ align:start position:0%
+I realize that I'm not showing I'm
+ 
+
+ align:start position:0%
+I realize that I'm not showing I'm
+showing you how they write a Million
+
+ align:start position:0%
+showing you how they write a Million
+ 
+
+ align:start position:0%
+showing you how they write a Million
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+and I realized that I didn't take the
+
+ align:start position:0%
+and I realized that I didn't take the
+ 
+
+ align:start position:0%
+and I realized that I didn't take the
+right graph so let me they write just as
+
+ align:start position:0%
+right graph so let me they write just as
+ 
+
+ align:start position:0%
+right graph so let me they write just as
+many number of its surroundable life
+
+ align:start position:0%
+many number of its surroundable life
+ 
+
+ align:start position:0%
+many number of its surroundable life
+it's non-runnerable they don't see and
+
+ align:start position:0%
+it's non-runnerable they don't see and
+ 
+
+ align:start position:0%
+it's non-runnerable they don't see and
+they don't they don't use the fact that
+
+ align:start position:0%
+they don't they don't use the fact that
+ 
+
+ align:start position:0%
+they don't they don't use the fact that
+it is rendable
+
+ align:start position:0%
+it is rendable
+ 
+
+ align:start position:0%
+it is rendable
+so the market kids have strategies that
+
+ align:start position:0%
+so the market kids have strategies that
+ 
+
+ align:start position:0%
+so the market kids have strategies that
+they can uh they can fall back to when
+
+ align:start position:0%
+they can uh they can fall back to when
+ 
+
+ align:start position:0%
+they can uh they can fall back to when
+the strategy is applicable they only
+
+ align:start position:0%
+the strategy is applicable they only
+ 
+
+ align:start position:0%
+the strategy is applicable they only
+think the Indian the school kids can do
+
+ align:start position:0%
+think the Indian the school kids can do
+ 
+
+ align:start position:0%
+think the Indian the school kids can do
+is just write down a bunch of numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and some of them might have figured out
+
+ align:start position:0%
+and some of them might have figured out
+ 
+
+ align:start position:0%
+and some of them might have figured out
+how to you know the algorithm you know
+
+ align:start position:0%
+how to you know the algorithm you know
+ 
+
+ align:start position:0%
+how to you know the algorithm you know
+these guys actually wrote it up this is
+
+ align:start position:0%
+these guys actually wrote it up this is
+ 
+
+ align:start position:0%
+these guys actually wrote it up this is
+it is written up properly so these guys
+
+ align:start position:0%
+it is written up properly so these guys
+ 
+
+ align:start position:0%
+it is written up properly so these guys
+know how to to do addition in a standard
+
+ align:start position:0%
+know how to to do addition in a standard
+ 
+
+ align:start position:0%
+know how to to do addition in a standard
+algorithmic way although he hasn't
+
+ align:start position:0%
+algorithmic way although he hasn't
+ 
+
+ align:start position:0%
+algorithmic way although he hasn't
+filled out the multiplication yet which
+
+ align:start position:0%
+filled out the multiplication yet which
+ 
+
+ align:start position:0%
+filled out the multiplication yet which
+finally Clips him up because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so the problem is deeper than the school
+
+ align:start position:0%
+so the problem is deeper than the school
+ 
+
+ align:start position:0%
+so the problem is deeper than the school
+not teaching much
+
+ align:start position:0%
+not teaching much
+ 
+
+ align:start position:0%
+not teaching much
+is that they uh don't recognize that
+
+ align:start position:0%
+is that they uh don't recognize that
+ 
+
+ align:start position:0%
+is that they uh don't recognize that
+there is existing knowledge uh abstract
+
+ align:start position:0%
+there is existing knowledge uh abstract
+ 
+
+ align:start position:0%
+there is existing knowledge uh abstract
+and concrete these kids
+
+ align:start position:0%
+and concrete these kids
+ 
+
+ align:start position:0%
+and concrete these kids
+uh in the market they have knowledge
+
+ align:start position:0%
+uh in the market they have knowledge
+ 
+
+ align:start position:0%
+uh in the market they have knowledge
+they know how to do mathematics to
+
+ align:start position:0%
+they know how to do mathematics to
+ 
+
+ align:start position:0%
+they know how to do mathematics to
+school is the schooling in in this
+
+ align:start position:0%
+school is the schooling in in this
+ 
+
+ align:start position:0%
+school is the schooling in in this
+instance impersonated by the the
+
+ align:start position:0%
+instance impersonated by the the
+ 
+
+ align:start position:0%
+instance impersonated by the the
+school-like presentation of the Assa
+
+ align:start position:0%
+school-like presentation of the Assa
+ 
+
+ align:start position:0%
+school-like presentation of the Assa
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+is unable to leverage that and basically
+
+ align:start position:0%
+is unable to leverage that and basically
+ 
+
+ align:start position:0%
+is unable to leverage that and basically
+what happens is that they see the thing
+
+ align:start position:0%
+what happens is that they see the thing
+ 
+
+ align:start position:0%
+what happens is that they see the thing
+and they say I'm not good at math
+
+ align:start position:0%
+and they say I'm not good at math
+ 
+
+ align:start position:0%
+and they say I'm not good at math
+I'm not I'm not uh I don't know how to
+
+ align:start position:0%
+I'm not I'm not uh I don't know how to
+ 
+
+ align:start position:0%
+I'm not I'm not uh I don't know how to
+do these things and the as soon as they
+
+ align:start position:0%
+do these things and the as soon as they
+ 
+
+ align:start position:0%
+do these things and the as soon as they
+see a written problem or even if you
+
+ align:start position:0%
+see a written problem or even if you
+ 
+
+ align:start position:0%
+see a written problem or even if you
+tell them or early the written problem
+
+ align:start position:0%
+tell them or early the written problem
+ 
+
+ align:start position:0%
+tell them or early the written problem
+because oral versus written doesn't make
+
+ align:start position:0%
+because oral versus written doesn't make
+ 
+
+ align:start position:0%
+because oral versus written doesn't make
+a difference there if they see an
+
+ align:start position:0%
+a difference there if they see an
+ 
+
+ align:start position:0%
+a difference there if they see an
+abstract problem in their mind what it
+
+ align:start position:0%
+abstract problem in their mind what it
+ 
+
+ align:start position:0%
+abstract problem in their mind what it
+evokes is that oh I better take out my
+
+ align:start position:0%
+evokes is that oh I better take out my
+ 
+
+ align:start position:0%
+evokes is that oh I better take out my
+you know toolbox of algorithm that I
+
+ align:start position:0%
+you know toolbox of algorithm that I
+ 
+
+ align:start position:0%
+you know toolbox of algorithm that I
+learned in school for how to teach this
+
+ align:start position:0%
+learned in school for how to teach this
+ 
+
+ align:start position:0%
+learned in school for how to teach this
+thing but in fact they are you know they
+
+ align:start position:0%
+thing but in fact they are you know they
+ 
+
+ align:start position:0%
+thing but in fact they are you know they
+misunderstood the algorithm to for
+
+ align:start position:0%
+misunderstood the algorithm to for
+ 
+
+ align:start position:0%
+misunderstood the algorithm to for
+example they do the subtraction in this
+
+ align:start position:0%
+example they do the subtraction in this
+ 
+
+ align:start position:0%
+example they do the subtraction in this
+algorithmic way but from the wrong part
+
+ align:start position:0%
+algorithmic way but from the wrong part
+ 
+
+ align:start position:0%
+algorithmic way but from the wrong part
+of the end or they do place value errors
+
+ align:start position:0%
+of the end or they do place value errors
+ 
+
+ align:start position:0%
+of the end or they do place value errors
+Etc
+
+ align:start position:0%
+Etc
+ 
+
+ align:start position:0%
+Etc
+that they never do in their real job
+
+ align:start position:0%
+that they never do in their real job
+ 
+
+ align:start position:0%
+that they never do in their real job
+because they
+
+ align:start position:0%
+because they
+ 
+
+ align:start position:0%
+because they
+they don't go back to this kind of
+
+ align:start position:0%
+they don't go back to this kind of
+ 
+
+ align:start position:0%
+they don't go back to this kind of
+half-baked algorithm that they have
+
+ align:start position:0%
+half-baked algorithm that they have
+ 
+
+ align:start position:0%
+half-baked algorithm that they have
+that they have learned
+
+ align:start position:0%
+that they have learned
+ 
+
+ align:start position:0%
+that they have learned
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so the school is unable to
+
+ align:start position:0%
+so the school is unable to
+ 
+
+ align:start position:0%
+so the school is unable to
+kind of see what's in right in front of
+
+ align:start position:0%
+kind of see what's in right in front of
+ 
+
+ align:start position:0%
+kind of see what's in right in front of
+it that the skills have these kids have
+
+ align:start position:0%
+it that the skills have these kids have
+ 
+
+ align:start position:0%
+it that the skills have these kids have
+the skills and they just but they don't
+
+ align:start position:0%
+the skills and they just but they don't
+ 
+
+ align:start position:0%
+the skills and they just but they don't
+their skills are not sufficient because
+
+ align:start position:0%
+their skills are not sufficient because
+ 
+
+ align:start position:0%
+their skills are not sufficient because
+they need to be able to go from this
+
+ align:start position:0%
+they need to be able to go from this
+ 
+
+ align:start position:0%
+they need to be able to go from this
+day-to-day apps you know manipulation of
+
+ align:start position:0%
+day-to-day apps you know manipulation of
+ 
+
+ align:start position:0%
+day-to-day apps you know manipulation of
+arithmetic tomorrow do you do need to go
+
+ align:start position:0%
+arithmetic tomorrow do you do need to go
+ 
+
+ align:start position:0%
+arithmetic tomorrow do you do need to go
+you do need to be able to go through the
+
+ align:start position:0%
+you do need to be able to go through the
+ 
+
+ align:start position:0%
+you do need to be able to go through the
+abstraction if you're going to do
+
+ align:start position:0%
+abstraction if you're going to do
+ 
+
+ align:start position:0%
+abstraction if you're going to do
+something more than doing a market kit
+
+ align:start position:0%
+something more than doing a market kit
+ 
+
+ align:start position:0%
+something more than doing a market kit
+you cannot learn algebra without
+
+ align:start position:0%
+you cannot learn algebra without
+ 
+
+ align:start position:0%
+you cannot learn algebra without
+understanding attraction
+
+ align:start position:0%
+understanding attraction
+ 
+
+ align:start position:0%
+understanding attraction
+but the school has come is completely
+
+ align:start position:0%
+but the school has come is completely
+ 
+
+ align:start position:0%
+but the school has come is completely
+unable to do this to do this transition
+
+ align:start position:0%
+unable to do this to do this transition
+ 
+
+ align:start position:0%
+unable to do this to do this transition
+and then on the other side is whatever
+
+ align:start position:0%
+and then on the other side is whatever
+ 
+
+ align:start position:0%
+and then on the other side is whatever
+schools teaches is completely useless
+
+ align:start position:0%
+schools teaches is completely useless
+ 
+
+ align:start position:0%
+schools teaches is completely useless
+for life because these poor kids who are
+
+ align:start position:0%
+for life because these poor kids who are
+ 
+
+ align:start position:0%
+for life because these poor kids who are
+school kids who are very good at doing
+
+ align:start position:0%
+school kids who are very good at doing
+ 
+
+ align:start position:0%
+school kids who are very good at doing
+are relatively good at doing the SR math
+
+ align:start position:0%
+are relatively good at doing the SR math
+ 
+
+ align:start position:0%
+are relatively good at doing the SR math
+one thing I didn't tell you is not only
+
+ align:start position:0%
+one thing I didn't tell you is not only
+ 
+
+ align:start position:0%
+one thing I didn't tell you is not only
+they get the market transaction right
+
+ align:start position:0%
+they get the market transaction right
+ 
+
+ align:start position:0%
+they get the market transaction right
+but it takes about 15 minutes for them
+
+ align:start position:0%
+but it takes about 15 minutes for them
+ 
+
+ align:start position:0%
+but it takes about 15 minutes for them
+to do the calculation because they have
+
+ align:start position:0%
+to do the calculation because they have
+ 
+
+ align:start position:0%
+to do the calculation because they have
+unlimited time so in 15 minutes they
+
+ align:start position:0%
+unlimited time so in 15 minutes they
+ 
+
+ align:start position:0%
+unlimited time so in 15 minutes they
+would have been you know run out of the
+
+ align:start position:0%
+would have been you know run out of the
+ 
+
+ align:start position:0%
+would have been you know run out of the
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+so they couldn't like whatever they have
+
+ align:start position:0%
+so they couldn't like whatever they have
+ 
+
+ align:start position:0%
+so they couldn't like whatever they have
+learned is not useful and in fact
+
+ align:start position:0%
+learned is not useful and in fact
+ 
+
+ align:start position:0%
+learned is not useful and in fact
+pratam did an assert survey for middle
+
+ align:start position:0%
+pratam did an assert survey for middle
+ 
+
+ align:start position:0%
+pratam did an assert survey for middle
+school students where they asked them
+
+ align:start position:0%
+school students where they asked them
+ 
+
+ align:start position:0%
+school students where they asked them
+things like you know
+
+ align:start position:0%
+things like you know
+ 
+
+ align:start position:0%
+things like you know
+um you have a bag of you have a bag of
+
+ align:start position:0%
+um you have a bag of you have a bag of
+ 
+
+ align:start position:0%
+um you have a bag of you have a bag of
+fertilizer that is uh enough for a field
+
+ align:start position:0%
+fertilizer that is uh enough for a field
+ 
+
+ align:start position:0%
+fertilizer that is uh enough for a field
+of three acre
+
+ align:start position:0%
+of three acre
+ 
+
+ align:start position:0%
+of three acre
+uh you know you you're
+
+ align:start position:0%
+uh you know you you're
+ 
+
+ align:start position:0%
+uh you know you you're
+your field is one and a half acre how
+
+ align:start position:0%
+your field is one and a half acre how
+ 
+
+ align:start position:0%
+your field is one and a half acre how
+much of the back of fertilizer should
+
+ align:start position:0%
+much of the back of fertilizer should
+ 
+
+ align:start position:0%
+much of the back of fertilizer should
+you use
+
+ align:start position:0%
+you use
+ 
+
+ align:start position:0%
+you use
+and the the kids are terrible at doing
+
+ align:start position:0%
+and the the kids are terrible at doing
+ 
+
+ align:start position:0%
+and the the kids are terrible at doing
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and even when they even the ones who can
+
+ align:start position:0%
+and even when they even the ones who can
+ 
+
+ align:start position:0%
+and even when they even the ones who can
+do division can still not do that do
+
+ align:start position:0%
+do division can still not do that do
+ 
+
+ align:start position:0%
+do division can still not do that do
+this type of so this is kind of a
+
+ align:start position:0%
+this type of so this is kind of a
+ 
+
+ align:start position:0%
+this type of so this is kind of a
+parallel thing of the whatever abstract
+
+ align:start position:0%
+parallel thing of the whatever abstract
+ 
+
+ align:start position:0%
+parallel thing of the whatever abstract
+so the concrete knowledge is not
+
+ align:start position:0%
+so the concrete knowledge is not
+ 
+
+ align:start position:0%
+so the concrete knowledge is not
+translated by the schools to abstract
+
+ align:start position:0%
+translated by the schools to abstract
+ 
+
+ align:start position:0%
+translated by the schools to abstract
+knowledge that would enable you to go
+
+ align:start position:0%
+knowledge that would enable you to go
+ 
+
+ align:start position:0%
+knowledge that would enable you to go
+further and the abstract knowledge that
+
+ align:start position:0%
+further and the abstract knowledge that
+ 
+
+ align:start position:0%
+further and the abstract knowledge that
+is impacted is not
+
+ align:start position:0%
+is impacted is not
+ 
+
+ align:start position:0%
+is impacted is not
+usable in a concrete way yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outcomes part of your children as much
+
+ align:start position:0%
+outcomes part of your children as much
+ 
+
+ align:start position:0%
+outcomes part of your children as much
+but the outcomes that the market
+
+ align:start position:0%
+but the outcomes that the market
+ 
+
+ align:start position:0%
+but the outcomes that the market
+shouldn't have are I wonder if they're
+
+ align:start position:0%
+shouldn't have are I wonder if they're
+ 
+
+ align:start position:0%
+shouldn't have are I wonder if they're
+actually related to accessing knowledge
+
+ align:start position:0%
+actually related to accessing knowledge
+ 
+
+ align:start position:0%
+actually related to accessing knowledge
+or something that they have no problems
+
+ align:start position:0%
+or something that they have no problems
+ 
+
+ align:start position:0%
+or something that they have no problems
+that they have learned on the job over
+
+ align:start position:0%
+that they have learned on the job over
+ 
+
+ align:start position:0%
+that they have learned on the job over
+the years so it's really been unfair to
+
+ align:start position:0%
+the years so it's really been unfair to
+ 
+
+ align:start position:0%
+the years so it's really been unfair to
+what it existing knowledge but something
+
+ align:start position:0%
+what it existing knowledge but something
+ 
+
+ align:start position:0%
+what it existing knowledge but something
+that we have knowledge yes but it's
+
+ align:start position:0%
+that we have knowledge yes but it's
+ 
+
+ align:start position:0%
+that we have knowledge yes but it's
+existing now right about two-thirds of
+
+ align:start position:0%
+existing now right about two-thirds of
+ 
+
+ align:start position:0%
+existing now right about two-thirds of
+these kids are in school the market kids
+
+ align:start position:0%
+these kids are in school the market kids
+ 
+
+ align:start position:0%
+these kids are in school the market kids
+are still in school so whatever maybe
+
+ align:start position:0%
+are still in school so whatever maybe
+ 
+
+ align:start position:0%
+are still in school so whatever maybe
+they took a long time to acquire it but
+
+ align:start position:0%
+they took a long time to acquire it but
+ 
+
+ align:start position:0%
+they took a long time to acquire it but
+now they have it and they are still they
+
+ align:start position:0%
+now they have it and they are still they
+ 
+
+ align:start position:0%
+now they have it and they are still they
+still can't do the SR test they have it
+
+ align:start position:0%
+still can't do the SR test they have it
+ 
+
+ align:start position:0%
+still can't do the SR test they have it
+in school the school could kind of use
+
+ align:start position:0%
+in school the school could kind of use
+ 
+
+ align:start position:0%
+in school the school could kind of use
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so do you think that this is a more of
+
+ align:start position:0%
+so do you think that this is a more of
+ 
+
+ align:start position:0%
+so do you think that this is a more of
+an issue with like the pedagogy of what
+
+ align:start position:0%
+an issue with like the pedagogy of what
+ 
+
+ align:start position:0%
+an issue with like the pedagogy of what
+the teachers are doing or do you think
+
+ align:start position:0%
+the teachers are doing or do you think
+ 
+
+ align:start position:0%
+the teachers are doing or do you think
+it's more of a measurement issue about
+
+ align:start position:0%
+it's more of a measurement issue about
+ 
+
+ align:start position:0%
+it's more of a measurement issue about
+like the Acer like things should be
+
+ align:start position:0%
+like the Acer like things should be
+ 
+
+ align:start position:0%
+like the Acer like things should be
+trying to measure different things or
+
+ align:start position:0%
+trying to measure different things or
+ 
+
+ align:start position:0%
+trying to measure different things or
+testing in ways like which of these two
+
+ align:start position:0%
+testing in ways like which of these two
+ 
+
+ align:start position:0%
+testing in ways like which of these two
+do you think it is or like which is more
+
+ align:start position:0%
+do you think it is or like which is more
+ 
+
+ align:start position:0%
+do you think it is or like which is more
+important both in a way which is on the
+
+ align:start position:0%
+important both in a way which is on the
+ 
+
+ align:start position:0%
+important both in a way which is on the
+one hand
+
+ align:start position:0%
+one hand
+ 
+
+ align:start position:0%
+one hand
+I do think that it's useful to know both
+
+ align:start position:0%
+I do think that it's useful to know both
+ 
+
+ align:start position:0%
+I do think that it's useful to know both
+for the SR testing but also for
+
+ align:start position:0%
+for the SR testing but also for
+ 
+
+ align:start position:0%
+for the SR testing but also for
+employers for example that they could
+
+ align:start position:0%
+employers for example that they could
+ 
+
+ align:start position:0%
+employers for example that they could
+start testing people that they might
+
+ align:start position:0%
+start testing people that they might
+ 
+
+ align:start position:0%
+start testing people that they might
+want to hire with tests that are less
+
+ align:start position:0%
+want to hire with tests that are less
+ 
+
+ align:start position:0%
+want to hire with tests that are less
+dependent on understanding and ability
+
+ align:start position:0%
+dependent on understanding and ability
+ 
+
+ align:start position:0%
+dependent on understanding and ability
+to rehash
+
+ align:start position:0%
+to rehash
+ 
+
+ align:start position:0%
+to rehash
+rehash
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the abstract the way the way the
+
+ align:start position:0%
+the abstract the way the way the
+ 
+
+ align:start position:0%
+the abstract the way the way the
+mathematics is being taught in schools
+
+ align:start position:0%
+mathematics is being taught in schools
+ 
+
+ align:start position:0%
+mathematics is being taught in schools
+so that's true from us there that's true
+
+ align:start position:0%
+so that's true from us there that's true
+ 
+
+ align:start position:0%
+so that's true from us there that's true
+more even even more true for you know
+
+ align:start position:0%
+more even even more true for you know
+ 
+
+ align:start position:0%
+more even even more true for you know
+emphasis or you know they want software
+
+ align:start position:0%
+emphasis or you know they want software
+ 
+
+ align:start position:0%
+emphasis or you know they want software
+engineer
+
+ align:start position:0%
+engineer
+ 
+
+ align:start position:0%
+engineer
+they want you know smart people who do a
+
+ align:start position:0%
+they want you know smart people who do a
+ 
+
+ align:start position:0%
+they want you know smart people who do a
+lot of things clearly mediating it by
+
+ align:start position:0%
+lot of things clearly mediating it by
+ 
+
+ align:start position:0%
+lot of things clearly mediating it by
+performance in schools or even by is or
+
+ align:start position:0%
+performance in schools or even by is or
+ 
+
+ align:start position:0%
+performance in schools or even by is or
+even by how you do well at school type
+
+ align:start position:0%
+even by how you do well at school type
+ 
+
+ align:start position:0%
+even by how you do well at school type
+exam is a problem in fact you see some
+
+ align:start position:0%
+exam is a problem in fact you see some
+ 
+
+ align:start position:0%
+exam is a problem in fact you see some
+software company like Infosys to run
+
+ align:start position:0%
+software company like Infosys to run
+ 
+
+ align:start position:0%
+software company like Infosys to run
+sort of testing camps
+
+ align:start position:0%
+sort of testing camps
+ 
+
+ align:start position:0%
+sort of testing camps
+that are trying to capture another form
+
+ align:start position:0%
+that are trying to capture another form
+ 
+
+ align:start position:0%
+that are trying to capture another form
+of knowledge precisely to to to get
+
+ align:start position:0%
+of knowledge precisely to to to get
+ 
+
+ align:start position:0%
+of knowledge precisely to to to get
+around that I don't know how successful
+
+ align:start position:0%
+around that I don't know how successful
+ 
+
+ align:start position:0%
+around that I don't know how successful
+they are haven't seen the test but
+
+ align:start position:0%
+they are haven't seen the test but
+ 
+
+ align:start position:0%
+they are haven't seen the test but
+that's so that's a great point however
+
+ align:start position:0%
+that's so that's a great point however
+ 
+
+ align:start position:0%
+that's so that's a great point however
+the second point is do I see this as a
+
+ align:start position:0%
+the second point is do I see this as a
+ 
+
+ align:start position:0%
+the second point is do I see this as a
+point of pedagogy yes because
+
+ align:start position:0%
+point of pedagogy yes because
+ 
+
+ align:start position:0%
+point of pedagogy yes because
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+the school is it is important for people
+
+ align:start position:0%
+the school is it is important for people
+ 
+
+ align:start position:0%
+the school is it is important for people
+to learn to solve abstract problems
+
+ align:start position:0%
+to learn to solve abstract problems
+ 
+
+ align:start position:0%
+to learn to solve abstract problems
+because otherwise you're you're limited
+
+ align:start position:0%
+because otherwise you're you're limited
+ 
+
+ align:start position:0%
+because otherwise you're you're limited
+once Infosys higher these people are
+
+ align:start position:0%
+once Infosys higher these people are
+ 
+
+ align:start position:0%
+once Infosys higher these people are
+based on their
+
+ align:start position:0%
+based on their
+ 
+
+ align:start position:0%
+based on their
+non-school-like test I assume they start
+
+ align:start position:0%
+non-school-like test I assume they start
+ 
+
+ align:start position:0%
+non-school-like test I assume they start
+to tell them you know some abstract
+
+ align:start position:0%
+to tell them you know some abstract
+ 
+
+ align:start position:0%
+to tell them you know some abstract
+skills otherwise they would never be
+
+ align:start position:0%
+skills otherwise they would never be
+ 
+
+ align:start position:0%
+skills otherwise they would never be
+able to could
+
+ align:start position:0%
+able to could
+ 
+
+ align:start position:0%
+able to could
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+so the schools also would need to be
+
+ align:start position:0%
+so the schools also would need to be
+ 
+
+ align:start position:0%
+so the schools also would need to be
+able to do that and also to to to to to
+
+ align:start position:0%
+able to do that and also to to to to to
+ 
+
+ align:start position:0%
+able to do that and also to to to to to
+help people use the abstract knowledge
+
+ align:start position:0%
+help people use the abstract knowledge
+ 
+
+ align:start position:0%
+help people use the abstract knowledge
+to apply the abstract knowledge in
+
+ align:start position:0%
+to apply the abstract knowledge in
+ 
+
+ align:start position:0%
+to apply the abstract knowledge in
+concrete situation seems to be part of
+
+ align:start position:0%
+concrete situation seems to be part of
+ 
+
+ align:start position:0%
+concrete situation seems to be part of
+the so I would say that this is a
+
+ align:start position:0%
+the so I would say that this is a
+ 
+
+ align:start position:0%
+the so I would say that this is a
+problem for both both things
+
+ align:start position:0%
+problem for both both things
+ 
+
+ align:start position:0%
+problem for both both things
+so that's the problem uh so the problem
+
+ align:start position:0%
+so that's the problem uh so the problem
+ 
+
+ align:start position:0%
+so that's the problem uh so the problem
+is deeper than the test scores are low
+
+ align:start position:0%
+is deeper than the test scores are low
+ 
+
+ align:start position:0%
+is deeper than the test scores are low
+that's what that's kind of what I was
+
+ align:start position:0%
+that's what that's kind of what I was
+ 
+
+ align:start position:0%
+that's what that's kind of what I was
+trying to say
+
+ align:start position:0%
+trying to say
+ 
+
+ align:start position:0%
+trying to say
+and so where does it come from
+
+ align:start position:0%
+and so where does it come from
+ 
+
+ align:start position:0%
+and so where does it come from
+so let me start by what it what it's not
+
+ align:start position:0%
+so let me start by what it what it's not
+ 
+
+ align:start position:0%
+so let me start by what it what it's not
+and sort of the general things that you
+
+ align:start position:0%
+and sort of the general things that you
+ 
+
+ align:start position:0%
+and sort of the general things that you
+hear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you have an Indian if you ask Indian
+
+ align:start position:0%
+if you have an Indian if you ask Indian
+ 
+
+ align:start position:0%
+if you have an Indian if you ask Indian
+teachers they'll always blame the
+
+ align:start position:0%
+teachers they'll always blame the
+ 
+
+ align:start position:0%
+teachers they'll always blame the
+parents or the kids
+
+ align:start position:0%
+parents or the kids
+ 
+
+ align:start position:0%
+parents or the kids
+I think basically some version of the
+
+ align:start position:0%
+I think basically some version of the
+ 
+
+ align:start position:0%
+I think basically some version of the
+kids don't want to learn or they are
+
+ align:start position:0%
+kids don't want to learn or they are
+ 
+
+ align:start position:0%
+kids don't want to learn or they are
+lazy or they are not too smart
+
+ align:start position:0%
+lazy or they are not too smart
+ 
+
+ align:start position:0%
+lazy or they are not too smart
+um to they can't learn
+
+ align:start position:0%
+um to they can't learn
+ 
+
+ align:start position:0%
+um to they can't learn
+so that's of course Very uh patronizing
+
+ align:start position:0%
+so that's of course Very uh patronizing
+ 
+
+ align:start position:0%
+so that's of course Very uh patronizing
+but it's actually more frequent than you
+
+ align:start position:0%
+but it's actually more frequent than you
+ 
+
+ align:start position:0%
+but it's actually more frequent than you
+hear for example Bill Gates had the
+
+ align:start position:0%
+hear for example Bill Gates had the
+ 
+
+ align:start position:0%
+hear for example Bill Gates had the
+whole thing
+
+ align:start position:0%
+whole thing
+ 
+
+ align:start position:0%
+whole thing
+on a nutrition program for young kids
+
+ align:start position:0%
+on a nutrition program for young kids
+ 
+
+ align:start position:0%
+on a nutrition program for young kids
+and basically he explained that school
+
+ align:start position:0%
+and basically he explained that school
+ 
+
+ align:start position:0%
+and basically he explained that school
+performance is low because kids are
+
+ align:start position:0%
+performance is low because kids are
+ 
+
+ align:start position:0%
+performance is low because kids are
+undernourished and therefore they can't
+
+ align:start position:0%
+undernourished and therefore they can't
+ 
+
+ align:start position:0%
+undernourished and therefore they can't
+learn which is basically the same you
+
+ align:start position:0%
+learn which is basically the same you
+ 
+
+ align:start position:0%
+learn which is basically the same you
+know sort of politically correct
+
+ align:start position:0%
+know sort of politically correct
+ 
+
+ align:start position:0%
+know sort of politically correct
+argument of the same version
+
+ align:start position:0%
+argument of the same version
+ 
+
+ align:start position:0%
+argument of the same version
+so I don't think it's that why I don't
+
+ align:start position:0%
+so I don't think it's that why I don't
+ 
+
+ align:start position:0%
+so I don't think it's that why I don't
+think it's that because of my preschool
+
+ align:start position:0%
+think it's that because of my preschool
+ 
+
+ align:start position:0%
+think it's that because of my preschool
+mathematician
+
+ align:start position:0%
+mathematician
+ 
+
+ align:start position:0%
+mathematician
+I'm taking those kids I'm learning them
+
+ align:start position:0%
+I'm taking those kids I'm learning them
+ 
+
+ align:start position:0%
+I'm taking those kids I'm learning them
+exactly I'm teaching them the same thing
+
+ align:start position:0%
+exactly I'm teaching them the same thing
+ 
+
+ align:start position:0%
+exactly I'm teaching them the same thing
+that the Cambridge kids teach and they
+
+ align:start position:0%
+that the Cambridge kids teach and they
+ 
+
+ align:start position:0%
+that the Cambridge kids teach and they
+are just as good when they were four so
+
+ align:start position:0%
+are just as good when they were four so
+ 
+
+ align:start position:0%
+are just as good when they were four so
+something has happened to them later
+
+ align:start position:0%
+something has happened to them later
+ 
+
+ align:start position:0%
+something has happened to them later
+so I don't believe you you cannot learn
+
+ align:start position:0%
+so I don't believe you you cannot learn
+ 
+
+ align:start position:0%
+so I don't believe you you cannot learn
+you cannot learn strategy
+
+ align:start position:0%
+you cannot learn strategy
+ 
+
+ align:start position:0%
+you cannot learn strategy
+that's one another thing you hear often
+
+ align:start position:0%
+that's one another thing you hear often
+ 
+
+ align:start position:0%
+that's one another thing you hear often
+especially in the education world is
+
+ align:start position:0%
+especially in the education world is
+ 
+
+ align:start position:0%
+especially in the education world is
+that it's all about resources the the
+
+ align:start position:0%
+that it's all about resources the the
+ 
+
+ align:start position:0%
+that it's all about resources the the
+the the systems are under resourced uh
+
+ align:start position:0%
+the the systems are under resourced uh
+ 
+
+ align:start position:0%
+the the systems are under resourced uh
+the teacher salary is too low and also
+
+ align:start position:0%
+the teacher salary is too low and also
+ 
+
+ align:start position:0%
+the teacher salary is too low and also
+there are no textbooks flip charts
+
+ align:start position:0%
+there are no textbooks flip charts
+ 
+
+ align:start position:0%
+there are no textbooks flip charts
+computers and so on and so forth in the
+
+ align:start position:0%
+computers and so on and so forth in the
+ 
+
+ align:start position:0%
+computers and so on and so forth in the
+school
+
+ align:start position:0%
+school
+ 
+
+ align:start position:0%
+school
+so we know a bunch about that because
+
+ align:start position:0%
+so we know a bunch about that because
+ 
+
+ align:start position:0%
+so we know a bunch about that because
+that's these are precisely where you
+
+ align:start position:0%
+that's these are precisely where you
+ 
+
+ align:start position:0%
+that's these are precisely where you
+have this like huge cluster of
+
+ align:start position:0%
+have this like huge cluster of
+ 
+
+ align:start position:0%
+have this like huge cluster of
+experiments that have been conducted
+
+ align:start position:0%
+experiments that have been conducted
+ 
+
+ align:start position:0%
+experiments that have been conducted
+over the year
+
+ align:start position:0%
+over the year
+ 
+
+ align:start position:0%
+over the year
+and what do we know well number one yeah
+
+ align:start position:0%
+and what do we know well number one yeah
+ 
+
+ align:start position:0%
+and what do we know well number one yeah
+and just thinking also about the issue
+
+ align:start position:0%
+and just thinking also about the issue
+ 
+
+ align:start position:0%
+and just thinking also about the issue
+you brought up earlier in lecture about
+
+ align:start position:0%
+you brought up earlier in lecture about
+ 
+
+ align:start position:0%
+you brought up earlier in lecture about
+attendance is there any argument or
+
+ align:start position:0%
+attendance is there any argument or
+ 
+
+ align:start position:0%
+attendance is there any argument or
+evidence in favor of attendance being
+
+ align:start position:0%
+evidence in favor of attendance being
+ 
+
+ align:start position:0%
+evidence in favor of attendance being
+faster as well where maybe there's
+
+ align:start position:0%
+faster as well where maybe there's
+ 
+
+ align:start position:0%
+faster as well where maybe there's
+secondary contacts return so you can go
+
+ align:start position:0%
+secondary contacts return so you can go
+ 
+
+ align:start position:0%
+secondary contacts return so you can go
+every day you can have a lot but if
+
+ align:start position:0%
+every day you can have a lot but if
+ 
+
+ align:start position:0%
+every day you can have a lot but if
+you're always starting there there is
+
+ align:start position:0%
+you're always starting there there is
+ 
+
+ align:start position:0%
+you're always starting there there is
+when kids go more to school in Israel
+
+ align:start position:0%
+when kids go more to school in Israel
+ 
+
+ align:start position:0%
+when kids go more to school in Israel
+because they are more present or they
+
+ align:start position:0%
+because they are more present or they
+ 
+
+ align:start position:0%
+because they are more present or they
+are Sharma president
+
+ align:start position:0%
+are Sharma president
+ 
+
+ align:start position:0%
+are Sharma president
+so there is something a little bit of
+
+ align:start position:0%
+so there is something a little bit of
+ 
+
+ align:start position:0%
+so there is something a little bit of
+something that happens in every day of
+
+ align:start position:0%
+something that happens in every day of
+ 
+
+ align:start position:0%
+something that happens in every day of
+school when kids are in early school
+
+ align:start position:0%
+school when kids are in early school
+ 
+
+ align:start position:0%
+school when kids are in early school
+they also learn more so something is
+
+ align:start position:0%
+they also learn more so something is
+ 
+
+ align:start position:0%
+they also learn more so something is
+happening so there is some amount of
+
+ align:start position:0%
+happening so there is some amount of
+ 
+
+ align:start position:0%
+happening so there is some amount of
+learning that's happening and you get
+
+ align:start position:0%
+learning that's happening and you get
+ 
+
+ align:start position:0%
+learning that's happening and you get
+fewer days of school you get fewer days
+
+ align:start position:0%
+fewer days of school you get fewer days
+ 
+
+ align:start position:0%
+fewer days of school you get fewer days
+of that and we saw it in you know it
+
+ align:start position:0%
+of that and we saw it in you know it
+ 
+
+ align:start position:0%
+of that and we saw it in you know it
+makes a big difference to to have a
+
+ align:start position:0%
+makes a big difference to to have a
+ 
+
+ align:start position:0%
+makes a big difference to to have a
+covet and and there is no school so
+
+ align:start position:0%
+covet and and there is no school so
+ 
+
+ align:start position:0%
+covet and and there is no school so
+something is happening in the school not
+
+ align:start position:0%
+something is happening in the school not
+ 
+
+ align:start position:0%
+something is happening in the school not
+nothing and then therefore attendance
+
+ align:start position:0%
+nothing and then therefore attendance
+ 
+
+ align:start position:0%
+nothing and then therefore attendance
+matters but
+
+ align:start position:0%
+matters but
+ 
+
+ align:start position:0%
+matters but
+maybe not as much as should be happening
+
+ align:start position:0%
+maybe not as much as should be happening
+ 
+
+ align:start position:0%
+maybe not as much as should be happening
+is what kind of what we are
+
+ align:start position:0%
+is what kind of what we are
+ 
+
+ align:start position:0%
+is what kind of what we are
+so the argument that teachers are poorly
+
+ align:start position:0%
+so the argument that teachers are poorly
+ 
+
+ align:start position:0%
+so the argument that teachers are poorly
+paid it definitely holds for France
+
+ align:start position:0%
+paid it definitely holds for France
+ 
+
+ align:start position:0%
+paid it definitely holds for France
+where teachers are very very poorly paid
+
+ align:start position:0%
+where teachers are very very poorly paid
+ 
+
+ align:start position:0%
+where teachers are very very poorly paid
+as a function of their education
+
+ align:start position:0%
+as a function of their education
+ 
+
+ align:start position:0%
+as a function of their education
+I think it holds in the U.S so someone
+
+ align:start position:0%
+I think it holds in the U.S so someone
+ 
+
+ align:start position:0%
+I think it holds in the U.S so someone
+would need to check that it does not
+
+ align:start position:0%
+would need to check that it does not
+ 
+
+ align:start position:0%
+would need to check that it does not
+hold in India
+
+ align:start position:0%
+hold in India
+ 
+
+ align:start position:0%
+hold in India
+where the the salary of a teacher uh you
+
+ align:start position:0%
+where the the salary of a teacher uh you
+ 
+
+ align:start position:0%
+where the the salary of a teacher uh you
+know in the distribution is super high
+
+ align:start position:0%
+know in the distribution is super high
+ 
+
+ align:start position:0%
+know in the distribution is super high
+and conditional on their on their
+
+ align:start position:0%
+and conditional on their on their
+ 
+
+ align:start position:0%
+and conditional on their on their
+education event is super high and after
+
+ align:start position:0%
+education event is super high and after
+ 
+
+ align:start position:0%
+education event is super high and after
+all we saw in Ghana how everybody is
+
+ align:start position:0%
+all we saw in Ghana how everybody is
+ 
+
+ align:start position:0%
+all we saw in Ghana how everybody is
+desperate to be a teacher because it's
+
+ align:start position:0%
+desperate to be a teacher because it's
+ 
+
+ align:start position:0%
+desperate to be a teacher because it's
+such a is such a rent seeking rent
+
+ align:start position:0%
+such a is such a rent seeking rent
+ 
+
+ align:start position:0%
+such a is such a rent seeking rent
+paying occupation
+
+ align:start position:0%
+paying occupation
+ 
+
+ align:start position:0%
+paying occupation
+teacher salary in the in the public
+
+ align:start position:0%
+teacher salary in the in the public
+ 
+
+ align:start position:0%
+teacher salary in the in the public
+schools are also much higher than what
+
+ align:start position:0%
+schools are also much higher than what
+ 
+
+ align:start position:0%
+schools are also much higher than what
+they are paid in private school which
+
+ align:start position:0%
+they are paid in private school which
+ 
+
+ align:start position:0%
+they are paid in private school which
+suggests that there is a huge wedge
+
+ align:start position:0%
+suggests that there is a huge wedge
+ 
+
+ align:start position:0%
+suggests that there is a huge wedge
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the so it's it's very unlikely to be due
+
+ align:start position:0%
+the so it's it's very unlikely to be due
+ 
+
+ align:start position:0%
+the so it's it's very unlikely to be due
+to teach your salary and in fact there
+
+ align:start position:0%
+to teach your salary and in fact there
+ 
+
+ align:start position:0%
+to teach your salary and in fact there
+is an experiment by Karthik maldon and
+
+ align:start position:0%
+is an experiment by Karthik maldon and
+ 
+
+ align:start position:0%
+is an experiment by Karthik maldon and
+others that demonstrated that in
+
+ align:start position:0%
+others that demonstrated that in
+ 
+
+ align:start position:0%
+others that demonstrated that in
+Indonesia super electrical experiment
+
+ align:start position:0%
+Indonesia super electrical experiment
+ 
+
+ align:start position:0%
+Indonesia super electrical experiment
+where the teacher salary was doubled
+
+ align:start position:0%
+where the teacher salary was doubled
+ 
+
+ align:start position:0%
+where the teacher salary was doubled
+and the impact on test causes nothing
+
+ align:start position:0%
+and the impact on test causes nothing
+ 
+
+ align:start position:0%
+and the impact on test causes nothing
+immediately nothing as you select more
+
+ align:start position:0%
+immediately nothing as you select more
+ 
+
+ align:start position:0%
+immediately nothing as you select more
+teachers and better teachers into the
+
+ align:start position:0%
+teachers and better teachers into the
+ 
+
+ align:start position:0%
+teachers and better teachers into the
+job
+
+ align:start position:0%
+job
+ 
+
+ align:start position:0%
+job
+so there's just no effect on teacher
+
+ align:start position:0%
+so there's just no effect on teacher
+ 
+
+ align:start position:0%
+so there's just no effect on teacher
+papers yeah
+
+ align:start position:0%
+papers yeah
+ 
+
+ align:start position:0%
+papers yeah
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so I'll go to incentives uh in a
+
+ align:start position:0%
+yeah so I'll go to incentives uh in a
+ 
+
+ align:start position:0%
+yeah so I'll go to incentives uh in a
+moment
+
+ align:start position:0%
+moment
+ 
+
+ align:start position:0%
+moment
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+before that in fact I'll go to incentive
+
+ align:start position:0%
+before that in fact I'll go to incentive
+ 
+
+ align:start position:0%
+before that in fact I'll go to incentive
+right away before that other resources
+
+ align:start position:0%
+right away before that other resources
+ 
+
+ align:start position:0%
+right away before that other resources
+so that's where this is like this line
+
+ align:start position:0%
+so that's where this is like this line
+ 
+
+ align:start position:0%
+so that's where this is like this line
+was about like
+
+ align:start position:0%
+was about like
+ 
+
+ align:start position:0%
+was about like
+20 years of research and education
+
+ align:start position:0%
+20 years of research and education
+ 
+
+ align:start position:0%
+20 years of research and education
+trying everything from
+
+ align:start position:0%
+trying everything from
+ 
+
+ align:start position:0%
+trying everything from
+textbooks to cutting class size into to
+
+ align:start position:0%
+textbooks to cutting class size into to
+ 
+
+ align:start position:0%
+textbooks to cutting class size into to
+anything you can think of any inputs
+
+ align:start position:0%
+anything you can think of any inputs
+ 
+
+ align:start position:0%
+anything you can think of any inputs
+except computers and I'll go back to the
+
+ align:start position:0%
+except computers and I'll go back to the
+ 
+
+ align:start position:0%
+except computers and I'll go back to the
+computers in a minute none of that makes
+
+ align:start position:0%
+computers in a minute none of that makes
+ 
+
+ align:start position:0%
+computers in a minute none of that makes
+any difference in fact the famous you
+
+ align:start position:0%
+any difference in fact the famous you
+ 
+
+ align:start position:0%
+any difference in fact the famous you
+know Michael Kramer textbook paper
+
+ align:start position:0%
+know Michael Kramer textbook paper
+ 
+
+ align:start position:0%
+know Michael Kramer textbook paper
+that's sort of launched us all
+
+ align:start position:0%
+that's sort of launched us all
+ 
+
+ align:start position:0%
+that's sort of launched us all
+was an extremely surprising result to
+
+ align:start position:0%
+was an extremely surprising result to
+ 
+
+ align:start position:0%
+was an extremely surprising result to
+even to to him and to all of us because
+
+ align:start position:0%
+even to to him and to all of us because
+ 
+
+ align:start position:0%
+even to to him and to all of us because
+it took no impact of providing textbooks
+
+ align:start position:0%
+it took no impact of providing textbooks
+ 
+
+ align:start position:0%
+it took no impact of providing textbooks
+in Kenyan school that didn't have
+
+ align:start position:0%
+in Kenyan school that didn't have
+ 
+
+ align:start position:0%
+in Kenyan school that didn't have
+textbooks so it's not about stuff it's
+
+ align:start position:0%
+textbooks so it's not about stuff it's
+ 
+
+ align:start position:0%
+textbooks so it's not about stuff it's
+not about teacher money it's not about
+
+ align:start position:0%
+not about teacher money it's not about
+ 
+
+ align:start position:0%
+not about teacher money it's not about
+things in the classes uh then you have
+
+ align:start position:0%
+things in the classes uh then you have
+ 
+
+ align:start position:0%
+things in the classes uh then you have
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+the incident the economists sort of
+
+ align:start position:0%
+the incident the economists sort of
+ 
+
+ align:start position:0%
+the incident the economists sort of
+knee-jerk reaction to the the first one
+
+ align:start position:0%
+knee-jerk reaction to the the first one
+ 
+
+ align:start position:0%
+knee-jerk reaction to the the first one
+about kids can't learn is the teachers
+
+ align:start position:0%
+about kids can't learn is the teachers
+ 
+
+ align:start position:0%
+about kids can't learn is the teachers
+need Jack reaction the second one is the
+
+ align:start position:0%
+need Jack reaction the second one is the
+ 
+
+ align:start position:0%
+need Jack reaction the second one is the
+you know Oxfam teacher reaction
+
+ align:start position:0%
+you know Oxfam teacher reaction
+ 
+
+ align:start position:0%
+you know Oxfam teacher reaction
+knee-jack reaction the incentive with
+
+ align:start position:0%
+knee-jack reaction the incentive with
+ 
+
+ align:start position:0%
+knee-jack reaction the incentive with
+the economist knee jock reaction it's
+
+ align:start position:0%
+the economist knee jock reaction it's
+ 
+
+ align:start position:0%
+the economist knee jock reaction it's
+got to be insensive
+
+ align:start position:0%
+got to be insensive
+ 
+
+ align:start position:0%
+got to be insensive
+and it's true that directive incentives
+
+ align:start position:0%
+and it's true that directive incentives
+ 
+
+ align:start position:0%
+and it's true that directive incentives
+to specific things has a small effect
+
+ align:start position:0%
+to specific things has a small effect
+ 
+
+ align:start position:0%
+to specific things has a small effect
+some effect for example uh going back to
+
+ align:start position:0%
+some effect for example uh going back to
+ 
+
+ align:start position:0%
+some effect for example uh going back to
+the attendance question you asked we
+
+ align:start position:0%
+the attendance question you asked we
+ 
+
+ align:start position:0%
+the attendance question you asked we
+have a paper with
+
+ align:start position:0%
+have a paper with
+ 
+
+ align:start position:0%
+have a paper with
+Stephen Ryan looking at providing
+
+ align:start position:0%
+Stephen Ryan looking at providing
+ 
+
+ align:start position:0%
+Stephen Ryan looking at providing
+incentives to teachers to show up
+
+ align:start position:0%
+incentives to teachers to show up
+ 
+
+ align:start position:0%
+incentives to teachers to show up
+and then if you give them incentive to
+
+ align:start position:0%
+and then if you give them incentive to
+ 
+
+ align:start position:0%
+and then if you give them incentive to
+show up more they show up more and if
+
+ align:start position:0%
+show up more they show up more and if
+ 
+
+ align:start position:0%
+show up more they show up more and if
+they show up more the kids learn more so
+
+ align:start position:0%
+they show up more the kids learn more so
+ 
+
+ align:start position:0%
+they show up more the kids learn more so
+that's that makes sense
+
+ align:start position:0%
+that's that makes sense
+ 
+
+ align:start position:0%
+that's that makes sense
+there is also a number of people based
+
+ align:start position:0%
+there is also a number of people based
+ 
+
+ align:start position:0%
+there is also a number of people based
+on providing incentive for test scores
+
+ align:start position:0%
+on providing incentive for test scores
+ 
+
+ align:start position:0%
+on providing incentive for test scores
+and then the literature is a bit more
+
+ align:start position:0%
+and then the literature is a bit more
+ 
+
+ align:start position:0%
+and then the literature is a bit more
+key some papers for example Michael
+
+ align:start position:0%
+key some papers for example Michael
+ 
+
+ align:start position:0%
+key some papers for example Michael
+Kramer shows that if you give incentive
+
+ align:start position:0%
+Kramer shows that if you give incentive
+ 
+
+ align:start position:0%
+Kramer shows that if you give incentive
+based on test scores
+
+ align:start position:0%
+based on test scores
+ 
+
+ align:start position:0%
+based on test scores
+you improve test scores that are
+
+ align:start position:0%
+you improve test scores that are
+ 
+
+ align:start position:0%
+you improve test scores that are
+targeted but you don't improve you
+
+ align:start position:0%
+targeted but you don't improve you
+ 
+
+ align:start position:0%
+targeted but you don't improve you
+improve the the performance on the exact
+
+ align:start position:0%
+improve the the performance on the exact
+ 
+
+ align:start position:0%
+improve the the performance on the exact
+test that is being targeted but not on
+
+ align:start position:0%
+test that is being targeted but not on
+ 
+
+ align:start position:0%
+test that is being targeted but not on
+any other measures of learning
+
+ align:start position:0%
+any other measures of learning
+ 
+
+ align:start position:0%
+any other measures of learning
+um to and then Karthik as another people
+
+ align:start position:0%
+um to and then Karthik as another people
+ 
+
+ align:start position:0%
+um to and then Karthik as another people
+that very argue that no no there is some
+
+ align:start position:0%
+that very argue that no no there is some
+ 
+
+ align:start position:0%
+that very argue that no no there is some
+gain in actual learning coming from the
+
+ align:start position:0%
+gain in actual learning coming from the
+ 
+
+ align:start position:0%
+gain in actual learning coming from the
+incentive so there is a bit of a dispute
+
+ align:start position:0%
+incentive so there is a bit of a dispute
+ 
+
+ align:start position:0%
+incentive so there is a bit of a dispute
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+it's a bit in the eyes of the beholder
+
+ align:start position:0%
+it's a bit in the eyes of the beholder
+ 
+
+ align:start position:0%
+it's a bit in the eyes of the beholder
+but I'll go into that if you give
+
+ align:start position:0%
+but I'll go into that if you give
+ 
+
+ align:start position:0%
+but I'll go into that if you give
+incentive on test scores there's going
+
+ align:start position:0%
+incentive on test scores there's going
+ 
+
+ align:start position:0%
+incentive on test scores there's going
+to be some increase in test scores
+
+ align:start position:0%
+to be some increase in test scores
+ 
+
+ align:start position:0%
+to be some increase in test scores
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+we can just put that aside and say well
+
+ align:start position:0%
+we can just put that aside and say well
+ 
+
+ align:start position:0%
+we can just put that aside and say well
+providing incentives to teachers on in
+
+ align:start position:0%
+providing incentives to teachers on in
+ 
+
+ align:start position:0%
+providing incentives to teachers on in
+public schools who are otherwise not
+
+ align:start position:0%
+public schools who are otherwise not
+ 
+
+ align:start position:0%
+public schools who are otherwise not
+very well incentivized
+
+ align:start position:0%
+very well incentivized
+ 
+
+ align:start position:0%
+very well incentivized
+is much less incentive than just the
+
+ align:start position:0%
+is much less incentive than just the
+ 
+
+ align:start position:0%
+is much less incentive than just the
+private schools you would think the
+
+ align:start position:0%
+private schools you would think the
+ 
+
+ align:start position:0%
+private schools you would think the
+private schools are the ones that are
+
+ align:start position:0%
+private schools are the ones that are
+ 
+
+ align:start position:0%
+private schools are the ones that are
+completely incentivized and in fact
+
+ align:start position:0%
+completely incentivized and in fact
+ 
+
+ align:start position:0%
+completely incentivized and in fact
+there is a literature in particular with
+
+ align:start position:0%
+there is a literature in particular with
+ 
+
+ align:start position:0%
+there is a literature in particular with
+jishnu by jishnu Das and Asim that is
+
+ align:start position:0%
+jishnu by jishnu Das and Asim that is
+ 
+
+ align:start position:0%
+jishnu by jishnu Das and Asim that is
+all about the fact that people parents
+
+ align:start position:0%
+all about the fact that people parents
+ 
+
+ align:start position:0%
+all about the fact that people parents
+are super
+
+ align:start position:0%
+are super
+ 
+
+ align:start position:0%
+are super
+demanding as customers and if they see
+
+ align:start position:0%
+demanding as customers and if they see
+ 
+
+ align:start position:0%
+demanding as customers and if they see
+that the performance of the school is
+
+ align:start position:0%
+that the performance of the school is
+ 
+
+ align:start position:0%
+that the performance of the school is
+low in the sense that they see low test
+
+ align:start position:0%
+low in the sense that they see low test
+ 
+
+ align:start position:0%
+low in the sense that they see low test
+scores around them they move the kids
+
+ align:start position:0%
+scores around them they move the kids
+ 
+
+ align:start position:0%
+scores around them they move the kids
+and so the you would think the private
+
+ align:start position:0%
+and so the you would think the private
+ 
+
+ align:start position:0%
+and so the you would think the private
+schools are where you would find
+
+ align:start position:0%
+schools are where you would find
+ 
+
+ align:start position:0%
+schools are where you would find
+that where the ins incentives are very
+
+ align:start position:0%
+that where the ins incentives are very
+ 
+
+ align:start position:0%
+that where the ins incentives are very
+steep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me know if you have like the supply
+
+ align:start position:0%
+let me know if you have like the supply
+ 
+
+ align:start position:0%
+let me know if you have like the supply
+of teachers in the sense that like how
+
+ align:start position:0%
+of teachers in the sense that like how
+ 
+
+ align:start position:0%
+of teachers in the sense that like how
+they are educated to begin with how are
+
+ align:start position:0%
+they are educated to begin with how are
+ 
+
+ align:start position:0%
+they are educated to begin with how are
+the teachers are educated themselves uh
+
+ align:start position:0%
+the teachers are educated themselves uh
+ 
+
+ align:start position:0%
+the teachers are educated themselves uh
+so yeah they go to they go to college
+
+ align:start position:0%
+so yeah they go to they go to college
+ 
+
+ align:start position:0%
+so yeah they go to they go to college
+so they are they have they they have
+
+ align:start position:0%
+so they are they have they they have
+ 
+
+ align:start position:0%
+so they are they have they they have
+they are well educated
+
+ align:start position:0%
+they are well educated
+ 
+
+ align:start position:0%
+they are well educated
+they don't do much but they are well
+
+ align:start position:0%
+they don't do much but they are well
+ 
+
+ align:start position:0%
+they don't do much but they are well
+educated they are able to do that job
+
+ align:start position:0%
+educated they are able to do that job
+ 
+
+ align:start position:0%
+educated they are able to do that job
+they are there I think it's much it
+
+ align:start position:0%
+they are there I think it's much it
+ 
+
+ align:start position:0%
+they are there I think it's much it
+becomes much more of an issue in
+
+ align:start position:0%
+becomes much more of an issue in
+ 
+
+ align:start position:0%
+becomes much more of an issue in
+secondary school if you remember we
+
+ align:start position:0%
+secondary school if you remember we
+ 
+
+ align:start position:0%
+secondary school if you remember we
+discussed that is that for second High
+
+ align:start position:0%
+discussed that is that for second High
+ 
+
+ align:start position:0%
+discussed that is that for second High
+School you start to have a competition
+
+ align:start position:0%
+School you start to have a competition
+ 
+
+ align:start position:0%
+School you start to have a competition
+between the labor market and and the
+
+ align:start position:0%
+between the labor market and and the
+ 
+
+ align:start position:0%
+between the labor market and and the
+schools
+
+ align:start position:0%
+schools
+ 
+
+ align:start position:0%
+schools
+uh and so the best peop the people who'd
+
+ align:start position:0%
+uh and so the best peop the people who'd
+ 
+
+ align:start position:0%
+uh and so the best peop the people who'd
+be best at teaching are also very good
+
+ align:start position:0%
+be best at teaching are also very good
+ 
+
+ align:start position:0%
+be best at teaching are also very good
+in the rest of the economy so in Middle
+
+ align:start position:0%
+in the rest of the economy so in Middle
+ 
+
+ align:start position:0%
+in the rest of the economy so in Middle
+income growing country like Ghana or
+
+ align:start position:0%
+income growing country like Ghana or
+ 
+
+ align:start position:0%
+income growing country like Ghana or
+India you start feeling that for
+
+ align:start position:0%
+India you start feeling that for
+ 
+
+ align:start position:0%
+India you start feeling that for
+secondary school but in Primary School
+
+ align:start position:0%
+secondary school but in Primary School
+ 
+
+ align:start position:0%
+secondary school but in Primary School
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+a vast supply of people who could do a
+
+ align:start position:0%
+a vast supply of people who could do a
+ 
+
+ align:start position:0%
+a vast supply of people who could do a
+perfectly good job educating kids and
+
+ align:start position:0%
+perfectly good job educating kids and
+ 
+
+ align:start position:0%
+perfectly good job educating kids and
+I'll go back I'll show you why I think
+
+ align:start position:0%
+I'll go back I'll show you why I think
+ 
+
+ align:start position:0%
+I'll go back I'll show you why I think
+they can do their job if they want to in
+
+ align:start position:0%
+they can do their job if they want to in
+ 
+
+ align:start position:0%
+they can do their job if they want to in
+a minute
+
+ align:start position:0%
+a minute
+ 
+
+ align:start position:0%
+a minute
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so how should we think or this would be
+
+ align:start position:0%
+so how should we think or this would be
+ 
+
+ align:start position:0%
+so how should we think or this would be
+like too big of a question for right now
+
+ align:start position:0%
+like too big of a question for right now
+ 
+
+ align:start position:0%
+like too big of a question for right now
+but how should we think about like all
+
+ align:start position:0%
+but how should we think about like all
+ 
+
+ align:start position:0%
+but how should we think about like all
+of this literature about like teacher
+
+ align:start position:0%
+of this literature about like teacher
+ 
+
+ align:start position:0%
+of this literature about like teacher
+incentives and like School quality and
+
+ align:start position:0%
+incentives and like School quality and
+ 
+
+ align:start position:0%
+incentives and like School quality and
+pedagogy or attendance or whatever
+
+ align:start position:0%
+pedagogy or attendance or whatever
+ 
+
+ align:start position:0%
+pedagogy or attendance or whatever
+um comparing the things that happen in
+
+ align:start position:0%
+um comparing the things that happen in
+ 
+
+ align:start position:0%
+um comparing the things that happen in
+the developing World versus I know a lot
+
+ align:start position:0%
+the developing World versus I know a lot
+ 
+
+ align:start position:0%
+the developing World versus I know a lot
+of Education literature exists for the
+
+ align:start position:0%
+of Education literature exists for the
+ 
+
+ align:start position:0%
+of Education literature exists for the
+United States or Europe or other
+
+ align:start position:0%
+United States or Europe or other
+ 
+
+ align:start position:0%
+United States or Europe or other
+subdeveloped countries and so how should
+
+ align:start position:0%
+subdeveloped countries and so how should
+ 
+
+ align:start position:0%
+subdeveloped countries and so how should
+we think about comparing like the
+
+ align:start position:0%
+we think about comparing like the
+ 
+
+ align:start position:0%
+we think about comparing like the
+findings from those two different
+
+ align:start position:0%
+findings from those two different
+ 
+
+ align:start position:0%
+findings from those two different
+literatures it's a great question and uh
+
+ align:start position:0%
+literatures it's a great question and uh
+ 
+
+ align:start position:0%
+literatures it's a great question and uh
+hold the sword I'll go back to it uh I
+
+ align:start position:0%
+hold the sword I'll go back to it uh I
+ 
+
+ align:start position:0%
+hold the sword I'll go back to it uh I
+think like in everything when we are
+
+ align:start position:0%
+think like in everything when we are
+ 
+
+ align:start position:0%
+think like in everything when we are
+wondering how to apply results from one
+
+ align:start position:0%
+wondering how to apply results from one
+ 
+
+ align:start position:0%
+wondering how to apply results from one
+context to another we have to think
+
+ align:start position:0%
+context to another we have to think
+ 
+
+ align:start position:0%
+context to another we have to think
+whether the context changes the model of
+
+ align:start position:0%
+whether the context changes the model of
+ 
+
+ align:start position:0%
+whether the context changes the model of
+what's being delivered in schools and in
+
+ align:start position:0%
+what's being delivered in schools and in
+ 
+
+ align:start position:0%
+what's being delivered in schools and in
+this particular instance I'm pretty sure
+
+ align:start position:0%
+this particular instance I'm pretty sure
+ 
+
+ align:start position:0%
+this particular instance I'm pretty sure
+it does and then I'll tell you exactly
+
+ align:start position:0%
+it does and then I'll tell you exactly
+ 
+
+ align:start position:0%
+it does and then I'll tell you exactly
+how in a moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're talking about the teacher side yes
+
+ align:start position:0%
+we're talking about the teacher side yes
+ 
+
+ align:start position:0%
+we're talking about the teacher side yes
+incentive for students themselves are
+
+ align:start position:0%
+incentive for students themselves are
+ 
+
+ align:start position:0%
+incentive for students themselves are
+are effective uh they increase the
+
+ align:start position:0%
+are effective uh they increase the
+ 
+
+ align:start position:0%
+are effective uh they increase the
+increased test scores they increase so
+
+ align:start position:0%
+increased test scores they increase so
+ 
+
+ align:start position:0%
+increased test scores they increase so
+if you give for example Michael cameras
+
+ align:start position:0%
+if you give for example Michael cameras
+ 
+
+ align:start position:0%
+if you give for example Michael cameras
+there is a paper on gold scholarship
+
+ align:start position:0%
+there is a paper on gold scholarship
+ 
+
+ align:start position:0%
+there is a paper on gold scholarship
+that are conditional and performance and
+
+ align:start position:0%
+that are conditional and performance and
+ 
+
+ align:start position:0%
+that are conditional and performance and
+you get an increase in performance
+
+ align:start position:0%
+you get an increase in performance
+ 
+
+ align:start position:0%
+you get an increase in performance
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um that relates to that that relates to
+
+ align:start position:0%
+um that relates to that that relates to
+ 
+
+ align:start position:0%
+um that relates to that that relates to
+the point I'll
+
+ align:start position:0%
+the point I'll
+ 
+
+ align:start position:0%
+the point I'll
+I'll
+
+ align:start position:0%
+I'll
+ 
+
+ align:start position:0%
+I'll
+again hold it so that's going to become
+
+ align:start position:0%
+again hold it so that's going to become
+ 
+
+ align:start position:0%
+again hold it so that's going to become
+relevant
+
+ align:start position:0%
+relevant
+ 
+
+ align:start position:0%
+relevant
+so let's go back to let's go back to my
+
+ align:start position:0%
+so let's go back to let's go back to my
+ 
+
+ align:start position:0%
+so let's go back to let's go back to my
+private schools so the private school
+
+ align:start position:0%
+private schools so the private school
+ 
+
+ align:start position:0%
+private schools so the private school
+you would think is like the most steeper
+
+ align:start position:0%
+you would think is like the most steeper
+ 
+
+ align:start position:0%
+you would think is like the most steeper
+incentive you could get is to just have
+
+ align:start position:0%
+incentive you could get is to just have
+ 
+
+ align:start position:0%
+incentive you could get is to just have
+to run a private schools which is
+
+ align:start position:0%
+to run a private schools which is
+ 
+
+ align:start position:0%
+to run a private schools which is
+entirely funded by parents and where
+
+ align:start position:0%
+entirely funded by parents and where
+ 
+
+ align:start position:0%
+entirely funded by parents and where
+parents are always willing to walk away
+
+ align:start position:0%
+parents are always willing to walk away
+ 
+
+ align:start position:0%
+parents are always willing to walk away
+so if incentives were powerful then
+
+ align:start position:0%
+so if incentives were powerful then
+ 
+
+ align:start position:0%
+so if incentives were powerful then
+private schools should do much better
+
+ align:start position:0%
+private schools should do much better
+ 
+
+ align:start position:0%
+private schools should do much better
+than public school
+
+ align:start position:0%
+than public school
+ 
+
+ align:start position:0%
+than public school
+make sense and in fact if you compare
+
+ align:start position:0%
+make sense and in fact if you compare
+ 
+
+ align:start position:0%
+make sense and in fact if you compare
+just at the correlations
+
+ align:start position:0%
+just at the correlations
+ 
+
+ align:start position:0%
+just at the correlations
+kids in private school do much better
+
+ align:start position:0%
+kids in private school do much better
+ 
+
+ align:start position:0%
+kids in private school do much better
+than kids in public schools but of
+
+ align:start position:0%
+than kids in public schools but of
+ 
+
+ align:start position:0%
+than kids in public schools but of
+course kids in private schools are
+
+ align:start position:0%
+course kids in private schools are
+ 
+
+ align:start position:0%
+course kids in private schools are
+selected their parents have the money
+
+ align:start position:0%
+selected their parents have the money
+ 
+
+ align:start position:0%
+selected their parents have the money
+and they also are interested enough to
+
+ align:start position:0%
+and they also are interested enough to
+ 
+
+ align:start position:0%
+and they also are interested enough to
+send them to private schools so we can't
+
+ align:start position:0%
+send them to private schools so we can't
+ 
+
+ align:start position:0%
+send them to private schools so we can't
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+so a Karthik
+
+ align:start position:0%
+so a Karthik
+ 
+
+ align:start position:0%
+so a Karthik
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+on an experiment on a private school
+
+ align:start position:0%
+on an experiment on a private school
+ 
+
+ align:start position:0%
+on an experiment on a private school
+attendance
+
+ align:start position:0%
+attendance
+ 
+
+ align:start position:0%
+attendance
+and here I'm going to
+
+ align:start position:0%
+and here I'm going to
+ 
+
+ align:start position:0%
+and here I'm going to
+I'm going to step back step aside one
+
+ align:start position:0%
+I'm going to step back step aside one
+ 
+
+ align:start position:0%
+I'm going to step back step aside one
+point that's going to be my one
+
+ align:start position:0%
+point that's going to be my one
+ 
+
+ align:start position:0%
+point that's going to be my one
+methodological point for the day which
+
+ align:start position:0%
+methodological point for the day which
+ 
+
+ align:start position:0%
+methodological point for the day which
+is he was not just interested in the
+
+ align:start position:0%
+is he was not just interested in the
+ 
+
+ align:start position:0%
+is he was not just interested in the
+impact of private schools on kids who
+
+ align:start position:0%
+impact of private schools on kids who
+ 
+
+ align:start position:0%
+impact of private schools on kids who
+attend private school
+
+ align:start position:0%
+attend private school
+ 
+
+ align:start position:0%
+attend private school
+but he was also interested which for us
+
+ align:start position:0%
+but he was also interested which for us
+ 
+
+ align:start position:0%
+but he was also interested which for us
+for today for the argument for today is
+
+ align:start position:0%
+for today for the argument for today is
+ 
+
+ align:start position:0%
+for today for the argument for today is
+all I need for today but he was also
+
+ align:start position:0%
+all I need for today but he was also
+ 
+
+ align:start position:0%
+all I need for today but he was also
+interested in another question that
+
+ align:start position:0%
+interested in another question that
+ 
+
+ align:start position:0%
+interested in another question that
+people for example in the U.S also in
+
+ align:start position:0%
+people for example in the U.S also in
+ 
+
+ align:start position:0%
+people for example in the U.S also in
+the U.S literature on Charter and
+
+ align:start position:0%
+the U.S literature on Charter and
+ 
+
+ align:start position:0%
+the U.S literature on Charter and
+voucher is continually asked which is
+
+ align:start position:0%
+voucher is continually asked which is
+ 
+
+ align:start position:0%
+voucher is continually asked which is
+what's the impact of having more kids in
+
+ align:start position:0%
+what's the impact of having more kids in
+ 
+
+ align:start position:0%
+what's the impact of having more kids in
+private school on kids that are around
+
+ align:start position:0%
+private school on kids that are around
+ 
+
+ align:start position:0%
+private school on kids that are around
+them either the other kids in private
+
+ align:start position:0%
+them either the other kids in private
+ 
+
+ align:start position:0%
+them either the other kids in private
+school that they are crowding out in
+
+ align:start position:0%
+school that they are crowding out in
+ 
+
+ align:start position:0%
+school that they are crowding out in
+their private school or the kids in
+
+ align:start position:0%
+their private school or the kids in
+ 
+
+ align:start position:0%
+their private school or the kids in
+public school that are left in the
+
+ align:start position:0%
+public school that are left in the
+ 
+
+ align:start position:0%
+public school that are left in the
+public school which might be a good
+
+ align:start position:0%
+public school which might be a good
+ 
+
+ align:start position:0%
+public school which might be a good
+thing because there are fewer kids
+
+ align:start position:0%
+thing because there are fewer kids
+ 
+
+ align:start position:0%
+thing because there are fewer kids
+around to compete with them or bad
+
+ align:start position:0%
+around to compete with them or bad
+ 
+
+ align:start position:0%
+around to compete with them or bad
+things because now they've lost their
+
+ align:start position:0%
+things because now they've lost their
+ 
+
+ align:start position:0%
+things because now they've lost their
+most motivated peers
+
+ align:start position:0%
+most motivated peers
+ 
+
+ align:start position:0%
+most motivated peers
+so this paper was really constructed to
+
+ align:start position:0%
+so this paper was really constructed to
+ 
+
+ align:start position:0%
+so this paper was really constructed to
+answer this question of the equilibrium
+
+ align:start position:0%
+answer this question of the equilibrium
+ 
+
+ align:start position:0%
+answer this question of the equilibrium
+effect of of having markets in private
+
+ align:start position:0%
+effect of of having markets in private
+ 
+
+ align:start position:0%
+effect of of having markets in private
+school in particular the equilibrium
+
+ align:start position:0%
+school in particular the equilibrium
+ 
+
+ align:start position:0%
+school in particular the equilibrium
+effect of a voucher program
+
+ align:start position:0%
+effect of a voucher program
+ 
+
+ align:start position:0%
+effect of a voucher program
+and uh and it's the first paper that did
+
+ align:start position:0%
+and uh and it's the first paper that did
+ 
+
+ align:start position:0%
+and uh and it's the first paper that did
+that I think around the world so what it
+
+ align:start position:0%
+that I think around the world so what it
+ 
+
+ align:start position:0%
+that I think around the world so what it
+did is that is he
+
+ align:start position:0%
+did is that is he
+ 
+
+ align:start position:0%
+did is that is he
+separated he first randomized at two
+
+ align:start position:0%
+separated he first randomized at two
+ 
+
+ align:start position:0%
+separated he first randomized at two
+levels you randomize at the level of the
+
+ align:start position:0%
+levels you randomize at the level of the
+ 
+
+ align:start position:0%
+levels you randomize at the level of the
+village and then you randomize at the
+
+ align:start position:0%
+village and then you randomize at the
+ 
+
+ align:start position:0%
+village and then you randomize at the
+individual level within the village
+
+ align:start position:0%
+individual level within the village
+ 
+
+ align:start position:0%
+individual level within the village
+so and the village is basically think of
+
+ align:start position:0%
+so and the village is basically think of
+ 
+
+ align:start position:0%
+so and the village is basically think of
+a village as a basically a school
+
+ align:start position:0%
+a village as a basically a school
+ 
+
+ align:start position:0%
+a village as a basically a school
+markets
+
+ align:start position:0%
+markets
+ 
+
+ align:start position:0%
+markets
+extended religion of to cover the whole
+
+ align:start position:0%
+extended religion of to cover the whole
+ 
+
+ align:start position:0%
+extended religion of to cover the whole
+school Market
+
+ align:start position:0%
+school Market
+ 
+
+ align:start position:0%
+school Market
+so you have random you have the control
+
+ align:start position:0%
+so you have random you have the control
+ 
+
+ align:start position:0%
+so you have random you have the control
+Villages and you have your treatment
+
+ align:start position:0%
+Villages and you have your treatment
+ 
+
+ align:start position:0%
+Villages and you have your treatment
+villages
+
+ align:start position:0%
+villages
+ 
+
+ align:start position:0%
+villages
+and then the treatment villagers you
+
+ align:start position:0%
+and then the treatment villagers you
+ 
+
+ align:start position:0%
+and then the treatment villagers you
+further have the kids who were in public
+
+ align:start position:0%
+further have the kids who were in public
+ 
+
+ align:start position:0%
+further have the kids who were in public
+school were in principle eligible they
+
+ align:start position:0%
+school were in principle eligible they
+ 
+
+ align:start position:0%
+school were in principle eligible they
+are to apply there was a lottery and
+
+ align:start position:0%
+are to apply there was a lottery and
+ 
+
+ align:start position:0%
+are to apply there was a lottery and
+some of them got it and some of them
+
+ align:start position:0%
+some of them got it and some of them
+ 
+
+ align:start position:0%
+some of them got it and some of them
+didn't get it
+
+ align:start position:0%
+didn't get it
+ 
+
+ align:start position:0%
+didn't get it
+so now we have randomization at two
+
+ align:start position:0%
+so now we have randomization at two
+ 
+
+ align:start position:0%
+so now we have randomization at two
+levels at the level of the market and at
+
+ align:start position:0%
+levels at the level of the market and at
+ 
+
+ align:start position:0%
+levels at the level of the market and at
+the level of the individual so if we
+
+ align:start position:0%
+the level of the individual so if we
+ 
+
+ align:start position:0%
+the level of the individual so if we
+want to know the impact of going to
+
+ align:start position:0%
+want to know the impact of going to
+ 
+
+ align:start position:0%
+want to know the impact of going to
+private school
+
+ align:start position:0%
+private school
+ 
+
+ align:start position:0%
+private school
+in an environment where there are some
+
+ align:start position:0%
+in an environment where there are some
+ 
+
+ align:start position:0%
+in an environment where there are some
+private schools and some vouchers around
+
+ align:start position:0%
+private schools and some vouchers around
+ 
+
+ align:start position:0%
+private schools and some vouchers around
+we can compare these two groups
+
+ align:start position:0%
+we can compare these two groups
+ 
+
+ align:start position:0%
+we can compare these two groups
+if we are interested in the impact of
+
+ align:start position:0%
+if we are interested in the impact of
+ 
+
+ align:start position:0%
+if we are interested in the impact of
+this voucher program on the kids left
+
+ align:start position:0%
+this voucher program on the kids left
+ 
+
+ align:start position:0%
+this voucher program on the kids left
+behind
+
+ align:start position:0%
+behind
+ 
+
+ align:start position:0%
+behind
+who were interested in also doing it we
+
+ align:start position:0%
+who were interested in also doing it we
+ 
+
+ align:start position:0%
+who were interested in also doing it we
+can compare this group to this entire
+
+ align:start position:0%
+can compare this group to this entire
+ 
+
+ align:start position:0%
+can compare this group to this entire
+control group
+
+ align:start position:0%
+control group
+ 
+
+ align:start position:0%
+control group
+so you know this group they're not
+
+ align:start position:0%
+so you know this group they're not
+ 
+
+ align:start position:0%
+so you know this group they're not
+awarded basically the control to the
+
+ align:start position:0%
+awarded basically the control to the
+ 
+
+ align:start position:0%
+awarded basically the control to the
+super control
+
+ align:start position:0%
+super control
+ 
+
+ align:start position:0%
+super control
+if we are interested in the impact on
+
+ align:start position:0%
+if we are interested in the impact on
+ 
+
+ align:start position:0%
+if we are interested in the impact on
+the private school kids who never wanted
+
+ align:start position:0%
+the private school kids who never wanted
+ 
+
+ align:start position:0%
+the private school kids who never wanted
+this in the first place we can compare
+
+ align:start position:0%
+this in the first place we can compare
+ 
+
+ align:start position:0%
+this in the first place we can compare
+them to their counterparts in other in
+
+ align:start position:0%
+them to their counterparts in other in
+ 
+
+ align:start position:0%
+them to their counterparts in other in
+in the control Villages and finally for
+
+ align:start position:0%
+in the control Villages and finally for
+ 
+
+ align:start position:0%
+in the control Villages and finally for
+the public school kids who were not
+
+ align:start position:0%
+the public school kids who were not
+ 
+
+ align:start position:0%
+the public school kids who were not
+interested in the program we can we can
+
+ align:start position:0%
+interested in the program we can we can
+ 
+
+ align:start position:0%
+interested in the program we can we can
+compare them here
+
+ align:start position:0%
+compare them here
+ 
+
+ align:start position:0%
+compare them here
+so that's a design this kind of two-step
+
+ align:start position:0%
+so that's a design this kind of two-step
+ 
+
+ align:start position:0%
+so that's a design this kind of two-step
+randomization to look at equilibrium is
+
+ align:start position:0%
+randomization to look at equilibrium is
+ 
+
+ align:start position:0%
+randomization to look at equilibrium is
+a design that I've also used to uh in in
+
+ align:start position:0%
+a design that I've also used to uh in in
+ 
+
+ align:start position:0%
+a design that I've also used to uh in in
+France to look at the spillover effect
+
+ align:start position:0%
+France to look at the spillover effect
+ 
+
+ align:start position:0%
+France to look at the spillover effect
+of a labor of active labor market policy
+
+ align:start position:0%
+of a labor of active labor market policy
+ 
+
+ align:start position:0%
+of a labor of active labor market policy
+program people are also look to to look
+
+ align:start position:0%
+program people are also look to to look
+ 
+
+ align:start position:0%
+program people are also look to to look
+at effects on you know allowing some
+
+ align:start position:0%
+at effects on you know allowing some
+ 
+
+ align:start position:0%
+at effects on you know allowing some
+people to migrate on other people Etc
+
+ align:start position:0%
+people to migrate on other people Etc
+ 
+
+ align:start position:0%
+people to migrate on other people Etc
+but that's one of the first people that
+
+ align:start position:0%
+but that's one of the first people that
+ 
+
+ align:start position:0%
+but that's one of the first people that
+did it yeah
+
+ align:start position:0%
+did it yeah
+ 
+
+ align:start position:0%
+did it yeah
+if you were to offer
+
+ align:start position:0%
+if you were to offer
+ 
+
+ align:start position:0%
+if you were to offer
+um the launcher later on to the control
+
+ align:start position:0%
+um the launcher later on to the control
+ 
+
+ align:start position:0%
+um the launcher later on to the control
+Court did you do some matching between
+
+ align:start position:0%
+Court did you do some matching between
+ 
+
+ align:start position:0%
+Court did you do some matching between
+the people who later on decided to apply
+
+ align:start position:0%
+the people who later on decided to apply
+ 
+
+ align:start position:0%
+the people who later on decided to apply
+or would you be concerned with something
+
+ align:start position:0%
+or would you be concerned with something
+ 
+
+ align:start position:0%
+or would you be concerned with something
+in that time spent change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is the what's the design that
+
+ align:start position:0%
+so what is the what's the design that
+ 
+
+ align:start position:0%
+so what is the what's the design that
+you're proposing instead
+
+ align:start position:0%
+you're proposing instead
+ 
+
+ align:start position:0%
+you're proposing instead
+so I think I would just be concerned
+
+ align:start position:0%
+so I think I would just be concerned
+ 
+
+ align:start position:0%
+so I think I would just be concerned
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+the non-africans
+
+ align:start position:0%
+the non-africans
+ 
+
+ align:start position:0%
+the non-africans
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh if we were there to
+
+ align:start position:0%
+uh if we were there to
+ 
+
+ align:start position:0%
+uh if we were there to
+considerably
+
+ align:start position:0%
+considerably
+ 
+
+ align:start position:0%
+considerably
+comparing the treatment you have right
+
+ align:start position:0%
+comparing the treatment you have right
+ 
+
+ align:start position:0%
+comparing the treatment you have right
+now to that controller if you layered
+
+ align:start position:0%
+now to that controller if you layered
+ 
+
+ align:start position:0%
+now to that controller if you layered
+give the voucher to the controller and
+
+ align:start position:0%
+give the voucher to the controller and
+ 
+
+ align:start position:0%
+give the voucher to the controller and
+then you just use the individuals who
+
+ align:start position:0%
+then you just use the individuals who
+ 
+
+ align:start position:0%
+then you just use the individuals who
+chose to apply yeah so you would be
+
+ align:start position:0%
+chose to apply yeah so you would be
+ 
+
+ align:start position:0%
+chose to apply yeah so you would be
+worried that the people who choose to
+
+ align:start position:0%
+worried that the people who choose to
+ 
+
+ align:start position:0%
+worried that the people who choose to
+apply the people who didn't are
+
+ align:start position:0%
+apply the people who didn't are
+ 
+
+ align:start position:0%
+apply the people who didn't are
+different in a way that are difficult to
+
+ align:start position:0%
+different in a way that are difficult to
+ 
+
+ align:start position:0%
+different in a way that are difficult to
+to control so a paper we didn't have
+
+ align:start position:0%
+to control so a paper we didn't have
+ 
+
+ align:start position:0%
+to control so a paper we didn't have
+time to cover but I sometimes cover is
+
+ align:start position:0%
+time to cover but I sometimes cover is
+ 
+
+ align:start position:0%
+time to cover but I sometimes cover is
+the the deworming paper
+
+ align:start position:0%
+the the deworming paper
+ 
+
+ align:start position:0%
+the the deworming paper
+where they were interested they tried to
+
+ align:start position:0%
+where they were interested they tried to
+ 
+
+ align:start position:0%
+where they were interested they tried to
+estimate externalities
+
+ align:start position:0%
+estimate externalities
+ 
+
+ align:start position:0%
+estimate externalities
+without having such a design so you try
+
+ align:start position:0%
+without having such a design so you try
+ 
+
+ align:start position:0%
+without having such a design so you try
+to construct a group of kids that is
+
+ align:start position:0%
+to construct a group of kids that is
+ 
+
+ align:start position:0%
+to construct a group of kids that is
+comparable of a situation where they are
+
+ align:start position:0%
+comparable of a situation where they are
+ 
+
+ align:start position:0%
+comparable of a situation where they are
+they are you know it's not perfect you
+
+ align:start position:0%
+they are you know it's not perfect you
+ 
+
+ align:start position:0%
+they are you know it's not perfect you
+don't have really perfectly comparable
+
+ align:start position:0%
+don't have really perfectly comparable
+ 
+
+ align:start position:0%
+don't have really perfectly comparable
+kids so this design avoids that you
+
+ align:start position:0%
+kids so this design avoids that you
+ 
+
+ align:start position:0%
+kids so this design avoids that you
+don't have to worry about can I make the
+
+ align:start position:0%
+don't have to worry about can I make the
+ 
+
+ align:start position:0%
+don't have to worry about can I make the
+non-applicant similar exposed
+
+ align:start position:0%
+non-applicant similar exposed
+ 
+
+ align:start position:0%
+non-applicant similar exposed
+uh you you basically in your design you
+
+ align:start position:0%
+uh you you basically in your design you
+ 
+
+ align:start position:0%
+uh you you basically in your design you
+would hope that the non-applicant two
+
+ align:start position:0%
+would hope that the non-applicant two
+ 
+
+ align:start position:0%
+would hope that the non-applicant two
+years later are comparable to the
+
+ align:start position:0%
+years later are comparable to the
+ 
+
+ align:start position:0%
+years later are comparable to the
+non-applicant you got you know that this
+
+ align:start position:0%
+non-applicant you got you know that this
+ 
+
+ align:start position:0%
+non-applicant you got you know that this
+one's two years later are comparable to
+
+ align:start position:0%
+one's two years later are comparable to
+ 
+
+ align:start position:0%
+one's two years later are comparable to
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+and then you would look at the
+
+ align:start position:0%
+and then you would look at the
+ 
+
+ align:start position:0%
+and then you would look at the
+externality on them but it's not clear
+
+ align:start position:0%
+externality on them but it's not clear
+ 
+
+ align:start position:0%
+externality on them but it's not clear
+that they are you know it's not clear
+
+ align:start position:0%
+that they are you know it's not clear
+ 
+
+ align:start position:0%
+that they are you know it's not clear
+that you can rely on that so that's why
+
+ align:start position:0%
+that you can rely on that so that's why
+ 
+
+ align:start position:0%
+that you can rely on that so that's why
+that those designs are because it's two
+
+ align:start position:0%
+that those designs are because it's two
+ 
+
+ align:start position:0%
+that those designs are because it's two
+years later who knows
+
+ align:start position:0%
+years later who knows
+ 
+
+ align:start position:0%
+years later who knows
+so that's why it was designs are better
+
+ align:start position:0%
+so that's why it was designs are better
+ 
+
+ align:start position:0%
+so that's why it was designs are better
+to measure your x19 so that was my kind
+
+ align:start position:0%
+to measure your x19 so that was my kind
+ 
+
+ align:start position:0%
+to measure your x19 so that was my kind
+of advertising uh pause
+
+ align:start position:0%
+of advertising uh pause
+ 
+
+ align:start position:0%
+of advertising uh pause
+it's finished it's a great design
+
+ align:start position:0%
+it's finished it's a great design
+ 
+
+ align:start position:0%
+it's finished it's a great design
+but it didn't come to be so useful in
+
+ align:start position:0%
+but it didn't come to be so useful in
+ 
+
+ align:start position:0%
+but it didn't come to be so useful in
+this particular instance because uh
+
+ align:start position:0%
+this particular instance because uh
+ 
+
+ align:start position:0%
+this particular instance because uh
+in fact the impact on the people so here
+
+ align:start position:0%
+in fact the impact on the people so here
+ 
+
+ align:start position:0%
+in fact the impact on the people so here
+now we are comparing
+
+ align:start position:0%
+now we are comparing
+ 
+
+ align:start position:0%
+now we are comparing
+the treated the people offer the voucher
+
+ align:start position:0%
+the treated the people offer the voucher
+ 
+
+ align:start position:0%
+the treated the people offer the voucher
+to people who are not a further voucher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and there is not much of an impact if
+
+ align:start position:0%
+um and there is not much of an impact if
+ 
+
+ align:start position:0%
+um and there is not much of an impact if
+anything so this is in in Andhra Pradesh
+
+ align:start position:0%
+anything so this is in in Andhra Pradesh
+ 
+
+ align:start position:0%
+anything so this is in in Andhra Pradesh
+the the medium of instruction is Telugu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Public School do not teach English
+
+ align:start position:0%
+Public School do not teach English
+ 
+
+ align:start position:0%
+Public School do not teach English
+and or and they do not teach Hindi
+
+ align:start position:0%
+and or and they do not teach Hindi
+ 
+
+ align:start position:0%
+and or and they do not teach Hindi
+uh or they might teach a tiny bit of
+
+ align:start position:0%
+uh or they might teach a tiny bit of
+ 
+
+ align:start position:0%
+uh or they might teach a tiny bit of
+English but very little
+
+ align:start position:0%
+English but very little
+ 
+
+ align:start position:0%
+English but very little
+so what do we find by year two
+
+ align:start position:0%
+so what do we find by year two
+ 
+
+ align:start position:0%
+so what do we find by year two
+of the program the kids offer a voucher
+
+ align:start position:0%
+of the program the kids offer a voucher
+ 
+
+ align:start position:0%
+of the program the kids offer a voucher
+actually do Works in uh in Telugu
+
+ align:start position:0%
+actually do Works in uh in Telugu
+ 
+
+ align:start position:0%
+actually do Works in uh in Telugu
+although that's not significant but then
+
+ align:start position:0%
+although that's not significant but then
+ 
+
+ align:start position:0%
+although that's not significant but then
+I don't know don't do any better
+
+ align:start position:0%
+I don't know don't do any better
+ 
+
+ align:start position:0%
+I don't know don't do any better
+and standard such that we can rule out
+
+ align:start position:0%
+and standard such that we can rule out
+ 
+
+ align:start position:0%
+and standard such that we can rule out
+even modest positive effect of this
+
+ align:start position:0%
+even modest positive effect of this
+ 
+
+ align:start position:0%
+even modest positive effect of this
+intervention on them
+
+ align:start position:0%
+intervention on them
+ 
+
+ align:start position:0%
+intervention on them
+similarly on math
+
+ align:start position:0%
+similarly on math
+ 
+
+ align:start position:0%
+similarly on math
+they do much better in English
+
+ align:start position:0%
+they do much better in English
+ 
+
+ align:start position:0%
+they do much better in English
+and overall the big fat zero
+
+ align:start position:0%
+and overall the big fat zero
+ 
+
+ align:start position:0%
+and overall the big fat zero
+you can now you know we saw IV last time
+
+ align:start position:0%
+you can now you know we saw IV last time
+ 
+
+ align:start position:0%
+you can now you know we saw IV last time
+so if you if you want you can instrument
+
+ align:start position:0%
+so if you if you want you can instrument
+ 
+
+ align:start position:0%
+so if you if you want you can instrument
+for actually going to school with
+
+ align:start position:0%
+for actually going to school with
+ 
+
+ align:start position:0%
+for actually going to school with
+receiving a voucher
+
+ align:start position:0%
+receiving a voucher
+ 
+
+ align:start position:0%
+receiving a voucher
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I think this is perfectly decent
+
+ align:start position:0%
+I think this is perfectly decent
+ 
+
+ align:start position:0%
+I think this is perfectly decent
+instrument I would not be too worried
+
+ align:start position:0%
+instrument I would not be too worried
+ 
+
+ align:start position:0%
+instrument I would not be too worried
+about the exclusional attraction but of
+
+ align:start position:0%
+about the exclusional attraction but of
+ 
+
+ align:start position:0%
+about the exclusional attraction but of
+course it's the same thing it's just
+
+ align:start position:0%
+course it's the same thing it's just
+ 
+
+ align:start position:0%
+course it's the same thing it's just
+like a just cosmetic now four years
+
+ align:start position:0%
+like a just cosmetic now four years
+ 
+
+ align:start position:0%
+like a just cosmetic now four years
+later something negative insignificant
+
+ align:start position:0%
+later something negative insignificant
+ 
+
+ align:start position:0%
+later something negative insignificant
+impact on Telugu and on math positive in
+
+ align:start position:0%
+impact on Telugu and on math positive in
+ 
+
+ align:start position:0%
+impact on Telugu and on math positive in
+English now he went and collected a bit
+
+ align:start position:0%
+English now he went and collected a bit
+ 
+
+ align:start position:0%
+English now he went and collected a bit
+more data on other things or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think that's environmental and science
+
+ align:start position:0%
+I think that's environmental and science
+ 
+
+ align:start position:0%
+I think that's environmental and science
+there is some positive impact
+
+ align:start position:0%
+there is some positive impact
+ 
+
+ align:start position:0%
+there is some positive impact
+insignificant impact there combine a
+
+ align:start position:0%
+insignificant impact there combine a
+ 
+
+ align:start position:0%
+insignificant impact there combine a
+cost-test explaining Hindi and then he
+
+ align:start position:0%
+cost-test explaining Hindi and then he
+ 
+
+ align:start position:0%
+cost-test explaining Hindi and then he
+went and collected Hindi which is not
+
+ align:start position:0%
+went and collected Hindi which is not
+ 
+
+ align:start position:0%
+went and collected Hindi which is not
+taught in a public school and when you
+
+ align:start position:0%
+taught in a public school and when you
+ 
+
+ align:start position:0%
+taught in a public school and when you
+add the Hindi you find a positive effect
+
+ align:start position:0%
+add the Hindi you find a positive effect
+ 
+
+ align:start position:0%
+add the Hindi you find a positive effect
+on the private school
+
+ align:start position:0%
+on the private school
+ 
+
+ align:start position:0%
+on the private school
+not to say he really wanted to have a
+
+ align:start position:0%
+not to say he really wanted to have a
+ 
+
+ align:start position:0%
+not to say he really wanted to have a
+positive headline number but maybe
+
+ align:start position:0%
+positive headline number but maybe
+ 
+
+ align:start position:0%
+positive headline number but maybe
+because this is like this is this is an
+
+ align:start position:0%
+because this is like this is this is an
+ 
+
+ align:start position:0%
+because this is like this is this is an
+effort
+
+ align:start position:0%
+effort
+ 
+
+ align:start position:0%
+effort
+but this is very interesting because
+
+ align:start position:0%
+but this is very interesting because
+ 
+
+ align:start position:0%
+but this is very interesting because
+what we have is that the private school
+
+ align:start position:0%
+what we have is that the private school
+ 
+
+ align:start position:0%
+what we have is that the private school
+are not
+
+ align:start position:0%
+are not
+ 
+
+ align:start position:0%
+are not
+teaching better at what you know they
+
+ align:start position:0%
+teaching better at what you know they
+ 
+
+ align:start position:0%
+teaching better at what you know they
+teach they also teach things that but
+
+ align:start position:0%
+teach they also teach things that but
+ 
+
+ align:start position:0%
+teach they also teach things that but
+they put more effort in different things
+
+ align:start position:0%
+they put more effort in different things
+ 
+
+ align:start position:0%
+they put more effort in different things
+so it's not that they are and presumably
+
+ align:start position:0%
+so it's not that they are and presumably
+ 
+
+ align:start position:0%
+so it's not that they are and presumably
+they are doing that because there is
+
+ align:start position:0%
+they are doing that because there is
+ 
+
+ align:start position:0%
+they are doing that because there is
+Parental demand to um to do it
+
+ align:start position:0%
+Parental demand to um to do it
+ 
+
+ align:start position:0%
+Parental demand to um to do it
+and so that kind of that kind of uh uh
+
+ align:start position:0%
+and so that kind of that kind of uh uh
+ 
+
+ align:start position:0%
+and so that kind of that kind of uh uh
+can is informative for us on what our
+
+ align:start position:0%
+can is informative for us on what our
+ 
+
+ align:start position:0%
+can is informative for us on what our
+parents demanding
+
+ align:start position:0%
+parents demanding
+ 
+
+ align:start position:0%
+parents demanding
+and what balance demanding is not good
+
+ align:start position:0%
+and what balance demanding is not good
+ 
+
+ align:start position:0%
+and what balance demanding is not good
+performance on mathematics and to look
+
+ align:start position:0%
+performance on mathematics and to look
+ 
+
+ align:start position:0%
+performance on mathematics and to look
+what parents are demanding is English
+
+ align:start position:0%
+what parents are demanding is English
+ 
+
+ align:start position:0%
+what parents are demanding is English
+and Hindi
+
+ align:start position:0%
+and Hindi
+ 
+
+ align:start position:0%
+and Hindi
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+there is surprisingly there is no so you
+
+ align:start position:0%
+there is surprisingly there is no so you
+ 
+
+ align:start position:0%
+there is surprisingly there is no so you
+know you can do all your fancy contrast
+
+ align:start position:0%
+know you can do all your fancy contrast
+ 
+
+ align:start position:0%
+know you can do all your fancy contrast
+of spit over it would have been nice
+
+ align:start position:0%
+of spit over it would have been nice
+ 
+
+ align:start position:0%
+of spit over it would have been nice
+since the impact had been positive of
+
+ align:start position:0%
+since the impact had been positive of
+ 
+
+ align:start position:0%
+since the impact had been positive of
+course there is no spillover of
+
+ align:start position:0%
+course there is no spillover of
+ 
+
+ align:start position:0%
+course there is no spillover of
+something that doesn't have a direct
+
+ align:start position:0%
+something that doesn't have a direct
+ 
+
+ align:start position:0%
+something that doesn't have a direct
+impact but it is what it is
+
+ align:start position:0%
+impact but it is what it is
+ 
+
+ align:start position:0%
+impact but it is what it is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the general rule out even large schools
+
+ align:start position:0%
+the general rule out even large schools
+ 
+
+ align:start position:0%
+the general rule out even large schools
+yeah at the speed of our because the
+
+ align:start position:0%
+yeah at the speed of our because the
+ 
+
+ align:start position:0%
+yeah at the speed of our because the
+main effects are are null
+
+ align:start position:0%
+main effects are are null
+ 
+
+ align:start position:0%
+main effects are are null
+and the speed of our become because the
+
+ align:start position:0%
+and the speed of our become because the
+ 
+
+ align:start position:0%
+and the speed of our become because the
+main effects are are zero the speed over
+
+ align:start position:0%
+main effects are are zero the speed over
+ 
+
+ align:start position:0%
+main effects are are zero the speed over
+become
+
+ align:start position:0%
+become
+ 
+
+ align:start position:0%
+become
+we're harmless people become
+
+ align:start position:0%
+we're harmless people become
+ 
+
+ align:start position:0%
+we're harmless people become
+a sort of uninteresting and and and
+
+ align:start position:0%
+a sort of uninteresting and and and
+ 
+
+ align:start position:0%
+a sort of uninteresting and and and
+uninformative
+
+ align:start position:0%
+uninformative
+ 
+
+ align:start position:0%
+uninformative
+I don't know if you would call them
+
+ align:start position:0%
+I don't know if you would call them
+ 
+
+ align:start position:0%
+I don't know if you would call them
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+this is uh 0.06 so that's you can rule
+
+ align:start position:0%
+this is uh 0.06 so that's you can rule
+ 
+
+ align:start position:0%
+this is uh 0.06 so that's you can rule
+out point 12.
+
+ align:start position:0%
+out point 12.
+ 
+
+ align:start position:0%
+out point 12.
+12 standard deviation if it's like you
+
+ align:start position:0%
+12 standard deviation if it's like you
+ 
+
+ align:start position:0%
+12 standard deviation if it's like you
+can rule out at 95 percent there's
+
+ align:start position:0%
+can rule out at 95 percent there's
+ 
+
+ align:start position:0%
+can rule out at 95 percent there's
+really nothing to write home about
+
+ align:start position:0%
+really nothing to write home about
+ 
+
+ align:start position:0%
+really nothing to write home about
+and negatively again you can rule out
+
+ align:start position:0%
+and negatively again you can rule out
+ 
+
+ align:start position:0%
+and negatively again you can rule out
+minus 0.12
+
+ align:start position:0%
+minus 0.12
+ 
+
+ align:start position:0%
+minus 0.12
+you know if it was a mean if it was a
+
+ align:start position:0%
+you know if it was a mean if it was a
+ 
+
+ align:start position:0%
+you know if it was a mean if it was a
+mean at Point 12 you could say well
+
+ align:start position:0%
+mean at Point 12 you could say well
+ 
+
+ align:start position:0%
+mean at Point 12 you could say well
+there is something there it's not a huge
+
+ align:start position:0%
+there is something there it's not a huge
+ 
+
+ align:start position:0%
+there is something there it's not a huge
+effect that it is an effect but if it's
+
+ align:start position:0%
+effect that it is an effect but if it's
+ 
+
+ align:start position:0%
+effect that it is an effect but if it's
+a 95 percent in confidence interval
+
+ align:start position:0%
+a 95 percent in confidence interval
+ 
+
+ align:start position:0%
+a 95 percent in confidence interval
+that's at Point 12. I wouldn't uh so I
+
+ align:start position:0%
+that's at Point 12. I wouldn't uh so I
+ 
+
+ align:start position:0%
+that's at Point 12. I wouldn't uh so I
+don't seem to stand on there are that
+
+ align:start position:0%
+don't seem to stand on there are that
+ 
+
+ align:start position:0%
+don't seem to stand on there are that
+huge it's just that it's not
+
+ align:start position:0%
+huge it's just that it's not
+ 
+
+ align:start position:0%
+huge it's just that it's not
+there's no direct effect so it would be
+
+ align:start position:0%
+there's no direct effect so it would be
+ 
+
+ align:start position:0%
+there's no direct effect so it would be
+surprising if they were spillover effect
+
+ align:start position:0%
+surprising if they were spillover effect
+ 
+
+ align:start position:0%
+surprising if they were spillover effect
+that's but you know that's bad luck it's
+
+ align:start position:0%
+that's but you know that's bad luck it's
+ 
+
+ align:start position:0%
+that's but you know that's bad luck it's
+I mean it's a bad look it's not bad luck
+
+ align:start position:0%
+I mean it's a bad look it's not bad luck
+ 
+
+ align:start position:0%
+I mean it's a bad look it's not bad luck
+it's interesting anyways but uh the
+
+ align:start position:0%
+it's interesting anyways but uh the
+ 
+
+ align:start position:0%
+it's interesting anyways but uh the
+results would have been more interesting
+
+ align:start position:0%
+results would have been more interesting
+ 
+
+ align:start position:0%
+results would have been more interesting
+in the setup where you have large direct
+
+ align:start position:0%
+in the setup where you have large direct
+ 
+
+ align:start position:0%
+in the setup where you have large direct
+effect which are undone by spillover
+
+ align:start position:0%
+effect which are undone by spillover
+ 
+
+ align:start position:0%
+effect which are undone by spillover
+in our paper on liberal Market policy in
+
+ align:start position:0%
+in our paper on liberal Market policy in
+ 
+
+ align:start position:0%
+in our paper on liberal Market policy in
+France that's what we have we have large
+
+ align:start position:0%
+France that's what we have we have large
+ 
+
+ align:start position:0%
+France that's what we have we have large
+labor of effect when we compare treated
+
+ align:start position:0%
+labor of effect when we compare treated
+ 
+
+ align:start position:0%
+labor of effect when we compare treated
+and control in the same labor market but
+
+ align:start position:0%
+and control in the same labor market but
+ 
+
+ align:start position:0%
+and control in the same labor market but
+it turns out they are all
+
+ align:start position:0%
+it turns out they are all
+ 
+
+ align:start position:0%
+it turns out they are all
+of a distribution within the group
+
+ align:start position:0%
+of a distribution within the group
+ 
+
+ align:start position:0%
+of a distribution within the group
+there is no effect compared to the
+
+ align:start position:0%
+there is no effect compared to the
+ 
+
+ align:start position:0%
+there is no effect compared to the
+control group it's uh
+
+ align:start position:0%
+control group it's uh
+ 
+
+ align:start position:0%
+control group it's uh
+the French French saying for that is a
+
+ align:start position:0%
+the French French saying for that is a
+ 
+
+ align:start position:0%
+the French French saying for that is a
+taking the clothes out of Peter's back
+
+ align:start position:0%
+taking the clothes out of Peter's back
+ 
+
+ align:start position:0%
+taking the clothes out of Peter's back
+to put them on pulls back
+
+ align:start position:0%
+to put them on pulls back
+ 
+
+ align:start position:0%
+to put them on pulls back
+so when
+
+ align:start position:0%
+so when
+ 
+
+ align:start position:0%
+so when
+so it's substantively more more fun but
+
+ align:start position:0%
+so it's substantively more more fun but
+ 
+
+ align:start position:0%
+so it's substantively more more fun but
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+but going back to the result so it's not
+
+ align:start position:0%
+but going back to the result so it's not
+ 
+
+ align:start position:0%
+but going back to the result so it's not
+that the the incentives don't work and
+
+ align:start position:0%
+that the the incentives don't work and
+ 
+
+ align:start position:0%
+that the the incentives don't work and
+that people are not responsive to the
+
+ align:start position:0%
+that people are not responsive to the
+ 
+
+ align:start position:0%
+that people are not responsive to the
+incentives is that they are is that the
+
+ align:start position:0%
+incentives is that they are is that the
+ 
+
+ align:start position:0%
+incentives is that they are is that the
+incentive themselves
+
+ align:start position:0%
+incentive themselves
+ 
+
+ align:start position:0%
+incentive themselves
+that that is the parental preferences
+
+ align:start position:0%
+that that is the parental preferences
+ 
+
+ align:start position:0%
+that that is the parental preferences
+are not going in the direction of
+
+ align:start position:0%
+are not going in the direction of
+ 
+
+ align:start position:0%
+are not going in the direction of
+are not going to uh I'm not targeting
+
+ align:start position:0%
+are not going to uh I'm not targeting
+ 
+
+ align:start position:0%
+are not going to uh I'm not targeting
+the fundamental learning
+
+ align:start position:0%
+the fundamental learning
+ 
+
+ align:start position:0%
+the fundamental learning
+and that's that's a
+
+ align:start position:0%
+and that's that's a
+ 
+
+ align:start position:0%
+and that's that's a
+com that's consistent very much to what
+
+ align:start position:0%
+com that's consistent very much to what
+ 
+
+ align:start position:0%
+com that's consistent very much to what
+we saw in Kenya where people don't see
+
+ align:start position:0%
+we saw in Kenya where people don't see
+ 
+
+ align:start position:0%
+we saw in Kenya where people don't see
+much value in primary education
+
+ align:start position:0%
+much value in primary education
+ 
+
+ align:start position:0%
+much value in primary education
+whatsoever they see value in secondary
+
+ align:start position:0%
+whatsoever they see value in secondary
+ 
+
+ align:start position:0%
+whatsoever they see value in secondary
+education to the extent that it's a
+
+ align:start position:0%
+education to the extent that it's a
+ 
+
+ align:start position:0%
+education to the extent that it's a
+ticket into tertiary education to the ex
+
+ align:start position:0%
+ticket into tertiary education to the ex
+ 
+
+ align:start position:0%
+ticket into tertiary education to the ex
+which is itself a ticket into into the
+
+ align:start position:0%
+which is itself a ticket into into the
+ 
+
+ align:start position:0%
+which is itself a ticket into into the
+rent seeking paying job
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+feels like emissions rewarded more
+
+ align:start position:0%
+feels like emissions rewarded more
+ 
+
+ align:start position:0%
+feels like emissions rewarded more
+marketing area that matters at least for
+
+ align:start position:0%
+marketing area that matters at least for
+ 
+
+ align:start position:0%
+marketing area that matters at least for
+like Sage yeah so that's not irrational
+
+ align:start position:0%
+like Sage yeah so that's not irrational
+ 
+
+ align:start position:0%
+like Sage yeah so that's not irrational
+I don't I think it's totally irrational
+
+ align:start position:0%
+I don't I think it's totally irrational
+ 
+
+ align:start position:0%
+I don't I think it's totally irrational
+even so English for example makes sense
+
+ align:start position:0%
+even so English for example makes sense
+ 
+
+ align:start position:0%
+even so English for example makes sense
+to have a little bit of English and even
+
+ align:start position:0%
+to have a little bit of English and even
+ 
+
+ align:start position:0%
+to have a little bit of English and even
+if you didn't have English if they cared
+
+ align:start position:0%
+if you didn't have English if they cared
+ 
+
+ align:start position:0%
+if you didn't have English if they cared
+about is uh you know doing great in uh
+
+ align:start position:0%
+about is uh you know doing great in uh
+ 
+
+ align:start position:0%
+about is uh you know doing great in uh
+is uh is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort of and we'll see in a moment it's
+
+ align:start position:0%
+sort of and we'll see in a moment it's
+ 
+
+ align:start position:0%
+sort of and we'll see in a moment it's
+doing at grade level you know being
+
+ align:start position:0%
+doing at grade level you know being
+ 
+
+ align:start position:0%
+doing at grade level you know being
+doing being able to take exams and not
+
+ align:start position:0%
+doing being able to take exams and not
+ 
+
+ align:start position:0%
+doing being able to take exams and not
+like the learning what parents seem to
+
+ align:start position:0%
+like the learning what parents seem to
+ 
+
+ align:start position:0%
+like the learning what parents seem to
+care about is what the what's going to
+
+ align:start position:0%
+care about is what the what's going to
+ 
+
+ align:start position:0%
+care about is what the what's going to
+be useful down the line so a little bit
+
+ align:start position:0%
+be useful down the line so a little bit
+ 
+
+ align:start position:0%
+be useful down the line so a little bit
+of English testing is useful you know we
+
+ align:start position:0%
+of English testing is useful you know we
+ 
+
+ align:start position:0%
+of English testing is useful you know we
+just saw that the math is not that is
+
+ align:start position:0%
+just saw that the math is not that is
+ 
+
+ align:start position:0%
+just saw that the math is not that is
+taught in school is not of any use
+
+ align:start position:0%
+taught in school is not of any use
+ 
+
+ align:start position:0%
+taught in school is not of any use
+anyway so why would they value it so I'm
+
+ align:start position:0%
+anyway so why would they value it so I'm
+ 
+
+ align:start position:0%
+anyway so why would they value it so I'm
+not saying it's irrational but that's
+
+ align:start position:0%
+not saying it's irrational but that's
+ 
+
+ align:start position:0%
+not saying it's irrational but that's
+the the parents are are interested not
+
+ align:start position:0%
+the the parents are are interested not
+ 
+
+ align:start position:0%
+the the parents are are interested not
+in fundamental learning but in what's
+
+ align:start position:0%
+in fundamental learning but in what's
+ 
+
+ align:start position:0%
+in fundamental learning but in what's
+going to be helpful to the kids or to
+
+ align:start position:0%
+going to be helpful to the kids or to
+ 
+
+ align:start position:0%
+going to be helpful to the kids or to
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+so on the one hand there is English and
+
+ align:start position:0%
+so on the one hand there is English and
+ 
+
+ align:start position:0%
+so on the one hand there is English and
+on the other hand there is doing well as
+
+ align:start position:0%
+on the other hand there is doing well as
+ 
+
+ align:start position:0%
+on the other hand there is doing well as
+in passing exams
+
+ align:start position:0%
+in passing exams
+ 
+
+ align:start position:0%
+in passing exams
+and so there on what the parents are
+
+ align:start position:0%
+and so there on what the parents are
+ 
+
+ align:start position:0%
+and so there on what the parents are
+responding to is the structure of the
+
+ align:start position:0%
+responding to is the structure of the
+ 
+
+ align:start position:0%
+responding to is the structure of the
+school system and how it's uh how its uh
+
+ align:start position:0%
+school system and how it's uh how its uh
+ 
+
+ align:start position:0%
+school system and how it's uh how its uh
+organized which is that and that's not
+
+ align:start position:0%
+organized which is that and that's not
+ 
+
+ align:start position:0%
+organized which is that and that's not
+just in India but that's true in most
+
+ align:start position:0%
+just in India but that's true in most
+ 
+
+ align:start position:0%
+just in India but that's true in most
+developing countries in particular all
+
+ align:start position:0%
+developing countries in particular all
+ 
+
+ align:start position:0%
+developing countries in particular all
+the former colonies is a curriculum that
+
+ align:start position:0%
+the former colonies is a curriculum that
+ 
+
+ align:start position:0%
+the former colonies is a curriculum that
+is extraordinarily demanding a much more
+
+ align:start position:0%
+is extraordinarily demanding a much more
+ 
+
+ align:start position:0%
+is extraordinarily demanding a much more
+demanding than our Primary School
+
+ align:start position:0%
+demanding than our Primary School
+ 
+
+ align:start position:0%
+demanding than our Primary School
+curriculum here in the U.S that's kind
+
+ align:start position:0%
+curriculum here in the U.S that's kind
+ 
+
+ align:start position:0%
+curriculum here in the U.S that's kind
+of going back to your question of what's
+
+ align:start position:0%
+of going back to your question of what's
+ 
+
+ align:start position:0%
+of going back to your question of what's
+the difference so this is a snapshot of
+
+ align:start position:0%
+the difference so this is a snapshot of
+ 
+
+ align:start position:0%
+the difference so this is a snapshot of
+grade 4 curriculum in haryana
+
+ align:start position:0%
+grade 4 curriculum in haryana
+ 
+
+ align:start position:0%
+grade 4 curriculum in haryana
+so I hope that you guys are kind of uh
+
+ align:start position:0%
+so I hope that you guys are kind of uh
+ 
+
+ align:start position:0%
+so I hope that you guys are kind of uh
+good about your table of table of
+
+ align:start position:0%
+good about your table of table of
+ 
+
+ align:start position:0%
+good about your table of table of
+multiplication up to 15 because
+
+ align:start position:0%
+multiplication up to 15 because
+ 
+
+ align:start position:0%
+multiplication up to 15 because
+otherwise you cannot if you don't know
+
+ align:start position:0%
+otherwise you cannot if you don't know
+ 
+
+ align:start position:0%
+otherwise you cannot if you don't know
+him like this you cannot do uh you
+
+ align:start position:0%
+him like this you cannot do uh you
+ 
+
+ align:start position:0%
+him like this you cannot do uh you
+cannot pass your you are not at grade
+
+ align:start position:0%
+cannot pass your you are not at grade
+ 
+
+ align:start position:0%
+cannot pass your you are not at grade
+level in grade four in in haryana
+
+ align:start position:0%
+level in grade four in in haryana
+ 
+
+ align:start position:0%
+level in grade four in in haryana
+um so you know by in October they are
+
+ align:start position:0%
+um so you know by in October they are
+ 
+
+ align:start position:0%
+um so you know by in October they are
+recognizing shape by November they are
+
+ align:start position:0%
+recognizing shape by November they are
+ 
+
+ align:start position:0%
+recognizing shape by November they are
+measuring the the area I mean this is
+
+ align:start position:0%
+measuring the the area I mean this is
+ 
+
+ align:start position:0%
+measuring the the area I mean this is
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+a bit crazy
+
+ align:start position:0%
+a bit crazy
+ 
+
+ align:start position:0%
+a bit crazy
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and the that the problem you're finding
+
+ align:start position:0%
+and the that the problem you're finding
+ 
+
+ align:start position:0%
+and the that the problem you're finding
+in in a lot of former colonies and the
+
+ align:start position:0%
+in in a lot of former colonies and the
+ 
+
+ align:start position:0%
+in in a lot of former colonies and the
+reason is that the the school system was
+
+ align:start position:0%
+reason is that the the school system was
+ 
+
+ align:start position:0%
+reason is that the the school system was
+was created not for educating everyone
+
+ align:start position:0%
+was created not for educating everyone
+ 
+
+ align:start position:0%
+was created not for educating everyone
+to be able to learn
+
+ align:start position:0%
+to be able to learn
+ 
+
+ align:start position:0%
+to be able to learn
+basic you know to read and to write and
+
+ align:start position:0%
+basic you know to read and to write and
+ 
+
+ align:start position:0%
+basic you know to read and to write and
+operate in their life but to educate a
+
+ align:start position:0%
+operate in their life but to educate a
+ 
+
+ align:start position:0%
+operate in their life but to educate a
+minority to become clerks for the
+
+ align:start position:0%
+minority to become clerks for the
+ 
+
+ align:start position:0%
+minority to become clerks for the
+colonial powers and that's what the
+
+ align:start position:0%
+colonial powers and that's what the
+ 
+
+ align:start position:0%
+colonial powers and that's what the
+system was for one at Independence when
+
+ align:start position:0%
+system was for one at Independence when
+ 
+
+ align:start position:0%
+system was for one at Independence when
+it was opened to everyone and scaled up
+
+ align:start position:0%
+it was opened to everyone and scaled up
+ 
+
+ align:start position:0%
+it was opened to everyone and scaled up
+it was open without a change in the
+
+ align:start position:0%
+it was open without a change in the
+ 
+
+ align:start position:0%
+it was open without a change in the
+curriculum
+
+ align:start position:0%
+curriculum
+ 
+
+ align:start position:0%
+curriculum
+partly because it's very difficult to
+
+ align:start position:0%
+partly because it's very difficult to
+ 
+
+ align:start position:0%
+partly because it's very difficult to
+say that oh no we are going to go back
+
+ align:start position:0%
+say that oh no we are going to go back
+ 
+
+ align:start position:0%
+say that oh no we are going to go back
+and and teach you know teach something
+
+ align:start position:0%
+and and teach you know teach something
+ 
+
+ align:start position:0%
+and and teach you know teach something
+simpler because that's that's sort of
+
+ align:start position:0%
+simpler because that's that's sort of
+ 
+
+ align:start position:0%
+simpler because that's that's sort of
+saying your your kids are not a little
+
+ align:start position:0%
+saying your your kids are not a little
+ 
+
+ align:start position:0%
+saying your your kids are not a little
+level of everything so politically it's
+
+ align:start position:0%
+level of everything so politically it's
+ 
+
+ align:start position:0%
+level of everything so politically it's
+very very difficult to say that it was
+
+ align:start position:0%
+very very difficult to say that it was
+ 
+
+ align:start position:0%
+very very difficult to say that it was
+difficult to say it independent it's
+
+ align:start position:0%
+difficult to say it independent it's
+ 
+
+ align:start position:0%
+difficult to say it independent it's
+still difficult to say today that the
+
+ align:start position:0%
+still difficult to say today that the
+ 
+
+ align:start position:0%
+still difficult to say today that the
+curriculum need to be scaled back
+
+ align:start position:0%
+curriculum need to be scaled back
+ 
+
+ align:start position:0%
+curriculum need to be scaled back
+um so you have this curriculum in India
+
+ align:start position:0%
+um so you have this curriculum in India
+ 
+
+ align:start position:0%
+um so you have this curriculum in India
+they passed the right to education in
+
+ align:start position:0%
+they passed the right to education in
+ 
+
+ align:start position:0%
+they passed the right to education in
+2010 saying that every kid has a right
+
+ align:start position:0%
+2010 saying that every kid has a right
+ 
+
+ align:start position:0%
+2010 saying that every kid has a right
+to primary education great
+
+ align:start position:0%
+to primary education great
+ 
+
+ align:start position:0%
+to primary education great
+but part of the right to education law
+
+ align:start position:0%
+but part of the right to education law
+ 
+
+ align:start position:0%
+but part of the right to education law
+was that the teachers have to complete
+
+ align:start position:0%
+was that the teachers have to complete
+ 
+
+ align:start position:0%
+was that the teachers have to complete
+the curriculum no matter what
+
+ align:start position:0%
+the curriculum no matter what
+ 
+
+ align:start position:0%
+the curriculum no matter what
+so they will come you know legally
+
+ align:start position:0%
+so they will come you know legally
+ 
+
+ align:start position:0%
+so they will come you know legally
+liable if they don't complete this crazy
+
+ align:start position:0%
+liable if they don't complete this crazy
+ 
+
+ align:start position:0%
+liable if they don't complete this crazy
+curriculum that almost none of their
+
+ align:start position:0%
+curriculum that almost none of their
+ 
+
+ align:start position:0%
+curriculum that almost none of their
+kids can follow so the result is a
+
+ align:start position:0%
+kids can follow so the result is a
+ 
+
+ align:start position:0%
+kids can follow so the result is a
+system where teachers are teaching to
+
+ align:start position:0%
+system where teachers are teaching to
+ 
+
+ align:start position:0%
+system where teachers are teaching to
+one or two people in a class
+
+ align:start position:0%
+one or two people in a class
+ 
+
+ align:start position:0%
+one or two people in a class
+at the very very top of the classroom
+
+ align:start position:0%
+at the very very top of the classroom
+ 
+
+ align:start position:0%
+at the very very top of the classroom
+which brings me to the U.S system the
+
+ align:start position:0%
+which brings me to the U.S system the
+ 
+
+ align:start position:0%
+which brings me to the U.S system the
+U.S system in primary school is not that
+
+ align:start position:0%
+U.S system in primary school is not that
+ 
+
+ align:start position:0%
+U.S system in primary school is not that
+it's a system of No Child Left Behind
+
+ align:start position:0%
+it's a system of No Child Left Behind
+ 
+
+ align:start position:0%
+it's a system of No Child Left Behind
+whether for good or for bad the Teaching
+
+ align:start position:0%
+whether for good or for bad the Teaching
+ 
+
+ align:start position:0%
+whether for good or for bad the Teaching
+Standards are extremely low
+
+ align:start position:0%
+Standards are extremely low
+ 
+
+ align:start position:0%
+Standards are extremely low
+and you're trying to get everyone to a
+
+ align:start position:0%
+and you're trying to get everyone to a
+ 
+
+ align:start position:0%
+and you're trying to get everyone to a
+minimum core so you might imagine that
+
+ align:start position:0%
+minimum core so you might imagine that
+ 
+
+ align:start position:0%
+minimum core so you might imagine that
+starting from systems that have
+
+ align:start position:0%
+starting from systems that have
+ 
+
+ align:start position:0%
+starting from systems that have
+different objective and different
+
+ align:start position:0%
+different objective and different
+ 
+
+ align:start position:0%
+different objective and different
+philosophy in mind the the effect of
+
+ align:start position:0%
+philosophy in mind the the effect of
+ 
+
+ align:start position:0%
+philosophy in mind the the effect of
+different intervention would also be
+
+ align:start position:0%
+different intervention would also be
+ 
+
+ align:start position:0%
+different intervention would also be
+quite different
+
+ align:start position:0%
+quite different
+ 
+
+ align:start position:0%
+quite different
+uh so that's the kind of the answer to
+
+ align:start position:0%
+uh so that's the kind of the answer to
+ 
+
+ align:start position:0%
+uh so that's the kind of the answer to
+your question
+
+ align:start position:0%
+your question
+ 
+
+ align:start position:0%
+your question
+so what's the possible answer to that is
+
+ align:start position:0%
+so what's the possible answer to that is
+ 
+
+ align:start position:0%
+so what's the possible answer to that is
+uh you know basically teaching is at the
+
+ align:start position:0%
+uh you know basically teaching is at the
+ 
+
+ align:start position:0%
+uh you know basically teaching is at the
+wrong level so you could go back and try
+
+ align:start position:0%
+wrong level so you could go back and try
+ 
+
+ align:start position:0%
+wrong level so you could go back and try
+and teach at the right level
+
+ align:start position:0%
+and teach at the right level
+ 
+
+ align:start position:0%
+and teach at the right level
+uh and so that's the basically the
+
+ align:start position:0%
+uh and so that's the basically the
+ 
+
+ align:start position:0%
+uh and so that's the basically the
+flagship uh the flagship program of the
+
+ align:start position:0%
+flagship uh the flagship program of the
+ 
+
+ align:start position:0%
+flagship uh the flagship program of the
+part-time uh the same people who do the
+
+ align:start position:0%
+part-time uh the same people who do the
+ 
+
+ align:start position:0%
+part-time uh the same people who do the
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+is the stitching at the right level
+
+ align:start position:0%
+is the stitching at the right level
+ 
+
+ align:start position:0%
+is the stitching at the right level
+approach where the uh um basically do
+
+ align:start position:0%
+approach where the uh um basically do
+ 
+
+ align:start position:0%
+approach where the uh um basically do
+regular testing of kids you know every
+
+ align:start position:0%
+regular testing of kids you know every
+ 
+
+ align:start position:0%
+regular testing of kids you know every
+month or so put them in groups by a
+
+ align:start position:0%
+month or so put them in groups by a
+ 
+
+ align:start position:0%
+month or so put them in groups by a
+level of
+
+ align:start position:0%
+level of
+ 
+
+ align:start position:0%
+level of
+by level of of competencies attack these
+
+ align:start position:0%
+by level of of competencies attack these
+ 
+
+ align:start position:0%
+by level of of competencies attack these
+competencies and then move them as they
+
+ align:start position:0%
+competencies and then move them as they
+ 
+
+ align:start position:0%
+competencies and then move them as they
+go along so it turns out that the kid
+
+ align:start position:0%
+go along so it turns out that the kid
+ 
+
+ align:start position:0%
+go along so it turns out that the kid
+who who reached grade four without
+
+ align:start position:0%
+who who reached grade four without
+ 
+
+ align:start position:0%
+who who reached grade four without
+learning to write or read can learn very
+
+ align:start position:0%
+learning to write or read can learn very
+ 
+
+ align:start position:0%
+learning to write or read can learn very
+fast if someone told them then because
+
+ align:start position:0%
+fast if someone told them then because
+ 
+
+ align:start position:0%
+fast if someone told them then because
+they are they are
+
+ align:start position:0%
+they are they are
+ 
+
+ align:start position:0%
+they are they are
+connectively quite ready
+
+ align:start position:0%
+connectively quite ready
+ 
+
+ align:start position:0%
+connectively quite ready
+so a kid can learn to to but if no one
+
+ align:start position:0%
+so a kid can learn to to but if no one
+ 
+
+ align:start position:0%
+so a kid can learn to to but if no one
+is ever teaching them then they won't
+
+ align:start position:0%
+is ever teaching them then they won't
+ 
+
+ align:start position:0%
+is ever teaching them then they won't
+learn so they make uh
+
+ align:start position:0%
+learn so they make uh
+ 
+
+ align:start position:0%
+learn so they make uh
+so this was my so something like that
+
+ align:start position:0%
+so this was my so something like that
+ 
+
+ align:start position:0%
+so this was my so something like that
+the ancestor of this program was the
+
+ align:start position:0%
+the ancestor of this program was the
+ 
+
+ align:start position:0%
+the ancestor of this program was the
+first randomized evolution I was
+
+ align:start position:0%
+first randomized evolution I was
+ 
+
+ align:start position:0%
+first randomized evolution I was
+involved with
+
+ align:start position:0%
+involved with
+ 
+
+ align:start position:0%
+involved with
+uh that was called the balsaki program
+
+ align:start position:0%
+uh that was called the balsaki program
+ 
+
+ align:start position:0%
+uh that was called the balsaki program
+in Baroda and Bombay and since then
+
+ align:start position:0%
+in Baroda and Bombay and since then
+ 
+
+ align:start position:0%
+in Baroda and Bombay and since then
+we've been evaluating some version of
+
+ align:start position:0%
+we've been evaluating some version of
+ 
+
+ align:start position:0%
+we've been evaluating some version of
+this program
+
+ align:start position:0%
+this program
+ 
+
+ align:start position:0%
+this program
+in rural areas in urban areas
+
+ align:start position:0%
+in rural areas in urban areas
+ 
+
+ align:start position:0%
+in rural areas in urban areas
+at some point we were ready to scale up
+
+ align:start position:0%
+at some point we were ready to scale up
+ 
+
+ align:start position:0%
+at some point we were ready to scale up
+a part I'm scaled up in Bihar
+
+ align:start position:0%
+a part I'm scaled up in Bihar
+ 
+
+ align:start position:0%
+a part I'm scaled up in Bihar
+in the context of their scaling up we
+
+ align:start position:0%
+in the context of their scaling up we
+ 
+
+ align:start position:0%
+in the context of their scaling up we
+were able to cover the control group
+
+ align:start position:0%
+were able to cover the control group
+ 
+
+ align:start position:0%
+were able to cover the control group
+so that's the opposite of your standard
+
+ align:start position:0%
+so that's the opposite of your standard
+ 
+
+ align:start position:0%
+so that's the opposite of your standard
+and then uh when you you know you have a
+
+ align:start position:0%
+and then uh when you you know you have a
+ 
+
+ align:start position:0%
+and then uh when you you know you have a
+status quo and then you do a new
+
+ align:start position:0%
+status quo and then you do a new
+ 
+
+ align:start position:0%
+status quo and then you do a new
+intervention It's A Small Piece here the
+
+ align:start position:0%
+intervention It's A Small Piece here the
+ 
+
+ align:start position:0%
+intervention It's A Small Piece here the
+new intervention was in a large place
+
+ align:start position:0%
+new intervention was in a large place
+ 
+
+ align:start position:0%
+new intervention was in a large place
+so you have all of the problems that
+
+ align:start position:0%
+so you have all of the problems that
+ 
+
+ align:start position:0%
+so you have all of the problems that
+will potentially arrive when you do
+
+ align:start position:0%
+will potentially arrive when you do
+ 
+
+ align:start position:0%
+will potentially arrive when you do
+something on large scale
+
+ align:start position:0%
+something on large scale
+ 
+
+ align:start position:0%
+something on large scale
+and we took out the control and it
+
+ align:start position:0%
+and we took out the control and it
+ 
+
+ align:start position:0%
+and we took out the control and it
+didn't work at all and until then we had
+
+ align:start position:0%
+didn't work at all and until then we had
+ 
+
+ align:start position:0%
+didn't work at all and until then we had
+great results and then it didn't work at
+
+ align:start position:0%
+great results and then it didn't work at
+ 
+
+ align:start position:0%
+great results and then it didn't work at
+all so we had to go back to the drawing
+
+ align:start position:0%
+all so we had to go back to the drawing
+ 
+
+ align:start position:0%
+all so we had to go back to the drawing
+boards
+
+ align:start position:0%
+boards
+ 
+
+ align:start position:0%
+boards
+um we try to understand why it wasn't
+
+ align:start position:0%
+um we try to understand why it wasn't
+ 
+
+ align:start position:0%
+um we try to understand why it wasn't
+working and to get a long story shot it
+
+ align:start position:0%
+working and to get a long story shot it
+ 
+
+ align:start position:0%
+working and to get a long story shot it
+wasn't working because the tyranny of
+
+ align:start position:0%
+wasn't working because the tyranny of
+ 
+
+ align:start position:0%
+wasn't working because the tyranny of
+the curriculum was still there so the
+
+ align:start position:0%
+the curriculum was still there so the
+ 
+
+ align:start position:0%
+the curriculum was still there so the
+teacher said I can't Implement your
+
+ align:start position:0%
+teacher said I can't Implement your
+ 
+
+ align:start position:0%
+teacher said I can't Implement your
+program you trained me to implement this
+
+ align:start position:0%
+program you trained me to implement this
+ 
+
+ align:start position:0%
+program you trained me to implement this
+program but I can't because I don't have
+
+ align:start position:0%
+program but I can't because I don't have
+ 
+
+ align:start position:0%
+program but I can't because I don't have
+the time because I have to finish the
+
+ align:start position:0%
+the time because I have to finish the
+ 
+
+ align:start position:0%
+the time because I have to finish the
+curriculum
+
+ align:start position:0%
+curriculum
+ 
+
+ align:start position:0%
+curriculum
+so the program could not catch with
+
+ align:start position:0%
+so the program could not catch with
+ 
+
+ align:start position:0%
+so the program could not catch with
+teacher even though and this goes back
+
+ align:start position:0%
+teacher even though and this goes back
+ 
+
+ align:start position:0%
+teacher even though and this goes back
+to your questions you asked earlier
+
+ align:start position:0%
+to your questions you asked earlier
+ 
+
+ align:start position:0%
+to your questions you asked earlier
+would they be capable of teaching yes
+
+ align:start position:0%
+would they be capable of teaching yes
+ 
+
+ align:start position:0%
+would they be capable of teaching yes
+because if you take the same teacher
+
+ align:start position:0%
+because if you take the same teacher
+ 
+
+ align:start position:0%
+because if you take the same teacher
+during summer
+
+ align:start position:0%
+during summer
+ 
+
+ align:start position:0%
+during summer
+we use the same teacher or partner Bihar
+
+ align:start position:0%
+we use the same teacher or partner Bihar
+ 
+
+ align:start position:0%
+we use the same teacher or partner Bihar
+to the state of BR recruited teacher to
+
+ align:start position:0%
+to the state of BR recruited teacher to
+ 
+
+ align:start position:0%
+to the state of BR recruited teacher to
+teach during summer and we experimented
+
+ align:start position:0%
+teach during summer and we experimented
+ 
+
+ align:start position:0%
+teach during summer and we experimented
+that and their kids during summer
+
+ align:start position:0%
+that and their kids during summer
+ 
+
+ align:start position:0%
+that and their kids during summer
+focusing on basic and TL approach did
+
+ align:start position:0%
+focusing on basic and TL approach did
+ 
+
+ align:start position:0%
+focusing on basic and TL approach did
+great progress so in one summer only
+
+ align:start position:0%
+great progress so in one summer only
+ 
+
+ align:start position:0%
+great progress so in one summer only
+made more progress than in an entire
+
+ align:start position:0%
+made more progress than in an entire
+ 
+
+ align:start position:0%
+made more progress than in an entire
+school year with the same teacher
+
+ align:start position:0%
+school year with the same teacher
+ 
+
+ align:start position:0%
+school year with the same teacher
+because during the summer it was very
+
+ align:start position:0%
+because during the summer it was very
+ 
+
+ align:start position:0%
+because during the summer it was very
+clear what they had to do and it was not
+
+ align:start position:0%
+clear what they had to do and it was not
+ 
+
+ align:start position:0%
+clear what they had to do and it was not
+the curriculum and when you move them
+
+ align:start position:0%
+the curriculum and when you move them
+ 
+
+ align:start position:0%
+the curriculum and when you move them
+back to the normal classroom they think
+
+ align:start position:0%
+back to the normal classroom they think
+ 
+
+ align:start position:0%
+back to the normal classroom they think
+I have to do my curriculum sorry I don't
+
+ align:start position:0%
+I have to do my curriculum sorry I don't
+ 
+
+ align:start position:0%
+I have to do my curriculum sorry I don't
+have time for this teaching and to learn
+
+ align:start position:0%
+have time for this teaching and to learn
+ 
+
+ align:start position:0%
+have time for this teaching and to learn
+to read and write things
+
+ align:start position:0%
+to read and write things
+ 
+
+ align:start position:0%
+to read and write things
+so then what we did is that we
+
+ align:start position:0%
+so then what we did is that we
+ 
+
+ align:start position:0%
+so then what we did is that we
+we went back on part time went back and
+
+ align:start position:0%
+we went back on part time went back and
+ 
+
+ align:start position:0%
+we went back on part time went back and
+thought basically it has to be it
+
+ align:start position:0%
+thought basically it has to be it
+ 
+
+ align:start position:0%
+thought basically it has to be it
+becomes a political economic problem
+
+ align:start position:0%
+becomes a political economic problem
+ 
+
+ align:start position:0%
+becomes a political economic problem
+which is how to uh get it to take hold
+
+ align:start position:0%
+which is how to uh get it to take hold
+ 
+
+ align:start position:0%
+which is how to uh get it to take hold
+in the system
+
+ align:start position:0%
+in the system
+ 
+
+ align:start position:0%
+in the system
+and uh so we saw that we needed the one
+
+ align:start position:0%
+and uh so we saw that we needed the one
+ 
+
+ align:start position:0%
+and uh so we saw that we needed the one
+the teachers needed to know that this is
+
+ align:start position:0%
+the teachers needed to know that this is
+ 
+
+ align:start position:0%
+the teachers needed to know that this is
+the time to do teaching at the right
+
+ align:start position:0%
+the time to do teaching at the right
+ 
+
+ align:start position:0%
+the time to do teaching at the right
+level and you cannot do anything else so
+
+ align:start position:0%
+level and you cannot do anything else so
+ 
+
+ align:start position:0%
+level and you cannot do anything else so
+they basically the government added a an
+
+ align:start position:0%
+they basically the government added a an
+ 
+
+ align:start position:0%
+they basically the government added a an
+hour in the school day
+
+ align:start position:0%
+hour in the school day
+ 
+
+ align:start position:0%
+hour in the school day
+both in treatment and control
+
+ align:start position:0%
+both in treatment and control
+ 
+
+ align:start position:0%
+both in treatment and control
+but in poncola just added an hour and
+
+ align:start position:0%
+but in poncola just added an hour and
+ 
+
+ align:start position:0%
+but in poncola just added an hour and
+treatment that said this hour is for
+
+ align:start position:0%
+treatment that said this hour is for
+ 
+
+ align:start position:0%
+treatment that said this hour is for
+teaching at the right level activity
+
+ align:start position:0%
+teaching at the right level activity
+ 
+
+ align:start position:0%
+teaching at the right level activity
+classes have to be mixed kids have to
+
+ align:start position:0%
+classes have to be mixed kids have to
+ 
+
+ align:start position:0%
+classes have to be mixed kids have to
+learn you know to go back to to do the
+
+ align:start position:0%
+learn you know to go back to to do the
+ 
+
+ align:start position:0%
+learn you know to go back to to do the
+teaching at the right level activities
+
+ align:start position:0%
+teaching at the right level activities
+ 
+
+ align:start position:0%
+teaching at the right level activities
+and they also an old the the school
+
+ align:start position:0%
+and they also an old the the school
+ 
+
+ align:start position:0%
+and they also an old the the school
+inspectors to serve as supervisor at the
+
+ align:start position:0%
+inspectors to serve as supervisor at the
+ 
+
+ align:start position:0%
+inspectors to serve as supervisor at the
+program and that worked nicely
+
+ align:start position:0%
+program and that worked nicely
+ 
+
+ align:start position:0%
+program and that worked nicely
+the other ways to say well forget the
+
+ align:start position:0%
+the other ways to say well forget the
+ 
+
+ align:start position:0%
+the other ways to say well forget the
+teachers let have it implemented by
+
+ align:start position:0%
+teachers let have it implemented by
+ 
+
+ align:start position:0%
+teachers let have it implemented by
+outside by Outsiders that was done in up
+
+ align:start position:0%
+outside by Outsiders that was done in up
+ 
+
+ align:start position:0%
+outside by Outsiders that was done in up
+that's a dysfunctional school system and
+
+ align:start position:0%
+that's a dysfunctional school system and
+ 
+
+ align:start position:0%
+that's a dysfunctional school system and
+that worked that also worked
+
+ align:start position:0%
+that worked that also worked
+ 
+
+ align:start position:0%
+that worked that also worked
+so now uh part-time has been scaled up
+
+ align:start position:0%
+so now uh part-time has been scaled up
+ 
+
+ align:start position:0%
+so now uh part-time has been scaled up
+in India uh the the teaching our right
+
+ align:start position:0%
+in India uh the the teaching our right
+ 
+
+ align:start position:0%
+in India uh the the teaching our right
+level has been scaled up in Africa and
+
+ align:start position:0%
+level has been scaled up in Africa and
+ 
+
+ align:start position:0%
+level has been scaled up in Africa and
+then it's a model that can
+
+ align:start position:0%
+then it's a model that can
+ 
+
+ align:start position:0%
+then it's a model that can
+either of these two models is robust
+
+ align:start position:0%
+either of these two models is robust
+ 
+
+ align:start position:0%
+either of these two models is robust
+enough can be implemented in other
+
+ align:start position:0%
+enough can be implemented in other
+ 
+
+ align:start position:0%
+enough can be implemented in other
+countries and is being implemented in in
+
+ align:start position:0%
+countries and is being implemented in in
+ 
+
+ align:start position:0%
+countries and is being implemented in in
+those places
+
+ align:start position:0%
+those places
+ 
+
+ align:start position:0%
+those places
+so let me conclude uh rapidly
+
+ align:start position:0%
+so let me conclude uh rapidly
+ 
+
+ align:start position:0%
+so let me conclude uh rapidly
+I've given everything I told you you
+
+ align:start position:0%
+I've given everything I told you you
+ 
+
+ align:start position:0%
+I've given everything I told you you
+know how do we go about fixing primary
+
+ align:start position:0%
+know how do we go about fixing primary
+ 
+
+ align:start position:0%
+know how do we go about fixing primary
+education
+
+ align:start position:0%
+education
+ 
+
+ align:start position:0%
+education
+so some people say well give up on the
+
+ align:start position:0%
+so some people say well give up on the
+ 
+
+ align:start position:0%
+so some people say well give up on the
+schools and in fact the founder of
+
+ align:start position:0%
+schools and in fact the founder of
+ 
+
+ align:start position:0%
+schools and in fact the founder of
+part-time madhav chavan that's kind of
+
+ align:start position:0%
+part-time madhav chavan that's kind of
+ 
+
+ align:start position:0%
+part-time madhav chavan that's kind of
+his view now it's like the schools are
+
+ align:start position:0%
+his view now it's like the schools are
+ 
+
+ align:start position:0%
+his view now it's like the schools are
+just a big waste of time
+
+ align:start position:0%
+just a big waste of time
+ 
+
+ align:start position:0%
+just a big waste of time
+and let's give tablets to the kids in in
+
+ align:start position:0%
+and let's give tablets to the kids in in
+ 
+
+ align:start position:0%
+and let's give tablets to the kids in in
+villages and then have them you know
+
+ align:start position:0%
+villages and then have them you know
+ 
+
+ align:start position:0%
+villages and then have them you know
+learn this way to
+
+ align:start position:0%
+learn this way to
+ 
+
+ align:start position:0%
+learn this way to
+material you you push to the tablet
+
+ align:start position:0%
+material you you push to the tablet
+ 
+
+ align:start position:0%
+material you you push to the tablet
+it has potential particularly with with
+
+ align:start position:0%
+it has potential particularly with with
+ 
+
+ align:start position:0%
+it has potential particularly with with
+digital education but it has a big
+
+ align:start position:0%
+digital education but it has a big
+ 
+
+ align:start position:0%
+digital education but it has a big
+problem which is at least the school's
+
+ align:start position:0%
+problem which is at least the school's
+ 
+
+ align:start position:0%
+problem which is at least the school's
+parents have bought in and they're
+
+ align:start position:0%
+parents have bought in and they're
+ 
+
+ align:start position:0%
+parents have bought in and they're
+sending the kids there so the kids are
+
+ align:start position:0%
+sending the kids there so the kids are
+ 
+
+ align:start position:0%
+sending the kids there so the kids are
+captive anything else you have to
+
+ align:start position:0%
+captive anything else you have to
+ 
+
+ align:start position:0%
+captive anything else you have to
+convince the parents that it's worth
+
+ align:start position:0%
+convince the parents that it's worth
+ 
+
+ align:start position:0%
+convince the parents that it's worth
+their while and it's very hard
+
+ align:start position:0%
+their while and it's very hard
+ 
+
+ align:start position:0%
+their while and it's very hard
+convincing the parents it's worth their
+
+ align:start position:0%
+convincing the parents it's worth their
+ 
+
+ align:start position:0%
+convincing the parents it's worth their
+while so Karthik did an experiment where
+
+ align:start position:0%
+while so Karthik did an experiment where
+ 
+
+ align:start position:0%
+while so Karthik did an experiment where
+he found absolutely spectacular effects
+
+ align:start position:0%
+he found absolutely spectacular effects
+ 
+
+ align:start position:0%
+he found absolutely spectacular effects
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+software-based mathematical intervention
+
+ align:start position:0%
+software-based mathematical intervention
+ 
+
+ align:start position:0%
+software-based mathematical intervention
+intervention on on math and Hindi
+
+ align:start position:0%
+intervention on on math and Hindi
+ 
+
+ align:start position:0%
+intervention on on math and Hindi
+67.67 standard deviation is like great
+
+ align:start position:0%
+67.67 standard deviation is like great
+ 
+
+ align:start position:0%
+67.67 standard deviation is like great
+but the problem is that even though it
+
+ align:start position:0%
+but the problem is that even though it
+ 
+
+ align:start position:0%
+but the problem is that even though it
+was 67 standard deviation
+
+ align:start position:0%
+was 67 standard deviation
+ 
+
+ align:start position:0%
+was 67 standard deviation
+when you ask the questions the type of
+
+ align:start position:0%
+when you ask the questions the type of
+ 
+
+ align:start position:0%
+when you ask the questions the type of
+question that are asked on exams that
+
+ align:start position:0%
+question that are asked on exams that
+ 
+
+ align:start position:0%
+question that are asked on exams that
+are the grade level question there is no
+
+ align:start position:0%
+are the grade level question there is no
+ 
+
+ align:start position:0%
+are the grade level question there is no
+impact on those at least on math that's
+
+ align:start position:0%
+impact on those at least on math that's
+ 
+
+ align:start position:0%
+impact on those at least on math that's
+because the kids are so far behind is
+
+ align:start position:0%
+because the kids are so far behind is
+ 
+
+ align:start position:0%
+because the kids are so far behind is
+that even though they progressed
+
+ align:start position:0%
+that even though they progressed
+ 
+
+ align:start position:0%
+that even though they progressed
+and all of them progressed they still
+
+ align:start position:0%
+and all of them progressed they still
+ 
+
+ align:start position:0%
+and all of them progressed they still
+haven't reached the point where the
+
+ align:start position:0%
+haven't reached the point where the
+ 
+
+ align:start position:0%
+haven't reached the point where the
+questions that are being asked at the
+
+ align:start position:0%
+questions that are being asked at the
+ 
+
+ align:start position:0%
+questions that are being asked at the
+exam are pertinent for them eventually
+
+ align:start position:0%
+exam are pertinent for them eventually
+ 
+
+ align:start position:0%
+exam are pertinent for them eventually
+you would think they they reached them
+
+ align:start position:0%
+you would think they they reached them
+ 
+
+ align:start position:0%
+you would think they they reached them
+and therefore the parents are totally
+
+ align:start position:0%
+and therefore the parents are totally
+ 
+
+ align:start position:0%
+and therefore the parents are totally
+not interested
+
+ align:start position:0%
+not interested
+ 
+
+ align:start position:0%
+not interested
+and what happened to this program
+
+ align:start position:0%
+and what happened to this program
+ 
+
+ align:start position:0%
+and what happened to this program
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+this is a long paragraph but it's likely
+
+ align:start position:0%
+this is a long paragraph but it's likely
+ 
+
+ align:start position:0%
+this is a long paragraph but it's likely
+to say at the very end of this program
+
+ align:start position:0%
+to say at the very end of this program
+ 
+
+ align:start position:0%
+to say at the very end of this program
+that shows this great result is at the
+
+ align:start position:0%
+that shows this great result is at the
+ 
+
+ align:start position:0%
+that shows this great result is at the
+moment the experiment was over the
+
+ align:start position:0%
+moment the experiment was over the
+ 
+
+ align:start position:0%
+moment the experiment was over the
+program was finished because the parents
+
+ align:start position:0%
+program was finished because the parents
+ 
+
+ align:start position:0%
+program was finished because the parents
+refused to spend like the few cents to
+
+ align:start position:0%
+refused to spend like the few cents to
+ 
+
+ align:start position:0%
+refused to spend like the few cents to
+keep it going uh because from there for
+
+ align:start position:0%
+keep it going uh because from there for
+ 
+
+ align:start position:0%
+keep it going uh because from there for
+their point of view it wasn't reaching
+
+ align:start position:0%
+their point of view it wasn't reaching
+ 
+
+ align:start position:0%
+their point of view it wasn't reaching
+it wasn't useful because it wasn't
+
+ align:start position:0%
+it wasn't useful because it wasn't
+ 
+
+ align:start position:0%
+it wasn't useful because it wasn't
+bringing the kids where they wanted them
+
+ align:start position:0%
+bringing the kids where they wanted them
+ 
+
+ align:start position:0%
+bringing the kids where they wanted them
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+so something that's not happening in the
+
+ align:start position:0%
+so something that's not happening in the
+ 
+
+ align:start position:0%
+so something that's not happening in the
+school is hard so I don't think we can
+
+ align:start position:0%
+school is hard so I don't think we can
+ 
+
+ align:start position:0%
+school is hard so I don't think we can
+give up on the schools changing the
+
+ align:start position:0%
+give up on the schools changing the
+ 
+
+ align:start position:0%
+give up on the schools changing the
+curriculum would of course be the Holy
+
+ align:start position:0%
+curriculum would of course be the Holy
+ 
+
+ align:start position:0%
+curriculum would of course be the Holy
+Grail it's a political year
+
+ align:start position:0%
+Grail it's a political year
+ 
+
+ align:start position:0%
+Grail it's a political year
+I've been trying uh you know a good part
+
+ align:start position:0%
+I've been trying uh you know a good part
+ 
+
+ align:start position:0%
+I've been trying uh you know a good part
+of my professional life with very
+
+ align:start position:0%
+of my professional life with very
+ 
+
+ align:start position:0%
+of my professional life with very
+limited success
+
+ align:start position:0%
+limited success
+ 
+
+ align:start position:0%
+limited success
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and then there is the final possibility
+
+ align:start position:0%
+and then there is the final possibility
+ 
+
+ align:start position:0%
+and then there is the final possibility
+which is what we started to do in uh
+
+ align:start position:0%
+which is what we started to do in uh
+ 
+
+ align:start position:0%
+which is what we started to do in uh
+with Liz which is to work anywhere where
+
+ align:start position:0%
+with Liz which is to work anywhere where
+ 
+
+ align:start position:0%
+with Liz which is to work anywhere where
+it's not yet you know in the margin
+
+ align:start position:0%
+it's not yet you know in the margin
+ 
+
+ align:start position:0%
+it's not yet you know in the margin
+to tutoring programs preschools uh
+
+ align:start position:0%
+to tutoring programs preschools uh
+ 
+
+ align:start position:0%
+to tutoring programs preschools uh
+um the completely different schools like
+
+ align:start position:0%
+um the completely different schools like
+ 
+
+ align:start position:0%
+um the completely different schools like
+they have in uttapadesh where there is
+
+ align:start position:0%
+they have in uttapadesh where there is
+ 
+
+ align:start position:0%
+they have in uttapadesh where there is
+no teaching happening anyway which you
+
+ align:start position:0%
+no teaching happening anyway which you
+ 
+
+ align:start position:0%
+no teaching happening anyway which you
+can sort of take over that kind of
+
+ align:start position:0%
+can sort of take over that kind of
+ 
+
+ align:start position:0%
+can sort of take over that kind of
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um I want to let you go so I won't get
+
+ align:start position:0%
+um I want to let you go so I won't get
+ 
+
+ align:start position:0%
+um I want to let you go so I won't get
+into the details of what we did with Liz
+
+ align:start position:0%
+into the details of what we did with Liz
+ 
+
+ align:start position:0%
+into the details of what we did with Liz
+but basically experiment after
+
+ align:start position:0%
+but basically experiment after
+ 
+
+ align:start position:0%
+but basically experiment after
+experiments we've developed an approach
+
+ align:start position:0%
+experiments we've developed an approach
+ 
+
+ align:start position:0%
+experiments we've developed an approach
+to teaching preschool mathematics that
+
+ align:start position:0%
+to teaching preschool mathematics that
+ 
+
+ align:start position:0%
+to teaching preschool mathematics that
+we think is good and can now be scaled
+
+ align:start position:0%
+we think is good and can now be scaled
+ 
+
+ align:start position:0%
+we think is good and can now be scaled
+up so now and more and more kids go to
+
+ align:start position:0%
+up so now and more and more kids go to
+ 
+
+ align:start position:0%
+up so now and more and more kids go to
+preschool so if at least they can you
+
+ align:start position:0%
+preschool so if at least they can you
+ 
+
+ align:start position:0%
+preschool so if at least they can you
+know they can be exposed to our program
+
+ align:start position:0%
+know they can be exposed to our program
+ 
+
+ align:start position:0%
+know they can be exposed to our program
+nobody cares that the simple people seem
+
+ align:start position:0%
+nobody cares that the simple people seem
+ 
+
+ align:start position:0%
+nobody cares that the simple people seem
+to be very happy to let us operate in
+
+ align:start position:0%
+to be very happy to let us operate in
+ 
+
+ align:start position:0%
+to be very happy to let us operate in
+preschools whereas anything like the
+
+ align:start position:0%
+preschools whereas anything like the
+ 
+
+ align:start position:0%
+preschools whereas anything like the
+teaching at the right level in primary
+
+ align:start position:0%
+teaching at the right level in primary
+ 
+
+ align:start position:0%
+teaching at the right level in primary
+school you have to fight with this
+
+ align:start position:0%
+school you have to fight with this
+ 
+
+ align:start position:0%
+school you have to fight with this
+existing existing pressure the one
+
+ align:start position:0%
+existing existing pressure the one
+ 
+
+ align:start position:0%
+existing existing pressure the one
+worries is though is that these are the
+
+ align:start position:0%
+worries is though is that these are the
+ 
+
+ align:start position:0%
+worries is though is that these are the
+detail doesn't matter the one worry is
+
+ align:start position:0%
+detail doesn't matter the one worry is
+ 
+
+ align:start position:0%
+detail doesn't matter the one worry is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+as this margin expands that's the
+
+ align:start position:0%
+as this margin expands that's the
+ 
+
+ align:start position:0%
+as this margin expands that's the
+trade-off this margin expands more and
+
+ align:start position:0%
+trade-off this margin expands more and
+ 
+
+ align:start position:0%
+trade-off this margin expands more and
+more schools go to primaries to
+
+ align:start position:0%
+more schools go to primaries to
+ 
+
+ align:start position:0%
+more schools go to primaries to
+preschool so that's great this gives us
+
+ align:start position:0%
+preschool so that's great this gives us
+ 
+
+ align:start position:0%
+preschool so that's great this gives us
+more space to do our stuff
+
+ align:start position:0%
+more space to do our stuff
+ 
+
+ align:start position:0%
+more space to do our stuff
+but then as it expands people start
+
+ align:start position:0%
+but then as it expands people start
+ 
+
+ align:start position:0%
+but then as it expands people start
+caring more about it
+
+ align:start position:0%
+caring more about it
+ 
+
+ align:start position:0%
+caring more about it
+so there are calls to regulate the
+
+ align:start position:0%
+so there are calls to regulate the
+ 
+
+ align:start position:0%
+so there are calls to regulate the
+coaching centers and what is being done
+
+ align:start position:0%
+coaching centers and what is being done
+ 
+
+ align:start position:0%
+coaching centers and what is being done
+there and they are called to regulate
+
+ align:start position:0%
+there and they are called to regulate
+ 
+
+ align:start position:0%
+there and they are called to regulate
+the preschool and have a curriculum for
+
+ align:start position:0%
+the preschool and have a curriculum for
+ 
+
+ align:start position:0%
+the preschool and have a curriculum for
+preschool so it's kind of a kind of
+
+ align:start position:0%
+preschool so it's kind of a kind of
+ 
+
+ align:start position:0%
+preschool so it's kind of a kind of
+permanent cat and mouse problem so the
+
+ align:start position:0%
+permanent cat and mouse problem so the
+ 
+
+ align:start position:0%
+permanent cat and mouse problem so the
+bottom line is that basically you need
+
+ align:start position:0%
+bottom line is that basically you need
+ 
+
+ align:start position:0%
+bottom line is that basically you need
+to be pretty patient which is I don't
+
+ align:start position:0%
+to be pretty patient which is I don't
+ 
+
+ align:start position:0%
+to be pretty patient which is I don't
+think there is going to be a silver
+
+ align:start position:0%
+think there is going to be a silver
+ 
+
+ align:start position:0%
+think there is going to be a silver
+bullet even though we Now understand the
+
+ align:start position:0%
+bullet even though we Now understand the
+ 
+
+ align:start position:0%
+bullet even though we Now understand the
+problem well
+
+ align:start position:0%
+problem well
+ 
+
+ align:start position:0%
+problem well
+we can't quite we can't fix it easily
+
+ align:start position:0%
+we can't quite we can't fix it easily
+ 
+
+ align:start position:0%
+we can't quite we can't fix it easily
+all you can do is having these programs
+
+ align:start position:0%
+all you can do is having these programs
+ 
+
+ align:start position:0%
+all you can do is having these programs
+that push a little bit demanding the
+
+ align:start position:0%
+that push a little bit demanding the
+ 
+
+ align:start position:0%
+that push a little bit demanding the
+gains are not enormous but they are
+
+ align:start position:0%
+gains are not enormous but they are
+ 
+
+ align:start position:0%
+gains are not enormous but they are
+there and it's a lot of kids so that's
+
+ align:start position:0%
+there and it's a lot of kids so that's
+ 
+
+ align:start position:0%
+there and it's a lot of kids so that's
+already something and there is not going
+
+ align:start position:0%
+already something and there is not going
+ 
+
+ align:start position:0%
+already something and there is not going
+to be a big uh Evolution where recently
+
+ align:start position:0%
+to be a big uh Evolution where recently
+ 
+
+ align:start position:0%
+to be a big uh Evolution where recently
+are going to make it work so much better
+
+ align:start position:0%
+are going to make it work so much better
+ 
+
+ align:start position:0%
+are going to make it work so much better
+and when I conclude like that if I give
+
+ align:start position:0%
+and when I conclude like that if I give
+ 
+
+ align:start position:0%
+and when I conclude like that if I give
+a similar presentation in India
+
+ align:start position:0%
+a similar presentation in India
+ 
+
+ align:start position:0%
+a similar presentation in India
+people are really upset and they come to
+
+ align:start position:0%
+people are really upset and they come to
+ 
+
+ align:start position:0%
+people are really upset and they come to
+me like a particular the tech people
+
+ align:start position:0%
+me like a particular the tech people
+ 
+
+ align:start position:0%
+me like a particular the tech people
+very well-intentioned they said how can
+
+ align:start position:0%
+very well-intentioned they said how can
+ 
+
+ align:start position:0%
+very well-intentioned they said how can
+you say that we don't have the time we
+
+ align:start position:0%
+you say that we don't have the time we
+ 
+
+ align:start position:0%
+you say that we don't have the time we
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+I think it's better to do that than to
+
+ align:start position:0%
+I think it's better to do that than to
+ 
+
+ align:start position:0%
+I think it's better to do that than to
+do nothing which is the alternative we
+
+ align:start position:0%
+do nothing which is the alternative we
+ 
+
+ align:start position:0%
+do nothing which is the alternative we
+have to act this generation blah blah
+
+ align:start position:0%
+have to act this generation blah blah
+ 
+
+ align:start position:0%
+have to act this generation blah blah
+blah so this is uh that's kind of the
+
+ align:start position:0%
+blah so this is uh that's kind of the
+ 
+
+ align:start position:0%
+blah so this is uh that's kind of the
+unpopular message of the only thing you
+
+ align:start position:0%
+unpopular message of the only thing you
+ 
+
+ align:start position:0%
+unpopular message of the only thing you
+can do is push a little bit the the
+
+ align:start position:0%
+can do is push a little bit the the
+ 
+
+ align:start position:0%
+can do is push a little bit the the
+envelope here and there and you're not
+
+ align:start position:0%
+envelope here and there and you're not
+ 
+
+ align:start position:0%
+envelope here and there and you're not
+going to get a revolution yeah
+
+ align:start position:0%
+going to get a revolution yeah
+ 
+
+ align:start position:0%
+going to get a revolution yeah
+yeah sort of thinking about the
+
+ align:start position:0%
+yeah sort of thinking about the
+ 
+
+ align:start position:0%
+yeah sort of thinking about the
+dialogue between
+
+ align:start position:0%
+dialogue between
+ 
+
+ align:start position:0%
+dialogue between
+the teaching at the red level program
+
+ align:start position:0%
+the teaching at the red level program
+ 
+
+ align:start position:0%
+the teaching at the red level program
+and sort of the literature on tracking
+
+ align:start position:0%
+and sort of the literature on tracking
+ 
+
+ align:start position:0%
+and sort of the literature on tracking
+is there a sense within the teaching of
+
+ align:start position:0%
+is there a sense within the teaching of
+ 
+
+ align:start position:0%
+is there a sense within the teaching of
+the right novel of how much of the
+
+ align:start position:0%
+the right novel of how much of the
+ 
+
+ align:start position:0%
+the right novel of how much of the
+effect of the program is due to like
+
+ align:start position:0%
+effect of the program is due to like
+ 
+
+ align:start position:0%
+effect of the program is due to like
+pure effects of like a new configuration
+
+ align:start position:0%
+pure effects of like a new configuration
+ 
+
+ align:start position:0%
+pure effects of like a new configuration
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+with whom the children are learning
+
+ align:start position:0%
+with whom the children are learning
+ 
+
+ align:start position:0%
+with whom the children are learning
+versus changes to the curriculum itself
+
+ align:start position:0%
+versus changes to the curriculum itself
+ 
+
+ align:start position:0%
+versus changes to the curriculum itself
+to the activities yeah so I think it's a
+
+ align:start position:0%
+to the activities yeah so I think it's a
+ 
+
+ align:start position:0%
+to the activities yeah so I think it's a
+lot to the farmer which is just a lot of
+
+ align:start position:0%
+lot to the farmer which is just a lot of
+ 
+
+ align:start position:0%
+lot to the farmer which is just a lot of
+being with a group of your same
+
+ align:start position:0%
+being with a group of your same
+ 
+
+ align:start position:0%
+being with a group of your same
+like-minded kids and so we have a paper
+
+ align:start position:0%
+like-minded kids and so we have a paper
+ 
+
+ align:start position:0%
+like-minded kids and so we have a paper
+in Kenya with Michael Kramer and
+
+ align:start position:0%
+in Kenya with Michael Kramer and
+ 
+
+ align:start position:0%
+in Kenya with Michael Kramer and
+pascalin where we kind of have both
+
+ align:start position:0%
+pascalin where we kind of have both
+ 
+
+ align:start position:0%
+pascalin where we kind of have both
+because we we track and then we have
+
+ align:start position:0%
+because we we track and then we have
+ 
+
+ align:start position:0%
+because we we track and then we have
+either the regular teacher or young
+
+ align:start position:0%
+either the regular teacher or young
+ 
+
+ align:start position:0%
+either the regular teacher or young
+enthusiastic teacher
+
+ align:start position:0%
+enthusiastic teacher
+ 
+
+ align:start position:0%
+enthusiastic teacher
+and and we do find effect of tracking
+
+ align:start position:0%
+and and we do find effect of tracking
+ 
+
+ align:start position:0%
+and and we do find effect of tracking
+and boosts cases both for the both would
+
+ align:start position:0%
+and boosts cases both for the both would
+ 
+
+ align:start position:0%
+and boosts cases both for the both would
+in the non-track school we have huge
+
+ align:start position:0%
+in the non-track school we have huge
+ 
+
+ align:start position:0%
+in the non-track school we have huge
+effect of the young enthusiastic teacher
+
+ align:start position:0%
+effect of the young enthusiastic teacher
+ 
+
+ align:start position:0%
+effect of the young enthusiastic teacher
+and in a track school we still have an
+
+ align:start position:0%
+and in a track school we still have an
+ 
+
+ align:start position:0%
+and in a track school we still have an
+effect of the young enthusiastic teacher
+
+ align:start position:0%
+effect of the young enthusiastic teacher
+ 
+
+ align:start position:0%
+effect of the young enthusiastic teacher
+but even in the regular school the
+
+ align:start position:0%
+but even in the regular school the
+ 
+
+ align:start position:0%
+but even in the regular school the
+tracking really helps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look at this
+
+ align:start position:0%
+look at this
+ 
+
+ align:start position:0%
+look at this
+education system was structured just to
+
+ align:start position:0%
+education system was structured just to
+ 
+
+ align:start position:0%
+education system was structured just to
+like capture the one currently in
+
+ align:start position:0%
+like capture the one currently in
+ 
+
+ align:start position:0%
+like capture the one currently in
+clinical students
+
+ align:start position:0%
+clinical students
+ 
+
+ align:start position:0%
+clinical students
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+academic skills now in the building is
+
+ align:start position:0%
+academic skills now in the building is
+ 
+
+ align:start position:0%
+academic skills now in the building is
+interesting fact is that that student
+
+ align:start position:0%
+interesting fact is that that student
+ 
+
+ align:start position:0%
+interesting fact is that that student
+also has a higher probability of living
+
+ align:start position:0%
+also has a higher probability of living
+ 
+
+ align:start position:0%
+also has a higher probability of living
+the country once after going through
+
+ align:start position:0%
+the country once after going through
+ 
+
+ align:start position:0%
+the country once after going through
+that nutrition there is that yes
+
+ align:start position:0%
+that nutrition there is that yes
+ 
+
+ align:start position:0%
+that nutrition there is that yes
+yes no no I think that you're absolutely
+
+ align:start position:0%
+yes no no I think that you're absolutely
+ 
+
+ align:start position:0%
+yes no no I think that you're absolutely
+right which is the the most brilliant of
+
+ align:start position:0%
+right which is the the most brilliant of
+ 
+
+ align:start position:0%
+right which is the the most brilliant of
+the the one kid who manages to you know
+
+ align:start position:0%
+the the one kid who manages to you know
+ 
+
+ align:start position:0%
+the the one kid who manages to you know
+make their way to the school system and
+
+ align:start position:0%
+make their way to the school system and
+ 
+
+ align:start position:0%
+make their way to the school system and
+not being crushed by it and go to
+
+ align:start position:0%
+not being crushed by it and go to
+ 
+
+ align:start position:0%
+not being crushed by it and go to
+universities probably somewhere here
+
+ align:start position:0%
+universities probably somewhere here
+ 
+
+ align:start position:0%
+universities probably somewhere here
+so they are contributing to the world
+
+ align:start position:0%
+so they are contributing to the world
+ 
+
+ align:start position:0%
+so they are contributing to the world
+but not necessarily to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay great thank you so we'll um uh see
+
+ align:start position:0%
+okay great thank you so we'll um uh see
+ 
+
+ align:start position:0%
+okay great thank you so we'll um uh see
+you next week oh it's a long weekend so
+
+ align:start position:0%
+you next week oh it's a long weekend so
+ 
+
+ align:start position:0%
+you next week oh it's a long weekend so
+we'll see you on Wednesday
\ No newline at end of file
diff --git a/Gv3fPjWiQhs.txt b/Gv3fPjWiQhs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..07861633485d6a7a488e99b9c68c49248a6ac1b1
--- /dev/null
+++ b/Gv3fPjWiQhs.txt
@@ -0,0 +1,195 @@
+align:start position:0%
+ 
+the personal reflective memo is a
+
+ align:start position:0%
+the personal reflective memo is a
+ 
+
+ align:start position:0%
+the personal reflective memo is a
+two-page document that I ask the
+
+ align:start position:0%
+two-page document that I ask the
+ 
+
+ align:start position:0%
+two-page document that I ask the
+students to write at the end of the
+
+ align:start position:0%
+students to write at the end of the
+ 
+
+ align:start position:0%
+students to write at the end of the
+class but before the oral exam so all
+
+ align:start position:0%
+class but before the oral exam so all
+ 
+
+ align:start position:0%
+class but before the oral exam so all
+the lectures we've had all the team
+
+ align:start position:0%
+the lectures we've had all the team
+ 
+
+ align:start position:0%
+the lectures we've had all the team
+assignments and all the material has
+
+ align:start position:0%
+assignments and all the material has
+ 
+
+ align:start position:0%
+assignments and all the material has
+been presented and at this point this
+
+ align:start position:0%
+been presented and at this point this
+ 
+
+ align:start position:0%
+been presented and at this point this
+reflective memo asks the students to
+
+ align:start position:0%
+reflective memo asks the students to
+ 
+
+ align:start position:0%
+reflective memo asks the students to
+think back on the material what really
+
+ align:start position:0%
+think back on the material what really
+ 
+
+ align:start position:0%
+think back on the material what really
+uh was the most important thing they
+
+ align:start position:0%
+uh was the most important thing they
+ 
+
+ align:start position:0%
+uh was the most important thing they
+learned uh what of what they learned in
+
+ align:start position:0%
+learned uh what of what they learned in
+ 
+
+ align:start position:0%
+learned uh what of what they learned in
+the class are they going to build into
+
+ align:start position:0%
+the class are they going to build into
+ 
+
+ align:start position:0%
+the class are they going to build into
+you know their own future projects their
+
+ align:start position:0%
+you know their own future projects their
+ 
+
+ align:start position:0%
+you know their own future projects their
+own careers if they're interested in
+
+ align:start position:0%
+own careers if they're interested in
+ 
+
+ align:start position:0%
+own careers if they're interested in
+systems engineering as a career choice
+
+ align:start position:0%
+systems engineering as a career choice
+ 
+
+ align:start position:0%
+systems engineering as a career choice
+whether it's in research or in Industry
+
+ align:start position:0%
+whether it's in research or in Industry
+ 
+
+ align:start position:0%
+whether it's in research or in Industry
+why is that the case and so they submit
+
+ align:start position:0%
+why is that the case and so they submit
+ 
+
+ align:start position:0%
+why is that the case and so they submit
+this uh one or two days before the oral
+
+ align:start position:0%
+this uh one or two days before the oral
+ 
+
+ align:start position:0%
+this uh one or two days before the oral
+exam and so we have a chance to to read
+
+ align:start position:0%
+exam and so we have a chance to to read
+ 
+
+ align:start position:0%
+exam and so we have a chance to to read
+those reflective memos and usually one
+
+ align:start position:0%
+those reflective memos and usually one
+ 
+
+ align:start position:0%
+those reflective memos and usually one
+of the very first questions in the oral
+
+ align:start position:0%
+of the very first questions in the oral
+ 
+
+ align:start position:0%
+of the very first questions in the oral
+exam is
+
+ align:start position:0%
+exam is
+ 
+
+ align:start position:0%
+exam is
+about some key ideas that they presented
+
+ align:start position:0%
+about some key ideas that they presented
+ 
+
+ align:start position:0%
+about some key ideas that they presented
+in their oral memo so it provides a
+
+ align:start position:0%
+in their oral memo so it provides a
+ 
+
+ align:start position:0%
+in their oral memo so it provides a
+great hook uh into the oral exam
\ No newline at end of file
diff --git a/H0xGKKpKaRE.txt b/H0xGKKpKaRE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cc0bc21cff4446054ba412e875c29c685b76fe6b
--- /dev/null
+++ b/H0xGKKpKaRE.txt
@@ -0,0 +1,641 @@
+There are many
+approaches to building
+
+a general-purpose computer that
+can be easily re-programmed
+
+for new problems.
+
+Almost all modern computers are
+based on the “stored program”
+
+computer architecture developed
+by John von Neumann in 1945,
+
+which is now commonly referred
+to as the “von Neumann model”.
+
+The von Neumann model
+has three components.
+
+There’s a central processing
+unit (aka the CPU) that
+
+contains a datapath and control
+FSM as described previously.
+
+The CPU is connected
+to a read/write memory
+
+that holds some number W
+of words, each with N bits.
+
+Nowadays, even small
+memories have a billion words
+
+and the width of each
+location is at least 32 bits
+
+(usually more).
+
+This memory is often referred to
+as “main memory” to distinguish
+
+it from other memories
+in the system.
+
+You can think of it as an array:
+when the CPU wishes to operate
+
+on values in memory , it sends
+the memory an array index,
+
+which we call the address, and,
+after a short delay (currently
+
+10’s of nanoseconds) the memory
+will return the N-bit value
+
+stored at that address.
+
+Writes to main memory
+follow the same protocol
+
+except, of course,
+the data flows
+
+in the opposite direction.
+
+We’ll talk about memory
+technologies a couple
+
+of lectures from now.
+
+And, finally, there are
+input/output devices
+
+that enable the computer
+system to communicate
+
+with the outside world or
+to access data storage that,
+
+unlike main memory, will
+remember values even when
+
+turned off.
+
+The key idea is
+to use main memory
+
+to hold the instructions
+for the CPU as well as data.
+
+Both instructions and data are,
+of course, just binary data
+
+stored in main memory.
+
+Interpreted as an
+instruction, a value in memory
+
+can be thought of as a set of
+fields containing one or bits
+
+encoding information
+about the actions
+
+to be performed by the CPU.
+
+The opcode field indicates
+the operation to be performed
+
+(e.g., ADD, XOR, COMPARE).
+
+Subsequent fields specify which
+registers supply the source
+
+operands and the
+destination register
+
+where the result is stored.
+
+The CPU interprets the
+information in the instruction
+
+fields and performs the
+requested operation.
+
+It would then move on to the
+next instruction in memory,
+
+executing the stored
+program step-by-step.
+
+The goal of this
+chapter is to discuss
+
+the details of what operations
+we want the CPU to perform,
+
+how many registers we
+should have, and so on.
+
+Of course, some values in
+memory are not instructions!
+
+They might be binary
+data representing
+
+numeric values, strings
+of characters, and so on.
+
+The CPU will read these values
+into its temporary registers
+
+when it needs to operate on them
+and write newly computed values
+
+back into memory.
+
+Mr. Blue is asking a
+good question: how do we
+
+know which words in
+memory are instructions
+
+and which are data?
+
+After all, they’re
+both binary values!
+
+The answer is that we can’t tell
+by looking at the values — it’s
+
+how they are used by the CPU
+that distinguishes instructions
+
+from data.
+
+If a value is loaded
+into the datapath,
+
+it’s being used as data.
+
+If a value is loaded
+by the control logic,
+
+it’s being used an instruction.
+
+So this is the digital
+system we’ll build to perform
+
+computations.
+
+We’ll start with a datapath
+that contains some number
+
+of registers to
+hold data values.
+
+We’ll be able to select which
+registers will supply operands
+
+for the arithmetic and
+logic unit that will perform
+
+an operation.
+
+The ALU produces a result
+and other status signals.
+
+The ALU result can
+be written back
+
+to one of the registers
+for later use.
+
+We’ll provide the datapath with
+means to move data to and from
+
+main memory.
+
+There will be a
+control unit that
+
+provides the necessary control
+signals to the datapath.
+
+In the example
+datapath shown here,
+
+the control unit would
+provide ASEL and BSEL
+
+to select two register
+values as operands
+
+and DEST to select
+the register where
+
+the ALU result will be written.
+
+If the datapath had, say,
+32 internal registers,
+
+ASEL, BSEL and DEST
+would be 5-bit values,
+
+each specifying a particular
+register number in the range
+
+0 to 31.
+
+The control unit also
+provides the FN function code
+
+that controls the operation
+performed by the ALU.
+
+The ALU we designed in
+Part 1 of the course
+
+requires a 6-bit
+function code to select
+
+between a variety of arithmetic,
+boolean and shift operations.
+
+The control unit would load
+values from main memory
+
+to be interpreted
+as instructions.
+
+The control unit
+contains a register,
+
+called the “program counter”,
+that keeps track of the address
+
+in main memory of the next
+instruction to be executed.
+
+The control unit also
+contains a (hopefully small)
+
+amount of logic to translate
+the instruction fields
+
+into the necessary
+control signals.
+
+Note the control unit
+receives status signals
+
+from the datapath that will
+enable programs to execute
+
+different sequences
+of instructions
+
+if, for example, a particular
+data value was zero.
+
+The datapath serves as the
+brawn of our digital system
+
+and is responsible for storing
+and manipulating data values.
+
+The control unit serves as
+the brain of our system,
+
+interpreting the program
+stored in main memory
+
+and generating the necessary
+sequence of control
+
+signals for the datapath.
+
+Instructions are the
+fundamental unit of work.
+
+They’re fetched by the control
+unit and executed one after
+
+another in the order
+they are fetched.
+
+Each instruction
+specifies the operation
+
+to be performed along
+with the registers
+
+to supply the source operands
+and destination register where
+
+the result will be stored.
+
+In a von Neumann machine,
+instruction execution
+
+involves the steps shown here:
+
+the instruction is
+loaded from the memory
+
+location whose address is
+specified by the program
+
+counter.
+
+When the requested data
+is returned by the memory,
+
+the instruction
+fields are converted
+
+to the appropriate control
+signals for the datapath,
+
+selecting the source operands
+from the specified registers,
+
+directing the ALU to perform
+the specified operation,
+
+and storing the result in the
+specified destination register.
+
+The final step in
+executing an instruction
+
+is updating the
+value of the program
+
+counter to be the address
+of the next instruction.
+
+This execution loop is
+performed again and again.
+
+Modern machines can execute
+up more than a billion
+
+instructions per second!
+
+The discussion so far
+has been a bit abstract.
+
+Now it’s time to roll up our
+sleeves and figure out what
+
+instructions we want
+our system to support.
+
+The specification of instruction
+fields and their meaning
+
+along with the details
+of the datapath design
+
+are collectively called the
+instruction set architecture
+
+(ISA) of the system.
+
+The ISA is a detailed functional
+specification of the operations
+
+and storage
+mechanisms and serves
+
+as a contract
+between the designers
+
+of the digital hardware
+and the programmers who
+
+will write the programs.
+
+Since the programs are stored
+in main memory and can hence be
+
+changed, we’ll
+call them software,
+
+to distinguish them from
+the digital logic which,
+
+once implemented,
+doesn’t change.
+
+It’s the combination of hardware
+and software that determine
+
+the behavior of our system.
+
+The ISA is a new
+layer of abstraction:
+
+we can write programs
+for the system
+
+without knowing
+the implementation
+
+details of the hardware.
+
+As hardware
+technology improves we
+
+can build faster systems without
+having to change the software.
+
+You can see here that over
+a fifteen year timespan,
+
+the hardware for executing
+the Intel x86 instruction set
+
+went from executing 300,000
+instructions per second
+
+to executing 5 billion
+instructions per second.
+
+Same software as before, we’ve
+just taken advantage of smaller
+
+and faster MOSFETs to build
+more complex circuits and faster
+
+execution engines.
+
+But a word of
+caution is in order!
+
+It’s tempting to make choices
+in the ISA that reflect
+
+the constraints of current
+technologies, e.g.,
+
+the number of
+internal registers,
+
+the width of the operands,
+or the maximum size of main
+
+memory.
+
+But it will be hard to change
+the ISA when technology
+
+improves since there’s a
+powerful economic incentive
+
+to ensure that old software
+can run on new machines,
+
+which means that a particular
+ISA can live for decades
+
+and span many generations
+of technology.
+
+If your ISA is successful,
+you’ll have to live with any
+
+bad choices you made
+for a very long time.
+
+Designing an ISA is hard!
+
+What are the operations
+that should be supported?
+
+How many internal registers?
+
+How much main memory?
+
+Should we design the
+instruction encoding
+
+to minimize program size or to
+keep the logic in the control
+
+unit as simple as possible?
+
+Looking into our
+crystal ball, what
+
+can we say about the computation
+and storage capabilities
+
+of future technologies?
+
+We’ll answer these questions by
+taking a quantitative approach.
+
+First we’ll choose a set
+of benchmark programs,
+
+chosen as representative of
+the many types of programs we
+
+expect to run on our system.
+
+So some of benchmark
+programs will
+
+perform scientific and
+engineering computations,
+
+some will manipulate
+large data sets
+
+or perform database
+operations, some
+
+will require specialized
+computations for graphics
+
+or communications, and so on.
+
+Happily, after many
+decades of computer use,
+
+several standardized
+benchmark suites
+
+are available for us to use.
+
+We’ll then implement the
+benchmark programs using
+
+our instruction set and simulate
+their execution on our proposed
+
+datapath.
+
+We’ll evaluate the results to
+measure how well the system
+
+performs.
+
+But what do we mean by “well”?
+
+That’s where it
+gets interesting:
+
+“well” could refer to execution
+speed, energy consumption,
+
+circuit size, system cost, etc.
+
+If you’re designing
+a smart watch,
+
+you’ll make different choices
+than if you’re designing
+
+a high-performance graphics
+card or a data-center server.
+
+Whatever metric you choose to
+evaluate your proposed system,
+
+there’s an important design
+principle we can follow:
+
+identify the common
+operations and focus on them
+
+as you optimize your design.
+
+For example, in
+general-purpose computing,
+
+almost all programs
+spend a lot of their time
+
+on simple arithmetic
+operations and accessing values
+
+in main memory.
+
+So those operations
+should be made as fast
+
+and energy efficient
+as possible.
+
+Now, let’s get to work designing
+our own instruction set
+
+and execution engine, a
+system we’ll call the Beta.
\ No newline at end of file
diff --git a/H44LyNdIi5E.txt b/H44LyNdIi5E.txt
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index 0000000000000000000000000000000000000000..65a66d1d7803896cf381a31687cc076c4e2f709a
--- /dev/null
+++ b/H44LyNdIi5E.txt
@@ -0,0 +1,3012 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK.
+
+Let's start.
+
+So for several
+lectures, we've been
+
+talking about the
+XY model, which
+
+is a collection of
+two component spins,
+
+for example defined
+on a square lattice,
+
+but it could be any
+type of lattice.
+
+And today we are going
+to compare and contrast
+
+that with the case of a solid.
+
+More specifically for
+simplicity, an isotropic solid.
+
+And a typical example of
+an isotropic solid in two
+
+dimension is the
+triangular lattice.
+
+So something like this.
+
+What both of these
+systems have in common
+
+is that there is an underlying
+continuous symmetry that
+
+is broken.
+
+In the case of the XY
+model, at low temperatures
+
+all of the spins would
+be pointing more or less
+
+in the same direction.
+
+Potentially with
+fluctuations, let's say, go
+
+around the direction
+where they're
+
+supposed to be
+pointing-- being, let's
+
+say, here in the
+vertical-- characterized
+
+by some kind of an angle.
+
+Let's call it theta.
+
+And essentially the uniform
+state at 0 temperature
+
+can be characterized
+by any theta.
+
+And because of the
+deformations, it's
+
+captured through these low
+energy Goldstone modes.
+
+And the probability of
+some particular deformation
+
+will be proportional at low
+temperature to the integral,
+
+let's say, in d
+dimensions of gradient,
+
+the change in theta within
+different spins squared.
+
+Of course, with some
+considerations as
+
+we discussed about topological
+defects, et cetera,
+
+being buried in
+this description.
+
+Now, similarly, away
+from 0 temperature
+
+the atoms of a solid
+will fluctuate around
+
+the position that
+corresponds to the minimum.
+
+And so the actual
+picture that you
+
+would see at any
+finite temperature
+
+would be distorted with respect
+to the perfect configuration
+
+and there would be some kind
+of a vector [INAUDIBLE] u
+
+at each location that would
+describe this fluctuation.
+
+Again, there is no cost in
+making a uniform distortion
+
+theta that is the
+same across space.
+
+And similarly here,
+there is no cost
+
+in uniformly translating things.
+
+So these would both imply that
+this row can [? continue ?]
+
+[INAUDIBLE] leads
+to Goldstone modes.
+
+And the corresponding
+energy cost
+
+in the case of the
+isotropically distorted system
+
+is typically returned
+as an integral involving
+
+elastic moduli, as we've seen.
+
+And the traditional
+way to write that
+
+is in this form where
+the same reason here
+
+that it wasn't theta
+that was appearing
+
+but gradient of theta,
+because a uniform theta
+
+does not make any cross.
+
+These strain fields are related
+derivatives of the distortion.
+
+But now we remember
+that this u is a vector
+
+and this strain field uij it
+was one half of the derivative
+
+of uj in the i direction
+derivative of ui
+
+in the j direction symmetrized.
+
+Actually, probably better
+to write this symmetrically
+
+as beta h equals
+to this quantity.
+
+And then the typical
+type of calculation
+
+that we did for the
+XY model was to go
+
+in terms of the independent
+spin wave modes.
+
+So we go to Fourier space.
+
+This becomes an integral
+ddq 2 pi to the d.
+
+The derivative here
+gave q squared.
+
+And then I had something like
+the Fourier transformed theta
+
+squared.
+
+Now I can also more
+clearly represent
+
+this in the Fourier description.
+
+I will get something like 1/2
+integral vdq 2 pi to the d.
+
+And a little bit of work
+shows that this form Fourier
+
+transforms to something
+that is proportional to mu.
+
+Again, it has to be
+proportionality to q squared
+
+because the energy
+should go to 0
+
+as q goes to 0 for very
+long wavelength modes.
+
+And so we'll have something
+like q squared mu tilde of q
+
+squared.
+
+This is a vector squared.
+
+u is a vector.
+
+q is a vector.
+
+And there is another component
+that gives you mu plus lambda.
+
+And consistent with
+rotational symmetry,
+
+we can have a term that is
+q dotted with u tilde of q,
+
+the whole thing squared.
+
+And again, you can
+reason that you
+
+can describe the isotropic
+system in terms of just two
+
+elastic moduli is that the
+only rotational invariant
+
+quantities are q squared,
+u squared, and q.u,
+
+that those are the only terms
+that you can [? find. ?]
+
+Now the next thing.
+
+Once you know this form, you
+can immediately say something
+
+about the fluctuations.
+
+So you say that expectation
+value of theta tilde q theta
+
+tilde q prime, if I assume
+that this is a Gaussian theory
+
+and these are the
+only fluctuations
+
+that I'm considering,
+the answer is
+
+going to be 2 pi to the d
+delta function q plus q prime.
+
+And then I will get a
+factor of 1 over kq squared.
+
+The corresponding thing here
+is a bit more complicated.
+
+Because as we said, this
+quantity u tilde is a vector.
+
+And I can look at the
+correlation between, say,
+
+the i-th component of
+that vector along mode
+
+q, the j-th component of
+that vector along mu 2 prime
+
+and ask what this is.
+
+And again, only the
+same values of q
+
+are coupled together, so we get
+the usual formula over here.
+
+If this term was the only
+term in the story, that
+
+is if we were dealing
+with vectors q and u that
+
+are orthogonal to
+each other, then we
+
+would just get the
+1 over q squared.
+
+And so there is actually
+a term that is like that.
+
+But because of this other
+term, there is the possibility
+
+that q and u are in the same
+direction, in which case,
+
+these two costs
+will add up and I
+
+will get something that
+is proportional to 2
+
+mu plus lambda.
+
+And so then I will get 2
+mu plus lambda q squared.
+
+And here I will have qi qj.
+
+This becomes q to the 4th.
+
+Let me make sure that I did
+not write this incorrectly.
+
+Yes, I did write it incorrectly.
+
+It turns out that there is a
+mu plus lambda out here too.
+
+But essentially there's
+just a small complication
+
+that we get because of the
+fact that you have a vector u.
+
+But overall the
+scaling is something
+
+that goes like 1 over q squared,
+which is characteristics
+
+of Goldstone modes here with
+additional vectorial things
+
+to worry about.
+
+Let me make sure I
+separate these two.
+
+Now one of the things that
+we have been concerned with
+
+is whether these fluctuations
+destroy long range order, so
+
+for long range order the
+information that we would like
+
+to have is that the
+entirety of the system
+
+is roughly pointing
+in the same direction,
+
+meaning that if I know
+that this beam here
+
+is pointed in the
+vertical direction,
+
+if I go very far away,
+it is still more or less
+
+pointed out-- pointing
+in the same direction.
+
+So for that, we could
+look, for example,
+
+as the degree which
+[? with ?] these two spins?
+
+Yes, question?
+
+AUDIENCE: [INAUDIBLE]
+q squared [INAUDIBLE]?
+
+PROFESSOR: This is 4.
+
+Is that what you're
+worried about?
+
+AUDIENCE: Yeah.
+
+It should be 2, I guess.
+
+PROFESSOR: No, because I have
+two powers of q out front.
+
+AUDIENCE: Right.
+
+PROFESSOR: So I
+think in the notes
+
+what I have is that
+I have actually
+
+written things this way.
+
+I put the factor of mu
+q squared out front.
+
+And then I had this
+as qi qj over q.
+
+And I think--
+
+AUDIENCE: [INAUDIBLE]
+q squared [INAUDIBLE]?
+
+PROFESSOR: q squared.
+
+Let me one more time check to
+make sure that that's not--
+
+actually there's a minus sign.
+
+All right.
+
+AUDIENCE: Wouldn't there
+be another factor of mu
+
+to compensate for
+the factoring out?
+
+PROFESSOR: Yeah.
+
+So let's check this in
+the following fashion.
+
+So I can look at modes
+where u and q are
+
+perpendicular to each other.
+
+When u and q are
+perpendicular to each other,
+
+I don't have this there.
+
+And so then what I should
+have is just a cost
+
+that is 1 over mu q squared.
+
+OK.
+
+So let's see if
+that comes about.
+
+What I can do is
+let's say imagine
+
+that I'm looking at a q that is
+oriented along the x direction.
+
+And I look at u's that
+are in the y direction.
+
+And I correlate two
+u's in the y direction.
+
+So I will definitely
+get a delta ij here.
+
+I would have a 1.
+
+Here I would get a
+factor of nothing,
+
+because this term is absent.
+
+The q's that I'm
+looking at don't
+
+have any component along the
+direction of u that I'm having.
+
+So this is absent
+and I will get a 1
+
+over mu q squared, which
+is consistent with that.
+
+Now let's look at the case
+where I look at u's that
+
+are aligned with the vector q.
+
+Let's say again in
+the x direction.
+
+Then, as far as the
+energy is concerned,
+
+both terms are
+present and the cost
+
+should be 2 mu plus lambda.
+
+So the answer that I
+should ultimately get
+
+should be 1 over
+2 mu plus lambda.
+
+So let's check.
+
+So here q squared-- and
+cancels with this q squared.
+
+All of the q's are in the
+direction of the indices
+
+that I'm looking at.
+
+So that cancels.
+
+This is 1.
+
+So I will get 1 minus mu plus
+lambda over 2 mu plus lambda.
+
+So then I will get 2 mu plus
+lambda minus mu minus lambda.
+
+So I will get a mu in
+front that cancels this.
+
+And I will be left with
+just the 2 mu plus lambda.
+
+So we've checked
+that this is correct.
+
+All right.
+
+So this is a proof, if
+you like, by induction.
+
+You knew that the only
+forms that are consistent
+
+are delta ij and qi
+qj over q squared.
+
+So we can give them two
+coefficients, a and b,
+
+and then adjust a and b so
+that these two limits that I
+
+considered are reproduced.
+
+So-- OK.
+
+I didn't have to
+resort to my notes
+
+if I was willing to spend
+the corresponding three
+
+minutes here.
+
+So going back here, in order
+to see the degree of alignment
+
+of the two spins that we have
+over here, what we need to do
+
+is to do is to look something
+like cosine of, say,
+
+theta at location x
+minus theta at location x
+
+prime, which is non
+other than the real part
+
+of the expectation value of
+e to the theta at location
+
+x minus theta at
+location x prime.
+
+And assuming that everything is
+governed by this Gaussian rate,
+
+the answer is going to obtain
+by computing this Gaussian
+
+as exponential of
+minus 1/2 the average
+
+of theta x minus
+theta x prime squared.
+
+So then my task is
+to replace theta x
+
+and theta x prime in terms of
+these theta tilde in Fourier
+
+space.
+
+And then this will give
+me some expectation
+
+that involves this average.
+
+And when I complete
+that, eventually I
+
+need to Fourier transform
+1 over q squared.
+
+And we've seen that the Fourier
+transform of the 1 over q
+
+squared is the
+Coulomb interaction.
+
+And so ultimately this becomes
+exponential of minus of 1
+
+over k.
+
+The Coulomb interaction
+as a function
+
+of x minus x prime with
+the appropriate cutoff
+
+included in this expression.
+
+And then the statement
+that we always make
+
+is that this entity
+at large distances,
+
+the Coulomb interaction saying
+three dimension, falls off as 1
+
+over separation.
+
+So in three dimensions,
+this at large distances
+
+goes to a constant 1
+over k is something that
+
+is proportional to temperature.
+
+So after doing
+enough temperature,
+
+this entity at large
+distances goes to a constant.
+
+So there is some knowledge
+about the correlation
+
+between these
+things that is left.
+
+Whereas in two
+dimensions and below,
+
+when I go to sufficiently
+large distances
+
+the Coulomb
+interaction diverges.
+
+This whole thing goes to
+0 and information is lost.
+
+So this is the in content
+that Goldstone modes
+
+destroy through long range order
+in two dimensions and below.
+
+Except that we saw
+that in two dimensions,
+
+because the Coulomb interaction
+grows logarithmically,
+
+this correlation
+fall off according
+
+to this description only as
+a power law with an exponent
+
+connected to k.
+
+And then the discussion
+that we had for the XY model
+
+was that at high
+temperatures you
+
+have exponential decay
+in two dimensions.
+
+At low temperature you
+have power law decay.
+
+Although there is no
+true long range order,
+
+there has to be a
+phase transition.
+
+And we saw that
+this transition was
+
+described by the unbinding
+of these topological defects.
+
+So we would like to state
+that something similar to that
+
+is going on over here.
+
+The only reason I
+went through this
+
+was to figure out what
+the analog of this entity
+
+should be in the
+case of the solid.
+
+So the analog of our theta is
+this vector u, the distortion.
+
+What should be the analog
+of e to the i theta?
+
+And the things that you should
+keep in mind is that theta,
+
+I can't really tell
+it's difference
+
+between theta and theta plus 2
+pi, theta of 4 pi, et cetera.
+
+So this e to the i
+theta captures that.
+
+If theta goes to theta
+plus a multiple of 2 pi, e
+
+to the i theta
+remains invariant.
+
+So it's a good
+measure of ordering.
+
+It's better than theta itself.
+
+So similarly, there's
+a better measure
+
+of deviation from
+perfect order here
+
+for the case of the lattice.
+
+You say, well, why
+should I worry about
+
+that since I can measure what
+u is from the perfect position?
+
+Well, my answer is
+this point here.
+
+Did it come from
+here or from there?
+
+Should you use for u this
+or should you use that?
+
+You don't know.
+
+So the u that you have the
+to use similar to the theta
+
+that you're using is
+somewhat arbitrary.
+
+And the arbitrariness of
+it is given by unit vectors
+
+along the original lattice.
+
+That is, u and any u that
+is increased or decreased
+
+by some lattice vector
+of the original lattice
+
+is the same thing.
+
+You can't take them apart
+in the same sense that theta
+
+and multiple of 2 pi you cannot.
+
+So then that suggest that I can
+construct some kind of an order
+
+parameter, I call it row
+G, which is like this.
+
+This e to i something.
+
+It's e to the iu
+but u is a vector.
+
+And what I do I multiple by a
+G, which is an inverse lattice
+
+vector.
+
+So G is an inverse
+lattice vector.
+
+And essentially the
+inverse lattice vectors
+
+are defined to have the property
+that when you multiply them
+
+with any of the original lattice
+vectors-- which are, let's say,
+
+parametrized by two
+integers, m and n--
+
+the answer is going to
+be some multiple of 2 pi.
+
+So you can see that
+irrespective of whether I choose
+
+u as distortion from one lattice
+position or any other lattice
+
+position that
+happens to be nearby,
+
+this measure is going to be
+giving you the same face.
+
+So in the same way as
+before for the spins where
+
+I asked whether spins
+at large distances
+
+are correlated long range,
+I can do the same thing here
+
+and define a long range
+correlations for a solid
+
+by looking at e to the iG dotted
+with, let's say, u at position
+
+x minus u at position x prime.
+
+And x and x prime are two
+points on the lattice.
+
+And again, the u's that I
+have are Gaussian distributed.
+
+So this I will
+complete the square.
+
+I will have
+exponential minus 1/2.
+
+Well, OK, let me be a little
+bit careful with this.
+
+I have G alpha G
+beta over 2 because I
+
+have two factors of G dot u.
+
+I will write them using
+Einstein's summation convention
+
+as G alpha times u alpha
+component times the u beta
+
+component.
+
+So once more what we
+can do is to then write
+
+these u's in terms of
+their Fourier vectors.
+
+So what I will have is
+exponential minus G alpha G
+
+beta over 2.
+
+I will need to
+integrate over q's.
+
+Because of these
+factors, I will get
+
+something like 2 minus 2
+cosine of qx minus x prime.
+
+So whenever you go to Fourier
+space, you will get e to the iq
+
+x minus e to the iq x prime.
+
+Different one for
+here with different q
+
+primes, but when you
+take the average,
+
+q prime is set to
+minus q so then you
+
+get this form as usual.
+
+And then I will have the average
+Fourier transform use, which
+
+is what I wrote over there.
+
+I will get a 1 over mu q square
+delta i delta alpha beta minus
+
+q alpha q beta q squared mu
+plus lambda over mu plus lambda.
+
+There is a little
+bit of subtlety here.
+
+So I will do something
+this is not quite kosher
+
+but gives me the right answer.
+
+Certainly I can take this
+G alpha a beta inside here.
+
+When it multiplies
+delta alpha beta,
+
+I will simply get G squared.
+
+I really G alpha G alpha.
+
+Sum over alpha.
+
+It will give me G squared.
+
+Here what I will
+get is a G dot q
+
+squared because I will have
+two Gq's divided by q squared.
+
+Ultimately I have to integrate
+over all values of q, including
+
+all angle values.
+
+So there will be, as far
+as the angle is concerned,
+
+something like a
+cosine squared here.
+
+And the rather
+unconventional thing to do
+
+is to angular
+averages that first
+
+and write this as
+G squared over 2.
+
+Once you do that,
+then essentially
+
+you can see that this structure
+just gives you a constant.
+
+And what you will need to
+do is the usual Fourier
+
+transformation of
+1 over q squared.
+
+So eventually you can
+see that the answer
+
+is going to be proportional
+to minus G squared.
+
+I will get a factor
+of 2 mu u from here.
+
+Once I have written this
+as G squared over 2,
+
+I will get 1 minus
+1/2 of this quantity.
+
+So that becomes 2
+mu plus lambda--
+
+or 4 mu plus lambda
+minus mu minus lambda.
+
+So I will get a 3 mu plus lambda
+divided by 2 2 mu plus lambda.
+
+And so there's a
+factor of 4 here.
+
+So that's just the numerics
+that goes out front.
+
+The key to the whole thing will
+be the usual integration of 1
+
+over q squared.
+
+Just as we had before, I will
+get again the same Coulomb
+
+interaction as a
+function of x minus x
+
+prime with appropriate
+lattice cut-off
+
+introduced so that
+the short distance
+
+behavior is controlled.
+
+This whole thing has a name.
+
+It's called a
+Debye-Waller factor.
+
+Well, almost.
+
+In 3D.
+
+And the point is
+that if I'm looking
+
+at this whole thing
+in three dimensions,
+
+at large enough separation
+this will go to a constant,
+
+just as we had before.
+
+And I will conclude
+that this entity, as I
+
+look at two points that are
+very far apart, at least that's
+
+sufficiently low temperature
+and all of my mus and lambdas
+
+are scaled inversely
+with temperature,
+
+so this whole thing is
+proportional to temperature.
+
+Essentially, you can see
+that this information
+
+at large distance goes
+to a finite constant,
+
+telling me that there's
+long range orders preserved.
+
+Again, when I go
+to two dimensions,
+
+you would say that this,
+at large distances,
+
+grows logarithmically.
+
+And so the correlations
+will fall off,
+
+but fall of as a power law.
+
+Now for the case
+of a solid, usually
+
+what you do in order to
+probe for the order is
+
+you shine x-rays and
+you see what comes out.
+
+So essentially, you
+will see that there
+
+will be some scattering.
+
+And the way that the wave
+vector of the light has changed
+
+is characterized by a vector q.
+
+And we discussed this already,
+that the structure factor
+
+s of q is going to be related to
+expectation value of the phase
+
+that you get from
+the different points.
+
+So I will get a factor
+of e to the i q.
+
+the location of the different
+atoms, let's call them r, of x.
+
+I have to do a sum over x.
+
+I have to scatter
+from all of the atoms.
+
+There's some overall form
+factor that if I'm not
+
+really interested,
+but this whole thing
+
+has to be first squished.
+
+So once I square this, I
+will be getting averages
+
+between pairs of points.
+
+Because of
+translational symmetry
+
+I can relate to that
+sum over pairs of points
+
+to a center of
+mass that typically
+
+would pick up the number
+of points that I have.
+
+And then the
+expectation value of e
+
+to the something like
+sum over all points, e
+
+to the i q.r r of x
+minus r of 0 average.
+
+This average I can
+certainly take out here.
+
+Yes?
+
+STUDENT: Sorry.
+
+Is r what you're
+calling u before?
+
+PROFESSOR: No.
+
+So r is the actual location of
+where the particle is location.
+
+So r, let's say for a particle
+that at zero temperature
+
+was sitting at lattice
+point-- that is,
+
+let's say, in two dimensions
+labeled by m and n--
+
+it is shifted by an
+amount that is u that I
+
+would assign to that point.
+
+So the r's that I put here are
+the actual physical position
+
+of the atom.
+
+Which is composed
+of where it was
+
+sitting at 0 temperature
+plus a little bit more.
+
+So when I do this, indeed I will
+get a sum over all positions.
+
+This could be a label mn,
+whatever, of e to the iq.
+
+The difference
+between the two r's
+
+would be, first of all, the
+difference between these two
+
+at 0 temperature, which
+would be some lattice
+
+vector of some variety.
+
+Let's call r 0 of x.
+
+And that quantity has
+[INAUDIBLE] fluctuations.
+
+The fluctuations go into e to
+the iq.u of x minus mu of 0.
+
+Now if I'm doing this at 0
+temperature or very close to 0
+
+temperature where this is either
+1 at 0 temperature or not too
+
+much fluctuating at
+high temperatures,
+
+I will essentially be
+adding a lot of e to iqr's.
+
+These are essentially phases.
+
+They can be positive, negative,
+all over the complex plane.
+
+And typically you would expect
+that for a randomly chosen q,
+
+the answer from adding all
+of these things will be 0.
+
+So the only time we're
+close to 0 temperature,
+
+you expect this to be
+something that is significant.
+
+Scattering is when q is one of
+these inverse lattice vectors.
+
+So if I was really doing this at
+0 temperature, this would be 1.
+
+And the answer that I
+would get is essentially
+
+I would get these delta
+function back peaks
+
+at the locations that correspond
+to the inverse lattice spacing.
+
+And that's presuming
+something that you have seen
+
+in crystallography or whatever.
+
+You take a solid and you
+scatter light from it
+
+and you will back points.
+
+So what I expect
+is that when I have
+
+a q that is roughly close to
+G but not necessarily sitting
+
+exactly at that point,
+what I would get
+
+is a scattering that these
+proportional to an integral
+
+over the entire
+lattice of something
+
+like how far I am away
+from the right position.
+
+And I should really write this
+as a sum over lattice points,
+
+but I can approximate
+this by an integral.
+
+The integral again has the
+property that it will give me 0
+
+unless q is exactly
+sitting at G.
+
+And then for here, I
+evaluate this quantity
+
+when q is close to
+G according to what
+
+I have calculated up there.
+
+So I will get
+exponential of minus G
+
+squared-- What do I have?
+
+Over 4 mu, three mu plus
+lambda, 2 mu plus lambda.
+
+The Coulomb interaction
+as a function of x.
+
+Yes?
+
+STUDENT: Are you missing
+an overall factor of m?
+
+PROFESSOR: That's why I
+wrote the proportionality.
+
+Because what I'm really
+interested is what you see.
+
+And what you see is how things
+are varying as a function of q.
+
+So I'll tell you
+what the answer is.
+
+So you do the Fourier
+transform from this.
+
+And in d equals to 3, what
+you find at 0 temperature,
+
+as we said, you
+will get Bragg spots
+
+at the locations of
+G's that correspond
+
+to the inverse lattice vectors,
+which actually themselves
+
+form a lattice.
+
+So this is essentially
+the space of q.
+
+And these are the
+different values of G.
+
+Now what happens is that
+the strength of each one
+
+of these delta functions
+is then modulated
+
+by this factor evaluated
+at the corresponding G.
+
+And since it is
+proportional to G squared,
+
+you find that the spots
+that are close to the origin
+
+are well defined.
+
+As you go further and further
+away, the become very weaker.
+
+And at some point you
+cease to see them.
+
+So that's the-- the
+Debye-Waller factor
+
+describes how these
+things vanish as you
+
+go further and further away.
+
+And essentially, you find
+that they go and diminish
+
+as e to the minus G squared.
+
+But clearly, this kind of
+scattering from a crystal
+
+is very different
+from the scattering
+
+that you expect from
+an liquid, which
+
+is essentially you will have
+a bright spot at q close to 0
+
+and things that would
+symmetrically fall off,
+
+maybe with a couple
+of oscillations
+
+due to the size of the
+particles, at cetera.
+
+Now what happens in d equals
+to 2 is kind of interesting.
+
+Because in d equals
+to 2, I'm doing a two
+
+dimensional integral,
+and this thing
+
+is growing as a power law.
+
+So basically what
+I end up having
+
+to deal with is something
+like e to the i q minus G x.
+
+And something that falls off
+as a over x to some power
+
+that I will simply cause eta G.
+So related to that combination.
+
+And when you
+integrate this, just
+
+dimensionally you
+can see that it
+
+is an integral that scales as
+x to the power of 2 minus eta.
+
+x is inverse to q minus G. So
+this is going to scale as 1
+
+over q minus g to the
+power of 2 minus eta.
+
+So as you go along some
+particular direction
+
+and ask what you see,
+you find that will
+
+see peaks close to the locations
+of the lattice vectors.
+
+So let's say they are equally
+spaced along the particular
+
+axis that I'm picking.
+
+In three dimension, you would
+have been seeing delta function
+
+at each one of these positions
+whose strength is governed
+
+by this Debye-Waller factor.
+
+In two dimensions,
+you will essentially
+
+see power laws close
+to each one of them.
+
+But as you go further, the
+exponent of the power law
+
+changes.
+
+So at some point you even
+cease to have a divergence.
+
+But you can essentially
+ignore anything
+
+like that [? happening. ?]
+
+So you can see that because
+we don't have true long range
+
+order into two
+dimensions because
+
+of these logarithmic
+divergences,
+
+et cetera, the
+traditional picture
+
+that we have of a solid that
+is characterized by Bragg
+
+scattering and delta
+function peaks is modified,
+
+but still it is
+something that looks
+
+very different from the liquid.
+
+So we expect that as
+we raise temperature
+
+there is a phase transition
+between scattering
+
+of this form and something
+that looks like liquid.
+
+And you can roughly
+guess that essentially it
+
+is going to be related
+with these etas becoming
+
+larger and larger so that
+these divergences disappear.
+
+But what is the mechanism?
+
+So let's go back and see what
+the mechanism was that we
+
+discovered for the XY model.
+
+So we are going to look at
+d equals to 2 from now on.
+
+That discussion so
+far was general.
+
+In d equals to 2, we said that
+we have topological defect.
+
+And the story here was that,
+as I have been discussing,
+
+the angle is
+undefined up to 2 pi.
+
+So it would configuration of
+angles that kind of radiate
+
+away from the origin.
+
+And the idea was that
+if I take a circuit
+
+and integrate around
+this circuit--
+
+let's call this the s gradient
+of theta-- the answer does not
+
+need to come back to 0.
+
+It will be some
+multiple of 2 pi .
+
+Some integer multiple.
+
+And similarly here, we
+said that the value of u
+
+is undefined up to
+a lattice spacing.
+
+That leads to topological
+defects, which
+
+I find it very difficult to
+draw for the triangular lattice,
+
+so I'll draw it for
+the square lattice.
+
+So at each one of
+these positions
+
+there's a particle sitting.
+
+And you look out here.
+
+You have a perfect
+square lattice.
+
+You look out here.
+
+You have a perfect
+square lattice.
+
+But clearly it is not a
+perfect square lattice.
+
+And the analog of the
+circuit that I drew over here
+
+that encloses a
+singlularty-- there's clearly
+
+some kind of a defect
+sitting over here--
+
+is that I can start with
+some point on the lattice
+
+and perform what is
+called a Burgers Circuit.
+
+What Burgers Circuit
+is is some walk
+
+that you would take
+on a lattice, which
+
+in a perfect lattice
+would bring you back
+
+to your starting point.
+
+So for example-- that was
+not a good starting point.
+
+Let me start from here.
+
+Let's say I take four steps
+up-- one, two, three, four.
+
+I take five steps to the right.
+
+One, two, three, four, five.
+
+I reverse my four steps.
+
+So I go four steps down.
+
+One, two, three, four.
+
+I reverse my five steps
+and I go five steps left.
+
+One, two, three, four, five.
+
+And you see that I did
+not end up where I was.
+
+I ended up here.
+
+And a failure to
+close my circuit
+
+has to be a lattice vector.
+
+And this is called d and
+it's called a Burgers Vector
+
+that characterize this defect,
+which is called a dislocation.
+
+So the uncertainty that I have
+in assigning a value for u
+
+because of being on a lattice
+or deforming a lattice
+
+gives rise to these
+kinds of ambiguity
+
+that are similar to
+the topological defects
+
+that you had over here.
+
+Whereas the defects here were
+characterized by an integer,
+
+the defects here
+are characterized
+
+by a lattice vector.
+
+And here the simplest things
+were, say, plus or minus.
+
+Clearly here on
+the square lattice
+
+the simplest things are plus b,
+minus b along the x direction
+
+and plus b minus b
+along the y direction.
+
+For example, on the
+triangular lattice
+
+it would be plus minus at
+any of the three directions
+
+that would define the lattice.
+
+So calculating the distortion
+field here was actually
+
+an easy matter because we said
+that the gradient of theta
+
+was something like 1 over r.
+
+And so the gradient of
+theta, which was 1 over r,
+
+I could in fact write--
+we saw as vector
+
+that is orthogonal to the vector
+that is going out of the plane.
+
+So we call that a z hat.
+
+It was also orthogonal to
+the direction of motion
+
+away from the defect,
+which we could characterize
+
+by looking at the gradient.
+
+The gradient vector
+for this distortion
+
+is clearly in the
+radial direction.
+
+And the answer that we
+had here for one defect
+
+was ni log of r minus ri.
+
+And since I'm taking the
+gradient it doesn't matter.
+
+I can't put or not
+put the cut off.
+
+And if I had multiple ones,
+I would simply sum over it.
+
+So this was the contribution
+to the distortion
+
+that came from a collection
+of defects such as this.
+
+Now you can see that essentially
+in some continuum sense,
+
+all I'm doing here is similar.
+
+I can be taking a big circuit.
+
+And as I go along
+that big circuit,
+
+I can take a gradient--
+So let's-- yeah.
+
+The s.
+
+gradient of the
+distortion field.
+
+Distortion field is,
+of course, a vector.
+
+So it has components that I
+can write as the x component
+
+or the y component.
+
+So this alpha could be the x
+component of the distortion
+
+or the y component
+of the distortion.
+
+And once I complete the circuit,
+here the answer was 2 pi n.
+
+Here the answer is
+a lattice vector,
+
+which is this Burgers Vector
+that could be in any direction
+
+that you want.
+
+Now as far as
+mathematics is concerned,
+
+this line and this line for each
+component are exactly the same.
+
+So the solution that I can
+write for gradient of u
+
+I can just copy from
+here for each component.
+
+So I can write that
+gradient of the u that
+
+is due to a collection
+of dislocations
+
+is something like z
+hat crossed with curl
+
+of a sum over all of
+the potential locations
+
+off my defect.
+
+Rather than n, I have b over 2.
+
+And it's a vector log of
+minus ri over [INAUDIBLE].
+
+So if I have a collection
+of these dislocations
+
+at different places on my
+lattice-- locations ri,
+
+strengths, b alpha
+which is a vector--
+
+then the distortion field
+that they would generate
+
+is given by this.
+
+It's very just following the
+answers that the [INAUDIBLE].
+
+So then what we did for the
+case of the overall system--
+
+in order to find how the
+different topological defects
+
+interact with each
+was to calculate
+
+beta h, which was an integral
+of gradient of theta squared.
+
+Yes?
+
+STUDENT: So the b alpha, you
+have an index i [? also? ?]
+
+PROFESSOR: b alpha
+have index i also.
+
+Like like the ni have index i.
+
+So maybe I write
+it in this fashion.
+
+Yeah.
+
+So this is the cost that
+we have to evaluate,
+
+except that we
+have to be somewhat
+
+careful with the meaning
+of this gradient of theta
+
+in that the gradient
+of theta, as we said,
+
+has a contribution that
+is from regular spin
+
+waves, the Goldstone modes,
+that can be deformed back
+
+to everybody pointing
+in the same direction
+
+without topological defect.
+
+Plus a contribution due to this
+topological defect that are
+
+categorized in that case by ni.
+
+Now similarly here for
+the case of the solid,
+
+we have the beta h.
+
+Slightly more complicated
+integral d 2x.
+
+We have mu uij uij plus
+lambda over 2 uii ujj.
+
+And what we can do is to
+say that our strain field
+
+uij has a component that
+is like the Goldstone modes
+
+that we have been
+calculating so far,
+
+essentially treating
+everything as Gaussians.
+
+Except that I will
+write it as phi ij.
+
+And then a part that would come
+from the distortion field u
+
+bar that I calculated.
+
+So I take that distortion field
+and then take derivatives of it
+
+to symmetrize
+appropriately to construct
+
+the strain that sums from them.
+
+So we substituted
+this form over here.
+
+And we found that beta h that we
+got had a part that was simply
+
+relate to the Goldstone modes.
+
+This was the part that could
+be treating as a Gaussian.
+
+And then we had a
+part that corresponded
+
+to the interactions
+among these defects.
+
+And that part we saw
+had the character
+
+of charges ni and
+nj plus minus 1
+
+characterizing these
+topological defects
+
+having a Coulomb interaction
+[? between them ?].
+
+And then, of course,
+this i less than j,
+
+we had to worry about what
+was happening when i was j.
+
+And that we considered
+to be the contributions
+
+of the core energy that,
+once exponentiated,
+
+we described as y.
+
+So it's beta h which is log
+of that would be log of y.
+
+And actually this k bar, by
+the way, was simply 2 pi k.
+
+And it was 2 pi k because each
+one of these charges is 2 pi n.
+
+So there's 2 pi 2 pi.
+
+But the Coulomb
+interaction really
+
+should be log divided by 2 pi.
+
+And so k bar becomes
+2 pi k times this.
+
+So I can do the same
+thing over here.
+
+And what I find happens is
+that my beta h gets decomposed
+
+as follows.
+
+There will be a part that is
+simply the original expression
+
+now for the field
+that is well behaved
+
+and has no dislocation piece.
+
+And then you
+wouldn't be surprised
+
+because this structure
+is no different
+
+from the other structure.
+
+There's essentially a
+gradient of this distortion
+
+field squared.
+
+And you can see that if I
+take a second derivative
+
+of this distortion field or one
+derivative of this, effectively
+
+I will have two
+derivatives of a log, which
+
+will give me a delta function.
+
+So essentially these
+things do behave
+
+like what you would get from
+Coulomb type of potential.
+
+[INAUDIBLE] plus [INAUDIBLE]
+if the potential is 0.
+
+So not surprisingly, I
+we get a minus k bar sum
+
+over pairs of where these
+dislocations are located.
+
+And then I will have b at
+location i, b at location j.
+
+And then I would have a log of
+ri minus rj with some cut off.
+
+Except that these b's
+are actually vector.
+
+So this term is a dot
+product of the two b's.
+
+And it turns out that when
+you go through the algebra,
+
+there is another
+term, which is bi.
+
+ri minus rj, bj dotted
+with ri minus rj
+
+divided by ri minus rj squared.
+
+So the charges that we
+had in our original theory
+
+were scalar quantities.
+
+These defects were characterized
+by a scalar value of n.
+
+And they were interacting
+with something
+
+that was like the ordinary
+Coulomb potential.
+
+Whereas now we are
+looking at a system
+
+that is characterized by
+charges that are vectors.
+
+And it turns out that
+what we have here
+
+is the vectorial analog
+of the Coulomb potential.
+
+And again, if you think about
+an isotropic system and vectors,
+
+this is a vector
+that you can form,
+
+but b.r is another
+vector that you can form.
+
+And so both of them do appear.
+
+And once you go through
+the whole algebra
+
+and through the inverse
+Fourier transform, et cetera,
+
+you get this
+additional contribution
+
+to this vector
+Coulomb interaction.
+
+That's really is
+the only difference.
+
+And of course,
+you will again get
+
+a sum over all locations
+of the core energies
+
+for creating these defects.
+
+And the value of k bar here
+is related to these parameters
+
+by mu mu plus lambda divided
+by pi 2u plus lambda.
+
+So this combination
+controls what you have.
+
+So the next thing
+that we did was
+
+to construct a perturbation.
+
+We essentially said that if
+I have these pairs of charges
+
+that can spontaneously
+appear at an energy
+
+cost but an entropy gain,
+they will effectively weaken
+
+the overall Coulomb potential.
+
+For example, if I
+have to test charges
+
+then there will be
+some polarization
+
+of the medium,
+some reorientation
+
+of these charges that
+appear, that weakens
+
+the effective charge here.
+
+And we could
+perturbatively calculate
+
+what the correction
+was, except that we
+
+found that that
+correction, which
+
+involves an integration over
+the separation of these things.
+
+There was an integration
+that was potentially
+
+divergent for us no matter
+how small we made the core
+
+energies here.
+
+And so what we did was
+eventually to construct an RG.
+
+And the RG was that the
+value of this parameter k
+
+bar-- actually more
+usefully its inverse that
+
+is related to
+temperature-- changed
+
+as a function of integrating
+out short distance
+
+degrees of freedom.
+
+It was something like 4 pi--
+I think it was 4 pi cubed,
+
+it doesn't matter-- y squared.
+
+And that the scaling
+of to core energy
+
+itself was determined
+by 2 minus pi k,
+
+which in terms of this k
+bar becomes 2 minus k bar
+
+over 2 times y.
+
+And we can do exactly
+the same thing over here,
+
+except for the
+complication of having
+
+to deal with the charges
+that are vectorial.
+
+And you get that the strength
+of the Coulomb interaction,
+
+it's inverse that is
+related temperature
+
+gets re-normalized by
+exactly the same process.
+
+That is, there will be
+charges that will appear.
+
+All the mathematics you
+can see is clearly similar.
+
+And there will be a
+reduction, which then you
+
+can think of as an increase
+in temperature, which will
+
+be proportional to y squared.
+
+I don't know what the constant
+of proportionality is.
+
+And that dy by dl--
+so essentially I
+
+focus on the simplest
+type of dislocations
+
+that I would have
+of unit spacing--
+
+has exactly the
+same [INAUDIBLE],
+
+2 minus k bar over 2 y.
+
+It turns out that there
+is actually a difference.
+
+And the difference
+is as follows.
+
+That while we did not
+calculate the next correction
+
+in this series, I said
+that this correction came
+
+from essentially what
+would a single dipole do,
+
+which would be some contribution
+that is order of y squared.
+
+And I expect that there
+will be correction
+
+if I look at a configuration
+that has pairs of dipoles.
+
+And this will change
+this by order of y
+
+to the fourth and this
+by order of y cubed.
+
+Whereas if I look at something
+like a triangular lattice,
+
+you can see that if I have
+two dislocations out there
+
+as test dislocations
+pointing out
+
+in opposite
+directions, which would
+
+have some kind of a
+interaction such as this.
+
+And I ask how that
+interaction is
+
+modified by the presence
+of dipoles of dislocation
+
+in the medium.
+
+I could put a pair
+of dislocations
+
+integrate over the
+separation between them.
+
+I will get, essentially,
+the same type
+
+of mathematical structure that
+would ultimately give me this.
+
+But then the next order
+term in this series
+
+is not for
+dislocations because I
+
+can have a neutral configuration
+of three dislocations,
+
+such as this.
+
+And so once you
+do that, you will
+
+find that the next
+correction here
+
+is order of y cubed and
+order of y squared here.
+
+But generically, both of
+them have a phase diagram
+
+for RG flows that involves
+the inverse of the interaction
+
+of these charges.
+
+That is a
+temperature-like quantity.
+
+And there is a critical value
+of that inverse, which is 1/4.
+
+And what happens is that--
+let's see, this other axis is y.
+
+Anything smaller than
+1/4 y tends to go to 0.
+
+Anything larger, y
+tends to get larger.
+
+And there is going to be
+some kind of a separatrix
+
+that he describes the transition
+between flows that go down here
+
+and the flows that go away.
+
+And presumably, as I heat up my
+original system-- my lattice,
+
+different types of lattices--
+at low temperature,
+
+I can figure out what this
+combination of mu an lambda is.
+
+That gives me some value of k.
+
+And there is some kind of the
+core energy for the vertices
+
+that I can calculate.
+
+So there will be some point
+in this phase diagram, which
+
+at low enough temperature I will
+go over here, which corresponds
+
+to a system that has an
+effective logarithmic
+
+interaction between
+dislocations.
+
+As I change the temperature,
+I will proceed around
+
+some trajectory such as this
+because everything will change.
+
+And presumably, at some
+point I will intersect this
+
+and I will go to
+the other phase.
+
+Now the characteristic
+of the other phase
+
+was that this parameter
+k was going to 0.
+
+It was essentially the
+logarithmic interaction
+
+was disappeared.
+
+And you can see that that
+parameter k going to 0
+
+means that mu, the shear
+modulus, has to go to 0.
+
+So basically this phase out
+here is definitely characterized
+
+by 0 shear modulus.
+
+So again, the two
+parameters mu and lambda, mu
+
+is the one that
+gives you the cost
+
+of trying to shear in a system.
+
+And essentially the presence
+of the resistance to shear
+
+is what defines a solid for you.
+
+So this is a solid to something
+that does not have rigidity
+
+transition.
+
+It turns out that there
+is one subtlety here.
+
+I don't know whether it's
+good to mention or not.
+
+But so in the case of alpha
+this superfluidity, for example,
+
+we said that this
+coupling strength as you
+
+approach the transition
+rose to a universal value.
+
+In these units it will be 4.
+
+But that it approaches
+that universal value
+
+with a logarithmic singularity.
+
+Sorry, with a square
+root singularly.
+
+Sorry.
+
+And we saw that this was
+experimentally observed
+
+in films of superfluid film.
+
+I also said that
+on the other side
+
+you have a finite correlations.
+
+The correlations will be
+decaying exponentially.
+
+And this correlation length has
+this very unusual signature,
+
+which is that it diverged as
+a square root of t minus tc
+
+in the exponent.
+
+It was giving rise to these
+essentially singularities.
+
+While everything kind of looks
+identical between this RG
+
+and the other RG, it
+turns out that once you
+
+keep track of these corrections,
+these corrections actually
+
+are important.
+
+And for the vectorial
+version of the Coulomb gas,
+
+you find that they shear modulus
+that is finite in this phase
+
+reaches its final
+value, which is not
+
+universal because the
+thing that the universal is
+
+that combination that
+involves both mu and lambda.
+
+But rather than stc
+minus t to the 1/2,
+
+stc minus t to
+some exponent that
+
+is called mu bar, which
+is 0.36963 [INAUDIBLE].
+
+So this is a kind
+of subtle thing
+
+that is buried in these
+recursion relationships
+
+once you go to a higher order.
+
+And accompanying that is
+a correlation length that
+
+also diverges with some behavior
+dominated by the same exponent.
+
+So once people understood
+the original [? Koster ?]
+
+[INAUDIBLE]
+transition, it was kind
+
+of a very natural
+next step for them
+
+to think about these
+locations in a two dimensional
+
+solid and say that
+in the same manner
+
+that the unbinding
+of these defects
+
+got rid of the residual
+long range order that
+
+was left in the XY model.
+
+That this kind of
+ordering that we said
+
+exists for the two
+dimensional solid,
+
+this appears as a result of
+unbinding of dislocations
+
+and you get a liquid.
+
+Turns out that
+that's not correct.
+
+And it was pointed
+out by Bert Halperin
+
+I think that if you
+look at a solid,
+
+there's two things that you.
+
+You have the
+translational order,
+
+but there's also
+orientational order.
+
+That is, you can
+look, for example,
+
+at a collection of
+spins here and the bonds
+
+are pointing along
+the x and y directions
+
+and you can look down here
+and the bonds are pointing
+
+in the x and y directions.
+
+And from the picture
+that I drew over here,
+
+you can kind of see that once
+I insert this dislocation which
+
+corresponds to an
+additional line,
+
+the positions here
+are distorted.
+
+Once I have many
+of these inserted,
+
+it is kind of
+obvious that I will
+
+lose any idea of how the
+position of this lattice point
+
+and something out
+there is related.
+
+It's not so obvious
+that inserting
+
+lots and lots of
+these lines will
+
+remove the knowledge
+that I have about
+
+the orientation of the bonds.
+
+And the insight that
+we will follow up--
+
+and maybe it's probably a
+good idea to do it next time--
+
+is that actually once
+the dislocations unbind,
+
+we will lose this
+kind of ordering.
+
+If I do this in two
+dimensions, these
+
+are power law decays
+at low temperatures.
+
+Once the dislocations
+unbind, this
+
+becomes an exponential
+decay, as I would expect.
+
+But I can also define locally
+some kind of an orientation.
+
+Let's again call it theta.
+
+But theta is, let's say, the
+orientation of the bond that
+
+connects two neighboring spins.
+
+Now what I can do is to look at
+the correlation of orientations
+
+at different positions.
+
+And it turns out that
+if I'm doing something
+
+like a triangular lattice,
+I can't just pick the angle
+
+and correlate the angle from
+one point to another point
+
+because let's say on the square
+lattice the angle itself,
+
+I don't know whether
+it was coming
+
+from a bond that was
+originally in the x direction
+
+or in the y direction.
+
+So this is unknown up to
+a factor of 90 degrees.
+
+In the triangular lattice
+it is an unknown up
+
+to a factor of 60 degrees.
+
+So what I should do is I should
+define e to the 6 i theta
+
+at each location as a measure
+of the orientational order.
+
+You can see that, again,
+if I'm at 0 temperature,
+
+I can reorient the lattice
+any way that I like.
+
+This phase would be the same
+across the entire system.
+
+So what I'm interested
+is to find out
+
+what is the expectation
+value of this object when
+
+I look at points that
+are further apart.
+
+And again, clearly if
+I'm at 0 temperature
+
+these thetas are the same.
+
+This will go to 1 at
+finite temperature.
+
+Because of the fluctuations
+it will start to move a bit.
+
+And what we can show-- and
+you will do it next time--
+
+is that as long as you are
+in the 0 temperature phase
+
+you will find that this
+goes to a constant,
+
+even in two dimensions.
+
+But once the dislocations
+unbind, what we will show
+
+is that it doesn't
+decay exponentially,
+
+but then it starts to decay
+as 1 over x to some power,
+
+let's call it eta theta.
+
+And then at some
+higher temperatures,
+
+it eventually starts
+to decay exponentially.
+
+So there is the
+original solid in two
+
+dimension that we started
+that has true long range
+
+order in the orientations.
+
+And that is reflected
+in these Fourier
+
+transforms that we make.
+
+So we said that when we do
+the Fourier transform and look
+
+at the x-ray scattering,
+let's say from a two
+
+dimensional crystal, you were
+seeing these kinds of pictures.
+
+And then these were
+becoming weaker
+
+as we went further
+and further out.
+
+But now you can see that
+this picture clearly
+
+has a very, very defined
+orientational aspect to it.
+
+Now once we go to this
+intermediate phase,
+
+all of these peaks disappear.
+
+But what you find is that
+when you look at this, rather
+
+than getting a ring
+that is uniform,
+
+you will a see a ring that has
+very well- defined variation.
+
+One, two, three,
+four, five, six.
+
+Six-fold symmetry to it.
+
+So this phase has no
+knowledge of where
+
+the particles are located,
+but knows the orientations.
+
+It's a kind of a liquid crystal.
+
+It actually has a name.
+
+It's called hexatic.
+
+But it's one of the family of
+different types of materials
+
+that have no translational
+order but some kind
+
+of orientational order
+that are hexatics.
+
+So the transition between
+this hexatic phase
+
+to this fully disordered phase,
+it turns out in two dimension
+
+to be another one of
+these dislocation--
+
+well, topology defect
+unbinding transition.
+
+So maybe we will finish
+with that next time around.
\ No newline at end of file
diff --git a/HZFIdpThd-s.txt b/HZFIdpThd-s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7ad1407d6e37f1b5a2db109a57f7ba256e04d428
--- /dev/null
+++ b/HZFIdpThd-s.txt
@@ -0,0 +1,1523 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+many chemistry and biochemistry
+
+ align:start position:0%
+many chemistry and biochemistry
+ 
+
+ align:start position:0%
+many chemistry and biochemistry
+procedures will require you to perform a
+
+ align:start position:0%
+procedures will require you to perform a
+ 
+
+ align:start position:0%
+procedures will require you to perform a
+reaction at a specific pH to accomplish
+
+ align:start position:0%
+reaction at a specific pH to accomplish
+ 
+
+ align:start position:0%
+reaction at a specific pH to accomplish
+this task you must understand how to
+
+ align:start position:0%
+this task you must understand how to
+ 
+
+ align:start position:0%
+this task you must understand how to
+both make a buffer and how to use a pH
+
+ align:start position:0%
+both make a buffer and how to use a pH
+ 
+
+ align:start position:0%
+both make a buffer and how to use a pH
+meter this video will demonstrate two
+
+ align:start position:0%
+meter this video will demonstrate two
+ 
+
+ align:start position:0%
+meter this video will demonstrate two
+methods of buffer preparation as well as
+
+ align:start position:0%
+methods of buffer preparation as well as
+ 
+
+ align:start position:0%
+methods of buffer preparation as well as
+proper use of the pH meter a buffer is
+
+ align:start position:0%
+proper use of the pH meter a buffer is
+ 
+
+ align:start position:0%
+proper use of the pH meter a buffer is
+an ionic compound that resists changes
+
+ align:start position:0%
+an ionic compound that resists changes
+ 
+
+ align:start position:0%
+an ionic compound that resists changes
+to its pH when strong acids or bases are
+
+ align:start position:0%
+to its pH when strong acids or bases are
+ 
+
+ align:start position:0%
+to its pH when strong acids or bases are
+added to it the amount of strong acid or
+
+ align:start position:0%
+added to it the amount of strong acid or
+ 
+
+ align:start position:0%
+added to it the amount of strong acid or
+strong base that can be neutralized by a
+
+ align:start position:0%
+strong base that can be neutralized by a
+ 
+
+ align:start position:0%
+strong base that can be neutralized by a
+particular buffer is dictated by the
+
+ align:start position:0%
+particular buffer is dictated by the
+ 
+
+ align:start position:0%
+particular buffer is dictated by the
+buffers capacity which is determined by
+
+ align:start position:0%
+buffers capacity which is determined by
+ 
+
+ align:start position:0%
+buffers capacity which is determined by
+the concentration of weak acid and weak
+
+ align:start position:0%
+the concentration of weak acid and weak
+ 
+
+ align:start position:0%
+the concentration of weak acid and weak
+base in the buffer a higher
+
+ align:start position:0%
+base in the buffer a higher
+ 
+
+ align:start position:0%
+base in the buffer a higher
+concentration of buffering reagents
+
+ align:start position:0%
+concentration of buffering reagents
+ 
+
+ align:start position:0%
+concentration of buffering reagents
+translates into greater buffering
+
+ align:start position:0%
+translates into greater buffering
+ 
+
+ align:start position:0%
+translates into greater buffering
+capacity in the first part of this video
+
+ align:start position:0%
+capacity in the first part of this video
+ 
+
+ align:start position:0%
+capacity in the first part of this video
+we will walk through two methods of
+
+ align:start position:0%
+we will walk through two methods of
+ 
+
+ align:start position:0%
+we will walk through two methods of
+buffer preparation in the first example
+
+ align:start position:0%
+buffer preparation in the first example
+ 
+
+ align:start position:0%
+buffer preparation in the first example
+you will need to prepare one liter of a
+
+ align:start position:0%
+you will need to prepare one liter of a
+ 
+
+ align:start position:0%
+you will need to prepare one liter of a
+50 mil Imola buffer for a protein that
+
+ align:start position:0%
+50 mil Imola buffer for a protein that
+ 
+
+ align:start position:0%
+50 mil Imola buffer for a protein that
+is stable at pH 7.3 the first step is
+
+ align:start position:0%
+is stable at pH 7.3 the first step is
+ 
+
+ align:start position:0%
+is stable at pH 7.3 the first step is
+choosing an appropriate buffer system
+
+ align:start position:0%
+choosing an appropriate buffer system
+ 
+
+ align:start position:0%
+choosing an appropriate buffer system
+this buffer system should produce a
+
+ align:start position:0%
+this buffer system should produce a
+ 
+
+ align:start position:0%
+this buffer system should produce a
+stable pH in the range needed and should
+
+ align:start position:0%
+stable pH in the range needed and should
+ 
+
+ align:start position:0%
+stable pH in the range needed and should
+have a capacity large enough to
+
+ align:start position:0%
+have a capacity large enough to
+ 
+
+ align:start position:0%
+have a capacity large enough to
+accommodate your solutions the weak acid
+
+ align:start position:0%
+accommodate your solutions the weak acid
+ 
+
+ align:start position:0%
+accommodate your solutions the weak acid
+used for the system must have a PKA that
+
+ align:start position:0%
+used for the system must have a PKA that
+ 
+
+ align:start position:0%
+used for the system must have a PKA that
+is plus or minus one unit of the desired
+
+ align:start position:0%
+is plus or minus one unit of the desired
+ 
+
+ align:start position:0%
+is plus or minus one unit of the desired
+pH the closer the better
+
+ align:start position:0%
+pH the closer the better
+ 
+
+ align:start position:0%
+pH the closer the better
+from this abbreviated list of weak acids
+
+ align:start position:0%
+from this abbreviated list of weak acids
+ 
+
+ align:start position:0%
+from this abbreviated list of weak acids
+the phosphate ion with a pKa of 6.8 - is
+
+ align:start position:0%
+the phosphate ion with a pKa of 6.8 - is
+ 
+
+ align:start position:0%
+the phosphate ion with a pKa of 6.8 - is
+cruely the best choice for a buffer with
+
+ align:start position:0%
+cruely the best choice for a buffer with
+ 
+
+ align:start position:0%
+cruely the best choice for a buffer with
+a desired pH of seven point three bear
+
+ align:start position:0%
+a desired pH of seven point three bear
+ 
+
+ align:start position:0%
+a desired pH of seven point three bear
+for the weak acid used for this system
+
+ align:start position:0%
+for the weak acid used for this system
+ 
+
+ align:start position:0%
+for the weak acid used for this system
+is h2 pure four - and the conjugate base
+
+ align:start position:0%
+is h2 pure four - and the conjugate base
+ 
+
+ align:start position:0%
+is h2 pure four - and the conjugate base
+is hpo4 two - which correspond to the
+
+ align:start position:0%
+is hpo4 two - which correspond to the
+ 
+
+ align:start position:0%
+is hpo4 two - which correspond to the
+salts sodium phosphate mono basic and
+
+ align:start position:0%
+salts sodium phosphate mono basic and
+ 
+
+ align:start position:0%
+salts sodium phosphate mono basic and
+sodium phosphate dibasic after
+
+ align:start position:0%
+sodium phosphate dibasic after
+ 
+
+ align:start position:0%
+sodium phosphate dibasic after
+determining an appropriate buffer system
+
+ align:start position:0%
+determining an appropriate buffer system
+ 
+
+ align:start position:0%
+determining an appropriate buffer system
+the Henderson Hasselbach equation is
+
+ align:start position:0%
+the Henderson Hasselbach equation is
+ 
+
+ align:start position:0%
+the Henderson Hasselbach equation is
+used to calculate the ratio of acid to
+
+ align:start position:0%
+used to calculate the ratio of acid to
+ 
+
+ align:start position:0%
+used to calculate the ratio of acid to
+conjugate base needed at your desired pH
+
+ align:start position:0%
+conjugate base needed at your desired pH
+ 
+
+ align:start position:0%
+conjugate base needed at your desired pH
+if your desired pH of seven point three
+
+ align:start position:0%
+if your desired pH of seven point three
+ 
+
+ align:start position:0%
+if your desired pH of seven point three
+and the pKa of the phosphate ion are
+
+ align:start position:0%
+and the pKa of the phosphate ion are
+ 
+
+ align:start position:0%
+and the pKa of the phosphate ion are
+substituted into this equation then the
+
+ align:start position:0%
+substituted into this equation then the
+ 
+
+ align:start position:0%
+substituted into this equation then the
+ratio of con
+
+ align:start position:0%
+ratio of con
+ 
+
+ align:start position:0%
+ratio of con
+to get bass to acid is calculated to be
+
+ align:start position:0%
+to get bass to acid is calculated to be
+ 
+
+ align:start position:0%
+to get bass to acid is calculated to be
+1.6 therefore your buffer must contain
+
+ align:start position:0%
+1.6 therefore your buffer must contain
+ 
+
+ align:start position:0%
+1.6 therefore your buffer must contain
+1.6 times the amount of sodium phosphate
+
+ align:start position:0%
+1.6 times the amount of sodium phosphate
+ 
+
+ align:start position:0%
+1.6 times the amount of sodium phosphate
+dibasic to sodium phosphate mono basic
+
+ align:start position:0%
+dibasic to sodium phosphate mono basic
+ 
+
+ align:start position:0%
+dibasic to sodium phosphate mono basic
+after determining the appropriate ratio
+
+ align:start position:0%
+after determining the appropriate ratio
+ 
+
+ align:start position:0%
+after determining the appropriate ratio
+of conjugate base to acid the exact
+
+ align:start position:0%
+of conjugate base to acid the exact
+ 
+
+ align:start position:0%
+of conjugate base to acid the exact
+amount of each reagent is calculated in
+
+ align:start position:0%
+amount of each reagent is calculated in
+ 
+
+ align:start position:0%
+amount of each reagent is calculated in
+the following way because you are
+
+ align:start position:0%
+the following way because you are
+ 
+
+ align:start position:0%
+the following way because you are
+planning to make one liter of a 50 mil
+
+ align:start position:0%
+planning to make one liter of a 50 mil
+ 
+
+ align:start position:0%
+planning to make one liter of a 50 mil
+Imola phosphate buffer at pH 7.3 50
+
+ align:start position:0%
+Imola phosphate buffer at pH 7.3 50
+ 
+
+ align:start position:0%
+Imola phosphate buffer at pH 7.3 50
+millimolar is equal to the concentration
+
+ align:start position:0%
+millimolar is equal to the concentration
+ 
+
+ align:start position:0%
+millimolar is equal to the concentration
+of acid plus the concentration of
+
+ align:start position:0%
+of acid plus the concentration of
+ 
+
+ align:start position:0%
+of acid plus the concentration of
+conjugate base in addition you already
+
+ align:start position:0%
+conjugate base in addition you already
+ 
+
+ align:start position:0%
+conjugate base in addition you already
+know that the ratio of base to acid is
+
+ align:start position:0%
+know that the ratio of base to acid is
+ 
+
+ align:start position:0%
+know that the ratio of base to acid is
+1.6 so the concentration of base is
+
+ align:start position:0%
+1.6 so the concentration of base is
+ 
+
+ align:start position:0%
+1.6 so the concentration of base is
+equal to 1.6 times the concentration of
+
+ align:start position:0%
+equal to 1.6 times the concentration of
+ 
+
+ align:start position:0%
+equal to 1.6 times the concentration of
+acid by substituting equation 2 into
+
+ align:start position:0%
+acid by substituting equation 2 into
+ 
+
+ align:start position:0%
+acid by substituting equation 2 into
+equation 1 you can see that the
+
+ align:start position:0%
+equation 1 you can see that the
+ 
+
+ align:start position:0%
+equation 1 you can see that the
+concentration of acid plus 1.6 times the
+
+ align:start position:0%
+concentration of acid plus 1.6 times the
+ 
+
+ align:start position:0%
+concentration of acid plus 1.6 times the
+concentration of acid is equal to 50
+
+ align:start position:0%
+concentration of acid is equal to 50
+ 
+
+ align:start position:0%
+concentration of acid is equal to 50
+millimolar through manipulation of this
+
+ align:start position:0%
+millimolar through manipulation of this
+ 
+
+ align:start position:0%
+millimolar through manipulation of this
+equation the concentration of acid
+
+ align:start position:0%
+equation the concentration of acid
+ 
+
+ align:start position:0%
+equation the concentration of acid
+needed for this particular buffer is
+
+ align:start position:0%
+needed for this particular buffer is
+ 
+
+ align:start position:0%
+needed for this particular buffer is
+nineteen point two millimolar and the
+
+ align:start position:0%
+nineteen point two millimolar and the
+ 
+
+ align:start position:0%
+nineteen point two millimolar and the
+concentration of base is 30.8 millimolar
+
+ align:start position:0%
+concentration of base is 30.8 millimolar
+ 
+
+ align:start position:0%
+concentration of base is 30.8 millimolar
+which corresponds to 2.30 and four point
+
+ align:start position:0%
+which corresponds to 2.30 and four point
+ 
+
+ align:start position:0%
+which corresponds to 2.30 and four point
+three seven grams respectively for a one
+
+ align:start position:0%
+three seven grams respectively for a one
+ 
+
+ align:start position:0%
+three seven grams respectively for a one
+liter solution to make the buffer simply
+
+ align:start position:0%
+liter solution to make the buffer simply
+ 
+
+ align:start position:0%
+liter solution to make the buffer simply
+dissolve 2.30 grams of sodium phosphate
+
+ align:start position:0%
+dissolve 2.30 grams of sodium phosphate
+ 
+
+ align:start position:0%
+dissolve 2.30 grams of sodium phosphate
+mono basic and four point three seven
+
+ align:start position:0%
+mono basic and four point three seven
+ 
+
+ align:start position:0%
+mono basic and four point three seven
+grams of sodium phosphate dibasic in one
+
+ align:start position:0%
+grams of sodium phosphate dibasic in one
+ 
+
+ align:start position:0%
+grams of sodium phosphate dibasic in one
+liter of distilled water an alternative
+
+ align:start position:0%
+liter of distilled water an alternative
+ 
+
+ align:start position:0%
+liter of distilled water an alternative
+method of buffer preparation is simple
+
+ align:start position:0%
+method of buffer preparation is simple
+ 
+
+ align:start position:0%
+method of buffer preparation is simple
+accurate and requires much less math to
+
+ align:start position:0%
+accurate and requires much less math to
+ 
+
+ align:start position:0%
+accurate and requires much less math to
+demonstrate this second method we will
+
+ align:start position:0%
+demonstrate this second method we will
+ 
+
+ align:start position:0%
+demonstrate this second method we will
+prepare one liter of a 1.0 millimolar
+
+ align:start position:0%
+prepare one liter of a 1.0 millimolar
+ 
+
+ align:start position:0%
+prepare one liter of a 1.0 millimolar
+Tris buffer at pH seven point six zero
+
+ align:start position:0%
+Tris buffer at pH seven point six zero
+ 
+
+ align:start position:0%
+Tris buffer at pH seven point six zero
+the first step involves the
+
+ align:start position:0%
+the first step involves the
+ 
+
+ align:start position:0%
+the first step involves the
+determination of the amount of weak acid
+
+ align:start position:0%
+determination of the amount of weak acid
+ 
+
+ align:start position:0%
+determination of the amount of weak acid
+or in this example weak base needed in
+
+ align:start position:0%
+or in this example weak base needed in
+ 
+
+ align:start position:0%
+or in this example weak base needed in
+the system to make one liter of a 1.0
+
+ align:start position:0%
+the system to make one liter of a 1.0
+ 
+
+ align:start position:0%
+the system to make one liter of a 1.0
+millimolar Tris buffer 1.0 millimoles or
+
+ align:start position:0%
+millimolar Tris buffer 1.0 millimoles or
+ 
+
+ align:start position:0%
+millimolar Tris buffer 1.0 millimoles or
+121 milligrams of Tris are required at
+
+ align:start position:0%
+121 milligrams of Tris are required at
+ 
+
+ align:start position:0%
+121 milligrams of Tris are required at
+approximately 800 milliliters of
+
+ align:start position:0%
+approximately 800 milliliters of
+ 
+
+ align:start position:0%
+approximately 800 milliliters of
+distilled water as well as a stir bar to
+
+ align:start position:0%
+distilled water as well as a stir bar to
+ 
+
+ align:start position:0%
+distilled water as well as a stir bar to
+the beaker then weigh 121 milligrams of
+
+ align:start position:0%
+the beaker then weigh 121 milligrams of
+ 
+
+ align:start position:0%
+the beaker then weigh 121 milligrams of
+Tris and transfer it to a one liter
+
+ align:start position:0%
+Tris and transfer it to a one liter
+ 
+
+ align:start position:0%
+Tris and transfer it to a one liter
+beaker ensure that all of the material
+
+ align:start position:0%
+beaker ensure that all of the material
+ 
+
+ align:start position:0%
+beaker ensure that all of the material
+has been transferred by rinsing the way
+
+ align:start position:0%
+has been transferred by rinsing the way
+ 
+
+ align:start position:0%
+has been transferred by rinsing the way
+boat and transferring the rinses into
+
+ align:start position:0%
+boat and transferring the rinses into
+ 
+
+ align:start position:0%
+boat and transferring the rinses into
+the beaker while stirring monitor the pH
+
+ align:start position:0%
+the beaker while stirring monitor the pH
+ 
+
+ align:start position:0%
+the beaker while stirring monitor the pH
+of this solution and add a sodium
+
+ align:start position:0%
+of this solution and add a sodium
+ 
+
+ align:start position:0%
+of this solution and add a sodium
+hydroxide solution drop-wise until the
+
+ align:start position:0%
+hydroxide solution drop-wise until the
+ 
+
+ align:start position:0%
+hydroxide solution drop-wise until the
+pH is exactly seven point six zero the
+
+ align:start position:0%
+pH is exactly seven point six zero the
+ 
+
+ align:start position:0%
+pH is exactly seven point six zero the
+concentration of the sodium hydroxide
+
+ align:start position:0%
+concentration of the sodium hydroxide
+ 
+
+ align:start position:0%
+concentration of the sodium hydroxide
+solution doesn't really matter however a
+
+ align:start position:0%
+solution doesn't really matter however a
+ 
+
+ align:start position:0%
+solution doesn't really matter however a
+solution that is to dilute may require
+
+ align:start position:0%
+solution that is to dilute may require
+ 
+
+ align:start position:0%
+solution that is to dilute may require
+an excessive volume to be added to the
+
+ align:start position:0%
+an excessive volume to be added to the
+ 
+
+ align:start position:0%
+an excessive volume to be added to the
+buffer while a solution that is too
+
+ align:start position:0%
+buffer while a solution that is too
+ 
+
+ align:start position:0%
+buffer while a solution that is too
+concentrated may cause you to overshoot
+
+ align:start position:0%
+concentrated may cause you to overshoot
+ 
+
+ align:start position:0%
+concentrated may cause you to overshoot
+the desired pH if you do happen to
+
+ align:start position:0%
+the desired pH if you do happen to
+ 
+
+ align:start position:0%
+the desired pH if you do happen to
+exceed the desired pH then add a
+
+ align:start position:0%
+exceed the desired pH then add a
+ 
+
+ align:start position:0%
+exceed the desired pH then add a
+hydrochloric acid solution to bring the
+
+ align:start position:0%
+hydrochloric acid solution to bring the
+ 
+
+ align:start position:0%
+hydrochloric acid solution to bring the
+pH back down transfer this solution to a
+
+ align:start position:0%
+pH back down transfer this solution to a
+ 
+
+ align:start position:0%
+pH back down transfer this solution to a
+one liter volumetric flask wash the
+
+ align:start position:0%
+one liter volumetric flask wash the
+ 
+
+ align:start position:0%
+one liter volumetric flask wash the
+beaker with distilled water several
+
+ align:start position:0%
+beaker with distilled water several
+ 
+
+ align:start position:0%
+beaker with distilled water several
+times and add these washings to the
+
+ align:start position:0%
+times and add these washings to the
+ 
+
+ align:start position:0%
+times and add these washings to the
+volumetric flask dilute the buffer to
+
+ align:start position:0%
+volumetric flask dilute the buffer to
+ 
+
+ align:start position:0%
+volumetric flask dilute the buffer to
+the mark on the volumetric flask and mix
+
+ align:start position:0%
+the mark on the volumetric flask and mix
+ 
+
+ align:start position:0%
+the mark on the volumetric flask and mix
+the solution by inverting the flask
+
+ align:start position:0%
+the solution by inverting the flask
+ 
+
+ align:start position:0%
+the solution by inverting the flask
+several times for the second method of
+
+ align:start position:0%
+several times for the second method of
+ 
+
+ align:start position:0%
+several times for the second method of
+buffer preparation you needed a pH meter
+
+ align:start position:0%
+buffer preparation you needed a pH meter
+ 
+
+ align:start position:0%
+buffer preparation you needed a pH meter
+the final part of this video will
+
+ align:start position:0%
+the final part of this video will
+ 
+
+ align:start position:0%
+the final part of this video will
+discuss the proper use of this equipment
+
+ align:start position:0%
+discuss the proper use of this equipment
+ 
+
+ align:start position:0%
+discuss the proper use of this equipment
+a pH meter allows the determination of
+
+ align:start position:0%
+a pH meter allows the determination of
+ 
+
+ align:start position:0%
+a pH meter allows the determination of
+hydrogen ion activity by apetencio
+
+ align:start position:0%
+hydrogen ion activity by apetencio
+ 
+
+ align:start position:0%
+hydrogen ion activity by apetencio
+metric measurement using a glass
+
+ align:start position:0%
+metric measurement using a glass
+ 
+
+ align:start position:0%
+metric measurement using a glass
+electrode coaxial II joined to a silver
+
+ align:start position:0%
+electrode coaxial II joined to a silver
+ 
+
+ align:start position:0%
+electrode coaxial II joined to a silver
+silver chloride reference electrode when
+
+ align:start position:0%
+silver chloride reference electrode when
+ 
+
+ align:start position:0%
+silver chloride reference electrode when
+the probe is immersed in solution the
+
+ align:start position:0%
+the probe is immersed in solution the
+ 
+
+ align:start position:0%
+the probe is immersed in solution the
+reference electrode makes contact with
+
+ align:start position:0%
+reference electrode makes contact with
+ 
+
+ align:start position:0%
+reference electrode makes contact with
+the sample which completes the
+
+ align:start position:0%
+the sample which completes the
+ 
+
+ align:start position:0%
+the sample which completes the
+electrical contact between the reference
+
+ align:start position:0%
+electrical contact between the reference
+ 
+
+ align:start position:0%
+electrical contact between the reference
+electrode sample and pH electrode if the
+
+ align:start position:0%
+electrode sample and pH electrode if the
+ 
+
+ align:start position:0%
+electrode sample and pH electrode if the
+unknown solution has a different pH from
+
+ align:start position:0%
+unknown solution has a different pH from
+ 
+
+ align:start position:0%
+unknown solution has a different pH from
+the solution in the probe an electrical
+
+ align:start position:0%
+the solution in the probe an electrical
+ 
+
+ align:start position:0%
+the solution in the probe an electrical
+potential results which is registered on
+
+ align:start position:0%
+potential results which is registered on
+ 
+
+ align:start position:0%
+potential results which is registered on
+the meter this video will demonstrate
+
+ align:start position:0%
+the meter this video will demonstrate
+ 
+
+ align:start position:0%
+the meter this video will demonstrate
+the use of an orion SI 520 pH meter the
+
+ align:start position:0%
+the use of an orion SI 520 pH meter the
+ 
+
+ align:start position:0%
+the use of an orion SI 520 pH meter the
+important components of a pH meter
+
+ align:start position:0%
+important components of a pH meter
+ 
+
+ align:start position:0%
+important components of a pH meter
+include the display the probe and the
+
+ align:start position:0%
+include the display the probe and the
+ 
+
+ align:start position:0%
+include the display the probe and the
+electrode tip the electrode tip contains
+
+ align:start position:0%
+electrode tip the electrode tip contains
+ 
+
+ align:start position:0%
+electrode tip the electrode tip contains
+a fragile glass bulb be extremely
+
+ align:start position:0%
+a fragile glass bulb be extremely
+ 
+
+ align:start position:0%
+a fragile glass bulb be extremely
+careful not to hit the probe on the side
+
+ align:start position:0%
+careful not to hit the probe on the side
+ 
+
+ align:start position:0%
+careful not to hit the probe on the side
+of a beaker and when using stir bars to
+
+ align:start position:0%
+of a beaker and when using stir bars to
+ 
+
+ align:start position:0%
+of a beaker and when using stir bars to
+operate the pH meter first make sure
+
+ align:start position:0%
+operate the pH meter first make sure
+ 
+
+ align:start position:0%
+operate the pH meter first make sure
+that the electrode is connected to the
+
+ align:start position:0%
+that the electrode is connected to the
+ 
+
+ align:start position:0%
+that the electrode is connected to the
+meter then calibrate the pH meter the pH
+
+ align:start position:0%
+meter then calibrate the pH meter the pH
+ 
+
+ align:start position:0%
+meter then calibrate the pH meter the pH
+meter must be recalibrated every time
+
+ align:start position:0%
+meter must be recalibrated every time
+ 
+
+ align:start position:0%
+meter must be recalibrated every time
+you turn it on and after three to four
+
+ align:start position:0%
+you turn it on and after three to four
+ 
+
+ align:start position:0%
+you turn it on and after three to four
+hours of use we will
+
+ align:start position:0%
+hours of use we will
+ 
+
+ align:start position:0%
+hours of use we will
+perform a two-point calibration this
+
+ align:start position:0%
+perform a two-point calibration this
+ 
+
+ align:start position:0%
+perform a two-point calibration this
+method involves calibrating the pH meter
+
+ align:start position:0%
+method involves calibrating the pH meter
+ 
+
+ align:start position:0%
+method involves calibrating the pH meter
+with two different buffers of known pH
+
+ align:start position:0%
+with two different buffers of known pH
+ 
+
+ align:start position:0%
+with two different buffers of known pH
+turn on the instrument and select the pH
+
+ align:start position:0%
+turn on the instrument and select the pH
+ 
+
+ align:start position:0%
+turn on the instrument and select the pH
+mode as 0.1 or 0.1 then press the ISO
+
+ align:start position:0%
+mode as 0.1 or 0.1 then press the ISO
+ 
+
+ align:start position:0%
+mode as 0.1 or 0.1 then press the ISO
+button and verify that the pH reads
+
+ align:start position:0%
+button and verify that the pH reads
+ 
+
+ align:start position:0%
+button and verify that the pH reads
+seven point zero zero rinse off the
+
+ align:start position:0%
+seven point zero zero rinse off the
+ 
+
+ align:start position:0%
+seven point zero zero rinse off the
+probe with distilled water into a waste
+
+ align:start position:0%
+probe with distilled water into a waste
+ 
+
+ align:start position:0%
+probe with distilled water into a waste
+beaker and gently blot it with a kimwipe
+
+ align:start position:0%
+beaker and gently blot it with a kimwipe
+ 
+
+ align:start position:0%
+beaker and gently blot it with a kimwipe
+place the probe into the first buffer
+
+ align:start position:0%
+place the probe into the first buffer
+ 
+
+ align:start position:0%
+place the probe into the first buffer
+and press the Cal button the number one
+
+ align:start position:0%
+and press the Cal button the number one
+ 
+
+ align:start position:0%
+and press the Cal button the number one
+should appear on the display the display
+
+ align:start position:0%
+should appear on the display the display
+ 
+
+ align:start position:0%
+should appear on the display the display
+will alternate between one and the pH
+
+ align:start position:0%
+will alternate between one and the pH
+ 
+
+ align:start position:0%
+will alternate between one and the pH
+value of the solution wait until the
+
+ align:start position:0%
+value of the solution wait until the
+ 
+
+ align:start position:0%
+value of the solution wait until the
+display stabilizes and press Enter the
+
+ align:start position:0%
+display stabilizes and press Enter the
+ 
+
+ align:start position:0%
+display stabilizes and press Enter the
+number two should then appear on the
+
+ align:start position:0%
+number two should then appear on the
+ 
+
+ align:start position:0%
+number two should then appear on the
+display rinse the probe with distilled
+
+ align:start position:0%
+display rinse the probe with distilled
+ 
+
+ align:start position:0%
+display rinse the probe with distilled
+water flat it with a kimwipe and place
+
+ align:start position:0%
+water flat it with a kimwipe and place
+ 
+
+ align:start position:0%
+water flat it with a kimwipe and place
+it into the second buffer if your
+
+ align:start position:0%
+it into the second buffer if your
+ 
+
+ align:start position:0%
+it into the second buffer if your
+solution has an acidic pH then use the
+
+ align:start position:0%
+solution has an acidic pH then use the
+ 
+
+ align:start position:0%
+solution has an acidic pH then use the
+4.01 buffer if it has a basic pH use the
+
+ align:start position:0%
+4.01 buffer if it has a basic pH use the
+ 
+
+ align:start position:0%
+4.01 buffer if it has a basic pH use the
+ten point zero one buffer the display
+
+ align:start position:0%
+ten point zero one buffer the display
+ 
+
+ align:start position:0%
+ten point zero one buffer the display
+will alternate between two and the pH
+
+ align:start position:0%
+will alternate between two and the pH
+ 
+
+ align:start position:0%
+will alternate between two and the pH
+value of the solution wait until the
+
+ align:start position:0%
+value of the solution wait until the
+ 
+
+ align:start position:0%
+value of the solution wait until the
+display stabilizes and press enter the
+
+ align:start position:0%
+display stabilizes and press enter the
+ 
+
+ align:start position:0%
+display stabilizes and press enter the
+letters pH will be displayed indicating
+
+ align:start position:0%
+letters pH will be displayed indicating
+ 
+
+ align:start position:0%
+letters pH will be displayed indicating
+that the pH meter is now ready to take
+
+ align:start position:0%
+that the pH meter is now ready to take
+ 
+
+ align:start position:0%
+that the pH meter is now ready to take
+measurements before taking a measurement
+
+ align:start position:0%
+measurements before taking a measurement
+ 
+
+ align:start position:0%
+measurements before taking a measurement
+make sure that your sample buffer is at
+
+ align:start position:0%
+make sure that your sample buffer is at
+ 
+
+ align:start position:0%
+make sure that your sample buffer is at
+the same temperature you'll be using in
+
+ align:start position:0%
+the same temperature you'll be using in
+ 
+
+ align:start position:0%
+the same temperature you'll be using in
+your experiments because pH is
+
+ align:start position:0%
+your experiments because pH is
+ 
+
+ align:start position:0%
+your experiments because pH is
+temperature dependent
+
+ align:start position:0%
+temperature dependent
+ 
+
+ align:start position:0%
+temperature dependent
+rinse and blot the probe and place it
+
+ align:start position:0%
+rinse and blot the probe and place it
+ 
+
+ align:start position:0%
+rinse and blot the probe and place it
+into the buffer wait for the display to
+
+ align:start position:0%
+into the buffer wait for the display to
+ 
+
+ align:start position:0%
+into the buffer wait for the display to
+stabilize and record the pH correct
+
+ align:start position:0%
+stabilize and record the pH correct
+ 
+
+ align:start position:0%
+stabilize and record the pH correct
+buffer preparation and pH meter
+
+ align:start position:0%
+buffer preparation and pH meter
+ 
+
+ align:start position:0%
+buffer preparation and pH meter
+technique are essential to ensure that
+
+ align:start position:0%
+technique are essential to ensure that
+ 
+
+ align:start position:0%
+technique are essential to ensure that
+your proteins and other sensitive
+
+ align:start position:0%
+your proteins and other sensitive
+ 
+
+ align:start position:0%
+your proteins and other sensitive
+chemicals live long functional lives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
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index 0000000000000000000000000000000000000000..22b8620586fab872aa863db9994e74df3f0f5aad
--- /dev/null
+++ b/H_k1w3cfny8.txt
@@ -0,0 +1,2294 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So today's agenda
+is to say a few more things
+
+about continuous random
+variables.
+
+Mainly we're going to talk a
+little bit about inference.
+
+This is a topic that we're going
+to revisit at the end of
+
+the semester.
+
+But there's a few things
+that we can
+
+already say at this point.
+
+And then the new topic for
+today is the subject of
+
+derived distributions.
+
+Basically if you know the
+distribution of one random
+
+variable, and you have a
+function of that random
+
+variable, how to find a
+
+distribution for that function.
+
+And it's a fairly mechanical
+skill, but that's an important
+
+one, so we're going
+to go through it.
+
+So let's see where we stand.
+
+Here is the big picture.
+
+That's all we have
+done so far.
+
+We have talked about discrete
+random variables, which we
+
+described by probability
+mass function.
+
+So if we have multiple random
+variables, we describe them
+
+with the a joint
+mass function.
+
+And then we define conditional
+probabilities, or conditional
+
+PMFs, and the three are related
+according to this
+
+formula, which is, you can
+think of it either as the
+
+definition of conditional
+probability.
+
+Or as the multiplication rule,
+the probability of two things
+
+happening is the product of the
+probabilities of the first
+
+thing happening, and then the
+second happening, given that
+
+the first has happened.
+
+There's another relation between
+this, which is the
+
+probability of x occurring, is
+the sum of the different
+
+probabilities of the different
+ways that x may occur, which
+
+is in conjunction with different
+values of y.
+
+And there's an analog of all
+that in the continuous world,
+
+where all you do is to replace
+p's by f's, and replace sums
+
+by integrals.
+
+So the formulas all
+look the same.
+
+The interpretations are a little
+more subtle, so the f's
+
+are not probabilities, they're
+probability densities.
+
+So they're probabilities per
+unit length, or in the case of
+
+joint PDf's, these are
+probabilities per unit area.
+
+So they're densities
+of some sort.
+
+Probably the more subtle concept
+to understand what it
+
+really is the conditional
+density.
+
+In some sense, it's simple.
+
+It's just the density of X in
+a world where you have been
+
+told the value of the random
+variable Y. It's a function
+
+that has two arguments, but the
+best way to think about it
+
+is to say that we fixed y.
+
+We're told the value of the
+random variable Y, and we look
+
+at it as a function of x.
+
+So as a function of x, the
+denominator is a constant, and
+
+it just looks like the
+joint density.
+
+when we keep y fixed.
+
+So it's really a function of
+one argument, just the
+
+argument x.
+
+And it has the same shape as the
+joint's density when you
+
+take that slice of it.
+
+So conditional PDFs are just
+slices of joint PDFs.
+
+There's a bunch of concepts,
+expectations, variances,
+
+cumulative distribution
+functions that apply equally
+
+well for to both universes
+of discrete or
+
+continuous random variables.
+
+So why is probability useful?
+
+Probability is useful because,
+among other things, we use it
+
+to make sense of the
+world around us.
+
+We use it to make inferences
+about things that we do not
+
+see directly.
+
+And this is done in a
+very simple manner
+
+using the base rule.
+
+We've already seen some of that,
+and now we're going to
+
+revisit it with a bunch of
+different variations.
+
+And the variations come because
+sometimes our random
+
+variable are discrete, sometimes
+they're continuous,
+
+or we can have a combination
+of the two.
+
+So the big picture is that
+there's some unknown random
+
+variable out of there, and we
+know the distribution that's
+
+random variable.
+
+And in the discrete case, it's
+going to be given by PMF.
+
+In the continuous case,
+it's given a PDF.
+
+Then we have some phenomenon,
+some noisy phenomenon or some
+
+measuring device, and that
+measuring device produces
+
+observable random variables Y.
+
+We don't know what x is, but we
+have some beliefs about how
+
+X is distributed.
+
+We observe the random variable
+Y. We need a
+
+model of this box.
+
+And the model of that box is
+going to be either a PMF, for
+
+the random variable Y. And that
+model tells us, if the
+
+true state of the world is X,
+how do we expect to Y to be
+
+distributed?
+
+That's for the case where
+Y is this discrete.
+
+If Y is a continuous, you might
+instead have a density
+
+for Y, or something
+of that form.
+
+So in either case, this
+should be a function
+
+that's known to us.
+
+This is our model of the
+measuring device.
+
+And now having observed
+y, we want to make
+
+inferences about x.
+
+What does it mean to
+make inferences?
+
+Well the most complete answer in
+the inference problem is to
+
+tell me the probability
+distribution
+
+of the unknown quantity.
+
+But when I say the probability
+distribution, I
+
+don't mean this one.
+
+I mean the probability
+distribution that takes into
+
+account the measurements
+that you got.
+
+So the output of an inference
+problem is to come up with the
+
+distribution of X, the unknown
+quantity, given what we have
+
+already observed.
+
+And in the discrete case, it
+would be an object like that.
+
+If X is continuous, it would
+be an object of this kind.
+
+OK, so we're given conditional
+probabilities of this type,
+
+and we want to get conditional
+distributions of the opposite
+
+type where the order of the
+
+conditioning is being reversed.
+
+So the starting point
+is always a formula
+
+such as this one.
+
+The probability of x happening,
+and then y
+
+happening given that
+x happens.
+
+This is the probability that
+a particular x and y happen
+
+simultaneously.
+
+But this is also equal to the
+probability that y happens,
+
+and then that x happens, given
+that y has happened.
+
+And you take this expression
+and send one term to the
+
+denominator of the other side,
+and this gives us the base
+
+rule for the discrete case.
+
+Which is this one that you have
+already seen, and you
+
+have played with it.
+
+So this is what the formula
+looks like in
+
+the discrete case.
+
+And the typical example where
+both random variables are
+
+discrete is the one we discussed
+some time ago.
+
+X is, let's say, a binary
+variable, or whether an
+
+airplane is present
+up there or not.
+
+Y is a discrete measurement, for
+example, whether our radar
+
+beeped or it didn't beep.
+
+And we make inferences and
+calculate the probability that
+
+the plane is there, or the
+probability that the plane is
+
+not there, given the measurement
+that we have made.
+
+And of course X and Y do not
+need to be just binary.
+
+They could be more general
+discrete random variables.
+
+So how does the story change
+in the continuous case?
+
+First, what's a possible
+application of
+
+the continuous case?
+
+Well, think of X as being some
+signal that takes values over
+
+a continuous range.
+
+Let's say X is the current
+through a resistor.
+
+And then you have some measuring
+device that measures
+
+currents, but that device is
+noisy, it gets hit, let's say
+
+for example, by Gaussian
+noise.
+
+And the Y that you observe is a
+noisy version of X. But your
+
+instruments are analog, so
+you measure things on
+
+a continuous scale.
+
+What are you going to
+do in that case?
+
+Well the inference problem, the
+output of the inference
+
+problem, is going to be the
+conditional distribution of X.
+
+What do you think your current
+is based on a particular value
+
+of Y that you have observed?
+
+So the output of our inference
+problem is, given the specific
+
+value of Y, to calculate this
+entire function as a function
+
+of x, and then go and plot it.
+
+How do we calculate it?
+
+You go through the same
+calculation as in the discrete
+
+case, except that all of the
+x's gets replaced by p's.
+
+In the continuous case, it's
+equally true that the joint's
+
+density is the product of the
+marginal density with the
+
+conditional density.
+
+So the formula is still
+valid with just a
+
+little change of notation.
+
+So we end up with the same
+formula here, except that we
+
+replace x's with p's.
+
+So all of these functions
+are known to us.
+
+We have formulas for them.
+
+We fix a specific value of y,
+we plug it in, so we're left
+
+with a function of x.
+
+And that gives us the posterior
+distribution.
+
+Actually there's also a
+denominator term that's not
+
+necessarily given to us, but we
+can always calculate it if
+
+we have the marginal of X,
+and we have the model for
+
+measuring device.
+
+Then we can always find the
+marginal distribution of Y. So
+
+this quantity, that number, is
+in general a known one, as
+
+well, and doesn't give
+us any problems.
+
+So to complicate things a little
+bit, we can also look
+
+into situations where our two
+random variables are of
+
+different kinds.
+
+For example, one random variable
+could be discrete,
+
+and the other it might
+be continuous.
+
+And there's two versions.
+
+Here one version is when X is
+discrete, but Y is continuous.
+
+What's an example of this?
+
+Well suppose that I send a
+single bit of information so
+
+my X is 0 or 1.
+
+And what I measure is Y,
+which is X plus, let's
+
+say, Gaussian noise.
+
+This is the standard example
+that shows up in any textbook
+
+on communication, or
+signal processing.
+
+You send a single bit, but what
+you observe is a noisy
+
+version of that bit.
+
+You start with a model
+of your x's.
+
+These would be your prior
+probabilities.
+
+For example, you might be
+believe that either 0 or 1 are
+
+equally likely, in which case
+your PMF gives equal weight to
+
+two possible values.
+
+And then we need a model of
+our measuring device.
+
+This is one specific model.
+
+The general model would have
+a shape such as follows.
+
+Y has a distribution,
+its density.
+
+And that density, however,
+depends on the value of X.
+
+So when x is 0, we might get
+a density of this kind.
+
+And when x is 1, we might
+get the density
+
+of a different kind.
+
+So these are the conditional
+densities of y in a universe
+
+that's specified by a particular
+value of x.
+
+And then we go ahead and
+do our inference.
+
+OK, what's the right formula
+for doing this inference?
+
+We need a formula that's sort of
+an analog of this one, but
+
+applies to the case where we
+have two random variables of
+
+different kinds.
+
+So let me just redo this
+calculation here.
+
+Except that I'm not going to
+have a probability of taking
+
+specific values.
+
+It will have to be something
+a little different.
+
+So here's how it goes.
+
+Let's look at the probability
+that X takes a specific value
+
+that makes sense in the discrete
+case, but for the
+
+continuous random variable,
+let's look at the probability
+
+that it takes values in
+some little interval.
+
+And now this probability of
+two things happening, I'm
+
+going to write it
+as a product.
+
+And I'm going to write
+this as a product in
+
+two different ways.
+
+So one way is to say that this
+is the probability that X
+
+takes that value and then given
+that X takes that value,
+
+the probability that Y falls
+inside that interval.
+
+So this is our usual
+multiplication rule for
+
+multiplying probabilities, but
+I can use the multiplication
+
+rule also in a different way.
+
+It's the probability
+that Y falls in
+
+the range of interest.
+
+And then the probability that X
+takes the value of interest
+
+given that Y satisfies
+the first condition.
+
+So this is something that's
+definitely true.
+
+We're just using the
+multiplication rule.
+
+And now let's translate it
+into PMF is PDF notation.
+
+So the entry up there is the
+PMF of X evaluated at x.
+
+The second entry, what is it?
+
+Well probabilities of
+little intervals are
+
+given to us by densities.
+
+But we are in the conditional
+universe where X takes on a
+
+particular value.
+
+So it's going to be the density
+of Y given the value
+
+of X times delta.
+
+So probabilities of little
+intervals are given by the
+
+density times the length of
+the little interval, but
+
+because we're working in the
+conditional universe, it has
+
+to be the conditional density.
+
+Now let's try the second
+expression.
+
+This is the probability
+that the Y falls
+
+into the little interval.
+
+So that's the density
+of Y times delta.
+
+And then here we have an
+object which is the
+
+conditional probability X in a
+universe where the value of Y
+
+is given to us.
+
+Now this relation is sort
+of approximate.
+
+This is true for very small
+delta in the limit.
+
+But we can cancel the deltas
+from both sides, and we're
+
+left with a formula that links
+together PMFs and PDFs.
+
+Now this may look terribly
+confusing because there's both
+
+p's and f's involved.
+
+But the logic should be clear.
+
+If a random variable
+is discrete, it's
+
+described by PMF.
+
+So here we're talking about
+the PMF of X in some
+
+particular universe.
+
+X is discrete, so
+it has a PMF.
+
+Similarly here.
+
+Y is continuous so it's
+described by a PDF.
+
+And even in the conditional
+universe where I tell you the
+
+value of X, Y is still a
+continuous random variable, so
+
+it's been described by a PDF.
+
+So this is the basic
+relation that links
+
+together PMF and PDFs.
+
+In this mixed the world.
+
+And now in this inequality,
+you can take this term and
+
+send it to the new denominator
+to the other side.
+
+And what you end up with
+is the formula
+
+that we have up here.
+
+And this is a formula that we
+can use to make inferences
+
+about the discrete random
+variable X when we're told the
+
+value of the continuous random
+variable Y. The probability
+
+that X takes on a particular
+value has something
+
+to do with the prior.
+
+And other than that, it's
+proportional to this quantity,
+
+the conditional of Y given X.
+So these are the quantities
+
+that we plotted here.
+
+Suppose that the x's are equally
+likely in your prior,
+
+so we don't really care
+about that term.
+
+It tells us that the posterior
+of X is proportional to that
+
+particular density under
+the given x's.
+
+So in this picture, if I were to
+get a particular y here, I
+
+would say that x equals 1
+has a probability that's
+
+proportional to this quantity.
+
+x equals 0 has a probability
+that's
+
+proportional to this quantity.
+
+So the ratio of these two
+quantities gives us the
+
+relative odds of the different
+x's given the y
+
+that we have observed.
+
+So we're going to come back to
+this topic and redo plenty of
+
+examples of these kinds towards
+the end of the class,
+
+when we spend some
+time dedicated
+
+to inference problems.
+
+But already at this stage, we
+sort of have the basic skills
+
+to deal with a lot of that.
+
+And it's useful at this
+point to pull all
+
+the formulas together.
+
+So finally let's look at the
+last case that's remaining.
+
+Here we have a continuous
+phenomenon that we're trying
+
+to measure, but our measurements
+are discrete.
+
+What's an example where
+this might happen?
+
+So you have some device that
+emits light, and you drive it
+
+with a current that has
+a certain intensity.
+
+You don't know what that
+current is, and it's a
+
+continuous random variable.
+
+But the device emits
+light by sending
+
+out individual photons.
+
+And your measurement is some
+other device that counts how
+
+many photons did you get
+in a single second.
+
+So if we have devices that emit
+a very low intensity you
+
+can actually start counting
+individual photons as they're
+
+being observed.
+
+So we have a discrete
+measurement, which is the
+
+number of problems, and we
+have a continuous hidden
+
+random variable that we're
+trying to estimate.
+
+What do we do in this case?
+
+Well we start again with a
+formula of this kind, and send
+
+the p term to the denominator.
+
+And that's the formula that we
+use there, except that the
+
+roles of x's and y's
+are interchanged.
+
+So since here we have Y being
+discrete, we should change all
+
+the subscripts.
+
+It would be p_Y f_X given
+y f_X, and P(Y given X).
+
+So just change all
+those subscripts.
+
+Because now what we're used to
+be continuous became discrete,
+
+and vice versa.
+
+Take that formula, send
+the other terms to the
+
+denominator, and we have a
+formula for the density, or X,
+
+given the particular
+measurements for Y that we
+
+have obtained.
+
+In some sense that's all there
+is in Bayesian inference.
+
+It's using these very simple
+one line formulas.
+
+But why are there people then
+who make their living solving
+
+inference problems?
+
+Well, the devil is
+in the details.
+
+As we're going to discuss,
+there are some real world
+
+issues of how exactly do you
+design your f's, how do you
+
+model your system, then how do
+you do your calculations.
+
+This might not be always easy.
+
+For example, there's certain
+integrals or sums that have to
+
+be evaluated, which may be
+hard to do and so on.
+
+So this object is
+a lot of richer
+
+than just these formulas.
+
+On the other hand, at the
+conceptual level, that's the
+
+basis for Bayesian inference,
+that these
+
+are the basic concepts.
+
+All right, so now let's change
+gear and move to the new
+
+subject, which is the topic of
+finding the distribution of a
+
+functional for a random
+variable.
+
+We call those distributions
+derived distributions, because
+
+we're given the distribution
+of X. We're interested in a
+
+function of X. We want to derive
+the distribution of
+
+that function based on
+the distribution
+
+that we already know.
+
+So it could be a function of
+just one random variable.
+
+It could be a function of
+several random variables.
+
+So one example that we are going
+to solve at some point,
+
+let's say you have to run the
+variables X and Y. Somebody
+
+tells you their distribution,
+for example, is a uniform of
+
+the square.
+
+For some reason, you're
+interested in the ratio of
+
+these two random variables,
+and you want to find the
+
+distribution of that ratio.
+
+You can think of lots of cases
+where your random variable of
+
+interest is created by taking
+some other unknown variables
+
+and taking a function of them.
+
+And so it's legitimate to care
+about the distribution of that
+
+random variable.
+
+A caveat, however.
+
+There's an important case where
+you don't need to find
+
+the distribution of that
+random variable.
+
+And this is when you want to
+calculate the expectations.
+
+If all you care about is the
+expected value of this
+
+function of the random
+variables, you can work
+
+directly with the distribution
+of the original random
+
+variables without ever having
+to find the PDF of g.
+
+So you don't do unnecessary work
+if it's not needed, but
+
+if it's needed, or if you're
+asked to do it,
+
+then you just do it.
+
+So how do we find the
+distribution of the function?
+
+As a warm-up, let's look
+at the discrete case.
+
+Suppose that X is a discrete
+random variable and takes
+
+certain values.
+
+We have a function g that
+maps x's into y's.
+
+And we want to find the
+probability mass function for
+
+Y.
+
+So for example, if I'm
+interested in finding the
+
+probability that Y takes on
+this particular value, how
+
+would they find it?
+
+Well I ask, what are the
+different ways that these
+
+particular y value can happen?
+
+And the different ways that it
+can happen is either if x
+
+takes this value, or if
+X takes that value.
+
+So we identify this event in the
+y space with that event in
+
+the x space.
+
+These two events
+are identical.
+
+X falls in this set if and only
+if Y falls in that set.
+
+Therefore, the probability of
+Y falling in that set is the
+
+probability of X falling
+in that set.
+
+The probability of X falling in
+that set is just the sum of
+
+the individual probabilities
+of the x's in this set.
+
+So we just add the probabilities
+of the different
+
+x's where the summation is taken
+over all x's that leads
+
+to that particular value of y.
+
+Very good.
+
+So that's all there is
+in the discrete case.
+
+It's a very nice and simple.
+
+So let's transfer
+these methods to
+
+the continuous case.
+
+Suppose we are in the
+continuous case.
+
+Suppose that X and Y now can
+take values anywhere.
+
+And I try to use same methods
+and I ask, what is the
+
+probability that Y is going
+to take this value?
+
+At least if the diagram is this
+way, you would say this
+
+is the same as the probability
+that X takes this value.
+
+So I can find the probability
+of Y being this in terms of
+
+the probability of
+X being that.
+
+Is this useful?
+
+In the continuous
+case, it's not.
+
+Because in the continuous case,
+any single value has 0
+
+probability.
+
+So what you're going to get out
+of this argument is that
+
+the probability Y takes this
+value is 0, is equal to the
+
+probability that X takes that
+value which also 0.
+
+That doesn't help us.
+
+We want to do something more.
+
+We want to actually find,
+perhaps, the density of Y, as
+
+opposed to the probabilities
+of individual y's.
+
+So to find the density of Y,
+you might argue as follows.
+
+I'm looking at an interval for
+y, and I ask what's the
+
+probability of falling
+in this interval.
+
+And you go back and find the
+corresponding set of x's that
+
+leads to those y's, and equate
+those two probabilities.
+
+The probability of all of those
+y's collectively should
+
+be equal to the probability of
+all of the x's that map into
+
+that interval collectively.
+
+And this way you can
+relate the two.
+
+As far as the mechanics go, in
+many cases it's easier to not
+
+to work with little intervals,
+but instead to work with
+
+cumulative distribution
+functions that used to work
+
+with sort of big intervals.
+
+So you can instead do
+a different picture.
+
+Look at this set of y's.
+
+This is the set of y's
+that are smaller
+
+than a certain value.
+
+The probability of this set
+is given by the cumulative
+
+distribution of the
+random variable Y.
+
+Now this set of y's gets
+produced by some corresponding
+
+set of x's.
+
+Maybe these are the x's that
+map into y's in that set.
+
+And then we argue as follows.
+
+The probability that the Y falls
+in this interval is the
+
+same as the probability that
+X falls in that interval.
+
+So the event of Y falling here
+and the event of X falling
+
+there are the same, so their
+probabilities must be equal.
+
+And then I do the calculations
+here.
+
+And I end up getting the
+cumulative distribution
+
+function of Y. Once I have the
+cumulative, I can get the
+
+density by just differentiating.
+
+So this is the general cookbook
+procedure that we
+
+will be using to calculate
+it derived distributions.
+
+We're interested in a random
+variable Y, which is a
+
+function of the x's.
+
+We will aim at obtaining the
+cumulative distribution of Y.
+
+Somehow, manage to calculate the
+probability of this event.
+
+Once we get it, and what I mean
+by get it, I don't mean
+
+getting it for a single
+value of little y.
+
+You need to get this
+for all little y's.
+
+So you need to get the
+function itself, the
+
+cumulative distribution.
+
+Once you get it in that form,
+then you can calculate the
+
+derivative at any particular
+point.
+
+And this is going to give
+you the density of Y.
+
+So a simple two-step
+procedure.
+
+The devil is in the details of
+how you carry the mechanics.
+
+So let's do one first example.
+
+Suppose that X is a uniform
+random variable, takes values
+
+between 0 and 2.
+
+We're interested in the random
+variable Y, which is the cube
+
+of X. What kind of distribution
+
+is it going to have?
+
+Now first notice that Y takes
+values between 0 and 8.
+
+So X is uniform, so all the
+x's are equally likely.
+
+You might then say, well, in
+that case, all the y's should
+
+be equally likely.
+
+So Y might also have a
+uniform distribution.
+
+Is this true?
+
+We'll find out.
+
+So let's start applying the
+cookbook procedure.
+
+We want to find first the
+cumulative distribution of the
+
+random variable Y, which by
+definition is the probability
+
+that the random variable is
+less than or equal to a
+
+certain number.
+
+That's what we want to find.
+
+What we have in our hands is the
+distribution of X. That's
+
+what we need to work with.
+
+So the first step that you need
+to do is to look at this
+
+events and translate it, and
+write it in terms of the
+
+random variable about which you
+know you have information.
+
+So Y is X cubed, so this event
+is the same as that event.
+
+So now we can forget
+about the y's.
+
+It's just an exercise involving
+a single random
+
+variable with a known
+distribution and we want to
+
+calculate the probability
+of some event.
+
+So we're looking
+at this event.
+
+X cubed being less than or equal
+to Y. We massage that
+
+expression so that's it involves
+X directly, so let's
+
+take cubic roots of both sides
+of this inequality.
+
+This event is the same as the
+event that X is less than or
+
+equal to Y to the 1/3.
+
+Now with a uniform distribution
+on [0,2], what is
+
+that probability going to be?
+
+It's the probability of being in
+the interval from 0 to y to
+
+the 1/3, so it's going to be in
+the area under the uniform
+
+going up to that point.
+
+And what's the area under
+that uniform?
+
+So here's x.
+
+Here is the distribution
+of X. It goes up to 2.
+
+The distribution of
+X is this one.
+
+We want to go up to
+y to the 1/3.
+
+So the probability for this
+event happening is this area.
+
+And the area is equal to the
+base, which is y to the 1/3
+
+times the height.
+
+What is the height?
+
+Well since the density must
+integrate to 1, the total area
+
+under the curve has to be 1.
+
+So the height here is 1/2, and
+that explains why we get the
+
+1/2 factor down there.
+
+So that's the formula for the
+cumulative distribution.
+
+And then the rest is easy.
+
+You just take derivatives.
+
+You differentiate this
+expression with respect to y
+
+1/2 times 1/3, and y
+drops by one power.
+
+So you get y to 2/3 in
+the denominator.
+
+So if you wish to plot this,
+it's 1/y to the 2/3.
+
+So when y goes to 0, it sort
+of blows up and it
+
+goes on this way.
+
+Is this picture correct
+the way I've drawn it?
+
+What's wrong with it?
+
+[? AUDIENCE:  Something. ?]
+
+PROFESSOR: Yes.
+
+y only takes values
+from 0 to 8.
+
+This formula that I wrote here
+is only correct when the
+
+preview picture applies.
+
+I took my y to the 1/3 to
+be between 0 and 2.
+
+So this formula here is only
+correct for y between 0 and 8.
+
+And for that reason, the formula
+for the derivative is
+
+also true only for a
+y between 0 and 8.
+
+And any other values of why are
+impossible, so they get
+
+zero density.
+
+So to complete the picture
+here, the PDF of y has a
+
+cut-off of 8, and it's also
+0 everywhere else.
+
+And one thing that we see is
+that the distribution of Y is
+
+not uniform.
+
+Certain y's are more likely than
+others, even though we
+
+started with a uniform random
+
+variable X. All right.
+
+So we will keep doing examples
+of this kind, a sequence of
+
+progressively more interesting
+or more complicated.
+
+So that's going to continue
+in the next lecture.
+
+You're going to see plenty of
+examples in your recitations
+
+and tutorials and so on.
+
+So let's do one that's pretty
+similar to the one that we
+
+did, but it's going to add to
+just a small twist in how we
+
+do the mechanics.
+
+OK so you set your
+cruise control
+
+when you start driving.
+
+And you keep driving at the
+constants based at the
+
+constant speed.
+
+Where you set your cruise
+control is somewhere
+
+between 30 and 60.
+
+You're going to drive
+a distance of 200.
+
+And so the time it's going to
+take for your trip is 200 over
+
+the setting of your
+cruise control.
+
+So it's 200/V.
+
+Somebody gives you the
+distribution of V, and they
+
+tell you not only it's between
+30 and 60, it's roughly
+
+equally likely to be anything
+between 30 and 60, so we have
+
+a uniform distribution
+over that range.
+
+So we have a distribution of
+V. We want to find the
+
+distribution of the random
+variable T, which is the time
+
+it takes till your trip ends.
+
+So how are we going
+to proceed?
+
+We'll use the exact same
+cookbook procedure.
+
+We're going to start by
+finding the cumulative
+
+distribution of T.
+What is this?
+
+By definition, the cumulative
+distribution is the
+
+probability that T is less
+than a certain number.
+
+OK.
+
+Now we don't know the
+distribution of T, so we
+
+cannot to work with these
+event directly.
+
+But we take that event and
+translate it into T-space.
+
+So we replace the t's by what we
+know T to be in terms of V
+
+or
+
+the v's All right.
+
+So we have the distribution
+of V. So now let's
+
+calculate this quantity.
+
+OK.
+
+Let's massage this event and
+rewrite it as the probability
+
+that V is larger or
+equal to 200/T.
+
+So what is this going to be?
+
+So let's say that 200/T
+is some number that
+
+falls inside the range.
+
+So that's going to be true if
+200/T is bigger than 30, and
+
+less than 60.
+
+Which means that t is
+less than 30/200.
+
+No, 200/30.
+
+And bigger than 200/60.
+
+So for t's inside that range,
+this number 200/t falls inside
+
+that range.
+
+This is the range of t's that
+are possible, given the
+
+description of the problem
+the we have set up.
+
+So for t's in that range, what
+is the probability that V is
+
+bigger than this number?
+
+So V being bigger than that
+number is the probability of
+
+this event, so it's going to be
+the area under this curve.
+
+So the area under that curve
+is the height of the curve,
+
+which is 1/3 over 30
+times the base.
+
+How big is the base?
+
+Well it's from that point to 60,
+so the base has a length
+
+of 60 minus 200/t.
+
+And this is a formula which is
+valid for those t's for which
+
+this picture is correct.
+
+And this picture is correct if
+200/T happens to fall in this
+
+interval, which is the same as
+T falling in that interval,
+
+which are the t's that
+are possible.
+
+So finally let's find the
+density of T, which is what
+
+we're looking for.
+
+We find this by taking the
+derivative in this expression
+
+with respect to t.
+
+We only get one term
+from here.
+
+And this is going to be 200/30,
+1 over t squared.
+
+And this is the formula for
+the density for t's in the
+
+allowed to range.
+
+OK, so that's the end of the
+solution to this particular
+
+problem as well.
+
+I said that there was a little
+twist compared to
+
+the previous one.
+
+What was the twist?
+
+Well the twist was that in the
+previous problem we dealt with
+
+the X cubed function, which was
+monotonically increasing.
+
+Here we dealt with the
+function that was
+
+monotonically decreasing.
+
+So when we had to find the
+probability that T is less
+
+than something, that translated
+into an event that
+
+V was bigger than something.
+
+Your time is less than something
+if and only if your
+
+velocity is bigger
+than something.
+
+So for when you're dealing
+with the monotonically
+
+decreasing function, at some
+point some inequalities will
+
+have to get reversed.
+
+Finally let's look at
+a very useful one.
+
+Which is the case where we take
+a linear function of a
+
+random variable.
+
+So X is a random variable with
+given distribution, and we can
+
+see there is a linear
+function.
+
+So in this particular instance,
+we take a to be
+
+equal to 2 and b equal to 5.
+
+And let us first argue
+just by picture.
+
+So X is a random variable that
+has a given distribution.
+
+Let's say it's this
+weird shape here.
+
+And x ranges from -1 to +2.
+
+Let's do things one
+step at the time.
+
+Let's first find the
+distribution of 2X.
+
+Why do you think you
+know about 2X?
+
+Well if x ranges from -1 to 2,
+then the random variable X is
+
+going to range from -2 to +4.
+
+So that's what the range
+is going to be.
+
+Now dealing with the random
+variable 2X, as opposed to the
+
+random variable X, in some sense
+it's just changing the
+
+units in which we measure
+that random variable.
+
+It's just changing the
+scale on which we
+
+draw and plot things.
+
+So if it's just a scale change,
+then intuition should
+
+tell you that the random
+variable X should have a PDF
+
+of the same shape, except that
+it's scaled out by a factor of
+
+2, because our random variable
+of 2X now has a range that's
+
+twice as large.
+
+So we take the same PDF and
+scale it up by stretching the
+
+x-axis by a factor of 2.
+
+So what does scaling
+correspond to
+
+in terms of a formula?
+
+So the distribution of 2X as a
+function, let's say, a generic
+
+argument z, is going to be the
+distribution of X, but scaled
+
+by a factor of 2.
+
+So taking a function and
+replacing its arguments by the
+
+argument over 2, what it
+does is it stretches it
+
+by a factor of 2.
+
+You have probably been tortured
+ever since middle
+
+school to figure out when need
+to stretch a function, whether
+
+you need to put 2z or z/2.
+
+And the one that actually does
+the stretching is to put the
+
+z/2 in that place.
+
+So that's what the
+stretching does.
+
+Could that to be the
+full answer?
+
+Well there's a catch.
+
+If you stretch this function by
+a factor of 2, what happens
+
+to the area under
+the function?
+
+It's going to get doubled.
+
+But the total probability must
+add up to 1, so we need to do
+
+something else to make sure that
+the area under the curve
+
+stays to 1.
+
+So we need to take that function
+and scale it down by
+
+this factor of 2.
+
+So when you're dealing with a
+multiple of a random variable,
+
+what happens to the PDF is you
+stretch it according to the
+
+multiple, and then scale it
+down by the same number so
+
+that you preserve the area
+under that curve.
+
+So now we found the distribution
+of 2X.
+
+How about the distribution
+of 2X + 5?
+
+Well what does adding 5
+to random variable do?
+
+You're going to get essentially
+the same values
+
+with the same probability,
+except that those values all
+
+get shifted by 5.
+
+So all that you need to do is
+to take this PDF here, and
+
+shift it by 5 units.
+
+So the range used to
+be from -2 to 4.
+
+The new range is going
+to be from 3 to 9.
+
+And that's the final answer.
+
+This is the distribution of
+2X + 5, starting with this
+
+particular distribution of X.
+
+Now shifting to the
+right by b, what
+
+does it do to a function?
+
+Shifting to the right to
+by a certain amount,
+
+mathematically, it corresponds
+to putting -b in the argument
+
+of the function.
+
+So I'm taking the formula that
+I had here, which is the
+
+scaling by a factor of a.
+
+The scaling down to keep the
+total area equal to 1.
+
+And then I need to introduce
+this extra
+
+term to do the shifting.
+
+So this is a plausible
+argument.
+
+The proof by picture that this
+should be the right answer.
+
+But just in order to keep our
+skills tuned and refined, let
+
+us do this derivation in a
+more formal way using our
+
+two-step cookbook procedure.
+
+And I'm going to do it under
+the assumption that a is
+
+positive, as in the example
+that's we just did.
+
+So what's the two-step
+procedure?
+
+We want to find the cumulative
+of Y, and after that we're
+
+going to differentiate.
+
+By definition the cumulative
+is the probability that the
+
+random variable takes values
+less than a certain number.
+
+And now we need to take this
+event and translate it, and
+
+express it in terms of the
+original random variables.
+
+So Y is, by definition,
+aX + b, so we're
+
+looking at this event.
+
+And now we want to express this
+event in a clean form
+
+where X shows up in
+a straight way.
+
+Let's say I'm going to massage
+this event and
+
+write it in this form.
+
+For this inequality to be true,
+x should be less than or
+
+equal to (y minus
+b) divided by a.
+
+OK, now what is this?
+
+This is the cumulative
+distribution of X evaluated at
+
+the particular point.
+
+So we got a formula for the
+cumulative Y based on the
+
+cumulative of X. What's
+the next step?
+
+Next step is to take derivatives
+of both sides.
+
+So the density of Y is going to
+be the derivative of this
+
+expression with respect to y.
+
+OK, so now here we need
+to use the chain rule.
+
+It's going to be the derivative
+of the F function
+
+with respect to its argument.
+
+And then we need to take the
+derivative of the argument
+
+with respect to y.
+
+What is the derivative
+of the cumulative?
+
+The derivative of
+the cumulative
+
+is the density itself.
+
+And we evaluate it at the
+point of interest.
+
+And then the chain rule tells
+us that we need to take the
+
+derivative of this with
+respect to y, and the
+
+derivative of this with
+respect to y is 1/a.
+
+And this gives us the formula
+which is consistent with what
+
+I had written down here,
+for the case where a
+
+is a positive number.
+
+What if a was a negative
+number?
+
+Could this formula be true?
+
+Of course not.
+
+Densities cannot be
+negative, right?
+
+So that formula cannot
+be true.
+
+Something needs to change.
+
+What should change?
+
+Where does this argument break
+down when a is negative?
+
+So when I write this inequality
+in this form, I
+
+divide by a.
+
+But when you divide by a
+negative number, the direction
+
+of an inequality is
+going to change.
+
+So when a is negative, this
+inequality becomes larger than
+
+or equal to.
+
+And in that case, the expression
+that I have up
+
+there would change when this
+is larger than here.
+
+Instead of getting the
+cumulative, I would get 1
+
+minus the cumulative of (y
+minus b) divided by a.
+
+So this is the probability that
+X is bigger than this
+
+particular number.
+
+And now when you take the
+derivatives, there's going to
+
+be a minus sign that shows up.
+
+And that minus sign will
+end up being here.
+
+And so we're taking the negative
+of a negative number,
+
+and that basically is equivalent
+to taking the
+
+absolute value of that number.
+
+So all that happens when we have
+a negative a is that we
+
+have to take the absolute value
+of the scaling factor
+
+instead of the factor itself.
+
+All right, so this general
+formula is quite useful for
+
+dealing with linear functions
+of random variables.
+
+And one nice application of it
+is to take the formula for a
+
+normal random variable, consider
+a linear function of
+
+a normal random variable, plug
+into this formula, and what
+
+you will find is that Y also
+has a normal distribution.
+
+So using this formula, now we
+can prove a statement that I
+
+had made a couple of lectures
+ago, that a linear function of
+
+a normal random variable
+is also linear.
+
+That's how you would prove it.
+
+I think this is it
+for today so.
\ No newline at end of file
diff --git a/HynldX56FHI.txt b/HynldX56FHI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fa2c24363fb5aea3f7be8dada1c4eeaf154d3ddd
--- /dev/null
+++ b/HynldX56FHI.txt
@@ -0,0 +1,1411 @@
+align:start position:0%
+ 
+welcome back to 8701
+
+ align:start position:0%
+welcome back to 8701
+ 
+
+ align:start position:0%
+welcome back to 8701
+um so in this second chapter chapter
+
+ align:start position:0%
+um so in this second chapter chapter
+ 
+
+ align:start position:0%
+um so in this second chapter chapter
+number one
+
+ align:start position:0%
+number one
+ 
+
+ align:start position:0%
+number one
+we start talking about quarks and
+
+ align:start position:0%
+we start talking about quarks and
+ 
+
+ align:start position:0%
+we start talking about quarks and
+leptons interactions and fears
+
+ align:start position:0%
+leptons interactions and fears
+ 
+
+ align:start position:0%
+leptons interactions and fears
+and we'll start by very general
+
+ align:start position:0%
+and we'll start by very general
+ 
+
+ align:start position:0%
+and we'll start by very general
+discussion of quantum fields and matter
+
+ align:start position:0%
+discussion of quantum fields and matter
+ 
+
+ align:start position:0%
+discussion of quantum fields and matter
+so you all know that what we mean by
+
+ align:start position:0%
+so you all know that what we mean by
+ 
+
+ align:start position:0%
+so you all know that what we mean by
+particles and forces in a classical
+
+ align:start position:0%
+particles and forces in a classical
+ 
+
+ align:start position:0%
+particles and forces in a classical
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+however we need now to see how they
+
+ align:start position:0%
+however we need now to see how they
+ 
+
+ align:start position:0%
+however we need now to see how they
+connect with quantum fields
+
+ align:start position:0%
+connect with quantum fields
+ 
+
+ align:start position:0%
+connect with quantum fields
+and how this helps us to consider matter
+
+ align:start position:0%
+and how this helps us to consider matter
+ 
+
+ align:start position:0%
+and how this helps us to consider matter
+and forces
+
+ align:start position:0%
+and forces
+ 
+
+ align:start position:0%
+and forces
+in a very similar way
+
+ align:start position:0%
+in a very similar way
+ 
+
+ align:start position:0%
+in a very similar way
+the modern view of the basic way that
+
+ align:start position:0%
+the modern view of the basic way that
+ 
+
+ align:start position:0%
+the modern view of the basic way that
+particles come to exist
+
+ align:start position:0%
+particles come to exist
+ 
+
+ align:start position:0%
+particles come to exist
+is in terms of quantized spheres which
+
+ align:start position:0%
+is in terms of quantized spheres which
+ 
+
+ align:start position:0%
+is in terms of quantized spheres which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+an extension of the quantum mechanics
+
+ align:start position:0%
+an extension of the quantum mechanics
+ 
+
+ align:start position:0%
+an extension of the quantum mechanics
+you love and know
+
+ align:start position:0%
+you love and know
+ 
+
+ align:start position:0%
+you love and know
+um which you have done before where you
+
+ align:start position:0%
+um which you have done before where you
+ 
+
+ align:start position:0%
+um which you have done before where you
+quantize
+
+ align:start position:0%
+quantize
+ 
+
+ align:start position:0%
+quantize
+particles these fields have quantum
+
+ align:start position:0%
+particles these fields have quantum
+ 
+
+ align:start position:0%
+particles these fields have quantum
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+for the field amplitudes which are
+
+ align:start position:0%
+for the field amplitudes which are
+ 
+
+ align:start position:0%
+for the field amplitudes which are
+basically like
+
+ align:start position:0%
+basically like
+ 
+
+ align:start position:0%
+basically like
+the quantum simple harmonic oscillator
+
+ align:start position:0%
+the quantum simple harmonic oscillator
+ 
+
+ align:start position:0%
+the quantum simple harmonic oscillator
+but there are an infinite number of them
+
+ align:start position:0%
+but there are an infinite number of them
+ 
+
+ align:start position:0%
+but there are an infinite number of them
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+for every possible frequency of wave in
+
+ align:start position:0%
+for every possible frequency of wave in
+ 
+
+ align:start position:0%
+for every possible frequency of wave in
+the field
+
+ align:start position:0%
+the field
+ 
+
+ align:start position:0%
+the field
+this means the amplitudes for the wave
+
+ align:start position:0%
+this means the amplitudes for the wave
+ 
+
+ align:start position:0%
+this means the amplitudes for the wave
+for each frequency are therefore
+
+ align:start position:0%
+for each frequency are therefore
+ 
+
+ align:start position:0%
+for each frequency are therefore
+quantized
+
+ align:start position:0%
+quantized
+ 
+
+ align:start position:0%
+quantized
+in integer steps uh just like
+
+ align:start position:0%
+in integer steps uh just like
+ 
+
+ align:start position:0%
+in integer steps uh just like
+a simple harmonic oscillator this is
+
+ align:start position:0%
+a simple harmonic oscillator this is
+ 
+
+ align:start position:0%
+a simple harmonic oscillator this is
+what we see as a particle the first
+
+ align:start position:0%
+what we see as a particle the first
+ 
+
+ align:start position:0%
+what we see as a particle the first
+excitation gives one particle of a
+
+ align:start position:0%
+excitation gives one particle of a
+ 
+
+ align:start position:0%
+excitation gives one particle of a
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+a further excitation of the amplitude
+
+ align:start position:0%
+a further excitation of the amplitude
+ 
+
+ align:start position:0%
+a further excitation of the amplitude
+for the same frequency corresponds to
+
+ align:start position:0%
+for the same frequency corresponds to
+ 
+
+ align:start position:0%
+for the same frequency corresponds to
+two particles
+
+ align:start position:0%
+two particles
+ 
+
+ align:start position:0%
+two particles
+etc etc so hence the concept of quantum
+
+ align:start position:0%
+etc etc so hence the concept of quantum
+ 
+
+ align:start position:0%
+etc etc so hence the concept of quantum
+field unlike normal quantum mechanics
+
+ align:start position:0%
+field unlike normal quantum mechanics
+ 
+
+ align:start position:0%
+field unlike normal quantum mechanics
+allows an arbitrary
+
+ align:start position:0%
+allows an arbitrary
+ 
+
+ align:start position:0%
+allows an arbitrary
+and changeable number of particles to
+
+ align:start position:0%
+and changeable number of particles to
+ 
+
+ align:start position:0%
+and changeable number of particles to
+exist
+
+ align:start position:0%
+exist
+ 
+
+ align:start position:0%
+exist
+this is necessary as you will see later
+
+ align:start position:0%
+this is necessary as you will see later
+ 
+
+ align:start position:0%
+this is necessary as you will see later
+such that we can create and annihilate
+
+ align:start position:0%
+such that we can create and annihilate
+ 
+
+ align:start position:0%
+such that we can create and annihilate
+part particles
+
+ align:start position:0%
+part particles
+ 
+
+ align:start position:0%
+part particles
+in reactions in the decays
+
+ align:start position:0%
+in reactions in the decays
+ 
+
+ align:start position:0%
+in reactions in the decays
+and the standard wave functions
+
+ align:start position:0%
+and the standard wave functions
+ 
+
+ align:start position:0%
+and the standard wave functions
+correspond to an equation of a
+
+ align:start position:0%
+correspond to an equation of a
+ 
+
+ align:start position:0%
+correspond to an equation of a
+particular frequency
+
+ align:start position:0%
+particular frequency
+ 
+
+ align:start position:0%
+particular frequency
+amplitude when it is exist and existed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now just let's consider a few cases
+
+ align:start position:0%
+so now just let's consider a few cases
+ 
+
+ align:start position:0%
+so now just let's consider a few cases
+here um
+
+ align:start position:0%
+here um
+ 
+
+ align:start position:0%
+here um
+um imagine you have you know two
+
+ align:start position:0%
+um imagine you have you know two
+ 
+
+ align:start position:0%
+um imagine you have you know two
+particles two fermions for example let's
+
+ align:start position:0%
+particles two fermions for example let's
+ 
+
+ align:start position:0%
+particles two fermions for example let's
+say two electrons
+
+ align:start position:0%
+say two electrons
+ 
+
+ align:start position:0%
+say two electrons
+um and you consider the wave function um
+
+ align:start position:0%
+um and you consider the wave function um
+ 
+
+ align:start position:0%
+um and you consider the wave function um
+quantum field theory um actually says
+
+ align:start position:0%
+quantum field theory um actually says
+ 
+
+ align:start position:0%
+quantum field theory um actually says
+that there's only
+
+ align:start position:0%
+that there's only
+ 
+
+ align:start position:0%
+that there's only
+one electron quantum field for the whole
+
+ align:start position:0%
+one electron quantum field for the whole
+ 
+
+ align:start position:0%
+one electron quantum field for the whole
+universe and every electron
+
+ align:start position:0%
+universe and every electron
+ 
+
+ align:start position:0%
+universe and every electron
+which has this is due to an excitation
+
+ align:start position:0%
+which has this is due to an excitation
+ 
+
+ align:start position:0%
+which has this is due to an excitation
+of the field
+
+ align:start position:0%
+of the field
+ 
+
+ align:start position:0%
+of the field
+and all electrons are identical in a
+
+ align:start position:0%
+and all electrons are identical in a
+ 
+
+ align:start position:0%
+and all electrons are identical in a
+quantum mechanical sense
+
+ align:start position:0%
+quantum mechanical sense
+ 
+
+ align:start position:0%
+quantum mechanical sense
+and they all arise from the same field
+
+ align:start position:0%
+and they all arise from the same field
+ 
+
+ align:start position:0%
+and they all arise from the same field
+now the theory says then that our
+
+ align:start position:0%
+now the theory says then that our
+ 
+
+ align:start position:0%
+now the theory says then that our
+particular properties or the resulting
+
+ align:start position:0%
+particular properties or the resulting
+ 
+
+ align:start position:0%
+particular properties or the resulting
+black equations namely their symmetry
+
+ align:start position:0%
+black equations namely their symmetry
+ 
+
+ align:start position:0%
+black equations namely their symmetry
+under exchange of these particles
+
+ align:start position:0%
+under exchange of these particles
+ 
+
+ align:start position:0%
+under exchange of these particles
+so the actual symmetry um depends on
+
+ align:start position:0%
+so the actual symmetry um depends on
+ 
+
+ align:start position:0%
+so the actual symmetry um depends on
+whether or not the particle is a fermion
+
+ align:start position:0%
+whether or not the particle is a fermion
+ 
+
+ align:start position:0%
+whether or not the particle is a fermion
+which means it has been one half or
+
+ align:start position:0%
+which means it has been one half or
+ 
+
+ align:start position:0%
+which means it has been one half or
+three halves or
+
+ align:start position:0%
+three halves or
+ 
+
+ align:start position:0%
+three halves or
+five halves etc or boson which means
+
+ align:start position:0%
+five halves etc or boson which means
+ 
+
+ align:start position:0%
+five halves etc or boson which means
+that it has been one
+
+ align:start position:0%
+that it has been one
+ 
+
+ align:start position:0%
+that it has been one
+zero one or two and so on so for any
+
+ align:start position:0%
+zero one or two and so on so for any
+ 
+
+ align:start position:0%
+zero one or two and so on so for any
+identical fermion an electron a quantum
+
+ align:start position:0%
+identical fermion an electron a quantum
+ 
+
+ align:start position:0%
+identical fermion an electron a quantum
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+theory says that their wave function
+
+ align:start position:0%
+theory says that their wave function
+ 
+
+ align:start position:0%
+theory says that their wave function
+must invade
+
+ align:start position:0%
+must invade
+ 
+
+ align:start position:0%
+must invade
+the property of anti-symmetry
+
+ align:start position:0%
+the property of anti-symmetry
+ 
+
+ align:start position:0%
+the property of anti-symmetry
+um this means that when we write an
+
+ align:start position:0%
+um this means that when we write an
+ 
+
+ align:start position:0%
+um this means that when we write an
+overall wave function and we replace two
+
+ align:start position:0%
+overall wave function and we replace two
+ 
+
+ align:start position:0%
+overall wave function and we replace two
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+to pick up a minus sign uh this property
+
+ align:start position:0%
+to pick up a minus sign uh this property
+ 
+
+ align:start position:0%
+to pick up a minus sign uh this property
+is just
+
+ align:start position:0%
+is just
+ 
+
+ align:start position:0%
+is just
+not just for for for electrons but for
+
+ align:start position:0%
+not just for for for electrons but for
+ 
+
+ align:start position:0%
+not just for for for electrons but for
+all fermions
+
+ align:start position:0%
+all fermions
+ 
+
+ align:start position:0%
+all fermions
+um that's all metaparticle as the
+
+ align:start position:0%
+um that's all metaparticle as the
+ 
+
+ align:start position:0%
+um that's all metaparticle as the
+smaller shoot
+
+ align:start position:0%
+smaller shoot
+ 
+
+ align:start position:0%
+smaller shoot
+so it also holds for composite particles
+
+ align:start position:0%
+so it also holds for composite particles
+ 
+
+ align:start position:0%
+so it also holds for composite particles
+a composite spin half particle
+
+ align:start position:0%
+a composite spin half particle
+ 
+
+ align:start position:0%
+a composite spin half particle
+um is subject to the same antisymmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this probably property of exchange
+
+ align:start position:0%
+this probably property of exchange
+ 
+
+ align:start position:0%
+this probably property of exchange
+antisymmetry leads to a well-known
+
+ align:start position:0%
+antisymmetry leads to a well-known
+ 
+
+ align:start position:0%
+antisymmetry leads to a well-known
+um principle namely the pauli principle
+
+ align:start position:0%
+um principle namely the pauli principle
+ 
+
+ align:start position:0%
+um principle namely the pauli principle
+which means that you cannot have two
+
+ align:start position:0%
+which means that you cannot have two
+ 
+
+ align:start position:0%
+which means that you cannot have two
+electrons of the same
+
+ align:start position:0%
+electrons of the same
+ 
+
+ align:start position:0%
+electrons of the same
+energy state or the same state um
+
+ align:start position:0%
+energy state or the same state um
+ 
+
+ align:start position:0%
+energy state or the same state um
+because when you would actually
+
+ align:start position:0%
+because when you would actually
+ 
+
+ align:start position:0%
+because when you would actually
+swap them you find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that they're identical which means
+
+ align:start position:0%
+that they're identical which means
+ 
+
+ align:start position:0%
+that they're identical which means
+there's dark contrast to the actual
+
+ align:start position:0%
+there's dark contrast to the actual
+ 
+
+ align:start position:0%
+there's dark contrast to the actual
+description of this wave function so
+
+ align:start position:0%
+description of this wave function so
+ 
+
+ align:start position:0%
+description of this wave function so
+this doesn't really work and therefore
+
+ align:start position:0%
+this doesn't really work and therefore
+ 
+
+ align:start position:0%
+this doesn't really work and therefore
+two electrons or two fermions cannot be
+
+ align:start position:0%
+two electrons or two fermions cannot be
+ 
+
+ align:start position:0%
+two electrons or two fermions cannot be
+in the same state
+
+ align:start position:0%
+in the same state
+ 
+
+ align:start position:0%
+in the same state
+in very general constructing a
+
+ align:start position:0%
+in very general constructing a
+ 
+
+ align:start position:0%
+in very general constructing a
+wave function or a total wave equation
+
+ align:start position:0%
+wave function or a total wave equation
+ 
+
+ align:start position:0%
+wave function or a total wave equation
+for two firms is not that hard
+
+ align:start position:0%
+for two firms is not that hard
+ 
+
+ align:start position:0%
+for two firms is not that hard
+you can simply do this by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by this construction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh important additional statement on
+
+ align:start position:0%
+uh important additional statement on
+ 
+
+ align:start position:0%
+uh important additional statement on
+note to take here is that an
+
+ align:start position:0%
+note to take here is that an
+ 
+
+ align:start position:0%
+note to take here is that an
+anti-particle such as a positron
+
+ align:start position:0%
+anti-particle such as a positron
+ 
+
+ align:start position:0%
+anti-particle such as a positron
+is not identical to a particle um
+
+ align:start position:0%
+is not identical to a particle um
+ 
+
+ align:start position:0%
+is not identical to a particle um
+such that the electron again
+
+ align:start position:0%
+such that the electron again
+ 
+
+ align:start position:0%
+such that the electron again
+if you move on to bosons both on
+
+ align:start position:0%
+if you move on to bosons both on
+ 
+
+ align:start position:0%
+if you move on to bosons both on
+exchange is symmetric
+
+ align:start position:0%
+exchange is symmetric
+ 
+
+ align:start position:0%
+exchange is symmetric
+meaning that you know if you replace two
+
+ align:start position:0%
+meaning that you know if you replace two
+ 
+
+ align:start position:0%
+meaning that you know if you replace two
+bosons defines identical
+
+ align:start position:0%
+bosons defines identical
+ 
+
+ align:start position:0%
+bosons defines identical
+wave function and then constructing a
+
+ align:start position:0%
+wave function and then constructing a
+ 
+
+ align:start position:0%
+wave function and then constructing a
+two boson
+
+ align:start position:0%
+two boson
+ 
+
+ align:start position:0%
+two boson
+uh total wave function you do this by
+
+ align:start position:0%
+uh total wave function you do this by
+ 
+
+ align:start position:0%
+uh total wave function you do this by
+adding those two functions together this
+
+ align:start position:0%
+adding those two functions together this
+ 
+
+ align:start position:0%
+adding those two functions together this
+is by definition
+
+ align:start position:0%
+is by definition
+ 
+
+ align:start position:0%
+is by definition
+the metric let's move now forwards to
+
+ align:start position:0%
+the metric let's move now forwards to
+ 
+
+ align:start position:0%
+the metric let's move now forwards to
+exchange particles again you have a very
+
+ align:start position:0%
+exchange particles again you have a very
+ 
+
+ align:start position:0%
+exchange particles again you have a very
+good idea of the classical picture
+
+ align:start position:0%
+good idea of the classical picture
+ 
+
+ align:start position:0%
+good idea of the classical picture
+how forces are transmitted um so the
+
+ align:start position:0%
+how forces are transmitted um so the
+ 
+
+ align:start position:0%
+how forces are transmitted um so the
+modern picture however
+
+ align:start position:0%
+modern picture however
+ 
+
+ align:start position:0%
+modern picture however
+of how a force acts under conservation
+
+ align:start position:0%
+of how a force acts under conservation
+ 
+
+ align:start position:0%
+of how a force acts under conservation
+is by admission and by absorption of a
+
+ align:start position:0%
+is by admission and by absorption of a
+ 
+
+ align:start position:0%
+is by admission and by absorption of a
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+what is shown in this diagram here where
+
+ align:start position:0%
+what is shown in this diagram here where
+ 
+
+ align:start position:0%
+what is shown in this diagram here where
+you let's say you have an electron and a
+
+ align:start position:0%
+you let's say you have an electron and a
+ 
+
+ align:start position:0%
+you let's say you have an electron and a
+second electron
+
+ align:start position:0%
+second electron
+ 
+
+ align:start position:0%
+second electron
+they see each other and they see each
+
+ align:start position:0%
+they see each other and they see each
+ 
+
+ align:start position:0%
+they see each other and they see each
+other by emitting
+
+ align:start position:0%
+other by emitting
+ 
+
+ align:start position:0%
+other by emitting
+and absorbing photons and you see this
+
+ align:start position:0%
+and absorbing photons and you see this
+ 
+
+ align:start position:0%
+and absorbing photons and you see this
+here so
+
+ align:start position:0%
+here so
+ 
+
+ align:start position:0%
+here so
+this electron comes along maybe emitting
+
+ align:start position:0%
+this electron comes along maybe emitting
+ 
+
+ align:start position:0%
+this electron comes along maybe emitting
+a photon
+
+ align:start position:0%
+a photon
+ 
+
+ align:start position:0%
+a photon
+this electron here emits it and by this
+
+ align:start position:0%
+this electron here emits it and by this
+ 
+
+ align:start position:0%
+this electron here emits it and by this
+exchange of emission
+
+ align:start position:0%
+exchange of emission
+ 
+
+ align:start position:0%
+exchange of emission
+and absorption of photon those two
+
+ align:start position:0%
+and absorption of photon those two
+ 
+
+ align:start position:0%
+and absorption of photon those two
+particles the electrostatic electrons
+
+ align:start position:0%
+particles the electrostatic electrons
+ 
+
+ align:start position:0%
+particles the electrostatic electrons
+see each other
+
+ align:start position:0%
+see each other
+ 
+
+ align:start position:0%
+see each other
+for this you know you can think about
+
+ align:start position:0%
+for this you know you can think about
+ 
+
+ align:start position:0%
+for this you know you can think about
+like you know two ships
+
+ align:start position:0%
+like you know two ships
+ 
+
+ align:start position:0%
+like you know two ships
+shooting cannons if you want but this
+
+ align:start position:0%
+shooting cannons if you want but this
+ 
+
+ align:start position:0%
+shooting cannons if you want but this
+would all um
+
+ align:start position:0%
+would all um
+ 
+
+ align:start position:0%
+would all um
+um but you also have to consider that
+
+ align:start position:0%
+um but you also have to consider that
+ 
+
+ align:start position:0%
+um but you also have to consider that
+there is not just repelling forces but
+
+ align:start position:0%
+there is not just repelling forces but
+ 
+
+ align:start position:0%
+there is not just repelling forces but
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+attracting forces could have replaced
+
+ align:start position:0%
+attracting forces could have replaced
+ 
+
+ align:start position:0%
+attracting forces could have replaced
+the electron with the positron and the
+
+ align:start position:0%
+the electron with the positron and the
+ 
+
+ align:start position:0%
+the electron with the positron and the
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+negative the negative and the positive
+
+ align:start position:0%
+negative the negative and the positive
+ 
+
+ align:start position:0%
+negative the negative and the positive
+charge attracting each other
+
+ align:start position:0%
+charge attracting each other
+ 
+
+ align:start position:0%
+charge attracting each other
+this is it for this uh for this short um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically an intro into the intro of the
+
+ align:start position:0%
+basically an intro into the intro of the
+ 
+
+ align:start position:0%
+basically an intro into the intro of the
+intro um
+
+ align:start position:0%
+intro um
+ 
+
+ align:start position:0%
+intro um
+i hope you enjoy this all of this
+
+ align:start position:0%
+i hope you enjoy this all of this
+ 
+
+ align:start position:0%
+i hope you enjoy this all of this
+concept we go into more detail
+
+ align:start position:0%
+concept we go into more detail
+ 
+
+ align:start position:0%
+concept we go into more detail
+this is really just the starting point
+
+ align:start position:0%
+this is really just the starting point
+ 
+
+ align:start position:0%
+this is really just the starting point
+um and in the next lecture you'll see
+
+ align:start position:0%
+um and in the next lecture you'll see
+ 
+
+ align:start position:0%
+um and in the next lecture you'll see
+how we can actually understand
+
+ align:start position:0%
+how we can actually understand
+ 
+
+ align:start position:0%
+how we can actually understand
+aspects of this diagram here which we
+
+ align:start position:0%
+aspects of this diagram here which we
+ 
+
+ align:start position:0%
+aspects of this diagram here which we
+call the final diagram
+
+ align:start position:0%
+call the final diagram
+ 
+
+ align:start position:0%
+call the final diagram
+you
\ No newline at end of file
diff --git a/Hzv9WuqIzA0.txt b/Hzv9WuqIzA0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3307dd135b6e2357c1e9241852b019d457a8d405
--- /dev/null
+++ b/Hzv9WuqIzA0.txt
@@ -0,0 +1,14547 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so today I'll talk about payment
+
+ align:start position:0%
+okay so today I'll talk about payment
+ 
+
+ align:start position:0%
+okay so today I'll talk about payment
+channels and the Lightning Network and I
+
+ align:start position:0%
+channels and the Lightning Network and I
+ 
+
+ align:start position:0%
+channels and the Lightning Network and I
+am sorry if I gloss over things I've
+
+ align:start position:0%
+am sorry if I gloss over things I've
+ 
+
+ align:start position:0%
+am sorry if I gloss over things I've
+explained this like a lot in the last
+
+ align:start position:0%
+explained this like a lot in the last
+ 
+
+ align:start position:0%
+explained this like a lot in the last
+two years because that's sort of my work
+
+ align:start position:0%
+two years because that's sort of my work
+ 
+
+ align:start position:0%
+two years because that's sort of my work
+on so I might like to skip over
+
+ align:start position:0%
+on so I might like to skip over
+ 
+
+ align:start position:0%
+on so I might like to skip over
+something you're like wait how did you
+
+ align:start position:0%
+something you're like wait how did you
+ 
+
+ align:start position:0%
+something you're like wait how did you
+get there so let me know so it'll have
+
+ align:start position:0%
+get there so let me know so it'll have
+ 
+
+ align:start position:0%
+get there so let me know so it'll have
+unidirectional payment channels and then
+
+ align:start position:0%
+unidirectional payment channels and then
+ 
+
+ align:start position:0%
+unidirectional payment channels and then
+lightning channel and then multi-hop
+
+ align:start position:0%
+lightning channel and then multi-hop
+ 
+
+ align:start position:0%
+lightning channel and then multi-hop
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the idea of payment channels why do
+
+ align:start position:0%
+so the idea of payment channels why do
+ 
+
+ align:start position:0%
+so the idea of payment channels why do
+we need to do all this complicated weird
+
+ align:start position:0%
+we need to do all this complicated weird
+ 
+
+ align:start position:0%
+we need to do all this complicated weird
+stuff with payment channels well the
+
+ align:start position:0%
+stuff with payment channels well the
+ 
+
+ align:start position:0%
+stuff with payment channels well the
+problem is these networks are really
+
+ align:start position:0%
+problem is these networks are really
+ 
+
+ align:start position:0%
+problem is these networks are really
+poor in scalability right every
+
+ align:start position:0%
+poor in scalability right every
+ 
+
+ align:start position:0%
+poor in scalability right every
+transaction on the blockchain
+
+ align:start position:0%
+transaction on the blockchain
+ 
+
+ align:start position:0%
+transaction on the blockchain
+you know that whole idea doesn't scale
+
+ align:start position:0%
+you know that whole idea doesn't scale
+ 
+
+ align:start position:0%
+you know that whole idea doesn't scale
+it's sort of people say it's o of N
+
+ align:start position:0%
+it's sort of people say it's o of N
+ 
+
+ align:start position:0%
+it's sort of people say it's o of N
+squared depends on what you define as N
+
+ align:start position:0%
+squared depends on what you define as N
+ 
+
+ align:start position:0%
+squared depends on what you define as N
+and things like that right so if you
+
+ align:start position:0%
+and things like that right so if you
+ 
+
+ align:start position:0%
+and things like that right so if you
+double the number of nodes it actually
+
+ align:start position:0%
+double the number of nodes it actually
+ 
+
+ align:start position:0%
+double the number of nodes it actually
+doesn't you can say well if you double
+
+ align:start position:0%
+doesn't you can say well if you double
+ 
+
+ align:start position:0%
+doesn't you can say well if you double
+the number of nodes each node is gonna
+
+ align:start position:0%
+the number of nodes each node is gonna
+ 
+
+ align:start position:0%
+the number of nodes each node is gonna
+be making some transactions right and
+
+ align:start position:0%
+be making some transactions right and
+ 
+
+ align:start position:0%
+be making some transactions right and
+then you're like okay yeah that's N
+
+ align:start position:0%
+then you're like okay yeah that's N
+ 
+
+ align:start position:0%
+then you're like okay yeah that's N
+squared if you count the total number of
+
+ align:start position:0%
+squared if you count the total number of
+ 
+
+ align:start position:0%
+squared if you count the total number of
+computations throughout the entire
+
+ align:start position:0%
+computations throughout the entire
+ 
+
+ align:start position:0%
+computations throughout the entire
+system but at the same time it's like
+
+ align:start position:0%
+system but at the same time it's like
+ 
+
+ align:start position:0%
+system but at the same time it's like
+well you've doubled the number of nodes
+
+ align:start position:0%
+well you've doubled the number of nodes
+ 
+
+ align:start position:0%
+well you've doubled the number of nodes
+so really it's o of n right like for any
+
+ align:start position:0%
+so really it's o of n right like for any
+ 
+
+ align:start position:0%
+so really it's o of n right like for any
+one computer your amount of computation
+
+ align:start position:0%
+one computer your amount of computation
+ 
+
+ align:start position:0%
+one computer your amount of computation
+you have to do scales with how many
+
+ align:start position:0%
+you have to do scales with how many
+ 
+
+ align:start position:0%
+you have to do scales with how many
+other computers that are so it's a
+
+ align:start position:0%
+other computers that are so it's a
+ 
+
+ align:start position:0%
+other computers that are so it's a
+little you know questionable but but
+
+ align:start position:0%
+little you know questionable but but
+ 
+
+ align:start position:0%
+little you know questionable but but
+basically it doesn't scale well right it
+
+ align:start position:0%
+basically it doesn't scale well right it
+ 
+
+ align:start position:0%
+basically it doesn't scale well right it
+doesn't scale to what you want and so I
+
+ align:start position:0%
+doesn't scale to what you want and so I
+ 
+
+ align:start position:0%
+doesn't scale to what you want and so I
+put a little history the first response
+
+ align:start position:0%
+put a little history the first response
+ 
+
+ align:start position:0%
+put a little history the first response
+of anyone ever referring to Bitcoin so
+
+ align:start position:0%
+of anyone ever referring to Bitcoin so
+ 
+
+ align:start position:0%
+of anyone ever referring to Bitcoin so
+there was a 2008 like October 30
+
+ align:start position:0%
+there was a 2008 like October 30
+ 
+
+ align:start position:0%
+there was a 2008 like October 30
+Halloween 2008 or like maybe after
+
+ align:start position:0%
+Halloween 2008 or like maybe after
+ 
+
+ align:start position:0%
+Halloween 2008 or like maybe after
+midnight so November 1st and Satoshi
+
+ align:start position:0%
+midnight so November 1st and Satoshi
+ 
+
+ align:start position:0%
+midnight so November 1st and Satoshi
+wrote I've been working on a new
+
+ align:start position:0%
+wrote I've been working on a new
+ 
+
+ align:start position:0%
+wrote I've been working on a new
+electronic cash system that's fully
+
+ align:start position:0%
+electronic cash system that's fully
+ 
+
+ align:start position:0%
+electronic cash system that's fully
+peer-to-peer with no trusted third party
+
+ align:start position:0%
+peer-to-peer with no trusted third party
+ 
+
+ align:start position:0%
+peer-to-peer with no trusted third party
+he has a little blurb the first reply on
+
+ align:start position:0%
+he has a little blurb the first reply on
+ 
+
+ align:start position:0%
+he has a little blurb the first reply on
+this mailing list was some guy James a
+
+ align:start position:0%
+this mailing list was some guy James a
+ 
+
+ align:start position:0%
+this mailing list was some guy James a
+Donald saying we very very much need
+
+ align:start position:0%
+Donald saying we very very much need
+ 
+
+ align:start position:0%
+Donald saying we very very much need
+such a system the way I understand your
+
+ align:start position:0%
+such a system the way I understand your
+ 
+
+ align:start position:0%
+such a system the way I understand your
+proposal it does not seem to scale to
+
+ align:start position:0%
+proposal it does not seem to scale to
+ 
+
+ align:start position:0%
+proposal it does not seem to scale to
+the required size so that was the first
+
+ align:start position:0%
+the required size so that was the first
+ 
+
+ align:start position:0%
+the required size so that was the first
+thing anyone's ever said about Bitcoin
+
+ align:start position:0%
+thing anyone's ever said about Bitcoin
+ 
+
+ align:start position:0%
+thing anyone's ever said about Bitcoin
+and we're still talking about it almost
+
+ align:start position:0%
+and we're still talking about it almost
+ 
+
+ align:start position:0%
+and we're still talking about it almost
+10 years later
+
+ align:start position:0%
+10 years later
+ 
+
+ align:start position:0%
+10 years later
+I wonder who James Donnell is maybe he's
+
+ align:start position:0%
+I wonder who James Donnell is maybe he's
+ 
+
+ align:start position:0%
+I wonder who James Donnell is maybe he's
+got a ton of Bitcoin now and he you know
+
+ align:start position:0%
+got a ton of Bitcoin now and he you know
+ 
+
+ align:start position:0%
+got a ton of Bitcoin now and he you know
+mined it this was so it was written
+
+ align:start position:0%
+mined it this was so it was written
+ 
+
+ align:start position:0%
+mined it this was so it was written
+about in late 2008 the actual software
+
+ align:start position:0%
+about in late 2008 the actual software
+ 
+
+ align:start position:0%
+about in late 2008 the actual software
+was released in 2009
+
+ align:start position:0%
+was released in 2009
+ 
+
+ align:start position:0%
+was released in 2009
+and no one really there's a couple males
+
+ align:start position:0%
+and no one really there's a couple males
+ 
+
+ align:start position:0%
+and no one really there's a couple males
+no one really looked into it much okay
+
+ align:start position:0%
+no one really looked into it much okay
+ 
+
+ align:start position:0%
+no one really looked into it much okay
+so you can start with a one way payment
+
+ align:start position:0%
+so you can start with a one way payment
+ 
+
+ align:start position:0%
+so you can start with a one way payment
+channel and this was I think Satoshi
+
+ align:start position:0%
+channel and this was I think Satoshi
+ 
+
+ align:start position:0%
+channel and this was I think Satoshi
+sort of mentioned these ideas never
+
+ align:start position:0%
+sort of mentioned these ideas never
+ 
+
+ align:start position:0%
+sort of mentioned these ideas never
+really implemented anything and this the
+
+ align:start position:0%
+really implemented anything and this the
+ 
+
+ align:start position:0%
+really implemented anything and this the
+way he talked about it didn't actually
+
+ align:start position:0%
+way he talked about it didn't actually
+ 
+
+ align:start position:0%
+way he talked about it didn't actually
+work some people in 2012 I remember
+
+ align:start position:0%
+work some people in 2012 I remember
+ 
+
+ align:start position:0%
+work some people in 2012 I remember
+looking at this I think blue mat and
+
+ align:start position:0%
+looking at this I think blue mat and
+ 
+
+ align:start position:0%
+looking at this I think blue mat and
+Mike Hearn gave a talk about like how
+
+ align:start position:0%
+Mike Hearn gave a talk about like how
+ 
+
+ align:start position:0%
+Mike Hearn gave a talk about like how
+you could make payment channels that
+
+ align:start position:0%
+you could make payment channels that
+ 
+
+ align:start position:0%
+you could make payment channels that
+didn't quite work either but the idea
+
+ align:start position:0%
+didn't quite work either but the idea
+ 
+
+ align:start position:0%
+didn't quite work either but the idea
+made sense so the idea is you have some
+
+ align:start position:0%
+made sense so the idea is you have some
+ 
+
+ align:start position:0%
+made sense so the idea is you have some
+kind of shared balance between two
+
+ align:start position:0%
+kind of shared balance between two
+ 
+
+ align:start position:0%
+kind of shared balance between two
+parties and you can move coins in one
+
+ align:start position:0%
+parties and you can move coins in one
+ 
+
+ align:start position:0%
+parties and you can move coins in one
+direction without making new
+
+ align:start position:0%
+direction without making new
+ 
+
+ align:start position:0%
+direction without making new
+transactions on the blockchain
+
+ align:start position:0%
+transactions on the blockchain
+ 
+
+ align:start position:0%
+transactions on the blockchain
+so one thing we haven't looked at but
+
+ align:start position:0%
+so one thing we haven't looked at but
+ 
+
+ align:start position:0%
+so one thing we haven't looked at but
+you might have seen in in the homework
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you look at like a transaction
+
+ align:start position:0%
+so if you look at like a transaction
+ 
+
+ align:start position:0%
+so if you look at like a transaction
+right probably have seen this kind of
+
+ align:start position:0%
+right probably have seen this kind of
+ 
+
+ align:start position:0%
+right probably have seen this kind of
+thing through the homework it's got a
+
+ align:start position:0%
+thing through the homework it's got a
+ 
+
+ align:start position:0%
+thing through the homework it's got a
+lock time and in this case the lock time
+
+ align:start position:0%
+lock time and in this case the lock time
+ 
+
+ align:start position:0%
+lock time and in this case the lock time
+is zero that means this transaction is
+
+ align:start position:0%
+is zero that means this transaction is
+ 
+
+ align:start position:0%
+is zero that means this transaction is
+valid
+
+ align:start position:0%
+valid
+ 
+
+ align:start position:0%
+valid
+at any point you know above height zero
+
+ align:start position:0%
+at any point you know above height zero
+ 
+
+ align:start position:0%
+at any point you know above height zero
+it's it's valid and every block is above
+
+ align:start position:0%
+it's it's valid and every block is above
+ 
+
+ align:start position:0%
+it's it's valid and every block is above
+height zero you can also find
+
+ align:start position:0%
+height zero you can also find
+ 
+
+ align:start position:0%
+height zero you can also find
+transactions which let's see yeah
+
+ align:start position:0%
+transactions which let's see yeah
+ 
+
+ align:start position:0%
+transactions which let's see yeah
+which has a lock time of this so this
+
+ align:start position:0%
+which has a lock time of this so this
+ 
+
+ align:start position:0%
+which has a lock time of this so this
+looks like a unix time where you you set
+
+ align:start position:0%
+looks like a unix time where you you set
+ 
+
+ align:start position:0%
+looks like a unix time where you you set
+a time this is like a unix time so you
+
+ align:start position:0%
+a time this is like a unix time so you
+ 
+
+ align:start position:0%
+a time this is like a unix time so you
+next time if you don't know it's like a
+
+ align:start position:0%
+next time if you don't know it's like a
+ 
+
+ align:start position:0%
+next time if you don't know it's like a
+30 well its seconds since january 1st
+
+ align:start position:0%
+30 well its seconds since january 1st
+ 
+
+ align:start position:0%
+30 well its seconds since january 1st
+1970 that's sort of like the you know
+
+ align:start position:0%
+1970 that's sort of like the you know
+ 
+
+ align:start position:0%
+1970 that's sort of like the you know
+first second and i don't know that's
+
+ align:start position:0%
+first second and i don't know that's
+ 
+
+ align:start position:0%
+first second and i don't know that's
+probably a week ago or something so you
+
+ align:start position:0%
+probably a week ago or something so you
+ 
+
+ align:start position:0%
+probably a week ago or something so you
+can you can have that filled in a
+
+ align:start position:0%
+can you can have that filled in a
+ 
+
+ align:start position:0%
+can you can have that filled in a
+transaction and the idea is the
+
+ align:start position:0%
+transaction and the idea is the
+ 
+
+ align:start position:0%
+transaction and the idea is the
+transactions only valid after that time
+
+ align:start position:0%
+transactions only valid after that time
+ 
+
+ align:start position:0%
+transactions only valid after that time
+or height it's a little weird below what
+
+ align:start position:0%
+or height it's a little weird below what
+ 
+
+ align:start position:0%
+or height it's a little weird below what
+is it 500 million it counts as a height
+
+ align:start position:0%
+is it 500 million it counts as a height
+ 
+
+ align:start position:0%
+is it 500 million it counts as a height
+above 500 million it counts as a you
+
+ align:start position:0%
+above 500 million it counts as a you
+ 
+
+ align:start position:0%
+above 500 million it counts as a you
+next time which ends up working because
+
+ align:start position:0%
+next time which ends up working because
+ 
+
+ align:start position:0%
+next time which ends up working because
+the idea the UNIX times below 500
+
+ align:start position:0%
+the idea the UNIX times below 500
+ 
+
+ align:start position:0%
+the idea the UNIX times below 500
+million or like in the 80s so you
+
+ align:start position:0%
+million or like in the 80s so you
+ 
+
+ align:start position:0%
+million or like in the 80s so you
+there's no Bitcoin didn't exist then
+
+ align:start position:0%
+there's no Bitcoin didn't exist then
+ 
+
+ align:start position:0%
+there's no Bitcoin didn't exist then
+there's no real need to have time walk
+
+ align:start position:0%
+there's no real need to have time walk
+ 
+
+ align:start position:0%
+there's no real need to have time walk
+think what's her about what five hundred
+
+ align:start position:0%
+think what's her about what five hundred
+ 
+
+ align:start position:0%
+think what's her about what five hundred
+million yeah a couple thousand years so
+
+ align:start position:0%
+million yeah a couple thousand years so
+ 
+
+ align:start position:0%
+million yeah a couple thousand years so
+ya know there's there's way more
+
+ align:start position:0%
+ya know there's there's way more
+ 
+
+ align:start position:0%
+ya know there's there's way more
+problems than Bitcoin before that the
+
+ align:start position:0%
+problems than Bitcoin before that the
+ 
+
+ align:start position:0%
+problems than Bitcoin before that the
+the time field in the headers for bytes
+
+ align:start position:0%
+the time field in the headers for bytes
+ 
+
+ align:start position:0%
+the time field in the headers for bytes
+so either so if it was signed it be 2038
+
+ align:start position:0%
+so either so if it was signed it be 2038
+ 
+
+ align:start position:0%
+so either so if it was signed it be 2038
+that it flips over and goes negative but
+
+ align:start position:0%
+that it flips over and goes negative but
+ 
+
+ align:start position:0%
+that it flips over and goes negative but
+it's unsigned so you got till 2000 106
+
+ align:start position:0%
+it's unsigned so you got till 2000 106
+ 
+
+ align:start position:0%
+it's unsigned so you got till 2000 106
+there's actually a hard fork to fix that
+
+ align:start position:0%
+there's actually a hard fork to fix that
+ 
+
+ align:start position:0%
+there's actually a hard fork to fix that
+but so it you know there's there's all
+
+ align:start position:0%
+but so it you know there's there's all
+ 
+
+ align:start position:0%
+but so it you know there's there's all
+sorts of weird like wait what do we do
+
+ align:start position:0%
+sorts of weird like wait what do we do
+ 
+
+ align:start position:0%
+sorts of weird like wait what do we do
+in the hundreds or thousands of years we
+
+ align:start position:0%
+in the hundreds or thousands of years we
+ 
+
+ align:start position:0%
+in the hundreds or thousands of years we
+have to make these little tweaks which
+
+ align:start position:0%
+have to make these little tweaks which
+ 
+
+ align:start position:0%
+have to make these little tweaks which
+hopefully wouldn't be super
+
+ align:start position:0%
+hopefully wouldn't be super
+ 
+
+ align:start position:0%
+hopefully wouldn't be super
+controversial because it's like well
+
+ align:start position:0%
+controversial because it's like well
+ 
+
+ align:start position:0%
+controversial because it's like well
+it'll stop working unless we change this
+
+ align:start position:0%
+it'll stop working unless we change this
+ 
+
+ align:start position:0%
+it'll stop working unless we change this
+little thing okay so yeah that you can
+
+ align:start position:0%
+little thing okay so yeah that you can
+ 
+
+ align:start position:0%
+little thing okay so yeah that you can
+have these lock times and you can use
+
+ align:start position:0%
+have these lock times and you can use
+ 
+
+ align:start position:0%
+have these lock times and you can use
+those so what you can do is make a
+
+ align:start position:0%
+those so what you can do is make a
+ 
+
+ align:start position:0%
+those so what you can do is make a
+channel and a channel is really just a
+
+ align:start position:0%
+channel and a channel is really just a
+ 
+
+ align:start position:0%
+channel and a channel is really just a
+multi-sig output multi-sig a lot of
+
+ align:start position:0%
+multi-sig output multi-sig a lot of
+ 
+
+ align:start position:0%
+multi-sig output multi-sig a lot of
+times is used for I want to say
+
+ align:start position:0%
+times is used for I want to say
+ 
+
+ align:start position:0%
+times is used for I want to say
+two-factor authentication but you know
+
+ align:start position:0%
+two-factor authentication but you know
+ 
+
+ align:start position:0%
+two-factor authentication but you know
+you could have two of two multi-sig
+
+ align:start position:0%
+you could have two of two multi-sig
+ 
+
+ align:start position:0%
+you could have two of two multi-sig
+where your phone needs to sign and your
+
+ align:start position:0%
+where your phone needs to sign and your
+ 
+
+ align:start position:0%
+where your phone needs to sign and your
+desktop needs to sign and then if
+
+ align:start position:0%
+desktop needs to sign and then if
+ 
+
+ align:start position:0%
+desktop needs to sign and then if
+someone steals your phone or you know
+
+ align:start position:0%
+someone steals your phone or you know
+ 
+
+ align:start position:0%
+someone steals your phone or you know
+hacks your phone and gets the key out
+
+ align:start position:0%
+hacks your phone and gets the key out
+ 
+
+ align:start position:0%
+hacks your phone and gets the key out
+well they have to also get your computer
+
+ align:start position:0%
+well they have to also get your computer
+ 
+
+ align:start position:0%
+well they have to also get your computer
+so this is useful but in these cases
+
+ align:start position:0%
+so this is useful but in these cases
+ 
+
+ align:start position:0%
+so this is useful but in these cases
+it's sort of adversarial multi-sig where
+
+ align:start position:0%
+it's sort of adversarial multi-sig where
+ 
+
+ align:start position:0%
+it's sort of adversarial multi-sig where
+it's not just you and you it's not like
+
+ align:start position:0%
+it's not just you and you it's not like
+ 
+
+ align:start position:0%
+it's not just you and you it's not like
+your phone and your computer it's okay
+
+ align:start position:0%
+your phone and your computer it's okay
+ 
+
+ align:start position:0%
+your phone and your computer it's okay
+it's Alice and Bob they're completely
+
+ align:start position:0%
+it's Alice and Bob they're completely
+ 
+
+ align:start position:0%
+it's Alice and Bob they're completely
+separate people they're not necessarily
+
+ align:start position:0%
+separate people they're not necessarily
+ 
+
+ align:start position:0%
+separate people they're not necessarily
+friends you know it could be customer
+
+ align:start position:0%
+friends you know it could be customer
+ 
+
+ align:start position:0%
+friends you know it could be customer
+merchants kind of thing and they create
+
+ align:start position:0%
+merchants kind of thing and they create
+ 
+
+ align:start position:0%
+merchants kind of thing and they create
+a transaction together so they fund it
+
+ align:start position:0%
+a transaction together so they fund it
+ 
+
+ align:start position:0%
+a transaction together so they fund it
+and Alice is funding this channel and so
+
+ align:start position:0%
+and Alice is funding this channel and so
+ 
+
+ align:start position:0%
+and Alice is funding this channel and so
+she takes her own coins write her own TX
+
+ align:start position:0%
+she takes her own coins write her own TX
+ 
+
+ align:start position:0%
+she takes her own coins write her own TX
+ID index her an output signs it and
+
+ align:start position:0%
+ID index her an output signs it and
+ 
+
+ align:start position:0%
+ID index her an output signs it and
+sends to an allison bob multi-sig and
+
+ align:start position:0%
+sends to an allison bob multi-sig and
+ 
+
+ align:start position:0%
+sends to an allison bob multi-sig and
+sends ten coins so in order to spend
+
+ align:start position:0%
+sends ten coins so in order to spend
+ 
+
+ align:start position:0%
+sends ten coins so in order to spend
+this they both have to cooperate um but
+
+ align:start position:0%
+this they both have to cooperate um but
+ 
+
+ align:start position:0%
+this they both have to cooperate um but
+before doing this Bob gives her a refund
+
+ align:start position:0%
+before doing this Bob gives her a refund
+ 
+
+ align:start position:0%
+before doing this Bob gives her a refund
+transaction so the idea is if Alice just
+
+ align:start position:0%
+transaction so the idea is if Alice just
+ 
+
+ align:start position:0%
+transaction so the idea is if Alice just
+broadcasts to this it says okay I'm
+
+ align:start position:0%
+broadcasts to this it says okay I'm
+ 
+
+ align:start position:0%
+broadcasts to this it says okay I'm
+taking my coins I'm sending it to Alice
+
+ align:start position:0%
+taking my coins I'm sending it to Alice
+ 
+
+ align:start position:0%
+taking my coins I'm sending it to Alice
+and Bob multi-sig Bob can just disappear
+
+ align:start position:0%
+and Bob multi-sig Bob can just disappear
+ 
+
+ align:start position:0%
+and Bob multi-sig Bob can just disappear
+and then Alice is stuck and the money
+
+ align:start position:0%
+and then Alice is stuck and the money
+ 
+
+ align:start position:0%
+and then Alice is stuck and the money
+stuck there forever because Bob
+
+ align:start position:0%
+stuck there forever because Bob
+ 
+
+ align:start position:0%
+stuck there forever because Bob
+never sign or Bob can say Oh Alice looks
+
+ align:start position:0%
+never sign or Bob can say Oh Alice looks
+ 
+
+ align:start position:0%
+never sign or Bob can say Oh Alice looks
+like you sent ten coins how about this
+
+ align:start position:0%
+like you sent ten coins how about this
+ 
+
+ align:start position:0%
+like you sent ten coins how about this
+I'll give you nine of them you just give
+
+ align:start position:0%
+I'll give you nine of them you just give
+ 
+
+ align:start position:0%
+I'll give you nine of them you just give
+me one of them and I don't you know
+
+ align:start position:0%
+me one of them and I don't you know
+ 
+
+ align:start position:0%
+me one of them and I don't you know
+you're not buying anything this is just
+
+ align:start position:0%
+you're not buying anything this is just
+ 
+
+ align:start position:0%
+you're not buying anything this is just
+I'm holding your coins hostage
+
+ align:start position:0%
+I'm holding your coins hostage
+ 
+
+ align:start position:0%
+I'm holding your coins hostage
+Bob could even make a even better threat
+
+ align:start position:0%
+Bob could even make a even better threat
+ 
+
+ align:start position:0%
+Bob could even make a even better threat
+and say I will sign a bunch of time lock
+
+ align:start position:0%
+and say I will sign a bunch of time lock
+ 
+
+ align:start position:0%
+and say I will sign a bunch of time lock
+transactions if you want your money
+
+ align:start position:0%
+transactions if you want your money
+ 
+
+ align:start position:0%
+transactions if you want your money
+today you only get one coin if you want
+
+ align:start position:0%
+today you only get one coin if you want
+ 
+
+ align:start position:0%
+today you only get one coin if you want
+your money in a week you'll get two
+
+ align:start position:0%
+your money in a week you'll get two
+ 
+
+ align:start position:0%
+your money in a week you'll get two
+coins and and you know sign these things
+
+ align:start position:0%
+coins and and you know sign these things
+ 
+
+ align:start position:0%
+coins and and you know sign these things
+with lock times and all the transactions
+
+ align:start position:0%
+with lock times and all the transactions
+ 
+
+ align:start position:0%
+with lock times and all the transactions
+over to Alice and say well you can pick
+
+ align:start position:0%
+over to Alice and say well you can pick
+ 
+
+ align:start position:0%
+over to Alice and say well you can pick
+you know how long do you want to wait to
+
+ align:start position:0%
+you know how long do you want to wait to
+ 
+
+ align:start position:0%
+you know how long do you want to wait to
+get your money back
+
+ align:start position:0%
+get your money back
+ 
+
+ align:start position:0%
+get your money back
+an analysis only response is oh shoot
+
+ align:start position:0%
+an analysis only response is oh shoot
+ 
+
+ align:start position:0%
+an analysis only response is oh shoot
+well if I wait years maybe I'll get most
+
+ align:start position:0%
+well if I wait years maybe I'll get most
+ 
+
+ align:start position:0%
+well if I wait years maybe I'll get most
+of my coins back but if I want my money
+
+ align:start position:0%
+of my coins back but if I want my money
+ 
+
+ align:start position:0%
+of my coins back but if I want my money
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+you know there's there's all sorts of
+
+ align:start position:0%
+you know there's there's all sorts of
+ 
+
+ align:start position:0%
+you know there's there's all sorts of
+horrible hostage situations even if
+
+ align:start position:0%
+horrible hostage situations even if
+ 
+
+ align:start position:0%
+horrible hostage situations even if
+they're both if they both have money at
+
+ align:start position:0%
+they're both if they both have money at
+ 
+
+ align:start position:0%
+they're both if they both have money at
+stake one one person could have less
+
+ align:start position:0%
+stake one one person could have less
+ 
+
+ align:start position:0%
+stake one one person could have less
+time value of money so they're like look
+
+ align:start position:0%
+time value of money so they're like look
+ 
+
+ align:start position:0%
+time value of money so they're like look
+I don't I don't need this anytime soon
+
+ align:start position:0%
+I don't I don't need this anytime soon
+ 
+
+ align:start position:0%
+I don't I don't need this anytime soon
+so I'm willing to wait so this is
+
+ align:start position:0%
+so I'm willing to wait so this is
+ 
+
+ align:start position:0%
+so I'm willing to wait so this is
+dangerous so what they do beforehand is
+
+ align:start position:0%
+dangerous so what they do beforehand is
+ 
+
+ align:start position:0%
+dangerous so what they do beforehand is
+Alice's hey Bob give me a refund
+
+ align:start position:0%
+Alice's hey Bob give me a refund
+ 
+
+ align:start position:0%
+Alice's hey Bob give me a refund
+transaction so Bob signs a refund
+
+ align:start position:0%
+transaction so Bob signs a refund
+ 
+
+ align:start position:0%
+transaction so Bob signs a refund
+transaction with a lock time of one week
+
+ align:start position:0%
+transaction with a lock time of one week
+ 
+
+ align:start position:0%
+transaction with a lock time of one week
+from now March 28th and the input is the
+
+ align:start position:0%
+from now March 28th and the input is the
+ 
+
+ align:start position:0%
+from now March 28th and the input is the
+fund transaction ID even though the fund
+
+ align:start position:0%
+fund transaction ID even though the fund
+ 
+
+ align:start position:0%
+fund transaction ID even though the fund
+transaction ID comes later
+
+ align:start position:0%
+transaction ID comes later
+ 
+
+ align:start position:0%
+transaction ID comes later
+thanks to segue you can say I know what
+
+ align:start position:0%
+thanks to segue you can say I know what
+ 
+
+ align:start position:0%
+thanks to segue you can say I know what
+the TX ID is gonna be I'm gonna you know
+
+ align:start position:0%
+the TX ID is gonna be I'm gonna you know
+ 
+
+ align:start position:0%
+the TX ID is gonna be I'm gonna you know
+reference a spend for that and Bob
+
+ align:start position:0%
+reference a spend for that and Bob
+ 
+
+ align:start position:0%
+reference a spend for that and Bob
+signature is gonna be on there bob signs
+
+ align:start position:0%
+signature is gonna be on there bob signs
+ 
+
+ align:start position:0%
+signature is gonna be on there bob signs
+it hands it over to Alice Alice's
+
+ align:start position:0%
+it hands it over to Alice Alice's
+ 
+
+ align:start position:0%
+it hands it over to Alice Alice's
+doesn't Alice's signatures not there yet
+
+ align:start position:0%
+doesn't Alice's signatures not there yet
+ 
+
+ align:start position:0%
+doesn't Alice's signatures not there yet
+right so Alice can sign it and store it
+
+ align:start position:0%
+right so Alice can sign it and store it
+ 
+
+ align:start position:0%
+right so Alice can sign it and store it
+on her drive or chicken sign later but
+
+ align:start position:0%
+on her drive or chicken sign later but
+ 
+
+ align:start position:0%
+on her drive or chicken sign later but
+until March 28th this transactions not
+
+ align:start position:0%
+until March 28th this transactions not
+ 
+
+ align:start position:0%
+until March 28th this transactions not
+happening right if you try to broadcast
+
+ align:start position:0%
+happening right if you try to broadcast
+ 
+
+ align:start position:0%
+happening right if you try to broadcast
+it everyone will reject it and the
+
+ align:start position:0%
+it everyone will reject it and the
+ 
+
+ align:start position:0%
+it everyone will reject it and the
+output from this refund transaction is
+
+ align:start position:0%
+output from this refund transaction is
+ 
+
+ align:start position:0%
+output from this refund transaction is
+it just sends to Alice's address all 10
+
+ align:start position:0%
+it just sends to Alice's address all 10
+ 
+
+ align:start position:0%
+it just sends to Alice's address all 10
+points yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh how does how do they know the fun its
+
+ align:start position:0%
+Oh how does how do they know the fun its
+ 
+
+ align:start position:0%
+Oh how does how do they know the fun its
+exid Alice can calculate it and tell Bob
+
+ align:start position:0%
+exid Alice can calculate it and tell Bob
+ 
+
+ align:start position:0%
+exid Alice can calculate it and tell Bob
+Alice can say I'm building a fund
+
+ align:start position:0%
+Alice can say I'm building a fund
+ 
+
+ align:start position:0%
+Alice can say I'm building a fund
+transaction Alice knows her inputs she
+
+ align:start position:0%
+transaction Alice knows her inputs she
+ 
+
+ align:start position:0%
+transaction Alice knows her inputs she
+knows she doesn't actually have to sign
+
+ align:start position:0%
+knows she doesn't actually have to sign
+ 
+
+ align:start position:0%
+knows she doesn't actually have to sign
+it all because the TX ID wasn't won't
+
+ align:start position:0%
+it all because the TX ID wasn't won't
+ 
+
+ align:start position:0%
+it all because the TX ID wasn't won't
+contain the signature and those you know
+
+ align:start position:0%
+contain the signature and those you know
+ 
+
+ align:start position:0%
+contain the signature and those you know
+what their key is so Alice can compute
+
+ align:start position:0%
+what their key is so Alice can compute
+ 
+
+ align:start position:0%
+what their key is so Alice can compute
+the TX ID and tell Bob hey sign this you
+
+ align:start position:0%
+the TX ID and tell Bob hey sign this you
+ 
+
+ align:start position:0%
+the TX ID and tell Bob hey sign this you
+know this is what the transactions gonna
+
+ align:start position:0%
+know this is what the transactions gonna
+ 
+
+ align:start position:0%
+know this is what the transactions gonna
+look like
+
+ align:start position:0%
+look like
+ 
+
+ align:start position:0%
+look like
+sign it and Bob right at this point has
+
+ align:start position:0%
+sign it and Bob right at this point has
+ 
+
+ align:start position:0%
+sign it and Bob right at this point has
+no no risk Bob I guess needs to make
+
+ align:start position:0%
+no no risk Bob I guess needs to make
+ 
+
+ align:start position:0%
+no no risk Bob I guess needs to make
+sure that he's not inadvertently signing
+
+ align:start position:0%
+sure that he's not inadvertently signing
+ 
+
+ align:start position:0%
+sure that he's not inadvertently signing
+his own money right so if Alice says hey
+
+ align:start position:0%
+his own money right so if Alice says hey
+ 
+
+ align:start position:0%
+his own money right so if Alice says hey
+here's the TX ID Bob should make sure
+
+ align:start position:0%
+here's the TX ID Bob should make sure
+ 
+
+ align:start position:0%
+here's the TX ID Bob should make sure
+okay this is not my TX ID right but it's
+
+ align:start position:0%
+okay this is not my TX ID right but it's
+ 
+
+ align:start position:0%
+okay this is not my TX ID right but it's
+actually doesn't matter since since he
+
+ align:start position:0%
+actually doesn't matter since since he
+ 
+
+ align:start position:0%
+actually doesn't matter since since he
+sort of commits to Alice's funky here so
+
+ align:start position:0%
+sort of commits to Alice's funky here so
+ 
+
+ align:start position:0%
+sort of commits to Alice's funky here so
+even if you've swapped the TX ID when
+
+ align:start position:0%
+even if you've swapped the TX ID when
+ 
+
+ align:start position:0%
+even if you've swapped the TX ID when
+you sign you're signing off of what to
+
+ align:start position:0%
+you sign you're signing off of what to
+ 
+
+ align:start position:0%
+you sign you're signing off of what to
+you say this is two of two multi-sig so
+
+ align:start position:0%
+you say this is two of two multi-sig so
+ 
+
+ align:start position:0%
+you say this is two of two multi-sig so
+if this was Bob's single key it wouldn't
+
+ align:start position:0%
+if this was Bob's single key it wouldn't
+ 
+
+ align:start position:0%
+if this was Bob's single key it wouldn't
+it wouldn't even work yeah so but so
+
+ align:start position:0%
+it wouldn't even work yeah so but so
+ 
+
+ align:start position:0%
+it wouldn't even work yeah so but so
+Alice sort of has to give some
+
+ align:start position:0%
+Alice sort of has to give some
+ 
+
+ align:start position:0%
+Alice sort of has to give some
+information about Bob signs hands the
+
+ align:start position:0%
+information about Bob signs hands the
+ 
+
+ align:start position:0%
+information about Bob signs hands the
+refund over to Alice then Alice is able
+
+ align:start position:0%
+refund over to Alice then Alice is able
+ 
+
+ align:start position:0%
+refund over to Alice then Alice is able
+to create this fun transaction and now
+
+ align:start position:0%
+to create this fun transaction and now
+ 
+
+ align:start position:0%
+to create this fun transaction and now
+Alice's risk is minimized because she
+
+ align:start position:0%
+Alice's risk is minimized because she
+ 
+
+ align:start position:0%
+Alice's risk is minimized because she
+says okay I'll send this to this channel
+
+ align:start position:0%
+says okay I'll send this to this channel
+ 
+
+ align:start position:0%
+says okay I'll send this to this channel
+and worst case after wait a week right
+
+ align:start position:0%
+and worst case after wait a week right
+ 
+
+ align:start position:0%
+and worst case after wait a week right
+if Bob disappears as soon as I broadcast
+
+ align:start position:0%
+if Bob disappears as soon as I broadcast
+ 
+
+ align:start position:0%
+if Bob disappears as soon as I broadcast
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+well then Bob's gone I can't do anything
+
+ align:start position:0%
+well then Bob's gone I can't do anything
+ 
+
+ align:start position:0%
+well then Bob's gone I can't do anything
+we can't sign but then next week I'll be
+
+ align:start position:0%
+we can't sign but then next week I'll be
+ 
+
+ align:start position:0%
+we can't sign but then next week I'll be
+able to use this transaction and get all
+
+ align:start position:0%
+able to use this transaction and get all
+ 
+
+ align:start position:0%
+able to use this transaction and get all
+my money back yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes which which transaction so there's
+
+ align:start position:0%
+yes which which transaction so there's
+ 
+
+ align:start position:0%
+yes which which transaction so there's
+there's the fund and the refund right no
+
+ align:start position:0%
+there's the fund and the refund right no
+ 
+
+ align:start position:0%
+there's the fund and the refund right no
+it needs to be created before the the
+
+ align:start position:0%
+it needs to be created before the the
+ 
+
+ align:start position:0%
+it needs to be created before the the
+fund right so it's not gonna be on the
+
+ align:start position:0%
+fund right so it's not gonna be on the
+ 
+
+ align:start position:0%
+fund right so it's not gonna be on the
+network but Bob creates this first signs
+
+ align:start position:0%
+network but Bob creates this first signs
+ 
+
+ align:start position:0%
+network but Bob creates this first signs
+it and gives it to Alice that way Alice
+
+ align:start position:0%
+it and gives it to Alice that way Alice
+ 
+
+ align:start position:0%
+it and gives it to Alice that way Alice
+knows well I have this that will be
+
+ align:start position:0%
+knows well I have this that will be
+ 
+
+ align:start position:0%
+knows well I have this that will be
+valid in a week and so that means it's
+
+ align:start position:0%
+valid in a week and so that means it's
+ 
+
+ align:start position:0%
+valid in a week and so that means it's
+safe to sign and broadcast this you know
+
+ align:start position:0%
+safe to sign and broadcast this you know
+ 
+
+ align:start position:0%
+safe to sign and broadcast this you know
+it's got Bob's signature and that's what
+
+ align:start position:0%
+it's got Bob's signature and that's what
+ 
+
+ align:start position:0%
+it's got Bob's signature and that's what
+hand you hand over and then Alice can
+
+ align:start position:0%
+hand you hand over and then Alice can
+ 
+
+ align:start position:0%
+hand you hand over and then Alice can
+sign later she can sign it immediately
+
+ align:start position:0%
+sign later she can sign it immediately
+ 
+
+ align:start position:0%
+sign later she can sign it immediately
+on reception and their store it or she
+
+ align:start position:0%
+on reception and their store it or she
+ 
+
+ align:start position:0%
+on reception and their store it or she
+can sign it on March 28th but the idea
+
+ align:start position:0%
+can sign it on March 28th but the idea
+ 
+
+ align:start position:0%
+can sign it on March 28th but the idea
+she's got Bob's signature endorsing this
+
+ align:start position:0%
+she's got Bob's signature endorsing this
+ 
+
+ align:start position:0%
+she's got Bob's signature endorsing this
+and it's not valid yet but she knows
+
+ align:start position:0%
+and it's not valid yet but she knows
+ 
+
+ align:start position:0%
+and it's not valid yet but she knows
+minimized risk right
+
+ align:start position:0%
+minimized risk right
+ 
+
+ align:start position:0%
+minimized risk right
+worst case wait a week okay so then what
+
+ align:start position:0%
+worst case wait a week okay so then what
+ 
+
+ align:start position:0%
+worst case wait a week okay so then what
+can you do with this you can make sort
+
+ align:start position:0%
+can you do with this you can make sort
+ 
+
+ align:start position:0%
+can you do with this you can make sort
+of similar to refund transactions but
+
+ align:start position:0%
+of similar to refund transactions but
+ 
+
+ align:start position:0%
+of similar to refund transactions but
+they give Bob more money so you make two
+
+ align:start position:0%
+they give Bob more money so you make two
+ 
+
+ align:start position:0%
+they give Bob more money so you make two
+outputs you say okay it's I'm spending
+
+ align:start position:0%
+outputs you say okay it's I'm spending
+ 
+
+ align:start position:0%
+outputs you say okay it's I'm spending
+the fun transaction ID I put Alice's
+
+ align:start position:0%
+the fun transaction ID I put Alice's
+ 
+
+ align:start position:0%
+the fun transaction ID I put Alice's
+signature and I say Alice gets nine
+
+ align:start position:0%
+signature and I say Alice gets nine
+ 
+
+ align:start position:0%
+signature and I say Alice gets nine
+coins Bob gets one coin and Alice hands
+
+ align:start position:0%
+coins Bob gets one coin and Alice hands
+ 
+
+ align:start position:0%
+coins Bob gets one coin and Alice hands
+that over to Bob right so you make a
+
+ align:start position:0%
+that over to Bob right so you make a
+ 
+
+ align:start position:0%
+that over to Bob right so you make a
+transaction like that right it spends
+
+ align:start position:0%
+transaction like that right it spends
+ 
+
+ align:start position:0%
+transaction like that right it spends
+the fun transaction output Alice and
+
+ align:start position:0%
+the fun transaction output Alice and
+ 
+
+ align:start position:0%
+the fun transaction output Alice and
+Bob's he is but are both needed and
+
+ align:start position:0%
+Bob's he is but are both needed and
+ 
+
+ align:start position:0%
+Bob's he is but are both needed and
+Alice signs this and says okay I get
+
+ align:start position:0%
+Alice signs this and says okay I get
+ 
+
+ align:start position:0%
+Alice signs this and says okay I get
+nine you get one hands it over to Bob
+
+ align:start position:0%
+nine you get one hands it over to Bob
+ 
+
+ align:start position:0%
+nine you get one hands it over to Bob
+and Bob says basically I just got the
+
+ align:start position:0%
+and Bob says basically I just got the
+ 
+
+ align:start position:0%
+and Bob says basically I just got the
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+I can broadcast this if I want right
+
+ align:start position:0%
+I can broadcast this if I want right
+ 
+
+ align:start position:0%
+I can broadcast this if I want right
+Bob's got Alice's signature Bob can add
+
+ align:start position:0%
+Bob's got Alice's signature Bob can add
+ 
+
+ align:start position:0%
+Bob's got Alice's signature Bob can add
+his signature broadcast this transaction
+
+ align:start position:0%
+his signature broadcast this transaction
+ 
+
+ align:start position:0%
+his signature broadcast this transaction
+and receive one Bitcoin okay but see Bob
+
+ align:start position:0%
+and receive one Bitcoin okay but see Bob
+ 
+
+ align:start position:0%
+and receive one Bitcoin okay but see Bob
+doesn't sign his side in broadcast Bob
+
+ align:start position:0%
+doesn't sign his side in broadcast Bob
+ 
+
+ align:start position:0%
+doesn't sign his side in broadcast Bob
+just waits Bob's like cool I've got this
+
+ align:start position:0%
+just waits Bob's like cool I've got this
+ 
+
+ align:start position:0%
+just waits Bob's like cool I've got this
+coin I'm not even gonna sign and
+
+ align:start position:0%
+coin I'm not even gonna sign and
+ 
+
+ align:start position:0%
+coin I'm not even gonna sign and
+broadcast this
+
+ align:start position:0%
+broadcast this
+ 
+
+ align:start position:0%
+broadcast this
+I know it's as good as having received
+
+ align:start position:0%
+I know it's as good as having received
+ 
+
+ align:start position:0%
+I know it's as good as having received
+the actual coin because there's no
+
+ align:start position:0%
+the actual coin because there's no
+ 
+
+ align:start position:0%
+the actual coin because there's no
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+thing else Alice can do on her own right
+
+ align:start position:0%
+thing else Alice can do on her own right
+ 
+
+ align:start position:0%
+thing else Alice can do on her own right
+she can't take these ten coins she can
+
+ align:start position:0%
+she can't take these ten coins she can
+ 
+
+ align:start position:0%
+she can't take these ten coins she can
+eventually get the refund in a week but
+
+ align:start position:0%
+eventually get the refund in a week but
+ 
+
+ align:start position:0%
+eventually get the refund in a week but
+for now
+
+ align:start position:0%
+for now
+ 
+
+ align:start position:0%
+for now
+Bob's safe and then maybe a day later
+
+ align:start position:0%
+Bob's safe and then maybe a day later
+ 
+
+ align:start position:0%
+Bob's safe and then maybe a day later
+Alice says okay
+
+ align:start position:0%
+Alice says okay
+ 
+
+ align:start position:0%
+Alice says okay
+I'm giving you another coin right I'm
+
+ align:start position:0%
+I'm giving you another coin right I'm
+ 
+
+ align:start position:0%
+I'm giving you another coin right I'm
+what I'm doing is I'm signing a new
+
+ align:start position:0%
+what I'm doing is I'm signing a new
+ 
+
+ align:start position:0%
+what I'm doing is I'm signing a new
+transaction it spends the same output
+
+ align:start position:0%
+transaction it spends the same output
+ 
+
+ align:start position:0%
+transaction it spends the same output
+this is still you know this is still
+
+ align:start position:0%
+this is still you know this is still
+ 
+
+ align:start position:0%
+this is still you know this is still
+there these have not been broadcast but
+
+ align:start position:0%
+there these have not been broadcast but
+ 
+
+ align:start position:0%
+there these have not been broadcast but
+in this one
+
+ align:start position:0%
+in this one
+ 
+
+ align:start position:0%
+in this one
+Alice gets eight coins Bob gets two
+
+ align:start position:0%
+Alice gets eight coins Bob gets two
+ 
+
+ align:start position:0%
+Alice gets eight coins Bob gets two
+coins Alice signs it hands that over to
+
+ align:start position:0%
+coins Alice signs it hands that over to
+ 
+
+ align:start position:0%
+coins Alice signs it hands that over to
+Bob bobs like great I got another coin I
+
+ align:start position:0%
+Bob bobs like great I got another coin I
+ 
+
+ align:start position:0%
+Bob bobs like great I got another coin I
+will also just wait Bob can actually
+
+ align:start position:0%
+will also just wait Bob can actually
+ 
+
+ align:start position:0%
+will also just wait Bob can actually
+delete this because well this is better
+
+ align:start position:0%
+delete this because well this is better
+ 
+
+ align:start position:0%
+delete this because well this is better
+right for from Bob's perspective I'd
+
+ align:start position:0%
+right for from Bob's perspective I'd
+ 
+
+ align:start position:0%
+right for from Bob's perspective I'd
+rather have two then one and there's no
+
+ align:start position:0%
+rather have two then one and there's no
+ 
+
+ align:start position:0%
+rather have two then one and there's no
+any of them are valid right according to
+
+ align:start position:0%
+any of them are valid right according to
+ 
+
+ align:start position:0%
+any of them are valid right according to
+the network the network itself no one's
+
+ align:start position:0%
+the network the network itself no one's
+ 
+
+ align:start position:0%
+the network the network itself no one's
+seen these things they're not broadcast
+
+ align:start position:0%
+seen these things they're not broadcast
+ 
+
+ align:start position:0%
+seen these things they're not broadcast
+only this exists as an output and you
+
+ align:start position:0%
+only this exists as an output and you
+ 
+
+ align:start position:0%
+only this exists as an output and you
+can keep doing this right you keep doing
+
+ align:start position:0%
+can keep doing this right you keep doing
+ 
+
+ align:start position:0%
+can keep doing this right you keep doing
+this as many times as you want well
+
+ align:start position:0%
+this as many times as you want well
+ 
+
+ align:start position:0%
+this as many times as you want well
+within limits right what what's the
+
+ align:start position:0%
+within limits right what what's the
+ 
+
+ align:start position:0%
+within limits right what what's the
+obvious limit here yeah sure
+
+ align:start position:0%
+obvious limit here yeah sure
+ 
+
+ align:start position:0%
+obvious limit here yeah sure
+once once once Bob gets all ten there's
+
+ align:start position:0%
+once once once Bob gets all ten there's
+ 
+
+ align:start position:0%
+once once once Bob gets all ten there's
+no reason to keep it open anymore also
+
+ align:start position:0%
+no reason to keep it open anymore also
+ 
+
+ align:start position:0%
+no reason to keep it open anymore also
+you can't you can't reverse right if you
+
+ align:start position:0%
+you can't you can't reverse right if you
+ 
+
+ align:start position:0%
+you can't you can't reverse right if you
+try if Alice says oh well so Alice Alice
+
+ align:start position:0%
+try if Alice says oh well so Alice Alice
+ 
+
+ align:start position:0%
+try if Alice says oh well so Alice Alice
+always sort of sending money if Bob says
+
+ align:start position:0%
+always sort of sending money if Bob says
+ 
+
+ align:start position:0%
+always sort of sending money if Bob says
+hey I'm gonna give you some money back
+
+ align:start position:0%
+hey I'm gonna give you some money back
+ 
+
+ align:start position:0%
+hey I'm gonna give you some money back
+and Bob signs something say hey no I
+
+ align:start position:0%
+and Bob signs something say hey no I
+ 
+
+ align:start position:0%
+and Bob signs something say hey no I
+have two coins and you have eight coins
+
+ align:start position:0%
+have two coins and you have eight coins
+ 
+
+ align:start position:0%
+have two coins and you have eight coins
+I was like yeah but you have this right
+
+ align:start position:0%
+I was like yeah but you have this right
+ 
+
+ align:start position:0%
+I was like yeah but you have this right
+you have this you out you know Alice
+
+ align:start position:0%
+you have this you out you know Alice
+ 
+
+ align:start position:0%
+you have this you out you know Alice
+seven Bob three transaction I know you
+
+ align:start position:0%
+seven Bob three transaction I know you
+ 
+
+ align:start position:0%
+seven Bob three transaction I know you
+can broadcast that whenever you want so
+
+ align:start position:0%
+can broadcast that whenever you want so
+ 
+
+ align:start position:0%
+can broadcast that whenever you want so
+there's no credible way for Bob to say
+
+ align:start position:0%
+there's no credible way for Bob to say
+ 
+
+ align:start position:0%
+there's no credible way for Bob to say
+like oh I'm giving you the money back in
+
+ align:start position:0%
+like oh I'm giving you the money back in
+ 
+
+ align:start position:0%
+like oh I'm giving you the money back in
+this channel right yes she gave one two
+
+ align:start position:0%
+this channel right yes she gave one two
+ 
+
+ align:start position:0%
+this channel right yes she gave one two
+and three
+
+ align:start position:0%
+and three
+ 
+
+ align:start position:0%
+and three
+and the next one she gets about 2.5 and
+
+ align:start position:0%
+and the next one she gets about 2.5 and
+ 
+
+ align:start position:0%
+and the next one she gets about 2.5 and
+yeah Bob Bob wouldn't bob would just
+
+ align:start position:0%
+yeah Bob Bob wouldn't bob would just
+ 
+
+ align:start position:0%
+yeah Bob Bob wouldn't bob would just
+ignore it right Bob would be like yeah
+
+ align:start position:0%
+ignore it right Bob would be like yeah
+ 
+
+ align:start position:0%
+ignore it right Bob would be like yeah
+but I already have three why would I
+
+ align:start position:0%
+but I already have three why would I
+ 
+
+ align:start position:0%
+but I already have three why would I
+want two and a half right like and and
+
+ align:start position:0%
+want two and a half right like and and
+ 
+
+ align:start position:0%
+want two and a half right like and and
+it's it's more like in that case if
+
+ align:start position:0%
+it's it's more like in that case if
+ 
+
+ align:start position:0%
+it's it's more like in that case if
+Alice says oh I have to you know Alice
+
+ align:start position:0%
+Alice says oh I have to you know Alice
+ 
+
+ align:start position:0%
+Alice says oh I have to you know Alice
+is trying to take some money back
+
+ align:start position:0%
+is trying to take some money back
+ 
+
+ align:start position:0%
+is trying to take some money back
+essentially Bob is paying Alice in that
+
+ align:start position:0%
+essentially Bob is paying Alice in that
+ 
+
+ align:start position:0%
+essentially Bob is paying Alice in that
+case but it's not credible right alice
+
+ align:start position:0%
+case but it's not credible right alice
+ 
+
+ align:start position:0%
+case but it's not credible right alice
+is like yeah I can sign this again or I
+
+ align:start position:0%
+is like yeah I can sign this again or I
+ 
+
+ align:start position:0%
+is like yeah I can sign this again or I
+can sign I have all ten again but you
+
+ align:start position:0%
+can sign I have all ten again but you
+ 
+
+ align:start position:0%
+can sign I have all ten again but you
+know Bob's idea is like I'm just gonna
+
+ align:start position:0%
+know Bob's idea is like I'm just gonna
+ 
+
+ align:start position:0%
+know Bob's idea is like I'm just gonna
+sign the one where I get the most money
+
+ align:start position:0%
+sign the one where I get the most money
+ 
+
+ align:start position:0%
+sign the one where I get the most money
+so so that's you know that's a
+
+ align:start position:0%
+so so that's you know that's a
+ 
+
+ align:start position:0%
+so so that's you know that's a
+limitation that's it's one direction
+
+ align:start position:0%
+limitation that's it's one direction
+ 
+
+ align:start position:0%
+limitation that's it's one direction
+right you Alice can keep paying Bob Bob
+
+ align:start position:0%
+right you Alice can keep paying Bob Bob
+ 
+
+ align:start position:0%
+right you Alice can keep paying Bob Bob
+can't pay back but that's still pretty
+
+ align:start position:0%
+can't pay back but that's still pretty
+ 
+
+ align:start position:0%
+can't pay back but that's still pretty
+useful in some cases if you're have some
+
+ align:start position:0%
+useful in some cases if you're have some
+ 
+
+ align:start position:0%
+useful in some cases if you're have some
+kind of recurrent payment you're
+
+ align:start position:0%
+kind of recurrent payment you're
+ 
+
+ align:start position:0%
+kind of recurrent payment you're
+streaming videos or something you open a
+
+ align:start position:0%
+streaming videos or something you open a
+ 
+
+ align:start position:0%
+streaming videos or something you open a
+channel you can keep paying one thing
+
+ align:start position:0%
+channel you can keep paying one thing
+ 
+
+ align:start position:0%
+channel you can keep paying one thing
+that's nice is these can be really fast
+
+ align:start position:0%
+that's nice is these can be really fast
+ 
+
+ align:start position:0%
+that's nice is these can be really fast
+so this you have to actually wait till
+
+ align:start position:0%
+so this you have to actually wait till
+ 
+
+ align:start position:0%
+so this you have to actually wait till
+it's in the blockchain but these
+
+ align:start position:0%
+it's in the blockchain but these
+ 
+
+ align:start position:0%
+it's in the blockchain but these
+transactions there's no blockchain
+
+ align:start position:0%
+transactions there's no blockchain
+ 
+
+ align:start position:0%
+transactions there's no blockchain
+involved you just sign it and hand it
+
+ align:start position:0%
+involved you just sign it and hand it
+ 
+
+ align:start position:0%
+involved you just sign it and hand it
+over to the other party and as soon as
+
+ align:start position:0%
+over to the other party and as soon as
+ 
+
+ align:start position:0%
+over to the other party and as soon as
+they've received it they're like it I
+
+ align:start position:0%
+they've received it they're like it I
+ 
+
+ align:start position:0%
+they've received it they're like it I
+got the money so this can be very low
+
+ align:start position:0%
+got the money so this can be very low
+ 
+
+ align:start position:0%
+got the money so this can be very low
+latency so this is pretty cool there are
+
+ align:start position:0%
+latency so this is pretty cool there are
+ 
+
+ align:start position:0%
+latency so this is pretty cool there are
+limitations right anyway so yeah Bob
+
+ align:start position:0%
+limitations right anyway so yeah Bob
+ 
+
+ align:start position:0%
+limitations right anyway so yeah Bob
+keeps getting these half signed
+
+ align:start position:0%
+keeps getting these half signed
+ 
+
+ align:start position:0%
+keeps getting these half signed
+transactions with more and more money
+
+ align:start position:0%
+transactions with more and more money
+ 
+
+ align:start position:0%
+transactions with more and more money
+going to him
+
+ align:start position:0%
+going to him
+ 
+
+ align:start position:0%
+going to him
+the old ones are useless right why would
+
+ align:start position:0%
+the old ones are useless right why would
+ 
+
+ align:start position:0%
+the old ones are useless right why would
+I keep this old transaction where I got
+
+ align:start position:0%
+I keep this old transaction where I got
+ 
+
+ align:start position:0%
+I keep this old transaction where I got
+one coin just delete it so Bob only
+
+ align:start position:0%
+one coin just delete it so Bob only
+ 
+
+ align:start position:0%
+one coin just delete it so Bob only
+actually has to store one thing Bob also
+
+ align:start position:0%
+actually has to store one thing Bob also
+ 
+
+ align:start position:0%
+actually has to store one thing Bob also
+has to be very careful though he's got a
+
+ align:start position:0%
+has to be very careful though he's got a
+ 
+
+ align:start position:0%
+has to be very careful though he's got a
+sign and broadcast one of these before
+
+ align:start position:0%
+sign and broadcast one of these before
+ 
+
+ align:start position:0%
+sign and broadcast one of these before
+next week if he doesn't
+
+ align:start position:0%
+next week if he doesn't
+ 
+
+ align:start position:0%
+next week if he doesn't
+Alice can just broadcast the refund
+
+ align:start position:0%
+Alice can just broadcast the refund
+ 
+
+ align:start position:0%
+Alice can just broadcast the refund
+transaction and you know he thinks he's
+
+ align:start position:0%
+transaction and you know he thinks he's
+ 
+
+ align:start position:0%
+transaction and you know he thinks he's
+getting three coins but Alice's like no
+
+ align:start position:0%
+getting three coins but Alice's like no
+ 
+
+ align:start position:0%
+getting three coins but Alice's like no
+I'm just taking all ten back and I was
+
+ align:start position:0%
+I'm just taking all ten back and I was
+ 
+
+ align:start position:0%
+I'm just taking all ten back and I was
+like shoot I just you know got ripped
+
+ align:start position:0%
+like shoot I just you know got ripped
+ 
+
+ align:start position:0%
+like shoot I just you know got ripped
+off and so you know from the network's
+
+ align:start position:0%
+off and so you know from the network's
+ 
+
+ align:start position:0%
+off and so you know from the network's
+point of view the Bitcoin networks point
+
+ align:start position:0%
+point of view the Bitcoin networks point
+ 
+
+ align:start position:0%
+point of view the Bitcoin networks point
+of view they no-one's seen any of this
+
+ align:start position:0%
+of view they no-one's seen any of this
+ 
+
+ align:start position:0%
+of view they no-one's seen any of this
+right all they see is the fun
+
+ align:start position:0%
+right all they see is the fun
+ 
+
+ align:start position:0%
+right all they see is the fun
+transaction nothing happens for days and
+
+ align:start position:0%
+transaction nothing happens for days and
+ 
+
+ align:start position:0%
+transaction nothing happens for days and
+then they see one of these payment
+
+ align:start position:0%
+then they see one of these payment
+ 
+
+ align:start position:0%
+then they see one of these payment
+channel closing transactions and they
+
+ align:start position:0%
+channel closing transactions and they
+ 
+
+ align:start position:0%
+channel closing transactions and they
+might see multiple right Bob could
+
+ align:start position:0%
+might see multiple right Bob could
+ 
+
+ align:start position:0%
+might see multiple right Bob could
+broadcast all three it would be dumb Bob
+
+ align:start position:0%
+broadcast all three it would be dumb Bob
+ 
+
+ align:start position:0%
+broadcast all three it would be dumb Bob
+Bob willing wants this one but you know
+
+ align:start position:0%
+Bob willing wants this one but you know
+ 
+
+ align:start position:0%
+Bob willing wants this one but you know
+you're basically using double spends to
+
+ align:start position:0%
+you're basically using double spends to
+ 
+
+ align:start position:0%
+you're basically using double spends to
+create these channels okay so yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you if it happens that means either
+
+ align:start position:0%
+yeah you if it happens that means either
+ 
+
+ align:start position:0%
+yeah you if it happens that means either
+Bob went down or Bob never you know like
+
+ align:start position:0%
+Bob went down or Bob never you know like
+ 
+
+ align:start position:0%
+Bob went down or Bob never you know like
+it's all it's it should never use it in
+
+ align:start position:0%
+it's all it's it should never use it in
+ 
+
+ align:start position:0%
+it's all it's it should never use it in
+real life right it's insurance so that
+
+ align:start position:0%
+real life right it's insurance so that
+ 
+
+ align:start position:0%
+real life right it's insurance so that
+you you're not you're not worried that
+
+ align:start position:0%
+you you're not you're not worried that
+ 
+
+ align:start position:0%
+you you're not you're not worried that
+Bob's just gonna run off and get your
+
+ align:start position:0%
+Bob's just gonna run off and get your
+ 
+
+ align:start position:0%
+Bob's just gonna run off and get your
+phone right but you can't keep using the
+
+ align:start position:0%
+phone right but you can't keep using the
+ 
+
+ align:start position:0%
+phone right but you can't keep using the
+chin like like at that point there's so
+
+ align:start position:0%
+chin like like at that point there's so
+ 
+
+ align:start position:0%
+chin like like at that point there's so
+much trust involved right if you keep
+
+ align:start position:0%
+much trust involved right if you keep
+ 
+
+ align:start position:0%
+much trust involved right if you keep
+trying to use the channel after the
+
+ align:start position:0%
+trying to use the channel after the
+ 
+
+ align:start position:0%
+trying to use the channel after the
+weeks gone by Bob now see like it's the
+
+ align:start position:0%
+weeks gone by Bob now see like it's the
+ 
+
+ align:start position:0%
+weeks gone by Bob now see like it's the
+same reason you can't make it
+
+ align:start position:0%
+same reason you can't make it
+ 
+
+ align:start position:0%
+same reason you can't make it
+bi-directional right if Bob says hey
+
+ align:start position:0%
+bi-directional right if Bob says hey
+ 
+
+ align:start position:0%
+bi-directional right if Bob says hey
+here's a transaction where you get more
+
+ align:start position:0%
+here's a transaction where you get more
+ 
+
+ align:start position:0%
+here's a transaction where you get more
+more of the money Alice's like yeah but
+
+ align:start position:0%
+more of the money Alice's like yeah but
+ 
+
+ align:start position:0%
+more of the money Alice's like yeah but
+that's not that's not credible right
+
+ align:start position:0%
+that's not that's not credible right
+ 
+
+ align:start position:0%
+that's not that's not credible right
+because I know you can broadcast and
+
+ align:start position:0%
+because I know you can broadcast and
+ 
+
+ align:start position:0%
+because I know you can broadcast and
+take more and similarly if Alice says
+
+ align:start position:0%
+take more and similarly if Alice says
+ 
+
+ align:start position:0%
+take more and similarly if Alice says
+let's just keep the channel open Bob's
+
+ align:start position:0%
+let's just keep the channel open Bob's
+ 
+
+ align:start position:0%
+let's just keep the channel open Bob's
+like no that's not credible right like I
+
+ align:start position:0%
+like no that's not credible right like I
+ 
+
+ align:start position:0%
+like no that's not credible right like I
+know you can just take all the money at
+
+ align:start position:0%
+know you can just take all the money at
+ 
+
+ align:start position:0%
+know you can just take all the money at
+any time so you handing me these new
+
+ align:start position:0%
+any time so you handing me these new
+ 
+
+ align:start position:0%
+any time so you handing me these new
+signatures like it's it's sort of
+
+ align:start position:0%
+signatures like it's it's sort of
+ 
+
+ align:start position:0%
+signatures like it's it's sort of
+meaningless it's not like there's so
+
+ align:start position:0%
+meaningless it's not like there's so
+ 
+
+ align:start position:0%
+meaningless it's not like there's so
+much trust involved it like why bother
+
+ align:start position:0%
+much trust involved it like why bother
+ 
+
+ align:start position:0%
+much trust involved it like why bother
+with this whole payment channel thing
+
+ align:start position:0%
+with this whole payment channel thing
+ 
+
+ align:start position:0%
+with this whole payment channel thing
+right so this this is nice in that you
+
+ align:start position:0%
+right so this this is nice in that you
+ 
+
+ align:start position:0%
+right so this this is nice in that you
+don't have to trust the counterparties
+
+ align:start position:0%
+don't have to trust the counterparties
+ 
+
+ align:start position:0%
+don't have to trust the counterparties
+the worst they can do is disappear they
+
+ align:start position:0%
+the worst they can do is disappear they
+ 
+
+ align:start position:0%
+the worst they can do is disappear they
+can't I mean yeah they can hurt
+
+ align:start position:0%
+can't I mean yeah they can hurt
+ 
+
+ align:start position:0%
+can't I mean yeah they can hurt
+themselves right Bob can broadcast this
+
+ align:start position:0%
+themselves right Bob can broadcast this
+ 
+
+ align:start position:0%
+themselves right Bob can broadcast this
+after this exists and now this is like
+
+ align:start position:0%
+after this exists and now this is like
+ 
+
+ align:start position:0%
+after this exists and now this is like
+okay that was dumb thanks for the two
+
+ align:start position:0%
+okay that was dumb thanks for the two
+ 
+
+ align:start position:0%
+okay that was dumb thanks for the two
+coins back or Bob can just disappear and
+
+ align:start position:0%
+coins back or Bob can just disappear and
+ 
+
+ align:start position:0%
+coins back or Bob can just disappear and
+now it's like hey I'm gonna do the
+
+ align:start position:0%
+now it's like hey I'm gonna do the
+ 
+
+ align:start position:0%
+now it's like hey I'm gonna do the
+refund like I know I'm you know you're
+
+ align:start position:0%
+refund like I know I'm you know you're
+ 
+
+ align:start position:0%
+refund like I know I'm you know you're
+supposed to get these three coins but
+
+ align:start position:0%
+supposed to get these three coins but
+ 
+
+ align:start position:0%
+supposed to get these three coins but
+you're gone and the refunds my only
+
+ align:start position:0%
+you're gone and the refunds my only
+ 
+
+ align:start position:0%
+you're gone and the refunds my only
+option so I'm broadcasting it so you
+
+ align:start position:0%
+option so I'm broadcasting it so you
+ 
+
+ align:start position:0%
+option so I'm broadcasting it so you
+don't have to worry about who is your
+
+ align:start position:0%
+don't have to worry about who is your
+ 
+
+ align:start position:0%
+don't have to worry about who is your
+counterparty and you don't have any like
+
+ align:start position:0%
+counterparty and you don't have any like
+ 
+
+ align:start position:0%
+counterparty and you don't have any like
+debt
+
+ align:start position:0%
+debt
+ 
+
+ align:start position:0%
+debt
+there's no custody or anything like that
+
+ align:start position:0%
+there's no custody or anything like that
+ 
+
+ align:start position:0%
+there's no custody or anything like that
+so that's really nice if you if you you
+
+ align:start position:0%
+so that's really nice if you if you you
+ 
+
+ align:start position:0%
+so that's really nice if you if you you
+can add trust but we already have that
+
+ align:start position:0%
+can add trust but we already have that
+ 
+
+ align:start position:0%
+can add trust but we already have that
+with like coinbase in the gemenon you
+
+ align:start position:0%
+with like coinbase in the gemenon you
+ 
+
+ align:start position:0%
+with like coinbase in the gemenon you
+know the exchanges okay so this is
+
+ align:start position:0%
+know the exchanges okay so this is
+ 
+
+ align:start position:0%
+know the exchanges okay so this is
+pretty useful time limits limits on you
+
+ align:start position:0%
+pretty useful time limits limits on you
+ 
+
+ align:start position:0%
+pretty useful time limits limits on you
+know back and forth refund transactions
+
+ align:start position:0%
+know back and forth refund transactions
+ 
+
+ align:start position:0%
+know back and forth refund transactions
+you have to be built before the trend
+
+ align:start position:0%
+you have to be built before the trend
+ 
+
+ align:start position:0%
+you have to be built before the trend
+the fun transaction because and so
+
+ align:start position:0%
+the fun transaction because and so
+ 
+
+ align:start position:0%
+the fun transaction because and so
+malleability hurts that right before seg
+
+ align:start position:0%
+malleability hurts that right before seg
+ 
+
+ align:start position:0%
+malleability hurts that right before seg
+wit this was very risky slushy couldn't
+
+ align:start position:0%
+wit this was very risky slushy couldn't
+ 
+
+ align:start position:0%
+wit this was very risky slushy couldn't
+do it
+
+ align:start position:0%
+do it
+ 
+
+ align:start position:0%
+do it
+the refund transaction has to spend the
+
+ align:start position:0%
+the refund transaction has to spend the
+ 
+
+ align:start position:0%
+the refund transaction has to spend the
+fun transaction and you don't really
+
+ align:start position:0%
+fun transaction and you don't really
+ 
+
+ align:start position:0%
+fun transaction and you don't really
+know without segue you don't know what
+
+ align:start position:0%
+know without segue you don't know what
+ 
+
+ align:start position:0%
+know without segue you don't know what
+that transaction ladies gonna be before
+
+ align:start position:0%
+that transaction ladies gonna be before
+ 
+
+ align:start position:0%
+that transaction ladies gonna be before
+it gets brought it gets confirmed and so
+
+ align:start position:0%
+it gets brought it gets confirmed and so
+ 
+
+ align:start position:0%
+it gets brought it gets confirmed and so
+you could try to anticipate oh well
+
+ align:start position:0%
+you could try to anticipate oh well
+ 
+
+ align:start position:0%
+you could try to anticipate oh well
+there might it might get Molly ated to
+
+ align:start position:0%
+there might it might get Molly ated to
+ 
+
+ align:start position:0%
+there might it might get Molly ated to
+these five different things let's do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's risky right so so let's segue
+
+ align:start position:0%
+but it's risky right so so let's segue
+ 
+
+ align:start position:0%
+but it's risky right so so let's segue
+it's nice you know what to worry about
+
+ align:start position:0%
+it's nice you know what to worry about
+ 
+
+ align:start position:0%
+it's nice you know what to worry about
+okay so any questions about the sort of
+
+ align:start position:0%
+okay so any questions about the sort of
+ 
+
+ align:start position:0%
+okay so any questions about the sort of
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+One Direction payments makes sense okay
+
+ align:start position:0%
+One Direction payments makes sense okay
+ 
+
+ align:start position:0%
+One Direction payments makes sense okay
+so how can you make it even better
+
+ align:start position:0%
+so how can you make it even better
+ 
+
+ align:start position:0%
+so how can you make it even better
+what if you want to make it
+
+ align:start position:0%
+what if you want to make it
+ 
+
+ align:start position:0%
+what if you want to make it
+bi-directional and last forever that
+
+ align:start position:0%
+bi-directional and last forever that
+ 
+
+ align:start position:0%
+bi-directional and last forever that
+would be much more useful right but like
+
+ align:start position:0%
+would be much more useful right but like
+ 
+
+ align:start position:0%
+would be much more useful right but like
+it's a tricky problem the refund
+
+ align:start position:0%
+it's a tricky problem the refund
+ 
+
+ align:start position:0%
+it's a tricky problem the refund
+transactions there and the clock's
+
+ align:start position:0%
+transactions there and the clock's
+ 
+
+ align:start position:0%
+transactions there and the clock's
+ticking also how do you delete or revoke
+
+ align:start position:0%
+ticking also how do you delete or revoke
+ 
+
+ align:start position:0%
+ticking also how do you delete or revoke
+these old transaction right if you've
+
+ align:start position:0%
+these old transaction right if you've
+ 
+
+ align:start position:0%
+these old transaction right if you've
+signed over okay you've got eight coins
+
+ align:start position:0%
+signed over okay you've got eight coins
+ 
+
+ align:start position:0%
+signed over okay you've got eight coins
+I've got two coins that's there forever
+
+ align:start position:0%
+I've got two coins that's there forever
+ 
+
+ align:start position:0%
+I've got two coins that's there forever
+and the blockchain doesn't know that
+
+ align:start position:0%
+and the blockchain doesn't know that
+ 
+
+ align:start position:0%
+and the blockchain doesn't know that
+it's not valid anymore right the whole
+
+ align:start position:0%
+it's not valid anymore right the whole
+ 
+
+ align:start position:0%
+it's not valid anymore right the whole
+point of the blockchain is to say okay
+
+ align:start position:0%
+point of the blockchain is to say okay
+ 
+
+ align:start position:0%
+point of the blockchain is to say okay
+this is gone actually but between this
+
+ align:start position:0%
+this is gone actually but between this
+ 
+
+ align:start position:0%
+this is gone actually but between this
+unidirectional and lightning I think how
+
+ align:start position:0%
+unidirectional and lightning I think how
+ 
+
+ align:start position:0%
+unidirectional and lightning I think how
+did the order go like christian decker
+
+ align:start position:0%
+did the order go like christian decker
+ 
+
+ align:start position:0%
+did the order go like christian decker
+wrote a thing about decrementing time
+
+ align:start position:0%
+wrote a thing about decrementing time
+ 
+
+ align:start position:0%
+wrote a thing about decrementing time
+locks and i don't think he published I
+
+ align:start position:0%
+locks and i don't think he published I
+ 
+
+ align:start position:0%
+locks and i don't think he published I
+think he published after we wrote
+
+ align:start position:0%
+think he published after we wrote
+ 
+
+ align:start position:0%
+think he published after we wrote
+lightning but the idea was like these
+
+ align:start position:0%
+lightning but the idea was like these
+ 
+
+ align:start position:0%
+lightning but the idea was like these
+would have lock times it's like you
+
+ align:start position:0%
+would have lock times it's like you
+ 
+
+ align:start position:0%
+would have lock times it's like you
+could broadcast this you could broadcast
+
+ align:start position:0%
+could broadcast this you could broadcast
+ 
+
+ align:start position:0%
+could broadcast this you could broadcast
+this on the 27th right all the three of
+
+ align:start position:0%
+this on the 27th right all the three of
+ 
+
+ align:start position:0%
+this on the 27th right all the three of
+these could be broadcast on the 27th and
+
+ align:start position:0%
+these could be broadcast on the 27th and
+ 
+
+ align:start position:0%
+these could be broadcast on the 27th and
+then the idea is Bob wants to send money
+
+ align:start position:0%
+then the idea is Bob wants to send money
+ 
+
+ align:start position:0%
+then the idea is Bob wants to send money
+back and you put a lock time on the 26th
+
+ align:start position:0%
+back and you put a lock time on the 26th
+ 
+
+ align:start position:0%
+back and you put a lock time on the 26th
+and the idea is like oh now now there's
+
+ align:start position:0%
+and the idea is like oh now now there's
+ 
+
+ align:start position:0%
+and the idea is like oh now now there's
+these all are 27th but now there's a bob
+
+ align:start position:0%
+these all are 27th but now there's a bob
+ 
+
+ align:start position:0%
+these all are 27th but now there's a bob
+to alice 8 over here that's broadcast on
+
+ align:start position:0%
+to alice 8 over here that's broadcast on
+ 
+
+ align:start position:0%
+to alice 8 over here that's broadcast on
+the 26th and so the idea is well Alice
+
+ align:start position:0%
+the 26th and so the idea is well Alice
+ 
+
+ align:start position:0%
+the 26th and so the idea is well Alice
+can get the money back you know Alice
+
+ align:start position:0%
+can get the money back you know Alice
+ 
+
+ align:start position:0%
+can get the money back you know Alice
+Bob can pay and go back to paying Alice
+
+ align:start position:0%
+Bob can pay and go back to paying Alice
+ 
+
+ align:start position:0%
+Bob can pay and go back to paying Alice
+because it's like sooner and now it's
+
+ align:start position:0%
+because it's like sooner and now it's
+ 
+
+ align:start position:0%
+because it's like sooner and now it's
+gonna like race so that helps a little
+
+ align:start position:0%
+gonna like race so that helps a little
+ 
+
+ align:start position:0%
+gonna like race so that helps a little
+and that you can switch back and forth a
+
+ align:start position:0%
+and that you can switch back and forth a
+ 
+
+ align:start position:0%
+and that you can switch back and forth a
+few times but each time you do it the
+
+ align:start position:0%
+few times but each time you do it the
+ 
+
+ align:start position:0%
+few times but each time you do it the
+time window gets like sooner so that's
+
+ align:start position:0%
+time window gets like sooner so that's
+ 
+
+ align:start position:0%
+time window gets like sooner so that's
+kind of cool idea
+
+ align:start position:0%
+kind of cool idea
+ 
+
+ align:start position:0%
+kind of cool idea
+but I think the Lightning one is nicer
+
+ align:start position:0%
+but I think the Lightning one is nicer
+ 
+
+ align:start position:0%
+but I think the Lightning one is nicer
+because it like makes it okay whoa the
+
+ align:start position:0%
+because it like makes it okay whoa the
+ 
+
+ align:start position:0%
+because it like makes it okay whoa the
+goal is back and forth between these two
+
+ align:start position:0%
+goal is back and forth between these two
+ 
+
+ align:start position:0%
+goal is back and forth between these two
+parties and lasts forever and you can do
+
+ align:start position:0%
+parties and lasts forever and you can do
+ 
+
+ align:start position:0%
+parties and lasts forever and you can do
+as many transactions as you want okay so
+
+ align:start position:0%
+as many transactions as you want okay so
+ 
+
+ align:start position:0%
+as many transactions as you want okay so
+how do you do that so there's two timing
+
+ align:start position:0%
+how do you do that so there's two timing
+ 
+
+ align:start position:0%
+how do you do that so there's two timing
+op coats that have been added to Bitcoin
+
+ align:start position:0%
+op coats that have been added to Bitcoin
+ 
+
+ align:start position:0%
+op coats that have been added to Bitcoin
+and like check sequence verifies is
+
+ align:start position:0%
+and like check sequence verifies is
+ 
+
+ align:start position:0%
+and like check sequence verifies is
+pretty much for lightning in my opinion
+
+ align:start position:0%
+pretty much for lightning in my opinion
+ 
+
+ align:start position:0%
+pretty much for lightning in my opinion
+that's that's the real use case there's
+
+ align:start position:0%
+that's that's the real use case there's
+ 
+
+ align:start position:0%
+that's that's the real use case there's
+also check check lock on verify so the
+
+ align:start position:0%
+also check check lock on verify so the
+ 
+
+ align:start position:0%
+also check check lock on verify so the
+idea of sequence verify is it's a
+
+ align:start position:0%
+idea of sequence verify is it's a
+ 
+
+ align:start position:0%
+idea of sequence verify is it's a
+relative lock time so it doesn't specify
+
+ align:start position:0%
+relative lock time so it doesn't specify
+ 
+
+ align:start position:0%
+relative lock time so it doesn't specify
+okay this transactions valid on March
+
+ align:start position:0%
+okay this transactions valid on March
+ 
+
+ align:start position:0%
+okay this transactions valid on March
+28th it says this transactions valid
+
+ align:start position:0%
+28th it says this transactions valid
+ 
+
+ align:start position:0%
+28th it says this transactions valid
+when the input is spending is a week old
+
+ align:start position:0%
+when the input is spending is a week old
+ 
+
+ align:start position:0%
+when the input is spending is a week old
+and by a week oh that's you know it's in
+
+ align:start position:0%
+and by a week oh that's you know it's in
+ 
+
+ align:start position:0%
+and by a week oh that's you know it's in
+a week's worth of blocks in the actual
+
+ align:start position:0%
+a week's worth of blocks in the actual
+ 
+
+ align:start position:0%
+a week's worth of blocks in the actual
+software we we don't usually use time we
+
+ align:start position:0%
+software we we don't usually use time we
+ 
+
+ align:start position:0%
+software we we don't usually use time we
+always use block ight it's sort of
+
+ align:start position:0%
+always use block ight it's sort of
+ 
+
+ align:start position:0%
+always use block ight it's sort of
+simpler to think about in a lot of ways
+
+ align:start position:0%
+simpler to think about in a lot of ways
+ 
+
+ align:start position:0%
+simpler to think about in a lot of ways
+but you can say okay well this you know
+
+ align:start position:0%
+but you can say okay well this you know
+ 
+
+ align:start position:0%
+but you can say okay well this you know
+this I sent to an output script and the
+
+ align:start position:0%
+this I sent to an output script and the
+ 
+
+ align:start position:0%
+this I sent to an output script and the
+output script specifies that you can
+
+ align:start position:0%
+output script specifies that you can
+ 
+
+ align:start position:0%
+output script specifies that you can
+only spend this these coins after the
+
+ align:start position:0%
+only spend this these coins after the
+ 
+
+ align:start position:0%
+only spend this these coins after the
+transaction creating them has been you
+
+ align:start position:0%
+transaction creating them has been you
+ 
+
+ align:start position:0%
+transaction creating them has been you
+know in a hundred block you know a
+
+ align:start position:0%
+know in a hundred block you know a
+ 
+
+ align:start position:0%
+know in a hundred block you know a
+hundred blocks deep so that's kind of an
+
+ align:start position:0%
+hundred blocks deep so that's kind of an
+ 
+
+ align:start position:0%
+hundred blocks deep so that's kind of an
+interesting useful thing requires yeah
+
+ align:start position:0%
+interesting useful thing requires yeah
+ 
+
+ align:start position:0%
+interesting useful thing requires yeah
+in confirmations if not you can't spend
+
+ align:start position:0%
+in confirmations if not you can't spend
+ 
+
+ align:start position:0%
+in confirmations if not you can't spend
+it I've checked long time verify it's a
+
+ align:start position:0%
+it I've checked long time verify it's a
+ 
+
+ align:start position:0%
+it I've checked long time verify it's a
+lot absolute long time off code so you
+
+ align:start position:0%
+lot absolute long time off code so you
+ 
+
+ align:start position:0%
+lot absolute long time off code so you
+require that the transaction be
+
+ align:start position:0%
+require that the transaction be
+ 
+
+ align:start position:0%
+require that the transaction be
+confirmed at high ten or or above and
+
+ align:start position:0%
+confirmed at high ten or or above and
+ 
+
+ align:start position:0%
+confirmed at high ten or or above and
+the difference between so what we said
+
+ align:start position:0%
+the difference between so what we said
+ 
+
+ align:start position:0%
+the difference between so what we said
+in the fund
+
+ align:start position:0%
+in the fund
+ 
+
+ align:start position:0%
+in the fund
+sorry the refunds transaction the refund
+
+ align:start position:0%
+sorry the refunds transaction the refund
+ 
+
+ align:start position:0%
+sorry the refunds transaction the refund
+transaction the transaction field has a
+
+ align:start position:0%
+transaction the transaction field has a
+ 
+
+ align:start position:0%
+transaction the transaction field has a
+lock time right so in this case here but
+
+ align:start position:0%
+lock time right so in this case here but
+ 
+
+ align:start position:0%
+lock time right so in this case here but
+the transaction itself has a long time
+
+ align:start position:0%
+the transaction itself has a long time
+ 
+
+ align:start position:0%
+the transaction itself has a long time
+and the OP but that's that's different
+
+ align:start position:0%
+and the OP but that's that's different
+ 
+
+ align:start position:0%
+and the OP but that's that's different
+from the OP code the what the off code
+
+ align:start position:0%
+from the OP code the what the off code
+ 
+
+ align:start position:0%
+from the OP code the what the off code
+does it says okay this output has a lock
+
+ align:start position:0%
+does it says okay this output has a lock
+ 
+
+ align:start position:0%
+does it says okay this output has a lock
+time because the output script ensures
+
+ align:start position:0%
+time because the output script ensures
+ 
+
+ align:start position:0%
+time because the output script ensures
+that the transaction itself has a long
+
+ align:start position:0%
+that the transaction itself has a long
+ 
+
+ align:start position:0%
+that the transaction itself has a long
+time right so basically what this off
+
+ align:start position:0%
+time right so basically what this off
+ 
+
+ align:start position:0%
+time right so basically what this off
+you know it says you say OP check lock
+
+ align:start position:0%
+you know it says you say OP check lock
+ 
+
+ align:start position:0%
+you know it says you say OP check lock
+time verify five hundred thousand and
+
+ align:start position:0%
+time verify five hundred thousand and
+ 
+
+ align:start position:0%
+time verify five hundred thousand and
+then it checks that the transactions
+
+ align:start position:0%
+then it checks that the transactions
+ 
+
+ align:start position:0%
+then it checks that the transactions
+lock time field is exactly equal to five
+
+ align:start position:0%
+lock time field is exactly equal to five
+ 
+
+ align:start position:0%
+lock time field is exactly equal to five
+hundred thousand
+
+ align:start position:0%
+hundred thousand
+ 
+
+ align:start position:0%
+hundred thousand
+so it's a way to enforce a transaction
+
+ align:start position:0%
+so it's a way to enforce a transaction
+ 
+
+ align:start position:0%
+so it's a way to enforce a transaction
+wide-field inside of an output it's a
+
+ align:start position:0%
+wide-field inside of an output it's a
+ 
+
+ align:start position:0%
+wide-field inside of an output it's a
+little weird but both of these become op
+
+ align:start position:0%
+little weird but both of these become op
+ 
+
+ align:start position:0%
+little weird but both of these become op
+codes that you can use in scripts and
+
+ align:start position:0%
+codes that you can use in scripts and
+ 
+
+ align:start position:0%
+codes that you can use in scripts and
+now you can specify like a make an
+
+ align:start position:0%
+now you can specify like a make an
+ 
+
+ align:start position:0%
+now you can specify like a make an
+address that has these weird timing
+
+ align:start position:0%
+address that has these weird timing
+ 
+
+ align:start position:0%
+address that has these weird timing
+properties okay any questions about
+
+ align:start position:0%
+properties okay any questions about
+ 
+
+ align:start position:0%
+properties okay any questions about
+these two yep
+
+ align:start position:0%
+these two yep
+ 
+
+ align:start position:0%
+these two yep
+you can mix them and match them check
+
+ align:start position:0%
+you can mix them and match them check
+ 
+
+ align:start position:0%
+you can mix them and match them check
+sequence verify is specific to an input
+
+ align:start position:0%
+sequence verify is specific to an input
+ 
+
+ align:start position:0%
+sequence verify is specific to an input
+so there's a sequence field in each
+
+ align:start position:0%
+so there's a sequence field in each
+ 
+
+ align:start position:0%
+so there's a sequence field in each
+input that was completely useless until
+
+ align:start position:0%
+input that was completely useless until
+ 
+
+ align:start position:0%
+input that was completely useless until
+like I said what well okay so if you
+
+ align:start position:0%
+like I said what well okay so if you
+ 
+
+ align:start position:0%
+like I said what well okay so if you
+look there's like a sequence and it was
+
+ align:start position:0%
+look there's like a sequence and it was
+ 
+
+ align:start position:0%
+look there's like a sequence and it was
+always just ffffff you know that's like
+
+ align:start position:0%
+always just ffffff you know that's like
+ 
+
+ align:start position:0%
+always just ffffff you know that's like
+2 to the 32 or whatever 2 to the 32
+
+ align:start position:0%
+2 to the 32 or whatever 2 to the 32
+ 
+
+ align:start position:0%
+2 to the 32 or whatever 2 to the 32
+minus 1 I think and it didn't do
+
+ align:start position:0%
+minus 1 I think and it didn't do
+ 
+
+ align:start position:0%
+minus 1 I think and it didn't do
+anything Satoshi put it in because he
+
+ align:start position:0%
+anything Satoshi put it in because he
+ 
+
+ align:start position:0%
+anything Satoshi put it in because he
+thought ok this will this will let you
+
+ align:start position:0%
+thought ok this will this will let you
+ 
+
+ align:start position:0%
+thought ok this will this will let you
+indicate finality right where you can
+
+ align:start position:0%
+indicate finality right where you can
+ 
+
+ align:start position:0%
+indicate finality right where you can
+increment the sequence number so you say
+
+ align:start position:0%
+increment the sequence number so you say
+ 
+
+ align:start position:0%
+increment the sequence number so you say
+ok this is sequence 1 and then I can
+
+ align:start position:0%
+ok this is sequence 1 and then I can
+ 
+
+ align:start position:0%
+ok this is sequence 1 and then I can
+replace it with sequence 2 and it didn't
+
+ align:start position:0%
+replace it with sequence 2 and it didn't
+ 
+
+ align:start position:0%
+replace it with sequence 2 and it didn't
+work because you can't have consensus on
+
+ align:start position:0%
+work because you can't have consensus on
+ 
+
+ align:start position:0%
+work because you can't have consensus on
+those things so this was a field that
+
+ align:start position:0%
+those things so this was a field that
+ 
+
+ align:start position:0%
+those things so this was a field that
+was sort of unused in the inputs and
+
+ align:start position:0%
+was sort of unused in the inputs and
+ 
+
+ align:start position:0%
+was sort of unused in the inputs and
+what they did is they said ok we'll make
+
+ align:start position:0%
+what they did is they said ok we'll make
+ 
+
+ align:start position:0%
+what they did is they said ok we'll make
+that a sequence number where if you now
+
+ align:start position:0%
+that a sequence number where if you now
+ 
+
+ align:start position:0%
+that a sequence number where if you now
+make this say you make the sequence
+
+ align:start position:0%
+make this say you make the sequence
+ 
+
+ align:start position:0%
+make this say you make the sequence
+number a hundred for example and then in
+
+ align:start position:0%
+number a hundred for example and then in
+ 
+
+ align:start position:0%
+number a hundred for example and then in
+your transaction it'll say ok this this
+
+ align:start position:0%
+your transaction it'll say ok this this
+ 
+
+ align:start position:0%
+your transaction it'll say ok this this
+this TX you know this transaction output
+
+ align:start position:0%
+this TX you know this transaction output
+ 
+
+ align:start position:0%
+this TX you know this transaction output
+that you're spending is it a hundred
+
+ align:start position:0%
+that you're spending is it a hundred
+ 
+
+ align:start position:0%
+that you're spending is it a hundred
+blocks old and if so we're good if not
+
+ align:start position:0%
+blocks old and if so we're good if not
+ 
+
+ align:start position:0%
+blocks old and if so we're good if not
+this input spending fails so it's
+
+ align:start position:0%
+this input spending fails so it's
+ 
+
+ align:start position:0%
+this input spending fails so it's
+another check in addition to the
+
+ align:start position:0%
+another check in addition to the
+ 
+
+ align:start position:0%
+another check in addition to the
+signature and then you can also ensure
+
+ align:start position:0%
+signature and then you can also ensure
+ 
+
+ align:start position:0%
+signature and then you can also ensure
+that that with the width check sequence
+
+ align:start position:0%
+that that with the width check sequence
+ 
+
+ align:start position:0%
+that that with the width check sequence
+verify you can put in the opcodes you
+
+ align:start position:0%
+verify you can put in the opcodes you
+ 
+
+ align:start position:0%
+verify you can put in the opcodes you
+can put in the script ok this must have
+
+ align:start position:0%
+can put in the script ok this must have
+ 
+
+ align:start position:0%
+can put in the script ok this must have
+a sequence of 100 and then check that
+
+ align:start position:0%
+a sequence of 100 and then check that
+ 
+
+ align:start position:0%
+a sequence of 100 and then check that
+the sequence is equal you know equal or
+
+ align:start position:0%
+the sequence is equal you know equal or
+ 
+
+ align:start position:0%
+the sequence is equal you know equal or
+greater to the you know depth of the
+
+ align:start position:0%
+greater to the you know depth of the
+ 
+
+ align:start position:0%
+greater to the you know depth of the
+transaction and yet you can mix them and
+
+ align:start position:0%
+transaction and yet you can mix them and
+ 
+
+ align:start position:0%
+transaction and yet you can mix them and
+match them in the same script it's a
+
+ align:start position:0%
+match them in the same script it's a
+ 
+
+ align:start position:0%
+match them in the same script it's a
+little ugly to use because it was
+
+ align:start position:0%
+little ugly to use because it was
+ 
+
+ align:start position:0%
+little ugly to use because it was
+introduced as a soft work and they they
+
+ align:start position:0%
+introduced as a soft work and they they
+ 
+
+ align:start position:0%
+introduced as a soft work and they they
+renamed and opted not write a no op op
+
+ align:start position:0%
+renamed and opted not write a no op op
+ 
+
+ align:start position:0%
+renamed and opted not write a no op op
+got renamed to this this is like no op3
+
+ align:start position:0%
+got renamed to this this is like no op3
+ 
+
+ align:start position:0%
+got renamed to this this is like no op3
+and so you have to push the the number
+
+ align:start position:0%
+and so you have to push the the number
+ 
+
+ align:start position:0%
+and so you have to push the the number
+you're checking on the stack up check
+
+ align:start position:0%
+you're checking on the stack up check
+ 
+
+ align:start position:0%
+you're checking on the stack up check
+sequence verify and then you have to
+
+ align:start position:0%
+sequence verify and then you have to
+ 
+
+ align:start position:0%
+sequence verify and then you have to
+drop the number off the stack because it
+
+ align:start position:0%
+drop the number off the stack because it
+ 
+
+ align:start position:0%
+drop the number off the stack because it
+the this opcode doesn't actually consume
+
+ align:start position:0%
+the this opcode doesn't actually consume
+ 
+
+ align:start position:0%
+the this opcode doesn't actually consume
+anything off the top of the stack so
+
+ align:start position:0%
+anything off the top of the stack so
+ 
+
+ align:start position:0%
+anything off the top of the stack so
+that it looks the same as a no op two
+
+ align:start position:0%
+that it looks the same as a no op two
+ 
+
+ align:start position:0%
+that it looks the same as a no op two
+nodes that don't know about it anyway so
+
+ align:start position:0%
+nodes that don't know about it anyway so
+ 
+
+ align:start position:0%
+nodes that don't know about it anyway so
+you've got these two ways to specify
+
+ align:start position:0%
+you've got these two ways to specify
+ 
+
+ align:start position:0%
+you've got these two ways to specify
+output timing okay good so then what you
+
+ align:start position:0%
+output timing okay good so then what you
+ 
+
+ align:start position:0%
+output timing okay good so then what you
+can do is you can revoke based on timing
+
+ align:start position:0%
+can do is you can revoke based on timing
+ 
+
+ align:start position:0%
+can do is you can revoke based on timing
+so the idea of the script and this is
+
+ align:start position:0%
+so the idea of the script and this is
+ 
+
+ align:start position:0%
+so the idea of the script and this is
+sort of in like see like notation not
+
+ align:start position:0%
+sort of in like see like notation not
+ 
+
+ align:start position:0%
+sort of in like see like notation not
+the actual op codes for Bitcoin because
+
+ align:start position:0%
+the actual op codes for Bitcoin because
+ 
+
+ align:start position:0%
+the actual op codes for Bitcoin because
+the actual op codes are kind of
+
+ align:start position:0%
+the actual op codes are kind of
+ 
+
+ align:start position:0%
+the actual op codes are kind of
+confusing the idea is okay you can spend
+
+ align:start position:0%
+confusing the idea is okay you can spend
+ 
+
+ align:start position:0%
+confusing the idea is okay you can spend
+with two of two multi-sig essentially
+
+ align:start position:0%
+with two of two multi-sig essentially
+ 
+
+ align:start position:0%
+with two of two multi-sig essentially
+right key a and key B or GC and wait a
+
+ align:start position:0%
+right key a and key B or GC and wait a
+ 
+
+ align:start position:0%
+right key a and key B or GC and wait a
+hundred blocks and buy wait a hundred
+
+ align:start position:0%
+hundred blocks and buy wait a hundred
+ 
+
+ align:start position:0%
+hundred blocks and buy wait a hundred
+blocks that means that this you know
+
+ align:start position:0%
+blocks that means that this you know
+ 
+
+ align:start position:0%
+blocks that means that this you know
+whatever you're spending has to be a
+
+ align:start position:0%
+whatever you're spending has to be a
+ 
+
+ align:start position:0%
+whatever you're spending has to be a
+hundred blocks you know confirmed a
+
+ align:start position:0%
+hundred blocks you know confirmed a
+ 
+
+ align:start position:0%
+hundred blocks you know confirmed a
+hundred blocks ago or more so a and B
+
+ align:start position:0%
+hundred blocks ago or more so a and B
+ 
+
+ align:start position:0%
+hundred blocks ago or more so a and B
+two that together they can spend any
+
+ align:start position:0%
+two that together they can spend any
+ 
+
+ align:start position:0%
+two that together they can spend any
+time they want secant it's together oops
+
+ align:start position:0%
+time they want secant it's together oops
+ 
+
+ align:start position:0%
+time they want secant it's together oops
+see you can spend but must wait and a
+
+ align:start position:0%
+see you can spend but must wait and a
+ 
+
+ align:start position:0%
+see you can spend but must wait and a
+and B can grab the coins first so this
+
+ align:start position:0%
+and B can grab the coins first so this
+ 
+
+ align:start position:0%
+and B can grab the coins first so this
+is a revocable transaction so the idea
+
+ align:start position:0%
+is a revocable transaction so the idea
+ 
+
+ align:start position:0%
+is a revocable transaction so the idea
+is you've got some and we call it a
+
+ align:start position:0%
+is you've got some and we call it a
+ 
+
+ align:start position:0%
+is you've got some and we call it a
+commitment transaction in the lightning
+
+ align:start position:0%
+commitment transaction in the lightning
+ 
+
+ align:start position:0%
+commitment transaction in the lightning
+paper you've got some input the funding
+
+ align:start position:0%
+paper you've got some input the funding
+ 
+
+ align:start position:0%
+paper you've got some input the funding
+transaction output you're spending that
+
+ align:start position:0%
+transaction output you're spending that
+ 
+
+ align:start position:0%
+transaction output you're spending that
+you've got you need to of to multi-sig
+
+ align:start position:0%
+you've got you need to of to multi-sig
+ 
+
+ align:start position:0%
+you've got you need to of to multi-sig
+so like Bob's signs and sends it over to
+
+ align:start position:0%
+so like Bob's signs and sends it over to
+ 
+
+ align:start position:0%
+so like Bob's signs and sends it over to
+Alice and then you've got that script
+
+ align:start position:0%
+Alice and then you've got that script
+ 
+
+ align:start position:0%
+Alice and then you've got that script
+where it's okay it's Alice's key and you
+
+ align:start position:0%
+where it's okay it's Alice's key and you
+ 
+
+ align:start position:0%
+where it's okay it's Alice's key and you
+wait a hundred blocks or Alice's key and
+
+ align:start position:0%
+wait a hundred blocks or Alice's key and
+ 
+
+ align:start position:0%
+wait a hundred blocks or Alice's key and
+you make a new key for Bob like the Bob
+
+ align:start position:0%
+you make a new key for Bob like the Bob
+ 
+
+ align:start position:0%
+you make a new key for Bob like the Bob
+revoke key and this has two coins this
+
+ align:start position:0%
+revoke key and this has two coins this
+ 
+
+ align:start position:0%
+revoke key and this has two coins this
+has eight coins
+
+ align:start position:0%
+has eight coins
+ 
+
+ align:start position:0%
+has eight coins
+Oh oops this should be our hold on I
+
+ align:start position:0%
+Oh oops this should be our hold on I
+ 
+
+ align:start position:0%
+Oh oops this should be our hold on I
+should change that that's kind of gonna
+
+ align:start position:0%
+should change that that's kind of gonna
+ 
+
+ align:start position:0%
+should change that that's kind of gonna
+be really confusing wait
+
+ align:start position:0%
+be really confusing wait
+ 
+
+ align:start position:0%
+be really confusing wait
+I put the R in the wrong place let me
+
+ align:start position:0%
+I put the R in the wrong place let me
+ 
+
+ align:start position:0%
+I put the R in the wrong place let me
+redo that's that's a typo but it's super
+
+ align:start position:0%
+redo that's that's a typo but it's super
+ 
+
+ align:start position:0%
+redo that's that's a typo but it's super
+confusing yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Elessar and Bob Allison wait did I so
+
+ align:start position:0%
+Elessar and Bob Allison wait did I so
+ 
+
+ align:start position:0%
+Elessar and Bob Allison wait did I so
+put the same thing on both right this
+
+ align:start position:0%
+put the same thing on both right this
+ 
+
+ align:start position:0%
+put the same thing on both right this
+wood is Alice R and Bob yeah and there's
+
+ align:start position:0%
+wood is Alice R and Bob yeah and there's
+ 
+
+ align:start position:0%
+wood is Alice R and Bob yeah and there's
+like when you're actually coding this
+
+ align:start position:0%
+like when you're actually coding this
+ 
+
+ align:start position:0%
+like when you're actually coding this
+stuff it's pretty easy to screw up
+
+ align:start position:0%
+stuff it's pretty easy to screw up
+ 
+
+ align:start position:0%
+stuff it's pretty easy to screw up
+there's a lot of like wait who's Allison
+
+ align:start position:0%
+there's a lot of like wait who's Allison
+ 
+
+ align:start position:0%
+there's a lot of like wait who's Allison
+who's Bob so I don't in any of the code
+
+ align:start position:0%
+who's Bob so I don't in any of the code
+ 
+
+ align:start position:0%
+who's Bob so I don't in any of the code
+I don't use Allison Bob I use like mine
+
+ align:start position:0%
+I don't use Allison Bob I use like mine
+ 
+
+ align:start position:0%
+I don't use Allison Bob I use like mine
+and theirs but a lot of times it's not
+
+ align:start position:0%
+and theirs but a lot of times it's not
+ 
+
+ align:start position:0%
+and theirs but a lot of times it's not
+clear because it's like held by us so
+
+ align:start position:0%
+clear because it's like held by us so
+ 
+
+ align:start position:0%
+clear because it's like held by us so
+this is the transaction that Bob creates
+
+ align:start position:0%
+this is the transaction that Bob creates
+ 
+
+ align:start position:0%
+this is the transaction that Bob creates
+Bob signs transfer balance and then it
+
+ align:start position:0%
+Bob signs transfer balance and then it
+ 
+
+ align:start position:0%
+Bob signs transfer balance and then it
+sits on Alice's hard drive yes okay so
+
+ align:start position:0%
+sits on Alice's hard drive yes okay so
+ 
+
+ align:start position:0%
+sits on Alice's hard drive yes okay so
+you don't you make these these separate
+
+ align:start position:0%
+you don't you make these these separate
+ 
+
+ align:start position:0%
+you don't you make these these separate
+keys right it's it's a key that Alice
+
+ align:start position:0%
+keys right it's it's a key that Alice
+ 
+
+ align:start position:0%
+keys right it's it's a key that Alice
+creates right Alice creates another pub
+
+ align:start position:0%
+creates right Alice creates another pub
+ 
+
+ align:start position:0%
+creates right Alice creates another pub
+key pair and tells the pub key to Bob it
+
+ align:start position:0%
+key pair and tells the pub key to Bob it
+ 
+
+ align:start position:0%
+key pair and tells the pub key to Bob it
+says and this is her sort of revocable
+
+ align:start position:0%
+says and this is her sort of revocable
+ 
+
+ align:start position:0%
+says and this is her sort of revocable
+key yeah where Alice kinland basically
+
+ align:start position:0%
+key yeah where Alice kinland basically
+ 
+
+ align:start position:0%
+key yeah where Alice kinland basically
+what else house is house gives the
+
+ align:start position:0%
+what else house is house gives the
+ 
+
+ align:start position:0%
+what else house is house gives the
+private key to Bob in order to revoke
+
+ align:start position:0%
+private key to Bob in order to revoke
+ 
+
+ align:start position:0%
+private key to Bob in order to revoke
+this transaction so there's sort of
+
+ align:start position:0%
+this transaction so there's sort of
+ 
+
+ align:start position:0%
+this transaction so there's sort of
+mirror images in both cases both parties
+
+ align:start position:0%
+mirror images in both cases both parties
+ 
+
+ align:start position:0%
+mirror images in both cases both parties
+agree look Alice has got two coins Bob's
+
+ align:start position:0%
+agree look Alice has got two coins Bob's
+ 
+
+ align:start position:0%
+agree look Alice has got two coins Bob's
+got eight coins
+
+ align:start position:0%
+got eight coins
+ 
+
+ align:start position:0%
+got eight coins
+right but the transaction that Bob
+
+ align:start position:0%
+right but the transaction that Bob
+ 
+
+ align:start position:0%
+right but the transaction that Bob
+creates and signs yes the transaction
+
+ align:start position:0%
+creates and signs yes the transaction
+ 
+
+ align:start position:0%
+creates and signs yes the transaction
+that Bob creates and signs sends Bob
+
+ align:start position:0%
+that Bob creates and signs sends Bob
+ 
+
+ align:start position:0%
+that Bob creates and signs sends Bob
+eight coins in the clear this is just a
+
+ align:start position:0%
+eight coins in the clear this is just a
+ 
+
+ align:start position:0%
+eight coins in the clear this is just a
+regular old pay to pub key hash where
+
+ align:start position:0%
+regular old pay to pub key hash where
+ 
+
+ align:start position:0%
+regular old pay to pub key hash where
+Bob gets eight coins the coins that are
+
+ align:start position:0%
+Bob gets eight coins the coins that are
+ 
+
+ align:start position:0%
+Bob gets eight coins the coins that are
+Alice's though Alice has to wait a
+
+ align:start position:0%
+Alice's though Alice has to wait a
+ 
+
+ align:start position:0%
+Alice's though Alice has to wait a
+hundred blocks if she broadcasts this
+
+ align:start position:0%
+hundred blocks if she broadcasts this
+ 
+
+ align:start position:0%
+hundred blocks if she broadcasts this
+commitment transaction
+
+ align:start position:0%
+commitment transaction
+ 
+
+ align:start position:0%
+commitment transaction
+she can't spend her money for a day like
+
+ align:start position:0%
+she can't spend her money for a day like
+ 
+
+ align:start position:0%
+she can't spend her money for a day like
+a hundred block whatever a hundred block
+
+ align:start position:0%
+a hundred block whatever a hundred block
+ 
+
+ align:start position:0%
+a hundred block whatever a hundred block
+day Bob can get the money but only if he
+
+ align:start position:0%
+day Bob can get the money but only if he
+ 
+
+ align:start position:0%
+day Bob can get the money but only if he
+knows Alice's are key Alice's were you
+
+ align:start position:0%
+knows Alice's are key Alice's were you
+ 
+
+ align:start position:0%
+knows Alice's are key Alice's were you
+know revocable key so you know Alice has
+
+ align:start position:0%
+know revocable key so you know Alice has
+ 
+
+ align:start position:0%
+know revocable key so you know Alice has
+this Bob doesn't and in the Bob case
+
+ align:start position:0%
+this Bob doesn't and in the Bob case
+ 
+
+ align:start position:0%
+this Bob doesn't and in the Bob case
+it's similar
+
+ align:start position:0%
+it's similar
+ 
+
+ align:start position:0%
+it's similar
+you know the outputs are the same but
+
+ align:start position:0%
+you know the outputs are the same but
+ 
+
+ align:start position:0%
+you know the outputs are the same but
+the ideas Alice creates this Alice signs
+
+ align:start position:0%
+the ideas Alice creates this Alice signs
+ 
+
+ align:start position:0%
+the ideas Alice creates this Alice signs
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+hands it over to Bob and in this case
+
+ align:start position:0%
+hands it over to Bob and in this case
+ 
+
+ align:start position:0%
+hands it over to Bob and in this case
+the transaction is well Alice gets two
+
+ align:start position:0%
+the transaction is well Alice gets two
+ 
+
+ align:start position:0%
+the transaction is well Alice gets two
+coins in the clear right
+
+ align:start position:0%
+coins in the clear right
+ 
+
+ align:start position:0%
+coins in the clear right
+this is immediately spendable no fancy
+
+ align:start position:0%
+this is immediately spendable no fancy
+ 
+
+ align:start position:0%
+this is immediately spendable no fancy
+scripts or anything Bob gets the money
+
+ align:start position:0%
+scripts or anything Bob gets the money
+ 
+
+ align:start position:0%
+scripts or anything Bob gets the money
+but he has to wait a day or Alice can
+
+ align:start position:0%
+but he has to wait a day or Alice can
+ 
+
+ align:start position:0%
+but he has to wait a day or Alice can
+spend the money if she knows Bob's
+
+ align:start position:0%
+spend the money if she knows Bob's
+ 
+
+ align:start position:0%
+spend the money if she knows Bob's
+revocable key this Bob our key right so
+
+ align:start position:0%
+revocable key this Bob our key right so
+ 
+
+ align:start position:0%
+revocable key this Bob our key right so
+either party at any time can broadcast
+
+ align:start position:0%
+either party at any time can broadcast
+ 
+
+ align:start position:0%
+either party at any time can broadcast
+these transactions the thing is the
+
+ align:start position:0%
+these transactions the thing is the
+ 
+
+ align:start position:0%
+these transactions the thing is the
+money they're supposed to get right so
+
+ align:start position:0%
+money they're supposed to get right so
+ 
+
+ align:start position:0%
+money they're supposed to get right so
+in in Bob's case Bob can add Bob's
+
+ align:start position:0%
+in in Bob's case Bob can add Bob's
+ 
+
+ align:start position:0%
+in in Bob's case Bob can add Bob's
+signature broadcast but now he has to
+
+ align:start position:0%
+signature broadcast but now he has to
+ 
+
+ align:start position:0%
+signature broadcast but now he has to
+wait no big deal wait a hundred blocks
+
+ align:start position:0%
+wait no big deal wait a hundred blocks
+ 
+
+ align:start position:0%
+wait no big deal wait a hundred blocks
+okay in Alice's case okay she can close
+
+ align:start position:0%
+okay in Alice's case okay she can close
+ 
+
+ align:start position:0%
+okay in Alice's case okay she can close
+it and you know put her signature on
+
+ align:start position:0%
+it and you know put her signature on
+ 
+
+ align:start position:0%
+it and you know put her signature on
+here broadcast wait a day spend the
+
+ align:start position:0%
+here broadcast wait a day spend the
+ 
+
+ align:start position:0%
+here broadcast wait a day spend the
+money but what's nice is you can revoke
+
+ align:start position:0%
+money but what's nice is you can revoke
+ 
+
+ align:start position:0%
+money but what's nice is you can revoke
+it right so Alice can say look I'm Alice
+
+ align:start position:0%
+it right so Alice can say look I'm Alice
+ 
+
+ align:start position:0%
+it right so Alice can say look I'm Alice
+can tell Bob I'm not gonna do this I'm
+
+ align:start position:0%
+can tell Bob I'm not gonna do this I'm
+ 
+
+ align:start position:0%
+can tell Bob I'm not gonna do this I'm
+not going to use this transaction the
+
+ align:start position:0%
+not going to use this transaction the
+ 
+
+ align:start position:0%
+not going to use this transaction the
+way I'll prove it to you the whale you
+
+ align:start position:0%
+way I'll prove it to you the whale you
+ 
+
+ align:start position:0%
+way I'll prove it to you the whale you
+know I deleted it and Bob's like yeah
+
+ align:start position:0%
+know I deleted it and Bob's like yeah
+ 
+
+ align:start position:0%
+know I deleted it and Bob's like yeah
+sure you deleted the way I'll prove you
+
+ align:start position:0%
+sure you deleted the way I'll prove you
+ 
+
+ align:start position:0%
+sure you deleted the way I'll prove you
+that I deleted this is I will tell you
+
+ align:start position:0%
+that I deleted this is I will tell you
+ 
+
+ align:start position:0%
+that I deleted this is I will tell you
+the private key I'll tell you Alice R so
+
+ align:start position:0%
+the private key I'll tell you Alice R so
+ 
+
+ align:start position:0%
+the private key I'll tell you Alice R so
+now you Bob knows Bob because Bob
+
+ align:start position:0%
+now you Bob knows Bob because Bob
+ 
+
+ align:start position:0%
+now you Bob knows Bob because Bob
+actually Bob created this transaction
+
+ align:start position:0%
+actually Bob created this transaction
+ 
+
+ align:start position:0%
+actually Bob created this transaction
+right Bob signed it Bob knows what it
+
+ align:start position:0%
+right Bob signed it Bob knows what it
+ 
+
+ align:start position:0%
+right Bob signed it Bob knows what it
+looks like and Bob knows well yeah this
+
+ align:start position:0%
+looks like and Bob knows well yeah this
+ 
+
+ align:start position:0%
+looks like and Bob knows well yeah this
+is the script since Bob knows Alice R
+
+ align:start position:0%
+is the script since Bob knows Alice R
+ 
+
+ align:start position:0%
+is the script since Bob knows Alice R
+and Bob knows his own key Bob Noah's
+
+ align:start position:0%
+and Bob knows his own key Bob Noah's
+ 
+
+ align:start position:0%
+and Bob knows his own key Bob Noah's
+look this money's mine this money's mine
+
+ align:start position:0%
+look this money's mine this money's mine
+ 
+
+ align:start position:0%
+look this money's mine this money's mine
+to write because I can do this
+
+ align:start position:0%
+to write because I can do this
+ 
+
+ align:start position:0%
+to write because I can do this
+immediately so if you brought this
+
+ align:start position:0%
+immediately so if you brought this
+ 
+
+ align:start position:0%
+immediately so if you brought this
+transaction I don't have to even touch
+
+ align:start position:0%
+transaction I don't have to even touch
+ 
+
+ align:start position:0%
+transaction I don't have to even touch
+this because it's just my money and this
+
+ align:start position:0%
+this because it's just my money and this
+ 
+
+ align:start position:0%
+this because it's just my money and this
+output I can spend immediately well you
+
+ align:start position:0%
+output I can spend immediately well you
+ 
+
+ align:start position:0%
+output I can spend immediately well you
+have to wait a hundred blocks so and you
+
+ align:start position:0%
+have to wait a hundred blocks so and you
+ 
+
+ align:start position:0%
+have to wait a hundred blocks so and you
+know my software's gonna automatically
+
+ align:start position:0%
+know my software's gonna automatically
+ 
+
+ align:start position:0%
+know my software's gonna automatically
+do that so I know Alice R its private
+
+ align:start position:0%
+do that so I know Alice R its private
+ 
+
+ align:start position:0%
+do that so I know Alice R its private
+key I know Bob's private key I just take
+
+ align:start position:0%
+key I know Bob's private key I just take
+ 
+
+ align:start position:0%
+key I know Bob's private key I just take
+these two coins as soon as I see this
+
+ align:start position:0%
+these two coins as soon as I see this
+ 
+
+ align:start position:0%
+these two coins as soon as I see this
+transaction I take these two coins I
+
+ align:start position:0%
+transaction I take these two coins I
+ 
+
+ align:start position:0%
+transaction I take these two coins I
+spend them back to Bob's address and get
+
+ align:start position:0%
+spend them back to Bob's address and get
+ 
+
+ align:start position:0%
+spend them back to Bob's address and get
+all 10 so that's a pretty convincing way
+
+ align:start position:0%
+all 10 so that's a pretty convincing way
+ 
+
+ align:start position:0%
+all 10 so that's a pretty convincing way
+for Alice to say look I'm not gonna use
+
+ align:start position:0%
+for Alice to say look I'm not gonna use
+ 
+
+ align:start position:0%
+for Alice to say look I'm not gonna use
+this I'm deleting and to show you know
+
+ align:start position:0%
+this I'm deleting and to show you know
+ 
+
+ align:start position:0%
+this I'm deleting and to show you know
+even if I do use it here here's the key
+
+ align:start position:0%
+even if I do use it here here's the key
+ 
+
+ align:start position:0%
+even if I do use it here here's the key
+okay any questions about this yep yeah
+
+ align:start position:0%
+okay any questions about this yep yeah
+ 
+
+ align:start position:0%
+okay any questions about this yep yeah
+so Alice has to hand it over right this
+
+ align:start position:0%
+so Alice has to hand it over right this
+ 
+
+ align:start position:0%
+so Alice has to hand it over right this
+is just a regular you know 32 byte
+
+ align:start position:0%
+is just a regular you know 32 byte
+ 
+
+ align:start position:0%
+is just a regular you know 32 byte
+private key
+
+ align:start position:0%
+private key
+ 
+
+ align:start position:0%
+private key
+that Alice created and similar you know
+
+ align:start position:0%
+that Alice created and similar you know
+ 
+
+ align:start position:0%
+that Alice created and similar you know
+same idea for Bob they both create you
+
+ align:start position:0%
+same idea for Bob they both create you
+ 
+
+ align:start position:0%
+same idea for Bob they both create you
+know essentially the same transaction
+
+ align:start position:0%
+know essentially the same transaction
+ 
+
+ align:start position:0%
+know essentially the same transaction
+but with things swapped Bob Bob can
+
+ align:start position:0%
+but with things swapped Bob Bob can
+ 
+
+ align:start position:0%
+but with things swapped Bob Bob can
+broadcast this if he does he has to wait
+
+ align:start position:0%
+broadcast this if he does he has to wait
+ 
+
+ align:start position:0%
+broadcast this if he does he has to wait
+a day but if he reveals Bob Bob our
+
+ align:start position:0%
+a day but if he reveals Bob Bob our
+ 
+
+ align:start position:0%
+a day but if he reveals Bob Bob our
+private key to Alice Alice knows okay I
+
+ align:start position:0%
+private key to Alice Alice knows okay I
+ 
+
+ align:start position:0%
+private key to Alice Alice knows okay I
+get two coins in the clear and then
+
+ align:start position:0%
+get two coins in the clear and then
+ 
+
+ align:start position:0%
+get two coins in the clear and then
+these eight coins I can sign this I can
+
+ align:start position:0%
+these eight coins I can sign this I can
+ 
+
+ align:start position:0%
+these eight coins I can sign this I can
+sign this I can get these eight coins
+
+ align:start position:0%
+sign this I can get these eight coins
+ 
+
+ align:start position:0%
+sign this I can get these eight coins
+immediately Bob's got away today so
+
+ align:start position:0%
+immediately Bob's got away today so
+ 
+
+ align:start position:0%
+immediately Bob's got away today so
+that's a way to sort of say look I'm not
+
+ align:start position:0%
+that's a way to sort of say look I'm not
+ 
+
+ align:start position:0%
+that's a way to sort of say look I'm not
+going to use this any other questions
+
+ align:start position:0%
+going to use this any other questions
+ 
+
+ align:start position:0%
+going to use this any other questions
+okay so what you do with that is yeah
+
+ align:start position:0%
+okay so what you do with that is yeah
+ 
+
+ align:start position:0%
+okay so what you do with that is yeah
+either party can broadcast that to wait
+
+ align:start position:0%
+either party can broadcast that to wait
+ 
+
+ align:start position:0%
+either party can broadcast that to wait
+they exchange these revoked and
+
+ align:start position:0%
+they exchange these revoked and
+ 
+
+ align:start position:0%
+they exchange these revoked and
+revocation private private keys and now
+
+ align:start position:0%
+revocation private private keys and now
+ 
+
+ align:start position:0%
+revocation private private keys and now
+if they broadcast the counterparty can
+
+ align:start position:0%
+if they broadcast the counterparty can
+ 
+
+ align:start position:0%
+if they broadcast the counterparty can
+take all the funds so it's pretty pretty
+
+ align:start position:0%
+take all the funds so it's pretty pretty
+ 
+
+ align:start position:0%
+take all the funds so it's pretty pretty
+good so the idea is this is a lightning
+
+ align:start position:0%
+good so the idea is this is a lightning
+ 
+
+ align:start position:0%
+good so the idea is this is a lightning
+channel you've got this output you
+
+ align:start position:0%
+channel you've got this output you
+ 
+
+ align:start position:0%
+channel you've got this output you
+create these states okay the first state
+
+ align:start position:0%
+create these states okay the first state
+ 
+
+ align:start position:0%
+create these states okay the first state
+is Alice gets one coin Bob gets nine
+
+ align:start position:0%
+is Alice gets one coin Bob gets nine
+ 
+
+ align:start position:0%
+is Alice gets one coin Bob gets nine
+coin then what Bob wants to pay Alice so
+
+ align:start position:0%
+coin then what Bob wants to pay Alice so
+ 
+
+ align:start position:0%
+coin then what Bob wants to pay Alice so
+Bob says hey Alice I'm paying you for
+
+ align:start position:0%
+Bob says hey Alice I'm paying you for
+ 
+
+ align:start position:0%
+Bob says hey Alice I'm paying you for
+coins here I'll sign and create this new
+
+ align:start position:0%
+coins here I'll sign and create this new
+ 
+
+ align:start position:0%
+coins here I'll sign and create this new
+output this new transaction in it to
+
+ align:start position:0%
+output this new transaction in it to
+ 
+
+ align:start position:0%
+output this new transaction in it to
+Alice and Bob's and Alice says okay but
+
+ align:start position:0%
+Alice and Bob's and Alice says okay but
+ 
+
+ align:start position:0%
+Alice and Bob's and Alice says okay but
+now we have to revoke this one right
+
+ align:start position:0%
+now we have to revoke this one right
+ 
+
+ align:start position:0%
+now we have to revoke this one right
+we've got you know Alice has this it's
+
+ align:start position:0%
+we've got you know Alice has this it's
+ 
+
+ align:start position:0%
+we've got you know Alice has this it's
+signed Alice can broadcast it but Alice
+
+ align:start position:0%
+signed Alice can broadcast it but Alice
+ 
+
+ align:start position:0%
+signed Alice can broadcast it but Alice
+also wants to be sure that Bob can't
+
+ align:start position:0%
+also wants to be sure that Bob can't
+ 
+
+ align:start position:0%
+also wants to be sure that Bob can't
+broadcast this anymore so they sort of
+
+ align:start position:0%
+broadcast this anymore so they sort of
+ 
+
+ align:start position:0%
+broadcast this anymore so they sort of
+trash it right they reveal there are
+
+ align:start position:0%
+trash it right they reveal there are
+ 
+
+ align:start position:0%
+trash it right they reveal there are
+private keys to each other so in
+
+ align:start position:0%
+private keys to each other so in
+ 
+
+ align:start position:0%
+private keys to each other so in
+practice right it could be well only Bob
+
+ align:start position:0%
+practice right it could be well only Bob
+ 
+
+ align:start position:0%
+practice right it could be well only Bob
+has to reveal the our private key in
+
+ align:start position:0%
+has to reveal the our private key in
+ 
+
+ align:start position:0%
+has to reveal the our private key in
+this case because Alice is never going
+
+ align:start position:0%
+this case because Alice is never going
+ 
+
+ align:start position:0%
+this case because Alice is never going
+to well you know alice is gonna
+
+ align:start position:0%
+to well you know alice is gonna
+ 
+
+ align:start position:0%
+to well you know alice is gonna
+broadcast this not this it's just so
+
+ align:start position:0%
+broadcast this not this it's just so
+ 
+
+ align:start position:0%
+broadcast this not this it's just so
+much simpler if they both if they both
+
+ align:start position:0%
+much simpler if they both if they both
+ 
+
+ align:start position:0%
+much simpler if they both if they both
+reveal the R keys because then you don't
+
+ align:start position:0%
+reveal the R keys because then you don't
+ 
+
+ align:start position:0%
+reveal the R keys because then you don't
+have to worry about like something you
+
+ align:start position:0%
+have to worry about like something you
+ 
+
+ align:start position:0%
+have to worry about like something you
+know what happens in the future when
+
+ align:start position:0%
+know what happens in the future when
+ 
+
+ align:start position:0%
+know what happens in the future when
+Alice has 0.5 and Alice still has this
+
+ align:start position:0%
+Alice has 0.5 and Alice still has this
+ 
+
+ align:start position:0%
+Alice has 0.5 and Alice still has this
+thing so it's really simple you just
+
+ align:start position:0%
+thing so it's really simple you just
+ 
+
+ align:start position:0%
+thing so it's really simple you just
+they both reveal and now this
+
+ align:start position:0%
+they both reveal and now this
+ 
+
+ align:start position:0%
+they both reveal and now this
+transaction this state one it's
+
+ align:start position:0%
+transaction this state one it's
+ 
+
+ align:start position:0%
+transaction this state one it's
+basically on broadcast you know you're
+
+ align:start position:0%
+basically on broadcast you know you're
+ 
+
+ align:start position:0%
+basically on broadcast you know you're
+not gonna use it and they can keep doing
+
+ align:start position:0%
+not gonna use it and they can keep doing
+ 
+
+ align:start position:0%
+not gonna use it and they can keep doing
+that and they can go back and forth
+
+ align:start position:0%
+that and they can go back and forth
+ 
+
+ align:start position:0%
+that and they can go back and forth
+right so now Alice phase Bob says hey or
+
+ align:start position:0%
+right so now Alice phase Bob says hey or
+ 
+
+ align:start position:0%
+right so now Alice phase Bob says hey or
+no oops
+
+ align:start position:0%
+no oops
+ 
+
+ align:start position:0%
+no oops
+go back and forth oh well oops anyway
+
+ align:start position:0%
+go back and forth oh well oops anyway
+ 
+
+ align:start position:0%
+go back and forth oh well oops anyway
+you can you can make this like Alice
+
+ align:start position:0%
+you can you can make this like Alice
+ 
+
+ align:start position:0%
+you can you can make this like Alice
+back to two and Bob back to eight or
+
+ align:start position:0%
+back to two and Bob back to eight or
+ 
+
+ align:start position:0%
+back to two and Bob back to eight or
+whatever you know basically arbitrary
+
+ align:start position:0%
+whatever you know basically arbitrary
+ 
+
+ align:start position:0%
+whatever you know basically arbitrary
+numbers you can keep going in both
+
+ align:start position:0%
+numbers you can keep going in both
+ 
+
+ align:start position:0%
+numbers you can keep going in both
+directions and you know deleting the old
+
+ align:start position:0%
+directions and you know deleting the old
+ 
+
+ align:start position:0%
+directions and you know deleting the old
+old so that's pretty useful there's no
+
+ align:start position:0%
+old so that's pretty useful there's no
+ 
+
+ align:start position:0%
+old so that's pretty useful there's no
+lock time for the transact for the
+
+ align:start position:0%
+lock time for the transact for the
+ 
+
+ align:start position:0%
+lock time for the transact for the
+channel itself the channel can just keep
+
+ align:start position:0%
+channel itself the channel can just keep
+ 
+
+ align:start position:0%
+channel itself the channel can just keep
+going on forever and Alice and Bob can
+
+ align:start position:0%
+going on forever and Alice and Bob can
+ 
+
+ align:start position:0%
+going on forever and Alice and Bob can
+keep sending these things it's a little
+
+ align:start position:0%
+keep sending these things it's a little
+ 
+
+ align:start position:0%
+keep sending these things it's a little
+more complicated I didn't put yeah I
+
+ align:start position:0%
+more complicated I didn't put yeah I
+ 
+
+ align:start position:0%
+more complicated I didn't put yeah I
+didn't put the the messages but they
+
+ align:start position:0%
+didn't put the the messages but they
+ 
+
+ align:start position:0%
+didn't put the the messages but they
+have to send four more messages you can
+
+ align:start position:0%
+have to send four more messages you can
+ 
+
+ align:start position:0%
+have to send four more messages you can
+optimize it to three because right so if
+
+ align:start position:0%
+optimize it to three because right so if
+ 
+
+ align:start position:0%
+optimize it to three because right so if
+you've Alice and Bob the first thing
+
+ align:start position:0%
+you've Alice and Bob the first thing
+ 
+
+ align:start position:0%
+you've Alice and Bob the first thing
+they do is Alice sends a signature so
+
+ align:start position:0%
+they do is Alice sends a signature so
+ 
+
+ align:start position:0%
+they do is Alice sends a signature so
+let's say they're you know they're at
+
+ align:start position:0%
+let's say they're you know they're at
+ 
+
+ align:start position:0%
+let's say they're you know they're at
+state five okay so she says here's a
+
+ align:start position:0%
+state five okay so she says here's a
+ 
+
+ align:start position:0%
+state five okay so she says here's a
+signature for state six and Bob says
+
+ align:start position:0%
+signature for state six and Bob says
+ 
+
+ align:start position:0%
+signature for state six and Bob says
+okay I'll give you a signature for state
+
+ align:start position:0%
+okay I'll give you a signature for state
+ 
+
+ align:start position:0%
+okay I'll give you a signature for state
+six so now they both build state six
+
+ align:start position:0%
+six so now they both build state six
+ 
+
+ align:start position:0%
+six so now they both build state six
+alright they've let's say you know go
+
+ align:start position:0%
+alright they've let's say you know go
+ 
+
+ align:start position:0%
+alright they've let's say you know go
+from five to six and then Alice can say
+
+ align:start position:0%
+from five to six and then Alice can say
+ 
+
+ align:start position:0%
+from five to six and then Alice can say
+okay I'll give you your you know
+
+ align:start position:0%
+okay I'll give you your you know
+ 
+
+ align:start position:0%
+okay I'll give you your you know
+revocation key for state five and then
+
+ align:start position:0%
+revocation key for state five and then
+ 
+
+ align:start position:0%
+revocation key for state five and then
+Bob can say okay I'll give you a
+
+ align:start position:0%
+Bob can say okay I'll give you a
+ 
+
+ align:start position:0%
+Bob can say okay I'll give you a
+revocation keep for Steve five and then
+
+ align:start position:0%
+revocation keep for Steve five and then
+ 
+
+ align:start position:0%
+revocation keep for Steve five and then
+they're done right then they've you know
+
+ align:start position:0%
+they're done right then they've you know
+ 
+
+ align:start position:0%
+they're done right then they've you know
+they've created the new state and
+
+ align:start position:0%
+they've created the new state and
+ 
+
+ align:start position:0%
+they've created the new state and
+revoked the old state you can't squish
+
+ align:start position:0%
+revoked the old state you can't squish
+ 
+
+ align:start position:0%
+revoked the old state you can't squish
+really if Alice cannot put Rev five here
+
+ align:start position:0%
+really if Alice cannot put Rev five here
+ 
+
+ align:start position:0%
+really if Alice cannot put Rev five here
+in the same message do you know why it
+
+ align:start position:0%
+in the same message do you know why it
+ 
+
+ align:start position:0%
+in the same message do you know why it
+why not so yeah well yeah Rev key just
+
+ align:start position:0%
+why not so yeah well yeah Rev key just
+ 
+
+ align:start position:0%
+why not so yeah well yeah Rev key just
+yeah abbreviate to Rev so why would this
+
+ align:start position:0%
+yeah abbreviate to Rev so why would this
+ 
+
+ align:start position:0%
+yeah abbreviate to Rev so why would this
+be bad if Alice says look here's state
+
+ align:start position:0%
+be bad if Alice says look here's state
+ 
+
+ align:start position:0%
+be bad if Alice says look here's state
+six and I'm revoking my claim on state
+
+ align:start position:0%
+six and I'm revoking my claim on state
+ 
+
+ align:start position:0%
+six and I'm revoking my claim on state
+five what what goes wrong if you do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no quiet Bob Bob broadcasting states
+
+ align:start position:0%
+no quiet Bob Bob broadcasting states
+ 
+
+ align:start position:0%
+no quiet Bob Bob broadcasting states
+sticks is okay in that case so you do
+
+ align:start position:0%
+sticks is okay in that case so you do
+ 
+
+ align:start position:0%
+sticks is okay in that case so you do
+that no because he doesn't he doesn't
+
+ align:start position:0%
+that no because he doesn't he doesn't
+ 
+
+ align:start position:0%
+that no because he doesn't he doesn't
+because because because state five is
+
+ align:start position:0%
+because because because state five is
+ 
+
+ align:start position:0%
+because because because state five is
+not broadcast right only Alice can sign
+
+ align:start position:0%
+not broadcast right only Alice can sign
+ 
+
+ align:start position:0%
+not broadcast right only Alice can sign
+in broadcast state five so the problem
+
+ align:start position:0%
+in broadcast state five so the problem
+ 
+
+ align:start position:0%
+in broadcast state five so the problem
+with this is if you do this Bob's fine
+
+ align:start position:0%
+with this is if you do this Bob's fine
+ 
+
+ align:start position:0%
+with this is if you do this Bob's fine
+alice is stuck right because Alice does
+
+ align:start position:0%
+alice is stuck right because Alice does
+ 
+
+ align:start position:0%
+alice is stuck right because Alice does
+not have state six on her drive right
+
+ align:start position:0%
+not have state six on her drive right
+ 
+
+ align:start position:0%
+not have state six on her drive right
+all Alice has on her drive is state five
+
+ align:start position:0%
+all Alice has on her drive is state five
+ 
+
+ align:start position:0%
+all Alice has on her drive is state five
+and she's just revealed the key for
+
+ align:start position:0%
+and she's just revealed the key for
+ 
+
+ align:start position:0%
+and she's just revealed the key for
+state five to revoke it so basically
+
+ align:start position:0%
+state five to revoke it so basically
+ 
+
+ align:start position:0%
+state five to revoke it so basically
+like alice has nothing at this point and
+
+ align:start position:0%
+like alice has nothing at this point and
+ 
+
+ align:start position:0%
+like alice has nothing at this point and
+Bob can just wait analysis stuck and
+
+ align:start position:0%
+Bob can just wait analysis stuck and
+ 
+
+ align:start position:0%
+Bob can just wait analysis stuck and
+then that's that's a really good
+
+ align:start position:0%
+then that's that's a really good
+ 
+
+ align:start position:0%
+then that's that's a really good
+position for Bob to be in because Bob is
+
+ align:start position:0%
+position for Bob to be in because Bob is
+ 
+
+ align:start position:0%
+position for Bob to be in because Bob is
+like hey I can close the channel I can
+
+ align:start position:0%
+like hey I can close the channel I can
+ 
+
+ align:start position:0%
+like hey I can close the channel I can
+close the channel at state five or state
+
+ align:start position:0%
+close the channel at state five or state
+ 
+
+ align:start position:0%
+close the channel at state five or state
+six probably he wants state six if
+
+ align:start position:0%
+six probably he wants state six if
+ 
+
+ align:start position:0%
+six probably he wants state six if
+usually you know you're sending money
+
+ align:start position:0%
+usually you know you're sending money
+ 
+
+ align:start position:0%
+usually you know you're sending money
+but I can close this channel and you can
+
+ align:start position:0%
+but I can close this channel and you can
+ 
+
+ align:start position:0%
+but I can close this channel and you can
+so give me some money you know you can
+
+ align:start position:0%
+so give me some money you know you can
+ 
+
+ align:start position:0%
+so give me some money you know you can
+close you know close the channel that
+
+ align:start position:0%
+close you know close the channel that
+ 
+
+ align:start position:0%
+close you know close the channel that
+kind of that's the attack right right
+
+ align:start position:0%
+kind of that's the attack right right
+ 
+
+ align:start position:0%
+kind of that's the attack right right
+and and you want it on your side right
+
+ align:start position:0%
+and and you want it on your side right
+ 
+
+ align:start position:0%
+and and you want it on your side right
+so this is creating a new state for Bob
+
+ align:start position:0%
+so this is creating a new state for Bob
+ 
+
+ align:start position:0%
+so this is creating a new state for Bob
+but it's revoking the old state for
+
+ align:start position:0%
+but it's revoking the old state for
+ 
+
+ align:start position:0%
+but it's revoking the old state for
+Alice if you want you do this so that's
+
+ align:start position:0%
+Alice if you want you do this so that's
+ 
+
+ align:start position:0%
+Alice if you want you do this so that's
+dangerous for you know Alice doesn't
+
+ align:start position:0%
+dangerous for you know Alice doesn't
+ 
+
+ align:start position:0%
+dangerous for you know Alice doesn't
+want to do that so the simplest way is
+
+ align:start position:0%
+want to do that so the simplest way is
+ 
+
+ align:start position:0%
+want to do that so the simplest way is
+okay create the new state by signing six
+
+ align:start position:0%
+okay create the new state by signing six
+ 
+
+ align:start position:0%
+okay create the new state by signing six
+revoking five revoking five you can
+
+ align:start position:0%
+revoking five revoking five you can
+ 
+
+ align:start position:0%
+revoking five revoking five you can
+optimize this though right can you guys
+
+ align:start position:0%
+optimize this though right can you guys
+ 
+
+ align:start position:0%
+optimize this though right can you guys
+see the reduces the three messages yeah
+
+ align:start position:0%
+see the reduces the three messages yeah
+ 
+
+ align:start position:0%
+see the reduces the three messages yeah
+he can send SIG's SIG's SIG's we have
+
+ align:start position:0%
+he can send SIG's SIG's SIG's we have
+ 
+
+ align:start position:0%
+he can send SIG's SIG's SIG's we have
+five at the same time so you get down
+
+ align:start position:0%
+five at the same time so you get down
+ 
+
+ align:start position:0%
+five at the same time so you get down
+into three messages so that's cool it's
+
+ align:start position:0%
+into three messages so that's cool it's
+ 
+
+ align:start position:0%
+into three messages so that's cool it's
+you know basically here's state six
+
+ align:start position:0%
+you know basically here's state six
+ 
+
+ align:start position:0%
+you know basically here's state six
+okay here's state six and I revoke my
+
+ align:start position:0%
+okay here's state six and I revoke my
+ 
+
+ align:start position:0%
+okay here's state six and I revoke my
+claim on say five okay overflow point
+
+ align:start position:0%
+claim on say five okay overflow point
+ 
+
+ align:start position:0%
+claim on say five okay overflow point
+claim let's say five then they both
+
+ align:start position:0%
+claim let's say five then they both
+ 
+
+ align:start position:0%
+claim let's say five then they both
+update their you know once this happens
+
+ align:start position:0%
+update their you know once this happens
+ 
+
+ align:start position:0%
+update their you know once this happens
+the UI is finished
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you end up it ends up being faster if
+
+ align:start position:0%
+you end up it ends up being faster if
+ 
+
+ align:start position:0%
+you end up it ends up being faster if
+you pre generate like one key ahead
+
+ align:start position:0%
+you pre generate like one key ahead
+ 
+
+ align:start position:0%
+you pre generate like one key ahead
+where you say like hey here's the next
+
+ align:start position:0%
+where you say like hey here's the next
+ 
+
+ align:start position:0%
+where you say like hey here's the next
+public key I'm gonna use all so that
+
+ align:start position:0%
+public key I'm gonna use all so that
+ 
+
+ align:start position:0%
+public key I'm gonna use all so that
+it'll do so that I can write cuz Alice
+
+ align:start position:0%
+it'll do so that I can write cuz Alice
+ 
+
+ align:start position:0%
+it'll do so that I can write cuz Alice
+one she's building state six she needs
+
+ align:start position:0%
+one she's building state six she needs
+ 
+
+ align:start position:0%
+one she's building state six she needs
+to know Bob's a revocation key in the
+
+ align:start position:0%
+to know Bob's a revocation key in the
+ 
+
+ align:start position:0%
+to know Bob's a revocation key in the
+state six so you pre share like one or
+
+ align:start position:0%
+state six so you pre share like one or
+ 
+
+ align:start position:0%
+state six so you pre share like one or
+two steps ahead so that you don't have
+
+ align:start position:0%
+two steps ahead so that you don't have
+ 
+
+ align:start position:0%
+two steps ahead so that you don't have
+to say hey can you get me into the next
+
+ align:start position:0%
+to say hey can you get me into the next
+ 
+
+ align:start position:0%
+to say hey can you get me into the next
+key okay you know otherwise you'd have
+
+ align:start position:0%
+key okay you know otherwise you'd have
+ 
+
+ align:start position:0%
+key okay you know otherwise you'd have
+this message where it's like request
+
+ align:start position:0%
+this message where it's like request
+ 
+
+ align:start position:0%
+this message where it's like request
+state six key send it send the signature
+
+ align:start position:0%
+state six key send it send the signature
+ 
+
+ align:start position:0%
+state six key send it send the signature
+back so there's all there's like more
+
+ align:start position:0%
+back so there's all there's like more
+ 
+
+ align:start position:0%
+back so there's all there's like more
+data in these messages but that like
+
+ align:start position:0%
+data in these messages but that like
+ 
+
+ align:start position:0%
+data in these messages but that like
+optimize yeah yeah so so you also put
+
+ align:start position:0%
+optimize yeah yeah so so you also put
+ 
+
+ align:start position:0%
+optimize yeah yeah so so you also put
+some public keys in here in this this is
+
+ align:start position:0%
+some public keys in here in this this is
+ 
+
+ align:start position:0%
+some public keys in here in this this is
+the private key yes in here right you're
+
+ align:start position:0%
+the private key yes in here right you're
+ 
+
+ align:start position:0%
+the private key yes in here right you're
+sending the signature but you can also
+
+ align:start position:0%
+sending the signature but you can also
+ 
+
+ align:start position:0%
+sending the signature but you can also
+send here's how much I'm giving you
+
+ align:start position:0%
+send here's how much I'm giving you
+ 
+
+ align:start position:0%
+send here's how much I'm giving you
+here's what the times and stuff are most
+
+ align:start position:0%
+here's what the times and stuff are most
+ 
+
+ align:start position:0%
+here's what the times and stuff are most
+of it can be computed because the
+
+ align:start position:0%
+of it can be computed because the
+ 
+
+ align:start position:0%
+of it can be computed because the
+transactions don't change that much
+
+ align:start position:0%
+transactions don't change that much
+ 
+
+ align:start position:0%
+transactions don't change that much
+right the scripts are the same everyone
+
+ align:start position:0%
+right the scripts are the same everyone
+ 
+
+ align:start position:0%
+right the scripts are the same everyone
+knows what this is gonna look like so
+
+ align:start position:0%
+knows what this is gonna look like so
+ 
+
+ align:start position:0%
+knows what this is gonna look like so
+you don't have to actually send too much
+
+ align:start position:0%
+you don't have to actually send too much
+ 
+
+ align:start position:0%
+you don't have to actually send too much
+data another optimization didn't put in
+
+ align:start position:0%
+data another optimization didn't put in
+ 
+
+ align:start position:0%
+data another optimization didn't put in
+is you're gonna potentially have to
+
+ align:start position:0%
+is you're gonna potentially have to
+ 
+
+ align:start position:0%
+is you're gonna potentially have to
+retain all of these are private keys so
+
+ align:start position:0%
+retain all of these are private keys so
+ 
+
+ align:start position:0%
+retain all of these are private keys so
+if you make a million states and you
+
+ align:start position:0%
+if you make a million states and you
+ 
+
+ align:start position:0%
+if you make a million states and you
+know you and 900 you know whatever are
+
+ align:start position:0%
+know you and 900 you know whatever are
+ 
+
+ align:start position:0%
+know you and 900 you know whatever are
+revoked Bob has to keep track of all
+
+ align:start position:0%
+revoked Bob has to keep track of all
+ 
+
+ align:start position:0%
+revoked Bob has to keep track of all
+those million old Alice private keys
+
+ align:start position:0%
+those million old Alice private keys
+ 
+
+ align:start position:0%
+those million old Alice private keys
+analysis to keep track of all those old
+
+ align:start position:0%
+analysis to keep track of all those old
+ 
+
+ align:start position:0%
+analysis to keep track of all those old
+Bob private keys that's kind of annoying
+
+ align:start position:0%
+Bob private keys that's kind of annoying
+ 
+
+ align:start position:0%
+Bob private keys that's kind of annoying
+not the end of the world but it's like
+
+ align:start position:0%
+not the end of the world but it's like
+ 
+
+ align:start position:0%
+not the end of the world but it's like
+32 bytes each can be a couple hundred
+
+ align:start position:0%
+32 bytes each can be a couple hundred
+ 
+
+ align:start position:0%
+32 bytes each can be a couple hundred
+megabytes if you use this channel a lot
+
+ align:start position:0%
+megabytes if you use this channel a lot
+ 
+
+ align:start position:0%
+megabytes if you use this channel a lot
+so you can make this so I thought I came
+
+ align:start position:0%
+so you can make this so I thought I came
+ 
+
+ align:start position:0%
+so you can make this so I thought I came
+up with it but at the same time when I
+
+ align:start position:0%
+up with it but at the same time when I
+ 
+
+ align:start position:0%
+up with it but at the same time when I
+was coming up with it I was like no I'm
+
+ align:start position:0%
+was coming up with it I was like no I'm
+ 
+
+ align:start position:0%
+was coming up with it I was like no I'm
+I'm pretty sure this isn't some paper
+
+ align:start position:0%
+I'm pretty sure this isn't some paper
+ 
+
+ align:start position:0%
+I'm pretty sure this isn't some paper
+somewhere and I can't find it and then
+
+ align:start position:0%
+somewhere and I can't find it and then
+ 
+
+ align:start position:0%
+somewhere and I can't find it and then
+talking to people here apparently like
+
+ align:start position:0%
+talking to people here apparently like
+ 
+
+ align:start position:0%
+talking to people here apparently like
+it's a gold wasö it likes a professor
+
+ align:start position:0%
+it's a gold wasö it likes a professor
+ 
+
+ align:start position:0%
+it's a gold wasö it likes a professor
+here came up with it in like the 80s I
+
+ align:start position:0%
+here came up with it in like the 80s I
+ 
+
+ align:start position:0%
+here came up with it in like the 80s I
+called it L chrome because spelled
+
+ align:start position:0%
+called it L chrome because spelled
+ 
+
+ align:start position:0%
+called it L chrome because spelled
+backwards it's Merkel right
+
+ align:start position:0%
+backwards it's Merkel right
+ 
+
+ align:start position:0%
+backwards it's Merkel right
+so you have a binary tree and you say
+
+ align:start position:0%
+so you have a binary tree and you say
+ 
+
+ align:start position:0%
+so you have a binary tree and you say
+like ok 0 1 2 3 4 5 6 is the root for
+
+ align:start position:0%
+like ok 0 1 2 3 4 5 6 is the root for
+ 
+
+ align:start position:0%
+like ok 0 1 2 3 4 5 6 is the root for
+example and when you want to when you
+
+ align:start position:0%
+example and when you want to when you
+ 
+
+ align:start position:0%
+example and when you want to when you
+want to descend to the left you take the
+
+ align:start position:0%
+want to descend to the left you take the
+ 
+
+ align:start position:0%
+want to descend to the left you take the
+value here append and L or like maybe
+
+ align:start position:0%
+value here append and L or like maybe
+ 
+
+ align:start position:0%
+value here append and L or like maybe
+you know 0 is left and one is right or
+
+ align:start position:0%
+you know 0 is left and one is right or
+ 
+
+ align:start position:0%
+you know 0 is left and one is right or
+something or L or R and you hash it so
+
+ align:start position:0%
+something or L or R and you hash it so
+ 
+
+ align:start position:0%
+something or L or R and you hash it so
+you say ok I'm taking this value
+
+ align:start position:0%
+you say ok I'm taking this value
+ 
+
+ align:start position:0%
+you say ok I'm taking this value
+sticking something on hashing to get
+
+ align:start position:0%
+sticking something on hashing to get
+ 
+
+ align:start position:0%
+sticking something on hashing to get
+down here and similarly you know through
+
+ align:start position:0%
+down here and similarly you know through
+ 
+
+ align:start position:0%
+down here and similarly you know through
+here you make a big tree the idea there
+
+ align:start position:0%
+here you make a big tree the idea there
+ 
+
+ align:start position:0%
+here you make a big tree the idea there
+is you can reveal things sequentially
+
+ align:start position:0%
+is you can reveal things sequentially
+ 
+
+ align:start position:0%
+is you can reveal things sequentially
+and say ok I reveal 0 fine I'll store it
+
+ align:start position:0%
+and say ok I reveal 0 fine I'll store it
+ 
+
+ align:start position:0%
+and say ok I reveal 0 fine I'll store it
+I'll reveal one store it I reveal two
+
+ align:start position:0%
+I'll reveal one store it I reveal two
+ 
+
+ align:start position:0%
+I'll reveal one store it I reveal two
+now you can delete 0 1 because you know
+
+ align:start position:0%
+now you can delete 0 1 because you know
+ 
+
+ align:start position:0%
+now you can delete 0 1 because you know
+the parent and you can compute 0 and 1
+
+ align:start position:0%
+the parent and you can compute 0 and 1
+ 
+
+ align:start position:0%
+the parent and you can compute 0 and 1
+from knowing to right so I give you 1 0
+
+ align:start position:0%
+from knowing to right so I give you 1 0
+ 
+
+ align:start position:0%
+from knowing to right so I give you 1 0
+give you 1 give you 2 you believe 0 1
+
+ align:start position:0%
+give you 1 give you 2 you believe 0 1
+ 
+
+ align:start position:0%
+give you 1 give you 2 you believe 0 1
+then I give you 3 4 5 you delete 3 & 4
+
+ align:start position:0%
+then I give you 3 4 5 you delete 3 & 4
+ 
+
+ align:start position:0%
+then I give you 3 4 5 you delete 3 & 4
+then I want to give you 6 you delete 2 &
+
+ align:start position:0%
+then I want to give you 6 you delete 2 &
+ 
+
+ align:start position:0%
+then I want to give you 6 you delete 2 &
+5 so that way you only have to store or
+
+ align:start position:0%
+5 so that way you only have to store or
+ 
+
+ align:start position:0%
+5 so that way you only have to store or
+log in secrets right but when you know
+
+ align:start position:0%
+log in secrets right but when you know
+ 
+
+ align:start position:0%
+log in secrets right but when you know
+you can't give in 0 & 1 you can't
+
+ align:start position:0%
+you can't give in 0 & 1 you can't
+ 
+
+ align:start position:0%
+you can't give in 0 & 1 you can't
+compute 2 and given 3 you know two three
+
+ align:start position:0%
+compute 2 and given 3 you know two three
+ 
+
+ align:start position:0%
+compute 2 and given 3 you know two three
+and four you can't compute 5 or 6 but
+
+ align:start position:0%
+and four you can't compute 5 or 6 but
+ 
+
+ align:start position:0%
+and four you can't compute 5 or 6 but
+once you've got them you can compute all
+
+ align:start position:0%
+once you've got them you can compute all
+ 
+
+ align:start position:0%
+once you've got them you can compute all
+the old ones so if we do that for the
+
+ align:start position:0%
+the old ones so if we do that for the
+ 
+
+ align:start position:0%
+the old ones so if we do that for the
+the secret Keys that like reduces
+
+ align:start position:0%
+the secret Keys that like reduces
+ 
+
+ align:start position:0%
+the secret Keys that like reduces
+storage a lot so that's kind of a nice
+
+ align:start position:0%
+storage a lot so that's kind of a nice
+ 
+
+ align:start position:0%
+storage a lot so that's kind of a nice
+optimization it's pretty quick and then
+
+ align:start position:0%
+optimization it's pretty quick and then
+ 
+
+ align:start position:0%
+optimization it's pretty quick and then
+so then you basically your your total
+
+ align:start position:0%
+so then you basically your your total
+ 
+
+ align:start position:0%
+so then you basically your your total
+data that you're storing for these
+
+ align:start position:0%
+data that you're storing for these
+ 
+
+ align:start position:0%
+data that you're storing for these
+channels never gets more than like a
+
+ align:start position:0%
+channels never gets more than like a
+ 
+
+ align:start position:0%
+channels never gets more than like a
+kilobyte or two so that's pretty useful
+
+ align:start position:0%
+kilobyte or two so that's pretty useful
+ 
+
+ align:start position:0%
+kilobyte or two so that's pretty useful
+ok other questions on this this alone
+
+ align:start position:0%
+ok other questions on this this alone
+ 
+
+ align:start position:0%
+ok other questions on this this alone
+actually is really complicated like yeah
+
+ align:start position:0%
+actually is really complicated like yeah
+ 
+
+ align:start position:0%
+actually is really complicated like yeah
+so there is a there is a sort of like
+
+ align:start position:0%
+so there is a there is a sort of like
+ 
+
+ align:start position:0%
+so there is a there is a sort of like
+superposition time here right we're at
+
+ align:start position:0%
+superposition time here right we're at
+ 
+
+ align:start position:0%
+superposition time here right we're at
+time so let's say this is x 0 this is
+
+ align:start position:0%
+time so let's say this is x 0 this is
+ 
+
+ align:start position:0%
+time so let's say this is x 0 this is
+time 1 this is time to this time 3 so at
+
+ align:start position:0%
+time 1 this is time to this time 3 so at
+ 
+
+ align:start position:0%
+time 1 this is time to this time 3 so at
+time 1 Bob's got a got two states he can
+
+ align:start position:0%
+time 1 Bob's got a got two states he can
+ 
+
+ align:start position:0%
+time 1 Bob's got a got two states he can
+broadcast right Bob's like I can do six
+
+ align:start position:0%
+broadcast right Bob's like I can do six
+ 
+
+ align:start position:0%
+broadcast right Bob's like I can do six
+or five
+
+ align:start position:0%
+or five
+ 
+
+ align:start position:0%
+or five
+Alice can only broadcast five but Alice
+
+ align:start position:0%
+Alice can only broadcast five but Alice
+ 
+
+ align:start position:0%
+Alice can only broadcast five but Alice
+knows that Bob can broadcast six right
+
+ align:start position:0%
+knows that Bob can broadcast six right
+ 
+
+ align:start position:0%
+knows that Bob can broadcast six right
+so Alice is also like well I'm not sure
+
+ align:start position:0%
+so Alice is also like well I'm not sure
+ 
+
+ align:start position:0%
+so Alice is also like well I'm not sure
+which it is if it's if I if you know
+
+ align:start position:0%
+which it is if it's if I if you know
+ 
+
+ align:start position:0%
+which it is if it's if I if you know
+from Alice's perspective if I close I'm
+
+ align:start position:0%
+from Alice's perspective if I close I'm
+ 
+
+ align:start position:0%
+from Alice's perspective if I close I'm
+gonna stay five if Bob closes he's at
+
+ align:start position:0%
+gonna stay five if Bob closes he's at
+ 
+
+ align:start position:0%
+gonna stay five if Bob closes he's at
+state six and then at state two Alice
+
+ align:start position:0%
+state six and then at state two Alice
+ 
+
+ align:start position:0%
+state six and then at state two Alice
+can only broadcast state six but Bob can
+
+ align:start position:0%
+can only broadcast state six but Bob can
+ 
+
+ align:start position:0%
+can only broadcast state six but Bob can
+broadcast sorry Alice can broadcast
+
+ align:start position:0%
+broadcast sorry Alice can broadcast
+ 
+
+ align:start position:0%
+broadcast sorry Alice can broadcast
+either but Bob can only broadcast one so
+
+ align:start position:0%
+either but Bob can only broadcast one so
+ 
+
+ align:start position:0%
+either but Bob can only broadcast one so
+yet during this process there's sort of
+
+ align:start position:0%
+yet during this process there's sort of
+ 
+
+ align:start position:0%
+yet during this process there's sort of
+it's not clear which state it is and you
+
+ align:start position:0%
+it's not clear which state it is and you
+ 
+
+ align:start position:0%
+it's not clear which state it is and you
+know if something happens like you know
+
+ align:start position:0%
+know if something happens like you know
+ 
+
+ align:start position:0%
+know if something happens like you know
+Bob goes offline you know Alice sends
+
+ align:start position:0%
+Bob goes offline you know Alice sends
+ 
+
+ align:start position:0%
+Bob goes offline you know Alice sends
+SIG's signature for six and Bob goes
+
+ align:start position:0%
+SIG's signature for six and Bob goes
+ 
+
+ align:start position:0%
+SIG's signature for six and Bob goes
+offline then it's like okay I never got
+
+ align:start position:0%
+offline then it's like okay I never got
+ 
+
+ align:start position:0%
+offline then it's like okay I never got
+a response I'll just try to close at
+
+ align:start position:0%
+a response I'll just try to close at
+ 
+
+ align:start position:0%
+a response I'll just try to close at
+state five I guess right and then I
+
+ align:start position:0%
+state five I guess right and then I
+ 
+
+ align:start position:0%
+state five I guess right and then I
+guess that payment never went through
+
+ align:start position:0%
+guess that payment never went through
+ 
+
+ align:start position:0%
+guess that payment never went through
+but then Bob could say no I got it and
+
+ align:start position:0%
+but then Bob could say no I got it and
+ 
+
+ align:start position:0%
+but then Bob could say no I got it and
+broadcast it like so that you know
+
+ align:start position:0%
+broadcast it like so that you know
+ 
+
+ align:start position:0%
+broadcast it like so that you know
+things can get weird where you're not
+
+ align:start position:0%
+things can get weird where you're not
+ 
+
+ align:start position:0%
+things can get weird where you're not
+really sure what happens here so like
+
+ align:start position:0%
+really sure what happens here so like
+ 
+
+ align:start position:0%
+really sure what happens here so like
+it's more a UI issue where in the UI
+
+ align:start position:0%
+it's more a UI issue where in the UI
+ 
+
+ align:start position:0%
+it's more a UI issue where in the UI
+like only show things after you get to
+
+ align:start position:0%
+like only show things after you get to
+ 
+
+ align:start position:0%
+like only show things after you get to
+the end hopefully in most cases this
+
+ align:start position:0%
+the end hopefully in most cases this
+ 
+
+ align:start position:0%
+the end hopefully in most cases this
+whole process takes a fraction of a
+
+ align:start position:0%
+whole process takes a fraction of a
+ 
+
+ align:start position:0%
+whole process takes a fraction of a
+second right because you're just sending
+
+ align:start position:0%
+second right because you're just sending
+ 
+
+ align:start position:0%
+second right because you're just sending
+some messages to each other so that's
+
+ align:start position:0%
+some messages to each other so that's
+ 
+
+ align:start position:0%
+some messages to each other so that's
+the nice part that's sort of the
+
+ align:start position:0%
+the nice part that's sort of the
+ 
+
+ align:start position:0%
+the nice part that's sort of the
+Lightning II thing is fast
+
+ align:start position:0%
+Lightning II thing is fast
+ 
+
+ align:start position:0%
+Lightning II thing is fast
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah right so they they're sending
+
+ align:start position:0%
+Yeah right so they they're sending
+ 
+
+ align:start position:0%
+Yeah right so they they're sending
+messages to each other they can't they
+
+ align:start position:0%
+messages to each other they can't they
+ 
+
+ align:start position:0%
+messages to each other they can't they
+can't really pre-compute these things
+
+ align:start position:0%
+can't really pre-compute these things
+ 
+
+ align:start position:0%
+can't really pre-compute these things
+because they don't know how much money
+
+ align:start position:0%
+because they don't know how much money
+ 
+
+ align:start position:0%
+because they don't know how much money
+is getting sent back and forth right so
+
+ align:start position:0%
+is getting sent back and forth right so
+ 
+
+ align:start position:0%
+is getting sent back and forth right so
+so when you're signing state six you're
+
+ align:start position:0%
+so when you're signing state six you're
+ 
+
+ align:start position:0%
+so when you're signing state six you're
+also signing the the value the output
+
+ align:start position:0%
+also signing the the value the output
+ 
+
+ align:start position:0%
+also signing the the value the output
+values and when Bob receives state six
+
+ align:start position:0%
+values and when Bob receives state six
+ 
+
+ align:start position:0%
+values and when Bob receives state six
+and signs his version of state six he
+
+ align:start position:0%
+and signs his version of state six he
+ 
+
+ align:start position:0%
+and signs his version of state six he
+also is like you know I don't know how
+
+ align:start position:0%
+also is like you know I don't know how
+ 
+
+ align:start position:0%
+also is like you know I don't know how
+much money I'm getting yet so I need to
+
+ align:start position:0%
+much money I'm getting yet so I need to
+ 
+
+ align:start position:0%
+much money I'm getting yet so I need to
+sign off on that
+
+ align:start position:0%
+sign off on that
+ 
+
+ align:start position:0%
+sign off on that
+so yeah both parties need to be online
+
+ align:start position:0%
+so yeah both parties need to be online
+ 
+
+ align:start position:0%
+so yeah both parties need to be online
+to receive which is different than
+
+ align:start position:0%
+to receive which is different than
+ 
+
+ align:start position:0%
+to receive which is different than
+normal in Bitcoin that's the same as
+
+ align:start position:0%
+normal in Bitcoin that's the same as
+ 
+
+ align:start position:0%
+normal in Bitcoin that's the same as
+that's the same as the unidirectional
+
+ align:start position:0%
+that's the same as the unidirectional
+ 
+
+ align:start position:0%
+that's the same as the unidirectional
+payment channels in the unidirectional
+
+ align:start position:0%
+payment channels in the unidirectional
+ 
+
+ align:start position:0%
+payment channels in the unidirectional
+one will were Bob the receiver he
+
+ align:start position:0%
+one will were Bob the receiver he
+ 
+
+ align:start position:0%
+one will were Bob the receiver he
+doesn't have to sign but he still has to
+
+ align:start position:0%
+doesn't have to sign but he still has to
+ 
+
+ align:start position:0%
+doesn't have to sign but he still has to
+be online because the the transaction
+
+ align:start position:0%
+be online because the the transaction
+ 
+
+ align:start position:0%
+be online because the the transaction
+just goes directly to him it doesn't go
+
+ align:start position:0%
+just goes directly to him it doesn't go
+ 
+
+ align:start position:0%
+just goes directly to him it doesn't go
+on to the blockchain right none of these
+
+ align:start position:0%
+on to the blockchain right none of these
+ 
+
+ align:start position:0%
+on to the blockchain right none of these
+are publicly known okay yes well what if
+
+ align:start position:0%
+are publicly known okay yes well what if
+ 
+
+ align:start position:0%
+are publicly known okay yes well what if
+what if you know this was state one
+
+ align:start position:0%
+what if you know this was state one
+ 
+
+ align:start position:0%
+what if you know this was state one
+right where Alice had one and bob had
+
+ align:start position:0%
+right where Alice had one and bob had
+ 
+
+ align:start position:0%
+right where Alice had one and bob had
+nine and then state you keep going and
+
+ align:start position:0%
+nine and then state you keep going and
+ 
+
+ align:start position:0%
+nine and then state you keep going and
+Bob keep in general the general trend is
+
+ align:start position:0%
+Bob keep in general the general trend is
+ 
+
+ align:start position:0%
+Bob keep in general the general trend is
+Bob's losing money right Bob's okay you
+
+ align:start position:0%
+Bob's losing money right Bob's okay you
+ 
+
+ align:start position:0%
+Bob's losing money right Bob's okay you
+know you go back and forth but at the
+
+ align:start position:0%
+know you go back and forth but at the
+ 
+
+ align:start position:0%
+know you go back and forth but at the
+end bob has one Bob needs to worry that
+
+ align:start position:0%
+end bob has one Bob needs to worry that
+ 
+
+ align:start position:0%
+end bob has one Bob needs to worry that
+Alice holds on to state one and then
+
+ align:start position:0%
+Alice holds on to state one and then
+ 
+
+ align:start position:0%
+Alice holds on to state one and then
+months later broadcasts it while Bob's
+
+ align:start position:0%
+months later broadcasts it while Bob's
+ 
+
+ align:start position:0%
+months later broadcasts it while Bob's
+not watching and then there's no right
+
+ align:start position:0%
+not watching and then there's no right
+ 
+
+ align:start position:0%
+not watching and then there's no right
+way no opposite Alice has to worry about
+
+ align:start position:0%
+way no opposite Alice has to worry about
+ 
+
+ align:start position:0%
+way no opposite Alice has to worry about
+Bob broadcasting state one in the future
+
+ align:start position:0%
+Bob broadcasting state one in the future
+ 
+
+ align:start position:0%
+Bob broadcasting state one in the future
+right but so you still need to keep the
+
+ align:start position:0%
+right but so you still need to keep the
+ 
+
+ align:start position:0%
+right but so you still need to keep the
+secret though it's revoked but that
+
+ align:start position:0%
+secret though it's revoked but that
+ 
+
+ align:start position:0%
+secret though it's revoked but that
+reveil the whole process of revocation
+
+ align:start position:0%
+reveil the whole process of revocation
+ 
+
+ align:start position:0%
+reveil the whole process of revocation
+is Bob gives a key to Alice
+
+ align:start position:0%
+is Bob gives a key to Alice
+ 
+
+ align:start position:0%
+is Bob gives a key to Alice
+so if Bob forgets that key then sorry if
+
+ align:start position:0%
+so if Bob forgets that key then sorry if
+ 
+
+ align:start position:0%
+so if Bob forgets that key then sorry if
+Alice forgets this key Bob can broadcast
+
+ align:start position:0%
+Alice forgets this key Bob can broadcast
+ 
+
+ align:start position:0%
+Alice forgets this key Bob can broadcast
+it and then Alice can't grab it yeah
+
+ align:start position:0%
+it and then Alice can't grab it yeah
+ 
+
+ align:start position:0%
+it and then Alice can't grab it yeah
+they can broadcast yeah they can anyone
+
+ align:start position:0%
+they can broadcast yeah they can anyone
+ 
+
+ align:start position:0%
+they can broadcast yeah they can anyone
+can brought so from the network's
+
+ align:start position:0%
+can brought so from the network's
+ 
+
+ align:start position:0%
+can brought so from the network's
+perspective these are all equally valid
+
+ align:start position:0%
+perspective these are all equally valid
+ 
+
+ align:start position:0%
+perspective these are all equally valid
+the network has no idea which came when
+
+ align:start position:0%
+the network has no idea which came when
+ 
+
+ align:start position:0%
+the network has no idea which came when
+and or anything like that the only way
+
+ align:start position:0%
+and or anything like that the only way
+ 
+
+ align:start position:0%
+and or anything like that the only way
+you enforce it is you know Bob broadcast
+
+ align:start position:0%
+you enforce it is you know Bob broadcast
+ 
+
+ align:start position:0%
+you enforce it is you know Bob broadcast
+this alice is like oh I'm taking this
+
+ align:start position:0%
+this alice is like oh I'm taking this
+ 
+
+ align:start position:0%
+this alice is like oh I'm taking this
+fund cuz I have the key so that's that's
+
+ align:start position:0%
+fund cuz I have the key so that's that's
+ 
+
+ align:start position:0%
+fund cuz I have the key so that's that's
+also a
+
+ align:start position:0%
+also a
+ 
+
+ align:start position:0%
+also a
+you know a pretty significant different
+
+ align:start position:0%
+you know a pretty significant different
+ 
+
+ align:start position:0%
+you know a pretty significant different
+security model it's a it's a security
+
+ align:start position:0%
+security model it's a it's a security
+ 
+
+ align:start position:0%
+security model it's a it's a security
+reduction right now you have to actively
+
+ align:start position:0%
+reduction right now you have to actively
+ 
+
+ align:start position:0%
+reduction right now you have to actively
+defend your channel because you if
+
+ align:start position:0%
+defend your channel because you if
+ 
+
+ align:start position:0%
+defend your channel because you if
+you're if you go offline I'm Alice I'm
+
+ align:start position:0%
+you're if you go offline I'm Alice I'm
+ 
+
+ align:start position:0%
+you're if you go offline I'm Alice I'm
+supposed to have nine coins I go on
+
+ align:start position:0%
+supposed to have nine coins I go on
+ 
+
+ align:start position:0%
+supposed to have nine coins I go on
+vacation I turn off my computer and Bob
+
+ align:start position:0%
+vacation I turn off my computer and Bob
+ 
+
+ align:start position:0%
+vacation I turn off my computer and Bob
+knows I've turned off my computer then
+
+ align:start position:0%
+knows I've turned off my computer then
+ 
+
+ align:start position:0%
+knows I've turned off my computer then
+I'll you know Bob can say Oh Alice is
+
+ align:start position:0%
+I'll you know Bob can say Oh Alice is
+ 
+
+ align:start position:0%
+I'll you know Bob can say Oh Alice is
+out like this this 100 block delay she's
+
+ align:start position:0%
+out like this this 100 block delay she's
+ 
+
+ align:start position:0%
+out like this this 100 block delay she's
+not gonna be online I'm just gonna
+
+ align:start position:0%
+not gonna be online I'm just gonna
+ 
+
+ align:start position:0%
+not gonna be online I'm just gonna
+broadcast this get the nine coins wait a
+
+ align:start position:0%
+broadcast this get the nine coins wait a
+ 
+
+ align:start position:0%
+broadcast this get the nine coins wait a
+hundred blocks and then you know sweep
+
+ align:start position:0%
+hundred blocks and then you know sweep
+ 
+
+ align:start position:0%
+hundred blocks and then you know sweep
+them as soon as I can
+
+ align:start position:0%
+them as soon as I can
+ 
+
+ align:start position:0%
+them as soon as I can
+and then Alice comes back plugs in and
+
+ align:start position:0%
+and then Alice comes back plugs in and
+ 
+
+ align:start position:0%
+and then Alice comes back plugs in and
+it's like oh you were wait no I
+
+ align:start position:0%
+it's like oh you were wait no I
+ 
+
+ align:start position:0%
+it's like oh you were wait no I
+oh it says I lost eight coins what
+
+ align:start position:0%
+oh it says I lost eight coins what
+ 
+
+ align:start position:0%
+oh it says I lost eight coins what
+because broad Bob defrauded so you have
+
+ align:start position:0%
+because broad Bob defrauded so you have
+ 
+
+ align:start position:0%
+because broad Bob defrauded so you have
+to be online I'm not I think I'm gonna
+
+ align:start position:0%
+to be online I'm not I think I'm gonna
+ 
+
+ align:start position:0%
+to be online I'm not I think I'm gonna
+get into it next time there's a way to
+
+ align:start position:0%
+get into it next time there's a way to
+ 
+
+ align:start position:0%
+get into it next time there's a way to
+outsource that so that you don't have to
+
+ align:start position:0%
+outsource that so that you don't have to
+ 
+
+ align:start position:0%
+outsource that so that you don't have to
+be watching you can have someone else
+
+ align:start position:0%
+be watching you can have someone else
+ 
+
+ align:start position:0%
+be watching you can have someone else
+watch for you and I'll probably talk
+
+ align:start position:0%
+watch for you and I'll probably talk
+ 
+
+ align:start position:0%
+watch for you and I'll probably talk
+about that next time but in the last 20
+
+ align:start position:0%
+about that next time but in the last 20
+ 
+
+ align:start position:0%
+about that next time but in the last 20
+minutes yeah so this is cool right this
+
+ align:start position:0%
+minutes yeah so this is cool right this
+ 
+
+ align:start position:0%
+minutes yeah so this is cool right this
+is light network channels to parties
+
+ align:start position:0%
+is light network channels to parties
+ 
+
+ align:start position:0%
+is light network channels to parties
+indefinite you still need to create a
+
+ align:start position:0%
+indefinite you still need to create a
+ 
+
+ align:start position:0%
+indefinite you still need to create a
+channel to pay people so you just do one
+
+ align:start position:0%
+channel to pay people so you just do one
+ 
+
+ align:start position:0%
+channel to pay people so you just do one
+on chain transaction to open the channel
+
+ align:start position:0%
+on chain transaction to open the channel
+ 
+
+ align:start position:0%
+on chain transaction to open the channel
+wanted to close the channel potentially
+
+ align:start position:0%
+wanted to close the channel potentially
+ 
+
+ align:start position:0%
+wanted to close the channel potentially
+two to close the channel but that's
+
+ align:start position:0%
+two to close the channel but that's
+ 
+
+ align:start position:0%
+two to close the channel but that's
+pretty rare right if you need to
+
+ align:start position:0%
+pretty rare right if you need to
+ 
+
+ align:start position:0%
+pretty rare right if you need to
+immediately grab it then you're time
+
+ align:start position:0%
+immediately grab it then you're time
+ 
+
+ align:start position:0%
+immediately grab it then you're time
+sensitive and you're gonna have to
+
+ align:start position:0%
+sensitive and you're gonna have to
+ 
+
+ align:start position:0%
+sensitive and you're gonna have to
+closing transactions if you closed
+
+ align:start position:0%
+closing transactions if you closed
+ 
+
+ align:start position:0%
+closing transactions if you closed
+normally like you close the current
+
+ align:start position:0%
+normally like you close the current
+ 
+
+ align:start position:0%
+normally like you close the current
+state you need to wait a hundred blocks
+
+ align:start position:0%
+state you need to wait a hundred blocks
+ 
+
+ align:start position:0%
+state you need to wait a hundred blocks
+for your money to be active but you
+
+ align:start position:0%
+for your money to be active but you
+ 
+
+ align:start position:0%
+for your money to be active but you
+don't have to spend it immediately after
+
+ align:start position:0%
+don't have to spend it immediately after
+ 
+
+ align:start position:0%
+don't have to spend it immediately after
+that you can just leave it because you
+
+ align:start position:0%
+that you can just leave it because you
+ 
+
+ align:start position:0%
+that you can just leave it because you
+know so so in this case let's say this
+
+ align:start position:0%
+know so so in this case let's say this
+ 
+
+ align:start position:0%
+know so so in this case let's say this
+is Bob's Held's transaction Bob
+
+ align:start position:0%
+is Bob's Held's transaction Bob
+ 
+
+ align:start position:0%
+is Bob's Held's transaction Bob
+broadcasts it Bob knows okay Alice gets
+
+ align:start position:0%
+broadcasts it Bob knows okay Alice gets
+ 
+
+ align:start position:0%
+broadcasts it Bob knows okay Alice gets
+her two coins I get my eight coins I
+
+ align:start position:0%
+her two coins I get my eight coins I
+ 
+
+ align:start position:0%
+her two coins I get my eight coins I
+have to wait a hundred blocks but I
+
+ align:start position:0%
+have to wait a hundred blocks but I
+ 
+
+ align:start position:0%
+have to wait a hundred blocks but I
+don't actually have to spend it after a
+
+ align:start position:0%
+don't actually have to spend it after a
+ 
+
+ align:start position:0%
+don't actually have to spend it after a
+hundred blocks I can just leave it in my
+
+ align:start position:0%
+hundred blocks I can just leave it in my
+ 
+
+ align:start position:0%
+hundred blocks I can just leave it in my
+wallet because Bob knows he never gave
+
+ align:start position:0%
+wallet because Bob knows he never gave
+ 
+
+ align:start position:0%
+wallet because Bob knows he never gave
+Alice this key so this this clause this
+
+ align:start position:0%
+Alice this key so this this clause this
+ 
+
+ align:start position:0%
+Alice this key so this this clause this
+or Alice and Bob are key it's just not
+
+ align:start position:0%
+or Alice and Bob are key it's just not
+ 
+
+ align:start position:0%
+or Alice and Bob are key it's just not
+gonna happen so Bob safe and just like
+
+ align:start position:0%
+gonna happen so Bob safe and just like
+ 
+
+ align:start position:0%
+gonna happen so Bob safe and just like
+leaves it so he doesn't meet you know he
+
+ align:start position:0%
+leaves it so he doesn't meet you know he
+ 
+
+ align:start position:0%
+leaves it so he doesn't meet you know he
+can just use that as well however if
+
+ align:start position:0%
+can just use that as well however if
+ 
+
+ align:start position:0%
+can just use that as well however if
+it's the like no you
+
+ align:start position:0%
+it's the like no you
+ 
+
+ align:start position:0%
+it's the like no you
+kind of thing then you have to do two
+
+ align:start position:0%
+kind of thing then you have to do two
+ 
+
+ align:start position:0%
+kind of thing then you have to do two
+transactions that's Rhoda so this is
+
+ align:start position:0%
+transactions that's Rhoda so this is
+ 
+
+ align:start position:0%
+transactions that's Rhoda so this is
+pretty good but you still have to do two
+
+ align:start position:0%
+pretty good but you still have to do two
+ 
+
+ align:start position:0%
+pretty good but you still have to do two
+transactions so if you use this you open
+
+ align:start position:0%
+transactions so if you use this you open
+ 
+
+ align:start position:0%
+transactions so if you use this you open
+a channel you use it once and then you
+
+ align:start position:0%
+a channel you use it once and then you
+ 
+
+ align:start position:0%
+a channel you use it once and then you
+close it well that was dumb you just
+
+ align:start position:0%
+close it well that was dumb you just
+ 
+
+ align:start position:0%
+close it well that was dumb you just
+paid twice as much on in fees that you
+
+ align:start position:0%
+paid twice as much on in fees that you
+ 
+
+ align:start position:0%
+paid twice as much on in fees that you
+needed to so it's useful for some things
+
+ align:start position:0%
+needed to so it's useful for some things
+ 
+
+ align:start position:0%
+needed to so it's useful for some things
+not for others could we do something
+
+ align:start position:0%
+not for others could we do something
+ 
+
+ align:start position:0%
+not for others could we do something
+like multiple party channels so there's
+
+ align:start position:0%
+like multiple party channels so there's
+ 
+
+ align:start position:0%
+like multiple party channels so there's
+research about this it gets real ugly
+
+ align:start position:0%
+research about this it gets real ugly
+ 
+
+ align:start position:0%
+research about this it gets real ugly
+real fast like I want a single channel
+
+ align:start position:0%
+real fast like I want a single channel
+ 
+
+ align:start position:0%
+real fast like I want a single channel
+with like three or four users or like a
+
+ align:start position:0%
+with like three or four users or like a
+ 
+
+ align:start position:0%
+with like three or four users or like a
+tree of channels where the first top you
+
+ align:start position:0%
+tree of channels where the first top you
+ 
+
+ align:start position:0%
+tree of channels where the first top you
+know output has 404 multi-sig and then
+
+ align:start position:0%
+know output has 404 multi-sig and then
+ 
+
+ align:start position:0%
+know output has 404 multi-sig and then
+it branches into these two of two multi
+
+ align:start position:0%
+it branches into these two of two multi
+ 
+
+ align:start position:0%
+it branches into these two of two multi
+six there's a lot of interesting ideas
+
+ align:start position:0%
+six there's a lot of interesting ideas
+ 
+
+ align:start position:0%
+six there's a lot of interesting ideas
+but it gets a little ugly so like the
+
+ align:start position:0%
+but it gets a little ugly so like the
+ 
+
+ align:start position:0%
+but it gets a little ugly so like the
+off chain scalability gets bad there's
+
+ align:start position:0%
+off chain scalability gets bad there's
+ 
+
+ align:start position:0%
+off chain scalability gets bad there's
+like a lot of N squared kind of stuff so
+
+ align:start position:0%
+like a lot of N squared kind of stuff so
+ 
+
+ align:start position:0%
+like a lot of N squared kind of stuff so
+what about a forwarding network of
+
+ align:start position:0%
+what about a forwarding network of
+ 
+
+ align:start position:0%
+what about a forwarding network of
+point-to-point channels so okay if we
+
+ align:start position:0%
+point-to-point channels so okay if we
+ 
+
+ align:start position:0%
+point-to-point channels so okay if we
+have these two party channels and people
+
+ align:start position:0%
+have these two party channels and people
+ 
+
+ align:start position:0%
+have these two party channels and people
+are connected with them so Alice and Bob
+
+ align:start position:0%
+are connected with them so Alice and Bob
+ 
+
+ align:start position:0%
+are connected with them so Alice and Bob
+have a channel and Bob and Carol have a
+
+ align:start position:0%
+have a channel and Bob and Carol have a
+ 
+
+ align:start position:0%
+have a channel and Bob and Carol have a
+channel so this would be cool Alice can
+
+ align:start position:0%
+channel so this would be cool Alice can
+ 
+
+ align:start position:0%
+channel so this would be cool Alice can
+just say hey Bob I will pay you if you
+
+ align:start position:0%
+just say hey Bob I will pay you if you
+ 
+
+ align:start position:0%
+just say hey Bob I will pay you if you
+pay Carol and you can do that right
+
+ align:start position:0%
+pay Carol and you can do that right
+ 
+
+ align:start position:0%
+pay Carol and you can do that right
+Alice says look I'm just making a new
+
+ align:start position:0%
+Alice says look I'm just making a new
+ 
+
+ align:start position:0%
+Alice says look I'm just making a new
+state where you have an extra coin now
+
+ align:start position:0%
+state where you have an extra coin now
+ 
+
+ align:start position:0%
+state where you have an extra coin now
+please give this extra going to Carol
+
+ align:start position:0%
+please give this extra going to Carol
+ 
+
+ align:start position:0%
+please give this extra going to Carol
+and Bob says yeah okay it does so the
+
+ align:start position:0%
+and Bob says yeah okay it does so the
+ 
+
+ align:start position:0%
+and Bob says yeah okay it does so the
+the the word there that should have
+
+ align:start position:0%
+the the word there that should have
+ 
+
+ align:start position:0%
+the the word there that should have
+immediately raised like oh no that's not
+
+ align:start position:0%
+immediately raised like oh no that's not
+ 
+
+ align:start position:0%
+immediately raised like oh no that's not
+how this stuff works is the word please
+
+ align:start position:0%
+how this stuff works is the word please
+ 
+
+ align:start position:0%
+how this stuff works is the word please
+you don't say please in Bitcoin uh so
+
+ align:start position:0%
+you don't say please in Bitcoin uh so
+ 
+
+ align:start position:0%
+you don't say please in Bitcoin uh so
+yeah the other option is Bob just keeps
+
+ align:start position:0%
+yeah the other option is Bob just keeps
+ 
+
+ align:start position:0%
+yeah the other option is Bob just keeps
+it right so Alice says okay here I'll
+
+ align:start position:0%
+it right so Alice says okay here I'll
+ 
+
+ align:start position:0%
+it right so Alice says okay here I'll
+you know add a coin to your output in
+
+ align:start position:0%
+you know add a coin to your output in
+ 
+
+ align:start position:0%
+you know add a coin to your output in
+this in this channel and please add a
+
+ align:start position:0%
+this in this channel and please add a
+ 
+
+ align:start position:0%
+this in this channel and please add a
+coin to Carol's output in your channel
+
+ align:start position:0%
+coin to Carol's output in your channel
+ 
+
+ align:start position:0%
+coin to Carol's output in your channel
+with her and Bob says yeah no I'm just
+
+ align:start position:0%
+with her and Bob says yeah no I'm just
+ 
+
+ align:start position:0%
+with her and Bob says yeah no I'm just
+gonna keep the coin thanks if your trust
+
+ align:start position:0%
+gonna keep the coin thanks if your trust
+ 
+
+ align:start position:0%
+gonna keep the coin thanks if your trust
+so this this might not be super crazy in
+
+ align:start position:0%
+so this this might not be super crazy in
+ 
+
+ align:start position:0%
+so this this might not be super crazy in
+that well you've got a channel with them
+
+ align:start position:0%
+that well you've got a channel with them
+ 
+
+ align:start position:0%
+that well you've got a channel with them
+maybe they're merchants also you can you
+
+ align:start position:0%
+maybe they're merchants also you can you
+ 
+
+ align:start position:0%
+maybe they're merchants also you can you
+can reduce the number of coins you send
+
+ align:start position:0%
+can reduce the number of coins you send
+ 
+
+ align:start position:0%
+can reduce the number of coins you send
+per update right you can say look I'm
+
+ align:start position:0%
+per update right you can say look I'm
+ 
+
+ align:start position:0%
+per update right you can say look I'm
+gonna send like one Satoshi at a time
+
+ align:start position:0%
+gonna send like one Satoshi at a time
+ 
+
+ align:start position:0%
+gonna send like one Satoshi at a time
+and so worst case you keep one Satoshi
+
+ align:start position:0%
+and so worst case you keep one Satoshi
+ 
+
+ align:start position:0%
+and so worst case you keep one Satoshi
+that you shouldn't have right you could
+
+ align:start position:0%
+that you shouldn't have right you could
+ 
+
+ align:start position:0%
+that you shouldn't have right you could
+write it's
+
+ align:start position:0%
+write it's
+ 
+
+ align:start position:0%
+write it's
+it's not a scalable though because let's
+
+ align:start position:0%
+it's not a scalable though because let's
+ 
+
+ align:start position:0%
+it's not a scalable though because let's
+say you want to send a lot of money to
+
+ align:start position:0%
+say you want to send a lot of money to
+ 
+
+ align:start position:0%
+say you want to send a lot of money to
+Carol okay you're gonna have to keep
+
+ align:start position:0%
+Carol okay you're gonna have to keep
+ 
+
+ align:start position:0%
+Carol okay you're gonna have to keep
+doing these little things it's kind of
+
+ align:start position:0%
+doing these little things it's kind of
+ 
+
+ align:start position:0%
+doing these little things it's kind of
+annoying also what if you want multiple
+
+ align:start position:0%
+annoying also what if you want multiple
+ 
+
+ align:start position:0%
+annoying also what if you want multiple
+hops where you're not even sure who's in
+
+ align:start position:0%
+hops where you're not even sure who's in
+ 
+
+ align:start position:0%
+hops where you're not even sure who's in
+the middle of your over your chain it
+
+ align:start position:0%
+the middle of your over your chain it
+ 
+
+ align:start position:0%
+the middle of your over your chain it
+doesn't work for that okay so you can
+
+ align:start position:0%
+doesn't work for that okay so you can
+ 
+
+ align:start position:0%
+doesn't work for that okay so you can
+have what's called HDFC's and these more
+
+ align:start position:0%
+have what's called HDFC's and these more
+ 
+
+ align:start position:0%
+have what's called HDFC's and these more
+complicated okay
+
+ align:start position:0%
+complicated okay
+ 
+
+ align:start position:0%
+complicated okay
+so the idea is it's hash time locked
+
+ align:start position:0%
+so the idea is it's hash time locked
+ 
+
+ align:start position:0%
+so the idea is it's hash time locked
+contract or a hex time walk contract
+
+ align:start position:0%
+contract or a hex time walk contract
+ 
+
+ align:start position:0%
+contract or a hex time walk contract
+whatever the script is essentially this
+
+ align:start position:0%
+whatever the script is essentially this
+ 
+
+ align:start position:0%
+whatever the script is essentially this
+key a and preimage are you need to
+
+ align:start position:0%
+key a and preimage are you need to
+ 
+
+ align:start position:0%
+key a and preimage are you need to
+present a pre-image of a hash or a key B
+
+ align:start position:0%
+present a pre-image of a hash or a key B
+ 
+
+ align:start position:0%
+present a pre-image of a hash or a key B
+and some absolute lock time check lock
+
+ align:start position:0%
+and some absolute lock time check lock
+ 
+
+ align:start position:0%
+and some absolute lock time check lock
+time verify it and it's it's important
+
+ align:start position:0%
+time verify it and it's it's important
+ 
+
+ align:start position:0%
+time verify it and it's it's important
+that this is an absolute time not a
+
+ align:start position:0%
+that this is an absolute time not a
+ 
+
+ align:start position:0%
+that this is an absolute time not a
+relative time because these should be
+
+ align:start position:0%
+relative time because these should be
+ 
+
+ align:start position:0%
+relative time because these should be
+able to expire regardless of when they
+
+ align:start position:0%
+able to expire regardless of when they
+ 
+
+ align:start position:0%
+able to expire regardless of when they
+get broadcast on to the blockchain so
+
+ align:start position:0%
+get broadcast on to the blockchain so
+ 
+
+ align:start position:0%
+get broadcast on to the blockchain so
+the idea is in this case Alice so let's
+
+ align:start position:0%
+the idea is in this case Alice so let's
+ 
+
+ align:start position:0%
+the idea is in this case Alice so let's
+say a is Alice B's Bob Alice gets the
+
+ align:start position:0%
+say a is Alice B's Bob Alice gets the
+ 
+
+ align:start position:0%
+say a is Alice B's Bob Alice gets the
+money if she knows this preimage are
+
+ align:start position:0%
+money if she knows this preimage are
+ 
+
+ align:start position:0%
+money if she knows this preimage are
+this 32 byte you know so what actually
+
+ align:start position:0%
+this 32 byte you know so what actually
+ 
+
+ align:start position:0%
+this 32 byte you know so what actually
+goes here is the hash of our right it's
+
+ align:start position:0%
+goes here is the hash of our right it's
+ 
+
+ align:start position:0%
+goes here is the hash of our right it's
+like it's like a pay to pub key hash
+
+ align:start position:0%
+like it's like a pay to pub key hash
+ 
+
+ align:start position:0%
+like it's like a pay to pub key hash
+where you say up you know up hash 160 up
+
+ align:start position:0%
+where you say up you know up hash 160 up
+ 
+
+ align:start position:0%
+where you say up you know up hash 160 up
+do pop hash 160 the thing people verify
+
+ align:start position:0%
+do pop hash 160 the thing people verify
+ 
+
+ align:start position:0%
+do pop hash 160 the thing people verify
+so you need to know some preimage and
+
+ align:start position:0%
+so you need to know some preimage and
+ 
+
+ align:start position:0%
+so you need to know some preimage and
+you need to sign or you can be Bob and
+
+ align:start position:0%
+you need to sign or you can be Bob and
+ 
+
+ align:start position:0%
+you need to sign or you can be Bob and
+then you can sign after a certain you
+
+ align:start position:0%
+then you can sign after a certain you
+ 
+
+ align:start position:0%
+then you can sign after a certain you
+know after a certain date so the way you
+
+ align:start position:0%
+know after a certain date so the way you
+ 
+
+ align:start position:0%
+know after a certain date so the way you
+build these so this is kind of nice it's
+
+ align:start position:0%
+build these so this is kind of nice it's
+ 
+
+ align:start position:0%
+build these so this is kind of nice it's
+like well if R is known then it's
+
+ align:start position:0%
+like well if R is known then it's
+ 
+
+ align:start position:0%
+like well if R is known then it's
+Alice's money if R is unknown then it's
+
+ align:start position:0%
+Alice's money if R is unknown then it's
+ 
+
+ align:start position:0%
+Alice's money if R is unknown then it's
+Bob's money after a certain period of
+
+ align:start position:0%
+Bob's money after a certain period of
+ 
+
+ align:start position:0%
+Bob's money after a certain period of
+time okay
+
+ align:start position:0%
+time okay
+ 
+
+ align:start position:0%
+time okay
+so this was the revocable transaction
+
+ align:start position:0%
+so this was the revocable transaction
+ 
+
+ align:start position:0%
+so this was the revocable transaction
+right where okay Alice got two coins
+
+ align:start position:0%
+right where okay Alice got two coins
+ 
+
+ align:start position:0%
+right where okay Alice got two coins
+Bob's got eight coins and then you add a
+
+ align:start position:0%
+Bob's got eight coins and then you add a
+ 
+
+ align:start position:0%
+Bob's got eight coins and then you add a
+third output this hdl-c output we're
+
+ align:start position:0%
+third output this hdl-c output we're
+ 
+
+ align:start position:0%
+third output this hdl-c output we're
+okay now Alice has two coins Bob has
+
+ align:start position:0%
+okay now Alice has two coins Bob has
+ 
+
+ align:start position:0%
+okay now Alice has two coins Bob has
+seven coins and Alice might be getting
+
+ align:start position:0%
+seven coins and Alice might be getting
+ 
+
+ align:start position:0%
+seven coins and Alice might be getting
+an extra coin if she learns our Bob gets
+
+ align:start position:0%
+an extra coin if she learns our Bob gets
+ 
+
+ align:start position:0%
+an extra coin if she learns our Bob gets
+the coin back after height 500,000 right
+
+ align:start position:0%
+the coin back after height 500,000 right
+ 
+
+ align:start position:0%
+the coin back after height 500,000 right
+so this is this similar to like when
+
+ align:start position:0%
+so this is this similar to like when
+ 
+
+ align:start position:0%
+so this is this similar to like when
+this is like okay this is Bob's money
+
+ align:start position:0%
+this is like okay this is Bob's money
+ 
+
+ align:start position:0%
+this is like okay this is Bob's money
+but if he does something bad Alice can
+
+ align:start position:0%
+but if he does something bad Alice can
+ 
+
+ align:start position:0%
+but if he does something bad Alice can
+grab it
+
+ align:start position:0%
+grab it
+ 
+
+ align:start position:0%
+grab it
+this is not
+
+ align:start position:0%
+this is not
+ 
+
+ align:start position:0%
+this is not
+this is this is Alice's money if she
+
+ align:start position:0%
+this is this is Alice's money if she
+ 
+
+ align:start position:0%
+this is this is Alice's money if she
+knows our if she doesn't Bob gets it
+
+ align:start position:0%
+knows our if she doesn't Bob gets it
+ 
+
+ align:start position:0%
+knows our if she doesn't Bob gets it
+back so there's no like mallet Liam this
+
+ align:start position:0%
+back so there's no like mallet Liam this
+ 
+
+ align:start position:0%
+back so there's no like mallet Liam this
+is sort of like really this is Bob's
+
+ align:start position:0%
+is sort of like really this is Bob's
+ 
+
+ align:start position:0%
+is sort of like really this is Bob's
+money right this only happens if
+
+ align:start position:0%
+money right this only happens if
+ 
+
+ align:start position:0%
+money right this only happens if
+something Horrible's you know someone's
+
+ align:start position:0%
+something Horrible's you know someone's
+ 
+
+ align:start position:0%
+something Horrible's you know someone's
+trying to rip someone off this on the
+
+ align:start position:0%
+trying to rip someone off this on the
+ 
+
+ align:start position:0%
+trying to rip someone off this on the
+other hand is well depends
+
+ align:start position:0%
+other hand is well depends
+ 
+
+ align:start position:0%
+other hand is well depends
+does Alice gonna learn our or not and
+
+ align:start position:0%
+does Alice gonna learn our or not and
+ 
+
+ align:start position:0%
+does Alice gonna learn our or not and
+what is our okay so the multi-party
+
+ align:start position:0%
+what is our okay so the multi-party
+ 
+
+ align:start position:0%
+what is our okay so the multi-party
+adversarial payment model so the
+
+ align:start position:0%
+adversarial payment model so the
+ 
+
+ align:start position:0%
+adversarial payment model so the
+lightning forwarding is Alice wants to
+
+ align:start position:0%
+lightning forwarding is Alice wants to
+ 
+
+ align:start position:0%
+lightning forwarding is Alice wants to
+pay Carol right she doesn't want to just
+
+ align:start position:0%
+pay Carol right she doesn't want to just
+ 
+
+ align:start position:0%
+pay Carol right she doesn't want to just
+ask Bob to keep forwarding the funds
+
+ align:start position:0%
+ask Bob to keep forwarding the funds
+ 
+
+ align:start position:0%
+ask Bob to keep forwarding the funds
+because she doesn't trust Bob so she
+
+ align:start position:0%
+because she doesn't trust Bob so she
+ 
+
+ align:start position:0%
+because she doesn't trust Bob so she
+connects to Carol and by connect I mean
+
+ align:start position:0%
+connects to Carol and by connect I mean
+ 
+
+ align:start position:0%
+connects to Carol and by connect I mean
+like regular TCP connection and says hey
+
+ align:start position:0%
+like regular TCP connection and says hey
+ 
+
+ align:start position:0%
+like regular TCP connection and says hey
+Carol make a random number R and send me
+
+ align:start position:0%
+Carol make a random number R and send me
+ 
+
+ align:start position:0%
+Carol make a random number R and send me
+the hash codes okay here you go
+
+ align:start position:0%
+the hash codes okay here you go
+ 
+
+ align:start position:0%
+the hash codes okay here you go
+Carol knows H which is the the hash and
+
+ align:start position:0%
+Carol knows H which is the the hash and
+ 
+
+ align:start position:0%
+Carol knows H which is the the hash and
+R which is the pretty much she sends
+
+ align:start position:0%
+R which is the pretty much she sends
+ 
+
+ align:start position:0%
+R which is the pretty much she sends
+over H to Alice Alice then says to Bob
+
+ align:start position:0%
+over H to Alice Alice then says to Bob
+ 
+
+ align:start position:0%
+over H to Alice Alice then says to Bob
+hey I'm going to add an HDL C to our our
+
+ align:start position:0%
+hey I'm going to add an HDL C to our our
+ 
+
+ align:start position:0%
+hey I'm going to add an HDL C to our our
+Channel so basically Bob if you know the
+
+ align:start position:0%
+Channel so basically Bob if you know the
+ 
+
+ align:start position:0%
+Channel so basically Bob if you know the
+preimage of h if you know R you can get
+
+ align:start position:0%
+preimage of h if you know R you can get
+ 
+
+ align:start position:0%
+preimage of h if you know R you can get
+this coin if not I get the coin back
+
+ align:start position:0%
+this coin if not I get the coin back
+ 
+
+ align:start position:0%
+this coin if not I get the coin back
+after five o'clock and then Bob says
+
+ align:start position:0%
+after five o'clock and then Bob says
+ 
+
+ align:start position:0%
+after five o'clock and then Bob says
+okay cool
+
+ align:start position:0%
+okay cool
+ 
+
+ align:start position:0%
+okay cool
+I know H now but I don't know R so I
+
+ align:start position:0%
+I know H now but I don't know R so I
+ 
+
+ align:start position:0%
+I know H now but I don't know R so I
+can't I can't grab this money right I
+
+ align:start position:0%
+can't I can't grab this money right I
+ 
+
+ align:start position:0%
+can't I can't grab this money right I
+don't know this so there's no way this
+
+ align:start position:0%
+don't know this so there's no way this
+ 
+
+ align:start position:0%
+don't know this so there's no way this
+is gonna be my money it's just gonna go
+
+ align:start position:0%
+is gonna be my money it's just gonna go
+ 
+
+ align:start position:0%
+is gonna be my money it's just gonna go
+back to you after five and Alice says
+
+ align:start position:0%
+back to you after five and Alice says
+ 
+
+ align:start position:0%
+back to you after five and Alice says
+yeah but you know Carol knows are so ask
+
+ align:start position:0%
+yeah but you know Carol knows are so ask
+ 
+
+ align:start position:0%
+yeah but you know Carol knows are so ask
+Carol
+
+ align:start position:0%
+Carol
+ 
+
+ align:start position:0%
+Carol
+Bob says okay I get it I will forward
+
+ align:start position:0%
+Bob says okay I get it I will forward
+ 
+
+ align:start position:0%
+Bob says okay I get it I will forward
+this on to Carol and then I create a
+
+ align:start position:0%
+this on to Carol and then I create a
+ 
+
+ align:start position:0%
+this on to Carol and then I create a
+similar output I make sure that these
+
+ align:start position:0%
+similar output I make sure that these
+ 
+
+ align:start position:0%
+similar output I make sure that these
+are the same R or the same H I don't
+
+ align:start position:0%
+are the same R or the same H I don't
+ 
+
+ align:start position:0%
+are the same R or the same H I don't
+know why yet but I say hey Carol if you
+
+ align:start position:0%
+know why yet but I say hey Carol if you
+ 
+
+ align:start position:0%
+know why yet but I say hey Carol if you
+know R if you know the preimage of H you
+
+ align:start position:0%
+know R if you know the preimage of H you
+ 
+
+ align:start position:0%
+know R if you know the preimage of H you
+can get this coin if not after four
+
+ align:start position:0%
+can get this coin if not after four
+ 
+
+ align:start position:0%
+can get this coin if not after four
+o'clock I get the money back and then
+
+ align:start position:0%
+o'clock I get the money back and then
+ 
+
+ align:start position:0%
+o'clock I get the money back and then
+Carol says oh cool
+
+ align:start position:0%
+Carol says oh cool
+ 
+
+ align:start position:0%
+Carol says oh cool
+well guess what I know R because I made
+
+ align:start position:0%
+well guess what I know R because I made
+ 
+
+ align:start position:0%
+well guess what I know R because I made
+up made made are up and I can
+
+ align:start position:0%
+up made made are up and I can
+ 
+
+ align:start position:0%
+up made made are up and I can
+so from careless perspective Carol could
+
+ align:start position:0%
+so from careless perspective Carol could
+ 
+
+ align:start position:0%
+so from careless perspective Carol could
+broadcast this on to the blockchain
+
+ align:start position:0%
+broadcast this on to the blockchain
+ 
+
+ align:start position:0%
+broadcast this on to the blockchain
+immediately and she will be able to grab
+
+ align:start position:0%
+immediately and she will be able to grab
+ 
+
+ align:start position:0%
+immediately and she will be able to grab
+the money right cuz she knows our she
+
+ align:start position:0%
+the money right cuz she knows our she
+ 
+
+ align:start position:0%
+the money right cuz she knows our she
+has to grab it soon because by 4 o'clock
+
+ align:start position:0%
+has to grab it soon because by 4 o'clock
+ 
+
+ align:start position:0%
+has to grab it soon because by 4 o'clock
+Bob can grab the money better than
+
+ align:start position:0%
+Bob can grab the money better than
+ 
+
+ align:start position:0%
+Bob can grab the money better than
+closing that
+
+ align:start position:0%
+closing that
+ 
+
+ align:start position:0%
+closing that
+and if carol if Carol does this she
+
+ align:start position:0%
+and if carol if Carol does this she
+ 
+
+ align:start position:0%
+and if carol if Carol does this she
+closes the channel she uses our because
+
+ align:start position:0%
+closes the channel she uses our because
+ 
+
+ align:start position:0%
+closes the channel she uses our because
+she knows it to take this coin from this
+
+ align:start position:0%
+she knows it to take this coin from this
+ 
+
+ align:start position:0%
+she knows it to take this coin from this
+output Carol doing that will reveal art
+
+ align:start position:0%
+output Carol doing that will reveal art
+ 
+
+ align:start position:0%
+output Carol doing that will reveal art
+to everyone in the world because it's on
+
+ align:start position:0%
+to everyone in the world because it's on
+ 
+
+ align:start position:0%
+to everyone in the world because it's on
+the blockchain now
+
+ align:start position:0%
+the blockchain now
+ 
+
+ align:start position:0%
+the blockchain now
+and so then Alice or certain that Bob
+
+ align:start position:0%
+and so then Alice or certain that Bob
+ 
+
+ align:start position:0%
+and so then Alice or certain that Bob
+can say ah I know R now I need to get
+
+ align:start position:0%
+can say ah I know R now I need to get
+ 
+
+ align:start position:0%
+can say ah I know R now I need to get
+this money so Bob can close the channel
+
+ align:start position:0%
+this money so Bob can close the channel
+ 
+
+ align:start position:0%
+this money so Bob can close the channel
+grab the money yes this offer yeah we
+
+ align:start position:0%
+grab the money yes this offer yeah we
+ 
+
+ align:start position:0%
+grab the money yes this offer yeah we
+use Heights you could do a time the the
+
+ align:start position:0%
+use Heights you could do a time the the
+ 
+
+ align:start position:0%
+use Heights you could do a time the the
+reason we the main reason for Heights is
+
+ align:start position:0%
+reason we the main reason for Heights is
+ 
+
+ align:start position:0%
+reason we the main reason for Heights is
+what if a blocks full and like height
+
+ align:start position:0%
+what if a blocks full and like height
+ 
+
+ align:start position:0%
+what if a blocks full and like height
+height seems because Heights sort of
+
+ align:start position:0%
+height seems because Heights sort of
+ 
+
+ align:start position:0%
+height seems because Heights sort of
+variable like maybe a bunch of blocks
+
+ align:start position:0%
+variable like maybe a bunch of blocks
+ 
+
+ align:start position:0%
+variable like maybe a bunch of blocks
+come out quickly maybe they come out
+
+ align:start position:0%
+come out quickly maybe they come out
+ 
+
+ align:start position:0%
+come out quickly maybe they come out
+slowly so time is a little dangerous in
+
+ align:start position:0%
+slowly so time is a little dangerous in
+ 
+
+ align:start position:0%
+slowly so time is a little dangerous in
+that you could say okay four o'clock but
+
+ align:start position:0%
+that you could say okay four o'clock but
+ 
+
+ align:start position:0%
+that you could say okay four o'clock but
+maybe in the next five hours only a
+
+ align:start position:0%
+maybe in the next five hours only a
+ 
+
+ align:start position:0%
+maybe in the next five hours only a
+couple blocks come out just by chance
+
+ align:start position:0%
+couple blocks come out just by chance
+ 
+
+ align:start position:0%
+couple blocks come out just by chance
+and they're full and you're not able to
+
+ align:start position:0%
+and they're full and you're not able to
+ 
+
+ align:start position:0%
+and they're full and you're not able to
+broadcast you know and you're not able
+
+ align:start position:0%
+broadcast you know and you're not able
+ 
+
+ align:start position:0%
+broadcast you know and you're not able
+to get this in then it's risky so the
+
+ align:start position:0%
+to get this in then it's risky so the
+ 
+
+ align:start position:0%
+to get this in then it's risky so the
+height sort of takes into account the
+
+ align:start position:0%
+height sort of takes into account the
+ 
+
+ align:start position:0%
+height sort of takes into account the
+variable nature of it a little bit
+
+ align:start position:0%
+variable nature of it a little bit
+ 
+
+ align:start position:0%
+variable nature of it a little bit
+better yeah well page for parent yeah so
+
+ align:start position:0%
+better yeah well page for parent yeah so
+ 
+
+ align:start position:0%
+better yeah well page for parent yeah so
+the question is well you know what if
+
+ align:start position:0%
+the question is well you know what if
+ 
+
+ align:start position:0%
+the question is well you know what if
+the fees get really high right what if
+
+ align:start position:0%
+the fees get really high right what if
+ 
+
+ align:start position:0%
+the fees get really high right what if
+these the thing is this whole process
+
+ align:start position:0%
+these the thing is this whole process
+ 
+
+ align:start position:0%
+these the thing is this whole process
+should take a few seconds so it's not
+
+ align:start position:0%
+should take a few seconds so it's not
+ 
+
+ align:start position:0%
+should take a few seconds so it's not
+like these outputs are have have weird
+
+ align:start position:0%
+like these outputs are have have weird
+ 
+
+ align:start position:0%
+like these outputs are have have weird
+fees that are like old right one that
+
+ align:start position:0%
+fees that are like old right one that
+ 
+
+ align:start position:0%
+fees that are like old right one that
+one issue is what if you're building
+
+ align:start position:0%
+one issue is what if you're building
+ 
+
+ align:start position:0%
+one issue is what if you're building
+these states back and forth and then you
+
+ align:start position:0%
+these states back and forth and then you
+ 
+
+ align:start position:0%
+these states back and forth and then you
+sit on one for a few weeks and then the
+
+ align:start position:0%
+sit on one for a few weeks and then the
+ 
+
+ align:start position:0%
+sit on one for a few weeks and then the
+fee rate goes way up and you're like
+
+ align:start position:0%
+fee rate goes way up and you're like
+ 
+
+ align:start position:0%
+fee rate goes way up and you're like
+shoot if I try to broadcast these
+
+ align:start position:0%
+shoot if I try to broadcast these
+ 
+
+ align:start position:0%
+shoot if I try to broadcast these
+transactions the fees too low and it
+
+ align:start position:0%
+transactions the fees too low and it
+ 
+
+ align:start position:0%
+transactions the fees too low and it
+might not get confirmed that's not it's
+
+ align:start position:0%
+might not get confirmed that's not it's
+ 
+
+ align:start position:0%
+might not get confirmed that's not it's
+not a huge risk because if you're not
+
+ align:start position:0%
+not a huge risk because if you're not
+ 
+
+ align:start position:0%
+not a huge risk because if you're not
+trying to rip people off you don't
+
+ align:start position:0%
+trying to rip people off you don't
+ 
+
+ align:start position:0%
+trying to rip people off you don't
+actually have any time risk in this case
+
+ align:start position:0%
+actually have any time risk in this case
+ 
+
+ align:start position:0%
+actually have any time risk in this case
+these this gets built this get spill
+
+ align:start position:0%
+these this gets built this get spill
+ 
+
+ align:start position:0%
+these this gets built this get spill
+these are sort of in real time and so
+
+ align:start position:0%
+these are sort of in real time and so
+ 
+
+ align:start position:0%
+these are sort of in real time and so
+you know what the fee rate is in the
+
+ align:start position:0%
+you know what the fee rate is in the
+ 
+
+ align:start position:0%
+you know what the fee rate is in the
+network so you can see can adapt to it
+
+ align:start position:0%
+network so you can see can adapt to it
+ 
+
+ align:start position:0%
+network so you can see can adapt to it
+but yeah that's not sure yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if some you know if you have like a
+
+ align:start position:0%
+if some you know if you have like a
+ 
+
+ align:start position:0%
+if some you know if you have like a
+number of nodes you mean a minimal
+
+ align:start position:0%
+number of nodes you mean a minimal
+ 
+
+ align:start position:0%
+number of nodes you mean a minimal
+number like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't need global consensus in that I
+
+ align:start position:0%
+don't need global consensus in that I
+ 
+
+ align:start position:0%
+don't need global consensus in that I
+didn't I did the only three so it you
+
+ align:start position:0%
+didn't I did the only three so it you
+ 
+
+ align:start position:0%
+didn't I did the only three so it you
+can't show if you have four you can sort
+
+ align:start position:0%
+can't show if you have four you can sort
+ 
+
+ align:start position:0%
+can't show if you have four you can sort
+of say let's say you have Alice Bob
+
+ align:start position:0%
+of say let's say you have Alice Bob
+ 
+
+ align:start position:0%
+of say let's say you have Alice Bob
+Carol Dave um Carol doesn't it like you
+
+ align:start position:0%
+Carol Dave um Carol doesn't it like you
+ 
+
+ align:start position:0%
+Carol Dave um Carol doesn't it like you
+don't actually have to know the whole
+
+ align:start position:0%
+don't actually have to know the whole
+ 
+
+ align:start position:0%
+don't actually have to know the whole
+thing you just have to know the person
+
+ align:start position:0%
+thing you just have to know the person
+ 
+
+ align:start position:0%
+thing you just have to know the person
+before you in the person after you you
+
+ align:start position:0%
+before you in the person after you you
+ 
+
+ align:start position:0%
+before you in the person after you you
+don't care what the actual end points
+
+ align:start position:0%
+don't care what the actual end points
+ 
+
+ align:start position:0%
+don't care what the actual end points
+are so to some extent Bob doesn't need
+
+ align:start position:0%
+are so to some extent Bob doesn't need
+ 
+
+ align:start position:0%
+are so to some extent Bob doesn't need
+to know maybe Alice got this hdl-c
+
+ align:start position:0%
+to know maybe Alice got this hdl-c
+ 
+
+ align:start position:0%
+to know maybe Alice got this hdl-c
+forwarded from someone else before and
+
+ align:start position:0%
+forwarded from someone else before and
+ 
+
+ align:start position:0%
+forwarded from someone else before and
+Bob's like all I know is Alice's you
+
+ align:start position:0%
+Bob's like all I know is Alice's you
+ 
+
+ align:start position:0%
+Bob's like all I know is Alice's you
+know I could get money from Alice I know
+
+ align:start position:0%
+know I could get money from Alice I know
+ 
+
+ align:start position:0%
+know I could get money from Alice I know
+R and Carol gets it for me if she knows
+
+ align:start position:0%
+R and Carol gets it for me if she knows
+ 
+
+ align:start position:0%
+R and Carol gets it for me if she knows
+R and if maybe that keeps going or
+
+ align:start position:0%
+R and if maybe that keeps going or
+ 
+
+ align:start position:0%
+R and if maybe that keeps going or
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+you don't need global consensus for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah you don't all you're all
+
+ align:start position:0%
+yeah yeah you don't all you're all
+ 
+
+ align:start position:0%
+yeah yeah you don't all you're all
+you're only concerned with the channels
+
+ align:start position:0%
+you're only concerned with the channels
+ 
+
+ align:start position:0%
+you're only concerned with the channels
+you're participating in if there's
+
+ align:start position:0%
+you're participating in if there's
+ 
+
+ align:start position:0%
+you're participating in if there's
+something else happening before it you
+
+ align:start position:0%
+something else happening before it you
+ 
+
+ align:start position:0%
+something else happening before it you
+might want to watch in case our shows up
+
+ align:start position:0%
+might want to watch in case our shows up
+ 
+
+ align:start position:0%
+might want to watch in case our shows up
+but you know you don't have to worry
+
+ align:start position:0%
+but you know you don't have to worry
+ 
+
+ align:start position:0%
+but you know you don't have to worry
+about it
+
+ align:start position:0%
+about it
+ 
+
+ align:start position:0%
+about it
+and then like these along get broadcast
+
+ align:start position:0%
+and then like these along get broadcast
+ 
+
+ align:start position:0%
+and then like these along get broadcast
+you know the sort of failure mode is
+
+ align:start position:0%
+you know the sort of failure mode is
+ 
+
+ align:start position:0%
+you know the sort of failure mode is
+broadcast everything onto the blockchain
+
+ align:start position:0%
+broadcast everything onto the blockchain
+ 
+
+ align:start position:0%
+broadcast everything onto the blockchain
+and let the blockchain sorted out and
+
+ align:start position:0%
+and let the blockchain sorted out and
+ 
+
+ align:start position:0%
+and let the blockchain sorted out and
+that's you know that's very highly and C
+
+ align:start position:0%
+that's you know that's very highly and C
+ 
+
+ align:start position:0%
+that's you know that's very highly and C
+because it's like ten minutes but the
+
+ align:start position:0%
+because it's like ten minutes but the
+ 
+
+ align:start position:0%
+because it's like ten minutes but the
+blockchain you know the idea is the
+
+ align:start position:0%
+blockchain you know the idea is the
+ 
+
+ align:start position:0%
+blockchain you know the idea is the
+blockchain already has that global
+
+ align:start position:0%
+blockchain already has that global
+ 
+
+ align:start position:0%
+blockchain already has that global
+consensus because it's really low
+
+ align:start position:0%
+consensus because it's really low
+ 
+
+ align:start position:0%
+consensus because it's really low
+latency and everyone can agree on it so
+
+ align:start position:0%
+latency and everyone can agree on it so
+ 
+
+ align:start position:0%
+latency and everyone can agree on it so
+I think that's yeah so what you could do
+
+ align:start position:0%
+I think that's yeah so what you could do
+ 
+
+ align:start position:0%
+I think that's yeah so what you could do
+here is you can just close it right you
+
+ align:start position:0%
+here is you can just close it right you
+ 
+
+ align:start position:0%
+here is you can just close it right you
+could broadcast this whole transaction
+
+ align:start position:0%
+could broadcast this whole transaction
+ 
+
+ align:start position:0%
+could broadcast this whole transaction
+on the blockchain
+
+ align:start position:0%
+on the blockchain
+ 
+
+ align:start position:0%
+on the blockchain
+and get the payment through that's
+
+ align:start position:0%
+and get the payment through that's
+ 
+
+ align:start position:0%
+and get the payment through that's
+really inefficient you want to keep your
+
+ align:start position:0%
+really inefficient you want to keep your
+ 
+
+ align:start position:0%
+really inefficient you want to keep your
+channels open so what instead happens in
+
+ align:start position:0%
+channels open so what instead happens in
+ 
+
+ align:start position:0%
+channels open so what instead happens in
+in you know when everything's working
+
+ align:start position:0%
+in you know when everything's working
+ 
+
+ align:start position:0%
+in you know when everything's working
+the idea is it could happen right Carol
+
+ align:start position:0%
+the idea is it could happen right Carol
+ 
+
+ align:start position:0%
+the idea is it could happen right Carol
+could just broadcast it okay that's
+
+ align:start position:0%
+could just broadcast it okay that's
+ 
+
+ align:start position:0%
+could just broadcast it okay that's
+annoying whatever but no one loses money
+
+ align:start position:0%
+annoying whatever but no one loses money
+ 
+
+ align:start position:0%
+annoying whatever but no one loses money
+or Carol can go offline at this point
+
+ align:start position:0%
+or Carol can go offline at this point
+ 
+
+ align:start position:0%
+or Carol can go offline at this point
+and then these things get stuck you know
+
+ align:start position:0%
+and then these things get stuck you know
+ 
+
+ align:start position:0%
+and then these things get stuck you know
+there's all sorts of weird things that
+
+ align:start position:0%
+there's all sorts of weird things that
+ 
+
+ align:start position:0%
+there's all sorts of weird things that
+can go wrong you know lose money but
+
+ align:start position:0%
+can go wrong you know lose money but
+ 
+
+ align:start position:0%
+can go wrong you know lose money but
+what happens when things go right is
+
+ align:start position:0%
+what happens when things go right is
+ 
+
+ align:start position:0%
+what happens when things go right is
+Carol says hey um Bob I know are and so
+
+ align:start position:0%
+Carol says hey um Bob I know are and so
+ 
+
+ align:start position:0%
+Carol says hey um Bob I know are and so
+really this whole crazy hdl-c thing it's
+
+ align:start position:0%
+really this whole crazy hdl-c thing it's
+ 
+
+ align:start position:0%
+really this whole crazy hdl-c thing it's
+just my money right I know what R is
+
+ align:start position:0%
+just my money right I know what R is
+ 
+
+ align:start position:0%
+just my money right I know what R is
+you're never you're not getting this
+
+ align:start position:0%
+you're never you're not getting this
+ 
+
+ align:start position:0%
+you're never you're not getting this
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+at 4 o'clock because I know our so here
+
+ align:start position:0%
+at 4 o'clock because I know our so here
+ 
+
+ align:start position:0%
+at 4 o'clock because I know our so here
+look I'll tell you our and when Carol
+
+ align:start position:0%
+look I'll tell you our and when Carol
+ 
+
+ align:start position:0%
+look I'll tell you our and when Carol
+tells Bob our she's doing two things
+
+ align:start position:0%
+tells Bob our she's doing two things
+ 
+
+ align:start position:0%
+tells Bob our she's doing two things
+she's proving that this hdl-c is her
+
+ align:start position:0%
+she's proving that this hdl-c is her
+ 
+
+ align:start position:0%
+she's proving that this hdl-c is her
+money she's also giving Bob our so that
+
+ align:start position:0%
+money she's also giving Bob our so that
+ 
+
+ align:start position:0%
+money she's also giving Bob our so that
+he can then grab Alice's money and so as
+
+ align:start position:0%
+he can then grab Alice's money and so as
+ 
+
+ align:start position:0%
+he can then grab Alice's money and so as
+soon as she reveals our to Bob Bob says
+
+ align:start position:0%
+soon as she reveals our to Bob Bob says
+ 
+
+ align:start position:0%
+soon as she reveals our to Bob Bob says
+yeah I agree
+
+ align:start position:0%
+yeah I agree
+ 
+
+ align:start position:0%
+yeah I agree
+this hdl-c is superfluous at this point
+
+ align:start position:0%
+this hdl-c is superfluous at this point
+ 
+
+ align:start position:0%
+this hdl-c is superfluous at this point
+I know you know our so this is just your
+
+ align:start position:0%
+I know you know our so this is just your
+ 
+
+ align:start position:0%
+I know you know our so this is just your
+money and you know if it gets close to 4
+
+ align:start position:0%
+money and you know if it gets close to 4
+ 
+
+ align:start position:0%
+money and you know if it gets close to 4
+o'clock I know you're gonna broadcast
+
+ align:start position:0%
+o'clock I know you're gonna broadcast
+ 
+
+ align:start position:0%
+o'clock I know you're gonna broadcast
+this channel onto the chain if I don't
+
+ align:start position:0%
+this channel onto the chain if I don't
+ 
+
+ align:start position:0%
+this channel onto the chain if I don't
+let you clear it out so let's just make
+
+ align:start position:0%
+let you clear it out so let's just make
+ 
+
+ align:start position:0%
+let you clear it out so let's just make
+a new state you know through these kind
+
+ align:start position:0%
+a new state you know through these kind
+ 
+
+ align:start position:0%
+a new state you know through these kind
+of state updates where you just have the
+
+ align:start position:0%
+of state updates where you just have the
+ 
+
+ align:start position:0%
+of state updates where you just have the
+extra money let's clear out that hdl-c
+
+ align:start position:0%
+extra money let's clear out that hdl-c
+ 
+
+ align:start position:0%
+extra money let's clear out that hdl-c
+so that one coin goes to you
+
+ align:start position:0%
+so that one coin goes to you
+ 
+
+ align:start position:0%
+so that one coin goes to you
+and goes like okay cool I agree we'll
+
+ align:start position:0%
+and goes like okay cool I agree we'll
+ 
+
+ align:start position:0%
+and goes like okay cool I agree we'll
+sign this and they let's get rid of the
+
+ align:start position:0%
+sign this and they let's get rid of the
+ 
+
+ align:start position:0%
+sign this and they let's get rid of the
+hdl-c output then Bob goes to Allison
+
+ align:start position:0%
+hdl-c output then Bob goes to Allison
+ 
+
+ align:start position:0%
+hdl-c output then Bob goes to Allison
+says hey Alice guess what I know R so
+
+ align:start position:0%
+says hey Alice guess what I know R so
+ 
+
+ align:start position:0%
+says hey Alice guess what I know R so
+this this part I'm gonna do it
+
+ align:start position:0%
+this this part I'm gonna do it
+ 
+
+ align:start position:0%
+this this part I'm gonna do it
+I know R and Bob this Alice after 5
+
+ align:start position:0%
+I know R and Bob this Alice after 5
+ 
+
+ align:start position:0%
+I know R and Bob this Alice after 5
+o'clock it's not happening right if you
+
+ align:start position:0%
+o'clock it's not happening right if you
+ 
+
+ align:start position:0%
+o'clock it's not happening right if you
+if you stop if you stop answering me and
+
+ align:start position:0%
+if you stop if you stop answering me and
+ 
+
+ align:start position:0%
+if you stop if you stop answering me and
+it gets to like 4:30 I'm just gonna
+
+ align:start position:0%
+it gets to like 4:30 I'm just gonna
+ 
+
+ align:start position:0%
+it gets to like 4:30 I'm just gonna
+broadcast the the the channel on chain
+
+ align:start position:0%
+broadcast the the the channel on chain
+ 
+
+ align:start position:0%
+broadcast the the the channel on chain
+and grab it that way and then out Bob
+
+ align:start position:0%
+and grab it that way and then out Bob
+ 
+
+ align:start position:0%
+and grab it that way and then out Bob
+reveals our to Alice Alice's oh yeah you
+
+ align:start position:0%
+reveals our to Alice Alice's oh yeah you
+ 
+
+ align:start position:0%
+reveals our to Alice Alice's oh yeah you
+do no heart okay will clear the hdl-c
+
+ align:start position:0%
+do no heart okay will clear the hdl-c
+ 
+
+ align:start position:0%
+do no heart okay will clear the hdl-c
+out and you get the money and then Alice
+
+ align:start position:0%
+out and you get the money and then Alice
+ 
+
+ align:start position:0%
+out and you get the money and then Alice
+gets R and that sort of a receipt for
+
+ align:start position:0%
+gets R and that sort of a receipt for
+ 
+
+ align:start position:0%
+gets R and that sort of a receipt for
+the payment and Alice knows well carol
+
+ align:start position:0%
+the payment and Alice knows well carol
+ 
+
+ align:start position:0%
+the payment and Alice knows well carol
+was the one who told me h carol must
+
+ align:start position:0%
+was the one who told me h carol must
+ 
+
+ align:start position:0%
+was the one who told me h carol must
+have gotten the money right so that's my
+
+ align:start position:0%
+have gotten the money right so that's my
+ 
+
+ align:start position:0%
+have gotten the money right so that's my
+my confirmation of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh so an input in the script but it's
+
+ align:start position:0%
+oh so an input in the script but it's
+ 
+
+ align:start position:0%
+oh so an input in the script but it's
+it's revocable the same way everything
+
+ align:start position:0%
+it's revocable the same way everything
+ 
+
+ align:start position:0%
+it's revocable the same way everything
+the the regular outputs are revocable
+
+ align:start position:0%
+the the regular outputs are revocable
+ 
+
+ align:start position:0%
+the the regular outputs are revocable
+there's also this you don't even have to
+
+ align:start position:0%
+there's also this you don't even have to
+ 
+
+ align:start position:0%
+there's also this you don't even have to
+do because the the idea is if the HDL
+
+ align:start position:0%
+do because the the idea is if the HDL
+ 
+
+ align:start position:0%
+do because the the idea is if the HDL
+sees are very small in comparison with
+
+ align:start position:0%
+sees are very small in comparison with
+ 
+
+ align:start position:0%
+sees are very small in comparison with
+the other outputs in the state that if
+
+ align:start position:0%
+the other outputs in the state that if
+ 
+
+ align:start position:0%
+the other outputs in the state that if
+you try to broadcast an old one you'll
+
+ align:start position:0%
+you try to broadcast an old one you'll
+ 
+
+ align:start position:0%
+you try to broadcast an old one you'll
+lose weigh more than the HDL see is
+
+ align:start position:0%
+lose weigh more than the HDL see is
+ 
+
+ align:start position:0%
+lose weigh more than the HDL see is
+worth but you can also tack on a or
+
+ align:start position:0%
+worth but you can also tack on a or
+ 
+
+ align:start position:0%
+worth but you can also tack on a or
+other Clause to the HDL C script with a
+
+ align:start position:0%
+other Clause to the HDL C script with a
+ 
+
+ align:start position:0%
+other Clause to the HDL C script with a
+relative lock time so there's actually a
+
+ align:start position:0%
+relative lock time so there's actually a
+ 
+
+ align:start position:0%
+relative lock time so there's actually a
+couple different ways to do it the
+
+ align:start position:0%
+couple different ways to do it the
+ 
+
+ align:start position:0%
+couple different ways to do it the
+simplest is you just say look the other
+
+ align:start position:0%
+simplest is you just say look the other
+ 
+
+ align:start position:0%
+simplest is you just say look the other
+the two you know I've got two coins
+
+ align:start position:0%
+the two you know I've got two coins
+ 
+
+ align:start position:0%
+the two you know I've got two coins
+eight coins or two point seven coins and
+
+ align:start position:0%
+eight coins or two point seven coins and
+ 
+
+ align:start position:0%
+eight coins or two point seven coins and
+then a one coin hdl-c I'm not gonna risk
+
+ align:start position:0%
+then a one coin hdl-c I'm not gonna risk
+ 
+
+ align:start position:0%
+then a one coin hdl-c I'm not gonna risk
+my seven coins to go back and try to get
+
+ align:start position:0%
+my seven coins to go back and try to get
+ 
+
+ align:start position:0%
+my seven coins to go back and try to get
+this one coin in the HLC but that's not
+
+ align:start position:0%
+this one coin in the HLC but that's not
+ 
+
+ align:start position:0%
+this one coin in the HLC but that's not
+how most of the software does it you
+
+ align:start position:0%
+how most of the software does it you
+ 
+
+ align:start position:0%
+how most of the software does it you
+just add a new clause okay so this is a
+
+ align:start position:0%
+just add a new clause okay so this is a
+ 
+
+ align:start position:0%
+just add a new clause okay so this is a
+multiple party adversarial so yeah that
+
+ align:start position:0%
+multiple party adversarial so yeah that
+ 
+
+ align:start position:0%
+multiple party adversarial so yeah that
+would be really useful right you you
+
+ align:start position:0%
+would be really useful right you you
+ 
+
+ align:start position:0%
+would be really useful right you you
+build lots of nodes with channels
+
+ align:start position:0%
+build lots of nodes with channels
+ 
+
+ align:start position:0%
+build lots of nodes with channels
+connecting and they form a big graph and
+
+ align:start position:0%
+connecting and they form a big graph and
+ 
+
+ align:start position:0%
+connecting and they form a big graph and
+then you can sort of request payment
+
+ align:start position:0%
+then you can sort of request payment
+ 
+
+ align:start position:0%
+then you can sort of request payment
+routing these these hdl-c outputs and if
+
+ align:start position:0%
+routing these these hdl-c outputs and if
+ 
+
+ align:start position:0%
+routing these these hdl-c outputs and if
+you open a few channels then you can pay
+
+ align:start position:0%
+you open a few channels then you can pay
+ 
+
+ align:start position:0%
+you open a few channels then you can pay
+lots of different users on the network
+
+ align:start position:0%
+lots of different users on the network
+ 
+
+ align:start position:0%
+lots of different users on the network
+yes Bob kid charged a fee or he could
+
+ align:start position:0%
+yes Bob kid charged a fee or he could
+ 
+
+ align:start position:0%
+yes Bob kid charged a fee or he could
+just be a nice guy
+
+ align:start position:0%
+just be a nice guy
+ 
+
+ align:start position:0%
+just be a nice guy
+that's basically the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please yeah so yeah so you can pay him
+
+ align:start position:0%
+please yeah so yeah so you can pay him
+ 
+
+ align:start position:0%
+please yeah so yeah so you can pay him
+um it's gonna be hard to pay him much
+
+ align:start position:0%
+um it's gonna be hard to pay him much
+ 
+
+ align:start position:0%
+um it's gonna be hard to pay him much
+because alice is gonna say look we've
+
+ align:start position:0%
+because alice is gonna say look we've
+ 
+
+ align:start position:0%
+because alice is gonna say look we've
+got a channel we're using it if you
+
+ align:start position:0%
+got a channel we're using it if you
+ 
+
+ align:start position:0%
+got a channel we're using it if you
+charge me a ton to forward payments to
+
+ align:start position:0%
+charge me a ton to forward payments to
+ 
+
+ align:start position:0%
+charge me a ton to forward payments to
+Carol I'm just gonna close the channel
+
+ align:start position:0%
+Carol I'm just gonna close the channel
+ 
+
+ align:start position:0%
+Carol I'm just gonna close the channel
+and open with someone who does it
+
+ align:start position:0%
+and open with someone who does it
+ 
+
+ align:start position:0%
+and open with someone who does it
+cheaper so yeah you can you can make the
+
+ align:start position:0%
+cheaper so yeah you can you can make the
+ 
+
+ align:start position:0%
+cheaper so yeah you can you can make the
+amounts slightly less right so Allah
+
+ align:start position:0%
+amounts slightly less right so Allah
+ 
+
+ align:start position:0%
+amounts slightly less right so Allah
+says I'm sending you one coin and Bob
+
+ align:start position:0%
+says I'm sending you one coin and Bob
+ 
+
+ align:start position:0%
+says I'm sending you one coin and Bob
+says okay I'm sending 0.9999 coins to
+
+ align:start position:0%
+says okay I'm sending 0.9999 coins to
+ 
+
+ align:start position:0%
+says okay I'm sending 0.9999 coins to
+Carol and I'm keeping the difference he
+
+ align:start position:0%
+Carol and I'm keeping the difference he
+ 
+
+ align:start position:0%
+Carol and I'm keeping the difference he
+can have that and then it's really up to
+
+ align:start position:0%
+can have that and then it's really up to
+ 
+
+ align:start position:0%
+can have that and then it's really up to
+Carol to decide if the fee because Alice
+
+ align:start position:0%
+Carol to decide if the fee because Alice
+ 
+
+ align:start position:0%
+Carol to decide if the fee because Alice
+all Alice knows is hey I'm sending one
+
+ align:start position:0%
+all Alice knows is hey I'm sending one
+ 
+
+ align:start position:0%
+all Alice knows is hey I'm sending one
+coin and then Carol sees what if Bob
+
+ align:start position:0%
+coin and then Carol sees what if Bob
+ 
+
+ align:start position:0%
+coin and then Carol sees what if Bob
+puts a crazy fee like half a coin Carol
+
+ align:start position:0%
+puts a crazy fee like half a coin Carol
+ 
+
+ align:start position:0%
+puts a crazy fee like half a coin Carol
+sees 0.5 and Carol is like no I that's
+
+ align:start position:0%
+sees 0.5 and Carol is like no I that's
+ 
+
+ align:start position:0%
+sees 0.5 and Carol is like no I that's
+that's way too low I don't know what
+
+ align:start position:0%
+that's way too low I don't know what
+ 
+
+ align:start position:0%
+that's way too low I don't know what
+happened if Alice sent 0.5 and Bob
+
+ align:start position:0%
+happened if Alice sent 0.5 and Bob
+ 
+
+ align:start position:0%
+happened if Alice sent 0.5 and Bob
+forwarded it to me or if Alice sent one
+
+ align:start position:0%
+forwarded it to me or if Alice sent one
+ 
+
+ align:start position:0%
+forwarded it to me or if Alice sent one
+and Bob Ford went five but I'm not
+
+ align:start position:0%
+and Bob Ford went five but I'm not
+ 
+
+ align:start position:0%
+and Bob Ford went five but I'm not
+accepting this right I'm not gonna
+
+ align:start position:0%
+accepting this right I'm not gonna
+ 
+
+ align:start position:0%
+accepting this right I'm not gonna
+reveal our to you I'm just gonna say no
+
+ align:start position:0%
+reveal our to you I'm just gonna say no
+ 
+
+ align:start position:0%
+reveal our to you I'm just gonna say no
+so you can do that right at this point
+
+ align:start position:0%
+so you can do that right at this point
+ 
+
+ align:start position:0%
+so you can do that right at this point
+Carol has not yet revealed are Carol can
+
+ align:start position:0%
+Carol has not yet revealed are Carol can
+ 
+
+ align:start position:0%
+Carol has not yet revealed are Carol can
+refuse and say look at Bob I'm not gonna
+
+ align:start position:0%
+refuse and say look at Bob I'm not gonna
+ 
+
+ align:start position:0%
+refuse and say look at Bob I'm not gonna
+accept this gauge steel see we can just
+
+ align:start position:0%
+accept this gauge steel see we can just
+ 
+
+ align:start position:0%
+accept this gauge steel see we can just
+clear it out right away without
+
+ align:start position:0%
+clear it out right away without
+ 
+
+ align:start position:0%
+clear it out right away without
+revealing our and and just basically
+
+ align:start position:0%
+revealing our and and just basically
+ 
+
+ align:start position:0%
+revealing our and and just basically
+undo what we just did yeah two photos -
+
+ align:start position:0%
+undo what we just did yeah two photos -
+ 
+
+ align:start position:0%
+undo what we just did yeah two photos -
+that the first is can there be a
+
+ align:start position:0%
+that the first is can there be a
+ 
+
+ align:start position:0%
+that the first is can there be a
+situation where it's an efficient market
+
+ align:start position:0%
+situation where it's an efficient market
+ 
+
+ align:start position:0%
+situation where it's an efficient market
+place for these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually wins and she rots it from that
+
+ align:start position:0%
+actually wins and she rots it from that
+ 
+
+ align:start position:0%
+actually wins and she rots it from that
+you can so if let's say Alice is
+
+ align:start position:0%
+you can so if let's say Alice is
+ 
+
+ align:start position:0%
+you can so if let's say Alice is
+connected to like you know three three
+
+ align:start position:0%
+connected to like you know three three
+ 
+
+ align:start position:0%
+connected to like you know three three
+Bob's in the middle and then asks all of
+
+ align:start position:0%
+Bob's in the middle and then asks all of
+ 
+
+ align:start position:0%
+Bob's in the middle and then asks all of
+them hey what are you gonna charge me to
+
+ align:start position:0%
+them hey what are you gonna charge me to
+ 
+
+ align:start position:0%
+them hey what are you gonna charge me to
+forward a coin to Carol
+
+ align:start position:0%
+forward a coin to Carol
+ 
+
+ align:start position:0%
+forward a coin to Carol
+then they can all answer it's a little
+
+ align:start position:0%
+then they can all answer it's a little
+ 
+
+ align:start position:0%
+then they can all answer it's a little
+weird because they can they can lie at
+
+ align:start position:0%
+weird because they can they can lie at
+ 
+
+ align:start position:0%
+weird because they can they can lie at
+that point because I haven't actually
+
+ align:start position:0%
+that point because I haven't actually
+ 
+
+ align:start position:0%
+that point because I haven't actually
+like signed anything and this fob can
+
+ align:start position:0%
+like signed anything and this fob can
+ 
+
+ align:start position:0%
+like signed anything and this fob can
+say oh I'll do it for free and this Bob
+
+ align:start position:0%
+say oh I'll do it for free and this Bob
+ 
+
+ align:start position:0%
+say oh I'll do it for free and this Bob
+says I'll do it for half a coin into
+
+ align:start position:0%
+says I'll do it for half a coin into
+ 
+
+ align:start position:0%
+says I'll do it for half a coin into
+this bob says I'll do it a tenth of a
+
+ align:start position:0%
+this bob says I'll do it a tenth of a
+ 
+
+ align:start position:0%
+this bob says I'll do it a tenth of a
+coin and then you try to go for the free
+
+ align:start position:0%
+coin and then you try to go for the free
+ 
+
+ align:start position:0%
+coin and then you try to go for the free
+one and Carol gets like some really low
+
+ align:start position:0%
+one and Carol gets like some really low
+ 
+
+ align:start position:0%
+one and Carol gets like some really low
+amount and says I'm not telling you are
+
+ align:start position:0%
+amount and says I'm not telling you are
+ 
+
+ align:start position:0%
+amount and says I'm not telling you are
+let's let's cancel this and then you can
+
+ align:start position:0%
+let's let's cancel this and then you can
+ 
+
+ align:start position:0%
+let's let's cancel this and then you can
+if Alice trusts Carol Cael can be like
+
+ align:start position:0%
+if Alice trusts Carol Cael can be like
+ 
+
+ align:start position:0%
+if Alice trusts Carol Cael can be like
+Alice Bob just tried to charge a
+
+ align:start position:0%
+Alice Bob just tried to charge a
+ 
+
+ align:start position:0%
+Alice Bob just tried to charge a
+ridiculous fee don't use this you know
+
+ align:start position:0%
+ridiculous fee don't use this you know
+ 
+
+ align:start position:0%
+ridiculous fee don't use this you know
+this Bob is bad and then you try the
+
+ align:start position:0%
+this Bob is bad and then you try the
+ 
+
+ align:start position:0%
+this Bob is bad and then you try the
+other Bob and the other Bob does the
+
+ align:start position:0%
+other Bob and the other Bob does the
+ 
+
+ align:start position:0%
+other Bob and the other Bob does the
+right thing yeah open the channel so
+
+ align:start position:0%
+right thing yeah open the channel so
+ 
+
+ align:start position:0%
+right thing yeah open the channel so
+yeah you could you just have to open a
+
+ align:start position:0%
+yeah you could you just have to open a
+ 
+
+ align:start position:0%
+yeah you could you just have to open a
+channel yeah you have to go on chain so
+
+ align:start position:0%
+channel yeah you have to go on chain so
+ 
+
+ align:start position:0%
+channel yeah you have to go on chain so
+the idea is long term like it we sort of
+
+ align:start position:0%
+the idea is long term like it we sort of
+ 
+
+ align:start position:0%
+the idea is long term like it we sort of
+saw a preview of it in November December
+
+ align:start position:0%
+saw a preview of it in November December
+ 
+
+ align:start position:0%
+saw a preview of it in November December
+January where it was actually kind of
+
+ align:start position:0%
+January where it was actually kind of
+ 
+
+ align:start position:0%
+January where it was actually kind of
+expensive to use Bitcoin now it's cheap
+
+ align:start position:0%
+expensive to use Bitcoin now it's cheap
+ 
+
+ align:start position:0%
+expensive to use Bitcoin now it's cheap
+again costs a few cents but for a month
+
+ align:start position:0%
+again costs a few cents but for a month
+ 
+
+ align:start position:0%
+again costs a few cents but for a month
+or two it was like oh shoot like this
+
+ align:start position:0%
+or two it was like oh shoot like this
+ 
+
+ align:start position:0%
+or two it was like oh shoot like this
+costs like five bucks to make a chain on
+
+ align:start position:0%
+costs like five bucks to make a chain on
+ 
+
+ align:start position:0%
+costs like five bucks to make a chain on
+chain transaction and so like creating a
+
+ align:start position:0%
+chain transaction and so like creating a
+ 
+
+ align:start position:0%
+chain transaction and so like creating a
+new direct channel from Alice to Carol
+
+ align:start position:0%
+new direct channel from Alice to Carol
+ 
+
+ align:start position:0%
+new direct channel from Alice to Carol
+it might cost five bucks or it might
+
+ align:start position:0%
+it might cost five bucks or it might
+ 
+
+ align:start position:0%
+it might cost five bucks or it might
+cost twenty bucks or you know like long
+
+ align:start position:0%
+cost twenty bucks or you know like long
+ 
+
+ align:start position:0%
+cost twenty bucks or you know like long
+term if everyone's trying to use the
+
+ align:start position:0%
+term if everyone's trying to use the
+ 
+
+ align:start position:0%
+term if everyone's trying to use the
+blockchain and the fees go really high
+
+ align:start position:0%
+blockchain and the fees go really high
+ 
+
+ align:start position:0%
+blockchain and the fees go really high
+it could be kind of expensive and so the
+
+ align:start position:0%
+it could be kind of expensive and so the
+ 
+
+ align:start position:0%
+it could be kind of expensive and so the
+idea is well if I've got a channel
+
+ align:start position:0%
+idea is well if I've got a channel
+ 
+
+ align:start position:0%
+idea is well if I've got a channel
+already I'd rather use that and move my
+
+ align:start position:0%
+already I'd rather use that and move my
+ 
+
+ align:start position:0%
+already I'd rather use that and move my
+money around that way without having to
+
+ align:start position:0%
+money around that way without having to
+ 
+
+ align:start position:0%
+money around that way without having to
+like touch the blockchain yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so scalability so like you can sort of
+
+ align:start position:0%
+so scalability so like you can sort of
+ 
+
+ align:start position:0%
+so scalability so like you can sort of
+so it's bone for it or it's like Jake's
+
+ align:start position:0%
+so it's bone for it or it's like Jake's
+ 
+
+ align:start position:0%
+so it's bone for it or it's like Jake's
+Torres kind of if you know the whole
+
+ align:start position:0%
+Torres kind of if you know the whole
+ 
+
+ align:start position:0%
+Torres kind of if you know the whole
+graph yeah well so that's one part is if
+
+ align:start position:0%
+graph yeah well so that's one part is if
+ 
+
+ align:start position:0%
+graph yeah well so that's one part is if
+you know the whole graph and you you can
+
+ align:start position:0%
+you know the whole graph and you you can
+ 
+
+ align:start position:0%
+you know the whole graph and you you can
+know the whole graph because the graph
+
+ align:start position:0%
+know the whole graph because the graph
+ 
+
+ align:start position:0%
+know the whole graph because the graph
+never gets bigger than the UT Exocet
+
+ align:start position:0%
+never gets bigger than the UT Exocet
+ 
+
+ align:start position:0%
+never gets bigger than the UT Exocet
+right every channel is a is a
+
+ align:start position:0%
+right every channel is a is a
+ 
+
+ align:start position:0%
+right every channel is a is a
+transaction output and so if you're
+
+ align:start position:0%
+transaction output and so if you're
+ 
+
+ align:start position:0%
+transaction output and so if you're
+running a full node and you have the
+
+ align:start position:0%
+running a full node and you have the
+ 
+
+ align:start position:0%
+running a full node and you have the
+whole UT Exocet well the entire graph is
+
+ align:start position:0%
+whole UT Exocet well the entire graph is
+ 
+
+ align:start position:0%
+whole UT Exocet well the entire graph is
+is on the order of that size so maybe
+
+ align:start position:0%
+is on the order of that size so maybe
+ 
+
+ align:start position:0%
+is on the order of that size so maybe
+it's twice as big I mean that you have
+
+ align:start position:0%
+it's twice as big I mean that you have
+ 
+
+ align:start position:0%
+it's twice as big I mean that you have
+to have some like extra metadata about
+
+ align:start position:0%
+to have some like extra metadata about
+ 
+
+ align:start position:0%
+to have some like extra metadata about
+what these outputs are and like Bob and
+
+ align:start position:0%
+what these outputs are and like Bob and
+ 
+
+ align:start position:0%
+what these outputs are and like Bob and
+Carol can make proofs they're like oh
+
+ align:start position:0%
+Carol can make proofs they're like oh
+ 
+
+ align:start position:0%
+Carol can make proofs they're like oh
+here's our channel and it's in the UT
+
+ align:start position:0%
+here's our channel and it's in the UT
+ 
+
+ align:start position:0%
+here's our channel and it's in the UT
+Exocet and we can sort of reveal our pop
+
+ align:start position:0%
+Exocet and we can sort of reveal our pop
+ 
+
+ align:start position:0%
+Exocet and we can sort of reveal our pop
+keys that they go in here so if you have
+
+ align:start position:0%
+keys that they go in here so if you have
+ 
+
+ align:start position:0%
+keys that they go in here so if you have
+the whole graph you can do some routing
+
+ align:start position:0%
+the whole graph you can do some routing
+ 
+
+ align:start position:0%
+the whole graph you can do some routing
+that's like n log n kind of speed but
+
+ align:start position:0%
+that's like n log n kind of speed but
+ 
+
+ align:start position:0%
+that's like n log n kind of speed but
+then it might not work and so that's the
+
+ align:start position:0%
+then it might not work and so that's the
+ 
+
+ align:start position:0%
+then it might not work and so that's the
+like so there's lots of ways there's
+
+ align:start position:0%
+like so there's lots of ways there's
+ 
+
+ align:start position:0%
+like so there's lots of ways there's
+there's actually tons of ways things can
+
+ align:start position:0%
+there's actually tons of ways things can
+ 
+
+ align:start position:0%
+there's actually tons of ways things can
+go wrong in this that's the sort of fun
+
+ align:start position:0%
+go wrong in this that's the sort of fun
+ 
+
+ align:start position:0%
+go wrong in this that's the sort of fun
+part of dealing with there's one of the
+
+ align:start position:0%
+part of dealing with there's one of the
+ 
+
+ align:start position:0%
+part of dealing with there's one of the
+ways it can it cannot work is you're
+
+ align:start position:0%
+ways it can it cannot work is you're
+ 
+
+ align:start position:0%
+ways it can it cannot work is you're
+like yeah I found a path the simplest is
+
+ align:start position:0%
+like yeah I found a path the simplest is
+ 
+
+ align:start position:0%
+like yeah I found a path the simplest is
+I found a path and I query Bob and Bob
+
+ align:start position:0%
+I found a path and I query Bob and Bob
+ 
+
+ align:start position:0%
+I found a path and I query Bob and Bob
+is just offline like oh okay well that's
+
+ align:start position:0%
+is just offline like oh okay well that's
+ 
+
+ align:start position:0%
+is just offline like oh okay well that's
+not an active path ok what's the second
+
+ align:start position:0%
+not an active path ok what's the second
+ 
+
+ align:start position:0%
+not an active path ok what's the second
+shortest fast ok this other Bob and and
+
+ align:start position:0%
+shortest fast ok this other Bob and and
+ 
+
+ align:start position:0%
+shortest fast ok this other Bob and and
+he says yes but the fee seems really
+
+ align:start position:0%
+he says yes but the fee seems really
+ 
+
+ align:start position:0%
+he says yes but the fee seems really
+high so ok I found the 30 so most of the
+
+ align:start position:0%
+high so ok I found the 30 so most of the
+ 
+
+ align:start position:0%
+high so ok I found the 30 so most of the
+algorithms though will will get you like
+
+ align:start position:0%
+algorithms though will will get you like
+ 
+
+ align:start position:0%
+algorithms though will will get you like
+the second and third and fourth and
+
+ align:start position:0%
+the second and third and fourth and
+ 
+
+ align:start position:0%
+the second and third and fourth and
+fifth shortest in much less time than
+
+ align:start position:0%
+fifth shortest in much less time than
+ 
+
+ align:start position:0%
+fifth shortest in much less time than
+recomputing the whole thing from scratch
+
+ align:start position:0%
+recomputing the whole thing from scratch
+ 
+
+ align:start position:0%
+recomputing the whole thing from scratch
+so you can get a you can get a bunch of
+
+ align:start position:0%
+so you can get a you can get a bunch of
+ 
+
+ align:start position:0%
+so you can get a you can get a bunch of
+pretty good ones and try them all by
+
+ align:start position:0%
+pretty good ones and try them all by
+ 
+
+ align:start position:0%
+pretty good ones and try them all by
+query and they're what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the thing is in practice it's all
+
+ align:start position:0%
+yeah the thing is in practice it's all
+ 
+
+ align:start position:0%
+yeah the thing is in practice it's all
+real fast right like there's well right
+
+ align:start position:0%
+real fast right like there's well right
+ 
+
+ align:start position:0%
+real fast right like there's well right
+now there's like you know for a small
+
+ align:start position:0%
+now there's like you know for a small
+ 
+
+ align:start position:0%
+now there's like you know for a small
+Network it's nothing but even total
+
+ align:start position:0%
+Network it's nothing but even total
+ 
+
+ align:start position:0%
+Network it's nothing but even total
+number of UT EXO's is on the order of
+
+ align:start position:0%
+number of UT EXO's is on the order of
+ 
+
+ align:start position:0%
+number of UT EXO's is on the order of
+like millions right so if you've got a
+
+ align:start position:0%
+like millions right so if you've got a
+ 
+
+ align:start position:0%
+like millions right so if you've got a
+graph with like millions of edges that's
+
+ align:start position:0%
+graph with like millions of edges that's
+ 
+
+ align:start position:0%
+graph with like millions of edges that's
+that's easy for a computer right they'll
+
+ align:start position:0%
+that's easy for a computer right they'll
+ 
+
+ align:start position:0%
+that's easy for a computer right they'll
+do it in like less than a second so and
+
+ align:start position:0%
+do it in like less than a second so and
+ 
+
+ align:start position:0%
+do it in like less than a second so and
+then you that your main thing here is
+
+ align:start position:0%
+then you that your main thing here is
+ 
+
+ align:start position:0%
+then you that your main thing here is
+network latency for all of these things
+
+ align:start position:0%
+network latency for all of these things
+ 
+
+ align:start position:0%
+network latency for all of these things
+for for building new states it's the the
+
+ align:start position:0%
+for for building new states it's the the
+ 
+
+ align:start position:0%
+for for building new states it's the the
+time taken for you know the data to get
+
+ align:start position:0%
+time taken for you know the data to get
+ 
+
+ align:start position:0%
+time taken for you know the data to get
+from one side of the other is much
+
+ align:start position:0%
+from one side of the other is much
+ 
+
+ align:start position:0%
+from one side of the other is much
+larger than computing the signatures
+
+ align:start position:0%
+larger than computing the signatures
+ 
+
+ align:start position:0%
+larger than computing the signatures
+verifying the signatures building the
+
+ align:start position:0%
+verifying the signatures building the
+ 
+
+ align:start position:0%
+verifying the signatures building the
+hash tree thing all that stuff is is
+
+ align:start position:0%
+hash tree thing all that stuff is is
+ 
+
+ align:start position:0%
+hash tree thing all that stuff is is
+real fast compared to network so same
+
+ align:start position:0%
+real fast compared to network so same
+ 
+
+ align:start position:0%
+real fast compared to network so same
+with routing looking at the look at the
+
+ align:start position:0%
+with routing looking at the look at the
+ 
+
+ align:start position:0%
+with routing looking at the look at the
+graph and detecting it is gonna be
+
+ align:start position:0%
+graph and detecting it is gonna be
+ 
+
+ align:start position:0%
+graph and detecting it is gonna be
+faster than contacting all the things
+
+ align:start position:0%
+faster than contacting all the things
+ 
+
+ align:start position:0%
+faster than contacting all the things
+there's a bunch of other things that can
+
+ align:start position:0%
+there's a bunch of other things that can
+ 
+
+ align:start position:0%
+there's a bunch of other things that can
+go wrong so for example this gets built
+
+ align:start position:0%
+go wrong so for example this gets built
+ 
+
+ align:start position:0%
+go wrong so for example this gets built
+you get to here and just Carol the stops
+
+ align:start position:0%
+you get to here and just Carol the stops
+ 
+
+ align:start position:0%
+you get to here and just Carol the stops
+responding right so now you've got these
+
+ align:start position:0%
+responding right so now you've got these
+ 
+
+ align:start position:0%
+responding right so now you've got these
+two HDL sees there there a third output
+
+ align:start position:0%
+two HDL sees there there a third output
+ 
+
+ align:start position:0%
+two HDL sees there there a third output
+in your channel transaction and Carol is
+
+ align:start position:0%
+in your channel transaction and Carol is
+ 
+
+ align:start position:0%
+in your channel transaction and Carol is
+just like not saying anything and then
+
+ align:start position:0%
+just like not saying anything and then
+ 
+
+ align:start position:0%
+just like not saying anything and then
+Alice goes to Bob it's like Bob what's
+
+ align:start position:0%
+Alice goes to Bob it's like Bob what's
+ 
+
+ align:start position:0%
+Alice goes to Bob it's like Bob what's
+up like we're gonna clear the stage teal
+
+ align:start position:0%
+up like we're gonna clear the stage teal
+ 
+
+ align:start position:0%
+up like we're gonna clear the stage teal
+see usually these only take a second and
+
+ align:start position:0%
+see usually these only take a second and
+ 
+
+ align:start position:0%
+see usually these only take a second and
+Bob's like oh yeah hold on and so it's
+
+ align:start position:0%
+Bob's like oh yeah hold on and so it's
+ 
+
+ align:start position:0%
+Bob's like oh yeah hold on and so it's
+kind of awkward right because now we've
+
+ align:start position:0%
+kind of awkward right because now we've
+ 
+
+ align:start position:0%
+kind of awkward right because now we've
+got the same she'll seen you don't know
+
+ align:start position:0%
+got the same she'll seen you don't know
+ 
+
+ align:start position:0%
+got the same she'll seen you don't know
+whose money it ends up being there's the
+
+ align:start position:0%
+whose money it ends up being there's the
+ 
+
+ align:start position:0%
+whose money it ends up being there's the
+way to mitigate that that rusty yeah I
+
+ align:start position:0%
+way to mitigate that that rusty yeah I
+ 
+
+ align:start position:0%
+way to mitigate that that rusty yeah I
+think it works
+
+ align:start position:0%
+think it works
+ 
+
+ align:start position:0%
+think it works
+Rusty's other guy who works on this
+
+ align:start position:0%
+Rusty's other guy who works on this
+ 
+
+ align:start position:0%
+Rusty's other guy who works on this
+stuff was that Alice were quite if he
+
+ align:start position:0%
+stuff was that Alice were quite if he
+ 
+
+ align:start position:0%
+stuff was that Alice were quite if he
+has like a timeout period I think 30
+
+ align:start position:0%
+has like a timeout period I think 30
+ 
+
+ align:start position:0%
+has like a timeout period I think 30
+seconds a minute whatever where Alice
+
+ align:start position:0%
+seconds a minute whatever where Alice
+ 
+
+ align:start position:0%
+seconds a minute whatever where Alice
+says okay Bob I made this hdl-c a minute
+
+ align:start position:0%
+says okay Bob I made this hdl-c a minute
+ 
+
+ align:start position:0%
+says okay Bob I made this hdl-c a minute
+ago minutes up you need to either shut
+
+ align:start position:0%
+ago minutes up you need to either shut
+ 
+
+ align:start position:0%
+ago minutes up you need to either shut
+down this channel right now because
+
+ align:start position:0%
+down this channel right now because
+ 
+
+ align:start position:0%
+down this channel right now because
+you're doing something bad or you need
+
+ align:start position:0%
+you're doing something bad or you need
+ 
+
+ align:start position:0%
+you're doing something bad or you need
+to shut down you need to prove to me
+
+ align:start position:0%
+to shut down you need to prove to me
+ 
+
+ align:start position:0%
+to shut down you need to prove to me
+that a channel has been shut down with
+
+ align:start position:0%
+that a channel has been shut down with
+ 
+
+ align:start position:0%
+that a channel has been shut down with
+this hdl-c this h value in it and then I
+
+ align:start position:0%
+this hdl-c this h value in it and then I
+ 
+
+ align:start position:0%
+this hdl-c this h value in it and then I
+know where to ascribe blame
+
+ align:start position:0%
+know where to ascribe blame
+ 
+
+ align:start position:0%
+know where to ascribe blame
+so if Bob's like yeah I can't contact
+
+ align:start position:0%
+so if Bob's like yeah I can't contact
+ 
+
+ align:start position:0%
+so if Bob's like yeah I can't contact
+Carol Carol's offline the analysis all
+
+ align:start position:0%
+Carol Carol's offline the analysis all
+ 
+
+ align:start position:0%
+Carol Carol's offline the analysis all
+right well then shut down the channel
+
+ align:start position:0%
+right well then shut down the channel
+ 
+
+ align:start position:0%
+right well then shut down the channel
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so it's that's the downside right well
+
+ align:start position:0%
+so it's that's the downside right well
+ 
+
+ align:start position:0%
+so it's that's the downside right well
+thing is if you don't do that you can in
+
+ align:start position:0%
+thing is if you don't do that you can in
+ 
+
+ align:start position:0%
+thing is if you don't do that you can in
+this world it's like being live really
+
+ align:start position:0%
+this world it's like being live really
+ 
+
+ align:start position:0%
+this world it's like being live really
+matters okay
+
+ align:start position:0%
+matters okay
+ 
+
+ align:start position:0%
+matters okay
+true okay one thing to mitigate that the
+
+ align:start position:0%
+true okay one thing to mitigate that the
+ 
+
+ align:start position:0%
+true okay one thing to mitigate that the
+only time care this is this is a Carol
+
+ align:start position:0%
+only time care this is this is a Carol
+ 
+
+ align:start position:0%
+only time care this is this is a Carol
+responded by signing off on the hdl-c
+
+ align:start position:0%
+responded by signing off on the hdl-c
+ 
+
+ align:start position:0%
+responded by signing off on the hdl-c
+and then immediately goes offline like
+
+ align:start position:0%
+and then immediately goes offline like
+ 
+
+ align:start position:0%
+and then immediately goes offline like
+so you know it's it's not like you
+
+ align:start position:0%
+so you know it's it's not like you
+ 
+
+ align:start position:0%
+so you know it's it's not like you
+accident well part of the protocol is if
+
+ align:start position:0%
+accident well part of the protocol is if
+ 
+
+ align:start position:0%
+accident well part of the protocol is if
+you have an HD LC and you don't remove
+
+ align:start position:0%
+you have an HD LC and you don't remove
+ 
+
+ align:start position:0%
+you have an HD LC and you don't remove
+it within 30 to 60 seconds it's like you
+
+ align:start position:0%
+it within 30 to 60 seconds it's like you
+ 
+
+ align:start position:0%
+it within 30 to 60 seconds it's like you
+know that's that's a violation of the
+
+ align:start position:0%
+know that's that's a violation of the
+ 
+
+ align:start position:0%
+know that's that's a violation of the
+rules and we're gonna close your chant
+
+ align:start position:0%
+rules and we're gonna close your chant
+ 
+
+ align:start position:0%
+rules and we're gonna close your chant
+there channels because if you're just
+
+ align:start position:0%
+there channels because if you're just
+ 
+
+ align:start position:0%
+there channels because if you're just
+offline straight-up offline and it's
+
+ align:start position:0%
+offline straight-up offline and it's
+ 
+
+ align:start position:0%
+offline straight-up offline and it's
+like well okay I'm not going to use that
+
+ align:start position:0%
+like well okay I'm not going to use that
+ 
+
+ align:start position:0%
+like well okay I'm not going to use that
+channel but it's like oh I accepted this
+
+ align:start position:0%
+channel but it's like oh I accepted this
+ 
+
+ align:start position:0%
+channel but it's like oh I accepted this
+and immediately said okay I'm not
+
+ align:start position:0%
+and immediately said okay I'm not
+ 
+
+ align:start position:0%
+and immediately said okay I'm not
+talking you anymore and they're like
+
+ align:start position:0%
+talking you anymore and they're like
+ 
+
+ align:start position:0%
+talking you anymore and they're like
+well now it's stuck because the the sort
+
+ align:start position:0%
+well now it's stuck because the the sort
+ 
+
+ align:start position:0%
+well now it's stuck because the the sort
+of attack vector is build a ton of HDL
+
+ align:start position:0%
+of attack vector is build a ton of HDL
+ 
+
+ align:start position:0%
+of attack vector is build a ton of HDL
+C's right you could have multiple per
+
+ align:start position:0%
+C's right you could have multiple per
+ 
+
+ align:start position:0%
+C's right you could have multiple per
+channel
+
+ align:start position:0%
+channel
+ 
+
+ align:start position:0%
+channel
+and like build them all and they all get
+
+ align:start position:0%
+and like build them all and they all get
+ 
+
+ align:start position:0%
+and like build them all and they all get
+stuck and one party's just not
+
+ align:start position:0%
+stuck and one party's just not
+ 
+
+ align:start position:0%
+stuck and one party's just not
+responding with there are values and
+
+ align:start position:0%
+responding with there are values and
+ 
+
+ align:start position:0%
+responding with there are values and
+then everyone's like okay if we try to
+
+ align:start position:0%
+then everyone's like okay if we try to
+ 
+
+ align:start position:0%
+then everyone's like okay if we try to
+close our transactions now have like 100
+
+ align:start position:0%
+close our transactions now have like 100
+ 
+
+ align:start position:0%
+close our transactions now have like 100
+outputs and they're huge and have all
+
+ align:start position:0%
+outputs and they're huge and have all
+ 
+
+ align:start position:0%
+outputs and they're huge and have all
+these fees also all these HDL sees yeah
+
+ align:start position:0%
+these fees also all these HDL sees yeah
+ 
+
+ align:start position:0%
+these fees also all these HDL sees yeah
+there might be really little and we have
+
+ align:start position:0%
+there might be really little and we have
+ 
+
+ align:start position:0%
+there might be really little and we have
+to like wait and then it charges a lot
+
+ align:start position:0%
+to like wait and then it charges a lot
+ 
+
+ align:start position:0%
+to like wait and then it charges a lot
+of fees to recover them and stuff so you
+
+ align:start position:0%
+of fees to recover them and stuff so you
+ 
+
+ align:start position:0%
+of fees to recover them and stuff so you
+don't you don't want people to be able
+
+ align:start position:0%
+don't you don't want people to be able
+ 
+
+ align:start position:0%
+don't you don't want people to be able
+to sort of bloat the number of HDL CS in
+
+ align:start position:0%
+to sort of bloat the number of HDL CS in
+ 
+
+ align:start position:0%
+to sort of bloat the number of HDL CS in
+your channels so the way to do it is
+
+ align:start position:0%
+your channels so the way to do it is
+ 
+
+ align:start position:0%
+your channels so the way to do it is
+okay if one of them stuck you need to
+
+ align:start position:0%
+okay if one of them stuck you need to
+ 
+
+ align:start position:0%
+okay if one of them stuck you need to
+find someone to blame and yeah it's it's
+
+ align:start position:0%
+find someone to blame and yeah it's it's
+ 
+
+ align:start position:0%
+find someone to blame and yeah it's it's
+possible right but but the thing is you
+
+ align:start position:0%
+possible right but but the thing is you
+ 
+
+ align:start position:0%
+possible right but but the thing is you
+you accurately find the person to blame
+
+ align:start position:0%
+you accurately find the person to blame
+ 
+
+ align:start position:0%
+you accurately find the person to blame
+if Carol accepts the HDL C and then a
+
+ align:start position:0%
+if Carol accepts the HDL C and then a
+ 
+
+ align:start position:0%
+if Carol accepts the HDL C and then a
+split second later unplugs their
+
+ align:start position:0%
+split second later unplugs their
+ 
+
+ align:start position:0%
+split second later unplugs their
+computer Bob's like wow okay fine I'm
+
+ align:start position:0%
+computer Bob's like wow okay fine I'm
+ 
+
+ align:start position:0%
+computer Bob's like wow okay fine I'm
+closing the channel you just did
+
+ align:start position:0%
+closing the channel you just did
+ 
+
+ align:start position:0%
+closing the channel you just did
+something really annoying and if I don't
+
+ align:start position:0%
+something really annoying and if I don't
+ 
+
+ align:start position:0%
+something really annoying and if I don't
+you know Bob's like if I don't close
+
+ align:start position:0%
+you know Bob's like if I don't close
+ 
+
+ align:start position:0%
+you know Bob's like if I don't close
+this channel Alice isn't gonna close the
+
+ align:start position:0%
+this channel Alice isn't gonna close the
+ 
+
+ align:start position:0%
+this channel Alice isn't gonna close the
+channel on me because alice is gonna
+
+ align:start position:0%
+channel on me because alice is gonna
+ 
+
+ align:start position:0%
+channel on me because alice is gonna
+think I'm the one acting weird so yeah
+
+ align:start position:0%
+think I'm the one acting weird so yeah
+ 
+
+ align:start position:0%
+think I'm the one acting weird so yeah
+there's there's all sorts of weird edge
+
+ align:start position:0%
+there's there's all sorts of weird edge
+ 
+
+ align:start position:0%
+there's there's all sorts of weird edge
+cases there's all sorts of weird stuff
+
+ align:start position:0%
+cases there's all sorts of weird stuff
+ 
+
+ align:start position:0%
+cases there's all sorts of weird stuff
+that could happen
+
+ align:start position:0%
+that could happen
+ 
+
+ align:start position:0%
+that could happen
+it's definitely more complicated than
+
+ align:start position:0%
+it's definitely more complicated than
+ 
+
+ align:start position:0%
+it's definitely more complicated than
+just the straight-up UTX I was in
+
+ align:start position:0%
+just the straight-up UTX I was in
+ 
+
+ align:start position:0%
+just the straight-up UTX I was in
+Bitcoin yes it was like couldn't counter
+
+ align:start position:0%
+Bitcoin yes it was like couldn't counter
+ 
+
+ align:start position:0%
+Bitcoin yes it was like couldn't counter
+will respond to bulb and then won't be
+
+ align:start position:0%
+will respond to bulb and then won't be
+ 
+
+ align:start position:0%
+will respond to bulb and then won't be
+malicious and close the channel and then
+
+ align:start position:0%
+malicious and close the channel and then
+ 
+
+ align:start position:0%
+malicious and close the channel and then
+say hey Alice yep
+
+ align:start position:0%
+say hey Alice yep
+ 
+
+ align:start position:0%
+say hey Alice yep
+it's okay Bob Bob blames Carol Carol
+
+ align:start position:0%
+it's okay Bob Bob blames Carol Carol
+ 
+
+ align:start position:0%
+it's okay Bob Bob blames Carol Carol
+says no was actually Bob from Alice's
+
+ align:start position:0%
+says no was actually Bob from Alice's
+ 
+
+ align:start position:0%
+says no was actually Bob from Alice's
+point of view like whatever like
+
+ align:start position:0%
+point of view like whatever like
+ 
+
+ align:start position:0%
+point of view like whatever like
+something got close there was a cost to
+
+ align:start position:0%
+something got close there was a cost to
+ 
+
+ align:start position:0%
+something got close there was a cost to
+adding this HT you know there was a cost
+
+ align:start position:0%
+adding this HT you know there was a cost
+ 
+
+ align:start position:0%
+adding this HT you know there was a cost
+to having me stuck with this hdl-c for
+
+ align:start position:0%
+to having me stuck with this hdl-c for
+ 
+
+ align:start position:0%
+to having me stuck with this hdl-c for
+five hours write something on chain
+
+ align:start position:0%
+five hours write something on chain
+ 
+
+ align:start position:0%
+five hours write something on chain
+happened so so like the thing is having
+
+ align:start position:0%
+happened so so like the thing is having
+ 
+
+ align:start position:0%
+happened so so like the thing is having
+one hdl-c stuck for a few hours it's no
+
+ align:start position:0%
+one hdl-c stuck for a few hours it's no
+ 
+
+ align:start position:0%
+one hdl-c stuck for a few hours it's no
+big deal
+
+ align:start position:0%
+big deal
+ 
+
+ align:start position:0%
+big deal
+after five o'clock Alice just goes to
+
+ align:start position:0%
+after five o'clock Alice just goes to
+ 
+
+ align:start position:0%
+after five o'clock Alice just goes to
+bombs like look well let's clear it
+
+ align:start position:0%
+bombs like look well let's clear it
+ 
+
+ align:start position:0%
+bombs like look well let's clear it
+right you don't know are you if you knew
+
+ align:start position:0%
+right you don't know are you if you knew
+ 
+
+ align:start position:0%
+right you don't know are you if you knew
+are you would have told me by now so
+
+ align:start position:0%
+are you would have told me by now so
+ 
+
+ align:start position:0%
+are you would have told me by now so
+let's just get rid of this thing and
+
+ align:start position:0%
+let's just get rid of this thing and
+ 
+
+ align:start position:0%
+let's just get rid of this thing and
+Bob's like yeah fine and they clear it
+
+ align:start position:0%
+Bob's like yeah fine and they clear it
+ 
+
+ align:start position:0%
+Bob's like yeah fine and they clear it
+out so the idea is it's it's not a big
+
+ align:start position:0%
+out so the idea is it's it's not a big
+ 
+
+ align:start position:0%
+out so the idea is it's it's not a big
+attack if you only have one of them it's
+
+ align:start position:0%
+attack if you only have one of them it's
+ 
+
+ align:start position:0%
+attack if you only have one of them it's
+a you want some cost to performing that
+
+ align:start position:0%
+a you want some cost to performing that
+ 
+
+ align:start position:0%
+a you want some cost to performing that
+and so if Bob closes the channel whether
+
+ align:start position:0%
+and so if Bob closes the channel whether
+ 
+
+ align:start position:0%
+and so if Bob closes the channel whether
+its kara's fault or Bob's fault
+
+ align:start position:0%
+its kara's fault or Bob's fault
+ 
+
+ align:start position:0%
+its kara's fault or Bob's fault
+alice is sort of like look well
+
+ align:start position:0%
+alice is sort of like look well
+ 
+
+ align:start position:0%
+alice is sort of like look well
+something happened so someone's bearing
+
+ align:start position:0%
+something happened so someone's bearing
+ 
+
+ align:start position:0%
+something happened so someone's bearing
+the cost for this so they're not going
+
+ align:start position:0%
+the cost for this so they're not going
+ 
+
+ align:start position:0%
+the cost for this so they're not going
+to keep doing it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you needed he actually need hours
+
+ align:start position:0%
+you needed he actually need hours
+ 
+
+ align:start position:0%
+you needed he actually need hours
+because Oh other attack let's say this
+
+ align:start position:0%
+because Oh other attack let's say this
+ 
+
+ align:start position:0%
+because Oh other attack let's say this
+was for let's say these were both five
+
+ align:start position:0%
+was for let's say these were both five
+ 
+
+ align:start position:0%
+was for let's say these were both five
+o'clock right and then Carol closes the
+
+ align:start position:0%
+o'clock right and then Carol closes the
+ 
+
+ align:start position:0%
+o'clock right and then Carol closes the
+channel right at five o'clock grabs the
+
+ align:start position:0%
+channel right at five o'clock grabs the
+ 
+
+ align:start position:0%
+channel right at five o'clock grabs the
+you know right before five o'clock Carol
+
+ align:start position:0%
+you know right before five o'clock Carol
+ 
+
+ align:start position:0%
+you know right before five o'clock Carol
+grabs it you know close to the channel
+
+ align:start position:0%
+grabs it you know close to the channel
+ 
+
+ align:start position:0%
+grabs it you know close to the channel
+uses are grabs it Bob then says oh shoot
+
+ align:start position:0%
+uses are grabs it Bob then says oh shoot
+ 
+
+ align:start position:0%
+uses are grabs it Bob then says oh shoot
+there's our Alice is like no Alice
+
+ align:start position:0%
+there's our Alice is like no Alice
+ 
+
+ align:start position:0%
+there's our Alice is like no Alice
+closes the channel right it right after
+
+ align:start position:0%
+closes the channel right it right after
+ 
+
+ align:start position:0%
+closes the channel right it right after
+five and grabs her by by signing with
+
+ align:start position:0%
+five and grabs her by by signing with
+ 
+
+ align:start position:0%
+five and grabs her by by signing with
+her key and above Bob screwed right
+
+ align:start position:0%
+her key and above Bob screwed right
+ 
+
+ align:start position:0%
+her key and above Bob screwed right
+Bob's like shoot wait Carol just got the
+
+ align:start position:0%
+Bob's like shoot wait Carol just got the
+ 
+
+ align:start position:0%
+Bob's like shoot wait Carol just got the
+money from me using our and then Alice
+
+ align:start position:0%
+money from me using our and then Alice
+ 
+
+ align:start position:0%
+money from me using our and then Alice
+closes got the money for me using the
+
+ align:start position:0%
+closes got the money for me using the
+ 
+
+ align:start position:0%
+closes got the money for me using the
+time out and I didn't get anything right
+
+ align:start position:0%
+time out and I didn't get anything right
+ 
+
+ align:start position:0%
+time out and I didn't get anything right
+I lost the money on this side and I
+
+ align:start position:0%
+I lost the money on this side and I
+ 
+
+ align:start position:0%
+I lost the money on this side and I
+didn't get the money on this side so Bob
+
+ align:start position:0%
+didn't get the money on this side so Bob
+ 
+
+ align:start position:0%
+didn't get the money on this side so Bob
+just got Bob just had a huge loss there
+
+ align:start position:0%
+just got Bob just had a huge loss there
+ 
+
+ align:start position:0%
+just got Bob just had a huge loss there
+so Bob really wants to make sure that
+
+ align:start position:0%
+so Bob really wants to make sure that
+ 
+
+ align:start position:0%
+so Bob really wants to make sure that
+this is later like Alice can't get the
+
+ align:start position:0%
+this is later like Alice can't get the
+ 
+
+ align:start position:0%
+this is later like Alice can't get the
+money until well after Carol can get the
+
+ align:start position:0%
+money until well after Carol can get the
+ 
+
+ align:start position:0%
+money until well after Carol can get the
+money with the timeout function I'm
+
+ align:start position:0%
+money with the timeout function I'm
+ 
+
+ align:start position:0%
+money with the timeout function I'm
+sorry that well after Bob can get his
+
+ align:start position:0%
+sorry that well after Bob can get his
+ 
+
+ align:start position:0%
+sorry that well after Bob can get his
+money with the time yeah well they all
+
+ align:start position:0%
+money with the time yeah well they all
+ 
+
+ align:start position:0%
+money with the time yeah well they all
+hold on Bob sets this time yes and Alice
+
+ align:start position:0%
+hold on Bob sets this time yes and Alice
+ 
+
+ align:start position:0%
+hold on Bob sets this time yes and Alice
+sets this time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah he has to make sure his is earlier
+
+ align:start position:0%
+yeah he has to make sure his is earlier
+ 
+
+ align:start position:0%
+yeah he has to make sure his is earlier
+and and continuing that right so if
+
+ align:start position:0%
+and and continuing that right so if
+ 
+
+ align:start position:0%
+and and continuing that right so if
+Carol opens a channel if Carol makes an
+
+ align:start position:0%
+Carol opens a channel if Carol makes an
+ 
+
+ align:start position:0%
+Carol opens a channel if Carol makes an
+HDL City today if she makes it at 3
+
+ align:start position:0%
+HDL City today if she makes it at 3
+ 
+
+ align:start position:0%
+HDL City today if she makes it at 3
+o'clock or whatever I don't remember
+
+ align:start position:0%
+o'clock or whatever I don't remember
+ 
+
+ align:start position:0%
+o'clock or whatever I don't remember
+what the defaults are and the different
+
+ align:start position:0%
+what the defaults are and the different
+ 
+
+ align:start position:0%
+what the defaults are and the different
+like like I do it all on test net and so
+
+ align:start position:0%
+like like I do it all on test net and so
+ 
+
+ align:start position:0%
+like like I do it all on test net and so
+in test net I do like five blocks
+
+ align:start position:0%
+in test net I do like five blocks
+ 
+
+ align:start position:0%
+in test net I do like five blocks
+because who cares but I think in the
+
+ align:start position:0%
+because who cares but I think in the
+ 
+
+ align:start position:0%
+because who cares but I think in the
+main net ones people are trying out they
+
+ align:start position:0%
+main net ones people are trying out they
+ 
+
+ align:start position:0%
+main net ones people are trying out they
+do quite a bit more because it's better
+
+ align:start position:0%
+do quite a bit more because it's better
+ 
+
+ align:start position:0%
+do quite a bit more because it's better
+to have your money stuck for a day than
+
+ align:start position:0%
+to have your money stuck for a day than
+ 
+
+ align:start position:0%
+to have your money stuck for a day than
+to lose it I guess so so you can make
+
+ align:start position:0%
+to lose it I guess so so you can make
+ 
+
+ align:start position:0%
+to lose it I guess so so you can make
+different time outs and stuff like that
+
+ align:start position:0%
+different time outs and stuff like that
+ 
+
+ align:start position:0%
+different time outs and stuff like that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+what else I'm basically done there's a
+
+ align:start position:0%
+what else I'm basically done there's a
+ 
+
+ align:start position:0%
+what else I'm basically done there's a
+whole bunch of other cool things you can
+
+ align:start position:0%
+whole bunch of other cool things you can
+ 
+
+ align:start position:0%
+whole bunch of other cool things you can
+do it and I'll I think I'll talk about
+
+ align:start position:0%
+do it and I'll I think I'll talk about
+ 
+
+ align:start position:0%
+do it and I'll I think I'll talk about
+that next time yeah you can do cross
+
+ align:start position:0%
+that next time yeah you can do cross
+ 
+
+ align:start position:0%
+that next time yeah you can do cross
+chain swaps so this is preview of after
+
+ align:start position:0%
+chain swaps so this is preview of after
+ 
+
+ align:start position:0%
+chain swaps so this is preview of after
+great this channel and this channel do
+
+ align:start position:0%
+great this channel and this channel do
+ 
+
+ align:start position:0%
+great this channel and this channel do
+not need to be on the same blockchain
+
+ align:start position:0%
+not need to be on the same blockchain
+ 
+
+ align:start position:0%
+not need to be on the same blockchain
+totally fine for this to be Bitcoin has
+
+ align:start position:0%
+totally fine for this to be Bitcoin has
+ 
+
+ align:start position:0%
+totally fine for this to be Bitcoin has
+to be like coin or this to be dogecoin
+
+ align:start position:0%
+to be like coin or this to be dogecoin
+ 
+
+ align:start position:0%
+to be like coin or this to be dogecoin
+you know like it actually totally works
+
+ align:start position:0%
+you know like it actually totally works
+ 
+
+ align:start position:0%
+you know like it actually totally works
+so that's kind of cool security so you
+
+ align:start position:0%
+so that's kind of cool security so you
+ 
+
+ align:start position:0%
+so that's kind of cool security so you
+can monitor you want to monitor your
+
+ align:start position:0%
+can monitor you want to monitor your
+ 
+
+ align:start position:0%
+can monitor you want to monitor your
+channels in case someone tries to rip
+
+ align:start position:0%
+channels in case someone tries to rip
+ 
+
+ align:start position:0%
+channels in case someone tries to rip
+you off you can outsource that in a nice
+
+ align:start position:0%
+you off you can outsource that in a nice
+ 
+
+ align:start position:0%
+you off you can outsource that in a nice
+way where you give it to a third party
+
+ align:start position:0%
+way where you give it to a third party
+ 
+
+ align:start position:0%
+way where you give it to a third party
+and say hey I've got this channel watch
+
+ align:start position:0%
+and say hey I've got this channel watch
+ 
+
+ align:start position:0%
+and say hey I've got this channel watch
+it for me not only that I've got a
+
+ align:start position:0%
+it for me not only that I've got a
+ 
+
+ align:start position:0%
+it for me not only that I've got a
+channel watch it for me I'm not gonna
+
+ align:start position:0%
+channel watch it for me I'm not gonna
+ 
+
+ align:start position:0%
+channel watch it for me I'm not gonna
+tell you what channel it is how much
+
+ align:start position:0%
+tell you what channel it is how much
+ 
+
+ align:start position:0%
+tell you what channel it is how much
+money you have basically anything and
+
+ align:start position:0%
+money you have basically anything and
+ 
+
+ align:start position:0%
+money you have basically anything and
+you can still protect it for me so
+
+ align:start position:0%
+you can still protect it for me so
+ 
+
+ align:start position:0%
+you can still protect it for me so
+that's kind of cool you can anonymously
+
+ align:start position:0%
+that's kind of cool you can anonymously
+ 
+
+ align:start position:0%
+that's kind of cool you can anonymously
+view that stuff case she'll sees I just
+
+ align:start position:0%
+view that stuff case she'll sees I just
+ 
+
+ align:start position:0%
+view that stuff case she'll sees I just
+talked about dust and fees gets really
+
+ align:start position:0%
+talked about dust and fees gets really
+ 
+
+ align:start position:0%
+talked about dust and fees gets really
+ugly there's a lot of cool stuff you can
+
+ align:start position:0%
+ugly there's a lot of cool stuff you can
+ 
+
+ align:start position:0%
+ugly there's a lot of cool stuff you can
+do so I think that the schedule is I'll
+
+ align:start position:0%
+do so I think that the schedule is I'll
+ 
+
+ align:start position:0%
+do so I think that the schedule is I'll
+talk about the rest of lightning on
+
+ align:start position:0%
+talk about the rest of lightning on
+ 
+
+ align:start position:0%
+talk about the rest of lightning on
+Monday after Spring Break and then go
+
+ align:start position:0%
+Monday after Spring Break and then go
+ 
+
+ align:start position:0%
+Monday after Spring Break and then go
+into discrete log contracts which is
+
+ align:start position:0%
+into discrete log contracts which is
+ 
+
+ align:start position:0%
+into discrete log contracts which is
+another similar construction on the
+
+ align:start position:0%
+another similar construction on the
+ 
+
+ align:start position:0%
+another similar construction on the
+Wednesday after ok any questions about
+
+ align:start position:0%
+Wednesday after ok any questions about
+ 
+
+ align:start position:0%
+Wednesday after ok any questions about
+all this stuff
+
+ align:start position:0%
+all this stuff
+ 
+
+ align:start position:0%
+all this stuff
+I'm sure yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+miners miners Kim can make timeouts not
+
+ align:start position:0%
+miners miners Kim can make timeouts not
+ 
+
+ align:start position:0%
+miners miners Kim can make timeouts not
+happen right if there's a lot of if
+
+ align:start position:0%
+happen right if there's a lot of if
+ 
+
+ align:start position:0%
+happen right if there's a lot of if
+there's their coordinated they can say
+
+ align:start position:0%
+there's their coordinated they can say
+ 
+
+ align:start position:0%
+there's their coordinated they can say
+we're just gonna not accept this
+
+ align:start position:0%
+we're just gonna not accept this
+ 
+
+ align:start position:0%
+we're just gonna not accept this
+transaction till later so that's bad
+
+ align:start position:0%
+transaction till later so that's bad
+ 
+
+ align:start position:0%
+transaction till later so that's bad
+yeah there's a there's there's all other
+
+ align:start position:0%
+yeah there's a there's there's all other
+ 
+
+ align:start position:0%
+yeah there's a there's there's all other
+weird attack vectors the one that I
+
+ align:start position:0%
+weird attack vectors the one that I
+ 
+
+ align:start position:0%
+weird attack vectors the one that I
+worry about most not most the one that I
+
+ align:start position:0%
+worry about most not most the one that I
+ 
+
+ align:start position:0%
+worry about most not most the one that I
+worry about is if you make a backup of
+
+ align:start position:0%
+worry about is if you make a backup of
+ 
+
+ align:start position:0%
+worry about is if you make a backup of
+your wallet and you restore it you lose
+
+ align:start position:0%
+your wallet and you restore it you lose
+ 
+
+ align:start position:0%
+your wallet and you restore it you lose
+all your money so you make a backup here
+
+ align:start position:0%
+all your money so you make a backup here
+ 
+
+ align:start position:0%
+all your money so you make a backup here
+at state two onto your USB stick and you
+
+ align:start position:0%
+at state two onto your USB stick and you
+ 
+
+ align:start position:0%
+at state two onto your USB stick and you
+go home and you drop your laptop in the
+
+ align:start position:0%
+go home and you drop your laptop in the
+ 
+
+ align:start position:0%
+go home and you drop your laptop in the
+pool and you're like shoot well good
+
+ align:start position:0%
+pool and you're like shoot well good
+ 
+
+ align:start position:0%
+pool and you're like shoot well good
+thing I got my backup and then you were
+
+ align:start position:0%
+thing I got my backup and then you were
+ 
+
+ align:start position:0%
+thing I got my backup and then you were
+well sorry you may come back up here at
+
+ align:start position:0%
+well sorry you may come back up here at
+ 
+
+ align:start position:0%
+well sorry you may come back up here at
+work on your USB stick and then you keep
+
+ align:start position:0%
+work on your USB stick and then you keep
+ 
+
+ align:start position:0%
+work on your USB stick and then you keep
+spending money and then you drop your
+
+ align:start position:0%
+spending money and then you drop your
+ 
+
+ align:start position:0%
+spending money and then you drop your
+laptop in the pool and then you restore
+
+ align:start position:0%
+laptop in the pool and then you restore
+ 
+
+ align:start position:0%
+laptop in the pool and then you restore
+from your USB stick to here and then you
+
+ align:start position:0%
+from your USB stick to here and then you
+ 
+
+ align:start position:0%
+from your USB stick to here and then you
+try to broadcast this but you've already
+
+ align:start position:0%
+try to broadcast this but you've already
+ 
+
+ align:start position:0%
+try to broadcast this but you've already
+revealed your private keys and so Bob's
+
+ align:start position:0%
+revealed your private keys and so Bob's
+ 
+
+ align:start position:0%
+revealed your private keys and so Bob's
+just like what like that's red like you
+
+ align:start position:0%
+just like what like that's red like you
+ 
+
+ align:start position:0%
+just like what like that's red like you
+you revealed it and then he takes all
+
+ align:start position:0%
+you revealed it and then he takes all
+ 
+
+ align:start position:0%
+you revealed it and then he takes all
+the money so yeah don't make backups
+
+ align:start position:0%
+the money so yeah don't make backups
+ 
+
+ align:start position:0%
+the money so yeah don't make backups
+it's like the the reason I worry about
+
+ align:start position:0%
+it's like the the reason I worry about
+ 
+
+ align:start position:0%
+it's like the the reason I worry about
+it is it's very counterintuitive there's
+
+ align:start position:0%
+it is it's very counterintuitive there's
+ 
+
+ align:start position:0%
+it is it's very counterintuitive there's
+nothing in the software that does this
+
+ align:start position:0%
+nothing in the software that does this
+ 
+
+ align:start position:0%
+nothing in the software that does this
+right the software I can write like you
+
+ align:start position:0%
+right the software I can write like you
+ 
+
+ align:start position:0%
+right the software I can write like you
+know don't make backups always only keep
+
+ align:start position:0%
+know don't make backups always only keep
+ 
+
+ align:start position:0%
+know don't make backups always only keep
+this but you just copy the files and it
+
+ align:start position:0%
+this but you just copy the files and it
+ 
+
+ align:start position:0%
+this but you just copy the files and it
+seems like the kind of thing people
+
+ align:start position:0%
+seems like the kind of thing people
+ 
+
+ align:start position:0%
+seems like the kind of thing people
+might do and you know put warnings and
+
+ align:start position:0%
+might do and you know put warnings and
+ 
+
+ align:start position:0%
+might do and you know put warnings and
+the readme is and stuff so that's kind
+
+ align:start position:0%
+the readme is and stuff so that's kind
+ 
+
+ align:start position:0%
+the readme is and stuff so that's kind
+of a big risk so there's a lot of like
+
+ align:start position:0%
+of a big risk so there's a lot of like
+ 
+
+ align:start position:0%
+of a big risk so there's a lot of like
+how do we make this safe how do and like
+
+ align:start position:0%
+how do we make this safe how do and like
+ 
+
+ align:start position:0%
+how do we make this safe how do and like
+a lot of people criticize it like this
+
+ align:start position:0%
+a lot of people criticize it like this
+ 
+
+ align:start position:0%
+a lot of people criticize it like this
+is too complicated there's like enormous
+
+ align:start position:0%
+is too complicated there's like enormous
+ 
+
+ align:start position:0%
+is too complicated there's like enormous
+communities on the internet that hate
+
+ align:start position:0%
+communities on the internet that hate
+ 
+
+ align:start position:0%
+communities on the internet that hate
+this and hate me and mmm go to our BTCC
+
+ align:start position:0%
+this and hate me and mmm go to our BTCC
+ 
+
+ align:start position:0%
+this and hate me and mmm go to our BTCC
+don't like the lightning Network I don't
+
+ align:start position:0%
+don't like the lightning Network I don't
+ 
+
+ align:start position:0%
+don't like the lightning Network I don't
+mean the other kind it's like well you
+
+ align:start position:0%
+mean the other kind it's like well you
+ 
+
+ align:start position:0%
+mean the other kind it's like well you
+don't like it you don't to use it right
+
+ align:start position:0%
+don't like it you don't to use it right
+ 
+
+ align:start position:0%
+don't like it you don't to use it right
+I'm just writing the software for free
+
+ align:start position:0%
+I'm just writing the software for free
+ 
+
+ align:start position:0%
+I'm just writing the software for free
+for you guys but anyway but yeah and and
+
+ align:start position:0%
+for you guys but anyway but yeah and and
+ 
+
+ align:start position:0%
+for you guys but anyway but yeah and and
+you know there's legitimate like this is
+
+ align:start position:0%
+you know there's legitimate like this is
+ 
+
+ align:start position:0%
+you know there's legitimate like this is
+kind of complicated this might not it's
+
+ align:start position:0%
+kind of complicated this might not it's
+ 
+
+ align:start position:0%
+kind of complicated this might not it's
+not gonna work for everything there's
+
+ align:start position:0%
+not gonna work for everything there's
+ 
+
+ align:start position:0%
+not gonna work for everything there's
+all sorts of you know things that that
+
+ align:start position:0%
+all sorts of you know things that that
+ 
+
+ align:start position:0%
+all sorts of you know things that that
+limit limits to this too
\ No newline at end of file
diff --git a/Ii6UtH6h2jY.txt b/Ii6UtH6h2jY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f889f4f401e7d4cae1c0e31f407b470c7737a9e7
--- /dev/null
+++ b/Ii6UtH6h2jY.txt
@@ -0,0 +1,11378 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay um I was at uh Atlanta
+
+ align:start position:0%
+ocw.mit.edu okay um I was at uh Atlanta
+ 
+
+ align:start position:0%
+ocw.mit.edu okay um I was at uh Atlanta
+yesterday and uh attending a conference
+
+ align:start position:0%
+yesterday and uh attending a conference
+ 
+
+ align:start position:0%
+yesterday and uh attending a conference
+at the expert uh from the disc drive
+
+ align:start position:0%
+at the expert uh from the disc drive
+ 
+
+ align:start position:0%
+at the expert uh from the disc drive
+industry I know I know her well and uh
+
+ align:start position:0%
+industry I know I know her well and uh
+ 
+
+ align:start position:0%
+industry I know I know her well and uh
+you remember I was just saying that the
+
+ align:start position:0%
+you remember I was just saying that the
+ 
+
+ align:start position:0%
+you remember I was just saying that the
+disc hat and separation is below 10 n do
+
+ align:start position:0%
+disc hat and separation is below 10 n do
+ 
+
+ align:start position:0%
+disc hat and separation is below 10 n do
+you know how much what's the separation
+
+ align:start position:0%
+you know how much what's the separation
+ 
+
+ align:start position:0%
+you know how much what's the separation
+now two that's just say about 1.5
+
+ align:start position:0%
+now two that's just say about 1.5
+ 
+
+ align:start position:0%
+now two that's just say about 1.5
+nmet that's the that's that's what
+
+ align:start position:0%
+nmet that's the that's that's what
+ 
+
+ align:start position:0%
+nmet that's the that's that's what
+everybody has in the computer it's
+
+ align:start position:0%
+everybody has in the computer it's
+ 
+
+ align:start position:0%
+everybody has in the computer it's
+amazing uh
+
+ align:start position:0%
+amazing uh
+ 
+
+ align:start position:0%
+amazing uh
+technology we just go for solid state
+
+ align:start position:0%
+technology we just go for solid state
+ 
+
+ align:start position:0%
+technology we just go for solid state
+huh we just go for solid
+
+ align:start position:0%
+huh we just go for solid
+ 
+
+ align:start position:0%
+huh we just go for solid
+well where you how much can push right
+
+ align:start position:0%
+well where you how much can push right
+ 
+
+ align:start position:0%
+well where you how much can push right
+but uh um the uh this is a this was
+
+ align:start position:0%
+but uh um the uh this is a this was
+ 
+
+ align:start position:0%
+but uh um the uh this is a this was
+actually a labmate of mine and uh uh she
+
+ align:start position:0%
+actually a labmate of mine and uh uh she
+ 
+
+ align:start position:0%
+actually a labmate of mine and uh uh she
+uh worked on N scale heat transfer and
+
+ align:start position:0%
+uh worked on N scale heat transfer and
+ 
+
+ align:start position:0%
+uh worked on N scale heat transfer and
+say that's a perfect place because what
+
+ align:start position:0%
+say that's a perfect place because what
+ 
+
+ align:start position:0%
+say that's a perfect place because what
+what they're doing is uh uh the magnatic
+
+ align:start position:0%
+what they're doing is uh uh the magnatic
+ 
+
+ align:start position:0%
+what they're doing is uh uh the magnatic
+when you make it a very small domain you
+
+ align:start position:0%
+when you make it a very small domain you
+ 
+
+ align:start position:0%
+when you make it a very small domain you
+actually cannot use a normal magnetic
+
+ align:start position:0%
+actually cannot use a normal magnetic
+ 
+
+ align:start position:0%
+actually cannot use a normal magnetic
+field to flip the uh magnetic domain
+
+ align:start position:0%
+field to flip the uh magnetic domain
+ 
+
+ align:start position:0%
+field to flip the uh magnetic domain
+because uh otherwise the at room
+
+ align:start position:0%
+because uh otherwise the at room
+ 
+
+ align:start position:0%
+because uh otherwise the at room
+temperature is just spontaneous flips
+
+ align:start position:0%
+temperature is just spontaneous flips
+ 
+
+ align:start position:0%
+temperature is just spontaneous flips
+back so they have to use very hard
+
+ align:start position:0%
+back so they have to use very hard
+ 
+
+ align:start position:0%
+back so they have to use very hard
+magnet magnet and uh in that case they
+
+ align:start position:0%
+magnet magnet and uh in that case they
+ 
+
+ align:start position:0%
+magnet magnet and uh in that case they
+have to heat up the domain so they have
+
+ align:start position:0%
+have to heat up the domain so they have
+ 
+
+ align:start position:0%
+have to heat up the domain so they have
+to heat up a nano domain first and then
+
+ align:start position:0%
+to heat up a nano domain first and then
+ 
+
+ align:start position:0%
+to heat up a nano domain first and then
+uh apply magnetic field to
+
+ align:start position:0%
+uh apply magnetic field to
+ 
+
+ align:start position:0%
+uh apply magnetic field to
+right um so I thought uh I'll share this
+
+ align:start position:0%
+right um so I thought uh I'll share this
+ 
+
+ align:start position:0%
+right um so I thought uh I'll share this
+story with you talk a little bit more
+
+ align:start position:0%
+story with you talk a little bit more
+ 
+
+ align:start position:0%
+story with you talk a little bit more
+about that technology later on as we
+
+ align:start position:0%
+about that technology later on as we
+ 
+
+ align:start position:0%
+about that technology later on as we
+learn so coming back to to um last
+
+ align:start position:0%
+learn so coming back to to um last
+ 
+
+ align:start position:0%
+learn so coming back to to um last
+lecture uh what we talked uh is the
+
+ align:start position:0%
+lecture uh what we talked uh is the
+ 
+
+ align:start position:0%
+lecture uh what we talked uh is the
+reciprocal space um the continuation and
+
+ align:start position:0%
+reciprocal space um the continuation and
+ 
+
+ align:start position:0%
+reciprocal space um the continuation and
+prove the bra condition and that's the
+
+ align:start position:0%
+prove the bra condition and that's the
+ 
+
+ align:start position:0%
+prove the bra condition and that's the
+uh uh say when you do a transmission
+
+ align:start position:0%
+uh uh say when you do a transmission
+ 
+
+ align:start position:0%
+uh uh say when you do a transmission
+electron microscope or you do a x-ray
+
+ align:start position:0%
+electron microscope or you do a x-ray
+ 
+
+ align:start position:0%
+electron microscope or you do a x-ray
+bra condition is the one when you look
+
+ align:start position:0%
+bra condition is the one when you look
+ 
+
+ align:start position:0%
+bra condition is the one when you look
+at defraction
+
+ align:start position:0%
+at defraction
+ 
+
+ align:start position:0%
+at defraction
+patterns and uh then we moved down to
+
+ align:start position:0%
+patterns and uh then we moved down to
+ 
+
+ align:start position:0%
+patterns and uh then we moved down to
+discuss the energy uh of the atomic
+
+ align:start position:0%
+discuss the energy uh of the atomic
+ 
+
+ align:start position:0%
+discuss the energy uh of the atomic
+vibration in
+
+ align:start position:0%
+vibration in
+ 
+
+ align:start position:0%
+vibration in
+crystals and uh uh um so we introduced
+
+ align:start position:0%
+crystals and uh uh um so we introduced
+ 
+
+ align:start position:0%
+crystals and uh uh um so we introduced
+the Fons right that's just the uh say we
+
+ align:start position:0%
+the Fons right that's just the uh say we
+ 
+
+ align:start position:0%
+the Fons right that's just the uh say we
+solve the Newton Second Law so it's a
+
+ align:start position:0%
+solve the Newton Second Law so it's a
+ 
+
+ align:start position:0%
+solve the Newton Second Law so it's a
+first is a Continuum approach it's a
+
+ align:start position:0%
+first is a Continuum approach it's a
+ 
+
+ align:start position:0%
+first is a Continuum approach it's a
+classical approach but the treating the
+
+ align:start position:0%
+classical approach but the treating the
+ 
+
+ align:start position:0%
+classical approach but the treating the
+atoms as disr and we got the dispersion
+
+ align:start position:0%
+atoms as disr and we got the dispersion
+ 
+
+ align:start position:0%
+atoms as disr and we got the dispersion
+between the vibrational
+
+ align:start position:0%
+between the vibrational
+ 
+
+ align:start position:0%
+between the vibrational
+frequency and the W vector and the V
+
+ align:start position:0%
+frequency and the W vector and the V
+ 
+
+ align:start position:0%
+frequency and the W vector and the V
+Vector is similarly as in the case of
+
+ align:start position:0%
+Vector is similarly as in the case of
+ 
+
+ align:start position:0%
+Vector is similarly as in the case of
+electron are discretized I have if I
+
+ align:start position:0%
+electron are discretized I have if I
+ 
+
+ align:start position:0%
+electron are discretized I have if I
+have n atoms in the chain and I have 2
+
+ align:start position:0%
+have n atoms in the chain and I have 2
+ 
+
+ align:start position:0%
+have n atoms in the chain and I have 2
+pi uh Over N this is the separation is 2
+
+ align:start position:0%
+pi uh Over N this is the separation is 2
+ 
+
+ align:start position:0%
+pi uh Over N this is the separation is 2
+pi over the length of the crystal n * a
+
+ align:start position:0%
+pi over the length of the crystal n * a
+ 
+
+ align:start position:0%
+pi over the length of the crystal n * a
+is the lens of the crystal right and uh
+
+ align:start position:0%
+is the lens of the crystal right and uh
+ 
+
+ align:start position:0%
+is the lens of the crystal right and uh
+uh we have acoustic branch and if I have
+
+ align:start position:0%
+uh we have acoustic branch and if I have
+ 
+
+ align:start position:0%
+uh we have acoustic branch and if I have
+more than one atom at the lest Point uh
+
+ align:start position:0%
+more than one atom at the lest Point uh
+ 
+
+ align:start position:0%
+more than one atom at the lest Point uh
+I have also after branch and acoustic
+
+ align:start position:0%
+I have also after branch and acoustic
+ 
+
+ align:start position:0%
+I have also after branch and acoustic
+branch has longitudinal and transverse
+
+ align:start position:0%
+branch has longitudinal and transverse
+ 
+
+ align:start position:0%
+branch has longitudinal and transverse
+typical longitudinal uh has a higher uh
+
+ align:start position:0%
+typical longitudinal uh has a higher uh
+ 
+
+ align:start position:0%
+typical longitudinal uh has a higher uh
+frequency and transverse lower
+
+ align:start position:0%
+frequency and transverse lower
+ 
+
+ align:start position:0%
+frequency and transverse lower
+frequency and in the case of op fullon
+
+ align:start position:0%
+frequency and in the case of op fullon
+ 
+
+ align:start position:0%
+frequency and in the case of op fullon
+this sometimes can cross over so it's
+
+ align:start position:0%
+this sometimes can cross over so it's
+ 
+
+ align:start position:0%
+this sometimes can cross over so it's
+hard to say which one has higher and
+
+ align:start position:0%
+hard to say which one has higher and
+ 
+
+ align:start position:0%
+hard to say which one has higher and
+lower but if I think if you deal with a
+
+ align:start position:0%
+lower but if I think if you deal with a
+ 
+
+ align:start position:0%
+lower but if I think if you deal with a
+polar Crystal like sodium chloride and
+
+ align:start position:0%
+polar Crystal like sodium chloride and
+ 
+
+ align:start position:0%
+polar Crystal like sodium chloride and
+uh you have always the transverse Fon
+
+ align:start position:0%
+uh you have always the transverse Fon
+ 
+
+ align:start position:0%
+uh you have always the transverse Fon
+lower and longitudal Fon op F on higher
+
+ align:start position:0%
+lower and longitudal Fon op F on higher
+ 
+
+ align:start position:0%
+lower and longitudal Fon op F on higher
+frequency so uh uh what's important
+
+ align:start position:0%
+frequency so uh uh what's important
+ 
+
+ align:start position:0%
+frequency so uh uh what's important
+later on is we simplify models and one
+
+ align:start position:0%
+later on is we simplify models and one
+ 
+
+ align:start position:0%
+later on is we simplify models and one
+way to simplify uh is the de buy so we
+
+ align:start position:0%
+way to simplify uh is the de buy so we
+ 
+
+ align:start position:0%
+way to simplify uh is the de buy so we
+trade this here uh although at the zoom
+
+ align:start position:0%
+trade this here uh although at the zoom
+ 
+
+ align:start position:0%
+trade this here uh although at the zoom
+boundary we see you can see we careful
+
+ align:start position:0%
+boundary we see you can see we careful
+ 
+
+ align:start position:0%
+boundary we see you can see we careful
+in drawing this almost like a
+
+ align:start position:0%
+in drawing this almost like a
+ 
+
+ align:start position:0%
+in drawing this almost like a
+perpendicular but say uh one
+
+ align:start position:0%
+perpendicular but say uh one
+ 
+
+ align:start position:0%
+perpendicular but say uh one
+approximation we use is approximate this
+
+ align:start position:0%
+approximation we use is approximate this
+ 
+
+ align:start position:0%
+approximation we use is approximate this
+by a street nine that's the buy model
+
+ align:start position:0%
+by a street nine that's the buy model
+ 
+
+ align:start position:0%
+by a street nine that's the buy model
+and uh the other uh is what original
+
+ align:start position:0%
+and uh the other uh is what original
+ 
+
+ align:start position:0%
+and uh the other uh is what original
+Einstein proposed just a constant
+
+ align:start position:0%
+Einstein proposed just a constant
+ 
+
+ align:start position:0%
+Einstein proposed just a constant
+frequency that's a Einstein model and
+
+ align:start position:0%
+frequency that's a Einstein model and
+ 
+
+ align:start position:0%
+frequency that's a Einstein model and
+you can see that Einstein model is
+
+ align:start position:0%
+you can see that Einstein model is
+ 
+
+ align:start position:0%
+you can see that Einstein model is
+closer for the optic fance or the buy
+
+ align:start position:0%
+closer for the optic fance or the buy
+ 
+
+ align:start position:0%
+closer for the optic fance or the buy
+model is closer for the uh um say um
+
+ align:start position:0%
+model is closer for the uh um say um
+ 
+
+ align:start position:0%
+model is closer for the uh um say um
+acoustic
+
+ align:start position:0%
+acoustic
+ 
+
+ align:start position:0%
+acoustic
+fance uh so that's uh uh where we were
+
+ align:start position:0%
+fance uh so that's uh uh where we were
+ 
+
+ align:start position:0%
+fance uh so that's uh uh where we were
+and uh with that uh if you recall what
+
+ align:start position:0%
+and uh with that uh if you recall what
+ 
+
+ align:start position:0%
+and uh with that uh if you recall what
+we have talked so far very fast right we
+
+ align:start position:0%
+we have talked so far very fast right we
+ 
+
+ align:start position:0%
+we have talked so far very fast right we
+talked about energy levels first in
+
+ align:start position:0%
+talked about energy levels first in
+ 
+
+ align:start position:0%
+talked about energy levels first in
+isolated atoms and
+
+ align:start position:0%
+isolated atoms and
+ 
+
+ align:start position:0%
+isolated atoms and
+molecules and that's vibrational
+
+ align:start position:0%
+molecules and that's vibrational
+ 
+
+ align:start position:0%
+molecules and that's vibrational
+translational and electronic rotational
+
+ align:start position:0%
+translational and electronic rotational
+ 
+
+ align:start position:0%
+translational and electronic rotational
+and then we extend to crystals and uh we
+
+ align:start position:0%
+and then we extend to crystals and uh we
+ 
+
+ align:start position:0%
+and then we extend to crystals and uh we
+view we say the the treatment the best
+
+ align:start position:0%
+view we say the the treatment the best
+ 
+
+ align:start position:0%
+view we say the the treatment the best
+treatment we've done is one dimension
+
+ align:start position:0%
+treatment we've done is one dimension
+ 
+
+ align:start position:0%
+treatment we've done is one dimension
+and then we say okay what's the if you
+
+ align:start position:0%
+and then we say okay what's the if you
+ 
+
+ align:start position:0%
+and then we say okay what's the if you
+look at the three dimension each
+
+ align:start position:0%
+look at the three dimension each
+ 
+
+ align:start position:0%
+look at the three dimension each
+Direction has different periodicity and
+
+ align:start position:0%
+Direction has different periodicity and
+ 
+
+ align:start position:0%
+Direction has different periodicity and
+different potential so your curve may
+
+ align:start position:0%
+different potential so your curve may
+ 
+
+ align:start position:0%
+different potential so your curve may
+look different right and uh uh with that
+
+ align:start position:0%
+look different right and uh uh with that
+ 
+
+ align:start position:0%
+look different right and uh uh with that
+you uh I hope you get appreciation for
+
+ align:start position:0%
+you uh I hope you get appreciation for
+ 
+
+ align:start position:0%
+you uh I hope you get appreciation for
+the energy levels of electrons in solid
+
+ align:start position:0%
+the energy levels of electrons in solid
+ 
+
+ align:start position:0%
+the energy levels of electrons in solid
+with that you can understand why there's
+
+ align:start position:0%
+with that you can understand why there's
+ 
+
+ align:start position:0%
+with that you can understand why there's
+insulator why there's semiconductor
+
+ align:start position:0%
+insulator why there's semiconductor
+ 
+
+ align:start position:0%
+insulator why there's semiconductor
+where there Metals right and uh also uh
+
+ align:start position:0%
+where there Metals right and uh also uh
+ 
+
+ align:start position:0%
+where there Metals right and uh also uh
+you uh can now also have some
+
+ align:start position:0%
+you uh can now also have some
+ 
+
+ align:start position:0%
+you uh can now also have some
+appreciation for the last
+
+ align:start position:0%
+appreciation for the last
+ 
+
+ align:start position:0%
+appreciation for the last
+vibration the Fons which is essentially
+
+ align:start position:0%
+vibration the Fons which is essentially
+ 
+
+ align:start position:0%
+vibration the Fons which is essentially
+here we do a classical treatment but
+
+ align:start position:0%
+here we do a classical treatment but
+ 
+
+ align:start position:0%
+here we do a classical treatment but
+what Fon is a quantized form of this
+
+ align:start position:0%
+what Fon is a quantized form of this
+ 
+
+ align:start position:0%
+what Fon is a quantized form of this
+frequency at each frequency for that
+
+ align:start position:0%
+frequency at each frequency for that
+ 
+
+ align:start position:0%
+frequency at each frequency for that
+mode you cannot have any energy you can
+
+ align:start position:0%
+mode you cannot have any energy you can
+ 
+
+ align:start position:0%
+mode you cannot have any energy you can
+only have discrete lber alha Fong the
+
+ align:start position:0%
+only have discrete lber alha Fong the
+ 
+
+ align:start position:0%
+only have discrete lber alha Fong the
+the energy is
+
+ align:start position:0%
+the energy is
+ 
+
+ align:start position:0%
+the energy is
+quantized right so uh those are the uh
+
+ align:start position:0%
+quantized right so uh those are the uh
+ 
+
+ align:start position:0%
+quantized right so uh those are the uh
+uh this give us some picture what are
+
+ align:start position:0%
+uh this give us some picture what are
+ 
+
+ align:start position:0%
+uh this give us some picture what are
+the quantum mechanical allowable energy
+
+ align:start position:0%
+the quantum mechanical allowable energy
+ 
+
+ align:start position:0%
+the quantum mechanical allowable energy
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+matters and what where we're going to
+
+ align:start position:0%
+matters and what where we're going to
+ 
+
+ align:start position:0%
+matters and what where we're going to
+move is to uh add the temperature this
+
+ align:start position:0%
+move is to uh add the temperature this
+ 
+
+ align:start position:0%
+move is to uh add the temperature this
+is a Quant mechanic allowable now if I
+
+ align:start position:0%
+is a Quant mechanic allowable now if I
+ 
+
+ align:start position:0%
+is a Quant mechanic allowable now if I
+have a object at certain temperature
+
+ align:start position:0%
+have a object at certain temperature
+ 
+
+ align:start position:0%
+have a object at certain temperature
+what's the uh um uh statistically
+
+ align:start position:0%
+what's the uh um uh statistically
+ 
+
+ align:start position:0%
+what's the uh um uh statistically
+average right and what what really
+
+ align:start position:0%
+average right and what what really
+ 
+
+ align:start position:0%
+average right and what what really
+what's the energy this object has so
+
+ align:start position:0%
+what's the energy this object has so
+ 
+
+ align:start position:0%
+what's the energy this object has so
+that's where we're moving and uh uh but
+
+ align:start position:0%
+that's where we're moving and uh uh but
+ 
+
+ align:start position:0%
+that's where we're moving and uh uh but
+before that uh I want to discuss a
+
+ align:start position:0%
+before that uh I want to discuss a
+ 
+
+ align:start position:0%
+before that uh I want to discuss a
+little more of the
+
+ align:start position:0%
+little more of the
+ 
+
+ align:start position:0%
+little more of the
+counting right and if you recall I said
+
+ align:start position:0%
+counting right and if you recall I said
+ 
+
+ align:start position:0%
+counting right and if you recall I said
+uh the I emphasized degeneracy a Quantum
+
+ align:start position:0%
+uh the I emphasized degeneracy a Quantum
+ 
+
+ align:start position:0%
+uh the I emphasized degeneracy a Quantum
+state right uh Quantum
+
+ align:start position:0%
+state right uh Quantum
+ 
+
+ align:start position:0%
+state right uh Quantum
+state right is defined by in the case of
+
+ align:start position:0%
+state right is defined by in the case of
+ 
+
+ align:start position:0%
+state right is defined by in the case of
+waves uh is if I have wave function
+
+ align:start position:0%
+waves uh is if I have wave function
+ 
+
+ align:start position:0%
+waves uh is if I have wave function
+right uh in let's say I have my wave
+
+ align:start position:0%
+right uh in let's say I have my wave
+ 
+
+ align:start position:0%
+right uh in let's say I have my wave
+function and KX KY
+
+ align:start position:0%
+function and KX KY
+ 
+
+ align:start position:0%
+function and KX KY
+KZ right each of this uh uh KX KY KZ so
+
+ align:start position:0%
+KZ right each of this uh uh KX KY KZ so
+ 
+
+ align:start position:0%
+KZ right each of this uh uh KX KY KZ so
+here in for example in One Direction I
+
+ align:start position:0%
+here in for example in One Direction I
+ 
+
+ align:start position:0%
+here in for example in One Direction I
+have discrete number of K values right
+
+ align:start position:0%
+have discrete number of K values right
+ 
+
+ align:start position:0%
+have discrete number of K values right
+each combination of K value gives me one
+
+ align:start position:0%
+each combination of K value gives me one
+ 
+
+ align:start position:0%
+each combination of K value gives me one
+specific wave a wave function right one
+
+ align:start position:0%
+specific wave a wave function right one
+ 
+
+ align:start position:0%
+specific wave a wave function right one
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+function is if I don't consider spin
+
+ align:start position:0%
+function is if I don't consider spin
+ 
+
+ align:start position:0%
+function is if I don't consider spin
+right electron I have to say one wave
+
+ align:start position:0%
+right electron I have to say one wave
+ 
+
+ align:start position:0%
+right electron I have to say one wave
+function because of the wave function
+
+ align:start position:0%
+function because of the wave function
+ 
+
+ align:start position:0%
+function because of the wave function
+itself doesn't include spin so uh one
+
+ align:start position:0%
+itself doesn't include spin so uh one
+ 
+
+ align:start position:0%
+itself doesn't include spin so uh one
+that's one Quantum
+
+ align:start position:0%
+that's one Quantum
+ 
+
+ align:start position:0%
+that's one Quantum
+State okay and uh uh in the case of uh
+
+ align:start position:0%
+State okay and uh uh in the case of uh
+ 
+
+ align:start position:0%
+State okay and uh uh in the case of uh
+discrete atoms uh we say quantum numbers
+
+ align:start position:0%
+discrete atoms uh we say quantum numbers
+ 
+
+ align:start position:0%
+discrete atoms uh we say quantum numbers
+right if you recall uh when we do
+
+ align:start position:0%
+right if you recall uh when we do
+ 
+
+ align:start position:0%
+right if you recall uh when we do
+electronic States we have uh n m uh NL
+
+ align:start position:0%
+electronic States we have uh n m uh NL
+ 
+
+ align:start position:0%
+electronic States we have uh n m uh NL
+M right that's the quantum number and we
+
+ align:start position:0%
+M right that's the quantum number and we
+ 
+
+ align:start position:0%
+M right that's the quantum number and we
+emphasize the Quant because different
+
+ align:start position:0%
+emphasize the Quant because different
+ 
+
+ align:start position:0%
+emphasize the Quant because different
+combination of nlm could actually have
+
+ align:start position:0%
+combination of nlm could actually have
+ 
+
+ align:start position:0%
+combination of nlm could actually have
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+energy that's where we say this is how
+
+ align:start position:0%
+energy that's where we say this is how
+ 
+
+ align:start position:0%
+energy that's where we say this is how
+you start understand the periodical
+
+ align:start position:0%
+you start understand the periodical
+ 
+
+ align:start position:0%
+you start understand the periodical
+table right the
+
+ align:start position:0%
+table right the
+ 
+
+ align:start position:0%
+table right the
+degeneracy now if you look at
+
+ align:start position:0%
+degeneracy now if you look at
+ 
+
+ align:start position:0%
+degeneracy now if you look at
+solid I'm only drawing in One Direction
+
+ align:start position:0%
+solid I'm only drawing in One Direction
+ 
+
+ align:start position:0%
+solid I'm only drawing in One Direction
+but we know that the real crystal solid
+
+ align:start position:0%
+but we know that the real crystal solid
+ 
+
+ align:start position:0%
+but we know that the real crystal solid
+is three
+
+ align:start position:0%
+is three
+ 
+
+ align:start position:0%
+is three
+directions and uh now if I count certain
+
+ align:start position:0%
+directions and uh now if I count certain
+ 
+
+ align:start position:0%
+directions and uh now if I count certain
+frequency or certain energy if you think
+
+ align:start position:0%
+frequency or certain energy if you think
+ 
+
+ align:start position:0%
+frequency or certain energy if you think
+about either frequency of energy because
+
+ align:start position:0%
+about either frequency of energy because
+ 
+
+ align:start position:0%
+about either frequency of energy because
+H Omega GES
+
+ align:start position:0%
+H Omega GES
+ 
+
+ align:start position:0%
+H Omega GES
+energy right and uh even in the same
+
+ align:start position:0%
+energy right and uh even in the same
+ 
+
+ align:start position:0%
+energy right and uh even in the same
+direction you can say here I have three
+
+ align:start position:0%
+direction you can say here I have three
+ 
+
+ align:start position:0%
+direction you can say here I have three
+states three wave
+
+ align:start position:0%
+states three wave
+ 
+
+ align:start position:0%
+states three wave
+vectors right that can have same Quantum
+
+ align:start position:0%
+vectors right that can have same Quantum
+ 
+
+ align:start position:0%
+vectors right that can have same Quantum
+state right same
+
+ align:start position:0%
+state right same
+ 
+
+ align:start position:0%
+state right same
+energy three wheel vectors three Quantum
+
+ align:start position:0%
+energy three wheel vectors three Quantum
+ 
+
+ align:start position:0%
+energy three wheel vectors three Quantum
+State can have same energy but if I look
+
+ align:start position:0%
+State can have same energy but if I look
+ 
+
+ align:start position:0%
+State can have same energy but if I look
+at the other directions right many many
+
+ align:start position:0%
+at the other directions right many many
+ 
+
+ align:start position:0%
+at the other directions right many many
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+directions I would have many other
+
+ align:start position:0%
+directions I would have many other
+ 
+
+ align:start position:0%
+directions I would have many other
+possible states that could have the same
+
+ align:start position:0%
+possible states that could have the same
+ 
+
+ align:start position:0%
+possible states that could have the same
+energy so that's the degeneracy and
+
+ align:start position:0%
+energy so that's the degeneracy and
+ 
+
+ align:start position:0%
+energy so that's the degeneracy and
+that's where I have to learn how to do
+
+ align:start position:0%
+that's where I have to learn how to do
+ 
+
+ align:start position:0%
+that's where I have to learn how to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+counting okay so this is uh a major
+
+ align:start position:0%
+counting okay so this is uh a major
+ 
+
+ align:start position:0%
+counting okay so this is uh a major
+emphasis today it's the idea of
+
+ align:start position:0%
+emphasis today it's the idea of
+ 
+
+ align:start position:0%
+emphasis today it's the idea of
+counting today
+
+ align:start position:0%
+counting today
+ 
+
+ align:start position:0%
+counting today
+we really doing the density of states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then when I say States I see this is
+
+ align:start position:0%
+and then when I say States I see this is
+ 
+
+ align:start position:0%
+and then when I say States I see this is
+like density of quantum
+
+ align:start position:0%
+like density of quantum
+ 
+
+ align:start position:0%
+like density of quantum
+States okay and uh uh I also hope at the
+
+ align:start position:0%
+States okay and uh uh I also hope at the
+ 
+
+ align:start position:0%
+States okay and uh uh I also hope at the
+end I have uh with that I'll get into uh
+
+ align:start position:0%
+end I have uh with that I'll get into uh
+ 
+
+ align:start position:0%
+end I have uh with that I'll get into uh
+Quantum statistics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is uh my plan
+
+ align:start position:0%
+so this is uh my plan
+ 
+
+ align:start position:0%
+so this is uh my plan
+today and uh let's
+
+ align:start position:0%
+today and uh let's
+ 
+
+ align:start position:0%
+today and uh let's
+start uh we have looked at a very
+
+ align:start position:0%
+start uh we have looked at a very
+ 
+
+ align:start position:0%
+start uh we have looked at a very
+complic say band structure for electrons
+
+ align:start position:0%
+complic say band structure for electrons
+ 
+
+ align:start position:0%
+complic say band structure for electrons
+for Fons this is like going to uh the
+
+ align:start position:0%
+for Fons this is like going to uh the
+ 
+
+ align:start position:0%
+for Fons this is like going to uh the
+Google and you look at all those
+
+ align:start position:0%
+Google and you look at all those
+ 
+
+ align:start position:0%
+Google and you look at all those
+different images right but say uh for
+
+ align:start position:0%
+different images right but say uh for
+ 
+
+ align:start position:0%
+different images right but say uh for
+the analytical purpose we're going to
+
+ align:start position:0%
+the analytical purpose we're going to
+ 
+
+ align:start position:0%
+the analytical purpose we're going to
+look at the simplest model like the buy
+
+ align:start position:0%
+look at the simplest model like the buy
+ 
+
+ align:start position:0%
+look at the simplest model like the buy
+model and for electrons uh we also say
+
+ align:start position:0%
+model and for electrons uh we also say
+ 
+
+ align:start position:0%
+model and for electrons uh we also say
+if it's the either minimum of the
+
+ align:start position:0%
+if it's the either minimum of the
+ 
+
+ align:start position:0%
+if it's the either minimum of the
+conduction band or the maximum of the
+
+ align:start position:0%
+conduction band or the maximum of the
+ 
+
+ align:start position:0%
+conduction band or the maximum of the
+bance band we expand that near that
+
+ align:start position:0%
+bance band we expand that near that
+ 
+
+ align:start position:0%
+bance band we expand that near that
+minimum maximum right so we have
+
+ align:start position:0%
+minimum maximum right so we have
+ 
+
+ align:start position:0%
+minimum maximum right so we have
+parabolic bands so uh uh
+
+ align:start position:0%
+parabolic bands so uh uh
+ 
+
+ align:start position:0%
+parabolic bands so uh uh
+let's we need uh uh this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so if you uh recall for electrons of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation and uh
+
+ align:start position:0%
+approximation and uh
+ 
+
+ align:start position:0%
+approximation and uh
+uh in the simplest picture this is my K
+
+ align:start position:0%
+uh in the simplest picture this is my K
+ 
+
+ align:start position:0%
+uh in the simplest picture this is my K
+and K you can think is KX KY k z and
+
+ align:start position:0%
+and K you can think is KX KY k z and
+ 
+
+ align:start position:0%
+and K you can think is KX KY k z and
+here is my conduction B and I write this
+
+ align:start position:0%
+here is my conduction B and I write this
+ 
+
+ align:start position:0%
+here is my conduction B and I write this
+at the minimum k equal Z minimum here
+
+ align:start position:0%
+at the minimum k equal Z minimum here
+ 
+
+ align:start position:0%
+at the minimum k equal Z minimum here
+and you can put that at a different
+
+ align:start position:0%
+and you can put that at a different
+ 
+
+ align:start position:0%
+and you can put that at a different
+point okay and uh uh this curvature
+
+ align:start position:0%
+point okay and uh uh this curvature
+ 
+
+ align:start position:0%
+point okay and uh uh this curvature
+gives me effective Mass so uh if I say
+
+ align:start position:0%
+gives me effective Mass so uh if I say
+ 
+
+ align:start position:0%
+gives me effective Mass so uh if I say
+this is the energy and I expand this at
+
+ align:start position:0%
+this is the energy and I expand this at
+ 
+
+ align:start position:0%
+this is the energy and I expand this at
+the minimum then the uh uh energy W
+
+ align:start position:0%
+the minimum then the uh uh energy W
+ 
+
+ align:start position:0%
+the minimum then the uh uh energy W
+Vector
+
+ align:start position:0%
+Vector
+ 
+
+ align:start position:0%
+Vector
+relation right and here is my e say the
+
+ align:start position:0%
+relation right and here is my e say the
+ 
+
+ align:start position:0%
+relation right and here is my e say the
+bottom here so energy Vector relation is
+
+ align:start position:0%
+bottom here so energy Vector relation is
+ 
+
+ align:start position:0%
+bottom here so energy Vector relation is
+e say plus h bar k
+
+ align:start position:0%
+e say plus h bar k
+ 
+
+ align:start position:0%
+e say plus h bar k
+squide by 2 m Star right so H bar k we
+
+ align:start position:0%
+squide by 2 m Star right so H bar k we
+ 
+
+ align:start position:0%
+squide by 2 m Star right so H bar k we
+see under this effective Mass concept
+
+ align:start position:0%
+see under this effective Mass concept
+ 
+
+ align:start position:0%
+see under this effective Mass concept
+it's really just like the 12 MV squ
+
+ align:start position:0%
+it's really just like the 12 MV squ
+ 
+
+ align:start position:0%
+it's really just like the 12 MV squ
+because h k gives me momentum p p IDE by
+
+ align:start position:0%
+because h k gives me momentum p p IDE by
+ 
+
+ align:start position:0%
+because h k gives me momentum p p IDE by
+uh Mass gives me uh say uh say gives me
+
+ align:start position:0%
+uh Mass gives me uh say uh say gives me
+ 
+
+ align:start position:0%
+uh Mass gives me uh say uh say gives me
+velocity right so uh that's the
+
+ align:start position:0%
+velocity right so uh that's the
+ 
+
+ align:start position:0%
+velocity right so uh that's the
+parabolic band
+
+ align:start position:0%
+parabolic band
+ 
+
+ align:start position:0%
+parabolic band
+approximation and what we need to keep
+
+ align:start position:0%
+approximation and what we need to keep
+ 
+
+ align:start position:0%
+approximation and what we need to keep
+in mind the
+
+ align:start position:0%
+in mind the
+ 
+
+ align:start position:0%
+in mind the
+K is Vector in 3D space
+
+ align:start position:0%
+K is Vector in 3D space
+ 
+
+ align:start position:0%
+K is Vector in 3D space
+right so KX we said if in the X
+
+ align:start position:0%
+right so KX we said if in the X
+ 
+
+ align:start position:0%
+right so KX we said if in the X
+Direction uh is 2 pi n *
+
+ align:start position:0%
+Direction uh is 2 pi n *
+ 
+
+ align:start position:0%
+Direction uh is 2 pi n *
+LX
+
+ align:start position:0%
+LX
+ 
+
+ align:start position:0%
+LX
+right and uh uh again the uh at the end
+
+ align:start position:0%
+right and uh uh again the uh at the end
+ 
+
+ align:start position:0%
+right and uh uh again the uh at the end
+if I do all this parabolic band
+
+ align:start position:0%
+if I do all this parabolic band
+ 
+
+ align:start position:0%
+if I do all this parabolic band
+approximation my zoom boundary is here
+
+ align:start position:0%
+approximation my zoom boundary is here
+ 
+
+ align:start position:0%
+approximation my zoom boundary is here
+this is a pi over
+
+ align:start position:0%
+this is a pi over
+ 
+
+ align:start position:0%
+this is a pi over
+ax right NX is how many atoms times this
+
+ align:start position:0%
+ax right NX is how many atoms times this
+ 
+
+ align:start position:0%
+ax right NX is how many atoms times this
+period ax
+
+ align:start position:0%
+period ax
+ 
+
+ align:start position:0%
+period ax
+okay so let's say LX equals n uh uh in
+
+ align:start position:0%
+okay so let's say LX equals n uh uh in
+ 
+
+ align:start position:0%
+okay so let's say LX equals n uh uh in
+the X Direction and periodicity in the X
+
+ align:start position:0%
+the X Direction and periodicity in the X
+ 
+
+ align:start position:0%
+the X Direction and periodicity in the X
+direction right that's our simple 1D
+
+ align:start position:0%
+direction right that's our simple 1D
+ 
+
+ align:start position:0%
+direction right that's our simple 1D
+model just to make a comment by passing
+
+ align:start position:0%
+model just to make a comment by passing
+ 
+
+ align:start position:0%
+model just to make a comment by passing
+now some of
+
+ align:start position:0%
+now some of
+ 
+
+ align:start position:0%
+now some of
+you uh probably do work in
+
+ align:start position:0%
+you uh probably do work in
+ 
+
+ align:start position:0%
+you uh probably do work in
+graphine um uh see what's special with
+
+ align:start position:0%
+graphine um uh see what's special with
+ 
+
+ align:start position:0%
+graphine um uh see what's special with
+graphine is that uh at uh
+
+ align:start position:0%
+graphine is that uh at uh
+ 
+
+ align:start position:0%
+graphine is that uh at uh
+uh the bottom
+
+ align:start position:0%
+uh the bottom
+ 
+
+ align:start position:0%
+uh the bottom
+here the uh band here is uh not qu see a
+
+ align:start position:0%
+here the uh band here is uh not qu see a
+ 
+
+ align:start position:0%
+here the uh band here is uh not qu see a
+parabola it's actually a straight
+
+ align:start position:0%
+parabola it's actually a straight
+ 
+
+ align:start position:0%
+parabola it's actually a straight
+line okay so uh a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graphing graphing the dispersion this is
+
+ align:start position:0%
+graphing graphing the dispersion this is
+ 
+
+ align:start position:0%
+graphing graphing the dispersion this is
+the energy this is V vector and in small
+
+ align:start position:0%
+the energy this is V vector and in small
+ 
+
+ align:start position:0%
+the energy this is V vector and in small
+region near the fir level right it's a
+
+ align:start position:0%
+region near the fir level right it's a
+ 
+
+ align:start position:0%
+region near the fir level right it's a
+zero Gap so the bank Gap happen to be
+
+ align:start position:0%
+zero Gap so the bank Gap happen to be
+ 
+
+ align:start position:0%
+zero Gap so the bank Gap happen to be
+zero and so at the fir level the
+
+ align:start position:0%
+zero and so at the fir level the
+ 
+
+ align:start position:0%
+zero and so at the fir level the
+dispersion is a
+
+ align:start position:0%
+dispersion is a
+ 
+
+ align:start position:0%
+dispersion is a
+linear and this linear dispersion make
+
+ align:start position:0%
+linear and this linear dispersion make
+ 
+
+ align:start position:0%
+linear and this linear dispersion make
+the very similar to the bi model for Fon
+
+ align:start position:0%
+the very similar to the bi model for Fon
+ 
+
+ align:start position:0%
+the very similar to the bi model for Fon
+and also Photon right photon is if you
+
+ align:start position:0%
+and also Photon right photon is if you
+ 
+
+ align:start position:0%
+and also Photon right photon is if you
+think about the model for photon is
+
+ align:start position:0%
+think about the model for photon is
+ 
+
+ align:start position:0%
+think about the model for photon is
+Omega equals
+
+ align:start position:0%
+Omega equals
+ 
+
+ align:start position:0%
+Omega equals
+CK right that's the speed of light and
+
+ align:start position:0%
+CK right that's the speed of light and
+ 
+
+ align:start position:0%
+CK right that's the speed of light and
+for foron Omega equals V K that
+
+ align:start position:0%
+for foron Omega equals V K that
+ 
+
+ align:start position:0%
+for foron Omega equals V K that
+V is the by velocity sometimes we
+
+ align:start position:0%
+V is the by velocity sometimes we
+ 
+
+ align:start position:0%
+V is the by velocity sometimes we
+associate with the sound
+
+ align:start position:0%
+associate with the sound
+ 
+
+ align:start position:0%
+associate with the sound
+velocity right so that makes the
+
+ align:start position:0%
+velocity right so that makes the
+ 
+
+ align:start position:0%
+velocity right so that makes the
+electron similar to
+
+ align:start position:0%
+electron similar to
+ 
+
+ align:start position:0%
+electron similar to
+Photon and uh similar to Fons so that's
+
+ align:start position:0%
+Photon and uh similar to Fons so that's
+ 
+
+ align:start position:0%
+Photon and uh similar to Fons so that's
+what special uh with the uh
+
+ align:start position:0%
+what special uh with the uh
+ 
+
+ align:start position:0%
+what special uh with the uh
+graphing uh so uh this is KX and of
+
+ align:start position:0%
+graphing uh so uh this is KX and of
+ 
+
+ align:start position:0%
+graphing uh so uh this is KX and of
+course I have similar K by KZ and K
+
+ align:start position:0%
+course I have similar K by KZ and K
+ 
+
+ align:start position:0%
+course I have similar K by KZ and K
+square is a com
+
+ align:start position:0%
+square is a com
+ 
+
+ align:start position:0%
+square is a com
+of KX
+
+ align:start position:0%
+of KX
+ 
+
+ align:start position:0%
+of KX
+s+ k y² + k z
+
+ align:start position:0%
+s+ k y² + k z
+ 
+
+ align:start position:0%
+s+ k y² + k z
+s okay so this means right my constant
+
+ align:start position:0%
+s okay so this means right my constant
+ 
+
+ align:start position:0%
+s okay so this means right my constant
+energy surface if I give K is a
+
+ align:start position:0%
+energy surface if I give K is a
+ 
+
+ align:start position:0%
+energy surface if I give K is a
+constant uh energy is a constant right
+
+ align:start position:0%
+constant uh energy is a constant right
+ 
+
+ align:start position:0%
+constant uh energy is a constant right
+KX KY KZ gives me a sphere so is a
+
+ align:start position:0%
+KX KY KZ gives me a sphere so is a
+ 
+
+ align:start position:0%
+KX KY KZ gives me a sphere so is a
+spherical uh uh say a constant energy
+
+ align:start position:0%
+spherical uh uh say a constant energy
+ 
+
+ align:start position:0%
+spherical uh uh say a constant energy
+surface uh sometimes you draw real
+
+ align:start position:0%
+surface uh sometimes you draw real
+ 
+
+ align:start position:0%
+surface uh sometimes you draw real
+constant energy surface in solid it look
+
+ align:start position:0%
+constant energy surface in solid it look
+ 
+
+ align:start position:0%
+constant energy surface in solid it look
+very complicated sometimes it look like
+
+ align:start position:0%
+very complicated sometimes it look like
+ 
+
+ align:start position:0%
+very complicated sometimes it look like
+a el SW or even other
+
+ align:start position:0%
+a el SW or even other
+ 
+
+ align:start position:0%
+a el SW or even other
+shapes okay but I'm doing the simplest
+
+ align:start position:0%
+shapes okay but I'm doing the simplest
+ 
+
+ align:start position:0%
+shapes okay but I'm doing the simplest
+model and uh so what uh you can say is
+
+ align:start position:0%
+model and uh so what uh you can say is
+ 
+
+ align:start position:0%
+model and uh so what uh you can say is
+there are many combination of KX KY KZ
+
+ align:start position:0%
+there are many combination of KX KY KZ
+ 
+
+ align:start position:0%
+there are many combination of KX KY KZ
+that could give me the same energy e and
+
+ align:start position:0%
+that could give me the same energy e and
+ 
+
+ align:start position:0%
+that could give me the same energy e and
+each combination is one Quantum State
+
+ align:start position:0%
+each combination is one Quantum State
+ 
+
+ align:start position:0%
+each combination is one Quantum State
+including a factor of two if I think
+
+ align:start position:0%
+including a factor of two if I think
+ 
+
+ align:start position:0%
+including a factor of two if I think
+about spin
+
+ align:start position:0%
+about spin
+ 
+
+ align:start position:0%
+about spin
+right so uh this is a uh the uh
+
+ align:start position:0%
+right so uh this is a uh the uh
+ 
+
+ align:start position:0%
+right so uh this is a uh the uh
+dispersion the energy with Vector
+
+ align:start position:0%
+dispersion the energy with Vector
+ 
+
+ align:start position:0%
+dispersion the energy with Vector
+relation is dispersion and uh for
+
+ align:start position:0%
+relation is dispersion and uh for
+ 
+
+ align:start position:0%
+relation is dispersion and uh for
+electrons and for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fons we already said Omega equals V K
+
+ align:start position:0%
+Fons we already said Omega equals V K
+ 
+
+ align:start position:0%
+Fons we already said Omega equals V K
+that's the by approximation and K now uh
+
+ align:start position:0%
+that's the by approximation and K now uh
+ 
+
+ align:start position:0%
+that's the by approximation and K now uh
+uh that's the k for we for the electron
+
+ align:start position:0%
+uh that's the k for we for the electron
+ 
+
+ align:start position:0%
+uh that's the k for we for the electron
+uh for the Fon W Vector but again uh
+
+ align:start position:0%
+uh for the Fon W Vector but again uh
+ 
+
+ align:start position:0%
+uh for the Fon W Vector but again uh
+based on discussion we have those are
+
+ align:start position:0%
+based on discussion we have those are
+ 
+
+ align:start position:0%
+based on discussion we have those are
+allowable
+
+ align:start position:0%
+allowable
+ 
+
+ align:start position:0%
+allowable
+values right so uh and for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Photon Omega equals c k like I just
+
+ align:start position:0%
+Photon Omega equals c k like I just
+ 
+
+ align:start position:0%
+Photon Omega equals c k like I just
+written
+
+ align:start position:0%
+written
+ 
+
+ align:start position:0%
+written
+down but say this k for
+
+ align:start position:0%
+down but say this k for
+ 
+
+ align:start position:0%
+down but say this k for
+Photon I I don't have upper
+
+ align:start position:0%
+Photon I I don't have upper
+ 
+
+ align:start position:0%
+Photon I I don't have upper
+limit uh it's a uh I haven't discussed
+
+ align:start position:0%
+limit uh it's a uh I haven't discussed
+ 
+
+ align:start position:0%
+limit uh it's a uh I haven't discussed
+uh so in in free space this K could be
+
+ align:start position:0%
+uh so in in free space this K could be
+ 
+
+ align:start position:0%
+uh so in in free space this K could be
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+large okay so uh those are the uh
+
+ align:start position:0%
+large okay so uh those are the uh
+ 
+
+ align:start position:0%
+large okay so uh those are the uh
+dispersion between frequency with vector
+
+ align:start position:0%
+dispersion between frequency with vector
+ 
+
+ align:start position:0%
+dispersion between frequency with vector
+or energy with Vector all those we call
+
+ align:start position:0%
+or energy with Vector all those we call
+ 
+
+ align:start position:0%
+or energy with Vector all those we call
+dispersion relations right now based on
+
+ align:start position:0%
+dispersion relations right now based on
+ 
+
+ align:start position:0%
+dispersion relations right now based on
+this I'm going to count how many states
+
+ align:start position:0%
+this I'm going to count how many states
+ 
+
+ align:start position:0%
+this I'm going to count how many states
+so it turns out uh for example I want to
+
+ align:start position:0%
+so it turns out uh for example I want to
+ 
+
+ align:start position:0%
+so it turns out uh for example I want to
+count uh a I have any electrons right
+
+ align:start position:0%
+count uh a I have any electrons right
+ 
+
+ align:start position:0%
+count uh a I have any electrons right
+where is the fir
+
+ align:start position:0%
+where is the fir
+ 
+
+ align:start position:0%
+where is the fir
+level if you recall when I did uh the
+
+ align:start position:0%
+level if you recall when I did uh the
+ 
+
+ align:start position:0%
+level if you recall when I did uh the
+simple onedimensional uh hydrogen Atomic
+
+ align:start position:0%
+simple onedimensional uh hydrogen Atomic
+ 
+
+ align:start position:0%
+simple onedimensional uh hydrogen Atomic
+chain right and we say this is
+
+ align:start position:0%
+chain right and we say this is
+ 
+
+ align:start position:0%
+chain right and we say this is
+the we say this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dispersion
+
+ align:start position:0%
+dispersion
+ 
+
+ align:start position:0%
+dispersion
+okay and uh I have between here minus Pi
+
+ align:start position:0%
+okay and uh I have between here minus Pi
+ 
+
+ align:start position:0%
+okay and uh I have between here minus Pi
+/ a to plus pi a symmetric and I have K
+
+ align:start position:0%
+/ a to plus pi a symmetric and I have K
+ 
+
+ align:start position:0%
+/ a to plus pi a symmetric and I have K
+points I say uh if it's 1D I go to the
+
+ align:start position:0%
+points I say uh if it's 1D I go to the
+ 
+
+ align:start position:0%
+points I say uh if it's 1D I go to the
+lowest States and because I have n
+
+ align:start position:0%
+lowest States and because I have n
+ 
+
+ align:start position:0%
+lowest States and because I have n
+States between pi a to minus Pi minus pi
+
+ align:start position:0%
+States between pi a to minus Pi minus pi
+ 
+
+ align:start position:0%
+States between pi a to minus Pi minus pi
+to plus pi I have n electrons and each
+
+ align:start position:0%
+to plus pi I have n electrons and each
+ 
+
+ align:start position:0%
+to plus pi I have n electrons and each
+of this wave function have spin up spin
+
+ align:start position:0%
+of this wave function have spin up spin
+ 
+
+ align:start position:0%
+of this wave function have spin up spin
+down so I fa to the
+
+ align:start position:0%
+down so I fa to the
+ 
+
+ align:start position:0%
+down so I fa to the
+middle right that's a 1D case now if I
+
+ align:start position:0%
+middle right that's a 1D case now if I
+ 
+
+ align:start position:0%
+middle right that's a 1D case now if I
+ask the same question if it's a 3D
+
+ align:start position:0%
+ask the same question if it's a 3D
+ 
+
+ align:start position:0%
+ask the same question if it's a 3D
+where does it go where is the
+
+ align:start position:0%
+where does it go where is the
+ 
+
+ align:start position:0%
+where does it go where is the
+fining
+
+ align:start position:0%
+fining
+ 
+
+ align:start position:0%
+fining
+right and uh uh in in that case uh
+
+ align:start position:0%
+right and uh uh in in that case uh
+ 
+
+ align:start position:0%
+right and uh uh in in that case uh
+because there are many KX KY KZ
+
+ align:start position:0%
+because there are many KX KY KZ
+ 
+
+ align:start position:0%
+because there are many KX KY KZ
+combination K give me the same energy
+
+ align:start position:0%
+combination K give me the same energy
+ 
+
+ align:start position:0%
+combination K give me the same energy
+level so I have to uh do this
+
+ align:start position:0%
+level so I have to uh do this
+ 
+
+ align:start position:0%
+level so I have to uh do this
+summation so this is total number of
+
+ align:start position:0%
+summation so this is total number of
+ 
+
+ align:start position:0%
+summation so this is total number of
+electrons let's say total number of
+
+ align:start position:0%
+electrons let's say total number of
+ 
+
+ align:start position:0%
+electrons let's say total number of
+atoms right if I say hydrogen each
+
+ align:start position:0%
+atoms right if I say hydrogen each
+ 
+
+ align:start position:0%
+atoms right if I say hydrogen each
+hydrogen give me one electron
+
+ align:start position:0%
+hydrogen give me one electron
+ 
+
+ align:start position:0%
+hydrogen give me one electron
+right and then I have to sum up what I
+
+ align:start position:0%
+right and then I have to sum up what I
+ 
+
+ align:start position:0%
+right and then I have to sum up what I
+know is let's say uh
+
+ align:start position:0%
+know is let's say uh
+ 
+
+ align:start position:0%
+know is let's say uh
+uh the at the zero
+
+ align:start position:0%
+uh the at the zero
+ 
+
+ align:start position:0%
+uh the at the zero
+temperature the lowest energy is field
+
+ align:start position:0%
+temperature the lowest energy is field
+ 
+
+ align:start position:0%
+temperature the lowest energy is field
+first right so I uh I have to think this
+
+ align:start position:0%
+first right so I uh I have to think this
+ 
+
+ align:start position:0%
+first right so I uh I have to think this
+now rather than 1 D I have to think
+
+ align:start position:0%
+now rather than 1 D I have to think
+ 
+
+ align:start position:0%
+now rather than 1 D I have to think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+3D three dimensional coordinate right
+
+ align:start position:0%
+3D three dimensional coordinate right
+ 
+
+ align:start position:0%
+3D three dimensional coordinate right
+and uh uh
+
+ align:start position:0%
+and uh uh
+ 
+
+ align:start position:0%
+and uh uh
+you will feel to the lowest and to the
+
+ align:start position:0%
+you will feel to the lowest and to the
+ 
+
+ align:start position:0%
+you will feel to the lowest and to the
+uppermost this is recall this is my
+
+ align:start position:0%
+uppermost this is recall this is my
+ 
+
+ align:start position:0%
+uppermost this is recall this is my
+EF right that's where my f level
+
+ align:start position:0%
+EF right that's where my f level
+ 
+
+ align:start position:0%
+EF right that's where my f level
+is and
+
+ align:start position:0%
+is and
+ 
+
+ align:start position:0%
+is and
+correspondingly this is my K if I say
+
+ align:start position:0%
+correspondingly this is my K if I say
+ 
+
+ align:start position:0%
+correspondingly this is my K if I say
+this is my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KF okay and my model is K XYZ all
+
+ align:start position:0%
+KF okay and my model is K XYZ all
+ 
+
+ align:start position:0%
+KF okay and my model is K XYZ all
+direction are the same if you look at
+
+ align:start position:0%
+direction are the same if you look at
+ 
+
+ align:start position:0%
+direction are the same if you look at
+what I written down right so uh KF so
+
+ align:start position:0%
+what I written down right so uh KF so
+ 
+
+ align:start position:0%
+what I written down right so uh KF so
+this is a coming uh constant energy
+
+ align:start position:0%
+this is a coming uh constant energy
+ 
+
+ align:start position:0%
+this is a coming uh constant energy
+sphere and the constant wave Vector uh
+
+ align:start position:0%
+sphere and the constant wave Vector uh
+ 
+
+ align:start position:0%
+sphere and the constant wave Vector uh
+also at that uh location so when they
+
+ align:start position:0%
+also at that uh location so when they
+ 
+
+ align:start position:0%
+also at that uh location so when they
+uh so each of this combination KX KY KZ
+
+ align:start position:0%
+uh so each of this combination KX KY KZ
+ 
+
+ align:start position:0%
+uh so each of this combination KX KY KZ
+gives me one Quantum State as long as
+
+ align:start position:0%
+gives me one Quantum State as long as
+ 
+
+ align:start position:0%
+gives me one Quantum State as long as
+this Quantum state lies below
+
+ align:start position:0%
+this Quantum state lies below
+ 
+
+ align:start position:0%
+this Quantum state lies below
+EF it has one
+
+ align:start position:0%
+EF it has one
+ 
+
+ align:start position:0%
+EF it has one
+electron so I add that total should give
+
+ align:start position:0%
+electron so I add that total should give
+ 
+
+ align:start position:0%
+electron so I add that total should give
+me total number of n total L of
+
+ align:start position:0%
+me total number of n total L of
+ 
+
+ align:start position:0%
+me total number of n total L of
+electrons okay and recall this is a huge
+
+ align:start position:0%
+electrons okay and recall this is a huge
+ 
+
+ align:start position:0%
+electrons okay and recall this is a huge
+L right if I say one more of God Conant
+
+ align:start position:0%
+L right if I say one more of God Conant
+ 
+
+ align:start position:0%
+L right if I say one more of God Conant
+10 to
+
+ align:start position:0%
+10 to
+ 
+
+ align:start position:0%
+10 to
+23rd okay it's it's going to be very
+
+ align:start position:0%
+23rd okay it's it's going to be very
+ 
+
+ align:start position:0%
+23rd okay it's it's going to be very
+large lber summation so what I have here
+
+ align:start position:0%
+large lber summation so what I have here
+ 
+
+ align:start position:0%
+large lber summation so what I have here
+is going to I say KX so any of this
+
+ align:start position:0%
+is going to I say KX so any of this
+ 
+
+ align:start position:0%
+is going to I say KX so any of this
+loable values below KF all that KX value
+
+ align:start position:0%
+loable values below KF all that KX value
+ 
+
+ align:start position:0%
+loable values below KF all that KX value
+right each I have many points
+
+ align:start position:0%
+right each I have many points
+ 
+
+ align:start position:0%
+right each I have many points
+there I have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KY
+
+ align:start position:0%
+KY
+ 
+
+ align:start position:0%
+KY
+same I have k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z
+
+ align:start position:0%
+z
+ 
+
+ align:start position:0%
+z
+right as as long as this KX squ + k y
+
+ align:start position:0%
+right as as long as this KX squ + k y
+ 
+
+ align:start position:0%
+right as as long as this KX squ + k y
+squ plus KZ
+
+ align:start position:0%
+squ plus KZ
+ 
+
+ align:start position:0%
+squ plus KZ
+squ uh uh is wi in this is KF squ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so as long as within this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+range that combination all those
+
+ align:start position:0%
+range that combination all those
+ 
+
+ align:start position:0%
+range that combination all those
+combination give me a Quantum State
+
+ align:start position:0%
+combination give me a Quantum State
+ 
+
+ align:start position:0%
+combination give me a Quantum State
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+fied right so I have each KX KY discrete
+
+ align:start position:0%
+fied right so I have each KX KY discrete
+ 
+
+ align:start position:0%
+fied right so I have each KX KY discrete
+Point KX KY
+
+ align:start position:0%
+Point KX KY
+ 
+
+ align:start position:0%
+Point KX KY
+KZ gives me one Quantum State except
+
+ align:start position:0%
+KZ gives me one Quantum State except
+ 
+
+ align:start position:0%
+KZ gives me one Quantum State except
+that doesn't count spin so I have factor
+
+ align:start position:0%
+that doesn't count spin so I have factor
+ 
+
+ align:start position:0%
+that doesn't count spin so I have factor
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+two right so each of this Quantum state
+
+ align:start position:0%
+two right so each of this Quantum state
+ 
+
+ align:start position:0%
+two right so each of this Quantum state
+has one electron
+
+ align:start position:0%
+has one electron
+ 
+
+ align:start position:0%
+has one electron
+right 2 plus KX KY KZ combination has
+
+ align:start position:0%
+right 2 plus KX KY KZ combination has
+ 
+
+ align:start position:0%
+right 2 plus KX KY KZ combination has
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+electron right each of this uh so what
+
+ align:start position:0%
+electron right each of this uh so what
+ 
+
+ align:start position:0%
+electron right each of this uh so what
+I'm really summing up that
+
+ align:start position:0%
+I'm really summing up that
+ 
+
+ align:start position:0%
+I'm really summing up that
+one one
+
+ align:start position:0%
+one one
+ 
+
+ align:start position:0%
+one one
+electron do you get me I'm doing
+
+ align:start position:0%
+electron do you get me I'm doing
+ 
+
+ align:start position:0%
+electron do you get me I'm doing
+counting it's basic
+
+ align:start position:0%
+counting it's basic
+ 
+
+ align:start position:0%
+counting it's basic
+counting okay now if later on I'm not
+
+ align:start position:0%
+counting okay now if later on I'm not
+ 
+
+ align:start position:0%
+counting okay now if later on I'm not
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+do one I'm going to do half field at a
+
+ align:start position:0%
+do one I'm going to do half field at a
+ 
+
+ align:start position:0%
+do one I'm going to do half field at a
+certain temperature for example some
+
+ align:start position:0%
+certain temperature for example some
+ 
+
+ align:start position:0%
+certain temperature for example some
+states could be empty right so I make it
+
+ align:start position:0%
+states could be empty right so I make it
+ 
+
+ align:start position:0%
+states could be empty right so I make it
+that say rather than one I may be a
+
+ align:start position:0%
+that say rather than one I may be a
+ 
+
+ align:start position:0%
+that say rather than one I may be a
+probability uh very soon at the end of
+
+ align:start position:0%
+probability uh very soon at the end of
+ 
+
+ align:start position:0%
+probability uh very soon at the end of
+lecture I hope I get there so this will
+
+ align:start position:0%
+lecture I hope I get there so this will
+ 
+
+ align:start position:0%
+lecture I hope I get there so this will
+be a function of energy and chemical
+
+ align:start position:0%
+be a function of energy and chemical
+ 
+
+ align:start position:0%
+be a function of energy and chemical
+potential and
+
+ align:start position:0%
+potential and
+ 
+
+ align:start position:0%
+potential and
+temperature right here I'm doing my
+
+ align:start position:0%
+temperature right here I'm doing my
+ 
+
+ align:start position:0%
+temperature right here I'm doing my
+simplest case at zero temperature any
+
+ align:start position:0%
+simplest case at zero temperature any
+ 
+
+ align:start position:0%
+simplest case at zero temperature any
+Quantom State below the fir level are
+
+ align:start position:0%
+Quantom State below the fir level are
+ 
+
+ align:start position:0%
+Quantom State below the fir level are
+fielded and I have my requirement I have
+
+ align:start position:0%
+fielded and I have my requirement I have
+ 
+
+ align:start position:0%
+fielded and I have my requirement I have
+total n
+
+ align:start position:0%
+total n
+ 
+
+ align:start position:0%
+total n
+electrons and I want to find out where
+
+ align:start position:0%
+electrons and I want to find out where
+ 
+
+ align:start position:0%
+electrons and I want to find out where
+is my KF where is my
+
+ align:start position:0%
+is my KF where is my
+ 
+
+ align:start position:0%
+is my KF where is my
+EF
+
+ align:start position:0%
+EF
+ 
+
+ align:start position:0%
+EF
+okay so now you go to do a
+
+ align:start position:0%
+okay so now you go to do a
+ 
+
+ align:start position:0%
+okay so now you go to do a
+summation how you do the
+
+ align:start position:0%
+summation how you do the
+ 
+
+ align:start position:0%
+summation how you do the
+summation
+
+ align:start position:0%
+summation
+ 
+
+ align:start position:0%
+summation
+right and uh doing
+
+ align:start position:0%
+right and uh doing
+ 
+
+ align:start position:0%
+right and uh doing
+summation when it has many unless it's a
+
+ align:start position:0%
+summation when it has many unless it's a
+ 
+
+ align:start position:0%
+summation when it has many unless it's a
+simple series it's not
+
+ align:start position:0%
+simple series it's not
+ 
+
+ align:start position:0%
+simple series it's not
+easy right so
+
+ align:start position:0%
+easy right so
+ 
+
+ align:start position:0%
+easy right so
+uh the way to do it is convert that
+
+ align:start position:0%
+uh the way to do it is convert that
+ 
+
+ align:start position:0%
+uh the way to do it is convert that
+summation into
+
+ align:start position:0%
+summation into
+ 
+
+ align:start position:0%
+summation into
+integration that's what we going to do
+
+ align:start position:0%
+integration that's what we going to do
+ 
+
+ align:start position:0%
+integration that's what we going to do
+next and uh the condition for converting
+
+ align:start position:0%
+next and uh the condition for converting
+ 
+
+ align:start position:0%
+next and uh the condition for converting
+a summation into integration right if I
+
+ align:start position:0%
+a summation into integration right if I
+ 
+
+ align:start position:0%
+a summation into integration right if I
+have a function here
+
+ align:start position:0%
+have a function here
+ 
+
+ align:start position:0%
+have a function here
+right and remember this is a k each set
+
+ align:start position:0%
+right and remember this is a k each set
+ 
+
+ align:start position:0%
+right and remember this is a k each set
+of point
+
+ align:start position:0%
+of point
+ 
+
+ align:start position:0%
+of point
+is one value I'm summing up those values
+
+ align:start position:0%
+is one value I'm summing up those values
+ 
+
+ align:start position:0%
+is one value I'm summing up those values
+when I do that summation right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now if this function does not vary
+
+ align:start position:0%
+and now if this function does not vary
+ 
+
+ align:start position:0%
+and now if this function does not vary
+rapidly between the
+
+ align:start position:0%
+rapidly between the
+ 
+
+ align:start position:0%
+rapidly between the
+points it's like you do trapezoidal
+
+ align:start position:0%
+points it's like you do trapezoidal
+ 
+
+ align:start position:0%
+points it's like you do trapezoidal
+rule you can actually do convert this
+
+ align:start position:0%
+rule you can actually do convert this
+ 
+
+ align:start position:0%
+rule you can actually do convert this
+some some back into
+
+ align:start position:0%
+some some back into
+ 
+
+ align:start position:0%
+some some back into
+integration so how we do it okay let's
+
+ align:start position:0%
+integration so how we do it okay let's
+ 
+
+ align:start position:0%
+integration so how we do it okay let's
+say KX right if I have a Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KX right right or dkx when I do
+
+ align:start position:0%
+KX right right or dkx when I do
+ 
+
+ align:start position:0%
+KX right right or dkx when I do
+integration I do dkx right so how many
+
+ align:start position:0%
+integration I do dkx right so how many
+ 
+
+ align:start position:0%
+integration I do dkx right so how many
+points there are in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dkx now I look at the spacing between
+
+ align:start position:0%
+dkx now I look at the spacing between
+ 
+
+ align:start position:0%
+dkx now I look at the spacing between
+two adjacent Point KX 2 pi
+
+ align:start position:0%
+two adjacent Point KX 2 pi
+ 
+
+ align:start position:0%
+two adjacent Point KX 2 pi
+n LX so what's the spacing between two
+
+ align:start position:0%
+n LX so what's the spacing between two
+ 
+
+ align:start position:0%
+n LX so what's the spacing between two
+adjacent
+
+ align:start position:0%
+adjacent
+ 
+
+ align:start position:0%
+adjacent
+Point 2 pi x RX right so I do dkx / by 2
+
+ align:start position:0%
+Point 2 pi x RX right so I do dkx / by 2
+ 
+
+ align:start position:0%
+Point 2 pi x RX right so I do dkx / by 2
+pi LX that's how many points over
+
+ align:start position:0%
+pi LX that's how many points over
+ 
+
+ align:start position:0%
+pi LX that's how many points over
+dkx okay so now I'm converting this one
+
+ align:start position:0%
+dkx okay so now I'm converting this one
+ 
+
+ align:start position:0%
+dkx okay so now I'm converting this one
+and rather than sum over D say KX I do
+
+ align:start position:0%
+and rather than sum over D say KX I do
+ 
+
+ align:start position:0%
+and rather than sum over D say KX I do
+integration
+
+ align:start position:0%
+integration
+ 
+
+ align:start position:0%
+integration
+over this is my integration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over uh KX so what's my limit if this is
+
+ align:start position:0%
+over uh KX so what's my limit if this is
+ 
+
+ align:start position:0%
+over uh KX so what's my limit if this is
+a kxf and minus kxf right so I have Min
+
+ align:start position:0%
+a kxf and minus kxf right so I have Min
+ 
+
+ align:start position:0%
+a kxf and minus kxf right so I have Min
+- K
+
+ align:start position:0%
+- K
+ 
+
+ align:start position:0%
+- K
+FX plus K FX remember
+
+ align:start position:0%
+FX plus K FX remember
+ 
+
+ align:start position:0%
+FX plus K FX remember
+I mean uh uh symmetry right K negative
+
+ align:start position:0%
+I mean uh uh symmetry right K negative
+ 
+
+ align:start position:0%
+I mean uh uh symmetry right K negative
+positive K
+
+ align:start position:0%
+positive K
+ 
+
+ align:start position:0%
+positive K
+symmetry okay and I do the
+
+ align:start position:0%
+symmetry okay and I do the
+ 
+
+ align:start position:0%
+symmetry okay and I do the
+same D
+
+ align:start position:0%
+same D
+ 
+
+ align:start position:0%
+same D
+KY and 2 pi l y
+
+ align:start position:0%
+KY and 2 pi l y
+ 
+
+ align:start position:0%
+KY and 2 pi l y
+KF y k
+
+ align:start position:0%
+KF y k
+ 
+
+ align:start position:0%
+KF y k
+FY
+
+ align:start position:0%
+FY
+ 
+
+ align:start position:0%
+FY
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+kfz K
+
+ align:start position:0%
+kfz K
+ 
+
+ align:start position:0%
+kfz K
+FZ
+
+ align:start position:0%
+FZ
+ 
+
+ align:start position:0%
+FZ
+dkz 2 pi l
+
+ align:start position:0%
+dkz 2 pi l
+ 
+
+ align:start position:0%
+dkz 2 pi l
+z and that integration is over one but
+
+ align:start position:0%
+z and that integration is over one but
+ 
+
+ align:start position:0%
+z and that integration is over one but
+you probably don't like one one is just
+
+ align:start position:0%
+you probably don't like one one is just
+ 
+
+ align:start position:0%
+you probably don't like one one is just
+look two th so let me just put any
+
+ align:start position:0%
+look two th so let me just put any
+ 
+
+ align:start position:0%
+look two th so let me just put any
+function as said before right say later
+
+ align:start position:0%
+function as said before right say later
+ 
+
+ align:start position:0%
+function as said before right say later
+on when I say the formula will I come
+
+ align:start position:0%
+on when I say the formula will I come
+ 
+
+ align:start position:0%
+on when I say the formula will I come
+back to fals 1 so the f as a function of
+
+ align:start position:0%
+back to fals 1 so the f as a function of
+ 
+
+ align:start position:0%
+back to fals 1 so the f as a function of
+e Mt right and turns out this F could be
+
+ align:start position:0%
+e Mt right and turns out this F could be
+ 
+
+ align:start position:0%
+e Mt right and turns out this F could be
+any function sometimes this F F could be
+
+ align:start position:0%
+any function sometimes this F F could be
+ 
+
+ align:start position:0%
+any function sometimes this F F could be
+a function of e sometimes this fun this
+
+ align:start position:0%
+a function of e sometimes this fun this
+ 
+
+ align:start position:0%
+a function of e sometimes this fun this
+could be a function of
+
+ align:start position:0%
+could be a function of
+ 
+
+ align:start position:0%
+could be a function of
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+okay and most of time when we do a deal
+
+ align:start position:0%
+okay and most of time when we do a deal
+ 
+
+ align:start position:0%
+okay and most of time when we do a deal
+with d States it's a function of
+
+ align:start position:0%
+with d States it's a function of
+ 
+
+ align:start position:0%
+with d States it's a function of
+e so you want convert the function e or
+
+ align:start position:0%
+e so you want convert the function e or
+ 
+
+ align:start position:0%
+e so you want convert the function e or
+a function of frequency but when you do
+
+ align:start position:0%
+a function of frequency but when you do
+ 
+
+ align:start position:0%
+a function of frequency but when you do
+transport I just want to warn you when
+
+ align:start position:0%
+transport I just want to warn you when
+ 
+
+ align:start position:0%
+transport I just want to warn you when
+you do
+
+ align:start position:0%
+you do
+ 
+
+ align:start position:0%
+you do
+transport this function is open function
+
+ align:start position:0%
+transport this function is open function
+ 
+
+ align:start position:0%
+transport this function is open function
+of K so the way I do that the summation
+
+ align:start position:0%
+of K so the way I do that the summation
+ 
+
+ align:start position:0%
+of K so the way I do that the summation
+sometimes in transport is actually not
+
+ align:start position:0%
+sometimes in transport is actually not
+ 
+
+ align:start position:0%
+sometimes in transport is actually not
+very useful but it's such a so common
+
+ align:start position:0%
+very useful but it's such a so common
+ 
+
+ align:start position:0%
+very useful but it's such a so common
+concept that's used every every time you
+
+ align:start position:0%
+concept that's used every every time you
+ 
+
+ align:start position:0%
+concept that's used every every time you
+go to read or discuss people say what's
+
+ align:start position:0%
+go to read or discuss people say what's
+ 
+
+ align:start position:0%
+go to read or discuss people say what's
+your D what's your D St
+
+ align:start position:0%
+your D what's your D St
+ 
+
+ align:start position:0%
+your D what's your D St
+States okay so this is I'm converting
+
+ align:start position:0%
+States okay so this is I'm converting
+ 
+
+ align:start position:0%
+States okay so this is I'm converting
+that of course I have factor of two I
+
+ align:start position:0%
+that of course I have factor of two I
+ 
+
+ align:start position:0%
+that of course I have factor of two I
+have my
+
+ align:start position:0%
+have my
+ 
+
+ align:start position:0%
+have my
+n this is the same I'm writing that
+
+ align:start position:0%
+n this is the same I'm writing that
+ 
+
+ align:start position:0%
+n this is the same I'm writing that
+summation into
+
+ align:start position:0%
+summation into
+ 
+
+ align:start position:0%
+summation into
+integration and uh so now with this you
+
+ align:start position:0%
+integration and uh so now with this you
+ 
+
+ align:start position:0%
+integration and uh so now with this you
+can say LX l y l z gives me
+
+ align:start position:0%
+can say LX l y l z gives me
+ 
+
+ align:start position:0%
+can say LX l y l z gives me
+volume right and 2 pi cubic so what I
+
+ align:start position:0%
+volume right and 2 pi cubic so what I
+ 
+
+ align:start position:0%
+volume right and 2 pi cubic so what I
+have is a two Volume 2 pi
+
+ align:start position:0%
+have is a two Volume 2 pi
+ 
+
+ align:start position:0%
+have is a two Volume 2 pi
+cubic and then say I have me let me
+
+ align:start position:0%
+cubic and then say I have me let me
+ 
+
+ align:start position:0%
+cubic and then say I have me let me
+skipe the uh uh the the integration
+
+ align:start position:0%
+skipe the uh uh the the integration
+ 
+
+ align:start position:0%
+skipe the uh uh the the integration
+limit and what I have here is
+
+ align:start position:0%
+limit and what I have here is
+ 
+
+ align:start position:0%
+limit and what I have here is
+dkx
+
+ align:start position:0%
+dkx
+ 
+
+ align:start position:0%
+dkx
+dky DK Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right triple
+
+ align:start position:0%
+right triple
+ 
+
+ align:start position:0%
+right triple
+integral so by this
+
+ align:start position:0%
+integral so by this
+ 
+
+ align:start position:0%
+integral so by this
+transformation assuming this function f
+
+ align:start position:0%
+transformation assuming this function f
+ 
+
+ align:start position:0%
+transformation assuming this function f
+does not change very rapidly between
+
+ align:start position:0%
+does not change very rapidly between
+ 
+
+ align:start position:0%
+does not change very rapidly between
+adjacent
+
+ align:start position:0%
+adjacent
+ 
+
+ align:start position:0%
+adjacent
+point I have converted this summation
+
+ align:start position:0%
+point I have converted this summation
+ 
+
+ align:start position:0%
+point I have converted this summation
+into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integration and uh uh now I have further
+
+ align:start position:0%
+integration and uh uh now I have further
+ 
+
+ align:start position:0%
+integration and uh uh now I have further
+freedom because uh you see here if I
+
+ align:start position:0%
+freedom because uh you see here if I
+ 
+
+ align:start position:0%
+freedom because uh you see here if I
+give you this function f in terms of e e
+
+ align:start position:0%
+give you this function f in terms of e e
+ 
+
+ align:start position:0%
+give you this function f in terms of e e
+is a function of K so you have the
+
+ align:start position:0%
+is a function of K so you have the
+ 
+
+ align:start position:0%
+is a function of K so you have the
+freedom how you do integration whether
+
+ align:start position:0%
+freedom how you do integration whether
+ 
+
+ align:start position:0%
+freedom how you do integration whether
+you integrate in terms of e or integrate
+
+ align:start position:0%
+you integrate in terms of e or integrate
+ 
+
+ align:start position:0%
+you integrate in terms of e or integrate
+in term of K you have to convert relate
+
+ align:start position:0%
+in term of K you have to convert relate
+ 
+
+ align:start position:0%
+in term of K you have to convert relate
+them right change into same variable so
+
+ align:start position:0%
+them right change into same variable so
+ 
+
+ align:start position:0%
+them right change into same variable so
+you can do your
+
+ align:start position:0%
+you can do your
+ 
+
+ align:start position:0%
+you can do your
+integration and all uh so what I can do
+
+ align:start position:0%
+integration and all uh so what I can do
+ 
+
+ align:start position:0%
+integration and all uh so what I can do
+is here is what I'm doing is in a ction
+
+ align:start position:0%
+is here is what I'm doing is in a ction
+ 
+
+ align:start position:0%
+is here is what I'm doing is in a ction
+coordinate dkx d KY dkz is a ction
+
+ align:start position:0%
+coordinate dkx d KY dkz is a ction
+ 
+
+ align:start position:0%
+coordinate dkx d KY dkz is a ction
+coordinate
+
+ align:start position:0%
+coordinate
+ 
+
+ align:start position:0%
+coordinate
+right and if this is a spherical
+
+ align:start position:0%
+right and if this is a spherical
+ 
+
+ align:start position:0%
+right and if this is a spherical
+symmetric so far if it's a function of e
+
+ align:start position:0%
+symmetric so far if it's a function of e
+ 
+
+ align:start position:0%
+symmetric so far if it's a function of e
+you can say if it's function of e is
+
+ align:start position:0%
+you can say if it's function of e is
+ 
+
+ align:start position:0%
+you can say if it's function of e is
+spherical
+
+ align:start position:0%
+spherical
+ 
+
+ align:start position:0%
+spherical
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+right I don't have so if the function of
+
+ align:start position:0%
+right I don't have so if the function of
+ 
+
+ align:start position:0%
+right I don't have so if the function of
+e uh uh for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fora here Omega is K
+
+ align:start position:0%
+fora here Omega is K
+ 
+
+ align:start position:0%
+fora here Omega is K
+so it does not depend on so in that case
+
+ align:start position:0%
+so it does not depend on so in that case
+ 
+
+ align:start position:0%
+so it does not depend on so in that case
+it's much easier if I
+
+ align:start position:0%
+it's much easier if I
+ 
+
+ align:start position:0%
+it's much easier if I
+do convert KX KY KZ into just a
+
+ align:start position:0%
+do convert KX KY KZ into just a
+ 
+
+ align:start position:0%
+do convert KX KY KZ into just a
+k into a spherical coordinate right
+
+ align:start position:0%
+k into a spherical coordinate right
+ 
+
+ align:start position:0%
+k into a spherical coordinate right
+rather than doing triple integral I do
+
+ align:start position:0%
+rather than doing triple integral I do
+ 
+
+ align:start position:0%
+rather than doing triple integral I do
+just uh say DK uh if it's a uh doing
+
+ align:start position:0%
+just uh say DK uh if it's a uh doing
+ 
+
+ align:start position:0%
+just uh say DK uh if it's a uh doing
+spherical if it's this one is another
+
+ align:start position:0%
+spherical if it's this one is another
+ 
+
+ align:start position:0%
+spherical if it's this one is another
+function it's only function of absolute
+
+ align:start position:0%
+function it's only function of absolute
+ 
+
+ align:start position:0%
+function it's only function of absolute
+value of
+
+ align:start position:0%
+value of
+ 
+
+ align:start position:0%
+value of
+K it's I so this is a 4 Pi can you tell
+
+ align:start position:0%
+K it's I so this is a 4 Pi can you tell
+ 
+
+ align:start position:0%
+K it's I so this is a 4 Pi can you tell
+me huh K squ
+
+ align:start position:0%
+me huh K squ
+ 
+
+ align:start position:0%
+me huh K squ
+DK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right try translating from a c into
+
+ align:start position:0%
+right try translating from a c into
+ 
+
+ align:start position:0%
+right try translating from a c into
+spheric so everything of here is a
+
+ align:start position:0%
+spheric so everything of here is a
+ 
+
+ align:start position:0%
+spheric so everything of here is a
+math but what's amazing is people this
+
+ align:start position:0%
+math but what's amazing is people this
+ 
+
+ align:start position:0%
+math but what's amazing is people this
+is such a convenient concept to talk
+
+ align:start position:0%
+is such a convenient concept to talk
+ 
+
+ align:start position:0%
+is such a convenient concept to talk
+about right so here is 4 Pi K squ DK and
+
+ align:start position:0%
+about right so here is 4 Pi K squ DK and
+ 
+
+ align:start position:0%
+about right so here is 4 Pi K squ DK and
+uh uh then I can group this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together okay now I'm going to group
+
+ align:start position:0%
+together okay now I'm going to group
+ 
+
+ align:start position:0%
+together okay now I'm going to group
+this back into here H so that uh uh uh
+
+ align:start position:0%
+this back into here H so that uh uh uh
+ 
+
+ align:start position:0%
+this back into here H so that uh uh uh
+my uh I like to write n over way but
+
+ align:start position:0%
+my uh I like to write n over way but
+ 
+
+ align:start position:0%
+my uh I like to write n over way but
+many people say so this in that case my
+
+ align:start position:0%
+many people say so this in that case my
+ 
+
+ align:start position:0%
+many people say so this in that case my
+D of this per unit volume so here on our
+
+ align:start position:0%
+D of this per unit volume so here on our
+ 
+
+ align:start position:0%
+D of this per unit volume so here on our
+way then is
+
+ align:start position:0%
+way then is
+ 
+
+ align:start position:0%
+way then is
+uh the
+
+ align:start position:0%
+uh the
+ 
+
+ align:start position:0%
+uh the
+integration integration and the F here I
+
+ align:start position:0%
+integration integration and the F here I
+ 
+
+ align:start position:0%
+integration integration and the F here I
+combine whatever all inside uh
+
+ align:start position:0%
+combine whatever all inside uh
+ 
+
+ align:start position:0%
+combine whatever all inside uh
+into uh you can say I have Pi Square K
+
+ align:start position:0%
+into uh you can say I have Pi Square K
+ 
+
+ align:start position:0%
+into uh you can say I have Pi Square K
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+DK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and uh so here K is zero to KF
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z
+
+ align:start position:0%
+Z
+ 
+
+ align:start position:0%
+Z
+KF because I'm doing spherical
+
+ align:start position:0%
+KF because I'm doing spherical
+ 
+
+ align:start position:0%
+KF because I'm doing spherical
+coordinate my radius is zero my KF I
+
+ align:start position:0%
+coordinate my radius is zero my KF I
+ 
+
+ align:start position:0%
+coordinate my radius is zero my KF I
+don't do negative positive because
+
+ align:start position:0%
+don't do negative positive because
+ 
+
+ align:start position:0%
+don't do negative positive because
+that's a condition coordinate you see
+
+ align:start position:0%
+that's a condition coordinate you see
+ 
+
+ align:start position:0%
+that's a condition coordinate you see
+what I'm doing okay so this one now is
+
+ align:start position:0%
+what I'm doing okay so this one now is
+ 
+
+ align:start position:0%
+what I'm doing okay so this one now is
+my density of
+
+ align:start position:0%
+my density of
+ 
+
+ align:start position:0%
+my density of
+States this is a density of stat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so it's a l of States per unit
+
+ align:start position:0%
+uh so it's a l of States per unit
+ 
+
+ align:start position:0%
+uh so it's a l of States per unit
+interval of
+
+ align:start position:0%
+interval of
+ 
+
+ align:start position:0%
+interval of
+K right how many states Quantum State I
+
+ align:start position:0%
+K right how many states Quantum State I
+ 
+
+ align:start position:0%
+K right how many states Quantum State I
+have per Delta
+
+ align:start position:0%
+have per Delta
+ 
+
+ align:start position:0%
+have per Delta
+K right because here I'm say in DK my
+
+ align:start position:0%
+K right because here I'm say in DK my
+ 
+
+ align:start position:0%
+K right because here I'm say in DK my
+integration is in DK so then this step
+
+ align:start position:0%
+integration is in DK so then this step
+ 
+
+ align:start position:0%
+integration is in DK so then this step
+States
+
+ align:start position:0%
+States
+ 
+
+ align:start position:0%
+States
+in if I write as in terms of K that
+
+ align:start position:0%
+in if I write as in terms of K that
+ 
+
+ align:start position:0%
+in if I write as in terms of K that
+means it's per Delta
+
+ align:start position:0%
+means it's per Delta
+ 
+
+ align:start position:0%
+means it's per Delta
+k okay okay but say uh if you go back
+
+ align:start position:0%
+k okay okay but say uh if you go back
+ 
+
+ align:start position:0%
+k okay okay but say uh if you go back
+to what uh I eluded here if my f is the
+
+ align:start position:0%
+to what uh I eluded here if my f is the
+ 
+
+ align:start position:0%
+to what uh I eluded here if my f is the
+function of e then you have to make your
+
+ align:start position:0%
+function of e then you have to make your
+ 
+
+ align:start position:0%
+function of e then you have to make your
+CH Choice whether you want to convert
+
+ align:start position:0%
+CH Choice whether you want to convert
+ 
+
+ align:start position:0%
+CH Choice whether you want to convert
+the e in this F F into K or you want to
+
+ align:start position:0%
+the e in this F F into K or you want to
+ 
+
+ align:start position:0%
+the e in this F F into K or you want to
+convert that DK into a function of
+
+ align:start position:0%
+convert that DK into a function of
+ 
+
+ align:start position:0%
+convert that DK into a function of
+e right it's just your choice there's no
+
+ align:start position:0%
+e right it's just your choice there's no
+ 
+
+ align:start position:0%
+e right it's just your choice there's no
+uh formula there it's whatever is a itic
+
+ align:start position:0%
+uh formula there it's whatever is a itic
+ 
+
+ align:start position:0%
+uh formula there it's whatever is a itic
+convenient for you so uh I could also
+
+ align:start position:0%
+convenient for you so uh I could also
+ 
+
+ align:start position:0%
+convenient for you so uh I could also
+convert if I want to do a convert into
+
+ align:start position:0%
+convert if I want to do a convert into
+ 
+
+ align:start position:0%
+convert if I want to do a convert into
+uh energy integration so I will do
+
+ align:start position:0%
+uh energy integration so I will do
+ 
+
+ align:start position:0%
+uh energy integration so I will do
+EF and F so in that case I'll write this
+
+ align:start position:0%
+EF and F so in that case I'll write this
+ 
+
+ align:start position:0%
+EF and F so in that case I'll write this
+uh into uh K Square Pi Pi Square
+
+ align:start position:0%
+uh into uh K Square Pi Pi Square
+ 
+
+ align:start position:0%
+uh into uh K Square Pi Pi Square
+DK
+
+ align:start position:0%
+DK
+ 
+
+ align:start position:0%
+DK
+D and D right at the the everything in
+
+ align:start position:0%
+D and D right at the the everything in
+ 
+
+ align:start position:0%
+D and D right at the the everything in
+this blob I'm going to convert right in
+
+ align:start position:0%
+this blob I'm going to convert right in
+ 
+
+ align:start position:0%
+this blob I'm going to convert right in
+terms of e so I have a relation between
+
+ align:start position:0%
+terms of e so I have a relation between
+ 
+
+ align:start position:0%
+terms of e so I have a relation between
+K
+
+ align:start position:0%
+K
+ 
+
+ align:start position:0%
+K
+right and E so I can convert this K into
+
+ align:start position:0%
+right and E so I can convert this K into
+ 
+
+ align:start position:0%
+right and E so I can convert this K into
+e so if I write this in in terms of e
+
+ align:start position:0%
+e so if I write this in in terms of e
+ 
+
+ align:start position:0%
+e so if I write this in in terms of e
+and i integrate over e this is my
+
+ align:start position:0%
+and i integrate over e this is my
+ 
+
+ align:start position:0%
+and i integrate over e this is my
+density of States per energy
+
+ align:start position:0%
+density of States per energy
+ 
+
+ align:start position:0%
+density of States per energy
+interval right here is my L of States
+
+ align:start position:0%
+interval right here is my L of States
+ 
+
+ align:start position:0%
+interval right here is my L of States
+per Delta k here is my dens stat per
+
+ align:start position:0%
+per Delta k here is my dens stat per
+ 
+
+ align:start position:0%
+per Delta k here is my dens stat per
+Delta e and say similarly you can write
+
+ align:start position:0%
+Delta e and say similarly you can write
+ 
+
+ align:start position:0%
+Delta e and say similarly you can write
+your per Delta Omega or per Delta NE or
+
+ align:start position:0%
+your per Delta Omega or per Delta NE or
+ 
+
+ align:start position:0%
+your per Delta Omega or per Delta NE or
+per Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda so with that I want to just to
+
+ align:start position:0%
+Lambda so with that I want to just to
+ 
+
+ align:start position:0%
+Lambda so with that I want to just to
+say you have the you feel that it's it's
+
+ align:start position:0%
+say you have the you feel that it's it's
+ 
+
+ align:start position:0%
+say you have the you feel that it's it's
+a mathematic concept and the case you
+
+ align:start position:0%
+a mathematic concept and the case you
+ 
+
+ align:start position:0%
+a mathematic concept and the case you
+can translate you can start from here
+
+ align:start position:0%
+can translate you can start from here
+ 
+
+ align:start position:0%
+can translate you can start from here
+you can write your summation and go
+
+ align:start position:0%
+you can write your summation and go
+ 
+
+ align:start position:0%
+you can write your summation and go
+through that I've done that probably 100
+
+ align:start position:0%
+through that I've done that probably 100
+ 
+
+ align:start position:0%
+through that I've done that probably 100
+of times so now I can I remember when I
+
+ align:start position:0%
+of times so now I can I remember when I
+ 
+
+ align:start position:0%
+of times so now I can I remember when I
+learned I always go to book and what's
+
+ align:start position:0%
+learned I always go to book and what's
+ 
+
+ align:start position:0%
+learned I always go to book and what's
+the formula gave in the book but if you
+
+ align:start position:0%
+the formula gave in the book but if you
+ 
+
+ align:start position:0%
+the formula gave in the book but if you
+get comfortable with that summation is
+
+ align:start position:0%
+get comfortable with that summation is
+ 
+
+ align:start position:0%
+get comfortable with that summation is
+translating summation into integration
+
+ align:start position:0%
+translating summation into integration
+ 
+
+ align:start position:0%
+translating summation into integration
+and particularly when later on when we
+
+ align:start position:0%
+and particularly when later on when we
+ 
+
+ align:start position:0%
+and particularly when later on when we
+do like a bman equation transport this
+
+ align:start position:0%
+do like a bman equation transport this
+ 
+
+ align:start position:0%
+do like a bman equation transport this
+is going to a function of KX KY
+
+ align:start position:0%
+is going to a function of KX KY
+ 
+
+ align:start position:0%
+is going to a function of KX KY
+KZ so I do not actually do D when I
+
+ align:start position:0%
+KZ so I do not actually do D when I
+ 
+
+ align:start position:0%
+KZ so I do not actually do D when I
+convert dkx dky dkz I do see f i do
+
+ align:start position:0%
+convert dkx dky dkz I do see f i do
+ 
+
+ align:start position:0%
+convert dkx dky dkz I do see f i do
+spherical coordinate but I don't have
+
+ align:start position:0%
+spherical coordinate but I don't have
+ 
+
+ align:start position:0%
+spherical coordinate but I don't have
+the function itself do not have
+
+ align:start position:0%
+the function itself do not have
+ 
+
+ align:start position:0%
+the function itself do not have
+spherical symmetry so I will have to do
+
+ align:start position:0%
+spherical symmetry so I will have to do
+ 
+
+ align:start position:0%
+spherical symmetry so I will have to do
+in the general case this one right if I
+
+ align:start position:0%
+in the general case this one right if I
+ 
+
+ align:start position:0%
+in the general case this one right if I
+do sperical coordinate is sin Theta D
+
+ align:start position:0%
+do sperical coordinate is sin Theta D
+ 
+
+ align:start position:0%
+do sperical coordinate is sin Theta D
+Theta d f d uh K and K Square so this
+
+ align:start position:0%
+Theta d f d uh K and K Square so this
+ 
+
+ align:start position:0%
+Theta d f d uh K and K Square so this
+will be my spherical converting a unit
+
+ align:start position:0%
+will be my spherical converting a unit
+ 
+
+ align:start position:0%
+will be my spherical converting a unit
+volume in ction into a unit volume in
+
+ align:start position:0%
+volume in ction into a unit volume in
+ 
+
+ align:start position:0%
+volume in ction into a unit volume in
+spheric right but we're not doing the
+
+ align:start position:0%
+spheric right but we're not doing the
+ 
+
+ align:start position:0%
+spheric right but we're not doing the
+now when you do transport this is is so
+
+ align:start position:0%
+now when you do transport this is is so
+ 
+
+ align:start position:0%
+now when you do transport this is is so
+common
+
+ align:start position:0%
+common
+ 
+
+ align:start position:0%
+common
+okay okay so that's the uh uh the the
+
+ align:start position:0%
+okay okay so that's the uh uh the the
+ 
+
+ align:start position:0%
+okay okay so that's the uh uh the the
+concept of den States and let's best uh
+
+ align:start position:0%
+concept of den States and let's best uh
+ 
+
+ align:start position:0%
+concept of den States and let's best uh
+uh use this concept and do a few
+
+ align:start position:0%
+uh use this concept and do a few
+ 
+
+ align:start position:0%
+uh use this concept and do a few
+examples to
+
+ align:start position:0%
+examples to
+ 
+
+ align:start position:0%
+examples to
+get fer more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comfortable so let's first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh look at that they continue our fir
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level right and uh uh I'm going
+
+ align:start position:0%
+level right and uh uh I'm going
+ 
+
+ align:start position:0%
+level right and uh uh I'm going
+to you can take in in this case it
+
+ align:start position:0%
+to you can take in in this case it
+ 
+
+ align:start position:0%
+to you can take in in this case it
+depends on whether you take where you
+
+ align:start position:0%
+depends on whether you take where you
+ 
+
+ align:start position:0%
+depends on whether you take where you
+take a reference e say right
+
+ align:start position:0%
+take a reference e say right
+ 
+
+ align:start position:0%
+take a reference e say right
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh uh if I write the way I'm writing 0
+
+ align:start position:0%
+uh uh if I write the way I'm writing 0
+ 
+
+ align:start position:0%
+uh uh if I write the way I'm writing 0
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+EF integration 0 to EF means zero the
+
+ align:start position:0%
+EF integration 0 to EF means zero the
+ 
+
+ align:start position:0%
+EF integration 0 to EF means zero the
+Finish start equal
+
+ align:start position:0%
+Finish start equal
+ 
+
+ align:start position:0%
+Finish start equal
+Z so in that case I cannot use EC
+
+ align:start position:0%
+Z so in that case I cannot use EC
+ 
+
+ align:start position:0%
+Z so in that case I cannot use EC
+because between
+
+ align:start position:0%
+because between
+ 
+
+ align:start position:0%
+because between
+zero and EC there's no energy state
+
+ align:start position:0%
+zero and EC there's no energy state
+ 
+
+ align:start position:0%
+zero and EC there's no energy state
+electron cannot fail between zero EC
+
+ align:start position:0%
+electron cannot fail between zero EC
+ 
+
+ align:start position:0%
+electron cannot fail between zero EC
+right so you have to be careful when you
+
+ align:start position:0%
+right so you have to be careful when you
+ 
+
+ align:start position:0%
+right so you have to be careful when you
+write those
+
+ align:start position:0%
+write those
+ 
+
+ align:start position:0%
+write those
+formulas uh and use yourself
+
+ align:start position:0%
+formulas uh and use yourself
+ 
+
+ align:start position:0%
+formulas uh and use yourself
+consistently what's your reference where
+
+ align:start position:0%
+consistently what's your reference where
+ 
+
+ align:start position:0%
+consistently what's your reference where
+you're doing your
+
+ align:start position:0%
+you're doing your
+ 
+
+ align:start position:0%
+you're doing your
+integration just a
+
+ align:start position:0%
+integration just a
+ 
+
+ align:start position:0%
+integration just a
+reminder and uh if I do following what I
+
+ align:start position:0%
+reminder and uh if I do following what I
+ 
+
+ align:start position:0%
+reminder and uh if I do following what I
+have here I have per unit volume I give
+
+ align:start position:0%
+have here I have per unit volume I give
+ 
+
+ align:start position:0%
+have here I have per unit volume I give
+you this number of
+
+ align:start position:0%
+you this number of
+ 
+
+ align:start position:0%
+you this number of
+electrons and I want to find at Absolute
+
+ align:start position:0%
+electrons and I want to find at Absolute
+ 
+
+ align:start position:0%
+electrons and I want to find at Absolute
+Zero temperature where is the uppermost
+
+ align:start position:0%
+Zero temperature where is the uppermost
+ 
+
+ align:start position:0%
+Zero temperature where is the uppermost
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+level right so my uh band then E equals
+
+ align:start position:0%
+level right so my uh band then E equals
+ 
+
+ align:start position:0%
+level right so my uh band then E equals
+h² k sare 2
+
+ align:start position:0%
+h² k sare 2
+ 
+
+ align:start position:0%
+h² k sare 2
+m because my uh energy start the fining
+
+ align:start position:0%
+m because my uh energy start the fining
+ 
+
+ align:start position:0%
+m because my uh energy start the fining
+start this is my e this is my K I'm
+
+ align:start position:0%
+start this is my e this is my K I'm
+ 
+
+ align:start position:0%
+start this is my e this is my K I'm
+trying to find out where is
+
+ align:start position:0%
+trying to find out where is
+ 
+
+ align:start position:0%
+trying to find out where is
+EF right this is the
+
+ align:start position:0%
+EF right this is the
+ 
+
+ align:start position:0%
+EF right this is the
+formula and uh so in that case what I
+
+ align:start position:0%
+formula and uh so in that case what I
+ 
+
+ align:start position:0%
+formula and uh so in that case what I
+have is FAL 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right uh that's below the formula will
+
+ align:start position:0%
+right uh that's below the formula will
+ 
+
+ align:start position:0%
+right uh that's below the formula will
+all the energy each state is uh uh spin
+
+ align:start position:0%
+all the energy each state is uh uh spin
+ 
+
+ align:start position:0%
+all the energy each state is uh uh spin
+up spin down so I have n equals n way
+
+ align:start position:0%
+up spin down so I have n equals n way
+ 
+
+ align:start position:0%
+up spin down so I have n equals n way
+equals z
+
+ align:start position:0%
+equals z
+ 
+
+ align:start position:0%
+equals z
+EF and uh uh one so the uh K Square so
+
+ align:start position:0%
+EF and uh uh one so the uh K Square so
+ 
+
+ align:start position:0%
+EF and uh uh one so the uh K Square so
+what's my K Square now I need to convert
+
+ align:start position:0%
+what's my K Square now I need to convert
+ 
+
+ align:start position:0%
+what's my K Square now I need to convert
+I want to convert into e
+
+ align:start position:0%
+I want to convert into e
+ 
+
+ align:start position:0%
+I want to convert into e
+okay this one is easy that's my if I do
+
+ align:start position:0%
+okay this one is easy that's my if I do
+ 
+
+ align:start position:0%
+okay this one is easy that's my if I do
+in terms of
+
+ align:start position:0%
+in terms of
+ 
+
+ align:start position:0%
+in terms of
+K but I want to do in terms of e and uh
+
+ align:start position:0%
+K but I want to do in terms of e and uh
+ 
+
+ align:start position:0%
+K but I want to do in terms of e and uh
+uh so what I have K Square uh is 2 m
+
+ align:start position:0%
+uh so what I have K Square uh is 2 m
+ 
+
+ align:start position:0%
+uh so what I have K Square uh is 2 m
+right so k equal 2 m star e over H bar
+
+ align:start position:0%
+right so k equal 2 m star e over H bar
+ 
+
+ align:start position:0%
+right so k equal 2 m star e over H bar
+Square 12 right based on the dispersion
+
+ align:start position:0%
+Square 12 right based on the dispersion
+ 
+
+ align:start position:0%
+Square 12 right based on the dispersion
+so I have two uh K square is 2 m uh star
+
+ align:start position:0%
+so I have two uh K square is 2 m uh star
+ 
+
+ align:start position:0%
+so I have two uh K square is 2 m uh star
+e h bar Square that's my K Square Pi
+
+ align:start position:0%
+e h bar Square that's my K Square Pi
+ 
+
+ align:start position:0%
+e h bar Square that's my K Square Pi
+Square so I will put a pi Square
+
+ align:start position:0%
+Square so I will put a pi Square
+ 
+
+ align:start position:0%
+Square so I will put a pi Square
+here and then I have my D
+
+ align:start position:0%
+here and then I have my D
+ 
+
+ align:start position:0%
+here and then I have my D
+KDE DK
+
+ align:start position:0%
+KDE DK
+ 
+
+ align:start position:0%
+KDE DK
+D this is my K this is my e so my dkd is
+
+ align:start position:0%
+D this is my K this is my e so my dkd is
+ 
+
+ align:start position:0%
+D this is my K this is my e so my dkd is
+12 uh 2 m star
+
+ align:start position:0%
+12 uh 2 m star
+ 
+
+ align:start position:0%
+12 uh 2 m star
+H bar square and uh uh DK D is this is a
+
+ align:start position:0%
+H bar square and uh uh DK D is this is a
+ 
+
+ align:start position:0%
+H bar square and uh uh DK D is this is a
+1 12 and e -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one2 so this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+overall integrate over
+
+ align:start position:0%
+overall integrate over
+ 
+
+ align:start position:0%
+overall integrate over
+de now I'm going to erase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so what I've written down is really
+
+ align:start position:0%
+this so what I've written down is really
+ 
+
+ align:start position:0%
+this so what I've written down is really
+what's
+
+ align:start position:0%
+what's
+ 
+
+ align:start position:0%
+what's
+inside the this I convert the K into E I
+
+ align:start position:0%
+inside the this I convert the K into E I
+ 
+
+ align:start position:0%
+inside the this I convert the K into E I
+convert DK D or write it also in terms
+
+ align:start position:0%
+convert DK D or write it also in terms
+ 
+
+ align:start position:0%
+convert DK D or write it also in terms
+of e so that at the end I have all that
+
+ align:start position:0%
+of e so that at the end I have all that
+ 
+
+ align:start position:0%
+of e so that at the end I have all that
+blob is my d sub
+
+ align:start position:0%
+blob is my d sub
+ 
+
+ align:start position:0%
+blob is my d sub
+state right so here is what's my dens of
+
+ align:start position:0%
+state right so here is what's my dens of
+ 
+
+ align:start position:0%
+state right so here is what's my dens of
+States you see 2 m h bar squ that's
+
+ align:start position:0%
+States you see 2 m h bar squ that's
+ 
+
+ align:start position:0%
+States you see 2 m h bar squ that's
+three halves and uh uh
+
+ align:start position:0%
+three halves and uh uh
+ 
+
+ align:start position:0%
+three halves and uh uh
+um so and the E and the E Min 12 so my
+
+ align:start position:0%
+um so and the E and the E Min 12 so my
+ 
+
+ align:start position:0%
+um so and the E and the E Min 12 so my
+density of states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is if you I just want to check
+
+ align:start position:0%
+is if you I just want to check
+ 
+
+ align:start position:0%
+is if you I just want to check
+everything is written it should be
+
+ align:start position:0%
+everything is written it should be
+ 
+
+ align:start position:0%
+everything is written it should be
+correct okay um so what I have here is 2
+
+ align:start position:0%
+correct okay um so what I have here is 2
+ 
+
+ align:start position:0%
+correct okay um so what I have here is 2
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+squar and u m
+
+ align:start position:0%
+squar and u m
+ 
+
+ align:start position:0%
+squar and u m
+star 2 m over H bar
+
+ align:start position:0%
+star 2 m over H bar
+ 
+
+ align:start position:0%
+star 2 m over H bar
+square and three
+
+ align:start position:0%
+square and three
+ 
+
+ align:start position:0%
+square and three
+halfes and uh
+
+ align:start position:0%
+halfes and uh
+ 
+
+ align:start position:0%
+halfes and uh
+e m E2 so this is my D
+
+ align:start position:0%
+e m E2 so this is my D
+ 
+
+ align:start position:0%
+e m E2 so this is my D
+substate and this e is referring to my
+
+ align:start position:0%
+substate and this e is referring to my
+ 
+
+ align:start position:0%
+substate and this e is referring to my
+uh zero is at the bottom e say if I take
+
+ align:start position:0%
+uh zero is at the bottom e say if I take
+ 
+
+ align:start position:0%
+uh zero is at the bottom e say if I take
+my zero at a different location I have
+
+ align:start position:0%
+my zero at a different location I have
+ 
+
+ align:start position:0%
+my zero at a different location I have
+to do e Min e
+
+ align:start position:0%
+to do e Min e
+ 
+
+ align:start position:0%
+to do e Min e
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+okay so if
+
+ align:start position:0%
+okay so if
+ 
+
+ align:start position:0%
+okay so if
+you many many times when I was just
+
+ align:start position:0%
+you many many times when I was just
+ 
+
+ align:start position:0%
+you many many times when I was just
+learning this I just say okay I forgot
+
+ align:start position:0%
+learning this I just say okay I forgot
+ 
+
+ align:start position:0%
+learning this I just say okay I forgot
+it I went back I to the book I do a
+
+ align:start position:0%
+it I went back I to the book I do a
+ 
+
+ align:start position:0%
+it I went back I to the book I do a
+derivation and I plug in here because at
+
+ align:start position:0%
+derivation and I plug in here because at
+ 
+
+ align:start position:0%
+derivation and I plug in here because at
+the end you want to do this f * D and
+
+ align:start position:0%
+the end you want to do this f * D and
+ 
+
+ align:start position:0%
+the end you want to do this f * D and
+integrate the over
+
+ align:start position:0%
+integrate the over
+ 
+
+ align:start position:0%
+integrate the over
+energy but say now I can comfortably sit
+
+ align:start position:0%
+energy but say now I can comfortably sit
+ 
+
+ align:start position:0%
+energy but say now I can comfortably sit
+there and every time I forget I say I
+
+ align:start position:0%
+there and every time I forget I say I
+ 
+
+ align:start position:0%
+there and every time I forget I say I
+redo my summation to integration
+
+ align:start position:0%
+redo my summation to integration
+ 
+
+ align:start position:0%
+redo my summation to integration
+conversion okay it takes many times
+
+ align:start position:0%
+conversion okay it takes many times
+ 
+
+ align:start position:0%
+conversion okay it takes many times
+so that's the den
+
+ align:start position:0%
+so that's the den
+ 
+
+ align:start position:0%
+so that's the den
+state right and uh of course now I want
+
+ align:start position:0%
+state right and uh of course now I want
+ 
+
+ align:start position:0%
+state right and uh of course now I want
+to find out where is EF right so here if
+
+ align:start position:0%
+to find out where is EF right so here if
+ 
+
+ align:start position:0%
+to find out where is EF right so here if
+you if you say this is your EF you put
+
+ align:start position:0%
+you if you say this is your EF you put
+ 
+
+ align:start position:0%
+you if you say this is your EF you put
+it in this D of states is d e d de right
+
+ align:start position:0%
+it in this D of states is d e d de right
+ 
+
+ align:start position:0%
+it in this D of states is d e d de right
+essentially what I have here is zero EF
+
+ align:start position:0%
+essentially what I have here is zero EF
+ 
+
+ align:start position:0%
+essentially what I have here is zero EF
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+d many times people get familiar this is
+
+ align:start position:0%
+d many times people get familiar this is
+ 
+
+ align:start position:0%
+d many times people get familiar this is
+where they start
+
+ align:start position:0%
+where they start
+ 
+
+ align:start position:0%
+where they start
+right I want to find out where is the EF
+
+ align:start position:0%
+right I want to find out where is the EF
+ 
+
+ align:start position:0%
+right I want to find out where is the EF
+give me the number of electron I write D
+
+ align:start position:0%
+give me the number of electron I write D
+ 
+
+ align:start position:0%
+give me the number of electron I write D
+of State I integrate over e that's how
+
+ align:start position:0%
+of State I integrate over e that's how
+ 
+
+ align:start position:0%
+of State I integrate over e that's how
+many states I have right each state I
+
+ align:start position:0%
+many states I have right each state I
+ 
+
+ align:start position:0%
+many states I have right each state I
+have one electron so that's the how many
+
+ align:start position:0%
+have one electron so that's the how many
+ 
+
+ align:start position:0%
+have one electron so that's the how many
+electron I have and with that you go to
+
+ align:start position:0%
+electron I have and with that you go to
+ 
+
+ align:start position:0%
+electron I have and with that you go to
+do your integration you say this is a
+
+ align:start position:0%
+do your integration you say this is a
+ 
+
+ align:start position:0%
+do your integration you say this is a
+constant you can take out it's really e
+
+ align:start position:0%
+constant you can take out it's really e
+ 
+
+ align:start position:0%
+constant you can take out it's really e
+half integration over
+
+ align:start position:0%
+half integration over
+ 
+
+ align:start position:0%
+half integration over
+e uh D and to zero to EF
+
+ align:start position:0%
+e uh D and to zero to EF
+ 
+
+ align:start position:0%
+e uh D and to zero to EF
+right so this will give you where is
+
+ align:start position:0%
+right so this will give you where is
+ 
+
+ align:start position:0%
+right so this will give you where is
+your form
+
+ align:start position:0%
+your form
+ 
+
+ align:start position:0%
+your form
+level you do your integration you find
+
+ align:start position:0%
+level you do your integration you find
+ 
+
+ align:start position:0%
+level you do your integration you find
+out your
+
+ align:start position:0%
+out your
+ 
+
+ align:start position:0%
+out your
+EF equal 3 Pi s n 23 uh and H bar Square
+
+ align:start position:0%
+EF equal 3 Pi s n 23 uh and H bar Square
+ 
+
+ align:start position:0%
+EF equal 3 Pi s n 23 uh and H bar Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m that's after you do your integration
+
+ align:start position:0%
+m that's after you do your integration
+ 
+
+ align:start position:0%
+m that's after you do your integration
+and inverse writing in terms of EF
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any question
+
+ align:start position:0%
+okay any question
+ 
+
+ align:start position:0%
+okay any question
+here it's converting summation into
+
+ align:start position:0%
+here it's converting summation into
+ 
+
+ align:start position:0%
+here it's converting summation into
+integration do the correct accounting
+
+ align:start position:0%
+integration do the correct accounting
+ 
+
+ align:start position:0%
+integration do the correct accounting
+the density of States tells you the L of
+
+ align:start position:0%
+the density of States tells you the L of
+ 
+
+ align:start position:0%
+the density of States tells you the L of
+quantum State per energy interval per V
+
+ align:start position:0%
+quantum State per energy interval per V
+ 
+
+ align:start position:0%
+quantum State per energy interval per V
+Vector interval per frequency interval
+
+ align:start position:0%
+Vector interval per frequency interval
+ 
+
+ align:start position:0%
+Vector interval per frequency interval
+many ways to write
+
+ align:start position:0%
+many ways to write
+ 
+
+ align:start position:0%
+many ways to write
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and just a
+
+ align:start position:0%
+and just a
+ 
+
+ align:start position:0%
+and just a
+comment right and let me write the let
+
+ align:start position:0%
+comment right and let me write the let
+ 
+
+ align:start position:0%
+comment right and let me write the let
+me draw the D self state for
+
+ align:start position:0%
+me draw the D self state for
+ 
+
+ align:start position:0%
+me draw the D self state for
+electron this is the
+
+ align:start position:0%
+electron this is the
+ 
+
+ align:start position:0%
+electron this is the
+energy this is
+
+ align:start position:0%
+energy this is
+ 
+
+ align:start position:0%
+energy this is
+d right and uh if I have energies
+
+ align:start position:0%
+d right and uh if I have energies
+ 
+
+ align:start position:0%
+d right and uh if I have energies
+relative to e say this is e minus E say
+
+ align:start position:0%
+relative to e say this is e minus E say
+ 
+
+ align:start position:0%
+relative to e say this is e minus E say
+so I I uh I put my e say not that the
+
+ align:start position:0%
+so I I uh I put my e say not that the
+ 
+
+ align:start position:0%
+so I I uh I put my e say not that the
+zero but at the arbitrary point then
+
+ align:start position:0%
+zero but at the arbitrary point then
+ 
+
+ align:start position:0%
+zero but at the arbitrary point then
+this is the paraba dens of state that's
+
+ align:start position:0%
+this is the paraba dens of state that's
+ 
+
+ align:start position:0%
+this is the paraba dens of state that's
+the shape of the install State because
+
+ align:start position:0%
+the shape of the install State because
+ 
+
+ align:start position:0%
+the shape of the install State because
+it's square
+
+ align:start position:0%
+it's square
+ 
+
+ align:start position:0%
+it's square
+root okay that's because if you see at
+
+ align:start position:0%
+root okay that's because if you see at
+ 
+
+ align:start position:0%
+root okay that's because if you see at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+bottom there are not many states but you
+
+ align:start position:0%
+bottom there are not many states but you
+ 
+
+ align:start position:0%
+bottom there are not many states but you
+increase energy there are a lot more
+
+ align:start position:0%
+increase energy there are a lot more
+ 
+
+ align:start position:0%
+increase energy there are a lot more
+State uh states that have same energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values okay so now let's do the same for
+
+ align:start position:0%
+values okay so now let's do the same for
+ 
+
+ align:start position:0%
+values okay so now let's do the same for
+Fong conceptually you follow the same
+
+ align:start position:0%
+Fong conceptually you follow the same
+ 
+
+ align:start position:0%
+Fong conceptually you follow the same
+same process
+
+ align:start position:0%
+same process
+ 
+
+ align:start position:0%
+same process
+converting this summation into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integration okay so uh I'm going to look
+
+ align:start position:0%
+integration okay so uh I'm going to look
+ 
+
+ align:start position:0%
+integration okay so uh I'm going to look
+at the Fong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm uh using the bu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model and the B model say Omega = way *
+
+ align:start position:0%
+model and the B model say Omega = way *
+ 
+
+ align:start position:0%
+model and the B model say Omega = way *
+K and this K is the
+
+ align:start position:0%
+K and this K is the
+ 
+
+ align:start position:0%
+K and this K is the
+magnitude of the V Vector right so it's
+
+ align:start position:0%
+magnitude of the V Vector right so it's
+ 
+
+ align:start position:0%
+magnitude of the V Vector right so it's
+a square root of KX s + k y sare plus KZ
+
+ align:start position:0%
+a square root of KX s + k y sare plus KZ
+ 
+
+ align:start position:0%
+a square root of KX s + k y sare plus KZ
+squ and also in this case the Fons are d
+
+ align:start position:0%
+squ and also in this case the Fons are d
+ 
+
+ align:start position:0%
+squ and also in this case the Fons are d
+generate three
+
+ align:start position:0%
+generate three
+ 
+
+ align:start position:0%
+generate three
+polarizations transverse to longitudinal
+
+ align:start position:0%
+polarizations transverse to longitudinal
+ 
+
+ align:start position:0%
+polarizations transverse to longitudinal
+one and thatby just collap the all the
+
+ align:start position:0%
+one and thatby just collap the all the
+ 
+
+ align:start position:0%
+one and thatby just collap the all the
+three into one line there so but you
+
+ align:start position:0%
+three into one line there so but you
+ 
+
+ align:start position:0%
+three into one line there so but you
+should still know there are three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polarizations okay so in that case if
+
+ align:start position:0%
+polarizations okay so in that case if
+ 
+
+ align:start position:0%
+polarizations okay so in that case if
+you go back to starting from my
+
+ align:start position:0%
+you go back to starting from my
+ 
+
+ align:start position:0%
+you go back to starting from my
+summation whatever function right and
+
+ align:start position:0%
+summation whatever function right and
+ 
+
+ align:start position:0%
+summation whatever function right and
+let's forget about the what I'm going to
+
+ align:start position:0%
+let's forget about the what I'm going to
+ 
+
+ align:start position:0%
+let's forget about the what I'm going to
+integrate because right now I don't have
+
+ align:start position:0%
+integrate because right now I don't have
+ 
+
+ align:start position:0%
+integrate because right now I don't have
+good L good stuff of f for you yet I'm
+
+ align:start position:0%
+good L good stuff of f for you yet I'm
+ 
+
+ align:start position:0%
+good L good stuff of f for you yet I'm
+going to we need to go to uh the uh say
+
+ align:start position:0%
+going to we need to go to uh the uh say
+ 
+
+ align:start position:0%
+going to we need to go to uh the uh say
+statistical distribution to say uh to
+
+ align:start position:0%
+statistical distribution to say uh to
+ 
+
+ align:start position:0%
+statistical distribution to say uh to
+actually give you f
+
+ align:start position:0%
+actually give you f
+ 
+
+ align:start position:0%
+actually give you f
+example right so I convert that
+
+ align:start position:0%
+example right so I convert that
+ 
+
+ align:start position:0%
+example right so I convert that
+summation into integration
+
+ align:start position:0%
+summation into integration
+ 
+
+ align:start position:0%
+summation into integration
+same but that factor of two which is a
+
+ align:start position:0%
+same but that factor of two which is a
+ 
+
+ align:start position:0%
+same but that factor of two which is a
+spin for
+
+ align:start position:0%
+spin for
+ 
+
+ align:start position:0%
+spin for
+electron need to become a factor of
+
+ align:start position:0%
+electron need to become a factor of
+ 
+
+ align:start position:0%
+electron need to become a factor of
+three because I have a polarization
+
+ align:start position:0%
+three because I have a polarization
+ 
+
+ align:start position:0%
+three because I have a polarization
+three the B model I have three
+
+ align:start position:0%
+three the B model I have three
+ 
+
+ align:start position:0%
+three the B model I have three
+polarization right
+
+ align:start position:0%
+polarization right
+ 
+
+ align:start position:0%
+polarization right
+okay for each KX KY KZ I have three
+
+ align:start position:0%
+okay for each KX KY KZ I have three
+ 
+
+ align:start position:0%
+okay for each KX KY KZ I have three
+polarization so I have three that's
+
+ align:start position:0%
+polarization so I have three that's
+ 
+
+ align:start position:0%
+polarization so I have three that's
+where my factor of three so if you look
+
+ align:start position:0%
+where my factor of three so if you look
+ 
+
+ align:start position:0%
+where my factor of three so if you look
+at my
+
+ align:start position:0%
+at my
+ 
+
+ align:start position:0%
+at my
+DK uh that's uh where is my DK here this
+
+ align:start position:0%
+DK uh that's uh where is my DK here this
+ 
+
+ align:start position:0%
+DK uh that's uh where is my DK here this
+is my dens of dek before is a factor of
+
+ align:start position:0%
+is my dens of dek before is a factor of
+ 
+
+ align:start position:0%
+is my dens of dek before is a factor of
+two now it's a factor of three so that
+
+ align:start position:0%
+two now it's a factor of three so that
+ 
+
+ align:start position:0%
+two now it's a factor of three so that
+should be three halfs of this so my DK
+
+ align:start position:0%
+should be three halfs of this so my DK
+ 
+
+ align:start position:0%
+should be three halfs of this so my DK
+density of states for forong
+
+ align:start position:0%
+density of states for forong
+ 
+
+ align:start position:0%
+density of states for forong
+is three halfes what I have here is K
+
+ align:start position:0%
+is three halfes what I have here is K
+ 
+
+ align:start position:0%
+is three halfes what I have here is K
+Square Pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+square right now my D
+
+ align:start position:0%
+square right now my D
+ 
+
+ align:start position:0%
+square right now my D
+Omega is
+
+ align:start position:0%
+Omega is
+ 
+
+ align:start position:0%
+Omega is
+DK and
+
+ align:start position:0%
+DK and
+ 
+
+ align:start position:0%
+DK and
+DK D Omega so this is written eventually
+
+ align:start position:0%
+DK D Omega so this is written eventually
+ 
+
+ align:start position:0%
+DK D Omega so this is written eventually
+has to be changed
+
+ align:start position:0%
+has to be changed
+ 
+
+ align:start position:0%
+has to be changed
+into K has to be changing into
+
+ align:start position:0%
+into K has to be changing into
+ 
+
+ align:start position:0%
+into K has to be changing into
+Omega right now I'm going to do
+
+ align:start position:0%
+Omega right now I'm going to do
+ 
+
+ align:start position:0%
+Omega right now I'm going to do
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+integration right for I normally don't
+
+ align:start position:0%
+integration right for I normally don't
+ 
+
+ align:start position:0%
+integration right for I normally don't
+do D my habit is typically do D Omega
+
+ align:start position:0%
+do D my habit is typically do D Omega
+ 
+
+ align:start position:0%
+do D my habit is typically do D Omega
+now I do DK D Omega right so DK D Omega
+
+ align:start position:0%
+now I do DK D Omega right so DK D Omega
+ 
+
+ align:start position:0%
+now I do DK D Omega right so DK D Omega
+so uh DK is 3 half K is Omega over V
+
+ align:start position:0%
+so uh DK is 3 half K is Omega over V
+ 
+
+ align:start position:0%
+so uh DK is 3 half K is Omega over V
+here Square Pi square and DK D
+
+ align:start position:0%
+here Square Pi square and DK D
+ 
+
+ align:start position:0%
+here Square Pi square and DK D
+Omega is 1
+
+ align:start position:0%
+Omega is 1
+ 
+
+ align:start position:0%
+Omega is 1
+weight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so with that I will get the
+
+ align:start position:0%
+right okay so with that I will get the
+ 
+
+ align:start position:0%
+right okay so with that I will get the
+three half pi Square V cubic Omega
+
+ align:start position:0%
+three half pi Square V cubic Omega
+ 
+
+ align:start position:0%
+three half pi Square V cubic Omega
+Square so this is den of
+
+ align:start position:0%
+Square so this is den of
+ 
+
+ align:start position:0%
+Square so this is den of
+states for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+and here is
+
+ align:start position:0%
+and here is
+ 
+
+ align:start position:0%
+and here is
+D Omega and here is Omega so it's a it's
+
+ align:start position:0%
+D Omega and here is Omega so it's a it's
+ 
+
+ align:start position:0%
+D Omega and here is Omega so it's a it's
+the uh Parabola it's not square root
+
+ align:start position:0%
+the uh Parabola it's not square root
+ 
+
+ align:start position:0%
+the uh Parabola it's not square root
+then of states for electron is square
+
+ align:start position:0%
+then of states for electron is square
+ 
+
+ align:start position:0%
+then of states for electron is square
+root of energy right here is actually
+
+ align:start position:0%
+root of energy right here is actually
+ 
+
+ align:start position:0%
+root of energy right here is actually
+square of
+
+ align:start position:0%
+square of
+ 
+
+ align:start position:0%
+square of
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+okay so different dispersion give you
+
+ align:start position:0%
+okay so different dispersion give you
+ 
+
+ align:start position:0%
+okay so different dispersion give you
+different density of
+
+ align:start position:0%
+different density of
+ 
+
+ align:start position:0%
+different density of
+States now this this could be easily
+
+ align:start position:0%
+States now this this could be easily
+ 
+
+ align:start position:0%
+States now this this could be easily
+converted into
+
+ align:start position:0%
+converted into
+ 
+
+ align:start position:0%
+converted into
+Photon
+
+ align:start position:0%
+Photon
+ 
+
+ align:start position:0%
+Photon
+Photon now try allow longitudinal
+
+ align:start position:0%
+Photon now try allow longitudinal
+ 
+
+ align:start position:0%
+Photon now try allow longitudinal
+electromagnetic wave right only two
+
+ align:start position:0%
+electromagnetic wave right only two
+ 
+
+ align:start position:0%
+electromagnetic wave right only two
+polarization two transverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+waves okay and that two transverse wave
+
+ align:start position:0%
+waves okay and that two transverse wave
+ 
+
+ align:start position:0%
+waves okay and that two transverse wave
+should not be three it should be
+
+ align:start position:0%
+should not be three it should be
+ 
+
+ align:start position:0%
+should not be three it should be
+two and the speed of sun becomes speed
+
+ align:start position:0%
+two and the speed of sun becomes speed
+ 
+
+ align:start position:0%
+two and the speed of sun becomes speed
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+light right so for photon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density of State in terms of frequency
+
+ align:start position:0%
+density of State in terms of frequency
+ 
+
+ align:start position:0%
+density of State in terms of frequency
+is just Omega Square Pi Square C
+
+ align:start position:0%
+is just Omega Square Pi Square C
+ 
+
+ align:start position:0%
+is just Omega Square Pi Square C
+cubic okay the best is so you see there
+
+ align:start position:0%
+cubic okay the best is so you see there
+ 
+
+ align:start position:0%
+cubic okay the best is so you see there
+and write through all
+
+ align:start position:0%
+and write through all
+ 
+
+ align:start position:0%
+and write through all
+this right getting yourself comfortable
+
+ align:start position:0%
+this right getting yourself comfortable
+ 
+
+ align:start position:0%
+this right getting yourself comfortable
+it's mathematics it's not much really
+
+ align:start position:0%
+it's mathematics it's not much really
+ 
+
+ align:start position:0%
+it's mathematics it's not much really
+not much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physics
+
+ align:start position:0%
+physics
+ 
+
+ align:start position:0%
+physics
+Okay so uh that's the uh case of 3D
+
+ align:start position:0%
+Okay so uh that's the uh case of 3D
+ 
+
+ align:start position:0%
+Okay so uh that's the uh case of 3D
+structure now let's do a
+
+ align:start position:0%
+structure now let's do a
+ 
+
+ align:start position:0%
+structure now let's do a
+2d I'm doing okay uh so we say uh let's
+
+ align:start position:0%
+2d I'm doing okay uh so we say uh let's
+ 
+
+ align:start position:0%
+2d I'm doing okay uh so we say uh let's
+look at a Quantum well let's look at
+
+ align:start position:0%
+look at a Quantum well let's look at
+ 
+
+ align:start position:0%
+look at a Quantum well let's look at
+thin film what will be the quantization
+
+ align:start position:0%
+thin film what will be the quantization
+ 
+
+ align:start position:0%
+thin film what will be the quantization
+effect on the density of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+States okay so let's do a
+
+ align:start position:0%
+States okay so let's do a
+ 
+
+ align:start position:0%
+States okay so let's do a
+2d
+
+ align:start position:0%
+2d
+ 
+
+ align:start position:0%
+2d
+uh I'm putting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this is best
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place uh I'm going to do a Quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay and before when we talk about
+
+ align:start position:0%
+well okay and before when we talk about
+ 
+
+ align:start position:0%
+well okay and before when we talk about
+Quantum well we say just a
+
+ align:start position:0%
+Quantum well we say just a
+ 
+
+ align:start position:0%
+Quantum well we say just a
+onedimensional Quantum well now I'm
+
+ align:start position:0%
+onedimensional Quantum well now I'm
+ 
+
+ align:start position:0%
+onedimensional Quantum well now I'm
+going to give you more realistic a f
+
+ align:start position:0%
+going to give you more realistic a f
+ 
+
+ align:start position:0%
+going to give you more realistic a f
+right in the case of film electron can
+
+ align:start position:0%
+right in the case of film electron can
+ 
+
+ align:start position:0%
+right in the case of film electron can
+move in
+
+ align:start position:0%
+move in
+ 
+
+ align:start position:0%
+move in
+XYZ three
+
+ align:start position:0%
+XYZ three
+ 
+
+ align:start position:0%
+XYZ three
+dimension and uh so if I have a
+
+ align:start position:0%
+dimension and uh so if I have a
+ 
+
+ align:start position:0%
+dimension and uh so if I have a
+film and in the thickness Direction I
+
+ align:start position:0%
+film and in the thickness Direction I
+ 
+
+ align:start position:0%
+film and in the thickness Direction I
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LZ
+
+ align:start position:0%
+LZ
+ 
+
+ align:start position:0%
+LZ
+okay and uh in the XY Direction uh I
+
+ align:start position:0%
+okay and uh in the XY Direction uh I
+ 
+
+ align:start position:0%
+okay and uh in the XY Direction uh I
+have have free Move Motion I don't have
+
+ align:start position:0%
+have have free Move Motion I don't have
+ 
+
+ align:start position:0%
+have have free Move Motion I don't have
+constraint right so uh uh my energy
+
+ align:start position:0%
+constraint right so uh uh my energy
+ 
+
+ align:start position:0%
+constraint right so uh uh my energy
+relation will be
+
+ align:start position:0%
+relation will be
+ 
+
+ align:start position:0%
+relation will be
+KX KY in the XY Direction I have discret
+
+ align:start position:0%
+KX KY in the XY Direction I have discret
+ 
+
+ align:start position:0%
+KX KY in the XY Direction I have discret
+Point as what we had before but say that
+
+ align:start position:0%
+Point as what we had before but say that
+ 
+
+ align:start position:0%
+Point as what we had before but say that
+2 pi LX 2 pi l y right that's my
+
+ align:start position:0%
+2 pi LX 2 pi l y right that's my
+ 
+
+ align:start position:0%
+2 pi LX 2 pi l y right that's my
+separation but my LX l y in the XY
+
+ align:start position:0%
+separation but my LX l y in the XY
+ 
+
+ align:start position:0%
+separation but my LX l y in the XY
+direction are minim
+
+ align:start position:0%
+direction are minim
+ 
+
+ align:start position:0%
+direction are minim
+M or right that's a
+
+ align:start position:0%
+M or right that's a
+ 
+
+ align:start position:0%
+M or right that's a
+macroscopic so that separation is very
+
+ align:start position:0%
+macroscopic so that separation is very
+ 
+
+ align:start position:0%
+macroscopic so that separation is very
+small on the Z Direction I'm unstr
+
+ align:start position:0%
+small on the Z Direction I'm unstr
+ 
+
+ align:start position:0%
+small on the Z Direction I'm unstr
+strong 100 unstr
+
+ align:start position:0%
+strong 100 unstr
+ 
+
+ align:start position:0%
+strong 100 unstr
+strong right so in that case recall that
+
+ align:start position:0%
+strong right so in that case recall that
+ 
+
+ align:start position:0%
+strong right so in that case recall that
+when we discuss the energy in this
+
+ align:start position:0%
+when we discuss the energy in this
+ 
+
+ align:start position:0%
+when we discuss the energy in this
+direction is standing wave right so uh n
+
+ align:start position:0%
+direction is standing wave right so uh n
+ 
+
+ align:start position:0%
+direction is standing wave right so uh n
+z and let me just use n Lambda / 2
+
+ align:start position:0%
+z and let me just use n Lambda / 2
+ 
+
+ align:start position:0%
+z and let me just use n Lambda / 2
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LZ right and uh that means Lambda equals
+
+ align:start position:0%
+LZ right and uh that means Lambda equals
+ 
+
+ align:start position:0%
+LZ right and uh that means Lambda equals
+l z
+
+ align:start position:0%
+l z
+ 
+
+ align:start position:0%
+l z
+2ide by n and you can convert this uh
+
+ align:start position:0%
+2ide by n and you can convert this uh
+ 
+
+ align:start position:0%
+2ide by n and you can convert this uh
+back into energy right HP say uh uh the
+
+ align:start position:0%
+back into energy right HP say uh uh the
+ 
+
+ align:start position:0%
+back into energy right HP say uh uh the
+momentum k = 2 pi/ Lambda and what do
+
+ align:start position:0%
+momentum k = 2 pi/ Lambda and what do
+ 
+
+ align:start position:0%
+momentum k = 2 pi/ Lambda and what do
+you have here uh 2 pi over Lambda Lambda
+
+ align:start position:0%
+you have here uh 2 pi over Lambda Lambda
+ 
+
+ align:start position:0%
+you have here uh 2 pi over Lambda Lambda
+is there so I have m pi over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LZ
+
+ align:start position:0%
+LZ
+ 
+
+ align:start position:0%
+LZ
+right and the separation between this is
+
+ align:start position:0%
+right and the separation between this is
+ 
+
+ align:start position:0%
+right and the separation between this is
+my K in the Z dire separation is become
+
+ align:start position:0%
+my K in the Z dire separation is become
+ 
+
+ align:start position:0%
+my K in the Z dire separation is become
+pi/
+
+ align:start position:0%
+pi/
+ 
+
+ align:start position:0%
+pi/
+LZ now if you look at the separation we
+
+ align:start position:0%
+LZ now if you look at the separation we
+ 
+
+ align:start position:0%
+LZ now if you look at the separation we
+say in the unconstraint case KX 2
+
+ align:start position:0%
+say in the unconstraint case KX 2
+ 
+
+ align:start position:0%
+say in the unconstraint case KX 2
+pi LX Over
+
+ align:start position:0%
+pi LX Over
+ 
+
+ align:start position:0%
+pi LX Over
+N
+
+ align:start position:0%
+N
+ 
+
+ align:start position:0%
+N
+right so in the unconstraint case is I
+
+ align:start position:0%
+right so in the unconstraint case is I
+ 
+
+ align:start position:0%
+right so in the unconstraint case is I
+have plus
+
+ align:start position:0%
+have plus
+ 
+
+ align:start position:0%
+have plus
+minus and the separation is 2 pi/ LX in
+
+ align:start position:0%
+minus and the separation is 2 pi/ LX in
+ 
+
+ align:start position:0%
+minus and the separation is 2 pi/ LX in
+the constraint case I have n is only
+
+ align:start position:0%
+the constraint case I have n is only
+ 
+
+ align:start position:0%
+the constraint case I have n is only
+plus okay and the separation is pi over
+
+ align:start position:0%
+plus okay and the separation is pi over
+ 
+
+ align:start position:0%
+plus okay and the separation is pi over
+LZ it's a is a factor of two difference
+
+ align:start position:0%
+LZ it's a is a factor of two difference
+ 
+
+ align:start position:0%
+LZ it's a is a factor of two difference
+that's because I'm using a traveling
+
+ align:start position:0%
+that's because I'm using a traveling
+ 
+
+ align:start position:0%
+that's because I'm using a traveling
+wave this traveling wave positive
+
+ align:start position:0%
+wave this traveling wave positive
+ 
+
+ align:start position:0%
+wave this traveling wave positive
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+direction to construct a standing wave
+
+ align:start position:0%
+direction to construct a standing wave
+ 
+
+ align:start position:0%
+direction to construct a standing wave
+right so it's actually equivalent
+
+ align:start position:0%
+right so it's actually equivalent
+ 
+
+ align:start position:0%
+right so it's actually equivalent
+whether I use plus
+
+ align:start position:0%
+whether I use plus
+ 
+
+ align:start position:0%
+whether I use plus
+minus in the case or whether I use
+
+ align:start position:0%
+minus in the case or whether I use
+ 
+
+ align:start position:0%
+minus in the case or whether I use
+standing way but in the case of small
+
+ align:start position:0%
+standing way but in the case of small
+ 
+
+ align:start position:0%
+standing way but in the case of small
+length l z I have to look at the
+
+ align:start position:0%
+length l z I have to look at the
+ 
+
+ align:start position:0%
+length l z I have to look at the
+separation because that summation cannot
+
+ align:start position:0%
+separation because that summation cannot
+ 
+
+ align:start position:0%
+separation because that summation cannot
+be converted into integration so this is
+
+ align:start position:0%
+be converted into integration so this is
+ 
+
+ align:start position:0%
+be converted into integration so this is
+the difference so if I write in that
+
+ align:start position:0%
+the difference so if I write in that
+ 
+
+ align:start position:0%
+the difference so if I write in that
+case I'll write my energy is
+
+ align:start position:0%
+case I'll write my energy is
+ 
+
+ align:start position:0%
+case I'll write my energy is
+h² uh say KX
+
+ align:start position:0%
+h² uh say KX
+ 
+
+ align:start position:0%
+h² uh say KX
+s+ k y 2 that's in the so effective mass
+
+ align:start position:0%
+s+ k y 2 that's in the so effective mass
+ 
+
+ align:start position:0%
+s+ k y 2 that's in the so effective mass
+in the implant
+
+ align:start position:0%
+in the implant
+ 
+
+ align:start position:0%
+in the implant
+Direction in the XY
+
+ align:start position:0%
+Direction in the XY
+ 
+
+ align:start position:0%
+Direction in the XY
+Direction okay and in the Z Direction
+
+ align:start position:0%
+Direction okay and in the Z Direction
+ 
+
+ align:start position:0%
+Direction okay and in the Z Direction
+and I have if I use this I can do uh my
+
+ align:start position:0%
+and I have if I use this I can do uh my
+ 
+
+ align:start position:0%
+and I have if I use this I can do uh my
+energy quantization right is HK / by HK
+
+ align:start position:0%
+energy quantization right is HK / by HK
+ 
+
+ align:start position:0%
+energy quantization right is HK / by HK
+2 / 2 m so 12 uh m h K Square
+
+ align:start position:0%
+2 / 2 m so 12 uh m h K Square
+ 
+
+ align:start position:0%
+2 / 2 m so 12 uh m h K Square
+h² K square is m pi/ l z square right n
+
+ align:start position:0%
+h² K square is m pi/ l z square right n
+ 
+
+ align:start position:0%
+h² K square is m pi/ l z square right n
+equals uh 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 okay so this is my energy level I'm
+
+ align:start position:0%
+2 okay so this is my energy level I'm
+ 
+
+ align:start position:0%
+2 okay so this is my energy level I'm
+still writing h² KZ Square KZ Square now
+
+ align:start position:0%
+still writing h² KZ Square KZ Square now
+ 
+
+ align:start position:0%
+still writing h² KZ Square KZ Square now
+I do a standing way
+
+ align:start position:0%
+I do a standing way
+ 
+
+ align:start position:0%
+I do a standing way
+and because my LZ is very
+
+ align:start position:0%
+and because my LZ is very
+ 
+
+ align:start position:0%
+and because my LZ is very
+small so between the two n uh uh
+
+ align:start position:0%
+small so between the two n uh uh
+ 
+
+ align:start position:0%
+small so between the two n uh uh
+consecutive n there could be many KX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KY okay so if you look at this what I
+
+ align:start position:0%
+KY okay so if you look at this what I
+ 
+
+ align:start position:0%
+KY okay so if you look at this what I
+what I have here recall in a
+
+ align:start position:0%
+what I have here recall in a
+ 
+
+ align:start position:0%
+what I have here recall in a
+3D right a spherical say we say a
+
+ align:start position:0%
+3D right a spherical say we say a
+ 
+
+ align:start position:0%
+3D right a spherical say we say a
+constant energy surface is a sphere
+
+ align:start position:0%
+constant energy surface is a sphere
+ 
+
+ align:start position:0%
+constant energy surface is a sphere
+right now I have a constant energy
+
+ align:start position:0%
+right now I have a constant energy
+ 
+
+ align:start position:0%
+right now I have a constant energy
+surface is XY plan is a circle but then
+
+ align:start position:0%
+surface is XY plan is a circle but then
+ 
+
+ align:start position:0%
+surface is XY plan is a circle but then
+depends on the N value I have jumps
+
+ align:start position:0%
+depends on the N value I have jumps
+ 
+
+ align:start position:0%
+depends on the N value I have jumps
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+values okay depends on the different
+
+ align:start position:0%
+values okay depends on the different
+ 
+
+ align:start position:0%
+values okay depends on the different
+energy so the other way to think about
+
+ align:start position:0%
+energy so the other way to think about
+ 
+
+ align:start position:0%
+energy so the other way to think about
+this Nal 1 so uh this is where we draw
+
+ align:start position:0%
+this Nal 1 so uh this is where we draw
+ 
+
+ align:start position:0%
+this Nal 1 so uh this is where we draw
+quantization effect this is you say
+
+ align:start position:0%
+quantization effect this is you say
+ 
+
+ align:start position:0%
+quantization effect this is you say
+before that's a
+
+ align:start position:0%
+before that's a
+ 
+
+ align:start position:0%
+before that's a
+bulk right that's a bulk of course I'm
+
+ align:start position:0%
+bulk right that's a bulk of course I'm
+ 
+
+ align:start position:0%
+bulk right that's a bulk of course I'm
+only drawing One Direction
+
+ align:start position:0%
+only drawing One Direction
+ 
+
+ align:start position:0%
+only drawing One Direction
+okay but you have to think this is a KX
+
+ align:start position:0%
+okay but you have to think this is a KX
+ 
+
+ align:start position:0%
+okay but you have to think this is a KX
+KY is a is like so you do a
+
+ align:start position:0%
+KY is a is like so you do a
+ 
+
+ align:start position:0%
+KY is a is like so you do a
+rotation right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and they when I have quantization
+
+ align:start position:0%
+here and they when I have quantization
+ 
+
+ align:start position:0%
+here and they when I have quantization
+it turns out that the minimum energy not
+
+ align:start position:0%
+it turns out that the minimum energy not
+ 
+
+ align:start position:0%
+it turns out that the minimum energy not
+can not longer be here because nals 1
+
+ align:start position:0%
+can not longer be here because nals 1
+ 
+
+ align:start position:0%
+can not longer be here because nals 1
+that gives me the first
+
+ align:start position:0%
+that gives me the first
+ 
+
+ align:start position:0%
+that gives me the first
+level right so the bottom of the
+
+ align:start position:0%
+level right so the bottom of the
+ 
+
+ align:start position:0%
+level right so the bottom of the
+conduction B actually will shift
+
+ align:start position:0%
+conduction B actually will shift
+ 
+
+ align:start position:0%
+conduction B actually will shift
+up right so that's why sometimes people
+
+ align:start position:0%
+up right so that's why sometimes people
+ 
+
+ align:start position:0%
+up right so that's why sometimes people
+say uh how I can open a
+
+ align:start position:0%
+say uh how I can open a
+ 
+
+ align:start position:0%
+say uh how I can open a
+gap when I have quantization I can
+
+ align:start position:0%
+gap when I have quantization I can
+ 
+
+ align:start position:0%
+gap when I have quantization I can
+artificially turn even a sem metal into
+
+ align:start position:0%
+artificially turn even a sem metal into
+ 
+
+ align:start position:0%
+artificially turn even a sem metal into
+semiconductor let me give you one one
+
+ align:start position:0%
+semiconductor let me give you one one
+ 
+
+ align:start position:0%
+semiconductor let me give you one one
+idea for example when we work on theral
+
+ align:start position:0%
+idea for example when we work on theral
+ 
+
+ align:start position:0%
+idea for example when we work on theral
+electrics uh there's a material bism
+
+ align:start position:0%
+electrics uh there's a material bism
+ 
+
+ align:start position:0%
+electrics uh there's a material bism
+turns out bism is like
+
+ align:start position:0%
+turns out bism is like
+ 
+
+ align:start position:0%
+turns out bism is like
+this right it's a Sim
+
+ align:start position:0%
+this right it's a Sim
+ 
+
+ align:start position:0%
+this right it's a Sim
+metal the uh there there's no Gap this
+
+ align:start position:0%
+metal the uh there there's no Gap this
+ 
+
+ align:start position:0%
+metal the uh there there's no Gap this
+is the top of Valance bottom conduction
+
+ align:start position:0%
+is the top of Valance bottom conduction
+ 
+
+ align:start position:0%
+is the top of Valance bottom conduction
+conduction band is below Valance band so
+
+ align:start position:0%
+conduction band is below Valance band so
+ 
+
+ align:start position:0%
+conduction band is below Valance band so
+in this the form level is around here
+
+ align:start position:0%
+in this the form level is around here
+ 
+
+ align:start position:0%
+in this the form level is around here
+and there's no Gap it's a s metal right
+
+ align:start position:0%
+and there's no Gap it's a s metal right
+ 
+
+ align:start position:0%
+and there's no Gap it's a s metal right
+s metal is not good for Thal
+
+ align:start position:0%
+s metal is not good for Thal
+ 
+
+ align:start position:0%
+s metal is not good for Thal
+electrics and uh because when
+
+ align:start position:0%
+electrics and uh because when
+ 
+
+ align:start position:0%
+electrics and uh because when
+electron in this H in this this still
+
+ align:start position:0%
+electron in this H in this this still
+ 
+
+ align:start position:0%
+electron in this H in this this still
+have you can still have electron
+
+ align:start position:0%
+have you can still have electron
+ 
+
+ align:start position:0%
+have you can still have electron
+holes and uh when they diffuse to the
+
+ align:start position:0%
+holes and uh when they diffuse to the
+ 
+
+ align:start position:0%
+holes and uh when they diffuse to the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+direction the heat they cancel each
+
+ align:start position:0%
+direction the heat they cancel each
+ 
+
+ align:start position:0%
+direction the heat they cancel each
+other so it's not good so how we can
+
+ align:start position:0%
+other so it's not good so how we can
+ 
+
+ align:start position:0%
+other so it's not good so how we can
+create a bank Gap out of this
+
+ align:start position:0%
+create a bank Gap out of this
+ 
+
+ align:start position:0%
+create a bank Gap out of this
+material and uh you do a size effect so
+
+ align:start position:0%
+material and uh you do a size effect so
+ 
+
+ align:start position:0%
+material and uh you do a size effect so
+you make it smaller and theoretically
+
+ align:start position:0%
+you make it smaller and theoretically
+ 
+
+ align:start position:0%
+you make it smaller and theoretically
+what happens is this one is a function
+
+ align:start position:0%
+what happens is this one is a function
+ 
+
+ align:start position:0%
+what happens is this one is a function
+of diameter or thickness so this will
+
+ align:start position:0%
+of diameter or thickness so this will
+ 
+
+ align:start position:0%
+of diameter or thickness so this will
+move
+
+ align:start position:0%
+move
+ 
+
+ align:start position:0%
+move
+up depend on thickness this one will
+
+ align:start position:0%
+up depend on thickness this one will
+ 
+
+ align:start position:0%
+up depend on thickness this one will
+move
+
+ align:start position:0%
+move
+ 
+
+ align:start position:0%
+move
+down right so now you can create a
+
+ align:start position:0%
+down right so now you can create a
+ 
+
+ align:start position:0%
+down right so now you can create a
+gap and there also discussion for
+
+ align:start position:0%
+gap and there also discussion for
+ 
+
+ align:start position:0%
+gap and there also discussion for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+silicon right silicon is like what you
+
+ align:start position:0%
+silicon right silicon is like what you
+ 
+
+ align:start position:0%
+silicon right silicon is like what you
+have here this is
+
+ align:start position:0%
+have here this is
+ 
+
+ align:start position:0%
+have here this is
+the this indirect Gap the valance band
+
+ align:start position:0%
+the this indirect Gap the valance band
+ 
+
+ align:start position:0%
+the this indirect Gap the valance band
+is here conduction band is here right
+
+ align:start position:0%
+is here conduction band is here right
+ 
+
+ align:start position:0%
+is here conduction band is here right
+there is another conduction band but
+
+ align:start position:0%
+there is another conduction band but
+ 
+
+ align:start position:0%
+there is another conduction band but
+it's it's not the minimum this is the
+
+ align:start position:0%
+it's it's not the minimum this is the
+ 
+
+ align:start position:0%
+it's it's not the minimum this is the
+minimum so now what you do you make a
+
+ align:start position:0%
+minimum so now what you do you make a
+ 
+
+ align:start position:0%
+minimum so now what you do you make a
+very small Doss and this will move up of
+
+ align:start position:0%
+very small Doss and this will move up of
+ 
+
+ align:start position:0%
+very small Doss and this will move up of
+course this will move down and this also
+
+ align:start position:0%
+course this will move down and this also
+ 
+
+ align:start position:0%
+course this will move down and this also
+move depends on the speed of moving
+
+ align:start position:0%
+move depends on the speed of moving
+ 
+
+ align:start position:0%
+move depends on the speed of moving
+that's related to the
+
+ align:start position:0%
+that's related to the
+ 
+
+ align:start position:0%
+that's related to the
+mass right and this could be move to
+
+ align:start position:0%
+mass right and this could be move to
+ 
+
+ align:start position:0%
+mass right and this could be move to
+here and this one move slower so this
+
+ align:start position:0%
+here and this one move slower so this
+ 
+
+ align:start position:0%
+here and this one move slower so this
+you can convert into direct
+
+ align:start position:0%
+you can convert into direct
+ 
+
+ align:start position:0%
+you can convert into direct
+Gap right so that's the beauty of this
+
+ align:start position:0%
+Gap right so that's the beauty of this
+ 
+
+ align:start position:0%
+Gap right so that's the beauty of this
+thinking about this Quantum size effect
+
+ align:start position:0%
+thinking about this Quantum size effect
+ 
+
+ align:start position:0%
+thinking about this Quantum size effect
+you can use that
+
+ align:start position:0%
+you can use that
+ 
+
+ align:start position:0%
+you can use that
+to tune the bank gap of the materials
+
+ align:start position:0%
+to tune the bank gap of the materials
+ 
+
+ align:start position:0%
+to tune the bank gap of the materials
+and that's uh when you make a say like
+
+ align:start position:0%
+and that's uh when you make a say like
+ 
+
+ align:start position:0%
+and that's uh when you make a say like
+Quantum dots like cat
+
+ align:start position:0%
+Quantum dots like cat
+ 
+
+ align:start position:0%
+Quantum dots like cat
+ter or cat uh uh uh
+
+ align:start position:0%
+ter or cat uh uh uh
+ 
+
+ align:start position:0%
+ter or cat uh uh uh
+sulfide canot cite cat sulfide or um if
+
+ align:start position:0%
+sulfide canot cite cat sulfide or um if
+ 
+
+ align:start position:0%
+sulfide canot cite cat sulfide or um if
+you look at the professor M Bend's
+
+ align:start position:0%
+you look at the professor M Bend's
+ 
+
+ align:start position:0%
+you look at the professor M Bend's
+website he has all this beautiful dots
+
+ align:start position:0%
+website he has all this beautiful dots
+ 
+
+ align:start position:0%
+website he has all this beautiful dots
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+colors and that's because the same
+
+ align:start position:0%
+colors and that's because the same
+ 
+
+ align:start position:0%
+colors and that's because the same
+material you change the size you can
+
+ align:start position:0%
+material you change the size you can
+ 
+
+ align:start position:0%
+material you change the size you can
+actually open make a different
+
+ align:start position:0%
+actually open make a different
+ 
+
+ align:start position:0%
+actually open make a different
+Gap
+
+ align:start position:0%
+Gap
+ 
+
+ align:start position:0%
+Gap
+okay so uh those are
+
+ align:start position:0%
+okay so uh those are
+ 
+
+ align:start position:0%
+okay so uh those are
+digression come come back to I want to
+
+ align:start position:0%
+digression come come back to I want to
+ 
+
+ align:start position:0%
+digression come come back to I want to
+find that what's the den sub state right
+
+ align:start position:0%
+find that what's the den sub state right
+ 
+
+ align:start position:0%
+find that what's the den sub state right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh let me again start with okay I have
+
+ align:start position:0%
+uh let me again start with okay I have
+ 
+
+ align:start position:0%
+uh let me again start with okay I have
+here is L of electrons I give to
+
+ align:start position:0%
+here is L of electrons I give to
+ 
+
+ align:start position:0%
+here is L of electrons I give to
+this how much how many electron in the
+
+ align:start position:0%
+this how much how many electron in the
+ 
+
+ align:start position:0%
+this how much how many electron in the
+material and I still do my
+
+ align:start position:0%
+material and I still do my
+ 
+
+ align:start position:0%
+material and I still do my
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+KX
+
+ align:start position:0%
+KX
+ 
+
+ align:start position:0%
+KX
+KY my
+
+ align:start position:0%
+KY my
+ 
+
+ align:start position:0%
+KY my
+KZ my f whatever F I have there function
+
+ align:start position:0%
+KZ my f whatever F I have there function
+ 
+
+ align:start position:0%
+KZ my f whatever F I have there function
+that I'm interested in
+
+ align:start position:0%
+that I'm interested in
+ 
+
+ align:start position:0%
+that I'm interested in
+integrating right and uh in
+
+ align:start position:0%
+integrating right and uh in
+ 
+
+ align:start position:0%
+integrating right and uh in
+3D I said this F is a very slow function
+
+ align:start position:0%
+3D I said this F is a very slow function
+ 
+
+ align:start position:0%
+3D I said this F is a very slow function
+of KX KY k z so I converted into
+
+ align:start position:0%
+of KX KY k z so I converted into
+ 
+
+ align:start position:0%
+of KX KY k z so I converted into
+integration but in 2D in the Z
+
+ align:start position:0%
+integration but in 2D in the Z
+ 
+
+ align:start position:0%
+integration but in 2D in the Z
+direction right turn two consecutive so
+
+ align:start position:0%
+direction right turn two consecutive so
+ 
+
+ align:start position:0%
+direction right turn two consecutive so
+this is you say and my first energy
+
+ align:start position:0%
+this is you say and my first energy
+ 
+
+ align:start position:0%
+this is you say and my first energy
+level is here my second energy level is
+
+ align:start position:0%
+level is here my second energy level is
+ 
+
+ align:start position:0%
+level is here my second energy level is
+here between these two there are many KX
+
+ align:start position:0%
+here between these two there are many KX
+ 
+
+ align:start position:0%
+here between these two there are many KX
+KY there are many states in between KX
+
+ align:start position:0%
+KY there are many states in between KX
+ 
+
+ align:start position:0%
+KY there are many states in between KX
+KY
+
+ align:start position:0%
+KY
+ 
+
+ align:start position:0%
+KY
+right so I cannot convert in the Z
+
+ align:start position:0%
+right so I cannot convert in the Z
+ 
+
+ align:start position:0%
+right so I cannot convert in the Z
+Direction into summation uh inte
+
+ align:start position:0%
+Direction into summation uh inte
+ 
+
+ align:start position:0%
+Direction into summation uh inte
+integration I need to keep that
+
+ align:start position:0%
+integration I need to keep that
+ 
+
+ align:start position:0%
+integration I need to keep that
+summation and then what I could do is
+
+ align:start position:0%
+summation and then what I could do is
+ 
+
+ align:start position:0%
+summation and then what I could do is
+only convert XY
+
+ align:start position:0%
+only convert XY
+ 
+
+ align:start position:0%
+only convert XY
+Direction into integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is what I'm going to do I'm
+
+ align:start position:0%
+so this is what I'm going to do I'm
+ 
+
+ align:start position:0%
+so this is what I'm going to do I'm
+going to keep my uh say uh summation in
+
+ align:start position:0%
+going to keep my uh say uh summation in
+ 
+
+ align:start position:0%
+going to keep my uh say uh summation in
+the X Direction I can still do so I have
+
+ align:start position:0%
+the X Direction I can still do so I have
+ 
+
+ align:start position:0%
+the X Direction I can still do so I have
+dkx 2 pi
+
+ align:start position:0%
+dkx 2 pi
+ 
+
+ align:start position:0%
+dkx 2 pi
+LX and Y Direction I still
+
+ align:start position:0%
+LX and Y Direction I still
+ 
+
+ align:start position:0%
+LX and Y Direction I still
+do dky 2 pi l y and z Direction I cannot
+
+ align:start position:0%
+do dky 2 pi l y and z Direction I cannot
+ 
+
+ align:start position:0%
+do dky 2 pi l y and z Direction I cannot
+do I'm going to keep my
+
+ align:start position:0%
+do I'm going to keep my
+ 
+
+ align:start position:0%
+do I'm going to keep my
+summation and rather than KZ I can also
+
+ align:start position:0%
+summation and rather than KZ I can also
+ 
+
+ align:start position:0%
+summation and rather than KZ I can also
+do n it's equivalent whether you do n
+
+ align:start position:0%
+do n it's equivalent whether you do n
+ 
+
+ align:start position:0%
+do n it's equivalent whether you do n
+notation or KZ notation
+
+ align:start position:0%
+notation or KZ notation
+ 
+
+ align:start position:0%
+notation or KZ notation
+right and uh whatever F I have a factor
+
+ align:start position:0%
+right and uh whatever F I have a factor
+ 
+
+ align:start position:0%
+right and uh whatever F I have a factor
+of two I move the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inside
+
+ align:start position:0%
+inside
+ 
+
+ align:start position:0%
+inside
+right so now rather than do a 3D
+
+ align:start position:0%
+right so now rather than do a 3D
+ 
+
+ align:start position:0%
+right so now rather than do a 3D
+cartisan coordinate your mathematics is
+
+ align:start position:0%
+cartisan coordinate your mathematics is
+ 
+
+ align:start position:0%
+cartisan coordinate your mathematics is
+in 2D KX KY integration
+
+ align:start position:0%
+in 2D KX KY integration
+ 
+
+ align:start position:0%
+in 2D KX KY integration
+so you do a either polar
+
+ align:start position:0%
+so you do a either polar
+ 
+
+ align:start position:0%
+so you do a either polar
+coordinate or say depends on your F
+
+ align:start position:0%
+coordinate or say depends on your F
+ 
+
+ align:start position:0%
+coordinate or say depends on your F
+what's your f f is function e or it's
+
+ align:start position:0%
+what's your f f is function e or it's
+ 
+
+ align:start position:0%
+what's your f f is function e or it's
+right so that's your choice but let me
+
+ align:start position:0%
+right so that's your choice but let me
+ 
+
+ align:start position:0%
+right so that's your choice but let me
+I'm going to do here you say I have area
+
+ align:start position:0%
+I'm going to do here you say I have area
+ 
+
+ align:start position:0%
+I'm going to do here you say I have area
+LX * l y and if I do uh dkx dky I
+
+ align:start position:0%
+LX * l y and if I do uh dkx dky I
+ 
+
+ align:start position:0%
+LX * l y and if I do uh dkx dky I
+convert it into a polar coordinate right
+
+ align:start position:0%
+convert it into a polar coordinate right
+ 
+
+ align:start position:0%
+convert it into a polar coordinate right
+dkx dky in a polar uh if it's a
+
+ align:start position:0%
+dkx dky in a polar uh if it's a
+ 
+
+ align:start position:0%
+dkx dky in a polar uh if it's a
+symmetric it's 2 pi K
+
+ align:start position:0%
+symmetric it's 2 pi K
+ 
+
+ align:start position:0%
+symmetric it's 2 pi K
+DK right let's say k i i just make a
+
+ align:start position:0%
+DK right let's say k i i just make a
+ 
+
+ align:start position:0%
+DK right let's say k i i just make a
+notation KX s + k y s so it's 2D K
+
+ align:start position:0%
+notation KX s + k y s so it's 2D K
+ 
+
+ align:start position:0%
+notation KX s + k y s so it's 2D K
+parallel so in this case I have 2 pi K
+
+ align:start position:0%
+parallel so in this case I have 2 pi K
+ 
+
+ align:start position:0%
+parallel so in this case I have 2 pi K
+parallel DK parallel and that's the dkx
+
+ align:start position:0%
+parallel DK parallel and that's the dkx
+ 
+
+ align:start position:0%
+parallel DK parallel and that's the dkx
+dky and then I have 2 pi squar that's
+
+ align:start position:0%
+dky and then I have 2 pi squar that's
+ 
+
+ align:start position:0%
+dky and then I have 2 pi squar that's
+here 2 pi Square then I have another two
+
+ align:start position:0%
+here 2 pi Square then I have another two
+ 
+
+ align:start position:0%
+here 2 pi Square then I have another two
+summation and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F right
+
+ align:start position:0%
+F right
+ 
+
+ align:start position:0%
+F right
+say I'm not jumping into dens of state
+
+ align:start position:0%
+say I'm not jumping into dens of state
+ 
+
+ align:start position:0%
+say I'm not jumping into dens of state
+I'm deriving dens States I'm comfortable
+
+ align:start position:0%
+I'm deriving dens States I'm comfortable
+ 
+
+ align:start position:0%
+I'm deriving dens States I'm comfortable
+doing that just converting the the
+
+ align:start position:0%
+doing that just converting the the
+ 
+
+ align:start position:0%
+doing that just converting the the
+concept just converting my summation
+
+ align:start position:0%
+concept just converting my summation
+ 
+
+ align:start position:0%
+concept just converting my summation
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+integration and uh uh what I can do
+
+ align:start position:0%
+integration and uh uh what I can do
+ 
+
+ align:start position:0%
+integration and uh uh what I can do
+right if I my f is energy so I can write
+
+ align:start position:0%
+right if I my f is energy so I can write
+ 
+
+ align:start position:0%
+right if I my f is energy so I can write
+my K parallel also in terms of
+
+ align:start position:0%
+my K parallel also in terms of
+ 
+
+ align:start position:0%
+my K parallel also in terms of
+energy right so now let go back to the
+
+ align:start position:0%
+energy right so now let go back to the
+ 
+
+ align:start position:0%
+energy right so now let go back to the
+dispersion let's say this is a this let
+
+ align:start position:0%
+dispersion let's say this is a this let
+ 
+
+ align:start position:0%
+dispersion let's say this is a this let
+me make a notation this is my n right
+
+ align:start position:0%
+me make a notation this is my n right
+ 
+
+ align:start position:0%
+me make a notation this is my n right
+that's the sub levels of quanti in Z
+
+ align:start position:0%
+that's the sub levels of quanti in Z
+ 
+
+ align:start position:0%
+that's the sub levels of quanti in Z
+Direction and this is my K
+
+ align:start position:0%
+Direction and this is my K
+ 
+
+ align:start position:0%
+Direction and this is my K
+parallel Square so my I can write this
+
+ align:start position:0%
+parallel Square so my I can write this
+ 
+
+ align:start position:0%
+parallel Square so my I can write this
+uh my K parallel square equals uh 2
+
+ align:start position:0%
+uh my K parallel square equals uh 2
+ 
+
+ align:start position:0%
+uh my K parallel square equals uh 2
+m star H bar square e Min
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+right so I have really you can say here
+
+ align:start position:0%
+right so I have really you can say here
+ 
+
+ align:start position:0%
+right so I have really you can say here
+I need to convert if I want to write
+
+ align:start position:0%
+I need to convert if I want to write
+ 
+
+ align:start position:0%
+I need to convert if I want to write
+into in terms of De I need to convert
+
+ align:start position:0%
+into in terms of De I need to convert
+ 
+
+ align:start position:0%
+into in terms of De I need to convert
+this K parallel into energy and I need
+
+ align:start position:0%
+this K parallel into energy and I need
+ 
+
+ align:start position:0%
+this K parallel into energy and I need
+to DK parallel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+de okay so if you do your math if you go
+
+ align:start position:0%
+de okay so if you do your math if you go
+ 
+
+ align:start position:0%
+de okay so if you do your math if you go
+to look at what we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there what I have
+
+ align:start position:0%
+there what I have
+ 
+
+ align:start position:0%
+there what I have
+is uh so this is a 2 pi cancel one and
+
+ align:start position:0%
+is uh so this is a 2 pi cancel one and
+ 
+
+ align:start position:0%
+is uh so this is a 2 pi cancel one and
+two canel one I have another
+
+ align:start position:0%
+two canel one I have another
+ 
+
+ align:start position:0%
+two canel one I have another
+PI right so I
+
+ align:start position:0%
+PI right so I
+ 
+
+ align:start position:0%
+PI right so I
+have um
+
+ align:start position:0%
+have um
+ 
+
+ align:start position:0%
+have um
+integration 1/ pi and sigma whatever n f
+
+ align:start position:0%
+integration 1/ pi and sigma whatever n f
+ 
+
+ align:start position:0%
+integration 1/ pi and sigma whatever n f
+and now I need to write uh here K
+
+ align:start position:0%
+and now I need to write uh here K
+ 
+
+ align:start position:0%
+and now I need to write uh here K
+parallel in fact if I put this in I do
+
+ align:start position:0%
+parallel in fact if I put this in I do
+ 
+
+ align:start position:0%
+parallel in fact if I put this in I do
+the DK Square parallel Square because DK
+
+ align:start position:0%
+the DK Square parallel Square because DK
+ 
+
+ align:start position:0%
+the DK Square parallel Square because DK
+parallel Square I have the here right so
+
+ align:start position:0%
+parallel Square I have the here right so
+ 
+
+ align:start position:0%
+parallel Square I have the here right so
+I have a DK parallel squar that means I
+
+ align:start position:0%
+I have a DK parallel squar that means I
+ 
+
+ align:start position:0%
+I have a DK parallel squar that means I
+have 1 12 I have 2 m bar star and h² and
+
+ align:start position:0%
+have 1 12 I have 2 m bar star and h² and
+ 
+
+ align:start position:0%
+have 1 12 I have 2 m bar star and h² and
+D I'm not sure whether you're following
+
+ align:start position:0%
+D I'm not sure whether you're following
+ 
+
+ align:start position:0%
+D I'm not sure whether you're following
+my conversion I'm writing
+
+ align:start position:0%
+my conversion I'm writing
+ 
+
+ align:start position:0%
+my conversion I'm writing
+this into e k parallel D par based on
+
+ align:start position:0%
+this into e k parallel D par based on
+ 
+
+ align:start position:0%
+this into e k parallel D par based on
+what I have
+
+ align:start position:0%
+what I have
+ 
+
+ align:start position:0%
+what I have
+here and of course uh I have a summation
+
+ align:start position:0%
+here and of course uh I have a summation
+ 
+
+ align:start position:0%
+here and of course uh I have a summation
+n that means when
+
+ align:start position:0%
+n that means when
+ 
+
+ align:start position:0%
+n that means when
+e e has to be larger than n right
+
+ align:start position:0%
+e e has to be larger than n right
+ 
+
+ align:start position:0%
+e e has to be larger than n right
+otherwise this is a uh say I I say you
+
+ align:start position:0%
+otherwise this is a uh say I I say you
+ 
+
+ align:start position:0%
+otherwise this is a uh say I I say you
+can say if I do if it's e is less than n
+
+ align:start position:0%
+can say if I do if it's e is less than n
+ 
+
+ align:start position:0%
+can say if I do if it's e is less than n
+my K parallel will be
+
+ align:start position:0%
+my K parallel will be
+ 
+
+ align:start position:0%
+my K parallel will be
+imagining okay so what I have here all
+
+ align:start position:0%
+imagining okay so what I have here all
+ 
+
+ align:start position:0%
+imagining okay so what I have here all
+this BL Lot F F is the one that I want
+
+ align:start position:0%
+this BL Lot F F is the one that I want
+ 
+
+ align:start position:0%
+this BL Lot F F is the one that I want
+to integrate my density of
+
+ align:start position:0%
+to integrate my density of
+ 
+
+ align:start position:0%
+to integrate my density of
+states is this cancel e n and M
+
+ align:start position:0%
+states is this cancel e n and M
+ 
+
+ align:start position:0%
+states is this cancel e n and M
+star and
+
+ align:start position:0%
+star and
+ 
+
+ align:start position:0%
+star and
+h² and I have another
+
+ align:start position:0%
+h² and I have another
+ 
+
+ align:start position:0%
+h² and I have another
+pi and that's my then substate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's a step function n = 1 and
+
+ align:start position:0%
+okay it's a step function n = 1 and
+ 
+
+ align:start position:0%
+okay it's a step function n = 1 and
+equal 2 you add another one and equals
+
+ align:start position:0%
+equal 2 you add another one and equals
+ 
+
+ align:start position:0%
+equal 2 you add another one and equals
+three you add another
+
+ align:start position:0%
+three you add another
+ 
+
+ align:start position:0%
+three you add another
+one right so what I have here is if I
+
+ align:start position:0%
+one right so what I have here is if I
+ 
+
+ align:start position:0%
+one right so what I have here is if I
+draw this is my e and uh say uh I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have and this is this is my uh e 1 E2
+
+ align:start position:0%
+have and this is this is my uh e 1 E2
+ 
+
+ align:start position:0%
+have and this is this is my uh e 1 E2
+that's the quantization energy level E3
+
+ align:start position:0%
+that's the quantization energy level E3
+ 
+
+ align:start position:0%
+that's the quantization energy level E3
+is Step
+
+ align:start position:0%
+is Step
+ 
+
+ align:start position:0%
+is Step
+function and before we draw the electron
+
+ align:start position:0%
+function and before we draw the electron
+ 
+
+ align:start position:0%
+function and before we draw the electron
+you go check your loads this is a
+
+ align:start position:0%
+you go check your loads this is a
+ 
+
+ align:start position:0%
+you go check your loads this is a
+parabola right this is like a e
+
+ align:start position:0%
+parabola right this is like a e
+ 
+
+ align:start position:0%
+parabola right this is like a e
+say that's the two that's a
+
+ align:start position:0%
+say that's the two that's a
+ 
+
+ align:start position:0%
+say that's the two that's a
+3D this is
+
+ align:start position:0%
+3D this is
+ 
+
+ align:start position:0%
+3D this is
+2D so you see now that there difference
+
+ align:start position:0%
+2D so you see now that there difference
+ 
+
+ align:start position:0%
+2D so you see now that there difference
+in this sub States and once you go to
+
+ align:start position:0%
+in this sub States and once you go to
+ 
+
+ align:start position:0%
+in this sub States and once you go to
+Quan mode you got a more sharp features
+
+ align:start position:0%
+Quan mode you got a more sharp features
+ 
+
+ align:start position:0%
+Quan mode you got a more sharp features
+right step function and you go to wire
+
+ align:start position:0%
+right step function and you go to wire
+ 
+
+ align:start position:0%
+right step function and you go to wire
+you got actually some Delta function the
+
+ align:start position:0%
+you got actually some Delta function the
+ 
+
+ align:start position:0%
+you got actually some Delta function the
+dots you got Delta function it's this
+
+ align:start position:0%
+dots you got Delta function it's this
+ 
+
+ align:start position:0%
+dots you got Delta function it's this
+kind of step and Delta or line that give
+
+ align:start position:0%
+kind of step and Delta or line that give
+ 
+
+ align:start position:0%
+kind of step and Delta or line that give
+you some very pecul characteristics for
+
+ align:start position:0%
+you some very pecul characteristics for
+ 
+
+ align:start position:0%
+you some very pecul characteristics for
+the quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems
+
+ align:start position:0%
+systems
+ 
+
+ align:start position:0%
+systems
+okay any
+
+ align:start position:0%
+okay any
+ 
+
+ align:start position:0%
+okay any
+questions it's
+
+ align:start position:0%
+questions it's
+ 
+
+ align:start position:0%
+questions it's
+math okay it's a
+
+ align:start position:0%
+math okay it's a
+ 
+
+ align:start position:0%
+math okay it's a
+counting now no no complicated physics
+
+ align:start position:0%
+counting now no no complicated physics
+ 
+
+ align:start position:0%
+counting now no no complicated physics
+yes your sum your n is restricted right
+
+ align:start position:0%
+yes your sum your n is restricted right
+ 
+
+ align:start position:0%
+yes your sum your n is restricted right
+so you have uh yeah so the the the right
+
+ align:start position:0%
+so you have uh yeah so the the the right
+ 
+
+ align:start position:0%
+so you have uh yeah so the the the right
+way to write it is I write a heavyside
+
+ align:start position:0%
+way to write it is I write a heavyside
+ 
+
+ align:start position:0%
+way to write it is I write a heavyside
+function so heite is a step
+
+ align:start position:0%
+function so heite is a step
+ 
+
+ align:start position:0%
+function so heite is a step
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh this so we spend uh most of today's
+
+ align:start position:0%
+uh this so we spend uh most of today's
+ 
+
+ align:start position:0%
+uh this so we spend uh most of today's
+lecture in doing the counting and say
+
+ align:start position:0%
+lecture in doing the counting and say
+ 
+
+ align:start position:0%
+lecture in doing the counting and say
+how I really is converting summation
+
+ align:start position:0%
+how I really is converting summation
+ 
+
+ align:start position:0%
+how I really is converting summation
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+integration and uh if the function
+
+ align:start position:0%
+integration and uh if the function
+ 
+
+ align:start position:0%
+integration and uh if the function
+doesn't change much over the summation I
+
+ align:start position:0%
+doesn't change much over the summation I
+ 
+
+ align:start position:0%
+doesn't change much over the summation I
+can convert in the quantum's case in the
+
+ align:start position:0%
+can convert in the quantum's case in the
+ 
+
+ align:start position:0%
+can convert in the quantum's case in the
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+quantization that conversion is usually
+
+ align:start position:0%
+quantization that conversion is usually
+ 
+
+ align:start position:0%
+quantization that conversion is usually
+have to be careful you you probably
+
+ align:start position:0%
+have to be careful you you probably
+ 
+
+ align:start position:0%
+have to be careful you you probably
+cannot do that conversion because there
+
+ align:start position:0%
+cannot do that conversion because there
+ 
+
+ align:start position:0%
+cannot do that conversion because there
+is a large change of that function in
+
+ align:start position:0%
+is a large change of that function in
+ 
+
+ align:start position:0%
+is a large change of that function in
+the uh summation Direction
+
+ align:start position:0%
+the uh summation Direction
+ 
+
+ align:start position:0%
+the uh summation Direction
+and uh uh What uh uh we go in next is do
+
+ align:start position:0%
+and uh uh What uh uh we go in next is do
+ 
+
+ align:start position:0%
+and uh uh What uh uh we go in next is do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+F okay in particular we're doing a
+
+ align:start position:0%
+F okay in particular we're doing a
+ 
+
+ align:start position:0%
+F okay in particular we're doing a
+system at certain
+
+ align:start position:0%
+system at certain
+ 
+
+ align:start position:0%
+system at certain
+temperature and uh what's the the
+
+ align:start position:0%
+temperature and uh what's the the
+ 
+
+ align:start position:0%
+temperature and uh what's the the
+answering the question at the one one
+
+ align:start position:0%
+answering the question at the one one
+ 
+
+ align:start position:0%
+answering the question at the one one
+Quantum State each Quantum state for
+
+ align:start position:0%
+Quantum State each Quantum state for
+ 
+
+ align:start position:0%
+Quantum State each Quantum state for
+example what's the average L of electron
+
+ align:start position:0%
+example what's the average L of electron
+ 
+
+ align:start position:0%
+example what's the average L of electron
+because it could be zero and one but at
+
+ align:start position:0%
+because it could be zero and one but at
+ 
+
+ align:start position:0%
+because it could be zero and one but at
+certain temperature there's statistical
+
+ align:start position:0%
+certain temperature there's statistical
+ 
+
+ align:start position:0%
+certain temperature there's statistical
+average what's that L this same for Fon
+
+ align:start position:0%
+average what's that L this same for Fon
+ 
+
+ align:start position:0%
+average what's that L this same for Fon
+right I can have 0 one infinite then
+
+ align:start position:0%
+right I can have 0 one infinite then
+ 
+
+ align:start position:0%
+right I can have 0 one infinite then
+what's the average L of Fon for each
+
+ align:start position:0%
+what's the average L of Fon for each
+ 
+
+ align:start position:0%
+what's the average L of Fon for each
+Quantum State now I know how to how I
+
+ align:start position:0%
+Quantum State now I know how to how I
+ 
+
+ align:start position:0%
+Quantum State now I know how to how I
+can count Quantum state right how many
+
+ align:start position:0%
+can count Quantum state right how many
+ 
+
+ align:start position:0%
+can count Quantum state right how many
+Quantum State I have what I want to say
+
+ align:start position:0%
+Quantum State I have what I want to say
+ 
+
+ align:start position:0%
+Quantum State I have what I want to say
+next is at each Quant State how many
+
+ align:start position:0%
+next is at each Quant State how many
+ 
+
+ align:start position:0%
+next is at each Quant State how many
+electrons how many Fons given a certain
+
+ align:start position:0%
+electrons how many Fons given a certain
+ 
+
+ align:start position:0%
+electrons how many Fons given a certain
+temperature now I'm going to get into
+
+ align:start position:0%
+temperature now I'm going to get into
+ 
+
+ align:start position:0%
+temperature now I'm going to get into
+Thal system
+
+ align:start position:0%
+Thal system
+ 
+
+ align:start position:0%
+Thal system
+right and how much energy you have
+
+ align:start position:0%
+right and how much energy you have
+ 
+
+ align:start position:0%
+right and how much energy you have
+so uh let me uh give a very uh say a
+
+ align:start position:0%
+so uh let me uh give a very uh say a
+ 
+
+ align:start position:0%
+so uh let me uh give a very uh say a
+beginning of
+
+ align:start position:0%
+beginning of
+ 
+
+ align:start position:0%
+beginning of
+that and uh in fact if you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recall we did in the first chapter we
+
+ align:start position:0%
+recall we did in the first chapter we
+ 
+
+ align:start position:0%
+recall we did in the first chapter we
+give you the bman factor right so uh
+
+ align:start position:0%
+give you the bman factor right so uh
+ 
+
+ align:start position:0%
+give you the bman factor right so uh
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+my Quantum statistics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh uh in uh the first uh uh chapter
+
+ align:start position:0%
+and uh uh in uh the first uh uh chapter
+ 
+
+ align:start position:0%
+and uh uh in uh the first uh uh chapter
+beginning we say the bman factor gives
+
+ align:start position:0%
+beginning we say the bman factor gives
+ 
+
+ align:start position:0%
+beginning we say the bman factor gives
+you the
+
+ align:start position:0%
+you the
+ 
+
+ align:start position:0%
+you the
+probability of a
+
+ align:start position:0%
+probability of a
+ 
+
+ align:start position:0%
+probability of a
+particle we were not we're see not
+
+ align:start position:0%
+particle we were not we're see not
+ 
+
+ align:start position:0%
+particle we were not we're see not
+discussing whether it's Quantum or
+
+ align:start position:0%
+discussing whether it's Quantum or
+ 
+
+ align:start position:0%
+discussing whether it's Quantum or
+classical probability of particle having
+
+ align:start position:0%
+classical probability of particle having
+ 
+
+ align:start position:0%
+classical probability of particle having
+certain energy at certain
+
+ align:start position:0%
+certain energy at certain
+ 
+
+ align:start position:0%
+certain energy at certain
+temperature is a normalization factor
+
+ align:start position:0%
+temperature is a normalization factor
+ 
+
+ align:start position:0%
+temperature is a normalization factor
+minus say exponential e
+
+ align:start position:0%
+minus say exponential e
+ 
+
+ align:start position:0%
+minus say exponential e
+KBT I said take it this is the uh uh the
+
+ align:start position:0%
+KBT I said take it this is the uh uh the
+ 
+
+ align:start position:0%
+KBT I said take it this is the uh uh the
+Borman Factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right You' seen many many say examples
+
+ align:start position:0%
+right You' seen many many say examples
+ 
+
+ align:start position:0%
+right You' seen many many say examples
+of this bardman Factor say the energy
+
+ align:start position:0%
+of this bardman Factor say the energy
+ 
+
+ align:start position:0%
+of this bardman Factor say the energy
+barriers arenus no or this related to
+
+ align:start position:0%
+barriers arenus no or this related to
+ 
+
+ align:start position:0%
+barriers arenus no or this related to
+the bman factor and next lecture I hope
+
+ align:start position:0%
+the bman factor and next lecture I hope
+ 
+
+ align:start position:0%
+the bman factor and next lecture I hope
+I give you a little bit r of this okay
+
+ align:start position:0%
+I give you a little bit r of this okay
+ 
+
+ align:start position:0%
+I give you a little bit r of this okay
+there is a beautiful uh statistical
+
+ align:start position:0%
+there is a beautiful uh statistical
+ 
+
+ align:start position:0%
+there is a beautiful uh statistical
+framework to do
+
+ align:start position:0%
+framework to do
+ 
+
+ align:start position:0%
+framework to do
+that and uh so we use this and then we
+
+ align:start position:0%
+that and uh so we use this and then we
+ 
+
+ align:start position:0%
+that and uh so we use this and then we
+went to the Maxwell
+
+ align:start position:0%
+went to the Maxwell
+ 
+
+ align:start position:0%
+went to the Maxwell
+distribution right if I have particle
+
+ align:start position:0%
+distribution right if I have particle
+ 
+
+ align:start position:0%
+distribution right if I have particle
+that has
+
+ align:start position:0%
+that has
+ 
+
+ align:start position:0%
+that has
+energy 12 m v x² + V y² + VZ s
+
+ align:start position:0%
+energy 12 m v x² + V y² + VZ s
+ 
+
+ align:start position:0%
+energy 12 m v x² + V y² + VZ s
+right I say okay I normalize this I put
+
+ align:start position:0%
+right I say okay I normalize this I put
+ 
+
+ align:start position:0%
+right I say okay I normalize this I put
+it in here and the a particle has the
+
+ align:start position:0%
+it in here and the a particle has the
+ 
+
+ align:start position:0%
+it in here and the a particle has the
+probability between minus infinite to
+
+ align:start position:0%
+probability between minus infinite to
+ 
+
+ align:start position:0%
+probability between minus infinite to
+plus infinite is one so with that I find
+
+ align:start position:0%
+plus infinite is one so with that I find
+ 
+
+ align:start position:0%
+plus infinite is one so with that I find
+that a normalization factor that's how I
+
+ align:start position:0%
+that a normalization factor that's how I
+ 
+
+ align:start position:0%
+that a normalization factor that's how I
+get the max wheel
+
+ align:start position:0%
+get the max wheel
+ 
+
+ align:start position:0%
+get the max wheel
+distribution right so you see in that
+
+ align:start position:0%
+distribution right so you see in that
+ 
+
+ align:start position:0%
+distribution right so you see in that
+process I did not consider the
+
+ align:start position:0%
+process I did not consider the
+ 
+
+ align:start position:0%
+process I did not consider the
+discontinuity of the Velocity any value
+
+ align:start position:0%
+discontinuity of the Velocity any value
+ 
+
+ align:start position:0%
+discontinuity of the Velocity any value
+between M infinite to plus
+
+ align:start position:0%
+between M infinite to plus
+ 
+
+ align:start position:0%
+between M infinite to plus
+infinite now I'm going to do a little
+
+ align:start position:0%
+infinite now I'm going to do a little
+ 
+
+ align:start position:0%
+infinite now I'm going to do a little
+bit say discontinuous
+
+ align:start position:0%
+bit say discontinuous
+ 
+
+ align:start position:0%
+bit say discontinuous
+right I'm going to ask for example if I
+
+ align:start position:0%
+right I'm going to ask for example if I
+ 
+
+ align:start position:0%
+right I'm going to ask for example if I
+have a Quantum state electron is in in
+
+ align:start position:0%
+have a Quantum state electron is in in
+ 
+
+ align:start position:0%
+have a Quantum state electron is in in
+thermal equilibrium with
+
+ align:start position:0%
+thermal equilibrium with
+ 
+
+ align:start position:0%
+thermal equilibrium with
+surrounding at the temperature
+
+ align:start position:0%
+surrounding at the temperature
+ 
+
+ align:start position:0%
+surrounding at the temperature
+T right and
+
+ align:start position:0%
+T right and
+ 
+
+ align:start position:0%
+T right and
+electron say uh uh say what's the
+
+ align:start position:0%
+electron say uh uh say what's the
+ 
+
+ align:start position:0%
+electron say uh uh say what's the
+average so this is now I'm looking at
+
+ align:start position:0%
+average so this is now I'm looking at
+ 
+
+ align:start position:0%
+average so this is now I'm looking at
+the one Quantum state right it's in
+
+ align:start position:0%
+the one Quantum state right it's in
+ 
+
+ align:start position:0%
+the one Quantum state right it's in
+seral equilibrium with surrounding I'm
+
+ align:start position:0%
+seral equilibrium with surrounding I'm
+ 
+
+ align:start position:0%
+seral equilibrium with surrounding I'm
+asking question what's the probability
+
+ align:start position:0%
+asking question what's the probability
+ 
+
+ align:start position:0%
+asking question what's the probability
+of this Quantum State how many electrons
+
+ align:start position:0%
+of this Quantum State how many electrons
+ 
+
+ align:start position:0%
+of this Quantum State how many electrons
+has right so that's the question I'm
+
+ align:start position:0%
+has right so that's the question I'm
+ 
+
+ align:start position:0%
+has right so that's the question I'm
+asking and uh now the difference of that
+
+ align:start position:0%
+asking and uh now the difference of that
+ 
+
+ align:start position:0%
+asking and uh now the difference of that
+question there are two difference
+
+ align:start position:0%
+question there are two difference
+ 
+
+ align:start position:0%
+question there are two difference
+compared to here one is that electron in
+
+ align:start position:0%
+compared to here one is that electron in
+ 
+
+ align:start position:0%
+compared to here one is that electron in
+that Quant state that you can go the
+
+ align:start position:0%
+that Quant state that you can go the
+ 
+
+ align:start position:0%
+that Quant state that you can go the
+electron can be in that Quant state or
+
+ align:start position:0%
+electron can be in that Quant state or
+ 
+
+ align:start position:0%
+electron can be in that Quant state or
+jump out to the surrounding so I have
+
+ align:start position:0%
+jump out to the surrounding so I have
+ 
+
+ align:start position:0%
+jump out to the surrounding so I have
+mass transfer a charge transfer whatever
+
+ align:start position:0%
+mass transfer a charge transfer whatever
+ 
+
+ align:start position:0%
+mass transfer a charge transfer whatever
+right it's open
+
+ align:start position:0%
+right it's open
+ 
+
+ align:start position:0%
+right it's open
+system so that's one second is the that
+
+ align:start position:0%
+system so that's one second is the that
+ 
+
+ align:start position:0%
+system so that's one second is the that
+electron that Quant State can only have
+
+ align:start position:0%
+electron that Quant State can only have
+ 
+
+ align:start position:0%
+electron that Quant State can only have
+zero and one
+
+ align:start position:0%
+zero and one
+ 
+
+ align:start position:0%
+zero and one
+discr okay so when I have here Boardman
+
+ align:start position:0%
+discr okay so when I have here Boardman
+ 
+
+ align:start position:0%
+discr okay so when I have here Boardman
+factor is for close system at constant
+
+ align:start position:0%
+factor is for close system at constant
+ 
+
+ align:start position:0%
+factor is for close system at constant
+temperature and when I deal with a open
+
+ align:start position:0%
+temperature and when I deal with a open
+ 
+
+ align:start position:0%
+temperature and when I deal with a open
+system at a constant temperature I have
+
+ align:start position:0%
+system at a constant temperature I have
+ 
+
+ align:start position:0%
+system at a constant temperature I have
+to modify this so I'm going to give you
+
+ align:start position:0%
+to modify this so I'm going to give you
+ 
+
+ align:start position:0%
+to modify this so I'm going to give you
+again just wait for next lecture uh see
+
+ align:start position:0%
+again just wait for next lecture uh see
+ 
+
+ align:start position:0%
+again just wait for next lecture uh see
+the Gibs Factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and GES factor for open system and the
+
+ align:start position:0%
+and GES factor for open system and the
+ 
+
+ align:start position:0%
+and GES factor for open system and the
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+of a system open system has certain
+
+ align:start position:0%
+of a system open system has certain
+ 
+
+ align:start position:0%
+of a system open system has certain
+energy and certain number of particle as
+
+ align:start position:0%
+energy and certain number of particle as
+ 
+
+ align:start position:0%
+energy and certain number of particle as
+at the temperature T is uh uh a again
+
+ align:start position:0%
+at the temperature T is uh uh a again
+ 
+
+ align:start position:0%
+at the temperature T is uh uh a again
+normalization Min the energy of the
+
+ align:start position:0%
+normalization Min the energy of the
+ 
+
+ align:start position:0%
+normalization Min the energy of the
+system Min the uh number particle times
+
+ align:start position:0%
+system Min the uh number particle times
+ 
+
+ align:start position:0%
+system Min the uh number particle times
+this constant mu and divide by
+
+ align:start position:0%
+this constant mu and divide by
+ 
+
+ align:start position:0%
+this constant mu and divide by
+KBT so now I add this mu which is the
+
+ align:start position:0%
+KBT so now I add this mu which is the
+ 
+
+ align:start position:0%
+KBT so now I add this mu which is the
+chemical potential that's say how much
+
+ align:start position:0%
+chemical potential that's say how much
+ 
+
+ align:start position:0%
+chemical potential that's say how much
+energy you need to take out or place a
+
+ align:start position:0%
+energy you need to take out or place a
+ 
+
+ align:start position:0%
+energy you need to take out or place a
+particle into the system that's chemical
+
+ align:start position:0%
+particle into the system that's chemical
+ 
+
+ align:start position:0%
+particle into the system that's chemical
+potential okay so mu is the chemical
+
+ align:start position:0%
+potential okay so mu is the chemical
+ 
+
+ align:start position:0%
+potential okay so mu is the chemical
+potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's the same CRA potential is uh
+
+ align:start position:0%
+and that's the same CRA potential is uh
+ 
+
+ align:start position:0%
+and that's the same CRA potential is uh
+essentially it gives free
+
+ align:start position:0%
+essentially it gives free
+ 
+
+ align:start position:0%
+essentially it gives free
+energy and uh uh it's a it's it doesn't
+
+ align:start position:0%
+energy and uh uh it's a it's it doesn't
+ 
+
+ align:start position:0%
+energy and uh uh it's a it's it doesn't
+include the the entropy part and uh
+
+ align:start position:0%
+include the the entropy part and uh
+ 
+
+ align:start position:0%
+include the the entropy part and uh
+gives free energy difference gives you
+
+ align:start position:0%
+gives free energy difference gives you
+ 
+
+ align:start position:0%
+gives free energy difference gives you
+how much work you can get out of the
+
+ align:start position:0%
+how much work you can get out of the
+ 
+
+ align:start position:0%
+how much work you can get out of the
+system okay so
+
+ align:start position:0%
+system okay so
+ 
+
+ align:start position:0%
+system okay so
+with that I'm considering one isolated
+
+ align:start position:0%
+with that I'm considering one isolated
+ 
+
+ align:start position:0%
+with that I'm considering one isolated
+electron uh Quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State this is the easiest so I have one
+
+ align:start position:0%
+State this is the easiest so I have one
+ 
+
+ align:start position:0%
+State this is the easiest so I have one
+Quantum state of
+
+ align:start position:0%
+Quantum state of
+ 
+
+ align:start position:0%
+Quantum state of
+electron right this is the solution you
+
+ align:start position:0%
+electron right this is the solution you
+ 
+
+ align:start position:0%
+electron right this is the solution you
+had before in Quantum from either for
+
+ align:start position:0%
+had before in Quantum from either for
+ 
+
+ align:start position:0%
+had before in Quantum from either for
+solid or for uh molecule or for atom
+
+ align:start position:0%
+solid or for uh molecule or for atom
+ 
+
+ align:start position:0%
+solid or for uh molecule or for atom
+right you have this solution of quantum
+
+ align:start position:0%
+right you have this solution of quantum
+ 
+
+ align:start position:0%
+right you have this solution of quantum
+State this is what we we've been doing
+
+ align:start position:0%
+State this is what we we've been doing
+ 
+
+ align:start position:0%
+State this is what we we've been doing
+the question is whether there is a
+
+ align:start position:0%
+the question is whether there is a
+ 
+
+ align:start position:0%
+the question is whether there is a
+electron in that Quantum state or not so
+
+ align:start position:0%
+electron in that Quantum state or not so
+ 
+
+ align:start position:0%
+electron in that Quantum state or not so
+what's the probability is zero or
+
+ align:start position:0%
+what's the probability is zero or
+ 
+
+ align:start position:0%
+what's the probability is zero or
+one right say this are the two states
+
+ align:start position:0%
+one right say this are the two states
+ 
+
+ align:start position:0%
+one right say this are the two states
+when n equals z or one when n equals z
+
+ align:start position:0%
+when n equals z or one when n equals z
+ 
+
+ align:start position:0%
+when n equals z or one when n equals z
+even though you have that Quantum state
+
+ align:start position:0%
+even though you have that Quantum state
+ 
+
+ align:start position:0%
+even though you have that Quantum state
+that state doesn't have real electron
+
+ align:start position:0%
+that state doesn't have real electron
+ 
+
+ align:start position:0%
+that state doesn't have real electron
+there doesn't have
+
+ align:start position:0%
+there doesn't have
+ 
+
+ align:start position:0%
+there doesn't have
+energy so the energy when this is zero
+
+ align:start position:0%
+energy so the energy when this is zero
+ 
+
+ align:start position:0%
+energy so the energy when this is zero
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+zero and when you have one particle that
+
+ align:start position:0%
+zero and when you have one particle that
+ 
+
+ align:start position:0%
+zero and when you have one particle that
+energy that state has energy EI right so
+
+ align:start position:0%
+energy that state has energy EI right so
+ 
+
+ align:start position:0%
+energy that state has energy EI right so
+eii now I use
+
+ align:start position:0%
+eii now I use
+ 
+
+ align:start position:0%
+eii now I use
+this to possibility I do my
+
+ align:start position:0%
+this to possibility I do my
+ 
+
+ align:start position:0%
+this to possibility I do my
+normalization factor for the Gibs Factor
+
+ align:start position:0%
+normalization factor for the Gibs Factor
+ 
+
+ align:start position:0%
+normalization factor for the Gibs Factor
+so add up it has to be has to be either
+
+ align:start position:0%
+so add up it has to be has to be either
+ 
+
+ align:start position:0%
+so add up it has to be has to be either
+zero or one
+
+ align:start position:0%
+zero or one
+ 
+
+ align:start position:0%
+zero or one
+right the add up has to be
+
+ align:start position:0%
+right the add up has to be
+ 
+
+ align:start position:0%
+right the add up has to be
+one so when it's zero
+
+ align:start position:0%
+one so when it's zero
+ 
+
+ align:start position:0%
+one so when it's zero
+p 0 0 t plus P here is
+
+ align:start position:0%
+p 0 0 t plus P here is
+ 
+
+ align:start position:0%
+p 0 0 t plus P here is
+EI one t that has to be one so the first
+
+ align:start position:0%
+EI one t that has to be one so the first
+ 
+
+ align:start position:0%
+EI one t that has to be one so the first
+when z z that's just a the second when
+
+ align:start position:0%
+when z z that's just a the second when
+ 
+
+ align:start position:0%
+when z z that's just a the second when
+uh EI so I have minus
+
+ align:start position:0%
+uh EI so I have minus
+ 
+
+ align:start position:0%
+uh EI so I have minus
+EI mu * n is just
+
+ align:start position:0%
+EI mu * n is just
+ 
+
+ align:start position:0%
+EI mu * n is just
+mu
+
+ align:start position:0%
+mu
+ 
+
+ align:start position:0%
+mu
+KBT equals 1 so this gives me a
+
+ align:start position:0%
+KBT equals 1 so this gives me a
+ 
+
+ align:start position:0%
+KBT equals 1 so this gives me a
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+exponential Mass EI mu
+
+ align:start position:0%
+exponential Mass EI mu
+ 
+
+ align:start position:0%
+exponential Mass EI mu
+KBT +
+
+ align:start position:0%
+KBT +
+ 
+
+ align:start position:0%
+KBT +
+one that's my normalization factor
+
+ align:start position:0%
+one that's my normalization factor
+ 
+
+ align:start position:0%
+one that's my normalization factor
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+right now my average L of particle F
+
+ align:start position:0%
+right now my average L of particle F
+ 
+
+ align:start position:0%
+right now my average L of particle F
+average L which is the average L of
+
+ align:start position:0%
+average L which is the average L of
+ 
+
+ align:start position:0%
+average L which is the average L of
+n right once I have distribution
+
+ align:start position:0%
+n right once I have distribution
+ 
+
+ align:start position:0%
+n right once I have distribution
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+can find the average any quantity
+
+ align:start position:0%
+can find the average any quantity
+ 
+
+ align:start position:0%
+can find the average any quantity
+average energy average L particle
+
+ align:start position:0%
+average energy average L particle
+ 
+
+ align:start position:0%
+average energy average L particle
+whatever average you want right so that
+
+ align:start position:0%
+whatever average you want right so that
+ 
+
+ align:start position:0%
+whatever average you want right so that
+should be zero because Z times this p 0
+
+ align:start position:0%
+should be zero because Z times this p 0
+ 
+
+ align:start position:0%
+should be zero because Z times this p 0
+0 t plus uh one I one particle time p uh
+
+ align:start position:0%
+0 t plus uh one I one particle time p uh
+ 
+
+ align:start position:0%
+0 t plus uh one I one particle time p uh
+EI 1 T so that's my average L of
+
+ align:start position:0%
+EI 1 T so that's my average L of
+ 
+
+ align:start position:0%
+EI 1 T so that's my average L of
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+right because this is the
+
+ align:start position:0%
+right because this is the
+ 
+
+ align:start position:0%
+right because this is the
+probability when a EI one fully
+
+ align:start position:0%
+probability when a EI one fully
+ 
+
+ align:start position:0%
+probability when a EI one fully
+empty and uh you go you know your a you
+
+ align:start position:0%
+empty and uh you go you know your a you
+ 
+
+ align:start position:0%
+empty and uh you go you know your a you
+know your uh p f uh a times this EI mu n
+
+ align:start position:0%
+know your uh p f uh a times this EI mu n
+ 
+
+ align:start position:0%
+know your uh p f uh a times this EI mu n
+so you can see this one and this one is
+
+ align:start position:0%
+so you can see this one and this one is
+ 
+
+ align:start position:0%
+so you can see this one and this one is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+right in the numerator I have this one
+
+ align:start position:0%
+right in the numerator I have this one
+ 
+
+ align:start position:0%
+right in the numerator I have this one
+in the gometer I have this one but I
+
+ align:start position:0%
+in the gometer I have this one but I
+ 
+
+ align:start position:0%
+in the gometer I have this one but I
+have plus Vector one
+
+ align:start position:0%
+have plus Vector one
+ 
+
+ align:start position:0%
+have plus Vector one
+right so I divide this so I can write
+
+ align:start position:0%
+right so I divide this so I can write
+ 
+
+ align:start position:0%
+right so I divide this so I can write
+the simpler and you will see now what I
+
+ align:start position:0%
+the simpler and you will see now what I
+ 
+
+ align:start position:0%
+the simpler and you will see now what I
+have is EI Mass mu
+
+ align:start position:0%
+have is EI Mass mu
+ 
+
+ align:start position:0%
+have is EI Mass mu
+KBT + one and this is the
+
+ align:start position:0%
+KBT + one and this is the
+ 
+
+ align:start position:0%
+KBT + one and this is the
+famor forid rock distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so in in three
+
+ align:start position:0%
+okay so in in three
+ 
+
+ align:start position:0%
+okay so in in three
+steps right you get the if you take that
+
+ align:start position:0%
+steps right you get the if you take that
+ 
+
+ align:start position:0%
+steps right you get the if you take that
+energy quantization probability
+
+ align:start position:0%
+energy quantization probability
+ 
+
+ align:start position:0%
+energy quantization probability
+normalization you got from a
+
+ align:start position:0%
+normalization you got from a
+ 
+
+ align:start position:0%
+normalization you got from a
+drug and the next lecture we'll
+
+ align:start position:0%
+drug and the next lecture we'll
+ 
+
+ align:start position:0%
+drug and the next lecture we'll
+get uh we'll go few more step to get the
+
+ align:start position:0%
+get uh we'll go few more step to get the
+ 
+
+ align:start position:0%
+get uh we'll go few more step to get the
+both Einstein distribution for Fons this
+
+ align:start position:0%
+both Einstein distribution for Fons this
+ 
+
+ align:start position:0%
+both Einstein distribution for Fons this
+are for electrons
\ No newline at end of file
diff --git a/JIjr9CmN5eI.txt b/JIjr9CmN5eI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ff8030056ef20d8cd8e419baa3dcf47aa249564d
--- /dev/null
+++ b/JIjr9CmN5eI.txt
@@ -0,0 +1,675 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu then I'll go and pick it up
+
+ align:start position:0%
+ocw.mit.edu then I'll go and pick it up
+ 
+
+ align:start position:0%
+ocw.mit.edu then I'll go and pick it up
+from the side like this and just press
+
+ align:start position:0%
+from the side like this and just press
+ 
+
+ align:start position:0%
+from the side like this and just press
+break it break it and sometimes it's
+
+ align:start position:0%
+break it break it and sometimes it's
+ 
+
+ align:start position:0%
+break it break it and sometimes it's
+it's a little inconsistent because
+
+ align:start position:0%
+it's a little inconsistent because
+ 
+
+ align:start position:0%
+it's a little inconsistent because
+depending on the waer and how well it
+
+ align:start position:0%
+depending on the waer and how well it
+ 
+
+ align:start position:0%
+depending on the waer and how well it
+released and how well cut some of them
+
+ align:start position:0%
+released and how well cut some of them
+ 
+
+ align:start position:0%
+released and how well cut some of them
+have real thin tabs that break you know
+
+ align:start position:0%
+have real thin tabs that break you know
+ 
+
+ align:start position:0%
+have real thin tabs that break you know
+instantly and some you have to really oh
+
+ align:start position:0%
+instantly and some you have to really oh
+ 
+
+ align:start position:0%
+instantly and some you have to really oh
+these are theong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on yeah that that that works sometimes
+
+ align:start position:0%
+on yeah that that that works sometimes
+ 
+
+ align:start position:0%
+on yeah that that that works sometimes
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find it helpful to put it back down and
+
+ align:start position:0%
+find it helpful to put it back down and
+ 
+
+ align:start position:0%
+find it helpful to put it back down and
+then grab it by the edges oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+sorry am I facing the right way yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah that looks pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enough take a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look mhm that looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good seting it back yeah sometimes I
+
+ align:start position:0%
+good seting it back yeah sometimes I
+ 
+
+ align:start position:0%
+good seting it back yeah sometimes I
+just check to make sure it's not back in
+
+ align:start position:0%
+just check to make sure it's not back in
+ 
+
+ align:start position:0%
+just check to make sure it's not back in
+there it helps with positioning the
+
+ align:start position:0%
+there it helps with positioning the
+ 
+
+ align:start position:0%
+there it helps with positioning the
+laser into cuz sometimes it's out
+
+ align:start position:0%
+laser into cuz sometimes it's out
+ 
+
+ align:start position:0%
+laser into cuz sometimes it's out
+farther and the angle is a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+yeah to use
+
+ align:start position:0%
+yeah to use
+ 
+
+ align:start position:0%
+yeah to use
+side yeah should be bing up on the side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in trouble with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this how do you like fli it over now
+
+ align:start position:0%
+this how do you like fli it over now
+ 
+
+ align:start position:0%
+this how do you like fli it over now
+what's kind of microscope well I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that might be good but I still think I
+
+ align:start position:0%
+that might be good but I still think I
+ 
+
+ align:start position:0%
+that might be good but I still think I
+need to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down there we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it used to be it used to be
+
+ align:start position:0%
+okay it used to be it used to be
+ 
+
+ align:start position:0%
+okay it used to be it used to be
+significantly no when using with vibrate
+
+ align:start position:0%
+significantly no when using with vibrate
+ 
+
+ align:start position:0%
+significantly no when using with vibrate
+but these On's not so bad I you can look
+
+ align:start position:0%
+but these On's not so bad I you can look
+ 
+
+ align:start position:0%
+but these On's not so bad I you can look
+I mean as far as as far as the recording
+
+ align:start position:0%
+I mean as far as as far as the recording
+ 
+
+ align:start position:0%
+I mean as far as as far as the recording
+spectum make a huge
+
+ align:start position:0%
+spectum make a huge
+ 
+
+ align:start position:0%
+spectum make a huge
+difference at yeah you'll be able to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't know if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good can I close sorry can you please
+
+ align:start position:0%
+good can I close sorry can you please
+ 
+
+ align:start position:0%
+good can I close sorry can you please
+close the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they can't deliver us here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I thought it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+pretty so now we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I want to
+
+ align:start position:0%
+so I want to
+ 
+
+ align:start position:0%
+so I want to
+be as close to the face
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I you want to be as
+
+ align:start position:0%
+I you want to be as
+ 
+
+ align:start position:0%
+I you want to be as
+far go as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+total
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so well I guess that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rightly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+NOP we just said one of these Pro late
+
+ align:start position:0%
+NOP we just said one of these Pro late
+ 
+
+ align:start position:0%
+NOP we just said one of these Pro late
+out nights a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you would have to do it in the
+
+ align:start position:0%
+yeah you would have to do it in the
+ 
+
+ align:start position:0%
+yeah you would have to do it in the
+middle of the air and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+on sores are really bad you know like
+
+ align:start position:0%
+on sores are really bad you know like
+ 
+
+ align:start position:0%
+on sores are really bad you know like
+how um the is is broken so very go
+
+ align:start position:0%
+how um the is is broken so very go
+ 
+
+ align:start position:0%
+how um the is is broken so very go
+grab
\ No newline at end of file
diff --git a/JRgIXyEPnbA.txt b/JRgIXyEPnbA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8e7d8f862f9d9ce7ca9b5ac90082c92e6de51d20
--- /dev/null
+++ b/JRgIXyEPnbA.txt
@@ -0,0 +1,2747 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Everything
+make sense?
+
+Are you guys good with Newton?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yes, really?
+
+I'm done.
+
+I'm going home.
+
+Are you guys good
+with Karatsuba?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Kara-what?
+
+[LAUGHTER]
+
+OK, so who is happy
+with Karatsuba?
+
+Good.
+
+Who is happy with Newton?
+
+Wait.
+
+I need to ask the other ones,
+because not enough people--
+
+who is not happy with Newton
+and wants to look over it?
+
+Who wants to look
+over Karatsuba?
+
+Oh, so you guy are
+paying attention.
+
+Good.
+
+OK.
+
+All right.
+
+So Newton and Karatsuba.
+
+Let's start.
+
+So Karatsuba real
+fast, and then we'll
+
+spend more time having
+fun with Newton.
+
+So suppose we don't
+know Karatsuba.
+
+We want to multiply two numbers.
+
+What's the method that we
+learned in elementary school?
+
+AUDIENCE: You take the first
+digit of the first number,
+
+and then you multiply
+it by the second number.
+
+And then you take
+the second digit
+
+and multiply it by the second
+number, but then you add a 0.
+
+And so on and so forth.
+
+PROFESSOR: So I'll
+take this digit
+
+and multiply it with this number
+and write the result down here,
+
+right?
+
+So whatever this thing happens
+to be, 1, 2, 3, 4 times 8,
+
+write the result.
+
+Then I take 1, 2, 3, 4 times
+7 and add the result here
+
+and the last digits are 0.
+
+1, 2, 3, 4 times 6, two 0s.
+
+1, 2, 3, 4 times 5, three 0s.
+
+Then I add these up
+and I know that I'm
+
+going to get the right result.
+
+What's the running
+time for this?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: OK.
+
+So why is it n squared?
+
+AUDIENCE: Because you go
+through every single thing
+
+for every digit below.
+
+PROFESSOR: Yup.
+
+So I'll have these
+partial products here,
+
+and I have as many
+partial products
+
+as digits in the second number.
+
+So if I have n digits here,
+I have n partial products.
+
+Each partial product is this
+first number here multiplied
+
+by a digit.
+
+So if this guy has
+n digits, then there
+
+are n digits everywhere here.
+
+And this thing will be
+2 n insides actually,
+
+but we're doing asymptotic,
+so we don't really
+
+care about constant factors.
+
+So in the end, you have
+to add up n numbers.
+
+All of them are order n in size.
+
+So n times order n squared.
+
+This is plain old
+multiplication.
+
+Does anyone know why
+Karatsuba's better?
+
+Yes?
+
+AUDIENCE: You do
+three multiplications
+
+or something like that?
+
+PROFESSOR: OK.
+
+So, let's go for
+a simple answer.
+
+AUDIENCE: It's better.
+
+PROFESSOR: So the simpler
+answer is it's faster.
+
+AUDIENCE: OK.
+
+PROFESSOR: n, n log 2--
+
+AUDIENCE: I said
+better, it's faster.
+
+PROFESSOR: I mean, some
+algorithms have the same speed
+
+but are simpler.
+
+We like this one
+because it's faster.
+
+It's definitely not simpler.
+
+So, it has this
+running time here.
+
+Log 2 of 3 is a weird number.
+
+It's somewhere
+between 1.5 and 2.
+
+So not revolutionary, but
+it's better than this guy.
+
+OK, why do we get to this?
+
+How do we get to this?
+
+Does anyone remember
+the recurrence for it?
+
+Yes?
+
+AUDIENCE: It's 3 times 2--
+
+PROFESSOR: You're
+not remembering it.
+
+You're cheating.
+
+AUDIENCE: No, I'm not.
+
+[LAUGHTER]
+
+PROFESSOR: So, let's see
+why it looks like this.
+
+Karatsuba takes 2 numbers that
+have n digits, splits both
+
+of them up into two-- n over 2n,
+n over 2, n over 2, n over 2--
+
+and then is able to compute the
+product of these two numbers
+
+by only using three
+multiplications, and then
+
+some additions.
+
+Multiplications are expensive,
+additions are cheap.
+
+So it does three multiplications
+that are of the form
+
+some number of n over
+2 digits multiplied
+
+by some number of
+n over or 2 digits.
+
+And exactly what the
+multiplications and what
+
+the additions are is, it's
+interesting to look over it.
+
+You can look over it, convince
+yourself that this is correct.
+
+Chances are you'll remember for
+the exam and forget afterwards.
+
+Please remember this.
+
+This is the essence
+of Karatsuba.
+
+And remember Karatsuba,
+because if you google this,
+
+you get the rest.
+
+So the multiplications
+are in the notes.
+
+I don't think it makes sense
+to spend some time on them
+
+and convince you
+that, yeah, there
+
+are three multiplications
+that will get you that.
+
+Instead, suppose I labeled
+these as a, b, c, d.
+
+If I evaluate the multiplication
+as using brute force,
+
+it's a times n over 2b plus
+c-- sorry, a plus-- no,
+
+this isn't good.
+
+10 to the power n over 2a plus
+b times 10-- assuming the base
+
+is ten, if it's not, you
+replace it-- n over 2 c plus d.
+
+And you get 10 to the n
+times, I think, ac plus 10
+
+to the n over 2 times
+ad plus bc plus bd.
+
+The problem with this is
+this is a multiplication,
+
+multiplication,
+multiplication, multiplication.
+
+So this uses four
+multiplications
+
+of size n over 2 to
+evaluate the answer one
+
+multiplication of size n.
+
+And if I have four
+multiplications,
+
+then the recursion becomes
+4t of n over 2 plus o of n.
+
+So this is t bad of n.
+
+So if you do this using
+the recursion tree,
+
+you're going to see that--
+yup, I hear whispers.
+
+n squared.
+
+So this isn't useful.
+
+This will give you
+insight on how to do it,
+
+but if you try to
+implement it this way,
+
+you don't get any speed up.
+
+The insight in Karatsuba
+is that the guy figured out
+
+how to do this with
+three multiplications.
+
+OK, makes sense?
+
+Is everyone happy
+with Karatsuba now?
+
+So that multiplying by 10 to
+the n over 2 is just shifting a?
+
+PROFESSOR: Yup.
+
+OK.
+
+Very good point.
+
+So this isn't an
+actual multiplication.
+
+If you have your number, say
+stored in a python list--
+
+so if these are
+your digits, then
+
+in order to multiply
+by 10 to the n,
+
+you append 10 to
+the n 0s at the end.
+
+0, 0, 0, 0, 0.
+
+So, this is append of 0 n times.
+
+So this is order n, so it
+counts as an addition, not as
+
+a multiplication.
+
+So, these are free.
+
+These are expensive.
+
+1, 2, 3, 4.
+
+OK.
+
+Who's happy with Karatsuba now?
+
+Let me feel like I did
+something useful today.
+
+AUDIENCE: I have a question.
+
+PROFESSOR: Yes.
+
+AUDIENCE: I didn't fully
+understand what [INAUDIBLE].
+
+PROFESSOR: So, I
+have this number
+
+and I'm splitting
+it up into 2 halves.
+
+The way split up is I say this
+is a number of size n over 2,
+
+and I have to shift
+it to the left.
+
+So n 10 to the power
+of n over 2 shifts
+
+it left by n over two digits.
+
+And then I add it to b.
+
+So this in a sense
+is just saying
+
+that this is the left half,
+this is the right half.
+
+AUDIENCE: This is
+actually that same number.
+
+PROFESSOR: Yup.
+
+It's exactly the same number.
+
+OK, so who is happy
+with Karatsuba now?
+
+AUDIENCE: Wait, but that's
+four multiplications though.
+
+PROFESSOR: Exactly.
+
+AUDIENCE: That's not three.
+
+PROFESSOR: Exactly.
+
+AUDIENCE: But we said
+there were three.
+
+PROFESSOR: So, I was
+saying that this,
+
+if you;re doing it the brute
+force way, you get four,
+
+and that is slow.
+
+So what Karatsuba
+did is he figured out
+
+the way to do this with
+just three multiplications.
+
+So it's not these three.
+
+You have to think
+a little bit more.
+
+But you google it, or you
+look at the lecture notes,
+
+or you think a little
+bit, then you find out
+
+the three multiplications
+that do the trick.
+
+So the difference between
+this 4 here and this 3
+
+here is important.
+
+All right, anything
+else on Karatsuba?
+
+Cool.
+
+Let's talk about Newton.
+
+That's the hard stuff.
+
+And let me see how
+we're doing on time.
+
+OK, doing well.
+
+So does anyone remember
+the point of Newton?
+
+OK, so I heard an
+application that
+
+lets you compute square roots.
+
+What else does it let you do?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: OK, we have
+Karatsuba for multiplication.
+
+You might be able to
+do it with Newton.
+
+Probably not going to be faster.
+
+But division, definitely.
+
+So square roots and division.
+
+So this is why we care about it.
+
+Now what does it do from
+a mathy perspective?
+
+So what's the mathy
+definition of Newton.
+
+AUDIENCE: Estimates--
+
+PROFESSOR: Estimates?
+
+AUDIENCE: The value--
+
+PROFESSOR: OK.
+
+So, we have a function.
+
+Suppose it looks like this.
+
+So, what Newton
+helps us do is it
+
+helps us find a root
+of the function.
+
+And the root is a value x 0
+so that f of x 0 equals 0.
+
+So this is what it does.
+
+So when you want
+to use Newton, you
+
+have to set up your
+function in such a way
+
+that your answer is a root.
+
+OK.
+
+How does Newton work?
+
+Yes?
+
+AUDIENCE: You
+start at some point
+
+where you actually
+know the answer to it,
+
+and then you kind of
+draw a approximation.
+
+So you're just drawing a line
+from the point to the root,
+
+and then just incrementing
+down that line.
+
+PROFESSOR: OK.
+
+So we start at
+some point, right?
+
+How do we call that point?
+
+Initial guess.
+
+Fancy name.
+
+So we have an initial guess
+for what the root might be.
+
+It's not going to be the right
+answer, because otherwise
+
+why am I bothering with this?
+
+But it can be too far off.
+
+We'll say that if
+you're too far off,
+
+you're not going to
+converge or you're not
+
+going to converge fast enough.
+
+So say we start somewhere
+here and, we think, you know,
+
+this is pretty close.
+
+It's not quite there,
+but it's pretty close.
+
+What I do from here
+on is, you said
+
+I approximate this function--
+
+AUDIENCE: The line.
+
+PROFESSOR: Yep.
+
+So what's of the best line?
+
+The best way to
+approximate the function
+
+with the line is to use
+is the tangent, right?
+
+So here, it sort
+of looks like this.
+
+And if the function
+were linear, this
+
+would be a perfect
+approximation and we'd
+
+get answer in one step.
+
+OK.
+
+So this is the tangent.
+
+And then what we do
+with this tangent?
+
+AUDIENCE: Well, after we
+get the equation for it,
+
+then we find the root, right?
+
+Or no?
+
+PROFESSOR: Well, I can't
+find the root right away.
+
+AUDIENCE: The root of that line.
+
+Of our tangent line.
+
+PROFESSOR: OK.
+
+So we find the root
+of the tangent, which
+
+is the point where
+it hits the x-axis.
+
+And what happens
+with this point?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: OK, so this
+is our next guess.
+
+And then we trade.
+
+So then we draw another
+tangent, and the idea
+
+is that eventually,
+you're going to get there.
+
+And if we go through
+the maths, we
+
+will see that you actually
+get there pretty fast.
+
+So that's why we
+like this method.
+
+So let's see how we convert this
+drawing thing into an equation
+
+that you can write into python.
+
+Let's label these quantities.
+
+So, x2, x1-- actually
+let's not use 1 and 2,
+
+because these are the
+first two guesses.
+
+Let's say our current guess is
+x and the next guess is x prime.
+
+So this line and is x1 minus
+x, so this guy over here.
+
+And what's this guy over here?
+
+f of x.
+
+Don't be shy.
+
+It's the right answer.
+
+So I have f of x here,
+x 1 minus x here.
+
+I also have this angle
+here, and this angle here
+
+is the same angle
+as the angle here
+
+because both of these
+lines are horizontal,
+
+so they're parallel.
+
+So what do I know
+about this angle?
+
+AUDIENCE: It's tangent.
+
+PROFESSOR: It's tangent.
+
+OK.
+
+The tangent, that's
+called the angle alpha.
+
+What's the tangent of the angle?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Sorry?
+
+AUDIENCE: F of x
+over x [INAUDIBLE].
+
+PROFESSOR: I think
+you're trying to give me
+
+the formula for x prime.
+
+Just the tangent.
+
+Just the tangent.
+
+AUDIENCE: Oh.
+
+PROFESSOR: Right?
+
+Can someone reassure me?
+
+This is right, right?
+
+[AUDIENCE AGREES]
+
+AUDIENCE: I was thinking
+the slope of the line.
+
+PROFESSOR: OK.
+
+So, yeah, you're
+going to give me
+
+the slope of the line
+which lets me compute this.
+
+OK, I was looking for this.
+
+OK.
+
+So now, let's get
+what you're saying.
+
+So this is the tangent, right?
+
+So, the tangent at a
+point of a function
+
+is the function's derivative.
+
+So now we're going to write
+all these things down and hope
+
+that we get an equation
+that make sense.
+
+So we have the
+tangent of this guy,
+
+also happens to
+be this over this.
+
+Right?
+
+This is a right angle
+triangle, so the tangent
+
+is f of x over--
+this is what you
+
+were trying to tell me, right?
+
+x1 minus x.
+
+So now I know that
+this is f prime of x.
+
+OK.
+
+So, we look at the picture,
+we put in everything we know,
+
+and then we write
+an equation here.
+
+And we solve for--
+sorry, this is x prime.
+
+So, if we solve
+for x prime, we're
+
+going to get x prime
+as a function of x.
+
+And this tells us,
+given a guess here,
+
+how do we compute
+the next guess?
+
+So once we have
+an initial guess,
+
+this lets us make the
+guess better and better
+
+and better, closer and
+closer and closer to x0.
+
+So, let's solve this
+equation reasonably quickly.
+
+x prime minus x equals f
+prime of x over f of x, so
+
+x prime is--
+
+AUDIENCE: Does it matter if it's
+x minus x prime or [INAUDIBLE],
+
+because technically
+it's x minus x prime.
+
+PROFESSOR: Yeah, it
+matters, because you're
+
+going to get the wrong sign.
+
+Which is exactly what
+I'm about to do here.
+
+AUDIENCE: Oh, OK.
+
+PROFESSOR: So, I'm not
+going very well, right?
+
+This is wrong.
+
+AUDIENCE: Yeah, it's because you
+flipped your x at your prime--
+
+AUDIENCE: x minus x prime
+instead of x prime--
+
+AUDIENCE: No, I think it's
+because f prime of x is on top.
+
+It should be on the bottom.
+
+In the second--
+no, third equation.
+
+Shouldn't those be flipped?
+
+Because if you move
+the subtraction,
+
+x prime to the left--
+
+PROFESSOR: f what?
+
+AUDIENCE: f of x over
+f minus x instead
+
+of f prime x over f of x.
+
+Yeah, there you go.
+
+PROFESSOR: OK, so I can do math.
+
+OK, so that's one issue.
+
+There's one more issue.
+
+So, there are too
+many issues here.
+
+Issue number one, this.
+
+Issue number two,
+I got this wrong.
+
+AUDIENCE: Oh, we get
+a negative number.
+
+AUDIENCE: 2x minus x prime.
+
+PROFESSOR: Yep.
+
+So the reason for
+that is we're going--
+
+AUDIENCE: Only if you start
+from the right, though.
+
+PROFESSOR: Yeah.
+
+AUDIENCE: If you
+start from the left,
+
+if your guess is to the
+left of the actual root,
+
+it may or may not be different.
+
+PROFESSOR: OK.
+
+So our guess should
+be to the right.
+
+So this is x minus x prime.
+
+So the reason it's x minus x
+prime, the way you remember
+
+this and you don't do the
+same mistake that I did
+
+is, you want to walk
+against the derivative.
+
+If you walk in the
+direction of the derivative,
+
+it's going to move
+you forward, right?
+
+So, if you go in the
+direction of the derivative,
+
+instead of going
+backwards like this,
+
+you're going to go
+forward like this.
+
+So you're going to go
+away from the solution.
+
+So, this will take us
+in the right direction,
+
+and this means that it's--
+
+OK.
+
+So two ways to remember this.
+
+One that you're going
+against the derivative.
+
+Another one is that
+you have your guess
+
+and you're subtracting
+something from it.
+
+AUDIENCE: You flipped
+your primes again.
+
+PROFESSOR: Again?
+
+Jesus.
+
+[LAUGHTER]
+
+AUDIENCE: I mean, I
+agree, the prime looks
+
+better on top part of
+the fraction, but still.
+
+PROFESSOR: OK.
+
+Well clearly, my hand
+thinks the same thing.
+
+So this is you'd
+iterate using Newton.
+
+So the way to remember
+that the signs are right
+
+is your x is somewhere
+here, and you
+
+know you have to subtract
+something from it so it looks
+
+like this figure.
+
+And this actually works in
+all the cases, turns out.
+
+Our guesses are usually
+smaller than the actual number,
+
+and this still works.
+
+OK, so let's go over Newton.
+
+What do we have, or
+what do we need in order
+
+to make Newton happen.
+
+So we need to be able
+to evaluate this, right?
+
+So we need to be
+able to evaluate
+
+f over f prime of x for
+any x that Newton gives us.
+
+And for Newton,
+this is a black box.
+
+So whichever way
+you use to implement
+
+this is fine, as long as
+it works reasonably fast.
+
+OK, what else do we
+need to use Newton.
+
+We need to remember this formula
+Let's start with something
+
+easy.
+
+Suppose we want to use
+it to compute a over b.
+
+How do I do that?
+
+What do I need?
+
+AUDIENCE: You need a
+line, a tangent line
+
+like you did before.
+
+PROFESSOR: Well, that's
+already taken care of here.
+
+So we have this, and
+we know that we'll
+
+have to compute this
+and plug it in here.
+
+So, what do I need to
+compute a/b using Newton?
+
+So, I need the function, right?
+
+This thing.
+
+I can't say it's something, I
+have to figure out what it is.
+
+I guess I was confusing because
+I said assume we have this.
+
+Well, sorry.
+
+We don't have this.
+
+We need to figure
+out the function
+
+so we can evaluate this.
+
+OK, so we need to come
+up with the function
+
+so we can evaluate
+that, and what property
+
+does the function need to meet?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, that
+would be nice, right?
+
+So we want the function
+so that f of a/b equals 0,
+
+because that's the number
+that Newton will give us.
+
+And we also need to be able
+to compute f over f prime of x
+
+without doing any
+division, right?
+
+If we did the divisions,
+it doesn't work.
+
+OK, so the first thing
+we're going to do
+
+is we're going to simplify this
+problem to 1 over b instead
+
+of a over b, because if
+you know what's 1 over b,
+
+you're going to
+multiply this by a,
+
+and you're going
+to get a over b.
+
+Suppose we work
+with integers and we
+
+don't want to touch
+floating point numbers.
+
+What would we actually compute?
+
+AUDIENCE: You shift
+it out, right?
+
+To get that 0.23, shift
+now to [INAUDIBLE].
+
+PROFESSOR: All right, all right.
+
+So 1 over b.
+
+Unless b is 1, in which
+case it's really boring.
+
+1 over b looks like this.
+
+0 point something.
+
+This is not an integer number.
+
+I don't like it.
+
+So what I do is,
+I decide that I'm
+
+going to need
+digits of precision,
+
+and I'm going to shift
+the decimal point
+
+right by d digits.
+
+So instead of 0
+point something, it's
+
+d digits here point
+something else.
+
+How do I do this?
+
+AUDIENCE: Multiply
+by 10 to the d?
+
+PROFESSOR: Multiply
+by 10 to the d.
+
+So instead of computing 1
+over b, 10 to the d over b.
+
+And we call this 10 to the
+d R in our station notes.
+
+So we're going to compute
+R. Over b multiplied
+
+by a, and then
+everything divided by R.
+
+So we talked about
+how you multiply
+
+by R. How do you divide by R?
+
+So, if I have a
+number with n digits
+
+and I want to divide by 10
+to the d, how do I do that?
+
+AUDIENCE: Shift.
+
+PROFESSOR: Shift right.
+
+If the number is a python list?
+
+AUDIENCE: Slice it.
+
+PROFESSOR: Yep.
+
+So kill the last d digits.
+
+So, if I add d
+digits to the right,
+
+I multiply by 10 to the d.
+
+If I slice the last digits,
+I divide by 10 to the d.
+
+So this is division,
+this is multiplication.
+
+And the reason I care
+about that is this
+
+is going to be an easy division,
+and whenever I have this,
+
+it's an easy multiplication.
+
+OK, now what function
+am I going to use?
+
+Does anyone know?
+
+Can I use x minus R
+over b equals zero?
+
+AUDIENCE: Sure?
+
+PROFESSOR: Well, so, this is
+f of x. f prime of x is what?
+
+AUDIENCE: Just
+negative R over b.
+
+Or no, 1.
+
+PROFESSOR: OK.
+
+So, f prime of x over--
+
+AUDIENCE: I think you
+switched it again.
+
+[LAUGHTER]
+
+PROFESSOR: Thank you.
+
+Because I was running ahead,
+and I was like, OK, this works.
+
+Why does it work?
+
+OK, so this is going to be
+x minus R over b, right?
+
+Can you evaluate this?
+
+If I can't evaluate this,
+I already know the answer.
+
+AUDIENCE: Your prime's
+not on the bottom one.
+
+PROFESSOR: So, it's x
+minus this divided by 1.
+
+So, it's this.
+
+So then, if you're trying to
+evaluate this far the guesses
+
+that Newton gives
+you, you can't.
+
+Because if you could, you'd
+have the answer already.
+
+So we can't use this function.
+
+This is a nice and easy
+function that doesn't work.
+
+So while I erase the
+board, one minute, someone
+
+figure out the right function.
+
+Sorry?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Man,
+that's hard math.
+
+No, that's too hard.
+
+That's too hard.
+
+OK, let's try this.
+
+Let's try instead
+of x minus R over b,
+
+let's try this 1/x minus b/R.
+And the intuition behind this
+
+is if I have to compute
+b/R, I can do that.
+
+Right?
+
+It's an easy division.
+
+If I somehow get rid of
+1/x and all I have to do
+
+is compute b/R, it's
+an easy division.
+
+Because dividing by
+2 to the R by R means
+
+you're going to shift by
+some digits to the right.
+
+So let's see if the math
+works out for this function.
+
+What's f prime of x?
+
+AUDIENCE: Negative
+1 over x prime?
+
+PROFESSOR: All right.
+
+Like, does no one know it?
+
+At least one student
+has to know it.
+
+OK, so f of x divided
+by f prime of x is what?
+
+AUDIENCE: Negative x
+plus x squared b/R.
+
+PROFESSOR: Plus x squared b R.
+
+AUDIENCE: Yeah.
+
+PROFESSOR: Is this right?
+
+AUDIENCE: Yes.
+
+PROFESSOR: OK.
+
+So if I have my initial guess--
+so if I want to get x prime,
+
+x prime is x minus f of x
+over f prime of x, right?
+
+So, what is it?
+
+AUDIENCE: 2x minus x
+squared over R. OK.
+
+Did this work?
+
+Did it get rid of all
+the hard divisions?
+
+[LAUGHS]
+
+Please nod so I know
+we're good to go.
+
+Tell me if we're not.
+
+So how many divisions
+did we have here?
+
+One division, this guy, right?
+
+AUDIENCE: But that's a shift.
+
+PROFESSOR: That's a shift.
+
+Because R is 10 to the d.
+
+AUDIENCE: What about the
+multiplication [INAUDIBLE]?
+
+PROFESSOR: So, we know
+how to do multiplication
+
+because we learned
+Karatsuba just now.
+
+So we wanted to get
+rid of division,
+
+because if you're
+trying to solve division
+
+by doing division,
+it's probably not
+
+I'm going to work unless you're
+doing divide and conquer.
+
+OK, so this is how it works.
+
+I'm not going to run into
+the error formulas for this
+
+because I want to do
+another case first.
+
+You can keep going on this
+and it's in the notes.
+
+The only thing that
+is useful to remember
+
+is that we use this trick.
+
+So, I want to look at this
+function, square root 3 of a,
+
+and I want to use
+Newton to compute it.
+
+So this is the third order root.
+
+It's not the regular square
+root that we had before.
+
+So we're trying to
+not be boring and not
+
+just repeat what's in the notes.
+
+How do I do this?
+
+Let's walk through the steps.
+
+So what's the first
+thing that we do?
+
+Very good.
+
+Look to the right.
+
+Find the first step,
+and let's put it here.
+
+What's the first step.
+
+AUDIENCE: Function f
+of 0 at cube root of a.
+
+PROFESSOR: OK.
+
+So we need a function
+f so that f of-- good.
+
+So before we start writing
+the actual function,
+
+what if I want to
+compute cube root
+
+of a up to d digits
+of precision?
+
+So if I want to
+compute cube root of 2,
+
+this is going to give me
+numbers that are below 1.
+
+I have to do with
+fractions again.
+
+I don't like that.
+
+If I want the digits of
+precision, what do I do?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Jumping ahead.
+
+But yeah.
+
+So you have the right answer,
+but you're speaking slowly
+
+because you're afraid you're
+going to do a mistake, right?
+
+So, the way to compute this
+to d digits of precision 10
+
+to the d, right?
+
+This shifts the
+dot to the right.
+
+So I have to get this
+10 to the d inside here,
+
+and I get and to the 3d times a.
+
+Perfect answer, by the way.
+
+Don't forget this 3 here.
+
+If you do, you're going
+to get something else.
+
+So now I take this guy,
+and this is the new number
+
+whose cube root I
+have to compute.
+
+Cube, cube, cube.
+
+OK.
+
+So I can do this
+in integer land,
+
+and then I'll get
+an integer result,
+
+and I shift it
+right by d digits,
+
+and I have a number with
+d digits of precision.
+
+Does this make sense?
+
+OK, what's f?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Let's go for that.
+
+Let's see if that works.
+
+x cubed minus a.
+
+Well, let's pretend.
+
+We're going to make
+this b the new a.
+
+So let's not to
+worry about this.
+
+This happens somewhere else.
+
+We went through
+it so that we know
+
+that we know how
+to deal with it.
+
+And now we're going
+to forget about it.
+
+So, it's x cubed minus a.
+
+Because we argued that
+this is an integer, right?
+
+So we don't have to do anything
+fancy like dividing by R
+
+that we had to do over there.
+
+So, what's f prime of x?
+
+OK.
+
+So, iteration?
+
+How do we iterate?
+
+AUDIENCE: x prime?
+
+PROFESSOR: Let's start
+with x prime equals
+
+x minus f of x
+over f prime of x.
+
+Right?
+
+Nice and easy so
+we have it here.
+
+And this becomes minus copy
+these two things, right?
+
+x cubed minus a over 3x squared.
+
+OK.
+
+Next thing, I bring this
+guy under the denominator,
+
+so it's 3x cubed minus x
+cubed plus a over 3x squared.
+
+So it's 2x cubed plus
+a over 3x squared.
+
+So this is 2/3 plus--
+
+AUDIENCE: 2 over 3x.
+
+You keep saying
+cubed and writing 2.
+
+PROFESSOR: Yeah, that's better.
+
+Thank you.
+
+Plus 1/3 times a over x.
+
+So this one's division.
+
+AUDIENCE: x squared.
+
+PROFESSOR: x squared.
+
+Ouch.
+
+So this guy wants division.
+
+By the time I do this, I better
+have division ready, right?
+
+OK, so that my iteration.
+
+x prime is 2/3 x plus
+1/3 and a over x squared.
+
+What else do I need?
+
+An initial guess
+would be nice, right?
+
+I can't do this if I
+don't have the first x.
+
+So let's try to think of a
+starting x that's reasonable.
+
+The better it is, the
+faster it's going to be.
+
+So let's try to come up with
+something reasonable that
+
+doesn't require too much
+thinking or too much.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Too much work.
+
+I have to compute a square root.
+
+So what's a?
+
+Let's start with that.
+
+What's an a, right?
+
+So, it's an n digit number.
+
+And say the digits are d1,
+d2, d3, all the way up to dn.
+
+So what's a good approximation?
+
+Well, the first
+approximation for this?
+
+AUDIENCE: You get a
+third as many digits.
+
+PROFESSOR: A third
+as many digits.
+
+OK.
+
+So something times
+10 to the n/3.
+
+Let's say that
+something is 1, right?
+
+So this is the
+first approximation.
+
+It's the right
+order of magnitude.
+
+Do people see why this
+is a good approximation?
+
+So this number,
+whatever it is, it
+
+has to be between 1,
+0, 0 0, 0, and 1, 0, 0.
+
+OK.
+
+So generally when
+we do this, what
+
+we have to have in
+an approximation
+
+is the right order of magnitude
+And maybe the first digit.
+
+If we can figure
+out the first digit,
+
+then we're in a good
+shape, or something really
+
+close to the first digit.
+
+How would we get
+the first digit?
+
+AUDIENCE: Cube root
+of the first digit?
+
+PROFESSOR: OK.
+
+Sure.
+
+How do we compute this?
+
+AUDIENCE: Get a formula?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: OK, so I'm not
+going to argue with that.
+
+AUDIENCE: I like that.
+
+PROFESSOR: So I want to reject
+the recursive argument first.
+
+So this is going
+to be small, right?
+
+This is going to be 10 if
+you're working with digits,
+
+or if you're a computer,
+maybe it's 256,
+
+or maybe it's 2 to
+the 16 or 2 to the 32.
+
+Not much bigger
+than that, right?
+
+Pretty small.
+
+So these algorithms really
+good for big numbers.
+
+Algorithms that are
+complicated but have
+
+nice asymptotic complexity
+are good for big numbers.
+
+They're awful for small numbers,
+as in they 10 to 100 times
+
+more times to run.
+
+So let's not to
+do that for this,
+
+because it's like
+bringing a tank
+
+and shooting it so you
+can hammer a nail in.
+
+Not the right tool.
+
+So, precomputed list.
+
+I like that.
+
+It's an option, especially
+if you're [INAUDIBLE] right?
+
+You can use pen and
+paper to get it.
+
+What if I don't want to do that.
+
+What if my base is
+more like this.?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: So this is
+a very good solution.
+
+I'm not arguing with it.
+
+If your power is this or this,
+by all means, use a table.
+
+So let's see what do we do here?
+
+I just want to think
+a little bit more.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: OK, so there's
+some approximation
+
+that comes from math
+that says that d1 over 3
+
+is not going to be
+such a bad guess.
+
+Now let's be CS people
+and do something better.
+
+AUDIENCE: [INAUDIBLE]
+the exponent.
+
+2 to the 14, divide--
+is that 14, right here
+
+AUDIENCE: 16.
+
+AUDIENCE: 16.
+
+Divide 16 by 3.
+
+Or I guess that's not
+quite right either.
+
+PROFESSOR: So you're saying
+2 to the power of, say, 5?
+
+15 over 3?
+
+AUDIENCE: It doesn't
+seem quite right.
+
+PROFESSOR: So, let's
+try to do better.
+
+This is math.
+
+Let's just try to
+do it in a CS way.
+
+So we're trying to guess a
+digit between 0 and 2 to the 16.
+
+I heard an "oh."
+
+Yes?
+
+You had your hand up?
+
+No?
+
+OK.
+
+AUDIENCE: You take the
+current time 2 to the 16.
+
+I mean--
+
+[LAUGHTER]
+
+PROFESSOR: So your
+algorithm is going
+
+to be fast with some
+probability, right?
+
+No, that's terrible.
+
+Let's not do that.
+
+Please don't make me
+grade code like that.
+
+AUDIENCE: Did you already
+cut out the recursive option?
+
+AUDIENCE: Yes.
+
+PROFESSOR: Yeah.
+
+Well, so I don't want to
+recurse on square roots.
+
+AUDIENCE: But you could
+recurse on that one.
+
+PROFESSOR: I mean,
+if you give me
+
+some algorithm that happens--
+
+AUDIENCE: You're
+already [INAUDIBLE].
+
+PROFESSOR: OK.
+
+So, what's the intuition?
+
+If you have a computer
+and you have register,
+
+bytes, bits, whatever.
+
+You don't know how
+to do square roots.
+
+That's not an instruction, but
+these are all instructions.
+
+Right?
+
+So if I have a guess,
+say I start with half
+
+and then I get my guess, what
+do I need for the binary search
+
+to work?
+
+Given a guess that's
+somewhere here,
+
+I have to be able to say whether
+this is too small, too big,
+
+or just the right number.
+
+So given a guess, I can multiply
+it by itself three times,
+
+right?
+
+Compute gets cubed.
+
+And I can see how does
+it compare to the number
+
+that I want.
+
+So I have the first digit, and
+I have an order of magnitude.
+
+Not bad, right?
+
+Pretty good initial guess.
+
+This is as much of an answer
+is you need to give out
+
+in physics problems, and you
+get full score, so that's good.
+
+OK, how are we doing so far?
+
+Following along?
+
+AUDIENCE: If we compute
+our guess cubed,
+
+we want only to compare
+it to our original number
+
+to see how close it is?
+
+PROFESSOR: Yup.
+
+AUDIENCE: And, do we just
+keep on doing that until--
+
+PROFESSOR: Well, so you're going
+have to guess a digit, right?
+
+Between 0 and 2 to the 16.
+
+So you choose the largest thing
+that's smaller than your guess,
+
+or something.
+
+AUDIENCE: Or until we
+get the first digit.
+
+PROFESSOR: Yeah.
+
+Just the first.
+
+And then you have a
+first digit, and then you
+
+have an order of magnitude.
+
+And then you feed
+that to Newton,
+
+which converges way faster.
+
+So you could the binary
+search for the whole thing,
+
+but that would be slower
+than Newton, turns out.
+
+Yes?
+
+AUDIENCE: So where'd
+you get the f of x here?
+
+I'm missing that stuff.
+
+PROFESSOR: Oh.
+
+AUDIENCE: Yeah, right there.
+
+PROFESSOR: Someone
+told me to use this.
+
+[LAUGHTER]
+
+One of you guys
+told me to use this.
+
+Well, so I tried it out.
+
+I put it here.
+
+And then I computed
+the derivative,
+
+and I looked to see if
+this looks reasonable.
+
+And this looks like
+something I can compute.
+
+AUDIENCE: And why
+was that reasonable?
+
+PROFESSOR: Because I know
+how to do the division
+
+and multiplication.
+
+So, say if I would have had
+the square root of 3 in here,
+
+that wouldn't be
+reasonable, right?
+
+Just like before.
+
+When you're trying
+to compute division,
+
+we can't have division.
+
+If you're trying to
+compute sine of x,
+
+you don't want to
+have sine of x.
+
+AUDIENCE: OK.
+
+and computing a over x
+squared is reasonable?
+
+PROFESSOR: Because
+we did it before.
+
+AUDIENCE: OK.
+
+So then you might use
+something else, maybe?
+
+PROFESSOR: Yeah.
+
+You can use something else as
+long as you know how to do it,
+
+and as long as it's
+reasonably fast.
+
+AUDIENCE: OK.
+
+PROFESSOR: Yes?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Oh, no that's fine.
+
+AUDIENCE: Oh, that fine?
+
+OK.
+
+PROFESSOR: So, the
+binary search is
+
+fine to get the
+first approximation.
+
+But after that--
+so I'm not going
+
+to do a binary search
+for the whole result,
+
+because Newton is
+faster than that.
+
+I'm just using this so
+that I have a decent guess
+
+to pass to Newton.
+
+And we'll see why we need that
+decent guess in two minutes
+
+total.
+
+So I'm going to try to
+spend two minutes to explain
+
+how the error thing
+works, and you'll
+
+have to look at the
+notes and make sense out
+
+of the rest of it.
+
+So, let's see.
+
+Errors.
+
+So with Newton, you start
+to with an initial guess,
+
+and then you get to a
+better guess, and a better
+
+guess, and a better guess,
+and so on and so forth
+
+until you're satisfied.
+
+By the way, if we're doing
+this one, are we satisfied?
+
+AUDIENCE: What do you mean,
+like, finding the guess?
+
+Are we satisfied?
+
+PROFESSOR: Oh, no.
+
+So, we have the initial guess.
+
+And we keep applying the formula
+that I just deleted to iterate.
+
+When do we stop?
+
+AUDIENCE: When we have
+enough digits of precision?
+
+PROFESSOR: So how do we know
+when we have enough digits,
+
+if we're working with integers?
+
+AUDIENCE: We iterate
+again and nothing changes.
+
+PROFESSOR: We iterate
+again and nothing changes.
+
+So I'm computing-- do
+I have this anywhere?
+
+Oh, no.
+
+I erased it.
+
+So I'm computing 10 t0
+some-- oh, I had it up here.
+
+So, I'm computing
+10 to the power
+
+of d times a square
+root of 3, because I
+
+want to work with integers.
+
+Just integers.
+
+I used Newton to iterate.
+
+My precision gets gets
+better and better and better.
+
+And I use integers.
+
+So I only have d
+digits of precision.
+
+Everything after that gets
+discarded automatically.
+
+When I get 2 x's that don't
+change-- so if I get x5,
+
+and then I run
+the thing and then
+
+I get x6 that is
+equal to x5, there's
+
+no point to keep
+running Newton, right?
+
+I;m stuck.
+
+And I'm also done
+because I have the answer
+
+with d digits of precision.
+
+So this is where I stop.
+
+OK.
+
+Now, my precision is how far
+I am from the right answer.
+
+And we write that
+by saying that x1
+
+is x, the true answer, times
+1 plus epsilon, epsilon 1.
+
+And then x2 is x times 1 plus
+epsilon 2, 1 plus epsilon 3,
+
+so on and so forth.
+
+Right?
+
+So, if we had a lot of time
+and not too much stuff to do,
+
+I could copy this thing here
+that we have in the notes.
+
+That's eight lines of math.
+
+And then we'd get something
+along the lines of x of i
+
+plus 1 is x times 1
+plus something times E
+
+squared-- I'm sorry, Ei squared.
+
+So this is also
+1 plus Ei plus 1.
+
+So what we get is that E of i
+plus 1 is roughly E i squared.
+
+And this is what's really
+called quadratic convergence.
+
+Now why is this good?
+
+Can anyone think intuitively
+why this is nice?
+
+In which cases?
+
+Yes?
+
+AUDIENCE: You're converging
+really quickly to your answer.
+
+PROFESSOR: OK.
+
+But when do I converge?
+
+, So what I want this to happen?
+
+What do I want this to be?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Well, you
+guys told me everything
+
+I need for the next two minutes.
+
+So, I want this to
+become 1, right?
+
+This has to go to 1 because I
+want this whole thing to be x.
+
+So in order for this to be 1,
+I want to epsilons to go to 0.
+
+So I want them to be
+as small as possible.
+
+Now, you said that if my
+epsilon is smaller than 1,
+
+then epsilon squared is
+smaller than epsilon.
+
+And intuitively,
+how this works is,
+
+suppose you start with
+an epsilon of 0.1.
+
+When you square
+it, you get 0.01.
+
+You square it again,
+you get 0.0001.
+
+Square it again.
+
+0.00000001.
+
+OK.
+
+This is step 0, step
+1, step 2, step 3.
+
+How many digits do I have here?
+
+Don't be shy.
+
+AUDIENCE: 2 to the i?
+
+PROFESSOR: Yup.
+
+2 to the i.
+
+So this is going
+to be equal to this
+
+when 1 plus x times 1 plus
+epsilon i over 1 plus epsilon--
+
+sorry, i plus 1 epsilon i
+when the floor of this thing
+
+is-- sorry, there is a
+delta somewhere here.
+
+So, something has
+to converge to 0.
+
+Sorry, this is what it is.
+
+1 plus e of i.
+
+So this is the difference
+between two terms, x.
+
+So this is x6 minus x5, right?
+
+Convincing?
+
+AUDIENCE: [INAUDIBLE].
+
+Let's write it again.
+
+Let's write it again.
+
+This is out of hand.
+
+So, x, x minus x5,
+or actually, xi
+
+plus 1 minus xi is equal
+to x times 1 plus epsilon i
+
+plus 1 minus x times 1
+plus epsilon i, right?
+
+So this is x times-- Sorry?
+
+AUDIENCE: Those are xi, x of i.
+
+AUDIENCE: No, those
+are the real x's.
+
+PROFESSOR: These are-- so
+these are the approximations,
+
+but then, this is the real x.
+
+AUDIENCE: I
+understand, thank you.
+
+PROFESSOR: OK.
+
+So, this is, the difference
+between them is this guy here.
+
+So if I take the floor
+because I work with integers,
+
+when this floor becomes
+0, we're done, right?
+
+So in order for the
+floor to become 0,
+
+this guy has to be
+canceled by this guy.
+
+So this guy has some number
+of digits, whatever that is.
+
+It's my number with d
+digits of precision.
+
+Well, that's OK
+because-- where my 0s?
+
+Did I erase my 0s?
+
+Oh, no.
+
+I have 0s here, right?
+
+The epsilons have a
+lot of 0s in them,
+
+so the 0s are going to
+cancel the digits in x.
+
+So as soon as I have enough 0s
+here to cancel this, I'm stuck.
+
+The number of 0s
+increases exponentially.
+
+So in each step the number
+of 0s I have doubles.
+
+So after log d steps, I'm done.
+
+If I have d digits
+in here, because I'm
+
+computing this with d
+digits of precision,
+
+after roughly log d steps,
+I'll have enough 0s here
+
+to reduce this and make
+the whole thing be 0.
+
+So this is how I
+know that it's fast.
+
+So in the end, what you
+want is the initial guess
+
+has to satisfy
+this, and then you
+
+want to be able to
+prove that this is true.
+
+So you want this factor
+here that tells you you're
+
+converging fast.
+
+So when you look at
+the recitation notes
+
+and you look at this
+long string of equations,
+
+make sure this is
+somewhere there,
+
+because this means you're
+on the right track.
+
+Yes?
+
+AUDIENCE: If it
+takes log d steps,
+
+doesn't the binary search
+also take log-- ah, OK.
+
+Log 10 steps.
+
+Got it.
+
+PROFESSOR: Yeah.
+
+Which is d.
+
+AUDIENCE: He's talking
+about binary search--
+
+PROFESSOR: Oh, for one digit.
+
+Yeah.
+
+Oh, sorry.
+
+I thought you meant
+for the whole thing.
+
+So if you wanted to do binary
+search for the whole thing,
+
+that's log of the whole number.
+
+So that's order d where d
+is the number of digits.
+
+AUDIENCE: Wait, he's talking
+about a binary [INAUDIBLE].
+
+AUDIENCE: [INAUDIBLE].
+
+AUDIENCE: [INAUDIBLE] wants
+to go for [INAUDIBLE], 10
+
+to the 20th.
+
+He wants to do a binary
+search over like a cube root--
+
+PROFESSOR: So, for this?
+
+Binary search for
+this or for one digit?
+
+Or binary search to
+compute the cube root?
+
+AUDIENCE: I think, yeah.
+
+PROFESSOR: So, if you do
+that, your entire thing is
+
+d digits, right?
+
+So 10 to the d.
+
+Binary search takes
+log of 10 to the d.
+
+AUDIENCE: Right, yeah.
+
+PROFESSOR: So the
+numbers that we're
+
+dealing with are d digits.
+
+So this d is the number
+of digits, not the number
+
+that you have.
+
+So if you look at the
+number that you have,
+
+this is log log n.
+
+AUDIENCE: Right,
+that makes sense.
+
+Sorry.
+
+PROFESSOR: So, it's faster.
+
+AUDIENCE: I like it.
+
+It is faster.
+
+PROFESSOR: OK.
+
+Cool.
+
+Thanks for the lesson.
+
+AUDIENCE: [INAUDIBLE].
\ No newline at end of file
diff --git a/Jfibd3L_E_o.txt b/Jfibd3L_E_o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..321eee348d3818f005523539162bf3e1cc29173f
--- /dev/null
+++ b/Jfibd3L_E_o.txt
@@ -0,0 +1,1708 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free to make a
+
+donation or view additional
+materials from hundreds of MIT
+
+courses, visit MIT
+OpenCourseWare at ocw.mit.edu.
+
+PROFESSOR: Ladies and gentlemen,
+welcome to this
+
+lecture on non-linear finite
+element analysis of solids and
+
+structures.
+
+In the previous lectures, we
+have considered quite a bit of
+
+theory related to non-linear
+finite element analysis in
+
+some example solutions.
+
+The objective in the next two
+lectures now, the last
+
+lectures of this video course,
+is to show how an actual
+
+finite element analysis is
+performed on the computer.
+
+We start with a linear solution
+in this lecture, and
+
+then consider a non-linear
+solution in the next lecture.
+
+We cannot discuss really, in
+this amount of time given, all
+
+the aspects of the analysis,
+but want to summarize and
+
+demonstrate on the computer
+the major steps of the
+
+analysis and concentrate on
+possible difficulties,
+
+possible pitfalls, and some
+general recommendations.
+
+As the example problem, we want
+to use the plate with a
+
+hole, that we already
+considered earlier.
+
+And we performed a linear
+analysis and then
+
+a non-linear analysis.
+
+Remember, I pointed out in the
+previous lectures that it is
+
+very important to always do
+linear analysis first before
+
+you go into a non-linear
+analysis.
+
+The elastic analysis is
+performed to obtain the stress
+
+concentration factor at the
+hole, then we do an
+
+elasto-plastic analysis to
+estimate the limit load, and
+
+an analysis also to investigate
+the effect of a
+
+shaft in the plate hole.
+
+These two analyses are being
+performed in the last lecture
+
+of the video course.
+
+The plate we are analyzing is
+shown on this view graph here.
+
+Notice it's a square plate.
+
+Here, we show the hole, the
+plate is loaded as shown up
+
+here, and down here.
+
+The material property for the
+elastic analysis are given
+
+here and the thickness of
+the plate is 0.01 meter.
+
+Because of symmetry conditions,
+we only need to
+
+consider this quarter here.
+
+Of course, using appropriate
+boundary conditions along
+
+these two lines. we will talk
+about that more later on.
+
+The first step for a finite
+element analysis is to select
+
+a computer program, and we, of
+course, use the ADINA system.
+
+ADINA-IN is the pre-processor
+to prepare, generate the
+
+finite element data.
+
+ADINA then solves the actual
+finite element model, and
+
+ADINA-PLOT is used to this
+display numerically or
+
+graphically the solution
+results.
+
+Schematically, we are sitting
+here at a terminal and we're
+
+inputting the data
+to ADINA-IN.
+
+We can also receive here,
+numerical output, and we can
+
+also plot on this terminal here,
+any of the information
+
+that we like to plot.
+
+This is a graphics terminal.
+
+Notice ADINA-IN, of course,
+communicates to a storage
+
+device and further on
+to ADINA, as we will
+
+discuss just now.
+
+The user inputs, in
+other words, or
+
+types into the terminal.
+
+ADINA-IN commands interactively
+or for batch
+
+processing and then the user
+checks also the input and the
+
+generated data on the graphics
+device, as I showed you on the
+
+previous view graph.
+
+ADINA-IN generates the
+input data for ADINA.
+
+The input data is checked
+internally in ADINA in for
+
+errors and inconsistency, and
+also is displayed as you are
+
+requesting it as a user.
+
+The degree of freedom numbers
+are generated and to obtain
+
+minimum bandwidth, we have a
+minimum bandwidth minimization
+
+algorithm in the program, as
+I will point out a bit
+
+stronger later on.
+
+ADINA data inputs then, is
+available to ADINA, and the
+
+user runs ADINA, and ADINA then
+stores the output data on
+
+a porthole file and
+on an output file.
+
+The output file, in other words,
+contains really the
+
+ADINA model data and the
+calculated results.
+
+We access ADINA porthole
+file using ADINA-PLOT.
+
+We can, of course, also look
+at the output file and see
+
+numerically the data that was
+calculated using ADINA.
+
+Here, we have the action
+displayed or schematically
+
+shown by the user.
+
+User uses ADINA-PLOT to fetch
+data from the ADINA porthole
+
+file and then ADINA-PLOT
+displays those data either
+
+numerically or graphically.
+
+Let's look very briefly at
+an overview of ADINA.
+
+The program can be used for
+static and dynamic solutions,
+
+for linear and non-linear
+analysis, for small and very
+
+large finite element models,
+and the formulations finite
+
+elements and numerical
+procedures used in the program
+
+have largely been discussed
+in this course.
+
+The displacement assumptions
+that can be employed for the
+
+finite element models are either
+infinitesimally small
+
+displacements, large
+displacements, large rotations
+
+but small strains, and large
+deformations, large strains.
+
+We discussed these assumptions,
+of course, also
+
+in the course.
+
+Material models that are
+available in isotropic linear
+
+elastic model, orthotropic
+linear elastic model,
+
+isotropic thermo-elastic model,
+a curve description
+
+model for analysis of geological
+materials, a
+
+concrete model, isothermal
+plasticity models,
+
+thermo-elastic-plastic and creep
+models, and non-linear
+
+elastic incompressible, and
+user-supplied models.
+
+The elements available in the
+program, is available number
+
+nodes tress element, an element
+that can have two
+
+nodes, three nodes,
+or four nodes.
+
+It can also be used
+as a ring element.
+
+A two-dimensional solid element
+that is used for plane
+
+stress axis symmetric and
+plane strain analysis.
+
+This also can have available
+number of nodes, from four
+
+nodes to nine nodes.
+
+Similarly, available number
+of nodes element for
+
+three-dimensional analysis.
+
+Then also a beam element, a
+2-node beam element, Hermitian
+
+beam element.
+
+And the isoparametric beam
+element that we talked about
+
+in the course.
+
+This element can carry, or can
+be used with two nodes, or
+
+three nodes, or four nodes.
+
+A pipe element that we did not
+discuss in the course, but you
+
+might be interested in reading
+about that element is a curved
+
+beam element, of course,
+of pipe section.
+
+Which however, also includes the
+effects of ovalization So
+
+this element also carries, if
+desired ovalization degrees of
+
+freedoms at the nodes.
+
+And shell elements, we talked
+about the use of the 16-node
+
+element, and the MITC 4,
+the 4-node element.
+
+We also talked briefly about
+transition elements that I
+
+used to model shells,
+or thin structures
+
+that couple into solids.
+
+Let us summarize some important
+observations
+
+regarding finite element
+analysis.
+
+It's important to check the
+finite element data, of
+
+course, very carefully.
+
+The data must be checked
+prior to the
+
+actual response solution.
+
+This is done, of course, with
+the pre-processor, by plotting
+
+the data, looking at it very
+carefully, typically.
+
+And then after the response
+solution, you still want to
+
+check the input data once more
+by seeing whether the boundary
+
+conditions are properly
+satisfied, that you want to
+
+impose on to the model, whether
+the displacement and
+
+stress solution is
+a reasonable.
+
+Once the analysis has been
+performed, you want to very
+
+carefully evaluate
+and interpret
+
+the calculate response.
+
+You want to start in detail the
+calculated displacement
+
+and stresses along
+certain lines.
+
+In particular, look
+at stress jumps.
+
+We pointed that out already in
+an earlier lecture, and we
+
+will do so in our example
+solution again, just now.
+
+And here, I'd like to add that
+stress averaging, stress
+
+smoothing should only be done
+after the above careful
+
+evaluation.
+
+That's something important
+to keep in mind.
+
+I believe that you should first
+look at the stresses,
+
+the way they have been
+calculated by the program and
+
+then start thinking about
+stress smoothing.
+
+Only after you've gone through
+this phase here.
+
+The data for the construction
+of the finite element mesh,
+
+that we want to deal with in the
+example solution is input
+
+for this quarter of
+the plate, as I
+
+pointed out earlier already.
+
+We have these elastic material
+constants, we're looking at a
+
+plane stress analysis.
+
+This is the thickness
+of the plate.
+
+And once again, here
+is a loading.
+
+Notice, we are putting this
+boundary on rollers, and we
+
+want to put this boundary as
+well on rollers to model the
+
+symmetry conditions that we
+need to model in order to
+
+consider a whole plate, where we
+actually analyze here, only
+
+one quarter of that plate.
+
+The finite element mesh that we
+will be using is shown on
+
+this view graph.
+
+It consists of 64 8-node
+isoparametric elements.
+
+Well, we performed this analysis
+on the computer in my
+
+laboratory at MIT a few weeks
+ago, and we have brought in a
+
+video crew to record all the
+actions that we have been
+
+performing to actually complete
+the analysis.
+
+I like to now share with you
+what we have recorded and
+
+narrate to you as we go step by
+step through the analysis
+
+of this plate on the computer.
+
+Our first step is to look at
+how we are generating using
+
+ADINA-IN, how we are generating
+this mesh, and also
+
+the other data that are required
+for use of ADINA.
+
+So let's look at this first step
+now, after which I will
+
+then introduce you to the next
+step and narrate continuous
+
+narration of the analysis.
+
+Here we show briefly the
+hardware equipment we are
+
+using in my MIT laboratory.
+
+A MASSCOMP minicomputer with two
+megabytes of real memory,
+
+and 330 megabytes
+of disk storage.
+
+We also have a tape drive.
+
+The computer features virtual
+memory, and we use a
+
+Unix-based operating system.
+
+Roughly, for our purposes,
+the computer is
+
+equivalent to a VAX 750.
+
+We use two terminals.
+
+One terminal for alphanumerical
+and numerical
+
+input and output, and one
+terminal, the one to the
+
+right, for graphical output.
+
+We also have a plotter.
+
+We use this plotter to generate
+the figures of finite
+
+element meshes, and results
+for this course.
+
+Here comes my student,
+Ted [? Sossman, ?]
+
+who will sit at the
+terminal to input
+
+the data to the program.
+
+In what follows, we will see the
+data input prepared by Ted
+
+on the terminal at
+which he sits.
+
+Non-graphical output is
+displayed by that same
+
+terminal, whereas we will see
+graphical output displayed on
+
+the right terminal.
+
+Here, we see the start of input
+
+preparation for ADINA-IN.
+
+We have opened the data base,
+on which the data input and
+
+generated will be stored and
+have already input the title
+
+for the analysis, quarter plate
+with hole, 64 elements.
+
+We have also defined master
+degrees of freedom conditions
+
+by specifying the
+values of IDOF.
+
+1 means of a deleted degree of
+freedom, 0 means a free,
+
+existing degree of freedom.
+
+Here, all degrees of freedom
+have been deleted except for
+
+the yz displacements.
+
+Notice also that at
+our request, all
+
+text appears twice.
+
+After we have typed a line, the
+line is echoed back by the
+
+program merely for checking.
+
+In what follows, we now specify
+the coordinates of a
+
+few key points that defines
+the outline of the
+
+quarter of the plate.
+
+Note we define the y-
+and z-coordinates.
+
+First of node 1, then for
+nodes 2, 3, 4, 5, and 6.
+
+Note that these coordinates
+are input in free format.
+
+Here the node 6 input is not
+aligned with the other nodal
+
+point coordinate input.
+
+We now want to look at the plot
+of these nodal points.
+
+This is achieved by the frame
+and mesh commands.
+
+Here they are, the six points.
+
+Point 1 is the center of the
+hole, points 2 and 3 defines
+
+the boundary of the hole.
+
+Points 4, 5, 6 defines the
+remaining corners of the
+
+quarter plate.
+
+And here, you see the first
+set of generated nodes.
+
+Note that the nodal points have
+consecutive numbers along
+
+the vertical symmetry edge,
+except for the top and bottom
+
+nodes, numbers 3 and 4,
+similarly for the horizontal
+
+symmetry edge.
+
+This would mean a large
+bandwidth unless we use a
+
+bandwidth minimizer.
+
+And we will do so, hence we
+are not concerned with the
+
+nodal point numbering
+used at this stage.
+
+Next, we generate also the nodal
+points on the remaining
+
+edges of the quarter plate.
+
+And here they are.
+
+We now want to generate the
+elements of the plate.
+
+For this we define, first the
+material to be a elastic.
+
+Young's modulus E, Poisson's
+ratio NU.
+
+We want a plane stress
+element group.
+
+The Gauss integration
+order is 3x3.
+
+The material set has a number 1,
+this is the material set we
+
+just defined.
+
+The G-surface command next
+generates the 8-node elements
+
+in the domain defined by the
+corner points, so to
+
+say 6, 4, 3, 2.
+
+We now want to plot the
+generated element mesh, and
+
+here, you see it.
+
+Note once again, we use 8-note
+isoparametric elements, around
+
+the hole, they are
+curved elements.
+
+Finally, we also define in the
+ADINA-IN input the elements
+
+thicknesses to be 0.01 and the
+loads which correspond to the
+
+pulling on the plate.
+
+This [? end ?] completes
+the input preparation
+
+for ADINA-IN .
+
+ADINA-IN has now all the
+information to generate a
+
+complete input file ADINA.
+
+In addition, we also want to
+ask ADINA-IN to assign
+
+equation numbers that correspond
+to a minimum
+
+bandwidth for the solution
+of this problem.
+
+So our next step is to have
+ADINA-IN go through these
+
+actions, and turn back to our
+laboratory and see what is
+
+happening now.
+
+Here, we see the end of the
+ADINA-IN input file that we
+
+saw already before.
+
+The command ADINA now generates
+the ADINA file.
+
+At the same, also, the bandwidth
+of the stiffness
+
+matrix is minimized.
+
+We use the reverse Cuthill-Mckee
+algorithm.
+
+Notice that the bandwidth has
+been reduced from 399 to 93.
+
+The original bandwidth was, of
+course, artificially large
+
+because our nodal point
+generation did not take
+
+account of any bandwidth
+considerations, as I pointed
+
+out before.
+
+Let us briefly look
+at the ADINA file
+
+generated by the ADINA-IN.
+
+Here, we see common cards,
+automatically inserted by
+
+ADINA-IN to explain
+the input cards.
+
+We see the master control card,
+the load control card,
+
+the Eigenvalue solution control
+card, and so on.
+
+Let us look a bit closer at
+the element data cards.
+
+Element 1 has eight nodes and
+the first three are 6, 64, 74.
+
+Element 2 has 8 nodes and the
+first three are 64, 62, 76.
+
+Note a maximum of nine
+nodes is possible.
+
+The last 0 is the node card
+signifies that the ninth node
+
+is not used.
+
+With a complete ADINA input
+file now available, we can
+
+call ADINA to execute this file
+and this gives us our
+
+first solution results.
+
+We look at the solution results
+and, in particular, we
+
+plot the deformed mesh onto the
+original mesh, and this
+
+shows, in fact, that we have
+made an error in the input
+
+description.
+
+It will show us that we have
+fixed all these nodes down
+
+here, whereas they should
+have been on a roller.
+
+This is shown by plotting the
+deformed mesh on to the
+
+original mesh, and it's
+also shown by
+
+looking at the stresses.
+
+We do so by using an option in
+the ADINA system for the
+
+stress vector outputs, and this
+is schematically shown
+
+here, this option.
+
+We plot maximum principle
+stresses--
+
+say tensile in this
+case here--
+
+as a line with two arrows, and
+principles stress that's
+
+compressive as simply a line.
+
+So we can see, in other words,
+how the stress flows through
+
+the material, and we can see,
+of course, compressive and
+
+tensile stress situations, and
+notice that the lengths of
+
+these lines corresponds or is
+proportional to the magnitude
+
+of the stresses.
+
+We can plot this stress vector
+output for all the integration
+
+points stresses in the mesh, and
+that, as I said already,
+
+indicates clearly once again,
+that we have used the wrong
+
+boundary conditions down here.
+
+So we go and correct the
+boundary conditions down here,
+
+and re-run the analysis.
+
+In other words, call ADINA again
+and those results that
+
+we obtained then, once again,
+displacements, in other words,
+
+are plotted by plotting the
+deformed mesh onto the
+
+original mesh.
+
+We see that we now got much
+better, much more
+
+realistically-looking results.
+
+And we also will look at the
+stresses using the stress
+
+vector plots again, in the
+elements, that show us also
+
+that the results are now quite
+realistic and that our mesh,
+
+including the boundary
+conditions have been quite
+
+properly defined.
+
+So let us now look at this
+step of the analysis.
+
+The command runadina
+calls ADINA to
+
+execute the input data.
+
+The data input file is
+in ADINA-IN F02.
+
+And here, we see now the
+deformed plotted onto the
+
+original mesh.
+
+The original mesh is plotted
+in dash lines.
+
+Of course, the deformations
+are magnified.
+
+Note that as expected, the top
+face has uniformly moved up.
+
+However, note that the nodal
+points on the horizontal
+
+symmetry line have not
+displaced at all.
+
+This is quite unphysical and
+shows that the wrong boundary
+
+conditions have been used.
+
+If we look at the stress vector
+plot over the mesh, the
+
+same conclusion is reached.
+
+For clarity, on the video, we
+show here the stress vectors
+
+just on the elements closest
+to the hole.
+
+And we can see in the element
+adjoining the horizontal
+
+symmetry line, a stress that
+acts normal to the whole.
+
+This is, of course,
+unphysical.
+
+Next, we show the stress vectors
+in the outer most
+
+elements of the quarter plate.
+
+And you can see here, a stress
+acting perpendicular to the
+
+free edge of the plate, when
+we look near the horizontal
+
+symmetry line.
+
+This is also unphysical and is
+due to having specified the
+
+wrong boundary conditions
+on the wrong
+
+horizontal symmetry line.
+
+The specification
+of the boundary
+
+conditions is shown here.
+
+The character, C, denotes the
+boundary condition on the
+
+horizontal symmetry line.
+
+The character B denotes the
+boundary condition on the
+
+vertical symmetry line.
+
+Where B means only the z
+displacement is free and C
+
+means all displacements
+are fixed.
+
+For the six possible
+displacements and
+
+[? flotatations, ?]
+
+a 1 means the degree of freedom
+is fixed, and 0 means
+
+the degree of freedom is free.
+
+We now correct the boundary
+conditions.
+
+And B on the horizontal symmetry
+line means now the v
+
+displacement is free.
+
+C on the vertical symmetry
+line means now the w
+
+displacement is free.
+
+We run ADINA again, and here
+you see the deformed mesh
+
+plotted on the original mesh.
+
+The deformations look
+very reasonable.
+
+The plate has contracted
+horizontally, and
+
+correspondingly, the hole
+has shrunk horizontally.
+
+The deformations closest to
+the hole are shown here.
+
+And here, we see the
+stress vector
+
+plots for these elements.
+
+The stresses align nicely
+with the hole.
+
+Notice that there is no stress
+perpendicular to the free
+
+surface of the hole when we look
+at the integration point
+
+layer closest as a hole.
+
+The value of the maximum
+stress is given here.
+
+It is 301.9 megapascal.
+
+Here, we look at the element
+which carries the largest
+
+stress, element 57.
+
+Once again, we can see that
+the stresses align
+
+nicely with the hole.
+
+We now recall is that the
+objective of our analysis is
+
+really the calculation of the
+stress concentration factor.
+
+And if we look at the problem
+once more, here, we have the
+
+plate with the hole.
+
+The plate subjected to the
+tractions, as shown here.
+
+We now need to, of course,
+predict the stresses
+
+accurately around the hole,
+and in particular, at this
+
+point here.
+
+Here, we have our
+finite element
+
+method used in the analysis.
+
+And so far, the only calculated
+stresses at the
+
+integration points
+in the elements.
+
+Now this is here, by the
+way, element number 57.
+
+And for this element, we have
+calculated so far, only the
+
+stresses at these integration
+points.
+
+However, these integration
+points do not lie on the
+
+circumference of the hole, on
+the boundary of the hole.
+
+And that is where the maximum
+stresses occur.
+
+Of particular interest is, of
+course, also this point here,
+
+where we anticipate to
+obtain the maximum
+
+stress in the analysis.
+
+If you look at, schematically,
+how the stresses would vary,
+
+say, through the element, to the
+boundary of the hole, we
+
+would see a schematic
+plot as shown here.
+
+Here is an actual element, the
+other elements lie next to it,
+
+and here you can see
+schematically shown the stress
+
+computed at the closest
+integration point to the
+
+boundary of the hole.
+
+And here, we would have
+the stress computed
+
+at the nodal point.
+
+That is actually the stress
+that we are interested in.
+
+Well, we can ask ADINA to
+calculate the stresses at the
+
+nodal points, and then we can
+ask ADINA-PLOT to enter with
+
+these nodal point stresses
+into this formula here.
+
+Sigma yy, sigma zz, and sigma
+yz are the stresses at the
+
+nodal points.
+
+To calculate, ADINA-PLOT
+calculate this Sigma 1, which
+
+is the maximum principle of
+stress at that nodal point.
+
+We can ask ADINA-PLOT to
+calculate sigma 1 at all the
+
+nodal points in the mesh, and by
+doing so, we obtained these
+
+stresses and then they can ask
+ADINA-PLOT to search through
+
+those nodal points stresses,
+these sigma 1 stresses, to
+
+find us the location, the
+element and the nodal point,
+
+to have the physical location
+of the maximum stress
+
+occurring in the mesh.
+
+We will see that doing so,
+ADINA-PLOT comes up to tell us
+
+that this is the point, element
+number 57, point
+
+number 4, that is this physical
+point here, where the
+
+maximum stress occurs and will
+also give us that maximum
+
+stress, and that maximum stress,
+of course, gives us
+
+then the stress concentration
+factor.
+
+So let us now look at this
+phase of the analysis.
+
+Here, we have input some
+information regarding
+
+variables that need be defined
+in ADINA plot.
+
+TYY refers to tau yy, TZZ
+refers to tau zz, TYZ
+
+refers to tau yz.
+
+We define the result and
+variable to calculate the
+
+maximum principle stress.
+
+Hence, when TYY, TZZ, and TYZ
+are defined [? smax ?]
+
+gives the maximum principle
+stress.
+
+Here, we now enter the command
+to look for the maximum
+
+principal stress in the mesh.
+
+First we make a small input
+error, obtain a message, we
+
+correct the input, and here
+comes the result.
+
+We see that indeed element
+57.4 carries a maximum
+
+principle stress and this value
+is 345.151 megapascal.
+
+We have now actually obtained
+an answer to the
+
+question that we asked.
+
+Originally, namely, we wanted
+to calculated the stress
+
+concentration factor
+around the hole.
+
+And we have obtained a number
+for that stress
+
+concentration factor.
+
+However, a valid question,
+certainly is to ask, how good
+
+is this number?
+
+After all, we used a finite
+element mesh to approximate
+
+the plate a particular finite
+element idealization was used,
+
+and we have only obtained
+an approximation
+
+to the exact result.
+
+Well, to evaluate that question,
+to obtain insight
+
+into that question, to evaluate
+how good our analysis
+
+results really are, we can plot
+stress jumps, the way we
+
+discussed it in an
+earlier lecture.
+
+And in particular, for the
+analysis that I'd like to show
+
+you in this final phase, we
+have plotted stress jumps
+
+along these two lines.
+
+Now, notice that, for example,
+at this node here, we have
+
+four elements coupling into this
+node, so at this node we
+
+get four different stress
+predictions
+
+for each stress component.
+
+At this node here, we would
+have only two stress
+
+predictions, for each stress
+component because only two
+
+elements couple into
+this node.
+
+That is one way to evaluate or
+to look at how accurate our
+
+results are.
+
+An alternative way is to plot
+pressure bands, and the
+
+pressure here is scalar.
+
+It's computed as shown here,
+and we can plot bands of
+
+constant pressure, the way we
+already have discussed it in
+
+an earlier lecture.
+
+Notice because this is a scalar,
+it can be used very
+
+nicely to plot these bands
+of constant pressure.
+
+Of course, we could also have
+used here, say, an effective
+
+stress, which is also a scalar,
+and we could plot
+
+bands of constant effective
+stresses.
+
+One example that you've seen
+already early, is this one
+
+here where we plotted pressure
+bands, with band magnitude of
+
+5 MPa, megapascal, and you can
+see here this white band, here
+
+a black band, in other words,
+we're going in steps 5 MPa
+
+from one band to the next.
+
+Notice that there's a pressure
+band discontinuity right here,
+
+which already indicates that we
+have a stress discontinuity
+
+here, and which indicates that
+the mesh that we used is
+
+really not a very fine mesh.
+
+And if we are interested in
+obtaining a very accurate
+
+result, then based on these
+pressure band plots, and also
+
+the stress jump plots that I
+will show you just now, we may
+
+actually decide to
+use a finer mesh.
+
+We discussed this issue already
+in an earlier lecture.
+
+So let us now then look at what
+happens, or what happened
+
+in this final phase
+of the analysis.
+
+Let's go back to the laboratory
+and share the
+
+experiences that we'll
+see there.
+
+Here, we see once more
+the mesh we're
+
+using in the analysis.
+
+We will plot the stresses, and
+hence, we can see the stress
+
+jumps along the horizontal
+symmetry line, and the
+
+diagonal line of the plate.
+
+Here, you see the stresses along
+the horizontal symmetry
+
+line, Tau zz is plotted.
+
+The horizontal axis measures
+distance along
+
+the symmetry line.
+
+And the vertical axis measures
+the stress values.
+
+Note that the stress predictions
+at the nodes, when
+
+calculated for the different
+elements are almost the same.
+
+Only at one node can we actually
+see a difference, and
+
+it is quite small.
+
+Note that two elements couple
+into this node.
+
+Hence, there are only small
+stress jumps along the
+
+horizontal symmetry
+axis of the plate.
+
+Next, we look at the stress plot
+along the diagonal line
+
+of the model.
+
+Here the maximum principle
+stress is plotted.
+
+Note that at one node into which
+four elements couple, we
+
+have four markedly different
+stress values.
+
+Indeed, we have significant
+stress jumps at that node, but
+
+otherwise the stress
+predictions do
+
+not show large jumps.
+
+Finally, we look at the
+pressure band plots.
+
+Here, they are drawn.
+
+To save time, we skipped some
+of the drawing process and
+
+jumped to a later
+picture here.
+
+We notice that the pressure
+bands are quite continuous,
+
+except between the first and
+second layer of elements
+
+around the hole.
+
+This corresponds to the stress
+discontinuity between these
+
+element layers that
+we saw earlier.
+
+We see now this is now
+completed, I'd like to look
+
+with you once more back on to
+two view graphs that we
+
+already have looked
+at earlier.
+
+On this you graph, we summarize
+some important
+
+observations.
+
+And we said that it is very
+important to check the finite
+
+element data input carefully
+prior to the actual response
+
+solution run.
+
+That, of course, means
+plotting the data.
+
+And we have done so, of course,
+in our analysis.
+
+And after the response solution
+has been obtained, by
+
+starting whether desired
+boundary conditions are
+
+satisfied, whether displacement
+and stress
+
+solution is reasonable.
+
+Remember, in our analysis, we
+did this, of course, as well
+
+and we found, by looking at the
+boundary conditions, the
+
+way they were represented in the
+actual solution, that we
+
+have actually made an error.
+
+In other words, we looked at
+the deformed mesh, and the
+
+boundary conditions on the
+deformed mesh in our first
+
+analysis showed that we had
+fixed the boundary at the
+
+bottom off the mesh,
+which was an error.
+
+So it is very important to go
+through this step, to look
+
+very closely whether the
+boundary conditions are
+
+actually satisfied on the mesh
+that you have been using, in
+
+the right way.
+
+Of course, the same holds for
+the stress and solution.
+
+Remember, that we looked at the
+stress plots for the mesh
+
+that was fixed at the bottom
+and we could directly see
+
+there were errors there, and,
+in other words, the error of
+
+having fixed the boundary at
+the bottom of the plate.
+
+So this step is most important,
+and we have seen an
+
+example in the analysis that
+we just completed.
+
+I also had this view graph
+already on, where we said that
+
+we want to carefully evaluate
+and interpret
+
+the calculated response.
+
+We want to study, in detail,
+the calculated displacement
+
+and stresses along certain
+lines, study stress jumps.
+
+Well, we saw an example of that
+in the analysis that we
+
+just completed, and we also
+pointed out that it is
+
+important to go through this
+step here first, prior to
+
+using a stress averaging because
+if you do average
+
+stresses, of course, you would
+never see stress jumps.
+
+And this can be an important
+step to gain confidence in the
+
+analysis results that
+you have obtained.
+
+This then completes what I
+wanted to share with you in
+
+this lecture.
+
+Thank you very much for
+your attention.
\ No newline at end of file
diff --git a/KO6GiBAK7cY.txt b/KO6GiBAK7cY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8e9368f676396bfba3a6af3b15c3e888ac4d599e
--- /dev/null
+++ b/KO6GiBAK7cY.txt
@@ -0,0 +1,163 @@
+align:start position:0%
+ 
+so my perspectives about language have
+
+ align:start position:0%
+so my perspectives about language have
+ 
+
+ align:start position:0%
+so my perspectives about language have
+changed significantly over the course of
+
+ align:start position:0%
+changed significantly over the course of
+ 
+
+ align:start position:0%
+changed significantly over the course of
+this class I think in awakening me and
+
+ align:start position:0%
+this class I think in awakening me and
+ 
+
+ align:start position:0%
+this class I think in awakening me and
+making me acknowledge biases and
+
+ align:start position:0%
+making me acknowledge biases and
+ 
+
+ align:start position:0%
+making me acknowledge biases and
+perceptions that I had and trying to
+
+ align:start position:0%
+perceptions that I had and trying to
+ 
+
+ align:start position:0%
+perceptions that I had and trying to
+recognize that all languages are equal
+
+ align:start position:0%
+recognize that all languages are equal
+ 
+
+ align:start position:0%
+recognize that all languages are equal
+you know in thinking about other aspects
+
+ align:start position:0%
+you know in thinking about other aspects
+ 
+
+ align:start position:0%
+you know in thinking about other aspects
+of my life where like you know wanting
+
+ align:start position:0%
+of my life where like you know wanting
+ 
+
+ align:start position:0%
+of my life where like you know wanting
+as like a minority woman of color like
+
+ align:start position:0%
+as like a minority woman of color like
+ 
+
+ align:start position:0%
+as like a minority woman of color like
+thinking of equality in that terms that
+
+ align:start position:0%
+thinking of equality in that terms that
+ 
+
+ align:start position:0%
+thinking of equality in that terms that
+I never thought to apply it to language
+
+ align:start position:0%
+I never thought to apply it to language
+ 
+
+ align:start position:0%
+I never thought to apply it to language
+and I never really considered how
+
+ align:start position:0%
+and I never really considered how
+ 
+
+ align:start position:0%
+and I never really considered how
+important languages as far as like
+
+ align:start position:0%
+important languages as far as like
+ 
+
+ align:start position:0%
+important languages as far as like
+identity and you know we learned a lot
+
+ align:start position:0%
+identity and you know we learned a lot
+ 
+
+ align:start position:0%
+identity and you know we learned a lot
+about how in this class like language is
+
+ align:start position:0%
+about how in this class like language is
+ 
+
+ align:start position:0%
+about how in this class like language is
+not just like their political social and
+
+ align:start position:0%
+not just like their political social and
+ 
+
+ align:start position:0%
+not just like their political social and
+economic implications and so I feel like
+
+ align:start position:0%
+economic implications and so I feel like
+ 
+
+ align:start position:0%
+economic implications and so I feel like
+this class has changed my perspective
+
+ align:start position:0%
+this class has changed my perspective
+ 
+
+ align:start position:0%
+this class has changed my perspective
+and making me aware of those things and
+
+ align:start position:0%
+and making me aware of those things and
+ 
+
+ align:start position:0%
+and making me aware of those things and
+realizing that language is important and
+
+ align:start position:0%
+realizing that language is important and
+ 
+
+ align:start position:0%
+realizing that language is important and
+that idea that all languages are equal
\ No newline at end of file
diff --git a/KUVB9S0QX-I.txt b/KUVB9S0QX-I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..55a32f0294e6c42c0747daa1d17955177d56ab82
--- /dev/null
+++ b/KUVB9S0QX-I.txt
@@ -0,0 +1,7520 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu last time we saw that these
+
+ align:start position:0%
+ocw.mit.edu last time we saw that these
+ 
+
+ align:start position:0%
+ocw.mit.edu last time we saw that these
+electron configurations that you've been
+
+ align:start position:0%
+electron configurations that you've been
+ 
+
+ align:start position:0%
+electron configurations that you've been
+writing down are
+
+ align:start position:0%
+writing down are
+ 
+
+ align:start position:0%
+writing down are
+uh nothing other than a shorthand way of
+
+ align:start position:0%
+uh nothing other than a shorthand way of
+ 
+
+ align:start position:0%
+uh nothing other than a shorthand way of
+writing down the wave functions
+
+ align:start position:0%
+writing down the wave functions
+ 
+
+ align:start position:0%
+writing down the wave functions
+for each electron in a multi-electron
+
+ align:start position:0%
+for each electron in a multi-electron
+ 
+
+ align:start position:0%
+for each electron in a multi-electron
+atom within the one electron wave
+
+ align:start position:0%
+atom within the one electron wave
+ 
+
+ align:start position:0%
+atom within the one electron wave
+approximation where we let every
+
+ align:start position:0%
+approximation where we let every
+ 
+
+ align:start position:0%
+approximation where we let every
+electron in the system or in the atom
+
+ align:start position:0%
+electron in the system or in the atom
+ 
+
+ align:start position:0%
+electron in the system or in the atom
+have its own wave
+
+ align:start position:0%
+have its own wave
+ 
+
+ align:start position:0%
+have its own wave
+function and as an approximation we gave
+
+ align:start position:0%
+function and as an approximation we gave
+ 
+
+ align:start position:0%
+function and as an approximation we gave
+it a hydrogen atom wave
+
+ align:start position:0%
+it a hydrogen atom wave
+ 
+
+ align:start position:0%
+it a hydrogen atom wave
+function but we also saw that we did not
+
+ align:start position:0%
+function but we also saw that we did not
+ 
+
+ align:start position:0%
+function but we also saw that we did not
+that at most we gave two electrons
+
+ align:start position:0%
+that at most we gave two electrons
+ 
+
+ align:start position:0%
+that at most we gave two electrons
+hydrogen atom wave function the same
+
+ align:start position:0%
+hydrogen atom wave function the same
+ 
+
+ align:start position:0%
+hydrogen atom wave function the same
+hydrogen atom wave
+
+ align:start position:0%
+hydrogen atom wave
+ 
+
+ align:start position:0%
+hydrogen atom wave
+function and of course you already know
+
+ align:start position:0%
+function and of course you already know
+ 
+
+ align:start position:0%
+function and of course you already know
+that the reason we did that is because
+
+ align:start position:0%
+that the reason we did that is because
+ 
+
+ align:start position:0%
+that the reason we did that is because
+of this quantum mechanical concept
+
+ align:start position:0%
+of this quantum mechanical concept
+ 
+
+ align:start position:0%
+of this quantum mechanical concept
+called spin quantum mechanical
+
+ align:start position:0%
+called spin quantum mechanical
+ 
+
+ align:start position:0%
+called spin quantum mechanical
+phenomenon called
+
+ align:start position:0%
+phenomenon called
+ 
+
+ align:start position:0%
+phenomenon called
+spin spin is the intrinsic angular
+
+ align:start position:0%
+spin spin is the intrinsic angular
+ 
+
+ align:start position:0%
+spin spin is the intrinsic angular
+momentum it is the angular momentum
+
+ align:start position:0%
+momentum it is the angular momentum
+ 
+
+ align:start position:0%
+momentum it is the angular momentum
+built in to the
+
+ align:start position:0%
+built in to the
+ 
+
+ align:start position:0%
+built in to the
+particle and then angular momentum comes
+
+ align:start position:0%
+particle and then angular momentum comes
+ 
+
+ align:start position:0%
+particle and then angular momentum comes
+in sort of two polarities a spin up and
+
+ align:start position:0%
+in sort of two polarities a spin up and
+ 
+
+ align:start position:0%
+in sort of two polarities a spin up and
+a spin
+
+ align:start position:0%
+a spin
+ 
+
+ align:start position:0%
+a spin
+down corresponding to the two possible
+
+ align:start position:0%
+down corresponding to the two possible
+ 
+
+ align:start position:0%
+down corresponding to the two possible
+values of the spin quantum number M Subs
+
+ align:start position:0%
+values of the spin quantum number M Subs
+ 
+
+ align:start position:0%
+values of the spin quantum number M Subs
+that we looked at last time M Subs can
+
+ align:start position:0%
+that we looked at last time M Subs can
+ 
+
+ align:start position:0%
+that we looked at last time M Subs can
+have the value plus2 or can have the
+
+ align:start position:0%
+have the value plus2 or can have the
+ 
+
+ align:start position:0%
+have the value plus2 or can have the
+value minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one2 all right so um we're about to talk
+
+ align:start position:0%
+one2 all right so um we're about to talk
+ 
+
+ align:start position:0%
+one2 all right so um we're about to talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+how spin was actually
+
+ align:start position:0%
+how spin was actually
+ 
+
+ align:start position:0%
+how spin was actually
+discovered and um was
+
+ align:start position:0%
+discovered and um was
+ 
+
+ align:start position:0%
+discovered and um was
+discovered by these two gentlemen here
+
+ align:start position:0%
+discovered by these two gentlemen here
+ 
+
+ align:start position:0%
+discovered by these two gentlemen here
+George umbeck and Sam hmid and they were
+
+ align:start position:0%
+George umbeck and Sam hmid and they were
+ 
+
+ align:start position:0%
+George umbeck and Sam hmid and they were
+uh really very young scientists they
+
+ align:start position:0%
+uh really very young scientists they
+ 
+
+ align:start position:0%
+uh really very young scientists they
+might have been post dos at the time and
+
+ align:start position:0%
+might have been post dos at the time and
+ 
+
+ align:start position:0%
+might have been post dos at the time and
+what they were looking at was the
+
+ align:start position:0%
+what they were looking at was the
+ 
+
+ align:start position:0%
+what they were looking at was the
+emission Spectra from uh sodium
+
+ align:start position:0%
+emission Spectra from uh sodium
+ 
+
+ align:start position:0%
+emission Spectra from uh sodium
+atoms and this is
+
+ align:start position:0%
+atoms and this is
+ 
+
+ align:start position:0%
+atoms and this is
+1925 and so they already knew
+
+ align:start position:0%
+1925 and so they already knew
+ 
+
+ align:start position:0%
+1925 and so they already knew
+enough about the electronics structure
+
+ align:start position:0%
+enough about the electronics structure
+ 
+
+ align:start position:0%
+enough about the electronics structure
+to anticipate where the the emission to
+
+ align:start position:0%
+to anticipate where the the emission to
+ 
+
+ align:start position:0%
+to anticipate where the the emission to
+anticipate at what frequency they ought
+
+ align:start position:0%
+anticipate at what frequency they ought
+ 
+
+ align:start position:0%
+anticipate at what frequency they ought
+to see emission from the sodium
+
+ align:start position:0%
+to see emission from the sodium
+ 
+
+ align:start position:0%
+to see emission from the sodium
+atoms and so they got a discharge going
+
+ align:start position:0%
+atoms and so they got a discharge going
+ 
+
+ align:start position:0%
+atoms and so they got a discharge going
+looked at the emission dispersed it and
+
+ align:start position:0%
+looked at the emission dispersed it and
+ 
+
+ align:start position:0%
+looked at the emission dispersed it and
+well they thought that they would see
+
+ align:start position:0%
+well they thought that they would see
+ 
+
+ align:start position:0%
+well they thought that they would see
+some emission at this particular
+
+ align:start position:0%
+some emission at this particular
+ 
+
+ align:start position:0%
+some emission at this particular
+frequency but instead what they saw was
+
+ align:start position:0%
+frequency but instead what they saw was
+ 
+
+ align:start position:0%
+frequency but instead what they saw was
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+emission a little bit lower in frequency
+
+ align:start position:0%
+emission a little bit lower in frequency
+ 
+
+ align:start position:0%
+emission a little bit lower in frequency
+were they expected and a little bit
+
+ align:start position:0%
+were they expected and a little bit
+ 
+
+ align:start position:0%
+were they expected and a little bit
+higher in energy than what they expected
+
+ align:start position:0%
+higher in energy than what they expected
+ 
+
+ align:start position:0%
+higher in energy than what they expected
+in spectroscopy this kind of emission
+
+ align:start position:0%
+in spectroscopy this kind of emission
+ 
+
+ align:start position:0%
+in spectroscopy this kind of emission
+here is called a
+
+ align:start position:0%
+here is called a
+ 
+
+ align:start position:0%
+here is called a
+doublet okay a little lower and a little
+
+ align:start position:0%
+doublet okay a little lower and a little
+ 
+
+ align:start position:0%
+doublet okay a little lower and a little
+higher well they uh looked at these
+
+ align:start position:0%
+higher well they uh looked at these
+ 
+
+ align:start position:0%
+higher well they uh looked at these
+results thought about it and said you
+
+ align:start position:0%
+results thought about it and said you
+ 
+
+ align:start position:0%
+results thought about it and said you
+know I think we can understand that
+
+ align:start position:0%
+know I think we can understand that
+ 
+
+ align:start position:0%
+know I think we can understand that
+those two lines those Missions at the
+
+ align:start position:0%
+those two lines those Missions at the
+ 
+
+ align:start position:0%
+those two lines those Missions at the
+two frequencies there if the electron in
+
+ align:start position:0%
+two frequencies there if the electron in
+ 
+
+ align:start position:0%
+two frequencies there if the electron in
+particular that extra s electron in the
+
+ align:start position:0%
+particular that extra s electron in the
+ 
+
+ align:start position:0%
+particular that extra s electron in the
+sodium if that existed in one of two
+
+ align:start position:0%
+sodium if that existed in one of two
+ 
+
+ align:start position:0%
+sodium if that existed in one of two
+spin
+
+ align:start position:0%
+spin
+ 
+
+ align:start position:0%
+spin
+States so this was revolutionary idea
+
+ align:start position:0%
+States so this was revolutionary idea
+ 
+
+ align:start position:0%
+States so this was revolutionary idea
+and uh so they were quite excited about
+
+ align:start position:0%
+and uh so they were quite excited about
+ 
+
+ align:start position:0%
+and uh so they were quite excited about
+it and they took the results of their
+
+ align:start position:0%
+it and they took the results of their
+ 
+
+ align:start position:0%
+it and they took the results of their
+experiment and their interpretation to
+
+ align:start position:0%
+experiment and their interpretation to
+ 
+
+ align:start position:0%
+experiment and their interpretation to
+the resident established scientist at
+
+ align:start position:0%
+the resident established scientist at
+ 
+
+ align:start position:0%
+the resident established scientist at
+the time that was closest to them this
+
+ align:start position:0%
+the time that was closest to them this
+ 
+
+ align:start position:0%
+the time that was closest to them this
+guy Wolf Gang
+
+ align:start position:0%
+guy Wolf Gang
+ 
+
+ align:start position:0%
+guy Wolf Gang
+poy Wolf Gang poy was not a nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+man so they showed him the data and they
+
+ align:start position:0%
+man so they showed him the data and they
+ 
+
+ align:start position:0%
+man so they showed him the data and they
+said oh yeah this this makes sense if
+
+ align:start position:0%
+said oh yeah this this makes sense if
+ 
+
+ align:start position:0%
+said oh yeah this this makes sense if
+the electrons in two different spin
+
+ align:start position:0%
+the electrons in two different spin
+ 
+
+ align:start position:0%
+the electrons in two different spin
+States and Wolf Gang poy said rubbish
+
+ align:start position:0%
+States and Wolf Gang poy said rubbish
+ 
+
+ align:start position:0%
+States and Wolf Gang poy said rubbish
+you publish that and you'll wreck your
+
+ align:start position:0%
+you publish that and you'll wreck your
+ 
+
+ align:start position:0%
+you publish that and you'll wreck your
+young Scientific
+
+ align:start position:0%
+young Scientific
+ 
+
+ align:start position:0%
+young Scientific
+careers so hoen Beck and ho left
+
+ align:start position:0%
+careers so hoen Beck and ho left
+ 
+
+ align:start position:0%
+careers so hoen Beck and ho left
+dejectedly no sooner than the door
+
+ align:start position:0%
+dejectedly no sooner than the door
+ 
+
+ align:start position:0%
+dejectedly no sooner than the door
+slamed shut and poie sits down and he
+
+ align:start position:0%
+slamed shut and poie sits down and he
+ 
+
+ align:start position:0%
+slamed shut and poie sits down and he
+writes a paper on the presence of the
+
+ align:start position:0%
+writes a paper on the presence of the
+ 
+
+ align:start position:0%
+writes a paper on the presence of the
+fourth quantum number M
+
+ align:start position:0%
+fourth quantum number M
+ 
+
+ align:start position:0%
+fourth quantum number M
+Subs this is one of the best well-known
+
+ align:start position:0%
+Subs this is one of the best well-known
+ 
+
+ align:start position:0%
+Subs this is one of the best well-known
+travesties in the history of science now
+
+ align:start position:0%
+travesties in the history of science now
+ 
+
+ align:start position:0%
+travesties in the history of science now
+well known
+
+ align:start position:0%
+well known
+ 
+
+ align:start position:0%
+well known
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+it and it actually took however another
+
+ align:start position:0%
+it and it actually took however another
+ 
+
+ align:start position:0%
+it and it actually took however another
+three years and it took another
+
+ align:start position:0%
+three years and it took another
+ 
+
+ align:start position:0%
+three years and it took another
+gentleman to rock
+
+ align:start position:0%
+gentleman to rock
+ 
+
+ align:start position:0%
+gentleman to rock
+uh it was dck who actually wrote down
+
+ align:start position:0%
+uh it was dck who actually wrote down
+ 
+
+ align:start position:0%
+uh it was dck who actually wrote down
+the relativistic schinger equation and
+
+ align:start position:0%
+the relativistic schinger equation and
+ 
+
+ align:start position:0%
+the relativistic schinger equation and
+solved it and when you do that out drops
+
+ align:start position:0%
+solved it and when you do that out drops
+ 
+
+ align:start position:0%
+solved it and when you do that out drops
+this fourth quantum number M Subs
+
+ align:start position:0%
+this fourth quantum number M Subs
+ 
+
+ align:start position:0%
+this fourth quantum number M Subs
+okay however poy did uh did contribute
+
+ align:start position:0%
+okay however poy did uh did contribute
+ 
+
+ align:start position:0%
+okay however poy did uh did contribute
+uh to this problem in the sense that uh
+
+ align:start position:0%
+uh to this problem in the sense that uh
+ 
+
+ align:start position:0%
+uh to this problem in the sense that uh
+he he worked on um the principles uh
+
+ align:start position:0%
+he he worked on um the principles uh
+ 
+
+ align:start position:0%
+he he worked on um the principles uh
+behind uh these problems with electrons
+
+ align:start position:0%
+behind uh these problems with electrons
+ 
+
+ align:start position:0%
+behind uh these problems with electrons
+being F Fons Etc which we won't go into
+
+ align:start position:0%
+being F Fons Etc which we won't go into
+ 
+
+ align:start position:0%
+being F Fons Etc which we won't go into
+but out of that work came something
+
+ align:start position:0%
+but out of that work came something
+ 
+
+ align:start position:0%
+but out of that work came something
+called this the poy Exclusion Principle
+
+ align:start position:0%
+called this the poy Exclusion Principle
+ 
+
+ align:start position:0%
+called this the poy Exclusion Principle
+right and the essence of that principle
+
+ align:start position:0%
+right and the essence of that principle
+ 
+
+ align:start position:0%
+right and the essence of that principle
+is that um no two electrons in the same
+
+ align:start position:0%
+is that um no two electrons in the same
+ 
+
+ align:start position:0%
+is that um no two electrons in the same
+atom can have the same electron wave
+
+ align:start position:0%
+atom can have the same electron wave
+ 
+
+ align:start position:0%
+atom can have the same electron wave
+function or the same and the same spin
+
+ align:start position:0%
+function or the same and the same spin
+ 
+
+ align:start position:0%
+function or the same and the same spin
+or another way to say that no two
+
+ align:start position:0%
+or another way to say that no two
+ 
+
+ align:start position:0%
+or another way to say that no two
+electrons can have the same set of four
+
+ align:start position:0%
+electrons can have the same set of four
+ 
+
+ align:start position:0%
+electrons can have the same set of four
+quantum numbers
+
+ align:start position:0%
+quantum numbers
+ 
+
+ align:start position:0%
+quantum numbers
+okay so for example in our electron
+
+ align:start position:0%
+okay so for example in our electron
+ 
+
+ align:start position:0%
+okay so for example in our electron
+configuration here of
+
+ align:start position:0%
+configuration here of
+ 
+
+ align:start position:0%
+configuration here of
+neon this electron has the quantum
+
+ align:start position:0%
+neon this electron has the quantum
+ 
+
+ align:start position:0%
+neon this electron has the quantum
+numbers 1 0 plus 12 for M Subs this
+
+ align:start position:0%
+numbers 1 0 plus 12 for M Subs this
+ 
+
+ align:start position:0%
+numbers 1 0 plus 12 for M Subs this
+electron has the quantum numbers 1 Z 0
+
+ align:start position:0%
+electron has the quantum numbers 1 Z 0
+ 
+
+ align:start position:0%
+electron has the quantum numbers 1 Z 0
+minus 12 for M Subs so these two
+
+ align:start position:0%
+minus 12 for M Subs so these two
+ 
+
+ align:start position:0%
+minus 12 for M Subs so these two
+electrons don't have the same set of
+
+ align:start position:0%
+electrons don't have the same set of
+ 
+
+ align:start position:0%
+electrons don't have the same set of
+four quantum numbers right and that's
+
+ align:start position:0%
+four quantum numbers right and that's
+ 
+
+ align:start position:0%
+four quantum numbers right and that's
+why we could only put two electrons here
+
+ align:start position:0%
+why we could only put two electrons here
+ 
+
+ align:start position:0%
+why we could only put two electrons here
+in this 1 s state
+
+ align:start position:0%
+in this 1 s state
+ 
+
+ align:start position:0%
+in this 1 s state
+okay likewise this uh electron here has
+
+ align:start position:0%
+okay likewise this uh electron here has
+ 
+
+ align:start position:0%
+okay likewise this uh electron here has
+the quantum numbers 2 1 minus one
+
+ align:start position:0%
+the quantum numbers 2 1 minus one
+ 
+
+ align:start position:0%
+the quantum numbers 2 1 minus one
++2 this electron has the quantum numbers
+
+ align:start position:0%
++2 this electron has the quantum numbers
+ 
+
+ align:start position:0%
++2 this electron has the quantum numbers
+2 1 - one
+
+ align:start position:0%
+2 1 - one
+ 
+
+ align:start position:0%
+2 1 - one
+-2 okay so that's the PO Exclusion
+
+ align:start position:0%
+-2 okay so that's the PO Exclusion
+ 
+
+ align:start position:0%
+-2 okay so that's the PO Exclusion
+Principle which prevents us from putting
+
+ align:start position:0%
+Principle which prevents us from putting
+ 
+
+ align:start position:0%
+Principle which prevents us from putting
+more than two electrons in each one of
+
+ align:start position:0%
+more than two electrons in each one of
+ 
+
+ align:start position:0%
+more than two electrons in each one of
+these states 2 S 2 S 2 PX 2 pz or 2 py
+
+ align:start position:0%
+these states 2 S 2 S 2 PX 2 pz or 2 py
+ 
+
+ align:start position:0%
+these states 2 S 2 S 2 PX 2 pz or 2 py
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so um now what I want to do is I
+
+ align:start position:0%
+okay so um now what I want to do is I
+ 
+
+ align:start position:0%
+okay so um now what I want to do is I
+want to try to look at the wave
+
+ align:start position:0%
+want to try to look at the wave
+ 
+
+ align:start position:0%
+want to try to look at the wave
+functions I want to look at uh what
+
+ align:start position:0%
+functions I want to look at uh what
+ 
+
+ align:start position:0%
+functions I want to look at uh what
+these wave functions look like for the
+
+ align:start position:0%
+these wave functions look like for the
+ 
+
+ align:start position:0%
+these wave functions look like for the
+electrons in the multi-electron atom and
+
+ align:start position:0%
+electrons in the multi-electron atom and
+ 
+
+ align:start position:0%
+electrons in the multi-electron atom and
+to look at their shapes what we're going
+
+ align:start position:0%
+to look at their shapes what we're going
+ 
+
+ align:start position:0%
+to look at their shapes what we're going
+to do is we're going to look at the
+
+ align:start position:0%
+to do is we're going to look at the
+ 
+
+ align:start position:0%
+to do is we're going to look at the
+radial probability distribution function
+
+ align:start position:0%
+radial probability distribution function
+ 
+
+ align:start position:0%
+radial probability distribution function
+because remember what the radial
+
+ align:start position:0%
+because remember what the radial
+ 
+
+ align:start position:0%
+because remember what the radial
+probability distribution function tells
+
+ align:start position:0%
+probability distribution function tells
+ 
+
+ align:start position:0%
+probability distribution function tells
+us it tells
+
+ align:start position:0%
+us it tells
+ 
+
+ align:start position:0%
+us it tells
+us the probability of finding the
+
+ align:start position:0%
+us the probability of finding the
+ 
+
+ align:start position:0%
+us the probability of finding the
+electron between R and R plus
+
+ align:start position:0%
+electron between R and R plus
+ 
+
+ align:start position:0%
+electron between R and R plus
+Dr okay so I plotted those radial
+
+ align:start position:0%
+Dr okay so I plotted those radial
+ 
+
+ align:start position:0%
+Dr okay so I plotted those radial
+probability distribution functions
+
+ align:start position:0%
+probability distribution functions
+ 
+
+ align:start position:0%
+probability distribution functions
+versus
+
+ align:start position:0%
+versus
+ 
+
+ align:start position:0%
+versus
+R for each one of the electrons in the
+
+ align:start position:0%
+R for each one of the electrons in the
+ 
+
+ align:start position:0%
+R for each one of the electrons in the
+different states for this multi-electron
+
+ align:start position:0%
+different states for this multi-electron
+ 
+
+ align:start position:0%
+different states for this multi-electron
+atom argon okay
+
+ align:start position:0%
+atom argon okay
+ 
+
+ align:start position:0%
+atom argon okay
+and what we want to do is we want to
+
+ align:start position:0%
+and what we want to do is we want to
+ 
+
+ align:start position:0%
+and what we want to do is we want to
+compare and contrast these wave
+
+ align:start position:0%
+compare and contrast these wave
+ 
+
+ align:start position:0%
+compare and contrast these wave
+functions for the individual electrons
+
+ align:start position:0%
+functions for the individual electrons
+ 
+
+ align:start position:0%
+functions for the individual electrons
+in this multi- electron atom to those of
+
+ align:start position:0%
+in this multi- electron atom to those of
+ 
+
+ align:start position:0%
+in this multi- electron atom to those of
+hydrogen all right all right well first
+
+ align:start position:0%
+hydrogen all right all right well first
+ 
+
+ align:start position:0%
+hydrogen all right all right well first
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+similarities if you look at this wave
+
+ align:start position:0%
+similarities if you look at this wave
+ 
+
+ align:start position:0%
+similarities if you look at this wave
+function or if you look at the radial
+
+ align:start position:0%
+function or if you look at the radial
+ 
+
+ align:start position:0%
+function or if you look at the radial
+probability distribution for the 1s wave
+
+ align:start position:0%
+probability distribution for the 1s wave
+ 
+
+ align:start position:0%
+probability distribution for the 1s wave
+function here what you see is that that
+
+ align:start position:0%
+function here what you see is that that
+ 
+
+ align:start position:0%
+function here what you see is that that
+radial probability distribution is zero
+
+ align:start position:0%
+radial probability distribution is zero
+ 
+
+ align:start position:0%
+radial probability distribution is zero
+at R equals z as all radial probabil
+
+ align:start position:0%
+at R equals z as all radial probabil
+ 
+
+ align:start position:0%
+at R equals z as all radial probabil
+ility distributions are that's not a
+
+ align:start position:0%
+ility distributions are that's not a
+ 
+
+ align:start position:0%
+ility distributions are that's not a
+radial node that probability
+
+ align:start position:0%
+radial node that probability
+ 
+
+ align:start position:0%
+radial node that probability
+distribution increases goes to a maximum
+
+ align:start position:0%
+distribution increases goes to a maximum
+ 
+
+ align:start position:0%
+distribution increases goes to a maximum
+and then decays exponentially with r hey
+
+ align:start position:0%
+and then decays exponentially with r hey
+ 
+
+ align:start position:0%
+and then decays exponentially with r hey
+that's exactly what a 1 s wave function
+
+ align:start position:0%
+that's exactly what a 1 s wave function
+ 
+
+ align:start position:0%
+that's exactly what a 1 s wave function
+looks like for a hydrogen
+
+ align:start position:0%
+looks like for a hydrogen
+ 
+
+ align:start position:0%
+looks like for a hydrogen
+atom if you looked at the 2s W function
+
+ align:start position:0%
+atom if you looked at the 2s W function
+ 
+
+ align:start position:0%
+atom if you looked at the 2s W function
+it starts at R equals 0 goes up a bit
+
+ align:start position:0%
+it starts at R equals 0 goes up a bit
+ 
+
+ align:start position:0%
+it starts at R equals 0 goes up a bit
+and then goes to zero here's a radial
+
+ align:start position:0%
+and then goes to zero here's a radial
+ 
+
+ align:start position:0%
+and then goes to zero here's a radial
+node in the 2s W function and then goes
+
+ align:start position:0%
+node in the 2s W function and then goes
+ 
+
+ align:start position:0%
+node in the 2s W function and then goes
+back up here's the most here's the most
+
+ align:start position:0%
+back up here's the most here's the most
+ 
+
+ align:start position:0%
+back up here's the most here's the most
+prob value of R then decays
+
+ align:start position:0%
+prob value of R then decays
+ 
+
+ align:start position:0%
+prob value of R then decays
+exponentially hey again it has the same
+
+ align:start position:0%
+exponentially hey again it has the same
+ 
+
+ align:start position:0%
+exponentially hey again it has the same
+structure as the 2s wave function in the
+
+ align:start position:0%
+structure as the 2s wave function in the
+ 
+
+ align:start position:0%
+structure as the 2s wave function in the
+hydrogen at so the similarity is that
+
+ align:start position:0%
+hydrogen at so the similarity is that
+ 
+
+ align:start position:0%
+hydrogen at so the similarity is that
+all of these wave functions have the
+
+ align:start position:0%
+all of these wave functions have the
+ 
+
+ align:start position:0%
+all of these wave functions have the
+same kind of basic structure as that in
+
+ align:start position:0%
+same kind of basic structure as that in
+ 
+
+ align:start position:0%
+same kind of basic structure as that in
+a hydrogen atom they have the same
+
+ align:start position:0%
+a hydrogen atom they have the same
+ 
+
+ align:start position:0%
+a hydrogen atom they have the same
+number of nodes same number of radial
+
+ align:start position:0%
+number of nodes same number of radial
+ 
+
+ align:start position:0%
+number of nodes same number of radial
+nodes same number of angular nodes all
+
+ align:start position:0%
+nodes same number of angular nodes all
+ 
+
+ align:start position:0%
+nodes same number of angular nodes all
+right the difference between these wave
+
+ align:start position:0%
+right the difference between these wave
+ 
+
+ align:start position:0%
+right the difference between these wave
+functions and those of the hydrogen atom
+
+ align:start position:0%
+functions and those of the hydrogen atom
+ 
+
+ align:start position:0%
+functions and those of the hydrogen atom
+is that all of these wave functions are
+
+ align:start position:0%
+is that all of these wave functions are
+ 
+
+ align:start position:0%
+is that all of these wave functions are
+closer in to the nucleus so for example
+
+ align:start position:0%
+closer in to the nucleus so for example
+ 
+
+ align:start position:0%
+closer in to the nucleus so for example
+if you looked here at what the most
+
+ align:start position:0%
+if you looked here at what the most
+ 
+
+ align:start position:0%
+if you looked here at what the most
+probable value of R is for that 1 s
+
+ align:start position:0%
+probable value of R is for that 1 s
+ 
+
+ align:start position:0%
+probable value of R is for that 1 s
+electron that most probable value in
+
+ align:start position:0%
+electron that most probable value in
+ 
+
+ align:start position:0%
+electron that most probable value in
+argon is .1 a knot what's the most
+
+ align:start position:0%
+argon is .1 a knot what's the most
+ 
+
+ align:start position:0%
+argon is .1 a knot what's the most
+probable value for R in the 1 s state of
+
+ align:start position:0%
+probable value for R in the 1 s state of
+ 
+
+ align:start position:0%
+probable value for R in the 1 s state of
+hydrogen a not this is 10 times closer
+
+ align:start position:0%
+hydrogen a not this is 10 times closer
+ 
+
+ align:start position:0%
+hydrogen a not this is 10 times closer
+closer all right this is much closer to
+
+ align:start position:0%
+closer all right this is much closer to
+ 
+
+ align:start position:0%
+closer all right this is much closer to
+the nucleus than it is in the hydrogen
+
+ align:start position:0%
+the nucleus than it is in the hydrogen
+ 
+
+ align:start position:0%
+the nucleus than it is in the hydrogen
+atom and if we went and we compared the
+
+ align:start position:0%
+atom and if we went and we compared the
+ 
+
+ align:start position:0%
+atom and if we went and we compared the
+most probable values for 2 s2p to those
+
+ align:start position:0%
+most probable values for 2 s2p to those
+ 
+
+ align:start position:0%
+most probable values for 2 s2p to those
+of hydrogen and 3 s3p for those of
+
+ align:start position:0%
+of hydrogen and 3 s3p for those of
+ 
+
+ align:start position:0%
+of hydrogen and 3 s3p for those of
+hydrogen we'd find that all of these are
+
+ align:start position:0%
+hydrogen we'd find that all of these are
+ 
+
+ align:start position:0%
+hydrogen we'd find that all of these are
+much closer in to the nucleus why
+
+ align:start position:0%
+much closer in to the nucleus why
+ 
+
+ align:start position:0%
+much closer in to the nucleus why
+because the nucleus has a
+
+ align:start position:0%
+because the nucleus has a
+ 
+
+ align:start position:0%
+because the nucleus has a
+larger uh positive charge on it right
+
+ align:start position:0%
+larger uh positive charge on it right
+ 
+
+ align:start position:0%
+larger uh positive charge on it right
+the coolant interaction here is the
+
+ align:start position:0%
+the coolant interaction here is the
+ 
+
+ align:start position:0%
+the coolant interaction here is the
+charge on the electron times the charge
+
+ align:start position:0%
+charge on the electron times the charge
+ 
+
+ align:start position:0%
+charge on the electron times the charge
+on the nucleus for Argon that charge is+
+
+ align:start position:0%
+on the nucleus for Argon that charge is+
+ 
+
+ align:start position:0%
+on the nucleus for Argon that charge is+
+18 * e that greater attractive
+
+ align:start position:0%
+18 * e that greater attractive
+ 
+
+ align:start position:0%
+18 * e that greater attractive
+interaction pulls those electrons in
+
+ align:start position:0%
+interaction pulls those electrons in
+ 
+
+ align:start position:0%
+interaction pulls those electrons in
+closer to the nucleus that's the bottom
+
+ align:start position:0%
+closer to the nucleus that's the bottom
+ 
+
+ align:start position:0%
+closer to the nucleus that's the bottom
+line okay so that's how these differ the
+
+ align:start position:0%
+line okay so that's how these differ the
+ 
+
+ align:start position:0%
+line okay so that's how these differ the
+structures the same n structures the
+
+ align:start position:0%
+structures the same n structures the
+ 
+
+ align:start position:0%
+structures the same n structures the
+same they're just all closer into to the
+
+ align:start position:0%
+same they're just all closer into to the
+ 
+
+ align:start position:0%
+same they're just all closer into to the
+nucleus because of that greater
+
+ align:start position:0%
+nucleus because of that greater
+ 
+
+ align:start position:0%
+nucleus because of that greater
+attractive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interaction okay so now that I have this
+
+ align:start position:0%
+interaction okay so now that I have this
+ 
+
+ align:start position:0%
+interaction okay so now that I have this
+radial probability distribution function
+
+ align:start position:0%
+radial probability distribution function
+ 
+
+ align:start position:0%
+radial probability distribution function
+up here I also want to use it to just
+
+ align:start position:0%
+up here I also want to use it to just
+ 
+
+ align:start position:0%
+up here I also want to use it to just
+illustrate a concept that I think you
+
+ align:start position:0%
+illustrate a concept that I think you
+ 
+
+ align:start position:0%
+illustrate a concept that I think you
+already know and that is this concept of
+
+ align:start position:0%
+already know and that is this concept of
+ 
+
+ align:start position:0%
+already know and that is this concept of
+a shell you know about the N equal one
+
+ align:start position:0%
+a shell you know about the N equal one
+ 
+
+ align:start position:0%
+a shell you know about the N equal one
+shell n equal 2 shell n equal 3 shell
+
+ align:start position:0%
+shell n equal 2 shell n equal 3 shell
+ 
+
+ align:start position:0%
+shell n equal 2 shell n equal 3 shell
+and the word shell also denotes kind
+
+ align:start position:0%
+and the word shell also denotes kind
+ 
+
+ align:start position:0%
+and the word shell also denotes kind
+some kind of spatial information right
+
+ align:start position:0%
+some kind of spatial information right
+ 
+
+ align:start position:0%
+some kind of spatial information right
+and when I and I want to show you how
+
+ align:start position:0%
+and when I and I want to show you how
+ 
+
+ align:start position:0%
+and when I and I want to show you how
+the spatial information is depicted here
+
+ align:start position:0%
+the spatial information is depicted here
+ 
+
+ align:start position:0%
+the spatial information is depicted here
+on this graph I want you to see that for
+
+ align:start position:0%
+on this graph I want you to see that for
+ 
+
+ align:start position:0%
+on this graph I want you to see that for
+the N equal three states 3s and
+
+ align:start position:0%
+the N equal three states 3s and
+ 
+
+ align:start position:0%
+the N equal three states 3s and
+3p well the most probable value isn't
+
+ align:start position:0%
+3p well the most probable value isn't
+ 
+
+ align:start position:0%
+3p well the most probable value isn't
+exactly in the same place but it's in
+
+ align:start position:0%
+exactly in the same place but it's in
+ 
+
+ align:start position:0%
+exactly in the same place but it's in
+the same place as when you compare it to
+
+ align:start position:0%
+the same place as when you compare it to
+ 
+
+ align:start position:0%
+the same place as when you compare it to
+the two s and the 2p right you can see
+
+ align:start position:0%
+the two s and the 2p right you can see
+ 
+
+ align:start position:0%
+the two s and the 2p right you can see
+how well the N equal 3 shell is
+
+ align:start position:0%
+how well the N equal 3 shell is
+ 
+
+ align:start position:0%
+how well the N equal 3 shell is
+separated in space from the N equal 2
+
+ align:start position:0%
+separated in space from the N equal 2
+ 
+
+ align:start position:0%
+separated in space from the N equal 2
+shell again the most probable value for
+
+ align:start position:0%
+shell again the most probable value for
+ 
+
+ align:start position:0%
+shell again the most probable value for
+2s and 2p aren't exactly in the same
+
+ align:start position:0%
+2s and 2p aren't exactly in the same
+ 
+
+ align:start position:0%
+2s and 2p aren't exactly in the same
+place right we saw the 2p is actually a
+
+ align:start position:0%
+place right we saw the 2p is actually a
+ 
+
+ align:start position:0%
+place right we saw the 2p is actually a
+little closer than to 2s but in terms of
+
+ align:start position:0%
+little closer than to 2s but in terms of
+ 
+
+ align:start position:0%
+little closer than to 2s but in terms of
+comparing it to where the most probable
+
+ align:start position:0%
+comparing it to where the most probable
+ 
+
+ align:start position:0%
+comparing it to where the most probable
+values are for 3s and 3p hey that's much
+
+ align:start position:0%
+values are for 3s and 3p hey that's much
+ 
+
+ align:start position:0%
+values are for 3s and 3p hey that's much
+closer in all right and so this graph
+
+ align:start position:0%
+closer in all right and so this graph
+ 
+
+ align:start position:0%
+closer in all right and so this graph
+here it shows you it gives you an idea
+
+ align:start position:0%
+here it shows you it gives you an idea
+ 
+
+ align:start position:0%
+here it shows you it gives you an idea
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+spatial information that is um denoted
+
+ align:start position:0%
+spatial information that is um denoted
+ 
+
+ align:start position:0%
+spatial information that is um denoted
+when we talk about shells the N equal 3
+
+ align:start position:0%
+when we talk about shells the N equal 3
+ 
+
+ align:start position:0%
+when we talk about shells the N equal 3
+shell is further out the N equal 2 shell
+
+ align:start position:0%
+shell is further out the N equal 2 shell
+ 
+
+ align:start position:0%
+shell is further out the N equal 2 shell
+is closer in and the N equal one shell
+
+ align:start position:0%
+is closer in and the N equal one shell
+ 
+
+ align:start position:0%
+is closer in and the N equal one shell
+even closer in all right I think that's
+
+ align:start position:0%
+even closer in all right I think that's
+ 
+
+ align:start position:0%
+even closer in all right I think that's
+a concept that you mostly know but here
+
+ align:start position:0%
+a concept that you mostly know but here
+ 
+
+ align:start position:0%
+a concept that you mostly know but here
+you see it on the radial probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+okay so now we've uh taken a quick look
+
+ align:start position:0%
+okay so now we've uh taken a quick look
+ 
+
+ align:start position:0%
+okay so now we've uh taken a quick look
+at those wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functions now it's time to actually look
+
+ align:start position:0%
+functions now it's time to actually look
+ 
+
+ align:start position:0%
+functions now it's time to actually look
+at the energies of the
+
+ align:start position:0%
+at the energies of the
+ 
+
+ align:start position:0%
+at the energies of the
+states we haven't done that
+
+ align:start position:0%
+states we haven't done that
+ 
+
+ align:start position:0%
+states we haven't done that
+yet so on the left here I show an energy
+
+ align:start position:0%
+yet so on the left here I show an energy
+ 
+
+ align:start position:0%
+yet so on the left here I show an energy
+level diagram for the hydrogen atom
+
+ align:start position:0%
+level diagram for the hydrogen atom
+ 
+
+ align:start position:0%
+level diagram for the hydrogen atom
+right we saw this before here's the N
+
+ align:start position:0%
+right we saw this before here's the N
+ 
+
+ align:start position:0%
+right we saw this before here's the N
+equal one
+
+ align:start position:0%
+equal one
+ 
+
+ align:start position:0%
+equal one
+state here at n equal two we've got four
+
+ align:start position:0%
+state here at n equal two we've got four
+ 
+
+ align:start position:0%
+state here at n equal two we've got four
+states four degenerate States here at n
+
+ align:start position:0%
+states four degenerate States here at n
+ 
+
+ align:start position:0%
+states four degenerate States here at n
+equal 3 we got nine degenerate States
+
+ align:start position:0%
+equal 3 we got nine degenerate States
+ 
+
+ align:start position:0%
+equal 3 we got nine degenerate States
+here at n equal 4 we got 14 16
+
+ align:start position:0%
+here at n equal 4 we got 14 16
+ 
+
+ align:start position:0%
+here at n equal 4 we got 14 16
+degenerate
+
+ align:start position:0%
+degenerate
+ 
+
+ align:start position:0%
+degenerate
+States okay but the difference between
+
+ align:start position:0%
+States okay but the difference between
+ 
+
+ align:start position:0%
+States okay but the difference between
+the hydrogen atom and any other
+
+ align:start position:0%
+the hydrogen atom and any other
+ 
+
+ align:start position:0%
+the hydrogen atom and any other
+multi-electron atom starting with helium
+
+ align:start position:0%
+multi-electron atom starting with helium
+ 
+
+ align:start position:0%
+multi-electron atom starting with helium
+two differences one is that the energies
+
+ align:start position:0%
+two differences one is that the energies
+ 
+
+ align:start position:0%
+two differences one is that the energies
+of these states in the multi-electron
+
+ align:start position:0%
+of these states in the multi-electron
+ 
+
+ align:start position:0%
+of these states in the multi-electron
+atom are all lower than they are in the
+
+ align:start position:0%
+atom are all lower than they are in the
+ 
+
+ align:start position:0%
+atom are all lower than they are in the
+hydrogen atom that is the one s State
+
+ align:start position:0%
+hydrogen atom that is the one s State
+ 
+
+ align:start position:0%
+hydrogen atom that is the one s State
+here is lower in energy than the 1s
+
+ align:start position:0%
+here is lower in energy than the 1s
+ 
+
+ align:start position:0%
+here is lower in energy than the 1s
+state in the hydrogen the 2s is lower
+
+ align:start position:0%
+state in the hydrogen the 2s is lower
+ 
+
+ align:start position:0%
+state in the hydrogen the 2s is lower
+than the 2s state in hydrogen the 3s is
+
+ align:start position:0%
+than the 2s state in hydrogen the 3s is
+ 
+
+ align:start position:0%
+than the 2s state in hydrogen the 3s is
+lower the 2p is lower the 3p is lower
+
+ align:start position:0%
+lower the 2p is lower the 3p is lower
+ 
+
+ align:start position:0%
+lower the 2p is lower the 3p is lower
+etc
+
+ align:start position:0%
+etc
+ 
+
+ align:start position:0%
+etc
+etc the energies of those states are all
+
+ align:start position:0%
+etc the energies of those states are all
+ 
+
+ align:start position:0%
+etc the energies of those states are all
+lower
+
+ align:start position:0%
+lower
+ 
+
+ align:start position:0%
+lower
+why because of the charge on the nucleus
+
+ align:start position:0%
+why because of the charge on the nucleus
+ 
+
+ align:start position:0%
+why because of the charge on the nucleus
+that potential energy of interaction is
+
+ align:start position:0%
+that potential energy of interaction is
+ 
+
+ align:start position:0%
+that potential energy of interaction is
+greater because the charge on the
+
+ align:start position:0%
+greater because the charge on the
+ 
+
+ align:start position:0%
+greater because the charge on the
+nucleus is
+
+ align:start position:0%
+nucleus is
+ 
+
+ align:start position:0%
+nucleus is
+larger that greater potential energy of
+
+ align:start position:0%
+larger that greater potential energy of
+ 
+
+ align:start position:0%
+larger that greater potential energy of
+interaction lowers the energy of the
+
+ align:start position:0%
+interaction lowers the energy of the
+ 
+
+ align:start position:0%
+interaction lowers the energy of the
+states makes those electrons more
+
+ align:start position:0%
+states makes those electrons more
+ 
+
+ align:start position:0%
+states makes those electrons more
+strongly bound so starting with helium
+
+ align:start position:0%
+strongly bound so starting with helium
+ 
+
+ align:start position:0%
+strongly bound so starting with helium
+all of these energies are lower than
+
+ align:start position:0%
+all of these energies are lower than
+ 
+
+ align:start position:0%
+all of these energies are lower than
+those in the hydrogen atom okay that's
+
+ align:start position:0%
+those in the hydrogen atom okay that's
+ 
+
+ align:start position:0%
+those in the hydrogen atom okay that's
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+difference the second difference is you
+
+ align:start position:0%
+difference the second difference is you
+ 
+
+ align:start position:0%
+difference the second difference is you
+can see now that the 2s state is lower
+
+ align:start position:0%
+can see now that the 2s state is lower
+ 
+
+ align:start position:0%
+can see now that the 2s state is lower
+in energy than the 2p
+
+ align:start position:0%
+in energy than the 2p
+ 
+
+ align:start position:0%
+in energy than the 2p
+State the degeneracy between 2s and 2p
+
+ align:start position:0%
+State the degeneracy between 2s and 2p
+ 
+
+ align:start position:0%
+State the degeneracy between 2s and 2p
+in a hydrogen atom is lifted or is
+
+ align:start position:0%
+in a hydrogen atom is lifted or is
+ 
+
+ align:start position:0%
+in a hydrogen atom is lifted or is
+broken as we say likewise the 3s state
+
+ align:start position:0%
+broken as we say likewise the 3s state
+ 
+
+ align:start position:0%
+broken as we say likewise the 3s state
+is lower in energy than the 3p State
+
+ align:start position:0%
+is lower in energy than the 3p State
+ 
+
+ align:start position:0%
+is lower in energy than the 3p State
+then the 3D State the degeneracy in
+
+ align:start position:0%
+then the 3D State the degeneracy in
+ 
+
+ align:start position:0%
+then the 3D State the degeneracy in
+those States is lifted or it's
+
+ align:start position:0%
+those States is lifted or it's
+ 
+
+ align:start position:0%
+those States is lifted or it's
+broken
+
+ align:start position:0%
+broken
+ 
+
+ align:start position:0%
+broken
+right so that's now what we have to talk
+
+ align:start position:0%
+right so that's now what we have to talk
+ 
+
+ align:start position:0%
+right so that's now what we have to talk
+about is why that is the case why is 2s
+
+ align:start position:0%
+about is why that is the case why is 2s
+ 
+
+ align:start position:0%
+about is why that is the case why is 2s
+for example lower in energy than
+
+ align:start position:0%
+for example lower in energy than
+ 
+
+ align:start position:0%
+for example lower in energy than
+2p and the reason for this has to do
+
+ align:start position:0%
+2p and the reason for this has to do
+ 
+
+ align:start position:0%
+2p and the reason for this has to do
+with the phenomenon called
+
+ align:start position:0%
+with the phenomenon called
+ 
+
+ align:start position:0%
+with the phenomenon called
+shielding so we have to uh talk about
+
+ align:start position:0%
+shielding so we have to uh talk about
+ 
+
+ align:start position:0%
+shielding so we have to uh talk about
+this phenomena
+
+ align:start position:0%
+this phenomena
+ 
+
+ align:start position:0%
+this phenomena
+shielding and uh we have to talk about
+
+ align:start position:0%
+shielding and uh we have to talk about
+ 
+
+ align:start position:0%
+shielding and uh we have to talk about
+how that leads to a concept called
+
+ align:start position:0%
+how that leads to a concept called
+ 
+
+ align:start position:0%
+how that leads to a concept called
+effective
+
+ align:start position:0%
+effective
+ 
+
+ align:start position:0%
+effective
+charge okay but to do
+
+ align:start position:0%
+charge okay but to do
+ 
+
+ align:start position:0%
+charge okay but to do
+that I'm going
+
+ align:start position:0%
+that I'm going
+ 
+
+ align:start position:0%
+that I'm going
+to do the following I'm going to realize
+
+ align:start position:0%
+to do the following I'm going to realize
+ 
+
+ align:start position:0%
+to do the following I'm going to realize
+that each one of these energies here e
+
+ align:start position:0%
+that each one of these energies here e
+ 
+
+ align:start position:0%
+that each one of these energies here e
+sub NL
+
+ align:start position:0%
+sub NL
+ 
+
+ align:start position:0%
+sub NL
+right so now these energies are labeled
+
+ align:start position:0%
+right so now these energies are labeled
+ 
+
+ align:start position:0%
+right so now these energies are labeled
+by both the principal quantum number and
+
+ align:start position:0%
+by both the principal quantum number and
+ 
+
+ align:start position:0%
+by both the principal quantum number and
+the angular momentum quantum
+
+ align:start position:0%
+the angular momentum quantum
+ 
+
+ align:start position:0%
+the angular momentum quantum
+number I'm going to realize that these
+
+ align:start position:0%
+number I'm going to realize that these
+ 
+
+ align:start position:0%
+number I'm going to realize that these
+energies here physically are minus the
+
+ align:start position:0%
+energies here physically are minus the
+ 
+
+ align:start position:0%
+energies here physically are minus the
+ionization
+
+ align:start position:0%
+ionization
+ 
+
+ align:start position:0%
+ionization
+energy right because because these
+
+ align:start position:0%
+energy right because because these
+ 
+
+ align:start position:0%
+energy right because because these
+energies are minus the energy it's going
+
+ align:start position:0%
+energies are minus the energy it's going
+ 
+
+ align:start position:0%
+energies are minus the energy it's going
+to require to rip the electron off from
+
+ align:start position:0%
+to require to rip the electron off from
+ 
+
+ align:start position:0%
+to require to rip the electron off from
+that particular
+
+ align:start position:0%
+that particular
+ 
+
+ align:start position:0%
+that particular
+State and I'm going to set those binding
+
+ align:start position:0%
+State and I'm going to set those binding
+ 
+
+ align:start position:0%
+State and I'm going to set those binding
+energies equal to a hydrogen atom like
+
+ align:start position:0%
+energies equal to a hydrogen atom like
+ 
+
+ align:start position:0%
+energies equal to a hydrogen atom like
+energy level here and now I'm going to
+
+ align:start position:0%
+energy level here and now I'm going to
+ 
+
+ align:start position:0%
+energy level here and now I'm going to
+use the board and we're going to explain
+
+ align:start position:0%
+use the board and we're going to explain
+ 
+
+ align:start position:0%
+use the board and we're going to explain
+that just a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops okay so I
+
+ align:start position:0%
+oops okay so I
+ 
+
+ align:start position:0%
+oops okay so I
+said these energies which are Now
+
+ align:start position:0%
+said these energies which are Now
+ 
+
+ align:start position:0%
+said these energies which are Now
+function of nnl
+
+ align:start position:0%
+function of nnl
+ 
+
+ align:start position:0%
+function of nnl
+they're minus the ionization
+
+ align:start position:0%
+they're minus the ionization
+ 
+
+ align:start position:0%
+they're minus the ionization
+energy from that NL State and I'm going
+
+ align:start position:0%
+energy from that NL State and I'm going
+ 
+
+ align:start position:0%
+energy from that NL State and I'm going
+to approximate that as a hydrogen atom
+
+ align:start position:0%
+to approximate that as a hydrogen atom
+ 
+
+ align:start position:0%
+to approximate that as a hydrogen atom
+kind of an energy scheme that is I'm
+
+ align:start position:0%
+kind of an energy scheme that is I'm
+ 
+
+ align:start position:0%
+kind of an energy scheme that is I'm
+going to set this equal to R subh the
+
+ align:start position:0%
+going to set this equal to R subh the
+ 
+
+ align:start position:0%
+going to set this equal to R subh the
+ridberg constant over
+
+ align:start position:0%
+ridberg constant over
+ 
+
+ align:start position:0%
+ridberg constant over
+N2 but out here there's going to be a
+
+ align:start position:0%
+N2 but out here there's going to be a
+ 
+
+ align:start position:0%
+N2 but out here there's going to be a
+z but this Z is going to be Z effective
+
+ align:start position:0%
+z but this Z is going to be Z effective
+ 
+
+ align:start position:0%
+z but this Z is going to be Z effective
+z e
+
+ align:start position:0%
+z e
+ 
+
+ align:start position:0%
+z e
+FF and it's going to be squared of
+
+ align:start position:0%
+FF and it's going to be squared of
+ 
+
+ align:start position:0%
+FF and it's going to be squared of
+course and that Z is going to depend on
+
+ align:start position:0%
+course and that Z is going to depend on
+ 
+
+ align:start position:0%
+course and that Z is going to depend on
+the particular NL state that you're in
+
+ align:start position:0%
+the particular NL state that you're in
+ 
+
+ align:start position:0%
+the particular NL state that you're in
+okay this Z effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is the effective nuclear
+
+ align:start position:0%
+here is the effective nuclear
+ 
+
+ align:start position:0%
+here is the effective nuclear
+charge it is not the nuclear
+
+ align:start position:0%
+charge it is not the nuclear
+ 
+
+ align:start position:0%
+charge it is not the nuclear
+charge it's the effective nuclear
+
+ align:start position:0%
+charge it's the effective nuclear
+ 
+
+ align:start position:0%
+charge it's the effective nuclear
+charge why well because of
+
+ align:start position:0%
+charge why well because of
+ 
+
+ align:start position:0%
+charge why well because of
+shielding so let's try to explain that
+
+ align:start position:0%
+shielding so let's try to explain that
+ 
+
+ align:start position:0%
+shielding so let's try to explain that
+so let's take helium all right helium Z
+
+ align:start position:0%
+so let's take helium all right helium Z
+ 
+
+ align:start position:0%
+so let's take helium all right helium Z
+is equal to + 2 e all right so we
+
+ align:start position:0%
+is equal to + 2 e all right so we
+ 
+
+ align:start position:0%
+is equal to + 2 e all right so we
+have plus 2 e here and now let's do a
+
+ align:start position:0%
+have plus 2 e here and now let's do a
+ 
+
+ align:start position:0%
+have plus 2 e here and now let's do a
+thought
+
+ align:start position:0%
+thought
+ 
+
+ align:start position:0%
+thought
+experiment in that we're going to take
+
+ align:start position:0%
+experiment in that we're going to take
+ 
+
+ align:start position:0%
+experiment in that we're going to take
+electron number two here right and we're
+
+ align:start position:0%
+electron number two here right and we're
+ 
+
+ align:start position:0%
+electron number two here right and we're
+going to place electron number two kind
+
+ align:start position:0%
+going to place electron number two kind
+ 
+
+ align:start position:0%
+going to place electron number two kind
+of close to the
+
+ align:start position:0%
+of close to the
+ 
+
+ align:start position:0%
+of close to the
+plus two charge
+
+ align:start position:0%
+plus two charge
+ 
+
+ align:start position:0%
+plus two charge
+nucleus and then we're going to have
+
+ align:start position:0%
+nucleus and then we're going to have
+ 
+
+ align:start position:0%
+nucleus and then we're going to have
+electron number one way out here
+
+ align:start position:0%
+electron number one way out here
+ 
+
+ align:start position:0%
+electron number one way out here
+right so in this case with electron
+
+ align:start position:0%
+right so in this case with electron
+ 
+
+ align:start position:0%
+right so in this case with electron
+number one way out here well the nuclear
+
+ align:start position:0%
+number one way out here well the nuclear
+ 
+
+ align:start position:0%
+number one way out here well the nuclear
+charge that electron number one
+
+ align:start position:0%
+charge that electron number one
+ 
+
+ align:start position:0%
+charge that electron number one
+experiences because it's so far out that
+
+ align:start position:0%
+experiences because it's so far out that
+ 
+
+ align:start position:0%
+experiences because it's so far out that
+nuclear charge kind of looks like a plus
+
+ align:start position:0%
+nuclear charge kind of looks like a plus
+ 
+
+ align:start position:0%
+nuclear charge kind of looks like a plus
+one charge right because this electron
+
+ align:start position:0%
+one charge right because this electron
+ 
+
+ align:start position:0%
+one charge right because this electron
+on the average is canceling one of the
+
+ align:start position:0%
+on the average is canceling one of the
+ 
+
+ align:start position:0%
+on the average is canceling one of the
+positive charges on the
+
+ align:start position:0%
+positive charges on the
+ 
+
+ align:start position:0%
+positive charges on the
+nucleus so the effective charge here for
+
+ align:start position:0%
+nucleus so the effective charge here for
+ 
+
+ align:start position:0%
+nucleus so the effective charge here for
+this electron way out there we're going
+
+ align:start position:0%
+this electron way out there we're going
+ 
+
+ align:start position:0%
+this electron way out there we're going
+to say is+
+
+ align:start position:0%
+to say is+
+ 
+
+ align:start position:0%
+to say is+
+one if that's the case well then The
+
+ align:start position:0%
+one if that's the case well then The
+ 
+
+ align:start position:0%
+one if that's the case well then The
+Binding energy of that electron right is
+
+ align:start position:0%
+Binding energy of that electron right is
+ 
+
+ align:start position:0%
+Binding energy of that electron right is
+1^ 2 * R subh over n 2 all right we're
+
+ align:start position:0%
+1^ 2 * R subh over n 2 all right we're
+ 
+
+ align:start position:0%
+1^ 2 * R subh over n 2 all right we're
+going to consider n equal 1 because
+
+ align:start position:0%
+going to consider n equal 1 because
+ 
+
+ align:start position:0%
+going to consider n equal 1 because
+we're going to talk about the ground
+
+ align:start position:0%
+we're going to talk about the ground
+ 
+
+ align:start position:0%
+we're going to talk about the ground
+state of the helium atom here but you
+
+ align:start position:0%
+state of the helium atom here but you
+ 
+
+ align:start position:0%
+state of the helium atom here but you
+know what this value is going to turn
+
+ align:start position:0%
+know what this value is going to turn
+ 
+
+ align:start position:0%
+know what this value is going to turn
+out to be it's going to turn out to be -
+
+ align:start position:0%
+out to be it's going to turn out to be -
+ 
+
+ align:start position:0%
+out to be it's going to turn out to be -
+2.18 * 10- 18 jewles Hey That's The
+
+ align:start position:0%
+2.18 * 10- 18 jewles Hey That's The
+ 
+
+ align:start position:0%
+2.18 * 10- 18 jewles Hey That's The
+Binding energy of an electron and a
+
+ align:start position:0%
+Binding energy of an electron and a
+ 
+
+ align:start position:0%
+Binding energy of an electron and a
+hydrogen atom okay when this is a
+
+ align:start position:0%
+hydrogen atom okay when this is a
+ 
+
+ align:start position:0%
+hydrogen atom okay when this is a
+thought experiment now right so this is
+
+ align:start position:0%
+thought experiment now right so this is
+ 
+
+ align:start position:0%
+thought experiment now right so this is
+helium this is just one electron way out
+
+ align:start position:0%
+helium this is just one electron way out
+ 
+
+ align:start position:0%
+helium this is just one electron way out
+here and it can't discriminate too well
+
+ align:start position:0%
+here and it can't discriminate too well
+ 
+
+ align:start position:0%
+here and it can't discriminate too well
+between the nucleus and this electron so
+
+ align:start position:0%
+between the nucleus and this electron so
+ 
+
+ align:start position:0%
+between the nucleus and this electron so
+the overall effective charge it sees is
+
+ align:start position:0%
+the overall effective charge it sees is
+ 
+
+ align:start position:0%
+the overall effective charge it sees is
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+one all right but now we take the other
+
+ align:start position:0%
+one all right but now we take the other
+ 
+
+ align:start position:0%
+one all right but now we take the other
+case The Other Extreme case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is we're going to bring in electron one
+
+ align:start position:0%
+is we're going to bring in electron one
+ 
+
+ align:start position:0%
+is we're going to bring in electron one
+really close to the nucleus right and
+
+ align:start position:0%
+really close to the nucleus right and
+ 
+
+ align:start position:0%
+really close to the nucleus right and
+electron 2 is way out here such that
+
+ align:start position:0%
+electron 2 is way out here such that
+ 
+
+ align:start position:0%
+electron 2 is way out here such that
+electron to doesn't do anything as far
+
+ align:start position:0%
+electron to doesn't do anything as far
+ 
+
+ align:start position:0%
+electron to doesn't do anything as far
+as this electron is concerned right and
+
+ align:start position:0%
+as this electron is concerned right and
+ 
+
+ align:start position:0%
+as this electron is concerned right and
+so this electron in this case is
+
+ align:start position:0%
+so this electron in this case is
+ 
+
+ align:start position:0%
+so this electron in this case is
+experiencing the total nuclear charge on
+
+ align:start position:0%
+experiencing the total nuclear charge on
+ 
+
+ align:start position:0%
+experiencing the total nuclear charge on
+the nucleus and so we say in
+
+ align:start position:0%
+the nucleus and so we say in
+ 
+
+ align:start position:0%
+the nucleus and so we say in
+this thought case here with this
+
+ align:start position:0%
+this thought case here with this
+ 
+
+ align:start position:0%
+this thought case here with this
+electron really close
+
+ align:start position:0%
+electron really close
+ 
+
+ align:start position:0%
+electron really close
+that the effective charge is equal to+ 2
+
+ align:start position:0%
+that the effective charge is equal to+ 2
+ 
+
+ align:start position:0%
+that the effective charge is equal to+ 2
+e for this
+
+ align:start position:0%
+e for this
+ 
+
+ align:start position:0%
+e for this
+electron well if that's the case we can
+
+ align:start position:0%
+electron well if that's the case we can
+ 
+
+ align:start position:0%
+electron well if that's the case we can
+calculate the binding energy of this
+
+ align:start position:0%
+calculate the binding energy of this
+ 
+
+ align:start position:0%
+calculate the binding energy of this
+electron and um that's going to be 2^
+
+ align:start position:0%
+electron and um that's going to be 2^
+ 
+
+ align:start position:0%
+electron and um that's going to be 2^
+2ar over uh time R subh over 1^
+
+ align:start position:0%
+2ar over uh time R subh over 1^
+ 
+
+ align:start position:0%
+2ar over uh time R subh over 1^
+2 we can plug in our subh and we're
+
+ align:start position:0%
+2 we can plug in our subh and we're
+ 
+
+ align:start position:0%
+2 we can plug in our subh and we're
+going to get minus 8
+
+ align:start position:0%
+going to get minus 8
+ 
+
+ align:start position:0%
+going to get minus 8
+72 * 10- 18 juw okay what this is is The
+
+ align:start position:0%
+72 * 10- 18 juw okay what this is is The
+ 
+
+ align:start position:0%
+72 * 10- 18 juw okay what this is is The
+Binding
+
+ align:start position:0%
+Binding
+ 
+
+ align:start position:0%
+Binding
+energy of a electron in helium plus
+
+ align:start position:0%
+energy of a electron in helium plus
+ 
+
+ align:start position:0%
+energy of a electron in helium plus
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay and so in this extreme case with
+
+ align:start position:0%
+okay and so in this extreme case with
+ 
+
+ align:start position:0%
+okay and so in this extreme case with
+the electron really close in That's The
+
+ align:start position:0%
+the electron really close in That's The
+ 
+
+ align:start position:0%
+the electron really close in That's The
+Binding energy with this extreme case
+
+ align:start position:0%
+Binding energy with this extreme case
+ 
+
+ align:start position:0%
+Binding energy with this extreme case
+with the electron way far out this is
+
+ align:start position:0%
+with the electron way far out this is
+ 
+
+ align:start position:0%
+with the electron way far out this is
+The Binding
+
+ align:start position:0%
+The Binding
+ 
+
+ align:start position:0%
+The Binding
+energy this is total
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shielding this case is no
+
+ align:start position:0%
+shielding this case is no
+ 
+
+ align:start position:0%
+shielding this case is no
+shielding no shielding the electron is
+
+ align:start position:0%
+shielding no shielding the electron is
+ 
+
+ align:start position:0%
+shielding no shielding the electron is
+much more strongly
+
+ align:start position:0%
+much more strongly
+ 
+
+ align:start position:0%
+much more strongly
+bound the reality is that The Binding
+
+ align:start position:0%
+bound the reality is that The Binding
+ 
+
+ align:start position:0%
+bound the reality is that The Binding
+energy of an electron in helium is
+
+ align:start position:0%
+energy of an electron in helium is
+ 
+
+ align:start position:0%
+energy of an electron in helium is
+somewhere in
+
+ align:start position:0%
+somewhere in
+ 
+
+ align:start position:0%
+somewhere in
+between right that is the ionization
+
+ align:start position:0%
+between right that is the ionization
+ 
+
+ align:start position:0%
+between right that is the ionization
+energy for helium for an electron in now
+
+ align:start position:0%
+energy for helium for an electron in now
+ 
+
+ align:start position:0%
+energy for helium for an electron in now
+neutral helium here the ionization
+
+ align:start position:0%
+neutral helium here the ionization
+ 
+
+ align:start position:0%
+neutral helium here the ionization
+energy is
+
+ align:start position:0%
+energy is
+ 
+
+ align:start position:0%
+energy is
+3.94 time 10- 18
+
+ align:start position:0%
+3.94 time 10- 18
+ 
+
+ align:start position:0%
+3.94 time 10- 18
+jewles somewhere in between this extreme
+
+ align:start position:0%
+jewles somewhere in between this extreme
+ 
+
+ align:start position:0%
+jewles somewhere in between this extreme
+case of total
+
+ align:start position:0%
+case of total
+ 
+
+ align:start position:0%
+case of total
+shielding and this extreme case of no
+
+ align:start position:0%
+shielding and this extreme case of no
+ 
+
+ align:start position:0%
+shielding and this extreme case of no
+shielding at
+
+ align:start position:0%
+shielding at
+ 
+
+ align:start position:0%
+shielding at
+all and that's because on the
+
+ align:start position:0%
+all and that's because on the
+ 
+
+ align:start position:0%
+all and that's because on the
+average right there is is another
+
+ align:start position:0%
+average right there is is another
+ 
+
+ align:start position:0%
+average right there is is another
+electron in between that electron and
+
+ align:start position:0%
+electron in between that electron and
+ 
+
+ align:start position:0%
+electron in between that electron and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+nucleus and we can calculate the
+
+ align:start position:0%
+nucleus and we can calculate the
+ 
+
+ align:start position:0%
+nucleus and we can calculate the
+effective charge then from the
+
+ align:start position:0%
+effective charge then from the
+ 
+
+ align:start position:0%
+effective charge then from the
+experimental binding energies by just
+
+ align:start position:0%
+experimental binding energies by just
+ 
+
+ align:start position:0%
+experimental binding energies by just
+taking this expression and rearranging
+
+ align:start position:0%
+taking this expression and rearranging
+ 
+
+ align:start position:0%
+taking this expression and rearranging
+it right so I'm going to solve that
+
+ align:start position:0%
+it right so I'm going to solve that
+ 
+
+ align:start position:0%
+it right so I'm going to solve that
+expression for the effective charge z e
+
+ align:start position:0%
+expression for the effective charge z e
+ 
+
+ align:start position:0%
+expression for the effective charge z e
+FF and when I do that that of course is
+
+ align:start position:0%
+FF and when I do that that of course is
+ 
+
+ align:start position:0%
+FF and when I do that that of course is
+s times then the ionization
+
+ align:start position:0%
+s times then the ionization
+ 
+
+ align:start position:0%
+s times then the ionization
+energy over the ridberg
+
+ align:start position:0%
+energy over the ridberg
+ 
+
+ align:start position:0%
+energy over the ridberg
+constant right n s is going to be one
+
+ align:start position:0%
+constant right n s is going to be one
+ 
+
+ align:start position:0%
+constant right n s is going to be one
+because we're talking about the ground
+
+ align:start position:0%
+because we're talking about the ground
+ 
+
+ align:start position:0%
+because we're talking about the ground
+state the ionization energy I said was
+
+ align:start position:0%
+state the ionization energy I said was
+ 
+
+ align:start position:0%
+state the ionization energy I said was
+3.94 * 10- 18 jewles redberg constant is
+
+ align:start position:0%
+3.94 * 10- 18 jewles redberg constant is
+ 
+
+ align:start position:0%
+3.94 * 10- 18 jewles redberg constant is
+2.18 * 10us 18 jewles right in the end I
+
+ align:start position:0%
+2.18 * 10us 18 jewles right in the end I
+ 
+
+ align:start position:0%
+2.18 * 10us 18 jewles right in the end I
+find an effective charge here of plus
+
+ align:start position:0%
+find an effective charge here of plus
+ 
+
+ align:start position:0%
+find an effective charge here of plus
+1.34 okay and again why is that the case
+
+ align:start position:0%
+1.34 okay and again why is that the case
+ 
+
+ align:start position:0%
+1.34 okay and again why is that the case
+well that's the case because if uh
+
+ align:start position:0%
+well that's the case because if uh
+ 
+
+ align:start position:0%
+well that's the case because if uh
+here's my
+
+ align:start position:0%
+here's my
+ 
+
+ align:start position:0%
+here's my
+electron here's my helium
+
+ align:start position:0%
+electron here's my helium
+ 
+
+ align:start position:0%
+electron here's my helium
+nucleus well just on the average right
+
+ align:start position:0%
+nucleus well just on the average right
+ 
+
+ align:start position:0%
+nucleus well just on the average right
+between this electron and the nucleus
+
+ align:start position:0%
+between this electron and the nucleus
+ 
+
+ align:start position:0%
+between this electron and the nucleus
+there's always another electron around
+
+ align:start position:0%
+there's always another electron around
+ 
+
+ align:start position:0%
+there's always another electron around
+this electron kind of partially Shields
+
+ align:start position:0%
+this electron kind of partially Shields
+ 
+
+ align:start position:0%
+this electron kind of partially Shields
+this nuclear charge partially Shields it
+
+ align:start position:0%
+this nuclear charge partially Shields it
+ 
+
+ align:start position:0%
+this nuclear charge partially Shields it
+so that we calculated from using this
+
+ align:start position:0%
+so that we calculated from using this
+ 
+
+ align:start position:0%
+so that we calculated from using this
+scheme and using the experimental
+
+ align:start position:0%
+scheme and using the experimental
+ 
+
+ align:start position:0%
+scheme and using the experimental
+ionization energies we calculated an
+
+ align:start position:0%
+ionization energies we calculated an
+ 
+
+ align:start position:0%
+ionization energies we calculated an
+effective charge of
+
+ align:start position:0%
+effective charge of
+ 
+
+ align:start position:0%
+effective charge of
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay all right so now we sort of
+
+ align:start position:0%
+okay all right so now we sort of
+ 
+
+ align:start position:0%
+okay all right so now we sort of
+understand shielding and effective
+
+ align:start position:0%
+understand shielding and effective
+ 
+
+ align:start position:0%
+understand shielding and effective
+charge
+
+ align:start position:0%
+charge
+ 
+
+ align:start position:0%
+charge
+right that's a square root thank
+
+ align:start position:0%
+right that's a square root thank
+ 
+
+ align:start position:0%
+right that's a square root thank
+you right
+
+ align:start position:0%
+you right
+ 
+
+ align:start position:0%
+you right
+okay all
+
+ align:start position:0%
+okay all
+ 
+
+ align:start position:0%
+okay all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay but now we have to use this idea of
+
+ align:start position:0%
+okay but now we have to use this idea of
+ 
+
+ align:start position:0%
+okay but now we have to use this idea of
+effective charge and shielding to
+
+ align:start position:0%
+effective charge and shielding to
+ 
+
+ align:start position:0%
+effective charge and shielding to
+understand why the 2s state is lower in
+
+ align:start position:0%
+understand why the 2s state is lower in
+ 
+
+ align:start position:0%
+understand why the 2s state is lower in
+energy than the 2p
+
+ align:start position:0%
+energy than the 2p
+ 
+
+ align:start position:0%
+energy than the 2p
+State all right and here comes that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's think about the lithium
+
+ align:start position:0%
+all right let's think about the lithium
+ 
+
+ align:start position:0%
+all right let's think about the lithium
+atom all right the electron
+
+ align:start position:0%
+atom all right the electron
+ 
+
+ align:start position:0%
+atom all right the electron
+configuration of lithium is 1 S2
+
+ align:start position:0%
+configuration of lithium is 1 S2
+ 
+
+ align:start position:0%
+configuration of lithium is 1 S2
+2s1 the electron configuration of
+
+ align:start position:0%
+2s1 the electron configuration of
+ 
+
+ align:start position:0%
+2s1 the electron configuration of
+lithium is not 1 S2 2 P1 why because 2s
+
+ align:start position:0%
+lithium is not 1 S2 2 P1 why because 2s
+ 
+
+ align:start position:0%
+lithium is not 1 S2 2 P1 why because 2s
+is lower in energy than
+
+ align:start position:0%
+is lower in energy than
+ 
+
+ align:start position:0%
+is lower in energy than
+2p but why is that the case well to look
+
+ align:start position:0%
+2p but why is that the case well to look
+ 
+
+ align:start position:0%
+2p but why is that the case well to look
+at that we got to look at the radial
+
+ align:start position:0%
+at that we got to look at the radial
+ 
+
+ align:start position:0%
+at that we got to look at the radial
+probability distribution functions for
+
+ align:start position:0%
+probability distribution functions for
+ 
+
+ align:start position:0%
+probability distribution functions for
+2s and 2
+
+ align:start position:0%
+2s and 2
+ 
+
+ align:start position:0%
+2s and 2
+p so here's the radial probability
+
+ align:start position:0%
+p so here's the radial probability
+ 
+
+ align:start position:0%
+p so here's the radial probability
+distribution function for
+
+ align:start position:0%
+distribution function for
+ 
+
+ align:start position:0%
+distribution function for
+2s here's the uh radial probability
+
+ align:start position:0%
+2s here's the uh radial probability
+ 
+
+ align:start position:0%
+2s here's the uh radial probability
+distribution function for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2p okay now you have to uh do a thought
+
+ align:start position:0%
+2p okay now you have to uh do a thought
+ 
+
+ align:start position:0%
+2p okay now you have to uh do a thought
+experiment here in this 2s radial
+
+ align:start position:0%
+experiment here in this 2s radial
+ 
+
+ align:start position:0%
+experiment here in this 2s radial
+probability distribution
+
+ align:start position:0%
+probability distribution
+ 
+
+ align:start position:0%
+probability distribution
+function what you see is that there is
+
+ align:start position:0%
+function what you see is that there is
+ 
+
+ align:start position:0%
+function what you see is that there is
+some finite
+
+ align:start position:0%
+some finite
+ 
+
+ align:start position:0%
+some finite
+probability of the electron in the 2s
+
+ align:start position:0%
+probability of the electron in the 2s
+ 
+
+ align:start position:0%
+probability of the electron in the 2s
+State being really close to the
+
+ align:start position:0%
+State being really close to the
+ 
+
+ align:start position:0%
+State being really close to the
+nucleus for the sake of the argument
+
+ align:start position:0%
+nucleus for the sake of the argument
+ 
+
+ align:start position:0%
+nucleus for the sake of the argument
+here I'm going to
+
+ align:start position:0%
+here I'm going to
+ 
+
+ align:start position:0%
+here I'm going to
+say that for this part of the
+
+ align:start position:0%
+say that for this part of the
+ 
+
+ align:start position:0%
+say that for this part of the
+probability distribution function for
+
+ align:start position:0%
+probability distribution function for
+ 
+
+ align:start position:0%
+probability distribution function for
+that part the effective charge Z
+
+ align:start position:0%
+that part the effective charge Z
+ 
+
+ align:start position:0%
+that part the effective charge Z
+effective is going to be plus
+
+ align:start position:0%
+effective is going to be plus
+ 
+
+ align:start position:0%
+effective is going to be plus
+3E okay I mean that's an exaggeration
+
+ align:start position:0%
+3E okay I mean that's an exaggeration
+ 
+
+ align:start position:0%
+3E okay I mean that's an exaggeration
+because obviously we have some s
+
+ align:start position:0%
+because obviously we have some s
+ 
+
+ align:start position:0%
+because obviously we have some s
+electrons but for the sake of this
+
+ align:start position:0%
+electrons but for the sake of this
+ 
+
+ align:start position:0%
+electrons but for the sake of this
+argument I'm going to say the effective
+
+ align:start position:0%
+argument I'm going to say the effective
+ 
+
+ align:start position:0%
+argument I'm going to say the effective
+charge for this part of the probability
+
+ align:start position:0%
+charge for this part of the probability
+ 
+
+ align:start position:0%
+charge for this part of the probability
+distribution function is plus
+
+ align:start position:0%
+distribution function is plus
+ 
+
+ align:start position:0%
+distribution function is plus
+3E for this part of the probability
+
+ align:start position:0%
+3E for this part of the probability
+ 
+
+ align:start position:0%
+3E for this part of the probability
+distribution function for 2s hey that's
+
+ align:start position:0%
+distribution function for 2s hey that's
+ 
+
+ align:start position:0%
+distribution function for 2s hey that's
+much further out and I have those 1s
+
+ align:start position:0%
+much further out and I have those 1s
+ 
+
+ align:start position:0%
+much further out and I have those 1s
+electrons closer in so for the sake of
+
+ align:start position:0%
+electrons closer in so for the sake of
+ 
+
+ align:start position:0%
+electrons closer in so for the sake of
+this argument I'm going to say that
+
+ align:start position:0%
+this argument I'm going to say that
+ 
+
+ align:start position:0%
+this argument I'm going to say that
+these s electrons completely Shield the
+
+ align:start position:0%
+these s electrons completely Shield the
+ 
+
+ align:start position:0%
+these s electrons completely Shield the
+nuclear charge and so the effective
+
+ align:start position:0%
+nuclear charge and so the effective
+ 
+
+ align:start position:0%
+nuclear charge and so the effective
+charge for this part of the distribution
+
+ align:start position:0%
+charge for this part of the distribution
+ 
+
+ align:start position:0%
+charge for this part of the distribution
+is plus one
+
+ align:start position:0%
+is plus one
+ 
+
+ align:start position:0%
+is plus one
+e okay now what about
+
+ align:start position:0%
+e okay now what about
+ 
+
+ align:start position:0%
+e okay now what about
+2p well in the case of 2p you can
+
+ align:start position:0%
+2p well in the case of 2p you can
+ 
+
+ align:start position:0%
+2p well in the case of 2p you can
+see that this 2p wave function although
+
+ align:start position:0%
+see that this 2p wave function although
+ 
+
+ align:start position:0%
+see that this 2p wave function although
+it's a little bit closer in hey for the
+
+ align:start position:0%
+it's a little bit closer in hey for the
+ 
+
+ align:start position:0%
+it's a little bit closer in hey for the
+most part it is about in the same place
+
+ align:start position:0%
+most part it is about in the same place
+ 
+
+ align:start position:0%
+most part it is about in the same place
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+this uh the second lobe here of the 2s
+
+ align:start position:0%
+this uh the second lobe here of the 2s
+ 
+
+ align:start position:0%
+this uh the second lobe here of the 2s
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+function so we're going to say that this
+
+ align:start position:0%
+function so we're going to say that this
+ 
+
+ align:start position:0%
+function so we're going to say that this
+effective
+
+ align:start position:0%
+effective
+ 
+
+ align:start position:0%
+effective
+charge is + one e just like this lobe of
+
+ align:start position:0%
+charge is + one e just like this lobe of
+ 
+
+ align:start position:0%
+charge is + one e just like this lobe of
+the 2s wave
+
+ align:start position:0%
+the 2s wave
+ 
+
+ align:start position:0%
+the 2s wave
+function but now to get the kind of
+
+ align:start position:0%
+function but now to get the kind of
+ 
+
+ align:start position:0%
+function but now to get the kind of
+total effective charge I'm going to have
+
+ align:start position:0%
+total effective charge I'm going to have
+ 
+
+ align:start position:0%
+total effective charge I'm going to have
+to take the effective charge and average
+
+ align:start position:0%
+to take the effective charge and average
+ 
+
+ align:start position:0%
+to take the effective charge and average
+it over this probability distribution
+
+ align:start position:0%
+it over this probability distribution
+ 
+
+ align:start position:0%
+it over this probability distribution
+function and so since in the 2s function
+
+ align:start position:0%
+function and so since in the 2s function
+ 
+
+ align:start position:0%
+function and so since in the 2s function
+I'm going to average over a part that
+
+ align:start position:0%
+I'm going to average over a part that
+ 
+
+ align:start position:0%
+I'm going to average over a part that
+has a plus three effective charge and a
+
+ align:start position:0%
+has a plus three effective charge and a
+ 
+
+ align:start position:0%
+has a plus three effective charge and a
+PL part that that has a plus one
+
+ align:start position:0%
+PL part that that has a plus one
+ 
+
+ align:start position:0%
+PL part that that has a plus one
+effective charge well if I average over
+
+ align:start position:0%
+effective charge well if I average over
+ 
+
+ align:start position:0%
+effective charge well if I average over
+that that's going to be larger than the
+
+ align:start position:0%
+that that's going to be larger than the
+ 
+
+ align:start position:0%
+that that's going to be larger than the
+effective charge of this 2p wave
+
+ align:start position:0%
+effective charge of this 2p wave
+ 
+
+ align:start position:0%
+effective charge of this 2p wave
+function right because the 2p everywhere
+
+ align:start position:0%
+function right because the 2p everywhere
+ 
+
+ align:start position:0%
+function right because the 2p everywhere
+is plus
+
+ align:start position:0%
+is plus
+ 
+
+ align:start position:0%
+is plus
+one so the effective charge here for the
+
+ align:start position:0%
+one so the effective charge here for the
+ 
+
+ align:start position:0%
+one so the effective charge here for the
+2s is going to be greater on the average
+
+ align:start position:0%
+2s is going to be greater on the average
+ 
+
+ align:start position:0%
+2s is going to be greater on the average
+than for the
+
+ align:start position:0%
+than for the
+ 
+
+ align:start position:0%
+than for the
+2p because of this part of the
+
+ align:start position:0%
+2p because of this part of the
+ 
+
+ align:start position:0%
+2p because of this part of the
+probability distribution function this
+
+ align:start position:0%
+probability distribution function this
+ 
+
+ align:start position:0%
+probability distribution function this
+part that's really close to the nucleus
+
+ align:start position:0%
+part that's really close to the nucleus
+ 
+
+ align:start position:0%
+part that's really close to the nucleus
+where the electrons can feel more of the
+
+ align:start position:0%
+where the electrons can feel more of the
+ 
+
+ align:start position:0%
+where the electrons can feel more of the
+nuclear charge or experience more of the
+
+ align:start position:0%
+nuclear charge or experience more of the
+ 
+
+ align:start position:0%
+nuclear charge or experience more of the
+nuclear charge than they could if they
+
+ align:start position:0%
+nuclear charge than they could if they
+ 
+
+ align:start position:0%
+nuclear charge than they could if they
+were a a 2p
+
+ align:start position:0%
+were a a 2p
+ 
+
+ align:start position:0%
+were a a 2p
+electron okay so therefore since the 2s
+
+ align:start position:0%
+electron okay so therefore since the 2s
+ 
+
+ align:start position:0%
+electron okay so therefore since the 2s
+electron has a greater effective charge
+
+ align:start position:0%
+electron has a greater effective charge
+ 
+
+ align:start position:0%
+electron has a greater effective charge
+here well what that's going to mean is
+
+ align:start position:0%
+here well what that's going to mean is
+ 
+
+ align:start position:0%
+here well what that's going to mean is
+that The Binding energy of the 2s state
+
+ align:start position:0%
+that The Binding energy of the 2s state
+ 
+
+ align:start position:0%
+that The Binding energy of the 2s state
+is going to be lower in energy it's
+
+ align:start position:0%
+is going to be lower in energy it's
+ 
+
+ align:start position:0%
+is going to be lower in energy it's
+going to be more negative Than The
+
+ align:start position:0%
+going to be more negative Than The
+ 
+
+ align:start position:0%
+going to be more negative Than The
+Binding energy of the 2p
+
+ align:start position:0%
+Binding energy of the 2p
+ 
+
+ align:start position:0%
+Binding energy of the 2p
+State same thing for 3s and
+
+ align:start position:0%
+State same thing for 3s and
+ 
+
+ align:start position:0%
+State same thing for 3s and
+3p all right same reasoning there and
+
+ align:start position:0%
+3p all right same reasoning there and
+ 
+
+ align:start position:0%
+3p all right same reasoning there and
+it's all because of this little part of
+
+ align:start position:0%
+it's all because of this little part of
+ 
+
+ align:start position:0%
+it's all because of this little part of
+the probability distribution function
+
+ align:start position:0%
+the probability distribution function
+ 
+
+ align:start position:0%
+the probability distribution function
+all right so now we can understand why
+
+ align:start position:0%
+all right so now we can understand why
+ 
+
+ align:start position:0%
+all right so now we can understand why
+the 2s is in fact lower in energy than
+
+ align:start position:0%
+the 2s is in fact lower in energy than
+ 
+
+ align:start position:0%
+the 2s is in fact lower in energy than
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+2p all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the three well because the 3s um
+
+ align:start position:0%
+yeah the three well because the 3s um
+ 
+
+ align:start position:0%
+yeah the three well because the 3s um
+although it does in fact have this it's
+
+ align:start position:0%
+although it does in fact have this it's
+ 
+
+ align:start position:0%
+although it does in fact have this it's
+a little bit further out here enough to
+
+ align:start position:0%
+a little bit further out here enough to
+ 
+
+ align:start position:0%
+a little bit further out here enough to
+make for this to compensate but again 3s
+
+ align:start position:0%
+make for this to compensate but again 3s
+ 
+
+ align:start position:0%
+make for this to compensate but again 3s
+is lower than 3p right so we're just
+
+ align:start position:0%
+is lower than 3p right so we're just
+ 
+
+ align:start position:0%
+is lower than 3p right so we're just
+going to compare 3s and 3p within the
+
+ align:start position:0%
+going to compare 3s and 3p within the
+ 
+
+ align:start position:0%
+going to compare 3s and 3p within the
+same shell all
+
+ align:start position:0%
+same shell all
+ 
+
+ align:start position:0%
+same shell all
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yes right it does have to do with
+
+ align:start position:0%
+okay yes right it does have to do with
+ 
+
+ align:start position:0%
+okay yes right it does have to do with
+the net area underneath if the
+
+ align:start position:0%
+the net area underneath if the
+ 
+
+ align:start position:0%
+the net area underneath if the
+probability were much higher and it's
+
+ align:start position:0%
+probability were much higher and it's
+ 
+
+ align:start position:0%
+probability were much higher and it's
+and it's not that much higher uh but if
+
+ align:start position:0%
+and it's not that much higher uh but if
+ 
+
+ align:start position:0%
+and it's not that much higher uh but if
+it were then you you're right it could
+
+ align:start position:0%
+it were then you you're right it could
+ 
+
+ align:start position:0%
+it were then you you're right it could
+cancel it out right right
+
+ align:start position:0%
+cancel it out right right
+ 
+
+ align:start position:0%
+cancel it out right right
+okay okay
+
+ align:start position:0%
+okay okay
+ 
+
+ align:start position:0%
+okay okay
+so now therefore we're ready to write
+
+ align:start position:0%
+so now therefore we're ready to write
+ 
+
+ align:start position:0%
+so now therefore we're ready to write
+the electron
+
+ align:start position:0%
+the electron
+ 
+
+ align:start position:0%
+the electron
+configurations of uh all the atoms in
+
+ align:start position:0%
+configurations of uh all the atoms in
+ 
+
+ align:start position:0%
+configurations of uh all the atoms in
+the on the periodic
+
+ align:start position:0%
+the on the periodic
+ 
+
+ align:start position:0%
+the on the periodic
+table and you already know that we use
+
+ align:start position:0%
+table and you already know that we use
+ 
+
+ align:start position:0%
+table and you already know that we use
+the albow principle to do
+
+ align:start position:0%
+the albow principle to do
+ 
+
+ align:start position:0%
+the albow principle to do
+that alow means building
+
+ align:start position:0%
+that alow means building
+ 
+
+ align:start position:0%
+that alow means building
+up so what do you do you take all the
+
+ align:start position:0%
+up so what do you do you take all the
+ 
+
+ align:start position:0%
+up so what do you do you take all the
+states the the allowed
+
+ align:start position:0%
+states the the allowed
+ 
+
+ align:start position:0%
+states the the allowed
+States and you order them according to
+
+ align:start position:0%
+States and you order them according to
+ 
+
+ align:start position:0%
+States and you order them according to
+their energy
+
+ align:start position:0%
+their energy
+ 
+
+ align:start position:0%
+their energy
+most strongly bound or most negative
+
+ align:start position:0%
+most strongly bound or most negative
+ 
+
+ align:start position:0%
+most strongly bound or most negative
+energy goes on the bottom and next most
+
+ align:start position:0%
+energy goes on the bottom and next most
+ 
+
+ align:start position:0%
+energy goes on the bottom and next most
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+energy on and on and we'll talk about an
+
+ align:start position:0%
+energy on and on and we'll talk about an
+ 
+
+ align:start position:0%
+energy on and on and we'll talk about an
+pneumonic for remembering those energies
+
+ align:start position:0%
+pneumonic for remembering those energies
+ 
+
+ align:start position:0%
+pneumonic for remembering those energies
+in a moment
+
+ align:start position:0%
+in a moment
+ 
+
+ align:start position:0%
+in a moment
+okay all right so we use the AL bow
+
+ align:start position:0%
+okay all right so we use the AL bow
+ 
+
+ align:start position:0%
+okay all right so we use the AL bow
+principle we start with the lowest
+
+ align:start position:0%
+principle we start with the lowest
+ 
+
+ align:start position:0%
+principle we start with the lowest
+energy State and we put an electron in
+
+ align:start position:0%
+energy State and we put an electron in
+ 
+
+ align:start position:0%
+energy State and we put an electron in
+for hydrogen there it is One S
+
+ align:start position:0%
+for hydrogen there it is One S
+ 
+
+ align:start position:0%
+for hydrogen there it is One S
+state for helium well we also put that
+
+ align:start position:0%
+state for helium well we also put that
+ 
+
+ align:start position:0%
+state for helium well we also put that
+in to the 1s State except as we fill
+
+ align:start position:0%
+in to the 1s State except as we fill
+ 
+
+ align:start position:0%
+in to the 1s State except as we fill
+these states we have to um heed the PO
+
+ align:start position:0%
+these states we have to um heed the PO
+ 
+
+ align:start position:0%
+these states we have to um heed the PO
+Exclusion Principle so this electron
+
+ align:start position:0%
+Exclusion Principle so this electron
+ 
+
+ align:start position:0%
+Exclusion Principle so this electron
+here goes in with the opposite
+
+ align:start position:0%
+here goes in with the opposite
+ 
+
+ align:start position:0%
+here goes in with the opposite
+spin all right next uh lithium 2s
+
+ align:start position:0%
+spin all right next uh lithium 2s
+ 
+
+ align:start position:0%
+spin all right next uh lithium 2s
+electron for brillium another 2s
+
+ align:start position:0%
+electron for brillium another 2s
+ 
+
+ align:start position:0%
+electron for brillium another 2s
+electron opposite
+
+ align:start position:0%
+electron opposite
+ 
+
+ align:start position:0%
+electron opposite
+Spin and then for um
+
+ align:start position:0%
+Spin and then for um
+ 
+
+ align:start position:0%
+Spin and then for um
+nitrogen electron here has to go into
+
+ align:start position:0%
+nitrogen electron here has to go into
+ 
+
+ align:start position:0%
+nitrogen electron here has to go into
+the 2p State now it doesn't matter
+
+ align:start position:0%
+the 2p State now it doesn't matter
+ 
+
+ align:start position:0%
+the 2p State now it doesn't matter
+whether you put it in 2px 2py or 2pz
+
+ align:start position:0%
+whether you put it in 2px 2py or 2pz
+ 
+
+ align:start position:0%
+whether you put it in 2px 2py or 2pz
+they're all the same energy
+
+ align:start position:0%
+they're all the same energy
+ 
+
+ align:start position:0%
+they're all the same energy
+okay all right but now the next um the
+
+ align:start position:0%
+okay all right but now the next um the
+ 
+
+ align:start position:0%
+okay all right but now the next um the
+next electron
+
+ align:start position:0%
+next electron
+ 
+
+ align:start position:0%
+next electron
+carbon uh what are we going to do here
+
+ align:start position:0%
+carbon uh what are we going to do here
+ 
+
+ align:start position:0%
+carbon uh what are we going to do here
+well here we have to obey something
+
+ align:start position:0%
+well here we have to obey something
+ 
+
+ align:start position:0%
+well here we have to obey something
+called Hunt's Rule and Hunt's rule says
+
+ align:start position:0%
+called Hunt's Rule and Hunt's rule says
+ 
+
+ align:start position:0%
+called Hunt's Rule and Hunt's rule says
+that when electrons are added to states
+
+ align:start position:0%
+that when electrons are added to states
+ 
+
+ align:start position:0%
+that when electrons are added to states
+of the same energy and that's what we're
+
+ align:start position:0%
+of the same energy and that's what we're
+ 
+
+ align:start position:0%
+of the same energy and that's what we're
+doing here in the
+
+ align:start position:0%
+doing here in the
+ 
+
+ align:start position:0%
+doing here in the
+2p a single electron enters each state
+
+ align:start position:0%
+2p a single electron enters each state
+ 
+
+ align:start position:0%
+2p a single electron enters each state
+before a second electron enters any
+
+ align:start position:0%
+before a second electron enters any
+ 
+
+ align:start position:0%
+before a second electron enters any
+state and those single electrons have to
+
+ align:start position:0%
+state and those single electrons have to
+ 
+
+ align:start position:0%
+state and those single electrons have to
+go in so that the resulting spins are
+
+ align:start position:0%
+go in so that the resulting spins are
+ 
+
+ align:start position:0%
+go in so that the resulting spins are
+parallel that is they have the same spin
+
+ align:start position:0%
+parallel that is they have the same spin
+ 
+
+ align:start position:0%
+parallel that is they have the same spin
+so do we put
+
+ align:start position:0%
+so do we put
+ 
+
+ align:start position:0%
+so do we put
+in do we put in an electron like this no
+
+ align:start position:0%
+in do we put in an electron like this no
+ 
+
+ align:start position:0%
+in do we put in an electron like this no
+do we put it in like that no do we put
+
+ align:start position:0%
+do we put it in like that no do we put
+ 
+
+ align:start position:0%
+do we put it in like that no do we put
+it in like this
+
+ align:start position:0%
+it in like this
+ 
+
+ align:start position:0%
+it in like this
+y okay according to Hunt's Rule and then
+
+ align:start position:0%
+y okay according to Hunt's Rule and then
+ 
+
+ align:start position:0%
+y okay according to Hunt's Rule and then
+the next electron has to go into that
+
+ align:start position:0%
+the next electron has to go into that
+ 
+
+ align:start position:0%
+the next electron has to go into that
+other empty P State before any of these
+
+ align:start position:0%
+other empty P State before any of these
+ 
+
+ align:start position:0%
+other empty P State before any of these
+states double up all right so then we
+
+ align:start position:0%
+states double up all right so then we
+ 
+
+ align:start position:0%
+states double up all right so then we
+keep doubling them up next electron has
+
+ align:start position:0%
+keep doubling them up next electron has
+ 
+
+ align:start position:0%
+keep doubling them up next electron has
+to go into the next state 3s again we
+
+ align:start position:0%
+to go into the next state 3s again we
+ 
+
+ align:start position:0%
+to go into the next state 3s again we
+double them up and now we're to the 3p
+
+ align:start position:0%
+double them up and now we're to the 3p
+ 
+
+ align:start position:0%
+double them up and now we're to the 3p
+State again one electron goes into 2px
+
+ align:start position:0%
+State again one electron goes into 2px
+ 
+
+ align:start position:0%
+State again one electron goes into 2px
+the next electron will go into either
+
+ align:start position:0%
+the next electron will go into either
+ 
+
+ align:start position:0%
+the next electron will go into either
+2py or 2pz according to Hunts Rule and
+
+ align:start position:0%
+2py or 2pz according to Hunts Rule and
+ 
+
+ align:start position:0%
+2py or 2pz according to Hunts Rule and
+the spins remain parallel to get the
+
+ align:start position:0%
+the spins remain parallel to get the
+ 
+
+ align:start position:0%
+the spins remain parallel to get the
+lowest energy
+
+ align:start position:0%
+lowest energy
+ 
+
+ align:start position:0%
+lowest energy
+configuration and then the next electron
+
+ align:start position:0%
+configuration and then the next electron
+ 
+
+ align:start position:0%
+configuration and then the next electron
+to pz and then we start doubling up all
+
+ align:start position:0%
+to pz and then we start doubling up all
+ 
+
+ align:start position:0%
+to pz and then we start doubling up all
+right and we keep going and you keep
+
+ align:start position:0%
+right and we keep going and you keep
+ 
+
+ align:start position:0%
+right and we keep going and you keep
+going in that way so that you write the
+
+ align:start position:0%
+going in that way so that you write the
+ 
+
+ align:start position:0%
+going in that way so that you write the
+electron configuration of all the atoms
+
+ align:start position:0%
+electron configuration of all the atoms
+ 
+
+ align:start position:0%
+electron configuration of all the atoms
+in the periodic
+
+ align:start position:0%
+in the periodic
+ 
+
+ align:start position:0%
+in the periodic
+table okay let's uh look at these
+
+ align:start position:0%
+table okay let's uh look at these
+ 
+
+ align:start position:0%
+table okay let's uh look at these
+electron configurations kind of quickly
+
+ align:start position:0%
+electron configurations kind of quickly
+ 
+
+ align:start position:0%
+electron configurations kind of quickly
+here let's start with uh let's start
+
+ align:start position:0%
+here let's start with uh let's start
+ 
+
+ align:start position:0%
+here let's start with uh let's start
+with the third period the third row
+
+ align:start position:0%
+with the third period the third row
+ 
+
+ align:start position:0%
+with the third period the third row
+here uh sodium going across here to
+
+ align:start position:0%
+here uh sodium going across here to
+ 
+
+ align:start position:0%
+here uh sodium going across here to
+argon here's the electron configuration
+
+ align:start position:0%
+argon here's the electron configuration
+ 
+
+ align:start position:0%
+argon here's the electron configuration
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+sodium notice here that I don't mind if
+
+ align:start position:0%
+sodium notice here that I don't mind if
+ 
+
+ align:start position:0%
+sodium notice here that I don't mind if
+you write that electron configuration is
+
+ align:start position:0%
+you write that electron configuration is
+ 
+
+ align:start position:0%
+you write that electron configuration is
+2p6 instead of 2px 2py 2pz because you
+
+ align:start position:0%
+2p6 instead of 2px 2py 2pz because you
+ 
+
+ align:start position:0%
+2p6 instead of 2px 2py 2pz because you
+can't tell the difference between X Y
+
+ align:start position:0%
+can't tell the difference between X Y
+ 
+
+ align:start position:0%
+can't tell the difference between X Y
+and Z anyway if you're not in a magnetic
+
+ align:start position:0%
+and Z anyway if you're not in a magnetic
+ 
+
+ align:start position:0%
+and Z anyway if you're not in a magnetic
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+okay these electrons here in sodium that
+
+ align:start position:0%
+okay these electrons here in sodium that
+ 
+
+ align:start position:0%
+okay these electrons here in sodium that
+make up the inner gas configuration
+
+ align:start position:0%
+make up the inner gas configuration
+ 
+
+ align:start position:0%
+make up the inner gas configuration
+argon of course are the core electrons
+
+ align:start position:0%
+argon of course are the core electrons
+ 
+
+ align:start position:0%
+argon of course are the core electrons
+so when we talk about core electrons
+
+ align:start position:0%
+so when we talk about core electrons
+ 
+
+ align:start position:0%
+so when we talk about core electrons
+we're talking about the electrons that
+
+ align:start position:0%
+we're talking about the electrons that
+ 
+
+ align:start position:0%
+we're talking about the electrons that
+make up the nearest rare gas config
+
+ align:start position:0%
+make up the nearest rare gas config
+ 
+
+ align:start position:0%
+make up the nearest rare gas config
+figuration and then the veence electron
+
+ align:start position:0%
+figuration and then the veence electron
+ 
+
+ align:start position:0%
+figuration and then the veence electron
+well the veence electron is the
+
+ align:start position:0%
+well the veence electron is the
+ 
+
+ align:start position:0%
+well the veence electron is the
+electrons that are beyond the nearest uh
+
+ align:start position:0%
+electrons that are beyond the nearest uh
+ 
+
+ align:start position:0%
+electrons that are beyond the nearest uh
+the nearest but lowest of in our gas
+
+ align:start position:0%
+the nearest but lowest of in our gas
+ 
+
+ align:start position:0%
+the nearest but lowest of in our gas
+configuration
+
+ align:start position:0%
+configuration
+ 
+
+ align:start position:0%
+configuration
+okay and also when you're writing these
+
+ align:start position:0%
+okay and also when you're writing these
+ 
+
+ align:start position:0%
+okay and also when you're writing these
+electron configurations say for sodium
+
+ align:start position:0%
+electron configurations say for sodium
+ 
+
+ align:start position:0%
+electron configurations say for sodium
+you can write it as the neon
+
+ align:start position:0%
+you can write it as the neon
+ 
+
+ align:start position:0%
+you can write it as the neon
+configuration and then just show the
+
+ align:start position:0%
+configuration and then just show the
+ 
+
+ align:start position:0%
+configuration and then just show the
+veence electron
+
+ align:start position:0%
+veence electron
+ 
+
+ align:start position:0%
+veence electron
+3s1 right so as we go across that third
+
+ align:start position:0%
+3s1 right so as we go across that third
+ 
+
+ align:start position:0%
+3s1 right so as we go across that third
+period here everything things very
+
+ align:start position:0%
+period here everything things very
+ 
+
+ align:start position:0%
+period here everything things very
+normal 3s fills up first then the 3 PS
+
+ align:start position:0%
+normal 3s fills up first then the 3 PS
+ 
+
+ align:start position:0%
+normal 3s fills up first then the 3 PS
+fill
+
+ align:start position:0%
+fill
+ 
+
+ align:start position:0%
+fill
+up all right but now we get to the
+
+ align:start position:0%
+up all right but now we get to the
+ 
+
+ align:start position:0%
+up all right but now we get to the
+fourth period from pottassium to
+
+ align:start position:0%
+fourth period from pottassium to
+ 
+
+ align:start position:0%
+fourth period from pottassium to
+Krypton now fourth period what happens
+
+ align:start position:0%
+Krypton now fourth period what happens
+ 
+
+ align:start position:0%
+Krypton now fourth period what happens
+here is that those first two electrons
+
+ align:start position:0%
+here is that those first two electrons
+ 
+
+ align:start position:0%
+here is that those first two electrons
+go into the S States they do not go into
+
+ align:start position:0%
+go into the S States they do not go into
+ 
+
+ align:start position:0%
+go into the S States they do not go into
+the 3D States they don't because those S
+
+ align:start position:0%
+the 3D States they don't because those S
+ 
+
+ align:start position:0%
+the 3D States they don't because those S
+electrons are lower in energy
+
+ align:start position:0%
+electrons are lower in energy
+ 
+
+ align:start position:0%
+electrons are lower in energy
+those S states are lower in energy than
+
+ align:start position:0%
+those S states are lower in energy than
+ 
+
+ align:start position:0%
+those S states are lower in energy than
+the 3D States and so these electron
+
+ align:start position:0%
+the 3D States and so these electron
+ 
+
+ align:start position:0%
+the 3D States and so these electron
+configurations are are gone 4s1 argone
+
+ align:start position:0%
+configurations are are gone 4s1 argone
+ 
+
+ align:start position:0%
+configurations are are gone 4s1 argone
+4s2 and then once we fill those 4S
+
+ align:start position:0%
+4s2 and then once we fill those 4S
+ 
+
+ align:start position:0%
+4s2 and then once we fill those 4S
+States well then we start filling the 3D
+
+ align:start position:0%
+States well then we start filling the 3D
+ 
+
+ align:start position:0%
+States well then we start filling the 3D
+States okay so here's Scandium here's
+
+ align:start position:0%
+States okay so here's Scandium here's
+ 
+
+ align:start position:0%
+States okay so here's Scandium here's
+titanium here's
+
+ align:start position:0%
+titanium here's
+ 
+
+ align:start position:0%
+titanium here's
+vadium everything's normal 3d1 3d2 3d3
+
+ align:start position:0%
+vadium everything's normal 3d1 3d2 3d3
+ 
+
+ align:start position:0%
+vadium everything's normal 3d1 3d2 3d3
+and then we get to Crypt uh uh
+
+ align:start position:0%
+and then we get to Crypt uh uh
+ 
+
+ align:start position:0%
+and then we get to Crypt uh uh
+chromium right we have an exception here
+
+ align:start position:0%
+chromium right we have an exception here
+ 
+
+ align:start position:0%
+chromium right we have an exception here
+chromium chromium is not what you would
+
+ align:start position:0%
+chromium chromium is not what you would
+ 
+
+ align:start position:0%
+chromium chromium is not what you would
+expect chromium is 4s2 3d4medical.com
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this is experimentally observed that
+
+ align:start position:0%
+but this is experimentally observed that
+ 
+
+ align:start position:0%
+but this is experimentally observed that
+this is the configuration why because
+
+ align:start position:0%
+this is the configuration why because
+ 
+
+ align:start position:0%
+this is the configuration why because
+it's lower in energy in total energy
+
+ align:start position:0%
+it's lower in energy in total energy
+ 
+
+ align:start position:0%
+it's lower in energy in total energy
+than this configuration all right it
+
+ align:start position:0%
+than this configuration all right it
+ 
+
+ align:start position:0%
+than this configuration all right it
+turns out that there's some extra
+
+ align:start position:0%
+turns out that there's some extra
+ 
+
+ align:start position:0%
+turns out that there's some extra
+stability in having a half fill 4S shell
+
+ align:start position:0%
+stability in having a half fill 4S shell
+ 
+
+ align:start position:0%
+stability in having a half fill 4S shell
+and a half fill 3D Shell
+
+ align:start position:0%
+and a half fill 3D Shell
+ 
+
+ align:start position:0%
+and a half fill 3D Shell
+subshell compared to having a filled 4S
+
+ align:start position:0%
+subshell compared to having a filled 4S
+ 
+
+ align:start position:0%
+subshell compared to having a filled 4S
+shell and a less than half filed 3D
+
+ align:start position:0%
+shell and a less than half filed 3D
+ 
+
+ align:start position:0%
+shell and a less than half filed 3D
+Shell
+
+ align:start position:0%
+Shell
+ 
+
+ align:start position:0%
+Shell
+okay this is an exception that you do
+
+ align:start position:0%
+okay this is an exception that you do
+ 
+
+ align:start position:0%
+okay this is an exception that you do
+have to know
+
+ align:start position:0%
+have to know
+ 
+
+ align:start position:0%
+have to know
+okay okay but after chromium
+
+ align:start position:0%
+okay okay but after chromium
+ 
+
+ align:start position:0%
+okay okay but after chromium
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh manganese behaves well iron behaves
+
+ align:start position:0%
+uh manganese behaves well iron behaves
+ 
+
+ align:start position:0%
+uh manganese behaves well iron behaves
+well Cobalt okay nickel okay and now we
+
+ align:start position:0%
+well Cobalt okay nickel okay and now we
+ 
+
+ align:start position:0%
+well Cobalt okay nickel okay and now we
+get to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+copper and we got a problem it is not
+
+ align:start position:0%
+copper and we got a problem it is not
+ 
+
+ align:start position:0%
+copper and we got a problem it is not
+what you would expect it is not 4s2
+
+ align:start position:0%
+what you would expect it is not 4s2
+ 
+
+ align:start position:0%
+what you would expect it is not 4s2
+3d9 and instead it's 4s1
+
+ align:start position:0%
+3d9 and instead it's 4s1
+ 
+
+ align:start position:0%
+3d9 and instead it's 4s1
+3d10 okay again this
+
+ align:start position:0%
+3d10 okay again this
+ 
+
+ align:start position:0%
+3d10 okay again this
+configuration is something you couldn't
+
+ align:start position:0%
+configuration is something you couldn't
+ 
+
+ align:start position:0%
+configuration is something you couldn't
+have predicted a priori if you do a
+
+ align:start position:0%
+have predicted a priori if you do a
+ 
+
+ align:start position:0%
+have predicted a priori if you do a
+sophisticated calculation you can see it
+
+ align:start position:0%
+sophisticated calculation you can see it
+ 
+
+ align:start position:0%
+sophisticated calculation you can see it
+but this is also experimentally observed
+
+ align:start position:0%
+but this is also experimentally observed
+ 
+
+ align:start position:0%
+but this is also experimentally observed
+we know this to be the configuration
+
+ align:start position:0%
+we know this to be the configuration
+ 
+
+ align:start position:0%
+we know this to be the configuration
+this is not the
+
+ align:start position:0%
+this is not the
+ 
+
+ align:start position:0%
+this is not the
+configuration all
+
+ align:start position:0%
+configuration all
+ 
+
+ align:start position:0%
+configuration all
+right this is the lower energy
+
+ align:start position:0%
+right this is the lower energy
+ 
+
+ align:start position:0%
+right this is the lower energy
+configuration here's another exception
+
+ align:start position:0%
+configuration here's another exception
+ 
+
+ align:start position:0%
+configuration here's another exception
+that you have to know no
+
+ align:start position:0%
+that you have to know no
+ 
+
+ align:start position:0%
+that you have to know no
+copper
+
+ align:start position:0%
+copper
+ 
+
+ align:start position:0%
+copper
+right okay and then after copper here to
+
+ align:start position:0%
+right okay and then after copper here to
+ 
+
+ align:start position:0%
+right okay and then after copper here to
+zinc Things become follow a pattern
+
+ align:start position:0%
+zinc Things become follow a pattern
+ 
+
+ align:start position:0%
+zinc Things become follow a pattern
+again the next electron then just fills
+
+ align:start position:0%
+again the next electron then just fills
+ 
+
+ align:start position:0%
+again the next electron then just fills
+up the 4s2
+
+ align:start position:0%
+up the 4s2
+ 
+
+ align:start position:0%
+up the 4s2
+3d10 now at gallium all of those are
+
+ align:start position:0%
+3d10 now at gallium all of those are
+ 
+
+ align:start position:0%
+3d10 now at gallium all of those are
+filled we start filling up the four P
+
+ align:start position:0%
+filled we start filling up the four P
+ 
+
+ align:start position:0%
+filled we start filling up the four P
+States all right and everything's fine
+
+ align:start position:0%
+States all right and everything's fine
+ 
+
+ align:start position:0%
+States all right and everything's fine
+until we as we get to Krypton all
+
+ align:start position:0%
+until we as we get to Krypton all
+ 
+
+ align:start position:0%
+until we as we get to Krypton all
+right so you got to know chromium and
+
+ align:start position:0%
+right so you got to know chromium and
+ 
+
+ align:start position:0%
+right so you got to know chromium and
+copper
+
+ align:start position:0%
+copper
+ 
+
+ align:start position:0%
+copper
+now the fifth row here starting with
+
+ align:start position:0%
+now the fifth row here starting with
+ 
+
+ align:start position:0%
+now the fifth row here starting with
+rubidium strum urbium zirconium Etc all
+
+ align:start position:0%
+rubidium strum urbium zirconium Etc all
+ 
+
+ align:start position:0%
+rubidium strum urbium zirconium Etc all
+the way across
+
+ align:start position:0%
+the way across
+ 
+
+ align:start position:0%
+the way across
+here well starting with uh
+
+ align:start position:0%
+here well starting with uh
+ 
+
+ align:start position:0%
+here well starting with uh
+rubidium again the electrons go into the
+
+ align:start position:0%
+rubidium again the electrons go into the
+ 
+
+ align:start position:0%
+rubidium again the electrons go into the
+5S shell they don't go into the 4D and
+
+ align:start position:0%
+5S shell they don't go into the 4D and
+ 
+
+ align:start position:0%
+5S shell they don't go into the 4D and
+that's because with rubidium and
+
+ align:start position:0%
+that's because with rubidium and
+ 
+
+ align:start position:0%
+that's because with rubidium and
+strum 5S is actually lower than 4D
+
+ align:start position:0%
+strum 5S is actually lower than 4D
+ 
+
+ align:start position:0%
+strum 5S is actually lower than 4D
+and it's only once you fill up the 5S
+
+ align:start position:0%
+and it's only once you fill up the 5S
+ 
+
+ align:start position:0%
+and it's only once you fill up the 5S
+states that you start filling up the 4D
+
+ align:start position:0%
+states that you start filling up the 4D
+ 
+
+ align:start position:0%
+states that you start filling up the 4D
+States right here all
+
+ align:start position:0%
+States right here all
+ 
+
+ align:start position:0%
+States right here all
+right now there are exceptions along
+
+ align:start position:0%
+right now there are exceptions along
+ 
+
+ align:start position:0%
+right now there are exceptions along
+this fifth row and the two
+
+ align:start position:0%
+this fifth row and the two
+ 
+
+ align:start position:0%
+this fifth row and the two
+exceptions malum and silver are the same
+
+ align:start position:0%
+exceptions malum and silver are the same
+ 
+
+ align:start position:0%
+exceptions malum and silver are the same
+kind of exceptions as chromium and
+
+ align:start position:0%
+kind of exceptions as chromium and
+ 
+
+ align:start position:0%
+kind of exceptions as chromium and
+copper all right you have to know the
+
+ align:start position:0%
+copper all right you have to know the
+ 
+
+ align:start position:0%
+copper all right you have to know the
+exceptions for silver silver and copper
+
+ align:start position:0%
+exceptions for silver silver and copper
+ 
+
+ align:start position:0%
+exceptions for silver silver and copper
+and maliban and chromium all right the
+
+ align:start position:0%
+and maliban and chromium all right the
+ 
+
+ align:start position:0%
+and maliban and chromium all right the
+same identical kind of exception as in
+
+ align:start position:0%
+same identical kind of exception as in
+ 
+
+ align:start position:0%
+same identical kind of exception as in
+the fourth row here there are other
+
+ align:start position:0%
+the fourth row here there are other
+ 
+
+ align:start position:0%
+the fourth row here there are other
+exceptions along this fifth row you
+
+ align:start position:0%
+exceptions along this fifth row you
+ 
+
+ align:start position:0%
+exceptions along this fifth row you
+don't have to know those there's really
+
+ align:start position:0%
+don't have to know those there's really
+ 
+
+ align:start position:0%
+don't have to know those there's really
+no way a priori for you to know that
+
+ align:start position:0%
+no way a priori for you to know that
+ 
+
+ align:start position:0%
+no way a priori for you to know that
+again it's an experimental observation a
+
+ align:start position:0%
+again it's an experimental observation a
+ 
+
+ align:start position:0%
+again it's an experimental observation a
+sophisticated hard calculation will also
+
+ align:start position:0%
+sophisticated hard calculation will also
+ 
+
+ align:start position:0%
+sophisticated hard calculation will also
+show that all right
+
+ align:start position:0%
+show that all right
+ 
+
+ align:start position:0%
+show that all right
+okay and then once you're done with
+
+ align:start position:0%
+okay and then once you're done with
+ 
+
+ align:start position:0%
+okay and then once you're done with
+cadmium well then the 5ps start filling
+
+ align:start position:0%
+cadmium well then the 5ps start filling
+ 
+
+ align:start position:0%
+cadmium well then the 5ps start filling
+and everything's normal and you get to
+
+ align:start position:0%
+and everything's normal and you get to
+ 
+
+ align:start position:0%
+and everything's normal and you get to
+the Xenon inner gas
+
+ align:start position:0%
+the Xenon inner gas
+ 
+
+ align:start position:0%
+the Xenon inner gas
+configuration
+
+ align:start position:0%
+configuration
+ 
+
+ align:start position:0%
+configuration
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay now how do you uh remember
+
+ align:start position:0%
+okay okay now how do you uh remember
+ 
+
+ align:start position:0%
+okay okay now how do you uh remember
+what the ordering is of these uh States
+
+ align:start position:0%
+what the ordering is of these uh States
+ 
+
+ align:start position:0%
+what the ordering is of these uh States
+the energy ordering well here's a
+
+ align:start position:0%
+the energy ordering well here's a
+ 
+
+ align:start position:0%
+the energy ordering well here's a
+pneumonic that
+
+ align:start position:0%
+pneumonic that
+ 
+
+ align:start position:0%
+pneumonic that
+maybe some of you have uh seen
+
+ align:start position:0%
+maybe some of you have uh seen
+ 
+
+ align:start position:0%
+maybe some of you have uh seen
+before but uh start out write one s then
+
+ align:start position:0%
+before but uh start out write one s then
+ 
+
+ align:start position:0%
+before but uh start out write one s then
+write 2 s right below it and then 2 p to
+
+ align:start position:0%
+write 2 s right below it and then 2 p to
+ 
+
+ align:start position:0%
+write 2 s right below it and then 2 p to
+the side of it and then write 3s 3p
+
+ align:start position:0%
+the side of it and then write 3s 3p
+ 
+
+ align:start position:0%
+the side of it and then write 3s 3p
+3D and then write 4S 4 P 4D
+
+ align:start position:0%
+3D and then write 4S 4 P 4D
+ 
+
+ align:start position:0%
+3D and then write 4S 4 P 4D
+4f and then write 5S 5 P 5D 5f and 6s 6
+
+ align:start position:0%
+4f and then write 5S 5 P 5D 5f and 6s 6
+ 
+
+ align:start position:0%
+4f and then write 5S 5 P 5D 5f and 6s 6
+P 6D and 7s
+
+ align:start position:0%
+P 6D and 7s
+ 
+
+ align:start position:0%
+P 6D and 7s
+7p and now to get the energy ordering
+
+ align:start position:0%
+7p and now to get the energy ordering
+ 
+
+ align:start position:0%
+7p and now to get the energy ordering
+we're going to draw diagonals well first
+
+ align:start position:0%
+we're going to draw diagonals well first
+ 
+
+ align:start position:0%
+we're going to draw diagonals well first
+of all the 1 s is the lowest energy
+
+ align:start position:0%
+of all the 1 s is the lowest energy
+ 
+
+ align:start position:0%
+of all the 1 s is the lowest energy
+State and then the next highest energy
+
+ align:start position:0%
+State and then the next highest energy
+ 
+
+ align:start position:0%
+State and then the next highest energy
+state is the 2s
+
+ align:start position:0%
+state is the 2s
+ 
+
+ align:start position:0%
+state is the 2s
+State and then the next highest energy
+
+ align:start position:0%
+State and then the next highest energy
+ 
+
+ align:start position:0%
+State and then the next highest energy
+state is the 2p so we're going to draw a
+
+ align:start position:0%
+state is the 2p so we're going to draw a
+ 
+
+ align:start position:0%
+state is the 2p so we're going to draw a
+diagonal so the next state to fill is 2p
+
+ align:start position:0%
+diagonal so the next state to fill is 2p
+ 
+
+ align:start position:0%
+diagonal so the next state to fill is 2p
+the next one is
+
+ align:start position:0%
+the next one is
+ 
+
+ align:start position:0%
+the next one is
+3s now we're going to draw a diagonal
+
+ align:start position:0%
+3s now we're going to draw a diagonal
+ 
+
+ align:start position:0%
+3s now we're going to draw a diagonal
+again the next one to fill is
+
+ align:start position:0%
+again the next one to fill is
+ 
+
+ align:start position:0%
+again the next one to fill is
+3p the next one to fill is
+
+ align:start position:0%
+3p the next one to fill is
+ 
+
+ align:start position:0%
+3p the next one to fill is
+4S draw another diagonal next one to
+
+ align:start position:0%
+4S draw another diagonal next one to
+ 
+
+ align:start position:0%
+4S draw another diagonal next one to
+fill is 3D 4 P
+
+ align:start position:0%
+fill is 3D 4 P
+ 
+
+ align:start position:0%
+fill is 3D 4 P
+5S 4D 5p 6s 4f 5D 6p 7s 5S 6D 7p and
+
+ align:start position:0%
+5S 4D 5p 6s 4f 5D 6p 7s 5S 6D 7p and
+ 
+
+ align:start position:0%
+5S 4D 5p 6s 4f 5D 6p 7s 5S 6D 7p and
+that's all that's going to be important
+
+ align:start position:0%
+that's all that's going to be important
+ 
+
+ align:start position:0%
+that's all that's going to be important
+all right so that's one way to remember
+
+ align:start position:0%
+all right so that's one way to remember
+ 
+
+ align:start position:0%
+all right so that's one way to remember
+the relative energy orderings here and
+
+ align:start position:0%
+the relative energy orderings here and
+ 
+
+ align:start position:0%
+the relative energy orderings here and
+you do have to be able to write this
+
+ align:start position:0%
+you do have to be able to write this
+ 
+
+ align:start position:0%
+you do have to be able to write this
+down on an exam okay without you'll have
+
+ align:start position:0%
+down on an exam okay without you'll have
+ 
+
+ align:start position:0%
+down on an exam okay without you'll have
+a periodic table but it won't have the
+
+ align:start position:0%
+a periodic table but it won't have the
+ 
+
+ align:start position:0%
+a periodic table but it won't have the
+electron configurations on it okay
+
+ align:start position:0%
+electron configurations on it okay
+ 
+
+ align:start position:0%
+electron configurations on it okay
+okay now I want to tell you something
+
+ align:start position:0%
+okay now I want to tell you something
+ 
+
+ align:start position:0%
+okay now I want to tell you something
+that uh sometimes people find uh a
+
+ align:start position:0%
+that uh sometimes people find uh a
+ 
+
+ align:start position:0%
+that uh sometimes people find uh a
+little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+confusing and that is uh the electron
+
+ align:start position:0%
+confusing and that is uh the electron
+ 
+
+ align:start position:0%
+confusing and that is uh the electron
+configuration of
+
+ align:start position:0%
+configuration of
+ 
+
+ align:start position:0%
+configuration of
+ions what I'm about to say has no effect
+
+ align:start position:0%
+ions what I'm about to say has no effect
+ 
+
+ align:start position:0%
+ions what I'm about to say has no effect
+on what I just said about how to write
+
+ align:start position:0%
+on what I just said about how to write
+ 
+
+ align:start position:0%
+on what I just said about how to write
+the electron configuration for
+
+ align:start position:0%
+the electron configuration for
+ 
+
+ align:start position:0%
+the electron configuration for
+neutrals okay this does not affect
+
+ align:start position:0%
+neutrals okay this does not affect
+ 
+
+ align:start position:0%
+neutrals okay this does not affect
+anything in your writing down the
+
+ align:start position:0%
+anything in your writing down the
+ 
+
+ align:start position:0%
+anything in your writing down the
+electron configuration for neutrals this
+
+ align:start position:0%
+electron configuration for neutrals this
+ 
+
+ align:start position:0%
+electron configuration for neutrals this
+is for
+
+ align:start position:0%
+is for
+ 
+
+ align:start position:0%
+is for
+ions okay but the point I want to make
+
+ align:start position:0%
+ions okay but the point I want to make
+ 
+
+ align:start position:0%
+ions okay but the point I want to make
+is that if you actually look at the
+
+ align:start position:0%
+is that if you actually look at the
+ 
+
+ align:start position:0%
+is that if you actually look at the
+energies of the individual 3D States and
+
+ align:start position:0%
+energies of the individual 3D States and
+ 
+
+ align:start position:0%
+energies of the individual 3D States and
+4S States
+
+ align:start position:0%
+4S States
+ 
+
+ align:start position:0%
+4S States
+across that fourth row this is what they
+
+ align:start position:0%
+across that fourth row this is what they
+ 
+
+ align:start position:0%
+across that fourth row this is what they
+look like so for
+
+ align:start position:0%
+look like so for
+ 
+
+ align:start position:0%
+look like so for
+example at pottassium that 4S state is
+
+ align:start position:0%
+example at pottassium that 4S state is
+ 
+
+ align:start position:0%
+example at pottassium that 4S state is
+lower in energy than the 3D State that's
+
+ align:start position:0%
+lower in energy than the 3D State that's
+ 
+
+ align:start position:0%
+lower in energy than the 3D State that's
+why we put the electron in the 4S State
+
+ align:start position:0%
+why we put the electron in the 4S State
+ 
+
+ align:start position:0%
+why we put the electron in the 4S State
+when we wrote the
+
+ align:start position:0%
+when we wrote the
+ 
+
+ align:start position:0%
+when we wrote the
+neutral and the same thing for calcium
+
+ align:start position:0%
+neutral and the same thing for calcium
+ 
+
+ align:start position:0%
+neutral and the same thing for calcium
+that's why we put that electron into the
+
+ align:start position:0%
+that's why we put that electron into the
+ 
+
+ align:start position:0%
+that's why we put that electron into the
+4S State and not the 3s
+
+ align:start position:0%
+4S State and not the 3s
+ 
+
+ align:start position:0%
+4S State and not the 3s
+state but lo and behold right here at
+
+ align:start position:0%
+state but lo and behold right here at
+ 
+
+ align:start position:0%
+state but lo and behold right here at
+Scandium Z equal
+
+ align:start position:0%
+Scandium Z equal
+ 
+
+ align:start position:0%
+Scandium Z equal
+21 what happens is that the 3D State
+
+ align:start position:0%
+21 what happens is that the 3D State
+ 
+
+ align:start position:0%
+21 what happens is that the 3D State
+actually drops below an energy than the
+
+ align:start position:0%
+actually drops below an energy than the
+ 
+
+ align:start position:0%
+actually drops below an energy than the
+4S State these are the energies of the
+
+ align:start position:0%
+4S State these are the energies of the
+ 
+
+ align:start position:0%
+4S State these are the energies of the
+individual State now
+
+ align:start position:0%
+individual State now
+ 
+
+ align:start position:0%
+individual State now
+okay and that continues all the way
+
+ align:start position:0%
+okay and that continues all the way
+ 
+
+ align:start position:0%
+okay and that continues all the way
+across the periodic
+
+ align:start position:0%
+across the periodic
+ 
+
+ align:start position:0%
+across the periodic
+table however that does not affect how
+
+ align:start position:0%
+table however that does not affect how
+ 
+
+ align:start position:0%
+table however that does not affect how
+you write the electron configuration of
+
+ align:start position:0%
+you write the electron configuration of
+ 
+
+ align:start position:0%
+you write the electron configuration of
+the neutrals so so for example if you're
+
+ align:start position:0%
+the neutrals so so for example if you're
+ 
+
+ align:start position:0%
+the neutrals so so for example if you're
+writing the electron configuration for
+
+ align:start position:0%
+writing the electron configuration for
+ 
+
+ align:start position:0%
+writing the electron configuration for
+titanium here it is it's the Argon core
+
+ align:start position:0%
+titanium here it is it's the Argon core
+ 
+
+ align:start position:0%
+titanium here it is it's the Argon core
+4s2
+
+ align:start position:0%
+4s2
+ 
+
+ align:start position:0%
+4s2
+3d2 okay and by the way I don't care
+
+ align:start position:0%
+3d2 okay and by the way I don't care
+ 
+
+ align:start position:0%
+3d2 okay and by the way I don't care
+whether you write 3d2 4s2 or 4s2
+
+ align:start position:0%
+whether you write 3d2 4s2 or 4s2
+ 
+
+ align:start position:0%
+whether you write 3d2 4s2 or 4s2
+3d2 okay you can write them in either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order all right now you might say well
+
+ align:start position:0%
+order all right now you might say well
+ 
+
+ align:start position:0%
+order all right now you might say well
+why is this the electron configuration
+
+ align:start position:0%
+why is this the electron configuration
+ 
+
+ align:start position:0%
+why is this the electron configuration
+if at this value for z z equal 22
+
+ align:start position:0%
+if at this value for z z equal 22
+ 
+
+ align:start position:0%
+if at this value for z z equal 22
+titanium the 3D state is lower than the
+
+ align:start position:0%
+titanium the 3D state is lower than the
+ 
+
+ align:start position:0%
+titanium the 3D state is lower than the
+4S State why don't these 4S electrons
+
+ align:start position:0%
+4S State why don't these 4S electrons
+ 
+
+ align:start position:0%
+4S State why don't these 4S electrons
+just hop into the 3D
+
+ align:start position:0%
+just hop into the 3D
+ 
+
+ align:start position:0%
+just hop into the 3D
+States well they don't do that they
+
+ align:start position:0%
+States well they don't do that they
+ 
+
+ align:start position:0%
+States well they don't do that they
+don't do that because this electron
+
+ align:start position:0%
+don't do that because this electron
+ 
+
+ align:start position:0%
+don't do that because this electron
+configuration actually minimizes the
+
+ align:start position:0%
+configuration actually minimizes the
+ 
+
+ align:start position:0%
+configuration actually minimizes the
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+repulsions if these four electrons were
+
+ align:start position:0%
+repulsions if these four electrons were
+ 
+
+ align:start position:0%
+repulsions if these four electrons were
+in the 3D
+
+ align:start position:0%
+in the 3D
+ 
+
+ align:start position:0%
+in the 3D
+State well then the repulsive
+
+ align:start position:0%
+State well then the repulsive
+ 
+
+ align:start position:0%
+State well then the repulsive
+interactions would be greater because
+
+ align:start position:0%
+interactions would be greater because
+ 
+
+ align:start position:0%
+interactions would be greater because
+they're in the same state
+
+ align:start position:0%
+they're in the same state
+ 
+
+ align:start position:0%
+they're in the same state
+now and therefore the entire energy of
+
+ align:start position:0%
+now and therefore the entire energy of
+ 
+
+ align:start position:0%
+now and therefore the entire energy of
+the of the atom will be larger all right
+
+ align:start position:0%
+the of the atom will be larger all right
+ 
+
+ align:start position:0%
+the of the atom will be larger all right
+and it is the entire energy the the
+
+ align:start position:0%
+and it is the entire energy the the
+ 
+
+ align:start position:0%
+and it is the entire energy the the
+total energy of the atom that's
+
+ align:start position:0%
+total energy of the atom that's
+ 
+
+ align:start position:0%
+total energy of the atom that's
+important when we look at the electron
+
+ align:start position:0%
+important when we look at the electron
+ 
+
+ align:start position:0%
+important when we look at the electron
+configurations in this particular case
+
+ align:start position:0%
+configurations in this particular case
+ 
+
+ align:start position:0%
+configurations in this particular case
+if we look at the individual D States
+
+ align:start position:0%
+if we look at the individual D States
+ 
+
+ align:start position:0%
+if we look at the individual D States
+and the four S States yeah the D states
+
+ align:start position:0%
+and the four S States yeah the D states
+ 
+
+ align:start position:0%
+and the four S States yeah the D states
+are lower in
+
+ align:start position:0%
+are lower in
+ 
+
+ align:start position:0%
+are lower in
+energy but what's important is when we
+
+ align:start position:0%
+energy but what's important is when we
+ 
+
+ align:start position:0%
+energy but what's important is when we
+sum up all of the energies of the
+
+ align:start position:0%
+sum up all of the energies of the
+ 
+
+ align:start position:0%
+sum up all of the energies of the
+interactions what is lower and what I'm
+
+ align:start position:0%
+interactions what is lower and what I'm
+ 
+
+ align:start position:0%
+interactions what is lower and what I'm
+saying to you is that when we do that
+
+ align:start position:0%
+saying to you is that when we do that
+ 
+
+ align:start position:0%
+saying to you is that when we do that
+when we sum up all of the interaction
+
+ align:start position:0%
+when we sum up all of the interaction
+ 
+
+ align:start position:0%
+when we sum up all of the interaction
+energies this still is the lower energy
+
+ align:start position:0%
+energies this still is the lower energy
+ 
+
+ align:start position:0%
+energies this still is the lower energy
+configuration even though the 3D
+
+ align:start position:0%
+configuration even though the 3D
+ 
+
+ align:start position:0%
+configuration even though the 3D
+electrons at this value of Z are those
+
+ align:start position:0%
+electrons at this value of Z are those
+ 
+
+ align:start position:0%
+electrons at this value of Z are those
+3D states are lower and energy than the
+
+ align:start position:0%
+3D states are lower and energy than the
+ 
+
+ align:start position:0%
+3D states are lower and energy than the
+4S States okay so that's why we don't
+
+ align:start position:0%
+4S States okay so that's why we don't
+ 
+
+ align:start position:0%
+4S States okay so that's why we don't
+have this hopping over into the 3D
+
+ align:start position:0%
+have this hopping over into the 3D
+ 
+
+ align:start position:0%
+have this hopping over into the 3D
+States for the
+
+ align:start position:0%
+States for the
+ 
+
+ align:start position:0%
+States for the
+neutral but now here comes the ion
+
+ align:start position:0%
+neutral but now here comes the ion
+ 
+
+ align:start position:0%
+neutral but now here comes the ion
+configuration if you have this
+
+ align:start position:0%
+configuration if you have this
+ 
+
+ align:start position:0%
+configuration if you have this
+configuration for the
+
+ align:start position:0%
+configuration for the
+ 
+
+ align:start position:0%
+configuration for the
+neutral and now you ionize titanium to
+
+ align:start position:0%
+neutral and now you ionize titanium to
+ 
+
+ align:start position:0%
+neutral and now you ionize titanium to
+make titanium
+
+ align:start position:0%
+make titanium
+ 
+
+ align:start position:0%
+make titanium
+plus the electron configuration is argon
+
+ align:start position:0%
+plus the electron configuration is argon
+ 
+
+ align:start position:0%
+plus the electron configuration is argon
+3d2 that that is it's the 4S electrons
+
+ align:start position:0%
+3d2 that that is it's the 4S electrons
+ 
+
+ align:start position:0%
+3d2 that that is it's the 4S electrons
+that come off that are plucked out right
+
+ align:start position:0%
+that come off that are plucked out right
+ 
+
+ align:start position:0%
+that come off that are plucked out right
+they're plucked out because they're the
+
+ align:start position:0%
+they're plucked out because they're the
+ 
+
+ align:start position:0%
+they're plucked out because they're the
+higher energy electrons
+
+ align:start position:0%
+higher energy electrons
+ 
+
+ align:start position:0%
+higher energy electrons
+now okay so this is the electron
+
+ align:start position:0%
+now okay so this is the electron
+ 
+
+ align:start position:0%
+now okay so this is the electron
+configuration for titanium plus 2 so
+
+ align:start position:0%
+configuration for titanium plus 2 so
+ 
+
+ align:start position:0%
+configuration for titanium plus 2 so
+we're going to pull out those higher
+
+ align:start position:0%
+we're going to pull out those higher
+ 
+
+ align:start position:0%
+we're going to pull out those higher
+energy electrons which are the 4S
+
+ align:start position:0%
+energy electrons which are the 4S
+ 
+
+ align:start position:0%
+energy electrons which are the 4S
+electrons and again this affects only
+
+ align:start position:0%
+electrons and again this affects only
+ 
+
+ align:start position:0%
+electrons and again this affects only
+the ion configuration
+
+ align:start position:0%
+the ion configuration
+ 
+
+ align:start position:0%
+the ion configuration
+same thing happens here on the fifth
+
+ align:start position:0%
+same thing happens here on the fifth
+ 
+
+ align:start position:0%
+same thing happens here on the fifth
+Row the fifth row starting here with
+
+ align:start position:0%
+Row the fifth row starting here with
+ 
+
+ align:start position:0%
+Row the fifth row starting here with
+rubidium and
+
+ align:start position:0%
+rubidium and
+ 
+
+ align:start position:0%
+rubidium and
+strum 5S is lower in energy than 4D
+
+ align:start position:0%
+strum 5S is lower in energy than 4D
+ 
+
+ align:start position:0%
+strum 5S is lower in energy than 4D
+that's why that rubidium electron went
+
+ align:start position:0%
+that's why that rubidium electron went
+ 
+
+ align:start position:0%
+that's why that rubidium electron went
+in the 5S State same thing with the
+
+ align:start position:0%
+in the 5S State same thing with the
+ 
+
+ align:start position:0%
+in the 5S State same thing with the
+strum electron went in the 5S state but
+
+ align:start position:0%
+strum electron went in the 5S state but
+ 
+
+ align:start position:0%
+strum electron went in the 5S state but
+right here at
+
+ align:start position:0%
+right here at
+ 
+
+ align:start position:0%
+right here at
+ubium the 4D State goes Below in energy
+
+ align:start position:0%
+ubium the 4D State goes Below in energy
+ 
+
+ align:start position:0%
+ubium the 4D State goes Below in energy
+the 5S
+
+ align:start position:0%
+the 5S
+ 
+
+ align:start position:0%
+the 5S
+State again that does not affect how you
+
+ align:start position:0%
+State again that does not affect how you
+ 
+
+ align:start position:0%
+State again that does not affect how you
+write the electron configuration of the
+
+ align:start position:0%
+write the electron configuration of the
+ 
+
+ align:start position:0%
+write the electron configuration of the
+neutral so for
+
+ align:start position:0%
+neutral so for
+ 
+
+ align:start position:0%
+neutral so for
+example silver which is way out here and
+
+ align:start position:0%
+example silver which is way out here and
+ 
+
+ align:start position:0%
+example silver which is way out here and
+which is one of those
+
+ align:start position:0%
+which is one of those
+ 
+
+ align:start position:0%
+which is one of those
+exceptions okay silver if you ionize it
+
+ align:start position:0%
+exceptions okay silver if you ionize it
+ 
+
+ align:start position:0%
+exceptions okay silver if you ionize it
+if you pluck off an electron from Silver
+
+ align:start position:0%
+if you pluck off an electron from Silver
+ 
+
+ align:start position:0%
+if you pluck off an electron from Silver
+which electron is going to go 5s and so
+
+ align:start position:0%
+which electron is going to go 5s and so
+ 
+
+ align:start position:0%
+which electron is going to go 5s and so
+the tip silver plus one electron
+
+ align:start position:0%
+the tip silver plus one electron
+ 
+
+ align:start position:0%
+the tip silver plus one electron
+configuration is the Krypton core 4 d10
+
+ align:start position:0%
+configuration is the Krypton core 4 d10
+ 
+
+ align:start position:0%
+configuration is the Krypton core 4 d10
+it's that 5S electron that's going to uh
+
+ align:start position:0%
+it's that 5S electron that's going to uh
+ 
+
+ align:start position:0%
+it's that 5S electron that's going to uh
+disappear okay so this is important
+
+ align:start position:0%
+disappear okay so this is important
+ 
+
+ align:start position:0%
+disappear okay so this is important
+don't let it confuse you with the
+
+ align:start position:0%
+don't let it confuse you with the
+ 
+
+ align:start position:0%
+don't let it confuse you with the
+writing the electron configurations of
+
+ align:start position:0%
+writing the electron configurations of
+ 
+
+ align:start position:0%
+writing the electron configurations of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+neutrals all
+
+ align:start position:0%
+neutrals all
+ 
+
+ align:start position:0%
+neutrals all
+right okie
+
+ align:start position:0%
+right okie
+ 
+
+ align:start position:0%
+right okie
+dokie see you Friday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
\ No newline at end of file
diff --git a/KXof0q88xbg.txt b/KXof0q88xbg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a1543065f1883bee7eb0110bd75793661631efa6
--- /dev/null
+++ b/KXof0q88xbg.txt
@@ -0,0 +1,1643 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+what I'd like you to do is use Green's
+
+ align:start position:0%
+what I'd like you to do is use Green's
+ 
+
+ align:start position:0%
+what I'd like you to do is use Green's
+theorem to find the area between one
+
+ align:start position:0%
+theorem to find the area between one
+ 
+
+ align:start position:0%
+theorem to find the area between one
+arch of the cyllid that is described by
+
+ align:start position:0%
+arch of the cyllid that is described by
+ 
+
+ align:start position:0%
+arch of the cyllid that is described by
+x = a * thean thetus sin Theta y = a *
+
+ align:start position:0%
+x = a * thean thetus sin Theta y = a *
+ 
+
+ align:start position:0%
+x = a * thean thetus sin Theta y = a *
+thean 1 - cosine Theta and the x-axis so
+
+ align:start position:0%
+thean 1 - cosine Theta and the x-axis so
+ 
+
+ align:start position:0%
+thean 1 - cosine Theta and the x-axis so
+probably it's helpful for you to draw a
+
+ align:start position:0%
+probably it's helpful for you to draw a
+ 
+
+ align:start position:0%
+probably it's helpful for you to draw a
+picture of this first so you have one
+
+ align:start position:0%
+picture of this first so you have one
+ 
+
+ align:start position:0%
+picture of this first so you have one
+arch of the C
+
+ align:start position:0%
+arch of the C
+ 
+
+ align:start position:0%
+arch of the C
+defined uh in terms of theta the X the x
+
+ align:start position:0%
+defined uh in terms of theta the X the x
+ 
+
+ align:start position:0%
+defined uh in terms of theta the X the x
+of theta and Y of theta are here and
+
+ align:start position:0%
+of theta and Y of theta are here and
+ 
+
+ align:start position:0%
+of theta and Y of theta are here and
+then the x axis will be the other bound
+
+ align:start position:0%
+then the x axis will be the other bound
+ 
+
+ align:start position:0%
+then the x axis will be the other bound
+and the big thing I want you to notice
+
+ align:start position:0%
+and the big thing I want you to notice
+ 
+
+ align:start position:0%
+and the big thing I want you to notice
+is you're going to use Green's theorem
+
+ align:start position:0%
+is you're going to use Green's theorem
+ 
+
+ align:start position:0%
+is you're going to use Green's theorem
+to find the area so why don't you pause
+
+ align:start position:0%
+to find the area so why don't you pause
+ 
+
+ align:start position:0%
+to find the area so why don't you pause
+the video work on the problem when
+
+ align:start position:0%
+the video work on the problem when
+ 
+
+ align:start position:0%
+the video work on the problem when
+you're ready to see my solution you can
+
+ align:start position:0%
+you're ready to see my solution you can
+ 
+
+ align:start position:0%
+you're ready to see my solution you can
+bring the video back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up okay welcome back so again what we
+
+ align:start position:0%
+up okay welcome back so again what we
+ 
+
+ align:start position:0%
+up okay welcome back so again what we
+want to do is we want to use green
+
+ align:start position:0%
+want to do is we want to use green
+ 
+
+ align:start position:0%
+want to do is we want to use green
+theorem to find an area okay and what
+
+ align:start position:0%
+theorem to find an area okay and what
+ 
+
+ align:start position:0%
+theorem to find an area okay and what
+I'm going to do first is I'm going to
+
+ align:start position:0%
+I'm going to do first is I'm going to
+ 
+
+ align:start position:0%
+I'm going to do first is I'm going to
+try and figure out what the picture
+
+ align:start position:0%
+try and figure out what the picture
+ 
+
+ align:start position:0%
+try and figure out what the picture
+looks like and then I'm going to figure
+
+ align:start position:0%
+looks like and then I'm going to figure
+ 
+
+ align:start position:0%
+looks like and then I'm going to figure
+out how to use green theorem in this in
+
+ align:start position:0%
+out how to use green theorem in this in
+ 
+
+ align:start position:0%
+out how to use green theorem in this in
+this region okay so let's first draw a
+
+ align:start position:0%
+this region okay so let's first draw a
+ 
+
+ align:start position:0%
+this region okay so let's first draw a
+sketch of the picture of what's going on
+
+ align:start position:0%
+sketch of the picture of what's going on
+ 
+
+ align:start position:0%
+sketch of the picture of what's going on
+and because I want the area between one
+
+ align:start position:0%
+and because I want the area between one
+ 
+
+ align:start position:0%
+and because I want the area between one
+arch of the cyllid and the x-axis what I
+
+ align:start position:0%
+arch of the cyllid and the x-axis what I
+ 
+
+ align:start position:0%
+arch of the cyllid and the x-axis what I
+really want to do first is figure out um
+
+ align:start position:0%
+really want to do first is figure out um
+ 
+
+ align:start position:0%
+really want to do first is figure out um
+what y value what Theta values will make
+
+ align:start position:0%
+what y value what Theta values will make
+ 
+
+ align:start position:0%
+what y value what Theta values will make
+y positive or greater than or equal to
+
+ align:start position:0%
+y positive or greater than or equal to
+ 
+
+ align:start position:0%
+y positive or greater than or equal to
+zero and go for from there so if I want
+
+ align:start position:0%
+zero and go for from there so if I want
+ 
+
+ align:start position:0%
+zero and go for from there so if I want
+y to be greater than or equal to
+
+ align:start position:0%
+y to be greater than or equal to
+ 
+
+ align:start position:0%
+y to be greater than or equal to
+zero then what I need is 1 - cosine
+
+ align:start position:0%
+zero then what I need is 1 - cosine
+ 
+
+ align:start position:0%
+zero then what I need is 1 - cosine
+Theta to be greater than or equal to
+
+ align:start position:0%
+Theta to be greater than or equal to
+ 
+
+ align:start position:0%
+Theta to be greater than or equal to
+zero okay and that's going to happen for
+
+ align:start position:0%
+zero okay and that's going to happen for
+ 
+
+ align:start position:0%
+zero okay and that's going to happen for
+every Theta from 0 to 2 pi and at0 and 2
+
+ align:start position:0%
+every Theta from 0 to 2 pi and at0 and 2
+ 
+
+ align:start position:0%
+every Theta from 0 to 2 pi and at0 and 2
+pi I get zero so we know we want Theta
+
+ align:start position:0%
+pi I get zero so we know we want Theta
+ 
+
+ align:start position:0%
+pi I get zero so we know we want Theta
+to go between 0o and 2
+
+ align:start position:0%
+to go between 0o and 2
+ 
+
+ align:start position:0%
+to go between 0o and 2
+pi that that's a good those are good
+
+ align:start position:0%
+pi that that's a good those are good
+ 
+
+ align:start position:0%
+pi that that's a good those are good
+parameters to have for Theta because
+
+ align:start position:0%
+parameters to have for Theta because
+ 
+
+ align:start position:0%
+parameters to have for Theta because
+this statement is always true but I get
+
+ align:start position:0%
+this statement is always true but I get
+ 
+
+ align:start position:0%
+this statement is always true but I get
+zero when Theta is zero and when Theta
+
+ align:start position:0%
+zero when Theta is zero and when Theta
+ 
+
+ align:start position:0%
+zero when Theta is zero and when Theta
+is 2 pi so I'm going to let Theta run
+
+ align:start position:0%
+is 2 pi so I'm going to let Theta run
+ 
+
+ align:start position:0%
+is 2 pi so I'm going to let Theta run
+between 0 and 2 pi as I mentioned okay
+
+ align:start position:0%
+between 0 and 2 pi as I mentioned okay
+ 
+
+ align:start position:0%
+between 0 and 2 pi as I mentioned okay
+so now let's think about what the
+
+ align:start position:0%
+so now let's think about what the
+ 
+
+ align:start position:0%
+so now let's think about what the
+picture is when Theta is zero if I come
+
+ align:start position:0%
+picture is when Theta is zero if I come
+ 
+
+ align:start position:0%
+picture is when Theta is zero if I come
+over to what x
+
+ align:start position:0%
+over to what x
+ 
+
+ align:start position:0%
+over to what x
+is X is a * 0 - 0 so x is 0 and Y we
+
+ align:start position:0%
+is X is a * 0 - 0 so x is 0 and Y we
+ 
+
+ align:start position:0%
+is X is a * 0 - 0 so x is 0 and Y we
+said was Zero
+
+ align:start position:0%
+said was Zero
+ 
+
+ align:start position:0%
+said was Zero
+okay I know that I'll achieve a maximum
+
+ align:start position:0%
+okay I know that I'll achieve a maximum
+ 
+
+ align:start position:0%
+okay I know that I'll achieve a maximum
+height at Theta equal Pi because that's
+
+ align:start position:0%
+height at Theta equal Pi because that's
+ 
+
+ align:start position:0%
+height at Theta equal Pi because that's
+where cosine Theta is minus 1 so the 1 -
+
+ align:start position:0%
+where cosine Theta is minus 1 so the 1 -
+ 
+
+ align:start position:0%
+where cosine Theta is minus 1 so the 1 -
+cosine Theta is 2
+
+ align:start position:0%
+cosine Theta is 2
+ 
+
+ align:start position:0%
+cosine Theta is 2
+and so if you look at what the Y value
+
+ align:start position:0%
+and so if you look at what the Y value
+ 
+
+ align:start position:0%
+and so if you look at what the Y value
+will be the Y value when Theta is pi is
+
+ align:start position:0%
+will be the Y value when Theta is pi is
+ 
+
+ align:start position:0%
+will be the Y value when Theta is pi is
+2 a and the x value is going to be a *
+
+ align:start position:0%
+2 a and the x value is going to be a *
+ 
+
+ align:start position:0%
+2 a and the x value is going to be a *
+pi minus sin Pi well s of Pi is zero so
+
+ align:start position:0%
+pi minus sin Pi well s of Pi is zero so
+ 
+
+ align:start position:0%
+pi minus sin Pi well s of Pi is zero so
+I just get a pi so I should go over a pi
+
+ align:start position:0%
+I just get a pi so I should go over a pi
+ 
+
+ align:start position:0%
+I just get a pi so I should go over a pi
+and I know there's a point at a pi comma
+
+ align:start position:0%
+and I know there's a point at a pi comma
+ 
+
+ align:start position:0%
+and I know there's a point at a pi comma
+I think I said 2 a
+
+ align:start position:0%
+I think I said 2 a
+ 
+
+ align:start position:0%
+I think I said 2 a
+right and then it's actually going to
+
+ align:start position:0%
+right and then it's actually going to
+ 
+
+ align:start position:0%
+right and then it's actually going to
+come back down the same way so let me
+
+ align:start position:0%
+come back down the same way so let me
+ 
+
+ align:start position:0%
+come back down the same way so let me
+draw the first part this is not a
+
+ align:start position:0%
+draw the first part this is not a
+ 
+
+ align:start position:0%
+draw the first part this is not a
+perfect drawing of this I don't have
+
+ align:start position:0%
+perfect drawing of this I don't have
+ 
+
+ align:start position:0%
+perfect drawing of this I don't have
+lots of points I'm having the smallest
+
+ align:start position:0%
+lots of points I'm having the smallest
+ 
+
+ align:start position:0%
+lots of points I'm having the smallest
+amount of points possible to figure out
+
+ align:start position:0%
+amount of points possible to figure out
+ 
+
+ align:start position:0%
+amount of points possible to figure out
+what's happening okay so then when Theta
+
+ align:start position:0%
+what's happening okay so then when Theta
+ 
+
+ align:start position:0%
+what's happening okay so then when Theta
+is 2 pi 1 - cosine Theta is is zero so I
+
+ align:start position:0%
+is 2 pi 1 - cosine Theta is is zero so I
+ 
+
+ align:start position:0%
+is 2 pi 1 - cosine Theta is is zero so I
+get here I get y equal 0 and then here I
+
+ align:start position:0%
+get here I get y equal 0 and then here I
+ 
+
+ align:start position:0%
+get here I get y equal 0 and then here I
+get 2 pi minus s of 2 pi s of 2 pi is
+
+ align:start position:0%
+get 2 pi minus s of 2 pi s of 2 pi is
+ 
+
+ align:start position:0%
+get 2 pi minus s of 2 pi s of 2 pi is
+Zer so I get 2 pi a so I come all the
+
+ align:start position:0%
+Zer so I get 2 pi a so I come all the
+ 
+
+ align:start position:0%
+Zer so I get 2 pi a so I come all the
+way over here and I get 2 pi
+
+ align:start position:0%
+way over here and I get 2 pi
+ 
+
+ align:start position:0%
+way over here and I get 2 pi
+a so this is yeah that's not maybe the
+
+ align:start position:0%
+a so this is yeah that's not maybe the
+ 
+
+ align:start position:0%
+a so this is yeah that's not maybe the
+most beautiful picture but it's a good
+
+ align:start position:0%
+most beautiful picture but it's a good
+ 
+
+ align:start position:0%
+most beautiful picture but it's a good
+it's a good start and so I'm interested
+
+ align:start position:0%
+it's a good start and so I'm interested
+ 
+
+ align:start position:0%
+it's a good start and so I'm interested
+in finding the area of this
+
+ align:start position:0%
+in finding the area of this
+ 
+
+ align:start position:0%
+in finding the area of this
+region right and what I want to do then
+
+ align:start position:0%
+region right and what I want to do then
+ 
+
+ align:start position:0%
+region right and what I want to do then
+is to find the area of that region I am
+
+ align:start position:0%
+is to find the area of that region I am
+ 
+
+ align:start position:0%
+is to find the area of that region I am
+going to use green theorem that's what
+
+ align:start position:0%
+going to use green theorem that's what
+ 
+
+ align:start position:0%
+going to use green theorem that's what
+we asked you to do so what I want to do
+
+ align:start position:0%
+we asked you to do so what I want to do
+ 
+
+ align:start position:0%
+we asked you to do so what I want to do
+is I want to pick a curve that's going
+
+ align:start position:0%
+is I want to pick a curve that's going
+ 
+
+ align:start position:0%
+is I want to pick a curve that's going
+to have two components it's going to
+
+ align:start position:0%
+to have two components it's going to
+ 
+
+ align:start position:0%
+to have two components it's going to
+have C1 will be this bottom part and C2
+
+ align:start position:0%
+have C1 will be this bottom part and C2
+ 
+
+ align:start position:0%
+have C1 will be this bottom part and C2
+will be this top part and I need to keep
+
+ align:start position:0%
+will be this top part and I need to keep
+ 
+
+ align:start position:0%
+will be this top part and I need to keep
+it oriented so I when I'm walking along
+
+ align:start position:0%
+it oriented so I when I'm walking along
+ 
+
+ align:start position:0%
+it oriented so I when I'm walking along
+the curve the region is on the left
+
+ align:start position:0%
+the curve the region is on the left
+ 
+
+ align:start position:0%
+the curve the region is on the left
+right and then I have to figure out how
+
+ align:start position:0%
+right and then I have to figure out how
+ 
+
+ align:start position:0%
+right and then I have to figure out how
+to use green the
+
+ align:start position:0%
+to use green the
+ 
+
+ align:start position:0%
+to use green the
+so to find the area of this region all I
+
+ align:start position:0%
+so to find the area of this region all I
+ 
+
+ align:start position:0%
+so to find the area of this region all I
+actually need is the integral over the
+
+ align:start position:0%
+actually need is the integral over the
+ 
+
+ align:start position:0%
+actually need is the integral over the
+region of Da right that would give me
+
+ align:start position:0%
+region of Da right that would give me
+ 
+
+ align:start position:0%
+region of Da right that would give me
+the area and so what quantities would
+
+ align:start position:0%
+the area and so what quantities would
+ 
+
+ align:start position:0%
+the area and so what quantities would
+that would would be uh what good what
+
+ align:start position:0%
+that would would be uh what good what
+ 
+
+ align:start position:0%
+that would would be uh what good what
+functions would be good sorry in order
+
+ align:start position:0%
+functions would be good sorry in order
+ 
+
+ align:start position:0%
+functions would be good sorry in order
+to find this well I believe you actually
+
+ align:start position:0%
+to find this well I believe you actually
+ 
+
+ align:start position:0%
+to find this well I believe you actually
+saw in class that you have two options
+
+ align:start position:0%
+saw in class that you have two options
+ 
+
+ align:start position:0%
+saw in class that you have two options
+you have minus
+
+ align:start position:0%
+you have minus
+ 
+
+ align:start position:0%
+you have minus
+ydx over the curve closed curve or you
+
+ align:start position:0%
+ydx over the curve closed curve or you
+ 
+
+ align:start position:0%
+ydx over the curve closed curve or you
+have uh xdy over the closed curve curve
+
+ align:start position:0%
+have uh xdy over the closed curve curve
+ 
+
+ align:start position:0%
+have uh xdy over the closed curve curve
+you have one of those two options okay
+
+ align:start position:0%
+you have one of those two options okay
+ 
+
+ align:start position:0%
+you have one of those two options okay
+now which one of those is better in this
+
+ align:start position:0%
+now which one of those is better in this
+ 
+
+ align:start position:0%
+now which one of those is better in this
+case we have a choice so let's make the
+
+ align:start position:0%
+case we have a choice so let's make the
+ 
+
+ align:start position:0%
+case we have a choice so let's make the
+best choice which one of those is better
+
+ align:start position:0%
+best choice which one of those is better
+ 
+
+ align:start position:0%
+best choice which one of those is better
+well if you notice that that on these
+
+ align:start position:0%
+well if you notice that that on these
+ 
+
+ align:start position:0%
+well if you notice that that on these
+two curves X is changing on both of them
+
+ align:start position:0%
+two curves X is changing on both of them
+ 
+
+ align:start position:0%
+two curves X is changing on both of them
+but Y is fixed on this one so it' be
+
+ align:start position:0%
+but Y is fixed on this one so it' be
+ 
+
+ align:start position:0%
+but Y is fixed on this one so it' be
+nicer for us if we could just if we
+
+ align:start position:0%
+nicer for us if we could just if we
+ 
+
+ align:start position:0%
+nicer for us if we could just if we
+could just integrate on the curve on
+
+ align:start position:0%
+could just integrate on the curve on
+ 
+
+ align:start position:0%
+could just integrate on the curve on
+this part which we would be able to do
+
+ align:start position:0%
+this part which we would be able to do
+ 
+
+ align:start position:0%
+this part which we would be able to do
+if we were choosing this one right
+
+ align:start position:0%
+if we were choosing this one right
+ 
+
+ align:start position:0%
+if we were choosing this one right
+because Y is constant and it is equal to
+
+ align:start position:0%
+because Y is constant and it is equal to
+ 
+
+ align:start position:0%
+because Y is constant and it is equal to
+zero along here okay so what you need to
+
+ align:start position:0%
+zero along here okay so what you need to
+ 
+
+ align:start position:0%
+zero along here okay so what you need to
+do to solve this problem is really you
+
+ align:start position:0%
+do to solve this problem is really you
+ 
+
+ align:start position:0%
+do to solve this problem is really you
+only need to integrate on
+
+ align:start position:0%
+only need to integrate on
+ 
+
+ align:start position:0%
+only need to integrate on
+C2 uh minus y DX that's going to give
+
+ align:start position:0%
+C2 uh minus y DX that's going to give
+ 
+
+ align:start position:0%
+C2 uh minus y DX that's going to give
+you the entire
+
+ align:start position:0%
+you the entire
+ 
+
+ align:start position:0%
+you the entire
+area and so now we have to figure out
+
+ align:start position:0%
+area and so now we have to figure out
+ 
+
+ align:start position:0%
+area and so now we have to figure out
+how to put everything in right well C2 I
+
+ align:start position:0%
+how to put everything in right well C2 I
+ 
+
+ align:start position:0%
+how to put everything in right well C2 I
+should parameterize I'm parameterized in
+
+ align:start position:0%
+should parameterize I'm parameterized in
+ 
+
+ align:start position:0%
+should parameterize I'm parameterized in
+Theta right and C2 parameterized in
+
+ align:start position:0%
+Theta right and C2 parameterized in
+ 
+
+ align:start position:0%
+Theta right and C2 parameterized in
+Theta if I start here I'm at 2 pi for
+
+ align:start position:0%
+Theta if I start here I'm at 2 pi for
+ 
+
+ align:start position:0%
+Theta if I start here I'm at 2 pi for
+Theta and if I go this direction I'm at
+
+ align:start position:0%
+Theta and if I go this direction I'm at
+ 
+
+ align:start position:0%
+Theta and if I go this direction I'm at
+zero for Theta so what I'm going to do
+
+ align:start position:0%
+zero for Theta so what I'm going to do
+ 
+
+ align:start position:0%
+zero for Theta so what I'm going to do
+is I'm going to do something that might
+
+ align:start position:0%
+is I'm going to do something that might
+ 
+
+ align:start position:0%
+is I'm going to do something that might
+seem tricky but it's quite natural I'm
+
+ align:start position:0%
+seem tricky but it's quite natural I'm
+ 
+
+ align:start position:0%
+seem tricky but it's quite natural I'm
+going to replace this minus by a plus
+
+ align:start position:0%
+going to replace this minus by a plus
+ 
+
+ align:start position:0%
+going to replace this minus by a plus
+and then integrate from 0 to 2 pi right
+
+ align:start position:0%
+and then integrate from 0 to 2 pi right
+ 
+
+ align:start position:0%
+and then integrate from 0 to 2 pi right
+because I was going to be integrating
+
+ align:start position:0%
+because I was going to be integrating
+ 
+
+ align:start position:0%
+because I was going to be integrating
+from 2 pi to zero and so I just flipped
+
+ align:start position:0%
+from 2 pi to zero and so I just flipped
+ 
+
+ align:start position:0%
+from 2 pi to zero and so I just flipped
+the order and made that sign of plus
+
+ align:start position:0%
+the order and made that sign of plus
+ 
+
+ align:start position:0%
+the order and made that sign of plus
+okay so that should be fine and then y I
+
+ align:start position:0%
+okay so that should be fine and then y I
+ 
+
+ align:start position:0%
+okay so that should be fine and then y I
+already know what it is it's a * 1 -
+
+ align:start position:0%
+already know what it is it's a * 1 -
+ 
+
+ align:start position:0%
+already know what it is it's a * 1 -
+cosine
+
+ align:start position:0%
+cosine
+ 
+
+ align:start position:0%
+cosine
+Theta and now I just have to figure out
+
+ align:start position:0%
+Theta and now I just have to figure out
+ 
+
+ align:start position:0%
+Theta and now I just have to figure out
+what is DX
+
+ align:start position:0%
+what is DX
+ 
+
+ align:start position:0%
+what is DX
+okay so we have to come back over for
+
+ align:start position:0%
+okay so we have to come back over for
+ 
+
+ align:start position:0%
+okay so we have to come back over for
+one second we're going to come over here
+
+ align:start position:0%
+one second we're going to come over here
+ 
+
+ align:start position:0%
+one second we're going to come over here
+and we're going to look at
+
+ align:start position:0%
+and we're going to look at
+ 
+
+ align:start position:0%
+and we're going to look at
+DX if x is equal to a * thetus sin Theta
+
+ align:start position:0%
+DX if x is equal to a * thetus sin Theta
+ 
+
+ align:start position:0%
+DX if x is equal to a * thetus sin Theta
+then DX is just a * 1 - cosine Theta so
+
+ align:start position:0%
+then DX is just a * 1 - cosine Theta so
+ 
+
+ align:start position:0%
+then DX is just a * 1 - cosine Theta so
+that's nice because that's actually what
+
+ align:start position:0%
+that's nice because that's actually what
+ 
+
+ align:start position:0%
+that's nice because that's actually what
+we already have so if you come back over
+
+ align:start position:0%
+we already have so if you come back over
+ 
+
+ align:start position:0%
+we already have so if you come back over
+here oh I should say also with the D
+
+ align:start position:0%
+here oh I should say also with the D
+ 
+
+ align:start position:0%
+here oh I should say also with the D
+Theta right if you come back over here
+
+ align:start position:0%
+Theta right if you come back over here
+ 
+
+ align:start position:0%
+Theta right if you come back over here
+DX gives you a squar a it gives you a
+
+ align:start position:0%
+DX gives you a squar a it gives you a
+ 
+
+ align:start position:0%
+DX gives you a squar a it gives you a
+square this and it gives you a d
+
+ align:start position:0%
+square this and it gives you a d
+ 
+
+ align:start position:0%
+square this and it gives you a d
+Theta so that actually gives you
+
+ align:start position:0%
+Theta so that actually gives you
+ 
+
+ align:start position:0%
+Theta so that actually gives you
+everything you need now I am not going
+
+ align:start position:0%
+everything you need now I am not going
+ 
+
+ align:start position:0%
+everything you need now I am not going
+to actually write out all the steps in
+
+ align:start position:0%
+to actually write out all the steps in
+ 
+
+ align:start position:0%
+to actually write out all the steps in
+order to do this but the way you could
+
+ align:start position:0%
+order to do this but the way you could
+ 
+
+ align:start position:0%
+order to do this but the way you could
+easily do this you can pull out the A
+
+ align:start position:0%
+easily do this you can pull out the A
+ 
+
+ align:start position:0%
+easily do this you can pull out the A
+squ and you're left with a 1us cosine
+
+ align:start position:0%
+squ and you're left with a 1us cosine
+ 
+
+ align:start position:0%
+squ and you're left with a 1us cosine
+Theta squar you might think about
+
+ align:start position:0%
+Theta squar you might think about
+ 
+
+ align:start position:0%
+Theta squar you might think about
+squaring all the terms and then you have
+
+ align:start position:0%
+squaring all the terms and then you have
+ 
+
+ align:start position:0%
+squaring all the terms and then you have
+one cosine squ Theta to deal with but
+
+ align:start position:0%
+one cosine squ Theta to deal with but
+ 
+
+ align:start position:0%
+one cosine squ Theta to deal with but
+ultimately when you get your answer I'm
+
+ align:start position:0%
+ultimately when you get your answer I'm
+ 
+
+ align:start position:0%
+ultimately when you get your answer I'm
+just going to write down what it is you
+
+ align:start position:0%
+just going to write down what it is you
+ 
+
+ align:start position:0%
+just going to write down what it is you
+get 3 Pi a 2 and you'll see you get a
+
+ align:start position:0%
+get 3 Pi a 2 and you'll see you get a
+ 
+
+ align:start position:0%
+get 3 Pi a 2 and you'll see you get a
+little bit of cancellation and it's not
+
+ align:start position:0%
+little bit of cancellation and it's not
+ 
+
+ align:start position:0%
+little bit of cancellation and it's not
+too hard to solve at this point since
+
+ align:start position:0%
+too hard to solve at this point since
+ 
+
+ align:start position:0%
+too hard to solve at this point since
+it's single variable going to assume I
+
+ align:start position:0%
+it's single variable going to assume I
+ 
+
+ align:start position:0%
+it's single variable going to assume I
+don't need to do it but you can check
+
+ align:start position:0%
+don't need to do it but you can check
+ 
+
+ align:start position:0%
+don't need to do it but you can check
+your final answer you should get I think
+
+ align:start position:0%
+your final answer you should get I think
+ 
+
+ align:start position:0%
+your final answer you should get I think
+yes I got 3 Pi a^ 2 so what we did was
+
+ align:start position:0%
+yes I got 3 Pi a^ 2 so what we did was
+ 
+
+ align:start position:0%
+yes I got 3 Pi a^ 2 so what we did was
+we took a problem again where we had a
+
+ align:start position:0%
+we took a problem again where we had a
+ 
+
+ align:start position:0%
+we took a problem again where we had a
+curve defined in terms of defined in
+
+ align:start position:0%
+curve defined in terms of defined in
+ 
+
+ align:start position:0%
+curve defined in terms of defined in
+terms of theta right we had a curve in X
+
+ align:start position:0%
+terms of theta right we had a curve in X
+ 
+
+ align:start position:0%
+terms of theta right we had a curve in X
+and Y was parameterized in Theta and we
+
+ align:start position:0%
+and Y was parameterized in Theta and we
+ 
+
+ align:start position:0%
+and Y was parameterized in Theta and we
+wanted to find an area between that
+
+ align:start position:0%
+wanted to find an area between that
+ 
+
+ align:start position:0%
+wanted to find an area between that
+curve and the x- axis and the reason we
+
+ align:start position:0%
+curve and the x- axis and the reason we
+ 
+
+ align:start position:0%
+curve and the x- axis and the reason we
+could use green theorem so easily is
+
+ align:start position:0%
+could use green theorem so easily is
+ 
+
+ align:start position:0%
+could use green theorem so easily is
+because area of a reg region of this
+
+ align:start position:0%
+because area of a reg region of this
+ 
+
+ align:start position:0%
+because area of a reg region of this
+connected region here is equal to the
+
+ align:start position:0%
+connected region here is equal to the
+ 
+
+ align:start position:0%
+connected region here is equal to the
+integral over the closed loop
+
+ align:start position:0%
+integral over the closed loop
+ 
+
+ align:start position:0%
+integral over the closed loop
+surrounding it of minus y DX or
+
+ align:start position:0%
+surrounding it of minus y DX or
+ 
+
+ align:start position:0%
+surrounding it of minus y DX or
+alternatively you could have done xdy
+
+ align:start position:0%
+alternatively you could have done xdy
+ 
+
+ align:start position:0%
+alternatively you could have done xdy
+and because I got to choose I picked the
+
+ align:start position:0%
+and because I got to choose I picked the
+ 
+
+ align:start position:0%
+and because I got to choose I picked the
+easier one and I picked the easier one
+
+ align:start position:0%
+easier one and I picked the easier one
+ 
+
+ align:start position:0%
+easier one and I picked the easier one
+in this case because Y is equal to zero
+
+ align:start position:0%
+in this case because Y is equal to zero
+ 
+
+ align:start position:0%
+in this case because Y is equal to zero
+on Parts on one part of the curve so I
+
+ align:start position:0%
+on Parts on one part of the curve so I
+ 
+
+ align:start position:0%
+on Parts on one part of the curve so I
+just ignored the C1 because that's where
+
+ align:start position:0%
+just ignored the C1 because that's where
+ 
+
+ align:start position:0%
+just ignored the C1 because that's where
+Y is zero and I looked along C2 and
+
+ align:start position:0%
+Y is zero and I looked along C2 and
+ 
+
+ align:start position:0%
+Y is zero and I looked along C2 and
+notice C2 is parameterized in this
+
+ align:start position:0%
+notice C2 is parameterized in this
+ 
+
+ align:start position:0%
+notice C2 is parameterized in this
+direction from Theta equal 2 pi to Theta
+
+ align:start position:0%
+direction from Theta equal 2 pi to Theta
+ 
+
+ align:start position:0%
+direction from Theta equal 2 pi to Theta
+equal 0
+
+ align:start position:0%
+equal 0
+ 
+
+ align:start position:0%
+equal 0
+so that's why I dropped the minus sign
+
+ align:start position:0%
+so that's why I dropped the minus sign
+ 
+
+ align:start position:0%
+so that's why I dropped the minus sign
+and changed it from 0 to 2 pi that's
+
+ align:start position:0%
+and changed it from 0 to 2 pi that's
+ 
+
+ align:start position:0%
+and changed it from 0 to 2 pi that's
+where that came from and then you end up
+
+ align:start position:0%
+where that came from and then you end up
+ 
+
+ align:start position:0%
+where that came from and then you end up
+having to just determine what Y is and
+
+ align:start position:0%
+having to just determine what Y is and
+ 
+
+ align:start position:0%
+having to just determine what Y is and
+what DX are in terms of theta which we
+
+ align:start position:0%
+what DX are in terms of theta which we
+ 
+
+ align:start position:0%
+what DX are in terms of theta which we
+have we had them already in terms of
+
+ align:start position:0%
+have we had them already in terms of
+ 
+
+ align:start position:0%
+have we had them already in terms of
+theta so we could just explicitly
+
+ align:start position:0%
+theta so we could just explicitly
+ 
+
+ align:start position:0%
+theta so we could just explicitly
+determine everything do all the
+
+ align:start position:0%
+determine everything do all the
+ 
+
+ align:start position:0%
+determine everything do all the
+substitution and then evaluate the
+
+ align:start position:0%
+substitution and then evaluate the
+ 
+
+ align:start position:0%
+substitution and then evaluate the
+integral and so then that's that's all
+
+ align:start position:0%
+integral and so then that's that's all
+ 
+
+ align:start position:0%
+integral and so then that's that's all
+there is to this problem so hopefully
+
+ align:start position:0%
+there is to this problem so hopefully
+ 
+
+ align:start position:0%
+there is to this problem so hopefully
+that taught you a little more about
+
+ align:start position:0%
+that taught you a little more about
+ 
+
+ align:start position:0%
+that taught you a little more about
+greens theorem and and actually now
+
+ align:start position:0%
+greens theorem and and actually now
+ 
+
+ align:start position:0%
+greens theorem and and actually now
+you've done problems going from the left
+
+ align:start position:0%
+you've done problems going from the left
+ 
+
+ align:start position:0%
+you've done problems going from the left
+to the right and from the right to the
+
+ align:start position:0%
+to the right and from the right to the
+ 
+
+ align:start position:0%
+to the right and from the right to the
+left so you've done a little of both so
+
+ align:start position:0%
+left so you've done a little of both so
+ 
+
+ align:start position:0%
+left so you've done a little of both so
+hopefully this revealed a little bit
+
+ align:start position:0%
+hopefully this revealed a little bit
+ 
+
+ align:start position:0%
+hopefully this revealed a little bit
+more to you than you knew before that's
+
+ align:start position:0%
+more to you than you knew before that's
+ 
+
+ align:start position:0%
+more to you than you knew before that's
+where I'll stop
\ No newline at end of file
diff --git a/Kj6iEzXsFkI.txt b/Kj6iEzXsFkI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..996dfba022927779fadb015796f4050d7edd5109
--- /dev/null
+++ b/Kj6iEzXsFkI.txt
@@ -0,0 +1,1179 @@
+align:start position:0%
+ 
+by now we have introduced all sorts of
+
+ align:start position:0%
+by now we have introduced all sorts of
+ 
+
+ align:start position:0%
+by now we have introduced all sorts of
+pmfs for the discrete case the joint pmf
+
+ align:start position:0%
+pmfs for the discrete case the joint pmf
+ 
+
+ align:start position:0%
+pmfs for the discrete case the joint pmf
+the conditional pmf given an event and
+
+ align:start position:0%
+the conditional pmf given an event and
+ 
+
+ align:start position:0%
+the conditional pmf given an event and
+the conditional pmf of one random
+
+ align:start position:0%
+the conditional pmf of one random
+ 
+
+ align:start position:0%
+the conditional pmf of one random
+variable given another and we're moving
+
+ align:start position:0%
+variable given another and we're moving
+ 
+
+ align:start position:0%
+variable given another and we're moving
+along with a program of defining
+
+ align:start position:0%
+along with a program of defining
+ 
+
+ align:start position:0%
+along with a program of defining
+analogous concepts for the continuous
+
+ align:start position:0%
+analogous concepts for the continuous
+ 
+
+ align:start position:0%
+analogous concepts for the continuous
+case we have already discussed the joint
+
+ align:start position:0%
+case we have already discussed the joint
+ 
+
+ align:start position:0%
+case we have already discussed the joint
+PDF and the conditional PDF given an
+
+ align:start position:0%
+PDF and the conditional PDF given an
+ 
+
+ align:start position:0%
+PDF and the conditional PDF given an
+event the next item in our menu is to
+
+ align:start position:0%
+event the next item in our menu is to
+ 
+
+ align:start position:0%
+event the next item in our menu is to
+define a conditional PDF of one random
+
+ align:start position:0%
+define a conditional PDF of one random
+ 
+
+ align:start position:0%
+define a conditional PDF of one random
+variable given another random variable
+
+ align:start position:0%
+variable given another random variable
+ 
+
+ align:start position:0%
+variable given another random variable
+we proceed by first looking at the
+
+ align:start position:0%
+we proceed by first looking at the
+ 
+
+ align:start position:0%
+we proceed by first looking at the
+definition for the discrete case a
+
+ align:start position:0%
+definition for the discrete case a
+ 
+
+ align:start position:0%
+definition for the discrete case a
+typical entry of the conditional PMF is
+
+ align:start position:0%
+typical entry of the conditional PMF is
+ 
+
+ align:start position:0%
+typical entry of the conditional PMF is
+just a conditional probability but in
+
+ align:start position:0%
+just a conditional probability but in
+ 
+
+ align:start position:0%
+just a conditional probability but in
+different notation and using the
+
+ align:start position:0%
+different notation and using the
+ 
+
+ align:start position:0%
+different notation and using the
+definition of conditional probabilities
+
+ align:start position:0%
+definition of conditional probabilities
+ 
+
+ align:start position:0%
+definition of conditional probabilities
+this is equal to the ratio of the joint
+
+ align:start position:0%
+this is equal to the ratio of the joint
+ 
+
+ align:start position:0%
+this is equal to the ratio of the joint
+divided by the probability of the
+
+ align:start position:0%
+divided by the probability of the
+ 
+
+ align:start position:0%
+divided by the probability of the
+conditioning event unfortunately in the
+
+ align:start position:0%
+conditioning event unfortunately in the
+ 
+
+ align:start position:0%
+conditioning event unfortunately in the
+continuous case a definition of this
+
+ align:start position:0%
+continuous case a definition of this
+ 
+
+ align:start position:0%
+continuous case a definition of this
+form would be problematic because the
+
+ align:start position:0%
+form would be problematic because the
+ 
+
+ align:start position:0%
+form would be problematic because the
+event that Y takes on a specific value
+
+ align:start position:0%
+event that Y takes on a specific value
+ 
+
+ align:start position:0%
+event that Y takes on a specific value
+is an event that has zero probability
+
+ align:start position:0%
+is an event that has zero probability
+ 
+
+ align:start position:0%
+is an event that has zero probability
+and we know that we cannot condition on
+
+ align:start position:0%
+and we know that we cannot condition on
+ 
+
+ align:start position:0%
+and we know that we cannot condition on
+a zero probability event however we can
+
+ align:start position:0%
+a zero probability event however we can
+ 
+
+ align:start position:0%
+a zero probability event however we can
+take this expression as a guide on how
+
+ align:start position:0%
+take this expression as a guide on how
+ 
+
+ align:start position:0%
+take this expression as a guide on how
+to define a conditional PDF in the
+
+ align:start position:0%
+to define a conditional PDF in the
+ 
+
+ align:start position:0%
+to define a conditional PDF in the
+continuous case and this is the
+
+ align:start position:0%
+continuous case and this is the
+ 
+
+ align:start position:0%
+continuous case and this is the
+definition which just mimics the formula
+
+ align:start position:0%
+definition which just mimics the formula
+ 
+
+ align:start position:0%
+definition which just mimics the formula
+that we have up here notice that this
+
+ align:start position:0%
+that we have up here notice that this
+ 
+
+ align:start position:0%
+that we have up here notice that this
+conditional PDF defined this way is
+
+ align:start position:0%
+conditional PDF defined this way is
+ 
+
+ align:start position:0%
+conditional PDF defined this way is
+well-defined as long as the denominator
+
+ align:start position:0%
+well-defined as long as the denominator
+ 
+
+ align:start position:0%
+well-defined as long as the denominator
+is a positive quantity let us now try to
+
+ align:start position:0%
+is a positive quantity let us now try to
+ 
+
+ align:start position:0%
+is a positive quantity let us now try to
+make sense of this definition let us
+
+ align:start position:0%
+make sense of this definition let us
+ 
+
+ align:start position:0%
+make sense of this definition let us
+first recall the interpretation of the
+
+ align:start position:0%
+first recall the interpretation of the
+ 
+
+ align:start position:0%
+first recall the interpretation of the
+conditional PDF given an event a that
+
+ align:start position:0%
+conditional PDF given an event a that
+ 
+
+ align:start position:0%
+conditional PDF given an event a that
+has positive probability we know that
+
+ align:start position:0%
+has positive probability we know that
+ 
+
+ align:start position:0%
+has positive probability we know that
+the PDF is used to determine the
+
+ align:start position:0%
+the PDF is used to determine the
+ 
+
+ align:start position:0%
+the PDF is used to determine the
+probability of a small interval and
+
+ align:start position:0%
+probability of a small interval and
+ 
+
+ align:start position:0%
+probability of a small interval and
+similarly the conditional PDF is used to
+
+ align:start position:0%
+similarly the conditional PDF is used to
+ 
+
+ align:start position:0%
+similarly the conditional PDF is used to
+calculate the conditional probability of
+
+ align:start position:0%
+calculate the conditional probability of
+ 
+
+ align:start position:0%
+calculate the conditional probability of
+a small interval given the conditioning
+
+ align:start position:0%
+a small interval given the conditioning
+ 
+
+ align:start position:0%
+a small interval given the conditioning
+event we would like to do something
+
+ align:start position:0%
+event we would like to do something
+ 
+
+ align:start position:0%
+event we would like to do something
+similar for the conditional PDF where we
+
+ align:start position:0%
+similar for the conditional PDF where we
+ 
+
+ align:start position:0%
+similar for the conditional PDF where we
+would like to take the event a to be
+
+ align:start position:0%
+would like to take the event a to be
+ 
+
+ align:start position:0%
+would like to take the event a to be
+something like the event that Y is equal
+
+ align:start position:0%
+something like the event that Y is equal
+ 
+
+ align:start position:0%
+something like the event that Y is equal
+to some particular value little
+
+ align:start position:0%
+to some particular value little
+ 
+
+ align:start position:0%
+to some particular value little
+why but as we said this is problematic
+
+ align:start position:0%
+why but as we said this is problematic
+ 
+
+ align:start position:0%
+why but as we said this is problematic
+because this event does not have
+
+ align:start position:0%
+because this event does not have
+ 
+
+ align:start position:0%
+because this event does not have
+positive probability so instead we can
+
+ align:start position:0%
+positive probability so instead we can
+ 
+
+ align:start position:0%
+positive probability so instead we can
+take a to be the event that y is
+
+ align:start position:0%
+take a to be the event that y is
+ 
+
+ align:start position:0%
+take a to be the event that y is
+approximately equal to a certain value
+
+ align:start position:0%
+approximately equal to a certain value
+ 
+
+ align:start position:0%
+approximately equal to a certain value
+so we're dealing with a little interval
+
+ align:start position:0%
+so we're dealing with a little interval
+ 
+
+ align:start position:0%
+so we're dealing with a little interval
+around this value little Y which in
+
+ align:start position:0%
+around this value little Y which in
+ 
+
+ align:start position:0%
+around this value little Y which in
+general would be an event of positive
+
+ align:start position:0%
+general would be an event of positive
+ 
+
+ align:start position:0%
+general would be an event of positive
+probability and we can try to have a
+
+ align:start position:0%
+probability and we can try to have a
+ 
+
+ align:start position:0%
+probability and we can try to have a
+similar interpretation let us see how
+
+ align:start position:0%
+similar interpretation let us see how
+ 
+
+ align:start position:0%
+similar interpretation let us see how
+this works out so what does it mean that
+
+ align:start position:0%
+this works out so what does it mean that
+ 
+
+ align:start position:0%
+this works out so what does it mean that
+Y is approximately equal to some
+
+ align:start position:0%
+Y is approximately equal to some
+ 
+
+ align:start position:0%
+Y is approximately equal to some
+particular value little Y we interpret
+
+ align:start position:0%
+particular value little Y we interpret
+ 
+
+ align:start position:0%
+particular value little Y we interpret
+that as follows we're told that the
+
+ align:start position:0%
+that as follows we're told that the
+ 
+
+ align:start position:0%
+that as follows we're told that the
+random variable Y takes a value that is
+
+ align:start position:0%
+random variable Y takes a value that is
+ 
+
+ align:start position:0%
+random variable Y takes a value that is
+within epsilon where epsilon is a small
+
+ align:start position:0%
+within epsilon where epsilon is a small
+ 
+
+ align:start position:0%
+within epsilon where epsilon is a small
+number of a given value little Y and
+
+ align:start position:0%
+number of a given value little Y and
+ 
+
+ align:start position:0%
+number of a given value little Y and
+given this conditioning information we
+
+ align:start position:0%
+given this conditioning information we
+ 
+
+ align:start position:0%
+given this conditioning information we
+want to calculate the probability of a
+
+ align:start position:0%
+want to calculate the probability of a
+ 
+
+ align:start position:0%
+want to calculate the probability of a
+small interval how do we do that
+
+ align:start position:0%
+small interval how do we do that
+ 
+
+ align:start position:0%
+small interval how do we do that
+well here because this in general will
+
+ align:start position:0%
+well here because this in general will
+ 
+
+ align:start position:0%
+well here because this in general will
+be a positive probability event we can
+
+ align:start position:0%
+be a positive probability event we can
+ 
+
+ align:start position:0%
+be a positive probability event we can
+use the definition of conditional
+
+ align:start position:0%
+use the definition of conditional
+ 
+
+ align:start position:0%
+use the definition of conditional
+probabilities and it would be equal to
+
+ align:start position:0%
+probabilities and it would be equal to
+ 
+
+ align:start position:0%
+probabilities and it would be equal to
+the probability of both events happening
+
+ align:start position:0%
+the probability of both events happening
+ 
+
+ align:start position:0%
+the probability of both events happening
+divided by the probability of the
+
+ align:start position:0%
+divided by the probability of the
+ 
+
+ align:start position:0%
+divided by the probability of the
+conditioning event what is the
+
+ align:start position:0%
+conditioning event what is the
+ 
+
+ align:start position:0%
+conditioning event what is the
+probability of both events happening
+
+ align:start position:0%
+probability of both events happening
+ 
+
+ align:start position:0%
+probability of both events happening
+this is a probability of a small
+
+ align:start position:0%
+this is a probability of a small
+ 
+
+ align:start position:0%
+this is a probability of a small
+rectangle in X Y space at that rectangle
+
+ align:start position:0%
+rectangle in X Y space at that rectangle
+ 
+
+ align:start position:0%
+rectangle in X Y space at that rectangle
+the joint PDF has a certain value and
+
+ align:start position:0%
+the joint PDF has a certain value and
+ 
+
+ align:start position:0%
+the joint PDF has a certain value and
+because we're integrating over that
+
+ align:start position:0%
+because we're integrating over that
+ 
+
+ align:start position:0%
+because we're integrating over that
+rectangle and that rectangle has
+
+ align:start position:0%
+rectangle and that rectangle has
+ 
+
+ align:start position:0%
+rectangle and that rectangle has
+dimensions Delta and epsilon that
+
+ align:start position:0%
+dimensions Delta and epsilon that
+ 
+
+ align:start position:0%
+dimensions Delta and epsilon that
+probability of that small rectangle is
+
+ align:start position:0%
+probability of that small rectangle is
+ 
+
+ align:start position:0%
+probability of that small rectangle is
+approximately equal to this then we need
+
+ align:start position:0%
+approximately equal to this then we need
+ 
+
+ align:start position:0%
+approximately equal to this then we need
+the denominator which is the probability
+
+ align:start position:0%
+the denominator which is the probability
+ 
+
+ align:start position:0%
+the denominator which is the probability
+of the conditional event and this is
+
+ align:start position:0%
+of the conditional event and this is
+ 
+
+ align:start position:0%
+of the conditional event and this is
+approximately equal to the density of Y
+
+ align:start position:0%
+approximately equal to the density of Y
+ 
+
+ align:start position:0%
+approximately equal to the density of Y
+evaluated at that point times the length
+
+ align:start position:0%
+evaluated at that point times the length
+ 
+
+ align:start position:0%
+evaluated at that point times the length
+of the small interval we cancel the
+
+ align:start position:0%
+of the small interval we cancel the
+ 
+
+ align:start position:0%
+of the small interval we cancel the
+absolutes
+
+ align:start position:0%
+absolutes
+ 
+
+ align:start position:0%
+absolutes
+and then we notice that the ratio we
+
+ align:start position:0%
+and then we notice that the ratio we
+ 
+
+ align:start position:0%
+and then we notice that the ratio we
+have here is what we defined as the
+
+ align:start position:0%
+have here is what we defined as the
+ 
+
+ align:start position:0%
+have here is what we defined as the
+conditional PDF so we get this relation
+
+ align:start position:0%
+conditional PDF so we get this relation
+ 
+
+ align:start position:0%
+conditional PDF so we get this relation
+times Delta so what do we see we see
+
+ align:start position:0%
+times Delta so what do we see we see
+ 
+
+ align:start position:0%
+times Delta so what do we see we see
+the probability of a small interval is
+
+ align:start position:0%
+the probability of a small interval is
+ 
+
+ align:start position:0%
+the probability of a small interval is
+equal to a PDF times the length of the
+
+ align:start position:0%
+equal to a PDF times the length of the
+ 
+
+ align:start position:0%
+equal to a PDF times the length of the
+small interval however because we are
+
+ align:start position:0%
+small interval however because we are
+ 
+
+ align:start position:0%
+small interval however because we are
+conditioning on Y being approximately
+
+ align:start position:0%
+conditioning on Y being approximately
+ 
+
+ align:start position:0%
+conditioning on Y being approximately
+equal to a certain value we end up using
+
+ align:start position:0%
+equal to a certain value we end up using
+ 
+
+ align:start position:0%
+equal to a certain value we end up using
+a corresponding conditional PDF where
+
+ align:start position:0%
+a corresponding conditional PDF where
+ 
+
+ align:start position:0%
+a corresponding conditional PDF where
+the conditional PDF is defined this way
+
+ align:start position:0%
+the conditional PDF is defined this way
+ 
+
+ align:start position:0%
+the conditional PDF is defined this way
+so we now have an interpretation of the
+
+ align:start position:0%
+so we now have an interpretation of the
+ 
+
+ align:start position:0%
+so we now have an interpretation of the
+conditional PDF in terms of
+
+ align:start position:0%
+conditional PDF in terms of
+ 
+
+ align:start position:0%
+conditional PDF in terms of
+probabilities of small intervals now
+
+ align:start position:0%
+probabilities of small intervals now
+ 
+
+ align:start position:0%
+probabilities of small intervals now
+that we have an intuitive interpretation
+
+ align:start position:0%
+that we have an intuitive interpretation
+ 
+
+ align:start position:0%
+that we have an intuitive interpretation
+of the conditional PDF we can also use
+
+ align:start position:0%
+of the conditional PDF we can also use
+ 
+
+ align:start position:0%
+of the conditional PDF we can also use
+it to calculate conditional
+
+ align:start position:0%
+it to calculate conditional
+ 
+
+ align:start position:0%
+it to calculate conditional
+probabilities of more general events not
+
+ align:start position:0%
+probabilities of more general events not
+ 
+
+ align:start position:0%
+probabilities of more general events not
+just intervals and we do this as follows
+
+ align:start position:0%
+just intervals and we do this as follows
+ 
+
+ align:start position:0%
+just intervals and we do this as follows
+in general for continuous random
+
+ align:start position:0%
+in general for continuous random
+ 
+
+ align:start position:0%
+in general for continuous random
+variables we can find the probability
+
+ align:start position:0%
+variables we can find the probability
+ 
+
+ align:start position:0%
+variables we can find the probability
+that X belongs to a certain set by
+
+ align:start position:0%
+that X belongs to a certain set by
+ 
+
+ align:start position:0%
+that X belongs to a certain set by
+integrating a PDF over that set because
+
+ align:start position:0%
+integrating a PDF over that set because
+ 
+
+ align:start position:0%
+integrating a PDF over that set because
+here we're dealing with a conditional
+
+ align:start position:0%
+here we're dealing with a conditional
+ 
+
+ align:start position:0%
+here we're dealing with a conditional
+situation where were given the value of
+
+ align:start position:0%
+situation where were given the value of
+ 
+
+ align:start position:0%
+situation where were given the value of
+y we use the conditional PDF instead of
+
+ align:start position:0%
+y we use the conditional PDF instead of
+ 
+
+ align:start position:0%
+y we use the conditional PDF instead of
+the true PDF and with this way we
+
+ align:start position:0%
+the true PDF and with this way we
+ 
+
+ align:start position:0%
+the true PDF and with this way we
+calculate the conditional probability
+
+ align:start position:0%
+calculate the conditional probability
+ 
+
+ align:start position:0%
+calculate the conditional probability
+now the difficulty is that this
+
+ align:start position:0%
+now the difficulty is that this
+ 
+
+ align:start position:0%
+now the difficulty is that this
+conditional probability is not a
+
+ align:start position:0%
+conditional probability is not a
+ 
+
+ align:start position:0%
+conditional probability is not a
+well-defined quantity according to what
+
+ align:start position:0%
+well-defined quantity according to what
+ 
+
+ align:start position:0%
+well-defined quantity according to what
+we did early on in this class we cannot
+
+ align:start position:0%
+we did early on in this class we cannot
+ 
+
+ align:start position:0%
+we did early on in this class we cannot
+condition on 0 probability events but we
+
+ align:start position:0%
+condition on 0 probability events but we
+ 
+
+ align:start position:0%
+condition on 0 probability events but we
+can get around this difficulty as
+
+ align:start position:0%
+can get around this difficulty as
+ 
+
+ align:start position:0%
+can get around this difficulty as
+follows this quantity is well-defined
+
+ align:start position:0%
+follows this quantity is well-defined
+ 
+
+ align:start position:0%
+follows this quantity is well-defined
+and we can use this quantity as the
+
+ align:start position:0%
+and we can use this quantity as the
+ 
+
+ align:start position:0%
+and we can use this quantity as the
+definition of this conditional
+
+ align:start position:0%
+definition of this conditional
+ 
+
+ align:start position:0%
+definition of this conditional
+probability and so we have managed to
+
+ align:start position:0%
+probability and so we have managed to
+ 
+
+ align:start position:0%
+probability and so we have managed to
+provide the definition of conditional
+
+ align:start position:0%
+provide the definition of conditional
+ 
+
+ align:start position:0%
+provide the definition of conditional
+probabilities given a 0 probability
+
+ align:start position:0%
+probabilities given a 0 probability
+ 
+
+ align:start position:0%
+probabilities given a 0 probability
+event of a certain type it turns out
+
+ align:start position:0%
+event of a certain type it turns out
+ 
+
+ align:start position:0%
+event of a certain type it turns out
+that this definition is sound and
+
+ align:start position:0%
+that this definition is sound and
+ 
+
+ align:start position:0%
+that this definition is sound and
+consistent with everything else that we
+
+ align:start position:0%
+consistent with everything else that we
+ 
+
+ align:start position:0%
+consistent with everything else that we
+are doing but when we are dealing with
+
+ align:start position:0%
+are doing but when we are dealing with
+ 
+
+ align:start position:0%
+are doing but when we are dealing with
+particular problems and applications we
+
+ align:start position:0%
+particular problems and applications we
+ 
+
+ align:start position:0%
+particular problems and applications we
+can generally forget about all these
+
+ align:start position:0%
+can generally forget about all these
+ 
+
+ align:start position:0%
+can generally forget about all these
+subtleties that we have been discussing
+
+ align:start position:0%
+subtleties that we have been discussing
+ 
+
+ align:start position:0%
+subtleties that we have been discussing
+here the bottom line is that we will be
+
+ align:start position:0%
+here the bottom line is that we will be
+ 
+
+ align:start position:0%
+here the bottom line is that we will be
+treating conditional PDFs given the
+
+ align:start position:0%
+treating conditional PDFs given the
+ 
+
+ align:start position:0%
+treating conditional PDFs given the
+value of a random variable Y just as
+
+ align:start position:0%
+value of a random variable Y just as
+ 
+
+ align:start position:0%
+value of a random variable Y just as
+ordinary PDFs
+
+ align:start position:0%
+ordinary PDFs
+ 
+
+ align:start position:0%
+ordinary PDFs
+but given the information that this
+
+ align:start position:0%
+but given the information that this
+ 
+
+ align:start position:0%
+but given the information that this
+random variable took on a specific value
+
+ align:start position:0%
+random variable took on a specific value
+ 
+
+ align:start position:0%
+random variable took on a specific value
+and in that conditional universe we will
+
+ align:start position:0%
+and in that conditional universe we will
+ 
+
+ align:start position:0%
+and in that conditional universe we will
+calculate probabilities than usual way
+
+ align:start position:0%
+calculate probabilities than usual way
+ 
+
+ align:start position:0%
+calculate probabilities than usual way
+by using conditional PDFs instead of
+
+ align:start position:0%
+by using conditional PDFs instead of
+ 
+
+ align:start position:0%
+by using conditional PDFs instead of
+ordinary PDFs
\ No newline at end of file
diff --git a/Kycmb2IwV-Y.txt b/Kycmb2IwV-Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4a55b6a2a269115df8796291fa47499ffe8be476
--- /dev/null
+++ b/Kycmb2IwV-Y.txt
@@ -0,0 +1,2307 @@
+align:start position:0%
+ 
+we will now study a problem which is
+
+ align:start position:0%
+we will now study a problem which is
+ 
+
+ align:start position:0%
+we will now study a problem which is
+quite difficult to approach in a direct
+
+ align:start position:0%
+quite difficult to approach in a direct
+ 
+
+ align:start position:0%
+quite difficult to approach in a direct
+brute-force manner but becomes tractable
+
+ align:start position:0%
+brute-force manner but becomes tractable
+ 
+
+ align:start position:0%
+brute-force manner but becomes tractable
+once we break it down into simpler
+
+ align:start position:0%
+once we break it down into simpler
+ 
+
+ align:start position:0%
+once we break it down into simpler
+pieces using several of the tricks that
+
+ align:start position:0%
+pieces using several of the tricks that
+ 
+
+ align:start position:0%
+pieces using several of the tricks that
+we have learned so far and this problem
+
+ align:start position:0%
+we have learned so far and this problem
+ 
+
+ align:start position:0%
+we have learned so far and this problem
+will also be a good opportunity for
+
+ align:start position:0%
+will also be a good opportunity for
+ 
+
+ align:start position:0%
+will also be a good opportunity for
+reviewing some of the tricks and
+
+ align:start position:0%
+reviewing some of the tricks and
+ 
+
+ align:start position:0%
+reviewing some of the tricks and
+techniques that we have developed the
+
+ align:start position:0%
+techniques that we have developed the
+ 
+
+ align:start position:0%
+techniques that we have developed the
+problem is the following there are n
+
+ align:start position:0%
+problem is the following there are n
+ 
+
+ align:start position:0%
+problem is the following there are n
+people and let's say for the purpose of
+
+ align:start position:0%
+people and let's say for the purpose of
+ 
+
+ align:start position:0%
+people and let's say for the purpose of
+illustration that we have three people
+
+ align:start position:0%
+illustration that we have three people
+ 
+
+ align:start position:0%
+illustration that we have three people
+persons 1 2 & 3 and each person has a
+
+ align:start position:0%
+persons 1 2 & 3 and each person has a
+ 
+
+ align:start position:0%
+persons 1 2 & 3 and each person has a
+hat they throw their hats inside a box
+
+ align:start position:0%
+hat they throw their hats inside a box
+ 
+
+ align:start position:0%
+hat they throw their hats inside a box
+and then each person picks a hat at
+
+ align:start position:0%
+and then each person picks a hat at
+ 
+
+ align:start position:0%
+and then each person picks a hat at
+random out of that box
+
+ align:start position:0%
+random out of that box
+ 
+
+ align:start position:0%
+random out of that box
+so here are the three hats and one
+
+ align:start position:0%
+so here are the three hats and one
+ 
+
+ align:start position:0%
+so here are the three hats and one
+possible outcome of this experiment is
+
+ align:start position:0%
+possible outcome of this experiment is
+ 
+
+ align:start position:0%
+possible outcome of this experiment is
+that person 1 ends up with hat number
+
+ align:start position:0%
+that person 1 ends up with hat number
+ 
+
+ align:start position:0%
+that person 1 ends up with hat number
+two person two ends up with hat number 1
+
+ align:start position:0%
+two person two ends up with hat number 1
+ 
+
+ align:start position:0%
+two person two ends up with hat number 1
+and person 3 ends up we had number three
+
+ align:start position:0%
+and person 3 ends up we had number three
+ 
+
+ align:start position:0%
+and person 3 ends up we had number three
+we could indicate the hats that each
+
+ align:start position:0%
+we could indicate the hats that each
+ 
+
+ align:start position:0%
+we could indicate the hats that each
+person got by noting the here the
+
+ align:start position:0%
+person got by noting the here the
+ 
+
+ align:start position:0%
+person got by noting the here the
+numbers associated with each person the
+
+ align:start position:0%
+numbers associated with each person the
+ 
+
+ align:start position:0%
+numbers associated with each person the
+hat numbers and notice that this
+
+ align:start position:0%
+hat numbers and notice that this
+ 
+
+ align:start position:0%
+hat numbers and notice that this
+sequence of numbers which is a
+
+ align:start position:0%
+sequence of numbers which is a
+ 
+
+ align:start position:0%
+sequence of numbers which is a
+description of the outcome of the
+
+ align:start position:0%
+description of the outcome of the
+ 
+
+ align:start position:0%
+description of the outcome of the
+experiment is just a permutation of the
+
+ align:start position:0%
+experiment is just a permutation of the
+ 
+
+ align:start position:0%
+experiment is just a permutation of the
+numbers 1 2 3 of the hats
+
+ align:start position:0%
+numbers 1 2 3 of the hats
+ 
+
+ align:start position:0%
+numbers 1 2 3 of the hats
+so we permute the hat numbers so that we
+
+ align:start position:0%
+so we permute the hat numbers so that we
+ 
+
+ align:start position:0%
+so we permute the hat numbers so that we
+can place them next to the person that
+
+ align:start position:0%
+can place them next to the person that
+ 
+
+ align:start position:0%
+can place them next to the person that
+got each one of the hats in particular
+
+ align:start position:0%
+got each one of the hats in particular
+ 
+
+ align:start position:0%
+got each one of the hats in particular
+we have n factorial possible outcomes
+
+ align:start position:0%
+we have n factorial possible outcomes
+ 
+
+ align:start position:0%
+we have n factorial possible outcomes
+this is the number of possible
+
+ align:start position:0%
+this is the number of possible
+ 
+
+ align:start position:0%
+this is the number of possible
+permutations what does it mean to pick
+
+ align:start position:0%
+permutations what does it mean to pick
+ 
+
+ align:start position:0%
+permutations what does it mean to pick
+hats at random one interpretation is
+
+ align:start position:0%
+hats at random one interpretation is
+ 
+
+ align:start position:0%
+hats at random one interpretation is
+that every permutation is equally likely
+
+ align:start position:0%
+that every permutation is equally likely
+ 
+
+ align:start position:0%
+that every permutation is equally likely
+and since we have n factorial
+
+ align:start position:0%
+and since we have n factorial
+ 
+
+ align:start position:0%
+and since we have n factorial
+permutations each permutation will have
+
+ align:start position:0%
+permutations each permutation will have
+ 
+
+ align:start position:0%
+permutations each permutation will have
+a probability of 1 over N factorial but
+
+ align:start position:0%
+a probability of 1 over N factorial but
+ 
+
+ align:start position:0%
+a probability of 1 over N factorial but
+there is another way of describing
+
+ align:start position:0%
+there is another way of describing
+ 
+
+ align:start position:0%
+there is another way of describing
+model which is the following person one
+
+ align:start position:0%
+model which is the following person one
+ 
+
+ align:start position:0%
+model which is the following person one
+gets a hat at random out of the three
+
+ align:start position:0%
+gets a hat at random out of the three
+ 
+
+ align:start position:0%
+gets a hat at random out of the three
+available then persons two gets a hat at
+
+ align:start position:0%
+available then persons two gets a hat at
+ 
+
+ align:start position:0%
+available then persons two gets a hat at
+random out of the remaining hats then
+
+ align:start position:0%
+random out of the remaining hats then
+ 
+
+ align:start position:0%
+random out of the remaining hats then
+person three gets the remaining hat each
+
+ align:start position:0%
+person three gets the remaining hat each
+ 
+
+ align:start position:0%
+person three gets the remaining hat each
+time that there is a choice each one of
+
+ align:start position:0%
+time that there is a choice each one of
+ 
+
+ align:start position:0%
+time that there is a choice each one of
+the available hats is equally likely to
+
+ align:start position:0%
+the available hats is equally likely to
+ 
+
+ align:start position:0%
+the available hats is equally likely to
+be picked as any other hat let us
+
+ align:start position:0%
+be picked as any other hat let us
+ 
+
+ align:start position:0%
+be picked as any other hat let us
+calculate the probability let's say that
+
+ align:start position:0%
+calculate the probability let's say that
+ 
+
+ align:start position:0%
+calculate the probability let's say that
+this particular permutation gets
+
+ align:start position:0%
+this particular permutation gets
+ 
+
+ align:start position:0%
+this particular permutation gets
+materialized the probability that person
+
+ align:start position:0%
+materialized the probability that person
+ 
+
+ align:start position:0%
+materialized the probability that person
+one yet hat number two is one-third then
+
+ align:start position:0%
+one yet hat number two is one-third then
+ 
+
+ align:start position:0%
+one yet hat number two is one-third then
+we're left with two hats person two has
+
+ align:start position:0%
+we're left with two hats person two has
+ 
+
+ align:start position:0%
+we're left with two hats person two has
+two hats to choose from the probability
+
+ align:start position:0%
+two hats to choose from the probability
+ 
+
+ align:start position:0%
+two hats to choose from the probability
+that it picks this particular hat is
+
+ align:start position:0%
+that it picks this particular hat is
+ 
+
+ align:start position:0%
+that it picks this particular hat is
+going to be one-half and finally person
+
+ align:start position:0%
+going to be one-half and finally person
+ 
+
+ align:start position:0%
+going to be one-half and finally person
+three has only one hat available so it
+
+ align:start position:0%
+three has only one hat available so it
+ 
+
+ align:start position:0%
+three has only one hat available so it
+will be picked with probability one so
+
+ align:start position:0%
+will be picked with probability one so
+ 
+
+ align:start position:0%
+will be picked with probability one so
+the probability of this particular
+
+ align:start position:0%
+the probability of this particular
+ 
+
+ align:start position:0%
+the probability of this particular
+permutation is one over three factorial
+
+ align:start position:0%
+permutation is one over three factorial
+ 
+
+ align:start position:0%
+permutation is one over three factorial
+but you can repeat this argument and
+
+ align:start position:0%
+but you can repeat this argument and
+ 
+
+ align:start position:0%
+but you can repeat this argument and
+consider any other permutation and you
+
+ align:start position:0%
+consider any other permutation and you
+ 
+
+ align:start position:0%
+consider any other permutation and you
+will always be getting the same answer
+
+ align:start position:0%
+will always be getting the same answer
+ 
+
+ align:start position:0%
+will always be getting the same answer
+any particular permutation has the same
+
+ align:start position:0%
+any particular permutation has the same
+ 
+
+ align:start position:0%
+any particular permutation has the same
+probability one over three factorial the
+
+ align:start position:0%
+probability one over three factorial the
+ 
+
+ align:start position:0%
+probability one over three factorial the
+same argument goes through for the case
+
+ align:start position:0%
+same argument goes through for the case
+ 
+
+ align:start position:0%
+same argument goes through for the case
+of general N and people and n hats and
+
+ align:start position:0%
+of general N and people and n hats and
+ 
+
+ align:start position:0%
+of general N and people and n hats and
+we will find that any permutation will
+
+ align:start position:0%
+we will find that any permutation will
+ 
+
+ align:start position:0%
+we will find that any permutation will
+have the same probability one over N
+
+ align:start position:0%
+have the same probability one over N
+ 
+
+ align:start position:0%
+have the same probability one over N
+factorial therefore the process of
+
+ align:start position:0%
+factorial therefore the process of
+ 
+
+ align:start position:0%
+factorial therefore the process of
+picking one hat at a time is
+
+ align:start position:0%
+picking one hat at a time is
+ 
+
+ align:start position:0%
+picking one hat at a time is
+probabilistically identical to a model
+
+ align:start position:0%
+probabilistically identical to a model
+ 
+
+ align:start position:0%
+probabilistically identical to a model
+in which we simply state that all
+
+ align:start position:0%
+in which we simply state that all
+ 
+
+ align:start position:0%
+in which we simply state that all
+permutations are equally likely now that
+
+ align:start position:0%
+permutations are equally likely now that
+ 
+
+ align:start position:0%
+permutations are equally likely now that
+we have described our model and our
+
+ align:start position:0%
+we have described our model and our
+ 
+
+ align:start position:0%
+we have described our model and our
+process and the associated probabilities
+
+ align:start position:0%
+process and the associated probabilities
+ 
+
+ align:start position:0%
+process and the associated probabilities
+let us consider the question we want to
+
+ align:start position:0%
+let us consider the question we want to
+ 
+
+ align:start position:0%
+let us consider the question we want to
+answer let X be the number of people who
+
+ align:start position:0%
+answer let X be the number of people who
+ 
+
+ align:start position:0%
+answer let X be the number of people who
+get their own hat back for example for
+
+ align:start position:0%
+get their own hat back for example for
+ 
+
+ align:start position:0%
+get their own hat back for example for
+the outcome that we have drawn here the
+
+ align:start position:0%
+the outcome that we have drawn here the
+ 
+
+ align:start position:0%
+the outcome that we have drawn here the
+only person who gets their own hat back
+
+ align:start position:0%
+only person who gets their own hat back
+ 
+
+ align:start position:0%
+only person who gets their own hat back
+is person 3 and so in this case X
+
+ align:start position:0%
+is person 3 and so in this case X
+ 
+
+ align:start position:0%
+is person 3 and so in this case X
+happens to take the value of 1
+
+ align:start position:0%
+happens to take the value of 1
+ 
+
+ align:start position:0%
+happens to take the value of 1
+what we want to do is to calculate the
+
+ align:start position:0%
+what we want to do is to calculate the
+ 
+
+ align:start position:0%
+what we want to do is to calculate the
+expected value of the random variable X
+
+ align:start position:0%
+expected value of the random variable X
+ 
+
+ align:start position:0%
+expected value of the random variable X
+the problem is difficult because if you
+
+ align:start position:0%
+the problem is difficult because if you
+ 
+
+ align:start position:0%
+the problem is difficult because if you
+try to calculate the PMF of the random
+
+ align:start position:0%
+try to calculate the PMF of the random
+ 
+
+ align:start position:0%
+try to calculate the PMF of the random
+variable X and then use the definition
+
+ align:start position:0%
+variable X and then use the definition
+ 
+
+ align:start position:0%
+variable X and then use the definition
+of the expectation to calculate this sum
+
+ align:start position:0%
+of the expectation to calculate this sum
+ 
+
+ align:start position:0%
+of the expectation to calculate this sum
+you will run into big difficulties
+
+ align:start position:0%
+you will run into big difficulties
+ 
+
+ align:start position:0%
+you will run into big difficulties
+calculating this quantity the PMF of X
+
+ align:start position:0%
+calculating this quantity the PMF of X
+ 
+
+ align:start position:0%
+calculating this quantity the PMF of X
+is difficult and it is difficult because
+
+ align:start position:0%
+is difficult and it is difficult because
+ 
+
+ align:start position:0%
+is difficult and it is difficult because
+there is no simple expression that
+
+ align:start position:0%
+there is no simple expression that
+ 
+
+ align:start position:0%
+there is no simple expression that
+describes it so we need to do something
+
+ align:start position:0%
+describes it so we need to do something
+ 
+
+ align:start position:0%
+describes it so we need to do something
+more intelligent find some other way of
+
+ align:start position:0%
+more intelligent find some other way of
+ 
+
+ align:start position:0%
+more intelligent find some other way of
+approaching the problem the trick that
+
+ align:start position:0%
+approaching the problem the trick that
+ 
+
+ align:start position:0%
+approaching the problem the trick that
+we will use is to employ indicator
+
+ align:start position:0%
+we will use is to employ indicator
+ 
+
+ align:start position:0%
+we will use is to employ indicator
+variables let X I be equal to 1 if
+
+ align:start position:0%
+variables let X I be equal to 1 if
+ 
+
+ align:start position:0%
+variables let X I be equal to 1 if
+person I selects their own hat and 0
+
+ align:start position:0%
+person I selects their own hat and 0
+ 
+
+ align:start position:0%
+person I selects their own hat and 0
+otherwise so then each one of the excise
+
+ align:start position:0%
+otherwise so then each one of the excise
+ 
+
+ align:start position:0%
+otherwise so then each one of the excise
+is 1 whenever a person has selected
+
+ align:start position:0%
+is 1 whenever a person has selected
+ 
+
+ align:start position:0%
+is 1 whenever a person has selected
+their own hat and by adding all the ones
+
+ align:start position:0%
+their own hat and by adding all the ones
+ 
+
+ align:start position:0%
+their own hat and by adding all the ones
+that we may get we obtain the total
+
+ align:start position:0%
+that we may get we obtain the total
+ 
+
+ align:start position:0%
+that we may get we obtain the total
+number of people who have selected their
+
+ align:start position:0%
+number of people who have selected their
+ 
+
+ align:start position:0%
+number of people who have selected their
+own hats this makes things easier
+
+ align:start position:0%
+own hats this makes things easier
+ 
+
+ align:start position:0%
+own hats this makes things easier
+because now to calculate the expected
+
+ align:start position:0%
+because now to calculate the expected
+ 
+
+ align:start position:0%
+because now to calculate the expected
+value of X it's sufficient to calculate
+
+ align:start position:0%
+value of X it's sufficient to calculate
+ 
+
+ align:start position:0%
+value of X it's sufficient to calculate
+the expected value of each one of those
+
+ align:start position:0%
+the expected value of each one of those
+ 
+
+ align:start position:0%
+the expected value of each one of those
+terms and add the expected values which
+
+ align:start position:0%
+terms and add the expected values which
+ 
+
+ align:start position:0%
+terms and add the expected values which
+were allowed to do because of linearity
+
+ align:start position:0%
+were allowed to do because of linearity
+ 
+
+ align:start position:0%
+were allowed to do because of linearity
+so let us look at a typical term here
+
+ align:start position:0%
+so let us look at a typical term here
+ 
+
+ align:start position:0%
+so let us look at a typical term here
+what is the expected value of x I if you
+
+ align:start position:0%
+what is the expected value of x I if you
+ 
+
+ align:start position:0%
+what is the expected value of x I if you
+consider the first description of our
+
+ align:start position:0%
+consider the first description of our
+ 
+
+ align:start position:0%
+consider the first description of our
+model all permutations are equally
+
+ align:start position:0%
+model all permutations are equally
+ 
+
+ align:start position:0%
+model all permutations are equally
+likely this description is symmetric
+
+ align:start position:0%
+likely this description is symmetric
+ 
+
+ align:start position:0%
+likely this description is symmetric
+with respect to all the persons so the
+
+ align:start position:0%
+with respect to all the persons so the
+ 
+
+ align:start position:0%
+with respect to all the persons so the
+expected value of X I should be the same
+
+ align:start position:0%
+expected value of X I should be the same
+ 
+
+ align:start position:0%
+expected value of X I should be the same
+as the expected value of x1 now to
+
+ align:start position:0%
+as the expected value of x1 now to
+ 
+
+ align:start position:0%
+as the expected value of x1 now to
+calculate the expected value of x1 we
+
+ align:start position:0%
+calculate the expected value of x1 we
+ 
+
+ align:start position:0%
+calculate the expected value of x1 we
+will consider the sequential description
+
+ align:start position:0%
+will consider the sequential description
+ 
+
+ align:start position:0%
+will consider the sequential description
+of the process in which one is the first
+
+ align:start position:0%
+of the process in which one is the first
+ 
+
+ align:start position:0%
+of the process in which one is the first
+person to pick a hat now since x1 is a
+
+ align:start position:0%
+person to pick a hat now since x1 is a
+ 
+
+ align:start position:0%
+person to pick a hat now since x1 is a
+Bernoulli random variable that takes
+
+ align:start position:0%
+Bernoulli random variable that takes
+ 
+
+ align:start position:0%
+Bernoulli random variable that takes
+values 0 or 1 the expected value of x1
+
+ align:start position:0%
+values 0 or 1 the expected value of x1
+ 
+
+ align:start position:0%
+values 0 or 1 the expected value of x1
+is just the probability that X
+
+ align:start position:0%
+is just the probability that X
+ 
+
+ align:start position:0%
+is just the probability that X
+one is equal to one and if person one is
+
+ align:start position:0%
+one is equal to one and if person one is
+ 
+
+ align:start position:0%
+one is equal to one and if person one is
+the first one to choose a hat that
+
+ align:start position:0%
+the first one to choose a hat that
+ 
+
+ align:start position:0%
+the first one to choose a hat that
+person has probability 1 over n of
+
+ align:start position:0%
+person has probability 1 over n of
+ 
+
+ align:start position:0%
+person has probability 1 over n of
+obtaining the correct hat so each one of
+
+ align:start position:0%
+obtaining the correct hat so each one of
+ 
+
+ align:start position:0%
+obtaining the correct hat so each one of
+these random variables has an expected
+
+ align:start position:0%
+these random variables has an expected
+ 
+
+ align:start position:0%
+these random variables has an expected
+value of 1 over n the expected value of
+
+ align:start position:0%
+value of 1 over n the expected value of
+ 
+
+ align:start position:0%
+value of 1 over n the expected value of
+x by linearity is going to be the sum of
+
+ align:start position:0%
+x by linearity is going to be the sum of
+ 
+
+ align:start position:0%
+x by linearity is going to be the sum of
+the expected values there is n of them
+
+ align:start position:0%
+the expected values there is n of them
+ 
+
+ align:start position:0%
+the expected values there is n of them
+each expected value is 1 over N and so
+
+ align:start position:0%
+each expected value is 1 over N and so
+ 
+
+ align:start position:0%
+each expected value is 1 over N and so
+the final answer is 1 this is the
+
+ align:start position:0%
+the final answer is 1 this is the
+ 
+
+ align:start position:0%
+the final answer is 1 this is the
+expected value of the random variable X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let us now move and try to calculate a
+
+ align:start position:0%
+let us now move and try to calculate a
+ 
+
+ align:start position:0%
+let us now move and try to calculate a
+more difficult quantity namely the
+
+ align:start position:0%
+more difficult quantity namely the
+ 
+
+ align:start position:0%
+more difficult quantity namely the
+variance of X how shall we proceed
+
+ align:start position:0%
+variance of X how shall we proceed
+ 
+
+ align:start position:0%
+variance of X how shall we proceed
+things would be easiest if the random
+
+ align:start position:0%
+things would be easiest if the random
+ 
+
+ align:start position:0%
+things would be easiest if the random
+variables X I were independent because
+
+ align:start position:0%
+variables X I were independent because
+ 
+
+ align:start position:0%
+variables X I were independent because
+in that case the variance of X would be
+
+ align:start position:0%
+in that case the variance of X would be
+ 
+
+ align:start position:0%
+in that case the variance of X would be
+the sum of the variances of the x i's
+
+ align:start position:0%
+the sum of the variances of the x i's
+ 
+
+ align:start position:0%
+the sum of the variances of the x i's
+but are the X is independent let us
+
+ align:start position:0%
+but are the X is independent let us
+ 
+
+ align:start position:0%
+but are the X is independent let us
+consider a special case suppose that we
+
+ align:start position:0%
+consider a special case suppose that we
+ 
+
+ align:start position:0%
+consider a special case suppose that we
+only have two persons and that I told
+
+ align:start position:0%
+only have two persons and that I told
+ 
+
+ align:start position:0%
+only have two persons and that I told
+you that the first person got their own
+
+ align:start position:0%
+you that the first person got their own
+ 
+
+ align:start position:0%
+you that the first person got their own
+hat back in that case the second person
+
+ align:start position:0%
+hat back in that case the second person
+ 
+
+ align:start position:0%
+hat back in that case the second person
+must have also gotten their own hat back
+
+ align:start position:0%
+must have also gotten their own hat back
+ 
+
+ align:start position:0%
+must have also gotten their own hat back
+if on the other hand person 1 did not
+
+ align:start position:0%
+if on the other hand person 1 did not
+ 
+
+ align:start position:0%
+if on the other hand person 1 did not
+get their own hat back then person 2
+
+ align:start position:0%
+get their own hat back then person 2
+ 
+
+ align:start position:0%
+get their own hat back then person 2
+will not get their own hat back either
+
+ align:start position:0%
+will not get their own hat back either
+ 
+
+ align:start position:0%
+will not get their own hat back either
+because in this scenario person one gets
+
+ align:start position:0%
+because in this scenario person one gets
+ 
+
+ align:start position:0%
+because in this scenario person one gets
+hat too and that means that person two
+
+ align:start position:0%
+hat too and that means that person two
+ 
+
+ align:start position:0%
+hat too and that means that person two
+gets hot one so we see that knowing the
+
+ align:start position:0%
+gets hot one so we see that knowing the
+ 
+
+ align:start position:0%
+gets hot one so we see that knowing the
+value of the random variable X 1 tells
+
+ align:start position:0%
+value of the random variable X 1 tells
+ 
+
+ align:start position:0%
+value of the random variable X 1 tells
+us a lot about the value of the random
+
+ align:start position:0%
+us a lot about the value of the random
+ 
+
+ align:start position:0%
+us a lot about the value of the random
+variable X 2 and that means that the
+
+ align:start position:0%
+variable X 2 and that means that the
+ 
+
+ align:start position:0%
+variable X 2 and that means that the
+random variables X 1 and X 2 are
+
+ align:start position:0%
+random variables X 1 and X 2 are
+ 
+
+ align:start position:0%
+random variables X 1 and X 2 are
+dependent more generally if I were to
+
+ align:start position:0%
+dependent more generally if I were to
+ 
+
+ align:start position:0%
+dependent more generally if I were to
+tell you that the
+
+ align:start position:0%
+tell you that the
+ 
+
+ align:start position:0%
+tell you that the
+first and -1 people got their own hats
+
+ align:start position:0%
+first and -1 people got their own hats
+ 
+
+ align:start position:0%
+first and -1 people got their own hats
+back then the last remaining person will
+
+ align:start position:0%
+back then the last remaining person will
+ 
+
+ align:start position:0%
+back then the last remaining person will
+have his or her own hat available to be
+
+ align:start position:0%
+have his or her own hat available to be
+ 
+
+ align:start position:0%
+have his or her own hat available to be
+picked that's going to be the only
+
+ align:start position:0%
+picked that's going to be the only
+ 
+
+ align:start position:0%
+picked that's going to be the only
+available hat and then person and will
+
+ align:start position:0%
+available hat and then person and will
+ 
+
+ align:start position:0%
+available hat and then person and will
+also get their hat back so we see that
+
+ align:start position:0%
+also get their hat back so we see that
+ 
+
+ align:start position:0%
+also get their hat back so we see that
+information about some of the excise
+
+ align:start position:0%
+information about some of the excise
+ 
+
+ align:start position:0%
+information about some of the excise
+gives us information about the remaining
+
+ align:start position:0%
+gives us information about the remaining
+ 
+
+ align:start position:0%
+gives us information about the remaining
+X and and again this means that the
+
+ align:start position:0%
+X and and again this means that the
+ 
+
+ align:start position:0%
+X and and again this means that the
+random variables are dependent since we
+
+ align:start position:0%
+random variables are dependent since we
+ 
+
+ align:start position:0%
+random variables are dependent since we
+do not have independence we cannot find
+
+ align:start position:0%
+do not have independence we cannot find
+ 
+
+ align:start position:0%
+do not have independence we cannot find
+the variance by just adding the
+
+ align:start position:0%
+the variance by just adding the
+ 
+
+ align:start position:0%
+the variance by just adding the
+variances of the different random
+
+ align:start position:0%
+variances of the different random
+ 
+
+ align:start position:0%
+variances of the different random
+variables but we need to do a lot more
+
+ align:start position:0%
+variables but we need to do a lot more
+ 
+
+ align:start position:0%
+variables but we need to do a lot more
+work in that direction in general
+
+ align:start position:0%
+work in that direction in general
+ 
+
+ align:start position:0%
+work in that direction in general
+whenever we need to calculate variances
+
+ align:start position:0%
+whenever we need to calculate variances
+ 
+
+ align:start position:0%
+whenever we need to calculate variances
+it is usually simpler to carry out the
+
+ align:start position:0%
+it is usually simpler to carry out the
+ 
+
+ align:start position:0%
+it is usually simpler to carry out the
+calculation using this alternative form
+
+ align:start position:0%
+calculation using this alternative form
+ 
+
+ align:start position:0%
+calculation using this alternative form
+for the variance so let us start towards
+
+ align:start position:0%
+for the variance so let us start towards
+ 
+
+ align:start position:0%
+for the variance so let us start towards
+a calculation of the expected value of x
+
+ align:start position:0%
+a calculation of the expected value of x
+ 
+
+ align:start position:0%
+a calculation of the expected value of x
+squared now the random variable x
+
+ align:start position:0%
+squared now the random variable x
+ 
+
+ align:start position:0%
+squared now the random variable x
+squared by simple algebra is this
+
+ align:start position:0%
+squared by simple algebra is this
+ 
+
+ align:start position:0%
+squared by simple algebra is this
+expression times itself and by expanding
+
+ align:start position:0%
+expression times itself and by expanding
+ 
+
+ align:start position:0%
+expression times itself and by expanding
+the product we get all sorts of cross
+
+ align:start position:0%
+the product we get all sorts of cross
+ 
+
+ align:start position:0%
+the product we get all sorts of cross
+terms some of these cross terms will be
+
+ align:start position:0%
+terms some of these cross terms will be
+ 
+
+ align:start position:0%
+terms some of these cross terms will be
+of the type X 1 times X 1 or X 2 times X
+
+ align:start position:0%
+of the type X 1 times X 1 or X 2 times X
+ 
+
+ align:start position:0%
+of the type X 1 times X 1 or X 2 times X
+2 these will be terms of this form and
+
+ align:start position:0%
+2 these will be terms of this form and
+ 
+
+ align:start position:0%
+2 these will be terms of this form and
+there is n of them and then we get cross
+
+ align:start position:0%
+there is n of them and then we get cross
+ 
+
+ align:start position:0%
+there is n of them and then we get cross
+terms such as X 1 times X 2 X 1 times X
+
+ align:start position:0%
+terms such as X 1 times X 2 X 1 times X
+ 
+
+ align:start position:0%
+terms such as X 1 times X 2 X 1 times X
+3 X 2 times X 1 and so on how many terms
+
+ align:start position:0%
+3 X 2 times X 1 and so on how many terms
+ 
+
+ align:start position:0%
+3 X 2 times X 1 and so on how many terms
+do we have here well if we have n terms
+
+ align:start position:0%
+do we have here well if we have n terms
+ 
+
+ align:start position:0%
+do we have here well if we have n terms
+multiplying another terms we have a
+
+ align:start position:0%
+multiplying another terms we have a
+ 
+
+ align:start position:0%
+multiplying another terms we have a
+total of n squared terms and are already
+
+ align:start position:0%
+total of n squared terms and are already
+ 
+
+ align:start position:0%
+total of n squared terms and are already
+here so the remaining terms which are
+
+ align:start position:0%
+here so the remaining terms which are
+ 
+
+ align:start position:0%
+here so the remaining terms which are
+the cross terms will be N squared minus
+
+ align:start position:0%
+the cross terms will be N squared minus
+ 
+
+ align:start position:0%
+the cross terms will be N squared minus
+n or in a simpler form it's n times n
+
+ align:start position:0%
+n or in a simpler form it's n times n
+ 
+
+ align:start position:0%
+n or in a simpler form it's n times n
+minus 1 so now how are we going to
+
+ align:start position:0%
+minus 1 so now how are we going to
+ 
+
+ align:start position:0%
+minus 1 so now how are we going to
+calculate the expected value of x
+
+ align:start position:0%
+calculate the expected value of x
+ 
+
+ align:start position:0%
+calculate the expected value of x
+squared well we will use linearity of
+
+ align:start position:0%
+squared well we will use linearity of
+ 
+
+ align:start position:0%
+squared well we will use linearity of
+expectations so we need to calculate the
+
+ align:start position:0%
+expectations so we need to calculate the
+ 
+
+ align:start position:0%
+expectations so we need to calculate the
+expected value of x I squared and we
+
+ align:start position:0%
+expected value of x I squared and we
+ 
+
+ align:start position:0%
+expected value of x I squared and we
+also need to calculate
+
+ align:start position:0%
+also need to calculate
+ 
+
+ align:start position:0%
+also need to calculate
+the expected value of x IX J when I is
+
+ align:start position:0%
+the expected value of x IX J when I is
+ 
+
+ align:start position:0%
+the expected value of x IX J when I is
+different from J let us start with X I
+
+ align:start position:0%
+different from J let us start with X I
+ 
+
+ align:start position:0%
+different from J let us start with X I
+squared first if we use the symmetric
+
+ align:start position:0%
+squared first if we use the symmetric
+ 
+
+ align:start position:0%
+squared first if we use the symmetric
+description of our model all
+
+ align:start position:0%
+description of our model all
+ 
+
+ align:start position:0%
+description of our model all
+permutations are equally likely then all
+
+ align:start position:0%
+permutations are equally likely then all
+ 
+
+ align:start position:0%
+permutations are equally likely then all
+persons play the same role there's
+
+ align:start position:0%
+persons play the same role there's
+ 
+
+ align:start position:0%
+persons play the same role there's
+symmetry in the problem so X I squared
+
+ align:start position:0%
+symmetry in the problem so X I squared
+ 
+
+ align:start position:0%
+symmetry in the problem so X I squared
+has the same distribution as x1 squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then x1 is a zero one random variable a
+
+ align:start position:0%
+then x1 is a zero one random variable a
+ 
+
+ align:start position:0%
+then x1 is a zero one random variable a
+Bernoulli random variable so x1 squared
+
+ align:start position:0%
+Bernoulli random variable so x1 squared
+ 
+
+ align:start position:0%
+Bernoulli random variable so x1 squared
+will always take the same numerical
+
+ align:start position:0%
+will always take the same numerical
+ 
+
+ align:start position:0%
+will always take the same numerical
+value as the random variable x1 this is
+
+ align:start position:0%
+value as the random variable x1 this is
+ 
+
+ align:start position:0%
+value as the random variable x1 this is
+a very special case which happens only
+
+ align:start position:0%
+a very special case which happens only
+ 
+
+ align:start position:0%
+a very special case which happens only
+because a random variable takes values
+
+ align:start position:0%
+because a random variable takes values
+ 
+
+ align:start position:0%
+because a random variable takes values
+in 0 1 & 0 squared is the same 0 1
+
+ align:start position:0%
+in 0 1 & 0 squared is the same 0 1
+ 
+
+ align:start position:0%
+in 0 1 & 0 squared is the same 0 1
+squared is the same as 1 this expected
+
+ align:start position:0%
+squared is the same as 1 this expected
+ 
+
+ align:start position:0%
+squared is the same as 1 this expected
+value is something that we have already
+
+ align:start position:0%
+value is something that we have already
+ 
+
+ align:start position:0%
+value is something that we have already
+calculated and it is 1 over N let us now
+
+ align:start position:0%
+calculated and it is 1 over N let us now
+ 
+
+ align:start position:0%
+calculated and it is 1 over N let us now
+move to the calculation of the
+
+ align:start position:0%
+move to the calculation of the
+ 
+
+ align:start position:0%
+move to the calculation of the
+expectation of a typical term inside
+
+ align:start position:0%
+expectation of a typical term inside
+ 
+
+ align:start position:0%
+expectation of a typical term inside
+this song so let a be different than J
+
+ align:start position:0%
+this song so let a be different than J
+ 
+
+ align:start position:0%
+this song so let a be different than J
+and look at the expected value of X I XJ
+
+ align:start position:0%
+and look at the expected value of X I XJ
+ 
+
+ align:start position:0%
+and look at the expected value of X I XJ
+once more because of the symmetry of the
+
+ align:start position:0%
+once more because of the symmetry of the
+ 
+
+ align:start position:0%
+once more because of the symmetry of the
+probabilistic model it doesn't matter
+
+ align:start position:0%
+probabilistic model it doesn't matter
+ 
+
+ align:start position:0%
+probabilistic model it doesn't matter
+which I and J we are considering so we
+
+ align:start position:0%
+which I and J we are considering so we
+ 
+
+ align:start position:0%
+which I and J we are considering so we
+might as well consider the product of x1
+
+ align:start position:0%
+might as well consider the product of x1
+ 
+
+ align:start position:0%
+might as well consider the product of x1
+with x2 now x1 and x2 take values 0 and
+
+ align:start position:0%
+with x2 now x1 and x2 take values 0 and
+ 
+
+ align:start position:0%
+with x2 now x1 and x2 take values 0 and
+1 and the product of the two also takes
+
+ align:start position:0%
+1 and the product of the two also takes
+ 
+
+ align:start position:0%
+1 and the product of the two also takes
+values 0 and 1 so this is a Bernoulli
+
+ align:start position:0%
+values 0 and 1 so this is a Bernoulli
+ 
+
+ align:start position:0%
+values 0 and 1 so this is a Bernoulli
+random variable and so the expectation
+
+ align:start position:0%
+random variable and so the expectation
+ 
+
+ align:start position:0%
+random variable and so the expectation
+of that random variable is just the
+
+ align:start position:0%
+of that random variable is just the
+ 
+
+ align:start position:0%
+of that random variable is just the
+probability that this random variable is
+
+ align:start position:0%
+probability that this random variable is
+ 
+
+ align:start position:0%
+probability that this random variable is
+equal to 1 but for the product to be
+
+ align:start position:0%
+equal to 1 but for the product to be
+ 
+
+ align:start position:0%
+equal to 1 but for the product to be
+equal to 1 the only way that this can
+
+ align:start position:0%
+equal to 1 the only way that this can
+ 
+
+ align:start position:0%
+equal to 1 the only way that this can
+happen is if both of these random
+
+ align:start position:0%
+happen is if both of these random
+ 
+
+ align:start position:0%
+happen is if both of these random
+variables happen to be equal to 1 let us
+
+ align:start position:0%
+variables happen to be equal to 1 let us
+ 
+
+ align:start position:0%
+variables happen to be equal to 1 let us
+now turn to the sequential description
+
+ align:start position:0%
+now turn to the sequential description
+ 
+
+ align:start position:0%
+now turn to the sequential description
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+the probability that the first person
+
+ align:start position:0%
+the probability that the first person
+ 
+
+ align:start position:0%
+the probability that the first person
+gets their own hot bath and the second
+
+ align:start position:0%
+gets their own hot bath and the second
+ 
+
+ align:start position:0%
+gets their own hot bath and the second
+person gets her own hot back
+
+ align:start position:0%
+person gets her own hot back
+ 
+
+ align:start position:0%
+person gets her own hot back
+he's the probability that the first one
+
+ align:start position:0%
+he's the probability that the first one
+ 
+
+ align:start position:0%
+he's the probability that the first one
+gets their own hat back and then
+
+ align:start position:0%
+gets their own hat back and then
+ 
+
+ align:start position:0%
+gets their own hat back and then
+multiplied by the conditional
+
+ align:start position:0%
+multiplied by the conditional
+ 
+
+ align:start position:0%
+multiplied by the conditional
+probability that the second person gets
+
+ align:start position:0%
+probability that the second person gets
+ 
+
+ align:start position:0%
+probability that the second person gets
+their own hat back given that the first
+
+ align:start position:0%
+their own hat back given that the first
+ 
+
+ align:start position:0%
+their own hat back given that the first
+person got their own hat back
+
+ align:start position:0%
+person got their own hat back
+ 
+
+ align:start position:0%
+person got their own hat back
+what are these probabilities the
+
+ align:start position:0%
+what are these probabilities the
+ 
+
+ align:start position:0%
+what are these probabilities the
+probability that the person gets their
+
+ align:start position:0%
+probability that the person gets their
+ 
+
+ align:start position:0%
+probability that the person gets their
+own hat back is one over n given that
+
+ align:start position:0%
+own hat back is one over n given that
+ 
+
+ align:start position:0%
+own hat back is one over n given that
+person one got their own hat back person
+
+ align:start position:0%
+person one got their own hat back person
+ 
+
+ align:start position:0%
+person one got their own hat back person
+two is faced with a situation where
+
+ align:start position:0%
+two is faced with a situation where
+ 
+
+ align:start position:0%
+two is faced with a situation where
+there are n minus one available hats and
+
+ align:start position:0%
+there are n minus one available hats and
+ 
+
+ align:start position:0%
+there are n minus one available hats and
+one of those is that person's hat so the
+
+ align:start position:0%
+one of those is that person's hat so the
+ 
+
+ align:start position:0%
+one of those is that person's hat so the
+probability that person two will also
+
+ align:start position:0%
+probability that person two will also
+ 
+
+ align:start position:0%
+probability that person two will also
+pick his or her own hat is one over n
+
+ align:start position:0%
+pick his or her own hat is one over n
+ 
+
+ align:start position:0%
+pick his or her own hat is one over n
+minus one now we are in a position to
+
+ align:start position:0%
+minus one now we are in a position to
+ 
+
+ align:start position:0%
+minus one now we are in a position to
+calculate the expected value of x
+
+ align:start position:0%
+calculate the expected value of x
+ 
+
+ align:start position:0%
+calculate the expected value of x
+squared the expected value of x squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consists of the sum of n expected values
+
+ align:start position:0%
+consists of the sum of n expected values
+ 
+
+ align:start position:0%
+consists of the sum of n expected values
+each one of which is equal to 1 over n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus so many expected values because we
+
+ align:start position:0%
+plus so many expected values because we
+ 
+
+ align:start position:0%
+plus so many expected values because we
+have so many terms each one of which by
+
+ align:start position:0%
+have so many terms each one of which by
+ 
+
+ align:start position:0%
+have so many terms each one of which by
+this calculation is 1 over n times 1
+
+ align:start position:0%
+this calculation is 1 over n times 1
+ 
+
+ align:start position:0%
+this calculation is 1 over n times 1
+over n minus 1 and we see that we get
+
+ align:start position:0%
+over n minus 1 and we see that we get
+ 
+
+ align:start position:0%
+over n minus 1 and we see that we get
+cancellations here and we obtain 1 plus
+
+ align:start position:0%
+cancellations here and we obtain 1 plus
+ 
+
+ align:start position:0%
+cancellations here and we obtain 1 plus
+1 which is equal to 2 on the other hand
+
+ align:start position:0%
+1 which is equal to 2 on the other hand
+ 
+
+ align:start position:0%
+1 which is equal to 2 on the other hand
+we have this term that we need to
+
+ align:start position:0%
+we have this term that we need to
+ 
+
+ align:start position:0%
+we have this term that we need to
+subtract we found previously that the
+
+ align:start position:0%
+subtract we found previously that the
+ 
+
+ align:start position:0%
+subtract we found previously that the
+expected value of x is equal to 1 so we
+
+ align:start position:0%
+expected value of x is equal to 1 so we
+ 
+
+ align:start position:0%
+expected value of x is equal to 1 so we
+need to subtract 1 and the final answer
+
+ align:start position:0%
+need to subtract 1 and the final answer
+ 
+
+ align:start position:0%
+need to subtract 1 and the final answer
+to our problem is that the variance of X
+
+ align:start position:0%
+to our problem is that the variance of X
+ 
+
+ align:start position:0%
+to our problem is that the variance of X
+is also equal to 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we saw in this problem is that
+
+ align:start position:0%
+so what we saw in this problem is that
+ 
+
+ align:start position:0%
+so what we saw in this problem is that
+we can deal with quite complicated
+
+ align:start position:0%
+we can deal with quite complicated
+ 
+
+ align:start position:0%
+we can deal with quite complicated
+models but by breaking them down into
+
+ align:start position:0%
+models but by breaking them down into
+ 
+
+ align:start position:0%
+models but by breaking them down into
+more manageable pieces first breakdown
+
+ align:start position:0%
+more manageable pieces first breakdown
+ 
+
+ align:start position:0%
+more manageable pieces first breakdown
+the random variable X as a sum of
+
+ align:start position:0%
+the random variable X as a sum of
+ 
+
+ align:start position:0%
+the random variable X as a sum of
+different random variables then taking
+
+ align:start position:0%
+different random variables then taking
+ 
+
+ align:start position:0%
+different random variables then taking
+the square of this and break it down
+
+ align:start position:0%
+the square of this and break it down
+ 
+
+ align:start position:0%
+the square of this and break it down
+into a number of different terms and
+
+ align:start position:0%
+into a number of different terms and
+ 
+
+ align:start position:0%
+into a number of different terms and
+then by considering one term at a time
+
+ align:start position:0%
+then by considering one term at a time
+ 
+
+ align:start position:0%
+then by considering one term at a time
+we can often end up with the solutions
+
+ align:start position:0%
+we can often end up with the solutions
+ 
+
+ align:start position:0%
+we can often end up with the solutions
+or the answers to problems that would
+
+ align:start position:0%
+or the answers to problems that would
+ 
+
+ align:start position:0%
+or the answers to problems that would
+have been otherwise quite difficult
\ No newline at end of file
diff --git a/L8N_KZBHeIA.txt b/L8N_KZBHeIA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..161d9577c04b409d6f836d73fa2550a5a79f9ff9
--- /dev/null
+++ b/L8N_KZBHeIA.txt
@@ -0,0 +1,283 @@
+align:start position:0%
+ 
+hello I'm David Newman and when I served
+
+ align:start position:0%
+hello I'm David Newman and when I served
+ 
+
+ align:start position:0%
+hello I'm David Newman and when I served
+as NASA deputy administrator that's the
+
+ align:start position:0%
+as NASA deputy administrator that's the
+ 
+
+ align:start position:0%
+as NASA deputy administrator that's the
+number two I became very familiar with
+
+ align:start position:0%
+number two I became very familiar with
+ 
+
+ align:start position:0%
+number two I became very familiar with
+our Earth observing satellites which
+
+ align:start position:0%
+our Earth observing satellites which
+ 
+
+ align:start position:0%
+our Earth observing satellites which
+tell us about the vital signs of our
+
+ align:start position:0%
+tell us about the vital signs of our
+ 
+
+ align:start position:0%
+tell us about the vital signs of our
+planet which I call spaceship earth eyes
+
+ align:start position:0%
+planet which I call spaceship earth eyes
+ 
+
+ align:start position:0%
+planet which I call spaceship earth eyes
+on Earth from this global perspective
+
+ align:start position:0%
+on Earth from this global perspective
+ 
+
+ align:start position:0%
+on Earth from this global perspective
+I saw warming temperatures melting ice
+
+ align:start position:0%
+I saw warming temperatures melting ice
+ 
+
+ align:start position:0%
+I saw warming temperatures melting ice
+intensifying natural disasters climate
+
+ align:start position:0%
+intensifying natural disasters climate
+ 
+
+ align:start position:0%
+intensifying natural disasters climate
+change is real and if we're going to
+
+ align:start position:0%
+change is real and if we're going to
+ 
+
+ align:start position:0%
+change is real and if we're going to
+solve climate change the moonshot of our
+
+ align:start position:0%
+solve climate change the moonshot of our
+ 
+
+ align:start position:0%
+solve climate change the moonshot of our
+generation we need everyone on board
+
+ align:start position:0%
+generation we need everyone on board
+ 
+
+ align:start position:0%
+generation we need everyone on board
+that's why with the support of the MIT
+
+ align:start position:0%
+that's why with the support of the MIT
+ 
+
+ align:start position:0%
+that's why with the support of the MIT
+Portugal program a partners and I
+
+ align:start position:0%
+Portugal program a partners and I
+ 
+
+ align:start position:0%
+Portugal program a partners and I
+started earth DNA data into action for
+
+ align:start position:0%
+started earth DNA data into action for
+ 
+
+ align:start position:0%
+started earth DNA data into action for
+the earth we want to unite the whole
+
+ align:start position:0%
+the earth we want to unite the whole
+ 
+
+ align:start position:0%
+the earth we want to unite the whole
+world and creating a sustainable
+
+ align:start position:0%
+world and creating a sustainable
+ 
+
+ align:start position:0%
+world and creating a sustainable
+relationship between humans and nature
+
+ align:start position:0%
+relationship between humans and nature
+ 
+
+ align:start position:0%
+relationship between humans and nature
+and we're so happy to have you with us
+
+ align:start position:0%
+and we're so happy to have you with us
+ 
+
+ align:start position:0%
+and we're so happy to have you with us
+you'll be our astronauts traveling to
+
+ align:start position:0%
+you'll be our astronauts traveling to
+ 
+
+ align:start position:0%
+you'll be our astronauts traveling to
+places we could never reach by ourselves
+
+ align:start position:0%
+places we could never reach by ourselves
+ 
+
+ align:start position:0%
+places we could never reach by ourselves
+and will be your Mission Control
+
+ align:start position:0%
+and will be your Mission Control
+ 
+
+ align:start position:0%
+and will be your Mission Control
+providing you with the tools and
+
+ align:start position:0%
+providing you with the tools and
+ 
+
+ align:start position:0%
+providing you with the tools and
+guidance you need to make an impact at
+
+ align:start position:0%
+guidance you need to make an impact at
+ 
+
+ align:start position:0%
+guidance you need to make an impact at
+the schools around you you'll teach
+
+ align:start position:0%
+the schools around you you'll teach
+ 
+
+ align:start position:0%
+the schools around you you'll teach
+students students will teach families
+
+ align:start position:0%
+students students will teach families
+ 
+
+ align:start position:0%
+students students will teach families
+and families will demand action with
+
+ align:start position:0%
+and families will demand action with
+ 
+
+ align:start position:0%
+and families will demand action with
+your help we can reach a destination a
+
+ align:start position:0%
+your help we can reach a destination a
+ 
+
+ align:start position:0%
+your help we can reach a destination a
+world that works for a hundred percent
+
+ align:start position:0%
+world that works for a hundred percent
+ 
+
+ align:start position:0%
+world that works for a hundred percent
+of humanity without ecological offense
+
+ align:start position:0%
+of humanity without ecological offense
+ 
+
+ align:start position:0%
+of humanity without ecological offense
+we're ready for lift up and we're
+
+ align:start position:0%
+we're ready for lift up and we're
+ 
+
+ align:start position:0%
+we're ready for lift up and we're
+thrilled to have you on board so let's
+
+ align:start position:0%
+thrilled to have you on board so let's
+ 
+
+ align:start position:0%
+thrilled to have you on board so let's
+get started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three two one launch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/LmiY4R6C2mM.txt b/LmiY4R6C2mM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6ff8ac5844036396d8b08094e8032c13abb6517d
--- /dev/null
+++ b/LmiY4R6C2mM.txt
@@ -0,0 +1,8307 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so you all should have uh
+
+ align:start position:0%
+ocw.mit.edu so you all should have uh
+ 
+
+ align:start position:0%
+ocw.mit.edu so you all should have uh
+these handouts ready to go now so let's
+
+ align:start position:0%
+these handouts ready to go now so let's
+ 
+
+ align:start position:0%
+these handouts ready to go now so let's
+review where we were last
+
+ align:start position:0%
+review where we were last
+ 
+
+ align:start position:0%
+review where we were last
+week so everyone uh can settle down a
+
+ align:start position:0%
+week so everyone uh can settle down a
+ 
+
+ align:start position:0%
+week so everyone uh can settle down a
+little bit you can discuss about who
+
+ align:start position:0%
+little bit you can discuss about who
+ 
+
+ align:start position:0%
+little bit you can discuss about who
+wants to be the top chemistry nature uh
+
+ align:start position:0%
+wants to be the top chemistry nature uh
+ 
+
+ align:start position:0%
+wants to be the top chemistry nature uh
+later on after class is over all right
+
+ align:start position:0%
+later on after class is over all right
+ 
+
+ align:start position:0%
+later on after class is over all right
+so octahedral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case so here is our octahedral
+
+ align:start position:0%
+case so here is our octahedral
+ 
+
+ align:start position:0%
+case so here is our octahedral
+molecule and again Crystal field theory
+
+ align:start position:0%
+molecule and again Crystal field theory
+ 
+
+ align:start position:0%
+molecule and again Crystal field theory
+is just an explanation for things that
+
+ align:start position:0%
+is just an explanation for things that
+ 
+
+ align:start position:0%
+is just an explanation for things that
+are observed
+
+ align:start position:0%
+are observed
+ 
+
+ align:start position:0%
+are observed
+experimentally so it's a fairly simple
+
+ align:start position:0%
+experimentally so it's a fairly simple
+ 
+
+ align:start position:0%
+experimentally so it's a fairly simple
+Theory and if you go on to study
+
+ align:start position:0%
+Theory and if you go on to study
+ 
+
+ align:start position:0%
+Theory and if you go on to study
+chemistry and you'll take more inorganic
+
+ align:start position:0%
+chemistry and you'll take more inorganic
+ 
+
+ align:start position:0%
+chemistry and you'll take more inorganic
+chemistry later on you'll learn about
+
+ align:start position:0%
+chemistry later on you'll learn about
+ 
+
+ align:start position:0%
+chemistry later on you'll learn about
+more complicated theories but this is
+
+ align:start position:0%
+more complicated theories but this is
+ 
+
+ align:start position:0%
+more complicated theories but this is
+really simple so this Simple Theory just
+
+ align:start position:0%
+really simple so this Simple Theory just
+ 
+
+ align:start position:0%
+really simple so this Simple Theory just
+thinks about each Lian uh each uh small
+
+ align:start position:0%
+thinks about each Lian uh each uh small
+ 
+
+ align:start position:0%
+thinks about each Lian uh each uh small
+molecule like NH3 group bound to a metal
+
+ align:start position:0%
+molecule like NH3 group bound to a metal
+ 
+
+ align:start position:0%
+molecule like NH3 group bound to a metal
+the metal is in the center position that
+
+ align:start position:0%
+the metal is in the center position that
+ 
+
+ align:start position:0%
+the metal is in the center position that
+each Lian it considers as a negative
+
+ align:start position:0%
+each Lian it considers as a negative
+ 
+
+ align:start position:0%
+each Lian it considers as a negative
+Point charge and so then the theory
+
+ align:start position:0%
+Point charge and so then the theory
+ 
+
+ align:start position:0%
+Point charge and so then the theory
+looks at whether that Li as a negative
+
+ align:start position:0%
+looks at whether that Li as a negative
+ 
+
+ align:start position:0%
+looks at whether that Li as a negative
+Point charge is pointing toward one of
+
+ align:start position:0%
+Point charge is pointing toward one of
+ 
+
+ align:start position:0%
+Point charge is pointing toward one of
+the D orbitals so you need to know about
+
+ align:start position:0%
+the D orbitals so you need to know about
+ 
+
+ align:start position:0%
+the D orbitals so you need to know about
+the shapes of the D orbitals and you
+
+ align:start position:0%
+the shapes of the D orbitals and you
+ 
+
+ align:start position:0%
+the shapes of the D orbitals and you
+need to know about the the shapes of the
+
+ align:start position:0%
+need to know about the the shapes of the
+ 
+
+ align:start position:0%
+need to know about the the shapes of the
+coordination complexes and then you need
+
+ align:start position:0%
+coordination complexes and then you need
+ 
+
+ align:start position:0%
+coordination complexes and then you need
+to just ask yourself is that Lian
+
+ align:start position:0%
+to just ask yourself is that Lian
+ 
+
+ align:start position:0%
+to just ask yourself is that Lian
+pointing toward directly toward a d
+
+ align:start position:0%
+pointing toward directly toward a d
+ 
+
+ align:start position:0%
+pointing toward directly toward a d
+orbital if it is then it'll be
+
+ align:start position:0%
+orbital if it is then it'll be
+ 
+
+ align:start position:0%
+orbital if it is then it'll be
+destabilized if it's not then those
+
+ align:start position:0%
+destabilized if it's not then those
+ 
+
+ align:start position:0%
+destabilized if it's not then those
+orbitals will be stabilized and so
+
+ align:start position:0%
+orbitals will be stabilized and so
+ 
+
+ align:start position:0%
+orbitals will be stabilized and so
+you're all you're talking about the
+
+ align:start position:0%
+you're all you're talking about the
+ 
+
+ align:start position:0%
+you're all you're talking about the
+stabilization relative to a imaginary uh
+
+ align:start position:0%
+stabilization relative to a imaginary uh
+ 
+
+ align:start position:0%
+stabilization relative to a imaginary uh
+spherical Crystal field where lians are
+
+ align:start position:0%
+spherical Crystal field where lians are
+ 
+
+ align:start position:0%
+spherical Crystal field where lians are
+just sort of everywhere all around the
+
+ align:start position:0%
+just sort of everywhere all around the
+ 
+
+ align:start position:0%
+just sort of everywhere all around the
+center metal so you consider that as
+
+ align:start position:0%
+center metal so you consider that as
+ 
+
+ align:start position:0%
+center metal so you consider that as
+sort of your standard case where all of
+
+ align:start position:0%
+sort of your standard case where all of
+ 
+
+ align:start position:0%
+sort of your standard case where all of
+the D orbitals have the same energy but
+
+ align:start position:0%
+the D orbitals have the same energy but
+ 
+
+ align:start position:0%
+the D orbitals have the same energy but
+then when you consider those lians as
+
+ align:start position:0%
+then when you consider those lians as
+ 
+
+ align:start position:0%
+then when you consider those lians as
+negative point charges in particular
+
+ align:start position:0%
+negative point charges in particular
+ 
+
+ align:start position:0%
+negative point charges in particular
+locations some D orbitals then get
+
+ align:start position:0%
+locations some D orbitals then get
+ 
+
+ align:start position:0%
+locations some D orbitals then get
+destabilized and other ones get
+
+ align:start position:0%
+destabilized and other ones get
+ 
+
+ align:start position:0%
+destabilized and other ones get
+stabilized in terms of
+
+ align:start position:0%
+stabilized in terms of
+ 
+
+ align:start position:0%
+stabilized in terms of
+energy so in the octahedral case then
+
+ align:start position:0%
+energy so in the octahedral case then
+ 
+
+ align:start position:0%
+energy so in the octahedral case then
+and here's our little cartoon for the
+
+ align:start position:0%
+and here's our little cartoon for the
+ 
+
+ align:start position:0%
+and here's our little cartoon for the
+octahedral case where one Lian there
+
+ align:start position:0%
+octahedral case where one Lian there
+ 
+
+ align:start position:0%
+octahedral case where one Lian there
+lians along uh the Z axis lians along
+
+ align:start position:0%
+lians along uh the Z axis lians along
+ 
+
+ align:start position:0%
+lians along uh the Z axis lians along
+the x axis and lians along the Y AIS and
+
+ align:start position:0%
+the x axis and lians along the Y AIS and
+ 
+
+ align:start position:0%
+the x axis and lians along the Y AIS and
+so if you look at dx^ 2 - y^2 you see
+
+ align:start position:0%
+so if you look at dx^ 2 - y^2 you see
+ 
+
+ align:start position:0%
+so if you look at dx^ 2 - y^2 you see
+that the lians will be pointing directly
+
+ align:start position:0%
+that the lians will be pointing directly
+ 
+
+ align:start position:0%
+that the lians will be pointing directly
+toward these D orbitals because lians
+
+ align:start position:0%
+toward these D orbitals because lians
+ 
+
+ align:start position:0%
+toward these D orbitals because lians
+are coming in along Y and along X and so
+
+ align:start position:0%
+are coming in along Y and along X and so
+ 
+
+ align:start position:0%
+are coming in along Y and along X and so
+there'll be a lot of
+
+ align:start position:0%
+there'll be a lot of
+ 
+
+ align:start position:0%
+there'll be a lot of
+destabilization for D um Z squared you
+
+ align:start position:0%
+destabilization for D um Z squared you
+ 
+
+ align:start position:0%
+destabilization for D um Z squared you
+have lians pointing directly toward
+
+ align:start position:0%
+have lians pointing directly toward
+ 
+
+ align:start position:0%
+have lians pointing directly toward
+those orbitals as well along the Z axis
+
+ align:start position:0%
+those orbitals as well along the Z axis
+ 
+
+ align:start position:0%
+those orbitals as well along the Z axis
+so these have large repulsions due to
+
+ align:start position:0%
+so these have large repulsions due to
+ 
+
+ align:start position:0%
+so these have large repulsions due to
+the negative point charges those
+
+ align:start position:0%
+the negative point charges those
+ 
+
+ align:start position:0%
+the negative point charges those
+negative point charges are heading right
+
+ align:start position:0%
+negative point charges are heading right
+ 
+
+ align:start position:0%
+negative point charges are heading right
+toward those D
+
+ align:start position:0%
+toward those D
+ 
+
+ align:start position:0%
+toward those D
+orbitals and these two are degenerate
+
+ align:start position:0%
+orbitals and these two are degenerate
+ 
+
+ align:start position:0%
+orbitals and these two are degenerate
+with respect to each other they have the
+
+ align:start position:0%
+with respect to each other they have the
+ 
+
+ align:start position:0%
+with respect to each other they have the
+same energy the same amount of
+
+ align:start position:0%
+same energy the same amount of
+ 
+
+ align:start position:0%
+same energy the same amount of
+destabilization and these are
+
+ align:start position:0%
+destabilization and these are
+ 
+
+ align:start position:0%
+destabilization and these are
+destabilized compared to this other set
+
+ align:start position:0%
+destabilized compared to this other set
+ 
+
+ align:start position:0%
+destabilized compared to this other set
+of D orbitals and in this set of D
+
+ align:start position:0%
+of D orbitals and in this set of D
+ 
+
+ align:start position:0%
+of D orbitals and in this set of D
+orbitals none of the orbitals are on
+
+ align:start position:0%
+orbitals none of the orbitals are on
+ 
+
+ align:start position:0%
+orbitals none of the orbitals are on
+axis they're 45° off axis the negative
+
+ align:start position:0%
+axis they're 45° off axis the negative
+ 
+
+ align:start position:0%
+axis they're 45° off axis the negative
+point charges are on axis so there's not
+
+ align:start position:0%
+point charges are on axis so there's not
+ 
+
+ align:start position:0%
+point charges are on axis so there's not
+as much destabilization the lians aren't
+
+ align:start position:0%
+as much destabilization the lians aren't
+ 
+
+ align:start position:0%
+as much destabilization the lians aren't
+pointing directly toward
+
+ align:start position:0%
+pointing directly toward
+ 
+
+ align:start position:0%
+pointing directly toward
+any of these D orbitals so you have
+
+ align:start position:0%
+any of these D orbitals so you have
+ 
+
+ align:start position:0%
+any of these D orbitals so you have
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+repulsion all of these three are of the
+
+ align:start position:0%
+repulsion all of these three are of the
+ 
+
+ align:start position:0%
+repulsion all of these three are of the
+same energy they're
+
+ align:start position:0%
+same energy they're
+ 
+
+ align:start position:0%
+same energy they're
+degenerate and they're all stabilized
+
+ align:start position:0%
+degenerate and they're all stabilized
+ 
+
+ align:start position:0%
+degenerate and they're all stabilized
+compared to this set so that's what we
+
+ align:start position:0%
+compared to this set so that's what we
+ 
+
+ align:start position:0%
+compared to this set so that's what we
+talked about last week and we also
+
+ align:start position:0%
+talked about last week and we also
+ 
+
+ align:start position:0%
+talked about last week and we also
+talked about how you can draw an
+
+ align:start position:0%
+talked about how you can draw an
+ 
+
+ align:start position:0%
+talked about how you can draw an
+octahedral Crystal field splitting
+
+ align:start position:0%
+octahedral Crystal field splitting
+ 
+
+ align:start position:0%
+octahedral Crystal field splitting
+diagram and here's the average energy of
+
+ align:start position:0%
+diagram and here's the average energy of
+ 
+
+ align:start position:0%
+diagram and here's the average energy of
+the D orbitals with this sort of uh
+
+ align:start position:0%
+the D orbitals with this sort of uh
+ 
+
+ align:start position:0%
+the D orbitals with this sort of uh
+spherical Crystal field where ligans are
+
+ align:start position:0%
+spherical Crystal field where ligans are
+ 
+
+ align:start position:0%
+spherical Crystal field where ligans are
+everywhere and so when lians are
+
+ align:start position:0%
+everywhere and so when lians are
+ 
+
+ align:start position:0%
+everywhere and so when lians are
+everywhere all of the D orbitals have
+
+ align:start position:0%
+everywhere all of the D orbitals have
+ 
+
+ align:start position:0%
+everywhere all of the D orbitals have
+the same energy but then when you put
+
+ align:start position:0%
+the same energy but then when you put
+ 
+
+ align:start position:0%
+the same energy but then when you put
+the lians in their locations in the
+
+ align:start position:0%
+the lians in their locations in the
+ 
+
+ align:start position:0%
+the lians in their locations in the
+octahedral geometry framework then these
+
+ align:start position:0%
+octahedral geometry framework then these
+ 
+
+ align:start position:0%
+octahedral geometry framework then these
+two uh sets of orbitals DX dx^ 2 minus
+
+ align:start position:0%
+two uh sets of orbitals DX dx^ 2 minus
+ 
+
+ align:start position:0%
+two uh sets of orbitals DX dx^ 2 minus
+y^2 and dz^2 are up in energy they're
+
+ align:start position:0%
+y^2 and dz^2 are up in energy they're
+ 
+
+ align:start position:0%
+y^2 and dz^2 are up in energy they're
+destabilized and these three go down in
+
+ align:start position:0%
+destabilized and these three go down in
+ 
+
+ align:start position:0%
+destabilized and these three go down in
+energy and the overall energy of the
+
+ align:start position:0%
+energy and the overall energy of the
+ 
+
+ align:start position:0%
+energy and the overall energy of the
+system is maintained so here's the
+
+ align:start position:0%
+system is maintained so here's the
+ 
+
+ align:start position:0%
+system is maintained so here's the
+crystal
+
+ align:start position:0%
+crystal
+ 
+
+ align:start position:0%
+crystal
+Crystal field splitting energy for the
+
+ align:start position:0%
+Crystal field splitting energy for the
+ 
+
+ align:start position:0%
+Crystal field splitting energy for the
+octahedral case o for octahedral and so
+
+ align:start position:0%
+octahedral case o for octahedral and so
+ 
+
+ align:start position:0%
+octahedral case o for octahedral and so
+it's split two orbitals go up in energy
+
+ align:start position:0%
+it's split two orbitals go up in energy
+ 
+
+ align:start position:0%
+it's split two orbitals go up in energy
+so they go up by three fifths three go
+
+ align:start position:0%
+so they go up by three fifths three go
+ 
+
+ align:start position:0%
+so they go up by three fifths three go
+down so they go down by two fifths to
+
+ align:start position:0%
+down so they go down by two fifths to
+ 
+
+ align:start position:0%
+down so they go down by two fifths to
+maintain the overall uh energy of the
+
+ align:start position:0%
+maintain the overall uh energy of the
+ 
+
+ align:start position:0%
+maintain the overall uh energy of the
+system so that's what we talked about
+
+ align:start position:0%
+system so that's what we talked about
+ 
+
+ align:start position:0%
+system so that's what we talked about
+last time and I just wanted to review it
+
+ align:start position:0%
+last time and I just wanted to review it
+ 
+
+ align:start position:0%
+last time and I just wanted to review it
+because we're going to go on and talk
+
+ align:start position:0%
+because we're going to go on and talk
+ 
+
+ align:start position:0%
+because we're going to go on and talk
+about other types of geometry and of
+
+ align:start position:0%
+about other types of geometry and of
+ 
+
+ align:start position:0%
+about other types of geometry and of
+course uh remember that exam three is on
+
+ align:start position:0%
+course uh remember that exam three is on
+ 
+
+ align:start position:0%
+course uh remember that exam three is on
+Wednesday uh extra problems are posted
+
+ align:start position:0%
+Wednesday uh extra problems are posted
+ 
+
+ align:start position:0%
+Wednesday uh extra problems are posted
+um I will mention that I actually posted
+
+ align:start position:0%
+um I will mention that I actually posted
+ 
+
+ align:start position:0%
+um I will mention that I actually posted
+the original exam last year and the exam
+
+ align:start position:0%
+the original exam last year and the exam
+ 
+
+ align:start position:0%
+the original exam last year and the exam
+that people took was slightly easier
+
+ align:start position:0%
+that people took was slightly easier
+ 
+
+ align:start position:0%
+that people took was slightly easier
+than the one I posted I did that
+
+ align:start position:0%
+than the one I posted I did that
+ 
+
+ align:start position:0%
+than the one I posted I did that
+actually by mistake but it turns out
+
+ align:start position:0%
+actually by mistake but it turns out
+ 
+
+ align:start position:0%
+actually by mistake but it turns out
+that if you do that the exam that's
+
+ align:start position:0%
+that if you do that the exam that's
+ 
+
+ align:start position:0%
+that if you do that the exam that's
+posted is a better indicator of how well
+
+ align:start position:0%
+posted is a better indicator of how well
+ 
+
+ align:start position:0%
+posted is a better indicator of how well
+you'll do on this next exam because the
+
+ align:start position:0%
+you'll do on this next exam because the
+ 
+
+ align:start position:0%
+you'll do on this next exam because the
+final exam the third exam last year was
+
+ align:start position:0%
+final exam the third exam last year was
+ 
+
+ align:start position:0%
+final exam the third exam last year was
+a bit too easy um I.E too too easy means
+
+ align:start position:0%
+a bit too easy um I.E too too easy means
+ 
+
+ align:start position:0%
+a bit too easy um I.E too too easy means
+that you know the sort of outstanding
+
+ align:start position:0%
+that you know the sort of outstanding
+ 
+
+ align:start position:0%
+that you know the sort of outstanding
+category was like 98 and above and if
+
+ align:start position:0%
+category was like 98 and above and if
+ 
+
+ align:start position:0%
+category was like 98 and above and if
+you got a 97 then that was no longer
+
+ align:start position:0%
+you got a 97 then that was no longer
+ 
+
+ align:start position:0%
+you got a 97 then that was no longer
+outstanding so whether you got three
+
+ align:start position:0%
+outstanding so whether you got three
+ 
+
+ align:start position:0%
+outstanding so whether you got three
+significant figures wrong or two made it
+
+ align:start position:0%
+significant figures wrong or two made it
+ 
+
+ align:start position:0%
+significant figures wrong or two made it
+some difference in your grade that that
+
+ align:start position:0%
+some difference in your grade that that
+ 
+
+ align:start position:0%
+some difference in your grade that that
+clustering I don't like I like to have
+
+ align:start position:0%
+clustering I don't like I like to have
+ 
+
+ align:start position:0%
+clustering I don't like I like to have
+the average such that people's uh
+
+ align:start position:0%
+the average such that people's uh
+ 
+
+ align:start position:0%
+the average such that people's uh
+performance on the exam really indicates
+
+ align:start position:0%
+performance on the exam really indicates
+ 
+
+ align:start position:0%
+performance on the exam really indicates
+more how well they know the the material
+
+ align:start position:0%
+more how well they know the the material
+ 
+
+ align:start position:0%
+more how well they know the the material
+so the exam that's posted is actually
+
+ align:start position:0%
+so the exam that's posted is actually
+ 
+
+ align:start position:0%
+so the exam that's posted is actually
+the the better review so even though
+
+ align:start position:0%
+the the better review so even though
+ 
+
+ align:start position:0%
+the the better review so even though
+that was an accident I'll pretend I did
+
+ align:start position:0%
+that was an accident I'll pretend I did
+ 
+
+ align:start position:0%
+that was an accident I'll pretend I did
+it on purpose because it's a better
+
+ align:start position:0%
+it on purpose because it's a better
+ 
+
+ align:start position:0%
+it on purpose because it's a better
+thing so uh extra problems on So today
+
+ align:start position:0%
+thing so uh extra problems on So today
+ 
+
+ align:start position:0%
+thing so uh extra problems on So today
+we're going to finish up Crystal field
+
+ align:start position:0%
+we're going to finish up Crystal field
+ 
+
+ align:start position:0%
+we're going to finish up Crystal field
+Theory and then talk about the relevance
+
+ align:start position:0%
+Theory and then talk about the relevance
+ 
+
+ align:start position:0%
+Theory and then talk about the relevance
+of Crystal field Theory and the
+
+ align:start position:0%
+of Crystal field Theory and the
+ 
+
+ align:start position:0%
+of Crystal field Theory and the
+relevance comes into explaining the
+
+ align:start position:0%
+relevance comes into explaining the
+ 
+
+ align:start position:0%
+relevance comes into explaining the
+colors of these transition uh compounds
+
+ align:start position:0%
+colors of these transition uh compounds
+ 
+
+ align:start position:0%
+colors of these transition uh compounds
+so they have these me compounds with
+
+ align:start position:0%
+so they have these me compounds with
+ 
+
+ align:start position:0%
+so they have these me compounds with
+metals have some really spectacular
+
+ align:start position:0%
+metals have some really spectacular
+ 
+
+ align:start position:0%
+metals have some really spectacular
+colors and you can explain or
+
+ align:start position:0%
+colors and you can explain or
+ 
+
+ align:start position:0%
+colors and you can explain or
+rationalize some of these Colors by this
+
+ align:start position:0%
+rationalize some of these Colors by this
+ 
+
+ align:start position:0%
+rationalize some of these Colors by this
+really very simple Theory so that's fun
+
+ align:start position:0%
+really very simple Theory so that's fun
+ 
+
+ align:start position:0%
+really very simple Theory so that's fun
+and you can also explain some of the
+
+ align:start position:0%
+and you can also explain some of the
+ 
+
+ align:start position:0%
+and you can also explain some of the
+properties and magnetism of these
+
+ align:start position:0%
+properties and magnetism of these
+ 
+
+ align:start position:0%
+properties and magnetism of these
+compounds by this fairly simple Le
+
+ align:start position:0%
+compounds by this fairly simple Le
+ 
+
+ align:start position:0%
+compounds by this fairly simple Le
+Theory okay so let's look at the uh
+
+ align:start position:0%
+Theory okay so let's look at the uh
+ 
+
+ align:start position:0%
+Theory okay so let's look at the uh
+tetrahedral case
+
+ align:start position:0%
+tetrahedral case
+ 
+
+ align:start position:0%
+tetrahedral case
+now so here we have our tetrahedral
+
+ align:start position:0%
+now so here we have our tetrahedral
+ 
+
+ align:start position:0%
+now so here we have our tetrahedral
+molecule I'll try to kind of hold it up
+
+ align:start position:0%
+molecule I'll try to kind of hold it up
+ 
+
+ align:start position:0%
+molecule I'll try to kind of hold it up
+as it's displayed on the on the board so
+
+ align:start position:0%
+as it's displayed on the on the board so
+ 
+
+ align:start position:0%
+as it's displayed on the on the board so
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+case we have two lians up one coming
+
+ align:start position:0%
+case we have two lians up one coming
+ 
+
+ align:start position:0%
+case we have two lians up one coming
+towards you one going back so coming to
+
+ align:start position:0%
+towards you one going back so coming to
+ 
+
+ align:start position:0%
+towards you one going back so coming to
+going coming towards you and going back
+
+ align:start position:0%
+going coming towards you and going back
+ 
+
+ align:start position:0%
+going coming towards you and going back
+and then we have two ligans in the plane
+
+ align:start position:0%
+and then we have two ligans in the plane
+ 
+
+ align:start position:0%
+and then we have two ligans in the plane
+of the screen and in this case the
+
+ align:start position:0%
+of the screen and in this case the
+ 
+
+ align:start position:0%
+of the screen and in this case the
+convention is to draw the Z axis coming
+
+ align:start position:0%
+convention is to draw the Z axis coming
+ 
+
+ align:start position:0%
+convention is to draw the Z axis coming
+down here and the Y AIS is kind of
+
+ align:start position:0%
+down here and the Y AIS is kind of
+ 
+
+ align:start position:0%
+down here and the Y AIS is kind of
+coming in from the side and the x- axis
+
+ align:start position:0%
+coming in from the side and the x- axis
+ 
+
+ align:start position:0%
+coming in from the side and the x- axis
+is coming out towards you here so that's
+
+ align:start position:0%
+is coming out towards you here so that's
+ 
+
+ align:start position:0%
+is coming out towards you here so that's
+uh what this what this picture
+
+ align:start position:0%
+uh what this what this picture
+ 
+
+ align:start position:0%
+uh what this what this picture
+indicates so the crystal field uh
+
+ align:start position:0%
+indicates so the crystal field uh
+ 
+
+ align:start position:0%
+indicates so the crystal field uh
+splitting energy tends to be smaller
+
+ align:start position:0%
+splitting energy tends to be smaller
+ 
+
+ align:start position:0%
+splitting energy tends to be smaller
+than the octahedral crystal field energy
+
+ align:start position:0%
+than the octahedral crystal field energy
+ 
+
+ align:start position:0%
+than the octahedral crystal field energy
+because because none of the point Lian
+
+ align:start position:0%
+because because none of the point Lian
+ 
+
+ align:start position:0%
+because because none of the point Lian
+point charges are really pointing toward
+
+ align:start position:0%
+point charges are really pointing toward
+ 
+
+ align:start position:0%
+point charges are really pointing toward
+any of the D orbitals and let's just
+
+ align:start position:0%
+any of the D orbitals and let's just
+ 
+
+ align:start position:0%
+any of the D orbitals and let's just
+take a look at all the D orbitals and
+
+ align:start position:0%
+take a look at all the D orbitals and
+ 
+
+ align:start position:0%
+take a look at all the D orbitals and
+consider then which ones are going to
+
+ align:start position:0%
+consider then which ones are going to
+ 
+
+ align:start position:0%
+consider then which ones are going to
+have more repulsion than other
+
+ align:start position:0%
+have more repulsion than other
+ 
+
+ align:start position:0%
+have more repulsion than other
+ones so if we go through and take a look
+
+ align:start position:0%
+ones so if we go through and take a look
+ 
+
+ align:start position:0%
+ones so if we go through and take a look
+at it and I've tried to indicate so here
+
+ align:start position:0%
+at it and I've tried to indicate so here
+ 
+
+ align:start position:0%
+at it and I've tried to indicate so here
+are our tetrahedral cases and here are
+
+ align:start position:0%
+are our tetrahedral cases and here are
+ 
+
+ align:start position:0%
+are our tetrahedral cases and here are
+our 5D orbitals and these little lines
+
+ align:start position:0%
+our 5D orbitals and these little lines
+ 
+
+ align:start position:0%
+our 5D orbitals and these little lines
+of the negative charge in the arrow is
+
+ align:start position:0%
+of the negative charge in the arrow is
+ 
+
+ align:start position:0%
+of the negative charge in the arrow is
+sort of a rough approximation of how
+
+ align:start position:0%
+sort of a rough approximation of how
+ 
+
+ align:start position:0%
+sort of a rough approximation of how
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+point charges are going to be coming in
+
+ align:start position:0%
+point charges are going to be coming in
+ 
+
+ align:start position:0%
+point charges are going to be coming in
+and pointing toward the D orbitals if
+
+ align:start position:0%
+and pointing toward the D orbitals if
+ 
+
+ align:start position:0%
+and pointing toward the D orbitals if
+they're coming in with this tetrahedral
+
+ align:start position:0%
+they're coming in with this tetrahedral
+ 
+
+ align:start position:0%
+they're coming in with this tetrahedral
+geometry is drawn and so you can see for
+
+ align:start position:0%
+geometry is drawn and so you can see for
+ 
+
+ align:start position:0%
+geometry is drawn and so you can see for
+the dx2 minus y^2 none of those lians
+
+ align:start position:0%
+the dx2 minus y^2 none of those lians
+ 
+
+ align:start position:0%
+the dx2 minus y^2 none of those lians
+are pointing right at any of the D
+
+ align:start position:0%
+are pointing right at any of the D
+ 
+
+ align:start position:0%
+are pointing right at any of the D
+orbitals NE and they're definitely not
+
+ align:start position:0%
+orbitals NE and they're definitely not
+ 
+
+ align:start position:0%
+orbitals NE and they're definitely not
+for the DZ squared either um a little
+
+ align:start position:0%
+for the DZ squared either um a little
+ 
+
+ align:start position:0%
+for the DZ squared either um a little
+bit more here but again not exactly uh
+
+ align:start position:0%
+bit more here but again not exactly uh
+ 
+
+ align:start position:0%
+bit more here but again not exactly uh
+pointing toward them although this
+
+ align:start position:0%
+pointing toward them although this
+ 
+
+ align:start position:0%
+pointing toward them although this
+picture looks like it is a little bit
+
+ align:start position:0%
+picture looks like it is a little bit
+ 
+
+ align:start position:0%
+picture looks like it is a little bit
+but again it's closer here but not
+
+ align:start position:0%
+but again it's closer here but not
+ 
+
+ align:start position:0%
+but again it's closer here but not
+exact so the result of this is that
+
+ align:start position:0%
+exact so the result of this is that
+ 
+
+ align:start position:0%
+exact so the result of this is that
+there's more a destabilization down here
+
+ align:start position:0%
+there's more a destabilization down here
+ 
+
+ align:start position:0%
+there's more a destabilization down here
+than there is up here so it turns out
+
+ align:start position:0%
+than there is up here so it turns out
+ 
+
+ align:start position:0%
+than there is up here so it turns out
+that this is then opposite of the
+
+ align:start position:0%
+that this is then opposite of the
+ 
+
+ align:start position:0%
+that this is then opposite of the
+octahedral case that we just talked
+
+ align:start position:0%
+octahedral case that we just talked
+ 
+
+ align:start position:0%
+octahedral case that we just talked
+about in octahedral these are the ones
+
+ align:start position:0%
+about in octahedral these are the ones
+ 
+
+ align:start position:0%
+about in octahedral these are the ones
+that are most
+
+ align:start position:0%
+that are most
+ 
+
+ align:start position:0%
+that are most
+destabilized in tetrahedral these are
+
+ align:start position:0%
+destabilized in tetrahedral these are
+ 
+
+ align:start position:0%
+destabilized in tetrahedral these are
+stabilized compared to the others so
+
+ align:start position:0%
+stabilized compared to the others so
+ 
+
+ align:start position:0%
+stabilized compared to the others so
+it's flipped exactly around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again there'd be more repulsion uh
+
+ align:start position:0%
+so again there'd be more repulsion uh
+ 
+
+ align:start position:0%
+so again there'd be more repulsion uh
+between the uh lens as negative point
+
+ align:start position:0%
+between the uh lens as negative point
+ 
+
+ align:start position:0%
+between the uh lens as negative point
+charges and the orbitals that are 45
+
+ align:start position:0%
+charges and the orbitals that are 45
+ 
+
+ align:start position:0%
+charges and the orbitals that are 45
+degree off axis because here the lians
+
+ align:start position:0%
+degree off axis because here the lians
+ 
+
+ align:start position:0%
+degree off axis because here the lians
+are off axis and also the orbitals are
+
+ align:start position:0%
+are off axis and also the orbitals are
+ 
+
+ align:start position:0%
+are off axis and also the orbitals are
+off axis they're not directly pointing
+
+ align:start position:0%
+off axis they're not directly pointing
+ 
+
+ align:start position:0%
+off axis they're not directly pointing
+at each other but it's definitely worse
+
+ align:start position:0%
+at each other but it's definitely worse
+ 
+
+ align:start position:0%
+at each other but it's definitely worse
+down here uh these guys are really far
+
+ align:start position:0%
+down here uh these guys are really far
+ 
+
+ align:start position:0%
+down here uh these guys are really far
+away from those Lian point charges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these two will have the same energy
+
+ align:start position:0%
+so these two will have the same energy
+ 
+
+ align:start position:0%
+so these two will have the same energy
+with respect to each other they will
+
+ align:start position:0%
+with respect to each other they will
+ 
+
+ align:start position:0%
+with respect to each other they will
+also be degenerate as they were before
+
+ align:start position:0%
+also be degenerate as they were before
+ 
+
+ align:start position:0%
+also be degenerate as they were before
+and these three have the same energy
+
+ align:start position:0%
+and these three have the same energy
+ 
+
+ align:start position:0%
+and these three have the same energy
+with respect to each other they are also
+
+ align:start position:0%
+with respect to each other they are also
+ 
+
+ align:start position:0%
+with respect to each other they are also
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degenerate so then we can draw what the
+
+ align:start position:0%
+degenerate so then we can draw what the
+ 
+
+ align:start position:0%
+degenerate so then we can draw what the
+diagram will look like for the
+
+ align:start position:0%
+diagram will look like for the
+ 
+
+ align:start position:0%
+diagram will look like for the
+tetrahedral case so again here was the
+
+ align:start position:0%
+tetrahedral case so again here was the
+ 
+
+ align:start position:0%
+tetrahedral case so again here was the
+octahedral case now this is the
+
+ align:start position:0%
+octahedral case now this is the
+ 
+
+ align:start position:0%
+octahedral case now this is the
+tetrahedral case and so we have the
+
+ align:start position:0%
+tetrahedral case and so we have the
+ 
+
+ align:start position:0%
+tetrahedral case and so we have the
+splitting energy which is the energy
+
+ align:start position:0%
+splitting energy which is the energy
+ 
+
+ align:start position:0%
+splitting energy which is the energy
+that splits the the orbitals um based on
+
+ align:start position:0%
+that splits the the orbitals um based on
+ 
+
+ align:start position:0%
+that splits the the orbitals um based on
+these negative point charges compared to
+
+ align:start position:0%
+these negative point charges compared to
+ 
+
+ align:start position:0%
+these negative point charges compared to
+this uh theoretical uh spherical Crystal
+
+ align:start position:0%
+this uh theoretical uh spherical Crystal
+ 
+
+ align:start position:0%
+this uh theoretical uh spherical Crystal
+field and we also have a uh tetrahedral
+
+ align:start position:0%
+field and we also have a uh tetrahedral
+ 
+
+ align:start position:0%
+field and we also have a uh tetrahedral
+Crystal field splitting energy so that's
+
+ align:start position:0%
+Crystal field splitting energy so that's
+ 
+
+ align:start position:0%
+Crystal field splitting energy so that's
+uh drawn here now the first thing which
+
+ align:start position:0%
+uh drawn here now the first thing which
+ 
+
+ align:start position:0%
+uh drawn here now the first thing which
+I emphasized that I'll point out again
+
+ align:start position:0%
+I emphasized that I'll point out again
+ 
+
+ align:start position:0%
+I emphasized that I'll point out again
+is that these guys are flipped around so
+
+ align:start position:0%
+is that these guys are flipped around so
+ 
+
+ align:start position:0%
+is that these guys are flipped around so
+in instead of being um destabilized as
+
+ align:start position:0%
+in instead of being um destabilized as
+ 
+
+ align:start position:0%
+in instead of being um destabilized as
+they are in the octahedral crystal field
+
+ align:start position:0%
+they are in the octahedral crystal field
+ 
+
+ align:start position:0%
+they are in the octahedral crystal field
+the dx^ 2us y^2 and DZ squared are now
+
+ align:start position:0%
+the dx^ 2us y^2 and DZ squared are now
+ 
+
+ align:start position:0%
+the dx^ 2us y^2 and DZ squared are now
+stabilized compared to the other orbital
+
+ align:start position:0%
+stabilized compared to the other orbital
+ 
+
+ align:start position:0%
+stabilized compared to the other orbital
+set so they've switched positions these
+
+ align:start position:0%
+set so they've switched positions these
+ 
+
+ align:start position:0%
+set so they've switched positions these
+instead of being stabilized are now more
+
+ align:start position:0%
+instead of being stabilized are now more
+ 
+
+ align:start position:0%
+instead of being stabilized are now more
+destabilized so it's a direct
+
+ align:start position:0%
+destabilized so it's a direct
+ 
+
+ align:start position:0%
+destabilized so it's a direct
+switch there's also a little change in
+
+ align:start position:0%
+switch there's also a little change in
+ 
+
+ align:start position:0%
+switch there's also a little change in
+in nomenclature here so you can still
+
+ align:start position:0%
+in nomenclature here so you can still
+ 
+
+ align:start position:0%
+in nomenclature here so you can still
+refer to this orbital Set uh with the
+
+ align:start position:0%
+refer to this orbital Set uh with the
+ 
+
+ align:start position:0%
+refer to this orbital Set uh with the
+term e but instead of EG we have e and
+
+ align:start position:0%
+term e but instead of EG we have e and
+ 
+
+ align:start position:0%
+term e but instead of EG we have e and
+I'll just point out that the book has uh
+
+ align:start position:0%
+I'll just point out that the book has uh
+ 
+
+ align:start position:0%
+I'll just point out that the book has uh
+calls this e too and sometimes it calls
+
+ align:start position:0%
+calls this e too and sometimes it calls
+ 
+
+ align:start position:0%
+calls this e too and sometimes it calls
+an e it should just be uh e but this is
+
+ align:start position:0%
+an e it should just be uh e but this is
+ 
+
+ align:start position:0%
+an e it should just be uh e but this is
+kind of a small point but I don't want
+
+ align:start position:0%
+kind of a small point but I don't want
+ 
+
+ align:start position:0%
+kind of a small point but I don't want
+people to get confused by that and
+
+ align:start position:0%
+people to get confused by that and
+ 
+
+ align:start position:0%
+people to get confused by that and
+instead of t2g we have T2 up here so
+
+ align:start position:0%
+instead of t2g we have T2 up here so
+ 
+
+ align:start position:0%
+instead of t2g we have T2 up here so
+basically the the G uh term is gone in
+
+ align:start position:0%
+basically the the G uh term is gone in
+ 
+
+ align:start position:0%
+basically the the G uh term is gone in
+this case and you'll learn a lot more
+
+ align:start position:0%
+this case and you'll learn a lot more
+ 
+
+ align:start position:0%
+this case and you'll learn a lot more
+about that if you go on and and take
+
+ align:start position:0%
+about that if you go on and and take
+ 
+
+ align:start position:0%
+about that if you go on and and take
+more inorganic chemistry so these are
+
+ align:start position:0%
+more inorganic chemistry so these are
+ 
+
+ align:start position:0%
+more inorganic chemistry so these are
+flipped what else is
+
+ align:start position:0%
+flipped what else is
+ 
+
+ align:start position:0%
+flipped what else is
+true well the other thing that's true is
+
+ align:start position:0%
+true well the other thing that's true is
+ 
+
+ align:start position:0%
+true well the other thing that's true is
+that this splitting energy is much
+
+ align:start position:0%
+that this splitting energy is much
+ 
+
+ align:start position:0%
+that this splitting energy is much
+smaller in the tetrahedral case than it
+
+ align:start position:0%
+smaller in the tetrahedral case than it
+ 
+
+ align:start position:0%
+smaller in the tetrahedral case than it
+is in the octahedral case so here
+
+ align:start position:0%
+is in the octahedral case so here
+ 
+
+ align:start position:0%
+is in the octahedral case so here
+there's a much bigger uh distance
+
+ align:start position:0%
+there's a much bigger uh distance
+ 
+
+ align:start position:0%
+there's a much bigger uh distance
+between the orbitals here it's a much
+
+ align:start position:0%
+between the orbitals here it's a much
+ 
+
+ align:start position:0%
+between the orbitals here it's a much
+smaller distance and that is because in
+
+ align:start position:0%
+smaller distance and that is because in
+ 
+
+ align:start position:0%
+smaller distance and that is because in
+the octahedral case there are lians
+
+ align:start position:0%
+the octahedral case there are lians
+ 
+
+ align:start position:0%
+the octahedral case there are lians
+pointing directly at the D orbitals so
+
+ align:start position:0%
+pointing directly at the D orbitals so
+ 
+
+ align:start position:0%
+pointing directly at the D orbitals so
+in this uh framework for octahedral
+
+ align:start position:0%
+in this uh framework for octahedral
+ 
+
+ align:start position:0%
+in this uh framework for octahedral
+their ligans right along Z along X and
+
+ align:start position:0%
+their ligans right along Z along X and
+ 
+
+ align:start position:0%
+their ligans right along Z along X and
+along Y and so they're along all of the
+
+ align:start position:0%
+along Y and so they're along all of the
+ 
+
+ align:start position:0%
+along Y and so they're along all of the
+orbitals Al pointing directly toward the
+
+ align:start position:0%
+orbitals Al pointing directly toward the
+ 
+
+ align:start position:0%
+orbitals Al pointing directly toward the
+orbitals in the tetrahedral case not
+
+ align:start position:0%
+orbitals in the tetrahedral case not
+ 
+
+ align:start position:0%
+orbitals in the tetrahedral case not
+really pointing directly toward they're
+
+ align:start position:0%
+really pointing directly toward they're
+ 
+
+ align:start position:0%
+really pointing directly toward they're
+closer to some than to others but it's
+
+ align:start position:0%
+closer to some than to others but it's
+ 
+
+ align:start position:0%
+closer to some than to others but it's
+not as direct so result of that is that
+
+ align:start position:0%
+not as direct so result of that is that
+ 
+
+ align:start position:0%
+not as direct so result of that is that
+there's just not split that much there's
+
+ align:start position:0%
+there's just not split that much there's
+ 
+
+ align:start position:0%
+there's just not split that much there's
+not such a huge difference between the
+
+ align:start position:0%
+not such a huge difference between the
+ 
+
+ align:start position:0%
+not such a huge difference between the
+energy levels of the D orbitals in this
+
+ align:start position:0%
+energy levels of the D orbitals in this
+ 
+
+ align:start position:0%
+energy levels of the D orbitals in this
+case so what is what does this mean well
+
+ align:start position:0%
+case so what is what does this mean well
+ 
+
+ align:start position:0%
+case so what is what does this mean well
+it means that uh a lot of tetrahedral uh
+
+ align:start position:0%
+it means that uh a lot of tetrahedral uh
+ 
+
+ align:start position:0%
+it means that uh a lot of tetrahedral uh
+complexes because the splitting energy
+
+ align:start position:0%
+complexes because the splitting energy
+ 
+
+ align:start position:0%
+complexes because the splitting energy
+is small a lot of them are called high
+
+ align:start position:0%
+is small a lot of them are called high
+ 
+
+ align:start position:0%
+is small a lot of them are called high
+Spin and we talked about this uh last
+
+ align:start position:0%
+Spin and we talked about this uh last
+ 
+
+ align:start position:0%
+Spin and we talked about this uh last
+Monday that in high spin you have the
+
+ align:start position:0%
+Monday that in high spin you have the
+ 
+
+ align:start position:0%
+Monday that in high spin you have the
+maximum number of unpaired
+
+ align:start position:0%
+maximum number of unpaired
+ 
+
+ align:start position:0%
+maximum number of unpaired
+electrons and um because this and the
+
+ align:start position:0%
+electrons and um because this and the
+ 
+
+ align:start position:0%
+electrons and um because this and the
+purpose of this you can just assume that
+
+ align:start position:0%
+purpose of this you can just assume that
+ 
+
+ align:start position:0%
+purpose of this you can just assume that
+if you have a tetrahedral complex it
+
+ align:start position:0%
+if you have a tetrahedral complex it
+ 
+
+ align:start position:0%
+if you have a tetrahedral complex it
+will be high spin so that will come in
+
+ align:start position:0%
+will be high spin so that will come in
+ 
+
+ align:start position:0%
+will be high spin so that will come in
+into play when you figure out how to put
+
+ align:start position:0%
+into play when you figure out how to put
+ 
+
+ align:start position:0%
+into play when you figure out how to put
+your electrons into this diagram whether
+
+ align:start position:0%
+your electrons into this diagram whether
+ 
+
+ align:start position:0%
+your electrons into this diagram whether
+you put them in singly to the fullest
+
+ align:start position:0%
+you put them in singly to the fullest
+ 
+
+ align:start position:0%
+you put them in singly to the fullest
+extent possible without pairing or if
+
+ align:start position:0%
+extent possible without pairing or if
+ 
+
+ align:start position:0%
+extent possible without pairing or if
+you start to pair so in this case you
+
+ align:start position:0%
+you start to pair so in this case you
+ 
+
+ align:start position:0%
+you start to pair so in this case you
+can put them in singly to the fullest
+
+ align:start position:0%
+can put them in singly to the fullest
+ 
+
+ align:start position:0%
+can put them in singly to the fullest
+extent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible okay and um as I mentioned
+
+ align:start position:0%
+possible okay and um as I mentioned
+ 
+
+ align:start position:0%
+possible okay and um as I mentioned
+before the overall uh energy of the
+
+ align:start position:0%
+before the overall uh energy of the
+ 
+
+ align:start position:0%
+before the overall uh energy of the
+system is maintained so in this case you
+
+ align:start position:0%
+system is maintained so in this case you
+ 
+
+ align:start position:0%
+system is maintained so in this case you
+have two orbitals that go up in energy
+
+ align:start position:0%
+have two orbitals that go up in energy
+ 
+
+ align:start position:0%
+have two orbitals that go up in energy
+so they go up by three fifths three that
+
+ align:start position:0%
+so they go up by three fifths three that
+ 
+
+ align:start position:0%
+so they go up by three fifths three that
+come down so they go come down by two
+
+ align:start position:0%
+come down so they go come down by two
+ 
+
+ align:start position:0%
+come down so they go come down by two
+fifths in this case you have three going
+
+ align:start position:0%
+fifths in this case you have three going
+ 
+
+ align:start position:0%
+fifths in this case you have three going
+up so they'll go up by two fifths and
+
+ align:start position:0%
+up so they'll go up by two fifths and
+ 
+
+ align:start position:0%
+up so they'll go up by two fifths and
+you have two going down in energy so
+
+ align:start position:0%
+you have two going down in energy so
+ 
+
+ align:start position:0%
+you have two going down in energy so
+they'll go down by three fifths to
+
+ align:start position:0%
+they'll go down by three fifths to
+ 
+
+ align:start position:0%
+they'll go down by three fifths to
+maintain the overall energy of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+oops okay so that's the tetrahedral case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's consider Square
+
+ align:start position:0%
+so now let's consider Square
+ 
+
+ align:start position:0%
+so now let's consider Square
+planer so here we have our Square planer
+
+ align:start position:0%
+planer so here we have our Square planer
+ 
+
+ align:start position:0%
+planer so here we have our Square planer
+molecule and we have uh lians along the
+
+ align:start position:0%
+molecule and we have uh lians along the
+ 
+
+ align:start position:0%
+molecule and we have uh lians along the
+Y AIS lians along the xaxis pointing out
+
+ align:start position:0%
+Y AIS lians along the xaxis pointing out
+ 
+
+ align:start position:0%
+Y AIS lians along the xaxis pointing out
+towards you one and one going back
+
+ align:start position:0%
+towards you one and one going back
+ 
+
+ align:start position:0%
+towards you one and one going back
+behind and Z then is coming up and down
+
+ align:start position:0%
+behind and Z then is coming up and down
+ 
+
+ align:start position:0%
+behind and Z then is coming up and down
+in this plane so with this uh lians a y
+
+ align:start position:0%
+in this plane so with this uh lians a y
+ 
+
+ align:start position:0%
+in this plane so with this uh lians a y
+and a
+
+ align:start position:0%
+and a
+ 
+
+ align:start position:0%
+and a
+X which would you predict which orbitals
+
+ align:start position:0%
+X which would you predict which orbitals
+ 
+
+ align:start position:0%
+X which would you predict which orbitals
+do you predict would be destabilized the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+most D I heard dxy that's one what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else dx2 minus y^2 right so those two so
+
+ align:start position:0%
+else dx2 minus y^2 right so those two so
+ 
+
+ align:start position:0%
+else dx2 minus y^2 right so those two so
+the ones that don't have the Z component
+
+ align:start position:0%
+the ones that don't have the Z component
+ 
+
+ align:start position:0%
+the ones that don't have the Z component
+in them so there's really not much
+
+ align:start position:0%
+in them so there's really not much
+ 
+
+ align:start position:0%
+in them so there's really not much
+destabilization along Z there no ligans
+
+ align:start position:0%
+destabilization along Z there no ligans
+ 
+
+ align:start position:0%
+destabilization along Z there no ligans
+along Z so orbitals that have amplitude
+
+ align:start position:0%
+along Z so orbitals that have amplitude
+ 
+
+ align:start position:0%
+along Z so orbitals that have amplitude
+along Z are not as affected so the ones
+
+ align:start position:0%
+along Z are not as affected so the ones
+ 
+
+ align:start position:0%
+along Z are not as affected so the ones
+that will be most affected are the
+
+ align:start position:0%
+that will be most affected are the
+ 
+
+ align:start position:0%
+that will be most affected are the
+orbitals that have component in the X
+
+ align:start position:0%
+orbitals that have component in the X
+ 
+
+ align:start position:0%
+orbitals that have component in the X
+and the y direction where the lians
+
+ align:start position:0%
+and the y direction where the lians
+ 
+
+ align:start position:0%
+and the y direction where the lians
+are so now we can consider the D
+
+ align:start position:0%
+are so now we can consider the D
+ 
+
+ align:start position:0%
+are so now we can consider the D
+orbitals and uh talk a little bit more
+
+ align:start position:0%
+orbitals and uh talk a little bit more
+ 
+
+ align:start position:0%
+orbitals and uh talk a little bit more
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+this so if we look at these two sets of
+
+ align:start position:0%
+this so if we look at these two sets of
+ 
+
+ align:start position:0%
+this so if we look at these two sets of
+orbitals now here as you uh correctly
+
+ align:start position:0%
+orbitals now here as you uh correctly
+ 
+
+ align:start position:0%
+orbitals now here as you uh correctly
+predicted there'll be lots of repulsion
+
+ align:start position:0%
+predicted there'll be lots of repulsion
+ 
+
+ align:start position:0%
+predicted there'll be lots of repulsion
+so the ligans are pointing directly at
+
+ align:start position:0%
+so the ligans are pointing directly at
+ 
+
+ align:start position:0%
+so the ligans are pointing directly at
+these de orbitals the lians are on axis
+
+ align:start position:0%
+these de orbitals the lians are on axis
+ 
+
+ align:start position:0%
+these de orbitals the lians are on axis
+the orbitals are on axis it's a direct
+
+ align:start position:0%
+the orbitals are on axis it's a direct
+ 
+
+ align:start position:0%
+the orbitals are on axis it's a direct
+hit so there's a lot of destabilization
+
+ align:start position:0%
+hit so there's a lot of destabilization
+ 
+
+ align:start position:0%
+hit so there's a lot of destabilization
+and this one now is going to be
+
+ align:start position:0%
+and this one now is going to be
+ 
+
+ align:start position:0%
+and this one now is going to be
+destabilized compared to all other ones
+
+ align:start position:0%
+destabilized compared to all other ones
+ 
+
+ align:start position:0%
+destabilized compared to all other ones
+so it's going to be by itself the most
+
+ align:start position:0%
+so it's going to be by itself the most
+ 
+
+ align:start position:0%
+so it's going to be by itself the most
+destabilized
+
+ align:start position:0%
+destabilized
+ 
+
+ align:start position:0%
+destabilized
+orbital DZ squared doesn't really have
+
+ align:start position:0%
+orbital DZ squared doesn't really have
+ 
+
+ align:start position:0%
+orbital DZ squared doesn't really have
+much destabilization
+
+ align:start position:0%
+much destabilization
+ 
+
+ align:start position:0%
+much destabilization
+uh at all in fact it'll be stabilized
+
+ align:start position:0%
+uh at all in fact it'll be stabilized
+ 
+
+ align:start position:0%
+uh at all in fact it'll be stabilized
+there's no lians along Z so there's no
+
+ align:start position:0%
+there's no lians along Z so there's no
+ 
+
+ align:start position:0%
+there's no lians along Z so there's no
+there's no real repulsion of the lians
+
+ align:start position:0%
+there's no real repulsion of the lians
+ 
+
+ align:start position:0%
+there's no real repulsion of the lians
+to uh DZ squared so it's going to be a
+
+ align:start position:0%
+to uh DZ squared so it's going to be a
+ 
+
+ align:start position:0%
+to uh DZ squared so it's going to be a
+lot less than for this guy and also less
+
+ align:start position:0%
+lot less than for this guy and also less
+ 
+
+ align:start position:0%
+lot less than for this guy and also less
+for the than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dxy so we can draw this now put in two
+
+ align:start position:0%
+dxy so we can draw this now put in two
+ 
+
+ align:start position:0%
+dxy so we can draw this now put in two
+of the orbitals this one is going to be
+
+ align:start position:0%
+of the orbitals this one is going to be
+ 
+
+ align:start position:0%
+of the orbitals this one is going to be
+way up it's going to be by far the most
+
+ align:start position:0%
+way up it's going to be by far the most
+ 
+
+ align:start position:0%
+way up it's going to be by far the most
+destabilized
+
+ align:start position:0%
+destabilized
+ 
+
+ align:start position:0%
+destabilized
+so it's going to even go up from where
+
+ align:start position:0%
+so it's going to even go up from where
+ 
+
+ align:start position:0%
+so it's going to even go up from where
+it was in the octahedral case whereas
+
+ align:start position:0%
+it was in the octahedral case whereas
+ 
+
+ align:start position:0%
+it was in the octahedral case whereas
+dz^2 which was up here degenerate with
+
+ align:start position:0%
+dz^2 which was up here degenerate with
+ 
+
+ align:start position:0%
+dz^2 which was up here degenerate with
+dx^ 2 minus y^2 in the octahedral case
+
+ align:start position:0%
+dx^ 2 minus y^2 in the octahedral case
+ 
+
+ align:start position:0%
+dx^ 2 minus y^2 in the octahedral case
+is now going to drop way down so these
+
+ align:start position:0%
+is now going to drop way down so these
+ 
+
+ align:start position:0%
+is now going to drop way down so these
+aren't equivalent at all
+
+ align:start position:0%
+aren't equivalent at all
+ 
+
+ align:start position:0%
+aren't equivalent at all
+anymore and so this makes sense the
+
+ align:start position:0%
+anymore and so this makes sense the
+ 
+
+ align:start position:0%
+anymore and so this makes sense the
+difference between the octahedral
+
+ align:start position:0%
+difference between the octahedral
+ 
+
+ align:start position:0%
+difference between the octahedral
+geometry is that there were lians along
+
+ align:start position:0%
+geometry is that there were lians along
+ 
+
+ align:start position:0%
+geometry is that there were lians along
+Z Now the lians along Z are gone in the
+
+ align:start position:0%
+Z Now the lians along Z are gone in the
+ 
+
+ align:start position:0%
+Z Now the lians along Z are gone in the
+Square planer case so there's a big
+
+ align:start position:0%
+Square planer case so there's a big
+ 
+
+ align:start position:0%
+Square planer case so there's a big
+difference between these two orbital
+
+ align:start position:0%
+difference between these two orbital
+ 
+
+ align:start position:0%
+difference between these two orbital
+sets in terms of
+
+ align:start position:0%
+sets in terms of
+ 
+
+ align:start position:0%
+sets in terms of
+energy now let's look at these three so
+
+ align:start position:0%
+energy now let's look at these three so
+ 
+
+ align:start position:0%
+energy now let's look at these three so
+this one as people correctly predicted
+
+ align:start position:0%
+this one as people correctly predicted
+ 
+
+ align:start position:0%
+this one as people correctly predicted
+is going to have a lot more repulsion
+
+ align:start position:0%
+is going to have a lot more repulsion
+ 
+
+ align:start position:0%
+is going to have a lot more repulsion
+than either of these because we have um
+
+ align:start position:0%
+than either of these because we have um
+ 
+
+ align:start position:0%
+than either of these because we have um
+amp the orbitals are have maximum
+
+ align:start position:0%
+amp the orbitals are have maximum
+ 
+
+ align:start position:0%
+amp the orbitals are have maximum
+amplitude along um X and Y they're
+
+ align:start position:0%
+amplitude along um X and Y they're
+ 
+
+ align:start position:0%
+amplitude along um X and Y they're
+actually 45 degrees off X and Y but
+
+ align:start position:0%
+actually 45 degrees off X and Y but
+ 
+
+ align:start position:0%
+actually 45 degrees off X and Y but
+still we don't have anything in the in
+
+ align:start position:0%
+still we don't have anything in the in
+ 
+
+ align:start position:0%
+still we don't have anything in the in
+the Z component here so this will be um
+
+ align:start position:0%
+the Z component here so this will be um
+ 
+
+ align:start position:0%
+the Z component here so this will be um
+this will be destabilized compared to
+
+ align:start position:0%
+this will be destabilized compared to
+ 
+
+ align:start position:0%
+this will be destabilized compared to
+these two and these two are stabilized
+
+ align:start position:0%
+these two and these two are stabilized
+ 
+
+ align:start position:0%
+these two and these two are stabilized
+compared to the D orbitals dxy D x^2
+
+ align:start position:0%
+compared to the D orbitals dxy D x^2
+ 
+
+ align:start position:0%
+compared to the D orbitals dxy D x^2
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+y^2 so now we can go and take a look at
+
+ align:start position:0%
+y^2 so now we can go and take a look at
+ 
+
+ align:start position:0%
+y^2 so now we can go and take a look at
+where these would be positioned
+
+ align:start position:0%
+where these would be positioned
+ 
+
+ align:start position:0%
+where these would be positioned
+approximately so if we look at this one
+
+ align:start position:0%
+approximately so if we look at this one
+ 
+
+ align:start position:0%
+approximately so if we look at this one
+it's not nearly as destabilized as this
+
+ align:start position:0%
+it's not nearly as destabilized as this
+ 
+
+ align:start position:0%
+it's not nearly as destabilized as this
+one but still it's a bit destabilized
+
+ align:start position:0%
+one but still it's a bit destabilized
+ 
+
+ align:start position:0%
+one but still it's a bit destabilized
+and above this this is this one is uh
+
+ align:start position:0%
+and above this this is this one is uh
+ 
+
+ align:start position:0%
+and above this this is this one is uh
+lower in energy and if you consider the
+
+ align:start position:0%
+lower in energy and if you consider the
+ 
+
+ align:start position:0%
+lower in energy and if you consider the
+here again dx^ 2us y^2 the lians are
+
+ align:start position:0%
+here again dx^ 2us y^2 the lians are
+ 
+
+ align:start position:0%
+here again dx^ 2us y^2 the lians are
+pointing directly at the orbitals it's
+
+ align:start position:0%
+pointing directly at the orbitals it's
+ 
+
+ align:start position:0%
+pointing directly at the orbitals it's
+on axis here it's 45 Dee off axis so
+
+ align:start position:0%
+on axis here it's 45 Dee off axis so
+ 
+
+ align:start position:0%
+on axis here it's 45 Dee off axis so
+it's not as destabilized but still it's
+
+ align:start position:0%
+it's not as destabilized but still it's
+ 
+
+ align:start position:0%
+it's not as destabilized but still it's
+up above where it was in the octahedral
+
+ align:start position:0%
+up above where it was in the octahedral
+ 
+
+ align:start position:0%
+up above where it was in the octahedral
+case and then finally these two guys uh
+
+ align:start position:0%
+case and then finally these two guys uh
+ 
+
+ align:start position:0%
+case and then finally these two guys uh
+don't have are going to be stabilized
+
+ align:start position:0%
+don't have are going to be stabilized
+ 
+
+ align:start position:0%
+don't have are going to be stabilized
+compared to this uh theoretical uh
+
+ align:start position:0%
+compared to this uh theoretical uh
+ 
+
+ align:start position:0%
+compared to this uh theoretical uh
+spherical Crystal field so they're going
+
+ align:start position:0%
+spherical Crystal field so they're going
+ 
+
+ align:start position:0%
+spherical Crystal field so they're going
+to be somewhere down down
+
+ align:start position:0%
+to be somewhere down down
+ 
+
+ align:start position:0%
+to be somewhere down down
+here so the big points here then are
+
+ align:start position:0%
+here so the big points here then are
+ 
+
+ align:start position:0%
+here so the big points here then are
+that when you get rid compared to the
+
+ align:start position:0%
+that when you get rid compared to the
+ 
+
+ align:start position:0%
+that when you get rid compared to the
+octahedral case you get rid of the
+
+ align:start position:0%
+octahedral case you get rid of the
+ 
+
+ align:start position:0%
+octahedral case you get rid of the
+ligans along Z this guy shoots up this
+
+ align:start position:0%
+ligans along Z this guy shoots up this
+ 
+
+ align:start position:0%
+ligans along Z this guy shoots up this
+one comes down it's
+
+ align:start position:0%
+one comes down it's
+ 
+
+ align:start position:0%
+one comes down it's
+stabilized uh the other D orbital that
+
+ align:start position:0%
+stabilized uh the other D orbital that
+ 
+
+ align:start position:0%
+stabilized uh the other D orbital that
+has maximum components along X and Y
+
+ align:start position:0%
+has maximum components along X and Y
+ 
+
+ align:start position:0%
+has maximum components along X and Y
+which is where those lians are goes up a
+
+ align:start position:0%
+which is where those lians are goes up a
+ 
+
+ align:start position:0%
+which is where those lians are goes up a
+little so these three are all sort of
+
+ align:start position:0%
+little so these three are all sort of
+ 
+
+ align:start position:0%
+little so these three are all sort of
+stabilized these two are destabilized
+
+ align:start position:0%
+stabilized these two are destabilized
+ 
+
+ align:start position:0%
+stabilized these two are destabilized
+but this one is destabilized quite a bit
+
+ align:start position:0%
+but this one is destabilized quite a bit
+ 
+
+ align:start position:0%
+but this one is destabilized quite a bit
+more these also will have
+
+ align:start position:0%
+more these also will have
+ 
+
+ align:start position:0%
+more these also will have
+um you can draw sort of splitting
+
+ align:start position:0%
+um you can draw sort of splitting
+ 
+
+ align:start position:0%
+um you can draw sort of splitting
+energies here but that's just too
+
+ align:start position:0%
+energies here but that's just too
+ 
+
+ align:start position:0%
+energies here but that's just too
+complicated we're only going to do this
+
+ align:start position:0%
+complicated we're only going to do this
+ 
+
+ align:start position:0%
+complicated we're only going to do this
+with the octahedral and tetrahedral case
+
+ align:start position:0%
+with the octahedral and tetrahedral case
+ 
+
+ align:start position:0%
+with the octahedral and tetrahedral case
+uh because there's many more layers here
+
+ align:start position:0%
+uh because there's many more layers here
+ 
+
+ align:start position:0%
+uh because there's many more layers here
+and uh these are a little bit different
+
+ align:start position:0%
+and uh these are a little bit different
+ 
+
+ align:start position:0%
+and uh these are a little bit different
+so all all you need to know is sort of
+
+ align:start position:0%
+so all all you need to know is sort of
+ 
+
+ align:start position:0%
+so all all you need to know is sort of
+this relative uh ratio this is the most
+
+ align:start position:0%
+this relative uh ratio this is the most
+ 
+
+ align:start position:0%
+this relative uh ratio this is the most
+destabilized this is next these guys are
+
+ align:start position:0%
+destabilized this is next these guys are
+ 
+
+ align:start position:0%
+destabilized this is next these guys are
+stabilized that's all you need to know
+
+ align:start position:0%
+stabilized that's all you need to know
+ 
+
+ align:start position:0%
+stabilized that's all you need to know
+we didn't we're not going to draw uh
+
+ align:start position:0%
+we didn't we're not going to draw uh
+ 
+
+ align:start position:0%
+we didn't we're not going to draw uh
+splitting energies going up by uh 1 and
+
+ align:start position:0%
+splitting energies going up by uh 1 and
+ 
+
+ align:start position:0%
+splitting energies going up by uh 1 and
+things like that for this case but
+
+ align:start position:0%
+things like that for this case but
+ 
+
+ align:start position:0%
+things like that for this case but
+you'll hear about this more if you go on
+
+ align:start position:0%
+you'll hear about this more if you go on
+ 
+
+ align:start position:0%
+you'll hear about this more if you go on
+in uh in chemistry so what I expect you
+
+ align:start position:0%
+in uh in chemistry so what I expect you
+ 
+
+ align:start position:0%
+in uh in chemistry so what I expect you
+to know is to be able to rationalize if
+
+ align:start position:0%
+to know is to be able to rationalize if
+ 
+
+ align:start position:0%
+to know is to be able to rationalize if
+you know something about the shape of a
+
+ align:start position:0%
+you know something about the shape of a
+ 
+
+ align:start position:0%
+you know something about the shape of a
+molecule suppose you had a linear
+
+ align:start position:0%
+molecule suppose you had a linear
+ 
+
+ align:start position:0%
+molecule suppose you had a linear
+molecule along the
+
+ align:start position:0%
+molecule along the
+ 
+
+ align:start position:0%
+molecule along the
+z-axis uh good test question uh might be
+
+ align:start position:0%
+z-axis uh good test question uh might be
+ 
+
+ align:start position:0%
+z-axis uh good test question uh might be
+which orbitals would be the most
+
+ align:start position:0%
+which orbitals would be the most
+ 
+
+ align:start position:0%
+which orbitals would be the most
+destabilized if you're linear along Z
+
+ align:start position:0%
+destabilized if you're linear along Z
+ 
+
+ align:start position:0%
+destabilized if you're linear along Z
+for example so you should be able to
+
+ align:start position:0%
+for example so you should be able to
+ 
+
+ align:start position:0%
+for example so you should be able to
+think about the shapes of the D orbitals
+
+ align:start position:0%
+think about the shapes of the D orbitals
+ 
+
+ align:start position:0%
+think about the shapes of the D orbitals
+think about the shapes of the molecules
+
+ align:start position:0%
+think about the shapes of the molecules
+ 
+
+ align:start position:0%
+think about the shapes of the molecules
+and predict the orbitals with the most
+
+ align:start position:0%
+and predict the orbitals with the most
+ 
+
+ align:start position:0%
+and predict the orbitals with the most
+stabilization and the most
+
+ align:start position:0%
+stabilization and the most
+ 
+
+ align:start position:0%
+stabilization and the most
+destabilization and to be able to
+
+ align:start position:0%
+destabilization and to be able to
+ 
+
+ align:start position:0%
+destabilization and to be able to
+explain your rationale for predicting uh
+
+ align:start position:0%
+explain your rationale for predicting uh
+ 
+
+ align:start position:0%
+explain your rationale for predicting uh
+these splitting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagrams now we're going to talk about
+
+ align:start position:0%
+diagrams now we're going to talk about
+ 
+
+ align:start position:0%
+diagrams now we're going to talk about
+how these diagrams and thinking about
+
+ align:start position:0%
+how these diagrams and thinking about
+ 
+
+ align:start position:0%
+how these diagrams and thinking about
+the splitting of the D orbitals can
+
+ align:start position:0%
+the splitting of the D orbitals can
+ 
+
+ align:start position:0%
+the splitting of the D orbitals can
+explain the beautiful colors of these
+
+ align:start position:0%
+explain the beautiful colors of these
+ 
+
+ align:start position:0%
+explain the beautiful colors of these
+coordination uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complexes so let's go back to the
+
+ align:start position:0%
+complexes so let's go back to the
+ 
+
+ align:start position:0%
+complexes so let's go back to the
+octahedral case for a minute and talk
+
+ align:start position:0%
+octahedral case for a minute and talk
+ 
+
+ align:start position:0%
+octahedral case for a minute and talk
+about two different octahedral
+
+ align:start position:0%
+about two different octahedral
+ 
+
+ align:start position:0%
+about two different octahedral
+complexes so we have iron plus three in
+
+ align:start position:0%
+complexes so we have iron plus three in
+ 
+
+ align:start position:0%
+complexes so we have iron plus three in
+two different complexes we have a high
+
+ align:start position:0%
+two different complexes we have a high
+ 
+
+ align:start position:0%
+two different complexes we have a high
+spin state with iron and six water
+
+ align:start position:0%
+spin state with iron and six water
+ 
+
+ align:start position:0%
+spin state with iron and six water
+ligans and a low spin molecule
+
+ align:start position:0%
+ligans and a low spin molecule
+ 
+
+ align:start position:0%
+ligans and a low spin molecule
+coordination compound with iron and six
+
+ align:start position:0%
+coordination compound with iron and six
+ 
+
+ align:start position:0%
+coordination compound with iron and six
+CID lians so the first thing you're
+
+ align:start position:0%
+CID lians so the first thing you're
+ 
+
+ align:start position:0%
+CID lians so the first thing you're
+going to do if you're going to be
+
+ align:start position:0%
+going to do if you're going to be
+ 
+
+ align:start position:0%
+going to do if you're going to be
+talking about the splitting is to figure
+
+ align:start position:0%
+talking about the splitting is to figure
+ 
+
+ align:start position:0%
+talking about the splitting is to figure
+out how many electrons you're talking
+
+ align:start position:0%
+out how many electrons you're talking
+ 
+
+ align:start position:0%
+out how many electrons you're talking
+about or come up with the D electron
+
+ align:start position:0%
+about or come up with the D electron
+ 
+
+ align:start position:0%
+about or come up with the D electron
+count so let's let's do
+
+ align:start position:0%
+count so let's let's do
+ 
+
+ align:start position:0%
+count so let's let's do
+that so if we have iron with six water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lians the overall charge on that is
+
+ align:start position:0%
+lians the overall charge on that is
+ 
+
+ align:start position:0%
+lians the overall charge on that is
+3+ so what is going to be our um and
+
+ align:start position:0%
+3+ so what is going to be our um and
+ 
+
+ align:start position:0%
+3+ so what is going to be our um and
+this is on the board too but what what
+
+ align:start position:0%
+this is on the board too but what what
+ 
+
+ align:start position:0%
+this is on the board too but what what
+will be the the oxidation number of
+
+ align:start position:0%
+will be the the oxidation number of
+ 
+
+ align:start position:0%
+will be the the oxidation number of
+iron plus
+
+ align:start position:0%
+iron plus
+ 
+
+ align:start position:0%
+iron plus
+three this is zero and so it all has to
+
+ align:start position:0%
+three this is zero and so it all has to
+ 
+
+ align:start position:0%
+three this is zero and so it all has to
+equal plus
+
+ align:start position:0%
+equal plus
+ 
+
+ align:start position:0%
+equal plus
+three so then the
+
+ align:start position:0%
+three so then the
+ 
+
+ align:start position:0%
+three so then the
+dcount is going to be equal to I'll put
+
+ align:start position:0%
+dcount is going to be equal to I'll put
+ 
+
+ align:start position:0%
+dcount is going to be equal to I'll put
+up a periodic table so the dcount will
+
+ align:start position:0%
+up a periodic table so the dcount will
+ 
+
+ align:start position:0%
+up a periodic table so the dcount will
+be equal to
+
+ align:start position:0%
+be equal to
+ 
+
+ align:start position:0%
+be equal to
+what five right so we look up the group
+
+ align:start position:0%
+what five right so we look up the group
+ 
+
+ align:start position:0%
+what five right so we look up the group
+number is 8 minus 3 is going to be
+
+ align:start position:0%
+number is 8 minus 3 is going to be
+ 
+
+ align:start position:0%
+number is 8 minus 3 is going to be
+five and our other iron complex will be
+
+ align:start position:0%
+five and our other iron complex will be
+ 
+
+ align:start position:0%
+five and our other iron complex will be
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same so this one has a charge of minus
+
+ align:start position:0%
+same so this one has a charge of minus
+ 
+
+ align:start position:0%
+same so this one has a charge of minus
+three cyanide is
+
+ align:start position:0%
+three cyanide is
+ 
+
+ align:start position:0%
+three cyanide is
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+minus1 so iron would also have to be+
+
+ align:start position:0%
+minus1 so iron would also have to be+
+ 
+
+ align:start position:0%
+minus1 so iron would also have to be+
+three to get the correct overall charge
+
+ align:start position:0%
+three to get the correct overall charge
+ 
+
+ align:start position:0%
+three to get the correct overall charge
+so our dcount over here as well is going
+
+ align:start position:0%
+so our dcount over here as well is going
+ 
+
+ align:start position:0%
+so our dcount over here as well is going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+D5 so we have the same number of
+
+ align:start position:0%
+D5 so we have the same number of
+ 
+
+ align:start position:0%
+D5 so we have the same number of
+electrons uh that we need to put into
+
+ align:start position:0%
+electrons uh that we need to put into
+ 
+
+ align:start position:0%
+electrons uh that we need to put into
+two different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagrams so we have one this is our high
+
+ align:start position:0%
+diagrams so we have one this is our high
+ 
+
+ align:start position:0%
+diagrams so we have one this is our high
+spin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case and so we can draw the crystal
+
+ align:start position:0%
+case and so we can draw the crystal
+ 
+
+ align:start position:0%
+case and so we can draw the crystal
+field splitting diagram for the high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Spin
+
+ align:start position:0%
+Spin
+ 
+
+ align:start position:0%
+Spin
+and put in our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbitals dx^ 2 - y^ 2 dz^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have our octahedral Crystal field
+
+ align:start position:0%
+we have our octahedral Crystal field
+ 
+
+ align:start position:0%
+we have our octahedral Crystal field
+splitting energy we're going
+
+ align:start position:0%
+splitting energy we're going
+ 
+
+ align:start position:0%
+splitting energy we're going
+up by 3
+
+ align:start position:0%
+up by 3
+ 
+
+ align:start position:0%
+up by 3
+fifths and down by two
+
+ align:start position:0%
+fifths and down by two
+ 
+
+ align:start position:0%
+fifths and down by two
+fths for these compared to this uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theoretical Crystal
+
+ align:start position:0%
+theoretical Crystal
+ 
+
+ align:start position:0%
+theoretical Crystal
+field and then we have our low spin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case and and
+
+ align:start position:0%
+case and and
+ 
+
+ align:start position:0%
+case and and
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see so in our low spin case we have a
+
+ align:start position:0%
+see so in our low spin case we have a
+ 
+
+ align:start position:0%
+see so in our low spin case we have a
+larger splitting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy and again some are going to go up
+
+ align:start position:0%
+energy and again some are going to go up
+ 
+
+ align:start position:0%
+energy and again some are going to go up
+by 3
+
+ align:start position:0%
+by 3
+ 
+
+ align:start position:0%
+by 3
+fths and these two three will go down by
+
+ align:start position:0%
+fths and these two three will go down by
+ 
+
+ align:start position:0%
+fths and these two three will go down by
+two fths
+
+ align:start position:0%
+two fths
+ 
+
+ align:start position:0%
+two fths
+all right so now we need to put in our
+
+ align:start position:0%
+all right so now we need to put in our
+ 
+
+ align:start position:0%
+all right so now we need to put in our
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+electrons so how am I going to uh put
+
+ align:start position:0%
+electrons so how am I going to uh put
+ 
+
+ align:start position:0%
+electrons so how am I going to uh put
+them in
+
+ align:start position:0%
+them in
+ 
+
+ align:start position:0%
+them in
+here will I fill up all the orbital all
+
+ align:start position:0%
+here will I fill up all the orbital all
+ 
+
+ align:start position:0%
+here will I fill up all the orbital all
+of the different energy levels with one
+
+ align:start position:0%
+of the different energy levels with one
+ 
+
+ align:start position:0%
+of the different energy levels with one
+before I pair or will I start to pair in
+
+ align:start position:0%
+before I pair or will I start to pair in
+ 
+
+ align:start position:0%
+before I pair or will I start to pair in
+the lower
+
+ align:start position:0%
+the lower
+ 
+
+ align:start position:0%
+the lower
+first we're going to put them in
+
+ align:start position:0%
+first we're going to put them in
+ 
+
+ align:start position:0%
+first we're going to put them in
+everywhere first so we'll put all five
+
+ align:start position:0%
+everywhere first so we'll put all five
+ 
+
+ align:start position:0%
+everywhere first so we'll put all five
+electrons we'll put one in each of the
+
+ align:start position:0%
+electrons we'll put one in each of the
+ 
+
+ align:start position:0%
+electrons we'll put one in each of the
+orbitals so I'm going to place them
+
+ align:start position:0%
+orbitals so I'm going to place them
+ 
+
+ align:start position:0%
+orbitals so I'm going to place them
+singly in and that's because in this
+
+ align:start position:0%
+singly in and that's because in this
+ 
+
+ align:start position:0%
+singly in and that's because in this
+case the splitting energy is
+
+ align:start position:0%
+case the splitting energy is
+ 
+
+ align:start position:0%
+case the splitting energy is
+small and since it's small it's less
+
+ align:start position:0%
+small and since it's small it's less
+ 
+
+ align:start position:0%
+small and since it's small it's less
+than the pairing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy so the pairing energy is the
+
+ align:start position:0%
+energy so the pairing energy is the
+ 
+
+ align:start position:0%
+energy so the pairing energy is the
+energy required to pair up these
+
+ align:start position:0%
+energy required to pair up these
+ 
+
+ align:start position:0%
+energy required to pair up these
+electrons there's a certain amount of
+
+ align:start position:0%
+electrons there's a certain amount of
+ 
+
+ align:start position:0%
+electrons there's a certain amount of
+repulsion all of the electrons would
+
+ align:start position:0%
+repulsion all of the electrons would
+ 
+
+ align:start position:0%
+repulsion all of the electrons would
+love to be alone in their orbital they'd
+
+ align:start position:0%
+love to be alone in their orbital they'd
+ 
+
+ align:start position:0%
+love to be alone in their orbital they'd
+prefer not for you to put another
+
+ align:start position:0%
+prefer not for you to put another
+ 
+
+ align:start position:0%
+prefer not for you to put another
+electron R in so there's a certain
+
+ align:start position:0%
+electron R in so there's a certain
+ 
+
+ align:start position:0%
+electron R in so there's a certain
+amount of energy required to do this if
+
+ align:start position:0%
+amount of energy required to do this if
+ 
+
+ align:start position:0%
+amount of energy required to do this if
+the energy level between the D orbitals
+
+ align:start position:0%
+the energy level between the D orbitals
+ 
+
+ align:start position:0%
+the energy level between the D orbitals
+is small then it's uh you put them all
+
+ align:start position:0%
+is small then it's uh you put them all
+ 
+
+ align:start position:0%
+is small then it's uh you put them all
+in singly and uh don't pair until you
+
+ align:start position:0%
+in singly and uh don't pair until you
+ 
+
+ align:start position:0%
+in singly and uh don't pair until you
+absolutely have to this is referred to
+
+ align:start position:0%
+absolutely have to this is referred to
+ 
+
+ align:start position:0%
+absolutely have to this is referred to
+as the high spin case where you have the
+
+ align:start position:0%
+as the high spin case where you have the
+ 
+
+ align:start position:0%
+as the high spin case where you have the
+most maximum number of unpaired
+
+ align:start position:0%
+most maximum number of unpaired
+ 
+
+ align:start position:0%
+most maximum number of unpaired
+electrons so in this case we have a
+
+ align:start position:0%
+electrons so in this case we have a
+ 
+
+ align:start position:0%
+electrons so in this case we have a
+large energy so that energy then is
+
+ align:start position:0%
+large energy so that energy then is
+ 
+
+ align:start position:0%
+large energy so that energy then is
+greater than the energy required to pair
+
+ align:start position:0%
+greater than the energy required to pair
+ 
+
+ align:start position:0%
+greater than the energy required to pair
+PE or the pairing energy so now we're
+
+ align:start position:0%
+PE or the pairing energy so now we're
+ 
+
+ align:start position:0%
+PE or the pairing energy so now we're
+going to put them all into the bottom
+
+ align:start position:0%
+going to put them all into the bottom
+ 
+
+ align:start position:0%
+going to put them all into the bottom
+until we have to go to the top so we'll
+
+ align:start position:0%
+until we have to go to the top so we'll
+ 
+
+ align:start position:0%
+until we have to go to the top so we'll
+first start out putting them in singly
+
+ align:start position:0%
+first start out putting them in singly
+ 
+
+ align:start position:0%
+first start out putting them in singly
+one two 3 and then we'll start pairing
+
+ align:start position:0%
+one two 3 and then we'll start pairing
+ 
+
+ align:start position:0%
+one two 3 and then we'll start pairing
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+five so now we fill up this bottom uh
+
+ align:start position:0%
+five so now we fill up this bottom uh
+ 
+
+ align:start position:0%
+five so now we fill up this bottom uh
+set I should put in the
+
+ align:start position:0%
+set I should put in the
+ 
+
+ align:start position:0%
+set I should put in the
+t2g and the
+
+ align:start position:0%
+t2g and the
+ 
+
+ align:start position:0%
+t2g and the
+EG labels
+
+ align:start position:0%
+EG labels
+ 
+
+ align:start position:0%
+EG labels
+so we'll put them in this bottom set in
+
+ align:start position:0%
+so we'll put them in this bottom set in
+ 
+
+ align:start position:0%
+so we'll put them in this bottom set in
+t2g until we have to go up to EG because
+
+ align:start position:0%
+t2g until we have to go up to EG because
+ 
+
+ align:start position:0%
+t2g until we have to go up to EG because
+this is a big energy difference and you
+
+ align:start position:0%
+this is a big energy difference and you
+ 
+
+ align:start position:0%
+this is a big energy difference and you
+don't want to do that until you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to all right so now we can look at the
+
+ align:start position:0%
+to all right so now we can look at the
+ 
+
+ align:start position:0%
+to all right so now we can look at the
+uh D electron count so where the
+
+ align:start position:0%
+uh D electron count so where the
+ 
+
+ align:start position:0%
+uh D electron count so where the
+electrons are so here it's
+
+ align:start position:0%
+electrons are so here it's
+ 
+
+ align:start position:0%
+electrons are so here it's
+t2g 3 there are three in the bottom and
+
+ align:start position:0%
+t2g 3 there are three in the bottom and
+ 
+
+ align:start position:0%
+t2g 3 there are three in the bottom and
+in EG there are
+
+ align:start position:0%
+in EG there are
+ 
+
+ align:start position:0%
+in EG there are
+two and over here in t2g we have five
+
+ align:start position:0%
+two and over here in t2g we have five
+ 
+
+ align:start position:0%
+two and over here in t2g we have five
+there's none in EG so those are our Del
+
+ align:start position:0%
+there's none in EG so those are our Del
+ 
+
+ align:start position:0%
+there's none in EG so those are our Del
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+counts and then we can calculate the
+
+ align:start position:0%
+counts and then we can calculate the
+ 
+
+ align:start position:0%
+counts and then we can calculate the
+crystal field stabilization energy which
+
+ align:start position:0%
+crystal field stabilization energy which
+ 
+
+ align:start position:0%
+crystal field stabilization energy which
+shouldn't be confused with the splitting
+
+ align:start position:0%
+shouldn't be confused with the splitting
+ 
+
+ align:start position:0%
+shouldn't be confused with the splitting
+energy so this considers how much
+
+ align:start position:0%
+energy so this considers how much
+ 
+
+ align:start position:0%
+energy so this considers how much
+stabilization you have as a result of
+
+ align:start position:0%
+stabilization you have as a result of
+ 
+
+ align:start position:0%
+stabilization you have as a result of
+the fact that the D orbitals are split
+
+ align:start position:0%
+the fact that the D orbitals are split
+ 
+
+ align:start position:0%
+the fact that the D orbitals are split
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+energy so in this case you want to count
+
+ align:start position:0%
+energy so in this case you want to count
+ 
+
+ align:start position:0%
+energy so in this case you want to count
+up how many are in the lower energy
+
+ align:start position:0%
+up how many are in the lower energy
+ 
+
+ align:start position:0%
+up how many are in the lower energy
+levels so they're three down
+
+ align:start position:0%
+levels so they're three down
+ 
+
+ align:start position:0%
+levels so they're three down
+here so 3 * - 25s the octahedral crystal
+
+ align:start position:0%
+here so 3 * - 25s the octahedral crystal
+ 
+
+ align:start position:0%
+here so 3 * - 25s the octahedral crystal
+field splitting energy and you have two
+
+ align:start position:0%
+field splitting energy and you have two
+ 
+
+ align:start position:0%
+field splitting energy and you have two
+above so two are up in energy by three F
+
+ align:start position:0%
+above so two are up in energy by three F
+ 
+
+ align:start position:0%
+above so two are up in energy by three F
+and so what do that
+
+ align:start position:0%
+and so what do that
+ 
+
+ align:start position:0%
+and so what do that
+equal zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and over here then you have five that
+
+ align:start position:0%
+and over here then you have five that
+ 
+
+ align:start position:0%
+and over here then you have five that
+are down in
+
+ align:start position:0%
+are down in
+ 
+
+ align:start position:0%
+are down in
+energy so you'd have minus 10 fths the
+
+ align:start position:0%
+energy so you'd have minus 10 fths the
+ 
+
+ align:start position:0%
+energy so you'd have minus 10 fths the
+octahedral crystal field splitting
+
+ align:start position:0%
+octahedral crystal field splitting
+ 
+
+ align:start position:0%
+octahedral crystal field splitting
+energy and sometimes in some books it
+
+ align:start position:0%
+energy and sometimes in some books it
+ 
+
+ align:start position:0%
+energy and sometimes in some books it
+also includes there is some energy to
+
+ align:start position:0%
+also includes there is some energy to
+ 
+
+ align:start position:0%
+also includes there is some energy to
+associated with pairing so occasionally
+
+ align:start position:0%
+associated with pairing so occasionally
+ 
+
+ align:start position:0%
+associated with pairing so occasionally
+you'll see this written as 2 PE
+
+ align:start position:0%
+you'll see this written as 2 PE
+ 
+
+ align:start position:0%
+you'll see this written as 2 PE
+indicating that there are two sets
+
+ align:start position:0%
+indicating that there are two sets
+ 
+
+ align:start position:0%
+indicating that there are two sets
+um with paired
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons so there's some energy
+
+ align:start position:0%
+electrons so there's some energy
+ 
+
+ align:start position:0%
+electrons so there's some energy
+associated with that so it's not as
+
+ align:start position:0%
+associated with that so it's not as
+ 
+
+ align:start position:0%
+associated with that so it's not as
+fantastic a situation as it looks like
+
+ align:start position:0%
+fantastic a situation as it looks like
+ 
+
+ align:start position:0%
+fantastic a situation as it looks like
+that there's lots of stabilization where
+
+ align:start position:0%
+that there's lots of stabilization where
+ 
+
+ align:start position:0%
+that there's lots of stabilization where
+the other has a zero stabilization um
+
+ align:start position:0%
+the other has a zero stabilization um
+ 
+
+ align:start position:0%
+the other has a zero stabilization um
+zero destabilization it's uh just about
+
+ align:start position:0%
+zero destabilization it's uh just about
+ 
+
+ align:start position:0%
+zero destabilization it's uh just about
+the same but there is some energy
+
+ align:start position:0%
+the same but there is some energy
+ 
+
+ align:start position:0%
+the same but there is some energy
+associated with this so sometimes you'll
+
+ align:start position:0%
+associated with this so sometimes you'll
+ 
+
+ align:start position:0%
+associated with this so sometimes you'll
+see that you only need to indicate that
+
+ align:start position:0%
+see that you only need to indicate that
+ 
+
+ align:start position:0%
+see that you only need to indicate that
+if it's asked for and I think your book
+
+ align:start position:0%
+if it's asked for and I think your book
+ 
+
+ align:start position:0%
+if it's asked for and I think your book
+doesn't ask ask for it but just so
+
+ align:start position:0%
+doesn't ask ask for it but just so
+ 
+
+ align:start position:0%
+doesn't ask ask for it but just so
+you're aware all right so that's kind of
+
+ align:start position:0%
+you're aware all right so that's kind of
+ 
+
+ align:start position:0%
+you're aware all right so that's kind of
+a review we talked about these things on
+
+ align:start position:0%
+a review we talked about these things on
+ 
+
+ align:start position:0%
+a review we talked about these things on
+Monday on last Monday but I just wanted
+
+ align:start position:0%
+Monday on last Monday but I just wanted
+ 
+
+ align:start position:0%
+Monday on last Monday but I just wanted
+to go through it again because now you
+
+ align:start position:0%
+to go through it again because now you
+ 
+
+ align:start position:0%
+to go through it again because now you
+need to see how this relates to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Colors okay so we have to introduce um
+
+ align:start position:0%
+Colors okay so we have to introduce um
+ 
+
+ align:start position:0%
+Colors okay so we have to introduce um
+this this idea that uh the relative
+
+ align:start position:0%
+this this idea that uh the relative
+ 
+
+ align:start position:0%
+this this idea that uh the relative
+ability of certain common lians to split
+
+ align:start position:0%
+ability of certain common lians to split
+ 
+
+ align:start position:0%
+ability of certain common lians to split
+the D orbital level is what's meant by
+
+ align:start position:0%
+the D orbital level is what's meant by
+ 
+
+ align:start position:0%
+the D orbital level is what's meant by
+this uh spect chemical Series so which
+
+ align:start position:0%
+this uh spect chemical Series so which
+ 
+
+ align:start position:0%
+this uh spect chemical Series so which
+lians there are in one case water and
+
+ align:start position:0%
+lians there are in one case water and
+ 
+
+ align:start position:0%
+lians there are in one case water and
+cyanide causes a difference and a strong
+
+ align:start position:0%
+cyanide causes a difference and a strong
+ 
+
+ align:start position:0%
+cyanide causes a difference and a strong
+field Lian and we talked about this a
+
+ align:start position:0%
+field Lian and we talked about this a
+ 
+
+ align:start position:0%
+field Lian and we talked about this a
+bit on Monday last Monday as well
+
+ align:start position:0%
+bit on Monday last Monday as well
+ 
+
+ align:start position:0%
+bit on Monday last Monday as well
+produces large energy separation so over
+
+ align:start position:0%
+produces large energy separation so over
+ 
+
+ align:start position:0%
+produces large energy separation so over
+here we have a large energy so this
+
+ align:start position:0%
+here we have a large energy so this
+ 
+
+ align:start position:0%
+here we have a large energy so this
+would be a strong a strong field over
+
+ align:start position:0%
+would be a strong a strong field over
+ 
+
+ align:start position:0%
+would be a strong a strong field over
+here so it's strong it splits those D
+
+ align:start position:0%
+here so it's strong it splits those D
+ 
+
+ align:start position:0%
+here so it's strong it splits those D
+orbitals a lot and and a weak field Lian
+
+ align:start position:0%
+orbitals a lot and and a weak field Lian
+ 
+
+ align:start position:0%
+orbitals a lot and and a weak field Lian
+produces a small separation it's pretty
+
+ align:start position:0%
+produces a small separation it's pretty
+ 
+
+ align:start position:0%
+produces a small separation it's pretty
+weak it can't really split those D
+
+ align:start position:0%
+weak it can't really split those D
+ 
+
+ align:start position:0%
+weak it can't really split those D
+orbitals very much it's weak so this
+
+ align:start position:0%
+orbitals very much it's weak so this
+ 
+
+ align:start position:0%
+orbitals very much it's weak so this
+would be a weak field case over here so
+
+ align:start position:0%
+would be a weak field case over here so
+ 
+
+ align:start position:0%
+would be a weak field case over here so
+there's not much splitting between the D
+
+ align:start position:0%
+there's not much splitting between the D
+ 
+
+ align:start position:0%
+there's not much splitting between the D
+orbitals so here are some various lians
+
+ align:start position:0%
+orbitals so here are some various lians
+ 
+
+ align:start position:0%
+orbitals so here are some various lians
+and how they fall into this series and
+
+ align:start position:0%
+and how they fall into this series and
+ 
+
+ align:start position:0%
+and how they fall into this series and
+you'll just you need to know this for
+
+ align:start position:0%
+you'll just you need to know this for
+ 
+
+ align:start position:0%
+you'll just you need to know this for
+the test only these uh sets of lians so
+
+ align:start position:0%
+the test only these uh sets of lians so
+ 
+
+ align:start position:0%
+the test only these uh sets of lians so
+there are three in sort of weak field
+
+ align:start position:0%
+there are three in sort of weak field
+ 
+
+ align:start position:0%
+there are three in sort of weak field
+category three in the intermediate
+
+ align:start position:0%
+category three in the intermediate
+ 
+
+ align:start position:0%
+category three in the intermediate
+category and three in the strong field
+
+ align:start position:0%
+category and three in the strong field
+ 
+
+ align:start position:0%
+category and three in the strong field
+category so when it's a weak field Lian
+
+ align:start position:0%
+category so when it's a weak field Lian
+ 
+
+ align:start position:0%
+category so when it's a weak field Lian
+you're going to have the small splitting
+
+ align:start position:0%
+you're going to have the small splitting
+ 
+
+ align:start position:0%
+you're going to have the small splitting
+as shown here and therefore you'll have
+
+ align:start position:0%
+as shown here and therefore you'll have
+ 
+
+ align:start position:0%
+as shown here and therefore you'll have
+a high spin system where you have the
+
+ align:start position:0%
+a high spin system where you have the
+ 
+
+ align:start position:0%
+a high spin system where you have the
+maximum number of unpaired electrons if
+
+ align:start position:0%
+maximum number of unpaired electrons if
+ 
+
+ align:start position:0%
+maximum number of unpaired electrons if
+you have a strong field you have a large
+
+ align:start position:0%
+you have a strong field you have a large
+ 
+
+ align:start position:0%
+you have a strong field you have a large
+splitting and then you're going to have
+
+ align:start position:0%
+splitting and then you're going to have
+ 
+
+ align:start position:0%
+splitting and then you're going to have
+a low spin system where you have the
+
+ align:start position:0%
+a low spin system where you have the
+ 
+
+ align:start position:0%
+a low spin system where you have the
+minimum number of unpaired
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons so in the example that we just
+
+ align:start position:0%
+electrons so in the example that we just
+ 
+
+ align:start position:0%
+electrons so in the example that we just
+had we had this is high spin so it's
+
+ align:start position:0%
+had we had this is high spin so it's
+ 
+
+ align:start position:0%
+had we had this is high spin so it's
+actually kind of an intermediate but it
+
+ align:start position:0%
+actually kind of an intermediate but it
+ 
+
+ align:start position:0%
+actually kind of an intermediate but it
+was determined to be high spin
+
+ align:start position:0%
+was determined to be high spin
+ 
+
+ align:start position:0%
+was determined to be high spin
+experimentally the intermediate ones are
+
+ align:start position:0%
+experimentally the intermediate ones are
+ 
+
+ align:start position:0%
+experimentally the intermediate ones are
+a little harder to predict uh these will
+
+ align:start position:0%
+a little harder to predict uh these will
+ 
+
+ align:start position:0%
+a little harder to predict uh these will
+be strong field these will be weak field
+
+ align:start position:0%
+be strong field these will be weak field
+ 
+
+ align:start position:0%
+be strong field these will be weak field
+these are harder to predict uh cyanide
+
+ align:start position:0%
+these are harder to predict uh cyanide
+ 
+
+ align:start position:0%
+these are harder to predict uh cyanide
+according to this list is the strongest
+
+ align:start position:0%
+according to this list is the strongest
+ 
+
+ align:start position:0%
+according to this list is the strongest
+field Lian so so uh that makes that
+
+ align:start position:0%
+field Lian so so uh that makes that
+ 
+
+ align:start position:0%
+field Lian so so uh that makes that
+makes sense that that was then a low
+
+ align:start position:0%
+makes sense that that was then a low
+ 
+
+ align:start position:0%
+makes sense that that was then a low
+spin uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+colors so colors are going to depend on
+
+ align:start position:0%
+colors so colors are going to depend on
+ 
+
+ align:start position:0%
+colors so colors are going to depend on
+uh on what photons are absorbed and the
+
+ align:start position:0%
+uh on what photons are absorbed and the
+ 
+
+ align:start position:0%
+uh on what photons are absorbed and the
+energy level it takes to get to that
+
+ align:start position:0%
+energy level it takes to get to that
+ 
+
+ align:start position:0%
+energy level it takes to get to that
+excited high energy state so here it's a
+
+ align:start position:0%
+excited high energy state so here it's a
+ 
+
+ align:start position:0%
+excited high energy state so here it's a
+very small difference here it's a big
+
+ align:start position:0%
+very small difference here it's a big
+ 
+
+ align:start position:0%
+very small difference here it's a big
+difference so you would need to absorb
+
+ align:start position:0%
+difference so you would need to absorb
+ 
+
+ align:start position:0%
+difference so you would need to absorb
+ABB um differently and then also
+
+ align:start position:0%
+ABB um differently and then also
+ 
+
+ align:start position:0%
+ABB um differently and then also
+transmit differently to excite those
+
+ align:start position:0%
+transmit differently to excite those
+ 
+
+ align:start position:0%
+transmit differently to excite those
+electrons and that's going to give rise
+
+ align:start position:0%
+electrons and that's going to give rise
+ 
+
+ align:start position:0%
+electrons and that's going to give rise
+to the different colors so let's just
+
+ align:start position:0%
+to the different colors so let's just
+ 
+
+ align:start position:0%
+to the different colors so let's just
+take a look at this so now we're
+
+ align:start position:0%
+take a look at this so now we're
+ 
+
+ align:start position:0%
+take a look at this so now we're
+reviewing back to uh the first half of
+
+ align:start position:0%
+reviewing back to uh the first half of
+ 
+
+ align:start position:0%
+reviewing back to uh the first half of
+the semester where you saw this so we
+
+ align:start position:0%
+the semester where you saw this so we
+ 
+
+ align:start position:0%
+the semester where you saw this so we
+have uh the energy of the absorbed light
+
+ align:start position:0%
+have uh the energy of the absorbed light
+ 
+
+ align:start position:0%
+have uh the energy of the absorbed light
+is equal to Plank's constant times the
+
+ align:start position:0%
+is equal to Plank's constant times the
+ 
+
+ align:start position:0%
+is equal to Plank's constant times the
+frequency and so we're back here again
+
+ align:start position:0%
+frequency and so we're back here again
+ 
+
+ align:start position:0%
+frequency and so we're back here again
+we're talking about splitting energies
+
+ align:start position:0%
+we're talking about splitting energies
+ 
+
+ align:start position:0%
+we're talking about splitting energies
+between the D orbitals amount of energy
+
+ align:start position:0%
+between the D orbitals amount of energy
+ 
+
+ align:start position:0%
+between the D orbitals amount of energy
+to excite an electron uh from one set of
+
+ align:start position:0%
+to excite an electron uh from one set of
+ 
+
+ align:start position:0%
+to excite an electron uh from one set of
+orbitals to the higher set of orbitals
+
+ align:start position:0%
+orbitals to the higher set of orbitals
+ 
+
+ align:start position:0%
+orbitals to the higher set of orbitals
+so we're we're back here but now we're
+
+ align:start position:0%
+so we're we're back here but now we're
+ 
+
+ align:start position:0%
+so we're we're back here but now we're
+going to have a little bit of a
+
+ align:start position:0%
+going to have a little bit of a
+ 
+
+ align:start position:0%
+going to have a little bit of a
+difference in that we're going to add
+
+ align:start position:0%
+difference in that we're going to add
+ 
+
+ align:start position:0%
+difference in that we're going to add
+another equal sign and say that that
+
+ align:start position:0%
+another equal sign and say that that
+ 
+
+ align:start position:0%
+another equal sign and say that that
+energy then is going to be in this case
+
+ align:start position:0%
+energy then is going to be in this case
+ 
+
+ align:start position:0%
+energy then is going to be in this case
+for the transition metal complexes
+
+ align:start position:0%
+for the transition metal complexes
+ 
+
+ align:start position:0%
+for the transition metal complexes
+octahedral coordination complexes is
+
+ align:start position:0%
+octahedral coordination complexes is
+ 
+
+ align:start position:0%
+octahedral coordination complexes is
+equal to this octahedral Crystal field
+
+ align:start position:0%
+equal to this octahedral Crystal field
+ 
+
+ align:start position:0%
+equal to this octahedral Crystal field
+splitting energy so again we're going to
+
+ align:start position:0%
+splitting energy so again we're going to
+ 
+
+ align:start position:0%
+splitting energy so again we're going to
+be talking about exciting electrons here
+
+ align:start position:0%
+be talking about exciting electrons here
+ 
+
+ align:start position:0%
+be talking about exciting electrons here
+up to here and so that depends then on
+
+ align:start position:0%
+up to here and so that depends then on
+ 
+
+ align:start position:0%
+up to here and so that depends then on
+how what the energy difference is
+
+ align:start position:0%
+how what the energy difference is
+ 
+
+ align:start position:0%
+how what the energy difference is
+between these sets of orbitals so we've
+
+ align:start position:0%
+between these sets of orbitals so we've
+ 
+
+ align:start position:0%
+between these sets of orbitals so we've
+seen this before and now we're just
+
+ align:start position:0%
+seen this before and now we're just
+ 
+
+ align:start position:0%
+seen this before and now we're just
+adding this new term on the other end
+
+ align:start position:0%
+adding this new term on the other end
+ 
+
+ align:start position:0%
+adding this new term on the other end
+the octahedral crystal field splitting
+
+ align:start position:0%
+the octahedral crystal field splitting
+ 
+
+ align:start position:0%
+the octahedral crystal field splitting
+energy all right so this we also saw in
+
+ align:start position:0%
+energy all right so this we also saw in
+ 
+
+ align:start position:0%
+energy all right so this we also saw in
+the first half of the course so if you
+
+ align:start position:0%
+the first half of the course so if you
+ 
+
+ align:start position:0%
+the first half of the course so if you
+have a high frequency of light is
+
+ align:start position:0%
+have a high frequency of light is
+ 
+
+ align:start position:0%
+have a high frequency of light is
+absorbed the wavelength of the absorbed
+
+ align:start position:0%
+absorbed the wavelength of the absorbed
+ 
+
+ align:start position:0%
+absorbed the wavelength of the absorbed
+light is going to be
+
+ align:start position:0%
+light is going to be
+ 
+
+ align:start position:0%
+light is going to be
+short and that's that equation which was
+
+ align:start position:0%
+short and that's that equation which was
+ 
+
+ align:start position:0%
+short and that's that equation which was
+I think these two equations were
+
+ align:start position:0%
+I think these two equations were
+ 
+
+ align:start position:0%
+I think these two equations were
+equations you needed to have memorized
+
+ align:start position:0%
+equations you needed to have memorized
+ 
+
+ align:start position:0%
+equations you needed to have memorized
+they weren't on the equation seed that
+
+ align:start position:0%
+they weren't on the equation seed that
+ 
+
+ align:start position:0%
+they weren't on the equation seed that
+indicates that they're of really
+
+ align:start position:0%
+indicates that they're of really
+ 
+
+ align:start position:0%
+indicates that they're of really
+fundamental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+importance and then the color of the
+
+ align:start position:0%
+importance and then the color of the
+ 
+
+ align:start position:0%
+importance and then the color of the
+transmitted light is complementary to
+
+ align:start position:0%
+transmitted light is complementary to
+ 
+
+ align:start position:0%
+transmitted light is complementary to
+the color of the absorbed light so here
+
+ align:start position:0%
+the color of the absorbed light so here
+ 
+
+ align:start position:0%
+the color of the absorbed light so here
+we need to think beyond the first half
+
+ align:start position:0%
+we need to think beyond the first half
+ 
+
+ align:start position:0%
+we need to think beyond the first half
+of this semester back to probably
+
+ align:start position:0%
+of this semester back to probably
+ 
+
+ align:start position:0%
+of this semester back to probably
+kindergarten when did you first learn
+
+ align:start position:0%
+kindergarten when did you first learn
+ 
+
+ align:start position:0%
+kindergarten when did you first learn
+about complimentary
+
+ align:start position:0%
+about complimentary
+ 
+
+ align:start position:0%
+about complimentary
+colors second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grade so I actually was uh talked into
+
+ align:start position:0%
+grade so I actually was uh talked into
+ 
+
+ align:start position:0%
+grade so I actually was uh talked into
+putting something like this on the exam
+
+ align:start position:0%
+putting something like this on the exam
+ 
+
+ align:start position:0%
+putting something like this on the exam
+so that you wouldn't have to have that
+
+ align:start position:0%
+so that you wouldn't have to have that
+ 
+
+ align:start position:0%
+so that you wouldn't have to have that
+material memorized but anyway here are
+
+ align:start position:0%
+material memorized but anyway here are
+ 
+
+ align:start position:0%
+material memorized but anyway here are
+your complimentary
+
+ align:start position:0%
+your complimentary
+ 
+
+ align:start position:0%
+your complimentary
+colors so if you know something about
+
+ align:start position:0%
+colors so if you know something about
+ 
+
+ align:start position:0%
+colors so if you know something about
+the color of the transition complex you
+
+ align:start position:0%
+the color of the transition complex you
+ 
+
+ align:start position:0%
+the color of the transition complex you
+can go back and calculate and estimate
+
+ align:start position:0%
+can go back and calculate and estimate
+ 
+
+ align:start position:0%
+can go back and calculate and estimate
+if you're given actual numbers you can
+
+ align:start position:0%
+if you're given actual numbers you can
+ 
+
+ align:start position:0%
+if you're given actual numbers you can
+calculate what the splitting energy
+
+ align:start position:0%
+calculate what the splitting energy
+ 
+
+ align:start position:0%
+calculate what the splitting energy
+difference was or you can approximate
+
+ align:start position:0%
+difference was or you can approximate
+ 
+
+ align:start position:0%
+difference was or you can approximate
+whether it's going to be small or large
+
+ align:start position:0%
+whether it's going to be small or large
+ 
+
+ align:start position:0%
+whether it's going to be small or large
+depending on the colors that the
+
+ align:start position:0%
+depending on the colors that the
+ 
+
+ align:start position:0%
+depending on the colors that the
+complexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have so let's let's take a look at uh
+
+ align:start position:0%
+have so let's let's take a look at uh
+ 
+
+ align:start position:0%
+have so let's let's take a look at uh
+some examples here of two different
+
+ align:start position:0%
+some examples here of two different
+ 
+
+ align:start position:0%
+some examples here of two different
+coordination complexes both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+octahedral so first we have to figure
+
+ align:start position:0%
+octahedral so first we have to figure
+ 
+
+ align:start position:0%
+octahedral so first we have to figure
+out the oxidation number so again this
+
+ align:start position:0%
+out the oxidation number so again this
+ 
+
+ align:start position:0%
+out the oxidation number so again this
+goes back to the uh the last unit on
+
+ align:start position:0%
+goes back to the uh the last unit on
+ 
+
+ align:start position:0%
+goes back to the uh the last unit on
+oxidation reduction uh we'll have on the
+
+ align:start position:0%
+oxidation reduction uh we'll have on the
+ 
+
+ align:start position:0%
+oxidation reduction uh we'll have on the
+useful for the exam on Wednesday so the
+
+ align:start position:0%
+useful for the exam on Wednesday so the
+ 
+
+ align:start position:0%
+useful for the exam on Wednesday so the
+uh the number here you're going to
+
+ align:start position:0%
+uh the number here you're going to
+ 
+
+ align:start position:0%
+uh the number here you're going to
+have plus three for both of these guys
+
+ align:start position:0%
+have plus three for both of these guys
+ 
+
+ align:start position:0%
+have plus three for both of these guys
+so this is this is zero and that's zero
+
+ align:start position:0%
+so this is this is zero and that's zero
+ 
+
+ align:start position:0%
+so this is this is zero and that's zero
+the overall charge is plus three so
+
+ align:start position:0%
+the overall charge is plus three so
+ 
+
+ align:start position:0%
+the overall charge is plus three so
+chromium has to be+ three in both cases
+
+ align:start position:0%
+chromium has to be+ three in both cases
+ 
+
+ align:start position:0%
+chromium has to be+ three in both cases
+then when we do the Del electron count
+
+ align:start position:0%
+then when we do the Del electron count
+ 
+
+ align:start position:0%
+then when we do the Del electron count
+we have to find chromium on our periodic
+
+ align:start position:0%
+we have to find chromium on our periodic
+ 
+
+ align:start position:0%
+we have to find chromium on our periodic
+table look up uh what group it's in to
+
+ align:start position:0%
+table look up uh what group it's in to
+ 
+
+ align:start position:0%
+table look up uh what group it's in to
+calculate the
+
+ align:start position:0%
+calculate the
+ 
+
+ align:start position:0%
+calculate the
+dcount so we have that here and we have
+
+ align:start position:0%
+dcount so we have that here and we have
+ 
+
+ align:start position:0%
+dcount so we have that here and we have
+a D3 case what does CN stand
+
+ align:start position:0%
+a D3 case what does CN stand
+ 
+
+ align:start position:0%
+a D3 case what does CN stand
+for coordination number and so what's
+
+ align:start position:0%
+for coordination number and so what's
+ 
+
+ align:start position:0%
+for coordination number and so what's
+the coordination number in this
+
+ align:start position:0%
+the coordination number in this
+ 
+
+ align:start position:0%
+the coordination number in this
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+six right so there's six things here six
+
+ align:start position:0%
+six right so there's six things here six
+ 
+
+ align:start position:0%
+six right so there's six things here six
+things coordinated and and that's not to
+
+ align:start position:0%
+things coordinated and and that's not to
+ 
+
+ align:start position:0%
+things coordinated and and that's not to
+be confused with the steric number which
+
+ align:start position:0%
+be confused with the steric number which
+ 
+
+ align:start position:0%
+be confused with the steric number which
+we talked about uh last Wednesday so the
+
+ align:start position:0%
+we talked about uh last Wednesday so the
+ 
+
+ align:start position:0%
+we talked about uh last Wednesday so the
+type of ligan here water was what what
+
+ align:start position:0%
+type of ligan here water was what what
+ 
+
+ align:start position:0%
+type of ligan here water was what what
+type of Lian in terms of weak to strong
+
+ align:start position:0%
+type of Lian in terms of weak to strong
+ 
+
+ align:start position:0%
+type of Lian in terms of weak to strong
+field it was intermediate and over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is stronger so these guys are
+
+ align:start position:0%
+here is stronger so these guys are
+ 
+
+ align:start position:0%
+here is stronger so these guys are
+actually not that far apart from each
+
+ align:start position:0%
+actually not that far apart from each
+ 
+
+ align:start position:0%
+actually not that far apart from each
+other uh water was sort of intermediate
+
+ align:start position:0%
+other uh water was sort of intermediate
+ 
+
+ align:start position:0%
+other uh water was sort of intermediate
+it is at least weaker than NH3 NH3 was
+
+ align:start position:0%
+it is at least weaker than NH3 NH3 was
+ 
+
+ align:start position:0%
+it is at least weaker than NH3 NH3 was
+in the strong category so it's at least
+
+ align:start position:0%
+in the strong category so it's at least
+ 
+
+ align:start position:0%
+in the strong category so it's at least
+stronger than water they're not that far
+
+ align:start position:0%
+stronger than water they're not that far
+ 
+
+ align:start position:0%
+stronger than water they're not that far
+apart from each other but this one
+
+ align:start position:0%
+apart from each other but this one
+ 
+
+ align:start position:0%
+apart from each other but this one
+should be a stronger field Lian than
+
+ align:start position:0%
+should be a stronger field Lian than
+ 
+
+ align:start position:0%
+should be a stronger field Lian than
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so if we consider a weaker field
+
+ align:start position:0%
+one so if we consider a weaker field
+ 
+
+ align:start position:0%
+one so if we consider a weaker field
+system and a stronger field
+
+ align:start position:0%
+system and a stronger field
+ 
+
+ align:start position:0%
+system and a stronger field
+system is this going to make any
+
+ align:start position:0%
+system is this going to make any
+ 
+
+ align:start position:0%
+system is this going to make any
+difference to how we put in electrons
+
+ align:start position:0%
+difference to how we put in electrons
+ 
+
+ align:start position:0%
+difference to how we put in electrons
+this time
+
+ align:start position:0%
+this time
+ 
+
+ align:start position:0%
+this time
+no it won't because we only have three
+
+ align:start position:0%
+no it won't because we only have three
+ 
+
+ align:start position:0%
+no it won't because we only have three
+so we would put them in the bottom
+
+ align:start position:0%
+so we would put them in the bottom
+ 
+
+ align:start position:0%
+so we would put them in the bottom
+regardless so the issue is when you get
+
+ align:start position:0%
+regardless so the issue is when you get
+ 
+
+ align:start position:0%
+regardless so the issue is when you get
+to the fourth one when you have the
+
+ align:start position:0%
+to the fourth one when you have the
+ 
+
+ align:start position:0%
+to the fourth one when you have the
+fourth electron you have to decide if
+
+ align:start position:0%
+fourth electron you have to decide if
+ 
+
+ align:start position:0%
+fourth electron you have to decide if
+you're going to put it up here or if
+
+ align:start position:0%
+you're going to put it up here or if
+ 
+
+ align:start position:0%
+you're going to put it up here or if
+you're going to pair but there're only
+
+ align:start position:0%
+you're going to pair but there're only
+ 
+
+ align:start position:0%
+you're going to pair but there're only
+three so the diagrams look the
+
+ align:start position:0%
+three so the diagrams look the
+ 
+
+ align:start position:0%
+three so the diagrams look the
+same but even though the diagrams look
+
+ align:start position:0%
+same but even though the diagrams look
+ 
+
+ align:start position:0%
+same but even though the diagrams look
+the same these compounds are going to
+
+ align:start position:0%
+the same these compounds are going to
+ 
+
+ align:start position:0%
+the same these compounds are going to
+have different properties because they
+
+ align:start position:0%
+have different properties because they
+ 
+
+ align:start position:0%
+have different properties because they
+have different splitting energy
+
+ align:start position:0%
+have different splitting energy
+ 
+
+ align:start position:0%
+have different splitting energy
+and so the um amount of energy required
+
+ align:start position:0%
+and so the um amount of energy required
+ 
+
+ align:start position:0%
+and so the um amount of energy required
+to bump an electron up here is going to
+
+ align:start position:0%
+to bump an electron up here is going to
+ 
+
+ align:start position:0%
+to bump an electron up here is going to
+be different than up here and so you'll
+
+ align:start position:0%
+be different than up here and so you'll
+ 
+
+ align:start position:0%
+be different than up here and so you'll
+have different colors as a result so
+
+ align:start position:0%
+have different colors as a result so
+ 
+
+ align:start position:0%
+have different colors as a result so
+let's take a look at
+
+ align:start position:0%
+let's take a look at
+ 
+
+ align:start position:0%
+let's take a look at
+that so again this is intermediate so
+
+ align:start position:0%
+that so again this is intermediate so
+ 
+
+ align:start position:0%
+that so again this is intermediate so
+this is smaller this is stronger it's
+
+ align:start position:0%
+this is smaller this is stronger it's
+ 
+
+ align:start position:0%
+this is smaller this is stronger it's
+larger it doesn't affect how the
+
+ align:start position:0%
+larger it doesn't affect how the
+ 
+
+ align:start position:0%
+larger it doesn't affect how the
+electrons go in but it does affect the
+
+ align:start position:0%
+electrons go in but it does affect the
+ 
+
+ align:start position:0%
+electrons go in but it does affect the
+property of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compound so let's go through this and
+
+ align:start position:0%
+compound so let's go through this and
+ 
+
+ align:start position:0%
+compound so let's go through this and
+see what what this means so water then
+
+ align:start position:0%
+see what what this means so water then
+ 
+
+ align:start position:0%
+see what what this means so water then
+is weaker it means the splitting energy
+
+ align:start position:0%
+is weaker it means the splitting energy
+ 
+
+ align:start position:0%
+is weaker it means the splitting energy
+is smaller so if the splitting energy is
+
+ align:start position:0%
+is smaller so if the splitting energy is
+ 
+
+ align:start position:0%
+is smaller so if the splitting energy is
+smaller that means you have a lower
+
+ align:start position:0%
+smaller that means you have a lower
+ 
+
+ align:start position:0%
+smaller that means you have a lower
+energy a smaller energy between them and
+
+ align:start position:0%
+energy a smaller energy between them and
+ 
+
+ align:start position:0%
+energy a smaller energy between them and
+a lower frequency that'll be
+
+ align:start position:0%
+a lower frequency that'll be
+ 
+
+ align:start position:0%
+a lower frequency that'll be
+absorbed in this case this is a strong
+
+ align:start position:0%
+absorbed in this case this is a strong
+ 
+
+ align:start position:0%
+absorbed in this case this is a strong
+field Lian so you'll have a larger
+
+ align:start position:0%
+field Lian so you'll have a larger
+ 
+
+ align:start position:0%
+field Lian so you'll have a larger
+energy and a higher frequency that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absorbed so so over here if we have the
+
+ align:start position:0%
+absorbed so so over here if we have the
+ 
+
+ align:start position:0%
+absorbed so so over here if we have the
+lower frequency absorbed we have a
+
+ align:start position:0%
+lower frequency absorbed we have a
+ 
+
+ align:start position:0%
+lower frequency absorbed we have a
+longer wavelength absorbed for the
+
+ align:start position:0%
+longer wavelength absorbed for the
+ 
+
+ align:start position:0%
+longer wavelength absorbed for the
+stronger field case we have somewhat of
+
+ align:start position:0%
+stronger field case we have somewhat of
+ 
+
+ align:start position:0%
+stronger field case we have somewhat of
+a higher frequency absorbed so we'll
+
+ align:start position:0%
+a higher frequency absorbed so we'll
+ 
+
+ align:start position:0%
+a higher frequency absorbed so we'll
+have somewhat of a shorter wavelength
+
+ align:start position:0%
+have somewhat of a shorter wavelength
+ 
+
+ align:start position:0%
+have somewhat of a shorter wavelength
+absorbed and then the color of the
+
+ align:start position:0%
+absorbed and then the color of the
+ 
+
+ align:start position:0%
+absorbed and then the color of the
+transmitted light is complementary to
+
+ align:start position:0%
+transmitted light is complementary to
+ 
+
+ align:start position:0%
+transmitted light is complementary to
+the color of the absorbed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+light so here you're going to have a
+
+ align:start position:0%
+light so here you're going to have a
+ 
+
+ align:start position:0%
+light so here you're going to have a
+transmitted light with a shorter
+
+ align:start position:0%
+transmitted light with a shorter
+ 
+
+ align:start position:0%
+transmitted light with a shorter
+frequency you you had a long you had a
+
+ align:start position:0%
+frequency you you had a long you had a
+ 
+
+ align:start position:0%
+frequency you you had a long you had a
+longer shorter wavelength you had a
+
+ align:start position:0%
+longer shorter wavelength you had a
+ 
+
+ align:start position:0%
+longer shorter wavelength you had a
+longer wavelength absorbed so you'll
+
+ align:start position:0%
+longer wavelength absorbed so you'll
+ 
+
+ align:start position:0%
+longer wavelength absorbed so you'll
+have a shorter wavelength
+
+ align:start position:0%
+have a shorter wavelength
+ 
+
+ align:start position:0%
+have a shorter wavelength
+transmitted and this compound is in fact
+
+ align:start position:0%
+transmitted and this compound is in fact
+ 
+
+ align:start position:0%
+transmitted and this compound is in fact
+Violet over here you're going to have um
+
+ align:start position:0%
+Violet over here you're going to have um
+ 
+
+ align:start position:0%
+Violet over here you're going to have um
+the shorter wavelength absorbed so the
+
+ align:start position:0%
+the shorter wavelength absorbed so the
+ 
+
+ align:start position:0%
+the shorter wavelength absorbed so the
+transmitted light will be complementary
+
+ align:start position:0%
+transmitted light will be complementary
+ 
+
+ align:start position:0%
+transmitted light will be complementary
+to that and will have a longer
+
+ align:start position:0%
+to that and will have a longer
+ 
+
+ align:start position:0%
+to that and will have a longer
+wavelength and this uh compound is in
+
+ align:start position:0%
+wavelength and this uh compound is in
+ 
+
+ align:start position:0%
+wavelength and this uh compound is in
+fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yellow so if we uh look again at uh the
+
+ align:start position:0%
+yellow so if we uh look again at uh the
+ 
+
+ align:start position:0%
+yellow so if we uh look again at uh the
+colors and um and their
+
+ align:start position:0%
+colors and um and their
+ 
+
+ align:start position:0%
+colors and um and their
+wavelengths this strong this complex
+
+ align:start position:0%
+wavelengths this strong this complex
+ 
+
+ align:start position:0%
+wavelengths this strong this complex
+with a strong field Li is
+
+ align:start position:0%
+with a strong field Li is
+ 
+
+ align:start position:0%
+with a strong field Li is
+yellow and the one with an intermediate
+
+ align:start position:0%
+yellow and the one with an intermediate
+ 
+
+ align:start position:0%
+yellow and the one with an intermediate
+field ligan is violet somewhere down in
+
+ align:start position:0%
+field ligan is violet somewhere down in
+ 
+
+ align:start position:0%
+field ligan is violet somewhere down in
+here so even though water and NH3 are
+
+ align:start position:0%
+here so even though water and NH3 are
+ 
+
+ align:start position:0%
+here so even though water and NH3 are
+close to each other the one that's
+
+ align:start position:0%
+close to each other the one that's
+ 
+
+ align:start position:0%
+close to each other the one that's
+stronger definitely has quite a distinct
+
+ align:start position:0%
+stronger definitely has quite a distinct
+ 
+
+ align:start position:0%
+stronger definitely has quite a distinct
+color from the one that's a bit weaker
+
+ align:start position:0%
+color from the one that's a bit weaker
+ 
+
+ align:start position:0%
+color from the one that's a bit weaker
+and unless you're given numbers you
+
+ align:start position:0%
+and unless you're given numbers you
+ 
+
+ align:start position:0%
+and unless you're given numbers you
+can't predict exactly which color you
+
+ align:start position:0%
+can't predict exactly which color you
+ 
+
+ align:start position:0%
+can't predict exactly which color you
+could just rationalize the relationship
+
+ align:start position:0%
+could just rationalize the relationship
+ 
+
+ align:start position:0%
+could just rationalize the relationship
+so if you said if you were told this is
+
+ align:start position:0%
+so if you said if you were told this is
+ 
+
+ align:start position:0%
+so if you said if you were told this is
+yellow and this is violet tell me why
+
+ align:start position:0%
+yellow and this is violet tell me why
+ 
+
+ align:start position:0%
+yellow and this is violet tell me why
+you would say this is a stronger field
+
+ align:start position:0%
+you would say this is a stronger field
+ 
+
+ align:start position:0%
+you would say this is a stronger field
+liin than this one so that's the kind of
+
+ align:start position:0%
+liin than this one so that's the kind of
+ 
+
+ align:start position:0%
+liin than this one so that's the kind of
+thing you can do but if you're given
+
+ align:start position:0%
+thing you can do but if you're given
+ 
+
+ align:start position:0%
+thing you can do but if you're given
+numbers and on problems and on the final
+
+ align:start position:0%
+numbers and on problems and on the final
+ 
+
+ align:start position:0%
+numbers and on problems and on the final
+you may be given numbers you can
+
+ align:start position:0%
+you may be given numbers you can
+ 
+
+ align:start position:0%
+you may be given numbers you can
+actually come up and calculate back and
+
+ align:start position:0%
+actually come up and calculate back and
+ 
+
+ align:start position:0%
+actually come up and calculate back and
+forth from the splitting energy to the
+
+ align:start position:0%
+forth from the splitting energy to the
+ 
+
+ align:start position:0%
+forth from the splitting energy to the
+color that you predict from a color back
+
+ align:start position:0%
+color that you predict from a color back
+ 
+
+ align:start position:0%
+color that you predict from a color back
+to the splitting energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what things would be
+
+ align:start position:0%
+so what things would be
+ 
+
+ align:start position:0%
+so what things would be
+colorless which kind of coordination
+
+ align:start position:0%
+colorless which kind of coordination
+ 
+
+ align:start position:0%
+colorless which kind of coordination
+complexes will be
+
+ align:start position:0%
+complexes will be
+ 
+
+ align:start position:0%
+complexes will be
+colorless and why would it be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+colorless this is where things written
+
+ align:start position:0%
+colorless this is where things written
+ 
+
+ align:start position:0%
+colorless this is where things written
+in your hand bout can be read back to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me unless you know but it's good to
+
+ align:start position:0%
+me unless you know but it's good to
+ 
+
+ align:start position:0%
+me unless you know but it's good to
+think about it a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if you filled up all your D
+
+ align:start position:0%
+okay so if you filled up all your D
+ 
+
+ align:start position:0%
+okay so if you filled up all your D
+orbitals and there's no room for things
+
+ align:start position:0%
+orbitals and there's no room for things
+ 
+
+ align:start position:0%
+orbitals and there's no room for things
+to move around when it's not possible to
+
+ align:start position:0%
+to move around when it's not possible to
+ 
+
+ align:start position:0%
+to move around when it's not possible to
+have a d Tod transition so you filled up
+
+ align:start position:0%
+have a d Tod transition so you filled up
+ 
+
+ align:start position:0%
+have a d Tod transition so you filled up
+everything so you're not going to be
+
+ align:start position:0%
+everything so you're not going to be
+ 
+
+ align:start position:0%
+everything so you're not going to be
+able to do this transition from one set
+
+ align:start position:0%
+able to do this transition from one set
+ 
+
+ align:start position:0%
+able to do this transition from one set
+of D orbitals to another one then uh you
+
+ align:start position:0%
+of D orbitals to another one then uh you
+ 
+
+ align:start position:0%
+of D orbitals to another one then uh you
+have colorless so here are some examples
+
+ align:start position:0%
+have colorless so here are some examples
+ 
+
+ align:start position:0%
+have colorless so here are some examples
+of things that will be colorless and
+
+ align:start position:0%
+of things that will be colorless and
+ 
+
+ align:start position:0%
+of things that will be colorless and
+let's just uh prove that that would be
+
+ align:start position:0%
+let's just uh prove that that would be
+ 
+
+ align:start position:0%
+let's just uh prove that that would be
+true that those are in fact filled so we
+
+ align:start position:0%
+true that those are in fact filled so we
+ 
+
+ align:start position:0%
+true that those are in fact filled so we
+have zinc and cadmium so if we look uh
+
+ align:start position:0%
+have zinc and cadmium so if we look uh
+ 
+
+ align:start position:0%
+have zinc and cadmium so if we look uh
+zinc and cadum are in group
+
+ align:start position:0%
+zinc and cadum are in group
+ 
+
+ align:start position:0%
+zinc and cadum are in group
+12 so 12 minus 2 they're both an oxida
+
+ align:start position:0%
+12 so 12 minus 2 they're both an oxida
+ 
+
+ align:start position:0%
+12 so 12 minus 2 they're both an oxida
+have oxidation numbers of plus two so 12
+
+ align:start position:0%
+have oxidation numbers of plus two so 12
+ 
+
+ align:start position:0%
+have oxidation numbers of plus two so 12
+U minus 2 is 10 you have a d10 system
+
+ align:start position:0%
+U minus 2 is 10 you have a d10 system
+ 
+
+ align:start position:0%
+U minus 2 is 10 you have a d10 system
+this one's also going to be a d10 system
+
+ align:start position:0%
+this one's also going to be a d10 system
+ 
+
+ align:start position:0%
+this one's also going to be a d10 system
+so you're going to have all 10 electrons
+
+ align:start position:0%
+so you're going to have all 10 electrons
+ 
+
+ align:start position:0%
+so you're going to have all 10 electrons
+already in and so you're not going to
+
+ align:start position:0%
+already in and so you're not going to
+ 
+
+ align:start position:0%
+already in and so you're not going to
+have these Transitions and so these in
+
+ align:start position:0%
+have these Transitions and so these in
+ 
+
+ align:start position:0%
+have these Transitions and so these in
+fact are are colorless zinc is is a
+
+ align:start position:0%
+fact are are colorless zinc is is a
+ 
+
+ align:start position:0%
+fact are are colorless zinc is is a
+really important U metal in biology and
+
+ align:start position:0%
+really important U metal in biology and
+ 
+
+ align:start position:0%
+really important U metal in biology and
+it plays structural roles it can play
+
+ align:start position:0%
+it plays structural roles it can play
+ 
+
+ align:start position:0%
+it plays structural roles it can play
+catalytic roles it's a very important
+
+ align:start position:0%
+catalytic roles it's a very important
+ 
+
+ align:start position:0%
+catalytic roles it's a very important
+metal and often when biochemists are
+
+ align:start position:0%
+metal and often when biochemists are
+ 
+
+ align:start position:0%
+metal and often when biochemists are
+trying to uh figure out how a protein
+
+ align:start position:0%
+trying to uh figure out how a protein
+ 
+
+ align:start position:0%
+trying to uh figure out how a protein
+Works they won't realize it's a zinc
+
+ align:start position:0%
+Works they won't realize it's a zinc
+ 
+
+ align:start position:0%
+Works they won't realize it's a zinc
+containing enzyme because the protein
+
+ align:start position:0%
+containing enzyme because the protein
+ 
+
+ align:start position:0%
+containing enzyme because the protein
+won't have any color in contrast there
+
+ align:start position:0%
+won't have any color in contrast there
+ 
+
+ align:start position:0%
+won't have any color in contrast there
+are um proteins and co-actors and metals
+
+ align:start position:0%
+are um proteins and co-actors and metals
+ 
+
+ align:start position:0%
+are um proteins and co-actors and metals
+that have a lot of color and uh then you
+
+ align:start position:0%
+that have a lot of color and uh then you
+ 
+
+ align:start position:0%
+that have a lot of color and uh then you
+can actually as you're purifying the
+
+ align:start position:0%
+can actually as you're purifying the
+ 
+
+ align:start position:0%
+can actually as you're purifying the
+enzyme it'll have this bright orange or
+
+ align:start position:0%
+enzyme it'll have this bright orange or
+ 
+
+ align:start position:0%
+enzyme it'll have this bright orange or
+red uh color and you realize it has some
+
+ align:start position:0%
+red uh color and you realize it has some
+ 
+
+ align:start position:0%
+red uh color and you realize it has some
+metal co-actor in it right from right
+
+ align:start position:0%
+metal co-actor in it right from right
+ 
+
+ align:start position:0%
+metal co-actor in it right from right
+from the very
+
+ align:start position:0%
+from the very
+ 
+
+ align:start position:0%
+from the very
+beginning okay so just to go through
+
+ align:start position:0%
+beginning okay so just to go through
+ 
+
+ align:start position:0%
+beginning okay so just to go through
+then and sort of summarize this whole
+
+ align:start position:0%
+then and sort of summarize this whole
+ 
+
+ align:start position:0%
+then and sort of summarize this whole
+procedure if you're on this end with the
+
+ align:start position:0%
+procedure if you're on this end with the
+ 
+
+ align:start position:0%
+procedure if you're on this end with the
+liggans and the weak field ligans then
+
+ align:start position:0%
+liggans and the weak field ligans then
+ 
+
+ align:start position:0%
+liggans and the weak field ligans then
+you're going to have a small splitting
+
+ align:start position:0%
+you're going to have a small splitting
+ 
+
+ align:start position:0%
+you're going to have a small splitting
+weak things can't split much they don't
+
+ align:start position:0%
+weak things can't split much they don't
+ 
+
+ align:start position:0%
+weak things can't split much they don't
+have enough strength to really split
+
+ align:start position:0%
+have enough strength to really split
+ 
+
+ align:start position:0%
+have enough strength to really split
+those de orbitals apart you'll have a
+
+ align:start position:0%
+those de orbitals apart you'll have a
+ 
+
+ align:start position:0%
+those de orbitals apart you'll have a
+high spin system in this case maximum
+
+ align:start position:0%
+high spin system in this case maximum
+ 
+
+ align:start position:0%
+high spin system in this case maximum
+number of unpaired
+
+ align:start position:0%
+number of unpaired
+ 
+
+ align:start position:0%
+number of unpaired
+electrons uh in terms of the complexes
+
+ align:start position:0%
+electrons uh in terms of the complexes
+ 
+
+ align:start position:0%
+electrons uh in terms of the complexes
+then they'll absorb low energy photons
+
+ align:start position:0%
+then they'll absorb low energy photons
+ 
+
+ align:start position:0%
+then they'll absorb low energy photons
+low frequency long
+
+ align:start position:0%
+low frequency long
+ 
+
+ align:start position:0%
+low frequency long
+wavelength and then they will transmit
+
+ align:start position:0%
+wavelength and then they will transmit
+ 
+
+ align:start position:0%
+wavelength and then they will transmit
+high frequency or short wavelength so
+
+ align:start position:0%
+high frequency or short wavelength so
+ 
+
+ align:start position:0%
+high frequency or short wavelength so
+they're going to be in this uh violet
+
+ align:start position:0%
+they're going to be in this uh violet
+ 
+
+ align:start position:0%
+they're going to be in this uh violet
+blue green end of the Spectra and let me
+
+ align:start position:0%
+blue green end of the Spectra and let me
+ 
+
+ align:start position:0%
+blue green end of the Spectra and let me
+just put uh this one up and actually let
+
+ align:start position:0%
+just put uh this one up and actually let
+ 
+
+ align:start position:0%
+just put uh this one up and actually let
+me just put all these guys up so they'll
+
+ align:start position:0%
+me just put all these guys up so they'll
+ 
+
+ align:start position:0%
+me just put all these guys up so they'll
+be on this end of the Spectra again you
+
+ align:start position:0%
+be on this end of the Spectra again you
+ 
+
+ align:start position:0%
+be on this end of the Spectra again you
+have it's all based on these two
+
+ align:start position:0%
+have it's all based on these two
+ 
+
+ align:start position:0%
+have it's all based on these two
+equations so if you have a small
+
+ align:start position:0%
+equations so if you have a small
+ 
+
+ align:start position:0%
+equations so if you have a small
+splitting small energy you're going to
+
+ align:start position:0%
+splitting small energy you're going to
+ 
+
+ align:start position:0%
+splitting small energy you're going to
+have a low frequency and then you'll
+
+ align:start position:0%
+have a low frequency and then you'll
+ 
+
+ align:start position:0%
+have a low frequency and then you'll
+have a long wavelength for absorbed and
+
+ align:start position:0%
+have a long wavelength for absorbed and
+ 
+
+ align:start position:0%
+have a long wavelength for absorbed and
+the complementary for the transmitted if
+
+ align:start position:0%
+the complementary for the transmitted if
+ 
+
+ align:start position:0%
+the complementary for the transmitted if
+you're strong field you'll have a large
+
+ align:start position:0%
+you're strong field you'll have a large
+ 
+
+ align:start position:0%
+you're strong field you'll have a large
+splitting energy it'll be low spin
+
+ align:start position:0%
+splitting energy it'll be low spin
+ 
+
+ align:start position:0%
+splitting energy it'll be low spin
+minimum number of unpaired
+
+ align:start position:0%
+minimum number of unpaired
+ 
+
+ align:start position:0%
+minimum number of unpaired
+electrons and you'll have uh a situation
+
+ align:start position:0%
+electrons and you'll have uh a situation
+ 
+
+ align:start position:0%
+electrons and you'll have uh a situation
+like this you know here you fill them up
+
+ align:start position:0%
+like this you know here you fill them up
+ 
+
+ align:start position:0%
+like this you know here you fill them up
+to maximum extent here they're low spin
+
+ align:start position:0%
+to maximum extent here they're low spin
+ 
+
+ align:start position:0%
+to maximum extent here they're low spin
+maximum paired uh so then you'll have
+
+ align:start position:0%
+maximum paired uh so then you'll have
+ 
+
+ align:start position:0%
+maximum paired uh so then you'll have
+the complimentary if you have short
+
+ align:start position:0%
+the complimentary if you have short
+ 
+
+ align:start position:0%
+the complimentary if you have short
+wavelength absorbed you'll have long
+
+ align:start position:0%
+wavelength absorbed you'll have long
+ 
+
+ align:start position:0%
+wavelength absorbed you'll have long
+wavelength trans um transmitted and
+
+ align:start position:0%
+wavelength trans um transmitted and
+ 
+
+ align:start position:0%
+wavelength trans um transmitted and
+you'll be on this end of the Spectra so
+
+ align:start position:0%
+you'll be on this end of the Spectra so
+ 
+
+ align:start position:0%
+you'll be on this end of the Spectra so
+you would expect yellow orange or red in
+
+ align:start position:0%
+you would expect yellow orange or red in
+ 
+
+ align:start position:0%
+you would expect yellow orange or red in
+this case so you can make predictions if
+
+ align:start position:0%
+this case so you can make predictions if
+ 
+
+ align:start position:0%
+this case so you can make predictions if
+you know something about the ligan You
+
+ align:start position:0%
+you know something about the ligan You
+ 
+
+ align:start position:0%
+you know something about the ligan You
+can predict the color of the
+
+ align:start position:0%
+can predict the color of the
+ 
+
+ align:start position:0%
+can predict the color of the
+coordination complex or at least
+
+ align:start position:0%
+coordination complex or at least
+ 
+
+ align:start position:0%
+coordination complex or at least
+rationalize the color of the
+
+ align:start position:0%
+rationalize the color of the
+ 
+
+ align:start position:0%
+rationalize the color of the
+coordination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complex so um just to show you sort of a
+
+ align:start position:0%
+complex so um just to show you sort of a
+ 
+
+ align:start position:0%
+complex so um just to show you sort of a
+real example these are all octahedral
+
+ align:start position:0%
+real example these are all octahedral
+ 
+
+ align:start position:0%
+real example these are all octahedral
+complexes with Cobalt and you can see
+
+ align:start position:0%
+complexes with Cobalt and you can see
+ 
+
+ align:start position:0%
+complexes with Cobalt and you can see
+the colors are really dramatically
+
+ align:start position:0%
+the colors are really dramatically
+ 
+
+ align:start position:0%
+the colors are really dramatically
+different so depending on the Lian to
+
+ align:start position:0%
+different so depending on the Lian to
+ 
+
+ align:start position:0%
+different so depending on the Lian to
+the Cobalt you can really get this
+
+ align:start position:0%
+the Cobalt you can really get this
+ 
+
+ align:start position:0%
+the Cobalt you can really get this
+beautiful range of colors
+
+ align:start position:0%
+beautiful range of colors
+ 
+
+ align:start position:0%
+beautiful range of colors
+Associated and uh one of the courses
+
+ align:start position:0%
+Associated and uh one of the courses
+ 
+
+ align:start position:0%
+Associated and uh one of the courses
+that's offered during IAP key that Dr
+
+ align:start position:0%
+that's offered during IAP key that Dr
+ 
+
+ align:start position:0%
+that's offered during IAP key that Dr
+shrank teaches you go through and
+
+ align:start position:0%
+shrank teaches you go through and
+ 
+
+ align:start position:0%
+shrank teaches you go through and
+actually do some of these experiments
+
+ align:start position:0%
+actually do some of these experiments
+ 
+
+ align:start position:0%
+actually do some of these experiments
+and see these colors and so it's a
+
+ align:start position:0%
+and see these colors and so it's a
+ 
+
+ align:start position:0%
+and see these colors and so it's a
+little lab component that complements
+
+ align:start position:0%
+little lab component that complements
+ 
+
+ align:start position:0%
+little lab component that complements
+nicely uh this part of the course as
+
+ align:start position:0%
+nicely uh this part of the course as
+ 
+
+ align:start position:0%
+nicely uh this part of the course as
+well as a few other parts of the course
+
+ align:start position:0%
+well as a few other parts of the course
+ 
+
+ align:start position:0%
+well as a few other parts of the course
+so those are of um these these
+
+ align:start position:0%
+so those are of um these these
+ 
+
+ align:start position:0%
+so those are of um these these
+coordination complexes and uh Cobalt is
+
+ align:start position:0%
+coordination complexes and uh Cobalt is
+ 
+
+ align:start position:0%
+coordination complexes and uh Cobalt is
+also in a
+
+ align:start position:0%
+also in a
+ 
+
+ align:start position:0%
+also in a
+vitamin can someone tell me what vitamin
+
+ align:start position:0%
+vitamin can someone tell me what vitamin
+ 
+
+ align:start position:0%
+vitamin can someone tell me what vitamin
+Cobalt is in the center
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of what's my favorite vitamin yes so
+
+ align:start position:0%
+of what's my favorite vitamin yes so
+ 
+
+ align:start position:0%
+of what's my favorite vitamin yes so
+these are colors of
+
+ align:start position:0%
+these are colors of
+ 
+
+ align:start position:0%
+these are colors of
+B12 so this is protein bound to
+
+ align:start position:0%
+B12 so this is protein bound to
+ 
+
+ align:start position:0%
+B12 so this is protein bound to
+different uh different forms of B12 so
+
+ align:start position:0%
+different uh different forms of B12 so
+ 
+
+ align:start position:0%
+different uh different forms of B12 so
+there's actually different lians to the
+
+ align:start position:0%
+there's actually different lians to the
+ 
+
+ align:start position:0%
+there's actually different lians to the
+Cobalt in these three cases and these
+
+ align:start position:0%
+Cobalt in these three cases and these
+ 
+
+ align:start position:0%
+Cobalt in these three cases and these
+are the actual colors it's really
+
+ align:start position:0%
+are the actual colors it's really
+ 
+
+ align:start position:0%
+are the actual colors it's really
+spectacular the colors of these and
+
+ align:start position:0%
+spectacular the colors of these and
+ 
+
+ align:start position:0%
+spectacular the colors of these and
+these are crystals of the of the
+
+ align:start position:0%
+these are crystals of the of the
+ 
+
+ align:start position:0%
+these are crystals of the of the
+proteins so the colors are really very
+
+ align:start position:0%
+proteins so the colors are really very
+ 
+
+ align:start position:0%
+proteins so the colors are really very
+rich so when you're doing experiments on
+
+ align:start position:0%
+rich so when you're doing experiments on
+ 
+
+ align:start position:0%
+rich so when you're doing experiments on
+a B12 system you know something about
+
+ align:start position:0%
+a B12 system you know something about
+ 
+
+ align:start position:0%
+a B12 system you know something about
+the form of B12 if you've some damage to
+
+ align:start position:0%
+the form of B12 if you've some damage to
+ 
+
+ align:start position:0%
+the form of B12 if you've some damage to
+your B12 uh you know it by actually
+
+ align:start position:0%
+your B12 uh you know it by actually
+ 
+
+ align:start position:0%
+your B12 uh you know it by actually
+looking at uh the color of the molecule
+
+ align:start position:0%
+looking at uh the color of the molecule
+ 
+
+ align:start position:0%
+looking at uh the color of the molecule
+you're working with of the crystals or
+
+ align:start position:0%
+you're working with of the crystals or
+ 
+
+ align:start position:0%
+you're working with of the crystals or
+the protein you're working
+
+ align:start position:0%
+the protein you're working
+ 
+
+ align:start position:0%
+the protein you're working
+with okay so very fast then
+
+ align:start position:0%
+with okay so very fast then
+ 
+
+ align:start position:0%
+with okay so very fast then
+magnetism
+
+ align:start position:0%
+magnetism
+ 
+
+ align:start position:0%
+magnetism
+so uh compounds comp that com um
+
+ align:start position:0%
+so uh compounds comp that com um
+ 
+
+ align:start position:0%
+so uh compounds comp that com um
+compounds that have unpaired electrons
+
+ align:start position:0%
+compounds that have unpaired electrons
+ 
+
+ align:start position:0%
+compounds that have unpaired electrons
+are paramagnetic attracted by a magnetic
+
+ align:start position:0%
+are paramagnetic attracted by a magnetic
+ 
+
+ align:start position:0%
+are paramagnetic attracted by a magnetic
+field and ones where they're pair are
+
+ align:start position:0%
+field and ones where they're pair are
+ 
+
+ align:start position:0%
+field and ones where they're pair are
+diamagnetic so they're repelled by a
+
+ align:start position:0%
+diamagnetic so they're repelled by a
+ 
+
+ align:start position:0%
+diamagnetic so they're repelled by a
+magnetic
+
+ align:start position:0%
+magnetic
+ 
+
+ align:start position:0%
+magnetic
+field so you can figure out something
+
+ align:start position:0%
+field so you can figure out something
+ 
+
+ align:start position:0%
+field so you can figure out something
+about the geometries often of your
+
+ align:start position:0%
+about the geometries often of your
+ 
+
+ align:start position:0%
+about the geometries often of your
+compounds by figuring out whether the
+
+ align:start position:0%
+compounds by figuring out whether the
+ 
+
+ align:start position:0%
+compounds by figuring out whether the
+compound is paramagnetic or diamagnetic
+
+ align:start position:0%
+compound is paramagnetic or diamagnetic
+ 
+
+ align:start position:0%
+compound is paramagnetic or diamagnetic
+all right well how would you do this
+
+ align:start position:0%
+all right well how would you do this
+ 
+
+ align:start position:0%
+all right well how would you do this
+well if for example you had a nickel two
+
+ align:start position:0%
+well if for example you had a nickel two
+ 
+
+ align:start position:0%
+well if for example you had a nickel two
+plus system in an enzyme so you have a
+
+ align:start position:0%
+plus system in an enzyme so you have a
+ 
+
+ align:start position:0%
+plus system in an enzyme so you have a
+d8 center in your enzyme and it's found
+
+ align:start position:0%
+d8 center in your enzyme and it's found
+ 
+
+ align:start position:0%
+d8 center in your enzyme and it's found
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+biomagnetic you could ask the question
+
+ align:start position:0%
+biomagnetic you could ask the question
+ 
+
+ align:start position:0%
+biomagnetic you could ask the question
+can I can I guess then whether it has
+
+ align:start position:0%
+can I can I guess then whether it has
+ 
+
+ align:start position:0%
+can I can I guess then whether it has
+Square planer geometry tetrahedral
+
+ align:start position:0%
+Square planer geometry tetrahedral
+ 
+
+ align:start position:0%
+Square planer geometry tetrahedral
+geometry or octahedral geometry because
+
+ align:start position:0%
+geometry or octahedral geometry because
+ 
+
+ align:start position:0%
+geometry or octahedral geometry because
+it is diamagnetic can I figure out the
+
+ align:start position:0%
+it is diamagnetic can I figure out the
+ 
+
+ align:start position:0%
+it is diamagnetic can I figure out the
+geometry knowing that fact knowing about
+
+ align:start position:0%
+geometry knowing that fact knowing about
+ 
+
+ align:start position:0%
+geometry knowing that fact knowing about
+unpaired or paired electrons in this
+
+ align:start position:0%
+unpaired or paired electrons in this
+ 
+
+ align:start position:0%
+unpaired or paired electrons in this
+case we'd have to have its diamagnetic
+
+ align:start position:0%
+case we'd have to have its diamagnetic
+ 
+
+ align:start position:0%
+case we'd have to have its diamagnetic
+all the electrons have to be
+
+ align:start position:0%
+all the electrons have to be
+ 
+
+ align:start position:0%
+all the electrons have to be
+paired so here are our splitting
+
+ align:start position:0%
+paired so here are our splitting
+ 
+
+ align:start position:0%
+paired so here are our splitting
+diagrams for all three cases let's look
+
+ align:start position:0%
+diagrams for all three cases let's look
+ 
+
+ align:start position:0%
+diagrams for all three cases let's look
+at octahedral again we have to put eight
+
+ align:start position:0%
+at octahedral again we have to put eight
+ 
+
+ align:start position:0%
+at octahedral again we have to put eight
+electrons in here are eight electrons
+
+ align:start position:0%
+electrons in here are eight electrons
+ 
+
+ align:start position:0%
+electrons in here are eight electrons
+does this matter if this was weak field
+
+ align:start position:0%
+does this matter if this was weak field
+ 
+
+ align:start position:0%
+does this matter if this was weak field
+or strong field in this case which which
+
+ align:start position:0%
+or strong field in this case which which
+ 
+
+ align:start position:0%
+or strong field in this case which which
+is it can you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tell same right because you would put in
+
+ align:start position:0%
+tell same right because you would put in
+ 
+
+ align:start position:0%
+tell same right because you would put in
+electrons whether you put them in 1 2 3
+
+ align:start position:0%
+electrons whether you put them in 1 2 3
+ 
+
+ align:start position:0%
+electrons whether you put them in 1 2 3
+four five six 78 or put them in 1 2 3 4
+
+ align:start position:0%
+four five six 78 or put them in 1 2 3 4
+ 
+
+ align:start position:0%
+four five six 78 or put them in 1 2 3 4
+5 6 7 8 it's the same
+
+ align:start position:0%
+5 6 7 8 it's the same
+ 
+
+ align:start position:0%
+5 6 7 8 it's the same
+so this could be either notice we have
+
+ align:start position:0%
+so this could be either notice we have
+ 
+
+ align:start position:0%
+so this could be either notice we have
+unpaired electrons so this cannot be the
+
+ align:start position:0%
+unpaired electrons so this cannot be the
+ 
+
+ align:start position:0%
+unpaired electrons so this cannot be the
+geometry of this unknown Center what
+
+ align:start position:0%
+geometry of this unknown Center what
+ 
+
+ align:start position:0%
+geometry of this unknown Center what
+about Square planer let's put them in
+
+ align:start position:0%
+about Square planer let's put them in
+ 
+
+ align:start position:0%
+about Square planer let's put them in
+starting at the bottom so we'll put them
+
+ align:start position:0%
+starting at the bottom so we'll put them
+ 
+
+ align:start position:0%
+starting at the bottom so we'll put them
+all in keep going just put them all in
+
+ align:start position:0%
+all in keep going just put them all in
+ 
+
+ align:start position:0%
+all in keep going just put them all in
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+eight so it didn't really matter too
+
+ align:start position:0%
+eight so it didn't really matter too
+ 
+
+ align:start position:0%
+eight so it didn't really matter too
+much the order I put them in down here
+
+ align:start position:0%
+much the order I put them in down here
+ 
+
+ align:start position:0%
+much the order I put them in down here
+the important point is I really didn't
+
+ align:start position:0%
+the important point is I really didn't
+ 
+
+ align:start position:0%
+the important point is I really didn't
+want to put any in here until I had to
+
+ align:start position:0%
+want to put any in here until I had to
+ 
+
+ align:start position:0%
+want to put any in here until I had to
+because this one if you recall is really
+
+ align:start position:0%
+because this one if you recall is really
+ 
+
+ align:start position:0%
+because this one if you recall is really
+destabilized compared to the rest all
+
+ align:start position:0%
+destabilized compared to the rest all
+ 
+
+ align:start position:0%
+destabilized compared to the rest all
+right so these are all paired up and
+
+ align:start position:0%
+right so these are all paired up and
+ 
+
+ align:start position:0%
+right so these are all paired up and
+let's look at tetrahedral tetrahedral
+
+ align:start position:0%
+let's look at tetrahedral tetrahedral
+ 
+
+ align:start position:0%
+let's look at tetrahedral tetrahedral
+tends to be what kind of
+
+ align:start position:0%
+tends to be what kind of
+ 
+
+ align:start position:0%
+tends to be what kind of
+spin High spin because the splitting
+
+ align:start position:0%
+spin High spin because the splitting
+ 
+
+ align:start position:0%
+spin High spin because the splitting
+energy is small because you don't have
+
+ align:start position:0%
+energy is small because you don't have
+ 
+
+ align:start position:0%
+energy is small because you don't have
+uh lians pointing directly at the D
+
+ align:start position:0%
+uh lians pointing directly at the D
+ 
+
+ align:start position:0%
+uh lians pointing directly at the D
+orbitals so we can put them in in a high
+
+ align:start position:0%
+orbitals so we can put them in in a high
+ 
+
+ align:start position:0%
+orbitals so we can put them in in a high
+spin fashion until we're
+
+ align:start position:0%
+spin fashion until we're
+ 
+
+ align:start position:0%
+spin fashion until we're
+done and uh that's our system it's going
+
+ align:start position:0%
+done and uh that's our system it's going
+ 
+
+ align:start position:0%
+done and uh that's our system it's going
+to this is small splitting energy
+
+ align:start position:0%
+to this is small splitting energy
+ 
+
+ align:start position:0%
+to this is small splitting energy
+and down here so we have unpaired
+
+ align:start position:0%
+and down here so we have unpaired
+ 
+
+ align:start position:0%
+and down here so we have unpaired
+electrons here so this is paramagnetic
+
+ align:start position:0%
+electrons here so this is paramagnetic
+ 
+
+ align:start position:0%
+electrons here so this is paramagnetic
+this is paramagnetic this is diamagnetic
+
+ align:start position:0%
+this is paramagnetic this is diamagnetic
+ 
+
+ align:start position:0%
+this is paramagnetic this is diamagnetic
+so then you could predict that the
+
+ align:start position:0%
+so then you could predict that the
+ 
+
+ align:start position:0%
+so then you could predict that the
+nickel in the enzyme must be square
+
+ align:start position:0%
+nickel in the enzyme must be square
+ 
+
+ align:start position:0%
+nickel in the enzyme must be square
+planer it can't be this and it can't be
+
+ align:start position:0%
+planer it can't be this and it can't be
+ 
+
+ align:start position:0%
+planer it can't be this and it can't be
+that so it tells you something about the
+
+ align:start position:0%
+that so it tells you something about the
+ 
+
+ align:start position:0%
+that so it tells you something about the
+geometry and I'll tell you that there
+
+ align:start position:0%
+geometry and I'll tell you that there
+ 
+
+ align:start position:0%
+geometry and I'll tell you that there
+are two square planer systems at least
+
+ align:start position:0%
+are two square planer systems at least
+ 
+
+ align:start position:0%
+are two square planer systems at least
+in enzymes of nickel and people
+
+ align:start position:0%
+in enzymes of nickel and people
+ 
+
+ align:start position:0%
+in enzymes of nickel and people
+predicted it using similar kinds of
+
+ align:start position:0%
+predicted it using similar kinds of
+ 
+
+ align:start position:0%
+predicted it using similar kinds of
+techniques to what you just learned
+
+ align:start position:0%
+techniques to what you just learned
+ 
+
+ align:start position:0%
+techniques to what you just learned
+about in freshman chemistry okay good
+
+ align:start position:0%
+about in freshman chemistry okay good
+ 
+
+ align:start position:0%
+about in freshman chemistry okay good
+good luck on the exam on Wednesday
\ No newline at end of file
diff --git a/LqwvVAtEIx8.txt b/LqwvVAtEIx8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bba069ec4c1b13f0a098cf702bd7feb7bee1f527
--- /dev/null
+++ b/LqwvVAtEIx8.txt
@@ -0,0 +1,1659 @@
+align:start position:0%
+ 
+hello everyone today I'm going to talk
+
+ align:start position:0%
+hello everyone today I'm going to talk
+ 
+
+ align:start position:0%
+hello everyone today I'm going to talk
+to you about crystallographic point
+
+ align:start position:0%
+to you about crystallographic point
+ 
+
+ align:start position:0%
+to you about crystallographic point
+groups and how to visualize them with
+
+ align:start position:0%
+groups and how to visualize them with
+ 
+
+ align:start position:0%
+groups and how to visualize them with
+Mathematica phone books are important in
+
+ align:start position:0%
+Mathematica phone books are important in
+ 
+
+ align:start position:0%
+Mathematica phone books are important in
+crystallography as they enable us to
+
+ align:start position:0%
+crystallography as they enable us to
+ 
+
+ align:start position:0%
+crystallography as they enable us to
+classify crystal symmetries of questions
+
+ align:start position:0%
+classify crystal symmetries of questions
+ 
+
+ align:start position:0%
+classify crystal symmetries of questions
+so what are point groups one group sets
+
+ align:start position:0%
+so what are point groups one group sets
+ 
+
+ align:start position:0%
+so what are point groups one group sets
+of symmetries which are in a variant
+
+ align:start position:0%
+of symmetries which are in a variant
+ 
+
+ align:start position:0%
+of symmetries which are in a variant
+around the center from meaning a prompt
+
+ align:start position:0%
+around the center from meaning a prompt
+ 
+
+ align:start position:0%
+around the center from meaning a prompt
+will not change if it's ended at the
+
+ align:start position:0%
+will not change if it's ended at the
+ 
+
+ align:start position:0%
+will not change if it's ended at the
+center and has all of these symmetries
+
+ align:start position:0%
+center and has all of these symmetries
+ 
+
+ align:start position:0%
+center and has all of these symmetries
+applied through three elements of point
+
+ align:start position:0%
+applied through three elements of point
+ 
+
+ align:start position:0%
+applied through three elements of point
+groups our mirror planes rotation axis
+
+ align:start position:0%
+groups our mirror planes rotation axis
+ 
+
+ align:start position:0%
+groups our mirror planes rotation axis
+and roto infusion Isis and mirror planes
+
+ align:start position:0%
+and roto infusion Isis and mirror planes
+ 
+
+ align:start position:0%
+and roto infusion Isis and mirror planes
+as you can be imagined are just taking
+
+ align:start position:0%
+as you can be imagined are just taking
+ 
+
+ align:start position:0%
+as you can be imagined are just taking
+in and then the image the mirror image
+
+ align:start position:0%
+in and then the image the mirror image
+ 
+
+ align:start position:0%
+in and then the image the mirror image
+of this point will be no symmetry mirror
+
+ align:start position:0%
+of this point will be no symmetry mirror
+ 
+
+ align:start position:0%
+of this point will be no symmetry mirror
+planes can be in three dimension meaning
+
+ align:start position:0%
+planes can be in three dimension meaning
+ 
+
+ align:start position:0%
+planes can be in three dimension meaning
+that they can be perpendicular to X
+
+ align:start position:0%
+that they can be perpendicular to X
+ 
+
+ align:start position:0%
+that they can be perpendicular to X
+perpendicular to Y and perpendicular to
+
+ align:start position:0%
+perpendicular to Y and perpendicular to
+ 
+
+ align:start position:0%
+perpendicular to Y and perpendicular to
+the z axis rotation axes are also found
+
+ align:start position:0%
+the z axis rotation axes are also found
+ 
+
+ align:start position:0%
+the z axis rotation axes are also found
+into three dimensions that they are
+
+ align:start position:0%
+into three dimensions that they are
+ 
+
+ align:start position:0%
+into three dimensions that they are
+rotations around this axis so for
+
+ align:start position:0%
+rotations around this axis so for
+ 
+
+ align:start position:0%
+rotations around this axis so for
+example a two-fold rotation would be
+
+ align:start position:0%
+example a two-fold rotation would be
+ 
+
+ align:start position:0%
+example a two-fold rotation would be
+taking a point and making a rotation of
+
+ align:start position:0%
+taking a point and making a rotation of
+ 
+
+ align:start position:0%
+taking a point and making a rotation of
+half a circle around a certain axis and
+
+ align:start position:0%
+half a circle around a certain axis and
+ 
+
+ align:start position:0%
+half a circle around a certain axis and
+this will be the symmetry 3 for rotation
+
+ align:start position:0%
+this will be the symmetry 3 for rotation
+ 
+
+ align:start position:0%
+this will be the symmetry 3 for rotation
+axis will be 3 atoms which are each
+
+ align:start position:0%
+axis will be 3 atoms which are each
+ 
+
+ align:start position:0%
+axis will be 3 atoms which are each
+rotated from by one third of a circle so
+
+ align:start position:0%
+rotated from by one third of a circle so
+ 
+
+ align:start position:0%
+rotated from by one third of a circle so
+brutal inversion axes are bit more
+
+ align:start position:0%
+brutal inversion axes are bit more
+ 
+
+ align:start position:0%
+brutal inversion axes are bit more
+complicated to visualize there are
+
+ align:start position:0%
+complicated to visualize there are
+ 
+
+ align:start position:0%
+complicated to visualize there are
+basically a rotation followed by what we
+
+ align:start position:0%
+basically a rotation followed by what we
+ 
+
+ align:start position:0%
+basically a rotation followed by what we
+call an inversion so for example me if
+
+ align:start position:0%
+call an inversion so for example me if
+ 
+
+ align:start position:0%
+call an inversion so for example me if
+we take a four-fold roto inversion axis
+
+ align:start position:0%
+we take a four-fold roto inversion axis
+ 
+
+ align:start position:0%
+we take a four-fold roto inversion axis
+we have to take album rotated by 1/4 of
+
+ align:start position:0%
+we have to take album rotated by 1/4 of
+ 
+
+ align:start position:0%
+we have to take album rotated by 1/4 of
+a circle and then invert this point
+
+ align:start position:0%
+a circle and then invert this point
+ 
+
+ align:start position:0%
+a circle and then invert this point
+through the origin
+
+ align:start position:0%
+through the origin
+ 
+
+ align:start position:0%
+through the origin
+so basically inverting would be taking
+
+ align:start position:0%
+so basically inverting would be taking
+ 
+
+ align:start position:0%
+so basically inverting would be taking
+opponent which has the coordinates 1 on
+
+ align:start position:0%
+opponent which has the coordinates 1 on
+ 
+
+ align:start position:0%
+opponent which has the coordinates 1 on
+1 and transforming it into minus 1 minus
+
+ align:start position:0%
+1 and transforming it into minus 1 minus
+ 
+
+ align:start position:0%
+1 and transforming it into minus 1 minus
+1 minus 1 when we come when we mix all
+
+ align:start position:0%
+1 minus 1 when we come when we mix all
+ 
+
+ align:start position:0%
+1 minus 1 when we come when we mix all
+of these elements we get the 32 point
+
+ align:start position:0%
+of these elements we get the 32 point
+ 
+
+ align:start position:0%
+of these elements we get the 32 point
+groups which are in crystal graphene as
+
+ align:start position:0%
+groups which are in crystal graphene as
+ 
+
+ align:start position:0%
+groups which are in crystal graphene as
+you can see in their routine notation
+
+ align:start position:0%
+you can see in their routine notation
+ 
+
+ align:start position:0%
+you can see in their routine notation
+like this so let's talk a bit about the
+
+ align:start position:0%
+like this so let's talk a bit about the
+ 
+
+ align:start position:0%
+like this so let's talk a bit about the
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+and it is fairly simple we take an M if
+
+ align:start position:0%
+and it is fairly simple we take an M if
+ 
+
+ align:start position:0%
+and it is fairly simple we take an M if
+we have a mirror plane two M's if we
+
+ align:start position:0%
+we have a mirror plane two M's if we
+ 
+
+ align:start position:0%
+we have a mirror plane two M's if we
+have two mirror planes Xterra if this
+
+ align:start position:0%
+have two mirror planes Xterra if this
+ 
+
+ align:start position:0%
+have two mirror planes Xterra if this
+mirror plane is perpendicular to an
+
+ align:start position:0%
+mirror plane is perpendicular to an
+ 
+
+ align:start position:0%
+mirror plane is perpendicular to an
+already existing rotation axis then we
+
+ align:start position:0%
+already existing rotation axis then we
+ 
+
+ align:start position:0%
+already existing rotation axis then we
+we noted slash air and a rotation axis
+
+ align:start position:0%
+we noted slash air and a rotation axis
+ 
+
+ align:start position:0%
+we noted slash air and a rotation axis
+is basically just a number which tells
+
+ align:start position:0%
+is basically just a number which tells
+ 
+
+ align:start position:0%
+is basically just a number which tells
+us the number of rotations so three four
+
+ align:start position:0%
+us the number of rotations so three four
+ 
+
+ align:start position:0%
+us the number of rotations so three four
+rotation axis would be three
+
+ align:start position:0%
+rotation axis would be three
+ 
+
+ align:start position:0%
+rotation axis would be three
+you know three rotation around the axis
+
+ align:start position:0%
+you know three rotation around the axis
+ 
+
+ align:start position:0%
+you know three rotation around the axis
+X bar is also antenatal four roto
+
+ align:start position:0%
+X bar is also antenatal four roto
+ 
+
+ align:start position:0%
+X bar is also antenatal four roto
+inversion axis so if we look at example
+
+ align:start position:0%
+inversion axis so if we look at example
+ 
+
+ align:start position:0%
+inversion axis so if we look at example
+examples in a couple of examples we can
+
+ align:start position:0%
+examples in a couple of examples we can
+ 
+
+ align:start position:0%
+examples in a couple of examples we can
+see the first point group which is named
+
+ align:start position:0%
+see the first point group which is named
+ 
+
+ align:start position:0%
+see the first point group which is named
+one which basically has no symmetry so
+
+ align:start position:0%
+one which basically has no symmetry so
+ 
+
+ align:start position:0%
+one which basically has no symmetry so
+we have a point and nothing happens with
+
+ align:start position:0%
+we have a point and nothing happens with
+ 
+
+ align:start position:0%
+we have a point and nothing happens with
+it then we have the two fold rotation
+
+ align:start position:0%
+it then we have the two fold rotation
+ 
+
+ align:start position:0%
+it then we have the two fold rotation
+axis so we take this point rotate it by
+
+ align:start position:0%
+axis so we take this point rotate it by
+ 
+
+ align:start position:0%
+axis so we take this point rotate it by
+half a circle and we get this pumped
+
+ align:start position:0%
+half a circle and we get this pumped
+ 
+
+ align:start position:0%
+half a circle and we get this pumped
+same for the 3/4 rotation axis one two
+
+ align:start position:0%
+same for the 3/4 rotation axis one two
+ 
+
+ align:start position:0%
+same for the 3/4 rotation axis one two
+and three and we're back to the original
+
+ align:start position:0%
+and three and we're back to the original
+ 
+
+ align:start position:0%
+and three and we're back to the original
+position and then we have here the
+
+ align:start position:0%
+position and then we have here the
+ 
+
+ align:start position:0%
+position and then we have here the
+fourfold rotation axis and here the six
+
+ align:start position:0%
+fourfold rotation axis and here the six
+ 
+
+ align:start position:0%
+fourfold rotation axis and here the six
+for rotation missus if we take something
+
+ align:start position:0%
+for rotation missus if we take something
+ 
+
+ align:start position:0%
+for rotation missus if we take something
+which has whenever planes this is mmm so
+
+ align:start position:0%
+which has whenever planes this is mmm so
+ 
+
+ align:start position:0%
+which has whenever planes this is mmm so
+for example we can take the cross which
+
+ align:start position:0%
+for example we can take the cross which
+ 
+
+ align:start position:0%
+for example we can take the cross which
+is the cross symbolizes an atom which is
+
+ align:start position:0%
+is the cross symbolizes an atom which is
+ 
+
+ align:start position:0%
+is the cross symbolizes an atom which is
+above the plane and a circle another
+
+ align:start position:0%
+above the plane and a circle another
+ 
+
+ align:start position:0%
+above the plane and a circle another
+which is below the plane so if we take
+
+ align:start position:0%
+which is below the plane so if we take
+ 
+
+ align:start position:0%
+which is below the plane so if we take
+this point and then say that there is a
+
+ align:start position:0%
+this point and then say that there is a
+ 
+
+ align:start position:0%
+this point and then say that there is a
+mirror plane here then we have of course
+
+ align:start position:0%
+mirror plane here then we have of course
+ 
+
+ align:start position:0%
+mirror plane here then we have of course
+to find a mirror image which is here
+
+ align:start position:0%
+to find a mirror image which is here
+ 
+
+ align:start position:0%
+to find a mirror image which is here
+then if we say it is a mirror plane on
+
+ align:start position:0%
+then if we say it is a mirror plane on
+ 
+
+ align:start position:0%
+then if we say it is a mirror plane on
+this direction then we have to take
+
+ align:start position:0%
+this direction then we have to take
+ 
+
+ align:start position:0%
+this direction then we have to take
+these two atoms and put them here and
+
+ align:start position:0%
+these two atoms and put them here and
+ 
+
+ align:start position:0%
+these two atoms and put them here and
+then we also have a third mirror plane
+
+ align:start position:0%
+then we also have a third mirror plane
+ 
+
+ align:start position:0%
+then we also have a third mirror plane
+which would be perpendicular to the x
+
+ align:start position:0%
+which would be perpendicular to the x
+ 
+
+ align:start position:0%
+which would be perpendicular to the x
+axis so the x axis in these images goes
+
+ align:start position:0%
+axis so the x axis in these images goes
+ 
+
+ align:start position:0%
+axis so the x axis in these images goes
+out of the screen and that's how we end
+
+ align:start position:0%
+out of the screen and that's how we end
+ 
+
+ align:start position:0%
+out of the screen and that's how we end
+up with four atoms on the top and four
+
+ align:start position:0%
+up with four atoms on the top and four
+ 
+
+ align:start position:0%
+up with four atoms on the top and four
+atoms below and then we can combine
+
+ align:start position:0%
+atoms below and then we can combine
+ 
+
+ align:start position:0%
+atoms below and then we can combine
+these with rotation axes so for example
+
+ align:start position:0%
+these with rotation axes so for example
+ 
+
+ align:start position:0%
+these with rotation axes so for example
+this is the two / M so basically we have
+
+ align:start position:0%
+this is the two / M so basically we have
+ 
+
+ align:start position:0%
+this is the two / M so basically we have
+a two for rotation and then we have a
+
+ align:start position:0%
+a two for rotation and then we have a
+ 
+
+ align:start position:0%
+a two for rotation and then we have a
+mirror plane which is perpendicular to
+
+ align:start position:0%
+mirror plane which is perpendicular to
+ 
+
+ align:start position:0%
+mirror plane which is perpendicular to
+the x axis so we get two atoms above and
+
+ align:start position:0%
+the x axis so we get two atoms above and
+ 
+
+ align:start position:0%
+the x axis so we get two atoms above and
+two atoms bill
+
+ align:start position:0%
+two atoms bill
+ 
+
+ align:start position:0%
+two atoms bill
+mm you can also play around with the
+
+ align:start position:0%
+mm you can also play around with the
+ 
+
+ align:start position:0%
+mm you can also play around with the
+rest and see if there if it works but we
+
+ align:start position:0%
+rest and see if there if it works but we
+ 
+
+ align:start position:0%
+rest and see if there if it works but we
+get it gets more and more complicated
+
+ align:start position:0%
+get it gets more and more complicated
+ 
+
+ align:start position:0%
+get it gets more and more complicated
+look to this one which is M power 3 M
+
+ align:start position:0%
+look to this one which is M power 3 M
+ 
+
+ align:start position:0%
+look to this one which is M power 3 M
+which is the most symmetric of these
+
+ align:start position:0%
+which is the most symmetric of these
+ 
+
+ align:start position:0%
+which is the most symmetric of these
+point groups so how do we use point
+
+ align:start position:0%
+point groups so how do we use point
+ 
+
+ align:start position:0%
+point groups so how do we use point
+groups it's basically if we combine the
+
+ align:start position:0%
+groups it's basically if we combine the
+ 
+
+ align:start position:0%
+groups it's basically if we combine the
+32 point groups with the transmission of
+
+ align:start position:0%
+32 point groups with the transmission of
+ 
+
+ align:start position:0%
+32 point groups with the transmission of
+symmetries after 14 bravais lattices and
+
+ align:start position:0%
+symmetries after 14 bravais lattices and
+ 
+
+ align:start position:0%
+symmetries after 14 bravais lattices and
+the light planes of complete screw axes
+
+ align:start position:0%
+the light planes of complete screw axes
+ 
+
+ align:start position:0%
+the light planes of complete screw axes
+which are which are found in an
+
+ align:start position:0%
+which are which are found in an
+ 
+
+ align:start position:0%
+which are which are found in an
+intuitive you start to combine point
+
+ align:start position:0%
+intuitive you start to combine point
+ 
+
+ align:start position:0%
+intuitive you start to combine point
+groups then we end up with the 270 space
+
+ align:start position:0%
+groups then we end up with the 270 space
+ 
+
+ align:start position:0%
+groups then we end up with the 270 space
+group to which all crystals belong and
+
+ align:start position:0%
+group to which all crystals belong and
+ 
+
+ align:start position:0%
+group to which all crystals belong and
+so how do we combine point groups and
+
+ align:start position:0%
+so how do we combine point groups and
+ 
+
+ align:start position:0%
+so how do we combine point groups and
+profit lattices so here is the list of
+
+ align:start position:0%
+profit lattices so here is the list of
+ 
+
+ align:start position:0%
+profit lattices so here is the list of
+the present this is the basically just
+
+ align:start position:0%
+the present this is the basically just
+ 
+
+ align:start position:0%
+the present this is the basically just
+taking a pond and transmitting it around
+
+ align:start position:0%
+taking a pond and transmitting it around
+ 
+
+ align:start position:0%
+taking a pond and transmitting it around
+a look this a cubic lattice tetragonal
+
+ align:start position:0%
+a look this a cubic lattice tetragonal
+ 
+
+ align:start position:0%
+a look this a cubic lattice tetragonal
+lattice exact and on everything the blue
+
+ align:start position:0%
+lattice exact and on everything the blue
+ 
+
+ align:start position:0%
+lattice exact and on everything the blue
+point will be the center of the point
+
+ align:start position:0%
+point will be the center of the point
+ 
+
+ align:start position:0%
+point will be the center of the point
+group and then we just translate this
+
+ align:start position:0%
+group and then we just translate this
+ 
+
+ align:start position:0%
+group and then we just translate this
+mass of atoms which are the signature on
+
+ align:start position:0%
+mass of atoms which are the signature on
+ 
+
+ align:start position:0%
+mass of atoms which are the signature on
+upon hoop and then transmitted around
+
+ align:start position:0%
+upon hoop and then transmitted around
+ 
+
+ align:start position:0%
+upon hoop and then transmitted around
+the lattice so let's look at the code
+
+ align:start position:0%
+the lattice so let's look at the code
+ 
+
+ align:start position:0%
+the lattice so let's look at the code
+and see how we visualize them so this is
+
+ align:start position:0%
+and see how we visualize them so this is
+ 
+
+ align:start position:0%
+and see how we visualize them so this is
+the manipulate which has the function
+
+ align:start position:0%
+the manipulate which has the function
+ 
+
+ align:start position:0%
+the manipulate which has the function
+embedded inside so we start with one
+
+ align:start position:0%
+embedded inside so we start with one
+ 
+
+ align:start position:0%
+embedded inside so we start with one
+atom which is the point group one if we
+
+ align:start position:0%
+atom which is the point group one if we
+ 
+
+ align:start position:0%
+atom which is the point group one if we
+decide to to make a mirror plane for
+
+ align:start position:0%
+decide to to make a mirror plane for
+ 
+
+ align:start position:0%
+decide to to make a mirror plane for
+support perpendicular to X then we end
+
+ align:start position:0%
+support perpendicular to X then we end
+ 
+
+ align:start position:0%
+support perpendicular to X then we end
+up with this this is a trust mode mirror
+
+ align:start position:0%
+up with this this is a trust mode mirror
+ 
+
+ align:start position:0%
+up with this this is a trust mode mirror
+plane which has an same name one then
+
+ align:start position:0%
+plane which has an same name one then
+ 
+
+ align:start position:0%
+plane which has an same name one then
+paint bench then we can have three
+
+ align:start position:0%
+paint bench then we can have three
+ 
+
+ align:start position:0%
+paint bench then we can have three
+mirror planes which would give us a
+
+ align:start position:0%
+mirror planes which would give us a
+ 
+
+ align:start position:0%
+mirror planes which would give us a
+patterns and and this is basically what
+
+ align:start position:0%
+patterns and and this is basically what
+ 
+
+ align:start position:0%
+patterns and and this is basically what
+the code does just taking or the or what
+
+ align:start position:0%
+the code does just taking or the or what
+ 
+
+ align:start position:0%
+the code does just taking or the or what
+will give it so if and so what we can
+
+ align:start position:0%
+will give it so if and so what we can
+ 
+
+ align:start position:0%
+will give it so if and so what we can
+take to to to which you can find is this
+
+ align:start position:0%
+take to to to which you can find is this
+ 
+
+ align:start position:0%
+take to to to which you can find is this
+one here
+
+ align:start position:0%
+one here
+ 
+
+ align:start position:0%
+one here
+two two two gives us this so this is two
+
+ align:start position:0%
+two two two gives us this so this is two
+ 
+
+ align:start position:0%
+two two two gives us this so this is two
+two two rotation axis symmetry two point
+
+ align:start position:0%
+two two rotation axis symmetry two point
+ 
+
+ align:start position:0%
+two two rotation axis symmetry two point
+group here in the function we also have
+
+ align:start position:0%
+group here in the function we also have
+ 
+
+ align:start position:0%
+group here in the function we also have
+the number of atoms which is four and we
+
+ align:start position:0%
+the number of atoms which is four and we
+ 
+
+ align:start position:0%
+the number of atoms which is four and we
+have the name of the point group which
+
+ align:start position:0%
+have the name of the point group which
+ 
+
+ align:start position:0%
+have the name of the point group which
+is a bit experimental because it's not
+
+ align:start position:0%
+is a bit experimental because it's not
+ 
+
+ align:start position:0%
+is a bit experimental because it's not
+easy to generate a name out of under the
+
+ align:start position:0%
+easy to generate a name out of under the
+ 
+
+ align:start position:0%
+easy to generate a name out of under the
+atomic chance and this code can generate
+
+ align:start position:0%
+atomic chance and this code can generate
+ 
+
+ align:start position:0%
+atomic chance and this code can generate
+for example this which is upon coop
+
+ align:start position:0%
+for example this which is upon coop
+ 
+
+ align:start position:0%
+for example this which is upon coop
+which doesn't
+
+ align:start position:0%
+which doesn't
+ 
+
+ align:start position:0%
+which doesn't
+exist six sixes it's just this is the
+
+ align:start position:0%
+exist six sixes it's just this is the
+ 
+
+ align:start position:0%
+exist six sixes it's just this is the
+first version of the code which might be
+
+ align:start position:0%
+first version of the code which might be
+ 
+
+ align:start position:0%
+first version of the code which might be
+improved of course we can also take both
+
+ align:start position:0%
+improved of course we can also take both
+ 
+
+ align:start position:0%
+improved of course we can also take both
+to a diversion axis here so if we try to
+
+ align:start position:0%
+to a diversion axis here so if we try to
+ 
+
+ align:start position:0%
+to a diversion axis here so if we try to
+understand what what's happening with
+
+ align:start position:0%
+understand what what's happening with
+ 
+
+ align:start position:0%
+understand what what's happening with
+this one is we have an atom then we
+
+ align:start position:0%
+this one is we have an atom then we
+ 
+
+ align:start position:0%
+this one is we have an atom then we
+trance
+
+ align:start position:0%
+trance
+ 
+
+ align:start position:0%
+trance
+so we said a wonderful rotation of
+
+ align:start position:0%
+so we said a wonderful rotation of
+ 
+
+ align:start position:0%
+so we said a wonderful rotation of
+rotoinversion axis would be at one for
+
+ align:start position:0%
+rotoinversion axis would be at one for
+ 
+
+ align:start position:0%
+rotoinversion axis would be at one for
+rotation so basically we end up at the
+
+ align:start position:0%
+rotation so basically we end up at the
+ 
+
+ align:start position:0%
+rotation so basically we end up at the
+same point and then we invert it through
+
+ align:start position:0%
+same point and then we invert it through
+ 
+
+ align:start position:0%
+same point and then we invert it through
+the origin and then weak this opposite
+
+ align:start position:0%
+the origin and then weak this opposite
+ 
+
+ align:start position:0%
+the origin and then weak this opposite
+atom as you can see if we get it maybe
+
+ align:start position:0%
+atom as you can see if we get it maybe
+ 
+
+ align:start position:0%
+atom as you can see if we get it maybe
+clearer to see if we have a three rotor
+
+ align:start position:0%
+clearer to see if we have a three rotor
+ 
+
+ align:start position:0%
+clearer to see if we have a three rotor
+in a version access so you can clearly
+
+ align:start position:0%
+in a version access so you can clearly
+ 
+
+ align:start position:0%
+in a version access so you can clearly
+see that at the three for rotation so we
+
+ align:start position:0%
+see that at the three for rotation so we
+ 
+
+ align:start position:0%
+see that at the three for rotation so we
+have three atoms on one side and three
+
+ align:start position:0%
+have three atoms on one side and three
+ 
+
+ align:start position:0%
+have three atoms on one side and three
+atoms on the other side so the atoms
+
+ align:start position:0%
+atoms on the other side so the atoms
+ 
+
+ align:start position:0%
+atoms on the other side so the atoms
+above and three atoms below and then and
+
+ align:start position:0%
+above and three atoms below and then and
+ 
+
+ align:start position:0%
+above and three atoms below and then and
+then we invert them each time so this is
+
+ align:start position:0%
+then we invert them each time so this is
+ 
+
+ align:start position:0%
+then we invert them each time so this is
+the code and now let's look at how it
+
+ align:start position:0%
+the code and now let's look at how it
+ 
+
+ align:start position:0%
+the code and now let's look at how it
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+so it is quite easy what the code does
+
+ align:start position:0%
+so it is quite easy what the code does
+ 
+
+ align:start position:0%
+so it is quite easy what the code does
+is taking inputs and then calculating
+
+ align:start position:0%
+is taking inputs and then calculating
+ 
+
+ align:start position:0%
+is taking inputs and then calculating
+all the matrices of molar
+
+ align:start position:0%
+all the matrices of molar
+ 
+
+ align:start position:0%
+all the matrices of molar
+transformations so the first line here
+
+ align:start position:0%
+transformations so the first line here
+ 
+
+ align:start position:0%
+transformations so the first line here
+would be taking the matrix of the BOK so
+
+ align:start position:0%
+would be taking the matrix of the BOK so
+ 
+
+ align:start position:0%
+would be taking the matrix of the BOK so
+with a function of reflection transform
+
+ align:start position:0%
+with a function of reflection transform
+ 
+
+ align:start position:0%
+with a function of reflection transform
+from Mathematica this line takes the
+
+ align:start position:0%
+from Mathematica this line takes the
+ 
+
+ align:start position:0%
+from Mathematica this line takes the
+rotation axis with the rotation
+
+ align:start position:0%
+rotation axis with the rotation
+ 
+
+ align:start position:0%
+rotation axis with the rotation
+transform function then these lines
+
+ align:start position:0%
+transform function then these lines
+ 
+
+ align:start position:0%
+transform function then these lines
+calculate all the rotation all the
+
+ align:start position:0%
+calculate all the rotation all the
+ 
+
+ align:start position:0%
+calculate all the rotation all the
+transformation matrices from each photo
+
+ align:start position:0%
+transformation matrices from each photo
+ 
+
+ align:start position:0%
+transformation matrices from each photo
+inversion X's in the as you can see is a
+
+ align:start position:0%
+inversion X's in the as you can see is a
+ 
+
+ align:start position:0%
+inversion X's in the as you can see is a
+bit more complicated to come up with and
+
+ align:start position:0%
+bit more complicated to come up with and
+ 
+
+ align:start position:0%
+bit more complicated to come up with and
+then taking all of these matrices which
+
+ align:start position:0%
+then taking all of these matrices which
+ 
+
+ align:start position:0%
+then taking all of these matrices which
+are found in the lines of matrices amira
+
+ align:start position:0%
+are found in the lines of matrices amira
+ 
+
+ align:start position:0%
+are found in the lines of matrices amira
+matrices reports and matrices in 402
+
+ align:start position:0%
+matrices reports and matrices in 402
+ 
+
+ align:start position:0%
+matrices reports and matrices in 402
+inversion we do the outer product of all
+
+ align:start position:0%
+inversion we do the outer product of all
+ 
+
+ align:start position:0%
+inversion we do the outer product of all
+of these matrices we get every possible
+
+ align:start position:0%
+of these matrices we get every possible
+ 
+
+ align:start position:0%
+of these matrices we get every possible
+combination of every possible symmetry
+
+ align:start position:0%
+combination of every possible symmetry
+ 
+
+ align:start position:0%
+combination of every possible symmetry
+so we can have all the put on the
+
+ align:start position:0%
+so we can have all the put on the
+ 
+
+ align:start position:0%
+so we can have all the put on the
+symmetry positions and then we are
+
+ align:start position:0%
+symmetry positions and then we are
+ 
+
+ align:start position:0%
+symmetry positions and then we are
+applying that to our initial position
+
+ align:start position:0%
+applying that to our initial position
+ 
+
+ align:start position:0%
+applying that to our initial position
+and we get all the symmetry positions
+
+ align:start position:0%
+and we get all the symmetry positions
+ 
+
+ align:start position:0%
+and we get all the symmetry positions
+then we delete duplicates of symmetry
+
+ align:start position:0%
+then we delete duplicates of symmetry
+ 
+
+ align:start position:0%
+then we delete duplicates of symmetry
+position we make sphere out of it and
+
+ align:start position:0%
+position we make sphere out of it and
+ 
+
+ align:start position:0%
+position we make sphere out of it and
+then we
+
+ align:start position:0%
+then we
+ 
+
+ align:start position:0%
+then we
+we display everything in a graphics 3d
+
+ align:start position:0%
+we display everything in a graphics 3d
+ 
+
+ align:start position:0%
+we display everything in a graphics 3d
+this bit here is to generate the name of
+
+ align:start position:0%
+this bit here is to generate the name of
+ 
+
+ align:start position:0%
+this bit here is to generate the name of
+the point group as I said experimental
+
+ align:start position:0%
+the point group as I said experimental
+ 
+
+ align:start position:0%
+the point group as I said experimental
+and this bit here is to calculate the
+
+ align:start position:0%
+and this bit here is to calculate the
+ 
+
+ align:start position:0%
+and this bit here is to calculate the
+number of atoms we have so this is
+
+ align:start position:0%
+number of atoms we have so this is
+ 
+
+ align:start position:0%
+number of atoms we have so this is
+basically the function which is not that
+
+ align:start position:0%
+basically the function which is not that
+ 
+
+ align:start position:0%
+basically the function which is not that
+complicated as I said and here is the
+
+ align:start position:0%
+complicated as I said and here is the
+ 
+
+ align:start position:0%
+complicated as I said and here is the
+result as we can have as you can see we
+
+ align:start position:0%
+result as we can have as you can see we
+ 
+
+ align:start position:0%
+result as we can have as you can see we
+can start combining everything and
+
+ align:start position:0%
+can start combining everything and
+ 
+
+ align:start position:0%
+can start combining everything and
+having your toolbar am to borrow to
+
+ align:start position:0%
+having your toolbar am to borrow to
+ 
+
+ align:start position:0%
+having your toolbar am to borrow to
+param and just play with it this is a
+
+ align:start position:0%
+param and just play with it this is a
+ 
+
+ align:start position:0%
+param and just play with it this is a
+this is why it is clever this code is
+
+ align:start position:0%
+this is why it is clever this code is
+ 
+
+ align:start position:0%
+this is why it is clever this code is
+quite because we can actually visualize
+
+ align:start position:0%
+quite because we can actually visualize
+ 
+
+ align:start position:0%
+quite because we can actually visualize
+pollen groups in 3d instead of seeing
+
+ align:start position:0%
+pollen groups in 3d instead of seeing
+ 
+
+ align:start position:0%
+pollen groups in 3d instead of seeing
+them as these 2d representations so I
+
+ align:start position:0%
+them as these 2d representations so I
+ 
+
+ align:start position:0%
+them as these 2d representations so I
+hope you had a fun time and thank you
+
+ align:start position:0%
+hope you had a fun time and thank you
+ 
+
+ align:start position:0%
+hope you had a fun time and thank you
+for your attention
\ No newline at end of file
diff --git a/LxDmWdOwIA8.txt b/LxDmWdOwIA8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ec2a0a84131969948c5f836f83d9bbd40af99e6b
--- /dev/null
+++ b/LxDmWdOwIA8.txt
@@ -0,0 +1,1979 @@
+align:start position:0%
+ 
+welcome you are about to do something
+
+ align:start position:0%
+welcome you are about to do something
+ 
+
+ align:start position:0%
+welcome you are about to do something
+very special which is to negotiate the
+
+ align:start position:0%
+very special which is to negotiate the
+ 
+
+ align:start position:0%
+very special which is to negotiate the
+future of work this video is designed to
+
+ align:start position:0%
+future of work this video is designed to
+ 
+
+ align:start position:0%
+future of work this video is designed to
+help you know what you need to know to
+
+ align:start position:0%
+help you know what you need to know to
+ 
+
+ align:start position:0%
+help you know what you need to know to
+nav naate the software and the tools and
+
+ align:start position:0%
+nav naate the software and the tools and
+ 
+
+ align:start position:0%
+nav naate the software and the tools and
+methods to help you be successful in
+
+ align:start position:0%
+methods to help you be successful in
+ 
+
+ align:start position:0%
+methods to help you be successful in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+process what you see on the screen are a
+
+ align:start position:0%
+process what you see on the screen are a
+ 
+
+ align:start position:0%
+process what you see on the screen are a
+series of slides uh we'll spend more
+
+ align:start position:0%
+series of slides uh we'll spend more
+ 
+
+ align:start position:0%
+series of slides uh we'll spend more
+time with some less with others but all
+
+ align:start position:0%
+time with some less with others but all
+ 
+
+ align:start position:0%
+time with some less with others but all
+of them will be available to you on the
+
+ align:start position:0%
+of them will be available to you on the
+ 
+
+ align:start position:0%
+of them will be available to you on the
+course website here's what you need to
+
+ align:start position:0%
+course website here's what you need to
+ 
+
+ align:start position:0%
+course website here's what you need to
+know at the
+
+ align:start position:0%
+know at the
+ 
+
+ align:start position:0%
+know at the
+beginning once you agree to be part of
+
+ align:start position:0%
+beginning once you agree to be part of
+ 
+
+ align:start position:0%
+beginning once you agree to be part of
+this negotiations we want you to sign up
+
+ align:start position:0%
+this negotiations we want you to sign up
+ 
+
+ align:start position:0%
+this negotiations we want you to sign up
+and we want you to commit because in the
+
+ align:start position:0%
+and we want you to commit because in the
+ 
+
+ align:start position:0%
+and we want you to commit because in the
+negotiations there will be yourself and
+
+ align:start position:0%
+negotiations there will be yourself and
+ 
+
+ align:start position:0%
+negotiations there will be yourself and
+three or four other people in
+
+ align:start position:0%
+three or four other people in
+ 
+
+ align:start position:0%
+three or four other people in
+appropriate roles and they'll all be
+
+ align:start position:0%
+appropriate roles and they'll all be
+ 
+
+ align:start position:0%
+appropriate roles and they'll all be
+depending on you to stay through uh to
+
+ align:start position:0%
+depending on you to stay through uh to
+ 
+
+ align:start position:0%
+depending on you to stay through uh to
+agreement and frankly that's how you'll
+
+ align:start position:0%
+agreement and frankly that's how you'll
+ 
+
+ align:start position:0%
+agreement and frankly that's how you'll
+all learn what are the roles the roles
+
+ align:start position:0%
+all learn what are the roles the roles
+ 
+
+ align:start position:0%
+all learn what are the roles the roles
+in the negotiation match key
+
+ align:start position:0%
+in the negotiation match key
+ 
+
+ align:start position:0%
+in the negotiation match key
+stakeholders in society Labor Management
+
+ align:start position:0%
+stakeholders in society Labor Management
+ 
+
+ align:start position:0%
+stakeholders in society Labor Management
+government and education and essentially
+
+ align:start position:0%
+government and education and essentially
+ 
+
+ align:start position:0%
+government and education and essentially
+each of you will be taking on one of
+
+ align:start position:0%
+each of you will be taking on one of
+ 
+
+ align:start position:0%
+each of you will be taking on one of
+these roles they'll be assigned through
+
+ align:start position:0%
+these roles they'll be assigned through
+ 
+
+ align:start position:0%
+these roles they'll be assigned through
+the course
+
+ align:start position:0%
+the course
+ 
+
+ align:start position:0%
+the course
+platform and that will tell you who
+
+ align:start position:0%
+platform and that will tell you who
+ 
+
+ align:start position:0%
+platform and that will tell you who
+you're going to represent in figuring
+
+ align:start position:0%
+you're going to represent in figuring
+ 
+
+ align:start position:0%
+you're going to represent in figuring
+out the future of work
+
+ align:start position:0%
+out the future of work
+ 
+
+ align:start position:0%
+out the future of work
+now once you're assigned to your role
+
+ align:start position:0%
+now once you're assigned to your role
+ 
+
+ align:start position:0%
+now once you're assigned to your role
+you'll come to the website uh platform
+
+ align:start position:0%
+you'll come to the website uh platform
+ 
+
+ align:start position:0%
+you'll come to the website uh platform
+for this negotiation that's what you see
+
+ align:start position:0%
+for this negotiation that's what you see
+ 
+
+ align:start position:0%
+for this negotiation that's what you see
+on the screen here it again reiterates
+
+ align:start position:0%
+on the screen here it again reiterates
+ 
+
+ align:start position:0%
+on the screen here it again reiterates
+what are the different roles in the
+
+ align:start position:0%
+what are the different roles in the
+ 
+
+ align:start position:0%
+what are the different roles in the
+exercise and gives you some background
+
+ align:start position:0%
+exercise and gives you some background
+ 
+
+ align:start position:0%
+exercise and gives you some background
+about the assignment and then for all
+
+ align:start position:0%
+about the assignment and then for all
+ 
+
+ align:start position:0%
+about the assignment and then for all
+four of the roles there's two here and
+
+ align:start position:0%
+four of the roles there's two here and
+ 
+
+ align:start position:0%
+four of the roles there's two here and
+two more uh you'll see some ex
+
+ align:start position:0%
+two more uh you'll see some ex
+ 
+
+ align:start position:0%
+two more uh you'll see some ex
+additional information to help you know
+
+ align:start position:0%
+additional information to help you know
+ 
+
+ align:start position:0%
+additional information to help you know
+what you need to know to be effective in
+
+ align:start position:0%
+what you need to know to be effective in
+ 
+
+ align:start position:0%
+what you need to know to be effective in
+your role you'll see there's a next
+
+ align:start position:0%
+your role you'll see there's a next
+ 
+
+ align:start position:0%
+your role you'll see there's a next
+button and I just checked it that will
+
+ align:start position:0%
+button and I just checked it that will
+ 
+
+ align:start position:0%
+button and I just checked it that will
+move you on to the next screen which is
+
+ align:start position:0%
+move you on to the next screen which is
+ 
+
+ align:start position:0%
+move you on to the next screen which is
+where you start to fill out some of the
+
+ align:start position:0%
+where you start to fill out some of the
+ 
+
+ align:start position:0%
+where you start to fill out some of the
+key information we need there's
+
+ align:start position:0%
+key information we need there's
+ 
+
+ align:start position:0%
+key information we need there's
+different universities that are
+
+ align:start position:0%
+different universities that are
+ 
+
+ align:start position:0%
+different universities that are
+participating in this check which one
+
+ align:start position:0%
+participating in this check which one
+ 
+
+ align:start position:0%
+participating in this check which one
+you're coming from you will be assigned
+
+ align:start position:0%
+you're coming from you will be assigned
+ 
+
+ align:start position:0%
+you're coming from you will be assigned
+a group number which you want to assign
+
+ align:start position:0%
+a group number which you want to assign
+ 
+
+ align:start position:0%
+a group number which you want to assign
+and then there's other demographic
+
+ align:start position:0%
+and then there's other demographic
+ 
+
+ align:start position:0%
+and then there's other demographic
+information that you'll fill out uh on
+
+ align:start position:0%
+information that you'll fill out uh on
+ 
+
+ align:start position:0%
+information that you'll fill out uh on
+education uh whether you've been a
+
+ align:start position:0%
+education uh whether you've been a
+ 
+
+ align:start position:0%
+education uh whether you've been a
+member of a union uh age and other
+
+ align:start position:0%
+member of a union uh age and other
+ 
+
+ align:start position:0%
+member of a union uh age and other
+factors uh they're all required except
+
+ align:start position:0%
+factors uh they're all required except
+ 
+
+ align:start position:0%
+factors uh they're all required except
+uh the gender item um which is optional
+
+ align:start position:0%
+uh the gender item um which is optional
+ 
+
+ align:start position:0%
+uh the gender item um which is optional
+but again once you finish uh filling out
+
+ align:start position:0%
+but again once you finish uh filling out
+ 
+
+ align:start position:0%
+but again once you finish uh filling out
+those different items you'll click next
+
+ align:start position:0%
+those different items you'll click next
+ 
+
+ align:start position:0%
+those different items you'll click next
+and you go onto a screen that now asks
+
+ align:start position:0%
+and you go onto a screen that now asks
+ 
+
+ align:start position:0%
+and you go onto a screen that now asks
+you to tell us about your preferences or
+
+ align:start position:0%
+you to tell us about your preferences or
+ 
+
+ align:start position:0%
+you to tell us about your preferences or
+priorities before negotiations begins
+
+ align:start position:0%
+priorities before negotiations begins
+ 
+
+ align:start position:0%
+priorities before negotiations begins
+you'll see that there's five different
+
+ align:start position:0%
+you'll see that there's five different
+ 
+
+ align:start position:0%
+you'll see that there's five different
+um issues about Workforce capability all
+
+ align:start position:0%
+um issues about Workforce capability all
+ 
+
+ align:start position:0%
+um issues about Workforce capability all
+of which could be subjects of
+
+ align:start position:0%
+of which could be subjects of
+ 
+
+ align:start position:0%
+of which could be subjects of
+negotiation and we want you to rank
+
+ align:start position:0%
+negotiation and we want you to rank
+ 
+
+ align:start position:0%
+negotiation and we want you to rank
+order them from your top priority to
+
+ align:start position:0%
+order them from your top priority to
+ 
+
+ align:start position:0%
+order them from your top priority to
+your second third fourth and fifth no
+
+ align:start position:0%
+your second third fourth and fifth no
+ 
+
+ align:start position:0%
+your second third fourth and fifth no
+ties here you have to pick one two 3
+
+ align:start position:0%
+ties here you have to pick one two 3
+ 
+
+ align:start position:0%
+ties here you have to pick one two 3
+four or five for each of the five items
+
+ align:start position:0%
+four or five for each of the five items
+ 
+
+ align:start position:0%
+four or five for each of the five items
+there's also some questions about
+
+ align:start position:0%
+there's also some questions about
+ 
+
+ align:start position:0%
+there's also some questions about
+representation about organizational
+
+ align:start position:0%
+representation about organizational
+ 
+
+ align:start position:0%
+representation about organizational
+performance uh about compensation uh and
+
+ align:start position:0%
+performance uh about compensation uh and
+ 
+
+ align:start position:0%
+performance uh about compensation uh and
+rewards and incentives for managers as
+
+ align:start position:0%
+rewards and incentives for managers as
+ 
+
+ align:start position:0%
+rewards and incentives for managers as
+well as work family kinds of issues all
+
+ align:start position:0%
+well as work family kinds of issues all
+ 
+
+ align:start position:0%
+well as work family kinds of issues all
+of these are questions that indicate
+
+ align:start position:0%
+of these are questions that indicate
+ 
+
+ align:start position:0%
+of these are questions that indicate
+your priorities going in and frankly
+
+ align:start position:0%
+your priorities going in and frankly
+ 
+
+ align:start position:0%
+your priorities going in and frankly
+that get you thinking about what's at
+
+ align:start position:0%
+that get you thinking about what's at
+ 
+
+ align:start position:0%
+that get you thinking about what's at
+stake as you think about the future of
+
+ align:start position:0%
+stake as you think about the future of
+ 
+
+ align:start position:0%
+stake as you think about the future of
+work finally before we go on to the next
+
+ align:start position:0%
+work finally before we go on to the next
+ 
+
+ align:start position:0%
+work finally before we go on to the next
+screen in each of the five big
+
+ align:start position:0%
+screen in each of the five big
+ 
+
+ align:start position:0%
+screen in each of the five big
+categories Each of which had five sub
+
+ align:start position:0%
+categories Each of which had five sub
+ 
+
+ align:start position:0%
+categories Each of which had five sub
+questions we want you to rank order
+
+ align:start position:0%
+questions we want you to rank order
+ 
+
+ align:start position:0%
+questions we want you to rank order
+those in terms of what's important in
+
+ align:start position:0%
+those in terms of what's important in
+ 
+
+ align:start position:0%
+those in terms of what's important in
+the role that you're playing and again
+
+ align:start position:0%
+the role that you're playing and again
+ 
+
+ align:start position:0%
+the role that you're playing and again
+you'll press next and go on to the next
+
+ align:start position:0%
+you'll press next and go on to the next
+ 
+
+ align:start position:0%
+you'll press next and go on to the next
+screen here there's a couple of short
+
+ align:start position:0%
+screen here there's a couple of short
+ 
+
+ align:start position:0%
+screen here there's a couple of short
+attitude questions about cooperation and
+
+ align:start position:0%
+attitude questions about cooperation and
+ 
+
+ align:start position:0%
+attitude questions about cooperation and
+competition again these will be quick
+
+ align:start position:0%
+competition again these will be quick
+ 
+
+ align:start position:0%
+competition again these will be quick
+and they give us your attitudes before
+
+ align:start position:0%
+and they give us your attitudes before
+ 
+
+ align:start position:0%
+and they give us your attitudes before
+we begin the
+
+ align:start position:0%
+we begin the
+ 
+
+ align:start position:0%
+we begin the
+bargaining that's the setup now we're
+
+ align:start position:0%
+bargaining that's the setup now we're
+ 
+
+ align:start position:0%
+bargaining that's the setup now we're
+getting ready to bargain you'll see that
+
+ align:start position:0%
+getting ready to bargain you'll see that
+ 
+
+ align:start position:0%
+getting ready to bargain you'll see that
+there's a slide that tells you and a set
+
+ align:start position:0%
+there's a slide that tells you and a set
+ 
+
+ align:start position:0%
+there's a slide that tells you and a set
+of materials about preparation the key
+
+ align:start position:0%
+of materials about preparation the key
+ 
+
+ align:start position:0%
+of materials about preparation the key
+thing about preparation is to not just
+
+ align:start position:0%
+thing about preparation is to not just
+ 
+
+ align:start position:0%
+thing about preparation is to not just
+think about your own priorities and
+
+ align:start position:0%
+think about your own priorities and
+ 
+
+ align:start position:0%
+think about your own priorities and
+frankly your underlying interest but to
+
+ align:start position:0%
+frankly your underlying interest but to
+ 
+
+ align:start position:0%
+frankly your underlying interest but to
+think about the priorities and the
+
+ align:start position:0%
+think about the priorities and the
+ 
+
+ align:start position:0%
+think about the priorities and the
+interest what's really at stake for the
+
+ align:start position:0%
+interest what's really at stake for the
+ 
+
+ align:start position:0%
+interest what's really at stake for the
+people in the other
+
+ align:start position:0%
+people in the other
+ 
+
+ align:start position:0%
+people in the other
+roles and so the prep preparation
+
+ align:start position:0%
+roles and so the prep preparation
+ 
+
+ align:start position:0%
+roles and so the prep preparation
+materials will get you up to speed I'm
+
+ align:start position:0%
+materials will get you up to speed I'm
+ 
+
+ align:start position:0%
+materials will get you up to speed I'm
+moving through it quickly but there's a
+
+ align:start position:0%
+moving through it quickly but there's a
+ 
+
+ align:start position:0%
+moving through it quickly but there's a
+lot here to read that will help you in
+
+ align:start position:0%
+lot here to read that will help you in
+ 
+
+ align:start position:0%
+lot here to read that will help you in
+negotiations we say the three things
+
+ align:start position:0%
+negotiations we say the three things
+ 
+
+ align:start position:0%
+negotiations we say the three things
+that are most important are preparation
+
+ align:start position:0%
+that are most important are preparation
+ 
+
+ align:start position:0%
+that are most important are preparation
+preparation and preparation just like in
+
+ align:start position:0%
+preparation and preparation just like in
+ 
+
+ align:start position:0%
+preparation and preparation just like in
+real estate um location location and
+
+ align:start position:0%
+real estate um location location and
+ 
+
+ align:start position:0%
+real estate um location location and
+location this time is time that's well
+
+ align:start position:0%
+location this time is time that's well
+ 
+
+ align:start position:0%
+location this time is time that's well
+spent at this point now you've committed
+
+ align:start position:0%
+spent at this point now you've committed
+ 
+
+ align:start position:0%
+spent at this point now you've committed
+to bargain You've Got Your Role you've
+
+ align:start position:0%
+to bargain You've Got Your Role you've
+ 
+
+ align:start position:0%
+to bargain You've Got Your Role you've
+done your preparation and we're ready to
+
+ align:start position:0%
+done your preparation and we're ready to
+ 
+
+ align:start position:0%
+done your preparation and we're ready to
+begin negotiations I'm going to say a
+
+ align:start position:0%
+begin negotiations I'm going to say a
+ 
+
+ align:start position:0%
+begin negotiations I'm going to say a
+little bit about the negotiations and
+
+ align:start position:0%
+little bit about the negotiations and
+ 
+
+ align:start position:0%
+little bit about the negotiations and
+then we're going to talk about um the
+
+ align:start position:0%
+then we're going to talk about um the
+ 
+
+ align:start position:0%
+then we're going to talk about um the
+what happens afterwards you'll see that
+
+ align:start position:0%
+what happens afterwards you'll see that
+ 
+
+ align:start position:0%
+what happens afterwards you'll see that
+there's a link to the settlement form
+
+ align:start position:0%
+there's a link to the settlement form
+ 
+
+ align:start position:0%
+there's a link to the settlement form
+which I'll show you in a minute but
+
+ align:start position:0%
+which I'll show you in a minute but
+ 
+
+ align:start position:0%
+which I'll show you in a minute but
+there's also um I'm sorry there's also a
+
+ align:start position:0%
+there's also um I'm sorry there's also a
+ 
+
+ align:start position:0%
+there's also um I'm sorry there's also a
+page that's not on here but that will
+
+ align:start position:0%
+page that's not on here but that will
+ 
+
+ align:start position:0%
+page that's not on here but that will
+come uh on your screen that will let you
+
+ align:start position:0%
+come uh on your screen that will let you
+ 
+
+ align:start position:0%
+come uh on your screen that will let you
+print out all of your preparation
+
+ align:start position:0%
+print out all of your preparation
+ 
+
+ align:start position:0%
+print out all of your preparation
+choices either in a PDF or in a printed
+
+ align:start position:0%
+choices either in a PDF or in a printed
+ 
+
+ align:start position:0%
+choices either in a PDF or in a printed
+document so that you've got that in
+
+ align:start position:0%
+document so that you've got that in
+ 
+
+ align:start position:0%
+document so that you've got that in
+front of you when it comes to the actual
+
+ align:start position:0%
+front of you when it comes to the actual
+ 
+
+ align:start position:0%
+front of you when it comes to the actual
+bargaining um I'm going to just give you
+
+ align:start position:0%
+bargaining um I'm going to just give you
+ 
+
+ align:start position:0%
+bargaining um I'm going to just give you
+a very simple
+
+ align:start position:0%
+a very simple
+ 
+
+ align:start position:0%
+a very simple
+example let's say in the opening
+
+ align:start position:0%
+example let's say in the opening
+ 
+
+ align:start position:0%
+example let's say in the opening
+statement and you'll all make opening
+
+ align:start position:0%
+statement and you'll all make opening
+ 
+
+ align:start position:0%
+statement and you'll all make opening
+state ments and this is of course
+
+ align:start position:0%
+state ments and this is of course
+ 
+
+ align:start position:0%
+state ments and this is of course
+virtual negotiation so you'll be writing
+
+ align:start position:0%
+virtual negotiation so you'll be writing
+ 
+
+ align:start position:0%
+virtual negotiation so you'll be writing
+it out online for the others in your
+
+ align:start position:0%
+it out online for the others in your
+ 
+
+ align:start position:0%
+it out online for the others in your
+group to see uh the folks who are in the
+
+ align:start position:0%
+group to see uh the folks who are in the
+ 
+
+ align:start position:0%
+group to see uh the folks who are in the
+workers role might say there ought to be
+
+ align:start position:0%
+workers role might say there ought to be
+ 
+
+ align:start position:0%
+workers role might say there ought to be
+more government grants for skills
+
+ align:start position:0%
+more government grants for skills
+ 
+
+ align:start position:0%
+more government grants for skills
+training the person in the government
+
+ align:start position:0%
+training the person in the government
+ 
+
+ align:start position:0%
+training the person in the government
+role may say we're willing to provide
+
+ align:start position:0%
+role may say we're willing to provide
+ 
+
+ align:start position:0%
+role may say we're willing to provide
+some funding but only in areas that are
+
+ align:start position:0%
+some funding but only in areas that are
+ 
+
+ align:start position:0%
+some funding but only in areas that are
+skill shortages in society management
+
+ align:start position:0%
+skill shortages in society management
+ 
+
+ align:start position:0%
+skill shortages in society management
+might say yes but the grant should be
+
+ align:start position:0%
+might say yes but the grant should be
+ 
+
+ align:start position:0%
+might say yes but the grant should be
+the to the employers since they know
+
+ align:start position:0%
+the to the employers since they know
+ 
+
+ align:start position:0%
+the to the employers since they know
+what the skills are not just to the
+
+ align:start position:0%
+what the skills are not just to the
+ 
+
+ align:start position:0%
+what the skills are not just to the
+individuals
+
+ align:start position:0%
+individuals
+ 
+
+ align:start position:0%
+individuals
+the education providers say this needs
+
+ align:start position:0%
+the education providers say this needs
+ 
+
+ align:start position:0%
+the education providers say this needs
+to be part of an integrated education
+
+ align:start position:0%
+to be part of an integrated education
+ 
+
+ align:start position:0%
+to be part of an integrated education
+system and so uh These funds for
+
+ align:start position:0%
+system and so uh These funds for
+ 
+
+ align:start position:0%
+system and so uh These funds for
+curriculum development ought to come to
+
+ align:start position:0%
+curriculum development ought to come to
+ 
+
+ align:start position:0%
+curriculum development ought to come to
+the education institutions so that they
+
+ align:start position:0%
+the education institutions so that they
+ 
+
+ align:start position:0%
+the education institutions so that they
+can provide the new training that's
+
+ align:start position:0%
+can provide the new training that's
+ 
+
+ align:start position:0%
+can provide the new training that's
+needed government may say that's all
+
+ align:start position:0%
+needed government may say that's all
+ 
+
+ align:start position:0%
+needed government may say that's all
+great but um we need to have a funding
+
+ align:start position:0%
+great but um we need to have a funding
+ 
+
+ align:start position:0%
+great but um we need to have a funding
+mechanism let's say one cent per hour
+
+ align:start position:0%
+mechanism let's say one cent per hour
+ 
+
+ align:start position:0%
+mechanism let's say one cent per hour
+for the people that work management as
+
+ align:start position:0%
+for the people that work management as
+ 
+
+ align:start position:0%
+for the people that work management as
+you see here might say well we're
+
+ align:start position:0%
+you see here might say well we're
+ 
+
+ align:start position:0%
+you see here might say well we're
+education providers so we should be able
+
+ align:start position:0%
+education providers so we should be able
+ 
+
+ align:start position:0%
+education providers so we should be able
+to get development funds too ultimately
+
+ align:start position:0%
+to get development funds too ultimately
+ 
+
+ align:start position:0%
+to get development funds too ultimately
+the management the workers and the
+
+ align:start position:0%
+the management the workers and the
+ 
+
+ align:start position:0%
+the management the workers and the
+education providers might come together
+
+ align:start position:0%
+education providers might come together
+ 
+
+ align:start position:0%
+education providers might come together
+and say we need to provide governance
+
+ align:start position:0%
+and say we need to provide governance
+ 
+
+ align:start position:0%
+and say we need to provide governance
+and insight and input into this
+
+ align:start position:0%
+and insight and input into this
+ 
+
+ align:start position:0%
+and insight and input into this
+government initiative and together they
+
+ align:start position:0%
+government initiative and together they
+ 
+
+ align:start position:0%
+government initiative and together they
+might then outline what an agreement is
+
+ align:start position:0%
+might then outline what an agreement is
+ 
+
+ align:start position:0%
+might then outline what an agreement is
+but as you can see it there's a series
+
+ align:start position:0%
+but as you can see it there's a series
+ 
+
+ align:start position:0%
+but as you can see it there's a series
+of iterative proposals and
+
+ align:start position:0%
+of iterative proposals and
+ 
+
+ align:start position:0%
+of iterative proposals and
+counterproposals that are all part of
+
+ align:start position:0%
+counterproposals that are all part of
+ 
+
+ align:start position:0%
+counterproposals that are all part of
+the negotiations and in the end we're
+
+ align:start position:0%
+the negotiations and in the end we're
+ 
+
+ align:start position:0%
+the negotiations and in the end we're
+not looking for a simple sentence we had
+
+ align:start position:0%
+not looking for a simple sentence we had
+ 
+
+ align:start position:0%
+not looking for a simple sentence we had
+an agreement on government funded
+
+ align:start position:0%
+an agreement on government funded
+ 
+
+ align:start position:0%
+an agreement on government funded
+education we're really looking for two
+
+ align:start position:0%
+education we're really looking for two
+ 
+
+ align:start position:0%
+education we're really looking for two
+or three paragraphs that says who does
+
+ align:start position:0%
+or three paragraphs that says who does
+ 
+
+ align:start position:0%
+or three paragraphs that says who does
+what what are they agreeing to how will
+
+ align:start position:0%
+what what are they agreeing to how will
+ 
+
+ align:start position:0%
+what what are they agreeing to how will
+be it funded and what are the outcomes
+
+ align:start position:0%
+be it funded and what are the outcomes
+ 
+
+ align:start position:0%
+be it funded and what are the outcomes
+involved
+
+ align:start position:0%
+involved
+ 
+
+ align:start position:0%
+involved
+now we've done this many times and it
+
+ align:start position:0%
+now we've done this many times and it
+ 
+
+ align:start position:0%
+now we've done this many times and it
+turns out this issue um support for
+
+ align:start position:0%
+turns out this issue um support for
+ 
+
+ align:start position:0%
+turns out this issue um support for
+worker training is a common issue that
+
+ align:start position:0%
+worker training is a common issue that
+ 
+
+ align:start position:0%
+worker training is a common issue that
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+pick we want you to push the envelope
+
+ align:start position:0%
+pick we want you to push the envelope
+ 
+
+ align:start position:0%
+pick we want you to push the envelope
+about what's needed in the future of
+
+ align:start position:0%
+about what's needed in the future of
+ 
+
+ align:start position:0%
+about what's needed in the future of
+work so we're going to say that at least
+
+ align:start position:0%
+work so we're going to say that at least
+ 
+
+ align:start position:0%
+work so we're going to say that at least
+for your first two agreements they
+
+ align:start position:0%
+for your first two agreements they
+ 
+
+ align:start position:0%
+for your first two agreements they
+cannot be agreements that are on this
+
+ align:start position:0%
+cannot be agreements that are on this
+ 
+
+ align:start position:0%
+cannot be agreements that are on this
+issue of government funded uh education
+
+ align:start position:0%
+issue of government funded uh education
+ 
+
+ align:start position:0%
+issue of government funded uh education
+but on other issues that are among the
+
+ align:start position:0%
+but on other issues that are among the
+ 
+
+ align:start position:0%
+but on other issues that are among the
+many 25 issues that we've highlighted in
+
+ align:start position:0%
+many 25 issues that we've highlighted in
+ 
+
+ align:start position:0%
+many 25 issues that we've highlighted in
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+categories uh and then then if you want
+
+ align:start position:0%
+categories uh and then then if you want
+ 
+
+ align:start position:0%
+categories uh and then then if you want
+to come back to this as part of a
+
+ align:start position:0%
+to come back to this as part of a
+ 
+
+ align:start position:0%
+to come back to this as part of a
+package great but the point is um push
+
+ align:start position:0%
+package great but the point is um push
+ 
+
+ align:start position:0%
+package great but the point is um push
+the envelope do something new once you
+
+ align:start position:0%
+the envelope do something new once you
+ 
+
+ align:start position:0%
+the envelope do something new once you
+have an agreement you'll then follow the
+
+ align:start position:0%
+have an agreement you'll then follow the
+ 
+
+ align:start position:0%
+have an agreement you'll then follow the
+URL to a screen that looks like what you
+
+ align:start position:0%
+URL to a screen that looks like what you
+ 
+
+ align:start position:0%
+URL to a screen that looks like what you
+see here it says it's part two and again
+
+ align:start position:0%
+see here it says it's part two and again
+ 
+
+ align:start position:0%
+see here it says it's part two and again
+It'll ask you what group number you are
+
+ align:start position:0%
+It'll ask you what group number you are
+ 
+
+ align:start position:0%
+It'll ask you what group number you are
+at what institution are you doing this
+
+ align:start position:0%
+at what institution are you doing this
+ 
+
+ align:start position:0%
+at what institution are you doing this
+and then you'll find that there's a
+
+ align:start position:0%
+and then you'll find that there's a
+ 
+
+ align:start position:0%
+and then you'll find that there's a
+question about what role are you in how
+
+ align:start position:0%
+question about what role are you in how
+ 
+
+ align:start position:0%
+question about what role are you in how
+many people are part of this agreement
+
+ align:start position:0%
+many people are part of this agreement
+ 
+
+ align:start position:0%
+many people are part of this agreement
+um and what were their roles so
+
+ align:start position:0%
+um and what were their roles so
+ 
+
+ align:start position:0%
+um and what were their roles so
+obviously if you are an education
+
+ align:start position:0%
+obviously if you are an education
+ 
+
+ align:start position:0%
+obviously if you are an education
+institution you would check management
+
+ align:start position:0%
+institution you would check management
+ 
+
+ align:start position:0%
+institution you would check management
+labor and federal government and leave
+
+ align:start position:0%
+labor and federal government and leave
+ 
+
+ align:start position:0%
+labor and federal government and leave
+education blank on question five but at
+
+ align:start position:0%
+education blank on question five but at
+ 
+
+ align:start position:0%
+education blank on question five but at
+that point you go to the next screen and
+
+ align:start position:0%
+that point you go to the next screen and
+ 
+
+ align:start position:0%
+that point you go to the next screen and
+this is your chance to indicate what you
+
+ align:start position:0%
+this is your chance to indicate what you
+ 
+
+ align:start position:0%
+this is your chance to indicate what you
+actually agreed to You'll click let's
+
+ align:start position:0%
+actually agreed to You'll click let's
+ 
+
+ align:start position:0%
+actually agreed to You'll click let's
+say fair treatment and a screen will
+
+ align:start position:0%
+say fair treatment and a screen will
+ 
+
+ align:start position:0%
+say fair treatment and a screen will
+open up saying write into this what you
+
+ align:start position:0%
+open up saying write into this what you
+ 
+
+ align:start position:0%
+open up saying write into this what you
+agreed upon this is important each of
+
+ align:start position:0%
+agreed upon this is important each of
+ 
+
+ align:start position:0%
+agreed upon this is important each of
+you will be entering the agreement
+
+ align:start position:0%
+you will be entering the agreement
+ 
+
+ align:start position:0%
+you will be entering the agreement
+separately so if there's four people in
+
+ align:start position:0%
+separately so if there's four people in
+ 
+
+ align:start position:0%
+separately so if there's four people in
+the negotiations there'll be four
+
+ align:start position:0%
+the negotiations there'll be four
+ 
+
+ align:start position:0%
+the negotiations there'll be four
+entries of the text it's perfectly okay
+
+ align:start position:0%
+entries of the text it's perfectly okay
+ 
+
+ align:start position:0%
+entries of the text it's perfectly okay
+for you to each cut and splice the same
+
+ align:start position:0%
+for you to each cut and splice the same
+ 
+
+ align:start position:0%
+for you to each cut and splice the same
+language um but the key thing and by the
+
+ align:start position:0%
+language um but the key thing and by the
+ 
+
+ align:start position:0%
+language um but the key thing and by the
+way if you put in different language
+
+ align:start position:0%
+way if you put in different language
+ 
+
+ align:start position:0%
+way if you put in different language
+that's evidence that it might not be a
+
+ align:start position:0%
+that's evidence that it might not be a
+ 
+
+ align:start position:0%
+that's evidence that it might not be a
+very stable agreement but the point is
+
+ align:start position:0%
+very stable agreement but the point is
+ 
+
+ align:start position:0%
+very stable agreement but the point is
+you each put in your language because we
+
+ align:start position:0%
+you each put in your language because we
+ 
+
+ align:start position:0%
+you each put in your language because we
+also ask you to each rate how important
+
+ align:start position:0%
+also ask you to each rate how important
+ 
+
+ align:start position:0%
+also ask you to each rate how important
+is this in terms of your role uh and how
+
+ align:start position:0%
+is this in terms of your role uh and how
+ 
+
+ align:start position:0%
+is this in terms of your role uh and how
+satisfied you are you with the process
+
+ align:start position:0%
+satisfied you are you with the process
+ 
+
+ align:start position:0%
+satisfied you are you with the process
+not just the substance to get to this
+
+ align:start position:0%
+not just the substance to get to this
+ 
+
+ align:start position:0%
+not just the substance to get to this
+agreement and this way we can hear from
+
+ align:start position:0%
+agreement and this way we can hear from
+ 
+
+ align:start position:0%
+agreement and this way we can hear from
+each of you in the negotiations and of
+
+ align:start position:0%
+each of you in the negotiations and of
+ 
+
+ align:start position:0%
+each of you in the negotiations and of
+course there's a space for you to say if
+
+ align:start position:0%
+course there's a space for you to say if
+ 
+
+ align:start position:0%
+course there's a space for you to say if
+there's anything else that you want to
+
+ align:start position:0%
+there's anything else that you want to
+ 
+
+ align:start position:0%
+there's anything else that you want to
+put and that completes uh the process
+
+ align:start position:0%
+put and that completes uh the process
+ 
+
+ align:start position:0%
+put and that completes uh the process
+there's a link here that will let you um
+
+ align:start position:0%
+there's a link here that will let you um
+ 
+
+ align:start position:0%
+there's a link here that will let you um
+come back and enter a second or third
+
+ align:start position:0%
+come back and enter a second or third
+ 
+
+ align:start position:0%
+come back and enter a second or third
+agreement and when you're done when when
+
+ align:start position:0%
+agreement and when you're done when when
+ 
+
+ align:start position:0%
+agreement and when you're done when when
+you're done you will have done something
+
+ align:start position:0%
+you're done you will have done something
+ 
+
+ align:start position:0%
+you're done you will have done something
+very special which is you will have
+
+ align:start position:0%
+very special which is you will have
+ 
+
+ align:start position:0%
+very special which is you will have
+negotiated an agreement about the future
+
+ align:start position:0%
+negotiated an agreement about the future
+ 
+
+ align:start position:0%
+negotiated an agreement about the future
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+work people who are in positions of
+
+ align:start position:0%
+work people who are in positions of
+ 
+
+ align:start position:0%
+work people who are in positions of
+power and authority are interested to
+
+ align:start position:0%
+power and authority are interested to
+ 
+
+ align:start position:0%
+power and authority are interested to
+see what comes out of the negotiations
+
+ align:start position:0%
+see what comes out of the negotiations
+ 
+
+ align:start position:0%
+see what comes out of the negotiations
+in this course we will try to sum up the
+
+ align:start position:0%
+in this course we will try to sum up the
+ 
+
+ align:start position:0%
+in this course we will try to sum up the
+agreements and look for insights and
+
+ align:start position:0%
+agreements and look for insights and
+ 
+
+ align:start position:0%
+agreements and look for insights and
+lessons around which there might be the
+
+ align:start position:0%
+lessons around which there might be the
+ 
+
+ align:start position:0%
+lessons around which there might be the
+kind of alignment that could actually
+
+ align:start position:0%
+kind of alignment that could actually
+ 
+
+ align:start position:0%
+kind of alignment that could actually
+change things in society and ensure that
+
+ align:start position:0%
+change things in society and ensure that
+ 
+
+ align:start position:0%
+change things in society and ensure that
+the institutions of work are better
+
+ align:start position:0%
+the institutions of work are better
+ 
+
+ align:start position:0%
+the institutions of work are better
+designed to serve the needs of yourself
+
+ align:start position:0%
+designed to serve the needs of yourself
+ 
+
+ align:start position:0%
+designed to serve the needs of yourself
+and others in the future Generations
+
+ align:start position:0%
+and others in the future Generations
+ 
+
+ align:start position:0%
+and others in the future Generations
+thank you very much
\ No newline at end of file
diff --git a/MCrDzhpu3-s.txt b/MCrDzhpu3-s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6fbc6cba187ed3b2bd7f9ee8d0cc6779b8b822d9
--- /dev/null
+++ b/MCrDzhpu3-s.txt
@@ -0,0 +1,2066 @@
+For the rest of the term,
+we are going to be studying not
+
+just one differential equation
+at a time, but rather what are
+
+called systems of differential
+equations.
+
+Those are like systems of
+linear equations.
+
+They have to be solved
+simultaneously,
+
+in other words,
+not just one at a time.
+
+So, how does a system look when
+you write it down?
+
+Well, since we are going to be
+talking about systems of
+
+ordinary differential equations,
+there still will be only one
+
+independent variable,
+but there will be several
+
+dependent variables.
+I am going to call,
+
+let's say two.
+The dependent variables are
+
+going to be, I will call them x
+and y, and then the first order
+
+system, something involving just
+first derivatives,
+
+will look like this.
+On the left-hand side 
+
+will be x prime,
+
+in other words.
+On the right-hand side will be
+
+the dependent variables and then
+also the independent variables.
+
+I will indicate that,
+I will separate it all from the
+
+others by putting a semicolon
+there.
+
+And the same way y prime,
+the derivative of y with
+
+respect to t,
+will be some other function of
+
+(x, y) and t.
+Let's write down explicitly
+
+that x and y are dependent
+variables.
+
+And what they depend upon is
+the independent variable t,
+
+time.
+A system like this is going to
+
+be called first order.
+And we are going to consider
+
+basically only first-order
+systems for a secret reason that
+
+I will explain at the end of the
+period.
+
+This is a first-order system,
+meaning that the only kind of
+
+derivatives that are up here are
+first derivatives.
+
+So x prime is dx over dt 
+and so on.
+
+Now, there is still more
+terminology.
+
+Of course, practically all the
+equations after the term
+
+started, virtually all the
+equations we have been
+
+considering are linear
+equations, so it must be true
+
+that linear systems are the best
+kind.
+
+And, boy, they certainly are.
+When are we going to call a
+
+system linear?
+I think in the beginning you
+
+should learn a little
+terminology before we launch in
+
+and actually try to start to
+solve these things.
+
+Well, the x and y,
+the dependent variables must
+
+occur linearly.
+In other words,
+
+it must look like this,
+ax plus by.
+
+Now, the t can be a mess.
+And so I will throw in an extra
+
+function of t there.
+And y prime will be some
+
+other linear combination of x
+and y, plus some other messy
+
+function of t.
+But even the a,
+
+b, c, and d are allowed to be
+functions of t.
+
+They could be one over t cubed
+or sine t
+
+or something like that.
+So I have to distinguish those
+
+cases.
+The case where a,
+
+b, c, and d are constants,
+that I will call --
+
+Well, there are different
+things you can call it.
+
+We will simply call it a
+constant coefficient system.
+
+A system with coefficients
+would probably be better
+
+English.
+On the other hand,
+
+a, b, c, and d,
+this system will still be
+
+called linear if these are
+functions of t.
+
+Can also be functions of t.
+
+So it would be a perfectly good
+linear system to have x prime
+
+equals tx plus sine t times y
+plus e to the minus t squared.
+
+You would never see something
+like that but it is okay.
+
+What else do you need to know?
+Well, what would a homogenous
+
+system be?
+A homogenous system is one
+
+without these extra guys.
+That doesn't mean there is no t
+
+in it.
+There could be t in the a,
+
+b, c and d, but these terms
+with no x and y in them must not
+
+occur.
+So, a linear homogenous.
+
+And that is the kind we are
+going to start studying first in
+
+the same way when we studied
+higher order equations.
+
+We studied first homogenous.
+You had to know how to solve
+
+those first, and then you could
+learn how to solve the more
+
+general kind.
+So linear homogenous means that
+
+r1 is zero and r2 is zero for
+all time.
+
+They are identically zero.
+They are not there.
+
+You don't see them.
+Have I left anything out?
+
+Yes, the initial conditions.
+Since that is quite general,
+
+let's talk about what would
+initial conditions look like?
+
+Well, in a general way,
+the reason you have to have
+
+initial conditions is to get
+values for the arbitrary
+
+constants that appear in the
+solution.
+
+The question is,
+how many arbitrary constants
+
+are going to appear in the
+solutions of these equations?
+
+Well, I will just give you the
+answer.
+
+Two.
+The number of arbitrary
+
+constants that appear is the
+total order of the system.
+
+For example,
+if this were a second
+
+derivative and this were a first
+derivative, I would expect three
+
+arbitrary constants in the
+system --
+
+-- because the total,
+the sum of two and one makes
+
+three.
+So you must have as many
+
+initial conditions as you have
+arbitrary constants in the
+
+solution.
+And that, of course,
+
+explains when we studied
+second-order equations,
+
+we had to have two initial
+conditions.
+
+I had to specify the initial
+starting point and the initial
+
+velocity.
+And the reason we had to have
+
+two conditions was because the
+general solution had two
+
+arbitrary constants in it.
+The same thing happens here but
+
+the answer is it is more
+natural, the conditions here are
+
+more natural.
+I don't have to specify the
+
+velocity.
+Why not?
+
+Well, because an initial
+condition, of course,
+
+would want me to say what the
+starting value of x is,
+
+some number,
+and it will also want to know
+
+what the starting value of y is
+at that same point.
+
+Well, there are my two
+conditions.
+
+And since this is going to have
+two arbitrary constants in it,
+
+it is these initial conditions
+that will satisfy,
+
+the arbitrary constants will
+have to be picked so as to
+
+satisfy those initial
+conditions.
+
+In some sense,
+the giving of initial
+
+conditions for a system is a
+more natural activity than
+
+giving the initial conditions of
+a second order system.
+
+You don't have to be the least
+bit cleaver about it.
+
+Anybody would give these two
+numbers.
+
+Whereas, somebody faced with a
+second order system might
+
+scratch his head.
+And, in fact,
+
+there are other kinds of
+conditions.
+
+There are boundary conditions
+you learned a little bit about
+
+instead of initial conditions
+for a second order equation.
+
+I cannot think of any more
+general terminology,
+
+so it sounds like we are going
+to actually have to get to work.
+
+Okay, let's get to work.
+I want to set up a system and
+
+solve it.
+And since one of the things in
+
+this course is supposed to be
+simple modeling,
+
+it should be a system that
+models something.
+
+In general, the kinds of models
+we are going to use when we
+
+study systems are the same ones
+we used in studying just
+
+first-order equations.
+Mixing, radioactive decay,
+
+temperature,
+the motion of temperature.
+
+Heat, heat conduction,
+in other words.
+
+Diffusion.
+I have given you a diffusion
+
+problem for your first homework
+on this subject.
+
+What else did we do?
+That's all I can think of for
+
+the moment, but I am sure they
+will occur to me.
+
+When, out of those physical
+ideas, are we going to get a
+
+system?
+The answer is,
+
+whenever there are two of
+something that there was only
+
+one of before.
+For example,
+
+if I have mixing with two tanks
+where the fluid goes like that.
+
+Say you want to have a big tank
+and a little tank here and you
+
+want to put some stuff into the
+little tank so that it will get
+
+mixed in the big tank without
+having to climb a big ladder and
+
+stop and drop the stuff in.
+That will require two tanks,
+
+the concentration of the
+substance in each tank,
+
+therefore, that will require a
+system of equations rather than
+
+just one.
+Or, to give something closer to
+
+home, closer to this backboard,
+anyway, suppose you have dah,
+
+dah, dah, don't groan,
+at least not audibly,
+
+something that looks like that.
+And next to it put an EMF
+
+there.
+That is just a first order.
+
+That just leads to a single
+first order equation.
+
+But suppose it is a two loop
+circuit.
+
+Now I need a pair of equations.
+Each of these loops gives a
+
+first order differential
+equation, but they have to be
+
+solved simultaneously to find
+the current or the charges on
+
+the condensers.
+And if I want a system of three
+
+equations, throw in another
+loop.
+
+Now, suppose I put in a coil
+instead.
+
+What is this going to lead to?
+This is going to give me a
+
+system of three equations of
+which this will be first order,
+
+first order.
+And this will be second order
+
+because it has a coil.
+You are up to that,
+
+right?
+You've had coils,
+
+inductance?
+Good.
+
+So the whole thing is going to
+count as first-order,
+
+first-order,
+second-order.
+
+To find out how complicated it
+is, you have to add up the
+
+orders.
+That is one and one,
+
+and two.
+This is really fourth-order
+
+stuff that we are talking about
+here.
+
+We can expect it to be a little
+complicated.
+
+Well, now let's take a modest
+little problem.
+
+I am going to return to a
+problem we considered earlier in
+
+the problem of heat conduction.
+I had forgotten whether it was
+
+on the problem set or I did it
+in class, but I am choosing it
+
+because it leads to something we
+will be able to solve.
+
+And because it illustrates how
+to add a little sophistication
+
+to something that was
+unsophisticated before.
+
+A pot of water.
+External temperature Te of t.
+
+I am talking about the
+
+temperature of something.
+And what I am talking about the
+
+temperature of will be an egg
+that is cooking inside,
+
+but with a difference.
+This egg is not homogenous
+
+inside.
+Instead it has a white and it
+
+has a yolk in the middle.
+In other words,
+
+it is a real egg and not a
+phony egg.
+
+That is a small pot,
+or it is an ostrich egg.
+
+[LAUGHTER] That is the yoke.
+The yolk is contained in a
+
+little membrane inside.
+And there are little yucky
+
+things that hold it in position.
+And we are going to let the
+
+temperature of the yolk,
+if you can see in the back of
+
+the room, be T1.
+That is the temperature of the
+
+yolk.
+The temperature of the white,
+
+which we will assume is
+uniform, is going to be T2.
+
+Oh, that's the water bath.
+The temperature of the white is
+
+T2, and then the temperature of
+the external water bath.
+
+In other words,
+the reason for introducing two
+
+variables instead of just the
+one variable for the overall
+
+temperature of the egg we had is
+because egg white is liquid pure
+
+protein, more or less,
+and the T1, the yolk has a lot
+
+of fat and cholesterol and other
+stuff like that which is
+
+supposed to be bad for you.
+It certainly has different
+
+conducting.
+It is liquid,
+
+at the beginning at any rate,
+but it certainly has different
+
+constants of conductivity than
+the egg white would.
+
+And the condition of heat
+through the shell of the egg
+
+would be different from the
+conduction of heat through the
+
+membrane that keeps the yoke
+together.
+
+So it is quite reasonable to
+consider that the white and the
+
+yolk will be at different
+temperatures and will have
+
+different conductivity
+properties.
+
+I am going to use Newton's laws
+but with this further
+
+refinement.
+In other words,
+
+introducing two temperatures.
+Whereas, before we only had one
+
+temperature.
+But let's use Newton's law.
+
+Let's see.
+The question is how does T1,
+
+the temperature of the yolk,
+vary with time?
+
+Well, the yolk is getting all
+its heat from the white.
+
+Therefore, Newton's law of
+conduction will be some constant
+
+of conductivity for the yolk
+times T2 minus T1.
+
+The yolk does not know anything
+about the external temperature
+
+of the water bath.
+It is completely surrounded,
+
+snug and secure within itself.
+But how about the temperature
+
+of the egg white?
+That gets heat and gives heat
+
+to two sources,
+from the external water and
+
+also from the internal yolk
+inside.
+
+So you have to take into
+account both of those.
+
+Its conduction of the heat
+through that membrane,
+
+we will use the same a,
+which is going to be a times T1
+
+minus T2.
+Remember the order in which you
+
+have to write these is governed
+by the yolk outside to the
+
+white.
+Therefore, that has to come
+
+first when I write it in order
+that a be a positive constant.
+
+But it is also getting heat
+from the water bath.
+
+And, presumably,
+the conductivity through the
+
+shell is different from what it
+is through this membrane around
+
+the yolk.
+So I am going to call that by a
+
+different constant.
+This is the conductivity
+
+through the shell into the
+white.
+
+And that is going to be T,
+the external temperature minus
+
+the temperature of the egg
+white.
+
+Here I have a system of
+equations because I want to make
+
+two dependent variables by
+refining the original problem.
+
+Now, you always have to write a
+system in standard form to solve
+
+it.
+You will see that the left-hand
+
+side will give the dependent
+variables in a certain order.
+
+In this case,
+the temperature of the yolk and
+
+then the temperature of the
+white.
+
+The law is that in order not to
+make mistakes --
+
+And it's a very frequent source
+of error so learn from the
+
+beginning not to do this.
+You must write the variables on
+
+the right-hand side in the same
+order left to right in which
+
+they occur top to bottom here.
+In other words,
+
+this is not a good way to leave
+that.
+
+This is the first attempt in
+writing this system,
+
+but the final version should
+like this.
+
+T1 prime,
+I won't bother writing dT / dt,
+
+is equal to --
+T1 must come first,
+
+so minus a times T1 plus a
+times T2.
+
+And the same law for the second
+one.
+
+It must come in the same order.
+Now, the coefficient of T1,
+
+that is easy.
+That's a times T1.
+
+The coefficient of T2 is minus
+a minus b,
+
+so minus (a plus b) times T2.
+
+But I am not done yet.
+There is still this external
+
+temperature I must put into the
+equation.
+
+Now, that is not a variable.
+This is some given function of
+
+t.
+And what the function of t is,
+
+of course, depends upon what
+the problem is.
+
+So that, for example,
+what might be some
+
+possibilities,
+well, suppose the problem was I
+
+wanted to coddle the egg.
+I think there is a generation
+
+gap here.
+How many of you know what a
+
+coddled egg is?
+How many of you don't know?
+
+Well, I'm just saying my
+daughter didn't know.
+
+I mentioned it to her.
+I said I think I'm going to do
+
+a coddled egg tomorrow in class.
+And she said what is that?
+
+And so I said a cuddled egg?
+She said why would someone
+
+cuddle an egg?
+I said coddle.
+
+And she said,
+oh, you mean like a person,
+
+like what you do to somebody
+you like or don't like or I
+
+don't know.
+Whatever.
+
+I thought a while and said,
+yeah, more like that.
+
+[LAUGHTER] Anyway,
+for the enrichment of your
+
+cooking skills,
+to coddle an egg,
+
+it is considered to produce a
+better quality product than
+
+boiling an egg.
+That is why people do it.
+
+You heat up the water to
+boiling, the egg should be at
+
+room temperature,
+and then you carefully lower
+
+the egg into the water.
+And you turn off the heat so
+
+the water bath cools
+exponentially while the egg
+
+inside is rising in temperature.
+And then you wait four minutes
+
+or six minutes or whatever and
+take it out.
+
+You have a perfect egg.
+So for coddling,
+
+spelled so, what will the
+external temperature be?
+
+Well, it starts out at time
+zero at 100 degrees centigrade
+
+because the water is supposed to
+be boiling.
+
+The reason you have it boiling
+is for calibration so that you
+
+can know what temperature it is
+without having to use a
+
+thermometer, unless you're on
+Pike's Peak or some place.
+
+It starts out at 100 degrees.
+And after that,
+
+since the light is off,
+it cools exponential because
+
+that is another law.
+You only have to know what K is
+
+for your particular pot and you
+will be able to solve the
+
+coddled egg problem.
+In other words,
+
+you will then be able to solve
+these equations and know how the
+
+temperature rises.
+I am going to solve a different
+
+problem because I don't want to
+have to deal with this
+
+inhomogeneous term.
+Let's use, as a different
+
+problem, a person cooks an egg.
+Coddles the egg by the first
+
+process, decides the egg is
+done, let's say hardboiled,
+
+and then you are supposed to
+drop a hardboiled egg into cold
+
+water.
+Not just to cool it but also
+
+because I think it prevents that
+dark thing from forming that
+
+looks sort of unattractive.
+Let's ice bath.
+
+The only reason for dropping
+the egg into an ice bath is so
+
+that you could have a homogenous
+equation to solve.
+
+And since this a first system
+we are going to solve,
+
+let's make life easy for
+ourselves.
+
+Now, all my work in preparing
+this example,
+
+and it took considerably longer
+time than actually solving the
+
+problem, was in picking values
+for a and b which would make
+
+everything come out nice.
+It's harder than it looks.
+
+The values that we are going to
+use, which make no physical
+
+sense whatsoever,
+but a equals 2 and b
+
+equals 3.
+These are called nice numbers.
+
+What is the equation?
+What is the system?
+
+Can somebody read it off for
+me?
+
+It is T1 prime equals, what
+is it, minus 2T1 plus 2T2.
+
+That's good.
+
+Minus 2T1 plus 2T2.
+
+T2 prime is,
+what is it?
+
+I think this is 2T1.
+And the other one is minus a
+
+plus b, so minus 5.
+
+This is a system.
+Now, on Wednesday I will teach
+
+you a fancy way of solving this.
+But, to be honest,
+
+the fancy way will take roughly
+about as long as the way I am
+
+going to do it now.
+The main reason for doing it is
+
+that it introduces new
+vocabulary which everyone wants
+
+you to have.
+And also, more important
+
+reasons, it gives more insight
+into the solution than this
+
+method.
+This method just produces the
+
+answer, but you want insight,
+also.
+
+And that is just as important.
+But for now,
+
+let's use a method which always
+works and which in 40 years,
+
+after you have forgotten all
+other fancy methods,
+
+will still be available to you
+because it is method you can
+
+figure out yourself.
+You don't have to remember
+
+anything.
+The method is to eliminate one
+
+of the dependent variables.
+It is just the way you solve
+
+systems of linear equations in
+general if you aren't doing
+
+something fancy with
+determinants and matrices.
+
+If you just eliminate
+variables.
+
+We are going to eliminate one
+of these variables.
+
+Let's eliminate T2.
+You could also eliminate T1.
+
+The main thing is eliminate one
+of them so you will have just
+
+one left to work with.
+How do I eliminate T2?
+
+Beg your pardon?
+Is something wrong?
+
+If somebody thinks something is
+wrong raise his hand.
+
+No?
+
+Why do I want to get rid of T1?
+Well, I can add them.
+
+But, on the left-hand side,
+I will have T1 prime plus T2
+
+prime. What good is that?
+
+[LAUGHTER]
+
+I think you will want to do it
+my way.
+
+[APPLAUSE]
+
+Solve for T2 in terms of T1.
+That is going to be T1 prime
+
+plus 2T1 divided by 2.
+
+Now, take that and substitute
+it into the second equation.
+
+Wherever you see a T2,
+put that in,
+
+and what you will be left with
+is something just in T1.
+
+To be honest,
+I don't know any other good way
+
+of doing this.
+There is a fancy method that I
+
+think is talked about in your
+book, which leads to extraneous
+
+solutions and so on,
+but you don't want to know
+
+about that.
+This will work for a simple
+
+linear equation with constant
+coefficients,
+
+always.
+Substitute in.
+
+What do I do?
+Now, here I do not advise doing
+
+this mentally.
+It is just too easy to make a
+
+mistake.
+Here, I will do it carefully,
+
+writing everything out just as
+you would.
+
+T1 prime plus 2T1 over 2,
+prime, equals 2T1 minus 5 time
+
+T1 prime plus 2T1 over two.
+
+I took that and substituted
+
+into this equation.
+Now, I don't like those two's.
+
+Let's get rid of them by
+multiplying.
+
+This will become 4.
+
+And now write this out.
+What is this when you look at
+
+it?
+This is an equation just in T1.
+
+It has constant coefficients.
+And what is its order?
+
+Its order is two because T1
+prime primed.
+
+In other words,
+I can eliminate T2 okay,
+
+but the equation I am going to
+get is no longer a first-order.
+
+It becomes a second-order
+differential equation.
+
+And that's a basic law.
+Even if you have a system of
+
+more equations,
+three or four or whatever,
+
+the law is that after you do
+the elimination successfully and
+
+end up with a single equation,
+normally the order of that
+
+equation will be the sum of the
+orders of the things you started
+
+with.
+So two first-order equations
+
+will always produce a
+second-order equation in just
+
+one dependent variable,
+three will produce a third
+
+order equation and so on.
+So you trade one complexity for
+
+another.
+You trade the complexity of
+
+having to deal with two
+equations simultaneously instead
+
+of just one for the complexity
+of having to deal with a single
+
+higher order equation which is
+more trouble to solve.
+
+It is like all mathematical
+problems.
+
+Unless you are very lucky,
+if you push them down one way,
+
+they are really simple now,
+they just pop up some place
+
+else.
+You say, oh,
+
+I didn't save anything after
+all.
+
+That is the law of conservation
+of mathematical difficulty.
+
+[LAUGHTER] You saw that even
+with the Laplace transform.
+
+In the beginning it looks
+great, you've got these tables,
+
+take the equation,
+horrible to solve.
+
+Take some transform,
+trivial to solve for capital Y.
+
+Now I have to find the inverse
+Laplace transform.
+
+And suddenly all the work is
+there, partial fractions,
+
+funny formulas and so on.
+It is very hard in mathematics
+
+to get away with something.
+It happens now and then and
+
+everybody cheers.
+Let's write this out now in the
+
+form in which it looks like an
+equation we can actually solve.
+
+Just be careful.
+Now it is all right to use the
+
+method by which you collect
+terms.
+
+There is only one term
+involving T1 double prime.
+
+It's the one that comes from
+here.
+
+How about the terms in T1
+prime?
+
+There is a 2.
+Here, there is minus 5 T1
+
+prime.
+If I put it on the other side
+
+it makes plus 5 T1 prime plus
+this two makes 7 T1 prime.
+
+And how many T1's are there?
+Well, none on the left-hand
+
+side.
+On the right-hand side I have 4
+
+here minus 10.
+4 minus 10 is negative 6.
+
+Negative 6 T1 put on this
+left-hand side the way we want
+
+to do makes plus 6 T1.
+
+There are no inhomogeneous
+terms, so that is equal to zero.
+
+If I had gotten a negative
+number for one of these
+
+coefficients,
+I would instantly know if I had
+
+made a mistake.
+Why?
+
+Why must those numbers come out
+to be positive?
+
+It is because the system must
+be, the system must be,
+
+fill in with one word,
+stable.
+
+And why must this system be
+stable?
+
+In other words,
+the long-term solutions must be
+
+zero, must all go to zero,
+whatever they are.
+
+Why is that?
+Well, because you are putting
+
+the egg into an ice bath.
+Or, because we know it was
+
+living but after being
+hardboiled it is dead and,
+
+therefore, dead systems are
+stable.
+
+That's not a good reason but it
+is, so to speak,
+
+the real one.
+It's clear anyway that all
+
+solutions must tend to zero
+physically.
+
+That's obvious.
+And, therefore,
+
+the differential equation must
+have the same property,
+
+and that means that its
+coefficients must be positive.
+
+All its coefficients must be
+positive.
+
+If this weren't there,
+I would get oscillating
+
+solutions, which wouldn't go to
+zero.
+
+That is physical impossible for
+this egg.
+
+Now the rest is just solving.
+The characteristic equation,
+
+if you can remember way,
+way back in prehistoric times
+
+when we were solving these
+equations, is this.
+
+And what you want to do is
+factor it.
+
+This is where all the work was,
+getting those numbers so that
+
+this would factor. So it's
+r plus 1 times r plus 6
+
+And so the solutions are,
+the roots are r equals 
+
+negative 1.
+I am just making marks on the
+
+board, but you have done this
+often enough,
+
+you know what I am talking
+about.
+
+So the characteristic roots are
+those two numbers.
+
+And, therefore,
+the solution is,
+
+I could write down immediately
+with its arbitrary constant as
+
+c1 times e to the negative t
+plus c2 times e to the negative
+
+6t. Now, I have got to get T2.
+
+Here the first worry is T2 is
+going to give me two more
+
+arbitrary constants.
+It better not.
+
+The system is only allowed to
+have two arbitrary constants in
+
+its solution because that is the
+initial conditions we are giving
+
+it.
+By the way, I forgot to give
+
+initial conditions.
+Let's give initial conditions.
+
+Let's say the initial
+temperature of the yolk,
+
+when it is put in the ice bath,
+is 40 degrees centigrade,
+
+Celsius.
+And T2, let's say the white
+
+ought to be a little hotter than
+the yolk is always cooler than
+
+the white for a soft boiled egg,
+I don't know,
+
+or a hardboiled egg if it
+hasn't been chilled too long.
+
+Let's make this 45.
+Realistic numbers.
+
+Now, the thing not to do is to
+say, hey, I found T1.
+
+Okay, I will find T2 by the
+same procedure.
+
+I will go through the whole
+thing.
+
+I will eliminate T1 instead.
+Then I will end up with an
+
+equation T2 and I will solve
+that and get T2 equals blah,
+
+blah, blah.
+That is no good,
+
+A, because you are working too
+hard and, B, because you are
+
+going to get two more arbitrary
+constants unrelated to these
+
+two.
+And that is no good.
+
+Because the correct solution
+only has two constants in it.
+
+Not four.
+So that procedure is wrong.
+
+You must calculate T2 from the
+T1 that you found,
+
+and that is the equation which
+does it.
+
+That's the one we have to have.
+Where is the chalk?
+
+Yes.
+Maybe I can have a little thing
+
+so I can just carry this around
+with me.
+
+That is the relation between T2
+and T1.
+
+Or, if you don't like it,
+either one of these equations
+
+will express T2 in terms of T1
+for you.
+
+It doesn't matter.
+Whichever one you use,
+
+however you do it,
+that's the way you must
+
+calculate T2.
+So what is it?
+
+T2 is calculated from that pink
+box.
+
+It is one-half of T1 prime plus
+T1.
+
+Now, if I take the derivative
+of this, I get minus c1 times
+
+the exponential.
+The coefficient is minus c1,
+
+take half of that,
+that is minus a half c1
+
+and add it to T1.
+Minus one-half c1 plus c1 gives
+
+me one-half c1.
+
+And here I take the derivative,
+it is minus 6 c2.
+
+Take half of that,
+minus 3 c2 and add this c2 to
+
+it, minus 3 plus 1 makes minus
+2.
+
+That is T2.
+And notice it uses the same
+
+arbitrary constants that T1
+uses.
+
+So we end up with just two
+because we calculated T2 from
+
+that formula or from the
+equation which is equivalent to
+
+it, not from scratch.
+We haven't put in the initial
+
+conditions yet,
+but that is easy to do.
+
+Everybody, when working with
+exponentials,
+
+of course, you always want the
+initial conditions to be when T
+
+is equal to zero
+because that makes all the
+
+exponentials one and you don't
+have to worry about them.
+
+But this you know.
+If I put in the initial
+
+conditions, at time zero,
+T1 has the value 40.
+
+So 40 should be equal to c1 +
+c2.
+
+And the other equation will say
+that 45 is equal to one-half c1
+
+minus 2 c2. 
+Now we are supposed to
+
+solve these.
+Well, this is called solving
+
+simultaneous linear equations.
+We could use Kramer's rule,
+
+inverse matrices,
+but why don't we just
+
+eliminate.
+Let me see.
+
+If I multiply by,
+45, so multiply by two,
+
+you get 90 equals c1 
+minus 4 c2.
+
+Then subtract this guy from
+that guy.
+
+So, 40 taken from 90 makes 50.
+And c1 taken from c1,
+
+because I multiplied by two,
+makes zero.
+
+And c2 taken from minus 4 c2,
+that makes minus 5 c2,
+
+I guess.
+
+I seem to get c2 is equal to
+negative 10.
+
+And if c2 is negative 10,
+then c1 must be 50.
+
+There are two ways of checking
+the answer.
+
+One is to plug it into the
+equations, and the other is to
+
+peak.
+Yes, that's right.
+
+[LAUGHTER]
+
+The final answer is,
+in other words,
+
+you put a 50 here,
+25 there, negative 10 here,
+
+and positive 20 there.
+That gives the answer to the
+
+problem.
+It tells you,
+
+in other words,
+how the temperature of the yolk
+
+varies with time and how the
+temperature of the white varies
+
+with time.
+As I said, we are going to
+
+learn a slick way of doing this
+problem, or at least a very
+
+different way of doing the same
+problem next time,
+
+but let's put that on ice for
+the moment.
+
+And instead I would like to
+spend the rest of the period
+
+doing for first order systems
+the same thing that I did for
+
+you the very first day of the
+term.
+
+Remember, I walked in assuming
+that you knew how to separate
+
+variables the first day of the
+term, and I did not talk to you
+
+about how to solve fancier
+equations by fancier methods.
+
+I instead talked to you about
+the geometric significance,
+
+what the geometric meaning of a
+single first order equation was
+
+and how that geometric meaning
+enabled you to solve it
+
+numerically.
+And we spent a little while
+
+working on such problems because
+nowadays with computers it is
+
+really important that you get a
+feeling for what these things
+
+mean as opposed to just
+algorithms for solving them.
+
+As I say, most differential
+equations, especially systems,
+
+are likely to be solved by a
+computer anyway.
+
+You have to be the guiding
+genius that interprets the
+
+answers and can see when
+mistakes are being made,
+
+stuff like that.
+The problem is,
+
+therefore, what is the meaning
+of this system?
+
+Well, you are not going to get
+anywhere interpreting it
+
+geometrically,
+unless you get rid of that t on
+
+the right-hand side.
+And the only way of getting rid
+
+of the t is to declare it is not
+there.
+
+So I hereby declare that I will
+only consider,
+
+for the rest of the period,
+that is only ten minutes,
+
+systems in which no t appears
+explicitly on the right-hand
+
+side.
+Because I don't know what to do
+
+if it does up here.
+We have a word for these.
+
+Remember what the first order
+word was?
+
+A first order equation where
+there was no t explicitly on the
+
+right-hand side,
+we called it,
+
+anybody remember?
+Just curious.
+
+Autonomous, right.
+
+This is an autonomous system.
+It is not a linear system
+
+because these are messy
+functions.
+
+This could be x times y
+or x squared minus 3y squared
+
+divided by sine of x plus y.
+
+It could be a mess.
+Definitely not linear.
+
+But autonomous means no t.
+t means the independent
+
+variable appears on the
+right-hand side.
+
+Of course, it is there.
+It is buried in the dx/dt and
+
+dy/dt.
+But it is not on the right-hand
+
+side.
+No t appears on the right-hand
+
+side.
+
+Because no t appears on the
+right-hand side,
+
+I can now draw a picture of
+this.
+
+But, let's see,
+what does a solution look like?
+
+I never even talked about what
+a solution was,
+
+did I?
+Well, pretend that immediately
+
+after I talked about that,
+I talked about this.
+
+What is the solution?
+Well, the solution,
+
+maybe you took it for granted,
+is a pair of functions,
+
+x of t, y of t if when 
+you plug it in
+
+it satisfies the equation.
+And so what else is new?
+
+The solution is x 
+equals x of t,
+
+y equals y of t.
+
+If I draw a picture of that
+what would it look like?
+
+This is where your previous
+knowledge of physics above all
+
+18.02, maybe 18.01 if you
+learned this in high school,
+
+what is x equals x of t and 
+y equals y of t?
+
+How do you draw a picture of
+
+that?
+What does it represent?
+
+A curve.
+And what will be the title of
+
+the chapter of the calculus book
+in which that is discussed?
+
+Parametric equations.
+This is a parameterized curve.
+
+So we know what the solution
+looks like.
+
+Our solution is a parameterized
+curve.
+
+And what does a parameterized
+curve look like?
+
+Well, it travels,
+and in a certain direction.
+
+Okay.
+That's enough.
+
+Why do I have several of those
+curves?
+
+Well, because I have several
+solutions.
+
+In fact, given any initial
+starting point,
+
+there is a solution that goes
+through it.
+
+I will put in possible starting
+points.
+
+And you can do this on the
+computer screen with a little
+
+program you will have,
+one of the visuals you'll have.
+
+It's being made right now.
+You put down starter point,
+
+put down a click,
+and then it just draws the
+
+curve passing through that
+point.
+
+Didn't we do this early in the
+term?
+
+Yes.
+But there is a difference now
+
+which I will explain.
+These are various possible
+
+starting points at time zero for
+this solution,
+
+and then you see what happens
+to it afterwards.
+
+In fact, through every point in
+the plane will pass a solution
+
+curve, parameterized curve.
+Now, what is then the
+
+representation of this?
+Well, what is the meaning of x
+
+prime of t and y prime of t?
+
+I am not going to worry for the
+moment about the right-hand
+
+side.
+What does this mean by itself?
+
+If this is the curve,
+the parameterized motion,
+
+then this represents its
+velocity vector.
+
+It is the velocity of the
+solution at time t.
+
+If I think of the solution as
+being a parameterized motion.
+
+All I have drawn here is the
+trace, the path of the motion.
+
+This hasn't indicated how fast
+it was going.
+
+One solution might go whoosh
+and another one might go rah.
+
+That is a velocity,
+and that velocity changes from
+
+point to point.
+It changes direction.
+
+Well, we know its direction at
+each point.
+
+That's tangent.
+What I cannot tell is the
+
+speed.
+From this picture,
+
+I cannot tell what the speed
+was.
+
+Too bad.
+Now, what is then the meaning
+
+of the system?
+What the system does,
+
+it prescribes at each point the
+velocity vector.
+
+If you tell me what the point
+(x, y) is in the plane then
+
+these equations give you the
+velocity vector at that point.
+
+And, therefore,
+what I end up with,
+
+the system is what you call in
+physics and what you call in
+
+18.02 a velocity field.
+So at each point there is a
+
+certain vector.
+The vector is always tangent to
+
+the solution curve through
+there, but I cannot predict from
+
+just this picture what its
+length will be because at some
+
+points, it might be going slow.
+The solution might be going
+
+slowly.
+In other words,
+
+the plane is filled up with
+these guys.
+
+Stop me.
+Not enough here.
+
+So on and so on.
+We can say a system of first
+
+order equations,
+ODEs of first order equations,
+
+autonomous because there must
+be no t on the right-hand side,
+
+is equal to a velocity field.
+A field of velocity.
+
+The plane covered with velocity
+vectors.
+
+And a solution is a
+parameterized curve with the
+
+right velocity everywhere.
+
+Now, there obviously must be a
+connection between that and the
+
+direction fields we studied at
+the beginning of the term.
+
+And there is.
+It is a very important
+
+connection.
+It is too important to talk
+
+about in minus one minute.
+When we need it,
+
+I will have to spend some time
+talking about it then.
\ No newline at end of file
diff --git a/ML5yVI18uaI.txt b/ML5yVI18uaI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fa14a28c48154c60c4f0d98c2f73f3835607b1ab
--- /dev/null
+++ b/ML5yVI18uaI.txt
@@ -0,0 +1,16735 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
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+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay so for the ones that
+
+ align:start position:0%
+ocw.mit.edu okay so for the ones that
+ 
+
+ align:start position:0%
+ocw.mit.edu okay so for the ones that
+have just arrived uh I'm going to be
+
+ align:start position:0%
+have just arrived uh I'm going to be
+ 
+
+ align:start position:0%
+have just arrived uh I'm going to be
+giving the lecture today but George is
+
+ align:start position:0%
+giving the lecture today but George is
+ 
+
+ align:start position:0%
+giving the lecture today but George is
+here so if You' got questions you can
+
+ align:start position:0%
+here so if You' got questions you can
+ 
+
+ align:start position:0%
+here so if You' got questions you can
+ask ask me I don't mind it being
+
+ align:start position:0%
+ask ask me I don't mind it being
+ 
+
+ align:start position:0%
+ask ask me I don't mind it being
+interrupted at any time but also uh if
+
+ align:start position:0%
+interrupted at any time but also uh if
+ 
+
+ align:start position:0%
+interrupted at any time but also uh if
+if you want George to answer something
+
+ align:start position:0%
+if you want George to answer something
+ 
+
+ align:start position:0%
+if you want George to answer something
+he's sitting here as well so he can also
+
+ align:start position:0%
+he's sitting here as well so he can also
+ 
+
+ align:start position:0%
+he's sitting here as well so he can also
+contribute uh so uh last time uh George
+
+ align:start position:0%
+contribute uh so uh last time uh George
+ 
+
+ align:start position:0%
+contribute uh so uh last time uh George
+was uh looking at the fer transforming
+
+ align:start position:0%
+was uh looking at the fer transforming
+ 
+
+ align:start position:0%
+was uh looking at the fer transforming
+property of a
+
+ align:start position:0%
+property of a
+ 
+
+ align:start position:0%
+property of a
+lens uh and he he he looked at the
+
+ align:start position:0%
+lens uh and he he he looked at the
+ 
+
+ align:start position:0%
+lens uh and he he he looked at the
+derived the 1D case uh where you've just
+
+ align:start position:0%
+derived the 1D case uh where you've just
+ 
+
+ align:start position:0%
+derived the 1D case uh where you've just
+got a function of X rather than a
+
+ align:start position:0%
+got a function of X rather than a
+ 
+
+ align:start position:0%
+got a function of X rather than a
+function of XY uh you've got this
+
+ align:start position:0%
+function of XY uh you've got this
+ 
+
+ align:start position:0%
+function of XY uh you've got this
+transparency a distance Z in front of
+
+ align:start position:0%
+transparency a distance Z in front of
+ 
+
+ align:start position:0%
+transparency a distance Z in front of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+lens uh and and then you've got a a
+
+ align:start position:0%
+lens uh and and then you've got a a
+ 
+
+ align:start position:0%
+lens uh and and then you've got a a
+screen placed a distance F behind the
+
+ align:start position:0%
+screen placed a distance F behind the
+ 
+
+ align:start position:0%
+screen placed a distance F behind the
+lens and so the question is what do you
+
+ align:start position:0%
+lens and so the question is what do you
+ 
+
+ align:start position:0%
+lens and so the question is what do you
+get on that screen uh and uh what I'm
+
+ align:start position:0%
+get on that screen uh and uh what I'm
+ 
+
+ align:start position:0%
+get on that screen uh and uh what I'm
+not going to go through all the algebra
+
+ align:start position:0%
+not going to go through all the algebra
+ 
+
+ align:start position:0%
+not going to go through all the algebra
+of that again because George did it last
+
+ align:start position:0%
+of that again because George did it last
+ 
+
+ align:start position:0%
+of that again because George did it last
+time this was the Cal this this was the
+
+ align:start position:0%
+time this was the Cal this this was the
+ 
+
+ align:start position:0%
+time this was the Cal this this was the
+answer what you find uh is that uh you
+
+ align:start position:0%
+answer what you find uh is that uh you
+ 
+
+ align:start position:0%
+answer what you find uh is that uh you
+what you get in in this plane here is
+
+ align:start position:0%
+what you get in in this plane here is
+ 
+
+ align:start position:0%
+what you get in in this plane here is
+actually the fer
+
+ align:start position:0%
+actually the fer
+ 
+
+ align:start position:0%
+actually the fer
+transform of the uh thin
+
+ align:start position:0%
+transform of the uh thin
+ 
+
+ align:start position:0%
+transform of the uh thin
+transparency right so G of X is this
+
+ align:start position:0%
+transparency right so G of X is this
+ 
+
+ align:start position:0%
+transparency right so G of X is this
+transparency here you get the fer
+
+ align:start position:0%
+transparency here you get the fer
+ 
+
+ align:start position:0%
+transparency here you get the fer
+transform of
+
+ align:start position:0%
+transform of
+ 
+
+ align:start position:0%
+transform of
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+and multiplied uh by a a parabolic phase
+
+ align:start position:0%
+and multiplied uh by a a parabolic phase
+ 
+
+ align:start position:0%
+and multiplied uh by a a parabolic phase
+Factor uh which depends on the position
+
+ align:start position:0%
+Factor uh which depends on the position
+ 
+
+ align:start position:0%
+Factor uh which depends on the position
+of this screen what the of the uh of the
+
+ align:start position:0%
+of this screen what the of the uh of the
+ 
+
+ align:start position:0%
+of this screen what the of the uh of the
+transparency
+
+ align:start position:0%
+transparency
+ 
+
+ align:start position:0%
+transparency
+what is the value of this Zed you'll
+
+ align:start position:0%
+what is the value of this Zed you'll
+ 
+
+ align:start position:0%
+what is the value of this Zed you'll
+notice that you get this uh Factor here
+
+ align:start position:0%
+notice that you get this uh Factor here
+ 
+
+ align:start position:0%
+notice that you get this uh Factor here
+1 - z/ F uh so if Z equals F uh this is
+
+ align:start position:0%
+1 - z/ F uh so if Z equals F uh this is
+ 
+
+ align:start position:0%
+1 - z/ F uh so if Z equals F uh this is
+going to be zero and this phase factor
+
+ align:start position:0%
+going to be zero and this phase factor
+ 
+
+ align:start position:0%
+going to be zero and this phase factor
+is going to disappear so for the special
+
+ align:start position:0%
+is going to disappear so for the special
+ 
+
+ align:start position:0%
+is going to disappear so for the special
+case where Z equals
+
+ align:start position:0%
+case where Z equals
+ 
+
+ align:start position:0%
+case where Z equals
+F all you see here is just the fer
+
+ align:start position:0%
+F all you see here is just the fer
+ 
+
+ align:start position:0%
+F all you see here is just the fer
+transform of this very simple very
+
+ align:start position:0%
+transform of this very simple very
+ 
+
+ align:start position:0%
+transform of this very simple very
+simple answer uh and um people actually
+
+ align:start position:0%
+simple answer uh and um people actually
+ 
+
+ align:start position:0%
+simple answer uh and um people actually
+have known this for quite a long time
+
+ align:start position:0%
+have known this for quite a long time
+ 
+
+ align:start position:0%
+have known this for quite a long time
+and at one time it did look really
+
+ align:start position:0%
+and at one time it did look really
+ 
+
+ align:start position:0%
+and at one time it did look really
+attractive that you could actually
+
+ align:start position:0%
+attractive that you could actually
+ 
+
+ align:start position:0%
+attractive that you could actually
+imagine using this as a real way of
+
+ align:start position:0%
+imagine using this as a real way of
+ 
+
+ align:start position:0%
+imagine using this as a real way of
+doing uh forer transforms uh especially
+
+ align:start position:0%
+doing uh forer transforms uh especially
+ 
+
+ align:start position:0%
+doing uh forer transforms uh especially
+as uh as we're now going to do you can
+
+ align:start position:0%
+as uh as we're now going to do you can
+ 
+
+ align:start position:0%
+as uh as we're now going to do you can
+immediately generalize that to the 2D
+
+ align:start position:0%
+immediately generalize that to the 2D
+ 
+
+ align:start position:0%
+immediately generalize that to the 2D
+case uh so you can do a 2d forer
+
+ align:start position:0%
+case uh so you can do a 2d forer
+ 
+
+ align:start position:0%
+case uh so you can do a 2d forer
+transform uh and when you think that um
+
+ align:start position:0%
+transform uh and when you think that um
+ 
+
+ align:start position:0%
+transform uh and when you think that um
+you know the the light propagates
+
+ align:start position:0%
+you know the the light propagates
+ 
+
+ align:start position:0%
+you know the the light propagates
+through this at the speed of light you
+
+ align:start position:0%
+through this at the speed of light you
+ 
+
+ align:start position:0%
+through this at the speed of light you
+can do a 2d forer transform at the speed
+
+ align:start position:0%
+can do a 2d forer transform at the speed
+ 
+
+ align:start position:0%
+can do a 2d forer transform at the speed
+of light uh and when people first
+
+ align:start position:0%
+of light uh and when people first
+ 
+
+ align:start position:0%
+of light uh and when people first
+realized this which was back in the
+
+ align:start position:0%
+realized this which was back in the
+ 
+
+ align:start position:0%
+realized this which was back in the
+1950s 50s or early
+
+ align:start position:0%
+1950s 50s or early
+ 
+
+ align:start position:0%
+1950s 50s or early
+60s uh you know computers were very slow
+
+ align:start position:0%
+60s uh you know computers were very slow
+ 
+
+ align:start position:0%
+60s uh you know computers were very slow
+then so doing a 2d forer transform was
+
+ align:start position:0%
+then so doing a 2d forer transform was
+ 
+
+ align:start position:0%
+then so doing a 2d forer transform was
+not trivial uh so a lot of effort was
+
+ align:start position:0%
+not trivial uh so a lot of effort was
+ 
+
+ align:start position:0%
+not trivial uh so a lot of effort was
+put into trying to design instruments to
+
+ align:start position:0%
+put into trying to design instruments to
+ 
+
+ align:start position:0%
+put into trying to design instruments to
+do that yes sure do you know who was the
+
+ align:start position:0%
+do that yes sure do you know who was the
+ 
+
+ align:start position:0%
+do that yes sure do you know who was the
+first one to realize this was it VL or
+
+ align:start position:0%
+first one to realize this was it VL or
+ 
+
+ align:start position:0%
+first one to realize this was it VL or
+uh uh the question is who was the first
+
+ align:start position:0%
+uh uh the question is who was the first
+ 
+
+ align:start position:0%
+uh uh the question is who was the first
+to recognize that yeah Vander Lutz well
+
+ align:start position:0%
+to recognize that yeah Vander Lutz well
+ 
+
+ align:start position:0%
+to recognize that yeah Vander Lutz well
+Vander Lutz was at um uh he was at
+
+ align:start position:0%
+Vander Lutz was at um uh he was at
+ 
+
+ align:start position:0%
+Vander Lutz was at um uh he was at
+Michigan wasn't he and an interestingly
+
+ align:start position:0%
+Michigan wasn't he and an interestingly
+ 
+
+ align:start position:0%
+Michigan wasn't he and an interestingly
+the um the holography guys were also in
+
+ align:start position:0%
+the um the holography guys were also in
+ 
+
+ align:start position:0%
+the um the holography guys were also in
+the same lab um what's the guy's name
+
+ align:start position:0%
+the same lab um what's the guy's name
+ 
+
+ align:start position:0%
+the same lab um what's the guy's name
+the one that em EMT Le uh and
+
+ align:start position:0%
+the one that em EMT Le uh and
+ 
+
+ align:start position:0%
+the one that em EMT Le uh and
+interestingly EMT LEF and Van
+
+ align:start position:0%
+interestingly EMT LEF and Van
+ 
+
+ align:start position:0%
+interestingly EMT LEF and Van
+delut uh both published virtually the
+
+ align:start position:0%
+delut uh both published virtually the
+ 
+
+ align:start position:0%
+delut uh both published virtually the
+same paper in the same year uh it's a
+
+ align:start position:0%
+same paper in the same year uh it's a
+ 
+
+ align:start position:0%
+same paper in the same year uh it's a
+very very interesting historical thing
+
+ align:start position:0%
+very very interesting historical thing
+ 
+
+ align:start position:0%
+very very interesting historical thing
+there they're both from the same lab and
+
+ align:start position:0%
+there they're both from the same lab and
+ 
+
+ align:start position:0%
+there they're both from the same lab and
+both invented almost the same idea as
+
+ align:start position:0%
+both invented almost the same idea as
+ 
+
+ align:start position:0%
+both invented almost the same idea as
+far as I can see uh and neither of them
+
+ align:start position:0%
+far as I can see uh and neither of them
+ 
+
+ align:start position:0%
+far as I can see uh and neither of them
+refer to the other guy very
+
+ align:start position:0%
+refer to the other guy very
+ 
+
+ align:start position:0%
+refer to the other guy very
+peculiar anyway um I don't know who
+
+ align:start position:0%
+peculiar anyway um I don't know who
+ 
+
+ align:start position:0%
+peculiar anyway um I don't know who
+really came up with this idea first but
+
+ align:start position:0%
+really came up with this idea first but
+ 
+
+ align:start position:0%
+really came up with this idea first but
+um but actually I think the I suspect
+
+ align:start position:0%
+um but actually I think the I suspect
+ 
+
+ align:start position:0%
+um but actually I think the I suspect
+that actually even uh an ABBA re
+
+ align:start position:0%
+that actually even uh an ABBA re
+ 
+
+ align:start position:0%
+that actually even uh an ABBA re
+realized this you know he uh an an daber
+
+ align:start position:0%
+realized this you know he uh an an daber
+ 
+
+ align:start position:0%
+realized this you know he uh an an daber
+was the
+
+ align:start position:0%
+was the
+ 
+
+ align:start position:0%
+was the
+scientist uh who designed the Zeiss
+
+ align:start position:0%
+scientist uh who designed the Zeiss
+ 
+
+ align:start position:0%
+scientist uh who designed the Zeiss
+microscopes
+
+ align:start position:0%
+microscopes
+ 
+
+ align:start position:0%
+microscopes
+uh 120 130 years ago and uh and and he
+
+ align:start position:0%
+uh 120 130 years ago and uh and and he
+ 
+
+ align:start position:0%
+uh 120 130 years ago and uh and and he
+came up with a theory for image
+
+ align:start position:0%
+came up with a theory for image
+ 
+
+ align:start position:0%
+came up with a theory for image
+formation and a microscope which is
+
+ align:start position:0%
+formation and a microscope which is
+ 
+
+ align:start position:0%
+formation and a microscope which is
+actually what we're going to be getting
+
+ align:start position:0%
+actually what we're going to be getting
+ 
+
+ align:start position:0%
+actually what we're going to be getting
+on to pretty well the next thing the um
+
+ align:start position:0%
+on to pretty well the next thing the um
+ 
+
+ align:start position:0%
+on to pretty well the next thing the um
+Imaging with a 4f system uh he he
+
+ align:start position:0%
+Imaging with a 4f system uh he he
+ 
+
+ align:start position:0%
+Imaging with a 4f system uh he he
+understood that 130 years ago uh and I
+
+ align:start position:0%
+understood that 130 years ago uh and I
+ 
+
+ align:start position:0%
+understood that 130 years ago uh and I
+don't think he's often given as much
+
+ align:start position:0%
+don't think he's often given as much
+ 
+
+ align:start position:0%
+don't think he's often given as much
+credit as he should get give anyway you
+
+ align:start position:0%
+credit as he should get give anyway you
+ 
+
+ align:start position:0%
+credit as he should get give anyway you
+can use this as a way of doing a a fer
+
+ align:start position:0%
+can use this as a way of doing a a fer
+ 
+
+ align:start position:0%
+can use this as a way of doing a a fer
+transform and even a 2d for a transform
+
+ align:start position:0%
+transform and even a 2d for a transform
+ 
+
+ align:start position:0%
+transform and even a 2d for a transform
+so you see going from this stage to this
+
+ align:start position:0%
+so you see going from this stage to this
+ 
+
+ align:start position:0%
+so you see going from this stage to this
+stage is is Trivial really uh all all
+
+ align:start position:0%
+stage is is Trivial really uh all all
+ 
+
+ align:start position:0%
+stage is is Trivial really uh all all
+you've all we've done here is assuming
+
+ align:start position:0%
+you've all we've done here is assuming
+ 
+
+ align:start position:0%
+you've all we've done here is assuming
+that it's a separable function of X and
+
+ align:start position:0%
+that it's a separable function of X and
+ 
+
+ align:start position:0%
+that it's a separable function of X and
+Y so you get exactly the same sort of
+
+ align:start position:0%
+Y so you get exactly the same sort of
+ 
+
+ align:start position:0%
+Y so you get exactly the same sort of
+integral for for y as you get get for X
+
+ align:start position:0%
+integral for for y as you get get for X
+ 
+
+ align:start position:0%
+integral for for y as you get get for X
+so it now becomes a a double integral
+
+ align:start position:0%
+so it now becomes a a double integral
+ 
+
+ align:start position:0%
+so it now becomes a a double integral
+this is a two the two-dimensional forer
+
+ align:start position:0%
+this is a two the two-dimensional forer
+ 
+
+ align:start position:0%
+this is a two the two-dimensional forer
+transform of G of G of
+
+ align:start position:0%
+transform of G of G of
+ 
+
+ align:start position:0%
+transform of G of G of
+XY and uh and you you can see uh you get
+
+ align:start position:0%
+XY and uh and you you can see uh you get
+ 
+
+ align:start position:0%
+XY and uh and you you can see uh you get
+again the phase Factor um here you
+
+ align:start position:0%
+again the phase Factor um here you
+ 
+
+ align:start position:0%
+again the phase Factor um here you
+because it's separable uh you got this e
+
+ align:start position:0%
+because it's separable uh you got this e
+ 
+
+ align:start position:0%
+because it's separable uh you got this e
+e to the I Pi x^2 and you've got an e to
+
+ align:start position:0%
+e to the I Pi x^2 and you've got an e to
+ 
+
+ align:start position:0%
+e to the I Pi x^2 and you've got an e to
+I Pi y^ 2 and of course x^2 + y^2 very
+
+ align:start position:0%
+I Pi y^ 2 and of course x^2 + y^2 very
+ 
+
+ align:start position:0%
+I Pi y^ 2 and of course x^2 + y^2 very
+nicely equals R 2 so this becomes a a a
+
+ align:start position:0%
+nicely equals R 2 so this becomes a a a
+ 
+
+ align:start position:0%
+nicely equals R 2 so this becomes a a a
+a spherical type um
+
+ align:start position:0%
+a spherical type um
+ 
+
+ align:start position:0%
+a spherical type um
+wave so we've still got this 1us Z over
+
+ align:start position:0%
+wave so we've still got this 1us Z over
+ 
+
+ align:start position:0%
+wave so we've still got this 1us Z over
+F so if Z equal f
+
+ align:start position:0%
+F so if Z equal f
+ 
+
+ align:start position:0%
+F so if Z equal f
+uh then again this this phase Factor
+
+ align:start position:0%
+uh then again this this phase Factor
+ 
+
+ align:start position:0%
+uh then again this this phase Factor
+vanishes and we end up with just the the
+
+ align:start position:0%
+vanishes and we end up with just the the
+ 
+
+ align:start position:0%
+vanishes and we end up with just the the
+pure fer
+
+ align:start position:0%
+pure fer
+ 
+
+ align:start position:0%
+pure fer
+transform yeah as I say so a lot of
+
+ align:start position:0%
+transform yeah as I say so a lot of
+ 
+
+ align:start position:0%
+transform yeah as I say so a lot of
+people thought that um this was quite a
+
+ align:start position:0%
+people thought that um this was quite a
+ 
+
+ align:start position:0%
+people thought that um this was quite a
+a neat way of doing fer transforms um
+
+ align:start position:0%
+a neat way of doing fer transforms um
+ 
+
+ align:start position:0%
+a neat way of doing fer transforms um
+there was a lot of work on optical
+
+ align:start position:0%
+there was a lot of work on optical
+ 
+
+ align:start position:0%
+there was a lot of work on optical
+computers all the way through the 60s
+
+ align:start position:0%
+computers all the way through the 60s
+ 
+
+ align:start position:0%
+computers all the way through the 60s
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+70s uh but the the trouble is that as
+
+ align:start position:0%
+70s uh but the the trouble is that as
+ 
+
+ align:start position:0%
+70s uh but the the trouble is that as
+fast as they could develop these systems
+
+ align:start position:0%
+fast as they could develop these systems
+ 
+
+ align:start position:0%
+fast as they could develop these systems
+the computer people
+
+ align:start position:0%
+the computer people
+ 
+
+ align:start position:0%
+the computer people
+develop their computers even faster so
+
+ align:start position:0%
+develop their computers even faster so
+ 
+
+ align:start position:0%
+develop their computers even faster so
+they were always one step behind I think
+
+ align:start position:0%
+they were always one step behind I think
+ 
+
+ align:start position:0%
+they were always one step behind I think
+uh so I think in the end people realized
+
+ align:start position:0%
+uh so I think in the end people realized
+ 
+
+ align:start position:0%
+uh so I think in the end people realized
+it was a waste of time and uh uh and and
+
+ align:start position:0%
+it was a waste of time and uh uh and and
+ 
+
+ align:start position:0%
+it was a waste of time and uh uh and and
+that it was never really going to become
+
+ align:start position:0%
+that it was never really going to become
+ 
+
+ align:start position:0%
+that it was never really going to become
+a uh a a
+
+ align:start position:0%
+a uh a a
+ 
+
+ align:start position:0%
+a uh a a
+um you know a a a practical way of doing
+
+ align:start position:0%
+um you know a a a practical way of doing
+ 
+
+ align:start position:0%
+um you know a a a practical way of doing
+real calculations but in the early days
+
+ align:start position:0%
+real calculations but in the early days
+ 
+
+ align:start position:0%
+real calculations but in the early days
+it was and emit Le we were just
+
+ align:start position:0%
+it was and emit Le we were just
+ 
+
+ align:start position:0%
+it was and emit Le we were just
+mentioning uh he first developed these
+
+ align:start position:0%
+mentioning uh he first developed these
+ 
+
+ align:start position:0%
+mentioning uh he first developed these
+systems for uh actually izing the um uh
+
+ align:start position:0%
+systems for uh actually izing the um uh
+ 
+
+ align:start position:0%
+systems for uh actually izing the um uh
+the images they took from um synthetic
+
+ align:start position:0%
+the images they took from um synthetic
+ 
+
+ align:start position:0%
+the images they took from um synthetic
+aperture they you know an airplane
+
+ align:start position:0%
+aperture they you know an airplane
+ 
+
+ align:start position:0%
+aperture they you know an airplane
+they'd fly an airplane over North
+
+ align:start position:0%
+they'd fly an airplane over North
+ 
+
+ align:start position:0%
+they'd fly an airplane over North
+Korea uh taking
+
+ align:start position:0%
+Korea uh taking
+ 
+
+ align:start position:0%
+Korea uh taking
+pictures uh and then the idea was that
+
+ align:start position:0%
+pictures uh and then the idea was that
+ 
+
+ align:start position:0%
+pictures uh and then the idea was that
+the the the the plane takes many
+
+ align:start position:0%
+the the the the plane takes many
+ 
+
+ align:start position:0%
+the the the the plane takes many
+pictures as it's traveling along uh and
+
+ align:start position:0%
+pictures as it's traveling along uh and
+ 
+
+ align:start position:0%
+pictures as it's traveling along uh and
+they're coherent with the respect to
+
+ align:start position:0%
+they're coherent with the respect to
+ 
+
+ align:start position:0%
+they're coherent with the respect to
+each other so you you can actually
+
+ align:start position:0%
+each other so you you can actually
+ 
+
+ align:start position:0%
+each other so you you can actually
+combine them digitally afterwards and
+
+ align:start position:0%
+combine them digitally afterwards and
+ 
+
+ align:start position:0%
+combine them digitally afterwards and
+get an image which has got amazing
+
+ align:start position:0%
+get an image which has got amazing
+ 
+
+ align:start position:0%
+get an image which has got amazing
+resolution and you can see the guy in
+
+ align:start position:0%
+resolution and you can see the guy in
+ 
+
+ align:start position:0%
+resolution and you can see the guy in
+North Korea reading his newspaper or
+
+ align:start position:0%
+North Korea reading his newspaper or
+ 
+
+ align:start position:0%
+North Korea reading his newspaper or
+whatever so they they really did that
+
+ align:start position:0%
+whatever so they they really did that
+ 
+
+ align:start position:0%
+whatever so they they really did that
+sort of thing way back then right so so
+
+ align:start position:0%
+sort of thing way back then right so so
+ 
+
+ align:start position:0%
+sort of thing way back then right so so
+that's the uh equation here then uh and
+
+ align:start position:0%
+that's the uh equation here then uh and
+ 
+
+ align:start position:0%
+that's the uh equation here then uh and
+um yeah so this is just going through
+
+ align:start position:0%
+um yeah so this is just going through
+ 
+
+ align:start position:0%
+um yeah so this is just going through
+how that thing was derived uh so we've
+
+ align:start position:0%
+how that thing was derived uh so we've
+ 
+
+ align:start position:0%
+how that thing was derived uh so we've
+got this um we've got the screen uh
+
+ align:start position:0%
+got this um we've got the screen uh
+ 
+
+ align:start position:0%
+got this um we've got the screen uh
+we've got the screen here the G of x
+
+ align:start position:0%
+we've got the screen here the G of x
+ 
+
+ align:start position:0%
+we've got the screen here the G of x
+by the time we get here there's a uh
+
+ align:start position:0%
+by the time we get here there's a uh
+ 
+
+ align:start position:0%
+by the time we get here there's a uh
+it's convolved with some phase parabolic
+
+ align:start position:0%
+it's convolved with some phase parabolic
+ 
+
+ align:start position:0%
+it's convolved with some phase parabolic
+phase function uh and then after it goes
+
+ align:start position:0%
+phase function uh and then after it goes
+ 
+
+ align:start position:0%
+phase function uh and then after it goes
+through here it's multiplied by another
+
+ align:start position:0%
+through here it's multiplied by another
+ 
+
+ align:start position:0%
+through here it's multiplied by another
+parabolic phase function and then as it
+
+ align:start position:0%
+parabolic phase function and then as it
+ 
+
+ align:start position:0%
+parabolic phase function and then as it
+propagates here it's convolved with
+
+ align:start position:0%
+propagates here it's convolved with
+ 
+
+ align:start position:0%
+propagates here it's convolved with
+another parabolic phase function uh and
+
+ align:start position:0%
+another parabolic phase function uh and
+ 
+
+ align:start position:0%
+another parabolic phase function uh and
+if we have that magic condition that
+
+ align:start position:0%
+if we have that magic condition that
+ 
+
+ align:start position:0%
+if we have that magic condition that
+this is f and this is f most of these
+
+ align:start position:0%
+this is f and this is f most of these
+ 
+
+ align:start position:0%
+this is f and this is f most of these
+parabolic phases cancel out and we're
+
+ align:start position:0%
+parabolic phases cancel out and we're
+ 
+
+ align:start position:0%
+parabolic phases cancel out and we're
+left with this very simple final answer
+
+ align:start position:0%
+left with this very simple final answer
+ 
+
+ align:start position:0%
+left with this very simple final answer
+so that's basically what's happening and
+
+ align:start position:0%
+so that's basically what's happening and
+ 
+
+ align:start position:0%
+so that's basically what's happening and
+George went through you know the the
+
+ align:start position:0%
+George went through you know the the
+ 
+
+ align:start position:0%
+George went through you know the the
+various stages of doing this of course
+
+ align:start position:0%
+various stages of doing this of course
+ 
+
+ align:start position:0%
+various stages of doing this of course
+you end up with a couple of integrals of
+
+ align:start position:0%
+you end up with a couple of integrals of
+ 
+
+ align:start position:0%
+you end up with a couple of integrals of
+of products of three phase functions
+
+ align:start position:0%
+of products of three phase functions
+ 
+
+ align:start position:0%
+of products of three phase functions
+here so uh the algebra was was quite um
+
+ align:start position:0%
+here so uh the algebra was was quite um
+ 
+
+ align:start position:0%
+here so uh the algebra was was quite um
+complicated well not really complicated
+
+ align:start position:0%
+complicated well not really complicated
+ 
+
+ align:start position:0%
+complicated well not really complicated
+but just lengthy uh and uh but but
+
+ align:start position:0%
+but just lengthy uh and uh but but
+ 
+
+ align:start position:0%
+but just lengthy uh and uh but but
+everything in the end
+
+ align:start position:0%
+everything in the end
+ 
+
+ align:start position:0%
+everything in the end
+cancels if you haven't got Z equals to F
+
+ align:start position:0%
+cancels if you haven't got Z equals to F
+ 
+
+ align:start position:0%
+cancels if you haven't got Z equals to F
+though uh then you can see uh that um
+
+ align:start position:0%
+though uh then you can see uh that um
+ 
+
+ align:start position:0%
+though uh then you can see uh that um
+you you do got got you have got this
+
+ align:start position:0%
+you you do got got you have got this
+ 
+
+ align:start position:0%
+you you do got got you have got this
+phase Factor so you don't actually get
+
+ align:start position:0%
+phase Factor so you don't actually get
+ 
+
+ align:start position:0%
+phase Factor so you don't actually get
+exactly the fuer transform in this plane
+
+ align:start position:0%
+exactly the fuer transform in this plane
+ 
+
+ align:start position:0%
+exactly the fuer transform in this plane
+in that case you get the fuer transform
+
+ align:start position:0%
+in that case you get the fuer transform
+ 
+
+ align:start position:0%
+in that case you get the fuer transform
+multiplied by this phase Factor uh and
+
+ align:start position:0%
+multiplied by this phase Factor uh and
+ 
+
+ align:start position:0%
+multiplied by this phase Factor uh and
+uh that can be important in some cases
+
+ align:start position:0%
+uh that can be important in some cases
+ 
+
+ align:start position:0%
+uh that can be important in some cases
+that's something that you need to take
+
+ align:start position:0%
+that's something that you need to take
+ 
+
+ align:start position:0%
+that's something that you need to take
+into account um there's another special
+
+ align:start position:0%
+into account um there's another special
+ 
+
+ align:start position:0%
+into account um there's another special
+case actually uh that's the case when Z
+
+ align:start position:0%
+case actually uh that's the case when Z
+ 
+
+ align:start position:0%
+case actually uh that's the case when Z
+equals not
+
+ align:start position:0%
+equals not
+ 
+
+ align:start position:0%
+equals not
+uh the case when Z equals not is if this
+
+ align:start position:0%
+uh the case when Z equals not is if this
+ 
+
+ align:start position:0%
+uh the case when Z equals not is if this
+screen coincides with the lens
+
+ align:start position:0%
+screen coincides with the lens
+ 
+
+ align:start position:0%
+screen coincides with the lens
+immediately close up to the lens uh and
+
+ align:start position:0%
+immediately close up to the lens uh and
+ 
+
+ align:start position:0%
+immediately close up to the lens uh and
+I think Goodman does that that one as
+
+ align:start position:0%
+I think Goodman does that that one as
+ 
+
+ align:start position:0%
+I think Goodman does that that one as
+well doesn't he uh and so if Z equals n
+
+ align:start position:0%
+well doesn't he uh and so if Z equals n
+ 
+
+ align:start position:0%
+well doesn't he uh and so if Z equals n
+this this goes uh and so we're still
+
+ align:start position:0%
+this this goes uh and so we're still
+ 
+
+ align:start position:0%
+this this goes uh and so we're still
+left with this phase Factor e to the I
+
+ align:start position:0%
+left with this phase Factor e to the I
+ 
+
+ align:start position:0%
+left with this phase Factor e to the I
+Pi X-2 over Lambda F right so and also
+
+ align:start position:0%
+Pi X-2 over Lambda F right so and also
+ 
+
+ align:start position:0%
+Pi X-2 over Lambda F right so and also
+Goodman does the case of the
+
+ align:start position:0%
+Goodman does the case of the
+ 
+
+ align:start position:0%
+Goodman does the case of the
+transparency after the lens which I did
+
+ align:start position:0%
+transparency after the lens which I did
+ 
+
+ align:start position:0%
+transparency after the lens which I did
+not do in the nodes right okay yeah so
+
+ align:start position:0%
+not do in the nodes right okay yeah so
+ 
+
+ align:start position:0%
+not do in the nodes right okay yeah so
+Goodman yeah Goodman does this case of
+
+ align:start position:0%
+Goodman yeah Goodman does this case of
+ 
+
+ align:start position:0%
+Goodman yeah Goodman does this case of
+the transparency placed in here that Z
+
+ align:start position:0%
+the transparency placed in here that Z
+ 
+
+ align:start position:0%
+the transparency placed in here that Z
+negative in yeah yeah but it's all it's
+
+ align:start position:0%
+negative in yeah yeah but it's all it's
+ 
+
+ align:start position:0%
+negative in yeah yeah but it's all it's
+very similar sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answers okay so
+
+ align:start position:0%
+answers okay so
+ 
+
+ align:start position:0%
+answers okay so
+um yeah so so this is just writing down
+
+ align:start position:0%
+um yeah so so this is just writing down
+ 
+
+ align:start position:0%
+um yeah so so this is just writing down
+finally then uh we're defining then the
+
+ align:start position:0%
+finally then uh we're defining then the
+ 
+
+ align:start position:0%
+finally then uh we're defining then the
+fer transform is called the fer
+
+ align:start position:0%
+fer transform is called the fer
+ 
+
+ align:start position:0%
+fer transform is called the fer
+transform of little G is Big G right so
+
+ align:start position:0%
+transform of little G is Big G right so
+ 
+
+ align:start position:0%
+transform of little G is Big G right so
+the final answer is that you've got this
+
+ align:start position:0%
+the final answer is that you've got this
+ 
+
+ align:start position:0%
+the final answer is that you've got this
+parabolic phase function times the the
+
+ align:start position:0%
+parabolic phase function times the the
+ 
+
+ align:start position:0%
+parabolic phase function times the the
+fer transform of of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G okay so um this is
+
+ align:start position:0%
+G okay so um this is
+ 
+
+ align:start position:0%
+G okay so um this is
+um uh pointing out that we've now looked
+
+ align:start position:0%
+um uh pointing out that we've now looked
+ 
+
+ align:start position:0%
+um uh pointing out that we've now looked
+at two different ways you can do a fer
+
+ align:start position:0%
+at two different ways you can do a fer
+ 
+
+ align:start position:0%
+at two different ways you can do a fer
+transform uh one way uh is to just
+
+ align:start position:0%
+transform uh one way uh is to just
+ 
+
+ align:start position:0%
+transform uh one way uh is to just
+propagate the light a very large
+
+ align:start position:0%
+propagate the light a very large
+ 
+
+ align:start position:0%
+propagate the light a very large
+distance you remember if you have frown
+
+ align:start position:0%
+distance you remember if you have frown
+ 
+
+ align:start position:0%
+distance you remember if you have frown
+off a defraction if your screen is a
+
+ align:start position:0%
+off a defraction if your screen is a
+ 
+
+ align:start position:0%
+off a defraction if your screen is a
+very long way away from the uh from the
+
+ align:start position:0%
+very long way away from the uh from the
+ 
+
+ align:start position:0%
+very long way away from the uh from the
+diffracting screen from the diffracting
+
+ align:start position:0%
+diffracting screen from the diffracting
+ 
+
+ align:start position:0%
+diffracting screen from the diffracting
+scre uh object whatever it was called uh
+
+ align:start position:0%
+scre uh object whatever it was called uh
+ 
+
+ align:start position:0%
+scre uh object whatever it was called uh
+transparency uh then again you get this
+
+ align:start position:0%
+transparency uh then again you get this
+ 
+
+ align:start position:0%
+transparency uh then again you get this
+for a transform relationship but of
+
+ align:start position:0%
+for a transform relationship but of
+ 
+
+ align:start position:0%
+for a transform relationship but of
+course here he's put a proportional sign
+
+ align:start position:0%
+course here he's put a proportional sign
+ 
+
+ align:start position:0%
+course here he's put a proportional sign
+there's some things out the front there
+
+ align:start position:0%
+there's some things out the front there
+ 
+
+ align:start position:0%
+there's some things out the front there
+uh and in particular there's going to be
+
+ align:start position:0%
+uh and in particular there's going to be
+ 
+
+ align:start position:0%
+uh and in particular there's going to be
+a again a parabolic phase term isn't
+
+ align:start position:0%
+a again a parabolic phase term isn't
+ 
+
+ align:start position:0%
+a again a parabolic phase term isn't
+there because in this case here what
+
+ align:start position:0%
+there because in this case here what
+ 
+
+ align:start position:0%
+there because in this case here what
+you'd expect actually is that this forer
+
+ align:start position:0%
+you'd expect actually is that this forer
+ 
+
+ align:start position:0%
+you'd expect actually is that this forer
+transform is going to be actually on the
+
+ align:start position:0%
+transform is going to be actually on the
+ 
+
+ align:start position:0%
+transform is going to be actually on the
+surface of of some curved surface uh not
+
+ align:start position:0%
+surface of of some curved surface uh not
+ 
+
+ align:start position:0%
+surface of of some curved surface uh not
+of a of a plain surface right so if you
+
+ align:start position:0%
+of a of a plain surface right so if you
+ 
+
+ align:start position:0%
+of a of a plain surface right so if you
+put the screen if the screen is plain
+
+ align:start position:0%
+put the screen if the screen is plain
+ 
+
+ align:start position:0%
+put the screen if the screen is plain
+then it's going to be multiplied by some
+
+ align:start position:0%
+then it's going to be multiplied by some
+ 
+
+ align:start position:0%
+then it's going to be multiplied by some
+parabolic phase term uh and now we've
+
+ align:start position:0%
+parabolic phase term uh and now we've
+ 
+
+ align:start position:0%
+parabolic phase term uh and now we've
+just looked at this other case where we
+
+ align:start position:0%
+just looked at this other case where we
+ 
+
+ align:start position:0%
+just looked at this other case where we
+don't have to uh have a very large Lab
+
+ align:start position:0%
+don't have to uh have a very large Lab
+ 
+
+ align:start position:0%
+don't have to uh have a very large Lab
+in order to do this
+
+ align:start position:0%
+in order to do this
+ 
+
+ align:start position:0%
+in order to do this
+experiment uh we can actually make the
+
+ align:start position:0%
+experiment uh we can actually make the
+ 
+
+ align:start position:0%
+experiment uh we can actually make the
+experiment quite small so that it fits
+
+ align:start position:0%
+experiment quite small so that it fits
+ 
+
+ align:start position:0%
+experiment quite small so that it fits
+on top of the table just by using a lens
+
+ align:start position:0%
+on top of the table just by using a lens
+ 
+
+ align:start position:0%
+on top of the table just by using a lens
+uh and you know really what you can see
+
+ align:start position:0%
+uh and you know really what you can see
+ 
+
+ align:start position:0%
+uh and you know really what you can see
+that that is actually doing according to
+
+ align:start position:0%
+that that is actually doing according to
+ 
+
+ align:start position:0%
+that that is actually doing according to
+your geometrical Optics ideas now you
+
+ align:start position:0%
+your geometrical Optics ideas now you
+ 
+
+ align:start position:0%
+your geometrical Optics ideas now you
+can see what this is doing uh this is
+
+ align:start position:0%
+can see what this is doing uh this is
+ 
+
+ align:start position:0%
+can see what this is doing uh this is
+producing an image of this at Infinity
+
+ align:start position:0%
+producing an image of this at Infinity
+ 
+
+ align:start position:0%
+producing an image of this at Infinity
+so you can see that the these these two
+
+ align:start position:0%
+so you can see that the these these two
+ 
+
+ align:start position:0%
+so you can see that the these these two
+things are actually equivalent what it's
+
+ align:start position:0%
+things are actually equivalent what it's
+ 
+
+ align:start position:0%
+things are actually equivalent what it's
+doing is bringing what would have been
+
+ align:start position:0%
+doing is bringing what would have been
+ 
+
+ align:start position:0%
+doing is bringing what would have been
+at Infinity uh to some finite plane
+
+ align:start position:0%
+at Infinity uh to some finite plane
+ 
+
+ align:start position:0%
+at Infinity uh to some finite plane
+isn't it right so that's that's that's
+
+ align:start position:0%
+isn't it right so that's that's that's
+ 
+
+ align:start position:0%
+isn't it right so that's that's that's
+all it's doing there uh but again we've
+
+ align:start position:0%
+all it's doing there uh but again we've
+ 
+
+ align:start position:0%
+all it's doing there uh but again we've
+got this uh this thing
+
+ align:start position:0%
+got this uh this thing
+ 
+
+ align:start position:0%
+got this uh this thing
+here uh this uh proportional sign which
+
+ align:start position:0%
+here uh this uh proportional sign which
+ 
+
+ align:start position:0%
+here uh this uh proportional sign which
+means there's some some other factors
+
+ align:start position:0%
+means there's some some other factors
+ 
+
+ align:start position:0%
+means there's some some other factors
+constant factors out there including in
+
+ align:start position:0%
+constant factors out there including in
+ 
+
+ align:start position:0%
+constant factors out there including in
+general uh a uh this parabolic phase
+
+ align:start position:0%
+general uh a uh this parabolic phase
+ 
+
+ align:start position:0%
+general uh a uh this parabolic phase
+factor which for the particular case
+
+ align:start position:0%
+factor which for the particular case
+ 
+
+ align:start position:0%
+factor which for the particular case
+when you got F and
+
+ align:start position:0%
+when you got F and
+ 
+
+ align:start position:0%
+when you got F and
+F
+
+ align:start position:0%
+F
+ 
+
+ align:start position:0%
+F
+uh disappears The parabolic Phase
+
+ align:start position:0%
+uh disappears The parabolic Phase
+ 
+
+ align:start position:0%
+uh disappears The parabolic Phase
+function disappears when you've got this
+
+ align:start position:0%
+function disappears when you've got this
+ 
+
+ align:start position:0%
+function disappears when you've got this
+uh special very very special case with
+
+ align:start position:0%
+uh special very very special case with
+ 
+
+ align:start position:0%
+uh special very very special case with
+the two FS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay now this one um what this is
+
+ align:start position:0%
+there okay now this one um what this is
+ 
+
+ align:start position:0%
+there okay now this one um what this is
+really trying to show is that really
+
+ align:start position:0%
+really trying to show is that really
+ 
+
+ align:start position:0%
+really trying to show is that really
+there's two ways of looking at this
+
+ align:start position:0%
+there's two ways of looking at this
+ 
+
+ align:start position:0%
+there's two ways of looking at this
+problem uh you can uh what these two
+
+ align:start position:0%
+problem uh you can uh what these two
+ 
+
+ align:start position:0%
+problem uh you can uh what these two
+diagrams here are really trying to show
+
+ align:start position:0%
+diagrams here are really trying to show
+ 
+
+ align:start position:0%
+diagrams here are really trying to show
+uh there's it's trying to show the same
+
+ align:start position:0%
+uh there's it's trying to show the same
+ 
+
+ align:start position:0%
+uh there's it's trying to show the same
+case but trying to get you thinking
+
+ align:start position:0%
+case but trying to get you thinking
+ 
+
+ align:start position:0%
+case but trying to get you thinking
+about a different way of of of um
+
+ align:start position:0%
+about a different way of of of um
+ 
+
+ align:start position:0%
+about a different way of of of um
+viewing the problem so in this case here
+
+ align:start position:0%
+viewing the problem so in this case here
+ 
+
+ align:start position:0%
+viewing the problem so in this case here
+uh you can think of any point on the
+
+ align:start position:0%
+uh you can think of any point on the
+ 
+
+ align:start position:0%
+uh you can think of any point on the
+screen on the on the the um uh what does
+
+ align:start position:0%
+screen on the on the the um uh what does
+ 
+
+ align:start position:0%
+screen on the on the the um uh what does
+he call it
+
+ align:start position:0%
+he call it
+ 
+
+ align:start position:0%
+he call it
+transparency uh is going to act like a
+
+ align:start position:0%
+transparency uh is going to act like a
+ 
+
+ align:start position:0%
+transparency uh is going to act like a
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+source uh so it's going to produce a
+
+ align:start position:0%
+source uh so it's going to produce a
+ 
+
+ align:start position:0%
+source uh so it's going to produce a
+spherical expanding wave uh and then
+
+ align:start position:0%
+spherical expanding wave uh and then
+ 
+
+ align:start position:0%
+spherical expanding wave uh and then
+this is a distance F so that spherical
+
+ align:start position:0%
+this is a distance F so that spherical
+ 
+
+ align:start position:0%
+this is a distance F so that spherical
+wave is going to be converted into a
+
+ align:start position:0%
+wave is going to be converted into a
+ 
+
+ align:start position:0%
+wave is going to be converted into a
+plane wave uh the angle of propagation
+
+ align:start position:0%
+plane wave uh the angle of propagation
+ 
+
+ align:start position:0%
+plane wave uh the angle of propagation
+of this plane wave depends on the
+
+ align:start position:0%
+of this plane wave depends on the
+ 
+
+ align:start position:0%
+of this plane wave depends on the
+distance at this point from the orig
+
+ align:start position:0%
+distance at this point from the orig
+ 
+
+ align:start position:0%
+distance at this point from the orig
+from the origin of course right uh and
+
+ align:start position:0%
+from the origin of course right uh and
+ 
+
+ align:start position:0%
+from the origin of course right uh and
+uh so you can think then of what you see
+
+ align:start position:0%
+uh so you can think then of what you see
+ 
+
+ align:start position:0%
+uh so you can think then of what you see
+on the screen as being made up of an
+
+ align:start position:0%
+on the screen as being made up of an
+ 
+
+ align:start position:0%
+on the screen as being made up of an
+angular Spectrum what's called an
+
+ align:start position:0%
+angular Spectrum what's called an
+ 
+
+ align:start position:0%
+angular Spectrum what's called an
+angular spectrum of plain waves
+
+ align:start position:0%
+angular spectrum of plain waves
+ 
+
+ align:start position:0%
+angular spectrum of plain waves
+uh where the strength of each of those
+
+ align:start position:0%
+uh where the strength of each of those
+ 
+
+ align:start position:0%
+uh where the strength of each of those
+angular Spectrum components uh comes
+
+ align:start position:0%
+angular Spectrum components uh comes
+ 
+
+ align:start position:0%
+angular Spectrum components uh comes
+about from the value of g at that point
+
+ align:start position:0%
+about from the value of g at that point
+ 
+
+ align:start position:0%
+about from the value of g at that point
+right so uh so that's one way of
+
+ align:start position:0%
+right so uh so that's one way of
+ 
+
+ align:start position:0%
+right so uh so that's one way of
+thinking about it uh and this way is
+
+ align:start position:0%
+thinking about it uh and this way is
+ 
+
+ align:start position:0%
+thinking about it uh and this way is
+thinking about it the other way this way
+
+ align:start position:0%
+thinking about it the other way this way
+ 
+
+ align:start position:0%
+thinking about it the other way this way
+you're thinking of the object is going
+
+ align:start position:0%
+you're thinking of the object is going
+ 
+
+ align:start position:0%
+you're thinking of the object is going
+to Def if you imagine your uh
+
+ align:start position:0%
+to Def if you imagine your uh
+ 
+
+ align:start position:0%
+to Def if you imagine your uh
+transparency as being like a gring it
+
+ align:start position:0%
+transparency as being like a gring it
+ 
+
+ align:start position:0%
+transparency as being like a gring it
+produces uh
+
+ align:start position:0%
+produces uh
+ 
+
+ align:start position:0%
+produces uh
+defraction uh it produces like grating
+
+ align:start position:0%
+defraction uh it produces like grating
+ 
+
+ align:start position:0%
+defraction uh it produces like grating
+orders for example if this this was a
+
+ align:start position:0%
+orders for example if this this was a
+ 
+
+ align:start position:0%
+orders for example if this this was a
+very simple case of a of a sinusoidal
+
+ align:start position:0%
+very simple case of a of a sinusoidal
+ 
+
+ align:start position:0%
+very simple case of a of a sinusoidal
+grating you'd expect it to produce some
+
+ align:start position:0%
+grating you'd expect it to produce some
+ 
+
+ align:start position:0%
+grating you'd expect it to produce some
+grating orders uh and these grating
+
+ align:start position:0%
+grating orders uh and these grating
+ 
+
+ align:start position:0%
+grating orders uh and these grating
+orders correspond to plane waves
+
+ align:start position:0%
+orders correspond to plane waves
+ 
+
+ align:start position:0%
+orders correspond to plane waves
+traveling in particular angles so this
+
+ align:start position:0%
+traveling in particular angles so this
+ 
+
+ align:start position:0%
+traveling in particular angles so this
+shows uh the angular spectrum of the
+
+ align:start position:0%
+shows uh the angular spectrum of the
+ 
+
+ align:start position:0%
+shows uh the angular spectrum of the
+defraction of the light uh given by uh
+
+ align:start position:0%
+defraction of the light uh given by uh
+ 
+
+ align:start position:0%
+defraction of the light uh given by uh
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+transparency and then the lens collects
+
+ align:start position:0%
+transparency and then the lens collects
+ 
+
+ align:start position:0%
+transparency and then the lens collects
+these uh the uh the different um these
+
+ align:start position:0%
+these uh the uh the different um these
+ 
+
+ align:start position:0%
+these uh the uh the different um these
+different plane wave components all of
+
+ align:start position:0%
+different plane wave components all of
+ 
+
+ align:start position:0%
+different plane wave components all of
+them are going to be converted uh into a
+
+ align:start position:0%
+them are going to be converted uh into a
+ 
+
+ align:start position:0%
+them are going to be converted uh into a
+spherical converging wave uh that
+
+ align:start position:0%
+spherical converging wave uh that
+ 
+
+ align:start position:0%
+spherical converging wave uh that
+converges a distance F away it doesn't
+
+ align:start position:0%
+converges a distance F away it doesn't
+ 
+
+ align:start position:0%
+converges a distance F away it doesn't
+say F but it this must be F uh and
+
+ align:start position:0%
+say F but it this must be F uh and
+ 
+
+ align:start position:0%
+say F but it this must be F uh and
+different the plane waves moving at
+
+ align:start position:0%
+different the plane waves moving at
+ 
+
+ align:start position:0%
+different the plane waves moving at
+different angles are going to converge
+
+ align:start position:0%
+different angles are going to converge
+ 
+
+ align:start position:0%
+different angles are going to converge
+to a point
+
+ align:start position:0%
+to a point
+ 
+
+ align:start position:0%
+to a point
+which of course is proportional to the
+
+ align:start position:0%
+which of course is proportional to the
+ 
+
+ align:start position:0%
+which of course is proportional to the
+uh the the sign of the angle of the
+
+ align:start position:0%
+uh the the sign of the angle of the
+ 
+
+ align:start position:0%
+uh the the sign of the angle of the
+propagation right so here at any point
+
+ align:start position:0%
+propagation right so here at any point
+ 
+
+ align:start position:0%
+propagation right so here at any point
+on the screen uh you're you're going to
+
+ align:start position:0%
+on the screen uh you're you're going to
+ 
+
+ align:start position:0%
+on the screen uh you're you're going to
+sum up these again these angular Spectra
+
+ align:start position:0%
+sum up these again these angular Spectra
+ 
+
+ align:start position:0%
+sum up these again these angular Spectra
+components Each of which is going to
+
+ align:start position:0%
+components Each of which is going to
+ 
+
+ align:start position:0%
+components Each of which is going to
+give a spherical weight uh so um you can
+
+ align:start position:0%
+give a spherical weight uh so um you can
+ 
+
+ align:start position:0%
+give a spherical weight uh so um you can
+see looking at that diagram again
+
+ align:start position:0%
+see looking at that diagram again
+ 
+
+ align:start position:0%
+see looking at that diagram again
+they're like sort of inverses of each
+
+ align:start position:0%
+they're like sort of inverses of each
+ 
+
+ align:start position:0%
+they're like sort of inverses of each
+other I think this is another example
+
+ align:start position:0%
+other I think this is another example
+ 
+
+ align:start position:0%
+other I think this is another example
+where uh very often you can think of um
+
+ align:start position:0%
+where uh very often you can think of um
+ 
+
+ align:start position:0%
+where uh very often you can think of um
+uh a reciprocal type
+
+ align:start position:0%
+uh a reciprocal type
+ 
+
+ align:start position:0%
+uh a reciprocal type
+behavior um you know you could yeah you
+
+ align:start position:0%
+behavior um you know you could yeah you
+ 
+
+ align:start position:0%
+behavior um you know you could yeah you
+could you can just flip this over and it
+
+ align:start position:0%
+could you can just flip this over and it
+ 
+
+ align:start position:0%
+could you can just flip this over and it
+it would look the same the other way
+
+ align:start position:0%
+it would look the same the other way
+ 
+
+ align:start position:0%
+it would look the same the other way
+wouldn't
+
+ align:start position:0%
+wouldn't
+ 
+
+ align:start position:0%
+wouldn't
+it okay so so this way here then we're
+
+ align:start position:0%
+it okay so so this way here then we're
+ 
+
+ align:start position:0%
+it okay so so this way here then we're
+thinking this this um here we're
+
+ align:start position:0%
+thinking this this um here we're
+ 
+
+ align:start position:0%
+thinking this this um here we're
+thinking of this as as um just like the
+
+ align:start position:0%
+thinking of this as as um just like the
+ 
+
+ align:start position:0%
+thinking of this as as um just like the
+hyan uh uh sense that we spoke about
+
+ align:start position:0%
+hyan uh uh sense that we spoke about
+ 
+
+ align:start position:0%
+hyan uh uh sense that we spoke about
+when we were first doing defraction then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um this is giving some nice
+
+ align:start position:0%
+okay so um this is giving some nice
+ 
+
+ align:start position:0%
+okay so um this is giving some nice
+pictures I'm going to I'm going to steal
+
+ align:start position:0%
+pictures I'm going to I'm going to steal
+ 
+
+ align:start position:0%
+pictures I'm going to I'm going to steal
+this um presentation afterwards because
+
+ align:start position:0%
+this um presentation afterwards because
+ 
+
+ align:start position:0%
+this um presentation afterwards because
+there's so many good displays in this
+
+ align:start position:0%
+there's so many good displays in this
+ 
+
+ align:start position:0%
+there's so many good displays in this
+thing that I'm going to use in my own
+
+ align:start position:0%
+thing that I'm going to use in my own
+ 
+
+ align:start position:0%
+thing that I'm going to use in my own
+lectures in the future uh so uh so this
+
+ align:start position:0%
+lectures in the future uh so uh so this
+ 
+
+ align:start position:0%
+lectures in the future uh so uh so this
+is giving some good ideas the uh so we
+
+ align:start position:0%
+is giving some good ideas the uh so we
+ 
+
+ align:start position:0%
+is giving some good ideas the uh so we
+start off then uh this is a a rectangle
+
+ align:start position:0%
+start off then uh this is a a rectangle
+ 
+
+ align:start position:0%
+start off then uh this is a a rectangle
+uh oh I'm I'm I'm going to say something
+
+ align:start position:0%
+uh oh I'm I'm I'm going to say something
+ 
+
+ align:start position:0%
+uh oh I'm I'm I'm going to say something
+in a minute though uh the so this is a
+
+ align:start position:0%
+in a minute though uh the so this is a
+ 
+
+ align:start position:0%
+in a minute though uh the so this is a
+distance F this is a distance F uh so
+
+ align:start position:0%
+distance F this is a distance F uh so
+ 
+
+ align:start position:0%
+distance F this is a distance F uh so
+this lens then as we just described is
+
+ align:start position:0%
+this lens then as we just described is
+ 
+
+ align:start position:0%
+this lens then as we just described is
+going to produce a fer transform of that
+
+ align:start position:0%
+going to produce a fer transform of that
+ 
+
+ align:start position:0%
+going to produce a fer transform of that
+so the fer transform of a of a of a rect
+
+ align:start position:0%
+so the fer transform of a of a of a rect
+ 
+
+ align:start position:0%
+so the fer transform of a of a of a rect
+is a is a sync so you'd expect to get
+
+ align:start position:0%
+is a is a sync so you'd expect to get
+ 
+
+ align:start position:0%
+is a is a sync so you'd expect to get
+this a syn in x syn in x times a syn in
+
+ align:start position:0%
+this a syn in x syn in x times a syn in
+ 
+
+ align:start position:0%
+this a syn in x syn in x times a syn in
+y uh now the thing I was going to say
+
+ align:start position:0%
+y uh now the thing I was going to say
+ 
+
+ align:start position:0%
+y uh now the thing I was going to say
+though George this looks to me that this
+
+ align:start position:0%
+though George this looks to me that this
+ 
+
+ align:start position:0%
+though George this looks to me that this
+is longer than that this is longer this
+
+ align:start position:0%
+is longer than that this is longer this
+ 
+
+ align:start position:0%
+is longer than that this is longer this
+way than that way so this should be
+
+ align:start position:0%
+way than that way so this should be
+ 
+
+ align:start position:0%
+way than that way so this should be
+longer that way than this way I think
+
+ align:start position:0%
+longer that way than this way I think
+ 
+
+ align:start position:0%
+longer that way than this way I think
+you know that's the aspect ratio of the
+
+ align:start position:0%
+you know that's the aspect ratio of the
+ 
+
+ align:start position:0%
+you know that's the aspect ratio of the
+screen actually yeah the aspect ratio of
+
+ align:start position:0%
+screen actually yeah the aspect ratio of
+ 
+
+ align:start position:0%
+screen actually yeah the aspect ratio of
+the screen ought to be 90 does not obey
+
+ align:start position:0%
+the screen ought to be 90 does not obey
+ 
+
+ align:start position:0%
+the screen ought to be 90 does not obey
+the full transform gu anyway so but this
+
+ align:start position:0%
+the full transform gu anyway so but this
+ 
+
+ align:start position:0%
+the full transform gu anyway so but this
+conversation is um uh bringing home I
+
+ align:start position:0%
+conversation is um uh bringing home I
+ 
+
+ align:start position:0%
+conversation is um uh bringing home I
+think uh a very important point that
+
+ align:start position:0%
+think uh a very important point that
+ 
+
+ align:start position:0%
+think uh a very important point that
+you've that we've mentioned before in
+
+ align:start position:0%
+you've that we've mentioned before in
+ 
+
+ align:start position:0%
+you've that we've mentioned before in
+the course uh that if you if you make a
+
+ align:start position:0%
+the course uh that if you if you make a
+ 
+
+ align:start position:0%
+the course uh that if you if you make a
+function smaller it's for a transform is
+
+ align:start position:0%
+function smaller it's for a transform is
+ 
+
+ align:start position:0%
+function smaller it's for a transform is
+wider if you if you make the function
+
+ align:start position:0%
+wider if you if you make the function
+ 
+
+ align:start position:0%
+wider if you if you make the function
+wider it foror transform is smaller
+
+ align:start position:0%
+wider it foror transform is smaller
+ 
+
+ align:start position:0%
+wider it foror transform is smaller
+right so uh and you'll notice then this
+
+ align:start position:0%
+right so uh and you'll notice then this
+ 
+
+ align:start position:0%
+right so uh and you'll notice then this
+product of these two sinks gives uh a
+
+ align:start position:0%
+product of these two sinks gives uh a
+ 
+
+ align:start position:0%
+product of these two sinks gives uh a
+bright spot in the center a series of
+
+ align:start position:0%
+bright spot in the center a series of
+ 
+
+ align:start position:0%
+bright spot in the center a series of
+bright spots along the the the axes uh
+
+ align:start position:0%
+bright spots along the the the axes uh
+ 
+
+ align:start position:0%
+bright spots along the the the axes uh
+there are also some bright spots in this
+
+ align:start position:0%
+there are also some bright spots in this
+ 
+
+ align:start position:0%
+there are also some bright spots in this
+region here uh but they're so weak that
+
+ align:start position:0%
+region here uh but they're so weak that
+ 
+
+ align:start position:0%
+region here uh but they're so weak that
+you can't actually see them you really
+
+ align:start position:0%
+you can't actually see them you really
+ 
+
+ align:start position:0%
+you can't actually see them you really
+you can only see the ones along the
+
+ align:start position:0%
+you can only see the ones along the
+ 
+
+ align:start position:0%
+you can only see the ones along the
+axes uh so that's the first example uh
+
+ align:start position:0%
+axes uh so that's the first example uh
+ 
+
+ align:start position:0%
+axes uh so that's the first example uh
+then this one's showing how if we make
+
+ align:start position:0%
+then this one's showing how if we make
+ 
+
+ align:start position:0%
+then this one's showing how if we make
+the uh if we make the transparency
+
+ align:start position:0%
+the uh if we make the transparency
+ 
+
+ align:start position:0%
+the uh if we make the transparency
+smaller the rectangle smaller so this
+
+ align:start position:0%
+smaller the rectangle smaller so this
+ 
+
+ align:start position:0%
+smaller the rectangle smaller so this
+pattern gets
+
+ align:start position:0%
+pattern gets
+ 
+
+ align:start position:0%
+pattern gets
+bigger uh now actually we can just about
+
+ align:start position:0%
+bigger uh now actually we can just about
+ 
+
+ align:start position:0%
+bigger uh now actually we can just about
+manage to maybe see some ones other than
+
+ align:start position:0%
+manage to maybe see some ones other than
+ 
+
+ align:start position:0%
+manage to maybe see some ones other than
+along the axis uh and then this one is
+
+ align:start position:0%
+along the axis uh and then this one is
+ 
+
+ align:start position:0%
+along the axis uh and then this one is
+an interesting one um so now we've got
+
+ align:start position:0%
+an interesting one um so now we've got
+ 
+
+ align:start position:0%
+an interesting one um so now we've got
+not just one
+
+ align:start position:0%
+not just one
+ 
+
+ align:start position:0%
+not just one
+aperture but three
+
+ align:start position:0%
+aperture but three
+ 
+
+ align:start position:0%
+aperture but three
+apertures uh and uh so so so now how can
+
+ align:start position:0%
+apertures uh and uh so so so now how can
+ 
+
+ align:start position:0%
+apertures uh and uh so so so now how can
+we work out what what the the fer
+
+ align:start position:0%
+we work out what what the the fer
+ 
+
+ align:start position:0%
+we work out what what the the fer
+transform of of three apertures would be
+
+ align:start position:0%
+transform of of three apertures would be
+ 
+
+ align:start position:0%
+transform of of three apertures would be
+anyone got some ideas I'm sure Shin will
+
+ align:start position:0%
+anyone got some ideas I'm sure Shin will
+ 
+
+ align:start position:0%
+anyone got some ideas I'm sure Shin will
+have an idea um anyone any how would
+
+ align:start position:0%
+have an idea um anyone any how would
+ 
+
+ align:start position:0%
+have an idea um anyone any how would
+anyone think of of doing this sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing have you come across a thing
+
+ align:start position:0%
+thing have you come across a thing
+ 
+
+ align:start position:0%
+thing have you come across a thing
+called the convolution theorem probably
+
+ align:start position:0%
+called the convolution theorem probably
+ 
+
+ align:start position:0%
+called the convolution theorem probably
+you should have done somewhere I would
+
+ align:start position:0%
+you should have done somewhere I would
+ 
+
+ align:start position:0%
+you should have done somewhere I would
+have thought so there's a thing in fua
+
+ align:start position:0%
+have thought so there's a thing in fua
+ 
+
+ align:start position:0%
+have thought so there's a thing in fua
+transforms called the convolution
+
+ align:start position:0%
+transforms called the convolution
+ 
+
+ align:start position:0%
+transforms called the convolution
+theorem uh so this is
+
+ align:start position:0%
+theorem uh so this is
+ 
+
+ align:start position:0%
+theorem uh so this is
+actually uh this is actually like three
+
+ align:start position:0%
+actually uh this is actually like three
+ 
+
+ align:start position:0%
+actually uh this is actually like three
+three spikes convolved with a square
+
+ align:start position:0%
+three spikes convolved with a square
+ 
+
+ align:start position:0%
+three spikes convolved with a square
+which it really means all it means is we
+
+ align:start position:0%
+which it really means all it means is we
+ 
+
+ align:start position:0%
+which it really means all it means is we
+place a square on each of the three SP
+
+ align:start position:0%
+place a square on each of the three SP
+ 
+
+ align:start position:0%
+place a square on each of the three SP
+spikes uh and the convolution
+
+ align:start position:0%
+spikes uh and the convolution
+ 
+
+ align:start position:0%
+spikes uh and the convolution
+theorem uh says that the for a transform
+
+ align:start position:0%
+theorem uh says that the for a transform
+ 
+
+ align:start position:0%
+theorem uh says that the for a transform
+of a convolution is the product of the
+
+ align:start position:0%
+of a convolution is the product of the
+ 
+
+ align:start position:0%
+of a convolution is the product of the
+FIA
+
+ align:start position:0%
+FIA
+ 
+
+ align:start position:0%
+FIA
+transforms so what you'd X is that the
+
+ align:start position:0%
+transforms so what you'd X is that the
+ 
+
+ align:start position:0%
+transforms so what you'd X is that the
+fer transform that you're going to see
+
+ align:start position:0%
+fer transform that you're going to see
+ 
+
+ align:start position:0%
+fer transform that you're going to see
+here is the fer transform of this of the
+
+ align:start position:0%
+here is the fer transform of this of the
+ 
+
+ align:start position:0%
+here is the fer transform of this of the
+rectangle which is
+
+ align:start position:0%
+rectangle which is
+ 
+
+ align:start position:0%
+rectangle which is
+this multiplied by something else uh
+
+ align:start position:0%
+this multiplied by something else uh
+ 
+
+ align:start position:0%
+this multiplied by something else uh
+which is the fer transform of the three
+
+ align:start position:0%
+which is the fer transform of the three
+ 
+
+ align:start position:0%
+which is the fer transform of the three
+spikes and the three spikes uh is like
+
+ align:start position:0%
+spikes and the three spikes uh is like
+ 
+
+ align:start position:0%
+spikes and the three spikes uh is like
+uh a Delta function and a A plus or
+
+ align:start position:0%
+uh a Delta function and a A plus or
+ 
+
+ align:start position:0%
+uh a Delta function and a A plus or
+minus Delta function the the plus or
+
+ align:start position:0%
+minus Delta function the the plus or
+ 
+
+ align:start position:0%
+minus Delta function the the plus or
+minus Delta function together e to the I
+
+ align:start position:0%
+minus Delta function together e to the I
+ 
+
+ align:start position:0%
+minus Delta function together e to the I
+something plus e to Theus I something
+
+ align:start position:0%
+something plus e to Theus I something
+ 
+
+ align:start position:0%
+something plus e to Theus I something
+gives C
+
+ align:start position:0%
+gives C
+ 
+
+ align:start position:0%
+gives C
+and the the the one at the center just
+
+ align:start position:0%
+and the the the one at the center just
+ 
+
+ align:start position:0%
+and the the the one at the center just
+gives a constant so the fua transform of
+
+ align:start position:0%
+gives a constant so the fua transform of
+ 
+
+ align:start position:0%
+gives a constant so the fua transform of
+these three Delta functions is is one
+
+ align:start position:0%
+these three Delta functions is is one
+ 
+
+ align:start position:0%
+these three Delta functions is is one
+plus a a cosine or something like that
+
+ align:start position:0%
+plus a a cosine or something like that
+ 
+
+ align:start position:0%
+plus a a cosine or something like that
+uh and uh so that's what we expect to
+
+ align:start position:0%
+uh and uh so that's what we expect to
+ 
+
+ align:start position:0%
+uh and uh so that's what we expect to
+see then this thing uh this pattern that
+
+ align:start position:0%
+see then this thing uh this pattern that
+ 
+
+ align:start position:0%
+see then this thing uh this pattern that
+we saw before is going to be multiplied
+
+ align:start position:0%
+we saw before is going to be multiplied
+ 
+
+ align:start position:0%
+we saw before is going to be multiplied
+by a
+
+ align:start position:0%
+by a
+ 
+
+ align:start position:0%
+by a
+cosign function which comes about
+
+ align:start position:0%
+cosign function which comes about
+ 
+
+ align:start position:0%
+cosign function which comes about
+because of the separation of this uh and
+
+ align:start position:0%
+because of the separation of this uh and
+ 
+
+ align:start position:0%
+because of the separation of this uh and
+of course because this this distance is
+
+ align:start position:0%
+of course because this this distance is
+ 
+
+ align:start position:0%
+of course because this this distance is
+actually much bigger than the width of
+
+ align:start position:0%
+actually much bigger than the width of
+ 
+
+ align:start position:0%
+actually much bigger than the width of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+rectangle the spacing of the of the
+
+ align:start position:0%
+rectangle the spacing of the of the
+ 
+
+ align:start position:0%
+rectangle the spacing of the of the
+cosine is much finer uh than the fora
+
+ align:start position:0%
+cosine is much finer uh than the fora
+ 
+
+ align:start position:0%
+cosine is much finer uh than the fora
+transform of the rectangle and so that's
+
+ align:start position:0%
+transform of the rectangle and so that's
+ 
+
+ align:start position:0%
+transform of the rectangle and so that's
+why these fringes you see these
+
+ align:start position:0%
+why these fringes you see these
+ 
+
+ align:start position:0%
+why these fringes you see these
+fringes very fine fringes become they
+
+ align:start position:0%
+fringes very fine fringes become they
+ 
+
+ align:start position:0%
+fringes very fine fringes become they
+become a a a a result of the fact that
+
+ align:start position:0%
+become a a a a result of the fact that
+ 
+
+ align:start position:0%
+become a a a a result of the fact that
+these components here are quite well
+
+ align:start position:0%
+these components here are quite well
+ 
+
+ align:start position:0%
+these components here are quite well
+separated uh so that's another very nice
+
+ align:start position:0%
+separated uh so that's another very nice
+ 
+
+ align:start position:0%
+separated uh so that's another very nice
+example uh and uh so all these all these
+
+ align:start position:0%
+example uh and uh so all these all these
+ 
+
+ align:start position:0%
+example uh and uh so all these all these
+um uh theorems that you learn in FIA
+
+ align:start position:0%
+um uh theorems that you learn in FIA
+ 
+
+ align:start position:0%
+um uh theorems that you learn in FIA
+transforms uh can all be directly taken
+
+ align:start position:0%
+transforms uh can all be directly taken
+ 
+
+ align:start position:0%
+transforms uh can all be directly taken
+over into Optics and uh sometimes they
+
+ align:start position:0%
+over into Optics and uh sometimes they
+ 
+
+ align:start position:0%
+over into Optics and uh sometimes they
+can save a lot of work because you can
+
+ align:start position:0%
+can save a lot of work because you can
+ 
+
+ align:start position:0%
+can save a lot of work because you can
+just use the standard forms for things
+
+ align:start position:0%
+just use the standard forms for things
+ 
+
+ align:start position:0%
+just use the standard forms for things
+that you can look up in a book of tables
+
+ align:start position:0%
+that you can look up in a book of tables
+ 
+
+ align:start position:0%
+that you can look up in a book of tables
+uh and uh would saves you a lot of
+
+ align:start position:0%
+uh and uh would saves you a lot of
+ 
+
+ align:start position:0%
+uh and uh would saves you a lot of
+algebra or even worse arithmetic
+
+ align:start position:0%
+algebra or even worse arithmetic
+ 
+
+ align:start position:0%
+algebra or even worse arithmetic
+right so this is another example so now
+
+ align:start position:0%
+right so this is another example so now
+ 
+
+ align:start position:0%
+right so this is another example so now
+we're back to the the bigger rectangle
+
+ align:start position:0%
+we're back to the the bigger rectangle
+ 
+
+ align:start position:0%
+we're back to the the bigger rectangle
+or something close to the bigger
+
+ align:start position:0%
+or something close to the bigger
+ 
+
+ align:start position:0%
+or something close to the bigger
+rectangle uh the fer transform of the
+
+ align:start position:0%
+rectangle uh the fer transform of the
+ 
+
+ align:start position:0%
+rectangle uh the fer transform of the
+rectangle we saw
+
+ align:start position:0%
+rectangle we saw
+ 
+
+ align:start position:0%
+rectangle we saw
+before uh but now this one you see the
+
+ align:start position:0%
+before uh but now this one you see the
+ 
+
+ align:start position:0%
+before uh but now this one you see the
+this is multiplied by some fringes so
+
+ align:start position:0%
+this is multiplied by some fringes so
+ 
+
+ align:start position:0%
+this is multiplied by some fringes so
+this is like the opposite of this one
+
+ align:start position:0%
+this is like the opposite of this one
+ 
+
+ align:start position:0%
+this is like the opposite of this one
+really so this is a this is a
+
+ align:start position:0%
+really so this is a this is a
+ 
+
+ align:start position:0%
+really so this is a this is a
+convolution this is a product so we use
+
+ align:start position:0%
+convolution this is a product so we use
+ 
+
+ align:start position:0%
+convolution this is a product so we use
+the same convolution theorem again uh
+
+ align:start position:0%
+the same convolution theorem again uh
+ 
+
+ align:start position:0%
+the same convolution theorem again uh
+the uh the fringes of course correspond
+
+ align:start position:0%
+the uh the fringes of course correspond
+ 
+
+ align:start position:0%
+the uh the fringes of course correspond
+just like we said before the fer
+
+ align:start position:0%
+just like we said before the fer
+ 
+
+ align:start position:0%
+just like we said before the fer
+transform of the three Delta functions
+
+ align:start position:0%
+transform of the three Delta functions
+ 
+
+ align:start position:0%
+transform of the three Delta functions
+with the fringes so the fer transform of
+
+ align:start position:0%
+with the fringes so the fer transform of
+ 
+
+ align:start position:0%
+with the fringes so the fer transform of
+the fringes is the is is like three
+
+ align:start position:0%
+the fringes is the is is like three
+ 
+
+ align:start position:0%
+the fringes is the is is like three
+Delta functions so what we'd expect this
+
+ align:start position:0%
+Delta functions so what we'd expect this
+ 
+
+ align:start position:0%
+Delta functions so what we'd expect this
+is a product of the fringes and the
+
+ align:start position:0%
+is a product of the fringes and the
+ 
+
+ align:start position:0%
+is a product of the fringes and the
+rectangle so we expect here to see the
+
+ align:start position:0%
+rectangle so we expect here to see the
+ 
+
+ align:start position:0%
+rectangle so we expect here to see the
+convolution of the fer transform of the
+
+ align:start position:0%
+convolution of the fer transform of the
+ 
+
+ align:start position:0%
+convolution of the fer transform of the
+fringes and the forer transform of the
+
+ align:start position:0%
+fringes and the forer transform of the
+ 
+
+ align:start position:0%
+fringes and the forer transform of the
+rectangle and that's that's what we see
+
+ align:start position:0%
+rectangle and that's that's what we see
+ 
+
+ align:start position:0%
+rectangle and that's that's what we see
+so we see three of these defraction
+
+ align:start position:0%
+so we see three of these defraction
+ 
+
+ align:start position:0%
+so we see three of these defraction
+patterns uh
+
+ align:start position:0%
+patterns uh
+ 
+
+ align:start position:0%
+patterns uh
+um situated on these three spots
+
+ align:start position:0%
+um situated on these three spots
+ 
+
+ align:start position:0%
+um situated on these three spots
+corresponding to the foror transform of
+
+ align:start position:0%
+corresponding to the foror transform of
+ 
+
+ align:start position:0%
+corresponding to the foror transform of
+that grating right so uh very nice uh
+
+ align:start position:0%
+that grating right so uh very nice uh
+ 
+
+ align:start position:0%
+that grating right so uh very nice uh
+display that one I like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one uh okay so yeah so this is now
+
+ align:start position:0%
+one uh okay so yeah so this is now
+ 
+
+ align:start position:0%
+one uh okay so yeah so this is now
+introducing um the idea of the What's
+
+ align:start position:0%
+introducing um the idea of the What's
+ 
+
+ align:start position:0%
+introducing um the idea of the What's
+called the 4f system so we're going to
+
+ align:start position:0%
+called the 4f system so we're going to
+ 
+
+ align:start position:0%
+called the 4f system so we're going to
+do not this not just once but do it
+
+ align:start position:0%
+do not this not just once but do it
+ 
+
+ align:start position:0%
+do not this not just once but do it
+twice so this is shows what we've had so
+
+ align:start position:0%
+twice so this is shows what we've had so
+ 
+
+ align:start position:0%
+twice so this is shows what we've had so
+far if we got some uh particular
+
+ align:start position:0%
+far if we got some uh particular
+ 
+
+ align:start position:0%
+far if we got some uh particular
+transparency we get some
+
+ align:start position:0%
+transparency we get some
+ 
+
+ align:start position:0%
+transparency we get some
+particular uh defraction pattern in the
+
+ align:start position:0%
+particular uh defraction pattern in the
+ 
+
+ align:start position:0%
+particular uh defraction pattern in the
+back focal
+
+ align:start position:0%
+back focal
+ 
+
+ align:start position:0%
+back focal
+plane and then in the 4f system we do
+
+ align:start position:0%
+plane and then in the 4f system we do
+ 
+
+ align:start position:0%
+plane and then in the 4f system we do
+the same again we now have another
+
+ align:start position:0%
+the same again we now have another
+ 
+
+ align:start position:0%
+the same again we now have another
+lens uh which is going to do exactly the
+
+ align:start position:0%
+lens uh which is going to do exactly the
+ 
+
+ align:start position:0%
+lens uh which is going to do exactly the
+same uh it's going to look at this
+
+ align:start position:0%
+same uh it's going to look at this
+ 
+
+ align:start position:0%
+same uh it's going to look at this
+pattern and produce its fer transform so
+
+ align:start position:0%
+pattern and produce its fer transform so
+ 
+
+ align:start position:0%
+pattern and produce its fer transform so
+if if uh remember if if the if this is f
+
+ align:start position:0%
+if if uh remember if if the if this is f
+ 
+
+ align:start position:0%
+if if uh remember if if the if this is f
+and this is f and this is f and this is
+
+ align:start position:0%
+and this is f and this is f and this is
+ 
+
+ align:start position:0%
+and this is f and this is f and this is
+f we won't have to worry anything about
+
+ align:start position:0%
+f we won't have to worry anything about
+ 
+
+ align:start position:0%
+f we won't have to worry anything about
+these parabolic phases it's just
+
+ align:start position:0%
+these parabolic phases it's just
+ 
+
+ align:start position:0%
+these parabolic phases it's just
+straight for a transforms with nothing
+
+ align:start position:0%
+straight for a transforms with nothing
+ 
+
+ align:start position:0%
+straight for a transforms with nothing
+else uh and uh so you can see what you
+
+ align:start position:0%
+else uh and uh so you can see what you
+ 
+
+ align:start position:0%
+else uh and uh so you can see what you
+get very simple you start off with this
+
+ align:start position:0%
+get very simple you start off with this
+ 
+
+ align:start position:0%
+get very simple you start off with this
+object so here you get uh is fer
+
+ align:start position:0%
+object so here you get uh is fer
+ 
+
+ align:start position:0%
+object so here you get uh is fer
+transform and if you take the fer
+
+ align:start position:0%
+transform and if you take the fer
+ 
+
+ align:start position:0%
+transform and if you take the fer
+transform of the F trans transform what
+
+ align:start position:0%
+transform of the F trans transform what
+ 
+
+ align:start position:0%
+transform of the F trans transform what
+do you get if you do a fer transform of
+
+ align:start position:0%
+do you get if you do a fer transform of
+ 
+
+ align:start position:0%
+do you get if you do a fer transform of
+a for
+
+ align:start position:0%
+a for
+ 
+
+ align:start position:0%
+a for
+transform yeah it's not quite is it you
+
+ align:start position:0%
+transform yeah it's not quite is it you
+ 
+
+ align:start position:0%
+transform yeah it's not quite is it you
+remember you're inverted that's right
+
+ align:start position:0%
+remember you're inverted that's right
+ 
+
+ align:start position:0%
+remember you're inverted that's right
+yeah so someone got that the um uh if
+
+ align:start position:0%
+yeah so someone got that the um uh if
+ 
+
+ align:start position:0%
+yeah so someone got that the um uh if
+you remember if you if you do a a fer
+
+ align:start position:0%
+you remember if you if you do a a fer
+ 
+
+ align:start position:0%
+you remember if you if you do a a fer
+transform of a fer transform you get the
+
+ align:start position:0%
+transform of a fer transform you get the
+ 
+
+ align:start position:0%
+transform of a fer transform you get the
+original function inverted you have to
+
+ align:start position:0%
+original function inverted you have to
+ 
+
+ align:start position:0%
+original function inverted you have to
+take for a transform four times and then
+
+ align:start position:0%
+take for a transform four times and then
+ 
+
+ align:start position:0%
+take for a transform four times and then
+you get back to where you
+
+ align:start position:0%
+you get back to where you
+ 
+
+ align:start position:0%
+you get back to where you
+start uh and uh so that's what we can
+
+ align:start position:0%
+start uh and uh so that's what we can
+ 
+
+ align:start position:0%
+start uh and uh so that's what we can
+see anyway so this is the uh inverted
+
+ align:start position:0%
+see anyway so this is the uh inverted
+ 
+
+ align:start position:0%
+see anyway so this is the uh inverted
+well of course inverted it's just what
+
+ align:start position:0%
+well of course inverted it's just what
+ 
+
+ align:start position:0%
+well of course inverted it's just what
+we expect isn't it because we know that
+
+ align:start position:0%
+we expect isn't it because we know that
+ 
+
+ align:start position:0%
+we expect isn't it because we know that
+when we have an IM Imaging system we get
+
+ align:start position:0%
+when we have an IM Imaging system we get
+ 
+
+ align:start position:0%
+when we have an IM Imaging system we get
+an inverted image so it's it everything
+
+ align:start position:0%
+an inverted image so it's it everything
+ 
+
+ align:start position:0%
+an inverted image so it's it everything
+fits together uh it gives exactly the
+
+ align:start position:0%
+fits together uh it gives exactly the
+ 
+
+ align:start position:0%
+fits together uh it gives exactly the
+same results that we expect from our
+
+ align:start position:0%
+same results that we expect from our
+ 
+
+ align:start position:0%
+same results that we expect from our
+geometrical
+
+ align:start position:0%
+geometrical
+ 
+
+ align:start position:0%
+geometrical
+Optics uh and um so in this case of
+
+ align:start position:0%
+Optics uh and um so in this case of
+ 
+
+ align:start position:0%
+Optics uh and um so in this case of
+course this is a rather symmetrical OB
+
+ align:start position:0%
+course this is a rather symmetrical OB
+ 
+
+ align:start position:0%
+course this is a rather symmetrical OB
+object so the fact that this is been
+
+ align:start position:0%
+object so the fact that this is been
+ 
+
+ align:start position:0%
+object so the fact that this is been
+inverted I guess you can't really even
+
+ align:start position:0%
+inverted I guess you can't really even
+ 
+
+ align:start position:0%
+inverted I guess you can't really even
+see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so this is saying then uh that
+
+ align:start position:0%
+okay so so this is saying then uh that
+ 
+
+ align:start position:0%
+okay so so this is saying then uh that
+you can um make a 4f system uh which
+
+ align:start position:0%
+you can um make a 4f system uh which
+ 
+
+ align:start position:0%
+you can um make a 4f system uh which
+produces then an uh an inverted version
+
+ align:start position:0%
+produces then an uh an inverted version
+ 
+
+ align:start position:0%
+produces then an uh an inverted version
+of the original object you might wonder
+
+ align:start position:0%
+of the original object you might wonder
+ 
+
+ align:start position:0%
+of the original object you might wonder
+what the point of that is I mean I guess
+
+ align:start position:0%
+what the point of that is I mean I guess
+ 
+
+ align:start position:0%
+what the point of that is I mean I guess
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+way uh there's no point in making an an
+
+ align:start position:0%
+way uh there's no point in making an an
+ 
+
+ align:start position:0%
+way uh there's no point in making an an
+image which is much the same as the
+
+ align:start position:0%
+image which is much the same as the
+ 
+
+ align:start position:0%
+image which is much the same as the
+object really um but one reason why you
+
+ align:start position:0%
+object really um but one reason why you
+ 
+
+ align:start position:0%
+object really um but one reason why you
+might want well there's two reasons one
+
+ align:start position:0%
+might want well there's two reasons one
+ 
+
+ align:start position:0%
+might want well there's two reasons one
+is that it's actually of course moved
+
+ align:start position:0%
+is that it's actually of course moved
+ 
+
+ align:start position:0%
+is that it's actually of course moved
+it's it's produced this image in a
+
+ align:start position:0%
+it's it's produced this image in a
+ 
+
+ align:start position:0%
+it's it's produced this image in a
+different plane so it's actually it's
+
+ align:start position:0%
+different plane so it's actually it's
+ 
+
+ align:start position:0%
+different plane so it's actually it's
+like transported the this distribution
+
+ align:start position:0%
+like transported the this distribution
+ 
+
+ align:start position:0%
+like transported the this distribution
+of light here from this plane to this
+
+ align:start position:0%
+of light here from this plane to this
+ 
+
+ align:start position:0%
+of light here from this plane to this
+plane uh so that's one type of
+
+ align:start position:0%
+plane uh so that's one type of
+ 
+
+ align:start position:0%
+plane uh so that's one type of
+application where you might want to do
+
+ align:start position:0%
+application where you might want to do
+ 
+
+ align:start position:0%
+application where you might want to do
+something like this um and the second
+
+ align:start position:0%
+something like this um and the second
+ 
+
+ align:start position:0%
+something like this um and the second
+thing of course uh is that although this
+
+ align:start position:0%
+thing of course uh is that although this
+ 
+
+ align:start position:0%
+thing of course uh is that although this
+is always called a 4f system uh the we
+
+ align:start position:0%
+is always called a 4f system uh the we
+ 
+
+ align:start position:0%
+is always called a 4f system uh the we
+we obviously have to have this and this
+
+ align:start position:0%
+we obviously have to have this and this
+ 
+
+ align:start position:0%
+we obviously have to have this and this
+F both equal for this to work we have to
+
+ align:start position:0%
+F both equal for this to work we have to
+ 
+
+ align:start position:0%
+F both equal for this to work we have to
+have this and this F to be equal for it
+
+ align:start position:0%
+have this and this F to be equal for it
+ 
+
+ align:start position:0%
+have this and this F to be equal for it
+to work but this F doesn't have to be
+
+ align:start position:0%
+to work but this F doesn't have to be
+ 
+
+ align:start position:0%
+to work but this F doesn't have to be
+the same as that F so you can actually
+
+ align:start position:0%
+the same as that F so you can actually
+ 
+
+ align:start position:0%
+the same as that F so you can actually
+have a system like this where you
+
+ align:start position:0%
+have a system like this where you
+ 
+
+ align:start position:0%
+have a system like this where you
+actually produce a magnified image or a
+
+ align:start position:0%
+actually produce a magnified image or a
+ 
+
+ align:start position:0%
+actually produce a magnified image or a
+demagnified image uh and now that of
+
+ align:start position:0%
+demagnified image uh and now that of
+ 
+
+ align:start position:0%
+demagnified image uh and now that of
+course is getting a lot more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useful uh so so that's how you can
+
+ align:start position:0%
+useful uh so so that's how you can
+ 
+
+ align:start position:0%
+useful uh so so that's how you can
+produce an image of a of an object in
+
+ align:start position:0%
+produce an image of a of an object in
+ 
+
+ align:start position:0%
+produce an image of a of an object in
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+plane uh now the next thing to note is
+
+ align:start position:0%
+plane uh now the next thing to note is
+ 
+
+ align:start position:0%
+plane uh now the next thing to note is
+of course so we're we're we're so far
+
+ align:start position:0%
+of course so we're we're we're so far
+ 
+
+ align:start position:0%
+of course so we're we're we're so far
+we've assumed that all this light gets
+
+ align:start position:0%
+we've assumed that all this light gets
+ 
+
+ align:start position:0%
+we've assumed that all this light gets
+through this Optical system and gets
+
+ align:start position:0%
+through this Optical system and gets
+ 
+
+ align:start position:0%
+through this Optical system and gets
+here uh so if that was the case you get
+
+ align:start position:0%
+here uh so if that was the case you get
+ 
+
+ align:start position:0%
+here uh so if that was the case you get
+a perfect image if all the information
+
+ align:start position:0%
+a perfect image if all the information
+ 
+
+ align:start position:0%
+a perfect image if all the information
+from the object was getting to the image
+
+ align:start position:0%
+from the object was getting to the image
+ 
+
+ align:start position:0%
+from the object was getting to the image
+uh then you wouldn't lose anything but
+
+ align:start position:0%
+uh then you wouldn't lose anything but
+ 
+
+ align:start position:0%
+uh then you wouldn't lose anything but
+in practice of course that's never going
+
+ align:start position:0%
+in practice of course that's never going
+ 
+
+ align:start position:0%
+in practice of course that's never going
+to be true um and um well one one way
+
+ align:start position:0%
+to be true um and um well one one way
+ 
+
+ align:start position:0%
+to be true um and um well one one way
+it's not going to be true of course is
+
+ align:start position:0%
+it's not going to be true of course is
+ 
+
+ align:start position:0%
+it's not going to be true of course is
+because in practice these lenses are
+
+ align:start position:0%
+because in practice these lenses are
+ 
+
+ align:start position:0%
+because in practice these lenses are
+never going to be infinitely large right
+
+ align:start position:0%
+never going to be infinitely large right
+ 
+
+ align:start position:0%
+never going to be infinitely large right
+so um but also uh we could if we wanted
+
+ align:start position:0%
+so um but also uh we could if we wanted
+ 
+
+ align:start position:0%
+so um but also uh we could if we wanted
+to actually put some sort of um mask in
+
+ align:start position:0%
+to actually put some sort of um mask in
+ 
+
+ align:start position:0%
+to actually put some sort of um mask in
+this plane here uh to actually stop some
+
+ align:start position:0%
+this plane here uh to actually stop some
+ 
+
+ align:start position:0%
+this plane here uh to actually stop some
+of that light getting through to the F
+
+ align:start position:0%
+of that light getting through to the F
+ 
+
+ align:start position:0%
+of that light getting through to the F
+to the image plane uh and so now we're
+
+ align:start position:0%
+to the image plane uh and so now we're
+ 
+
+ align:start position:0%
+to the image plane uh and so now we're
+going to look at what happens
+
+ align:start position:0%
+going to look at what happens
+ 
+
+ align:start position:0%
+going to look at what happens
+uh if we do that uh this is much the
+
+ align:start position:0%
+uh if we do that uh this is much the
+ 
+
+ align:start position:0%
+uh if we do that uh this is much the
+same overall effect as George spoke
+
+ align:start position:0%
+same overall effect as George spoke
+ 
+
+ align:start position:0%
+same overall effect as George spoke
+about in previous lectures actually not
+
+ align:start position:0%
+about in previous lectures actually not
+ 
+
+ align:start position:0%
+about in previous lectures actually not
+Imaging case but he spoke about you
+
+ align:start position:0%
+Imaging case but he spoke about you
+ 
+
+ align:start position:0%
+Imaging case but he spoke about you
+remember the the results with the the
+
+ align:start position:0%
+remember the the results with the the
+ 
+
+ align:start position:0%
+remember the the results with the the
+building with the windows that you could
+
+ align:start position:0%
+building with the windows that you could
+ 
+
+ align:start position:0%
+building with the windows that you could
+actually uh you could actually but by
+
+ align:start position:0%
+actually uh you could actually but by
+ 
+
+ align:start position:0%
+actually uh you could actually but by
+just by doing processing digital
+
+ align:start position:0%
+just by doing processing digital
+ 
+
+ align:start position:0%
+just by doing processing digital
+processing on the fer transforms you can
+
+ align:start position:0%
+processing on the fer transforms you can
+ 
+
+ align:start position:0%
+processing on the fer transforms you can
+manipulate the strength of the grading
+
+ align:start position:0%
+manipulate the strength of the grading
+ 
+
+ align:start position:0%
+manipulate the strength of the grading
+components in the final image uh so the
+
+ align:start position:0%
+components in the final image uh so the
+ 
+
+ align:start position:0%
+components in the final image uh so the
+same is true here except now we're doing
+
+ align:start position:0%
+same is true here except now we're doing
+ 
+
+ align:start position:0%
+same is true here except now we're doing
+it optically uh rather than digitally
+
+ align:start position:0%
+it optically uh rather than digitally
+ 
+
+ align:start position:0%
+it optically uh rather than digitally
+right so what you'd expect then is if we
+
+ align:start position:0%
+right so what you'd expect then is if we
+ 
+
+ align:start position:0%
+right so what you'd expect then is if we
+put something in here so here this is
+
+ align:start position:0%
+put something in here so here this is
+ 
+
+ align:start position:0%
+put something in here so here this is
+showing a a a pass band so let's say you
+
+ align:start position:0%
+showing a a a pass band so let's say you
+ 
+
+ align:start position:0%
+showing a a a pass band so let's say you
+put in here some uh opak screen with a
+
+ align:start position:0%
+put in here some uh opak screen with a
+ 
+
+ align:start position:0%
+put in here some uh opak screen with a
+small hole in the hole is this pass band
+
+ align:start position:0%
+small hole in the hole is this pass band
+ 
+
+ align:start position:0%
+small hole in the hole is this pass band
+uh and the screen is the Block band so
+
+ align:start position:0%
+uh and the screen is the Block band so
+ 
+
+ align:start position:0%
+uh and the screen is the Block band so
+it only lets through the region in the
+
+ align:start position:0%
+it only lets through the region in the
+ 
+
+ align:start position:0%
+it only lets through the region in the
+center
+
+ align:start position:0%
+center
+ 
+
+ align:start position:0%
+center
+according to how big that uh pass band
+
+ align:start position:0%
+according to how big that uh pass band
+ 
+
+ align:start position:0%
+according to how big that uh pass band
+is you'll get different answers in the
+
+ align:start position:0%
+is you'll get different answers in the
+ 
+
+ align:start position:0%
+is you'll get different answers in the
+uh in the um image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane yeah of course it says uh the
+
+ align:start position:0%
+plane yeah of course it says uh the
+ 
+
+ align:start position:0%
+plane yeah of course it says uh the
+transparency may be a gray scale uh it
+
+ align:start position:0%
+transparency may be a gray scale uh it
+ 
+
+ align:start position:0%
+transparency may be a gray scale uh it
+doesn't have to be a binary type thing
+
+ align:start position:0%
+doesn't have to be a binary type thing
+ 
+
+ align:start position:0%
+doesn't have to be a binary type thing
+black and white uh or it could even be a
+
+ align:start position:0%
+black and white uh or it could even be a
+ 
+
+ align:start position:0%
+black and white uh or it could even be a
+phase mask it could be that uh that this
+
+ align:start position:0%
+phase mask it could be that uh that this
+ 
+
+ align:start position:0%
+phase mask it could be that uh that this
+is uh changing the phase by let's say uh
+
+ align:start position:0%
+is uh changing the phase by let's say uh
+ 
+
+ align:start position:0%
+is uh changing the phase by let's say uh
+pi by2 relative to this or Pi relative
+
+ align:start position:0%
+pi by2 relative to this or Pi relative
+ 
+
+ align:start position:0%
+pi by2 relative to this or Pi relative
+to this or whatever and you'll get
+
+ align:start position:0%
+to this or whatever and you'll get
+ 
+
+ align:start position:0%
+to this or whatever and you'll get
+you'll get different answers according
+
+ align:start position:0%
+you'll get different answers according
+ 
+
+ align:start position:0%
+you'll get different answers according
+to what you choose obviously for the
+
+ align:start position:0%
+to what you choose obviously for the
+ 
+
+ align:start position:0%
+to what you choose obviously for the
+geometry of this what we call spatial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+filter okay so um yeah so this is going
+
+ align:start position:0%
+filter okay so um yeah so this is going
+ 
+
+ align:start position:0%
+filter okay so um yeah so this is going
+back to this idea of these two ways of
+
+ align:start position:0%
+back to this idea of these two ways of
+ 
+
+ align:start position:0%
+back to this idea of these two ways of
+thinking about the same problem uh so uh
+
+ align:start position:0%
+thinking about the same problem uh so uh
+ 
+
+ align:start position:0%
+thinking about the same problem uh so uh
+this is the first way where we think of
+
+ align:start position:0%
+this is the first way where we think of
+ 
+
+ align:start position:0%
+this is the first way where we think of
+our objects as being made up of lots of
+
+ align:start position:0%
+our objects as being made up of lots of
+ 
+
+ align:start position:0%
+our objects as being made up of lots of
+Point scatterers each of these
+
+ align:start position:0%
+Point scatterers each of these
+ 
+
+ align:start position:0%
+Point scatterers each of these
+scatterers gives way uh gives rise to uh
+
+ align:start position:0%
+scatterers gives way uh gives rise to uh
+ 
+
+ align:start position:0%
+scatterers gives way uh gives rise to uh
+like hyan spherical
+
+ align:start position:0%
+like hyan spherical
+ 
+
+ align:start position:0%
+like hyan spherical
+wavelets uh these are each of these is
+
+ align:start position:0%
+wavelets uh these are each of these is
+ 
+
+ align:start position:0%
+wavelets uh these are each of these is
+collected by a lens uh the lens converts
+
+ align:start position:0%
+collected by a lens uh the lens converts
+ 
+
+ align:start position:0%
+collected by a lens uh the lens converts
+that to a plain
+
+ align:start position:0%
+that to a plain
+ 
+
+ align:start position:0%
+that to a plain
+wave the plain wave reaches the second
+
+ align:start position:0%
+wave the plain wave reaches the second
+ 
+
+ align:start position:0%
+wave the plain wave reaches the second
+lens uh and because it's a plain Wave
+
+ align:start position:0%
+lens uh and because it's a plain Wave
+ 
+
+ align:start position:0%
+lens uh and because it's a plain Wave
+It's converted back to a spherical wave
+
+ align:start position:0%
+It's converted back to a spherical wave
+ 
+
+ align:start position:0%
+It's converted back to a spherical wave
+that converges a distance F uh away from
+
+ align:start position:0%
+that converges a distance F uh away from
+ 
+
+ align:start position:0%
+that converges a distance F uh away from
+that and now uh we've actually
+
+ align:start position:0%
+that and now uh we've actually
+ 
+
+ align:start position:0%
+that and now uh we've actually
+introduced the fact that these FS can be
+
+ align:start position:0%
+introduced the fact that these FS can be
+ 
+
+ align:start position:0%
+introduced the fact that these FS can be
+different so fub1 FS2 fub1 sorry fub1
+
+ align:start position:0%
+different so fub1 FS2 fub1 sorry fub1
+ 
+
+ align:start position:0%
+different so fub1 FS2 fub1 sorry fub1
+F2 this has to be equal to this and this
+
+ align:start position:0%
+F2 this has to be equal to this and this
+ 
+
+ align:start position:0%
+F2 this has to be equal to this and this
+has to be equal to this otherwise the uh
+
+ align:start position:0%
+has to be equal to this otherwise the uh
+ 
+
+ align:start position:0%
+has to be equal to this otherwise the uh
+the phases won't cancel out
+
+ align:start position:0%
+the phases won't cancel out
+ 
+
+ align:start position:0%
+the phases won't cancel out
+properly and um so you can see that what
+
+ align:start position:0%
+properly and um so you can see that what
+ 
+
+ align:start position:0%
+properly and um so you can see that what
+you'd expect then uh is that because in
+
+ align:start position:0%
+you'd expect then uh is that because in
+ 
+
+ align:start position:0%
+you'd expect then uh is that because in
+this diagram here F1 one is bigger than
+
+ align:start position:0%
+this diagram here F1 one is bigger than
+ 
+
+ align:start position:0%
+this diagram here F1 one is bigger than
+F2 this image is actually uh smaller
+
+ align:start position:0%
+F2 this image is actually uh smaller
+ 
+
+ align:start position:0%
+F2 this image is actually uh smaller
+than the original
+
+ align:start position:0%
+than the original
+ 
+
+ align:start position:0%
+than the original
+object uh and and note now you can also
+
+ align:start position:0%
+object uh and and note now you can also
+ 
+
+ align:start position:0%
+object uh and and note now you can also
+see directly the um the geometry showing
+
+ align:start position:0%
+see directly the um the geometry showing
+ 
+
+ align:start position:0%
+see directly the um the geometry showing
+the inversion the point above the axis
+
+ align:start position:0%
+the inversion the point above the axis
+ 
+
+ align:start position:0%
+the inversion the point above the axis
+has come to an image uh below the axis
+
+ align:start position:0%
+has come to an image uh below the axis
+ 
+
+ align:start position:0%
+has come to an image uh below the axis
+here right so that's the one way of
+
+ align:start position:0%
+here right so that's the one way of
+ 
+
+ align:start position:0%
+here right so that's the one way of
+thinking about it uh and and then the
+
+ align:start position:0%
+thinking about it uh and and then the
+ 
+
+ align:start position:0%
+thinking about it uh and and then the
+other way is to think in terms of
+
+ align:start position:0%
+other way is to think in terms of
+ 
+
+ align:start position:0%
+other way is to think in terms of
+spatial frequencies we think of this
+
+ align:start position:0%
+spatial frequencies we think of this
+ 
+
+ align:start position:0%
+spatial frequencies we think of this
+object as being like a grating which is
+
+ align:start position:0%
+object as being like a grating which is
+ 
+
+ align:start position:0%
+object as being like a grating which is
+going to produce grating orders which
+
+ align:start position:0%
+going to produce grating orders which
+ 
+
+ align:start position:0%
+going to produce grating orders which
+travel in different directions each of
+
+ align:start position:0%
+travel in different directions each of
+ 
+
+ align:start position:0%
+travel in different directions each of
+these grating orders is like a a plain
+
+ align:start position:0%
+these grating orders is like a a plain
+ 
+
+ align:start position:0%
+these grating orders is like a a plain
+wave uh and when it reaches the lens
+
+ align:start position:0%
+wave uh and when it reaches the lens
+ 
+
+ align:start position:0%
+wave uh and when it reaches the lens
+it's going to um produce a converging
+
+ align:start position:0%
+it's going to um produce a converging
+ 
+
+ align:start position:0%
+it's going to um produce a converging
+spherical wave which comes to a focus a
+
+ align:start position:0%
+spherical wave which comes to a focus a
+ 
+
+ align:start position:0%
+spherical wave which comes to a focus a
+distance F behind the
+
+ align:start position:0%
+distance F behind the
+ 
+
+ align:start position:0%
+distance F behind the
+lens uh and then after that of course it
+
+ align:start position:0%
+lens uh and then after that of course it
+ 
+
+ align:start position:0%
+lens uh and then after that of course it
+doesn't stop but it Carries On diverges
+
+ align:start position:0%
+doesn't stop but it Carries On diverges
+ 
+
+ align:start position:0%
+doesn't stop but it Carries On diverges
+Again reaches the second lens uh and
+
+ align:start position:0%
+Again reaches the second lens uh and
+ 
+
+ align:start position:0%
+Again reaches the second lens uh and
+then the second lens because this is a
+
+ align:start position:0%
+then the second lens because this is a
+ 
+
+ align:start position:0%
+then the second lens because this is a
+spherical wave coming from a distance
+
+ align:start position:0%
+spherical wave coming from a distance
+ 
+
+ align:start position:0%
+spherical wave coming from a distance
+half away is converted into a plane wave
+
+ align:start position:0%
+half away is converted into a plane wave
+ 
+
+ align:start position:0%
+half away is converted into a plane wave
+again right so again you got this this
+
+ align:start position:0%
+again right so again you got this this
+ 
+
+ align:start position:0%
+again right so again you got this this
+nice symmetry uh between the the what
+
+ align:start position:0%
+nice symmetry uh between the the what
+ 
+
+ align:start position:0%
+nice symmetry uh between the the what
+goes in and what comes out uh so there
+
+ align:start position:0%
+goes in and what comes out uh so there
+ 
+
+ align:start position:0%
+goes in and what comes out uh so there
+are these two different um really
+
+ align:start position:0%
+are these two different um really
+ 
+
+ align:start position:0%
+are these two different um really
+different ways of U thinking about how
+
+ align:start position:0%
+different ways of U thinking about how
+ 
+
+ align:start position:0%
+different ways of U thinking about how
+this is all going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on end of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+show right
+
+ align:start position:0%
+show right
+ 
+
+ align:start position:0%
+show right
+then right okay so so all that was U
+
+ align:start position:0%
+then right okay so so all that was U
+ 
+
+ align:start position:0%
+then right okay so so all that was U
+that was just a warmup uh that was last
+
+ align:start position:0%
+that was just a warmup uh that was last
+ 
+
+ align:start position:0%
+that was just a warmup uh that was last
+week's lecture last Monday's lecture
+
+ align:start position:0%
+week's lecture last Monday's lecture
+ 
+
+ align:start position:0%
+week's lecture last Monday's lecture
+we've done so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right ah oh yeah there LS lots of
+
+ align:start position:0%
+right ah oh yeah there LS lots of
+ 
+
+ align:start position:0%
+right ah oh yeah there LS lots of
+interesting things coming up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later okay uh so we're going to carry on
+
+ align:start position:0%
+later okay uh so we're going to carry on
+ 
+
+ align:start position:0%
+later okay uh so we're going to carry on
+straight away with this more of this 4f
+
+ align:start position:0%
+straight away with this more of this 4f
+ 
+
+ align:start position:0%
+straight away with this more of this 4f
+system and spatial filtering so um we're
+
+ align:start position:0%
+system and spatial filtering so um we're
+ 
+
+ align:start position:0%
+system and spatial filtering so um we're
+just getting stting on this and so
+
+ align:start position:0%
+just getting stting on this and so
+ 
+
+ align:start position:0%
+just getting stting on this and so
+there's lots of very interesting things
+
+ align:start position:0%
+there's lots of very interesting things
+ 
+
+ align:start position:0%
+there's lots of very interesting things
+you can do with these uh so this is back
+
+ align:start position:0%
+you can do with these uh so this is back
+ 
+
+ align:start position:0%
+you can do with these uh so this is back
+to the same thing again Ren showing
+
+ align:start position:0%
+to the same thing again Ren showing
+ 
+
+ align:start position:0%
+to the same thing again Ren showing
+again uh but bit more detailed now
+
+ align:start position:0%
+again uh but bit more detailed now
+ 
+
+ align:start position:0%
+again uh but bit more detailed now
+because we're actually going to really
+
+ align:start position:0%
+because we're actually going to really
+ 
+
+ align:start position:0%
+because we're actually going to really
+uh look in more detail of where these
+
+ align:start position:0%
+uh look in more detail of where these
+ 
+
+ align:start position:0%
+uh look in more detail of where these
+orders are are formed and what you can
+
+ align:start position:0%
+orders are are formed and what you can
+ 
+
+ align:start position:0%
+orders are are formed and what you can
+do with them uh
+
+ align:start position:0%
+do with them uh
+ 
+
+ align:start position:0%
+do with them uh
+so we have a greatting
+
+ align:start position:0%
+so we have a greatting
+ 
+
+ align:start position:0%
+so we have a greatting
+objects uh let's imagine this is just a
+
+ align:start position:0%
+objects uh let's imagine this is just a
+ 
+
+ align:start position:0%
+objects uh let's imagine this is just a
+1 plus a cosine uh which means then it
+
+ align:start position:0%
+1 plus a cosine uh which means then it
+ 
+
+ align:start position:0%
+1 plus a cosine uh which means then it
+produces a zero order and then a plus
+
+ align:start position:0%
+produces a zero order and then a plus
+ 
+
+ align:start position:0%
+produces a zero order and then a plus
+and minus one order uh so three plane
+
+ align:start position:0%
+and minus one order uh so three plane
+ 
+
+ align:start position:0%
+and minus one order uh so three plane
+waves uh and as we said each of those
+
+ align:start position:0%
+waves uh and as we said each of those
+ 
+
+ align:start position:0%
+waves uh and as we said each of those
+plain waves is going to be converted to
+
+ align:start position:0%
+plain waves is going to be converted to
+ 
+
+ align:start position:0%
+plain waves is going to be converted to
+a a converging spherical wave and so in
+
+ align:start position:0%
+a a converging spherical wave and so in
+ 
+
+ align:start position:0%
+a a converging spherical wave and so in
+this back focal plane uh you'll see
+
+ align:start position:0%
+this back focal plane uh you'll see
+ 
+
+ align:start position:0%
+this back focal plane uh you'll see
+three spots corresponding to the three
+
+ align:start position:0%
+three spots corresponding to the three
+ 
+
+ align:start position:0%
+three spots corresponding to the three
+orders uh and uh and then carrying on uh
+
+ align:start position:0%
+orders uh and uh and then carrying on uh
+ 
+
+ align:start position:0%
+orders uh and uh and then carrying on uh
+these plane waves then converted back
+
+ align:start position:0%
+these plane waves then converted back
+ 
+
+ align:start position:0%
+these plane waves then converted back
+into a sperical wave and you get an
+
+ align:start position:0%
+into a sperical wave and you get an
+ 
+
+ align:start position:0%
+into a sperical wave and you get an
+image which is back to the grating again
+
+ align:start position:0%
+image which is back to the grating again
+ 
+
+ align:start position:0%
+image which is back to the grating again
+right so at the moment the optical
+
+ align:start position:0%
+right so at the moment the optical
+ 
+
+ align:start position:0%
+right so at the moment the optical
+system has transmitted all the
+
+ align:start position:0%
+system has transmitted all the
+ 
+
+ align:start position:0%
+system has transmitted all the
+information and so what we would expect
+
+ align:start position:0%
+information and so what we would expect
+ 
+
+ align:start position:0%
+information and so what we would expect
+is that the image uh is exactly the same
+
+ align:start position:0%
+is that the image uh is exactly the same
+ 
+
+ align:start position:0%
+is that the image uh is exactly the same
+as the object apart from the fact it's
+
+ align:start position:0%
+as the object apart from the fact it's
+ 
+
+ align:start position:0%
+as the object apart from the fact it's
+inverted and it might be magnified or or
+
+ align:start position:0%
+inverted and it might be magnified or or
+ 
+
+ align:start position:0%
+inverted and it might be magnified or or
+the opposite uh so but the the
+
+ align:start position:0%
+the opposite uh so but the the
+ 
+
+ align:start position:0%
+the opposite uh so but the the
+resolution you'd expect would be the
+
+ align:start position:0%
+resolution you'd expect would be the
+ 
+
+ align:start position:0%
+resolution you'd expect would be the
+same all the detail in here you'd expect
+
+ align:start position:0%
+same all the detail in here you'd expect
+ 
+
+ align:start position:0%
+same all the detail in here you'd expect
+to see in there right now so the next
+
+ align:start position:0%
+to see in there right now so the next
+ 
+
+ align:start position:0%
+to see in there right now so the next
+thing to look at is what happens if we
+
+ align:start position:0%
+thing to look at is what happens if we
+ 
+
+ align:start position:0%
+thing to look at is what happens if we
+now Place something in this plane that
+
+ align:start position:0%
+now Place something in this plane that
+ 
+
+ align:start position:0%
+now Place something in this plane that
+changes the relative strength of these
+
+ align:start position:0%
+changes the relative strength of these
+ 
+
+ align:start position:0%
+changes the relative strength of these
+different orders and there are lots of
+
+ align:start position:0%
+different orders and there are lots of
+ 
+
+ align:start position:0%
+different orders and there are lots of
+things that we could try uh the first
+
+ align:start position:0%
+things that we could try uh the first
+ 
+
+ align:start position:0%
+things that we could try uh the first
+one the simplest one to look at uh is
+
+ align:start position:0%
+one the simplest one to look at uh is
+ 
+
+ align:start position:0%
+one the simplest one to look at uh is
+what happens if we just put in something
+
+ align:start position:0%
+what happens if we just put in something
+ 
+
+ align:start position:0%
+what happens if we just put in something
+uh a mask here that lets through the
+
+ align:start position:0%
+uh a mask here that lets through the
+ 
+
+ align:start position:0%
+uh a mask here that lets through the
+zero order and not the others the two
+
+ align:start position:0%
+zero order and not the others the two
+ 
+
+ align:start position:0%
+zero order and not the others the two
+two the plus one and the minus one order
+
+ align:start position:0%
+two the plus one and the minus one order
+ 
+
+ align:start position:0%
+two the plus one and the minus one order
+are obstructed by this screen so all we
+
+ align:start position:0%
+are obstructed by this screen so all we
+ 
+
+ align:start position:0%
+are obstructed by this screen so all we
+let through is this single order uh
+
+ align:start position:0%
+let through is this single order uh
+ 
+
+ align:start position:0%
+let through is this single order uh
+which is going to be converted to a
+
+ align:start position:0%
+which is going to be converted to a
+ 
+
+ align:start position:0%
+which is going to be converted to a
+plain wave and so on your screen here
+
+ align:start position:0%
+plain wave and so on your screen here
+ 
+
+ align:start position:0%
+plain wave and so on your screen here
+all you'll see is the plane
+
+ align:start position:0%
+all you'll see is the plane
+ 
+
+ align:start position:0%
+all you'll see is the plane
+wave right so the the image that you see
+
+ align:start position:0%
+wave right so the the image that you see
+ 
+
+ align:start position:0%
+wave right so the the image that you see
+well I called it an image but it's not
+
+ align:start position:0%
+well I called it an image but it's not
+ 
+
+ align:start position:0%
+well I called it an image but it's not
+really much of an image it's completely
+
+ align:start position:0%
+really much of an image it's completely
+ 
+
+ align:start position:0%
+really much of an image it's completely
+featureless it's just like a a a a well
+
+ align:start position:0%
+featureless it's just like a a a a well
+ 
+
+ align:start position:0%
+featureless it's just like a a a a well
+gray spot a gray region there's no
+
+ align:start position:0%
+gray spot a gray region there's no
+ 
+
+ align:start position:0%
+gray spot a gray region there's no
+detail there so we've lost we've lost
+
+ align:start position:0%
+detail there so we've lost we've lost
+ 
+
+ align:start position:0%
+detail there so we've lost we've lost
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+structure uh the structure actually
+
+ align:start position:0%
+structure uh the structure actually
+ 
+
+ align:start position:0%
+structure uh the structure actually
+because we put this mask in here uh the
+
+ align:start position:0%
+because we put this mask in here uh the
+ 
+
+ align:start position:0%
+because we put this mask in here uh the
+structure is Bel is beyond the uh
+
+ align:start position:0%
+structure is Bel is beyond the uh
+ 
+
+ align:start position:0%
+structure is Bel is beyond the uh
+resolution limit of the optical system
+
+ align:start position:0%
+resolution limit of the optical system
+ 
+
+ align:start position:0%
+resolution limit of the optical system
+and so we can't see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay so uh this is what we might call
+
+ align:start position:0%
+it okay so uh this is what we might call
+ 
+
+ align:start position:0%
+it okay so uh this is what we might call
+a low pass filter
+
+ align:start position:0%
+a low pass filter
+ 
+
+ align:start position:0%
+a low pass filter
+uh so if you think of uh these as being
+
+ align:start position:0%
+uh so if you think of uh these as being
+ 
+
+ align:start position:0%
+uh so if you think of uh these as being
+like these grating orders basically
+
+ align:start position:0%
+like these grating orders basically
+ 
+
+ align:start position:0%
+like these grating orders basically
+represent different spatial frequencies
+
+ align:start position:0%
+represent different spatial frequencies
+ 
+
+ align:start position:0%
+represent different spatial frequencies
+so just in analogy with what you have in
+
+ align:start position:0%
+so just in analogy with what you have in
+ 
+
+ align:start position:0%
+so just in analogy with what you have in
+electricity uh where you've got
+
+ align:start position:0%
+electricity uh where you've got
+ 
+
+ align:start position:0%
+electricity uh where you've got
+frequencies and time uh in space we
+
+ align:start position:0%
+frequencies and time uh in space we
+ 
+
+ align:start position:0%
+frequencies and time uh in space we
+think of uh we we've got distance and
+
+ align:start position:0%
+think of uh we we've got distance and
+ 
+
+ align:start position:0%
+think of uh we we've got distance and
+we've got spatial frequencies so this is
+
+ align:start position:0%
+we've got spatial frequencies so this is
+ 
+
+ align:start position:0%
+we've got spatial frequencies so this is
+why we we could talk about uh low pass
+
+ align:start position:0%
+why we we could talk about uh low pass
+ 
+
+ align:start position:0%
+why we we could talk about uh low pass
+filtering uh we're filtering the spatial
+
+ align:start position:0%
+filtering uh we're filtering the spatial
+ 
+
+ align:start position:0%
+filtering uh we're filtering the spatial
+frequencies and just like in in uh in in
+
+ align:start position:0%
+frequencies and just like in in uh in in
+ 
+
+ align:start position:0%
+frequencies and just like in in uh in in
+time you remember when you when you got
+
+ align:start position:0%
+time you remember when you when you got
+ 
+
+ align:start position:0%
+time you remember when you when you got
+your your Hi-Fi system if you turn turn
+
+ align:start position:0%
+your your Hi-Fi system if you turn turn
+ 
+
+ align:start position:0%
+your your Hi-Fi system if you turn turn
+down the
+
+ align:start position:0%
+down the
+ 
+
+ align:start position:0%
+down the
+treble that's acting like a a low pass
+
+ align:start position:0%
+treble that's acting like a a low pass
+ 
+
+ align:start position:0%
+treble that's acting like a a low pass
+filter it's it's cutting out the high
+
+ align:start position:0%
+filter it's it's cutting out the high
+ 
+
+ align:start position:0%
+filter it's it's cutting out the high
+frequency sound and letting through the
+
+ align:start position:0%
+frequency sound and letting through the
+ 
+
+ align:start position:0%
+frequency sound and letting through the
+low frequency sound only isn't it so
+
+ align:start position:0%
+low frequency sound only isn't it so
+ 
+
+ align:start position:0%
+low frequency sound only isn't it so
+that's what we call a low pass filter uh
+
+ align:start position:0%
+that's what we call a low pass filter uh
+ 
+
+ align:start position:0%
+that's what we call a low pass filter uh
+and this is exactly the same we put in
+
+ align:start position:0%
+and this is exactly the same we put in
+ 
+
+ align:start position:0%
+and this is exactly the same we put in
+The Mask uh it's a bit different in a
+
+ align:start position:0%
+The Mask uh it's a bit different in a
+ 
+
+ align:start position:0%
+The Mask uh it's a bit different in a
+way uh from the electronic case because
+
+ align:start position:0%
+way uh from the electronic case because
+ 
+
+ align:start position:0%
+way uh from the electronic case because
+in Optics we've got a lot more freedom
+
+ align:start position:0%
+in Optics we've got a lot more freedom
+ 
+
+ align:start position:0%
+in Optics we've got a lot more freedom
+as to what we can do uh we can actually
+
+ align:start position:0%
+as to what we can do uh we can actually
+ 
+
+ align:start position:0%
+as to what we can do uh we can actually
+put in something here which has got real
+
+ align:start position:0%
+put in something here which has got real
+ 
+
+ align:start position:0%
+put in something here which has got real
+sharp edges to it uh in in electronics
+
+ align:start position:0%
+sharp edges to it uh in in electronics
+ 
+
+ align:start position:0%
+sharp edges to it uh in in electronics
+if you try to make a filter uh there's
+
+ align:start position:0%
+if you try to make a filter uh there's
+ 
+
+ align:start position:0%
+if you try to make a filter uh there's
+there's always a limit to how much you
+
+ align:start position:0%
+there's always a limit to how much you
+ 
+
+ align:start position:0%
+there's always a limit to how much you
+can uh make the roll off of the filter
+
+ align:start position:0%
+can uh make the roll off of the filter
+ 
+
+ align:start position:0%
+can uh make the roll off of the filter
+all right so you can't get something
+
+ align:start position:0%
+all right so you can't get something
+ 
+
+ align:start position:0%
+all right so you can't get something
+that suddenly cuts off like that very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+easily okay so this is going through the
+
+ align:start position:0%
+easily okay so this is going through the
+ 
+
+ align:start position:0%
+easily okay so this is going through the
+math of this uh our original
+
+ align:start position:0%
+math of this uh our original
+ 
+
+ align:start position:0%
+math of this uh our original
+transparency then is a 1 plus
+
+ align:start position:0%
+transparency then is a 1 plus
+ 
+
+ align:start position:0%
+transparency then is a 1 plus
+cosine uh and the 1 plus cosine uh we F
+
+ align:start position:0%
+cosine uh and the 1 plus cosine uh we F
+ 
+
+ align:start position:0%
+cosine uh and the 1 plus cosine uh we F
+transform that to find the what we call
+
+ align:start position:0%
+transform that to find the what we call
+ 
+
+ align:start position:0%
+transform that to find the what we call
+the object
+
+ align:start position:0%
+the object
+ 
+
+ align:start position:0%
+the object
+Spectrum uh and um so in this case
+
+ align:start position:0%
+Spectrum uh and um so in this case
+ 
+
+ align:start position:0%
+Spectrum uh and um so in this case
+finding the fer transform of cosine is
+
+ align:start position:0%
+finding the fer transform of cosine is
+ 
+
+ align:start position:0%
+finding the fer transform of cosine is
+very straightforward because we just
+
+ align:start position:0%
+very straightforward because we just
+ 
+
+ align:start position:0%
+very straightforward because we just
+expand cosine as e to the I something
+
+ align:start position:0%
+expand cosine as e to the I something
+ 
+
+ align:start position:0%
+expand cosine as e to the I something
+plus e to Theus SI something over two uh
+
+ align:start position:0%
+plus e to Theus SI something over two uh
+ 
+
+ align:start position:0%
+plus e to Theus SI something over two uh
+and each of those e to the I type terms
+
+ align:start position:0%
+and each of those e to the I type terms
+ 
+
+ align:start position:0%
+and each of those e to the I type terms
+uh will correspond to a single uh
+
+ align:start position:0%
+uh will correspond to a single uh
+ 
+
+ align:start position:0%
+uh will correspond to a single uh
+frequency right so we can end up now
+
+ align:start position:0%
+frequency right so we can end up now
+ 
+
+ align:start position:0%
+frequency right so we can end up now
+with three terms at different
+
+ align:start position:0%
+with three terms at different
+ 
+
+ align:start position:0%
+with three terms at different
+frequencies the one for transforms to a
+
+ align:start position:0%
+frequencies the one for transforms to a
+ 
+
+ align:start position:0%
+frequencies the one for transforms to a
+Delta function of U which is a spike
+
+ align:start position:0%
+Delta function of U which is a spike
+ 
+
+ align:start position:0%
+Delta function of U which is a spike
+where U equals zero uh and the two
+
+ align:start position:0%
+where U equals zero uh and the two
+ 
+
+ align:start position:0%
+where U equals zero uh and the two
+components of the cosine correspond to
+
+ align:start position:0%
+components of the cosine correspond to
+ 
+
+ align:start position:0%
+components of the cosine correspond to
+another two uh another two Delta
+
+ align:start position:0%
+another two uh another two Delta
+ 
+
+ align:start position:0%
+another two uh another two Delta
+functions uh each
+
+ align:start position:0%
+functions uh each
+ 
+
+ align:start position:0%
+functions uh each
+situated this one's at at U equals some
+
+ align:start position:0%
+situated this one's at at U equals some
+ 
+
+ align:start position:0%
+situated this one's at at U equals some
+value u u and this one is some value U
+
+ align:start position:0%
+value u u and this one is some value U
+ 
+
+ align:start position:0%
+value u u and this one is some value U
+equals minus U right so you've got these
+
+ align:start position:0%
+equals minus U right so you've got these
+ 
+
+ align:start position:0%
+equals minus U right so you've got these
+three three spikes that we've been
+
+ align:start position:0%
+three three spikes that we've been
+ 
+
+ align:start position:0%
+three three spikes that we've been
+talking about uh for the last few slides
+
+ align:start position:0%
+talking about uh for the last few slides
+ 
+
+ align:start position:0%
+talking about uh for the last few slides
+now uh so this is the uh this is the the
+
+ align:start position:0%
+now uh so this is the uh this is the the
+ 
+
+ align:start position:0%
+now uh so this is the uh this is the the
+object Spectrum it's the angular
+
+ align:start position:0%
+object Spectrum it's the angular
+ 
+
+ align:start position:0%
+object Spectrum it's the angular
+Spectrum uh that we've got here so
+
+ align:start position:0%
+Spectrum uh that we've got here so
+ 
+
+ align:start position:0%
+Spectrum uh that we've got here so
+actually you can see that you here it
+
+ align:start position:0%
+actually you can see that you here it
+ 
+
+ align:start position:0%
+actually you can see that you here it
+basically represents the angle that
+
+ align:start position:0%
+basically represents the angle that
+ 
+
+ align:start position:0%
+basically represents the angle that
+these uh these plane waves are traveling
+
+ align:start position:0%
+these uh these plane waves are traveling
+ 
+
+ align:start position:0%
+these uh these plane waves are traveling
+in and there's three different angles
+
+ align:start position:0%
+in and there's three different angles
+ 
+
+ align:start position:0%
+in and there's three different angles
+that that the light can travel
+
+ align:start position:0%
+that that the light can travel
+ 
+
+ align:start position:0%
+that that the light can travel
+in uh and uh
+
+ align:start position:0%
+in uh and uh
+ 
+
+ align:start position:0%
+in uh and uh
+so um yeah so that will propagate then
+
+ align:start position:0%
+so um yeah so that will propagate then
+ 
+
+ align:start position:0%
+so um yeah so that will propagate then
+uh and uh so what as we've said before
+
+ align:start position:0%
+uh and uh so what as we've said before
+ 
+
+ align:start position:0%
+uh and uh so what as we've said before
+you can see that uh these these rays are
+
+ align:start position:0%
+you can see that uh these these rays are
+ 
+
+ align:start position:0%
+you can see that uh these these rays are
+moving at an angle uh and so uh as you
+
+ align:start position:0%
+moving at an angle uh and so uh as you
+ 
+
+ align:start position:0%
+moving at an angle uh and so uh as you
+trans as you go along a distance F uh
+
+ align:start position:0%
+trans as you go along a distance F uh
+ 
+
+ align:start position:0%
+trans as you go along a distance F uh
+you get a shift in the X position which
+
+ align:start position:0%
+you get a shift in the X position which
+ 
+
+ align:start position:0%
+you get a shift in the X position which
+is given by of course the this the slope
+
+ align:start position:0%
+is given by of course the this the slope
+ 
+
+ align:start position:0%
+is given by of course the this the slope
+of this the more the slope the more it
+
+ align:start position:0%
+of this the more the slope the more it
+ 
+
+ align:start position:0%
+of this the more the slope the more it
+deflects uh by the time you travel a
+
+ align:start position:0%
+deflects uh by the time you travel a
+ 
+
+ align:start position:0%
+deflects uh by the time you travel a
+distance F so this then gives the shifts
+
+ align:start position:0%
+distance F so this then gives the shifts
+ 
+
+ align:start position:0%
+distance F so this then gives the shifts
+of these two things so that's before the
+
+ align:start position:0%
+of these two things so that's before the
+ 
+
+ align:start position:0%
+of these two things so that's before the
+screen uh then then um sorry before the
+
+ align:start position:0%
+screen uh then then um sorry before the
+ 
+
+ align:start position:0%
+screen uh then then um sorry before the
+mask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happened did anything happen
+
+ align:start position:0%
+what happened did anything happen
+ 
+
+ align:start position:0%
+what happened did anything happen
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry nothing
+
+ align:start position:0%
+sorry nothing
+ 
+
+ align:start position:0%
+sorry nothing
+happening oh something happened then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we ah okay right so yeah so this is
+
+ align:start position:0%
+we ah okay right so yeah so this is
+ 
+
+ align:start position:0%
+we ah okay right so yeah so this is
+showing then uh so these Rays then uh as
+
+ align:start position:0%
+showing then uh so these Rays then uh as
+ 
+
+ align:start position:0%
+showing then uh so these Rays then uh as
+they come down here um we put in this
+
+ align:start position:0%
+they come down here um we put in this
+ 
+
+ align:start position:0%
+they come down here um we put in this
+pupil mask which is going to get rid of
+
+ align:start position:0%
+pupil mask which is going to get rid of
+ 
+
+ align:start position:0%
+pupil mask which is going to get rid of
+these two and it just leaves the other
+
+ align:start position:0%
+these two and it just leaves the other
+ 
+
+ align:start position:0%
+these two and it just leaves the other
+one so we just left them with our single
+
+ align:start position:0%
+one so we just left them with our single
+ 
+
+ align:start position:0%
+one so we just left them with our single
+um beam uh which um as we said said
+
+ align:start position:0%
+um beam uh which um as we said said
+ 
+
+ align:start position:0%
+um beam uh which um as we said said
+before gives an image which is not
+
+ align:start position:0%
+before gives an image which is not
+ 
+
+ align:start position:0%
+before gives an image which is not
+really an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+image right yeah so after the pupil mask
+
+ align:start position:0%
+image right yeah so after the pupil mask
+ 
+
+ align:start position:0%
+image right yeah so after the pupil mask
+uh we multiply by The Mask gets rid of
+
+ align:start position:0%
+uh we multiply by The Mask gets rid of
+ 
+
+ align:start position:0%
+uh we multiply by The Mask gets rid of
+those two just leaves the other one uh
+
+ align:start position:0%
+those two just leaves the other one uh
+ 
+
+ align:start position:0%
+those two just leaves the other one uh
+and then finally then um the final image
+
+ align:start position:0%
+and then finally then um the final image
+ 
+
+ align:start position:0%
+and then finally then um the final image
+you you'll see is going to be the fua
+
+ align:start position:0%
+you you'll see is going to be the fua
+ 
+
+ align:start position:0%
+you you'll see is going to be the fua
+transform of that uh and the fer
+
+ align:start position:0%
+transform of that uh and the fer
+ 
+
+ align:start position:0%
+transform of that uh and the fer
+transform of a Delta function is a
+
+ align:start position:0%
+transform of a Delta function is a
+ 
+
+ align:start position:0%
+transform of a Delta function is a
+constant uh and so you see something
+
+ align:start position:0%
+constant uh and so you see something
+ 
+
+ align:start position:0%
+constant uh and so you see something
+which has got no no detail in it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um this gives another example
+
+ align:start position:0%
+okay so um this gives another example
+ 
+
+ align:start position:0%
+okay so um this gives another example
+then uh of um here we're looking at some
+
+ align:start position:0%
+then uh of um here we're looking at some
+ 
+
+ align:start position:0%
+then uh of um here we're looking at some
+a binary amplitude grating so this is a
+
+ align:start position:0%
+a binary amplitude grating so this is a
+ 
+
+ align:start position:0%
+a binary amplitude grating so this is a
+particular example um another example so
+
+ align:start position:0%
+particular example um another example so
+ 
+
+ align:start position:0%
+particular example um another example so
+last time we looked at the cosine type
+
+ align:start position:0%
+last time we looked at the cosine type
+ 
+
+ align:start position:0%
+last time we looked at the cosine type
+thing so this one is now a binary
+
+ align:start position:0%
+thing so this one is now a binary
+ 
+
+ align:start position:0%
+thing so this one is now a binary
+grating which means that the object is
+
+ align:start position:0%
+grating which means that the object is
+ 
+
+ align:start position:0%
+grating which means that the object is
+something which is either black or
+
+ align:start position:0%
+something which is either black or
+ 
+
+ align:start position:0%
+something which is either black or
+white and we shine light onto this so uh
+
+ align:start position:0%
+white and we shine light onto this so uh
+ 
+
+ align:start position:0%
+white and we shine light onto this so uh
+it's like a square wave grating uh and
+
+ align:start position:0%
+it's like a square wave grating uh and
+ 
+
+ align:start position:0%
+it's like a square wave grating uh and
+uh so unlike the previous case where
+
+ align:start position:0%
+uh so unlike the previous case where
+ 
+
+ align:start position:0%
+uh so unlike the previous case where
+coign of course just produced those
+
+ align:start position:0%
+coign of course just produced those
+ 
+
+ align:start position:0%
+coign of course just produced those
+three three grating components uh in
+
+ align:start position:0%
+three three grating components uh in
+ 
+
+ align:start position:0%
+three three grating components uh in
+this case there's going to be a whole
+
+ align:start position:0%
+this case there's going to be a whole
+ 
+
+ align:start position:0%
+this case there's going to be a whole
+load of grating components they're going
+
+ align:start position:0%
+load of grating components they're going
+ 
+
+ align:start position:0%
+load of grating components they're going
+to go on forever uh and but they get
+
+ align:start position:0%
+to go on forever uh and but they get
+ 
+
+ align:start position:0%
+to go on forever uh and but they get
+weaker and weaker uh and uh so you can
+
+ align:start position:0%
+weaker and weaker uh and uh so you can
+ 
+
+ align:start position:0%
+weaker and weaker uh and uh so you can
+see here it shows a few of them uh the
+
+ align:start position:0%
+see here it shows a few of them uh the
+ 
+
+ align:start position:0%
+see here it shows a few of them uh the
+first the second so there'll be the
+
+ align:start position:0%
+first the second so there'll be the
+ 
+
+ align:start position:0%
+first the second so there'll be the
+third the fourth and so on and then
+
+ align:start position:0%
+third the fourth and so on and then
+ 
+
+ align:start position:0%
+third the fourth and so on and then
+minus one and so on and so on and each
+
+ align:start position:0%
+minus one and so on and so on and each
+ 
+
+ align:start position:0%
+minus one and so on and so on and each
+of these is moving at a different angle
+
+ align:start position:0%
+of these is moving at a different angle
+ 
+
+ align:start position:0%
+of these is moving at a different angle
+uh so when when the plane wave gets to
+
+ align:start position:0%
+uh so when when the plane wave gets to
+ 
+
+ align:start position:0%
+uh so when when the plane wave gets to
+the pupil mask uh it's sorry when the uh
+
+ align:start position:0%
+the pupil mask uh it's sorry when the uh
+ 
+
+ align:start position:0%
+the pupil mask uh it's sorry when the uh
+the plane wave is focused to the pupil
+
+ align:start position:0%
+the plane wave is focused to the pupil
+ 
+
+ align:start position:0%
+the plane wave is focused to the pupil
+mask it's going to reach there at a
+
+ align:start position:0%
+mask it's going to reach there at a
+ 
+
+ align:start position:0%
+mask it's going to reach there at a
+point the distance from the axis of
+
+ align:start position:0%
+point the distance from the axis of
+ 
+
+ align:start position:0%
+point the distance from the axis of
+course is going to depend on the angle
+
+ align:start position:0%
+course is going to depend on the angle
+ 
+
+ align:start position:0%
+course is going to depend on the angle
+of this uh uh plane wave component the
+
+ align:start position:0%
+of this uh uh plane wave component the
+ 
+
+ align:start position:0%
+of this uh uh plane wave component the
+gracing component right so
+
+ align:start position:0%
+gracing component right so
+ 
+
+ align:start position:0%
+gracing component right so
+so if you look here you're going to see
+
+ align:start position:0%
+so if you look here you're going to see
+ 
+
+ align:start position:0%
+so if you look here you're going to see
+all these different grating orders all
+
+ align:start position:0%
+all these different grating orders all
+ 
+
+ align:start position:0%
+all these different grating orders all
+arrayed in this position here uh and uh
+
+ align:start position:0%
+arrayed in this position here uh and uh
+ 
+
+ align:start position:0%
+arrayed in this position here uh and uh
+so uh by putting some sort of uh phase
+
+ align:start position:0%
+so uh by putting some sort of uh phase
+ 
+
+ align:start position:0%
+so uh by putting some sort of uh phase
+or all sort of mask here we can monitor
+
+ align:start position:0%
+or all sort of mask here we can monitor
+ 
+
+ align:start position:0%
+or all sort of mask here we can monitor
+and change uh the relative strength or
+
+ align:start position:0%
+and change uh the relative strength or
+ 
+
+ align:start position:0%
+and change uh the relative strength or
+phase or whatever we like of those
+
+ align:start position:0%
+phase or whatever we like of those
+ 
+
+ align:start position:0%
+phase or whatever we like of those
+different components and then they'll be
+
+ align:start position:0%
+different components and then they'll be
+ 
+
+ align:start position:0%
+different components and then they'll be
+added together and produce some nice
+
+ align:start position:0%
+added together and produce some nice
+ 
+
+ align:start position:0%
+added together and produce some nice
+effect uh that we might want to look at
+
+ align:start position:0%
+effect uh that we might want to look at
+ 
+
+ align:start position:0%
+effect uh that we might want to look at
+so uh let's see uh what we're going to
+
+ align:start position:0%
+so uh let's see uh what we're going to
+ 
+
+ align:start position:0%
+so uh let's see uh what we're going to
+get in this case so in this particular
+
+ align:start position:0%
+get in this case so in this particular
+ 
+
+ align:start position:0%
+get in this case so in this particular
+case in the picture uh the size of this
+
+ align:start position:0%
+case in the picture uh the size of this
+ 
+
+ align:start position:0%
+case in the picture uh the size of this
+aperture is enough to let through the
+
+ align:start position:0%
+aperture is enough to let through the
+ 
+
+ align:start position:0%
+aperture is enough to let through the
+central three components the zero order
+
+ align:start position:0%
+central three components the zero order
+ 
+
+ align:start position:0%
+central three components the zero order
+and the plus and minus one
+
+ align:start position:0%
+and the plus and minus one
+ 
+
+ align:start position:0%
+and the plus and minus one
+order uh but it's stopped all the other
+
+ align:start position:0%
+order uh but it's stopped all the other
+ 
+
+ align:start position:0%
+order uh but it's stopped all the other
+ones right so what you'll see here is
+
+ align:start position:0%
+ones right so what you'll see here is
+ 
+
+ align:start position:0%
+ones right so what you'll see here is
+the fer transform of this uh We've
+
+ align:start position:0%
+the fer transform of this uh We've
+ 
+
+ align:start position:0%
+the fer transform of this uh We've
+before it's the three it's these three
+
+ align:start position:0%
+before it's the three it's these three
+ 
+
+ align:start position:0%
+before it's the three it's these three
+spikes again the fer transform of the
+
+ align:start position:0%
+spikes again the fer transform of the
+ 
+
+ align:start position:0%
+spikes again the fer transform of the
+three spikes is just uh a a one plus a
+
+ align:start position:0%
+three spikes is just uh a a one plus a
+ 
+
+ align:start position:0%
+three spikes is just uh a a one plus a
+cosine the relative strengths of these
+
+ align:start position:0%
+cosine the relative strengths of these
+ 
+
+ align:start position:0%
+cosine the relative strengths of these
+might change according to uh the
+
+ align:start position:0%
+might change according to uh the
+ 
+
+ align:start position:0%
+might change according to uh the
+properties of these uh uh of the
+
+ align:start position:0%
+properties of these uh uh of the
+ 
+
+ align:start position:0%
+properties of these uh uh of the
+transmission of the Mask uh but anyway
+
+ align:start position:0%
+transmission of the Mask uh but anyway
+ 
+
+ align:start position:0%
+transmission of the Mask uh but anyway
+so what you see finally uh is uh an
+
+ align:start position:0%
+so what you see finally uh is uh an
+ 
+
+ align:start position:0%
+so what you see finally uh is uh an
+object which is like a uh you see the 1
+
+ align:start position:0%
+object which is like a uh you see the 1
+ 
+
+ align:start position:0%
+object which is like a uh you see the 1
+plus cosine type uh variation in
+
+ align:start position:0%
+plus cosine type uh variation in
+ 
+
+ align:start position:0%
+plus cosine type uh variation in
+amplitude
+
+ align:start position:0%
+amplitude
+ 
+
+ align:start position:0%
+amplitude
+and uh so you notice that this thing
+
+ align:start position:0%
+and uh so you notice that this thing
+ 
+
+ align:start position:0%
+and uh so you notice that this thing
+here started with these um very Square
+
+ align:start position:0%
+here started with these um very Square
+ 
+
+ align:start position:0%
+here started with these um very Square
+edges we no longer see the very Square
+
+ align:start position:0%
+edges we no longer see the very Square
+ 
+
+ align:start position:0%
+edges we no longer see the very Square
+edges so this is an example of how we've
+
+ align:start position:0%
+edges so this is an example of how we've
+ 
+
+ align:start position:0%
+edges so this is an example of how we've
+um lost resolution the optical system
+
+ align:start position:0%
+um lost resolution the optical system
+ 
+
+ align:start position:0%
+um lost resolution the optical system
+has got a certain finite resolution
+
+ align:start position:0%
+has got a certain finite resolution
+ 
+
+ align:start position:0%
+has got a certain finite resolution
+there's detail uh in this original
+
+ align:start position:0%
+there's detail uh in this original
+ 
+
+ align:start position:0%
+there's detail uh in this original
+object that we can't actually see in the
+
+ align:start position:0%
+object that we can't actually see in the
+ 
+
+ align:start position:0%
+object that we can't actually see in the
+final image and this is because not all
+
+ align:start position:0%
+final image and this is because not all
+ 
+
+ align:start position:0%
+final image and this is because not all
+the light has got through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system okay so we're going to look at a
+
+ align:start position:0%
+system okay so we're going to look at a
+ 
+
+ align:start position:0%
+system okay so we're going to look at a
+particular uh case now uh this is the
+
+ align:start position:0%
+particular uh case now uh this is the
+ 
+
+ align:start position:0%
+particular uh case now uh this is the
+bit I was saying I wasn't very keen on
+
+ align:start position:0%
+bit I was saying I wasn't very keen on
+ 
+
+ align:start position:0%
+bit I was saying I wasn't very keen on
+uh no no it's all right uh but anyway
+
+ align:start position:0%
+uh no no it's all right uh but anyway
+ 
+
+ align:start position:0%
+uh no no it's all right uh but anyway
+there's a load of U maths here uh which
+
+ align:start position:0%
+there's a load of U maths here uh which
+ 
+
+ align:start position:0%
+there's a load of U maths here uh which
+I might uh actually gloss over a bit and
+
+ align:start position:0%
+I might uh actually gloss over a bit and
+ 
+
+ align:start position:0%
+I might uh actually gloss over a bit and
+let you look at it yourself later uh but
+
+ align:start position:0%
+let you look at it yourself later uh but
+ 
+
+ align:start position:0%
+let you look at it yourself later uh but
+basically then we're looking at a
+
+ align:start position:0%
+basically then we're looking at a
+ 
+
+ align:start position:0%
+basically then we're looking at a
+particular example uh the the it's a
+
+ align:start position:0%
+particular example uh the the it's a
+ 
+
+ align:start position:0%
+particular example uh the the it's a
+binary grating with perfect contrast m
+
+ align:start position:0%
+binary grating with perfect contrast m
+ 
+
+ align:start position:0%
+binary grating with perfect contrast m
+equal 1 I.E this goes from black to
+
+ align:start position:0%
+equal 1 I.E this goes from black to
+ 
+
+ align:start position:0%
+equal 1 I.E this goes from black to
+white that's what that means it's got a
+
+ align:start position:0%
+white that's what that means it's got a
+ 
+
+ align:start position:0%
+white that's what that means it's got a
+period of 10 microns right the spacing
+
+ align:start position:0%
+period of 10 microns right the spacing
+ 
+
+ align:start position:0%
+period of 10 microns right the spacing
+that the period is the distance between
+
+ align:start position:0%
+that the period is the distance between
+ 
+
+ align:start position:0%
+that the period is the distance between
+the repeat on this this
+
+ align:start position:0%
+the repeat on this this
+ 
+
+ align:start position:0%
+the repeat on this this
+grating uh and it's got a duty cycle of
+
+ align:start position:0%
+grating uh and it's got a duty cycle of
+ 
+
+ align:start position:0%
+grating uh and it's got a duty cycle of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+third uh which means that the the um the
+
+ align:start position:0%
+third uh which means that the the um the
+ 
+
+ align:start position:0%
+third uh which means that the the um the
+white bit is a third of the black bits
+
+ align:start position:0%
+white bit is a third of the black bits
+ 
+
+ align:start position:0%
+white bit is a third of the black bits
+is that what that means a third of the
+
+ align:start position:0%
+is that what that means a third of the
+ 
+
+ align:start position:0%
+is that what that means a third of the
+whole yeah a third of the
+
+ align:start position:0%
+whole yeah a third of the
+ 
+
+ align:start position:0%
+whole yeah a third of the
+period uh
+
+ align:start position:0%
+period uh
+ 
+
+ align:start position:0%
+period uh
+okay uh and and then we're also told
+
+ align:start position:0%
+okay uh and and then we're also told
+ 
+
+ align:start position:0%
+okay uh and and then we're also told
+that the 4f system consists of two
+
+ align:start position:0%
+that the 4f system consists of two
+ 
+
+ align:start position:0%
+that the 4f system consists of two
+identical lenses of focal length FAL 20
+
+ align:start position:0%
+identical lenses of focal length FAL 20
+ 
+
+ align:start position:0%
+identical lenses of focal length FAL 20
+cm so both F1 and F2 are 20 cm uh and we
+
+ align:start position:0%
+cm so both F1 and F2 are 20 cm uh and we
+ 
+
+ align:start position:0%
+cm so both F1 and F2 are 20 cm uh and we
+put a pupil mask of diameter 3 cm
+
+ align:start position:0%
+put a pupil mask of diameter 3 cm
+ 
+
+ align:start position:0%
+put a pupil mask of diameter 3 cm
+here at the at the fer plane what is the
+
+ align:start position:0%
+here at the at the fer plane what is the
+ 
+
+ align:start position:0%
+here at the at the fer plane what is the
+intensity observed at the output image
+
+ align:start position:0%
+intensity observed at the output image
+ 
+
+ align:start position:0%
+intensity observed at the output image
+plane so that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question okay the sequence to solve this
+
+ align:start position:0%
+question okay the sequence to solve this
+ 
+
+ align:start position:0%
+question okay the sequence to solve this
+kind of problem uh what you got to do is
+
+ align:start position:0%
+kind of problem uh what you got to do is
+ 
+
+ align:start position:0%
+kind of problem uh what you got to do is
+to work out what you're going to get in
+
+ align:start position:0%
+to work out what you're going to get in
+ 
+
+ align:start position:0%
+to work out what you're going to get in
+this plane which is basically the for a
+
+ align:start position:0%
+this plane which is basically the for a
+ 
+
+ align:start position:0%
+this plane which is basically the for a
+transform of this uh and then you're
+
+ align:start position:0%
+transform of this uh and then you're
+ 
+
+ align:start position:0%
+transform of this uh and then you're
+going to have to
+
+ align:start position:0%
+going to have to
+ 
+
+ align:start position:0%
+going to have to
+uh multiply by the mask and see which of
+
+ align:start position:0%
+uh multiply by the mask and see which of
+ 
+
+ align:start position:0%
+uh multiply by the mask and see which of
+those orders get through right so the
+
+ align:start position:0%
+those orders get through right so the
+ 
+
+ align:start position:0%
+those orders get through right so the
+relative scaling of this defraction
+
+ align:start position:0%
+relative scaling of this defraction
+ 
+
+ align:start position:0%
+relative scaling of this defraction
+pattern and the mass uh is obviously all
+
+ align:start position:0%
+pattern and the mass uh is obviously all
+ 
+
+ align:start position:0%
+pattern and the mass uh is obviously all
+important for that if you don't get that
+
+ align:start position:0%
+important for that if you don't get that
+ 
+
+ align:start position:0%
+important for that if you don't get that
+right uh then you'll get the wrong
+
+ align:start position:0%
+right uh then you'll get the wrong
+ 
+
+ align:start position:0%
+right uh then you'll get the wrong
+answer obviously because uh you you you
+
+ align:start position:0%
+answer obviously because uh you you you
+ 
+
+ align:start position:0%
+answer obviously because uh you you you
+you'll you you might get orders getting
+
+ align:start position:0%
+you'll you you might get orders getting
+ 
+
+ align:start position:0%
+you'll you you might get orders getting
+through that shouldn't or the other way
+
+ align:start position:0%
+through that shouldn't or the other way
+ 
+
+ align:start position:0%
+through that shouldn't or the other way
+around uh and
+
+ align:start position:0%
+around uh and
+ 
+
+ align:start position:0%
+around uh and
+um so once we've done that we know now
+
+ align:start position:0%
+um so once we've done that we know now
+ 
+
+ align:start position:0%
+um so once we've done that we know now
+what the um grating orders the the the
+
+ align:start position:0%
+what the um grating orders the the the
+ 
+
+ align:start position:0%
+what the um grating orders the the the
+the fer components in the final image
+
+ align:start position:0%
+the fer components in the final image
+ 
+
+ align:start position:0%
+the fer components in the final image
+are going to be and we then do another
+
+ align:start position:0%
+are going to be and we then do another
+ 
+
+ align:start position:0%
+are going to be and we then do another
+forer transform and we got the image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amplitude there we are right again we
+
+ align:start position:0%
+amplitude there we are right again we
+ 
+
+ align:start position:0%
+amplitude there we are right again we
+got to do scaling to get it to the right
+
+ align:start position:0%
+got to do scaling to get it to the right
+ 
+
+ align:start position:0%
+got to do scaling to get it to the right
+size normally of course at the very end
+
+ align:start position:0%
+size normally of course at the very end
+ 
+
+ align:start position:0%
+size normally of course at the very end
+we would be interested in intensity not
+
+ align:start position:0%
+we would be interested in intensity not
+ 
+
+ align:start position:0%
+we would be interested in intensity not
+amplitude as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay so this is our example low
+
+ align:start position:0%
+well okay so this is our example low
+ 
+
+ align:start position:0%
+well okay so this is our example low
+pass filtering a binary amplitude
+
+ align:start position:0%
+pass filtering a binary amplitude
+ 
+
+ align:start position:0%
+pass filtering a binary amplitude
+grating uh so this is this grating as
+
+ align:start position:0%
+grating uh so this is this grating as
+ 
+
+ align:start position:0%
+grating uh so this is this grating as
+we've
+
+ align:start position:0%
+we've
+ 
+
+ align:start position:0%
+we've
+chosen uh and um so you can see here's
+
+ align:start position:0%
+chosen uh and um so you can see here's
+ 
+
+ align:start position:0%
+chosen uh and um so you can see here's
+the dimensions in in
+
+ align:start position:0%
+the dimensions in in
+ 
+
+ align:start position:0%
+the dimensions in in
+microns uh so uh this is quite a fine
+
+ align:start position:0%
+microns uh so uh this is quite a fine
+ 
+
+ align:start position:0%
+microns uh so uh this is quite a fine
+grating
+
+ align:start position:0%
+grating
+ 
+
+ align:start position:0%
+grating
+so uh you can see that it's not
+
+ align:start position:0%
+so uh you can see that it's not
+ 
+
+ align:start position:0%
+so uh you can see that it's not
+symmetrical by the way the um the um dut
+
+ align:start position:0%
+symmetrical by the way the um the um dut
+ 
+
+ align:start position:0%
+symmetrical by the way the um the um dut
+duty cycle is not a half right so the
+
+ align:start position:0%
+duty cycle is not a half right so the
+ 
+
+ align:start position:0%
+duty cycle is not a half right so the
+the width of the uh bright regions is
+
+ align:start position:0%
+the width of the uh bright regions is
+ 
+
+ align:start position:0%
+the width of the uh bright regions is
+smaller than the width of the dark
+
+ align:start position:0%
+smaller than the width of the dark
+ 
+
+ align:start position:0%
+smaller than the width of the dark
+regions uh and that's important when it
+
+ align:start position:0%
+regions uh and that's important when it
+ 
+
+ align:start position:0%
+regions uh and that's important when it
+comes to looking at the fer transform
+
+ align:start position:0%
+comes to looking at the fer transform
+ 
+
+ align:start position:0%
+comes to looking at the fer transform
+and therefore the spectrum of that uh
+
+ align:start position:0%
+and therefore the spectrum of that uh
+ 
+
+ align:start position:0%
+and therefore the spectrum of that uh
+and then uh the pupil mask uh that we're
+
+ align:start position:0%
+and then uh the pupil mask uh that we're
+ 
+
+ align:start position:0%
+and then uh the pupil mask uh that we're
+going to look at looks something like
+
+ align:start position:0%
+going to look at looks something like
+ 
+
+ align:start position:0%
+going to look at looks something like
+that we let through the frequencies near
+
+ align:start position:0%
+that we let through the frequencies near
+ 
+
+ align:start position:0%
+that we let through the frequencies near
+the center uh and we keep out reject the
+
+ align:start position:0%
+the center uh and we keep out reject the
+ 
+
+ align:start position:0%
+the center uh and we keep out reject the
+frequencies which are further from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+center
+
+ align:start position:0%
+center
+ 
+
+ align:start position:0%
+center
+okay uh so we we got a do the fer
+
+ align:start position:0%
+okay uh so we we got a do the fer
+ 
+
+ align:start position:0%
+okay uh so we we got a do the fer
+transform of that this is a repetitive
+
+ align:start position:0%
+transform of that this is a repetitive
+ 
+
+ align:start position:0%
+transform of that this is a repetitive
+function so the fer transform just
+
+ align:start position:0%
+function so the fer transform just
+ 
+
+ align:start position:0%
+function so the fer transform just
+becomes a fuer
+
+ align:start position:0%
+becomes a fuer
+ 
+
+ align:start position:0%
+becomes a fuer
+series uh and uh this is an expression
+
+ align:start position:0%
+series uh and uh this is an expression
+ 
+
+ align:start position:0%
+series uh and uh this is an expression
+for the fer series of this uh it
+
+ align:start position:0%
+for the fer series of this uh it
+ 
+
+ align:start position:0%
+for the fer series of this uh it
+basically consists of um two parts uh
+
+ align:start position:0%
+basically consists of um two parts uh
+ 
+
+ align:start position:0%
+basically consists of um two parts uh
+there's it's it's got a a sort of
+
+ align:start position:0%
+there's it's it's got a a sort of
+ 
+
+ align:start position:0%
+there's it's it's got a a sort of
+envelope which is a
+
+ align:start position:0%
+envelope which is a
+ 
+
+ align:start position:0%
+envelope which is a
+sync uh basically this is going to
+
+ align:start position:0%
+sync uh basically this is going to
+ 
+
+ align:start position:0%
+sync uh basically this is going to
+consist of a infinite number of uh of
+
+ align:start position:0%
+consist of a infinite number of uh of
+ 
+
+ align:start position:0%
+consist of a infinite number of uh of
+discrete frequencies isn't it it's going
+
+ align:start position:0%
+discrete frequencies isn't it it's going
+ 
+
+ align:start position:0%
+discrete frequencies isn't it it's going
+to consist of a a a constant term which
+
+ align:start position:0%
+to consist of a a a constant term which
+ 
+
+ align:start position:0%
+to consist of a a a constant term which
+is the zero order term it's going to
+
+ align:start position:0%
+is the zero order term it's going to
+ 
+
+ align:start position:0%
+is the zero order term it's going to
+consist of a a a a first harmonic and
+
+ align:start position:0%
+consist of a a a a first harmonic and
+ 
+
+ align:start position:0%
+consist of a a a a first harmonic and
+then a second harmonic and a third
+
+ align:start position:0%
+then a second harmonic and a third
+ 
+
+ align:start position:0%
+then a second harmonic and a third
+harmonic and so on if the if the duty
+
+ align:start position:0%
+harmonic and so on if the if the duty
+ 
+
+ align:start position:0%
+harmonic and so on if the if the duty
+cycle had been chosen to be a half I it
+
+ align:start position:0%
+cycle had been chosen to be a half I it
+ 
+
+ align:start position:0%
+cycle had been chosen to be a half I it
+was a square wave then by symmetry it
+
+ align:start position:0%
+was a square wave then by symmetry it
+ 
+
+ align:start position:0%
+was a square wave then by symmetry it
+turns out that the second harmonic and
+
+ align:start position:0%
+turns out that the second harmonic and
+ 
+
+ align:start position:0%
+turns out that the second harmonic and
+the fourth harmonic and all those all
+
+ align:start position:0%
+the fourth harmonic and all those all
+ 
+
+ align:start position:0%
+the fourth harmonic and all those all
+vanish so you'd only end up with the
+
+ align:start position:0%
+vanish so you'd only end up with the
+ 
+
+ align:start position:0%
+vanish so you'd only end up with the
+zero the first the third fifth and so on
+
+ align:start position:0%
+zero the first the third fifth and so on
+ 
+
+ align:start position:0%
+zero the first the third fifth and so on
+uh but in general uh there will be all
+
+ align:start position:0%
+uh but in general uh there will be all
+ 
+
+ align:start position:0%
+uh but in general uh there will be all
+the orders there uh and the the relative
+
+ align:start position:0%
+the orders there uh and the the relative
+ 
+
+ align:start position:0%
+the orders there uh and the the relative
+strength of those orders uh here you can
+
+ align:start position:0%
+strength of those orders uh here you can
+ 
+
+ align:start position:0%
+strength of those orders uh here you can
+um you can see is um decide is it
+
+ align:start position:0%
+um you can see is um decide is it
+ 
+
+ align:start position:0%
+um you can see is um decide is it
+depends on the value of this sync
+
+ align:start position:0%
+depends on the value of this sync
+ 
+
+ align:start position:0%
+depends on the value of this sync
+function actually that's that's a very
+
+ align:start position:0%
+function actually that's that's a very
+ 
+
+ align:start position:0%
+function actually that's that's a very
+easy way of seeing about the even orders
+
+ align:start position:0%
+easy way of seeing about the even orders
+ 
+
+ align:start position:0%
+easy way of seeing about the even orders
+cancelling uh because uh what happens is
+
+ align:start position:0%
+cancelling uh because uh what happens is
+ 
+
+ align:start position:0%
+cancelling uh because uh what happens is
+if the duty uh the duty factor is a half
+
+ align:start position:0%
+if the duty uh the duty factor is a half
+ 
+
+ align:start position:0%
+if the duty uh the duty factor is a half
+it turns out that the even uh the even
+
+ align:start position:0%
+it turns out that the even uh the even
+ 
+
+ align:start position:0%
+it turns out that the even uh the even
+orders when cuticles even number
+
+ align:start position:0%
+orders when cuticles even number
+ 
+
+ align:start position:0%
+orders when cuticles even number
+coincide
+
+ align:start position:0%
+coincide
+ 
+
+ align:start position:0%
+coincide
+with the zeros of the sync function and
+
+ align:start position:0%
+with the zeros of the sync function and
+ 
+
+ align:start position:0%
+with the zeros of the sync function and
+that's why they vanish right uh
+
+ align:start position:0%
+that's why they vanish right uh
+ 
+
+ align:start position:0%
+that's why they vanish right uh
+so um so where this comes from uh is uh
+
+ align:start position:0%
+so um so where this comes from uh is uh
+ 
+
+ align:start position:0%
+so um so where this comes from uh is uh
+that uh so we're saying that this
+
+ align:start position:0%
+that uh so we're saying that this
+ 
+
+ align:start position:0%
+that uh so we're saying that this
+function is
+
+ align:start position:0%
+function is
+ 
+
+ align:start position:0%
+function is
+a uh maybe it's easier if I go on to the
+
+ align:start position:0%
+a uh maybe it's easier if I go on to the
+ 
+
+ align:start position:0%
+a uh maybe it's easier if I go on to the
+next line I think which is the fer
+
+ align:start position:0%
+next line I think which is the fer
+ 
+
+ align:start position:0%
+next line I think which is the fer
+transform yeah the fer transform uh so
+
+ align:start position:0%
+transform yeah the fer transform uh so
+ 
+
+ align:start position:0%
+transform yeah the fer transform uh so
+the the the fer transform the strength
+
+ align:start position:0%
+the the the fer transform the strength
+ 
+
+ align:start position:0%
+the the the fer transform the strength
+of of these components is what we're
+
+ align:start position:0%
+of of these components is what we're
+ 
+
+ align:start position:0%
+of of these components is what we're
+going to find out uh and uh so this
+
+ align:start position:0%
+going to find out uh and uh so this
+ 
+
+ align:start position:0%
+going to find out uh and uh so this
+function for transforms to something uh
+
+ align:start position:0%
+function for transforms to something uh
+ 
+
+ align:start position:0%
+function for transforms to something uh
+which is a series of Delta functions uh
+
+ align:start position:0%
+which is a series of Delta functions uh
+ 
+
+ align:start position:0%
+which is a series of Delta functions uh
+corresponding to the different orders
+
+ align:start position:0%
+corresponding to the different orders
+ 
+
+ align:start position:0%
+corresponding to the different orders
+different values of Q uh and um the
+
+ align:start position:0%
+different values of Q uh and um the
+ 
+
+ align:start position:0%
+different values of Q uh and um the
+strength of the different components is
+
+ align:start position:0%
+strength of the different components is
+ 
+
+ align:start position:0%
+strength of the different components is
+given by the value of the
+
+ align:start position:0%
+given by the value of the
+ 
+
+ align:start position:0%
+given by the value of the
+sync right so you can see again U if um
+
+ align:start position:0%
+sync right so you can see again U if um
+ 
+
+ align:start position:0%
+sync right so you can see again U if um
+if there are some values of alpha Q
+
+ align:start position:0%
+if there are some values of alpha Q
+ 
+
+ align:start position:0%
+if there are some values of alpha Q
+which can be uh zero and therefore uh
+
+ align:start position:0%
+which can be uh zero and therefore uh
+ 
+
+ align:start position:0%
+which can be uh zero and therefore uh
+would um mean that those components
+
+ align:start position:0%
+would um mean that those components
+ 
+
+ align:start position:0%
+would um mean that those components
+wouldn't be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay so uh so when it gets to the
+
+ align:start position:0%
+there okay so uh so when it gets to the
+ 
+
+ align:start position:0%
+there okay so uh so when it gets to the
+uh to the pupil
+
+ align:start position:0%
+uh to the pupil
+ 
+
+ align:start position:0%
+uh to the pupil
+mask uh all that's happening uh maybe
+
+ align:start position:0%
+mask uh all that's happening uh maybe
+ 
+
+ align:start position:0%
+mask uh all that's happening uh maybe
+you want to go back to
+
+ align:start position:0%
+you want to go back to
+ 
+
+ align:start position:0%
+you want to go back to
+the we go back to
+
+ align:start position:0%
+the we go back to
+ 
+
+ align:start position:0%
+the we go back to
+this diagram uh so you can see that the
+
+ align:start position:0%
+this diagram uh so you can see that the
+ 
+
+ align:start position:0%
+this diagram uh so you can see that the
+um what we what we need to know is this
+
+ align:start position:0%
+um what we what we need to know is this
+ 
+
+ align:start position:0%
+um what we what we need to know is this
+this is coming to a focus at this point
+
+ align:start position:0%
+this is coming to a focus at this point
+ 
+
+ align:start position:0%
+this is coming to a focus at this point
+here but we need to know what that
+
+ align:start position:0%
+here but we need to know what that
+ 
+
+ align:start position:0%
+here but we need to know what that
+distance here is but we need to know um
+
+ align:start position:0%
+distance here is but we need to know um
+ 
+
+ align:start position:0%
+distance here is but we need to know um
+the relative scaling of of where where
+
+ align:start position:0%
+the relative scaling of of where where
+ 
+
+ align:start position:0%
+the relative scaling of of where where
+that defraction order appears
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on oh that was what appeared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay so it's this is this Lambda F
+
+ align:start position:0%
+there okay so it's this is this Lambda F
+ 
+
+ align:start position:0%
+there okay so it's this is this Lambda F
+that comes in here because it's going
+
+ align:start position:0%
+that comes in here because it's going
+ 
+
+ align:start position:0%
+that comes in here because it's going
+through a distance F so that gives the
+
+ align:start position:0%
+through a distance F so that gives the
+ 
+
+ align:start position:0%
+through a distance F so that gives the
+uh the scaling of this distribution you
+
+ align:start position:0%
+uh the scaling of this distribution you
+ 
+
+ align:start position:0%
+uh the scaling of this distribution you
+get there uh and uh so uh so that's
+
+ align:start position:0%
+get there uh and uh so uh so that's
+ 
+
+ align:start position:0%
+get there uh and uh so uh so that's
+where U now is replaced by this x Double
+
+ align:start position:0%
+where U now is replaced by this x Double
+ 
+
+ align:start position:0%
+where U now is replaced by this x Double
+Dash over Lambda F right the scaling of
+
+ align:start position:0%
+Dash over Lambda F right the scaling of
+ 
+
+ align:start position:0%
+Dash over Lambda F right the scaling of
+that size of that defraction
+
+ align:start position:0%
+that size of that defraction
+ 
+
+ align:start position:0%
+that size of that defraction
+pattern uh and uh and then this is
+
+ align:start position:0%
+pattern uh and uh and then this is
+ 
+
+ align:start position:0%
+pattern uh and uh and then this is
+putting the answer in uh is that you get
+
+ align:start position:0%
+putting the answer in uh is that you get
+ 
+
+ align:start position:0%
+putting the answer in uh is that you get
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um oh yeah we're told that Alpha is the
+
+ align:start position:0%
+um oh yeah we're told that Alpha is the
+ 
+
+ align:start position:0%
+um oh yeah we're told that Alpha is the
+duty F uh uh cycle the uh so that's the
+
+ align:start position:0%
+duty F uh uh cycle the uh so that's the
+ 
+
+ align:start position:0%
+duty F uh uh cycle the uh so that's the
+third uh so that becomes Alpha is a
+
+ align:start position:0%
+third uh so that becomes Alpha is a
+ 
+
+ align:start position:0%
+third uh so that becomes Alpha is a
+third in
+
+ align:start position:0%
+third in
+ 
+
+ align:start position:0%
+third in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh and where do we get the 1 cm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from yeah I think I saw something like
+
+ align:start position:0%
+from yeah I think I saw something like
+ 
+
+ align:start position:0%
+from yeah I think I saw something like
+this on the crib sheet which you've all
+
+ align:start position:0%
+this on the crib sheet which you've all
+ 
+
+ align:start position:0%
+this on the crib sheet which you've all
+had by the
+
+ align:start position:0%
+had by the
+ 
+
+ align:start position:0%
+had by the
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+uh so we've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got right
+
+ align:start position:0%
+got right
+ 
+
+ align:start position:0%
+got right
+here we've got Lambda equal
+
+ align:start position:0%
+here we've got Lambda equal
+ 
+
+ align:start position:0%
+here we've got Lambda equal
+0.5
+
+ align:start position:0%
+0.5
+ 
+
+ align:start position:0%
+0.5
+microns F = 20
+
+ align:start position:0%
+microns F = 20
+ 
+
+ align:start position:0%
+microns F = 20
+cm
+
+ align:start position:0%
+cm
+ 
+
+ align:start position:0%
+cm
+Lambda period is equal to 10
+
+ align:start position:0%
+Lambda period is equal to 10
+ 
+
+ align:start position:0%
+Lambda period is equal to 10
+microns so that gives that Lambda F over
+
+ align:start position:0%
+microns so that gives that Lambda F over
+ 
+
+ align:start position:0%
+microns so that gives that Lambda F over
+Capital Lambda is
+
+ align:start position:0%
+Capital Lambda is
+ 
+
+ align:start position:0%
+Capital Lambda is
+0.5 uh time
+
+ align:start position:0%
+0.5 uh time
+ 
+
+ align:start position:0%
+0.5 uh time
+20 over
+
+ align:start position:0%
+20 over
+ 
+
+ align:start position:0%
+20 over
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+um um that's not that's this is this is
+
+ align:start position:0%
+um um that's not that's this is this is
+ 
+
+ align:start position:0%
+um um that's not that's this is this is
+microns
+
+ align:start position:0%
+microns
+ 
+
+ align:start position:0%
+microns
+lamb oh yeah that's the these are in
+
+ align:start position:0%
+lamb oh yeah that's the these are in
+ 
+
+ align:start position:0%
+lamb oh yeah that's the these are in
+microns these are in microns these are
+
+ align:start position:0%
+microns these are in microns these are
+ 
+
+ align:start position:0%
+microns these are in microns these are
+in centimet so this is in centimet
+
+ align:start position:0%
+in centimet so this is in centimet
+ 
+
+ align:start position:0%
+in centimet so this is in centimet
+and this is equal to 1
+
+ align:start position:0%
+and this is equal to 1
+ 
+
+ align:start position:0%
+and this is equal to 1
+cm right okay so so that's
+
+ align:start position:0%
+cm right okay so so that's
+ 
+
+ align:start position:0%
+cm right okay so so that's
+the uh what's going on there then so
+
+ align:start position:0%
+the uh what's going on there then so
+ 
+
+ align:start position:0%
+the uh what's going on there then so
+that's the 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cm okay that's so that's just plotting
+
+ align:start position:0%
+cm okay that's so that's just plotting
+ 
+
+ align:start position:0%
+cm okay that's so that's just plotting
+then these different
+
+ align:start position:0%
+then these different
+ 
+
+ align:start position:0%
+then these different
+orders uh and so you can see here the
+
+ align:start position:0%
+orders uh and so you can see here the
+ 
+
+ align:start position:0%
+orders uh and so you can see here the
+zero order + one + two plus three so on
+
+ align:start position:0%
+zero order + one + two plus three so on
+ 
+
+ align:start position:0%
+zero order + one + two plus three so on
+uh but uh
+
+ align:start position:0%
+uh but uh
+ 
+
+ align:start position:0%
+uh but uh
+the screen blocks out all the ones
+
+ align:start position:0%
+the screen blocks out all the ones
+ 
+
+ align:start position:0%
+the screen blocks out all the ones
+except for these Central
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ones uh and uh so this thing these these
+
+ align:start position:0%
+ones uh and uh so this thing these these
+ 
+
+ align:start position:0%
+ones uh and uh so this thing these these
+relative
+
+ align:start position:0%
+relative
+ 
+
+ align:start position:0%
+relative
+strengths uh must come from well there's
+
+ align:start position:0%
+strengths uh must come from well there's
+ 
+
+ align:start position:0%
+strengths uh must come from well there's
+a the fact of third at the front is this
+
+ align:start position:0%
+a the fact of third at the front is this
+ 
+
+ align:start position:0%
+a the fact of third at the front is this
+one and then this is multiplied by the
+
+ align:start position:0%
+one and then this is multiplied by the
+ 
+
+ align:start position:0%
+one and then this is multiplied by the
+value of SN of of um a third which must
+
+ align:start position:0%
+value of SN of of um a third which must
+ 
+
+ align:start position:0%
+value of SN of of um a third which must
+give this this the rest of this thing
+
+ align:start position:0%
+give this this the rest of this thing
+ 
+
+ align:start position:0%
+give this this the rest of this thing
+here uh um so I have posted in the
+
+ align:start position:0%
+here uh um so I have posted in the
+ 
+
+ align:start position:0%
+here uh um so I have posted in the
+website a supplement to this lecture so
+
+ align:start position:0%
+website a supplement to this lecture so
+ 
+
+ align:start position:0%
+website a supplement to this lecture so
+in the supplement I have worked out all
+
+ align:start position:0%
+in the supplement I have worked out all
+ 
+
+ align:start position:0%
+in the supplement I have worked out all
+these calculations how you compute the
+
+ align:start position:0%
+these calculations how you compute the
+ 
+
+ align:start position:0%
+these calculations how you compute the
+sync of 1/3 sync of two over3 and so on
+
+ align:start position:0%
+sync of 1/3 sync of two over3 and so on
+ 
+
+ align:start position:0%
+sync of 1/3 sync of two over3 and so on
+so you can see some more details in the
+
+ align:start position:0%
+so you can see some more details in the
+ 
+
+ align:start position:0%
+so you can see some more details in the
+in the in the website yeah okay you
+
+ align:start position:0%
+in the in the website yeah okay you
+ 
+
+ align:start position:0%
+in the in the website yeah okay you
+remember sync you've defined as s of pix
+
+ align:start position:0%
+remember sync you've defined as s of pix
+ 
+
+ align:start position:0%
+remember sync you've defined as s of pix
+over pix remember that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so that's the that's the why that
+
+ align:start position:0%
+um so that's the that's the why that
+ 
+
+ align:start position:0%
+um so that's the that's the why that
+people usually Define it syn of x equal
+
+ align:start position:0%
+people usually Define it syn of x equal
+ 
+
+ align:start position:0%
+people usually Define it syn of x equal
+sin of PX over
+
+ align:start position:0%
+sin of PX over
+ 
+
+ align:start position:0%
+sin of PX over
+pix right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's it's it's defined in that way
+
+ align:start position:0%
+so it's it's it's defined in that way
+ 
+
+ align:start position:0%
+so it's it's it's defined in that way
+because then then lots of n nasty pies
+
+ align:start position:0%
+because then then lots of n nasty pies
+ 
+
+ align:start position:0%
+because then then lots of n nasty pies
+and things cancel out and everything
+
+ align:start position:0%
+and things cancel out and everything
+ 
+
+ align:start position:0%
+and things cancel out and everything
+else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh so we got to then multiply that
+
+ align:start position:0%
+okay uh so we got to then multiply that
+ 
+
+ align:start position:0%
+okay uh so we got to then multiply that
+uh by the
+
+ align:start position:0%
+uh by the
+ 
+
+ align:start position:0%
+uh by the
+um the size of the Mask uh so as it
+
+ align:start position:0%
+um the size of the Mask uh so as it
+ 
+
+ align:start position:0%
+um the size of the Mask uh so as it
+shows here the mask going fromus 1.5 cm
+
+ align:start position:0%
+shows here the mask going fromus 1.5 cm
+ 
+
+ align:start position:0%
+shows here the mask going fromus 1.5 cm
+to 1 plus 1.5 CM which means that this
+
+ align:start position:0%
+to 1 plus 1.5 CM which means that this
+ 
+
+ align:start position:0%
+to 1 plus 1.5 CM which means that this
+grating component which is at 2 cm
+
+ align:start position:0%
+grating component which is at 2 cm
+ 
+
+ align:start position:0%
+grating component which is at 2 cm
+doesn't get through right so so that's
+
+ align:start position:0%
+doesn't get through right so so that's
+ 
+
+ align:start position:0%
+doesn't get through right so so that's
+what the what gets through the
+
+ align:start position:0%
+what the what gets through the
+ 
+
+ align:start position:0%
+what the what gets through the
+aperture uh and uh then we for transform
+
+ align:start position:0%
+aperture uh and uh then we for transform
+ 
+
+ align:start position:0%
+aperture uh and uh then we for transform
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+again uh and uh so the Delta function
+
+ align:start position:0%
+again uh and uh so the Delta function
+ 
+
+ align:start position:0%
+again uh and uh so the Delta function
+transforms to an exponential shifted
+
+ align:start position:0%
+transforms to an exponential shifted
+ 
+
+ align:start position:0%
+transforms to an exponential shifted
+Delta function corresponds to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponential and therefore our output uh
+
+ align:start position:0%
+exponential and therefore our output uh
+ 
+
+ align:start position:0%
+exponential and therefore our output uh
+of course this this F was the same in
+
+ align:start position:0%
+of course this this F was the same in
+ 
+
+ align:start position:0%
+of course this this F was the same in
+this case the two FS of the two two
+
+ align:start position:0%
+this case the two FS of the two two
+ 
+
+ align:start position:0%
+this case the two FS of the two two
+lenses were the same so we get a 1 over
+
+ align:start position:0%
+lenses were the same so we get a 1 over
+ 
+
+ align:start position:0%
+lenses were the same so we get a 1 over
+Lambda f again there
+
+ align:start position:0%
+Lambda f again there
+ 
+
+ align:start position:0%
+Lambda f again there
+R uh what will happen if we make the
+
+ align:start position:0%
+R uh what will happen if we make the
+ 
+
+ align:start position:0%
+R uh what will happen if we make the
+width of the uh this mask uh minus 2 to
+
+ align:start position:0%
+width of the uh this mask uh minus 2 to
+ 
+
+ align:start position:0%
+width of the uh this mask uh minus 2 to
++2 will there be any deflection due to
+
+ align:start position:0%
++2 will there be any deflection due to
+ 
+
+ align:start position:0%
++2 will there be any deflection due to
+this uh second
+
+ align:start position:0%
+this uh second
+ 
+
+ align:start position:0%
+this uh second
+order um well if it was exactly minus 2
+
+ align:start position:0%
+order um well if it was exactly minus 2
+ 
+
+ align:start position:0%
+order um well if it was exactly minus 2
+to plus two yes then uh I guess if it
+
+ align:start position:0%
+to plus two yes then uh I guess if it
+ 
+
+ align:start position:0%
+to plus two yes then uh I guess if it
+really was exactly there you'd expect
+
+ align:start position:0%
+really was exactly there you'd expect
+ 
+
+ align:start position:0%
+really was exactly there you'd expect
+half of it to get through wouldn't you
+
+ align:start position:0%
+half of it to get through wouldn't you
+ 
+
+ align:start position:0%
+half of it to get through wouldn't you
+this order but I mean normally we we we
+
+ align:start position:0%
+this order but I mean normally we we we
+ 
+
+ align:start position:0%
+this order but I mean normally we we we
+would assume it either lets it through
+
+ align:start position:0%
+would assume it either lets it through
+ 
+
+ align:start position:0%
+would assume it either lets it through
+or it doesn't let it through but so if
+
+ align:start position:0%
+or it doesn't let it through but so if
+ 
+
+ align:start position:0%
+or it doesn't let it through but so if
+you let if if you made the the size of
+
+ align:start position:0%
+you let if if you made the the size of
+ 
+
+ align:start position:0%
+you let if if you made the the size of
+the aperture 2 2.5 then of course this
+
+ align:start position:0%
+the aperture 2 2.5 then of course this
+ 
+
+ align:start position:0%
+the aperture 2 2.5 then of course this
+next order would get through wouldn't
+
+ align:start position:0%
+next order would get through wouldn't
+ 
+
+ align:start position:0%
+next order would get through wouldn't
+it yeah but if it is exit will there
+
+ align:start position:0%
+it yeah but if it is exit will there
+ 
+
+ align:start position:0%
+it yeah but if it is exit will there
+means do we have to consider a
+
+ align:start position:0%
+means do we have to consider a
+ 
+
+ align:start position:0%
+means do we have to consider a
+deflection
+
+ align:start position:0%
+deflection
+ 
+
+ align:start position:0%
+deflection
+of uh no I think that basically you know
+
+ align:start position:0%
+of uh no I think that basically you know
+ 
+
+ align:start position:0%
+of uh no I think that basically you know
+I think that effectively you I think
+
+ align:start position:0%
+I think that effectively you I think
+ 
+
+ align:start position:0%
+I think that effectively you I think
+you'd have to say that half of it got
+
+ align:start position:0%
+you'd have to say that half of it got
+ 
+
+ align:start position:0%
+you'd have to say that half of it got
+through and actually that's correct
+
+ align:start position:0%
+through and actually that's correct
+ 
+
+ align:start position:0%
+through and actually that's correct
+because in actuality the Great is finite
+
+ align:start position:0%
+because in actuality the Great is finite
+ 
+
+ align:start position:0%
+because in actuality the Great is finite
+so these are not Delta functions they're
+
+ align:start position:0%
+so these are not Delta functions they're
+ 
+
+ align:start position:0%
+so these are not Delta functions they're
+sync patterns so if you place the grade
+
+ align:start position:0%
+sync patterns so if you place the grade
+ 
+
+ align:start position:0%
+sync patterns so if you place the grade
+in at exactly two then you allow one
+
+ align:start position:0%
+in at exactly two then you allow one
+ 
+
+ align:start position:0%
+in at exactly two then you allow one
+half of the S to go through right so
+
+ align:start position:0%
+half of the S to go through right so
+ 
+
+ align:start position:0%
+half of the S to go through right so
+therefore one half is yeah yeah that's a
+
+ align:start position:0%
+therefore one half is yeah yeah that's a
+ 
+
+ align:start position:0%
+therefore one half is yeah yeah that's a
+very good way of thinking here we
+
+ align:start position:0%
+very good way of thinking here we
+ 
+
+ align:start position:0%
+very good way of thinking here we
+started off by saying that this is a um
+
+ align:start position:0%
+started off by saying that this is a um
+ 
+
+ align:start position:0%
+started off by saying that this is a um
+a continuous a repetitive grating and so
+
+ align:start position:0%
+a continuous a repetitive grating and so
+ 
+
+ align:start position:0%
+a continuous a repetitive grating and so
+we can think of it in terms of a Furious
+
+ align:start position:0%
+we can think of it in terms of a Furious
+ 
+
+ align:start position:0%
+we can think of it in terms of a Furious
+series but of course it's not actually
+
+ align:start position:0%
+series but of course it's not actually
+ 
+
+ align:start position:0%
+series but of course it's not actually
+infinitely
+
+ align:start position:0%
+infinitely
+ 
+
+ align:start position:0%
+infinitely
+big uh I guess it's not going to be more
+
+ align:start position:0%
+big uh I guess it's not going to be more
+ 
+
+ align:start position:0%
+big uh I guess it's not going to be more
+than a few
+
+ align:start position:0%
+than a few
+ 
+
+ align:start position:0%
+than a few
+uh like years across so this is
+
+ align:start position:0%
+uh like years across so this is
+ 
+
+ align:start position:0%
+uh like years across so this is
+multiplied by another rect function
+
+ align:start position:0%
+multiplied by another rect function
+ 
+
+ align:start position:0%
+multiplied by another rect function
+really right so the fora transform of
+
+ align:start position:0%
+really right so the fora transform of
+ 
+
+ align:start position:0%
+really right so the fora transform of
+this whole thing multiplied by re is
+
+ align:start position:0%
+this whole thing multiplied by re is
+ 
+
+ align:start position:0%
+this whole thing multiplied by re is
+something convolved with a sync so each
+
+ align:start position:0%
+something convolved with a sync so each
+ 
+
+ align:start position:0%
+something convolved with a sync so each
+of these these things is not really a
+
+ align:start position:0%
+of these these things is not really a
+ 
+
+ align:start position:0%
+of these these things is not really a
+Delta function but it's really a very
+
+ align:start position:0%
+Delta function but it's really a very
+ 
+
+ align:start position:0%
+Delta function but it's really a very
+narrow sync which depends on the size of
+
+ align:start position:0%
+narrow sync which depends on the size of
+ 
+
+ align:start position:0%
+narrow sync which depends on the size of
+our grating so yeah so the point George
+
+ align:start position:0%
+our grating so yeah so the point George
+ 
+
+ align:start position:0%
+our grating so yeah so the point George
+is making is if you think of it as a
+
+ align:start position:0%
+is making is if you think of it as a
+ 
+
+ align:start position:0%
+is making is if you think of it as a
+sync
+
+ align:start position:0%
+sync
+ 
+
+ align:start position:0%
+sync
+uh then you it really would be letting
+
+ align:start position:0%
+uh then you it really would be letting
+ 
+
+ align:start position:0%
+uh then you it really would be letting
+letting through half of it right um I
+
+ align:start position:0%
+letting through half of it right um I
+ 
+
+ align:start position:0%
+letting through half of it right um I
+think mathematically it have to be like
+
+ align:start position:0%
+think mathematically it have to be like
+ 
+
+ align:start position:0%
+think mathematically it have to be like
+that as well you get used to these when
+
+ align:start position:0%
+that as well you get used to these when
+ 
+
+ align:start position:0%
+that as well you get used to these when
+you do you you must remember from um
+
+ align:start position:0%
+you do you you must remember from um
+ 
+
+ align:start position:0%
+you do you you must remember from um
+solving partial differential equations
+
+ align:start position:0%
+solving partial differential equations
+ 
+
+ align:start position:0%
+solving partial differential equations
+when you do the boundary conditions you
+
+ align:start position:0%
+when you do the boundary conditions you
+ 
+
+ align:start position:0%
+when you do the boundary conditions you
+always have to do that sort of thing uh
+
+ align:start position:0%
+always have to do that sort of thing uh
+ 
+
+ align:start position:0%
+always have to do that sort of thing uh
+it seems a bit of a cheap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+okay okay so this is putting the numbers
+
+ align:start position:0%
+okay okay so this is putting the numbers
+ 
+
+ align:start position:0%
+okay okay so this is putting the numbers
+in then so this is the uh the three
+
+ align:start position:0%
+in then so this is the uh the three
+ 
+
+ align:start position:0%
+in then so this is the uh the three
+components these are these root3 over 2
+
+ align:start position:0%
+components these are these root3 over 2
+ 
+
+ align:start position:0%
+components these are these root3 over 2
+pi we had there uh and uh and then
+
+ align:start position:0%
+pi we had there uh and uh and then
+ 
+
+ align:start position:0%
+pi we had there uh and uh and then
+finally these two combine together to
+
+ align:start position:0%
+finally these two combine together to
+ 
+
+ align:start position:0%
+finally these two combine together to
+make a
+
+ align:start position:0%
+make a
+ 
+
+ align:start position:0%
+make a
+cosine uh and our final uh amplitude of
+
+ align:start position:0%
+cosine uh and our final uh amplitude of
+ 
+
+ align:start position:0%
+cosine uh and our final uh amplitude of
+our image is going to be a constant plus
+
+ align:start position:0%
+our image is going to be a constant plus
+ 
+
+ align:start position:0%
+our image is going to be a constant plus
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+cosine you notice that it's not the the
+
+ align:start position:0%
+cosine you notice that it's not the the
+ 
+
+ align:start position:0%
+cosine you notice that it's not the the
+the amplitude of this is not the same as
+
+ align:start position:0%
+the amplitude of this is not the same as
+ 
+
+ align:start position:0%
+the amplitude of this is not the same as
+the amplitude of that of course because
+
+ align:start position:0%
+the amplitude of that of course because
+ 
+
+ align:start position:0%
+the amplitude of that of course because
+of the uh the fact that it was a
+
+ align:start position:0%
+of the uh the fact that it was a
+ 
+
+ align:start position:0%
+of the uh the fact that it was a
+uh this um um rectangular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grating yeah then finally though uh as I
+
+ align:start position:0%
+grating yeah then finally though uh as I
+ 
+
+ align:start position:0%
+grating yeah then finally though uh as I
+just uh mentioned briefly a little while
+
+ align:start position:0%
+just uh mentioned briefly a little while
+ 
+
+ align:start position:0%
+just uh mentioned briefly a little while
+ago what you actually see is not the
+
+ align:start position:0%
+ago what you actually see is not the
+ 
+
+ align:start position:0%
+ago what you actually see is not the
+amplitude what you see is the
+
+ align:start position:0%
+amplitude what you see is the
+ 
+
+ align:start position:0%
+amplitude what you see is the
+intensity uh which is the modulus square
+
+ align:start position:0%
+intensity uh which is the modulus square
+ 
+
+ align:start position:0%
+intensity uh which is the modulus square
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+amplitude right so uh you remember we
+
+ align:start position:0%
+amplitude right so uh you remember we
+ 
+
+ align:start position:0%
+amplitude right so uh you remember we
+said that what we we normally are going
+
+ align:start position:0%
+said that what we we normally are going
+ 
+
+ align:start position:0%
+said that what we we normally are going
+to call the intensity just the modulus
+
+ align:start position:0%
+to call the intensity just the modulus
+ 
+
+ align:start position:0%
+to call the intensity just the modulus
+square of the amplitude there perhaps
+
+ align:start position:0%
+square of the amplitude there perhaps
+ 
+
+ align:start position:0%
+square of the amplitude there perhaps
+should be some some halves and funny
+
+ align:start position:0%
+should be some some halves and funny
+ 
+
+ align:start position:0%
+should be some some halves and funny
+things out there if we were really doing
+
+ align:start position:0%
+things out there if we were really doing
+ 
+
+ align:start position:0%
+things out there if we were really doing
+it according to uh the pointing Vector
+
+ align:start position:0%
+it according to uh the pointing Vector
+ 
+
+ align:start position:0%
+it according to uh the pointing Vector
+uh but normally we don't bother with
+
+ align:start position:0%
+uh but normally we don't bother with
+ 
+
+ align:start position:0%
+uh but normally we don't bother with
+that we just say is the modulus Square
+
+ align:start position:0%
+that we just say is the modulus Square
+ 
+
+ align:start position:0%
+that we just say is the modulus Square
+so the modulus square of this uh we're
+
+ align:start position:0%
+so the modulus square of this uh we're
+ 
+
+ align:start position:0%
+so the modulus square of this uh we're
+going to get this squared uh and uh
+
+ align:start position:0%
+going to get this squared uh and uh
+ 
+
+ align:start position:0%
+going to get this squared uh and uh
+twice the product of these two and then
+
+ align:start position:0%
+twice the product of these two and then
+ 
+
+ align:start position:0%
+twice the product of these two and then
+this one squared so we get this terming
+
+ align:start position:0%
+this one squared so we get this terming
+ 
+
+ align:start position:0%
+this one squared so we get this terming
+cos
+
+ align:start position:0%
+cos
+ 
+
+ align:start position:0%
+cos
+squar uh and then you have to remember
+
+ align:start position:0%
+squar uh and then you have to remember
+ 
+
+ align:start position:0%
+squar uh and then you have to remember
+your formula uh that you learned in Mass
+
+ align:start position:0%
+your formula uh that you learned in Mass
+ 
+
+ align:start position:0%
+your formula uh that you learned in Mass
+cos 2 Theta = 1 - 2 cosine 2 Theta which
+
+ align:start position:0%
+cos 2 Theta = 1 - 2 cosine 2 Theta which
+ 
+
+ align:start position:0%
+cos 2 Theta = 1 - 2 cosine 2 Theta which
+allows us to write cos s Theta is 1 +
+
+ align:start position:0%
+allows us to write cos s Theta is 1 +
+ 
+
+ align:start position:0%
+allows us to write cos s Theta is 1 +
+cos Theta / 2 uh so this cos squ uh we
+
+ align:start position:0%
+cos Theta / 2 uh so this cos squ uh we
+ 
+
+ align:start position:0%
+cos Theta / 2 uh so this cos squ uh we
+can now replace uh by a constant plus a
+
+ align:start position:0%
+can now replace uh by a constant plus a
+ 
+
+ align:start position:0%
+can now replace uh by a constant plus a
+cosine of twice the angle uh and uh so
+
+ align:start position:0%
+cosine of twice the angle uh and uh so
+ 
+
+ align:start position:0%
+cosine of twice the angle uh and uh so
+that this is the constant
+
+ align:start position:0%
+that this is the constant
+ 
+
+ align:start position:0%
+that this is the constant
+bit uh and this is the cosine of twice
+
+ align:start position:0%
+bit uh and this is the cosine of twice
+ 
+
+ align:start position:0%
+bit uh and this is the cosine of twice
+the angle
+
+ align:start position:0%
+the angle
+ 
+
+ align:start position:0%
+the angle
+right so that likes gives another
+
+ align:start position:0%
+right so that likes gives another
+ 
+
+ align:start position:0%
+right so that likes gives another
+harmonic in the image uh so that's
+
+ align:start position:0%
+harmonic in the image uh so that's
+ 
+
+ align:start position:0%
+harmonic in the image uh so that's
+something that people are a bit confused
+
+ align:start position:0%
+something that people are a bit confused
+ 
+
+ align:start position:0%
+something that people are a bit confused
+by sometimes first of all because we've
+
+ align:start position:0%
+by sometimes first of all because we've
+ 
+
+ align:start position:0%
+by sometimes first of all because we've
+gone through a lot of talk about how
+
+ align:start position:0%
+gone through a lot of talk about how
+ 
+
+ align:start position:0%
+gone through a lot of talk about how
+it's only the first harmonic that's got
+
+ align:start position:0%
+it's only the first harmonic that's got
+ 
+
+ align:start position:0%
+it's only the first harmonic that's got
+through uh but actually now when we look
+
+ align:start position:0%
+through uh but actually now when we look
+ 
+
+ align:start position:0%
+through uh but actually now when we look
+at the
+
+ align:start position:0%
+at the
+ 
+
+ align:start position:0%
+at the
+intensity uh We've now got a second
+
+ align:start position:0%
+intensity uh We've now got a second
+ 
+
+ align:start position:0%
+intensity uh We've now got a second
+harmonic that's that's appearing in the
+
+ align:start position:0%
+harmonic that's that's appearing in the
+ 
+
+ align:start position:0%
+harmonic that's that's appearing in the
+final
+
+ align:start position:0%
+final
+ 
+
+ align:start position:0%
+final
+intensity so note the second harmonic
+
+ align:start position:0%
+intensity so note the second harmonic
+ 
+
+ align:start position:0%
+intensity so note the second harmonic
+term intensity due to the magnitude
+
+ align:start position:0%
+term intensity due to the magnitude
+ 
+
+ align:start position:0%
+term intensity due to the magnitude
+Square operation
+
+ align:start position:0%
+Square operation
+ 
+
+ align:start position:0%
+Square operation
+uh this term explains the ringing in
+
+ align:start position:0%
+uh this term explains the ringing in
+ 
+
+ align:start position:0%
+uh this term explains the ringing in
+coherent low pass filtering systems
+
+ align:start position:0%
+coherent low pass filtering systems
+ 
+
+ align:start position:0%
+coherent low pass filtering systems
+right so yeah so it's
+
+ align:start position:0%
+right so yeah so it's
+ 
+
+ align:start position:0%
+right so yeah so it's
+um the ringing is the the the
+
+ align:start position:0%
+um the ringing is the the the
+ 
+
+ align:start position:0%
+um the ringing is the the the
+um Wiggles you get on a on a sharp
+
+ align:start position:0%
+um Wiggles you get on a on a sharp
+ 
+
+ align:start position:0%
+um Wiggles you get on a on a sharp
+edge right and that's a sketch of what
+
+ align:start position:0%
+edge right and that's a sketch of what
+ 
+
+ align:start position:0%
+edge right and that's a sketch of what
+it looks like uh so it doesn't look
+
+ align:start position:0%
+it looks like uh so it doesn't look
+ 
+
+ align:start position:0%
+it looks like uh so it doesn't look
+quite like a a a cosine grating anymore
+
+ align:start position:0%
+quite like a a a cosine grating anymore
+ 
+
+ align:start position:0%
+quite like a a a cosine grating anymore
+uh because when you Square it the the
+
+ align:start position:0%
+uh because when you Square it the the
+ 
+
+ align:start position:0%
+uh because when you Square it the the
+low values get depressed more uh than
+
+ align:start position:0%
+low values get depressed more uh than
+ 
+
+ align:start position:0%
+low values get depressed more uh than
+the high values right so it become makes
+
+ align:start position:0%
+the high values right so it become makes
+ 
+
+ align:start position:0%
+the high values right so it become makes
+it look more
+
+ align:start position:0%
+it look more
+ 
+
+ align:start position:0%
+it look more
+peaky like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay so perhaps we ought to start
+
+ align:start position:0%
+that okay so perhaps we ought to start
+ 
+
+ align:start position:0%
+that okay so perhaps we ought to start
+again I was just waiting for one of our
+
+ align:start position:0%
+again I was just waiting for one of our
+ 
+
+ align:start position:0%
+again I was just waiting for one of our
+people to come back ah well there we are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just in
+
+ align:start position:0%
+so just in
+ 
+
+ align:start position:0%
+so just in
+time okay so um yeah before we carry on
+
+ align:start position:0%
+time okay so um yeah before we carry on
+ 
+
+ align:start position:0%
+time okay so um yeah before we carry on
+then uh there was a question just before
+
+ align:start position:0%
+then uh there was a question just before
+ 
+
+ align:start position:0%
+then uh there was a question just before
+the break so we're going to have a
+
+ align:start position:0%
+the break so we're going to have a
+ 
+
+ align:start position:0%
+the break so we're going to have a
+question okay actually I have two
+
+ align:start position:0%
+question okay actually I have two
+ 
+
+ align:start position:0%
+question okay actually I have two
+question the first question is regarding
+
+ align:start position:0%
+question the first question is regarding
+ 
+
+ align:start position:0%
+question the first question is regarding
+the physical meaning of the low pass
+
+ align:start position:0%
+the physical meaning of the low pass
+ 
+
+ align:start position:0%
+the physical meaning of the low pass
+filter just now in the previous slide
+
+ align:start position:0%
+filter just now in the previous slide
+ 
+
+ align:start position:0%
+filter just now in the previous slide
+yeah okay so the question is about the
+
+ align:start position:0%
+yeah okay so the question is about the
+ 
+
+ align:start position:0%
+yeah okay so the question is about the
+low pass
+
+ align:start position:0%
+low pass
+ 
+
+ align:start position:0%
+low pass
+filter uh so you you remember in you
+
+ align:start position:0%
+filter uh so you you remember in you
+ 
+
+ align:start position:0%
+filter uh so you you remember in you
+know in um perhaps I'll Draw Something
+
+ align:start position:0%
+know in um perhaps I'll Draw Something
+ 
+
+ align:start position:0%
+know in um perhaps I'll Draw Something
+from uh electronics so you know you you
+
+ align:start position:0%
+from uh electronics so you know you you
+ 
+
+ align:start position:0%
+from uh electronics so you know you you
+remember from uh your high-fi
+
+ align:start position:0%
+remember from uh your high-fi
+ 
+
+ align:start position:0%
+remember from uh your high-fi
+amplifier so this is
+
+ align:start position:0%
+amplifier so this is
+ 
+
+ align:start position:0%
+amplifier so this is
+frequency uh so these These are high
+
+ align:start position:0%
+frequency uh so these These are high
+ 
+
+ align:start position:0%
+frequency uh so these These are high
+frequencies and these are low
+
+ align:start position:0%
+frequencies and these are low
+ 
+
+ align:start position:0%
+frequencies and these are low
+frequencies so um so this corresponds
+
+ align:start position:0%
+frequencies so um so this corresponds
+ 
+
+ align:start position:0%
+frequencies so um so this corresponds
+to and this corresponds
+
+ align:start position:0%
+to and this corresponds
+ 
+
+ align:start position:0%
+to and this corresponds
+to and if we if we multiply this by some
+
+ align:start position:0%
+to and if we if we multiply this by some
+ 
+
+ align:start position:0%
+to and if we if we multiply this by some
+function that looks like that this is
+
+ align:start position:0%
+function that looks like that this is
+ 
+
+ align:start position:0%
+function that looks like that this is
+what we call a low pass filter because
+
+ align:start position:0%
+what we call a low pass filter because
+ 
+
+ align:start position:0%
+what we call a low pass filter because
+we we let through the low low
+
+ align:start position:0%
+we we let through the low low
+ 
+
+ align:start position:0%
+we we let through the low low
+frequencies and we stop the high
+
+ align:start position:0%
+frequencies and we stop the high
+ 
+
+ align:start position:0%
+frequencies and we stop the high
+frequency right um so the same is true
+
+ align:start position:0%
+frequency right um so the same is true
+ 
+
+ align:start position:0%
+frequency right um so the same is true
+here so when we say low low
+
+ align:start position:0%
+here so when we say low low
+ 
+
+ align:start position:0%
+here so when we say low low
+pass uh we we mean that the uh we let
+
+ align:start position:0%
+pass uh we we mean that the uh we let
+ 
+
+ align:start position:0%
+pass uh we we mean that the uh we let
+through the the um the spots which are
+
+ align:start position:0%
+through the the um the spots which are
+ 
+
+ align:start position:0%
+through the the um the spots which are
+close to the axis and stop the ones that
+
+ align:start position:0%
+close to the axis and stop the ones that
+ 
+
+ align:start position:0%
+close to the axis and stop the ones that
+are far from the axis right so that's
+
+ align:start position:0%
+are far from the axis right so that's
+ 
+
+ align:start position:0%
+are far from the axis right so that's
+the first question then there's another
+
+ align:start position:0%
+the first question then there's another
+ 
+
+ align:start position:0%
+the first question then there's another
+one uh the second one is regarding the a
+
+ align:start position:0%
+one uh the second one is regarding the a
+ 
+
+ align:start position:0%
+one uh the second one is regarding the a
+base rule because a Bas rule tell us if
+
+ align:start position:0%
+base rule because a Bas rule tell us if
+ 
+
+ align:start position:0%
+base rule because a Bas rule tell us if
+if we can collect two ERS of the weave
+
+ align:start position:0%
+if we can collect two ERS of the weave
+ 
+
+ align:start position:0%
+if we can collect two ERS of the weave
+we can form one image but just now we
+
+ align:start position:0%
+we can form one image but just now we
+ 
+
+ align:start position:0%
+we can form one image but just now we
+notice that even with the three orders I
+
+ align:start position:0%
+notice that even with the three orders I
+ 
+
+ align:start position:0%
+notice that even with the three orders I
+mean the wave we still get very strange
+
+ align:start position:0%
+mean the wave we still get very strange
+ 
+
+ align:start position:0%
+mean the wave we still get very strange
+weave compared to the original one so I
+
+ align:start position:0%
+weave compared to the original one so I
+ 
+
+ align:start position:0%
+weave compared to the original one so I
+not want to check it what's the reason
+
+ align:start position:0%
+not want to check it what's the reason
+ 
+
+ align:start position:0%
+not want to check it what's the reason
+right okay yeah so um so this is going
+
+ align:start position:0%
+right okay yeah so um so this is going
+ 
+
+ align:start position:0%
+right okay yeah so um so this is going
+back to ABBA's rule which I I I don't
+
+ align:start position:0%
+back to ABBA's rule which I I I don't
+ 
+
+ align:start position:0%
+back to ABBA's rule which I I I don't
+know um I've never really heard what he
+
+ align:start position:0%
+know um I've never really heard what he
+ 
+
+ align:start position:0%
+know um I've never really heard what he
+said actually but have you got that in a
+
+ align:start position:0%
+said actually but have you got that in a
+ 
+
+ align:start position:0%
+said actually but have you got that in a
+book or something it's probably in
+
+ align:start position:0%
+book or something it's probably in
+ 
+
+ align:start position:0%
+book or something it's probably in
+Chinese is it
+
+ align:start position:0%
+Chinese is it
+ 
+
+ align:start position:0%
+Chinese is it
+uh but anyway um the Chinese abber came
+
+ align:start position:0%
+uh but anyway um the Chinese abber came
+ 
+
+ align:start position:0%
+uh but anyway um the Chinese abber came
+up with this rule that you must have at
+
+ align:start position:0%
+up with this rule that you must have at
+ 
+
+ align:start position:0%
+up with this rule that you must have at
+least well we gave an example just now
+
+ align:start position:0%
+least well we gave an example just now
+ 
+
+ align:start position:0%
+least well we gave an example just now
+didn't we of one where you only had one
+
+ align:start position:0%
+didn't we of one where you only had one
+ 
+
+ align:start position:0%
+didn't we of one where you only had one
+beam one order got through and we didn't
+
+ align:start position:0%
+beam one order got through and we didn't
+ 
+
+ align:start position:0%
+beam one order got through and we didn't
+get an image uh so yeah because you're
+
+ align:start position:0%
+get an image uh so yeah because you're
+ 
+
+ align:start position:0%
+get an image uh so yeah because you're
+not obviously not going to get any
+
+ align:start position:0%
+not obviously not going to get any
+ 
+
+ align:start position:0%
+not obviously not going to get any
+interference if you've only got one beam
+
+ align:start position:0%
+interference if you've only got one beam
+ 
+
+ align:start position:0%
+interference if you've only got one beam
+uh so
+
+ align:start position:0%
+uh so
+ 
+
+ align:start position:0%
+uh so
+abbath according to Abba you've got to
+
+ align:start position:0%
+abbath according to Abba you've got to
+ 
+
+ align:start position:0%
+abbath according to Abba you've got to
+have two beams interfering in order to
+
+ align:start position:0%
+have two beams interfering in order to
+ 
+
+ align:start position:0%
+have two beams interfering in order to
+get some variation in in amplitude in
+
+ align:start position:0%
+get some variation in in amplitude in
+ 
+
+ align:start position:0%
+get some variation in in amplitude in
+the image uh and um so he he says at
+
+ align:start position:0%
+the image uh and um so he he says at
+ 
+
+ align:start position:0%
+the image uh and um so he he says at
+least two I guess so uh it could be you
+
+ align:start position:0%
+least two I guess so uh it could be you
+ 
+
+ align:start position:0%
+least two I guess so uh it could be you
+know if you think of these it could be
+
+ align:start position:0%
+know if you think of these it could be
+ 
+
+ align:start position:0%
+know if you think of these it could be
+you could let through the uh we last
+
+ align:start position:0%
+you could let through the uh we last
+ 
+
+ align:start position:0%
+you could let through the uh we last
+time we had the zero and the plus one
+
+ align:start position:0%
+time we had the zero and the plus one
+ 
+
+ align:start position:0%
+time we had the zero and the plus one
+and the minus one uh which is three
+
+ align:start position:0%
+and the minus one uh which is three
+ 
+
+ align:start position:0%
+and the minus one uh which is three
+beams uh and the the point that was made
+
+ align:start position:0%
+beams uh and the the point that was made
+ 
+
+ align:start position:0%
+beams uh and the the point that was made
+in the question was that although we got
+
+ align:start position:0%
+in the question was that although we got
+ 
+
+ align:start position:0%
+in the question was that although we got
+an image it was wasn't a very good image
+
+ align:start position:0%
+an image it was wasn't a very good image
+ 
+
+ align:start position:0%
+an image it was wasn't a very good image
+so um I think that's probably right that
+
+ align:start position:0%
+so um I think that's probably right that
+ 
+
+ align:start position:0%
+so um I think that's probably right that
+that um you know uh I guess Abus
+
+ align:start position:0%
+that um you know uh I guess Abus
+ 
+
+ align:start position:0%
+that um you know uh I guess Abus
+Criterion is is is aba's rule is all to
+
+ align:start position:0%
+Criterion is is is aba's rule is all to
+ 
+
+ align:start position:0%
+Criterion is is is aba's rule is all to
+do with resolution of an optical system
+
+ align:start position:0%
+do with resolution of an optical system
+ 
+
+ align:start position:0%
+do with resolution of an optical system
+the smallest detail you can see but it
+
+ align:start position:0%
+the smallest detail you can see but it
+ 
+
+ align:start position:0%
+the smallest detail you can see but it
+doesn't necessarily mean that you're
+
+ align:start position:0%
+doesn't necessarily mean that you're
+ 
+
+ align:start position:0%
+doesn't necessarily mean that you're
+going to get a good image uh and
+
+ align:start position:0%
+going to get a good image uh and
+ 
+
+ align:start position:0%
+going to get a good image uh and
+changing the relative strengths we're
+
+ align:start position:0%
+changing the relative strengths we're
+ 
+
+ align:start position:0%
+changing the relative strengths we're
+going to see this in lots of examples
+
+ align:start position:0%
+going to see this in lots of examples
+ 
+
+ align:start position:0%
+going to see this in lots of examples
+now actually uh I guess the the whole of
+
+ align:start position:0%
+now actually uh I guess the the whole of
+ 
+
+ align:start position:0%
+now actually uh I guess the the whole of
+the rest of this lecture will be about
+
+ align:start position:0%
+the rest of this lecture will be about
+ 
+
+ align:start position:0%
+the rest of this lecture will be about
+these uh more examples
+
+ align:start position:0%
+these uh more examples
+ 
+
+ align:start position:0%
+these uh more examples
+of stopping beams and so on and changing
+
+ align:start position:0%
+of stopping beams and so on and changing
+ 
+
+ align:start position:0%
+of stopping beams and so on and changing
+beams and seeing what it does to the
+
+ align:start position:0%
+beams and seeing what it does to the
+ 
+
+ align:start position:0%
+beams and seeing what it does to the
+pattern and uh so very often what you'll
+
+ align:start position:0%
+pattern and uh so very often what you'll
+ 
+
+ align:start position:0%
+pattern and uh so very often what you'll
+find then is you get something which may
+
+ align:start position:0%
+find then is you get something which may
+ 
+
+ align:start position:0%
+find then is you get something which may
+be not a good image of the uh original
+
+ align:start position:0%
+be not a good image of the uh original
+ 
+
+ align:start position:0%
+be not a good image of the uh original
+objects but it it's um an image which is
+
+ align:start position:0%
+objects but it it's um an image which is
+ 
+
+ align:start position:0%
+objects but it it's um an image which is
+perhaps better than
+
+ align:start position:0%
+perhaps better than
+ 
+
+ align:start position:0%
+perhaps better than
+nothing okay so is that all right that
+
+ align:start position:0%
+nothing okay so is that all right that
+ 
+
+ align:start position:0%
+nothing okay so is that all right that
+can that answer the
+
+ align:start position:0%
+can that answer the
+ 
+
+ align:start position:0%
+can that answer the
+question okay so we're now looking at a
+
+ align:start position:0%
+question okay so we're now looking at a
+ 
+
+ align:start position:0%
+question okay so we're now looking at a
+a a band pass filter so going back to
+
+ align:start position:0%
+a a band pass filter so going back to
+ 
+
+ align:start position:0%
+a a band pass filter so going back to
+what I was saying here the band pass
+
+ align:start position:0%
+what I was saying here the band pass
+ 
+
+ align:start position:0%
+what I was saying here the band pass
+filter of
+
+ align:start position:0%
+filter of
+ 
+
+ align:start position:0%
+filter of
+course uh is is something that looks
+
+ align:start position:0%
+course uh is is something that looks
+ 
+
+ align:start position:0%
+course uh is is something that looks
+like this it's it a band pass filter uh
+
+ align:start position:0%
+like this it's it a band pass filter uh
+ 
+
+ align:start position:0%
+like this it's it a band pass filter uh
+stops the low frequencies and also the
+
+ align:start position:0%
+stops the low frequencies and also the
+ 
+
+ align:start position:0%
+stops the low frequencies and also the
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+frequencies and so you can see here the
+
+ align:start position:0%
+frequencies and so you can see here the
+ 
+
+ align:start position:0%
+frequencies and so you can see here the
+uh the optical equivalent of this it's
+
+ align:start position:0%
+uh the optical equivalent of this it's
+ 
+
+ align:start position:0%
+uh the optical equivalent of this it's
+now stopping the zero order but allowing
+
+ align:start position:0%
+now stopping the zero order but allowing
+ 
+
+ align:start position:0%
+now stopping the zero order but allowing
+the first orders to get through uh and
+
+ align:start position:0%
+the first orders to get through uh and
+ 
+
+ align:start position:0%
+the first orders to get through uh and
+then the later ones would also uh not
+
+ align:start position:0%
+then the later ones would also uh not
+ 
+
+ align:start position:0%
+then the later ones would also uh not
+get through uh oh yeah that was another
+
+ align:start position:0%
+get through uh oh yeah that was another
+ 
+
+ align:start position:0%
+get through uh oh yeah that was another
+point that George mentioned to me during
+
+ align:start position:0%
+point that George mentioned to me during
+ 
+
+ align:start position:0%
+point that George mentioned to me during
+the break that I hadn't appreciated
+
+ align:start position:0%
+the break that I hadn't appreciated
+ 
+
+ align:start position:0%
+the break that I hadn't appreciated
+fully uh and that is that this
+
+ align:start position:0%
+fully uh and that is that this
+ 
+
+ align:start position:0%
+fully uh and that is that this
+particular example which had this um
+
+ align:start position:0%
+particular example which had this um
+ 
+
+ align:start position:0%
+particular example which had this um
+duty cycle of a
+
+ align:start position:0%
+duty cycle of a
+ 
+
+ align:start position:0%
+duty cycle of a
+third uh actually it turns out that the
+
+ align:start position:0%
+third uh actually it turns out that the
+ 
+
+ align:start position:0%
+third uh actually it turns out that the
+third order of this one vanishes so I
+
+ align:start position:0%
+third order of this one vanishes so I
+ 
+
+ align:start position:0%
+third order of this one vanishes so I
+guess the third the sixth the ninth all
+
+ align:start position:0%
+guess the third the sixth the ninth all
+ 
+
+ align:start position:0%
+guess the third the sixth the ninth all
+these and this is just like we we said
+
+ align:start position:0%
+these and this is just like we we said
+ 
+
+ align:start position:0%
+these and this is just like we we said
+that for a square wave grating all the
+
+ align:start position:0%
+that for a square wave grating all the
+ 
+
+ align:start position:0%
+that for a square wave grating all the
+even orders cancel so it's all to do
+
+ align:start position:0%
+even orders cancel so it's all to do
+ 
+
+ align:start position:0%
+even orders cancel so it's all to do
+with the the zeros of of that sync
+
+ align:start position:0%
+with the the zeros of of that sync
+ 
+
+ align:start position:0%
+with the the zeros of of that sync
+function we had sync of alpha Q right so
+
+ align:start position:0%
+function we had sync of alpha Q right so
+ 
+
+ align:start position:0%
+function we had sync of alpha Q right so
+where Alpha is the duty cycle so for any
+
+ align:start position:0%
+where Alpha is the duty cycle so for any
+ 
+
+ align:start position:0%
+where Alpha is the duty cycle so for any
+duty cycle there will be particular uh
+
+ align:start position:0%
+duty cycle there will be particular uh
+ 
+
+ align:start position:0%
+duty cycle there will be particular uh
+values of the uh
+
+ align:start position:0%
+values of the uh
+ 
+
+ align:start position:0%
+values of the uh
+particular uh integers for the order
+
+ align:start position:0%
+particular uh integers for the order
+ 
+
+ align:start position:0%
+particular uh integers for the order
+which would vanish in the forer
+
+ align:start position:0%
+which would vanish in the forer
+ 
+
+ align:start position:0%
+which would vanish in the forer
+transform right okay so um we here with
+
+ align:start position:0%
+transform right okay so um we here with
+ 
+
+ align:start position:0%
+transform right okay so um we here with
+we're letting through the plus one and
+
+ align:start position:0%
+we're letting through the plus one and
+ 
+
+ align:start position:0%
+we're letting through the plus one and
+the minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one what did something do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then ah right yeah okay so okay so the
+
+ align:start position:0%
+then ah right yeah okay so okay so the
+ 
+
+ align:start position:0%
+then ah right yeah okay so okay so the
+amplitude is one going to be a 1 plus
+
+ align:start position:0%
+amplitude is one going to be a 1 plus
+ 
+
+ align:start position:0%
+amplitude is one going to be a 1 plus
+cosine uh and intensity we're going to
+
+ align:start position:0%
+cosine uh and intensity we're going to
+ 
+
+ align:start position:0%
+cosine uh and intensity we're going to
+get a second harmonic in it just like we
+
+ align:start position:0%
+get a second harmonic in it just like we
+ 
+
+ align:start position:0%
+get a second harmonic in it just like we
+had with the previous
+
+ align:start position:0%
+had with the previous
+ 
+
+ align:start position:0%
+had with the previous
+case Okay and then we now we're going to
+
+ align:start position:0%
+case Okay and then we now we're going to
+ 
+
+ align:start position:0%
+case Okay and then we now we're going to
+go through this in uh more detail so
+
+ align:start position:0%
+go through this in uh more detail so
+ 
+
+ align:start position:0%
+go through this in uh more detail so
+it's the same grating as before so we
+
+ align:start position:0%
+it's the same grating as before so we
+ 
+
+ align:start position:0%
+it's the same grating as before so we
+haven't got to work out all that stuff
+
+ align:start position:0%
+haven't got to work out all that stuff
+ 
+
+ align:start position:0%
+haven't got to work out all that stuff
+again uh the you remember it was 1 cm
+
+ align:start position:0%
+again uh the you remember it was 1 cm
+ 
+
+ align:start position:0%
+again uh the you remember it was 1 cm
+was where the first order was so we got
+
+ align:start position:0%
+was where the first order was so we got
+ 
+
+ align:start position:0%
+was where the first order was so we got
+this series of these uh um different um
+
+ align:start position:0%
+this series of these uh um different um
+ 
+
+ align:start position:0%
+this series of these uh um different um
+grating
+
+ align:start position:0%
+grating
+ 
+
+ align:start position:0%
+grating
+components and uh these ones are
+
+ align:start position:0%
+components and uh these ones are
+ 
+
+ align:start position:0%
+components and uh these ones are
+zero as I just described the next one
+
+ align:start position:0%
+zero as I just described the next one
+ 
+
+ align:start position:0%
+zero as I just described the next one
+would wouldn't be zero though and and we
+
+ align:start position:0%
+would wouldn't be zero though and and we
+ 
+
+ align:start position:0%
+would wouldn't be zero though and and we
+are putting this mask in which is just
+
+ align:start position:0%
+are putting this mask in which is just
+ 
+
+ align:start position:0%
+are putting this mask in which is just
+going to let through these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two and uh so we mathematically we can
+
+ align:start position:0%
+two and uh so we mathematically we can
+ 
+
+ align:start position:0%
+two and uh so we mathematically we can
+write the mask as being the sum of two
+
+ align:start position:0%
+write the mask as being the sum of two
+ 
+
+ align:start position:0%
+write the mask as being the sum of two
+rectangles rectangle and another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectangle so then uh it lets through
+
+ align:start position:0%
+rectangle so then uh it lets through
+ 
+
+ align:start position:0%
+rectangle so then uh it lets through
+those two components and stops the
+
+ align:start position:0%
+those two components and stops the
+ 
+
+ align:start position:0%
+those two components and stops the
+others so we got the these two two Delta
+
+ align:start position:0%
+others so we got the these two two Delta
+ 
+
+ align:start position:0%
+others so we got the these two two Delta
+functions and then we just got to do a
+
+ align:start position:0%
+functions and then we just got to do a
+ 
+
+ align:start position:0%
+functions and then we just got to do a
+for a transform again uh each of the
+
+ align:start position:0%
+for a transform again uh each of the
+ 
+
+ align:start position:0%
+for a transform again uh each of the
+Delta functions produces a a a a plain
+
+ align:start position:0%
+Delta functions produces a a a a plain
+ 
+
+ align:start position:0%
+Delta functions produces a a a a plain
+uh wave an a complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponential we then got to add those
+
+ align:start position:0%
+exponential we then got to add those
+ 
+
+ align:start position:0%
+exponential we then got to add those
+together well we got to got got to
+
+ align:start position:0%
+together well we got to got got to
+ 
+
+ align:start position:0%
+together well we got to got got to
+change the um um into distance of course
+
+ align:start position:0%
+change the um um into distance of course
+ 
+
+ align:start position:0%
+change the um um into distance of course
+uh and then uh combine these two complex
+
+ align:start position:0%
+uh and then uh combine these two complex
+ 
+
+ align:start position:0%
+uh and then uh combine these two complex
+exponentials to make a cosine and then
+
+ align:start position:0%
+exponentials to make a cosine and then
+ 
+
+ align:start position:0%
+exponentials to make a cosine and then
+finally we've got to square it again in
+
+ align:start position:0%
+finally we've got to square it again in
+ 
+
+ align:start position:0%
+finally we've got to square it again in
+order to get the intensity
+
+ align:start position:0%
+order to get the intensity
+ 
+
+ align:start position:0%
+order to get the intensity
+out and so now notice what we get
+
+ align:start position:0%
+out and so now notice what we get
+ 
+
+ align:start position:0%
+out and so now notice what we get
+now uh you see we get the constant
+
+ align:start position:0%
+now uh you see we get the constant
+ 
+
+ align:start position:0%
+now uh you see we get the constant
+term you see here is just cosine there's
+
+ align:start position:0%
+term you see here is just cosine there's
+ 
+
+ align:start position:0%
+term you see here is just cosine there's
+no constant term anymore because the
+
+ align:start position:0%
+no constant term anymore because the
+ 
+
+ align:start position:0%
+no constant term anymore because the
+constant terms gone so the COS when we
+
+ align:start position:0%
+constant terms gone so the COS when we
+ 
+
+ align:start position:0%
+constant terms gone so the COS when we
+Square it we get cos squar
+
+ align:start position:0%
+Square it we get cos squar
+ 
+
+ align:start position:0%
+Square it we get cos squar
+the COS squ we go into double angles
+
+ align:start position:0%
+the COS squ we go into double angles
+ 
+
+ align:start position:0%
+the COS squ we go into double angles
+again we get a constant plus a
+
+ align:start position:0%
+again we get a constant plus a
+ 
+
+ align:start position:0%
+again we get a constant plus a
+cosine and uh so you see that actually
+
+ align:start position:0%
+cosine and uh so you see that actually
+ 
+
+ align:start position:0%
+cosine and uh so you see that actually
+uh we get an image where the uh first
+
+ align:start position:0%
+uh we get an image where the uh first
+ 
+
+ align:start position:0%
+uh we get an image where the uh first
+harmonic doesn't appear at all but the
+
+ align:start position:0%
+harmonic doesn't appear at all but the
+ 
+
+ align:start position:0%
+harmonic doesn't appear at all but the
+second harmonic does so uh this comes
+
+ align:start position:0%
+second harmonic does so uh this comes
+ 
+
+ align:start position:0%
+second harmonic does so uh this comes
+back to your question in a way uh you
+
+ align:start position:0%
+back to your question in a way uh you
+ 
+
+ align:start position:0%
+back to your question in a way uh you
+end up with getting an image which is
+
+ align:start position:0%
+end up with getting an image which is
+ 
+
+ align:start position:0%
+end up with getting an image which is
+actually really not like the objects
+
+ align:start position:0%
+actually really not like the objects
+ 
+
+ align:start position:0%
+actually really not like the objects
+because you see that this has got twice
+
+ align:start position:0%
+because you see that this has got twice
+ 
+
+ align:start position:0%
+because you see that this has got twice
+the frequency of this
+
+ align:start position:0%
+the frequency of this
+ 
+
+ align:start position:0%
+the frequency of this
+right so uh although Abba uh says that
+
+ align:start position:0%
+right so uh although Abba uh says that
+ 
+
+ align:start position:0%
+right so uh although Abba uh says that
+you can get an image he doesn't say that
+
+ align:start position:0%
+you can get an image he doesn't say that
+ 
+
+ align:start position:0%
+you can get an image he doesn't say that
+you can get a correct image and in this
+
+ align:start position:0%
+you can get a correct image and in this
+ 
+
+ align:start position:0%
+you can get a correct image and in this
+case you could be very confused by this
+
+ align:start position:0%
+case you could be very confused by this
+ 
+
+ align:start position:0%
+case you could be very confused by this
+couldn't you you could look at in your
+
+ align:start position:0%
+couldn't you you could look at in your
+ 
+
+ align:start position:0%
+couldn't you you could look at in your
+microscope at something and you could
+
+ align:start position:0%
+microscope at something and you could
+ 
+
+ align:start position:0%
+microscope at something and you could
+see this uh and uh and you'd be
+
+ align:start position:0%
+see this uh and uh and you'd be
+ 
+
+ align:start position:0%
+see this uh and uh and you'd be
+completely mistaken about the object
+
+ align:start position:0%
+completely mistaken about the object
+ 
+
+ align:start position:0%
+completely mistaken about the object
+that was actually producing this because
+
+ align:start position:0%
+that was actually producing this because
+ 
+
+ align:start position:0%
+that was actually producing this because
+uh it's actually twice as big as what
+
+ align:start position:0%
+uh it's actually twice as big as what
+ 
+
+ align:start position:0%
+uh it's actually twice as big as what
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+expect uh so a question that's oh yeah
+
+ align:start position:0%
+expect uh so a question that's oh yeah
+ 
+
+ align:start position:0%
+expect uh so a question that's oh yeah
+um youen me if you grab just the zero
+
+ align:start position:0%
+um youen me if you grab just the zero
+ 
+
+ align:start position:0%
+um youen me if you grab just the zero
+order and say the first order but not
+
+ align:start position:0%
+order and say the first order but not
+ 
+
+ align:start position:0%
+order and say the first order but not
+the minus one then you get the same
+
+ align:start position:0%
+the minus one then you get the same
+ 
+
+ align:start position:0%
+the minus one then you get the same
+period as the original
+
+ align:start position:0%
+period as the original
+ 
+
+ align:start position:0%
+period as the original
+grading uh the yeah I guess so would
+
+ align:start position:0%
+grading uh the yeah I guess so would
+ 
+
+ align:start position:0%
+grading uh the yeah I guess so would
+that be right George if you take this
+
+ align:start position:0%
+that be right George if you take this
+ 
+
+ align:start position:0%
+that be right George if you take this
+one and this one uh so you got and then
+
+ align:start position:0%
+one and this one uh so you got and then
+ 
+
+ align:start position:0%
+one and this one uh so you got and then
+you square
+
+ align:start position:0%
+you square
+ 
+
+ align:start position:0%
+you square
+it uh you're going to get one plus an e
+
+ align:start position:0%
+it uh you're going to get one plus an e
+ 
+
+ align:start position:0%
+it uh you're going to get one plus an e
+to the I you're going
+
+ align:start position:0%
+to the I you're going
+ 
+
+ align:start position:0%
+to the I you're going
+to uh uh I don't yeah he's working it
+
+ align:start position:0%
+to uh uh I don't yeah he's working it
+ 
+
+ align:start position:0%
+to uh uh I don't yeah he's working it
+out he's working it out we have a race
+
+ align:start position:0%
+out he's working it out we have a race
+ 
+
+ align:start position:0%
+out he's working it out we have a race
+shall we
+
+ align:start position:0%
+shall we
+ 
+
+ align:start position:0%
+shall we
+um you're going to have a 1 plus e to
+
+ align:start position:0%
+um you're going to have a 1 plus e to
+ 
+
+ align:start position:0%
+um you're going to have a 1 plus e to
+the I um something or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other and then this modulus
+
+ align:start position:0%
+other and then this modulus
+ 
+
+ align:start position:0%
+other and then this modulus
+squared so and then you can take out an
+
+ align:start position:0%
+squared so and then you can take out an
+ 
+
+ align:start position:0%
+squared so and then you can take out an
+e to the ey something over two e you got
+
+ align:start position:0%
+e to the ey something over two e you got
+ 
+
+ align:start position:0%
+e to the ey something over two e you got
+the answer yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something like that so this is cosine so
+
+ align:start position:0%
+something like that so this is cosine so
+ 
+
+ align:start position:0%
+something like that so this is cosine so
+you're going to end that with cosine
+
+ align:start position:0%
+you're going to end that with cosine
+ 
+
+ align:start position:0%
+you're going to end that with cosine
+squared um it's the same as this isn't
+
+ align:start position:0%
+squared um it's the same as this isn't
+ 
+
+ align:start position:0%
+squared um it's the same as this isn't
+it the image with just with a phase term
+
+ align:start position:0%
+it the image with just with a phase term
+ 
+
+ align:start position:0%
+it the image with just with a phase term
+no it can't be because it's half as far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+apart yeah you get the first harmonic
+
+ align:start position:0%
+apart yeah you get the first harmonic
+ 
+
+ align:start position:0%
+apart yeah you get the first harmonic
+yeah because it's the square of half of
+
+ align:start position:0%
+yeah because it's the square of half of
+ 
+
+ align:start position:0%
+yeah because it's the square of half of
+it yeah okay so it's a it's it's double
+
+ align:start position:0%
+it yeah okay so it's a it's it's double
+ 
+
+ align:start position:0%
+it yeah okay so it's a it's it's double
+half of it so you do get the first
+
+ align:start position:0%
+half of it so you do get the first
+ 
+
+ align:start position:0%
+half of it so you do get the first
+harmonic yeah you're quite correct so
+
+ align:start position:0%
+harmonic yeah you're quite correct so
+ 
+
+ align:start position:0%
+harmonic yeah you're quite correct so
+but you know I mean it might work for
+
+ align:start position:0%
+but you know I mean it might work for
+ 
+
+ align:start position:0%
+but you know I mean it might work for
+this object but I guess there' be other
+
+ align:start position:0%
+this object but I guess there' be other
+ 
+
+ align:start position:0%
+this object but I guess there' be other
+objects which it would also uh produce
+
+ align:start position:0%
+objects which it would also uh produce
+ 
+
+ align:start position:0%
+objects which it would also uh produce
+funny results uh and uh and of course as
+
+ align:start position:0%
+funny results uh and uh and of course as
+ 
+
+ align:start position:0%
+funny results uh and uh and of course as
+we know um well some of us know uh most
+
+ align:start position:0%
+we know um well some of us know uh most
+ 
+
+ align:start position:0%
+we know um well some of us know uh most
+of you won't know but for example shalim
+
+ align:start position:0%
+of you won't know but for example shalim
+ 
+
+ align:start position:0%
+of you won't know but for example shalim
+will know uh that if you have uh uh a
+
+ align:start position:0%
+will know uh that if you have uh uh a
+ 
+
+ align:start position:0%
+will know uh that if you have uh uh a
+mask which is uh asymmetric like that
+
+ align:start position:0%
+mask which is uh asymmetric like that
+ 
+
+ align:start position:0%
+mask which is uh asymmetric like that
+it's going to have some quite
+
+ align:start position:0%
+it's going to have some quite
+ 
+
+ align:start position:0%
+it's going to have some quite
+interesting in properties so I don't
+
+ align:start position:0%
+interesting in properties so I don't
+ 
+
+ align:start position:0%
+interesting in properties so I don't
+know whether you go Ono these at some
+
+ align:start position:0%
+know whether you go Ono these at some
+ 
+
+ align:start position:0%
+know whether you go Ono these at some
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+point maybe in the exam okay so all
+
+ align:start position:0%
+point maybe in the exam okay so all
+ 
+
+ align:start position:0%
+point maybe in the exam okay so all
+everyone SWAT up on asymmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gratings yeah yes single Side Band
+
+ align:start position:0%
+gratings yeah yes single Side Band
+ 
+
+ align:start position:0%
+gratings yeah yes single Side Band
+modulation yeah um and what's the other
+
+ align:start position:0%
+modulation yeah um and what's the other
+ 
+
+ align:start position:0%
+modulation yeah um and what's the other
+word for it what's this um when they um
+
+ align:start position:0%
+word for it what's this um when they um
+ 
+
+ align:start position:0%
+word for it what's this um when they um
+measure the um flow of the uh in
+
+ align:start position:0%
+measure the um flow of the uh in
+ 
+
+ align:start position:0%
+measure the um flow of the uh in
+aerodynamics scheren schen it's it's
+
+ align:start position:0%
+aerodynamics scheren schen it's it's
+ 
+
+ align:start position:0%
+aerodynamics scheren schen it's it's
+it's basically
+
+ align:start position:0%
+it's basically
+ 
+
+ align:start position:0%
+it's basically
+schen
+
+ align:start position:0%
+schen
+ 
+
+ align:start position:0%
+schen
+okay uh now we're looking at uh tilted
+
+ align:start position:0%
+okay uh now we're looking at uh tilted
+ 
+
+ align:start position:0%
+okay uh now we're looking at uh tilted
+illumination so same sort of system as
+
+ align:start position:0%
+illumination so same sort of system as
+ 
+
+ align:start position:0%
+illumination so same sort of system as
+the last one uh but we're now not
+
+ align:start position:0%
+the last one uh but we're now not
+ 
+
+ align:start position:0%
+the last one uh but we're now not
+Illuminating it with a plane wave along
+
+ align:start position:0%
+Illuminating it with a plane wave along
+ 
+
+ align:start position:0%
+Illuminating it with a plane wave along
+the a axis we're going to tilt this uh
+
+ align:start position:0%
+the a axis we're going to tilt this uh
+ 
+
+ align:start position:0%
+the a axis we're going to tilt this uh
+and um so what we find what do we find
+
+ align:start position:0%
+and um so what we find what do we find
+ 
+
+ align:start position:0%
+and um so what we find what do we find
+if we uh if we got a grating and we
+
+ align:start position:0%
+if we uh if we got a grating and we
+ 
+
+ align:start position:0%
+if we uh if we got a grating and we
+illuminate it with a plain wave
+
+ align:start position:0%
+illuminate it with a plain wave
+ 
+
+ align:start position:0%
+illuminate it with a plain wave
+what what do we find happens if we tilt
+
+ align:start position:0%
+what what do we find happens if we tilt
+ 
+
+ align:start position:0%
+what what do we find happens if we tilt
+the the plane
+
+ align:start position:0%
+the the plane
+ 
+
+ align:start position:0%
+the the plane
+wave have you come across this it was
+
+ align:start position:0%
+wave have you come across this it was
+ 
+
+ align:start position:0%
+wave have you come across this it was
+you did this earlier on did you I don't
+
+ align:start position:0%
+you did this earlier on did you I don't
+ 
+
+ align:start position:0%
+you did this earlier on did you I don't
+think I was there for this one but
+
+ align:start position:0%
+think I was there for this one but
+ 
+
+ align:start position:0%
+think I was there for this one but
+actually all that happens is it just
+
+ align:start position:0%
+actually all that happens is it just
+ 
+
+ align:start position:0%
+actually all that happens is it just
+tilts the defraction pattern very simple
+
+ align:start position:0%
+tilts the defraction pattern very simple
+ 
+
+ align:start position:0%
+tilts the defraction pattern very simple
+uh so you can see now the the zero
+
+ align:start position:0%
+uh so you can see now the the zero
+ 
+
+ align:start position:0%
+uh so you can see now the the zero
+order uh is still in this this
+
+ align:start position:0%
+order uh is still in this this
+ 
+
+ align:start position:0%
+order uh is still in this this
+direction uh and um and all the other
+
+ align:start position:0%
+direction uh and um and all the other
+ 
+
+ align:start position:0%
+direction uh and um and all the other
+orders just move bodily they all rotate
+
+ align:start position:0%
+orders just move bodily they all rotate
+ 
+
+ align:start position:0%
+orders just move bodily they all rotate
+through the same angle this is actually
+
+ align:start position:0%
+through the same angle this is actually
+ 
+
+ align:start position:0%
+through the same angle this is actually
+only true if you can think of this as
+
+ align:start position:0%
+only true if you can think of this as
+ 
+
+ align:start position:0%
+only true if you can think of this as
+being a thin
+
+ align:start position:0%
+being a thin
+ 
+
+ align:start position:0%
+being a thin
+grating and uh you know if you if you go
+
+ align:start position:0%
+grating and uh you know if you if you go
+ 
+
+ align:start position:0%
+grating and uh you know if you if you go
+into a theory of volume Holograms and
+
+ align:start position:0%
+into a theory of volume Holograms and
+ 
+
+ align:start position:0%
+into a theory of volume Holograms and
+things like that then you'll find that
+
+ align:start position:0%
+things like that then you'll find that
+ 
+
+ align:start position:0%
+things like that then you'll find that
+Things become much more complicated the
+
+ align:start position:0%
+Things become much more complicated the
+ 
+
+ align:start position:0%
+Things become much more complicated the
+relative strengths of the grading can
+
+ align:start position:0%
+relative strengths of the grading can
+ 
+
+ align:start position:0%
+relative strengths of the grading can
+change and so on but if this is a a thin
+
+ align:start position:0%
+change and so on but if this is a a thin
+ 
+
+ align:start position:0%
+change and so on but if this is a a thin
+grading so that you can uh use this uh
+
+ align:start position:0%
+grading so that you can uh use this uh
+ 
+
+ align:start position:0%
+grading so that you can uh use this uh
+property that you just multiply by the
+
+ align:start position:0%
+property that you just multiply by the
+ 
+
+ align:start position:0%
+property that you just multiply by the
+transm transmission of the Great
+
+ align:start position:0%
+transm transmission of the Great
+ 
+
+ align:start position:0%
+transm transmission of the Great
+uh then that will be the case uh so you
+
+ align:start position:0%
+uh then that will be the case uh so you
+ 
+
+ align:start position:0%
+uh then that will be the case uh so you
+can see what that's going to do all the
+
+ align:start position:0%
+can see what that's going to do all the
+ 
+
+ align:start position:0%
+can see what that's going to do all the
+gratings move up uh which means that
+
+ align:start position:0%
+gratings move up uh which means that
+ 
+
+ align:start position:0%
+gratings move up uh which means that
+they all get moved up there as well so
+
+ align:start position:0%
+they all get moved up there as well so
+ 
+
+ align:start position:0%
+they all get moved up there as well so
+the uh you see the zero order
+
+ align:start position:0%
+the uh you see the zero order
+ 
+
+ align:start position:0%
+the uh you see the zero order
+grating which was appearing down at the
+
+ align:start position:0%
+grating which was appearing down at the
+ 
+
+ align:start position:0%
+grating which was appearing down at the
+origin uh is now tilted upwards uh and
+
+ align:start position:0%
+origin uh is now tilted upwards uh and
+ 
+
+ align:start position:0%
+origin uh is now tilted upwards uh and
+appears at this point here so with this
+
+ align:start position:0%
+appears at this point here so with this
+ 
+
+ align:start position:0%
+appears at this point here so with this
+band pass filter uh that we've chosen uh
+
+ align:start position:0%
+band pass filter uh that we've chosen uh
+ 
+
+ align:start position:0%
+band pass filter uh that we've chosen uh
+we now get the zero order through so
+
+ align:start position:0%
+we now get the zero order through so
+ 
+
+ align:start position:0%
+we now get the zero order through so
+we're getting the the zero order
+
+ align:start position:0%
+we're getting the the zero order
+ 
+
+ align:start position:0%
+we're getting the the zero order
+through through this one and we get in
+
+ align:start position:0%
+through through this one and we get in
+ 
+
+ align:start position:0%
+through through this one and we get in
+the minus two order through this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one right so it's we illuminate it with
+
+ align:start position:0%
+one right so it's we illuminate it with
+ 
+
+ align:start position:0%
+one right so it's we illuminate it with
+a uh uh we illiminate the grating with
+
+ align:start position:0%
+a uh uh we illiminate the grating with
+ 
+
+ align:start position:0%
+a uh uh we illiminate the grating with
+an off-axis plane wave at an angle of
+
+ align:start position:0%
+an off-axis plane wave at an angle of
+ 
+
+ align:start position:0%
+an off-axis plane wave at an angle of
+2.86
+
+ align:start position:0%
+2.86
+ 
+
+ align:start position:0%
+2.86
+5° uh which is is obviously uh very
+
+ align:start position:0%
+5° uh which is is obviously uh very
+ 
+
+ align:start position:0%
+5° uh which is is obviously uh very
+carefully designed uh so that this this
+
+ align:start position:0%
+carefully designed uh so that this this
+ 
+
+ align:start position:0%
+carefully designed uh so that this this
+grazing this gracing order moves from
+
+ align:start position:0%
+grazing this gracing order moves from
+ 
+
+ align:start position:0%
+grazing this gracing order moves from
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh so what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens okay so yeah so it's just
+
+ align:start position:0%
+happens okay so yeah so it's just
+ 
+
+ align:start position:0%
+happens okay so yeah so it's just
+describing uh what what I just
+
+ align:start position:0%
+describing uh what what I just
+ 
+
+ align:start position:0%
+describing uh what what I just
+said um yeah this is just describing why
+
+ align:start position:0%
+said um yeah this is just describing why
+ 
+
+ align:start position:0%
+said um yeah this is just describing why
+that happens then in terms of um
+
+ align:start position:0%
+that happens then in terms of um
+ 
+
+ align:start position:0%
+that happens then in terms of um
+multiplying the um
+
+ align:start position:0%
+multiplying the um
+ 
+
+ align:start position:0%
+multiplying the um
+the the uh you see this tilted wave is
+
+ align:start position:0%
+the the uh you see this tilted wave is
+ 
+
+ align:start position:0%
+the the uh you see this tilted wave is
+just going to have a a
+
+ align:start position:0%
+just going to have a a
+ 
+
+ align:start position:0%
+just going to have a a
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+uh a complex exponential phase variation
+
+ align:start position:0%
+uh a complex exponential phase variation
+ 
+
+ align:start position:0%
+uh a complex exponential phase variation
+like this so you multiply that by the
+
+ align:start position:0%
+like this so you multiply that by the
+ 
+
+ align:start position:0%
+like this so you multiply that by the
+grating uh and then the the uh it's just
+
+ align:start position:0%
+grating uh and then the the uh it's just
+ 
+
+ align:start position:0%
+grating uh and then the the uh it's just
+as this result of rotating the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing okay so um so there there are the
+
+ align:start position:0%
+thing okay so um so there there are the
+ 
+
+ align:start position:0%
+thing okay so um so there there are the
+rating
+
+ align:start position:0%
+rating
+ 
+
+ align:start position:0%
+rating
+orders uh the zero order one uh is this
+
+ align:start position:0%
+orders uh the zero order one uh is this
+ 
+
+ align:start position:0%
+orders uh the zero order one uh is this
+one uh and this is the plus and minus
+
+ align:start position:0%
+one uh and this is the plus and minus
+ 
+
+ align:start position:0%
+one uh and this is the plus and minus
+one and the plus and minus
+
+ align:start position:0%
+one and the plus and minus
+ 
+
+ align:start position:0%
+one and the plus and minus
+two uh and uh so we get let through
+
+ align:start position:0%
+two uh and uh so we get let through
+ 
+
+ align:start position:0%
+two uh and uh so we get let through
+those two so this is a bit like um so
+
+ align:start position:0%
+those two so this is a bit like um so
+ 
+
+ align:start position:0%
+those two so this is a bit like um so
+we're now letting through the uh the
+
+ align:start position:0%
+we're now letting through the uh the
+ 
+
+ align:start position:0%
+we're now letting through the uh the
+we're letting through the zero order and
+
+ align:start position:0%
+we're letting through the zero order and
+ 
+
+ align:start position:0%
+we're letting through the zero order and
+the minus two order uh so it's a bit
+
+ align:start position:0%
+the minus two order uh so it's a bit
+ 
+
+ align:start position:0%
+the minus two order uh so it's a bit
+like the the one in the question but uh
+
+ align:start position:0%
+like the the one in the question but uh
+ 
+
+ align:start position:0%
+like the the one in the question but uh
+but now it's the minus two order not the
+
+ align:start position:0%
+but now it's the minus two order not the
+ 
+
+ align:start position:0%
+but now it's the minus two order not the
+plus the not the minus one order uh so
+
+ align:start position:0%
+plus the not the minus one order uh so
+ 
+
+ align:start position:0%
+plus the not the minus one order uh so
+this is going to be another example
+
+ align:start position:0%
+this is going to be another example
+ 
+
+ align:start position:0%
+this is going to be another example
+where it doesn't give a very good image
+
+ align:start position:0%
+where it doesn't give a very good image
+ 
+
+ align:start position:0%
+where it doesn't give a very good image
+I think from that
+
+ align:start position:0%
+I think from that
+ 
+
+ align:start position:0%
+I think from that
+result uh okay
+
+ align:start position:0%
+result uh okay
+ 
+
+ align:start position:0%
+result uh okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um yeah that's just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really right here we are so it's it's 1
+
+ align:start position:0%
+really right here we are so it's it's 1
+ 
+
+ align:start position:0%
+really right here we are so it's it's 1
+cm the the
+
+ align:start position:0%
+cm the the
+ 
+
+ align:start position:0%
+cm the the
+um the magic figure that magic angle was
+
+ align:start position:0%
+um the magic figure that magic angle was
+ 
+
+ align:start position:0%
+um the magic figure that magic angle was
+designed so that they're all shifted by
+
+ align:start position:0%
+designed so that they're all shifted by
+ 
+
+ align:start position:0%
+designed so that they're all shifted by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cm so after passing through the mask we
+
+ align:start position:0%
+cm so after passing through the mask we
+ 
+
+ align:start position:0%
+cm so after passing through the mask we
+just get those two
+
+ align:start position:0%
+just get those two
+ 
+
+ align:start position:0%
+just get those two
+components uh and so these are the two
+
+ align:start position:0%
+components uh and so these are the two
+ 
+
+ align:start position:0%
+components uh and so these are the two
+components uh oh yeah
+
+ align:start position:0%
+components uh oh yeah
+ 
+
+ align:start position:0%
+components uh oh yeah
+so ah but they no it isn't yeah that's
+
+ align:start position:0%
+so ah but they no it isn't yeah that's
+ 
+
+ align:start position:0%
+so ah but they no it isn't yeah that's
+right because there're still ah so it's
+
+ align:start position:0%
+right because there're still ah so it's
+ 
+
+ align:start position:0%
+right because there're still ah so it's
+bit more complicated than what I was ah
+
+ align:start position:0%
+bit more complicated than what I was ah
+ 
+
+ align:start position:0%
+bit more complicated than what I was ah
+It's Tricky this so not only of course
+
+ align:start position:0%
+It's Tricky this so not only of course
+ 
+
+ align:start position:0%
+It's Tricky this so not only of course
+uh do we let through the the zero order
+
+ align:start position:0%
+uh do we let through the the zero order
+ 
+
+ align:start position:0%
+uh do we let through the the zero order
+and the minus two order but those orders
+
+ align:start position:0%
+and the minus two order but those orders
+ 
+
+ align:start position:0%
+and the minus two order but those orders
+have got this complex phase shift is
+
+ align:start position:0%
+have got this complex phase shift is
+ 
+
+ align:start position:0%
+have got this complex phase shift is
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah exactly exactly because of the
+
+ align:start position:0%
+um yeah exactly exactly because of the
+ 
+
+ align:start position:0%
+um yeah exactly exactly because of the
+pH because of the yeah okay so that's
+
+ align:start position:0%
+pH because of the yeah okay so that's
+ 
+
+ align:start position:0%
+pH because of the yeah okay so that's
+what I'm same so although this is a a
+
+ align:start position:0%
+what I'm same so although this is a a
+ 
+
+ align:start position:0%
+what I'm same so although this is a a
+zero order and aus2 order they're
+
+ align:start position:0%
+zero order and aus2 order they're
+ 
+
+ align:start position:0%
+zero order and aus2 order they're
+actually shifted uh and so when you do
+
+ align:start position:0%
+actually shifted uh and so when you do
+ 
+
+ align:start position:0%
+actually shifted uh and so when you do
+the fer transform uh
+
+ align:start position:0%
+the fer transform uh
+ 
+
+ align:start position:0%
+the fer transform uh
+they're they're just as though they were
+
+ align:start position:0%
+they're they're just as though they were
+ 
+
+ align:start position:0%
+they're they're just as though they were
+the plus one and the minus one order
+
+ align:start position:0%
+the plus one and the minus one order
+ 
+
+ align:start position:0%
+the plus one and the minus one order
+that's neat very
+
+ align:start position:0%
+that's neat very
+ 
+
+ align:start position:0%
+that's neat very
+interesting but with different
+
+ align:start position:0%
+interesting but with different
+ 
+
+ align:start position:0%
+interesting but with different
+amplitudes given by these two strengths
+
+ align:start position:0%
+amplitudes given by these two strengths
+ 
+
+ align:start position:0%
+amplitudes given by these two strengths
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right uh and then uh so um
+
+ align:start position:0%
+right uh and then uh so um
+ 
+
+ align:start position:0%
+right uh and then uh so um
+yeah so then then we have to um put the
+
+ align:start position:0%
+yeah so then then we have to um put the
+ 
+
+ align:start position:0%
+yeah so then then we have to um put the
+values of U in terms of the X and then
+
+ align:start position:0%
+values of U in terms of the X and then
+ 
+
+ align:start position:0%
+values of U in terms of the X and then
+we combine the two exponentials well we
+
+ align:start position:0%
+we combine the two exponentials well we
+ 
+
+ align:start position:0%
+we combine the two exponentials well we
+can't do that anymore can we oh yes we
+
+ align:start position:0%
+can't do that anymore can we oh yes we
+ 
+
+ align:start position:0%
+can't do that anymore can we oh yes we
+can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh uh yeah exactly so how have you how
+
+ align:start position:0%
+uh uh yeah exactly so how have you how
+ 
+
+ align:start position:0%
+uh uh yeah exactly so how have you how
+have you actually done that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then right so you got to do the the the
+
+ align:start position:0%
+then right so you got to do the the the
+ 
+
+ align:start position:0%
+then right so you got to do the the the
+modulus square of this so you're going
+
+ align:start position:0%
+modulus square of this so you're going
+ 
+
+ align:start position:0%
+modulus square of this so you're going
+to have this squared plus this squared
+
+ align:start position:0%
+to have this squared plus this squared
+ 
+
+ align:start position:0%
+to have this squared plus this squared
+oh yeah okay so that of course you are
+
+ align:start position:0%
+oh yeah okay so that of course you are
+ 
+
+ align:start position:0%
+oh yeah okay so that of course you are
+so then twice the products of these
+
+ align:start position:0%
+so then twice the products of these
+ 
+
+ align:start position:0%
+so then twice the products of these
+two uh and um
+
+ align:start position:0%
+two uh and um
+ 
+
+ align:start position:0%
+two uh and um
+okay that right uh no sorry that's not
+
+ align:start position:0%
+okay that right uh no sorry that's not
+ 
+
+ align:start position:0%
+okay that right uh no sorry that's not
+right is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it yeah that's right
+
+ align:start position:0%
+it yeah that's right
+ 
+
+ align:start position:0%
+it yeah that's right
+yeah yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and this is what it looks like
+
+ align:start position:0%
+okay and this is what it looks like
+ 
+
+ align:start position:0%
+okay and this is what it looks like
+T so uh okay so the field is the first
+
+ align:start position:0%
+T so uh okay so the field is the first
+ 
+
+ align:start position:0%
+T so uh okay so the field is the first
+harmonic the intensity is the second
+
+ align:start position:0%
+harmonic the intensity is the second
+ 
+
+ align:start position:0%
+harmonic the intensity is the second
+harmonic because of the squaring and the
+
+ align:start position:0%
+harmonic because of the squaring and the
+ 
+
+ align:start position:0%
+harmonic because of the squaring and the
+contrast is
+
+ align:start position:0%
+contrast is
+ 
+
+ align:start position:0%
+contrast is
+.7 right so again we end up with a bad
+
+ align:start position:0%
+.7 right so again we end up with a bad
+ 
+
+ align:start position:0%
+.7 right so again we end up with a bad
+image because it's shifted uh because
+
+ align:start position:0%
+image because it's shifted uh because
+ 
+
+ align:start position:0%
+image because it's shifted uh because
+it's double frequency and also the
+
+ align:start position:0%
+it's double frequency and also the
+ 
+
+ align:start position:0%
+it's double frequency and also the
+contrast is reduced in this case because
+
+ align:start position:0%
+contrast is reduced in this case because
+ 
+
+ align:start position:0%
+contrast is reduced in this case because
+the strength of the two beams was not
+
+ align:start position:0%
+the strength of the two beams was not
+ 
+
+ align:start position:0%
+the strength of the two beams was not
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+uh this is calculating here the contrast
+
+ align:start position:0%
+uh this is calculating here the contrast
+ 
+
+ align:start position:0%
+uh this is calculating here the contrast
+this is the normal definition of
+
+ align:start position:0%
+this is the normal definition of
+ 
+
+ align:start position:0%
+this is the normal definition of
+contrast of
+
+ align:start position:0%
+contrast of
+ 
+
+ align:start position:0%
+contrast of
+fringes uh the difference over the
+
+ align:start position:0%
+fringes uh the difference over the
+ 
+
+ align:start position:0%
+fringes uh the difference over the
+sum uh and it comes to 7062 the previous
+
+ align:start position:0%
+sum uh and it comes to 7062 the previous
+ 
+
+ align:start position:0%
+sum uh and it comes to 7062 the previous
+case of course it was uh the contrast
+
+ align:start position:0%
+case of course it was uh the contrast
+ 
+
+ align:start position:0%
+case of course it was uh the contrast
+was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one right another example a new pupil
+
+ align:start position:0%
+one right another example a new pupil
+ 
+
+ align:start position:0%
+one right another example a new pupil
+mask consisting of two holes each of Di
+
+ align:start position:0%
+mask consisting of two holes each of Di
+ 
+
+ align:start position:0%
+mask consisting of two holes each of Di
+1 cm and centered further away from the
+
+ align:start position:0%
+1 cm and centered further away from the
+ 
+
+ align:start position:0%
+1 cm and centered further away from the
+axis at plus orus 2 cm from the optical
+
+ align:start position:0%
+axis at plus orus 2 cm from the optical
+ 
+
+ align:start position:0%
+axis at plus orus 2 cm from the optical
+axis respectively what is the intensity
+
+ align:start position:0%
+axis respectively what is the intensity
+ 
+
+ align:start position:0%
+axis respectively what is the intensity
+observed at the output image plane right
+
+ align:start position:0%
+observed at the output image plane right
+ 
+
+ align:start position:0%
+observed at the output image plane right
+so at least it's told us the 2 cm we
+
+ align:start position:0%
+so at least it's told us the 2 cm we
+ 
+
+ align:start position:0%
+so at least it's told us the 2 cm we
+know where that is we don't have to
+
+ align:start position:0%
+know where that is we don't have to
+ 
+
+ align:start position:0%
+know where that is we don't have to
+worry about working out what
+
+ align:start position:0%
+worry about working out what
+ 
+
+ align:start position:0%
+worry about working out what
+3479 degrees is uh we know that the the
+
+ align:start position:0%
+3479 degrees is uh we know that the the
+ 
+
+ align:start position:0%
+3479 degrees is uh we know that the the
+first one first uh order was at 1 C CM
+
+ align:start position:0%
+first one first uh order was at 1 C CM
+ 
+
+ align:start position:0%
+first one first uh order was at 1 C CM
+so uh this this is the second order is
+
+ align:start position:0%
+so uh this this is the second order is
+ 
+
+ align:start position:0%
+so uh this this is the second order is
+where the aperture is so the second
+
+ align:start position:0%
+where the aperture is so the second
+ 
+
+ align:start position:0%
+where the aperture is so the second
+order is going to get through the plus
+
+ align:start position:0%
+order is going to get through the plus
+ 
+
+ align:start position:0%
+order is going to get through the plus
+two and the minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two uh and did that did that appear then
+
+ align:start position:0%
+two uh and did that did that appear then
+ 
+
+ align:start position:0%
+two uh and did that did that appear then
+up there right okay so the second
+
+ align:start position:0%
+up there right okay so the second
+ 
+
+ align:start position:0%
+up there right okay so the second
+harmonic is going to get through and
+
+ align:start position:0%
+harmonic is going to get through and
+ 
+
+ align:start position:0%
+harmonic is going to get through and
+when you do the square of that you're
+
+ align:start position:0%
+when you do the square of that you're
+ 
+
+ align:start position:0%
+when you do the square of that you're
+going to get the fourth Harmony
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so this is going through the mass of
+
+ align:start position:0%
+uh so this is going through the mass of
+ 
+
+ align:start position:0%
+uh so this is going through the mass of
+that then uh so we got these just these
+
+ align:start position:0%
+that then uh so we got these just these
+ 
+
+ align:start position:0%
+that then uh so we got these just these
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+components um so these have now got two
+
+ align:start position:0%
+components um so these have now got two
+ 
+
+ align:start position:0%
+components um so these have now got two
+cm in rather than 1
+
+ align:start position:0%
+cm in rather than 1
+ 
+
+ align:start position:0%
+cm in rather than 1
+cm uh so that means that you get a two
+
+ align:start position:0%
+cm uh so that means that you get a two
+ 
+
+ align:start position:0%
+cm uh so that means that you get a two
+multiplied in here that wasn't there
+
+ align:start position:0%
+multiplied in here that wasn't there
+ 
+
+ align:start position:0%
+multiplied in here that wasn't there
+before uh so that's the where the
+
+ align:start position:0%
+before uh so that's the where the
+ 
+
+ align:start position:0%
+before uh so that's the where the
+um second harmonic comes in and then
+
+ align:start position:0%
+um second harmonic comes in and then
+ 
+
+ align:start position:0%
+um second harmonic comes in and then
+when you do the square again you're only
+
+ align:start position:0%
+when you do the square again you're only
+ 
+
+ align:start position:0%
+when you do the square again you're only
+going to get the cosine and no constant
+
+ align:start position:0%
+going to get the cosine and no constant
+ 
+
+ align:start position:0%
+going to get the cosine and no constant
+term and then you do cos squar and
+
+ align:start position:0%
+term and then you do cos squar and
+ 
+
+ align:start position:0%
+term and then you do cos squar and
+change that into uh double angles or for
+
+ align:start position:0%
+change that into uh double angles or for
+ 
+
+ align:start position:0%
+change that into uh double angles or for
+four angles actually uh and now we're
+
+ align:start position:0%
+four angles actually uh and now we're
+ 
+
+ align:start position:0%
+four angles actually uh and now we're
+going to see what it looks like uh and
+
+ align:start position:0%
+going to see what it looks like uh and
+ 
+
+ align:start position:0%
+going to see what it looks like uh and
+now it's it's even worse an image of
+
+ align:start position:0%
+now it's it's even worse an image of
+ 
+
+ align:start position:0%
+now it's it's even worse an image of
+what we wanted so this I guess this is
+
+ align:start position:0%
+what we wanted so this I guess this is
+ 
+
+ align:start position:0%
+what we wanted so this I guess this is
+mainly telling us what we shouldn't do
+
+ align:start position:0%
+mainly telling us what we shouldn't do
+ 
+
+ align:start position:0%
+mainly telling us what we shouldn't do
+rather than what we should do yeah
+
+ align:start position:0%
+rather than what we should do yeah
+ 
+
+ align:start position:0%
+rather than what we should do yeah
+another question uh is this still
+
+ align:start position:0%
+another question uh is this still
+ 
+
+ align:start position:0%
+another question uh is this still
+assuming F1 equals FS2 and what happens
+
+ align:start position:0%
+assuming F1 equals FS2 and what happens
+ 
+
+ align:start position:0%
+assuming F1 equals FS2 and what happens
+if FS2 is smaller than F1
+
+ align:start position:0%
+if FS2 is smaller than F1
+ 
+
+ align:start position:0%
+if FS2 is smaller than F1
+uh all it would do if you change the
+
+ align:start position:0%
+uh all it would do if you change the
+ 
+
+ align:start position:0%
+uh all it would do if you change the
+relative values of F and F1 and F2 all
+
+ align:start position:0%
+relative values of F and F1 and F2 all
+ 
+
+ align:start position:0%
+relative values of F and F1 and F2 all
+it would do uh is is is change the the
+
+ align:start position:0%
+it would do uh is is is change the the
+ 
+
+ align:start position:0%
+it would do uh is is is change the the
+size of the final image right if you if
+
+ align:start position:0%
+size of the final image right if you if
+ 
+
+ align:start position:0%
+size of the final image right if you if
+you think about this system um let's go
+
+ align:start position:0%
+you think about this system um let's go
+ 
+
+ align:start position:0%
+you think about this system um let's go
+back to one where it shows that here we
+
+ align:start position:0%
+back to one where it shows that here we
+ 
+
+ align:start position:0%
+back to one where it shows that here we
+are uh you can see that um it's only the
+
+ align:start position:0%
+are uh you can see that um it's only the
+ 
+
+ align:start position:0%
+are uh you can see that um it's only the
+relative sizes of the the rest relative
+
+ align:start position:0%
+relative sizes of the the rest relative
+ 
+
+ align:start position:0%
+relative sizes of the the rest relative
+distances uh from the
+
+ align:start position:0%
+distances uh from the
+ 
+
+ align:start position:0%
+distances uh from the
+axis uh
+
+ align:start position:0%
+axis uh
+ 
+
+ align:start position:0%
+axis uh
+only depend on the this part of the
+
+ align:start position:0%
+only depend on the this part of the
+ 
+
+ align:start position:0%
+only depend on the this part of the
+optical system and then after the after
+
+ align:start position:0%
+optical system and then after the after
+ 
+
+ align:start position:0%
+optical system and then after the after
+the the pupil mask we've already decided
+
+ align:start position:0%
+the the pupil mask we've already decided
+ 
+
+ align:start position:0%
+the the pupil mask we've already decided
+then what orders get into the final
+
+ align:start position:0%
+then what orders get into the final
+ 
+
+ align:start position:0%
+then what orders get into the final
+image uh and then the final part all
+
+ align:start position:0%
+image uh and then the final part all
+ 
+
+ align:start position:0%
+image uh and then the final part all
+that's going to do is just change the
+
+ align:start position:0%
+that's going to do is just change the
+ 
+
+ align:start position:0%
+that's going to do is just change the
+relative size of the final image you see
+
+ align:start position:0%
+relative size of the final image you see
+ 
+
+ align:start position:0%
+relative size of the final image you see
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now we're going to do another bit
+
+ align:start position:0%
+right now we're going to do another bit
+ 
+
+ align:start position:0%
+right now we're going to do another bit
+more complicated one a phase pupil
+
+ align:start position:0%
+more complicated one a phase pupil
+ 
+
+ align:start position:0%
+more complicated one a phase pupil
+mask uh and so what is what this is
+
+ align:start position:0%
+mask uh and so what is what this is
+ 
+
+ align:start position:0%
+mask uh and so what is what this is
+shown as uh is you can see it's got a an
+
+ align:start position:0%
+shown as uh is you can see it's got a an
+ 
+
+ align:start position:0%
+shown as uh is you can see it's got a an
+opaque part of the screen here uh and
+
+ align:start position:0%
+opaque part of the screen here uh and
+ 
+
+ align:start position:0%
+opaque part of the screen here uh and
+then in the central part it's it's
+
+ align:start position:0%
+then in the central part it's it's
+ 
+
+ align:start position:0%
+then in the central part it's it's
+transparent uh but it's got some uh some
+
+ align:start position:0%
+transparent uh but it's got some uh some
+ 
+
+ align:start position:0%
+transparent uh but it's got some uh some
+sort of structure there uh some some
+
+ align:start position:0%
+sort of structure there uh some some
+ 
+
+ align:start position:0%
+sort of structure there uh some some
+diffractive uh dialect element which
+
+ align:start position:0%
+diffractive uh dialect element which
+ 
+
+ align:start position:0%
+diffractive uh dialect element which
+changes the relative phase of this
+
+ align:start position:0%
+changes the relative phase of this
+ 
+
+ align:start position:0%
+changes the relative phase of this
+order compared with the other
+
+ align:start position:0%
+order compared with the other
+ 
+
+ align:start position:0%
+order compared with the other
+orders uh so the question is what's that
+
+ align:start position:0%
+orders uh so the question is what's that
+ 
+
+ align:start position:0%
+orders uh so the question is what's that
+going to do to your your your image uh
+
+ align:start position:0%
+going to do to your your your image uh
+ 
+
+ align:start position:0%
+going to do to your your your image uh
+so the rest of the system is completely
+
+ align:start position:0%
+so the rest of the system is completely
+ 
+
+ align:start position:0%
+so the rest of the system is completely
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same uh so this is this is what we're
+
+ align:start position:0%
+same uh so this is this is what we're
+ 
+
+ align:start position:0%
+same uh so this is this is what we're
+considering putting in there uh it
+
+ align:start position:0%
+considering putting in there uh it
+ 
+
+ align:start position:0%
+considering putting in there uh it
+doesn't matter what the thickness of
+
+ align:start position:0%
+doesn't matter what the thickness of
+ 
+
+ align:start position:0%
+doesn't matter what the thickness of
+this is because all that's going to do
+
+ align:start position:0%
+this is because all that's going to do
+ 
+
+ align:start position:0%
+this is because all that's going to do
+is change the relative phase of all of
+
+ align:start position:0%
+is change the relative phase of all of
+ 
+
+ align:start position:0%
+is change the relative phase of all of
+these so it won't affect how they
+
+ align:start position:0%
+these so it won't affect how they
+ 
+
+ align:start position:0%
+these so it won't affect how they
+interfere with each other it just Chang
+
+ align:start position:0%
+interfere with each other it just Chang
+ 
+
+ align:start position:0%
+interfere with each other it just Chang
+the phase of the final image which you
+
+ align:start position:0%
+the phase of the final image which you
+ 
+
+ align:start position:0%
+the phase of the final image which you
+don't see anyway uh but what is
+
+ align:start position:0%
+don't see anyway uh but what is
+ 
+
+ align:start position:0%
+don't see anyway uh but what is
+important uh is this bit here uh the
+
+ align:start position:0%
+important uh is this bit here uh the
+ 
+
+ align:start position:0%
+important uh is this bit here uh the
+thickness of this uh s equal .25
+
+ align:start position:0%
+thickness of this uh s equal .25
+ 
+
+ align:start position:0%
+thickness of this uh s equal .25
+microns uh and the wavelength was half
+
+ align:start position:0%
+microns uh and the wavelength was half
+ 
+
+ align:start position:0%
+microns uh and the wavelength was half
+of5
+
+ align:start position:0%
+of5
+ 
+
+ align:start position:0%
+of5
+microns uh so that's Lambda by two uh so
+
+ align:start position:0%
+microns uh so that's Lambda by two uh so
+ 
+
+ align:start position:0%
+microns uh so that's Lambda by two uh so
+that means changes the phase uh it by
+
+ align:start position:0%
+that means changes the phase uh it by
+ 
+
+ align:start position:0%
+that means changes the phase uh it by
+180° right
+
+ align:start position:0%
+180° right
+ 
+
+ align:start position:0%
+180° right
+so M ah n minus one
+
+ align:start position:0%
+so M ah n minus one
+ 
+
+ align:start position:0%
+so M ah n minus one
+uh oh yeah n minus one so it's not going
+
+ align:start position:0%
+uh oh yeah n minus one so it's not going
+ 
+
+ align:start position:0%
+uh oh yeah n minus one so it's not going
+to do that take it back okay it's Pi by
+
+ align:start position:0%
+to do that take it back okay it's Pi by
+ 
+
+ align:start position:0%
+to do that take it back okay it's Pi by
+twoing right okay uh
+
+ align:start position:0%
+twoing right okay uh
+ 
+
+ align:start position:0%
+twoing right okay uh
+so okay this is known as a phase pupil
+
+ align:start position:0%
+so okay this is known as a phase pupil
+ 
+
+ align:start position:0%
+so okay this is known as a phase pupil
+mask or a pupil phase mask or a mask
+
+ align:start position:0%
+mask or a pupil phase mask or a mask
+ 
+
+ align:start position:0%
+mask or a pupil phase mask or a mask
+pupil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phe yeah it yeah that's right so that
+
+ align:start position:0%
+phe yeah it yeah that's right so that
+ 
+
+ align:start position:0%
+phe yeah it yeah that's right so that
+must be in the next lecture because it's
+
+ align:start position:0%
+must be in the next lecture because it's
+ 
+
+ align:start position:0%
+must be in the next lecture because it's
+not in this one uh so that is getting on
+
+ align:start position:0%
+not in this one uh so that is getting on
+ 
+
+ align:start position:0%
+not in this one uh so that is getting on
+to the real applications okay so George
+
+ align:start position:0%
+to the real applications okay so George
+ 
+
+ align:start position:0%
+to the real applications okay so George
+George said that I would have just
+
+ align:start position:0%
+George said that I would have just
+ 
+
+ align:start position:0%
+George said that I would have just
+failed the exam uh because I I forgot
+
+ align:start position:0%
+failed the exam uh because I I forgot
+ 
+
+ align:start position:0%
+failed the exam uh because I I forgot
+the minus one so of course this light
+
+ align:start position:0%
+the minus one so of course this light
+ 
+
+ align:start position:0%
+the minus one so of course this light
+this light goes through the glass but
+
+ align:start position:0%
+this light goes through the glass but
+ 
+
+ align:start position:0%
+this light goes through the glass but
+this light goes through the glass and
+
+ align:start position:0%
+this light goes through the glass and
+ 
+
+ align:start position:0%
+this light goes through the glass and
+then the air right so to work out the
+
+ align:start position:0%
+then the air right so to work out the
+ 
+
+ align:start position:0%
+then the air right so to work out the
+relative phases of these you have to uh
+
+ align:start position:0%
+relative phases of these you have to uh
+ 
+
+ align:start position:0%
+relative phases of these you have to uh
+look at the relative uh change in the
+
+ align:start position:0%
+look at the relative uh change in the
+ 
+
+ align:start position:0%
+look at the relative uh change in the
+refractive index times the optical
+
+ align:start position:0%
+refractive index times the optical
+ 
+
+ align:start position:0%
+refractive index times the optical
+thickness right so um this is 0.25
+
+ align:start position:0%
+thickness right so um this is 0.25
+ 
+
+ align:start position:0%
+thickness right so um this is 0.25
+microns uh and um this is a025 microns
+
+ align:start position:0%
+microns uh and um this is a025 microns
+ 
+
+ align:start position:0%
+microns uh and um this is a025 microns
+divided by the wavelength and it's going
+
+ align:start position:0%
+divided by the wavelength and it's going
+ 
+
+ align:start position:0%
+divided by the wavelength and it's going
+to be multiplied by 1.5 minus uh one so
+
+ align:start position:0%
+to be multiplied by 1.5 minus uh one so
+ 
+
+ align:start position:0%
+to be multiplied by 1.5 minus uh one so
+this is assuming it's glass uh so uh
+
+ align:start position:0%
+this is assuming it's glass uh so uh
+ 
+
+ align:start position:0%
+this is assuming it's glass uh so uh
+this means that the uh phase change is
+
+ align:start position:0%
+this means that the uh phase change is
+ 
+
+ align:start position:0%
+this means that the uh phase change is
+pi over
+
+ align:start position:0%
+pi over
+ 
+
+ align:start position:0%
+pi over
+two right so not not Pi but pi over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two okay so exactly the same grating
+
+ align:start position:0%
+two okay so exactly the same grating
+ 
+
+ align:start position:0%
+two okay so exactly the same grating
+these are all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orders uh and uh so you now you see um
+
+ align:start position:0%
+orders uh and uh so you now you see um
+ 
+
+ align:start position:0%
+orders uh and uh so you now you see um
+first of all we get rid of these outer
+
+ align:start position:0%
+first of all we get rid of these outer
+ 
+
+ align:start position:0%
+first of all we get rid of these outer
+ones we let through just these three uh
+
+ align:start position:0%
+ones we let through just these three uh
+ 
+
+ align:start position:0%
+ones we let through just these three uh
+but of those uh we're also going to to
+
+ align:start position:0%
+but of those uh we're also going to to
+ 
+
+ align:start position:0%
+but of those uh we're also going to to
+uh change the relative phase uh of this
+
+ align:start position:0%
+uh change the relative phase uh of this
+ 
+
+ align:start position:0%
+uh change the relative phase uh of this
+one relative to the other two that
+
+ align:start position:0%
+one relative to the other two that
+ 
+
+ align:start position:0%
+one relative to the other two that
+doesn't matter of course if you uh in
+
+ align:start position:0%
+doesn't matter of course if you uh in
+ 
+
+ align:start position:0%
+doesn't matter of course if you uh in
+your sum whether you change the the
+
+ align:start position:0%
+your sum whether you change the the
+ 
+
+ align:start position:0%
+your sum whether you change the the
+phase of this or you change the phase of
+
+ align:start position:0%
+phase of this or you change the phase of
+ 
+
+ align:start position:0%
+phase of this or you change the phase of
+the other two it's only the relative
+
+ align:start position:0%
+the other two it's only the relative
+ 
+
+ align:start position:0%
+the other two it's only the relative
+phase uh which is the important
+
+ align:start position:0%
+phase uh which is the important
+ 
+
+ align:start position:0%
+phase uh which is the important
+thing okay
+
+ align:start position:0%
+thing okay
+ 
+
+ align:start position:0%
+thing okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay so these are the three
+
+ align:start position:0%
+uh okay so these are the three
+ 
+
+ align:start position:0%
+uh okay so these are the three
+conditions then for the ones that are
+
+ align:start position:0%
+conditions then for the ones that are
+ 
+
+ align:start position:0%
+conditions then for the ones that are
+not don't get through at all the
+
+ align:start position:0%
+not don't get through at all the
+ 
+
+ align:start position:0%
+not don't get through at all the
+strength of those is zero then is here
+
+ align:start position:0%
+strength of those is zero then is here
+ 
+
+ align:start position:0%
+strength of those is zero then is here
+we're taking this these ones to be of
+
+ align:start position:0%
+we're taking this these ones to be of
+ 
+
+ align:start position:0%
+we're taking this these ones to be of
+strength
+
+ align:start position:0%
+strength
+ 
+
+ align:start position:0%
+strength
+one and this one in the center uh to be
+
+ align:start position:0%
+one and this one in the center uh to be
+ 
+
+ align:start position:0%
+one and this one in the center uh to be
+a strength of e to the
+
+ align:start position:0%
+a strength of e to the
+ 
+
+ align:start position:0%
+a strength of e to the
+if5 uh and uh we know that e to the uh
+
+ align:start position:0%
+if5 uh and uh we know that e to the uh
+ 
+
+ align:start position:0%
+if5 uh and uh we know that e to the uh
+we know that f is pi/ 2 so this is e to
+
+ align:start position:0%
+we know that f is pi/ 2 so this is e to
+ 
+
+ align:start position:0%
+we know that f is pi/ 2 so this is e to
+the I pi over 2 uh which is just I is
+
+ align:start position:0%
+the I pi over 2 uh which is just I is
+ 
+
+ align:start position:0%
+the I pi over 2 uh which is just I is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+right um why have we got this IUS one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then so one way to write this pupil
+
+ align:start position:0%
+then so one way to write this pupil
+ 
+
+ align:start position:0%
+then so one way to write this pupil
+function is as a rect that is as big as
+
+ align:start position:0%
+function is as a rect that is as big as
+ 
+
+ align:start position:0%
+function is as a rect that is as big as
+the opening yeah yeah okay sorry yeah um
+
+ align:start position:0%
+the opening yeah yeah okay sorry yeah um
+ 
+
+ align:start position:0%
+the opening yeah yeah okay sorry yeah um
+so yeah so you can think of this as
+
+ align:start position:0%
+so yeah so you can think of this as
+ 
+
+ align:start position:0%
+so yeah so you can think of this as
+being um uh the whole thing uh uh the
+
+ align:start position:0%
+being um uh the whole thing uh uh the
+ 
+
+ align:start position:0%
+being um uh the whole thing uh uh the
+minus well this this this on top of the
+
+ align:start position:0%
+minus well this this this on top of the
+ 
+
+ align:start position:0%
+minus well this this this on top of the
+whole rectangle right otherwise you'd
+
+ align:start position:0%
+whole rectangle right otherwise you'd
+ 
+
+ align:start position:0%
+whole rectangle right otherwise you'd
+have to do this little bit of rectangle
+
+ align:start position:0%
+have to do this little bit of rectangle
+ 
+
+ align:start position:0%
+have to do this little bit of rectangle
+and this bit of rectangle and this bit
+
+ align:start position:0%
+and this bit of rectangle and this bit
+ 
+
+ align:start position:0%
+and this bit of rectangle and this bit
+of rectangle there three things so you
+
+ align:start position:0%
+of rectangle there three things so you
+ 
+
+ align:start position:0%
+of rectangle there three things so you
+could do it either of those ways I guess
+
+ align:start position:0%
+could do it either of those ways I guess
+ 
+
+ align:start position:0%
+could do it either of those ways I guess
+but the way that George has said done it
+
+ align:start position:0%
+but the way that George has said done it
+ 
+
+ align:start position:0%
+but the way that George has said done it
+here it's the rectangle the whole lot
+
+ align:start position:0%
+here it's the rectangle the whole lot
+ 
+
+ align:start position:0%
+here it's the rectangle the whole lot
+it's all of this uh minus the central
+
+ align:start position:0%
+it's all of this uh minus the central
+ 
+
+ align:start position:0%
+it's all of this uh minus the central
+one plus the central one with the phase
+
+ align:start position:0%
+one plus the central one with the phase
+ 
+
+ align:start position:0%
+one plus the central one with the phase
+change right so that's the minus the one
+
+ align:start position:0%
+change right so that's the minus the one
+ 
+
+ align:start position:0%
+change right so that's the minus the one
+that's not there plus the one that is
+
+ align:start position:0%
+that's not there plus the one that is
+ 
+
+ align:start position:0%
+that's not there plus the one that is
+there with a phase change
+
+ align:start position:0%
+there with a phase change
+ 
+
+ align:start position:0%
+there with a phase change
+and uh yeah so now we we well of course
+
+ align:start position:0%
+and uh yeah so now we we well of course
+ 
+
+ align:start position:0%
+and uh yeah so now we we well of course
+we still
+
+ align:start position:0%
+we still
+ 
+
+ align:start position:0%
+we still
+get uh all these Delta functions but now
+
+ align:start position:0%
+get uh all these Delta functions but now
+ 
+
+ align:start position:0%
+get uh all these Delta functions but now
+we've got some eyes coming
+
+ align:start position:0%
+we've got some eyes coming
+ 
+
+ align:start position:0%
+we've got some eyes coming
+in sorry just one ey just one eye yeah
+
+ align:start position:0%
+in sorry just one ey just one eye yeah
+ 
+
+ align:start position:0%
+in sorry just one ey just one eye yeah
+uh and uh and then uh these two combin
+
+ align:start position:0%
+uh and uh and then uh these two combin
+ 
+
+ align:start position:0%
+uh and uh and then uh these two combin
+to produce cosine still I guess if you
+
+ align:start position:0%
+to produce cosine still I guess if you
+ 
+
+ align:start position:0%
+to produce cosine still I guess if you
+change the pH of one relative to the
+
+ align:start position:0%
+change the pH of one relative to the
+ 
+
+ align:start position:0%
+change the pH of one relative to the
+other it' be more complicated uh but if
+
+ align:start position:0%
+other it' be more complicated uh but if
+ 
+
+ align:start position:0%
+other it' be more complicated uh but if
+these two produce a cosine so we've got
+
+ align:start position:0%
+these two produce a cosine so we've got
+ 
+
+ align:start position:0%
+these two produce a cosine so we've got
+an i plus a
+
+ align:start position:0%
+an i plus a
+ 
+
+ align:start position:0%
+an i plus a
+cosine uh and then we do the modulus
+
+ align:start position:0%
+cosine uh and then we do the modulus
+ 
+
+ align:start position:0%
+cosine uh and then we do the modulus
+square of that uh and the modulus square
+
+ align:start position:0%
+square of that uh and the modulus square
+ 
+
+ align:start position:0%
+square of that uh and the modulus square
+of that of course is um you're not going
+
+ align:start position:0%
+of that of course is um you're not going
+ 
+
+ align:start position:0%
+of that of course is um you're not going
+to get a cross product term are you
+
+ align:start position:0%
+to get a cross product term are you
+ 
+
+ align:start position:0%
+to get a cross product term are you
+because these two uh are in Phase
+
+ align:start position:0%
+because these two uh are in Phase
+ 
+
+ align:start position:0%
+because these two uh are in Phase
+quadrature so when you do the modulus
+
+ align:start position:0%
+quadrature so when you do the modulus
+ 
+
+ align:start position:0%
+quadrature so when you do the modulus
+Square uh you're only going to is that
+
+ align:start position:0%
+Square uh you're only going to is that
+ 
+
+ align:start position:0%
+Square uh you're only going to is that
+right yeah you're going to get this
+
+ align:start position:0%
+right yeah you're going to get this
+ 
+
+ align:start position:0%
+right yeah you're going to get this
+squar plus this squared and this squared
+
+ align:start position:0%
+squar plus this squared and this squared
+ 
+
+ align:start position:0%
+squar plus this squared and this squared
+you can write as these two
+
+ align:start position:0%
+you can write as these two
+ 
+
+ align:start position:0%
+you can write as these two
+terms uh when you do the the double
+
+ align:start position:0%
+terms uh when you do the the double
+ 
+
+ align:start position:0%
+terms uh when you do the the double
+angle and I guess the next one we're
+
+ align:start position:0%
+angle and I guess the next one we're
+ 
+
+ align:start position:0%
+angle and I guess the next one we're
+going to see what it looks like T this
+
+ align:start position:0%
+going to see what it looks like T this
+ 
+
+ align:start position:0%
+going to see what it looks like T this
+is what it looks like uh first harmonic
+
+ align:start position:0%
+is what it looks like uh first harmonic
+ 
+
+ align:start position:0%
+is what it looks like uh first harmonic
+in field second harmonic in intensity
+
+ align:start position:0%
+in field second harmonic in intensity
+ 
+
+ align:start position:0%
+in field second harmonic in intensity
+because of the
+
+ align:start position:0%
+because of the
+ 
+
+ align:start position:0%
+because of the
+squarey uh and again the contrast is now
+
+ align:start position:0%
+squarey uh and again the contrast is now
+ 
+
+ align:start position:0%
+squarey uh and again the contrast is now
+much reduced actually in this case uh
+
+ align:start position:0%
+much reduced actually in this case uh
+ 
+
+ align:start position:0%
+much reduced actually in this case uh
+down to
+
+ align:start position:0%
+down to
+ 
+
+ align:start position:0%
+down to
+0.25 um so I guess this hasn't turned
+
+ align:start position:0%
+0.25 um so I guess this hasn't turned
+ 
+
+ align:start position:0%
+0.25 um so I guess this hasn't turned
+out to be a very good strategy this this
+
+ align:start position:0%
+out to be a very good strategy this this
+ 
+
+ align:start position:0%
+out to be a very good strategy this this
+lecture seems to be mainly showing you
+
+ align:start position:0%
+lecture seems to be mainly showing you
+ 
+
+ align:start position:0%
+lecture seems to be mainly showing you
+what you shouldn't do when you make your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+microscope okay uh right
+
+ align:start position:0%
+microscope okay uh right
+ 
+
+ align:start position:0%
+microscope okay uh right
+so uh so now we're going to go on to
+
+ align:start position:0%
+so uh so now we're going to go on to
+ 
+
+ align:start position:0%
+so uh so now we're going to go on to
+think of this in terms of um what we
+
+ align:start position:0%
+think of this in terms of um what we
+ 
+
+ align:start position:0%
+think of this in terms of um what we
+call a point spread function of the low
+
+ align:start position:0%
+call a point spread function of the low
+ 
+
+ align:start position:0%
+call a point spread function of the low
+pass filter so do you remember that um
+
+ align:start position:0%
+pass filter so do you remember that um
+ 
+
+ align:start position:0%
+pass filter so do you remember that um
+going back to our analogies with
+
+ align:start position:0%
+going back to our analogies with
+ 
+
+ align:start position:0%
+going back to our analogies with
+electronics uh we can think of in
+
+ align:start position:0%
+electronics uh we can think of in
+ 
+
+ align:start position:0%
+electronics uh we can think of in
+electronics we think of um you can
+
+ align:start position:0%
+electronics we think of um you can
+ 
+
+ align:start position:0%
+electronics we think of um you can
+either think
+
+ align:start position:0%
+either think
+ 
+
+ align:start position:0%
+either think
+of you you think of your high-fi
+
+ align:start position:0%
+of you you think of your high-fi
+ 
+
+ align:start position:0%
+of you you think of your high-fi
+amplifier as being like a black box
+
+ align:start position:0%
+amplifier as being like a black box
+ 
+
+ align:start position:0%
+amplifier as being like a black box
+don't you and you put in something and
+
+ align:start position:0%
+don't you and you put in something and
+ 
+
+ align:start position:0%
+don't you and you put in something and
+you get out
+
+ align:start position:0%
+you get out
+ 
+
+ align:start position:0%
+you get out
+something uh and you can either think of
+
+ align:start position:0%
+something uh and you can either think of
+ 
+
+ align:start position:0%
+something uh and you can either think of
+what happens inside there as being like
+
+ align:start position:0%
+what happens inside there as being like
+ 
+
+ align:start position:0%
+what happens inside there as being like
+a h of T an Impulse response or you can
+
+ align:start position:0%
+a h of T an Impulse response or you can
+ 
+
+ align:start position:0%
+a h of T an Impulse response or you can
+think of it as being a um a a frequency
+
+ align:start position:0%
+think of it as being a um a a frequency
+ 
+
+ align:start position:0%
+think of it as being a um a a frequency
+response right so uh there are two two
+
+ align:start position:0%
+response right so uh there are two two
+ 
+
+ align:start position:0%
+response right so uh there are two two
+different ways of thinking about this
+
+ align:start position:0%
+different ways of thinking about this
+ 
+
+ align:start position:0%
+different ways of thinking about this
+black box the same is true in this case
+
+ align:start position:0%
+black box the same is true in this case
+ 
+
+ align:start position:0%
+black box the same is true in this case
+so up until now we've been thinking of
+
+ align:start position:0%
+so up until now we've been thinking of
+ 
+
+ align:start position:0%
+so up until now we've been thinking of
+this in terms of uh the frequency
+
+ align:start position:0%
+this in terms of uh the frequency
+ 
+
+ align:start position:0%
+this in terms of uh the frequency
+response what frequencies get into the
+
+ align:start position:0%
+response what frequencies get into the
+ 
+
+ align:start position:0%
+response what frequencies get into the
+image uh and now we're going to think of
+
+ align:start position:0%
+image uh and now we're going to think of
+ 
+
+ align:start position:0%
+image uh and now we're going to think of
+what that means in terms of the point
+
+ align:start position:0%
+what that means in terms of the point
+ 
+
+ align:start position:0%
+what that means in terms of the point
+spread function we've come across the
+
+ align:start position:0%
+spread function we've come across the
+ 
+
+ align:start position:0%
+spread function we've come across the
+point spread function before of course
+
+ align:start position:0%
+point spread function before of course
+ 
+
+ align:start position:0%
+point spread function before of course
+uh so um so we can the point spread
+
+ align:start position:0%
+uh so um so we can the point spread
+ 
+
+ align:start position:0%
+uh so um so we can the point spread
+function is
+
+ align:start position:0%
+function is
+ 
+
+ align:start position:0%
+function is
+basically uh the image of a point object
+
+ align:start position:0%
+basically uh the image of a point object
+ 
+
+ align:start position:0%
+basically uh the image of a point object
+object and our Point objects we make by
+
+ align:start position:0%
+object and our Point objects we make by
+ 
+
+ align:start position:0%
+object and our Point objects we make by
+having a screen with a very small hole
+
+ align:start position:0%
+having a screen with a very small hole
+ 
+
+ align:start position:0%
+having a screen with a very small hole
+in right so this then is going to
+
+ align:start position:0%
+in right so this then is going to
+ 
+
+ align:start position:0%
+in right so this then is going to
+expand
+
+ align:start position:0%
+expand
+ 
+
+ align:start position:0%
+expand
+uh re reach the lens it's going to be
+
+ align:start position:0%
+uh re reach the lens it's going to be
+ 
+
+ align:start position:0%
+uh re reach the lens it's going to be
+cated because we've assumed this to be
+
+ align:start position:0%
+cated because we've assumed this to be
+ 
+
+ align:start position:0%
+cated because we've assumed this to be
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+axis uh this cated
+
+ align:start position:0%
+axis uh this cated
+ 
+
+ align:start position:0%
+axis uh this cated
+beam excuse me uh is going to arrive at
+
+ align:start position:0%
+beam excuse me uh is going to arrive at
+ 
+
+ align:start position:0%
+beam excuse me uh is going to arrive at
+our pupil mask part of this cated beam
+
+ align:start position:0%
+our pupil mask part of this cated beam
+ 
+
+ align:start position:0%
+our pupil mask part of this cated beam
+is going to go through the aperture it's
+
+ align:start position:0%
+is going to go through the aperture it's
+ 
+
+ align:start position:0%
+is going to go through the aperture it's
+going to get to a lens uh it's then
+
+ align:start position:0%
+going to get to a lens uh it's then
+ 
+
+ align:start position:0%
+going to get to a lens uh it's then
+going to be focused down uh and produce
+
+ align:start position:0%
+going to be focused down uh and produce
+ 
+
+ align:start position:0%
+going to be focused down uh and produce
+a uh a converging wave to form a a spot
+
+ align:start position:0%
+a uh a converging wave to form a a spot
+ 
+
+ align:start position:0%
+a uh a converging wave to form a a spot
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+screen right so this is what we think of
+
+ align:start position:0%
+screen right so this is what we think of
+ 
+
+ align:start position:0%
+screen right so this is what we think of
+as uh the final spot is going to be what
+
+ align:start position:0%
+as uh the final spot is going to be what
+ 
+
+ align:start position:0%
+as uh the final spot is going to be what
+we call the point spread function uh h
+
+ align:start position:0%
+we call the point spread function uh h
+ 
+
+ align:start position:0%
+we call the point spread function uh h
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XY okay so how do we uh how do we work
+
+ align:start position:0%
+XY okay so how do we uh how do we work
+ 
+
+ align:start position:0%
+XY okay so how do we uh how do we work
+out this point spread function
+
+ align:start position:0%
+out this point spread function
+ 
+
+ align:start position:0%
+out this point spread function
+uh so what we do is we can again work
+
+ align:start position:0%
+uh so what we do is we can again work
+ 
+
+ align:start position:0%
+uh so what we do is we can again work
+through this system in terms of forer
+
+ align:start position:0%
+through this system in terms of forer
+ 
+
+ align:start position:0%
+through this system in terms of forer
+transforms this is a Delta function so
+
+ align:start position:0%
+transforms this is a Delta function so
+ 
+
+ align:start position:0%
+transforms this is a Delta function so
+the fer transform of a Delta function is
+
+ align:start position:0%
+the fer transform of a Delta function is
+ 
+
+ align:start position:0%
+the fer transform of a Delta function is
+just a constant we multiply the constant
+
+ align:start position:0%
+just a constant we multiply the constant
+ 
+
+ align:start position:0%
+just a constant we multiply the constant
+uh by the pupil
+
+ align:start position:0%
+uh by the pupil
+ 
+
+ align:start position:0%
+uh by the pupil
+mask uh and uh and then we got another
+
+ align:start position:0%
+mask uh and uh and then we got another
+ 
+
+ align:start position:0%
+mask uh and uh and then we got another
+system here uh which does another fer
+
+ align:start position:0%
+system here uh which does another fer
+ 
+
+ align:start position:0%
+system here uh which does another fer
+transform uh so what what we're going to
+
+ align:start position:0%
+transform uh so what what we're going to
+ 
+
+ align:start position:0%
+transform uh so what what we're going to
+get uh in the in the plane the image of
+
+ align:start position:0%
+get uh in the in the plane the image of
+ 
+
+ align:start position:0%
+get uh in the in the plane the image of
+a point object is going to be the fer
+
+ align:start position:0%
+a point object is going to be the fer
+ 
+
+ align:start position:0%
+a point object is going to be the fer
+transform of the pupil
+
+ align:start position:0%
+transform of the pupil
+ 
+
+ align:start position:0%
+transform of the pupil
+mask uh and uh yeah so it makes the
+
+ align:start position:0%
+mask uh and uh yeah so it makes the
+ 
+
+ align:start position:0%
+mask uh and uh yeah so it makes the
+point here that we have to be careful of
+
+ align:start position:0%
+point here that we have to be careful of
+ 
+
+ align:start position:0%
+point here that we have to be careful of
+course how we scale things uh and of
+
+ align:start position:0%
+course how we scale things uh and of
+ 
+
+ align:start position:0%
+course how we scale things uh and of
+course the scaling uh is going to depend
+
+ align:start position:0%
+course the scaling uh is going to depend
+ 
+
+ align:start position:0%
+course the scaling uh is going to depend
+on the relative sizes of these F1 and F2
+
+ align:start position:0%
+on the relative sizes of these F1 and F2
+ 
+
+ align:start position:0%
+on the relative sizes of these F1 and F2
+as well of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so example if we got the low pass
+
+ align:start position:0%
+right so example if we got the low pass
+ 
+
+ align:start position:0%
+right so example if we got the low pass
+filter right so zero is in the center it
+
+ align:start position:0%
+filter right so zero is in the center it
+ 
+
+ align:start position:0%
+filter right so zero is in the center it
+lets through the low frequencies stops
+
+ align:start position:0%
+lets through the low frequencies stops
+ 
+
+ align:start position:0%
+lets through the low frequencies stops
+the outer
+
+ align:start position:0%
+the outer
+ 
+
+ align:start position:0%
+the outer
+frequencies uh so this is the uh this is
+
+ align:start position:0%
+frequencies uh so this is the uh this is
+ 
+
+ align:start position:0%
+frequencies uh so this is the uh this is
+the uh pupil mask what does the point
+
+ align:start position:0%
+the uh pupil mask what does the point
+ 
+
+ align:start position:0%
+the uh pupil mask what does the point
+spread function of that uh
+
+ align:start position:0%
+spread function of that uh
+ 
+
+ align:start position:0%
+spread function of that uh
+give uh and
+
+ align:start position:0%
+give uh and
+ 
+
+ align:start position:0%
+give uh and
+um so we're assuming that the input uh
+
+ align:start position:0%
+um so we're assuming that the input uh
+ 
+
+ align:start position:0%
+um so we're assuming that the input uh
+uh the input transparency is Delta X IE
+
+ align:start position:0%
+uh the input transparency is Delta X IE
+ 
+
+ align:start position:0%
+uh the input transparency is Delta X IE
+on the axis so this is illuminated on
+
+ align:start position:0%
+on the axis so this is illuminated on
+ 
+
+ align:start position:0%
+on the axis so this is illuminated on
+axis uh the field after the uh after the
+
+ align:start position:0%
+axis uh the field after the uh after the
+ 
+
+ align:start position:0%
+axis uh the field after the uh after the
+pupil mask is just the same as the as
+
+ align:start position:0%
+pupil mask is just the same as the as
+ 
+
+ align:start position:0%
+pupil mask is just the same as the as
+the pupil mask uh and then we FIA
+
+ align:start position:0%
+the pupil mask uh and then we FIA
+ 
+
+ align:start position:0%
+the pupil mask uh and then we FIA
+transform that and it's going to give uh
+
+ align:start position:0%
+transform that and it's going to give uh
+ 
+
+ align:start position:0%
+transform that and it's going to give uh
+a syn the fer Transformer of rect is
+
+ align:start position:0%
+a syn the fer Transformer of rect is
+ 
+
+ align:start position:0%
+a syn the fer Transformer of rect is
+sync uh and uh and here we've got the
+
+ align:start position:0%
+sync uh and uh and here we've got the
+ 
+
+ align:start position:0%
+sync uh and uh and here we've got the
+the relative sizes of this as well uh so
+
+ align:start position:0%
+the relative sizes of this as well uh so
+ 
+
+ align:start position:0%
+the relative sizes of this as well uh so
+that we know how big it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and uh so the amplitude point spread
+
+ align:start position:0%
+uh and uh so the amplitude point spread
+ 
+
+ align:start position:0%
+uh and uh so the amplitude point spread
+function then is is the is this thing
+
+ align:start position:0%
+function then is is the is this thing
+ 
+
+ align:start position:0%
+function then is is the is this thing
+this for transform uh
+
+ align:start position:0%
+this for transform uh
+ 
+
+ align:start position:0%
+this for transform uh
+rescaled with this x- over Lambda F we
+
+ align:start position:0%
+rescaled with this x- over Lambda F we
+ 
+
+ align:start position:0%
+rescaled with this x- over Lambda F we
+replace the U by the x- over Lambda F uh
+
+ align:start position:0%
+replace the U by the x- over Lambda F uh
+ 
+
+ align:start position:0%
+replace the U by the x- over Lambda F uh
+and this finally then is our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer uh
+
+ align:start position:0%
+answer uh
+ 
+
+ align:start position:0%
+answer uh
+and that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um what which three which three times is
+
+ align:start position:0%
+um what which three which three times is
+ 
+
+ align:start position:0%
+um what which three which three times is
+it saying there this this three is that
+
+ align:start position:0%
+it saying there this this three is that
+ 
+
+ align:start position:0%
+it saying there this this three is that
+what that three yeah yeah okay yeah of
+
+ align:start position:0%
+what that three yeah yeah okay yeah of
+ 
+
+ align:start position:0%
+what that three yeah yeah okay yeah of
+course the um energy has to be conserved
+
+ align:start position:0%
+course the um energy has to be conserved
+ 
+
+ align:start position:0%
+course the um energy has to be conserved
+by this thing so you remember there's
+
+ align:start position:0%
+by this thing so you remember there's
+ 
+
+ align:start position:0%
+by this thing so you remember there's
+this theorem in for a transforms again
+
+ align:start position:0%
+this theorem in for a transforms again
+ 
+
+ align:start position:0%
+this theorem in for a transforms again
+that says the area under the uh function
+
+ align:start position:0%
+that says the area under the uh function
+ 
+
+ align:start position:0%
+that says the area under the uh function
+squared is equal to the area under the
+
+ align:start position:0%
+squared is equal to the area under the
+ 
+
+ align:start position:0%
+squared is equal to the area under the
+fora transform squared right so it's
+
+ align:start position:0%
+fora transform squared right so it's
+ 
+
+ align:start position:0%
+fora transform squared right so it's
+it's conservation of
+
+ align:start position:0%
+it's conservation of
+ 
+
+ align:start position:0%
+it's conservation of
+energy uh and um so this is the
+
+ align:start position:0%
+energy uh and um so this is the
+ 
+
+ align:start position:0%
+energy uh and um so this is the
+amplitude point spread function uh it's
+
+ align:start position:0%
+amplitude point spread function uh it's
+ 
+
+ align:start position:0%
+amplitude point spread function uh it's
+sync uh so it goes negative syn sync is
+
+ align:start position:0%
+sync uh so it goes negative syn sync is
+ 
+
+ align:start position:0%
+sync uh so it goes negative syn sync is
+sin pix over pix so it goes negative so
+
+ align:start position:0%
+sin pix over pix so it goes negative so
+ 
+
+ align:start position:0%
+sin pix over pix so it goes negative so
+that's why it's plotted here this is
+
+ align:start position:0%
+that's why it's plotted here this is
+ 
+
+ align:start position:0%
+that's why it's plotted here this is
+zero okay it Wiggles up and down above
+
+ align:start position:0%
+zero okay it Wiggles up and down above
+ 
+
+ align:start position:0%
+zero okay it Wiggles up and down above
+uh zero uh the zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L uh and uh so what you'd actually see
+
+ align:start position:0%
+L uh and uh so what you'd actually see
+ 
+
+ align:start position:0%
+L uh and uh so what you'd actually see
+of course if you looked at the image of
+
+ align:start position:0%
+of course if you looked at the image of
+ 
+
+ align:start position:0%
+of course if you looked at the image of
+a point object you'd see the modulus
+
+ align:start position:0%
+a point object you'd see the modulus
+ 
+
+ align:start position:0%
+a point object you'd see the modulus
+square of this wouldn't you right just
+
+ align:start position:0%
+square of this wouldn't you right just
+ 
+
+ align:start position:0%
+square of this wouldn't you right just
+like when we looked at our examples of
+
+ align:start position:0%
+like when we looked at our examples of
+ 
+
+ align:start position:0%
+like when we looked at our examples of
+um the
+
+ align:start position:0%
+um the
+ 
+
+ align:start position:0%
+um the
+gratings uh we we we finally look at the
+
+ align:start position:0%
+gratings uh we we we finally look at the
+ 
+
+ align:start position:0%
+gratings uh we we we finally look at the
+actual intensity rather than the
+
+ align:start position:0%
+actual intensity rather than the
+ 
+
+ align:start position:0%
+actual intensity rather than the
+amplitude the intensity of course is
+
+ align:start position:0%
+amplitude the intensity of course is
+ 
+
+ align:start position:0%
+amplitude the intensity of course is
+always positive uh so you'd actually be
+
+ align:start position:0%
+always positive uh so you'd actually be
+ 
+
+ align:start position:0%
+always positive uh so you'd actually be
+looking at the square of that but if
+
+ align:start position:0%
+looking at the square of that but if
+ 
+
+ align:start position:0%
+looking at the square of that but if
+you're trying so think of this thing as
+
+ align:start position:0%
+you're trying so think of this thing as
+ 
+
+ align:start position:0%
+you're trying so think of this thing as
+being um you know what we're going to
+
+ align:start position:0%
+being um you know what we're going to
+ 
+
+ align:start position:0%
+being um you know what we're going to
+carry on to say of course is in Furious
+
+ align:start position:0%
+carry on to say of course is in Furious
+ 
+
+ align:start position:0%
+carry on to say of course is in Furious
+space uh fuor domain uh the spatial
+
+ align:start position:0%
+space uh fuor domain uh the spatial
+ 
+
+ align:start position:0%
+space uh fuor domain uh the spatial
+frequencies of the object are multiplied
+
+ align:start position:0%
+frequencies of the object are multiplied
+ 
+
+ align:start position:0%
+frequencies of the object are multiplied
+by the
+
+ align:start position:0%
+by the
+ 
+
+ align:start position:0%
+by the
+mask in in in terms of of uh this of um
+
+ align:start position:0%
+mask in in in terms of of uh this of um
+ 
+
+ align:start position:0%
+mask in in in terms of of uh this of um
+uh real space you're going to get a
+
+ align:start position:0%
+uh real space you're going to get a
+ 
+
+ align:start position:0%
+uh real space you're going to get a
+convolution the product becomes a
+
+ align:start position:0%
+convolution the product becomes a
+ 
+
+ align:start position:0%
+convolution the product becomes a
+convolution so we're going to convolve
+
+ align:start position:0%
+convolution so we're going to convolve
+ 
+
+ align:start position:0%
+convolution so we're going to convolve
+our objects with an with an amplitude
+
+ align:start position:0%
+our objects with an with an amplitude
+ 
+
+ align:start position:0%
+our objects with an with an amplitude
+point spread function right so but we
+
+ align:start position:0%
+point spread function right so but we
+ 
+
+ align:start position:0%
+point spread function right so but we
+have to do it with the amplitude point
+
+ align:start position:0%
+have to do it with the amplitude point
+ 
+
+ align:start position:0%
+have to do it with the amplitude point
+spread function find the find the total
+
+ align:start position:0%
+spread function find the find the total
+ 
+
+ align:start position:0%
+spread function find the find the total
+amplitude in the image and then do the
+
+ align:start position:0%
+amplitude in the image and then do the
+ 
+
+ align:start position:0%
+amplitude in the image and then do the
+modular Square uh to find the final
+
+ align:start position:0%
+modular Square uh to find the final
+ 
+
+ align:start position:0%
+modular Square uh to find the final
+intensity okay and this is an example of
+
+ align:start position:0%
+intensity okay and this is an example of
+ 
+
+ align:start position:0%
+intensity okay and this is an example of
+the point spread function of this um
+
+ align:start position:0%
+the point spread function of this um
+ 
+
+ align:start position:0%
+the point spread function of this um
+face filter we looked at uh the the
+
+ align:start position:0%
+face filter we looked at uh the the
+ 
+
+ align:start position:0%
+face filter we looked at uh the the
+pupil mask this is the same as we had
+
+ align:start position:0%
+pupil mask this is the same as we had
+ 
+
+ align:start position:0%
+pupil mask this is the same as we had
+before uh so it's this is its modulus
+
+ align:start position:0%
+before uh so it's this is its modulus
+ 
+
+ align:start position:0%
+before uh so it's this is its modulus
+this is the phase uh and uh if you
+
+ align:start position:0%
+this is the phase uh and uh if you
+ 
+
+ align:start position:0%
+this is the phase uh and uh if you
+calculate the point spread function of
+
+ align:start position:0%
+calculate the point spread function of
+ 
+
+ align:start position:0%
+calculate the point spread function of
+this it comes to this this is the
+
+ align:start position:0%
+this it comes to this this is the
+ 
+
+ align:start position:0%
+this it comes to this this is the
+modulus this is the phase uh so you can
+
+ align:start position:0%
+modulus this is the phase uh so you can
+ 
+
+ align:start position:0%
+modulus this is the phase uh so you can
+see that that is why we got a pretty
+
+ align:start position:0%
+see that that is why we got a pretty
+ 
+
+ align:start position:0%
+see that that is why we got a pretty
+horrible image it's because it's got a
+
+ align:start position:0%
+horrible image it's because it's got a
+ 
+
+ align:start position:0%
+horrible image it's because it's got a
+very nasty point spread function uh it's
+
+ align:start position:0%
+very nasty point spread function uh it's
+ 
+
+ align:start position:0%
+very nasty point spread function uh it's
+point spread function for a start that's
+
+ align:start position:0%
+point spread function for a start that's
+ 
+
+ align:start position:0%
+point spread function for a start that's
+got these very large side loes which
+
+ align:start position:0%
+got these very large side loes which
+ 
+
+ align:start position:0%
+got these very large side loes which
+normally we don't like we normally like
+
+ align:start position:0%
+normally we don't like we normally like
+ 
+
+ align:start position:0%
+normally we don't like we normally like
+to have our point spread function to be
+
+ align:start position:0%
+to have our point spread function to be
+ 
+
+ align:start position:0%
+to have our point spread function to be
+nicely narrow and smooth and without big
+
+ align:start position:0%
+nicely narrow and smooth and without big
+ 
+
+ align:start position:0%
+nicely narrow and smooth and without big
+side loses and then more than that it's
+
+ align:start position:0%
+side loses and then more than that it's
+ 
+
+ align:start position:0%
+side loses and then more than that it's
+also got these horrible phase jumps uh
+
+ align:start position:0%
+also got these horrible phase jumps uh
+ 
+
+ align:start position:0%
+also got these horrible phase jumps uh
+which I think are very likely to produce
+
+ align:start position:0%
+which I think are very likely to produce
+ 
+
+ align:start position:0%
+which I think are very likely to produce
+pretty awful image uh which is probably
+
+ align:start position:0%
+pretty awful image uh which is probably
+ 
+
+ align:start position:0%
+pretty awful image uh which is probably
+what we saw uh so this goes through the
+
+ align:start position:0%
+what we saw uh so this goes through the
+ 
+
+ align:start position:0%
+what we saw uh so this goes through the
+the the sum of actually doing that so
+
+ align:start position:0%
+the the sum of actually doing that so
+ 
+
+ align:start position:0%
+the the sum of actually doing that so
+this is the same as we had before then
+
+ align:start position:0%
+this is the same as we had before then
+ 
+
+ align:start position:0%
+this is the same as we had before then
+uh the the big rectangle minus the
+
+ align:start position:0%
+uh the the big rectangle minus the
+ 
+
+ align:start position:0%
+uh the the big rectangle minus the
+little rectangle with a phase uh and um
+
+ align:start position:0%
+little rectangle with a phase uh and um
+ 
+
+ align:start position:0%
+little rectangle with a phase uh and um
+then we got to do the fer transform of
+
+ align:start position:0%
+then we got to do the fer transform of
+ 
+
+ align:start position:0%
+then we got to do the fer transform of
+that uh and um so the way we've done it
+
+ align:start position:0%
+that uh and um so the way we've done it
+ 
+
+ align:start position:0%
+that uh and um so the way we've done it
+here then we just got this the sum of
+
+ align:start position:0%
+here then we just got this the sum of
+ 
+
+ align:start position:0%
+here then we just got this the sum of
+two rectangles each of them becomes a
+
+ align:start position:0%
+two rectangles each of them becomes a
+ 
+
+ align:start position:0%
+two rectangles each of them becomes a
+sync uh but you got a you've got this
+
+ align:start position:0%
+sync uh but you got a you've got this
+ 
+
+ align:start position:0%
+sync uh but you got a you've got this
+eye here you have to be careful of uh
+
+ align:start position:0%
+eye here you have to be careful of uh
+ 
+
+ align:start position:0%
+eye here you have to be careful of uh
+and then finally um we work out the the
+
+ align:start position:0%
+and then finally um we work out the the
+ 
+
+ align:start position:0%
+and then finally um we work out the the
+the modulus square of the of the of the
+
+ align:start position:0%
+the modulus square of the of the of the
+ 
+
+ align:start position:0%
+the modulus square of the of the of the
+point spread function and the phase of
+
+ align:start position:0%
+point spread function and the phase of
+ 
+
+ align:start position:0%
+point spread function and the phase of
+the point spread function right so this
+
+ align:start position:0%
+the point spread function right so this
+ 
+
+ align:start position:0%
+the point spread function right so this
+is the modulus square of the point
+
+ align:start position:0%
+is the modulus square of the point
+ 
+
+ align:start position:0%
+is the modulus square of the point
+spread function so these side loes are
+
+ align:start position:0%
+spread function so these side loes are
+ 
+
+ align:start position:0%
+spread function so these side loes are
+actually quite
+
+ align:start position:0%
+actually quite
+ 
+
+ align:start position:0%
+actually quite
+huge um
+
+ align:start position:0%
+huge um
+ 
+
+ align:start position:0%
+huge um
+quite quite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+big okay yeah that's just looking at the
+
+ align:start position:0%
+big okay yeah that's just looking at the
+ 
+
+ align:start position:0%
+big okay yeah that's just looking at the
+difference between the two then uh so uh
+
+ align:start position:0%
+difference between the two then uh so uh
+ 
+
+ align:start position:0%
+difference between the two then uh so uh
+if we have our low pass filter uh so
+
+ align:start position:0%
+if we have our low pass filter uh so
+ 
+
+ align:start position:0%
+if we have our low pass filter uh so
+this is what I'm was saying about these
+
+ align:start position:0%
+this is what I'm was saying about these
+ 
+
+ align:start position:0%
+this is what I'm was saying about these
+being huge you see the the the low pass
+
+ align:start position:0%
+being huge you see the the the low pass
+ 
+
+ align:start position:0%
+being huge you see the the the low pass
+filter uh these side loes are pretty
+
+ align:start position:0%
+filter uh these side loes are pretty
+ 
+
+ align:start position:0%
+filter uh these side loes are pretty
+small by comparison I guess you could
+
+ align:start position:0%
+small by comparison I guess you could
+ 
+
+ align:start position:0%
+small by comparison I guess you could
+you you could use some sort of shaded
+
+ align:start position:0%
+you you could use some sort of shaded
+ 
+
+ align:start position:0%
+you you could use some sort of shaded
+aperture or maybe uh an aperture with
+
+ align:start position:0%
+aperture or maybe uh an aperture with
+ 
+
+ align:start position:0%
+aperture or maybe uh an aperture with
+some structure that would allow you to
+
+ align:start position:0%
+some structure that would allow you to
+ 
+
+ align:start position:0%
+some structure that would allow you to
+make those those um side loes even
+
+ align:start position:0%
+make those those um side loes even
+ 
+
+ align:start position:0%
+make those those um side loes even
+smaller uh this is this process that's
+
+ align:start position:0%
+smaller uh this is this process that's
+ 
+
+ align:start position:0%
+smaller uh this is this process that's
+sometimes called
+
+ align:start position:0%
+sometimes called
+ 
+
+ align:start position:0%
+sometimes called
+apodization um apodization means to uh
+
+ align:start position:0%
+apodization um apodization means to uh
+ 
+
+ align:start position:0%
+apodization um apodization means to uh
+cut off the feet I I think if George was
+
+ align:start position:0%
+cut off the feet I I think if George was
+ 
+
+ align:start position:0%
+cut off the feet I I think if George was
+giving the talk he'd say something about
+
+ align:start position:0%
+giving the talk he'd say something about
+ 
+
+ align:start position:0%
+giving the talk he'd say something about
+the Greek for Feats being something to
+
+ align:start position:0%
+the Greek for Feats being something to
+ 
+
+ align:start position:0%
+the Greek for Feats being something to
+do with
+
+ align:start position:0%
+do with
+ 
+
+ align:start position:0%
+do with
+pod right right there we are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay are we we we're over time really
+
+ align:start position:0%
+so okay are we we we're over time really
+ 
+
+ align:start position:0%
+so okay are we we we're over time really
+you want to stop
+
+ align:start position:0%
+you want to stop
+ 
+
+ align:start position:0%
+you want to stop
+now yeah maybe that's a good point I
+
+ align:start position:0%
+now yeah maybe that's a good point I
+ 
+
+ align:start position:0%
+now yeah maybe that's a good point I
+think that's good you've got the a
+
+ align:start position:0%
+think that's good you've got the a
+ 
+
+ align:start position:0%
+think that's good you've got the a
+concept of the point spread function uh
+
+ align:start position:0%
+concept of the point spread function uh
+ 
+
+ align:start position:0%
+concept of the point spread function uh
+now you've got a week to think about the
+
+ align:start position:0%
+now you've got a week to think about the
+ 
+
+ align:start position:0%
+now you've got a week to think about the
+point spread function and and then next
+
+ align:start position:0%
+point spread function and and then next
+ 
+
+ align:start position:0%
+point spread function and and then next
+time it'll all be very
+
+ align:start position:0%
+time it'll all be very
+ 
+
+ align:start position:0%
+time it'll all be very
+clear okay so any questions from either
+
+ align:start position:0%
+clear okay so any questions from either
+ 
+
+ align:start position:0%
+clear okay so any questions from either
+side
\ No newline at end of file
diff --git a/MMWqGD4Urso.txt b/MMWqGD4Urso.txt
new file mode 100644
index 0000000000000000000000000000000000000000..940282e5098c12c69dd9330fdcb934ed5c872ca1
--- /dev/null
+++ b/MMWqGD4Urso.txt
@@ -0,0 +1,1123 @@
+align:start position:0%
+ 
+hi there welcome back to recitation in
+
+ align:start position:0%
+hi there welcome back to recitation in
+ 
+
+ align:start position:0%
+hi there welcome back to recitation in
+lecture you've been learning about when
+
+ align:start position:0%
+lecture you've been learning about when
+ 
+
+ align:start position:0%
+lecture you've been learning about when
+vectors are
+
+ align:start position:0%
+vectors are
+ 
+
+ align:start position:0%
+vectors are
+dependent when they span a space what a
+
+ align:start position:0%
+dependent when they span a space what a
+ 
+
+ align:start position:0%
+dependent when they span a space what a
+basis is what a dimension of a vector
+
+ align:start position:0%
+basis is what a dimension of a vector
+ 
+
+ align:start position:0%
+basis is what a dimension of a vector
+space is and the problem for today is
+
+ align:start position:0%
+space is and the problem for today is
+ 
+
+ align:start position:0%
+space is and the problem for today is
+exactly about that we have a vector
+
+ align:start position:0%
+exactly about that we have a vector
+ 
+
+ align:start position:0%
+exactly about that we have a vector
+space that is given it's spanned by
+
+ align:start position:0%
+space that is given it's spanned by
+ 
+
+ align:start position:0%
+space that is given it's spanned by
+these four vectors and we're asked to
+
+ align:start position:0%
+these four vectors and we're asked to
+ 
+
+ align:start position:0%
+these four vectors and we're asked to
+find the dimension of that vector space
+
+ align:start position:0%
+find the dimension of that vector space
+ 
+
+ align:start position:0%
+find the dimension of that vector space
+and the basis for it well why don't you
+
+ align:start position:0%
+and the basis for it well why don't you
+ 
+
+ align:start position:0%
+and the basis for it well why don't you
+hit pause on the video and work on it
+
+ align:start position:0%
+hit pause on the video and work on it
+ 
+
+ align:start position:0%
+hit pause on the video and work on it
+for a while and I'll come back in a
+
+ align:start position:0%
+for a while and I'll come back in a
+ 
+
+ align:start position:0%
+for a while and I'll come back in a
+little bit to help you out with it all
+
+ align:start position:0%
+little bit to help you out with it all
+ 
+
+ align:start position:0%
+little bit to help you out with it all
+right we're back let's work on it well
+
+ align:start position:0%
+right we're back let's work on it well
+ 
+
+ align:start position:0%
+right we're back let's work on it well
+so we need to find the dimension and the
+
+ align:start position:0%
+so we need to find the dimension and the
+ 
+
+ align:start position:0%
+so we need to find the dimension and the
+basis remember what the dimension is
+
+ align:start position:0%
+basis remember what the dimension is
+ 
+
+ align:start position:0%
+basis remember what the dimension is
+it's simply the number of vectors in a
+
+ align:start position:0%
+it's simply the number of vectors in a
+ 
+
+ align:start position:0%
+it's simply the number of vectors in a
+basis for the vector space so actually
+
+ align:start position:0%
+basis for the vector space so actually
+ 
+
+ align:start position:0%
+basis for the vector space so actually
+the problems is backwards we want to
+
+ align:start position:0%
+the problems is backwards we want to
+ 
+
+ align:start position:0%
+the problems is backwards we want to
+find the basis for the space first and
+
+ align:start position:0%
+find the basis for the space first and
+ 
+
+ align:start position:0%
+find the basis for the space first and
+then find the dimension all right all
+
+ align:start position:0%
+then find the dimension all right all
+ 
+
+ align:start position:0%
+then find the dimension all right all
+right first here and second here all
+
+ align:start position:0%
+right first here and second here all
+ 
+
+ align:start position:0%
+right first here and second here all
+right so we want to find a basis for the
+
+ align:start position:0%
+right so we want to find a basis for the
+ 
+
+ align:start position:0%
+right so we want to find a basis for the
+vector space spanned by these four
+
+ align:start position:0%
+vector space spanned by these four
+ 
+
+ align:start position:0%
+vector space spanned by these four
+vectors all right so you might be
+
+ align:start position:0%
+vectors all right so you might be
+ 
+
+ align:start position:0%
+vectors all right so you might be
+tempted to just say that a basis for
+
+ align:start position:0%
+tempted to just say that a basis for
+ 
+
+ align:start position:0%
+tempted to just say that a basis for
+this vector space is those four vectors
+
+ align:start position:0%
+this vector space is those four vectors
+ 
+
+ align:start position:0%
+this vector space is those four vectors
+because they span the vector space but
+
+ align:start position:0%
+because they span the vector space but
+ 
+
+ align:start position:0%
+because they span the vector space but
+there's another thing that a basis has
+
+ align:start position:0%
+there's another thing that a basis has
+ 
+
+ align:start position:0%
+there's another thing that a basis has
+to satisfy and it is the elements of the
+
+ align:start position:0%
+to satisfy and it is the elements of the
+ 
+
+ align:start position:0%
+to satisfy and it is the elements of the
+basis have to be linearly independent
+
+ align:start position:0%
+basis have to be linearly independent
+ 
+
+ align:start position:0%
+basis have to be linearly independent
+and we don't know that these are so we
+
+ align:start position:0%
+and we don't know that these are so we
+ 
+
+ align:start position:0%
+and we don't know that these are so we
+have to check how do we check that four
+
+ align:start position:0%
+have to check how do we check that four
+ 
+
+ align:start position:0%
+have to check how do we check that four
+vectors are linearly independent well
+
+ align:start position:0%
+vectors are linearly independent well
+ 
+
+ align:start position:0%
+vectors are linearly independent well
+there's a couple of different ways but
+
+ align:start position:0%
+there's a couple of different ways but
+ 
+
+ align:start position:0%
+there's a couple of different ways but
+here's what we're going to do we're
+
+ align:start position:0%
+here's what we're going to do we're
+ 
+
+ align:start position:0%
+here's what we're going to do we're
+going to put these vectors as rows of a
+
+ align:start position:0%
+going to put these vectors as rows of a
+ 
+
+ align:start position:0%
+going to put these vectors as rows of a
+matrix and then we'll do elimination and
+
+ align:start position:0%
+matrix and then we'll do elimination and
+ 
+
+ align:start position:0%
+matrix and then we'll do elimination and
+when we get to the end the rows that
+
+ align:start position:0%
+when we get to the end the rows that
+ 
+
+ align:start position:0%
+when we get to the end the rows that
+have pivots are the independent ones so
+
+ align:start position:0%
+have pivots are the independent ones so
+ 
+
+ align:start position:0%
+have pivots are the independent ones so
+let's do that
+
+ align:start position:0%
+let's do that
+ 
+
+ align:start position:0%
+let's do that
+1 1 plus 2 0 minus 1 1 2 0 minus 4 1 0 1
+
+ align:start position:0%
+1 1 plus 2 0 minus 1 1 2 0 minus 4 1 0 1
+ 
+
+ align:start position:0%
+1 1 plus 2 0 minus 1 1 2 0 minus 4 1 0 1
+3 2
+
+ align:start position:0%
+3 2
+ 
+
+ align:start position:0%
+3 2
+- 3 0 - 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right by now you must have done
+
+ align:start position:0%
+all right by now you must have done
+ 
+
+ align:start position:0%
+all right by now you must have done
+elimination a million times so I'll go a
+
+ align:start position:0%
+elimination a million times so I'll go a
+ 
+
+ align:start position:0%
+elimination a million times so I'll go a
+little bit faster - its 1 0 1 0 + 2 - 4
+
+ align:start position:0%
+little bit faster - its 1 0 1 0 + 2 - 4
+ 
+
+ align:start position:0%
+little bit faster - its 1 0 1 0 + 2 - 4
+- it's already done 1 3 minutes 3 - 2
+
+ align:start position:0%
+- it's already done 1 3 minutes 3 - 2
+ 
+
+ align:start position:0%
+- it's already done 1 3 minutes 3 - 2
+minutes - 3 - 2 0 + 4 - 2 & 2 alright
+
+ align:start position:0%
+minutes - 3 - 2 0 + 4 - 2 & 2 alright
+ 
+
+ align:start position:0%
+minutes - 3 - 2 0 + 4 - 2 & 2 alright
+one more step 1 1 - 2 0 - 1 I'll do done
+
+ align:start position:0%
+one more step 1 1 - 2 0 - 1 I'll do done
+ 
+
+ align:start position:0%
+one more step 1 1 - 2 0 - 1 I'll do done
+0 1 2 1 2 0 1 minus 1 is 0 3 minus 2 is
+
+ align:start position:0%
+0 1 2 1 2 0 1 minus 1 is 0 3 minus 2 is
+ 
+
+ align:start position:0%
+0 1 2 1 2 0 1 minus 1 is 0 3 minus 2 is
+1 - 3 + 4 is 1 2 minus 2 is 0 1 minus 1
+
+ align:start position:0%
+1 - 3 + 4 is 1 2 minus 2 is 0 1 minus 1
+ 
+
+ align:start position:0%
+1 - 3 + 4 is 1 2 minus 2 is 0 1 minus 1
+is 0 - 2 again and 0 oh you can see
+
+ align:start position:0%
+is 0 - 2 again and 0 oh you can see
+ 
+
+ align:start position:0%
+is 0 - 2 again and 0 oh you can see
+where this is going
+
+ align:start position:0%
+where this is going
+ 
+
+ align:start position:0%
+where this is going
+and the next step this row is going to
+
+ align:start position:0%
+and the next step this row is going to
+ 
+
+ align:start position:0%
+and the next step this row is going to
+disappear - 2 0 1 0 1 - 2 0 0 1 1 0 0 0
+
+ align:start position:0%
+disappear - 2 0 1 0 1 - 2 0 0 1 1 0 0 0
+ 
+
+ align:start position:0%
+disappear - 2 0 1 0 1 - 2 0 0 1 1 0 0 0
+0 0 alright we're done with elimination
+
+ align:start position:0%
+0 0 alright we're done with elimination
+ 
+
+ align:start position:0%
+0 0 alright we're done with elimination
+and so let's circle our pivots and here
+
+ align:start position:0%
+and so let's circle our pivots and here
+ 
+
+ align:start position:0%
+and so let's circle our pivots and here
+our pivots we have three pivots and so
+
+ align:start position:0%
+our pivots we have three pivots and so
+ 
+
+ align:start position:0%
+our pivots we have three pivots and so
+these 3 rows are linearly independent no
+
+ align:start position:0%
+these 3 rows are linearly independent no
+ 
+
+ align:start position:0%
+these 3 rows are linearly independent no
+and in fact these rows still span the
+
+ align:start position:0%
+and in fact these rows still span the
+ 
+
+ align:start position:0%
+and in fact these rows still span the
+same space that the initial four rows
+
+ align:start position:0%
+same space that the initial four rows
+ 
+
+ align:start position:0%
+same space that the initial four rows
+did because when you do elimination all
+
+ align:start position:0%
+did because when you do elimination all
+ 
+
+ align:start position:0%
+did because when you do elimination all
+that you're doing is recombining a rose
+
+ align:start position:0%
+that you're doing is recombining a rose
+ 
+
+ align:start position:0%
+that you're doing is recombining a rose
+well by doing linear combinations of
+
+ align:start position:0%
+well by doing linear combinations of
+ 
+
+ align:start position:0%
+well by doing linear combinations of
+them so for example your first first row
+
+ align:start position:0%
+them so for example your first first row
+ 
+
+ align:start position:0%
+them so for example your first first row
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+same throughout your second row was
+
+ align:start position:0%
+same throughout your second row was
+ 
+
+ align:start position:0%
+same throughout your second row was
+replaced by Row 2 minus Row 1 but it's
+
+ align:start position:0%
+replaced by Row 2 minus Row 1 but it's
+ 
+
+ align:start position:0%
+replaced by Row 2 minus Row 1 but it's
+really still spanning the same space and
+
+ align:start position:0%
+really still spanning the same space and
+ 
+
+ align:start position:0%
+really still spanning the same space and
+it goes on and then the fourth row it
+
+ align:start position:0%
+it goes on and then the fourth row it
+ 
+
+ align:start position:0%
+it goes on and then the fourth row it
+turns out was useless you only needed
+
+ align:start position:0%
+turns out was useless you only needed
+ 
+
+ align:start position:0%
+turns out was useless you only needed
+the first three so the elements for a
+
+ align:start position:0%
+the first three so the elements for a
+ 
+
+ align:start position:0%
+the first three so the elements for a
+basis well they will be these three so
+
+ align:start position:0%
+basis well they will be these three so
+ 
+
+ align:start position:0%
+basis well they will be these three so
+let me write that zero one one zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could you have used the first three rows
+
+ align:start position:0%
+could you have used the first three rows
+ 
+
+ align:start position:0%
+could you have used the first three rows
+yes you could you can't always do that
+
+ align:start position:0%
+yes you could you can't always do that
+ 
+
+ align:start position:0%
+yes you could you can't always do that
+sometimes in elimination you have to
+
+ align:start position:0%
+sometimes in elimination you have to
+ 
+
+ align:start position:0%
+sometimes in elimination you have to
+switch rows because there's a zero where
+
+ align:start position:0%
+switch rows because there's a zero where
+ 
+
+ align:start position:0%
+switch rows because there's a zero where
+a pivot should be when that happens you
+
+ align:start position:0%
+a pivot should be when that happens you
+ 
+
+ align:start position:0%
+a pivot should be when that happens you
+have to use these three or you have to
+
+ align:start position:0%
+have to use these three or you have to
+ 
+
+ align:start position:0%
+have to use these three or you have to
+keep track of which row you switched to
+
+ align:start position:0%
+keep track of which row you switched to
+ 
+
+ align:start position:0%
+keep track of which row you switched to
+go back and use the initial ones but
+
+ align:start position:0%
+go back and use the initial ones but
+ 
+
+ align:start position:0%
+go back and use the initial ones but
+it's really safe to use these ones and
+
+ align:start position:0%
+it's really safe to use these ones and
+ 
+
+ align:start position:0%
+it's really safe to use these ones and
+also they're simpler than the ones that
+
+ align:start position:0%
+also they're simpler than the ones that
+ 
+
+ align:start position:0%
+also they're simpler than the ones that
+you started with so why not the other
+
+ align:start position:0%
+you started with so why not the other
+ 
+
+ align:start position:0%
+you started with so why not the other
+question that we had was what is the
+
+ align:start position:0%
+question that we had was what is the
+ 
+
+ align:start position:0%
+question that we had was what is the
+dimension of the vector space well this
+
+ align:start position:0%
+dimension of the vector space well this
+ 
+
+ align:start position:0%
+dimension of the vector space well this
+is the easy part
+
+ align:start position:0%
+is the easy part
+ 
+
+ align:start position:0%
+is the easy part
+the dimension of the vector space is 1 2
+
+ align:start position:0%
+the dimension of the vector space is 1 2
+ 
+
+ align:start position:0%
+the dimension of the vector space is 1 2
+3 and that solves the problem but
+
+ align:start position:0%
+3 and that solves the problem but
+ 
+
+ align:start position:0%
+3 and that solves the problem but
+there's one more thing that I want to
+
+ align:start position:0%
+there's one more thing that I want to
+ 
+
+ align:start position:0%
+there's one more thing that I want to
+tell you I told you that there's a
+
+ align:start position:0%
+tell you I told you that there's a
+ 
+
+ align:start position:0%
+tell you I told you that there's a
+couple of ways to find out which of
+
+ align:start position:0%
+couple of ways to find out which of
+ 
+
+ align:start position:0%
+couple of ways to find out which of
+those four vectors are linearly
+
+ align:start position:0%
+those four vectors are linearly
+ 
+
+ align:start position:0%
+those four vectors are linearly
+independent and the one that I used was
+
+ align:start position:0%
+independent and the one that I used was
+ 
+
+ align:start position:0%
+independent and the one that I used was
+I put them in two rows and perform the
+
+ align:start position:0%
+I put them in two rows and perform the
+ 
+
+ align:start position:0%
+I put them in two rows and perform the
+elimination and picked out the rows that
+
+ align:start position:0%
+elimination and picked out the rows that
+ 
+
+ align:start position:0%
+elimination and picked out the rows that
+have pivots on them another way to do it
+
+ align:start position:0%
+have pivots on them another way to do it
+ 
+
+ align:start position:0%
+have pivots on them another way to do it
+is to write the initial vectors as
+
+ align:start position:0%
+is to write the initial vectors as
+ 
+
+ align:start position:0%
+is to write the initial vectors as
+columns of the matrix and then perform
+
+ align:start position:0%
+columns of the matrix and then perform
+ 
+
+ align:start position:0%
+columns of the matrix and then perform
+elimination that also works and as you
+
+ align:start position:0%
+elimination that also works and as you
+ 
+
+ align:start position:0%
+elimination that also works and as you
+know because you're only working with
+
+ align:start position:0%
+know because you're only working with
+ 
+
+ align:start position:0%
+know because you're only working with
+the transpose of this matrix you'll get
+
+ align:start position:0%
+the transpose of this matrix you'll get
+ 
+
+ align:start position:0%
+the transpose of this matrix you'll get
+the same number of pivots let's go over
+
+ align:start position:0%
+the same number of pivots let's go over
+ 
+
+ align:start position:0%
+the same number of pivots let's go over
+here where I have the same while the
+
+ align:start position:0%
+here where I have the same while the
+ 
+
+ align:start position:0%
+here where I have the same while the
+transpose of that matrix I have the same
+
+ align:start position:0%
+transpose of that matrix I have the same
+ 
+
+ align:start position:0%
+transpose of that matrix I have the same
+vectors but now written as columns my
+
+ align:start position:0%
+vectors but now written as columns my
+ 
+
+ align:start position:0%
+vectors but now written as columns my
+four initial vector is written as
+
+ align:start position:0%
+four initial vector is written as
+ 
+
+ align:start position:0%
+four initial vector is written as
+columns and here I have performed
+
+ align:start position:0%
+columns and here I have performed
+ 
+
+ align:start position:0%
+columns and here I have performed
+elimination
+
+ align:start position:0%
+elimination
+ 
+
+ align:start position:0%
+elimination
+and this is the final result let me
+
+ align:start position:0%
+and this is the final result let me
+ 
+
+ align:start position:0%
+and this is the final result let me
+circle the pivots again here they are
+
+ align:start position:0%
+circle the pivots again here they are
+ 
+
+ align:start position:0%
+circle the pivots again here they are
+three which is going to give me three
+
+ align:start position:0%
+three which is going to give me three
+ 
+
+ align:start position:0%
+three which is going to give me three
+independent three linearly independent
+
+ align:start position:0%
+independent three linearly independent
+ 
+
+ align:start position:0%
+independent three linearly independent
+vectors and hence three elements of the
+
+ align:start position:0%
+vectors and hence three elements of the
+ 
+
+ align:start position:0%
+vectors and hence three elements of the
+basis and hence dimension three for the
+
+ align:start position:0%
+basis and hence dimension three for the
+ 
+
+ align:start position:0%
+basis and hence dimension three for the
+vector space but I can no longer use
+
+ align:start position:0%
+vector space but I can no longer use
+ 
+
+ align:start position:0%
+vector space but I can no longer use
+these three these three columns as
+
+ align:start position:0%
+these three these three columns as
+ 
+
+ align:start position:0%
+these three these three columns as
+elements of the basis because when I did
+
+ align:start position:0%
+elements of the basis because when I did
+ 
+
+ align:start position:0%
+elements of the basis because when I did
+elimination I changed the column space
+
+ align:start position:0%
+elimination I changed the column space
+ 
+
+ align:start position:0%
+elimination I changed the column space
+so in the column space of this vectors
+
+ align:start position:0%
+so in the column space of this vectors
+ 
+
+ align:start position:0%
+so in the column space of this vectors
+of this matrix is not the same as the
+
+ align:start position:0%
+of this matrix is not the same as the
+ 
+
+ align:start position:0%
+of this matrix is not the same as the
+column space of the eliminated version
+
+ align:start position:0%
+column space of the eliminated version
+ 
+
+ align:start position:0%
+column space of the eliminated version
+so I cannot use these in fact if you
+
+ align:start position:0%
+so I cannot use these in fact if you
+ 
+
+ align:start position:0%
+so I cannot use these in fact if you
+look at them you can probably understand
+
+ align:start position:0%
+look at them you can probably understand
+ 
+
+ align:start position:0%
+look at them you can probably understand
+that they're not going to span the same
+
+ align:start position:0%
+that they're not going to span the same
+ 
+
+ align:start position:0%
+that they're not going to span the same
+space as these because all that I have
+
+ align:start position:0%
+space as these because all that I have
+ 
+
+ align:start position:0%
+space as these because all that I have
+done here are zeros and I get a lot more
+
+ align:start position:0%
+done here are zeros and I get a lot more
+ 
+
+ align:start position:0%
+done here are zeros and I get a lot more
+than just zeros in the last two entries
+
+ align:start position:0%
+than just zeros in the last two entries
+ 
+
+ align:start position:0%
+than just zeros in the last two entries
+of the vectors so what I need to do is
+
+ align:start position:0%
+of the vectors so what I need to do is
+ 
+
+ align:start position:0%
+of the vectors so what I need to do is
+the pivots are in the first second and
+
+ align:start position:0%
+the pivots are in the first second and
+ 
+
+ align:start position:0%
+the pivots are in the first second and
+third columns I need to use these three
+
+ align:start position:0%
+third columns I need to use these three
+ 
+
+ align:start position:0%
+third columns I need to use these three
+columns as my basis I'll just write
+
+ align:start position:0%
+columns as my basis I'll just write
+ 
+
+ align:start position:0%
+columns as my basis I'll just write
+basis down here and that will work too
+
+ align:start position:0%
+basis down here and that will work too
+ 
+
+ align:start position:0%
+basis down here and that will work too
+so see I have produced two different
+
+ align:start position:0%
+so see I have produced two different
+ 
+
+ align:start position:0%
+so see I have produced two different
+basis for the same vector space which is
+
+ align:start position:0%
+basis for the same vector space which is
+ 
+
+ align:start position:0%
+basis for the same vector space which is
+totally fine
+
+ align:start position:0%
+totally fine
+ 
+
+ align:start position:0%
+totally fine
+you can pick the basis that you prefer
+
+ align:start position:0%
+you can pick the basis that you prefer
+ 
+
+ align:start position:0%
+you can pick the basis that you prefer
+alright we're done thank you
\ No newline at end of file
diff --git a/MXTA8HlhnuM.txt b/MXTA8HlhnuM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..29abbab17ad097c5a8365df5ea8286d09a635389
--- /dev/null
+++ b/MXTA8HlhnuM.txt
@@ -0,0 +1,16027 @@
+align:start position:0%
+ 
+go ahead and uh turn turn to your
+
+ align:start position:0%
+go ahead and uh turn turn to your
+ 
+
+ align:start position:0%
+go ahead and uh turn turn to your
+neighbor and start. Uh one thing you
+
+ align:start position:0%
+neighbor and start. Uh one thing you
+ 
+
+ align:start position:0%
+neighbor and start. Uh one thing you
+could do is pull out the main reading
+
+ align:start position:0%
+could do is pull out the main reading
+ 
+
+ align:start position:0%
+could do is pull out the main reading
+that we did about situated learning
+
+ align:start position:0%
+that we did about situated learning
+ 
+
+ align:start position:0%
+that we did about situated learning
+because we'll do kind of a close read of
+
+ align:start position:0%
+because we'll do kind of a close read of
+ 
+
+ align:start position:0%
+because we'll do kind of a close read of
+that today. So, um, pull that up on
+
+ align:start position:0%
+that today. So, um, pull that up on
+ 
+
+ align:start position:0%
+that today. So, um, pull that up on
+something and then, um, in the minutes
+
+ align:start position:0%
+something and then, um, in the minutes
+ 
+
+ align:start position:0%
+something and then, um, in the minutes
+that we have, we usually start 105, but
+
+ align:start position:0%
+that we have, we usually start 105, but
+ 
+
+ align:start position:0%
+that we have, we usually start 105, but
+in the minutes that we have, uh, turn to
+
+ align:start position:0%
+in the minutes that we have, uh, turn to
+ 
+
+ align:start position:0%
+in the minutes that we have, uh, turn to
+your, uh, turn to your neighbor and
+
+ align:start position:0%
+your, uh, turn to your neighbor and
+ 
+
+ align:start position:0%
+your, uh, turn to your neighbor and
+start thinking about why why babies
+
+ align:start position:0%
+start thinking about why why babies
+ 
+
+ align:start position:0%
+start thinking about why why babies
+would give, uh, cognitive load theorist
+
+ align:start position:0%
+would give, uh, cognitive load theorist
+ 
+
+ align:start position:0%
+would give, uh, cognitive load theorist
+conions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. as a just just as one level
+
+ align:start position:0%
+All right. as a just just as one level
+ 
+
+ align:start position:0%
+All right. as a just just as one level
+setting thing in case you haven't hung
+
+ align:start position:0%
+setting thing in case you haven't hung
+ 
+
+ align:start position:0%
+setting thing in case you haven't hung
+out with babies in a while. Like in
+
+ align:start position:0%
+out with babies in a while. Like in
+ 
+
+ align:start position:0%
+out with babies in a while. Like in
+their first few years of life, how would
+
+ align:start position:0%
+their first few years of life, how would
+ 
+
+ align:start position:0%
+their first few years of life, how would
+you characterize the amount and rate of
+
+ align:start position:0%
+you characterize the amount and rate of
+ 
+
+ align:start position:0%
+you characterize the amount and rate of
+learning that babies do? Insane. Insane.
+
+ align:start position:0%
+learning that babies do? Insane. Insane.
+ 
+
+ align:start position:0%
+learning that babies do? Insane. Insane.
+It is bonkers how much babies learn. I
+
+ align:start position:0%
+It is bonkers how much babies learn. I
+ 
+
+ align:start position:0%
+It is bonkers how much babies learn. I
+mean, a very strong feeling I had when I
+
+ align:start position:0%
+mean, a very strong feeling I had when I
+ 
+
+ align:start position:0%
+mean, a very strong feeling I had when I
+was first father was like like I I do
+
+ align:start position:0%
+was first father was like like I I do
+ 
+
+ align:start position:0%
+was first father was like like I I do
+not improve at all in a week or in a
+
+ align:start position:0%
+not improve at all in a week or in a
+ 
+
+ align:start position:0%
+not improve at all in a week or in a
+month or really most years. I'm really
+
+ align:start position:0%
+month or really most years. I'm really
+ 
+
+ align:start position:0%
+month or really most years. I'm really
+like not that much better than I was the
+
+ align:start position:0%
+like not that much better than I was the
+ 
+
+ align:start position:0%
+like not that much better than I was the
+beginning of the year. And you're just
+
+ align:start position:0%
+beginning of the year. And you're just
+ 
+
+ align:start position:0%
+beginning of the year. And you're just
+watching these infants who are totally
+
+ align:start position:0%
+watching these infants who are totally
+ 
+
+ align:start position:0%
+watching these infants who are totally
+transformed because they are learning
+
+ align:start position:0%
+transformed because they are learning
+ 
+
+ align:start position:0%
+transformed because they are learning
+things at an amazing rate that you can
+
+ align:start position:0%
+things at an amazing rate that you can
+ 
+
+ align:start position:0%
+things at an amazing rate that you can
+see daily, weekly, monthly, you know,
+
+ align:start position:0%
+see daily, weekly, monthly, you know,
+ 
+
+ align:start position:0%
+see daily, weekly, monthly, you know,
+incredibly accelerated learning. Um so
+
+ align:start position:0%
+incredibly accelerated learning. Um so
+ 
+
+ align:start position:0%
+incredibly accelerated learning. Um so
+let's use we'll just use that to level
+
+ align:start position:0%
+let's use we'll just use that to level
+ 
+
+ align:start position:0%
+let's use we'll just use that to level
+set. Um let's let's let's take it as a
+
+ align:start position:0%
+set. Um let's let's let's take it as a
+ 
+
+ align:start position:0%
+set. Um let's let's let's take it as a
+given that babies learn an amazing
+
+ align:start position:0%
+given that babies learn an amazing
+ 
+
+ align:start position:0%
+given that babies learn an amazing
+amount in their early years. Um why now
+
+ align:start position:0%
+amount in their early years. Um why now
+ 
+
+ align:start position:0%
+amount in their early years. Um why now
+keep talking why would that prove to be
+
+ align:start position:0%
+keep talking why would that prove to be
+ 
+
+ align:start position:0%
+keep talking why would that prove to be
+such why would that give cognitive load
+
+ align:start position:0%
+such why would that give cognitive load
+ 
+
+ align:start position:0%
+such why would that give cognitive load
+theorist such a
+
+ align:start position:0%
+theorist such a
+ 
+
+ align:start position:0%
+theorist such a
+conipion and and you can think about um
+
+ align:start position:0%
+conipion and and you can think about um
+ 
+
+ align:start position:0%
+conipion and and you can think about um
+how it connects to some of the stuff
+
+ align:start position:0%
+how it connects to some of the stuff
+ 
+
+ align:start position:0%
+how it connects to some of the stuff
+that you've been reading about situated
+
+ align:start position:0%
+that you've been reading about situated
+ 
+
+ align:start position:0%
+that you've been reading about situated
+load theory keep talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right good what are some what are
+
+ align:start position:0%
+all right good what are some what are
+ 
+
+ align:start position:0%
+all right good what are some what are
+some observations that people made
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are what are baby babies are babies
+
+ align:start position:0%
+what are what are baby babies are babies
+ 
+
+ align:start position:0%
+what are what are baby babies are babies
+are significant so what are what are
+
+ align:start position:0%
+are significant so what are what are
+ 
+
+ align:start position:0%
+are significant so what are what are
+what are some of the observations that
+
+ align:start position:0%
+what are some of the observations that
+ 
+
+ align:start position:0%
+what are some of the observations that
+that you
+
+ align:start position:0%
+that you
+ 
+
+ align:start position:0%
+that you
+made. What were you guys talking about
+
+ align:start position:0%
+made. What were you guys talking about
+ 
+
+ align:start position:0%
+made. What were you guys talking about
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+back? What was your group talking about,
+
+ align:start position:0%
+back? What was your group talking about,
+ 
+
+ align:start position:0%
+back? What was your group talking about,
+Gloria? Um, I was saying that if like
+
+ align:start position:0%
+Gloria? Um, I was saying that if like
+ 
+
+ align:start position:0%
+Gloria? Um, I was saying that if like
+cognitive load theory was true, then
+
+ align:start position:0%
+cognitive load theory was true, then
+ 
+
+ align:start position:0%
+cognitive load theory was true, then
+that would say that babies probably
+
+ align:start position:0%
+that would say that babies probably
+ 
+
+ align:start position:0%
+that would say that babies probably
+can't learn like anything because
+
+ align:start position:0%
+can't learn like anything because
+ 
+
+ align:start position:0%
+can't learn like anything because
+everything is extraneous knowledge to
+
+ align:start position:0%
+everything is extraneous knowledge to
+ 
+
+ align:start position:0%
+everything is extraneous knowledge to
+them and they don't have any long-term
+
+ align:start position:0%
+them and they don't have any long-term
+ 
+
+ align:start position:0%
+them and they don't have any long-term
+memory. They haven't formed any skills
+
+ align:start position:0%
+memory. They haven't formed any skills
+ 
+
+ align:start position:0%
+memory. They haven't formed any skills
+yet. All right. Yep. So, they're so
+
+ align:start position:0%
+yet. All right. Yep. So, they're so
+ 
+
+ align:start position:0%
+yet. All right. Yep. So, they're so
+they're not drawing in they don't have a
+
+ align:start position:0%
+they're not drawing in they don't have a
+ 
+
+ align:start position:0%
+they're not drawing in they don't have a
+lot of long-term memory to draw on.
+
+ align:start position:0%
+lot of long-term memory to draw on.
+ 
+
+ align:start position:0%
+lot of long-term memory to draw on.
+They, you know, they are like the
+
+ align:start position:0%
+They, you know, they are like the
+ 
+
+ align:start position:0%
+They, you know, they are like the
+canonical us looking at Sanskrit letters
+
+ align:start position:0%
+canonical us looking at Sanskrit letters
+ 
+
+ align:start position:0%
+canonical us looking at Sanskrit letters
+where like everything is its own sort of
+
+ align:start position:0%
+where like everything is its own sort of
+ 
+
+ align:start position:0%
+where like everything is its own sort of
+discrete part like um so you would think
+
+ align:start position:0%
+discrete part like um so you would think
+ 
+
+ align:start position:0%
+discrete part like um so you would think
+they're working memory. I mean, you
+
+ align:start position:0%
+they're working memory. I mean, you
+ 
+
+ align:start position:0%
+they're working memory. I mean, you
+know, this video I think is sort of
+
+ align:start position:0%
+know, this video I think is sort of
+ 
+
+ align:start position:0%
+know, this video I think is sort of
+helpful for that. Like everything on
+
+ align:start position:0%
+helpful for that. Like everything on
+ 
+
+ align:start position:0%
+helpful for that. Like everything on
+this screen is brand new to them.
+
+ align:start position:0%
+this screen is brand new to them.
+ 
+
+ align:start position:0%
+this screen is brand new to them.
+There's nothing that they've ever seen
+
+ align:start position:0%
+There's nothing that they've ever seen
+ 
+
+ align:start position:0%
+There's nothing that they've ever seen
+before and it's filled like there's a
+
+ align:start position:0%
+before and it's filled like there's a
+ 
+
+ align:start position:0%
+before and it's filled like there's a
+slide and a dad and that other thing
+
+ align:start position:0%
+slide and a dad and that other thing
+ 
+
+ align:start position:0%
+slide and a dad and that other thing
+back there and all this stuff on the
+
+ align:start position:0%
+back there and all this stuff on the
+ 
+
+ align:start position:0%
+back there and all this stuff on the
+ground and people are talking and the
+
+ align:start position:0%
+ground and people are talking and the
+ 
+
+ align:start position:0%
+ground and people are talking and the
+sun is out and all these things are
+
+ align:start position:0%
+sun is out and all these things are
+ 
+
+ align:start position:0%
+sun is out and all these things are
+happening at once. Good. What else did
+
+ align:start position:0%
+happening at once. Good. What else did
+ 
+
+ align:start position:0%
+happening at once. Good. What else did
+people talk about?
+
+ align:start position:0%
+people talk about?
+ 
+
+ align:start position:0%
+people talk about?
+Um it's also like the the speed with
+
+ align:start position:0%
+Um it's also like the the speed with
+ 
+
+ align:start position:0%
+Um it's also like the the speed with
+which they learn doesn't really connect
+
+ align:start position:0%
+which they learn doesn't really connect
+ 
+
+ align:start position:0%
+which they learn doesn't really connect
+with like the bottleneck theory and like
+
+ align:start position:0%
+with like the bottleneck theory and like
+ 
+
+ align:start position:0%
+with like the bottleneck theory and like
+um the theory of like it takes a while
+
+ align:start position:0%
+um the theory of like it takes a while
+ 
+
+ align:start position:0%
+um the theory of like it takes a while
+for you to like compile all of this
+
+ align:start position:0%
+for you to like compile all of this
+ 
+
+ align:start position:0%
+for you to like compile all of this
+information but it almost seems like a
+
+ align:start position:0%
+information but it almost seems like a
+ 
+
+ align:start position:0%
+information but it almost seems like a
+baby sees it one time and is like able
+
+ align:start position:0%
+baby sees it one time and is like able
+ 
+
+ align:start position:0%
+baby sees it one time and is like able
+to retain it. Yeah. babies seem to do
+
+ align:start position:0%
+to retain it. Yeah. babies seem to do
+ 
+
+ align:start position:0%
+to retain it. Yeah. babies seem to do
+exactly the thing that Sweller said um
+
+ align:start position:0%
+exactly the thing that Sweller said um
+ 
+
+ align:start position:0%
+exactly the thing that Sweller said um
+people should not be able to do, which
+
+ align:start position:0%
+people should not be able to do, which
+ 
+
+ align:start position:0%
+people should not be able to do, which
+is to be um I mean, would you gen like
+
+ align:start position:0%
+is to be um I mean, would you gen like
+ 
+
+ align:start position:0%
+is to be um I mean, would you gen like
+this baby learning stuff, would you
+
+ align:start position:0%
+this baby learning stuff, would you
+ 
+
+ align:start position:0%
+this baby learning stuff, would you
+generally characterize their experience
+
+ align:start position:0%
+generally characterize their experience
+ 
+
+ align:start position:0%
+generally characterize their experience
+as sort of open-ended problem solving or
+
+ align:start position:0%
+as sort of open-ended problem solving or
+ 
+
+ align:start position:0%
+as sort of open-ended problem solving or
+like being carefully walked through a
+
+ align:start position:0%
+like being carefully walked through a
+ 
+
+ align:start position:0%
+like being carefully walked through a
+series of worked
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples? How would you describe it?
+
+ align:start position:0%
+examples? How would you describe it?
+ 
+
+ align:start position:0%
+examples? How would you describe it?
+Open. Yeah, this I mean like I'm just
+
+ align:start position:0%
+Open. Yeah, this I mean like I'm just
+ 
+
+ align:start position:0%
+Open. Yeah, this I mean like I'm just
+like going on the slide and going down,
+
+ align:start position:0%
+like going on the slide and going down,
+ 
+
+ align:start position:0%
+like going on the slide and going down,
+you know? It's not like dad's like, you
+
+ align:start position:0%
+you know? It's not like dad's like, you
+ 
+
+ align:start position:0%
+you know? It's not like dad's like, you
+know, I mean, I think I think you'd find
+
+ align:start position:0%
+know, I mean, I think I think you'd find
+ 
+
+ align:start position:0%
+know, I mean, I think I think you'd find
+more structure and stuff like that, but
+
+ align:start position:0%
+more structure and stuff like that, but
+ 
+
+ align:start position:0%
+more structure and stuff like that, but
+there's a lot of just like, wow, I'm a
+
+ align:start position:0%
+there's a lot of just like, wow, I'm a
+ 
+
+ align:start position:0%
+there's a lot of just like, wow, I'm a
+baby. I'm out there. I'm doing my thing.
+
+ align:start position:0%
+baby. I'm out there. I'm doing my thing.
+ 
+
+ align:start position:0%
+baby. I'm out there. I'm doing my thing.
+Um, you know, and and the worked example
+
+ align:start position:0%
+Um, you know, and and the worked example
+ 
+
+ align:start position:0%
+Um, you know, and and the worked example
+effect and the expert reversal effect
+
+ align:start position:0%
+effect and the expert reversal effect
+ 
+
+ align:start position:0%
+effect and the expert reversal effect
+suggests that that should not be very
+
+ align:start position:0%
+suggests that that should not be very
+ 
+
+ align:start position:0%
+suggests that that should not be very
+effective. You know, the most effective
+
+ align:start position:0%
+effective. You know, the most effective
+ 
+
+ align:start position:0%
+effective. You know, the most effective
+way to teach babies should be, you know,
+
+ align:start position:0%
+way to teach babies should be, you know,
+ 
+
+ align:start position:0%
+way to teach babies should be, you know,
+through like careful, you know,
+
+ align:start position:0%
+through like careful, you know,
+ 
+
+ align:start position:0%
+through like careful, you know,
+devolving scaffolding of language and
+
+ align:start position:0%
+devolving scaffolding of language and
+ 
+
+ align:start position:0%
+devolving scaffolding of language and
+things like that. And that's not what we
+
+ align:start position:0%
+things like that. And that's not what we
+ 
+
+ align:start position:0%
+things like that. And that's not what we
+do. We just like throw babies in with
+
+ align:start position:0%
+do. We just like throw babies in with
+ 
+
+ align:start position:0%
+do. We just like throw babies in with
+people all the time. Um and they uh and
+
+ align:start position:0%
+people all the time. Um and they uh and
+ 
+
+ align:start position:0%
+people all the time. Um and they uh and
+they learn language, they learn
+
+ align:start position:0%
+they learn language, they learn
+ 
+
+ align:start position:0%
+they learn language, they learn
+movement, they learn a few other things
+
+ align:start position:0%
+movement, they learn a few other things
+ 
+
+ align:start position:0%
+movement, they learn a few other things
+at sort of an extraordinary rate. Um so
+
+ align:start position:0%
+at sort of an extraordinary rate. Um so
+ 
+
+ align:start position:0%
+at sort of an extraordinary rate. Um so
+for how do how does how does what
+
+ align:start position:0%
+for how do how does how does what
+ 
+
+ align:start position:0%
+for how do how does how does what
+connections do you see between this set
+
+ align:start position:0%
+connections do you see between this set
+ 
+
+ align:start position:0%
+connections do you see between this set
+of ideas and situated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+learning? There's a lot of like trial
+
+ align:start position:0%
+learning? There's a lot of like trial
+ 
+
+ align:start position:0%
+learning? There's a lot of like trial
+and error in it. Like we were talking
+
+ align:start position:0%
+and error in it. Like we were talking
+ 
+
+ align:start position:0%
+and error in it. Like we were talking
+about like hey when they they see a
+
+ align:start position:0%
+about like hey when they they see a
+ 
+
+ align:start position:0%
+about like hey when they they see a
+block they want to go get they start to
+
+ align:start position:0%
+block they want to go get they start to
+ 
+
+ align:start position:0%
+block they want to go get they start to
+figure out the different ways that they
+
+ align:start position:0%
+figure out the different ways that they
+ 
+
+ align:start position:0%
+figure out the different ways that they
+can go get that block. Like but through
+
+ align:start position:0%
+can go get that block. Like but through
+ 
+
+ align:start position:0%
+can go get that block. Like but through
+trial and error trying to stand up,
+
+ align:start position:0%
+trial and error trying to stand up,
+ 
+
+ align:start position:0%
+trial and error trying to stand up,
+trying to crawl, trying to drag
+
+ align:start position:0%
+trying to crawl, trying to drag
+ 
+
+ align:start position:0%
+trying to crawl, trying to drag
+themselves. Yeah. all that kind of
+
+ align:start position:0%
+themselves. Yeah. all that kind of
+ 
+
+ align:start position:0%
+themselves. Yeah. all that kind of
+stuff. Kadus, come on in. Sit with me.
+
+ align:start position:0%
+stuff. Kadus, come on in. Sit with me.
+ 
+
+ align:start position:0%
+stuff. Kadus, come on in. Sit with me.
+No, no, delighted to have you. Um, yeah.
+
+ align:start position:0%
+No, no, delighted to have you. Um, yeah.
+ 
+
+ align:start position:0%
+No, no, delighted to have you. Um, yeah.
+Um, yeah. I mean, this this certainly
+
+ align:start position:0%
+Um, yeah. I mean, this this certainly
+ 
+
+ align:start position:0%
+Um, yeah. I mean, this this certainly
+looks a lot more like situated learning
+
+ align:start position:0%
+looks a lot more like situated learning
+ 
+
+ align:start position:0%
+looks a lot more like situated learning
+than it does look like a sort of
+
+ align:start position:0%
+than it does look like a sort of
+ 
+
+ align:start position:0%
+than it does look like a sort of
+carefully sculpted classroom. Um, and
+
+ align:start position:0%
+carefully sculpted classroom. Um, and
+ 
+
+ align:start position:0%
+carefully sculpted classroom. Um, and
+uh, so for situated learning people, and
+
+ align:start position:0%
+uh, so for situated learning people, and
+ 
+
+ align:start position:0%
+uh, so for situated learning people, and
+you know, we'll we'll I think we'll see
+
+ align:start position:0%
+you know, we'll we'll I think we'll see
+ 
+
+ align:start position:0%
+you know, we'll we'll I think we'll see
+this more in some stuff that we read.
+
+ align:start position:0%
+this more in some stuff that we read.
+ 
+
+ align:start position:0%
+this more in some stuff that we read.
+Um, the experience of babies seems like
+
+ align:start position:0%
+Um, the experience of babies seems like
+ 
+
+ align:start position:0%
+Um, the experience of babies seems like
+something that's pretty important to
+
+ align:start position:0%
+something that's pretty important to
+ 
+
+ align:start position:0%
+something that's pretty important to
+draw from. Um, how would you how would
+
+ align:start position:0%
+draw from. Um, how would you how would
+ 
+
+ align:start position:0%
+draw from. Um, how would you how would
+you how would you
+
+ align:start position:0%
+you how would you
+ 
+
+ align:start position:0%
+you how would you
+characterize like the feelings that
+
+ align:start position:0%
+characterize like the feelings that
+ 
+
+ align:start position:0%
+characterize like the feelings that
+babies have as they learn language? Like
+
+ align:start position:0%
+babies have as they learn language? Like
+ 
+
+ align:start position:0%
+babies have as they learn language? Like
+are they happy? Are they sad? Are they
+
+ align:start position:0%
+are they happy? Are they sad? Are they
+ 
+
+ align:start position:0%
+are they happy? Are they sad? Are they
+angry? Are they frustrated? Are they
+
+ align:start position:0%
+angry? Are they frustrated? Are they
+ 
+
+ align:start position:0%
+angry? Are they frustrated? Are they
+joyful? Are they playful? Like what kind
+
+ align:start position:0%
+joyful? Are they playful? Like what kind
+ 
+
+ align:start position:0%
+joyful? Are they playful? Like what kind
+of feelings do babies seem to have as
+
+ align:start position:0%
+of feelings do babies seem to have as
+ 
+
+ align:start position:0%
+of feelings do babies seem to have as
+they're learning words?
+
+ align:start position:0%
+they're learning words?
+ 
+
+ align:start position:0%
+they're learning words?
+What were you going to say, Jared? I was
+
+ align:start position:0%
+What were you going to say, Jared? I was
+ 
+
+ align:start position:0%
+What were you going to say, Jared? I was
+going to say like they seem kind of
+
+ align:start position:0%
+going to say like they seem kind of
+ 
+
+ align:start position:0%
+going to say like they seem kind of
+fearless and like there there's no like
+
+ align:start position:0%
+fearless and like there there's no like
+ 
+
+ align:start position:0%
+fearless and like there there's no like
+social pressure to like try and
+
+ align:start position:0%
+social pressure to like try and
+ 
+
+ align:start position:0%
+social pressure to like try and
+pronounce this word correctly. They'll
+
+ align:start position:0%
+pronounce this word correctly. They'll
+ 
+
+ align:start position:0%
+pronounce this word correctly. They'll
+just say the word be like, "Oh, good
+
+ align:start position:0%
+just say the word be like, "Oh, good
+ 
+
+ align:start position:0%
+just say the word be like, "Oh, good
+job. make noises come out of our mouths
+
+ align:start position:0%
+job. make noises come out of our mouths
+ 
+
+ align:start position:0%
+job. make noises come out of our mouths
+whenever. Yeah. Do you want to grab
+
+ align:start position:0%
+whenever. Yeah. Do you want to grab
+ 
+
+ align:start position:0%
+whenever. Yeah. Do you want to grab
+another chair? There's no It doesn't
+
+ align:start position:0%
+another chair? There's no It doesn't
+ 
+
+ align:start position:0%
+another chair? There's no It doesn't
+seem like there's there's a lot of fear
+
+ align:start position:0%
+seem like there's there's a lot of fear
+ 
+
+ align:start position:0%
+seem like there's there's a lot of fear
+behind trying to practice what they're
+
+ align:start position:0%
+behind trying to practice what they're
+ 
+
+ align:start position:0%
+behind trying to practice what they're
+learning. Uhhuh. Um but I think like in
+
+ align:start position:0%
+learning. Uhhuh. Um but I think like in
+ 
+
+ align:start position:0%
+learning. Uhhuh. Um but I think like in
+addition to that, there can be like a
+
+ align:start position:0%
+addition to that, there can be like a
+ 
+
+ align:start position:0%
+addition to that, there can be like a
+lot of frustration as well. The
+
+ align:start position:0%
+lot of frustration as well. The
+ 
+
+ align:start position:0%
+lot of frustration as well. The
+consequences of like not knowing how to
+
+ align:start position:0%
+consequences of like not knowing how to
+ 
+
+ align:start position:0%
+consequences of like not knowing how to
+say a specific thing. Yeah. Or or you
+
+ align:start position:0%
+say a specific thing. Yeah. Or or you
+ 
+
+ align:start position:0%
+say a specific thing. Yeah. Or or you
+watch babies when they're you know I
+
+ align:start position:0%
+watch babies when they're you know I
+ 
+
+ align:start position:0%
+watch babies when they're you know I
+mean they cry when they can't articulate
+
+ align:start position:0%
+mean they cry when they can't articulate
+ 
+
+ align:start position:0%
+mean they cry when they can't articulate
+the thing that they want to be able to
+
+ align:start position:0%
+the thing that they want to be able to
+ 
+
+ align:start position:0%
+the thing that they want to be able to
+say or Yeah. And in addition to
+
+ align:start position:0%
+say or Yeah. And in addition to
+ 
+
+ align:start position:0%
+say or Yeah. And in addition to
+frustration, I think there's a bit of
+
+ align:start position:0%
+frustration, I think there's a bit of
+ 
+
+ align:start position:0%
+frustration, I think there's a bit of
+like happiness when they actually
+
+ align:start position:0%
+like happiness when they actually
+ 
+
+ align:start position:0%
+like happiness when they actually
+achieve what they're trying to create
+
+ align:start position:0%
+achieve what they're trying to create
+ 
+
+ align:start position:0%
+achieve what they're trying to create
+and then they feel understood. I think
+
+ align:start position:0%
+and then they feel understood. I think
+ 
+
+ align:start position:0%
+and then they feel understood. I think
+there's some some sort of some sort of
+
+ align:start position:0%
+there's some some sort of some sort of
+ 
+
+ align:start position:0%
+there's some some sort of some sort of
+pride in that. What were you going to
+
+ align:start position:0%
+pride in that. What were you going to
+ 
+
+ align:start position:0%
+pride in that. What were you going to
+say, Courtney? Um, same kind. I wonder
+
+ align:start position:0%
+say, Courtney? Um, same kind. I wonder
+ 
+
+ align:start position:0%
+say, Courtney? Um, same kind. I wonder
+my my daughter, we used to uh we used to
+
+ align:start position:0%
+my my daughter, we used to uh we used to
+ 
+
+ align:start position:0%
+my my daughter, we used to uh we used to
+just my I guess it was my younger one,
+
+ align:start position:0%
+just my I guess it was my younger one,
+ 
+
+ align:start position:0%
+just my I guess it was my younger one,
+we used to just list vegetables and list
+
+ align:start position:0%
+we used to just list vegetables and list
+ 
+
+ align:start position:0%
+we used to just list vegetables and list
+things you get at the supermarket and
+
+ align:start position:0%
+things you get at the supermarket and
+ 
+
+ align:start position:0%
+things you get at the supermarket and
+she thought that was the funniest thing
+
+ align:start position:0%
+she thought that was the funniest thing
+ 
+
+ align:start position:0%
+she thought that was the funniest thing
+ever. you you would just be like
+
+ align:start position:0%
+ever. you you would just be like
+ 
+
+ align:start position:0%
+ever. you you would just be like
+pears in the back of the car just like
+
+ align:start position:0%
+pears in the back of the car just like
+ 
+
+ align:start position:0%
+pears in the back of the car just like
+saying stuff and she's giggling the
+
+ align:start position:0%
+saying stuff and she's giggling the
+ 
+
+ align:start position:0%
+saying stuff and she's giggling the
+whole time. Um you know I I mean if you
+
+ align:start position:0%
+whole time. Um you know I I mean if you
+ 
+
+ align:start position:0%
+whole time. Um you know I I mean if you
+watch a video like this like this is
+
+ align:start position:0%
+watch a video like this like this is
+ 
+
+ align:start position:0%
+watch a video like this like this is
+clearly a delightful um you know there's
+
+ align:start position:0%
+clearly a delightful um you know there's
+ 
+
+ align:start position:0%
+clearly a delightful um you know there's
+there's not a lot that Sweller and
+
+ align:start position:0%
+there's not a lot that Sweller and
+ 
+
+ align:start position:0%
+there's not a lot that Sweller and
+colleagues have to say about like being
+
+ align:start position:0%
+colleagues have to say about like being
+ 
+
+ align:start position:0%
+colleagues have to say about like being
+delighted. Um you know I I I think if
+
+ align:start position:0%
+delighted. Um you know I I I think if
+ 
+
+ align:start position:0%
+delighted. Um you know I I I think if
+you were to if you were to situate like
+
+ align:start position:0%
+you were to if you were to situate like
+ 
+
+ align:start position:0%
+you were to if you were to situate like
+the kind of like moral ethic of work
+
+ align:start position:0%
+the kind of like moral ethic of work
+ 
+
+ align:start position:0%
+the kind of like moral ethic of work
+around learning in cognitive load
+
+ align:start position:0%
+around learning in cognitive load
+ 
+
+ align:start position:0%
+around learning in cognitive load
+theory, it's very like learning is hard.
+
+ align:start position:0%
+theory, it's very like learning is hard.
+ 
+
+ align:start position:0%
+theory, it's very like learning is hard.
+we persevere through a hard thing. Um,
+
+ align:start position:0%
+we persevere through a hard thing. Um,
+ 
+
+ align:start position:0%
+we persevere through a hard thing. Um,
+and we control the hardness of it so
+
+ align:start position:0%
+and we control the hardness of it so
+ 
+
+ align:start position:0%
+and we control the hardness of it so
+that we can scaffold it for people. Um,
+
+ align:start position:0%
+that we can scaffold it for people. Um,
+ 
+
+ align:start position:0%
+that we can scaffold it for people. Um,
+and for situated learning people, these
+
+ align:start position:0%
+and for situated learning people, these
+ 
+
+ align:start position:0%
+and for situated learning people, these
+these aren't really I wouldn't even
+
+ align:start position:0%
+these aren't really I wouldn't even
+ 
+
+ align:start position:0%
+these aren't really I wouldn't even
+these aren't like arguments. And
+
+ align:start position:0%
+these aren't like arguments. And
+ 
+
+ align:start position:0%
+these aren't like arguments. And
+sometimes they're explicit arguments.
+
+ align:start position:0%
+sometimes they're explicit arguments.
+ 
+
+ align:start position:0%
+sometimes they're explicit arguments.
+Sometimes they're just tones that you
+
+ align:start position:0%
+Sometimes they're just tones that you
+ 
+
+ align:start position:0%
+Sometimes they're just tones that you
+find in the way people talk about these
+
+ align:start position:0%
+find in the way people talk about these
+ 
+
+ align:start position:0%
+find in the way people talk about these
+things. They'd be like, "Oh, you know,
+
+ align:start position:0%
+things. They'd be like, "Oh, you know,
+ 
+
+ align:start position:0%
+things. They'd be like, "Oh, you know,
+learning is great. Learning is the thing
+
+ align:start position:0%
+learning is great. Learning is the thing
+ 
+
+ align:start position:0%
+learning is great. Learning is the thing
+that we do and get better at stuff. It's
+
+ align:start position:0%
+that we do and get better at stuff. It's
+ 
+
+ align:start position:0%
+that we do and get better at stuff. It's
+like nice and natural and things like
+
+ align:start position:0%
+like nice and natural and things like
+ 
+
+ align:start position:0%
+like nice and natural and things like
+that." Um, can anybody think of a thing
+
+ align:start position:0%
+that." Um, can anybody think of a thing
+ 
+
+ align:start position:0%
+that." Um, can anybody think of a thing
+that you've learned in which you like
+
+ align:start position:0%
+that you've learned in which you like
+ 
+
+ align:start position:0%
+that you've learned in which you like
+got better at the thing and it was just
+
+ align:start position:0%
+got better at the thing and it was just
+ 
+
+ align:start position:0%
+got better at the thing and it was just
+like playful, enjoyable, natural to get
+
+ align:start position:0%
+like playful, enjoyable, natural to get
+ 
+
+ align:start position:0%
+like playful, enjoyable, natural to get
+better at it? Anybody can shout out one
+
+ align:start position:0%
+better at it? Anybody can shout out one
+ 
+
+ align:start position:0%
+better at it? Anybody can shout out one
+or two things that was like that for
+
+ align:start position:0%
+or two things that was like that for
+ 
+
+ align:start position:0%
+or two things that was like that for
+you?
+
+ align:start position:0%
+you?
+ 
+
+ align:start position:0%
+you?
+When I first learned how to use like a
+
+ align:start position:0%
+When I first learned how to use like a
+ 
+
+ align:start position:0%
+When I first learned how to use like a
+power drill. Awesome. Great. Learning
+
+ align:start position:0%
+power drill. Awesome. Great. Learning
+ 
+
+ align:start position:0%
+power drill. Awesome. Great. Learning
+how to use power drill like very
+
+ align:start position:0%
+how to use power drill like very
+ 
+
+ align:start position:0%
+how to use power drill like very
+satisfying immediate feedback things
+
+ align:start position:0%
+satisfying immediate feedback things
+ 
+
+ align:start position:0%
+satisfying immediate feedback things
+like that. Yeah. Other things that
+
+ align:start position:0%
+like that. Yeah. Other things that
+ 
+
+ align:start position:0%
+like that. Yeah. Other things that
+people really enjoyed learning? Um, I
+
+ align:start position:0%
+people really enjoyed learning? Um, I
+ 
+
+ align:start position:0%
+people really enjoyed learning? Um, I
+think similarly like like tactical
+
+ align:start position:0%
+think similarly like like tactical
+ 
+
+ align:start position:0%
+think similarly like like tactical
+things like learning how to do pottery.
+
+ align:start position:0%
+things like learning how to do pottery.
+ 
+
+ align:start position:0%
+things like learning how to do pottery.
+Oh, great. Yep. Pottery seems like a
+
+ align:start position:0%
+Oh, great. Yep. Pottery seems like a
+ 
+
+ align:start position:0%
+Oh, great. Yep. Pottery seems like a
+good one. Learning how to swim. Learning
+
+ align:start position:0%
+good one. Learning how to swim. Learning
+ 
+
+ align:start position:0%
+good one. Learning how to swim. Learning
+how to swim was all right. We're saying
+
+ align:start position:0%
+how to swim was all right. We're saying
+ 
+
+ align:start position:0%
+how to swim was all right. We're saying
+a lot of physical things. Good. Video
+
+ align:start position:0%
+a lot of physical things. Good. Video
+ 
+
+ align:start position:0%
+a lot of physical things. Good. Video
+games. Video video games. Video games
+
+ align:start position:0%
+games. Video video games. Video games
+ 
+
+ align:start position:0%
+games. Video video games. Video games
+are a there is a whole science. Um
+
+ align:start position:0%
+are a there is a whole science. Um
+ 
+
+ align:start position:0%
+are a there is a whole science. Um
+there's a there we won't read it.
+
+ align:start position:0%
+there's a there we won't read it.
+ 
+
+ align:start position:0%
+there's a there we won't read it.
+There's a guy named James G um who wrote
+
+ align:start position:0%
+There's a guy named James G um who wrote
+ 
+
+ align:start position:0%
+There's a guy named James G um who wrote
+a great book about learning in video
+
+ align:start position:0%
+a great book about learning in video
+ 
+
+ align:start position:0%
+a great book about learning in video
+games. It's a little bit like Toqueville
+
+ align:start position:0%
+games. It's a little bit like Toqueville
+ 
+
+ align:start position:0%
+games. It's a little bit like Toqueville
+coming to America if that's a reference
+
+ align:start position:0%
+coming to America if that's a reference
+ 
+
+ align:start position:0%
+coming to America if that's a reference
+that you know. Um, but Toqueville was
+
+ align:start position:0%
+that you know. Um, but Toqueville was
+ 
+
+ align:start position:0%
+that you know. Um, but Toqueville was
+this European who came to America. Um,
+
+ align:start position:0%
+this European who came to America. Um,
+ 
+
+ align:start position:0%
+this European who came to America. Um,
+and he saw America incredibly intimately
+
+ align:start position:0%
+and he saw America incredibly intimately
+ 
+
+ align:start position:0%
+and he saw America incredibly intimately
+in a way that sort of only an outsider
+
+ align:start position:0%
+in a way that sort of only an outsider
+ 
+
+ align:start position:0%
+in a way that sort of only an outsider
+could by in part by becoming an insider.
+
+ align:start position:0%
+could by in part by becoming an insider.
+ 
+
+ align:start position:0%
+could by in part by becoming an insider.
+Um, James G is an old guy who was like,
+
+ align:start position:0%
+Um, James G is an old guy who was like,
+ 
+
+ align:start position:0%
+Um, James G is an old guy who was like,
+"Why do my kids like video games so
+
+ align:start position:0%
+"Why do my kids like video games so
+ 
+
+ align:start position:0%
+"Why do my kids like video games so
+much?" And he starts playing them a
+
+ align:start position:0%
+much?" And he starts playing them a
+ 
+
+ align:start position:0%
+much?" And he starts playing them a
+bunch. He's like, "These are amazing
+
+ align:start position:0%
+bunch. He's like, "These are amazing
+ 
+
+ align:start position:0%
+bunch. He's like, "These are amazing
+learning experiences." Um, think like
+
+ align:start position:0%
+learning experiences." Um, think like
+ 
+
+ align:start position:0%
+learning experiences." Um, think like
+think about someone learning a really
+
+ align:start position:0%
+think about someone learning a really
+ 
+
+ align:start position:0%
+think about someone learning a really
+hard game like Civilization 6 or
+
+ align:start position:0%
+hard game like Civilization 6 or
+ 
+
+ align:start position:0%
+hard game like Civilization 6 or
+Stellaris or put in whatever game you've
+
+ align:start position:0%
+Stellaris or put in whatever game you've
+ 
+
+ align:start position:0%
+Stellaris or put in whatever game you've
+been playing recently that just has like
+
+ align:start position:0%
+been playing recently that just has like
+ 
+
+ align:start position:0%
+been playing recently that just has like
+incredibly complicated systems in them.
+
+ align:start position:0%
+incredibly complicated systems in them.
+ 
+
+ align:start position:0%
+incredibly complicated systems in them.
+There aren't a lot of people who are
+
+ align:start position:0%
+There aren't a lot of people who are
+ 
+
+ align:start position:0%
+There aren't a lot of people who are
+like, you know,
+
+ align:start position:0%
+like, you know,
+ 
+
+ align:start position:0%
+like, you know,
+Minecraft like redstone building in
+
+ align:start position:0%
+Minecraft like redstone building in
+ 
+
+ align:start position:0%
+Minecraft like redstone building in
+Minecraft, stuff like that. There aren't
+
+ align:start position:0%
+Minecraft, stuff like that. There aren't
+ 
+
+ align:start position:0%
+Minecraft, stuff like that. There aren't
+people who are like, "God, it was such a
+
+ align:start position:0%
+people who are like, "God, it was such a
+ 
+
+ align:start position:0%
+people who are like, "God, it was such a
+drag that I had to take all those
+
+ align:start position:0%
+drag that I had to take all those
+ 
+
+ align:start position:0%
+drag that I had to take all those
+classes on redstone to be able to, you
+
+ align:start position:0%
+classes on redstone to be able to, you
+ 
+
+ align:start position:0%
+classes on redstone to be able to, you
+know, um these games have have systems
+
+ align:start position:0%
+know, um these games have have systems
+ 
+
+ align:start position:0%
+know, um these games have have systems
+built within them. They're sort of canot
+
+ align:start position:0%
+built within them. They're sort of canot
+ 
+
+ align:start position:0%
+built within them. They're sort of canot
+almost all them canonically situated
+
+ align:start position:0%
+almost all them canonically situated
+ 
+
+ align:start position:0%
+almost all them canonically situated
+kinds of things. Um where you're just
+
+ align:start position:0%
+kinds of things. Um where you're just
+ 
+
+ align:start position:0%
+kinds of things. Um where you're just
+immersed in the environment, you're
+
+ align:start position:0%
+immersed in the environment, you're
+ 
+
+ align:start position:0%
+immersed in the environment, you're
+encouraged to play. There are some peer
+
+ align:start position:0%
+encouraged to play. There are some peer
+ 
+
+ align:start position:0%
+encouraged to play. There are some peer
+structures around to help you learn and
+
+ align:start position:0%
+structures around to help you learn and
+ 
+
+ align:start position:0%
+structures around to help you learn and
+stuff like that. But it's extremely
+
+ align:start position:0%
+stuff like that. But it's extremely
+ 
+
+ align:start position:0%
+stuff like that. But it's extremely
+pleasant. um you know even even when um
+
+ align:start position:0%
+pleasant. um you know even even when um
+ 
+
+ align:start position:0%
+pleasant. um you know even even when um
+you know people might find it
+
+ align:start position:0%
+you know people might find it
+ 
+
+ align:start position:0%
+you know people might find it
+frustrating or things like that. I think
+
+ align:start position:0%
+frustrating or things like that. I think
+ 
+
+ align:start position:0%
+frustrating or things like that. I think
+a lot of in families cooking is
+
+ align:start position:0%
+a lot of in families cooking is
+ 
+
+ align:start position:0%
+a lot of in families cooking is
+something that learning how to cook
+
+ align:start position:0%
+something that learning how to cook
+ 
+
+ align:start position:0%
+something that learning how to cook
+which has both tactile and kind of
+
+ align:start position:0%
+which has both tactile and kind of
+ 
+
+ align:start position:0%
+which has both tactile and kind of
+scientific ma you know measurement
+
+ align:start position:0%
+scientific ma you know measurement
+ 
+
+ align:start position:0%
+scientific ma you know measurement
+mathematical language components um that
+
+ align:start position:0%
+mathematical language components um that
+ 
+
+ align:start position:0%
+mathematical language components um that
+people often find quite pleasurable. Uh
+
+ align:start position:0%
+people often find quite pleasurable. Uh
+ 
+
+ align:start position:0%
+people often find quite pleasurable. Uh
+and this connects a lot to like the
+
+ align:start position:0%
+and this connects a lot to like the
+ 
+
+ align:start position:0%
+and this connects a lot to like the
+material I'm learning in CMS 587 about
+
+ align:start position:0%
+material I'm learning in CMS 587 about
+ 
+
+ align:start position:0%
+material I'm learning in CMS 587 about
+assessments. We're learning like the
+
+ align:start position:0%
+assessments. We're learning like the
+ 
+
+ align:start position:0%
+assessments. We're learning like the
+different theories of intelligence and
+
+ align:start position:0%
+different theories of intelligence and
+ 
+
+ align:start position:0%
+different theories of intelligence and
+how um if you believe that your
+
+ align:start position:0%
+how um if you believe that your
+ 
+
+ align:start position:0%
+how um if you believe that your
+intelligence isn't fixed and like it can
+
+ align:start position:0%
+intelligence isn't fixed and like it can
+ 
+
+ align:start position:0%
+intelligence isn't fixed and like it can
+expand then you can learn a lot more.
+
+ align:start position:0%
+expand then you can learn a lot more.
+ 
+
+ align:start position:0%
+expand then you can learn a lot more.
+And that's kind of like young children
+
+ align:start position:0%
+And that's kind of like young children
+ 
+
+ align:start position:0%
+And that's kind of like young children
+or babies because they're not really
+
+ align:start position:0%
+or babies because they're not really
+ 
+
+ align:start position:0%
+or babies because they're not really
+afraid of failure and like they just
+
+ align:start position:0%
+afraid of failure and like they just
+ 
+
+ align:start position:0%
+afraid of failure and like they just
+like they're very resilient. So yeah.
+
+ align:start position:0%
+like they're very resilient. So yeah.
+ 
+
+ align:start position:0%
+like they're very resilient. So yeah.
+Yeah. Yeah. They don't they don't care
+
+ align:start position:0%
+Yeah. Yeah. They don't they don't care
+ 
+
+ align:start position:0%
+Yeah. Yeah. They don't they don't care
+what's going on. They're just trying to
+
+ align:start position:0%
+what's going on. They're just trying to
+ 
+
+ align:start position:0%
+what's going on. They're just trying to
+figure things out. Um how many of you
+
+ align:start position:0%
+figure things out. Um how many of you
+ 
+
+ align:start position:0%
+figure things out. Um how many of you
+have have had uh experiences that you're
+
+ align:start position:0%
+have have had uh experiences that you're
+ 
+
+ align:start position:0%
+have have had uh experiences that you're
+really happy with where learning was
+
+ align:start position:0%
+really happy with where learning was
+ 
+
+ align:start position:0%
+really happy with where learning was
+hard where you like persevered through
+
+ align:start position:0%
+hard where you like persevered through
+ 
+
+ align:start position:0%
+hard where you like persevered through
+sort of a challenging set of learning
+
+ align:start position:0%
+sort of a challenging set of learning
+ 
+
+ align:start position:0%
+sort of a challenging set of learning
+experiences and got better at it and you
+
+ align:start position:0%
+experiences and got better at it and you
+ 
+
+ align:start position:0%
+experiences and got better at it and you
+were like, "Yeah, that's great. I'm
+
+ align:start position:0%
+were like, "Yeah, that's great. I'm
+ 
+
+ align:start position:0%
+were like, "Yeah, that's great. I'm
+super glad I did that." What what things
+
+ align:start position:0%
+super glad I did that." What what things
+ 
+
+ align:start position:0%
+super glad I did that." What what things
+come to mind for that for you? I think
+
+ align:start position:0%
+come to mind for that for you? I think
+ 
+
+ align:start position:0%
+come to mind for that for you? I think
+for me learning to code was a bit like
+
+ align:start position:0%
+for me learning to code was a bit like
+ 
+
+ align:start position:0%
+for me learning to code was a bit like
+that. I think differently from some
+
+ align:start position:0%
+that. I think differently from some
+ 
+
+ align:start position:0%
+that. I think differently from some
+people in the room like I didn't learn
+
+ align:start position:0%
+people in the room like I didn't learn
+ 
+
+ align:start position:0%
+people in the room like I didn't learn
+to code in middle school. I learned it
+
+ align:start position:0%
+to code in middle school. I learned it
+ 
+
+ align:start position:0%
+to code in middle school. I learned it
+in university. So there were like
+
+ align:start position:0%
+in university. So there were like
+ 
+
+ align:start position:0%
+in university. So there were like
+degrees associated with it and things
+
+ align:start position:0%
+degrees associated with it and things
+ 
+
+ align:start position:0%
+degrees associated with it and things
+like that. Yeah. Yeah. You watched a
+
+ align:start position:0%
+like that. Yeah. Yeah. You watched a
+ 
+
+ align:start position:0%
+like that. Yeah. Yeah. You watched a
+bunch of lectures and did pet sets and
+
+ align:start position:0%
+bunch of lectures and did pet sets and
+ 
+
+ align:start position:0%
+bunch of lectures and did pet sets and
+turn them in and but I remember like the
+
+ align:start position:0%
+turn them in and but I remember like the
+ 
+
+ align:start position:0%
+turn them in and but I remember like the
+first very complex pet that I completed
+
+ align:start position:0%
+first very complex pet that I completed
+ 
+
+ align:start position:0%
+first very complex pet that I completed
+and like my program worked perfectly and
+
+ align:start position:0%
+and like my program worked perfectly and
+ 
+
+ align:start position:0%
+and like my program worked perfectly and
+I was like it's amazing feeling. It felt
+
+ align:start position:0%
+I was like it's amazing feeling. It felt
+ 
+
+ align:start position:0%
+I was like it's amazing feeling. It felt
+it felt very satisfying even though some
+
+ align:start position:0%
+it felt very satisfying even though some
+ 
+
+ align:start position:0%
+it felt very satisfying even though some
+of the learning experience of doing
+
+ align:start position:0%
+of the learning experience of doing
+ 
+
+ align:start position:0%
+of the learning experience of doing
+that. Yeah. Yeah. So that that kind of
+
+ align:start position:0%
+that. Yeah. Yeah. So that that kind of
+ 
+
+ align:start position:0%
+that. Yeah. Yeah. So that that kind of
+that you know I think there's sort of a
+
+ align:start position:0%
+that you know I think there's sort of a
+ 
+
+ align:start position:0%
+that you know I think there's sort of a
+moral story that emerges around a lot of
+
+ align:start position:0%
+moral story that emerges around a lot of
+ 
+
+ align:start position:0%
+moral story that emerges around a lot of
+instructionist learning which is like it
+
+ align:start position:0%
+instructionist learning which is like it
+ 
+
+ align:start position:0%
+instructionist learning which is like it
+was hard we put our nose to the
+
+ align:start position:0%
+was hard we put our nose to the
+ 
+
+ align:start position:0%
+was hard we put our nose to the
+grindstoneone we sacrificed but after
+
+ align:start position:0%
+grindstoneone we sacrificed but after
+ 
+
+ align:start position:0%
+grindstoneone we sacrificed but after
+that sacrifice we had this great feeling
+
+ align:start position:0%
+that sacrifice we had this great feeling
+ 
+
+ align:start position:0%
+that sacrifice we had this great feeling
+of relief and I think most of us have
+
+ align:start position:0%
+of relief and I think most of us have
+ 
+
+ align:start position:0%
+of relief and I think most of us have
+some kind of learning experience that
+
+ align:start position:0%
+some kind of learning experience that
+ 
+
+ align:start position:0%
+some kind of learning experience that
+goes like that and then situated
+
+ align:start position:0%
+goes like that and then situated
+ 
+
+ align:start position:0%
+goes like that and then situated
+learning people have more of this story
+
+ align:start position:0%
+learning people have more of this story
+ 
+
+ align:start position:0%
+learning people have more of this story
+of like we just naturally found
+
+ align:start position:0%
+of like we just naturally found
+ 
+
+ align:start position:0%
+of like we just naturally found
+ourselves in this space surrounded by
+
+ align:start position:0%
+ourselves in this space surrounded by
+ 
+
+ align:start position:0%
+ourselves in this space surrounded by
+opportunities to learn and it was
+
+ align:start position:0%
+opportunities to learn and it was
+ 
+
+ align:start position:0%
+opportunities to learn and it was
+playful and it felt easy and natural and
+
+ align:start position:0%
+playful and it felt easy and natural and
+ 
+
+ align:start position:0%
+playful and it felt easy and natural and
+that's what we're trying to sort of
+
+ align:start position:0%
+that's what we're trying to sort of
+ 
+
+ align:start position:0%
+that's what we're trying to sort of
+restore So actually the cognitive load
+
+ align:start position:0%
+restore So actually the cognitive load
+ 
+
+ align:start position:0%
+restore So actually the cognitive load
+theorists have to me what I think is
+
+ align:start position:0%
+theorists have to me what I think is
+ 
+
+ align:start position:0%
+theorists have to me what I think is
+sort of a funny way of dealing with
+
+ align:start position:0%
+sort of a funny way of dealing with
+ 
+
+ align:start position:0%
+sort of a funny way of dealing with
+this. Um there was just a guy who
+
+ align:start position:0%
+this. Um there was just a guy who
+ 
+
+ align:start position:0%
+this. Um there was just a guy who
+proposed that there's two categories of
+
+ align:start position:0%
+proposed that there's two categories of
+ 
+
+ align:start position:0%
+proposed that there's two categories of
+things that are learned called
+
+ align:start position:0%
+things that are learned called
+ 
+
+ align:start position:0%
+things that are learned called
+biologically primary and biologically
+
+ align:start position:0%
+biologically primary and biologically
+ 
+
+ align:start position:0%
+biologically primary and biologically
+secondary kinds of things. Um and uh
+
+ align:start position:0%
+secondary kinds of things. Um and uh
+ 
+
+ align:start position:0%
+secondary kinds of things. Um and uh
+we're evolutionarily wired to naturally
+
+ align:start position:0%
+we're evolutionarily wired to naturally
+ 
+
+ align:start position:0%
+we're evolutionarily wired to naturally
+learn biologically primary kinds of
+
+ align:start position:0%
+learn biologically primary kinds of
+ 
+
+ align:start position:0%
+learn biologically primary kinds of
+things and everything else is
+
+ align:start position:0%
+things and everything else is
+ 
+
+ align:start position:0%
+things and everything else is
+biologically secondary and is much
+
+ align:start position:0%
+biologically secondary and is much
+ 
+
+ align:start position:0%
+biologically secondary and is much
+harder. So that you're sort of naturally
+
+ align:start position:0%
+harder. So that you're sort of naturally
+ 
+
+ align:start position:0%
+harder. So that you're sort of naturally
+wired to learn how to walk, how to eat,
+
+ align:start position:0%
+wired to learn how to walk, how to eat,
+ 
+
+ align:start position:0%
+wired to learn how to walk, how to eat,
+some basic parts of socializing,
+
+ align:start position:0%
+some basic parts of socializing,
+ 
+
+ align:start position:0%
+some basic parts of socializing,
+recognizing faces. Language ends up
+
+ align:start position:0%
+recognizing faces. Language ends up
+ 
+
+ align:start position:0%
+recognizing faces. Language ends up
+being a real problem for this because
+
+ align:start position:0%
+being a real problem for this because
+ 
+
+ align:start position:0%
+being a real problem for this because
+it's like are you biologically primed to
+
+ align:start position:0%
+it's like are you biologically primed to
+ 
+
+ align:start position:0%
+it's like are you biologically primed to
+learn your first language to learn
+
+ align:start position:0%
+learn your first language to learn
+ 
+
+ align:start position:0%
+learn your first language to learn
+multiple languages? Why would you be
+
+ align:start position:0%
+multiple languages? Why would you be
+ 
+
+ align:start position:0%
+multiple languages? Why would you be
+biologic? Like why was it easy for me to
+
+ align:start position:0%
+biologic? Like why was it easy for me to
+ 
+
+ align:start position:0%
+biologic? Like why was it easy for me to
+learn English when I was young, but not
+
+ align:start position:0%
+learn English when I was young, but not
+ 
+
+ align:start position:0%
+learn English when I was young, but not
+Spanish was really hard when I was
+
+ align:start position:0%
+Spanish was really hard when I was
+ 
+
+ align:start position:0%
+Spanish was really hard when I was
+older? Like my brain changed? Did
+
+ align:start position:0%
+older? Like my brain changed? Did
+ 
+
+ align:start position:0%
+older? Like my brain changed? Did
+evolution? Like anyway, um I actually
+
+ align:start position:0%
+evolution? Like anyway, um I actually
+ 
+
+ align:start position:0%
+evolution? Like anyway, um I actually
+find this theory totally unsatisfying.
+
+ align:start position:0%
+find this theory totally unsatisfying.
+ 
+
+ align:start position:0%
+find this theory totally unsatisfying.
+Um do do you are familiar with the idea
+
+ align:start position:0%
+Um do do you are familiar with the idea
+ 
+
+ align:start position:0%
+Um do do you are familiar with the idea
+of epicycles? Um like before the
+
+ align:start position:0%
+of epicycles? Um like before the
+ 
+
+ align:start position:0%
+of epicycles? Um like before the
+capernican revolution uh we uh everybody
+
+ align:start position:0%
+capernican revolution uh we uh everybody
+ 
+
+ align:start position:0%
+capernican revolution uh we uh everybody
+thought orbits were circles not you know
+
+ align:start position:0%
+thought orbits were circles not you know
+ 
+
+ align:start position:0%
+thought orbits were circles not you know
+uh ovals or or whatever it is that
+
+ align:start position:0%
+uh ovals or or whatever it is that
+ 
+
+ align:start position:0%
+uh ovals or or whatever it is that
+they're what is it? What's the shape of
+
+ align:start position:0%
+they're what is it? What's the shape of
+ 
+
+ align:start position:0%
+they're what is it? What's the shape of
+them? Ellipses. Um and so there was a
+
+ align:start position:0%
+them? Ellipses. Um and so there was a
+ 
+
+ align:start position:0%
+them? Ellipses. Um and so there was a
+period of time when they realized like
+
+ align:start position:0%
+period of time when they realized like
+ 
+
+ align:start position:0%
+period of time when they realized like
+oh circle measurements don't work. And
+
+ align:start position:0%
+oh circle measurements don't work. And
+ 
+
+ align:start position:0%
+oh circle measurements don't work. And
+so they added circles to the circles. Um
+
+ align:start position:0%
+so they added circles to the circles. Um
+ 
+
+ align:start position:0%
+so they added circles to the circles. Um
+there they like believed that there had
+
+ align:start position:0%
+there they like believed that there had
+ 
+
+ align:start position:0%
+there they like believed that there had
+to be sort of perfect circles making the
+
+ align:start position:0%
+to be sort of perfect circles making the
+ 
+
+ align:start position:0%
+to be sort of perfect circles making the
+orbits. And so they believed that
+
+ align:start position:0%
+orbits. And so they believed that
+ 
+
+ align:start position:0%
+orbits. And so they believed that
+somehow there were like orbits within
+
+ align:start position:0%
+somehow there were like orbits within
+ 
+
+ align:start position:0%
+somehow there were like orbits within
+the orbits. um you know and then I think
+
+ align:start position:0%
+the orbits. um you know and then I think
+ 
+
+ align:start position:0%
+the orbits. um you know and then I think
+it was capergus who came around was like
+
+ align:start position:0%
+it was capergus who came around was like
+ 
+
+ align:start position:0%
+it was capergus who came around was like
+actually it's just like this and that
+
+ align:start position:0%
+actually it's just like this and that
+ 
+
+ align:start position:0%
+actually it's just like this and that
+works a lot better but to me sort of
+
+ align:start position:0%
+works a lot better but to me sort of
+ 
+
+ align:start position:0%
+works a lot better but to me sort of
+biologically primary and biologically
+
+ align:start position:0%
+biologically primary and biologically
+ 
+
+ align:start position:0%
+biologically primary and biologically
+secondary thing sort of operate that
+
+ align:start position:0%
+secondary thing sort of operate that
+ 
+
+ align:start position:0%
+secondary thing sort of operate that
+like that seems a little bit like an
+
+ align:start position:0%
+like that seems a little bit like an
+ 
+
+ align:start position:0%
+like that seems a little bit like an
+epicycle to me like we haven't quite
+
+ align:start position:0%
+epicycle to me like we haven't quite
+ 
+
+ align:start position:0%
+epicycle to me like we haven't quite
+figured out um what's going on there but
+
+ align:start position:0%
+figured out um what's going on there but
+ 
+
+ align:start position:0%
+figured out um what's going on there but
+that is how um canonically the the
+
+ align:start position:0%
+that is how um canonically the the
+ 
+
+ align:start position:0%
+that is how um canonically the the
+cognitive load theory people just wave
+
+ align:start position:0%
+cognitive load theory people just wave
+ 
+
+ align:start position:0%
+cognitive load theory people just wave
+all this away and say ah but babies
+
+ align:start position:0%
+all this away and say ah but babies
+ 
+
+ align:start position:0%
+all this away and say ah but babies
+whatever biologically primary we don't
+
+ align:start position:0%
+whatever biologically primary we don't
+ 
+
+ align:start position:0%
+whatever biologically primary we don't
+have to worry about them um everything
+
+ align:start position:0%
+have to worry about them um everything
+ 
+
+ align:start position:0%
+have to worry about them um everything
+after you're four years old or something
+
+ align:start position:0%
+after you're four years old or something
+ 
+
+ align:start position:0%
+after you're four years old or something
+like that is uh cognitive load theory
+
+ align:start position:0%
+like that is uh cognitive load theory
+ 
+
+ align:start position:0%
+like that is uh cognitive load theory
+works um But for the situated learning
+
+ align:start position:0%
+works um But for the situated learning
+ 
+
+ align:start position:0%
+works um But for the situated learning
+people, you know, not not exactly, but
+
+ align:start position:0%
+people, you know, not not exactly, but
+ 
+
+ align:start position:0%
+people, you know, not not exactly, but
+in a lot of ways, they're trying to sort
+
+ align:start position:0%
+in a lot of ways, they're trying to sort
+ 
+
+ align:start position:0%
+in a lot of ways, they're trying to sort
+of recapture the learning experiences
+
+ align:start position:0%
+of recapture the learning experiences
+ 
+
+ align:start position:0%
+of recapture the learning experiences
+that we have when we're very young. Um,
+
+ align:start position:0%
+that we have when we're very young. Um,
+ 
+
+ align:start position:0%
+that we have when we're very young. Um,
+where where learning is natural,
+
+ align:start position:0%
+where where learning is natural,
+ 
+
+ align:start position:0%
+where where learning is natural,
+playful, not always happy, but often
+
+ align:start position:0%
+playful, not always happy, but often
+ 
+
+ align:start position:0%
+playful, not always happy, but often
+sort of socially satisfying. Um, and
+
+ align:start position:0%
+sort of socially satisfying. Um, and
+ 
+
+ align:start position:0%
+sort of socially satisfying. Um, and
+extremely effective. I mean, what babies
+
+ align:start position:0%
+extremely effective. I mean, what babies
+ 
+
+ align:start position:0%
+extremely effective. I mean, what babies
+learn in a short period of time is just
+
+ align:start position:0%
+learn in a short period of time is just
+ 
+
+ align:start position:0%
+learn in a short period of time is just
+bonkers. Um, it's one of the most fun
+
+ align:start position:0%
+bonkers. Um, it's one of the most fun
+ 
+
+ align:start position:0%
+bonkers. Um, it's one of the most fun
+things about being a parent or an auntie
+
+ align:start position:0%
+things about being a parent or an auntie
+ 
+
+ align:start position:0%
+things about being a parent or an auntie
+or a uncle or all the other ways you get
+
+ align:start position:0%
+or a uncle or all the other ways you get
+ 
+
+ align:start position:0%
+or a uncle or all the other ways you get
+to spend a lot of time with kids. Okay.
+
+ align:start position:0%
+to spend a lot of time with kids. Okay.
+ 
+
+ align:start position:0%
+to spend a lot of time with kids. Okay.
+Um, let's just get oriented
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here. So, again, we're in foundations.
+
+ align:start position:0%
+here. So, again, we're in foundations.
+ 
+
+ align:start position:0%
+here. So, again, we're in foundations.
+Um, we're trying to get a hand of these
+
+ align:start position:0%
+Um, we're trying to get a hand of these
+ 
+
+ align:start position:0%
+Um, we're trying to get a hand of these
+two sort of contemporary learning
+
+ align:start position:0%
+two sort of contemporary learning
+ 
+
+ align:start position:0%
+two sort of contemporary learning
+theories. Cognitive load theory,
+
+ align:start position:0%
+theories. Cognitive load theory,
+ 
+
+ align:start position:0%
+theories. Cognitive load theory,
+situated learning. Um, that these two
+
+ align:start position:0%
+situated learning. Um, that these two
+ 
+
+ align:start position:0%
+situated learning. Um, that these two
+ideas about how people learn are
+
+ align:start position:0%
+ideas about how people learn are
+ 
+
+ align:start position:0%
+ideas about how people learn are
+ancient. Um, that you can find people
+
+ align:start position:0%
+ancient. Um, that you can find people
+ 
+
+ align:start position:0%
+ancient. Um, that you can find people
+like Plutarch for the mind does not
+
+ align:start position:0%
+like Plutarch for the mind does not
+ 
+
+ align:start position:0%
+like Plutarch for the mind does not
+require filling like a bottle, but
+
+ align:start position:0%
+require filling like a bottle, but
+ 
+
+ align:start position:0%
+require filling like a bottle, but
+rather like wood. It only requires
+
+ align:start position:0%
+rather like wood. It only requires
+ 
+
+ align:start position:0%
+rather like wood. It only requires
+kindling to create in it an impulse to
+
+ align:start position:0%
+kindling to create in it an impulse to
+ 
+
+ align:start position:0%
+kindling to create in it an impulse to
+think independently and an ardent desire
+
+ align:start position:0%
+think independently and an ardent desire
+ 
+
+ align:start position:0%
+think independently and an ardent desire
+for truth. That's the sort of like this
+
+ align:start position:0%
+for truth. That's the sort of like this
+ 
+
+ align:start position:0%
+for truth. That's the sort of like this
+is Plutarch making a case for situated
+
+ align:start position:0%
+is Plutarch making a case for situated
+ 
+
+ align:start position:0%
+is Plutarch making a case for situated
+learning and against cognitive load
+
+ align:start position:0%
+learning and against cognitive load
+ 
+
+ align:start position:0%
+learning and against cognitive load
+theory, though he wouldn't have known
+
+ align:start position:0%
+theory, though he wouldn't have known
+ 
+
+ align:start position:0%
+theory, though he wouldn't have known
+those terms because they didn't show up
+
+ align:start position:0%
+those terms because they didn't show up
+ 
+
+ align:start position:0%
+those terms because they didn't show up
+for another 2,000 years. Um, but you can
+
+ align:start position:0%
+for another 2,000 years. Um, but you can
+ 
+
+ align:start position:0%
+for another 2,000 years. Um, but you can
+hear the resonance of the debate in his
+
+ align:start position:0%
+hear the resonance of the debate in his
+ 
+
+ align:start position:0%
+hear the resonance of the debate in his
+mind. Here's a little chunk from a 2017
+
+ align:start position:0%
+mind. Here's a little chunk from a 2017
+ 
+
+ align:start position:0%
+mind. Here's a little chunk from a 2017
+New Yorker article. For nearly a
+
+ align:start position:0%
+New Yorker article. For nearly a
+ 
+
+ align:start position:0%
+New Yorker article. For nearly a
+century, public education in America has
+
+ align:start position:0%
+century, public education in America has
+ 
+
+ align:start position:0%
+century, public education in America has
+been influenced by two opposing
+
+ align:start position:0%
+been influenced by two opposing
+ 
+
+ align:start position:0%
+been influenced by two opposing
+pedagogical approaches. Traditionalism
+
+ align:start position:0%
+pedagogical approaches. Traditionalism
+ 
+
+ align:start position:0%
+pedagogical approaches. Traditionalism
+and progressivism. The thing that you
+
+ align:start position:0%
+and progressivism. The thing that you
+ 
+
+ align:start position:0%
+and progressivism. The thing that you
+got to catch is that there are these two
+
+ align:start position:0%
+got to catch is that there are these two
+ 
+
+ align:start position:0%
+got to catch is that there are these two
+ideas that have like each of them has
+
+ align:start position:0%
+ideas that have like each of them has
+ 
+
+ align:start position:0%
+ideas that have like each of them has
+8,000 different names. But anytime you
+
+ align:start position:0%
+8,000 different names. But anytime you
+ 
+
+ align:start position:0%
+8,000 different names. But anytime you
+sort of notice this dichconomy, broadly
+
+ align:start position:0%
+sort of notice this dichconomy, broadly
+ 
+
+ align:start position:0%
+sort of notice this dichconomy, broadly
+speaking, in the traditional approach to
+
+ align:start position:0%
+speaking, in the traditional approach to
+ 
+
+ align:start position:0%
+speaking, in the traditional approach to
+education, a teacher imparts knowledge
+
+ align:start position:0%
+education, a teacher imparts knowledge
+ 
+
+ align:start position:0%
+education, a teacher imparts knowledge
+to students through direct instruction
+
+ align:start position:0%
+to students through direct instruction
+ 
+
+ align:start position:0%
+to students through direct instruction
+and embodies a disciplinary culture in
+
+ align:start position:0%
+and embodies a disciplinary culture in
+ 
+
+ align:start position:0%
+and embodies a disciplinary culture in
+which obedience is both prized and
+
+ align:start position:0%
+which obedience is both prized and
+ 
+
+ align:start position:0%
+which obedience is both prized and
+rewarded. That's a that's a nice both
+
+ align:start position:0%
+rewarded. That's a that's a nice both
+ 
+
+ align:start position:0%
+rewarded. That's a that's a nice both
+like so like she frames it here's a
+
+ align:start position:0%
+like so like she frames it here's a
+ 
+
+ align:start position:0%
+like so like she frames it here's a
+pedagogical piece. Knowledge is imparted
+
+ align:start position:0%
+pedagogical piece. Knowledge is imparted
+ 
+
+ align:start position:0%
+pedagogical piece. Knowledge is imparted
+through direct instruction and embodies
+
+ align:start position:0%
+through direct instruction and embodies
+ 
+
+ align:start position:0%
+through direct instruction and embodies
+a disciplinary culture in which
+
+ align:start position:0%
+a disciplinary culture in which
+ 
+
+ align:start position:0%
+a disciplinary culture in which
+obedience is prized and rewarded. like
+
+ align:start position:0%
+obedience is prized and rewarded. like
+ 
+
+ align:start position:0%
+obedience is prized and rewarded. like
+obedience was not prized and rewarded
+
+ align:start position:0%
+obedience was not prized and rewarded
+ 
+
+ align:start position:0%
+obedience was not prized and rewarded
+amongst the baby on the playground. What
+
+ align:start position:0%
+amongst the baby on the playground. What
+ 
+
+ align:start position:0%
+amongst the baby on the playground. What
+was rewarded was screwing around. Um the
+
+ align:start position:0%
+was rewarded was screwing around. Um the
+ 
+
+ align:start position:0%
+was rewarded was screwing around. Um the
+purpose of the classroom is to equip all
+
+ align:start position:0%
+purpose of the classroom is to equip all
+ 
+
+ align:start position:0%
+purpose of the classroom is to equip all
+students to meet measurable academic
+
+ align:start position:0%
+students to meet measurable academic
+ 
+
+ align:start position:0%
+students to meet measurable academic
+standards. At progressive institutions,
+
+ align:start position:0%
+standards. At progressive institutions,
+ 
+
+ align:start position:0%
+standards. At progressive institutions,
+a teacher develops a curriculum but
+
+ align:start position:0%
+a teacher develops a curriculum but
+ 
+
+ align:start position:0%
+a teacher develops a curriculum but
+urges students to treat it as a staging
+
+ align:start position:0%
+urges students to treat it as a staging
+ 
+
+ align:start position:0%
+urges students to treat it as a staging
+ground for their own intellectual
+
+ align:start position:0%
+ground for their own intellectual
+ 
+
+ align:start position:0%
+ground for their own intellectual
+discoveries, often through hands-on
+
+ align:start position:0%
+discoveries, often through hands-on
+ 
+
+ align:start position:0%
+discoveries, often through hands-on
+activity and group work. Allowances are
+
+ align:start position:0%
+activity and group work. Allowances are
+ 
+
+ align:start position:0%
+activity and group work. Allowances are
+made for differences in the way
+
+ align:start position:0%
+made for differences in the way
+ 
+
+ align:start position:0%
+made for differences in the way
+individual students learn. Progressivism
+
+ align:start position:0%
+individual students learn. Progressivism
+ 
+
+ align:start position:0%
+individual students learn. Progressivism
+was inspired in large part by the work
+
+ align:start position:0%
+was inspired in large part by the work
+ 
+
+ align:start position:0%
+was inspired in large part by the work
+of John Dwey, the American philosopher
+
+ align:start position:0%
+of John Dwey, the American philosopher
+ 
+
+ align:start position:0%
+of John Dwey, the American philosopher
+and education theorist. Um maybe I'll
+
+ align:start position:0%
+and education theorist. Um maybe I'll
+ 
+
+ align:start position:0%
+and education theorist. Um maybe I'll
+say that last name. For Dwey, the
+
+ align:start position:0%
+say that last name. For Dwey, the
+ 
+
+ align:start position:0%
+say that last name. For Dwey, the
+classroom was not simply a place for
+
+ align:start position:0%
+classroom was not simply a place for
+ 
+
+ align:start position:0%
+classroom was not simply a place for
+acquiring academic credentials. It was
+
+ align:start position:0%
+acquiring academic credentials. It was
+ 
+
+ align:start position:0%
+acquiring academic credentials. It was
+also a venue in which students learned
+
+ align:start position:0%
+also a venue in which students learned
+ 
+
+ align:start position:0%
+also a venue in which students learned
+crucial values about being citizens in a
+
+ align:start position:0%
+crucial values about being citizens in a
+ 
+
+ align:start position:0%
+crucial values about being citizens in a
+democracy. So maybe maybe these things
+
+ align:start position:0%
+democracy. So maybe maybe these things
+ 
+
+ align:start position:0%
+democracy. So maybe maybe these things
+are laden not just with pedagogical
+
+ align:start position:0%
+are laden not just with pedagogical
+ 
+
+ align:start position:0%
+are laden not just with pedagogical
+ideas, beliefs about human architecture,
+
+ align:start position:0%
+ideas, beliefs about human architecture,
+ 
+
+ align:start position:0%
+ideas, beliefs about human architecture,
+um cultural sort of values, but even
+
+ align:start position:0%
+um cultural sort of values, but even
+ 
+
+ align:start position:0%
+um cultural sort of values, but even
+maybe the outcomes of education. Maybe
+
+ align:start position:0%
+maybe the outcomes of education. Maybe
+ 
+
+ align:start position:0%
+maybe the outcomes of education. Maybe
+we believe differently about that,
+
+ align:start position:0%
+we believe differently about that,
+ 
+
+ align:start position:0%
+we believe differently about that,
+though not necessarily. Um the person
+
+ align:start position:0%
+though not necessarily. Um the person
+ 
+
+ align:start position:0%
+though not necessarily. Um the person
+who's probably the best counterpoint to
+
+ align:start position:0%
+who's probably the best counterpoint to
+ 
+
+ align:start position:0%
+who's probably the best counterpoint to
+John Dwey is this guy Ed Thorndikeke. um
+
+ align:start position:0%
+John Dwey is this guy Ed Thorndikeke. um
+ 
+
+ align:start position:0%
+John Dwey is this guy Ed Thorndikeke. um
+who is a very early educational
+
+ align:start position:0%
+who is a very early educational
+ 
+
+ align:start position:0%
+who is a very early educational
+psychologist. I often think of him as
+
+ align:start position:0%
+psychologist. I often think of him as
+ 
+
+ align:start position:0%
+psychologist. I often think of him as
+the guy who is like no no no pale
+
+ align:start position:0%
+the guy who is like no no no pale
+ 
+
+ align:start position:0%
+the guy who is like no no no pale
+filling is great. Um like a particularly
+
+ align:start position:0%
+filling is great. Um like a particularly
+ 
+
+ align:start position:0%
+filling is great. Um like a particularly
+great thing about pale filling is that
+
+ align:start position:0%
+great thing about pale filling is that
+ 
+
+ align:start position:0%
+great thing about pale filling is that
+we can measure pale filling. You can
+
+ align:start position:0%
+we can measure pale filling. You can
+ 
+
+ align:start position:0%
+we can measure pale filling. You can
+measure like the rate at which you bore
+
+ align:start position:0%
+measure like the rate at which you bore
+ 
+
+ align:start position:0%
+measure like the rate at which you bore
+things into people and the rate at which
+
+ align:start position:0%
+things into people and the rate at which
+ 
+
+ align:start position:0%
+things into people and the rate at which
+it falls out and how leaky people are um
+
+ align:start position:0%
+it falls out and how leaky people are um
+ 
+
+ align:start position:0%
+it falls out and how leaky people are um
+and some of those kinds of things. So he
+
+ align:start position:0%
+and some of those kinds of things. So he
+ 
+
+ align:start position:0%
+and some of those kinds of things. So he
+was very involved in testing. Um he
+
+ align:start position:0%
+was very involved in testing. Um he
+ 
+
+ align:start position:0%
+was very involved in testing. Um he
+actually um played a really important
+
+ align:start position:0%
+actually um played a really important
+ 
+
+ align:start position:0%
+actually um played a really important
+role in developing ideas that
+
+ align:start position:0%
+role in developing ideas that
+ 
+
+ align:start position:0%
+role in developing ideas that
+educational progressives uh hold dearly.
+
+ align:start position:0%
+educational progressives uh hold dearly.
+ 
+
+ align:start position:0%
+educational progressives uh hold dearly.
+He's one of the things he studied which
+
+ align:start position:0%
+He's one of the things he studied which
+ 
+
+ align:start position:0%
+He's one of the things he studied which
+we'll talk about the course goes on is
+
+ align:start position:0%
+we'll talk about the course goes on is
+ 
+
+ align:start position:0%
+we'll talk about the course goes on is
+this idea of transfer. Um so uh uh you
+
+ align:start position:0%
+this idea of transfer. Um so uh uh you
+ 
+
+ align:start position:0%
+this idea of transfer. Um so uh uh you
+know in the 18th 19th century people in
+
+ align:start position:0%
+know in the 18th 19th century people in
+ 
+
+ align:start position:0%
+know in the 18th 19th century people in
+America Europe believed that a great
+
+ align:start position:0%
+America Europe believed that a great
+ 
+
+ align:start position:0%
+America Europe believed that a great
+thing about learning Latin and Greek was
+
+ align:start position:0%
+thing about learning Latin and Greek was
+ 
+
+ align:start position:0%
+thing about learning Latin and Greek was
+it sort of strengthened these kind of
+
+ align:start position:0%
+it sort of strengthened these kind of
+ 
+
+ align:start position:0%
+it sort of strengthened these kind of
+like generic thinking muscles. Like if
+
+ align:start position:0%
+like generic thinking muscles. Like if
+ 
+
+ align:start position:0%
+like generic thinking muscles. Like if
+you got really good at learning Latin
+
+ align:start position:0%
+you got really good at learning Latin
+ 
+
+ align:start position:0%
+you got really good at learning Latin
+and Greek you would just be a good
+
+ align:start position:0%
+and Greek you would just be a good
+ 
+
+ align:start position:0%
+and Greek you would just be a good
+thinker. And he was like that's dumb. Um
+
+ align:start position:0%
+thinker. And he was like that's dumb. Um
+ 
+
+ align:start position:0%
+thinker. And he was like that's dumb. Um
+if you learn Latin and Greek you're good
+
+ align:start position:0%
+if you learn Latin and Greek you're good
+ 
+
+ align:start position:0%
+if you learn Latin and Greek you're good
+at Latin and Greek but you're not
+
+ align:start position:0%
+at Latin and Greek but you're not
+ 
+
+ align:start position:0%
+at Latin and Greek but you're not
+actually good at anything else. um like
+
+ align:start position:0%
+actually good at anything else. um like
+ 
+
+ align:start position:0%
+actually good at anything else. um like
+the brain is not general purpose like
+
+ align:start position:0%
+the brain is not general purpose like
+ 
+
+ align:start position:0%
+the brain is not general purpose like
+that but that kind of thinking that kind
+
+ align:start position:0%
+that but that kind of thinking that kind
+ 
+
+ align:start position:0%
+that but that kind of thinking that kind
+of thinking if I learn this thing it'll
+
+ align:start position:0%
+of thinking if I learn this thing it'll
+ 
+
+ align:start position:0%
+of thinking if I learn this thing it'll
+help me like generically with these
+
+ align:start position:0%
+help me like generically with these
+ 
+
+ align:start position:0%
+help me like generically with these
+other things shows up all the time. Um
+
+ align:start position:0%
+other things shows up all the time. Um
+ 
+
+ align:start position:0%
+other things shows up all the time. Um
+the most contemporary uh version of this
+
+ align:start position:0%
+the most contemporary uh version of this
+ 
+
+ align:start position:0%
+the most contemporary uh version of this
+is have any of you ever encountered the
+
+ align:start position:0%
+is have any of you ever encountered the
+ 
+
+ align:start position:0%
+is have any of you ever encountered the
+idea of computational thinking. What
+
+ align:start position:0%
+idea of computational thinking. What
+ 
+
+ align:start position:0%
+idea of computational thinking. What
+people mean by computational thinking
+
+ align:start position:0%
+people mean by computational thinking
+ 
+
+ align:start position:0%
+people mean by computational thinking
+almost all the time is like we're going
+
+ align:start position:0%
+almost all the time is like we're going
+ 
+
+ align:start position:0%
+almost all the time is like we're going
+to teach you computer programming and if
+
+ align:start position:0%
+to teach you computer programming and if
+ 
+
+ align:start position:0%
+to teach you computer programming and if
+you learn about computer programming
+
+ align:start position:0%
+you learn about computer programming
+ 
+
+ align:start position:0%
+you learn about computer programming
+you're going to learn how to like break
+
+ align:start position:0%
+you're going to learn how to like break
+ 
+
+ align:start position:0%
+you're going to learn how to like break
+ideas down into smaller parts and you're
+
+ align:start position:0%
+ideas down into smaller parts and you're
+ 
+
+ align:start position:0%
+ideas down into smaller parts and you're
+going to learn how to think
+
+ align:start position:0%
+going to learn how to think
+ 
+
+ align:start position:0%
+going to learn how to think
+algorithmically and do all these other
+
+ align:start position:0%
+algorithmically and do all these other
+ 
+
+ align:start position:0%
+algorithmically and do all these other
+sort of and it's like no you're going to
+
+ align:start position:0%
+sort of and it's like no you're going to
+ 
+
+ align:start position:0%
+sort of and it's like no you're going to
+be good at programming computers. Um you
+
+ align:start position:0%
+be good at programming computers. Um you
+ 
+
+ align:start position:0%
+be good at programming computers. Um you
+know if you want to be able to break
+
+ align:start position:0%
+know if you want to be able to break
+ 
+
+ align:start position:0%
+know if you want to be able to break
+ideas down in poetry learning computer
+
+ align:start position:0%
+ideas down in poetry learning computer
+ 
+
+ align:start position:0%
+ideas down in poetry learning computer
+programming will not help you do that
+
+ align:start position:0%
+programming will not help you do that
+ 
+
+ align:start position:0%
+programming will not help you do that
+anymore. I mean it will help you about
+
+ align:start position:0%
+anymore. I mean it will help you about
+ 
+
+ align:start position:0%
+anymore. I mean it will help you about
+as much as learning Latin and Greek will
+
+ align:start position:0%
+as much as learning Latin and Greek will
+ 
+
+ align:start position:0%
+as much as learning Latin and Greek will
+help you do that which is to say like
+
+ align:start position:0%
+help you do that which is to say like
+ 
+
+ align:start position:0%
+help you do that which is to say like
+not that much. um that a frustrating
+
+ align:start position:0%
+not that much. um that a frustrating
+ 
+
+ align:start position:0%
+not that much. um that a frustrating
+thing about teaching is the things we
+
+ align:start position:0%
+thing about teaching is the things we
+ 
+
+ align:start position:0%
+thing about teaching is the things we
+learn um tend to only help us in like
+
+ align:start position:0%
+learn um tend to only help us in like
+ 
+
+ align:start position:0%
+learn um tend to only help us in like
+very near cognate areas. Um so these are
+
+ align:start position:0%
+very near cognate areas. Um so these are
+ 
+
+ align:start position:0%
+very near cognate areas. Um so these are
+sort of the two kind of you know again
+
+ align:start position:0%
+sort of the two kind of you know again
+ 
+
+ align:start position:0%
+sort of the two kind of you know again
+I'm trying to give you the sense that
+
+ align:start position:0%
+I'm trying to give you the sense that
+ 
+
+ align:start position:0%
+I'm trying to give you the sense that
+like these two big ideas are millennia
+
+ align:start position:0%
+like these two big ideas are millennia
+ 
+
+ align:start position:0%
+like these two big ideas are millennia
+old. They have a scientific basis that's
+
+ align:start position:0%
+old. They have a scientific basis that's
+ 
+
+ align:start position:0%
+old. They have a scientific basis that's
+at least a century old. Um and you're
+
+ align:start position:0%
+at least a century old. Um and you're
+ 
+
+ align:start position:0%
+at least a century old. Um and you're
+getting what I think are some of the
+
+ align:start position:0%
+getting what I think are some of the
+ 
+
+ align:start position:0%
+getting what I think are some of the
+best most recent contemporary uh
+
+ align:start position:0%
+best most recent contemporary uh
+ 
+
+ align:start position:0%
+best most recent contemporary uh
+formulations. Um like the work of John
+
+ align:start position:0%
+formulations. Um like the work of John
+ 
+
+ align:start position:0%
+formulations. Um like the work of John
+Sweller and some of these other folks
+
+ align:start position:0%
+Sweller and some of these other folks
+ 
+
+ align:start position:0%
+Sweller and some of these other folks
+like the little piece you read from
+
+ align:start position:0%
+like the little piece you read from
+ 
+
+ align:start position:0%
+like the little piece you read from
+Mitch Resnik for today. Um and then
+
+ align:start position:0%
+Mitch Resnik for today. Um and then
+ 
+
+ align:start position:0%
+Mitch Resnik for today. Um and then
+maybe just to give you like a broader
+
+ align:start position:0%
+maybe just to give you like a broader
+ 
+
+ align:start position:0%
+maybe just to give you like a broader
+overview like overwhelmingly Thorndikeke
+
+ align:start position:0%
+overview like overwhelmingly Thorndikeke
+ 
+
+ align:start position:0%
+overview like overwhelmingly Thorndikeke
+is one. Um if you were to walk through a
+
+ align:start position:0%
+is one. Um if you were to walk through a
+ 
+
+ align:start position:0%
+is one. Um if you were to walk through a
+typical American school in a typical
+
+ align:start position:0%
+typical American school in a typical
+ 
+
+ align:start position:0%
+typical American school in a typical
+American day, you would see very little
+
+ align:start position:0%
+American day, you would see very little
+ 
+
+ align:start position:0%
+American day, you would see very little
+education is life itself and you would
+
+ align:start position:0%
+education is life itself and you would
+ 
+
+ align:start position:0%
+education is life itself and you would
+see a lot of direct instruction. Um like
+
+ align:start position:0%
+see a lot of direct instruction. Um like
+ 
+
+ align:start position:0%
+see a lot of direct instruction. Um like
+the the canonical experience of students
+
+ align:start position:0%
+the the canonical experience of students
+ 
+
+ align:start position:0%
+the the canonical experience of students
+in schools is very organized around
+
+ align:start position:0%
+in schools is very organized around
+ 
+
+ align:start position:0%
+in schools is very organized around
+direct instruction. However, if you were
+
+ align:start position:0%
+direct instruction. However, if you were
+ 
+
+ align:start position:0%
+direct instruction. However, if you were
+to ask teachers who their favorite um
+
+ align:start position:0%
+to ask teachers who their favorite um
+ 
+
+ align:start position:0%
+to ask teachers who their favorite um
+educational philosopher is, you would
+
+ align:start position:0%
+educational philosopher is, you would
+ 
+
+ align:start position:0%
+educational philosopher is, you would
+get a lot of answers that are Dewey and
+
+ align:start position:0%
+get a lot of answers that are Dewey and
+ 
+
+ align:start position:0%
+get a lot of answers that are Dewey and
+you would not get a lot of answers that
+
+ align:start position:0%
+you would not get a lot of answers that
+ 
+
+ align:start position:0%
+you would not get a lot of answers that
+were Thorndikeke. Um so the um Dewey is
+
+ align:start position:0%
+were Thorndikeke. Um so the um Dewey is
+ 
+
+ align:start position:0%
+were Thorndikeke. Um so the um Dewey is
+beloved in a way that Thorndikeke is
+
+ align:start position:0%
+beloved in a way that Thorndikeke is
+ 
+
+ align:start position:0%
+beloved in a way that Thorndikeke is
+not. But Thorndikeke is like actually
+
+ align:start position:0%
+not. But Thorndikeke is like actually
+ 
+
+ align:start position:0%
+not. But Thorndikeke is like actually
+the person who uh inspires more of our
+
+ align:start position:0%
+the person who uh inspires more of our
+ 
+
+ align:start position:0%
+the person who uh inspires more of our
+ideas. All right, let's do just a little
+
+ align:start position:0%
+ideas. All right, let's do just a little
+ 
+
+ align:start position:0%
+ideas. All right, let's do just a little
+bit of close reading together, which is
+
+ align:start position:0%
+bit of close reading together, which is
+ 
+
+ align:start position:0%
+bit of close reading together, which is
+mostly me telling you about some things
+
+ align:start position:0%
+mostly me telling you about some things
+ 
+
+ align:start position:0%
+mostly me telling you about some things
+that you should read closely. This is
+
+ align:start position:0%
+that you should read closely. This is
+ 
+
+ align:start position:0%
+that you should read closely. This is
+what we looked at yesterday. Here's um
+
+ align:start position:0%
+what we looked at yesterday. Here's um
+ 
+
+ align:start position:0%
+what we looked at yesterday. Here's um
+one thing that's fun about the um
+
+ align:start position:0%
+one thing that's fun about the um
+ 
+
+ align:start position:0%
+one thing that's fun about the um
+cognitive load theory people is that
+
+ align:start position:0%
+cognitive load theory people is that
+ 
+
+ align:start position:0%
+cognitive load theory people is that
+they have they're really good at stating
+
+ align:start position:0%
+they have they're really good at stating
+ 
+
+ align:start position:0%
+they have they're really good at stating
+clearly what their models of human
+
+ align:start position:0%
+clearly what their models of human
+ 
+
+ align:start position:0%
+clearly what their models of human
+cognitive architecture are. I think the
+
+ align:start position:0%
+cognitive architecture are. I think the
+ 
+
+ align:start position:0%
+cognitive architecture are. I think the
+situated learning people have cognates.
+
+ align:start position:0%
+situated learning people have cognates.
+ 
+
+ align:start position:0%
+situated learning people have cognates.
+I think they have things that they
+
+ align:start position:0%
+I think they have things that they
+ 
+
+ align:start position:0%
+I think they have things that they
+believe are central about the brain, how
+
+ align:start position:0%
+believe are central about the brain, how
+ 
+
+ align:start position:0%
+believe are central about the brain, how
+learning works. Um but they would draw a
+
+ align:start position:0%
+learning works. Um but they would draw a
+ 
+
+ align:start position:0%
+learning works. Um but they would draw a
+different model like this is not what
+
+ align:start position:0%
+different model like this is not what
+ 
+
+ align:start position:0%
+different model like this is not what
+they were draw and and but and they're
+
+ align:start position:0%
+they were draw and and but and they're
+ 
+
+ align:start position:0%
+they were draw and and but and they're
+less explicit about it which makes our
+
+ align:start position:0%
+less explicit about it which makes our
+ 
+
+ align:start position:0%
+less explicit about it which makes our
+job a little bit harder but a thing that
+
+ align:start position:0%
+job a little bit harder but a thing that
+ 
+
+ align:start position:0%
+job a little bit harder but a thing that
+you can be thinking about now um is like
+
+ align:start position:0%
+you can be thinking about now um is like
+ 
+
+ align:start position:0%
+you can be thinking about now um is like
+what would be you know what is the what
+
+ align:start position:0%
+what would be you know what is the what
+ 
+
+ align:start position:0%
+what would be you know what is the what
+is the situated learning cognate of this
+
+ align:start position:0%
+is the situated learning cognate of this
+ 
+
+ align:start position:0%
+is the situated learning cognate of this
+like what would be the pieces that they
+
+ align:start position:0%
+like what would be the pieces that they
+ 
+
+ align:start position:0%
+like what would be the pieces that they
+would put in the model that would be
+
+ align:start position:0%
+would put in the model that would be
+ 
+
+ align:start position:0%
+would put in the model that would be
+most important um for their
+
+ align:start position:0%
+most important um for their
+ 
+
+ align:start position:0%
+most important um for their
+developmental learning. We'll play with
+
+ align:start position:0%
+developmental learning. We'll play with
+ 
+
+ align:start position:0%
+developmental learning. We'll play with
+that as we go along a little bit. Okay.
+
+ align:start position:0%
+that as we go along a little bit. Okay.
+ 
+
+ align:start position:0%
+that as we go along a little bit. Okay.
+Um how many of you ever use the logo
+
+ align:start position:0%
+Um how many of you ever use the logo
+ 
+
+ align:start position:0%
+Um how many of you ever use the logo
+programming language?
+
+ align:start position:0%
+programming language?
+ 
+
+ align:start position:0%
+programming language?
+Oh good. More than there. How many of
+
+ align:start position:0%
+Oh good. More than there. How many of
+ 
+
+ align:start position:0%
+Oh good. More than there. How many of
+you use Scratch? Okay, there we got
+
+ align:start position:0%
+you use Scratch? Okay, there we got
+ 
+
+ align:start position:0%
+you use Scratch? Okay, there we got
+everybody. Um, so Scratch is a
+
+ align:start position:0%
+everybody. Um, so Scratch is a
+ 
+
+ align:start position:0%
+everybody. Um, so Scratch is a
+descendant of Logo. Um, Logo is a
+
+ align:start position:0%
+descendant of Logo. Um, Logo is a
+ 
+
+ align:start position:0%
+descendant of Logo. Um, Logo is a
+programming language that was uh
+
+ align:start position:0%
+programming language that was uh
+ 
+
+ align:start position:0%
+programming language that was uh
+developed by Seymour Papert um in the
+
+ align:start position:0%
+developed by Seymour Papert um in the
+ 
+
+ align:start position:0%
+developed by Seymour Papert um in the
+media lab. Uh, one of the first efforts
+
+ align:start position:0%
+media lab. Uh, one of the first efforts
+ 
+
+ align:start position:0%
+media lab. Uh, one of the first efforts
+to bring computer programming to um kids
+
+ align:start position:0%
+to bring computer programming to um kids
+ 
+
+ align:start position:0%
+to bring computer programming to um kids
+in schools when I was in the fourth
+
+ align:start position:0%
+in schools when I was in the fourth
+ 
+
+ align:start position:0%
+in schools when I was in the fourth
+grade at a monastery school in South NIC
+
+ align:start position:0%
+grade at a monastery school in South NIC
+ 
+
+ align:start position:0%
+grade at a monastery school in South NIC
+not far from here. We had a little
+
+ align:start position:0%
+not far from here. We had a little
+ 
+
+ align:start position:0%
+not far from here. We had a little
+computer lab and logo was the language
+
+ align:start position:0%
+computer lab and logo was the language
+ 
+
+ align:start position:0%
+computer lab and logo was the language
+that I learned to do a little bit of
+
+ align:start position:0%
+that I learned to do a little bit of
+ 
+
+ align:start position:0%
+that I learned to do a little bit of
+programming anyway with um you'll see
+
+ align:start position:0%
+programming anyway with um you'll see
+ 
+
+ align:start position:0%
+programming anyway with um you'll see
+that a lot of it um is about shapes and
+
+ align:start position:0%
+that a lot of it um is about shapes and
+ 
+
+ align:start position:0%
+that a lot of it um is about shapes and
+geometry. Um but what I really loved
+
+ align:start position:0%
+geometry. Um but what I really loved
+ 
+
+ align:start position:0%
+geometry. Um but what I really loved
+about it was uh choose your own
+
+ align:start position:0%
+about it was uh choose your own
+ 
+
+ align:start position:0%
+about it was uh choose your own
+adventures. Um so you could essentially
+
+ align:start position:0%
+adventures. Um so you could essentially
+ 
+
+ align:start position:0%
+adventures. Um so you could essentially
+like like write a program or function
+
+ align:start position:0%
+like like write a program or function
+ 
+
+ align:start position:0%
+like like write a program or function
+whatever it is in which uh someone types
+
+ align:start position:0%
+whatever it is in which uh someone types
+ 
+
+ align:start position:0%
+whatever it is in which uh someone types
+a word and that triggers the the display
+
+ align:start position:0%
+a word and that triggers the the display
+ 
+
+ align:start position:0%
+a word and that triggers the the display
+of a set of text. Um, and so it wasn't
+
+ align:start position:0%
+of a set of text. Um, and so it wasn't
+ 
+
+ align:start position:0%
+of a set of text. Um, and so it wasn't
+that hard to make choose your own
+
+ align:start position:0%
+that hard to make choose your own
+ 
+
+ align:start position:0%
+that hard to make choose your own
+adventures, you know, you know, like
+
+ align:start position:0%
+adventures, you know, you know, like
+ 
+
+ align:start position:0%
+adventures, you know, you know, like
+you're you're you're at the front of the
+
+ align:start position:0%
+you're you're you're at the front of the
+ 
+
+ align:start position:0%
+you're you're you're at the front of the
+house. Do you want to walk up to the,
+
+ align:start position:0%
+house. Do you want to walk up to the,
+ 
+
+ align:start position:0%
+house. Do you want to walk up to the,
+you know, type porch if you want to walk
+
+ align:start position:0%
+you know, type porch if you want to walk
+ 
+
+ align:start position:0%
+you know, type porch if you want to walk
+into porch? Um, type, uh, knock if you
+
+ align:start position:0%
+into porch? Um, type, uh, knock if you
+ 
+
+ align:start position:0%
+into porch? Um, type, uh, knock if you
+want to knock on the door. And then
+
+ align:start position:0%
+want to knock on the door. And then
+ 
+
+ align:start position:0%
+want to knock on the door. And then
+knock is a program that releases another
+
+ align:start position:0%
+knock is a program that releases another
+ 
+
+ align:start position:0%
+knock is a program that releases another
+set of text and you can make choose your
+
+ align:start position:0%
+set of text and you can make choose your
+ 
+
+ align:start position:0%
+set of text and you can make choose your
+own adventure that way. How important is
+
+ align:start position:0%
+own adventure that way. How important is
+ 
+
+ align:start position:0%
+own adventure that way. How important is
+that for you to know? I don't know. Here
+
+ align:start position:0%
+that for you to know? I don't know. Here
+ 
+
+ align:start position:0%
+that for you to know? I don't know. Here
+um is a few minutes of Seymour Papert
+
+ align:start position:0%
+um is a few minutes of Seymour Papert
+ 
+
+ align:start position:0%
+um is a few minutes of Seymour Papert
+um who was a student of Jean PG who's
+
+ align:start position:0%
+um who was a student of Jean PG who's
+ 
+
+ align:start position:0%
+um who was a student of Jean PG who's
+another kind of major social
+
+ align:start position:0%
+another kind of major social
+ 
+
+ align:start position:0%
+another kind of major social
+constructivist sort of thinker. Here's
+
+ align:start position:0%
+constructivist sort of thinker. Here's
+ 
+
+ align:start position:0%
+constructivist sort of thinker. Here's
+um what uh logo was supposed to look
+
+ align:start position:0%
+um what uh logo was supposed to look
+ 
+
+ align:start position:0%
+um what uh logo was supposed to look
+like in the classroom in the 1980s about
+
+ align:start position:0%
+like in the classroom in the 1980s about
+ 
+
+ align:start position:0%
+like in the classroom in the 1980s about
+when I was a kid.
+
+ align:start position:0%
+when I was a kid.
+ 
+
+ align:start position:0%
+when I was a kid.
+The idea is quite
+
+ align:start position:0%
+The idea is quite
+ 
+
+ align:start position:0%
+The idea is quite
+simple. Let learn mathematics by
+
+ align:start position:0%
+simple. Let learn mathematics by
+ 
+
+ align:start position:0%
+simple. Let learn mathematics by
+speaking in mathematics about things
+
+ align:start position:0%
+speaking in mathematics about things
+ 
+
+ align:start position:0%
+speaking in mathematics about things
+that really matter to him. So at MIT,
+
+ align:start position:0%
+that really matter to him. So at MIT,
+ 
+
+ align:start position:0%
+that really matter to him. So at MIT,
+we've given computers the power to turn
+
+ align:start position:0%
+we've given computers the power to turn
+ 
+
+ align:start position:0%
+we've given computers the power to turn
+motors, to make sounds, to draw
+
+ align:start position:0%
+motors, to make sounds, to draw
+ 
+
+ align:start position:0%
+motors, to make sounds, to draw
+pictures, and we've found ways of giving
+
+ align:start position:0%
+pictures, and we've found ways of giving
+ 
+
+ align:start position:0%
+pictures, and we've found ways of giving
+children the power to control the
+
+ align:start position:0%
+children the power to control the
+ 
+
+ align:start position:0%
+children the power to control the
+computer. So the child can make the
+
+ align:start position:0%
+computer. So the child can make the
+ 
+
+ align:start position:0%
+computer. So the child can make the
+computer do anything that he can
+
+ align:start position:0%
+computer do anything that he can
+ 
+
+ align:start position:0%
+computer do anything that he can
+describe in a suitable mathematical
+
+ align:start position:0%
+describe in a suitable mathematical
+ 
+
+ align:start position:0%
+describe in a suitable mathematical
+language by typing on a keyboard like
+
+ align:start position:0%
+language by typing on a keyboard like
+ 
+
+ align:start position:0%
+language by typing on a keyboard like
+this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's what um P1 sounds like.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+P2. That's P2 and P3.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+A computer controlled turtle is made to
+
+ align:start position:0%
+A computer controlled turtle is made to
+ 
+
+ align:start position:0%
+A computer controlled turtle is made to
+draw and dance by programs so simple
+
+ align:start position:0%
+draw and dance by programs so simple
+ 
+
+ align:start position:0%
+draw and dance by programs so simple
+that all children invent them in the
+
+ align:start position:0%
+that all children invent them in the
+ 
+
+ align:start position:0%
+that all children invent them in the
+first days of the course. Thus, the
+
+ align:start position:0%
+first days of the course. Thus, the
+ 
+
+ align:start position:0%
+first days of the course. Thus, the
+child acquires a taste of math power
+
+ align:start position:0%
+child acquires a taste of math power
+ 
+
+ align:start position:0%
+child acquires a taste of math power
+that grows and grows as his projects
+
+ align:start position:0%
+that grows and grows as his projects
+ 
+
+ align:start position:0%
+that grows and grows as his projects
+become more original, more complex, and
+
+ align:start position:0%
+become more original, more complex, and
+ 
+
+ align:start position:0%
+become more original, more complex, and
+more varied. So, you have like the um
+
+ align:start position:0%
+more varied. So, you have like the um
+ 
+
+ align:start position:0%
+more varied. So, you have like the um
+first one, then the second one, then the
+
+ align:start position:0%
+first one, then the second one, then the
+ 
+
+ align:start position:0%
+first one, then the second one, then the
+third one, then the first one again for
+
+ align:start position:0%
+third one, then the first one again for
+ 
+
+ align:start position:0%
+third one, then the first one again for
+the ending. Okay. Now they'll put their
+
+ align:start position:0%
+the ending. Okay. Now they'll put their
+ 
+
+ align:start position:0%
+the ending. Okay. Now they'll put their
+little tunes together to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make now. I'm telling it to do it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I know.
+
+ align:start position:0%
+I know.
+ 
+
+ align:start position:0%
+I know.
+Sometimes I get into bugs like this and
+
+ align:start position:0%
+Sometimes I get into bugs like this and
+ 
+
+ align:start position:0%
+Sometimes I get into bugs like this and
+it'll
+
+ align:start position:0%
+it'll
+ 
+
+ align:start position:0%
+it'll
+um when it was doing it in his mind, the
+
+ align:start position:0%
+um when it was doing it in his mind, the
+ 
+
+ align:start position:0%
+um when it was doing it in his mind, the
+little turtle, it's the little triangle
+
+ align:start position:0%
+little turtle, it's the little triangle
+ 
+
+ align:start position:0%
+little turtle, it's the little triangle
+thing um was on an angle. So it drew the
+
+ align:start position:0%
+thing um was on an angle. So it drew the
+ 
+
+ align:start position:0%
+thing um was on an angle. So it drew the
+picture on on an angle. So now I'll go
+
+ align:start position:0%
+picture on on an angle. So now I'll go
+ 
+
+ align:start position:0%
+picture on on an angle. So now I'll go
+back and have it draw it in its mind
+
+ align:start position:0%
+back and have it draw it in its mind
+ 
+
+ align:start position:0%
+back and have it draw it in its mind
+again while it's in the right position.
+
+ align:start position:0%
+again while it's in the right position.
+ 
+
+ align:start position:0%
+again while it's in the right position.
+And so the child doesn't have to be told
+
+ align:start position:0%
+And so the child doesn't have to be told
+ 
+
+ align:start position:0%
+And so the child doesn't have to be told
+by a teacher whether he's right or
+
+ align:start position:0%
+by a teacher whether he's right or
+ 
+
+ align:start position:0%
+by a teacher whether he's right or
+wrong. He can see for himself whether it
+
+ align:start position:0%
+wrong. He can see for himself whether it
+ 
+
+ align:start position:0%
+wrong. He can see for himself whether it
+works. That's what science and knowledge
+
+ align:start position:0%
+works. That's what science and knowledge
+ 
+
+ align:start position:0%
+works. That's what science and knowledge
+is about. Super procedure is named
+
+ align:start position:0%
+is about. Super procedure is named
+ 
+
+ align:start position:0%
+is about. Super procedure is named
+fancy. And then you have an input which
+
+ align:start position:0%
+fancy. And then you have an input which
+ 
+
+ align:start position:0%
+fancy. And then you have an input which
+means you can vary the size. I'm going
+
+ align:start position:0%
+means you can vary the size. I'm going
+ 
+
+ align:start position:0%
+means you can vary the size. I'm going
+to make it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+100. Right now it's doing a procedure
+
+ align:start position:0%
+100. Right now it's doing a procedure
+ 
+
+ align:start position:0%
+100. Right now it's doing a procedure
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+top. And each one of those little fins
+
+ align:start position:0%
+top. And each one of those little fins
+ 
+
+ align:start position:0%
+top. And each one of those little fins
+is called fin. And that's another sub
+
+ align:start position:0%
+is called fin. And that's another sub
+ 
+
+ align:start position:0%
+is called fin. And that's another sub
+procedure in top. Now it's doing inside.
+
+ align:start position:0%
+procedure in top. Now it's doing inside.
+ 
+
+ align:start position:0%
+procedure in top. Now it's doing inside.
+They are identifiable techniques for
+
+ align:start position:0%
+They are identifiable techniques for
+ 
+
+ align:start position:0%
+They are identifiable techniques for
+working on a problem. One of these is
+
+ align:start position:0%
+working on a problem. One of these is
+ 
+
+ align:start position:0%
+working on a problem. One of these is
+known by these children as writing
+
+ align:start position:0%
+known by these children as writing
+ 
+
+ align:start position:0%
+known by these children as writing
+procedures as subrocedures. Inside and
+
+ align:start position:0%
+procedures as subrocedures. Inside and
+ 
+
+ align:start position:0%
+procedures as subrocedures. Inside and
+top are the two main
+
+ align:start position:0%
+top are the two main
+ 
+
+ align:start position:0%
+top are the two main
+subprocedures and the other one the tail
+
+ align:start position:0%
+subprocedures and the other one the tail
+ 
+
+ align:start position:0%
+subprocedures and the other one the tail
+is made out of odds and ends. just put
+
+ align:start position:0%
+is made out of odds and ends. just put
+ 
+
+ align:start position:0%
+is made out of odds and ends. just put
+just put together the techniques really
+
+ align:start position:0%
+just put together the techniques really
+ 
+
+ align:start position:0%
+just put together the techniques really
+well known. Subdivide the problem. Split
+
+ align:start position:0%
+well known. Subdivide the problem. Split
+ 
+
+ align:start position:0%
+well known. Subdivide the problem. Split
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+difficulties. Make a procedure out of
+
+ align:start position:0%
+difficulties. Make a procedure out of
+ 
+
+ align:start position:0%
+difficulties. Make a procedure out of
+subprocedures. Make a whole I'll just
+
+ align:start position:0%
+subprocedures. Make a whole I'll just
+ 
+
+ align:start position:0%
+subprocedures. Make a whole I'll just
+tell you one second about this little
+
+ align:start position:0%
+tell you one second about this little
+ 
+
+ align:start position:0%
+tell you one second about this little
+robot which again is like iconic my
+
+ align:start position:0%
+robot which again is like iconic my
+ 
+
+ align:start position:0%
+robot which again is like iconic my
+childhood. I I had a commercialized
+
+ align:start position:0%
+childhood. I I had a commercialized
+ 
+
+ align:start position:0%
+childhood. I I had a commercialized
+version of this. Um but it it t it it
+
+ align:start position:0%
+version of this. Um but it it t it it
+ 
+
+ align:start position:0%
+version of this. Um but it it t it it
+takes the same commands and uses the
+
+ align:start position:0%
+takes the same commands and uses the
+ 
+
+ align:start position:0%
+takes the same commands and uses the
+same language as the turtle that's on
+
+ align:start position:0%
+same language as the turtle that's on
+ 
+
+ align:start position:0%
+same language as the turtle that's on
+the screen. So you can tell it like
+
+ align:start position:0%
+the screen. So you can tell it like
+ 
+
+ align:start position:0%
+the screen. So you can tell it like
+forward 10 and there's some equivalent
+
+ align:start position:0%
+forward 10 and there's some equivalent
+ 
+
+ align:start position:0%
+forward 10 and there's some equivalent
+to forward 10 that also shows up on the
+
+ align:start position:0%
+to forward 10 that also shows up on the
+ 
+
+ align:start position:0%
+to forward 10 that also shows up on the
+screen. It has a pen that's mounted in
+
+ align:start position:0%
+screen. It has a pen that's mounted in
+ 
+
+ align:start position:0%
+screen. It has a pen that's mounted in
+it that's controlled with pen up and pen
+
+ align:start position:0%
+it that's controlled with pen up and pen
+ 
+
+ align:start position:0%
+it that's controlled with pen up and pen
+down. Um, so you can like make varying
+
+ align:start position:0%
+down. Um, so you can like make varying
+ 
+
+ align:start position:0%
+down. Um, so you can like make varying
+kinds of shapes using that. And then if
+
+ align:start position:0%
+kinds of shapes using that. And then if
+ 
+
+ align:start position:0%
+kinds of shapes using that. And then if
+you see the cable that the person is
+
+ align:start position:0%
+you see the cable that the person is
+ 
+
+ align:start position:0%
+you see the cable that the person is
+walking around with, that was a serial
+
+ align:start position:0%
+walking around with, that was a serial
+ 
+
+ align:start position:0%
+walking around with, that was a serial
+cable which is the primary thing we used
+
+ align:start position:0%
+cable which is the primary thing we used
+ 
+
+ align:start position:0%
+cable which is the primary thing we used
+to use to connect computers to
+
+ align:start position:0%
+to use to connect computers to
+ 
+
+ align:start position:0%
+to use to connect computers to
+peripherals. So that like before
+
+ align:start position:0%
+peripherals. So that like before
+ 
+
+ align:start position:0%
+peripherals. So that like before
+wireless or before you know USB or other
+
+ align:start position:0%
+wireless or before you know USB or other
+ 
+
+ align:start position:0%
+wireless or before you know USB or other
+things like that that was the cable that
+
+ align:start position:0%
+things like that that was the cable that
+ 
+
+ align:start position:0%
+things like that that was the cable that
+they were using to move things around
+
+ align:start position:0%
+they were using to move things around
+ 
+
+ align:start position:0%
+they were using to move things around
+procedure out of sub procedures, make a
+
+ align:start position:0%
+procedure out of sub procedures, make a
+ 
+
+ align:start position:0%
+procedure out of sub procedures, make a
+hold out of parts. Understand each
+
+ align:start position:0%
+hold out of parts. Understand each
+ 
+
+ align:start position:0%
+hold out of parts. Understand each
+separately. Everybody knows that, but
+
+ align:start position:0%
+separately. Everybody knows that, but
+ 
+
+ align:start position:0%
+separately. Everybody knows that, but
+they don't do it. Now, it's moving
+
+ align:start position:0%
+they don't do it. Now, it's moving
+ 
+
+ align:start position:0%
+they don't do it. Now, it's moving
+across the screen the way I um told you
+
+ align:start position:0%
+across the screen the way I um told you
+ 
+
+ align:start position:0%
+across the screen the way I um told you
+it did it before, but this time, this is
+
+ align:start position:0%
+it did it before, but this time, this is
+ 
+
+ align:start position:0%
+it did it before, but this time, this is
+like the way I taught myself to get it
+
+ align:start position:0%
+like the way I taught myself to get it
+ 
+
+ align:start position:0%
+like the way I taught myself to get it
+across the screen. It's the first time I
+
+ align:start position:0%
+across the screen. It's the first time I
+ 
+
+ align:start position:0%
+across the screen. It's the first time I
+had done it. And so, the way I have the
+
+ align:start position:0%
+had done it. And so, the way I have the
+ 
+
+ align:start position:0%
+had done it. And so, the way I have the
+little one to go is every time it moves
+
+ align:start position:0%
+little one to go is every time it moves
+ 
+
+ align:start position:0%
+little one to go is every time it moves
+up a little, it subtracts a number, a
+
+ align:start position:0%
+up a little, it subtracts a number, a
+ 
+
+ align:start position:0%
+up a little, it subtracts a number, a
+little bit of a number, and then until
+
+ align:start position:0%
+little bit of a number, and then until
+ 
+
+ align:start position:0%
+little bit of a number, and then until
+it it's a small number. And when it's a
+
+ align:start position:0%
+it it's a small number. And when it's a
+ 
+
+ align:start position:0%
+it it's a small number. And when it's a
+certain number, I tell it that it should
+
+ align:start position:0%
+certain number, I tell it that it should
+ 
+
+ align:start position:0%
+certain number, I tell it that it should
+stop.
+
+ align:start position:0%
+stop.
+ 
+
+ align:start position:0%
+stop.
+Martha's getting mathematical knowledge
+
+ align:start position:0%
+Martha's getting mathematical knowledge
+ 
+
+ align:start position:0%
+Martha's getting mathematical knowledge
+in a meaningful context for use. Now,
+
+ align:start position:0%
+in a meaningful context for use. Now,
+ 
+
+ align:start position:0%
+in a meaningful context for use. Now,
+it just told me I can't move off the
+
+ align:start position:0%
+it just told me I can't move off the
+ 
+
+ align:start position:0%
+it just told me I can't move off the
+screen. When I was at school, they told
+
+ align:start position:0%
+screen. When I was at school, they told
+ 
+
+ align:start position:0%
+screen. When I was at school, they told
+me to learn long division because I
+
+ align:start position:0%
+me to learn long division because I
+ 
+
+ align:start position:0%
+me to learn long division because I
+would need it when I grew up. And I
+
+ align:start position:0%
+would need it when I grew up. And I
+ 
+
+ align:start position:0%
+would need it when I grew up. And I
+think I knew it was a
+
+ align:start position:0%
+think I knew it was a
+ 
+
+ align:start position:0%
+think I knew it was a
+lie. It was to make me despise the
+
+ align:start position:0%
+lie. It was to make me despise the
+ 
+
+ align:start position:0%
+lie. It was to make me despise the
+teachers a little more. Now it's drawing
+
+ align:start position:0%
+teachers a little more. Now it's drawing
+ 
+
+ align:start position:0%
+teachers a little more. Now it's drawing
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+gill a
+
+ align:start position:0%
+gill a
+ 
+
+ align:start position:0%
+gill a
+subrocedure. Now the bottom of the fish
+
+ align:start position:0%
+subrocedure. Now the bottom of the fish
+ 
+
+ align:start position:0%
+subrocedure. Now the bottom of the fish
+Steven is using the ideas of angle of
+
+ align:start position:0%
+Steven is using the ideas of angle of
+ 
+
+ align:start position:0%
+Steven is using the ideas of angle of
+subrocedure of arc and of circle in a
+
+ align:start position:0%
+subrocedure of arc and of circle in a
+ 
+
+ align:start position:0%
+subrocedure of arc and of circle in a
+confident purposeful way. The tail the
+
+ align:start position:0%
+confident purposeful way. The tail the
+ 
+
+ align:start position:0%
+confident purposeful way. The tail the
+triangle part is made out of a procedure
+
+ align:start position:0%
+triangle part is made out of a procedure
+ 
+
+ align:start position:0%
+triangle part is made out of a procedure
+called try one. First you got to do
+
+ align:start position:0%
+called try one. First you got to do
+ 
+
+ align:start position:0%
+called try one. First you got to do
+right 60, then forward 50, back 50, left
+
+ align:start position:0%
+right 60, then forward 50, back 50, left
+ 
+
+ align:start position:0%
+right 60, then forward 50, back 50, left
+60, forward 50, back 50, left 60,
+
+ align:start position:0%
+60, forward 50, back 50, left 60,
+ 
+
+ align:start position:0%
+60, forward 50, back 50, left 60,
+forward 50, back 50, and so on.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now it's doing a
+
+ align:start position:0%
+Now it's doing a
+ 
+
+ align:start position:0%
+Now it's doing a
+firm. That's a radius of 300 and a um
+
+ align:start position:0%
+firm. That's a radius of 300 and a um
+ 
+
+ align:start position:0%
+firm. That's a radius of 300 and a um
+arc of 90. I made a big radius. And then
+
+ align:start position:0%
+arc of 90. I made a big radius. And then
+ 
+
+ align:start position:0%
+arc of 90. I made a big radius. And then
+I went sector left which will go right
+
+ align:start position:0%
+I went sector left which will go right
+ 
+
+ align:start position:0%
+I went sector left which will go right
+over it and bring it back. Then I made a
+
+ align:start position:0%
+over it and bring it back. Then I made a
+ 
+
+ align:start position:0%
+over it and bring it back. Then I made a
+smaller radius of the same arc and then
+
+ align:start position:0%
+smaller radius of the same arc and then
+ 
+
+ align:start position:0%
+smaller radius of the same arc and then
+it would do that again. Then it's even
+
+ align:start position:0%
+it would do that again. Then it's even
+ 
+
+ align:start position:0%
+it would do that again. Then it's even
+smaller one. It will do that again. And
+
+ align:start position:0%
+smaller one. It will do that again. And
+ 
+
+ align:start position:0%
+smaller one. It will do that again. And
+that's how I got the
+
+ align:start position:0%
+that's how I got the
+ 
+
+ align:start position:0%
+that's how I got the
+fern. There we are. There's the finished
+
+ align:start position:0%
+fern. There we are. There's the finished
+ 
+
+ align:start position:0%
+fern. There we are. There's the finished
+picture.
+
+ align:start position:0%
+picture.
+ 
+
+ align:start position:0%
+picture.
+I made a big song and I used that for
+
+ align:start position:0%
+I made a big song and I used that for
+ 
+
+ align:start position:0%
+I made a big song and I used that for
+part of it and then I made an
+
+ align:start position:0%
+part of it and then I made an
+ 
+
+ align:start position:0%
+part of it and then I made an
+accompanying with it with the drum and
+
+ align:start position:0%
+accompanying with it with the drum and
+ 
+
+ align:start position:0%
+accompanying with it with the drum and
+that's um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The kids told me that's a spiral. I
+
+ align:start position:0%
+The kids told me that's a spiral. I
+ 
+
+ align:start position:0%
+The kids told me that's a spiral. I
+think there was a new mathematical word
+
+ align:start position:0%
+think there was a new mathematical word
+ 
+
+ align:start position:0%
+think there was a new mathematical word
+that was born there that's going to
+
+ align:start position:0%
+that was born there that's going to
+ 
+
+ align:start position:0%
+that was born there that's going to
+stick. I'd call that real discovery.
+
+ align:start position:0%
+stick. I'd call that real discovery.
+ 
+
+ align:start position:0%
+stick. I'd call that real discovery.
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Good. Don't spend time with this. Um,
+
+ align:start position:0%
+Good. Don't spend time with this. Um,
+ 
+
+ align:start position:0%
+Good. Don't spend time with this. Um,
+turn the people next to you. Talk to
+
+ align:start position:0%
+turn the people next to you. Talk to
+ 
+
+ align:start position:0%
+turn the people next to you. Talk to
+them a little bit. What are what are the
+
+ align:start position:0%
+them a little bit. What are what are the
+ 
+
+ align:start position:0%
+them a little bit. What are what are the
+things that you saw in there that coher
+
+ align:start position:0%
+things that you saw in there that coher
+ 
+
+ align:start position:0%
+things that you saw in there that coher
+with ideas that you read about from
+
+ align:start position:0%
+with ideas that you read about from
+ 
+
+ align:start position:0%
+with ideas that you read about from
+other communities of situated learning?
+
+ align:start position:0%
+other communities of situated learning?
+ 
+
+ align:start position:0%
+other communities of situated learning?
+What are some things that you saw in
+
+ align:start position:0%
+What are some things that you saw in
+ 
+
+ align:start position:0%
+What are some things that you saw in
+there that cohered with cognitive load
+
+ align:start position:0%
+there that cohered with cognitive load
+ 
+
+ align:start position:0%
+there that cohered with cognitive load
+theory? Do you see sort of evidence of
+
+ align:start position:0%
+theory? Do you see sort of evidence of
+ 
+
+ align:start position:0%
+theory? Do you see sort of evidence of
+direct instruction that was in there
+
+ align:start position:0%
+direct instruction that was in there
+ 
+
+ align:start position:0%
+direct instruction that was in there
+anywhere? Um and then what kind of
+
+ align:start position:0%
+anywhere? Um and then what kind of
+ 
+
+ align:start position:0%
+anywhere? Um and then what kind of
+learning environments have you been like
+
+ align:start position:0%
+learning environments have you been like
+ 
+
+ align:start position:0%
+learning environments have you been like
+um where you learned in this kind of way
+
+ align:start position:0%
+um where you learned in this kind of way
+ 
+
+ align:start position:0%
+um where you learned in this kind of way
+that was pleasurable? And have people
+
+ align:start position:0%
+that was pleasurable? And have people
+ 
+
+ align:start position:0%
+that was pleasurable? And have people
+been in learning environments where
+
+ align:start position:0%
+been in learning environments where
+ 
+
+ align:start position:0%
+been in learning environments where
+you've sort of learned in this way that
+
+ align:start position:0%
+you've sort of learned in this way that
+ 
+
+ align:start position:0%
+you've sort of learned in this way that
+you found very unpleasurable and
+
+ align:start position:0%
+you found very unpleasurable and
+ 
+
+ align:start position:0%
+you found very unpleasurable and
+unlikable? Then discuss that for a
+
+ align:start position:0%
+unlikable? Then discuss that for a
+ 
+
+ align:start position:0%
+unlikable? Then discuss that for a
+couple minutes. Ready? Go.
+
+ align:start position:0%
+couple minutes. Ready? Go.
+ 
+
+ align:start position:0%
+couple minutes. Ready? Go.
+Every good. What are what are what are
+
+ align:start position:0%
+Every good. What are what are what are
+ 
+
+ align:start position:0%
+Every good. What are what are what are
+some connections that people made? What
+
+ align:start position:0%
+some connections that people made? What
+ 
+
+ align:start position:0%
+some connections that people made? What
+are some things that uh where you saw
+
+ align:start position:0%
+are some things that uh where you saw
+ 
+
+ align:start position:0%
+are some things that uh where you saw
+examples of uh situated learning or
+
+ align:start position:0%
+examples of uh situated learning or
+ 
+
+ align:start position:0%
+examples of uh situated learning or
+cognitive load theory or things that
+
+ align:start position:0%
+cognitive load theory or things that
+ 
+
+ align:start position:0%
+cognitive load theory or things that
+seem pleasurable or or frustrating? What
+
+ align:start position:0%
+seem pleasurable or or frustrating? What
+ 
+
+ align:start position:0%
+seem pleasurable or or frustrating? What
+did you talk about in your groups? We
+
+ align:start position:0%
+did you talk about in your groups? We
+ 
+
+ align:start position:0%
+did you talk about in your groups? We
+were talking about learning like
+
+ align:start position:0%
+were talking about learning like
+ 
+
+ align:start position:0%
+were talking about learning like
+programming in general or it seems like
+
+ align:start position:0%
+programming in general or it seems like
+ 
+
+ align:start position:0%
+programming in general or it seems like
+you always need some base level of
+
+ align:start position:0%
+you always need some base level of
+ 
+
+ align:start position:0%
+you always need some base level of
+whether it's the instructions or knowing
+
+ align:start position:0%
+whether it's the instructions or knowing
+ 
+
+ align:start position:0%
+whether it's the instructions or knowing
+whatever commands there are in logo and
+
+ align:start position:0%
+whatever commands there are in logo and
+ 
+
+ align:start position:0%
+whatever commands there are in logo and
+that most likely comes from more of an
+
+ align:start position:0%
+that most likely comes from more of an
+ 
+
+ align:start position:0%
+that most likely comes from more of an
+instructional place but then you can get
+
+ align:start position:0%
+instructional place but then you can get
+ 
+
+ align:start position:0%
+instructional place but then you can get
+into these situations like we saw in the
+
+ align:start position:0%
+into these situations like we saw in the
+ 
+
+ align:start position:0%
+into these situations like we saw in the
+video where it becomes open world but it
+
+ align:start position:0%
+video where it becomes open world but it
+ 
+
+ align:start position:0%
+video where it becomes open world but it
+still seems like you need some base
+
+ align:start position:0%
+still seems like you need some base
+ 
+
+ align:start position:0%
+still seems like you need some base
+level where CLT needs to come in. All
+
+ align:start position:0%
+level where CLT needs to come in. All
+ 
+
+ align:start position:0%
+level where CLT needs to come in. All
+right. Yeah. Or or some kind of direct
+
+ align:start position:0%
+right. Yeah. Or or some kind of direct
+ 
+
+ align:start position:0%
+right. Yeah. Or or some kind of direct
+instruction. Where where did where what
+
+ align:start position:0%
+instruction. Where where did where what
+ 
+
+ align:start position:0%
+instruction. Where where did where what
+what evidence of direct instruction did
+
+ align:start position:0%
+what evidence of direct instruction did
+ 
+
+ align:start position:0%
+what evidence of direct instruction did
+people um did people see? Like where
+
+ align:start position:0%
+people um did people see? Like where
+ 
+
+ align:start position:0%
+people um did people see? Like where
+were you like h that kid didn't figure
+
+ align:start position:0%
+were you like h that kid didn't figure
+ 
+
+ align:start position:0%
+were you like h that kid didn't figure
+that out on their own? I mean just the
+
+ align:start position:0%
+that out on their own? I mean just the
+ 
+
+ align:start position:0%
+that out on their own? I mean just the
+terminology they figured out like
+
+ align:start position:0%
+terminology they figured out like
+ 
+
+ align:start position:0%
+terminology they figured out like
+procedure subrocedure all of these
+
+ align:start position:0%
+procedure subrocedure all of these
+ 
+
+ align:start position:0%
+procedure subrocedure all of these
+things are a kid a kid wouldn't just
+
+ align:start position:0%
+things are a kid a kid wouldn't just
+ 
+
+ align:start position:0%
+things are a kid a kid wouldn't just
+figure these out. Yeah. Yeah. It doesn't
+
+ align:start position:0%
+figure these out. Yeah. Yeah. It doesn't
+ 
+
+ align:start position:0%
+figure these out. Yeah. Yeah. It doesn't
+seem like Steven came up with the term
+
+ align:start position:0%
+seem like Steven came up with the term
+ 
+
+ align:start position:0%
+seem like Steven came up with the term
+procedure and subrocedure. Like pretty
+
+ align:start position:0%
+procedure and subrocedure. Like pretty
+ 
+
+ align:start position:0%
+procedure and subrocedure. Like pretty
+sure somebody taught him you know sat
+
+ align:start position:0%
+sure somebody taught him you know sat
+ 
+
+ align:start position:0%
+sure somebody taught him you know sat
+down and said this is you know here are
+
+ align:start position:0%
+down and said this is you know here are
+ 
+
+ align:start position:0%
+down and said this is you know here are
+a couple of useful definitions that will
+
+ align:start position:0%
+a couple of useful definitions that will
+ 
+
+ align:start position:0%
+a couple of useful definitions that will
+allow us communicate with us more
+
+ align:start position:0%
+allow us communicate with us more
+ 
+
+ align:start position:0%
+allow us communicate with us more
+clearly. Um also we were talking about
+
+ align:start position:0%
+clearly. Um also we were talking about
+ 
+
+ align:start position:0%
+clearly. Um also we were talking about
+like when the two girls were talking to
+
+ align:start position:0%
+like when the two girls were talking to
+ 
+
+ align:start position:0%
+like when the two girls were talking to
+each other it was like one at the
+
+ align:start position:0%
+each other it was like one at the
+ 
+
+ align:start position:0%
+each other it was like one at the
+beginning was like instruct instructing
+
+ align:start position:0%
+beginning was like instruct instructing
+ 
+
+ align:start position:0%
+beginning was like instruct instructing
+the other. Yeah.
+
+ align:start position:0%
+the other. Yeah.
+ 
+
+ align:start position:0%
+the other. Yeah.
+So, I guess that's kind of like Oh, very
+
+ align:start position:0%
+So, I guess that's kind of like Oh, very
+ 
+
+ align:start position:0%
+So, I guess that's kind of like Oh, very
+direct instruction. Yeah. Instruction
+
+ align:start position:0%
+direct instruction. Yeah. Instruction
+ 
+
+ align:start position:0%
+direct instruction. Yeah. Instruction
+within like a situated learning
+
+ align:start position:0%
+within like a situated learning
+ 
+
+ align:start position:0%
+within like a situated learning
+environment. Yeah. Yeah. I mean, it's
+
+ align:start position:0%
+environment. Yeah. Yeah. I mean, it's
+ 
+
+ align:start position:0%
+environment. Yeah. Yeah. I mean, it's
+it's Yeah. Yeah. It's a it's a kind of
+
+ align:start position:0%
+it's Yeah. Yeah. It's a it's a kind of
+ 
+
+ align:start position:0%
+it's Yeah. Yeah. It's a it's a kind of
+worked example like, oh, I'm going to
+
+ align:start position:0%
+worked example like, oh, I'm going to
+ 
+
+ align:start position:0%
+worked example like, oh, I'm going to
+show you how I you know, I made a thing
+
+ align:start position:0%
+show you how I you know, I made a thing
+ 
+
+ align:start position:0%
+show you how I you know, I made a thing
+like I'm going to, you know, we're going
+
+ align:start position:0%
+like I'm going to, you know, we're going
+ 
+
+ align:start position:0%
+like I'm going to, you know, we're going
+to make this thing together right now by
+
+ align:start position:0%
+to make this thing together right now by
+ 
+
+ align:start position:0%
+to make this thing together right now by
+first of all, play each of the pieces.
+
+ align:start position:0%
+first of all, play each of the pieces.
+ 
+
+ align:start position:0%
+first of all, play each of the pieces.
+Now, we're going to play all the pieces
+
+ align:start position:0%
+Now, we're going to play all the pieces
+ 
+
+ align:start position:0%
+Now, we're going to play all the pieces
+together. I've already learned how to do
+
+ align:start position:0%
+together. I've already learned how to do
+ 
+
+ align:start position:0%
+together. I've already learned how to do
+that. you know what makes it a kind of
+
+ align:start position:0%
+that. you know what makes it a kind of
+ 
+
+ align:start position:0%
+that. you know what makes it a kind of
+peer learning uh uh situated learning
+
+ align:start position:0%
+peer learning uh uh situated learning
+ 
+
+ align:start position:0%
+peer learning uh uh situated learning
+kind of thing is it's one young person
+
+ align:start position:0%
+kind of thing is it's one young person
+ 
+
+ align:start position:0%
+kind of thing is it's one young person
+teaching it to another person but does
+
+ align:start position:0%
+teaching it to another person but does
+ 
+
+ align:start position:0%
+teaching it to another person but does
+seem to be you know direct instruction
+
+ align:start position:0%
+seem to be you know direct instruction
+ 
+
+ align:start position:0%
+seem to be you know direct instruction
+for sure. Um that kind of led us into a
+
+ align:start position:0%
+for sure. Um that kind of led us into a
+ 
+
+ align:start position:0%
+for sure. Um that kind of led us into a
+conversation about how like within
+
+ align:start position:0%
+conversation about how like within
+ 
+
+ align:start position:0%
+conversation about how like within
+situated learning like that there's like
+
+ align:start position:0%
+situated learning like that there's like
+ 
+
+ align:start position:0%
+situated learning like that there's like
+kind of two ways that it can be seen as
+
+ align:start position:0%
+kind of two ways that it can be seen as
+ 
+
+ align:start position:0%
+kind of two ways that it can be seen as
+like you have someone who's like an
+
+ align:start position:0%
+like you have someone who's like an
+ 
+
+ align:start position:0%
+like you have someone who's like an
+old-timer like the the other girl like
+
+ align:start position:0%
+old-timer like the the other girl like
+ 
+
+ align:start position:0%
+old-timer like the the other girl like
+explaining to the other the like the
+
+ align:start position:0%
+explaining to the other the like the
+ 
+
+ align:start position:0%
+explaining to the other the like the
+other girl about um the situation that
+
+ align:start position:0%
+other girl about um the situation that
+ 
+
+ align:start position:0%
+other girl about um the situation that
+they were working with. But then there's
+
+ align:start position:0%
+they were working with. But then there's
+ 
+
+ align:start position:0%
+they were working with. But then there's
+also the instances when it was just like
+
+ align:start position:0%
+also the instances when it was just like
+ 
+
+ align:start position:0%
+also the instances when it was just like
+the student and the computer and that
+
+ align:start position:0%
+the student and the computer and that
+ 
+
+ align:start position:0%
+the student and the computer and that
+like you kind of lost that like social
+
+ align:start position:0%
+like you kind of lost that like social
+ 
+
+ align:start position:0%
+like you kind of lost that like social
+aspect that you have of like learning
+
+ align:start position:0%
+aspect that you have of like learning
+ 
+
+ align:start position:0%
+aspect that you have of like learning
+from another person. Um and then we like
+
+ align:start position:0%
+from another person. Um and then we like
+ 
+
+ align:start position:0%
+from another person. Um and then we like
+went into like an interesting
+
+ align:start position:0%
+went into like an interesting
+ 
+
+ align:start position:0%
+went into like an interesting
+conversation about whether like maybe
+
+ align:start position:0%
+conversation about whether like maybe
+ 
+
+ align:start position:0%
+conversation about whether like maybe
+the student was like having a social
+
+ align:start position:0%
+the student was like having a social
+ 
+
+ align:start position:0%
+the student was like having a social
+interaction from themsel and like
+
+ align:start position:0%
+interaction from themsel and like
+ 
+
+ align:start position:0%
+interaction from themsel and like
+learning with the computer as a tool or
+
+ align:start position:0%
+learning with the computer as a tool or
+ 
+
+ align:start position:0%
+learning with the computer as a tool or
+maybe they were having a social
+
+ align:start position:0%
+maybe they were having a social
+ 
+
+ align:start position:0%
+maybe they were having a social
+interaction with the computer itself and
+
+ align:start position:0%
+interaction with the computer itself and
+ 
+
+ align:start position:0%
+interaction with the computer itself and
+like they were learning from the
+
+ align:start position:0%
+like they were learning from the
+ 
+
+ align:start position:0%
+like they were learning from the
+computer and the computer was like
+
+ align:start position:0%
+computer and the computer was like
+ 
+
+ align:start position:0%
+computer and the computer was like
+learning what like they really wanted
+
+ align:start position:0%
+learning what like they really wanted
+ 
+
+ align:start position:0%
+learning what like they really wanted
+the outcome to be. So yeah. Yeah, good.
+
+ align:start position:0%
+the outcome to be. So yeah. Yeah, good.
+ 
+
+ align:start position:0%
+the outcome to be. So yeah. Yeah, good.
+Yeah, that's definitely something we'll
+
+ align:start position:0%
+Yeah, that's definitely something we'll
+ 
+
+ align:start position:0%
+Yeah, that's definitely something we'll
+think about more as we go along. Like
+
+ align:start position:0%
+think about more as we go along. Like
+ 
+
+ align:start position:0%
+think about more as we go along. Like
+what kind of agent is the machine? What
+
+ align:start position:0%
+what kind of agent is the machine? What
+ 
+
+ align:start position:0%
+what kind of agent is the machine? What
+kind of relationship do we have uh to
+
+ align:start position:0%
+kind of relationship do we have uh to
+ 
+
+ align:start position:0%
+kind of relationship do we have uh to
+the machines? How does the machine
+
+ align:start position:0%
+the machines? How does the machine
+ 
+
+ align:start position:0%
+the machines? How does the machine
+motivate? How does the machine explain?
+
+ align:start position:0%
+motivate? How does the machine explain?
+ 
+
+ align:start position:0%
+motivate? How does the machine explain?
+The thing that seems pretty rad here
+
+ align:start position:0%
+The thing that seems pretty rad here
+ 
+
+ align:start position:0%
+The thing that seems pretty rad here
+that that seem more pepper is the
+
+ align:start position:0%
+that that seem more pepper is the
+ 
+
+ align:start position:0%
+that that seem more pepper is the
+machine gives some great feedback.
+
+ align:start position:0%
+machine gives some great feedback.
+ 
+
+ align:start position:0%
+machine gives some great feedback.
+Although lots of other things do. Um uh
+
+ align:start position:0%
+Although lots of other things do. Um uh
+ 
+
+ align:start position:0%
+Although lots of other things do. Um uh
+hand drills give great feedback. You
+
+ align:start position:0%
+hand drills give great feedback. You
+ 
+
+ align:start position:0%
+hand drills give great feedback. You
+know, when you like go through the wall,
+
+ align:start position:0%
+know, when you like go through the wall,
+ 
+
+ align:start position:0%
+know, when you like go through the wall,
+you know it. And when you like, you
+
+ align:start position:0%
+you know it. And when you like, you
+ 
+
+ align:start position:0%
+you know it. And when you like, you
+know, hit something metal or something
+
+ align:start position:0%
+know, hit something metal or something
+ 
+
+ align:start position:0%
+know, hit something metal or something
+like that, you know it and you get that
+
+ align:start position:0%
+like that, you know it and you get that
+ 
+
+ align:start position:0%
+like that, you know it and you get that
+kind of instant feedback. Um there are
+
+ align:start position:0%
+kind of instant feedback. Um there are
+ 
+
+ align:start position:0%
+kind of instant feedback. Um there are
+other things that we teach people where
+
+ align:start position:0%
+other things that we teach people where
+ 
+
+ align:start position:0%
+other things that we teach people where
+it's just hard to imagine where that
+
+ align:start position:0%
+it's just hard to imagine where that
+ 
+
+ align:start position:0%
+it's just hard to imagine where that
+instant feedback might come from. Um
+
+ align:start position:0%
+instant feedback might come from. Um
+ 
+
+ align:start position:0%
+instant feedback might come from. Um
+writing is often that way especially
+
+ align:start position:0%
+writing is often that way especially
+ 
+
+ align:start position:0%
+writing is often that way especially
+like writing other people. There's
+
+ align:start position:0%
+like writing other people. There's
+ 
+
+ align:start position:0%
+like writing other people. There's
+nothing that a sort of screen right we
+
+ align:start position:0%
+nothing that a sort of screen right we
+ 
+
+ align:start position:0%
+nothing that a sort of screen right we
+haven't built things very well where a
+
+ align:start position:0%
+haven't built things very well where a
+ 
+
+ align:start position:0%
+haven't built things very well where a
+machine can tell you like oh that's a
+
+ align:start position:0%
+machine can tell you like oh that's a
+ 
+
+ align:start position:0%
+machine can tell you like oh that's a
+compelling way of expressing that idea
+
+ align:start position:0%
+compelling way of expressing that idea
+ 
+
+ align:start position:0%
+compelling way of expressing that idea
+um in the same way that I can be like oh
+
+ align:start position:0%
+um in the same way that I can be like oh
+ 
+
+ align:start position:0%
+um in the same way that I can be like oh
+my swan is on its side. Um so sort of
+
+ align:start position:0%
+my swan is on its side. Um so sort of
+ 
+
+ align:start position:0%
+my swan is on its side. Um so sort of
+different you know different
+
+ align:start position:0%
+different you know different
+ 
+
+ align:start position:0%
+different you know different
+technologies or and different in you
+
+ align:start position:0%
+technologies or and different in you
+ 
+
+ align:start position:0%
+technologies or and different in you
+know different things that we study have
+
+ align:start position:0%
+know different things that we study have
+ 
+
+ align:start position:0%
+know different things that we study have
+have different capacity to give us
+
+ align:start position:0%
+have different capacity to give us
+ 
+
+ align:start position:0%
+have different capacity to give us
+immediate feedback about what we're
+
+ align:start position:0%
+immediate feedback about what we're
+ 
+
+ align:start position:0%
+immediate feedback about what we're
+doing. Um good other has anybody ever
+
+ align:start position:0%
+doing. Um good other has anybody ever
+ 
+
+ align:start position:0%
+doing. Um good other has anybody ever
+been in an environment like this where
+
+ align:start position:0%
+been in an environment like this where
+ 
+
+ align:start position:0%
+been in an environment like this where
+you're like oh my gosh this is the worst
+
+ align:start position:0%
+you're like oh my gosh this is the worst
+ 
+
+ align:start position:0%
+you're like oh my gosh this is the worst
+do students have experience in this kind
+
+ align:start position:0%
+do students have experience in this kind
+ 
+
+ align:start position:0%
+do students have experience in this kind
+of like open-ended learning where you're
+
+ align:start position:0%
+of like open-ended learning where you're
+ 
+
+ align:start position:0%
+of like open-ended learning where you're
+like this is terrible. Yeah, I remember
+
+ align:start position:0%
+like this is terrible. Yeah, I remember
+ 
+
+ align:start position:0%
+like this is terrible. Yeah, I remember
+this like one or I guess the some more
+
+ align:start position:0%
+this like one or I guess the some more
+ 
+
+ align:start position:0%
+this like one or I guess the some more
+recent MIT experience where basically
+
+ align:start position:0%
+recent MIT experience where basically
+ 
+
+ align:start position:0%
+recent MIT experience where basically
+one of the classes like final project
+
+ align:start position:0%
+one of the classes like final project
+ 
+
+ align:start position:0%
+one of the classes like final project
+was very like open-ended and they were
+
+ align:start position:0%
+was very like open-ended and they were
+ 
+
+ align:start position:0%
+was very like open-ended and they were
+like, "Oh, like just like design this
+
+ align:start position:0%
+like, "Oh, like just like design this
+ 
+
+ align:start position:0%
+like, "Oh, like just like design this
+game." And I was like, "Wow, like it
+
+ align:start position:0%
+game." And I was like, "Wow, like it
+ 
+
+ align:start position:0%
+game." And I was like, "Wow, like it
+would be nice to get some kind of Yeah,
+
+ align:start position:0%
+would be nice to get some kind of Yeah,
+ 
+
+ align:start position:0%
+would be nice to get some kind of Yeah,
+will you please show me how to design
+
+ align:start position:0%
+will you please show me how to design
+ 
+
+ align:start position:0%
+will you please show me how to design
+this game? Like I don't like someone has
+
+ align:start position:0%
+this game? Like I don't like someone has
+ 
+
+ align:start position:0%
+this game? Like I don't like someone has
+figured this out before. Like I don't I
+
+ align:start position:0%
+figured this out before. Like I don't I
+ 
+
+ align:start position:0%
+figured this out before. Like I don't I
+don't want to explore this space
+
+ align:start position:0%
+don't want to explore this space
+ 
+
+ align:start position:0%
+don't want to explore this space
+forever." I've definitely have people
+
+ align:start position:0%
+forever." I've definitely have people
+ 
+
+ align:start position:0%
+forever." I've definitely have people
+who who have taken this class and they
+
+ align:start position:0%
+who who have taken this class and they
+ 
+
+ align:start position:0%
+who who have taken this class and they
+watch this video and they're like, "Give
+
+ align:start position:0%
+watch this video and they're like, "Give
+ 
+
+ align:start position:0%
+watch this video and they're like, "Give
+me a break." Like just show me how to
+
+ align:start position:0%
+me a break." Like just show me how to
+ 
+
+ align:start position:0%
+me a break." Like just show me how to
+use the turtle. them. Um I would say in
+
+ align:start position:0%
+use the turtle. them. Um I would say in
+ 
+
+ align:start position:0%
+use the turtle. them. Um I would say in
+high school um a lot of the AP computer
+
+ align:start position:0%
+high school um a lot of the AP computer
+ 
+
+ align:start position:0%
+high school um a lot of the AP computer
+science classes are like very into like
+
+ align:start position:0%
+science classes are like very into like
+ 
+
+ align:start position:0%
+science classes are like very into like
+this kind of situated learning. But then
+
+ align:start position:0%
+this kind of situated learning. But then
+ 
+
+ align:start position:0%
+this kind of situated learning. But then
+if you have certain classrooms where
+
+ align:start position:0%
+if you have certain classrooms where
+ 
+
+ align:start position:0%
+if you have certain classrooms where
+like in my instance it was like just
+
+ align:start position:0%
+like in my instance it was like just
+ 
+
+ align:start position:0%
+like in my instance it was like just
+overloaded with people who just need an
+
+ align:start position:0%
+overloaded with people who just need an
+ 
+
+ align:start position:0%
+overloaded with people who just need an
+elective and they were like you have to
+
+ align:start position:0%
+elective and they were like you have to
+ 
+
+ align:start position:0%
+elective and they were like you have to
+take this class then it becomes that um
+
+ align:start position:0%
+take this class then it becomes that um
+ 
+
+ align:start position:0%
+take this class then it becomes that um
+like peer-to-peer interaction becomes an
+
+ align:start position:0%
+like peer-to-peer interaction becomes an
+ 
+
+ align:start position:0%
+like peer-to-peer interaction becomes an
+issue where it's like okay you have
+
+ align:start position:0%
+issue where it's like okay you have
+ 
+
+ align:start position:0%
+issue where it's like okay you have
+three people who are trying to teach
+
+ align:start position:0%
+three people who are trying to teach
+ 
+
+ align:start position:0%
+three people who are trying to teach
+like 30 other people how to do a
+
+ align:start position:0%
+like 30 other people how to do a
+ 
+
+ align:start position:0%
+like 30 other people how to do a
+specific thing because you're in the
+
+ align:start position:0%
+specific thing because you're in the
+ 
+
+ align:start position:0%
+specific thing because you're in the
+same like group and they have to pass
+
+ align:start position:0%
+same like group and they have to pass
+ 
+
+ align:start position:0%
+same like group and they have to pass
+and they don't really care anyway. Good.
+
+ align:start position:0%
+and they don't really care anyway. Good.
+ 
+
+ align:start position:0%
+and they don't really care anyway. Good.
+people have different motivations or I
+
+ align:start position:0%
+people have different motivations or I
+ 
+
+ align:start position:0%
+people have different motivations or I
+mean a huge problem that computer
+
+ align:start position:0%
+mean a huge problem that computer
+ 
+
+ align:start position:0%
+mean a huge problem that computer
+science education has is that people
+
+ align:start position:0%
+science education has is that people
+ 
+
+ align:start position:0%
+science education has is that people
+unlike other subjects people come to it
+
+ align:start position:0%
+unlike other subjects people come to it
+ 
+
+ align:start position:0%
+unlike other subjects people come to it
+with very different levels of background
+
+ align:start position:0%
+with very different levels of background
+ 
+
+ align:start position:0%
+with very different levels of background
+experience. Um so like none of you
+
+ align:start position:0%
+experience. Um so like none of you
+ 
+
+ align:start position:0%
+experience. Um so like none of you
+probably ever took a geology class where
+
+ align:start position:0%
+probably ever took a geology class where
+ 
+
+ align:start position:0%
+probably ever took a geology class where
+like a third of the kids were like man I
+
+ align:start position:0%
+like a third of the kids were like man I
+ 
+
+ align:start position:0%
+like a third of the kids were like man I
+just love geology like I do I do geology
+
+ align:start position:0%
+just love geology like I do I do geology
+ 
+
+ align:start position:0%
+just love geology like I do I do geology
+all the time in my spare time. I'm way
+
+ align:start position:0%
+all the time in my spare time. I'm way
+ 
+
+ align:start position:0%
+all the time in my spare time. I'm way
+ahead of you guys. But that is
+
+ align:start position:0%
+ahead of you guys. But that is
+ 
+
+ align:start position:0%
+ahead of you guys. But that is
+essentially what just about every
+
+ align:start position:0%
+essentially what just about every
+ 
+
+ align:start position:0%
+essentially what just about every
+computer science class we teach is like
+
+ align:start position:0%
+computer science class we teach is like
+ 
+
+ align:start position:0%
+computer science class we teach is like
+where a chunk of people are like way
+
+ align:start position:0%
+where a chunk of people are like way
+ 
+
+ align:start position:0%
+where a chunk of people are like way
+into it know a bunch more already. Um,
+
+ align:start position:0%
+into it know a bunch more already. Um,
+ 
+
+ align:start position:0%
+into it know a bunch more already. Um,
+and in fact, those open-ended
+
+ align:start position:0%
+and in fact, those open-ended
+ 
+
+ align:start position:0%
+and in fact, those open-ended
+environments can be can be really great
+
+ align:start position:0%
+environments can be can be really great
+ 
+
+ align:start position:0%
+environments can be can be really great
+for those folks who have that extra
+
+ align:start position:0%
+for those folks who have that extra
+ 
+
+ align:start position:0%
+for those folks who have that extra
+expertise, and they can be a real bummer
+
+ align:start position:0%
+expertise, and they can be a real bummer
+ 
+
+ align:start position:0%
+expertise, and they can be a real bummer
+for people who like can't jump in as
+
+ align:start position:0%
+for people who like can't jump in as
+ 
+
+ align:start position:0%
+for people who like can't jump in as
+naturally. Harmon, what was you going to
+
+ align:start position:0%
+naturally. Harmon, what was you going to
+ 
+
+ align:start position:0%
+naturally. Harmon, what was you going to
+say? Uh, I think what this made me think
+
+ align:start position:0%
+say? Uh, I think what this made me think
+ 
+
+ align:start position:0%
+say? Uh, I think what this made me think
+of is how CLT and situated learning
+
+ align:start position:0%
+of is how CLT and situated learning
+ 
+
+ align:start position:0%
+of is how CLT and situated learning
+cannot be really separated from each
+
+ align:start position:0%
+cannot be really separated from each
+ 
+
+ align:start position:0%
+cannot be really separated from each
+other. Sometimes you need CLT to give
+
+ align:start position:0%
+other. Sometimes you need CLT to give
+ 
+
+ align:start position:0%
+other. Sometimes you need CLT to give
+framework for students and then from
+
+ align:start position:0%
+framework for students and then from
+ 
+
+ align:start position:0%
+framework for students and then from
+that I guess you can fire the wood and
+
+ align:start position:0%
+that I guess you can fire the wood and
+ 
+
+ align:start position:0%
+that I guess you can fire the wood and
+the situated. Yeah. Good. Good. I like
+
+ align:start position:0%
+the situated. Yeah. Good. Good. I like
+ 
+
+ align:start position:0%
+the situated. Yeah. Good. Good. I like
+it. I like it. Yeah. Yeah. What are the
+
+ align:start position:0%
+it. I like it. Yeah. Yeah. What are the
+ 
+
+ align:start position:0%
+it. I like it. Yeah. Yeah. What are the
+I think that's a great question to ask.
+
+ align:start position:0%
+I think that's a great question to ask.
+ 
+
+ align:start position:0%
+I think that's a great question to ask.
+What are the different sort of
+
+ align:start position:0%
+What are the different sort of
+ 
+
+ align:start position:0%
+What are the different sort of
+combination and permutations like the
+
+ align:start position:0%
+combination and permutations like the
+ 
+
+ align:start position:0%
+combination and permutations like the
+reason why these ideas have existed that
+
+ align:start position:0%
+reason why these ideas have existed that
+ 
+
+ align:start position:0%
+reason why these ideas have existed that
+we can find evidence of them for 2,000
+
+ align:start position:0%
+we can find evidence of them for 2,000
+ 
+
+ align:start position:0%
+we can find evidence of them for 2,000
+years is that like they both seem pretty
+
+ align:start position:0%
+years is that like they both seem pretty
+ 
+
+ align:start position:0%
+years is that like they both seem pretty
+good. Um they both seem useful in
+
+ align:start position:0%
+good. Um they both seem useful in
+ 
+
+ align:start position:0%
+good. Um they both seem useful in
+different ways. You know, here you know
+
+ align:start position:0%
+different ways. You know, here you know
+ 
+
+ align:start position:0%
+different ways. You know, here you know
+here is here you know um Seymour Papard
+
+ align:start position:0%
+here is here you know um Seymour Papard
+ 
+
+ align:start position:0%
+here is here you know um Seymour Papard
+is once talking about like his teachers
+
+ align:start position:0%
+is once talking about like his teachers
+ 
+
+ align:start position:0%
+is once talking about like his teachers
+lying to them and despising schools. But
+
+ align:start position:0%
+lying to them and despising schools. But
+ 
+
+ align:start position:0%
+lying to them and despising schools. But
+you can also find sort of school things
+
+ align:start position:0%
+you can also find sort of school things
+ 
+
+ align:start position:0%
+you can also find sort of school things
+like we're going to need some
+
+ align:start position:0%
+like we're going to need some
+ 
+
+ align:start position:0%
+like we're going to need some
+definitions that I teach you um that are
+
+ align:start position:0%
+definitions that I teach you um that are
+ 
+
+ align:start position:0%
+definitions that I teach you um that are
+kind of woven even in this sort of
+
+ align:start position:0%
+kind of woven even in this sort of
+ 
+
+ align:start position:0%
+kind of woven even in this sort of
+extreme example. Um let me give you a
+
+ align:start position:0%
+extreme example. Um let me give you a
+ 
+
+ align:start position:0%
+extreme example. Um let me give you a
+few pieces from the thing that you read
+
+ align:start position:0%
+few pieces from the thing that you read
+ 
+
+ align:start position:0%
+few pieces from the thing that you read
+u from a guy named Jean Le um who with
+
+ align:start position:0%
+u from a guy named Jean Le um who with
+ 
+
+ align:start position:0%
+u from a guy named Jean Le um who with
+another person named Eddiad Winganger um
+
+ align:start position:0%
+another person named Eddiad Winganger um
+ 
+
+ align:start position:0%
+another person named Eddiad Winganger um
+really advanced some of these ideas. Um
+
+ align:start position:0%
+really advanced some of these ideas. Um
+ 
+
+ align:start position:0%
+really advanced some of these ideas. Um
+and I want you to like be thinking about
+
+ align:start position:0%
+and I want you to like be thinking about
+ 
+
+ align:start position:0%
+and I want you to like be thinking about
+like so how is the like what are the
+
+ align:start position:0%
+like so how is the like what are the
+ 
+
+ align:start position:0%
+like so how is the like what are the
+methods that this person uses to study?
+
+ align:start position:0%
+methods that this person uses to study?
+ 
+
+ align:start position:0%
+methods that this person uses to study?
+What are the kind of arguments they
+
+ align:start position:0%
+What are the kind of arguments they
+ 
+
+ align:start position:0%
+What are the kind of arguments they
+make? What are the implications for
+
+ align:start position:0%
+make? What are the implications for
+ 
+
+ align:start position:0%
+make? What are the implications for
+pedagogy? what's their framework about
+
+ align:start position:0%
+pedagogy? what's their framework about
+ 
+
+ align:start position:0%
+pedagogy? what's their framework about
+um human beings and how they learn and
+
+ align:start position:0%
+um human beings and how they learn and
+ 
+
+ align:start position:0%
+um human beings and how they learn and
+where do these things lap and overlap
+
+ align:start position:0%
+where do these things lap and overlap
+ 
+
+ align:start position:0%
+where do these things lap and overlap
+you know some like it can often seem
+
+ align:start position:0%
+you know some like it can often seem
+ 
+
+ align:start position:0%
+you know some like it can often seem
+like when you're writing about you know
+
+ align:start position:0%
+like when you're writing about you know
+ 
+
+ align:start position:0%
+like when you're writing about you know
+if you read a bunch of stuff on
+
+ align:start position:0%
+if you read a bunch of stuff on
+ 
+
+ align:start position:0%
+if you read a bunch of stuff on
+cognitive load theory it seems like
+
+ align:start position:0%
+cognitive load theory it seems like
+ 
+
+ align:start position:0%
+cognitive load theory it seems like
+they're just talking about instruction
+
+ align:start position:0%
+they're just talking about instruction
+ 
+
+ align:start position:0%
+they're just talking about instruction
+and they mostly are but they're ways at
+
+ align:start position:0%
+and they mostly are but they're ways at
+ 
+
+ align:start position:0%
+and they mostly are but they're ways at
+talking about instruction that evoke
+
+ align:start position:0%
+talking about instruction that evoke
+ 
+
+ align:start position:0%
+talking about instruction that evoke
+their beliefs about culture that evoke
+
+ align:start position:0%
+their beliefs about culture that evoke
+ 
+
+ align:start position:0%
+their beliefs about culture that evoke
+their beliefs about values that evoke
+
+ align:start position:0%
+their beliefs about values that evoke
+ 
+
+ align:start position:0%
+their beliefs about values that evoke
+their beliefs around methods and
+
+ align:start position:0%
+their beliefs around methods and
+ 
+
+ align:start position:0%
+their beliefs around methods and
+outcomes even if they don't talk about
+
+ align:start position:0%
+outcomes even if they don't talk about
+ 
+
+ align:start position:0%
+outcomes even if they don't talk about
+those things as much in this chapter I
+
+ align:start position:0%
+those things as much in this chapter I
+ 
+
+ align:start position:0%
+those things as much in this chapter I
+propose to consider learning not as a
+
+ align:start position:0%
+propose to consider learning not as a
+ 
+
+ align:start position:0%
+propose to consider learning not as a
+process process of socially shared
+
+ align:start position:0%
+process process of socially shared
+ 
+
+ align:start position:0%
+process process of socially shared
+cognition that results in the end in the
+
+ align:start position:0%
+cognition that results in the end in the
+ 
+
+ align:start position:0%
+cognition that results in the end in the
+internalization of knowledge by
+
+ align:start position:0%
+internalization of knowledge by
+ 
+
+ align:start position:0%
+internalization of knowledge by
+individuals but as a process of becoming
+
+ align:start position:0%
+individuals but as a process of becoming
+ 
+
+ align:start position:0%
+individuals but as a process of becoming
+a member of a sustained community of
+
+ align:start position:0%
+a member of a sustained community of
+ 
+
+ align:start position:0%
+a member of a sustained community of
+practice. Um so anytime you read
+
+ align:start position:0%
+practice. Um so anytime you read
+ 
+
+ align:start position:0%
+practice. Um so anytime you read
+anything a thing that you're almost all
+
+ align:start position:0%
+anything a thing that you're almost all
+ 
+
+ align:start position:0%
+anything a thing that you're almost all
+probably trained to do is try to figure
+
+ align:start position:0%
+probably trained to do is try to figure
+ 
+
+ align:start position:0%
+probably trained to do is try to figure
+out like what is the person's core
+
+ align:start position:0%
+out like what is the person's core
+ 
+
+ align:start position:0%
+out like what is the person's core
+argument like what is the thing they're
+
+ align:start position:0%
+argument like what is the thing they're
+ 
+
+ align:start position:0%
+argument like what is the thing they're
+arguing for. An equally useful thing to
+
+ align:start position:0%
+arguing for. An equally useful thing to
+ 
+
+ align:start position:0%
+arguing for. An equally useful thing to
+do almost anytime you read anything is
+
+ align:start position:0%
+do almost anytime you read anything is
+ 
+
+ align:start position:0%
+do almost anytime you read anything is
+to try to figure out what is this person
+
+ align:start position:0%
+to try to figure out what is this person
+ 
+
+ align:start position:0%
+to try to figure out what is this person
+arguing against. Um, and people are
+
+ align:start position:0%
+arguing against. Um, and people are
+ 
+
+ align:start position:0%
+arguing against. Um, and people are
+often not that explicit. Um, you know,
+
+ align:start position:0%
+often not that explicit. Um, you know,
+ 
+
+ align:start position:0%
+often not that explicit. Um, you know,
+he's not sort of saying like these jerks
+
+ align:start position:0%
+he's not sort of saying like these jerks
+ 
+
+ align:start position:0%
+he's not sort of saying like these jerks
+who are really like big on schools and
+
+ align:start position:0%
+who are really like big on schools and
+ 
+
+ align:start position:0%
+who are really like big on schools and
+direct instruction have totally missed
+
+ align:start position:0%
+direct instruction have totally missed
+ 
+
+ align:start position:0%
+direct instruction have totally missed
+this stuff. But there's that's kind of
+
+ align:start position:0%
+this stuff. But there's that's kind of
+ 
+
+ align:start position:0%
+this stuff. But there's that's kind of
+what he's he's getting at in here. And
+
+ align:start position:0%
+what he's he's getting at in here. And
+ 
+
+ align:start position:0%
+what he's he's getting at in here. And
+it's and it's a radical statement.
+
+ align:start position:0%
+it's and it's a radical statement.
+ 
+
+ align:start position:0%
+it's and it's a radical statement.
+Learning is not the internalization of
+
+ align:start position:0%
+Learning is not the internalization of
+ 
+
+ align:start position:0%
+Learning is not the internalization of
+knowledge. You know, last week I told
+
+ align:start position:0%
+knowledge. You know, last week I told
+ 
+
+ align:start position:0%
+knowledge. You know, last week I told
+you that for some of these kind of
+
+ align:start position:0%
+you that for some of these kind of
+ 
+
+ align:start position:0%
+you that for some of these kind of
+educational psychology people, memory is
+
+ align:start position:0%
+educational psychology people, memory is
+ 
+
+ align:start position:0%
+educational psychology people, memory is
+the residue of thought. Like the entire
+
+ align:start position:0%
+the residue of thought. Like the entire
+ 
+
+ align:start position:0%
+the residue of thought. Like the entire
+end point of cognitive load theory is to
+
+ align:start position:0%
+end point of cognitive load theory is to
+ 
+
+ align:start position:0%
+end point of cognitive load theory is to
+store memories facts as memories in our
+
+ align:start position:0%
+store memories facts as memories in our
+ 
+
+ align:start position:0%
+store memories facts as memories in our
+long-term memory. Um not as the
+
+ align:start position:0%
+long-term memory. Um not as the
+ 
+
+ align:start position:0%
+long-term memory. Um not as the
+internalization of knowledge as
+
+ align:start position:0%
+internalization of knowledge as
+ 
+
+ align:start position:0%
+internalization of knowledge as
+individuals but as a process of becoming
+
+ align:start position:0%
+individuals but as a process of becoming
+ 
+
+ align:start position:0%
+individuals but as a process of becoming
+a member of a sustained community of
+
+ align:start position:0%
+a member of a sustained community of
+ 
+
+ align:start position:0%
+a member of a sustained community of
+practice developing an identity as a
+
+ align:start position:0%
+practice developing an identity as a
+ 
+
+ align:start position:0%
+practice developing an identity as a
+member of a community and becoming
+
+ align:start position:0%
+member of a community and becoming
+ 
+
+ align:start position:0%
+member of a community and becoming
+knowledgeably skillful are part of the
+
+ align:start position:0%
+knowledgeably skillful are part of the
+ 
+
+ align:start position:0%
+knowledgeably skillful are part of the
+same process. You cannot separate
+
+ align:start position:0%
+same process. You cannot separate
+ 
+
+ align:start position:0%
+same process. You cannot separate
+storing things in long-term memory from
+
+ align:start position:0%
+storing things in long-term memory from
+ 
+
+ align:start position:0%
+storing things in long-term memory from
+building relationships with other
+
+ align:start position:0%
+building relationships with other
+ 
+
+ align:start position:0%
+building relationships with other
+people. Um with the former motivating
+
+ align:start position:0%
+people. Um with the former motivating
+ 
+
+ align:start position:0%
+people. Um with the former motivating
+one of the key things that we remember
+
+ align:start position:0%
+one of the key things that we remember
+ 
+
+ align:start position:0%
+one of the key things that we remember
+our colleague Michael Pashan you know
+
+ align:start position:0%
+our colleague Michael Pashan you know
+ 
+
+ align:start position:0%
+our colleague Michael Pashan you know
+not a theory of everything where is the
+
+ align:start position:0%
+not a theory of everything where is the
+ 
+
+ align:start position:0%
+not a theory of everything where is the
+motivation with the former motivating
+
+ align:start position:0%
+motivation with the former motivating
+ 
+
+ align:start position:0%
+motivation with the former motivating
+shaping and giving meaning to the latter
+
+ align:start position:0%
+shaping and giving meaning to the latter
+ 
+
+ align:start position:0%
+shaping and giving meaning to the latter
+which it subsumes it is difficult to
+
+ align:start position:0%
+which it subsumes it is difficult to
+ 
+
+ align:start position:0%
+which it subsumes it is difficult to
+move from peripheral to full
+
+ align:start position:0%
+move from peripheral to full
+ 
+
+ align:start position:0%
+move from peripheral to full
+participation in today's world including
+
+ align:start position:0%
+participation in today's world including
+ 
+
+ align:start position:0%
+participation in today's world including
+workplaces and schools thereby
+
+ align:start position:0%
+workplaces and schools thereby
+ 
+
+ align:start position:0%
+workplaces and schools thereby
+developing knowledgeably skilled
+
+ align:start position:0%
+developing knowledgeably skilled
+ 
+
+ align:start position:0%
+developing knowledgeably skilled
+identities. This is because the
+
+ align:start position:0%
+identities. This is because the
+ 
+
+ align:start position:0%
+identities. This is because the
+processes by which we divide and sell
+
+ align:start position:0%
+processes by which we divide and sell
+ 
+
+ align:start position:0%
+processes by which we divide and sell
+labor, which are ubiquitous in our way
+
+ align:start position:0%
+labor, which are ubiquitous in our way
+ 
+
+ align:start position:0%
+labor, which are ubiquitous in our way
+of producing goods and services,
+
+ align:start position:0%
+of producing goods and services,
+ 
+
+ align:start position:0%
+of producing goods and services,
+including knowledge, truncate both the
+
+ align:start position:0%
+including knowledge, truncate both the
+ 
+
+ align:start position:0%
+including knowledge, truncate both the
+movement from peripheral to full
+
+ align:start position:0%
+movement from peripheral to full
+ 
+
+ align:start position:0%
+movement from peripheral to full
+participation in the scope of
+
+ align:start position:0%
+participation in the scope of
+ 
+
+ align:start position:0%
+participation in the scope of
+knowledgeable skill. Taken to an
+
+ align:start position:0%
+knowledgeable skill. Taken to an
+ 
+
+ align:start position:0%
+knowledgeable skill. Taken to an
+extreme, these processes separate
+
+ align:start position:0%
+extreme, these processes separate
+ 
+
+ align:start position:0%
+extreme, these processes separate
+identity from intended forms of
+
+ align:start position:0%
+identity from intended forms of
+ 
+
+ align:start position:0%
+identity from intended forms of
+knowledgeable practice. This view
+
+ align:start position:0%
+knowledgeable practice. This view
+ 
+
+ align:start position:0%
+knowledgeable practice. This view
+implies that learning and failure to
+
+ align:start position:0%
+implies that learning and failure to
+ 
+
+ align:start position:0%
+implies that learning and failure to
+learn are aspects of the same social
+
+ align:start position:0%
+learn are aspects of the same social
+ 
+
+ align:start position:0%
+learn are aspects of the same social
+historical processes and points to
+
+ align:start position:0%
+historical processes and points to
+ 
+
+ align:start position:0%
+historical processes and points to
+relationships between knowledgeability
+
+ align:start position:0%
+relationships between knowledgeability
+ 
+
+ align:start position:0%
+relationships between knowledgeability
+and identity as important focus for
+
+ align:start position:0%
+and identity as important focus for
+ 
+
+ align:start position:0%
+and identity as important focus for
+research. These jerks, these education
+
+ align:start position:0%
+research. These jerks, these education
+ 
+
+ align:start position:0%
+research. These jerks, these education
+psychologists keep trying to convince
+
+ align:start position:0%
+psychologists keep trying to convince
+ 
+
+ align:start position:0%
+psychologists keep trying to convince
+you that what learning is is just
+
+ align:start position:0%
+you that what learning is is just
+ 
+
+ align:start position:0%
+you that what learning is is just
+shoving stuff in your brain. It's not.
+
+ align:start position:0%
+shoving stuff in your brain. It's not.
+ 
+
+ align:start position:0%
+shoving stuff in your brain. It's not.
+There are always people around when
+
+ align:start position:0%
+There are always people around when
+ 
+
+ align:start position:0%
+There are always people around when
+we're learning. Even when we're learning
+
+ align:start position:0%
+we're learning. Even when we're learning
+ 
+
+ align:start position:0%
+we're learning. Even when we're learning
+by ourselves, reading books and stuff
+
+ align:start position:0%
+by ourselves, reading books and stuff
+ 
+
+ align:start position:0%
+by ourselves, reading books and stuff
+like that, there are people in our minds
+
+ align:start position:0%
+like that, there are people in our minds
+ 
+
+ align:start position:0%
+like that, there are people in our minds
+or communities that we see ourselves
+
+ align:start position:0%
+or communities that we see ourselves
+ 
+
+ align:start position:0%
+or communities that we see ourselves
+being part of. Um try, you know, trying
+
+ align:start position:0%
+being part of. Um try, you know, trying
+ 
+
+ align:start position:0%
+being part of. Um try, you know, trying
+to understand how learning happens in
+
+ align:start position:0%
+to understand how learning happens in
+ 
+
+ align:start position:0%
+to understand how learning happens in
+schools or any other learning
+
+ align:start position:0%
+schools or any other learning
+ 
+
+ align:start position:0%
+schools or any other learning
+environment without thinking about the
+
+ align:start position:0%
+environment without thinking about the
+ 
+
+ align:start position:0%
+environment without thinking about the
+social environment that people learn is
+
+ align:start position:0%
+social environment that people learn is
+ 
+
+ align:start position:0%
+social environment that people learn is
+bonkers, is nuts. Um, it just it it it
+
+ align:start position:0%
+bonkers, is nuts. Um, it just it it it
+ 
+
+ align:start position:0%
+bonkers, is nuts. Um, it just it it it
+denies a crucial part of our humanity.
+
+ align:start position:0%
+denies a crucial part of our humanity.
+ 
+
+ align:start position:0%
+denies a crucial part of our humanity.
+Um, here's a a blog post that you can
+
+ align:start position:0%
+Um, here's a a blog post that you can
+ 
+
+ align:start position:0%
+Um, here's a a blog post that you can
+look at later if you sort of follow
+
+ align:start position:0%
+look at later if you sort of follow
+ 
+
+ align:start position:0%
+look at later if you sort of follow
+this. It's by a wonderful math educator
+
+ align:start position:0%
+this. It's by a wonderful math educator
+ 
+
+ align:start position:0%
+this. It's by a wonderful math educator
+named Dan Meyer. Um, who has been trying
+
+ align:start position:0%
+named Dan Meyer. Um, who has been trying
+ 
+
+ align:start position:0%
+named Dan Meyer. Um, who has been trying
+to explain to people why he thinks AI
+
+ align:start position:0%
+to explain to people why he thinks AI
+ 
+
+ align:start position:0%
+to explain to people why he thinks AI
+chat bots are a stupid idea and will not
+
+ align:start position:0%
+chat bots are a stupid idea and will not
+ 
+
+ align:start position:0%
+chat bots are a stupid idea and will not
+work. Um, and and uh and the you know
+
+ align:start position:0%
+work. Um, and and uh and the you know
+ 
+
+ align:start position:0%
+work. Um, and and uh and the you know
+his core issue is like nobody wants to
+
+ align:start position:0%
+his core issue is like nobody wants to
+ 
+
+ align:start position:0%
+his core issue is like nobody wants to
+talk to a computer. Like maybe the
+
+ align:start position:0%
+talk to a computer. Like maybe the
+ 
+
+ align:start position:0%
+talk to a computer. Like maybe the
+computer can provide a sort of perfect
+
+ align:start position:0%
+computer can provide a sort of perfect
+ 
+
+ align:start position:0%
+computer can provide a sort of perfect
+direct instructional sequence, but like
+
+ align:start position:0%
+direct instructional sequence, but like
+ 
+
+ align:start position:0%
+direct instructional sequence, but like
+the kids who are in my eighth grade
+
+ align:start position:0%
+the kids who are in my eighth grade
+ 
+
+ align:start position:0%
+the kids who are in my eighth grade
+algebra classroom, they don't want to be
+
+ align:start position:0%
+algebra classroom, they don't want to be
+ 
+
+ align:start position:0%
+algebra classroom, they don't want to be
+there. They're not interested in
+
+ align:start position:0%
+there. They're not interested in
+ 
+
+ align:start position:0%
+there. They're not interested in
+algebra. Um I love this framing. He's,
+
+ align:start position:0%
+algebra. Um I love this framing. He's,
+ 
+
+ align:start position:0%
+algebra. Um I love this framing. He's,
+you know, he a students attend school to
+
+ align:start position:0%
+you know, he a students attend school to
+ 
+
+ align:start position:0%
+you know, he a students attend school to
+answer two questions. Who am I? And how
+
+ align:start position:0%
+answer two questions. Who am I? And how
+ 
+
+ align:start position:0%
+answer two questions. Who am I? And how
+do I do this? Those are the two things
+
+ align:start position:0%
+do I do this? Those are the two things
+ 
+
+ align:start position:0%
+do I do this? Those are the two things
+they're thinking about all the time. Who
+
+ align:start position:0%
+they're thinking about all the time. Who
+ 
+
+ align:start position:0%
+they're thinking about all the time. Who
+am I? And how do I do this? A chatbot
+
+ align:start position:0%
+am I? And how do I do this? A chatbot
+ 
+
+ align:start position:0%
+am I? And how do I do this? A chatbot
+cannot help you at all with the first
+
+ align:start position:0%
+cannot help you at all with the first
+ 
+
+ align:start position:0%
+cannot help you at all with the first
+question. Um but the other thing I want
+
+ align:start position:0%
+question. Um but the other thing I want
+ 
+
+ align:start position:0%
+question. Um but the other thing I want
+to bring up here and you can disagree
+
+ align:start position:0%
+to bring up here and you can disagree
+ 
+
+ align:start position:0%
+to bring up here and you can disagree
+with that and we'll talk about more when
+
+ align:start position:0%
+with that and we'll talk about more when
+ 
+
+ align:start position:0%
+with that and we'll talk about more when
+we talk about chatbots but um who am I
+
+ align:start position:0%
+we talk about chatbots but um who am I
+ 
+
+ align:start position:0%
+we talk about chatbots but um who am I
+and how do I do this? This is exactly
+
+ align:start position:0%
+and how do I do this? This is exactly
+ 
+
+ align:start position:0%
+and how do I do this? This is exactly
+what Jean La was discussing that
+
+ align:start position:0%
+what Jean La was discussing that
+ 
+
+ align:start position:0%
+what Jean La was discussing that
+identity cannot be separated from the
+
+ align:start position:0%
+identity cannot be separated from the
+ 
+
+ align:start position:0%
+identity cannot be separated from the
+acquisition of knowledge. Um and I think
+
+ align:start position:0%
+acquisition of knowledge. Um and I think
+ 
+
+ align:start position:0%
+acquisition of knowledge. Um and I think
+most of you probably if you think of
+
+ align:start position:0%
+most of you probably if you think of
+ 
+
+ align:start position:0%
+most of you probably if you think of
+your own classroom exper you know think
+
+ align:start position:0%
+your own classroom exper you know think
+ 
+
+ align:start position:0%
+your own classroom exper you know think
+of your own school experience like I
+
+ align:start position:0%
+of your own school experience like I
+ 
+
+ align:start position:0%
+of your own school experience like I
+spent a lot of time in middle school and
+
+ align:start position:0%
+spent a lot of time in middle school and
+ 
+
+ align:start position:0%
+spent a lot of time in middle school and
+high school thinking to myself in one
+
+ align:start position:0%
+high school thinking to myself in one
+ 
+
+ align:start position:0%
+high school thinking to myself in one
+form or another who am I? Um what do
+
+ align:start position:0%
+form or another who am I? Um what do
+ 
+
+ align:start position:0%
+form or another who am I? Um what do
+people think of me? What kinds of
+
+ align:start position:0%
+people think of me? What kinds of
+ 
+
+ align:start position:0%
+people think of me? What kinds of
+relationships do I have? Why am I here?
+
+ align:start position:0%
+relationships do I have? Why am I here?
+ 
+
+ align:start position:0%
+relationships do I have? Why am I here?
+What am I supposed to be doing?
+
+ align:start position:0%
+What am I supposed to be doing?
+ 
+
+ align:start position:0%
+What am I supposed to be doing?
+Um uh Jordan has carried out extensive
+
+ align:start position:0%
+Um uh Jordan has carried out extensive
+ 
+
+ align:start position:0%
+Um uh Jordan has carried out extensive
+field research in the Yakatan Maya wavel
+
+ align:start position:0%
+field research in the Yakatan Maya wavel
+ 
+
+ align:start position:0%
+field research in the Yakatan Maya wavel
+whose apprenticeship is quite different
+
+ align:start position:0%
+whose apprenticeship is quite different
+ 
+
+ align:start position:0%
+whose apprenticeship is quite different
+more effective and less exploitative
+
+ align:start position:0%
+more effective and less exploitative
+ 
+
+ align:start position:0%
+more effective and less exploitative
+than the butchers of marshall study. The
+
+ align:start position:0%
+than the butchers of marshall study. The
+ 
+
+ align:start position:0%
+than the butchers of marshall study. The
+apprentices are peripheral participants
+
+ align:start position:0%
+apprentices are peripheral participants
+ 
+
+ align:start position:0%
+apprentices are peripheral participants
+legitimate peripherence and legitimate
+
+ align:start position:0%
+legitimate peripherence and legitimate
+ 
+
+ align:start position:0%
+legitimate peripherence and legitimate
+peripheral to the practice of midy. What
+
+ align:start position:0%
+peripheral to the practice of midy. What
+ 
+
+ align:start position:0%
+peripheral to the practice of midy. What
+did you all take away from what you
+
+ align:start position:0%
+did you all take away from what you
+ 
+
+ align:start position:0%
+did you all take away from what you
+think like what is legitimate peripheral
+
+ align:start position:0%
+think like what is legitimate peripheral
+ 
+
+ align:start position:0%
+think like what is legitimate peripheral
+practice or periphery? Like what does
+
+ align:start position:0%
+practice or periphery? Like what does
+ 
+
+ align:start position:0%
+practice or periphery? Like what does
+that mean sort of in your own words?
+
+ align:start position:0%
+that mean sort of in your own words?
+ 
+
+ align:start position:0%
+that mean sort of in your own words?
+What do you think Dana? Like they're
+
+ align:start position:0%
+What do you think Dana? Like they're
+ 
+
+ align:start position:0%
+What do you think Dana? Like they're
+doing work that like matters, but
+
+ align:start position:0%
+doing work that like matters, but
+ 
+
+ align:start position:0%
+doing work that like matters, but
+they're not like doing the main work.
+
+ align:start position:0%
+they're not like doing the main work.
+ 
+
+ align:start position:0%
+they're not like doing the main work.
+Like they're doing side tasks that are
+
+ align:start position:0%
+Like they're doing side tasks that are
+ 
+
+ align:start position:0%
+Like they're doing side tasks that are
+like helping them understand the main
+
+ align:start position:0%
+like helping them understand the main
+ 
+
+ align:start position:0%
+like helping them understand the main
+process, but like they themselves are
+
+ align:start position:0%
+process, but like they themselves are
+ 
+
+ align:start position:0%
+process, but like they themselves are
+not like giving birth to the child.
+
+ align:start position:0%
+not like giving birth to the child.
+ 
+
+ align:start position:0%
+not like giving birth to the child.
+Good. Good. And and there's a space
+
+ align:start position:0%
+Good. Good. And and there's a space
+ 
+
+ align:start position:0%
+Good. Good. And and there's a space
+there. A space is held for those people.
+
+ align:start position:0%
+there. A space is held for those people.
+ 
+
+ align:start position:0%
+there. A space is held for those people.
+It is expected that there are going to
+
+ align:start position:0%
+It is expected that there are going to
+ 
+
+ align:start position:0%
+It is expected that there are going to
+be some folks who are hanging around
+
+ align:start position:0%
+be some folks who are hanging around
+ 
+
+ align:start position:0%
+be some folks who are hanging around
+midwives who are not quite midwives yet.
+
+ align:start position:0%
+midwives who are not quite midwives yet.
+ 
+
+ align:start position:0%
+midwives who are not quite midwives yet.
+And that's normal. They're supposed to
+
+ align:start position:0%
+And that's normal. They're supposed to
+ 
+
+ align:start position:0%
+And that's normal. They're supposed to
+be there. Um, it's not a classroom of 20
+
+ align:start position:0%
+be there. Um, it's not a classroom of 20
+ 
+
+ align:start position:0%
+be there. Um, it's not a classroom of 20
+people all lined up who are supposed to
+
+ align:start position:0%
+people all lined up who are supposed to
+ 
+
+ align:start position:0%
+people all lined up who are supposed to
+be doing the same thing all the time.
+
+ align:start position:0%
+be doing the same thing all the time.
+ 
+
+ align:start position:0%
+be doing the same thing all the time.
+There's supposed to be some people in
+
+ align:start position:0%
+There's supposed to be some people in
+ 
+
+ align:start position:0%
+There's supposed to be some people in
+the middle and there's supposed to be
+
+ align:start position:0%
+the middle and there's supposed to be
+ 
+
+ align:start position:0%
+the middle and there's supposed to be
+some people on the outside. I want to
+
+ align:start position:0%
+some people on the outside. I want to
+ 
+
+ align:start position:0%
+some people on the outside. I want to
+pose a question too to think of the
+
+ align:start position:0%
+pose a question too to think of the
+ 
+
+ align:start position:0%
+pose a question too to think of the
+relationship between what uh Gene Le was
+
+ align:start position:0%
+relationship between what uh Gene Le was
+ 
+
+ align:start position:0%
+relationship between what uh Gene Le was
+talking about the midwives and the
+
+ align:start position:0%
+talking about the midwives and the
+ 
+
+ align:start position:0%
+talking about the midwives and the
+butchers in the thinking. What's the
+
+ align:start position:0%
+butchers in the thinking. What's the
+ 
+
+ align:start position:0%
+butchers in the thinking. What's the
+difference between peripheral
+
+ align:start position:0%
+difference between peripheral
+ 
+
+ align:start position:0%
+difference between peripheral
+participants and legitimately peripheral
+
+ align:start position:0%
+participants and legitimately peripheral
+ 
+
+ align:start position:0%
+participants and legitimately peripheral
+participants? Do folks remember what
+
+ align:start position:0%
+participants? Do folks remember what
+ 
+
+ align:start position:0%
+participants? Do folks remember what
+they described about the butchers? Yeah.
+
+ align:start position:0%
+they described about the butchers? Yeah.
+ 
+
+ align:start position:0%
+they described about the butchers? Yeah.
+Yeah. Yeah. Was that the butchers even
+
+ align:start position:0%
+Yeah. Yeah. Was that the butchers even
+ 
+
+ align:start position:0%
+Yeah. Yeah. Was that the butchers even
+though like they were doing peripheral
+
+ align:start position:0%
+though like they were doing peripheral
+ 
+
+ align:start position:0%
+though like they were doing peripheral
+work, they were separated in space from
+
+ align:start position:0%
+work, they were separated in space from
+ 
+
+ align:start position:0%
+work, they were separated in space from
+the like
+
+ align:start position:0%
+the like
+ 
+
+ align:start position:0%
+the like
+the experts. So they didn't they
+
+ align:start position:0%
+the experts. So they didn't they
+ 
+
+ align:start position:0%
+the experts. So they didn't they
+wouldn't really pick up on things as
+
+ align:start position:0%
+wouldn't really pick up on things as
+ 
+
+ align:start position:0%
+wouldn't really pick up on things as
+opposed to midwives who still observe
+
+ align:start position:0%
+opposed to midwives who still observe
+ 
+
+ align:start position:0%
+opposed to midwives who still observe
+what the legitimate the expert was
+
+ align:start position:0%
+what the legitimate the expert was
+ 
+
+ align:start position:0%
+what the legitimate the expert was
+doing. Yeah. So what does that mean in
+
+ align:start position:0%
+doing. Yeah. So what does that mean in
+ 
+
+ align:start position:0%
+doing. Yeah. So what does that mean in
+terms of being a part of that community
+
+ align:start position:0%
+terms of being a part of that community
+ 
+
+ align:start position:0%
+terms of being a part of that community
+and then shaping the learning that
+
+ align:start position:0%
+and then shaping the learning that
+ 
+
+ align:start position:0%
+and then shaping the learning that
+they're able to
+
+ align:start position:0%
+they're able to
+ 
+
+ align:start position:0%
+they're able to
+acquire? If I'm a butcher and I'm I'm
+
+ align:start position:0%
+acquire? If I'm a butcher and I'm I'm
+ 
+
+ align:start position:0%
+acquire? If I'm a butcher and I'm I'm
+part of the community, if I'm standing
+
+ align:start position:0%
+part of the community, if I'm standing
+ 
+
+ align:start position:0%
+part of the community, if I'm standing
+over here cutting my meat, using my
+
+ align:start position:0%
+over here cutting my meat, using my
+ 
+
+ align:start position:0%
+over here cutting my meat, using my
+tool, that's all I get to do. And then
+
+ align:start position:0%
+tool, that's all I get to do. And then
+ 
+
+ align:start position:0%
+tool, that's all I get to do. And then
+Justin's over there, you know, hanging
+
+ align:start position:0%
+Justin's over there, you know, hanging
+ 
+
+ align:start position:0%
+Justin's over there, you know, hanging
+out with the pig or whatever it is,
+
+ align:start position:0%
+out with the pig or whatever it is,
+ 
+
+ align:start position:0%
+out with the pig or whatever it is,
+right? What am I losing then? The social
+
+ align:start position:0%
+right? What am I losing then? The social
+ 
+
+ align:start position:0%
+right? What am I losing then? The social
+aspect. The social aspect, right? Am I
+
+ align:start position:0%
+aspect. The social aspect, right? Am I
+ 
+
+ align:start position:0%
+aspect. The social aspect, right? Am I
+able to observe him? Can I see what he's
+
+ align:start position:0%
+able to observe him? Can I see what he's
+ 
+
+ align:start position:0%
+able to observe him? Can I see what he's
+doing when he leaves? Can I pick it up
+
+ align:start position:0%
+doing when he leaves? Can I pick it up
+ 
+
+ align:start position:0%
+doing when he leaves? Can I pick it up
+from watching? Totally miss that. But
+
+ align:start position:0%
+from watching? Totally miss that. But
+ 
+
+ align:start position:0%
+from watching? Totally miss that. But
+then what about the midwife? How's that
+
+ align:start position:0%
+then what about the midwife? How's that
+ 
+
+ align:start position:0%
+then what about the midwife? How's that
+different?
+
+ align:start position:0%
+different?
+ 
+
+ align:start position:0%
+different?
+How do they describe the midwife
+
+ align:start position:0%
+How do they describe the midwife
+ 
+
+ align:start position:0%
+How do they describe the midwife
+relationship? Justin, I hope this is
+
+ align:start position:0%
+relationship? Justin, I hope this is
+ 
+
+ align:start position:0%
+relationship? Justin, I hope this is
+okay. I love this book. So, yeah. Go
+
+ align:start position:0%
+okay. I love this book. So, yeah. Go
+ 
+
+ align:start position:0%
+okay. I love this book. So, yeah. Go
+ahead. Um, so I think the one of the
+
+ align:start position:0%
+ahead. Um, so I think the one of the
+ 
+
+ align:start position:0%
+ahead. Um, so I think the one of the
+main differences is beyond the fact that
+
+ align:start position:0%
+main differences is beyond the fact that
+ 
+
+ align:start position:0%
+main differences is beyond the fact that
+it wasn't supposed to be more efficient.
+
+ align:start position:0%
+it wasn't supposed to be more efficient.
+ 
+
+ align:start position:0%
+it wasn't supposed to be more efficient.
+So there was no capitalist aspect to it.
+
+ align:start position:0%
+So there was no capitalist aspect to it.
+ 
+
+ align:start position:0%
+So there was no capitalist aspect to it.
+There was a lot of culture embedded in
+
+ align:start position:0%
+There was a lot of culture embedded in
+ 
+
+ align:start position:0%
+There was a lot of culture embedded in
+it. So like the daughter of a midwife
+
+ align:start position:0%
+it. So like the daughter of a midwife
+ 
+
+ align:start position:0%
+it. So like the daughter of a midwife
+would become midwife, meaning that at 5
+
+ align:start position:0%
+would become midwife, meaning that at 5
+ 
+
+ align:start position:0%
+would become midwife, meaning that at 5
+years old, they would already kind of be
+
+ align:start position:0%
+years old, they would already kind of be
+ 
+
+ align:start position:0%
+years old, they would already kind of be
+present in that situation and start like
+
+ align:start position:0%
+present in that situation and start like
+ 
+
+ align:start position:0%
+present in that situation and start like
+picking up on what was going on and then
+
+ align:start position:0%
+picking up on what was going on and then
+ 
+
+ align:start position:0%
+picking up on what was going on and then
+progressively have a more like
+
+ align:start position:0%
+progressively have a more like
+ 
+
+ align:start position:0%
+progressively have a more like
+protagonist role to that experience. So
+
+ align:start position:0%
+protagonist role to that experience. So
+ 
+
+ align:start position:0%
+protagonist role to that experience. So
+yeah. So like although both could be
+
+ align:start position:0%
+yeah. So like although both could be
+ 
+
+ align:start position:0%
+yeah. So like although both could be
+argued as peripheral, right? We're we're
+
+ align:start position:0%
+argued as peripheral, right? We're we're
+ 
+
+ align:start position:0%
+argued as peripheral, right? We're we're
+in the same space. We're hanging out.
+
+ align:start position:0%
+in the same space. We're hanging out.
+ 
+
+ align:start position:0%
+in the same space. We're hanging out.
+Like who's welcome in the community and
+
+ align:start position:0%
+Like who's welcome in the community and
+ 
+
+ align:start position:0%
+Like who's welcome in the community and
+then what type of knowledge are you able
+
+ align:start position:0%
+then what type of knowledge are you able
+ 
+
+ align:start position:0%
+then what type of knowledge are you able
+to gain from that type of peripheral
+
+ align:start position:0%
+to gain from that type of peripheral
+ 
+
+ align:start position:0%
+to gain from that type of peripheral
+participation? It's kind of cool. It's
+
+ align:start position:0%
+participation? It's kind of cool. It's
+ 
+
+ align:start position:0%
+participation? It's kind of cool. It's
+subtle, right? Yeah. All right. That's
+
+ align:start position:0%
+subtle, right? Yeah. All right. That's
+ 
+
+ align:start position:0%
+subtle, right? Yeah. All right. That's
+all I got. I have Can I make Okay.
+
+ align:start position:0%
+all I got. I have Can I make Okay.
+ 
+
+ align:start position:0%
+all I got. I have Can I make Okay.
+um the the previous paragraph I had a
+
+ align:start position:0%
+um the the previous paragraph I had a
+ 
+
+ align:start position:0%
+um the the previous paragraph I had a
+lot of reflection about it and I don't
+
+ align:start position:0%
+lot of reflection about it and I don't
+ 
+
+ align:start position:0%
+lot of reflection about it and I don't
+nec like kind of that in some aspects
+
+ align:start position:0%
+nec like kind of that in some aspects
+ 
+
+ align:start position:0%
+nec like kind of that in some aspects
+I'm not sure how you feel about it but
+
+ align:start position:0%
+I'm not sure how you feel about it but
+ 
+
+ align:start position:0%
+I'm not sure how you feel about it but
+like I really like the point that he
+
+ align:start position:0%
+like I really like the point that he
+ 
+
+ align:start position:0%
+like I really like the point that he
+makes about like learning kind of makes
+
+ align:start position:0%
+makes about like learning kind of makes
+ 
+
+ align:start position:0%
+makes about like learning kind of makes
+forms your identity as part of this
+
+ align:start position:0%
+forms your identity as part of this
+ 
+
+ align:start position:0%
+forms your identity as part of this
+social group right and I think that
+
+ align:start position:0%
+social group right and I think that
+ 
+
+ align:start position:0%
+social group right and I think that
+really applies to kids for example kind
+
+ align:start position:0%
+really applies to kids for example kind
+ 
+
+ align:start position:0%
+really applies to kids for example kind
+of like they come from this per
+
+ align:start position:0%
+of like they come from this per
+ 
+
+ align:start position:0%
+of like they come from this per
+peripheral existence and develop their
+
+ align:start position:0%
+peripheral existence and develop their
+ 
+
+ align:start position:0%
+peripheral existence and develop their
+own identities and become like a
+
+ align:start position:0%
+own identities and become like a
+ 
+
+ align:start position:0%
+own identities and become like a
+committed like functioning part of
+
+ align:start position:0%
+committed like functioning part of
+ 
+
+ align:start position:0%
+committed like functioning part of
+society. But then it really made me
+
+ align:start position:0%
+society. But then it really made me
+ 
+
+ align:start position:0%
+society. But then it really made me
+think like oh how do we think about it
+
+ align:start position:0%
+think like oh how do we think about it
+ 
+
+ align:start position:0%
+think like oh how do we think about it
+like from an abbleist um perspective
+
+ align:start position:0%
+like from an abbleist um perspective
+ 
+
+ align:start position:0%
+like from an abbleist um perspective
+right where people cannot acquire
+
+ align:start position:0%
+right where people cannot acquire
+ 
+
+ align:start position:0%
+right where people cannot acquire
+certain knowledges or certain abilities
+
+ align:start position:0%
+certain knowledges or certain abilities
+ 
+
+ align:start position:0%
+certain knowledges or certain abilities
+and does that mean they have less of an
+
+ align:start position:0%
+and does that mean they have less of an
+ 
+
+ align:start position:0%
+and does that mean they have less of an
+identity like I really thought about
+
+ align:start position:0%
+identity like I really thought about
+ 
+
+ align:start position:0%
+identity like I really thought about
+that for a while and at the same time
+
+ align:start position:0%
+that for a while and at the same time
+ 
+
+ align:start position:0%
+that for a while and at the same time
+there's like a criticism in the book
+
+ align:start position:0%
+there's like a criticism in the book
+ 
+
+ align:start position:0%
+there's like a criticism in the book
+about like commoditization of knowledge
+
+ align:start position:0%
+about like commoditization of knowledge
+ 
+
+ align:start position:0%
+about like commoditization of knowledge
+because before like with midwives etc
+
+ align:start position:0%
+because before like with midwives etc
+ 
+
+ align:start position:0%
+because before like with midwives etc
+like okay it was this really specific
+
+ align:start position:0%
+like okay it was this really specific
+ 
+
+ align:start position:0%
+like okay it was this really specific
+group of people teaching this very kind
+
+ align:start position:0%
+group of people teaching this very kind
+ 
+
+ align:start position:0%
+group of people teaching this very kind
+of like expertise u whereas today we
+
+ align:start position:0%
+of like expertise u whereas today we
+ 
+
+ align:start position:0%
+of like expertise u whereas today we
+have universities and we have schools or
+
+ align:start position:0%
+have universities and we have schools or
+ 
+
+ align:start position:0%
+have universities and we have schools or
+you can kind of get to whatever class
+
+ align:start position:0%
+you can kind of get to whatever class
+ 
+
+ align:start position:0%
+you can kind of get to whatever class
+and learn things, but it's not
+
+ align:start position:0%
+and learn things, but it's not
+ 
+
+ align:start position:0%
+and learn things, but it's not
+necessarily all bad, right? Because that
+
+ align:start position:0%
+necessarily all bad, right? Because that
+ 
+
+ align:start position:0%
+necessarily all bad, right? Because that
+would imply that if you're the daughter
+
+ align:start position:0%
+would imply that if you're the daughter
+ 
+
+ align:start position:0%
+would imply that if you're the daughter
+of the midwife, you don't really have a
+
+ align:start position:0%
+of the midwife, you don't really have a
+ 
+
+ align:start position:0%
+of the midwife, you don't really have a
+lot of say into becoming or not a
+
+ align:start position:0%
+lot of say into becoming or not a
+ 
+
+ align:start position:0%
+lot of say into becoming or not a
+midwife, right? Like the way that
+
+ align:start position:0%
+midwife, right? Like the way that
+ 
+
+ align:start position:0%
+midwife, right? Like the way that
+society was structured back then likely
+
+ align:start position:0%
+society was structured back then likely
+ 
+
+ align:start position:0%
+society was structured back then likely
+you would kind of become one because
+
+ align:start position:0%
+you would kind of become one because
+ 
+
+ align:start position:0%
+you would kind of become one because
+that's what expected of you. Whereas
+
+ align:start position:0%
+that's what expected of you. Whereas
+ 
+
+ align:start position:0%
+that's what expected of you. Whereas
+like when you kind of can choose that
+
+ align:start position:0%
+like when you kind of can choose that
+ 
+
+ align:start position:0%
+like when you kind of can choose that
+you have some sort of agency and power
+
+ align:start position:0%
+you have some sort of agency and power
+ 
+
+ align:start position:0%
+you have some sort of agency and power
+even if you won't have that exposure as
+
+ align:start position:0%
+even if you won't have that exposure as
+ 
+
+ align:start position:0%
+even if you won't have that exposure as
+a peripheral participant since a since
+
+ align:start position:0%
+a peripheral participant since a since
+ 
+
+ align:start position:0%
+a peripheral participant since a since
+you were a kid. So like it really made
+
+ align:start position:0%
+you were a kid. So like it really made
+ 
+
+ align:start position:0%
+you were a kid. So like it really made
+me think of many things. Great. Good.
+
+ align:start position:0%
+me think of many things. Great. Good.
+ 
+
+ align:start position:0%
+me think of many things. Great. Good.
+Good. And and none of them have to be
+
+ align:start position:0%
+Good. And and none of them have to be
+ 
+
+ align:start position:0%
+Good. And and none of them have to be
+resolved either. Um you know that that
+
+ align:start position:0%
+resolved either. Um you know that that
+ 
+
+ align:start position:0%
+resolved either. Um you know that that
+uh um probably probably some important
+
+ align:start position:0%
+uh um probably probably some important
+ 
+
+ align:start position:0%
+uh um probably probably some important
+things to take away are like how Jean
+
+ align:start position:0%
+things to take away are like how Jean
+ 
+
+ align:start position:0%
+things to take away are like how Jean
+assigns values to these different kinds
+
+ align:start position:0%
+assigns values to these different kinds
+ 
+
+ align:start position:0%
+assigns values to these different kinds
+of institutions. like he thinks it's a
+
+ align:start position:0%
+of institutions. like he thinks it's a
+ 
+
+ align:start position:0%
+of institutions. like he thinks it's a
+big problem, you know, a big problem
+
+ align:start position:0%
+big problem, you know, a big problem
+ 
+
+ align:start position:0%
+big problem, you know, a big problem
+with schools and university is sort of
+
+ align:start position:0%
+with schools and university is sort of
+ 
+
+ align:start position:0%
+with schools and university is sort of
+ripping knowledge away from these
+
+ align:start position:0%
+ripping knowledge away from these
+ 
+
+ align:start position:0%
+ripping knowledge away from these
+broader social contexts. Um that you go
+
+ align:start position:0%
+broader social contexts. Um that you go
+ 
+
+ align:start position:0%
+broader social contexts. Um that you go
+and take a physics class and in the vast
+
+ align:start position:0%
+and take a physics class and in the vast
+ 
+
+ align:start position:0%
+and take a physics class and in the vast
+majority of physics 101 classes, no one
+
+ align:start position:0%
+majority of physics 101 classes, no one
+ 
+
+ align:start position:0%
+majority of physics 101 classes, no one
+is trying to get you to be a physicist.
+
+ align:start position:0%
+is trying to get you to be a physicist.
+ 
+
+ align:start position:0%
+is trying to get you to be a physicist.
+They're not trying to get you to develop
+
+ align:start position:0%
+They're not trying to get you to develop
+ 
+
+ align:start position:0%
+They're not trying to get you to develop
+the identity of a physicist. They're
+
+ align:start position:0%
+the identity of a physicist. They're
+ 
+
+ align:start position:0%
+the identity of a physicist. They're
+just trying to teach you the physics.
+
+ align:start position:0%
+just trying to teach you the physics.
+ 
+
+ align:start position:0%
+just trying to teach you the physics.
+And what is lost sort of in that? Of
+
+ align:start position:0%
+And what is lost sort of in that? Of
+ 
+
+ align:start position:0%
+And what is lost sort of in that? Of
+course, what's pretty rad about like
+
+ align:start position:0%
+course, what's pretty rad about like
+ 
+
+ align:start position:0%
+course, what's pretty rad about like
+walking into a campus full of people who
+
+ align:start position:0%
+walking into a campus full of people who
+ 
+
+ align:start position:0%
+walking into a campus full of people who
+will be like, "Yeah, I'll teach you any
+
+ align:start position:0%
+will be like, "Yeah, I'll teach you any
+ 
+
+ align:start position:0%
+will be like, "Yeah, I'll teach you any
+of these atomized little things for you
+
+ align:start position:0%
+of these atomized little things for you
+ 
+
+ align:start position:0%
+of these atomized little things for you
+to learn." like that seems kind of cool
+
+ align:start position:0%
+to learn." like that seems kind of cool
+ 
+
+ align:start position:0%
+to learn." like that seems kind of cool
+too. Um it is worth noting that it would
+
+ align:start position:0%
+too. Um it is worth noting that it would
+ 
+
+ align:start position:0%
+too. Um it is worth noting that it would
+be difficult to find evidence that
+
+ align:start position:0%
+be difficult to find evidence that
+ 
+
+ align:start position:0%
+be difficult to find evidence that
+teaching is the mode of knowledge
+
+ align:start position:0%
+teaching is the mode of knowledge
+ 
+
+ align:start position:0%
+teaching is the mode of knowledge
+transmission amongst the midwives. Um he
+
+ align:start position:0%
+transmission amongst the midwives. Um he
+ 
+
+ align:start position:0%
+transmission amongst the midwives. Um he
+makes this claim that like you wouldn't
+
+ align:start position:0%
+makes this claim that like you wouldn't
+ 
+
+ align:start position:0%
+makes this claim that like you wouldn't
+find direct instruction amongst the
+
+ align:start position:0%
+find direct instruction amongst the
+ 
+
+ align:start position:0%
+find direct instruction amongst the
+midwives. Um I mean Jordan did the fil
+
+ align:start position:0%
+midwives. Um I mean Jordan did the fil
+ 
+
+ align:start position:0%
+midwives. Um I mean Jordan did the fil
+work and not me. That seems totally
+
+ align:start position:0%
+work and not me. That seems totally
+ 
+
+ align:start position:0%
+work and not me. That seems totally
+laughable to me. I've spent time with
+
+ align:start position:0%
+laughable to me. I've spent time with
+ 
+
+ align:start position:0%
+laughable to me. I've spent time with
+lots of people of lots of ages, learns
+
+ align:start position:0%
+lots of people of lots of ages, learns
+ 
+
+ align:start position:0%
+lots of people of lots of ages, learns
+lots of kinds of things and people are
+
+ align:start position:0%
+lots of kinds of things and people are
+ 
+
+ align:start position:0%
+lots of kinds of things and people are
+always transmitting and explaining
+
+ align:start position:0%
+always transmitting and explaining
+ 
+
+ align:start position:0%
+always transmitting and explaining
+stuff. It's always sort of nested in
+
+ align:start position:0%
+stuff. It's always sort of nested in
+ 
+
+ align:start position:0%
+stuff. It's always sort of nested in
+there. Um but there's a kind of politics
+
+ align:start position:0%
+there. Um but there's a kind of politics
+ 
+
+ align:start position:0%
+there. Um but there's a kind of politics
+of John Lave like we don't even need to
+
+ align:start position:0%
+of John Lave like we don't even need to
+ 
+
+ align:start position:0%
+of John Lave like we don't even need to
+explain these things. We don't even need
+
+ align:start position:0%
+explain these things. We don't even need
+ 
+
+ align:start position:0%
+explain these things. We don't even need
+to teach these people. We can learn it
+
+ align:start position:0%
+to teach these people. We can learn it
+ 
+
+ align:start position:0%
+to teach these people. We can learn it
+just like babies learn it sort of in
+
+ align:start position:0%
+just like babies learn it sort of in
+ 
+
+ align:start position:0%
+just like babies learn it sort of in
+their natural environment. You just you
+
+ align:start position:0%
+their natural environment. You just you
+ 
+
+ align:start position:0%
+their natural environment. You just you
+know just like you have to surround
+
+ align:start position:0%
+know just like you have to surround
+ 
+
+ align:start position:0%
+know just like you have to surround
+babies with language and they'll learn
+
+ align:start position:0%
+babies with language and they'll learn
+ 
+
+ align:start position:0%
+babies with language and they'll learn
+language. You surround young girls with
+
+ align:start position:0%
+language. You surround young girls with
+ 
+
+ align:start position:0%
+language. You surround young girls with
+birth and pregnancy and they learn
+
+ align:start position:0%
+birth and pregnancy and they learn
+ 
+
+ align:start position:0%
+birth and pregnancy and they learn
+midwiffery. Um
+
+ align:start position:0%
+midwiffery. Um
+ 
+
+ align:start position:0%
+midwiffery. Um
+uh apprenticeship happens as a way in
+
+ align:start position:0%
+uh apprenticeship happens as a way in
+ 
+
+ align:start position:0%
+uh apprenticeship happens as a way in
+the course of daily life. It may not be
+
+ align:start position:0%
+the course of daily life. It may not be
+ 
+
+ align:start position:0%
+the course of daily life. It may not be
+recognized as teaching effort at all.
+
+ align:start position:0%
+recognized as teaching effort at all.
+ 
+
+ align:start position:0%
+recognized as teaching effort at all.
+Again sort of doubling down like there's
+
+ align:start position:0%
+Again sort of doubling down like there's
+ 
+
+ align:start position:0%
+Again sort of doubling down like there's
+no instruction here. If there
+
+ align:start position:0%
+no instruction here. If there
+ 
+
+ align:start position:0%
+no instruction here. If there
+instruction, the people are lying to you
+
+ align:start position:0%
+instruction, the people are lying to you
+ 
+
+ align:start position:0%
+instruction, the people are lying to you
+and you should despise them. Um, a Maya
+
+ align:start position:0%
+and you should despise them. Um, a Maya
+ 
+
+ align:start position:0%
+and you should despise them. Um, a Maya
+girl who eventually became a midwife
+
+ align:start position:0%
+girl who eventually became a midwife
+ 
+
+ align:start position:0%
+girl who eventually became a midwife
+most likely as a mother, a grandmother
+
+ align:start position:0%
+most likely as a mother, a grandmother
+ 
+
+ align:start position:0%
+most likely as a mother, a grandmother
+as a midwife. Girls in such families
+
+ align:start position:0%
+as a midwife. Girls in such families
+ 
+
+ align:start position:0%
+as a midwife. Girls in such families
+without being identified as apprentice
+
+ align:start position:0%
+without being identified as apprentice
+ 
+
+ align:start position:0%
+without being identified as apprentice
+midwives absorb the effence of midwife
+
+ align:start position:0%
+midwives absorb the effence of midwife
+ 
+
+ align:start position:0%
+midwives absorb the effence of midwife
+practice as well as specific knowledge
+
+ align:start position:0%
+practice as well as specific knowledge
+ 
+
+ align:start position:0%
+practice as well as specific knowledge
+about many procedures simply in the
+
+ align:start position:0%
+about many procedures simply in the
+ 
+
+ align:start position:0%
+about many procedures simply in the
+process of growing up. They know what
+
+ align:start position:0%
+process of growing up. They know what
+ 
+
+ align:start position:0%
+process of growing up. They know what
+the life of a midwife is like, what
+
+ align:start position:0%
+the life of a midwife is like, what
+ 
+
+ align:start position:0%
+the life of a midwife is like, what
+kinds of stories the women and men who
+
+ align:start position:0%
+kinds of stories the women and men who
+ 
+
+ align:start position:0%
+kinds of stories the women and men who
+come to consult her tell, what kind of
+
+ align:start position:0%
+come to consult her tell, what kind of
+ 
+
+ align:start position:0%
+come to consult her tell, what kind of
+herbs and other remedies might be needed
+
+ align:start position:0%
+herbs and other remedies might be needed
+ 
+
+ align:start position:0%
+herbs and other remedies might be needed
+to collected. As young children, they
+
+ align:start position:0%
+to collected. As young children, they
+ 
+
+ align:start position:0%
+to collected. As young children, they
+might be sitting quietly in their
+
+ align:start position:0%
+might be sitting quietly in their
+ 
+
+ align:start position:0%
+might be sitting quietly in their
+corner. As their minister mother
+
+ align:start position:0%
+corner. As their minister mother
+ 
+
+ align:start position:0%
+corner. As their minister mother
+administers a prenatal massage, they
+
+ align:start position:0%
+administers a prenatal massage, they
+ 
+
+ align:start position:0%
+administers a prenatal massage, they
+would hear stories of difficult cases of
+
+ align:start position:0%
+would hear stories of difficult cases of
+ 
+
+ align:start position:0%
+would hear stories of difficult cases of
+miraculous outcomes and the like. As
+
+ align:start position:0%
+miraculous outcomes and the like. As
+ 
+
+ align:start position:0%
+miraculous outcomes and the like. As
+they grow older, they may be passing
+
+ align:start position:0%
+they grow older, they may be passing
+ 
+
+ align:start position:0%
+they grow older, they may be passing
+messages, running errands, getting
+
+ align:start position:0%
+messages, running errands, getting
+ 
+
+ align:start position:0%
+messages, running errands, getting
+needed supplies. A young girl might be
+
+ align:start position:0%
+needed supplies. A young girl might be
+ 
+
+ align:start position:0%
+needed supplies. A young girl might be
+present as her mother stops for a
+
+ align:start position:0%
+present as her mother stops for a
+ 
+
+ align:start position:0%
+present as her mother stops for a
+postpartum visit after the daily
+
+ align:start position:0%
+postpartum visit after the daily
+ 
+
+ align:start position:0%
+postpartum visit after the daily
+shopping trip to the market. Eventually,
+
+ align:start position:0%
+shopping trip to the market. Eventually,
+ 
+
+ align:start position:0%
+shopping trip to the market. Eventually,
+after she has a child herself, she might
+
+ align:start position:0%
+after she has a child herself, she might
+ 
+
+ align:start position:0%
+after she has a child herself, she might
+come along to her birth, perhaps because
+
+ align:start position:0%
+come along to her birth, perhaps because
+ 
+
+ align:start position:0%
+come along to her birth, perhaps because
+her alien grandmother needs someone to
+
+ align:start position:0%
+her alien grandmother needs someone to
+ 
+
+ align:start position:0%
+her alien grandmother needs someone to
+walk with, and thus finds herself doing
+
+ align:start position:0%
+walk with, and thus finds herself doing
+ 
+
+ align:start position:0%
+walk with, and thus finds herself doing
+for the woman in labor what other women
+
+ align:start position:0%
+for the woman in labor what other women
+ 
+
+ align:start position:0%
+for the woman in labor what other women
+had done for her when she gave birth.
+
+ align:start position:0%
+had done for her when she gave birth.
+ 
+
+ align:start position:0%
+had done for her when she gave birth.
+That is, she may take a turn at
+
+ align:start position:0%
+That is, she may take a turn at
+ 
+
+ align:start position:0%
+That is, she may take a turn at
+supporting the laboring woman.
+
+ align:start position:0%
+supporting the laboring woman.
+ 
+
+ align:start position:0%
+supporting the laboring woman.
+Eventually, she may even administer
+
+ align:start position:0%
+Eventually, she may even administer
+ 
+
+ align:start position:0%
+Eventually, she may even administer
+prenatal massages to the selected
+
+ align:start position:0%
+prenatal massages to the selected
+ 
+
+ align:start position:0%
+prenatal massages to the selected
+clients. At some point, she may decide
+
+ align:start position:0%
+clients. At some point, she may decide
+ 
+
+ align:start position:0%
+clients. At some point, she may decide
+she actually wants to do this kind of
+
+ align:start position:0%
+she actually wants to do this kind of
+ 
+
+ align:start position:0%
+she actually wants to do this kind of
+work. She then pays more attention, but
+
+ align:start position:0%
+work. She then pays more attention, but
+ 
+
+ align:start position:0%
+work. She then pays more attention, but
+only rarely does she ask questions. Her
+
+ align:start position:0%
+only rarely does she ask questions. Her
+ 
+
+ align:start position:0%
+only rarely does she ask questions. Her
+mentor sees their association, primarily
+
+ align:start position:0%
+mentor sees their association, primarily
+ 
+
+ align:start position:0%
+mentor sees their association, primarily
+one that is of some use to her. Rosa
+
+ align:start position:0%
+one that is of some use to her. Rosa
+ 
+
+ align:start position:0%
+one that is of some use to her. Rosa
+already knows how to do a massage, so I
+
+ align:start position:0%
+already knows how to do a massage, so I
+ 
+
+ align:start position:0%
+already knows how to do a massage, so I
+can send her if I'm too busy. Um, that
+
+ align:start position:0%
+can send her if I'm too busy. Um, that
+ 
+
+ align:start position:0%
+can send her if I'm too busy. Um, that
+is just a beautiful description of kind
+
+ align:start position:0%
+is just a beautiful description of kind
+ 
+
+ align:start position:0%
+is just a beautiful description of kind
+of legitimate peripheral participation,
+
+ align:start position:0%
+of legitimate peripheral participation,
+ 
+
+ align:start position:0%
+of legitimate peripheral participation,
+moving from the periphery to the center.
+
+ align:start position:0%
+moving from the periphery to the center.
+ 
+
+ align:start position:0%
+moving from the periphery to the center.
+You just watch this thing for a while
+
+ align:start position:0%
+You just watch this thing for a while
+ 
+
+ align:start position:0%
+You just watch this thing for a while
+and then your mom's hands are a little
+
+ align:start position:0%
+and then your mom's hands are a little
+ 
+
+ align:start position:0%
+and then your mom's hands are a little
+sore and so you do the massage this time
+
+ align:start position:0%
+sore and so you do the massage this time
+ 
+
+ align:start position:0%
+sore and so you do the massage this time
+and you know how to move the massage cuz
+
+ align:start position:0%
+and you know how to move the massage cuz
+ 
+
+ align:start position:0%
+and you know how to move the massage cuz
+it happened to you. You've seen it a
+
+ align:start position:0%
+it happened to you. You've seen it a
+ 
+
+ align:start position:0%
+it happened to you. You've seen it a
+zillion times. Are any of you part of
+
+ align:start position:0%
+zillion times. Are any of you part of
+ 
+
+ align:start position:0%
+zillion times. Are any of you part of
+sort of clubs or groups at MIT that have
+
+ align:start position:0%
+sort of clubs or groups at MIT that have
+ 
+
+ align:start position:0%
+sort of clubs or groups at MIT that have
+learning that feels like this?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess like technically a lot of
+
+ align:start position:0%
+I guess like technically a lot of
+ 
+
+ align:start position:0%
+I guess like technically a lot of
+theater clubs are similar where people
+
+ align:start position:0%
+theater clubs are similar where people
+ 
+
+ align:start position:0%
+theater clubs are similar where people
+are just doing this like how do you
+
+ align:start position:0%
+are just doing this like how do you
+ 
+
+ align:start position:0%
+are just doing this like how do you
+become a stage manager? I don't know.
+
+ align:start position:0%
+become a stage manager? I don't know.
+ 
+
+ align:start position:0%
+become a stage manager? I don't know.
+Look at what the stage hand. Oh, and and
+
+ align:start position:0%
+Look at what the stage hand. Oh, and and
+ 
+
+ align:start position:0%
+Look at what the stage hand. Oh, and and
+the other thing is like you start as a
+
+ align:start position:0%
+the other thing is like you start as a
+ 
+
+ align:start position:0%
+the other thing is like you start as a
+stage hand like Yeah. Yeah. Yeah. Come,
+
+ align:start position:0%
+stage hand like Yeah. Yeah. Yeah. Come,
+ 
+
+ align:start position:0%
+stage hand like Yeah. Yeah. Yeah. Come,
+you know, you watch some theater. Yeah.
+
+ align:start position:0%
+you know, you watch some theater. Yeah.
+ 
+
+ align:start position:0%
+you know, you watch some theater. Yeah.
+You know, just stand there and like
+
+ align:start position:0%
+You know, just stand there and like
+ 
+
+ align:start position:0%
+You know, just stand there and like
+you're like between the second and third
+
+ align:start position:0%
+you're like between the second and third
+ 
+
+ align:start position:0%
+you're like between the second and third
+act like hand this prop to that person.
+
+ align:start position:0%
+act like hand this prop to that person.
+ 
+
+ align:start position:0%
+act like hand this prop to that person.
+Um and you're probably never going to
+
+ align:start position:0%
+Um and you're probably never going to
+ 
+
+ align:start position:0%
+Um and you're probably never going to
+take stage manager class. You're just
+
+ align:start position:0%
+take stage manager class. You're just
+ 
+
+ align:start position:0%
+take stage manager class. You're just
+going to hand that prop once and then
+
+ align:start position:0%
+going to hand that prop once and then
+ 
+
+ align:start position:0%
+going to hand that prop once and then
+you're the prop master and then the
+
+ align:start position:0%
+you're the prop master and then the
+ 
+
+ align:start position:0%
+you're the prop master and then the
+stage manager gets sick and you do it
+
+ align:start position:0%
+stage manager gets sick and you do it
+ 
+
+ align:start position:0%
+stage manager gets sick and you do it
+for the night and then you're the stage
+
+ align:start position:0%
+for the night and then you're the stage
+ 
+
+ align:start position:0%
+for the night and then you're the stage
+manager. Yeah, I think theater has a ton
+
+ align:start position:0%
+manager. Yeah, I think theater has a ton
+ 
+
+ align:start position:0%
+manager. Yeah, I think theater has a ton
+of stuff like this. That's a great
+
+ align:start position:0%
+of stuff like this. That's a great
+ 
+
+ align:start position:0%
+of stuff like this. That's a great
+example. What are you going to say,
+
+ align:start position:0%
+example. What are you going to say,
+ 
+
+ align:start position:0%
+example. What are you going to say,
+Omar? In the tech and technique, we have
+
+ align:start position:0%
+Omar? In the tech and technique, we have
+ 
+
+ align:start position:0%
+Omar? In the tech and technique, we have
+what's called like shadowing. So, when
+
+ align:start position:0%
+what's called like shadowing. So, when
+ 
+
+ align:start position:0%
+what's called like shadowing. So, when
+we go out for photo assignments where
+
+ align:start position:0%
+we go out for photo assignments where
+ 
+
+ align:start position:0%
+we go out for photo assignments where
+there's a studio photography assignment
+
+ align:start position:0%
+there's a studio photography assignment
+ 
+
+ align:start position:0%
+there's a studio photography assignment
+or something out in the field, um we can
+
+ align:start position:0%
+or something out in the field, um we can
+ 
+
+ align:start position:0%
+or something out in the field, um we can
+always have like a someone shadowing us
+
+ align:start position:0%
+always have like a someone shadowing us
+ 
+
+ align:start position:0%
+always have like a someone shadowing us
+and they can also be taking photos with
+
+ align:start position:0%
+and they can also be taking photos with
+ 
+
+ align:start position:0%
+and they can also be taking photos with
+their own camera and sometimes we will
+
+ align:start position:0%
+their own camera and sometimes we will
+ 
+
+ align:start position:0%
+their own camera and sometimes we will
+use their work as well. So, they can
+
+ align:start position:0%
+use their work as well. So, they can
+ 
+
+ align:start position:0%
+use their work as well. So, they can
+also do legitimate periphery work. I
+
+ align:start position:0%
+also do legitimate periphery work. I
+ 
+
+ align:start position:0%
+also do legitimate periphery work. I
+love it. and you have intentionally sort
+
+ align:start position:0%
+love it. and you have intentionally sort
+ 
+
+ align:start position:0%
+love it. and you have intentionally sort
+of held space for that. You've kind of
+
+ align:start position:0%
+of held space for that. You've kind of
+ 
+
+ align:start position:0%
+of held space for that. You've kind of
+designed like, oh yeah, come, you know,
+
+ align:start position:0%
+designed like, oh yeah, come, you know,
+ 
+
+ align:start position:0%
+designed like, oh yeah, come, you know,
+come along, hang out with us. Um, and
+
+ align:start position:0%
+come along, hang out with us. Um, and
+ 
+
+ align:start position:0%
+come along, hang out with us. Um, and
+you probably have parties and other
+
+ align:start position:0%
+you probably have parties and other
+ 
+
+ align:start position:0%
+you probably have parties and other
+kinds of things like that where it's
+
+ align:start position:0%
+kinds of things like that where it's
+ 
+
+ align:start position:0%
+kinds of things like that where it's
+like, oh, you know, where like some of
+
+ align:start position:0%
+like, oh, you know, where like some of
+ 
+
+ align:start position:0%
+like, oh, you know, where like some of
+you are just goofing around, but some of
+
+ align:start position:0%
+you are just goofing around, but some of
+ 
+
+ align:start position:0%
+you are just goofing around, but some of
+it you're like, ah, the story that we
+
+ align:start position:0%
+it you're like, ah, the story that we
+ 
+
+ align:start position:0%
+it you're like, ah, the story that we
+gota d, you know, I'm sure like them
+
+ align:start position:0%
+gota d, you know, I'm sure like them
+ 
+
+ align:start position:0%
+gota d, you know, I'm sure like them
+telling the stories of of difficult
+
+ align:start position:0%
+telling the stories of of difficult
+ 
+
+ align:start position:0%
+telling the stories of of difficult
+cases and miraculous outcomes. I'm sure
+
+ align:start position:0%
+cases and miraculous outcomes. I'm sure
+ 
+
+ align:start position:0%
+cases and miraculous outcomes. I'm sure
+the tech has other similar kinds of
+
+ align:start position:0%
+the tech has other similar kinds of
+ 
+
+ align:start position:0%
+the tech has other similar kinds of
+difficult cases and miraculous outcomes.
+
+ align:start position:0%
+difficult cases and miraculous outcomes.
+ 
+
+ align:start position:0%
+difficult cases and miraculous outcomes.
+I was going to say like on sports teams
+
+ align:start position:0%
+I was going to say like on sports teams
+ 
+
+ align:start position:0%
+I was going to say like on sports teams
+like when people become captains like
+
+ align:start position:0%
+like when people become captains like
+ 
+
+ align:start position:0%
+like when people become captains like
+not often is the coach sitting them down
+
+ align:start position:0%
+not often is the coach sitting them down
+ 
+
+ align:start position:0%
+not often is the coach sitting them down
+and being like this is how you be a
+
+ align:start position:0%
+and being like this is how you be a
+ 
+
+ align:start position:0%
+and being like this is how you be a
+captain, this is how you lead people.
+
+ align:start position:0%
+captain, this is how you lead people.
+ 
+
+ align:start position:0%
+captain, this is how you lead people.
+It's more like they just like naturally
+
+ align:start position:0%
+It's more like they just like naturally
+ 
+
+ align:start position:0%
+It's more like they just like naturally
+have this like personality of doing that
+
+ align:start position:0%
+have this like personality of doing that
+ 
+
+ align:start position:0%
+have this like personality of doing that
+of like maybe they grew up and like
+
+ align:start position:0%
+of like maybe they grew up and like
+ 
+
+ align:start position:0%
+of like maybe they grew up and like
+their their mom was like a girl boss or
+
+ align:start position:0%
+their their mom was like a girl boss or
+ 
+
+ align:start position:0%
+their their mom was like a girl boss or
+like they like just grew up seeing stuff
+
+ align:start position:0%
+like they like just grew up seeing stuff
+ 
+
+ align:start position:0%
+like they like just grew up seeing stuff
+like that. So then like you kind of have
+
+ align:start position:0%
+like that. So then like you kind of have
+ 
+
+ align:start position:0%
+like that. So then like you kind of have
+like that natural progression into like
+
+ align:start position:0%
+like that natural progression into like
+ 
+
+ align:start position:0%
+like that natural progression into like
+just learning by doing. Good. Yeah.
+
+ align:start position:0%
+just learning by doing. Good. Yeah.
+ 
+
+ align:start position:0%
+just learning by doing. Good. Yeah.
+Yeah. Pretty. What were you going to
+
+ align:start position:0%
+Yeah. Pretty. What were you going to
+ 
+
+ align:start position:0%
+Yeah. Pretty. What were you going to
+say, Sabrina? Okay, this is kind of a
+
+ align:start position:0%
+say, Sabrina? Okay, this is kind of a
+ 
+
+ align:start position:0%
+say, Sabrina? Okay, this is kind of a
+dumb example, but I like I'm really bad
+
+ align:start position:0%
+dumb example, but I like I'm really bad
+ 
+
+ align:start position:0%
+dumb example, but I like I'm really bad
+at Smash, so I always get placed with
+
+ align:start position:0%
+at Smash, so I always get placed with
+ 
+
+ align:start position:0%
+at Smash, so I always get placed with
+the best Smash player, and then we're on
+
+ align:start position:0%
+the best Smash player, and then we're on
+ 
+
+ align:start position:0%
+the best Smash player, and then we're on
+a team against two other people who are
+
+ align:start position:0%
+a team against two other people who are
+ 
+
+ align:start position:0%
+a team against two other people who are
+also really good, but this person is so
+
+ align:start position:0%
+also really good, but this person is so
+ 
+
+ align:start position:0%
+also really good, but this person is so
+good that like they carry they carry,
+
+ align:start position:0%
+good that like they carry they carry,
+ 
+
+ align:start position:0%
+good that like they carry they carry,
+but I'm kind of learning along with
+
+ align:start position:0%
+but I'm kind of learning along with
+ 
+
+ align:start position:0%
+but I'm kind of learning along with
+them. Um, and like I kind of like hold
+
+ align:start position:0%
+them. Um, and like I kind of like hold
+ 
+
+ align:start position:0%
+them. Um, and like I kind of like hold
+off onto the side where I just kind of
+
+ align:start position:0%
+off onto the side where I just kind of
+ 
+
+ align:start position:0%
+off onto the side where I just kind of
+like try to like hold lives while they
+
+ align:start position:0%
+like try to like hold lives while they
+ 
+
+ align:start position:0%
+like try to like hold lives while they
+like destroy the other people. Um, and I
+
+ align:start position:0%
+like destroy the other people. Um, and I
+ 
+
+ align:start position:0%
+like destroy the other people. Um, and I
+think that's kind of periphery. Oh yeah,
+
+ align:start position:0%
+think that's kind of periphery. Oh yeah,
+ 
+
+ align:start position:0%
+think that's kind of periphery. Oh yeah,
+yeah, yeah, yeah. I mean in and in that
+
+ align:start position:0%
+yeah, yeah, yeah. I mean in and in that
+ 
+
+ align:start position:0%
+yeah, yeah, yeah. I mean in and in that
+particular community it's a space of
+
+ align:start position:0%
+particular community it's a space of
+ 
+
+ align:start position:0%
+particular community it's a space of
+legitimate peripheral participation
+
+ align:start position:0%
+legitimate peripheral participation
+ 
+
+ align:start position:0%
+legitimate peripheral participation
+which somewhat exists because of this
+
+ align:start position:0%
+which somewhat exists because of this
+ 
+
+ align:start position:0%
+which somewhat exists because of this
+like fairness balancing kinds of things
+
+ align:start position:0%
+like fairness balancing kinds of things
+ 
+
+ align:start position:0%
+like fairness balancing kinds of things
+and so you know like every learning
+
+ align:start position:0%
+and so you know like every learning
+ 
+
+ align:start position:0%
+and so you know like every learning
+environment like the substance of uh
+
+ align:start position:0%
+environment like the substance of uh
+ 
+
+ align:start position:0%
+environment like the substance of uh
+Super Smash Brothers determines like
+
+ align:start position:0%
+Super Smash Brothers determines like
+ 
+
+ align:start position:0%
+Super Smash Brothers determines like
+where the legitimate you know and it
+
+ align:start position:0%
+where the legitimate you know and it
+ 
+
+ align:start position:0%
+where the legitimate you know and it
+determines spaces for peripheral
+
+ align:start position:0%
+determines spaces for peripheral
+ 
+
+ align:start position:0%
+determines spaces for peripheral
+partition that's different than
+
+ align:start position:0%
+partition that's different than
+ 
+
+ align:start position:0%
+partition that's different than
+journalism that different than sports
+
+ align:start position:0%
+journalism that different than sports
+ 
+
+ align:start position:0%
+journalism that different than sports
+that different but this theory is giving
+
+ align:start position:0%
+that different but this theory is giving
+ 
+
+ align:start position:0%
+that different but this theory is giving
+us commonality where we can talk about
+
+ align:start position:0%
+us commonality where we can talk about
+ 
+
+ align:start position:0%
+us commonality where we can talk about
+really different things that might arise
+
+ align:start position:0%
+really different things that might arise
+ 
+
+ align:start position:0%
+really different things that might arise
+in different circumstances be like I I
+
+ align:start position:0%
+in different circumstances be like I I
+ 
+
+ align:start position:0%
+in different circumstances be like I I
+think that's actually kind of the same
+
+ align:start position:0%
+think that's actually kind of the same
+ 
+
+ align:start position:0%
+think that's actually kind of the same
+thing and it's kind of spaces that I'm
+
+ align:start position:0%
+thing and it's kind of spaces that I'm
+ 
+
+ align:start position:0%
+thing and it's kind of spaces that I'm
+finding for learning.
+
+ align:start position:0%
+finding for learning.
+ 
+
+ align:start position:0%
+finding for learning.
+Um, in short, when official channels
+
+ align:start position:0%
+Um, in short, when official channels
+ 
+
+ align:start position:0%
+Um, in short, when official channels
+offer only a possibility to participate
+
+ align:start position:0%
+offer only a possibility to participate
+ 
+
+ align:start position:0%
+offer only a possibility to participate
+in institutionally mandated forms of
+
+ align:start position:0%
+in institutionally mandated forms of
+ 
+
+ align:start position:0%
+in institutionally mandated forms of
+commoditized activity, genuine
+
+ align:start position:0%
+commoditized activity, genuine
+ 
+
+ align:start position:0%
+commoditized activity, genuine
+participation, membership, and
+
+ align:start position:0%
+participation, membership, and
+ 
+
+ align:start position:0%
+participation, membership, and
+legitimate access to ongoing practice of
+
+ align:start position:0%
+legitimate access to ongoing practice of
+ 
+
+ align:start position:0%
+legitimate access to ongoing practice of
+a practice considered worthy to the name
+
+ align:start position:0%
+a practice considered worthy to the name
+ 
+
+ align:start position:0%
+a practice considered worthy to the name
+are rare. Practice is not to be found in
+
+ align:start position:0%
+are rare. Practice is not to be found in
+ 
+
+ align:start position:0%
+are rare. Practice is not to be found in
+schools and workplaces. At the same
+
+ align:start position:0%
+schools and workplaces. At the same
+ 
+
+ align:start position:0%
+schools and workplaces. At the same
+time, schools and school-like workplace
+
+ align:start position:0%
+time, schools and school-like workplace
+ 
+
+ align:start position:0%
+time, schools and school-like workplace
+educational enterprises accord knowledge
+
+ align:start position:0%
+educational enterprises accord knowledge
+ 
+
+ align:start position:0%
+educational enterprises accord knowledge
+skill a reified existed turning it from
+
+ align:start position:0%
+skill a reified existed turning it from
+ 
+
+ align:start position:0%
+skill a reified existed turning it from
+into something to be acquired and its
+
+ align:start position:0%
+into something to be acquired and its
+ 
+
+ align:start position:0%
+into something to be acquired and its
+transmission into an institutional
+
+ align:start position:0%
+transmission into an institutional
+ 
+
+ align:start position:0%
+transmission into an institutional
+motive. This process generates pressures
+
+ align:start position:0%
+motive. This process generates pressures
+ 
+
+ align:start position:0%
+motive. This process generates pressures
+towards the trivializing decomposing of
+
+ align:start position:0%
+towards the trivializing decomposing of
+ 
+
+ align:start position:0%
+towards the trivializing decomposing of
+forms or activity. The result is a
+
+ align:start position:0%
+forms or activity. The result is a
+ 
+
+ align:start position:0%
+forms or activity. The result is a
+widespread generation of negative
+
+ align:start position:0%
+widespread generation of negative
+ 
+
+ align:start position:0%
+widespread generation of negative
+identities of misrecognized or
+
+ align:start position:0%
+identities of misrecognized or
+ 
+
+ align:start position:0%
+identities of misrecognized or
+institutionally disapproved insistential
+
+ align:start position:0%
+institutionally disapproved insistential
+ 
+
+ align:start position:0%
+institutionally disapproved insistential
+communities of practice. um that some of
+
+ align:start position:0%
+communities of practice. um that some of
+ 
+
+ align:start position:0%
+communities of practice. um that some of
+the things that might feel most academic
+
+ align:start position:0%
+the things that might feel most academic
+ 
+
+ align:start position:0%
+the things that might feel most academic
+might feel less or least identity
+
+ align:start position:0%
+might feel less or least identity
+ 
+
+ align:start position:0%
+might feel less or least identity
+oriented to you. Um because there's not,
+
+ align:start position:0%
+oriented to you. Um because there's not,
+ 
+
+ align:start position:0%
+oriented to you. Um because there's not,
+you know, think about like what like
+
+ align:start position:0%
+you know, think about like what like
+ 
+
+ align:start position:0%
+you know, think about like what like
+what degrees here would be like I'm not
+
+ align:start position:0%
+what degrees here would be like I'm not
+ 
+
+ align:start position:0%
+what degrees here would be like I'm not
+sure there's a way to be a legitimate
+
+ align:start position:0%
+sure there's a way to be a legitimate
+ 
+
+ align:start position:0%
+sure there's a way to be a legitimate
+peripheral participant there. Like
+
+ align:start position:0%
+peripheral participant there. Like
+ 
+
+ align:start position:0%
+peripheral participant there. Like
+there's a way to learn the stuff.
+
+ align:start position:0%
+there's a way to learn the stuff.
+ 
+
+ align:start position:0%
+there's a way to learn the stuff.
+There's a way to be taught the discreet
+
+ align:start position:0%
+There's a way to be taught the discreet
+ 
+
+ align:start position:0%
+There's a way to be taught the discreet
+parts of this course or subject or
+
+ align:start position:0%
+parts of this course or subject or
+ 
+
+ align:start position:0%
+parts of this course or subject or
+major, but I I like I'm not learning how
+
+ align:start position:0%
+major, but I I like I'm not learning how
+ 
+
+ align:start position:0%
+major, but I I like I'm not learning how
+to be a part of this community. Um
+
+ align:start position:0%
+to be a part of this community. Um
+ 
+
+ align:start position:0%
+to be a part of this community. Um
+uh okay.
+
+ align:start position:0%
+uh okay.
+ 
+
+ align:start position:0%
+uh okay.
+Um, here are three things that I'll have
+
+ align:start position:0%
+Um, here are three things that I'll have
+ 
+
+ align:start position:0%
+Um, here are three things that I'll have
+you do together um for five or 10
+
+ align:start position:0%
+you do together um for five or 10
+ 
+
+ align:start position:0%
+you do together um for five or 10
+minutes, which might involve some
+
+ align:start position:0%
+minutes, which might involve some
+ 
+
+ align:start position:0%
+minutes, which might involve some
+drawing. Um,
+
+ align:start position:0%
+drawing. Um,
+ 
+
+ align:start position:0%
+drawing. Um,
+uh, so grab grab some paper or some
+
+ align:start position:0%
+uh, so grab grab some paper or some
+ 
+
+ align:start position:0%
+uh, so grab grab some paper or some
+board space. Um, what see if you could
+
+ align:start position:0%
+board space. Um, what see if you could
+ 
+
+ align:start position:0%
+board space. Um, what see if you could
+draw sort of the equivalent of human
+
+ align:start position:0%
+draw sort of the equivalent of human
+ 
+
+ align:start position:0%
+draw sort of the equivalent of human
+cognitive architecture. Um, see if you
+
+ align:start position:0%
+cognitive architecture. Um, see if you
+ 
+
+ align:start position:0%
+cognitive architecture. Um, see if you
+could draw like just just like just like
+
+ align:start position:0%
+could draw like just just like just like
+ 
+
+ align:start position:0%
+could draw like just just like just like
+you drew these diagrams for um, uh,
+
+ align:start position:0%
+you drew these diagrams for um, uh,
+ 
+
+ align:start position:0%
+you drew these diagrams for um, uh,
+cognitive load theory. What is the
+
+ align:start position:0%
+cognitive load theory. What is the
+ 
+
+ align:start position:0%
+cognitive load theory. What is the
+diagram you would draw for um situated
+
+ align:start position:0%
+diagram you would draw for um situated
+ 
+
+ align:start position:0%
+diagram you would draw for um situated
+learning? Um what is um based on that
+
+ align:start position:0%
+learning? Um what is um based on that
+ 
+
+ align:start position:0%
+learning? Um what is um based on that
+cognitive architecture? Um what is the
+
+ align:start position:0%
+cognitive architecture? Um what is the
+ 
+
+ align:start position:0%
+cognitive architecture? Um what is the
+pedagogy that follows? So based on like
+
+ align:start position:0%
+pedagogy that follows? So based on like
+ 
+
+ align:start position:0%
+pedagogy that follows? So based on like
+the sort of key fundamental principles
+
+ align:start position:0%
+the sort of key fundamental principles
+ 
+
+ align:start position:0%
+the sort of key fundamental principles
+of of situated learning, cognitive load
+
+ align:start position:0%
+of of situated learning, cognitive load
+ 
+
+ align:start position:0%
+of of situated learning, cognitive load
+theory said like here's a model of human
+
+ align:start position:0%
+theory said like here's a model of human
+ 
+
+ align:start position:0%
+theory said like here's a model of human
+cognitive architecture. Here are series
+
+ align:start position:0%
+cognitive architecture. Here are series
+ 
+
+ align:start position:0%
+cognitive architecture. Here are series
+of like clearly defined effects. The
+
+ align:start position:0%
+of like clearly defined effects. The
+ 
+
+ align:start position:0%
+of like clearly defined effects. The
+situated learning people are not as good
+
+ align:start position:0%
+situated learning people are not as good
+ 
+
+ align:start position:0%
+situated learning people are not as good
+as like enumerating in bullet points all
+
+ align:start position:0%
+as like enumerating in bullet points all
+ 
+
+ align:start position:0%
+as like enumerating in bullet points all
+of their pieces, but it's all in there.
+
+ align:start position:0%
+of their pieces, but it's all in there.
+ 
+
+ align:start position:0%
+of their pieces, but it's all in there.
+um what are some of the what are some of
+
+ align:start position:0%
+um what are some of the what are some of
+ 
+
+ align:start position:0%
+um what are some of the what are some of
+the like instructional practices that
+
+ align:start position:0%
+the like instructional practices that
+ 
+
+ align:start position:0%
+the like instructional practices that
+follow from this model? Um think about
+
+ align:start position:0%
+follow from this model? Um think about
+ 
+
+ align:start position:0%
+follow from this model? Um think about
+those two things and then also see if
+
+ align:start position:0%
+those two things and then also see if
+ 
+
+ align:start position:0%
+those two things and then also see if
+you can sort of recreate some of your
+
+ align:start position:0%
+you can sort of recreate some of your
+ 
+
+ align:start position:0%
+you can sort of recreate some of your
+ven diagrams um of what are the
+
+ align:start position:0%
+ven diagrams um of what are the
+ 
+
+ align:start position:0%
+ven diagrams um of what are the
+categories of things that seem separate
+
+ align:start position:0%
+categories of things that seem separate
+ 
+
+ align:start position:0%
+categories of things that seem separate
+from um cognitive learning and situated
+
+ align:start position:0%
+from um cognitive learning and situated
+ 
+
+ align:start position:0%
+from um cognitive learning and situated
+learning and what are the things that
+
+ align:start position:0%
+learning and what are the things that
+ 
+
+ align:start position:0%
+learning and what are the things that
+they seem to be quite similar on um or
+
+ align:start position:0%
+they seem to be quite similar on um or
+ 
+
+ align:start position:0%
+they seem to be quite similar on um or
+quite together on. Um take 10 minutes to
+
+ align:start position:0%
+quite together on. Um take 10 minutes to
+ 
+
+ align:start position:0%
+quite together on. Um take 10 minutes to
+again grab one person or two other
+
+ align:start position:0%
+again grab one person or two other
+ 
+
+ align:start position:0%
+again grab one person or two other
+people do some drawing, do some
+
+ align:start position:0%
+people do some drawing, do some
+ 
+
+ align:start position:0%
+people do some drawing, do some
+composing. Feel free to pull up your
+
+ align:start position:0%
+composing. Feel free to pull up your
+ 
+
+ align:start position:0%
+composing. Feel free to pull up your
+notes from your learning journal where
+
+ align:start position:0%
+notes from your learning journal where
+ 
+
+ align:start position:0%
+notes from your learning journal where
+you should have done some of this uh
+
+ align:start position:0%
+you should have done some of this uh
+ 
+
+ align:start position:0%
+you should have done some of this uh
+things. And if any of these questions,
+
+ align:start position:0%
+things. And if any of these questions,
+ 
+
+ align:start position:0%
+things. And if any of these questions,
+you don't have to you don't have to
+
+ align:start position:0%
+you don't have to you don't have to
+ 
+
+ align:start position:0%
+you don't have to you don't have to
+spend equal time on all three questions.
+
+ align:start position:0%
+spend equal time on all three questions.
+ 
+
+ align:start position:0%
+spend equal time on all three questions.
+If you dive in on one, that's fine. But
+
+ align:start position:0%
+If you dive in on one, that's fine. But
+ 
+
+ align:start position:0%
+If you dive in on one, that's fine. But
+those three should keep you busy for
+
+ align:start position:0%
+those three should keep you busy for
+ 
+
+ align:start position:0%
+those three should keep you busy for
+eight minutes or something like that.
+
+ align:start position:0%
+eight minutes or something like that.
+ 
+
+ align:start position:0%
+eight minutes or something like that.
+Make sense? Ready? You go.
+
+ align:start position:0%
+Make sense? Ready? You go.
+ 
+
+ align:start position:0%
+Make sense? Ready? You go.
+So, one one thing I love about almost
+
+ align:start position:0%
+So, one one thing I love about almost
+ 
+
+ align:start position:0%
+So, one one thing I love about almost
+all of these drawings is it's kind of
+
+ align:start position:0%
+all of these drawings is it's kind of
+ 
+
+ align:start position:0%
+all of these drawings is it's kind of
+impossible to draw these models without
+
+ align:start position:0%
+impossible to draw these models without
+ 
+
+ align:start position:0%
+impossible to draw these models without
+drawing other people. Um, that when you
+
+ align:start position:0%
+drawing other people. Um, that when you
+ 
+
+ align:start position:0%
+drawing other people. Um, that when you
+all developed a kind of human cognitive
+
+ align:start position:0%
+all developed a kind of human cognitive
+ 
+
+ align:start position:0%
+all developed a kind of human cognitive
+architecture in cognitive load theory,
+
+ align:start position:0%
+architecture in cognitive load theory,
+ 
+
+ align:start position:0%
+architecture in cognitive load theory,
+you were sort of drawing like one brain.
+
+ align:start position:0%
+you were sort of drawing like one brain.
+ 
+
+ align:start position:0%
+you were sort of drawing like one brain.
+And actually like actually most of your
+
+ align:start position:0%
+And actually like actually most of your
+ 
+
+ align:start position:0%
+And actually like actually most of your
+drawings you didn't even really
+
+ align:start position:0%
+drawings you didn't even really
+ 
+
+ align:start position:0%
+drawings you didn't even really
+represent the rest of the world. But in
+
+ align:start position:0%
+represent the rest of the world. But in
+ 
+
+ align:start position:0%
+represent the rest of the world. But in
+this model it's impossible not to
+
+ align:start position:0%
+this model it's impossible not to
+ 
+
+ align:start position:0%
+this model it's impossible not to
+represent the rest of the world and in
+
+ align:start position:0%
+represent the rest of the world and in
+ 
+
+ align:start position:0%
+represent the rest of the world and in
+particular other people um because
+
+ align:start position:0%
+particular other people um because
+ 
+
+ align:start position:0%
+particular other people um because
+learning fundamentally is social and
+
+ align:start position:0%
+learning fundamentally is social and
+ 
+
+ align:start position:0%
+learning fundamentally is social and
+your identity is fundamentally
+
+ align:start position:0%
+your identity is fundamentally
+ 
+
+ align:start position:0%
+your identity is fundamentally
+reflective of your connections with uh
+
+ align:start position:0%
+reflective of your connections with uh
+ 
+
+ align:start position:0%
+reflective of your connections with uh
+with other people. So these are good. Um
+
+ align:start position:0%
+with other people. So these are good. Um
+ 
+
+ align:start position:0%
+with other people. So these are good. Um
+you read a little piece of um give P's a
+
+ align:start position:0%
+you read a little piece of um give P's a
+ 
+
+ align:start position:0%
+you read a little piece of um give P's a
+chance. So four P's from Mitch Resnik
+
+ align:start position:0%
+chance. So four P's from Mitch Resnik
+ 
+
+ align:start position:0%
+chance. So four P's from Mitch Resnik
+about projects passion uh play and
+
+ align:start position:0%
+about projects passion uh play and
+ 
+
+ align:start position:0%
+about projects passion uh play and
+peers. Hopefully, you can now start
+
+ align:start position:0%
+peers. Hopefully, you can now start
+ 
+
+ align:start position:0%
+peers. Hopefully, you can now start
+mapping some of these ideas to what we
+
+ align:start position:0%
+mapping some of these ideas to what we
+ 
+
+ align:start position:0%
+mapping some of these ideas to what we
+talked about the reason, you know,
+
+ align:start position:0%
+talked about the reason, you know,
+ 
+
+ align:start position:0%
+talked about the reason, you know,
+projects, kind of open-ended
+
+ align:start position:0%
+projects, kind of open-ended
+ 
+
+ align:start position:0%
+projects, kind of open-ended
+explorations, making music, making uh
+
+ align:start position:0%
+explorations, making music, making uh
+ 
+
+ align:start position:0%
+explorations, making music, making uh
+funny shape, having a robot draw funny
+
+ align:start position:0%
+funny shape, having a robot draw funny
+ 
+
+ align:start position:0%
+funny shape, having a robot draw funny
+shape somewhere. Um, those are spaces
+
+ align:start position:0%
+shape somewhere. Um, those are spaces
+ 
+
+ align:start position:0%
+shape somewhere. Um, those are spaces
+for open-ended exploration, for doing
+
+ align:start position:0%
+for open-ended exploration, for doing
+ 
+
+ align:start position:0%
+for open-ended exploration, for doing
+multiple kinds of things. Um, projects
+
+ align:start position:0%
+multiple kinds of things. Um, projects
+ 
+
+ align:start position:0%
+multiple kinds of things. Um, projects
+have more space for peripheral
+
+ align:start position:0%
+have more space for peripheral
+ 
+
+ align:start position:0%
+have more space for peripheral
+participation, like multiple people can
+
+ align:start position:0%
+participation, like multiple people can
+ 
+
+ align:start position:0%
+participation, like multiple people can
+be making music, even if someone's a
+
+ align:start position:0%
+be making music, even if someone's a
+ 
+
+ align:start position:0%
+be making music, even if someone's a
+little bit better at making music than
+
+ align:start position:0%
+little bit better at making music than
+ 
+
+ align:start position:0%
+little bit better at making music than
+the other person. um that they are um
+
+ align:start position:0%
+the other person. um that they are um
+ 
+
+ align:start position:0%
+the other person. um that they are um
+that that learning environments here are
+
+ align:start position:0%
+that that learning environments here are
+ 
+
+ align:start position:0%
+that that learning environments here are
+are driven by interests. Um you know
+
+ align:start position:0%
+are driven by interests. Um you know
+ 
+
+ align:start position:0%
+are driven by interests. Um you know
+there's very little reference in
+
+ align:start position:0%
+there's very little reference in
+ 
+
+ align:start position:0%
+there's very little reference in
+cognitive load theory to things like
+
+ align:start position:0%
+cognitive load theory to things like
+ 
+
+ align:start position:0%
+cognitive load theory to things like
+well yeah and sometimes the kids don't
+
+ align:start position:0%
+well yeah and sometimes the kids don't
+ 
+
+ align:start position:0%
+well yeah and sometimes the kids don't
+like learning math so they just don't.
+
+ align:start position:0%
+like learning math so they just don't.
+ 
+
+ align:start position:0%
+like learning math so they just don't.
+Um although that's very real. Um some
+
+ align:start position:0%
+Um although that's very real. Um some
+ 
+
+ align:start position:0%
+Um although that's very real. Um some
+some of the young w some of the
+
+ align:start position:0%
+some of the young w some of the
+ 
+
+ align:start position:0%
+some of the young w some of the
+daughters and midwives wanted to become
+
+ align:start position:0%
+daughters and midwives wanted to become
+ 
+
+ align:start position:0%
+daughters and midwives wanted to become
+midwives and some didn't. Um and for the
+
+ align:start position:0%
+midwives and some didn't. Um and for the
+ 
+
+ align:start position:0%
+midwives and some didn't. Um and for the
+ones who did want to become midwives
+
+ align:start position:0%
+ones who did want to become midwives
+ 
+
+ align:start position:0%
+ones who did want to become midwives
+they followed that interest and those
+
+ align:start position:0%
+they followed that interest and those
+ 
+
+ align:start position:0%
+they followed that interest and those
+who didn't went and did other things.
+
+ align:start position:0%
+who didn't went and did other things.
+ 
+
+ align:start position:0%
+who didn't went and did other things.
+Um, and in these kinds of models of
+
+ align:start position:0%
+Um, and in these kinds of models of
+ 
+
+ align:start position:0%
+Um, and in these kinds of models of
+learning, that's actually okay and
+
+ align:start position:0%
+learning, that's actually okay and
+ 
+
+ align:start position:0%
+learning, that's actually okay and
+really important. We're not supposed to
+
+ align:start position:0%
+really important. We're not supposed to
+ 
+
+ align:start position:0%
+really important. We're not supposed to
+make everyone better at everything.
+
+ align:start position:0%
+make everyone better at everything.
+ 
+
+ align:start position:0%
+make everyone better at everything.
+We're supposed to let people follow
+
+ align:start position:0%
+We're supposed to let people follow
+ 
+
+ align:start position:0%
+We're supposed to let people follow
+their interests and get good at the
+
+ align:start position:0%
+their interests and get good at the
+ 
+
+ align:start position:0%
+their interests and get good at the
+things that they want to get good at. um
+
+ align:start position:0%
+things that they want to get good at. um
+ 
+
+ align:start position:0%
+things that they want to get good at. um
+that in environments in which there is a
+
+ align:start position:0%
+that in environments in which there is a
+ 
+
+ align:start position:0%
+that in environments in which there is a
+kind of lightness to the environment
+
+ align:start position:0%
+kind of lightness to the environment
+ 
+
+ align:start position:0%
+kind of lightness to the environment
+where uh you know lightness play creates
+
+ align:start position:0%
+where uh you know lightness play creates
+ 
+
+ align:start position:0%
+where uh you know lightness play creates
+space for multiple forms of
+
+ align:start position:0%
+space for multiple forms of
+ 
+
+ align:start position:0%
+space for multiple forms of
+participation like like things don't
+
+ align:start position:0%
+participation like like things don't
+ 
+
+ align:start position:0%
+participation like like things don't
+have to be optimized
+
+ align:start position:0%
+have to be optimized
+ 
+
+ align:start position:0%
+have to be optimized
+um to to get to the the you know fastest
+
+ align:start position:0%
+um to to get to the the you know fastest
+ 
+
+ align:start position:0%
+um to to get to the the you know fastest
+best trajectory for all people. There
+
+ align:start position:0%
+best trajectory for all people. There
+ 
+
+ align:start position:0%
+best trajectory for all people. There
+can be like room to to play and mess
+
+ align:start position:0%
+can be like room to to play and mess
+ 
+
+ align:start position:0%
+can be like room to to play and mess
+around and try other things. And then
+
+ align:start position:0%
+around and try other things. And then
+ 
+
+ align:start position:0%
+around and try other things. And then
+you know doing it with other people is
+
+ align:start position:0%
+you know doing it with other people is
+ 
+
+ align:start position:0%
+you know doing it with other people is
+essential as you can see in kind of all
+
+ align:start position:0%
+essential as you can see in kind of all
+ 
+
+ align:start position:0%
+essential as you can see in kind of all
+of these kinds of things you know and
+
+ align:start position:0%
+of these kinds of things you know and
+ 
+
+ align:start position:0%
+of these kinds of things you know and
+part of what uh um you know in some ways
+
+ align:start position:0%
+part of what uh um you know in some ways
+ 
+
+ align:start position:0%
+part of what uh um you know in some ways
+the real genius Jean Leave was a woman I
+
+ align:start position:0%
+the real genius Jean Leave was a woman I
+ 
+
+ align:start position:0%
+the real genius Jean Leave was a woman I
+misrepresented her as a man before and
+
+ align:start position:0%
+misrepresented her as a man before and
+ 
+
+ align:start position:0%
+misrepresented her as a man before and
+Aaron hopefully corrected me. Um Eddie
+
+ align:start position:0%
+Aaron hopefully corrected me. Um Eddie
+ 
+
+ align:start position:0%
+Aaron hopefully corrected me. Um Eddie
+Wanger her partner is a co-writer as a
+
+ align:start position:0%
+Wanger her partner is a co-writer as a
+ 
+
+ align:start position:0%
+Wanger her partner is a co-writer as a
+guy. Um is is it's not it's not just
+
+ align:start position:0%
+guy. Um is is it's not it's not just
+ 
+
+ align:start position:0%
+guy. Um is is it's not it's not just
+like people hanging out with each other.
+
+ align:start position:0%
+like people hanging out with each other.
+ 
+
+ align:start position:0%
+like people hanging out with each other.
+we can describe repeated patterns we see
+
+ align:start position:0%
+we can describe repeated patterns we see
+ 
+
+ align:start position:0%
+we can describe repeated patterns we see
+of legitimate peripheral participation
+
+ align:start position:0%
+of legitimate peripheral participation
+ 
+
+ align:start position:0%
+of legitimate peripheral participation
+um of old-timers and newcomers um of uh
+
+ align:start position:0%
+um of old-timers and newcomers um of uh
+ 
+
+ align:start position:0%
+um of old-timers and newcomers um of uh
+there's lots in Le's work that you
+
+ align:start position:0%
+there's lots in Le's work that you
+ 
+
+ align:start position:0%
+there's lots in Le's work that you
+probably read that was about trying to
+
+ align:start position:0%
+probably read that was about trying to
+ 
+
+ align:start position:0%
+probably read that was about trying to
+trying to find new language to get away
+
+ align:start position:0%
+trying to find new language to get away
+ 
+
+ align:start position:0%
+trying to find new language to get away
+from the experts and noviceses because
+
+ align:start position:0%
+from the experts and noviceses because
+ 
+
+ align:start position:0%
+from the experts and noviceses because
+it's not ju that's part of it but it's
+
+ align:start position:0%
+it's not ju that's part of it but it's
+ 
+
+ align:start position:0%
+it's not ju that's part of it but it's
+not just that um it's our time in its
+
+ align:start position:0%
+not just that um it's our time in its
+ 
+
+ align:start position:0%
+not just that um it's our time in its
+community it's our space in community
+
+ align:start position:0%
+community it's our space in community
+ 
+
+ align:start position:0%
+community it's our space in community
+those kinds of things so there's some so
+
+ align:start position:0%
+those kinds of things so there's some so
+ 
+
+ align:start position:0%
+those kinds of things so there's some so
+just like in cognitive load theory you
+
+ align:start position:0%
+just like in cognitive load theory you
+ 
+
+ align:start position:0%
+just like in cognitive load theory you
+could say here's a human cognitive
+
+ align:start position:0%
+could say here's a human cognitive
+ 
+
+ align:start position:0%
+could say here's a human cognitive
+architecture here's a set of pedagogical
+
+ align:start position:0%
+architecture here's a set of pedagogical
+ 
+
+ align:start position:0%
+architecture here's a set of pedagogical
+principles that follow from that. Um,
+
+ align:start position:0%
+principles that follow from that. Um,
+ 
+
+ align:start position:0%
+principles that follow from that. Um,
+Jean Leave can describe these social
+
+ align:start position:0%
+Jean Leave can describe these social
+ 
+
+ align:start position:0%
+Jean Leave can describe these social
+interactions. We can as you can abstract
+
+ align:start position:0%
+interactions. We can as you can abstract
+ 
+
+ align:start position:0%
+interactions. We can as you can abstract
+from them some models of uh of human
+
+ align:start position:0%
+from them some models of uh of human
+ 
+
+ align:start position:0%
+from them some models of uh of human
+cognitive architecture and say well okay
+
+ align:start position:0%
+cognitive architecture and say well okay
+ 
+
+ align:start position:0%
+cognitive architecture and say well okay
+from those models there are some
+
+ align:start position:0%
+from those models there are some
+ 
+
+ align:start position:0%
+from those models there are some
+instructional principles that follow. Um
+
+ align:start position:0%
+instructional principles that follow. Um
+ 
+
+ align:start position:0%
+instructional principles that follow. Um
+if I were to draw one of these I think a
+
+ align:start position:0%
+if I were to draw one of these I think a
+ 
+
+ align:start position:0%
+if I were to draw one of these I think a
+thing that I would pay a bunch of
+
+ align:start position:0%
+thing that I would pay a bunch of
+ 
+
+ align:start position:0%
+thing that I would pay a bunch of
+attention to is that um you know the
+
+ align:start position:0%
+attention to is that um you know the
+ 
+
+ align:start position:0%
+attention to is that um you know the
+thing in in both learning models like
+
+ align:start position:0%
+thing in in both learning models like
+ 
+
+ align:start position:0%
+thing in in both learning models like
+you learn what you attend to. Um seeing
+
+ align:start position:0%
+you learn what you attend to. Um seeing
+ 
+
+ align:start position:0%
+you learn what you attend to. Um seeing
+is really important. Um, a key insight
+
+ align:start position:0%
+is really important. Um, a key insight
+ 
+
+ align:start position:0%
+is really important. Um, a key insight
+of of uh situated learning is that we
+
+ align:start position:0%
+of of uh situated learning is that we
+ 
+
+ align:start position:0%
+of of uh situated learning is that we
+attend to things that interest us and
+
+ align:start position:0%
+attend to things that interest us and
+ 
+
+ align:start position:0%
+attend to things that interest us and
+motivate us and where where we find our
+
+ align:start position:0%
+motivate us and where where we find our
+ 
+
+ align:start position:0%
+motivate us and where where we find our
+identity and care about like how you
+
+ align:start position:0%
+identity and care about like how you
+ 
+
+ align:start position:0%
+identity and care about like how you
+know if looking at something is
+
+ align:start position:0%
+know if looking at something is
+ 
+
+ align:start position:0%
+know if looking at something is
+essential to get people to learn about
+
+ align:start position:0%
+essential to get people to learn about
+ 
+
+ align:start position:0%
+essential to get people to learn about
+it then we ought to think very carefully
+
+ align:start position:0%
+it then we ought to think very carefully
+ 
+
+ align:start position:0%
+it then we ought to think very carefully
+about what motivates us to look at a
+
+ align:start position:0%
+about what motivates us to look at a
+ 
+
+ align:start position:0%
+about what motivates us to look at a
+thing. Um, uh, T-ball for me is a,
+
+ align:start position:0%
+thing. Um, uh, T-ball for me is a,
+ 
+
+ align:start position:0%
+thing. Um, uh, T-ball for me is a,
+um, a a a canonical example of a kind of
+
+ align:start position:0%
+um, a a a canonical example of a kind of
+ 
+
+ align:start position:0%
+um, a a a canonical example of a kind of
+activity which it would be almost
+
+ align:start position:0%
+activity which it would be almost
+ 
+
+ align:start position:0%
+activity which it would be almost
+impossible to teach primarily through
+
+ align:start position:0%
+impossible to teach primarily through
+ 
+
+ align:start position:0%
+impossible to teach primarily through
+cognitive load theory. Um, like it's
+
+ align:start position:0%
+cognitive load theory. Um, like it's
+ 
+
+ align:start position:0%
+cognitive load theory. Um, like it's
+really hard to imagine teaching kids
+
+ align:start position:0%
+really hard to imagine teaching kids
+ 
+
+ align:start position:0%
+really hard to imagine teaching kids
+baseball where you're like, "All right,
+
+ align:start position:0%
+baseball where you're like, "All right,
+ 
+
+ align:start position:0%
+baseball where you're like, "All right,
+sit down everyone. Like we're all going
+
+ align:start position:0%
+sit down everyone. Like we're all going
+ 
+
+ align:start position:0%
+sit down everyone. Like we're all going
+to watch a worked example of how you,
+
+ align:start position:0%
+to watch a worked example of how you,
+ 
+
+ align:start position:0%
+to watch a worked example of how you,
+you know, hit a ball or like like we
+
+ align:start position:0%
+you know, hit a ball or like like we
+ 
+
+ align:start position:0%
+you know, hit a ball or like like we
+have to learn the rule book of
+
+ align:start position:0%
+have to learn the rule book of
+ 
+
+ align:start position:0%
+have to learn the rule book of
+baseball." Like the way we teach kids
+
+ align:start position:0%
+baseball." Like the way we teach kids
+ 
+
+ align:start position:0%
+baseball." Like the way we teach kids
+baseball is we're like, "What is the
+
+ align:start position:0%
+baseball is we're like, "What is the
+ 
+
+ align:start position:0%
+baseball is we're like, "What is the
+fastest way we can get young people with
+
+ align:start position:0%
+fastest way we can get young people with
+ 
+
+ align:start position:0%
+fastest way we can get young people with
+limited coordination and no knowledge of
+
+ align:start position:0%
+limited coordination and no knowledge of
+ 
+
+ align:start position:0%
+limited coordination and no knowledge of
+the rules to play something like
+
+ align:start position:0%
+the rules to play something like
+ 
+
+ align:start position:0%
+the rules to play something like
+baseball? How do we get them baseballing
+
+ align:start position:0%
+baseball? How do we get them baseballing
+ 
+
+ align:start position:0%
+baseball? How do we get them baseballing
+as soon as we possibly can?" And some
+
+ align:start position:0%
+as soon as we possibly can?" And some
+ 
+
+ align:start position:0%
+as soon as we possibly can?" And some
+genius was like, "Don't do the pitching.
+
+ align:start position:0%
+genius was like, "Don't do the pitching.
+ 
+
+ align:start position:0%
+genius was like, "Don't do the pitching.
+Like, get rid of the pitching. Just put
+
+ align:start position:0%
+Like, get rid of the pitching. Just put
+ 
+
+ align:start position:0%
+Like, get rid of the pitching. Just put
+the ball on the stick and they can just
+
+ align:start position:0%
+the ball on the stick and they can just
+ 
+
+ align:start position:0%
+the ball on the stick and they can just
+hit the ball." Um, it h it it it has
+
+ align:start position:0%
+hit the ball." Um, it h it it it has
+ 
+
+ align:start position:0%
+hit the ball." Um, it h it it it has
+some kind of cognitive relationship to
+
+ align:start position:0%
+some kind of cognitive relationship to
+ 
+
+ align:start position:0%
+some kind of cognitive relationship to
+sort of part whole practice um to
+
+ align:start position:0%
+sort of part whole practice um to
+ 
+
+ align:start position:0%
+sort of part whole practice um to
+devolving scaffolding and things like
+
+ align:start position:0%
+devolving scaffolding and things like
+ 
+
+ align:start position:0%
+devolving scaffolding and things like
+that. There's a there's a researcher at
+
+ align:start position:0%
+that. There's a there's a researcher at
+ 
+
+ align:start position:0%
+that. There's a there's a researcher at
+Harvard uh who wrote a book called
+
+ align:start position:0%
+Harvard uh who wrote a book called
+ 
+
+ align:start position:0%
+Harvard uh who wrote a book called
+Making Learning Whole. Um where he said
+
+ align:start position:0%
+Making Learning Whole. Um where he said
+ 
+
+ align:start position:0%
+Making Learning Whole. Um where he said
+that that one of the things we can often
+
+ align:start position:0%
+that that one of the things we can often
+ 
+
+ align:start position:0%
+that that one of the things we can often
+do in curriculum that we underestimate
+
+ align:start position:0%
+do in curriculum that we underestimate
+ 
+
+ align:start position:0%
+do in curriculum that we underestimate
+is get people playing the whole game as
+
+ align:start position:0%
+is get people playing the whole game as
+ 
+
+ align:start position:0%
+is get people playing the whole game as
+early as possible. Um you could we'll
+
+ align:start position:0%
+early as possible. Um you could we'll
+ 
+
+ align:start position:0%
+early as possible. Um you could we'll
+talk about this more, but think about
+
+ align:start position:0%
+talk about this more, but think about
+ 
+
+ align:start position:0%
+talk about this more, but think about
+like what subjects have you taken in MIT
+
+ align:start position:0%
+like what subjects have you taken in MIT
+ 
+
+ align:start position:0%
+like what subjects have you taken in MIT
+that let you start playing the whole
+
+ align:start position:0%
+that let you start playing the whole
+ 
+
+ align:start position:0%
+that let you start playing the whole
+game as soon as possible and what
+
+ align:start position:0%
+game as soon as possible and what
+ 
+
+ align:start position:0%
+game as soon as possible and what
+require you to sort of build up lots of
+
+ align:start position:0%
+require you to sort of build up lots of
+ 
+
+ align:start position:0%
+require you to sort of build up lots of
+elementary pieces before you can do the
+
+ align:start position:0%
+elementary pieces before you can do the
+ 
+
+ align:start position:0%
+elementary pieces before you can do the
+thing that that whole discipline does.
+
+ align:start position:0%
+thing that that whole discipline does.
+ 
+
+ align:start position:0%
+thing that that whole discipline does.
+Um but ba baseball instruction in the
+
+ align:start position:0%
+Um but ba baseball instruction in the
+ 
+
+ align:start position:0%
+Um but ba baseball instruction in the
+United States like very difficult to
+
+ align:start position:0%
+United States like very difficult to
+ 
+
+ align:start position:0%
+United States like very difficult to
+imagine in a cognitive load theory
+
+ align:start position:0%
+imagine in a cognitive load theory
+ 
+
+ align:start position:0%
+imagine in a cognitive load theory
+framework. Um like very pleasant for
+
+ align:start position:0%
+framework. Um like very pleasant for
+ 
+
+ align:start position:0%
+framework. Um like very pleasant for
+millions of young people in a more
+
+ align:start position:0%
+millions of young people in a more
+ 
+
+ align:start position:0%
+millions of young people in a more
+experiential situated kind of way. All
+
+ align:start position:0%
+experiential situated kind of way. All
+ 
+
+ align:start position:0%
+experiential situated kind of way. All
+right. You did this a little bit. Um
+
+ align:start position:0%
+right. You did this a little bit. Um
+ 
+
+ align:start position:0%
+right. You did this a little bit. Um
+which is good. Here is one thing that I
+
+ align:start position:0%
+which is good. Here is one thing that I
+ 
+
+ align:start position:0%
+which is good. Here is one thing that I
+would like to have in the center of your
+
+ align:start position:0%
+would like to have in the center of your
+ 
+
+ align:start position:0%
+would like to have in the center of your
+ven diagrams of things that are similar.
+
+ align:start position:0%
+ven diagrams of things that are similar.
+ 
+
+ align:start position:0%
+ven diagrams of things that are similar.
+Um this I this is a misconception that
+
+ align:start position:0%
+Um this I this is a misconception that
+ 
+
+ align:start position:0%
+Um this I this is a misconception that
+my students have had over the years that
+
+ align:start position:0%
+my students have had over the years that
+ 
+
+ align:start position:0%
+my students have had over the years that
+I want to correct.
+
+ align:start position:0%
+I want to correct.
+ 
+
+ align:start position:0%
+I want to correct.
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+they're the cognitive loads theorists
+
+ align:start position:0%
+they're the cognitive loads theorists
+ 
+
+ align:start position:0%
+they're the cognitive loads theorists
+and the situated learning people agree
+
+ align:start position:0%
+and the situated learning people agree
+ 
+
+ align:start position:0%
+and the situated learning people agree
+on what expertise looks like. They agree
+
+ align:start position:0%
+on what expertise looks like. They agree
+ 
+
+ align:start position:0%
+on what expertise looks like. They agree
+on what high quality practice looks
+
+ align:start position:0%
+on what high quality practice looks
+ 
+
+ align:start position:0%
+on what high quality practice looks
+like. I don't think you'd find these
+
+ align:start position:0%
+like. I don't think you'd find these
+ 
+
+ align:start position:0%
+like. I don't think you'd find these
+people. They would not disagree about
+
+ align:start position:0%
+people. They would not disagree about
+ 
+
+ align:start position:0%
+people. They would not disagree about
+what a great body player or a great
+
+ align:start position:0%
+what a great body player or a great
+ 
+
+ align:start position:0%
+what a great body player or a great
+carpenter or a great surgeon or a great
+
+ align:start position:0%
+carpenter or a great surgeon or a great
+ 
+
+ align:start position:0%
+carpenter or a great surgeon or a great
+lawyer looks like. Um they would believe
+
+ align:start position:0%
+lawyer looks like. Um they would believe
+ 
+
+ align:start position:0%
+lawyer looks like. Um they would believe
+that sometimes people think that the
+
+ align:start position:0%
+that sometimes people think that the
+ 
+
+ align:start position:0%
+that sometimes people think that the
+cognitive load theorists want people who
+
+ align:start position:0%
+cognitive load theorists want people who
+ 
+
+ align:start position:0%
+cognitive load theorists want people who
+are experts to be really like rigid and
+
+ align:start position:0%
+are experts to be really like rigid and
+ 
+
+ align:start position:0%
+are experts to be really like rigid and
+disciplined and pattern repeating and
+
+ align:start position:0%
+disciplined and pattern repeating and
+ 
+
+ align:start position:0%
+disciplined and pattern repeating and
+that is not the case. That is not what
+
+ align:start position:0%
+that is not the case. That is not what
+ 
+
+ align:start position:0%
+that is not the case. That is not what
+they want as the end point. You know
+
+ align:start position:0%
+they want as the end point. You know
+ 
+
+ align:start position:0%
+they want as the end point. You know
+they they want your cancer surgeon to be
+
+ align:start position:0%
+they they want your cancer surgeon to be
+ 
+
+ align:start position:0%
+they they want your cancer surgeon to be
+dynamic and flexible when they cut open
+
+ align:start position:0%
+dynamic and flexible when they cut open
+ 
+
+ align:start position:0%
+dynamic and flexible when they cut open
+your belly um and find cancerous tumors
+
+ align:start position:0%
+your belly um and find cancerous tumors
+ 
+
+ align:start position:0%
+your belly um and find cancerous tumors
+and are pulling them out of there. Um
+
+ align:start position:0%
+and are pulling them out of there. Um
+ 
+
+ align:start position:0%
+and are pulling them out of there. Um
+they want poets to be creative and
+
+ align:start position:0%
+they want poets to be creative and
+ 
+
+ align:start position:0%
+they want poets to be creative and
+imaginative. They just think that the
+
+ align:start position:0%
+imaginative. They just think that the
+ 
+
+ align:start position:0%
+imaginative. They just think that the
+way that you develop the knowledge base
+
+ align:start position:0%
+way that you develop the knowledge base
+ 
+
+ align:start position:0%
+way that you develop the knowledge base
+that lets you be creative and flexible
+
+ align:start position:0%
+that lets you be creative and flexible
+ 
+
+ align:start position:0%
+that lets you be creative and flexible
+and dynamic and strategic is through
+
+ align:start position:0%
+and dynamic and strategic is through
+ 
+
+ align:start position:0%
+and dynamic and strategic is through
+really disciplined instruction. Um
+
+ align:start position:0%
+really disciplined instruction. Um
+ 
+
+ align:start position:0%
+really disciplined instruction. Um
+because if you don't go through a
+
+ align:start position:0%
+because if you don't go through a
+ 
+
+ align:start position:0%
+because if you don't go through a
+process of really disciplined
+
+ align:start position:0%
+process of really disciplined
+ 
+
+ align:start position:0%
+process of really disciplined
+instruction, um it's hard to get good at
+
+ align:start position:0%
+instruction, um it's hard to get good at
+ 
+
+ align:start position:0%
+instruction, um it's hard to get good at
+things because no one no one has showed
+
+ align:start position:0%
+things because no one no one has showed
+ 
+
+ align:start position:0%
+things because no one no one has showed
+you how to do fundamental pieces um in
+
+ align:start position:0%
+you how to do fundamental pieces um in
+ 
+
+ align:start position:0%
+you how to do fundamental pieces um in
+clear ways. Um I have a couple
+
+ align:start position:0%
+clear ways. Um I have a couple
+ 
+
+ align:start position:0%
+clear ways. Um I have a couple
+colleagues, Jal Meta and Sarah Fine. Um
+
+ align:start position:0%
+colleagues, Jal Meta and Sarah Fine. Um
+ 
+
+ align:start position:0%
+colleagues, Jal Meta and Sarah Fine. Um
+J still at Harvard. uh s was there for a
+
+ align:start position:0%
+J still at Harvard. uh s was there for a
+ 
+
+ align:start position:0%
+J still at Harvard. uh s was there for a
+while in his uh was it high-tech high
+
+ align:start position:0%
+while in his uh was it high-tech high
+ 
+
+ align:start position:0%
+while in his uh was it high-tech high
+graduate school of education for a while
+
+ align:start position:0%
+graduate school of education for a while
+ 
+
+ align:start position:0%
+graduate school of education for a while
+who said who studied schools a lot
+
+ align:start position:0%
+who said who studied schools a lot
+ 
+
+ align:start position:0%
+who said who studied schools a lot
+studied very different schools with very
+
+ align:start position:0%
+studied very different schools with very
+ 
+
+ align:start position:0%
+studied very different schools with very
+different pedagogical philosophies and
+
+ align:start position:0%
+different pedagogical philosophies and
+ 
+
+ align:start position:0%
+different pedagogical philosophies and
+found that across all of them they
+
+ align:start position:0%
+found that across all of them they
+ 
+
+ align:start position:0%
+found that across all of them they
+tended to believe that expertise
+
+ align:start position:0%
+tended to believe that expertise
+ 
+
+ align:start position:0%
+tended to believe that expertise
+consisted of mastery identity and
+
+ align:start position:0%
+consisted of mastery identity and
+ 
+
+ align:start position:0%
+consisted of mastery identity and
+creativity that you knew a bunch of
+
+ align:start position:0%
+creativity that you knew a bunch of
+ 
+
+ align:start position:0%
+creativity that you knew a bunch of
+stuff in a domain um that you developed
+
+ align:start position:0%
+stuff in a domain um that you developed
+ 
+
+ align:start position:0%
+stuff in a domain um that you developed
+an identity in that domain and that you
+
+ align:start position:0%
+an identity in that domain and that you
+ 
+
+ align:start position:0%
+an identity in that domain and that you
+were able to do flexible creative work
+
+ align:start position:0%
+were able to do flexible creative work
+ 
+
+ align:start position:0%
+were able to do flexible creative work
+um you know a bunch of physics equations
+
+ align:start position:0%
+um you know a bunch of physics equations
+ 
+
+ align:start position:0%
+um you know a bunch of physics equations
+and when to apply them you feel like
+
+ align:start position:0%
+and when to apply them you feel like
+ 
+
+ align:start position:0%
+and when to apply them you feel like
+you're kind of a physicist and a
+
+ align:start position:0%
+you're kind of a physicist and a
+ 
+
+ align:start position:0%
+you're kind of a physicist and a
+scientist and when you need to do
+
+ align:start position:0%
+scientist and when you need to do
+ 
+
+ align:start position:0%
+scientist and when you need to do
+something novel like build a bridge um
+
+ align:start position:0%
+something novel like build a bridge um
+ 
+
+ align:start position:0%
+something novel like build a bridge um
+or launch a rocket or something like
+
+ align:start position:0%
+or launch a rocket or something like
+ 
+
+ align:start position:0%
+or launch a rocket or something like
+that, you're not just following steps,
+
+ align:start position:0%
+that, you're not just following steps,
+ 
+
+ align:start position:0%
+that, you're not just following steps,
+but you're doing things that are that
+
+ align:start position:0%
+but you're doing things that are that
+ 
+
+ align:start position:0%
+but you're doing things that are that
+are creative um and expressive. One one
+
+ align:start position:0%
+are creative um and expressive. One one
+ 
+
+ align:start position:0%
+are creative um and expressive. One one
+way that I would um I think the
+
+ align:start position:0%
+way that I would um I think the
+ 
+
+ align:start position:0%
+way that I would um I think the
+cognitive load theorists and situated
+
+ align:start position:0%
+cognitive load theorists and situated
+ 
+
+ align:start position:0%
+cognitive load theorists and situated
+learning people tend to imagine
+
+ align:start position:0%
+learning people tend to imagine
+ 
+
+ align:start position:0%
+learning people tend to imagine
+different pathways at getting at these
+
+ align:start position:0%
+different pathways at getting at these
+ 
+
+ align:start position:0%
+different pathways at getting at these
+goals. Um, so the cognitive load
+
+ align:start position:0%
+goals. Um, so the cognitive load
+ 
+
+ align:start position:0%
+goals. Um, so the cognitive load
+theorists tend to think that mastery is
+
+ align:start position:0%
+theorists tend to think that mastery is
+ 
+
+ align:start position:0%
+theorists tend to think that mastery is
+like the starting point. If you know the
+
+ align:start position:0%
+like the starting point. If you know the
+ 
+
+ align:start position:0%
+like the starting point. If you know the
+stuff, if you can do the pieces, then a
+
+ align:start position:0%
+stuff, if you can do the pieces, then a
+ 
+
+ align:start position:0%
+stuff, if you can do the pieces, then a
+we often most enjoy things that we're
+
+ align:start position:0%
+we often most enjoy things that we're
+ 
+
+ align:start position:0%
+we often most enjoy things that we're
+good at. So like get you good at doing
+
+ align:start position:0%
+good at. So like get you good at doing
+ 
+
+ align:start position:0%
+good at. So like get you good at doing
+things. There's, you know, there's there
+
+ align:start position:0%
+things. There's, you know, there's there
+ 
+
+ align:start position:0%
+things. There's, you know, there's there
+there's there's lots of debates in the
+
+ align:start position:0%
+there's there's lots of debates in the
+ 
+
+ align:start position:0%
+there's there's lots of debates in the
+country right now, we'll talk about them
+
+ align:start position:0%
+country right now, we'll talk about them
+ 
+
+ align:start position:0%
+country right now, we'll talk about them
+some, about teaching kids to read. Um,
+
+ align:start position:0%
+some, about teaching kids to read. Um,
+ 
+
+ align:start position:0%
+some, about teaching kids to read. Um,
+and there's some folks who say like we
+
+ align:start position:0%
+and there's some folks who say like we
+ 
+
+ align:start position:0%
+and there's some folks who say like we
+just have to let kids explore books and
+
+ align:start position:0%
+just have to let kids explore books and
+ 
+
+ align:start position:0%
+just have to let kids explore books and
+find what they're interested in. And
+
+ align:start position:0%
+find what they're interested in. And
+ 
+
+ align:start position:0%
+find what they're interested in. And
+there other folks are like, you know
+
+ align:start position:0%
+there other folks are like, you know
+ 
+
+ align:start position:0%
+there other folks are like, you know
+what's fun about reading is actually
+
+ align:start position:0%
+what's fun about reading is actually
+ 
+
+ align:start position:0%
+what's fun about reading is actually
+being able to read. So like teach them a
+
+ align:start position:0%
+being able to read. So like teach them a
+ 
+
+ align:start position:0%
+being able to read. So like teach them a
+bunch of phonics and explain to them the
+
+ align:start position:0%
+bunch of phonics and explain to them the
+ 
+
+ align:start position:0%
+bunch of phonics and explain to them the
+basics of how to construct words. And
+
+ align:start position:0%
+basics of how to construct words. And
+ 
+
+ align:start position:0%
+basics of how to construct words. And
+that's what makes reading enjoyable.
+
+ align:start position:0%
+that's what makes reading enjoyable.
+ 
+
+ align:start position:0%
+that's what makes reading enjoyable.
+That would make people feel like
+
+ align:start position:0%
+That would make people feel like
+ 
+
+ align:start position:0%
+That would make people feel like
+readers, you know, not when they have
+
+ align:start position:0%
+readers, you know, not when they have
+ 
+
+ align:start position:0%
+readers, you know, not when they have
+like a beautiful library of things to
+
+ align:start position:0%
+like a beautiful library of things to
+ 
+
+ align:start position:0%
+like a beautiful library of things to
+choose from, whatever they want, but
+
+ align:start position:0%
+choose from, whatever they want, but
+ 
+
+ align:start position:0%
+choose from, whatever they want, but
+when they can actually make sense of
+
+ align:start position:0%
+when they can actually make sense of
+ 
+
+ align:start position:0%
+when they can actually make sense of
+what's in there. There's some sense in
+
+ align:start position:0%
+what's in there. There's some sense in
+ 
+
+ align:start position:0%
+what's in there. There's some sense in
+that. Um, you develop some kind of
+
+ align:start position:0%
+that. Um, you develop some kind of
+ 
+
+ align:start position:0%
+that. Um, you develop some kind of
+identity and then you get then you have
+
+ align:start position:0%
+identity and then you get then you have
+ 
+
+ align:start position:0%
+identity and then you get then you have
+the opportunity to do creative practice
+
+ align:start position:0%
+the opportunity to do creative practice
+ 
+
+ align:start position:0%
+the opportunity to do creative practice
+that builds that mastery. There are
+
+ align:start position:0%
+that builds that mastery. There are
+ 
+
+ align:start position:0%
+that builds that mastery. There are
+other people who say start with things
+
+ align:start position:0%
+other people who say start with things
+ 
+
+ align:start position:0%
+other people who say start with things
+like creativity. Start by getting people
+
+ align:start position:0%
+like creativity. Start by getting people
+ 
+
+ align:start position:0%
+like creativity. Start by getting people
+to play around in the space as much as
+
+ align:start position:0%
+to play around in the space as much as
+ 
+
+ align:start position:0%
+to play around in the space as much as
+possible so that they're motivated. Um
+
+ align:start position:0%
+possible so that they're motivated. Um
+ 
+
+ align:start position:0%
+possible so that they're motivated. Um
+so that they say, "Man, like I am a I am
+
+ align:start position:0%
+so that they say, "Man, like I am a I am
+ 
+
+ align:start position:0%
+so that they say, "Man, like I am a I am
+a this. I want, you know, I'm a I'm a
+
+ align:start position:0%
+a this. I want, you know, I'm a I'm a
+ 
+
+ align:start position:0%
+a this. I want, you know, I'm a I'm a
+baseball player. Like I, you know, I
+
+ align:start position:0%
+baseball player. Like I, you know, I
+ 
+
+ align:start position:0%
+baseball player. Like I, you know, I
+swung on a ball on a stick a few times."
+
+ align:start position:0%
+swung on a ball on a stick a few times."
+ 
+
+ align:start position:0%
+swung on a ball on a stick a few times."
+Um but now I am a baseball player. Um,
+
+ align:start position:0%
+Um but now I am a baseball player. Um,
+ 
+
+ align:start position:0%
+Um but now I am a baseball player. Um,
+and because I'm a baseball player, like
+
+ align:start position:0%
+and because I'm a baseball player, like
+ 
+
+ align:start position:0%
+and because I'm a baseball player, like
+in my heart, um, I'll memorize all the
+
+ align:start position:0%
+in my heart, um, I'll memorize all the
+ 
+
+ align:start position:0%
+in my heart, um, I'll memorize all the
+statistics and learn the rules and go to
+
+ align:start position:0%
+statistics and learn the rules and go to
+ 
+
+ align:start position:0%
+statistics and learn the rules and go to
+practice, you know, and eventually do
+
+ align:start position:0%
+practice, you know, and eventually do
+ 
+
+ align:start position:0%
+practice, you know, and eventually do
+like really boring learning kinds of
+
+ align:start position:0%
+like really boring learning kinds of
+ 
+
+ align:start position:0%
+like really boring learning kinds of
+things. Um, the sort of masteryoriented
+
+ align:start position:0%
+things. Um, the sort of masteryoriented
+ 
+
+ align:start position:0%
+things. Um, the sort of masteryoriented
+discipline kinds of things, but because
+
+ align:start position:0%
+discipline kinds of things, but because
+ 
+
+ align:start position:0%
+discipline kinds of things, but because
+I know how fun it is to play around in
+
+ align:start position:0%
+I know how fun it is to play around in
+ 
+
+ align:start position:0%
+I know how fun it is to play around in
+this space. Um, what what do you think
+
+ align:start position:0%
+this space. Um, what what do you think
+ 
+
+ align:start position:0%
+this space. Um, what what do you think
+at MIT are the are the subjects or
+
+ align:start position:0%
+at MIT are the are the subjects or
+ 
+
+ align:start position:0%
+at MIT are the are the subjects or
+courses that you would take that would
+
+ align:start position:0%
+courses that you would take that would
+ 
+
+ align:start position:0%
+courses that you would take that would
+be more canonically sort of mastery
+
+ align:start position:0%
+be more canonically sort of mastery
+ 
+
+ align:start position:0%
+be more canonically sort of mastery
+first oriented?
+
+ align:start position:0%
+first oriented?
+ 
+
+ align:start position:0%
+first oriented?
+What are what are the subjects you would
+
+ align:start position:0%
+What are what are the subjects you would
+ 
+
+ align:start position:0%
+What are what are the subjects you would
+take that you would like start with the
+
+ align:start position:0%
+take that you would like start with the
+ 
+
+ align:start position:0%
+take that you would like start with the
+smallest pieces or or by contrast if
+
+ align:start position:0%
+smallest pieces or or by contrast if
+ 
+
+ align:start position:0%
+smallest pieces or or by contrast if
+it's easier? What are the ones that seem
+
+ align:start position:0%
+it's easier? What are the ones that seem
+ 
+
+ align:start position:0%
+it's easier? What are the ones that seem
+to be more creativity first?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think more like bioheavy classes would
+
+ align:start position:0%
+I think more like bioheavy classes would
+ 
+
+ align:start position:0%
+I think more like bioheavy classes would
+definitely be like mastery first because
+
+ align:start position:0%
+definitely be like mastery first because
+ 
+
+ align:start position:0%
+definitely be like mastery first because
+if you don't understand like the basic
+
+ align:start position:0%
+if you don't understand like the basic
+ 
+
+ align:start position:0%
+if you don't understand like the basic
+of cells like you're not getting
+
+ align:start position:0%
+of cells like you're not getting
+ 
+
+ align:start position:0%
+of cells like you're not getting
+anywhere like you can't go like chapter
+
+ align:start position:0%
+anywhere like you can't go like chapter
+ 
+
+ align:start position:0%
+anywhere like you can't go like chapter
+2 without understanding like good. So it
+
+ align:start position:0%
+2 without understanding like good. So it
+ 
+
+ align:start position:0%
+2 without understanding like good. So it
+seems to be, you know, so eventually you
+
+ align:start position:0%
+seems to be, you know, so eventually you
+ 
+
+ align:start position:0%
+seems to be, you know, so eventually you
+can do some like pretty rad
+
+ align:start position:0%
+can do some like pretty rad
+ 
+
+ align:start position:0%
+can do some like pretty rad
+computational biology, biological
+
+ align:start position:0%
+computational biology, biological
+ 
+
+ align:start position:0%
+computational biology, biological
+engineering here, but there's not a lot
+
+ align:start position:0%
+engineering here, but there's not a lot
+ 
+
+ align:start position:0%
+engineering here, but there's not a lot
+in bio 101 where they're like, "Yeah,
+
+ align:start position:0%
+in bio 101 where they're like, "Yeah,
+ 
+
+ align:start position:0%
+in bio 101 where they're like, "Yeah,
+let's like have cells start generating
+
+ align:start position:0%
+let's like have cells start generating
+ 
+
+ align:start position:0%
+let's like have cells start generating
+novel proteins or things like that." I
+
+ align:start position:0%
+novel proteins or things like that." I
+ 
+
+ align:start position:0%
+novel proteins or things like that." I
+would say most of the general
+
+ align:start position:0%
+would say most of the general
+ 
+
+ align:start position:0%
+would say most of the general
+requirements like especially like the
+
+ align:start position:0%
+requirements like especially like the
+ 
+
+ align:start position:0%
+requirements like especially like the
+chemistry requirements and the biology
+
+ align:start position:0%
+chemistry requirements and the biology
+ 
+
+ align:start position:0%
+chemistry requirements and the biology
+requirements are like with the hopes
+
+ align:start position:0%
+requirements are like with the hopes
+ 
+
+ align:start position:0%
+requirements are like with the hopes
+that hey if you learn a little bit about
+
+ align:start position:0%
+that hey if you learn a little bit about
+ 
+
+ align:start position:0%
+that hey if you learn a little bit about
+this maybe then you become interested
+
+ align:start position:0%
+this maybe then you become interested
+ 
+
+ align:start position:0%
+this maybe then you become interested
+and want to go further and want that to
+
+ align:start position:0%
+and want to go further and want that to
+ 
+
+ align:start position:0%
+and want to go further and want that to
+be your major. But yeah, so so which
+
+ align:start position:0%
+be your major. But yeah, so so which
+ 
+
+ align:start position:0%
+be your major. But yeah, so so which
+which ones do that through like giving
+
+ align:start position:0%
+which ones do that through like giving
+ 
+
+ align:start position:0%
+which ones do that through like giving
+you a bunch of facts and which ones do
+
+ align:start position:0%
+you a bunch of facts and which ones do
+ 
+
+ align:start position:0%
+you a bunch of facts and which ones do
+that by letting you sort of play the
+
+ align:start position:0%
+that by letting you sort of play the
+ 
+
+ align:start position:0%
+that by letting you sort of play the
+whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game? I mean my understanding is that a
+
+ align:start position:0%
+game? I mean my understanding is that a
+ 
+
+ align:start position:0%
+game? I mean my understanding is that a
+number of the engineering departments
+
+ align:start position:0%
+number of the engineering departments
+ 
+
+ align:start position:0%
+number of the engineering departments
+like in mechanical engineering you'd be
+
+ align:start position:0%
+like in mechanical engineering you'd be
+ 
+
+ align:start position:0%
+like in mechanical engineering you'd be
+more likely earlier in your career to be
+
+ align:start position:0%
+more likely earlier in your career to be
+ 
+
+ align:start position:0%
+more likely earlier in your career to be
+like we're going to build a robot. Um
+
+ align:start position:0%
+like we're going to build a robot. Um
+ 
+
+ align:start position:0%
+like we're going to build a robot. Um
+and like do you know how to build a
+
+ align:start position:0%
+and like do you know how to build a
+ 
+
+ align:start position:0%
+and like do you know how to build a
+robot? No. Are you going to be good at
+
+ align:start position:0%
+robot? No. Are you going to be good at
+ 
+
+ align:start position:0%
+robot? No. Are you going to be good at
+building a robot? No. You're going to
+
+ align:start position:0%
+building a robot? No. You're going to
+ 
+
+ align:start position:0%
+building a robot? No. You're going to
+build a lousy robot. We're going to let
+
+ align:start position:0%
+build a lousy robot. We're going to let
+ 
+
+ align:start position:0%
+build a lousy robot. We're going to let
+you build a crummy robot. and some TA is
+
+ align:start position:0%
+you build a crummy robot. and some TA is
+ 
+
+ align:start position:0%
+you build a crummy robot. and some TA is
+going to put their arm around your
+
+ align:start position:0%
+going to put their arm around your
+ 
+
+ align:start position:0%
+going to put their arm around your
+shoulder and be like, "That robot's
+
+ align:start position:0%
+shoulder and be like, "That robot's
+ 
+
+ align:start position:0%
+shoulder and be like, "That robot's
+okay. That robot's only okay because you
+
+ align:start position:0%
+okay. That robot's only okay because you
+ 
+
+ align:start position:0%
+okay. That robot's only okay because you
+don't know anything about control
+
+ align:start position:0%
+don't know anything about control
+ 
+
+ align:start position:0%
+don't know anything about control
+systems." But guess what? Guess what?
+
+ align:start position:0%
+systems." But guess what? Guess what?
+ 
+
+ align:start position:0%
+systems." But guess what? Guess what?
+One of our junior classes is control
+
+ align:start position:0%
+One of our junior classes is control
+ 
+
+ align:start position:0%
+One of our junior classes is control
+systems. You're like, "Ah, I can't wait
+
+ align:start position:0%
+systems. You're like, "Ah, I can't wait
+ 
+
+ align:start position:0%
+systems. You're like, "Ah, I can't wait
+to take control system. It's going to be
+
+ align:start position:0%
+to take control system. It's going to be
+ 
+
+ align:start position:0%
+to take control system. It's going to be
+boring. It's going to be like a bunch of
+
+ align:start position:0%
+boring. It's going to be like a bunch of
+ 
+
+ align:start position:0%
+boring. It's going to be like a bunch of
+equations and other pets and things like
+
+ align:start position:0%
+equations and other pets and things like
+ 
+
+ align:start position:0%
+equations and other pets and things like
+that." But there's a robot that you want
+
+ align:start position:0%
+that." But there's a robot that you want
+ 
+
+ align:start position:0%
+that." But there's a robot that you want
+to drive. Um, the neat program I think
+
+ align:start position:0%
+to drive. Um, the neat program I think
+ 
+
+ align:start position:0%
+to drive. Um, the neat program I think
+at MIT is really about trying to create
+
+ align:start position:0%
+at MIT is really about trying to create
+ 
+
+ align:start position:0%
+at MIT is really about trying to create
+a bunch of these like experiential
+
+ align:start position:0%
+a bunch of these like experiential
+ 
+
+ align:start position:0%
+a bunch of these like experiential
+experiences. I mean, historically, if
+
+ align:start position:0%
+experiences. I mean, historically, if
+ 
+
+ align:start position:0%
+experiences. I mean, historically, if
+you were to look at our curriculum
+
+ align:start position:0%
+you were to look at our curriculum
+ 
+
+ align:start position:0%
+you were to look at our curriculum
+across MIT, many more things would be
+
+ align:start position:0%
+across MIT, many more things would be
+ 
+
+ align:start position:0%
+across MIT, many more things would be
+much more like this. I mean, like our
+
+ align:start position:0%
+much more like this. I mean, like our
+ 
+
+ align:start position:0%
+much more like this. I mean, like our
+math curriculum, I think, is very much
+
+ align:start position:0%
+math curriculum, I think, is very much
+ 
+
+ align:start position:0%
+math curriculum, I think, is very much
+this way. Like, you're just going to do
+
+ align:start position:0%
+this way. Like, you're just going to do
+ 
+
+ align:start position:0%
+this way. Like, you're just going to do
+math that other people have figured out
+
+ align:start position:0%
+math that other people have figured out
+ 
+
+ align:start position:0%
+math that other people have figured out
+for years and years, and maybe by the
+
+ align:start position:0%
+for years and years, and maybe by the
+ 
+
+ align:start position:0%
+for years and years, and maybe by the
+time you get to the end of MIT, but you
+
+ align:start position:0%
+time you get to the end of MIT, but you
+ 
+
+ align:start position:0%
+time you get to the end of MIT, but you
+might have to wait till graduate school
+
+ align:start position:0%
+might have to wait till graduate school
+ 
+
+ align:start position:0%
+might have to wait till graduate school
+that you can do some new math that
+
+ align:start position:0%
+that you can do some new math that
+ 
+
+ align:start position:0%
+that you can do some new math that
+someone else has never done before. Um,
+
+ align:start position:0%
+someone else has never done before. Um,
+ 
+
+ align:start position:0%
+someone else has never done before. Um,
+my uh my wife teaches the material
+
+ align:start position:0%
+my uh my wife teaches the material
+ 
+
+ align:start position:0%
+my uh my wife teaches the material
+science department. Um, and uh some of
+
+ align:start position:0%
+science department. Um, and uh some of
+ 
+
+ align:start position:0%
+science department. Um, and uh some of
+the stuff with like the Breaker Lab that
+
+ align:start position:0%
+the stuff with like the Breaker Lab that
+ 
+
+ align:start position:0%
+the stuff with like the Breaker Lab that
+they just developed and things like
+
+ align:start position:0%
+they just developed and things like
+ 
+
+ align:start position:0%
+they just developed and things like
+that. um where like they did an early
+
+ align:start position:0%
+that. um where like they did an early
+ 
+
+ align:start position:0%
+that. um where like they did an early
+exercise in one of our classes which is
+
+ align:start position:0%
+exercise in one of our classes which is
+ 
+
+ align:start position:0%
+exercise in one of our classes which is
+build products from the worst possible
+
+ align:start position:0%
+build products from the worst possible
+ 
+
+ align:start position:0%
+build products from the worst possible
+materials. Um so like phone cases that
+
+ align:start position:0%
+materials. Um so like phone cases that
+ 
+
+ align:start position:0%
+materials. Um so like phone cases that
+were made of sponges and absorbed water
+
+ align:start position:0%
+were made of sponges and absorbed water
+ 
+
+ align:start position:0%
+were made of sponges and absorbed water
+or um locks that were made of clear
+
+ align:start position:0%
+or um locks that were made of clear
+ 
+
+ align:start position:0%
+or um locks that were made of clear
+plastic where you could see all the
+
+ align:start position:0%
+plastic where you could see all the
+ 
+
+ align:start position:0%
+plastic where you could see all the
+tumblers and things like basically like
+
+ align:start position:0%
+tumblers and things like basically like
+ 
+
+ align:start position:0%
+tumblers and things like basically like
+play around with materials, do stuff
+
+ align:start position:0%
+play around with materials, do stuff
+ 
+
+ align:start position:0%
+play around with materials, do stuff
+with materials and then you're going to
+
+ align:start position:0%
+with materials and then you're going to
+ 
+
+ align:start position:0%
+with materials and then you're going to
+take like some super boring really hard
+
+ align:start position:0%
+take like some super boring really hard
+ 
+
+ align:start position:0%
+take like some super boring really hard
+classes but you're motivated to take
+
+ align:start position:0%
+classes but you're motivated to take
+ 
+
+ align:start position:0%
+classes but you're motivated to take
+those things. So I think you can look
+
+ align:start position:0%
+those things. So I think you can look
+ 
+
+ align:start position:0%
+those things. So I think you can look
+across environments um and see how they
+
+ align:start position:0%
+across environments um and see how they
+ 
+
+ align:start position:0%
+across environments um and see how they
+choose different pathways um through
+
+ align:start position:0%
+choose different pathways um through
+ 
+
+ align:start position:0%
+choose different pathways um through
+these uh these different if you look at
+
+ align:start position:0%
+these uh these different if you look at
+ 
+
+ align:start position:0%
+these uh these different if you look at
+reading instruction in the United States
+
+ align:start position:0%
+reading instruction in the United States
+ 
+
+ align:start position:0%
+reading instruction in the United States
+there's a huge debate right now about do
+
+ align:start position:0%
+there's a huge debate right now about do
+ 
+
+ align:start position:0%
+there's a huge debate right now about do
+you start with mastery and facts and
+
+ align:start position:0%
+you start with mastery and facts and
+ 
+
+ align:start position:0%
+you start with mastery and facts and
+pieces and build up to readers um or do
+
+ align:start position:0%
+pieces and build up to readers um or do
+ 
+
+ align:start position:0%
+pieces and build up to readers um or do
+you start by exposing people to books
+
+ align:start position:0%
+you start by exposing people to books
+ 
+
+ align:start position:0%
+you start by exposing people to books
+and letters and words and the things
+
+ align:start position:0%
+and letters and words and the things
+ 
+
+ align:start position:0%
+and letters and words and the things
+they love and and lots of time um you
+
+ align:start position:0%
+they love and and lots of time um you
+ 
+
+ align:start position:0%
+they love and and lots of time um you
+know and almost no course of study is
+
+ align:start position:0%
+know and almost no course of study is
+ 
+
+ align:start position:0%
+know and almost no course of study is
+the answer only one of those things like
+
+ align:start position:0%
+the answer only one of those things like
+ 
+
+ align:start position:0%
+the answer only one of those things like
+nobody believes you should just do
+
+ align:start position:0%
+nobody believes you should just do
+ 
+
+ align:start position:0%
+nobody believes you should just do
+creativity I think almost all of our
+
+ align:start position:0%
+creativity I think almost all of our
+ 
+
+ align:start position:0%
+creativity I think almost all of our
+subjects like have classes which are
+
+ align:start position:0%
+subjects like have classes which are
+ 
+
+ align:start position:0%
+subjects like have classes which are
+like okay time to buckle down and learn
+
+ align:start position:0%
+like okay time to buckle down and learn
+ 
+
+ align:start position:0%
+like okay time to buckle down and learn
+this thing. But we can often think about
+
+ align:start position:0%
+this thing. But we can often think about
+ 
+
+ align:start position:0%
+this thing. But we can often think about
+like how we order these things
+
+ align:start position:0%
+like how we order these things
+ 
+
+ align:start position:0%
+like how we order these things
+differently to produce more motivation
+
+ align:start position:0%
+differently to produce more motivation
+ 
+
+ align:start position:0%
+differently to produce more motivation
+or develop identity or other kinds of
+
+ align:start position:0%
+or develop identity or other kinds of
+ 
+
+ align:start position:0%
+or develop identity or other kinds of
+things like that. Um but again the like
+
+ align:start position:0%
+things like that. Um but again the like
+ 
+
+ align:start position:0%
+things like that. Um but again the like
+across different pedagogical
+
+ align:start position:0%
+across different pedagogical
+ 
+
+ align:start position:0%
+across different pedagogical
+philosophies is almost always the case
+
+ align:start position:0%
+philosophies is almost always the case
+ 
+
+ align:start position:0%
+philosophies is almost always the case
+that people have a very shared idea
+
+ align:start position:0%
+that people have a very shared idea
+ 
+
+ align:start position:0%
+that people have a very shared idea
+about what expertise is. Um so I think
+
+ align:start position:0%
+about what expertise is. Um so I think
+ 
+
+ align:start position:0%
+about what expertise is. Um so I think
+even people who you know um are situated
+
+ align:start position:0%
+even people who you know um are situated
+ 
+
+ align:start position:0%
+even people who you know um are situated
+learning folks um you know they like
+
+ align:start position:0%
+learning folks um you know they like
+ 
+
+ align:start position:0%
+learning folks um you know they like
+they they they don't want you to like
+
+ align:start position:0%
+they they they don't want you to like
+ 
+
+ align:start position:0%
+they they they don't want you to like
+invent midwiffery a new like they want
+
+ align:start position:0%
+invent midwiffery a new like they want
+ 
+
+ align:start position:0%
+invent midwiffery a new like they want
+the babies consistently delivered in
+
+ align:start position:0%
+the babies consistently delivered in
+ 
+
+ align:start position:0%
+the babies consistently delivered in
+safe healthy ways. Um uh so that so it's
+
+ align:start position:0%
+safe healthy ways. Um uh so that so it's
+ 
+
+ align:start position:0%
+safe healthy ways. Um uh so that so it's
+that it's different beliefs about how
+
+ align:start position:0%
+that it's different beliefs about how
+ 
+
+ align:start position:0%
+that it's different beliefs about how
+you get there. Um there are efforts to
+
+ align:start position:0%
+you get there. Um there are efforts to
+ 
+
+ align:start position:0%
+you get there. Um there are efforts to
+reconcile these things which I didn't
+
+ align:start position:0%
+reconcile these things which I didn't
+ 
+
+ align:start position:0%
+reconcile these things which I didn't
+make you read but if you wanted to
+
+ align:start position:0%
+make you read but if you wanted to
+ 
+
+ align:start position:0%
+make you read but if you wanted to
+explore a little bit more I'll give you
+
+ align:start position:0%
+explore a little bit more I'll give you
+ 
+
+ align:start position:0%
+explore a little bit more I'll give you
+an introduction to one of them um in the
+
+ align:start position:0%
+an introduction to one of them um in the
+ 
+
+ align:start position:0%
+an introduction to one of them um in the
+rabbit hole for this week. Ken Kadinger
+
+ align:start position:0%
+rabbit hole for this week. Ken Kadinger
+ 
+
+ align:start position:0%
+rabbit hole for this week. Ken Kadinger
+has a a couple of things you can look
+
+ align:start position:0%
+has a a couple of things you can look
+ 
+
+ align:start position:0%
+has a a couple of things you can look
+at. The the lecture he gives is actually
+
+ align:start position:0%
+at. The the lecture he gives is actually
+ 
+
+ align:start position:0%
+at. The the lecture he gives is actually
+the easiest way of getting it. There's a
+
+ align:start position:0%
+the easiest way of getting it. There's a
+ 
+
+ align:start position:0%
+the easiest way of getting it. There's a
+video in there. It's quite good. Um the
+
+ align:start position:0%
+video in there. It's quite good. Um the
+ 
+
+ align:start position:0%
+video in there. It's quite good. Um the
+knowledge learning instruction framework
+
+ align:start position:0%
+knowledge learning instruction framework
+ 
+
+ align:start position:0%
+knowledge learning instruction framework
+and he says one useful way to think
+
+ align:start position:0%
+and he says one useful way to think
+ 
+
+ align:start position:0%
+and he says one useful way to think
+about this um is that there are um uh
+
+ align:start position:0%
+about this um is that there are um uh
+ 
+
+ align:start position:0%
+about this um is that there are um uh
+more complex and less complex knowledge
+
+ align:start position:0%
+more complex and less complex knowledge
+ 
+
+ align:start position:0%
+more complex and less complex knowledge
+components in the things we learn. So
+
+ align:start position:0%
+components in the things we learn. So
+ 
+
+ align:start position:0%
+components in the things we learn. So
+there are things like um you know
+
+ align:start position:0%
+there are things like um you know
+ 
+
+ align:start position:0%
+there are things like um you know
+Chinese characters and there are things
+
+ align:start position:0%
+Chinese characters and there are things
+ 
+
+ align:start position:0%
+Chinese characters and there are things
+like you know um anthropological
+
+ align:start position:0%
+like you know um anthropological
+ 
+
+ align:start position:0%
+like you know um anthropological
+principles about how society are
+
+ align:start position:0%
+principles about how society are
+ 
+
+ align:start position:0%
+principles about how society are
+organized um and there different levels
+
+ align:start position:0%
+organized um and there different levels
+ 
+
+ align:start position:0%
+organized um and there different levels
+of complexity. There's also um sort of
+
+ align:start position:0%
+of complexity. There's also um sort of
+ 
+
+ align:start position:0%
+of complexity. There's also um sort of
+learning processes and there's things
+
+ align:start position:0%
+learning processes and there's things
+ 
+
+ align:start position:0%
+learning processes and there's things
+like flashc cards um and then you know
+
+ align:start position:0%
+like flashc cards um and then you know
+ 
+
+ align:start position:0%
+like flashc cards um and then you know
+which is just for memorizing stuff um
+
+ align:start position:0%
+which is just for memorizing stuff um
+ 
+
+ align:start position:0%
+which is just for memorizing stuff um
+and then there's things like um talk and
+
+ align:start position:0%
+and then there's things like um talk and
+ 
+
+ align:start position:0%
+and then there's things like um talk and
+explaining and sense making and stuff
+
+ align:start position:0%
+explaining and sense making and stuff
+ 
+
+ align:start position:0%
+explaining and sense making and stuff
+like that um and he has a theory that
+
+ align:start position:0%
+like that um and he has a theory that
+ 
+
+ align:start position:0%
+like that um and he has a theory that
+basically um you know you should be
+
+ align:start position:0%
+basically um you know you should be
+ 
+
+ align:start position:0%
+basically um you know you should be
+matching instructional components to how
+
+ align:start position:0%
+matching instructional components to how
+ 
+
+ align:start position:0%
+matching instructional components to how
+complex um the knowledge component
+
+ align:start position:0%
+complex um the knowledge component
+ 
+
+ align:start position:0%
+complex um the knowledge component
+learning processes to how complex the
+
+ align:start position:0%
+learning processes to how complex the
+ 
+
+ align:start position:0%
+learning processes to how complex the
+knowledge components are. Um he has a
+
+ align:start position:0%
+knowledge components are. Um he has a
+ 
+
+ align:start position:0%
+knowledge components are. Um he has a
+nice uh sort of this is kind of like a
+
+ align:start position:0%
+nice uh sort of this is kind of like a
+ 
+
+ align:start position:0%
+nice uh sort of this is kind of like a
+giant science which is in process where
+
+ align:start position:0%
+giant science which is in process where
+ 
+
+ align:start position:0%
+giant science which is in process where
+here are a bunch of things that people
+
+ align:start position:0%
+here are a bunch of things that people
+ 
+
+ align:start position:0%
+here are a bunch of things that people
+were trying to learn. Chinese vocab,
+
+ align:start position:0%
+were trying to learn. Chinese vocab,
+ 
+
+ align:start position:0%
+were trying to learn. Chinese vocab,
+French articles, chem models, pressure
+
+ align:start position:0%
+French articles, chem models, pressure
+ 
+
+ align:start position:0%
+French articles, chem models, pressure
+concept. Here are a bunch of uh
+
+ align:start position:0%
+concept. Here are a bunch of uh
+ 
+
+ align:start position:0%
+concept. Here are a bunch of uh
+instructional strategies, optimal
+
+ align:start position:0%
+instructional strategies, optimal
+ 
+
+ align:start position:0%
+instructional strategies, optimal
+scheduling, feedback, worked examples,
+
+ align:start position:0%
+scheduling, feedback, worked examples,
+ 
+
+ align:start position:0%
+scheduling, feedback, worked examples,
+accountable talk, collaboration and you
+
+ align:start position:0%
+accountable talk, collaboration and you
+ 
+
+ align:start position:0%
+accountable talk, collaboration and you
+find that like the you know these are
+
+ align:start position:0%
+find that like the you know these are
+ 
+
+ align:start position:0%
+find that like the you know these are
+less complex to more complex teaching.
+
+ align:start position:0%
+less complex to more complex teaching.
+ 
+
+ align:start position:0%
+less complex to more complex teaching.
+this is less complex to more complex um
+
+ align:start position:0%
+this is less complex to more complex um
+ 
+
+ align:start position:0%
+this is less complex to more complex um
+uh uh knowledge components and that like
+
+ align:start position:0%
+uh uh knowledge components and that like
+ 
+
+ align:start position:0%
+uh uh knowledge components and that like
+basically where you get uh studies with
+
+ align:start position:0%
+basically where you get uh studies with
+ 
+
+ align:start position:0%
+basically where you get uh studies with
+statistically significant effects on
+
+ align:start position:0%
+statistically significant effects on
+ 
+
+ align:start position:0%
+statistically significant effects on
+learning is when you kind of move
+
+ align:start position:0%
+learning is when you kind of move
+ 
+
+ align:start position:0%
+learning is when you kind of move
+through the middle of this space when
+
+ align:start position:0%
+through the middle of this space when
+ 
+
+ align:start position:0%
+through the middle of this space when
+you map the right knowledge component to
+
+ align:start position:0%
+you map the right knowledge component to
+ 
+
+ align:start position:0%
+you map the right knowledge component to
+the right learning process. I don't know
+
+ align:start position:0%
+the right learning process. I don't know
+ 
+
+ align:start position:0%
+the right learning process. I don't know
+that Ken Kinger and his colleagues have
+
+ align:start position:0%
+that Ken Kinger and his colleagues have
+ 
+
+ align:start position:0%
+that Ken Kinger and his colleagues have
+totally figured this out either. Um but
+
+ align:start position:0%
+totally figured this out either. Um but
+ 
+
+ align:start position:0%
+totally figured this out either. Um but
+it's one way to start sort of
+
+ align:start position:0%
+it's one way to start sort of
+ 
+
+ align:start position:0%
+it's one way to start sort of
+reconciling some of these ideas. Okay.
+
+ align:start position:0%
+reconciling some of these ideas. Okay.
+ 
+
+ align:start position:0%
+reconciling some of these ideas. Okay.
+Um the the most important thing for
+
+ align:start position:0%
+Um the the most important thing for
+ 
+
+ align:start position:0%
+Um the the most important thing for
+Wednesday is that we're meeting at the
+
+ align:start position:0%
+Wednesday is that we're meeting at the
+ 
+
+ align:start position:0%
+Wednesday is that we're meeting at the
+MIT Museum. Please try to be at the MIT
+
+ align:start position:0%
+MIT Museum. Please try to be at the MIT
+ 
+
+ align:start position:0%
+MIT Museum. Please try to be at the MIT
+Museum. Like if you could if you can get
+
+ align:start position:0%
+Museum. Like if you could if you can get
+ 
+
+ align:start position:0%
+Museum. Like if you could if you can get
+there by 1 and get checked in and put
+
+ align:start position:0%
+there by 1 and get checked in and put
+ 
+
+ align:start position:0%
+there by 1 and get checked in and put
+your bag in the locker, then we can
+
+ align:start position:0%
+your bag in the locker, then we can
+ 
+
+ align:start position:0%
+your bag in the locker, then we can
+start class at 105. So make every effort
+
+ align:start position:0%
+start class at 105. So make every effort
+ 
+
+ align:start position:0%
+start class at 105. So make every effort
+to get there as soon as you can. There's
+
+ align:start position:0%
+to get there as soon as you can. There's
+ 
+
+ align:start position:0%
+to get there as soon as you can. There's
+a few pieces of reading. Um the Steven
+
+ align:start position:0%
+a few pieces of reading. Um the Steven
+ 
+
+ align:start position:0%
+a few pieces of reading. Um the Steven
+Wolf thing is totally worth your time
+
+ align:start position:0%
+Wolf thing is totally worth your time
+ 
+
+ align:start position:0%
+Wolf thing is totally worth your time
+and it will require a little attention.
+
+ align:start position:0%
+and it will require a little attention.
+ 
+
+ align:start position:0%
+and it will require a little attention.
+Like you'll have to sort of move your
+
+ align:start position:0%
+Like you'll have to sort of move your
+ 
+
+ align:start position:0%
+Like you'll have to sort of move your
+way through it, but he does just a
+
+ align:start position:0%
+way through it, but he does just a
+ 
+
+ align:start position:0%
+way through it, but he does just a
+beautiful job explaining the
+
+ align:start position:0%
+beautiful job explaining the
+ 
+
+ align:start position:0%
+beautiful job explaining the
+fundamentals of generative pre-trained
+
+ align:start position:0%
+fundamentals of generative pre-trained
+ 
+
+ align:start position:0%
+fundamentals of generative pre-trained
+models. um a little bit about neural
+
+ align:start position:0%
+models. um a little bit about neural
+ 
+
+ align:start position:0%
+models. um a little bit about neural
+networks and things like that. And then
+
+ align:start position:0%
+networks and things like that. And then
+ 
+
+ align:start position:0%
+networks and things like that. And then
+there's a bunch of other readings that
+
+ align:start position:0%
+there's a bunch of other readings that
+ 
+
+ align:start position:0%
+there's a bunch of other readings that
+are in there. Some of which are about
+
+ align:start position:0%
+are in there. Some of which are about
+ 
+
+ align:start position:0%
+are in there. Some of which are about
+the mu the exhibits you'll see at the
+
+ align:start position:0%
+the mu the exhibits you'll see at the
+ 
+
+ align:start position:0%
+the mu the exhibits you'll see at the
+museum and some are some other
+
+ align:start position:0%
+museum and some are some other
+ 
+
+ align:start position:0%
+museum and some are some other
+educational things that me and some
+
+ align:start position:0%
+educational things that me and some
+ 
+
+ align:start position:0%
+educational things that me and some
+other folks at MIT have written about uh
+
+ align:start position:0%
+other folks at MIT have written about uh
+ 
+
+ align:start position:0%
+other folks at MIT have written about uh
+GPT. Um and then be sure you refresh
+
+ align:start position:0%
+GPT. Um and then be sure you refresh
+ 
+
+ align:start position:0%
+GPT. Um and then be sure you refresh
+yourself and you start thinking about
+
+ align:start position:0%
+yourself and you start thinking about
+ 
+
+ align:start position:0%
+yourself and you start thinking about
+working on the assignment because you
+
+ align:start position:0%
+working on the assignment because you
+ 
+
+ align:start position:0%
+working on the assignment because you
+now have two of the crucial building
+
+ align:start position:0%
+now have two of the crucial building
+ 
+
+ align:start position:0%
+now have two of the crucial building
+blocks that you'll need for the
+
+ align:start position:0%
+blocks that you'll need for the
+ 
+
+ align:start position:0%
+blocks that you'll need for the
+assignment. Um which is some sense of
+
+ align:start position:0%
+assignment. Um which is some sense of
+ 
+
+ align:start position:0%
+assignment. Um which is some sense of
+direct instruction, cognitive load
+
+ align:start position:0%
+direct instruction, cognitive load
+ 
+
+ align:start position:0%
+direct instruction, cognitive load
+theory, and some sense of
+
+ align:start position:0%
+theory, and some sense of
+ 
+
+ align:start position:0%
+theory, and some sense of
+constructionism, situated learning, um
+
+ align:start position:0%
+constructionism, situated learning, um
+ 
+
+ align:start position:0%
+constructionism, situated learning, um
+progressive learning kinds of things.
+
+ align:start position:0%
+progressive learning kinds of things.
+ 
+
+ align:start position:0%
+progressive learning kinds of things.
+And you'll need both of those ideas to
+
+ align:start position:0%
+And you'll need both of those ideas to
+ 
+
+ align:start position:0%
+And you'll need both of those ideas to
+do assignment number one. And we'll talk
+
+ align:start position:0%
+do assignment number one. And we'll talk
+ 
+
+ align:start position:0%
+do assignment number one. And we'll talk
+a little bit about uh how we want to do
+
+ align:start position:0%
+a little bit about uh how we want to do
+ 
+
+ align:start position:0%
+a little bit about uh how we want to do
+assignment number one on Wednesday. Stay
+
+ align:start position:0%
+assignment number one on Wednesday. Stay
+ 
+
+ align:start position:0%
+assignment number one on Wednesday. Stay
+safe in the snow. Have a wonderful uh
+
+ align:start position:0%
+safe in the snow. Have a wonderful uh
+ 
+
+ align:start position:0%
+safe in the snow. Have a wonderful uh
+next couple days. And I'll see you at
+
+ align:start position:0%
+next couple days. And I'll see you at
+ 
+
+ align:start position:0%
+next couple days. And I'll see you at
+the museum on Wednesday.
\ No newline at end of file
diff --git a/Mge-sj1UVFM.txt b/Mge-sj1UVFM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..258c909621b966e7c4c19f6fd36b7a703044a8fa
--- /dev/null
+++ b/Mge-sj1UVFM.txt
@@ -0,0 +1,843 @@
+align:start position:0%
+ 
+this is a lecture of how IBM build a
+
+ align:start position:0%
+this is a lecture of how IBM build a
+ 
+
+ align:start position:0%
+this is a lecture of how IBM build a
+computer that plays a very popular game
+
+ align:start position:0%
+computer that plays a very popular game
+ 
+
+ align:start position:0%
+computer that plays a very popular game
+of Jeopardy in 2004 IBM vice president
+
+ align:start position:0%
+of Jeopardy in 2004 IBM vice president
+ 
+
+ align:start position:0%
+of Jeopardy in 2004 IBM vice president
+Charlie CO and co-workers were having
+
+ align:start position:0%
+Charlie CO and co-workers were having
+ 
+
+ align:start position:0%
+Charlie CO and co-workers were having
+dinner at the restaurant all of a sudden
+
+ align:start position:0%
+dinner at the restaurant all of a sudden
+ 
+
+ align:start position:0%
+dinner at the restaurant all of a sudden
+the restaurant fell silent everyone was
+
+ align:start position:0%
+the restaurant fell silent everyone was
+ 
+
+ align:start position:0%
+the restaurant fell silent everyone was
+watching the game jeopardy on the
+
+ align:start position:0%
+watching the game jeopardy on the
+ 
+
+ align:start position:0%
+watching the game jeopardy on the
+television a contention Ken Jennings was
+
+ align:start position:0%
+television a contention Ken Jennings was
+ 
+
+ align:start position:0%
+television a contention Ken Jennings was
+setting the record for the longest
+
+ align:start position:0%
+setting the record for the longest
+ 
+
+ align:start position:0%
+setting the record for the longest
+winning streak of all times 75 days why
+
+ align:start position:0%
+winning streak of all times 75 days why
+ 
+
+ align:start position:0%
+winning streak of all times 75 days why
+was everyone so interested Joe Pardy is
+
+ align:start position:0%
+was everyone so interested Joe Pardy is
+ 
+
+ align:start position:0%
+was everyone so interested Joe Pardy is
+a quiz show that asks complex and clever
+
+ align:start position:0%
+a quiz show that asks complex and clever
+ 
+
+ align:start position:0%
+a quiz show that asks complex and clever
+questions like pans of score facts and
+
+ align:start position:0%
+questions like pans of score facts and
+ 
+
+ align:start position:0%
+questions like pans of score facts and
+uncommon words it originally aired in
+
+ align:start position:0%
+uncommon words it originally aired in
+ 
+
+ align:start position:0%
+uncommon words it originally aired in
+1964 it covers a huge variety of topics
+
+ align:start position:0%
+1964 it covers a huge variety of topics
+ 
+
+ align:start position:0%
+1964 it covers a huge variety of topics
+and is generally viewed as an impressive
+
+ align:start position:0%
+and is generally viewed as an impressive
+ 
+
+ align:start position:0%
+and is generally viewed as an impressive
+feat to do well in this game no computer
+
+ align:start position:0%
+feat to do well in this game no computer
+ 
+
+ align:start position:0%
+feat to do well in this game no computer
+system has ever been developed that
+
+ align:start position:0%
+system has ever been developed that
+ 
+
+ align:start position:0%
+system has ever been developed that
+could even come close to competing with
+
+ align:start position:0%
+could even come close to competing with
+ 
+
+ align:start position:0%
+could even come close to competing with
+humans on Jeopardy IBM Research strives
+
+ align:start position:0%
+humans on Jeopardy IBM Research strives
+ 
+
+ align:start position:0%
+humans on Jeopardy IBM Research strives
+to push the limits of science it has a
+
+ align:start position:0%
+to push the limits of science it has a
+ 
+
+ align:start position:0%
+to push the limits of science it has a
+tradition of addressing inspiring and
+
+ align:start position:0%
+tradition of addressing inspiring and
+ 
+
+ align:start position:0%
+tradition of addressing inspiring and
+difficult challenges over the years in
+
+ align:start position:0%
+difficult challenges over the years in
+ 
+
+ align:start position:0%
+difficult challenges over the years in
+the mid-90s it built deep-blue a
+
+ align:start position:0%
+the mid-90s it built deep-blue a
+ 
+
+ align:start position:0%
+the mid-90s it built deep-blue a
+computer to compete against the best
+
+ align:start position:0%
+computer to compete against the best
+ 
+
+ align:start position:0%
+computer to compete against the best
+human chess players and then the mid-90s
+
+ align:start position:0%
+human chess players and then the mid-90s
+ 
+
+ align:start position:0%
+human chess players and then the mid-90s
+the blue bit Garry Kasparov who was at
+
+ align:start position:0%
+the blue bit Garry Kasparov who was at
+ 
+
+ align:start position:0%
+the blue bit Garry Kasparov who was at
+that time world champion in chess later
+
+ align:start position:0%
+that time world champion in chess later
+ 
+
+ align:start position:0%
+that time world champion in chess later
+it built Blue Gene a computer to map the
+
+ align:start position:0%
+it built Blue Gene a computer to map the
+ 
+
+ align:start position:0%
+it built Blue Gene a computer to map the
+human human genome in 2005 a team at IBM
+
+ align:start position:0%
+human human genome in 2005 a team at IBM
+ 
+
+ align:start position:0%
+human human genome in 2005 a team at IBM
+research started creating a computer
+
+ align:start position:0%
+research started creating a computer
+ 
+
+ align:start position:0%
+research started creating a computer
+that would compete at jeopardy of course
+
+ align:start position:0%
+that would compete at jeopardy of course
+ 
+
+ align:start position:0%
+that would compete at jeopardy of course
+no one knew at the time how to beat
+
+ align:start position:0%
+no one knew at the time how to beat
+ 
+
+ align:start position:0%
+no one knew at the time how to beat
+humans or even if it was even possible
+
+ align:start position:0%
+humans or even if it was even possible
+ 
+
+ align:start position:0%
+humans or even if it was even possible
+six years later a two-game exhibition
+
+ align:start position:0%
+six years later a two-game exhibition
+ 
+
+ align:start position:0%
+six years later a two-game exhibition
+match aired on television the winner
+
+ align:start position:0%
+match aired on television the winner
+ 
+
+ align:start position:0%
+match aired on television the winner
+would receive a million dollars the
+
+ align:start position:0%
+would receive a million dollars the
+ 
+
+ align:start position:0%
+would receive a million dollars the
+contentions were Ken Jennings the
+
+ align:start position:0%
+contentions were Ken Jennings the
+ 
+
+ align:start position:0%
+contentions were Ken Jennings the
+longest winning champion whose longest
+
+ align:start position:0%
+longest winning champion whose longest
+ 
+
+ align:start position:0%
+longest winning champion whose longest
+winning streak was 75 days Brad Rutter
+
+ align:start position:0%
+winning streak was 75 days Brad Rutter
+ 
+
+ align:start position:0%
+winning streak was 75 days Brad Rutter
+who was the biggest money winner of over
+
+ align:start position:0%
+who was the biggest money winner of over
+ 
+
+ align:start position:0%
+who was the biggest money winner of over
+3.5 million and watch on a supercomputer
+
+ align:start position:0%
+3.5 million and watch on a supercomputer
+ 
+
+ align:start position:0%
+3.5 million and watch on a supercomputer
+with 3000
+
+ align:start position:0%
+with 3000
+ 
+
+ align:start position:0%
+with 3000
+and processors in a database of 200
+
+ align:start position:0%
+and processors in a database of 200
+ 
+
+ align:start position:0%
+and processors in a database of 200
+million pages of information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+and welcome everyone to a very special
+
+ align:start position:0%
+and welcome everyone to a very special
+ 
+
+ align:start position:0%
+and welcome everyone to a very special
+jeopardy event for the next three days
+
+ align:start position:0%
+jeopardy event for the next three days
+ 
+
+ align:start position:0%
+jeopardy event for the next three days
+we're gonna be coming to you from this
+
+ align:start position:0%
+we're gonna be coming to you from this
+ 
+
+ align:start position:0%
+we're gonna be coming to you from this
+IBM research facility just outside of
+
+ align:start position:0%
+IBM research facility just outside of
+ 
+
+ align:start position:0%
+IBM research facility just outside of
+New York City
+
+ align:start position:0%
+New York City
+ 
+
+ align:start position:0%
+New York City
+let me tell you why a little over three
+
+ align:start position:0%
+let me tell you why a little over three
+ 
+
+ align:start position:0%
+let me tell you why a little over three
+years ago the folks at IBM came to us
+
+ align:start position:0%
+years ago the folks at IBM came to us
+ 
+
+ align:start position:0%
+years ago the folks at IBM came to us
+with a proposal that they considered to
+
+ align:start position:0%
+with a proposal that they considered to
+ 
+
+ align:start position:0%
+with a proposal that they considered to
+be the next grand challenge in computing
+
+ align:start position:0%
+be the next grand challenge in computing
+ 
+
+ align:start position:0%
+be the next grand challenge in computing
+and that was designing a computer system
+
+ align:start position:0%
+and that was designing a computer system
+ 
+
+ align:start position:0%
+and that was designing a computer system
+that could understand the complexities
+
+ align:start position:0%
+that could understand the complexities
+ 
+
+ align:start position:0%
+that could understand the complexities
+of natural language well enough to
+
+ align:start position:0%
+of natural language well enough to
+ 
+
+ align:start position:0%
+of natural language well enough to
+compete against Jeopardy's best players
+
+ align:start position:0%
+compete against Jeopardy's best players
+ 
+
+ align:start position:0%
+compete against Jeopardy's best players
+well they think they've succeeded and
+
+ align:start position:0%
+well they think they've succeeded and
+ 
+
+ align:start position:0%
+well they think they've succeeded and
+that's why we're here today so you are
+
+ align:start position:0%
+that's why we're here today so you are
+ 
+
+ align:start position:0%
+that's why we're here today so you are
+about to witness what may prove to be an
+
+ align:start position:0%
+about to witness what may prove to be an
+ 
+
+ align:start position:0%
+about to witness what may prove to be an
+historic competition an exhibition match
+
+ align:start position:0%
+historic competition an exhibition match
+ 
+
+ align:start position:0%
+historic competition an exhibition match
+pitting an IBM computer system against
+
+ align:start position:0%
+pitting an IBM computer system against
+ 
+
+ align:start position:0%
+pitting an IBM computer system against
+the two most celebrated and successful
+
+ align:start position:0%
+the two most celebrated and successful
+ 
+
+ align:start position:0%
+the two most celebrated and successful
+players in jeopardy history sounds like
+
+ align:start position:0%
+players in jeopardy history sounds like
+ 
+
+ align:start position:0%
+players in jeopardy history sounds like
+a lot of fun doesn't it developed and
+
+ align:start position:0%
+a lot of fun doesn't it developed and
+ 
+
+ align:start position:0%
+a lot of fun doesn't it developed and
+programmed especially for this moment
+
+ align:start position:0%
+programmed especially for this moment
+ 
+
+ align:start position:0%
+programmed especially for this moment
+making its first appearance on our
+
+ align:start position:0%
+making its first appearance on our
+ 
+
+ align:start position:0%
+making its first appearance on our
+national television program ladies and
+
+ align:start position:0%
+national television program ladies and
+ 
+
+ align:start position:0%
+national television program ladies and
+gentlemen this is Watson
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just as I expected that was a very warm
+
+ align:start position:0%
+just as I expected that was a very warm
+ 
+
+ align:start position:0%
+just as I expected that was a very warm
+reception and I'm sure Watson would have
+
+ align:start position:0%
+reception and I'm sure Watson would have
+ 
+
+ align:start position:0%
+reception and I'm sure Watson would have
+appreciated the applause except for one
+
+ align:start position:0%
+appreciated the applause except for one
+ 
+
+ align:start position:0%
+appreciated the applause except for one
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+Watson can neither hear nor see it will
+
+ align:start position:0%
+Watson can neither hear nor see it will
+ 
+
+ align:start position:0%
+Watson can neither hear nor see it will
+be receiving all of its information late
+
+ align:start position:0%
+be receiving all of its information late
+ 
+
+ align:start position:0%
+be receiving all of its information late
+and as a matter of fact what you're
+
+ align:start position:0%
+and as a matter of fact what you're
+ 
+
+ align:start position:0%
+and as a matter of fact what you're
+looking at right now is not the real
+
+ align:start position:0%
+looking at right now is not the real
+ 
+
+ align:start position:0%
+looking at right now is not the real
+Watson this is an avatar this is a
+
+ align:start position:0%
+Watson this is an avatar this is a
+ 
+
+ align:start position:0%
+Watson this is an avatar this is a
+representation of Watson Watson of
+
+ align:start position:0%
+representation of Watson Watson of
+ 
+
+ align:start position:0%
+representation of Watson Watson of
+course is a sophisticated computer
+
+ align:start position:0%
+course is a sophisticated computer
+ 
+
+ align:start position:0%
+course is a sophisticated computer
+system too big and too heavy to fit
+
+ align:start position:0%
+system too big and too heavy to fit
+ 
+
+ align:start position:0%
+system too big and too heavy to fit
+behind that lecture on our stage but it
+
+ align:start position:0%
+behind that lecture on our stage but it
+ 
+
+ align:start position:0%
+behind that lecture on our stage but it
+is close by it's right next door and a
+
+ align:start position:0%
+is close by it's right next door and a
+ 
+
+ align:start position:0%
+is close by it's right next door and a
+little while ago I paid it a visit the
+
+ align:start position:0%
+little while ago I paid it a visit the
+ 
+
+ align:start position:0%
+little while ago I paid it a visit the
+very first thing you will notice as I
+
+ align:start position:0%
+very first thing you will notice as I
+ 
+
+ align:start position:0%
+very first thing you will notice as I
+come in to Watson's space is noise there
+
+ align:start position:0%
+come in to Watson's space is noise there
+ 
+
+ align:start position:0%
+come in to Watson's space is noise there
+is a lot of noise a little bit comes
+
+ align:start position:0%
+is a lot of noise a little bit comes
+ 
+
+ align:start position:0%
+is a lot of noise a little bit comes
+from Watson himself but most of the
+
+ align:start position:0%
+from Watson himself but most of the
+ 
+
+ align:start position:0%
+from Watson himself but most of the
+noise comes from two very large
+
+ align:start position:0%
+noise comes from two very large
+ 
+
+ align:start position:0%
+noise comes from two very large
+refrigerator units that help to keep
+
+ align:start position:0%
+refrigerator units that help to keep
+ 
+
+ align:start position:0%
+refrigerator units that help to keep
+Watson cool now as you can see Watson
+
+ align:start position:0%
+Watson cool now as you can see Watson
+ 
+
+ align:start position:0%
+Watson cool now as you can see Watson
+has been set up in two units each half
+
+ align:start position:0%
+has been set up in two units each half
+ 
+
+ align:start position:0%
+has been set up in two units each half
+contains five separate Rex each of these
+
+ align:start position:0%
+contains five separate Rex each of these
+ 
+
+ align:start position:0%
+contains five separate Rex each of these
+racks contains ten IBM power 750 servers
+
+ align:start position:0%
+racks contains ten IBM power 750 servers
+ 
+
+ align:start position:0%
+racks contains ten IBM power 750 servers
+now when you link all of these servers
+
+ align:start position:0%
+now when you link all of these servers
+ 
+
+ align:start position:0%
+now when you link all of these servers
+together as they have done for Watson
+
+ align:start position:0%
+together as they have done for Watson
+ 
+
+ align:start position:0%
+together as they have done for Watson
+you create a deep analytic system that
+
+ align:start position:0%
+you create a deep analytic system that
+ 
+
+ align:start position:0%
+you create a deep analytic system that
+is the equivalent of two thousand eight
+
+ align:start position:0%
+is the equivalent of two thousand eight
+ 
+
+ align:start position:0%
+is the equivalent of two thousand eight
+hundred powerful computers tied together
+
+ align:start position:0%
+hundred powerful computers tied together
+ 
+
+ align:start position:0%
+hundred powerful computers tied together
+in a super high-speed network
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/MjRb8R33Ucc.txt b/MjRb8R33Ucc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a299b427bba21e6e6a562641eb741d6ecbad0877
--- /dev/null
+++ b/MjRb8R33Ucc.txt
@@ -0,0 +1,11363 @@
+align:start position:0%
+ 
+Okay. So let's so assume that again that
+
+ align:start position:0%
+Okay. So let's so assume that again that
+ 
+
+ align:start position:0%
+Okay. So let's so assume that again that
+we have a so this here is a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we can form from a sequence we can
+
+ align:start position:0%
+then we can form from a sequence we can
+ 
+
+ align:start position:0%
+then we can form from a sequence we can
+find we can form another sequence. So
+
+ align:start position:0%
+find we can form another sequence. So
+ 
+
+ align:start position:0%
+find we can form another sequence. So
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+from a end we can form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh at least if um at least
+
+ align:start position:0%
+uh at least if um at least
+ 
+
+ align:start position:0%
+uh at least if um at least
+if a end is bounded from above.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we can form another sequence and
+
+ align:start position:0%
+So we can form another sequence and
+ 
+
+ align:start position:0%
+So we can form another sequence and
+that's what we we take
+
+ align:start position:0%
+that's what we we take
+ 
+
+ align:start position:0%
+that's what we we take
+uh bn
+
+ align:start position:0%
+uh bn
+ 
+
+ align:start position:0%
+uh bn
+is going to be the soup of the set
+
+ align:start position:0%
+is going to be the soup of the set
+ 
+
+ align:start position:0%
+is going to be the soup of the set
+of a starting at n. So this here is is
+
+ align:start position:0%
+of a starting at n. So this here is is
+ 
+
+ align:start position:0%
+of a starting at n. So this here is is
+oops this here is the the sequence bn.
+
+ align:start position:0%
+oops this here is the the sequence bn.
+ 
+
+ align:start position:0%
+oops this here is the the sequence bn.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And so right again implicitly here we
+
+ align:start position:0%
+And so right again implicitly here we
+ 
+
+ align:start position:0%
+And so right again implicitly here we
+are assuming so assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh that there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some c so that for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh a n is less than c in other words c
+
+ align:start position:0%
+uh a n is less than c in other words c
+ 
+
+ align:start position:0%
+uh a n is less than c in other words c
+are bounded from above right so if we If
+
+ align:start position:0%
+are bounded from above right so if we If
+ 
+
+ align:start position:0%
+are bounded from above right so if we If
+we if the sequence a n is bounded from
+
+ align:start position:0%
+we if the sequence a n is bounded from
+ 
+
+ align:start position:0%
+we if the sequence a n is bounded from
+above then this here gives us a real
+
+ align:start position:0%
+above then this here gives us a real
+ 
+
+ align:start position:0%
+above then this here gives us a real
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+uh and we see
+
+ align:start position:0%
+uh and we see
+ 
+
+ align:start position:0%
+uh and we see
+and we see that since if you're looking
+
+ align:start position:0%
+and we see that since if you're looking
+ 
+
+ align:start position:0%
+and we see that since if you're looking
+at uh bn + one this is now soup of a n +
+
+ align:start position:0%
+at uh bn + one this is now soup of a n +
+ 
+
+ align:start position:0%
+at uh bn + one this is now soup of a n +
+one a n + 2
+
+ align:start position:0%
+one a n + 2
+ 
+
+ align:start position:0%
+one a n + 2
+and this here is soup over a smaller
+
+ align:start position:0%
+and this here is soup over a smaller
+ 
+
+ align:start position:0%
+and this here is soup over a smaller
+set. So this here is less than the soup
+
+ align:start position:0%
+set. So this here is less than the soup
+ 
+
+ align:start position:0%
+set. So this here is less than the soup
+where we do it over where we take soup
+
+ align:start position:0%
+where we do it over where we take soup
+ 
+
+ align:start position:0%
+where we do it over where we take soup
+over a larger set.
+
+ align:start position:0%
+over a larger set.
+ 
+
+ align:start position:0%
+over a larger set.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+And that here is BN.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we have that if you take any sequence
+
+ align:start position:0%
+So we have that if you take any sequence
+ 
+
+ align:start position:0%
+So we have that if you take any sequence
+then you can and let's say that that
+
+ align:start position:0%
+then you can and let's say that that
+ 
+
+ align:start position:0%
+then you can and let's say that that
+sequence is bounded from above then you
+
+ align:start position:0%
+sequence is bounded from above then you
+ 
+
+ align:start position:0%
+sequence is bounded from above then you
+can find another you can form another
+
+ align:start position:0%
+can find another you can form another
+ 
+
+ align:start position:0%
+can find another you can form another
+sequence BN and BN here is mono
+
+ align:start position:0%
+sequence BN and BN here is mono
+ 
+
+ align:start position:0%
+sequence BN and BN here is mono
+decreasing right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+if also if the sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+BN is bound from below
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then uh then the BN here in the sequence
+
+ align:start position:0%
+then uh then the BN here in the sequence
+ 
+
+ align:start position:0%
+then uh then the BN here in the sequence
+here converge and it converts to the
+
+ align:start position:0%
+here converge and it converts to the
+ 
+
+ align:start position:0%
+here converge and it converts to the
+infam right this is this uh with mono
+
+ align:start position:0%
+infam right this is this uh with mono
+ 
+
+ align:start position:0%
+infam right this is this uh with mono
+convergent sequences it's converging to
+
+ align:start position:0%
+convergent sequences it's converging to
+ 
+
+ align:start position:0%
+convergent sequences it's converging to
+the infimum of the BI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that.
+
+ align:start position:0%
+like that.
+ 
+
+ align:start position:0%
+like that.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now, um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+and and likewise, so likewise, although
+
+ align:start position:0%
+and and likewise, so likewise, although
+ 
+
+ align:start position:0%
+and and likewise, so likewise, although
+we won't really use this here. So,
+
+ align:start position:0%
+we won't really use this here. So,
+ 
+
+ align:start position:0%
+we won't really use this here. So,
+likewise, but likewise,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um again if you take if a n is any
+
+ align:start position:0%
+Um again if you take if a n is any
+ 
+
+ align:start position:0%
+Um again if you take if a n is any
+sequence any sequence
+
+ align:start position:0%
+sequence any sequence
+ 
+
+ align:start position:0%
+sequence any sequence
+this time I want it to be bounded from
+
+ align:start position:0%
+this time I want it to be bounded from
+ 
+
+ align:start position:0%
+this time I want it to be bounded from
+below
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you can find a sequence then you
+
+ align:start position:0%
+then you can find a sequence then you
+ 
+
+ align:start position:0%
+then you can find a sequence then you
+can form from a n you can form a
+
+ align:start position:0%
+can form from a n you can form a
+ 
+
+ align:start position:0%
+can form from a n you can form a
+sequence uh cn and cn is just where
+
+ align:start position:0%
+sequence uh cn and cn is just where
+ 
+
+ align:start position:0%
+sequence uh cn and cn is just where
+you're taking the infam one starting at
+
+ align:start position:0%
+you're taking the infam one starting at
+ 
+
+ align:start position:0%
+you're taking the infam one starting at
+a end,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? And you see that if you're
+
+ align:start position:0%
+right? And you see that if you're
+ 
+
+ align:start position:0%
+right? And you see that if you're
+looking at CN + one, then you take the
+
+ align:start position:0%
+looking at CN + one, then you take the
+ 
+
+ align:start position:0%
+looking at CN + one, then you take the
+infom over a smaller set.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is a smaller set and so this
+
+ align:start position:0%
+So this is a smaller set and so this
+ 
+
+ align:start position:0%
+So this is a smaller set and so this
+here is bigger than where you're taking
+
+ align:start position:0%
+here is bigger than where you're taking
+ 
+
+ align:start position:0%
+here is bigger than where you're taking
+the info from a end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's CN. So the sequence CN is
+
+ align:start position:0%
+and that's CN. So the sequence CN is
+ 
+
+ align:start position:0%
+and that's CN. So the sequence CN is
+therefore monotone increasing and if it
+
+ align:start position:0%
+therefore monotone increasing and if it
+ 
+
+ align:start position:0%
+therefore monotone increasing and if it
+is bounded. So if CN is bounded from
+
+ align:start position:0%
+is bounded. So if CN is bounded from
+ 
+
+ align:start position:0%
+is bounded. So if CN is bounded from
+above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bounded from above.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then the sequence CN converge to some C.
+
+ align:start position:0%
+Then the sequence CN converge to some C.
+ 
+
+ align:start position:0%
+Then the sequence CN converge to some C.
+And that sea is just a soup of the of
+
+ align:start position:0%
+And that sea is just a soup of the of
+ 
+
+ align:start position:0%
+And that sea is just a soup of the of
+the seas,
+
+ align:start position:0%
+the seas,
+ 
+
+ align:start position:0%
+the seas,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+And so and we talked a little bit about
+
+ align:start position:0%
+And so and we talked a little bit about
+ 
+
+ align:start position:0%
+And so and we talked a little bit about
+this earlier, right? And the thing is
+
+ align:start position:0%
+this earlier, right? And the thing is
+ 
+
+ align:start position:0%
+this earlier, right? And the thing is
+that but now we will use it in just a
+
+ align:start position:0%
+that but now we will use it in just a
+ 
+
+ align:start position:0%
+that but now we will use it in just a
+second.
+
+ align:start position:0%
+second.
+ 
+
+ align:start position:0%
+second.
+The thing is so that in the first case
+
+ align:start position:0%
+The thing is so that in the first case
+ 
+
+ align:start position:0%
+The thing is so that in the first case
+here we call B here B is written as a
+
+ align:start position:0%
+here we call B here B is written as a
+ 
+
+ align:start position:0%
+here we call B here B is written as a
+lem
+
+ align:start position:0%
+lem
+ 
+
+ align:start position:0%
+lem
+soup of of the of the an
+
+ align:start position:0%
+soup of of the of the an
+ 
+
+ align:start position:0%
+soup of of the of the an
+and in the second case it's called the
+
+ align:start position:0%
+and in the second case it's called the
+ 
+
+ align:start position:0%
+and in the second case it's called the
+lem in
+
+ align:start position:0%
+lem in
+ 
+
+ align:start position:0%
+lem in
+uh of of the a
+
+ align:start position:0%
+uh of of the a
+ 
+
+ align:start position:0%
+uh of of the a
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so why is this relevant here for us so
+
+ align:start position:0%
+so why is this relevant here for us so
+ 
+
+ align:start position:0%
+so why is this relevant here for us so
+what we were looking at last time So
+
+ align:start position:0%
+what we were looking at last time So
+ 
+
+ align:start position:0%
+what we were looking at last time So
+last time and I'm only going to use the
+
+ align:start position:0%
+last time and I'm only going to use the
+ 
+
+ align:start position:0%
+last time and I'm only going to use the
+lem soup. So last time
+
+ align:start position:0%
+lem soup. So last time
+ 
+
+ align:start position:0%
+lem soup. So last time
+we had a sequence. So a n is a sequence
+
+ align:start position:0%
+we had a sequence. So a n is a sequence
+ 
+
+ align:start position:0%
+we had a sequence. So a n is a sequence
+or was a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we looked we defined what we call a
+
+ align:start position:0%
+and we looked we defined what we call a
+ 
+
+ align:start position:0%
+and we looked we defined what we call a
+power series. And again power series
+
+ align:start position:0%
+power series. And again power series
+ 
+
+ align:start position:0%
+power series. And again power series
+think about that x as being just some
+
+ align:start position:0%
+think about that x as being just some
+ 
+
+ align:start position:0%
+think about that x as being just some
+fixed number
+
+ align:start position:0%
+fixed number
+ 
+
+ align:start position:0%
+fixed number
+and you have the sequence a n x is some
+
+ align:start position:0%
+and you have the sequence a n x is some
+ 
+
+ align:start position:0%
+and you have the sequence a n x is some
+fixed number and then you form the
+
+ align:start position:0%
+fixed number and then you form the
+ 
+
+ align:start position:0%
+fixed number and then you form the
+sequence a n xn right
+
+ align:start position:0%
+sequence a n xn right
+ 
+
+ align:start position:0%
+sequence a n xn right
+and so for each x fixed this gives you
+
+ align:start position:0%
+and so for each x fixed this gives you
+ 
+
+ align:start position:0%
+and so for each x fixed this gives you
+some number maybe if it converge I mean
+
+ align:start position:0%
+some number maybe if it converge I mean
+ 
+
+ align:start position:0%
+some number maybe if it converge I mean
+you can ask for each x you can ask does
+
+ align:start position:0%
+you can ask for each x you can ask does
+ 
+
+ align:start position:0%
+you can ask for each x you can ask does
+this sequence converge or
+
+ align:start position:0%
+this sequence converge or
+ 
+
+ align:start position:0%
+this sequence converge or
+And this here is called a power series.
+
+ align:start position:0%
+And this here is called a power series.
+ 
+
+ align:start position:0%
+And this here is called a power series.
+So you're suming from zero to whatever
+
+ align:start position:0%
+So you're suming from zero to whatever
+ 
+
+ align:start position:0%
+So you're suming from zero to whatever
+or you're signing from one or whatever
+
+ align:start position:0%
+or you're signing from one or whatever
+ 
+
+ align:start position:0%
+or you're signing from one or whatever
+you're starting with up to infinity. So
+
+ align:start position:0%
+you're starting with up to infinity. So
+ 
+
+ align:start position:0%
+you're starting with up to infinity. So
+this here is a power series.
+
+ align:start position:0%
+this here is a power series.
+ 
+
+ align:start position:0%
+this here is a power series.
+And so now it for power says the the the
+
+ align:start position:0%
+And so now it for power says the the the
+ 
+
+ align:start position:0%
+And so now it for power says the the the
+question is
+
+ align:start position:0%
+question is
+ 
+
+ align:start position:0%
+question is
+how serious is the question is what
+
+ align:start position:0%
+how serious is the question is what
+ 
+
+ align:start position:0%
+how serious is the question is what
+about for which
+
+ align:start position:0%
+about for which
+ 
+
+ align:start position:0%
+about for which
+for which
+
+ align:start position:0%
+for which
+ 
+
+ align:start position:0%
+for which
+X does it converge.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that's what we're interested in
+
+ align:start position:0%
+Okay, so that's what we're interested in
+ 
+
+ align:start position:0%
+Okay, so that's what we're interested in
+and what we looked at last time.
+
+ align:start position:0%
+and what we looked at last time.
+ 
+
+ align:start position:0%
+and what we looked at last time.
+So just let me remind you because we're
+
+ align:start position:0%
+So just let me remind you because we're
+ 
+
+ align:start position:0%
+So just let me remind you because we're
+going to use that anyway in a minute
+
+ align:start position:0%
+going to use that anyway in a minute
+ 
+
+ align:start position:0%
+going to use that anyway in a minute
+last time. So example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, the example we looked at last time
+
+ align:start position:0%
+Well, the example we looked at last time
+ 
+
+ align:start position:0%
+Well, the example we looked at last time
+was we're looking at xn. I mean, we
+
+ align:start position:0%
+was we're looking at xn. I mean, we
+ 
+
+ align:start position:0%
+was we're looking at xn. I mean, we
+looked at some other examples too, but
+
+ align:start position:0%
+looked at some other examples too, but
+ 
+
+ align:start position:0%
+looked at some other examples too, but
+this was the one we focused on.
+
+ align:start position:0%
+this was the one we focused on.
+ 
+
+ align:start position:0%
+this was the one we focused on.
+So, this here is a power series. The a n
+
+ align:start position:0%
+So, this here is a power series. The a n
+ 
+
+ align:start position:0%
+So, this here is a power series. The a n
+in this case here
+
+ align:start position:0%
+in this case here
+ 
+
+ align:start position:0%
+in this case here
+are one over n factorial, right?
+
+ align:start position:0%
+are one over n factorial, right?
+ 
+
+ align:start position:0%
+are one over n factorial, right?
+So now uh and we and for each fixed x so
+
+ align:start position:0%
+So now uh and we and for each fixed x so
+ 
+
+ align:start position:0%
+So now uh and we and for each fixed x so
+for for x fixed
+
+ align:start position:0%
+for for x fixed
+ 
+
+ align:start position:0%
+for for x fixed
+we looked at whether or not this
+
+ align:start position:0%
+we looked at whether or not this
+ 
+
+ align:start position:0%
+we looked at whether or not this
+sequence converge and so we defined we
+
+ align:start position:0%
+sequence converge and so we defined we
+ 
+
+ align:start position:0%
+sequence converge and so we defined we
+think about this thing here we thought
+
+ align:start position:0%
+think about this thing here we thought
+ 
+
+ align:start position:0%
+think about this thing here we thought
+this here we thought about it as just a
+
+ align:start position:0%
+this here we thought about it as just a
+ 
+
+ align:start position:0%
+this here we thought about it as just a
+sequence like this
+
+ align:start position:0%
+sequence like this
+ 
+
+ align:start position:0%
+sequence like this
+sum of of a sequence so this is as a
+
+ align:start position:0%
+sum of of a sequence so this is as a
+ 
+
+ align:start position:0%
+sum of of a sequence so this is as a
+series like is where the dn here is now
+
+ align:start position:0%
+series like is where the dn here is now
+ 
+
+ align:start position:0%
+series like is where the dn here is now
+x to the n / n factorial right
+
+ align:start position:0%
+x to the n / n factorial right
+ 
+
+ align:start position:0%
+x to the n / n factorial right
+and so in order to determine for which x
+
+ align:start position:0%
+and so in order to determine for which x
+ 
+
+ align:start position:0%
+and so in order to determine for which x
+it converge so just think about x as
+
+ align:start position:0%
+it converge so just think about x as
+ 
+
+ align:start position:0%
+it converge so just think about x as
+being fixed we use the ratio test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we use the ratio test
+
+ align:start position:0%
+so we use the ratio test
+ 
+
+ align:start position:0%
+so we use the ratio test
+and the ratio test um said that If
+
+ align:start position:0%
+and the ratio test um said that If
+ 
+
+ align:start position:0%
+and the ratio test um said that If
+you're looking at dn + 1 / dn,
+
+ align:start position:0%
+you're looking at dn + 1 / dn,
+ 
+
+ align:start position:0%
+you're looking at dn + 1 / dn,
+this here is well dn is just x to the n
+
+ align:start position:0%
+this here is well dn is just x to the n
+ 
+
+ align:start position:0%
+this here is well dn is just x to the n
++ 1 / n + 1 factorial divided by x to
+
+ align:start position:0%
++ 1 / n + 1 factorial divided by x to
+ 
+
+ align:start position:0%
++ 1 / n + 1 factorial divided by x to
+the n / n factorial.
+
+ align:start position:0%
+the n / n factorial.
+ 
+
+ align:start position:0%
+the n / n factorial.
+And that's the same, right? So when you
+
+ align:start position:0%
+And that's the same, right? So when you
+ 
+
+ align:start position:0%
+And that's the same, right? So when you
+divide by a fraction, you just switch,
+
+ align:start position:0%
+divide by a fraction, you just switch,
+ 
+
+ align:start position:0%
+divide by a fraction, you just switch,
+right? So this is the same as x to the n
+
+ align:start position:0%
+right? So this is the same as x to the n
+ 
+
+ align:start position:0%
+right? So this is the same as x to the n
++ 1 / n + 1 factorial * n factorial * x
+
+ align:start position:0%
++ 1 / n + 1 factorial * n factorial * x
+ 
+
+ align:start position:0%
++ 1 / n + 1 factorial * n factorial * x
+to the n. And you just think about this
+
+ align:start position:0%
+to the n. And you just think about this
+ 
+
+ align:start position:0%
+to the n. And you just think about this
+the top here as x n * x * n factorial.
+
+ align:start position:0%
+the top here as x n * x * n factorial.
+ 
+
+ align:start position:0%
+the top here as x n * x * n factorial.
+And the denominator you think about as n
+
+ align:start position:0%
+And the denominator you think about as n
+ 
+
+ align:start position:0%
+And the denominator you think about as n
++1 * n factorial * x. You see that this
+
+ align:start position:0%
++1 * n factorial * x. You see that this
+ 
+
+ align:start position:0%
++1 * n factorial * x. You see that this
+here and this here cancel with those two
+
+ align:start position:0%
+here and this here cancel with those two
+ 
+
+ align:start position:0%
+here and this here cancel with those two
+and so you get x / n +1
+
+ align:start position:0%
+and so you get x / n +1
+ 
+
+ align:start position:0%
+and so you get x / n +1
+and this here converts to zero right so
+
+ align:start position:0%
+and this here converts to zero right so
+ 
+
+ align:start position:0%
+and this here converts to zero right so
+therefore the power series is convergent
+
+ align:start position:0%
+therefore the power series is convergent
+ 
+
+ align:start position:0%
+therefore the power series is convergent
+for all x
+
+ align:start position:0%
+for all x
+ 
+
+ align:start position:0%
+for all x
+now so that was a particular example of
+
+ align:start position:0%
+now so that was a particular example of
+ 
+
+ align:start position:0%
+now so that was a particular example of
+a power series right but so uh and and
+
+ align:start position:0%
+a power series right but so uh and and
+ 
+
+ align:start position:0%
+a power series right but so uh and and
+and it worked uh well with ratio test,
+
+ align:start position:0%
+and it worked uh well with ratio test,
+ 
+
+ align:start position:0%
+and it worked uh well with ratio test,
+but but the root test actually is
+
+ align:start position:0%
+but but the root test actually is
+ 
+
+ align:start position:0%
+but but the root test actually is
+better. And this was related to a point
+
+ align:start position:0%
+better. And this was related to a point
+ 
+
+ align:start position:0%
+better. And this was related to a point
+somebody raised uh last time. And the
+
+ align:start position:0%
+somebody raised uh last time. And the
+ 
+
+ align:start position:0%
+somebody raised uh last time. And the
+point was like you know like for the
+
+ align:start position:0%
+point was like you know like for the
+ 
+
+ align:start position:0%
+point was like you know like for the
+ratio test it was you know implicitly
+
+ align:start position:0%
+ratio test it was you know implicitly
+ 
+
+ align:start position:0%
+ratio test it was you know implicitly
+somehow in the ratio test was something
+
+ align:start position:0%
+somehow in the ratio test was something
+ 
+
+ align:start position:0%
+somehow in the ratio test was something
+about that from a some stage on the next
+
+ align:start position:0%
+about that from a some stage on the next
+ 
+
+ align:start position:0%
+about that from a some stage on the next
+element is smaller than the previous one
+
+ align:start position:0%
+element is smaller than the previous one
+ 
+
+ align:start position:0%
+element is smaller than the previous one
+and you don't really need to have that
+
+ align:start position:0%
+and you don't really need to have that
+ 
+
+ align:start position:0%
+and you don't really need to have that
+uh uh you know I mean you certainly
+
+ align:start position:0%
+uh uh you know I mean you certainly
+ 
+
+ align:start position:0%
+uh uh you know I mean you certainly
+don't need it for a series to converge
+
+ align:start position:0%
+don't need it for a series to converge
+ 
+
+ align:start position:0%
+don't need it for a series to converge
+but but it's not even necessary if you
+
+ align:start position:0%
+but but it's not even necessary if you
+ 
+
+ align:start position:0%
+but but it's not even necessary if you
+apply the right test right
+
+ align:start position:0%
+apply the right test right
+ 
+
+ align:start position:0%
+apply the right test right
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+so this come this this this bring us to
+
+ align:start position:0%
+so this come this this this bring us to
+ 
+
+ align:start position:0%
+so this come this this this bring us to
+what's called the radius of convergence
+
+ align:start position:0%
+what's called the radius of convergence
+ 
+
+ align:start position:0%
+what's called the radius of convergence
+so so this is a a crucial concept
+
+ align:start position:0%
+so so this is a a crucial concept
+ 
+
+ align:start position:0%
+so so this is a a crucial concept
+and why it is crucial concept because
+
+ align:start position:0%
+and why it is crucial concept because
+ 
+
+ align:start position:0%
+and why it is crucial concept because
+you see appro what you could imagine so
+
+ align:start position:0%
+you see appro what you could imagine so
+ 
+
+ align:start position:0%
+you see appro what you could imagine so
+suppose you just take
+
+ align:start position:0%
+suppose you just take
+ 
+
+ align:start position:0%
+suppose you just take
+suppose you just write down a power
+
+ align:start position:0%
+suppose you just write down a power
+ 
+
+ align:start position:0%
+suppose you just write down a power
+shares like this
+
+ align:start position:0%
+shares like this
+ 
+
+ align:start position:0%
+shares like this
+appro
+
+ align:start position:0%
+appro
+ 
+
+ align:start position:0%
+appro
+maybe like that it's convergent for at
+
+ align:start position:0%
+maybe like that it's convergent for at
+ 
+
+ align:start position:0%
+maybe like that it's convergent for at
+when x is equal to 5 it's divergent when
+
+ align:start position:0%
+when x is equal to 5 it's divergent when
+ 
+
+ align:start position:0%
+when x is equal to 5 it's divergent when
+x is equal to 10 and maybe it's
+
+ align:start position:0%
+x is equal to 10 and maybe it's
+ 
+
+ align:start position:0%
+x is equal to 10 and maybe it's
+convergent again if x is equal to 20
+
+ align:start position:0%
+convergent again if x is equal to 20
+ 
+
+ align:start position:0%
+convergent again if x is equal to 20
+right that's not actually going to be
+
+ align:start position:0%
+right that's not actually going to be
+ 
+
+ align:start position:0%
+right that's not actually going to be
+the case so there's something called
+
+ align:start position:0%
+the case so there's something called
+ 
+
+ align:start position:0%
+the case so there's something called
+radius of convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the radius of convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the thing is that what you get out
+
+ align:start position:0%
+And the thing is that what you get out
+ 
+
+ align:start position:0%
+And the thing is that what you get out
+of this radius of convergence is that a
+
+ align:start position:0%
+of this radius of convergence is that a
+ 
+
+ align:start position:0%
+of this radius of convergence is that a
+power series like this is convergent on
+
+ align:start position:0%
+power series like this is convergent on
+ 
+
+ align:start position:0%
+power series like this is convergent on
+some interval and then outside this
+
+ align:start position:0%
+some interval and then outside this
+ 
+
+ align:start position:0%
+some interval and then outside this
+interval it's divergent.
+
+ align:start position:0%
+interval it's divergent.
+ 
+
+ align:start position:0%
+interval it's divergent.
+So it's not like you have some that is
+
+ align:start position:0%
+So it's not like you have some that is
+ 
+
+ align:start position:0%
+So it's not like you have some that is
+convergent here it's divergent there and
+
+ align:start position:0%
+convergent here it's divergent there and
+ 
+
+ align:start position:0%
+convergent here it's divergent there and
+then it's like converging again. Right?
+
+ align:start position:0%
+then it's like converging again. Right?
+ 
+
+ align:start position:0%
+then it's like converging again. Right?
+That's not what's going to happen. Okay,
+
+ align:start position:0%
+That's not what's going to happen. Okay,
+ 
+
+ align:start position:0%
+That's not what's going to happen. Okay,
+part of this is also we already saw this
+
+ align:start position:0%
+part of this is also we already saw this
+ 
+
+ align:start position:0%
+part of this is also we already saw this
+in the different test that there is at
+
+ align:start position:0%
+in the different test that there is at
+ 
+
+ align:start position:0%
+in the different test that there is at
+the boundary of this interval it's it's
+
+ align:start position:0%
+the boundary of this interval it's it's
+ 
+
+ align:start position:0%
+the boundary of this interval it's it's
+not it's it's the test is inconclusive.
+
+ align:start position:0%
+not it's it's the test is inconclusive.
+ 
+
+ align:start position:0%
+not it's it's the test is inconclusive.
+So you have to check the boundary
+
+ align:start position:0%
+So you have to check the boundary
+ 
+
+ align:start position:0%
+So you have to check the boundary
+separately. Okay.
+
+ align:start position:0%
+separately. Okay.
+ 
+
+ align:start position:0%
+separately. Okay.
+And so so the idea is that you take so
+
+ align:start position:0%
+And so so the idea is that you take so
+ 
+
+ align:start position:0%
+And so so the idea is that you take so
+you you have a power series like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you think about again you're
+
+ align:start position:0%
+and you think about again you're
+ 
+
+ align:start position:0%
+and you think about again you're
+thinking about dn as x to the n x again
+
+ align:start position:0%
+thinking about dn as x to the n x again
+ 
+
+ align:start position:0%
+thinking about dn as x to the n x again
+is is thought of being fixed and now you
+
+ align:start position:0%
+is is thought of being fixed and now you
+ 
+
+ align:start position:0%
+is is thought of being fixed and now you
+apply the root test. So apply the root
+
+ align:start position:0%
+apply the root test. So apply the root
+ 
+
+ align:start position:0%
+apply the root test. So apply the root
+test but I'm going to apply it in a in a
+
+ align:start position:0%
+test but I'm going to apply it in a in a
+ 
+
+ align:start position:0%
+test but I'm going to apply it in a in a
+better form than what we did last time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Maybe I'll just state first first the
+
+ align:start position:0%
+Maybe I'll just state first first the
+ 
+
+ align:start position:0%
+Maybe I'll just state first first the
+better form of the root test. So here's
+
+ align:start position:0%
+better form of the root test. So here's
+ 
+
+ align:start position:0%
+better form of the root test. So here's
+the sort of
+
+ align:start position:0%
+the sort of
+ 
+
+ align:start position:0%
+the sort of
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+here's the the real version of the root
+
+ align:start position:0%
+here's the the real version of the root
+ 
+
+ align:start position:0%
+here's the the real version of the root
+test.
+
+ align:start position:0%
+test.
+ 
+
+ align:start position:0%
+test.
+So suppose you take a series.
+
+ align:start position:0%
+So suppose you take a series.
+ 
+
+ align:start position:0%
+So suppose you take a series.
+Suppose you have some serious here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is let's call it the end.
+
+ align:start position:0%
+This is let's call it the end.
+ 
+
+ align:start position:0%
+This is let's call it the end.
+Suppose you take a series like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you're looking at so now you the root
+
+ align:start position:0%
+if you're looking at so now you the root
+ 
+
+ align:start position:0%
+if you're looking at so now you the root
+test right you took dn you took the
+
+ align:start position:0%
+test right you took dn you took the
+ 
+
+ align:start position:0%
+test right you took dn you took the
+absolute value and you took the nth root
+
+ align:start position:0%
+absolute value and you took the nth root
+ 
+
+ align:start position:0%
+absolute value and you took the nth root
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+when I looked at the root test last time
+
+ align:start position:0%
+when I looked at the root test last time
+ 
+
+ align:start position:0%
+when I looked at the root test last time
+we looked at whether this is convergent
+
+ align:start position:0%
+we looked at whether this is convergent
+ 
+
+ align:start position:0%
+we looked at whether this is convergent
+or not right so we said if it was
+
+ align:start position:0%
+or not right so we said if it was
+ 
+
+ align:start position:0%
+or not right so we said if it was
+converging to something, right? But you
+
+ align:start position:0%
+converging to something, right? But you
+ 
+
+ align:start position:0%
+converging to something, right? But you
+could just take you could form this
+
+ align:start position:0%
+could just take you could form this
+ 
+
+ align:start position:0%
+could just take you could form this
+thing here. So you could form from from
+
+ align:start position:0%
+thing here. So you could form from from
+ 
+
+ align:start position:0%
+thing here. So you could form from from
+this here you could form this. This is
+
+ align:start position:0%
+this here you could form this. This is
+ 
+
+ align:start position:0%
+this here you could form this. This is
+now a sequence and you could look at lim
+
+ align:start position:0%
+now a sequence and you could look at lim
+ 
+
+ align:start position:0%
+now a sequence and you could look at lim
+soup of this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This these here are all non- negative
+
+ align:start position:0%
+This these here are all non- negative
+ 
+
+ align:start position:0%
+This these here are all non- negative
+numbers. Right? So um so uh and this le
+
+ align:start position:0%
+numbers. Right? So um so uh and this le
+ 
+
+ align:start position:0%
+numbers. Right? So um so uh and this le
+soup here is now going to be either
+
+ align:start position:0%
+soup here is now going to be either
+ 
+
+ align:start position:0%
+soup here is now going to be either
+infinite or it's going to be some real
+
+ align:start position:0%
+infinite or it's going to be some real
+ 
+
+ align:start position:0%
+infinite or it's going to be some real
+non- negative number right this here is
+
+ align:start position:0%
+non- negative number right this here is
+ 
+
+ align:start position:0%
+non- negative number right this here is
+going to be infinite usually we don't
+
+ align:start position:0%
+going to be infinite usually we don't
+ 
+
+ align:start position:0%
+going to be infinite usually we don't
+talk about that it's converging if it's
+
+ align:start position:0%
+talk about that it's converging if it's
+ 
+
+ align:start position:0%
+talk about that it's converging if it's
+infinite or it's it's some number
+
+ align:start position:0%
+infinite or it's it's some number
+ 
+
+ align:start position:0%
+infinite or it's it's some number
+um let's call it let's call it d I guess
+
+ align:start position:0%
+um let's call it let's call it d I guess
+ 
+
+ align:start position:0%
+um let's call it let's call it d I guess
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And the thing is that if you're looking
+
+ align:start position:0%
+And the thing is that if you're looking
+ 
+
+ align:start position:0%
+And the thing is that if you're looking
+at if you set r equal to 1 /d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right sorry no if you're setting uh if
+
+ align:start position:0%
+right sorry no if you're setting uh if
+ 
+
+ align:start position:0%
+right sorry no if you're setting uh if
+so so so this is just the root test the
+
+ align:start position:0%
+so so so this is just the root test the
+ 
+
+ align:start position:0%
+so so so this is just the root test the
+sort of adult version of the root test
+
+ align:start position:0%
+sort of adult version of the root test
+ 
+
+ align:start position:0%
+sort of adult version of the root test
+because this apply to all sequences
+
+ align:start position:0%
+because this apply to all sequences
+ 
+
+ align:start position:0%
+because this apply to all sequences
+right for any sequence you have this for
+
+ align:start position:0%
+right for any sequence you have this for
+ 
+
+ align:start position:0%
+right for any sequence you have this for
+any sequence dn if you're looking at
+
+ align:start position:0%
+any sequence dn if you're looking at
+ 
+
+ align:start position:0%
+any sequence dn if you're looking at
+this series you can look at this right
+
+ align:start position:0%
+this series you can look at this right
+ 
+
+ align:start position:0%
+this series you can look at this right
+and it's either infinity or d
+
+ align:start position:0%
+and it's either infinity or d
+ 
+
+ align:start position:0%
+and it's either infinity or d
+and then if d here is less than one then
+
+ align:start position:0%
+and then if d here is less than one then
+ 
+
+ align:start position:0%
+and then if d here is less than one then
+the series is convergent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If d is bigger than one, the series is
+
+ align:start position:0%
+If d is bigger than one, the series is
+ 
+
+ align:start position:0%
+If d is bigger than one, the series is
+divergent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And if d is equal to one, it's
+
+ align:start position:0%
+And if d is equal to one, it's
+ 
+
+ align:start position:0%
+And if d is equal to one, it's
+inconclusion,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? The difference between this and
+
+ align:start position:0%
+right? The difference between this and
+ 
+
+ align:start position:0%
+right? The difference between this and
+what we talked about last time was that
+
+ align:start position:0%
+what we talked about last time was that
+ 
+
+ align:start position:0%
+what we talked about last time was that
+last time we assume that this thing here
+
+ align:start position:0%
+last time we assume that this thing here
+ 
+
+ align:start position:0%
+last time we assume that this thing here
+converge here I'm not assuming it but
+
+ align:start position:0%
+converge here I'm not assuming it but
+ 
+
+ align:start position:0%
+converge here I'm not assuming it but
+I'm then I'm looking at the lem soup
+
+ align:start position:0%
+I'm then I'm looking at the lem soup
+ 
+
+ align:start position:0%
+I'm then I'm looking at the lem soup
+instead. Right? So this is does give us
+
+ align:start position:0%
+instead. Right? So this is does give us
+ 
+
+ align:start position:0%
+instead. Right? So this is does give us
+a number.
+
+ align:start position:0%
+a number.
+ 
+
+ align:start position:0%
+a number.
+Okay. And it's just a matter of whether
+
+ align:start position:0%
+Okay. And it's just a matter of whether
+ 
+
+ align:start position:0%
+Okay. And it's just a matter of whether
+the slim soup is smaller than one
+
+ align:start position:0%
+the slim soup is smaller than one
+ 
+
+ align:start position:0%
+the slim soup is smaller than one
+and then it's convergent or bigger than
+
+ align:start position:0%
+and then it's convergent or bigger than
+ 
+
+ align:start position:0%
+and then it's convergent or bigger than
+one then it's divergent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now I'll come back to to the proof
+
+ align:start position:0%
+Okay. Now I'll come back to to the proof
+ 
+
+ align:start position:0%
+Okay. Now I'll come back to to the proof
+but the proof is really kind of the same
+
+ align:start position:0%
+but the proof is really kind of the same
+ 
+
+ align:start position:0%
+but the proof is really kind of the same
+as the one we gave. the one we gave
+
+ align:start position:0%
+as the one we gave. the one we gave
+ 
+
+ align:start position:0%
+as the one we gave. the one we gave
+really, you know, the if you kind of
+
+ align:start position:0%
+really, you know, the if you kind of
+ 
+
+ align:start position:0%
+really, you know, the if you kind of
+mimic what we did uh in the special case
+
+ align:start position:0%
+mimic what we did uh in the special case
+ 
+
+ align:start position:0%
+mimic what we did uh in the special case
+last time, then the proof would still
+
+ align:start position:0%
+last time, then the proof would still
+ 
+
+ align:start position:0%
+last time, then the proof would still
+apply to this case here and give this
+
+ align:start position:0%
+apply to this case here and give this
+ 
+
+ align:start position:0%
+apply to this case here and give this
+result.
+
+ align:start position:0%
+result.
+ 
+
+ align:start position:0%
+result.
+Okay. So now, but let's let's take this
+
+ align:start position:0%
+Okay. So now, but let's let's take this
+ 
+
+ align:start position:0%
+Okay. So now, but let's let's take this
+this more fancy version of uh the root
+
+ align:start position:0%
+this more fancy version of uh the root
+ 
+
+ align:start position:0%
+this more fancy version of uh the root
+test. Let's take that for granted.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so
+
+ align:start position:0%
+And so
+ 
+
+ align:start position:0%
+And so
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+so now I have
+
+ align:start position:0%
+so now I have
+ 
+
+ align:start position:0%
+so now I have
+a power shares like this. I just for for
+
+ align:start position:0%
+a power shares like this. I just for for
+ 
+
+ align:start position:0%
+a power shares like this. I just for for
+you know for for clarity I define dn to
+
+ align:start position:0%
+you know for for clarity I define dn to
+ 
+
+ align:start position:0%
+you know for for clarity I define dn to
+be just a n
+
+ align:start position:0%
+be just a n
+ 
+
+ align:start position:0%
+be just a n
+time xn and I'm interested in is for
+
+ align:start position:0%
+time xn and I'm interested in is for
+ 
+
+ align:start position:0%
+time xn and I'm interested in is for
+what x
+
+ align:start position:0%
+what x
+ 
+
+ align:start position:0%
+what x
+for what x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does it converge does the power series
+
+ align:start position:0%
+does it converge does the power series
+ 
+
+ align:start position:0%
+does it converge does the power series
+convert
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now,
+
+ align:start position:0%
+Okay. Now,
+ 
+
+ align:start position:0%
+Okay. Now,
+so now you see that so lem soup.
+
+ align:start position:0%
+so now you see that so lem soup.
+ 
+
+ align:start position:0%
+so now you see that so lem soup.
+So you you were looking at lim soup of
+
+ align:start position:0%
+So you you were looking at lim soup of
+ 
+
+ align:start position:0%
+So you you were looking at lim soup of
+the nth root of d n is a n * xn
+
+ align:start position:0%
+the nth root of d n is a n * xn
+ 
+
+ align:start position:0%
+the nth root of d n is a n * xn
+and you take the absolute value of that
+
+ align:start position:0%
+and you take the absolute value of that
+ 
+
+ align:start position:0%
+and you take the absolute value of that
+right that's that's what you're looking
+
+ align:start position:0%
+right that's that's what you're looking
+ 
+
+ align:start position:0%
+right that's that's what you're looking
+at and you asking is this smaller than
+
+ align:start position:0%
+at and you asking is this smaller than
+ 
+
+ align:start position:0%
+at and you asking is this smaller than
+one or bigger than one
+
+ align:start position:0%
+one or bigger than one
+ 
+
+ align:start position:0%
+one or bigger than one
+but this thing here
+
+ align:start position:0%
+but this thing here
+ 
+
+ align:start position:0%
+but this thing here
+right this is the same as sou right if
+
+ align:start position:0%
+right this is the same as sou right if
+ 
+
+ align:start position:0%
+right this is the same as sou right if
+you're looking at this thing here let's
+
+ align:start position:0%
+you're looking at this thing here let's
+ 
+
+ align:start position:0%
+you're looking at this thing here let's
+do a
+
+ align:start position:0%
+do a
+ 
+
+ align:start position:0%
+do a
+side calculation. If you're looking at
+
+ align:start position:0%
+side calculation. If you're looking at
+ 
+
+ align:start position:0%
+side calculation. If you're looking at
+the nth root
+
+ align:start position:0%
+the nth root
+ 
+
+ align:start position:0%
+the nth root
+of uh a n * xn,
+
+ align:start position:0%
+of uh a n * xn,
+ 
+
+ align:start position:0%
+of uh a n * xn,
+this thing here is the same as the nth
+
+ align:start position:0%
+this thing here is the same as the nth
+ 
+
+ align:start position:0%
+this thing here is the same as the nth
+root of this product here. Absolute
+
+ align:start position:0%
+root of this product here. Absolute
+ 
+
+ align:start position:0%
+root of this product here. Absolute
+value is the same as this times x
+
+ align:start position:0%
+value is the same as this times x
+ 
+
+ align:start position:0%
+value is the same as this times x
+absolute value to the n.
+
+ align:start position:0%
+absolute value to the n.
+ 
+
+ align:start position:0%
+absolute value to the n.
+And when you take the nth root, you may
+
+ align:start position:0%
+And when you take the nth root, you may
+ 
+
+ align:start position:0%
+And when you take the nth root, you may
+as well take the nth root of each of
+
+ align:start position:0%
+as well take the nth root of each of
+ 
+
+ align:start position:0%
+as well take the nth root of each of
+those two factors individually.
+
+ align:start position:0%
+those two factors individually.
+ 
+
+ align:start position:0%
+those two factors individually.
+So this is what you get.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But this thing here, you see this thing
+
+ align:start position:0%
+But this thing here, you see this thing
+ 
+
+ align:start position:0%
+But this thing here, you see this thing
+here, the end root, this here is
+
+ align:start position:0%
+here, the end root, this here is
+ 
+
+ align:start position:0%
+here, the end root, this here is
+whatever it is.
+
+ align:start position:0%
+whatever it is.
+ 
+
+ align:start position:0%
+whatever it is.
+Can't do much about that.
+
+ align:start position:0%
+Can't do much about that.
+ 
+
+ align:start position:0%
+Can't do much about that.
+But this thing here, that's just the
+
+ align:start position:0%
+But this thing here, that's just the
+ 
+
+ align:start position:0%
+But this thing here, that's just the
+norm of x, right? The norm of x has the
+
+ align:start position:0%
+norm of x, right? The norm of x has the
+ 
+
+ align:start position:0%
+norm of x, right? The norm of x has the
+property that when you raise it to the n
+
+ align:start position:0%
+property that when you raise it to the n
+ 
+
+ align:start position:0%
+property that when you raise it to the n
+power you're getting this right. So this
+
+ align:start position:0%
+power you're getting this right. So this
+ 
+
+ align:start position:0%
+power you're getting this right. So this
+is the end.
+
+ align:start position:0%
+is the end.
+ 
+
+ align:start position:0%
+is the end.
+Okay. So this means that this thing here
+
+ align:start position:0%
+Okay. So this means that this thing here
+ 
+
+ align:start position:0%
+Okay. So this means that this thing here
+is the same as the norm of x limb soup
+
+ align:start position:0%
+is the same as the norm of x limb soup
+ 
+
+ align:start position:0%
+is the same as the norm of x limb soup
+of the nth root of a n.
+
+ align:start position:0%
+of the nth root of a n.
+ 
+
+ align:start position:0%
+of the nth root of a n.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+Often you do it like this. You don't
+
+ align:start position:0%
+Often you do it like this. You don't
+ 
+
+ align:start position:0%
+Often you do it like this. You don't
+have to do this. It's usually clear
+
+ align:start position:0%
+have to do this. It's usually clear
+ 
+
+ align:start position:0%
+have to do this. It's usually clear
+anyway. But it off you write like that.
+
+ align:start position:0%
+anyway. But it off you write like that.
+ 
+
+ align:start position:0%
+anyway. But it off you write like that.
+Okay. So now what you do is so you you
+
+ align:start position:0%
+Okay. So now what you do is so you you
+ 
+
+ align:start position:0%
+Okay. So now what you do is so you you
+want you asking when is this number here
+
+ align:start position:0%
+want you asking when is this number here
+ 
+
+ align:start position:0%
+want you asking when is this number here
+smaller than one when is it bigger than
+
+ align:start position:0%
+smaller than one when is it bigger than
+ 
+
+ align:start position:0%
+smaller than one when is it bigger than
+one right? And so you have that you see
+
+ align:start position:0%
+one right? And so you have that you see
+ 
+
+ align:start position:0%
+one right? And so you have that you see
+now you define something that's called
+
+ align:start position:0%
+now you define something that's called
+ 
+
+ align:start position:0%
+now you define something that's called
+the radius of convergence.
+
+ align:start position:0%
+the radius of convergence.
+ 
+
+ align:start position:0%
+the radius of convergence.
+And so this is the following. So the
+
+ align:start position:0%
+And so this is the following. So the
+ 
+
+ align:start position:0%
+And so this is the following. So the
+radius of convergence
+
+ align:start position:0%
+radius of convergence
+ 
+
+ align:start position:0%
+radius of convergence
+is oops
+
+ align:start position:0%
+is oops
+ 
+
+ align:start position:0%
+is oops
+radius of convergence is
+
+ align:start position:0%
+radius of convergence is
+ 
+
+ align:start position:0%
+radius of convergence is
+so this is just radius
+
+ align:start position:0%
+so this is just radius
+ 
+
+ align:start position:0%
+so this is just radius
+of convergent.
+
+ align:start position:0%
+of convergent.
+ 
+
+ align:start position:0%
+of convergent.
+The radius of convergence is just a
+
+ align:start position:0%
+The radius of convergence is just a
+ 
+
+ align:start position:0%
+The radius of convergence is just a
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that number is radius of convergence
+
+ align:start position:0%
+and that number is radius of convergence
+ 
+
+ align:start position:0%
+and that number is radius of convergence
+and we have to just interpret it a
+
+ align:start position:0%
+and we have to just interpret it a
+ 
+
+ align:start position:0%
+and we have to just interpret it a
+little bit. So it's one over lim super
+
+ align:start position:0%
+little bit. So it's one over lim super
+ 
+
+ align:start position:0%
+little bit. So it's one over lim super
+of of the nth root.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This thing here could of course be
+
+ align:start position:0%
+This thing here could of course be
+ 
+
+ align:start position:0%
+This thing here could of course be
+infinite.
+
+ align:start position:0%
+infinite.
+ 
+
+ align:start position:0%
+infinite.
+If this here is infinite then the radius
+
+ align:start position:0%
+If this here is infinite then the radius
+ 
+
+ align:start position:0%
+If this here is infinite then the radius
+by definition this here would be zero.
+
+ align:start position:0%
+by definition this here would be zero.
+ 
+
+ align:start position:0%
+by definition this here would be zero.
+Right? Right? Where this here is equal
+
+ align:start position:0%
+Right? Right? Where this here is equal
+ 
+
+ align:start position:0%
+Right? Right? Where this here is equal
+to zero. If
+
+ align:start position:0%
+to zero. If
+ 
+
+ align:start position:0%
+to zero. If
+there's lean soup uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is infinite and otherwise right it's a
+
+ align:start position:0%
+is infinite and otherwise right it's a
+ 
+
+ align:start position:0%
+is infinite and otherwise right it's a
+it's always a right otherwise yeah
+
+ align:start position:0%
+it's always a right otherwise yeah
+ 
+
+ align:start position:0%
+it's always a right otherwise yeah
+there's one other case you have to
+
+ align:start position:0%
+there's one other case you have to
+ 
+
+ align:start position:0%
+there's one other case you have to
+define that if uh it's infinite if the
+
+ align:start position:0%
+define that if uh it's infinite if the
+ 
+
+ align:start position:0%
+define that if uh it's infinite if the
+lem soup
+
+ align:start position:0%
+lem soup
+ 
+
+ align:start position:0%
+lem soup
+sorry this should be absolute value if
+
+ align:start position:0%
+sorry this should be absolute value if
+ 
+
+ align:start position:0%
+sorry this should be absolute value if
+this lem soup
+
+ align:start position:0%
+this lem soup
+ 
+
+ align:start position:0%
+this lem soup
+is true and otherwise otherwise it's a
+
+ align:start position:0%
+is true and otherwise otherwise it's a
+ 
+
+ align:start position:0%
+is true and otherwise otherwise it's a
+you know otherwise there's nothing to
+
+ align:start position:0%
+you know otherwise there's nothing to
+ 
+
+ align:start position:0%
+you know otherwise there's nothing to
+you know it's a well you know that's the
+
+ align:start position:0%
+you know it's a well you know that's the
+ 
+
+ align:start position:0%
+you know it's a well you know that's the
+only thing you have to comment right
+
+ align:start position:0%
+only thing you have to comment right
+ 
+
+ align:start position:0%
+only thing you have to comment right
+because otherwise it's it's it's always
+
+ align:start position:0%
+because otherwise it's it's it's always
+ 
+
+ align:start position:0%
+because otherwise it's it's it's always
+a non- negative number but it could be
+
+ align:start position:0%
+a non- negative number but it could be
+ 
+
+ align:start position:0%
+a non- negative number but it could be
+zero or it could be infinity but if it's
+
+ align:start position:0%
+zero or it could be infinity but if it's
+ 
+
+ align:start position:0%
+zero or it could be infinity but if it's
+any other number then it is just what
+
+ align:start position:0%
+any other number then it is just what
+ 
+
+ align:start position:0%
+any other number then it is just what
+you think it should be is one over that
+
+ align:start position:0%
+you think it should be is one over that
+ 
+
+ align:start position:0%
+you think it should be is one over that
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+okay so this gives you this is this here
+
+ align:start position:0%
+okay so this gives you this is this here
+ 
+
+ align:start position:0%
+okay so this gives you this is this here
+r here is the radius of convergence okay
+
+ align:start position:0%
+r here is the radius of convergence okay
+ 
+
+ align:start position:0%
+r here is the radius of convergence okay
+and Now the the thing is that now we
+
+ align:start position:0%
+and Now the the thing is that now we
+ 
+
+ align:start position:0%
+and Now the the thing is that now we
+have the following symbol picture.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now we have that. So you have this
+
+ align:start position:0%
+So now we have that. So you have this
+ 
+
+ align:start position:0%
+So now we have that. So you have this
+power series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again it doesn't matter what you start
+
+ align:start position:0%
+again it doesn't matter what you start
+ 
+
+ align:start position:0%
+again it doesn't matter what you start
+with the sum matters what you start with
+
+ align:start position:0%
+with the sum matters what you start with
+ 
+
+ align:start position:0%
+with the sum matters what you start with
+but not the convergence. So you have
+
+ align:start position:0%
+but not the convergence. So you have
+ 
+
+ align:start position:0%
+but not the convergence. So you have
+this power series you are forming a
+
+ align:start position:0%
+this power series you are forming a
+ 
+
+ align:start position:0%
+this power series you are forming a
+This is the radius of convergence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the claim is and again this
+
+ align:start position:0%
+And then the claim is and again this
+ 
+
+ align:start position:0%
+And then the claim is and again this
+could be zero it could be infinity but
+
+ align:start position:0%
+could be zero it could be infinity but
+ 
+
+ align:start position:0%
+could be zero it could be infinity but
+often it's just a a real number non-
+
+ align:start position:0%
+often it's just a a real number non-
+ 
+
+ align:start position:0%
+often it's just a a real number non-
+negative real positive real number and
+
+ align:start position:0%
+negative real positive real number and
+ 
+
+ align:start position:0%
+negative real positive real number and
+so it say that if you take the interval
+
+ align:start position:0%
+so it say that if you take the interval
+ 
+
+ align:start position:0%
+so it say that if you take the interval
+here around zero in the interval
+
+ align:start position:0%
+here around zero in the interval
+ 
+
+ align:start position:0%
+here around zero in the interval
+from minus r to r then inside this
+
+ align:start position:0%
+from minus r to r then inside this
+ 
+
+ align:start position:0%
+from minus r to r then inside this
+interval here inside here when x is in
+
+ align:start position:0%
+interval here inside here when x is in
+ 
+
+ align:start position:0%
+interval here inside here when x is in
+here then the Power series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when X is here or here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power series is divergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then when X's is here or here at
+
+ align:start position:0%
+and then when X's is here or here at
+ 
+
+ align:start position:0%
+and then when X's is here or here at
+those two points then it's and clear and
+
+ align:start position:0%
+those two points then it's and clear and
+ 
+
+ align:start position:0%
+those two points then it's and clear and
+further test is needed.
+
+ align:start position:0%
+further test is needed.
+ 
+
+ align:start position:0%
+further test is needed.
+Further test is needed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Test are needed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Okay.
+
+ align:start position:0%
+>> Okay.
+ 
+
+ align:start position:0%
+>> Okay.
+>> Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+less than one.
+
+ align:start position:0%
+less than one.
+ 
+
+ align:start position:0%
+less than one.
+>> Yeah. So that's right. So so let's come
+
+ align:start position:0%
+>> Yeah. So that's right. So so let's come
+ 
+
+ align:start position:0%
+>> Yeah. So that's right. So so let's come
+to the proof. Yeah. So this is what
+
+ align:start position:0%
+to the proof. Yeah. So this is what
+ 
+
+ align:start position:0%
+to the proof. Yeah. So this is what
+you're talking about. So
+
+ align:start position:0%
+you're talking about. So
+ 
+
+ align:start position:0%
+you're talking about. So
+So this is this is the the radius of
+
+ align:start position:0%
+So this is this is the the radius of
+ 
+
+ align:start position:0%
+So this is this is the the radius of
+convergence, right? And so as you say
+
+ align:start position:0%
+convergence, right? And so as you say
+ 
+
+ align:start position:0%
+convergence, right? And so as you say
+um all we need to do is right but we
+
+ align:start position:0%
+um all we need to do is right but we
+ 
+
+ align:start position:0%
+um all we need to do is right but we
+know from this from the more fancy
+
+ align:start position:0%
+know from this from the more fancy
+ 
+
+ align:start position:0%
+know from this from the more fancy
+version of the ratio test that is in
+
+ align:start position:0%
+version of the ratio test that is in
+ 
+
+ align:start position:0%
+version of the ratio test that is in
+terms of leap soup we know that so so
+
+ align:start position:0%
+terms of leap soup we know that so so
+ 
+
+ align:start position:0%
+terms of leap soup we know that so so
+prove here
+
+ align:start position:0%
+prove here
+ 
+
+ align:start position:0%
+prove here
+power series is convergent by the ratio
+
+ align:start position:0%
+power series is convergent by the ratio
+ 
+
+ align:start position:0%
+power series is convergent by the ratio
+test by the by the ratio test,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not a ratio test. Sorry, the root test
+
+ align:start position:0%
+not a ratio test. Sorry, the root test
+ 
+
+ align:start position:0%
+not a ratio test. Sorry, the root test
+by the root test.
+
+ align:start position:0%
+by the root test.
+ 
+
+ align:start position:0%
+by the root test.
+So again, the version the version the
+
+ align:start position:0%
+So again, the version the version the
+ 
+
+ align:start position:0%
+So again, the version the version the
+lem soup version,
+
+ align:start position:0%
+lem soup version,
+ 
+
+ align:start position:0%
+lem soup version,
+not the one I talked about last time,
+
+ align:start position:0%
+not the one I talked about last time,
+ 
+
+ align:start position:0%
+not the one I talked about last time,
+but this one we just talked about, but
+
+ align:start position:0%
+but this one we just talked about, but
+ 
+
+ align:start position:0%
+but this one we just talked about, but
+the lem soup version of the ratio root
+
+ align:start position:0%
+the lem soup version of the ratio root
+ 
+
+ align:start position:0%
+the lem soup version of the ratio root
+test,
+
+ align:start position:0%
+test,
+ 
+
+ align:start position:0%
+test,
+then the power series is converging. If
+
+ align:start position:0%
+then the power series is converging. If
+ 
+
+ align:start position:0%
+then the power series is converging. If
+this thing here, so this means that this
+
+ align:start position:0%
+this thing here, so this means that this
+ 
+
+ align:start position:0%
+this thing here, so this means that this
+thing here. So if this thing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+li
+
+ align:start position:0%
+li
+ 
+
+ align:start position:0%
+li
+of a nth
+
+ align:start position:0%
+of a nth
+ 
+
+ align:start position:0%
+of a nth
+root
+
+ align:start position:0%
+root
+ 
+
+ align:start position:0%
+root
+if this thing here is less than one,
+
+ align:start position:0%
+if this thing here is less than one,
+ 
+
+ align:start position:0%
+if this thing here is less than one,
+it's divergent.
+
+ align:start position:0%
+it's divergent.
+ 
+
+ align:start position:0%
+it's divergent.
+If this thing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bigger than one and it's inconclusive
+
+ align:start position:0%
+is bigger than one and it's inconclusive
+ 
+
+ align:start position:0%
+is bigger than one and it's inconclusive
+and it's and it's inconclusive if this
+
+ align:start position:0%
+and it's and it's inconclusive if this
+ 
+
+ align:start position:0%
+and it's and it's inconclusive if this
+thing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to one here it's inconclusive.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But now you see that this here this here
+
+ align:start position:0%
+But now you see that this here this here
+ 
+
+ align:start position:0%
+But now you see that this here this here
+just means that the norm of X should be
+
+ align:start position:0%
+just means that the norm of X should be
+ 
+
+ align:start position:0%
+just means that the norm of X should be
+smaller than one over that. Right? So
+
+ align:start position:0%
+smaller than one over that. Right? So
+ 
+
+ align:start position:0%
+smaller than one over that. Right? So
+this here is is is
+
+ align:start position:0%
+this here is is is
+ 
+
+ align:start position:0%
+this here is is is
+the same as saying that the norm of X is
+
+ align:start position:0%
+the same as saying that the norm of X is
+ 
+
+ align:start position:0%
+the same as saying that the norm of X is
+smaller than R the radius of
+
+ align:start position:0%
+smaller than R the radius of
+ 
+
+ align:start position:0%
+smaller than R the radius of
+convergence. Right?
+
+ align:start position:0%
+convergence. Right?
+ 
+
+ align:start position:0%
+convergence. Right?
+This here is saying this is equivalent
+
+ align:start position:0%
+This here is saying this is equivalent
+ 
+
+ align:start position:0%
+This here is saying this is equivalent
+to saying that the norm of x is bigger
+
+ align:start position:0%
+to saying that the norm of x is bigger
+ 
+
+ align:start position:0%
+to saying that the norm of x is bigger
+than uh than r
+
+ align:start position:0%
+than uh than r
+ 
+
+ align:start position:0%
+than uh than r
+right and this here is equivalent to
+
+ align:start position:0%
+right and this here is equivalent to
+ 
+
+ align:start position:0%
+right and this here is equivalent to
+saying that the norm of x is equal to r.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So so that is the that is the so
+
+ align:start position:0%
+Okay. So so that is the that is the so
+ 
+
+ align:start position:0%
+Okay. So so that is the that is the so
+that's a radius of convergence. So you
+
+ align:start position:0%
+that's a radius of convergence. So you
+ 
+
+ align:start position:0%
+that's a radius of convergence. So you
+see so this is like you know a pure this
+
+ align:start position:0%
+see so this is like you know a pure this
+ 
+
+ align:start position:0%
+see so this is like you know a pure this
+is not at all clear
+
+ align:start position:0%
+is not at all clear
+ 
+
+ align:start position:0%
+is not at all clear
+that it couldn't be that a power series
+
+ align:start position:0%
+that it couldn't be that a power series
+ 
+
+ align:start position:0%
+that it couldn't be that a power series
+couldn't be convergent for like you know
+
+ align:start position:0%
+couldn't be convergent for like you know
+ 
+
+ align:start position:0%
+couldn't be convergent for like you know
+some sort of discrete set of of x but
+
+ align:start position:0%
+some sort of discrete set of of x but
+ 
+
+ align:start position:0%
+some sort of discrete set of of x but
+that's not the case right it's it's
+
+ align:start position:0%
+that's not the case right it's it's
+ 
+
+ align:start position:0%
+that's not the case right it's it's
+convergent on some interval it's unclear
+
+ align:start position:0%
+convergent on some interval it's unclear
+ 
+
+ align:start position:0%
+convergent on some interval it's unclear
+at the at the end of that interval but
+
+ align:start position:0%
+at the at the end of that interval but
+ 
+
+ align:start position:0%
+at the at the end of that interval but
+it is convergence on an interval and
+
+ align:start position:0%
+it is convergence on an interval and
+ 
+
+ align:start position:0%
+it is convergence on an interval and
+divergent outside that interval now that
+
+ align:start position:0%
+divergent outside that interval now that
+ 
+
+ align:start position:0%
+divergent outside that interval now that
+interval could be just zero
+
+ align:start position:0%
+interval could be just zero
+ 
+
+ align:start position:0%
+interval could be just zero
+Or it could be all of R. Right.
+
+ align:start position:0%
+Or it could be all of R. Right.
+ 
+
+ align:start position:0%
+Or it could be all of R. Right.
+But it is also symmetric around zero.
+
+ align:start position:0%
+But it is also symmetric around zero.
+ 
+
+ align:start position:0%
+But it is also symmetric around zero.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Right. So it's so it's one over this
+
+ align:start position:0%
+>> Right. So it's so it's one over this
+ 
+
+ align:start position:0%
+>> Right. So it's so it's one over this
+here. But remember how R was defined. R
+
+ align:start position:0%
+here. But remember how R was defined. R
+ 
+
+ align:start position:0%
+here. But remember how R was defined. R
+is up there.
+
+ align:start position:0%
+is up there.
+ 
+
+ align:start position:0%
+is up there.
+>> Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+um let me just say a word
+
+ align:start position:0%
+um let me just say a word
+ 
+
+ align:start position:0%
+um let me just say a word
+about why does the proof from last time
+
+ align:start position:0%
+about why does the proof from last time
+ 
+
+ align:start position:0%
+about why does the proof from last time
+why does it really prove this more you
+
+ align:start position:0%
+why does it really prove this more you
+ 
+
+ align:start position:0%
+why does it really prove this more you
+know I mean the sort of argument we gave
+
+ align:start position:0%
+know I mean the sort of argument we gave
+ 
+
+ align:start position:0%
+know I mean the sort of argument we gave
+last time
+
+ align:start position:0%
+last time
+ 
+
+ align:start position:0%
+last time
+why does it give you this much more sat
+
+ align:start position:0%
+why does it give you this much more sat
+ 
+
+ align:start position:0%
+why does it give you this much more sat
+I mean it's much more satisfying this
+
+ align:start position:0%
+I mean it's much more satisfying this
+ 
+
+ align:start position:0%
+I mean it's much more satisfying this
+version of the root test because it
+
+ align:start position:0%
+version of the root test because it
+ 
+
+ align:start position:0%
+version of the root test because it
+apply to any series right the because
+
+ align:start position:0%
+apply to any series right the because
+ 
+
+ align:start position:0%
+apply to any series right the because
+otherwise we talk about whether some
+
+ align:start position:0%
+otherwise we talk about whether some
+ 
+
+ align:start position:0%
+otherwise we talk about whether some
+ratio was convergent but it may not
+
+ align:start position:0%
+ratio was convergent but it may not
+ 
+
+ align:start position:0%
+ratio was convergent but it may not
+converge right so this is much more
+
+ align:start position:0%
+converge right so this is much more
+ 
+
+ align:start position:0%
+converge right so this is much more
+satisfying so suppose again you have a
+
+ align:start position:0%
+satisfying so suppose again you have a
+ 
+
+ align:start position:0%
+satisfying so suppose again you have a
+series like this
+
+ align:start position:0%
+series like this
+ 
+
+ align:start position:0%
+series like this
+and so now you form you're looking at
+
+ align:start position:0%
+and so now you form you're looking at
+ 
+
+ align:start position:0%
+and so now you form you're looking at
+lem soup so this here is again this is
+
+ align:start position:0%
+lem soup so this here is again this is
+ 
+
+ align:start position:0%
+lem soup so this here is again this is
+the root test
+
+ align:start position:0%
+the root test
+ 
+
+ align:start position:0%
+the root test
+root
+
+ align:start position:0%
+root
+ 
+
+ align:start position:0%
+root
+test
+
+ align:start position:0%
+test
+ 
+
+ align:start position:0%
+test
+version, let's call it version 2.0,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? And so it take um series like
+
+ align:start position:0%
+right? And so it take um series like
+ 
+
+ align:start position:0%
+right? And so it take um series like
+this and it's
+
+ align:start position:0%
+this and it's
+ 
+
+ align:start position:0%
+this and it's
+it's looking at le soup and then the nth
+
+ align:start position:0%
+it's looking at le soup and then the nth
+ 
+
+ align:start position:0%
+it's looking at le soup and then the nth
+root of the absolute value of dn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again it say that if this thing here
+
+ align:start position:0%
+and again it say that if this thing here
+ 
+
+ align:start position:0%
+and again it say that if this thing here
+is e is less than one it's convergent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If it's bigger than one, it's diverging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if it's equal to one, it's
+
+ align:start position:0%
+and if it's equal to one, it's
+ 
+
+ align:start position:0%
+and if it's equal to one, it's
+inconclusion.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now let's let's try to see why
+
+ align:start position:0%
+Okay. Now let's let's try to see why
+ 
+
+ align:start position:0%
+Okay. Now let's let's try to see why
+this here why this here is the case. So
+
+ align:start position:0%
+this here why this here is the case. So
+ 
+
+ align:start position:0%
+this here why this here is the case. So
+proof of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of root test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+version 2.0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now may maybe I won't do all of it
+
+ align:start position:0%
+So now may maybe I won't do all of it
+ 
+
+ align:start position:0%
+So now may maybe I won't do all of it
+but let's just say let's just look at
+
+ align:start position:0%
+but let's just say let's just look at
+ 
+
+ align:start position:0%
+but let's just say let's just look at
+because you see in a minute you see that
+
+ align:start position:0%
+because you see in a minute you see that
+ 
+
+ align:start position:0%
+because you see in a minute you see that
+it's really kind of super similar to
+
+ align:start position:0%
+it's really kind of super similar to
+ 
+
+ align:start position:0%
+it's really kind of super similar to
+last time. So suppose that this limit
+
+ align:start position:0%
+last time. So suppose that this limit
+ 
+
+ align:start position:0%
+last time. So suppose that this limit
+suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this limb soup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the nth root here of dn suppos
+
+ align:start position:0%
+of the nth root here of dn suppos
+ 
+
+ align:start position:0%
+of the nth root here of dn suppos
+supposed that this thing here
+
+ align:start position:0%
+supposed that this thing here
+ 
+
+ align:start position:0%
+supposed that this thing here
+is equal to some d which is strictly
+
+ align:start position:0%
+is equal to some d which is strictly
+ 
+
+ align:start position:0%
+is equal to some d which is strictly
+less than one.
+
+ align:start position:0%
+less than one.
+ 
+
+ align:start position:0%
+less than one.
+Okay. So this means that there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+they exist.
+
+ align:start position:0%
+they exist.
+ 
+
+ align:start position:0%
+they exist.
+So choose if you will choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh d
+
+ align:start position:0%
+uh d
+ 
+
+ align:start position:0%
+uh d
+bar
+
+ align:start position:0%
+bar
+ 
+
+ align:start position:0%
+bar
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+uh d less than d bar strictly less than
+
+ align:start position:0%
+uh d less than d bar strictly less than
+ 
+
+ align:start position:0%
+uh d less than d bar strictly less than
+strictly less than one.
+
+ align:start position:0%
+strictly less than one.
+ 
+
+ align:start position:0%
+strictly less than one.
+Right? So I can choose it like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But now you see that if I choose it like
+
+ align:start position:0%
+But now you see that if I choose it like
+ 
+
+ align:start position:0%
+But now you see that if I choose it like
+this then there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so remember that let's just remind
+
+ align:start position:0%
+that so remember that let's just remind
+ 
+
+ align:start position:0%
+that so remember that let's just remind
+ourselves that
+
+ align:start position:0%
+ourselves that
+ 
+
+ align:start position:0%
+ourselves that
+how was the lim soup defined
+
+ align:start position:0%
+how was the lim soup defined
+ 
+
+ align:start position:0%
+how was the lim soup defined
+the limb soup was defined
+
+ align:start position:0%
+the limb soup was defined
+ 
+
+ align:start position:0%
+the limb soup was defined
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+that you take this new sequence so
+
+ align:start position:0%
+that you take this new sequence so
+ 
+
+ align:start position:0%
+that you take this new sequence so
+you're taking this sequence here
+
+ align:start position:0%
+you're taking this sequence here
+ 
+
+ align:start position:0%
+you're taking this sequence here
+to You're taking
+
+ align:start position:0%
+to You're taking
+ 
+
+ align:start position:0%
+to You're taking
+these guys here.
+
+ align:start position:0%
+these guys here.
+ 
+
+ align:start position:0%
+these guys here.
+So you're looking at now these guys here
+
+ align:start position:0%
+So you're looking at now these guys here
+ 
+
+ align:start position:0%
+So you're looking at now these guys here
+and you are taking a you define a
+
+ align:start position:0%
+and you are taking a you define a
+ 
+
+ align:start position:0%
+and you are taking a you define a
+sequence that is like the soup starting
+
+ align:start position:0%
+sequence that is like the soup starting
+ 
+
+ align:start position:0%
+sequence that is like the soup starting
+at the nth guy
+
+ align:start position:0%
+at the nth guy
+ 
+
+ align:start position:0%
+at the nth guy
+and like this here.
+
+ align:start position:0%
+and like this here.
+ 
+
+ align:start position:0%
+and like this here.
+Sorry this here is n plus one
+
+ align:start position:0%
+Sorry this here is n plus one
+ 
+
+ align:start position:0%
+Sorry this here is n plus one
+etc. Right.
+
+ align:start position:0%
+etc. Right.
+ 
+
+ align:start position:0%
+etc. Right.
+Right. This is the soup of the tail,
+
+ align:start position:0%
+Right. This is the soup of the tail,
+ 
+
+ align:start position:0%
+Right. This is the soup of the tail,
+right? And so this was this was that it
+
+ align:start position:0%
+right? And so this was this was that it
+ 
+
+ align:start position:0%
+right? And so this was this was that it
+was soup on as you're going further out,
+
+ align:start position:0%
+was soup on as you're going further out,
+ 
+
+ align:start position:0%
+was soup on as you're going further out,
+you're taking soup over a smaller set.
+
+ align:start position:0%
+you're taking soup over a smaller set.
+ 
+
+ align:start position:0%
+you're taking soup over a smaller set.
+So these this sequence going down,
+
+ align:start position:0%
+So these this sequence going down,
+ 
+
+ align:start position:0%
+So these this sequence going down,
+right? So now if this limit here is some
+
+ align:start position:0%
+right? So now if this limit here is some
+ 
+
+ align:start position:0%
+right? So now if this limit here is some
+D which is strictly less than D bar then
+
+ align:start position:0%
+D which is strictly less than D bar then
+ 
+
+ align:start position:0%
+D which is strictly less than D bar then
+it means that there exist so there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capital N. So that if little n is bigger
+
+ align:start position:0%
+capital N. So that if little n is bigger
+ 
+
+ align:start position:0%
+capital N. So that if little n is bigger
+than capital n then all of these guys
+
+ align:start position:0%
+than capital n then all of these guys
+ 
+
+ align:start position:0%
+than capital n then all of these guys
+here is less than d bar. Right? So this
+
+ align:start position:0%
+here is less than d bar. Right? So this
+ 
+
+ align:start position:0%
+here is less than d bar. Right? So this
+here is so that so if this here then all
+
+ align:start position:0%
+here is so that so if this here then all
+ 
+
+ align:start position:0%
+here is so that so if this here then all
+of these guys here is less or equal to d
+
+ align:start position:0%
+of these guys here is less or equal to d
+ 
+
+ align:start position:0%
+of these guys here is less or equal to d
+bar this is if little n if you starting
+
+ align:start position:0%
+bar this is if little n if you starting
+ 
+
+ align:start position:0%
+bar this is if little n if you starting
+that far out right
+
+ align:start position:0%
+that far out right
+ 
+
+ align:start position:0%
+that far out right
+but so now you see that so you have that
+
+ align:start position:0%
+but so now you see that so you have that
+ 
+
+ align:start position:0%
+but so now you see that so you have that
+when n is bigger than this you have that
+
+ align:start position:0%
+when n is bigger than this you have that
+ 
+
+ align:start position:0%
+when n is bigger than this you have that
+this so you have that for all these guys
+
+ align:start position:0%
+this so you have that for all these guys
+ 
+
+ align:start position:0%
+this so you have that for all these guys
+here dn the nth root is less then d bar
+
+ align:start position:0%
+here dn the nth root is less then d bar
+ 
+
+ align:start position:0%
+here dn the nth root is less then d bar
+less or equal to d bar.
+
+ align:start position:0%
+less or equal to d bar.
+ 
+
+ align:start position:0%
+less or equal to d bar.
+But now you take the nth root the nth
+
+ align:start position:0%
+But now you take the nth root the nth
+ 
+
+ align:start position:0%
+But now you take the nth root the nth
+power on both sides. So you have that dn
+
+ align:start position:0%
+power on both sides. So you have that dn
+ 
+
+ align:start position:0%
+power on both sides. So you have that dn
+absolute value is less than d bar the n
+
+ align:start position:0%
+absolute value is less than d bar the n
+ 
+
+ align:start position:0%
+absolute value is less than d bar the n
+power. This here is d is is and n is
+
+ align:start position:0%
+power. This here is d is is and n is
+ 
+
+ align:start position:0%
+power. This here is d is is and n is
+this is even actually not negative. So
+
+ align:start position:0%
+this is even actually not negative. So
+ 
+
+ align:start position:0%
+this is even actually not negative. So
+you don't even need this absolute value
+
+ align:start position:0%
+you don't even need this absolute value
+ 
+
+ align:start position:0%
+you don't even need this absolute value
+sign. So you're having this but this is
+
+ align:start position:0%
+sign. So you're having this but this is
+ 
+
+ align:start position:0%
+sign. So you're having this but this is
+a number that is strictly less than one.
+
+ align:start position:0%
+a number that is strictly less than one.
+ 
+
+ align:start position:0%
+a number that is strictly less than one.
+So this here is a geometric series right
+
+ align:start position:0%
+So this here is a geometric series right
+ 
+
+ align:start position:0%
+So this here is a geometric series right
+geometric series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with where where where
+
+ align:start position:0%
+with where where where
+ 
+
+ align:start position:0%
+with where where where
+d bar is less than one. So it's is a
+
+ align:start position:0%
+d bar is less than one. So it's is a
+ 
+
+ align:start position:0%
+d bar is less than one. So it's is a
+convergent geometric series. Right? So
+
+ align:start position:0%
+convergent geometric series. Right? So
+ 
+
+ align:start position:0%
+convergent geometric series. Right? So
+this is you see that it was it's
+
+ align:start position:0%
+this is you see that it was it's
+ 
+
+ align:start position:0%
+this is you see that it was it's
+basically the same proof we did last
+
+ align:start position:0%
+basically the same proof we did last
+ 
+
+ align:start position:0%
+basically the same proof we did last
+time but last time we were assuming that
+
+ align:start position:0%
+time but last time we were assuming that
+ 
+
+ align:start position:0%
+time but last time we were assuming that
+some ratio was convert you know or some
+
+ align:start position:0%
+some ratio was convert you know or some
+ 
+
+ align:start position:0%
+some ratio was convert you know or some
+we were consuming assuming that this
+
+ align:start position:0%
+we were consuming assuming that this
+ 
+
+ align:start position:0%
+we were consuming assuming that this
+this here converge to something but you
+
+ align:start position:0%
+this here converge to something but you
+ 
+
+ align:start position:0%
+this here converge to something but you
+don't need it to converge you just need
+
+ align:start position:0%
+don't need it to converge you just need
+ 
+
+ align:start position:0%
+don't need it to converge you just need
+that this soup is is um is is less than
+
+ align:start position:0%
+that this soup is is um is is less than
+ 
+
+ align:start position:0%
+that this soup is is um is is less than
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and so likewise if you examine what this
+
+ align:start position:0%
+and so likewise if you examine what this
+ 
+
+ align:start position:0%
+and so likewise if you examine what this
+case here say then just like last time
+
+ align:start position:0%
+case here say then just like last time
+ 
+
+ align:start position:0%
+case here say then just like last time
+it's going to say that if this here is
+
+ align:start position:0%
+it's going to say that if this here is
+ 
+
+ align:start position:0%
+it's going to say that if this here is
+bigger than one then the ordinary
+
+ align:start position:0%
+bigger than one then the ordinary
+ 
+
+ align:start position:0%
+bigger than one then the ordinary
+element doesn't even go to zero. Okay.
+
+ align:start position:0%
+element doesn't even go to zero. Okay.
+ 
+
+ align:start position:0%
+element doesn't even go to zero. Okay.
+So it it fails the most basic test for
+
+ align:start position:0%
+So it it fails the most basic test for
+ 
+
+ align:start position:0%
+So it it fails the most basic test for
+being convergent. Okay. So and that was
+
+ align:start position:0%
+being convergent. Okay. So and that was
+ 
+
+ align:start position:0%
+being convergent. Okay. So and that was
+just like last time also and and again
+
+ align:start position:0%
+just like last time also and and again
+ 
+
+ align:start position:0%
+just like last time also and and again
+the advantage is saying you were the one
+
+ align:start position:0%
+the advantage is saying you were the one
+ 
+
+ align:start position:0%
+the advantage is saying you were the one
+that was asking yesterday. Yeah. I mean
+
+ align:start position:0%
+that was asking yesterday. Yeah. I mean
+ 
+
+ align:start position:0%
+that was asking yesterday. Yeah. I mean
+like last time this with a ratio test
+
+ align:start position:0%
+like last time this with a ratio test
+ 
+
+ align:start position:0%
+like last time this with a ratio test
+and the root test and and like in the
+
+ align:start position:0%
+and the root test and and like in the
+ 
+
+ align:start position:0%
+and the root test and and like in the
+ratio test it's something about that the
+
+ align:start position:0%
+ratio test it's something about that the
+ 
+
+ align:start position:0%
+ratio test it's something about that the
+next element is some you know is going
+
+ align:start position:0%
+next element is some you know is going
+ 
+
+ align:start position:0%
+next element is some you know is going
+down with some fraction right and here
+
+ align:start position:0%
+down with some fraction right and here
+ 
+
+ align:start position:0%
+down with some fraction right and here
+and you very much see that like this
+
+ align:start position:0%
+and you very much see that like this
+ 
+
+ align:start position:0%
+and you very much see that like this
+here works for all series right and it's
+
+ align:start position:0%
+here works for all series right and it's
+ 
+
+ align:start position:0%
+here works for all series right and it's
+really just because you don't compare
+
+ align:start position:0%
+really just because you don't compare
+ 
+
+ align:start position:0%
+really just because you don't compare
+the element to the next but you're
+
+ align:start position:0%
+the element to the next but you're
+ 
+
+ align:start position:0%
+the element to the next but you're
+comparing it to this fixed um
+
+ align:start position:0%
+comparing it to this fixed um
+ 
+
+ align:start position:0%
+comparing it to this fixed um
+series which is a geometric is
+
+ align:start position:0%
+series which is a geometric is
+ 
+
+ align:start position:0%
+series which is a geometric is
+okay.
+
+ align:start position:0%
+okay.
+ 
+
+ align:start position:0%
+okay.
+So that's that's like the
+
+ align:start position:0%
+So that's that's like the
+ 
+
+ align:start position:0%
+So that's that's like the
+uh that's the the the the real version
+
+ align:start position:0%
+uh that's the the the the real version
+ 
+
+ align:start position:0%
+uh that's the the the the real version
+uh so to speak of the of the boot test.
+
+ align:start position:0%
+uh so to speak of the of the boot test.
+ 
+
+ align:start position:0%
+uh so to speak of the of the boot test.
+So now let's
+
+ align:start position:0%
+So now let's
+ 
+
+ align:start position:0%
+So now let's
+let's talk a little bit more about power
+
+ align:start position:0%
+let's talk a little bit more about power
+ 
+
+ align:start position:0%
+let's talk a little bit more about power
+series.
+
+ align:start position:0%
+series.
+ 
+
+ align:start position:0%
+series.
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I want to talk about so like there's
+
+ align:start position:0%
+and I want to talk about so like there's
+ 
+
+ align:start position:0%
+and I want to talk about so like there's
+one function that is particular
+
+ align:start position:0%
+one function that is particular
+ 
+
+ align:start position:0%
+one function that is particular
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+and I mean like all of these sort of
+
+ align:start position:0%
+and I mean like all of these sort of
+ 
+
+ align:start position:0%
+and I mean like all of these sort of
+basic functions are of course important
+
+ align:start position:0%
+basic functions are of course important
+ 
+
+ align:start position:0%
+basic functions are of course important
+but they are somewhat similar and uh the
+
+ align:start position:0%
+but they are somewhat similar and uh the
+ 
+
+ align:start position:0%
+but they are somewhat similar and uh the
+one I want to talk about is the
+
+ align:start position:0%
+one I want to talk about is the
+ 
+
+ align:start position:0%
+one I want to talk about is the
+exponential function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And and there's various way that you
+
+ align:start position:0%
+And and there's various way that you
+ 
+
+ align:start position:0%
+And and there's various way that you
+could define so what is the exponential
+
+ align:start position:0%
+could define so what is the exponential
+ 
+
+ align:start position:0%
+could define so what is the exponential
+function? There's various ways that you
+
+ align:start position:0%
+function? There's various ways that you
+ 
+
+ align:start position:0%
+function? There's various ways that you
+could define the exponential function.
+
+ align:start position:0%
+could define the exponential function.
+ 
+
+ align:start position:0%
+could define the exponential function.
+You can define it, you know, like two
+
+ align:start position:0%
+You can define it, you know, like two
+ 
+
+ align:start position:0%
+You can define it, you know, like two
+that comes to mind, but there's others
+
+ align:start position:0%
+that comes to mind, but there's others
+ 
+
+ align:start position:0%
+that comes to mind, but there's others
+too. One is that you could define it to
+
+ align:start position:0%
+too. One is that you could define it to
+ 
+
+ align:start position:0%
+too. One is that you could define it to
+be a function that's satisfying a
+
+ align:start position:0%
+be a function that's satisfying a
+ 
+
+ align:start position:0%
+be a function that's satisfying a
+certain differential equation and that
+
+ align:start position:0%
+certain differential equation and that
+ 
+
+ align:start position:0%
+certain differential equation and that
+would be a good way of defining it.
+
+ align:start position:0%
+would be a good way of defining it.
+ 
+
+ align:start position:0%
+would be a good way of defining it.
+Another way of defining it which is more
+
+ align:start position:0%
+Another way of defining it which is more
+ 
+
+ align:start position:0%
+Another way of defining it which is more
+relevant to what we're doing here is
+
+ align:start position:0%
+relevant to what we're doing here is
+ 
+
+ align:start position:0%
+relevant to what we're doing here is
+defining it as a power series.
+
+ align:start position:0%
+defining it as a power series.
+ 
+
+ align:start position:0%
+defining it as a power series.
+So I'm looking at
+
+ align:start position:0%
+So I'm looking at
+ 
+
+ align:start position:0%
+So I'm looking at
+but at e to the x
+
+ align:start position:0%
+but at e to the x
+ 
+
+ align:start position:0%
+but at e to the x
+and um and I'm looking at e to the x. So
+
+ align:start position:0%
+and um and I'm looking at e to the x. So
+ 
+
+ align:start position:0%
+and um and I'm looking at e to the x. So
+I define e capital e of x as this power
+
+ align:start position:0%
+I define e capital e of x as this power
+ 
+
+ align:start position:0%
+I define e capital e of x as this power
+series that we looked at before.
+
+ align:start position:0%
+series that we looked at before.
+ 
+
+ align:start position:0%
+series that we looked at before.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now I want to prove that this here is
+
+ align:start position:0%
+Now I want to prove that this here is
+ 
+
+ align:start position:0%
+Now I want to prove that this here is
+really what you should think of this.
+
+ align:start position:0%
+really what you should think of this.
+ 
+
+ align:start position:0%
+really what you should think of this.
+This here is the exponential function.
+
+ align:start position:0%
+This here is the exponential function.
+ 
+
+ align:start position:0%
+This here is the exponential function.
+So so I want to show but what does it
+
+ align:start position:0%
+So so I want to show but what does it
+ 
+
+ align:start position:0%
+So so I want to show but what does it
+mean that it is expon want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+the exponential function. So what do I
+
+ align:start position:0%
+the exponential function. So what do I
+ 
+
+ align:start position:0%
+the exponential function. So what do I
+mean by I mean of course I could
+
+ align:start position:0%
+mean by I mean of course I could
+ 
+
+ align:start position:0%
+mean by I mean of course I could
+you know I could define any function to
+
+ align:start position:0%
+you know I could define any function to
+ 
+
+ align:start position:0%
+you know I could define any function to
+be the exponential function but there
+
+ align:start position:0%
+be the exponential function but there
+ 
+
+ align:start position:0%
+be the exponential function but there
+are certain properties of the
+
+ align:start position:0%
+are certain properties of the
+ 
+
+ align:start position:0%
+are certain properties of the
+exponential function that you would want
+
+ align:start position:0%
+exponential function that you would want
+ 
+
+ align:start position:0%
+exponential function that you would want
+right and so um well the first thing I
+
+ align:start position:0%
+right and so um well the first thing I
+ 
+
+ align:start position:0%
+right and so um well the first thing I
+observe is that e of zero
+
+ align:start position:0%
+observe is that e of zero
+ 
+
+ align:start position:0%
+observe is that e of zero
+is equal to if if all of these if x is
+
+ align:start position:0%
+is equal to if if all of these if x is
+ 
+
+ align:start position:0%
+is equal to if if all of these if x is
+zero then all of these are zero except
+
+ align:start position:0%
+zero then all of these are zero except
+ 
+
+ align:start position:0%
+zero then all of these are zero except
+when n is equal to zero and then x to
+
+ align:start position:0%
+when n is equal to zero and then x to
+ 
+
+ align:start position:0%
+when n is equal to zero and then x to
+the zero this here is by definition one
+
+ align:start position:0%
+the zero this here is by definition one
+ 
+
+ align:start position:0%
+the zero this here is by definition one
+okay and this here is is zero factorial
+
+ align:start position:0%
+okay and this here is is zero factorial
+ 
+
+ align:start position:0%
+okay and this here is is zero factorial
+is by definition one so this here is is
+
+ align:start position:0%
+is by definition one so this here is is
+ 
+
+ align:start position:0%
+is by definition one so this here is is
+one by definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we know already by the way that this
+
+ align:start position:0%
+and we know already by the way that this
+ 
+
+ align:start position:0%
+and we know already by the way that this
+here we have already seen that the
+
+ align:start position:0%
+here we have already seen that the
+ 
+
+ align:start position:0%
+here we have already seen that the
+radius of convergence for this power
+
+ align:start position:0%
+radius of convergence for this power
+ 
+
+ align:start position:0%
+radius of convergence for this power
+series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to infinity right we have
+
+ align:start position:0%
+is equal to infinity right we have
+ 
+
+ align:start position:0%
+is equal to infinity right we have
+already seen that right so it's a well-
+
+ align:start position:0%
+already seen that right so it's a well-
+ 
+
+ align:start position:0%
+already seen that right so it's a well-
+definfined function for all x okay now
+
+ align:start position:0%
+definfined function for all x okay now
+ 
+
+ align:start position:0%
+definfined function for all x okay now
+I'm later going to prove so next time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we will show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if you define it like that that
+
+ align:start position:0%
+that if you define it like that that
+ 
+
+ align:start position:0%
+that if you define it like that that
+that that this function here defined
+
+ align:start position:0%
+that that this function here defined
+ 
+
+ align:start position:0%
+that that this function here defined
+like that has a property that x e to x +
+
+ align:start position:0%
+like that has a property that x e to x +
+ 
+
+ align:start position:0%
+like that has a property that x e to x +
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+is equal to this product here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now uh using this well the first thing I
+
+ align:start position:0%
+Now uh using this well the first thing I
+ 
+
+ align:start position:0%
+Now uh using this well the first thing I
+can observe is I haven't really gotten
+
+ align:start position:0%
+can observe is I haven't really gotten
+ 
+
+ align:start position:0%
+can observe is I haven't really gotten
+to the property yet but I'm just at the
+
+ align:start position:0%
+to the property yet but I'm just at the
+ 
+
+ align:start position:0%
+to the property yet but I'm just at the
+moment I'm just examining that
+
+ align:start position:0%
+moment I'm just examining that
+ 
+
+ align:start position:0%
+moment I'm just examining that
+particular function you know some
+
+ align:start position:0%
+particular function you know some
+ 
+
+ align:start position:0%
+particular function you know some
+properties that it has
+
+ align:start position:0%
+properties that it has
+ 
+
+ align:start position:0%
+properties that it has
+and so the first thing I will observe is
+
+ align:start position:0%
+and so the first thing I will observe is
+ 
+
+ align:start position:0%
+and so the first thing I will observe is
+that if x here is positive or non-
+
+ align:start position:0%
+that if x here is positive or non-
+ 
+
+ align:start position:0%
+that if x here is positive or non-
+negative right then all of these numbers
+
+ align:start position:0%
+negative right then all of these numbers
+ 
+
+ align:start position:0%
+negative right then all of these numbers
+are non- negative so you're summing non-
+
+ align:start position:0%
+are non- negative so you're summing non-
+ 
+
+ align:start position:0%
+are non- negative so you're summing non-
+negative numbers so the sum is non-
+
+ align:start position:0%
+negative numbers so the sum is non-
+ 
+
+ align:start position:0%
+negative numbers so the sum is non-
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+So if
+
+ align:start position:0%
+So if
+ 
+
+ align:start position:0%
+So if
+x is bigger equal to zero then it
+
+ align:start position:0%
+x is bigger equal to zero then it
+ 
+
+ align:start position:0%
+x is bigger equal to zero then it
+implies that e of x is big is actually
+
+ align:start position:0%
+implies that e of x is big is actually
+ 
+
+ align:start position:0%
+implies that e of x is big is actually
+strictly positive
+
+ align:start position:0%
+strictly positive
+ 
+
+ align:start position:0%
+strictly positive
+right in fact the smallest one is where
+
+ align:start position:0%
+right in fact the smallest one is where
+ 
+
+ align:start position:0%
+right in fact the smallest one is where
+you x was equal to zero but in that case
+
+ align:start position:0%
+you x was equal to zero but in that case
+ 
+
+ align:start position:0%
+you x was equal to zero but in that case
+you got one right
+
+ align:start position:0%
+you got one right
+ 
+
+ align:start position:0%
+you got one right
+now if x here is negative then it's not
+
+ align:start position:0%
+now if x here is negative then it's not
+ 
+
+ align:start position:0%
+now if x here is negative then it's not
+super clear right if x is negative you
+
+ align:start position:0%
+super clear right if x is negative you
+ 
+
+ align:start position:0%
+super clear right if x is negative you
+know some of these numbers that you'll
+
+ align:start position:0%
+know some of these numbers that you'll
+ 
+
+ align:start position:0%
+know some of these numbers that you'll
+be summing are positive and some of them
+
+ align:start position:0%
+be summing are positive and some of them
+ 
+
+ align:start position:0%
+be summing are positive and some of them
+are negative. So it's not at all clear
+
+ align:start position:0%
+are negative. So it's not at all clear
+ 
+
+ align:start position:0%
+are negative. So it's not at all clear
+what happened to the sum. But if if you
+
+ align:start position:0%
+what happened to the sum. But if if you
+ 
+
+ align:start position:0%
+what happened to the sum. But if if you
+grant me this for the for the moment
+
+ align:start position:0%
+grant me this for the for the moment
+ 
+
+ align:start position:0%
+grant me this for the for the moment
+this relationship here then we would
+
+ align:start position:0%
+this relationship here then we would
+ 
+
+ align:start position:0%
+this relationship here then we would
+have that e to the x minus e to minus
+
+ align:start position:0%
+have that e to the x minus e to minus
+ 
+
+ align:start position:0%
+have that e to the x minus e to minus
+sorry e in x - x. So that's the same as
+
+ align:start position:0%
+sorry e in x - x. So that's the same as
+ 
+
+ align:start position:0%
+sorry e in x - x. So that's the same as
+let me just make a little more space
+
+ align:start position:0%
+let me just make a little more space
+ 
+
+ align:start position:0%
+let me just make a little more space
+here. So e of zero which I already know
+
+ align:start position:0%
+here. So e of zero which I already know
+ 
+
+ align:start position:0%
+here. So e of zero which I already know
+is one. This here can think about that
+
+ align:start position:0%
+is one. This here can think about that
+ 
+
+ align:start position:0%
+is one. This here can think about that
+as x - x
+
+ align:start position:0%
+as x - x
+ 
+
+ align:start position:0%
+as x - x
+or if you will you could think about it
+
+ align:start position:0%
+or if you will you could think about it
+ 
+
+ align:start position:0%
+or if you will you could think about it
+as x + - x.
+
+ align:start position:0%
+as x + - x.
+ 
+
+ align:start position:0%
+as x + - x.
+And now if you grant me this this thing
+
+ align:start position:0%
+And now if you grant me this this thing
+ 
+
+ align:start position:0%
+And now if you grant me this this thing
+here that we prove next time then I can
+
+ align:start position:0%
+here that we prove next time then I can
+ 
+
+ align:start position:0%
+here that we prove next time then I can
+write this here as e
+
+ align:start position:0%
+write this here as e
+ 
+
+ align:start position:0%
+write this here as e
+of x * e of minus x right
+
+ align:start position:0%
+of x * e of minus x right
+ 
+
+ align:start position:0%
+of x * e of minus x right
+uh yeah sorry yeah
+
+ align:start position:0%
+uh yeah sorry yeah
+ 
+
+ align:start position:0%
+uh yeah sorry yeah
+okay and now if x here is negative then
+
+ align:start position:0%
+okay and now if x here is negative then
+ 
+
+ align:start position:0%
+okay and now if x here is negative then
+of course minus x is positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this thing here. So now I know by
+
+ align:start position:0%
+So this thing here. So now I know by
+ 
+
+ align:start position:0%
+So this thing here. So now I know by
+this thing here that this here is
+
+ align:start position:0%
+this thing here that this here is
+ 
+
+ align:start position:0%
+this thing here that this here is
+positive.
+
+ align:start position:0%
+positive.
+ 
+
+ align:start position:0%
+positive.
+And so since the product of these two
+
+ align:start position:0%
+And so since the product of these two
+ 
+
+ align:start position:0%
+And so since the product of these two
+things is one, this here must be
+
+ align:start position:0%
+things is one, this here must be
+ 
+
+ align:start position:0%
+things is one, this here must be
+strictly positive as well. Right? So
+
+ align:start position:0%
+strictly positive as well. Right? So
+ 
+
+ align:start position:0%
+strictly positive as well. Right? So
+this imply that e to the x is also
+
+ align:start position:0%
+this imply that e to the x is also
+ 
+
+ align:start position:0%
+this imply that e to the x is also
+strictly positive.
+
+ align:start position:0%
+strictly positive.
+ 
+
+ align:start position:0%
+strictly positive.
+Okay?
+
+ align:start position:0%
+Okay?
+ 
+
+ align:start position:0%
+Okay?
+So this is just a couple of observation.
+
+ align:start position:0%
+So this is just a couple of observation.
+ 
+
+ align:start position:0%
+So this is just a couple of observation.
+Now, of course, I'm using that
+
+ align:start position:0%
+Now, of course, I'm using that
+ 
+
+ align:start position:0%
+Now, of course, I'm using that
+relationship that I haven't established
+
+ align:start position:0%
+relationship that I haven't established
+ 
+
+ align:start position:0%
+relationship that I haven't established
+yet, but I will establish that next
+
+ align:start position:0%
+yet, but I will establish that next
+ 
+
+ align:start position:0%
+yet, but I will establish that next
+time.
+
+ align:start position:0%
+time.
+ 
+
+ align:start position:0%
+time.
+The next thing is that I want to define
+
+ align:start position:0%
+The next thing is that I want to define
+ 
+
+ align:start position:0%
+The next thing is that I want to define
+the number E.
+
+ align:start position:0%
+the number E.
+ 
+
+ align:start position:0%
+the number E.
+And so I define this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So E that is 2.7 whatever I don't
+
+ align:start position:0%
+So E that is 2.7 whatever I don't
+ 
+
+ align:start position:0%
+So E that is 2.7 whatever I don't
+remember. Uh but so E we define so
+
+ align:start position:0%
+remember. Uh but so E we define so
+ 
+
+ align:start position:0%
+remember. Uh but so E we define so
+little E. So I define it as this
+
+ align:start position:0%
+little E. So I define it as this
+ 
+
+ align:start position:0%
+little E. So I define it as this
+function here
+
+ align:start position:0%
+function here
+ 
+
+ align:start position:0%
+function here
+evaluated in one. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now I want to define so I have my
+
+ align:start position:0%
+Now I want to define so I have my
+ 
+
+ align:start position:0%
+Now I want to define so I have my
+function capital E but I want to define
+
+ align:start position:0%
+function capital E but I want to define
+ 
+
+ align:start position:0%
+function capital E but I want to define
+a second function that is E. So, so want
+
+ align:start position:0%
+a second function that is E. So, so want
+ 
+
+ align:start position:0%
+a second function that is E. So, so want
+to define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a second function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is e to the x like this, right?
+
+ align:start position:0%
+and that is e to the x like this, right?
+ 
+
+ align:start position:0%
+and that is e to the x like this, right?
+And that should have the kind of
+
+ align:start position:0%
+And that should have the kind of
+ 
+
+ align:start position:0%
+And that should have the kind of
+properties that you uh that you think it
+
+ align:start position:0%
+properties that you uh that you think it
+ 
+
+ align:start position:0%
+properties that you uh that you think it
+should have. Okay? So but first before I
+
+ align:start position:0%
+should have. Okay? So but first before I
+ 
+
+ align:start position:0%
+should have. Okay? So but first before I
+do that let me just think if if you take
+
+ align:start position:0%
+do that let me just think if if you take
+ 
+
+ align:start position:0%
+do that let me just think if if you take
+e to the power m m here
+
+ align:start position:0%
+e to the power m m here
+ 
+
+ align:start position:0%
+e to the power m m here
+m is let's say that m here
+
+ align:start position:0%
+m is let's say that m here
+ 
+
+ align:start position:0%
+m is let's say that m here
+uh let's say that m is a is a integer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if if um this here this here should just
+
+ align:start position:0%
+if if um this here this here should just
+ 
+
+ align:start position:0%
+if if um this here this here should just
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+e * E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M*s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+note that this here is this here I can
+
+ align:start position:0%
+note that this here is this here I can
+ 
+
+ align:start position:0%
+note that this here is this here I can
+of course write as E
+
+ align:start position:0%
+of course write as E
+ 
+
+ align:start position:0%
+of course write as E
+this is what E is so I can write it as
+
+ align:start position:0%
+this is what E is so I can write it as
+ 
+
+ align:start position:0%
+this is what E is so I can write it as
+this here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now I can use this hair that I will
+
+ align:start position:0%
+but now I can use this hair that I will
+ 
+
+ align:start position:0%
+but now I can use this hair that I will
+prove next time again. So if I take E of
+
+ align:start position:0%
+prove next time again. So if I take E of
+ 
+
+ align:start position:0%
+prove next time again. So if I take E of
+1 * E of 1 then that's E of two. And if
+
+ align:start position:0%
+1 * E of 1 then that's E of two. And if
+ 
+
+ align:start position:0%
+1 * E of 1 then that's E of two. And if
+I take E here three times then it's E of
+
+ align:start position:0%
+I take E here three times then it's E of
+ 
+
+ align:start position:0%
+I take E here three times then it's E of
+three. Right? So this thing here is
+
+ align:start position:0%
+three. Right? So this thing here is
+ 
+
+ align:start position:0%
+three. Right? So this thing here is
+actually the same as capital E of M.
+
+ align:start position:0%
+actually the same as capital E of M.
+ 
+
+ align:start position:0%
+actually the same as capital E of M.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+So I have that.
+
+ align:start position:0%
+So I have that.
+ 
+
+ align:start position:0%
+So I have that.
+I also by definition so
+
+ align:start position:0%
+I also by definition so
+ 
+
+ align:start position:0%
+I also by definition so
+e to the zero this here I'm setting
+
+ align:start position:0%
+e to the zero this here I'm setting
+ 
+
+ align:start position:0%
+e to the zero this here I'm setting
+equal to one but I already have that one
+
+ align:start position:0%
+equal to one but I already have that one
+ 
+
+ align:start position:0%
+equal to one but I already have that one
+was equal to this capital e in in in
+
+ align:start position:0%
+was equal to this capital e in in in
+ 
+
+ align:start position:0%
+was equal to this capital e in in in
+zero right
+
+ align:start position:0%
+zero right
+ 
+
+ align:start position:0%
+zero right
+okay now what about if m here is a
+
+ align:start position:0%
+okay now what about if m here is a
+ 
+
+ align:start position:0%
+okay now what about if m here is a
+negative integer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So suppose that m here is a negative
+
+ align:start position:0%
+So suppose that m here is a negative
+ 
+
+ align:start position:0%
+So suppose that m here is a negative
+integer. Suppose that m here is
+
+ align:start position:0%
+integer. Suppose that m here is
+ 
+
+ align:start position:0%
+integer. Suppose that m here is
+negative.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So sorry what should e to the m here be?
+
+ align:start position:0%
+So sorry what should e to the m here be?
+ 
+
+ align:start position:0%
+So sorry what should e to the m here be?
+This here is just one over e to the
+
+ align:start position:0%
+This here is just one over e to the
+ 
+
+ align:start position:0%
+This here is just one over e to the
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+uh m. Okay, minus m is a positive
+
+ align:start position:0%
+uh m. Okay, minus m is a positive
+ 
+
+ align:start position:0%
+uh m. Okay, minus m is a positive
+integer, right? So this so this makes
+
+ align:start position:0%
+integer, right? So this so this makes
+ 
+
+ align:start position:0%
+integer, right? So this so this makes
+sense.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+if you're looking at
+
+ align:start position:0%
+if you're looking at
+ 
+
+ align:start position:0%
+if you're looking at
+E
+
+ align:start position:0%
+E
+ 
+
+ align:start position:0%
+E
+to the again using this relationship
+
+ align:start position:0%
+to the again using this relationship
+ 
+
+ align:start position:0%
+to the again using this relationship
+here E the one and in fact the one we
+
+ align:start position:0%
+here E the one and in fact the one we
+ 
+
+ align:start position:0%
+here E the one and in fact the one we
+just did.
+
+ align:start position:0%
+just did.
+ 
+
+ align:start position:0%
+just did.
+So this is on integers
+
+ align:start position:0%
+So this is on integers
+ 
+
+ align:start position:0%
+So this is on integers
+um this here is now equal to E of zero
+
+ align:start position:0%
+um this here is now equal to E of zero
+ 
+
+ align:start position:0%
+um this here is now equal to E of zero
+which is equal to one.
+
+ align:start position:0%
+which is equal to one.
+ 
+
+ align:start position:0%
+which is equal to one.
+And so this imply and this is by this by
+
+ align:start position:0%
+And so this imply and this is by this by
+ 
+
+ align:start position:0%
+And so this imply and this is by this by
+that relationship over there. It's E of
+
+ align:start position:0%
+that relationship over there. It's E of
+ 
+
+ align:start position:0%
+that relationship over there. It's E of
+M * E of minus M. And so you see that
+
+ align:start position:0%
+M * E of minus M. And so you see that
+ 
+
+ align:start position:0%
+M * E of minus M. And so you see that
+this implies that E of minus M is equal
+
+ align:start position:0%
+this implies that E of minus M is equal
+ 
+
+ align:start position:0%
+this implies that E of minus M is equal
+to 1 / E of M by just dividing this on
+
+ align:start position:0%
+to 1 / E of M by just dividing this on
+ 
+
+ align:start position:0%
+to 1 / E of M by just dividing this on
+both sides. So you have this and this
+
+ align:start position:0%
+both sides. So you have this and this
+ 
+
+ align:start position:0%
+both sides. So you have this and this
+thing here. But this thing here,
+
+ align:start position:0%
+thing here. But this thing here,
+ 
+
+ align:start position:0%
+thing here. But this thing here,
+sorry, this is not what I wanted. Uh, if
+
+ align:start position:0%
+sorry, this is not what I wanted. Uh, if
+ 
+
+ align:start position:0%
+sorry, this is not what I wanted. Uh, if
+I take M negative, I just use the other
+
+ align:start position:0%
+I take M negative, I just use the other
+ 
+
+ align:start position:0%
+I take M negative, I just use the other
+one. Sorry, e of M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to 1 / E of minus M like that,
+
+ align:start position:0%
+is equal to 1 / E of minus M like that,
+ 
+
+ align:start position:0%
+is equal to 1 / E of minus M like that,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+M is M was supposed to be negative. So,
+
+ align:start position:0%
+M is M was supposed to be negative. So,
+ 
+
+ align:start position:0%
+M is M was supposed to be negative. So,
+this means that minus M is a positive
+
+ align:start position:0%
+this means that minus M is a positive
+ 
+
+ align:start position:0%
+this means that minus M is a positive
+integer. And this one here is then this
+
+ align:start position:0%
+integer. And this one here is then this
+ 
+
+ align:start position:0%
+integer. And this one here is then this
+one. I know that this here already agree
+
+ align:start position:0%
+one. I know that this here already agree
+ 
+
+ align:start position:0%
+one. I know that this here already agree
+with uh
+
+ align:start position:0%
+with uh
+ 
+
+ align:start position:0%
+with uh
+with um with uh this little function of
+
+ align:start position:0%
+with um with uh this little function of
+ 
+
+ align:start position:0%
+with um with uh this little function of
+e. So you see that this thing here is
+
+ align:start position:0%
+e. So you see that this thing here is
+ 
+
+ align:start position:0%
+e. So you see that this thing here is
+agrees with e to the power m. Right.
+
+ align:start position:0%
+agrees with e to the power m. Right.
+ 
+
+ align:start position:0%
+agrees with e to the power m. Right.
+Right. Because we we defined it like
+
+ align:start position:0%
+Right. Because we we defined it like
+ 
+
+ align:start position:0%
+Right. Because we we defined it like
+this. And now just checking that also on
+
+ align:start position:0%
+this. And now just checking that also on
+ 
+
+ align:start position:0%
+this. And now just checking that also on
+the negative integer this function here
+
+ align:start position:0%
+the negative integer this function here
+ 
+
+ align:start position:0%
+the negative integer this function here
+and this function here agree. Okay. So,
+
+ align:start position:0%
+and this function here agree. Okay. So,
+ 
+
+ align:start position:0%
+and this function here agree. Okay. So,
+so I now have these two different
+
+ align:start position:0%
+so I now have these two different
+ 
+
+ align:start position:0%
+so I now have these two different
+functions. Well, one I haven't really
+
+ align:start position:0%
+functions. Well, one I haven't really
+ 
+
+ align:start position:0%
+functions. Well, one I haven't really
+defined yet. I've only defined it now on
+
+ align:start position:0%
+defined yet. I've only defined it now on
+ 
+
+ align:start position:0%
+defined yet. I've only defined it now on
+all integers.
+
+ align:start position:0%
+all integers.
+ 
+
+ align:start position:0%
+all integers.
+But, but so far these two functions
+
+ align:start position:0%
+But, but so far these two functions
+ 
+
+ align:start position:0%
+But, but so far these two functions
+agree.
+
+ align:start position:0%
+agree.
+ 
+
+ align:start position:0%
+agree.
+Now what I also should have is that I
+
+ align:start position:0%
+Now what I also should have is that I
+ 
+
+ align:start position:0%
+Now what I also should have is that I
+should have so suppose you're looking at
+
+ align:start position:0%
+should have so suppose you're looking at
+ 
+
+ align:start position:0%
+should have so suppose you're looking at
+a rational number.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So suppose you take a rational number.
+
+ align:start position:0%
+So suppose you take a rational number.
+ 
+
+ align:start position:0%
+So suppose you take a rational number.
+Remember we usually write a rational
+
+ align:start position:0%
+Remember we usually write a rational
+ 
+
+ align:start position:0%
+Remember we usually write a rational
+number. So suppose that Q here is a
+
+ align:start position:0%
+number. So suppose that Q here is a
+ 
+
+ align:start position:0%
+number. So suppose that Q here is a
+rational number. We usually write a
+
+ align:start position:0%
+rational number. We usually write a
+ 
+
+ align:start position:0%
+rational number. We usually write a
+rational number as
+
+ align:start position:0%
+rational number as
+ 
+
+ align:start position:0%
+rational number as
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as an element in set. So it could be
+
+ align:start position:0%
+as an element in set. So it could be
+ 
+
+ align:start position:0%
+as an element in set. So it could be
+negative, it could be zero and n here is
+
+ align:start position:0%
+negative, it could be zero and n here is
+ 
+
+ align:start position:0%
+negative, it could be zero and n here is
+a positive integer. So fraction like
+
+ align:start position:0%
+a positive integer. So fraction like
+ 
+
+ align:start position:0%
+a positive integer. So fraction like
+this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now what should E
+
+ align:start position:0%
+Now what should E
+ 
+
+ align:start position:0%
+Now what should E
+of Q be? Right?
+
+ align:start position:0%
+of Q be? Right?
+ 
+
+ align:start position:0%
+of Q be? Right?
+Well, E of Q um this here should be
+
+ align:start position:0%
+Well, E of Q um this here should be
+ 
+
+ align:start position:0%
+Well, E of Q um this here should be
+right how you would think about it is
+
+ align:start position:0%
+right how you would think about it is
+ 
+
+ align:start position:0%
+right how you would think about it is
+that it really should be something
+
+ align:start position:0%
+that it really should be something
+ 
+
+ align:start position:0%
+that it really should be something
+it should be something this here should
+
+ align:start position:0%
+it should be something this here should
+ 
+
+ align:start position:0%
+it should be something this here should
+be a number should be a number alpha and
+
+ align:start position:0%
+be a number should be a number alpha and
+ 
+
+ align:start position:0%
+be a number should be a number alpha and
+this should have the property that is
+
+ align:start position:0%
+this should have the property that is
+ 
+
+ align:start position:0%
+this should have the property that is
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+and it should have the property so let's
+
+ align:start position:0%
+and it should have the property so let's
+ 
+
+ align:start position:0%
+and it should have the property so let's
+just write it so so E of Q this is m /
+
+ align:start position:0%
+just write it so so E of Q this is m /
+ 
+
+ align:start position:0%
+just write it so so E of Q this is m /
+n. It should have the property that if
+
+ align:start position:0%
+n. It should have the property that if
+ 
+
+ align:start position:0%
+n. It should have the property that if
+you raise it alpha here suppose you were
+
+ align:start position:0%
+you raise it alpha here suppose you were
+ 
+
+ align:start position:0%
+you raise it alpha here suppose you were
+raising it to the power n then you
+
+ align:start position:0%
+raising it to the power n then you
+ 
+
+ align:start position:0%
+raising it to the power n then you
+should get this number that we have
+
+ align:start position:0%
+should get this number that we have
+ 
+
+ align:start position:0%
+should get this number that we have
+already defined right. So should have it
+
+ align:start position:0%
+already defined right. So should have it
+ 
+
+ align:start position:0%
+already defined right. So should have it
+should be positive and when you raise it
+
+ align:start position:0%
+should be positive and when you raise it
+ 
+
+ align:start position:0%
+should be positive and when you raise it
+like this um then it should give you
+
+ align:start position:0%
+like this um then it should give you
+ 
+
+ align:start position:0%
+like this um then it should give you
+that and just like with square root of
+
+ align:start position:0%
+that and just like with square root of
+ 
+
+ align:start position:0%
+that and just like with square root of
+two it's just one element with this
+
+ align:start position:0%
+two it's just one element with this
+ 
+
+ align:start position:0%
+two it's just one element with this
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+okay so that's defined uh what it so so
+
+ align:start position:0%
+okay so that's defined uh what it so so
+ 
+
+ align:start position:0%
+okay so that's defined uh what it so so
+this way you see this way we have now
+
+ align:start position:0%
+this way you see this way we have now
+ 
+
+ align:start position:0%
+this way you see this way we have now
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+this function e on all rational numbers
+
+ align:start position:0%
+this function e on all rational numbers
+ 
+
+ align:start position:0%
+this function e on all rational numbers
+but now we need to check right we need
+
+ align:start position:0%
+but now we need to check right we need
+ 
+
+ align:start position:0%
+but now we need to check right we need
+to check that this thing here need to
+
+ align:start position:0%
+to check that this thing here need to
+ 
+
+ align:start position:0%
+to check that this thing here need to
+check. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that that
+
+ align:start position:0%
+that that
+ 
+
+ align:start position:0%
+that that
+EQ
+
+ align:start position:0%
+EQ
+ 
+
+ align:start position:0%
+EQ
+is equal
+
+ align:start position:0%
+is equal
+ 
+
+ align:start position:0%
+is equal
+like that. Right? So I need to check
+
+ align:start position:0%
+like that. Right? So I need to check
+ 
+
+ align:start position:0%
+like that. Right? So I need to check
+that. Okay?
+
+ align:start position:0%
+that. Okay?
+ 
+
+ align:start position:0%
+that. Okay?
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+I want to say that that E to the Q is
+
+ align:start position:0%
+I want to say that that E to the Q is
+ 
+
+ align:start position:0%
+I want to say that that E to the Q is
+that alpha, right?
+
+ align:start position:0%
+that alpha, right?
+ 
+
+ align:start position:0%
+that alpha, right?
+So this means that
+
+ align:start position:0%
+So this means that
+ 
+
+ align:start position:0%
+So this means that
+I want to show
+
+ align:start position:0%
+I want to show
+ 
+
+ align:start position:0%
+I want to show
+so I need to show two things
+
+ align:start position:0%
+so I need to show two things
+ 
+
+ align:start position:0%
+so I need to show two things
+E
+
+ align:start position:0%
+E
+ 
+
+ align:start position:0%
+E
+to Q is positive. Well, I've already
+
+ align:start position:0%
+to Q is positive. Well, I've already
+ 
+
+ align:start position:0%
+to Q is positive. Well, I've already
+checked that right because you check at
+
+ align:start position:0%
+checked that right because you check at
+ 
+
+ align:start position:0%
+checked that right because you check at
+at E capital E at anything is positive.
+
+ align:start position:0%
+at E capital E at anything is positive.
+ 
+
+ align:start position:0%
+at E capital E at anything is positive.
+So this is okay. The second thing I need
+
+ align:start position:0%
+So this is okay. The second thing I need
+ 
+
+ align:start position:0%
+So this is okay. The second thing I need
+to check is that it has the property
+
+ align:start position:0%
+to check is that it has the property
+ 
+
+ align:start position:0%
+to check is that it has the property
+that if you raise it to the n power then
+
+ align:start position:0%
+that if you raise it to the n power then
+ 
+
+ align:start position:0%
+that if you raise it to the n power then
+you're getting uh then you're getting e
+
+ align:start position:0%
+you're getting uh then you're getting e
+ 
+
+ align:start position:0%
+you're getting uh then you're getting e
+um e to the to the m
+
+ align:start position:0%
+um e to the to the m
+ 
+
+ align:start position:0%
+um e to the to the m
+right now e to the m that's an integer.
+
+ align:start position:0%
+right now e to the m that's an integer.
+ 
+
+ align:start position:0%
+right now e to the m that's an integer.
+It could be negative
+
+ align:start position:0%
+It could be negative
+ 
+
+ align:start position:0%
+It could be negative
+but e to any negative integer whether
+
+ align:start position:0%
+but e to any negative integer whether
+ 
+
+ align:start position:0%
+but e to any negative integer whether
+it's ne positive or or negative we
+
+ align:start position:0%
+it's ne positive or or negative we
+ 
+
+ align:start position:0%
+it's ne positive or or negative we
+already checked that this is equal to
+
+ align:start position:0%
+already checked that this is equal to
+ 
+
+ align:start position:0%
+already checked that this is equal to
+capital e of m.
+
+ align:start position:0%
+capital e of m.
+ 
+
+ align:start position:0%
+capital e of m.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So now I need to so this here is so now
+
+ align:start position:0%
+So now I need to so this here is so now
+ 
+
+ align:start position:0%
+So now I need to so this here is so now
+what is this? So what do I need to
+
+ align:start position:0%
+what is this? So what do I need to
+ 
+
+ align:start position:0%
+what is this? So what do I need to
+check? So I need to check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that e
+
+ align:start position:0%
+that e
+ 
+
+ align:start position:0%
+that e
+to the m / n. This thing here raised to
+
+ align:start position:0%
+to the m / n. This thing here raised to
+ 
+
+ align:start position:0%
+to the m / n. This thing here raised to
+the power n is equal to this. But but
+
+ align:start position:0%
+the power n is equal to this. But but
+ 
+
+ align:start position:0%
+the power n is equal to this. But but
+what is this here? This here is just e
+
+ align:start position:0%
+what is this here? This here is just e
+ 
+
+ align:start position:0%
+what is this here? This here is just e
+to the m / n
+
+ align:start position:0%
+to the m / n
+ 
+
+ align:start position:0%
+to the m / n
+time multiply itself n times.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is now n times.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But now I can use again this thing that
+
+ align:start position:0%
+But now I can use again this thing that
+ 
+
+ align:start position:0%
+But now I can use again this thing that
+I proved next time that when I do it
+
+ align:start position:0%
+I proved next time that when I do it
+ 
+
+ align:start position:0%
+I proved next time that when I do it
+like here I'm just doing it two times
+
+ align:start position:0%
+like here I'm just doing it two times
+ 
+
+ align:start position:0%
+like here I'm just doing it two times
+and here I'm just doing it for I'm doing
+
+ align:start position:0%
+and here I'm just doing it for I'm doing
+ 
+
+ align:start position:0%
+and here I'm just doing it for I'm doing
+it for different x and y. But if I do it
+
+ align:start position:0%
+it for different x and y. But if I do it
+ 
+
+ align:start position:0%
+it for different x and y. But if I do it
+n times with the same x then I'm just
+
+ align:start position:0%
+n times with the same x then I'm just
+ 
+
+ align:start position:0%
+n times with the same x then I'm just
+adding that x together n times.
+
+ align:start position:0%
+adding that x together n times.
+ 
+
+ align:start position:0%
+adding that x together n times.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+And so this thing here is the same as e
+
+ align:start position:0%
+And so this thing here is the same as e
+ 
+
+ align:start position:0%
+And so this thing here is the same as e
+by that rule over there n * m / n but
+
+ align:start position:0%
+by that rule over there n * m / n but
+ 
+
+ align:start position:0%
+by that rule over there n * m / n but
+this is just e of m as it should be
+
+ align:start position:0%
+this is just e of m as it should be
+ 
+
+ align:start position:0%
+this is just e of m as it should be
+right. So you see that these two
+
+ align:start position:0%
+right. So you see that these two
+ 
+
+ align:start position:0%
+right. So you see that these two
+functions here. So the conclusion so far
+
+ align:start position:0%
+functions here. So the conclusion so far
+ 
+
+ align:start position:0%
+functions here. So the conclusion so far
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the conclusion now is that
+
+ align:start position:0%
+the conclusion now is that
+ 
+
+ align:start position:0%
+the conclusion now is that
+this function here
+
+ align:start position:0%
+this function here
+ 
+
+ align:start position:0%
+this function here
+is equal to this function here for all
+
+ align:start position:0%
+is equal to this function here for all
+ 
+
+ align:start position:0%
+is equal to this function here for all
+Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all rational numbers. Okay.
+
+ align:start position:0%
+for all rational numbers. Okay.
+ 
+
+ align:start position:0%
+for all rational numbers. Okay.
+Now what other property should this
+
+ align:start position:0%
+Now what other property should this
+ 
+
+ align:start position:0%
+Now what other property should this
+exponential? So this here you know so
+
+ align:start position:0%
+exponential? So this here you know so
+ 
+
+ align:start position:0%
+exponential? So this here you know so
+far this is kind of the property that
+
+ align:start position:0%
+far this is kind of the property that
+ 
+
+ align:start position:0%
+far this is kind of the property that
+you want of the exponential function
+
+ align:start position:0%
+you want of the exponential function
+ 
+
+ align:start position:0%
+you want of the exponential function
+right but what other property should the
+
+ align:start position:0%
+right but what other property should the
+ 
+
+ align:start position:0%
+right but what other property should the
+exponential function have it should have
+
+ align:start position:0%
+exponential function have it should have
+ 
+
+ align:start position:0%
+exponential function have it should have
+one other property and that's enough to
+
+ align:start position:0%
+one other property and that's enough to
+ 
+
+ align:start position:0%
+one other property and that's enough to
+determine it and that is it should be
+
+ align:start position:0%
+determine it and that is it should be
+ 
+
+ align:start position:0%
+determine it and that is it should be
+continuous. So one more property is that
+
+ align:start position:0%
+continuous. So one more property is that
+ 
+
+ align:start position:0%
+continuous. So one more property is that
+this function e to the x when x is
+
+ align:start position:0%
+this function e to the x when x is
+ 
+
+ align:start position:0%
+this function e to the x when x is
+defined like this this function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should be continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll talk a little bit more about
+
+ align:start position:0%
+and we'll talk a little bit more about
+ 
+
+ align:start position:0%
+and we'll talk a little bit more about
+continuous function in just a second.
+
+ align:start position:0%
+continuous function in just a second.
+ 
+
+ align:start position:0%
+continuous function in just a second.
+Okay. Now, now then I have a theorem
+
+ align:start position:0%
+Okay. Now, now then I have a theorem
+ 
+
+ align:start position:0%
+Okay. Now, now then I have a theorem
+that we prove next time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the next times and and that is
+
+ align:start position:0%
+one of the next times and and that is
+ 
+
+ align:start position:0%
+one of the next times and and that is
+that suppose you take two functions.
+
+ align:start position:0%
+that suppose you take two functions.
+ 
+
+ align:start position:0%
+that suppose you take two functions.
+So so we then can appeal to the
+
+ align:start position:0%
+So so we then can appeal to the
+ 
+
+ align:start position:0%
+So so we then can appeal to the
+following theorem.
+
+ align:start position:0%
+following theorem.
+ 
+
+ align:start position:0%
+following theorem.
+If f and g are two
+
+ align:start position:0%
+If f and g are two
+ 
+
+ align:start position:0%
+If f and g are two
+continuous functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on a
+
+ align:start position:0%
+on a
+ 
+
+ align:start position:0%
+on a
+that agree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on all
+
+ align:start position:0%
+on all
+ 
+
+ align:start position:0%
+on all
+of do.
+
+ align:start position:0%
+of do.
+ 
+
+ align:start position:0%
+of do.
+So if you have two continuous functions
+
+ align:start position:0%
+So if you have two continuous functions
+ 
+
+ align:start position:0%
+So if you have two continuous functions
+and they if you restrict it to the
+
+ align:start position:0%
+and they if you restrict it to the
+ 
+
+ align:start position:0%
+and they if you restrict it to the
+rational number then the two functions
+
+ align:start position:0%
+rational number then the two functions
+ 
+
+ align:start position:0%
+rational number then the two functions
+are the same.
+
+ align:start position:0%
+are the same.
+ 
+
+ align:start position:0%
+are the same.
+If they're both continuous then the
+
+ align:start position:0%
+If they're both continuous then the
+ 
+
+ align:start position:0%
+If they're both continuous then the
+function has to be the same. So this
+
+ align:start position:0%
+function has to be the same. So this
+ 
+
+ align:start position:0%
+function has to be the same. So this
+implies that f is equal to g everywhere
+
+ align:start position:0%
+implies that f is equal to g everywhere
+ 
+
+ align:start position:0%
+implies that f is equal to g everywhere
+not just on the rational function
+
+ align:start position:0%
+not just on the rational function
+ 
+
+ align:start position:0%
+not just on the rational function
+rational numbers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So we'll prove that either next
+
+ align:start position:0%
+Okay. So we'll prove that either next
+ 
+
+ align:start position:0%
+Okay. So we'll prove that either next
+time or the following time. Let me just
+
+ align:start position:0%
+time or the following time. Let me just
+ 
+
+ align:start position:0%
+time or the following time. Let me just
+go back and remind you
+
+ align:start position:0%
+go back and remind you
+ 
+
+ align:start position:0%
+go back and remind you
+about what it means for a function to be
+
+ align:start position:0%
+about what it means for a function to be
+ 
+
+ align:start position:0%
+about what it means for a function to be
+continuous.
+
+ align:start position:0%
+continuous.
+ 
+
+ align:start position:0%
+continuous.
+Uh so
+
+ align:start position:0%
+Uh so
+ 
+
+ align:start position:0%
+Uh so
+so this is the fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So suppose you take a function and the
+
+ align:start position:0%
+So suppose you take a function and the
+ 
+
+ align:start position:0%
+So suppose you take a function and the
+function uh is it doesn't even need to
+
+ align:start position:0%
+function uh is it doesn't even need to
+ 
+
+ align:start position:0%
+function uh is it doesn't even need to
+be defined on an interval. Um
+
+ align:start position:0%
+be defined on an interval. Um
+ 
+
+ align:start position:0%
+be defined on an interval. Um
+I but you may as well assume that it's
+
+ align:start position:0%
+I but you may as well assume that it's
+ 
+
+ align:start position:0%
+I but you may as well assume that it's
+interval but it doesn't need to be
+
+ align:start position:0%
+interval but it doesn't need to be
+ 
+
+ align:start position:0%
+interval but it doesn't need to be
+defined on the interval.
+
+ align:start position:0%
+defined on the interval.
+ 
+
+ align:start position:0%
+defined on the interval.
+So a function here f is set to be
+
+ align:start position:0%
+So a function here f is set to be
+ 
+
+ align:start position:0%
+So a function here f is set to be
+continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x here
+
+ align:start position:0%
+at x here
+ 
+
+ align:start position:0%
+at x here
+in the domain where it's defined.
+
+ align:start position:0%
+in the domain where it's defined.
+ 
+
+ align:start position:0%
+in the domain where it's defined.
+If
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+epsilon greater than zero
+
+ align:start position:0%
+epsilon greater than zero
+ 
+
+ align:start position:0%
+epsilon greater than zero
+there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta greater than zero such that
+
+ align:start position:0%
+delta greater than zero such that
+ 
+
+ align:start position:0%
+delta greater than zero such that
+if x - x0
+
+ align:start position:0%
+if x - x0
+ 
+
+ align:start position:0%
+if x - x0
+is smaller than delta then the images
+
+ align:start position:0%
+is smaller than delta then the images
+ 
+
+ align:start position:0%
+is smaller than delta then the images
+are epsilon close to each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so again this delta typically
+
+ align:start position:0%
+And so again this delta typically
+ 
+
+ align:start position:0%
+And so again this delta typically
+depends not just on epsilon but also on
+
+ align:start position:0%
+depends not just on epsilon but also on
+ 
+
+ align:start position:0%
+depends not just on epsilon but also on
+x0 right and so the function so this is
+
+ align:start position:0%
+x0 right and so the function so this is
+ 
+
+ align:start position:0%
+x0 right and so the function so this is
+so it's continuous at a point x0 if this
+
+ align:start position:0%
+so it's continuous at a point x0 if this
+ 
+
+ align:start position:0%
+so it's continuous at a point x0 if this
+here is the case and the function f here
+
+ align:start position:0%
+here is the case and the function f here
+ 
+
+ align:start position:0%
+here is the case and the function f here
+is set to be continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If
+
+ align:start position:0%
+If
+ 
+
+ align:start position:0%
+If
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at all points.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now let's just let's let's look at two
+
+ align:start position:0%
+Now let's just let's let's look at two
+ 
+
+ align:start position:0%
+Now let's just let's let's look at two
+simple examples and and and and
+
+ align:start position:0%
+simple examples and and and and
+ 
+
+ align:start position:0%
+simple examples and and and and
+then once we have those
+
+ align:start position:0%
+then once we have those
+ 
+
+ align:start position:0%
+then once we have those
+uh then together with some algebraic
+
+ align:start position:0%
+uh then together with some algebraic
+ 
+
+ align:start position:0%
+uh then together with some algebraic
+rules that are similar to the algebraic
+
+ align:start position:0%
+rules that are similar to the algebraic
+ 
+
+ align:start position:0%
+rules that are similar to the algebraic
+rules that we had for sequences
+
+ align:start position:0%
+rules that we had for sequences
+ 
+
+ align:start position:0%
+rules that we had for sequences
+then we get a huge
+
+ align:start position:0%
+then we get a huge
+ 
+
+ align:start position:0%
+then we get a huge
+number of examples of you get a large uh
+
+ align:start position:0%
+number of examples of you get a large uh
+ 
+
+ align:start position:0%
+number of examples of you get a large uh
+collection of examples of continuous
+
+ align:start position:0%
+collection of examples of continuous
+ 
+
+ align:start position:0%
+collection of examples of continuous
+functions.
+
+ align:start position:0%
+functions.
+ 
+
+ align:start position:0%
+functions.
+So the first example is like the
+
+ align:start position:0%
+So the first example is like the
+ 
+
+ align:start position:0%
+So the first example is like the
+simplest of all example
+
+ align:start position:0%
+simplest of all example
+ 
+
+ align:start position:0%
+simplest of all example
+where f here is is the constant
+
+ align:start position:0%
+where f here is is the constant
+ 
+
+ align:start position:0%
+where f here is is the constant
+function.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I'm thinking about f here is to be
+
+ align:start position:0%
+So I'm thinking about f here is to be
+ 
+
+ align:start position:0%
+So I'm thinking about f here is to be
+defined from r into r and for each x in
+
+ align:start position:0%
+defined from r into r and for each x in
+ 
+
+ align:start position:0%
+defined from r into r and for each x in
+r it's equal to the same constant. Okay.
+
+ align:start position:0%
+r it's equal to the same constant. Okay.
+ 
+
+ align:start position:0%
+r it's equal to the same constant. Okay.
+So that's f. I want to show that this f
+
+ align:start position:0%
+So that's f. I want to show that this f
+ 
+
+ align:start position:0%
+So that's f. I want to show that this f
+is that a constant function is
+
+ align:start position:0%
+is that a constant function is
+ 
+
+ align:start position:0%
+is that a constant function is
+continuous. So given so proof
+
+ align:start position:0%
+continuous. So given so proof
+ 
+
+ align:start position:0%
+continuous. So given so proof
+of continuity.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So given epsilon
+
+ align:start position:0%
+So given epsilon
+ 
+
+ align:start position:0%
+So given epsilon
+given epsilon greater than zero in this
+
+ align:start position:0%
+given epsilon greater than zero in this
+ 
+
+ align:start position:0%
+given epsilon greater than zero in this
+part says you can pick any delta you
+
+ align:start position:0%
+part says you can pick any delta you
+ 
+
+ align:start position:0%
+part says you can pick any delta you
+want. I'm just picking
+
+ align:start position:0%
+want. I'm just picking
+ 
+
+ align:start position:0%
+want. I'm just picking
+let
+
+ align:start position:0%
+let
+ 
+
+ align:start position:0%
+let
+delta be equal to one but you could pick
+
+ align:start position:0%
+delta be equal to one but you could pick
+ 
+
+ align:start position:0%
+delta be equal to one but you could pick
+anything you want. It has to be positive
+
+ align:start position:0%
+anything you want. It has to be positive
+ 
+
+ align:start position:0%
+anything you want. It has to be positive
+but you can pick anything you want. Then
+
+ align:start position:0%
+but you can pick anything you want. Then
+ 
+
+ align:start position:0%
+but you can pick anything you want. Then
+you have that if x minus x0
+
+ align:start position:0%
+you have that if x minus x0
+ 
+
+ align:start position:0%
+you have that if x minus x0
+is less than one.
+
+ align:start position:0%
+is less than one.
+ 
+
+ align:start position:0%
+is less than one.
+Well then of course f ofx
+
+ align:start position:0%
+Well then of course f ofx
+ 
+
+ align:start position:0%
+Well then of course f ofx
+minus f of x0 both of these numbers is
+
+ align:start position:0%
+minus f of x0 both of these numbers is
+ 
+
+ align:start position:0%
+minus f of x0 both of these numbers is
+c. So the difference so this is c minus
+
+ align:start position:0%
+c. So the difference so this is c minus
+ 
+
+ align:start position:0%
+c. So the difference so this is c minus
+c.
+
+ align:start position:0%
+c.
+ 
+
+ align:start position:0%
+c.
+So this is zero. So this is surely less
+
+ align:start position:0%
+So this is zero. So this is surely less
+ 
+
+ align:start position:0%
+So this is zero. So this is surely less
+than epsilon. Right? So they show that
+
+ align:start position:0%
+than epsilon. Right? So they show that
+ 
+
+ align:start position:0%
+than epsilon. Right? So they show that
+it's the function is continuous at all
+
+ align:start position:0%
+it's the function is continuous at all
+ 
+
+ align:start position:0%
+it's the function is continuous at all
+point. And you see that you could pick
+
+ align:start position:0%
+point. And you see that you could pick
+ 
+
+ align:start position:0%
+point. And you see that you could pick
+delta anything you want. And of course
+
+ align:start position:0%
+delta anything you want. And of course
+ 
+
+ align:start position:0%
+delta anything you want. And of course
+in particular it's it's doesn't even
+
+ align:start position:0%
+in particular it's it's doesn't even
+ 
+
+ align:start position:0%
+in particular it's it's doesn't even
+depend on x0. It doesn't depend on
+
+ align:start position:0%
+depend on x0. It doesn't depend on
+ 
+
+ align:start position:0%
+depend on x0. It doesn't depend on
+epsilon and it doesn't depend on x0.
+
+ align:start position:0%
+epsilon and it doesn't depend on x0.
+ 
+
+ align:start position:0%
+epsilon and it doesn't depend on x0.
+Okay. So the constant functions are for
+
+ align:start position:0%
+Okay. So the constant functions are for
+ 
+
+ align:start position:0%
+Okay. So the constant functions are for
+continuous.
+
+ align:start position:0%
+continuous.
+ 
+
+ align:start position:0%
+continuous.
+What about then next simple the next
+
+ align:start position:0%
+What about then next simple the next
+ 
+
+ align:start position:0%
+What about then next simple the next
+simplest function would be the linear
+
+ align:start position:0%
+simplest function would be the linear
+ 
+
+ align:start position:0%
+simplest function would be the linear
+function or just x function x.
+
+ align:start position:0%
+function or just x function x.
+ 
+
+ align:start position:0%
+function or just x function x.
+So suppose you take
+
+ align:start position:0%
+So suppose you take
+ 
+
+ align:start position:0%
+So suppose you take
+because you're looking at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the function f on r to r
+
+ align:start position:0%
+at the function f on r to r
+ 
+
+ align:start position:0%
+at the function f on r to r
+where f of x is equal to x. So this is
+
+ align:start position:0%
+where f of x is equal to x. So this is
+ 
+
+ align:start position:0%
+where f of x is equal to x. So this is
+also continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the proof of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+delta equal to epsilon
+
+ align:start position:0%
+delta equal to epsilon
+ 
+
+ align:start position:0%
+delta equal to epsilon
+then you see that if x - x0
+
+ align:start position:0%
+then you see that if x - x0
+ 
+
+ align:start position:0%
+then you see that if x - x0
+is less than epsilon then
+
+ align:start position:0%
+is less than epsilon then
+ 
+
+ align:start position:0%
+is less than epsilon then
+uh f ofx minus f of x0 but f of x is
+
+ align:start position:0%
+uh f ofx minus f of x0 but f of x is
+ 
+
+ align:start position:0%
+uh f ofx minus f of x0 but f of x is
+equal to x and f of x0 is equal to x0 so
+
+ align:start position:0%
+equal to x and f of x0 is equal to x0 so
+ 
+
+ align:start position:0%
+equal to x and f of x0 is equal to x0 so
+this thing here is of course less than
+
+ align:start position:0%
+this thing here is of course less than
+ 
+
+ align:start position:0%
+this thing here is of course less than
+epsilon not right
+
+ align:start position:0%
+epsilon not right
+ 
+
+ align:start position:0%
+epsilon not right
+so this is so so so that's kind of
+
+ align:start position:0%
+so this is so so so that's kind of
+ 
+
+ align:start position:0%
+so this is so so so that's kind of
+trivial okay
+
+ align:start position:0%
+trivial okay
+ 
+
+ align:start position:0%
+trivial okay
+now the next thing is that we have uh
+
+ align:start position:0%
+now the next thing is that we have uh
+ 
+
+ align:start position:0%
+now the next thing is that we have uh
+the algebraic uh property of continuous
+
+ align:start position:0%
+the algebraic uh property of continuous
+ 
+
+ align:start position:0%
+the algebraic uh property of continuous
+functions. So we have some as a break
+
+ align:start position:0%
+functions. So we have some as a break
+ 
+
+ align:start position:0%
+functions. So we have some as a break
+property.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of continuous function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I will prove a couple of these and
+
+ align:start position:0%
+and I will prove a couple of these and
+ 
+
+ align:start position:0%
+and I will prove a couple of these and
+but the proofs you see in just a second
+
+ align:start position:0%
+but the proofs you see in just a second
+ 
+
+ align:start position:0%
+but the proofs you see in just a second
+that the proof is like I mean the
+
+ align:start position:0%
+that the proof is like I mean the
+ 
+
+ align:start position:0%
+that the proof is like I mean the
+properties is is is and There's good
+
+ align:start position:0%
+properties is is is and There's good
+ 
+
+ align:start position:0%
+properties is is is and There's good
+reasons for that. They're very similar
+
+ align:start position:0%
+reasons for that. They're very similar
+ 
+
+ align:start position:0%
+reasons for that. They're very similar
+to the property we had for for limits of
+
+ align:start position:0%
+to the property we had for for limits of
+ 
+
+ align:start position:0%
+to the property we had for for limits of
+sequences and the proofs are are very
+
+ align:start position:0%
+sequences and the proofs are are very
+ 
+
+ align:start position:0%
+sequences and the proofs are are very
+similar to those proofs. So the first
+
+ align:start position:0%
+similar to those proofs. So the first
+ 
+
+ align:start position:0%
+similar to those proofs. So the first
+one is that if
+
+ align:start position:0%
+one is that if
+ 
+
+ align:start position:0%
+one is that if
+f and g are continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the sum of these two functions is
+
+ align:start position:0%
+then the sum of these two functions is
+ 
+
+ align:start position:0%
+then the sum of these two functions is
+also continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The next one is that if um
+
+ align:start position:0%
+The next one is that if um
+ 
+
+ align:start position:0%
+The next one is that if um
+f is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and c is a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then c * f is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The third property is
+
+ align:start position:0%
+The third property is
+ 
+
+ align:start position:0%
+The third property is
+that again if
+
+ align:start position:0%
+that again if
+ 
+
+ align:start position:0%
+that again if
+uh f comma g are continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the product
+
+ align:start position:0%
+then the product
+ 
+
+ align:start position:0%
+then the product
+then the product f * d is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The fourth property is that if
+
+ align:start position:0%
+The fourth property is that if
+ 
+
+ align:start position:0%
+The fourth property is that if
+f is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and uh and f is never equal to zero
+
+ align:start position:0%
+and and uh and f is never equal to zero
+ 
+
+ align:start position:0%
+and and uh and f is never equal to zero
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+1 / f is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the fifth property that's a little
+
+ align:start position:0%
+And the fifth property that's a little
+ 
+
+ align:start position:0%
+And the fifth property that's a little
+bit different and we didn't have that
+
+ align:start position:0%
+bit different and we didn't have that
+ 
+
+ align:start position:0%
+bit different and we didn't have that
+for sequences.
+
+ align:start position:0%
+for sequences.
+ 
+
+ align:start position:0%
+for sequences.
+The fifth property is that if you take a
+
+ align:start position:0%
+The fifth property is that if you take a
+ 
+
+ align:start position:0%
+The fifth property is that if you take a
+map f of take a function f.
+
+ align:start position:0%
+map f of take a function f.
+ 
+
+ align:start position:0%
+map f of take a function f.
+Let's think about it as a function from
+
+ align:start position:0%
+Let's think about it as a function from
+ 
+
+ align:start position:0%
+Let's think about it as a function from
+R to R. And then you have another
+
+ align:start position:0%
+R to R. And then you have another
+ 
+
+ align:start position:0%
+R to R. And then you have another
+function G from R to R.
+
+ align:start position:0%
+function G from R to R.
+ 
+
+ align:start position:0%
+function G from R to R.
+And now you could look at where you take
+
+ align:start position:0%
+And now you could look at where you take
+ 
+
+ align:start position:0%
+And now you could look at where you take
+first. You could look at the
+
+ align:start position:0%
+first. You could look at the
+ 
+
+ align:start position:0%
+first. You could look at the
+composition. So you could look at the
+
+ align:start position:0%
+composition. So you could look at the
+ 
+
+ align:start position:0%
+composition. So you could look at the
+function H of X which is where you first
+
+ align:start position:0%
+function H of X which is where you first
+ 
+
+ align:start position:0%
+function H of X which is where you first
+apply F of X F to X and then you apply G
+
+ align:start position:0%
+apply F of X F to X and then you apply G
+ 
+
+ align:start position:0%
+apply F of X F to X and then you apply G
+to it. Right? So if both f so if this
+
+ align:start position:0%
+to it. Right? So if both f so if this
+ 
+
+ align:start position:0%
+to it. Right? So if both f so if this
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and the function g are continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the composition here is also
+
+ align:start position:0%
+then the composition here is also
+ 
+
+ align:start position:0%
+then the composition here is also
+continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+When you have a composition of function
+
+ align:start position:0%
+When you have a composition of function
+ 
+
+ align:start position:0%
+When you have a composition of function
+you always have to be careful that it
+
+ align:start position:0%
+you always have to be careful that it
+ 
+
+ align:start position:0%
+you always have to be careful that it
+makes sense. So to make sense means that
+
+ align:start position:0%
+makes sense. So to make sense means that
+ 
+
+ align:start position:0%
+makes sense. So to make sense means that
+the function g the one that the second
+
+ align:start position:0%
+the function g the one that the second
+ 
+
+ align:start position:0%
+the function g the one that the second
+function that you apply is that the
+
+ align:start position:0%
+function that you apply is that the
+ 
+
+ align:start position:0%
+function that you apply is that the
+image of when you use the first function
+
+ align:start position:0%
+image of when you use the first function
+ 
+
+ align:start position:0%
+image of when you use the first function
+you have to make sure that what you get
+
+ align:start position:0%
+you have to make sure that what you get
+ 
+
+ align:start position:0%
+you have to make sure that what you get
+here is uh at some point where G is
+
+ align:start position:0%
+here is uh at some point where G is
+ 
+
+ align:start position:0%
+here is uh at some point where G is
+defined. Right? So I just for simplicity
+
+ align:start position:0%
+defined. Right? So I just for simplicity
+ 
+
+ align:start position:0%
+defined. Right? So I just for simplicity
+I just uh looked at maps into um
+
+ align:start position:0%
+I just uh looked at maps into um
+ 
+
+ align:start position:0%
+I just uh looked at maps into um
+functions into R where G also was
+
+ align:start position:0%
+functions into R where G also was
+ 
+
+ align:start position:0%
+functions into R where G also was
+defined on all of our but of course it
+
+ align:start position:0%
+defined on all of our but of course it
+ 
+
+ align:start position:0%
+defined on all of our but of course it
+doesn't have to be defined but you just
+
+ align:start position:0%
+doesn't have to be defined but you just
+ 
+
+ align:start position:0%
+doesn't have to be defined but you just
+have to make sure
+
+ align:start position:0%
+have to make sure
+ 
+
+ align:start position:0%
+have to make sure
+that G is defined where F and X end up
+
+ align:start position:0%
+that G is defined where F and X end up
+ 
+
+ align:start position:0%
+that G is defined where F and X end up
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay I'll talk a little bit about you
+
+ align:start position:0%
+okay I'll talk a little bit about you
+ 
+
+ align:start position:0%
+okay I'll talk a little bit about you
+know these uh how to prove these but
+
+ align:start position:0%
+know these uh how to prove these but
+ 
+
+ align:start position:0%
+know these uh how to prove these but
+it's very similar to what we did for
+
+ align:start position:0%
+it's very similar to what we did for
+ 
+
+ align:start position:0%
+it's very similar to what we did for
+sequences let me just apply apply it.
+
+ align:start position:0%
+sequences let me just apply apply it.
+ 
+
+ align:start position:0%
+sequences let me just apply apply it.
+So let me look at an example where I
+
+ align:start position:0%
+So let me look at an example where I
+ 
+
+ align:start position:0%
+So let me look at an example where I
+apply it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So suppose you take x2 + one. Suppose
+
+ align:start position:0%
+So suppose you take x2 + one. Suppose
+ 
+
+ align:start position:0%
+So suppose you take x2 + one. Suppose
+you take this function here. I'll take
+
+ align:start position:0%
+you take this function here. I'll take
+ 
+
+ align:start position:0%
+you take this function here. I'll take
+look at two examples.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Suppose you take this function here.
+
+ align:start position:0%
+Suppose you take this function here.
+ 
+
+ align:start position:0%
+Suppose you take this function here.
+I claim that this here is continuous.
+
+ align:start position:0%
+I claim that this here is continuous.
+ 
+
+ align:start position:0%
+I claim that this here is continuous.
+I'm not going to go through the proof
+
+ align:start position:0%
+I'm not going to go through the proof
+ 
+
+ align:start position:0%
+I'm not going to go through the proof
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+because we already actually so if this
+
+ align:start position:0%
+because we already actually so if this
+ 
+
+ align:start position:0%
+because we already actually so if this
+here prove at least some of these
+
+ align:start position:0%
+here prove at least some of these
+ 
+
+ align:start position:0%
+here prove at least some of these
+properties but once you have that then
+
+ align:start position:0%
+properties but once you have that then
+ 
+
+ align:start position:0%
+properties but once you have that then
+you see that well you have that g of x
+
+ align:start position:0%
+you see that well you have that g of x
+ 
+
+ align:start position:0%
+you see that well you have that g of x
+equal to x this here is continuous.
+
+ align:start position:0%
+equal to x this here is continuous.
+ 
+
+ align:start position:0%
+equal to x this here is continuous.
+This is what we proved
+
+ align:start position:0%
+This is what we proved
+ 
+
+ align:start position:0%
+This is what we proved
+just a little while ago. And if you take
+
+ align:start position:0%
+just a little while ago. And if you take
+ 
+
+ align:start position:0%
+just a little while ago. And if you take
+the function that is constant and in
+
+ align:start position:0%
+the function that is constant and in
+ 
+
+ align:start position:0%
+the function that is constant and in
+this case constant one, we already
+
+ align:start position:0%
+this case constant one, we already
+ 
+
+ align:start position:0%
+this case constant one, we already
+proved that that's continuous. Right?
+
+ align:start position:0%
+proved that that's continuous. Right?
+ 
+
+ align:start position:0%
+proved that that's continuous. Right?
+Now this means that if you take a
+
+ align:start position:0%
+Now this means that if you take a
+ 
+
+ align:start position:0%
+Now this means that if you take a
+continuous function
+
+ align:start position:0%
+continuous function
+ 
+
+ align:start position:0%
+continuous function
+by by by whatever root three or
+
+ align:start position:0%
+by by by whatever root three or
+ 
+
+ align:start position:0%
+by by by whatever root three or
+something like that over there uh and
+
+ align:start position:0%
+something like that over there uh and
+ 
+
+ align:start position:0%
+something like that over there uh and
+you take the function where it's like
+
+ align:start position:0%
+you take the function where it's like
+ 
+
+ align:start position:0%
+you take the function where it's like
+multiply by itself this function here
+
+ align:start position:0%
+multiply by itself this function here
+ 
+
+ align:start position:0%
+multiply by itself this function here
+right because g is continuous this
+
+ align:start position:0%
+right because g is continuous this
+ 
+
+ align:start position:0%
+right because g is continuous this
+function here is also continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then once you have that you can add
+
+ align:start position:0%
+and then once you have that you can add
+ 
+
+ align:start position:0%
+and then once you have that you can add
+another. So you can look at G ^2
+
+ align:start position:0%
+another. So you can look at G ^2
+ 
+
+ align:start position:0%
+another. So you can look at G ^2
+plus H.
+
+ align:start position:0%
+plus H.
+ 
+
+ align:start position:0%
+plus H.
+This is you now have established this is
+
+ align:start position:0%
+This is you now have established this is
+ 
+
+ align:start position:0%
+This is you now have established this is
+continuous. This here is a constant
+
+ align:start position:0%
+continuous. This here is a constant
+ 
+
+ align:start position:0%
+continuous. This here is a constant
+function. So we already proven that this
+
+ align:start position:0%
+function. So we already proven that this
+ 
+
+ align:start position:0%
+function. So we already proven that this
+is continuous. So the sum by rule one
+
+ align:start position:0%
+is continuous. So the sum by rule one
+ 
+
+ align:start position:0%
+is continuous. So the sum by rule one
+over there this here is continuous.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So this means that so okay. So this show
+
+ align:start position:0%
+So this means that so okay. So this show
+ 
+
+ align:start position:0%
+So this means that so okay. So this show
+that this function here this quadratic
+
+ align:start position:0%
+that this function here this quadratic
+ 
+
+ align:start position:0%
+that this function here this quadratic
+function is continuous. But in fact of
+
+ align:start position:0%
+function is continuous. But in fact of
+ 
+
+ align:start position:0%
+function is continuous. But in fact of
+course this argument gives you that any
+
+ align:start position:0%
+course this argument gives you that any
+ 
+
+ align:start position:0%
+course this argument gives you that any
+polomium any polomial is continuous
+
+ align:start position:0%
+polomium any polomial is continuous
+ 
+
+ align:start position:0%
+polomium any polomial is continuous
+right so this here proves that any
+
+ align:start position:0%
+right so this here proves that any
+ 
+
+ align:start position:0%
+right so this here proves that any
+polomium
+
+ align:start position:0%
+polomium
+ 
+
+ align:start position:0%
+polomium
+right so this the you know like the
+
+ align:start position:0%
+right so this the you know like the
+ 
+
+ align:start position:0%
+right so this the you know like the
+similar argument right so if you're
+
+ align:start position:0%
+similar argument right so if you're
+ 
+
+ align:start position:0%
+similar argument right so if you're
+using so if you're using one two and
+
+ align:start position:0%
+using so if you're using one two and
+ 
+
+ align:start position:0%
+using so if you're using one two and
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+then just starting at the constant
+
+ align:start position:0%
+then just starting at the constant
+ 
+
+ align:start position:0%
+then just starting at the constant
+function and the function x you can get
+
+ align:start position:0%
+function and the function x you can get
+ 
+
+ align:start position:0%
+function and the function x you can get
+to any polomium and and and using these
+
+ align:start position:0%
+to any polomium and and and using these
+ 
+
+ align:start position:0%
+to any polomium and and and using these
+operations and so it means that any
+
+ align:start position:0%
+operations and so it means that any
+ 
+
+ align:start position:0%
+operations and so it means that any
+polomial is continuous right so so you
+
+ align:start position:0%
+polomial is continuous right so so you
+ 
+
+ align:start position:0%
+polomial is continuous right so so you
+have the following theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all polomials
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And in fact, so this is just using
+
+ align:start position:0%
+Okay. And in fact, so this is just using
+ 
+
+ align:start position:0%
+Okay. And in fact, so this is just using
+one, two, and three over here. If you
+
+ align:start position:0%
+one, two, and three over here. If you
+ 
+
+ align:start position:0%
+one, two, and three over here. If you
+now also bring in four
+
+ align:start position:0%
+now also bring in four
+ 
+
+ align:start position:0%
+now also bring in four
+then you have then so so this is this is
+
+ align:start position:0%
+then you have then so so this is this is
+ 
+
+ align:start position:0%
+then you have then so so this is this is
+proof,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? So it follows it uses the two
+
+ align:start position:0%
+right? So it follows it uses the two
+ 
+
+ align:start position:0%
+right? So it follows it uses the two
+examples that we gave and then
+
+ align:start position:0%
+examples that we gave and then
+ 
+
+ align:start position:0%
+examples that we gave and then
+in addition to that it follows from
+
+ align:start position:0%
+in addition to that it follows from
+ 
+
+ align:start position:0%
+in addition to that it follows from
+the algebraic rules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one through uh one through three.
+
+ align:start position:0%
+one through uh one through three.
+ 
+
+ align:start position:0%
+one through uh one through three.
+If you bring in alt four, five is
+
+ align:start position:0%
+If you bring in alt four, five is
+ 
+
+ align:start position:0%
+If you bring in alt four, five is
+something slightly different. But if you
+
+ align:start position:0%
+something slightly different. But if you
+ 
+
+ align:start position:0%
+something slightly different. But if you
+bring in four here, then you you get
+
+ align:start position:0%
+bring in four here, then you you get
+ 
+
+ align:start position:0%
+bring in four here, then you you get
+that what's called any rational function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh any
+
+ align:start position:0%
+uh any
+ 
+
+ align:start position:0%
+uh any
+all rational function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are continuous. So what is a a rational
+
+ align:start position:0%
+are continuous. So what is a a rational
+ 
+
+ align:start position:0%
+are continuous. So what is a a rational
+function?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A rational function is just where you're
+
+ align:start position:0%
+A rational function is just where you're
+ 
+
+ align:start position:0%
+A rational function is just where you're
+taking a polomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you're dividing by another
+
+ align:start position:0%
+and then you're dividing by another
+ 
+
+ align:start position:0%
+and then you're dividing by another
+polinomial.
+
+ align:start position:0%
+polinomial.
+ 
+
+ align:start position:0%
+polinomial.
+Right? So we know that any polomial is
+
+ align:start position:0%
+Right? So we know that any polomial is
+ 
+
+ align:start position:0%
+Right? So we know that any polomial is
+continuous. If you take another polomium
+
+ align:start position:0%
+continuous. If you take another polomium
+ 
+
+ align:start position:0%
+continuous. If you take another polomium
+and let's look at the that other
+
+ align:start position:0%
+and let's look at the that other
+ 
+
+ align:start position:0%
+and let's look at the that other
+polinomial away from the roots away from
+
+ align:start position:0%
+polinomial away from the roots away from
+ 
+
+ align:start position:0%
+polinomial away from the roots away from
+where it is zero away from it where it's
+
+ align:start position:0%
+where it is zero away from it where it's
+ 
+
+ align:start position:0%
+where it is zero away from it where it's
+zero this is I mean it's of course even
+
+ align:start position:0%
+zero this is I mean it's of course even
+ 
+
+ align:start position:0%
+zero this is I mean it's of course even
+continuous where it's zero but you can't
+
+ align:start position:0%
+continuous where it's zero but you can't
+ 
+
+ align:start position:0%
+continuous where it's zero but you can't
+divide by it right so away from it this
+
+ align:start position:0%
+divide by it right so away from it this
+ 
+
+ align:start position:0%
+divide by it right so away from it this
+function here is not zero and it's
+
+ align:start position:0%
+function here is not zero and it's
+ 
+
+ align:start position:0%
+function here is not zero and it's
+continuous this is continuous rule four
+
+ align:start position:0%
+continuous this is continuous rule four
+ 
+
+ align:start position:0%
+continuous this is continuous rule four
+so this is proved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh the theorem above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+rule four,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. In that case, exactly. In that
+
+ align:start position:0%
+>> Yeah. In that case, exactly. In that
+ 
+
+ align:start position:0%
+>> Yeah. In that case, exactly. In that
+case, I chose delta to be simply
+
+ align:start position:0%
+case, I chose delta to be simply
+ 
+
+ align:start position:0%
+case, I chose delta to be simply
+epsilon. Yeah. Yeah.
+
+ align:start position:0%
+epsilon. Yeah. Yeah.
+ 
+
+ align:start position:0%
+epsilon. Yeah. Yeah.
+>> Anything with that first?
+
+ align:start position:0%
+>> Anything with that first?
+ 
+
+ align:start position:0%
+>> Anything with that first?
+>> That's not a problem, right? But it's
+
+ align:start position:0%
+>> That's not a problem, right? But it's
+ 
+
+ align:start position:0%
+>> That's not a problem, right? But it's
+just like if you give me an epsilon,
+
+ align:start position:0%
+just like if you give me an epsilon,
+ 
+
+ align:start position:0%
+just like if you give me an epsilon,
+then I have to pick a a delta. And
+
+ align:start position:0%
+then I have to pick a a delta. And
+ 
+
+ align:start position:0%
+then I have to pick a a delta. And
+typically the delta will depend on
+
+ align:start position:0%
+typically the delta will depend on
+ 
+
+ align:start position:0%
+typically the delta will depend on
+epsilon.
+
+ align:start position:0%
+epsilon.
+ 
+
+ align:start position:0%
+epsilon.
+Typically, it also depends on x. Let me
+
+ align:start position:0%
+Typically, it also depends on x. Let me
+ 
+
+ align:start position:0%
+Typically, it also depends on x. Let me
+give you an example of the last. I don't
+
+ align:start position:0%
+give you an example of the last. I don't
+ 
+
+ align:start position:0%
+give you an example of the last. I don't
+think I I I might not get to to proving
+
+ align:start position:0%
+think I I I might not get to to proving
+ 
+
+ align:start position:0%
+think I I I might not get to to proving
+this, but that's fine. I mean they
+
+ align:start position:0%
+this, but that's fine. I mean they
+ 
+
+ align:start position:0%
+this, but that's fine. I mean they
+actually the proof I'm not even sure I
+
+ align:start position:0%
+actually the proof I'm not even sure I
+ 
+
+ align:start position:0%
+actually the proof I'm not even sure I
+would go through it but the proof is if
+
+ align:start position:0%
+would go through it but the proof is if
+ 
+
+ align:start position:0%
+would go through it but the proof is if
+maybe maybe if I have a minutes I will
+
+ align:start position:0%
+maybe maybe if I have a minutes I will
+ 
+
+ align:start position:0%
+maybe maybe if I have a minutes I will
+talk about one of them.
+
+ align:start position:0%
+talk about one of them.
+ 
+
+ align:start position:0%
+talk about one of them.
+So let me give you an example also where
+
+ align:start position:0%
+So let me give you an example also where
+ 
+
+ align:start position:0%
+So let me give you an example also where
+so typically
+
+ align:start position:0%
+so typically
+ 
+
+ align:start position:0%
+so typically
+typically it's it's highly unusual in
+
+ align:start position:0%
+typically it's it's highly unusual in
+ 
+
+ align:start position:0%
+typically it's it's highly unusual in
+the first example with a constant
+
+ align:start position:0%
+the first example with a constant
+ 
+
+ align:start position:0%
+the first example with a constant
+function that it doesn't really matter
+
+ align:start position:0%
+function that it doesn't really matter
+ 
+
+ align:start position:0%
+function that it doesn't really matter
+you could pick delta anything. Okay. Now
+
+ align:start position:0%
+you could pick delta anything. Okay. Now
+ 
+
+ align:start position:0%
+you could pick delta anything. Okay. Now
+suppose you're looking at the function f
+
+ align:start position:0%
+suppose you're looking at the function f
+ 
+
+ align:start position:0%
+suppose you're looking at the function f
+ofx = 1 /x. This is a rational function
+
+ align:start position:0%
+ofx = 1 /x. This is a rational function
+ 
+
+ align:start position:0%
+ofx = 1 /x. This is a rational function
+because it's a polomial. In that case
+
+ align:start position:0%
+because it's a polomial. In that case
+ 
+
+ align:start position:0%
+because it's a polomial. In that case
+the polomial in the denominator is the
+
+ align:start position:0%
+the polomial in the denominator is the
+ 
+
+ align:start position:0%
+the polomial in the denominator is the
+constant function one and then the
+
+ align:start position:0%
+constant function one and then the
+ 
+
+ align:start position:0%
+constant function one and then the
+denominator is is is x. If you're
+
+ align:start position:0%
+denominator is is is x. If you're
+ 
+
+ align:start position:0%
+denominator is is is x. If you're
+looking at this function let's just look
+
+ align:start position:0%
+looking at this function let's just look
+ 
+
+ align:start position:0%
+looking at this function let's just look
+at this function where it's pos strictly
+
+ align:start position:0%
+at this function where it's pos strictly
+ 
+
+ align:start position:0%
+at this function where it's pos strictly
+positive. Right? And then you see now
+
+ align:start position:0%
+positive. Right? And then you see now
+ 
+
+ align:start position:0%
+positive. Right? And then you see now
+the graphs looks basically like this.
+
+ align:start position:0%
+the graphs looks basically like this.
+ 
+
+ align:start position:0%
+the graphs looks basically like this.
+So in particular if you go close to zero
+
+ align:start position:0%
+So in particular if you go close to zero
+ 
+
+ align:start position:0%
+So in particular if you go close to zero
+it's not defined as zero but if you go
+
+ align:start position:0%
+it's not defined as zero but if you go
+ 
+
+ align:start position:0%
+it's not defined as zero but if you go
+close to zero then the image varies a
+
+ align:start position:0%
+close to zero then the image varies a
+ 
+
+ align:start position:0%
+close to zero then the image varies a
+lot right. So if you take some fixed
+
+ align:start position:0%
+lot right. So if you take some fixed
+ 
+
+ align:start position:0%
+lot right. So if you take some fixed
+thing here suppose you take suppose you
+
+ align:start position:0%
+thing here suppose you take suppose you
+ 
+
+ align:start position:0%
+thing here suppose you take suppose you
+take suppose you take you want to prove
+
+ align:start position:0%
+take suppose you take you want to prove
+ 
+
+ align:start position:0%
+take suppose you take you want to prove
+that it's continuous at some extreme.
+
+ align:start position:0%
+that it's continuous at some extreme.
+ 
+
+ align:start position:0%
+that it's continuous at some extreme.
+So this means that you have to pick some
+
+ align:start position:0%
+So this means that you have to pick some
+ 
+
+ align:start position:0%
+So this means that you have to pick some
+delta. So given an epsilon you have to
+
+ align:start position:0%
+delta. So given an epsilon you have to
+ 
+
+ align:start position:0%
+delta. So given an epsilon you have to
+pick a delta. So that if you are in this
+
+ align:start position:0%
+pick a delta. So that if you are in this
+ 
+
+ align:start position:0%
+pick a delta. So that if you are in this
+little interval then image lie in that
+
+ align:start position:0%
+little interval then image lie in that
+ 
+
+ align:start position:0%
+little interval then image lie in that
+little interval. But you see that as x0
+
+ align:start position:0%
+little interval. But you see that as x0
+ 
+
+ align:start position:0%
+little interval. But you see that as x0
+becomes very close to zero then in any
+
+ align:start position:0%
+becomes very close to zero then in any
+ 
+
+ align:start position:0%
+becomes very close to zero then in any
+small interval the function varies a
+
+ align:start position:0%
+small interval the function varies a
+ 
+
+ align:start position:0%
+small interval the function varies a
+lot. So this means that that if if you
+
+ align:start position:0%
+lot. So this means that that if if you
+ 
+
+ align:start position:0%
+lot. So this means that that if if you
+take some fixed epsilon
+
+ align:start position:0%
+take some fixed epsilon
+ 
+
+ align:start position:0%
+take some fixed epsilon
+then you expect that if the x0 was close
+
+ align:start position:0%
+then you expect that if the x0 was close
+ 
+
+ align:start position:0%
+then you expect that if the x0 was close
+to zero then the delta had to be really
+
+ align:start position:0%
+to zero then the delta had to be really
+ 
+
+ align:start position:0%
+to zero then the delta had to be really
+really really small right for this to
+
+ align:start position:0%
+really really small right for this to
+ 
+
+ align:start position:0%
+really really small right for this to
+work right so typically delta depends
+
+ align:start position:0%
+work right so typically delta depends
+ 
+
+ align:start position:0%
+work right so typically delta depends
+not just on epsilon which it's I mean
+
+ align:start position:0%
+not just on epsilon which it's I mean
+ 
+
+ align:start position:0%
+not just on epsilon which it's I mean
+it's highly unusual it doesn't it also
+
+ align:start position:0%
+it's highly unusual it doesn't it also
+ 
+
+ align:start position:0%
+it's highly unusual it doesn't it also
+depends on x and in fact if it doesn't
+
+ align:start position:0%
+depends on x and in fact if it doesn't
+ 
+
+ align:start position:0%
+depends on x and in fact if it doesn't
+depend on x or extra then it has a
+
+ align:start position:0%
+depend on x or extra then it has a
+ 
+
+ align:start position:0%
+depend on x or extra then it has a
+particular name. We'll get to that
+
+ align:start position:0%
+particular name. We'll get to that
+ 
+
+ align:start position:0%
+particular name. We'll get to that
+later. It's called uniform continuity.
+
+ align:start position:0%
+later. It's called uniform continuity.
+ 
+
+ align:start position:0%
+later. It's called uniform continuity.
+Uniform continuity have some nice extra
+
+ align:start position:0%
+Uniform continuity have some nice extra
+ 
+
+ align:start position:0%
+Uniform continuity have some nice extra
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+and and and and you will see later on
+
+ align:start position:0%
+and and and and you will see later on
+ 
+
+ align:start position:0%
+and and and and you will see later on
+that there's a good reason why the
+
+ align:start position:0%
+that there's a good reason why the
+ 
+
+ align:start position:0%
+that there's a good reason why the
+domain here was did not include zero. If
+
+ align:start position:0%
+domain here was did not include zero. If
+ 
+
+ align:start position:0%
+domain here was did not include zero. If
+somehow this is would have been a
+
+ align:start position:0%
+somehow this is would have been a
+ 
+
+ align:start position:0%
+somehow this is would have been a
+continuous function defined on an
+
+ align:start position:0%
+continuous function defined on an
+ 
+
+ align:start position:0%
+continuous function defined on an
+interval that included the end point
+
+ align:start position:0%
+interval that included the end point
+ 
+
+ align:start position:0%
+interval that included the end point
+then actually it would automatically be
+
+ align:start position:0%
+then actually it would automatically be
+ 
+
+ align:start position:0%
+then actually it would automatically be
+uniform continuous. So so it was the
+
+ align:start position:0%
+uniform continuous. So so it was the
+ 
+
+ align:start position:0%
+uniform continuous. So so it was the
+good reason this example here it didn't
+
+ align:start position:0%
+good reason this example here it didn't
+ 
+
+ align:start position:0%
+good reason this example here it didn't
+include the the the point zero. Okay.
+
+ align:start position:0%
+include the the the point zero. Okay.
+ 
+
+ align:start position:0%
+include the the the point zero. Okay.
+Now let me just so I have like three
+
+ align:start position:0%
+Now let me just so I have like three
+ 
+
+ align:start position:0%
+Now let me just so I have like three
+minutes left. Let me just talk about
+
+ align:start position:0%
+minutes left. Let me just talk about
+ 
+
+ align:start position:0%
+minutes left. Let me just talk about
+one particular of these like the first
+
+ align:start position:0%
+one particular of these like the first
+ 
+
+ align:start position:0%
+one particular of these like the first
+one and the second one super easy and
+
+ align:start position:0%
+one and the second one super easy and
+ 
+
+ align:start position:0%
+one and the second one super easy and
+the third one is also easy but and it
+
+ align:start position:0%
+the third one is also easy but and it
+ 
+
+ align:start position:0%
+the third one is also easy but and it
+uses exactly the same trick that we
+
+ align:start position:0%
+uses exactly the same trick that we
+ 
+
+ align:start position:0%
+uses exactly the same trick that we
+looked at before. So let me just talk
+
+ align:start position:0%
+looked at before. So let me just talk
+ 
+
+ align:start position:0%
+looked at before. So let me just talk
+about that for a minute just because
+
+ align:start position:0%
+about that for a minute just because
+ 
+
+ align:start position:0%
+about that for a minute just because
+it's it's it's a little bit more
+
+ align:start position:0%
+it's it's it's a little bit more
+ 
+
+ align:start position:0%
+it's it's it's a little bit more
+interesting than one and two is is
+
+ align:start position:0%
+interesting than one and two is is
+ 
+
+ align:start position:0%
+interesting than one and two is is
+barely interesting. So suppose I'm
+
+ align:start position:0%
+barely interesting. So suppose I'm
+ 
+
+ align:start position:0%
+barely interesting. So suppose I'm
+looking at the product of these two
+
+ align:start position:0%
+looking at the product of these two
+ 
+
+ align:start position:0%
+looking at the product of these two
+functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know so remember that you give
+
+ align:start position:0%
+and you know so remember that you give
+ 
+
+ align:start position:0%
+and you know so remember that you give
+me an epsilon I had to find a delta so I
+
+ align:start position:0%
+me an epsilon I had to find a delta so I
+ 
+
+ align:start position:0%
+me an epsilon I had to find a delta so I
+have to find a delta so that this
+
+ align:start position:0%
+have to find a delta so that this
+ 
+
+ align:start position:0%
+have to find a delta so that this
+difference here
+
+ align:start position:0%
+difference here
+ 
+
+ align:start position:0%
+difference here
+is smaller
+
+ align:start position:0%
+is smaller
+ 
+
+ align:start position:0%
+is smaller
+I want to find a delta so that if x
+
+ align:start position:0%
+I want to find a delta so that if x
+ 
+
+ align:start position:0%
+I want to find a delta so that if x
+minus x0 is smaller if it's smaller than
+
+ align:start position:0%
+minus x0 is smaller if it's smaller than
+ 
+
+ align:start position:0%
+minus x0 is smaller if it's smaller than
+delta then this difference here is
+
+ align:start position:0%
+delta then this difference here is
+ 
+
+ align:start position:0%
+delta then this difference here is
+smaller than epsilon right that's what
+
+ align:start position:0%
+smaller than epsilon right that's what
+ 
+
+ align:start position:0%
+smaller than epsilon right that's what
+I'm supposed to do
+
+ align:start position:0%
+I'm supposed to do
+ 
+
+ align:start position:0%
+I'm supposed to do
+just knowing that f and g are continuous
+
+ align:start position:0%
+just knowing that f and g are continuous
+ 
+
+ align:start position:0%
+just knowing that f and g are continuous
+right and so I do so this just like when
+
+ align:start position:0%
+right and so I do so this just like when
+ 
+
+ align:start position:0%
+right and so I do so this just like when
+we had this for sequences
+
+ align:start position:0%
+we had this for sequences
+ 
+
+ align:start position:0%
+we had this for sequences
+the similar thing for sequences it's too
+
+ align:start position:0%
+the similar thing for sequences it's too
+ 
+
+ align:start position:0%
+the similar thing for sequences it's too
+much it's too complicated if you just
+
+ align:start position:0%
+much it's too complicated if you just
+ 
+
+ align:start position:0%
+much it's too complicated if you just
+look at like this. So what you do is
+
+ align:start position:0%
+look at like this. So what you do is
+ 
+
+ align:start position:0%
+look at like this. So what you do is
+that you take f ofx times g of x. You
+
+ align:start position:0%
+that you take f ofx times g of x. You
+ 
+
+ align:start position:0%
+that you take f ofx times g of x. You
+insert something and so you insert. It
+
+ align:start position:0%
+insert something and so you insert. It
+ 
+
+ align:start position:0%
+insert something and so you insert. It
+doesn't really matter which way you do
+
+ align:start position:0%
+doesn't really matter which way you do
+ 
+
+ align:start position:0%
+doesn't really matter which way you do
+it, but this is like halfway between
+
+ align:start position:0%
+it, but this is like halfway between
+ 
+
+ align:start position:0%
+it, but this is like halfway between
+this and that where you take one point
+
+ align:start position:0%
+this and that where you take one point
+ 
+
+ align:start position:0%
+this and that where you take one point
+to be x0 the other two x. Of course you
+
+ align:start position:0%
+to be x0 the other two x. Of course you
+ 
+
+ align:start position:0%
+to be x0 the other two x. Of course you
+didn't have that. So you have to add it
+
+ align:start position:0%
+didn't have that. So you have to add it
+ 
+
+ align:start position:0%
+didn't have that. So you have to add it
+again.
+
+ align:start position:0%
+again.
+ 
+
+ align:start position:0%
+again.
+But now the thing is that what you've
+
+ align:start position:0%
+But now the thing is that what you've
+ 
+
+ align:start position:0%
+But now the thing is that what you've
+done here is you sort of have split the
+
+ align:start position:0%
+done here is you sort of have split the
+ 
+
+ align:start position:0%
+done here is you sort of have split the
+difference if you will.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now when you want to estimate
+
+ align:start position:0%
+And so now when you want to estimate
+ 
+
+ align:start position:0%
+And so now when you want to estimate
+this you estimate this thing here first.
+
+ align:start position:0%
+this you estimate this thing here first.
+ 
+
+ align:start position:0%
+this you estimate this thing here first.
+So this is g of x * f ofx
+
+ align:start position:0%
+So this is g of x * f ofx
+ 
+
+ align:start position:0%
+So this is g of x * f ofx
+- f of x0
+
+ align:start position:0%
+- f of x0
+ 
+
+ align:start position:0%
+- f of x0
+and you take the absolute value of this
+
+ align:start position:0%
+and you take the absolute value of this
+ 
+
+ align:start position:0%
+and you take the absolute value of this
+plus and then this here here you can
+
+ align:start position:0%
+plus and then this here here you can
+ 
+
+ align:start position:0%
+plus and then this here here you can
+factor out f of x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh g of x minus g of x0.
+
+ align:start position:0%
+uh g of x minus g of x0.
+ 
+
+ align:start position:0%
+uh g of x minus g of x0.
+And now you see now you can sort of do
+
+ align:start position:0%
+And now you see now you can sort of do
+ 
+
+ align:start position:0%
+And now you see now you can sort of do
+like we did before. This here is now
+
+ align:start position:0%
+like we did before. This here is now
+ 
+
+ align:start position:0%
+like we did before. This here is now
+fixed. So you just you can you can also
+
+ align:start position:0%
+fixed. So you just you can you can also
+ 
+
+ align:start position:0%
+fixed. So you just you can you can also
+take the absolute value sign like that.
+
+ align:start position:0%
+take the absolute value sign like that.
+ 
+
+ align:start position:0%
+take the absolute value sign like that.
+And now this here is like just x here is
+
+ align:start position:0%
+And now this here is like just x here is
+ 
+
+ align:start position:0%
+And now this here is like just x here is
+fixed. So this is just some fixed
+
+ align:start position:0%
+fixed. So this is just some fixed
+ 
+
+ align:start position:0%
+fixed. So this is just some fixed
+number. So this means that this thing
+
+ align:start position:0%
+number. So this means that this thing
+ 
+
+ align:start position:0%
+number. So this means that this thing
+here has to be maybe even smaller
+
+ align:start position:0%
+here has to be maybe even smaller
+ 
+
+ align:start position:0%
+here has to be maybe even smaller
+depending on what this constant is. But
+
+ align:start position:0%
+depending on what this constant is. But
+ 
+
+ align:start position:0%
+depending on what this constant is. But
+that's easy to achieve with some delta.
+
+ align:start position:0%
+that's easy to achieve with some delta.
+ 
+
+ align:start position:0%
+that's easy to achieve with some delta.
+Right? Here it's a little bit more
+
+ align:start position:0%
+Right? Here it's a little bit more
+ 
+
+ align:start position:0%
+Right? Here it's a little bit more
+complicated because this one here is not
+
+ align:start position:0%
+complicated because this one here is not
+ 
+
+ align:start position:0%
+complicated because this one here is not
+fixed. Right? But you have to then say
+
+ align:start position:0%
+fixed. Right? But you have to then say
+ 
+
+ align:start position:0%
+fixed. Right? But you have to then say
+that once you are close to x0 then this
+
+ align:start position:0%
+that once you are close to x0 then this
+ 
+
+ align:start position:0%
+that once you are close to x0 then this
+here there's a bound for this. You see
+
+ align:start position:0%
+here there's a bound for this. You see
+ 
+
+ align:start position:0%
+here there's a bound for this. You see
+it's sort of like what we did before. So
+
+ align:start position:0%
+it's sort of like what we did before. So
+ 
+
+ align:start position:0%
+it's sort of like what we did before. So
+we are out of time so I just leave it
+
+ align:start position:0%
+we are out of time so I just leave it
+ 
+
+ align:start position:0%
+we are out of time so I just leave it
+there.
+
+ align:start position:0%
+there.
+ 
+
+ align:start position:0%
+there.
+So next time we'll talk more about this
+
+ align:start position:0%
+So next time we'll talk more about this
+ 
+
+ align:start position:0%
+So next time we'll talk more about this
+with exponential function. Yeah. So a
+
+ align:start position:0%
+with exponential function. Yeah. So a
+ 
+
+ align:start position:0%
+with exponential function. Yeah. So a
+rational function said to be continuous
+
+ align:start position:0%
+rational function said to be continuous
+ 
+
+ align:start position:0%
+rational function said to be continuous
+or do we not call it continuous? No, a
+
+ align:start position:0%
+or do we not call it continuous? No, a
+ 
+
+ align:start position:0%
+or do we not call it continuous? No, a
+rational function any rational function
+
+ align:start position:0%
+rational function any rational function
+ 
+
+ align:start position:0%
+rational function any rational function
+is continuous. It's defined
+
+ align:start position:0%
+is continuous. It's defined
+ 
+
+ align:start position:0%
+is continuous. It's defined
+at points where the where the polinomial
+
+ align:start position:0%
+at points where the where the polinomial
+ 
+
+ align:start position:0%
+at points where the where the polinomial
+in the denominator
+
+ align:start position:0%
+in the denominator
+ 
+
+ align:start position:0%
+in the denominator
+away from the roots of the of the
+
+ align:start position:0%
+away from the roots of the of the
+ 
+
+ align:start position:0%
+away from the roots of the of the
+polomial in the denominator.
+
+ align:start position:0%
+polomial in the denominator.
+ 
+
+ align:start position:0%
+polomial in the denominator.
+>> It's continuous. What
+
+ align:start position:0%
+>> It's continuous. What
+ 
+
+ align:start position:0%
+>> It's continuous. What
+>> are they said to be continu
+
+ align:start position:0%
+>> are they said to be continu
+ 
+
+ align:start position:0%
+>> are they said to be continu
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+one what yeah I mean any rational
+
+ align:start position:0%
+one what yeah I mean any rational
+ 
+
+ align:start position:0%
+one what yeah I mean any rational
+function is continuous. It's just not
+
+ align:start position:0%
+function is continuous. It's just not
+ 
+
+ align:start position:0%
+function is continuous. It's just not
+defined at the roots.
+
+ align:start position:0%
+defined at the roots.
+ 
+
+ align:start position:0%
+defined at the roots.
+Okay. Now for some polomium you could
+
+ align:start position:0%
+Okay. Now for some polomium you could
+ 
+
+ align:start position:0%
+Okay. Now for some polomium you could
+some rational functions if you were sort
+
+ align:start position:0%
+some rational functions if you were sort
+ 
+
+ align:start position:0%
+some rational functions if you were sort
+of silly and you wrote a if you wrote
+
+ align:start position:0%
+of silly and you wrote a if you wrote
+ 
+
+ align:start position:0%
+of silly and you wrote a if you wrote
+this thing here right this is a polomial
+
+ align:start position:0%
+this thing here right this is a polomial
+ 
+
+ align:start position:0%
+this thing here right this is a polomial
+that's a polomial this one have a root
+
+ align:start position:0%
+that's a polomial this one have a root
+ 
+
+ align:start position:0%
+that's a polomial this one have a root
+as zero but really this function here
+
+ align:start position:0%
+as zero but really this function here
+ 
+
+ align:start position:0%
+as zero but really this function here
+you would probably think about as being
+
+ align:start position:0%
+you would probably think about as being
+ 
+
+ align:start position:0%
+you would probably think about as being
+the constant function one right so it's
+
+ align:start position:0%
+the constant function one right so it's
+ 
+
+ align:start position:0%
+the constant function one right so it's
+still right but it's not a pure it's
+
+ align:start position:0%
+still right but it's not a pure it's
+ 
+
+ align:start position:0%
+still right but it's not a pure it's
+it's continuous
+
+ align:start position:0%
+it's continuous
+ 
+
+ align:start position:0%
+it's continuous
+away from the root. It doesn't say
+
+ align:start position:0%
+away from the root. It doesn't say
+ 
+
+ align:start position:0%
+away from the root. It doesn't say
+whether it's continuous at the root.
+
+ align:start position:0%
+whether it's continuous at the root.
+ 
+
+ align:start position:0%
+whether it's continuous at the root.
+It's just not defined at the root of the
+
+ align:start position:0%
+It's just not defined at the root of the
+ 
+
+ align:start position:0%
+It's just not defined at the root of the
+denominator.
+
+ align:start position:0%
+denominator.
+ 
+
+ align:start position:0%
+denominator.
+>> Yep.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah, that's right. That's right. So
+
+ align:start position:0%
+>> Yeah, that's right. That's right. So
+ 
+
+ align:start position:0%
+>> Yeah, that's right. That's right. So
+that's right. So if you have a polomial
+
+ align:start position:0%
+that's right. So if you have a polomial
+ 
+
+ align:start position:0%
+that's right. So if you have a polomial
+in the denominator, right, there's
+
+ align:start position:0%
+in the denominator, right, there's
+ 
+
+ align:start position:0%
+in the denominator, right, there's
+there's like finite many points where
+
+ align:start position:0%
+there's like finite many points where
+ 
+
+ align:start position:0%
+there's like finite many points where
+where where you have roots and at those
+
+ align:start position:0%
+where where you have roots and at those
+ 
+
+ align:start position:0%
+where where you have roots and at those
+point it's appro defined. You might be
+
+ align:start position:0%
+point it's appro defined. You might be
+ 
+
+ align:start position:0%
+point it's appro defined. You might be
+able to extend it in a continuous way to
+
+ align:start position:0%
+able to extend it in a continuous way to
+ 
+
+ align:start position:0%
+able to extend it in a continuous way to
+those points, but typically it's not
+
+ align:start position:0%
+those points, but typically it's not
+ 
+
+ align:start position:0%
+those points, but typically it's not
+defined in those points.
\ No newline at end of file
diff --git a/Mv2aDOe1o4w.txt b/Mv2aDOe1o4w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..63ea482ed162d379dce1e84cef0ca4a19a20b788
--- /dev/null
+++ b/Mv2aDOe1o4w.txt
@@ -0,0 +1,22595 @@
+align:start position:0%
+ 
+so we have uh we're going to spend most
+
+ align:start position:0%
+so we have uh we're going to spend most
+ 
+
+ align:start position:0%
+so we have uh we're going to spend most
+of today debriefing the
+
+ align:start position:0%
+of today debriefing the
+ 
+
+ align:start position:0%
+of today debriefing the
+trip and and
+
+ align:start position:0%
+trip and and
+ 
+
+ align:start position:0%
+trip and and
+uh we have a little uh going to have it
+
+ align:start position:0%
+uh we have a little uh going to have it
+ 
+
+ align:start position:0%
+uh we have a little uh going to have it
+broken down to three parts one is a a
+
+ align:start position:0%
+broken down to three parts one is a a
+ 
+
+ align:start position:0%
+broken down to three parts one is a a
+little reflection experience we want you
+
+ align:start position:0%
+little reflection experience we want you
+ 
+
+ align:start position:0%
+little reflection experience we want you
+to do then we want to do a debrief of
+
+ align:start position:0%
+to do then we want to do a debrief of
+ 
+
+ align:start position:0%
+to do then we want to do a debrief of
+the interviews that happened and then a
+
+ align:start position:0%
+the interviews that happened and then a
+ 
+
+ align:start position:0%
+the interviews that happened and then a
+debrief of the inventory work you did
+
+ align:start position:0%
+debrief of the inventory work you did
+ 
+
+ align:start position:0%
+debrief of the inventory work you did
+and then we're going to do uh kind of
+
+ align:start position:0%
+and then we're going to do uh kind of
+ 
+
+ align:start position:0%
+and then we're going to do uh kind of
+two discussions one a discussion about
+
+ align:start position:0%
+two discussions one a discussion about
+ 
+
+ align:start position:0%
+two discussions one a discussion about
+populationbased approaches to Economic
+
+ align:start position:0%
+populationbased approaches to Economic
+ 
+
+ align:start position:0%
+populationbased approaches to Economic
+Development and then another of kind of
+
+ align:start position:0%
+Development and then another of kind of
+ 
+
+ align:start position:0%
+Development and then another of kind of
+setting up for the work that we have to
+
+ align:start position:0%
+setting up for the work that we have to
+ 
+
+ align:start position:0%
+setting up for the work that we have to
+do that right so those are the kind of
+
+ align:start position:0%
+do that right so those are the kind of
+ 
+
+ align:start position:0%
+do that right so those are the kind of
+five steps we hope to get through today
+
+ align:start position:0%
+five steps we hope to get through today
+ 
+
+ align:start position:0%
+five steps we hope to get through today
+and if we don't get through all of them
+
+ align:start position:0%
+and if we don't get through all of them
+ 
+
+ align:start position:0%
+and if we don't get through all of them
+um we'll you know continue next session
+
+ align:start position:0%
+um we'll you know continue next session
+ 
+
+ align:start position:0%
+um we'll you know continue next session
+I think we have enough time next session
+
+ align:start position:0%
+I think we have enough time next session
+ 
+
+ align:start position:0%
+I think we have enough time next session
+to to sort of complete this this work
+
+ align:start position:0%
+to to sort of complete this this work
+ 
+
+ align:start position:0%
+to to sort of complete this this work
+and cover the the material for the next
+
+ align:start position:0%
+and cover the the material for the next
+ 
+
+ align:start position:0%
+and cover the the material for the next
+session too so uh I need I need a tester
+
+ align:start position:0%
+session too so uh I need I need a tester
+ 
+
+ align:start position:0%
+session too so uh I need I need a tester
+and can you me can you just test that
+
+ align:start position:0%
+and can you me can you just test that
+ 
+
+ align:start position:0%
+and can you me can you just test that
+and see if it'll actually stick on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board yeah will if you push hard huh you
+
+ align:start position:0%
+board yeah will if you push hard huh you
+ 
+
+ align:start position:0%
+board yeah will if you push hard huh you
+push if you push hard it'll stick okay
+
+ align:start position:0%
+push if you push hard it'll stick okay
+ 
+
+ align:start position:0%
+push if you push hard it'll stick okay
+good okay
+
+ align:start position:0%
+good okay
+ 
+
+ align:start position:0%
+good okay
+so can people just take
+
+ align:start position:0%
+so can people just take
+ 
+
+ align:start position:0%
+so can people just take
+like a few of these like six or seven or
+
+ align:start position:0%
+like a few of these like six or seven or
+ 
+
+ align:start position:0%
+like a few of these like six or seven or
+so of those
+
+ align:start position:0%
+so of those
+ 
+
+ align:start position:0%
+so of those
+uh then pass him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around so take a set and then pass him
+
+ align:start position:0%
+around so take a set and then pass him
+ 
+
+ align:start position:0%
+around so take a set and then pass him
+around then we have supportive tape in
+
+ align:start position:0%
+around then we have supportive tape in
+ 
+
+ align:start position:0%
+around then we have supportive tape in
+case we need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and also you might want to get out a
+
+ align:start position:0%
+it and also you might want to get out a
+ 
+
+ align:start position:0%
+it and also you might want to get out a
+piece of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paper everybody got a stack everyone
+
+ align:start position:0%
+paper everybody got a stack everyone
+ 
+
+ align:start position:0%
+paper everybody got a stack everyone
+have a stack good James you have a stack
+
+ align:start position:0%
+have a stack good James you have a stack
+ 
+
+ align:start position:0%
+have a stack good James you have a stack
+I don't have a stack
+
+ align:start position:0%
+I don't have a stack
+ 
+
+ align:start position:0%
+I don't have a stack
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good a want some sure only one color oh
+
+ align:start position:0%
+good a want some sure only one color oh
+ 
+
+ align:start position:0%
+good a want some sure only one color oh
+that's more color would you like Green
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead color you want great okay so
+
+ align:start position:0%
+instead color you want great okay so
+ 
+
+ align:start position:0%
+instead color you want great okay so
+there are two parts to this and I want
+
+ align:start position:0%
+there are two parts to this and I want
+ 
+
+ align:start position:0%
+there are two parts to this and I want
+people to kind of concentrate on for the
+
+ align:start position:0%
+people to kind of concentrate on for the
+ 
+
+ align:start position:0%
+people to kind of concentrate on for the
+next like five minutes or so so
+
+ align:start position:0%
+next like five minutes or so so
+ 
+
+ align:start position:0%
+next like five minutes or so so
+um and that's why I asked you to
+
+ align:start position:0%
+um and that's why I asked you to
+ 
+
+ align:start position:0%
+um and that's why I asked you to
+actually have a piece of paper out then
+
+ align:start position:0%
+actually have a piece of paper out then
+ 
+
+ align:start position:0%
+actually have a piece of paper out then
+also have one of these the piece of
+
+ align:start position:0%
+also have one of these the piece of
+ 
+
+ align:start position:0%
+also have one of these the piece of
+paper you all have to share with us but
+
+ align:start position:0%
+paper you all have to share with us but
+ 
+
+ align:start position:0%
+paper you all have to share with us but
+these we're going to put up what I'd
+
+ align:start position:0%
+these we're going to put up what I'd
+ 
+
+ align:start position:0%
+these we're going to put up what I'd
+like you to do is just uh take a few
+
+ align:start position:0%
+like you to do is just uh take a few
+ 
+
+ align:start position:0%
+like you to do is just uh take a few
+minutes and write down from your
+
+ align:start position:0%
+minutes and write down from your
+ 
+
+ align:start position:0%
+minutes and write down from your
+perspective kind of five observations
+
+ align:start position:0%
+perspective kind of five observations
+ 
+
+ align:start position:0%
+perspective kind of five observations
+that you thought were the most important
+
+ align:start position:0%
+that you thought were the most important
+ 
+
+ align:start position:0%
+that you thought were the most important
+observations you made during your trip
+
+ align:start position:0%
+observations you made during your trip
+ 
+
+ align:start position:0%
+observations you made during your trip
+in Springfield just Things You observe
+
+ align:start position:0%
+in Springfield just Things You observe
+ 
+
+ align:start position:0%
+in Springfield just Things You observe
+saw things that happen
+
+ align:start position:0%
+saw things that happen
+ 
+
+ align:start position:0%
+saw things that happen
+Okay and
+
+ align:start position:0%
+Okay and
+ 
+
+ align:start position:0%
+Okay and
+it can be from any perspective it could
+
+ align:start position:0%
+it can be from any perspective it could
+ 
+
+ align:start position:0%
+it can be from any perspective it could
+be something it may not be related to
+
+ align:start position:0%
+be something it may not be related to
+ 
+
+ align:start position:0%
+be something it may not be related to
+Economic Development it could just be
+
+ align:start position:0%
+Economic Development it could just be
+ 
+
+ align:start position:0%
+Economic Development it could just be
+related to relationships whatever it is
+
+ align:start position:0%
+related to relationships whatever it is
+ 
+
+ align:start position:0%
+related to relationships whatever it is
+but you know try to think of from your
+
+ align:start position:0%
+but you know try to think of from your
+ 
+
+ align:start position:0%
+but you know try to think of from your
+own perspective there five really kind
+
+ align:start position:0%
+own perspective there five really kind
+ 
+
+ align:start position:0%
+own perspective there five really kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+key Impressions things you came back
+
+ align:start position:0%
+key Impressions things you came back
+ 
+
+ align:start position:0%
+key Impressions things you came back
+from in terms of your visit to the North
+
+ align:start position:0%
+from in terms of your visit to the North
+ 
+
+ align:start position:0%
+from in terms of your visit to the North
+End
+
+ align:start position:0%
+End
+ 
+
+ align:start position:0%
+End
+okay and then after you get those five
+
+ align:start position:0%
+okay and then after you get those five
+ 
+
+ align:start position:0%
+okay and then after you get those five
+down I'm going to ask you to do one
+
+ align:start position:0%
+down I'm going to ask you to do one
+ 
+
+ align:start position:0%
+down I'm going to ask you to do one
+other thing okay so I'm going to give
+
+ align:start position:0%
+other thing okay so I'm going to give
+ 
+
+ align:start position:0%
+other thing okay so I'm going to give
+you a few minutes to do that
+
+ align:start position:0%
+you a few minutes to do that
+ 
+
+ align:start position:0%
+you a few minutes to do that
+one pet please
+
+ align:start position:0%
+one pet please
+ 
+
+ align:start position:0%
+one pet please
+one yeah one ped on these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people finished
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+TR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+almost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finished D just right next to it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so after you've done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that then in your own note book or
+
+ align:start position:0%
+that then in your own note book or
+ 
+
+ align:start position:0%
+that then in your own note book or
+another piece of paper I want you to
+
+ align:start position:0%
+another piece of paper I want you to
+ 
+
+ align:start position:0%
+another piece of paper I want you to
+write one more
+
+ align:start position:0%
+write one more
+ 
+
+ align:start position:0%
+write one more
+thing given your a whole experience
+
+ align:start position:0%
+thing given your a whole experience
+ 
+
+ align:start position:0%
+thing given your a whole experience
+there giving your
+
+ align:start position:0%
+there giving your
+ 
+
+ align:start position:0%
+there giving your
+experience that uh in the North End I
+
+ align:start position:0%
+experience that uh in the North End I
+ 
+
+ align:start position:0%
+experience that uh in the North End I
+want you to just kind of think back to
+
+ align:start position:0%
+want you to just kind of think back to
+ 
+
+ align:start position:0%
+want you to just kind of think back to
+any other experiences or events or uh
+
+ align:start position:0%
+any other experiences or events or uh
+ 
+
+ align:start position:0%
+any other experiences or events or uh
+places you know
+
+ align:start position:0%
+places you know
+ 
+
+ align:start position:0%
+places you know
+of that when you were there it reminded
+
+ align:start position:0%
+of that when you were there it reminded
+ 
+
+ align:start position:0%
+of that when you were there it reminded
+you of it's kind of like wow you know
+
+ align:start position:0%
+you of it's kind of like wow you know
+ 
+
+ align:start position:0%
+you of it's kind of like wow you know
+when I was walking around this
+
+ align:start position:0%
+when I was walking around this
+ 
+
+ align:start position:0%
+when I was walking around this
+experience or this event or this thing
+
+ align:start position:0%
+experience or this event or this thing
+ 
+
+ align:start position:0%
+experience or this event or this thing
+kind of popped up in my mind it could be
+
+ align:start position:0%
+kind of popped up in my mind it could be
+ 
+
+ align:start position:0%
+kind of popped up in my mind it could be
+something you actually live through or
+
+ align:start position:0%
+something you actually live through or
+ 
+
+ align:start position:0%
+something you actually live through or
+something you maybe have read about but
+
+ align:start position:0%
+something you maybe have read about but
+ 
+
+ align:start position:0%
+something you maybe have read about but
+there was a connection with something
+
+ align:start position:0%
+there was a connection with something
+ 
+
+ align:start position:0%
+there was a connection with something
+outside of the north end is that clear
+
+ align:start position:0%
+outside of the north end is that clear
+ 
+
+ align:start position:0%
+outside of the north end is that clear
+what I mean and just jot yourself a note
+
+ align:start position:0%
+what I mean and just jot yourself a note
+ 
+
+ align:start position:0%
+what I mean and just jot yourself a note
+down about what that
+
+ align:start position:0%
+down about what that
+ 
+
+ align:start position:0%
+down about what that
+was don't put it on no just totally
+
+ align:start position:0%
+was don't put it on no just totally
+ 
+
+ align:start position:0%
+was don't put it on no just totally
+independent of those things it doesn't
+
+ align:start position:0%
+independent of those things it doesn't
+ 
+
+ align:start position:0%
+independent of those things it doesn't
+have anything it doesn't have to have
+
+ align:start position:0%
+have anything it doesn't have to have
+ 
+
+ align:start position:0%
+have anything it doesn't have to have
+anything to do with those cards
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay is everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ready
+
+ align:start position:0%
+ready
+ 
+
+ align:start position:0%
+ready
+so what I'm looking for at this point in
+
+ align:start position:0%
+so what I'm looking for at this point in
+ 
+
+ align:start position:0%
+so what I'm looking for at this point in
+time is
+
+ align:start position:0%
+time is
+ 
+
+ align:start position:0%
+time is
+volunteers person to come up and just
+
+ align:start position:0%
+volunteers person to come up and just
+ 
+
+ align:start position:0%
+volunteers person to come up and just
+tell us quickly about the five things
+
+ align:start position:0%
+tell us quickly about the five things
+ 
+
+ align:start position:0%
+tell us quickly about the five things
+that you have that you laid out and what
+
+ align:start position:0%
+that you have that you laid out and what
+ 
+
+ align:start position:0%
+that you have that you laid out and what
+I'd like you to do is when you do it
+
+ align:start position:0%
+I'd like you to do is when you do it
+ 
+
+ align:start position:0%
+I'd like you to do is when you do it
+if the thing you saw was positive you
+
+ align:start position:0%
+if the thing you saw was positive you
+ 
+
+ align:start position:0%
+if the thing you saw was positive you
+thought it was a positive thing
+
+ align:start position:0%
+thought it was a positive thing
+ 
+
+ align:start position:0%
+thought it was a positive thing
+experience it's all subjective put it on
+
+ align:start position:0%
+experience it's all subjective put it on
+ 
+
+ align:start position:0%
+experience it's all subjective put it on
+this board if it's something that you
+
+ align:start position:0%
+this board if it's something that you
+ 
+
+ align:start position:0%
+this board if it's something that you
+thought was negative put it on this
+
+ align:start position:0%
+thought was negative put it on this
+ 
+
+ align:start position:0%
+thought was negative put it on this
+board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what it's kind of like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay neutral gets the biggest board only
+
+ align:start position:0%
+okay neutral gets the biggest board only
+ 
+
+ align:start position:0%
+okay neutral gets the biggest board only
+because that's not a suggestion about
+
+ align:start position:0%
+because that's not a suggestion about
+ 
+
+ align:start position:0%
+because that's not a suggestion about
+where you place things neutral and mixed
+
+ align:start position:0%
+where you place things neutral and mixed
+ 
+
+ align:start position:0%
+where you place things neutral and mixed
+bag this is neutral mixed bag bag no one
+
+ align:start position:0%
+bag this is neutral mixed bag bag no one
+ 
+
+ align:start position:0%
+bag this is neutral mixed bag bag no one
+side is neutral one side is mix bag oh
+
+ align:start position:0%
+side is neutral one side is mix bag oh
+ 
+
+ align:start position:0%
+side is neutral one side is mix bag oh
+okay mixed bag okay you want to give us
+
+ align:start position:0%
+okay mixed bag okay you want to give us
+ 
+
+ align:start position:0%
+okay mixed bag okay you want to give us
+a little sign write us one that says
+
+ align:start position:0%
+a little sign write us one that says
+ 
+
+ align:start position:0%
+a little sign write us one that says
+mixed bag one says neutral and then
+
+ align:start position:0%
+mixed bag one says neutral and then
+ 
+
+ align:start position:0%
+mixed bag one says neutral and then
+we'll make this one over here
+
+ align:start position:0%
+we'll make this one over here
+ 
+
+ align:start position:0%
+we'll make this one over here
+positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay just a remind everyone you got a
+
+ align:start position:0%
+okay just a remind everyone you got a
+ 
+
+ align:start position:0%
+okay just a remind everyone you got a
+mix bag neutral neutral okay here's
+
+ align:start position:0%
+mix bag neutral neutral okay here's
+ 
+
+ align:start position:0%
+mix bag neutral neutral okay here's
+neutral and give us a mixed bag so who
+
+ align:start position:0%
+neutral and give us a mixed bag so who
+ 
+
+ align:start position:0%
+neutral and give us a mixed bag so who
+wants to go first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is like a graduate class we
+
+ align:start position:0%
+okay this is like a graduate class we
+ 
+
+ align:start position:0%
+okay this is like a graduate class we
+don't have to point people out right
+
+ align:start position:0%
+don't have to point people out right
+ 
+
+ align:start position:0%
+don't have to point people out right
+okay okay let's go come on up and put
+
+ align:start position:0%
+okay okay let's go come on up and put
+ 
+
+ align:start position:0%
+okay okay let's go come on up and put
+your things in case you don't stick just
+
+ align:start position:0%
+your things in case you don't stick just
+ 
+
+ align:start position:0%
+your things in case you don't stick just
+grab a piece of tape to put them up
+
+ align:start position:0%
+grab a piece of tape to put them up
+ 
+
+ align:start position:0%
+grab a piece of tape to put them up
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay the first thing was was very
+
+ align:start position:0%
+okay okay the first thing was was very
+ 
+
+ align:start position:0%
+okay okay the first thing was was very
+strong sociocultural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infrastructure sry could you repeat that
+
+ align:start position:0%
+infrastructure sry could you repeat that
+ 
+
+ align:start position:0%
+infrastructure sry could you repeat that
+I a strong soci cultural infrastructure
+
+ align:start position:0%
+I a strong soci cultural infrastructure
+ 
+
+ align:start position:0%
+I a strong soci cultural infrastructure
+um underutilized parks and Open
+
+ align:start position:0%
+um underutilized parks and Open
+ 
+
+ align:start position:0%
+um underutilized parks and Open
+Spaces here I guess because is it
+
+ align:start position:0%
+Spaces here I guess because is it
+ 
+
+ align:start position:0%
+Spaces here I guess because is it
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+there so it could be a mixed bag could
+
+ align:start position:0%
+there so it could be a mixed bag could
+ 
+
+ align:start position:0%
+there so it could be a mixed bag could
+be a mixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bag you guys you guys would be
+
+ align:start position:0%
+bag you guys you guys would be
+ 
+
+ align:start position:0%
+bag you guys you guys would be
+helpful we could vote in
+
+ align:start position:0%
+helpful we could vote in
+ 
+
+ align:start position:0%
+helpful we could vote in
+a A diversity in housing is stock with
+
+ align:start position:0%
+a A diversity in housing is stock with
+ 
+
+ align:start position:0%
+a A diversity in housing is stock with
+the strong presence of public
+
+ align:start position:0%
+the strong presence of public
+ 
+
+ align:start position:0%
+the strong presence of public
+housing you can put it where you think
+
+ align:start position:0%
+housing you can put it where you think
+ 
+
+ align:start position:0%
+housing you can put it where you think
+it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrong it's
+
+ align:start position:0%
+wrong it's
+ 
+
+ align:start position:0%
+wrong it's
+okay stronger presence of medical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+industry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and
+
+ align:start position:0%
+here and
+ 
+
+ align:start position:0%
+here and
+teral rivers side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what was that last one the riv side the
+
+ align:start position:0%
+what was that last one the riv side the
+ 
+
+ align:start position:0%
+what was that last one the riv side the
+wall the
+
+ align:start position:0%
+wall the
+ 
+
+ align:start position:0%
+wall the
+side that big wall that goes uhhuh cool
+
+ align:start position:0%
+side that big wall that goes uhhuh cool
+ 
+
+ align:start position:0%
+side that big wall that goes uhhuh cool
+now um okay that's fine we're just going
+
+ align:start position:0%
+now um okay that's fine we're just going
+ 
+
+ align:start position:0%
+now um okay that's fine we're just going
+to go through these okay those are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next just jump up you know don't raise
+
+ align:start position:0%
+next just jump up you know don't raise
+ 
+
+ align:start position:0%
+next just jump up you know don't raise
+your hand just jump up and do it you
+
+ align:start position:0%
+your hand just jump up and do it you
+ 
+
+ align:start position:0%
+your hand just jump up and do it you
+know sees the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment okay uh for first one I have uh
+
+ align:start position:0%
+moment okay uh for first one I have uh
+ 
+
+ align:start position:0%
+moment okay uh for first one I have uh
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+Springfield shows some as a city shows
+
+ align:start position:0%
+Springfield shows some as a city shows
+ 
+
+ align:start position:0%
+Springfield shows some as a city shows
+some economic dynamism and represents
+
+ align:start position:0%
+some economic dynamism and represents
+ 
+
+ align:start position:0%
+some economic dynamism and represents
+potential demand for the work and
+
+ align:start position:0%
+potential demand for the work and
+ 
+
+ align:start position:0%
+potential demand for the work and
+services of the people in the North
+
+ align:start position:0%
+services of the people in the North
+ 
+
+ align:start position:0%
+services of the people in the North
+End um another positive that I had is
+
+ align:start position:0%
+End um another positive that I had is
+ 
+
+ align:start position:0%
+End um another positive that I had is
+that the people in neon are ready to
+
+ align:start position:0%
+that the people in neon are ready to
+ 
+
+ align:start position:0%
+that the people in neon are ready to
+work on this ready to be pretty
+
+ align:start position:0%
+work on this ready to be pretty
+ 
+
+ align:start position:0%
+work on this ready to be pretty
+active um one neutral observation is
+
+ align:start position:0%
+active um one neutral observation is
+ 
+
+ align:start position:0%
+active um one neutral observation is
+that I found it seems that a lot of
+
+ align:start position:0%
+that I found it seems that a lot of
+ 
+
+ align:start position:0%
+that I found it seems that a lot of
+small local businesses are very like
+
+ align:start position:0%
+small local businesses are very like
+ 
+
+ align:start position:0%
+small local businesses are very like
+almost intentionally or at least
+
+ align:start position:0%
+almost intentionally or at least
+ 
+
+ align:start position:0%
+almost intentionally or at least
+knowingly volatile contingency plans
+
+ align:start position:0%
+knowingly volatile contingency plans
+ 
+
+ align:start position:0%
+knowingly volatile contingency plans
+where the owner knows in advance there's
+
+ align:start position:0%
+where the owner knows in advance there's
+ 
+
+ align:start position:0%
+where the owner knows in advance there's
+a high chance it'll close quickly and is
+
+ align:start position:0%
+a high chance it'll close quickly and is
+ 
+
+ align:start position:0%
+a high chance it'll close quickly and is
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+actually trying necessarily or intending
+
+ align:start position:0%
+actually trying necessarily or intending
+ 
+
+ align:start position:0%
+actually trying necessarily or intending
+to make it last a long
+
+ align:start position:0%
+to make it last a long
+ 
+
+ align:start position:0%
+to make it last a long
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+um as a mixed bag I have uh given State
+
+ align:start position:0%
+um as a mixed bag I have uh given State
+ 
+
+ align:start position:0%
+um as a mixed bag I have uh given State
+given take between uh the community and
+
+ align:start position:0%
+given take between uh the community and
+ 
+
+ align:start position:0%
+given take between uh the community and
+Bay State Medical so while there's a
+
+ align:start position:0%
+Bay State Medical so while there's a
+ 
+
+ align:start position:0%
+Bay State Medical so while there's a
+positive that I think B state is willing
+
+ align:start position:0%
+positive that I think B state is willing
+ 
+
+ align:start position:0%
+positive that I think B state is willing
+to come to the table with people there
+
+ align:start position:0%
+to come to the table with people there
+ 
+
+ align:start position:0%
+to come to the table with people there
+I'm not sure that there's that anyone's
+
+ align:start position:0%
+I'm not sure that there's that anyone's
+ 
+
+ align:start position:0%
+I'm not sure that there's that anyone's
+operating with a very coherent game plan
+
+ align:start position:0%
+operating with a very coherent game plan
+ 
+
+ align:start position:0%
+operating with a very coherent game plan
+of what the community wants from B
+
+ align:start position:0%
+of what the community wants from B
+ 
+
+ align:start position:0%
+of what the community wants from B
+State uh another mixed bag in a way is
+
+ align:start position:0%
+State uh another mixed bag in a way is
+ 
+
+ align:start position:0%
+State uh another mixed bag in a way is
+that there's it sounds negative the way
+
+ align:start position:0%
+that there's it sounds negative the way
+ 
+
+ align:start position:0%
+that there's it sounds negative the way
+I wrote it because I wrote language Gap
+
+ align:start position:0%
+I wrote it because I wrote language Gap
+ 
+
+ align:start position:0%
+I wrote it because I wrote language Gap
+but I think it's a mixed bag also
+
+ align:start position:0%
+but I think it's a mixed bag also
+ 
+
+ align:start position:0%
+but I think it's a mixed bag also
+because it shows some internal Unity
+
+ align:start position:0%
+because it shows some internal Unity
+ 
+
+ align:start position:0%
+because it shows some internal Unity
+cultural Unity um and then another
+
+ align:start position:0%
+cultural Unity um and then another
+ 
+
+ align:start position:0%
+cultural Unity um and then another
+positive was uh that the North End has
+
+ align:start position:0%
+positive was uh that the North End has
+ 
+
+ align:start position:0%
+positive was uh that the North End has
+been identified by the state as an
+
+ align:start position:0%
+been identified by the state as an
+ 
+
+ align:start position:0%
+been identified by the state as an
+anchor neighborhood so it shows that the
+
+ align:start position:0%
+anchor neighborhood so it shows that the
+ 
+
+ align:start position:0%
+anchor neighborhood so it shows that the
+state ready maybe to 20 up to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area I'm going to put this one in
+
+ align:start position:0%
+area I'm going to put this one in
+ 
+
+ align:start position:0%
+area I'm going to put this one in
+positive that I think it really was was
+
+ align:start position:0%
+positive that I think it really was was
+ 
+
+ align:start position:0%
+positive that I think it really was was
+a bit intimidating I said we received a
+
+ align:start position:0%
+a bit intimidating I said we received a
+ 
+
+ align:start position:0%
+a bit intimidating I said we received a
+very warm welcome in the north end but I
+
+ align:start position:0%
+very warm welcome in the north end but I
+ 
+
+ align:start position:0%
+very warm welcome in the north end but I
+think that it was still intimidating
+
+ align:start position:0%
+think that it was still intimidating
+ 
+
+ align:start position:0%
+think that it was still intimidating
+because it seemed
+
+ align:start position:0%
+because it seemed
+ 
+
+ align:start position:0%
+because it seemed
+like uh symptomatic of expectations of
+
+ align:start position:0%
+like uh symptomatic of expectations of
+ 
+
+ align:start position:0%
+like uh symptomatic of expectations of
+us uh this is definitely a mixed bag is
+
+ align:start position:0%
+us uh this is definitely a mixed bag is
+ 
+
+ align:start position:0%
+us uh this is definitely a mixed bag is
+I said we seem to have joined the
+
+ align:start position:0%
+I said we seem to have joined the
+ 
+
+ align:start position:0%
+I said we seem to have joined the
+conversation concerning the future of
+
+ align:start position:0%
+conversation concerning the future of
+ 
+
+ align:start position:0%
+conversation concerning the future of
+the north and at a very Advanced
+
+ align:start position:0%
+the north and at a very Advanced
+ 
+
+ align:start position:0%
+the north and at a very Advanced
+stage um this is I think positive could
+
+ align:start position:0%
+stage um this is I think positive could
+ 
+
+ align:start position:0%
+stage um this is I think positive could
+be considered mix bag too uh neon
+
+ align:start position:0%
+be considered mix bag too uh neon
+ 
+
+ align:start position:0%
+be considered mix bag too uh neon
+workers are deeply concerned about
+
+ align:start position:0%
+workers are deeply concerned about
+ 
+
+ align:start position:0%
+workers are deeply concerned about
+environmental and Public Health in the
+
+ align:start position:0%
+environmental and Public Health in the
+ 
+
+ align:start position:0%
+environmental and Public Health in the
+North
+
+ align:start position:0%
+North
+ 
+
+ align:start position:0%
+North
+End last
+
+ align:start position:0%
+End last
+ 
+
+ align:start position:0%
+End last
+I would say more
+
+ align:start position:0%
+I would say more
+ 
+
+ align:start position:0%
+I would say more
+negative um I felt that Jeff had really
+
+ align:start position:0%
+negative um I felt that Jeff had really
+ 
+
+ align:start position:0%
+negative um I felt that Jeff had really
+sort of impenetrable set of thoughts
+
+ align:start position:0%
+sort of impenetrable set of thoughts
+ 
+
+ align:start position:0%
+sort of impenetrable set of thoughts
+about what the ideal relationship
+
+ align:start position:0%
+about what the ideal relationship
+ 
+
+ align:start position:0%
+about what the ideal relationship
+between the Northend and Bas state was
+
+ align:start position:0%
+between the Northend and Bas state was
+ 
+
+ align:start position:0%
+between the Northend and Bas state was
+and I really couldn't get much of a
+
+ align:start position:0%
+and I really couldn't get much of a
+ 
+
+ align:start position:0%
+and I really couldn't get much of a
+handle of the way he thought about that
+
+ align:start position:0%
+handle of the way he thought about that
+ 
+
+ align:start position:0%
+handle of the way he thought about that
+relationship as it might move forward or
+
+ align:start position:0%
+relationship as it might move forward or
+ 
+
+ align:start position:0%
+relationship as it might move forward or
+does it not move forward he of talked
+
+ align:start position:0%
+does it not move forward he of talked
+ 
+
+ align:start position:0%
+does it not move forward he of talked
+about but wouldn't get into the details
+
+ align:start position:0%
+about but wouldn't get into the details
+ 
+
+ align:start position:0%
+about but wouldn't get into the details
+about seing rightwood from B St um so I
+
+ align:start position:0%
+about seing rightwood from B St um so I
+ 
+
+ align:start position:0%
+about seing rightwood from B St um so I
+feel that till that black box is somehow
+
+ align:start position:0%
+feel that till that black box is somehow
+ 
+
+ align:start position:0%
+feel that till that black box is somehow
+cracked open it's it's negative and then
+
+ align:start position:0%
+cracked open it's it's negative and then
+ 
+
+ align:start position:0%
+cracked open it's it's negative and then
+I thought the highway interchange is
+
+ align:start position:0%
+I thought the highway interchange is
+ 
+
+ align:start position:0%
+I thought the highway interchange is
+very dangerous which one the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+highway I have a
+
+ align:start position:0%
+highway I have a
+ 
+
+ align:start position:0%
+highway I have a
+few but first I found a wide range of
+
+ align:start position:0%
+few but first I found a wide range of
+ 
+
+ align:start position:0%
+few but first I found a wide range of
+community activities going on in the
+
+ align:start position:0%
+community activities going on in the
+ 
+
+ align:start position:0%
+community activities going on in the
+area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+iot just speak up just a little louder
+
+ align:start position:0%
+iot just speak up just a little louder
+ 
+
+ align:start position:0%
+iot just speak up just a little louder
+I'm having a hard time hearing
+
+ align:start position:0%
+I'm having a hard time hearing
+ 
+
+ align:start position:0%
+I'm having a hard time hearing
+and um there was an absence of close
+
+ align:start position:0%
+and um there was an absence of close
+ 
+
+ align:start position:0%
+and um there was an absence of close
+Community initiatives although I saw a
+
+ align:start position:0%
+Community initiatives although I saw a
+ 
+
+ align:start position:0%
+Community initiatives although I saw a
+lot of activities going on within the
+
+ align:start position:0%
+lot of activities going on within the
+ 
+
+ align:start position:0%
+lot of activities going on within the
+community I asked sever people and they
+
+ align:start position:0%
+community I asked sever people and they
+ 
+
+ align:start position:0%
+community I asked sever people and they
+didn't see that there were um a lot
+
+ align:start position:0%
+didn't see that there were um a lot
+ 
+
+ align:start position:0%
+didn't see that there were um a lot
+going on with other
+
+ align:start position:0%
+going on with other
+ 
+
+ align:start position:0%
+going on with other
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's and then um somebody told me that
+
+ align:start position:0%
+that's and then um somebody told me that
+ 
+
+ align:start position:0%
+that's and then um somebody told me that
+the health issue was a serious concern
+
+ align:start position:0%
+the health issue was a serious concern
+ 
+
+ align:start position:0%
+the health issue was a serious concern
+that they have the highest
+
+ align:start position:0%
+that they have the highest
+ 
+
+ align:start position:0%
+that they have the highest
+industrial um in the area okay this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is and then I thought there's not enough
+
+ align:start position:0%
+is and then I thought there's not enough
+ 
+
+ align:start position:0%
+is and then I thought there's not enough
+internal demand within the the community
+
+ align:start position:0%
+internal demand within the the community
+ 
+
+ align:start position:0%
+internal demand within the the community
+like I didn't see that there was like an
+
+ align:start position:0%
+like I didn't see that there was like an
+ 
+
+ align:start position:0%
+like I didn't see that there was like an
+excess demand for the ex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can I ask a question quick when it says
+
+ align:start position:0%
+can I ask a question quick when it says
+ 
+
+ align:start position:0%
+can I ask a question quick when it says
+n of demand you mean like commercial for
+
+ align:start position:0%
+n of demand you mean like commercial for
+ 
+
+ align:start position:0%
+n of demand you mean like commercial for
+services or yeah for servic Goods
+
+ align:start position:0%
+services or yeah for servic Goods
+ 
+
+ align:start position:0%
+services or yeah for servic Goods
+business but then also I Seth mentioned
+
+ align:start position:0%
+business but then also I Seth mentioned
+ 
+
+ align:start position:0%
+business but then also I Seth mentioned
+that too that I saw a strong sense of
+
+ align:start position:0%
+that too that I saw a strong sense of
+ 
+
+ align:start position:0%
+that too that I saw a strong sense of
+unity among the people because they
+
+ align:start position:0%
+unity among the people because they
+ 
+
+ align:start position:0%
+unity among the people because they
+speak the same language because they
+
+ align:start position:0%
+speak the same language because they
+ 
+
+ align:start position:0%
+speak the same language because they
+minority majority and I think
+
+ align:start position:0%
+minority majority and I think
+ 
+
+ align:start position:0%
+minority majority and I think
+that's the same oh um they speak most
+
+ align:start position:0%
+that's the same oh um they speak most
+ 
+
+ align:start position:0%
+that's the same oh um they speak most
+most of them speak Spanish and um I
+
+ align:start position:0%
+most of them speak Spanish and um I
+ 
+
+ align:start position:0%
+most of them speak Spanish and um I
+guess it is a minority language in the
+
+ align:start position:0%
+guess it is a minority language in the
+ 
+
+ align:start position:0%
+guess it is a minority language in the
+country but in the area that's the
+
+ align:start position:0%
+country but in the area that's the
+ 
+
+ align:start position:0%
+country but in the area that's the
+majority speak
+
+ align:start position:0%
+majority speak
+ 
+
+ align:start position:0%
+majority speak
+so sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next okay let's see
+
+ align:start position:0%
+next okay let's see
+ 
+
+ align:start position:0%
+next okay let's see
+here um
+
+ align:start position:0%
+here um
+ 
+
+ align:start position:0%
+here um
+the first I have year is that not end
+
+ align:start position:0%
+the first I have year is that not end
+ 
+
+ align:start position:0%
+the first I have year is that not end
+didn't seem to be too poor to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me that's interesting I mean I that's
+
+ align:start position:0%
+me that's interesting I mean I that's
+ 
+
+ align:start position:0%
+me that's interesting I mean I that's
+compared
+
+ align:start position:0%
+compared
+ 
+
+ align:start position:0%
+compared
+toity Philadelphia the summer
+
+ align:start position:0%
+toity Philadelphia the summer
+ 
+
+ align:start position:0%
+toity Philadelphia the summer
+I anyway I don't know where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+POS um
+
+ align:start position:0%
+POS um
+ 
+
+ align:start position:0%
+POS um
+then uh two things actually on Neo one
+
+ align:start position:0%
+then uh two things actually on Neo one
+ 
+
+ align:start position:0%
+then uh two things actually on Neo one
+of them was I was a little bit concerned
+
+ align:start position:0%
+of them was I was a little bit concerned
+ 
+
+ align:start position:0%
+of them was I was a little bit concerned
+about the financial sustainability of
+
+ align:start position:0%
+about the financial sustainability of
+ 
+
+ align:start position:0%
+about the financial sustainability of
+neon for a long period of time and I
+
+ align:start position:0%
+neon for a long period of time and I
+ 
+
+ align:start position:0%
+neon for a long period of time and I
+thought it was a little bit concerned so
+
+ align:start position:0%
+thought it was a little bit concerned so
+ 
+
+ align:start position:0%
+thought it was a little bit concerned so
+um I don't know what to put that
+
+ align:start position:0%
+um I don't know what to put that
+ 
+
+ align:start position:0%
+um I don't know what to put that
+but just some concerns I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+um then also I had a they appear to be a
+
+ align:start position:0%
+um then also I had a they appear to be a
+ 
+
+ align:start position:0%
+um then also I had a they appear to be a
+small number of people compared to the
+
+ align:start position:0%
+small number of people compared to the
+ 
+
+ align:start position:0%
+small number of people compared to the
+size of the city I mean in said it seem
+
+ align:start position:0%
+size of the city I mean in said it seem
+ 
+
+ align:start position:0%
+size of the city I mean in said it seem
+to be to be too big and too few people
+
+ align:start position:0%
+to be to be too big and too few people
+ 
+
+ align:start position:0%
+to be to be too big and too few people
+you know so in a way you might say that
+
+ align:start position:0%
+you know so in a way you might say that
+ 
+
+ align:start position:0%
+you know so in a way you might say that
+the city's capacity was greater than you
+
+ align:start position:0%
+the city's capacity was greater than you
+ 
+
+ align:start position:0%
+the city's capacity was greater than you
+know the available resource use or
+
+ align:start position:0%
+know the available resource use or
+ 
+
+ align:start position:0%
+know the available resource use or
+whatever so
+
+ align:start position:0%
+whatever so
+ 
+
+ align:start position:0%
+whatever so
+um you are very good
+
+ align:start position:0%
+um you are very good
+ 
+
+ align:start position:0%
+um you are very good
+aty so I don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know then another concern I had
+
+ align:start position:0%
+know then another concern I had
+ 
+
+ align:start position:0%
+know then another concern I had
+um was I had a concern about the
+
+ align:start position:0%
+um was I had a concern about the
+ 
+
+ align:start position:0%
+um was I had a concern about the
+technical capacity of the neon staff
+
+ align:start position:0%
+technical capacity of the neon staff
+ 
+
+ align:start position:0%
+technical capacity of the neon staff
+Beyond providing Social Services I mean
+
+ align:start position:0%
+Beyond providing Social Services I mean
+ 
+
+ align:start position:0%
+Beyond providing Social Services I mean
+like I kept thinking if we were to come
+
+ align:start position:0%
+like I kept thinking if we were to come
+ 
+
+ align:start position:0%
+like I kept thinking if we were to come
+up with any other project Beyond Social
+
+ align:start position:0%
+up with any other project Beyond Social
+ 
+
+ align:start position:0%
+up with any other project Beyond Social
+Services I would it be implemented and
+
+ align:start position:0%
+Services I would it be implemented and
+ 
+
+ align:start position:0%
+Services I would it be implemented and
+in my mind it was this question about
+
+ align:start position:0%
+in my mind it was this question about
+ 
+
+ align:start position:0%
+in my mind it was this question about
+what have the people I saw and talk with
+
+ align:start position:0%
+what have the people I saw and talk with
+ 
+
+ align:start position:0%
+what have the people I saw and talk with
+you know how to keep technical
+
+ align:start position:0%
+you know how to keep technical
+ 
+
+ align:start position:0%
+you know how to keep technical
+capacity so that it's a negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and my last observ Vision was that I
+
+ align:start position:0%
+and my last observ Vision was that I
+ 
+
+ align:start position:0%
+and my last observ Vision was that I
+mean like um shean I think Jeff had a
+
+ align:start position:0%
+mean like um shean I think Jeff had a
+ 
+
+ align:start position:0%
+mean like um shean I think Jeff had a
+very strong opinion about bringing the B
+
+ align:start position:0%
+very strong opinion about bringing the B
+ 
+
+ align:start position:0%
+very strong opinion about bringing the B
+employees out into the community and he
+
+ align:start position:0%
+employees out into the community and he
+ 
+
+ align:start position:0%
+employees out into the community and he
+kept saying that over and over I said
+
+ align:start position:0%
+kept saying that over and over I said
+ 
+
+ align:start position:0%
+kept saying that over and over I said
+this is the plan I have you know so I I
+
+ align:start position:0%
+this is the plan I have you know so I I
+ 
+
+ align:start position:0%
+this is the plan I have you know so I I
+felt a little bit uncomfortable with
+
+ align:start position:0%
+felt a little bit uncomfortable with
+ 
+
+ align:start position:0%
+felt a little bit uncomfortable with
+that that's a positive positive oh sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first thing I it doesn't look
+
+ align:start position:0%
+the first thing I it doesn't look
+ 
+
+ align:start position:0%
+the first thing I it doesn't look
+that expected it I'll just put that as
+
+ align:start position:0%
+that expected it I'll just put that as
+ 
+
+ align:start position:0%
+that expected it I'll just put that as
+neutral because looks be
+
+ align:start position:0%
+neutral because looks be
+ 
+
+ align:start position:0%
+neutral because looks be
+deceiving and um another thing is um
+
+ align:start position:0%
+deceiving and um another thing is um
+ 
+
+ align:start position:0%
+deceiving and um another thing is um
+drugs like nobody really talk nobody
+
+ align:start position:0%
+drugs like nobody really talk nobody
+ 
+
+ align:start position:0%
+drugs like nobody really talk nobody
+that I spoke to talk directly about it
+
+ align:start position:0%
+that I spoke to talk directly about it
+ 
+
+ align:start position:0%
+that I spoke to talk directly about it
+but there's you know methodone Clinic
+
+ align:start position:0%
+but there's you know methodone Clinic
+ 
+
+ align:start position:0%
+but there's you know methodone Clinic
+there's such huge race of incarceration
+
+ align:start position:0%
+there's such huge race of incarceration
+ 
+
+ align:start position:0%
+there's such huge race of incarceration
+you can kind of tell that there's
+
+ align:start position:0%
+you can kind of tell that there's
+ 
+
+ align:start position:0%
+you can kind of tell that there's
+something with drugs going on people are
+
+ align:start position:0%
+something with drugs going on people are
+ 
+
+ align:start position:0%
+something with drugs going on people are
+talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the next one is the scary Highway ever
+
+ align:start position:0%
+the next one is the scary Highway ever
+ 
+
+ align:start position:0%
+the next one is the scary Highway ever
+pass
+
+ align:start position:0%
+pass
+ 
+
+ align:start position:0%
+pass
+too that was very
+
+ align:start position:0%
+too that was very
+ 
+
+ align:start position:0%
+too that was very
+traumatized um and next one everybody
+
+ align:start position:0%
+traumatized um and next one everybody
+ 
+
+ align:start position:0%
+traumatized um and next one everybody
+knows everybody people pick up each
+
+ align:start position:0%
+knows everybody people pick up each
+ 
+
+ align:start position:0%
+knows everybody people pick up each
+other's kids that asking like people are
+
+ align:start position:0%
+other's kids that asking like people are
+ 
+
+ align:start position:0%
+other's kids that asking like people are
+just really kind of you you can tell
+
+ align:start position:0%
+just really kind of you you can tell
+ 
+
+ align:start position:0%
+just really kind of you you can tell
+when you walk in stores and everything
+
+ align:start position:0%
+when you walk in stores and everything
+ 
+
+ align:start position:0%
+when you walk in stores and everything
+everybody part of it we're walking
+
+ align:start position:0%
+everybody part of it we're walking
+ 
+
+ align:start position:0%
+everybody part of it we're walking
+around with
+
+ align:start position:0%
+around with
+ 
+
+ align:start position:0%
+around with
+Myra and also women seem to write a lot
+
+ align:start position:0%
+Myra and also women seem to write a lot
+ 
+
+ align:start position:0%
+Myra and also women seem to write a lot
+of the datto day community activities
+
+ align:start position:0%
+of the datto day community activities
+ 
+
+ align:start position:0%
+of the datto day community activities
+like just like in the shops the
+
+ align:start position:0%
+like just like in the shops the
+ 
+
+ align:start position:0%
+like just like in the shops the
+shopkeepers to be wom people on stuff
+
+ align:start position:0%
+shopkeepers to be wom people on stuff
+ 
+
+ align:start position:0%
+shopkeepers to be wom people on stuff
+like B maybe that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could oh like women tend to run they
+
+ align:start position:0%
+could oh like women tend to run they
+ 
+
+ align:start position:0%
+could oh like women tend to run they
+just seem to be a lot of like women tend
+
+ align:start position:0%
+just seem to be a lot of like women tend
+ 
+
+ align:start position:0%
+just seem to be a lot of like women tend
+to have like a really positive strong
+
+ align:start position:0%
+to have like a really positive strong
+ 
+
+ align:start position:0%
+to have like a really positive strong
+role in the community like just walking
+
+ align:start position:0%
+role in the community like just walking
+ 
+
+ align:start position:0%
+role in the community like just walking
+around like even a lot of people that
+
+ align:start position:0%
+around like even a lot of people that
+ 
+
+ align:start position:0%
+around like even a lot of people that
+work at stores are tend to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be the first thing that I thought would
+
+ align:start position:0%
+be the first thing that I thought would
+ 
+
+ align:start position:0%
+be the first thing that I thought would
+be important was that they seem very
+
+ align:start position:0%
+be important was that they seem very
+ 
+
+ align:start position:0%
+be important was that they seem very
+interesting what we have to say I'm
+
+ align:start position:0%
+interesting what we have to say I'm
+ 
+
+ align:start position:0%
+interesting what we have to say I'm
+going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put um another thing I guess maybe that
+
+ align:start position:0%
+put um another thing I guess maybe that
+ 
+
+ align:start position:0%
+put um another thing I guess maybe that
+there is some State involvement that
+
+ align:start position:0%
+there is some State involvement that
+ 
+
+ align:start position:0%
+there is some State involvement that
+they're not talking about but it seemed
+
+ align:start position:0%
+they're not talking about but it seemed
+ 
+
+ align:start position:0%
+they're not talking about but it seemed
+like they weren't really engaging with
+
+ align:start position:0%
+like they weren't really engaging with
+ 
+
+ align:start position:0%
+like they weren't really engaging with
+the state that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seem and uh in the same way they seem to
+
+ align:start position:0%
+seem and uh in the same way they seem to
+ 
+
+ align:start position:0%
+seem and uh in the same way they seem to
+not really be connecting with the rest
+
+ align:start position:0%
+not really be connecting with the rest
+ 
+
+ align:start position:0%
+not really be connecting with the rest
+of the city either on social or
+
+ align:start position:0%
+of the city either on social or
+ 
+
+ align:start position:0%
+of the city either on social or
+political level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative I mean maybe it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Neal might want to believe people seem
+
+ align:start position:0%
+Neal might want to believe people seem
+ 
+
+ align:start position:0%
+Neal might want to believe people seem
+very interested in making the most of
+
+ align:start position:0%
+very interested in making the most of
+ 
+
+ align:start position:0%
+very interested in making the most of
+the infrastructure they're part of so
+
+ align:start position:0%
+the infrastructure they're part of so
+ 
+
+ align:start position:0%
+the infrastructure they're part of so
+meaning whatever that thing was called
+
+ align:start position:0%
+meaning whatever that thing was called
+ 
+
+ align:start position:0%
+meaning whatever that thing was called
+the the school and all those Community
+
+ align:start position:0%
+the the school and all those Community
+ 
+
+ align:start position:0%
+the the school and all those Community
+rooms but that seemed like that could be
+
+ align:start position:0%
+rooms but that seemed like that could be
+ 
+
+ align:start position:0%
+rooms but that seemed like that could be
+positive or negative because maybe
+
+ align:start position:0%
+positive or negative because maybe
+ 
+
+ align:start position:0%
+positive or negative because maybe
+that's not really the way to go so
+
+ align:start position:0%
+that's not really the way to go so
+ 
+
+ align:start position:0%
+that's not really the way to go so
+mix
+
+ align:start position:0%
+mix
+ 
+
+ align:start position:0%
+mix
+bag and uh finally I felt like they were
+
+ align:start position:0%
+bag and uh finally I felt like they were
+ 
+
+ align:start position:0%
+bag and uh finally I felt like they were
+very helpful for the future of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Community First I have that the staff at
+
+ align:start position:0%
+Community First I have that the staff at
+ 
+
+ align:start position:0%
+Community First I have that the staff at
+neon is very committed and knowledgeable
+
+ align:start position:0%
+neon is very committed and knowledgeable
+ 
+
+ align:start position:0%
+neon is very committed and knowledgeable
+and capable and that came out very
+
+ align:start position:0%
+and capable and that came out very
+ 
+
+ align:start position:0%
+and capable and that came out very
+positive but I meant it actually more as
+
+ align:start position:0%
+positive but I meant it actually more as
+ 
+
+ align:start position:0%
+positive but I meant it actually more as
+a mixed bag
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean I think I was that my first
+
+ align:start position:0%
+I mean I think I was that my first
+ 
+
+ align:start position:0%
+I mean I think I was that my first
+impression but then I after back that's
+
+ align:start position:0%
+impression but then I after back that's
+ 
+
+ align:start position:0%
+impression but then I after back that's
+can be a dangerous thing especially when
+
+ align:start position:0%
+can be a dangerous thing especially when
+ 
+
+ align:start position:0%
+can be a dangerous thing especially when
+there're our client and we working for
+
+ align:start position:0%
+there're our client and we working for
+ 
+
+ align:start position:0%
+there're our client and we working for
+them you yeah I'm trying to find what
+
+ align:start position:0%
+them you yeah I'm trying to find what
+ 
+
+ align:start position:0%
+them you yeah I'm trying to find what
+the what well just because there's a
+
+ align:start position:0%
+the what well just because there's a
+ 
+
+ align:start position:0%
+the what well just because there's a
+danger that we completely accept their
+
+ align:start position:0%
+danger that we completely accept their
+ 
+
+ align:start position:0%
+danger that we completely accept their
+perceptions of things that they give us
+
+ align:start position:0%
+perceptions of things that they give us
+ 
+
+ align:start position:0%
+perceptions of things that they give us
+only one side of isues like Jeff the B
+
+ align:start position:0%
+only one side of isues like Jeff the B
+ 
+
+ align:start position:0%
+only one side of isues like Jeff the B
+St and I think that that can be
+
+ align:start position:0%
+St and I think that that can be
+ 
+
+ align:start position:0%
+St and I think that that can be
+dangerous uh second there was a Vibrance
+
+ align:start position:0%
+dangerous uh second there was a Vibrance
+ 
+
+ align:start position:0%
+dangerous uh second there was a Vibrance
+to the school area that really be When
+
+ align:start position:0%
+to the school area that really be When
+ 
+
+ align:start position:0%
+to the school area that really be When
+the Children weren't there so it was
+
+ align:start position:0%
+the Children weren't there so it was
+ 
+
+ align:start position:0%
+the Children weren't there so it was
+easy to see it when you we got of school
+
+ align:start position:0%
+easy to see it when you we got of school
+ 
+
+ align:start position:0%
+easy to see it when you we got of school
+and there was like everyone R around but
+
+ align:start position:0%
+and there was like everyone R around but
+ 
+
+ align:start position:0%
+and there was like everyone R around but
+even when uh we were there before the
+
+ align:start position:0%
+even when uh we were there before the
+ 
+
+ align:start position:0%
+even when uh we were there before the
+the whole complex was not nearly as bad
+
+ align:start position:0%
+the whole complex was not nearly as bad
+ 
+
+ align:start position:0%
+the whole complex was not nearly as bad
+as I pictured it to be so I thought that
+
+ align:start position:0%
+as I pictured it to be so I thought that
+ 
+
+ align:start position:0%
+as I pictured it to be so I thought that
+was a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing uh the change of Main Street um
+
+ align:start position:0%
+thing uh the change of Main Street um
+ 
+
+ align:start position:0%
+thing uh the change of Main Street um
+was really drastic throughout the city
+
+ align:start position:0%
+was really drastic throughout the city
+ 
+
+ align:start position:0%
+was really drastic throughout the city
+and I think that's also Mi B I think I
+
+ align:start position:0%
+and I think that's also Mi B I think I
+ 
+
+ align:start position:0%
+and I think that's also Mi B I think I
+don't think M Street needs or should
+
+ align:start position:0%
+don't think M Street needs or should
+ 
+
+ align:start position:0%
+don't think M Street needs or should
+necessarily be one continous supporter
+
+ align:start position:0%
+necessarily be one continous supporter
+ 
+
+ align:start position:0%
+necessarily be one continous supporter
+throughout the whole city you that have
+
+ align:start position:0%
+throughout the whole city you that have
+ 
+
+ align:start position:0%
+throughout the whole city you that have
+different strengths and character um but
+
+ align:start position:0%
+different strengths and character um but
+ 
+
+ align:start position:0%
+different strengths and character um but
+at the same time it was um it was not
+
+ align:start position:0%
+at the same time it was um it was not
+ 
+
+ align:start position:0%
+at the same time it was um it was not
+necessarily A thriving kind of like
+
+ align:start position:0%
+necessarily A thriving kind of like
+ 
+
+ align:start position:0%
+necessarily A thriving kind of like
+retail or commercial area in the north
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+east uh there's a lot of vacant
+
+ align:start position:0%
+east uh there's a lot of vacant
+ 
+
+ align:start position:0%
+east uh there's a lot of vacant
+developable land developable developable
+
+ align:start position:0%
+developable land developable developable
+ 
+
+ align:start position:0%
+developable land developable developable
+land uh the North End also I think a
+
+ align:start position:0%
+land uh the North End also I think a
+ 
+
+ align:start position:0%
+land uh the North End also I think a
+mixed value I think at the time at
+
+ align:start position:0%
+mixed value I think at the time at
+ 
+
+ align:start position:0%
+mixed value I think at the time at
+present it's not the best in we need but
+
+ align:start position:0%
+present it's not the best in we need but
+ 
+
+ align:start position:0%
+present it's not the best in we need but
+that means a lot of opportunity for
+
+ align:start position:0%
+that means a lot of opportunity for
+ 
+
+ align:start position:0%
+that means a lot of opportunity for
+us and will describe the
+
+ align:start position:0%
+us and will describe the
+ 
+
+ align:start position:0%
+us and will describe the
+change the the Brightway Development
+
+ align:start position:0%
+change the the Brightway Development
+ 
+
+ align:start position:0%
+change the the Brightway Development
+Corporation like the change in their
+
+ align:start position:0%
+Corporation like the change in their
+ 
+
+ align:start position:0%
+Corporation like the change in their
+presence in the community and I still
+
+ align:start position:0%
+presence in the community and I still
+ 
+
+ align:start position:0%
+presence in the community and I still
+fully understand the story simply there
+
+ align:start position:0%
+fully understand the story simply there
+ 
+
+ align:start position:0%
+fully understand the story simply there
+was kind of a lot of politics around
+
+ align:start position:0%
+was kind of a lot of politics around
+ 
+
+ align:start position:0%
+was kind of a lot of politics around
+that um so but I think just the whole
+
+ align:start position:0%
+that um so but I think just the whole
+ 
+
+ align:start position:0%
+that um so but I think just the whole
+part Development Corporation presence
+
+ align:start position:0%
+part Development Corporation presence
+ 
+
+ align:start position:0%
+part Development Corporation presence
+might be a negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay positive uh
+
+ align:start position:0%
+okay positive uh
+ 
+
+ align:start position:0%
+okay positive uh
+the um the midday s of community
+
+ align:start position:0%
+the um the midday s of community
+ 
+
+ align:start position:0%
+the um the midday s of community
+Vitality that we saw we got there you
+
+ align:start position:0%
+Vitality that we saw we got there you
+ 
+
+ align:start position:0%
+Vitality that we saw we got there you
+know at night was kind of calm was kind
+
+ align:start position:0%
+know at night was kind of calm was kind
+ 
+
+ align:start position:0%
+know at night was kind of calm was kind
+of calm day people walking around it was
+
+ align:start position:0%
+of calm day people walking around it was
+ 
+
+ align:start position:0%
+of calm day people walking around it was
+like very positive energy um a negative
+
+ align:start position:0%
+like very positive energy um a negative
+ 
+
+ align:start position:0%
+like very positive energy um a negative
+uh the condition of the elementary
+
+ align:start position:0%
+uh the condition of the elementary
+ 
+
+ align:start position:0%
+uh the condition of the elementary
+school and the flooding made me very
+
+ align:start position:0%
+school and the flooding made me very
+ 
+
+ align:start position:0%
+school and the flooding made me very
+nervous I wasn't really comfortable with
+
+ align:start position:0%
+nervous I wasn't really comfortable with
+ 
+
+ align:start position:0%
+nervous I wasn't really comfortable with
+sort of um I mean it's it's definitely
+
+ align:start position:0%
+sort of um I mean it's it's definitely
+ 
+
+ align:start position:0%
+sort of um I mean it's it's definitely
+an asset and they a lot with it but as
+
+ align:start position:0%
+an asset and they a lot with it but as
+ 
+
+ align:start position:0%
+an asset and they a lot with it but as
+far as how it might be used any plans we
+
+ align:start position:0%
+far as how it might be used any plans we
+ 
+
+ align:start position:0%
+far as how it might be used any plans we
+make um just something that keep in mind
+
+ align:start position:0%
+make um just something that keep in mind
+ 
+
+ align:start position:0%
+make um just something that keep in mind
+that are
+
+ align:start position:0%
+that are
+ 
+
+ align:start position:0%
+that are
+there so um what else uh mixed bag
+
+ align:start position:0%
+there so um what else uh mixed bag
+ 
+
+ align:start position:0%
+there so um what else uh mixed bag
+majority of the neon folks that um I saw
+
+ align:start position:0%
+majority of the neon folks that um I saw
+ 
+
+ align:start position:0%
+majority of the neon folks that um I saw
+I interacted with were women which I
+
+ align:start position:0%
+I interacted with were women which I
+ 
+
+ align:start position:0%
+I interacted with were women which I
+think you know are self- importantly is
+
+ align:start position:0%
+think you know are self- importantly is
+ 
+
+ align:start position:0%
+think you know are self- importantly is
+great but at the same time you know it's
+
+ align:start position:0%
+great but at the same time you know it's
+ 
+
+ align:start position:0%
+great but at the same time you know it's
+not just so something
+
+ align:start position:0%
+not just so something
+ 
+
+ align:start position:0%
+not just so something
+that positive strength of all the
+
+ align:start position:0%
+that positive strength of all the
+ 
+
+ align:start position:0%
+that positive strength of all the
+relationships that I saw familial
+
+ align:start position:0%
+relationships that I saw familial
+ 
+
+ align:start position:0%
+relationships that I saw familial
+professional and general community and a
+
+ align:start position:0%
+professional and general community and a
+ 
+
+ align:start position:0%
+professional and general community and a
+negative last one the palpable well
+
+ align:start position:0%
+negative last one the palpable well
+ 
+
+ align:start position:0%
+negative last one the palpable well
+maybe mix bag um the difference in the
+
+ align:start position:0%
+maybe mix bag um the difference in the
+ 
+
+ align:start position:0%
+maybe mix bag um the difference in the
+feel between the Brightwood and the
+
+ align:start position:0%
+feel between the Brightwood and the
+ 
+
+ align:start position:0%
+feel between the Brightwood and the
+memorial Square size um and as we try to
+
+ align:start position:0%
+memorial Square size um and as we try to
+ 
+
+ align:start position:0%
+memorial Square size um and as we try to
+figure out what to do you know it's
+
+ align:start position:0%
+figure out what to do you know it's
+ 
+
+ align:start position:0%
+figure out what to do you know it's
+possible that we decide to
+
+ align:start position:0%
+possible that we decide to
+ 
+
+ align:start position:0%
+possible that we decide to
+have ideas things that will maintain
+
+ align:start position:0%
+have ideas things that will maintain
+ 
+
+ align:start position:0%
+have ideas things that will maintain
+that difference because it's something
+
+ align:start position:0%
+that difference because it's something
+ 
+
+ align:start position:0%
+that difference because it's something
+that we really can tackle or I don't
+
+ align:start position:0%
+that we really can tackle or I don't
+ 
+
+ align:start position:0%
+that we really can tackle or I don't
+know it could be an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead
+
+ align:start position:0%
+ahead
+ 
+
+ align:start position:0%
+ahead
+um I have lots of vacant buildings and
+
+ align:start position:0%
+um I have lots of vacant buildings and
+ 
+
+ align:start position:0%
+um I have lots of vacant buildings and
+lots I'm going to put that as a negative
+
+ align:start position:0%
+lots I'm going to put that as a negative
+ 
+
+ align:start position:0%
+lots I'm going to put that as a negative
+although John classified it as a mixed
+
+ align:start position:0%
+although John classified it as a mixed
+ 
+
+ align:start position:0%
+although John classified it as a mixed
+bag but think now it's kind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um kind of used a fancy planning word
+
+ align:start position:0%
+um kind of used a fancy planning word
+ 
+
+ align:start position:0%
+um kind of used a fancy planning word
+but I uh I call the dominance of
+
+ align:start position:0%
+but I uh I call the dominance of
+ 
+
+ align:start position:0%
+but I uh I call the dominance of
+automobility between neighborhoods so
+
+ align:start position:0%
+automobility between neighborhoods so
+ 
+
+ align:start position:0%
+automobility between neighborhoods so
+that scary overcat pets um which is the
+
+ align:start position:0%
+that scary overcat pets um which is the
+ 
+
+ align:start position:0%
+that scary overcat pets um which is the
+negative in my you know my own
+
+ align:start position:0%
+negative in my you know my own
+ 
+
+ align:start position:0%
+negative in my you know my own
+perspective
+
+ align:start position:0%
+perspective
+ 
+
+ align:start position:0%
+perspective
+um I have a Bay State Suburban campus
+
+ align:start position:0%
+um I have a Bay State Suburban campus
+ 
+
+ align:start position:0%
+um I have a Bay State Suburban campus
+versus the neighborhood's Urban
+
+ align:start position:0%
+versus the neighborhood's Urban
+ 
+
+ align:start position:0%
+versus the neighborhood's Urban
+grid which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's just kind of a disconnect and
+
+ align:start position:0%
+but it's just kind of a disconnect and
+ 
+
+ align:start position:0%
+but it's just kind of a disconnect and
+then kind of similar I I felt similarly
+
+ align:start position:0%
+then kind of similar I I felt similarly
+ 
+
+ align:start position:0%
+then kind of similar I I felt similarly
+to an did about the neighbor the
+
+ align:start position:0%
+to an did about the neighbor the
+ 
+
+ align:start position:0%
+to an did about the neighbor the
+different neighborhoods as well um the
+
+ align:start position:0%
+different neighborhoods as well um the
+ 
+
+ align:start position:0%
+different neighborhoods as well um the
+positive is the deep roots of neon in
+
+ align:start position:0%
+positive is the deep roots of neon in
+ 
+
+ align:start position:0%
+positive is the deep roots of neon in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+neighborhood and then my final one is uh
+
+ align:start position:0%
+neighborhood and then my final one is uh
+ 
+
+ align:start position:0%
+neighborhood and then my final one is uh
+which I'm going to put as a mixed bag is
+
+ align:start position:0%
+which I'm going to put as a mixed bag is
+ 
+
+ align:start position:0%
+which I'm going to put as a mixed bag is
+the resilience of the underground
+
+ align:start position:0%
+the resilience of the underground
+ 
+
+ align:start position:0%
+the resilience of the underground
+school I think there's something just
+
+ align:start position:0%
+school I think there's something just
+ 
+
+ align:start position:0%
+school I think there's something just
+weird about having a school underground
+
+ align:start position:0%
+weird about having a school underground
+ 
+
+ align:start position:0%
+weird about having a school underground
+um and that it's flooded yet um people
+
+ align:start position:0%
+um and that it's flooded yet um people
+ 
+
+ align:start position:0%
+um and that it's flooded yet um people
+are committed to it um but it also kind
+
+ align:start position:0%
+are committed to it um but it also kind
+ 
+
+ align:start position:0%
+are committed to it um but it also kind
+of buries Vitality underground in a way
+
+ align:start position:0%
+of buries Vitality underground in a way
+ 
+
+ align:start position:0%
+of buries Vitality underground in a way
+um but that's something I think we we
+
+ align:start position:0%
+um but that's something I think we we
+ 
+
+ align:start position:0%
+um but that's something I think we we
+need to discuss and
+
+ align:start position:0%
+need to discuss and
+ 
+
+ align:start position:0%
+need to discuss and
+Tackle so M are kind of experiences I
+
+ align:start position:0%
+Tackle so M are kind of experiences I
+ 
+
+ align:start position:0%
+Tackle so M are kind of experiences I
+been there's so many so many times um
+
+ align:start position:0%
+been there's so many so many times um
+ 
+
+ align:start position:0%
+been there's so many so many times um
+but actually one new one for me was when
+
+ align:start position:0%
+but actually one new one for me was when
+ 
+
+ align:start position:0%
+but actually one new one for me was when
+we left the herena school and walked up
+
+ align:start position:0%
+we left the herena school and walked up
+ 
+
+ align:start position:0%
+we left the herena school and walked up
+Main Street under the highway into the
+
+ align:start position:0%
+Main Street under the highway into the
+ 
+
+ align:start position:0%
+Main Street under the highway into the
+complex area where state is and just the
+
+ align:start position:0%
+complex area where state is and just the
+ 
+
+ align:start position:0%
+complex area where state is and just the
+difference of walking from one side of
+
+ align:start position:0%
+difference of walking from one side of
+ 
+
+ align:start position:0%
+difference of walking from one side of
+that underpass overpass to the other
+
+ align:start position:0%
+that underpass overpass to the other
+ 
+
+ align:start position:0%
+that underpass overpass to the other
+side uh and what was there and I I it's
+
+ align:start position:0%
+side uh and what was there and I I it's
+ 
+
+ align:start position:0%
+side uh and what was there and I I it's
+for me it's a negative because it's
+
+ align:start position:0%
+for me it's a negative because it's
+ 
+
+ align:start position:0%
+for me it's a negative because it's
+really about things just not
+
+ align:start position:0%
+really about things just not
+ 
+
+ align:start position:0%
+really about things just not
+connecting
+
+ align:start position:0%
+connecting
+ 
+
+ align:start position:0%
+connecting
+uh this is just always the truth it's
+
+ align:start position:0%
+uh this is just always the truth it's
+ 
+
+ align:start position:0%
+uh this is just always the truth it's
+really the kind of warmth with which
+
+ align:start position:0%
+really the kind of warmth with which
+ 
+
+ align:start position:0%
+really the kind of warmth with which
+people greet everyone and us and folks
+
+ align:start position:0%
+people greet everyone and us and folks
+ 
+
+ align:start position:0%
+people greet everyone and us and folks
+that they don't
+
+ align:start position:0%
+that they don't
+ 
+
+ align:start position:0%
+that they don't
+know uh the scary Bridge experience of
+
+ align:start position:0%
+know uh the scary Bridge experience of
+ 
+
+ align:start position:0%
+know uh the scary Bridge experience of
+walking across from Memorial Square to
+
+ align:start position:0%
+walking across from Memorial Square to
+ 
+
+ align:start position:0%
+walking across from Memorial Square to
+Brightwood the top of the highway you
+
+ align:start position:0%
+Brightwood the top of the highway you
+ 
+
+ align:start position:0%
+Brightwood the top of the highway you
+know in single file like the Little D
+
+ align:start position:0%
+know in single file like the Little D
+ 
+
+ align:start position:0%
+know in single file like the Little D
+ducklings and uh that was very scary um
+
+ align:start position:0%
+ducklings and uh that was very scary um
+ 
+
+ align:start position:0%
+ducklings and uh that was very scary um
+I also thought the lack of variety in
+
+ align:start position:0%
+I also thought the lack of variety in
+ 
+
+ align:start position:0%
+I also thought the lack of variety in
+the kinds of small businesses they were
+
+ align:start position:0%
+the kinds of small businesses they were
+ 
+
+ align:start position:0%
+the kinds of small businesses they were
+either grocery stores or grocery stores
+
+ align:start position:0%
+either grocery stores or grocery stores
+ 
+
+ align:start position:0%
+either grocery stores or grocery stores
+or restaurants and that was basically it
+
+ align:start position:0%
+or restaurants and that was basically it
+ 
+
+ align:start position:0%
+or restaurants and that was basically it
+and that didn't seem very viable uh to
+
+ align:start position:0%
+and that didn't seem very viable uh to
+ 
+
+ align:start position:0%
+and that didn't seem very viable uh to
+me I think that's
+
+ align:start position:0%
+me I think that's
+ 
+
+ align:start position:0%
+me I think that's
+fire oh this one is oh and the number of
+
+ align:start position:0%
+fire oh this one is oh and the number of
+ 
+
+ align:start position:0%
+fire oh this one is oh and the number of
+board I was actually very surprised by
+
+ align:start position:0%
+board I was actually very surprised by
+ 
+
+ align:start position:0%
+board I was actually very surprised by
+but the number of boarded up houses from
+
+ align:start position:0%
+but the number of boarded up houses from
+ 
+
+ align:start position:0%
+but the number of boarded up houses from
+fire there were actually
+
+ align:start position:0%
+fire there were actually
+ 
+
+ align:start position:0%
+fire there were actually
+that was actually quite a change from
+
+ align:start position:0%
+that was actually quite a change from
+ 
+
+ align:start position:0%
+that was actually quite a change from
+the last time I had walked through the
+
+ align:start position:0%
+the last time I had walked through the
+ 
+
+ align:start position:0%
+the last time I had walked through the
+neighborhood
+
+ align:start position:0%
+neighborhood
+ 
+
+ align:start position:0%
+neighborhood
+so uh it was last
+
+ align:start position:0%
+so uh it was last
+ 
+
+ align:start position:0%
+so uh it was last
+spring actually was it last spring or
+
+ align:start position:0%
+spring actually was it last spring or
+ 
+
+ align:start position:0%
+spring actually was it last spring or
+well it was in January so that's not
+
+ align:start position:0%
+well it was in January so that's not
+ 
+
+ align:start position:0%
+well it was in January so that's not
+really spring that's winter isn't it
+
+ align:start position:0%
+really spring that's winter isn't it
+ 
+
+ align:start position:0%
+really spring that's winter isn't it
+yeah spring semester months
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay how much you feel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would it seemed double at least you know
+
+ align:start position:0%
+would it seemed double at least you know
+ 
+
+ align:start position:0%
+would it seemed double at least you know
+just was it in one area more than yeah
+
+ align:start position:0%
+just was it in one area more than yeah
+ 
+
+ align:start position:0%
+just was it in one area more than yeah
+in the in the square
+
+ align:start position:0%
+in the in the square
+ 
+
+ align:start position:0%
+in the in the square
+area um I thought that the scale of the
+
+ align:start position:0%
+area um I thought that the scale of the
+ 
+
+ align:start position:0%
+area um I thought that the scale of the
+vacant industrial buildings um you know
+
+ align:start position:0%
+vacant industrial buildings um you know
+ 
+
+ align:start position:0%
+vacant industrial buildings um you know
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+were quite large um some in pretty bad
+
+ align:start position:0%
+were quite large um some in pretty bad
+ 
+
+ align:start position:0%
+were quite large um some in pretty bad
+shape you know clearly some serious
+
+ align:start position:0%
+shape you know clearly some serious
+ 
+
+ align:start position:0%
+shape you know clearly some serious
+Brownfield issues so that that was going
+
+ align:start position:0%
+Brownfield issues so that that was going
+ 
+
+ align:start position:0%
+Brownfield issues so that that was going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+be and I thought it
+
+ align:start position:0%
+be and I thought it
+ 
+
+ align:start position:0%
+be and I thought it
+um while they weren't at the center of
+
+ align:start position:0%
+um while they weren't at the center of
+ 
+
+ align:start position:0%
+um while they weren't at the center of
+the neighborhood they certainly you know
+
+ align:start position:0%
+the neighborhood they certainly you know
+ 
+
+ align:start position:0%
+the neighborhood they certainly you know
+had a strong a strong impact um and then
+
+ align:start position:0%
+had a strong a strong impact um and then
+ 
+
+ align:start position:0%
+had a strong a strong impact um and then
+another negative The Limited knowledge
+
+ align:start position:0%
+another negative The Limited knowledge
+ 
+
+ align:start position:0%
+another negative The Limited knowledge
+of businesses and residents at least
+
+ align:start position:0%
+of businesses and residents at least
+ 
+
+ align:start position:0%
+of businesses and residents at least
+among the Outreach worker and our tour
+
+ align:start position:0%
+among the Outreach worker and our tour
+ 
+
+ align:start position:0%
+among the Outreach worker and our tour
+um I was I was very surprised how little
+
+ align:start position:0%
+um I was I was very surprised how little
+ 
+
+ align:start position:0%
+um I was I was very surprised how little
+he seemed to know about you know who
+
+ align:start position:0%
+he seemed to know about you know who
+ 
+
+ align:start position:0%
+he seemed to know about you know who
+were these businesses who did they
+
+ align:start position:0%
+were these businesses who did they
+ 
+
+ align:start position:0%
+were these businesses who did they
+employ where did people work um and I I
+
+ align:start position:0%
+employ where did people work um and I I
+ 
+
+ align:start position:0%
+employ where did people work um and I I
+sort of fear it's kind of emblematic of
+
+ align:start position:0%
+sort of fear it's kind of emblematic of
+ 
+
+ align:start position:0%
+sort of fear it's kind of emblematic of
+the lack of relationships between some
+
+ align:start position:0%
+the lack of relationships between some
+ 
+
+ align:start position:0%
+the lack of relationships between some
+of the organizations and The Business
+
+ align:start position:0%
+of the organizations and The Business
+ 
+
+ align:start position:0%
+of the organizations and The Business
+Community although I don't really know
+
+ align:start position:0%
+Community although I don't really know
+ 
+
+ align:start position:0%
+Community although I don't really know
+that um I think on a positive side um I
+
+ align:start position:0%
+that um I think on a positive side um I
+ 
+
+ align:start position:0%
+that um I think on a positive side um I
+I was actually quite surprised by the
+
+ align:start position:0%
+I was actually quite surprised by the
+ 
+
+ align:start position:0%
+I was actually quite surprised by the
+level and diversity of economic activity
+
+ align:start position:0%
+level and diversity of economic activity
+ 
+
+ align:start position:0%
+level and diversity of economic activity
+in the neighborhood when you really add
+
+ align:start position:0%
+in the neighborhood when you really add
+ 
+
+ align:start position:0%
+in the neighborhood when you really add
+everything up with with base state with
+
+ align:start position:0%
+everything up with with base state with
+ 
+
+ align:start position:0%
+everything up with with base state with
+the small scale retail there's even some
+
+ align:start position:0%
+the small scale retail there's even some
+ 
+
+ align:start position:0%
+the small scale retail there's even some
+Distributors there you have all those
+
+ align:start position:0%
+Distributors there you have all those
+ 
+
+ align:start position:0%
+Distributors there you have all those
+Transportation businesses and then you
+
+ align:start position:0%
+Transportation businesses and then you
+ 
+
+ align:start position:0%
+Transportation businesses and then you
+have industry you know um um um it was
+
+ align:start position:0%
+have industry you know um um um it was
+ 
+
+ align:start position:0%
+have industry you know um um um it was
+it was quite diverse and and probably if
+
+ align:start position:0%
+it was quite diverse and and probably if
+ 
+
+ align:start position:0%
+it was quite diverse and and probably if
+you counted up all those jobs you know
+
+ align:start position:0%
+you counted up all those jobs you know
+ 
+
+ align:start position:0%
+you counted up all those jobs you know
+there's there's probably um you know a
+
+ align:start position:0%
+there's there's probably um you know a
+ 
+
+ align:start position:0%
+there's there's probably um you know a
+number of jobs that may equal or exceed
+
+ align:start position:0%
+number of jobs that may equal or exceed
+ 
+
+ align:start position:0%
+number of jobs that may equal or exceed
+you know the workforce that's in the
+
+ align:start position:0%
+you know the workforce that's in the
+ 
+
+ align:start position:0%
+you know the workforce that's in the
+neighborhood um I think probably the
+
+ align:start position:0%
+neighborhood um I think probably the
+ 
+
+ align:start position:0%
+neighborhood um I think probably the
+thing that impressed me the most was the
+
+ align:start position:0%
+thing that impressed me the most was the
+ 
+
+ align:start position:0%
+thing that impressed me the most was the
+accomplishments of neon and the
+
+ align:start position:0%
+accomplishments of neon and the
+ 
+
+ align:start position:0%
+accomplishments of neon and the
+Brightwood Health Center um and bringing
+
+ align:start position:0%
+Brightwood Health Center um and bringing
+ 
+
+ align:start position:0%
+Brightwood Health Center um and bringing
+back about some of the systematic change
+
+ align:start position:0%
+back about some of the systematic change
+ 
+
+ align:start position:0%
+back about some of the systematic change
+in the health care bringing you know
+
+ align:start position:0%
+in the health care bringing you know
+ 
+
+ align:start position:0%
+in the health care bringing you know
+getting the UN insurance rate cut in
+
+ align:start position:0%
+getting the UN insurance rate cut in
+ 
+
+ align:start position:0%
+getting the UN insurance rate cut in
+half um you know changing the model in
+
+ align:start position:0%
+half um you know changing the model in
+ 
+
+ align:start position:0%
+half um you know changing the model in
+which Healthcare was delivered getting
+
+ align:start position:0%
+which Healthcare was delivered getting
+ 
+
+ align:start position:0%
+which Healthcare was delivered getting
+better health care for the prison
+
+ align:start position:0%
+better health care for the prison
+ 
+
+ align:start position:0%
+better health care for the prison
+population that sure could really shows
+
+ align:start position:0%
+population that sure could really shows
+ 
+
+ align:start position:0%
+population that sure could really shows
+some some creative thinking and some
+
+ align:start position:0%
+some some creative thinking and some
+ 
+
+ align:start position:0%
+some some creative thinking and some
+significant capacity to get things done
+
+ align:start position:0%
+significant capacity to get things done
+ 
+
+ align:start position:0%
+significant capacity to get things done
+um and this I'll say is sort of neutral
+
+ align:start position:0%
+um and this I'll say is sort of neutral
+ 
+
+ align:start position:0%
+um and this I'll say is sort of neutral
+that the contrast between the two parts
+
+ align:start position:0%
+that the contrast between the two parts
+ 
+
+ align:start position:0%
+that the contrast between the two parts
+of the neighborhood I mean it was it was
+
+ align:start position:0%
+of the neighborhood I mean it was it was
+ 
+
+ align:start position:0%
+of the neighborhood I mean it was it was
+even after reading about it it did they
+
+ align:start position:0%
+even after reading about it it did they
+ 
+
+ align:start position:0%
+even after reading about it it did they
+really felt with two different worlds um
+
+ align:start position:0%
+really felt with two different worlds um
+ 
+
+ align:start position:0%
+really felt with two different worlds um
+the sort of very maybe it was because of
+
+ align:start position:0%
+the sort of very maybe it was because of
+ 
+
+ align:start position:0%
+the sort of very maybe it was because of
+of the time of day but this's very very
+
+ align:start position:0%
+of the time of day but this's very very
+ 
+
+ align:start position:0%
+of the time of day but this's very very
+quiet residential neighborhood with not
+
+ align:start position:0%
+quiet residential neighborhood with not
+ 
+
+ align:start position:0%
+quiet residential neighborhood with not
+many people out not much traffic and
+
+ align:start position:0%
+many people out not much traffic and
+ 
+
+ align:start position:0%
+many people out not much traffic and
+then Memorial Square you know with all
+
+ align:start position:0%
+then Memorial Square you know with all
+ 
+
+ align:start position:0%
+then Memorial Square you know with all
+that traffic and activity and everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so overall thoughts Impressions after
+
+ align:start position:0%
+so overall thoughts Impressions after
+ 
+
+ align:start position:0%
+so overall thoughts Impressions after
+kind of hearing everyone report out you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+commonalities what's the story you would
+
+ align:start position:0%
+commonalities what's the story you would
+ 
+
+ align:start position:0%
+commonalities what's the story you would
+take from what you just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heard I thought a lot of the positive
+
+ align:start position:0%
+heard I thought a lot of the positive
+ 
+
+ align:start position:0%
+heard I thought a lot of the positive
+comments have something to do with the
+
+ align:start position:0%
+comments have something to do with the
+ 
+
+ align:start position:0%
+comments have something to do with the
+human asset kind like a lot of people
+
+ align:start position:0%
+human asset kind like a lot of people
+ 
+
+ align:start position:0%
+human asset kind like a lot of people
+made positive observations about the
+
+ align:start position:0%
+made positive observations about the
+ 
+
+ align:start position:0%
+made positive observations about the
+human Network that existed in the area
+
+ align:start position:0%
+human Network that existed in the area
+ 
+
+ align:start position:0%
+human Network that existed in the area
+while a lot of the negative comments had
+
+ align:start position:0%
+while a lot of the negative comments had
+ 
+
+ align:start position:0%
+while a lot of the negative comments had
+more to do with the physical
+
+ align:start position:0%
+more to do with the physical
+ 
+
+ align:start position:0%
+more to do with the physical
+infrastructures or I don't know if
+
+ align:start position:0%
+infrastructures or I don't know if
+ 
+
+ align:start position:0%
+infrastructures or I don't know if
+economic activities are part of the
+
+ align:start position:0%
+economic activities are part of the
+ 
+
+ align:start position:0%
+economic activities are part of the
+physical infrastructures but um how the
+
+ align:start position:0%
+physical infrastructures but um how the
+ 
+
+ align:start position:0%
+physical infrastructures but um how the
+physical setting was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+present some people think about that as
+
+ align:start position:0%
+present some people think about that as
+ 
+
+ align:start position:0%
+present some people think about that as
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+observation that's good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pleas let me ask us um last week we
+
+ align:start position:0%
+pleas let me ask us um last week we
+ 
+
+ align:start position:0%
+pleas let me ask us um last week we
+talked a little about um how people are
+
+ align:start position:0%
+talked a little about um how people are
+ 
+
+ align:start position:0%
+talked a little about um how people are
+feeling about the sort of charge we've
+
+ align:start position:0%
+feeling about the sort of charge we've
+ 
+
+ align:start position:0%
+feeling about the sort of charge we've
+been given by Neon before they went out
+
+ align:start position:0%
+been given by Neon before they went out
+ 
+
+ align:start position:0%
+been given by Neon before they went out
+there and I'm curious now that you've
+
+ align:start position:0%
+there and I'm curious now that you've
+ 
+
+ align:start position:0%
+there and I'm curious now that you've
+been out in the neighborhood um and have
+
+ align:start position:0%
+been out in the neighborhood um and have
+ 
+
+ align:start position:0%
+been out in the neighborhood um and have
+you know have actually seen it and met
+
+ align:start position:0%
+you know have actually seen it and met
+ 
+
+ align:start position:0%
+you know have actually seen it and met
+the people people and have you know a
+
+ align:start position:0%
+the people people and have you know a
+ 
+
+ align:start position:0%
+the people people and have you know a
+richer sense of of um you know the the
+
+ align:start position:0%
+richer sense of of um you know the the
+ 
+
+ align:start position:0%
+richer sense of of um you know the the
+client and the community how how do that
+
+ align:start position:0%
+client and the community how how do that
+ 
+
+ align:start position:0%
+client and the community how how do that
+changed your thinking about about the
+
+ align:start position:0%
+changed your thinking about about the
+ 
+
+ align:start position:0%
+changed your thinking about about the
+project and your sort of optimism or
+
+ align:start position:0%
+project and your sort of optimism or
+ 
+
+ align:start position:0%
+project and your sort of optimism or
+pessimism about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I was the only one last week who said
+
+ align:start position:0%
+it I was the only one last week who said
+ 
+
+ align:start position:0%
+it I was the only one last week who said
+anything pessimistic or explicitly
+
+ align:start position:0%
+anything pessimistic or explicitly
+ 
+
+ align:start position:0%
+anything pessimistic or explicitly
+pessimist but I felt a lot more positive
+
+ align:start position:0%
+pessimist but I felt a lot more positive
+ 
+
+ align:start position:0%
+pessimist but I felt a lot more positive
+after having been there I I was really I
+
+ align:start position:0%
+after having been there I I was really I
+ 
+
+ align:start position:0%
+after having been there I I was really I
+guess kind of skeptical about what they
+
+ align:start position:0%
+guess kind of skeptical about what they
+ 
+
+ align:start position:0%
+guess kind of skeptical about what they
+expected from us in terms of whether
+
+ align:start position:0%
+expected from us in terms of whether
+ 
+
+ align:start position:0%
+expected from us in terms of whether
+they were really excited about being
+
+ align:start position:0%
+they were really excited about being
+ 
+
+ align:start position:0%
+they were really excited about being
+involved and like I gu didn't really
+
+ align:start position:0%
+involved and like I gu didn't really
+ 
+
+ align:start position:0%
+involved and like I gu didn't really
+realize that they had saw us out that
+
+ align:start position:0%
+realize that they had saw us out that
+ 
+
+ align:start position:0%
+realize that they had saw us out that
+there was kind of long relationship
+
+ align:start position:0%
+there was kind of long relationship
+ 
+
+ align:start position:0%
+there was kind of long relationship
+so I don't know I think that um just
+
+ align:start position:0%
+so I don't know I think that um just
+ 
+
+ align:start position:0%
+so I don't know I think that um just
+they're being excited about working with
+
+ align:start position:0%
+they're being excited about working with
+ 
+
+ align:start position:0%
+they're being excited about working with
+us it makes me excited about working
+
+ align:start position:0%
+us it makes me excited about working
+ 
+
+ align:start position:0%
+us it makes me excited about working
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+them um I'm still really positive but
+
+ align:start position:0%
+them um I'm still really positive but
+ 
+
+ align:start position:0%
+them um I'm still really positive but
+especially with all these colorful posts
+
+ align:start position:0%
+especially with all these colorful posts
+ 
+
+ align:start position:0%
+especially with all these colorful posts
+up no idea how we will accomplish
+
+ align:start position:0%
+up no idea how we will accomplish
+ 
+
+ align:start position:0%
+up no idea how we will accomplish
+anything by the end of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+St I ear as well I think that I felt
+
+ align:start position:0%
+St I ear as well I think that I felt
+ 
+
+ align:start position:0%
+St I ear as well I think that I felt
+very and I think that I I know I felt
+
+ align:start position:0%
+very and I think that I I know I felt
+ 
+
+ align:start position:0%
+very and I think that I I know I felt
+very um strongly about all the potential
+
+ align:start position:0%
+very um strongly about all the potential
+ 
+
+ align:start position:0%
+very um strongly about all the potential
+for what we as a group could
+
+ align:start position:0%
+for what we as a group could
+ 
+
+ align:start position:0%
+for what we as a group could
+do you know crafting and economic
+
+ align:start position:0%
+do you know crafting and economic
+ 
+
+ align:start position:0%
+do you know crafting and economic
+development plan once we got there
+
+ align:start position:0%
+development plan once we got there
+ 
+
+ align:start position:0%
+development plan once we got there
+walked around with a sense of what sort
+
+ align:start position:0%
+walked around with a sense of what sort
+ 
+
+ align:start position:0%
+walked around with a sense of what sort
+of of facilities and and business exist
+
+ align:start position:0%
+of of facilities and and business exist
+ 
+
+ align:start position:0%
+of of facilities and and business exist
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+community but then every time a neon
+
+ align:start position:0%
+community but then every time a neon
+ 
+
+ align:start position:0%
+community but then every time a neon
+worker would talk about any of those
+
+ align:start position:0%
+worker would talk about any of those
+ 
+
+ align:start position:0%
+worker would talk about any of those
+businesses or facilities or talk about
+
+ align:start position:0%
+businesses or facilities or talk about
+ 
+
+ align:start position:0%
+businesses or facilities or talk about
+their ideas what was you know what they
+
+ align:start position:0%
+their ideas what was you know what they
+ 
+
+ align:start position:0%
+their ideas what was you know what they
+com to consisted of it was quite
+
+ align:start position:0%
+com to consisted of it was quite
+ 
+
+ align:start position:0%
+com to consisted of it was quite
+worrisome because it seems almost like
+
+ align:start position:0%
+worrisome because it seems almost like
+ 
+
+ align:start position:0%
+worrisome because it seems almost like
+one of our biggest obstacles is going to
+
+ align:start position:0%
+one of our biggest obstacles is going to
+ 
+
+ align:start position:0%
+one of our biggest obstacles is going to
+be our
+
+ align:start position:0%
+be our
+ 
+
+ align:start position:0%
+be our
+client and reminds me of this at the
+
+ align:start position:0%
+client and reminds me of this at the
+ 
+
+ align:start position:0%
+client and reminds me of this at the
+time would seemed like a really weird
+
+ align:start position:0%
+time would seemed like a really weird
+ 
+
+ align:start position:0%
+time would seemed like a really weird
+question that our Gateway take home fin
+
+ align:start position:0%
+question that our Gateway take home fin
+ 
+
+ align:start position:0%
+question that our Gateway take home fin
+which is like what do you do if the
+
+ align:start position:0%
+which is like what do you do if the
+ 
+
+ align:start position:0%
+which is like what do you do if the
+community group you work for doesn't
+
+ align:start position:0%
+community group you work for doesn't
+ 
+
+ align:start position:0%
+community group you work for doesn't
+want you to do what you think you should
+
+ align:start position:0%
+want you to do what you think you should
+ 
+
+ align:start position:0%
+want you to do what you think you should
+be doing in their best
+
+ align:start position:0%
+be doing in their best
+ 
+
+ align:start position:0%
+be doing in their best
+interest like look up the code of ethics
+
+ align:start position:0%
+interest like look up the code of ethics
+ 
+
+ align:start position:0%
+interest like look up the code of ethics
+to answer that question as well the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I actually I would I mean I I don't want
+
+ align:start position:0%
+I actually I would I mean I I don't want
+ 
+
+ align:start position:0%
+I actually I would I mean I I don't want
+to dwell on one topic too much but I I
+
+ align:start position:0%
+to dwell on one topic too much but I I
+ 
+
+ align:start position:0%
+to dwell on one topic too much but I I
+just there was an anecdote I was
+
+ align:start position:0%
+just there was an anecdote I was
+ 
+
+ align:start position:0%
+just there was an anecdote I was
+thinking of that do tells what both Shan
+
+ align:start position:0%
+thinking of that do tells what both Shan
+ 
+
+ align:start position:0%
+thinking of that do tells what both Shan
+and Anna were saying which is that
+
+ align:start position:0%
+and Anna were saying which is that
+ 
+
+ align:start position:0%
+and Anna were saying which is that
+uh at lunch uh the kind of questions we
+
+ align:start position:0%
+uh at lunch uh the kind of questions we
+ 
+
+ align:start position:0%
+uh at lunch uh the kind of questions we
+were getting were making me wonder you
+
+ align:start position:0%
+were getting were making me wonder you
+ 
+
+ align:start position:0%
+were getting were making me wonder you
+know how free we were to give any plan
+
+ align:start position:0%
+know how free we were to give any plan
+ 
+
+ align:start position:0%
+know how free we were to give any plan
+that we felt appropriate or I mean
+
+ align:start position:0%
+that we felt appropriate or I mean
+ 
+
+ align:start position:0%
+that we felt appropriate or I mean
+granted we're probably free to say
+
+ align:start position:0%
+granted we're probably free to say
+ 
+
+ align:start position:0%
+granted we're probably free to say
+anything but it made me wonder how
+
+ align:start position:0%
+anything but it made me wonder how
+ 
+
+ align:start position:0%
+anything but it made me wonder how
+receptive um the clients would be to
+
+ align:start position:0%
+receptive um the clients would be to
+ 
+
+ align:start position:0%
+receptive um the clients would be to
+anything you know cuz we sat down and it
+
+ align:start position:0%
+anything you know cuz we sat down and it
+ 
+
+ align:start position:0%
+anything you know cuz we sat down and it
+seemed like the first question out of
+
+ align:start position:0%
+seemed like the first question out of
+ 
+
+ align:start position:0%
+seemed like the first question out of
+first thing out of anyone's mouth was so
+
+ align:start position:0%
+first thing out of anyone's mouth was so
+ 
+
+ align:start position:0%
+first thing out of anyone's mouth was so
+what do we do about all the vacant
+
+ align:start position:0%
+what do we do about all the vacant
+ 
+
+ align:start position:0%
+what do we do about all the vacant
+houses here and um so
+
+ align:start position:0%
+houses here and um so
+ 
+
+ align:start position:0%
+houses here and um so
+I'm and I'm not and that just
+
+ align:start position:0%
+I'm and I'm not and that just
+ 
+
+ align:start position:0%
+I'm and I'm not and that just
+immediately was seemed to narrow the
+
+ align:start position:0%
+immediately was seemed to narrow the
+ 
+
+ align:start position:0%
+immediately was seemed to narrow the
+whole discourse that we were
+
+ align:start position:0%
+whole discourse that we were
+ 
+
+ align:start position:0%
+whole discourse that we were
+participating in about Economic
+
+ align:start position:0%
+participating in about Economic
+ 
+
+ align:start position:0%
+participating in about Economic
+Development and our project there and
+
+ align:start position:0%
+Development and our project there and
+ 
+
+ align:start position:0%
+Development and our project there and
+then there were a series of other very
+
+ align:start position:0%
+then there were a series of other very
+ 
+
+ align:start position:0%
+then there were a series of other very
+specific questions so I'm uncertain as
+
+ align:start position:0%
+specific questions so I'm uncertain as
+ 
+
+ align:start position:0%
+specific questions so I'm uncertain as
+to whether or not uh even though there's
+
+ align:start position:0%
+to whether or not uh even though there's
+ 
+
+ align:start position:0%
+to whether or not uh even though there's
+a lot of community capacity I think to
+
+ align:start position:0%
+a lot of community capacity I think to
+ 
+
+ align:start position:0%
+a lot of community capacity I think to
+do Grassroots and do good
+
+ align:start position:0%
+do Grassroots and do good
+ 
+
+ align:start position:0%
+do Grassroots and do good
+work I just wonder
+
+ align:start position:0%
+work I just wonder
+ 
+
+ align:start position:0%
+work I just wonder
+if there is a trust or a level of
+
+ align:start position:0%
+if there is a trust or a level of
+ 
+
+ align:start position:0%
+if there is a trust or a level of
+openness
+
+ align:start position:0%
+openness
+ 
+
+ align:start position:0%
+openness
+to for the partners to want to really
+
+ align:start position:0%
+to for the partners to want to really
+ 
+
+ align:start position:0%
+to for the partners to want to really
+act on plans that we a variety of plans
+
+ align:start position:0%
+act on plans that we a variety of plans
+ 
+
+ align:start position:0%
+act on plans that we a variety of plans
+that we might potentially provide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them I didn't have that negative
+
+ align:start position:0%
+them I didn't have that negative
+ 
+
+ align:start position:0%
+them I didn't have that negative
+impression about what we could do given
+
+ align:start position:0%
+impression about what we could do given
+ 
+
+ align:start position:0%
+impression about what we could do given
+like that they have defin sense that you
+
+ align:start position:0%
+like that they have defin sense that you
+ 
+
+ align:start position:0%
+like that they have defin sense that you
+know like getting Bas employees into
+
+ align:start position:0%
+know like getting Bas employees into
+ 
+
+ align:start position:0%
+know like getting Bas employees into
+town Los and housing and all that but I
+
+ align:start position:0%
+town Los and housing and all that but I
+ 
+
+ align:start position:0%
+town Los and housing and all that but I
+don't know I got I I I feel like we I
+
+ align:start position:0%
+don't know I got I I I feel like we I
+ 
+
+ align:start position:0%
+don't know I got I I I feel like we I
+think that we can benefit from the prior
+
+ align:start position:0%
+think that we can benefit from the prior
+ 
+
+ align:start position:0%
+think that we can benefit from the prior
+experiences with students because they
+
+ align:start position:0%
+experiences with students because they
+ 
+
+ align:start position:0%
+experiences with students because they
+seem at least s like really pleased with
+
+ align:start position:0%
+seem at least s like really pleased with
+ 
+
+ align:start position:0%
+seem at least s like really pleased with
+the word that they got and I mean I feel
+
+ align:start position:0%
+the word that they got and I mean I feel
+ 
+
+ align:start position:0%
+the word that they got and I mean I feel
+confident us that we can drive an agenda
+
+ align:start position:0%
+confident us that we can drive an agenda
+ 
+
+ align:start position:0%
+confident us that we can drive an agenda
+we think that there's a different one
+
+ align:start position:0%
+we think that there's a different one
+ 
+
+ align:start position:0%
+we think that there's a different one
+than there out there um I don't I mean I
+
+ align:start position:0%
+than there out there um I don't I mean I
+ 
+
+ align:start position:0%
+than there out there um I don't I mean I
+think I was really impressed with them I
+
+ align:start position:0%
+think I was really impressed with them I
+ 
+
+ align:start position:0%
+think I was really impressed with them I
+didn't get I didn't hear Jeff as much
+
+ align:start position:0%
+didn't get I didn't hear Jeff as much
+ 
+
+ align:start position:0%
+didn't get I didn't hear Jeff as much
+people because we came in late to the
+
+ align:start position:0%
+people because we came in late to the
+ 
+
+ align:start position:0%
+people because we came in late to the
+lunch um but yeah there's this dominant
+
+ align:start position:0%
+lunch um but yeah there's this dominant
+ 
+
+ align:start position:0%
+lunch um but yeah there's this dominant
+personality aspect but I I don't feel
+
+ align:start position:0%
+personality aspect but I I don't feel
+ 
+
+ align:start position:0%
+personality aspect but I I don't feel
+like just cuz there there are find that
+
+ align:start position:0%
+like just cuz there there are find that
+ 
+
+ align:start position:0%
+like just cuz there there are find that
+we can't at them and kind of for we
+
+ align:start position:0%
+we can't at them and kind of for we
+ 
+
+ align:start position:0%
+we can't at them and kind of for we
+think is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important so so listening to this I'm
+
+ align:start position:0%
+important so so listening to this I'm
+ 
+
+ align:start position:0%
+important so so listening to this I'm
+I'm curious if if um if People's
+
+ align:start position:0%
+I'm curious if if um if People's
+ 
+
+ align:start position:0%
+I'm curious if if um if People's
+thinking about what what the nature of
+
+ align:start position:0%
+thinking about what what the nature of
+ 
+
+ align:start position:0%
+thinking about what what the nature of
+your work
+
+ align:start position:0%
+your work
+ 
+
+ align:start position:0%
+your work
+is at least over the next few weeks is
+
+ align:start position:0%
+is at least over the next few weeks is
+ 
+
+ align:start position:0%
+is at least over the next few weeks is
+different now than it might have been
+
+ align:start position:0%
+different now than it might have been
+ 
+
+ align:start position:0%
+different now than it might have been
+last week are there things that are seem
+
+ align:start position:0%
+last week are there things that are seem
+ 
+
+ align:start position:0%
+last week are there things that are seem
+to be more of a priority for us in how
+
+ align:start position:0%
+to be more of a priority for us in how
+ 
+
+ align:start position:0%
+to be more of a priority for us in how
+we tackle this based upon either what
+
+ align:start position:0%
+we tackle this based upon either what
+ 
+
+ align:start position:0%
+we tackle this based upon either what
+you saw there or or some of the you know
+
+ align:start position:0%
+you saw there or or some of the you know
+ 
+
+ align:start position:0%
+you saw there or or some of the you know
+um client relationship issues people
+
+ align:start position:0%
+um client relationship issues people
+ 
+
+ align:start position:0%
+um client relationship issues people
+have talked about anything say wow you
+
+ align:start position:0%
+have talked about anything say wow you
+ 
+
+ align:start position:0%
+have talked about anything say wow you
+know this I wasn't really thinking that
+
+ align:start position:0%
+know this I wasn't really thinking that
+ 
+
+ align:start position:0%
+know this I wasn't really thinking that
+we had to do this but we we better make
+
+ align:start position:0%
+we had to do this but we we better make
+ 
+
+ align:start position:0%
+we had to do this but we we better make
+sure we understand this so we better
+
+ align:start position:0%
+sure we understand this so we better
+ 
+
+ align:start position:0%
+sure we understand this so we better
+make sure we learn about this to any any
+
+ align:start position:0%
+make sure we learn about this to any any
+ 
+
+ align:start position:0%
+make sure we learn about this to any any
+sort of epiphanies like like that happen
+
+ align:start position:0%
+sort of epiphanies like like that happen
+ 
+
+ align:start position:0%
+sort of epiphanies like like that happen
+or any reflection lead you to think
+
+ align:start position:0%
+or any reflection lead you to think
+ 
+
+ align:start position:0%
+or any reflection lead you to think
+something's more important than
+
+ align:start position:0%
+something's more important than
+ 
+
+ align:start position:0%
+something's more important than
+something else and and what we tackle or
+
+ align:start position:0%
+something else and and what we tackle or
+ 
+
+ align:start position:0%
+something else and and what we tackle or
+how we think about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work I don't think this is necess
+
+ align:start position:0%
+work I don't think this is necess
+ 
+
+ align:start position:0%
+work I don't think this is necess
+specific to this project but I think
+
+ align:start position:0%
+specific to this project but I think
+ 
+
+ align:start position:0%
+specific to this project but I think
+it's just real important that we
+
+ align:start position:0%
+it's just real important that we
+ 
+
+ align:start position:0%
+it's just real important that we
+have as soon as possible we have some
+
+ align:start position:0%
+have as soon as possible we have some
+ 
+
+ align:start position:0%
+have as soon as possible we have some
+sort of B agenda or concept what we're
+
+ align:start position:0%
+sort of B agenda or concept what we're
+ 
+
+ align:start position:0%
+sort of B agenda or concept what we're
+doing and just really run by them and
+
+ align:start position:0%
+doing and just really run by them and
+ 
+
+ align:start position:0%
+doing and just really run by them and
+have them and and have them not just be
+
+ align:start position:0%
+have them and and have them not just be
+ 
+
+ align:start position:0%
+have them and and have them not just be
+J or not just be one person different
+
+ align:start position:0%
+J or not just be one person different
+ 
+
+ align:start position:0%
+J or not just be one person different
+people um different members of the
+
+ align:start position:0%
+people um different members of the
+ 
+
+ align:start position:0%
+people um different members of the
+different organizations this um just
+
+ align:start position:0%
+different organizations this um just
+ 
+
+ align:start position:0%
+different organizations this um just
+like as soon as possible early on back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for I mean I don't know what our agenda
+
+ align:start position:0%
+for I mean I don't know what our agenda
+ 
+
+ align:start position:0%
+for I mean I don't know what our agenda
+was previously I don't think that it be
+
+ align:start position:0%
+was previously I don't think that it be
+ 
+
+ align:start position:0%
+was previously I don't think that it be
+completely shaky after Friday but I do
+
+ align:start position:0%
+completely shaky after Friday but I do
+ 
+
+ align:start position:0%
+completely shaky after Friday but I do
+feel
+
+ align:start position:0%
+feel
+ 
+
+ align:start position:0%
+feel
+that there might be communication
+
+ align:start position:0%
+that there might be communication
+ 
+
+ align:start position:0%
+that there might be communication
+problems they and about whether Cent
+
+ align:start position:0%
+problems they and about whether Cent
+ 
+
+ align:start position:0%
+problems they and about whether Cent
+will continue to work with us but at
+
+ align:start position:0%
+will continue to work with us but at
+ 
+
+ align:start position:0%
+will continue to work with us but at
+some deeper level just feel that this
+
+ align:start position:0%
+some deeper level just feel that this
+ 
+
+ align:start position:0%
+some deeper level just feel that this
+isn't really going in the
+
+ align:start position:0%
+isn't really going in the
+ 
+
+ align:start position:0%
+isn't really going in the
+direction out and hope that a different
+
+ align:start position:0%
+direction out and hope that a different
+ 
+
+ align:start position:0%
+direction out and hope that a different
+group shows up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in one of the things that keeps popping
+
+ align:start position:0%
+in one of the things that keeps popping
+ 
+
+ align:start position:0%
+in one of the things that keeps popping
+up for me and I think it was very well
+
+ align:start position:0%
+up for me and I think it was very well
+ 
+
+ align:start position:0%
+up for me and I think it was very well
+kind of Illustrated both through the
+
+ align:start position:0%
+kind of Illustrated both through the
+ 
+
+ align:start position:0%
+kind of Illustrated both through the
+visit and and uh through some previous
+
+ align:start position:0%
+visit and and uh through some previous
+ 
+
+ align:start position:0%
+visit and and uh through some previous
+dists we've had and that is that this
+
+ align:start position:0%
+dists we've had and that is that this
+ 
+
+ align:start position:0%
+dists we've had and that is that this
+kind of language of and kind of thinking
+
+ align:start position:0%
+kind of language of and kind of thinking
+ 
+
+ align:start position:0%
+kind of language of and kind of thinking
+about economic development is not
+
+ align:start position:0%
+about economic development is not
+ 
+
+ align:start position:0%
+about economic development is not
+something that's just you know as a
+
+ align:start position:0%
+something that's just you know as a
+ 
+
+ align:start position:0%
+something that's just you know as a
+planful thing it's not something just
+
+ align:start position:0%
+planful thing it's not something just
+ 
+
+ align:start position:0%
+planful thing it's not something just
+the community doesn't have experience in
+
+ align:start position:0%
+the community doesn't have experience in
+ 
+
+ align:start position:0%
+the community doesn't have experience in
+but it's also not kind of the language
+
+ align:start position:0%
+but it's also not kind of the language
+ 
+
+ align:start position:0%
+but it's also not kind of the language
+of politics and economic development in
+
+ align:start position:0%
+of politics and economic development in
+ 
+
+ align:start position:0%
+of politics and economic development in
+the city as a whole right so there's
+
+ align:start position:0%
+the city as a whole right so there's
+ 
+
+ align:start position:0%
+the city as a whole right so there's
+this really interesting problem I think
+
+ align:start position:0%
+this really interesting problem I think
+ 
+
+ align:start position:0%
+this really interesting problem I think
+when someone steps up and says well we
+
+ align:start position:0%
+when someone steps up and says well we
+ 
+
+ align:start position:0%
+when someone steps up and says well we
+think we need to do
+
+ align:start position:0%
+think we need to do
+ 
+
+ align:start position:0%
+think we need to do
+this uh then the question is a set of
+
+ align:start position:0%
+this uh then the question is a set of
+ 
+
+ align:start position:0%
+this uh then the question is a set of
+people who who have a set of skills
+
+ align:start position:0%
+people who who have a set of skills
+ 
+
+ align:start position:0%
+people who who have a set of skills
+about helping to do that is how much of
+
+ align:start position:0%
+about helping to do that is how much of
+ 
+
+ align:start position:0%
+about helping to do that is how much of
+your work is about coming up with a plan
+
+ align:start position:0%
+your work is about coming up with a plan
+ 
+
+ align:start position:0%
+your work is about coming up with a plan
+and how much of it is about helping the
+
+ align:start position:0%
+and how much of it is about helping the
+ 
+
+ align:start position:0%
+and how much of it is about helping the
+client really understand what does it
+
+ align:start position:0%
+client really understand what does it
+ 
+
+ align:start position:0%
+client really understand what does it
+mean to try to do Economic Development
+
+ align:start position:0%
+mean to try to do Economic Development
+ 
+
+ align:start position:0%
+mean to try to do Economic Development
+work and how do you what role do you
+
+ align:start position:0%
+work and how do you what role do you
+ 
+
+ align:start position:0%
+work and how do you what role do you
+have in kind of the development of their
+
+ align:start position:0%
+have in kind of the development of their
+ 
+
+ align:start position:0%
+have in kind of the development of their
+thinking and does that become a
+
+ align:start position:0%
+thinking and does that become a
+ 
+
+ align:start position:0%
+thinking and does that become a
+strategic part part of what does it mean
+
+ align:start position:0%
+strategic part part of what does it mean
+ 
+
+ align:start position:0%
+strategic part part of what does it mean
+to actually create a plan you know do
+
+ align:start position:0%
+to actually create a plan you know do
+ 
+
+ align:start position:0%
+to actually create a plan you know do
+you have the responsibility of creating
+
+ align:start position:0%
+you have the responsibility of creating
+ 
+
+ align:start position:0%
+you have the responsibility of creating
+the context where they can be receptive
+
+ align:start position:0%
+the context where they can be receptive
+ 
+
+ align:start position:0%
+the context where they can be receptive
+to it as opposed to you know assuming
+
+ align:start position:0%
+to it as opposed to you know assuming
+ 
+
+ align:start position:0%
+to it as opposed to you know assuming
+that well it's about getting the right
+
+ align:start position:0%
+that well it's about getting the right
+ 
+
+ align:start position:0%
+that well it's about getting the right
+plan of which they'll be acceptive to
+
+ align:start position:0%
+plan of which they'll be acceptive to
+ 
+
+ align:start position:0%
+plan of which they'll be acceptive to
+but that
+
+ align:start position:0%
+but that
+ 
+
+ align:start position:0%
+but that
+somehow there's a responsibility or
+
+ align:start position:0%
+somehow there's a responsibility or
+ 
+
+ align:start position:0%
+somehow there's a responsibility or
+there's a a need a requirement to really
+
+ align:start position:0%
+there's a a need a requirement to really
+ 
+
+ align:start position:0%
+there's a a need a requirement to really
+kind of help them in their own thinking
+
+ align:start position:0%
+kind of help them in their own thinking
+ 
+
+ align:start position:0%
+kind of help them in their own thinking
+in the development of their thinking so
+
+ align:start position:0%
+in the development of their thinking so
+ 
+
+ align:start position:0%
+in the development of their thinking so
+that they can be in the position to
+
+ align:start position:0%
+that they can be in the position to
+ 
+
+ align:start position:0%
+that they can be in the position to
+really kind of grapple with the plan in
+
+ align:start position:0%
+really kind of grapple with the plan in
+ 
+
+ align:start position:0%
+really kind of grapple with the plan in
+the ways in which you think would be
+
+ align:start position:0%
+the ways in which you think would be
+ 
+
+ align:start position:0%
+the ways in which you think would be
+most helpful to them I mean I think I
+
+ align:start position:0%
+most helpful to them I mean I think I
+ 
+
+ align:start position:0%
+most helpful to them I mean I think I
+think that's a very good point I think
+
+ align:start position:0%
+think that's a very good point I think
+ 
+
+ align:start position:0%
+think that's a very good point I think
+it picks up on John I definitely left
+
+ align:start position:0%
+it picks up on John I definitely left
+ 
+
+ align:start position:0%
+it picks up on John I definitely left
+with the sense that you know there's
+
+ align:start position:0%
+with the sense that you know there's
+ 
+
+ align:start position:0%
+with the sense that you know there's
+really a lot
+
+ align:start position:0%
+really a lot
+ 
+
+ align:start position:0%
+really a lot
+more uh discussion and back and forth
+
+ align:start position:0%
+more uh discussion and back and forth
+ 
+
+ align:start position:0%
+more uh discussion and back and forth
+communication I think involved in in in
+
+ align:start position:0%
+communication I think involved in in in
+ 
+
+ align:start position:0%
+communication I think involved in in in
+figuring out what our work should be
+
+ align:start position:0%
+figuring out what our work should be
+ 
+
+ align:start position:0%
+figuring out what our work should be
+than us going off and coming back in
+
+ align:start position:0%
+than us going off and coming back in
+ 
+
+ align:start position:0%
+than us going off and coming back in
+October and I think October is probably
+
+ align:start position:0%
+October and I think October is probably
+ 
+
+ align:start position:0%
+October and I think October is probably
+too late in some ways um um for us to be
+
+ align:start position:0%
+too late in some ways um um for us to be
+ 
+
+ align:start position:0%
+too late in some ways um um for us to be
+the discussion about what we see our
+
+ align:start position:0%
+the discussion about what we see our
+ 
+
+ align:start position:0%
+the discussion about what we see our
+task but that but I think Caesar's
+
+ align:start position:0%
+task but that but I think Caesar's
+ 
+
+ align:start position:0%
+task but that but I think Caesar's
+Point's really an excellent one is that
+
+ align:start position:0%
+Point's really an excellent one is that
+ 
+
+ align:start position:0%
+Point's really an excellent one is that
+I think
+
+ align:start position:0%
+I think
+ 
+
+ align:start position:0%
+I think
+um you know what is the what is the
+
+ align:start position:0%
+um you know what is the what is the
+ 
+
+ align:start position:0%
+um you know what is the what is the
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+process um and and how do we we think
+
+ align:start position:0%
+process um and and how do we we think
+ 
+
+ align:start position:0%
+process um and and how do we we think
+about Framing and
+
+ align:start position:0%
+about Framing and
+ 
+
+ align:start position:0%
+about Framing and
+conceptualizing what we're going to be
+
+ align:start position:0%
+conceptualizing what we're going to be
+ 
+
+ align:start position:0%
+conceptualizing what we're going to be
+doing in a way that that's developmental
+
+ align:start position:0%
+doing in a way that that's developmental
+ 
+
+ align:start position:0%
+doing in a way that that's developmental
+for them that that helps them understand
+
+ align:start position:0%
+for them that that helps them understand
+ 
+
+ align:start position:0%
+for them that that helps them understand
+why we've we're talking about things in
+
+ align:start position:0%
+why we've we're talking about things in
+ 
+
+ align:start position:0%
+why we've we're talking about things in
+certain ways why we see these things as
+
+ align:start position:0%
+certain ways why we see these things as
+ 
+
+ align:start position:0%
+certain ways why we see these things as
+either why we why we endorse some of
+
+ align:start position:0%
+either why we why we endorse some of
+ 
+
+ align:start position:0%
+either why we why we endorse some of
+their ideas or if we are proposing
+
+ align:start position:0%
+their ideas or if we are proposing
+ 
+
+ align:start position:0%
+their ideas or if we are proposing
+different sort of ideas you know what is
+
+ align:start position:0%
+different sort of ideas you know what is
+ 
+
+ align:start position:0%
+different sort of ideas you know what is
+the thinking behind that um I think you
+
+ align:start position:0%
+the thinking behind that um I think you
+ 
+
+ align:start position:0%
+the thinking behind that um I think you
+know that's that that sort of the the
+
+ align:start position:0%
+know that's that that sort of the the
+ 
+
+ align:start position:0%
+know that's that that sort of the the
+sort of deeper communication of of why
+
+ align:start position:0%
+sort of deeper communication of of why
+ 
+
+ align:start position:0%
+sort of deeper communication of of why
+we arrived at what we are and and and
+
+ align:start position:0%
+we arrived at what we are and and and
+ 
+
+ align:start position:0%
+we arrived at what we are and and and
+having that challenge somewhat and
+
+ align:start position:0%
+having that challenge somewhat and
+ 
+
+ align:start position:0%
+having that challenge somewhat and
+having people take
+
+ align:start position:0%
+having people take
+ 
+
+ align:start position:0%
+having people take
+ownership uh and of that is going to be
+
+ align:start position:0%
+ownership uh and of that is going to be
+ 
+
+ align:start position:0%
+ownership uh and of that is going to be
+I think I think important
+
+ align:start position:0%
+I think I think important
+ 
+
+ align:start position:0%
+I think I think important
+um you know because um I think there is
+
+ align:start position:0%
+um you know because um I think there is
+ 
+
+ align:start position:0%
+um you know because um I think there is
+a big there is a big
+
+ align:start position:0%
+a big there is a big
+ 
+
+ align:start position:0%
+a big there is a big
+um um certainly disconnect in terms of
+
+ align:start position:0%
+um um certainly disconnect in terms of
+ 
+
+ align:start position:0%
+um um certainly disconnect in terms of
+the the work people are doing in the
+
+ align:start position:0%
+the the work people are doing in the
+ 
+
+ align:start position:0%
+the the work people are doing in the
+community now the type of relationships
+
+ align:start position:0%
+community now the type of relationships
+ 
+
+ align:start position:0%
+community now the type of relationships
+they have um and what what at least
+
+ align:start position:0%
+they have um and what what at least
+ 
+
+ align:start position:0%
+they have um and what what at least
+typical Economic Development work sort
+
+ align:start position:0%
+typical Economic Development work sort
+ 
+
+ align:start position:0%
+typical Economic Development work sort
+of entails so I think I think there's a
+
+ align:start position:0%
+of entails so I think I think there's a
+ 
+
+ align:start position:0%
+of entails so I think I think there's a
+lot of there's a lot of potential you
+
+ align:start position:0%
+lot of there's a lot of potential you
+ 
+
+ align:start position:0%
+lot of there's a lot of potential you
+know disconnect we just move ahead
+
+ align:start position:0%
+know disconnect we just move ahead
+ 
+
+ align:start position:0%
+know disconnect we just move ahead
+without engaging in that type of
+
+ align:start position:0%
+without engaging in that type of
+ 
+
+ align:start position:0%
+without engaging in that type of
+discussion POs to have three working
+
+ align:start position:0%
+discussion POs to have three working
+ 
+
+ align:start position:0%
+discussion POs to have three working
+simultanously like because I cannot see
+
+ align:start position:0%
+simultanously like because I cannot see
+ 
+
+ align:start position:0%
+simultanously like because I cannot see
+them having ownership role unless they
+
+ align:start position:0%
+them having ownership role unless they
+ 
+
+ align:start position:0%
+them having ownership role unless they
+see some some change going on and then
+
+ align:start position:0%
+see some some change going on and then
+ 
+
+ align:start position:0%
+see some some change going on and then
+they will be more receptive for what
+
+ align:start position:0%
+they will be more receptive for what
+ 
+
+ align:start position:0%
+they will be more receptive for what
+what change might because to them so I'm
+
+ align:start position:0%
+what change might because to them so I'm
+ 
+
+ align:start position:0%
+what change might because to them so I'm
+I'm just wondering like is it possible
+
+ align:start position:0%
+I'm just wondering like is it possible
+ 
+
+ align:start position:0%
+I'm just wondering like is it possible
+to have something changed while still
+
+ align:start position:0%
+to have something changed while still
+ 
+
+ align:start position:0%
+to have something changed while still
+dealing with them like convincing them
+
+ align:start position:0%
+dealing with them like convincing them
+ 
+
+ align:start position:0%
+dealing with them like convincing them
+and yeah during the learning process
+
+ align:start position:0%
+and yeah during the learning process
+ 
+
+ align:start position:0%
+and yeah during the learning process
+yeah I mean that's an interesting idea I
+
+ align:start position:0%
+yeah I mean that's an interesting idea I
+ 
+
+ align:start position:0%
+yeah I mean that's an interesting idea I
+know I've definitely worked on Project
+
+ align:start position:0%
+know I've definitely worked on Project
+ 
+
+ align:start position:0%
+know I've definitely worked on Project
+where you where you you try and identify
+
+ align:start position:0%
+where you where you you try and identify
+ 
+
+ align:start position:0%
+where you where you you try and identify
+a project people can start working on
+
+ align:start position:0%
+a project people can start working on
+ 
+
+ align:start position:0%
+a project people can start working on
+early so that you sort of break down the
+
+ align:start position:0%
+early so that you sort of break down the
+ 
+
+ align:start position:0%
+early so that you sort of break down the
+sort of thinking between you do a plan
+
+ align:start position:0%
+sort of thinking between you do a plan
+ 
+
+ align:start position:0%
+sort of thinking between you do a plan
+and then you begin to implement the plan
+
+ align:start position:0%
+and then you begin to implement the plan
+ 
+
+ align:start position:0%
+and then you begin to implement the plan
+um and that's something we might want to
+
+ align:start position:0%
+um and that's something we might want to
+ 
+
+ align:start position:0%
+um and that's something we might want to
+keep in mind um if we see something like
+
+ align:start position:0%
+keep in mind um if we see something like
+ 
+
+ align:start position:0%
+keep in mind um if we see something like
+that I mean I think that's a huge
+
+ align:start position:0%
+that I mean I think that's a huge
+ 
+
+ align:start position:0%
+that I mean I think that's a huge
+challenge um you know for for the class
+
+ align:start position:0%
+challenge um you know for for the class
+ 
+
+ align:start position:0%
+challenge um you know for for the class
+in the period we
+
+ align:start position:0%
+in the period we
+ 
+
+ align:start position:0%
+in the period we
+have you know to both do a piece of
+
+ align:start position:0%
+have you know to both do a piece of
+ 
+
+ align:start position:0%
+have you know to both do a piece of
+planning work and and sort of get a
+
+ align:start position:0%
+planning work and and sort of get a
+ 
+
+ align:start position:0%
+planning work and and sort of get a
+project going that will bring about
+
+ align:start position:0%
+project going that will bring about
+ 
+
+ align:start position:0%
+project going that will bring about
+change but I do think I do think that's
+
+ align:start position:0%
+change but I do think I do think that's
+ 
+
+ align:start position:0%
+change but I do think I do think that's
+an issue we should be asking ourselves
+
+ align:start position:0%
+an issue we should be asking ourselves
+ 
+
+ align:start position:0%
+an issue we should be asking ourselves
+are there ways we can begin to move
+
+ align:start position:0%
+are there ways we can begin to move
+ 
+
+ align:start position:0%
+are there ways we can begin to move
+forward on action without necessarily
+
+ align:start position:0%
+forward on action without necessarily
+ 
+
+ align:start position:0%
+forward on action without necessarily
+having completed a plan and that might
+
+ align:start position:0%
+having completed a plan and that might
+ 
+
+ align:start position:0%
+having completed a plan and that might
+that might
+
+ align:start position:0%
+that might
+ 
+
+ align:start position:0%
+that might
+involve how we engage with with neon and
+
+ align:start position:0%
+involve how we engage with with neon and
+ 
+
+ align:start position:0%
+involve how we engage with with neon and
+campus committee members and
+
+ align:start position:0%
+campus committee members and
+ 
+
+ align:start position:0%
+campus committee members and
+undertaking the research or having the
+
+ align:start position:0%
+undertaking the research or having the
+ 
+
+ align:start position:0%
+undertaking the research or having the
+discussions or participating in the
+
+ align:start position:0%
+discussions or participating in the
+ 
+
+ align:start position:0%
+discussions or participating in the
+meetings we have in developing the plan
+
+ align:start position:0%
+meetings we have in developing the plan
+ 
+
+ align:start position:0%
+meetings we have in developing the plan
+I mean that might you know that might be
+
+ align:start position:0%
+I mean that might you know that might be
+ 
+
+ align:start position:0%
+I mean that might you know that might be
+one way you know we use the work we're
+
+ align:start position:0%
+one way you know we use the work we're
+ 
+
+ align:start position:0%
+one way you know we use the work we're
+doing to facilitate some relationship
+
+ align:start position:0%
+doing to facilitate some relationship
+ 
+
+ align:start position:0%
+doing to facilitate some relationship
+building if if if we're going to be
+
+ align:start position:0%
+building if if if we're going to be
+ 
+
+ align:start position:0%
+building if if if we're going to be
+meeting with people in the business
+
+ align:start position:0%
+meeting with people in the business
+ 
+
+ align:start position:0%
+meeting with people in the business
+Community inviting a neon worker or
+
+ align:start position:0%
+Community inviting a neon worker or
+ 
+
+ align:start position:0%
+Community inviting a neon worker or
+inviting someone think to attend so you
+
+ align:start position:0%
+inviting someone think to attend so you
+ 
+
+ align:start position:0%
+inviting someone think to attend so you
+know I mean I think there are things we
+
+ align:start position:0%
+know I mean I think there are things we
+ 
+
+ align:start position:0%
+know I mean I think there are things we
+can do in the way we do the work that
+
+ align:start position:0%
+can do in the way we do the work that
+ 
+
+ align:start position:0%
+can do in the way we do the work that
+that will contribute to that somewhat
+
+ align:start position:0%
+that will contribute to that somewhat
+ 
+
+ align:start position:0%
+that will contribute to that somewhat
+um um you know um and and we may find we
+
+ align:start position:0%
+um um you know um and and we may find we
+ 
+
+ align:start position:0%
+um um you know um and and we may find we
+may find by October we have some ideas
+
+ align:start position:0%
+may find by October we have some ideas
+ 
+
+ align:start position:0%
+may find by October we have some ideas
+on some project and we we really want to
+
+ align:start position:0%
+on some project and we we really want to
+ 
+
+ align:start position:0%
+on some project and we we really want to
+begin working with them and implemented
+
+ align:start position:0%
+begin working with them and implemented
+ 
+
+ align:start position:0%
+begin working with them and implemented
+I think we should be very open to that
+
+ align:start position:0%
+I think we should be very open to that
+ 
+
+ align:start position:0%
+I think we should be very open to that
+approach you know if it if it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+emerge it Puerto Rican
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and I don't know what kind
+
+ align:start position:0%
+um and I don't know what kind
+ 
+
+ align:start position:0%
+um and I don't know what kind
+of like you know if those are people
+
+ align:start position:0%
+of like you know if those are people
+ 
+
+ align:start position:0%
+of like you know if those are people
+were Bor here
+
+ align:start position:0%
+were Bor here
+ 
+
+ align:start position:0%
+were Bor here
+second here or do you know mostly Second
+
+ align:start position:0%
+second here or do you know mostly Second
+ 
+
+ align:start position:0%
+second here or do you know mostly Second
+Generation and third generation a pretty
+
+ align:start position:0%
+Generation and third generation a pretty
+ 
+
+ align:start position:0%
+Generation and third generation a pretty
+stable community what kind of Lifestyle
+
+ align:start position:0%
+stable community what kind of Lifestyle
+ 
+
+ align:start position:0%
+stable community what kind of Lifestyle
+the first generation had I think have a
+
+ align:start position:0%
+the first generation had I think have a
+ 
+
+ align:start position:0%
+the first generation had I think have a
+lot to do because a lot of times we just
+
+ align:start position:0%
+lot to do because a lot of times we just
+ 
+
+ align:start position:0%
+lot to do because a lot of times we just
+don't have the vision of what it is that
+
+ align:start position:0%
+don't have the vision of what it is that
+ 
+
+ align:start position:0%
+don't have the vision of what it is that
+you're going to see after that we can
+
+ align:start position:0%
+you're going to see after that we can
+ 
+
+ align:start position:0%
+you're going to see after that we can
+come and see this neighborhood needs
+
+ align:start position:0%
+come and see this neighborhood needs
+ 
+
+ align:start position:0%
+come and see this neighborhood needs
+some work but some of those people is
+
+ align:start position:0%
+some work but some of those people is
+ 
+
+ align:start position:0%
+some work but some of those people is
+this is this is good this is it used to
+
+ align:start position:0%
+this is this is good this is it used to
+ 
+
+ align:start position:0%
+this is this is good this is it used to
+be work in situations like that so
+
+ align:start position:0%
+be work in situations like that so
+ 
+
+ align:start position:0%
+be work in situations like that so
+sometimes a different
+
+ align:start position:0%
+sometimes a different
+ 
+
+ align:start position:0%
+sometimes a different
+Vision um so sometimes helping compare
+
+ align:start position:0%
+Vision um so sometimes helping compare
+ 
+
+ align:start position:0%
+Vision um so sometimes helping compare
+what this could be see the past and see
+
+ align:start position:0%
+what this could be see the past and see
+ 
+
+ align:start position:0%
+what this could be see the past and see
+the future what what it is right now and
+
+ align:start position:0%
+the future what what it is right now and
+ 
+
+ align:start position:0%
+the future what what it is right now and
+what it could be helps people take more
+
+ align:start position:0%
+what it could be helps people take more
+ 
+
+ align:start position:0%
+what it could be helps people take more
+initiative of where they want to go next
+
+ align:start position:0%
+initiative of where they want to go next
+ 
+
+ align:start position:0%
+initiative of where they want to go next
+we in a neighbor work in a neighborhood
+
+ align:start position:0%
+we in a neighbor work in a neighborhood
+ 
+
+ align:start position:0%
+we in a neighbor work in a neighborhood
+before there was before there was
+
+ align:start position:0%
+before there was before there was
+ 
+
+ align:start position:0%
+before there was before there was
+absolutely all the stores was closed and
+
+ align:start position:0%
+absolutely all the stores was closed and
+ 
+
+ align:start position:0%
+absolutely all the stores was closed and
+much like the came they start open their
+
+ align:start position:0%
+much like the came they start open their
+ 
+
+ align:start position:0%
+much like the came they start open their
+stores and of course they had no
+
+ align:start position:0%
+stores and of course they had no
+ 
+
+ align:start position:0%
+stores and of course they had no
+business plan they had no IDE is the the
+
+ align:start position:0%
+business plan they had no IDE is the the
+ 
+
+ align:start position:0%
+business plan they had no IDE is the the
+man will come to start to do and if they
+
+ align:start position:0%
+man will come to start to do and if they
+ 
+
+ align:start position:0%
+man will come to start to do and if they
+see this business was working then
+
+ align:start position:0%
+see this business was working then
+ 
+
+ align:start position:0%
+see this business was working then
+everybody else would go like right now
+
+ align:start position:0%
+everybody else would go like right now
+ 
+
+ align:start position:0%
+everybody else would go like right now
+we have 15
+
+ align:start position:0%
+we have 15
+ 
+
+ align:start position:0%
+we have 15
+head not including the people that doing
+
+ align:start position:0%
+head not including the people that doing
+ 
+
+ align:start position:0%
+head not including the people that doing
+this in the houses so now the people had
+
+ align:start position:0%
+this in the houses so now the people had
+ 
+
+ align:start position:0%
+this in the houses so now the people had
+5,000 U you know
+
+ align:start position:0%
+5,000 U you know
+ 
+
+ align:start position:0%
+5,000 U you know
+$50,000 open up their business it's in a
+
+ align:start position:0%
+$50,000 open up their business it's in a
+ 
+
+ align:start position:0%
+$50,000 open up their business it's in a
+huge Dr now once all this development
+
+ align:start position:0%
+huge Dr now once all this development
+ 
+
+ align:start position:0%
+huge Dr now once all this development
+start to happen the people owns the
+
+ align:start position:0%
+start to happen the people owns the
+ 
+
+ align:start position:0%
+start to happen the people owns the
+business oh this is great you know
+
+ align:start position:0%
+business oh this is great you know
+ 
+
+ align:start position:0%
+business oh this is great you know
+everybody we have business this looks
+
+ align:start position:0%
+everybody we have business this looks
+ 
+
+ align:start position:0%
+everybody we have business this looks
+good now I can another development to of
+
+ align:start position:0%
+good now I can another development to of
+ 
+
+ align:start position:0%
+good now I can another development to of
+this so now they're going to invest
+
+ align:start position:0%
+this so now they're going to invest
+ 
+
+ align:start position:0%
+this so now they're going to invest
+about 65 to 70,000
+
+ align:start position:0%
+about 65 to 70,000
+ 
+
+ align:start position:0%
+about 65 to 70,000
+million and then all those business
+
+ align:start position:0%
+million and then all those business
+ 
+
+ align:start position:0%
+million and then all those business
+that's there so now is only the
+
+ align:start position:0%
+that's there so now is only the
+ 
+
+ align:start position:0%
+that's there so now is only the
+this new developers only going to be not
+
+ align:start position:0%
+this new developers only going to be not
+ 
+
+ align:start position:0%
+this new developers only going to be not
+bra because the r going be so high so
+
+ align:start position:0%
+bra because the r going be so high so
+ 
+
+ align:start position:0%
+bra because the r going be so high so
+and less than 20 years I mean we say for
+
+ align:start position:0%
+and less than 20 years I mean we say for
+ 
+
+ align:start position:0%
+and less than 20 years I mean we say for
+the Last 5 Years something really good
+
+ align:start position:0%
+the Last 5 Years something really good
+ 
+
+ align:start position:0%
+the Last 5 Years something really good
+happened of helping them open their own
+
+ align:start position:0%
+happened of helping them open their own
+ 
+
+ align:start position:0%
+happened of helping them open their own
+business but they didn't have a plan of
+
+ align:start position:0%
+business but they didn't have a plan of
+ 
+
+ align:start position:0%
+business but they didn't have a plan of
+how is this going what is this going
+
+ align:start position:0%
+how is this going what is this going
+ 
+
+ align:start position:0%
+how is this going what is this going
+what kind of impact is going to be now
+
+ align:start position:0%
+what kind of impact is going to be now
+ 
+
+ align:start position:0%
+what kind of impact is going to be now
+and what is going to be five 10 years 20
+
+ align:start position:0%
+and what is going to be five 10 years 20
+ 
+
+ align:start position:0%
+and what is going to be five 10 years 20
+years from now CU for some of those
+
+ align:start position:0%
+years from now CU for some of those
+ 
+
+ align:start position:0%
+years from now CU for some of those
+business in order for them to make of
+
+ align:start position:0%
+business in order for them to make of
+ 
+
+ align:start position:0%
+business in order for them to make of
+what they had already invest they need
+
+ align:start position:0%
+what they had already invest they need
+ 
+
+ align:start position:0%
+what they had already invest they need
+to be in business at least for five
+
+ align:start position:0%
+to be in business at least for five
+ 
+
+ align:start position:0%
+to be in business at least for five
+years so some of those not going for the
+
+ align:start position:0%
+years so some of those not going for the
+ 
+
+ align:start position:0%
+years so some of those not going for the
+next years so help can people to think
+
+ align:start position:0%
+next years so help can people to think
+ 
+
+ align:start position:0%
+next years so help can people to think
+about it what the plan in long term it
+
+ align:start position:0%
+about it what the plan in long term it
+ 
+
+ align:start position:0%
+about it what the plan in long term it
+could be better this because this
+
+ align:start position:0%
+could be better this because this
+ 
+
+ align:start position:0%
+could be better this because this
+particular Community they could L the
+
+ align:start position:0%
+particular Community they could L the
+ 
+
+ align:start position:0%
+particular Community they could L the
+business on the next
+
+ align:start position:0%
+business on the next
+ 
+
+ align:start position:0%
+business on the next
+years so that connects a lot with what
+
+ align:start position:0%
+years so that connects a lot with what
+ 
+
+ align:start position:0%
+years so that connects a lot with what
+you saw when you were talking to one in
+
+ align:start position:0%
+you saw when you were talking to one in
+ 
+
+ align:start position:0%
+you saw when you were talking to one in
+the business can you say a little bit
+
+ align:start position:0%
+the business can you say a little bit
+ 
+
+ align:start position:0%
+the business can you say a little bit
+about that story you had when you talked
+
+ align:start position:0%
+about that story you had when you talked
+ 
+
+ align:start position:0%
+about that story you had when you talked
+with the guy about the store yeah um I
+
+ align:start position:0%
+with the guy about the store yeah um I
+ 
+
+ align:start position:0%
+with the guy about the store yeah um I
+was walking with Bill and we stopped in
+
+ align:start position:0%
+was walking with Bill and we stopped in
+ 
+
+ align:start position:0%
+was walking with Bill and we stopped in
+one of the little local bodegas and I
+
+ align:start position:0%
+one of the little local bodegas and I
+ 
+
+ align:start position:0%
+one of the little local bodegas and I
+asked the owner about
+
+ align:start position:0%
+asked the owner about
+ 
+
+ align:start position:0%
+asked the owner about
+um just about his business and it's
+
+ align:start position:0%
+um just about his business and it's
+ 
+
+ align:start position:0%
+um just about his business and it's
+history
+
+ align:start position:0%
+history
+ 
+
+ align:start position:0%
+history
+and uh because there's a for sale sign
+
+ align:start position:0%
+and uh because there's a for sale sign
+ 
+
+ align:start position:0%
+and uh because there's a for sale sign
+on it and we were curious as to why the
+
+ align:start position:0%
+on it and we were curious as to why the
+ 
+
+ align:start position:0%
+on it and we were curious as to why the
+business was for sale and he said well I
+
+ align:start position:0%
+business was for sale and he said well I
+ 
+
+ align:start position:0%
+business was for sale and he said well I
+started it 3 years
+
+ align:start position:0%
+started it 3 years
+ 
+
+ align:start position:0%
+started it 3 years
+ago and after a year or so sold it and
+
+ align:start position:0%
+ago and after a year or so sold it and
+ 
+
+ align:start position:0%
+ago and after a year or so sold it and
+then bought it back and now I'm selling
+
+ align:start position:0%
+then bought it back and now I'm selling
+ 
+
+ align:start position:0%
+then bought it back and now I'm selling
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+again and um like really well
+
+ align:start position:0%
+again and um like really well
+ 
+
+ align:start position:0%
+again and um like really well
+why you know what did you do when you
+
+ align:start position:0%
+why you know what did you do when you
+ 
+
+ align:start position:0%
+why you know what did you do when you
+didn't know that and uh he said well I
+
+ align:start position:0%
+didn't know that and uh he said well I
+ 
+
+ align:start position:0%
+didn't know that and uh he said well I
+have this other store and it's much
+
+ align:start position:0%
+have this other store and it's much
+ 
+
+ align:start position:0%
+have this other store and it's much
+bigger than this one and and what came
+
+ align:start position:0%
+bigger than this one and and what came
+ 
+
+ align:start position:0%
+bigger than this one and and what came
+through in the conversation eventually
+
+ align:start position:0%
+through in the conversation eventually
+ 
+
+ align:start position:0%
+through in the conversation eventually
+was that he sort of bases himself on the
+
+ align:start position:0%
+was that he sort of bases himself on the
+ 
+
+ align:start position:0%
+was that he sort of bases himself on the
+one big story that he owns and that's
+
+ align:start position:0%
+one big story that he owns and that's
+ 
+
+ align:start position:0%
+one big story that he owns and that's
+like his foundation his entrepreneurial
+
+ align:start position:0%
+like his foundation his entrepreneurial
+ 
+
+ align:start position:0%
+like his foundation his entrepreneurial
+Foundation I guess and then
+
+ align:start position:0%
+Foundation I guess and then
+ 
+
+ align:start position:0%
+Foundation I guess and then
+this store when he feels like he has the
+
+ align:start position:0%
+this store when he feels like he has the
+ 
+
+ align:start position:0%
+this store when he feels like he has the
+money and it's like a good time or I
+
+ align:start position:0%
+money and it's like a good time or I
+ 
+
+ align:start position:0%
+money and it's like a good time or I
+don't know all of the conditions that
+
+ align:start position:0%
+don't know all of the conditions that
+ 
+
+ align:start position:0%
+don't know all of the conditions that
+decide this for but he buys this other
+
+ align:start position:0%
+decide this for but he buys this other
+ 
+
+ align:start position:0%
+decide this for but he buys this other
+store and runs it and just sells little
+
+ align:start position:0%
+store and runs it and just sells little
+ 
+
+ align:start position:0%
+store and runs it and just sells little
+foods and things there the other
+
+ align:start position:0%
+foods and things there the other
+ 
+
+ align:start position:0%
+foods and things there the other
+business is larger appliances I think or
+
+ align:start position:0%
+business is larger appliances I think or
+ 
+
+ align:start position:0%
+business is larger appliances I think or
+at least includes them and um but then
+
+ align:start position:0%
+at least includes them and um but then
+ 
+
+ align:start position:0%
+at least includes them and um but then
+when things get tight he sells the
+
+ align:start position:0%
+when things get tight he sells the
+ 
+
+ align:start position:0%
+when things get tight he sells the
+smaller business because he needs the
+
+ align:start position:0%
+smaller business because he needs the
+ 
+
+ align:start position:0%
+smaller business because he needs the
+fast cash and goes back and runs only
+
+ align:start position:0%
+fast cash and goes back and runs only
+ 
+
+ align:start position:0%
+fast cash and goes back and runs only
+the bigger one and he's he seemed
+
+ align:start position:0%
+the bigger one and he's he seemed
+ 
+
+ align:start position:0%
+the bigger one and he's he seemed
+perfectly comfortable with moving in and
+
+ align:start position:0%
+perfectly comfortable with moving in and
+ 
+
+ align:start position:0%
+perfectly comfortable with moving in and
+out of that and there wasn't like any
+
+ align:start position:0%
+out of that and there wasn't like any
+ 
+
+ align:start position:0%
+out of that and there wasn't like any
+big scheme to you know there wasn't any
+
+ align:start position:0%
+big scheme to you know there wasn't any
+ 
+
+ align:start position:0%
+big scheme to you know there wasn't any
+it didn't seem to be like part of some
+
+ align:start position:0%
+it didn't seem to be like part of some
+ 
+
+ align:start position:0%
+it didn't seem to be like part of some
+larger plan it was just well sometimes I
+
+ align:start position:0%
+larger plan it was just well sometimes I
+ 
+
+ align:start position:0%
+larger plan it was just well sometimes I
+own this store when I can afford it and
+
+ align:start position:0%
+own this store when I can afford it and
+ 
+
+ align:start position:0%
+own this store when I can afford it and
+sometimes I don't but things get a
+
+ align:start position:0%
+sometimes I don't but things get a
+ 
+
+ align:start position:0%
+sometimes I don't but things get a
+little rough and it moves in and out of
+
+ align:start position:0%
+little rough and it moves in and out of
+ 
+
+ align:start position:0%
+little rough and it moves in and out of
+that that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interesting another issue that sort of
+
+ align:start position:0%
+interesting another issue that sort of
+ 
+
+ align:start position:0%
+interesting another issue that sort of
+came to mind U as U we had a um train as
+
+ align:start position:0%
+came to mind U as U we had a um train as
+ 
+
+ align:start position:0%
+came to mind U as U we had a um train as
+well this morning that the conversations
+
+ align:start position:0%
+well this morning that the conversations
+ 
+
+ align:start position:0%
+well this morning that the conversations
+with the state or with City official to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+produce interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conversations or at least Center has
+
+ align:start position:0%
+conversations or at least Center has
+ 
+
+ align:start position:0%
+conversations or at least Center has
+information on if such conversations
+
+ align:start position:0%
+information on if such conversations
+ 
+
+ align:start position:0%
+information on if such conversations
+took place between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have not a lot that would really uh
+
+ align:start position:0%
+we have not a lot that would really uh
+ 
+
+ align:start position:0%
+we have not a lot that would really uh
+impact on this I'm actually want to just
+
+ align:start position:0%
+impact on this I'm actually want to just
+ 
+
+ align:start position:0%
+impact on this I'm actually want to just
+show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops I want a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+computer recalling some the things that
+
+ align:start position:0%
+computer recalling some the things that
+ 
+
+ align:start position:0%
+computer recalling some the things that
+je said it sounds like they've actually
+
+ align:start position:0%
+je said it sounds like they've actually
+ 
+
+ align:start position:0%
+je said it sounds like they've actually
+very impressive relationship with the
+
+ align:start position:0%
+very impressive relationship with the
+ 
+
+ align:start position:0%
+very impressive relationship with the
+state with some some elements of the
+
+ align:start position:0%
+state with some some elements of the
+ 
+
+ align:start position:0%
+state with some some elements of the
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+self highly specialized programs they've
+
+ align:start position:0%
+self highly specialized programs they've
+ 
+
+ align:start position:0%
+self highly specialized programs they've
+done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+withy so obviously there are some
+
+ align:start position:0%
+withy so obviously there are some
+ 
+
+ align:start position:0%
+withy so obviously there are some
+departments within State apparatus that
+
+ align:start position:0%
+departments within State apparatus that
+ 
+
+ align:start position:0%
+departments within State apparatus that
+they have been very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+successful for development
+
+ align:start position:0%
+successful for development
+ 
+
+ align:start position:0%
+successful for development
+feel that those are at least if we were
+
+ align:start position:0%
+feel that those are at least if we were
+ 
+
+ align:start position:0%
+feel that those are at least if we were
+to have those convers at least Avenues
+
+ align:start position:0%
+to have those convers at least Avenues
+ 
+
+ align:start position:0%
+to have those convers at least Avenues
+in which we could point to and say
+
+ align:start position:0%
+in which we could point to and say
+ 
+
+ align:start position:0%
+in which we could point to and say
+actually successful around a whole set
+
+ align:start position:0%
+actually successful around a whole set
+ 
+
+ align:start position:0%
+actually successful around a whole set
+of Economic Development activities
+
+ align:start position:0%
+of Economic Development activities
+ 
+
+ align:start position:0%
+of Economic Development activities
+potentially a set of activities that
+
+ align:start position:0%
+potentially a set of activities that
+ 
+
+ align:start position:0%
+potentially a set of activities that
+have some economic development
+
+ align:start position:0%
+have some economic development
+ 
+
+ align:start position:0%
+have some economic development
+effect yeah another way to look at that
+
+ align:start position:0%
+effect yeah another way to look at that
+ 
+
+ align:start position:0%
+effect yeah another way to look at that
+which I've been thinking about is
+
+ align:start position:0%
+which I've been thinking about is
+ 
+
+ align:start position:0%
+which I've been thinking about is
+they've clearly accomplished a lot um
+
+ align:start position:0%
+they've clearly accomplished a lot um
+ 
+
+ align:start position:0%
+they've clearly accomplished a lot um
+and they clearly have some real
+
+ align:start position:0%
+and they clearly have some real
+ 
+
+ align:start position:0%
+and they clearly have some real
+organizational strengths and to what
+
+ align:start position:0%
+organizational strengths and to what
+ 
+
+ align:start position:0%
+organizational strengths and to what
+extent and and that's sort of this
+
+ align:start position:0%
+extent and and that's sort of this
+ 
+
+ align:start position:0%
+extent and and that's sort of this
+question of of you know how do we take
+
+ align:start position:0%
+question of of you know how do we take
+ 
+
+ align:start position:0%
+question of of you know how do we take
+this how do we perhaps apply this
+
+ align:start position:0%
+this how do we perhaps apply this
+ 
+
+ align:start position:0%
+this how do we perhaps apply this
+populationbased approach in other words
+
+ align:start position:0%
+populationbased approach in other words
+ 
+
+ align:start position:0%
+populationbased approach in other words
+what are their
+
+ align:start position:0%
+what are their
+ 
+
+ align:start position:0%
+what are their
+strengths
+
+ align:start position:0%
+strengths
+ 
+
+ align:start position:0%
+strengths
+uh and and how could that inform the
+
+ align:start position:0%
+uh and and how could that inform the
+ 
+
+ align:start position:0%
+uh and and how could that inform the
+approach we take you know if we realiz
+
+ align:start position:0%
+approach we take you know if we realiz
+ 
+
+ align:start position:0%
+approach we take you know if we realiz
+if our if our first step forward in any
+
+ align:start position:0%
+if our if our first step forward in any
+ 
+
+ align:start position:0%
+if our if our first step forward in any
+sort of Economic Development initiative
+
+ align:start position:0%
+sort of Economic Development initiative
+ 
+
+ align:start position:0%
+sort of Economic Development initiative
+is going to be built around the campus
+
+ align:start position:0%
+is going to be built around the campus
+ 
+
+ align:start position:0%
+is going to be built around the campus
+committee
+
+ align:start position:0%
+committee
+ 
+
+ align:start position:0%
+committee
+organizations then we have you know
+
+ align:start position:0%
+organizations then we have you know
+ 
+
+ align:start position:0%
+organizations then we have you know
+trying to understand how they approach
+
+ align:start position:0%
+trying to understand how they approach
+ 
+
+ align:start position:0%
+trying to understand how they approach
+their work think about their work how we
+
+ align:start position:0%
+their work think about their work how we
+ 
+
+ align:start position:0%
+their work think about their work how we
+might be able to translate that approach
+
+ align:start position:0%
+might be able to translate that approach
+ 
+
+ align:start position:0%
+might be able to translate that approach
+into Economic Development work so so
+
+ align:start position:0%
+into Economic Development work so so
+ 
+
+ align:start position:0%
+into Economic Development work so so
+that we can we can sort of build on
+
+ align:start position:0%
+that we can we can sort of build on
+ 
+
+ align:start position:0%
+that we can we can sort of build on
+their own their own capacities their own
+
+ align:start position:0%
+their own their own capacities their own
+ 
+
+ align:start position:0%
+their own their own capacities their own
+relationships their own way of doing
+
+ align:start position:0%
+relationships their own way of doing
+ 
+
+ align:start position:0%
+relationships their own way of doing
+things we may have more success um in
+
+ align:start position:0%
+things we may have more success um in
+ 
+
+ align:start position:0%
+things we may have more success um in
+getting the work accepted and getting
+
+ align:start position:0%
+getting the work accepted and getting
+ 
+
+ align:start position:0%
+getting the work accepted and getting
+the work U forward and and that's one
+
+ align:start position:0%
+the work U forward and and that's one
+ 
+
+ align:start position:0%
+the work U forward and and that's one
+approach I mean um you know so and I
+
+ align:start position:0%
+approach I mean um you know so and I
+ 
+
+ align:start position:0%
+approach I mean um you know so and I
+think it's worth exploring that on the
+
+ align:start position:0%
+think it's worth exploring that on the
+ 
+
+ align:start position:0%
+think it's worth exploring that on the
+other hand people you you might come to
+
+ align:start position:0%
+other hand people you you might come to
+ 
+
+ align:start position:0%
+other hand people you you might come to
+the feeling that that's just too big a
+
+ align:start position:0%
+the feeling that that's just too big a
+ 
+
+ align:start position:0%
+the feeling that that's just too big a
+disconnect that's that's not and you
+
+ align:start position:0%
+disconnect that's that's not and you
+ 
+
+ align:start position:0%
+disconnect that's that's not and you
+know the the tasks they need to do are
+
+ align:start position:0%
+know the the tasks they need to do are
+ 
+
+ align:start position:0%
+know the the tasks they need to do are
+so different that we really have to
+
+ align:start position:0%
+so different that we really have to
+ 
+
+ align:start position:0%
+so different that we really have to
+approach the work in a different way and
+
+ align:start position:0%
+approach the work in a different way and
+ 
+
+ align:start position:0%
+approach the work in a different way and
+I think I think that you might come to
+
+ align:start position:0%
+I think I think that you might come to
+ 
+
+ align:start position:0%
+I think I think that you might come to
+that conclusion as well but I think it's
+
+ align:start position:0%
+that conclusion as well but I think it's
+ 
+
+ align:start position:0%
+that conclusion as well but I think it's
+a good question to ask where are they
+
+ align:start position:0%
+a good question to ask where are they
+ 
+
+ align:start position:0%
+a good question to ask where are they
+starting from and how do we engage with
+
+ align:start position:0%
+starting from and how do we engage with
+ 
+
+ align:start position:0%
+starting from and how do we engage with
+them or where they're starting from um
+
+ align:start position:0%
+them or where they're starting from um
+ 
+
+ align:start position:0%
+them or where they're starting from um
+in terms of thinking about an economic
+
+ align:start position:0%
+in terms of thinking about an economic
+ 
+
+ align:start position:0%
+in terms of thinking about an economic
+development um um but but I would
+
+ align:start position:0%
+development um um but but I would
+ 
+
+ align:start position:0%
+development um um but but I would
+generally
+
+ align:start position:0%
+generally
+ 
+
+ align:start position:0%
+generally
+think setting aside some time to have a
+
+ align:start position:0%
+think setting aside some time to have a
+ 
+
+ align:start position:0%
+think setting aside some time to have a
+broader set of discussions s fairly soon
+
+ align:start position:0%
+broader set of discussions s fairly soon
+ 
+
+ align:start position:0%
+broader set of discussions s fairly soon
+is going to be important to that work
+
+ align:start position:0%
+is going to be important to that work
+ 
+
+ align:start position:0%
+is going to be important to that work
+both within the community and and within
+
+ align:start position:0%
+both within the community and and within
+ 
+
+ align:start position:0%
+both within the community and and within
+quote other stakeholders in the city the
+
+ align:start position:0%
+quote other stakeholders in the city the
+ 
+
+ align:start position:0%
+quote other stakeholders in the city the
+region the state um because I think it's
+
+ align:start position:0%
+region the state um because I think it's
+ 
+
+ align:start position:0%
+region the state um because I think it's
+going to be hard to to feel like we have
+
+ align:start position:0%
+going to be hard to to feel like we have
+ 
+
+ align:start position:0%
+going to be hard to to feel like we have
+a good understanding of of the
+
+ align:start position:0%
+a good understanding of of the
+ 
+
+ align:start position:0%
+a good understanding of of the
+opportunities for the community and
+
+ align:start position:0%
+opportunities for the community and
+ 
+
+ align:start position:0%
+opportunities for the community and
+where resources might be and why things
+
+ align:start position:0%
+where resources might be and why things
+ 
+
+ align:start position:0%
+where resources might be and why things
+may have worked or not worked in the
+
+ align:start position:0%
+may have worked or not worked in the
+ 
+
+ align:start position:0%
+may have worked or not worked in the
+past so that's probably one activity we
+
+ align:start position:0%
+past so that's probably one activity we
+ 
+
+ align:start position:0%
+past so that's probably one activity we
+should be be thinking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tackling I had been looking on my
+
+ align:start position:0%
+tackling I had been looking on my
+ 
+
+ align:start position:0%
+tackling I had been looking on my
+computer because I know I got an email
+
+ align:start position:0%
+computer because I know I got an email
+ 
+
+ align:start position:0%
+computer because I know I got an email
+from Jeff yesterday and I couldn't
+
+ align:start position:0%
+from Jeff yesterday and I couldn't
+ 
+
+ align:start position:0%
+from Jeff yesterday and I couldn't
+remember exactly what it said but part
+
+ align:start position:0%
+remember exactly what it said but part
+ 
+
+ align:start position:0%
+remember exactly what it said but part
+of it was basically that oh we need to
+
+ align:start position:0%
+of it was basically that oh we need to
+ 
+
+ align:start position:0%
+of it was basically that oh we need to
+make sure the students get to talk to
+
+ align:start position:0%
+make sure the students get to talk to
+ 
+
+ align:start position:0%
+make sure the students get to talk to
+Katie and Carlos and
+
+ align:start position:0%
+Katie and Carlos and
+ 
+
+ align:start position:0%
+Katie and Carlos and
+to Steve at Bay State and stuff like
+
+ align:start position:0%
+to Steve at Bay State and stuff like
+ 
+
+ align:start position:0%
+to Steve at Bay State and stuff like
+that so I think in some sense he's
+
+ align:start position:0%
+that so I think in some sense he's
+ 
+
+ align:start position:0%
+that so I think in some sense he's
+recognizing also the need to make sure
+
+ align:start position:0%
+recognizing also the need to make sure
+ 
+
+ align:start position:0%
+recognizing also the need to make sure
+there's a broader audience uh one part
+
+ align:start position:0%
+there's a broader audience uh one part
+ 
+
+ align:start position:0%
+there's a broader audience uh one part
+about this I just want to uh kind of
+
+ align:start position:0%
+about this I just want to uh kind of
+ 
+
+ align:start position:0%
+about this I just want to uh kind of
+reaffirm what uh affirm What
+
+ align:start position:0%
+reaffirm what uh affirm What
+ 
+
+ align:start position:0%
+reaffirm what uh affirm What
+U uh Carlo said is and thinking about
+
+ align:start position:0%
+U uh Carlo said is and thinking about
+ 
+
+ align:start position:0%
+U uh Carlo said is and thinking about
+this as you're kind of you know being
+
+ align:start position:0%
+this as you're kind of you know being
+ 
+
+ align:start position:0%
+this as you're kind of you know being
+the The Firm organization that's saying
+
+ align:start position:0%
+the The Firm organization that's saying
+ 
+
+ align:start position:0%
+the The Firm organization that's saying
+you know it's been asked to do this work
+
+ align:start position:0%
+you know it's been asked to do this work
+ 
+
+ align:start position:0%
+you know it's been asked to do this work
+uh for this community is I think it's
+
+ align:start position:0%
+uh for this community is I think it's
+ 
+
+ align:start position:0%
+uh for this community is I think it's
+really important that you're clear about
+
+ align:start position:0%
+really important that you're clear about
+ 
+
+ align:start position:0%
+really important that you're clear about
+what you need in order to be
+
+ align:start position:0%
+what you need in order to be
+ 
+
+ align:start position:0%
+what you need in order to be
+successful and that you can kind of
+
+ align:start position:0%
+successful and that you can kind of
+ 
+
+ align:start position:0%
+successful and that you can kind of
+communicate that to folks and right now
+
+ align:start position:0%
+communicate that to folks and right now
+ 
+
+ align:start position:0%
+communicate that to folks and right now
+you know I mean you have the attention
+
+ align:start position:0%
+you know I mean you have the attention
+ 
+
+ align:start position:0%
+you know I mean you have the attention
+of a few people who are part of the
+
+ align:start position:0%
+of a few people who are part of the
+ 
+
+ align:start position:0%
+of a few people who are part of the
+campus committee and I I think being
+
+ align:start position:0%
+campus committee and I I think being
+ 
+
+ align:start position:0%
+campus committee and I I think being
+able to say you know this is the
+
+ align:start position:0%
+able to say you know this is the
+ 
+
+ align:start position:0%
+able to say you know this is the
+accesses we need access we need there
+
+ align:start position:0%
+accesses we need access we need there
+ 
+
+ align:start position:0%
+accesses we need access we need there
+people we need to talk to this time
+
+ align:start position:0%
+people we need to talk to this time
+ 
+
+ align:start position:0%
+people we need to talk to this time
+commitment we need these are the things
+
+ align:start position:0%
+commitment we need these are the things
+ 
+
+ align:start position:0%
+commitment we need these are the things
+we kind of need in order to be able to
+
+ align:start position:0%
+we kind of need in order to be able to
+ 
+
+ align:start position:0%
+we kind of need in order to be able to
+do what we're trying to do is a
+
+ align:start position:0%
+do what we're trying to do is a
+ 
+
+ align:start position:0%
+do what we're trying to do is a
+reasonable thing for you to communicate
+
+ align:start position:0%
+reasonable thing for you to communicate
+ 
+
+ align:start position:0%
+reasonable thing for you to communicate
+back to the group uh that you know it
+
+ align:start position:0%
+back to the group uh that you know it
+ 
+
+ align:start position:0%
+back to the group uh that you know it
+doesn't have to be kind of a passive
+
+ align:start position:0%
+doesn't have to be kind of a passive
+ 
+
+ align:start position:0%
+doesn't have to be kind of a passive
+thing that you only have to deal with
+
+ align:start position:0%
+thing that you only have to deal with
+ 
+
+ align:start position:0%
+thing that you only have to deal with
+what's presented but I think folks need
+
+ align:start position:0%
+what's presented but I think folks need
+ 
+
+ align:start position:0%
+what's presented but I think folks need
+to know you know what you require in
+
+ align:start position:0%
+to know you know what you require in
+ 
+
+ align:start position:0%
+to know you know what you require in
+order to be
+
+ align:start position:0%
+order to be
+ 
+
+ align:start position:0%
+order to be
+successful and that they will I think
+
+ align:start position:0%
+successful and that they will I think
+ 
+
+ align:start position:0%
+successful and that they will I think
+they will help you do that if they kind
+
+ align:start position:0%
+they will help you do that if they kind
+ 
+
+ align:start position:0%
+they will help you do that if they kind
+of know what it is and we're very clear
+
+ align:start position:0%
+of know what it is and we're very clear
+ 
+
+ align:start position:0%
+of know what it is and we're very clear
+about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's a communication challenge I
+
+ align:start position:0%
+so it's a communication challenge I
+ 
+
+ align:start position:0%
+so it's a communication challenge I
+think you have with the with the campus
+
+ align:start position:0%
+think you have with the with the campus
+ 
+
+ align:start position:0%
+think you have with the with the campus
+committee with this work group that I
+
+ align:start position:0%
+committee with this work group that I
+ 
+
+ align:start position:0%
+committee with this work group that I
+think you need to establish really kind
+
+ align:start position:0%
+think you need to establish really kind
+ 
+
+ align:start position:0%
+think you need to establish really kind
+of early
+
+ align:start position:0%
+of early
+ 
+
+ align:start position:0%
+of early
+on how to do that and I think we're
+
+ align:start position:0%
+on how to do that and I think we're
+ 
+
+ align:start position:0%
+on how to do that and I think we're
+moving to a place where Carl and I don't
+
+ align:start position:0%
+moving to a place where Carl and I don't
+ 
+
+ align:start position:0%
+moving to a place where Carl and I don't
+want to be
+
+ align:start position:0%
+want to be
+ 
+
+ align:start position:0%
+want to be
+the the the uh interveners in that
+
+ align:start position:0%
+the the the uh interveners in that
+ 
+
+ align:start position:0%
+the the the uh interveners in that
+process but having it really be the
+
+ align:start position:0%
+process but having it really be the
+ 
+
+ align:start position:0%
+process but having it really be the
+negotiators around that
+
+ align:start position:0%
+negotiators around that
+ 
+
+ align:start position:0%
+negotiators around that
+process I one of our gos for this week
+
+ align:start position:0%
+process I one of our gos for this week
+ 
+
+ align:start position:0%
+process I one of our gos for this week
+between today and and tomorrow I mean
+
+ align:start position:0%
+between today and and tomorrow I mean
+ 
+
+ align:start position:0%
+between today and and tomorrow I mean
+then Thursday is to begin to sort of
+
+ align:start position:0%
+then Thursday is to begin to sort of
+ 
+
+ align:start position:0%
+then Thursday is to begin to sort of
+figure out how we want to tackle the
+
+ align:start position:0%
+figure out how we want to tackle the
+ 
+
+ align:start position:0%
+figure out how we want to tackle the
+work and how we're going to organize
+
+ align:start position:0%
+work and how we're going to organize
+ 
+
+ align:start position:0%
+work and how we're going to organize
+ourselves around it um at least over the
+
+ align:start position:0%
+ourselves around it um at least over the
+ 
+
+ align:start position:0%
+ourselves around it um at least over the
+first phase um so that will hopefully
+
+ align:start position:0%
+first phase um so that will hopefully
+ 
+
+ align:start position:0%
+first phase um so that will hopefully
+Empower everyone to to go out and and
+
+ align:start position:0%
+Empower everyone to to go out and and
+ 
+
+ align:start position:0%
+Empower everyone to to go out and and
+begin to to take the initiative around
+
+ align:start position:0%
+begin to to take the initiative around
+ 
+
+ align:start position:0%
+begin to to take the initiative around
+around contact with neon and
+
+ align:start position:0%
+around contact with neon and
+ 
+
+ align:start position:0%
+around contact with neon and
+Etc I guess question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you talk a little bit
+
+ align:start position:0%
+you talk a little bit
+ 
+
+ align:start position:0%
+you talk a little bit
+about you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+involved for a few
+
+ align:start position:0%
+involved for a few
+ 
+
+ align:start position:0%
+involved for a few
+years I don't even know um and I guess
+
+ align:start position:0%
+years I don't even know um and I guess
+ 
+
+ align:start position:0%
+years I don't even know um and I guess
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+curious
+
+ align:start position:0%
+curious
+ 
+
+ align:start position:0%
+curious
+how the student products have been used
+
+ align:start position:0%
+how the student products have been used
+ 
+
+ align:start position:0%
+how the student products have been used
+by this past have they been um realize
+
+ align:start position:0%
+by this past have they been um realize
+ 
+
+ align:start position:0%
+by this past have they been um realize
+that they' been completely different
+
+ align:start position:0%
+that they' been completely different
+ 
+
+ align:start position:0%
+that they' been completely different
+types of t ask but the product of Sol
+
+ align:start position:0%
+types of t ask but the product of Sol
+ 
+
+ align:start position:0%
+types of t ask but the product of Sol
+has been viewed as actionable by the
+
+ align:start position:0%
+has been viewed as actionable by the
+ 
+
+ align:start position:0%
+has been viewed as actionable by the
+recipients or more like education piece
+
+ align:start position:0%
+recipients or more like education piece
+ 
+
+ align:start position:0%
+recipients or more like education piece
+or you know how would you describe well
+
+ align:start position:0%
+or you know how would you describe well
+ 
+
+ align:start position:0%
+or you know how would you describe well
+let me take the the the last course on
+
+ align:start position:0%
+let me take the the the last course on
+ 
+
+ align:start position:0%
+let me take the the the last course on
+the campus concept we did that
+
+ align:start position:0%
+the campus concept we did that
+ 
+
+ align:start position:0%
+the campus concept we did that
+uh one of the things that was very clear
+
+ align:start position:0%
+uh one of the things that was very clear
+ 
+
+ align:start position:0%
+uh one of the things that was very clear
+and that the community asked for and the
+
+ align:start position:0%
+and that the community asked for and the
+ 
+
+ align:start position:0%
+and that the community asked for and the
+class went back and forth with a morning
+
+ align:start position:0%
+class went back and forth with a morning
+ 
+
+ align:start position:0%
+class went back and forth with a morning
+around is that the community is very
+
+ align:start position:0%
+around is that the community is very
+ 
+
+ align:start position:0%
+around is that the community is very
+clear that they wanted actionable
+
+ align:start position:0%
+clear that they wanted actionable
+ 
+
+ align:start position:0%
+clear that they wanted actionable
+items on the plan they wanted things
+
+ align:start position:0%
+items on the plan they wanted things
+ 
+
+ align:start position:0%
+items on the plan they wanted things
+that they could do within the next 6 to
+
+ align:start position:0%
+that they could do within the next 6 to
+ 
+
+ align:start position:0%
+that they could do within the next 6 to
+12 months as well as a broader plan that
+
+ align:start position:0%
+12 months as well as a broader plan that
+ 
+
+ align:start position:0%
+12 months as well as a broader plan that
+that fit
+
+ align:start position:0%
+that fit
+ 
+
+ align:start position:0%
+that fit
+into and there were a number of
+
+ align:start position:0%
+into and there were a number of
+ 
+
+ align:start position:0%
+into and there were a number of
+recommendations actually that the class
+
+ align:start position:0%
+recommendations actually that the class
+ 
+
+ align:start position:0%
+recommendations actually that the class
+worked on that they thought could be
+
+ align:start position:0%
+worked on that they thought could be
+ 
+
+ align:start position:0%
+worked on that they thought could be
+accomplished in the next 6 to 12 months
+
+ align:start position:0%
+accomplished in the next 6 to 12 months
+ 
+
+ align:start position:0%
+accomplished in the next 6 to 12 months
+of which I think most of the they the
+
+ align:start position:0%
+of which I think most of the they the
+ 
+
+ align:start position:0%
+of which I think most of the they the
+community has acted on uh I'll give you
+
+ align:start position:0%
+community has acted on uh I'll give you
+ 
+
+ align:start position:0%
+community has acted on uh I'll give you
+three examples it used to be that there
+
+ align:start position:0%
+three examples it used to be that there
+ 
+
+ align:start position:0%
+three examples it used to be that there
+was a campus committee and then there
+
+ align:start position:0%
+was a campus committee and then there
+ 
+
+ align:start position:0%
+was a campus committee and then there
+was a steering committee that ran neon
+
+ align:start position:0%
+was a steering committee that ran neon
+ 
+
+ align:start position:0%
+was a steering committee that ran neon
+and neon was actually separate from the
+
+ align:start position:0%
+and neon was actually separate from the
+ 
+
+ align:start position:0%
+and neon was actually separate from the
+campus committee and one of the things
+
+ align:start position:0%
+campus committee and one of the things
+ 
+
+ align:start position:0%
+campus committee and one of the things
+that came out of is is the group said
+
+ align:start position:0%
+that came out of is is the group said
+ 
+
+ align:start position:0%
+that came out of is is the group said
+look neon needs to be responsive
+
+ align:start position:0%
+look neon needs to be responsive
+ 
+
+ align:start position:0%
+look neon needs to be responsive
+response needs to be a subset of the
+
+ align:start position:0%
+response needs to be a subset of the
+ 
+
+ align:start position:0%
+response needs to be a subset of the
+campus committee not a separate thing
+
+ align:start position:0%
+campus committee not a separate thing
+ 
+
+ align:start position:0%
+campus committee not a separate thing
+and actually the director of neon needs
+
+ align:start position:0%
+and actually the director of neon needs
+ 
+
+ align:start position:0%
+and actually the director of neon needs
+to be hired by the campus committee and
+
+ align:start position:0%
+to be hired by the campus committee and
+ 
+
+ align:start position:0%
+to be hired by the campus committee and
+be responsible to the campus committee
+
+ align:start position:0%
+be responsible to the campus committee
+ 
+
+ align:start position:0%
+be responsible to the campus committee
+and so they actually changed that
+
+ align:start position:0%
+and so they actually changed that
+ 
+
+ align:start position:0%
+and so they actually changed that
+organizational Arrangement they also
+
+ align:start position:0%
+organizational Arrangement they also
+ 
+
+ align:start position:0%
+organizational Arrangement they also
+talked about the need to hire someone
+
+ align:start position:0%
+talked about the need to hire someone
+ 
+
+ align:start position:0%
+talked about the need to hire someone
+who is going to be a coordinator for the
+
+ align:start position:0%
+who is going to be a coordinator for the
+ 
+
+ align:start position:0%
+who is going to be a coordinator for the
+campus itself which Vanessa I think some
+
+ align:start position:0%
+campus itself which Vanessa I think some
+ 
+
+ align:start position:0%
+campus itself which Vanessa I think some
+of you met Vanessa they actually then
+
+ align:start position:0%
+of you met Vanessa they actually then
+ 
+
+ align:start position:0%
+of you met Vanessa they actually then
+put money into hiring her to do that
+
+ align:start position:0%
+put money into hiring her to do that
+ 
+
+ align:start position:0%
+put money into hiring her to do that
+there were a set of other activities
+
+ align:start position:0%
+there were a set of other activities
+ 
+
+ align:start position:0%
+there were a set of other activities
+that they thought could happen and some
+
+ align:start position:0%
+that they thought could happen and some
+ 
+
+ align:start position:0%
+that they thought could happen and some
+changes in the building that could
+
+ align:start position:0%
+changes in the building that could
+ 
+
+ align:start position:0%
+changes in the building that could
+happen so when Peter took us on the tour
+
+ align:start position:0%
+happen so when Peter took us on the tour
+ 
+
+ align:start position:0%
+happen so when Peter took us on the tour
+and you remember the room he said there
+
+ align:start position:0%
+and you remember the room he said there
+ 
+
+ align:start position:0%
+and you remember the room he said there
+the playscape was in was in that
+
+ align:start position:0%
+the playscape was in was in that
+ 
+
+ align:start position:0%
+the playscape was in was in that
+actually was a classroom last year and
+
+ align:start position:0%
+actually was a classroom last year and
+ 
+
+ align:start position:0%
+actually was a classroom last year and
+it was suggested that that room be
+
+ align:start position:0%
+it was suggested that that room be
+ 
+
+ align:start position:0%
+it was suggested that that room be
+cleared out and actually be made as a
+
+ align:start position:0%
+cleared out and actually be made as a
+ 
+
+ align:start position:0%
+cleared out and actually be made as a
+central space for the community to do
+
+ align:start position:0%
+central space for the community to do
+ 
+
+ align:start position:0%
+central space for the community to do
+certain kinds of activity so the school
+
+ align:start position:0%
+certain kinds of activity so the school
+ 
+
+ align:start position:0%
+certain kinds of activity so the school
+acted on that and the idea was that the
+
+ align:start position:0%
+acted on that and the idea was that the
+ 
+
+ align:start position:0%
+acted on that and the idea was that the
+school released all the bill all the
+
+ align:start position:0%
+school released all the bill all the
+ 
+
+ align:start position:0%
+school released all the bill all the
+space on that floor for community activ
+
+ align:start position:0%
+space on that floor for community activ
+ 
+
+ align:start position:0%
+space on that floor for community activ
+ities and none of for educational
+
+ align:start position:0%
+ities and none of for educational
+ 
+
+ align:start position:0%
+ities and none of for educational
+activities from the school uh as a way
+
+ align:start position:0%
+activities from the school uh as a way
+ 
+
+ align:start position:0%
+activities from the school uh as a way
+of setting the base for and some of the
+
+ align:start position:0%
+of setting the base for and some of the
+ 
+
+ align:start position:0%
+of setting the base for and some of the
+other things they wanted to do so there
+
+ align:start position:0%
+other things they wanted to do so there
+ 
+
+ align:start position:0%
+other things they wanted to do so there
+were a number of steps that I think then
+
+ align:start position:0%
+were a number of steps that I think then
+ 
+
+ align:start position:0%
+were a number of steps that I think then
+people felt like oh well we can act on
+
+ align:start position:0%
+people felt like oh well we can act on
+ 
+
+ align:start position:0%
+people felt like oh well we can act on
+those things we can make that happen and
+
+ align:start position:0%
+those things we can make that happen and
+ 
+
+ align:start position:0%
+those things we can make that happen and
+they then kind of went on and started to
+
+ align:start position:0%
+they then kind of went on and started to
+ 
+
+ align:start position:0%
+they then kind of went on and started to
+do that so I think in the in the the way
+
+ align:start position:0%
+do that so I think in the in the the way
+ 
+
+ align:start position:0%
+do that so I think in the in the the way
+they work
+
+ align:start position:0%
+they work
+ 
+
+ align:start position:0%
+they work
+is is that they you know they really do
+
+ align:start position:0%
+is is that they you know they really do
+ 
+
+ align:start position:0%
+is is that they you know they really do
+need clear next steps and it doesn't
+
+ align:start position:0%
+need clear next steps and it doesn't
+ 
+
+ align:start position:0%
+need clear next steps and it doesn't
+matter how big or how small they are and
+
+ align:start position:0%
+matter how big or how small they are and
+ 
+
+ align:start position:0%
+matter how big or how small they are and
+then they need to be connected
+
+ align:start position:0%
+then they need to be connected
+ 
+
+ align:start position:0%
+then they need to be connected
+something much larger now I can tell you
+
+ align:start position:0%
+something much larger now I can tell you
+ 
+
+ align:start position:0%
+something much larger now I can tell you
+one of the problems we had last year
+
+ align:start position:0%
+one of the problems we had last year
+ 
+
+ align:start position:0%
+one of the problems we had last year
+which I think is a clear communication
+
+ align:start position:0%
+which I think is a clear communication
+ 
+
+ align:start position:0%
+which I think is a clear communication
+problem uh you remember the entrance
+
+ align:start position:0%
+problem uh you remember the entrance
+ 
+
+ align:start position:0%
+problem uh you remember the entrance
+into the school the
+
+ align:start position:0%
+into the school the
+ 
+
+ align:start position:0%
+into the school the
+park okay a very funny thing happened
+
+ align:start position:0%
+park okay a very funny thing happened
+ 
+
+ align:start position:0%
+park okay a very funny thing happened
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+year uh the class got together and they
+
+ align:start position:0%
+year uh the class got together and they
+ 
+
+ align:start position:0%
+year uh the class got together and they
+were trying to work on this much larger
+
+ align:start position:0%
+were trying to work on this much larger
+ 
+
+ align:start position:0%
+were trying to work on this much larger
+issue of how do you create let see if I
+
+ align:start position:0%
+issue of how do you create let see if I
+ 
+
+ align:start position:0%
+issue of how do you create let see if I
+have it here
+
+ align:start position:0%
+have it here
+ 
+
+ align:start position:0%
+have it here
+I'm not sure I do so may not have to
+
+ align:start position:0%
+I'm not sure I do so may not have to
+ 
+
+ align:start position:0%
+I'm not sure I do so may not have to
+hold anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+uh yeah actually I can use this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one can you hold this up for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me so they were worried you know the
+
+ align:start position:0%
+me so they were worried you know the
+ 
+
+ align:start position:0%
+me so they were worried you know the
+class last year was worried about this
+
+ align:start position:0%
+class last year was worried about this
+ 
+
+ align:start position:0%
+class last year was worried about this
+here's a herena school right and they
+
+ align:start position:0%
+here's a herena school right and they
+ 
+
+ align:start position:0%
+here's a herena school right and they
+were worried about this flow they were
+
+ align:start position:0%
+were worried about this flow they were
+ 
+
+ align:start position:0%
+were worried about this flow they were
+worried about how do you open up this
+
+ align:start position:0%
+worried about how do you open up this
+ 
+
+ align:start position:0%
+worried about how do you open up this
+school concept so that it really feels
+
+ align:start position:0%
+school concept so that it really feels
+ 
+
+ align:start position:0%
+school concept so that it really feels
+like it's an inviting Place coming in
+
+ align:start position:0%
+like it's an inviting Place coming in
+ 
+
+ align:start position:0%
+like it's an inviting Place coming in
+because you remember when you come down
+
+ align:start position:0%
+because you remember when you come down
+ 
+
+ align:start position:0%
+because you remember when you come down
+off the highway and you're there even
+
+ align:start position:0%
+off the highway and you're there even
+ 
+
+ align:start position:0%
+off the highway and you're there even
+now the park it does you know it's a
+
+ align:start position:0%
+now the park it does you know it's a
+ 
+
+ align:start position:0%
+now the park it does you know it's a
+park and you can't even unless you know
+
+ align:start position:0%
+park and you can't even unless you know
+ 
+
+ align:start position:0%
+park and you can't even unless you know
+there's a school there you would never
+
+ align:start position:0%
+there's a school there you would never
+ 
+
+ align:start position:0%
+there's a school there you would never
+know right unless somebody told you so
+
+ align:start position:0%
+know right unless somebody told you so
+ 
+
+ align:start position:0%
+know right unless somebody told you so
+uh one of the things that the class
+
+ align:start position:0%
+uh one of the things that the class
+ 
+
+ align:start position:0%
+uh one of the things that the class
+worked on was the design of a that space
+
+ align:start position:0%
+worked on was the design of a that space
+ 
+
+ align:start position:0%
+worked on was the design of a that space
+so that it would actually be an
+
+ align:start position:0%
+so that it would actually be an
+ 
+
+ align:start position:0%
+so that it would actually be an
+extension of Main
+
+ align:start position:0%
+extension of Main
+ 
+
+ align:start position:0%
+extension of Main
+Street right and they had a whole idea
+
+ align:start position:0%
+Street right and they had a whole idea
+ 
+
+ align:start position:0%
+Street right and they had a whole idea
+about both how push cars could be used
+
+ align:start position:0%
+about both how push cars could be used
+ 
+
+ align:start position:0%
+about both how push cars could be used
+how that one apartment building that's
+
+ align:start position:0%
+how that one apartment building that's
+ 
+
+ align:start position:0%
+how that one apartment building that's
+there could actually you could turn the
+
+ align:start position:0%
+there could actually you could turn the
+ 
+
+ align:start position:0%
+there could actually you could turn the
+first floor into a business space and
+
+ align:start position:0%
+first floor into a business space and
+ 
+
+ align:start position:0%
+first floor into a business space and
+keep apartments above it a whole kind of
+
+ align:start position:0%
+keep apartments above it a whole kind of
+ 
+
+ align:start position:0%
+keep apartments above it a whole kind of
+set of things like that
+
+ align:start position:0%
+set of things like that
+ 
+
+ align:start position:0%
+set of things like that
+unbeknownst to the class after several
+
+ align:start position:0%
+unbeknownst to the class after several
+ 
+
+ align:start position:0%
+unbeknownst to the class after several
+meetings with people the community
+
+ align:start position:0%
+meetings with people the community
+ 
+
+ align:start position:0%
+meetings with people the community
+actually had a plan that you can put
+
+ align:start position:0%
+actually had a plan that you can put
+ 
+
+ align:start position:0%
+actually had a plan that you can put
+that down had been
+
+ align:start position:0%
+that down had been
+ 
+
+ align:start position:0%
+that down had been
+developed uh two years ago three years
+
+ align:start position:0%
+developed uh two years ago three years
+ 
+
+ align:start position:0%
+developed uh two years ago three years
+ago that had been kind of
+
+ align:start position:0%
+ago that had been kind of
+ 
+
+ align:start position:0%
+ago that had been kind of
+sitting uh in a back room somewhere
+
+ align:start position:0%
+sitting uh in a back room somewhere
+ 
+
+ align:start position:0%
+sitting uh in a back room somewhere
+about redeveloping that
+
+ align:start position:0%
+about redeveloping that
+ 
+
+ align:start position:0%
+about redeveloping that
+Park okay now what you see now is
+
+ align:start position:0%
+Park okay now what you see now is
+ 
+
+ align:start position:0%
+Park okay now what you see now is
+actually the actualization of that plan
+
+ align:start position:0%
+actually the actualization of that plan
+ 
+
+ align:start position:0%
+actually the actualization of that plan
+not the one the students did right of
+
+ align:start position:0%
+not the one the students did right of
+ 
+
+ align:start position:0%
+not the one the students did right of
+the old plan because it had been on a
+
+ align:start position:0%
+the old plan because it had been on a
+ 
+
+ align:start position:0%
+the old plan because it had been on a
+track but nobody talked about it they
+
+ align:start position:0%
+track but nobody talked about it they
+ 
+
+ align:start position:0%
+track but nobody talked about it they
+would put it up and said they did show
+
+ align:start position:0%
+would put it up and said they did show
+ 
+
+ align:start position:0%
+would put it up and said they did show
+the plan said well we have these
+
+ align:start position:0%
+the plan said well we have these
+ 
+
+ align:start position:0%
+the plan said well we have these
+ideas but nobody was saying well we've
+
+ align:start position:0%
+ideas but nobody was saying well we've
+ 
+
+ align:start position:0%
+ideas but nobody was saying well we've
+got something going where this actually
+
+ align:start position:0%
+got something going where this actually
+ 
+
+ align:start position:0%
+got something going where this actually
+may happen it's actually in the parks
+
+ align:start position:0%
+may happen it's actually in the parks
+ 
+
+ align:start position:0%
+may happen it's actually in the parks
+department bud and they're starting to
+
+ align:start position:0%
+department bud and they're starting to
+ 
+
+ align:start position:0%
+department bud and they're starting to
+do something right right so the students
+
+ align:start position:0%
+do something right right so the students
+ 
+
+ align:start position:0%
+do something right right so the students
+are working on this plan and stuff and
+
+ align:start position:0%
+are working on this plan and stuff and
+ 
+
+ align:start position:0%
+are working on this plan and stuff and
+then when they came to one meeting with
+
+ align:start position:0%
+then when they came to one meeting with
+ 
+
+ align:start position:0%
+then when they came to one meeting with
+the new new North Citizens Council and
+
+ align:start position:0%
+the new new North Citizens Council and
+ 
+
+ align:start position:0%
+the new new North Citizens Council and
+they're laying out the concept of all of
+
+ align:start position:0%
+they're laying out the concept of all of
+ 
+
+ align:start position:0%
+they're laying out the concept of all of
+this and they had a whole set about what
+
+ align:start position:0%
+this and they had a whole set about what
+ 
+
+ align:start position:0%
+this and they had a whole set about what
+was going to happen on the Brightwood
+
+ align:start position:0%
+was going to happen on the Brightwood
+ 
+
+ align:start position:0%
+was going to happen on the Brightwood
+side and there was
+
+ align:start position:0%
+side and there was
+ 
+
+ align:start position:0%
+side and there was
+a there was basically a little battle
+
+ align:start position:0%
+a there was basically a little battle
+ 
+
+ align:start position:0%
+a there was basically a little battle
+that happened because the person who was
+
+ align:start position:0%
+that happened because the person who was
+ 
+
+ align:start position:0%
+that happened because the person who was
+head of the new citizen Council that
+
+ align:start position:0%
+head of the new citizen Council that
+ 
+
+ align:start position:0%
+head of the new citizen Council that
+time Barbera Rivera felt like well she
+
+ align:start position:0%
+time Barbera Rivera felt like well she
+ 
+
+ align:start position:0%
+time Barbera Rivera felt like well she
+had been dismissed because they had an
+
+ align:start position:0%
+had been dismissed because they had an
+ 
+
+ align:start position:0%
+had been dismissed because they had an
+idea and though it was
+
+ align:start position:0%
+idea and though it was
+ 
+
+ align:start position:0%
+idea and though it was
+communicated to the class as something
+
+ align:start position:0%
+communicated to the class as something
+ 
+
+ align:start position:0%
+communicated to the class as something
+they and I don't think this was
+
+ align:start position:0%
+they and I don't think this was
+ 
+
+ align:start position:0%
+they and I don't think this was
+because people were trying to set up the
+
+ align:start position:0%
+because people were trying to set up the
+ 
+
+ align:start position:0%
+because people were trying to set up the
+class I think it's because people didn't
+
+ align:start position:0%
+class I think it's because people didn't
+ 
+
+ align:start position:0%
+class I think it's because people didn't
+hold the information that way they just
+
+ align:start position:0%
+hold the information that way they just
+ 
+
+ align:start position:0%
+hold the information that way they just
+didn't hold it that way it that oh yeah
+
+ align:start position:0%
+didn't hold it that way it that oh yeah
+ 
+
+ align:start position:0%
+didn't hold it that way it that oh yeah
+there was this even and I think the
+
+ align:start position:0%
+there was this even and I think the
+ 
+
+ align:start position:0%
+there was this even and I think the
+other problem that they got caught up in
+
+ align:start position:0%
+other problem that they got caught up in
+ 
+
+ align:start position:0%
+other problem that they got caught up in
+is the person who set all that emotion
+
+ align:start position:0%
+is the person who set all that emotion
+ 
+
+ align:start position:0%
+is the person who set all that emotion
+Katie uh who's now the economic
+
+ align:start position:0%
+Katie uh who's now the economic
+ 
+
+ align:start position:0%
+Katie uh who's now the economic
+development person who was a senior
+
+ align:start position:0%
+development person who was a senior
+ 
+
+ align:start position:0%
+development person who was a senior
+planner was out on maternity to leave
+
+ align:start position:0%
+planner was out on maternity to leave
+ 
+
+ align:start position:0%
+planner was out on maternity to leave
+that whole semester so there was and the
+
+ align:start position:0%
+that whole semester so there was and the
+ 
+
+ align:start position:0%
+that whole semester so there was and the
+other person who was head of the plan
+
+ align:start position:0%
+other person who was head of the plan
+ 
+
+ align:start position:0%
+other person who was head of the plan
+Department who we would normally work
+
+ align:start position:0%
+Department who we would normally work
+ 
+
+ align:start position:0%
+Department who we would normally work
+with was actually Al CLE because she had
+
+ align:start position:0%
+with was actually Al CLE because she had
+ 
+
+ align:start position:0%
+with was actually Al CLE because she had
+cancer so the normal people who would
+
+ align:start position:0%
+cancer so the normal people who would
+ 
+
+ align:start position:0%
+cancer so the normal people who would
+have provided that information weren't
+
+ align:start position:0%
+have provided that information weren't
+ 
+
+ align:start position:0%
+have provided that information weren't
+in the picture there was no one in the
+
+ align:start position:0%
+in the picture there was no one in the
+ 
+
+ align:start position:0%
+in the picture there was no one in the
+picture who could do that connection for
+
+ align:start position:0%
+picture who could do that connection for
+ 
+
+ align:start position:0%
+picture who could do that connection for
+the class uh and I think the class what
+
+ align:start position:0%
+the class uh and I think the class what
+ 
+
+ align:start position:0%
+the class uh and I think the class what
+was interesting about it though in the
+
+ align:start position:0%
+was interesting about it though in the
+ 
+
+ align:start position:0%
+was interesting about it though in the
+public meetings that they had in the
+
+ align:start position:0%
+public meetings that they had in the
+ 
+
+ align:start position:0%
+public meetings that they had in the
+meeting with the campus committee folks
+
+ align:start position:0%
+meeting with the campus committee folks
+ 
+
+ align:start position:0%
+meeting with the campus committee folks
+wanted to do the
+
+ align:start position:0%
+wanted to do the
+ 
+
+ align:start position:0%
+wanted to do the
+plan that the students said they thought
+
+ align:start position:0%
+plan that the students said they thought
+ 
+
+ align:start position:0%
+plan that the students said they thought
+that that made sense
+
+ align:start position:0%
+that that made sense
+ 
+
+ align:start position:0%
+that that made sense
+and it could have been very easy for the
+
+ align:start position:0%
+and it could have been very easy for the
+ 
+
+ align:start position:0%
+and it could have been very easy for the
+students to have said well what's the
+
+ align:start position:0%
+students to have said well what's the
+ 
+
+ align:start position:0%
+students to have said well what's the
+transition from what you have and what's
+
+ align:start position:0%
+transition from what you have and what's
+ 
+
+ align:start position:0%
+transition from what you have and what's
+going to happen to this next stage and
+
+ align:start position:0%
+going to happen to this next stage and
+ 
+
+ align:start position:0%
+going to happen to this next stage and
+they could have built it as a
+
+ align:start position:0%
+they could have built it as a
+ 
+
+ align:start position:0%
+they could have built it as a
+transitional plan as opposed to well
+
+ align:start position:0%
+transitional plan as opposed to well
+ 
+
+ align:start position:0%
+transitional plan as opposed to well
+this is what you need to do next to
+
+ align:start position:0%
+this is what you need to do next to
+ 
+
+ align:start position:0%
+this is what you need to do next to
+clean up this area but there wasn't even
+
+ align:start position:0%
+clean up this area but there wasn't even
+ 
+
+ align:start position:0%
+clean up this area but there wasn't even
+that that that piece so there is
+
+ align:start position:0%
+that that that piece so there is
+ 
+
+ align:start position:0%
+that that that piece so there is
+some I think this important point is
+
+ align:start position:0%
+some I think this important point is
+ 
+
+ align:start position:0%
+some I think this important point is
+often you know in the politics of
+
+ align:start position:0%
+often you know in the politics of
+ 
+
+ align:start position:0%
+often you know in the politics of
+getting PL except that and acted on um
+
+ align:start position:0%
+getting PL except that and acted on um
+ 
+
+ align:start position:0%
+getting PL except that and acted on um
+understanding what people already
+
+ align:start position:0%
+understanding what people already
+ 
+
+ align:start position:0%
+understanding what people already
+invested in and sort of acknowledging at
+
+ align:start position:0%
+invested in and sort of acknowledging at
+ 
+
+ align:start position:0%
+invested in and sort of acknowledging at
+least acknowledging that and and perhaps
+
+ align:start position:0%
+least acknowledging that and and perhaps
+ 
+
+ align:start position:0%
+least acknowledging that and and perhaps
+even incorporating that you know can be
+
+ align:start position:0%
+even incorporating that you know can be
+ 
+
+ align:start position:0%
+even incorporating that you know can be
+very important because you know a lot of
+
+ align:start position:0%
+very important because you know a lot of
+ 
+
+ align:start position:0%
+very important because you know a lot of
+people will read will read the plan for
+
+ align:start position:0%
+people will read will read the plan for
+ 
+
+ align:start position:0%
+people will read will read the plan for
+where they're in it and how it
+
+ align:start position:0%
+where they're in it and how it
+ 
+
+ align:start position:0%
+where they're in it and how it
+influences resources for them and their
+
+ align:start position:0%
+influences resources for them and their
+ 
+
+ align:start position:0%
+influences resources for them and their
+organization so you know you do you have
+
+ align:start position:0%
+organization so you know you do you have
+ 
+
+ align:start position:0%
+organization so you know you do you have
+to sort of be be be conscious of that
+
+ align:start position:0%
+to sort of be be be conscious of that
+ 
+
+ align:start position:0%
+to sort of be be be conscious of that
+but I I do think in terms of of of
+
+ align:start position:0%
+but I I do think in terms of of of
+ 
+
+ align:start position:0%
+but I I do think in terms of of of
+action that um you know it's it's pretty
+
+ align:start position:0%
+action that um you know it's it's pretty
+ 
+
+ align:start position:0%
+action that um you know it's it's pretty
+much a given where our client is now
+
+ align:start position:0%
+much a given where our client is now
+ 
+
+ align:start position:0%
+much a given where our client is now
+that that um you know thinking about how
+
+ align:start position:0%
+that that um you know thinking about how
+ 
+
+ align:start position:0%
+that that um you know thinking about how
+they organize themselves to do Economic
+
+ align:start position:0%
+they organize themselves to do Economic
+ 
+
+ align:start position:0%
+they organize themselves to do Economic
+Development work and what sort of
+
+ align:start position:0%
+Development work and what sort of
+ 
+
+ align:start position:0%
+Development work and what sort of
+capacity and relationships they're going
+
+ align:start position:0%
+capacity and relationships they're going
+ 
+
+ align:start position:0%
+capacity and relationships they're going
+to need to act on you know
+
+ align:start position:0%
+to need to act on you know
+ 
+
+ align:start position:0%
+to need to act on you know
+whatever um we work with them to decide
+
+ align:start position:0%
+whatever um we work with them to decide
+ 
+
+ align:start position:0%
+whatever um we work with them to decide
+is their Economic Development agenda is
+
+ align:start position:0%
+is their Economic Development agenda is
+ 
+
+ align:start position:0%
+is their Economic Development agenda is
+going to be I think a big part of what
+
+ align:start position:0%
+going to be I think a big part of what
+ 
+
+ align:start position:0%
+going to be I think a big part of what
+we're going to be have to thinking about
+
+ align:start position:0%
+we're going to be have to thinking about
+ 
+
+ align:start position:0%
+we're going to be have to thinking about
+and and doing and so I think in that's a
+
+ align:start position:0%
+and and doing and so I think in that's a
+ 
+
+ align:start position:0%
+and and doing and so I think in that's a
+that's something once again to be
+
+ align:start position:0%
+that's something once again to be
+ 
+
+ align:start position:0%
+that's something once again to be
+thinking about as we begin to collect
+
+ align:start position:0%
+thinking about as we begin to collect
+ 
+
+ align:start position:0%
+thinking about as we begin to collect
+information you know what's important to
+
+ align:start position:0%
+information you know what's important to
+ 
+
+ align:start position:0%
+information you know what's important to
+help us plan the sort of capacity
+
+ align:start position:0%
+help us plan the sort of capacity
+ 
+
+ align:start position:0%
+help us plan the sort of capacity
+building you know the organization
+
+ align:start position:0%
+building you know the organization
+ 
+
+ align:start position:0%
+building you know the organization
+capacity building sort of aspect of of
+
+ align:start position:0%
+capacity building sort of aspect of of
+ 
+
+ align:start position:0%
+capacity building sort of aspect of of
+what what we're going to need to do
+
+ align:start position:0%
+what what we're going to need to do
+ 
+
+ align:start position:0%
+what what we're going to need to do
+because the um I guess to the extent
+
+ align:start position:0%
+because the um I guess to the extent
+ 
+
+ align:start position:0%
+because the um I guess to the extent
+Brightwood Development Corporation is
+
+ align:start position:0%
+Brightwood Development Corporation is
+ 
+
+ align:start position:0%
+Brightwood Development Corporation is
+doing something and to the extent that
+
+ align:start position:0%
+doing something and to the extent that
+ 
+
+ align:start position:0%
+doing something and to the extent that
+maybe um the Hispanic chamber is doing
+
+ align:start position:0%
+maybe um the Hispanic chamber is doing
+ 
+
+ align:start position:0%
+maybe um the Hispanic chamber is doing
+something that there there doesn't seem
+
+ align:start position:0%
+something that there there doesn't seem
+ 
+
+ align:start position:0%
+something that there there doesn't seem
+seem to be much capacity even something
+
+ align:start position:0%
+seem to be much capacity even something
+ 
+
+ align:start position:0%
+seem to be much capacity even something
+that I was sort of surprised when I
+
+ align:start position:0%
+that I was sort of surprised when I
+ 
+
+ align:start position:0%
+that I was sort of surprised when I
+asked about was well what's been done
+
+ align:start position:0%
+asked about was well what's been done
+ 
+
+ align:start position:0%
+asked about was well what's been done
+around employment programs so that the
+
+ align:start position:0%
+around employment programs so that the
+ 
+
+ align:start position:0%
+around employment programs so that the
+jobs that bait the state I mean they're
+
+ align:start position:0%
+jobs that bait the state I mean they're
+ 
+
+ align:start position:0%
+jobs that bait the state I mean they're
+just beginning to do something around
+
+ align:start position:0%
+just beginning to do something around
+ 
+
+ align:start position:0%
+just beginning to do something around
+that and that you think that would have
+
+ align:start position:0%
+that and that you think that would have
+ 
+
+ align:start position:0%
+that and that you think that would have
+been something that the employment and
+
+ align:start position:0%
+been something that the employment and
+ 
+
+ align:start position:0%
+been something that the employment and
+training the schools the employment and
+
+ align:start position:0%
+training the schools the employment and
+ 
+
+ align:start position:0%
+training the schools the employment and
+training programs and people in the city
+
+ align:start position:0%
+training programs and people in the city
+ 
+
+ align:start position:0%
+training programs and people in the city
+in the neighborhood would have been
+
+ align:start position:0%
+in the neighborhood would have been
+ 
+
+ align:start position:0%
+in the neighborhood would have been
+thinking about and working on so so I do
+
+ align:start position:0%
+thinking about and working on so so I do
+ 
+
+ align:start position:0%
+thinking about and working on so so I do
+I do think that's something you know we
+
+ align:start position:0%
+I do think that's something you know we
+ 
+
+ align:start position:0%
+I do think that's something you know we
+we should recognize it's going to be
+
+ align:start position:0%
+we should recognize it's going to be
+ 
+
+ align:start position:0%
+we should recognize it's going to be
+important important part of the the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actions quick break yeah um sure yeah
+
+ align:start position:0%
+actions quick break yeah um sure yeah
+ 
+
+ align:start position:0%
+actions quick break yeah um sure yeah
+why don't we take a quick break then we
+
+ align:start position:0%
+why don't we take a quick break then we
+ 
+
+ align:start position:0%
+why don't we take a quick break then we
+could come back and Report out a little
+
+ align:start position:0%
+could come back and Report out a little
+ 
+
+ align:start position:0%
+could come back and Report out a little
+bit on the interviews and data
+
+ align:start position:0%
+bit on the interviews and data
+ 
+
+ align:start position:0%
+bit on the interviews and data
+collection okay and also I would like if
+
+ align:start position:0%
+collection okay and also I would like if
+ 
+
+ align:start position:0%
+collection okay and also I would like if
+somebody would take responsibility for
+
+ align:start position:0%
+somebody would take responsibility for
+ 
+
+ align:start position:0%
+somebody would take responsibility for
+like typing up those notes for the class
+
+ align:start position:0%
+like typing up those notes for the class
+ 
+
+ align:start position:0%
+like typing up those notes for the class
+under each of the categories and you can
+
+ align:start position:0%
+under each of the categories and you can
+ 
+
+ align:start position:0%
+under each of the categories and you can
+figure that out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for like some of those procedural things
+
+ align:start position:0%
+for like some of those procedural things
+ 
+
+ align:start position:0%
+for like some of those procedural things
+outside um healthare I understand the
+
+ align:start position:0%
+outside um healthare I understand the
+ 
+
+ align:start position:0%
+outside um healthare I understand the
+definition of healthare is
+
+ align:start position:0%
+definition of healthare is
+ 
+
+ align:start position:0%
+definition of healthare is
+very well why don't we just pay
+
+ align:start position:0%
+very well why don't we just pay
+ 
+
+ align:start position:0%
+very well why don't we just pay
+attention to this this question for a
+
+ align:start position:0%
+attention to this this question for a
+ 
+
+ align:start position:0%
+attention to this this question for a
+second because I think it's an
+
+ align:start position:0%
+second because I think it's an
+ 
+
+ align:start position:0%
+second because I think it's an
+interesting one because I can give you a
+
+ align:start position:0%
+interesting one because I can give you a
+ 
+
+ align:start position:0%
+interesting one because I can give you a
+little more detail about that particular
+
+ align:start position:0%
+little more detail about that particular
+ 
+
+ align:start position:0%
+little more detail about that particular
+experience the person that they had
+
+ align:start position:0%
+experience the person that they had
+ 
+
+ align:start position:0%
+experience the person that they had
+worked a lot with last year was Michael
+
+ align:start position:0%
+worked a lot with last year was Michael
+ 
+
+ align:start position:0%
+worked a lot with last year was Michael
+Denny who's not part of neon he's
+
+ align:start position:0%
+Denny who's not part of neon he's
+ 
+
+ align:start position:0%
+Denny who's not part of neon he's
+actually with the new North Citizens
+
+ align:start position:0%
+actually with the new North Citizens
+ 
+
+ align:start position:0%
+actually with the new North Citizens
+Council he not an executive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+director he had been part of all the
+
+ align:start position:0%
+director he had been part of all the
+ 
+
+ align:start position:0%
+director he had been part of all the
+meetings with the students when they
+
+ align:start position:0%
+meetings with the students when they
+ 
+
+ align:start position:0%
+meetings with the students when they
+came back and reported and let the stuff
+
+ align:start position:0%
+came back and reported and let the stuff
+ 
+
+ align:start position:0%
+came back and reported and let the stuff
+everything like
+
+ align:start position:0%
+everything like
+ 
+
+ align:start position:0%
+everything like
+this and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh he had been part of that whole
+
+ align:start position:0%
+uh he had been part of that whole
+ 
+
+ align:start position:0%
+uh he had been part of that whole
+process and I think one of the things
+
+ align:start position:0%
+process and I think one of the things
+ 
+
+ align:start position:0%
+process and I think one of the things
+that came up was one of the questions
+
+ align:start position:0%
+that came up was one of the questions
+ 
+
+ align:start position:0%
+that came up was one of the questions
+that I guess the point I'm trying to
+
+ align:start position:0%
+that I guess the point I'm trying to
+ 
+
+ align:start position:0%
+that I guess the point I'm trying to
+make by that is that I don't think it's
+
+ align:start position:0%
+make by that is that I don't think it's
+ 
+
+ align:start position:0%
+make by that is that I don't think it's
+neon that really is the the issue here
+
+ align:start position:0%
+neon that really is the the issue here
+ 
+
+ align:start position:0%
+neon that really is the the issue here
+because I think you're right there are
+
+ align:start position:0%
+because I think you're right there are
+ 
+
+ align:start position:0%
+because I think you're right there are
+certain things that the neon workers are
+
+ align:start position:0%
+certain things that the neon workers are
+ 
+
+ align:start position:0%
+certain things that the neon workers are
+involved in not involved in but even
+
+ align:start position:0%
+involved in not involved in but even
+ 
+
+ align:start position:0%
+involved in not involved in but even
+when you're involved with a broader set
+
+ align:start position:0%
+when you're involved with a broader set
+ 
+
+ align:start position:0%
+when you're involved with a broader set
+of players in the community who kind of
+
+ align:start position:0%
+of players in the community who kind of
+ 
+
+ align:start position:0%
+of players in the community who kind of
+know some things and have a hold of some
+
+ align:start position:0%
+know some things and have a hold of some
+ 
+
+ align:start position:0%
+know some things and have a hold of some
+things there's a there's a question of
+
+ align:start position:0%
+things there's a there's a question of
+ 
+
+ align:start position:0%
+things there's a there's a question of
+you know how is how do people
+
+ align:start position:0%
+you know how is how do people
+ 
+
+ align:start position:0%
+you know how is how do people
+communicate what's real versus what is
+
+ align:start position:0%
+communicate what's real versus what is
+ 
+
+ align:start position:0%
+communicate what's real versus what is
+desired and sometimes those things get I
+
+ align:start position:0%
+desired and sometimes those things get I
+ 
+
+ align:start position:0%
+desired and sometimes those things get I
+think get mixed up and they were they
+
+ align:start position:0%
+think get mixed up and they were they
+ 
+
+ align:start position:0%
+think get mixed up and they were they
+were hard I think for the students to
+
+ align:start position:0%
+were hard I think for the students to
+ 
+
+ align:start position:0%
+were hard I think for the students to
+really kind of uh kind of make their way
+
+ align:start position:0%
+really kind of uh kind of make their way
+ 
+
+ align:start position:0%
+really kind of uh kind of make their way
+through I also think it's really true
+
+ align:start position:0%
+through I also think it's really true
+ 
+
+ align:start position:0%
+through I also think it's really true
+that no one in the community holds this
+
+ align:start position:0%
+that no one in the community holds this
+ 
+
+ align:start position:0%
+that no one in the community holds this
+Economic Development perspective and no
+
+ align:start position:0%
+Economic Development perspective and no
+ 
+
+ align:start position:0%
+Economic Development perspective and no
+one holds a more even though new
+
+ align:start position:0%
+one holds a more even though new
+ 
+
+ align:start position:0%
+one holds a more even though new
+Citizens
+
+ align:start position:0%
+Citizens
+ 
+
+ align:start position:0%
+Citizens
+Council has it in their purview there is
+
+ align:start position:0%
+Council has it in their purview there is
+ 
+
+ align:start position:0%
+Council has it in their purview there is
+really no agency that really have holds
+
+ align:start position:0%
+really no agency that really have holds
+ 
+
+ align:start position:0%
+really no agency that really have holds
+the kind of planning process for the
+
+ align:start position:0%
+the kind of planning process for the
+ 
+
+ align:start position:0%
+the kind of planning process for the
+neighborhood it does fall under the new
+
+ align:start position:0%
+neighborhood it does fall under the new
+ 
+
+ align:start position:0%
+neighborhood it does fall under the new
+North Citizens Council but if you kind
+
+ align:start position:0%
+North Citizens Council but if you kind
+ 
+
+ align:start position:0%
+North Citizens Council but if you kind
+of then think about the size of their
+
+ align:start position:0%
+of then think about the size of their
+ 
+
+ align:start position:0%
+of then think about the size of their
+budget and what the majority of their
+
+ align:start position:0%
+budget and what the majority of their
+ 
+
+ align:start position:0%
+budget and what the majority of their
+work is it's not around that right it's
+
+ align:start position:0%
+work is it's not around that right it's
+ 
+
+ align:start position:0%
+work is it's not around that right it's
+around something else and so I think
+
+ align:start position:0%
+around something else and so I think
+ 
+
+ align:start position:0%
+around something else and so I think
+there is a you know a little bit of a
+
+ align:start position:0%
+there is a you know a little bit of a
+ 
+
+ align:start position:0%
+there is a you know a little bit of a
+golf up between where people can put
+
+ align:start position:0%
+golf up between where people can put
+ 
+
+ align:start position:0%
+golf up between where people can put
+their attention and I think actually the
+
+ align:start position:0%
+their attention and I think actually the
+ 
+
+ align:start position:0%
+their attention and I think actually the
+folks who interview Jeff got some of
+
+ align:start position:0%
+folks who interview Jeff got some of
+ 
+
+ align:start position:0%
+folks who interview Jeff got some of
+that in the interview what I mean not
+
+ align:start position:0%
+that in the interview what I mean not
+ 
+
+ align:start position:0%
+that in the interview what I mean not
+Jeff but I mean uh Michael got some of
+
+ align:start position:0%
+Jeff but I mean uh Michael got some of
+ 
+
+ align:start position:0%
+Jeff but I mean uh Michael got some of
+that in the interview I think he was
+
+ align:start position:0%
+that in the interview I think he was
+ 
+
+ align:start position:0%
+that in the interview I think he was
+very Frank uh in the in in the interview
+
+ align:start position:0%
+very Frank uh in the in in the interview
+ 
+
+ align:start position:0%
+very Frank uh in the in in the interview
+about some of those things so Al if I
+
+ align:start position:0%
+about some of those things so Al if I
+ 
+
+ align:start position:0%
+about some of those things so Al if I
+recall I wasn't involved in the last
+
+ align:start position:0%
+recall I wasn't involved in the last
+ 
+
+ align:start position:0%
+recall I wasn't involved in the last
+year's classes but in some of the
+
+ align:start position:0%
+year's classes but in some of the
+ 
+
+ align:start position:0%
+year's classes but in some of the
+discussions you had I remember process
+
+ align:start position:0%
+discussions you had I remember process
+ 
+
+ align:start position:0%
+discussions you had I remember process
+began with a little bit of a conflict in
+
+ align:start position:0%
+began with a little bit of a conflict in
+ 
+
+ align:start position:0%
+began with a little bit of a conflict in
+agenda wasn't there the new North
+
+ align:start position:0%
+agenda wasn't there the new North
+ 
+
+ align:start position:0%
+agenda wasn't there the new North
+citizen Council had been pushing this
+
+ align:start position:0%
+citizen Council had been pushing this
+ 
+
+ align:start position:0%
+citizen Council had been pushing this
+idea of a community center yes and the
+
+ align:start position:0%
+idea of a community center yes and the
+ 
+
+ align:start position:0%
+idea of a community center yes and the
+idea of a of a campus connecting all of
+
+ align:start position:0%
+idea of a of a campus connecting all of
+ 
+
+ align:start position:0%
+idea of a of a campus connecting all of
+the other organizations was somewhat
+
+ align:start position:0%
+the other organizations was somewhat
+ 
+
+ align:start position:0%
+the other organizations was somewhat
+controversial so there were some
+
+ align:start position:0%
+controversial so there were some
+ 
+
+ align:start position:0%
+controversial so there were some
+divisions there were some division in
+
+ align:start position:0%
+divisions there were some division in
+ 
+
+ align:start position:0%
+divisions there were some division in
+the community even when the project
+
+ align:start position:0%
+the community even when the project
+ 
+
+ align:start position:0%
+the community even when the project
+started and I don't know if that played
+
+ align:start position:0%
+started and I don't know if that played
+ 
+
+ align:start position:0%
+started and I don't know if that played
+into how open some people might have
+
+ align:start position:0%
+into how open some people might have
+ 
+
+ align:start position:0%
+into how open some people might have
+been or not been you know with the
+
+ align:start position:0%
+been or not been you know with the
+ 
+
+ align:start position:0%
+been or not been you know with the
+community but but they did walk into a
+
+ align:start position:0%
+community but but they did walk into a
+ 
+
+ align:start position:0%
+community but but they did walk into a
+situation um where there were some
+
+ align:start position:0%
+situation um where there were some
+ 
+
+ align:start position:0%
+situation um where there were some
+conflicting agendas if I were to be
+
+ align:start position:0%
+conflicting agendas if I were to be
+ 
+
+ align:start position:0%
+conflicting agendas if I were to be
+going forward and so I think at least
+
+ align:start position:0%
+going forward and so I think at least
+ 
+
+ align:start position:0%
+going forward and so I think at least
+have your antennas up for that you know
+
+ align:start position:0%
+have your antennas up for that you know
+ 
+
+ align:start position:0%
+have your antennas up for that you know
+there might be segments of the community
+
+ align:start position:0%
+there might be segments of the community
+ 
+
+ align:start position:0%
+there might be segments of the community
+that think an economic development plan
+
+ align:start position:0%
+that think an economic development plan
+ 
+
+ align:start position:0%
+that think an economic development plan
+isn't what people should be working on
+
+ align:start position:0%
+isn't what people should be working on
+ 
+
+ align:start position:0%
+isn't what people should be working on
+now they might be they might feel
+
+ align:start position:0%
+now they might be they might feel
+ 
+
+ align:start position:0%
+now they might be they might feel
+dealing with vacant housing is is much
+
+ align:start position:0%
+dealing with vacant housing is is much
+ 
+
+ align:start position:0%
+dealing with vacant housing is is much
+more of an important issue or something
+
+ align:start position:0%
+more of an important issue or something
+ 
+
+ align:start position:0%
+more of an important issue or something
+like that so you know you should be you
+
+ align:start position:0%
+like that so you know you should be you
+ 
+
+ align:start position:0%
+like that so you know you should be you
+should be attentive to where there might
+
+ align:start position:0%
+should be attentive to where there might
+ 
+
+ align:start position:0%
+should be attentive to where there might
+be might the conflex of Divisions around
+
+ align:start position:0%
+be might the conflex of Divisions around
+ 
+
+ align:start position:0%
+be might the conflex of Divisions around
+the agenda you're working
+
+ align:start position:0%
+the agenda you're working
+ 
+
+ align:start position:0%
+the agenda you're working
+on why don't we um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh do some debriefing around the
+
+ align:start position:0%
+uh do some debriefing around the
+ 
+
+ align:start position:0%
+uh do some debriefing around the
+interviews that people had and uh who
+
+ align:start position:0%
+interviews that people had and uh who
+ 
+
+ align:start position:0%
+interviews that people had and uh who
+got to interview whom and tell us about
+
+ align:start position:0%
+got to interview whom and tell us about
+ 
+
+ align:start position:0%
+got to interview whom and tell us about
+your interview and what you learned and
+
+ align:start position:0%
+your interview and what you learned and
+ 
+
+ align:start position:0%
+your interview and what you learned and
+what you think is important for us to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know and are there any of the teams here
+
+ align:start position:0%
+know and are there any of the teams here
+ 
+
+ align:start position:0%
+know and are there any of the teams here
+who let see who was interviewed Jeff was
+
+ align:start position:0%
+who let see who was interviewed Jeff was
+ 
+
+ align:start position:0%
+who let see who was interviewed Jeff was
+interviewed Robert Bailey was
+
+ align:start position:0%
+interviewed Robert Bailey was
+ 
+
+ align:start position:0%
+interviewed Robert Bailey was
+interviewed I guess or he spoke I'm not
+
+ align:start position:0%
+interviewed I guess or he spoke I'm not
+ 
+
+ align:start position:0%
+interviewed I guess or he spoke I'm not
+sure which one that was really
+
+ align:start position:0%
+sure which one that was really
+ 
+
+ align:start position:0%
+sure which one that was really
+interviewed he wasn't interviewed uh my
+
+ align:start position:0%
+interviewed he wasn't interviewed uh my
+ 
+
+ align:start position:0%
+interviewed he wasn't interviewed uh my
+Michael was
+
+ align:start position:0%
+Michael was
+ 
+
+ align:start position:0%
+Michael was
+interviewed Michael Denny Jeff anyone
+
+ align:start position:0%
+interviewed Michael Denny Jeff anyone
+ 
+
+ align:start position:0%
+interviewed Michael Denny Jeff anyone
+else Peter Peter Lon was interview so
+
+ align:start position:0%
+else Peter Peter Lon was interview so
+ 
+
+ align:start position:0%
+else Peter Peter Lon was interview so
+those are the three
+
+ align:start position:0%
+those are the three
+ 
+
+ align:start position:0%
+those are the three
+interviews cool so why don't we start
+
+ align:start position:0%
+interviews cool so why don't we start
+ 
+
+ align:start position:0%
+interviews cool so why don't we start
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+Peter who did Peter yeah we did okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually try to suiz
+
+ align:start position:0%
+actually try to suiz
+ 
+
+ align:start position:0%
+actually try to suiz
+something I hope uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think he's a principal from school
+
+ align:start position:0%
+I think he's a principal from school
+ 
+
+ align:start position:0%
+I think he's a principal from school
+sorry Phil did I give you my notes yeah
+
+ align:start position:0%
+sorry Phil did I give you my notes yeah
+ 
+
+ align:start position:0%
+sorry Phil did I give you my notes yeah
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+did yes he's the principal for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this yeah I mean I I I didn't really
+
+ align:start position:0%
+this yeah I mean I I I didn't really
+ 
+
+ align:start position:0%
+this yeah I mean I I I didn't really
+like organize in any particular fashion
+
+ align:start position:0%
+like organize in any particular fashion
+ 
+
+ align:start position:0%
+like organize in any particular fashion
+I just kind like type up what I talk
+
+ align:start position:0%
+I just kind like type up what I talk
+ 
+
+ align:start position:0%
+I just kind like type up what I talk
+about the issues and just sort of pull
+
+ align:start position:0%
+about the issues and just sort of pull
+ 
+
+ align:start position:0%
+about the issues and just sort of pull
+up points you know is there extra one
+
+ align:start position:0%
+up points you know is there extra one
+ 
+
+ align:start position:0%
+up points you know is there extra one
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we share okay okay and we can share
+
+ align:start position:0%
+we share okay okay and we can share
+ 
+
+ align:start position:0%
+we share okay okay and we can share
+we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fine yeah so um in the beginning one of
+
+ align:start position:0%
+fine yeah so um in the beginning one of
+ 
+
+ align:start position:0%
+fine yeah so um in the beginning one of
+the the first thing he talk about was
+
+ align:start position:0%
+the the first thing he talk about was
+ 
+
+ align:start position:0%
+the the first thing he talk about was
+just his connection with the community
+
+ align:start position:0%
+just his connection with the community
+ 
+
+ align:start position:0%
+just his connection with the community
+and he said that he's been working there
+
+ align:start position:0%
+and he said that he's been working there
+ 
+
+ align:start position:0%
+and he said that he's been working there
+um since since in
+
+ align:start position:0%
+um since since in
+ 
+
+ align:start position:0%
+um since since in
+1967 as a community activist and used to
+
+ align:start position:0%
+1967 as a community activist and used to
+ 
+
+ align:start position:0%
+1967 as a community activist and used to
+be the director for community services
+
+ align:start position:0%
+be the director for community services
+ 
+
+ align:start position:0%
+be the director for community services
+and people becoming principle he was a
+
+ align:start position:0%
+and people becoming principle he was a
+ 
+
+ align:start position:0%
+and people becoming principle he was a
+number two man for education I believe
+
+ align:start position:0%
+number two man for education I believe
+ 
+
+ align:start position:0%
+number two man for education I believe
+in spr I'm not sure of that but I think
+
+ align:start position:0%
+in spr I'm not sure of that but I think
+ 
+
+ align:start position:0%
+in spr I'm not sure of that but I think
+that's why I heard
+
+ align:start position:0%
+that's why I heard
+ 
+
+ align:start position:0%
+that's why I heard
+um and then he has been principal for
+
+ align:start position:0%
+um and then he has been principal for
+ 
+
+ align:start position:0%
+um and then he has been principal for
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+um there was no specific order to our
+
+ align:start position:0%
+um there was no specific order to our
+ 
+
+ align:start position:0%
+um there was no specific order to our
+sort of interview just went around you
+
+ align:start position:0%
+sort of interview just went around you
+ 
+
+ align:start position:0%
+sort of interview just went around you
+know looking at issues that came up in
+
+ align:start position:0%
+know looking at issues that came up in
+ 
+
+ align:start position:0%
+know looking at issues that came up in
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+so one of the big things you talk about
+
+ align:start position:0%
+so one of the big things you talk about
+ 
+
+ align:start position:0%
+so one of the big things you talk about
+uh in the beginning was this issue of
+
+ align:start position:0%
+uh in the beginning was this issue of
+ 
+
+ align:start position:0%
+uh in the beginning was this issue of
+Housing and it was very clear from the
+
+ align:start position:0%
+Housing and it was very clear from the
+ 
+
+ align:start position:0%
+Housing and it was very clear from the
+very beginning that housing was the
+
+ align:start position:0%
+very beginning that housing was the
+ 
+
+ align:start position:0%
+very beginning that housing was the
+biggest his biggest concern uh in the
+
+ align:start position:0%
+biggest his biggest concern uh in the
+ 
+
+ align:start position:0%
+biggest his biggest concern uh in the
+beginning uh he talk about housing for
+
+ align:start position:0%
+beginning uh he talk about housing for
+ 
+
+ align:start position:0%
+beginning uh he talk about housing for
+the Ed as well and he did say um that
+
+ align:start position:0%
+the Ed as well and he did say um that
+ 
+
+ align:start position:0%
+the Ed as well and he did say um that
+from the bridal side of things the
+
+ align:start position:0%
+from the bridal side of things the
+ 
+
+ align:start position:0%
+from the bridal side of things the
+housing stock was pretty much stable and
+
+ align:start position:0%
+housing stock was pretty much stable and
+ 
+
+ align:start position:0%
+housing stock was pretty much stable and
+okay but that he felt that uh some of
+
+ align:start position:0%
+okay but that he felt that uh some of
+ 
+
+ align:start position:0%
+okay but that he felt that uh some of
+the housing on the mor Square side
+
+ align:start position:0%
+the housing on the mor Square side
+ 
+
+ align:start position:0%
+the housing on the mor Square side
+needed some attention
+
+ align:start position:0%
+needed some attention
+ 
+
+ align:start position:0%
+needed some attention
+uh in fact he they talk about some of
+
+ align:start position:0%
+uh in fact he they talk about some of
+ 
+
+ align:start position:0%
+uh in fact he they talk about some of
+those areas being completely clear out
+
+ align:start position:0%
+those areas being completely clear out
+ 
+
+ align:start position:0%
+those areas being completely clear out
+and new housing in put in
+
+ align:start position:0%
+and new housing in put in
+ 
+
+ align:start position:0%
+and new housing in put in
+there and then we talk a little bit
+
+ align:start position:0%
+there and then we talk a little bit
+ 
+
+ align:start position:0%
+there and then we talk a little bit
+about the school um and the environment
+
+ align:start position:0%
+about the school um and the environment
+ 
+
+ align:start position:0%
+about the school um and the environment
+there basically three elementary schools
+
+ align:start position:0%
+there basically three elementary schools
+ 
+
+ align:start position:0%
+there basically three elementary schools
+and one Middle School in the area and
+
+ align:start position:0%
+and one Middle School in the area and
+ 
+
+ align:start position:0%
+and one Middle School in the area and
+most high schools are in downtown the
+
+ align:start position:0%
+most high schools are in downtown the
+ 
+
+ align:start position:0%
+most high schools are in downtown the
+downtown area um the school in
+
+ align:start position:0%
+downtown area um the school in
+ 
+
+ align:start position:0%
+downtown area um the school in
+particular is mostly Hispanic and has
+
+ align:start position:0%
+particular is mostly Hispanic and has
+ 
+
+ align:start position:0%
+particular is mostly Hispanic and has
+and that group also also has the highest
+
+ align:start position:0%
+and that group also also has the highest
+ 
+
+ align:start position:0%
+and that group also also has the highest
+drug out
+
+ align:start position:0%
+drug out
+ 
+
+ align:start position:0%
+drug out
+rate um he did say that there were like
+
+ align:start position:0%
+rate um he did say that there were like
+ 
+
+ align:start position:0%
+rate um he did say that there were like
+92% free lunch introduced in the school
+
+ align:start position:0%
+92% free lunch introduced in the school
+ 
+
+ align:start position:0%
+92% free lunch introduced in the school
+uh he talk about how the school had made
+
+ align:start position:0%
+uh he talk about how the school had made
+ 
+
+ align:start position:0%
+uh he talk about how the school had made
+some progress in the last couple of in
+
+ align:start position:0%
+some progress in the last couple of in
+ 
+
+ align:start position:0%
+some progress in the last couple of in
+the last couple of years for example
+
+ align:start position:0%
+the last couple of years for example
+ 
+
+ align:start position:0%
+the last couple of years for example
+they used to place two from the bottom
+
+ align:start position:0%
+they used to place two from the bottom
+ 
+
+ align:start position:0%
+they used to place two from the bottom
+you know couple of years ago and now
+
+ align:start position:0%
+you know couple of years ago and now
+ 
+
+ align:start position:0%
+you know couple of years ago and now
+they're like 16 in math and 18 in
+
+ align:start position:0%
+they're like 16 in math and 18 in
+ 
+
+ align:start position:0%
+they're like 16 in math and 18 in
+English in massachusett
+
+ align:start position:0%
+English in massachusett
+ 
+
+ align:start position:0%
+English in massachusett
+so um just couple of curious point he
+
+ align:start position:0%
+so um just couple of curious point he
+ 
+
+ align:start position:0%
+so um just couple of curious point he
+talk about you know African-Americans is
+
+ align:start position:0%
+talk about you know African-Americans is
+ 
+
+ align:start position:0%
+talk about you know African-Americans is
+doing well incast as compared to other
+
+ align:start position:0%
+doing well incast as compared to other
+ 
+
+ align:start position:0%
+doing well incast as compared to other
+uh groups there it talks about how they
+
+ align:start position:0%
+uh groups there it talks about how they
+ 
+
+ align:start position:0%
+uh groups there it talks about how they
+were limited inage proficiency among
+
+ align:start position:0%
+were limited inage proficiency among
+ 
+
+ align:start position:0%
+were limited inage proficiency among
+students and then he also talk a lot
+
+ align:start position:0%
+students and then he also talk a lot
+ 
+
+ align:start position:0%
+students and then he also talk a lot
+about his the partnership the school had
+
+ align:start position:0%
+about his the partnership the school had
+ 
+
+ align:start position:0%
+about his the partnership the school had
+with Smith college uh which provide
+
+ align:start position:0%
+with Smith college uh which provide
+ 
+
+ align:start position:0%
+with Smith college uh which provide
+after school Tut and sports uh for the
+
+ align:start position:0%
+after school Tut and sports uh for the
+ 
+
+ align:start position:0%
+after school Tut and sports uh for the
+kids and there a couple of issue on the
+
+ align:start position:0%
+kids and there a couple of issue on the
+ 
+
+ align:start position:0%
+kids and there a couple of issue on the
+demographic um basically he talk about
+
+ align:start position:0%
+demographic um basically he talk about
+ 
+
+ align:start position:0%
+demographic um basically he talk about
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+1950s how the area was set up by
+
+ align:start position:0%
+1950s how the area was set up by
+ 
+
+ align:start position:0%
+1950s how the area was set up by
+recruits from Puerto Rico for the
+
+ align:start position:0%
+recruits from Puerto Rico for the
+ 
+
+ align:start position:0%
+recruits from Puerto Rico for the
+tobacco
+
+ align:start position:0%
+tobacco
+ 
+
+ align:start position:0%
+tobacco
+Farms um and then the North End being
+
+ align:start position:0%
+Farms um and then the North End being
+ 
+
+ align:start position:0%
+Farms um and then the North End being
+the Forest
+
+ align:start position:0%
+the Forest
+ 
+
+ align:start position:0%
+the Forest
+community in the area but at the same
+
+ align:start position:0%
+community in the area but at the same
+ 
+
+ align:start position:0%
+community in the area but at the same
+time serve as a gway into the region uh
+
+ align:start position:0%
+time serve as a gway into the region uh
+ 
+
+ align:start position:0%
+time serve as a gway into the region uh
+he talk about a lot about how um
+
+ align:start position:0%
+he talk about a lot about how um
+ 
+
+ align:start position:0%
+he talk about a lot about how um
+pollution has taking place a lot in the
+
+ align:start position:0%
+pollution has taking place a lot in the
+ 
+
+ align:start position:0%
+pollution has taking place a lot in the
+area that has led to a high incidence of
+
+ align:start position:0%
+area that has led to a high incidence of
+ 
+
+ align:start position:0%
+area that has led to a high incidence of
+asthma uh we talk about new influx of
+
+ align:start position:0%
+asthma uh we talk about new influx of
+ 
+
+ align:start position:0%
+asthma uh we talk about new influx of
+immigrants from Mexico and Salvador
+
+ align:start position:0%
+immigrants from Mexico and Salvador
+ 
+
+ align:start position:0%
+immigrants from Mexico and Salvador
+Guatemala Dominican Republic in addition
+
+ align:start position:0%
+Guatemala Dominican Republic in addition
+ 
+
+ align:start position:0%
+Guatemala Dominican Republic in addition
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the more traditional uh Puerto Rican in
+
+ align:start position:0%
+the more traditional uh Puerto Rican in
+ 
+
+ align:start position:0%
+the more traditional uh Puerto Rican in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+community and one important thing he
+
+ align:start position:0%
+community and one important thing he
+ 
+
+ align:start position:0%
+community and one important thing he
+said was that I mean in a question I
+
+ align:start position:0%
+said was that I mean in a question I
+ 
+
+ align:start position:0%
+said was that I mean in a question I
+think it was uh James who asked a
+
+ align:start position:0%
+think it was uh James who asked a
+ 
+
+ align:start position:0%
+think it was uh James who asked a
+question or something like that
+
+ align:start position:0%
+question or something like that
+ 
+
+ align:start position:0%
+question or something like that
+concerning the political environment and
+
+ align:start position:0%
+concerning the political environment and
+ 
+
+ align:start position:0%
+concerning the political environment and
+he did say that uh there was a control
+
+ align:start position:0%
+he did say that uh there was a control
+ 
+
+ align:start position:0%
+he did say that uh there was a control
+go composed of five
+
+ align:start position:0%
+go composed of five
+ 
+
+ align:start position:0%
+go composed of five
+members and that three of those members
+
+ align:start position:0%
+members and that three of those members
+ 
+
+ align:start position:0%
+members and that three of those members
+were government appointees and they're
+
+ align:start position:0%
+were government appointees and they're
+ 
+
+ align:start position:0%
+were government appointees and they're
+particularly conservative you know state
+
+ align:start position:0%
+particularly conservative you know state
+ 
+
+ align:start position:0%
+particularly conservative you know state
+government state
+
+ align:start position:0%
+government state
+ 
+
+ align:start position:0%
+government state
+I didn't quite understand all of that
+
+ align:start position:0%
+I didn't quite understand all of that
+ 
+
+ align:start position:0%
+I didn't quite understand all of that
+but um but maybe you guys do
+
+ align:start position:0%
+but um but maybe you guys do
+ 
+
+ align:start position:0%
+but um but maybe you guys do
+anyway um and he also talk about the
+
+ align:start position:0%
+anyway um and he also talk about the
+ 
+
+ align:start position:0%
+anyway um and he also talk about the
+neighor drawing a lot of churches and
+
+ align:start position:0%
+neighor drawing a lot of churches and
+ 
+
+ align:start position:0%
+neighor drawing a lot of churches and
+Clinics uh on the health side the issues
+
+ align:start position:0%
+Clinics uh on the health side the issues
+ 
+
+ align:start position:0%
+Clinics uh on the health side the issues
+included HIV diabetes asthma and
+
+ align:start position:0%
+included HIV diabetes asthma and
+ 
+
+ align:start position:0%
+included HIV diabetes asthma and
+obesity from the employment side talk
+
+ align:start position:0%
+obesity from the employment side talk
+ 
+
+ align:start position:0%
+obesity from the employment side talk
+about B State um but he did mention that
+
+ align:start position:0%
+about B State um but he did mention that
+ 
+
+ align:start position:0%
+about B State um but he did mention that
+there was no concered effort by the
+
+ align:start position:0%
+there was no concered effort by the
+ 
+
+ align:start position:0%
+there was no concered effort by the
+community to push for job
+
+ align:start position:0%
+community to push for job
+ 
+
+ align:start position:0%
+community to push for job
+creation um and then mag workers of
+
+ align:start position:0%
+creation um and then mag workers of
+ 
+
+ align:start position:0%
+creation um and then mag workers of
+course work on farms along the colica
+
+ align:start position:0%
+course work on farms along the colica
+ 
+
+ align:start position:0%
+course work on farms along the colica
+river um terms of families you talk
+
+ align:start position:0%
+river um terms of families you talk
+ 
+
+ align:start position:0%
+river um terms of families you talk
+about how the the need
+
+ align:start position:0%
+about how the the need
+ 
+
+ align:start position:0%
+about how the the need
+for some kind of stabilization for
+
+ align:start position:0%
+for some kind of stabilization for
+ 
+
+ align:start position:0%
+for some kind of stabilization for
+families and he saw that as basically
+
+ align:start position:0%
+families and he saw that as basically
+ 
+
+ align:start position:0%
+families and he saw that as basically
+coming from the economic Foundation uh
+
+ align:start position:0%
+coming from the economic Foundation uh
+ 
+
+ align:start position:0%
+coming from the economic Foundation uh
+people getting jobs and having income to
+
+ align:start position:0%
+people getting jobs and having income to
+ 
+
+ align:start position:0%
+people getting jobs and having income to
+support their families talk a lot about
+
+ align:start position:0%
+support their families talk a lot about
+ 
+
+ align:start position:0%
+support their families talk a lot about
+broken families and how basically you
+
+ align:start position:0%
+broken families and how basically you
+ 
+
+ align:start position:0%
+broken families and how basically you
+had a situation where kids were raising
+
+ align:start position:0%
+had a situation where kids were raising
+ 
+
+ align:start position:0%
+had a situation where kids were raising
+kids
+
+ align:start position:0%
+kids
+ 
+
+ align:start position:0%
+kids
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+lastly if I can just add one thing to
+
+ align:start position:0%
+lastly if I can just add one thing to
+ 
+
+ align:start position:0%
+lastly if I can just add one thing to
+that you talked a lot about adult
+
+ align:start position:0%
+that you talked a lot about adult
+ 
+
+ align:start position:0%
+that you talked a lot about adult
+literacy as well and trying to to to get
+
+ align:start position:0%
+literacy as well and trying to to to get
+ 
+
+ align:start position:0%
+literacy as well and trying to to to get
+that I
+
+ align:start position:0%
+that I
+ 
+
+ align:start position:0%
+that I
+mean kids having kids kind of if how can
+
+ align:start position:0%
+mean kids having kids kind of if how can
+ 
+
+ align:start position:0%
+mean kids having kids kind of if how can
+the kids kind of I mean based on the
+
+ align:start position:0%
+the kids kind of I mean based on the
+ 
+
+ align:start position:0%
+the kids kind of I mean based on the
+idea that how can the kids really um
+
+ align:start position:0%
+idea that how can the kids really um
+ 
+
+ align:start position:0%
+idea that how can the kids really um
+grow and learn if their parents aren't
+
+ align:start position:0%
+grow and learn if their parents aren't
+ 
+
+ align:start position:0%
+grow and learn if their parents aren't
+um don't have the capacity to help teach
+
+ align:start position:0%
+um don't have the capacity to help teach
+ 
+
+ align:start position:0%
+um don't have the capacity to help teach
+them um so they kind of teaching in the
+
+ align:start position:0%
+them um so they kind of teaching in the
+ 
+
+ align:start position:0%
+them um so they kind of teaching in the
+home thing so I think he I don't know if
+
+ align:start position:0%
+home thing so I think he I don't know if
+ 
+
+ align:start position:0%
+home thing so I think he I don't know if
+it's current or if it's a recent
+
+ align:start position:0%
+it's current or if it's a recent
+ 
+
+ align:start position:0%
+it's current or if it's a recent
+initiative but to do adult literacy in
+
+ align:start position:0%
+initiative but to do adult literacy in
+ 
+
+ align:start position:0%
+initiative but to do adult literacy in
+not only English but also in
+
+ align:start position:0%
+not only English but also in
+ 
+
+ align:start position:0%
+not only English but also in
+Spanish actually have some of that read
+
+ align:start position:0%
+Spanish actually have some of that read
+ 
+
+ align:start position:0%
+Spanish actually have some of that read
+okay sorry where you have challenges
+
+ align:start position:0%
+okay sorry where you have challenges
+ 
+
+ align:start position:0%
+okay sorry where you have challenges
+opportunities
+
+ align:start position:0%
+opportunities
+ 
+
+ align:start position:0%
+opportunities
+plans uh Peter thinks that business is a
+
+ align:start position:0%
+plans uh Peter thinks that business is a
+ 
+
+ align:start position:0%
+plans uh Peter thinks that business is a
+way to go I mean he is very strong on
+
+ align:start position:0%
+way to go I mean he is very strong on
+ 
+
+ align:start position:0%
+way to go I mean he is very strong on
+that he believes there are lots of
+
+ align:start position:0%
+that he believes there are lots of
+ 
+
+ align:start position:0%
+that he believes there are lots of
+entrepreneurs in the area for example
+
+ align:start position:0%
+entrepreneurs in the area for example
+ 
+
+ align:start position:0%
+entrepreneurs in the area for example
+talk about artist uh massage followers
+
+ align:start position:0%
+talk about artist uh massage followers
+ 
+
+ align:start position:0%
+talk about artist uh massage followers
+or viers even though most are illegal
+
+ align:start position:0%
+or viers even though most are illegal
+ 
+
+ align:start position:0%
+or viers even though most are illegal
+restaurants
+
+ align:start position:0%
+restaurants
+ 
+
+ align:start position:0%
+restaurants
+H all shops okay so when that St pet
+
+ align:start position:0%
+H all shops okay so when that St pet
+ 
+
+ align:start position:0%
+H all shops okay so when that St pet
+thinks business is the way to go yeah
+
+ align:start position:0%
+thinks business is the way to go yeah
+ 
+
+ align:start position:0%
+thinks business is the way to go yeah
+that that's helping people form
+
+ align:start position:0%
+that that's helping people form
+ 
+
+ align:start position:0%
+that that's helping people form
+businesses is is really should be a
+
+ align:start position:0%
+businesses is is really should be a
+ 
+
+ align:start position:0%
+businesses is is really should be a
+priority for any economic development
+
+ align:start position:0%
+priority for any economic development
+ 
+
+ align:start position:0%
+priority for any economic development
+plan is that sort of what you mean there
+
+ align:start position:0%
+plan is that sort of what you mean there
+ 
+
+ align:start position:0%
+plan is that sort of what you mean there
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+um and then also you talk up a little
+
+ align:start position:0%
+um and then also you talk up a little
+ 
+
+ align:start position:0%
+um and then also you talk up a little
+bit about this whole idea of business
+
+ align:start position:0%
+bit about this whole idea of business
+ 
+
+ align:start position:0%
+bit about this whole idea of business
+incubation I think we you also talk
+
+ align:start position:0%
+incubation I think we you also talk
+ 
+
+ align:start position:0%
+incubation I think we you also talk
+about during the lunch time uh selecting
+
+ align:start position:0%
+about during the lunch time uh selecting
+ 
+
+ align:start position:0%
+about during the lunch time uh selecting
+or desting a place in the school for
+
+ align:start position:0%
+or desting a place in the school for
+ 
+
+ align:start position:0%
+or desting a place in the school for
+that uh so he talked about that and he
+
+ align:start position:0%
+that uh so he talked about that and he
+ 
+
+ align:start position:0%
+that uh so he talked about that and he
+felt that this whole idea will really be
+
+ align:start position:0%
+felt that this whole idea will really be
+ 
+
+ align:start position:0%
+felt that this whole idea will really be
+appealing to the three government
+
+ align:start position:0%
+appealing to the three government
+ 
+
+ align:start position:0%
+appealing to the three government
+appointees on this board that it will be
+
+ align:start position:0%
+appointees on this board that it will be
+ 
+
+ align:start position:0%
+appointees on this board that it will be
+really one way of getting them involved
+
+ align:start position:0%
+really one way of getting them involved
+ 
+
+ align:start position:0%
+really one way of getting them involved
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+community
+
+ align:start position:0%
+community
+ 
+
+ align:start position:0%
+community
+um in terms of I mean one challenge you
+
+ align:start position:0%
+um in terms of I mean one challenge you
+ 
+
+ align:start position:0%
+um in terms of I mean one challenge you
+talk about was just the homeschool
+
+ align:start position:0%
+talk about was just the homeschool
+ 
+
+ align:start position:0%
+talk about was just the homeschool
+connection how do you connect the school
+
+ align:start position:0%
+connection how do you connect the school
+ 
+
+ align:start position:0%
+connection how do you connect the school
+to the home and some of the issues that
+
+ align:start position:0%
+to the home and some of the issues that
+ 
+
+ align:start position:0%
+to the home and some of the issues that
+Jim just talked about um how to engage
+
+ align:start position:0%
+Jim just talked about um how to engage
+ 
+
+ align:start position:0%
+Jim just talked about um how to engage
+the community and some ideas um he had
+
+ align:start position:0%
+the community and some ideas um he had
+ 
+
+ align:start position:0%
+the community and some ideas um he had
+was to provide um rural health care for
+
+ align:start position:0%
+was to provide um rural health care for
+ 
+
+ align:start position:0%
+was to provide um rural health care for
+students he estimated that about 90% of
+
+ align:start position:0%
+students he estimated that about 90% of
+ 
+
+ align:start position:0%
+students he estimated that about 90% of
+the students needed oral healthare and
+
+ align:start position:0%
+the students needed oral healthare and
+ 
+
+ align:start position:0%
+the students needed oral healthare and
+he also had his idea of opening the
+
+ align:start position:0%
+he also had his idea of opening the
+ 
+
+ align:start position:0%
+he also had his idea of opening the
+dental clinic for otherly people in the
+
+ align:start position:0%
+dental clinic for otherly people in the
+ 
+
+ align:start position:0%
+dental clinic for otherly people in the
+evening hours uh at
+
+ align:start position:0%
+evening hours uh at
+ 
+
+ align:start position:0%
+evening hours uh at
+school and then uh some ideas included
+
+ align:start position:0%
+school and then uh some ideas included
+ 
+
+ align:start position:0%
+school and then uh some ideas included
+providing English and Spanish literacy
+
+ align:start position:0%
+providing English and Spanish literacy
+ 
+
+ align:start position:0%
+providing English and Spanish literacy
+classes for
+
+ align:start position:0%
+classes for
+ 
+
+ align:start position:0%
+classes for
+parents uh where parents his idea was
+
+ align:start position:0%
+parents uh where parents his idea was
+ 
+
+ align:start position:0%
+parents uh where parents his idea was
+get a group of parents train them and
+
+ align:start position:0%
+get a group of parents train them and
+ 
+
+ align:start position:0%
+get a group of parents train them and
+and these parents then will be
+
+ align:start position:0%
+and these parents then will be
+ 
+
+ align:start position:0%
+and these parents then will be
+responsible to teach other
+
+ align:start position:0%
+responsible to teach other
+ 
+
+ align:start position:0%
+responsible to teach other
+parents uh and then he also talk about
+
+ align:start position:0%
+parents uh and then he also talk about
+ 
+
+ align:start position:0%
+parents uh and then he also talk about
+plans to research into how to deliver
+
+ align:start position:0%
+plans to research into how to deliver
+ 
+
+ align:start position:0%
+plans to research into how to deliver
+literacy classes for families and this
+
+ align:start position:0%
+literacy classes for families and this
+ 
+
+ align:start position:0%
+literacy classes for families and this
+would be I guess done by dis
+
+ align:start position:0%
+would be I guess done by dis
+ 
+
+ align:start position:0%
+would be I guess done by dis
+College um his idea on new was that
+
+ align:start position:0%
+College um his idea on new was that
+ 
+
+ align:start position:0%
+College um his idea on new was that
+they're very powerful and they get very
+
+ align:start position:0%
+they're very powerful and they get very
+ 
+
+ align:start position:0%
+they're very powerful and they get very
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+response he talk about State Rep living
+
+ align:start position:0%
+response he talk about State Rep living
+ 
+
+ align:start position:0%
+response he talk about State Rep living
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+neighborhood and there was a very good
+
+ align:start position:0%
+neighborhood and there was a very good
+ 
+
+ align:start position:0%
+neighborhood and there was a very good
+connection to the mayor and and there're
+
+ align:start position:0%
+connection to the mayor and and there're
+ 
+
+ align:start position:0%
+connection to the mayor and and there're
+also funding for social services
+
+ align:start position:0%
+also funding for social services
+ 
+
+ align:start position:0%
+also funding for social services
+so just want to go back to one thing
+
+ align:start position:0%
+so just want to go back to one thing
+ 
+
+ align:start position:0%
+so just want to go back to one thing
+real quick do people understand what it
+
+ align:start position:0%
+real quick do people understand what it
+ 
+
+ align:start position:0%
+real quick do people understand what it
+means under the school thing it says 92%
+
+ align:start position:0%
+means under the school thing it says 92%
+ 
+
+ align:start position:0%
+means under the school thing it says 92%
+free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lot is that clear to everyone what that
+
+ align:start position:0%
+lot is that clear to everyone what that
+ 
+
+ align:start position:0%
+lot is that clear to everyone what that
+actually means no in order in to qualify
+
+ align:start position:0%
+actually means no in order in to qualify
+ 
+
+ align:start position:0%
+actually means no in order in to qualify
+for kids to get free lunch at the school
+
+ align:start position:0%
+for kids to get free lunch at the school
+ 
+
+ align:start position:0%
+for kids to get free lunch at the school
+they basically they have to come from a
+
+ align:start position:0%
+they basically they have to come from a
+ 
+
+ align:start position:0%
+they basically they have to come from a
+family that lives within a certain
+
+ align:start position:0%
+family that lives within a certain
+ 
+
+ align:start position:0%
+family that lives within a certain
+percentage of the pover
+
+ align:start position:0%
+percentage of the pover
+ 
+
+ align:start position:0%
+percentage of the pover
+level uh set by the federal government
+
+ align:start position:0%
+level uh set by the federal government
+ 
+
+ align:start position:0%
+level uh set by the federal government
+so this is actually a measure of poverty
+
+ align:start position:0%
+so this is actually a measure of poverty
+ 
+
+ align:start position:0%
+so this is actually a measure of poverty
+of school kids who are in school that
+
+ align:start position:0%
+of school kids who are in school that
+ 
+
+ align:start position:0%
+of school kids who are in school that
+are actually
+
+ align:start position:0%
+are actually
+ 
+
+ align:start position:0%
+are actually
+living um yeah that doesn't necessarily
+
+ align:start position:0%
+living um yeah that doesn't necessarily
+ 
+
+ align:start position:0%
+living um yeah that doesn't necessarily
+represent everyone in the community
+
+ align:start position:0%
+represent everyone in the community
+ 
+
+ align:start position:0%
+represent everyone in the community
+because some people might be sending
+
+ align:start position:0%
+because some people might be sending
+ 
+
+ align:start position:0%
+because some people might be sending
+their kids to private schools or other
+
+ align:start position:0%
+their kids to private schools or other
+ 
+
+ align:start position:0%
+their kids to private schools or other
+schools but it's C it's certainly an
+
+ align:start position:0%
+schools but it's C it's certainly an
+ 
+
+ align:start position:0%
+schools but it's C it's certainly an
+indicator um any anyone else at the
+
+ align:start position:0%
+indicator um any anyone else at the
+ 
+
+ align:start position:0%
+indicator um any anyone else at the
+interview want to add anything any
+
+ align:start position:0%
+interview want to add anything any
+ 
+
+ align:start position:0%
+interview want to add anything any
+J um can I also do people understand the
+
+ align:start position:0%
+J um can I also do people understand the
+ 
+
+ align:start position:0%
+J um can I also do people understand the
+the the financial control board
+
+ align:start position:0%
+the the financial control board
+ 
+
+ align:start position:0%
+the the financial control board
+situation don't need any more
+
+ align:start position:0%
+situation don't need any more
+ 
+
+ align:start position:0%
+situation don't need any more
+clarification that okay yeah I think I
+
+ align:start position:0%
+clarification that okay yeah I think I
+ 
+
+ align:start position:0%
+clarification that okay yeah I think I
+mean just my big kind of global
+
+ align:start position:0%
+mean just my big kind of global
+ 
+
+ align:start position:0%
+mean just my big kind of global
+takeaway um was it was really you know
+
+ align:start position:0%
+takeaway um was it was really you know
+ 
+
+ align:start position:0%
+takeaway um was it was really you know
+Peter obviously has really deep roots in
+
+ align:start position:0%
+Peter obviously has really deep roots in
+ 
+
+ align:start position:0%
+Peter obviously has really deep roots in
+in the community um has been in
+
+ align:start position:0%
+in the community um has been in
+ 
+
+ align:start position:0%
+in the community um has been in
+positions you know I think you know even
+
+ align:start position:0%
+positions you know I think you know even
+ 
+
+ align:start position:0%
+positions you know I think you know even
+at lunchtime he kind of said oh yeah
+
+ align:start position:0%
+at lunchtime he kind of said oh yeah
+ 
+
+ align:start position:0%
+at lunchtime he kind of said oh yeah
+headed up the Redevelopment you know
+
+ align:start position:0%
+headed up the Redevelopment you know
+ 
+
+ align:start position:0%
+headed up the Redevelopment you know
+Authority and that didn't come out
+
+ align:start position:0%
+Authority and that didn't come out
+ 
+
+ align:start position:0%
+Authority and that didn't come out
+intervie at all um so and then you know
+
+ align:start position:0%
+intervie at all um so and then you know
+ 
+
+ align:start position:0%
+intervie at all um so and then you know
+he was talking about how you know he was
+
+ align:start position:0%
+he was talking about how you know he was
+ 
+
+ align:start position:0%
+he was talking about how you know he was
+in a construction you know had and like
+
+ align:start position:0%
+in a construction you know had and like
+ 
+
+ align:start position:0%
+in a construction you know had and like
+with this the school and build you know
+
+ align:start position:0%
+with this the school and build you know
+ 
+
+ align:start position:0%
+with this the school and build you know
+really building the school so um I think
+
+ align:start position:0%
+really building the school so um I think
+ 
+
+ align:start position:0%
+really building the school so um I think
+he feels um personally um responsible
+
+ align:start position:0%
+he feels um personally um responsible
+ 
+
+ align:start position:0%
+he feels um personally um responsible
+you know for a lot of the stuff that
+
+ align:start position:0%
+you know for a lot of the stuff that
+ 
+
+ align:start position:0%
+you know for a lot of the stuff that
+goes on um but he really did focus on
+
+ align:start position:0%
+goes on um but he really did focus on
+ 
+
+ align:start position:0%
+goes on um but he really did focus on
+the you know the small businesses and
+
+ align:start position:0%
+the you know the small businesses and
+ 
+
+ align:start position:0%
+the you know the small businesses and
+the entrepreneurship microenterprises
+
+ align:start position:0%
+the entrepreneurship microenterprises
+ 
+
+ align:start position:0%
+the entrepreneurship microenterprises
+the the kind of way way to go in the
+
+ align:start position:0%
+the the kind of way way to go in the
+ 
+
+ align:start position:0%
+the the kind of way way to go in the
+neighborhood so that was that was really
+
+ align:start position:0%
+neighborhood so that was that was really
+ 
+
+ align:start position:0%
+neighborhood so that was that was really
+his very clear uh
+
+ align:start position:0%
+his very clear uh
+ 
+
+ align:start position:0%
+his very clear uh
+agenda you're going to ask a question
+
+ align:start position:0%
+agenda you're going to ask a question
+ 
+
+ align:start position:0%
+agenda you're going to ask a question
+yeah I have a question about absente
+
+ align:start position:0%
+yeah I have a question about absente
+ 
+
+ align:start position:0%
+yeah I have a question about absente
+landlords did he say who are these and
+
+ align:start position:0%
+landlords did he say who are these and
+ 
+
+ align:start position:0%
+landlords did he say who are these and
+where are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they I know he did talk a little bit
+
+ align:start position:0%
+they I know he did talk a little bit
+ 
+
+ align:start position:0%
+they I know he did talk a little bit
+about people living I think in Bost or
+
+ align:start position:0%
+about people living I think in Bost or
+ 
+
+ align:start position:0%
+about people living I think in Bost or
+something only properties there or
+
+ align:start position:0%
+something only properties there or
+ 
+
+ align:start position:0%
+something only properties there or
+something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I interview Michael that that AOW
+
+ align:start position:0%
+that I interview Michael that that AOW
+ 
+
+ align:start position:0%
+that I interview Michael that that AOW
+theost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+juster so is it investment just to the
+
+ align:start position:0%
+juster so is it investment just to the
+ 
+
+ align:start position:0%
+juster so is it investment just to the
+prop few years
+
+ align:start position:0%
+prop few years
+ 
+
+ align:start position:0%
+prop few years
+or yeah how did Michael talk about that
+
+ align:start position:0%
+or yeah how did Michael talk about that
+ 
+
+ align:start position:0%
+or yeah how did Michael talk about that
+I mean he he did talk about that
+
+ align:start position:0%
+I mean he he did talk about that
+ 
+
+ align:start position:0%
+I mean he he did talk about that
+specifically about what they were doing
+
+ align:start position:0%
+specifically about what they were doing
+ 
+
+ align:start position:0%
+specifically about what they were doing
+yeah I mean basically like you can get
+
+ align:start position:0%
+yeah I mean basically like you can get
+ 
+
+ align:start position:0%
+yeah I mean basically like you can get
+you know it's the some of the cheapest
+
+ align:start position:0%
+you know it's the some of the cheapest
+ 
+
+ align:start position:0%
+you know it's the some of the cheapest
+property you can get in in Massachusetts
+
+ align:start position:0%
+property you can get in in Massachusetts
+ 
+
+ align:start position:0%
+property you can get in in Massachusetts
+and you can buy house for 100 or under
+
+ align:start position:0%
+and you can buy house for 100 or under
+ 
+
+ align:start position:0%
+and you can buy house for 100 or under
+Grand and there's buying they just
+
+ align:start position:0%
+Grand and there's buying they just
+ 
+
+ align:start position:0%
+Grand and there's buying they just
+letting housing interior
+
+ align:start position:0%
+letting housing interior
+ 
+
+ align:start position:0%
+letting housing interior
+um and there was like lots of turnover
+
+ align:start position:0%
+um and there was like lots of turnover
+ 
+
+ align:start position:0%
+um and there was like lots of turnover
+um you know
+
+ align:start position:0%
+um you know
+ 
+
+ align:start position:0%
+um you know
+people the house not well maintain at
+
+ align:start position:0%
+people the house not well maintain at
+ 
+
+ align:start position:0%
+people the house not well maintain at
+all been a huge problem I me there's
+
+ align:start position:0%
+all been a huge problem I me there's
+ 
+
+ align:start position:0%
+all been a huge problem I me there's
+probably a lot of money pour out of
+
+ align:start position:0%
+probably a lot of money pour out of
+ 
+
+ align:start position:0%
+probably a lot of money pour out of
+Boston because if you look at the
+
+ align:start position:0%
+Boston because if you look at the
+ 
+
+ align:start position:0%
+Boston because if you look at the
+situation of Boston right now you have
+
+ align:start position:0%
+situation of Boston right now you have
+ 
+
+ align:start position:0%
+situation of Boston right now you have
+there's been this huge run up in
+
+ align:start position:0%
+there's been this huge run up in
+ 
+
+ align:start position:0%
+there's been this huge run up in
+property values and there's a
+
+ align:start position:0%
+property values and there's a
+ 
+
+ align:start position:0%
+property values and there's a
+disjunction between the
+
+ align:start position:0%
+disjunction between the
+ 
+
+ align:start position:0%
+disjunction between the
+property the value the property is sell
+
+ align:start position:0%
+property the value the property is sell
+ 
+
+ align:start position:0%
+property the value the property is sell
+for and the rents that properties is are
+
+ align:start position:0%
+for and the rents that properties is are
+ 
+
+ align:start position:0%
+for and the rents that properties is are
+earning you can't really support a unit
+
+ align:start position:0%
+earning you can't really support a unit
+ 
+
+ align:start position:0%
+earning you can't really support a unit
+based on the rents the right now because
+
+ align:start position:0%
+based on the rents the right now because
+ 
+
+ align:start position:0%
+based on the rents the right now because
+properties have gone up so you may well
+
+ align:start position:0%
+properties have gone up so you may well
+ 
+
+ align:start position:0%
+properties have gone up so you may well
+see Property Owners saying H you know if
+
+ align:start position:0%
+see Property Owners saying H you know if
+ 
+
+ align:start position:0%
+see Property Owners saying H you know if
+I take my money out of Boston I'm gonna
+
+ align:start position:0%
+I take my money out of Boston I'm gonna
+ 
+
+ align:start position:0%
+I take my money out of Boston I'm gonna
+make a lot of money on this investment
+
+ align:start position:0%
+make a lot of money on this investment
+ 
+
+ align:start position:0%
+make a lot of money on this investment
+now and I can move into a market where
+
+ align:start position:0%
+now and I can move into a market where
+ 
+
+ align:start position:0%
+now and I can move into a market where
+values are lower and the rents will cash
+
+ align:start position:0%
+values are lower and the rents will cash
+ 
+
+ align:start position:0%
+values are lower and the rents will cash
+flow better for me so it doesn't surp
+
+ align:start position:0%
+flow better for me so it doesn't surp
+ 
+
+ align:start position:0%
+flow better for me so it doesn't surp
+it's sort of like Arbitrage in the state
+
+ align:start position:0%
+it's sort of like Arbitrage in the state
+ 
+
+ align:start position:0%
+it's sort of like Arbitrage in the state
+you know you have a very expensive
+
+ align:start position:0%
+you know you have a very expensive
+ 
+
+ align:start position:0%
+you know you have a very expensive
+housing market and a lost housing market
+
+ align:start position:0%
+housing market and a lost housing market
+ 
+
+ align:start position:0%
+housing market and a lost housing market
+and people are shifting some of their
+
+ align:start position:0%
+and people are shifting some of their
+ 
+
+ align:start position:0%
+and people are shifting some of their
+investment dollars to capitalize on that
+
+ align:start position:0%
+investment dollars to capitalize on that
+ 
+
+ align:start position:0%
+investment dollars to capitalize on that
+wouldn't surprise me at
+
+ align:start position:0%
+wouldn't surprise me at
+ 
+
+ align:start position:0%
+wouldn't surprise me at
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+great good
+
+ align:start position:0%
+great good
+ 
+
+ align:start position:0%
+great good
+job
+
+ align:start position:0%
+job
+ 
+
+ align:start position:0%
+job
+good um who else going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ask
+
+ align:start position:0%
+ask
+ 
+
+ align:start position:0%
+ask
+okay so SE I
+
+ align:start position:0%
+okay so SE I
+ 
+
+ align:start position:0%
+okay so SE I
+interviewed head of the new Citizens
+
+ align:start position:0%
+interviewed head of the new Citizens
+ 
+
+ align:start position:0%
+interviewed head of the new Citizens
+Council he had a lot to
+
+ align:start position:0%
+Council he had a lot to
+ 
+
+ align:start position:0%
+Council he had a lot to
+say anyone not have a lot to
+
+ align:start position:0%
+say anyone not have a lot to
+ 
+
+ align:start position:0%
+say anyone not have a lot to
+that's problem I I I think our initial
+
+ align:start position:0%
+that's problem I I I think our initial
+ 
+
+ align:start position:0%
+that's problem I I I think our initial
+question was answered within like 40
+
+ align:start position:0%
+question was answered within like 40
+ 
+
+ align:start position:0%
+question was answered within like 40
+minutes um but he he was really good he
+
+ align:start position:0%
+minutes um but he he was really good he
+ 
+
+ align:start position:0%
+minutes um but he he was really good he
+just like real information um some of
+
+ align:start position:0%
+just like real information um some of
+ 
+
+ align:start position:0%
+just like real information um some of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+highlights basic so new North he really
+
+ align:start position:0%
+highlights basic so new North he really
+ 
+
+ align:start position:0%
+highlights basic so new North he really
+emphasized kind of Social Service
+
+ align:start position:0%
+emphasized kind of Social Service
+ 
+
+ align:start position:0%
+emphasized kind of Social Service
+aspects of what they do and there was
+
+ align:start position:0%
+aspects of what they do and there was
+ 
+
+ align:start position:0%
+aspects of what they do and there was
+kind point about how how much of a
+
+ align:start position:0%
+kind point about how how much of a
+ 
+
+ align:start position:0%
+kind point about how how much of a
+planning organization are they um like
+
+ align:start position:0%
+planning organization are they um like
+ 
+
+ align:start position:0%
+planning organization are they um like
+with key and actually another worker
+
+ align:start position:0%
+with key and actually another worker
+ 
+
+ align:start position:0%
+with key and actually another worker
+there Maria sat in us on the interview
+
+ align:start position:0%
+there Maria sat in us on the interview
+ 
+
+ align:start position:0%
+there Maria sat in us on the interview
+and she was showing us their uh kind of
+
+ align:start position:0%
+and she was showing us their uh kind of
+ 
+
+ align:start position:0%
+and she was showing us their uh kind of
+like the their scope of work their
+
+ align:start position:0%
+like the their scope of work their
+ 
+
+ align:start position:0%
+like the their scope of work their
+mission work as an organization and so
+
+ align:start position:0%
+mission work as an organization and so
+ 
+
+ align:start position:0%
+mission work as an organization and so
+much of it was Social Service based so
+
+ align:start position:0%
+much of it was Social Service based so
+ 
+
+ align:start position:0%
+much of it was Social Service based so
+they do like all sorts of like Child
+
+ align:start position:0%
+they do like all sorts of like Child
+ 
+
+ align:start position:0%
+they do like all sorts of like Child
+Care parenting issues family um tutoring
+
+ align:start position:0%
+Care parenting issues family um tutoring
+ 
+
+ align:start position:0%
+Care parenting issues family um tutoring
+job
+
+ align:start position:0%
+job
+ 
+
+ align:start position:0%
+job
+placement uh advocacy around Youth and
+
+ align:start position:0%
+placement uh advocacy around Youth and
+ 
+
+ align:start position:0%
+placement uh advocacy around Youth and
+family issues
+
+ align:start position:0%
+family issues
+ 
+
+ align:start position:0%
+family issues
+Healthcare um they do resource and
+
+ align:start position:0%
+Healthcare um they do resource and
+ 
+
+ align:start position:0%
+Healthcare um they do resource and
+referrals substance abuse programs HIV
+
+ align:start position:0%
+referrals substance abuse programs HIV
+ 
+
+ align:start position:0%
+referrals substance abuse programs HIV
+Aid prevention educ and
+
+ align:start position:0%
+Aid prevention educ and
+ 
+
+ align:start position:0%
+Aid prevention educ and
+education um school programs anyway like
+
+ align:start position:0%
+education um school programs anyway like
+ 
+
+ align:start position:0%
+education um school programs anyway like
+if for for a good like 10 minutes you
+
+ align:start position:0%
+if for for a good like 10 minutes you
+ 
+
+ align:start position:0%
+if for for a good like 10 minutes you
+wouldn't know that they actually do
+
+ align:start position:0%
+wouldn't know that they actually do
+ 
+
+ align:start position:0%
+wouldn't know that they actually do
+planning as well or do development or
+
+ align:start position:0%
+planning as well or do development or
+ 
+
+ align:start position:0%
+planning as well or do development or
+you know are the main um you know kind
+
+ align:start position:0%
+you know are the main um you know kind
+ 
+
+ align:start position:0%
+you know are the main um you know kind
+of yes or no on a lot of development
+
+ align:start position:0%
+of yes or no on a lot of development
+ 
+
+ align:start position:0%
+of yes or no on a lot of development
+projects in in the North End um so
+
+ align:start position:0%
+projects in in the North End um so
+ 
+
+ align:start position:0%
+projects in in the North End um so
+that's kind of a big issue that there's
+
+ align:start position:0%
+that's kind of a big issue that there's
+ 
+
+ align:start position:0%
+that's kind of a big issue that there's
+all this other activities going on
+
+ align:start position:0%
+all this other activities going on
+ 
+
+ align:start position:0%
+all this other activities going on
+within the
+
+ align:start position:0%
+within the
+ 
+
+ align:start position:0%
+within the
+organization um they so as I think
+
+ align:start position:0%
+organization um they so as I think
+ 
+
+ align:start position:0%
+organization um they so as I think
+described previously it's I'm not
+
+ align:start position:0%
+described previously it's I'm not
+ 
+
+ align:start position:0%
+described previously it's I'm not
+completely clear but the mechanism is
+
+ align:start position:0%
+completely clear but the mechanism is
+ 
+
+ align:start position:0%
+completely clear but the mechanism is
+that they have um any any new
+
+ align:start position:0%
+that they have um any any new
+ 
+
+ align:start position:0%
+that they have um any any new
+development goes through them so they
+
+ align:start position:0%
+development goes through them so they
+ 
+
+ align:start position:0%
+development goes through them so they
+have pretty much if not not official but
+
+ align:start position:0%
+have pretty much if not not official but
+ 
+
+ align:start position:0%
+have pretty much if not not official but
+they have a de facto um decision making
+
+ align:start position:0%
+they have a de facto um decision making
+ 
+
+ align:start position:0%
+they have a de facto um decision making
+role in development that happens um in
+
+ align:start position:0%
+role in development that happens um in
+ 
+
+ align:start position:0%
+role in development that happens um in
+the North End so are definitely the key
+
+ align:start position:0%
+the North End so are definitely the key
+ 
+
+ align:start position:0%
+the North End so are definitely the key
+player and they have the the city's ear
+
+ align:start position:0%
+player and they have the the city's ear
+ 
+
+ align:start position:0%
+player and they have the the city's ear
+when it comes to new
+
+ align:start position:0%
+when it comes to new
+ 
+
+ align:start position:0%
+when it comes to new
+projects tough a lot about again like
+
+ align:start position:0%
+projects tough a lot about again like
+ 
+
+ align:start position:0%
+projects tough a lot about again like
+abute landlords and the housing and how
+
+ align:start position:0%
+abute landlords and the housing and how
+ 
+
+ align:start position:0%
+abute landlords and the housing and how
+that's a big problem um but again show
+
+ align:start position:0%
+that's a big problem um but again show
+ 
+
+ align:start position:0%
+that's a big problem um but again show
+like the Memorial square and briwood and
+
+ align:start position:0%
+like the Memorial square and briwood and
+ 
+
+ align:start position:0%
+like the Memorial square and briwood and
+how like you know the how stock Memorial
+
+ align:start position:0%
+how like you know the how stock Memorial
+ 
+
+ align:start position:0%
+how like you know the how stock Memorial
+square is not really what briwood is he
+
+ align:start position:0%
+square is not really what briwood is he
+ 
+
+ align:start position:0%
+square is not really what briwood is he
+said he lives in Brightwood yeah he
+
+ align:start position:0%
+said he lives in Brightwood yeah he
+ 
+
+ align:start position:0%
+said he lives in Brightwood yeah he
+lives in Brightwood he's been there
+
+ align:start position:0%
+lives in Brightwood he's been there
+ 
+
+ align:start position:0%
+lives in Brightwood he's been there
+for several years 20 years or something
+
+ align:start position:0%
+for several years 20 years or something
+ 
+
+ align:start position:0%
+for several years 20 years or something
+and uh he justes you totally different
+
+ align:start position:0%
+and uh he justes you totally different
+ 
+
+ align:start position:0%
+and uh he justes you totally different
+place thanal
+
+ align:start position:0%
+place thanal
+ 
+
+ align:start position:0%
+place thanal
+Square uh new North is actually one of
+
+ align:start position:0%
+Square uh new North is actually one of
+ 
+
+ align:start position:0%
+Square uh new North is actually one of
+the largest employers in the
+
+ align:start position:0%
+the largest employers in the
+ 
+
+ align:start position:0%
+the largest employers in the
+north um we do with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but how many did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say uh one of a couple of like successes
+
+ align:start position:0%
+say uh one of a couple of like successes
+ 
+
+ align:start position:0%
+say uh one of a couple of like successes
+he he pointed out that they've done one
+
+ align:start position:0%
+he he pointed out that they've done one
+ 
+
+ align:start position:0%
+he he pointed out that they've done one
+that was interesting that they turned a
+
+ align:start position:0%
+that was interesting that they turned a
+ 
+
+ align:start position:0%
+that was interesting that they turned a
+liquor store on Main Street into a child
+
+ align:start position:0%
+liquor store on Main Street into a child
+ 
+
+ align:start position:0%
+liquor store on Main Street into a child
+care center
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um ecomic is development
+
+ align:start position:0%
+um ecomic is development
+ 
+
+ align:start position:0%
+um ecomic is development
+issues he points it out some of the same
+
+ align:start position:0%
+issues he points it out some of the same
+ 
+
+ align:start position:0%
+issues he points it out some of the same
+on been talking about limited skills
+
+ align:start position:0%
+on been talking about limited skills
+ 
+
+ align:start position:0%
+on been talking about limited skills
+education language issues um kind of
+
+ align:start position:0%
+education language issues um kind of
+ 
+
+ align:start position:0%
+education language issues um kind of
+like anywhere can be better on subsidies
+
+ align:start position:0%
+like anywhere can be better on subsidies
+ 
+
+ align:start position:0%
+like anywhere can be better on subsidies
+than they can be by working get the type
+
+ align:start position:0%
+than they can be by working get the type
+ 
+
+ align:start position:0%
+than they can be by working get the type
+of jobs that are available then another
+
+ align:start position:0%
+of jobs that are available then another
+ 
+
+ align:start position:0%
+of jobs that are available then another
+interesting thing is
+
+ align:start position:0%
+interesting thing is
+ 
+
+ align:start position:0%
+interesting thing is
+that initial development reports read is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that tool group with the largest
+
+ align:start position:0%
+that tool group with the largest
+ 
+
+ align:start position:0%
+that tool group with the largest
+employer
+
+ align:start position:0%
+employer
+ 
+
+ align:start position:0%
+employer
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+right rightwood they left so they're no
+
+ align:start position:0%
+right rightwood they left so they're no
+ 
+
+ align:start position:0%
+right rightwood they left so they're no
+longer in the North End so that's that's
+
+ align:start position:0%
+longer in the North End so that's that's
+ 
+
+ align:start position:0%
+longer in the North End so that's that's
+a major potential issue that
+
+ align:start position:0%
+a major potential issue that
+ 
+
+ align:start position:0%
+a major potential issue that
+um employers gone uh we talked a little
+
+ align:start position:0%
+um employers gone uh we talked a little
+ 
+
+ align:start position:0%
+um employers gone uh we talked a little
+bit about crime and safety on crime
+
+ align:start position:0%
+bit about crime and safety on crime
+ 
+
+ align:start position:0%
+bit about crime and safety on crime
+perceptions from of of crime and safety
+
+ align:start position:0%
+perceptions from of of crime and safety
+ 
+
+ align:start position:0%
+perceptions from of of crime and safety
+um and he thought that the perception
+
+ align:start position:0%
+um and he thought that the perception
+ 
+
+ align:start position:0%
+um and he thought that the perception
+isn't completely match with reality he
+
+ align:start position:0%
+isn't completely match with reality he
+ 
+
+ align:start position:0%
+isn't completely match with reality he
+thought that um it actually as as was a
+
+ align:start position:0%
+thought that um it actually as as was a
+ 
+
+ align:start position:0%
+thought that um it actually as as was a
+lot more safe was a lot safer than the
+
+ align:start position:0%
+lot more safe was a lot safer than the
+ 
+
+ align:start position:0%
+lot more safe was a lot safer than the
+people may make it out to
+
+ align:start position:0%
+people may make it out to
+ 
+
+ align:start position:0%
+people may make it out to
+be that's a lot about their relationship
+
+ align:start position:0%
+be that's a lot about their relationship
+ 
+
+ align:start position:0%
+be that's a lot about their relationship
+with B state which is interesting he
+
+ align:start position:0%
+with B state which is interesting he
+ 
+
+ align:start position:0%
+with B state which is interesting he
+said really adversarial for
+
+ align:start position:0%
+said really adversarial for
+ 
+
+ align:start position:0%
+said really adversarial for
+forever I guess um but that in the past
+
+ align:start position:0%
+forever I guess um but that in the past
+ 
+
+ align:start position:0%
+forever I guess um but that in the past
+like two to three years it's it's been
+
+ align:start position:0%
+like two to three years it's it's been
+ 
+
+ align:start position:0%
+like two to three years it's it's been
+improving significantly uh he thought
+
+ align:start position:0%
+improving significantly uh he thought
+ 
+
+ align:start position:0%
+improving significantly uh he thought
+that pretty much had to the change
+
+ align:start position:0%
+that pretty much had to the change
+ 
+
+ align:start position:0%
+that pretty much had to the change
+leadership um
+
+ align:start position:0%
+leadership um
+ 
+
+ align:start position:0%
+leadership um
+and there was
+
+ align:start position:0%
+and there was
+ 
+
+ align:start position:0%
+and there was
+a there was something that
+
+ align:start position:0%
+a there was something that
+ 
+
+ align:start position:0%
+a there was something that
+brought there something that brought
+
+ align:start position:0%
+brought there something that brought
+ 
+
+ align:start position:0%
+brought there something that brought
+them together they did um basic needed
+
+ align:start position:0%
+them together they did um basic needed
+ 
+
+ align:start position:0%
+them together they did um basic needed
+something from from
+
+ align:start position:0%
+something from from
+ 
+
+ align:start position:0%
+something from from
+new said point being that Rel are to new
+
+ align:start position:0%
+new said point being that Rel are to new
+ 
+
+ align:start position:0%
+new said point being that Rel are to new
+North that they St
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um he he he deped Bas St is pretty much
+
+ align:start position:0%
+um he he he deped Bas St is pretty much
+ 
+
+ align:start position:0%
+um he he he deped Bas St is pretty much
+like it should in land and property
+
+ align:start position:0%
+like it should in land and property
+ 
+
+ align:start position:0%
+like it should in land and property
+money um not necessarily a good
+
+ align:start position:0%
+money um not necessarily a good
+ 
+
+ align:start position:0%
+money um not necessarily a good
+Community partner but again that's that
+
+ align:start position:0%
+Community partner but again that's that
+ 
+
+ align:start position:0%
+Community partner but again that's that
+been improving over the past
+
+ align:start position:0%
+been improving over the past
+ 
+
+ align:start position:0%
+been improving over the past
+years uh they don't employ locally which
+
+ align:start position:0%
+years uh they don't employ locally which
+ 
+
+ align:start position:0%
+years uh they don't employ locally which
+is a big problem um as you know that it
+
+ align:start position:0%
+is a big problem um as you know that it
+ 
+
+ align:start position:0%
+is a big problem um as you know that it
+also has to do with the skills though
+
+ align:start position:0%
+also has to do with the skills though
+ 
+
+ align:start position:0%
+also has to do with the skills though
+exist in the community for the type of
+
+ align:start position:0%
+exist in the community for the type of
+ 
+
+ align:start position:0%
+exist in the community for the type of
+jobs that b is looking for at least good
+
+ align:start position:0%
+jobs that b is looking for at least good
+ 
+
+ align:start position:0%
+jobs that b is looking for at least good
+type of
+
+ align:start position:0%
+type of
+ 
+
+ align:start position:0%
+type of
+jobs um but so one one of the indicators
+
+ align:start position:0%
+jobs um but so one one of the indicators
+ 
+
+ align:start position:0%
+jobs um but so one one of the indicators
+that things are kind of changing is that
+
+ align:start position:0%
+that things are kind of changing is that
+ 
+
+ align:start position:0%
+that things are kind of changing is that
+Bas I'm working with to the link and one
+
+ align:start position:0%
+Bas I'm working with to the link and one
+ 
+
+ align:start position:0%
+Bas I'm working with to the link and one
+of the high schools on training programs
+
+ align:start position:0%
+of the high schools on training programs
+ 
+
+ align:start position:0%
+of the high schools on training programs
+so like we want to see continue was
+
+ align:start position:0%
+so like we want to see continue was
+ 
+
+ align:start position:0%
+so like we want to see continue was
+linking base data with the schools for
+
+ align:start position:0%
+linking base data with the schools for
+ 
+
+ align:start position:0%
+linking base data with the schools for
+um unification schools for real job
+
+ align:start position:0%
+um unification schools for real job
+ 
+
+ align:start position:0%
+um unification schools for real job
+training that would prepare High States
+
+ align:start position:0%
+training that would prepare High States
+ 
+
+ align:start position:0%
+training that would prepare High States
+for aate type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jobs oh this is sorry this is the issue
+
+ align:start position:0%
+jobs oh this is sorry this is the issue
+ 
+
+ align:start position:0%
+jobs oh this is sorry this is the issue
+from is that they're landlocked so they
+
+ align:start position:0%
+from is that they're landlocked so they
+ 
+
+ align:start position:0%
+from is that they're landlocked so they
+don't have any way to expand directly
+
+ align:start position:0%
+don't have any way to expand directly
+ 
+
+ align:start position:0%
+don't have any way to expand directly
+around them so that they in his View at
+
+ align:start position:0%
+around them so that they in his View at
+ 
+
+ align:start position:0%
+around them so that they in his View at
+least they're BEC playing more
+
+ align:start position:0%
+least they're BEC playing more
+ 
+
+ align:start position:0%
+least they're BEC playing more
+interested in the neighborhood as a
+
+ align:start position:0%
+interested in the neighborhood as a
+ 
+
+ align:start position:0%
+interested in the neighborhood as a
+whole to offer them more opportunities
+
+ align:start position:0%
+whole to offer them more opportunities
+ 
+
+ align:start position:0%
+whole to offer them more opportunities
+for expansion because they pretty much
+
+ align:start position:0%
+for expansion because they pretty much
+ 
+
+ align:start position:0%
+for expansion because they pretty much
+take expanded everywhere they can in
+
+ align:start position:0%
+take expanded everywhere they can in
+ 
+
+ align:start position:0%
+take expanded everywhere they can in
+their you know directly around their
+
+ align:start position:0%
+their you know directly around their
+ 
+
+ align:start position:0%
+their you know directly around their
+existing
+
+ align:start position:0%
+existing
+ 
+
+ align:start position:0%
+existing
+property uh another interesting thing is
+
+ align:start position:0%
+property uh another interesting thing is
+ 
+
+ align:start position:0%
+property uh another interesting thing is
+he talks about the private Development
+
+ align:start position:0%
+he talks about the private Development
+ 
+
+ align:start position:0%
+he talks about the private Development
+Corporation how it's changed um and how
+
+ align:start position:0%
+Corporation how it's changed um and how
+ 
+
+ align:start position:0%
+Corporation how it's changed um and how
+it really was like a strong CBC in the
+
+ align:start position:0%
+it really was like a strong CBC in the
+ 
+
+ align:start position:0%
+it really was like a strong CBC in the
+neighborhood and now um I guess
+
+ align:start position:0%
+neighborhood and now um I guess
+ 
+
+ align:start position:0%
+neighborhood and now um I guess
+I guess their new leadership or at some
+
+ align:start position:0%
+I guess their new leadership or at some
+ 
+
+ align:start position:0%
+I guess their new leadership or at some
+point where existing leadership kind of
+
+ align:start position:0%
+point where existing leadership kind of
+ 
+
+ align:start position:0%
+point where existing leadership kind of
+changed and they're just completely you
+
+ align:start position:0%
+changed and they're just completely you
+ 
+
+ align:start position:0%
+changed and they're just completely you
+know not interested in the neigh or
+
+ align:start position:0%
+know not interested in the neigh or
+ 
+
+ align:start position:0%
+know not interested in the neigh or
+don't AR are not seen as a good
+
+ align:start position:0%
+don't AR are not seen as a good
+ 
+
+ align:start position:0%
+don't AR are not seen as a good
+Community Builder um but now their
+
+ align:start position:0%
+Community Builder um but now their
+ 
+
+ align:start position:0%
+Community Builder um but now their
+interests are a lot work outside
+
+ align:start position:0%
+interests are a lot work outside
+ 
+
+ align:start position:0%
+interests are a lot work outside
+Springfield so they're doing a lot of
+
+ align:start position:0%
+Springfield so they're doing a lot of
+ 
+
+ align:start position:0%
+Springfield so they're doing a lot of
+development work where either outside
+
+ align:start position:0%
+development work where either outside
+ 
+
+ align:start position:0%
+development work where either outside
+the North End or outside Springfield as
+
+ align:start position:0%
+the North End or outside Springfield as
+ 
+
+ align:start position:0%
+the North End or outside Springfield as
+well in other parts of Massachusetts and
+
+ align:start position:0%
+well in other parts of Massachusetts and
+ 
+
+ align:start position:0%
+well in other parts of Massachusetts and
+it seems like the impression is that
+
+ align:start position:0%
+it seems like the impression is that
+ 
+
+ align:start position:0%
+it seems like the impression is that
+they gotten kind of like too big and no
+
+ align:start position:0%
+they gotten kind of like too big and no
+ 
+
+ align:start position:0%
+they gotten kind of like too big and no
+longer as interested in
+
+ align:start position:0%
+longer as interested in
+ 
+
+ align:start position:0%
+longer as interested in
+north um so he really really stressed
+
+ align:start position:0%
+north um so he really really stressed
+ 
+
+ align:start position:0%
+north um so he really really stressed
+that the north needs a strong CDC and he
+
+ align:start position:0%
+that the north needs a strong CDC and he
+ 
+
+ align:start position:0%
+that the north needs a strong CDC and he
+was thr about this idea that the north
+
+ align:start position:0%
+was thr about this idea that the north
+ 
+
+ align:start position:0%
+was thr about this idea that the north
+the new North his organization could
+
+ align:start position:0%
+the new North his organization could
+ 
+
+ align:start position:0%
+the new North his organization could
+play that role um as
+
+ align:start position:0%
+play that role um as
+ 
+
+ align:start position:0%
+play that role um as
+developer um and soar about that or is
+
+ align:start position:0%
+developer um and soar about that or is
+ 
+
+ align:start position:0%
+developer um and soar about that or is
+is there need to be like a founding of a
+
+ align:start position:0%
+is there need to be like a founding of a
+ 
+
+ align:start position:0%
+is there need to be like a founding of a
+new CBC clear that was a huge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+uh um and we had we as some kind like
+
+ align:start position:0%
+uh um and we had we as some kind like
+ 
+
+ align:start position:0%
+uh um and we had we as some kind like
+what if you you you're doing plan what
+
+ align:start position:0%
+what if you you you're doing plan what
+ 
+
+ align:start position:0%
+what if you you you're doing plan what
+you priorities you we talk about those
+
+ align:start position:0%
+you priorities you we talk about those
+ 
+
+ align:start position:0%
+you priorities you we talk about those
+kind of bigger issues but I mean he he
+
+ align:start position:0%
+kind of bigger issues but I mean he he
+ 
+
+ align:start position:0%
+kind of bigger issues but I mean he he
+would asked that question directly he
+
+ align:start position:0%
+would asked that question directly he
+ 
+
+ align:start position:0%
+would asked that question directly he
+said he doesn't really know um but some
+
+ align:start position:0%
+said he doesn't really know um but some
+ 
+
+ align:start position:0%
+said he doesn't really know um but some
+of the things he pointed out were just
+
+ align:start position:0%
+of the things he pointed out were just
+ 
+
+ align:start position:0%
+of the things he pointed out were just
+you know no destination shopping so
+
+ align:start position:0%
+you know no destination shopping so
+ 
+
+ align:start position:0%
+you know no destination shopping so
+nothing floring people from the outside
+
+ align:start position:0%
+nothing floring people from the outside
+ 
+
+ align:start position:0%
+nothing floring people from the outside
+in um not even enough convenience
+
+ align:start position:0%
+in um not even enough convenience
+ 
+
+ align:start position:0%
+in um not even enough convenience
+shopping so there's not like drugs for
+
+ align:start position:0%
+shopping so there's not like drugs for
+ 
+
+ align:start position:0%
+shopping so there's not like drugs for
+dry cleaners um it's not like the kind
+
+ align:start position:0%
+dry cleaners um it's not like the kind
+ 
+
+ align:start position:0%
+dry cleaners um it's not like the kind
+of diversity of commun some
+
+ align:start position:0%
+of diversity of commun some
+ 
+
+ align:start position:0%
+of diversity of commun some
+uh we asked a bit about that and he
+
+ align:start position:0%
+uh we asked a bit about that and he
+ 
+
+ align:start position:0%
+uh we asked a bit about that and he
+thought just kind as we've discussed
+
+ align:start position:0%
+thought just kind as we've discussed
+ 
+
+ align:start position:0%
+thought just kind as we've discussed
+before that um people kind of don't know
+
+ align:start position:0%
+before that um people kind of don't know
+ 
+
+ align:start position:0%
+before that um people kind of don't know
+what else to do so they start local
+
+ align:start position:0%
+what else to do so they start local
+ 
+
+ align:start position:0%
+what else to do so they start local
+business and they don't know what other
+
+ align:start position:0%
+business and they don't know what other
+ 
+
+ align:start position:0%
+business and they don't know what other
+local business starts they do with
+
+ align:start position:0%
+local business starts they do with
+ 
+
+ align:start position:0%
+local business starts they do with
+Bodega um and that's not necessarily
+
+ align:start position:0%
+Bodega um and that's not necessarily
+ 
+
+ align:start position:0%
+Bodega um and that's not necessarily
+obviously the best thing uh he did talk
+
+ align:start position:0%
+obviously the best thing uh he did talk
+ 
+
+ align:start position:0%
+obviously the best thing uh he did talk
+about how there's this opportunity to
+
+ align:start position:0%
+about how there's this opportunity to
+ 
+
+ align:start position:0%
+about how there's this opportunity to
+build around kind of like the E thing
+
+ align:start position:0%
+build around kind of like the E thing
+ 
+
+ align:start position:0%
+build around kind of like the E thing
+where um um emphasis of the nor event
+
+ align:start position:0%
+where um um emphasis of the nor event
+ 
+
+ align:start position:0%
+where um um emphasis of the nor event
+and he thought that that was an
+
+ align:start position:0%
+and he thought that that was an
+ 
+
+ align:start position:0%
+and he thought that that was an
+opportunity that might people um from
+
+ align:start position:0%
+opportunity that might people um from
+ 
+
+ align:start position:0%
+opportunity that might people um from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+outside we know about um yeah so a
+
+ align:start position:0%
+outside we know about um yeah so a
+ 
+
+ align:start position:0%
+outside we know about um yeah so a
+marketing packaging issue of branding
+
+ align:start position:0%
+marketing packaging issue of branding
+ 
+
+ align:start position:0%
+marketing packaging issue of branding
+like the new North and again like I I
+
+ align:start position:0%
+like the new North and again like I I
+ 
+
+ align:start position:0%
+like the new North and again like I I
+think he recognize the potential
+
+ align:start position:0%
+think he recognize the potential
+ 
+
+ align:start position:0%
+think he recognize the potential
+pitfalls of that but just saw that that
+
+ align:start position:0%
+pitfalls of that but just saw that that
+ 
+
+ align:start position:0%
+pitfalls of that but just saw that that
+was an opportunity that that would might
+
+ align:start position:0%
+was an opportunity that that would might
+ 
+
+ align:start position:0%
+was an opportunity that that would might
+distinguish the North End from other
+
+ align:start position:0%
+distinguish the North End from other
+ 
+
+ align:start position:0%
+distinguish the North End from other
+parts of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Springfield also I think notic that b
+
+ align:start position:0%
+Springfield also I think notic that b
+ 
+
+ align:start position:0%
+Springfield also I think notic that b
+this but something that was he know he
+
+ align:start position:0%
+this but something that was he know he
+ 
+
+ align:start position:0%
+this but something that was he know he
+noted was that in the past like four or
+
+ align:start position:0%
+noted was that in the past like four or
+ 
+
+ align:start position:0%
+noted was that in the past like four or
+five years there been a real influx of
+
+ align:start position:0%
+five years there been a real influx of
+ 
+
+ align:start position:0%
+five years there been a real influx of
+um of immigrants from guala salor Mexico
+
+ align:start position:0%
+um of immigrants from guala salor Mexico
+ 
+
+ align:start position:0%
+um of immigrants from guala salor Mexico
+and that so while the neighbor is
+
+ align:start position:0%
+and that so while the neighbor is
+ 
+
+ align:start position:0%
+and that so while the neighbor is
+definitely probably Puerto Rican is that
+
+ align:start position:0%
+definitely probably Puerto Rican is that
+ 
+
+ align:start position:0%
+definitely probably Puerto Rican is that
+it might be changing or at least there's
+
+ align:start position:0%
+it might be changing or at least there's
+ 
+
+ align:start position:0%
+it might be changing or at least there's
+kind of new groups coming in um and a
+
+ align:start position:0%
+kind of new groups coming in um and a
+ 
+
+ align:start position:0%
+kind of new groups coming in um and a
+lot of them are UND
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+immigrants I guess I'll stop
+
+ align:start position:0%
+immigrants I guess I'll stop
+ 
+
+ align:start position:0%
+immigrants I guess I'll stop
+it uh I think those are the big things
+
+ align:start position:0%
+it uh I think those are the big things
+ 
+
+ align:start position:0%
+it uh I think those are the big things
+he also he he mentioned this guy I don't
+
+ align:start position:0%
+he also he he mentioned this guy I don't
+ 
+
+ align:start position:0%
+he also he he mentioned this guy I don't
+know Gonzalez who is an example of uh a
+
+ align:start position:0%
+know Gonzalez who is an example of uh a
+ 
+
+ align:start position:0%
+know Gonzalez who is an example of uh a
+successful businessman
+
+ align:start position:0%
+successful businessman
+ 
+
+ align:start position:0%
+successful businessman
+who I guess he owns or runs several
+
+ align:start position:0%
+who I guess he owns or runs several
+ 
+
+ align:start position:0%
+who I guess he owns or runs several
+stores in the north end but doesn't give
+
+ align:start position:0%
+stores in the north end but doesn't give
+ 
+
+ align:start position:0%
+stores in the north end but doesn't give
+back to the community so again just kind
+
+ align:start position:0%
+back to the community so again just kind
+ 
+
+ align:start position:0%
+back to the community so again just kind
+of like Bas there's all these like
+
+ align:start position:0%
+of like Bas there's all these like
+ 
+
+ align:start position:0%
+of like Bas there's all these like
+strong presences whether like
+
+ align:start position:0%
+strong presences whether like
+ 
+
+ align:start position:0%
+strong presences whether like
+institutional or individual in the
+
+ align:start position:0%
+institutional or individual in the
+ 
+
+ align:start position:0%
+institutional or individual in the
+neighborhood that are not good um
+
+ align:start position:0%
+neighborhood that are not good um
+ 
+
+ align:start position:0%
+neighborhood that are not good um
+Community are not good neighbors
+
+ align:start position:0%
+Community are not good neighbors
+ 
+
+ align:start position:0%
+Community are not good neighbors
+basically and really could do a lot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more one of the things I said in on the
+
+ align:start position:0%
+more one of the things I said in on the
+ 
+
+ align:start position:0%
+more one of the things I said in on the
+interview one of the things I thought
+
+ align:start position:0%
+interview one of the things I thought
+ 
+
+ align:start position:0%
+interview one of the things I thought
+was very interesting that Michael said
+
+ align:start position:0%
+was very interesting that Michael said
+ 
+
+ align:start position:0%
+was very interesting that Michael said
+was about this whole thing about working
+
+ align:start position:0%
+was about this whole thing about working
+ 
+
+ align:start position:0%
+was about this whole thing about working
+with Bay State and B you know the change
+
+ align:start position:0%
+with Bay State and B you know the change
+ 
+
+ align:start position:0%
+with Bay State and B you know the change
+in their relationship and what was
+
+ align:start position:0%
+in their relationship and what was
+ 
+
+ align:start position:0%
+in their relationship and what was
+fascinating to me is his stance that
+
+ align:start position:0%
+fascinating to me is his stance that
+ 
+
+ align:start position:0%
+fascinating to me is his stance that
+they don't want anything from Bay State
+
+ align:start position:0%
+they don't want anything from Bay State
+ 
+
+ align:start position:0%
+they don't want anything from Bay State
+you it was very interesting that they've
+
+ align:start position:0%
+you it was very interesting that they've
+ 
+
+ align:start position:0%
+you it was very interesting that they've
+never really said we want you to do this
+
+ align:start position:0%
+never really said we want you to do this
+ 
+
+ align:start position:0%
+never really said we want you to do this
+that what they've said is we want you to
+
+ align:start position:0%
+that what they've said is we want you to
+ 
+
+ align:start position:0%
+that what they've said is we want you to
+recognize
+
+ align:start position:0%
+recognize
+ 
+
+ align:start position:0%
+recognize
+us you know and then come and present
+
+ align:start position:0%
+us you know and then come and present
+ 
+
+ align:start position:0%
+us you know and then come and present
+and recognize our Authority around some
+
+ align:start position:0%
+and recognize our Authority around some
+ 
+
+ align:start position:0%
+and recognize our Authority around some
+of this planning stuff but they have not
+
+ align:start position:0%
+of this planning stuff but they have not
+ 
+
+ align:start position:0%
+of this planning stuff but they have not
+made any demands really as a community
+
+ align:start position:0%
+made any demands really as a community
+ 
+
+ align:start position:0%
+made any demands really as a community
+on Bay
+
+ align:start position:0%
+on Bay
+ 
+
+ align:start position:0%
+on Bay
+State which I think is kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interesting any other comments from that
+
+ align:start position:0%
+interesting any other comments from that
+ 
+
+ align:start position:0%
+interesting any other comments from that
+from other
+
+ align:start position:0%
+from other
+ 
+
+ align:start position:0%
+from other
+participant all said I don't know if you
+
+ align:start position:0%
+participant all said I don't know if you
+ 
+
+ align:start position:0%
+participant all said I don't know if you
+disappeared okay um so move on to
+
+ align:start position:0%
+disappeared okay um so move on to
+ 
+
+ align:start position:0%
+disappeared okay um so move on to
+Jeff summarize that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Jeff what did Jeff have to say I feel
+
+ align:start position:0%
+Jeff what did Jeff have to say I feel
+ 
+
+ align:start position:0%
+Jeff what did Jeff have to say I feel
+there were a lot of us
+
+ align:start position:0%
+there were a lot of us
+ 
+
+ align:start position:0%
+there were a lot of us
+there there were a lot of so I'll say a
+
+ align:start position:0%
+there there were a lot of so I'll say a
+ 
+
+ align:start position:0%
+there there were a lot of so I'll say a
+couple of things and I'll invite all of
+
+ align:start position:0%
+couple of things and I'll invite all of
+ 
+
+ align:start position:0%
+couple of things and I'll invite all of
+those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+present that I might leave out
+
+ align:start position:0%
+present that I might leave out
+ 
+
+ align:start position:0%
+present that I might leave out
+um he also started out talking a lot
+
+ align:start position:0%
+um he also started out talking a lot
+ 
+
+ align:start position:0%
+um he also started out talking a lot
+about his history um both at the health
+
+ align:start position:0%
+about his history um both at the health
+ 
+
+ align:start position:0%
+about his history um both at the health
+clinic um and just in the neighborhood
+
+ align:start position:0%
+clinic um and just in the neighborhood
+ 
+
+ align:start position:0%
+clinic um and just in the neighborhood
+um about of
+
+ align:start position:0%
+um about of
+ 
+
+ align:start position:0%
+um about of
+his activist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he what else he talked about we talked a
+
+ align:start position:0%
+he what else he talked about we talked a
+ 
+
+ align:start position:0%
+he what else he talked about we talked a
+lot about the history um then he went on
+
+ align:start position:0%
+lot about the history um then he went on
+ 
+
+ align:start position:0%
+lot about the history um then he went on
+to say I guess we didn't really get a
+
+ align:start position:0%
+to say I guess we didn't really get a
+ 
+
+ align:start position:0%
+to say I guess we didn't really get a
+lot of information about
+
+ align:start position:0%
+lot of information about
+ 
+
+ align:start position:0%
+lot of information about
+heal St thing I know you even tried to
+
+ align:start position:0%
+heal St thing I know you even tried to
+ 
+
+ align:start position:0%
+heal St thing I know you even tried to
+see the conversation that way a couple
+
+ align:start position:0%
+see the conversation that way a couple
+ 
+
+ align:start position:0%
+see the conversation that way a couple
+of points then that didn't really P out
+
+ align:start position:0%
+of points then that didn't really P out
+ 
+
+ align:start position:0%
+of points then that didn't really P out
+um but it does sound like he is
+
+ align:start position:0%
+um but it does sound like he is
+ 
+
+ align:start position:0%
+um but it does sound like he is
+something like he is very committed to
+
+ align:start position:0%
+something like he is very committed to
+ 
+
+ align:start position:0%
+something like he is very committed to
+his staff and so that
+
+ align:start position:0%
+his staff and so that
+ 
+
+ align:start position:0%
+his staff and so that
+is that's an
+
+ align:start position:0%
+is that's an
+ 
+
+ align:start position:0%
+is that's an
+ass um let see he it is Affiliated
+
+ align:start position:0%
+ass um let see he it is Affiliated
+ 
+
+ align:start position:0%
+ass um let see he it is Affiliated
+officially with B State um and has
+
+ align:start position:0%
+officially with B State um and has
+ 
+
+ align:start position:0%
+officially with B State um and has
+always been it
+
+ align:start position:0%
+always been it
+ 
+
+ align:start position:0%
+always been it
+has basically does not want the clinic
+
+ align:start position:0%
+has basically does not want the clinic
+ 
+
+ align:start position:0%
+has basically does not want the clinic
+to be an independent Clinic although
+
+ align:start position:0%
+to be an independent Clinic although
+ 
+
+ align:start position:0%
+to be an independent Clinic although
+Jeff said that he has should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mentioned trying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to he said
+
+ align:start position:0%
+to he said
+ 
+
+ align:start position:0%
+to he said
+that there were three and this is I
+
+ align:start position:0%
+that there were three and this is I
+ 
+
+ align:start position:0%
+that there were three and this is I
+guess I wasn't really clear
+
+ align:start position:0%
+guess I wasn't really clear
+ 
+
+ align:start position:0%
+guess I wasn't really clear
+that neon is a
+
+ align:start position:0%
+that neon is a
+ 
+
+ align:start position:0%
+that neon is a
+product this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+program the okay so there are two other
+
+ align:start position:0%
+program the okay so there are two other
+ 
+
+ align:start position:0%
+program the okay so there are two other
+programs that he mentioned um one uh was
+
+ align:start position:0%
+programs that he mentioned um one uh was
+ 
+
+ align:start position:0%
+programs that he mentioned um one uh was
+s of a new approach to Primary Care team
+
+ align:start position:0%
+s of a new approach to Primary Care team
+ 
+
+ align:start position:0%
+s of a new approach to Primary Care team
+based
+
+ align:start position:0%
+based
+ 
+
+ align:start position:0%
+based
+not yeah sort of like that organization
+
+ align:start position:0%
+not yeah sort of like that organization
+ 
+
+ align:start position:0%
+not yeah sort of like that organization
+of professionals all working for one
+
+ align:start position:0%
+of professionals all working for one
+ 
+
+ align:start position:0%
+of professionals all working for one
+individual was one of the other programs
+
+ align:start position:0%
+individual was one of the other programs
+ 
+
+ align:start position:0%
+individual was one of the other programs
+mention the other wasal
+
+ align:start position:0%
+mention the other wasal
+ 
+
+ align:start position:0%
+mention the other wasal
+healthare um he then he went on to talk
+
+ align:start position:0%
+healthare um he then he went on to talk
+ 
+
+ align:start position:0%
+healthare um he then he went on to talk
+about so he talked about his history
+
+ align:start position:0%
+about so he talked about his history
+ 
+
+ align:start position:0%
+about so he talked about his history
+about history of the clinic uh and then
+
+ align:start position:0%
+about history of the clinic uh and then
+ 
+
+ align:start position:0%
+about history of the clinic uh and then
+he started talking about um s what he
+
+ align:start position:0%
+he started talking about um s what he
+ 
+
+ align:start position:0%
+he started talking about um s what he
+saw for other
+
+ align:start position:0%
+saw for other
+ 
+
+ align:start position:0%
+saw for other
+and he talked about personal care that
+
+ align:start position:0%
+and he talked about personal care that
+ 
+
+ align:start position:0%
+and he talked about personal care that
+was one of the things he talked about
+
+ align:start position:0%
+was one of the things he talked about
+ 
+
+ align:start position:0%
+was one of the things he talked about
+that being a possible area
+
+ align:start position:0%
+that being a possible area
+ 
+
+ align:start position:0%
+that being a possible area
+for both training um and then creating a
+
+ align:start position:0%
+for both training um and then creating a
+ 
+
+ align:start position:0%
+for both training um and then creating a
+supply of workers and then firstand
+
+ align:start position:0%
+supply of workers and then firstand
+ 
+
+ align:start position:0%
+supply of workers and then firstand
+problem um he also then spent a fair
+
+ align:start position:0%
+problem um he also then spent a fair
+ 
+
+ align:start position:0%
+problem um he also then spent a fair
+amount of time oh we talk similarly
+
+ align:start position:0%
+amount of time oh we talk similarly
+ 
+
+ align:start position:0%
+amount of time oh we talk similarly
+about Co-op daycare
+
+ align:start position:0%
+about Co-op daycare
+ 
+
+ align:start position:0%
+about Co-op daycare
+uh he then spent a amount of time
+
+ align:start position:0%
+uh he then spent a amount of time
+ 
+
+ align:start position:0%
+uh he then spent a amount of time
+talking about turning the North End um
+
+ align:start position:0%
+talking about turning the North End um
+ 
+
+ align:start position:0%
+talking about turning the North End um
+exp business small bus type of
+
+ align:start position:0%
+exp business small bus type of
+ 
+
+ align:start position:0%
+exp business small bus type of
+topic retail support area for
+
+ align:start position:0%
+topic retail support area for
+ 
+
+ align:start position:0%
+topic retail support area for
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+for recreational shopping but as well as
+
+ align:start position:0%
+for recreational shopping but as well as
+ 
+
+ align:start position:0%
+for recreational shopping but as well as
+serving U what he sees to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be stff uh he talked about also brought
+
+ align:start position:0%
+be stff uh he talked about also brought
+ 
+
+ align:start position:0%
+be stff uh he talked about also brought
+corporation uh very similar opinions
+
+ align:start position:0%
+corporation uh very similar opinions
+ 
+
+ align:start position:0%
+corporation uh very similar opinions
+obstacle r as at this
+
+ align:start position:0%
+obstacle r as at this
+ 
+
+ align:start position:0%
+obstacle r as at this
+point Al that came up
+
+ align:start position:0%
+point Al that came up
+ 
+
+ align:start position:0%
+point Al that came up
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+yeah that was that was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interesting yeah kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+changed what happened tell us some of us
+
+ align:start position:0%
+changed what happened tell us some of us
+ 
+
+ align:start position:0%
+changed what happened tell us some of us
+wenten there so why was it interesting
+
+ align:start position:0%
+wenten there so why was it interesting
+ 
+
+ align:start position:0%
+wenten there so why was it interesting
+well Robert came in and I guess it just
+
+ align:start position:0%
+well Robert came in and I guess it just
+ 
+
+ align:start position:0%
+well Robert came in and I guess it just
+changed it it must have been more just
+
+ align:start position:0%
+changed it it must have been more just
+ 
+
+ align:start position:0%
+changed it it must have been more just
+sort of was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really we asked ask talk about the land
+
+ align:start position:0%
+really we asked ask talk about the land
+ 
+
+ align:start position:0%
+really we asked ask talk about the land
+trust idea
+
+ align:start position:0%
+trust idea
+ 
+
+ align:start position:0%
+trust idea
+right is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else he also talked about kind of this
+
+ align:start position:0%
+else he also talked about kind of this
+ 
+
+ align:start position:0%
+else he also talked about kind of this
+idea of from he's part of like this
+
+ align:start position:0%
+idea of from he's part of like this
+ 
+
+ align:start position:0%
+idea of from he's part of like this
+whole we call it like the community he
+
+ align:start position:0%
+whole we call it like the community he
+ 
+
+ align:start position:0%
+whole we call it like the community he
+Center movement which was a whole um
+
+ align:start position:0%
+Center movement which was a whole um
+ 
+
+ align:start position:0%
+Center movement which was a whole um
+kind of idea I guess getting out of like
+
+ align:start position:0%
+kind of idea I guess getting out of like
+ 
+
+ align:start position:0%
+kind of idea I guess getting out of like
+major hospitals where patients go to
+
+ align:start position:0%
+major hospitals where patients go to
+ 
+
+ align:start position:0%
+major hospitals where patients go to
+hospital to try like having a community
+
+ align:start position:0%
+hospital to try like having a community
+ 
+
+ align:start position:0%
+hospital to try like having a community
+area that service by Clinic that's in a
+
+ align:start position:0%
+area that service by Clinic that's in a
+ 
+
+ align:start position:0%
+area that service by Clinic that's in a
+community and is kind of more the
+
+ align:start position:0%
+community and is kind of more the
+ 
+
+ align:start position:0%
+community and is kind of more the
+community is kind of on a board and like
+
+ align:start position:0%
+community is kind of on a board and like
+ 
+
+ align:start position:0%
+community is kind of on a board and like
+it's like the community kind of runs it
+
+ align:start position:0%
+it's like the community kind of runs it
+ 
+
+ align:start position:0%
+it's like the community kind of runs it
+in the way boards and associations and
+
+ align:start position:0%
+in the way boards and associations and
+ 
+
+ align:start position:0%
+in the way boards and associations and
+things kind of um and that that kind of
+
+ align:start position:0%
+things kind of um and that that kind of
+ 
+
+ align:start position:0%
+things kind of um and that that kind of
+movement also has an idea of like
+
+ align:start position:0%
+movement also has an idea of like
+ 
+
+ align:start position:0%
+movement also has an idea of like
+population based healthare which is what
+
+ align:start position:0%
+population based healthare which is what
+ 
+
+ align:start position:0%
+population based healthare which is what
+kind of his clinic and a lot of clinics
+
+ align:start position:0%
+kind of his clinic and a lot of clinics
+ 
+
+ align:start position:0%
+kind of his clinic and a lot of clinics
+that are involved in kind of this
+
+ align:start position:0%
+that are involved in kind of this
+ 
+
+ align:start position:0%
+that are involved in kind of this
+movement the 60s kind um which is like
+
+ align:start position:0%
+movement the 60s kind um which is like
+ 
+
+ align:start position:0%
+movement the 60s kind um which is like
+not looking it not saying okay how many
+
+ align:start position:0%
+not looking it not saying okay how many
+ 
+
+ align:start position:0%
+not looking it not saying okay how many
+we have 50 people who came to our clinic
+
+ align:start position:0%
+we have 50 people who came to our clinic
+ 
+
+ align:start position:0%
+we have 50 people who came to our clinic
+and 20 of them got well it's it's like
+
+ align:start position:0%
+and 20 of them got well it's it's like
+ 
+
+ align:start position:0%
+and 20 of them got well it's it's like
+looking at like the whole community so
+
+ align:start position:0%
+looking at like the whole community so
+ 
+
+ align:start position:0%
+looking at like the whole community so
+even if you don't see that person in
+
+ align:start position:0%
+even if you don't see that person in
+ 
+
+ align:start position:0%
+even if you don't see that person in
+your clinic that's the clinic
+
+ align:start position:0%
+your clinic that's the clinic
+ 
+
+ align:start position:0%
+your clinic that's the clinic
+responsibility to bring that person in
+
+ align:start position:0%
+responsibility to bring that person in
+ 
+
+ align:start position:0%
+responsibility to bring that person in
+the clinic and still give care to that
+
+ align:start position:0%
+the clinic and still give care to that
+ 
+
+ align:start position:0%
+the clinic and still give care to that
+person even if that person isn't on
+
+ align:start position:0%
+person even if that person isn't on
+ 
+
+ align:start position:0%
+person even if that person isn't on
+their own come to the clinic like
+
+ align:start position:0%
+their own come to the clinic like
+ 
+
+ align:start position:0%
+their own come to the clinic like
+looking at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whole so um and then well like what is
+
+ align:start position:0%
+whole so um and then well like what is
+ 
+
+ align:start position:0%
+whole so um and then well like what is
+that and and this is like something that
+
+ align:start position:0%
+that and and this is like something that
+ 
+
+ align:start position:0%
+that and and this is like something that
+um like like um I've asked this question
+
+ align:start position:0%
+um like like um I've asked this question
+ 
+
+ align:start position:0%
+um like like um I've asked this question
+because like people at neon also I've
+
+ align:start position:0%
+because like people at neon also I've
+ 
+
+ align:start position:0%
+because like people at neon also I've
+heard this several times and I talked to
+
+ align:start position:0%
+heard this several times and I talked to
+ 
+
+ align:start position:0%
+heard this several times and I talked to
+Myra about like what it was because she
+
+ align:start position:0%
+Myra about like what it was because she
+ 
+
+ align:start position:0%
+Myra about like what it was because she
+she stressed again like a coule stressed
+
+ align:start position:0%
+she stressed again like a coule stressed
+ 
+
+ align:start position:0%
+she stressed again like a coule stressed
+like neon is kind of a population based
+
+ align:start position:0%
+like neon is kind of a population based
+ 
+
+ align:start position:0%
+like neon is kind of a population based
+organization has a population based
+
+ align:start position:0%
+organization has a population based
+ 
+
+ align:start position:0%
+organization has a population based
+approach which is you know they knock on
+
+ align:start position:0%
+approach which is you know they knock on
+ 
+
+ align:start position:0%
+approach which is you know they knock on
+like the way my's been it's like you
+
+ align:start position:0%
+like the way my's been it's like you
+ 
+
+ align:start position:0%
+like the way my's been it's like you
+knock on the door every you know and try
+
+ align:start position:0%
+knock on the door every you know and try
+ 
+
+ align:start position:0%
+knock on the door every you know and try
+to reach everybody it's not just the
+
+ align:start position:0%
+to reach everybody it's not just the
+ 
+
+ align:start position:0%
+to reach everybody it's not just the
+person that aners the door it's like
+
+ align:start position:0%
+person that aners the door it's like
+ 
+
+ align:start position:0%
+person that aners the door it's like
+everybody in that house is part of the
+
+ align:start position:0%
+everybody in that house is part of the
+ 
+
+ align:start position:0%
+everybody in that house is part of the
+community and hopefully they can access
+
+ align:start position:0%
+community and hopefully they can access
+ 
+
+ align:start position:0%
+community and hopefully they can access
+all of people to it's not just people
+
+ align:start position:0%
+all of people to it's not just people
+ 
+
+ align:start position:0%
+all of people to it's not just people
+that show to Mee programs like that so
+
+ align:start position:0%
+that show to Mee programs like that so
+ 
+
+ align:start position:0%
+that show to Mee programs like that so
+then call asked a question like what
+
+ align:start position:0%
+then call asked a question like what
+ 
+
+ align:start position:0%
+then call asked a question like what
+would that mean for like Economic
+
+ align:start position:0%
+would that mean for like Economic
+ 
+
+ align:start position:0%
+would that mean for like Economic
+Development so then he kind of talked
+
+ align:start position:0%
+Development so then he kind of talked
+ 
+
+ align:start position:0%
+Development so then he kind of talked
+about maybe an um maybe what this kind
+
+ align:start position:0%
+about maybe an um maybe what this kind
+ 
+
+ align:start position:0%
+about maybe an um maybe what this kind
+of community based approach would for
+
+ align:start position:0%
+of community based approach would for
+ 
+
+ align:start position:0%
+of community based approach would for
+economic development is looking at maybe
+
+ align:start position:0%
+economic development is looking at maybe
+ 
+
+ align:start position:0%
+economic development is looking at maybe
+things that wouldn't Target like not
+
+ align:start position:0%
+things that wouldn't Target like not
+ 
+
+ align:start position:0%
+things that wouldn't Target like not
+like a Workforce program that would
+
+ align:start position:0%
+like a Workforce program that would
+ 
+
+ align:start position:0%
+like a Workforce program that would
+Target Like A specific group were
+
+ align:start position:0%
+Target Like A specific group were
+ 
+
+ align:start position:0%
+Target Like A specific group were
+interested but things that would make a
+
+ align:start position:0%
+interested but things that would make a
+ 
+
+ align:start position:0%
+interested but things that would make a
+large change for everybody in the
+
+ align:start position:0%
+large change for everybody in the
+ 
+
+ align:start position:0%
+large change for everybody in the
+neighborhood and he kind of talked about
+
+ align:start position:0%
+neighborhood and he kind of talked about
+ 
+
+ align:start position:0%
+neighborhood and he kind of talked about
+this idea that kind of like in most
+
+ align:start position:0%
+this idea that kind of like in most
+ 
+
+ align:start position:0%
+this idea that kind of like in most
+places like the community he was talking
+
+ align:start position:0%
+places like the community he was talking
+ 
+
+ align:start position:0%
+places like the community he was talking
+about where he lived in like where he
+
+ align:start position:0%
+about where he lived in like where he
+ 
+
+ align:start position:0%
+about where he lived in like where he
+grab in Queens it was like there were
+
+ align:start position:0%
+grab in Queens it was like there were
+ 
+
+ align:start position:0%
+grab in Queens it was like there were
+like 70% of people that that were pretty
+
+ align:start position:0%
+like 70% of people that that were pretty
+ 
+
+ align:start position:0%
+like 70% of people that that were pretty
+well out and doing okay and then like
+
+ align:start position:0%
+well out and doing okay and then like
+ 
+
+ align:start position:0%
+well out and doing okay and then like
+30% of people that were really
+
+ align:start position:0%
+30% of people that were really
+ 
+
+ align:start position:0%
+30% of people that were really
+struggling and that 70% really helped
+
+ align:start position:0%
+struggling and that 70% really helped
+ 
+
+ align:start position:0%
+struggling and that 70% really helped
+with 30% that were struggling so the
+
+ align:start position:0%
+with 30% that were struggling so the
+ 
+
+ align:start position:0%
+with 30% that were struggling so the
+commun was was great was well off and he
+
+ align:start position:0%
+commun was was great was well off and he
+ 
+
+ align:start position:0%
+commun was was great was well off and he
+said that that that's a little bit
+
+ align:start position:0%
+said that that that's a little bit
+ 
+
+ align:start position:0%
+said that that that's a little bit
+reversed in the North End so you have
+
+ align:start position:0%
+reversed in the North End so you have
+ 
+
+ align:start position:0%
+reversed in the North End so you have
+like 70% of people who aren't doing okay
+
+ align:start position:0%
+like 70% of people who aren't doing okay
+ 
+
+ align:start position:0%
+like 70% of people who aren't doing okay
+and 30% % of people who are doing okay
+
+ align:start position:0%
+and 30% % of people who are doing okay
+ 
+
+ align:start position:0%
+and 30% % of people who are doing okay
+but that 70% the massive kind of um
+
+ align:start position:0%
+but that 70% the massive kind of um
+ 
+
+ align:start position:0%
+but that 70% the massive kind of um
+that's kind of the big presence of opin
+
+ align:start position:0%
+that's kind of the big presence of opin
+ 
+
+ align:start position:0%
+that's kind of the big presence of opin
+kind of brings that 30% down so the
+
+ align:start position:0%
+kind of brings that 30% down so the
+ 
+
+ align:start position:0%
+kind of brings that 30% down so the
+whole Community isn't doing well so he
+
+ align:start position:0%
+whole Community isn't doing well so he
+ 
+
+ align:start position:0%
+whole Community isn't doing well so he
+kind of talking about approaches that
+
+ align:start position:0%
+kind of talking about approaches that
+ 
+
+ align:start position:0%
+kind of talking about approaches that
+would maybe um change the community kind
+
+ align:start position:0%
+would maybe um change the community kind
+ 
+
+ align:start position:0%
+would maybe um change the community kind
+of like on a larger scale and kind of
+
+ align:start position:0%
+of like on a larger scale and kind of
+ 
+
+ align:start position:0%
+of like on a larger scale and kind of
+get it to that 70% of people that were
+
+ align:start position:0%
+get it to that 70% of people that were
+ 
+
+ align:start position:0%
+get it to that 70% of people that were
+doing okay so the whole Community get
+
+ align:start position:0%
+doing okay so the whole Community get
+ 
+
+ align:start position:0%
+doing okay so the whole Community get
+kind of benefit from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that one thing I would add is
+
+ align:start position:0%
+that one thing I would add is
+ 
+
+ align:start position:0%
+that one thing I would add is
+that one of the um the population based
+
+ align:start position:0%
+that one of the um the population based
+ 
+
+ align:start position:0%
+that one of the um the population based
+approach and the Outreach through
+
+ align:start position:0%
+approach and the Outreach through
+ 
+
+ align:start position:0%
+approach and the Outreach through
+through neon produced real Financial
+
+ align:start position:0%
+through neon produced real Financial
+ 
+
+ align:start position:0%
+through neon produced real Financial
+benefits for base a because they were
+
+ align:start position:0%
+benefits for base a because they were
+ 
+
+ align:start position:0%
+benefits for base a because they were
+able to sign everyone up who was
+
+ align:start position:0%
+able to sign everyone up who was
+ 
+
+ align:start position:0%
+able to sign everyone up who was
+eligible for Medicaid or some other
+
+ align:start position:0%
+eligible for Medicaid or some other
+ 
+
+ align:start position:0%
+eligible for Medicaid or some other
+health insurance plan so B they dropped
+
+ align:start position:0%
+health insurance plan so B they dropped
+ 
+
+ align:start position:0%
+health insurance plan so B they dropped
+Bas States uninsured percentage of of
+
+ align:start position:0%
+Bas States uninsured percentage of of
+ 
+
+ align:start position:0%
+Bas States uninsured percentage of of
+patients from 16% to 18% as were all the
+
+ align:start position:0%
+patients from 16% to 18% as were all the
+ 
+
+ align:start position:0%
+patients from 16% to 18% as were all the
+other community health clinics still
+
+ align:start position:0%
+other community health clinics still
+ 
+
+ align:start position:0%
+other community health clinics still
+have this 16% uninsured so it it it sort
+
+ align:start position:0%
+have this 16% uninsured so it it it sort
+ 
+
+ align:start position:0%
+have this 16% uninsured so it it it sort
+of did have this benefit for base Aid
+
+ align:start position:0%
+of did have this benefit for base Aid
+ 
+
+ align:start position:0%
+of did have this benefit for base Aid
+and and at least you know one of his
+
+ align:start position:0%
+and and at least you know one of his
+ 
+
+ align:start position:0%
+and and at least you know one of his
+other themes were there there's enough
+
+ align:start position:0%
+other themes were there there's enough
+ 
+
+ align:start position:0%
+other themes were there there's enough
+money in the healthare system that if
+
+ align:start position:0%
+money in the healthare system that if
+ 
+
+ align:start position:0%
+money in the healthare system that if
+you find ways to save money through
+
+ align:start position:0%
+you find ways to save money through
+ 
+
+ align:start position:0%
+you find ways to save money through
+actually delivering Better Health Care
+
+ align:start position:0%
+actually delivering Better Health Care
+ 
+
+ align:start position:0%
+actually delivering Better Health Care
+that does free them up some resources to
+
+ align:start position:0%
+that does free them up some resources to
+ 
+
+ align:start position:0%
+that does free them up some resources to
+do some other type of things um so that
+
+ align:start position:0%
+do some other type of things um so that
+ 
+
+ align:start position:0%
+do some other type of things um so that
+that that I thought was kind of
+
+ align:start position:0%
+that that I thought was kind of
+ 
+
+ align:start position:0%
+that that I thought was kind of
+interesting um um and that they were
+
+ align:start position:0%
+interesting um um and that they were
+ 
+
+ align:start position:0%
+interesting um um and that they were
+able to sort of bring about these kind
+
+ align:start position:0%
+able to sort of bring about these kind
+ 
+
+ align:start position:0%
+able to sort of bring about these kind
+of changes they sort of were able to
+
+ align:start position:0%
+of changes they sort of were able to
+ 
+
+ align:start position:0%
+of changes they sort of were able to
+sort of change the healthcare Del system
+
+ align:start position:0%
+sort of change the healthcare Del system
+ 
+
+ align:start position:0%
+sort of change the healthcare Del system
+and in what seemed to be you know
+
+ align:start position:0%
+and in what seemed to be you know
+ 
+
+ align:start position:0%
+and in what seemed to be you know
+overcome a lot of organizational
+
+ align:start position:0%
+overcome a lot of organizational
+ 
+
+ align:start position:0%
+overcome a lot of organizational
+obstacles he did walk us through this
+
+ align:start position:0%
+obstacles he did walk us through this
+ 
+
+ align:start position:0%
+obstacles he did walk us through this
+process he used to eventually get the
+
+ align:start position:0%
+process he used to eventually get the
+ 
+
+ align:start position:0%
+process he used to eventually get the
+the community health centers in the
+
+ align:start position:0%
+the community health centers in the
+ 
+
+ align:start position:0%
+the community health centers in the
+Springfield area to take responsibility
+
+ align:start position:0%
+Springfield area to take responsibility
+ 
+
+ align:start position:0%
+Springfield area to take responsibility
+for the healthc care of
+
+ align:start position:0%
+for the healthc care of
+ 
+
+ align:start position:0%
+for the healthc care of
+prisoners um so that they weren't you
+
+ align:start position:0%
+prisoners um so that they weren't you
+ 
+
+ align:start position:0%
+prisoners um so that they weren't you
+know having AIDS going into prison stop
+
+ align:start position:0%
+know having AIDS going into prison stop
+ 
+
+ align:start position:0%
+know having AIDS going into prison stop
+getting care and then coming back out
+
+ align:start position:0%
+getting care and then coming back out
+ 
+
+ align:start position:0%
+getting care and then coming back out
+with really deteriorated Health that
+
+ align:start position:0%
+with really deteriorated Health that
+ 
+
+ align:start position:0%
+with really deteriorated Health that
+also kind of interesting no I just want
+
+ align:start position:0%
+also kind of interesting no I just want
+ 
+
+ align:start position:0%
+also kind of interesting no I just want
+to say something on that because I think
+
+ align:start position:0%
+to say something on that because I think
+ 
+
+ align:start position:0%
+to say something on that because I think
+it's one of the interesting things about
+
+ align:start position:0%
+it's one of the interesting things about
+ 
+
+ align:start position:0%
+it's one of the interesting things about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+health uh work that they're doing
+
+ align:start position:0%
+health uh work that they're doing
+ 
+
+ align:start position:0%
+health uh work that they're doing
+because I think often when we look at it
+
+ align:start position:0%
+because I think often when we look at it
+ 
+
+ align:start position:0%
+because I think often when we look at it
+we talk about it and think about it in
+
+ align:start position:0%
+we talk about it and think about it in
+ 
+
+ align:start position:0%
+we talk about it and think about it in
+that but this is about Healthcare it's
+
+ align:start position:0%
+that but this is about Healthcare it's
+ 
+
+ align:start position:0%
+that but this is about Healthcare it's
+about the Social Service delivery
+
+ align:start position:0%
+about the Social Service delivery
+ 
+
+ align:start position:0%
+about the Social Service delivery
+component of things but there have been
+
+ align:start position:0%
+component of things but there have been
+ 
+
+ align:start position:0%
+component of things but there have been
+some very interesting experimental
+
+ align:start position:0%
+some very interesting experimental
+ 
+
+ align:start position:0%
+some very interesting experimental
+business ideas you know economic ideas
+
+ align:start position:0%
+business ideas you know economic ideas
+ 
+
+ align:start position:0%
+business ideas you know economic ideas
+and what they've been doing with
+
+ align:start position:0%
+and what they've been doing with
+ 
+
+ align:start position:0%
+and what they've been doing with
+Healthcare that I think they haven't
+
+ align:start position:0%
+Healthcare that I think they haven't
+ 
+
+ align:start position:0%
+Healthcare that I think they haven't
+figured out how to leverage in really
+
+ align:start position:0%
+figured out how to leverage in really
+ 
+
+ align:start position:0%
+figured out how to leverage in really
+powerful ways so for example the
+
+ align:start position:0%
+powerful ways so for example the
+ 
+
+ align:start position:0%
+powerful ways so for example the
+Medicaid one that they're
+
+ align:start position:0%
+Medicaid one that they're
+ 
+
+ align:start position:0%
+Medicaid one that they're
+doing you know if you ask Jeff if
+
+ align:start position:0%
+doing you know if you ask Jeff if
+ 
+
+ align:start position:0%
+doing you know if you ask Jeff if
+they've been able to recoup an equal
+
+ align:start position:0%
+they've been able to recoup an equal
+ 
+
+ align:start position:0%
+they've been able to recoup an equal
+amount of the savings for them as
+
+ align:start position:0%
+amount of the savings for them as
+ 
+
+ align:start position:0%
+amount of the savings for them as
+opposed to going to Bay State they don't
+
+ align:start position:0%
+opposed to going to Bay State they don't
+ 
+
+ align:start position:0%
+opposed to going to Bay State they don't
+feel that they have been able to uh the
+
+ align:start position:0%
+feel that they have been able to uh the
+ 
+
+ align:start position:0%
+feel that they have been able to uh the
+same thing with with the insurance if
+
+ align:start position:0%
+same thing with with the insurance if
+ 
+
+ align:start position:0%
+same thing with with the insurance if
+Bay State gets a savings what's the
+
+ align:start position:0%
+Bay State gets a savings what's the
+ 
+
+ align:start position:0%
+Bay State gets a savings what's the
+benefit for the community clearly
+
+ align:start position:0%
+benefit for the community clearly
+ 
+
+ align:start position:0%
+benefit for the community clearly
+there's a health benefit but if there's
+
+ align:start position:0%
+there's a health benefit but if there's
+ 
+
+ align:start position:0%
+there's a health benefit but if there's
+a financial benefit for Bay State you
+
+ align:start position:0%
+a financial benefit for Bay State you
+ 
+
+ align:start position:0%
+a financial benefit for Bay State you
+know the community doesn't they don't
+
+ align:start position:0%
+know the community doesn't they don't
+ 
+
+ align:start position:0%
+know the community doesn't they don't
+they can't monetize you know get any
+
+ align:start position:0%
+they can't monetize you know get any
+ 
+
+ align:start position:0%
+they can't monetize you know get any
+value they trying aren't they trying to
+
+ align:start position:0%
+value they trying aren't they trying to
+ 
+
+ align:start position:0%
+value they trying aren't they trying to
+negotiate some cost sharing Arrangements
+
+ align:start position:0%
+negotiate some cost sharing Arrangements
+ 
+
+ align:start position:0%
+negotiate some cost sharing Arrangements
+they're trying to negotiate some of that
+
+ align:start position:0%
+they're trying to negotiate some of that
+ 
+
+ align:start position:0%
+they're trying to negotiate some of that
+but don't kind of have it but I think
+
+ align:start position:0%
+but don't kind of have it but I think
+ 
+
+ align:start position:0%
+but don't kind of have it but I think
+it's and then there's a third one thing
+
+ align:start position:0%
+it's and then there's a third one thing
+ 
+
+ align:start position:0%
+it's and then there's a third one thing
+with the prison thing is interesting
+
+ align:start position:0%
+with the prison thing is interesting
+ 
+
+ align:start position:0%
+with the prison thing is interesting
+because part of what they did with their
+
+ align:start position:0%
+because part of what they did with their
+ 
+
+ align:start position:0%
+because part of what they did with their
+model with the prison is because so many
+
+ align:start position:0%
+model with the prison is because so many
+ 
+
+ align:start position:0%
+model with the prison is because so many
+what's happened is is that a lot of the
+
+ align:start position:0%
+what's happened is is that a lot of the
+ 
+
+ align:start position:0%
+what's happened is is that a lot of the
+prisoners have gone to contract it their
+
+ align:start position:0%
+prisoners have gone to contract it their
+ 
+
+ align:start position:0%
+prisoners have gone to contract it their
+health care out to private and they've
+
+ align:start position:0%
+health care out to private and they've
+ 
+
+ align:start position:0%
+health care out to private and they've
+been able to show that they can provide
+
+ align:start position:0%
+been able to show that they can provide
+ 
+
+ align:start position:0%
+been able to show that they can provide
+the same care better care for less money
+
+ align:start position:0%
+the same care better care for less money
+ 
+
+ align:start position:0%
+the same care better care for less money
+you know into this contract ser and
+
+ align:start position:0%
+you know into this contract ser and
+ 
+
+ align:start position:0%
+you know into this contract ser and
+there's an interesting there's a model
+
+ align:start position:0%
+there's an interesting there's a model
+ 
+
+ align:start position:0%
+there's an interesting there's a model
+there so I just think it's interesting
+
+ align:start position:0%
+there so I just think it's interesting
+ 
+
+ align:start position:0%
+there so I just think it's interesting
+you have kind of like three different
+
+ align:start position:0%
+you have kind of like three different
+ 
+
+ align:start position:0%
+you have kind of like three different
+things that have happened Happ around
+
+ align:start position:0%
+things that have happened Happ around
+ 
+
+ align:start position:0%
+things that have happened Happ around
+the health thing where they're able to
+
+ align:start position:0%
+the health thing where they're able to
+ 
+
+ align:start position:0%
+the health thing where they're able to
+demonstrate that there's some way which
+
+ align:start position:0%
+demonstrate that there's some way which
+ 
+
+ align:start position:0%
+demonstrate that there's some way which
+financial benefits they Financial
+
+ align:start position:0%
+financial benefits they Financial
+ 
+
+ align:start position:0%
+financial benefits they Financial
+benefits they don't they don't capture
+
+ align:start position:0%
+benefits they don't they don't capture
+ 
+
+ align:start position:0%
+benefits they don't they don't capture
+they don't capture that cost savings and
+
+ align:start position:0%
+they don't capture that cost savings and
+ 
+
+ align:start position:0%
+they don't capture that cost savings and
+so that does raise interest if if they
+
+ align:start position:0%
+so that does raise interest if if they
+ 
+
+ align:start position:0%
+so that does raise interest if if they
+could capture some of that could that be
+
+ align:start position:0%
+could capture some of that could that be
+ 
+
+ align:start position:0%
+could capture some of that could that be
+a revenue stream that could help support
+
+ align:start position:0%
+a revenue stream that could help support
+ 
+
+ align:start position:0%
+a revenue stream that could help support
+you know other activities all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right it was actually and just as a side
+
+ align:start position:0%
+right it was actually and just as a side
+ 
+
+ align:start position:0%
+right it was actually and just as a side
+note I don't when Massachusetts Housing
+
+ align:start position:0%
+note I don't when Massachusetts Housing
+ 
+
+ align:start position:0%
+note I don't when Massachusetts Housing
+Finance
+
+ align:start position:0%
+Finance
+ 
+
+ align:start position:0%
+Finance
+agency mhf when they were when they were
+
+ align:start position:0%
+agency mhf when they were when they were
+ 
+
+ align:start position:0%
+agency mhf when they were when they were
+mhfa they called Mass housing there was
+
+ align:start position:0%
+mhfa they called Mass housing there was
+ 
+
+ align:start position:0%
+mhfa they called Mass housing there was
+a gentleman called Tony flare who uh
+
+ align:start position:0%
+a gentleman called Tony flare who uh
+ 
+
+ align:start position:0%
+a gentleman called Tony flare who uh
+worked for them doing uh kind of
+
+ align:start position:0%
+worked for them doing uh kind of
+ 
+
+ align:start position:0%
+worked for them doing uh kind of
+community outreach and he got very
+
+ align:start position:0%
+community outreach and he got very
+ 
+
+ align:start position:0%
+community outreach and he got very
+interested
+
+ align:start position:0%
+interested
+ 
+
+ align:start position:0%
+interested
+in uh the insurance cost that they had
+
+ align:start position:0%
+in uh the insurance cost that they had
+ 
+
+ align:start position:0%
+in uh the insurance cost that they had
+to pay on buildings that they had and
+
+ align:start position:0%
+to pay on buildings that they had and
+ 
+
+ align:start position:0%
+to pay on buildings that they had and
+that in places where there were you know
+
+ align:start position:0%
+that in places where there were you know
+ 
+
+ align:start position:0%
+that in places where there were you know
+kind of high poverty and issues of you
+
+ align:start position:0%
+kind of high poverty and issues of you
+ 
+
+ align:start position:0%
+kind of high poverty and issues of you
+know drugs and things like that that you
+
+ align:start position:0%
+know drugs and things like that that you
+ 
+
+ align:start position:0%
+know drugs and things like that that you
+know the insurance premiums were high
+
+ align:start position:0%
+know the insurance premiums were high
+ 
+
+ align:start position:0%
+know the insurance premiums were high
+and he actually struck this deal with
+
+ align:start position:0%
+and he actually struck this deal with
+ 
+
+ align:start position:0%
+and he actually struck this deal with
+some of the insurance companies that if
+
+ align:start position:0%
+some of the insurance companies that if
+ 
+
+ align:start position:0%
+some of the insurance companies that if
+he could lower their loss
+
+ align:start position:0%
+he could lower their loss
+ 
+
+ align:start position:0%
+he could lower their loss
+rate right would they split with him
+
+ align:start position:0%
+rate right would they split with him
+ 
+
+ align:start position:0%
+rate right would they split with him
+5050 the savings and they actually ended
+
+ align:start position:0%
+5050 the savings and they actually ended
+ 
+
+ align:start position:0%
+5050 the savings and they actually ended
+up building the whole
+
+ align:start position:0%
+up building the whole
+ 
+
+ align:start position:0%
+up building the whole
+Community uh service program out of mhfa
+
+ align:start position:0%
+Community uh service program out of mhfa
+ 
+
+ align:start position:0%
+Community uh service program out of mhfa
+out of that whole insurance program
+
+ align:start position:0%
+out of that whole insurance program
+ 
+
+ align:start position:0%
+out of that whole insurance program
+which actually became a Mainstay of what
+
+ align:start position:0%
+which actually became a Mainstay of what
+ 
+
+ align:start position:0%
+which actually became a Mainstay of what
+Mass housing does now which is uh so
+
+ align:start position:0%
+Mass housing does now which is uh so
+ 
+
+ align:start position:0%
+Mass housing does now which is uh so
+there's some ways in which that can
+
+ align:start position:0%
+there's some ways in which that can
+ 
+
+ align:start position:0%
+there's some ways in which that can
+happen so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I you want to move on to this
+
+ align:start position:0%
+but I you want to move on to this
+ 
+
+ align:start position:0%
+but I you want to move on to this
+population base yeah if people want to
+
+ align:start position:0%
+population base yeah if people want to
+ 
+
+ align:start position:0%
+population base yeah if people want to
+take a few minutes to talk about the
+
+ align:start position:0%
+take a few minutes to talk about the
+ 
+
+ align:start position:0%
+take a few minutes to talk about the
+inventory or do you want to maybe maybe
+
+ align:start position:0%
+inventory or do you want to maybe maybe
+ 
+
+ align:start position:0%
+inventory or do you want to maybe maybe
+it's more of a segue to go into this
+
+ align:start position:0%
+it's more of a segue to go into this
+ 
+
+ align:start position:0%
+it's more of a segue to go into this
+population based discussion yeah okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um Bailey
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you want to name them both yeah so
+
+ align:start position:0%
+okay you want to name them both yeah so
+ 
+
+ align:start position:0%
+okay you want to name them both yeah so
+so first was we were walking
+
+ align:start position:0%
+so first was we were walking
+ 
+
+ align:start position:0%
+so first was we were walking
+by the physical site
+
+ align:start position:0%
+by the physical site
+ 
+
+ align:start position:0%
+by the physical site
+where located and W quite sure which
+
+ align:start position:0%
+where located and W quite sure which
+ 
+
+ align:start position:0%
+where located and W quite sure which
+agency it was it
+
+ align:start position:0%
+agency it was it
+ 
+
+ align:start position:0%
+agency it was it
+just outside and I actually different
+
+ align:start position:0%
+just outside and I actually different
+ 
+
+ align:start position:0%
+just outside and I actually different
+agency that was out of the whole of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+campus and Kam was like no no no we are
+
+ align:start position:0%
+campus and Kam was like no no no we are
+ 
+
+ align:start position:0%
+campus and Kam was like no no no we are
+under there umbrella on let's go
+
+ align:start position:0%
+under there umbrella on let's go
+ 
+
+ align:start position:0%
+under there umbrella on let's go
+inside don't have time but she of
+
+ align:start position:0%
+inside don't have time but she of
+ 
+
+ align:start position:0%
+inside don't have time but she of
+dragged Us in and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+and he gave us about 10 minutes time and
+
+ align:start position:0%
+and he gave us about 10 minutes time and
+ 
+
+ align:start position:0%
+and he gave us about 10 minutes time and
+actually was just getting wound up
+
+ align:start position:0%
+actually was just getting wound up
+ 
+
+ align:start position:0%
+actually was just getting wound up
+really all the work they had been doing
+
+ align:start position:0%
+really all the work they had been doing
+ 
+
+ align:start position:0%
+really all the work they had been doing
+and how they had come every conceivable
+
+ align:start position:0%
+and how they had come every conceivable
+ 
+
+ align:start position:0%
+and how they had come every conceivable
+vibe from
+
+ align:start position:0%
+vibe from
+ 
+
+ align:start position:0%
+vibe from
+development prevention to car the
+
+ align:start position:0%
+development prevention to car the
+ 
+
+ align:start position:0%
+development prevention to car the
+seniors and the interesting thing of saw
+
+ align:start position:0%
+seniors and the interesting thing of saw
+ 
+
+ align:start position:0%
+seniors and the interesting thing of saw
+that car seniors is the way
+
+ align:start position:0%
+that car seniors is the way
+ 
+
+ align:start position:0%
+that car seniors is the way
+in and smashion work
+
+ align:start position:0%
+in and smashion work
+ 
+
+ align:start position:0%
+in and smashion work
+together and a little taste of them you
+
+ align:start position:0%
+together and a little taste of them you
+ 
+
+ align:start position:0%
+together and a little taste of them you
+know of seeing their organization as
+
+ align:start position:0%
+know of seeing their organization as
+ 
+
+ align:start position:0%
+know of seeing their organization as
+a hybrid commity based organization
+
+ align:start position:0%
+a hybrid commity based organization
+ 
+
+ align:start position:0%
+a hybrid commity based organization
+CDC trying to do pieces of work that
+
+ align:start position:0%
+CDC trying to do pieces of work that
+ 
+
+ align:start position:0%
+CDC trying to do pieces of work that
+might otherwise be
+
+ align:start position:0%
+might otherwise be
+ 
+
+ align:start position:0%
+might otherwise be
+a types and then when he turned
+
+ align:start position:0%
+a types and then when he turned
+ 
+
+ align:start position:0%
+a types and then when he turned
+up almost unexpectedly at lunch he prob
+
+ align:start position:0%
+up almost unexpectedly at lunch he prob
+ 
+
+ align:start position:0%
+up almost unexpectedly at lunch he prob
+wasn't going to have time to and it
+
+ align:start position:0%
+wasn't going to have time to and it
+ 
+
+ align:start position:0%
+wasn't going to have time to and it
+didn't seem like Tak care of the that
+
+ align:start position:0%
+didn't seem like Tak care of the that
+ 
+
+ align:start position:0%
+didn't seem like Tak care of the that
+keeping away so I don't think that any
+
+ align:start position:0%
+keeping away so I don't think that any
+ 
+
+ align:start position:0%
+keeping away so I don't think that any
+of that of pressure had really been
+
+ align:start position:0%
+of that of pressure had really been
+ 
+
+ align:start position:0%
+of that of pressure had really been
+released um I think he really wanted to
+
+ align:start position:0%
+released um I think he really wanted to
+ 
+
+ align:start position:0%
+released um I think he really wanted to
+talk about the need for a strong CDC in
+
+ align:start position:0%
+talk about the need for a strong CDC in
+ 
+
+ align:start position:0%
+talk about the need for a strong CDC in
+the area and
+
+ align:start position:0%
+the area and
+ 
+
+ align:start position:0%
+the area and
+that he had very specific ideas of what
+
+ align:start position:0%
+that he had very specific ideas of what
+ 
+
+ align:start position:0%
+that he had very specific ideas of what
+their mandate would be how that would
+
+ align:start position:0%
+their mandate would be how that would
+ 
+
+ align:start position:0%
+their mandate would be how that would
+support existing
+
+ align:start position:0%
+support existing
+ 
+
+ align:start position:0%
+support existing
+organizations there are two things about
+
+ align:start position:0%
+organizations there are two things about
+ 
+
+ align:start position:0%
+organizations there are two things about
+that that I struck by one and this again
+
+ align:start position:0%
+that that I struck by one and this again
+ 
+
+ align:start position:0%
+that that I struck by one and this again
+Taste of this even
+
+ align:start position:0%
+Taste of this even
+ 
+
+ align:start position:0%
+Taste of this even
+earlier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relationship
+
+ align:start position:0%
+relationship
+ 
+
+ align:start position:0%
+relationship
+very the whole day previous night
+
+ align:start position:0%
+very the whole day previous night
+ 
+
+ align:start position:0%
+very the whole day previous night
+actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he seemed really around him in I don't
+
+ align:start position:0%
+he seemed really around him in I don't
+ 
+
+ align:start position:0%
+he seemed really around him in I don't
+know what the history there is and the
+
+ align:start position:0%
+know what the history there is and the
+ 
+
+ align:start position:0%
+know what the history there is and the
+second was almost like he was to Spanish
+
+ align:start position:0%
+second was almost like he was to Spanish
+ 
+
+ align:start position:0%
+second was almost like he was to Spanish
+Amer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CC interesting but that's our that's a
+
+ align:start position:0%
+CC interesting but that's our that's a
+ 
+
+ align:start position:0%
+CC interesting but that's our that's a
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+different everything we' talked about
+
+ align:start position:0%
+different everything we' talked about
+ 
+
+ align:start position:0%
+different everything we' talked about
+so also did kind of introduce himself in
+
+ align:start position:0%
+so also did kind of introduce himself in
+ 
+
+ align:start position:0%
+so also did kind of introduce himself in
+an unusual I thought an unusual way
+
+ align:start position:0%
+an unusual I thought an unusual way
+ 
+
+ align:start position:0%
+an unusual I thought an unusual way
+because he emphasized
+
+ align:start position:0%
+because he emphasized
+ 
+
+ align:start position:0%
+because he emphasized
+his
+
+ align:start position:0%
+his
+ 
+
+ align:start position:0%
+his
+accounting background he was kind of
+
+ align:start position:0%
+accounting background he was kind of
+ 
+
+ align:start position:0%
+accounting background he was kind of
+like you know I've been I forget the
+
+ align:start position:0%
+like you know I've been I forget the
+ 
+
+ align:start position:0%
+like you know I've been I forget the
+fiscal administrator or something like
+
+ align:start position:0%
+fiscal administrator or something like
+ 
+
+ align:start position:0%
+fiscal administrator or something like
+that and you know I kind of ended up as
+
+ align:start position:0%
+that and you know I kind of ended up as
+ 
+
+ align:start position:0%
+that and you know I kind of ended up as
+executive director because everyone else
+
+ align:start position:0%
+executive director because everyone else
+ 
+
+ align:start position:0%
+executive director because everyone else
+came and went was almost how he told the
+
+ align:start position:0%
+came and went was almost how he told the
+ 
+
+ align:start position:0%
+came and went was almost how he told the
+story and and I still do the fiscal work
+
+ align:start position:0%
+story and and I still do the fiscal work
+ 
+
+ align:start position:0%
+story and and I still do the fiscal work
+and I really like the fiscal work it was
+
+ align:start position:0%
+and I really like the fiscal work it was
+ 
+
+ align:start position:0%
+and I really like the fiscal work it was
+it was it was an unusual way to
+
+ align:start position:0%
+it was it was an unusual way to
+ 
+
+ align:start position:0%
+it was it was an unusual way to
+introduce yourself was director for a
+
+ align:start position:0%
+introduce yourself was director for a
+ 
+
+ align:start position:0%
+introduce yourself was director for a
+while and
+
+ align:start position:0%
+while and
+ 
+
+ align:start position:0%
+while and
+actually a buch g us old business Cs and
+
+ align:start position:0%
+actually a buch g us old business Cs and
+ 
+
+ align:start position:0%
+actually a buch g us old business Cs and
+said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scratched yeah well see that's that's
+
+ align:start position:0%
+scratched yeah well see that's that's
+ 
+
+ align:start position:0%
+scratched yeah well see that's that's
+the thing I had gone up to him and just
+
+ align:start position:0%
+the thing I had gone up to him and just
+ 
+
+ align:start position:0%
+the thing I had gone up to him and just
+to get the business cards and he you
+
+ align:start position:0%
+to get the business cards and he you
+ 
+
+ align:start position:0%
+to get the business cards and he you
+know each one he he very methodically
+
+ align:start position:0%
+know each one he he very methodically
+ 
+
+ align:start position:0%
+know each one he he very methodically
+crossed off the um and he also kind of
+
+ align:start position:0%
+crossed off the um and he also kind of
+ 
+
+ align:start position:0%
+crossed off the um and he also kind of
+talked me up and I think he mentioned it
+
+ align:start position:0%
+talked me up and I think he mentioned it
+ 
+
+ align:start position:0%
+talked me up and I think he mentioned it
+a little bit at lunch his the kind of
+
+ align:start position:0%
+a little bit at lunch his the kind of
+ 
+
+ align:start position:0%
+a little bit at lunch his the kind of
+land trust idea I guess I don't know if
+
+ align:start position:0%
+land trust idea I guess I don't know if
+ 
+
+ align:start position:0%
+land trust idea I guess I don't know if
+they've gotten money for that but it
+
+ align:start position:0%
+they've gotten money for that but it
+ 
+
+ align:start position:0%
+they've gotten money for that but it
+seemed that what he was emphasizing to
+
+ align:start position:0%
+seemed that what he was emphasizing to
+ 
+
+ align:start position:0%
+seemed that what he was emphasizing to
+me and maybe this is is the role that
+
+ align:start position:0%
+me and maybe this is is the role that
+ 
+
+ align:start position:0%
+me and maybe this is is the role that
+that where neon comes in that it's not
+
+ align:start position:0%
+that where neon comes in that it's not
+ 
+
+ align:start position:0%
+that where neon comes in that it's not
+so much you know the Spanish American
+
+ align:start position:0%
+so much you know the Spanish American
+ 
+
+ align:start position:0%
+so much you know the Spanish American
+Union that has to do the work of of kind
+
+ align:start position:0%
+Union that has to do the work of of kind
+ 
+
+ align:start position:0%
+Union that has to do the work of of kind
+of land banking but that the community
+
+ align:start position:0%
+of land banking but that the community
+ 
+
+ align:start position:0%
+of land banking but that the community
+itself has to kind of see the value and
+
+ align:start position:0%
+itself has to kind of see the value and
+ 
+
+ align:start position:0%
+itself has to kind of see the value and
+land trust and really take um the the
+
+ align:start position:0%
+land trust and really take um the the
+ 
+
+ align:start position:0%
+land trust and really take um the the
+Reigns and and and uh move that concept
+
+ align:start position:0%
+Reigns and and and uh move that concept
+ 
+
+ align:start position:0%
+Reigns and and and uh move that concept
+forward so there was it seemed kind of
+
+ align:start position:0%
+forward so there was it seemed kind of
+ 
+
+ align:start position:0%
+forward so there was it seemed kind of
+like it was a big idea a lot of work to
+
+ align:start position:0%
+like it was a big idea a lot of work to
+ 
+
+ align:start position:0%
+like it was a big idea a lot of work to
+be done and he was really kind of
+
+ align:start position:0%
+be done and he was really kind of
+ 
+
+ align:start position:0%
+be done and he was really kind of
+looking to spread that Work Out Among
+
+ align:start position:0%
+looking to spread that Work Out Among
+ 
+
+ align:start position:0%
+looking to spread that Work Out Among
+the community and using it as a
+
+ align:start position:0%
+the community and using it as a
+ 
+
+ align:start position:0%
+the community and using it as a
+community organiz
+
+ align:start position:0%
+community organiz
+ 
+
+ align:start position:0%
+community organiz
+kind of concept but I guess it didn't
+
+ align:start position:0%
+kind of concept but I guess it didn't
+ 
+
+ align:start position:0%
+kind of concept but I guess it didn't
+you know he did it seemed like he wasn't
+
+ align:start position:0%
+you know he did it seemed like he wasn't
+ 
+
+ align:start position:0%
+you know he did it seemed like he wasn't
+necessarily too sure about how to
+
+ align:start position:0%
+necessarily too sure about how to
+ 
+
+ align:start position:0%
+necessarily too sure about how to
+execute that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea very good
+
+ align:start position:0%
+idea very good
+ 
+
+ align:start position:0%
+idea very good
+observations I'll leave it at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I think no I think they're very
+
+ align:start position:0%
+that I think no I think they're very
+ 
+
+ align:start position:0%
+that I think no I think they're very
+good observations about what's what's
+
+ align:start position:0%
+good observations about what's what's
+ 
+
+ align:start position:0%
+good observations about what's what's
+what's going I'm sorry just what is the
+
+ align:start position:0%
+what's going I'm sorry just what is the
+ 
+
+ align:start position:0%
+what's going I'm sorry just what is the
+Spanish American un I was so kind of czy
+
+ align:start position:0%
+Spanish American un I was so kind of czy
+ 
+
+ align:start position:0%
+Spanish American un I was so kind of czy
+at the end like what like it's not like
+
+ align:start position:0%
+at the end like what like it's not like
+ 
+
+ align:start position:0%
+at the end like what like it's not like
+is it it's not like when you are
+
+ align:start position:0%
+is it it's not like when you are
+ 
+
+ align:start position:0%
+is it it's not like when you are
+Citizens Council it's
+
+ align:start position:0%
+Citizens Council it's
+ 
+
+ align:start position:0%
+Citizens Council it's
+it it is a Social Service
+
+ align:start position:0%
+it it is a Social Service
+ 
+
+ align:start position:0%
+it it is a Social Service
+Agency uh and it's independent of the
+
+ align:start position:0%
+Agency uh and it's independent of the
+ 
+
+ align:start position:0%
+Agency uh and it's independent of the
+new North Citizens Council the New York
+
+ align:start position:0%
+new North Citizens Council the New York
+ 
+
+ align:start position:0%
+new North Citizens Council the New York
+Citizens Council actually has uh a much
+
+ align:start position:0%
+Citizens Council actually has uh a much
+ 
+
+ align:start position:0%
+Citizens Council actually has uh a much
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+uh you know it has kind of an official
+
+ align:start position:0%
+uh you know it has kind of an official
+ 
+
+ align:start position:0%
+uh you know it has kind of an official
+role around its you know because of it's
+
+ align:start position:0%
+role around its you know because of it's
+ 
+
+ align:start position:0%
+role around its you know because of it's
+elected representative organization and
+
+ align:start position:0%
+elected representative organization and
+ 
+
+ align:start position:0%
+elected representative organization and
+what it does and it's tied into state
+
+ align:start position:0%
+what it does and it's tied into state
+ 
+
+ align:start position:0%
+what it does and it's tied into state
+government around how it gets funds and
+
+ align:start position:0%
+government around how it gets funds and
+ 
+
+ align:start position:0%
+government around how it gets funds and
+stuff like that Spanish American Union
+
+ align:start position:0%
+stuff like that Spanish American Union
+ 
+
+ align:start position:0%
+stuff like that Spanish American Union
+is very independent organization it does
+
+ align:start position:0%
+is very independent organization it does
+ 
+
+ align:start position:0%
+is very independent organization it does
+on Social Service side does some of the
+
+ align:start position:0%
+on Social Service side does some of the
+ 
+
+ align:start position:0%
+on Social Service side does some of the
+same kinds of things so it focused very
+
+ align:start position:0%
+same kinds of things so it focused very
+ 
+
+ align:start position:0%
+same kinds of things so it focused very
+heavily in two areas uh one was
+
+ align:start position:0%
+heavily in two areas uh one was
+ 
+
+ align:start position:0%
+heavily in two areas uh one was
+providing uh support for elders and the
+
+ align:start position:0%
+providing uh support for elders and the
+ 
+
+ align:start position:0%
+providing uh support for elders and the
+other was the training and
+
+ align:start position:0%
+other was the training and
+ 
+
+ align:start position:0%
+other was the training and
+preparation uh and certification of
+
+ align:start position:0%
+preparation uh and certification of
+ 
+
+ align:start position:0%
+preparation uh and certification of
+childcare workers in the community they
+
+ align:start position:0%
+childcare workers in the community they
+ 
+
+ align:start position:0%
+childcare workers in the community they
+had a whole program around there as a
+
+ align:start position:0%
+had a whole program around there as a
+ 
+
+ align:start position:0%
+had a whole program around there as a
+matter of fact they had developed a
+
+ align:start position:0%
+matter of fact they had developed a
+ 
+
+ align:start position:0%
+matter of fact they had developed a
+whole Spanish language program for
+
+ align:start position:0%
+whole Spanish language program for
+ 
+
+ align:start position:0%
+whole Spanish language program for
+actually training people to get uh
+
+ align:start position:0%
+actually training people to get uh
+ 
+
+ align:start position:0%
+actually training people to get uh
+certified as child care workers uh under
+
+ align:start position:0%
+certified as child care workers uh under
+ 
+
+ align:start position:0%
+certified as child care workers uh under
+the old director
+
+ align:start position:0%
+the old director
+ 
+
+ align:start position:0%
+the old director
+uh when the the last bust happened in
+
+ align:start position:0%
+uh when the the last bust happened in
+ 
+
+ align:start position:0%
+uh when the the last bust happened in
+the uh economy and there was all the
+
+ align:start position:0%
+the uh economy and there was all the
+ 
+
+ align:start position:0%
+the uh economy and there was all the
+cuts five years ago four years ago from
+
+ align:start position:0%
+cuts five years ago four years ago from
+ 
+
+ align:start position:0%
+cuts five years ago four years ago from
+the state I can't remember the dates or
+
+ align:start position:0%
+the state I can't remember the dates or
+ 
+
+ align:start position:0%
+the state I can't remember the dates or
+anything but uh they lost almost all
+
+ align:start position:0%
+anything but uh they lost almost all
+ 
+
+ align:start position:0%
+anything but uh they lost almost all
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+funding and so they became like a
+
+ align:start position:0%
+funding and so they became like a
+ 
+
+ align:start position:0%
+funding and so they became like a
+dormant institution in some sense kept
+
+ align:start position:0%
+dormant institution in some sense kept
+ 
+
+ align:start position:0%
+dormant institution in some sense kept
+together by the board only uh existing
+
+ align:start position:0%
+together by the board only uh existing
+ 
+
+ align:start position:0%
+together by the board only uh existing
+they weren't really running any programs
+
+ align:start position:0%
+they weren't really running any programs
+ 
+
+ align:start position:0%
+they weren't really running any programs
+and now they're trying to come back and
+
+ align:start position:0%
+and now they're trying to come back and
+ 
+
+ align:start position:0%
+and now they're trying to come back and
+I think they're searching for
+
+ align:start position:0%
+I think they're searching for
+ 
+
+ align:start position:0%
+I think they're searching for
+what kind of organization they're going
+
+ align:start position:0%
+what kind of organization they're going
+ 
+
+ align:start position:0%
+what kind of organization they're going
+to be and what what can they be as an
+
+ align:start position:0%
+to be and what what can they be as an
+ 
+
+ align:start position:0%
+to be and what what can they be as an
+organization that's going to let them
+
+ align:start position:0%
+organization that's going to let them
+ 
+
+ align:start position:0%
+organization that's going to let them
+sustain themselves I did get the
+
+ align:start position:0%
+sustain themselves I did get the
+ 
+
+ align:start position:0%
+sustain themselves I did get the
+impression that they're very
+
+ align:start position:0%
+impression that they're very
+ 
+
+ align:start position:0%
+impression that they're very
+oriented in
+
+ align:start position:0%
+oriented in
+ 
+
+ align:start position:0%
+oriented in
+towards State grant funding and that
+
+ align:start position:0%
+towards State grant funding and that
+ 
+
+ align:start position:0%
+towards State grant funding and that
+finding opportunities for State Grand
+
+ align:start position:0%
+finding opportunities for State Grand
+ 
+
+ align:start position:0%
+finding opportunities for State Grand
+funding you know he had talked about uh
+
+ align:start position:0%
+funding you know he had talked about uh
+ 
+
+ align:start position:0%
+funding you know he had talked about uh
+doing a lot of work now around tobacco
+
+ align:start position:0%
+doing a lot of work now around tobacco
+ 
+
+ align:start position:0%
+doing a lot of work now around tobacco
+prevention smoking
+
+ align:start position:0%
+prevention smoking
+ 
+
+ align:start position:0%
+prevention smoking
+prevention I I think because there was
+
+ align:start position:0%
+prevention I I think because there was
+ 
+
+ align:start position:0%
+prevention I I think because there was
+funding available from the the
+
+ align:start position:0%
+funding available from the the
+ 
+
+ align:start position:0%
+funding available from the the
+settlements with the tobacco industry
+
+ align:start position:0%
+settlements with the tobacco industry
+ 
+
+ align:start position:0%
+settlements with the tobacco industry
+and stuff like that so I I did get the
+
+ align:start position:0%
+and stuff like that so I I did get the
+ 
+
+ align:start position:0%
+and stuff like that so I I did get the
+sense they were sort of in a more
+
+ align:start position:0%
+sense they were sort of in a more
+ 
+
+ align:start position:0%
+sense they were sort of in a more
+opportunistic mode right now based on
+
+ align:start position:0%
+opportunistic mode right now based on
+ 
+
+ align:start position:0%
+opportunistic mode right now based on
+where they could get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+funded it's a 20 year something like a
+
+ align:start position:0%
+funded it's a 20 year something like a
+ 
+
+ align:start position:0%
+funded it's a 20 year something like a
+20-year funding
+
+ align:start position:0%
+20-year funding
+ 
+
+ align:start position:0%
+20-year funding
+stream I'm asking about this is the New
+
+ align:start position:0%
+stream I'm asking about this is the New
+ 
+
+ align:start position:0%
+stream I'm asking about this is the New
+York
+
+ align:start position:0%
+York
+ 
+
+ align:start position:0%
+York
+State cbos and cbcs can get the money to
+
+ align:start position:0%
+State cbos and cbcs can get the money to
+ 
+
+ align:start position:0%
+State cbos and cbcs can get the money to
+sign people up for subsidized health
+
+ align:start position:0%
+sign people up for subsidized health
+ 
+
+ align:start position:0%
+sign people up for subsidized health
+insurance
+
+ align:start position:0%
+insurance
+ 
+
+ align:start position:0%
+insurance
+that all comes out yeah each State's
+
+ align:start position:0%
+that all comes out yeah each State's
+ 
+
+ align:start position:0%
+that all comes out yeah each State's
+using that money
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differently yeah I mean there's a
+
+ align:start position:0%
+differently yeah I mean there's a
+ 
+
+ align:start position:0%
+differently yeah I mean there's a
+there's a long-term funding stream but
+
+ align:start position:0%
+there's a long-term funding stream but
+ 
+
+ align:start position:0%
+there's a long-term funding stream but
+I'm not really sure where how in
+
+ align:start position:0%
+I'm not really sure where how in
+ 
+
+ align:start position:0%
+I'm not really sure where how in
+Massachusetts that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's I I thought it was kind of ironic
+
+ align:start position:0%
+that's I I thought it was kind of ironic
+ 
+
+ align:start position:0%
+that's I I thought it was kind of ironic
+that that they were doing so much anti
+
+ align:start position:0%
+that that they were doing so much anti
+ 
+
+ align:start position:0%
+that that they were doing so much anti
+tobacco stuff cuz everyone was saying
+
+ align:start position:0%
+tobacco stuff cuz everyone was saying
+ 
+
+ align:start position:0%
+tobacco stuff cuz everyone was saying
+that a lot of the migrant workers in the
+
+ align:start position:0%
+that a lot of the migrant workers in the
+ 
+
+ align:start position:0%
+that a lot of the migrant workers in the
+area work in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it's too bad when we're in the health
+
+ align:start position:0%
+uh it's too bad when we're in the health
+ 
+
+ align:start position:0%
+uh it's too bad when we're in the health
+CL we didn't meet in the community room
+
+ align:start position:0%
+CL we didn't meet in the community room
+ 
+
+ align:start position:0%
+CL we didn't meet in the community room
+because it's actually a huge display up
+
+ align:start position:0%
+because it's actually a huge display up
+ 
+
+ align:start position:0%
+because it's actually a huge display up
+on the wall they have about the health
+
+ align:start position:0%
+on the wall they have about the health
+ 
+
+ align:start position:0%
+on the wall they have about the health
+hazards of tobacco uh working the
+
+ align:start position:0%
+hazards of tobacco uh working the
+ 
+
+ align:start position:0%
+hazards of tobacco uh working the
+tobacco Fields
+
+ align:start position:0%
+tobacco Fields
+ 
+
+ align:start position:0%
+tobacco Fields
+smoking and everything like that and yet
+
+ align:start position:0%
+smoking and everything like that and yet
+ 
+
+ align:start position:0%
+smoking and everything like that and yet
+if you say that's where kind of a lot of
+
+ align:start position:0%
+if you say that's where kind of a lot of
+ 
+
+ align:start position:0%
+if you say that's where kind of a lot of
+people work they actually have a photo
+
+ align:start position:0%
+people work they actually have a photo
+ 
+
+ align:start position:0%
+people work they actually have a photo
+of Clinton standing in front of that
+
+ align:start position:0%
+of Clinton standing in front of that
+ 
+
+ align:start position:0%
+of Clinton standing in front of that
+sign and Jeff K saying I'm gonna send
+
+ align:start position:0%
+sign and Jeff K saying I'm gonna send
+ 
+
+ align:start position:0%
+sign and Jeff K saying I'm gonna send
+him a picture of that and then the one
+
+ align:start position:0%
+him a picture of that and then the one
+ 
+
+ align:start position:0%
+him a picture of that and then the one
+of him in the official you know cigar
+
+ align:start position:0%
+of him in the official you know cigar
+ 
+
+ align:start position:0%
+of him in the official you know cigar
+offici Auto
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+magazine send it to him and remind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+him so anyway coming back to this issue
+
+ align:start position:0%
+him so anyway coming back to this issue
+ 
+
+ align:start position:0%
+him so anyway coming back to this issue
+of of populationbased
+
+ align:start position:0%
+of of populationbased
+ 
+
+ align:start position:0%
+of of populationbased
+approach um I thought it'd be useful to
+
+ align:start position:0%
+approach um I thought it'd be useful to
+ 
+
+ align:start position:0%
+approach um I thought it'd be useful to
+spend a little bit of time sort of
+
+ align:start position:0%
+spend a little bit of time sort of
+ 
+
+ align:start position:0%
+spend a little bit of time sort of
+talking about whether a what do you
+
+ align:start position:0%
+talking about whether a what do you
+ 
+
+ align:start position:0%
+talking about whether a what do you
+think that concept's useful um in
+
+ align:start position:0%
+think that concept's useful um in
+ 
+
+ align:start position:0%
+think that concept's useful um in
+thinking about or approach to Economic
+
+ align:start position:0%
+thinking about or approach to Economic
+ 
+
+ align:start position:0%
+thinking about or approach to Economic
+Development and if so what might it
+
+ align:start position:0%
+Development and if so what might it
+ 
+
+ align:start position:0%
+Development and if so what might it
+suggest about about how we might frame
+
+ align:start position:0%
+suggest about about how we might frame
+ 
+
+ align:start position:0%
+suggest about about how we might frame
+our war I don't know what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it well let me let me give my
+
+ align:start position:0%
+it well let me let me give my
+ 
+
+ align:start position:0%
+it well let me let me give my
+interpretation of it I I I interpret it
+
+ align:start position:0%
+interpretation of it I I I interpret it
+ 
+
+ align:start position:0%
+interpretation of it I I I interpret it
+to mean that um you know a commitment to
+
+ align:start position:0%
+to mean that um you know a commitment to
+ 
+
+ align:start position:0%
+to mean that um you know a commitment to
+improve outcomes for as many people in
+
+ align:start position:0%
+improve outcomes for as many people in
+ 
+
+ align:start position:0%
+improve outcomes for as many people in
+the community as
+
+ align:start position:0%
+the community as
+ 
+
+ align:start position:0%
+the community as
+possible um and that the way that's
+
+ align:start position:0%
+possible um and that the way that's
+ 
+
+ align:start position:0%
+possible um and that the way that's
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+implemented is through neon and that's
+
+ align:start position:0%
+implemented is through neon and that's
+ 
+
+ align:start position:0%
+implemented is through neon and that's
+through actually trying
+
+ align:start position:0%
+through actually trying
+ 
+
+ align:start position:0%
+through actually trying
+to develop a relationship with everyone
+
+ align:start position:0%
+to develop a relationship with everyone
+ 
+
+ align:start position:0%
+to develop a relationship with everyone
+in the community be able to sort of
+
+ align:start position:0%
+in the community be able to sort of
+ 
+
+ align:start position:0%
+in the community be able to sort of
+reach out to every household and
+
+ align:start position:0%
+reach out to every household and
+ 
+
+ align:start position:0%
+reach out to every household and
+understand what their health needs are
+
+ align:start position:0%
+understand what their health needs are
+ 
+
+ align:start position:0%
+understand what their health needs are
+understand what services might be
+
+ align:start position:0%
+understand what services might be
+ 
+
+ align:start position:0%
+understand what services might be
+available to address those Health needs
+
+ align:start position:0%
+available to address those Health needs
+ 
+
+ align:start position:0%
+available to address those Health needs
+and sort of connect them up to them
+
+ align:start position:0%
+and sort of connect them up to them
+ 
+
+ align:start position:0%
+and sort of connect them up to them
+so I mean at least two aspects of that
+
+ align:start position:0%
+so I mean at least two aspects of that
+ 
+
+ align:start position:0%
+so I mean at least two aspects of that
+seem useful at least uh important one
+
+ align:start position:0%
+seem useful at least uh important one
+ 
+
+ align:start position:0%
+seem useful at least uh important one
+the sort of notion that you're really
+
+ align:start position:0%
+the sort of notion that you're really
+ 
+
+ align:start position:0%
+the sort of notion that you're really
+trying to to measure outcomes not just
+
+ align:start position:0%
+trying to to measure outcomes not just
+ 
+
+ align:start position:0%
+trying to to measure outcomes not just
+uh you know by for a small segment but
+
+ align:start position:0%
+uh you know by for a small segment but
+ 
+
+ align:start position:0%
+uh you know by for a small segment but
+how everyone's conditions improved and
+
+ align:start position:0%
+how everyone's conditions improved and
+ 
+
+ align:start position:0%
+how everyone's conditions improved and
+the idea of of of having this Service
+
+ align:start position:0%
+the idea of of of having this Service
+ 
+
+ align:start position:0%
+the idea of of of having this Service
+delivery model where you actually have
+
+ align:start position:0%
+delivery model where you actually have
+ 
+
+ align:start position:0%
+delivery model where you actually have
+relationships with everyone in the
+
+ align:start position:0%
+relationships with everyone in the
+ 
+
+ align:start position:0%
+relationships with everyone in the
+community you really try and have an
+
+ align:start position:0%
+community you really try and have an
+ 
+
+ align:start position:0%
+community you really try and have an
+Outreach Network that can try and
+
+ align:start position:0%
+Outreach Network that can try and
+ 
+
+ align:start position:0%
+Outreach Network that can try and
+connect now I don't I know you've said
+
+ align:start position:0%
+connect now I don't I know you've said
+ 
+
+ align:start position:0%
+connect now I don't I know you've said
+in the past that really only only about
+
+ align:start position:0%
+in the past that really only only about
+ 
+
+ align:start position:0%
+in the past that really only only about
+40% of the people have actually
+
+ align:start position:0%
+40% of the people have actually
+ 
+
+ align:start position:0%
+40% of the people have actually
+participated in a meaningful way in that
+
+ align:start position:0%
+participated in a meaningful way in that
+ 
+
+ align:start position:0%
+participated in a meaningful way in that
+so they're not to they're not to 100% at
+
+ align:start position:0%
+so they're not to they're not to 100% at
+ 
+
+ align:start position:0%
+so they're not to they're not to 100% at
+this point yeah I think there's other
+
+ align:start position:0%
+this point yeah I think there's other
+ 
+
+ align:start position:0%
+this point yeah I think there's other
+couple of things two ways to think about
+
+ align:start position:0%
+couple of things two ways to think about
+ 
+
+ align:start position:0%
+couple of things two ways to think about
+it one is
+
+ align:start position:0%
+it one is
+ 
+
+ align:start position:0%
+it one is
+that uh and I me you said this quite
+
+ align:start position:0%
+that uh and I me you said this quite
+ 
+
+ align:start position:0%
+that uh and I me you said this quite
+clear but it's the the kind of indicator
+
+ align:start position:0%
+clear but it's the the kind of indicator
+ 
+
+ align:start position:0%
+clear but it's the the kind of indicator
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+success for them and the indicators for
+
+ align:start position:0%
+success for them and the indicators for
+ 
+
+ align:start position:0%
+success for them and the indicators for
+Progress are not based on who they serve
+
+ align:start position:0%
+Progress are not based on who they serve
+ 
+
+ align:start position:0%
+Progress are not based on who they serve
+but who resides in the community so it's
+
+ align:start position:0%
+but who resides in the community so it's
+ 
+
+ align:start position:0%
+but who resides in the community so it's
+a very different model because most
+
+ align:start position:0%
+a very different model because most
+ 
+
+ align:start position:0%
+a very different model because most
+people kind of think about look if
+
+ align:start position:0%
+people kind of think about look if
+ 
+
+ align:start position:0%
+people kind of think about look if
+we if we if we Service as a clinic for
+
+ align:start position:0%
+we if we if we Service as a clinic for
+ 
+
+ align:start position:0%
+we if we if we Service as a clinic for
+example 100 people and 80% of them get
+
+ align:start position:0%
+example 100 people and 80% of them get
+ 
+
+ align:start position:0%
+example 100 people and 80% of them get
+well we're doing a good job but their
+
+ align:start position:0%
+well we're doing a good job but their
+ 
+
+ align:start position:0%
+well we're doing a good job but their
+notion is because they have this
+
+ align:start position:0%
+notion is because they have this
+ 
+
+ align:start position:0%
+notion is because they have this
+population B if we serve a 100 people
+
+ align:start position:0%
+population B if we serve a 100 people
+ 
+
+ align:start position:0%
+population B if we serve a 100 people
+and and 80% get well but there 300 we're
+
+ align:start position:0%
+and and 80% get well but there 300 we're
+ 
+
+ align:start position:0%
+and and 80% get well but there 300 we're
+not serving then we're not doing a good
+
+ align:start position:0%
+not serving then we're not doing a good
+ 
+
+ align:start position:0%
+not serving then we're not doing a good
+job so they have a it's a different you
+
+ align:start position:0%
+job so they have a it's a different you
+ 
+
+ align:start position:0%
+job so they have a it's a different you
+kind of cast a broader net of how you
+
+ align:start position:0%
+kind of cast a broader net of how you
+ 
+
+ align:start position:0%
+kind of cast a broader net of how you
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+measure uh what you're paying attention
+
+ align:start position:0%
+measure uh what you're paying attention
+ 
+
+ align:start position:0%
+measure uh what you're paying attention
+to as an indicator of success the other
+
+ align:start position:0%
+to as an indicator of success the other
+ 
+
+ align:start position:0%
+to as an indicator of success the other
+part that they talk about is where you
+
+ align:start position:0%
+part that they talk about is where you
+ 
+
+ align:start position:0%
+part that they talk about is where you
+put your emphasis on
+
+ align:start position:0%
+put your emphasis on
+ 
+
+ align:start position:0%
+put your emphasis on
+uh on your strategy for doing that
+
+ align:start position:0%
+uh on your strategy for doing that
+ 
+
+ align:start position:0%
+uh on your strategy for doing that
+and part of that is an assumption that
+
+ align:start position:0%
+and part of that is an assumption that
+ 
+
+ align:start position:0%
+and part of that is an assumption that
+you need to figure out why the people
+
+ align:start position:0%
+you need to figure out why the people
+ 
+
+ align:start position:0%
+you need to figure out why the people
+who are disconnected or disconnected and
+
+ align:start position:0%
+who are disconnected or disconnected and
+ 
+
+ align:start position:0%
+who are disconnected or disconnected and
+how do you kind of bring
+
+ align:start position:0%
+how do you kind of bring
+ 
+
+ align:start position:0%
+how do you kind of bring
+them you know if you have 300 people who
+
+ align:start position:0%
+them you know if you have 300 people who
+ 
+
+ align:start position:0%
+them you know if you have 300 people who
+are aren't serving and really trying to
+
+ align:start position:0%
+are aren't serving and really trying to
+ 
+
+ align:start position:0%
+are aren't serving and really trying to
+understand how you connect and really
+
+ align:start position:0%
+understand how you connect and really
+ 
+
+ align:start position:0%
+understand how you connect and really
+bring them into what you're doing with
+
+ align:start position:0%
+bring them into what you're doing with
+ 
+
+ align:start position:0%
+bring them into what you're doing with
+some assumption that you have a way of
+
+ align:start position:0%
+some assumption that you have a way of
+ 
+
+ align:start position:0%
+some assumption that you have a way of
+knowing how to do what you do in a good
+
+ align:start position:0%
+knowing how to do what you do in a good
+ 
+
+ align:start position:0%
+knowing how to do what you do in a good
+way so it works quite well in the
+
+ align:start position:0%
+way so it works quite well in the
+ 
+
+ align:start position:0%
+way so it works quite well in the
+medical work because they actually they
+
+ align:start position:0%
+medical work because they actually they
+ 
+
+ align:start position:0%
+medical work because they actually they
+know how to provide care and so if they
+
+ align:start position:0%
+know how to provide care and so if they
+ 
+
+ align:start position:0%
+know how to provide care and so if they
+can get people into the
+
+ align:start position:0%
+can get people into the
+ 
+
+ align:start position:0%
+can get people into the
+system then they can do a lot for
+
+ align:start position:0%
+system then they can do a lot for
+ 
+
+ align:start position:0%
+system then they can do a lot for
+them around the economic model is a
+
+ align:start position:0%
+them around the economic model is a
+ 
+
+ align:start position:0%
+them around the economic model is a
+different thing because they don't
+
+ align:start position:0%
+different thing because they don't
+ 
+
+ align:start position:0%
+different thing because they don't
+necessarily have something to get people
+
+ align:start position:0%
+necessarily have something to get people
+ 
+
+ align:start position:0%
+necessarily have something to get people
+into so it may you know present a
+
+ align:start position:0%
+into so it may you know present a
+ 
+
+ align:start position:0%
+into so it may you know present a
+different set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems so I think it's much more of a
+
+ align:start position:0%
+problems so I think it's much more of a
+ 
+
+ align:start position:0%
+problems so I think it's much more of a
+strategy of what who you're holding as
+
+ align:start position:0%
+strategy of what who you're holding as
+ 
+
+ align:start position:0%
+strategy of what who you're holding as
+important to pay attention to and how
+
+ align:start position:0%
+important to pay attention to and how
+ 
+
+ align:start position:0%
+important to pay attention to and how
+you kind of
+
+ align:start position:0%
+you kind of
+ 
+
+ align:start position:0%
+you kind of
+measure and what are the indicators you
+
+ align:start position:0%
+measure and what are the indicators you
+ 
+
+ align:start position:0%
+measure and what are the indicators you
+look for for success
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about some of
+
+ align:start position:0%
+about some of
+ 
+
+ align:start position:0%
+about some of
+this third world and stories about
+
+ align:start position:0%
+this third world and stories about
+ 
+
+ align:start position:0%
+this third world and stories about
+how they
+
+ align:start position:0%
+how they
+ 
+
+ align:start position:0%
+how they
+found Scholars
+
+ align:start position:0%
+found Scholars
+ 
+
+ align:start position:0%
+found Scholars
+found a really successful cases of
+
+ align:start position:0%
+found a really successful cases of
+ 
+
+ align:start position:0%
+found a really successful cases of
+poverty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deviation were made up of families where
+
+ align:start position:0%
+deviation were made up of families where
+ 
+
+ align:start position:0%
+deviation were made up of families where
+different members of the families did
+
+ align:start position:0%
+different members of the families did
+ 
+
+ align:start position:0%
+different members of the families did
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+differentes some of managment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unfur a men of things that different
+
+ align:start position:0%
+unfur a men of things that different
+ 
+
+ align:start position:0%
+unfur a men of things that different
+members of each household
+
+ align:start position:0%
+members of each household
+ 
+
+ align:start position:0%
+members of each household
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+way to yeah from the household
+
+ align:start position:0%
+way to yeah from the household
+ 
+
+ align:start position:0%
+way to yeah from the household
+perspective right what could be a
+
+ align:start position:0%
+perspective right what could be a
+ 
+
+ align:start position:0%
+perspective right what could be a
+strategy what could be the set of
+
+ align:start position:0%
+strategy what could be the set of
+ 
+
+ align:start position:0%
+strategy what could be the set of
+activities that that you're looking at
+
+ align:start position:0%
+activities that that you're looking at
+ 
+
+ align:start position:0%
+activities that that you're looking at
+as a household might help bring them out
+
+ align:start position:0%
+as a household might help bring them out
+ 
+
+ align:start position:0%
+as a household might help bring them out
+of poverty I'm guessing that it's
+
+ align:start position:0%
+of poverty I'm guessing that it's
+ 
+
+ align:start position:0%
+of poverty I'm guessing that it's
+precisely not just saying that we were
+
+ align:start position:0%
+precisely not just saying that we were
+ 
+
+ align:start position:0%
+precisely not just saying that we were
+able to
+
+ align:start position:0%
+able to
+ 
+
+ align:start position:0%
+able to
+create
+
+ align:start position:0%
+create
+ 
+
+ align:start position:0%
+create
+100 jobs for people for the community
+
+ align:start position:0%
+100 jobs for people for the community
+ 
+
+ align:start position:0%
+100 jobs for people for the community
+then the community the nature of that
+
+ align:start position:0%
+then the community the nature of that
+ 
+
+ align:start position:0%
+then the community the nature of that
+work for bringing home $5,000 a year
+
+ align:start position:0%
+work for bringing home $5,000 a year
+ 
+
+ align:start position:0%
+work for bringing home $5,000 a year
+that brought 100
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+households could be a it could be a
+
+ align:start position:0%
+households could be a it could be a
+ 
+
+ align:start position:0%
+households could be a it could be a
+difference yeah that is a very different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approach thoughts about any
+
+ align:start position:0%
+approach thoughts about any
+ 
+
+ align:start position:0%
+approach thoughts about any
+is this useful how might it be
+
+ align:start position:0%
+is this useful how might it be
+ 
+
+ align:start position:0%
+is this useful how might it be
+useful or is it really
+
+ align:start position:0%
+useful or is it really
+ 
+
+ align:start position:0%
+useful or is it really
+outside the way we should be thinking
+
+ align:start position:0%
+outside the way we should be thinking
+ 
+
+ align:start position:0%
+outside the way we should be thinking
+about Economic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Development the Alterna taking more
+
+ align:start position:0%
+Development the Alterna taking more
+ 
+
+ align:start position:0%
+Development the Alterna taking more
+macro approach
+
+ align:start position:0%
+macro approach
+ 
+
+ align:start position:0%
+macro approach
+looking is that kind like I guess I'm
+
+ align:start position:0%
+looking is that kind like I guess I'm
+ 
+
+ align:start position:0%
+looking is that kind like I guess I'm
+looking I mean this this feels very
+
+ align:start position:0%
+looking I mean this this feels very
+ 
+
+ align:start position:0%
+looking I mean this this feels very
+intuitive do
+
+ align:start position:0%
+intuitive do
+ 
+
+ align:start position:0%
+intuitive do
+this iess how do
+
+ align:start position:0%
+this iess how do
+ 
+
+ align:start position:0%
+this iess how do
+you that even that they couple with
+
+ align:start position:0%
+you that even that they couple with
+ 
+
+ align:start position:0%
+you that even that they couple with
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+approaches because it's it strikes me
+
+ align:start position:0%
+approaches because it's it strikes me
+ 
+
+ align:start position:0%
+approaches because it's it strikes me
+someone interesting because the list of
+
+ align:start position:0%
+someone interesting because the list of
+ 
+
+ align:start position:0%
+someone interesting because the list of
+projects that they give us doesn't
+
+ align:start position:0%
+projects that they give us doesn't
+ 
+
+ align:start position:0%
+projects that they give us doesn't
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+connect at least explicitly with the
+
+ align:start position:0%
+connect at least explicitly with the
+ 
+
+ align:start position:0%
+connect at least explicitly with the
+sort of population approach I mean they
+
+ align:start position:0%
+sort of population approach I mean they
+ 
+
+ align:start position:0%
+sort of population approach I mean they
+may have
+
+ align:start position:0%
+may have
+ 
+
+ align:start position:0%
+may have
+connections in their mind somewhere but
+
+ align:start position:0%
+connections in their mind somewhere but
+ 
+
+ align:start position:0%
+connections in their mind somewhere but
+I mean you know um creating a creating a
+
+ align:start position:0%
+I mean you know um creating a creating a
+ 
+
+ align:start position:0%
+I mean you know um creating a creating a
+d a destination for people outside the
+
+ align:start position:0%
+d a destination for people outside the
+ 
+
+ align:start position:0%
+d a destination for people outside the
+community well where is the connection
+
+ align:start position:0%
+community well where is the connection
+ 
+
+ align:start position:0%
+community well where is the connection
+of that to the improved outcomes to
+
+ align:start position:0%
+of that to the improved outcomes to
+ 
+
+ align:start position:0%
+of that to the improved outcomes to
+people in the community now there might
+
+ align:start position:0%
+people in the community now there might
+ 
+
+ align:start position:0%
+people in the community now there might
+be a set of assumptions playing out in
+
+ align:start position:0%
+be a set of assumptions playing out in
+ 
+
+ align:start position:0%
+be a set of assumptions playing out in
+people's mind about it um um or reusing
+
+ align:start position:0%
+people's mind about it um um or reusing
+ 
+
+ align:start position:0%
+people's mind about it um um or reusing
+vacant buildings or things like that
+
+ align:start position:0%
+vacant buildings or things like that
+ 
+
+ align:start position:0%
+vacant buildings or things like that
+they don't they haven't their thinking
+
+ align:start position:0%
+they don't they haven't their thinking
+ 
+
+ align:start position:0%
+they don't they haven't their thinking
+hasn't started from
+
+ align:start position:0%
+hasn't started from
+ 
+
+ align:start position:0%
+hasn't started from
+okay what are the what are the the
+
+ align:start position:0%
+okay what are the what are the the
+ 
+
+ align:start position:0%
+okay what are the what are the the
+challenges to improving incomes of of
+
+ align:start position:0%
+challenges to improving incomes of of
+ 
+
+ align:start position:0%
+challenges to improving incomes of of
+the people we're working with what what
+
+ align:start position:0%
+the people we're working with what what
+ 
+
+ align:start position:0%
+the people we're working with what what
+the set of of economic opportunities
+
+ align:start position:0%
+the set of of economic opportunities
+ 
+
+ align:start position:0%
+the set of of economic opportunities
+that might support that I guess maybe
+
+ align:start position:0%
+that might support that I guess maybe
+ 
+
+ align:start position:0%
+that might support that I guess maybe
+Peter conception might be closest to
+
+ align:start position:0%
+Peter conception might be closest to
+ 
+
+ align:start position:0%
+Peter conception might be closest to
+that and then he's looking at the at the
+
+ align:start position:0%
+that and then he's looking at the at the
+ 
+
+ align:start position:0%
+that and then he's looking at the at the
+entrepreneurial activity around that um
+
+ align:start position:0%
+entrepreneurial activity around that um
+ 
+
+ align:start position:0%
+entrepreneurial activity around that um
+so um the thing that really struck me
+
+ align:start position:0%
+so um the thing that really struck me
+ 
+
+ align:start position:0%
+so um the thing that really struck me
+about it is that in a lot of the
+
+ align:start position:0%
+about it is that in a lot of the
+ 
+
+ align:start position:0%
+about it is that in a lot of the
+literature about at least obstacles to
+
+ align:start position:0%
+literature about at least obstacles to
+ 
+
+ align:start position:0%
+literature about at least obstacles to
+employment um in in poor households and
+
+ align:start position:0%
+employment um in in poor households and
+ 
+
+ align:start position:0%
+employment um in in poor households and
+especially households where you have you
+
+ align:start position:0%
+especially households where you have you
+ 
+
+ align:start position:0%
+especially households where you have you
+know multigenerational poverty and and
+
+ align:start position:0%
+know multigenerational poverty and and
+ 
+
+ align:start position:0%
+know multigenerational poverty and and
+um low educational attainment is that
+
+ align:start position:0%
+um low educational attainment is that
+ 
+
+ align:start position:0%
+um low educational attainment is that
+there are there are very complicated
+
+ align:start position:0%
+there are there are very complicated
+ 
+
+ align:start position:0%
+there are there are very complicated
+obstacles and Myriad obstacles to
+
+ align:start position:0%
+obstacles and Myriad obstacles to
+ 
+
+ align:start position:0%
+obstacles and Myriad obstacles to
+employment that include you know
+
+ align:start position:0%
+employment that include you know
+ 
+
+ align:start position:0%
+employment that include you know
+language barriers Health barriers um
+
+ align:start position:0%
+language barriers Health barriers um
+ 
+
+ align:start position:0%
+language barriers Health barriers um
+education um child care you know some
+
+ align:start position:0%
+education um child care you know some
+ 
+
+ align:start position:0%
+education um child care you know some
+sometimes
+
+ align:start position:0%
+sometimes
+ 
+
+ align:start position:0%
+sometimes
+Transportation um and that um you know
+
+ align:start position:0%
+Transportation um and that um you know
+ 
+
+ align:start position:0%
+Transportation um and that um you know
+getting those people in in employment
+
+ align:start position:0%
+getting those people in in employment
+ 
+
+ align:start position:0%
+getting those people in in employment
+and staying in employment and then
+
+ align:start position:0%
+and staying in employment and then
+ 
+
+ align:start position:0%
+and staying in employment and then
+ultimately moving up to higher level
+
+ align:start position:0%
+ultimately moving up to higher level
+ 
+
+ align:start position:0%
+ultimately moving up to higher level
+incomes requires a pretty um um strong
+
+ align:start position:0%
+incomes requires a pretty um um strong
+ 
+
+ align:start position:0%
+incomes requires a pretty um um strong
+involvement with them and you often a
+
+ align:start position:0%
+involvement with them and you often a
+ 
+
+ align:start position:0%
+involvement with them and you often a
+complicated mix of services so it did
+
+ align:start position:0%
+complicated mix of services so it did
+ 
+
+ align:start position:0%
+complicated mix of services so it did
+strike me that least in that you know
+
+ align:start position:0%
+strike me that least in that you know
+ 
+
+ align:start position:0%
+strike me that least in that you know
+some of the same issues they're facing
+
+ align:start position:0%
+some of the same issues they're facing
+ 
+
+ align:start position:0%
+some of the same issues they're facing
+around Healthcare in terms of the
+
+ align:start position:0%
+around Healthcare in terms of the
+ 
+
+ align:start position:0%
+around Healthcare in terms of the
+obstacles of getting people connected to
+
+ align:start position:0%
+obstacles of getting people connected to
+ 
+
+ align:start position:0%
+obstacles of getting people connected to
+healthare um are probably there on on
+
+ align:start position:0%
+healthare um are probably there on on
+ 
+
+ align:start position:0%
+healthare um are probably there on on
+the employment side and and I would
+
+ align:start position:0%
+the employment side and and I would
+ 
+
+ align:start position:0%
+the employment side and and I would
+imagine even on the small business
+
+ align:start position:0%
+imagine even on the small business
+ 
+
+ align:start position:0%
+imagine even on the small business
+development side that some of those same
+
+ align:start position:0%
+development side that some of those same
+ 
+
+ align:start position:0%
+development side that some of those same
+issues and obstacles
+
+ align:start position:0%
+issues and obstacles
+ 
+
+ align:start position:0%
+issues and obstacles
+you know are going to get in the way so
+
+ align:start position:0%
+you know are going to get in the way so
+ 
+
+ align:start position:0%
+you know are going to get in the way so
+I do think there's some potential
+
+ align:start position:0%
+I do think there's some potential
+ 
+
+ align:start position:0%
+I do think there's some potential
+analogy even though the system's very
+
+ align:start position:0%
+analogy even though the system's very
+ 
+
+ align:start position:0%
+analogy even though the system's very
+different you know there there isn't
+
+ align:start position:0%
+different you know there there isn't
+ 
+
+ align:start position:0%
+different you know there there isn't
+there isn't a health care delivery
+
+ align:start position:0%
+there isn't a health care delivery
+ 
+
+ align:start position:0%
+there isn't a health care delivery
+system and an insurance system that at
+
+ align:start position:0%
+system and an insurance system that at
+ 
+
+ align:start position:0%
+system and an insurance system that at
+least makes it a little easier to know
+
+ align:start position:0%
+least makes it a little easier to know
+ 
+
+ align:start position:0%
+least makes it a little easier to know
+what you're trying to connect people to
+
+ align:start position:0%
+what you're trying to connect people to
+ 
+
+ align:start position:0%
+what you're trying to connect people to
+um there isn't a business development
+
+ align:start position:0%
+um there isn't a business development
+ 
+
+ align:start position:0%
+um there isn't a business development
+system that you could plug people into
+
+ align:start position:0%
+system that you could plug people into
+ 
+
+ align:start position:0%
+system that you could plug people into
+with the same type of employment and
+
+ align:start position:0%
+with the same type of employment and
+ 
+
+ align:start position:0%
+with the same type of employment and
+training system is but at least in terms
+
+ align:start position:0%
+training system is but at least in terms
+ 
+
+ align:start position:0%
+training system is but at least in terms
+of the barriers to accessing that
+
+ align:start position:0%
+of the barriers to accessing that
+ 
+
+ align:start position:0%
+of the barriers to accessing that
+opportunity I I think there's going to
+
+ align:start position:0%
+opportunity I I think there's going to
+ 
+
+ align:start position:0%
+opportunity I I think there's going to
+be some analogies to what they've
+
+ align:start position:0%
+be some analogies to what they've
+ 
+
+ align:start position:0%
+be some analogies to what they've
+learned um on on the healthc care side
+
+ align:start position:0%
+learned um on on the healthc care side
+ 
+
+ align:start position:0%
+learned um on on the healthc care side
+um that's translation translatable um I
+
+ align:start position:0%
+um that's translation translatable um I
+ 
+
+ align:start position:0%
+um that's translation translatable um I
+think the other thing too is it does it
+
+ align:start position:0%
+think the other thing too is it does it
+ 
+
+ align:start position:0%
+think the other thing too is it does it
+gives us at least one potential screen
+
+ align:start position:0%
+gives us at least one potential screen
+ 
+
+ align:start position:0%
+gives us at least one potential screen
+to think about as we look at these ideas
+
+ align:start position:0%
+to think about as we look at these ideas
+ 
+
+ align:start position:0%
+to think about as we look at these ideas
+and these proposals which is how do we
+
+ align:start position:0%
+and these proposals which is how do we
+ 
+
+ align:start position:0%
+and these proposals which is how do we
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+them actually improving economic
+
+ align:start position:0%
+them actually improving economic
+ 
+
+ align:start position:0%
+them actually improving economic
+outcomes for the residents of the
+
+ align:start position:0%
+outcomes for the residents of the
+ 
+
+ align:start position:0%
+outcomes for the residents of the
+neighborhood that that should be a
+
+ align:start position:0%
+neighborhood that that should be a
+ 
+
+ align:start position:0%
+neighborhood that that should be a
+screen where thinking about um in
+
+ align:start position:0%
+screen where thinking about um in
+ 
+
+ align:start position:0%
+screen where thinking about um in
+deciding which activities to focus on
+
+ align:start position:0%
+deciding which activities to focus on
+ 
+
+ align:start position:0%
+deciding which activities to focus on
+you know we should be able to make a
+
+ align:start position:0%
+you know we should be able to make a
+ 
+
+ align:start position:0%
+you know we should be able to make a
+case um about how these activities will
+
+ align:start position:0%
+case um about how these activities will
+ 
+
+ align:start position:0%
+case um about how these activities will
+generate improved outcomes for people in
+
+ align:start position:0%
+generate improved outcomes for people in
+ 
+
+ align:start position:0%
+generate improved outcomes for people in
+the community you know we we should be
+
+ align:start position:0%
+the community you know we we should be
+ 
+
+ align:start position:0%
+the community you know we we should be
+uh or thinking about how our plan will
+
+ align:start position:0%
+uh or thinking about how our plan will
+ 
+
+ align:start position:0%
+uh or thinking about how our plan will
+help connect those activities to ways
+
+ align:start position:0%
+help connect those activities to ways
+ 
+
+ align:start position:0%
+help connect those activities to ways
+that will will lead to improve outcomes
+
+ align:start position:0%
+that will will lead to improve outcomes
+ 
+
+ align:start position:0%
+that will will lead to improve outcomes
+of residence since that's that's their
+
+ align:start position:0%
+of residence since that's that's their
+ 
+
+ align:start position:0%
+of residence since that's that's their
+overriding objective you know I think we
+
+ align:start position:0%
+overriding objective you know I think we
+ 
+
+ align:start position:0%
+overriding objective you know I think we
+need to to be applying that lens to what
+
+ align:start position:0%
+need to to be applying that lens to what
+ 
+
+ align:start position:0%
+need to to be applying that lens to what
+we're thinking about doing
+
+ align:start position:0%
+we're thinking about doing
+ 
+
+ align:start position:0%
+we're thinking about doing
+yeah I think you know in my mind is you
+
+ align:start position:0%
+yeah I think you know in my mind is you
+ 
+
+ align:start position:0%
+yeah I think you know in my mind is you
+know if you take this population base
+
+ align:start position:0%
+know if you take this population base
+ 
+
+ align:start position:0%
+know if you take this population base
+that's very active you know you're not
+
+ align:start position:0%
+that's very active you know you're not
+ 
+
+ align:start position:0%
+that's very active you know you're not
+doing door knocking and in the way I'm
+
+ align:start position:0%
+doing door knocking and in the way I'm
+ 
+
+ align:start position:0%
+doing door knocking and in the way I'm
+thinking maybe it's just another added
+
+ align:start position:0%
+thinking maybe it's just another added
+ 
+
+ align:start position:0%
+thinking maybe it's just another added
+component so they have this health care
+
+ align:start position:0%
+component so they have this health care
+ 
+
+ align:start position:0%
+component so they have this health care
+or Social Service kind of component now
+
+ align:start position:0%
+or Social Service kind of component now
+ 
+
+ align:start position:0%
+or Social Service kind of component now
+it's kind of like maybe that's the first
+
+ align:start position:0%
+it's kind of like maybe that's the first
+ 
+
+ align:start position:0%
+it's kind of like maybe that's the first
+layer and then Economic Development
+
+ align:start position:0%
+layer and then Economic Development
+ 
+
+ align:start position:0%
+layer and then Economic Development
+comes on top of that and so it's
+
+ align:start position:0%
+comes on top of that and so it's
+ 
+
+ align:start position:0%
+comes on top of that and so it's
+connecting you know um you know talked
+
+ align:start position:0%
+connecting you know um you know talked
+ 
+
+ align:start position:0%
+connecting you know um you know talked
+with some folks that that work um in uh
+
+ align:start position:0%
+with some folks that that work um in uh
+ 
+
+ align:start position:0%
+with some folks that that work um in uh
+kind of career uh computer centers for
+
+ align:start position:0%
+kind of career uh computer centers for
+ 
+
+ align:start position:0%
+kind of career uh computer centers for
+cdcs and and they often say you know
+
+ align:start position:0%
+cdcs and and they often say you know
+ 
+
+ align:start position:0%
+cdcs and and they often say you know
+we're we're going to meet people where
+
+ align:start position:0%
+we're we're going to meet people where
+ 
+
+ align:start position:0%
+we're we're going to meet people where
+they're at and uh so it's really kind of
+
+ align:start position:0%
+they're at and uh so it's really kind of
+ 
+
+ align:start position:0%
+they're at and uh so it's really kind of
+taking stock of where someone's at um
+
+ align:start position:0%
+taking stock of where someone's at um
+ 
+
+ align:start position:0%
+taking stock of where someone's at um
+based on their skills based on their
+
+ align:start position:0%
+based on their skills based on their
+ 
+
+ align:start position:0%
+based on their skills based on their
+their just kind of their emotions and
+
+ align:start position:0%
+their just kind of their emotions and
+ 
+
+ align:start position:0%
+their just kind of their emotions and
+their thinking about themselves and
+
+ align:start position:0%
+their thinking about themselves and
+ 
+
+ align:start position:0%
+their thinking about themselves and
+where their opportunities are and so so
+
+ align:start position:0%
+where their opportunities are and so so
+ 
+
+ align:start position:0%
+where their opportunities are and so so
+you know if it's getting
+
+ align:start position:0%
+you know if it's getting
+ 
+
+ align:start position:0%
+you know if it's getting
+esol program that is getting an esol Pro
+
+ align:start position:0%
+esol program that is getting an esol Pro
+ 
+
+ align:start position:0%
+esol program that is getting an esol Pro
+program so I guess it's you know and
+
+ align:start position:0%
+program so I guess it's you know and
+ 
+
+ align:start position:0%
+program so I guess it's you know and
+there's a framework um uh like the
+
+ align:start position:0%
+there's a framework um uh like the
+ 
+
+ align:start position:0%
+there's a framework um uh like the
+self-sufficiency framework I don't know
+
+ align:start position:0%
+self-sufficiency framework I don't know
+ 
+
+ align:start position:0%
+self-sufficiency framework I don't know
+if if people have have looked at that
+
+ align:start position:0%
+if if people have have looked at that
+ 
+
+ align:start position:0%
+if if people have have looked at that
+but that's a that's something that's
+
+ align:start position:0%
+but that's a that's something that's
+ 
+
+ align:start position:0%
+but that's a that's something that's
+been developed in the in the state of
+
+ align:start position:0%
+been developed in the in the state of
+ 
+
+ align:start position:0%
+been developed in the in the state of
+the work in the Workforce Development
+
+ align:start position:0%
+the work in the Workforce Development
+ 
+
+ align:start position:0%
+the work in the Workforce Development
+world that it's really kind of career
+
+ align:start position:0%
+world that it's really kind of career
+ 
+
+ align:start position:0%
+world that it's really kind of career
+development is is a stepped process and
+
+ align:start position:0%
+development is is a stepped process and
+ 
+
+ align:start position:0%
+development is is a stepped process and
+people go through stages so um it might
+
+ align:start position:0%
+people go through stages so um it might
+ 
+
+ align:start position:0%
+people go through stages so um it might
+be useful to kind of apply that to to
+
+ align:start position:0%
+be useful to kind of apply that to to
+ 
+
+ align:start position:0%
+be useful to kind of apply that to to
+the kind of population population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+base com observation
\ No newline at end of file
diff --git a/NnDqJhtUqjw.txt b/NnDqJhtUqjw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ae442a6b73861501e119ee0e2d38f9ac7a21a94c
--- /dev/null
+++ b/NnDqJhtUqjw.txt
@@ -0,0 +1,15475 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu today what we're going to do
+
+ align:start position:0%
+ocw.mit.edu today what we're going to do
+ 
+
+ align:start position:0%
+ocw.mit.edu today what we're going to do
+is uh is we're going to finish off our
+
+ align:start position:0%
+is uh is we're going to finish off our
+ 
+
+ align:start position:0%
+is uh is we're going to finish off our
+discussion about oscillators in
+
+ align:start position:0%
+discussion about oscillators in
+ 
+
+ align:start position:0%
+discussion about oscillators in
+particular we're going to talk about
+
+ align:start position:0%
+particular we're going to talk about
+ 
+
+ align:start position:0%
+particular we're going to talk about
+alternative designs for oscillators so
+
+ align:start position:0%
+alternative designs for oscillators so
+ 
+
+ align:start position:0%
+alternative designs for oscillators so
+rather than having uh these Loops that
+
+ align:start position:0%
+rather than having uh these Loops that
+ 
+
+ align:start position:0%
+rather than having uh these Loops that
+are purely composed of negative U
+
+ align:start position:0%
+are purely composed of negative U
+ 
+
+ align:start position:0%
+are purely composed of negative U
+negative interactions negative feedback
+
+ align:start position:0%
+negative interactions negative feedback
+ 
+
+ align:start position:0%
+negative interactions negative feedback
+instead we're going to talk about cases
+
+ align:start position:0%
+instead we're going to talk about cases
+ 
+
+ align:start position:0%
+instead we're going to talk about cases
+where you have both positive and
+
+ align:start position:0%
+where you have both positive and
+ 
+
+ align:start position:0%
+where you have both positive and
+negative interactions all right so in
+
+ align:start position:0%
+negative interactions all right so in
+ 
+
+ align:start position:0%
+negative interactions all right so in
+using these uh this kind of combined
+
+ align:start position:0%
+using these uh this kind of combined
+ 
+
+ align:start position:0%
+using these uh this kind of combined
+Network structure you can generate what
+
+ align:start position:0%
+Network structure you can generate what
+ 
+
+ align:start position:0%
+Network structure you can generate what
+are known as relaxation oscillators
+
+ align:start position:0%
+are known as relaxation oscillators
+ 
+
+ align:start position:0%
+are known as relaxation oscillators
+which have uh some really um some
+
+ align:start position:0%
+which have uh some really um some
+ 
+
+ align:start position:0%
+which have uh some really um some
+wonderful properties in particular you
+
+ align:start position:0%
+wonderful properties in particular you
+ 
+
+ align:start position:0%
+wonderful properties in particular you
+can get more robust oscillations
+
+ align:start position:0%
+can get more robust oscillations
+ 
+
+ align:start position:0%
+can get more robust oscillations
+relative to the parameters but also you
+
+ align:start position:0%
+relative to the parameters but also you
+ 
+
+ align:start position:0%
+relative to the parameters but also you
+can uh the the oscillations become
+
+ align:start position:0%
+can uh the the oscillations become
+ 
+
+ align:start position:0%
+can uh the the oscillations become
+tunable I.E you can change the frequency
+
+ align:start position:0%
+tunable I.E you can change the frequency
+ 
+
+ align:start position:0%
+tunable I.E you can change the frequency
+without compromising for example the
+
+ align:start position:0%
+without compromising for example the
+ 
+
+ align:start position:0%
+without compromising for example the
+amplitude of the oscillations right so
+
+ align:start position:0%
+amplitude of the oscillations right so
+ 
+
+ align:start position:0%
+amplitude of the oscillations right so
+for many both uh natural and synthetic
+
+ align:start position:0%
+for many both uh natural and synthetic
+ 
+
+ align:start position:0%
+for many both uh natural and synthetic
+oscillators these these so-called
+
+ align:start position:0%
+oscillators these these so-called
+ 
+
+ align:start position:0%
+oscillators these these so-called
+synthetic oscillators are perhaps uh the
+
+ align:start position:0%
+synthetic oscillators are perhaps uh the
+ 
+
+ align:start position:0%
+synthetic oscillators are perhaps uh the
+way to
+
+ align:start position:0%
+way to
+ 
+
+ align:start position:0%
+way to
+go then we're going to transition to
+
+ align:start position:0%
+go then we're going to transition to
+ 
+
+ align:start position:0%
+go then we're going to transition to
+more of the global structure of U of
+
+ align:start position:0%
+more of the global structure of U of
+ 
+
+ align:start position:0%
+more of the global structure of U of
+some of these uh these networks in the
+
+ align:start position:0%
+some of these uh these networks in the
+ 
+
+ align:start position:0%
+some of these uh these networks in the
+context of transcription networks within
+
+ align:start position:0%
+context of transcription networks within
+ 
+
+ align:start position:0%
+context of transcription networks within
+within cells and and discuss this paper
+
+ align:start position:0%
+within cells and and discuss this paper
+ 
+
+ align:start position:0%
+within cells and and discuss this paper
+that you guys just read the barabasi
+
+ align:start position:0%
+that you guys just read the barabasi
+ 
+
+ align:start position:0%
+that you guys just read the barabasi
+paper which is uh one of the world's
+
+ align:start position:0%
+paper which is uh one of the world's
+ 
+
+ align:start position:0%
+paper which is uh one of the world's
+most cited papers I think right and
+
+ align:start position:0%
+most cited papers I think right and
+ 
+
+ align:start position:0%
+most cited papers I think right and
+um and then and then uh and then after
+
+ align:start position:0%
+um and then and then uh and then after
+ 
+
+ align:start position:0%
+um and then and then uh and then after
+thinking about this Global structure of
+
+ align:start position:0%
+thinking about this Global structure of
+ 
+
+ align:start position:0%
+thinking about this Global structure of
+how you might be able to generate these
+
+ align:start position:0%
+how you might be able to generate these
+ 
+
+ align:start position:0%
+how you might be able to generate these
+so-called power law structures uh we're
+
+ align:start position:0%
+so-called power law structures uh we're
+ 
+
+ align:start position:0%
+so-called power law structures uh we're
+going to look a little bit more detailed
+
+ align:start position:0%
+going to look a little bit more detailed
+ 
+
+ align:start position:0%
+going to look a little bit more detailed
+as that to try to understand something
+
+ align:start position:0%
+as that to try to understand something
+ 
+
+ align:start position:0%
+as that to try to understand something
+about these Network motifs we've already
+
+ align:start position:0%
+about these Network motifs we've already
+ 
+
+ align:start position:0%
+about these Network motifs we've already
+talked about them a little bit in the
+
+ align:start position:0%
+talked about them a little bit in the
+ 
+
+ align:start position:0%
+talked about them a little bit in the
+context of uh Auto regulatory Loops but
+
+ align:start position:0%
+context of uh Auto regulatory Loops but
+ 
+
+ align:start position:0%
+context of uh Auto regulatory Loops but
+now we'll talk about them in in in a
+
+ align:start position:0%
+now we'll talk about them in in in a
+ 
+
+ align:start position:0%
+now we'll talk about them in in in a
+little a little bit more generality in
+
+ align:start position:0%
+little a little bit more generality in
+ 
+
+ align:start position:0%
+little a little bit more generality in
+particular this cont in the context of
+
+ align:start position:0%
+particular this cont in the context of
+ 
+
+ align:start position:0%
+particular this cont in the context of
+feed forward
+
+ align:start position:0%
+feed forward
+ 
+
+ align:start position:0%
+feed forward
+loops and then and then on Thursday we
+
+ align:start position:0%
+loops and then and then on Thursday we
+ 
+
+ align:start position:0%
+loops and then and then on Thursday we
+will get into you know what some of the
+
+ align:start position:0%
+will get into you know what some of the
+ 
+
+ align:start position:0%
+will get into you know what some of the
+the possible beneficial features of feed
+
+ align:start position:0%
+the possible beneficial features of feed
+ 
+
+ align:start position:0%
+the possible beneficial features of feed
+forward loops on Thursday we talked
+
+ align:start position:0%
+forward loops on Thursday we talked
+ 
+
+ align:start position:0%
+forward loops on Thursday we talked
+about about the
+
+ align:start position:0%
+about about the
+ 
+
+ align:start position:0%
+about about the
+repressilator right so if you have x
+
+ align:start position:0%
+repressilator right so if you have x
+ 
+
+ align:start position:0%
+repressilator right so if you have x
+inhibiting y inhibiting z coming back
+
+ align:start position:0%
+inhibiting y inhibiting z coming back
+ 
+
+ align:start position:0%
+inhibiting y inhibiting z coming back
+and inhibiting X that this thing can is
+
+ align:start position:0%
+and inhibiting X that this thing can is
+ 
+
+ align:start position:0%
+and inhibiting X that this thing can is
+you know it's reasonable to expect that
+
+ align:start position:0%
+you know it's reasonable to expect that
+ 
+
+ align:start position:0%
+you know it's reasonable to expect that
+it might generate oscillations right and
+
+ align:start position:0%
+it might generate oscillations right and
+ 
+
+ align:start position:0%
+it might generate oscillations right and
+indeed in in the elowitz paper that we
+
+ align:start position:0%
+indeed in in the elowitz paper that we
+ 
+
+ align:start position:0%
+indeed in in the elowitz paper that we
+read uh such a such a synthetic circuit
+
+ align:start position:0%
+read uh such a such a synthetic circuit
+ 
+
+ align:start position:0%
+read uh such a such a synthetic circuit
+did indeed uh generate oscillations but
+
+ align:start position:0%
+did indeed uh generate oscillations but
+ 
+
+ align:start position:0%
+did indeed uh generate oscillations but
+uh there were perhaps a few problems
+
+ align:start position:0%
+uh there were perhaps a few problems
+ 
+
+ align:start position:0%
+uh there were perhaps a few problems
+there right so one is that only about
+
+ align:start position:0%
+there right so one is that only about
+ 
+
+ align:start position:0%
+there right so one is that only about
+40% % of the cells actually oscillated
+
+ align:start position:0%
+40% % of the cells actually oscillated
+ 
+
+ align:start position:0%
+40% % of the cells actually oscillated
+uh right uh who knows why not right but
+
+ align:start position:0%
+uh right uh who knows why not right but
+ 
+
+ align:start position:0%
+uh right uh who knows why not right but
+also there were there were other
+
+ align:start position:0%
+also there were there were other
+ 
+
+ align:start position:0%
+also there were there were other
+problems that the the oscillations
+
+ align:start position:0%
+problems that the the oscillations
+ 
+
+ align:start position:0%
+problems that the the oscillations
+seemed rather noisy there was relatively
+
+ align:start position:0%
+seemed rather noisy there was relatively
+ 
+
+ align:start position:0%
+seemed rather noisy there was relatively
+rapid uh U kind of
+
+ align:start position:0%
+rapid uh U kind of
+ 
+
+ align:start position:0%
+rapid uh U kind of
+desynchronization uh
+
+ align:start position:0%
+desynchronization uh
+ 
+
+ align:start position:0%
+desynchronization uh
+moreover if you if you go and you you
+
+ align:start position:0%
+moreover if you if you go and you you
+ 
+
+ align:start position:0%
+moreover if you if you go and you you
+ask well is it possible or how easy
+
+ align:start position:0%
+ask well is it possible or how easy
+ 
+
+ align:start position:0%
+ask well is it possible or how easy
+would it be to change the period of the
+
+ align:start position:0%
+would it be to change the period of the
+ 
+
+ align:start position:0%
+would it be to change the period of the
+oscillations just by changing something
+
+ align:start position:0%
+oscillations just by changing something
+ 
+
+ align:start position:0%
+oscillations just by changing something
+like the degradation rate what you'll
+
+ align:start position:0%
+like the degradation rate what you'll
+ 
+
+ align:start position:0%
+like the degradation rate what you'll
+find is that the oscillation
+
+ align:start position:0%
+find is that the oscillation
+ 
+
+ align:start position:0%
+find is that the oscillation
+are not very tunable okay so so I'll say
+
+ align:start position:0%
+are not very tunable okay so so I'll say
+ 
+
+ align:start position:0%
+are not very tunable okay so so I'll say
+the period or the frequency is not very
+
+ align:start position:0%
+the period or the frequency is not very
+ 
+
+ align:start position:0%
+the period or the frequency is not very
+tunable
+
+ align:start position:0%
+tunable
+ 
+
+ align:start position:0%
+tunable
+okay and indeed this is a general
+
+ align:start position:0%
+okay and indeed this is a general
+ 
+
+ align:start position:0%
+okay and indeed this is a general
+feature of os oscillatory networks that
+
+ align:start position:0%
+feature of os oscillatory networks that
+ 
+
+ align:start position:0%
+feature of os oscillatory networks that
+that have purely negative uh
+
+ align:start position:0%
+that have purely negative uh
+ 
+
+ align:start position:0%
+that have purely negative uh
+interactions right so we talked about a
+
+ align:start position:0%
+interactions right so we talked about a
+ 
+
+ align:start position:0%
+interactions right so we talked about a
+couple of these cases so for example you
+
+ align:start position:0%
+couple of these cases so for example you
+ 
+
+ align:start position:0%
+couple of these cases so for example you
+can get oscillations just with negative
+
+ align:start position:0%
+can get oscillations just with negative
+ 
+
+ align:start position:0%
+can get oscillations just with negative
+Auto regulation and what what is it
+
+ align:start position:0%
+Auto regulation and what what is it
+ 
+
+ align:start position:0%
+Auto regulation and what what is it
+that's necessary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's
+
+ align:start position:0%
+what's
+ 
+
+ align:start position:0%
+what's
+that high coordination you mean oh
+
+ align:start position:0%
+that high coordination you mean oh
+ 
+
+ align:start position:0%
+that high coordination you mean oh
+you're you're you're cooperativity in
+
+ align:start position:0%
+you're you're you're cooperativity in
+ 
+
+ align:start position:0%
+you're you're you're cooperativity in
+the repression all right so so that I
+
+ align:start position:0%
+the repression all right so so that I
+ 
+
+ align:start position:0%
+the repression all right so so that I
+think is necessary but is it is it going
+
+ align:start position:0%
+think is necessary but is it is it going
+ 
+
+ align:start position:0%
+think is necessary but is it is it going
+to be is it
+
+ align:start position:0%
+to be is it
+ 
+
+ align:start position:0%
+to be is it
+sufficient right I mean even in this
+
+ align:start position:0%
+sufficient right I mean even in this
+ 
+
+ align:start position:0%
+sufficient right I mean even in this
+case where I just have let's say that I
+
+ align:start position:0%
+case where I just have let's say that I
+ 
+
+ align:start position:0%
+case where I just have let's say that I
+I say okay x dot the rate of production
+
+ align:start position:0%
+I say okay x dot the rate of production
+ 
+
+ align:start position:0%
+I say okay x dot the rate of production
+if this thing is just as a function of X
+
+ align:start position:0%
+if this thing is just as a function of X
+ 
+
+ align:start position:0%
+if this thing is just as a function of X
+the sharpest it could be right this is
+
+ align:start position:0%
+the sharpest it could be right this is
+ 
+
+ align:start position:0%
+the sharpest it could be right this is
+kind of infinite cooperativity so it's
+
+ align:start position:0%
+kind of infinite cooperativity so it's
+ 
+
+ align:start position:0%
+kind of infinite cooperativity so it's
+maximal ression then when you get above
+
+ align:start position:0%
+maximal ression then when you get above
+ 
+
+ align:start position:0%
+maximal ression then when you get above
+some X critical all of a sudden you
+
+ align:start position:0%
+some X critical all of a sudden you
+ 
+
+ align:start position:0%
+some X critical all of a sudden you
+fully repress okay if I just have this
+
+ align:start position:0%
+fully repress okay if I just have this
+ 
+
+ align:start position:0%
+fully repress okay if I just have this
+be the formula do you guys understand
+
+ align:start position:0%
+be the formula do you guys understand
+ 
+
+ align:start position:0%
+be the formula do you guys understand
+what I'm referring to here right would
+
+ align:start position:0%
+what I'm referring to here right would
+ 
+
+ align:start position:0%
+what I'm referring to here right would
+would this generate would this generate
+
+ align:start position:0%
+would this generate would this generate
+ 
+
+ align:start position:0%
+would this generate would this generate
+oscillations so it actually doesn't
+
+ align:start position:0%
+oscillations so it actually doesn't
+ 
+
+ align:start position:0%
+oscillations so it actually doesn't
+right so if in the simple equation where
+
+ align:start position:0%
+right so if in the simple equation where
+ 
+
+ align:start position:0%
+right so if in the simple equation where
+we if we have x dot is equal to this
+
+ align:start position:0%
+we if we have x dot is equal to this
+ 
+
+ align:start position:0%
+we if we have x dot is equal to this
+function so I guess this is a
+
+ align:start position:0%
+function so I guess this is a
+ 
+
+ align:start position:0%
+function so I guess this is a
+Theta I want to make sure I get this x
+
+ align:start position:0%
+Theta I want to make sure I get this x
+ 
+
+ align:start position:0%
+Theta I want to make sure I get this x
+less than x critical that's what that's
+
+ align:start position:0%
+less than x critical that's what that's
+ 
+
+ align:start position:0%
+less than x critical that's what that's
+what this means right so with some B
+
+ align:start position:0%
+what this means right so with some B
+ 
+
+ align:start position:0%
+what this means right so with some B
+rate beta minus some alpha
+
+ align:start position:0%
+rate beta minus some alpha
+ 
+
+ align:start position:0%
+rate beta minus some alpha
+x did does this thing
+
+ align:start position:0%
+x did does this thing
+ 
+
+ align:start position:0%
+x did does this thing
+oscillate no and and we had a simple
+
+ align:start position:0%
+oscillate no and and we had a simple
+ 
+
+ align:start position:0%
+oscillate no and and we had a simple
+argument for why it did not oscillate as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well yes right can yell it out somebody
+
+ align:start position:0%
+well yes right can yell it out somebody
+ 
+
+ align:start position:0%
+well yes right can yell it out somebody
+somebody that was you know I'm sure
+
+ align:start position:0%
+somebody that was you know I'm sure
+ 
+
+ align:start position:0%
+somebody that was you know I'm sure
+somebody was here on Thursday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that's right the T yeah so this is
+
+ align:start position:0%
+um that's right the T yeah so this is
+ 
+
+ align:start position:0%
+um that's right the T yeah so this is
+just this is a single this is just an x
+
+ align:start position:0%
+just this is a single this is just an x
+ 
+
+ align:start position:0%
+just this is a single this is just an x
+dot there's no X double dot right so
+
+ align:start position:0%
+dot there's no X double dot right so
+ 
+
+ align:start position:0%
+dot there's no X double dot right so
+that means the derivative of x is single
+
+ align:start position:0%
+that means the derivative of x is single
+ 
+
+ align:start position:0%
+that means the derivative of x is single
+value is a function of X that means that
+
+ align:start position:0%
+value is a function of X that means that
+ 
+
+ align:start position:0%
+value is a function of X that means that
+we can't get any that looks any any
+
+ align:start position:0%
+we can't get any that looks any any
+ 
+
+ align:start position:0%
+we can't get any that looks any any
+oscillation
+
+ align:start position:0%
+oscillation
+ 
+
+ align:start position:0%
+oscillation
+here right then we remember we analyze
+
+ align:start position:0%
+here right then we remember we analyze
+ 
+
+ align:start position:0%
+here right then we remember we analyze
+this model where we explicitly included
+
+ align:start position:0%
+this model where we explicitly included
+ 
+
+ align:start position:0%
+this model where we explicitly included
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+MRNA right so then we just had that X
+
+ align:start position:0%
+MRNA right so then we just had that X
+ 
+
+ align:start position:0%
+MRNA right so then we just had that X
+comes and what it does is it represses
+
+ align:start position:0%
+comes and what it does is it represses
+ 
+
+ align:start position:0%
+comes and what it does is it represses
+produ expression of this mRNA for x and
+
+ align:start position:0%
+produ expression of this mRNA for x and
+ 
+
+ align:start position:0%
+produ expression of this mRNA for x and
+then this mRNA comes back and makes
+
+ align:start position:0%
+then this mRNA comes back and makes
+ 
+
+ align:start position:0%
+then this mRNA comes back and makes
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+right and uh in this model was this
+
+ align:start position:0%
+right and uh in this model was this
+ 
+
+ align:start position:0%
+right and uh in this model was this
+sufficient did this give
+
+ align:start position:0%
+sufficient did this give
+ 
+
+ align:start position:0%
+sufficient did this give
+oscillations no all right so this Al so
+
+ align:start position:0%
+oscillations no all right so this Al so
+ 
+
+ align:start position:0%
+oscillations no all right so this Al so
+here there was no
+
+ align:start position:0%
+here there was no
+ 
+
+ align:start position:0%
+here there was no
+oscillations again here there were no
+
+ align:start position:0%
+oscillations again here there were no
+ 
+
+ align:start position:0%
+oscillations again here there were no
+oscillations but I did tell you that
+
+ align:start position:0%
+oscillations but I did tell you that
+ 
+
+ align:start position:0%
+oscillations but I did tell you that
+there was something that that you could
+
+ align:start position:0%
+there was something that that you could
+ 
+
+ align:start position:0%
+there was something that that you could
+do something more to get oscillations
+
+ align:start position:0%
+do something more to get oscillations
+ 
+
+ align:start position:0%
+do something more to get oscillations
+just with a single protein repressing
+
+ align:start position:0%
+just with a single protein repressing
+ 
+
+ align:start position:0%
+just with a single protein repressing
+itself right so yeah so you need more
+
+ align:start position:0%
+itself right so yeah so you need more
+ 
+
+ align:start position:0%
+itself right so yeah so you need more
+delays all right so if you add
+
+ align:start position:0%
+delays all right so if you add
+ 
+
+ align:start position:0%
+delays all right so if you add
+delays then it's possible
+
+ align:start position:0%
+delays then it's possible
+ 
+
+ align:start position:0%
+delays then it's possible
+to get um to get oscillations
+
+ align:start position:0%
+to get um to get oscillations
+ 
+
+ align:start position:0%
+to get um to get oscillations
+okay all right so those delays uh could
+
+ align:start position:0%
+okay all right so those delays uh could
+ 
+
+ align:start position:0%
+okay all right so those delays uh could
+be in the form of having a model where
+
+ align:start position:0%
+be in the form of having a model where
+ 
+
+ align:start position:0%
+be in the form of having a model where
+you explicitly take into account that
+
+ align:start position:0%
+you explicitly take into account that
+ 
+
+ align:start position:0%
+you explicitly take into account that
+that first the MRNA is made and then
+
+ align:start position:0%
+that first the MRNA is made and then
+ 
+
+ align:start position:0%
+that first the MRNA is made and then
+that goes and then you translate that to
+
+ align:start position:0%
+that goes and then you translate that to
+ 
+
+ align:start position:0%
+that goes and then you translate that to
+make some monomer and then the monomer
+
+ align:start position:0%
+make some monomer and then the monomer
+ 
+
+ align:start position:0%
+make some monomer and then the monomer
+has to maybe fold and then the folded
+
+ align:start position:0%
+has to maybe fold and then the folded
+ 
+
+ align:start position:0%
+has to maybe fold and then the folded
+protein maybe has to dimerize in order
+
+ align:start position:0%
+protein maybe has to dimerize in order
+ 
+
+ align:start position:0%
+protein maybe has to dimerize in order
+to do repression right so if you have a
+
+ align:start position:0%
+to do repression right so if you have a
+ 
+
+ align:start position:0%
+to do repression right so if you have a
+more detailed mechanistic model that
+
+ align:start position:0%
+more detailed mechanistic model that
+ 
+
+ align:start position:0%
+more detailed mechanistic model that
+includes all these steps that kind of
+
+ align:start position:0%
+includes all these steps that kind of
+ 
+
+ align:start position:0%
+includes all these steps that kind of
+introduces some sort of delay that can
+
+ align:start position:0%
+introduces some sort of delay that can
+ 
+
+ align:start position:0%
+introduces some sort of delay that can
+that in principle can lead to
+
+ align:start position:0%
+that in principle can lead to
+ 
+
+ align:start position:0%
+that in principle can lead to
+oscillations in such a circuit or if you
+
+ align:start position:0%
+oscillations in such a circuit or if you
+ 
+
+ align:start position:0%
+oscillations in such a circuit or if you
+want to you could just explicitly put in
+
+ align:start position:0%
+want to you could just explicitly put in
+ 
+
+ align:start position:0%
+want to you could just explicitly put in
+a delay right so you could say that x
+
+ align:start position:0%
+a delay right so you could say that x
+ 
+
+ align:start position:0%
+a delay right so you could say that x
+dot instead of being a function of
+
+ align:start position:0%
+dot instead of being a function of
+ 
+
+ align:start position:0%
+dot instead of being a function of
+X right instead what you can do is you
+
+ align:start position:0%
+X right instead what you can do is you
+ 
+
+ align:start position:0%
+X right instead what you can do is you
+can say all right well it's actually a
+
+ align:start position:0%
+can say all right well it's actually a
+ 
+
+ align:start position:0%
+can say all right well it's actually a
+function of X at some time uh T minus
+
+ align:start position:0%
+function of X at some time uh T minus
+ 
+
+ align:start position:0%
+function of X at some time uh T minus
+to all right so instead of having the
+
+ align:start position:0%
+to all right so instead of having the
+ 
+
+ align:start position:0%
+to all right so instead of having the
+rate of production of X be a function of
+
+ align:start position:0%
+rate of production of X be a function of
+ 
+
+ align:start position:0%
+rate of production of X be a function of
+X at that moment of time instead it
+
+ align:start position:0%
+X at that moment of time instead it
+ 
+
+ align:start position:0%
+X at that moment of time instead it
+could be a function of X at some
+
+ align:start position:0%
+could be a function of X at some
+ 
+
+ align:start position:0%
+could be a function of X at some
+previous time doing that that's a very
+
+ align:start position:0%
+previous time doing that that's a very
+ 
+
+ align:start position:0%
+previous time doing that that's a very
+explicit form of delay and that can Al
+
+ align:start position:0%
+explicit form of delay and that can Al
+ 
+
+ align:start position:0%
+explicit form of delay and that can Al
+be used to generate oscillations in a
+
+ align:start position:0%
+be used to generate oscillations in a
+ 
+
+ align:start position:0%
+be used to generate oscillations in a
+simple negative a auto regulatory
+
+ align:start position:0%
+simple negative a auto regulatory
+ 
+
+ align:start position:0%
+simple negative a auto regulatory
+Loop
+
+ align:start position:0%
+Loop
+ 
+
+ align:start position:0%
+Loop
+okay all right so these are all
+
+ align:start position:0%
+okay all right so these are all
+ 
+
+ align:start position:0%
+okay all right so these are all
+different kind of approaches for uh for
+
+ align:start position:0%
+different kind of approaches for uh for
+ 
+
+ align:start position:0%
+different kind of approaches for uh for
+encoding oscill or encoding delays into
+
+ align:start position:0%
+encoding oscill or encoding delays into
+ 
+
+ align:start position:0%
+encoding oscill or encoding delays into
+uh into uh the into a model and and and
+
+ align:start position:0%
+uh into uh the into a model and and and
+ 
+
+ align:start position:0%
+uh into uh the into a model and and and
+various approaches will give you
+
+ align:start position:0%
+various approaches will give you
+ 
+
+ align:start position:0%
+various approaches will give you
+oscillations okay
+
+ align:start position:0%
+oscillations okay
+ 
+
+ align:start position:0%
+oscillations okay
+yesod is
+
+ align:start position:0%
+yesod is
+ 
+
+ align:start position:0%
+yesod is
+notable because the LIF is very all
+
+ align:start position:0%
+notable because the LIF is very all
+ 
+
+ align:start position:0%
+notable because the LIF is very all
+right so when when we say yeah model in
+
+ align:start position:0%
+right so when when we say yeah model in
+ 
+
+ align:start position:0%
+right so when when we say yeah model in
+the model can yes that's right so in the
+
+ align:start position:0%
+the model can yes that's right so in the
+ 
+
+ align:start position:0%
+the model can yes that's right so in the
+model you can in principle T it so what
+
+ align:start position:0%
+model you can in principle T it so what
+ 
+
+ align:start position:0%
+model you can in principle T it so what
+what I mean when I say this is that um
+
+ align:start position:0%
+what I mean when I say this is that um
+ 
+
+ align:start position:0%
+what I mean when I say this is that um
+in this class of models so you can also
+
+ align:start position:0%
+in this class of models so you can also
+ 
+
+ align:start position:0%
+in this class of models so you can also
+have instead of this repated with three
+
+ align:start position:0%
+have instead of this repated with three
+ 
+
+ align:start position:0%
+have instead of this repated with three
+you can have the so-called pentil where
+
+ align:start position:0%
+you can have the so-called pentil where
+ 
+
+ align:start position:0%
+you can have the so-called pentil where
+you have five proteins and each is
+
+ align:start position:0%
+you have five proteins and each is
+ 
+
+ align:start position:0%
+you have five proteins and each is
+repressing itself right so there these
+
+ align:start position:0%
+repressing itself right so there these
+ 
+
+ align:start position:0%
+repressing itself right so there these
+are all have you know have similar
+
+ align:start position:0%
+are all have you know have similar
+ 
+
+ align:start position:0%
+are all have you know have similar
+features they all have like these odd
+
+ align:start position:0%
+features they all have like these odd
+ 
+
+ align:start position:0%
+features they all have like these odd
+numbers of proteins going around and
+
+ align:start position:0%
+numbers of proteins going around and
+ 
+
+ align:start position:0%
+numbers of proteins going around and
+repressing one another right so you can
+
+ align:start position:0%
+repressing one another right so you can
+ 
+
+ align:start position:0%
+repressing one another right so you can
+write down the model of seven if you
+
+ align:start position:0%
+write down the model of seven if you
+ 
+
+ align:start position:0%
+write down the model of seven if you
+want right
+
+ align:start position:0%
+want right
+ 
+
+ align:start position:0%
+want right
+but in all these in all these cases um
+
+ align:start position:0%
+but in all these in all these cases um
+ 
+
+ align:start position:0%
+but in all these in all these cases um
+there it's it's not tunable what we mean
+
+ align:start position:0%
+there it's it's not tunable what we mean
+ 
+
+ align:start position:0%
+there it's it's not tunable what we mean
+and what we mean by that is that if you
+
+ align:start position:0%
+and what we mean by that is that if you
+ 
+
+ align:start position:0%
+and what we mean by that is that if you
+when you tune the when you when you tune
+
+ align:start position:0%
+when you tune the when you when you tune
+ 
+
+ align:start position:0%
+when you tune the when you when you tune
+the frequency you in general uh lose uh
+
+ align:start position:0%
+the frequency you in general uh lose uh
+ 
+
+ align:start position:0%
+the frequency you in general uh lose uh
+the amplitude of the oscillation so the
+
+ align:start position:0%
+the amplitude of the oscillation so the
+ 
+
+ align:start position:0%
+the amplitude of the oscillation so the
+amplitude will go down right there's I
+
+ align:start position:0%
+amplitude will go down right there's I
+ 
+
+ align:start position:0%
+amplitude will go down right there's I
+think a very nice uh paper that was
+
+ align:start position:0%
+think a very nice uh paper that was
+ 
+
+ align:start position:0%
+think a very nice uh paper that was
+written in 2008 on this topic uh written
+
+ align:start position:0%
+written in 2008 on this topic uh written
+ 
+
+ align:start position:0%
+written in 2008 on this topic uh written
+by Jim Ferell at Stanford all right so I
+
+ align:start position:0%
+by Jim Ferell at Stanford all right so I
+ 
+
+ align:start position:0%
+by Jim Ferell at Stanford all right so I
+just want to mention this okay so it's
+
+ align:start position:0%
+just want to mention this okay so it's
+ 
+
+ align:start position:0%
+just want to mention this okay so it's
+um feral uh at Stanford
+
+ align:start position:0%
+um feral uh at Stanford
+ 
+
+ align:start position:0%
+um feral uh at Stanford
+uh this is an a paper in science
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2008 and um you know and it's called Uh
+
+ align:start position:0%
+2008 and um you know and it's called Uh
+ 
+
+ align:start position:0%
+2008 and um you know and it's called Uh
+robust tunable biological oscillations
+
+ align:start position:0%
+robust tunable biological oscillations
+ 
+
+ align:start position:0%
+robust tunable biological oscillations
+from inter interl positive and negative
+
+ align:start position:0%
+from inter interl positive and negative
+ 
+
+ align:start position:0%
+from inter interl positive and negative
+feedback loops right it's a nice title
+
+ align:start position:0%
+feedback loops right it's a nice title
+ 
+
+ align:start position:0%
+feedback loops right it's a nice title
+right I like titles that say something
+
+ align:start position:0%
+right I like titles that say something
+ 
+
+ align:start position:0%
+right I like titles that say something
+right so it's it's sort of a ultimate
+
+ align:start position:0%
+right so it's it's sort of a ultimate
+ 
+
+ align:start position:0%
+right so it's it's sort of a ultimate
+short version of an abstract right if
+
+ align:start position:0%
+short version of an abstract right if
+ 
+
+ align:start position:0%
+short version of an abstract right if
+you can if you can do it I recommend it
+
+ align:start position:0%
+you can if you can do it I recommend it
+ 
+
+ align:start position:0%
+you can if you can do it I recommend it
+incidentally in graduate school I once
+
+ align:start position:0%
+incidentally in graduate school I once
+ 
+
+ align:start position:0%
+incidentally in graduate school I once
+wrote a paper with four words short
+
+ align:start position:0%
+wrote a paper with four words short
+ 
+
+ align:start position:0%
+wrote a paper with four words short
+words DNA overwinds when stretched right
+
+ align:start position:0%
+words DNA overwinds when stretched right
+ 
+
+ align:start position:0%
+words DNA overwinds when stretched right
+nice statement okay you may or may not
+
+ align:start position:0%
+nice statement okay you may or may not
+ 
+
+ align:start position:0%
+nice statement okay you may or may not
+actually know what I mean by that but
+
+ align:start position:0%
+actually know what I mean by that but
+ 
+
+ align:start position:0%
+actually know what I mean by that but
+you know it's a nice short title it's a
+
+ align:start position:0%
+you know it's a nice short title it's a
+ 
+
+ align:start position:0%
+you know it's a nice short title it's a
+statement right so um I encourage you to
+
+ align:start position:0%
+statement right so um I encourage you to
+ 
+
+ align:start position:0%
+statement right so um I encourage you to
+to think about that when you're writing
+
+ align:start position:0%
+to think about that when you're writing
+ 
+
+ align:start position:0%
+to think about that when you're writing
+your papers
+
+ align:start position:0%
+your papers
+ 
+
+ align:start position:0%
+your papers
+okay all right so so Jim farell he he
+
+ align:start position:0%
+okay all right so so Jim farell he he
+ 
+
+ align:start position:0%
+okay all right so so Jim farell he he
+wrote he wrote this paper where he said
+
+ align:start position:0%
+wrote he wrote this paper where he said
+ 
+
+ align:start position:0%
+wrote he wrote this paper where he said
+all right well you know oscillations are
+
+ align:start position:0%
+all right well you know oscillations are
+ 
+
+ align:start position:0%
+all right well you know oscillations are
+really important right thinking about
+
+ align:start position:0%
+really important right thinking about
+ 
+
+ align:start position:0%
+really important right thinking about
+context of heart rhythms or cell cycle
+
+ align:start position:0%
+context of heart rhythms or cell cycle
+ 
+
+ align:start position:0%
+context of heart rhythms or cell cycle
+or this or that right so oscillations
+
+ align:start position:0%
+or this or that right so oscillations
+ 
+
+ align:start position:0%
+or this or that right so oscillations
+are important but if you go and you look
+
+ align:start position:0%
+are important but if you go and you look
+ 
+
+ align:start position:0%
+are important but if you go and you look
+at uh the the circuits that are
+
+ align:start position:0%
+at uh the the circuits that are
+ 
+
+ align:start position:0%
+at uh the the circuits that are
+generating oscillations in biology they
+
+ align:start position:0%
+generating oscillations in biology they
+ 
+
+ align:start position:0%
+generating oscillations in biology they
+often have so-called interl positive and
+
+ align:start position:0%
+often have so-called interl positive and
+ 
+
+ align:start position:0%
+often have so-called interl positive and
+negative feedback loops right so there
+
+ align:start position:0%
+negative feedback loops right so there
+ 
+
+ align:start position:0%
+negative feedback loops right so there
+are many cases where um you have some X
+
+ align:start position:0%
+are many cases where um you have some X
+ 
+
+ align:start position:0%
+are many cases where um you have some X
+that actually has is is positively it's
+
+ align:start position:0%
+that actually has is is positively it's
+ 
+
+ align:start position:0%
+that actually has is is positively it's
+kind of activating itself right and this
+
+ align:start position:0%
+kind of activating itself right and this
+ 
+
+ align:start position:0%
+kind of activating itself right and this
+is very much something that will not
+
+ align:start position:0%
+is very much something that will not
+ 
+
+ align:start position:0%
+is very much something that will not
+lead to oscillations on its own right it
+
+ align:start position:0%
+lead to oscillations on its own right it
+ 
+
+ align:start position:0%
+lead to oscillations on its own right it
+might be bable which is interesting but
+
+ align:start position:0%
+might be bable which is interesting but
+ 
+
+ align:start position:0%
+might be bable which is interesting but
+it not oscillations on its own but then
+
+ align:start position:0%
+it not oscillations on its own but then
+ 
+
+ align:start position:0%
+it not oscillations on its own but then
+there's there's also maybe a negative
+
+ align:start position:0%
+there's there's also maybe a negative
+ 
+
+ align:start position:0%
+there's there's also maybe a negative
+feedback loop through another another
+
+ align:start position:0%
+feedback loop through another another
+ 
+
+ align:start position:0%
+feedback loop through another another
+protein and the idea is that this one
+
+ align:start position:0%
+protein and the idea is that this one
+ 
+
+ align:start position:0%
+protein and the idea is that this one
+somehow operates uh this one's fast and
+
+ align:start position:0%
+somehow operates uh this one's fast and
+ 
+
+ align:start position:0%
+somehow operates uh this one's fast and
+this one's
+
+ align:start position:0%
+this one's
+ 
+
+ align:start position:0%
+this one's
+slow right the key feature of these
+
+ align:start position:0%
+slow right the key feature of these
+ 
+
+ align:start position:0%
+slow right the key feature of these
+relaxation oscillators is there are two
+
+ align:start position:0%
+relaxation oscillators is there are two
+ 
+
+ align:start position:0%
+relaxation oscillators is there are two
+time scales
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and it's the it's the slow time
+
+ align:start position:0%
+okay and it's the it's the slow time
+ 
+
+ align:start position:0%
+okay and it's the it's the slow time
+scale that specifies the the period of
+
+ align:start position:0%
+scale that specifies the the period of
+ 
+
+ align:start position:0%
+scale that specifies the the period of
+the oscillation and this fast one kind
+
+ align:start position:0%
+the oscillation and this fast one kind
+ 
+
+ align:start position:0%
+the oscillation and this fast one kind
+of locks the system into these
+
+ align:start position:0%
+of locks the system into these
+ 
+
+ align:start position:0%
+of locks the system into these
+alternative States right so you kind of
+
+ align:start position:0%
+alternative States right so you kind of
+ 
+
+ align:start position:0%
+alternative States right so you kind of
+you and this helps maintain the
+
+ align:start position:0%
+you and this helps maintain the
+ 
+
+ align:start position:0%
+you and this helps maintain the
+amplitude because it's it has this
+
+ align:start position:0%
+amplitude because it's it has this
+ 
+
+ align:start position:0%
+amplitude because it's it has this
+nature of being bable right so it's on
+
+ align:start position:0%
+nature of being bable right so it's on
+ 
+
+ align:start position:0%
+nature of being bable right so it's on
+or off okay so this helps you maintain
+
+ align:start position:0%
+or off okay so this helps you maintain
+ 
+
+ align:start position:0%
+or off okay so this helps you maintain
+amplitude all right so this is kind of
+
+ align:start position:0%
+amplitude all right so this is kind of
+ 
+
+ align:start position:0%
+amplitude all right so this is kind of
+in charge of
+
+ align:start position:0%
+in charge of
+ 
+
+ align:start position:0%
+in charge of
+amplitude and this one over here is in
+
+ align:start position:0%
+amplitude and this one over here is in
+ 
+
+ align:start position:0%
+amplitude and this one over here is in
+charge of the
+
+ align:start position:0%
+charge of the
+ 
+
+ align:start position:0%
+charge of the
+period okay so what you can imagine that
+
+ align:start position:0%
+period okay so what you can imagine that
+ 
+
+ align:start position:0%
+period okay so what you can imagine that
+by changing this time scale you can
+
+ align:start position:0%
+by changing this time scale you can
+ 
+
+ align:start position:0%
+by changing this time scale you can
+change the period of the oscillation
+
+ align:start position:0%
+change the period of the oscillation
+ 
+
+ align:start position:0%
+change the period of the oscillation
+whereas this Loop allows you to maintain
+
+ align:start position:0%
+whereas this Loop allows you to maintain
+ 
+
+ align:start position:0%
+whereas this Loop allows you to maintain
+uh maintain the
+
+ align:start position:0%
+uh maintain the
+ 
+
+ align:start position:0%
+uh maintain the
+amplitude Okay and what uh what Jim's
+
+ align:start position:0%
+amplitude Okay and what uh what Jim's
+ 
+
+ align:start position:0%
+amplitude Okay and what uh what Jim's
+group did computationally in this paper
+
+ align:start position:0%
+group did computationally in this paper
+ 
+
+ align:start position:0%
+group did computationally in this paper
+is uh they analyzed uh many different
+
+ align:start position:0%
+is uh they analyzed uh many different
+ 
+
+ align:start position:0%
+is uh they analyzed uh many different
+circuit designs that can lead to
+
+ align:start position:0%
+circuit designs that can lead to
+ 
+
+ align:start position:0%
+circuit designs that can lead to
+oscillations and they showed that for
+
+ align:start position:0%
+oscillations and they showed that for
+ 
+
+ align:start position:0%
+oscillations and they showed that for
+the the loop the loops that are made of
+
+ align:start position:0%
+the the loop the loops that are made of
+ 
+
+ align:start position:0%
+the the loop the loops that are made of
+purely negative interactions like this
+
+ align:start position:0%
+purely negative interactions like this
+ 
+
+ align:start position:0%
+purely negative interactions like this
+if you change if you change a parameter
+
+ align:start position:0%
+if you change if you change a parameter
+ 
+
+ align:start position:0%
+if you change if you change a parameter
+in order to change the period you'll
+
+ align:start position:0%
+in order to change the period you'll
+ 
+
+ align:start position:0%
+in order to change the period you'll
+also in general make the amplitude of
+
+ align:start position:0%
+also in general make the amplitude of
+ 
+
+ align:start position:0%
+also in general make the amplitude of
+the oscillations will drop dramatically
+
+ align:start position:0%
+the oscillations will drop dramatically
+ 
+
+ align:start position:0%
+the oscillations will drop dramatically
+right so that that's so that's the sense
+
+ align:start position:0%
+right so that that's so that's the sense
+ 
+
+ align:start position:0%
+right so that that's so that's the sense
+in which they're not tunable whereas if
+
+ align:start position:0%
+in which they're not tunable whereas if
+ 
+
+ align:start position:0%
+in which they're not tunable whereas if
+you have this kind of design you can
+
+ align:start position:0%
+you have this kind of design you can
+ 
+
+ align:start position:0%
+you have this kind of design you can
+actually uh tune over in some cases a
+
+ align:start position:0%
+actually uh tune over in some cases a
+ 
+
+ align:start position:0%
+actually uh tune over in some cases a
+very wide range but maintain the
+
+ align:start position:0%
+very wide range but maintain the
+ 
+
+ align:start position:0%
+very wide range but maintain the
+amplitude of the oscillation okay and in
+
+ align:start position:0%
+amplitude of the oscillation okay and in
+ 
+
+ align:start position:0%
+amplitude of the oscillation okay and in
+addition to being tunable these things
+
+ align:start position:0%
+addition to being tunable these things
+ 
+
+ align:start position:0%
+addition to being tunable these things
+also end up being robust in various ways
+
+ align:start position:0%
+also end up being robust in various ways
+ 
+
+ align:start position:0%
+also end up being robust in various ways
+right that the oscillation uh is
+
+ align:start position:0%
+right that the oscillation uh is
+ 
+
+ align:start position:0%
+right that the oscillation uh is
+maintained subject to various kinds of
+
+ align:start position:0%
+maintained subject to various kinds of
+ 
+
+ align:start position:0%
+maintained subject to various kinds of
+if you if you twiddle with the
+
+ align:start position:0%
+if you if you twiddle with the
+ 
+
+ align:start position:0%
+if you if you twiddle with the
+parameters you know you double this you
+
+ align:start position:0%
+parameters you know you double this you
+ 
+
+ align:start position:0%
+parameters you know you double this you
+have that you can still get nice
+
+ align:start position:0%
+have that you can still get nice
+ 
+
+ align:start position:0%
+have that you can still get nice
+oscillations here whereas um in in those
+
+ align:start position:0%
+oscillations here whereas um in in those
+ 
+
+ align:start position:0%
+oscillations here whereas um in in those
+designs you tend to you tend to lose the
+
+ align:start position:0%
+designs you tend to you tend to lose the
+ 
+
+ align:start position:0%
+designs you tend to you tend to lose the
+oscillations more easily right so they
+
+ align:start position:0%
+oscillations more easily right so they
+ 
+
+ align:start position:0%
+oscillations more easily right so they
+claim that based on that that these
+
+ align:start position:0%
+claim that based on that that these
+ 
+
+ align:start position:0%
+claim that based on that that these
+might be more evolvable okay so even in
+
+ align:start position:0%
+might be more evolvable okay so even in
+ 
+
+ align:start position:0%
+might be more evolvable okay so even in
+cases where you don't need to tune the
+
+ align:start position:0%
+cases where you don't need to tune the
+ 
+
+ align:start position:0%
+cases where you don't need to tune the
+period maybe you still end up evolving
+
+ align:start position:0%
+period maybe you still end up evolving
+ 
+
+ align:start position:0%
+period maybe you still end up evolving
+towards this design just because it's
+
+ align:start position:0%
+towards this design just because it's
+ 
+
+ align:start position:0%
+towards this design just because it's
+robust to stochastic fluctuations and
+
+ align:start position:0%
+robust to stochastic fluctuations and
+ 
+
+ align:start position:0%
+robust to stochastic fluctuations and
+the concentrations of things but also it
+
+ align:start position:0%
+the concentrations of things but also it
+ 
+
+ align:start position:0%
+the concentrations of things but also it
+might be easier to evolve these sorts of
+
+ align:start position:0%
+might be easier to evolve these sorts of
+ 
+
+ align:start position:0%
+might be easier to evolve these sorts of
+U these sorts of oscillations
+
+ align:start position:0%
+U these sorts of oscillations
+ 
+
+ align:start position:0%
+U these sorts of oscillations
+okay um are there any questions about
+
+ align:start position:0%
+okay um are there any questions about
+ 
+
+ align:start position:0%
+okay um are there any questions about
+the the kind of intuition behind this
+
+ align:start position:0%
+the the kind of intuition behind this
+ 
+
+ align:start position:0%
+the the kind of intuition behind this
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+now there's there's a nice kind of
+
+ align:start position:0%
+now there's there's a nice kind of
+ 
+
+ align:start position:0%
+now there's there's a nice kind of
+circuit analogy that people talk about
+
+ align:start position:0%
+circuit analogy that people talk about
+ 
+
+ align:start position:0%
+circuit analogy that people talk about
+in the context of um of this s right so
+
+ align:start position:0%
+in the context of um of this s right so
+ 
+
+ align:start position:0%
+in the context of um of this s right so
+if you imagine you have some battery
+
+ align:start position:0%
+if you imagine you have some battery
+ 
+
+ align:start position:0%
+if you imagine you have some battery
+with some voltage V well say we'll say V
+
+ align:start position:0%
+with some voltage V well say we'll say V
+ 
+
+ align:start position:0%
+with some voltage V well say we'll say V
+battery all
+
+ align:start position:0%
+battery all
+ 
+
+ align:start position:0%
+battery all
+right some capacitor over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+right but over here you
+
+ align:start position:0%
+right but over here you
+ 
+
+ align:start position:0%
+right but over here you
+have something
+
+ align:start position:0%
+have something
+ 
+
+ align:start position:0%
+have something
+that uh will uh
+
+ align:start position:0%
+that uh will uh
+ 
+
+ align:start position:0%
+that uh will uh
+spark at some voltage some VT you get a
+
+ align:start position:0%
+spark at some voltage some VT you get a
+ 
+
+ align:start position:0%
+spark at some voltage some VT you get a
+you get a
+
+ align:start position:0%
+you get a
+ 
+
+ align:start position:0%
+you get a
+spark all right now the question is well
+
+ align:start position:0%
+spark all right now the question is well
+ 
+
+ align:start position:0%
+spark all right now the question is well
+um what happens over time if V threshold
+
+ align:start position:0%
+um what happens over time if V threshold
+ 
+
+ align:start position:0%
+um what happens over time if V threshold
+is less than V battery okay so oh no we
+
+ align:start position:0%
+is less than V battery okay so oh no we
+ 
+
+ align:start position:0%
+is less than V battery okay so oh no we
+maybe should have a resistor in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for so V threshold is Le less than V
+
+ align:start position:0%
+for so V threshold is Le less than V
+ 
+
+ align:start position:0%
+for so V threshold is Le less than V
+battery then um this can generate nice
+
+ align:start position:0%
+battery then um this can generate nice
+ 
+
+ align:start position:0%
+battery then um this can generate nice
+um nice oscillations in the voltage say
+
+ align:start position:0%
+um nice oscillations in the voltage say
+ 
+
+ align:start position:0%
+um nice oscillations in the voltage say
+across the capacitor as a function of
+
+ align:start position:0%
+across the capacitor as a function of
+ 
+
+ align:start position:0%
+across the capacitor as a function of
+time that are tunable right because if
+
+ align:start position:0%
+time that are tunable right because if
+ 
+
+ align:start position:0%
+time that are tunable right because if
+you plot as a function of
+
+ align:start position:0%
+you plot as a function of
+ 
+
+ align:start position:0%
+you plot as a function of
+time this is the voltage across the
+
+ align:start position:0%
+time this is the voltage across the
+ 
+
+ align:start position:0%
+time this is the voltage across the
+capacitor where up here we might have
+
+ align:start position:0%
+capacitor where up here we might have
+ 
+
+ align:start position:0%
+capacitor where up here we might have
+the V of the battery here we might have
+
+ align:start position:0%
+the V of the battery here we might have
+ 
+
+ align:start position:0%
+the V of the battery here we might have
+v v threshold okay now in the absence of
+
+ align:start position:0%
+v v threshold okay now in the absence of
+ 
+
+ align:start position:0%
+v v threshold okay now in the absence of
+this thing that's going to short
+
+ align:start position:0%
+this thing that's going to short
+ 
+
+ align:start position:0%
+this thing that's going to short
+periodically we're just going to charge
+
+ align:start position:0%
+periodically we're just going to charge
+ 
+
+ align:start position:0%
+periodically we're just going to charge
+up the capacitor right so in principle
+
+ align:start position:0%
+up the capacitor right so in principle
+ 
+
+ align:start position:0%
+up the capacitor right so in principle
+there's going to be this standard RC
+
+ align:start position:0%
+there's going to be this standard RC
+ 
+
+ align:start position:0%
+there's going to be this standard RC
+time constant coming up to here right
+
+ align:start position:0%
+time constant coming up to here right
+ 
+
+ align:start position:0%
+time constant coming up to here right
+but instead of before we get there we
+
+ align:start position:0%
+but instead of before we get there we
+ 
+
+ align:start position:0%
+but instead of before we get there we
+get the spark right so then we get we
+
+ align:start position:0%
+get the spark right so then we get we
+ 
+
+ align:start position:0%
+get the spark right so then we get we
+discharge across here and then we this
+
+ align:start position:0%
+discharge across here and then we this
+ 
+
+ align:start position:0%
+discharge across here and then we this
+drops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so you get something that looks
+
+ align:start position:0%
+right so you get something that looks
+ 
+
+ align:start position:0%
+right so you get something that looks
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this all right now you can imagine by
+
+ align:start position:0%
+this all right now you can imagine by
+ 
+
+ align:start position:0%
+this all right now you can imagine by
+changing for example the
+
+ align:start position:0%
+changing for example the
+ 
+
+ align:start position:0%
+changing for example the
+resistor you can change the the rate
+
+ align:start position:0%
+resistor you can change the the rate
+ 
+
+ align:start position:0%
+resistor you can change the the rate
+that this thing the capacitor will
+
+ align:start position:0%
+that this thing the capacitor will
+ 
+
+ align:start position:0%
+that this thing the capacitor will
+charge up right but the amplitude of the
+
+ align:start position:0%
+charge up right but the amplitude of the
+ 
+
+ align:start position:0%
+charge up right but the amplitude of the
+oscillations stay constant because
+
+ align:start position:0%
+oscillations stay constant because
+ 
+
+ align:start position:0%
+oscillations stay constant because
+that's set by uh the voltage threshold
+
+ align:start position:0%
+that's set by uh the voltage threshold
+ 
+
+ align:start position:0%
+that's set by uh the voltage threshold
+across this um
+
+ align:start position:0%
+across this um
+ 
+
+ align:start position:0%
+across this um
+uh where it where it shorts okay right
+
+ align:start position:0%
+uh where it where it shorts okay right
+ 
+
+ align:start position:0%
+uh where it where it shorts okay right
+so this is and this is capturing this
+
+ align:start position:0%
+so this is and this is capturing this
+ 
+
+ align:start position:0%
+so this is and this is capturing this
+Dynamic of the separation of time scales
+
+ align:start position:0%
+Dynamic of the separation of time scales
+ 
+
+ align:start position:0%
+Dynamic of the separation of time scales
+right so there's a slow time scale which
+
+ align:start position:0%
+right so there's a slow time scale which
+ 
+
+ align:start position:0%
+right so there's a slow time scale which
+is this RC time constant and then
+
+ align:start position:0%
+is this RC time constant and then
+ 
+
+ align:start position:0%
+is this RC time constant and then
+there's the rapid time scale is where
+
+ align:start position:0%
+there's the rapid time scale is where
+ 
+
+ align:start position:0%
+there's the rapid time scale is where
+where this shorts off okay and so you
+
+ align:start position:0%
+where this shorts off okay and so you
+ 
+
+ align:start position:0%
+where this shorts off okay and so you
+can imagine that this is an example of
+
+ align:start position:0%
+can imagine that this is an example of
+ 
+
+ align:start position:0%
+can imagine that this is an example of
+an oscillatory signal that we can we can
+
+ align:start position:0%
+an oscillatory signal that we can we can
+ 
+
+ align:start position:0%
+an oscillatory signal that we can we can
+tune the frequency without sacrificing
+
+ align:start position:0%
+tune the frequency without sacrificing
+ 
+
+ align:start position:0%
+tune the frequency without sacrificing
+the amplitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right so
+
+ align:start position:0%
+right right so
+ 
+
+ align:start position:0%
+right right so
+what we what we've said so far is that
+
+ align:start position:0%
+what we what we've said so far is that
+ 
+
+ align:start position:0%
+what we what we've said so far is that
+uh you know there they're engineering
+
+ align:start position:0%
+uh you know there they're engineering
+ 
+
+ align:start position:0%
+uh you know there they're engineering
+analoges to these sorts of relaxation
+
+ align:start position:0%
+analoges to these sorts of relaxation
+ 
+
+ align:start position:0%
+analoges to these sorts of relaxation
+oscillators we can model various
+
+ align:start position:0%
+oscillators we can model various
+ 
+
+ align:start position:0%
+oscillators we can model various
+synthetic circuits or we can look at
+
+ align:start position:0%
+synthetic circuits or we can look at
+ 
+
+ align:start position:0%
+synthetic circuits or we can look at
+natural uh at natural oscillatory
+
+ align:start position:0%
+natural uh at natural oscillatory
+ 
+
+ align:start position:0%
+natural uh at natural oscillatory
+networks in order to get a sense of
+
+ align:start position:0%
+networks in order to get a sense of
+ 
+
+ align:start position:0%
+networks in order to get a sense of
+what's going on right but of course uh a
+
+ align:start position:0%
+what's going on right but of course uh a
+ 
+
+ align:start position:0%
+what's going on right but of course uh a
+major goal of this kind of system
+
+ align:start position:0%
+major goal of this kind of system
+ 
+
+ align:start position:0%
+major goal of this kind of system
+synthetic approach to uh to the field is
+
+ align:start position:0%
+synthetic approach to uh to the field is
+ 
+
+ align:start position:0%
+synthetic approach to uh to the field is
+it you know if if all this stuff is
+
+ align:start position:0%
+it you know if if all this stuff is
+ 
+
+ align:start position:0%
+it you know if if all this stuff is
+really true we should be able to build
+
+ align:start position:0%
+really true we should be able to build
+ 
+
+ align:start position:0%
+really true we should be able to build
+it right and and there's a very nice
+
+ align:start position:0%
+it right and and there's a very nice
+ 
+
+ align:start position:0%
+it right and and there's a very nice
+demonstration of this also in 2008 by
+
+ align:start position:0%
+demonstration of this also in 2008 by
+ 
+
+ align:start position:0%
+demonstration of this also in 2008 by
+Jeff Hasty's
+
+ align:start position:0%
+Jeff Hasty's
+ 
+
+ align:start position:0%
+Jeff Hasty's
+group all right so Jeff
+
+ align:start position:0%
+group all right so Jeff
+ 
+
+ align:start position:0%
+group all right so Jeff
+Hasty uh was uh was actually trained as
+
+ align:start position:0%
+Hasty uh was uh was actually trained as
+ 
+
+ align:start position:0%
+Hasty uh was uh was actually trained as
+a high energy
+
+ align:start position:0%
+a high energy
+ 
+
+ align:start position:0%
+a high energy
+theorist uh and then I think guess it
+
+ align:start position:0%
+theorist uh and then I think guess it
+ 
+
+ align:start position:0%
+theorist uh and then I think guess it
+was during his postto maybe switched
+
+ align:start position:0%
+was during his postto maybe switched
+ 
+
+ align:start position:0%
+was during his postto maybe switched
+into uh experimental biology wenton did
+
+ align:start position:0%
+into uh experimental biology wenton did
+ 
+
+ align:start position:0%
+into uh experimental biology wenton did
+his postto I think with uh with Jim
+
+ align:start position:0%
+his postto I think with uh with Jim
+ 
+
+ align:start position:0%
+his postto I think with uh with Jim
+Collins and then uh and then eventually
+
+ align:start position:0%
+Collins and then uh and then eventually
+ 
+
+ align:start position:0%
+Collins and then uh and then eventually
+now has his own group doing systems
+
+ align:start position:0%
+now has his own group doing systems
+ 
+
+ align:start position:0%
+now has his own group doing systems
+synthetic biology right so in this paper
+
+ align:start position:0%
+synthetic biology right so in this paper
+ 
+
+ align:start position:0%
+synthetic biology right so in this paper
+it was a it was a nature paper in 2008
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it's called again a fast robust and
+
+ align:start position:0%
+um it's called again a fast robust and
+ 
+
+ align:start position:0%
+um it's called again a fast robust and
+tunable synthetic Gene oscillator right
+
+ align:start position:0%
+tunable synthetic Gene oscillator right
+ 
+
+ align:start position:0%
+tunable synthetic Gene oscillator right
+it's a nice statement tells you what
+
+ align:start position:0%
+it's a nice statement tells you what
+ 
+
+ align:start position:0%
+it's a nice statement tells you what
+he's about to do right but um the data
+
+ align:start position:0%
+he's about to do right but um the data
+ 
+
+ align:start position:0%
+he's about to do right but um the data
+here so this is again um it's it's using
+
+ align:start position:0%
+here so this is again um it's it's using
+ 
+
+ align:start position:0%
+here so this is again um it's it's using
+these B this basic Insight of uh having
+
+ align:start position:0%
+these B this basic Insight of uh having
+ 
+
+ align:start position:0%
+these B this basic Insight of uh having
+both interl positive negative feedback
+
+ align:start position:0%
+both interl positive negative feedback
+ 
+
+ align:start position:0%
+both interl positive negative feedback
+loops in eoli he demonstrated that uh
+
+ align:start position:0%
+loops in eoli he demonstrated that uh
+ 
+
+ align:start position:0%
+loops in eoli he demonstrated that uh
+that he can get really beautiful
+
+ align:start position:0%
+that he can get really beautiful
+ 
+
+ align:start position:0%
+that he can get really beautiful
+oscillations in essentially all the
+
+ align:start position:0%
+oscillations in essentially all the
+ 
+
+ align:start position:0%
+oscillations in essentially all the
+cells and that they're tunable in Period
+
+ align:start position:0%
+cells and that they're tunable in Period
+ 
+
+ align:start position:0%
+cells and that they're tunable in Period
+by a factor of three or four or so right
+
+ align:start position:0%
+by a factor of three or four or so right
+ 
+
+ align:start position:0%
+by a factor of three or four or so right
+so by a by a fair amount and indeed uh
+
+ align:start position:0%
+so by a by a fair amount and indeed uh
+ 
+
+ align:start position:0%
+so by a by a fair amount and indeed uh
+as as fast as 13 minutes the the
+
+ align:start position:0%
+as as fast as 13 minutes the the
+ 
+
+ align:start position:0%
+as as fast as 13 minutes the the
+oscillatory period right which is pretty
+
+ align:start position:0%
+oscillatory period right which is pretty
+ 
+
+ align:start position:0%
+oscillatory period right which is pretty
+nice right um so I encourage you to to
+
+ align:start position:0%
+nice right um so I encourage you to to
+ 
+
+ align:start position:0%
+nice right um so I encourage you to to
+to check out this paper U this paper was
+
+ align:start position:0%
+to check out this paper U this paper was
+ 
+
+ align:start position:0%
+to check out this paper U this paper was
+um was also an example of
+
+ align:start position:0%
+um was also an example of
+ 
+
+ align:start position:0%
+um was also an example of
+uh how it was in principle possible to
+
+ align:start position:0%
+uh how it was in principle possible to
+ 
+
+ align:start position:0%
+uh how it was in principle possible to
+get oscillations just uh by doing
+
+ align:start position:0%
+get oscillations just uh by doing
+ 
+
+ align:start position:0%
+get oscillations just uh by doing
+negative Auto regulation right so this
+
+ align:start position:0%
+negative Auto regulation right so this
+ 
+
+ align:start position:0%
+negative Auto regulation right so this
+was case where they they designed a gene
+
+ align:start position:0%
+was case where they they designed a gene
+ 
+
+ align:start position:0%
+was case where they they designed a gene
+Network that would uh that they could
+
+ align:start position:0%
+Network that would uh that they could
+ 
+
+ align:start position:0%
+Network that would uh that they could
+tune and had this wonderful property but
+
+ align:start position:0%
+tune and had this wonderful property but
+ 
+
+ align:start position:0%
+tune and had this wonderful property but
+then after they did that they noticed
+
+ align:start position:0%
+then after they did that they noticed
+ 
+
+ align:start position:0%
+then after they did that they noticed
+that in their model at least they could
+
+ align:start position:0%
+that in their model at least they could
+ 
+
+ align:start position:0%
+that in their model at least they could
+get oscillations in some parameter
+
+ align:start position:0%
+get oscillations in some parameter
+ 
+
+ align:start position:0%
+get oscillations in some parameter
+regime just by having a negative Auto
+
+ align:start position:0%
+regime just by having a negative Auto
+ 
+
+ align:start position:0%
+regime just by having a negative Auto
+regulatory Loop but and as a result of
+
+ align:start position:0%
+regulatory Loop but and as a result of
+ 
+
+ align:start position:0%
+regulatory Loop but and as a result of
+all these uh intermediate processes of
+
+ align:start position:0%
+all these uh intermediate processes of
+ 
+
+ align:start position:0%
+all these uh intermediate processes of
+protein maturation and so forth and they
+
+ align:start position:0%
+protein maturation and so forth and they
+ 
+
+ align:start position:0%
+protein maturation and so forth and they
+went and they constructed that Network
+
+ align:start position:0%
+went and they constructed that Network
+ 
+
+ align:start position:0%
+went and they constructed that Network
+and they showed that that could also
+
+ align:start position:0%
+and they showed that that could also
+ 
+
+ align:start position:0%
+and they showed that that could also
+oscillate right so again this is an
+
+ align:start position:0%
+oscillate right so again this is an
+ 
+
+ align:start position:0%
+oscillate right so again this is an
+example of the interplay between
+
+ align:start position:0%
+example of the interplay between
+ 
+
+ align:start position:0%
+example of the interplay between
+modeling experiment Theory modeling and
+
+ align:start position:0%
+modeling experiment Theory modeling and
+ 
+
+ align:start position:0%
+modeling experiment Theory modeling and
+and Jeff has gone on to to write another
+
+ align:start position:0%
+and Jeff has gone on to to write another
+ 
+
+ align:start position:0%
+and Jeff has gone on to to write another
+uh several really beautiful papers uh
+
+ align:start position:0%
+uh several really beautiful papers uh
+ 
+
+ align:start position:0%
+uh several really beautiful papers uh
+looking at at these sorts of
+
+ align:start position:0%
+looking at at these sorts of
+ 
+
+ align:start position:0%
+looking at at these sorts of
+oscillations looking at how you can get
+
+ align:start position:0%
+oscillations looking at how you can get
+ 
+
+ align:start position:0%
+oscillations looking at how you can get
+um synchronization of oscillators and
+
+ align:start position:0%
+um synchronization of oscillators and
+ 
+
+ align:start position:0%
+um synchronization of oscillators and
+you get period doubling ideas you know
+
+ align:start position:0%
+you get period doubling ideas you know
+ 
+
+ align:start position:0%
+you get period doubling ideas you know
+it's really a whole string of wonderful
+
+ align:start position:0%
+it's really a whole string of wonderful
+ 
+
+ align:start position:0%
+it's really a whole string of wonderful
+uh wonderful papers so I I encourage you
+
+ align:start position:0%
+uh wonderful papers so I I encourage you
+ 
+
+ align:start position:0%
+uh wonderful papers so I I encourage you
+to if you're interested in oscillations
+
+ align:start position:0%
+to if you're interested in oscillations
+ 
+
+ align:start position:0%
+to if you're interested in oscillations
+to look at look at Jeff Hasty's work
+
+ align:start position:0%
+to look at look at Jeff Hasty's work
+ 
+
+ align:start position:0%
+to look at look at Jeff Hasty's work
+over the years um and uh right so so um
+
+ align:start position:0%
+over the years um and uh right so so um
+ 
+
+ align:start position:0%
+over the years um and uh right so so um
+and you know and if you if you want to a
+
+ align:start position:0%
+and you know and if you if you want to a
+ 
+
+ align:start position:0%
+and you know and if you if you want to a
+quick introduction to these papers I I
+
+ align:start position:0%
+quick introduction to these papers I I
+ 
+
+ align:start position:0%
+quick introduction to these papers I I
+also wrote a News and Views and nature
+
+ align:start position:0%
+also wrote a News and Views and nature
+ 
+
+ align:start position:0%
+also wrote a News and Views and nature
+on these two papers so you can you can
+
+ align:start position:0%
+on these two papers so you can you can
+ 
+
+ align:start position:0%
+on these two papers so you can you can
+read that it's only um a page uh so um
+
+ align:start position:0%
+read that it's only um a page uh so um
+ 
+
+ align:start position:0%
+read that it's only um a page uh so um
+so that's although I guess you won't
+
+ align:start position:0%
+so that's although I guess you won't
+ 
+
+ align:start position:0%
+so that's although I guess you won't
+hear anything that you haven't already
+
+ align:start position:0%
+hear anything that you haven't already
+ 
+
+ align:start position:0%
+hear anything that you haven't already
+heard probably um but um yeah any any
+
+ align:start position:0%
+heard probably um but um yeah any any
+ 
+
+ align:start position:0%
+heard probably um but um yeah any any
+other any other questions about this
+
+ align:start position:0%
+other any other questions about this
+ 
+
+ align:start position:0%
+other any other questions about this
+idea of uh how how we can use both
+
+ align:start position:0%
+idea of uh how how we can use both
+ 
+
+ align:start position:0%
+idea of uh how how we can use both
+positive and negative feedback in order
+
+ align:start position:0%
+positive and negative feedback in order
+ 
+
+ align:start position:0%
+positive and negative feedback in order
+to get some nice oscillatory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties okay then let's um let's move
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on all right what did you guys think of
+
+ align:start position:0%
+on all right what did you guys think of
+ 
+
+ align:start position:0%
+on all right what did you guys think of
+um of this paper the barasi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paper good bad difficult Easy Does It
+
+ align:start position:0%
+paper good bad difficult Easy Does It
+ 
+
+ align:start position:0%
+paper good bad difficult Easy Does It
+citations why does it have so many
+
+ align:start position:0%
+citations why does it have so many
+ 
+
+ align:start position:0%
+citations why does it have so many
+citations all right that's yeah no and
+
+ align:start position:0%
+citations all right that's yeah no and
+ 
+
+ align:start position:0%
+citations all right that's yeah no and
+you you should look at how many I mean
+
+ align:start position:0%
+you you should look at how many I mean
+ 
+
+ align:start position:0%
+you you should look at how many I mean
+according to Google Scholar I haven't
+
+ align:start position:0%
+according to Google Scholar I haven't
+ 
+
+ align:start position:0%
+according to Google Scholar I haven't
+checked this year but it's probably like
+
+ align:start position:0%
+checked this year but it's probably like
+ 
+
+ align:start position:0%
+checked this year but it's probably like
+20,000 citations I mean it's a c thing
+
+ align:start position:0%
+20,000 citations I mean it's a c thing
+ 
+
+ align:start position:0%
+20,000 citations I mean it's a c thing
+or um it's a cult thing um well I I I I
+
+ align:start position:0%
+or um it's a cult thing um well I I I I
+ 
+
+ align:start position:0%
+or um it's a cult thing um well I I I I
+don't know that might exaggerating um
+
+ align:start position:0%
+don't know that might exaggerating um
+ 
+
+ align:start position:0%
+don't know that might exaggerating um
+it's a nice yeah right um no right so
+
+ align:start position:0%
+it's a nice yeah right um no right so
+ 
+
+ align:start position:0%
+it's a nice yeah right um no right so
+this is interesting I think that the
+
+ align:start position:0%
+this is interesting I think that the
+ 
+
+ align:start position:0%
+this is interesting I think that the
+basic answer is that um there are
+
+ align:start position:0%
+basic answer is that um there are
+ 
+
+ align:start position:0%
+basic answer is that um there are
+networks that are relevant in many many
+
+ align:start position:0%
+networks that are relevant in many many
+ 
+
+ align:start position:0%
+networks that are relevant in many many
+many fields which they allude to and um
+
+ align:start position:0%
+many fields which they allude to and um
+ 
+
+ align:start position:0%
+many fields which they allude to and um
+and there are many researchers that have
+
+ align:start position:0%
+and there are many researchers that have
+ 
+
+ align:start position:0%
+and there are many researchers that have
+been excited about studying those
+
+ align:start position:0%
+been excited about studying those
+ 
+
+ align:start position:0%
+been excited about studying those
+networks in many many fields and uh many
+
+ align:start position:0%
+networks in many many fields and uh many
+ 
+
+ align:start position:0%
+networks in many many fields and uh many
+many many of the networks that are
+
+ align:start position:0%
+many many of the networks that are
+ 
+
+ align:start position:0%
+many many of the networks that are
+observed in nature social
+
+ align:start position:0%
+observed in nature social
+ 
+
+ align:start position:0%
+observed in nature social
+science the web everywhere they have
+
+ align:start position:0%
+science the web everywhere they have
+ 
+
+ align:start position:0%
+science the web everywhere they have
+these power power LW structures and and
+
+ align:start position:0%
+these power power LW structures and and
+ 
+
+ align:start position:0%
+these power power LW structures and and
+and this is
+
+ align:start position:0%
+and this is
+ 
+
+ align:start position:0%
+and this is
+um the the the you know the first clear
+
+ align:start position:0%
+um the the the you know the first clear
+ 
+
+ align:start position:0%
+um the the the you know the first clear
+simple mechanism to generate it my my
+
+ align:start position:0%
+simple mechanism to generate it my my
+ 
+
+ align:start position:0%
+simple mechanism to generate it my my
+understanding is actually that some you
+
+ align:start position:0%
+understanding is actually that some you
+ 
+
+ align:start position:0%
+understanding is actually that some you
+know that actually a mathematician
+
+ align:start position:0%
+know that actually a mathematician
+ 
+
+ align:start position:0%
+know that actually a mathematician
+decades before actually did demonstrate
+
+ align:start position:0%
+decades before actually did demonstrate
+ 
+
+ align:start position:0%
+decades before actually did demonstrate
+that this kind of thing could be
+
+ align:start position:0%
+that this kind of thing could be
+ 
+
+ align:start position:0%
+that this kind of thing could be
+constructed that would lead to this but
+
+ align:start position:0%
+constructed that would lead to this but
+ 
+
+ align:start position:0%
+constructed that would lead to this but
+um but that paper doesn't have 20,000
+
+ align:start position:0%
+um but that paper doesn't have 20,000
+ 
+
+ align:start position:0%
+um but that paper doesn't have 20,000
+citations you know I mean like it's a
+
+ align:start position:0%
+citations you know I mean like it's a
+ 
+
+ align:start position:0%
+citations you know I mean like it's a
+lot of these things you have to be at
+
+ align:start position:0%
+lot of these things you have to be at
+ 
+
+ align:start position:0%
+lot of these things you have to be at
+the right time the right place and have
+
+ align:start position:0%
+the right time the right place and have
+ 
+
+ align:start position:0%
+the right time the right place and have
+the right idea and you know um yeah I
+
+ align:start position:0%
+the right idea and you know um yeah I
+ 
+
+ align:start position:0%
+the right idea and you know um yeah I
+guess my my main thought about paper is
+
+ align:start position:0%
+guess my my main thought about paper is
+ 
+
+ align:start position:0%
+guess my my main thought about paper is
+exactly that
+
+ align:start position:0%
+exactly that
+ 
+
+ align:start position:0%
+exactly that
+the interesting thing about it was it
+
+ align:start position:0%
+the interesting thing about it was it
+ 
+
+ align:start position:0%
+the interesting thing about it was it
+was it came out at about the time that
+
+ align:start position:0%
+was it came out at about the time that
+ 
+
+ align:start position:0%
+was it came out at about the time that
+data on laun networks was available
+
+ align:start position:0%
+data on laun networks was available
+ 
+
+ align:start position:0%
+data on laun networks was available
+that's right yeah there's a re there's a
+
+ align:start position:0%
+that's right yeah there's a re there's a
+ 
+
+ align:start position:0%
+that's right yeah there's a re there's a
+reason that this paper was U published
+
+ align:start position:0%
+reason that this paper was U published
+ 
+
+ align:start position:0%
+reason that this paper was U published
+at this time and you know and of course
+
+ align:start position:0%
+at this time and you know and of course
+ 
+
+ align:start position:0%
+at this time and you know and of course
+you know if barosi didn't do it here
+
+ align:start position:0%
+you know if barosi didn't do it here
+ 
+
+ align:start position:0%
+you know if barosi didn't do it here
+someone else would have done it a year
+
+ align:start position:0%
+someone else would have done it a year
+ 
+
+ align:start position:0%
+someone else would have done it a year
+or two later right but it was it was
+
+ align:start position:0%
+or two later right but it was it was
+ 
+
+ align:start position:0%
+or two later right but it was it was
+really that that the data were available
+
+ align:start position:0%
+really that that the data were available
+ 
+
+ align:start position:0%
+really that that the data were available
+everywhere and so then that and we were
+
+ align:start position:0%
+everywhere and so then that and we were
+ 
+
+ align:start position:0%
+everywhere and so then that and we were
+seeing these power law distributions and
+
+ align:start position:0%
+seeing these power law distributions and
+ 
+
+ align:start position:0%
+seeing these power law distributions and
+it's really crying out for for an
+
+ align:start position:0%
+it's really crying out for for an
+ 
+
+ align:start position:0%
+it's really crying out for for an
+explanation okay I think it it's you
+
+ align:start position:0%
+explanation okay I think it it's you
+ 
+
+ align:start position:0%
+explanation okay I think it it's you
+know sometimes people complain that they
+
+ align:start position:0%
+know sometimes people complain that they
+ 
+
+ align:start position:0%
+know sometimes people complain that they
+say oh yeah you know I could have come
+
+ align:start position:0%
+say oh yeah you know I could have come
+ 
+
+ align:start position:0%
+say oh yeah you know I could have come
+up with this idea you know it's not that
+
+ align:start position:0%
+up with this idea you know it's not that
+ 
+
+ align:start position:0%
+up with this idea you know it's not that
+deep you know and yeah maybe you could
+
+ align:start position:0%
+deep you know and yeah maybe you could
+ 
+
+ align:start position:0%
+deep you know and yeah maybe you could
+have but you know but you didn't you
+
+ align:start position:0%
+have but you know but you didn't you
+ 
+
+ align:start position:0%
+have but you know but you didn't you
+know uh you know and and also I'd say
+
+ align:start position:0%
+know uh you know and and also I'd say
+ 
+
+ align:start position:0%
+know uh you know and and also I'd say
+that you know you know barabasi has a
+
+ align:start position:0%
+that you know you know barabasi has a
+ 
+
+ align:start position:0%
+that you know you know barabasi has a
+has a record of doing interesting
+
+ align:start position:0%
+has a record of doing interesting
+ 
+
+ align:start position:0%
+has a record of doing interesting
+things and being the first to point out
+
+ align:start position:0%
+things and being the first to point out
+ 
+
+ align:start position:0%
+things and being the first to point out
+a simple idea you know and and you know
+
+ align:start position:0%
+a simple idea you know and and you know
+ 
+
+ align:start position:0%
+a simple idea you know and and you know
+and if if you can reliably be the first
+
+ align:start position:0%
+and if if you can reliably be the first
+ 
+
+ align:start position:0%
+and if if you can reliably be the first
+to point out a simple explanation for
+
+ align:start position:0%
+to point out a simple explanation for
+ 
+
+ align:start position:0%
+to point out a simple explanation for
+important things and that's um that's
+
+ align:start position:0%
+important things and that's um that's
+ 
+
+ align:start position:0%
+important things and that's um that's
+another kind of Genius right I mean you
+
+ align:start position:0%
+another kind of Genius right I mean you
+ 
+
+ align:start position:0%
+another kind of Genius right I mean you
+know and it's um and it's the kind of
+
+ align:start position:0%
+know and it's um and it's the kind of
+ 
+
+ align:start position:0%
+know and it's um and it's the kind of
+Genius that I I would you know I aspire
+
+ align:start position:0%
+Genius that I I would you know I aspire
+ 
+
+ align:start position:0%
+Genius that I I would you know I aspire
+to because I know that I'm not going to
+
+ align:start position:0%
+to because I know that I'm not going to
+ 
+
+ align:start position:0%
+to because I know that I'm not going to
+do the I'm not going to um reach the
+
+ align:start position:0%
+do the I'm not going to um reach the
+ 
+
+ align:start position:0%
+do the I'm not going to um reach the
+other kind of Genius right you know so
+
+ align:start position:0%
+other kind of Genius right you know so
+ 
+
+ align:start position:0%
+other kind of Genius right you know so
+you know I mean you know I mean there
+
+ align:start position:0%
+you know I mean you know I mean there
+ 
+
+ align:start position:0%
+you know I mean you know I mean there
+there I mean there are some things that
+
+ align:start position:0%
+there I mean there are some things that
+ 
+
+ align:start position:0%
+there I mean there are some things that
+you know you look at you're like oh well
+
+ align:start position:0%
+you know you look at you're like oh well
+ 
+
+ align:start position:0%
+you know you look at you're like oh well
+you know I would never be able to do
+
+ align:start position:0%
+you know I would never be able to do
+ 
+
+ align:start position:0%
+you know I would never be able to do
+that right um and uh and those you know
+
+ align:start position:0%
+that right um and uh and those you know
+ 
+
+ align:start position:0%
+that right um and uh and those you know
+everyone agrees that's hard but um but I
+
+ align:start position:0%
+everyone agrees that's hard but um but I
+ 
+
+ align:start position:0%
+everyone agrees that's hard but um but I
+think that there there is something
+
+ align:start position:0%
+think that there there is something
+ 
+
+ align:start position:0%
+think that there there is something
+about being able to see what the
+
+ align:start position:0%
+about being able to see what the
+ 
+
+ align:start position:0%
+about being able to see what the
+scientific opportunities are at a given
+
+ align:start position:0%
+scientific opportunities are at a given
+ 
+
+ align:start position:0%
+scientific opportunities are at a given
+time and you don't have to come up with
+
+ align:start position:0%
+time and you don't have to come up with
+ 
+
+ align:start position:0%
+time and you don't have to come up with
+a really complicated
+
+ align:start position:0%
+a really complicated
+ 
+
+ align:start position:0%
+a really complicated
+model or proof in order to have have
+
+ align:start position:0%
+model or proof in order to have have
+ 
+
+ align:start position:0%
+model or proof in order to have have
+really important impact uh and yeah and
+
+ align:start position:0%
+really important impact uh and yeah and
+ 
+
+ align:start position:0%
+really important impact uh and yeah and
+this paper is um is you know way I mean
+
+ align:start position:0%
+this paper is um is you know way I mean
+ 
+
+ align:start position:0%
+this paper is um is you know way I mean
+Way Beyond and you know in terms of like
+
+ align:start position:0%
+Way Beyond and you know in terms of like
+ 
+
+ align:start position:0%
+Way Beyond and you know in terms of like
+number of people that have read it cited
+
+ align:start position:0%
+number of people that have read it cited
+ 
+
+ align:start position:0%
+number of people that have read it cited
+it and so forth It's you know Way Beyond
+
+ align:start position:0%
+it and so forth It's you know Way Beyond
+ 
+
+ align:start position:0%
+it and so forth It's you know Way Beyond
+probably any other paper you'll likely
+
+ align:start position:0%
+probably any other paper you'll likely
+ 
+
+ align:start position:0%
+probably any other paper you'll likely
+read in your life uh yes uh just more
+
+ align:start position:0%
+read in your life uh yes uh just more
+ 
+
+ align:start position:0%
+read in your life uh yes uh just more
+thoughts more thoughts yeah that's fine
+
+ align:start position:0%
+thoughts more thoughts yeah that's fine
+ 
+
+ align:start position:0%
+thoughts more thoughts yeah that's fine
+yeah yeah I mean I guess what's
+
+ align:start position:0%
+yeah yeah I mean I guess what's
+ 
+
+ align:start position:0%
+yeah yeah I mean I guess what's
+interesting is yeah it starts the
+
+ align:start position:0%
+interesting is yeah it starts the
+ 
+
+ align:start position:0%
+interesting is yeah it starts the
+conversation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah no I think that's that's a totally
+
+ align:start position:0%
+yeah no I think that's that's a totally
+ 
+
+ align:start position:0%
+yeah no I think that's that's a totally
+um so this is the barosi and ra Albert
+
+ align:start position:0%
+um so this is the barosi and ra Albert
+ 
+
+ align:start position:0%
+um so this is the barosi and ra Albert
+um so um so barosi is a professor over
+
+ align:start position:0%
+um so um so barosi is a professor over
+ 
+
+ align:start position:0%
+um so um so barosi is a professor over
+at nor Eastern now um ra Albert is a
+
+ align:start position:0%
+at nor Eastern now um ra Albert is a
+ 
+
+ align:start position:0%
+at nor Eastern now um ra Albert is a
+professor at Penn State and I think
+
+ align:start position:0%
+professor at Penn State and I think
+ 
+
+ align:start position:0%
+professor at Penn State and I think
+they've both gone on to do what I I
+
+ align:start position:0%
+they've both gone on to do what I I
+ 
+
+ align:start position:0%
+they've both gone on to do what I I
+think are really very interesting things
+
+ align:start position:0%
+think are really very interesting things
+ 
+
+ align:start position:0%
+think are really very interesting things
+you know in this network space but you
+
+ align:start position:0%
+you know in this network space but you
+ 
+
+ align:start position:0%
+you know in this network space but you
+know and more generally so I you I
+
+ align:start position:0%
+know and more generally so I you I
+ 
+
+ align:start position:0%
+know and more generally so I you I
+encourage you to to check out what what
+
+ align:start position:0%
+encourage you to to check out what what
+ 
+
+ align:start position:0%
+encourage you to to check out what what
+each of them have been doing over the
+
+ align:start position:0%
+each of them have been doing over the
+ 
+
+ align:start position:0%
+each of them have been doing over the
+years uh all right so so all right so
+
+ align:start position:0%
+years uh all right so so all right so
+ 
+
+ align:start position:0%
+years uh all right so so all right so
+this is the this model okay what what
+
+ align:start position:0%
+this is the this model okay what what
+ 
+
+ align:start position:0%
+this is the this model okay what what
+are the two key ingredients of of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model right so all right so the two
+
+ align:start position:0%
+model right so all right so the two
+ 
+
+ align:start position:0%
+model right so all right so the two
+things that you should be able
+
+ align:start position:0%
+things that you should be able
+ 
+
+ align:start position:0%
+things that you should be able
+to recapitulate on an exam is that there
+
+ align:start position:0%
+to recapitulate on an exam is that there
+ 
+
+ align:start position:0%
+to recapitulate on an exam is that there
+are two assumptions here there's growth
+
+ align:start position:0%
+are two assumptions here there's growth
+ 
+
+ align:start position:0%
+are two assumptions here there's growth
+and there's preferential attachment okay
+
+ align:start position:0%
+and there's preferential attachment okay
+ 
+
+ align:start position:0%
+and there's preferential attachment okay
+and we'll we'll talk about the degree to
+
+ align:start position:0%
+and we'll we'll talk about the degree to
+ 
+
+ align:start position:0%
+and we'll we'll talk about the degree to
+which we think each of those things
+
+ align:start position:0%
+which we think each of those things
+ 
+
+ align:start position:0%
+which we think each of those things
+might be necessary but um what's the
+
+ align:start position:0%
+might be necessary but um what's the
+ 
+
+ align:start position:0%
+might be necessary but um what's the
+what's the
+
+ align:start position:0%
+what's the
+ 
+
+ align:start position:0%
+what's the
+key yeah can somebody be a little more
+
+ align:start position:0%
+key yeah can somebody be a little more
+ 
+
+ align:start position:0%
+key yeah can somebody be a little more
+explicit than what we've been so far
+
+ align:start position:0%
+explicit than what we've been so far
+ 
+
+ align:start position:0%
+explicit than what we've been so far
+about what the key kind of observation
+
+ align:start position:0%
+about what the key kind of observation
+ 
+
+ align:start position:0%
+about what the key kind of observation
+is that we're trying to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explain that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges random right Perfect Right
+
+ align:start position:0%
+edges random right Perfect Right
+ 
+
+ align:start position:0%
+edges random right Perfect Right
+observation right all right so some
+
+ align:start position:0%
+observation right all right so some
+ 
+
+ align:start position:0%
+observation right all right so some
+nodes have lots of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges it is kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+met yes it you it it indeed it is um it
+
+ align:start position:0%
+met yes it you it it indeed it is um it
+ 
+
+ align:start position:0%
+met yes it you it it indeed it is um it
+is ironic and and and we'll we'll we'll
+
+ align:start position:0%
+is ironic and and and we'll we'll we'll
+ 
+
+ align:start position:0%
+is ironic and and and we'll we'll we'll
+talk about how how the scaling of the
+
+ align:start position:0%
+talk about how how the scaling of the
+ 
+
+ align:start position:0%
+talk about how how the scaling of the
+citation networks go in a moment um
+
+ align:start position:0%
+citation networks go in a moment um
+ 
+
+ align:start position:0%
+citation networks go in a moment um
+right so some nodes have lots of edges
+
+ align:start position:0%
+right so some nodes have lots of edges
+ 
+
+ align:start position:0%
+right so some nodes have lots of edges
+all right and um and then you know you
+
+ align:start position:0%
+all right and um and then you know you
+ 
+
+ align:start position:0%
+all right and um and then you know you
+you have you want to be very clear about
+
+ align:start position:0%
+you have you want to be very clear about
+ 
+
+ align:start position:0%
+you have you want to be very clear about
+this this is what the you know you're
+
+ align:start position:0%
+this this is what the you know you're
+ 
+
+ align:start position:0%
+this this is what the you know you're
+trying to explain right so uh it's power
+
+ align:start position:0%
+trying to explain right so uh it's power
+ 
+
+ align:start position:0%
+trying to explain right so uh it's power
+law distribution right so in particular
+
+ align:start position:0%
+law distribution right so in particular
+ 
+
+ align:start position:0%
+law distribution right so in particular
+you can quantify this thing right that
+
+ align:start position:0%
+you can quantify this thing right that
+ 
+
+ align:start position:0%
+you can quantify this thing right that
+the probability of having K nodes or
+
+ align:start position:0%
+the probability of having K nodes or
+ 
+
+ align:start position:0%
+the probability of having K nodes or
+sorry the probability that a node has K
+
+ align:start position:0%
+sorry the probability that a node has K
+ 
+
+ align:start position:0%
+sorry the probability that a node has K
+edges falls off as a power law you know
+
+ align:start position:0%
+edges falls off as a power law you know
+ 
+
+ align:start position:0%
+edges falls off as a power law you know
+1 over K to some power 2 3 4 right so
+
+ align:start position:0%
+1 over K to some power 2 3 4 right so
+ 
+
+ align:start position:0%
+1 over K to some power 2 3 4 right so
+the probability having K edges um goes
+
+ align:start position:0%
+the probability having K edges um goes
+ 
+
+ align:start position:0%
+the probability having K edges um goes
+as 1 over K to some power Alpha right
+
+ align:start position:0%
+as 1 over K to some power Alpha right
+ 
+
+ align:start position:0%
+as 1 over K to some power Alpha right
+where Alpha is kind of you know maybe
+
+ align:start position:0%
+where Alpha is kind of you know maybe
+ 
+
+ align:start position:0%
+where Alpha is kind of you know maybe
+between two and four for a lot of these
+
+ align:start position:0%
+between two and four for a lot of these
+ 
+
+ align:start position:0%
+between two and four for a lot of these
+okay now you know it's important to make
+
+ align:start position:0%
+okay now you know it's important to make
+ 
+
+ align:start position:0%
+okay now you know it's important to make
+sure
+
+ align:start position:0%
+sure
+ 
+
+ align:start position:0%
+sure
+that you you keep this qualitative
+
+ align:start position:0%
+that you you keep this qualitative
+ 
+
+ align:start position:0%
+that you you keep this qualitative
+statement in mind though right because
+
+ align:start position:0%
+statement in mind though right because
+ 
+
+ align:start position:0%
+statement in mind though right because
+you know it's true that it falls off and
+
+ align:start position:0%
+you know it's true that it falls off and
+ 
+
+ align:start position:0%
+you know it's true that it falls off and
+and you know and sort of rapidly right
+
+ align:start position:0%
+and you know and sort of rapidly right
+ 
+
+ align:start position:0%
+and you know and sort of rapidly right
+you know one over K2 K cubed or k to the
+
+ align:start position:0%
+you know one over K2 K cubed or k to the
+ 
+
+ align:start position:0%
+you know one over K2 K cubed or k to the
+4th you'd say oh that's that that's a
+
+ align:start position:0%
+4th you'd say oh that's that that's a
+ 
+
+ align:start position:0%
+4th you'd say oh that's that that's a
+pretty rapid fallof right but it's not
+
+ align:start position:0%
+pretty rapid fallof right but it's not
+ 
+
+ align:start position:0%
+pretty rapid fallof right but it's not
+rapid compared to
+
+ align:start position:0%
+rapid compared to
+ 
+
+ align:start position:0%
+rapid compared to
+what expon right so the for these other
+
+ align:start position:0%
+what expon right so the for these other
+ 
+
+ align:start position:0%
+what expon right so the for these other
+yeah for these other models then it
+
+ align:start position:0%
+yeah for these other models then it
+ 
+
+ align:start position:0%
+yeah for these other models then it
+falls off exponential
+
+ align:start position:0%
+falls off exponential
+ 
+
+ align:start position:0%
+falls off exponential
+right so even faster okay so you know
+
+ align:start position:0%
+right so even faster okay so you know
+ 
+
+ align:start position:0%
+right so even faster okay so you know
+you know it's easy to kind of look at oh
+
+ align:start position:0%
+you know it's easy to kind of look at oh
+ 
+
+ align:start position:0%
+you know it's easy to kind of look at oh
+one k to 4th and think oh that's a fast
+
+ align:start position:0%
+one k to 4th and think oh that's a fast
+ 
+
+ align:start position:0%
+one k to 4th and think oh that's a fast
+fallof right but just we have to
+
+ align:start position:0%
+fallof right but just we have to
+ 
+
+ align:start position:0%
+fallof right but just we have to
+remember that it's uh it's slow compared
+
+ align:start position:0%
+remember that it's uh it's slow compared
+ 
+
+ align:start position:0%
+remember that it's uh it's slow compared
+to some other things right so um in
+
+ align:start position:0%
+to some other things right so um in
+ 
+
+ align:start position:0%
+to some other things right so um in
+particular if you look at the if you
+
+ align:start position:0%
+particular if you look at the if you
+ 
+
+ align:start position:0%
+particular if you look at the if you
+look at the data for real networks right
+
+ align:start position:0%
+look at the data for real networks right
+ 
+
+ align:start position:0%
+look at the data for real networks right
+you see that the probability
+
+ align:start position:0%
+you see that the probability
+ 
+
+ align:start position:0%
+you see that the probability
+distribution in many cases goes over
+
+ align:start position:0%
+distribution in many cases goes over
+ 
+
+ align:start position:0%
+distribution in many cases goes over
+orders of magnitude in terms of this
+
+ align:start position:0%
+orders of magnitude in terms of this
+ 
+
+ align:start position:0%
+orders of magnitude in terms of this
+probability right so you think oh that's
+
+ align:start position:0%
+probability right so you think oh that's
+ 
+
+ align:start position:0%
+probability right so you think oh that's
+a big that's a big range and it is a big
+
+ align:start position:0%
+a big that's a big range and it is a big
+ 
+
+ align:start position:0%
+a big that's a big range and it is a big
+range but uh the fact is that you
+
+ align:start position:0%
+range but uh the fact is that you
+ 
+
+ align:start position:0%
+range but uh the fact is that you
+actually see some no
+
+ align:start position:0%
+actually see some no
+ 
+
+ align:start position:0%
+actually see some no
+with you know the Thousand edges or
+
+ align:start position:0%
+with you know the Thousand edges or
+ 
+
+ align:start position:0%
+with you know the Thousand edges or
+whatnot right which is something you
+
+ align:start position:0%
+whatnot right which is something you
+ 
+
+ align:start position:0%
+whatnot right which is something you
+would just never see if it were a random
+
+ align:start position:0%
+would just never see if it were a random
+ 
+
+ align:start position:0%
+would just never see if it were a random
+Network or if it were you know if it
+
+ align:start position:0%
+Network or if it were you know if it
+ 
+
+ align:start position:0%
+Network or if it were you know if it
+were not a power law distributed Network
+
+ align:start position:0%
+were not a power law distributed Network
+ 
+
+ align:start position:0%
+were not a power law distributed Network
+okay and I think that this is also
+
+ align:start position:0%
+okay and I think that this is also
+ 
+
+ align:start position:0%
+okay and I think that this is also
+highlighting another statement which is
+
+ align:start position:0%
+highlighting another statement which is
+ 
+
+ align:start position:0%
+highlighting another statement which is
+that a powerful way to make a difference
+
+ align:start position:0%
+that a powerful way to make a difference
+ 
+
+ align:start position:0%
+that a powerful way to make a difference
+for example if you're going to write
+
+ align:start position:0%
+for example if you're going to write
+ 
+
+ align:start position:0%
+for example if you're going to write
+down a model or you're going to do
+
+ align:start position:0%
+down a model or you're going to do
+ 
+
+ align:start position:0%
+down a model or you're going to do
+theory is that it's nice if you start if
+
+ align:start position:0%
+theory is that it's nice if you start if
+ 
+
+ align:start position:0%
+theory is that it's nice if you start if
+there's a clear observation that needs
+
+ align:start position:0%
+there's a clear observation that needs
+ 
+
+ align:start position:0%
+there's a clear observation that needs
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+explained okay because you can always
+
+ align:start position:0%
+explained okay because you can always
+ 
+
+ align:start position:0%
+explained okay because you can always
+write down a model of something
+
+ align:start position:0%
+write down a model of something
+ 
+
+ align:start position:0%
+write down a model of something
+and and maybe you'll find something
+
+ align:start position:0%
+and and maybe you'll find something
+ 
+
+ align:start position:0%
+and and maybe you'll find something
+interesting right uh but uh a way to I
+
+ align:start position:0%
+interesting right uh but uh a way to I
+ 
+
+ align:start position:0%
+interesting right uh but uh a way to I
+think massively increase the probability
+
+ align:start position:0%
+think massively increase the probability
+ 
+
+ align:start position:0%
+think massively increase the probability
+that you're going to um discover
+
+ align:start position:0%
+that you're going to um discover
+ 
+
+ align:start position:0%
+that you're going to um discover
+something interesting is if there's all
+
+ align:start position:0%
+something interesting is if there's all
+ 
+
+ align:start position:0%
+something interesting is if there's all
+if you already know there's something
+
+ align:start position:0%
+if you already know there's something
+ 
+
+ align:start position:0%
+if you already know there's something
+interesting there and that you're trying
+
+ align:start position:0%
+interesting there and that you're trying
+ 
+
+ align:start position:0%
+interesting there and that you're trying
+to explain it okay and I think that this
+
+ align:start position:0%
+to explain it okay and I think that this
+ 
+
+ align:start position:0%
+to explain it okay and I think that this
+is an example of that right there was
+
+ align:start position:0%
+is an example of that right there was
+ 
+
+ align:start position:0%
+is an example of that right there was
+already an observation it was already
+
+ align:start position:0%
+already an observation it was already
+ 
+
+ align:start position:0%
+already an observation it was already
+known right it's not that he was the
+
+ align:start position:0%
+known right it's not that he was the
+ 
+
+ align:start position:0%
+known right it's not that he was the
+first person to make those plots right
+
+ align:start position:0%
+first person to make those plots right
+ 
+
+ align:start position:0%
+first person to make those plots right
+there were other plots of citation
+
+ align:start position:0%
+there were other plots of citation
+ 
+
+ align:start position:0%
+there were other plots of citation
+networks before right so Sid rner for
+
+ align:start position:0%
+networks before right so Sid rner for
+ 
+
+ align:start position:0%
+networks before right so Sid rner for
+example had already done some analyses
+
+ align:start position:0%
+example had already done some analyses
+ 
+
+ align:start position:0%
+example had already done some analyses
+of citation networks over uh he's a
+
+ align:start position:0%
+of citation networks over uh he's a
+ 
+
+ align:start position:0%
+of citation networks over uh he's a
+theoretical statistical physicist over
+
+ align:start position:0%
+theoretical statistical physicist over
+ 
+
+ align:start position:0%
+theoretical statistical physicist over
+at bu uh but just now I guess moving uh
+
+ align:start position:0%
+at bu uh but just now I guess moving uh
+ 
+
+ align:start position:0%
+at bu uh but just now I guess moving uh
+over to the um Santa Fe Institute okay
+
+ align:start position:0%
+over to the um Santa Fe Institute okay
+ 
+
+ align:start position:0%
+over to the um Santa Fe Institute okay
+but so it's not that he was the first
+
+ align:start position:0%
+but so it's not that he was the first
+ 
+
+ align:start position:0%
+but so it's not that he was the first
+person to make that observation but he
+
+ align:start position:0%
+person to make that observation but he
+ 
+
+ align:start position:0%
+person to make that observation but he
+knew that there but the obser you know
+
+ align:start position:0%
+knew that there but the obser you know
+ 
+
+ align:start position:0%
+knew that there but the obser you know
+he knew there was something interesting
+
+ align:start position:0%
+he knew there was something interesting
+ 
+
+ align:start position:0%
+he knew there was something interesting
+that needed to be explained right so I'd
+
+ align:start position:0%
+that needed to be explained right so I'd
+ 
+
+ align:start position:0%
+that needed to be explained right so I'd
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+that whatever you know for for any of
+
+ align:start position:0%
+that whatever you know for for any of
+ 
+
+ align:start position:0%
+that whatever you know for for any of
+you that are going thinking about doing
+
+ align:start position:0%
+you that are going thinking about doing
+ 
+
+ align:start position:0%
+you that are going thinking about doing
+Theory or writing down models I I I
+
+ align:start position:0%
+Theory or writing down models I I I
+ 
+
+ align:start position:0%
+Theory or writing down models I I I
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+say whenever possible start start with
+
+ align:start position:0%
+say whenever possible start start with
+ 
+
+ align:start position:0%
+say whenever possible start start with
+an interesting observation
+
+ align:start position:0%
+an interesting observation
+ 
+
+ align:start position:0%
+an interesting observation
+okay all right so can somebody maybe you
+
+ align:start position:0%
+okay all right so can somebody maybe you
+ 
+
+ align:start position:0%
+okay all right so can somebody maybe you
+guys could just throw out what are some
+
+ align:start position:0%
+guys could just throw out what are some
+ 
+
+ align:start position:0%
+guys could just throw out what are some
+examples of nodes and edges that were
+
+ align:start position:0%
+examples of nodes and edges that were
+ 
+
+ align:start position:0%
+examples of nodes and edges that were
+given there or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elsewhere pages and links all right web
+
+ align:start position:0%
+elsewhere pages and links all right web
+ 
+
+ align:start position:0%
+elsewhere pages and links all right web
+pages and links
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and uh is this a directed or
+
+ align:start position:0%
+all right and uh is this a directed or
+ 
+
+ align:start position:0%
+all right and uh is this a directed or
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+undirected yes so this is indeed
+
+ align:start position:0%
+undirected yes so this is indeed
+ 
+
+ align:start position:0%
+undirected yes so this is indeed
+directed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right some
+
+ align:start position:0%
+right right some
+ 
+
+ align:start position:0%
+right right some
+others movies movie stars and movies
+
+ align:start position:0%
+others movies movie stars and movies
+ 
+
+ align:start position:0%
+others movies movie stars and movies
+yeah this one's a funny one right okay
+
+ align:start position:0%
+yeah this one's a funny one right okay
+ 
+
+ align:start position:0%
+yeah this one's a funny one right okay
+yeah so movie
+
+ align:start position:0%
+yeah so movie
+ 
+
+ align:start position:0%
+yeah so movie
+stars and then um right and this this is
+
+ align:start position:0%
+stars and then um right and this this is
+ 
+
+ align:start position:0%
+stars and then um right and this this is
+this is um this is like being in a movie
+
+ align:start position:0%
+this is um this is like being in a movie
+ 
+
+ align:start position:0%
+this is um this is like being in a movie
+together right so co-starring or so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+others articles and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+citations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+articles
+
+ align:start position:0%
+articles
+ 
+
+ align:start position:0%
+articles
+citations all right and this is again
+
+ align:start position:0%
+citations all right and this is again
+ 
+
+ align:start position:0%
+citations all right and this is again
+directed and this is not directed
+
+ align:start position:0%
+directed and this is not directed
+ 
+
+ align:start position:0%
+directed and this is not directed
+right um and and we can maybe even try
+
+ align:start position:0%
+right um and and we can maybe even try
+ 
+
+ align:start position:0%
+right um and and we can maybe even try
+to remind ourselves this this fell off
+
+ align:start position:0%
+to remind ourselves this this fell off
+ 
+
+ align:start position:0%
+to remind ourselves this this fell off
+as alpha alpha was equal to what I guess
+
+ align:start position:0%
+as alpha alpha was equal to what I guess
+ 
+
+ align:start position:0%
+as alpha alpha was equal to what I guess
+it was three I think they
+
+ align:start position:0%
+it was three I think they
+ 
+
+ align:start position:0%
+it was three I think they
+said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actors were around 2.3 I guess they
+
+ align:start position:0%
+actors were around 2.3 I guess they
+ 
+
+ align:start position:0%
+actors were around 2.3 I guess they
+said all right the web was 2.1 okay all
+
+ align:start position:0%
+said all right the web was 2.1 okay all
+ 
+
+ align:start position:0%
+said all right the web was 2.1 okay all
+right so you know just because it's a
+
+ align:start position:0%
+right so you know just because it's a
+ 
+
+ align:start position:0%
+right so you know just because it's a
+power law doesn't mean that it's always
+
+ align:start position:0%
+power law doesn't mean that it's always
+ 
+
+ align:start position:0%
+power law doesn't mean that it's always
+going to have the same Alpha right um
+
+ align:start position:0%
+going to have the same Alpha right um
+ 
+
+ align:start position:0%
+going to have the same Alpha right um
+but for example what this means is
+
+ align:start position:0%
+but for example what this means is
+ 
+
+ align:start position:0%
+but for example what this means is
+that for every paper that has
+
+ align:start position:0%
+that for every paper that has
+ 
+
+ align:start position:0%
+that for every paper that has
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+say 200 citations there are going to be
+
+ align:start position:0%
+say 200 citations there are going to be
+ 
+
+ align:start position:0%
+say 200 citations there are going to be
+roughly 10 papers that have 100
+
+ align:start position:0%
+roughly 10 papers that have 100
+ 
+
+ align:start position:0%
+roughly 10 papers that have 100
+citations right because if you increase
+
+ align:start position:0%
+citations right because if you increase
+ 
+
+ align:start position:0%
+citations right because if you increase
+K by factor of two you get almost an
+
+ align:start position:0%
+K by factor of two you get almost an
+ 
+
+ align:start position:0%
+K by factor of two you get almost an
+order of magnitude in term in terms of
+
+ align:start position:0%
+order of magnitude in term in terms of
+ 
+
+ align:start position:0%
+order of magnitude in term in terms of
+the probability
+
+ align:start position:0%
+the probability
+ 
+
+ align:start position:0%
+the probability
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so so all right so this
+
+ align:start position:0%
+okay all right so so all right so this
+ 
+
+ align:start position:0%
+okay all right so so all right so this
+is an observation and and where barbos
+
+ align:start position:0%
+is an observation and and where barbos
+ 
+
+ align:start position:0%
+is an observation and and where barbos
+came in and said all right well what
+
+ align:start position:0%
+came in and said all right well what
+ 
+
+ align:start position:0%
+came in and said all right well what
+would be a model that would recapitulate
+
+ align:start position:0%
+would be a model that would recapitulate
+ 
+
+ align:start position:0%
+would be a model that would recapitulate
+this okay and and what are the models
+
+ align:start position:0%
+this okay and and what are the models
+ 
+
+ align:start position:0%
+this okay and and what are the models
+that uh that did not recapitulate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it right so the Eros sheni okay so uh so
+
+ align:start position:0%
+it right so the Eros sheni okay so uh so
+ 
+
+ align:start position:0%
+it right so the Eros sheni okay so uh so
+other um other models right there was
+
+ align:start position:0%
+other um other models right there was
+ 
+
+ align:start position:0%
+other um other models right there was
+the ER other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+models there was the soal Eros reny
+
+ align:start position:0%
+models there was the soal Eros reny
+ 
+
+ align:start position:0%
+models there was the soal Eros reny
+Network um random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Network okay right and that's uh because
+
+ align:start position:0%
+Network okay right and that's uh because
+ 
+
+ align:start position:0%
+Network okay right and that's uh because
+the here the the degree distribution is
+
+ align:start position:0%
+the here the the degree distribution is
+ 
+
+ align:start position:0%
+the here the the degree distribution is
+peaked around something and then falls
+
+ align:start position:0%
+peaked around something and then falls
+ 
+
+ align:start position:0%
+peaked around something and then falls
+off exponentially as you go above that
+
+ align:start position:0%
+off exponentially as you go above that
+ 
+
+ align:start position:0%
+off exponentially as you go above that
+um and this is actually where the I
+
+ align:start position:0%
+um and this is actually where the I
+ 
+
+ align:start position:0%
+um and this is actually where the I
+think the equations are wrong in terms
+
+ align:start position:0%
+think the equations are wrong in terms
+ 
+
+ align:start position:0%
+think the equations are wrong in terms
+in this in this paper um because you
+
+ align:start position:0%
+in this in this paper um because you
+ 
+
+ align:start position:0%
+in this in this paper um because you
+know if if you look at the paper page
+
+ align:start position:0%
+know if if you look at the paper page
+ 
+
+ align:start position:0%
+know if if you look at the paper page
+510 right they say the Eros Reni uh you
+
+ align:start position:0%
+510 right they say the Eros Reni uh you
+ 
+
+ align:start position:0%
+510 right they say the Eros Reni uh you
+connect the edges with p and then they
+
+ align:start position:0%
+connect the edges with p and then they
+ 
+
+ align:start position:0%
+connect the edges with p and then they
+say uh you get a Pon distribution P of K
+
+ align:start position:0%
+say uh you get a Pon distribution P of K
+ 
+
+ align:start position:0%
+say uh you get a Pon distribution P of K
+where you where Lambda the mean is
+
+ align:start position:0%
+where you where Lambda the mean is
+ 
+
+ align:start position:0%
+where you where Lambda the mean is
+something but then they say oh Lambda is
+
+ align:start position:0%
+something but then they say oh Lambda is
+ 
+
+ align:start position:0%
+something but then they say oh Lambda is
+equal to some binomial something of K
+
+ align:start position:0%
+equal to some binomial something of K
+ 
+
+ align:start position:0%
+equal to some binomial something of K
+and so forth um so I think that this is
+
+ align:start position:0%
+and so forth um so I think that this is
+ 
+
+ align:start position:0%
+and so forth um so I think that this is
+all not true but rather that it um you
+
+ align:start position:0%
+all not true but rather that it um you
+ 
+
+ align:start position:0%
+all not true but rather that it um you
+can approximate the binomial with a Pon
+
+ align:start position:0%
+can approximate the binomial with a Pon
+ 
+
+ align:start position:0%
+can approximate the binomial with a Pon
+and the limit of small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PS okay so beware if you're um looking
+
+ align:start position:0%
+PS okay so beware if you're um looking
+ 
+
+ align:start position:0%
+PS okay so beware if you're um looking
+at that
+
+ align:start position:0%
+at that
+ 
+
+ align:start position:0%
+at that
+um all right there there was another
+
+ align:start position:0%
+um all right there there was another
+ 
+
+ align:start position:0%
+um all right there there was another
+Network that uh that oh do you have a
+
+ align:start position:0%
+Network that uh that oh do you have a
+ 
+
+ align:start position:0%
+Network that uh that oh do you have a
+question um all right so we'll you know
+
+ align:start position:0%
+question um all right so we'll you know
+ 
+
+ align:start position:0%
+question um all right so we'll you know
+we'll you know we we're going to spend a
+
+ align:start position:0%
+we'll you know we we're going to spend a
+ 
+
+ align:start position:0%
+we'll you know we we're going to spend a
+lot of time talking about probity
+
+ align:start position:0%
+lot of time talking about probity
+ 
+
+ align:start position:0%
+lot of time talking about probity
+distributions in the coming weeks but I
+
+ align:start position:0%
+distributions in the coming weeks but I
+ 
+
+ align:start position:0%
+distributions in the coming weeks but I
+just wanted to highlight that there is
+
+ align:start position:0%
+just wanted to highlight that there is
+ 
+
+ align:start position:0%
+just wanted to highlight that there is
+as far as I can tell that that is not
+
+ align:start position:0%
+as far as I can tell that that is not
+ 
+
+ align:start position:0%
+as far as I can tell that that is not
+true what they say um all right but
+
+ align:start position:0%
+true what they say um all right but
+ 
+
+ align:start position:0%
+true what they say um all right but
+there there there was one other uh model
+
+ align:start position:0%
+there there there was one other uh model
+ 
+
+ align:start position:0%
+there there there was one other uh model
+for a network that they they talk about
+
+ align:start position:0%
+for a network that they they talk about
+ 
+
+ align:start position:0%
+for a network that they they talk about
+or they mention does any anybody small
+
+ align:start position:0%
+or they mention does any anybody small
+ 
+
+ align:start position:0%
+or they mention does any anybody small
+the so-called small world Network right
+
+ align:start position:0%
+the so-called small world Network right
+ 
+
+ align:start position:0%
+the so-called small world Network right
+um and this is
+
+ align:start position:0%
+um and this is
+ 
+
+ align:start position:0%
+um and this is
+um small world Network and this this is
+
+ align:start position:0%
+um small world Network and this this is
+ 
+
+ align:start position:0%
+um small world Network and this this is
+based on a paper by
+
+ align:start position:0%
+based on a paper by
+ 
+
+ align:start position:0%
+based on a paper by
+stroets
+
+ align:start position:0%
+stroets
+ 
+
+ align:start position:0%
+stroets
+and yeah watts and stroat Okay small
+
+ align:start position:0%
+and yeah watts and stroat Okay small
+ 
+
+ align:start position:0%
+and yeah watts and stroat Okay small
+world that's
+
+ align:start position:0%
+world that's
+ 
+
+ align:start position:0%
+world that's
+watts and
+
+ align:start position:0%
+watts and
+ 
+
+ align:start position:0%
+watts and
+stroots right and and and and this this
+
+ align:start position:0%
+stroots right and and and and this this
+ 
+
+ align:start position:0%
+stroots right and and and and this this
+is this was a paper where they they
+
+ align:start position:0%
+is this was a paper where they they
+ 
+
+ align:start position:0%
+is this was a paper where they they
+demonstrated that there was a very
+
+ align:start position:0%
+demonstrated that there was a very
+ 
+
+ align:start position:0%
+demonstrated that there was a very
+simple mechanism uh just by kind of like
+
+ align:start position:0%
+simple mechanism uh just by kind of like
+ 
+
+ align:start position:0%
+simple mechanism uh just by kind of like
+rewind ing a network that you could get
+
+ align:start position:0%
+rewind ing a network that you could get
+ 
+
+ align:start position:0%
+rewind ing a network that you could get
+this so-called small world phenomenon
+
+ align:start position:0%
+this so-called small world phenomenon
+ 
+
+ align:start position:0%
+this so-called small world phenomenon
+right where uh you know the Kevin Bacon
+
+ align:start position:0%
+right where uh you know the Kevin Bacon
+ 
+
+ align:start position:0%
+right where uh you know the Kevin Bacon
+thing where you can take any you can
+
+ align:start position:0%
+thing where you can take any you can
+ 
+
+ align:start position:0%
+thing where you can take any you can
+right from Kevin Bacon and this is
+
+ align:start position:0%
+right from Kevin Bacon and this is
+ 
+
+ align:start position:0%
+right from Kevin Bacon and this is
+actually the actor Network right so you
+
+ align:start position:0%
+actually the actor Network right so you
+ 
+
+ align:start position:0%
+actually the actor Network right so you
+can say starting with Kevin Bacon can
+
+ align:start position:0%
+can say starting with Kevin Bacon can
+ 
+
+ align:start position:0%
+can say starting with Kevin Bacon can
+you construct um a list of actors that
+
+ align:start position:0%
+you construct um a list of actors that
+ 
+
+ align:start position:0%
+you construct um a list of actors that
+co-starred with each person that gets
+
+ align:start position:0%
+co-starred with each person that gets
+ 
+
+ align:start position:0%
+co-starred with each person that gets
+you to Any Given actor and the statement
+
+ align:start position:0%
+you to Any Given actor and the statement
+ 
+
+ align:start position:0%
+you to Any Given actor and the statement
+is you're supposed to be able to do that
+
+ align:start position:0%
+is you're supposed to be able to do that
+ 
+
+ align:start position:0%
+is you're supposed to be able to do that
+from you know a path of six right so
+
+ align:start position:0%
+from you know a path of six right so
+ 
+
+ align:start position:0%
+from you know a path of six right so
+that you know all the actors are
+
+ align:start position:0%
+that you know all the actors are
+ 
+
+ align:start position:0%
+that you know all the actors are
+supposed to be connected to Kevin Bacon
+
+ align:start position:0%
+supposed to be connected to Kevin Bacon
+ 
+
+ align:start position:0%
+supposed to be connected to Kevin Bacon
+by six right um although maybe you guys
+
+ align:start position:0%
+by six right um although maybe you guys
+ 
+
+ align:start position:0%
+by six right um although maybe you guys
+don't even remember who Kevin Kevin
+
+ align:start position:0%
+don't even remember who Kevin Kevin
+ 
+
+ align:start position:0%
+don't even remember who Kevin Kevin
+Bacon is anymore is it oh you do okay
+
+ align:start position:0%
+Bacon is anymore is it oh you do okay
+ 
+
+ align:start position:0%
+Bacon is anymore is it oh you do okay
+all right um no but this rule works for
+
+ align:start position:0%
+all right um no but this rule works for
+ 
+
+ align:start position:0%
+all right um no but this rule works for
+anybody so just you know in you know
+
+ align:start position:0%
+anybody so just you know in you know
+ 
+
+ align:start position:0%
+anybody so just you know in you know
+insert your favorite actor into that
+
+ align:start position:0%
+insert your favorite actor into that
+ 
+
+ align:start position:0%
+insert your favorite actor into that
+sentence
+
+ align:start position:0%
+sentence
+ 
+
+ align:start position:0%
+sentence
+um okay and it's important I just just
+
+ align:start position:0%
+um okay and it's important I just just
+ 
+
+ align:start position:0%
+um okay and it's important I just just
+to mention that just because something
+
+ align:start position:0%
+to mention that just because something
+ 
+
+ align:start position:0%
+to mention that just because something
+is a small world network does not mean
+
+ align:start position:0%
+is a small world network does not mean
+ 
+
+ align:start position:0%
+is a small world network does not mean
+that it's it has power law distributions
+
+ align:start position:0%
+that it's it has power law distributions
+ 
+
+ align:start position:0%
+that it's it has power law distributions
+right it may be the case that many power
+
+ align:start position:0%
+right it may be the case that many power
+ 
+
+ align:start position:0%
+right it may be the case that many power
+law networks also have this small world
+
+ align:start position:0%
+law networks also have this small world
+ 
+
+ align:start position:0%
+law networks also have this small world
+character
+
+ align:start position:0%
+character
+ 
+
+ align:start position:0%
+character
+and I'd say maybe even most of them
+
+ align:start position:0%
+and I'd say maybe even most of them
+ 
+
+ align:start position:0%
+and I'd say maybe even most of them
+right because some of those highly
+
+ align:start position:0%
+right because some of those highly
+ 
+
+ align:start position:0%
+right because some of those highly
+connected nodes are going to be useful
+
+ align:start position:0%
+connected nodes are going to be useful
+ 
+
+ align:start position:0%
+connected nodes are going to be useful
+for connecting any anybody to anybody
+
+ align:start position:0%
+for connecting any anybody to anybody
+ 
+
+ align:start position:0%
+for connecting any anybody to anybody
+else but that's not required to get the
+
+ align:start position:0%
+else but that's not required to get the
+ 
+
+ align:start position:0%
+else but that's not required to get the
+small world
+
+ align:start position:0%
+small world
+ 
+
+ align:start position:0%
+small world
+character
+
+ align:start position:0%
+character
+ 
+
+ align:start position:0%
+character
+okay any questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statement question so you can't go from
+
+ align:start position:0%
+statement question so you can't go from
+ 
+
+ align:start position:0%
+statement question so you can't go from
+this small statement strong statement
+
+ align:start position:0%
+this small statement strong statement
+ 
+
+ align:start position:0%
+this small statement strong statement
+conc
+
+ align:start position:0%
+conc
+ 
+
+ align:start position:0%
+conc
+connectivity um
+
+ align:start position:0%
+connectivity um
+ 
+
+ align:start position:0%
+connectivity um
+well I I guess the strong statement is
+
+ align:start position:0%
+well I I guess the strong statement is
+ 
+
+ align:start position:0%
+well I I guess the strong statement is
+that um that this property does not
+
+ align:start position:0%
+that um that this property does not
+ 
+
+ align:start position:0%
+that um that this property does not
+imply that property right I guess yeah
+
+ align:start position:0%
+imply that property right I guess yeah
+ 
+
+ align:start position:0%
+imply that property right I guess yeah
+you're not say the
+
+ align:start position:0%
+you're not say the
+ 
+
+ align:start position:0%
+you're not say the
+invers yeah you know and that seems
+
+ align:start position:0%
+invers yeah you know and that seems
+ 
+
+ align:start position:0%
+invers yeah you know and that seems
+Seems
+
+ align:start position:0%
+Seems
+ 
+
+ align:start position:0%
+Seems
+exed yeah no I I AG I think that this
+
+ align:start position:0%
+exed yeah no I I AG I think that this
+ 
+
+ align:start position:0%
+exed yeah no I I AG I think that this
+small world property that's why I was
+
+ align:start position:0%
+small world property that's why I was
+ 
+
+ align:start position:0%
+small world property that's why I was
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+it's okay what I do not know is whether
+
+ align:start position:0%
+it's okay what I do not know is whether
+ 
+
+ align:start position:0%
+it's okay what I do not know is whether
+it would be possible to construct a uh a
+
+ align:start position:0%
+it would be possible to construct a uh a
+ 
+
+ align:start position:0%
+it would be possible to construct a uh a
+power law distributed Network that does
+
+ align:start position:0%
+power law distributed Network that does
+ 
+
+ align:start position:0%
+power law distributed Network that does
+not have the small world property but
+
+ align:start position:0%
+not have the small world property but
+ 
+
+ align:start position:0%
+not have the small world property but
+what I would say is that uh the ones
+
+ align:start position:0%
+what I would say is that uh the ones
+ 
+
+ align:start position:0%
+what I would say is that uh the ones
+that I'm aware of would have the small
+
+ align:start position:0%
+that I'm aware of would have the small
+ 
+
+ align:start position:0%
+that I'm aware of would have the small
+world property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right any other questions about where
+
+ align:start position:0%
+right any other questions about where
+ 
+
+ align:start position:0%
+right any other questions about where
+where we are right so there's
+
+ align:start position:0%
+where we are right so there's
+ 
+
+ align:start position:0%
+where we are right so there's
+interesting properties of networks that
+
+ align:start position:0%
+interesting properties of networks that
+ 
+
+ align:start position:0%
+interesting properties of networks that
+we would like to explain right and um I
+
+ align:start position:0%
+we would like to explain right and um I
+ 
+
+ align:start position:0%
+we would like to explain right and um I
+would say that what uh what this paper
+
+ align:start position:0%
+would say that what uh what this paper
+ 
+
+ align:start position:0%
+would say that what uh what this paper
+does I think kind of convincingly is
+
+ align:start position:0%
+does I think kind of convincingly is
+ 
+
+ align:start position:0%
+does I think kind of convincingly is
+that they demonstrate that at least this
+
+ align:start position:0%
+that they demonstrate that at least this
+ 
+
+ align:start position:0%
+that they demonstrate that at least this
+model and we'll get into the assumptions
+
+ align:start position:0%
+model and we'll get into the assumptions
+ 
+
+ align:start position:0%
+model and we'll get into the assumptions
+does lead to a power law distributed
+
+ align:start position:0%
+does lead to a power law distributed
+ 
+
+ align:start position:0%
+does lead to a power law distributed
+Network okay um now uh in the um there
+
+ align:start position:0%
+Network okay um now uh in the um there
+ 
+
+ align:start position:0%
+Network okay um now uh in the um there
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+uh yeah there the the answer to the
+
+ align:start position:0%
+uh yeah there the the answer to the
+ 
+
+ align:start position:0%
+uh yeah there the the answer to the
+reading questions about about whether
+
+ align:start position:0%
+reading questions about about whether
+ 
+
+ align:start position:0%
+reading questions about about whether
+both of these is strictly necessary I
+
+ align:start position:0%
+both of these is strictly necessary I
+ 
+
+ align:start position:0%
+both of these is strictly necessary I
+think was it was an interesting one
+
+ align:start position:0%
+think was it was an interesting one
+ 
+
+ align:start position:0%
+think was it was an interesting one
+right and and I I'd say that this this
+
+ align:start position:0%
+right and and I I'd say that this this
+ 
+
+ align:start position:0%
+right and and I I'd say that this this
+gets into the wider issue of um you know
+
+ align:start position:0%
+gets into the wider issue of um you know
+ 
+
+ align:start position:0%
+gets into the wider issue of um you know
+there's a observation that is maybe
+
+ align:start position:0%
+there's a observation that is maybe
+ 
+
+ align:start position:0%
+there's a observation that is maybe
+interesting okay and then we want to
+
+ align:start position:0%
+interesting okay and then we want to
+ 
+
+ align:start position:0%
+interesting okay and then we want to
+understand why that might be and you
+
+ align:start position:0%
+understand why that might be and you
+ 
+
+ align:start position:0%
+understand why that might be and you
+then then what you can do is you can
+
+ align:start position:0%
+then then what you can do is you can
+ 
+
+ align:start position:0%
+then then what you can do is you can
+write down a model that leads to that
+
+ align:start position:0%
+write down a model that leads to that
+ 
+
+ align:start position:0%
+write down a model that leads to that
+behavior okay we've already talked about
+
+ align:start position:0%
+behavior okay we've already talked about
+ 
+
+ align:start position:0%
+behavior okay we've already talked about
+this does that prove that the
+
+ align:start position:0%
+this does that prove that the
+ 
+
+ align:start position:0%
+this does that prove that the
+assumptions of the model are
+
+ align:start position:0%
+assumptions of the model are
+ 
+
+ align:start position:0%
+assumptions of the model are
+correct no in this case these are pretty
+
+ align:start position:0%
+correct no in this case these are pretty
+ 
+
+ align:start position:0%
+correct no in this case these are pretty
+generic features of lots and lots of the
+
+ align:start position:0%
+generic features of lots and lots of the
+ 
+
+ align:start position:0%
+generic features of lots and lots of the
+network so we we tend not so we I'd say
+
+ align:start position:0%
+network so we we tend not so we I'd say
+ 
+
+ align:start position:0%
+network so we we tend not so we I'd say
+when you read it you kind of believe
+
+ align:start position:0%
+when you read it you kind of believe
+ 
+
+ align:start position:0%
+when you read it you kind of believe
+that this is a dominant mechanism but it
+
+ align:start position:0%
+that this is a dominant mechanism but it
+ 
+
+ align:start position:0%
+that this is a dominant mechanism but it
+it very much does not prove that these
+
+ align:start position:0%
+it very much does not prove that these
+ 
+
+ align:start position:0%
+it very much does not prove that these
+are the only this you know this is not
+
+ align:start position:0%
+are the only this you know this is not
+ 
+
+ align:start position:0%
+are the only this you know this is not
+at all the only way to get a power law
+
+ align:start position:0%
+at all the only way to get a power law
+ 
+
+ align:start position:0%
+at all the only way to get a power law
+distributed Network right and I'd say
+
+ align:start position:0%
+distributed Network right and I'd say
+ 
+
+ align:start position:0%
+distributed Network right and I'd say
+that some of the language in the paper
+
+ align:start position:0%
+that some of the language in the paper
+ 
+
+ align:start position:0%
+that some of the language in the paper
+might kind of lead you to believe that
+
+ align:start position:0%
+might kind of lead you to believe that
+ 
+
+ align:start position:0%
+might kind of lead you to believe that
+that is the case and I think that that's
+
+ align:start position:0%
+that is the case and I think that that's
+ 
+
+ align:start position:0%
+that is the case and I think that that's
+you know this is a standard logical
+
+ align:start position:0%
+you know this is a standard logical
+ 
+
+ align:start position:0%
+you know this is a standard logical
+fallacy that we have to be careful of
+
+ align:start position:0%
+fallacy that we have to be careful of
+ 
+
+ align:start position:0%
+fallacy that we have to be careful of
+and some of and I think that some of the
+
+ align:start position:0%
+and some of and I think that some of the
+ 
+
+ align:start position:0%
+and some of and I think that some of the
+language is a little bit dangerous you
+
+ align:start position:0%
+language is a little bit dangerous you
+ 
+
+ align:start position:0%
+language is a little bit dangerous you
+know so the de development of the power
+
+ align:start position:0%
+know so the de development of the power
+ 
+
+ align:start position:0%
+know so the de development of the power
+law scaling of the model indicates that
+
+ align:start position:0%
+law scaling of the model indicates that
+ 
+
+ align:start position:0%
+law scaling of the model indicates that
+growth and preferential attachment play
+
+ align:start position:0%
+growth and preferential attachment play
+ 
+
+ align:start position:0%
+growth and preferential attachment play
+an important role ink you know I you
+
+ align:start position:0%
+an important role ink you know I you
+ 
+
+ align:start position:0%
+an important role ink you know I you
+know I would say that it's it's I think
+
+ align:start position:0%
+know I would say that it's it's I think
+ 
+
+ align:start position:0%
+know I would say that it's it's I think
+it's probably true but you know but once
+
+ align:start position:0%
+it's probably true but you know but once
+ 
+
+ align:start position:0%
+it's probably true but you know but once
+again you know it's a question of this
+
+ align:start position:0%
+again you know it's a question of this
+ 
+
+ align:start position:0%
+again you know it's a question of this
+is certainly not a proof that th that
+
+ align:start position:0%
+is certainly not a proof that th that
+ 
+
+ align:start position:0%
+is certainly not a proof that th that
+those assumptions are relevant for any
+
+ align:start position:0%
+those assumptions are relevant for any
+ 
+
+ align:start position:0%
+those assumptions are relevant for any
+given network of
+
+ align:start position:0%
+given network of
+ 
+
+ align:start position:0%
+given network of
+course in all these cases the network
+
+ align:start position:0%
+course in all these cases the network
+ 
+
+ align:start position:0%
+course in all these cases the network
+does grow and there is preferential ATT
+
+ align:start position:0%
+does grow and there is preferential ATT
+ 
+
+ align:start position:0%
+does grow and there is preferential ATT
+attachment um but you know it's also
+
+ align:start position:0%
+attachment um but you know it's also
+ 
+
+ align:start position:0%
+attachment um but you know it's also
+there are other things that are also
+
+ align:start position:0%
+there are other things that are also
+ 
+
+ align:start position:0%
+there are other things that are also
+true that may be important for example
+
+ align:start position:0%
+true that may be important for example
+ 
+
+ align:start position:0%
+true that may be important for example
+in determining exactly what Alpha is or
+
+ align:start position:0%
+in determining exactly what Alpha is or
+ 
+
+ align:start position:0%
+in determining exactly what Alpha is or
+other things and and I think that as
+
+ align:start position:0%
+other things and and I think that as
+ 
+
+ align:start position:0%
+other things and and I think that as
+indicated that there are uh other ways
+
+ align:start position:0%
+indicated that there are uh other ways
+ 
+
+ align:start position:0%
+indicated that there are uh other ways
+of getting power lot networks without
+
+ align:start position:0%
+of getting power lot networks without
+ 
+
+ align:start position:0%
+of getting power lot networks without
+making the exact assumptions that are
+
+ align:start position:0%
+making the exact assumptions that are
+ 
+
+ align:start position:0%
+making the exact assumptions that are
+here but I think it it's um it's in my
+
+ align:start position:0%
+here but I think it it's um it's in my
+ 
+
+ align:start position:0%
+here but I think it it's um it's in my
+mind probably you know a or the dominant
+
+ align:start position:0%
+mind probably you know a or the dominant
+ 
+
+ align:start position:0%
+mind probably you know a or the dominant
+mechanism for in a lot of these networks
+
+ align:start position:0%
+mechanism for in a lot of these networks
+ 
+
+ align:start position:0%
+mechanism for in a lot of these networks
+so I I I think it's a it's a fine paper
+
+ align:start position:0%
+so I I I think it's a it's a fine paper
+ 
+
+ align:start position:0%
+so I I I think it's a it's a fine paper
+but just remember that it doesn't it
+
+ align:start position:0%
+but just remember that it doesn't it
+ 
+
+ align:start position:0%
+but just remember that it doesn't it
+doesn't prove that those are the two the
+
+ align:start position:0%
+doesn't prove that those are the two the
+ 
+
+ align:start position:0%
+doesn't prove that those are the two the
+only two important things right
+
+ align:start position:0%
+only two important things right
+ 
+
+ align:start position:0%
+only two important things right
+um yes just about the preferential
+
+ align:start position:0%
+um yes just about the preferential
+ 
+
+ align:start position:0%
+um yes just about the preferential
+attachments like I think you mentioned
+
+ align:start position:0%
+attachments like I think you mentioned
+ 
+
+ align:start position:0%
+attachments like I think you mentioned
+that we tried yes only yeah yeah this is
+
+ align:start position:0%
+that we tried yes only yeah yeah this is
+ 
+
+ align:start position:0%
+that we tried yes only yeah yeah this is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+troubling yeah yeah I I agree I agree uh
+
+ align:start position:0%
+troubling yeah yeah I I agree I agree uh
+ 
+
+ align:start position:0%
+troubling yeah yeah I I agree I agree uh
+right so uh right and what they what
+
+ align:start position:0%
+right so uh right and what they what
+ 
+
+ align:start position:0%
+right so uh right and what they what
+they assume
+
+ align:start position:0%
+they assume
+ 
+
+ align:start position:0%
+they assume
+in in the model here is that that the
+
+ align:start position:0%
+in in the model here is that that the
+ 
+
+ align:start position:0%
+in in the model here is that that the
+preferential attachment goes linearly
+
+ align:start position:0%
+preferential attachment goes linearly
+ 
+
+ align:start position:0%
+preferential attachment goes linearly
+with the um the number of existing uh
+
+ align:start position:0%
+with the um the number of existing uh
+ 
+
+ align:start position:0%
+with the um the number of existing uh
+edges right and I would say that I very
+
+ align:start position:0%
+edges right and I would say that I very
+ 
+
+ align:start position:0%
+edges right and I would say that I very
+much believe that preferential
+
+ align:start position:0%
+much believe that preferential
+ 
+
+ align:start position:0%
+much believe that preferential
+attachment is present in all those
+
+ align:start position:0%
+attachment is present in all those
+ 
+
+ align:start position:0%
+attachment is present in all those
+things but I'm sure that if you go and
+
+ align:start position:0%
+things but I'm sure that if you go and
+ 
+
+ align:start position:0%
+things but I'm sure that if you go and
+you measure it you're not going to find
+
+ align:start position:0%
+you measure it you're not going to find
+ 
+
+ align:start position:0%
+you measure it you're not going to find
+that it's linear with the number of
+
+ align:start position:0%
+that it's linear with the number of
+ 
+
+ align:start position:0%
+that it's linear with the number of
+edges it's going to I mean okay I
+
+ align:start position:0%
+edges it's going to I mean okay I
+ 
+
+ align:start position:0%
+edges it's going to I mean okay I
+actually I don't know what you'll find
+
+ align:start position:0%
+actually I don't know what you'll find
+ 
+
+ align:start position:0%
+actually I don't know what you'll find
+in each of those cases but there's no
+
+ align:start position:0%
+in each of those cases but there's no
+ 
+
+ align:start position:0%
+in each of those cases but there's no
+reason to believe it has to be linear
+
+ align:start position:0%
+reason to believe it has to be linear
+ 
+
+ align:start position:0%
+reason to believe it has to be linear
+right that being said it may be the
+
+ align:start position:0%
+right that being said it may be the
+ 
+
+ align:start position:0%
+right that being said it may be the
+question is how strong of a deviation
+
+ align:start position:0%
+question is how strong of a deviation
+ 
+
+ align:start position:0%
+question is how strong of a deviation
+from linearity is there and then how
+
+ align:start position:0%
+from linearity is there and then how
+ 
+
+ align:start position:0%
+from linearity is there and then how
+sensitive is the power law Behavior to
+
+ align:start position:0%
+sensitive is the power law Behavior to
+ 
+
+ align:start position:0%
+sensitive is the power law Behavior to
+that and and that's the kind of thing
+
+ align:start position:0%
+that and and that's the kind of thing
+ 
+
+ align:start position:0%
+that and and that's the kind of thing
+that I'm sure that that uh one of the
+
+ align:start position:0%
+that I'm sure that that uh one of the
+ 
+
+ align:start position:0%
+that I'm sure that that uh one of the
+20,000 papers that have cited this paper
+
+ align:start position:0%
+20,000 papers that have cited this paper
+ 
+
+ align:start position:0%
+20,000 papers that have cited this paper
+in the last 15 years address this issue
+
+ align:start position:0%
+in the last 15 years address this issue
+ 
+
+ align:start position:0%
+in the last 15 years address this issue
+right um yeah no but I mean this is also
+
+ align:start position:0%
+right um yeah no but I mean this is also
+ 
+
+ align:start position:0%
+right um yeah no but I mean this is also
+why there are so many papers I mean it's
+
+ align:start position:0%
+why there are so many papers I mean it's
+ 
+
+ align:start position:0%
+why there are so many papers I mean it's
+like you read thiser like oh you know it
+
+ align:start position:0%
+like you read thiser like oh you know it
+ 
+
+ align:start position:0%
+like you read thiser like oh you know it
+would be really interesting to do this
+
+ align:start position:0%
+would be really interesting to do this
+ 
+
+ align:start position:0%
+would be really interesting to do this
+that you know and and people have been
+
+ align:start position:0%
+that you know and and people have been
+ 
+
+ align:start position:0%
+that you know and and people have been
+following that interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay let let's go and uh I think
+
+ align:start position:0%
+right okay let let's go and uh I think
+ 
+
+ align:start position:0%
+right okay let let's go and uh I think
+that the derivation is is a little bit
+
+ align:start position:0%
+that the derivation is is a little bit
+ 
+
+ align:start position:0%
+that the derivation is is a little bit
+tricky U so I think it's worth you know
+
+ align:start position:0%
+tricky U so I think it's worth you know
+ 
+
+ align:start position:0%
+tricky U so I think it's worth you know
+just walking through
+
+ align:start position:0%
+just walking through
+ 
+
+ align:start position:0%
+just walking through
+it um especially since some people
+
+ align:start position:0%
+it um especially since some people
+ 
+
+ align:start position:0%
+it um especially since some people
+apparently couldn't even get the
+
+ align:start position:0%
+apparently couldn't even get the
+ 
+
+ align:start position:0%
+apparently couldn't even get the
+equations which are going to be is going
+
+ align:start position:0%
+equations which are going to be is going
+ 
+
+ align:start position:0%
+equations which are going to be is going
+to it's going to be a problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh and maybe while we're on this
+
+ align:start position:0%
+oh and maybe while we're on this
+ 
+
+ align:start position:0%
+oh and maybe while we're on this
+question of preferential attachment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um how do you guys feel about this
+
+ align:start position:0%
+um how do you guys feel about this
+ 
+
+ align:start position:0%
+um how do you guys feel about this
+question of uh networks within say the
+
+ align:start position:0%
+question of uh networks within say the
+ 
+
+ align:start position:0%
+question of uh networks within say the
+trans the transcriptional network of
+
+ align:start position:0%
+trans the transcriptional network of
+ 
+
+ align:start position:0%
+trans the transcriptional network of
+eoli or other cells I mean do you think
+
+ align:start position:0%
+eoli or other cells I mean do you think
+ 
+
+ align:start position:0%
+eoli or other cells I mean do you think
+that these these properties are are are
+
+ align:start position:0%
+that these these properties are are are
+ 
+
+ align:start position:0%
+that these these properties are are are
+relevant in the cell or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so what would what would growth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean right so growth would correspond to
+
+ align:start position:0%
+mean right so growth would correspond to
+ 
+
+ align:start position:0%
+mean right so growth would correspond to
+adding a new Gene does that ever
+
+ align:start position:0%
+adding a new Gene does that ever
+ 
+
+ align:start position:0%
+adding a new Gene does that ever
+happen okay and what uh can someone give
+
+ align:start position:0%
+happen okay and what uh can someone give
+ 
+
+ align:start position:0%
+happen okay and what uh can someone give
+an a possible mechanism by which a new
+
+ align:start position:0%
+an a possible mechanism by which a new
+ 
+
+ align:start position:0%
+an a possible mechanism by which a new
+Gene is added to the
+
+ align:start position:0%
+Gene is added to the
+ 
+
+ align:start position:0%
+Gene is added to the
+genome right so for example duplication
+
+ align:start position:0%
+genome right so for example duplication
+ 
+
+ align:start position:0%
+genome right so for example duplication
+is common
+
+ align:start position:0%
+is common
+ 
+
+ align:start position:0%
+is common
+right EG
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+duplication and so what is this
+
+ align:start position:0%
+duplication and so what is this
+ 
+
+ align:start position:0%
+duplication and so what is this
+mean for preferential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attachment sorry my phone is we have d
+
+ align:start position:0%
+attachment sorry my phone is we have d
+ 
+
+ align:start position:0%
+attachment sorry my phone is we have d
+the probably also duplicate the
+
+ align:start position:0%
+the probably also duplicate the
+ 
+
+ align:start position:0%
+the probably also duplicate the
+which right so this I think is very
+
+ align:start position:0%
+which right so this I think is very
+ 
+
+ align:start position:0%
+which right so this I think is very
+interesting um right so
+
+ align:start position:0%
+interesting um right so
+ 
+
+ align:start position:0%
+interesting um right so
+duplication you know in general you'll
+
+ align:start position:0%
+duplication you know in general you'll
+ 
+
+ align:start position:0%
+duplication you know in general you'll
+duplicate both the coding region that
+
+ align:start position:0%
+duplicate both the coding region that
+ 
+
+ align:start position:0%
+duplicate both the coding region that
+makes the protein but also maybe the
+
+ align:start position:0%
+makes the protein but also maybe the
+ 
+
+ align:start position:0%
+makes the protein but also maybe the
+promoter region that specifies the
+
+ align:start position:0%
+promoter region that specifies the
+ 
+
+ align:start position:0%
+promoter region that specifies the
+regulation right so if you imagine you
+
+ align:start position:0%
+regulation right so if you imagine you
+ 
+
+ align:start position:0%
+regulation right so if you imagine you
+have some X here that is right and and
+
+ align:start position:0%
+have some X here that is right and and
+ 
+
+ align:start position:0%
+have some X here that is right and and
+we can remind ourselves uh are both the
+
+ align:start position:0%
+we can remind ourselves uh are both the
+ 
+
+ align:start position:0%
+we can remind ourselves uh are both the
+incoming and outgoing edges power LW
+
+ align:start position:0%
+incoming and outgoing edges power LW
+ 
+
+ align:start position:0%
+incoming and outgoing edges power LW
+distributed and transcription networks
+
+ align:start position:0%
+distributed and transcription networks
+ 
+
+ align:start position:0%
+distributed and transcription networks
+no I know this was in the this was the
+
+ align:start position:0%
+no I know this was in the this was the
+ 
+
+ align:start position:0%
+no I know this was in the this was the
+pre-class reading but just in case right
+
+ align:start position:0%
+pre-class reading but just in case right
+ 
+
+ align:start position:0%
+pre-class reading but just in case right
+so it the what you find is that some
+
+ align:start position:0%
+so it the what you find is that some
+ 
+
+ align:start position:0%
+so it the what you find is that some
+transcription factors regulate many
+
+ align:start position:0%
+transcription factors regulate many
+ 
+
+ align:start position:0%
+transcription factors regulate many
+genes but we don't have any any proteins
+
+ align:start position:0%
+genes but we don't have any any proteins
+ 
+
+ align:start position:0%
+genes but we don't have any any proteins
+that are regulated by 200 genes right so
+
+ align:start position:0%
+that are regulated by 200 genes right so
+ 
+
+ align:start position:0%
+that are regulated by 200 genes right so
+in that sense there
+
+ align:start position:0%
+in that sense there
+ 
+
+ align:start position:0%
+in that sense there
+typically right we have things that are
+
+ align:start position:0%
+typically right we have things that are
+ 
+
+ align:start position:0%
+typically right we have things that are
+regulated X there's maybe some X1
+
+ align:start position:0%
+regulated X there's maybe some X1
+ 
+
+ align:start position:0%
+regulated X there's maybe some X1
+X2 X3 right and there might be a few
+
+ align:start position:0%
+X2 X3 right and there might be a few
+ 
+
+ align:start position:0%
+X2 X3 right and there might be a few
+incoming edges right so expression of a
+
+ align:start position:0%
+incoming edges right so expression of a
+ 
+
+ align:start position:0%
+incoming edges right so expression of a
+gene is is typically specified by a few
+
+ align:start position:0%
+gene is is typically specified by a few
+ 
+
+ align:start position:0%
+gene is is typically specified by a few
+transcription factors right whereas some
+
+ align:start position:0%
+transcription factors right whereas some
+ 
+
+ align:start position:0%
+transcription factors right whereas some
+transcription factors might have 100
+
+ align:start position:0%
+transcription factors might have 100
+ 
+
+ align:start position:0%
+transcription factors might have 100
+outgoing edges okay so it's the outgoing
+
+ align:start position:0%
+outgoing edges okay so it's the outgoing
+ 
+
+ align:start position:0%
+outgoing edges okay so it's the outgoing
+edges that are power lot distributed and
+
+ align:start position:0%
+edges that are power lot distributed and
+ 
+
+ align:start position:0%
+edges that are power lot distributed and
+the ingoing you know are closer to being
+
+ align:start position:0%
+the ingoing you know are closer to being
+ 
+
+ align:start position:0%
+the ingoing you know are closer to being
+kind of Plus on or so all right so you
+
+ align:start position:0%
+kind of Plus on or so all right so you
+ 
+
+ align:start position:0%
+kind of Plus on or so all right so you
+can imagine that we have this guy might
+
+ align:start position:0%
+can imagine that we have this guy might
+ 
+
+ align:start position:0%
+can imagine that we have this guy might
+you know have 100 or so and whereas over
+
+ align:start position:0%
+you know have 100 or so and whereas over
+ 
+
+ align:start position:0%
+you know have 100 or so and whereas over
+here some y transcription factor that is
+
+ align:start position:0%
+here some y transcription factor that is
+ 
+
+ align:start position:0%
+here some y transcription factor that is
+just regulating two genes say y1 and Y
+
+ align:start position:0%
+just regulating two genes say y1 and Y
+ 
+
+ align:start position:0%
+just regulating two genes say y1 and Y
+two okay
+
+ align:start position:0%
+two okay
+ 
+
+ align:start position:0%
+two okay
+now question is if Gene duplication
+
+ align:start position:0%
+now question is if Gene duplication
+ 
+
+ align:start position:0%
+now question is if Gene duplication
+occurs kind of randomly throughout the
+
+ align:start position:0%
+occurs kind of randomly throughout the
+ 
+
+ align:start position:0%
+occurs kind of randomly throughout the
+genome you know
+
+ align:start position:0%
+genome you know
+ 
+
+ align:start position:0%
+genome you know
+which Target or you know which which
+
+ align:start position:0%
+which Target or you know which which
+ 
+
+ align:start position:0%
+which Target or you know which which
+transcription Factor X or Y is more
+
+ align:start position:0%
+transcription Factor X or Y is more
+ 
+
+ align:start position:0%
+transcription Factor X or Y is more
+likely to have a Target that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+duplicated X all right interestingly how
+
+ align:start position:0%
+duplicated X all right interestingly how
+ 
+
+ align:start position:0%
+duplicated X all right interestingly how
+does that scale with the number of
+
+ align:start position:0%
+does that scale with the number of
+ 
+
+ align:start position:0%
+does that scale with the number of
+targets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linear this actually is linear right so
+
+ align:start position:0%
+linear this actually is linear right so
+ 
+
+ align:start position:0%
+linear this actually is linear right so
+so I'd say that that Gene
+
+ align:start position:0%
+so I'd say that that Gene
+ 
+
+ align:start position:0%
+so I'd say that that Gene
+duplication does
+
+ align:start position:0%
+duplication does
+ 
+
+ align:start position:0%
+duplication does
+give growth and preferential attachment
+
+ align:start position:0%
+give growth and preferential attachment
+ 
+
+ align:start position:0%
+give growth and preferential attachment
+that is basically linear with the number
+
+ align:start position:0%
+that is basically linear with the number
+ 
+
+ align:start position:0%
+that is basically linear with the number
+of targets um it's interesting I I'd say
+
+ align:start position:0%
+of targets um it's interesting I I'd say
+ 
+
+ align:start position:0%
+of targets um it's interesting I I'd say
+I find
+
+ align:start position:0%
+I find
+ 
+
+ align:start position:0%
+I find
+this kind of
+
+ align:start position:0%
+this kind of
+ 
+
+ align:start position:0%
+this kind of
+observation quite interesting and
+
+ align:start position:0%
+observation quite interesting and
+ 
+
+ align:start position:0%
+observation quite interesting and
+compelling and makes me feel kind of
+
+ align:start position:0%
+compelling and makes me feel kind of
+ 
+
+ align:start position:0%
+compelling and makes me feel kind of
+comfortable about this as a mechanism
+
+ align:start position:0%
+comfortable about this as a mechanism
+ 
+
+ align:start position:0%
+comfortable about this as a mechanism
+for uh some of the global properties you
+
+ align:start position:0%
+for uh some of the global properties you
+ 
+
+ align:start position:0%
+for uh some of the global properties you
+know I mean this of course there's no
+
+ align:start position:0%
+know I mean this of course there's no
+ 
+
+ align:start position:0%
+know I mean this of course there's no
+selection there's no way to explain you
+
+ align:start position:0%
+selection there's no way to explain you
+ 
+
+ align:start position:0%
+selection there's no way to explain you
+know the interesting Network motifs and
+
+ align:start position:0%
+know the interesting Network motifs and
+ 
+
+ align:start position:0%
+know the interesting Network motifs and
+so forth here but I'd say just in terms
+
+ align:start position:0%
+so forth here but I'd say just in terms
+ 
+
+ align:start position:0%
+so forth here but I'd say just in terms
+of some general properties I think it's
+
+ align:start position:0%
+of some general properties I think it's
+ 
+
+ align:start position:0%
+of some general properties I think it's
+it's interesting of course once again
+
+ align:start position:0%
+it's interesting of course once again
+ 
+
+ align:start position:0%
+it's interesting of course once again
+not approve Evolution can do whatever it
+
+ align:start position:0%
+not approve Evolution can do whatever it
+ 
+
+ align:start position:0%
+not approve Evolution can do whatever it
+wants with these Gene duplication events
+
+ align:start position:0%
+wants with these Gene duplication events
+ 
+
+ align:start position:0%
+wants with these Gene duplication events
+um but you know so I would say you know
+
+ align:start position:0%
+um but you know so I would say you know
+ 
+
+ align:start position:0%
+um but you know so I would say you know
+not everybody finds this argument very
+
+ align:start position:0%
+not everybody finds this argument very
+ 
+
+ align:start position:0%
+not everybody finds this argument very
+uh very compelling but I'd say I think
+
+ align:start position:0%
+uh very compelling but I'd say I think
+ 
+
+ align:start position:0%
+uh very compelling but I'd say I think
+it's kind of I get a warm fuzzy feeling
+
+ align:start position:0%
+it's kind of I get a warm fuzzy feeling
+ 
+
+ align:start position:0%
+it's kind of I get a warm fuzzy feeling
+inside yeah about transcription Network
+
+ align:start position:0%
+inside yeah about transcription Network
+ 
+
+ align:start position:0%
+inside yeah about transcription Network
+it's different from the other networks
+
+ align:start position:0%
+it's different from the other networks
+ 
+
+ align:start position:0%
+it's different from the other networks
+we talking about that also lose Gen Y so
+
+ align:start position:0%
+we talking about that also lose Gen Y so
+ 
+
+ align:start position:0%
+we talking about that also lose Gen Y so
+is there any discussion well you know
+
+ align:start position:0%
+is there any discussion well you know
+ 
+
+ align:start position:0%
+is there any discussion well you know
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+lose you can lose web pages you can you
+
+ align:start position:0%
+lose you can lose web pages you can you
+ 
+
+ align:start position:0%
+lose you can lose web pages you can you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+areast
+
+ align:start position:0%
+areast
+ 
+
+ align:start position:0%
+areast
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+um yeah I I don't know um I find that
+
+ align:start position:0%
+um yeah I I don't know um I find that
+ 
+
+ align:start position:0%
+um yeah I I don't know um I find that
+you know you know lots of links to my
+
+ align:start position:0%
+you know you know lots of links to my
+ 
+
+ align:start position:0%
+you know you know lots of links to my
+web pages just disappear over time and I
+
+ align:start position:0%
+web pages just disappear over time and I
+ 
+
+ align:start position:0%
+web pages just disappear over time and I
+don't know yeah I I it's it's a
+
+ align:start position:0%
+don't know yeah I I it's it's a
+ 
+
+ align:start position:0%
+don't know yeah I I it's it's a
+reasonable question I um I don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right you know in some of these you'd
+
+ align:start position:0%
+right you know in some of these you'd
+ 
+
+ align:start position:0%
+right you know in some of these you'd
+say oh well right so the the web has
+
+ align:start position:0%
+say oh well right so the the web has
+ 
+
+ align:start position:0%
+say oh well right so the the web has
+been growing a lot recently and and and
+
+ align:start position:0%
+been growing a lot recently and and and
+ 
+
+ align:start position:0%
+been growing a lot recently and and and
+so then we'd say that birth dominates
+
+ align:start position:0%
+so then we'd say that birth dominates
+ 
+
+ align:start position:0%
+so then we'd say that birth dominates
+over death there whereas if you talk
+
+ align:start position:0%
+over death there whereas if you talk
+ 
+
+ align:start position:0%
+over death there whereas if you talk
+about genome sizes along different
+
+ align:start position:0%
+about genome sizes along different
+ 
+
+ align:start position:0%
+about genome sizes along different
+lineages it certainly is not growing
+
+ align:start position:0%
+lineages it certainly is not growing
+ 
+
+ align:start position:0%
+lineages it certainly is not growing
+exponentially the way the web yeah I
+
+ align:start position:0%
+exponentially the way the web yeah I
+ 
+
+ align:start position:0%
+exponentially the way the web yeah I
+think that that's fair and true um but
+
+ align:start position:0%
+think that that's fair and true um but
+ 
+
+ align:start position:0%
+think that that's fair and true um but
+we we haven't really actually specified
+
+ align:start position:0%
+we we haven't really actually specified
+ 
+
+ align:start position:0%
+we we haven't really actually specified
+or made clear within a model what
+
+ align:start position:0%
+or made clear within a model what
+ 
+
+ align:start position:0%
+or made clear within a model what
+happens if you allow for birth and death
+
+ align:start position:0%
+happens if you allow for birth and death
+ 
+
+ align:start position:0%
+happens if you allow for birth and death
+right um but I think that uh you you
+
+ align:start position:0%
+right um but I think that uh you you
+ 
+
+ align:start position:0%
+right um but I think that uh you you
+could introduce death and and
+
+ align:start position:0%
+could introduce death and and
+ 
+
+ align:start position:0%
+could introduce death and and
+recapitulate these behaviors so it's not
+
+ align:start position:0%
+recapitulate these behaviors so it's not
+ 
+
+ align:start position:0%
+recapitulate these behaviors so it's not
+I think that it's just because some
+
+ align:start position:0%
+I think that it's just because some
+ 
+
+ align:start position:0%
+I think that it's just because some
+nodes disappear doesn't mean that the
+
+ align:start position:0%
+nodes disappear doesn't mean that the
+ 
+
+ align:start position:0%
+nodes disappear doesn't mean that the
+whole we have to throw the whole idea
+
+ align:start position:0%
+whole we have to throw the whole idea
+ 
+
+ align:start position:0%
+whole we have to throw the whole idea
+out the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+window but um but you know evolu you
+
+ align:start position:0%
+window but um but you know evolu you
+ 
+
+ align:start position:0%
+window but um but you know evolu you
+know in the presence of evolution this
+
+ align:start position:0%
+know in the presence of evolution this
+ 
+
+ align:start position:0%
+know in the presence of evolution this
+is all very complicated right so I you
+
+ align:start position:0%
+is all very complicated right so I you
+ 
+
+ align:start position:0%
+is all very complicated right so I you
+know you can't carry this argument too
+
+ align:start position:0%
+know you can't carry this argument too
+ 
+
+ align:start position:0%
+know you can't carry this argument too
+far
+
+ align:start position:0%
+far
+ 
+
+ align:start position:0%
+far
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+okay so it's linear
+
+ align:start position:0%
+okay so it's linear
+ 
+
+ align:start position:0%
+okay so it's linear
+if has
+
+ align:start position:0%
+if has
+ 
+
+ align:start position:0%
+if has
+one if well what we're assuming is that
+
+ align:start position:0%
+one if well what we're assuming is that
+ 
+
+ align:start position:0%
+one if well what we're assuming is that
+right there's
+
+ align:start position:0%
+right there's
+ 
+
+ align:start position:0%
+right there's
+some you know some segment of DNA that's
+
+ align:start position:0%
+some you know some segment of DNA that's
+ 
+
+ align:start position:0%
+some you know some segment of DNA that's
+in front of the gene that specifi gives
+
+ align:start position:0%
+in front of the gene that specifi gives
+ 
+
+ align:start position:0%
+in front of the gene that specifi gives
+instructions of when to make when to
+
+ align:start position:0%
+instructions of when to make when to
+ 
+
+ align:start position:0%
+instructions of when to make when to
+when to transcribe the the
+
+ align:start position:0%
+when to transcribe the the
+ 
+
+ align:start position:0%
+when to transcribe the the
+gene right so the linearity is just
+
+ align:start position:0%
+gene right so the linearity is just
+ 
+
+ align:start position:0%
+gene right so the linearity is just
+assuming that that's really just
+
+ align:start position:0%
+assuming that that's really just
+ 
+
+ align:start position:0%
+assuming that that's really just
+assuming that genes have kind of the
+
+ align:start position:0%
+assuming that genes have kind of the
+ 
+
+ align:start position:0%
+assuming that genes have kind of the
+same rate of being duplicated on average
+
+ align:start position:0%
+same rate of being duplicated on average
+ 
+
+ align:start position:0%
+same rate of being duplicated on average
+you know and this is a very Global
+
+ align:start position:0%
+you know and this is a very Global
+ 
+
+ align:start position:0%
+you know and this is a very Global
+property so I I think
+
+ align:start position:0%
+property so I I think
+ 
+
+ align:start position:0%
+property so I I think
+that it's you know it's kind of roughly
+
+ align:start position:0%
+that it's you know it's kind of roughly
+ 
+
+ align:start position:0%
+that it's you know it's kind of roughly
+it's a it's a it's I would say it's the
+
+ align:start position:0%
+it's a it's a it's I would say it's the
+ 
+
+ align:start position:0%
+it's a it's a it's I would say it's the
+n model that you would use if you're
+
+ align:start position:0%
+n model that you would use if you're
+ 
+
+ align:start position:0%
+n model that you would use if you're
+going if you had to write down a null
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model um
+
+ align:start position:0%
+model um
+ 
+
+ align:start position:0%
+model um
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+support yeah that's an interesting
+
+ align:start position:0%
+support yeah that's an interesting
+ 
+
+ align:start position:0%
+support yeah that's an interesting
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+uh you know and it's hard to know what
+
+ align:start position:0%
+uh you know and it's hard to know what
+ 
+
+ align:start position:0%
+uh you know and it's hard to know what
+it would even mean to quite be evidenced
+
+ align:start position:0%
+it would even mean to quite be evidenced
+ 
+
+ align:start position:0%
+it would even mean to quite be evidenced
+to support it in the sense that uh
+
+ align:start position:0%
+to support it in the sense that uh
+ 
+
+ align:start position:0%
+to support it in the sense that uh
+you're you're saying along different
+
+ align:start position:0%
+you're you're saying along different
+ 
+
+ align:start position:0%
+you're you're saying along different
+evolutionary lineages could we um say
+
+ align:start position:0%
+evolutionary lineages could we um say
+ 
+
+ align:start position:0%
+evolutionary lineages could we um say
+that it's more likely to grow you know
+
+ align:start position:0%
+that it's more likely to grow you know
+ 
+
+ align:start position:0%
+that it's more likely to grow you know
+of course the other thing to say is that
+
+ align:start position:0%
+of course the other thing to say is that
+ 
+
+ align:start position:0%
+of course the other thing to say is that
+the the rate of of death would also
+
+ align:start position:0%
+the the rate of of death would also
+ 
+
+ align:start position:0%
+the the rate of of death would also
+scale linearly I mean the sense that if
+
+ align:start position:0%
+scale linearly I mean the sense that if
+ 
+
+ align:start position:0%
+scale linearly I mean the sense that if
+a gene being uh stochastically um
+
+ align:start position:0%
+a gene being uh stochastically um
+ 
+
+ align:start position:0%
+a gene being uh stochastically um
+removed from the genome should also
+
+ align:start position:0%
+removed from the genome should also
+ 
+
+ align:start position:0%
+removed from the genome should also
+scale linearly right so it's not that um
+
+ align:start position:0%
+scale linearly right so it's not that um
+ 
+
+ align:start position:0%
+scale linearly right so it's not that um
+you don't actually then expect there to
+
+ align:start position:0%
+you don't actually then expect there to
+ 
+
+ align:start position:0%
+you don't actually then expect there to
+be any um systematic change I mean it's
+
+ align:start position:0%
+be any um systematic change I mean it's
+ 
+
+ align:start position:0%
+be any um systematic change I mean it's
+not as simple as just saying oh the the
+
+ align:start position:0%
+not as simple as just saying oh the the
+ 
+
+ align:start position:0%
+not as simple as just saying oh the the
+the number of targets of um a
+
+ align:start position:0%
+the number of targets of um a
+ 
+
+ align:start position:0%
+the number of targets of um a
+transcription factor with many targets
+
+ align:start position:0%
+transcription factor with many targets
+ 
+
+ align:start position:0%
+transcription factor with many targets
+should grow faster you know it's really
+
+ align:start position:0%
+should grow faster you know it's really
+ 
+
+ align:start position:0%
+should grow faster you know it's really
+that the expectations is it should be
+
+ align:start position:0%
+that the expectations is it should be
+ 
+
+ align:start position:0%
+that the expectations is it should be
+changing faster because they're because
+
+ align:start position:0%
+changing faster because they're because
+ 
+
+ align:start position:0%
+changing faster because they're because
+both duplication and removal would both
+
+ align:start position:0%
+both duplication and removal would both
+ 
+
+ align:start position:0%
+both duplication and removal would both
+be increasing so I think the signature
+
+ align:start position:0%
+be increasing so I think the signature
+ 
+
+ align:start position:0%
+be increasing so I think the signature
+is not totally obvious in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense all right so how many people
+
+ align:start position:0%
+sense all right so how many people
+ 
+
+ align:start position:0%
+sense all right so how many people
+actually tried to piece the piece this
+
+ align:start position:0%
+actually tried to piece the piece this
+ 
+
+ align:start position:0%
+actually tried to piece the piece this
+derivation apart
+
+ align:start position:0%
+derivation apart
+ 
+
+ align:start position:0%
+derivation apart
+anybody all right and did were you happy
+
+ align:start position:0%
+anybody all right and did were you happy
+ 
+
+ align:start position:0%
+anybody all right and did were you happy
+with it at the end of your I think so an
+
+ align:start position:0%
+with it at the end of your I think so an
+ 
+
+ align:start position:0%
+with it at the end of your I think so an
+assumtion near the very end that I was a
+
+ align:start position:0%
+assumtion near the very end that I was a
+ 
+
+ align:start position:0%
+assumtion near the very end that I was a
+little bit okay yeah know it kind of you
+
+ align:start position:0%
+little bit okay yeah know it kind of you
+ 
+
+ align:start position:0%
+little bit okay yeah know it kind of you
+know there is like a Croc of the climb
+
+ align:start position:0%
+know there is like a Croc of the climb
+ 
+
+ align:start position:0%
+know there is like a Croc of the climb
+at the end all right um okay so um all
+
+ align:start position:0%
+at the end all right um okay so um all
+ 
+
+ align:start position:0%
+at the end all right um okay so um all
+right let's just make sure that we um
+
+ align:start position:0%
+right let's just make sure that we um
+ 
+
+ align:start position:0%
+right let's just make sure that we um
+you know we can understand kind of what
+
+ align:start position:0%
+you know we can understand kind of what
+ 
+
+ align:start position:0%
+you know we can understand kind of what
+happened there because it's it's worth
+
+ align:start position:0%
+happened there because it's it's worth
+ 
+
+ align:start position:0%
+happened there because it's it's worth
+you know since we read the paper it's
+
+ align:start position:0%
+you know since we read the paper it's
+ 
+
+ align:start position:0%
+you know since we read the paper it's
+worth trying to figure it out all right
+
+ align:start position:0%
+worth trying to figure it out all right
+ 
+
+ align:start position:0%
+worth trying to figure it out all right
+um okay so so what we're going to assume
+
+ align:start position:0%
+um okay so so what we're going to assume
+ 
+
+ align:start position:0%
+um okay so so what we're going to assume
+is that we
+
+ align:start position:0%
+is that we
+ 
+
+ align:start position:0%
+is that we
+start with uh M uh
+
+ align:start position:0%
+start with uh M uh
+ 
+
+ align:start position:0%
+start with uh M uh
+nodes okay so they're going to be here
+
+ align:start position:0%
+nodes okay so they're going to be here
+ 
+
+ align:start position:0%
+nodes okay so they're going to be here
+and the idea is that doesn't really
+
+ align:start position:0%
+and the idea is that doesn't really
+ 
+
+ align:start position:0%
+and the idea is that doesn't really
+matter how we start this thing they
+
+ align:start position:0%
+matter how we start this thing they
+ 
+
+ align:start position:0%
+matter how we start this thing they
+might start out being unconnected or
+
+ align:start position:0%
+might start out being unconnected or
+ 
+
+ align:start position:0%
+might start out being unconnected or
+they might be connected you know and
+
+ align:start position:0%
+they might be connected you know and
+ 
+
+ align:start position:0%
+they might be connected you know and
+over time you know the signature of how
+
+ align:start position:0%
+over time you know the signature of how
+ 
+
+ align:start position:0%
+over time you know the signature of how
+we start is not supposed to be that
+
+ align:start position:0%
+we start is not supposed to be that
+ 
+
+ align:start position:0%
+we start is not supposed to be that
+important right um and then what we're
+
+ align:start position:0%
+important right um and then what we're
+ 
+
+ align:start position:0%
+important right um and then what we're
+going to do is um at each time point
+
+ align:start position:0%
+going to do is um at each time point
+ 
+
+ align:start position:0%
+going to do is um at each time point
+we're going to add one more
+
+ align:start position:0%
+we're going to add one more
+ 
+
+ align:start position:0%
+we're going to add one more
+node and uh as we do that we're going to
+
+ align:start position:0%
+node and uh as we do that we're going to
+ 
+
+ align:start position:0%
+node and uh as we do that we're going to
+add uh M edges as well okay right so we
+
+ align:start position:0%
+add uh M edges as well okay right so we
+ 
+
+ align:start position:0%
+add uh M edges as well okay right so we
+can uh we then have the number of uh
+
+ align:start position:0%
+can uh we then have the number of uh
+ 
+
+ align:start position:0%
+can uh we then have the number of uh
+we'll say nodes and
+
+ align:start position:0%
+we'll say nodes and
+ 
+
+ align:start position:0%
+we'll say nodes and
+uh as a function of
+
+ align:start position:0%
+uh as a function of
+ 
+
+ align:start position:0%
+uh as a function of
+time is going to be equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what all right this is just going to be
+
+ align:start position:0%
+what all right this is just going to be
+ 
+
+ align:start position:0%
+what all right this is just going to be
+we're going to start at m not and it's
+
+ align:start position:0%
+we're going to start at m not and it's
+ 
+
+ align:start position:0%
+we're going to start at m not and it's
+going to be we're going to add one each
+
+ align:start position:0%
+going to be we're going to add one each
+ 
+
+ align:start position:0%
+going to be we're going to add one each
+time m not plus T number of
+
+ align:start position:0%
+time m not plus T number of
+ 
+
+ align:start position:0%
+time m not plus T number of
+edges is just going to be equal to the
+
+ align:start position:0%
+edges is just going to be equal to the
+ 
+
+ align:start position:0%
+edges is just going to be equal to the
+number that we add each time Point times
+
+ align:start position:0%
+number that we add each time Point times
+ 
+
+ align:start position:0%
+number that we add each time Point times
+times the time okay right so here we're
+
+ align:start position:0%
+times the time okay right so here we're
+ 
+
+ align:start position:0%
+times the time okay right so here we're
+assuming that we start out with these
+
+ align:start position:0%
+assuming that we start out with these
+ 
+
+ align:start position:0%
+assuming that we start out with these
+nodes being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unconnected now uh we're we're given the
+
+ align:start position:0%
+unconnected now uh we're we're given the
+ 
+
+ align:start position:0%
+unconnected now uh we're we're given the
+assumption that there's preferential
+
+ align:start position:0%
+assumption that there's preferential
+ 
+
+ align:start position:0%
+assumption that there's preferential
+attachment right so that means that the
+
+ align:start position:0%
+attachment right so that means that the
+ 
+
+ align:start position:0%
+attachment right so that means that the
+probability of connecting to uh this to
+
+ align:start position:0%
+probability of connecting to uh this to
+ 
+
+ align:start position:0%
+probability of connecting to uh this to
+some I node that has K edges is going to
+
+ align:start position:0%
+some I node that has K edges is going to
+ 
+
+ align:start position:0%
+some I node that has K edges is going to
+be K the I divided by the sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over um all of
+
+ align:start position:0%
+over um all of
+ 
+
+ align:start position:0%
+over um all of
+all of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes all right so the assumption is that
+
+ align:start position:0%
+yes all right so the assumption is that
+ 
+
+ align:start position:0%
+yes all right so the assumption is that
+at each time point we add a new node
+
+ align:start position:0%
+at each time point we add a new node
+ 
+
+ align:start position:0%
+at each time point we add a new node
+let's say this node and with that we
+
+ align:start position:0%
+let's say this node and with that we
+ 
+
+ align:start position:0%
+let's say this node and with that we
+bring in some number M of new edges all
+
+ align:start position:0%
+bring in some number M of new edges all
+ 
+
+ align:start position:0%
+bring in some number M of new edges all
+right so this could be three and then we
+
+ align:start position:0%
+right so this could be three and then we
+ 
+
+ align:start position:0%
+right so this could be three and then we
+go randomly to three of the existing
+
+ align:start position:0%
+go randomly to three of the existing
+ 
+
+ align:start position:0%
+go randomly to three of the existing
+three of the existing nodes right so
+
+ align:start position:0%
+three of the existing nodes right so
+ 
+
+ align:start position:0%
+three of the existing nodes right so
+each time point we add M edges you add
+
+ align:start position:0%
+each time point we add M edges you add
+ 
+
+ align:start position:0%
+each time point we add M edges you add
+you necessarily add them to the
+
+ align:start position:0%
+you necessarily add them to the
+ 
+
+ align:start position:0%
+you necessarily add them to the
+new you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+connect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I'm sorry I don't understand oh yeah
+
+ align:start position:0%
+um I'm sorry I don't understand oh yeah
+ 
+
+ align:start position:0%
+um I'm sorry I don't understand oh yeah
+right so the assumption is that um is
+
+ align:start position:0%
+right so the assumption is that um is
+ 
+
+ align:start position:0%
+right so the assumption is that um is
+that the new the new node is indeed
+
+ align:start position:0%
+that the new the new node is indeed
+ 
+
+ align:start position:0%
+that the new the new node is indeed
+being connected to U right that all M
+
+ align:start position:0%
+being connected to U right that all M
+ 
+
+ align:start position:0%
+being connected to U right that all M
+edges that we're adding are to this new
+
+ align:start position:0%
+edges that we're adding are to this new
+ 
+
+ align:start position:0%
+edges that we're adding are to this new
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+yeah okay all right so this is the
+
+ align:start position:0%
+yeah okay all right so this is the
+ 
+
+ align:start position:0%
+yeah okay all right so this is the
+linear preferential attachment that we
+
+ align:start position:0%
+linear preferential attachment that we
+ 
+
+ align:start position:0%
+linear preferential attachment that we
+were talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right all right so what we want to know
+
+ align:start position:0%
+right all right so what we want to know
+ 
+
+ align:start position:0%
+right all right so what we want to know
+uh first is how um a after a node is is
+
+ align:start position:0%
+uh first is how um a after a node is is
+ 
+
+ align:start position:0%
+uh first is how um a after a node is is
+connected how is it that the number of
+
+ align:start position:0%
+connected how is it that the number of
+ 
+
+ align:start position:0%
+connected how is it that the number of
+edges will grow over
+
+ align:start position:0%
+edges will grow over
+ 
+
+ align:start position:0%
+edges will grow over
+time right what we know is that at when
+
+ align:start position:0%
+time right what we know is that at when
+ 
+
+ align:start position:0%
+time right what we know is that at when
+it's first added it has exactly M uh M
+
+ align:start position:0%
+it's first added it has exactly M uh M
+ 
+
+ align:start position:0%
+it's first added it has exactly M uh M
+edges right so but then but then as new
+
+ align:start position:0%
+edges right so but then but then as new
+ 
+
+ align:start position:0%
+edges right so but then but then as new
+nodes come then we'll maybe get some
+
+ align:start position:0%
+nodes come then we'll maybe get some
+ 
+
+ align:start position:0%
+nodes come then we'll maybe get some
+more and then it'll it'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grow and in particular we want to get um
+
+ align:start position:0%
+grow and in particular we want to get um
+ 
+
+ align:start position:0%
+grow and in particular we want to get um
+you know we're told that there's that
+
+ align:start position:0%
+you know we're told that there's that
+ 
+
+ align:start position:0%
+you know we're told that there's that
+it's going to grow as this differential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation okay so we want we want to kind
+
+ align:start position:0%
+equation okay so we want we want to kind
+ 
+
+ align:start position:0%
+equation okay so we want we want to kind
+of get to this all right and and the way
+
+ align:start position:0%
+of get to this all right and and the way
+ 
+
+ align:start position:0%
+of get to this all right and and the way
+to think about this is that all right
+
+ align:start position:0%
+to think about this is that all right
+ 
+
+ align:start position:0%
+to think about this is that all right
+well how is it that the number of edges
+
+ align:start position:0%
+well how is it that the number of edges
+ 
+
+ align:start position:0%
+well how is it that the number of edges
+will change at each time Point some
+
+ align:start position:0%
+will change at each time Point some
+ 
+
+ align:start position:0%
+will change at each time Point some
+Delta Ki right
+
+ align:start position:0%
+Delta Ki right
+ 
+
+ align:start position:0%
+Delta Ki right
+well the expected number of of edges
+
+ align:start position:0%
+well the expected number of of edges
+ 
+
+ align:start position:0%
+well the expected number of of edges
+that will be attached to some uh to some
+
+ align:start position:0%
+that will be attached to some uh to some
+ 
+
+ align:start position:0%
+that will be attached to some uh to some
+node well that's going to be uh the M
+
+ align:start position:0%
+node well that's going to be uh the M
+ 
+
+ align:start position:0%
+node well that's going to be uh the M
+this is the number of uh the number of
+
+ align:start position:0%
+this is the number of uh the number of
+ 
+
+ align:start position:0%
+this is the number of uh the number of
+edges that were attached by this
+
+ align:start position:0%
+edges that were attached by this
+ 
+
+ align:start position:0%
+edges that were attached by this
+incoming node and times this
+
+ align:start position:0%
+incoming node and times this
+ 
+
+ align:start position:0%
+incoming node and times this
+probability of attaching to this um to
+
+ align:start position:0%
+probability of attaching to this um to
+ 
+
+ align:start position:0%
+probability of attaching to this um to
+this node right so this is is the
+
+ align:start position:0%
+this node right so this is is the
+ 
+
+ align:start position:0%
+this node right so this is is the
+probability of
+
+ align:start position:0%
+probability of
+ 
+
+ align:start position:0%
+probability of
+Ki right now this is in one time
+
+ align:start position:0%
+Ki right now this is in one time
+ 
+
+ align:start position:0%
+Ki right now this is in one time
+step right so this is really a Delta Ki
+
+ align:start position:0%
+step right so this is really a Delta Ki
+ 
+
+ align:start position:0%
+step right so this is really a Delta Ki
+if we want we could say over some delta
+
+ align:start position:0%
+if we want we could say over some delta
+ 
+
+ align:start position:0%
+if we want we could say over some delta
+T which is one
+
+ align:start position:0%
+T which is one
+ 
+
+ align:start position:0%
+T which is one
+right so from that standpoint we can
+
+ align:start position:0%
+right so from that standpoint we can
+ 
+
+ align:start position:0%
+right so from that standpoint we can
+actually then write as a differential
+
+ align:start position:0%
+actually then write as a differential
+ 
+
+ align:start position:0%
+actually then write as a differential
+equation we you say the change in this
+
+ align:start position:0%
+equation we you say the change in this
+ 
+
+ align:start position:0%
+equation we you say the change in this
+number of edges with respect to time is
+
+ align:start position:0%
+number of edges with respect to time is
+ 
+
+ align:start position:0%
+number of edges with respect to time is
+indeed going to be equal to M
+
+ align:start position:0%
+indeed going to be equal to M
+ 
+
+ align:start position:0%
+indeed going to be equal to M
+* this guy
+
+ align:start position:0%
+* this guy
+ 
+
+ align:start position:0%
+* this guy
+here which
+
+ align:start position:0%
+here which
+ 
+
+ align:start position:0%
+here which
+is the number of edges that that that
+
+ align:start position:0%
+is the number of edges that that that
+ 
+
+ align:start position:0%
+is the number of edges that that that
+note has at this time divided by this
+
+ align:start position:0%
+note has at this time divided by this
+ 
+
+ align:start position:0%
+note has at this time divided by this
+sum
+
+ align:start position:0%
+sum
+ 
+
+ align:start position:0%
+sum
+over all those
+
+ align:start position:0%
+over all those
+ 
+
+ align:start position:0%
+over all those
+edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so this is just the kind
+
+ align:start position:0%
+okay all right so this is just the kind
+ 
+
+ align:start position:0%
+okay all right so this is just the kind
+of the expected number of edges to be
+
+ align:start position:0%
+of the expected number of edges to be
+ 
+
+ align:start position:0%
+of the expected number of edges to be
+added to that node at each time Point
+
+ align:start position:0%
+added to that node at each time Point
+ 
+
+ align:start position:0%
+added to that node at each time Point
+okay all right so but what what is this
+
+ align:start position:0%
+okay all right so but what what is this
+ 
+
+ align:start position:0%
+okay all right so but what what is this
+thing uh what is that thing equal to yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did yeah so so this is kind of the
+
+ align:start position:0%
+did yeah so so this is kind of the
+ 
+
+ align:start position:0%
+did yeah so so this is kind of the
+discreet version of the differential of
+
+ align:start position:0%
+discreet version of the differential of
+ 
+
+ align:start position:0%
+discreet version of the differential of
+this differential equation right yeah
+
+ align:start position:0%
+this differential equation right yeah
+ 
+
+ align:start position:0%
+this differential equation right yeah
+that's right that's right yeah um and of
+
+ align:start position:0%
+that's right that's right yeah um and of
+ 
+
+ align:start position:0%
+that's right that's right yeah um and of
+course uh the beginning could be highly
+
+ align:start position:0%
+course uh the beginning could be highly
+ 
+
+ align:start position:0%
+course uh the beginning could be highly
+stochastic right but we're just we're
+
+ align:start position:0%
+stochastic right but we're just we're
+ 
+
+ align:start position:0%
+stochastic right but we're just we're
+just thinking about it in the limit of
+
+ align:start position:0%
+just thinking about it in the limit of
+ 
+
+ align:start position:0%
+just thinking about it in the limit of
+if if it's deterministic
+
+ align:start position:0%
+if if it's deterministic
+ 
+
+ align:start position:0%
+if if it's deterministic
+right right so what is this
+
+ align:start position:0%
+right right so what is this
+ 
+
+ align:start position:0%
+right right so what is this
+thing in terms I mean so from here this
+
+ align:start position:0%
+thing in terms I mean so from here this
+ 
+
+ align:start position:0%
+thing in terms I mean so from here this
+was just a normalization constant right
+
+ align:start position:0%
+was just a normalization constant right
+ 
+
+ align:start position:0%
+was just a normalization constant right
+because you know each Edge has to be
+
+ align:start position:0%
+because you know each Edge has to be
+ 
+
+ align:start position:0%
+because you know each Edge has to be
+attached somewhere we're assuming it's
+
+ align:start position:0%
+attached somewhere we're assuming it's
+ 
+
+ align:start position:0%
+attached somewhere we're assuming it's
+linear with respect to the number of
+
+ align:start position:0%
+linear with respect to the number of
+ 
+
+ align:start position:0%
+linear with respect to the number of
+edges at each node right and that means
+
+ align:start position:0%
+edges at each node right and that means
+ 
+
+ align:start position:0%
+edges at each node right and that means
+that for normalization we have
+
+ align:start position:0%
+that for normalization we have
+ 
+
+ align:start position:0%
+that for normalization we have
+to divide by the sum over all those
+
+ align:start position:0%
+to divide by the sum over all those
+ 
+
+ align:start position:0%
+to divide by the sum over all those
+edges right that the edges that each of
+
+ align:start position:0%
+edges right that the edges that each of
+ 
+
+ align:start position:0%
+edges right that the edges that each of
+the each of the nodes might have but how
+
+ align:start position:0%
+the each of the nodes might have but how
+ 
+
+ align:start position:0%
+the each of the nodes might have but how
+what is this thing equal to in terms of
+
+ align:start position:0%
+what is this thing equal to in terms of
+ 
+
+ align:start position:0%
+what is this thing equal to in terms of
+something else that we might have on the
+
+ align:start position:0%
+something else that we might have on the
+ 
+
+ align:start position:0%
+something else that we might have on the
+board yeah edges
+
+ align:start position:0%
+board yeah edges
+ 
+
+ align:start position:0%
+board yeah edges
+to right okay so I guess the question is
+
+ align:start position:0%
+to right okay so I guess the question is
+ 
+
+ align:start position:0%
+to right okay so I guess the question is
+well is this can we write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this you know e where e is a function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time is is is that
+
+ align:start position:0%
+time is is is that
+ 
+
+ align:start position:0%
+time is is is that
+correct so we're getting
+
+ align:start position:0%
+correct so we're getting
+ 
+
+ align:start position:0%
+correct so we're getting
+shakes right so it's actually 2
+
+ align:start position:0%
+shakes right so it's actually 2
+ 
+
+ align:start position:0%
+shakes right so it's actually 2
+e right because what you notice here is
+
+ align:start position:0%
+e right because what you notice here is
+ 
+
+ align:start position:0%
+e right because what you notice here is
+that this is the sum over all of the
+
+ align:start position:0%
+that this is the sum over all of the
+ 
+
+ align:start position:0%
+that this is the sum over all of the
+edges that each of the nodes have right
+
+ align:start position:0%
+edges that each of the nodes have right
+ 
+
+ align:start position:0%
+edges that each of the nodes have right
+but each Edge is connecting two nodes
+
+ align:start position:0%
+but each Edge is connecting two nodes
+ 
+
+ align:start position:0%
+but each Edge is connecting two nodes
+right so the sum over all these Edge
+
+ align:start position:0%
+right so the sum over all these Edge
+ 
+
+ align:start position:0%
+right so the sum over all these Edge
+distributions is twice the number of
+
+ align:start position:0%
+distributions is twice the number of
+ 
+
+ align:start position:0%
+distributions is twice the number of
+edges okay now I would say as a
+
+ align:start position:0%
+edges okay now I would say as a
+ 
+
+ align:start position:0%
+edges okay now I would say as a
+physicist you know working in biology my
+
+ align:start position:0%
+physicist you know working in biology my
+ 
+
+ align:start position:0%
+physicist you know working in biology my
+general attitude is that a factor of two
+
+ align:start position:0%
+general attitude is that a factor of two
+ 
+
+ align:start position:0%
+general attitude is that a factor of two
+here factor of two there doesn't really
+
+ align:start position:0%
+here factor of two there doesn't really
+ 
+
+ align:start position:0%
+here factor of two there doesn't really
+matter right um but this Factor two
+
+ align:start position:0%
+matter right um but this Factor two
+ 
+
+ align:start position:0%
+matter right um but this Factor two
+actually is relevant because it ends up
+
+ align:start position:0%
+actually is relevant because it ends up
+ 
+
+ align:start position:0%
+actually is relevant because it ends up
+determining the scaling over time right
+
+ align:start position:0%
+determining the scaling over time right
+ 
+
+ align:start position:0%
+determining the scaling over time right
+so um so this is you know you know not
+
+ align:start position:0%
+so um so this is you know you know not
+ 
+
+ align:start position:0%
+so um so this is you know you know not
+all factors of two are created equal and
+
+ align:start position:0%
+all factors of two are created equal and
+ 
+
+ align:start position:0%
+all factors of two are created equal and
+this this is one that is worth that is
+
+ align:start position:0%
+this this is one that is worth that is
+ 
+
+ align:start position:0%
+this this is one that is worth that is
+worth paying attention to okay all right
+
+ align:start position:0%
+worth paying attention to okay all right
+ 
+
+ align:start position:0%
+worth paying attention to okay all right
+does everybody understand why there's
+
+ align:start position:0%
+does everybody understand why there's
+ 
+
+ align:start position:0%
+does everybody understand why there's
+why this is two times the number of
+
+ align:start position:0%
+why this is two times the number of
+ 
+
+ align:start position:0%
+why this is two times the number of
+edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right K1 is equal to 1 K2 is equal
+
+ align:start position:0%
+right right K1 is equal to 1 K2 is equal
+ 
+
+ align:start position:0%
+right right K1 is equal to 1 K2 is equal
+to 1 number of edges is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one yep okay so that means we're in an
+
+ align:start position:0%
+one yep okay so that means we're in an
+ 
+
+ align:start position:0%
+one yep okay so that means we're in an
+undirected network if you were in a
+
+ align:start position:0%
+undirected network if you were in a
+ 
+
+ align:start position:0%
+undirected network if you were in a
+directed Network then you would not have
+
+ align:start position:0%
+directed Network then you would not have
+ 
+
+ align:start position:0%
+directed Network then you would not have
+that fact yes so we are indeed in an
+
+ align:start position:0%
+that fact yes so we are indeed in an
+ 
+
+ align:start position:0%
+that fact yes so we are indeed in an
+undirected i' say in a directed Network
+
+ align:start position:0%
+undirected i' say in a directed Network
+ 
+
+ align:start position:0%
+undirected i' say in a directed Network
+you have to then be more careful about
+
+ align:start position:0%
+you have to then be more careful about
+ 
+
+ align:start position:0%
+you have to then be more careful about
+what you I mean you have to specify the
+
+ align:start position:0%
+what you I mean you have to specify the
+ 
+
+ align:start position:0%
+what you I mean you have to specify the
+K's in and K's out so actually already
+
+ align:start position:0%
+K's in and K's out so actually already
+ 
+
+ align:start position:0%
+K's in and K's out so actually already
+just by writing this we've already
+
+ align:start position:0%
+just by writing this we've already
+ 
+
+ align:start position:0%
+just by writing this we've already
+assumed it's undirected because we
+
+ align:start position:0%
+assumed it's undirected because we
+ 
+
+ align:start position:0%
+assumed it's undirected because we
+haven't specified what we mean by K
+
+ align:start position:0%
+haven't specified what we mean by K
+ 
+
+ align:start position:0%
+haven't specified what we mean by K
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um okay all right um we're here but you
+
+ align:start position:0%
+um okay all right um we're here but you
+ 
+
+ align:start position:0%
+um okay all right um we're here but you
+know very we already know how how many
+
+ align:start position:0%
+know very we already know how how many
+ 
+
+ align:start position:0%
+know very we already know how how many
+edges there are as a function of time
+
+ align:start position:0%
+edges there are as a function of time
+ 
+
+ align:start position:0%
+edges there are as a function of time
+right this is just equal to M * T all
+
+ align:start position:0%
+right this is just equal to M * T all
+ 
+
+ align:start position:0%
+right this is just equal to M * T all
+right so we get something that's very
+
+ align:start position:0%
+right so we get something that's very
+ 
+
+ align:start position:0%
+right so we get something that's very
+convenient Ki / 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T right from here we can uh you know we
+
+ align:start position:0%
+T right from here we can uh you know we
+ 
+
+ align:start position:0%
+T right from here we can uh you know we
+can solve the differential equation
+
+ align:start position:0%
+can solve the differential equation
+ 
+
+ align:start position:0%
+can solve the differential equation
+right so this is what we were what we
+
+ align:start position:0%
+right so this is what we were what we
+ 
+
+ align:start position:0%
+right so this is what we were what we
+wanted to show right so uh the fact that
+
+ align:start position:0%
+wanted to show right so uh the fact that
+ 
+
+ align:start position:0%
+wanted to show right so uh the fact that
+we're doing partials doesn't really
+
+ align:start position:0%
+we're doing partials doesn't really
+ 
+
+ align:start position:0%
+we're doing partials doesn't really
+matter because it's just time here right
+
+ align:start position:0%
+matter because it's just time here right
+ 
+
+ align:start position:0%
+matter because it's just time here right
+so it's really so we have d k i over k i
+
+ align:start position:0%
+so it's really so we have d k i over k i
+ 
+
+ align:start position:0%
+so it's really so we have d k i over k i
+is equal to DT over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2T right so this two really again is
+
+ align:start position:0%
+2T right so this two really again is
+ 
+
+ align:start position:0%
+2T right so this two really again is
+going to make a difference because you
+
+ align:start position:0%
+going to make a difference because you
+ 
+
+ align:start position:0%
+going to make a difference because you
+know when we're when we go and we
+
+ align:start position:0%
+know when we're when we go and we
+ 
+
+ align:start position:0%
+know when we're when we go and we
+integrate we get the logs and so forth
+
+ align:start position:0%
+integrate we get the logs and so forth
+ 
+
+ align:start position:0%
+integrate we get the logs and so forth
+right and so we get that Ki as a
+
+ align:start position:0%
+right and so we get that Ki as a
+ 
+
+ align:start position:0%
+right and so we get that Ki as a
+function time is going to grow with time
+
+ align:start position:0%
+function time is going to grow with time
+ 
+
+ align:start position:0%
+function time is going to grow with time
+with some constant C proportionality to
+
+ align:start position:0%
+with some constant C proportionality to
+ 
+
+ align:start position:0%
+with some constant C proportionality to
+the square root of
+
+ align:start position:0%
+the square root of
+ 
+
+ align:start position:0%
+the square root of
+time right so if we didn't have the half
+
+ align:start position:0%
+time right so if we didn't have the half
+ 
+
+ align:start position:0%
+time right so if we didn't have the half
+it would just be linear with time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now uh how how do we know what c in
+
+ align:start position:0%
+now uh how how do we know what c in
+ 
+
+ align:start position:0%
+now uh how how do we know what c in
+general how how do we get constants of
+
+ align:start position:0%
+general how how do we get constants of
+ 
+
+ align:start position:0%
+general how how do we get constants of
+integration in
+
+ align:start position:0%
+integration in
+ 
+
+ align:start position:0%
+integration in
+life yeah boundary conditions in this
+
+ align:start position:0%
+life yeah boundary conditions in this
+ 
+
+ align:start position:0%
+life yeah boundary conditions in this
+case the initial condition what is it
+
+ align:start position:0%
+case the initial condition what is it
+ 
+
+ align:start position:0%
+case the initial condition what is it
+that we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know right so what we know is that Ki so
+
+ align:start position:0%
+know right so what we know is that Ki so
+ 
+
+ align:start position:0%
+know right so what we know is that Ki so
+this this I node when it's added at time
+
+ align:start position:0%
+this this I node when it's added at time
+ 
+
+ align:start position:0%
+this this I node when it's added at time
+TI should be equal to what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M yeah it's equal to M so when it's
+
+ align:start position:0%
+M yeah it's equal to M so when it's
+ 
+
+ align:start position:0%
+M yeah it's equal to M so when it's
+first added at sometime TI its number of
+
+ align:start position:0%
+first added at sometime TI its number of
+ 
+
+ align:start position:0%
+first added at sometime TI its number of
+edges is equal to M because that's
+
+ align:start position:0%
+edges is equal to M because that's
+ 
+
+ align:start position:0%
+edges is equal to M because that's
+that's what we've assumed is that we add
+
+ align:start position:0%
+that's what we've assumed is that we add
+ 
+
+ align:start position:0%
+that's what we've assumed is that we add
+we add a node we connect it randomly to
+
+ align:start position:0%
+we add a node we connect it randomly to
+ 
+
+ align:start position:0%
+we add a node we connect it randomly to
+M other things so it it has M edges
+
+ align:start position:0%
+M other things so it it has M edges
+ 
+
+ align:start position:0%
+M other things so it it has M edges
+initially right so from this K of T this
+
+ align:start position:0%
+initially right so from this K of T this
+ 
+
+ align:start position:0%
+initially right so from this K of T this
+is then equal to M * the sare < TK of T
+
+ align:start position:0%
+is then equal to M * the sare < TK of T
+ 
+
+ align:start position:0%
+is then equal to M * the sare < TK of T
+/ T initial right where TI is the time
+
+ align:start position:0%
+/ T initial right where TI is the time
+ 
+
+ align:start position:0%
+/ T initial right where TI is the time
+that the I node was added to the network
+
+ align:start position:0%
+that the I node was added to the network
+ 
+
+ align:start position:0%
+that the I node was added to the network
+okay are there any questions about how
+
+ align:start position:0%
+okay are there any questions about how
+ 
+
+ align:start position:0%
+okay are there any questions about how
+we got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there all right um so I think that this
+
+ align:start position:0%
+there all right um so I think that this
+ 
+
+ align:start position:0%
+there all right um so I think that this
+is relatively straightforward I think
+
+ align:start position:0%
+is relatively straightforward I think
+ 
+
+ align:start position:0%
+is relatively straightforward I think
+the part that gets confusing are is the
+
+ align:start position:0%
+the part that gets confusing are is the
+ 
+
+ align:start position:0%
+the part that gets confusing are is the
+this this later part about the
+
+ align:start position:0%
+this this later part about the
+ 
+
+ align:start position:0%
+this this later part about the
+probabilities and kind of keeping
+
+ align:start position:0%
+probabilities and kind of keeping
+ 
+
+ align:start position:0%
+probabilities and kind of keeping
+keeping everything straight right so the
+
+ align:start position:0%
+keeping everything straight right so the
+ 
+
+ align:start position:0%
+keeping everything straight right so the
+the what what barasi did next is he said
+
+ align:start position:0%
+the what what barasi did next is he said
+ 
+
+ align:start position:0%
+the what what barasi did next is he said
+all right well what we're going to do is
+
+ align:start position:0%
+all right well what we're going to do is
+ 
+
+ align:start position:0%
+all right well what we're going to do is
+we're going to talk about the
+
+ align:start position:0%
+we're going to talk about the
+ 
+
+ align:start position:0%
+we're going to talk about the
+probability P right right now this is an
+
+ align:start position:0%
+probability P right right now this is an
+ 
+
+ align:start position:0%
+probability P right right now this is an
+actual honest to goodness
+
+ align:start position:0%
+actual honest to goodness
+ 
+
+ align:start position:0%
+actual honest to goodness
+probability okay the big p is actually a
+
+ align:start position:0%
+probability okay the big p is actually a
+ 
+
+ align:start position:0%
+probability okay the big p is actually a
+probability and that's as compared to a
+
+ align:start position:0%
+probability and that's as compared to a
+ 
+
+ align:start position:0%
+probability and that's as compared to a
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+distribution Little
+
+ align:start position:0%
+distribution Little
+ 
+
+ align:start position:0%
+distribution Little
+P and I'll put in a little curly here
+
+ align:start position:0%
+P and I'll put in a little curly here
+ 
+
+ align:start position:0%
+P and I'll put in a little curly here
+thing so that's a little p all right
+
+ align:start position:0%
+thing so that's a little p all right
+ 
+
+ align:start position:0%
+thing so that's a little p all right
+this is saying if you want to get an
+
+ align:start position:0%
+this is saying if you want to get an
+ 
+
+ align:start position:0%
+this is saying if you want to get an
+actual probability here then you have to
+
+ align:start position:0%
+actual probability here then you have to
+ 
+
+ align:start position:0%
+actual probability here then you have to
+multiply that probability distribution
+
+ align:start position:0%
+multiply that probability distribution
+ 
+
+ align:start position:0%
+multiply that probability distribution
+times some range Delta K right so if you
+
+ align:start position:0%
+times some range Delta K right so if you
+ 
+
+ align:start position:0%
+times some range Delta K right so if you
+want to know that the probability that
+
+ align:start position:0%
+want to know that the probability that
+ 
+
+ align:start position:0%
+want to know that the probability that
+some node has between some number and
+
+ align:start position:0%
+some node has between some number and
+ 
+
+ align:start position:0%
+some node has between some number and
+some number of of edges then you
+
+ align:start position:0%
+some number of of edges then you
+ 
+
+ align:start position:0%
+some number of of edges then you
+multiply it by that that
+
+ align:start position:0%
+multiply it by that that
+ 
+
+ align:start position:0%
+multiply it by that that
+range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right probability distribution this is
+
+ align:start position:0%
+right probability distribution this is
+ 
+
+ align:start position:0%
+right probability distribution this is
+an actual probability right and and as
+
+ align:start position:0%
+an actual probability right and and as
+ 
+
+ align:start position:0%
+an actual probability right and and as
+befits an actual probability we're going
+
+ align:start position:0%
+befits an actual probability we're going
+ 
+
+ align:start position:0%
+befits an actual probability we're going
+to say okay the probability that the I
+
+ align:start position:0%
+to say okay the probability that the I
+ 
+
+ align:start position:0%
+to say okay the probability that the I
+the I node has K edges that are less
+
+ align:start position:0%
+the I node has K edges that are less
+ 
+
+ align:start position:0%
+the I node has K edges that are less
+than some value
+
+ align:start position:0%
+than some value
+ 
+
+ align:start position:0%
+than some value
+K and remember this thing is actually a
+
+ align:start position:0%
+K and remember this thing is actually a
+ 
+
+ align:start position:0%
+K and remember this thing is actually a
+function of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but we have an expression for KI as
+
+ align:start position:0%
+okay but we have an expression for KI as
+ 
+
+ align:start position:0%
+okay but we have an expression for KI as
+function of time it's equal to
+
+ align:start position:0%
+function of time it's equal to
+ 
+
+ align:start position:0%
+function of time it's equal to
+this okay so we can kind of we can solve
+
+ align:start position:0%
+this okay so we can kind of we can solve
+ 
+
+ align:start position:0%
+this okay so we can kind of we can solve
+we can show that this probability is
+
+ align:start position:0%
+we can show that this probability is
+ 
+
+ align:start position:0%
+we can show that this probability is
+also the same as this other probability
+
+ align:start position:0%
+also the same as this other probability
+ 
+
+ align:start position:0%
+also the same as this other probability
+that that the node the I node was added
+
+ align:start position:0%
+that that the node the I node was added
+ 
+
+ align:start position:0%
+that that the node the I node was added
+after sometime T that is can be written
+
+ align:start position:0%
+after sometime T that is can be written
+ 
+
+ align:start position:0%
+after sometime T that is can be written
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay so this is saying the
+
+ align:start position:0%
+this okay so this is saying the
+ 
+
+ align:start position:0%
+this okay so this is saying the
+probability that some random say I node
+
+ align:start position:0%
+probability that some random say I node
+ 
+
+ align:start position:0%
+probability that some random say I node
+has fewer than K edges is the same as
+
+ align:start position:0%
+has fewer than K edges is the same as
+ 
+
+ align:start position:0%
+has fewer than K edges is the same as
+saying that the it's the probability
+
+ align:start position:0%
+saying that the it's the probability
+ 
+
+ align:start position:0%
+saying that the it's the probability
+that the I node was added after sometime
+
+ align:start position:0%
+that the I node was added after sometime
+ 
+
+ align:start position:0%
+that the I node was added after sometime
+T which is which is this
+
+ align:start position:0%
+T which is which is this
+ 
+
+ align:start position:0%
+T which is which is this
+thing okay because the number of edges
+
+ align:start position:0%
+thing okay because the number of edges
+ 
+
+ align:start position:0%
+thing okay because the number of edges
+will grow over time for each of each of
+
+ align:start position:0%
+will grow over time for each of each of
+ 
+
+ align:start position:0%
+will grow over time for each of each of
+these nodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay do you guys do you understand the
+
+ align:start position:0%
+okay do you guys do you understand the
+ 
+
+ align:start position:0%
+okay do you guys do you understand the
+the kind of conceptual statement that
+
+ align:start position:0%
+the kind of conceptual statement that
+ 
+
+ align:start position:0%
+the kind of conceptual statement that
+was made there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes any any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions all right so the probability
+
+ align:start position:0%
+questions all right so the probability
+ 
+
+ align:start position:0%
+questions all right so the probability
+that this I node was added after this
+
+ align:start position:0%
+that this I node was added after this
+ 
+
+ align:start position:0%
+that this I node was added after this
+time is also of course one
+
+ align:start position:0%
+time is also of course one
+ 
+
+ align:start position:0%
+time is also of course one
+minus the probability that it was added
+
+ align:start position:0%
+minus the probability that it was added
+ 
+
+ align:start position:0%
+minus the probability that it was added
+before that time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right where whereas time Little T
+
+ align:start position:0%
+right right where whereas time Little T
+ 
+
+ align:start position:0%
+right right where whereas time Little T
+here this is at the time that you're
+
+ align:start position:0%
+here this is at the time that you're
+ 
+
+ align:start position:0%
+here this is at the time that you're
+actually looking right so this is saying
+
+ align:start position:0%
+actually looking right so this is saying
+ 
+
+ align:start position:0%
+actually looking right so this is saying
+oh well if Little T is 100 for example
+
+ align:start position:0%
+oh well if Little T is 100 for example
+ 
+
+ align:start position:0%
+oh well if Little T is 100 for example
+it's saying oh at at that time point
+
+ align:start position:0%
+it's saying oh at at that time point
+ 
+
+ align:start position:0%
+it's saying oh at at that time point
+after we've added 100 nodes right we
+
+ align:start position:0%
+after we've added 100 nodes right we
+ 
+
+ align:start position:0%
+after we've added 100 nodes right we
+want to say all right what's the
+
+ align:start position:0%
+want to say all right what's the
+ 
+
+ align:start position:0%
+want to say all right what's the
+probability that some random I node was
+
+ align:start position:0%
+probability that some random I node was
+ 
+
+ align:start position:0%
+probability that some random I node was
+added before this quantity and this is
+
+ align:start position:0%
+added before this quantity and this is
+ 
+
+ align:start position:0%
+added before this quantity and this is
+just again some other kind of time if
+
+ align:start position:0%
+just again some other kind of time if
+ 
+
+ align:start position:0%
+just again some other kind of time if
+you'd
+
+ align:start position:0%
+you'd
+ 
+
+ align:start position:0%
+you'd
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay and I think this is the part
+
+ align:start position:0%
+okay okay and I think this is the part
+ 
+
+ align:start position:0%
+okay okay and I think this is the part
+that is especially kind of weird all
+
+ align:start position:0%
+that is especially kind of weird all
+ 
+
+ align:start position:0%
+that is especially kind of weird all
+right so this is also equal to this
+
+ align:start position:0%
+right so this is also equal to this
+ 
+
+ align:start position:0%
+right so this is also equal to this
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+um and I think you know reasonable
+
+ align:start position:0%
+um and I think you know reasonable
+ 
+
+ align:start position:0%
+um and I think you know reasonable
+people can argue about exactly what you
+
+ align:start position:0%
+people can argue about exactly what you
+ 
+
+ align:start position:0%
+people can argue about exactly what you
+should write here uh but we we let's
+
+ align:start position:0%
+should write here uh but we we let's
+ 
+
+ align:start position:0%
+should write here uh but we we let's
+figure out the basic argument first all
+
+ align:start position:0%
+figure out the basic argument first all
+ 
+
+ align:start position:0%
+figure out the basic argument first all
+right so there's this probability is
+
+ align:start position:0%
+right so there's this probability is
+ 
+
+ align:start position:0%
+right so there's this probability is
+equal to this thing okay so the the
+
+ align:start position:0%
+equal to this thing okay so the the
+ 
+
+ align:start position:0%
+equal to this thing okay so the the
+statement is really that at some time
+
+ align:start position:0%
+statement is really that at some time
+ 
+
+ align:start position:0%
+statement is really that at some time
+sometime
+
+ align:start position:0%
+sometime
+ 
+
+ align:start position:0%
+sometime
+T we have how many nodes we have we have
+
+ align:start position:0%
+T we have how many nodes we have we have
+ 
+
+ align:start position:0%
+T we have how many nodes we have we have
+M plus T nodes right so this is this is
+
+ align:start position:0%
+M plus T nodes right so this is this is
+ 
+
+ align:start position:0%
+M plus T nodes right so this is this is
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+here and of course there are edges going
+
+ align:start position:0%
+here and of course there are edges going
+ 
+
+ align:start position:0%
+here and of course there are edges going
+around doing things right and what we
+
+ align:start position:0%
+around doing things right and what we
+ 
+
+ align:start position:0%
+around doing things right and what we
+want to know is what's the probability
+
+ align:start position:0%
+want to know is what's the probability
+ 
+
+ align:start position:0%
+want to know is what's the probability
+if I grab one of them you know we're
+
+ align:start position:0%
+if I grab one of them you know we're
+ 
+
+ align:start position:0%
+if I grab one of them you know we're
+going to call that the I node okay so
+
+ align:start position:0%
+going to call that the I node okay so
+ 
+
+ align:start position:0%
+going to call that the I node okay so
+what's the probability if I grab one of
+
+ align:start position:0%
+what's the probability if I grab one of
+ 
+
+ align:start position:0%
+what's the probability if I grab one of
+them that it was added
+
+ align:start position:0%
+them that it was added
+ 
+
+ align:start position:0%
+them that it was added
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+sometime
+
+ align:start position:0%
+sometime
+ 
+
+ align:start position:0%
+sometime
+here okay and and it's useful to just
+
+ align:start position:0%
+here okay and and it's useful to just
+ 
+
+ align:start position:0%
+here okay and and it's useful to just
+imagine this as just being sometime T
+
+ align:start position:0%
+imagine this as just being sometime T
+ 
+
+ align:start position:0%
+imagine this as just being sometime T
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+will you know just just so that we don't
+
+ align:start position:0%
+will you know just just so that we don't
+ 
+
+ align:start position:0%
+will you know just just so that we don't
+get confused by
+
+ align:start position:0%
+get confused by
+ 
+
+ align:start position:0%
+get confused by
+all the symbols right then you say oh
+
+ align:start position:0%
+all the symbols right then you say oh
+ 
+
+ align:start position:0%
+all the symbols right then you say oh
+well that Pro that probability is really
+
+ align:start position:0%
+well that Pro that probability is really
+ 
+
+ align:start position:0%
+well that Pro that probability is really
+just the probability well how how many
+
+ align:start position:0%
+just the probability well how how many
+ 
+
+ align:start position:0%
+just the probability well how how many
+nodes were how many nodes total do we
+
+ align:start position:0%
+nodes were how many nodes total do we
+ 
+
+ align:start position:0%
+nodes were how many nodes total do we
+have we have M plus T how many nodes
+
+ align:start position:0%
+have we have M plus T how many nodes
+ 
+
+ align:start position:0%
+have we have M plus T how many nodes
+were there that were added before this
+
+ align:start position:0%
+were there that were added before this
+ 
+
+ align:start position:0%
+were there that were added before this
+time T well that's going to
+
+ align:start position:0%
+time T well that's going to
+ 
+
+ align:start position:0%
+time T well that's going to
+be T if you want you might want to say t
+
+ align:start position:0%
+be T if you want you might want to say t
+ 
+
+ align:start position:0%
+be T if you want you might want to say t
+plus M there's a question of whether you
+
+ align:start position:0%
+plus M there's a question of whether you
+ 
+
+ align:start position:0%
+plus M there's a question of whether you
+include those nodes that started there
+
+ align:start position:0%
+include those nodes that started there
+ 
+
+ align:start position:0%
+include those nodes that started there
+or not right um given the equations that
+
+ align:start position:0%
+or not right um given the equations that
+ 
+
+ align:start position:0%
+or not right um given the equations that
+barabasi wrote down he kind of assumes
+
+ align:start position:0%
+barabasi wrote down he kind of assumes
+ 
+
+ align:start position:0%
+barabasi wrote down he kind of assumes
+that we're only counting the that were
+
+ align:start position:0%
+that we're only counting the that were
+ 
+
+ align:start position:0%
+that we're only counting the that were
+added later right but you know so so I'd
+
+ align:start position:0%
+added later right but you know so so I'd
+ 
+
+ align:start position:0%
+added later right but you know so so I'd
+say if you want you could either add an
+
+ align:start position:0%
+say if you want you could either add an
+ 
+
+ align:start position:0%
+say if you want you could either add an
+mot up there or get rid of this m notot
+
+ align:start position:0%
+mot up there or get rid of this m notot
+ 
+
+ align:start position:0%
+mot up there or get rid of this m notot
+depending on what you like right but
+
+ align:start position:0%
+depending on what you like right but
+ 
+
+ align:start position:0%
+depending on what you like right but
+broadly there's this idea that we have
+
+ align:start position:0%
+broadly there's this idea that we have
+ 
+
+ align:start position:0%
+broadly there's this idea that we have
+this many nodes and this many of them
+
+ align:start position:0%
+this many nodes and this many of them
+ 
+
+ align:start position:0%
+this many nodes and this many of them
+were added before some time T and that's
+
+ align:start position:0%
+were added before some time T and that's
+ 
+
+ align:start position:0%
+were added before some time T and that's
+how we get this m^2 T over K squ which
+
+ align:start position:0%
+how we get this m^2 T over K squ which
+ 
+
+ align:start position:0%
+how we get this m^2 T over K squ which
+just that time T divided by the total
+
+ align:start position:0%
+just that time T divided by the total
+ 
+
+ align:start position:0%
+just that time T divided by the total
+number of of
+
+ align:start position:0%
+number of of
+ 
+
+ align:start position:0%
+number of of
+nodes
+
+ align:start position:0%
+nodes
+ 
+
+ align:start position:0%
+nodes
+okay and this whole discussion about
+
+ align:start position:0%
+okay and this whole discussion about
+ 
+
+ align:start position:0%
+okay and this whole discussion about
+whether you count the initial m not
+
+ align:start position:0%
+whether you count the initial m not
+ 
+
+ align:start position:0%
+whether you count the initial m not
+nodes or not it doesn't matter because
+
+ align:start position:0%
+nodes or not it doesn't matter because
+ 
+
+ align:start position:0%
+nodes or not it doesn't matter because
+we're going to be taking the limit as T
+
+ align:start position:0%
+we're going to be taking the limit as T
+ 
+
+ align:start position:0%
+we're going to be taking the limit as T
+goes to infinity and that all goes away
+
+ align:start position:0%
+goes to infinity and that all goes away
+ 
+
+ align:start position:0%
+goes to infinity and that all goes away
+right are there are there questions
+
+ align:start position:0%
+right are there are there questions
+ 
+
+ align:start position:0%
+right are there are there questions
+about this
+
+ align:start position:0%
+about this
+ 
+
+ align:start position:0%
+about this
+this there there are
+
+ align:start position:0%
+this there there are
+ 
+
+ align:start position:0%
+this there there are
+there's something kind of mind twisting
+
+ align:start position:0%
+there's something kind of mind twisting
+ 
+
+ align:start position:0%
+there's something kind of mind twisting
+about this argument even though we're
+
+ align:start position:0%
+about this argument even though we're
+ 
+
+ align:start position:0%
+about this argument even though we're
+really just
+
+ align:start position:0%
+really just
+ 
+
+ align:start position:0%
+really just
+picking Big T objects out of essentially
+
+ align:start position:0%
+picking Big T objects out of essentially
+ 
+
+ align:start position:0%
+picking Big T objects out of essentially
+Little T objects right but somehow that
+
+ align:start position:0%
+Little T objects right but somehow that
+ 
+
+ align:start position:0%
+Little T objects right but somehow that
+something funny goes on
+
+ align:start position:0%
+something funny goes on
+ 
+
+ align:start position:0%
+something funny goes on
+there all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions about about
+
+ align:start position:0%
+any questions about about
+ 
+
+ align:start position:0%
+any questions about about
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um you just go through the argument one
+
+ align:start position:0%
+um you just go through the argument one
+ 
+
+ align:start position:0%
+um you just go through the argument one
+more time yeah yeah yeah sure sure um
+
+ align:start position:0%
+more time yeah yeah yeah sure sure um
+ 
+
+ align:start position:0%
+more time yeah yeah yeah sure sure um
+right so I think that what's confusing
+
+ align:start position:0%
+right so I think that what's confusing
+ 
+
+ align:start position:0%
+right so I think that what's confusing
+about it is is the fact that we're
+
+ align:start position:0%
+about it is is the fact that we're
+ 
+
+ align:start position:0%
+about it is is the fact that we're
+asking whether this whether the I node
+
+ align:start position:0%
+asking whether this whether the I node
+ 
+
+ align:start position:0%
+asking whether this whether the I node
+was added before some time T and and and
+
+ align:start position:0%
+was added before some time T and and and
+ 
+
+ align:start position:0%
+was added before some time T and and and
+this time T is equal to something that's
+
+ align:start position:0%
+this time T is equal to something that's
+ 
+
+ align:start position:0%
+this time T is equal to something that's
+funny based on this other what we've
+
+ align:start position:0%
+funny based on this other what we've
+ 
+
+ align:start position:0%
+funny based on this other what we've
+just done but I think it's useful to
+
+ align:start position:0%
+just done but I think it's useful to
+ 
+
+ align:start position:0%
+just done but I think it's useful to
+just ask if if at time Little
+
+ align:start position:0%
+just ask if if at time Little
+ 
+
+ align:start position:0%
+just ask if if at time Little
+T you have you know you look at you look
+
+ align:start position:0%
+T you have you know you look at you look
+ 
+
+ align:start position:0%
+T you have you know you look at you look
+at this network and I ask you all right
+
+ align:start position:0%
+at this network and I ask you all right
+ 
+
+ align:start position:0%
+at this network and I ask you all right
+well was it added before this time Big T
+
+ align:start position:0%
+well was it added before this time Big T
+ 
+
+ align:start position:0%
+well was it added before this time Big T
+I.E let's just for concreteness say you
+
+ align:start position:0%
+I.E let's just for concreteness say you
+ 
+
+ align:start position:0%
+I.E let's just for concreteness say you
+know m is equal to we start with 10
+
+ align:start position:0%
+know m is equal to we start with 10
+ 
+
+ align:start position:0%
+know m is equal to we start with 10
+nodes and we say okay at time t equal to
+
+ align:start position:0%
+nodes and we say okay at time t equal to
+ 
+
+ align:start position:0%
+nodes and we say okay at time t equal to
+100 I want I ask you what's the
+
+ align:start position:0%
+100 I want I ask you what's the
+ 
+
+ align:start position:0%
+100 I want I ask you what's the
+probability that I grab if I grab a
+
+ align:start position:0%
+probability that I grab if I grab a
+ 
+
+ align:start position:0%
+probability that I grab if I grab a
+random node what's the probability it
+
+ align:start position:0%
+random node what's the probability it
+ 
+
+ align:start position:0%
+random node what's the probability it
+was added before some time Big T equal
+
+ align:start position:0%
+was added before some time Big T equal
+ 
+
+ align:start position:0%
+was added before some time Big T equal
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10 okay well you would say um you know
+
+ align:start position:0%
+10 okay well you would say um you know
+ 
+
+ align:start position:0%
+10 okay well you would say um you know
+very roughly actually you we can say
+
+ align:start position:0%
+very roughly actually you we can say
+ 
+
+ align:start position:0%
+very roughly actually you we can say
+let's let's actually we can even just if
+
+ align:start position:0%
+let's let's actually we can even just if
+ 
+
+ align:start position:0%
+let's let's actually we can even just if
+we'd like say we're not going to count
+
+ align:start position:0%
+we'd like say we're not going to count
+ 
+
+ align:start position:0%
+we'd like say we're not going to count
+we're not going to we're not going to
+
+ align:start position:0%
+we're not going to we're not going to
+ 
+
+ align:start position:0%
+we're not going to we're not going to
+count those m not initial nodes so we're
+
+ align:start position:0%
+count those m not initial nodes so we're
+ 
+
+ align:start position:0%
+count those m not initial nodes so we're
+just going to be looking at nodes we
+
+ align:start position:0%
+just going to be looking at nodes we
+ 
+
+ align:start position:0%
+just going to be looking at nodes we
+added later if you'd like right and then
+
+ align:start position:0%
+added later if you'd like right and then
+ 
+
+ align:start position:0%
+added later if you'd like right and then
+then you would say all right well at
+
+ align:start position:0%
+then you would say all right well at
+ 
+
+ align:start position:0%
+then you would say all right well at
+time T 100 we've added 100 nodes right
+
+ align:start position:0%
+time T 100 we've added 100 nodes right
+ 
+
+ align:start position:0%
+time T 100 we've added 100 nodes right
+and I'm asking you what's the if I grab
+
+ align:start position:0%
+and I'm asking you what's the if I grab
+ 
+
+ align:start position:0%
+and I'm asking you what's the if I grab
+one of the noes what's the probability
+
+ align:start position:0%
+one of the noes what's the probability
+ 
+
+ align:start position:0%
+one of the noes what's the probability
+that I that the node I grab was added in
+
+ align:start position:0%
+that I that the node I grab was added in
+ 
+
+ align:start position:0%
+that I that the node I grab was added in
+the first 10 time steps right well you
+
+ align:start position:0%
+the first 10 time steps right well you
+ 
+
+ align:start position:0%
+the first 10 time steps right well you
+would say it's going to be 10% right
+
+ align:start position:0%
+would say it's going to be 10% right
+ 
+
+ align:start position:0%
+would say it's going to be 10% right
+because there were 10 nodes that were
+
+ align:start position:0%
+because there were 10 nodes that were
+ 
+
+ align:start position:0%
+because there were 10 nodes that were
+added Before Time Big T and we added 100
+
+ align:start position:0%
+added Before Time Big T and we added 100
+ 
+
+ align:start position:0%
+added Before Time Big T and we added 100
+so it's really just this divided by this
+
+ align:start position:0%
+so it's really just this divided by this
+ 
+
+ align:start position:0%
+so it's really just this divided by this
+and you know with the question of
+
+ align:start position:0%
+and you know with the question of
+ 
+
+ align:start position:0%
+and you know with the question of
+whether you want to include M knots or
+
+ align:start position:0%
+whether you want to include M knots or
+ 
+
+ align:start position:0%
+whether you want to include M knots or
+not right so I think that that argument
+
+ align:start position:0%
+not right so I think that that argument
+ 
+
+ align:start position:0%
+not right so I think that that argument
+is surprisingly straightforward but then
+
+ align:start position:0%
+is surprisingly straightforward but then
+ 
+
+ align:start position:0%
+is surprisingly straightforward but then
+somehow what gets really confusing is
+
+ align:start position:0%
+somehow what gets really confusing is
+ 
+
+ align:start position:0%
+somehow what gets really confusing is
+that you know the time T we're referring
+
+ align:start position:0%
+that you know the time T we're referring
+ 
+
+ align:start position:0%
+that you know the time T we're referring
+to it it it's depending on the the K's
+
+ align:start position:0%
+to it it it's depending on the the K's
+ 
+
+ align:start position:0%
+to it it it's depending on the the K's
+and the t's and so forth right but
+
+ align:start position:0%
+and the t's and so forth right but
+ 
+
+ align:start position:0%
+and the t's and so forth right but
+that's that's a way of keeping track of
+
+ align:start position:0%
+that's that's a way of keeping track of
+ 
+
+ align:start position:0%
+that's that's a way of keeping track of
+how how everything is scaling as a
+
+ align:start position:0%
+how how everything is scaling as a
+ 
+
+ align:start position:0%
+how how everything is scaling as a
+function of time right but if you just
+
+ align:start position:0%
+function of time right but if you just
+ 
+
+ align:start position:0%
+function of time right but if you just
+if you boil the argument down to this
+
+ align:start position:0%
+if you boil the argument down to this
+ 
+
+ align:start position:0%
+if you boil the argument down to this
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+it it makes sense but then of course
+
+ align:start position:0%
+it it makes sense but then of course
+ 
+
+ align:start position:0%
+it it makes sense but then of course
+then you look back at this and you get
+
+ align:start position:0%
+then you look back at this and you get
+ 
+
+ align:start position:0%
+then you look back at this and you get
+confused again right um which is um how
+
+ align:start position:0%
+confused again right um which is um how
+ 
+
+ align:start position:0%
+confused again right um which is um how
+I feel every year when I prepare this
+
+ align:start position:0%
+I feel every year when I prepare this
+ 
+
+ align:start position:0%
+I feel every year when I prepare this
+lecture but but I think it but it's all
+
+ align:start position:0%
+lecture but but I think it but it's all
+ 
+
+ align:start position:0%
+lecture but but I think it but it's all
+I think it's all it all does make sense
+
+ align:start position:0%
+I think it's all it all does make sense
+ 
+
+ align:start position:0%
+I think it's all it all does make sense
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+um okay
+
+ align:start position:0%
+um okay
+ 
+
+ align:start position:0%
+um okay
+did any questions about this argument or
+
+ align:start position:0%
+did any questions about this argument or
+ 
+
+ align:start position:0%
+did any questions about this argument or
+that argument or any part of it um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes all right
+
+ align:start position:0%
+yes yes all right
+ 
+
+ align:start position:0%
+yes yes all right
+so right so okay so this is TI this is
+
+ align:start position:0%
+so right so okay so this is TI this is
+ 
+
+ align:start position:0%
+so right so okay so this is TI this is
+just saying that if I pick some random
+
+ align:start position:0%
+just saying that if I pick some random
+ 
+
+ align:start position:0%
+just saying that if I pick some random
+node we're we're calling it The I node
+
+ align:start position:0%
+node we're we're calling it The I node
+ 
+
+ align:start position:0%
+node we're we're calling it The I node
+I'm asking what's the probability that
+
+ align:start position:0%
+I'm asking what's the probability that
+ 
+
+ align:start position:0%
+I'm asking what's the probability that
+that the time it was added was before
+
+ align:start position:0%
+that the time it was added was before
+ 
+
+ align:start position:0%
+that the time it was added was before
+something right so this is just this is
+
+ align:start position:0%
+something right so this is just this is
+ 
+
+ align:start position:0%
+something right so this is just this is
+is not one of the variables and you'll
+
+ align:start position:0%
+is not one of the variables and you'll
+ 
+
+ align:start position:0%
+is not one of the variables and you'll
+see the ti doesn't appear down here
+
+ align:start position:0%
+see the ti doesn't appear down here
+ 
+
+ align:start position:0%
+see the ti doesn't appear down here
+because this is just saying because I'm
+
+ align:start position:0%
+because this is just saying because I'm
+ 
+
+ align:start position:0%
+because this is just saying because I'm
+just I'm I'm asking you if I grab some
+
+ align:start position:0%
+just I'm I'm asking you if I grab some
+ 
+
+ align:start position:0%
+just I'm I'm asking you if I grab some
+random node the I node I'm asking you
+
+ align:start position:0%
+random node the I node I'm asking you
+ 
+
+ align:start position:0%
+random node the I node I'm asking you
+what's the probability that it was added
+
+ align:start position:0%
+what's the probability that it was added
+ 
+
+ align:start position:0%
+what's the probability that it was added
+before some other time which is which is
+
+ align:start position:0%
+before some other time which is which is
+ 
+
+ align:start position:0%
+before some other time which is which is
+all this right so and what you can see
+
+ align:start position:0%
+all this right so and what you can see
+ 
+
+ align:start position:0%
+all this right so and what you can see
+is that it it's a function of of you
+
+ align:start position:0%
+is that it it's a function of of you
+ 
+
+ align:start position:0%
+is that it it's a function of of you
+know the time that we look right because
+
+ align:start position:0%
+know the time that we look right because
+ 
+
+ align:start position:0%
+know the time that we look right because
+if if I go to longer
+
+ align:start position:0%
+if if I go to longer
+ 
+
+ align:start position:0%
+if if I go to longer
+times you know then indeed this
+
+ align:start position:0%
+times you know then indeed this
+ 
+
+ align:start position:0%
+times you know then indeed this
+probability should have go what should
+
+ align:start position:0%
+probability should have go what should
+ 
+
+ align:start position:0%
+probability should have go what should
+it do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but it depends on KS as well
+
+ align:start position:0%
+okay but it depends on KS as well
+ 
+
+ align:start position:0%
+okay but it depends on KS as well
+right what do I want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say all right because ultimately what
+
+ align:start position:0%
+say all right because ultimately what
+ 
+
+ align:start position:0%
+say all right because ultimately what
+what we what we see here is that as as
+
+ align:start position:0%
+what we what we see here is that as as
+ 
+
+ align:start position:0%
+what we what we see here is that as as
+as time goes to Infinity so as after a
+
+ align:start position:0%
+as time goes to Infinity so as after a
+ 
+
+ align:start position:0%
+as time goes to Infinity so as after a
+long time then we reach this stationary
+
+ align:start position:0%
+long time then we reach this stationary
+ 
+
+ align:start position:0%
+long time then we reach this stationary
+distribution where uh the the base
+
+ align:start position:0%
+distribution where uh the the base
+ 
+
+ align:start position:0%
+distribution where uh the the base
+structure of the network is not changing
+
+ align:start position:0%
+structure of the network is not changing
+ 
+
+ align:start position:0%
+structure of the network is not changing
+anymore right and that's because the
+
+ align:start position:0%
+anymore right and that's because the
+ 
+
+ align:start position:0%
+anymore right and that's because the
+there's a t in both the numerator and
+
+ align:start position:0%
+there's a t in both the numerator and
+ 
+
+ align:start position:0%
+there's a t in both the numerator and
+the denominator so then the only thing
+
+ align:start position:0%
+the denominator so then the only thing
+ 
+
+ align:start position:0%
+the denominator so then the only thing
+that kind of is left is this Behavior as
+
+ align:start position:0%
+that kind of is left is this Behavior as
+ 
+
+ align:start position:0%
+that kind of is left is this Behavior as
+a function of K right so this is and
+
+ align:start position:0%
+a function of K right so this is and
+ 
+
+ align:start position:0%
+a function of K right so this is and
+this is really saying that you know the
+
+ align:start position:0%
+this is really saying that you know the
+ 
+
+ align:start position:0%
+this is really saying that you know the
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+that some node was added before some
+
+ align:start position:0%
+that some node was added before some
+ 
+
+ align:start position:0%
+that some node was added before some
+time is is kind of the same as saying
+
+ align:start position:0%
+time is is kind of the same as saying
+ 
+
+ align:start position:0%
+time is is kind of the same as saying
+that well that you have a lot of edges
+
+ align:start position:0%
+that well that you have a lot of edges
+ 
+
+ align:start position:0%
+that well that you have a lot of edges
+and and that's how we got here to begin
+
+ align:start position:0%
+and and that's how we got here to begin
+ 
+
+ align:start position:0%
+and and that's how we got here to begin
+with right because the the nodes that
+
+ align:start position:0%
+with right because the the nodes that
+ 
+
+ align:start position:0%
+with right because the the nodes that
+were added early end up with a lot of
+
+ align:start position:0%
+were added early end up with a lot of
+ 
+
+ align:start position:0%
+were added early end up with a lot of
+edges this is the so-called Rich get
+
+ align:start position:0%
+edges this is the so-called Rich get
+ 
+
+ align:start position:0%
+edges this is the so-called Rich get
+richer phenom phenomenon all right so if
+
+ align:start position:0%
+richer phenom phenomenon all right so if
+ 
+
+ align:start position:0%
+richer phenom phenomenon all right so if
+you're sitting on a manuscript and
+
+ align:start position:0%
+you're sitting on a manuscript and
+ 
+
+ align:start position:0%
+you're sitting on a manuscript and
+you're not submitting it for publication
+
+ align:start position:0%
+you're not submitting it for publication
+ 
+
+ align:start position:0%
+you're not submitting it for publication
+you should kind of get on it because you
+
+ align:start position:0%
+you should kind of get on it because you
+ 
+
+ align:start position:0%
+you should kind of get on it because you
+know the earlier that it's published the
+
+ align:start position:0%
+know the earlier that it's published the
+ 
+
+ align:start position:0%
+know the earlier that it's published the
+more citations it's going to get okay
+
+ align:start position:0%
+more citations it's going to get okay
+ 
+
+ align:start position:0%
+more citations it's going to get okay
+right but this is saying that right the
+
+ align:start position:0%
+right but this is saying that right the
+ 
+
+ align:start position:0%
+right but this is saying that right the
+probability that some random node has a
+
+ align:start position:0%
+probability that some random node has a
+ 
+
+ align:start position:0%
+probability that some random node has a
+small number of
+
+ align:start position:0%
+small number of
+ 
+
+ align:start position:0%
+small number of
+edges is the same as that the
+
+ align:start position:0%
+edges is the same as that the
+ 
+
+ align:start position:0%
+edges is the same as that the
+probability that the node was added
+
+ align:start position:0%
+probability that the node was added
+ 
+
+ align:start position:0%
+probability that the node was added
+late right and that makes sense because
+
+ align:start position:0%
+late right and that makes sense because
+ 
+
+ align:start position:0%
+late right and that makes sense because
+if it's added late doesn't have very
+
+ align:start position:0%
+if it's added late doesn't have very
+ 
+
+ align:start position:0%
+if it's added late doesn't have very
+many edges hasn't had time to grow right
+
+ align:start position:0%
+many edges hasn't had time to grow right
+ 
+
+ align:start position:0%
+many edges hasn't had time to grow right
+and then you know just you know from th
+
+ align:start position:0%
+and then you know just you know from th
+ 
+
+ align:start position:0%
+and then you know just you know from th
+those uh those calculations you can get
+
+ align:start position:0%
+those uh those calculations you can get
+ 
+
+ align:start position:0%
+those uh those calculations you can get
+it at this degree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution okay yes in this analytical
+
+ align:start position:0%
+distribution okay yes in this analytical
+ 
+
+ align:start position:0%
+distribution okay yes in this analytical
+Anis assuming that the links could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Beal non yeah okay right
+
+ align:start position:0%
+Beal non yeah okay right
+ 
+
+ align:start position:0%
+Beal non yeah okay right
+so yes so we're we're taking in
+
+ align:start position:0%
+so yes so we're we're taking in
+ 
+
+ align:start position:0%
+so yes so we're we're taking in
+principle it's a discret problem and
+
+ align:start position:0%
+principle it's a discret problem and
+ 
+
+ align:start position:0%
+principle it's a discret problem and
+converting it into into a differential
+
+ align:start position:0%
+converting it into into a differential
+ 
+
+ align:start position:0%
+converting it into into a differential
+equation right um you know and it's an
+
+ align:start position:0%
+equation right um you know and it's an
+ 
+
+ align:start position:0%
+equation right um you know and it's an
+interesting question of of I don't know
+
+ align:start position:0%
+interesting question of of I don't know
+ 
+
+ align:start position:0%
+interesting question of of I don't know
+how big of an error this ends up making
+
+ align:start position:0%
+how big of an error this ends up making
+ 
+
+ align:start position:0%
+how big of an error this ends up making
+right U and and of
+
+ align:start position:0%
+right U and and of
+ 
+
+ align:start position:0%
+right U and and of
+course this expression doesn't actually
+
+ align:start position:0%
+course this expression doesn't actually
+ 
+
+ align:start position:0%
+course this expression doesn't actually
+end up being integ you know having
+
+ align:start position:0%
+end up being integ you know having
+ 
+
+ align:start position:0%
+end up being integ you know having
+integers right but this is a this is a
+
+ align:start position:0%
+integers right but this is a this is a
+ 
+
+ align:start position:0%
+integers right but this is a this is a
+way of making it so that the errors
+
+ align:start position:0%
+way of making it so that the errors
+ 
+
+ align:start position:0%
+way of making it so that the errors
+don't grow or so right um you know so I
+
+ align:start position:0%
+don't grow or so right um you know so I
+ 
+
+ align:start position:0%
+don't grow or so right um you know so I
+think that it it you know it basically
+
+ align:start position:0%
+think that it it you know it basically
+ 
+
+ align:start position:0%
+think that it it you know it basically
+works I think you if you'd like you
+
+ align:start position:0%
+works I think you if you'd like you
+ 
+
+ align:start position:0%
+works I think you if you'd like you
+could you know you can sit down actually
+
+ align:start position:0%
+could you know you can sit down actually
+ 
+
+ align:start position:0%
+could you know you can sit down actually
+do the simulation with all the discrete
+
+ align:start position:0%
+do the simulation with all the discrete
+ 
+
+ align:start position:0%
+do the simulation with all the discrete
+I think that it's actually going to be
+
+ align:start position:0%
+I think that it's actually going to be
+ 
+
+ align:start position:0%
+I think that it's actually going to be
+the stochastic dynamics that end up
+
+ align:start position:0%
+the stochastic dynamics that end up
+ 
+
+ align:start position:0%
+the stochastic dynamics that end up
+being more relevant than the the integer
+
+ align:start position:0%
+being more relevant than the the integer
+ 
+
+ align:start position:0%
+being more relevant than the the integer
+kind of issue um but I I haven't
+
+ align:start position:0%
+kind of issue um but I I haven't
+ 
+
+ align:start position:0%
+kind of issue um but I I haven't
+actually looked into that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+though okay um all right any other
+
+ align:start position:0%
+though okay um all right any other
+ 
+
+ align:start position:0%
+though okay um all right any other
+questions about about that so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes right so there's no loss of edges no
+
+ align:start position:0%
+yes right so there's no loss of edges no
+ 
+
+ align:start position:0%
+yes right so there's no loss of edges no
+loss of nodes strictly verboten
+
+ align:start position:0%
+loss of nodes strictly verboten
+ 
+
+ align:start position:0%
+loss of nodes strictly verboten
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I spent a lot of time trying to plan an
+
+ align:start position:0%
+I spent a lot of time trying to plan an
+ 
+
+ align:start position:0%
+I spent a lot of time trying to plan an
+upcoming trip to Germany last night so
+
+ align:start position:0%
+upcoming trip to Germany last night so
+ 
+
+ align:start position:0%
+upcoming trip to Germany last night so
+I'm I'm German is on my
+
+ align:start position:0%
+I'm I'm German is on my
+ 
+
+ align:start position:0%
+I'm I'm German is on my
+mind
+
+ align:start position:0%
+mind
+ 
+
+ align:start position:0%
+mind
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um all right so are are We Done Yet
+
+ align:start position:0%
+um all right so are are We Done Yet
+ 
+
+ align:start position:0%
+um all right so are are We Done Yet
+incidentally uh nearly right because we
+
+ align:start position:0%
+incidentally uh nearly right because we
+ 
+
+ align:start position:0%
+incidentally uh nearly right because we
+have um now this but but what we really
+
+ align:start position:0%
+have um now this but but what we really
+ 
+
+ align:start position:0%
+have um now this but but what we really
+wanted is the is the degree distribution
+
+ align:start position:0%
+wanted is the is the degree distribution
+ 
+
+ align:start position:0%
+wanted is the is the degree distribution
+not this probability
+
+ align:start position:0%
+not this probability
+ 
+
+ align:start position:0%
+not this probability
+right so we have to take a derivative
+
+ align:start position:0%
+right so we have to take a derivative
+ 
+
+ align:start position:0%
+right so we have to take a derivative
+still right but as as T goes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity regardless of how you treat the
+
+ align:start position:0%
+Infinity regardless of how you treat the
+ 
+
+ align:start position:0%
+Infinity regardless of how you treat the
+M knots um oh actually well we maybe
+
+ align:start position:0%
+M knots um oh actually well we maybe
+ 
+
+ align:start position:0%
+M knots um oh actually well we maybe
+we'll sorry maybe we'll take take the
+
+ align:start position:0%
+we'll sorry maybe we'll take take the
+ 
+
+ align:start position:0%
+we'll sorry maybe we'll take take the
+derivative first okay so the this
+
+ align:start position:0%
+derivative first okay so the this
+ 
+
+ align:start position:0%
+derivative first okay so the this
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+density right is going to be uh the
+
+ align:start position:0%
+density right is going to be uh the
+ 
+
+ align:start position:0%
+density right is going to be uh the
+derivative with respect to K of the
+
+ align:start position:0%
+derivative with respect to K of the
+ 
+
+ align:start position:0%
+derivative with respect to K of the
+actual
+
+ align:start position:0%
+actual
+ 
+
+ align:start position:0%
+actual
+probability here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we take a derivative this
+
+ align:start position:0%
+all right so we take a derivative this
+ 
+
+ align:start position:0%
+all right so we take a derivative this
+one derivative nothing happens K2 it's
+
+ align:start position:0%
+one derivative nothing happens K2 it's
+ 
+
+ align:start position:0%
+one derivative nothing happens K2 it's
+going to turn into a k a k cubed right
+
+ align:start position:0%
+going to turn into a k a k cubed right
+ 
+
+ align:start position:0%
+going to turn into a k a k cubed right
+so we get 2 m^ 2 T over K
+
+ align:start position:0%
+so we get 2 m^ 2 T over K
+ 
+
+ align:start position:0%
+so we get 2 m^ 2 T over K
+cubed we still have the m t plus
+
+ align:start position:0%
+cubed we still have the m t plus
+ 
+
+ align:start position:0%
+cubed we still have the m t plus
+M all right but when we uh when we let T
+
+ align:start position:0%
+M all right but when we uh when we let T
+ 
+
+ align:start position:0%
+M all right but when we uh when we let T
+go to Infinity so after this thing is
+
+ align:start position:0%
+go to Infinity so after this thing is
+ 
+
+ align:start position:0%
+go to Infinity so after this thing is
+reached stationary distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we end up just getting 2 m^2 over K
+
+ align:start position:0%
+then we end up just getting 2 m^2 over K
+ 
+
+ align:start position:0%
+then we end up just getting 2 m^2 over K
+Cub
+
+ align:start position:0%
+Cub
+ 
+
+ align:start position:0%
+Cub
+right I just want to be clear this is to
+
+ align:start position:0%
+right I just want to be clear this is to
+ 
+
+ align:start position:0%
+right I just want to be clear this is to
+the K right the key feature here is that
+
+ align:start position:0%
+the K right the key feature here is that
+ 
+
+ align:start position:0%
+the K right the key feature here is that
+um the probability distribution goes as
+
+ align:start position:0%
+um the probability distribution goes as
+ 
+
+ align:start position:0%
+um the probability distribution goes as
+um 1 over K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cubed um what is interesting is that you
+
+ align:start position:0%
+cubed um what is interesting is that you
+ 
+
+ align:start position:0%
+cubed um what is interesting is that you
+know when I first read the paper I
+
+ align:start position:0%
+know when I first read the paper I
+ 
+
+ align:start position:0%
+know when I first read the paper I
+actually thought
+
+ align:start position:0%
+actually thought
+ 
+
+ align:start position:0%
+actually thought
+that this exponent here would be a
+
+ align:start position:0%
+that this exponent here would be a
+ 
+
+ align:start position:0%
+that this exponent here would be a
+function of the linearity of the
+
+ align:start position:0%
+function of the linearity of the
+ 
+
+ align:start position:0%
+function of the linearity of the
+preferential attachment so I actually I
+
+ align:start position:0%
+preferential attachment so I actually I
+ 
+
+ align:start position:0%
+preferential attachment so I actually I
+you know and of course they say that
+
+ align:start position:0%
+you know and of course they say that
+ 
+
+ align:start position:0%
+you know and of course they say that
+it's not true right but when I was
+
+ align:start position:0%
+it's not true right but when I was
+ 
+
+ align:start position:0%
+it's not true right but when I was
+halfway through the paper I thought oh
+
+ align:start position:0%
+halfway through the paper I thought oh
+ 
+
+ align:start position:0%
+halfway through the paper I thought oh
+well if you just let this go as some
+
+ align:start position:0%
+well if you just let this go as some
+ 
+
+ align:start position:0%
+well if you just let this go as some
+power to the beta or so then you would
+
+ align:start position:0%
+power to the beta or so then you would
+ 
+
+ align:start position:0%
+power to the beta or so then you would
+maybe get something like oh this was you
+
+ align:start position:0%
+maybe get something like oh this was you
+ 
+
+ align:start position:0%
+maybe get something like oh this was you
+know 2 plus beta you know I thought
+
+ align:start position:0%
+know 2 plus beta you know I thought
+ 
+
+ align:start position:0%
+know 2 plus beta you know I thought
+something like that uh but apparently
+
+ align:start position:0%
+something like that uh but apparently
+ 
+
+ align:start position:0%
+something like that uh but apparently
+it's not true right that uh if if you uh
+
+ align:start position:0%
+it's not true right that uh if if you uh
+ 
+
+ align:start position:0%
+it's not true right that uh if if you uh
+if you do not have linear attachment
+
+ align:start position:0%
+if you do not have linear attachment
+ 
+
+ align:start position:0%
+if you do not have linear attachment
+here then you just don't get power law
+
+ align:start position:0%
+here then you just don't get power law
+ 
+
+ align:start position:0%
+here then you just don't get power law
+distributions right they suggest other
+
+ align:start position:0%
+distributions right they suggest other
+ 
+
+ align:start position:0%
+distributions right they suggest other
+ways that you could maybe get different
+
+ align:start position:0%
+ways that you could maybe get different
+ 
+
+ align:start position:0%
+ways that you could maybe get different
+exponents which is very relevant given
+
+ align:start position:0%
+exponents which is very relevant given
+ 
+
+ align:start position:0%
+exponents which is very relevant given
+the fact that different real networks
+
+ align:start position:0%
+the fact that different real networks
+ 
+
+ align:start position:0%
+the fact that different real networks
+indeed have different exponents right um
+
+ align:start position:0%
+indeed have different exponents right um
+ 
+
+ align:start position:0%
+indeed have different exponents right um
+but I'd say that their their proferred
+
+ align:start position:0%
+but I'd say that their their proferred
+ 
+
+ align:start position:0%
+but I'd say that their their proferred
+explanation which is to include directed
+
+ align:start position:0%
+explanation which is to include directed
+ 
+
+ align:start position:0%
+explanation which is to include directed
+edges feels uh unsatisfying because not
+
+ align:start position:0%
+edges feels uh unsatisfying because not
+ 
+
+ align:start position:0%
+edges feels uh unsatisfying because not
+all networks are directed right uh and
+
+ align:start position:0%
+all networks are directed right uh and
+ 
+
+ align:start position:0%
+all networks are directed right uh and
+this network here is not directed and
+
+ align:start position:0%
+this network here is not directed and
+ 
+
+ align:start position:0%
+this network here is not directed and
+has different has an exponents closer to
+
+ align:start position:0%
+has different has an exponents closer to
+ 
+
+ align:start position:0%
+has different has an exponents closer to
+two right so you would you really want
+
+ align:start position:0%
+two right so you would you really want
+ 
+
+ align:start position:0%
+two right so you would you really want
+to have other other mechanisms but you
+
+ align:start position:0%
+to have other other mechanisms but you
+ 
+
+ align:start position:0%
+to have other other mechanisms but you
+know this as we've mentioned is it's a
+
+ align:start position:0%
+know this as we've mentioned is it's a
+ 
+
+ align:start position:0%
+know this as we've mentioned is it's a
+thriving field and uh and people have
+
+ align:start position:0%
+thriving field and uh and people have
+ 
+
+ align:start position:0%
+thriving field and uh and people have
+explored many different aspects of this
+
+ align:start position:0%
+explored many different aspects of this
+ 
+
+ align:start position:0%
+explored many different aspects of this
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um are there any any other
+
+ align:start position:0%
+okay um are there any any other
+ 
+
+ align:start position:0%
+okay um are there any any other
+questions about this derivation how we
+
+ align:start position:0%
+questions about this derivation how we
+ 
+
+ align:start position:0%
+questions about this derivation how we
+got there how convincing we maybe you
+
+ align:start position:0%
+got there how convincing we maybe you
+ 
+
+ align:start position:0%
+got there how convincing we maybe you
+think it should be or not be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I want I want us to to spend the
+
+ align:start position:0%
+okay so I want I want us to to spend the
+ 
+
+ align:start position:0%
+okay so I want I want us to to spend the
+the last five minutes of the class kind
+
+ align:start position:0%
+the last five minutes of the class kind
+ 
+
+ align:start position:0%
+the last five minutes of the class kind
+of setting up the discussion of uh how
+
+ align:start position:0%
+of setting up the discussion of uh how
+ 
+
+ align:start position:0%
+of setting up the discussion of uh how
+we should be searching for network
+
+ align:start position:0%
+we should be searching for network
+ 
+
+ align:start position:0%
+we should be searching for network
+motifs okay in particular there's a
+
+ align:start position:0%
+motifs okay in particular there's a
+ 
+
+ align:start position:0%
+motifs okay in particular there's a
+natural question which is um we have to
+
+ align:start position:0%
+natural question which is um we have to
+ 
+
+ align:start position:0%
+natural question which is um we have to
+decide what the right null model is in
+
+ align:start position:0%
+decide what the right null model is in
+ 
+
+ align:start position:0%
+decide what the right null model is in
+terms of deciding uh kind of what the
+
+ align:start position:0%
+terms of deciding uh kind of what the
+ 
+
+ align:start position:0%
+terms of deciding uh kind of what the
+expected frequency of a network Motif
+
+ align:start position:0%
+expected frequency of a network Motif
+ 
+
+ align:start position:0%
+expected frequency of a network Motif
+like a feed forward Loop might
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be so first of
+
+ align:start position:0%
+be so first of
+ 
+
+ align:start position:0%
+be so first of
+all why why is it that we think that you
+
+ align:start position:0%
+all why why is it that we think that you
+ 
+
+ align:start position:0%
+all why why is it that we think that you
+know why why is it that we we maybe
+
+ align:start position:0%
+know why why is it that we we maybe
+ 
+
+ align:start position:0%
+know why why is it that we we maybe
+should not use an OS Ry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Network yes doesn't it's not very good
+
+ align:start position:0%
+Network yes doesn't it's not very good
+ 
+
+ align:start position:0%
+Network yes doesn't it's not very good
+for handling
+
+ align:start position:0%
+for handling
+ 
+
+ align:start position:0%
+for handling
+direct right okay so you oh not very
+
+ align:start position:0%
+direct right okay so you oh not very
+ 
+
+ align:start position:0%
+direct right okay so you oh not very
+good I mean I can maybe make I mean I
+
+ align:start position:0%
+good I mean I can maybe make I mean I
+ 
+
+ align:start position:0%
+good I mean I can maybe make I mean I
+can there's a clear analog to a a you
+
+ align:start position:0%
+can there's a clear analog to a a you
+ 
+
+ align:start position:0%
+can there's a clear analog to a a you
+know you can take a a random undirected
+
+ align:start position:0%
+know you can take a a random undirected
+ 
+
+ align:start position:0%
+know you can take a a random undirected
+ER Network and and say you know D you
+
+ align:start position:0%
+ER Network and and say you know D you
+ 
+
+ align:start position:0%
+ER Network and and say you know D you
+know put arrows randomly on each you
+
+ align:start position:0%
+know put arrows randomly on each you
+ 
+
+ align:start position:0%
+know put arrows randomly on each you
+know I mean I think that there's there's
+
+ align:start position:0%
+know I mean I think that there's there's
+ 
+
+ align:start position:0%
+know I mean I think that there's there's
+a natural ER version of a directed
+
+ align:start position:0%
+a natural ER version of a directed
+ 
+
+ align:start position:0%
+a natural ER version of a directed
+Network there
+
+ align:start position:0%
+Network there
+ 
+
+ align:start position:0%
+Network there
+con like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what duplication you don't Rand
+
+ align:start position:0%
+what duplication you don't Rand
+ 
+
+ align:start position:0%
+what duplication you don't Rand
+ass Ed that's right okay so one thing is
+
+ align:start position:0%
+ass Ed that's right okay so one thing is
+ 
+
+ align:start position:0%
+ass Ed that's right okay so one thing is
+it may be that that biologically there
+
+ align:start position:0%
+it may be that that biologically there
+ 
+
+ align:start position:0%
+it may be that that biologically there
+are constraints um but you know and then
+
+ align:start position:0%
+are constraints um but you know and then
+ 
+
+ align:start position:0%
+are constraints um but you know and then
+but that should manifest itself somehow
+
+ align:start position:0%
+but that should manifest itself somehow
+ 
+
+ align:start position:0%
+but that should manifest itself somehow
+in the sense that if you know all that
+
+ align:start position:0%
+in the sense that if you know all that
+ 
+
+ align:start position:0%
+in the sense that if you know all that
+may be well and good it may be true what
+
+ align:start position:0%
+may be well and good it may be true what
+ 
+
+ align:start position:0%
+may be well and good it may be true what
+you're saying but if we go and we look
+
+ align:start position:0%
+you're saying but if we go and we look
+ 
+
+ align:start position:0%
+you're saying but if we go and we look
+at a transcription network if it looks
+
+ align:start position:0%
+at a transcription network if it looks
+ 
+
+ align:start position:0%
+at a transcription network if it looks
+like an ER Network then I would say it
+
+ align:start position:0%
+like an ER Network then I would say it
+ 
+
+ align:start position:0%
+like an ER Network then I would say it
+just doesn't matter right you know the
+
+ align:start position:0%
+just doesn't matter right you know the
+ 
+
+ align:start position:0%
+just doesn't matter right you know the
+fact that that there's microscopic
+
+ align:start position:0%
+fact that that there's microscopic
+ 
+
+ align:start position:0%
+fact that that there's microscopic
+things going on I mean if at the end of
+
+ align:start position:0%
+things going on I mean if at the end of
+ 
+
+ align:start position:0%
+things going on I mean if at the end of
+the day it looks like an ER Network
+
+ align:start position:0%
+the day it looks like an ER Network
+ 
+
+ align:start position:0%
+the day it looks like an ER Network
+then then maybe then maybe it's fine
+
+ align:start position:0%
+then then maybe then maybe it's fine
+ 
+
+ align:start position:0%
+then then maybe then maybe it's fine
+anyways
+
+ align:start position:0%
+anyways
+ 
+
+ align:start position:0%
+anyways
+right or maybe not you know yeah you can
+
+ align:start position:0%
+right or maybe not you know yeah you can
+ 
+
+ align:start position:0%
+right or maybe not you know yeah you can
+argue either way if if a particular I
+
+ align:start position:0%
+argue either way if if a particular I
+ 
+
+ align:start position:0%
+argue either way if if a particular I
+mean it depends on what you want if a
+
+ align:start position:0%
+mean it depends on what you want if a
+ 
+
+ align:start position:0%
+mean it depends on what you want if a
+particular Motif occurs a lot it might
+
+ align:start position:0%
+particular Motif occurs a lot it might
+ 
+
+ align:start position:0%
+particular Motif occurs a lot it might
+be because of the you know it might be
+
+ align:start position:0%
+be because of the you know it might be
+ 
+
+ align:start position:0%
+be because of the you know it might be
+because it's selected for evolution or
+
+ align:start position:0%
+because it's selected for evolution or
+ 
+
+ align:start position:0%
+because it's selected for evolution or
+for some other reason that's right okay
+
+ align:start position:0%
+for some other reason that's right okay
+ 
+
+ align:start position:0%
+for some other reason that's right okay
+so this is an important point that you
+
+ align:start position:0%
+so this is an important point that you
+ 
+
+ align:start position:0%
+so this is an important point that you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+that right I would say that in in er's
+
+ align:start position:0%
+that right I would say that in in er's
+ 
+
+ align:start position:0%
+that right I would say that in in er's
+approach he basically says if if we see
+
+ align:start position:0%
+approach he basically says if if we see
+ 
+
+ align:start position:0%
+approach he basically says if if we see
+a network Motif more frequently than we
+
+ align:start position:0%
+a network Motif more frequently than we
+ 
+
+ align:start position:0%
+a network Motif more frequently than we
+would expect based on some null model
+
+ align:start position:0%
+would expect based on some null model
+ 
+
+ align:start position:0%
+would expect based on some null model
+some null Network then uh then it's kind
+
+ align:start position:0%
+some null Network then uh then it's kind
+ 
+
+ align:start position:0%
+some null Network then uh then it's kind
+of Prim aish evidence that Evolution was
+
+ align:start position:0%
+of Prim aish evidence that Evolution was
+ 
+
+ align:start position:0%
+of Prim aish evidence that Evolution was
+selecting for it for some reason right
+
+ align:start position:0%
+selecting for it for some reason right
+ 
+
+ align:start position:0%
+selecting for it for some reason right
+and what you're saying is that it could
+
+ align:start position:0%
+and what you're saying is that it could
+ 
+
+ align:start position:0%
+and what you're saying is that it could
+be that that there's a microscopic
+
+ align:start position:0%
+be that that there's a microscopic
+ 
+
+ align:start position:0%
+be that that there's a microscopic
+mechanism that just leads to those
+
+ align:start position:0%
+mechanism that just leads to those
+ 
+
+ align:start position:0%
+mechanism that just leads to those
+things happening and it so it doesn't
+
+ align:start position:0%
+things happening and it so it doesn't
+ 
+
+ align:start position:0%
+things happening and it so it doesn't
+have to be selection it could be just
+
+ align:start position:0%
+have to be selection it could be just
+ 
+
+ align:start position:0%
+have to be selection it could be just
+due to the the mechanistic processes
+
+ align:start position:0%
+due to the the mechanistic processes
+ 
+
+ align:start position:0%
+due to the the mechanistic processes
+below right I think that's a that's a
+
+ align:start position:0%
+below right I think that's a that's a
+ 
+
+ align:start position:0%
+below right I think that's a that's a
+fair concern and it's related to a lot
+
+ align:start position:0%
+fair concern and it's related to a lot
+ 
+
+ align:start position:0%
+fair concern and it's related to a lot
+of these other things and that uh just
+
+ align:start position:0%
+of these other things and that uh just
+ 
+
+ align:start position:0%
+of these other things and that uh just
+for example duplication will naturally
+
+ align:start position:0%
+for example duplication will naturally
+ 
+
+ align:start position:0%
+for example duplication will naturally
+lead to something I mean if you start
+
+ align:start position:0%
+lead to something I mean if you start
+ 
+
+ align:start position:0%
+lead to something I mean if you start
+out with X regulating Y and Y is
+
+ align:start position:0%
+out with X regulating Y and Y is
+ 
+
+ align:start position:0%
+out with X regulating Y and Y is
+duplicated then now you have X
+
+ align:start position:0%
+duplicated then now you have X
+ 
+
+ align:start position:0%
+duplicated then now you have X
+regulating some y1 and also some
+
+ align:start position:0%
+regulating some y1 and also some
+ 
+
+ align:start position:0%
+regulating some y1 and also some
+Y2 right and this is the beginnings of a
+
+ align:start position:0%
+Y2 right and this is the beginnings of a
+ 
+
+ align:start position:0%
+Y2 right and this is the beginnings of a
+network Motif right um and and so it's a
+
+ align:start position:0%
+network Motif right um and and so it's a
+ 
+
+ align:start position:0%
+network Motif right um and and so it's a
+reasonable it's a reasonable thing to
+
+ align:start position:0%
+reasonable it's a reasonable thing to
+ 
+
+ align:start position:0%
+reasonable it's a reasonable thing to
+worry about but maybe we can correct for
+
+ align:start position:0%
+worry about but maybe we can correct for
+ 
+
+ align:start position:0%
+worry about but maybe we can correct for
+at least a majority of this by using the
+
+ align:start position:0%
+at least a majority of this by using the
+ 
+
+ align:start position:0%
+at least a majority of this by using the
+proper null model at least that would be
+
+ align:start position:0%
+proper null model at least that would be
+ 
+
+ align:start position:0%
+proper null model at least that would be
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+hope well right but that's why you don't
+
+ align:start position:0%
+hope well right but that's why you don't
+ 
+
+ align:start position:0%
+hope well right but that's why you don't
+want necessarily okay that's why you
+
+ align:start position:0%
+want necessarily okay that's why you
+ 
+
+ align:start position:0%
+want necessarily okay that's why you
+don't yeah okay that's fair you know but
+
+ align:start position:0%
+don't yeah okay that's fair you know but
+ 
+
+ align:start position:0%
+don't yeah okay that's fair you know but
+then the question is what null model
+
+ align:start position:0%
+then the question is what null model
+ 
+
+ align:start position:0%
+then the question is what null model
+should we be using
+
+ align:start position:0%
+should we be using
+ 
+
+ align:start position:0%
+should we be using
+yeah so I feel like having the
+
+ align:start position:0%
+yeah so I feel like having the
+ 
+
+ align:start position:0%
+yeah so I feel like having the
+microscopic constraints does not
+
+ align:start position:0%
+microscopic constraints does not
+ 
+
+ align:start position:0%
+microscopic constraints does not
+necessarily need to be in the null model
+
+ align:start position:0%
+necessarily need to be in the null model
+ 
+
+ align:start position:0%
+necessarily need to be in the null model
+I feel like we can have a norel without
+
+ align:start position:0%
+I feel like we can have a norel without
+ 
+
+ align:start position:0%
+I feel like we can have a norel without
+using the microscopic constraints and
+
+ align:start position:0%
+using the microscopic constraints and
+ 
+
+ align:start position:0%
+using the microscopic constraints and
+then just say oh well that's another
+
+ align:start position:0%
+then just say oh well that's another
+ 
+
+ align:start position:0%
+then just say oh well that's another
+possibility for why we might have these
+
+ align:start position:0%
+possibility for why we might have these
+ 
+
+ align:start position:0%
+possibility for why we might have these
+divergencies I I don't think they need
+
+ align:start position:0%
+divergencies I I don't think they need
+ 
+
+ align:start position:0%
+divergencies I I don't think they need
+to be in the N model yeah it's just that
+
+ align:start position:0%
+to be in the N model yeah it's just that
+ 
+
+ align:start position:0%
+to be in the N model yeah it's just that
+then you can't say anything about
+
+ align:start position:0%
+then you can't say anything about
+ 
+
+ align:start position:0%
+then you can't say anything about
+Evolution well fair but I don't think
+
+ align:start position:0%
+Evolution well fair but I don't think
+ 
+
+ align:start position:0%
+Evolution well fair but I don't think
+you should have to be I don't think you
+
+ align:start position:0%
+you should have to be I don't think you
+ 
+
+ align:start position:0%
+you should have to be I don't think you
+have to say something about Evolution
+
+ align:start position:0%
+have to say something about Evolution
+ 
+
+ align:start position:0%
+have to say something about Evolution
+afterwards NE yeah and I think that this
+
+ align:start position:0%
+afterwards NE yeah and I think that this
+ 
+
+ align:start position:0%
+afterwards NE yeah and I think that this
+question about how strongly you can
+
+ align:start position:0%
+question about how strongly you can
+ 
+
+ align:start position:0%
+question about how strongly you can
+argue that Evolution selected for
+
+ align:start position:0%
+argue that Evolution selected for
+ 
+
+ align:start position:0%
+argue that Evolution selected for
+something um this is a little bit of a
+
+ align:start position:0%
+something um this is a little bit of a
+ 
+
+ align:start position:0%
+something um this is a little bit of a
+judgment call all right because most of
+
+ align:start position:0%
+judgment call all right because most of
+ 
+
+ align:start position:0%
+judgment call all right because most of
+these evolutionary arguments are not
+
+ align:start position:0%
+these evolutionary arguments are not
+ 
+
+ align:start position:0%
+these evolutionary arguments are not
+Ironclad you know there it's more a
+
+ align:start position:0%
+Ironclad you know there it's more a
+ 
+
+ align:start position:0%
+Ironclad you know there it's more a
+matter of making you feel yeah kind of
+
+ align:start position:0%
+matter of making you feel yeah kind of
+ 
+
+ align:start position:0%
+matter of making you feel yeah kind of
+comfortable with looking for what the
+
+ align:start position:0%
+comfortable with looking for what the
+ 
+
+ align:start position:0%
+comfortable with looking for what the
+evolution explanation might have been
+
+ align:start position:0%
+evolution explanation might have been
+ 
+
+ align:start position:0%
+evolution explanation might have been
+you know and that this is just I mean
+
+ align:start position:0%
+you know and that this is just I mean
+ 
+
+ align:start position:0%
+you know and that this is just I mean
+the nature of looking at I mean of
+
+ align:start position:0%
+the nature of looking at I mean of
+ 
+
+ align:start position:0%
+the nature of looking at I mean of
+historical science right um I mean you
+
+ align:start position:0%
+historical science right um I mean you
+ 
+
+ align:start position:0%
+historical science right um I mean you
+can speculate about what would have
+
+ align:start position:0%
+can speculate about what would have
+ 
+
+ align:start position:0%
+can speculate about what would have
+happened if Napoleon had done something
+
+ align:start position:0%
+happened if Napoleon had done something
+ 
+
+ align:start position:0%
+happened if Napoleon had done something
+else or whatever right but uh you know
+
+ align:start position:0%
+else or whatever right but uh you know
+ 
+
+ align:start position:0%
+else or whatever right but uh you know
+it's a it's you speculation I mean of
+
+ align:start position:0%
+it's a it's you speculation I mean of
+ 
+
+ align:start position:0%
+it's a it's you speculation I mean of
+course you know the hope is that we can
+
+ align:start position:0%
+course you know the hope is that we can
+ 
+
+ align:start position:0%
+course you know the hope is that we can
+collect multiple pieces of evidence that
+
+ align:start position:0%
+collect multiple pieces of evidence that
+ 
+
+ align:start position:0%
+collect multiple pieces of evidence that
+make us more and more comfortable with
+
+ align:start position:0%
+make us more and more comfortable with
+ 
+
+ align:start position:0%
+make us more and more comfortable with
+it in some cases we can do laboratory
+
+ align:start position:0%
+it in some cases we can do laboratory
+ 
+
+ align:start position:0%
+it in some cases we can do laboratory
+Evolution to get more Comfort right but
+
+ align:start position:0%
+Evolution to get more Comfort right but
+ 
+
+ align:start position:0%
+Evolution to get more Comfort right but
+you know laboratory Evolution doesn't
+
+ align:start position:0%
+you know laboratory Evolution doesn't
+ 
+
+ align:start position:0%
+you know laboratory Evolution doesn't
+prove that that's what happened you know
+
+ align:start position:0%
+prove that that's what happened you know
+ 
+
+ align:start position:0%
+prove that that's what happened you know
+a million years ago either right but I'd
+
+ align:start position:0%
+a million years ago either right but I'd
+ 
+
+ align:start position:0%
+a million years ago either right but I'd
+say it's it's more the accumulation of
+
+ align:start position:0%
+say it's it's more the accumulation of
+ 
+
+ align:start position:0%
+say it's it's more the accumulation of
+evidence to make you feel comfortable
+
+ align:start position:0%
+evidence to make you feel comfortable
+ 
+
+ align:start position:0%
+evidence to make you feel comfortable
+with an argument um but we you know
+
+ align:start position:0%
+with an argument um but we you know
+ 
+
+ align:start position:0%
+with an argument um but we you know
+let's first maybe make sure we
+
+ align:start position:0%
+let's first maybe make sure we
+ 
+
+ align:start position:0%
+let's first maybe make sure we
+understand what the null model is and
+
+ align:start position:0%
+understand what the null model is and
+ 
+
+ align:start position:0%
+understand what the null model is and
+then we can maybe and then you know and
+
+ align:start position:0%
+then we can maybe and then you know and
+ 
+
+ align:start position:0%
+then we can maybe and then you know and
+then on Thursday we'll decide whether
+
+ align:start position:0%
+then on Thursday we'll decide whether
+ 
+
+ align:start position:0%
+then on Thursday we'll decide whether
+well decide and we'll we'll we'll
+
+ align:start position:0%
+well decide and we'll we'll we'll
+ 
+
+ align:start position:0%
+well decide and we'll we'll we'll
+discuss what we think that means about
+
+ align:start position:0%
+discuss what we think that means about
+ 
+
+ align:start position:0%
+discuss what we think that means about
+Evolution yeah yeah so I think um what
+
+ align:start position:0%
+Evolution yeah yeah so I think um what
+ 
+
+ align:start position:0%
+Evolution yeah yeah so I think um what
+we the other part and the PEX that we
+
+ align:start position:0%
+we the other part and the PEX that we
+ 
+
+ align:start position:0%
+we the other part and the PEX that we
+read about the in and out distributions
+
+ align:start position:0%
+read about the in and out distributions
+ 
+
+ align:start position:0%
+read about the in and out distributions
+is important for the N model
+
+ align:start position:0%
+is important for the N model
+ 
+
+ align:start position:0%
+is important for the N model
+yes it seems to me
+
+ align:start position:0%
+yes it seems to me
+ 
+
+ align:start position:0%
+yes it seems to me
+that Network might be a good model for
+
+ align:start position:0%
+that Network might be a good model for
+ 
+
+ align:start position:0%
+that Network might be a good model for
+the IND
+
+ align:start position:0%
+the IND
+ 
+
+ align:start position:0%
+the IND
+distributions but not for the out
+
+ align:start position:0%
+distributions but not for the out
+ 
+
+ align:start position:0%
+distributions but not for the out
+distribtion that's
+
+ align:start position:0%
+distribtion that's
+ 
+
+ align:start position:0%
+distribtion that's
+right yeah and I think this is this is
+
+ align:start position:0%
+right yeah and I think this is this is
+ 
+
+ align:start position:0%
+right yeah and I think this is this is
+really important I think that it it's
+
+ align:start position:0%
+really important I think that it it's
+ 
+
+ align:start position:0%
+really important I think that it it's
+clear that the that the actual
+
+ align:start position:0%
+clear that the that the actual
+ 
+
+ align:start position:0%
+clear that the that the actual
+transcription network of eai for example
+
+ align:start position:0%
+transcription network of eai for example
+ 
+
+ align:start position:0%
+transcription network of eai for example
+is not well described as an erish or any
+
+ align:start position:0%
+is not well described as an erish or any
+ 
+
+ align:start position:0%
+is not well described as an erish or any
+kind of random Network U but then it
+
+ align:start position:0%
+kind of random Network U but then it
+ 
+
+ align:start position:0%
+kind of random Network U but then it
+kind of does big the question of of what
+
+ align:start position:0%
+kind of does big the question of of what
+ 
+
+ align:start position:0%
+kind of does big the question of of what
+should we be using and you could say
+
+ align:start position:0%
+should we be using and you could say
+ 
+
+ align:start position:0%
+should we be using and you could say
+well we just we just make a power law
+
+ align:start position:0%
+well we just we just make a power law
+ 
+
+ align:start position:0%
+well we just we just make a power law
+network but then you say oh but there's
+
+ align:start position:0%
+network but then you say oh but there's
+ 
+
+ align:start position:0%
+network but then you say oh but there's
+the in degree and the out degree you
+
+ align:start position:0%
+the in degree and the out degree you
+ 
+
+ align:start position:0%
+the in degree and the out degree you
+know how much do you want to keep track
+
+ align:start position:0%
+know how much do you want to keep track
+ 
+
+ align:start position:0%
+know how much do you want to keep track
+of that and I think that there's a a
+
+ align:start position:0%
+of that and I think that there's a a
+ 
+
+ align:start position:0%
+of that and I think that there's a a
+fairly strong argument that what you
+
+ align:start position:0%
+fairly strong argument that what you
+ 
+
+ align:start position:0%
+fairly strong argument that what you
+should do is what they call this degree
+
+ align:start position:0%
+should do is what they call this degree
+ 
+
+ align:start position:0%
+should do is what they call this degree
+preserving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Network and in particular what that
+
+ align:start position:0%
+Network and in particular what that
+ 
+
+ align:start position:0%
+Network and in particular what that
+means is
+
+ align:start position:0%
+means is
+ 
+
+ align:start position:0%
+means is
+that you take all of you take the real
+
+ align:start position:0%
+that you take all of you take the real
+ 
+
+ align:start position:0%
+that you take all of you take the real
+Network right so you take the actual
+
+ align:start position:0%
+Network right so you take the actual
+ 
+
+ align:start position:0%
+Network right so you take the actual
+Network that you're going to be
+
+ align:start position:0%
+Network that you're going to be
+ 
+
+ align:start position:0%
+Network that you're going to be
+analyzing and there there is some
+
+ align:start position:0%
+analyzing and there there is some
+ 
+
+ align:start position:0%
+analyzing and there there is some
+actual degree distribution right so
+
+ align:start position:0%
+actual degree distribution right so
+ 
+
+ align:start position:0%
+actual degree distribution right so
+there's you know one node has you know
+
+ align:start position:0%
+there's you know one node has you know
+ 
+
+ align:start position:0%
+there's you know one node has you know
+so K1 might be
+
+ align:start position:0%
+so K1 might be
+ 
+
+ align:start position:0%
+so K1 might be
+106 K2 might be 7
+
+ align:start position:0%
+106 K2 might be 7
+ 
+
+ align:start position:0%
+106 K2 might be 7
+73 dot dott dot dot you know up to KNN
+
+ align:start position:0%
+73 dot dott dot dot you know up to KNN
+ 
+
+ align:start position:0%
+73 dot dott dot dot you know up to KNN
+which is equal to one and of course I'm
+
+ align:start position:0%
+which is equal to one and of course I'm
+ 
+
+ align:start position:0%
+which is equal to one and of course I'm
+not even talking about it being directed
+
+ align:start position:0%
+not even talking about it being directed
+ 
+
+ align:start position:0%
+not even talking about it being directed
+but you can do the same thing with
+
+ align:start position:0%
+but you can do the same thing with
+ 
+
+ align:start position:0%
+but you can do the same thing with
+directed right um but then what you do
+
+ align:start position:0%
+directed right um but then what you do
+ 
+
+ align:start position:0%
+directed right um but then what you do
+is you kind of mix things up so you
+
+ align:start position:0%
+is you kind of mix things up so you
+ 
+
+ align:start position:0%
+is you kind of mix things up so you
+start with the real Network and then you
+
+ align:start position:0%
+start with the real Network and then you
+ 
+
+ align:start position:0%
+start with the real Network and then you
+do something to randomize it right and
+
+ align:start position:0%
+do something to randomize it right and
+ 
+
+ align:start position:0%
+do something to randomize it right and
+and it's a rather clever scheme I'm just
+
+ align:start position:0%
+and it's a rather clever scheme I'm just
+ 
+
+ align:start position:0%
+and it's a rather clever scheme I'm just
+going to describe it briefly here and
+
+ align:start position:0%
+going to describe it briefly here and
+ 
+
+ align:start position:0%
+going to describe it briefly here and
+then we'll talk more about it on
+
+ align:start position:0%
+then we'll talk more about it on
+ 
+
+ align:start position:0%
+then we'll talk more about it on
+Thursday what you do is you take all of
+
+ align:start position:0%
+Thursday what you do is you take all of
+ 
+
+ align:start position:0%
+Thursday what you do is you take all of
+the actual
+
+ align:start position:0%
+the actual
+ 
+
+ align:start position:0%
+the actual
+uh so let's say we have some X1 some X2
+
+ align:start position:0%
+uh so let's say we have some X1 some X2
+ 
+
+ align:start position:0%
+uh so let's say we have some X1 some X2
+and some here we have a y y 1 a
+
+ align:start position:0%
+and some here we have a y y 1 a
+ 
+
+ align:start position:0%
+and some here we have a y y 1 a
+Y2 a Y3 okay now let's say that these
+
+ align:start position:0%
+Y2 a Y3 okay now let's say that these
+ 
+
+ align:start position:0%
+Y2 a Y3 okay now let's say that these
+guys are regulating something like this
+
+ align:start position:0%
+guys are regulating something like this
+ 
+
+ align:start position:0%
+guys are regulating something like this
+what you do is you take two edges
+
+ align:start position:0%
+what you do is you take two edges
+ 
+
+ align:start position:0%
+what you do is you take two edges
+randomly we'll claim we CL pick this one
+
+ align:start position:0%
+randomly we'll claim we CL pick this one
+ 
+
+ align:start position:0%
+randomly we'll claim we CL pick this one
+and that one what we do is we
+
+ align:start position:0%
+and that one what we do is we
+ 
+
+ align:start position:0%
+and that one what we do is we
+swap the um the targets okay so what we
+
+ align:start position:0%
+swap the um the targets okay so what we
+ 
+
+ align:start position:0%
+swap the um the targets okay so what we
+do is we make this guy come over here
+
+ align:start position:0%
+do is we make this guy come over here
+ 
+
+ align:start position:0%
+do is we make this guy come over here
+and then this one comes over
+
+ align:start position:0%
+and then this one comes over
+ 
+
+ align:start position:0%
+and then this one comes over
+here okay so now what we do is we erase
+
+ align:start position:0%
+here okay so now what we do is we erase
+ 
+
+ align:start position:0%
+here okay so now what we do is we erase
+this we erase this now we have a new
+
+ align:start position:0%
+this we erase this now we have a new
+ 
+
+ align:start position:0%
+this we erase this now we have a new
+network but intriguingly the degree
+
+ align:start position:0%
+network but intriguingly the degree
+ 
+
+ align:start position:0%
+network but intriguingly the degree
+distributions for both incoming and
+
+ align:start position:0%
+distributions for both incoming and
+ 
+
+ align:start position:0%
+distributions for both incoming and
+outgoing edges are identical to what we
+
+ align:start position:0%
+outgoing edges are identical to what we
+ 
+
+ align:start position:0%
+outgoing edges are identical to what we
+had before this right you know every guy
+
+ align:start position:0%
+had before this right you know every guy
+ 
+
+ align:start position:0%
+had before this right you know every guy
+has the same outgoing edges incoming
+
+ align:start position:0%
+has the same outgoing edges incoming
+ 
+
+ align:start position:0%
+has the same outgoing edges incoming
+edges but they're just they have
+
+ align:start position:0%
+edges but they're just they have
+ 
+
+ align:start position:0%
+edges but they're just they have
+different targets right so if you just
+
+ align:start position:0%
+different targets right so if you just
+ 
+
+ align:start position:0%
+different targets right so if you just
+do this procedure many many times then
+
+ align:start position:0%
+do this procedure many many times then
+ 
+
+ align:start position:0%
+do this procedure many many times then
+what you do is you achieve some
+
+ align:start position:0%
+what you do is you achieve some
+ 
+
+ align:start position:0%
+what you do is you achieve some
+randomized version of the real Network
+
+ align:start position:0%
+randomized version of the real Network
+ 
+
+ align:start position:0%
+randomized version of the real Network
+okay and then what you can do is you can
+
+ align:start position:0%
+okay and then what you can do is you can
+ 
+
+ align:start position:0%
+okay and then what you can do is you can
+ask you can ask how many feed forward
+
+ align:start position:0%
+ask you can ask how many feed forward
+ 
+
+ align:start position:0%
+ask you can ask how many feed forward
+Loops are there how many you know this
+
+ align:start position:0%
+Loops are there how many you know this
+ 
+
+ align:start position:0%
+Loops are there how many you know this
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+right and so I think that there's a fair
+
+ align:start position:0%
+right and so I think that there's a fair
+ 
+
+ align:start position:0%
+right and so I think that there's a fair
+argument that this is in some ways the
+
+ align:start position:0%
+argument that this is in some ways the
+ 
+
+ align:start position:0%
+argument that this is in some ways the
+proper null model to be asking the
+
+ align:start position:0%
+proper null model to be asking the
+ 
+
+ align:start position:0%
+proper null model to be asking the
+question and indeed for example there
+
+ align:start position:0%
+question and indeed for example there
+ 
+
+ align:start position:0%
+question and indeed for example there
+are many more feed forward Loops than
+
+ align:start position:0%
+are many more feed forward Loops than
+ 
+
+ align:start position:0%
+are many more feed forward Loops than
+there would be in an Eros reny but still
+
+ align:start position:0%
+there would be in an Eros reny but still
+ 
+
+ align:start position:0%
+there would be in an Eros reny but still
+what you see is that you lose many feed
+
+ align:start position:0%
+what you see is that you lose many feed
+ 
+
+ align:start position:0%
+what you see is that you lose many feed
+forward Loops so this is this is then
+
+ align:start position:0%
+forward Loops so this is this is then
+ 
+
+ align:start position:0%
+forward Loops so this is this is then
+the argument for U for feed for Loops
+
+ align:start position:0%
+the argument for U for feed for Loops
+ 
+
+ align:start position:0%
+the argument for U for feed for Loops
+being selected for right we'll talk
+
+ align:start position:0%
+being selected for right we'll talk
+ 
+
+ align:start position:0%
+being selected for right we'll talk
+about this and we'll quantify it on
+
+ align:start position:0%
+about this and we'll quantify it on
+ 
+
+ align:start position:0%
+about this and we'll quantify it on
+Thursday but I'm available for the next
+
+ align:start position:0%
+Thursday but I'm available for the next
+ 
+
+ align:start position:0%
+Thursday but I'm available for the next
+half hour if anybody has any questions
+
+ align:start position:0%
+half hour if anybody has any questions
+ 
+
+ align:start position:0%
+half hour if anybody has any questions
+all right
\ No newline at end of file
diff --git a/Posv6O0845c.txt b/Posv6O0845c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cf74e89157c4ef0f08974a8d8acef4d0098296d7
--- /dev/null
+++ b/Posv6O0845c.txt
@@ -0,0 +1,2900 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+TIM RAY: I guess
+first of all I wanted
+
+to entertain any questions you
+might've had about the concert.
+
+I know Mark is having you
+write up some reports.
+
+Actually I got an advanced
+copy of one person's report
+
+that had some really
+interesting comments.
+
+One of the comments
+that this person wrote
+
+was about hearing--
+trying to listen
+
+for the difference between
+the improvised sections
+
+and the written sections.
+
+What was your feeling on that?
+
+Did you feel like you had
+a pretty good sense of when
+
+we were improvising and when
+we were playing written music?
+
+Was it a little hard to
+tell sometimes, right?
+
+I actually tell-- we hear
+that comment a lot, actually.
+
+Including from symphony players.
+
+It might have been hard for you
+to tell, don't think that means
+
+anything negative.
+
+Like I say, a lot of musicians
+come up to us afterwards
+
+and they go, I don't know
+what you guys were doing,
+
+or how you were
+blending the composition
+
+and the improvisation.
+
+And that's, to me, is sort
+of an affirmation of one
+
+of my goals for this group,
+is to blend composition
+
+and improvisation in
+kind of a seamless way.
+
+I mean, it's obviously
+not seamless,
+
+but to make that-- make
+those lines blurry.
+
+And I think a lot of
+composers of modern music--
+
+I know Mark Harvey's
+compositions do somewhat
+
+the same thing, as well
+as of course Greg's.
+
+And a lot of people
+I know sometimes
+
+look for that kind of blurry
+line between composition
+
+improvisation.
+
+Because it's really all
+the same thing, right?
+
+It's just composition,
+you write it down.
+
+Improvisation is
+spontaneous, but still it's
+
+all kind of the same thing.
+
+The piece that you transcribed
+from an improvisation,
+
+did you play that--
+were you playing it
+
+exactly how it
+sounded originally?
+
+Or did you kind
+of reinterpret it?
+
+Because it sounded
+like a real piece.
+
+[LAUGHTER]
+
+Yeah, that's--
+
+GREG HOPKINS: (LAUGHING)
+What do you mean by that?
+
+TIM RAY: Yeah, right.
+
+GREG HOPKINS: I
+know what you mean.
+
+I know exactly what you mean.
+
+TIM RAY: Sounded like real
+music, not improvisation.
+
+No, I'm teasing.
+
+No, that's a good question.
+
+That's another one
+people ask a lot.
+
+Yeah, that was, again,
+that was sort of Eugene's.
+
+That was something
+that he had improvised
+
+with a different piano player
+years ago in this cathedral.
+
+Now he talked about it
+a little bit, I know.
+
+GREG HOPKINS: Oh, you're talking
+about the piano-cello piece.
+
+TIM RAY: Yeah, the
+piano-cello piece, right.
+
+And as he said,
+they wrote it out.
+
+I mean, they wrote it out.
+
+Eugene kind of just
+memorized his cello part.
+
+And his part was
+pretty much as played,
+
+as improvised back however
+many years ago that was.
+
+And then the piano part, they
+wrote it out and of course,
+
+being a jazz player
+I changed it.
+
+So I mean I basically
+followed the intent of it,
+
+you know, and I played
+something specific to what
+
+was played back then, as
+according to the music.
+
+But then I did some other--
+I changed it up a little bit.
+
+Made it a little
+bit more-- gave it
+
+a little bit of a personal
+thing, a personal touch.
+
+But yeah, that's
+one of the things.
+
+I know you weren't
+here last week
+
+when we were doing the thing
+with diatonic improvisation,
+
+but basically that's
+what that was.
+
+It was a whole thing
+about just improvising
+
+in the key of D major.
+
+And Eugene and this
+guy, Paul Halley,
+
+was the pianist, basically
+did an amazing job of kind
+
+of creating this thing.
+
+And as you said, it
+sounded like real music.
+
+It sounded like something
+that could have been composed.
+
+It had sections and
+melody in the cello,
+
+melody in the piano,
+all kinds of variations
+
+and accompaniments.
+
+And like I said,
+that was just one
+
+of those things that kind
+of worked out really well
+
+improvisationally and
+happened to be recorded.
+
+And so that that's why
+it keeps getting played.
+
+But yeah, so I don't know if
+that answered your question,
+
+but that's kind of
+the genesis of that.
+
+So, cool.
+
+And then Greg and I--
+
+GREG HOPKINS: He probably played
+the piece though, many times,
+
+right?
+
+TIM RAY: Yeah, yeah.
+
+Eugene's played that
+piece many times.
+
+GREG HOPKINS: So it's not
+improvisation of the moment,
+
+it's a creation that he
+recreates many times over
+
+and over and over.
+
+So they kind of played
+it similar each time.
+
+TIM RAY: Right, yeah.
+
+You know, and
+sometimes it's funny
+
+because we, Greg and I and Mark,
+are kind of jazz-- you know,
+
+what we might call
+hardcore jazz guys.
+
+Who sort of believe
+in the sanctity
+
+of spontaneous improvisation.
+
+But actually, if you look back
+not that long ago in history
+
+that happened a lot.
+
+Duke Ellington spans
+a perfect example.
+
+Cootie Williams would
+take a trumpet solo
+
+and Duke would say, I like
+that, do that solo again.
+
+The next thing you know,
+that Cootie Williams solo
+
+becomes part of the book.
+
+What started off as an
+improvisation, or at least
+
+largely as an improvisation,
+became part of the music.
+
+So there's a little bit of
+history even in the jazz
+
+world--
+
+GREG HOPKINS: Well,
+a lot of jazz music
+
+starts out as improvisation
+and becomes concrete.
+
+Like some of Charlie
+Parker's tunes.
+
+And he would play them
+the same each time.
+
+OK, this is the melody.
+
+And they're nothing but,
+really, improvisations
+
+that become part of history.
+
+TIM RAY: Indeed.
+
+And then, the duet
+that Greg and I
+
+did, I made a little comment
+at the beginning about I
+
+didn't know what
+was going to happen.
+
+And it's kind of
+true, I don't really
+
+know what's going to happen.
+
+That's one of those
+moments, which
+
+I like to do in our program, and
+Greg and I have done this a lot
+
+over the course of our--
+
+GREG HOPKINS: We never decide
+what tune we're going to play.
+
+TIM RAY: Yeah, well
+we don't decide it.
+
+I'm happy to have Greg start.
+
+And I don't know, did you--
+when you started did you know--
+
+GREG HOPKINS: I had no idea.
+
+TIM RAY: I had a
+feeling you were--
+
+GREG HOPKINS: I was
+searching around,
+
+I was kind of doing a
+little prelude stuff.
+
+Saying, now what do I feel
+like I want to play here?
+
+Well, we just played something
+in sharp key so I said,
+
+we're going to go into flats.
+
+Because I wanted to
+have a different taste.
+
+And A-flat came out, OK, well
+let's-- I know this tune.
+
+And, hey let's play
+rhythm changes in A-flat,
+
+and then we went into
+the Thelonious Monk
+
+tune "Little Rootie Tootie".
+
+Which we-- I know that
+Tim knows and I know.
+
+So basically after a
+little fooling around,
+
+OK, let's do that, no problem.
+
+But we had fun
+with Monk's riffs,
+
+so then we really
+played the composition.
+
+And as a composer, I think
+that's-- I really appreciate
+
+that, when an improviser or a
+soloist plays the composition.
+
+Because that's a strong way
+to approach a improvisation--
+
+playing the musical composition
+instead of just playing
+
+your horn, your instrument.
+
+And playing a bunch of licks
+and making the changes is fine,
+
+but what does it all mean
+related to Mr. Monk's music?
+
+Because I put myself not
+as so much a soloist,
+
+it's not about me
+as much as it's
+
+about how can I interpret
+his composition.
+
+So I'm more like the conduit
+instead of the focal point.
+
+So we had a lot of
+fun with his riffs.
+
+TIM RAY: Yeah, we did.
+
+And that gets a little bit back
+to what we were talking about
+
+with the assignment,
+which is this tune
+
+of Greg's, [? "Karagassian". ?]
+
+GREG HOPKINS: Oh,
+you have that one?
+
+TIM RAY: Yeah, you guys
+all brought it, right?
+
+All right, so we're going to
+start playing in just a second.
+
+But the idea, being to--
+obviously, get the foundation.
+
+In other words,
+learn the melody,
+
+get comfortable with the minor
+blues progression-- which
+
+is what the improvisation
+is based on-- if you're not
+
+already comfortable
+with that, and then use
+
+some of the motifs in the melody
+to inform your improvisation.
+
+Use to improvise in the motivic
+fashion, as much as you can.
+
+I mean, you don't--
+obviously, no one-- well,
+
+I shouldn't say no one.
+
+It would be rare to hear
+an improvisation created
+
+completely out of motivic
+stuff, although I'm
+
+sure it's been done.
+
+GREG HOPKINS: Sure it is.
+
+TIM RAY: Some of my favorite
+improvisers do that.
+
+I mean they don't--
+
+GREG HOPKINS: I'm always
+playing the melody up here.
+
+Even when I play a standard
+tune, I'm on the melody.
+
+So then you're never at
+a loss for what to do.
+
+I don't really have
+to think of something.
+
+It's here.
+
+Do something with that.
+
+TIM RAY: Yeah, that's true.
+
+GREG HOPKINS: But then
+what do you do with it?
+
+You have to know your
+compositional techniques.
+
+Repetition, sequence,
+transposition, elongation,
+
+augmentation, diminution,
+transformation, embellishment,
+
+all that stuff.
+
+TIM RAY: Yeah, absolutely.
+
+GREG HOPKINS: And
+then sometimes we
+
+play stuff, little
+cannons back and forth.
+
+Question and answer,
+question and answer.
+
+TIM RAY: Yeah, cool.
+
+So, should we jump
+into this piece?
+
+What do we think?
+
+Yeah, we've got plenty of time.
+
+OK, so [? "Karagassian". ?] I
+know I suggested maybe we have
+
+you guys do some-- you
+know, pair up to do some
+
+improvisations.
+
+But maybe just for
+rehearsal sake,
+
+why don't we all
+play the melody.
+
+And we'll see if we're
+on the same page.
+
+GREG HOPKINS: So, as you know
+this is written for my cat.
+
+My late cat [? Karagassian. ?]
+I wrote the piece probably
+
+in 15 minutes.
+
+It just came out.
+
+Because the cat
+had so much spirit.
+
+And it's all here.
+
+You know cats,
+they're very playful.
+
+So this melody's very playful.
+
+It's meant to be had
+a lot of fun with.
+
+TIM RAY: Yes, indeed.
+
+So yeah, so let's
+all play the melody.
+
+If you guys on guitar
+want to do some chord
+
+changes in the
+three-four measure
+
+you can, or you can just
+stay with the melody
+
+if you want to do that.
+
+Let's just do that and
+see where we're at.
+
+And then we'll get
+into some improv.
+
+Do you want to
+count it off, Greg?
+
+GREG HOPKINS: One,
+two, a one, two, three.
+
+[MUSIC PLAYING]
+
+TIM RAY: That's a hard one.
+
+[MUSIC PLAYING]
+
+All right.
+
+Not bad.
+
+GREG HOPKINS: Not bad at all.
+
+But the inflection
+is pretty good.
+
+Yeah, it's really
+soft and distant.
+
+And then in the third measure
+we can clobber that note.
+
+Actually, play a different
+note than E-flat.
+
+That's like a crash.
+
+One more time.
+
+A one, two, a one, two.
+
+Yeah, but softer.
+
+Much softer.
+
+Just touch it.
+
+One, two, a one, two.
+
+That's it.
+
+One, two.
+
+Loud.
+
+Two, three,four.
+
+One, two.
+
+So I always put a doit on that.
+
+You know what a doit is?
+
+Where you fall up?
+
+It's a fall up instead
+of a fall down.
+
+TIM RAY: Yeah, it's always
+hard on a piano, right?
+
+I usually just
+[INAUDIBLE] short little--
+
+GREG HOPKINS:
+That's an old term ,
+
+nobody talks about
+that stuff anymore.
+
+D-O-I-T it's called doit.
+
+Doy-eet.
+
+TIM RAY: Where are we?
+
+GREG HOPKINS: Bar nine.
+
+Third line.
+
+Two, a one, two, three.
+
+Two, three.
+
+Three, four.
+
+Two, three.
+
+Three, four.
+
+Good.
+
+A two, a one, two.
+
+Quiet.
+
+Two, three.
+
+Yeah, nice.
+
+So the fermata would
+just be for the ending.
+
+And then we would go
+to that three four bar
+
+and then go right back to the
+beginning and start the blues.
+
+TIM RAY: The blues is
+in four four by the way,
+
+and I know the chart's
+not clear about that.
+
+But, yeah four four blues.
+
+For the improv.
+
+GREG HOPKINS: Yeah.
+
+So the whole ending
+part is supposed
+
+to create this tension,
+a little angst.
+
+With the rhythm, four against
+three, and then the four
+
+goes faster than you think.
+
+And then when we start
+to play the blues form,
+
+it relaxes back
+to regular tempo.
+
+So the cat's kind of clawing
+its way up the curtain.
+
+But we don't play-- we
+don't improvise on that,
+
+but you could certainly
+include the motifs
+
+in your improvisations.
+
+TIM RAY: Cool.
+
+GREG HOPKINS: Should we
+do it with some solos?
+
+TIM RAY: Yeah, let's
+do it with some solos.
+
+Yeah.
+
+GREG HOPKINS: Now, we perform
+it as a totally conversational
+
+piece.
+
+There's no accompaniment.
+
+Everybody's just soloing
+at the same time, which
+
+is an interesting
+style which I like.
+
+I tend to play a lot less when
+I'm playing conversationally.
+
+Because you want the
+person to talk back to you.
+
+You can't be like
+some professors who
+
+just talk and talk
+and talk and talk
+
+and you can't say anything.
+
+OK.
+
+Just take notes.
+
+TIM RAY: Cool.
+
+But you want to-- maybe
+we'll start with-- well,
+
+let's play the melody again.
+
+And then, and then maybe we'll
+do a little bit of soloing.
+
+I'll maybe keep the form--
+
+GREG HOPKINS: It's going to
+be tough with this many people
+
+to play conversationally.
+
+TIM RAY: Yeah, well maybe
+by the end we'll get there.
+
+We won't start there, though.
+
+But I would like to hear
+some people kind of pair off.
+
+But you want-- maybe we should
+do, like, individually first.
+
+GREG HOPKINS: Yeah, I think so.
+
+Let's do a chorus each.
+
+TIM RAY: Cool, all right.
+
+GREG HOPKINS: And will you comp?
+
+TIM RAY: Yeah,
+I'll do some comp.
+
+GREG HOPKINS: Yeah, do
+some typical comping.
+
+Base notes, you play the melody.
+
+I mean, all you need
+really is base and melody.
+
+Two parts to have counterpoint.
+
+Any two lines could
+be counterpointal.
+
+Then there's conversational.
+
+Much more fun than
+playing alone.
+
+GUEST SPEAKER: And we've
+all-- everybody's assignment
+
+was to prepare, right?
+
+Some thoughts about how
+you would treat the motif.
+
+So why don't we start there?
+
+Then we see how that expands.
+
+TIM RAY: Cool.
+
+GREG HOPKINS: So, do the melody
+once and then we'll start.
+
+So just go around,
+you want to go first?
+
+We'll go around.
+
+We can start there.
+
+A one, two.
+
+[MUSIC PLAYING]
+
+TIM RAY: Yeah, all right.
+
+Cool.
+
+Let's stop there.
+
+Nice, all right.
+
+Great, it's great to
+hear all of you play.
+
+Excellent, thank you.
+
+GREG HOPKINS: So we
+all played one chorus.
+
+TIM RAY: Yeah, so we
+all did one chorus.
+
+While I heard a lot
+of really nice ideas,
+
+I didn't hear a whole
+lot of use of the motifs.
+
+Let's look at those real quick.
+
+GREG HOPKINS: I heard
+the first motif a lot.
+
+TIM RAY: Did you?
+
+OK.
+
+GREG HOPKINS: Yeah,
+some of you played
+
+that opening, which
+I did five times.
+
+But I transposed it each time.
+
+So it kind of created a
+little line cliche, as we say.
+
+TIM RAY: Indeed.
+
+Indeed.
+
+Right.
+
+So that first one, I think
+we looked at these just
+
+briefly last time.
+
+Yeah, the first one
+is a good one to grab.
+
+The repeated note,
+that's a nice one.
+
+GREG HOPKINS: Number
+two, number two.
+
+That's funky.
+
+TIM RAY: That's
+pretty funky, yeah.
+
+GREG HOPKINS: You
+could go [PLAYS MUSIC].
+
+You could go [PLAYS MUSIC].
+
+You could go [PLAYS MUSIC].
+
+You could go [PLAYS MUSIC].
+
+You could go [PLAYS MUSIC].
+
+Just play it, you
+could do-- yeah,
+
+we could do several
+choruses just on that.
+
+TIM RAY: Just on that, I know.
+
+And we probably have.
+
+GREG HOPKINS: By
+changing notes, I'm
+
+using the rhythmic
+contours of motif.
+
+So, the da da da da, I could
+do anything I want there.
+
+[PLAYS MUSIC]
+
+Yeah.
+
+You could work your way through
+creating interesting melodies
+
+by changing the notes.
+
+TIM RAY: Yeah, absolutely.
+
+Do you want to do a little
+motivic exercise, maybe?
+
+We'll go-- we'll
+do the same thing.
+
+We'll go around the--
+
+GREG HOPKINS: Let's
+just play that motif.
+
+Da da da da.
+
+TIM RAY: Yeah.
+
+GREG HOPKINS: So you
+can play four notes.
+
+One two three four.
+
+You can play any
+intervals, though.
+
+TIM RAY: Cool.
+
+GREG HOPKINS: Not yet.
+
+This is my warm up,
+Mark, for the day.
+
+[LAUGHTER]
+
+GUEST SPEAKER: Pretty good.
+
+GREG HOPKINS: It's a
+good tune to warm up on.
+
+TIM RAY: It is.
+
+So, you want to do
+everybody four measures?
+
+GREG HOPKINS: Let's do--
+
+TIM RAY: [INAUDIBLE]
+
+Sure.
+
+Four bars each.
+
+TIM RAY: What do you think?
+
+OK.
+
+Just doing that motif.
+
+Just the repeated note motif.
+
+All right.
+
+Why don't you start.
+
+GREG HOPKINS: A two, a one, two.
+
+Good Nice idea.
+
+Yeah.
+
+Do another one.
+
+You go.
+
+One.
+
+AUDIENCE: From this [INAUDIBLE]?
+
+GREG HOPKINS: Yeah.
+
+Flute.
+
+TIM RAY: You ready?
+
+Yeah, nice.
+
+GREG HOPKINS: Next solo.
+
+[LAUGHTER]
+
+Yeah.
+
+So we're setting parameters now.
+
+You have to use that material
+and create with that.
+
+It's like, I mean we're
+sculptors, Let's face it,
+
+we're just shaping stuff
+out of these materials.
+
+So sometimes it's really
+good to limit yourself.
+
+That's what an etude
+is, an etude is always
+
+like one idea for
+the whole page.
+
+And the composer of
+the etude does it
+
+in all the different
+keys so you'll learn it.
+
+So it's really good to set the
+parameters like that I think.
+
+TIM RAY: Yeah, oh
+I think so too.
+
+I think it's a great
+way to-- you know,
+
+there's all kinds of parameters.
+
+You can obviously-- we're
+doing the little motivic thing
+
+with the four
+notes, but you can,
+
+obviously-- there's any
+number of other motifs
+
+you could do that with.
+
+You can do set
+parameters, as far
+
+as the range of
+your instruments,
+
+or dynamics, or
+rhythmic density,
+
+you know, do a solo
+with all quarter notes.
+
+Right?
+
+Or do a solo with all
+quarter note triplets, right?
+
+Something like that,
+that's another great way
+
+to kind of expand your range.
+
+In other words,
+expand your range
+
+of what you're doing
+with improvisation.
+
+Let's do another one of those.
+
+Let's see, what's another
+good motif to grab?
+
+GREG HOPKINS: Bar
+nine is pretty good.
+
+That might be a little hard.
+
+Well, the opening motif is good.
+
+TIM RAY: Cool.
+
+Cool.
+
+Yeah, let's do the same thing.
+
+Four measures again?
+
+GREG HOPKINS: Four measures.
+
+We'll do the opening motif.
+
+Two, a one, two, three.
+
+Nice.
+
+Nice.
+
+Go ahead.
+
+Change direction.
+
+Nice.
+
+TIM RAY: Yeah.
+
+GREG HOPKINS: OK.
+
+So, I mean, how would you
+practice something like that?
+
+Well, let's play that motif.
+
+Just those three notes.
+
+OK, let's go up in half steps.
+
+So I'm going to sequence it, I'm
+going to play it in every key.
+
+OK, and then we
+go (PLAYS MUSIC).
+
+Yeah.
+
+So the first one, D
+G, D G, D G D. Now,
+
+what am I-- I'm
+hearing in my head,
+
+I'm hearing five one five.
+
+So I'm hearing it in the key.
+
+Up a half.
+
+So an A-flat now.
+
+Let's do it in A. A.
+
+Next key.
+
+Next key.
+
+Next key.
+
+Next key.
+
+Yeah, good.
+
+OK?
+
+So then we could (PLAYS MUSIC).
+
+You can put it in, and we could
+do the same thing going down.
+
+We could do the motif down.
+
+I mean, that's what you
+do when you practice.
+
+You do really mundane--
+maybe not mundane,
+
+you do really small,
+little things.
+
+I mean, it might
+take me 10 minutes
+
+to really feel comfortable
+with that, just those intervals
+
+going up in sequences like that.
+
+TIM RAY: Yeah, absolutely.
+
+GREG HOPKINS: And then
+you could sequence
+
+things four different ways.
+
+Let's sequence it
+in whole steps.
+
+Up a whole step, I'm going to
+go up a whole step each time.
+
+Too high?
+
+Yeah.
+
+So the person is going
+to be in G then A then B
+
+then C-sharp, then E-flat,
+then F, and then G again.
+
+Right?
+
+TIM RAY: Yeah.
+
+Absolutely.
+
+GREG HOPKINS: Can we do that?
+
+TIM RAY: Sure.
+
+GREG HOPKINS: Let's just go up.
+
+Skip the first note.
+
+Now I'm going to sequence
+just the first measure.
+
+Right.
+
+That's it.
+
+There I go.
+
+It's the whole thing, now
+it's a whole different animal.
+
+Now it sounds like a
+progression, right?
+
+TIM RAY: It does.
+
+Yeah, absolutely.
+
+GREG HOPKINS: So
+that creates it.
+
+And we can do it
+in minor thirds.
+
+OK?
+
+Let's do that over a G pedal.
+
+Yeah, that creates kind
+of a bluesy feeling.
+
+It's like a G diminished chord.
+
+TIM RAY: Yeah, absolutely.
+
+Right, yeah.
+
+GREG HOPKINS: So now I'm
+creating counterpoint just
+
+with the motif.
+
+Then we could do
+it in major thirds.
+
+That's an interesting one too--
+
+TIM RAY: It is.
+
+GREG HOPKINS: You think?
+
+TIM RAY: Oh yeah.
+
+Absolutely.
+
+GREG HOPKINS: This is-- I
+learned all this from him.
+
+[LAUGHTER]
+
+Let's do that over a D pedal.
+
+TIM RAY: Sure.
+
+GREG HOPKINS: One, two.
+
+Then we could do cycle four.
+
+So we did half steps,
+whole steps, minor thirds,
+
+major thirds, what's
+the next interval?
+
+Above a major third
+is a perfect fourth.
+
+So this is going-- there's
+going to be 12 of them.
+
+This is cycle five, right?
+
+TIM RAY: Sure, yeah.
+
+Yeah, right.
+
+Or you can just--
+
+GREG HOPKINS: Now we're
+going to expand it.
+
+We're going to
+play a minor triad.
+
+Instead of just one five, we're
+going to play one three five.
+
+Let's play up and
+down a minor triad.
+
+So we embellished the lick.
+
+That's fine.
+
+You can add notes
+whenever you want.
+
+Why'd you do that?
+
+I wanted to.
+
+G minor, so now we're
+going to do cycles,
+
+so we're going to go a forth
+up to C minor, fourth up to F
+
+minor, B-flat minor, E-flat
+minor, A-flat minor, D-flat
+
+minor, G-flat minor, B minor,
+E minor, A minor, D minor,
+
+back to G. Slowly.
+
+Ready, go.
+
+So now I'm going to
+take that same idea
+
+and do it in whole steps.
+
+And so on.
+
+It's all just grunt work.
+
+But that's what Coltrane did.
+
+He used to practice in his
+apartment eight hours a day.
+
+Eight hours a day just on
+these-- what he was playing.
+
+He made up his own etudes.
+
+Yeah, he did.
+
+Which is what all the good--
+all the great players do.
+
+TIM RAY: Yeah, absolutely.
+
+I mean, certainly--
+
+GREG HOPKINS: This is the model.
+
+This is the model.
+
+This has dozens of ideas.
+
+TIM RAY: Yeah, and
+certainly that's
+
+the idea of any kind of
+work on improvisation.
+
+You know, when you're sitting
+alone at home thinking,
+
+you know, because
+everyone always says,
+
+well I don't know how to
+practice improvisation.
+
+GREG HOPKINS: Yeah,
+what should I do?
+
+Oh, I'm going to play
+my scales every day.
+
+OK, that's fine.
+
+TIM RAY: Because
+it's spontaneous.
+
+GREG HOPKINS: You got make
+goals, a set of goals.
+
+And we can tell you what goals,
+what projects to work on.
+
+TIM RAY: But yeah.
+
+But a lot of it's just about
+coming up with stuff like this.
+
+Obviously, as Greg said,
+we can tell you stuff
+
+or you could go
+buy books that have
+
+patterns and stuff like that.
+
+And that's all great,
+but sometimes it's
+
+just about what
+we're doing, which
+
+is like, OK, let's try that.
+
+Now let's try it up a fourth.
+
+And let's find this
+little two bar thing.
+
+I mean, if you want
+to get more difficult
+
+you can find something
+even in a tune like this.
+
+Something that's a
+little more difficult
+
+and try that in all 12 keys.
+
+GREG HOPKINS: Let's
+do bar 17, you know.
+
+[LAUGHTER]
+
+TIM RAY: Yeah, right.
+
+No, I'm not going to try it.
+
+GREG HOPKINS:
+That's a-- basically
+
+it's this a B-flat lick.
+
+Yeah, that was my
+idea, I want to go
+
+from B-flat to B-flat with some
+kind of maybe 12 tone idea,
+
+I don't know what it is.
+
+TIM RAY: Yeah, so
+that's, as Greg says,
+
+a lot of just sitting alone
+at home work that's, I think,
+
+that's really helpful.
+
+All the great players did it.
+
+They all spent 10,000 hours.
+
+Is that the current idea?
+
+GREG HOPKINS: I
+do the same thing.
+
+I do the same thing
+with my scales.
+
+How do you practice your scales?
+
+Well, you do them in intervals.
+
+I mean, what is a melody?
+
+Let's define melody.
+
+This is a good place to do it.
+
+Let's have a real technical
+definition of melody.
+
+Anybody, what is melody?
+
+First thing that
+comes into your head.
+
+What's the melody?
+
+AUDIENCE: Whatever
+you'd sing after you're
+
+done listening to it.
+
+GREG HOPKINS: Yeah, whatever
+you hear-- what did you say?
+
+AUDIENCE: Whatever
+you would sing
+
+after you were done
+listening to it.
+
+GREG HOPKINS: Good, yeah,
+whatever you'd sing.
+
+You're a melody player, violin,
+you're all melody players.
+
+Yeah.
+
+You guys, too.
+
+What's melody to you?
+
+AUDIENCE: It's
+kind of the song--
+
+GREG HOPKINS: It's
+the song, very good.
+
+AUDIENCE: [INAUDIBLE]
+
+GREG HOPKINS: Many
+people say that.
+
+It's the main idea.
+
+It's the meaning.
+
+Technically, is this music?
+
+No, this is paper
+with ink on it.
+
+This is graph paper.
+
+This is graph paper.
+
+Pitch goes up and down,
+time goes that way.
+
+This is not music.
+
+It's only music when you
+realize it, when you play it.
+
+So, the better you are
+at creating intervals,
+
+the better you'll be
+at melody playing.
+
+A melody is a
+series of intervals
+
+in some kind of rhythm.
+
+So if I play-- that's the sixth.
+
+So six down, fourth
+up, third up,
+
+minor sixth down, half step
+up, half step, half step.
+
+That's what a melody is,
+it's a series of intervals,
+
+that's all.
+
+In some kind of time, right?
+
+Every melody-- that's a
+third, and then a fourth.
+
+Another third, second
+second, major seventh.
+
+So, when we're playing
+our scales, right?
+
+That's all the
+same scale, I just
+
+played different intervals.
+
+I'll play the scale
+in seconds, I'll
+
+play the scale in thirds,
+fourths, fifths, sixths,
+
+and sevenths.
+
+Let's play G melodic minor.
+
+No, G-natural minor.
+
+Good, yeah, up and down.
+
+One note in the top.
+
+Go.
+
+Now play it in thirds.
+
+Now play it in fourths, slowly.
+
+Now in fifths.
+
+Nice.
+
+Sixth is really pretty.
+
+Sevenths is even more diverse,
+a little obtuse, maybe?
+
+Yeah.
+
+Octaves.
+
+Ninths.
+
+I mean, you could
+expand it even further.
+
+TIM RAY: Sure.
+
+GREG HOPKINS: You
+do that, right?
+
+TIM RAY: Yeah.
+
+GREG HOPKINS: You've got
+to learn your intervals.
+
+TIM RAY: Of course.
+
+Yeah, absolutely.
+
+GREG HOPKINS: And also
+inherent in the scale
+
+is diatonic triads and
+diatonic seventh chords.
+
+Do you do that in class?
+
+GUEST SPEAKER: We
+haven't done that.
+
+Have you done that with Tom?
+
+GREG HOPKINS: Yeah,
+play up all the triads
+
+in the G minor scale.
+
+TIM RAY: Yeah, well, right.
+
+If you're doing natural minor.
+
+GREG HOPKINS: Let's do that.
+
+It's just building blocks.
+
+This is the building blocks
+of melody and harmony.
+
+TIM RAY: Yeah, that's true.
+
+GREG HOPKINS: And then
+as you study each scale,
+
+each scale is different.
+
+Each scale has
+characteristic notes
+
+that make it function
+different than other scales.
+
+That's what makes
+the scales different,
+
+is the different notes.
+
+And how the architecture
+of the scale
+
+works and draws things together.
+
+So, I mean that's what we
+study when we practice.
+
+I'll practice
+scales and I'll try
+
+to really get the
+meaning out of the scale.
+
+This scale, natural
+minor, is-- Yeah, I
+
+mean there's certain things that
+make that scale work, right?
+
+TIM RAY: Sure, absolutely.
+
+GREG HOPKINS: Flat sixth, right?
+
+TIM RAY: Yeah, yeah.
+
+Absolutely.
+
+GREG HOPKINS: So if I'm
+playing a natural minor,
+
+I immediately know that the flat
+sixth is a real strong note.
+
+Let's just play a natural--
+we'll play a natural minor just
+
+for a minute.
+
+TIM RAY: Sure.
+
+GREG HOPKINS: G, so it'll
+be like C minor, right?
+
+Another chord?
+
+TIM RAY: Right, yeah.
+
+GREG HOPKINS: So one,
+two, a one, two, three.
+
+Yeah.
+
+TIM RAY: Yeah, all right.
+
+GREG HOPKINS: So
+you're using D seven?
+
+TIM RAY: Yeah, I used D seven.
+
+GREG HOPKINS: Oh,
+you used D seven, OK.
+
+TIM RAY: Yeah, I threw that in.
+
+Which is not technically part--
+
+GUEST SPEAKER: We did
+this with [INAUDIBLE],
+
+and so you're already
+talking [INAUDIBLE].
+
+GREG HOPKINS: This
+is aeolian mode.
+
+It's called the aeolian mode.
+
+Let's just play G minor C minor.
+
+TIM RAY: Yeah.
+
+GREG HOPKINS: One bar each.
+
+One two three four--
+
+I think modes is a great way
+to start learning harmony.
+
+TIM RAY: Absolutely, yeah.
+
+GREG HOPKINS: Because
+there's only one note,
+
+really, that's really strong.
+
+So here were playing G minor
+for a bar and C minor for a bar.
+
+G minor, C minor.
+
+What's the note that
+changes the most?
+
+When you play the C minor
+it's going to be the E-flat.
+
+The E-flat.
+
+So the G minor has
+a D in it, right?
+
+In then you go to C minor.
+
+[SINGS NOTE]
+
+So that's the
+meaning of aeolian.
+
+TIM RAY: Absolutely, yeah.
+
+GREG HOPKINS: You could
+play E-flat major,
+
+would be a good
+chord too, I think.
+
+Let's play a bar each,
+G minor and C minor.
+
+Let's start over here, guitar.
+
+One, a two, a one,
+two, three, four.
+
+Good.
+
+Yeah.
+
+Yeah, OK.
+
+Got the idea?
+
+Yeah, that's good.
+
+I mean that's really
+good for your ear.
+
+Now I'm really working
+on a small slice
+
+of harmonic information
+that I could put to use.
+
+Now you played D seven before,
+what scale would that be?
+
+TIM RAY: Yeah, right?
+
+So, D seven has got
+what note in it--
+
+GREG HOPKINS: What
+note does D seven have?
+
+TIM RAY: --that doesn't
+belong in the aeolian--
+
+GREG HOPKINS: That's different.
+
+TIM RAY: Yeah, right.
+
+You played it, Chris.
+
+F-sharp, right?
+
+GREG HOPKINS: F-sharp.
+
+Yeah.
+
+So that's kind of
+like G-- now we've
+
+got to learn G
+harmonic minor scale.
+
+Which has that very interesting
+augmented second interval.
+
+Gives it an exotic, Middle
+Eastern or Detroit flavor.
+
+Let's play harmonic minor.
+
+One, two, three.
+
+Let's play the triads in
+harmonic minor-- slowly.
+
+One, two-- Yeah.
+
+The three chord's very
+interesting, augmented chord.
+
+And the four chord
+is still minor.
+
+So it's similar to aeolian
+but it has the much preferred
+
+leading tone, the F-sharp.
+
+TIM RAY: Yes, indeed.
+
+GREG HOPKINS: Just for fun, now
+let's play G minor for a bar
+
+and D seven flat nine for a bar.
+
+What do you think?
+
+TIM RAY: Yeah.
+
+GREG HOPKINS: Flute first.
+
+Nah, I'll start.
+
+Two, a one, two, three--
+Yeah, yeah, nice.
+
+Yeah, and so on.
+
+It's another small
+slice of harmony
+
+but it's different
+than the first one.
+
+So you practice that and you
+practice it, and then it sinks
+
+in your ear.
+
+Because this is nothing
+but ear training.
+
+All this is just ear training
+so you can pick your flavors.
+
+OK, I want this flavor, I
+want that color, that mood,
+
+that sound.
+
+Then there's melodic minor.
+
+Yeah, because when
+you play a minor key
+
+you don't just
+play one scale, we
+
+mix four or five
+minor scales together.
+
+And if I play a
+certain note, he'll
+
+hear it and play the voicing
+behind me, or whatever.
+
+TIM RAY: Exactly.
+
+That's where listening
+comes into play.
+
+Listening to the
+person you're with.
+
+GREG HOPKINS: When Wayne
+Shorter was in the Army
+
+he used to spend a
+month on one scale.
+
+He would practice the
+key of D-flat for months.
+
+He'd play every tune
+he knew in D-flat.
+
+He'd practice the scales,
+he'd practice the chords,
+
+he'd play rhythm changes,
+blues, everything in one key.
+
+And Coltrane did the same thing.
+
+All the guys that practiced.
+
+I have a tape of Clifford
+Brown practicing the bridge
+
+to "Cherokee" for an hour.
+
+And you know he
+did it every day.
+
+Played with his mute.
+
+TIM RAY: Cool.
+
+So I also wanted
+to get back to--
+
+and this great
+information, certainly-- I
+
+wanted to get back the idea
+of having you guys pair up
+
+a little bit.
+
+And maybe try it without me
+doing the accompaniment, which
+
+of course is about listening, as
+I was saying just a second ago,
+
+listening to who you're with.
+
+Without the accompaniment
+it becomes--
+
+what becomes more important?
+
+This is like as Greg
+and I and Eugene
+
+were doing with
+the song, where we
+
+were all kind of soloing
+at the same time.
+
+That's what I want to try to
+get you guys to do a little bit.
+
+And what aspect of
+music becomes more
+
+important in that situation.
+
+Something we haven't really
+talked about yet today.
+
+GREG HOPKINS: So let's have
+flute, sax, and guitar.
+
+TIM RAY: What I was getting
+at was rhythm, right?
+
+Again, getting back to the
+idea that we're all time
+
+keepers, right.
+
+I mean, when you hear
+somebody like Greg who
+
+is a great improviser, his
+rhythmic ideas are very clear.
+
+His rhythmic ideas
+are very clear,
+
+and if he does
+something intentionally
+
+that's a little less
+clear, he follows it up
+
+with something that's more clear
+so that the people around him
+
+know where the beats are, right?
+
+So that's another thing that's
+really important to work on
+
+and I know we did a little
+thing with rhythm with Eugene
+
+last time.
+
+AUDIENCE: So are we doing
+an accompaniment solo type
+
+thing or more like
+a conversational?
+
+TIM RAY: I think we should try
+doing like a conversational--
+
+GREG HOPKINS: Conversation.
+
+So nobody's really
+comping, you're
+
+all playing your own ideas.
+
+I'm leaving space for
+other people's ideas.
+
+TIM RAY: Right.
+
+So what we'll do is
+maybe have you guys play.
+
+You're all improvising again,
+leaving space, conversing.
+
+I'll do a baseline for 12
+bars and then I'll drop
+
+and you guys keep going.
+
+OK?
+
+So this will be improv.
+
+We're not going
+to do the melody,
+
+just starting right
+with the improv.
+
+Feel free to throw in
+some motivic stuff, some
+
+of the things Greg was talking
+about in terms of the scales,
+
+obviously G minor scale can
+figure prominently in this.
+
+OK, so here we go.
+
+Right at the top of the improv.
+
+One, a two, a one, two, three--
+
+GREG HOPKINS: One more?
+
+One more.
+
+Not bad.
+
+That was good.
+
+TIM RAY: That was good.
+
+Everybody feel where
+the time was, right?
+
+Felt pretty secure to me.
+
+And then listening, really nice.
+
+One of the motifs we
+haven't touched on,
+
+which is the quarter
+note triplets, right?
+
+Quarter note
+triplets are tricky,
+
+because that's against
+the feeling of duple.
+
+Against the feeling
+of two and four,
+
+which is-- any
+song in four four,
+
+most songs tend to
+spend most of their time
+
+either quarter
+notes, eight notes.
+
+Any kind of triplet feeling
+is sort of against that.
+
+So when there's
+not accompaniment,
+
+you have to be
+really careful to--
+
+I mean I'm not saying don't play
+them, I think they're great--
+
+but just be really careful to
+articulate where your landing
+
+them.
+
+Because that's usually the thing
+that gets rushed or dragged
+
+and that sometimes
+can send you--
+
+GREG HOPKINS: And sometimes if
+somebody's playing quarter note
+
+triplets, maybe the other
+person would play quarter notes
+
+against that.
+
+Just to be obstinate, or
+to have that counterpoint
+
+so I can tell that
+they're really triplets.
+
+I mean, sometimes you don't
+want to use mimicry too much.
+
+If somebody plays an idea, don't
+just play the same idea back.
+
+Play something different.
+
+If I say hello, you
+don't say hello.
+
+Well, I guess you do.
+
+What's your name?
+
+What's your name?
+
+Yeah, you have to
+have an answer.
+
+So let's do a flute,
+guitar, and violin.
+
+TIM RAY: We'll do
+the same thing.
+
+I'll start off with the
+baseline and then I'll drop out.
+
+But you guys keep going.
+
+OK, here we go.
+
+One, a two, a one,
+two, three, four--
+
+GREG HOPKINS: Not
+bad, yeah it was good.
+
+TIM RAY: OK, nice.
+
+So-- oh no, go ahead.
+
+GREG HOPKINS: Same as before,
+nice use of the motifs.
+
+Sometimes I'll just
+play the melody.
+
+And Tim and Eugene
+will play around it,
+
+and sometimes Tim will
+quote some of the melody.
+
+TIM RAY: Yeah, absolutely.
+
+A couple things to
+just be careful of,
+
+I know you guys
+are, to some degree,
+
+kind of hanging
+on to the rhythm.
+
+I know, which is, of
+course, what we all
+
+do in this situation.
+
+You're like, sometimes
+you're kind of white
+
+knuckling the beats instead of
+just kind of letting it flow.
+
+And I think sometimes
+when that happens,
+
+you start to lose a
+little bit of linear flow.
+
+I felt like there was a lot
+of root improvisation based
+
+on the roots going on.
+
+GREG HOPKINS: It was
+a little block style.
+
+TIM RAY: Yeah, right.
+
+And again, it's not to say
+that if you did it again
+
+you might do something
+entirely different.
+
+But it's just one thing
+to be aware of, right?
+
+And this is one of these
+situations where you try it
+
+again and you say,
+OK I'm going to not
+
+focus on the root
+so much I'm going
+
+to try to do more linear
+stuff, more scales.
+
+Maybe focus on the third or the
+fifth, or just, like I said,
+
+be a little bit more free
+with what you're doing.
+
+So, again it's nice stuff.
+
+GREG HOPKINS: Let's
+do flute and piano,
+
+and you get another chance.
+
+TIM RAY: All right.
+
+Same thing.
+
+One, two, a one,
+two, three, four--
+
+GREG HOPKINS: Bang!
+
+OK, you stopped before the end.
+
+We're still playing the fourth.
+
+We're still playing
+12 bar forms, right?
+
+Did they stop before the end?
+
+TIM RAY: Yeah , we--
+
+GREG HOPKINS: Or maybe it was
+just really good use of space.
+
+TIM RAY: Yeah.
+
+It's either that or you
+owe us three measures.
+
+I don't know.
+
+We'll come back and
+collect next year.
+
+GREG HOPKINS: Let
+me show you-- here's
+
+an interesting way to practice.
+
+This is going to be
+a revolving trio.
+
+I'm going to start
+with you three, OK.
+
+Then you're going to drop
+out, you're going to join in,
+
+and then you're
+going to drop out,
+
+then you're going to join in.
+
+Then you're going to--
+whatever three people.
+
+And no base line.
+
+A one, two, a one,
+two, three, four--
+
+OK.
+
+TIM RAY: Yeah, all right.
+
+GREG HOPKINS: To you?
+
+Yeah.
+
+It's a nice way to practice and
+then you don't-- everyone's not
+
+jamming in your ear, and again
+you're setting parameters.
+
+We're going to have three people
+playing or two people playing.
+
+TIM RAY: Yeah.
+
+Yeah, you guys are
+doing a great job.
+
+I mean, I can tell--
+
+GREG HOPKINS: You're keeping the
+form and your ideas are clear.
+
+TIM RAY: Very nice.
+
+And again, hearing some of
+the motifs come into play,
+
+that's very cool.
+
+GREG HOPKINS: I'm thrilled.
+
+TIM RAY: Yeah, I--
+
+GREG HOPKINS: [? Karagassian ?]
+will be very happy.
+
+TIM RAY: I know we're
+getting close to out of time.
+
+Are there any
+questions about some
+
+of this stuff we've been
+talking about, scales, modes?
+
+GREG HOPKINS: I need to
+stress what Tim said before.
+
+Melodies and harmonies are fine,
+but the most important thing
+
+in this music is rhythm.
+
+Rhythm.
+
+Rhythm.
+
+It's like location
+in real estate.
+
+Rhythm.
+
+Rhythm.
+
+You could play any
+note, it doesn't matter,
+
+if it's in the right time and
+it swings, people will buy it.
+
+TIM RAY: That's true.
+
+GREG HOPKINS: It's
+absolutely true.
+
+It's a rhythmic art form.
+
+Came from dancing.
+
+TIM RAY: Yeah, that's true.
+
+GREG HOPKINS: I do
+an analogy my class.
+
+Let me just get to the
+board right behind you
+
+for one second.
+
+Chalk, mighty chalk.
+
+Harmony.
+
+We study all this harmony.
+
+I'm going to give
+it an H that big.
+
+But I'm a melody guy, so
+melody is more important.
+
+But rhythm is-- and
+actually it should
+
+go to the top of the building
+to under the basement,
+
+and make an R out to
+Mass Ave and back.
+
+TIM RAY: Very cool, thank you.
+
+That's-- I would
+agree with the that.
+
+GREG HOPKINS: Rhythm is--
+
+TIM RAY: So work on rhythm.
+
+GREG HOPKINS: Sometimes
+I just play one note.
+
+TIM RAY: Yeah, I know.
+
+GREG HOPKINS: Let's play
+a minimalistic chorus,
+
+just me and you.
+
+TIM RAY: OK.
+
+GREG HOPKINS: Two, a
+one, two, three-- Yeah,
+
+so we left a lot of
+space, but when we came in
+
+with the rhythms, they
+were very strong that time.
+
+So sometimes I think I'm
+playing like a melodic drummer.
+
+I want to lay that melody
+down so people know right
+
+where it is.
+
+And sometimes I don't,
+sometimes I'll float.
+
+TIM RAY: Right.
+
+And I think most of the
+good players did that.
+
+They'd float for
+awhile and then they'd
+
+lock it in with something
+really specific.
+
+That's one of things I work
+on with some of my students.
+
+Play a phrase, it
+floats, and then play
+
+something that really locks in.
+
+So that you know the difference,
+you can hear the difference,
+
+and you can feel the
+difference in your hands
+
+as to what the different--
+whatever your instrument is.
+
+So you can feel the difference,
+how it affects the music
+
+and how it affects
+your improvisation.
+
+So, yeah that's
+another great-- there's
+
+all these exercises, etudes,
+whatever you want to call them,
+
+for improvisations
+which are great to do.
+
+GREG HOPKINS: Transcribing
+is really good,
+
+because you can't really
+notate jazz rhythms.
+
+You can write the
+notes down, but you
+
+can't notate how
+they're playing them.
+
+So you've got to listen.
+
+And now copy Miles'
+articulation,
+
+or Clifford Brown's
+articulation, or whoever,
+
+Chet Baker.
+
+Because they would all
+play a little differently,
+
+but-- it's all the tongue.
+
+It's all articulation.
+
+Because it's wind
+instruments, I mean
+
+that's where a lot of
+the language comes from.
+
+And piano.
+
+TIM RAY: But even with
+piano or guitar, still,
+
+the articulation makes
+all the difference.
+
+You could do a whole solo
+just based on two notes.
+
+And be somewhat interesting.
+
+I mean, it's not going
+to be super interesting,
+
+but just two notes with
+articulation and strong
+
+rhythms, you can make
+an interesting solo.
+
+Like I say, on any instrument.
+
+I think that's true.
+
+Drummers do it.
+
+That's how they solo.
+
+It's all about how
+they hit the thing.
+
+They don't have 88
+keys to play with,
+
+they've just got four
+drums and a couple symbols.
+
+GREG HOPKINS: And for
+the wind instruments
+
+it's really just a matter
+of slurring and tonguing.
+
+Some short notes,
+some long notes,
+
+some slurred notes
+in the middle.
+
+You've got to
+tongue but it can't
+
+be-- you can't
+tongue too hard or it
+
+sounds too much
+like a classical.
+
+It's got to have the funkiness
+and looseness of the swing.
+
+So yeah, working on your
+articulation is very important.
+
+That's what we do, right?
+
+GUEST SPEAKER:
+Unfortunately I think
+
+we have to wrap because
+it's the end of the period.
+
+GREG HOPKINS: Is it
+3 o'clock already?
+
+GUEST SPEAKER: It's 3:30.
+
+GREG HOPKINS: It's 3:30?
+
+I'm going to get a ticket.
+
+GUEST SPEAKER: So let's give
+a round of applause for Greg.
+
+GREG HOPKINS: Thank you.
+
+Yeah, good play.
+
+TIM RAY: Yeah, nice play.
+
+GREG HOPKINS: And have no fear.
+
+Have no fear.
+
+Play whatever you want.
+
+And try and hear it.
\ No newline at end of file
diff --git a/QKXAd2PhZGY.txt b/QKXAd2PhZGY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6340c92660f087528a37fba0c44358a59fd90788
--- /dev/null
+++ b/QKXAd2PhZGY.txt
@@ -0,0 +1,1128 @@
+align:start position:0%
+ 
+hi welcome back to recitation in lecture
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+ 
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+Professor jarrison was teaching you
+
+ align:start position:0%
+Professor jarrison was teaching you
+ 
+
+ align:start position:0%
+Professor jarrison was teaching you
+about lal's Rule and one thing that he
+
+ align:start position:0%
+about lal's Rule and one thing that he
+ 
+
+ align:start position:0%
+about lal's Rule and one thing that he
+mentioned several times was that when
+
+ align:start position:0%
+mentioned several times was that when
+ 
+
+ align:start position:0%
+mentioned several times was that when
+you have when you apply lal's rule it's
+
+ align:start position:0%
+you have when you apply lal's rule it's
+ 
+
+ align:start position:0%
+you have when you apply lal's rule it's
+really important that the second limit
+
+ align:start position:0%
+really important that the second limit
+ 
+
+ align:start position:0%
+really important that the second limit
+exists in order for lal's rule to be
+
+ align:start position:0%
+exists in order for lal's rule to be
+ 
+
+ align:start position:0%
+exists in order for lal's rule to be
+true in order for the first limit to
+
+ align:start position:0%
+true in order for the first limit to
+ 
+
+ align:start position:0%
+true in order for the first limit to
+equal the second limit so I have a uh
+
+ align:start position:0%
+equal the second limit so I have a uh
+ 
+
+ align:start position:0%
+equal the second limit so I have a uh
+but he didn't he didn't give you any
+
+ align:start position:0%
+but he didn't he didn't give you any
+ 
+
+ align:start position:0%
+but he didn't he didn't give you any
+examples of of uh what can go wrong um
+
+ align:start position:0%
+examples of of uh what can go wrong um
+ 
+
+ align:start position:0%
+examples of of uh what can go wrong um
+so I have here a limit for you to to
+
+ align:start position:0%
+so I have here a limit for you to to
+ 
+
+ align:start position:0%
+so I have here a limit for you to to
+work on um so what I'd like you to do is
+
+ align:start position:0%
+work on um so what I'd like you to do is
+ 
+
+ align:start position:0%
+work on um so what I'd like you to do is
+is try lall's rule see what happens and
+
+ align:start position:0%
+is try lall's rule see what happens and
+ 
+
+ align:start position:0%
+is try lall's rule see what happens and
+then try to solve it a different way not
+
+ align:start position:0%
+then try to solve it a different way not
+ 
+
+ align:start position:0%
+then try to solve it a different way not
+using lyall's rule so why don't you
+
+ align:start position:0%
+using lyall's rule so why don't you
+ 
+
+ align:start position:0%
+using lyall's rule so why don't you
+pause the video uh spend a couple
+
+ align:start position:0%
+pause the video uh spend a couple
+ 
+
+ align:start position:0%
+pause the video uh spend a couple
+minutes working on that come back and we
+
+ align:start position:0%
+minutes working on that come back and we
+ 
+
+ align:start position:0%
+minutes working on that come back and we
+can work on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together welcome back hopefully you had
+
+ align:start position:0%
+together welcome back hopefully you had
+ 
+
+ align:start position:0%
+together welcome back hopefully you had
+some fun working on this limit Let's uh
+
+ align:start position:0%
+some fun working on this limit Let's uh
+ 
+
+ align:start position:0%
+some fun working on this limit Let's uh
+let's go through it and and see what
+
+ align:start position:0%
+let's go through it and and see what
+ 
+
+ align:start position:0%
+let's go through it and and see what
+happens when we when we try to apply
+
+ align:start position:0%
+happens when we when we try to apply
+ 
+
+ align:start position:0%
+happens when we when we try to apply
+lal's rule to it so the first thing to
+
+ align:start position:0%
+lal's rule to it so the first thing to
+ 
+
+ align:start position:0%
+lal's rule to it so the first thing to
+notice is that as X goes to Infinity uh
+
+ align:start position:0%
+notice is that as X goes to Infinity uh
+ 
+
+ align:start position:0%
+notice is that as X goes to Infinity uh
+X plus cosine X well cosine X is is
+
+ align:start position:0%
+X plus cosine X well cosine X is is
+ 
+
+ align:start position:0%
+X plus cosine X well cosine X is is
+small you know between minus one and 1 x
+
+ align:start position:0%
+small you know between minus one and 1 x
+ 
+
+ align:start position:0%
+small you know between minus one and 1 x
+is going to Infinity so the top is going
+
+ align:start position:0%
+is going to Infinity so the top is going
+ 
+
+ align:start position:0%
+is going to Infinity so the top is going
+to infinity and the bottom is going to
+
+ align:start position:0%
+to infinity and the bottom is going to
+ 
+
+ align:start position:0%
+to infinity and the bottom is going to
+Infinity so this is an Infinity over
+
+ align:start position:0%
+Infinity so this is an Infinity over
+ 
+
+ align:start position:0%
+Infinity so this is an Infinity over
+infinity in determinate form so it is a
+
+ align:start position:0%
+infinity in determinate form so it is a
+ 
+
+ align:start position:0%
+infinity in determinate form so it is a
+a context in which we can try to apply
+
+ align:start position:0%
+a context in which we can try to apply
+ 
+
+ align:start position:0%
+a context in which we can try to apply
+lal's rules so that's that's fine it's
+
+ align:start position:0%
+lal's rules so that's that's fine it's
+ 
+
+ align:start position:0%
+lal's rules so that's that's fine it's
+it's an indeterminate ratio we can we
+
+ align:start position:0%
+it's an indeterminate ratio we can we
+ 
+
+ align:start position:0%
+it's an indeterminate ratio we can we
+can look at applying lal's rule so let's
+
+ align:start position:0%
+can look at applying lal's rule so let's
+ 
+
+ align:start position:0%
+can look at applying lal's rule so let's
+let's try to do that so lal's rule says
+
+ align:start position:0%
+let's try to do that so lal's rule says
+ 
+
+ align:start position:0%
+let's try to do that so lal's rule says
+that the limit as X goes to Infinity of
+
+ align:start position:0%
+that the limit as X goes to Infinity of
+ 
+
+ align:start position:0%
+that the limit as X goes to Infinity of
+our expression x + cosine x / X is equal
+
+ align:start position:0%
+our expression x + cosine x / X is equal
+ 
+
+ align:start position:0%
+our expression x + cosine x / X is equal
+and I'm going to put a little question
+
+ align:start position:0%
+and I'm going to put a little question
+ 
+
+ align:start position:0%
+and I'm going to put a little question
+mark here because what lal's rule says
+
+ align:start position:0%
+mark here because what lal's rule says
+ 
+
+ align:start position:0%
+mark here because what lal's rule says
+is that it's equal provided it's equal
+
+ align:start position:0%
+is that it's equal provided it's equal
+ 
+
+ align:start position:0%
+is that it's equal provided it's equal
+to what I'm going to write over here
+
+ align:start position:0%
+to what I'm going to write over here
+ 
+
+ align:start position:0%
+to what I'm going to write over here
+provided that the second limit exists so
+
+ align:start position:0%
+provided that the second limit exists so
+ 
+
+ align:start position:0%
+provided that the second limit exists so
+what goes over here well it's the limit
+
+ align:start position:0%
+what goes over here well it's the limit
+ 
+
+ align:start position:0%
+what goes over here well it's the limit
+as X goes to the same place as X go to
+
+ align:start position:0%
+as X goes to the same place as X go to
+ 
+
+ align:start position:0%
+as X goes to the same place as X go to
+Infinity of the the ratio of the
+
+ align:start position:0%
+Infinity of the the ratio of the
+ 
+
+ align:start position:0%
+Infinity of the the ratio of the
+derivative so the derivative of the top
+
+ align:start position:0%
+derivative so the derivative of the top
+ 
+
+ align:start position:0%
+derivative so the derivative of the top
+divided by the derivative of the bottom
+
+ align:start position:0%
+divided by the derivative of the bottom
+ 
+
+ align:start position:0%
+divided by the derivative of the bottom
+so in this case that's
+
+ align:start position:0%
+so in this case that's
+ 
+
+ align:start position:0%
+so in this case that's
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+minus sin x is the derivative of the top
+
+ align:start position:0%
+minus sin x is the derivative of the top
+ 
+
+ align:start position:0%
+minus sin x is the derivative of the top
+and 1 is the derivative of the
+
+ align:start position:0%
+and 1 is the derivative of the
+ 
+
+ align:start position:0%
+and 1 is the derivative of the
+bottom okay now let's look at this limit
+
+ align:start position:0%
+bottom okay now let's look at this limit
+ 
+
+ align:start position:0%
+bottom okay now let's look at this limit
+what happens well okay the over one part
+
+ align:start position:0%
+what happens well okay the over one part
+ 
+
+ align:start position:0%
+what happens well okay the over one part
+is irrelevant the the one minus part
+
+ align:start position:0%
+is irrelevant the the one minus part
+ 
+
+ align:start position:0%
+is irrelevant the the one minus part
+okay who cares the the only thing that's
+
+ align:start position:0%
+okay who cares the the only thing that's
+ 
+
+ align:start position:0%
+okay who cares the the only thing that's
+changing in this limit is the
+
+ align:start position:0%
+changing in this limit is the
+ 
+
+ align:start position:0%
+changing in this limit is the
+sinx so as X goes to Infinity what this
+
+ align:start position:0%
+sinx so as X goes to Infinity what this
+ 
+
+ align:start position:0%
+sinx so as X goes to Infinity what this
+does is it is it oscillates just like
+
+ align:start position:0%
+does is it is it oscillates just like
+ 
+
+ align:start position:0%
+does is it is it oscillates just like
+sinx does I mean it's it's offset and
+
+ align:start position:0%
+sinx does I mean it's it's offset and
+ 
+
+ align:start position:0%
+sinx does I mean it's it's offset and
+flipped upside down because of this one
+
+ align:start position:0%
+flipped upside down because of this one
+ 
+
+ align:start position:0%
+flipped upside down because of this one
+minus but um so in particular it you
+
+ align:start position:0%
+minus but um so in particular it you
+ 
+
+ align:start position:0%
+minus but um so in particular it you
+know sometimes it's near one sometimes
+
+ align:start position:0%
+know sometimes it's near one sometimes
+ 
+
+ align:start position:0%
+know sometimes it's near one sometimes
+it's near negative 1 sometimes it's near
+
+ align:start position:0%
+it's near negative 1 sometimes it's near
+ 
+
+ align:start position:0%
+it's near negative 1 sometimes it's near
+zero and it and it oscillates back and
+
+ align:start position:0%
+zero and it and it oscillates back and
+ 
+
+ align:start position:0%
+zero and it and it oscillates back and
+forth in between um so in particular
+
+ align:start position:0%
+forth in between um so in particular
+ 
+
+ align:start position:0%
+forth in between um so in particular
+because it's oscillating it's not
+
+ align:start position:0%
+because it's oscillating it's not
+ 
+
+ align:start position:0%
+because it's oscillating it's not
+approaching any value so this this limit
+
+ align:start position:0%
+approaching any value so this this limit
+ 
+
+ align:start position:0%
+approaching any value so this this limit
+doesn't exist uh it's not equal to any
+
+ align:start position:0%
+doesn't exist uh it's not equal to any
+ 
+
+ align:start position:0%
+doesn't exist uh it's not equal to any
+real number it's not equal to Infinity
+
+ align:start position:0%
+real number it's not equal to Infinity
+ 
+
+ align:start position:0%
+real number it's not equal to Infinity
+it's not equal to minus infinity it does
+
+ align:start position:0%
+it's not equal to minus infinity it does
+ 
+
+ align:start position:0%
+it's not equal to minus infinity it does
+not exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the the statement of lal's
+
+ align:start position:0%
+okay so the the statement of lal's
+ 
+
+ align:start position:0%
+okay so the the statement of lal's
+theorem says that thise equality is
+
+ align:start position:0%
+theorem says that thise equality is
+ 
+
+ align:start position:0%
+theorem says that thise equality is
+really wrong okay what it what it means
+
+ align:start position:0%
+really wrong okay what it what it means
+ 
+
+ align:start position:0%
+really wrong okay what it what it means
+is that low rule tells you nothing you
+
+ align:start position:0%
+is that low rule tells you nothing you
+ 
+
+ align:start position:0%
+is that low rule tells you nothing you
+don't learn anything here so if we want
+
+ align:start position:0%
+don't learn anything here so if we want
+ 
+
+ align:start position:0%
+don't learn anything here so if we want
+to compute this first limit we can't use
+
+ align:start position:0%
+to compute this first limit we can't use
+ 
+
+ align:start position:0%
+to compute this first limit we can't use
+lal's rule we have to come up with some
+
+ align:start position:0%
+lal's rule we have to come up with some
+ 
+
+ align:start position:0%
+lal's rule we have to come up with some
+better way to do it okay um so so that's
+
+ align:start position:0%
+better way to do it okay um so so that's
+ 
+
+ align:start position:0%
+better way to do it okay um so so that's
+what's going wrong now let's see about
+
+ align:start position:0%
+what's going wrong now let's see about
+ 
+
+ align:start position:0%
+what's going wrong now let's see about
+doing this even though we don't have
+
+ align:start position:0%
+doing this even though we don't have
+ 
+
+ align:start position:0%
+doing this even though we don't have
+this tool so if we try and and solve
+
+ align:start position:0%
+this tool so if we try and and solve
+ 
+
+ align:start position:0%
+this tool so if we try and and solve
+this limit without lal's rule so we want
+
+ align:start position:0%
+this limit without lal's rule so we want
+ 
+
+ align:start position:0%
+this limit without lal's rule so we want
+to look at the limit as X goes to
+
+ align:start position:0%
+to look at the limit as X goes to
+ 
+
+ align:start position:0%
+to look at the limit as X goes to
+Infinity of X plus cosine x / X um well
+
+ align:start position:0%
+Infinity of X plus cosine x / X um well
+ 
+
+ align:start position:0%
+Infinity of X plus cosine x / X um well
+think about what's important in this
+
+ align:start position:0%
+think about what's important in this
+ 
+
+ align:start position:0%
+think about what's important in this
+limit as X is getting big well X is
+
+ align:start position:0%
+limit as X is getting big well X is
+ 
+
+ align:start position:0%
+limit as X is getting big well X is
+getting big and X is getting big and
+
+ align:start position:0%
+getting big and X is getting big and
+ 
+
+ align:start position:0%
+getting big and X is getting big and
+what's cosine X doing well cosine X is
+
+ align:start position:0%
+what's cosine X doing well cosine X is
+ 
+
+ align:start position:0%
+what's cosine X doing well cosine X is
+behaving like a constant but but wigger
+
+ align:start position:0%
+behaving like a constant but but wigger
+ 
+
+ align:start position:0%
+behaving like a constant but but wigger
+right we could we could say so cosine X
+
+ align:start position:0%
+right we could we could say so cosine X
+ 
+
+ align:start position:0%
+right we could we could say so cosine X
+is is always between minus one and one
+
+ align:start position:0%
+is is always between minus one and one
+ 
+
+ align:start position:0%
+is is always between minus one and one
+but you know it's oscillating but it's
+
+ align:start position:0%
+but you know it's oscillating but it's
+ 
+
+ align:start position:0%
+but you know it's oscillating but it's
+in some bounded interval there um
+
+ align:start position:0%
+in some bounded interval there um
+ 
+
+ align:start position:0%
+in some bounded interval there um
+whereas x and x
+
+ align:start position:0%
+whereas x and x
+ 
+
+ align:start position:0%
+whereas x and x
+are both going to Infinity at exactly
+
+ align:start position:0%
+are both going to Infinity at exactly
+ 
+
+ align:start position:0%
+are both going to Infinity at exactly
+the same speed
+
+ align:start position:0%
+the same speed
+ 
+
+ align:start position:0%
+the same speed
+so this suggests a manipulation that
+
+ align:start position:0%
+so this suggests a manipulation that
+ 
+
+ align:start position:0%
+so this suggests a manipulation that
+that sort of allows us to quantify that
+
+ align:start position:0%
+that sort of allows us to quantify that
+ 
+
+ align:start position:0%
+that sort of allows us to quantify that
+explicitly and so one thing that we can
+
+ align:start position:0%
+explicitly and so one thing that we can
+ 
+
+ align:start position:0%
+explicitly and so one thing that we can
+do is we can divide top and bottom of
+
+ align:start position:0%
+do is we can divide top and bottom of
+ 
+
+ align:start position:0%
+do is we can divide top and bottom of
+this limit by X um so if we do that or
+
+ align:start position:0%
+this limit by X um so if we do that or
+ 
+
+ align:start position:0%
+this limit by X um so if we do that or
+or equivalently we can just divide this
+
+ align:start position:0%
+or equivalently we can just divide this
+ 
+
+ align:start position:0%
+or equivalently we can just divide this
+x into the into the fraction above split
+
+ align:start position:0%
+x into the into the fraction above split
+ 
+
+ align:start position:0%
+x into the into the fraction above split
+it into two fractions
+
+ align:start position:0%
+it into two fractions
+ 
+
+ align:start position:0%
+it into two fractions
+so we have I'm just going to rewrite it
+
+ align:start position:0%
+so we have I'm just going to rewrite it
+ 
+
+ align:start position:0%
+so we have I'm just going to rewrite it
+one more time the limit as X goes to to
+
+ align:start position:0%
+one more time the limit as X goes to to
+ 
+
+ align:start position:0%
+one more time the limit as X goes to to
+Infinity of x + cosine x / X is equal to
+
+ align:start position:0%
+Infinity of x + cosine x / X is equal to
+ 
+
+ align:start position:0%
+Infinity of x + cosine x / X is equal to
+the Limit as X goes to Infinity of 1
+
+ align:start position:0%
+the Limit as X goes to Infinity of 1
+ 
+
+ align:start position:0%
+the Limit as X goes to Infinity of 1
++ cosine
+
+ align:start position:0%
++ cosine
+ 
+
+ align:start position:0%
++ cosine
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+overx all right so what's happening here
+
+ align:start position:0%
+overx all right so what's happening here
+ 
+
+ align:start position:0%
+overx all right so what's happening here
+well all I've done is I've divided that
+
+ align:start position:0%
+well all I've done is I've divided that
+ 
+
+ align:start position:0%
+well all I've done is I've divided that
+X in and now you see that this one that
+
+ align:start position:0%
+X in and now you see that this one that
+ 
+
+ align:start position:0%
+X in and now you see that this one that
+was from the X overx so that's a
+
+ align:start position:0%
+was from the X overx so that's a
+ 
+
+ align:start position:0%
+was from the X overx so that's a
+constant that's going to one and as X
+
+ align:start position:0%
+constant that's going to one and as X
+ 
+
+ align:start position:0%
+constant that's going to one and as X
+goes to Infinity cosine X again is we
+
+ align:start position:0%
+goes to Infinity cosine X again is we
+ 
+
+ align:start position:0%
+goes to Infinity cosine X again is we
+can think of it like a constant but
+
+ align:start position:0%
+can think of it like a constant but
+ 
+
+ align:start position:0%
+can think of it like a constant but
+wigger X is going to Infinity so cosine
+
+ align:start position:0%
+wigger X is going to Infinity so cosine
+ 
+
+ align:start position:0%
+wigger X is going to Infinity so cosine
+XX is going to zero as X goes to
+
+ align:start position:0%
+XX is going to zero as X goes to
+ 
+
+ align:start position:0%
+XX is going to zero as X goes to
+Infinity so at so I guess I wouldn't
+
+ align:start position:0%
+Infinity so at so I guess I wouldn't
+ 
+
+ align:start position:0%
+Infinity so at so I guess I wouldn't
+call this plugging in but it's you know
+
+ align:start position:0%
+call this plugging in but it's you know
+ 
+
+ align:start position:0%
+call this plugging in but it's you know
+sort of just like plugging in so this
+
+ align:start position:0%
+sort of just like plugging in so this
+ 
+
+ align:start position:0%
+sort of just like plugging in so this
+part is going to zero so we're left with
+
+ align:start position:0%
+part is going to zero so we're left with
+ 
+
+ align:start position:0%
+part is going to zero so we're left with
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay so we can evaluate this limit
+
+ align:start position:0%
+one okay so we can evaluate this limit
+ 
+
+ align:start position:0%
+one okay so we can evaluate this limit
+fairly easily just took a couple steps
+
+ align:start position:0%
+fairly easily just took a couple steps
+ 
+
+ align:start position:0%
+fairly easily just took a couple steps
+but we can't evaluate it with lal's rule
+
+ align:start position:0%
+but we can't evaluate it with lal's rule
+ 
+
+ align:start position:0%
+but we can't evaluate it with lal's rule
+so this is why you have that that that
+
+ align:start position:0%
+so this is why you have that that that
+ 
+
+ align:start position:0%
+so this is why you have that that that
+extra thing in in the statement of the
+
+ align:start position:0%
+extra thing in in the statement of the
+ 
+
+ align:start position:0%
+extra thing in in the statement of the
+theorem that Professor Jaron kept saying
+
+ align:start position:0%
+theorem that Professor Jaron kept saying
+ 
+
+ align:start position:0%
+theorem that Professor Jaron kept saying
+and and that I'll say every time I use
+
+ align:start position:0%
+and and that I'll say every time I use
+ 
+
+ align:start position:0%
+and and that I'll say every time I use
+it which is lal's Rule says that the
+
+ align:start position:0%
+it which is lal's Rule says that the
+ 
+
+ align:start position:0%
+it which is lal's Rule says that the
+limit of the ratio is equal to the limit
+
+ align:start position:0%
+limit of the ratio is equal to the limit
+ 
+
+ align:start position:0%
+limit of the ratio is equal to the limit
+of the ratio of the derivatives provided
+
+ align:start position:0%
+of the ratio of the derivatives provided
+ 
+
+ align:start position:0%
+of the ratio of the derivatives provided
+the second limit exists okay so here's
+
+ align:start position:0%
+the second limit exists okay so here's
+ 
+
+ align:start position:0%
+the second limit exists okay so here's
+an example where the second limit didn't
+
+ align:start position:0%
+an example where the second limit didn't
+ 
+
+ align:start position:0%
+an example where the second limit didn't
+exist and so we can't say that the two
+
+ align:start position:0%
+exist and so we can't say that the two
+ 
+
+ align:start position:0%
+exist and so we can't say that the two
+are actually equal to each other and we
+
+ align:start position:0%
+are actually equal to each other and we
+ 
+
+ align:start position:0%
+are actually equal to each other and we
+need some other tools to evaluate the
+
+ align:start position:0%
+need some other tools to evaluate the
+ 
+
+ align:start position:0%
+need some other tools to evaluate the
+limit in question so I'll end there
\ No newline at end of file
diff --git a/QuZL5IKpO_U.txt b/QuZL5IKpO_U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dcd4408f4251102719f2c15eae65e6d740613967
--- /dev/null
+++ b/QuZL5IKpO_U.txt
@@ -0,0 +1,6171 @@
+align:start position:0%
+ 
+okay this is quiz review day the quiz
+
+ align:start position:0%
+okay this is quiz review day the quiz
+ 
+
+ align:start position:0%
+okay this is quiz review day the quiz
+coming up on Wednesday will be for this
+
+ align:start position:0%
+coming up on Wednesday will be for this
+ 
+
+ align:start position:0%
+coming up on Wednesday will be for this
+lecture the quiz will be this our one
+
+ align:start position:0%
+lecture the quiz will be this our one
+ 
+
+ align:start position:0%
+lecture the quiz will be this our one
+o'clock Wednesday in Walker
+
+ align:start position:0%
+o'clock Wednesday in Walker
+ 
+
+ align:start position:0%
+o'clock Wednesday in Walker
+top floor of Walker closed book all
+
+ align:start position:0%
+top floor of Walker closed book all
+ 
+
+ align:start position:0%
+top floor of Walker closed book all
+normal I wrote down what we've covered
+
+ align:start position:0%
+normal I wrote down what we've covered
+ 
+
+ align:start position:0%
+normal I wrote down what we've covered
+in this second part of the course and
+
+ align:start position:0%
+in this second part of the course and
+ 
+
+ align:start position:0%
+in this second part of the course and
+actually I've impressed as I write it so
+
+ align:start position:0%
+actually I've impressed as I write it so
+ 
+
+ align:start position:0%
+actually I've impressed as I write it so
+that's chapter 4 on orthogonality and
+
+ align:start position:0%
+that's chapter 4 on orthogonality and
+ 
+
+ align:start position:0%
+that's chapter 4 on orthogonality and
+you're remembering these what this is
+
+ align:start position:0%
+you're remembering these what this is
+ 
+
+ align:start position:0%
+you're remembering these what this is
+suggesting these are those columns are
+
+ align:start position:0%
+suggesting these are those columns are
+ 
+
+ align:start position:0%
+suggesting these are those columns are
+orthonormal vectors and then we call
+
+ align:start position:0%
+orthonormal vectors and then we call
+ 
+
+ align:start position:0%
+orthonormal vectors and then we call
+that matrix Q and the what's the key how
+
+ align:start position:0%
+that matrix Q and the what's the key how
+ 
+
+ align:start position:0%
+that matrix Q and the what's the key how
+do we state the fact that those those
+
+ align:start position:0%
+do we state the fact that those those
+ 
+
+ align:start position:0%
+do we state the fact that those those
+columns are orthonormal in terms of Q it
+
+ align:start position:0%
+columns are orthonormal in terms of Q it
+ 
+
+ align:start position:0%
+columns are orthonormal in terms of Q it
+means that Q transpose Q is the identity
+
+ align:start position:0%
+means that Q transpose Q is the identity
+ 
+
+ align:start position:0%
+means that Q transpose Q is the identity
+so that's the matrix statement of the of
+
+ align:start position:0%
+so that's the matrix statement of the of
+ 
+
+ align:start position:0%
+so that's the matrix statement of the of
+the property that the columns are
+
+ align:start position:0%
+the property that the columns are
+ 
+
+ align:start position:0%
+the property that the columns are
+orthonormal the dot products are either
+
+ align:start position:0%
+orthonormal the dot products are either
+ 
+
+ align:start position:0%
+orthonormal the dot products are either
+1 or 0 and then we computed the
+
+ align:start position:0%
+1 or 0 and then we computed the
+ 
+
+ align:start position:0%
+1 or 0 and then we computed the
+projections onto lines and onto
+
+ align:start position:0%
+projections onto lines and onto
+ 
+
+ align:start position:0%
+projections onto lines and onto
+subspaces and we use that to solve
+
+ align:start position:0%
+subspaces and we use that to solve
+ 
+
+ align:start position:0%
+subspaces and we use that to solve
+problems ax equal B in in the least
+
+ align:start position:0%
+problems ax equal B in in the least
+ 
+
+ align:start position:0%
+problems ax equal B in in the least
+square sense when there was no solution
+
+ align:start position:0%
+square sense when there was no solution
+ 
+
+ align:start position:0%
+square sense when there was no solution
+we found the best solution and then
+
+ align:start position:0%
+we found the best solution and then
+ 
+
+ align:start position:0%
+we found the best solution and then
+finally this gram-schmidt idea which
+
+ align:start position:0%
+finally this gram-schmidt idea which
+ 
+
+ align:start position:0%
+finally this gram-schmidt idea which
+takes independent vectors and lines them
+
+ align:start position:0%
+takes independent vectors and lines them
+ 
+
+ align:start position:0%
+takes independent vectors and lines them
+up takes subtracts off the projections
+
+ align:start position:0%
+up takes subtracts off the projections
+ 
+
+ align:start position:0%
+up takes subtracts off the projections
+of the part you've already done so that
+
+ align:start position:0%
+of the part you've already done so that
+ 
+
+ align:start position:0%
+of the part you've already done so that
+the new part is orthogonal and so it
+
+ align:start position:0%
+the new part is orthogonal and so it
+ 
+
+ align:start position:0%
+the new part is orthogonal and so it
+takes a basis to an orthonormal basis
+
+ align:start position:0%
+takes a basis to an orthonormal basis
+ 
+
+ align:start position:0%
+takes a basis to an orthonormal basis
+and you those calculations involve
+
+ align:start position:0%
+and you those calculations involve
+ 
+
+ align:start position:0%
+and you those calculations involve
+square roots a lot because you're making
+
+ align:start position:0%
+square roots a lot because you're making
+ 
+
+ align:start position:0%
+square roots a lot because you're making
+things unit vectors but you should know
+
+ align:start position:0%
+things unit vectors but you should know
+ 
+
+ align:start position:0%
+things unit vectors but you should know
+that step
+
+ align:start position:0%
+that step
+ 
+
+ align:start position:0%
+that step
+okay four determinants the three big the
+
+ align:start position:0%
+okay four determinants the three big the
+ 
+
+ align:start position:0%
+okay four determinants the three big the
+big picture is the properties of the
+
+ align:start position:0%
+big picture is the properties of the
+ 
+
+ align:start position:0%
+big picture is the properties of the
+determinants one two three diff
+
+ align:start position:0%
+determinants one two three diff
+ 
+
+ align:start position:0%
+determinants one two three diff
+properties one two and three that define
+
+ align:start position:0%
+properties one two and three that define
+ 
+
+ align:start position:0%
+properties one two and three that define
+the determinants and then four five six
+
+ align:start position:0%
+the determinants and then four five six
+ 
+
+ align:start position:0%
+the determinants and then four five six
+through ten were consequences in the big
+
+ align:start position:0%
+through ten were consequences in the big
+ 
+
+ align:start position:0%
+through ten were consequences in the big
+formula that has n factorial terms half
+
+ align:start position:0%
+formula that has n factorial terms half
+ 
+
+ align:start position:0%
+formula that has n factorial terms half
+of them have plus signs and half minus
+
+ align:start position:0%
+of them have plus signs and half minus
+ 
+
+ align:start position:0%
+of them have plus signs and half minus
+signs and then the cofactor formula so
+
+ align:start position:0%
+signs and then the cofactor formula so
+ 
+
+ align:start position:0%
+signs and then the cofactor formula so
+and which led us to a formula for the
+
+ align:start position:0%
+and which led us to a formula for the
+ 
+
+ align:start position:0%
+and which led us to a formula for the
+inverse and finally just so you know
+
+ align:start position:0%
+inverse and finally just so you know
+ 
+
+ align:start position:0%
+inverse and finally just so you know
+what's covered in from Chapter three
+
+ align:start position:0%
+what's covered in from Chapter three
+ 
+
+ align:start position:0%
+what's covered in from Chapter three
+it's section six point one and two so
+
+ align:start position:0%
+it's section six point one and two so
+ 
+
+ align:start position:0%
+it's section six point one and two so
+that's the basic idea of eigenvalues and
+
+ align:start position:0%
+that's the basic idea of eigenvalues and
+ 
+
+ align:start position:0%
+that's the basic idea of eigenvalues and
+eigenvectors the equation for the
+
+ align:start position:0%
+eigenvectors the equation for the
+ 
+
+ align:start position:0%
+eigenvectors the equation for the
+eigenvalues the mechanical step this is
+
+ align:start position:0%
+eigenvalues the mechanical step this is
+ 
+
+ align:start position:0%
+eigenvalues the mechanical step this is
+really ax equal lambda X for all n
+
+ align:start position:0%
+really ax equal lambda X for all n
+ 
+
+ align:start position:0%
+really ax equal lambda X for all n
+eigenvectors at once if we have n
+
+ align:start position:0%
+eigenvectors at once if we have n
+ 
+
+ align:start position:0%
+eigenvectors at once if we have n
+independent eigenvectors and then using
+
+ align:start position:0%
+independent eigenvectors and then using
+ 
+
+ align:start position:0%
+independent eigenvectors and then using
+that to compute powers of a matrix so
+
+ align:start position:0%
+that to compute powers of a matrix so
+ 
+
+ align:start position:0%
+that to compute powers of a matrix so
+you notice the differential equations
+
+ align:start position:0%
+you notice the differential equations
+ 
+
+ align:start position:0%
+you notice the differential equations
+not on this list because that's six
+
+ align:start position:0%
+not on this list because that's six
+ 
+
+ align:start position:0%
+not on this list because that's six
+point three that that's for the third
+
+ align:start position:0%
+point three that that's for the third
+ 
+
+ align:start position:0%
+point three that that's for the third
+quiz okay so like what i usually do for
+
+ align:start position:0%
+quiz okay so like what i usually do for
+ 
+
+ align:start position:0%
+quiz okay so like what i usually do for
+review is to take an old exam and just
+
+ align:start position:0%
+review is to take an old exam and just
+ 
+
+ align:start position:0%
+review is to take an old exam and just
+try to pick out questions that are
+
+ align:start position:0%
+try to pick out questions that are
+ 
+
+ align:start position:0%
+try to pick out questions that are
+significant and write them quickly on
+
+ align:start position:0%
+significant and write them quickly on
+ 
+
+ align:start position:0%
+significant and write them quickly on
+the board shall I shall I proceed that
+
+ align:start position:0%
+the board shall I shall I proceed that
+ 
+
+ align:start position:0%
+the board shall I shall I proceed that
+way again this this exam is really old
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+November 19 1984 so that was before the
+
+ align:start position:0%
+November 19 1984 so that was before the
+ 
+
+ align:start position:0%
+November 19 1984 so that was before the
+web existed so not only where the
+
+ align:start position:0%
+web existed so not only where the
+ 
+
+ align:start position:0%
+web existed so not only where the
+lectures are not on the web
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nobody even had a web page my god okay
+
+ align:start position:0%
+nobody even had a web page my god okay
+ 
+
+ align:start position:0%
+nobody even had a web page my god okay
+so can I nevertheless linear algebra was
+
+ align:start position:0%
+so can I nevertheless linear algebra was
+ 
+
+ align:start position:0%
+so can I nevertheless linear algebra was
+still as great as ever
+
+ align:start position:0%
+still as great as ever
+ 
+
+ align:start position:0%
+still as great as ever
+so may I and that wasn't meant to be a
+
+ align:start position:0%
+so may I and that wasn't meant to be a
+ 
+
+ align:start position:0%
+so may I and that wasn't meant to be a
+joke okay all right so let me just take
+
+ align:start position:0%
+joke okay all right so let me just take
+ 
+
+ align:start position:0%
+joke okay all right so let me just take
+these questions as they come all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the first questions about
+
+ align:start position:0%
+okay so the first questions about
+ 
+
+ align:start position:0%
+okay so the first questions about
+projections it says we're given the line
+
+ align:start position:0%
+projections it says we're given the line
+ 
+
+ align:start position:0%
+projections it says we're given the line
+the vector a is the vector 2 1 2 and I
+
+ align:start position:0%
+the vector a is the vector 2 1 2 and I
+ 
+
+ align:start position:0%
+the vector a is the vector 2 1 2 and I
+want to find the projection matrix P
+
+ align:start position:0%
+want to find the projection matrix P
+ 
+
+ align:start position:0%
+want to find the projection matrix P
+that projects onto the line through a so
+
+ align:start position:0%
+that projects onto the line through a so
+ 
+
+ align:start position:0%
+that projects onto the line through a so
+my picture is well I'm in three
+
+ align:start position:0%
+my picture is well I'm in three
+ 
+
+ align:start position:0%
+my picture is well I'm in three
+dimensions of course so there's a vector
+
+ align:start position:0%
+dimensions of course so there's a vector
+ 
+
+ align:start position:0%
+dimensions of course so there's a vector
+- there's the vector a 2 1 2 let me draw
+
+ align:start position:0%
+- there's the vector a 2 1 2 let me draw
+ 
+
+ align:start position:0%
+- there's the vector a 2 1 2 let me draw
+the whole line through it and I want to
+
+ align:start position:0%
+the whole line through it and I want to
+ 
+
+ align:start position:0%
+the whole line through it and I want to
+project any vector B onto that line and
+
+ align:start position:0%
+project any vector B onto that line and
+ 
+
+ align:start position:0%
+project any vector B onto that line and
+I'm looking for the projection matrix so
+
+ align:start position:0%
+I'm looking for the projection matrix so
+ 
+
+ align:start position:0%
+I'm looking for the projection matrix so
+so this the projection matrix is the
+
+ align:start position:0%
+so this the projection matrix is the
+ 
+
+ align:start position:0%
+so this the projection matrix is the
+matrix that I multiply B by to get here
+
+ align:start position:0%
+matrix that I multiply B by to get here
+ 
+
+ align:start position:0%
+matrix that I multiply B by to get here
+and I guess this first part this is just
+
+ align:start position:0%
+and I guess this first part this is just
+ 
+
+ align:start position:0%
+and I guess this first part this is just
+part one a I'm really asking you the
+
+ align:start position:0%
+part one a I'm really asking you the
+ 
+
+ align:start position:0%
+part one a I'm really asking you the
+quick way to answer to find P is just to
+
+ align:start position:0%
+quick way to answer to find P is just to
+ 
+
+ align:start position:0%
+quick way to answer to find P is just to
+remember what the formula is and and
+
+ align:start position:0%
+remember what the formula is and and
+ 
+
+ align:start position:0%
+remember what the formula is and and
+we're in we're projecting onto a line so
+
+ align:start position:0%
+we're in we're projecting onto a line so
+ 
+
+ align:start position:0%
+we're in we're projecting onto a line so
+our formula our usual formula is a a
+
+ align:start position:0%
+our formula our usual formula is a a
+ 
+
+ align:start position:0%
+our formula our usual formula is a a
+transpose a inverse a transpose
+
+ align:start position:0%
+transpose a inverse a transpose
+ 
+
+ align:start position:0%
+transpose a inverse a transpose
+but now a is just a column one column
+
+ align:start position:0%
+but now a is just a column one column
+ 
+
+ align:start position:0%
+but now a is just a column one column
+matrix so it'll be just a so I'll just
+
+ align:start position:0%
+matrix so it'll be just a so I'll just
+ 
+
+ align:start position:0%
+matrix so it'll be just a so I'll just
+call it little a little a transpose and
+
+ align:start position:0%
+call it little a little a transpose and
+ 
+
+ align:start position:0%
+call it little a little a transpose and
+this is just a number now one by one so
+
+ align:start position:0%
+this is just a number now one by one so
+ 
+
+ align:start position:0%
+this is just a number now one by one so
+I can put it in the denominator so
+
+ align:start position:0%
+I can put it in the denominator so
+ 
+
+ align:start position:0%
+I can put it in the denominator so
+there's our that's really what we want
+
+ align:start position:0%
+there's our that's really what we want
+ 
+
+ align:start position:0%
+there's our that's really what we want
+to remember and using that - one - what
+
+ align:start position:0%
+to remember and using that - one - what
+ 
+
+ align:start position:0%
+to remember and using that - one - what
+will I get
+
+ align:start position:0%
+will I get
+ 
+
+ align:start position:0%
+will I get
+I'm dividing by what's the length
+
+ align:start position:0%
+I'm dividing by what's the length
+ 
+
+ align:start position:0%
+I'm dividing by what's the length
+squared of that vector so what's a
+
+ align:start position:0%
+squared of that vector so what's a
+ 
+
+ align:start position:0%
+squared of that vector so what's a
+transpose a looks like 9 and what's the
+
+ align:start position:0%
+transpose a looks like 9 and what's the
+ 
+
+ align:start position:0%
+transpose a looks like 9 and what's the
+matrix well I'm doing 2 1 2 against 2 1
+
+ align:start position:0%
+matrix well I'm doing 2 1 2 against 2 1
+ 
+
+ align:start position:0%
+matrix well I'm doing 2 1 2 against 2 1
+2 so it's 1/9
+
+ align:start position:0%
+2 so it's 1/9
+ 
+
+ align:start position:0%
+2 so it's 1/9
+of this matrix 4 2 4 2 1 2 4 2 4 now the
+
+ align:start position:0%
+of this matrix 4 2 4 2 1 2 4 2 4 now the
+ 
+
+ align:start position:0%
+of this matrix 4 2 4 2 1 2 4 2 4 now the
+next part asked about eigenvalues so you
+
+ align:start position:0%
+next part asked about eigenvalues so you
+ 
+
+ align:start position:0%
+next part asked about eigenvalues so you
+see where since we're learning we know a
+
+ align:start position:0%
+see where since we're learning we know a
+ 
+
+ align:start position:0%
+see where since we're learning we know a
+lot more
+
+ align:start position:0%
+lot more
+ 
+
+ align:start position:0%
+lot more
+now we can make connections between
+
+ align:start position:0%
+now we can make connections between
+ 
+
+ align:start position:0%
+now we can make connections between
+these chapters so what's the eigenvector
+
+ align:start position:0%
+these chapters so what's the eigenvector
+ 
+
+ align:start position:0%
+these chapters so what's the eigenvector
+what are the eigenvalues of p I could
+
+ align:start position:0%
+what are the eigenvalues of p I could
+ 
+
+ align:start position:0%
+what are the eigenvalues of p I could
+ask what's the rank of P what's the rank
+
+ align:start position:0%
+ask what's the rank of P what's the rank
+ 
+
+ align:start position:0%
+ask what's the rank of P what's the rank
+of that matrix the one rank is one
+
+ align:start position:0%
+of that matrix the one rank is one
+ 
+
+ align:start position:0%
+of that matrix the one rank is one
+what's the column space if I apply P to
+
+ align:start position:0%
+what's the column space if I apply P to
+ 
+
+ align:start position:0%
+what's the column space if I apply P to
+all vectors then I fill up the column
+
+ align:start position:0%
+all vectors then I fill up the column
+ 
+
+ align:start position:0%
+all vectors then I fill up the column
+space its combinations of the column so
+
+ align:start position:0%
+space its combinations of the column so
+ 
+
+ align:start position:0%
+space its combinations of the column so
+what's the column space well it's just
+
+ align:start position:0%
+what's the column space well it's just
+ 
+
+ align:start position:0%
+what's the column space well it's just
+this line the column space is the line
+
+ align:start position:0%
+this line the column space is the line
+ 
+
+ align:start position:0%
+this line the column space is the line
+through two one two and now what's the
+
+ align:start position:0%
+through two one two and now what's the
+ 
+
+ align:start position:0%
+through two one two and now what's the
+eigenvalue so or since that matrix has
+
+ align:start position:0%
+eigenvalue so or since that matrix has
+ 
+
+ align:start position:0%
+eigenvalue so or since that matrix has
+rank one so tell me the eigenvalues of
+
+ align:start position:0%
+rank one so tell me the eigenvalues of
+ 
+
+ align:start position:0%
+rank one so tell me the eigenvalues of
+this matrix it's a singular matrix so it
+
+ align:start position:0%
+this matrix it's a singular matrix so it
+ 
+
+ align:start position:0%
+this matrix it's a singular matrix so it
+certainly has an eigenvalue zero
+
+ align:start position:0%
+certainly has an eigenvalue zero
+ 
+
+ align:start position:0%
+certainly has an eigenvalue zero
+actually the rank is only one so that
+
+ align:start position:0%
+actually the rank is only one so that
+ 
+
+ align:start position:0%
+actually the rank is only one so that
+means that there's like going to be a
+
+ align:start position:0%
+means that there's like going to be a
+ 
+
+ align:start position:0%
+means that there's like going to be a
+two dimensional null space there be at
+
+ align:start position:0%
+two dimensional null space there be at
+ 
+
+ align:start position:0%
+two dimensional null space there be at
+least two this land this lambda equal
+
+ align:start position:0%
+least two this land this lambda equal
+ 
+
+ align:start position:0%
+least two this land this lambda equal
+zero will be repeated twice because I
+
+ align:start position:0%
+zero will be repeated twice because I
+ 
+
+ align:start position:0%
+zero will be repeated twice because I
+could find two independent eigenvectors
+
+ align:start position:0%
+could find two independent eigenvectors
+ 
+
+ align:start position:0%
+could find two independent eigenvectors
+with lambda equals zero and then of
+
+ align:start position:0%
+with lambda equals zero and then of
+ 
+
+ align:start position:0%
+with lambda equals zero and then of
+course since it's got three eigenvalues
+
+ align:start position:0%
+course since it's got three eigenvalues
+ 
+
+ align:start position:0%
+course since it's got three eigenvalues
+what's the third one it's one how do I
+
+ align:start position:0%
+what's the third one it's one how do I
+ 
+
+ align:start position:0%
+what's the third one it's one how do I
+know it's one either from the trace
+
+ align:start position:0%
+know it's one either from the trace
+ 
+
+ align:start position:0%
+know it's one either from the trace
+which is nine over nine which is one or
+
+ align:start position:0%
+which is nine over nine which is one or
+ 
+
+ align:start position:0%
+which is nine over nine which is one or
+by remembering what what is the
+
+ align:start position:0%
+by remembering what what is the
+ 
+
+ align:start position:0%
+by remembering what what is the
+eigenvector and actually now it's going
+
+ align:start position:0%
+eigenvector and actually now it's going
+ 
+
+ align:start position:0%
+eigenvector and actually now it's going
+to ask for the eigenvector so what's the
+
+ align:start position:0%
+to ask for the eigenvector so what's the
+ 
+
+ align:start position:0%
+to ask for the eigenvector so what's the
+eigenvector for that eigenvalue what's
+
+ align:start position:0%
+eigenvector for that eigenvalue what's
+ 
+
+ align:start position:0%
+eigenvector for that eigenvalue what's
+the eigenvector for that eigenvalue it's
+
+ align:start position:0%
+the eigenvector for that eigenvalue it's
+ 
+
+ align:start position:0%
+the eigenvector for that eigenvalue it's
+the vector it's the it's the vector that
+
+ align:start position:0%
+the vector it's the it's the vector that
+ 
+
+ align:start position:0%
+the vector it's the it's the vector that
+doesn't move I can value one so the
+
+ align:start position:0%
+doesn't move I can value one so the
+ 
+
+ align:start position:0%
+doesn't move I can value one so the
+vector that doesn't move is a this a is
+
+ align:start position:0%
+vector that doesn't move is a this a is
+ 
+
+ align:start position:0%
+vector that doesn't move is a this a is
+the is also the eigenvector with lambda
+
+ align:start position:0%
+the is also the eigenvector with lambda
+ 
+
+ align:start position:0%
+the is also the eigenvector with lambda
+equal one because if I apply the
+
+ align:start position:0%
+equal one because if I apply the
+ 
+
+ align:start position:0%
+equal one because if I apply the
+projection matrix to a I get a again
+
+ align:start position:0%
+projection matrix to a I get a again
+ 
+
+ align:start position:0%
+projection matrix to a I get a again
+everybody sees it if I apply that matrix
+
+ align:start position:0%
+everybody sees it if I apply that matrix
+ 
+
+ align:start position:0%
+everybody sees it if I apply that matrix
+to a can I do it in little letters if I
+
+ align:start position:0%
+to a can I do it in little letters if I
+ 
+
+ align:start position:0%
+to a can I do it in little letters if I
+apply that matrix to a then I have a
+
+ align:start position:0%
+apply that matrix to a then I have a
+ 
+
+ align:start position:0%
+apply that matrix to a then I have a
+transpose a canceling a transpose a and
+
+ align:start position:0%
+transpose a canceling a transpose a and
+ 
+
+ align:start position:0%
+transpose a canceling a transpose a and
+I get a again so sure enough PA equals a
+
+ align:start position:0%
+I get a again so sure enough PA equals a
+ 
+
+ align:start position:0%
+I get a again so sure enough PA equals a
+and the eigenvalue is one okay good now
+
+ align:start position:0%
+and the eigenvalue is one okay good now
+ 
+
+ align:start position:0%
+and the eigenvalue is one okay good now
+actually it asks you further to solve
+
+ align:start position:0%
+actually it asks you further to solve
+ 
+
+ align:start position:0%
+actually it asks you further to solve
+this difference equation so this will be
+
+ align:start position:0%
+this difference equation so this will be
+ 
+
+ align:start position:0%
+this difference equation so this will be
+this is this is solve you k plus 1
+
+ align:start position:0%
+this is this is solve you k plus 1
+ 
+
+ align:start position:0%
+this is this is solve you k plus 1
+equals PUK starting from u 0 equal 9 9 0
+
+ align:start position:0%
+equals PUK starting from u 0 equal 9 9 0
+ 
+
+ align:start position:0%
+equals PUK starting from u 0 equal 9 9 0
+and find you K so so what's up so we
+
+ align:start position:0%
+and find you K so so what's up so we
+ 
+
+ align:start position:0%
+and find you K so so what's up so we
+find you one first of all so just to get
+
+ align:start position:0%
+find you one first of all so just to get
+ 
+
+ align:start position:0%
+find you one first of all so just to get
+started so what is u 1
+
+ align:start position:0%
+started so what is u 1
+ 
+
+ align:start position:0%
+started so what is u 1
+it's PU 0 of course
+
+ align:start position:0%
+it's PU 0 of course
+ 
+
+ align:start position:0%
+it's PU 0 of course
+so if I do the projection of this vector
+
+ align:start position:0%
+so if I do the projection of this vector
+ 
+
+ align:start position:0%
+so if I do the projection of this vector
+onto the line so this is like my vector
+
+ align:start position:0%
+onto the line so this is like my vector
+ 
+
+ align:start position:0%
+onto the line so this is like my vector
+B now that I'm projecting onto the line
+
+ align:start position:0%
+B now that I'm projecting onto the line
+ 
+
+ align:start position:0%
+B now that I'm projecting onto the line
+I get a times a transpose u 0 over a
+
+ align:start position:0%
+I get a times a transpose u 0 over a
+ 
+
+ align:start position:0%
+I get a times a transpose u 0 over a
+transpose a well in one way or another I
+
+ align:start position:0%
+transpose a well in one way or another I
+ 
+
+ align:start position:0%
+transpose a well in one way or another I
+just do this multiplication but maybe
+
+ align:start position:0%
+just do this multiplication but maybe
+ 
+
+ align:start position:0%
+just do this multiplication but maybe
+this is the easiest way to do it
+
+ align:start position:0%
+this is the easiest way to do it
+ 
+
+ align:start position:0%
+this is the easiest way to do it
+a transpose can I remember what a is on
+
+ align:start position:0%
+a transpose can I remember what a is on
+ 
+
+ align:start position:0%
+a transpose can I remember what a is on
+this board 2 1 2 so I'm projecting onto
+
+ align:start position:0%
+this board 2 1 2 so I'm projecting onto
+ 
+
+ align:start position:0%
+this board 2 1 2 so I'm projecting onto
+the line through there this is the
+
+ align:start position:0%
+the line through there this is the
+ 
+
+ align:start position:0%
+the line through there this is the
+projection it's P times the vector u 0
+
+ align:start position:0%
+projection it's P times the vector u 0
+ 
+
+ align:start position:0%
+projection it's P times the vector u 0
+so what do I have for a transpose u 0
+
+ align:start position:0%
+so what do I have for a transpose u 0
+ 
+
+ align:start position:0%
+so what do I have for a transpose u 0
+looks like 18 looks like 27 and a
+
+ align:start position:0%
+looks like 18 looks like 27 and a
+ 
+
+ align:start position:0%
+looks like 18 looks like 27 and a
+transpose a we figured was 9 so it's 3 a
+
+ align:start position:0%
+transpose a we figured was 9 so it's 3 a
+ 
+
+ align:start position:0%
+transpose a we figured was 9 so it's 3 a
+so that this is the this is the X hat
+
+ align:start position:0%
+so that this is the this is the X hat
+ 
+
+ align:start position:0%
+so that this is the this is the X hat
+the the multiple of a in our formulas
+
+ align:start position:0%
+the the multiple of a in our formulas
+ 
+
+ align:start position:0%
+the the multiple of a in our formulas
+and of course that's 6 3 6
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's you one computed out directly
+
+ align:start position:0%
+so that's you one computed out directly
+ 
+
+ align:start position:0%
+so that's you one computed out directly
+that's on the line through a and it's
+
+ align:start position:0%
+that's on the line through a and it's
+ 
+
+ align:start position:0%
+that's on the line through a and it's
+the closest point to you zero and it's
+
+ align:start position:0%
+the closest point to you zero and it's
+ 
+
+ align:start position:0%
+the closest point to you zero and it's
+just pu zero you just straight forward
+
+ align:start position:0%
+just pu zero you just straight forward
+ 
+
+ align:start position:0%
+just pu zero you just straight forward
+multiplication produces that okay now
+
+ align:start position:0%
+multiplication produces that okay now
+ 
+
+ align:start position:0%
+multiplication produces that okay now
+what's you two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you two is P you one I agree
+
+ align:start position:0%
+well you two is P you one I agree
+ 
+
+ align:start position:0%
+well you two is P you one I agree
+do I need to compute that again no
+
+ align:start position:0%
+do I need to compute that again no
+ 
+
+ align:start position:0%
+do I need to compute that again no
+because once I'm already on the line
+
+ align:start position:0%
+because once I'm already on the line
+ 
+
+ align:start position:0%
+because once I'm already on the line
+through a UK will be I could do the
+
+ align:start position:0%
+through a UK will be I could do the
+ 
+
+ align:start position:0%
+through a UK will be I could do the
+projection K times but it's enough just
+
+ align:start position:0%
+projection K times but it's enough just
+ 
+
+ align:start position:0%
+projection K times but it's enough just
+to do it once it's the same it's this
+
+ align:start position:0%
+to do it once it's the same it's this
+ 
+
+ align:start position:0%
+to do it once it's the same it's this
+same six three six so this is a case
+
+ align:start position:0%
+same six three six so this is a case
+ 
+
+ align:start position:0%
+same six three six so this is a case
+where I could and actually on the quiz
+
+ align:start position:0%
+where I could and actually on the quiz
+ 
+
+ align:start position:0%
+where I could and actually on the quiz
+if you see one of these which could very
+
+ align:start position:0%
+if you see one of these which could very
+ 
+
+ align:start position:0%
+if you see one of these which could very
+well be there and it could very well be
+
+ align:start position:0%
+well be there and it could very well be
+ 
+
+ align:start position:0%
+well be there and it could very well be
+not a projection matrix then we would
+
+ align:start position:0%
+not a projection matrix then we would
+ 
+
+ align:start position:0%
+not a projection matrix then we would
+use all the eigenvalues and eigenvectors
+
+ align:start position:0%
+use all the eigenvalues and eigenvectors
+ 
+
+ align:start position:0%
+use all the eigenvalues and eigenvectors
+let's think for a moment how do you do
+
+ align:start position:0%
+let's think for a moment how do you do
+ 
+
+ align:start position:0%
+let's think for a moment how do you do
+those the point of this small part of a
+
+ align:start position:0%
+those the point of this small part of a
+ 
+
+ align:start position:0%
+those the point of this small part of a
+question was that when p is a projection
+
+ align:start position:0%
+question was that when p is a projection
+ 
+
+ align:start position:0%
+question was that when p is a projection
+matrix so that p squared equals p and p
+
+ align:start position:0%
+matrix so that p squared equals p and p
+ 
+
+ align:start position:0%
+matrix so that p squared equals p and p
+cubed equals p then then we don't need
+
+ align:start position:0%
+cubed equals p then then we don't need
+ 
+
+ align:start position:0%
+cubed equals p then then we don't need
+to get into the mechanics of all knowing
+
+ align:start position:0%
+to get into the mechanics of all knowing
+ 
+
+ align:start position:0%
+to get into the mechanics of all knowing
+all the other eigenvalues and
+
+ align:start position:0%
+all the other eigenvalues and
+ 
+
+ align:start position:0%
+all the other eigenvalues and
+eigenvectors we just can go directly but
+
+ align:start position:0%
+eigenvectors we just can go directly but
+ 
+
+ align:start position:0%
+eigenvectors we just can go directly but
+if p was now some other matrix can you
+
+ align:start position:0%
+if p was now some other matrix can you
+ 
+
+ align:start position:0%
+if p was now some other matrix can you
+just just just remember from these very
+
+ align:start position:0%
+just just just remember from these very
+ 
+
+ align:start position:0%
+just just just remember from these very
+recent lectures how you would proceed
+
+ align:start position:0%
+recent lectures how you would proceed
+ 
+
+ align:start position:0%
+recent lectures how you would proceed
+from these very recent lectures we know
+
+ align:start position:0%
+from these very recent lectures we know
+ 
+
+ align:start position:0%
+from these very recent lectures we know
+that UK we would we would expand u 0 as
+
+ align:start position:0%
+that UK we would we would expand u 0 as
+ 
+
+ align:start position:0%
+that UK we would we would expand u 0 as
+a combination of eigenvectors let me
+
+ align:start position:0%
+a combination of eigenvectors let me
+ 
+
+ align:start position:0%
+a combination of eigenvectors let me
+leave ya as a combination of
+
+ align:start position:0%
+leave ya as a combination of
+ 
+
+ align:start position:0%
+leave ya as a combination of
+eigenvectors c 1 x 1 some multiple of
+
+ align:start position:0%
+eigenvectors c 1 x 1 some multiple of
+ 
+
+ align:start position:0%
+eigenvectors c 1 x 1 some multiple of
+the second eigenvector some multiple of
+
+ align:start position:0%
+the second eigenvector some multiple of
+ 
+
+ align:start position:0%
+the second eigenvector some multiple of
+a third eigenvector and then a to the k
+
+ align:start position:0%
+a third eigenvector and then a to the k
+ 
+
+ align:start position:0%
+a third eigenvector and then a to the k
+u 0
+
+ align:start position:0%
+u 0
+ 
+
+ align:start position:0%
+u 0
+would be c1 so this we have to find
+
+ align:start position:0%
+would be c1 so this we have to find
+ 
+
+ align:start position:0%
+would be c1 so this we have to find
+these numbers here that's the work
+
+ align:start position:0%
+these numbers here that's the work
+ 
+
+ align:start position:0%
+these numbers here that's the work
+actually the work is find the
+
+ align:start position:0%
+actually the work is find the
+ 
+
+ align:start position:0%
+actually the work is find the
+eigenvalues find the eigenvectors and
+
+ align:start position:0%
+eigenvalues find the eigenvectors and
+ 
+
+ align:start position:0%
+eigenvalues find the eigenvectors and
+find the C's because they all come into
+
+ align:start position:0%
+find the C's because they all come into
+ 
+
+ align:start position:0%
+find the C's because they all come into
+the formula we have so so to do this you
+
+ align:start position:0%
+the formula we have so so to do this you
+ 
+
+ align:start position:0%
+the formula we have so so to do this you
+can see what you have to compute you
+
+ align:start position:0%
+can see what you have to compute you
+ 
+
+ align:start position:0%
+can see what you have to compute you
+have to compute the eigenvalues you have
+
+ align:start position:0%
+have to compute the eigenvalues you have
+ 
+
+ align:start position:0%
+have to compute the eigenvalues you have
+to compute the eigenvectors and then to
+
+ align:start position:0%
+to compute the eigenvectors and then to
+ 
+
+ align:start position:0%
+to compute the eigenvectors and then to
+match you not you compute the C's and
+
+ align:start position:0%
+match you not you compute the C's and
+ 
+
+ align:start position:0%
+match you not you compute the C's and
+then you've got it so it's it's just
+
+ align:start position:0%
+then you've got it so it's it's just
+ 
+
+ align:start position:0%
+then you've got it so it's it's just
+that's a formula that shows what pieces
+
+ align:start position:0%
+that's a formula that shows what pieces
+ 
+
+ align:start position:0%
+that's a formula that shows what pieces
+we need and what would actually happen
+
+ align:start position:0%
+we need and what would actually happen
+ 
+
+ align:start position:0%
+we need and what would actually happen
+in the case of this projection matrix if
+
+ align:start position:0%
+in the case of this projection matrix if
+ 
+
+ align:start position:0%
+in the case of this projection matrix if
+this a is a projection matrix then a
+
+ align:start position:0%
+this a is a projection matrix then a
+ 
+
+ align:start position:0%
+this a is a projection matrix then a
+couple of eigenvalues are 0 that's why
+
+ align:start position:0%
+couple of eigenvalues are 0 that's why
+ 
+
+ align:start position:0%
+couple of eigenvalues are 0 that's why
+we just throw those away the other
+
+ align:start position:0%
+we just throw those away the other
+ 
+
+ align:start position:0%
+we just throw those away the other
+eigenvalue is a 1 so that we got the
+
+ align:start position:0%
+eigenvalue is a 1 so that we got the
+ 
+
+ align:start position:0%
+eigenvalue is a 1 so that we got the
+same thing every time see 3x3 from the
+
+ align:start position:0%
+same thing every time see 3x3 from the
+ 
+
+ align:start position:0%
+same thing every time see 3x3 from the
+first time second time third all
+
+ align:start position:0%
+first time second time third all
+ 
+
+ align:start position:0%
+first time second time third all
+iterations press with this constant left
+
+ align:start position:0%
+iterations press with this constant left
+ 
+
+ align:start position:0%
+iterations press with this constant left
+us right here at 6:36 but maybe I take
+
+ align:start position:0%
+us right here at 6:36 but maybe I take
+ 
+
+ align:start position:0%
+us right here at 6:36 but maybe I take
+I'm taking this chance to remind you of
+
+ align:start position:0%
+I'm taking this chance to remind you of
+ 
+
+ align:start position:0%
+I'm taking this chance to remind you of
+what to do for other matrices ok so
+
+ align:start position:0%
+what to do for other matrices ok so
+ 
+
+ align:start position:0%
+what to do for other matrices ok so
+that's a part way through ok the next
+
+ align:start position:0%
+that's a part way through ok the next
+ 
+
+ align:start position:0%
+that's a part way through ok the next
+question in 1984 is fitting a straight
+
+ align:start position:0%
+question in 1984 is fitting a straight
+ 
+
+ align:start position:0%
+question in 1984 is fitting a straight
+line to points and actually a straight
+
+ align:start position:0%
+line to points and actually a straight
+ 
+
+ align:start position:0%
+line to points and actually a straight
+line through the origin a straight line
+
+ align:start position:0%
+line through the origin a straight line
+ 
+
+ align:start position:0%
+line through the origin a straight line
+through the origin so can I go to
+
+ align:start position:0%
+through the origin so can I go to
+ 
+
+ align:start position:0%
+through the origin so can I go to
+question two so this is fitting a
+
+ align:start position:0%
+question two so this is fitting a
+ 
+
+ align:start position:0%
+question two so this is fitting a
+straight line to these points can I I'll
+
+ align:start position:0%
+straight line to these points can I I'll
+ 
+
+ align:start position:0%
+straight line to these points can I I'll
+just give you the points at T equal 1
+
+ align:start position:0%
+just give you the points at T equal 1
+ 
+
+ align:start position:0%
+just give you the points at T equal 1
+the Y is 4 at T equal to 2 y is 5 at t
+
+ align:start position:0%
+the Y is 4 at T equal to 2 y is 5 at t
+ 
+
+ align:start position:0%
+the Y is 4 at T equal to 2 y is 5 at t
+equal to 3 y is 8
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we've got points one two three four
+
+ align:start position:0%
+so we've got points one two three four
+ 
+
+ align:start position:0%
+so we've got points one two three four
+five and eight and I'm trying to fit a
+
+ align:start position:0%
+five and eight and I'm trying to fit a
+ 
+
+ align:start position:0%
+five and eight and I'm trying to fit a
+straight line through the origin to
+
+ align:start position:0%
+straight line through the origin to
+ 
+
+ align:start position:0%
+straight line through the origin to
+these three values okay so my equation
+
+ align:start position:0%
+these three values okay so my equation
+ 
+
+ align:start position:0%
+these three values okay so my equation
+that I'm allowing myself is just y equal
+
+ align:start position:0%
+that I'm allowing myself is just y equal
+ 
+
+ align:start position:0%
+that I'm allowing myself is just y equal
+DT so I have only one unknown one degree
+
+ align:start position:0%
+DT so I have only one unknown one degree
+ 
+
+ align:start position:0%
+DT so I have only one unknown one degree
+of freedom one parameter D so I'm
+
+ align:start position:0%
+of freedom one parameter D so I'm
+ 
+
+ align:start position:0%
+of freedom one parameter D so I'm
+expecting to end up my matrix so my my
+
+ align:start position:0%
+expecting to end up my matrix so my my
+ 
+
+ align:start position:0%
+expecting to end up my matrix so my my
+when I try to when I try to fit a
+
+ align:start position:0%
+when I try to when I try to fit a
+ 
+
+ align:start position:0%
+when I try to when I try to fit a
+straight line that goes through the
+
+ align:start position:0%
+straight line that goes through the
+ 
+
+ align:start position:0%
+straight line that goes through the
+origin that's because it goes through
+
+ align:start position:0%
+origin that's because it goes through
+ 
+
+ align:start position:0%
+origin that's because it goes through
+the origin I've lost the constant C here
+
+ align:start position:0%
+the origin I've lost the constant C here
+ 
+
+ align:start position:0%
+the origin I've lost the constant C here
+so I have just this should be a quick
+
+ align:start position:0%
+so I have just this should be a quick
+ 
+
+ align:start position:0%
+so I have just this should be a quick
+calculation and I can write down the
+
+ align:start position:0%
+calculation and I can write down the
+ 
+
+ align:start position:0%
+calculation and I can write down the
+three equations that that would I'd like
+
+ align:start position:0%
+three equations that that would I'd like
+ 
+
+ align:start position:0%
+three equations that that would I'd like
+to solve if the line went through the
+
+ align:start position:0%
+to solve if the line went through the
+ 
+
+ align:start position:0%
+to solve if the line went through the
+points that's a good start because that
+
+ align:start position:0%
+points that's a good start because that
+ 
+
+ align:start position:0%
+points that's a good start because that
+displays the matrix so can I continue
+
+ align:start position:0%
+displays the matrix so can I continue
+ 
+
+ align:start position:0%
+displays the matrix so can I continue
+that problem we would like to solve so
+
+ align:start position:0%
+that problem we would like to solve so
+ 
+
+ align:start position:0%
+that problem we would like to solve so
+why is DT so I'd like to solve D times
+
+ align:start position:0%
+why is DT so I'd like to solve D times
+ 
+
+ align:start position:0%
+why is DT so I'd like to solve D times
+one times D equals four two times D
+
+ align:start position:0%
+one times D equals four two times D
+ 
+
+ align:start position:0%
+one times D equals four two times D
+equals five and three times D equals
+
+ align:start position:0%
+equals five and three times D equals
+ 
+
+ align:start position:0%
+equals five and three times D equals
+eight
+
+ align:start position:0%
+eight
+ 
+
+ align:start position:0%
+eight
+that would be perfection if I could find
+
+ align:start position:0%
+that would be perfection if I could find
+ 
+
+ align:start position:0%
+that would be perfection if I could find
+such a D then the line y equal DT would
+
+ align:start position:0%
+such a D then the line y equal DT would
+ 
+
+ align:start position:0%
+such a D then the line y equal DT would
+satisfy all three equations would go
+
+ align:start position:0%
+satisfy all three equations would go
+ 
+
+ align:start position:0%
+satisfy all three equations would go
+through all three points but it doesn't
+
+ align:start position:0%
+through all three points but it doesn't
+ 
+
+ align:start position:0%
+through all three points but it doesn't
+exist so so I have to solve this so that
+
+ align:start position:0%
+exist so so I have to solve this so that
+ 
+
+ align:start position:0%
+exist so so I have to solve this so that
+my matrix is now you can see my matrix
+
+ align:start position:0%
+my matrix is now you can see my matrix
+ 
+
+ align:start position:0%
+my matrix is now you can see my matrix
+it just has one column multiplying a
+
+ align:start position:0%
+it just has one column multiplying a
+ 
+
+ align:start position:0%
+it just has one column multiplying a
+scalar D and you can see the right-hand
+
+ align:start position:0%
+scalar D and you can see the right-hand
+ 
+
+ align:start position:0%
+scalar D and you can see the right-hand
+side this is my a X equal B I don't need
+
+ align:start position:0%
+side this is my a X equal B I don't need
+ 
+
+ align:start position:0%
+side this is my a X equal B I don't need
+three equal signs now cuz I've got
+
+ align:start position:0%
+three equal signs now cuz I've got
+ 
+
+ align:start position:0%
+three equal signs now cuz I've got
+vectors okay
+
+ align:start position:0%
+vectors okay
+ 
+
+ align:start position:0%
+vectors okay
+there's a X equal B and you take it from
+
+ align:start position:0%
+there's a X equal B and you take it from
+ 
+
+ align:start position:0%
+there's a X equal B and you take it from
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+you the best
+
+ align:start position:0%
+you the best
+ 
+
+ align:start position:0%
+you the best
+we'll be we'll come from so what's the
+
+ align:start position:0%
+we'll be we'll come from so what's the
+ 
+
+ align:start position:0%
+we'll be we'll come from so what's the
+the key equation so here this is the a
+
+ align:start position:0%
+the key equation so here this is the a
+ 
+
+ align:start position:0%
+the key equation so here this is the a
+this is the ax hat equal B equation
+
+ align:start position:0%
+this is the ax hat equal B equation
+ 
+
+ align:start position:0%
+this is the ax hat equal B equation
+well ax equal B and what's the equation
+
+ align:start position:0%
+well ax equal B and what's the equation
+ 
+
+ align:start position:0%
+well ax equal B and what's the equation
+for x hat the best D so to find the best
+
+ align:start position:0%
+for x hat the best D so to find the best
+ 
+
+ align:start position:0%
+for x hat the best D so to find the best
+D the best X the equation is a transpose
+
+ align:start position:0%
+D the best X the equation is a transpose
+ 
+
+ align:start position:0%
+D the best X the equation is a transpose
+a the best D is a transpose times the
+
+ align:start position:0%
+a the best D is a transpose times the
+ 
+
+ align:start position:0%
+a the best D is a transpose times the
+right hand side this is all coming from
+
+ align:start position:0%
+right hand side this is all coming from
+ 
+
+ align:start position:0%
+right hand side this is all coming from
+projection on a line or our matrix only
+
+ align:start position:0%
+projection on a line or our matrix only
+ 
+
+ align:start position:0%
+projection on a line or our matrix only
+has one column so a transpose a would be
+
+ align:start position:0%
+has one column so a transpose a would be
+ 
+
+ align:start position:0%
+has one column so a transpose a would be
+maybe 14 D hat and a transpose B I'm
+
+ align:start position:0%
+maybe 14 D hat and a transpose B I'm
+ 
+
+ align:start position:0%
+maybe 14 D hat and a transpose B I'm
+getting four ten and twenty four is that
+
+ align:start position:0%
+getting four ten and twenty four is that
+ 
+
+ align:start position:0%
+getting four ten and twenty four is that
+right for ten and twenty four so thirty
+
+ align:start position:0%
+right for ten and twenty four so thirty
+ 
+
+ align:start position:0%
+right for ten and twenty four so thirty
+eight so that tells me the best D hat is
+
+ align:start position:0%
+eight so that tells me the best D hat is
+ 
+
+ align:start position:0%
+eight so that tells me the best D hat is
+d hat is 38 over fourteen okay fine
+
+ align:start position:0%
+d hat is 38 over fourteen okay fine
+ 
+
+ align:start position:0%
+d hat is 38 over fourteen okay fine
+alright so we found the best line and
+
+ align:start position:0%
+alright so we found the best line and
+ 
+
+ align:start position:0%
+alright so we found the best line and
+now here's a here's the next question
+
+ align:start position:0%
+now here's a here's the next question
+ 
+
+ align:start position:0%
+now here's a here's the next question
+what vector did I just project onto what
+
+ align:start position:0%
+what vector did I just project onto what
+ 
+
+ align:start position:0%
+what vector did I just project onto what
+line see in this section on least
+
+ align:start position:0%
+line see in this section on least
+ 
+
+ align:start position:0%
+line see in this section on least
+squares here's the key point
+
+ align:start position:0%
+squares here's the key point
+ 
+
+ align:start position:0%
+squares here's the key point
+I'm asking you to think of the least
+
+ align:start position:0%
+I'm asking you to think of the least
+ 
+
+ align:start position:0%
+I'm asking you to think of the least
+squares problem in two ways two
+
+ align:start position:0%
+squares problem in two ways two
+ 
+
+ align:start position:0%
+squares problem in two ways two
+different pictures two different graphs
+
+ align:start position:0%
+different pictures two different graphs
+ 
+
+ align:start position:0%
+different pictures two different graphs
+one graph is this this is a graph in the
+
+ align:start position:0%
+one graph is this this is a graph in the
+ 
+
+ align:start position:0%
+one graph is this this is a graph in the
+in the B and the TB flame T Y plane the
+
+ align:start position:0%
+in the B and the TB flame T Y plane the
+ 
+
+ align:start position:0%
+in the B and the TB flame T Y plane the
+line itself the other picture I'm asking
+
+ align:start position:0%
+line itself the other picture I'm asking
+ 
+
+ align:start position:0%
+line itself the other picture I'm asking
+you to think of is like my projection
+
+ align:start position:0%
+you to think of is like my projection
+ 
+
+ align:start position:0%
+you to think of is like my projection
+picture what what what projection what
+
+ align:start position:0%
+picture what what what projection what
+ 
+
+ align:start position:0%
+picture what what what projection what
+what vector am I am i projecting onto
+
+ align:start position:0%
+what vector am I am i projecting onto
+ 
+
+ align:start position:0%
+what vector am I am i projecting onto
+what line or what subspace when i when i
+
+ align:start position:0%
+what line or what subspace when i when i
+ 
+
+ align:start position:0%
+what line or what subspace when i when i
+do this so is my second picture is a
+
+ align:start position:0%
+do this so is my second picture is a
+ 
+
+ align:start position:0%
+do this so is my second picture is a
+projection picture that sees the whole
+
+ align:start position:0%
+projection picture that sees the whole
+ 
+
+ align:start position:0%
+projection picture that sees the whole
+thing with vectors here's my vector of
+
+ align:start position:0%
+thing with vectors here's my vector of
+ 
+
+ align:start position:0%
+thing with vectors here's my vector of
+course that I'm projecting I'm
+
+ align:start position:0%
+course that I'm projecting I'm
+ 
+
+ align:start position:0%
+course that I'm projecting I'm
+projecting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that vector B onto the column space of a
+
+ align:start position:0%
+that vector B onto the column space of a
+ 
+
+ align:start position:0%
+that vector B onto the column space of a
+or if you like it's just a line on two
+
+ align:start position:0%
+or if you like it's just a line on two
+ 
+
+ align:start position:0%
+or if you like it's just a line on two
+that's the line it's just a line of
+
+ align:start position:0%
+that's the line it's just a line of
+ 
+
+ align:start position:0%
+that's the line it's just a line of
+course that's what this calculation is
+
+ align:start position:0%
+course that's what this calculation is
+ 
+
+ align:start position:0%
+course that's what this calculation is
+doing this is computing the best D which
+
+ align:start position:0%
+doing this is computing the best D which
+ 
+
+ align:start position:0%
+doing this is computing the best D which
+is this is the X hat so so seeing it as
+
+ align:start position:0%
+is this is the X hat so so seeing it as
+ 
+
+ align:start position:0%
+is this is the X hat so so seeing it as
+a projection means I don't see the
+
+ align:start position:0%
+a projection means I don't see the
+ 
+
+ align:start position:0%
+a projection means I don't see the
+projection in this figure right in this
+
+ align:start position:0%
+projection in this figure right in this
+ 
+
+ align:start position:0%
+projection in this figure right in this
+figure I'm not projecting those points
+
+ align:start position:0%
+figure I'm not projecting those points
+ 
+
+ align:start position:0%
+figure I'm not projecting those points
+onto that line or anything of the sort
+
+ align:start position:0%
+onto that line or anything of the sort
+ 
+
+ align:start position:0%
+onto that line or anything of the sort
+the projection picture for for least
+
+ align:start position:0%
+the projection picture for for least
+ 
+
+ align:start position:0%
+the projection picture for for least
+squares is in the plane in the space
+
+ align:start position:0%
+squares is in the plane in the space
+ 
+
+ align:start position:0%
+squares is in the plane in the space
+where B lies the whole vector B and the
+
+ align:start position:0%
+where B lies the whole vector B and the
+ 
+
+ align:start position:0%
+where B lies the whole vector B and the
+columns of a and then the X is the best
+
+ align:start position:0%
+columns of a and then the X is the best
+ 
+
+ align:start position:0%
+columns of a and then the X is the best
+combination that gives the projection
+
+ align:start position:0%
+combination that gives the projection
+ 
+
+ align:start position:0%
+combination that gives the projection
+okay so that's a chance to tell me that
+
+ align:start position:0%
+okay so that's a chance to tell me that
+ 
+
+ align:start position:0%
+okay so that's a chance to tell me that
+okay I'll go okay now finally in
+
+ align:start position:0%
+okay I'll go okay now finally in
+ 
+
+ align:start position:0%
+okay I'll go okay now finally in
+orthogonality there's the gram-schmidt
+
+ align:start position:0%
+orthogonality there's the gram-schmidt
+ 
+
+ align:start position:0%
+orthogonality there's the gram-schmidt
+idea so that's problem 2d here it asks
+
+ align:start position:0%
+idea so that's problem 2d here it asks
+ 
+
+ align:start position:0%
+idea so that's problem 2d here it asks
+me if I have two vectors a1 equal 1 2 3
+
+ align:start position:0%
+me if I have two vectors a1 equal 1 2 3
+ 
+
+ align:start position:0%
+me if I have two vectors a1 equal 1 2 3
+and a 2 equal 1 1 1 find two orthogonal
+
+ align:start position:0%
+and a 2 equal 1 1 1 find two orthogonal
+ 
+
+ align:start position:0%
+and a 2 equal 1 1 1 find two orthogonal
+vectors in that plane so those two
+
+ align:start position:0%
+vectors in that plane so those two
+ 
+
+ align:start position:0%
+vectors in that plane so those two
+vectors give a plane they give a plane
+
+ align:start position:0%
+vectors give a plane they give a plane
+ 
+
+ align:start position:0%
+vectors give a plane they give a plane
+which is of course the column space of
+
+ align:start position:0%
+which is of course the column space of
+ 
+
+ align:start position:0%
+which is of course the column space of
+the of the matrix and I'm looking for an
+
+ align:start position:0%
+the of the matrix and I'm looking for an
+ 
+
+ align:start position:0%
+the of the matrix and I'm looking for an
+orthogonal basis for that plane so I'm
+
+ align:start position:0%
+orthogonal basis for that plane so I'm
+ 
+
+ align:start position:0%
+orthogonal basis for that plane so I'm
+looking for two orthogonal vectors and
+
+ align:start position:0%
+looking for two orthogonal vectors and
+ 
+
+ align:start position:0%
+looking for two orthogonal vectors and
+of course there were lots of I mean I've
+
+ align:start position:0%
+of course there were lots of I mean I've
+ 
+
+ align:start position:0%
+of course there were lots of I mean I've
+got a plane there if I get one
+
+ align:start position:0%
+got a plane there if I get one
+ 
+
+ align:start position:0%
+got a plane there if I get one
+orthogonal pair I can rotate it there's
+
+ align:start position:0%
+orthogonal pair I can rotate it there's
+ 
+
+ align:start position:0%
+orthogonal pair I can rotate it there's
+not just one answer here but gram
+
+ align:start position:0%
+not just one answer here but gram
+ 
+
+ align:start position:0%
+not just one answer here but gram
+Schmidt says okay start with the first
+
+ align:start position:0%
+Schmidt says okay start with the first
+ 
+
+ align:start position:0%
+Schmidt says okay start with the first
+vector and let that be and keep that one
+
+ align:start position:0%
+vector and let that be and keep that one
+ 
+
+ align:start position:0%
+vector and let that be and keep that one
+and then take the second one orthogonal
+
+ align:start position:0%
+and then take the second one orthogonal
+ 
+
+ align:start position:0%
+and then take the second one orthogonal
+to this so so gram schmidt says start
+
+ align:start position:0%
+to this so so gram schmidt says start
+ 
+
+ align:start position:0%
+to this so so gram schmidt says start
+with this one and then make a second
+
+ align:start position:0%
+with this one and then make a second
+ 
+
+ align:start position:0%
+with this one and then make a second
+vector B can I call that second vector B
+
+ align:start position:0%
+vector B can I call that second vector B
+ 
+
+ align:start position:0%
+vector B can I call that second vector B
+this is going to be orthogonal to so
+
+ align:start position:0%
+this is going to be orthogonal to so
+ 
+
+ align:start position:0%
+this is going to be orthogonal to so
+perpendicular to a-1 if I could with my
+
+ align:start position:0%
+perpendicular to a-1 if I could with my
+ 
+
+ align:start position:0%
+perpendicular to a-1 if I could with my
+chalk create the key equation this
+
+ align:start position:0%
+chalk create the key equation this
+ 
+
+ align:start position:0%
+chalk create the key equation this
+vector B is going to be this 1 1 1 but
+
+ align:start position:0%
+vector B is going to be this 1 1 1 but
+ 
+
+ align:start position:0%
+vector B is going to be this 1 1 1 but
+that 1 1 1 1 1 is not perpendicular to a
+
+ align:start position:0%
+that 1 1 1 1 1 is not perpendicular to a
+ 
+
+ align:start position:0%
+that 1 1 1 1 1 is not perpendicular to a
+1 so I have to subtract off its
+
+ align:start position:0%
+1 so I have to subtract off its
+ 
+
+ align:start position:0%
+1 so I have to subtract off its
+projection I have to subtract off the be
+
+ align:start position:0%
+projection I have to subtract off the be
+ 
+
+ align:start position:0%
+projection I have to subtract off the be
+the the be transfer or yeah the B I
+
+ align:start position:0%
+the the be transfer or yeah the B I
+ 
+
+ align:start position:0%
+the the be transfer or yeah the B I
+should say the a 1 transpose B over a 1
+
+ align:start position:0%
+should say the a 1 transpose B over a 1
+ 
+
+ align:start position:0%
+should say the a 1 transpose B over a 1
+transpose a 1 that multiple of a 1 I've
+
+ align:start position:0%
+transpose a 1 that multiple of a 1 I've
+ 
+
+ align:start position:0%
+transpose a 1 that multiple of a 1 I've
+got to remove so I just have to compute
+
+ align:start position:0%
+got to remove so I just have to compute
+ 
+
+ align:start position:0%
+got to remove so I just have to compute
+what that is and I get in I get a vector
+
+ align:start position:0%
+what that is and I get in I get a vector
+ 
+
+ align:start position:0%
+what that is and I get in I get a vector
+B that's orthogonal to a-1 it's the it's
+
+ align:start position:0%
+B that's orthogonal to a-1 it's the it's
+ 
+
+ align:start position:0%
+B that's orthogonal to a-1 it's the it's
+it's the original vector minus its
+
+ align:start position:0%
+it's the original vector minus its
+ 
+
+ align:start position:0%
+it's the original vector minus its
+projection oh so what is I mean this to
+
+ align:start position:0%
+projection oh so what is I mean this to
+ 
+
+ align:start position:0%
+projection oh so what is I mean this to
+be a 2
+
+ align:start position:0%
+be a 2
+ 
+
+ align:start position:0%
+be a 2
+yeah so I'm projecting a 2 onto the line
+
+ align:start position:0%
+yeah so I'm projecting a 2 onto the line
+ 
+
+ align:start position:0%
+yeah so I'm projecting a 2 onto the line
+through a 1 that's the part that I don't
+
+ align:start position:0%
+through a 1 that's the part that I don't
+ 
+
+ align:start position:0%
+through a 1 that's the part that I don't
+want cuz that's in the direction I
+
+ align:start position:0%
+want cuz that's in the direction I
+ 
+
+ align:start position:0%
+want cuz that's in the direction I
+already have so I subtract off that
+
+ align:start position:0%
+already have so I subtract off that
+ 
+
+ align:start position:0%
+already have so I subtract off that
+projection and I get the part I want the
+
+ align:start position:0%
+projection and I get the part I want the
+ 
+
+ align:start position:0%
+projection and I get the part I want the
+orthogonal part okay so that's the
+
+ align:start position:0%
+orthogonal part okay so that's the
+ 
+
+ align:start position:0%
+orthogonal part okay so that's the
+gram-schmidt thing and we can put
+
+ align:start position:0%
+gram-schmidt thing and we can put
+ 
+
+ align:start position:0%
+gram-schmidt thing and we can put
+numbers in 1 1 1 take away a 1 transpose
+
+ align:start position:0%
+numbers in 1 1 1 take away a 1 transpose
+ 
+
+ align:start position:0%
+numbers in 1 1 1 take away a 1 transpose
+a 2 is 6 a 1 transpose a 1 is 14
+
+ align:start position:0%
+a 2 is 6 a 1 transpose a 1 is 14
+ 
+
+ align:start position:0%
+a 2 is 6 a 1 transpose a 1 is 14
+multiplying a 1 and that gives us the
+
+ align:start position:0%
+multiplying a 1 and that gives us the
+ 
+
+ align:start position:0%
+multiplying a 1 and that gives us the
+new orthogonal vector B because I only
+
+ align:start position:0%
+new orthogonal vector B because I only
+ 
+
+ align:start position:0%
+new orthogonal vector B because I only
+asked for orthogonal right now I don't
+
+ align:start position:0%
+asked for orthogonal right now I don't
+ 
+
+ align:start position:0%
+asked for orthogonal right now I don't
+have to divide by the length which will
+
+ align:start position:0%
+have to divide by the length which will
+ 
+
+ align:start position:0%
+have to divide by the length which will
+involve a square root ok
+
+ align:start position:0%
+involve a square root ok
+ 
+
+ align:start position:0%
+involve a square root ok
+third question third question alright
+
+ align:start position:0%
+third question third question alright
+ 
+
+ align:start position:0%
+third question third question alright
+let me I'll move this board up third
+
+ align:start position:0%
+let me I'll move this board up third
+ 
+
+ align:start position:0%
+let me I'll move this board up third
+question I'll probably be about
+
+ align:start position:0%
+question I'll probably be about
+ 
+
+ align:start position:0%
+question I'll probably be about
+eigenvalues okay three this is a four by
+
+ align:start position:0%
+eigenvalues okay three this is a four by
+ 
+
+ align:start position:0%
+eigenvalues okay three this is a four by
+four matrix its eigenvalues are lambda 1
+
+ align:start position:0%
+four matrix its eigenvalues are lambda 1
+ 
+
+ align:start position:0%
+four matrix its eigenvalues are lambda 1
+lambda 2 lambda 3 lambda 4 question 1
+
+ align:start position:0%
+lambda 2 lambda 3 lambda 4 question 1
+ 
+
+ align:start position:0%
+lambda 2 lambda 3 lambda 4 question 1
+what's the condition on the lambdas so
+
+ align:start position:0%
+what's the condition on the lambdas so
+ 
+
+ align:start position:0%
+what's the condition on the lambdas so
+that the matrix is invertible okay so
+
+ align:start position:0%
+that the matrix is invertible okay so
+ 
+
+ align:start position:0%
+that the matrix is invertible okay so
+under what conditions on the lambdas
+
+ align:start position:0%
+under what conditions on the lambdas
+ 
+
+ align:start position:0%
+under what conditions on the lambdas
+will the matrix be invertible so that's
+
+ align:start position:0%
+will the matrix be invertible so that's
+ 
+
+ align:start position:0%
+will the matrix be invertible so that's
+easy invertible if what's the condition
+
+ align:start position:0%
+easy invertible if what's the condition
+ 
+
+ align:start position:0%
+easy invertible if what's the condition
+on the lambdas none of them are zero a
+
+ align:start position:0%
+on the lambdas none of them are zero a
+ 
+
+ align:start position:0%
+on the lambdas none of them are zero a
+zero eigenvalue would mean something in
+
+ align:start position:0%
+zero eigenvalue would mean something in
+ 
+
+ align:start position:0%
+zero eigenvalue would mean something in
+the null space would be in a solution to
+
+ align:start position:0%
+the null space would be in a solution to
+ 
+
+ align:start position:0%
+the null space would be in a solution to
+ax equals zero X but we're invertible so
+
+ align:start position:0%
+ax equals zero X but we're invertible so
+ 
+
+ align:start position:0%
+ax equals zero X but we're invertible so
+none of them is 0 the product however
+
+ align:start position:0%
+none of them is 0 the product however
+ 
+
+ align:start position:0%
+none of them is 0 the product however
+you want to say no no zero eigenvalues
+
+ align:start position:0%
+you want to say no no zero eigenvalues
+ 
+
+ align:start position:0%
+you want to say no no zero eigenvalues
+good ok what's the determinant of a
+
+ align:start position:0%
+good ok what's the determinant of a
+ 
+
+ align:start position:0%
+good ok what's the determinant of a
+inverse the determinant of a inverse so
+
+ align:start position:0%
+inverse the determinant of a inverse so
+ 
+
+ align:start position:0%
+inverse the determinant of a inverse so
+where's that going to come from well if
+
+ align:start position:0%
+where's that going to come from well if
+ 
+
+ align:start position:0%
+where's that going to come from well if
+we knew the eigenvalues of a inverse we
+
+ align:start position:0%
+we knew the eigenvalues of a inverse we
+ 
+
+ align:start position:0%
+we knew the eigenvalues of a inverse we
+could multiply them together to find the
+
+ align:start position:0%
+could multiply them together to find the
+ 
+
+ align:start position:0%
+could multiply them together to find the
+determinant and we do know the
+
+ align:start position:0%
+determinant and we do know the
+ 
+
+ align:start position:0%
+determinant and we do know the
+eigenvalues of a inverse what are they
+
+ align:start position:0%
+eigenvalues of a inverse what are they
+ 
+
+ align:start position:0%
+eigenvalues of a inverse what are they
+they're just 1 over lambda 1 times 1
+
+ align:start position:0%
+they're just 1 over lambda 1 times 1
+ 
+
+ align:start position:0%
+they're just 1 over lambda 1 times 1
+over lambda 2 that's the second
+
+ align:start position:0%
+over lambda 2 that's the second
+ 
+
+ align:start position:0%
+over lambda 2 that's the second
+eigenvalue the third eigenvalue and the
+
+ align:start position:0%
+eigenvalue the third eigenvalue and the
+ 
+
+ align:start position:0%
+eigenvalue the third eigenvalue and the
+fourth so the product of the four
+
+ align:start position:0%
+fourth so the product of the four
+ 
+
+ align:start position:0%
+fourth so the product of the four
+eigenvalues of the inverse will give us
+
+ align:start position:0%
+eigenvalues of the inverse will give us
+ 
+
+ align:start position:0%
+eigenvalues of the inverse will give us
+the determinant of the inverse fine okay
+
+ align:start position:0%
+the determinant of the inverse fine okay
+ 
+
+ align:start position:0%
+the determinant of the inverse fine okay
+and what's the trace of a plus I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what do we know about trace it's the
+
+ align:start position:0%
+so what do we know about trace it's the
+ 
+
+ align:start position:0%
+so what do we know about trace it's the
+sum down the diagonal but we don't know
+
+ align:start position:0%
+sum down the diagonal but we don't know
+ 
+
+ align:start position:0%
+sum down the diagonal but we don't know
+what our matrix is the trace is also the
+
+ align:start position:0%
+what our matrix is the trace is also the
+ 
+
+ align:start position:0%
+what our matrix is the trace is also the
+sum of the eigenvalues and we do know
+
+ align:start position:0%
+sum of the eigenvalues and we do know
+ 
+
+ align:start position:0%
+sum of the eigenvalues and we do know
+the eigenvalues of a plus I so we just
+
+ align:start position:0%
+the eigenvalues of a plus I so we just
+ 
+
+ align:start position:0%
+the eigenvalues of a plus I so we just
+add them up so what's the first
+
+ align:start position:0%
+add them up so what's the first
+ 
+
+ align:start position:0%
+add them up so what's the first
+eigenvalue of a plus I when the matrix a
+
+ align:start position:0%
+eigenvalue of a plus I when the matrix a
+ 
+
+ align:start position:0%
+eigenvalue of a plus I when the matrix a
+has eigenvalues lambda 1 2 3 & 4 then
+
+ align:start position:0%
+has eigenvalues lambda 1 2 3 & 4 then
+ 
+
+ align:start position:0%
+has eigenvalues lambda 1 2 3 & 4 then
+the eigenvalues if I add the identity
+
+ align:start position:0%
+the eigenvalues if I add the identity
+ 
+
+ align:start position:0%
+the eigenvalues if I add the identity
+that moves all the eigenvalues by 1 so I
+
+ align:start position:0%
+that moves all the eigenvalues by 1 so I
+ 
+
+ align:start position:0%
+that moves all the eigenvalues by 1 so I
+just add up lambda 1 plus 1 lambda 2
+
+ align:start position:0%
+just add up lambda 1 plus 1 lambda 2
+ 
+
+ align:start position:0%
+just add up lambda 1 plus 1 lambda 2
+plus 1 and so on lambda 3 plus 1 lambda
+
+ align:start position:0%
+plus 1 and so on lambda 3 plus 1 lambda
+ 
+
+ align:start position:0%
+plus 1 and so on lambda 3 plus 1 lambda
+4 plus 1 so it's lambda 1 plus lambda 2
+
+ align:start position:0%
+4 plus 1 so it's lambda 1 plus lambda 2
+ 
+
+ align:start position:0%
+4 plus 1 so it's lambda 1 plus lambda 2
+plus lambda 3 plus lambda 4 plus 4 right
+
+ align:start position:0%
+plus lambda 3 plus lambda 4 plus 4 right
+ 
+
+ align:start position:0%
+plus lambda 3 plus lambda 4 plus 4 right
+that movement by the identity moved all
+
+ align:start position:0%
+that movement by the identity moved all
+ 
+
+ align:start position:0%
+that movement by the identity moved all
+the eigenvalues by 1 so it moved the
+
+ align:start position:0%
+the eigenvalues by 1 so it moved the
+ 
+
+ align:start position:0%
+the eigenvalues by 1 so it moved the
+whole trace by 4 so that was the trace
+
+ align:start position:0%
+whole trace by 4 so that was the trace
+ 
+
+ align:start position:0%
+whole trace by 4 so that was the trace
+of a plus 4 more ok let's see we may be
+
+ align:start position:0%
+of a plus 4 more ok let's see we may be
+ 
+
+ align:start position:0%
+of a plus 4 more ok let's see we may be
+finished this quiz 20 minutes early nope
+
+ align:start position:0%
+finished this quiz 20 minutes early nope
+ 
+
+ align:start position:0%
+finished this quiz 20 minutes early nope
+there's another question oh god ok how
+
+ align:start position:0%
+there's another question oh god ok how
+ 
+
+ align:start position:0%
+there's another question oh god ok how
+did this class ever do it well you'll
+
+ align:start position:0%
+did this class ever do it well you'll
+ 
+
+ align:start position:0%
+did this class ever do it well you'll
+see you'll see yeah you'll be able to do
+
+ align:start position:0%
+see you'll see yeah you'll be able to do
+ 
+
+ align:start position:0%
+see you'll see yeah you'll be able to do
+it ok
+
+ align:start position:0%
+it ok
+ 
+
+ align:start position:0%
+it ok
+this has got to be a determinate
+
+ align:start position:0%
+this has got to be a determinate
+ 
+
+ align:start position:0%
+this has got to be a determinate
+question all right amaura determinants
+
+ align:start position:0%
+question all right amaura determinants
+ 
+
+ align:start position:0%
+question all right amaura determinants
+and cofactors and big formula question
+
+ align:start position:0%
+and cofactors and big formula question
+ 
+
+ align:start position:0%
+and cofactors and big formula question
+ok let me do that so it's about a matrix
+
+ align:start position:0%
+ok let me do that so it's about a matrix
+ 
+
+ align:start position:0%
+ok let me do that so it's about a matrix
+or a whole family of matrices here's the
+
+ align:start position:0%
+or a whole family of matrices here's the
+ 
+
+ align:start position:0%
+or a whole family of matrices here's the
+4 by 4 1 the 4 by 4 1 is and all the
+
+ align:start position:0%
+4 by 4 1 the 4 by 4 1 is and all the
+ 
+
+ align:start position:0%
+4 by 4 1 the 4 by 4 1 is and all the
+matrices in this family are tridiagonal
+
+ align:start position:0%
+matrices in this family are tridiagonal
+ 
+
+ align:start position:0%
+matrices in this family are tridiagonal
+with with ones otherwise zeros so that's
+
+ align:start position:0%
+with with ones otherwise zeros so that's
+ 
+
+ align:start position:0%
+with with ones otherwise zeros so that's
+the pattern and we've seen this matrix I
+
+ align:start position:0%
+the pattern and we've seen this matrix I
+ 
+
+ align:start position:0%
+the pattern and we've seen this matrix I
+guess
+
+ align:start position:0%
+guess
+ 
+
+ align:start position:0%
+guess
+okay so the it's tridiagonal with ones
+
+ align:start position:0%
+okay so the it's tridiagonal with ones
+ 
+
+ align:start position:0%
+okay so the it's tridiagonal with ones
+on the diagonal ones above and ones
+
+ align:start position:0%
+on the diagonal ones above and ones
+ 
+
+ align:start position:0%
+on the diagonal ones above and ones
+below and you see the general formula am
+
+ align:start position:0%
+below and you see the general formula am
+ 
+
+ align:start position:0%
+below and you see the general formula am
+so I'll use DN for the determinant of a
+
+ align:start position:0%
+so I'll use DN for the determinant of a
+ 
+
+ align:start position:0%
+so I'll use DN for the determinant of a
+and okay alright so I'm gonna do a coke
+
+ align:start position:0%
+and okay alright so I'm gonna do a coke
+ 
+
+ align:start position:0%
+and okay alright so I'm gonna do a coke
+the first question is use cofactors to
+
+ align:start position:0%
+the first question is use cofactors to
+ 
+
+ align:start position:0%
+the first question is use cofactors to
+show that DN is something times DN minus
+
+ align:start position:0%
+show that DN is something times DN minus
+ 
+
+ align:start position:0%
+show that DN is something times DN minus
+one plus something times DN minus two
+
+ align:start position:0%
+one plus something times DN minus two
+ 
+
+ align:start position:0%
+one plus something times DN minus two
+and find those something's okay so this
+
+ align:start position:0%
+and find those something's okay so this
+ 
+
+ align:start position:0%
+and find those something's okay so this
+the fact that it's tri diagonal with
+
+ align:start position:0%
+the fact that it's tri diagonal with
+ 
+
+ align:start position:0%
+the fact that it's tri diagonal with
+these constant diagonals means that
+
+ align:start position:0%
+these constant diagonals means that
+ 
+
+ align:start position:0%
+these constant diagonals means that
+there is such a recurrence formula and
+
+ align:start position:0%
+there is such a recurrence formula and
+ 
+
+ align:start position:0%
+there is such a recurrence formula and
+so the first question is find it what's
+
+ align:start position:0%
+so the first question is find it what's
+ 
+
+ align:start position:0%
+so the first question is find it what's
+the recurrence formula okay how does it
+
+ align:start position:0%
+the recurrence formula okay how does it
+ 
+
+ align:start position:0%
+the recurrence formula okay how does it
+go so I'll use cofactors along the first
+
+ align:start position:0%
+go so I'll use cofactors along the first
+ 
+
+ align:start position:0%
+go so I'll use cofactors along the first
+row so I take that number times its
+
+ align:start position:0%
+row so I take that number times its
+ 
+
+ align:start position:0%
+row so I take that number times its
+cofactor so it's one times its cofactor
+
+ align:start position:0%
+cofactor so it's one times its cofactor
+ 
+
+ align:start position:0%
+cofactor so it's one times its cofactor
+and what is its cofactor DN minus 1
+
+ align:start position:0%
+and what is its cofactor DN minus 1
+ 
+
+ align:start position:0%
+and what is its cofactor DN minus 1
+right exactly the cofactor is this is
+
+ align:start position:0%
+right exactly the cofactor is this is
+ 
+
+ align:start position:0%
+right exactly the cofactor is this is
+that this guy uses up Row one and column
+
+ align:start position:0%
+that this guy uses up Row one and column
+ 
+
+ align:start position:0%
+that this guy uses up Row one and column
+one so the cofactor is down here so it's
+
+ align:start position:0%
+one so the cofactor is down here so it's
+ 
+
+ align:start position:0%
+one so the cofactor is down here so it's
+one of those okay that's the first
+
+ align:start position:0%
+one of those okay that's the first
+ 
+
+ align:start position:0%
+one of those okay that's the first
+cofactor term now the other cofactor
+
+ align:start position:0%
+cofactor term now the other cofactor
+ 
+
+ align:start position:0%
+cofactor term now the other cofactor
+term is this guy which uses up Row one
+
+ align:start position:0%
+term is this guy which uses up Row one
+ 
+
+ align:start position:0%
+term is this guy which uses up Row one
+and column two and what's surprising
+
+ align:start position:0%
+and column two and what's surprising
+ 
+
+ align:start position:0%
+and column two and what's surprising
+about that when you use Row one and
+
+ align:start position:0%
+about that when you use Row one and
+ 
+
+ align:start position:0%
+about that when you use Row one and
+column two that brings in a minus
+
+ align:start position:0%
+column two that brings in a minus
+ 
+
+ align:start position:0%
+column two that brings in a minus
+there'll be a minus because the the
+
+ align:start position:0%
+there'll be a minus because the the
+ 
+
+ align:start position:0%
+there'll be a minus because the the
+cofactor is this determinant times minus
+
+ align:start position:0%
+cofactor is this determinant times minus
+ 
+
+ align:start position:0%
+cofactor is this determinant times minus
+one the the code the one to cofactor is
+
+ align:start position:0%
+one the the code the one to cofactor is
+ 
+
+ align:start position:0%
+one the the code the one to cofactor is
+that determinant with its sign changed
+
+ align:start position:0%
+that determinant with its sign changed
+ 
+
+ align:start position:0%
+that determinant with its sign changed
+okay so I have to look at that
+
+ align:start position:0%
+okay so I have to look at that
+ 
+
+ align:start position:0%
+okay so I have to look at that
+determinant I have to remember in my
+
+ align:start position:0%
+determinant I have to remember in my
+ 
+
+ align:start position:0%
+determinant I have to remember in my
+head a sign is going to get changed okay
+
+ align:start position:0%
+head a sign is going to get changed okay
+ 
+
+ align:start position:0%
+head a sign is going to get changed okay
+now how do I do that determinant how do
+
+ align:start position:0%
+now how do I do that determinant how do
+ 
+
+ align:start position:0%
+now how do I do that determinant how do
+I make that one clear
+
+ align:start position:0%
+I make that one clear
+ 
+
+ align:start position:0%
+I make that one clear
+I the the neat way to do is here I see
+
+ align:start position:0%
+I the the neat way to do is here I see
+ 
+
+ align:start position:0%
+I the the neat way to do is here I see
+I'll use cofactors down the first column
+
+ align:start position:0%
+I'll use cofactors down the first column
+ 
+
+ align:start position:0%
+I'll use cofactors down the first column
+because the first column is all zeros
+
+ align:start position:0%
+because the first column is all zeros
+ 
+
+ align:start position:0%
+because the first column is all zeros
+except for that one so this one is now
+
+ align:start position:0%
+except for that one so this one is now
+ 
+
+ align:start position:0%
+except for that one so this one is now
+and what's its cofactor within this
+
+ align:start position:0%
+and what's its cofactor within this
+ 
+
+ align:start position:0%
+and what's its cofactor within this
+three by three its cofactor will be 2 by
+
+ align:start position:0%
+three by three its cofactor will be 2 by
+ 
+
+ align:start position:0%
+three by three its cofactor will be 2 by
+2 and what is it it's this right so so
+
+ align:start position:0%
+2 and what is it it's this right so so
+ 
+
+ align:start position:0%
+2 and what is it it's this right so so
+that part is all gone so I'm taking that
+
+ align:start position:0%
+that part is all gone so I'm taking that
+ 
+
+ align:start position:0%
+that part is all gone so I'm taking that
+times its cofactor then 0 times whatever
+
+ align:start position:0%
+times its cofactor then 0 times whatever
+ 
+
+ align:start position:0%
+times its cofactor then 0 times whatever
+its cofactor is so it's really just 1
+
+ align:start position:0%
+its cofactor is so it's really just 1
+ 
+
+ align:start position:0%
+its cofactor is so it's really just 1
+times and what's this in the general
+
+ align:start position:0%
+times and what's this in the general
+ 
+
+ align:start position:0%
+times and what's this in the general
+end-by-end case it's D and minus 2 but
+
+ align:start position:0%
+end-by-end case it's D and minus 2 but
+ 
+
+ align:start position:0%
+end-by-end case it's D and minus 2 but
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+so is this a plus or a sign or a minus
+
+ align:start position:0%
+so is this a plus or a sign or a minus
+ 
+
+ align:start position:0%
+so is this a plus or a sign or a minus
+sign it's it's just a 1 because there's
+
+ align:start position:0%
+sign it's it's just a 1 because there's
+ 
+
+ align:start position:0%
+sign it's it's just a 1 because there's
+a 1 from there and a 1 from there and is
+
+ align:start position:0%
+a 1 from there and a 1 from there and is
+ 
+
+ align:start position:0%
+a 1 from there and a 1 from there and is
+it a plus or a minus
+
+ align:start position:0%
+it a plus or a minus
+ 
+
+ align:start position:0%
+it a plus or a minus
+it's - I guess because it was a minus
+
+ align:start position:0%
+it's - I guess because it was a minus
+ 
+
+ align:start position:0%
+it's - I guess because it was a minus
+the first time and then the second time
+
+ align:start position:0%
+the first time and then the second time
+ 
+
+ align:start position:0%
+the first time and then the second time
+it's a plus so it's overall it's a minus
+
+ align:start position:0%
+it's a plus so it's overall it's a minus
+ 
+
+ align:start position:0%
+it's a plus so it's overall it's a minus
+so there's my a and B were 1 and minus 1
+
+ align:start position:0%
+so there's my a and B were 1 and minus 1
+ 
+
+ align:start position:0%
+so there's my a and B were 1 and minus 1
+that was constants that's the that's the
+
+ align:start position:0%
+that was constants that's the that's the
+ 
+
+ align:start position:0%
+that was constants that's the that's the
+recurrence ok and oh then it asks you to
+
+ align:start position:0%
+recurrence ok and oh then it asks you to
+ 
+
+ align:start position:0%
+recurrence ok and oh then it asks you to
+and then it asks you to solve this thing
+
+ align:start position:0%
+and then it asks you to solve this thing
+ 
+
+ align:start position:0%
+and then it asks you to solve this thing
+first by writing it as a as a system so
+
+ align:start position:0%
+first by writing it as a as a system so
+ 
+
+ align:start position:0%
+first by writing it as a as a system so
+now I'd like to know these solution I
+
+ align:start position:0%
+now I'd like to know these solution I
+ 
+
+ align:start position:0%
+now I'd like to know these solution I
+better know how it starts right
+
+ align:start position:0%
+better know how it starts right
+ 
+
+ align:start position:0%
+better know how it starts right
+it starts with D 1 what was D 1 that's
+
+ align:start position:0%
+it starts with D 1 what was D 1 that's
+ 
+
+ align:start position:0%
+it starts with D 1 what was D 1 that's
+just a one by one case so D 1 is 1 and
+
+ align:start position:0%
+just a one by one case so D 1 is 1 and
+ 
+
+ align:start position:0%
+just a one by one case so D 1 is 1 and
+what is d 2 just to get us started and
+
+ align:start position:0%
+what is d 2 just to get us started and
+ 
+
+ align:start position:0%
+what is d 2 just to get us started and
+then this would give us d3 d4 and
+
+ align:start position:0%
+then this would give us d3 d4 and
+ 
+
+ align:start position:0%
+then this would give us d3 d4 and
+forever D 2 is this 2 by 2 that I'm
+
+ align:start position:0%
+forever D 2 is this 2 by 2 that I'm
+ 
+
+ align:start position:0%
+forever D 2 is this 2 by 2 that I'm
+seeing here and that determinant is
+
+ align:start position:0%
+seeing here and that determinant is
+ 
+
+ align:start position:0%
+seeing here and that determinant is
+obviously 0 so those little ones will
+
+ align:start position:0%
+obviously 0 so those little ones will
+ 
+
+ align:start position:0%
+obviously 0 so those little ones will
+start the recurrence and then we take
+
+ align:start position:0%
+start the recurrence and then we take
+ 
+
+ align:start position:0%
+start the recurrence and then we take
+off and then the idea is to write this
+
+ align:start position:0%
+off and then the idea is to write this
+ 
+
+ align:start position:0%
+off and then the idea is to write this
+recurrence as a as a DND n minus 1 is
+
+ align:start position:0%
+recurrence as a as a DND n minus 1 is
+ 
+
+ align:start position:0%
+recurrence as a as a DND n minus 1 is
+some matrix times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the one before the DN minus 1 DN minus 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the matrix you see you remember
+
+ align:start position:0%
+what's the matrix you see you remember
+ 
+
+ align:start position:0%
+what's the matrix you see you remember
+this step of taking a single
+
+ align:start position:0%
+this step of taking a single
+ 
+
+ align:start position:0%
+this step of taking a single
+second-order equation and by introducing
+
+ align:start position:0%
+second-order equation and by introducing
+ 
+
+ align:start position:0%
+second-order equation and by introducing
+a vector unknown to make it into a to a
+
+ align:start position:0%
+a vector unknown to make it into a to a
+ 
+
+ align:start position:0%
+a vector unknown to make it into a to a
+first-order system okay
+
+ align:start position:0%
+first-order system okay
+ 
+
+ align:start position:0%
+first-order system okay
+so DN is one of DN minus 1 minus 1 I
+
+ align:start position:0%
+so DN is one of DN minus 1 minus 1 I
+ 
+
+ align:start position:0%
+so DN is one of DN minus 1 minus 1 I
+think that that goes in the first row
+
+ align:start position:0%
+think that that goes in the first row
+ 
+
+ align:start position:0%
+think that that goes in the first row
+right from the equation above and the
+
+ align:start position:0%
+right from the equation above and the
+ 
+
+ align:start position:0%
+right from the equation above and the
+second one is this is the same as this
+
+ align:start position:0%
+second one is this is the same as this
+ 
+
+ align:start position:0%
+second one is this is the same as this
+so 1 and 0 are fine so there's the
+
+ align:start position:0%
+so 1 and 0 are fine so there's the
+ 
+
+ align:start position:0%
+so 1 and 0 are fine so there's the
+matrix ok so now how do I proceed we can
+
+ align:start position:0%
+matrix ok so now how do I proceed we can
+ 
+
+ align:start position:0%
+matrix ok so now how do I proceed we can
+guess what this examiner's got in his
+
+ align:start position:0%
+guess what this examiner's got in his
+ 
+
+ align:start position:0%
+guess what this examiner's got in his
+little mind well find the eigenvalues
+
+ align:start position:0%
+little mind well find the eigenvalues
+ 
+
+ align:start position:0%
+little mind well find the eigenvalues
+and actually it tells us that the sixth
+
+ align:start position:0%
+and actually it tells us that the sixth
+ 
+
+ align:start position:0%
+and actually it tells us that the sixth
+power of these eigenvalues turns out to
+
+ align:start position:0%
+power of these eigenvalues turns out to
+ 
+
+ align:start position:0%
+power of these eigenvalues turns out to
+be 1 well can can we get the equation
+
+ align:start position:0%
+be 1 well can can we get the equation
+ 
+
+ align:start position:0%
+be 1 well can can we get the equation
+for the eigenvalues let's do it and
+
+ align:start position:0%
+for the eigenvalues let's do it and
+ 
+
+ align:start position:0%
+for the eigenvalues let's do it and
+let's get a formula for them okay so
+
+ align:start position:0%
+let's get a formula for them okay so
+ 
+
+ align:start position:0%
+let's get a formula for them okay so
+what are the eigenvalues I look at the
+
+ align:start position:0%
+what are the eigenvalues I look at the
+ 
+
+ align:start position:0%
+what are the eigenvalues I look at the
+the matrix this determinant 1 minus
+
+ align:start position:0%
+the matrix this determinant 1 minus
+ 
+
+ align:start position:0%
+the matrix this determinant 1 minus
+lambda and 0 minus lambda and these guys
+
+ align:start position:0%
+lambda and 0 minus lambda and these guys
+ 
+
+ align:start position:0%
+lambda and 0 minus lambda and these guys
+are still there i compute that
+
+ align:start position:0%
+are still there i compute that
+ 
+
+ align:start position:0%
+are still there i compute that
+determinant I get lambda squared minus
+
+ align:start position:0%
+determinant I get lambda squared minus
+ 
+
+ align:start position:0%
+determinant I get lambda squared minus
+lambda and then plus 1 and I set that to
+
+ align:start position:0%
+lambda and then plus 1 and I set that to
+ 
+
+ align:start position:0%
+lambda and then plus 1 and I set that to
+0 okay so we're not Fibonacci here we're
+
+ align:start position:0%
+0 okay so we're not Fibonacci here we're
+ 
+
+ align:start position:0%
+0 okay so we're not Fibonacci here we're
+not seeing Fibonacci numbers because the
+
+ align:start position:0%
+not seeing Fibonacci numbers because the
+ 
+
+ align:start position:0%
+not seeing Fibonacci numbers because the
+sine we had a sign change there and it's
+
+ align:start position:0%
+sine we had a sign change there and it's
+ 
+
+ align:start position:0%
+sine we had a sign change there and it's
+not clear right away whether these
+
+ align:start position:0%
+not clear right away whether these
+ 
+
+ align:start position:0%
+not clear right away whether these
+whether this is it clear is this matrix
+
+ align:start position:0%
+whether this is it clear is this matrix
+ 
+
+ align:start position:0%
+whether this is it clear is this matrix
+stable or unstable when we take when we
+
+ align:start position:0%
+stable or unstable when we take when we
+ 
+
+ align:start position:0%
+stable or unstable when we take when we
+go further and further out are these D
+
+ align:start position:0%
+go further and further out are these D
+ 
+
+ align:start position:0%
+go further and further out are these D
+is increasing are they going to zero are
+
+ align:start position:0%
+is increasing are they going to zero are
+ 
+
+ align:start position:0%
+is increasing are they going to zero are
+they bouncing around periodically the
+
+ align:start position:0%
+they bouncing around periodically the
+ 
+
+ align:start position:0%
+they bouncing around periodically the
+answers have to be here I I would like
+
+ align:start position:0%
+answers have to be here I I would like
+ 
+
+ align:start position:0%
+answers have to be here I I would like
+to know how big these lambdas are right
+
+ align:start position:0%
+to know how big these lambdas are right
+ 
+
+ align:start position:0%
+to know how big these lambdas are right
+and the point is probably these let's
+
+ align:start position:0%
+and the point is probably these let's
+ 
+
+ align:start position:0%
+and the point is probably these let's
+let's see what's lambda from the
+
+ align:start position:0%
+let's see what's lambda from the
+ 
+
+ align:start position:0%
+let's see what's lambda from the
+quadratic formula lambda is one I
+
+ align:start position:0%
+quadratic formula lambda is one I
+ 
+
+ align:start position:0%
+quadratic formula lambda is one I
+switched the sign of that plus or minus
+
+ align:start position:0%
+switched the sign of that plus or minus
+ 
+
+ align:start position:0%
+switched the sign of that plus or minus
+the square root of one minus 4ac am I
+
+ align:start position:0%
+the square root of one minus 4ac am I
+ 
+
+ align:start position:0%
+the square root of one minus 4ac am I
+getting a minus three there / - what's
+
+ align:start position:0%
+getting a minus three there / - what's
+ 
+
+ align:start position:0%
+getting a minus three there / - what's
+up there complex the eigenvalues are 1
+
+ align:start position:0%
+up there complex the eigenvalues are 1
+ 
+
+ align:start position:0%
+up there complex the eigenvalues are 1
+plus square root of 3i over 2 and 1
+
+ align:start position:0%
+plus square root of 3i over 2 and 1
+ 
+
+ align:start position:0%
+plus square root of 3i over 2 and 1
+minus square root of 3i over 2 what's
+
+ align:start position:0%
+minus square root of 3i over 2 what's
+ 
+
+ align:start position:0%
+minus square root of 3i over 2 what's
+the magnitude of lambda that's the key
+
+ align:start position:0%
+the magnitude of lambda that's the key
+ 
+
+ align:start position:0%
+the magnitude of lambda that's the key
+point for stability these these these
+
+ align:start position:0%
+point for stability these these these
+ 
+
+ align:start position:0%
+point for stability these these these
+are two numbers in the complex plane 1
+
+ align:start position:0%
+are two numbers in the complex plane 1
+ 
+
+ align:start position:0%
+are two numbers in the complex plane 1
+plus some somewhere here and it's
+
+ align:start position:0%
+plus some somewhere here and it's
+ 
+
+ align:start position:0%
+plus some somewhere here and it's
+complex conjugate there I want to know
+
+ align:start position:0%
+complex conjugate there I want to know
+ 
+
+ align:start position:0%
+complex conjugate there I want to know
+how far from the origin are those
+
+ align:start position:0%
+how far from the origin are those
+ 
+
+ align:start position:0%
+how far from the origin are those
+numbers what's the magnitude of lambda
+
+ align:start position:0%
+numbers what's the magnitude of lambda
+ 
+
+ align:start position:0%
+numbers what's the magnitude of lambda
+and you see what it is
+
+ align:start position:0%
+and you see what it is
+ 
+
+ align:start position:0%
+and you see what it is
+you recognize this a number like that
+
+ align:start position:0%
+you recognize this a number like that
+ 
+
+ align:start position:0%
+you recognize this a number like that
+take the real part squared and the
+
+ align:start position:0%
+take the real part squared and the
+ 
+
+ align:start position:0%
+take the real part squared and the
+imaginary part squared and add what do
+
+ align:start position:0%
+imaginary part squared and add what do
+ 
+
+ align:start position:0%
+imaginary part squared and add what do
+you get so the real part squared is of
+
+ align:start position:0%
+you get so the real part squared is of
+ 
+
+ align:start position:0%
+you get so the real part squared is of
+quarter the imaginary part squared is
+
+ align:start position:0%
+quarter the imaginary part squared is
+ 
+
+ align:start position:0%
+quarter the imaginary part squared is
+3/4 they add to 1 that's a number with
+
+ align:start position:0%
+3/4 they add to 1 that's a number with
+ 
+
+ align:start position:0%
+3/4 they add to 1 that's a number with
+that's on the unit circle that's an e to
+
+ align:start position:0%
+that's on the unit circle that's an e to
+ 
+
+ align:start position:0%
+that's on the unit circle that's an e to
+the I theta
+
+ align:start position:0%
+the I theta
+ 
+
+ align:start position:0%
+the I theta
+that's a cos theta plus I sine theta and
+
+ align:start position:0%
+that's a cos theta plus I sine theta and
+ 
+
+ align:start position:0%
+that's a cos theta plus I sine theta and
+what's theta is so this this is like a
+
+ align:start position:0%
+what's theta is so this this is like a
+ 
+
+ align:start position:0%
+what's theta is so this this is like a
+complex number that's worth knowing it's
+
+ align:start position:0%
+complex number that's worth knowing it's
+ 
+
+ align:start position:0%
+complex number that's worth knowing it's
+not totally obvious but it's nice that's
+
+ align:start position:0%
+not totally obvious but it's nice that's
+ 
+
+ align:start position:0%
+not totally obvious but it's nice that's
+that I should see that as cos theta plus
+
+ align:start position:0%
+that I should see that as cos theta plus
+ 
+
+ align:start position:0%
+that I should see that as cos theta plus
+I sine theta and the angle that would do
+
+ align:start position:0%
+I sine theta and the angle that would do
+ 
+
+ align:start position:0%
+I sine theta and the angle that would do
+that is 60 degrees PI over 3 so that's a
+
+ align:start position:0%
+that is 60 degrees PI over 3 so that's a
+ 
+
+ align:start position:0%
+that is 60 degrees PI over 3 so that's a
+let me improve my picture
+
+ align:start position:0%
+let me improve my picture
+ 
+
+ align:start position:0%
+let me improve my picture
+so those that's e to the I PI over six
+
+ align:start position:0%
+so those that's e to the I PI over six
+ 
+
+ align:start position:0%
+so those that's e to the I PI over six
+be PI over three
+
+ align:start position:0%
+be PI over three
+ 
+
+ align:start position:0%
+be PI over three
+this is this number is e to the I PI
+
+ align:start position:0%
+this is this number is e to the I PI
+ 
+
+ align:start position:0%
+this is this number is e to the I PI
+over three and he to the minus I PI over
+
+ align:start position:0%
+over three and he to the minus I PI over
+ 
+
+ align:start position:0%
+over three and he to the minus I PI over
+three will be doing more complex numbers
+
+ align:start position:0%
+three will be doing more complex numbers
+ 
+
+ align:start position:0%
+three will be doing more complex numbers
+briefly but a little more in the next
+
+ align:start position:0%
+briefly but a little more in the next
+ 
+
+ align:start position:0%
+briefly but a little more in the next
+two days next two lectures anyway so
+
+ align:start position:0%
+two days next two lectures anyway so
+ 
+
+ align:start position:0%
+two days next two lectures anyway so
+what's the deal with stability what do
+
+ align:start position:0%
+what's the deal with stability what do
+ 
+
+ align:start position:0%
+what's the deal with stability what do
+the d-ends do well look if if I take the
+
+ align:start position:0%
+the d-ends do well look if if I take the
+ 
+
+ align:start position:0%
+the d-ends do well look if if I take the
+sixth power I'm around at 1 the problem
+
+ align:start position:0%
+sixth power I'm around at 1 the problem
+ 
+
+ align:start position:0%
+sixth power I'm around at 1 the problem
+actually told me this the sixth power of
+
+ align:start position:0%
+actually told me this the sixth power of
+ 
+
+ align:start position:0%
+actually told me this the sixth power of
+those eigenvalues brings me around to 1
+
+ align:start position:0%
+those eigenvalues brings me around to 1
+ 
+
+ align:start position:0%
+those eigenvalues brings me around to 1
+what does that tell you about the matrix
+
+ align:start position:0%
+what does that tell you about the matrix
+ 
+
+ align:start position:0%
+what does that tell you about the matrix
+by the way suppose you know this was a
+
+ align:start position:0%
+by the way suppose you know this was a
+ 
+
+ align:start position:0%
+by the way suppose you know this was a
+great quiz question so I should never
+
+ align:start position:0%
+great quiz question so I should never
+ 
+
+ align:start position:0%
+great quiz question so I should never
+have just said it but popped out suppose
+
+ align:start position:0%
+have just said it but popped out suppose
+ 
+
+ align:start position:0%
+have just said it but popped out suppose
+lambda 1 to the sixth and lambda 2 to
+
+ align:start position:0%
+lambda 1 to the sixth and lambda 2 to
+ 
+
+ align:start position:0%
+lambda 1 to the sixth and lambda 2 to
+the sixth or 1 which they are what does
+
+ align:start position:0%
+the sixth or 1 which they are what does
+ 
+
+ align:start position:0%
+the sixth or 1 which they are what does
+that tell me about a matrix about my
+
+ align:start position:0%
+that tell me about a matrix about my
+ 
+
+ align:start position:0%
+that tell me about a matrix about my
+matrix a here well what what matrix is
+
+ align:start position:0%
+matrix a here well what what matrix is
+ 
+
+ align:start position:0%
+matrix a here well what what matrix is
+connected with lambda 1 to the sixth and
+
+ align:start position:0%
+connected with lambda 1 to the sixth and
+ 
+
+ align:start position:0%
+connected with lambda 1 to the sixth and
+lambda 2 to the 6 it's got to be the
+
+ align:start position:0%
+lambda 2 to the 6 it's got to be the
+ 
+
+ align:start position:0%
+lambda 2 to the 6 it's got to be the
+matrix a to the sixth so what is a to
+
+ align:start position:0%
+matrix a to the sixth so what is a to
+ 
+
+ align:start position:0%
+matrix a to the sixth so what is a to
+the sixth for that matrix it's got I
+
+ align:start position:0%
+the sixth for that matrix it's got I
+ 
+
+ align:start position:0%
+the sixth for that matrix it's got I
+ghen values one in one cuz when I take
+
+ align:start position:0%
+ghen values one in one cuz when I take
+ 
+
+ align:start position:0%
+ghen values one in one cuz when I take
+the sixth power actually yeah if I take
+
+ align:start position:0%
+the sixth power actually yeah if I take
+ 
+
+ align:start position:0%
+the sixth power actually yeah if I take
+the sixth power both all the sixth power
+
+ align:start position:0%
+the sixth power both all the sixth power
+ 
+
+ align:start position:0%
+the sixth power both all the sixth power
+of that is one and the sixth power of
+
+ align:start position:0%
+of that is one and the sixth power of
+ 
+
+ align:start position:0%
+of that is one and the sixth power of
+that is one the sixth power of this is e
+
+ align:start position:0%
+that is one the sixth power of this is e
+ 
+
+ align:start position:0%
+that is one the sixth power of this is e
+to the 2 pi that's one the sixth power
+
+ align:start position:0%
+to the 2 pi that's one the sixth power
+ 
+
+ align:start position:0%
+to the 2 pi that's one the sixth power
+of this is e to the minus 2 pi that's
+
+ align:start position:0%
+of this is e to the minus 2 pi that's
+ 
+
+ align:start position:0%
+of this is e to the minus 2 pi that's
+one so the sixth powers the the 6th
+
+ align:start position:0%
+one so the sixth powers the the 6th
+ 
+
+ align:start position:0%
+one so the sixth powers the the 6th
+power of that matrix has eigenvalues one
+
+ align:start position:0%
+power of that matrix has eigenvalues one
+ 
+
+ align:start position:0%
+power of that matrix has eigenvalues one
+and one so what is it it's the identity
+
+ align:start position:0%
+and one so what is it it's the identity
+ 
+
+ align:start position:0%
+and one so what is it it's the identity
+right so if I operate this if I run this
+
+ align:start position:0%
+right so if I operate this if I run this
+ 
+
+ align:start position:0%
+right so if I operate this if I run this
+thing six times I'm back where I was the
+
+ align:start position:0%
+thing six times I'm back where I was the
+ 
+
+ align:start position:0%
+thing six times I'm back where I was the
+sixth power of that matrix is the
+
+ align:start position:0%
+sixth power of that matrix is the
+ 
+
+ align:start position:0%
+sixth power of that matrix is the
+identity good okay so it'll loop around
+
+ align:start position:0%
+identity good okay so it'll loop around
+ 
+
+ align:start position:0%
+identity good okay so it'll loop around
+it's it doesn't go to zero it doesn't
+
+ align:start position:0%
+it's it doesn't go to zero it doesn't
+ 
+
+ align:start position:0%
+it's it doesn't go to zero it doesn't
+blow up it just periodically goes around
+
+ align:start position:0%
+blow up it just periodically goes around
+ 
+
+ align:start position:0%
+blow up it just periodically goes around
+with period six okay
+
+ align:start position:0%
+with period six okay
+ 
+
+ align:start position:0%
+with period six okay
+let's just see if there's a alright
+
+ align:start position:0%
+let's just see if there's a alright
+ 
+
+ align:start position:0%
+let's just see if there's a alright
+oh let's see can I also look at a at a
+
+ align:start position:0%
+oh let's see can I also look at a at a
+ 
+
+ align:start position:0%
+oh let's see can I also look at a at a
+final exam from 1992 I think that's yeah
+
+ align:start position:0%
+final exam from 1992 I think that's yeah
+ 
+
+ align:start position:0%
+final exam from 1992 I think that's yeah
+let me do that on this last board it
+
+ align:start position:0%
+let me do that on this last board it
+ 
+
+ align:start position:0%
+let me do that on this last board it
+starts a lot of the questions in this
+
+ align:start position:0%
+starts a lot of the questions in this
+ 
+
+ align:start position:0%
+starts a lot of the questions in this
+exam are about a family of matrices let
+
+ align:start position:0%
+exam are about a family of matrices let
+ 
+
+ align:start position:0%
+exam are about a family of matrices let
+me give you the fourth the fourth guy in
+
+ align:start position:0%
+me give you the fourth the fourth guy in
+ 
+
+ align:start position:0%
+me give you the fourth the fourth guy in
+the family is has a 1 so it's zeros on
+
+ align:start position:0%
+the family is has a 1 so it's zeros on
+ 
+
+ align:start position:0%
+the family is has a 1 so it's zeros on
+the diagonal but these are going 1 2 3
+
+ align:start position:0%
+the diagonal but these are going 1 2 3
+ 
+
+ align:start position:0%
+the diagonal but these are going 1 2 3
+and so on 1 2 3 and so on
+
+ align:start position:0%
+and so on 1 2 3 and so on
+ 
+
+ align:start position:0%
+and so on 1 2 3 and so on
+but for the 4 by 4 case I'm stopping at
+
+ align:start position:0%
+but for the 4 by 4 case I'm stopping at
+ 
+
+ align:start position:0%
+but for the 4 by 4 case I'm stopping at
+4 you see the pattern it's it's a family
+
+ align:start position:0%
+4 you see the pattern it's it's a family
+ 
+
+ align:start position:0%
+4 you see the pattern it's it's a family
+of matrices which is growing and
+
+ align:start position:0%
+of matrices which is growing and
+ 
+
+ align:start position:0%
+of matrices which is growing and
+actually the numbers it's symmetric
+
+ align:start position:0%
+actually the numbers it's symmetric
+ 
+
+ align:start position:0%
+actually the numbers it's symmetric
+right it's equal to a for transpose and
+
+ align:start position:0%
+right it's equal to a for transpose and
+ 
+
+ align:start position:0%
+right it's equal to a for transpose and
+we can ask all sorts of questions about
+
+ align:start position:0%
+we can ask all sorts of questions about
+ 
+
+ align:start position:0%
+we can ask all sorts of questions about
+its null space its range its column
+
+ align:start position:0%
+its null space its range its column
+ 
+
+ align:start position:0%
+its null space its range its column
+space find the projection matrix under
+
+ align:start position:0%
+space find the projection matrix under
+ 
+
+ align:start position:0%
+space find the projection matrix under
+the column space of a 3 for example is
+
+ align:start position:0%
+the column space of a 3 for example is
+ 
+
+ align:start position:0%
+the column space of a 3 for example is
+in here so so one so a 3 is 0 1 0 1 0 2
+
+ align:start position:0%
+in here so so one so a 3 is 0 1 0 1 0 2
+ 
+
+ align:start position:0%
+in here so so one so a 3 is 0 1 0 1 0 2
+0 2 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay find the projection matrix onto the
+
+ align:start position:0%
+okay find the projection matrix onto the
+ 
+
+ align:start position:0%
+okay find the projection matrix onto the
+column space by the way is that matrix
+
+ align:start position:0%
+column space by the way is that matrix
+ 
+
+ align:start position:0%
+column space by the way is that matrix
+singular or invertible singular why do
+
+ align:start position:0%
+singular or invertible singular why do
+ 
+
+ align:start position:0%
+singular or invertible singular why do
+we know it's singular
+
+ align:start position:0%
+we know it's singular
+ 
+
+ align:start position:0%
+we know it's singular
+I see the column three is a cut is a
+
+ align:start position:0%
+I see the column three is a cut is a
+ 
+
+ align:start position:0%
+I see the column three is a cut is a
+multiple of column one or we could take
+
+ align:start position:0%
+multiple of column one or we could take
+ 
+
+ align:start position:0%
+multiple of column one or we could take
+its determinant so it's certainly
+
+ align:start position:0%
+its determinant so it's certainly
+ 
+
+ align:start position:0%
+its determinant so it's certainly
+singular the project so the projection
+
+ align:start position:0%
+singular the project so the projection
+ 
+
+ align:start position:0%
+singular the project so the projection
+will be matrix will be three by three
+
+ align:start position:0%
+will be matrix will be three by three
+ 
+
+ align:start position:0%
+will be matrix will be three by three
+but it will project onto the column
+
+ align:start position:0%
+but it will project onto the column
+ 
+
+ align:start position:0%
+but it will project onto the column
+space it'll project onto this plane the
+
+ align:start position:0%
+space it'll project onto this plane the
+ 
+
+ align:start position:0%
+space it'll project onto this plane the
+column space of a three and I guess I
+
+ align:start position:0%
+column space of a three and I guess I
+ 
+
+ align:start position:0%
+column space of a three and I guess I
+would find it from the formula a eight a
+
+ align:start position:0%
+would find it from the formula a eight a
+ 
+
+ align:start position:0%
+would find it from the formula a eight a
+a transpose a inverse I would have to I
+
+ align:start position:0%
+a transpose a inverse I would have to I
+ 
+
+ align:start position:0%
+a transpose a inverse I would have to I
+would I guess I would do all this there
+
+ align:start position:0%
+would I guess I would do all this there
+ 
+
+ align:start position:0%
+would I guess I would do all this there
+may be a better way perhaps like yeah I
+
+ align:start position:0%
+may be a better way perhaps like yeah I
+ 
+
+ align:start position:0%
+may be a better way perhaps like yeah I
+could think there might be a slightly
+
+ align:start position:0%
+could think there might be a slightly
+ 
+
+ align:start position:0%
+could think there might be a slightly
+quicker way but that would come out
+
+ align:start position:0%
+quicker way but that would come out
+ 
+
+ align:start position:0%
+quicker way but that would come out
+pretty fast okay so that's me the
+
+ align:start position:0%
+pretty fast okay so that's me the
+ 
+
+ align:start position:0%
+pretty fast okay so that's me the
+projection matrix
+
+ align:start position:0%
+projection matrix
+ 
+
+ align:start position:0%
+projection matrix
+next question find the eigenvalues and
+
+ align:start position:0%
+next question find the eigenvalues and
+ 
+
+ align:start position:0%
+next question find the eigenvalues and
+eigenvectors of that matrix okay there's
+
+ align:start position:0%
+eigenvectors of that matrix okay there's
+ 
+
+ align:start position:0%
+eigenvectors of that matrix okay there's
+a three by three matrix oh yes so what
+
+ align:start position:0%
+a three by three matrix oh yes so what
+ 
+
+ align:start position:0%
+a three by three matrix oh yes so what
+are its eigenvalues and eigenvectors we
+
+ align:start position:0%
+are its eigenvalues and eigenvectors we
+ 
+
+ align:start position:0%
+are its eigenvalues and eigenvectors we
+haven't done any three by threes let's
+
+ align:start position:0%
+haven't done any three by threes let's
+ 
+
+ align:start position:0%
+haven't done any three by threes let's
+do one I want to find so how do I find
+
+ align:start position:0%
+do one I want to find so how do I find
+ 
+
+ align:start position:0%
+do one I want to find so how do I find
+eigenvalues I take the determinant of a
+
+ align:start position:0%
+eigenvalues I take the determinant of a
+ 
+
+ align:start position:0%
+eigenvalues I take the determinant of a
+3 minus lambda hi so this is you just
+
+ align:start position:0%
+3 minus lambda hi so this is you just
+ 
+
+ align:start position:0%
+3 minus lambda hi so this is you just
+have to so I'm subtracting lambda from
+
+ align:start position:0%
+have to so I'm subtracting lambda from
+ 
+
+ align:start position:0%
+have to so I'm subtracting lambda from
+the diagonal and I have a 1 1 0 0 2 2
+
+ align:start position:0%
+the diagonal and I have a 1 1 0 0 2 2
+ 
+
+ align:start position:0%
+the diagonal and I have a 1 1 0 0 2 2
+there and I just have to find that
+
+ align:start position:0%
+there and I just have to find that
+ 
+
+ align:start position:0%
+there and I just have to find that
+determinant okay since it's 3x3 I'll
+
+ align:start position:0%
+determinant okay since it's 3x3 I'll
+ 
+
+ align:start position:0%
+determinant okay since it's 3x3 I'll
+just go for it this way gives me minus
+
+ align:start position:0%
+just go for it this way gives me minus
+ 
+
+ align:start position:0%
+just go for it this way gives me minus
+lambda cubed and a 0 and a 0 then in
+
+ align:start position:0%
+lambda cubed and a 0 and a 0 then in
+ 
+
+ align:start position:0%
+lambda cubed and a 0 and a 0 then in
+this direction which has the minus sign
+
+ align:start position:0%
+this direction which has the minus sign
+ 
+
+ align:start position:0%
+this direction which has the minus sign
+that's a zero for lambdas i mean- for
+
+ align:start position:0%
+that's a zero for lambdas i mean- for
+ 
+
+ align:start position:0%
+that's a zero for lambdas i mean- for
+lambdas and - another lambda so that's
+
+ align:start position:0%
+lambdas and - another lambda so that's
+ 
+
+ align:start position:0%
+lambdas and - another lambda so that's
+-5 lambdas but that direction goes with
+
+ align:start position:0%
+-5 lambdas but that direction goes with
+ 
+
+ align:start position:0%
+-5 lambdas but that direction goes with
+a minus sign so I think it's plus 5
+
+ align:start position:0%
+a minus sign so I think it's plus 5
+ 
+
+ align:start position:0%
+a minus sign so I think it's plus 5
+lambda that looks like the determinant
+
+ align:start position:0%
+lambda that looks like the determinant
+ 
+
+ align:start position:0%
+lambda that looks like the determinant
+of a 3 minus lambda I so I set it to 0
+
+ align:start position:0%
+of a 3 minus lambda I so I set it to 0
+ 
+
+ align:start position:0%
+of a 3 minus lambda I so I set it to 0
+so what are the eigenvalues
+
+ align:start position:0%
+so what are the eigenvalues
+ 
+
+ align:start position:0%
+so what are the eigenvalues
+well lambda equals 0 lambda factors out
+
+ align:start position:0%
+well lambda equals 0 lambda factors out
+ 
+
+ align:start position:0%
+well lambda equals 0 lambda factors out
+of this times minus lambda squared plus
+
+ align:start position:0%
+of this times minus lambda squared plus
+ 
+
+ align:start position:0%
+of this times minus lambda squared plus
+4 so the eigenvalues are 5 thanks thanks
+
+ align:start position:0%
+4 so the eigenvalues are 5 thanks thanks
+ 
+
+ align:start position:0%
+4 so the eigenvalues are 5 thanks thanks
+so the eigenvalues are 0 square root of
+
+ align:start position:0%
+so the eigenvalues are 0 square root of
+ 
+
+ align:start position:0%
+so the eigenvalues are 0 square root of
+5 and minus square root of 5 and I would
+
+ align:start position:0%
+5 and minus square root of 5 and I would
+ 
+
+ align:start position:0%
+5 and minus square root of 5 and I would
+never write down those three eigenvalues
+
+ align:start position:0%
+never write down those three eigenvalues
+ 
+
+ align:start position:0%
+never write down those three eigenvalues
+without checking the trace to tell the
+
+ align:start position:0%
+without checking the trace to tell the
+ 
+
+ align:start position:0%
+without checking the trace to tell the
+truth because because we did a bunch of
+
+ align:start position:0%
+truth because because we did a bunch of
+ 
+
+ align:start position:0%
+truth because because we did a bunch of
+calculations here but then I can quickly
+
+ align:start position:0%
+calculations here but then I can quickly
+ 
+
+ align:start position:0%
+calculations here but then I can quickly
+add up the eigenvalues to get 0 add up
+
+ align:start position:0%
+add up the eigenvalues to get 0 add up
+ 
+
+ align:start position:0%
+add up the eigenvalues to get 0 add up
+the trace to get 0 and feel that I'm
+
+ align:start position:0%
+the trace to get 0 and feel that I'm
+ 
+
+ align:start position:0%
+the trace to get 0 and feel that I'm
+well I guess that wouldn't have caught
+
+ align:start position:0%
+well I guess that wouldn't have caught
+ 
+
+ align:start position:0%
+well I guess that wouldn't have caught
+my error if I made it if that had been a
+
+ align:start position:0%
+my error if I made it if that had been a
+ 
+
+ align:start position:0%
+my error if I made it if that had been a
+4 I wouldn't have noticed the
+
+ align:start position:0%
+4 I wouldn't have noticed the
+ 
+
+ align:start position:0%
+4 I wouldn't have noticed the
+determinant isn't anything greatly
+
+ align:start position:0%
+determinant isn't anything greatly
+ 
+
+ align:start position:0%
+determinant isn't anything greatly
+useful here right because the
+
+ align:start position:0%
+useful here right because the
+ 
+
+ align:start position:0%
+useful here right because the
+determinant is just 0 and so I never
+
+ align:start position:0%
+determinant is just 0 and so I never
+ 
+
+ align:start position:0%
+determinant is just 0 and so I never
+would know whether that 5 was right or
+
+ align:start position:0%
+would know whether that 5 was right or
+ 
+
+ align:start position:0%
+would know whether that 5 was right or
+wrong but thanks for making it right ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+huh question to see whoever wrote this
+
+ align:start position:0%
+huh question to see whoever wrote this
+ 
+
+ align:start position:0%
+huh question to see whoever wrote this
+probably me said this is not difficult I
+
+ align:start position:0%
+probably me said this is not difficult I
+ 
+
+ align:start position:0%
+probably me said this is not difficult I
+don't know why I put that in it asks for
+
+ align:start position:0%
+don't know why I put that in it asks for
+ 
+
+ align:start position:0%
+don't know why I put that in it asks for
+the projection matrix onto the column
+
+ align:start position:0%
+the projection matrix onto the column
+ 
+
+ align:start position:0%
+the projection matrix onto the column
+space of a 4 how could I have thought
+
+ align:start position:0%
+space of a 4 how could I have thought
+ 
+
+ align:start position:0%
+space of a 4 how could I have thought
+that wasn't difficult it looks extremely
+
+ align:start position:0%
+that wasn't difficult it looks extremely
+ 
+
+ align:start position:0%
+that wasn't difficult it looks extremely
+difficult what's the projection matrix
+
+ align:start position:0%
+difficult what's the projection matrix
+ 
+
+ align:start position:0%
+difficult what's the projection matrix
+under the column space of a 4 I don't
+
+ align:start position:0%
+under the column space of a 4 I don't
+ 
+
+ align:start position:0%
+under the column space of a 4 I don't
+know whether that this is now difficult
+
+ align:start position:0%
+know whether that this is now difficult
+ 
+
+ align:start position:0%
+know whether that this is now difficult
+it's just like helpful or or insulting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what do you think there what's the
+
+ align:start position:0%
+and what do you think there what's the
+ 
+
+ align:start position:0%
+and what do you think there what's the
+column space of a 4 here well what's our
+
+ align:start position:0%
+column space of a 4 here well what's our
+ 
+
+ align:start position:0%
+column space of a 4 here well what's our
+first question is is the matrix singular
+
+ align:start position:0%
+first question is is the matrix singular
+ 
+
+ align:start position:0%
+first question is is the matrix singular
+or invertible if the answer is
+
+ align:start position:0%
+or invertible if the answer is
+ 
+
+ align:start position:0%
+or invertible if the answer is
+invertible then what's the column space
+
+ align:start position:0%
+invertible then what's the column space
+ 
+
+ align:start position:0%
+invertible then what's the column space
+if this matrix a for is invertible so
+
+ align:start position:0%
+if this matrix a for is invertible so
+ 
+
+ align:start position:0%
+if this matrix a for is invertible so
+that's my guess if this problem is easy
+
+ align:start position:0%
+that's my guess if this problem is easy
+ 
+
+ align:start position:0%
+that's my guess if this problem is easy
+it has to be because this matrix is
+
+ align:start position:0%
+it has to be because this matrix is
+ 
+
+ align:start position:0%
+it has to be because this matrix is
+probably invertible then it's column
+
+ align:start position:0%
+probably invertible then it's column
+ 
+
+ align:start position:0%
+probably invertible then it's column
+spaces are for good column spaces the
+
+ align:start position:0%
+spaces are for good column spaces the
+ 
+
+ align:start position:0%
+spaces are for good column spaces the
+whole space and the answer to this easy
+
+ align:start position:0%
+whole space and the answer to this easy
+ 
+
+ align:start position:0%
+whole space and the answer to this easy
+question is the projection matrix is the
+
+ align:start position:0%
+question is the projection matrix is the
+ 
+
+ align:start position:0%
+question is the projection matrix is the
+identity it's the 4 by 4 identity matrix
+
+ align:start position:0%
+identity it's the 4 by 4 identity matrix
+ 
+
+ align:start position:0%
+identity it's the 4 by 4 identity matrix
+if this matrix is invertible shall we
+
+ align:start position:0%
+if this matrix is invertible shall we
+ 
+
+ align:start position:0%
+if this matrix is invertible shall we
+check invertibility how would you find
+
+ align:start position:0%
+check invertibility how would you find
+ 
+
+ align:start position:0%
+check invertibility how would you find
+its determinant can we just like take
+
+ align:start position:0%
+its determinant can we just like take
+ 
+
+ align:start position:0%
+its determinant can we just like take
+the determinant of that matrix I could
+
+ align:start position:0%
+the determinant of that matrix I could
+ 
+
+ align:start position:0%
+the determinant of that matrix I could
+ask you how so there there are 24 terms
+
+ align:start position:0%
+ask you how so there there are 24 terms
+ 
+
+ align:start position:0%
+ask you how so there there are 24 terms
+do we want to write all 24 terms down
+
+ align:start position:0%
+do we want to write all 24 terms down
+ 
+
+ align:start position:0%
+do we want to write all 24 terms down
+not in the remaining 10 seconds better
+
+ align:start position:0%
+not in the remaining 10 seconds better
+ 
+
+ align:start position:0%
+not in the remaining 10 seconds better
+to use cofactors so I go along Row 1 I
+
+ align:start position:0%
+to use cofactors so I go along Row 1 I
+ 
+
+ align:start position:0%
+to use cofactors so I go along Row 1 I
+see one the only nonzero is this guy so
+
+ align:start position:0%
+see one the only nonzero is this guy so
+ 
+
+ align:start position:0%
+see one the only nonzero is this guy so
+I should take that 1 times the cofactor
+
+ align:start position:0%
+I should take that 1 times the cofactor
+ 
+
+ align:start position:0%
+I should take that 1 times the cofactor
+now so I'm down to this determinant okay
+
+ align:start position:0%
+now so I'm down to this determinant okay
+ 
+
+ align:start position:0%
+now so I'm down to this determinant okay
+so now I'm look at this for his column I
+
+ align:start position:0%
+so now I'm look at this for his column I
+ 
+
+ align:start position:0%
+so now I'm look at this for his column I
+see 1 times this there's the cofactor of
+
+ align:start position:0%
+see 1 times this there's the cofactor of
+ 
+
+ align:start position:0%
+see 1 times this there's the cofactor of
+the one so I'm using up Row 1 Row 1 and
+
+ align:start position:0%
+the one so I'm using up Row 1 Row 1 and
+ 
+
+ align:start position:0%
+the one so I'm using up Row 1 Row 1 and
+column 1 of this 3 by 3 matrix I'm down
+
+ align:start position:0%
+column 1 of this 3 by 3 matrix I'm down
+ 
+
+ align:start position:0%
+column 1 of this 3 by 3 matrix I'm down
+to this cofactor and by the way those
+
+ align:start position:0%
+to this cofactor and by the way those
+ 
+
+ align:start position:0%
+to this cofactor and by the way those
+were both plus signs right no they
+
+ align:start position:0%
+were both plus signs right no they
+ 
+
+ align:start position:0%
+were both plus signs right no they
+weren't that was a minus sign that was a
+
+ align:start position:0%
+weren't that was a minus sign that was a
+ 
+
+ align:start position:0%
+weren't that was a minus sign that was a
+that was a minus and then that was a
+
+ align:start position:0%
+that was a minus and then that was a
+ 
+
+ align:start position:0%
+that was a minus and then that was a
+plus and then this so what's the
+
+ align:start position:0%
+plus and then this so what's the
+ 
+
+ align:start position:0%
+plus and then this so what's the
+determinant 9 no determinate is not the
+
+ align:start position:0%
+determinant 9 no determinate is not the
+ 
+
+ align:start position:0%
+determinant 9 no determinate is not the
+determinate of a for is not okay where a
+
+ align:start position:0%
+determinate of a for is not okay where a
+ 
+
+ align:start position:0%
+determinate of a for is not okay where a
+3 so my guess is I'll put that on the
+
+ align:start position:0%
+3 so my guess is I'll put that on the
+ 
+
+ align:start position:0%
+3 so my guess is I'll put that on the
+final this year the probably the
+
+ align:start position:0%
+final this year the probably the
+ 
+
+ align:start position:0%
+final this year the probably the
+odd-numbered ones are singular and the
+
+ align:start position:0%
+odd-numbered ones are singular and the
+ 
+
+ align:start position:0%
+odd-numbered ones are singular and the
+even-numbered ones are invertible and I
+
+ align:start position:0%
+even-numbered ones are invertible and I
+ 
+
+ align:start position:0%
+even-numbered ones are invertible and I
+don't know what the determinants are but
+
+ align:start position:0%
+don't know what the determinants are but
+ 
+
+ align:start position:0%
+don't know what the determinants are but
+I'm betting that they have some nice
+
+ align:start position:0%
+I'm betting that they have some nice
+ 
+
+ align:start position:0%
+I'm betting that they have some nice
+formula okay so recitations this week
+
+ align:start position:0%
+formula okay so recitations this week
+ 
+
+ align:start position:0%
+formula okay so recitations this week
+will also be quiz review and then the
+
+ align:start position:0%
+will also be quiz review and then the
+ 
+
+ align:start position:0%
+will also be quiz review and then the
+quiz is Wednesday at 1 o'clock thanks
\ No newline at end of file
diff --git a/R4nGGs0m7lo.txt b/R4nGGs0m7lo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..03d931671824cdf65108cf9bc20285ee77c89bf3
--- /dev/null
+++ b/R4nGGs0m7lo.txt
@@ -0,0 +1,571 @@
+align:start position:0%
+ 
+when we have independence does anything
+
+ align:start position:0%
+when we have independence does anything
+ 
+
+ align:start position:0%
+when we have independence does anything
+interesting happen to expectations we
+
+ align:start position:0%
+interesting happen to expectations we
+ 
+
+ align:start position:0%
+interesting happen to expectations we
+know that in general the expected value
+
+ align:start position:0%
+know that in general the expected value
+ 
+
+ align:start position:0%
+know that in general the expected value
+of a function of random variables is not
+
+ align:start position:0%
+of a function of random variables is not
+ 
+
+ align:start position:0%
+of a function of random variables is not
+the same as applying the function to the
+
+ align:start position:0%
+the same as applying the function to the
+ 
+
+ align:start position:0%
+the same as applying the function to the
+expected values and we also know that
+
+ align:start position:0%
+expected values and we also know that
+ 
+
+ align:start position:0%
+expected values and we also know that
+there are some exceptions where we do
+
+ align:start position:0%
+there are some exceptions where we do
+ 
+
+ align:start position:0%
+there are some exceptions where we do
+get equality this is the case where we
+
+ align:start position:0%
+get equality this is the case where we
+ 
+
+ align:start position:0%
+get equality this is the case where we
+are dealing with linear functions of one
+
+ align:start position:0%
+are dealing with linear functions of one
+ 
+
+ align:start position:0%
+are dealing with linear functions of one
+or more random variables
+
+ align:start position:0%
+or more random variables
+ 
+
+ align:start position:0%
+or more random variables
+note that this last property is always
+
+ align:start position:0%
+note that this last property is always
+ 
+
+ align:start position:0%
+note that this last property is always
+true and does not require any
+
+ align:start position:0%
+true and does not require any
+ 
+
+ align:start position:0%
+true and does not require any
+independence assumptions when we have
+
+ align:start position:0%
+independence assumptions when we have
+ 
+
+ align:start position:0%
+independence assumptions when we have
+independence there is one additional
+
+ align:start position:0%
+independence there is one additional
+ 
+
+ align:start position:0%
+independence there is one additional
+property that turns out to be true the
+
+ align:start position:0%
+property that turns out to be true the
+ 
+
+ align:start position:0%
+property that turns out to be true the
+expected value of the product of two
+
+ align:start position:0%
+expected value of the product of two
+ 
+
+ align:start position:0%
+expected value of the product of two
+independent random variables is the
+
+ align:start position:0%
+independent random variables is the
+ 
+
+ align:start position:0%
+independent random variables is the
+product of their expected values let us
+
+ align:start position:0%
+product of their expected values let us
+ 
+
+ align:start position:0%
+product of their expected values let us
+verify this relation we are dealing here
+
+ align:start position:0%
+verify this relation we are dealing here
+ 
+
+ align:start position:0%
+verify this relation we are dealing here
+with the expected value of a function of
+
+ align:start position:0%
+with the expected value of a function of
+ 
+
+ align:start position:0%
+with the expected value of a function of
+random variables where the function is
+
+ align:start position:0%
+random variables where the function is
+ 
+
+ align:start position:0%
+random variables where the function is
+defined to be the product function so to
+
+ align:start position:0%
+defined to be the product function so to
+ 
+
+ align:start position:0%
+defined to be the product function so to
+calculate this expected value you can
+
+ align:start position:0%
+calculate this expected value you can
+ 
+
+ align:start position:0%
+calculate this expected value you can
+use the expected value rule and we are
+
+ align:start position:0%
+use the expected value rule and we are
+ 
+
+ align:start position:0%
+use the expected value rule and we are
+going to get the sum over all X the sum
+
+ align:start position:0%
+going to get the sum over all X the sum
+ 
+
+ align:start position:0%
+going to get the sum over all X the sum
+over all Y of G of X Y but in this case
+
+ align:start position:0%
+over all Y of G of X Y but in this case
+ 
+
+ align:start position:0%
+over all Y of G of X Y but in this case
+G of XY is x times y and then we weigh
+
+ align:start position:0%
+G of XY is x times y and then we weigh
+ 
+
+ align:start position:0%
+G of XY is x times y and then we weigh
+all those values according to the
+
+ align:start position:0%
+all those values according to the
+ 
+
+ align:start position:0%
+all those values according to the
+probabilities as given by the joint PMF
+
+ align:start position:0%
+probabilities as given by the joint PMF
+ 
+
+ align:start position:0%
+probabilities as given by the joint PMF
+now using independence this sum can be
+
+ align:start position:0%
+now using independence this sum can be
+ 
+
+ align:start position:0%
+now using independence this sum can be
+changed into the following form the
+
+ align:start position:0%
+changed into the following form the
+ 
+
+ align:start position:0%
+changed into the following form the
+joint PMF is the product of the marginal
+
+ align:start position:0%
+joint PMF is the product of the marginal
+ 
+
+ align:start position:0%
+joint PMF is the product of the marginal
+pmfs and now when we look at the inner
+
+ align:start position:0%
+pmfs and now when we look at the inner
+ 
+
+ align:start position:0%
+pmfs and now when we look at the inner
+sum over all values of Y we can take
+
+ align:start position:0%
+sum over all values of Y we can take
+ 
+
+ align:start position:0%
+sum over all values of Y we can take
+outside the summation those terms
+
+ align:start position:0%
+outside the summation those terms
+ 
+
+ align:start position:0%
+outside the summation those terms
+do not depend on why and so this term
+
+ align:start position:0%
+do not depend on why and so this term
+ 
+
+ align:start position:0%
+do not depend on why and so this term
+and that term and this is going to yield
+
+ align:start position:0%
+and that term and this is going to yield
+ 
+
+ align:start position:0%
+and that term and this is going to yield
+a summation over X of x times the
+
+ align:start position:0%
+a summation over X of x times the
+ 
+
+ align:start position:0%
+a summation over X of x times the
+marginal PMF of X and then the summation
+
+ align:start position:0%
+marginal PMF of X and then the summation
+ 
+
+ align:start position:0%
+marginal PMF of X and then the summation
+over all y of Y times the marginal PMF
+
+ align:start position:0%
+over all y of Y times the marginal PMF
+ 
+
+ align:start position:0%
+over all y of Y times the marginal PMF
+of Y but now we recognize that here we
+
+ align:start position:0%
+of Y but now we recognize that here we
+ 
+
+ align:start position:0%
+of Y but now we recognize that here we
+have just the expected value of y and
+
+ align:start position:0%
+have just the expected value of y and
+ 
+
+ align:start position:0%
+have just the expected value of y and
+then on we will be left with another
+
+ align:start position:0%
+then on we will be left with another
+ 
+
+ align:start position:0%
+then on we will be left with another
+expression which is the expected value
+
+ align:start position:0%
+expression which is the expected value
+ 
+
+ align:start position:0%
+expression which is the expected value
+of x and this completes the argument now
+
+ align:start position:0%
+of x and this completes the argument now
+ 
+
+ align:start position:0%
+of x and this completes the argument now
+consider a function of x and another
+
+ align:start position:0%
+consider a function of x and another
+ 
+
+ align:start position:0%
+consider a function of x and another
+function of y x and y are independent
+
+ align:start position:0%
+function of y x and y are independent
+ 
+
+ align:start position:0%
+function of y x and y are independent
+intuitively the value of x does not give
+
+ align:start position:0%
+intuitively the value of x does not give
+ 
+
+ align:start position:0%
+intuitively the value of x does not give
+you any new information about Y so the
+
+ align:start position:0%
+you any new information about Y so the
+ 
+
+ align:start position:0%
+you any new information about Y so the
+value of G of X does not give you any
+
+ align:start position:0%
+value of G of X does not give you any
+ 
+
+ align:start position:0%
+value of G of X does not give you any
+new information about H of Y so on the
+
+ align:start position:0%
+new information about H of Y so on the
+ 
+
+ align:start position:0%
+new information about H of Y so on the
+basis of this intuitive argument the
+
+ align:start position:0%
+basis of this intuitive argument the
+ 
+
+ align:start position:0%
+basis of this intuitive argument the
+functions G of X and H of Y are also
+
+ align:start position:0%
+functions G of X and H of Y are also
+ 
+
+ align:start position:0%
+functions G of X and H of Y are also
+independent of each other therefore we
+
+ align:start position:0%
+independent of each other therefore we
+ 
+
+ align:start position:0%
+independent of each other therefore we
+can apply the fact that we have already
+
+ align:start position:0%
+can apply the fact that we have already
+ 
+
+ align:start position:0%
+can apply the fact that we have already
+proved but with G of X in the place of X
+
+ align:start position:0%
+proved but with G of X in the place of X
+ 
+
+ align:start position:0%
+proved but with G of X in the place of X
+and H of Y in the place of Y and this
+
+ align:start position:0%
+and H of Y in the place of Y and this
+ 
+
+ align:start position:0%
+and H of Y in the place of Y and this
+gives us this more general fact that the
+
+ align:start position:0%
+gives us this more general fact that the
+ 
+
+ align:start position:0%
+gives us this more general fact that the
+expected value of the product of two
+
+ align:start position:0%
+expected value of the product of two
+ 
+
+ align:start position:0%
+expected value of the product of two
+functions of independent random
+
+ align:start position:0%
+functions of independent random
+ 
+
+ align:start position:0%
+functions of independent random
+variables is equal to the product of the
+
+ align:start position:0%
+variables is equal to the product of the
+ 
+
+ align:start position:0%
+variables is equal to the product of the
+expectations of these functions we could
+
+ align:start position:0%
+expectations of these functions we could
+ 
+
+ align:start position:0%
+expectations of these functions we could
+also prove this property directly
+
+ align:start position:0%
+also prove this property directly
+ 
+
+ align:start position:0%
+also prove this property directly
+without relying on the intuitive
+
+ align:start position:0%
+without relying on the intuitive
+ 
+
+ align:start position:0%
+without relying on the intuitive
+argument we could just follow the same
+
+ align:start position:0%
+argument we could just follow the same
+ 
+
+ align:start position:0%
+argument we could just follow the same
+steps as in this derivation wherever
+
+ align:start position:0%
+steps as in this derivation wherever
+ 
+
+ align:start position:0%
+steps as in this derivation wherever
+there's an X we would write G of X and
+
+ align:start position:0%
+there's an X we would write G of X and
+ 
+
+ align:start position:0%
+there's an X we would write G of X and
+wherever there is a Y we would write H
+
+ align:start position:0%
+wherever there is a Y we would write H
+ 
+
+ align:start position:0%
+wherever there is a Y we would write H
+of Y and the same algebra would go
+
+ align:start position:0%
+of Y and the same algebra would go
+ 
+
+ align:start position:0%
+of Y and the same algebra would go
+through and we would end up with the
+
+ align:start position:0%
+through and we would end up with the
+ 
+
+ align:start position:0%
+through and we would end up with the
+expected value of G of x times the
+
+ align:start position:0%
+expected value of G of x times the
+ 
+
+ align:start position:0%
+expected value of G of x times the
+expected value of H of Y
\ No newline at end of file
diff --git a/RcAkiv8Bkpo.txt b/RcAkiv8Bkpo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4dc5ecd5023731cf24dfd2f72192ebc4008d2f73
--- /dev/null
+++ b/RcAkiv8Bkpo.txt
@@ -0,0 +1,99 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how does diversity strengthen science
+
+ align:start position:0%
+how does diversity strengthen science
+ 
+
+ align:start position:0%
+how does diversity strengthen science
+can freezing your credit card help you
+
+ align:start position:0%
+can freezing your credit card help you
+ 
+
+ align:start position:0%
+can freezing your credit card help you
+spend less what is a seed librarian and
+
+ align:start position:0%
+spend less what is a seed librarian and
+ 
+
+ align:start position:0%
+spend less what is a seed librarian and
+what can they teach us is nuclear
+
+ align:start position:0%
+what can they teach us is nuclear
+ 
+
+ align:start position:0%
+what can they teach us is nuclear
+warfare still the greatest threat to
+
+ align:start position:0%
+warfare still the greatest threat to
+ 
+
+ align:start position:0%
+warfare still the greatest threat to
+life on Earth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+welcome to chalk radio season four tune
+
+ align:start position:0%
+welcome to chalk radio season four tune
+ 
+
+ align:start position:0%
+welcome to chalk radio season four tune
+in soon to hear candid personal and
+
+ align:start position:0%
+in soon to hear candid personal and
+ 
+
+ align:start position:0%
+in soon to hear candid personal and
+eye-opening conversations with some of
+
+ align:start position:0%
+eye-opening conversations with some of
+ 
+
+ align:start position:0%
+eye-opening conversations with some of
+mit's most passionate Educators
+
+ align:start position:0%
+mit's most passionate Educators
+ 
+
+ align:start position:0%
+mit's most passionate Educators
+subscribe to our channel to never miss
+
+ align:start position:0%
+subscribe to our channel to never miss
+ 
+
+ align:start position:0%
+subscribe to our channel to never miss
+an episode
\ No newline at end of file
diff --git a/RwDQWPhNZ8U.txt b/RwDQWPhNZ8U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..14428fb351aefaa37d52003a279172fd50199904
--- /dev/null
+++ b/RwDQWPhNZ8U.txt
@@ -0,0 +1,6062 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: When did
+you arrive at MIT?
+
+ROSALIND WILLIAMS: I was
+a post-doc in 1980.
+
+PROFESSOR: Yeah, I just
+remember that.
+
+PROFESSOR: So Ros is also a
+historian of technology.
+
+But she practices the craft
+a little different
+
+than David and I do.
+
+She focuses on the cultural
+side of things and is an
+
+expert in literature and what
+writers have said about
+
+technological change
+and has written a
+
+lot about those subjects.
+
+But also, she served
+as the dean of
+
+undergraduate education.
+
+ROSALIND WILLIAMS: And
+student affairs.
+
+I did both jobs.
+
+PROFESSOR: I didn't know
+if I had the title.
+
+There was one time when you
+didn't have two deans.
+
+You didn't a dean for
+residential life.
+
+You had them combined
+in one office.
+
+And she got stuck with that
+job, which is as you might
+
+imagine, is a lot of work.
+
+And so Ross did that
+for at least six--
+
+ROSALIND WILLIAMS: Five years.
+
+PROFESSOR: Five years.
+
+So that's been a big
+item on her agenda.
+
+And now, she's back
+in the department.
+
+And today, she's going to talk
+about chemical engineering
+
+basically, in the early
+20th century.
+
+And this is extremely
+interesting.
+
+She gave a lecture about
+it last year.
+
+Because her grandfather
+was Warren K. Lewis.
+
+If any of are familiar with the
+"Lewis Report" of the late
+
+1940s, that's the report that in
+effect that established the
+
+School of Humanities and
+Social Sciences.
+
+But here's a chemical engineer
+who is a very much involved
+
+and looking at all aspects of
+life at MIT and coming up with
+
+this report.
+
+And as they say, the
+rest is history.
+
+So Ros has a long lineage here,
+that your grandfather
+
+goes back to the early
+1900s, I would say.
+
+Didn't he get here--
+
+ROSALIND WILLIAMS: He
+was class of '05.
+
+PROFESSOR: Yeah.
+
+So she's going to talk
+about this area.
+
+And she's brought some very
+interesting materials I'm
+
+anxious to look at.
+
+ROSALIND WILLIAMS: So I wanted
+to do something new this time.
+
+And that's why in the
+last hour, I went
+
+though my Lewis box.
+
+Archives are just
+boxes of stuff.
+
+This is from my attic.
+
+And the library's is just
+not that different.
+
+And I pulled out some little
+treasures, at least I think
+
+they're treasures, that will
+give you a flavor of what
+
+archives are like and when
+you're doing history, what you
+
+learn from archives that you
+don't learn online, can't
+
+learn online.
+
+I may overstate that.
+
+I may take that back.
+
+But I'll stand by it for
+a talking point.
+
+So I'm going to start with
+giving you an overview of
+
+intertwined biography of Warren
+K. Lewis and of the
+
+world here in the Boston area,
+Cambridge, and MIT
+
+specifically, as they
+intertwined.
+
+And in discussing afterwards, we
+can talk about him, we can
+
+talk about chemical
+engineering.
+
+We can also talk about
+deanly things.
+
+If you're interested in student
+life history, I've
+
+done a little boning up on that
+for a documentary that
+
+was being shot last week
+about the evolution of
+
+student life at MIT.
+
+So I sort of refreshed my memory
+about some points on
+
+that topic.
+
+So we talk about anything
+you want to talk about.
+
+But first of all, let me give
+you some what my grandfather
+
+used to say, you want to put
+the fodder down where the
+
+calves can get at it.
+
+So I'm going to put
+out some fodder.
+
+Fodder is food, so cow food.
+
+They say you've got
+to put it down.
+
+So I'm putting it down.
+
+And we'll chew on this
+together and then see
+
+where it takes us.
+
+So this is this kind of
+biographical history of
+
+chemical engineering at MIT.
+
+I remember my grandfather
+sitting in the living room
+
+holding forth, as he was
+wont to do, in Newton,
+
+Massachusetts.
+
+This is where he lived with my
+grandmother and mother and
+
+three other siblings.
+
+He was a boarder in
+the household
+
+and married the daughter.
+
+And this is a little part
+history right there.
+
+Most MIT students, there
+weren't residences.
+
+So you boarded with families or
+you were in a fraternity.
+
+So boarding was very common.
+
+Let me just me just mention
+something about his family.
+
+You see his dates.
+
+His father was born in 1845,
+in Laurel, Delaware.
+
+And his father, my grandfather's
+grandfather, had
+
+been born in the kind of,
+well, mid to late 1700s.
+
+He had three wives.
+
+My grandfather's father
+was the last child
+
+of the third wife.
+
+So there's a huge gap in the
+half-brothers, between Henry
+
+Clay Lewis, Henry Clay Lewis,
+that's the name of my
+
+grandfather's father, and the
+first wife's, first child.
+
+Many of these children died.
+
+But this is just a part of
+history, the fact that if I go
+
+from my grandfather, to his
+father, to his father, I'm
+
+back to the Revolutionary War.
+
+Because his grandfather had a
+brother who died in a prison
+
+ship, moored in the Hudson
+River during the
+
+Revolutionary War.
+
+So it's just amazing to me that
+you just take a few steps
+
+and you're back in
+time, like that.
+
+This is Delaware.
+
+Delaware was a slave state.
+
+It was a slave-owning family.
+
+Also an abolitionist family,
+which is a strange
+
+combination.
+
+But it's one of those, it's a
+nice idea, but not until I die
+
+will I free my slaves, family.
+
+And that's what happened.
+
+But his father was one of the
+two votes for Abraham Lincoln
+
+in his county in Delaware
+in 1860.
+
+And his father--
+
+God, these dates don't
+seem right.
+
+Because if his father
+is born in 18--
+
+OK.
+
+It was his grandfather, his last
+vote was for Abe Lincoln,
+
+that's it, in Laurel,
+Delaware.
+
+If you look at the history of
+slavery in Laurel, what's
+
+fascinating is that next door
+was Maryland, where slaves
+
+could be traded, but
+not in Delaware,
+
+after a certain date.
+
+You may know that.
+
+But in Delaware, you could
+hold slaves, but you
+
+couldn't sell them.
+
+So there's a huge kidnapping
+ring, where people from
+
+Maryland would go just over the
+border to Laurel, kidnap
+
+either free blacks or slaves,
+take them back to Maryland,
+
+where they could be sold
+for a huge profit.
+
+Because at that time, they could
+still be sold to other
+
+parts of the United States.
+
+So Delaware, Laurel was the
+site of the Patty Cannon
+
+kidnapping ring, which is
+a fascinating story.
+
+But it's not the story
+I'm here to tell.
+
+But it does give context.
+
+This is a farm boy.
+
+Kenny was raised on the farm
+in Laurel, Delaware.
+
+Expecting to say on the farm,
+and his life, he got hijacked
+
+by the 20th century.
+
+These are just some more
+pictures holding forth.
+
+That's a very familiar
+pose, very familiar.
+
+PROFESSOR: You know it well.
+
+ROSALIND WILLIAMS: Yeah.
+
+I mean as a granddaughter,
+you knew this guy.
+
+Students were terrified of him
+because he'd get you up here.
+
+And you'd start doing something
+on the board.
+
+And you wouldn't know
+what you were doing
+
+and he would pounce.
+
+But as a granddaughter, it was
+just a very affectionate
+
+relationship.
+
+I was aware how much he
+terrified other people.
+
+But that was not my relationship
+with him.
+
+That's the farmhouse, still
+in a Laurel, Delaware.
+
+It used to be a bed and
+breakfast not that long ago.
+
+I don't think it's in
+business anymore.
+
+That's my brother.
+
+That's more Warren K. Lewis,
+Jr., my uncle, and my
+
+grandfather.
+
+This is in 1952.
+
+He has just sold the farm.
+
+Heart breaking, because it had
+been in the family back to the
+
+late 1700s.
+
+But a part of the farm was cut
+through by a road, the dual,
+
+they call it there,
+a dual highway.
+
+Route 14 cut through a corner of
+the farm and he realized it
+
+was never going to be a
+working farm again.
+
+And the irony is of course that
+part of the reason for
+
+putting in that highway is that
+DuPont had established
+
+big factories in northern
+Delaware.
+
+And there's more commuter
+traffic from south to north.
+
+So chemical engineering,
+in a sense,
+
+destroyed the family farm.
+
+And I say there's
+a sort of irony.
+
+There's quite a bit
+of irony there.
+
+Not to mention the fact that the
+whole automobile age was
+
+in part made possible through
+new methods of refining
+
+petroleum, using catalytic
+cracking, that my grandfather
+
+directly worked on.
+
+This is not the best-- but this
+is the Eastern Shore,
+
+this peninsula.
+
+The Chesapeake Bay is here.
+
+So Baltimore is up
+around here.
+
+Washington is kind of off
+the map, over here.
+
+And Philadelphia is
+to the north.
+
+But this is the Eastern Shore.
+
+And it's Virginia down here.
+
+You can't see the map--
+
+the split division.
+
+So last time I went, I go to
+the airport in Baltimore, I
+
+drive over the Chesapeake Bay
+Bridge, I go down to roads,
+
+about right in the middle.
+
+And that takes me two hours.
+
+So you go from one end to the
+other in a couple hours.
+
+With the dual, you
+go fast, yeah.
+
+So there is a Maryland
+over here.
+
+Oh, you can see the
+dotted line, OK.
+
+So this is Maryland over here.
+
+This is where like Dick Cheney
+lives now, in Easton.
+
+It's very high, upper crust.
+
+And this is Delaware,
+which is much more
+
+farming, much more rural.
+
+And then Virginia down here.
+
+It's pretty rustic.
+
+The Chincoteague ponies,
+Chincoteague is one of these
+
+islands off of here.
+
+So this is a garden spot in the
+18th and 19th centuries.
+
+It is the truck garden area
+for the Philadelphia and
+
+Baltimore markets, raising
+mainly corn, fruits,
+
+vegetables, peaches, tomatoes,
+live stock.
+
+It's mixed farming.
+
+And I'll tell you some more
+about that as we go on.
+
+But the reason I have this map--
+this is from Bob Post--
+
+the railroad comes to
+Laurel in 1859.
+
+And that opens up the whole
+area to commercial
+
+farming much more.
+
+I mean it had always been
+such, but even more.
+
+Now, my grandfather's
+grandfather was a sea captain.
+
+Farming was his--
+
+that's where the wife
+and kids stayed.
+
+But he made his money in the
+trade, starting from the
+
+Chesapeake, doing a lot of
+trade of the Caribbean.
+
+So that's where his
+money came from.
+
+I mean he was a large,
+established farmer and the
+
+state legislator.
+
+So he was a politician.
+
+But he was a well-off person
+for Delaware, but still
+
+basically a sea captain
+and a farmer.
+
+So the railroad comes.
+
+And this is sort of getting
+ahead of the story.
+
+But my grandfather born in
+1882, he goes through the
+
+three-year high school
+in Laurel, Delaware.
+
+And learns everything you learn
+there, because there's
+
+one teacher for all grades,
+in one classroom.
+
+And his parents want him to
+get a better education.
+
+He's an only child.
+
+He's obviously going to
+inherit the farm.
+
+So they want him to go to a
+better high school than the
+
+Laurel one.
+
+So his cousin, she's actually
+a cousin I guess.
+
+He had an older female cousin
+named Mary Witherby, who had
+
+left Laurel to teach school,
+like her father, and she was
+
+teaching school at the Lasell
+Female seminary, which still
+
+exists around here.
+
+Do any of you--
+
+you know what I'm
+talking about.
+
+PROFESSOR: Oh, sure.
+
+ROSALIND WILLIAMS: It's
+now Lasell College.
+
+It used to be junior college,
+now college.
+
+Yeah, and it's in West Newton,
+just a stone's
+
+throw from your place.
+
+So my grandfather was sent up
+by his parents to live in
+
+Newton, go to high school.
+
+Newton High was famous even
+then as a good school.
+
+He would board with
+the family.
+
+But he had his cousin in town.
+
+And she would look after him
+and make sure he didn't get
+
+into too much trouble.
+
+This house is a block away
+from where I live now.
+
+I go there all the time.
+
+So that's still there, one of
+the older houses in the
+
+neighborhood.
+
+So this is where he boarded.
+
+Now, I happen to have his diary
+from his first full
+
+winter at Hunnewell
+Avenue in Newton.
+
+And it starts January
+10, 1898 and it
+
+goes through the spring.
+
+So I'm a little mixed up about
+the timing, because I believe
+
+this is his second year I
+believe at Newton High.
+
+His first year he came up, he
+got an A in arithmetic, a D in
+
+drawing, and F's in
+everything else.
+
+So it was not a good high school
+he was coming from.
+
+And he really had to catch up.
+
+By this time, I think it's the
+second year, he's got his feet
+
+under him and he's
+doing better.
+
+So he's boarding in
+the winter of '98.
+
+And I just want to read a few
+little details that will give
+
+you a sense of what life was
+like, daily life was like for
+
+him at that time.
+
+This is the Second Industrial
+Revolution, is what we call it
+
+from up here.
+
+But down here, this
+is what it's like.
+
+After school, this is high
+school, he says, this is
+
+January 12, I went up to Lasell
+and read Cicero with
+
+cousin Mary.
+
+Who's Cicero?
+
+What does this tell you?
+
+You read Cicero in Latin.
+
+You start with doing Cicero.
+
+You wind up with Cicero
+and Virgil.
+
+So he's reading his Latin
+with his cousin.
+
+And then she gave me a supper
+of canned chicken, cocoa,
+
+bread, butter, crackers,
+and peanut butter.
+
+I had a fine time.
+
+OK, canned chicken?
+
+I mean I don't have
+to rub this in.
+
+You can figure this out.
+
+This is not off the farm.
+
+Canned chicken, cocoa, you know
+we're dealing with the
+
+Caribbean at least, if that's
+not the East Indies.
+
+Bread, butter, all
+right, crackers--
+
+packaged food-- and
+peanut butter.
+
+OK.
+
+So he mentions that-- at home,
+he got a letter from home.
+
+And the letter from home says
+four factories were going up
+
+in Laurel and vicinity
+for canning.
+
+He, my father--
+
+this is my grandfather's father,
+he is going to put out
+
+10 acres of tomatoes.
+
+He has only four cows now.
+
+So there's a lot of agricultural
+history there.
+
+There's a new canning factory,
+more tomatoes, fewer cows.
+
+So just to jump ahead, my
+grandfather would say that he
+
+paid for his MIT tuition when he
+got to MIT, with tomatoes,
+
+sold to a cannery at $4 a ton.
+
+PROFESSOR: Jesus, $4 a ton.
+
+ROSALIND WILLIAMS: $4 a ton.
+
+Now, he had the bright
+idea, during his
+
+college years, of recycling.
+
+That is, using the tomato skins,
+which are removed in
+
+the canning process, or they
+tried to remove them, using
+
+those skins to feed to
+the cows as fodder.
+
+And they tried it.
+
+The cows ate them.
+
+But then they gave pink milk.
+
+So it didn't work.
+
+OK, just a few more of
+these from his diary.
+
+We're still back in
+January 1898.
+
+Today, as I was walking home
+from school, cousin Mary in
+
+the electrics--
+
+so what are the electrics?
+
+PROFESSOR: Trolleys.
+
+ROSALIND WILLIAMS: Trolleys.
+
+OK, the street car suburbs--
+
+this is a little digression.
+
+But this is showing how the
+electric trolley system was
+
+being extended at the time.
+
+This is the Sam Best Warner's
+classic study.
+
+And the trolley, which I
+remember from my childhood,
+
+near Hunewell Avenue, where he
+lived, is just a block away.
+
+You can just walk.
+
+In fact, now it's
+a bus system.
+
+But it's the same route.
+
+And you can get on where
+we live and go to
+
+Fenway Park in one stop.
+
+PROFESSOR: No wonder you live
+in that neighborhood.
+
+ROSALIND WILLIAMS: Of
+course, you got it.
+
+Then we went into Boston.
+
+Cousin Mary in the electrics,
+saw me, got out and walked
+
+home with me.
+
+Then we went into Boston.
+
+Now, this would have been on the
+train track, which is the
+
+other side of the hill
+that he's looking on.
+
+Went into Boston.
+
+And she bought two tin basins,
+a pie pan, a strainer, and a
+
+dozen knives and forks.
+
+She carried it in a mug strainer
+belonging to the
+
+coffee pot, to fit the strainer
+she brought to it.
+
+So she's buying a piece
+for her coffee pot.
+
+She's buying all this
+stuff, taking the
+
+electrics into Boston.
+
+So this tells you a lot
+about technological
+
+systems of the day.
+
+But I think my favorite
+entry from this
+
+diary, this is in February.
+
+He says, I went downtown.
+
+This would be Newton Corner.
+
+I went downtown in the evening
+and rode, R-O-D-E, underlined.
+
+I asked a man passing, for
+a ride, and he consented.
+
+It was the first time,
+underlined, I've ridden,
+
+underlined, on or behind a horse
+since last September,
+
+and I a farmer's boy.
+
+So there's cars, there's
+trolleys, there's trains.
+
+But he wants to ride the horse,
+because that's what
+
+farmers; boys did.
+
+There's a lot.
+
+I could go on and on
+about what you find
+
+out from this diary.
+
+There's a lot of reading,
+Cicero, Shakespeare.
+
+There's a lot of magazines.
+
+He's reading magazines a lot.
+
+He's going to church.
+
+There are church plays.
+
+There are glee club performances
+at Lasell.
+
+He goes into Boston for lectures
+at the temple,
+
+Fremont Temple.
+
+He goes to the Museum of Fine
+Arts, still with us, discusses
+
+modern illustrators who
+are exhibited there.
+
+Then cousin Mary gives
+him some pictures.
+
+But I mean it is an information
+
+age, in its own way.
+
+It's just a different
+kind of media.
+
+But he's very connected.
+
+So, for example, on January
+20, he says he goes into
+
+Boston to hear a lecture
+on imperialism
+
+by Dr. Lyman Abbott.
+
+Now why in 1898, is he going to
+a lecture on imperialism?
+
+What's going on?
+
+What's the news?
+
+Anybody know?
+
+AUDIENCE: Spanish-American
+War.
+
+ROSALIND WILLIAMS: OK?
+
+Which--
+
+PROFESSOR: He said it.
+
+ROSALIND WILLIAMS:
+Spanish-American War, go to
+
+the head of the class, yeah.
+
+And it's interesting.
+
+He says the lecture was a fine
+one in favor of staying to
+
+help them, the Filipinos in
+this case, learn to govern
+
+themselves.
+
+And then he goes to another
+lecture the next week, same
+
+topic, another speaker, who
+also make good points.
+
+But cousin Mary said
+some bad ones.
+
+He attacked, the second speaker,
+Dr. Abbott, the first
+
+speaker, saying he had made some
+misstatements concerning
+
+the arguments on Californian
+annexation and made McKinley
+
+out as having imperial power.
+
+So there's debate going on.
+
+And then on February 7, we
+received our first news
+
+yesterday of the Battle
+of Manila.
+
+Reports of dead and wounded,
+the gunboats
+
+did a fearful execution.
+
+Then there's Washington's
+birthday soon after, the
+
+church bells ring all day.
+
+And my grandfather writes, these
+are signs to me that it
+
+is the anniversary of the
+birth of the greatest
+
+American, underlined,
+ever borne.
+
+OK, anyway.
+
+PROFESSOR: It wasn't
+Abe Lincoln.
+
+ROSALIND WILLIAMS: Um, true.
+
+PROFESSOR: It was GW.
+
+ROSALIND WILLIAMS: It was GW.
+
+How about that.
+
+AUDIENCE: [INAUDIBLE].
+
+ROSALIND WILLIAMS: Yeah.
+
+PROFESSOR: Well, her--
+
+yeah, but her--
+
+it would be your great
+grandfather's--
+
+whose name is Henry Clay.
+
+Now, Henry Clay--
+
+ROSALIND WILLIAMS:
+That's another--
+
+yeah.
+
+PROFESSOR: But Henry Clay
+was Abraham Lincoln's
+
+great idol in a way.
+
+ROSALIND WILLIAMS: I mean the
+story of this family and
+
+slavery is just fascinating.
+
+PROFESSOR: Yeah, it's very
+interesting, very interesting.
+
+ROSALIND WILLIAMS: Well, I just
+showed you this paper of
+
+my grandmother's, my
+grandfather's wife, on the
+
+Negro problem in 1921.
+
+Because my grandfather, he
+wanted to go back to the farm
+
+and improve race relations by
+starting that farm up again in
+
+the right way.
+
+And that never happened.
+
+But that was the idea.
+
+OK, instead what happens?
+
+In the spring, he asked two
+teachers at Newton High what
+
+they thought would be best for
+him to do about college?
+
+They will think it
+over, he writes.
+
+But the former advised either
+Amherst Agricultural--
+
+what's that?
+
+PROFESSOR: New Mass.
+
+ROSALIND WILLIAMS: Yeah, it's
+the University of Amherst now,
+
+the Ag School-- other Amherst
+agriculture, or as even
+
+better, tech.
+
+One of them mentioned
+Cornell, but tech.
+
+Here we are.
+
+So he thinks about it.
+
+By the way, this is just a
+picture of downtown Boston,
+
+when they take the
+train in there.
+
+I was there Friday, meeting
+my son and his girlfriend.
+
+It's not--
+
+they're not people
+like I know.
+
+And I was saying to my son, oh
+gee, my grandparent's would be
+
+so distressed to see this.
+
+And he said-- he has a place
+in Fort Point, he said.
+
+But that's up and coming.
+
+That needs to be [INAUDIBLE].
+
+And now, it's happening.
+
+But let me just mention, I mean
+these are quick reminders
+
+that the occupation of
+engineering was growing very
+
+quickly at the time.
+
+And that the people who went
+into engineering--
+
+my grandfather is very typical,
+in being off the farm
+
+and not particularly
+well educated.
+
+This is the way for young men,
+almost always young men, to
+
+have a professional or
+quasi-professional career,
+
+without having to consider
+postgraduate study, like law
+
+or divinity or medicine
+required.
+
+So here's Boston Tech.
+
+You must have seen this picture
+
+somewhat, in this class.
+
+Here's Trinity Church
+in Copley Square.
+
+This is Boston Tech?
+
+PROFESSOR: It's Boston Tech.
+
+ROSALIND WILLIAMS: Yeah.
+
+And I've seen other photos where
+I can't really place it.
+
+So I would love to see somebody
+do a sort of up to
+
+date GPS showing exactly--
+
+AUDIENCE: So that's
+still there.
+
+ROSALIND WILLIAMS: That's
+there, yeah.
+
+AUDIENCE: And then across the
+street from that building is
+
+Brooks Brothers, on Berkeley
+Street, across from
+
+[INAUDIBLE].
+
+ROSALIND WILLIAMS: This is all
+one big building there.
+
+AUDIENCE: Yeah, that's
+the [INAUDIBLE].
+
+PROFESSOR: There's actually a
+plaque on the front of that
+
+office building
+
+ROSALIND WILLIAMS: But there was
+another building, not the
+
+Rogers Building, but
+another building,
+
+like off to the side.
+
+PROFESSOR: Yeah.
+
+It would be in that direction.
+
+AUDIENCE: There's a
+bunch of stuff.
+
+Mark Jarzombek showed us a map,
+and sort of to the right
+
+of where the photograph is.
+
+There's train tracks
+and stuff there.
+
+ROSALIND WILLIAMS: Now, the
+steep steps, was that on this
+
+building, on the Rogers
+Building, or the second one?
+
+PROFESSOR: I think
+it's right there.
+
+ROSALIND WILLIAMS: Oh, there.
+
+PROFESSOR: Right there.
+
+ROSALIND WILLIAMS: Oh, OK.
+
+OK.
+
+Because again, my grandfather
+had a story about a kind of a
+
+riot involving Harvard and MIT
+students and a fire and he was
+
+on the witness stand.
+
+And it had to do
+with the steps.
+
+Some things don't change.
+
+AUDIENCE: Mark talked
+about the difference
+
+between those two--
+
+ROSALIND WILLIAMS: These
+two buildings.
+
+AUDIENCE: --buildings.
+
+But they're separated by
+a couple of decades.
+
+But closer is a custom-built
+laboratory, where you can see
+
+the fumes of the vents coming
+at the top there.
+
+ROSALIND WILLIAMS: Oh, that
+has happened here.
+
+That's fascinating.
+
+So in the subway spot at
+Kimball, it says the second
+
+building MIT build was
+a gym, a gymnasium?
+
+Does anybody--
+
+I just read it there the
+other day, thinking
+
+that's the first I knew.
+
+So Warren K. Lewis enters MIT
+in 1901, planning to study
+
+chemical engineer-- excuse me,
+mechanical engineering, still
+
+the dominant engineering, kind
+of the default mode.
+
+But he had a friend, this friend
+that he was boarding
+
+with in Newton, whose sister he
+eventually married, urged
+
+him to try chemical
+engineering.
+
+It seemed more interesting
+and so on and so forth.
+
+So as you know from your
+reading, something like
+
+industrial chemistry
+had begun.
+
+Actually, it was 1888, I think
+was the first offerings in
+
+industrial chemistry.
+
+And by 1893, there was a lab.
+
+This is sort of like the
+first start of chemical
+
+engineering at MIT.
+
+But then because of deaths and
+
+departures, it sort of declined.
+
+But just when my grandfather's
+was entering, actually in
+
+1903, this is when Walker
+comes back.
+
+And Noyes had been there
+for a couple years.
+
+So it's sort of like a
+false start early on.
+
+And then it kind of
+restarted around
+
+the turn of the century.
+
+And this is something that he
+wrote many years later, that I
+
+think captures the overall
+feeling of the time.
+
+Lewis wrote, the stimulus of
+these concepts, and he's
+
+referring to unit operations
+and these related concepts,
+
+the stimulus of these concepts
+made work in chemical
+
+engineering at the Institute
+from 1902 to the outbreak of
+
+World War I an inspiration for
+both staff and student, which
+
+it is impossible to describe.
+
+So these are happening years.
+
+I mean the tension between
+Noyes and Walker is a
+
+productive tension.
+
+They had each other
+to play off of.
+
+And they certainly did.
+
+By the way, you know
+Walker, that's not
+
+Walker, Memorial Walker.
+
+Walker Memorial is named after
+Francis Amasa Walker, one of
+
+the early presidents.
+
+Have I got it right?
+
+PROFESSOR: Yup.
+
+ROSALIND WILLIAMS: And we're
+talking about William Walker.
+
+It's no relation.
+
+So it's important to
+those straight.
+
+So you have these two very
+strong personalities.
+
+This is Noyes, trained in
+Germany, a physical chemist.
+
+And really brought in serious
+chemistry to the program,
+
+beginning in 1902.
+
+And then you have William H.
+Walker, who had also been
+
+educated in Germany, Penn State
+and Gottingen, both.
+
+And was teaching analytical
+chemistry, the partner of A.D.
+
+Little, which was originally
+Little and Walker.
+
+So he was entrusted with
+Course 10 in 1903.
+
+And was entrusted with building
+it up into a chemical
+
+engineering curriculum.
+
+Now this, you can't read.
+
+But I will read to you, because
+this is Walker's
+
+statement written years later.
+
+This was after he
+had left MIT.
+
+This is either from the late
+'20s or early '30s--
+
+well, he died in the '30s.
+
+So this is his statement of
+what he was trying to do.
+
+It's a fascinating statement.
+
+So I'm going to read you
+what Walker wrote.
+
+What an industry needed was not
+a man who had been taught
+
+what the industry already knew,
+but rather a man who was
+
+trained to do what the
+industry had not
+
+been able to do.
+
+The ideal man for the industries
+was one who had
+
+been given a sound knowledge
+of chemistry and physics.
+
+And then as a part of the
+curriculum, had been given
+
+systematic experience in the
+application of this knowledge
+
+to the solution of industrial
+problems.
+
+That he should not be a
+specialist, but a solver of
+
+problems, any kind of problem
+that industry might present.
+
+And then he goes on to say, this
+idea met opposition, both
+
+from established courses
+of chemical
+
+instruction and from industry.
+
+And the industry thought
+it was too theoretical.
+
+But the scientists thought it
+was too industry oriented.
+
+So Walker is on this very nice
+edge between not trying to
+
+give into one or the other.
+
+And then he goes on and says--
+
+this at the top of the second
+paragraph, I love this--
+
+to prove the soundness
+of this idea, I
+
+returned to MIT in 1903.
+
+And after a hot fight with
+both the chemical and the
+
+engineering faculties, I
+reconstructed Course X as a
+
+general educational course
+without options.
+
+And without options, that turns
+out to be important.
+
+So this is a feisty guy.
+
+And I'm sure that's one reason
+he and my grandfather got
+
+along very well.
+
+They were both feisty people,
+very self assured.
+
+But my grandfather always would
+say, it is Walker who
+
+invented chemical engineering
+in this country.
+
+He did not claim that
+for himself at all.
+
+But again, my grandfather
+studied.
+
+With Noyes.
+
+You know, I was just reminding
+you, this is particularly in
+
+Servos's article.
+
+My grandfather studied with
+Noyes, took P-Chem from him,
+
+and graduating in the
+class of '05.
+
+My grandfather's is this kind of
+this grim-- he looks-- kind
+
+of a grim looking guy.
+
+And you'll see another
+picture.
+
+I'll pass it around.
+
+In the spring of his senior
+year, he expected to go back
+
+to the farm, as much as you and
+I expect the Sun to come
+
+up tomorrow.
+
+However, he got a job in the
+lab, I think with Noyes.
+
+And then that led to somebody,
+I don't know whether it was
+
+Noyes or Walker, one of them
+suggested that he apply for a
+
+traveling fellowship which
+was being offered.
+
+And it was $1,000 stipend, which
+is that day and age was
+
+a lot of money.
+
+A traveling fellowship,
+he could go
+
+anywhere for a doctorate.
+
+And so he really was
+not interested.
+
+But one of them basically
+appealed to his competitive
+
+spirit and kind of said well, if
+you don't get it, somebody
+
+else is going to get it.
+
+And $1,000 sounded very nice.
+
+He applied, got it and was on
+his way to Breslau, in what is
+
+now Germany, it's kind of on the
+Polish-German border, for
+
+graduate school the next year.
+
+Later, he found he was in fact
+the only applicant that year.
+
+PROFESSOR: Well, it's
+interesting.
+
+Think about what the Harvard
+class of 1905, where they
+
+might have chosen to have
+their picture taken.
+
+ROSALIND WILLIAMS: Aah.
+
+AUDIENCE: I'm sure it was
+not in the laboratory.
+
+ROSALIND WILLIAMS: Yeah, yeah.
+
+I mean this is a good example,
+where it tells you so much.
+
+It does.
+
+Began with the names
+and faces.
+
+AUDIENCE: Books piled up
+in the front of them.
+
+ROSALIND WILLIAMS: Yeah.
+
+So--
+
+AUDIENCE: What's in the
+books on the front?
+
+ROSALIND WILLIAMS: Yeah.
+
+Oh yeah, that's great.
+
+So this is his dissertation in
+German, from Breslau, three
+
+years later.
+
+He wrote it in Florence, because
+he thought Florence
+
+was the most beautiful city in
+the world, and why not write
+
+your dissertation there?
+
+I recommend that highly,
+if any of you write
+
+dissertations.
+
+But this is Germany.
+
+And just keep that in mind when
+we get to World War II.
+
+PROFESSOR: Yeah, yeah.
+
+AUDIENCE: World War I.
+
+PROFESSOR: And he was
+sufficiently literate in
+
+German to be able to write
+a dissertation.
+
+ROSALIND WILLIAMS: Yeah.
+
+Yeah.
+
+Well, he never felt his
+German was that great.
+
+And in fact, back to Latin, a
+story he tells us taking the
+
+train to Italy, or maybe
+back from Italy.
+
+But in any case, he was seated
+next to somebody-- maybe they
+
+were like Polish or something.
+
+But German didn't work.
+
+The other person didn't
+know English.
+
+So they conversed in Latin.
+
+PROFESSOR: Is that right?
+
+ROSALIND WILLIAMS:
+You never know.
+
+PROFESSOR: It's fascinating.
+
+ROSALIND WILLIAMS: It
+may come in handy.
+
+So then he comes back to--
+
+well, he has a year working
+at a tannery in
+
+Manchester, New Hampshire.
+
+And as a result of that
+experience, he always said
+
+tanneries do not have
+to pollute.
+
+It's not necessary, if
+you run them right.
+
+And they don't have to smell
+either, that's the other thing
+
+you associate was a tannery.
+
+So he comes back.
+
+And you can see how chemical
+engineering around 1910,
+
+there's this kind of reversal
+of who was majoring in what.
+
+And this is before the war.
+
+Because when World War I comes,
+even before the US
+
+enters World War I, the Great
+War, in 1917, there's a
+
+tremendous demand for
+military equipment.
+
+And chemical engineering is
+connected with gas warfare,
+
+which was used right near the
+beginning of the war.
+
+It was in the spring of 1915
+that chlorine was first used
+
+on the battlefield
+as a poison gas.
+
+Chlorine is not the most
+effective, by any means.
+
+It dissipates pretty quickly.
+
+But the surprise factor was such
+that it really did work
+
+in the initial use.
+
+And it had a tremendous
+psychological effect in
+
+scaring people on both sides.
+
+So Walker, William Walker, was
+put in charge of the Edgewood
+
+Arsenal, once the US
+entered the war, to
+
+manufacture toxic gases.
+
+And my grandfather was put
+in charge of gas defense.
+
+So he worked on the masks.
+
+And there's all sorts of--
+
+I mean this is very specialized
+equipment.
+
+And to try to design equipment
+that made it possible to keep
+
+fighting and yet would protect
+the soldier from poison gas,
+
+not just the soldier but--
+
+do I have some of the--
+the animals too.
+
+In fact, there's a whole long
+story about the horses being
+
+affected by mustard gas,
+which is a vesicant.
+
+And it's a much nastier gas.
+
+And it would affect
+the animals too.
+
+So the one story that I need
+to tell you about my
+
+grandfather and gas defense,
+this made such an
+
+impression on me.
+
+We had this conversation
+was I was a teenager.
+
+Let's see, he said there was not
+a single Allied soldier--
+
+am I taking too much?
+
+PROFESSOR: No, no.
+
+ROSALIND WILLIAMS: It won't
+take much longer.
+
+There's not a single Allied
+soldier is World War I who
+
+died from poison gas when they
+had the gas mask and other
+
+equipment on.
+
+And I grandpa, you must been so
+proud because you designed
+
+something that was fail-safe.
+
+It worked every time.
+
+And he said no, it means
+I over designed.
+
+And what he meant was the
+cost of putting on a
+
+mask is quite high.
+
+It's makes it hard to breathe.
+
+And it does encumber you.
+
+So in designing the gas
+mask, you have to make
+
+it just on the edge.
+
+Because then, soldiers are more
+likely to put it on in
+
+the first place.
+
+So by over designing it, it
+meant that he was surmising
+
+that more people had died
+but not putting
+
+on the mask at all.
+
+Because it was such
+a pain to put on.
+
+And for an engineer to think
+that way about human life, it
+
+just really took me aback.
+
+And I thought, boy, that's
+responsibility.
+
+After he died in 1975, you clean
+out the house of the
+
+person who has passed on.
+
+And down in the cellar, big
+basement, in the furnace room
+
+there are these shelves.
+
+And there were all these gas
+masks lined up on the shelves.
+
+And it turned out at the end of
+the war, the Allied troops
+
+have given him a model of each
+of the gas masks that had been
+
+used by the Allies in the war.
+
+So he had this collection of
+gas masks that were just
+
+sitting down there.
+
+And I called the Smithsonian and
+I called the MIT Museum,
+
+and I said I think this
+is really interesting.
+
+But nobody took the gas masks.
+
+So they have thrown out,
+because I tried.
+
+I tried.
+
+AUDIENCE: You weren't tempted to
+just mount them on wall in
+
+your living room?
+
+ROSALIND WILLIAMS: Well,
+they're odd.
+
+Well, I mean we'd been looking
+at pictures from Japan,
+
+testing children.
+
+And when you get in a haz
+suit, it's really scary.
+
+It's just very curious,
+period.
+
+So no, I was not inclined
+to keep them around.
+
+I was just surprised somebody
+didn't want them.
+
+Well, actually now
+I can go back to
+
+gas masks for a minute.
+
+You've read about the tension
+between Noyes and Walker,
+
+Walker finally leaving.
+
+My grandfather finally becoming
+head of the chemical
+
+engineering department in 1920,
+
+known as Walker's protege.
+
+But also the real appreciation
+for the science-based
+
+engineering.
+
+And the more I read Servos's
+article, the more I would love
+
+to look at his headship of
+Course 10 in that period.
+
+I think it's a really
+interesting story.
+
+I don't know it.
+
+But I'm almost sure
+it's there.
+
+OK, he it comes back.
+
+Heads the department for 10
+years, but that isn't what he
+
+wants to do.
+
+He's not an administrative
+type.
+
+He doesn't like it.
+
+He loves teaching and he's
+famous for his teaching.
+
+And that's where he really
+made his mark.
+
+But he did a lot of consulting
+for what was what was then
+
+Standard Oil in New Jersey,
+Esso, Exxon.
+
+And one thing your articles
+didn't mention I think is the
+
+relationship between the
+university and industry
+
+through consulting
+work and how that
+
+fits into the picture.
+
+And he was a great believer in
+the value of consulting.
+
+That's how you find out what's
+happening in the world and it
+
+keeps you on your toes.
+
+And it's also useful
+for industry.
+
+So he, to his death, he got a
+check every month from Exxon.
+
+I mean it wasn't a lot,
+but it was a retainer.
+
+And he died at what, 94.
+
+So they were very loyal
+to him and vice versa.
+
+So this is a drawing of the
+catalytic cracking process.
+
+Let's see, have you been to
+the MIT Museum exhibit?
+
+You must have been.
+
+AUDIENCE: I have.
+
+ROSALIND WILLIAMS: OK.
+
+And you go through
+the whole thing.
+
+And just when you're going to
+leave when to go out of the
+
+exhibit in that back room, on
+the left, is a picture of my
+
+grandfather and a couple other
+gentlemen at a refinery in
+
+Venezuela where catalytic
+cracking has been put into
+
+production in 1939.
+
+And there's a barrel
+above there, an
+
+empty barrel I trust.
+
+But anyway, just to
+make the exhibit
+
+about catalytic cracking.
+
+But the timing, 1939, means that
+once the war broke out in
+
+1940, the demand for aviation
+fuel was huge.
+
+I mean catalytic cracking began
+as a way to get higher
+
+octane for automobiles.
+
+And it was the automobile
+race that instigated it.
+
+AUDIENCE: Does everybody know
+what catalytic cracking is?
+
+ROSALIND WILLIAMS: So let me
+give my brief, nontechnical--
+
+actually this is very
+interesting.
+
+He did the work in the basement
+of Building 12.
+
+And you need some kind
+of a catalytic agent
+
+to promote the cracking.
+
+It's usually a powder and its
+mixed in with the petroleum to
+
+get more higher octane fractions
+or lighter weight
+
+fractions out of a certain
+amount of petroleum.
+
+So if you have the same amount
+of petroleum and the cracking
+
+works efficiently, you get more
+usable high octane fuel
+
+than you do without it.
+
+So you have this--
+
+AUDIENCE: You take crude oil,
+basically, and separating out
+
+all the parts.
+
+ROSALIND WILLIAMS: It's part of
+the distillation process.
+
+And a higher octane means you
+can run engines faster and get
+
+more power out of them, without
+knocking and so forth.
+
+You know when you need higher
+octane, if you fill up your
+
+car and your car starts
+knocking.
+
+That's a sign that things
+are not going well.
+
+It's true in cars.
+
+It's true in airplanes.
+
+So they were trying to blow
+the catalyst through the
+
+petroleum stream.
+
+But as a pattern, it
+kept settling out.
+
+It didn't stay mixed
+in with the stream.
+
+So after months and months of
+work, on trying to get it to
+
+hold into the stream, my
+grandfather, who was famously
+
+profane, said damn it,
+let it settle out.
+
+And in other words, if you let
+it settle out, then you get a
+
+fluid bed at kind of the
+bottom of the reactor.
+
+And it mixes the fumes, the
+petroleum fumes with, or
+
+gases, with the catalyst, better
+than if you try to blow
+
+it along with the stream.
+
+So it's fluid-bed catalytic
+cracking that he and his
+
+students are known for and
+brought a huge fortune to
+
+Exxon, which is one of
+the early adopters.
+
+What he never imagined
+was that--
+
+again, it comes on
+line in 1939.
+
+Within a year, the tankers are
+going to Venezuela to fill up
+
+with a high octane aviation
+fuel, going to the docks of
+
+Liverpool, and pumping
+the fuel into
+
+the tanks of Spitfires.
+
+They don't even put it
+in the holding tank.
+
+They put it right in the
+tanks of the airplanes.
+
+And the Spitfires go
+up to do battle in
+
+the Battle of Britain.
+
+So it's a dramatic example of
+what you do and then how
+
+things happen to change the
+implications of what you do,
+
+that are entirely out
+of your control.
+
+That of course is also
+the story of
+
+the Manhattan Project.
+
+When the Manhattan Project
+got under way--
+
+do I have any slides
+about this?
+
+Oh, this goes back, OK--
+
+basically my grandfather is
+asked to head up the series of
+
+committees making
+recommendations about the
+
+extraction and refinement
+of fissionable material.
+
+In other words, the chemical
+engineering problems of the
+
+atomic weapons, they require
+high grade ore, high grade
+
+uranium or plutonium.
+
+And how do you get it?
+
+That's an engineering problem.
+
+That's a chemical engineering
+problem.
+
+So if you go to the MIT archives
+and ask for Warren K.
+
+Lewis material, a lot of it is
+still classified from World
+
+War II, but there is a notebook
+that he kept when he
+
+was going around to, trying
+to figure out--
+
+I think this is 1941.
+
+When was the chain reaction
+started? '42, right, in Stagg
+
+Field, Chicago?
+
+AUDIENCE: Chicago?
+
+ROSALIND WILLIAMS: Chicago.
+
+Was that earlier?
+
+AUDIENCE: Earlier.
+
+ROSALIND WILLIAMS:
+It was earlier.
+
+AUDIENCE: Before the
+war I think.
+
+ROSALIND WILLIAMS: In the
+middle of this notebook,
+
+appears that event.
+
+And he's going around to
+DuPont, to Oak Ridge.
+
+He's going out to Berkeley,
+Lawrence Lab, talking to all
+
+these people, trying to figure
+out how to do the refining to
+
+get the material that they would
+need for these weapons.
+
+And he served on a series
+of committees.
+
+Was gone all during the war,
+kind of overseeing the
+
+construction and the development
+of these vast
+
+facilities, especially at Oak
+Ridge, also out in Hanford.
+
+AUDIENCE: If you look at the
+Manhattan Project, which my
+
+favorite statistics would be
+the size of the US auto
+
+industry at the time, a huge
+project, less that 10% of it
+
+is concentrated at Los Alamos
+or [INAUDIBLE].
+
+Brilliant physicists are--
+
+and most of it were chemical
+engineering plants in
+
+Tennessee and in Washington
+state, huge plants making the
+
+actual material.
+
+ROSALIND WILLIAMS: So he told
+his wife, my grandmother, just
+
+don't ask where I am.
+
+But if you need me in an
+emergency, you call General
+
+Groves in Washington, and gave
+her the phone number.
+
+And again, I presume the
+students have already heard
+
+this, but my mother was
+married in 1940 and
+
+I was born in 1944.
+
+So this was kind of
+like the next
+
+generation was coming along.
+
+And my mother tells me that
+when she heard the Lowell
+
+Thomas announcement of the
+bomb being dropped on
+
+Hiroshima, on the radio, she
+said now I know where pop's
+
+been, all the war.
+
+And I'm a baby.
+
+And we're back to Japan
+these days.
+
+OK, I have to think he was
+deeply troubled by his role in
+
+the Manhattan Project because
+he didn't talk about it.
+
+He talked a lot about World
+War I and gas masks.
+
+But World War II, he just--
+
+I mean I wish I had pressed
+him more, but I didn't.
+
+My mother said that
+after the war--
+
+for example, at those days if
+you got a watch, a wrist
+
+watch, and you wanted it to glow
+in the dark, they put a
+
+little radium on the dial just
+to make it glow in the dark.
+
+And he would scrape it off.
+
+He didn't want any of
+that stuff near him.
+
+Anyway, so I'm surmising.
+
+But he chaired the Lewis
+committee, and you'll hear a
+
+lot more about that, kept
+teaching at MIT.
+
+My husband had him as a kind
+of senior thesis adviser in
+
+the early 1960s.
+
+And there's a lot of letters
+that he wrote about the role
+
+of the engineer and
+civilization, the profession
+
+of engineering.
+
+And this quote from
+the Lewis Report I
+
+think really captures--
+
+I mean we don't know who
+actually wrote it.
+
+Maybe it Morrison or somebody.
+
+But he really believes that.
+
+He said, if I could come back,
+it would be as a social
+
+scientist, because that's where
+the big problems are,
+
+the really intractable ones.
+
+I can see after World War II
+why you would say that.
+
+So that's the--
+
+yeah, the Spring Garden
+farm again.
+
+OK, so back to the farm.
+
+So what I did in about 15
+minutes before class was just
+
+go through my box of stuff.
+
+And I'm just going to
+pass this around.
+
+Obviously, just collect
+it back there, when it
+
+gets back to you.
+
+The point is what you learn from
+archives that you don't
+
+learn from reading articles
+or so forth.
+
+Monthly Report, Laurel City
+Schools, Laurel, Delaware,
+
+Report of Warren Lewis, 1895.
+
+This tells you sort of, not only
+what his grades are, but
+
+what they're teaching.
+
+PROFESSOR: Is that the
+original document?
+
+ROSALIND WILLIAMS: That's
+the document.
+
+Why do I have this stuff?
+
+I have no idea.
+
+I gave a lot of it
+to the archives.
+
+And they have copies of this.
+
+And I kept a few original
+documents.
+
+There's a lot more.
+
+I mean I am from a very
+literate family.
+
+I don't know how
+else to put it.
+
+Now Ross Basset told you about
+going through MIT yearbooks
+
+and looking at where
+people are from?
+
+PROFESSOR: A little bit.
+
+ROSALIND WILLIAMS: This is my
+grandfather on the left.
+
+So this is what Ross was looking
+at, hometown and list.
+
+My grandfather's list
+is very brief.
+
+But again, I just thought
+you'd like to see.
+
+And Breslau, here are
+photographs of Breslau, where
+
+he studied, got his Ph.D.
+I mean it got bombed to
+
+smithereens in the war.
+
+None of this is here anymore.
+
+But this is old Germany.
+
+PROFESSOR: Did you ever go back
+to try to visit there?
+
+ROSALIND WILLIAMS:
+Not Breslau, no.
+
+I think it blew all
+to smithereens.
+
+PROFESSOR: Probably
+nothing to see.
+
+ROSALIND WILLIAMS: And I had a
+couple of bigger photos, that
+
+are really beauties, that I
+have framed it at home.
+
+And here's his dissertation.
+
+I'm not sure, my German
+not being workable.
+
+But it's signed Rosalind D.
+Kenway, from Warren, July '05,
+
+that's my grandmother.
+
+The Tech, special chemistry
+and chemical engineering
+
+issue, 1910.
+
+So remember that chart showing
+chemistry is going down and
+
+chemical-- so this is published
+at that time.
+
+I have no idea why I have
+this, but I do.
+
+And it's so interesting.
+
+Few industries not founded
+on chemistry, it says.
+
+Now, this is a Xerox.
+
+This is his father basically
+selling off the stock of the
+
+farm, public sale of
+valuable cows.
+
+And this is what his father
+writes in 1917, back in
+
+Laurel, Delaware.
+
+I have sailed life's storm-swept
+sea for 74 years
+
+and I am now nearing port.
+
+I smell the land.
+
+It is wise that I should take
+in-- and I can't read it.
+
+But it must be take
+in the sails--
+
+Therefore on--
+
+He's going to sell
+his milk cows.
+
+This is the start of the decline
+of agriculture in the
+
+United States right here,
+the family farm.
+
+This is the high school, now
+Newton North, Newton high
+
+school kind of review
+magazine.
+
+This is 1918.
+
+A lot of young men are
+going over to Europe.
+
+But it talks about a Newton
+high school scientist.
+
+Of the many capable men on the
+defense side of chemical
+
+warfare service, perhaps none
+has contributed more practical
+
+ideas that Dr. Lewis.
+
+This is his high school,
+hall of fame, kind of.
+
+This is page 10.
+
+My kids went to the
+same school.
+
+PROFESSOR: Newton North?
+
+ROSALIND WILLIAMS:
+Yeah, of course.
+
+OK, this is March 5, 1920.
+
+PROFESSOR: Of course.
+
+ROSALIND WILLIAMS: You
+got to show spirit.
+
+PROFESSOR: Of course.
+
+Boy if live in Newton,
+there's a difference.
+
+I know that.
+
+ROSALIND WILLIAMS: A
+different Newton.
+
+It matters whether it's
+north or south.
+
+OK, Debbie K. Lewis, required
+Course 10, 1920.
+
+His time here seems
+very interesting.
+
+AUDIENCE: [INAUDIBLE].
+
+ROSALIND WILLIAMS: Well,
+actually I won't pass this
+
+around because he-- well,
+maybe I will.
+
+This is Spring Garden farm.
+
+I showed you the photo
+actually earlier.
+
+OK, here we have-- oh look,
+August 5, 1946.
+
+Anybody know what happened
+on August 5, 19--
+
+you know what happened
+on August 6, 1945?
+
+It's Hiroshima.
+
+A year minus a day later, James
+R. Killian writes to Dr.
+
+Compton, during the summer,
+there have been a number of
+
+discussions of the need to
+promote here at the Institute,
+
+more interest in the study of
+educational objectives and
+
+procedures.
+
+This calls for the Lewis
+Commission essentially.
+
+And it's a letter saying
+Lewis should head it.
+
+And here's some people who
+should be on it, and here's
+
+the budget.
+
+And then a second letter,
+outlining in more detail what
+
+the Lewis Commission would do.
+
+It follows shortly thereafter.
+
+Then I just have a bunch of,
+again my grandfather's
+
+thoughts about the history
+of chemical engineering;
+
+engineering as a profession; my
+favorite title, "The Place
+
+of Engineering in Society and
+Civilization." This is from
+
+Tech Review.
+
+And I thought you would enjoy
+this title, "Chemical
+
+Engineering, A New Science,"
+a new science, 1953.
+
+And so these are all published
+in one form or another.
+
+But then there are letters.
+
+And there are quite a few
+letters to me, to my mother,
+
+to my father, when my father's
+trying to figure out-- this is
+
+1945 and my father notes that
+at GE, so many younger
+
+engineers are getting offers
+from small companies and
+
+should be thinking about this?
+
+And my grandfather writes
+this long letter
+
+back, in long hand.
+
+In 1970, somebody has asked
+him for conversations.
+
+He wants to discuss the
+fundamental differences
+
+between Greek philosophy and
+modern science on the purely
+
+intellectual level.
+
+And he wants me to come
+up and help him write
+
+something about this.
+
+And this is very moving because
+he says, I am getting
+
+older and it's hard for people
+to understand me.
+
+You, however, have heard enough
+of it over the years so
+
+you know at least
+the direction in
+
+which my mind is working.
+
+PROFESSOR: Ah, interesting.
+
+High compliment.
+
+ROSALIND WILLIAMS: Yeah.
+
+It's a huge compliment.
+
+Anyway, if you don't get
+the personality,
+
+you're missing things.
+
+Thanksgiving dinner.
+
+Actually this would be 1963,
+the fall of 1963.
+
+So what happened in
+the fall of 1963?
+
+PROFESSOR: Oh, Kennedy.
+
+ROSALIND WILLIAMS: It was
+right after Kennedy's
+
+assassination.
+
+And my grandfather
+is saying grace.
+
+I remember this like
+yesterday.
+
+He had his usual grace and he
+gave thanks for the American
+
+family, because in such
+difficult times like these,
+
+that's the rock on which the
+country is founded, the
+
+American family.
+
+This is my then boyfriend,
+between me and my mother.
+
+PROFESSOR: It's not Gary.
+
+ROSALIND WILLIAMS: Yeah, yeah.
+
+Have you see the actual
+Lewis Report?
+
+PROFESSOR: I have
+never seen that.
+
+ROSALIND WILLIAMS: It's nice,
+nice binding job.
+
+And this is A Dollar to a
+Doughnut, which are stories
+
+about my grandfather's
+teaching.
+
+And this is what the chemical
+engineering department put
+
+together for him when he retired
+as a feitschrift,
+
+because they felt the normal,
+staid one was not appropriate
+
+for such a character.
+
+PROFESSOR: What year
+did he retire?
+
+ROSALIND WILLIAMS: Well, this
+is the official retirement.
+
+So this is like 1950 or so.
+
+But as I say, he's like Leo.
+
+He just kept teaching.
+
+This is a CD.
+
+Just so you know, in the
+archives they have-- this is
+
+from tape, the original
+tape, now on CD.
+
+At the 50th anniversary of the
+Department of Chemical
+
+Engineering, so in 1970,
+he gave a talk about
+
+reminiscences and the
+fascinating history of
+
+chemical engineering in the 19th
+century, where he has a
+
+whole theory about the time
+lag between discovery and
+
+implementation, both in
+electrical and chemical
+
+engineering.
+
+For example, the role of
+batteries in running the
+
+telegraph system, which I had
+never thought about it as an
+
+incentive to chemical
+engineering.
+
+ROSALIND WILLIAMS: Oh,
+very interesting.
+
+AUDIENCE: You know the great
+mentors of the chemical
+
+industry that got [INAUDIBLE]?
+
+PROFESSOR: No.
+
+AUDIENCE: Paper making.
+
+A lot of early involvement.
+
+[INAUDIBLE]
+
+to some degree, much less than
+they were a national center of
+
+paper making.
+
+A lot of the early MIT chemical
+engineers were with
+
+the paper industry.
+
+ROSALIND WILLIAMS: I
+didn't know that.
+
+And this last thing, and I
+bring this along just in
+
+serendipity.
+
+This is an obituary in 1975.
+
+He died on March 9.
+
+This is the Tech Talk,
+when we used to have
+
+a printed MIT newspaper.
+
+But what struck me
+as I was picking
+
+it up, OK, an obituary.
+
+And then I look on the back of
+the first page, "Response
+
+Awaited on Proposal to Train
+Iranian Nuclear Engineers."
+
+And it just struck me, this
+is why I love hard copy.
+
+Because you' come across
+things you don't
+
+plan to come across.
+
+And this is a reminder
+of this is happening.
+
+And of course this had my
+attention, but on the back we
+
+were being friendly with Iran.
+
+The Shah was still around.
+
+OK.
+
+So that's my show and tell.
+
+Do you have any questions?
+
+PROFESSOR: Yeah.
+
+Thank you for bringing
+all this stuff.
+
+ROSALIND WILLIAMS: Well,
+I just love stuff.
+
+PROFESSOR: It reminds me that
+I think historians have a
+
+special feeling for
+stuff like this.
+
+But I remember when I was
+working on my dissertation at
+
+the National Archives, I was
+writing about a topic that
+
+dated back to the end
+of the War of 1812.
+
+So it was a long time ago.
+
+And I was getting materials out
+of the archives that were
+
+still bound in the original
+red tape.
+
+And you'd pull those strings
+apart and they would
+
+disintegrate.
+
+I don't know, it's a weird
+feeling thinking that I'm the
+
+first one to look at the stuff
+in over 200 years.
+
+ROSALIND WILLIAMS: It's kind
+of creepy, but it's also
+
+exhilarating.
+
+PROFESSOR: Yeah, it is.
+
+ROSALIND WILLIAMS: Exploration,
+right.
+
+PROFESSOR: And then we had a
+colleague that Ros and I knew,
+
+and I think you may have
+known him too, David.
+
+His name was Brooke Hindle.
+
+He was the former director of
+the Museum of American History
+
+at the Smithsonian.
+
+But he wrote an article one time
+called "What is a Piece
+
+of the True Cross Worth." Do
+you remember that article,
+
+about the importance of
+artifacts in the study of
+
+technology particularly?
+
+ROSALIND WILLIAMS: The story
+is that they had four
+
+children, two daughters,
+two sons.
+
+The other daughter, besides my
+mother, Mary, married a guy
+
+named Cherry Emerson, who
+went into plastics
+
+after World War II.
+
+Plastics, and to quote Chambers,
+made quite a bit of
+
+money in chemical engineering.
+
+And he studied with Doc
+during the war.
+
+So he gave the money to renovate
+the library, naming
+
+it in honor of my grandmother,
+Warren K Lewis' wife.
+
+And he always claimed
+it was because she
+
+loved music so much.
+
+And I must say I never
+heard her listen
+
+or talk about music.
+
+So I think it was more
+Cherry's love
+
+of music, than her's.
+
+But that doesn't matter.
+
+I think it's a great library.
+
+And I think my grandmother would
+particularly be happy
+
+that students can sleep
+on the couches there.
+
+She's a very gentle soul.
+
+AUDIENCE: Does anybody here have
+parents who went to MIT
+
+or other relatives?
+
+So one think you do see is,
+any institution that lasts
+
+this long has this kind
+of family connection.
+
+Universities are sort of famous
+for keeping track of
+
+that sort of thig.
+
+And that's true among
+faculty, as well.
+
+And there's the genealogies
+of our blood families.
+
+And then we'll talk a bit about
+this, but not to much
+
+explicitly yet.
+
+We'll talk about it in the
+second half, the academic
+
+genealogies of so and so's
+teacher was so and so's
+
+student, was so and
+so's student,
+
+was so and so's student.
+
+And then our colleague, Leo
+Marx, who was my teacher, Who
+
+said that, how does it go?
+
+His adviser from Harvard in the
+'40s-- it's only two steps
+
+back to Ralph Waldo Emerson.
+
+You can trace four academic
+generations today from Leo
+
+Marx to Ralph Waldo Emerson.
+
+I'm sure there are people
+here, some of the senior
+
+faculty who were students
+of your grandfather's.
+
+ROSALIND WILLIAMS: If
+I go to Chemical
+
+Engineering, they just--
+
+oh, Warren K--
+
+AUDIENCE: And that's a person
+who started here in 1896.
+
+And more than 100 years later,
+there are still that person's
+
+students around.
+
+ROSALIND WILLIAMS: That's been
+a great been pleasure of
+
+university life.
+
+It's a sense of continuity.
+
+I mean it would drive
+me crazy too.
+
+PROFESSOR: Ros, your grandfather
+was born in
+
+Delaware and pretty
+much raised there.
+
+He obviously was a
+religious person.
+
+What persuasion?
+
+ROSALIND WILLIAMS: I think in
+Delaware, he was Methodist.
+
+PROFESSOR: Methodist.
+
+Yeah, that makes sense.
+
+ROSALIND WILLIAMS: And one of
+the most fascinating books I
+
+have is of an uncle of his who
+was a Methodist circuit rider
+
+in Delaware, in the 1850s,
+setting up black churches.
+
+They were separate,--
+
+PROFESSOR: Really.
+
+ROSALIND WILLIAMS: --but
+setting them up.
+
+Oh, it's fascinating.
+
+And my grandfather then joined
+the Congregational church up
+
+here, Elliott church
+in Newton.
+
+Because Methodism up here is a
+little different from what it
+
+was in the South.
+
+But you get the point.
+
+It's a low church.
+
+It's not Episcopalian.
+
+And he taught Sunday school
+every Sunday,
+
+as long as he could.
+
+And his religious faith
+meant a lot to him.
+
+He was not a fundamentalist,
+at all.
+
+He said, I take the Bible
+seriously, but not literally.
+
+But I mean he knew his
+Bible up one side
+
+and down the other.
+
+And it was really fundamental
+to him.
+
+In his old age, he became good
+friends with John Crocker, who
+
+was the Episcopal chaplain
+here at MIT.
+
+And they had a lot of talks.
+
+And I mean again, I think maybe
+whether it was guilt
+
+about the Manhattan Project or
+just trying to kind of talk
+
+about matters of faith and
+other matters too.
+
+So Crocker led his funeral
+service, which I was glad that
+
+he was able to do.
+
+So I think religion is one of
+the great untapped kind of
+
+untapped, unappreciated sources
+of motivation at MIT.
+
+And I don't think my
+grandfather's unusual.
+
+And it's not necessarily any
+particular religion.
+
+But people from outside MIT are
+always amazed to find how
+
+strong the religious groups are
+here and how many there
+
+are and how active they are.
+
+It's not their vision of MIT,
+but it's very true.
+
+OK.
+
+ROSALIND WILLIAMS: Well,
+thank you very much.
+
+PROFESSOR: Thank
+you very much.
+
+PROFESSOR: OK, I want to just
+talk today a little bit more
+
+about the '30s, the
+'20s and the '30s.
+
+And again, kind of like Ros's
+talk, use a specific case of a
+
+particular faculty member and
+a particular machine to
+
+illustrate some of the general
+ideas about where MIT moved
+
+between about 1925 and 1935 and
+why that's interesting.
+
+And you of course know from the
+readings, and the more you
+
+look at this, everybody says it
+and the more I read about
+
+it, the more you really feel
+like Karl Compton coming here
+
+in 1930 was a major
+turning point.
+
+There was this kind of
+internal warfare.
+
+What was the word that Lewis
+used, hot fights about the
+
+relation of science
+and engineering.
+
+And the Corporation definitely
+has an opinion about it.
+
+And one thing they do--
+
+they don't have a lot of control
+over the faculty, but
+
+they do decide who
+the president is.
+
+And so they bring
+in Karl Compton.
+
+He's 42 years old--
+
+and it probably sounds
+old to you.
+
+It sounds young to me--
+
+in 1930.
+
+And one of the young people who
+was already here was this
+
+guy then Vannevar Bush, who
+we've also heard about, and
+
+we'll hear about a bunch more,
+who was a young electrical
+
+engineering professor.
+
+And he was building this
+device called a
+
+differential analyzer.
+
+And what I want to do today--
+this is again, a sort of
+
+prototype for what a paper topic
+might be, is to look at
+
+this instrument and how this
+instrument was handled and how
+
+the instrument itself changed
+as the goals of the
+
+Institution changed, from the
+'20s through the '30s.
+
+So here's Bush and there's
+the analyzer.
+
+And when we go to the MIT
+Museum, one of the 150 objects
+
+is that part of the
+analyzer that's in
+
+the wooden box there.
+
+I'll tell you more about
+what that is.
+
+But it's sitting right there
+on the front of the floor.
+
+And when I was first doing this
+research, I asked them if
+
+they had a piece of it and
+they didn't really know.
+
+And Debbie Douglas and I went
+back in the storerooms and we
+
+found that the original
+integrator was there.
+
+So if you go into the
+1920s, Bush is here.
+
+He's a young professor.
+
+He had gotten his Ph.D. here.
+
+And he was a student of
+Kennelly, who I mentioned
+
+before, who was Edison's
+assistant.
+
+And they were very much in the
+kind of technology plan world
+
+of MIT, solving problems for
+big industrial partners.
+
+And what is the problem that
+the big industrial partners
+
+are having?
+
+Well, in the electrical world,
+and you've got to remember
+
+electrical engineering for a--
+
+how people here are Core 6,
+in one way or another?
+
+OK, so about a third.
+
+Electrical engineering, for its
+first 100 years, really
+
+was electrical, without a lot of
+electronics or any of that
+
+solid state physics
+or certainly no
+
+computers and stuff.
+
+It was building big machines
+to make big generators, and
+
+big generators, transmission
+lines, large electric motors,
+
+to drive factories and other
+kinds of things.
+
+And anybody ever hear of the
+IEEE, Institute of Electrical
+
+and Electronic Engineers?
+
+This is a little
+bit of trivia.
+
+But there was the AIEE,
+American Institute of
+
+Electrical Engineers.
+
+Those are the big electric
+power people.
+
+In fact, in German universities
+they still divide
+
+the curriculum into big signals
+and a little signals.
+
+And so big signals
+was the AIEE.
+
+Little signals was the IRE,
+Institute of Radio
+
+Engineering, lots of little
+tiny, little small signals.
+
+And in 1964, they merged
+in the IEEE.
+
+It's to electrical and
+electronic engineers.
+
+Even though it's probably one of
+the two major professional
+
+societies for computation, but
+the word "computer" doesn't
+
+appear in the title at all.
+
+And so, this is back in the
+days of electric power.
+
+And the problem with the
+electric power industry is the
+
+electric generators start out as
+basically local phenomena.
+
+A local entrepreneur will build
+a generator, either a
+
+hydro plant or steam powered,
+in one way or
+
+another, in a town.
+
+And they'll create lighting in
+the town and maybe run some
+
+motors in factories.
+
+And it's all centralized and
+it was all nonuniform.
+
+Every town had a different
+
+voltage, a different frequency.
+
+Some of them were running
+on direct current versus
+
+alternating current.
+
+These are all big battles they
+were having at the time.
+
+But over the course of the
+teens and the '20s, those
+
+systems are becoming
+standardized and they're
+
+becoming connected into what
+today we would call grids.
+
+So they have a big electric
+power grid.
+
+And they're not quite
+national yet, but
+
+they're very much regional.
+
+And so in the '20s, General
+Electric starts to build a big
+
+grid that brings hydroelectric
+power from in Canada and also
+
+from Niagara Falls, through
+very, very long transmission
+
+lines, hundreds and hundreds
+of miles, down into the New
+
+York City area, which is where
+most of the population and
+
+most of the energy
+usage is from.
+
+And those lines begin
+to have problems.
+
+And the problems are, if you've
+got either a lightning
+
+strike at one part of the line,
+you had a bad electrical
+
+storm, or even if you had a
+short circuit and part of the
+
+grid tripped off and had just to
+sort of save itself, you'd
+
+get these transients
+on the line.
+
+And the transients would
+travel great distances.
+
+They were just like big wave
+power spikes on the line and
+
+create blackouts all
+over the place.
+
+And there a couple of famous
+blackouts that happened in the
+
+early '20s that really
+caused a big problem.
+
+So this was like a critical
+issue about how do you figure
+
+out, how do you model the
+performance of these systems
+
+under this kind of stress?
+
+And General Electric, and this
+has come up in the readings in
+
+places, had a very close
+relationship with MIT.
+
+There were a lot of young
+engineers who would go there,
+
+what they called on-test,
+to Schenectady.
+
+In fact, that's where
+Ros's father worked.
+
+I don't if she mention that,
+Doc Lewis's son went to
+
+Schenectady and worked
+for General Electric.
+
+And then they would come back
+to MIT sometimes, to get a
+
+master's degree.
+
+And they began looking at this
+problem of how do you
+
+understand these systems.
+
+Now, Bush had done earlier work
+in his career, which was
+
+also based on this whole
+idea of modeling.
+
+I may have mentioned
+this before where--
+
+how many of you have taken an
+engineering class where you
+
+use a spring mass damper
+system and model a RLC
+
+circuit with it?
+
+Ring a bell for anybody?
+
+OK, maybe a few too
+many times.
+
+Or, there are other analogies,
+different kinds
+
+of hydraulic analogies.
+
+Well, that whole idea basically
+comes from the first
+
+book that Vannevar Bush wrote,
+which is called Operational
+
+Circuit Analysis, where first
+of all he applies a thing
+
+called Oliver Heaviside's
+operational calculus.
+
+Anybody ever heard of the
+Heaviside step function?
+
+And Heaviside was a sort of
+somewhat outlandish English
+
+engineer around the turn of the
+century, who came up with
+
+these ideas.
+
+Mathematicians didn't like them
+because they couldn't
+
+prove they were valid.
+
+Heaviside just didn't care about
+it at all because he
+
+could show that they
+were useful.
+
+And they told you a lot about
+how transients go down lines.
+
+And Bush really took the
+Heaviside work and he put it
+
+on a rigorous mathematical
+foundation.
+
+And said among other things,
+you can use these analogies
+
+and you can model a second order
+system in any of these
+
+different fields with
+a set of equations.
+
+And that can be either RLC
+circuit or a spring mass
+
+damper or there are also
+hydraulic versions of it, I'm
+
+sure any number of other ones.
+
+And what that basic idea allows
+you to do is to make
+
+models of different
+kinds of circuits.
+
+And so what they said
+is here's this
+
+electric power problem.
+
+Let's look at this problem and
+let's build a model of it.
+
+And what this thing is, is
+called a network analyzer.
+
+And this picture is probably
+about 1927.
+
+And all it is, is-- well, first
+thing they make a model
+
+of just the electric
+power line between
+
+Niagara Falls and Boston.
+
+So there might be a couple of
+generators on the line in
+
+Niagara Falls, then there's a
+long transmission line, then
+
+there's a whole bunch of
+different users, and maybe you
+
+make one circuit that's
+50,000 times
+
+smaller than the original.
+
+And you use that as a model.
+
+And anybody know what
+the big problem
+
+with that was actually?
+
+The hardest thing about making
+these small models was
+
+measuring the output.
+
+If you go to the actual electric
+power system and you
+
+put a voltmeter on the line,
+that voltmeter is going to
+
+load the line by some amount.
+
+But it's negligible, it
+really has no impact.
+
+If you make it 50,000 times
+smaller, you've still got the
+
+same voltmeter.
+
+And you put it on the line and
+it's the equivalent of like
+
+putting a whole factory
+on the line.
+
+And it affects the performance
+of it in ways
+
+that it wouldn't otherwise.
+
+So it's one thing to
+make this model.
+
+And they did that rather
+successfully and it helped
+
+them describe.
+
+And they then reported the
+results to GE, this is how the
+
+thing would behave under
+a lightning strike.
+
+And these are some strategies
+you can take to make it a
+
+little more robust.
+
+Well, once the word out about
+that, all these different
+
+power companies came and
+said, we would like you
+
+to model our system.
+
+And so what did they do?
+
+Did they constantly build
+a new one for
+
+everybody's power system?
+
+No.
+
+They built a little set up.
+
+Actually, I don't even have to
+draw it, because it's here.
+
+Where they said OK, we're going
+to put a bunch of models
+
+of transmission lines and a
+bunch of models of generators
+
+and a bunch of models
+of other things.
+
+And they're actually connected
+together by
+
+telephone plug boards.
+
+And you bring your system here
+and we'll plug it together in
+
+a certain way, much
+like a telephone
+
+operator connects circuits.
+
+At that time, it was
+done manually.
+
+And we'll create this thing.
+
+And this thing, they actually
+called it a network computer,
+
+which is a nice word for it,
+that comes up later in MIT
+
+culture, about 50 years later.
+
+And electric power companies
+would come here.
+
+And students would write their
+theses by designing this
+
+system and describing it for
+a particular power company.
+
+And saying here, I modeled
+your circuit.
+
+And this thing actually
+was around until the
+
+'50s, it turns out.
+
+We'll talk about it getting shut
+down when Gordon Brown
+
+shut it down.
+
+But it was again this kind of
+classic MIT in the 1920s,
+
+early '30s, model of close
+relationships with industry,
+
+solving very particular
+problems, almost in a literal
+
+consulting role.
+
+Tell us what your issue is?
+
+We'll model it and we'll help
+you solve the problem.
+
+So we read a lot about that.
+
+Then there was another approach,
+which was to
+
+calculate the progress of these
+transients directly.
+
+And how did they do that?
+
+Well, they could do it
+analytically with algebra.
+
+It was extremely difficult
+because it was not easy to
+
+write the equations.
+
+But it was much easier
+to build an analog
+
+computer to model it.
+
+And it turned out, and you
+probably recognize this, that
+
+the integral of the product
+of two functions
+
+is a critical piece.
+
+Today, you find it in all kinds
+of signals processing
+
+and convolution algorithms.
+
+And they said we'll build
+basically these machines that
+
+will model the key
+function of it.
+
+And this is an early version
+of it, which is also a
+
+specific machine modeled
+to evaluate
+
+the specific integral.
+
+They called it a product
+intergraph.
+
+And it didn't use equations
+at all.
+
+It just took curves in
+and drew curves out.
+
+There you can see Bush.
+
+This is actually the output
+device, which
+
+is a watt/hour meter.
+
+Why would they use
+a watt/hour meter
+
+from an electric utility?
+
+Because a watt/hour meter does
+the same thing, right.
+
+It evaluates the integral of
+the product of the current.
+
+And the voltage is the
+amount of power that
+
+you get billed for.
+
+So they take this thing and
+they just stick there.
+
+And then there's these kind of
+funky mechanical linkages.
+
+And there's all these
+people involved.
+
+And actually they have
+big high-power
+
+resistors, so they use a--
+
+anybody want to guess what
+that thing hanging
+
+up on the top is?
+
+AUDIENCE: Radiator.
+
+PROFESSOR: Close.
+
+AUDIENCE: Radiator.
+
+PROFESSOR: It's a
+radiator, from?
+
+AUDIENCE: Model T.
+
+PROFESSOR: It's a radiator
+from a Model T Ford, that
+
+they're using to provide cooling
+water to this machine,
+
+which evaluates this particular
+integral for this
+
+particular electric
+power problem.
+
+In fact, some of these
+are Bush's students.
+
+This one particularly is a guy
+named Harold Hazen, who we
+
+will talk about later.
+
+In fact, he's also the guy
+sitting in the middle there,
+
+in that picture.
+
+Here's another picture of it.
+
+You can see the watt/hour meter,
+just taken right out of
+
+an electric power measurement
+facility.
+
+Again, you sort of work
+with what you have.
+
+They were working with
+electric companies.
+
+They had these electrical
+things, a whole bunch of
+
+different motor and gears
+and interconnections.
+
+And this was probably
+in Building--
+
+somewhere in the main group.
+
+I'm forgetting exactly.
+
+Building 10, I believe
+was this lab.
+
+I liked, you still have the
+pencil sharpener there.
+
+This is probably the one part
+of what was in the lab that
+
+you might still find in
+a laboratory today.
+
+There's a picture
+of Bush with it.
+
+You can see he looks
+pretty young.
+
+And so there's the
+first product
+
+intergraph, is this device.
+
+And what it does is all those
+little graph chart holders
+
+basically, move under these
+three independent needles.
+
+And the operators just follow
+the first two curves and then
+
+the output plots the integral
+of those two curves.
+
+So it's literally a graphical
+user interface
+
+for an analog computer.
+
+And then, they actually bring
+it up to one more level of
+
+complication.
+
+And there's a way that you can
+make it solve a differential
+
+equation, as well as just
+evaluating an integral.
+
+And so this thing is called the
+second product intergraph,
+
+where it's the same
+kind of thing.
+
+There's two different pieces and
+then you can sort of tie
+
+the output back to the input.
+
+And this is about where things
+stood when Karl Compton
+
+becomes president of MIT.
+
+And Compton basically says,
+we're not going to do that
+
+kind of stuff anymore.
+
+It's too focused on
+just one problem.
+
+It's too simple.
+
+And Bush responds in a
+very energetic way.
+
+And he builds this machine
+about 1931.
+
+And this is called the
+differential analyzer.
+
+Anybody ever heard of
+that term before?
+
+And really it's kind of nothing
+more than this, but
+
+made in a fully general
+purpose way.
+
+Or like I mentioned before, they
+did with the simulator,
+
+they first started building a
+custom one and then they built
+
+a general one.
+
+And what you see here is, these
+guys here are called
+
+integrators.
+
+That's the core of
+the problem.
+
+Again, it's primarily an
+integral thing you're trying
+
+to evaluate.
+
+An integrator is nothing more
+than, they call it a wheel and
+
+disk integrator.
+
+There's a disk that
+spins around.
+
+In a mechanical sense, that's
+just a transmission, but a
+
+continuously variable one.
+
+Then there's a wheel that sits
+on the transmission.
+
+And if the disk is spinning at
+a fixed rate and the wheel
+
+goes in and out, the number of
+turns on the upper end of
+
+wheel is the integral of the
+curve of the position of the
+
+wheel that pulls it off.
+
+But it's a very simple idea
+mechanically, very hard to do
+
+that in a way that
+is mechanically
+
+robust and very accurate.
+
+And that's the piece--
+
+actually it was so critical to
+make it accurate, they covered
+
+these with those wooden boxes.
+
+That's the piece that's
+in the MIT Museum.
+
+And then there's all these
+other elements.
+
+I may have a picture of it.
+
+So there are all these
+other elements.
+
+You can take these integrators
+and then you have a
+
+multiplier, which is nothing but
+a gear that connects one
+
+rod to another in a ratio.
+
+And you have these rods that
+go through the middle.
+
+They're almost like the
+bus on a computer.
+
+And you can connect these things
+in all different ways
+
+to evaluate a particular
+equation.
+
+In this case, this is just a
+second order equation for a
+
+falling body problem.
+
+But you can mix and match this
+thing and essentially program
+
+it by rebuilding it around
+these connecting rods.
+
+And so, I'll show you a couple
+of pictures of the--
+
+oops.
+
+Here is another view
+of the integrator.
+
+Here you can see the
+disk and the little
+
+wheel that takes off.
+
+It actually has a real
+knife edge on it, to
+
+try to make it accurate.
+
+One of the real problems with
+those integrators is that they
+
+can't drive much of a load.
+
+If they slip at all, they
+lose a lot of accuracy.
+
+So here they have put these
+things called torque
+
+amplifiers, which are these very
+clunky, exotic, kind of
+
+cached in like devices that
+amplify the torque.
+
+And then they connect them in.
+
+And where you might have in an
+electrical analog computer,
+
+there's a voltage that gets
+pushed around, in a mechanical
+
+analogue computer it's just the
+rotation of these shafts
+
+that carry the data from
+one place to another.
+
+And they do that by going into
+this matrix of mechanical rods
+
+that you see over there
+on the left.
+
+And each time they wanted, they
+could kind of reprogram
+
+the whole thing.
+
+And here's another shot.
+
+So here's a gear ratio that
+would perform the
+
+multiplication.
+
+You can see that this stuff is
+beautifully machined, very
+
+interesting and carefully
+done.
+
+Yeah?
+
+AUDIENCE: And they were doing
+this in the electrical
+
+department.
+
+PROFESSOR: This is in electrical
+engineering
+
+department, right.
+
+AUDIENCE: It seems very much
+like a mechanical project.
+
+PROFESSOR: It does seem like
+a mechanical project.
+
+That's a very good point.
+
+And Bush actually said, he was
+very clear, he said, I want my
+
+engineers to be able to design
+mathematical equations the way
+
+they design circuits.
+
+And he tried to make a
+circuit design-type
+
+language, visual language--
+
+I redrew this picture.
+
+But I redrew it from one
+of their papers.
+
+It's the same terminology--
+
+that you could actually design
+these equations and make these
+
+big kind of systems.
+
+And already you're beginning
+to see a move toward
+
+generality.
+
+So he says, this is not a device
+to evaluate integrals
+
+for studying transience in the
+electric power industry.
+
+This is a research device
+for a general
+
+purpose calculating machine.
+
+And it's interesting, he goes
+to the Rockefeller--
+
+well, I'll cover that
+in a minute.
+
+So already you're beginning to
+see this guy beginning to
+
+think in a more general, kind
+of fundamental terms, as
+
+opposed to in these
+specific terms.
+
+And this is within just a couple
+of years of Compton
+
+coming here to MIT.
+
+Here's the output
+of the device.
+
+You can see it's basically
+creating a family of curves.
+
+And they were very into
+the fact that they
+
+didn't need any algebra.
+
+They didn't need
+any equations.
+
+They said the world is
+basically analog.
+
+They didn't use that term.
+
+And said, the world
+is continuous.
+
+Our integrator is
+continuous and
+
+produces continuous outputs.
+
+And again, you can
+see this kind of
+
+graphical user interface.
+
+There's a little magnifying
+glass there.
+
+And he's kind of following these
+curves, which was a kind
+
+of manual input.
+
+Bush is kind of looking over
+the shoulder there.
+
+And they would evaluate
+all these
+
+different kinds of curves.
+
+Here's another view, where
+they're all connected by an
+
+electrical audio system.
+
+And there's one guy in the
+center, telling everybody OK,
+
+follow your curves now.
+
+And here, he's not doing it
+by hand so much anymore.
+
+He's turning a little crank
+to trace all the curves.
+
+And you can begin to see by the
+curves, they can do some
+
+pretty complicated things.
+
+And there's a whole kind of
+science of analog computing
+
+that comes up in the '30s around
+these machines, where
+
+they measure the number of
+integrators the way you would
+
+measure the number of megahertz
+of processor that
+
+you have in your computer.
+
+Because the integrator was the
+expensive thing that kind of
+
+described what order equation
+you could possibly model with
+
+these things.
+
+And people start to use them
+to model electron orbits in
+
+atomic physics.
+
+They used them particularly
+for ballistics.
+
+The Army gets really
+interested.
+
+And they have to calculate
+ballistic equations for all
+
+different kinds of
+guns and shells.
+
+And this makes it a lot
+more convenient.
+
+And so you begin to see the move
+away from, even with the
+
+same research group, the same
+people literally, from this
+
+kind of specific industry
+oriented work toward more
+
+general work in what
+they think of as a
+
+general purpose computing.
+
+This is kind of the most famous
+picture of the device.
+
+And you can see there
+three integrators
+
+inside their glass cases.
+
+Those integrated became so
+precise that you had to have
+
+them covered, free of dust, and
+
+really very well protected.
+
+And it turns out there was a
+integrator that was developed
+
+secretly by the Navy for
+controlling the big guns on
+
+battleships, that was better
+than this one, that they
+
+weren't really aware yet.
+
+And has nobody ever see
+a tubal integrator?
+
+It's a whole other kind of
+mechanism that you can use to
+
+do mechanical integration.
+
+So then this project spurs a
+whole bunch of different other
+
+kinds of projects.
+
+One is called the cinema
+intergraph, where the idea is
+
+instead of integrating with
+these kind of problematic
+
+mechanical integrators, you
+integrate using this exotic
+
+new technology.
+
+Anybody want to guess what
+that is over on the left?
+
+It's a photo cell.
+
+And they would actually plot
+the mathematical curves as
+
+images on this 35
+millimeter film.
+
+And then shine a light through
+it and plot the area under the
+
+curves by integrating the charge
+that came through the
+
+photo cell.
+
+And this is the guy
+who made it.
+
+As he said, it was mostly
+a machine for producing
+
+dissertations.
+
+It had essentially no
+practical output.
+
+But it was important in that,
+this guy is named Gordon
+
+Brown, who is a student of
+Harold Hazen, and becomes the
+
+dean of engineering right
+at the end of the
+
+Second World War.
+
+And is the guy who closes down
+all that old-fashioned
+
+electrical machinery.
+
+We read about him
+a little bit.
+
+I think it was in the
+[? Laquier ?]
+
+article.
+
+And kind of is the dean of
+engineering when they kind of
+
+formalized a lot of things after
+the Second World War.
+
+And there's another picture
+of the cinema intergraph.
+
+Also one of his advisers on
+there was Norbert Wiener, who
+
+was also very closely related
+to Bush's work.
+
+And a lot of his earlier ideas
+of cybernetics also came out
+
+of this work.
+
+This is Harold Hazen again.
+
+It's called an automatic
+curve follower.
+
+And his idea is, gee, maybe I
+could make these photo cells
+
+just follow these curves
+automatically.
+
+And today, you can go to the
+Science Museum and buy a
+
+little robot kit with a
+robot that follows a
+
+line across the floor.
+
+This is the first
+one of those.
+
+But what's much more interesting
+and important than
+
+that about this, was that in
+order to do this and order to
+
+make the differential analyzer
+work, it's the amount of
+
+friction that builds up
+in the mechanisms.
+
+And it gets to a point where you
+basically just can't turn
+
+the crank anymore.
+
+And you start to lose
+a lot of accuracy.
+
+You don't lose it
+in the gears.
+
+Eventually you would, because
+they would break.
+
+But you lose it in all these
+other systems, particularly
+
+the integrator.
+
+So what they do is they put what
+they call followers or
+
+servomechanisms between the
+stages, where they can kind of
+
+renew the signal and add
+energy to the system.
+
+Because with a mechanical
+system, if you don't have any
+
+energy, it's just going
+to eventually--
+
+the energy is all dissipated.
+
+But if you can carry the data
+from one point to another and
+
+just add energy and make it
+constantly stronger, you can
+
+build them as big as you want.
+
+And it's between that problem
+and this problem that Hazen
+
+actually writes the first paper
+ever on what he calls
+
+the theory of servomechanisms,
+which you now what know as
+
+feedback control theory.
+
+And anybody take a course on
+that, or probably in every
+
+engineering course you're taking
+something in feedback
+
+control theory.
+
+And he became interested in
+these basic problems.
+
+Until that point, people had
+governors on steam engines.
+
+They had different kinds of
+regulators in this electric
+
+power network they
+were working on.
+
+But nobody had thought of, let's
+write about the theory
+
+of how this feedback mechanism
+works overall.
+
+And there again, there's another
+one of these, a little
+
+more detailed example of an
+intellectual way that
+
+Compton's move was not just
+administrative, he didn't just
+
+say let's stop working
+with industry
+
+and think about science.
+
+He actually influenced these
+people in their labs very
+
+quickly, within a couple years,
+to start thinking about
+
+fundamental problems as opposed
+to just these kind of
+
+immediate problems.
+
+Hazen also becomes dean of
+engineering at MIT during the
+
+Second World War and head of
+the electrical engineering
+
+department.
+
+Here's his model of
+servomechanisms.
+
+Also in that group, looking at
+again this electric power
+
+problem, and saw something
+literally in the electrical
+
+power problem that was
+bigger than simply
+
+the immediate problem.
+
+Anybody want to get
+who this is?
+
+Let me describe what
+he's doing and
+
+maybe then you'll guess?
+
+So you can actually see in this
+picture, he says, I'm
+
+going to look at these
+generators.
+
+And the problem is when
+they have these
+
+transients of these--
+
+they fall out of step, so that
+in an A/C system, everything
+
+has to be running in
+perfect synchrony.
+
+And if it's not running
+synchronized, you get all
+
+kinds of issues.
+
+And he says, I'm going to tape
+cardboard N and S. So that I'm
+
+going to tape them to each of
+the poles on the generator and
+
+then let the generator
+spin really fast.
+
+And then I'm going to shine a
+light on it and I'm going to
+
+pulse the light at exactly
+the same frequency as the
+
+generator is supposed
+to be spinning.
+
+And that will freeze the
+N and S in your eye
+
+when you look at it.
+
+And then if there's a phasing
+problem, you'll see the N and
+
+the S moving back and forth.
+
+Now, anybody want to
+guess who this is?
+
+AUDIENCE: Edgerton.
+
+PROFESSOR: This is
+Edgerton, right?
+
+And this is the first
+application he have of this
+
+stroboscope.
+
+And very soon, he says hey,
+you know what, this
+
+stroboscope thing is
+really interesting.
+
+I can make some innovations
+there.
+
+Forget about electric
+power stuff.
+
+I'm interested in high-speed
+photography and generally
+
+high-speed electrical
+discharge.
+
+AUDIENCE: It's like the first
+timing light for a car.
+
+PROFESSOR: Yeah.
+
+It's exactly the same as the
+timing light for a car.
+
+Most of which are made
+by EG&G, which
+
+was Edgerton's company.
+
+And so there again, he gets
+interested in a bunch of
+
+different things.
+
+But all of them have in common
+this idea of like how even
+
+most of the flashes--
+
+you don't see it so much in your
+digital camera, with the
+
+little teeny ones.
+
+But if you ever have a big
+flash, it fires and then you
+
+hear it charging up.
+
+And then it fires all again.
+
+And Edgerton really became an
+expert at very rapid discharge
+
+of electrical energy.
+
+I work a lot at the Undersea
+World, where Edgerton did a
+
+lot of work with sonar.
+
+But the particular kind of sonar
+he built was very much
+
+like the flash bulb, in
+that it was a sonar
+
+that flashed the sound.
+
+It's called side-scan sonar,
+rather than continuous wave
+
+sonar, would just gave
+it all the time.
+
+So for the plutonium bomb in
+particular, the one during
+
+World War II, and I think they
+still are spherical, and you
+
+had to implode this device.
+
+And a guy at Harvard,
+Kistiakowsky, made these
+
+explosive lenses.
+
+And you had to trigger them
+all around this sphere at
+
+exactly the same moment.
+
+Otherwise, you were going to get
+a lopsided shock wave and
+
+you weren't going to implode
+the thing perfectly.
+
+And it was Edgerton's company
+that designed the triggering
+
+mechanisms for that
+atomic bomb.
+
+They also did high-speed
+photography of the actual
+
+mushroom clouds.
+
+And it's amazing, sort of
+frightening imagery that
+
+they've collected all through
+the Cold War about that.
+
+And that was EG&G. It was
+founded by Edgerton,
+
+Germeshausen, and Grier,
+two of his colleagues.
+
+And the-- let's see,
+what is it--
+
+Building 37 is the building
+they gave.
+
+And there's a Grier room and
+the Germeshausen room.
+
+And I forget which the
+auditorium is called.
+
+But that work started here.
+
+And then Edgerton
+developed that.
+
+And interestingly, one of the
+students, a guy named Marty
+
+Klein, who is the sort of the
+father of that side-scan
+
+sonar, is a good
+friend of mine.
+
+And he always says, Edgerton
+was a time domain man.
+
+He never thought in the
+frequency domain.
+
+For those of you who are
+EEs, you'll know
+
+what that refers to.
+
+And that really came out this
+legacy from Bush's lab of
+
+thinking about transience
+on these lines.
+
+There's nothing to say about
+electric power systems in the
+
+frequency domain, because
+it's all 60 Hertz.
+
+It's all exactly the same
+frequency, unlike radio which
+
+is all about frequency domain.
+
+He thought in the time domain.
+
+And everything about
+the electronics--
+
+anybody work in the Edgerton
+lab these days or
+
+take a class there?
+
+All that stuff is time domain
+stuff, kind of epitomized by
+
+the high-speed photography.
+
+Here's an image again of the
+Army getting interested at the
+
+Aberdeen Proving Ground, down
+in Maryland, which did a lot
+
+of the measurement
+for ballistics.
+
+They bought five or six of these
+or they hired people and
+
+they made their own
+copies of them.
+
+Within a few years, during the
+'30s, they were all over the
+
+place, not just in
+electric power.
+
+Yeah?
+
+AUDIENCE: When do you begin
+to see military
+
+funding of this work?
+
+Does it start with Bush's
+differential?
+
+No, OK.
+
+PROFESSOR: Really not
+until the war.
+
+So I'll come to the funding
+issue in a second, because
+
+it's pretty interesting.
+
+They also, with Bush's
+consulting, built the control
+
+system for the Palomar
+telescope, which at the time
+
+was the biggest telescope
+ever built.
+
+It didn't even become
+operational until after the
+
+Second World War.
+
+Anybody ever been there?
+
+It's in California, outside
+of San Diego.
+
+And you have this enormous,
+three-story high telescope.
+
+And you've got to point it
+with great accuracy.
+
+And it actually had a lot of
+similarities to the problems
+
+they were working on there.
+
+So there's also a funding
+story here.
+
+Warren Weaver is also
+mentioned in the--
+
+I'm forgetting if it was the
+Servos or the [? Laquier ?]
+
+article from the Rockefeller
+Foundation.
+
+And they talk about it.
+
+It was [? Laquier. ?]
+
+He said, as soon as Compton
+came in, he went to the
+
+Rockefeller Foundation and said,
+I need $175,000 for this
+
+new initiative.
+
+And if you guys back
+me on this--
+
+at the time, there was no
+National Science Foundation.
+
+There was no public money other
+than from the military,
+
+available for research.
+
+But the Rockefeller Foundation
+was basically the equivalent
+
+of the NSF today, a
+private foundation
+
+handing out these checks.
+
+And Bush went to Weaver.
+
+And he went to Weaver with
+this early version of the
+
+differential analyzer.
+
+And it was about 1931.
+
+And Weaver says,
+not interested.
+
+That engineering stuff is best
+handled by industrial funding.
+
+We don't support anything
+that looks
+
+like engineering research.
+
+We only support fundamental
+research.
+
+Why don't you go find an
+electric power company or
+
+somebody to give it to you?
+
+Two years later, Bush goes back
+to Weaver and says oh,
+
+this is not a machine for
+electric power research.
+
+This is a machine for
+
+fundamental research in computing.
+
+And Weaver says, oh, well if
+you're going to put it that
+
+way, here's $100,000.
+
+At the depths of the Depression,
+that a lot of
+
+money for a research program,
+far beyond what anybody-- in
+
+fact, I think there's a
+statistic in there that before
+
+the war, the entire federal
+funding for all of MIT was
+
+only $40,000 a year.
+
+And they gave Bush, not just
+$100,000, but about $250,000
+
+in the middle of the '30s, to
+build the next version, which
+
+became known as the Rockefeller
+
+differential analyzer.
+
+And here you see, it looks a
+little bit more sophisticated.
+
+Instead of those earlier tables,
+they called them input
+
+tables, here you have
+a rotating drum.
+
+There's still a person required
+to sit there and turn
+
+the handle.
+
+But the basic model was
+a lot more electrical.
+
+And also interestingly, the
+operators of these machines
+
+changed from men to women.
+
+So they're no longer graduate
+students operating them.
+
+They're much more what they
+called human computers at the
+
+time, operating them.
+
+But you can see there,
+a similar idea.
+
+There are curves on this drum.
+
+The person looks at the curves
+and is providing the input to
+
+the machine by matching the
+pointer to the curve.
+
+And the way this machine
+worked, is also really
+
+interesting.
+
+A lot like the other one, but
+instead of that matrix of
+
+circular rods in the middle,
+it's a crossbar switch.
+
+Anybody know what industry a
+crossbar switch comes from?
+
+It's a telephone switch.
+
+And its electrical switch that
+basically says, I got all
+
+these inputs across the top and
+all these inputs across
+
+the bottom.
+
+I can connect anyone to anyone,
+in fact in this case
+
+using a punched paper tape.
+
+And so they get the
+prototype crossbar
+
+switch from Bell Labs.
+
+It was a pretty big revolution
+in telephone
+
+switching at the time.
+
+They had built this crossbar
+and donated it to MIT.
+
+And what they did was they
+said, we're just going to
+
+adapt each of these mechanical
+elements-- in fact, the
+
+integrators were still
+mechanical--
+
+but we're going to give them
+electrical outputs.
+
+Instead of the quantities
+being represented by the
+
+rotation angle of the
+rod, it's now
+
+represented by a voltage.
+
+We'll feed all the voltages
+into the crossbar switch.
+
+And then you configure the
+crossbar switch by reading a
+
+paper tape into it.
+
+And so you can basically model
+any equation by some set of
+
+switch closings on the crossbar
+switch and you
+
+program those by a paper tape.
+
+And now, you're beginning to see
+the beginning of digital
+
+switching coming into -- there
+wasn't even a word for
+
+"digital" at the time--
+
+coming into this idea of
+analogue computing.
+
+And so then the problem for the
+programmer becomes, they
+
+have this continuous analog
+equation across the top.
+
+I need to translate it into
+these paper tapes.
+
+And that's kind of an
+interesting problem, how do I
+
+think about the transformation
+from a set of equations into a
+
+set of switch closures?
+
+And this young master student
+looks at it and he says well,
+
+I can actually make
+this kind of--
+
+he calls it a relay algebra.
+
+And I'm going to design a little
+kind of mechanical
+
+notation that will allow me
+to design these circuits.
+
+And you know that totally
+useless stuff that I studied
+
+in mathematics they called
+Boolean algebra, from the 19th
+
+century, is actually kind
+of useful here.
+
+And I'm going to call a closed
+switch, a 1 and an open
+
+switch, a 0.
+
+And that allows you to
+manipulate the whole thing
+
+mathematically.
+
+Anybody know who this is?
+
+You maybe the name flash by.
+
+AUDIENCE: You mean
+Claude Shannon?
+
+PROFESSOR: Yeah, it's actually
+Claude Shannon, writes his
+
+master's thesis on exactly
+this problem.
+
+And many people call this the
+most significant master's
+
+thesis ever written in
+electrical engineering.
+
+The master's thesis basically
+lays down the entire
+
+groundwork for the design of
+digital systems in 1936 and
+
+based on the problems that are
+raised by designing this
+
+computational machine.
+
+And he immediately gets hired by
+Bell Labs and starts to go
+
+work there and think about how
+to design switching circuits.
+
+And the kind of counterpart at
+Bell Labs right at that moment
+
+reads this thesis and says, I'm
+going to call this kind of
+
+electronics digital.
+
+And actually invents the word
+"digital" to describe that
+
+kind of electronics.
+
+So here's a case of--
+
+again, 1936, Karl Compton
+has only been
+
+at MIT for six years.
+
+But he's already pushed this
+particular laboratory and this
+
+particular set of students to
+start thinking about their
+
+work in a different way.
+
+Much less specific to one
+industry specific to solving
+
+particular applications, and
+more generally thinking about
+
+the fundamentals, the
+mathematics, with applications
+
+to lots and lots
+of other areas.
+
+So that's just one case there,
+I thought I would show you.
+
+And then, all those people are
+also then people who get very
+
+involved in the early
+digital computing.
+
+Once the war starts, basically
+they all go to
+
+Washington with Bush.
+
+Some of them stay here and
+get very involved.
+
+But we'll cover that in the next
+time we actually meet.
+
+Questions, comments
+about that?
+
+AUDIENCE: Is that the same
+servomechanism laboratory that
+
+goes and creates
+the Whirlwind?
+
+PROFESSOR: Yeah.
+
+The earlier question, it's
+exactly that laboratory.
+
+So Gordon Brown starts
+the Servomechanism
+
+Laboratory in 1940.
+
+He the first course ever
+on feedback control
+
+theory at MIT in 1939.
+
+And he writes this one paper.
+
+In fact, it's called "Transient
+Analysis of
+
+Servomechanisms." So it still
+carries that transient idea
+
+from the early electric
+power work.
+
+And Warren Weaver shows up in
+his lab and says, guess what?
+
+I work for the government now.
+
+I don't work for the
+
+Rockefeller Foundation anymore.
+
+That paper that you just wrote,
+that you're about to
+
+publish, it's classified.
+
+You're not allowed to
+publish it anymore.
+
+And here's $500,000
+to start your lab.
+
+And Brown sort of takes it in.
+
+And if it happens for an
+historian, very valuable that
+
+they classified that paper.
+
+Because then, anyone who
+got a copy of it,
+
+had to sign it out.
+
+So he writes this fundamental
+paper.
+
+And then you can actually trace
+week by week, out in the
+
+community, who's reading the
+paper and see how they are
+
+changing their work.
+
+And they begin to have this
+idea, again if you look at
+
+feedback control, there's
+governors on steam engines.
+
+There's regulators
+on arc lights.
+
+There's automatic pilots
+in airplanes.
+
+And is even feedback amplifiers
+in electrical
+
+engineering.
+
+But there's nobody who says,
+hey, you know what, all that
+
+stuff is really the same.
+
+And now, we take for granted
+as that's what you study in
+
+control theory.
+
+You don't study any one
+of those areas.
+
+You study the basic
+phenomenon.
+
+And that was the beginning
+of what Brown was doing.
+
+And it was really a coincidence
+that right about
+
+that moment, it goes underground
+and it stays
+
+underground for the whole war.
+
+And that's really where when
+Norbert Wiener comes out in
+
+1948, and says, cybernetics,
+feedback control, it's all
+
+about this, he was just saying
+something that had been secret
+
+for eight years already
+at that point.
+
+But one of the things that got
+me interested in this research
+
+was, why was MIT's first digital
+computer made by the
+
+Servomechanisms Lab?
+
+Because you don't necessarily
+associate those two
+
+things in your mind.
+
+A servo, you think of as an
+analog, mechanical thing and a
+
+digital computer as this
+funny electronic thing.
+
+But during the war, it sort of--
+it actually happens after
+
+the war, but right
+after the war.
\ No newline at end of file
diff --git a/SAgWL1G5Bcw.txt b/SAgWL1G5Bcw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..71ab374aec1a3520ef47c2d67914738c0b66f196
--- /dev/null
+++ b/SAgWL1G5Bcw.txt
@@ -0,0 +1,1507 @@
+align:start position:0%
+ 
+my name is an margules I'm the executive
+
+ align:start position:0%
+my name is an margules I'm the executive
+ 
+
+ align:start position:0%
+my name is an margules I'm the executive
+director of MIT open courseware in our
+
+ align:start position:0%
+director of MIT open courseware in our
+ 
+
+ align:start position:0%
+director of MIT open courseware in our
+session on open courseware you'll
+
+ align:start position:0%
+session on open courseware you'll
+ 
+
+ align:start position:0%
+session on open courseware you'll
+actually be spending some time on the
+
+ align:start position:0%
+actually be spending some time on the
+ 
+
+ align:start position:0%
+actually be spending some time on the
+site but I'll describe also how open
+
+ align:start position:0%
+site but I'll describe also how open
+ 
+
+ align:start position:0%
+site but I'll describe also how open
+courseware was developed a little bit
+
+ align:start position:0%
+courseware was developed a little bit
+ 
+
+ align:start position:0%
+courseware was developed a little bit
+about its history and we'll talk about
+
+ align:start position:0%
+about its history and we'll talk about
+ 
+
+ align:start position:0%
+about its history and we'll talk about
+some of the challenges for open
+
+ align:start position:0%
+some of the challenges for open
+ 
+
+ align:start position:0%
+some of the challenges for open
+courseware going forward for now I'd
+
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+courseware going forward for now I'd
+ 
+
+ align:start position:0%
+courseware going forward for now I'd
+like to tell you a little bit about what
+
+ align:start position:0%
+like to tell you a little bit about what
+ 
+
+ align:start position:0%
+like to tell you a little bit about what
+open course Weare is and also share with
+
+ align:start position:0%
+open course Weare is and also share with
+ 
+
+ align:start position:0%
+open course Weare is and also share with
+you some of our experience with our
+
+ align:start position:0%
+you some of our experience with our
+ 
+
+ align:start position:0%
+you some of our experience with our
+first public launch of the site I'll
+
+ align:start position:0%
+first public launch of the site I'll
+ 
+
+ align:start position:0%
+first public launch of the site I'll
+then post some of the questions or the
+
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+then post some of the questions or the
+ 
+
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+then post some of the questions or the
+challenges we're facing in the area of
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+challenges we're facing in the area of
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+challenges we're facing in the area of
+access and
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+access and
+ 
+
+ align:start position:0%
+access and
+sustainability MIT open courseware was
+
+ align:start position:0%
+sustainability MIT open courseware was
+ 
+
+ align:start position:0%
+sustainability MIT open courseware was
+announced about a year and a half ago
+
+ align:start position:0%
+announced about a year and a half ago
+ 
+
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+announced about a year and a half ago
+with an overwhelmingly positive response
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+with an overwhelmingly positive response
+ 
+
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+with an overwhelmingly positive response
+with that tremendous response however
+
+ align:start position:0%
+with that tremendous response however
+ 
+
+ align:start position:0%
+with that tremendous response however
+came a lot of confusion about what MIT
+
+ align:start position:0%
+came a lot of confusion about what MIT
+ 
+
+ align:start position:0%
+came a lot of confusion about what MIT
+open courseware is and what it
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+ align:start position:0%
+open courseware is and what it
+ 
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+ align:start position:0%
+open courseware is and what it
+isn't oh CW is a large-scale web-based
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+isn't oh CW is a large-scale web-based
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+isn't oh CW is a large-scale web-based
+publication of all of mit's course
+
+ align:start position:0%
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+site so that's what ocw is we just
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+site so that's what ocw is we just
+ 
+
+ align:start position:0%
+site so that's what ocw is we just
+launched the site uh three weeks ago we
+
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+launched the site uh three weeks ago we
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+launched the site uh three weeks ago we
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+we've received once again an over inly
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+we've received once again an over inly
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+3,000 email messages have been received
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+those email messages have given us lots
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+value in being able to use the site to
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+they can now spend their energy on
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+creating new ideas instead of
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+Reinventing ideas that other people have
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+Reinventing ideas that other people have
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+also interested in using ocw to be able
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+also interested in using ocw to be able
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+to share best teaching practices so we
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+expect over time for the for there to be
+much more
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+much more
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+much more
+collaboration and potentially much more
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+collaboration and potentially much more
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+Innovation many self-learners have also
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+Innovation many self-learners have also
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+Innovation many self-learners have also
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+visited the site and told us some of the
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+visited the site and told us some of the
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+ways that they'll be using it
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+self-learners are coming to ocw to
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+ align:start position:0%
+self-learners are coming to ocw to
+explore whole new areas of study as well
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+explore whole new areas of study as well
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+ align:start position:0%
+explore whole new areas of study as well
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+as to brush up on subjects that they
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+took a while ago and perhaps have gotten
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+rust
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+rust
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+rust
+on self- Learners have also told us that
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+ align:start position:0%
+on self- Learners have also told us that
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+
+ align:start position:0%
+on self- Learners have also told us that
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+they e eager to come to ocw often in
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+they e eager to come to ocw often in
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+order to keep current on the latest on
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+be measuring over time more about how
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+people are using the site and what their
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+impact may be in class we'll have more
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+what the potential impact will be we
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+
+ align:start position:0%
+what the potential impact will be we
+have great hopes for ocw but they're
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+have great hopes for ocw but they're
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+ align:start position:0%
+have great hopes for ocw but they're
+also great challenges our first area of
+
+ align:start position:0%
+also great challenges our first area of
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+challenge is in Access we can think of
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+accessing two ways there's technical
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+access just how do you get to the site
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+access just how do you get to the site
+and then there's cultural access let's
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+and then there's cultural access let's
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+and then there's cultural access let's
+talk first about technical
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+talk first about technical
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+access although people have accessed the
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+site from 177 different countries there
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+site from 177 different countries there
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+site from 177 different countries there
+are plenty of remote Villages and other
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+are plenty of remote Villages and other
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+are plenty of remote Villages and other
+locations that just don't have the
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+locations that just don't have the
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+locations that just don't have the
+network infrastructure need needed to be
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+network infrastructure need needed to be
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+network infrastructure need needed to be
+able to truly access all the depth in
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+able to truly access all the depth in
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+able to truly access all the depth in
+open course Weare what should we do
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+open course Weare what should we do
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+open course Weare what should we do
+about that we'll talk about that when we
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+about that we'll talk about that when we
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+about that we'll talk about that when we
+get together cultural access is perhaps
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+get together cultural access is perhaps
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+get together cultural access is perhaps
+even more
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+even more
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+even more
+challenging those areas that are most
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+challenging those areas that are most
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+eager to get to the content say they
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+might have difficulty using it because
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+not make sense within their culture what
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+not make sense within their culture what
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+
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+either encourage or facilitate local
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+ align:start position:0%
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+
+ align:start position:0%
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+ 
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+materials with any Innovation it's
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+materials with any Innovation it's
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+materials with any Innovation it's
+important not only to launch it properly
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+important not only to launch it properly
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+important not only to launch it properly
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+but also to consider how to sustain it
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+but also to consider how to sustain it
+over
+
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+over
+ 
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+over
+time we
+
+ align:start position:0%
+time we
+ 
+
+ align:start position:0%
+time we
+know that many of the for profit models
+
+ align:start position:0%
+know that many of the for profit models
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+
+ align:start position:0%
+know that many of the for profit models
+have struggled in fact many of them have
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+ align:start position:0%
+have struggled in fact many of them have
+ 
+
+ align:start position:0%
+have struggled in fact many of them have
+folded and I would be willing to predict
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+ align:start position:0%
+folded and I would be willing to predict
+ 
+
+ align:start position:0%
+folded and I would be willing to predict
+that many still will not make it and
+
+ align:start position:0%
+that many still will not make it and
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+
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+that many still will not make it and
+will
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+will
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+
+ align:start position:0%
+will
+fold how do we make the for free model
+
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+fold how do we make the for free model
+ 
+
+ align:start position:0%
+fold how do we make the for free model
+survive and be sustainable over
+
+ align:start position:0%
+survive and be sustainable over
+ 
+
+ align:start position:0%
+survive and be sustainable over
+time let's think about it in terms of
+
+ align:start position:0%
+time let's think about it in terms of
+ 
+
+ align:start position:0%
+time let's think about it in terms of
+the local level and then perhaps at the
+
+ align:start position:0%
+the local level and then perhaps at the
+ 
+
+ align:start position:0%
+the local level and then perhaps at the
+national and international level at the
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+national and international level at the
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+
+ align:start position:0%
+national and international level at the
+local level for ocw to survive and to be
+
+ align:start position:0%
+local level for ocw to survive and to be
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+ align:start position:0%
+local level for ocw to survive and to be
+sustainable it first of all has to be
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+ align:start position:0%
+sustainable it first of all has to be
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+ align:start position:0%
+sustainable it first of all has to be
+part of the way our faculty work it has
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+ align:start position:0%
+part of the way our faculty work it has
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+ align:start position:0%
+part of the way our faculty work it has
+to be part of their normal way of
+
+ align:start position:0%
+to be part of their normal way of
+ 
+
+ align:start position:0%
+to be part of their normal way of
+preparing their course materials
+
+ align:start position:0%
+preparing their course materials
+ 
+
+ align:start position:0%
+preparing their course materials
+ocw will not succeed if we place any
+
+ align:start position:0%
+ocw will not succeed if we place any
+ 
+
+ align:start position:0%
+ocw will not succeed if we place any
+additional burden on the
+
+ align:start position:0%
+additional burden on the
+ 
+
+ align:start position:0%
+additional burden on the
+faculty secondly we need to be as
+
+ align:start position:0%
+faculty secondly we need to be as
+ 
+
+ align:start position:0%
+faculty secondly we need to be as
+efficient and as cost effective as
+
+ align:start position:0%
+efficient and as cost effective as
+ 
+
+ align:start position:0%
+efficient and as cost effective as
+possible so that there aren't barriers
+
+ align:start position:0%
+possible so that there aren't barriers
+ 
+
+ align:start position:0%
+possible so that there aren't barriers
+for other campuses to join in the
+
+ align:start position:0%
+for other campuses to join in the
+ 
+
+ align:start position:0%
+for other campuses to join in the
+effort which takes us to the next level
+
+ align:start position:0%
+effort which takes us to the next level
+ 
+
+ align:start position:0%
+effort which takes us to the next level
+of concern around
+
+ align:start position:0%
+of concern around
+ 
+
+ align:start position:0%
+of concern around
+sustainability if our vision is truly
+
+ align:start position:0%
+sustainability if our vision is truly
+ 
+
+ align:start position:0%
+sustainability if our vision is truly
+realized and there are open coursewares
+
+ align:start position:0%
+realized and there are open coursewares
+ 
+
+ align:start position:0%
+realized and there are open coursewares
+not just in MIT but on every campus if
+
+ align:start position:0%
+not just in MIT but on every campus if
+ 
+
+ align:start position:0%
+not just in MIT but on every campus if
+open courseware becomes a a real
+
+ align:start position:0%
+open courseware becomes a a real
+ 
+
+ align:start position:0%
+open courseware becomes a a real
+movement then how do we allow people to
+
+ align:start position:0%
+movement then how do we allow people to
+ 
+
+ align:start position:0%
+movement then how do we allow people to
+navigate across different open course
+
+ align:start position:0%
+navigate across different open course
+ 
+
+ align:start position:0%
+navigate across different open course
+word platforms there will need to be
+
+ align:start position:0%
+word platforms there will need to be
+ 
+
+ align:start position:0%
+word platforms there will need to be
+some kind of organizing structures or
+
+ align:start position:0%
+some kind of organizing structures or
+ 
+
+ align:start position:0%
+some kind of organizing structures or
+Frameworks or standard bodies that exist
+
+ align:start position:0%
+Frameworks or standard bodies that exist
+ 
+
+ align:start position:0%
+Frameworks or standard bodies that exist
+to coordinate that in class I'd love to
+
+ align:start position:0%
+to coordinate that in class I'd love to
+ 
+
+ align:start position:0%
+to coordinate that in class I'd love to
+hear your ideas about how we here at
+
+ align:start position:0%
+hear your ideas about how we here at
+ 
+
+ align:start position:0%
+hear your ideas about how we here at
+Team might help lead that
+
+ align:start position:0%
+Team might help lead that
+ 
+
+ align:start position:0%
+Team might help lead that
+effort those are just a few of the many
+
+ align:start position:0%
+effort those are just a few of the many
+ 
+
+ align:start position:0%
+effort those are just a few of the many
+challenges we face in the future we're
+
+ align:start position:0%
+challenges we face in the future we're
+ 
+
+ align:start position:0%
+challenges we face in the future we're
+really just at the very beginning of
+
+ align:start position:0%
+really just at the very beginning of
+ 
+
+ align:start position:0%
+really just at the very beginning of
+open courseware but it's a very exciting
+
+ align:start position:0%
+open courseware but it's a very exciting
+ 
+
+ align:start position:0%
+open courseware but it's a very exciting
+time and I look forward to seeing you
+
+ align:start position:0%
+time and I look forward to seeing you
+ 
+
+ align:start position:0%
+time and I look forward to seeing you
+class seeing you in class and we'll talk
+
+ align:start position:0%
+class seeing you in class and we'll talk
+ 
+
+ align:start position:0%
+class seeing you in class and we'll talk
+more about this thank you
\ No newline at end of file
diff --git a/SbtqjZk80Qc.txt b/SbtqjZk80Qc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f5d1e84b8d57334deb771279da7876d40629636b
--- /dev/null
+++ b/SbtqjZk80Qc.txt
@@ -0,0 +1,13251 @@
+align:start position:0%
+ 
+one more lecture from me and so remember
+
+ align:start position:0%
+one more lecture from me and so remember
+ 
+
+ align:start position:0%
+one more lecture from me and so remember
+then on Thursday we'll be here and Chris
+
+ align:start position:0%
+then on Thursday we'll be here and Chris
+ 
+
+ align:start position:0%
+then on Thursday we'll be here and Chris
+Wolverton from Ford will be
+
+ align:start position:0%
+Wolverton from Ford will be
+ 
+
+ align:start position:0%
+Wolverton from Ford will be
+lecturing Straight live direct from Fort
+
+ align:start position:0%
+lecturing Straight live direct from Fort
+ 
+
+ align:start position:0%
+lecturing Straight live direct from Fort
+and so you better have good questions
+
+ align:start position:0%
+and so you better have good questions
+ 
+
+ align:start position:0%
+and so you better have good questions
+for him because he only lectures about
+
+ align:start position:0%
+for him because he only lectures about
+ 
+
+ align:start position:0%
+for him because he only lectures about
+an hour and so we usually in the past
+
+ align:start position:0%
+an hour and so we usually in the past
+ 
+
+ align:start position:0%
+an hour and so we usually in the past
+we've had quite some good discussion
+
+ align:start position:0%
+we've had quite some good discussion
+ 
+
+ align:start position:0%
+we've had quite some good discussion
+afterwards but that's going to depend on
+
+ align:start position:0%
+afterwards but that's going to depend on
+ 
+
+ align:start position:0%
+afterwards but that's going to depend on
+you um so what I'm going to do today is
+
+ align:start position:0%
+you um so what I'm going to do today is
+ 
+
+ align:start position:0%
+you um so what I'm going to do today is
+um a variety of topics but they all have
+
+ align:start position:0%
+um a variety of topics but they all have
+ 
+
+ align:start position:0%
+um a variety of topics but they all have
+to kind of do with the same idea of
+
+ align:start position:0%
+to kind of do with the same idea of
+ 
+
+ align:start position:0%
+to kind of do with the same idea of
+bigger and faster and better not
+
+ align:start position:0%
+bigger and faster and better not
+ 
+
+ align:start position:0%
+bigger and faster and better not
+necessarily better but um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know when you deal with atoms uh
+
+ align:start position:0%
+so you know when you deal with atoms uh
+ 
+
+ align:start position:0%
+so you know when you deal with atoms uh
+both because of the size and the time um
+
+ align:start position:0%
+both because of the size and the time um
+ 
+
+ align:start position:0%
+both because of the size and the time um
+if you go away especially if you go away
+
+ align:start position:0%
+if you go away especially if you go away
+ 
+
+ align:start position:0%
+if you go away especially if you go away
+from periodic systems uh you'll always
+
+ align:start position:0%
+from periodic systems uh you'll always
+ 
+
+ align:start position:0%
+from periodic systems uh you'll always
+run into this problem that it's um too
+
+ align:start position:0%
+run into this problem that it's um too
+ 
+
+ align:start position:0%
+run into this problem that it's um too
+small your system that the simulation is
+
+ align:start position:0%
+small your system that the simulation is
+ 
+
+ align:start position:0%
+small your system that the simulation is
+too short um I always like to quote
+
+ align:start position:0%
+too short um I always like to quote
+ 
+
+ align:start position:0%
+too short um I always like to quote
+Professor marzari on this when people
+
+ align:start position:0%
+Professor marzari on this when people
+ 
+
+ align:start position:0%
+Professor marzari on this when people
+come to him with Nano Nano problems and
+
+ align:start position:0%
+come to him with Nano Nano problems and
+ 
+
+ align:start position:0%
+come to him with Nano Nano problems and
+he always says Nano is just a little too
+
+ align:start position:0%
+he always says Nano is just a little too
+ 
+
+ align:start position:0%
+he always says Nano is just a little too
+big for us um and so I think that's
+
+ align:start position:0%
+big for us um and so I think that's
+ 
+
+ align:start position:0%
+big for us um and so I think that's
+telling you something about the state of
+
+ align:start position:0%
+telling you something about the state of
+ 
+
+ align:start position:0%
+telling you something about the state of
+what we do um so what you've actually
+
+ align:start position:0%
+what we do um so what you've actually
+ 
+
+ align:start position:0%
+what we do um so what you've actually
+seen certain Solutions already to the
+
+ align:start position:0%
+seen certain Solutions already to the
+ 
+
+ align:start position:0%
+seen certain Solutions already to the
+sort of size and time problem um maybe
+
+ align:start position:0%
+sort of size and time problem um maybe
+ 
+
+ align:start position:0%
+sort of size and time problem um maybe
+they were fairly obvious but if you
+
+ align:start position:0%
+they were fairly obvious but if you
+ 
+
+ align:start position:0%
+they were fairly obvious but if you
+think of the time
+
+ align:start position:0%
+think of the time
+ 
+
+ align:start position:0%
+think of the time
+problem um what I've already showed you
+
+ align:start position:0%
+problem um what I've already showed you
+ 
+
+ align:start position:0%
+problem um what I've already showed you
+is how to essentially Co grain that away
+
+ align:start position:0%
+is how to essentially Co grain that away
+ 
+
+ align:start position:0%
+is how to essentially Co grain that away
+um which is it's one thing to C grain
+
+ align:start position:0%
+um which is it's one thing to C grain
+ 
+
+ align:start position:0%
+um which is it's one thing to C grain
+over time and space it's another thing
+
+ align:start position:0%
+over time and space it's another thing
+ 
+
+ align:start position:0%
+over time and space it's another thing
+and it's actually easier to almost
+
+ align:start position:0%
+and it's actually easier to almost
+ 
+
+ align:start position:0%
+and it's actually easier to almost
+remove it by integrating it away and
+
+ align:start position:0%
+remove it by integrating it away and
+ 
+
+ align:start position:0%
+remove it by integrating it away and
+when you essentially integrate time away
+
+ align:start position:0%
+when you essentially integrate time away
+ 
+
+ align:start position:0%
+when you essentially integrate time away
+completely you end up with
+
+ align:start position:0%
+completely you end up with
+ 
+
+ align:start position:0%
+completely you end up with
+thermodynamics I mean think about that's
+
+ align:start position:0%
+thermodynamics I mean think about that's
+ 
+
+ align:start position:0%
+thermodynamics I mean think about that's
+what integration over the partition
+
+ align:start position:0%
+what integration over the partition
+ 
+
+ align:start position:0%
+what integration over the partition
+function is you're essentially assuming
+
+ align:start position:0%
+function is you're essentially assuming
+ 
+
+ align:start position:0%
+function is you're essentially assuming
+the system has had enough time to sample
+
+ align:start position:0%
+the system has had enough time to sample
+ 
+
+ align:start position:0%
+the system has had enough time to sample
+all its excitations so you essentially
+
+ align:start position:0%
+all its excitations so you essentially
+ 
+
+ align:start position:0%
+all its excitations so you essentially
+integrate over that Ensemble you
+
+ align:start position:0%
+integrate over that Ensemble you
+ 
+
+ align:start position:0%
+integrate over that Ensemble you
+integrate over all the excitations and
+
+ align:start position:0%
+integrate over all the excitations and
+ 
+
+ align:start position:0%
+integrate over all the excitations and
+you end up with the thermodynamic
+
+ align:start position:0%
+you end up with the thermodynamic
+ 
+
+ align:start position:0%
+you end up with the thermodynamic
+functions and the examples that I showed
+
+ align:start position:0%
+functions and the examples that I showed
+ 
+
+ align:start position:0%
+functions and the examples that I showed
+you with the cluster expansion were
+
+ align:start position:0%
+you with the cluster expansion were
+ 
+
+ align:start position:0%
+you with the cluster expansion were
+essentially examples like that so that
+
+ align:start position:0%
+essentially examples like that so that
+ 
+
+ align:start position:0%
+essentially examples like that so that
+part I would say for crystalline system
+
+ align:start position:0%
+part I would say for crystalline system
+ 
+
+ align:start position:0%
+part I would say for crystalline system
+is a solved problem it's not a trivial
+
+ align:start position:0%
+is a solved problem it's not a trivial
+ 
+
+ align:start position:0%
+is a solved problem it's not a trivial
+solution it's still a lot of work but
+
+ align:start position:0%
+solution it's still a lot of work but
+ 
+
+ align:start position:0%
+solution it's still a lot of work but
+it's essentially a solved problem um I
+
+ align:start position:0%
+it's essentially a solved problem um I
+ 
+
+ align:start position:0%
+it's essentially a solved problem um I
+would say most of
+
+ align:start position:0%
+would say most of
+ 
+
+ align:start position:0%
+would say most of
+the spatial problem is solved if you're
+
+ align:start position:0%
+the spatial problem is solved if you're
+ 
+
+ align:start position:0%
+the spatial problem is solved if you're
+going to deal with static properties
+
+ align:start position:0%
+going to deal with static properties
+ 
+
+ align:start position:0%
+going to deal with static properties
+static properties and things such as
+
+ align:start position:0%
+static properties and things such as
+ 
+
+ align:start position:0%
+static properties and things such as
+elastic Behavior
+
+ align:start position:0%
+elastic Behavior
+ 
+
+ align:start position:0%
+elastic Behavior
+uh you know you essentially cor grain
+
+ align:start position:0%
+uh you know you essentially cor grain
+ 
+
+ align:start position:0%
+uh you know you essentially cor grain
+fairly easily and end up with Continuum
+
+ align:start position:0%
+fairly easily and end up with Continuum
+ 
+
+ align:start position:0%
+fairly easily and end up with Continuum
+Theory um the real problem lies in you
+
+ align:start position:0%
+Theory um the real problem lies in you
+ 
+
+ align:start position:0%
+Theory um the real problem lies in you
+know what should have happens in between
+
+ align:start position:0%
+know what should have happens in between
+ 
+
+ align:start position:0%
+know what should have happens in between
+here um when when you want to keep some
+
+ align:start position:0%
+here um when when you want to keep some
+ 
+
+ align:start position:0%
+here um when when you want to keep some
+level of detail that's not Continuum or
+
+ align:start position:0%
+level of detail that's not Continuum or
+ 
+
+ align:start position:0%
+level of detail that's not Continuum or
+that's in the time axis not
+
+ align:start position:0%
+that's in the time axis not
+ 
+
+ align:start position:0%
+that's in the time axis not
+thermodynamic but you can't afford to
+
+ align:start position:0%
+thermodynamic but you can't afford to
+ 
+
+ align:start position:0%
+thermodynamic but you can't afford to
+stay all the way down at the atomistic
+
+ align:start position:0%
+stay all the way down at the atomistic
+ 
+
+ align:start position:0%
+stay all the way down at the atomistic
+scale and the scale of the electrons
+
+ align:start position:0%
+scale and the scale of the electrons
+ 
+
+ align:start position:0%
+scale and the scale of the electrons
+that's where um I think the real
+
+ align:start position:0%
+that's where um I think the real
+ 
+
+ align:start position:0%
+that's where um I think the real
+challenge
+
+ align:start position:0%
+challenge
+ 
+
+ align:start position:0%
+challenge
+exists and I'll tell you a little more
+
+ align:start position:0%
+exists and I'll tell you a little more
+ 
+
+ align:start position:0%
+exists and I'll tell you a little more
+about that
+
+ align:start position:0%
+about that
+ 
+
+ align:start position:0%
+about that
+um that's when you break your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+computer um so first I'm going to tell
+
+ align:start position:0%
+computer um so first I'm going to tell
+ 
+
+ align:start position:0%
+computer um so first I'm going to tell
+you there's obviously the Brute Force
+
+ align:start position:0%
+you there's obviously the Brute Force
+ 
+
+ align:start position:0%
+you there's obviously the Brute Force
+approaches um which is you know just
+
+ align:start position:0%
+approaches um which is you know just
+ 
+
+ align:start position:0%
+approaches um which is you know just
+throw more computer power at it and
+
+ align:start position:0%
+throw more computer power at it and
+ 
+
+ align:start position:0%
+throw more computer power at it and
+these days the way you do that is not
+
+ align:start position:0%
+these days the way you do that is not
+ 
+
+ align:start position:0%
+these days the way you do that is not
+buying faster computers you buy more of
+
+ align:start position:0%
+buying faster computers you buy more of
+ 
+
+ align:start position:0%
+buying faster computers you buy more of
+them so you have to parallel
+
+ align:start position:0%
+them so you have to parallel
+ 
+
+ align:start position:0%
+them so you have to parallel
+ize um parallelization over space is
+
+ align:start position:0%
+ize um parallelization over space is
+ 
+
+ align:start position:0%
+ize um parallelization over space is
+obviously the most obvious one if you
+
+ align:start position:0%
+obviously the most obvious one if you
+ 
+
+ align:start position:0%
+obviously the most obvious one if you
+have a really big system you can divide
+
+ align:start position:0%
+have a really big system you can divide
+ 
+
+ align:start position:0%
+have a really big system you can divide
+it in chunks
+
+ align:start position:0%
+it in chunks
+ 
+
+ align:start position:0%
+it in chunks
+okay you know you'd probably do it a
+
+ align:start position:0%
+okay you know you'd probably do it a
+ 
+
+ align:start position:0%
+okay you know you'd probably do it a
+little more systematic but you can
+
+ align:start position:0%
+little more systematic but you can
+ 
+
+ align:start position:0%
+little more systematic but you can
+divide it in chunks and give each chunk
+
+ align:start position:0%
+divide it in chunks and give each chunk
+ 
+
+ align:start position:0%
+divide it in chunks and give each chunk
+of atoms to a CPU you know CPU 1 CPU 2
+
+ align:start position:0%
+of atoms to a CPU you know CPU 1 CPU 2
+ 
+
+ align:start position:0%
+of atoms to a CPU you know CPU 1 CPU 2
+cpu3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Etc of course what
+
+ align:start position:0%
+Etc of course what
+ 
+
+ align:start position:0%
+Etc of course what
+that means that implies that the
+
+ align:start position:0%
+that means that implies that the
+ 
+
+ align:start position:0%
+that means that implies that the
+coupling between regions is not too
+
+ align:start position:0%
+coupling between regions is not too
+ 
+
+ align:start position:0%
+coupling between regions is not too
+severe because when you
+
+ align:start position:0%
+severe because when you
+ 
+
+ align:start position:0%
+severe because when you
+calculate uh say let's say you're doing
+
+ align:start position:0%
+calculate uh say let's say you're doing
+ 
+
+ align:start position:0%
+calculate uh say let's say you're doing
+molecular Dynamics when you calculate
+
+ align:start position:0%
+molecular Dynamics when you calculate
+ 
+
+ align:start position:0%
+molecular Dynamics when you calculate
+forces on the atoms in the region of
+
+ align:start position:0%
+forces on the atoms in the region of
+ 
+
+ align:start position:0%
+forces on the atoms in the region of
+cpu1 the atoms that live in the boundary
+
+ align:start position:0%
+cpu1 the atoms that live in the boundary
+ 
+
+ align:start position:0%
+cpu1 the atoms that live in the boundary
+layer of obviously
+
+ align:start position:0%
+layer of obviously
+ 
+
+ align:start position:0%
+layer of obviously
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+see see forces coming from atoms in the
+
+ align:start position:0%
+see see forces coming from atoms in the
+ 
+
+ align:start position:0%
+see see forces coming from atoms in the
+other regions so how efficient this this
+
+ align:start position:0%
+other regions so how efficient this this
+ 
+
+ align:start position:0%
+other regions so how efficient this this
+method is will depend very much on how
+
+ align:start position:0%
+method is will depend very much on how
+ 
+
+ align:start position:0%
+method is will depend very much on how
+well you can divide the sort of spatial
+
+ align:start position:0%
+well you can divide the sort of spatial
+ 
+
+ align:start position:0%
+well you can divide the sort of spatial
+origin of the forces and the energy so
+
+ align:start position:0%
+origin of the forces and the energy so
+ 
+
+ align:start position:0%
+origin of the forces and the energy so
+you can already see that this is going
+
+ align:start position:0%
+you can already see that this is going
+ 
+
+ align:start position:0%
+you can already see that this is going
+to be easier when you do it with pair
+
+ align:start position:0%
+to be easier when you do it with pair
+ 
+
+ align:start position:0%
+to be easier when you do it with pair
+potential say with pair potentials you
+
+ align:start position:0%
+potential say with pair potentials you
+ 
+
+ align:start position:0%
+potential say with pair potentials you
+can directly
+
+ align:start position:0%
+can directly
+ 
+
+ align:start position:0%
+can directly
+assign when you have the force on an
+
+ align:start position:0%
+assign when you have the force on an
+ 
+
+ align:start position:0%
+assign when you have the force on an
+atom the component coming from other
+
+ align:start position:0%
+atom the component coming from other
+ 
+
+ align:start position:0%
+atom the component coming from other
+atoms okay you can say the force on this
+
+ align:start position:0%
+atoms okay you can say the force on this
+ 
+
+ align:start position:0%
+atoms okay you can say the force on this
+atom comes you know have a piece coming
+
+ align:start position:0%
+atom comes you know have a piece coming
+ 
+
+ align:start position:0%
+atom comes you know have a piece coming
+from the potential with that atom the
+
+ align:start position:0%
+from the potential with that atom the
+ 
+
+ align:start position:0%
+from the potential with that atom the
+potential with that atom Etc um you'll
+
+ align:start position:0%
+potential with that atom Etc um you'll
+ 
+
+ align:start position:0%
+potential with that atom Etc um you'll
+see that in the standard approximation
+
+ align:start position:0%
+see that in the standard approximation
+ 
+
+ align:start position:0%
+see that in the standard approximation
+for example to Quantum Mechanics this is
+
+ align:start position:0%
+for example to Quantum Mechanics this is
+ 
+
+ align:start position:0%
+for example to Quantum Mechanics this is
+virtually
+
+ align:start position:0%
+virtually
+ 
+
+ align:start position:0%
+virtually
+impossible when we work with um block
+
+ align:start position:0%
+impossible when we work with um block
+ 
+
+ align:start position:0%
+impossible when we work with um block
+States those are by definition extended
+
+ align:start position:0%
+States those are by definition extended
+ 
+
+ align:start position:0%
+States those are by definition extended
+over the whole
+
+ align:start position:0%
+over the whole
+ 
+
+ align:start position:0%
+over the whole
+system okay so you can partition them
+
+ align:start position:0%
+system okay so you can partition them
+ 
+
+ align:start position:0%
+system okay so you can partition them
+over pieces of space so to do this sort
+
+ align:start position:0%
+over pieces of space so to do this sort
+ 
+
+ align:start position:0%
+over pieces of space so to do this sort
+of divide and coner approach with
+
+ align:start position:0%
+of divide and coner approach with
+ 
+
+ align:start position:0%
+of divide and coner approach with
+quantum mechanics um you have to go to
+
+ align:start position:0%
+quantum mechanics um you have to go to
+ 
+
+ align:start position:0%
+quantum mechanics um you have to go to
+Alternative approaches and these are
+
+ align:start position:0%
+Alternative approaches and these are
+ 
+
+ align:start position:0%
+Alternative approaches and these are
+either um people invest a lot of time
+
+ align:start position:0%
+either um people invest a lot of time
+ 
+
+ align:start position:0%
+either um people invest a lot of time
+now in just real space
+
+ align:start position:0%
+now in just real space
+ 
+
+ align:start position:0%
+now in just real space
+grids uh you know in theory the Shing
+
+ align:start position:0%
+grids uh you know in theory the Shing
+ 
+
+ align:start position:0%
+grids uh you know in theory the Shing
+equation is a partial differential
+
+ align:start position:0%
+equation is a partial differential
+ 
+
+ align:start position:0%
+equation is a partial differential
+equation like any other partial
+
+ align:start position:0%
+equation like any other partial
+ 
+
+ align:start position:0%
+equation like any other partial
+differential equation you should be able
+
+ align:start position:0%
+differential equation you should be able
+ 
+
+ align:start position:0%
+differential equation you should be able
+to solve it on a real space grid there
+
+ align:start position:0%
+to solve it on a real space grid there
+ 
+
+ align:start position:0%
+to solve it on a real space grid there
+Al all kinds of complications that arise
+
+ align:start position:0%
+Al all kinds of complications that arise
+ 
+
+ align:start position:0%
+Al all kinds of complications that arise
+but people are doing a lot there's a lot
+
+ align:start position:0%
+but people are doing a lot there's a lot
+ 
+
+ align:start position:0%
+but people are doing a lot there's a lot
+of work actually being done on that um
+
+ align:start position:0%
+of work actually being done on that um
+ 
+
+ align:start position:0%
+of work actually being done on that um
+the other is to go to localized basis
+
+ align:start position:0%
+the other is to go to localized basis
+ 
+
+ align:start position:0%
+the other is to go to localized basis
+sets and you know one year functions
+
+ align:start position:0%
+sets and you know one year functions
+ 
+
+ align:start position:0%
+sets and you know one year functions
+maximally localized one functions fall
+
+ align:start position:0%
+maximally localized one functions fall
+ 
+
+ align:start position:0%
+maximally localized one functions fall
+in that category and Professor marar is
+
+ align:start position:0%
+in that category and Professor marar is
+ 
+
+ align:start position:0%
+in that category and Professor marar is
+an expert on that almost essentially
+
+ align:start position:0%
+an expert on that almost essentially
+ 
+
+ align:start position:0%
+an expert on that almost essentially
+invented them um uh tight binding
+
+ align:start position:0%
+invented them um uh tight binding
+ 
+
+ align:start position:0%
+invented them um uh tight binding
+approaches so you'll see a lot of work
+
+ align:start position:0%
+approaches so you'll see a lot of work
+ 
+
+ align:start position:0%
+approaches so you'll see a lot of work
+being done on real space methods which
+
+ align:start position:0%
+being done on real space methods which
+ 
+
+ align:start position:0%
+being done on real space methods which
+is in essence directed largely toward
+
+ align:start position:0%
+is in essence directed largely toward
+ 
+
+ align:start position:0%
+is in essence directed largely toward
+this sort of divide and conquer approach
+
+ align:start position:0%
+this sort of divide and conquer approach
+ 
+
+ align:start position:0%
+this sort of divide and conquer approach
+if you can go real space in quantum
+
+ align:start position:0%
+if you can go real space in quantum
+ 
+
+ align:start position:0%
+if you can go real space in quantum
+mechanics you can um divide space up so
+
+ align:start position:0%
+mechanics you can um divide space up so
+ 
+
+ align:start position:0%
+mechanics you can um divide space up so
+space is maybe in the end not the
+
+ align:start position:0%
+space is maybe in the end not the
+ 
+
+ align:start position:0%
+space is maybe in the end not the
+biggest problem we have to deal with um
+
+ align:start position:0%
+biggest problem we have to deal with um
+ 
+
+ align:start position:0%
+biggest problem we have to deal with um
+time is a much harder one because um how
+
+ align:start position:0%
+time is a much harder one because um how
+ 
+
+ align:start position:0%
+time is a much harder one because um how
+do you paralyze over time time is by
+
+ align:start position:0%
+do you paralyze over time time is by
+ 
+
+ align:start position:0%
+do you paralyze over time time is by
+nature sequential
+
+ align:start position:0%
+nature sequential
+ 
+
+ align:start position:0%
+nature sequential
+um so it's really hard to do
+
+ align:start position:0%
+um so it's really hard to do
+ 
+
+ align:start position:0%
+um so it's really hard to do
+something um that's in the future when
+
+ align:start position:0%
+something um that's in the future when
+ 
+
+ align:start position:0%
+something um that's in the future when
+you don't know the present yet um but
+
+ align:start position:0%
+you don't know the present yet um but
+ 
+
+ align:start position:0%
+you don't know the present yet um but
+you'll see in a second uh or not in a
+
+ align:start position:0%
+you'll see in a second uh or not in a
+ 
+
+ align:start position:0%
+you'll see in a second uh or not in a
+second a little more than a second but
+
+ align:start position:0%
+second a little more than a second but
+ 
+
+ align:start position:0%
+second a little more than a second but
+later in the lecture there are some
+
+ align:start position:0%
+later in the lecture there are some
+ 
+
+ align:start position:0%
+later in the lecture there are some
+approaches to paralyzing time but
+
+ align:start position:0%
+approaches to paralyzing time but
+ 
+
+ align:start position:0%
+approaches to paralyzing time but
+they're all I would say much more
+
+ align:start position:0%
+they're all I would say much more
+ 
+
+ align:start position:0%
+they're all I would say much more
+limited in scope um than um than the
+
+ align:start position:0%
+limited in scope um than um than the
+ 
+
+ align:start position:0%
+limited in scope um than um than the
+methods for paralyzing over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space so you see time will be the big
+
+ align:start position:0%
+space so you see time will be the big
+ 
+
+ align:start position:0%
+space so you see time will be the big
+problem time time is easier to deal with
+
+ align:start position:0%
+problem time time is easier to deal with
+ 
+
+ align:start position:0%
+problem time time is easier to deal with
+when it's either short or very long
+
+ align:start position:0%
+when it's either short or very long
+ 
+
+ align:start position:0%
+when it's either short or very long
+because when it's very long you
+
+ align:start position:0%
+because when it's very long you
+ 
+
+ align:start position:0%
+because when it's very long you
+essentially integrate it away but in
+
+ align:start position:0%
+essentially integrate it away but in
+ 
+
+ align:start position:0%
+essentially integrate it away but in
+between is where it uh tends to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+harder so let me give you sort of a
+
+ align:start position:0%
+harder so let me give you sort of a
+ 
+
+ align:start position:0%
+harder so let me give you sort of a
+couple of examples
+
+ align:start position:0%
+couple of examples
+ 
+
+ align:start position:0%
+couple of examples
+of ideas that have been kicked around
+
+ align:start position:0%
+of ideas that have been kicked around
+ 
+
+ align:start position:0%
+of ideas that have been kicked around
+for uh Co graining space and then I'll
+
+ align:start position:0%
+for uh Co graining space and then I'll
+ 
+
+ align:start position:0%
+for uh Co graining space and then I'll
+say a little more about the time and and
+
+ align:start position:0%
+say a little more about the time and and
+ 
+
+ align:start position:0%
+say a little more about the time and and
+with time comes temperature problem so
+
+ align:start position:0%
+with time comes temperature problem so
+ 
+
+ align:start position:0%
+with time comes temperature problem so
+you know you could imagine if you
+
+ align:start position:0%
+you know you could imagine if you
+ 
+
+ align:start position:0%
+you know you could imagine if you
+if you do an impurity calculation so you
+
+ align:start position:0%
+if you do an impurity calculation so you
+ 
+
+ align:start position:0%
+if you do an impurity calculation so you
+know you take a sort of Crystal of these
+
+ align:start position:0%
+know you take a sort of Crystal of these
+ 
+
+ align:start position:0%
+know you take a sort of Crystal of these
+bluish atoms and you stick a big red
+
+ align:start position:0%
+bluish atoms and you stick a big red
+ 
+
+ align:start position:0%
+bluish atoms and you stick a big red
+atom in you you want to calculate the
+
+ align:start position:0%
+atom in you you want to calculate the
+ 
+
+ align:start position:0%
+atom in you you want to calculate the
+energy of that with quantum mechanics
+
+ align:start position:0%
+energy of that with quantum mechanics
+ 
+
+ align:start position:0%
+energy of that with quantum mechanics
+well you know those NE those shells
+
+ align:start position:0%
+well you know those NE those shells
+ 
+
+ align:start position:0%
+well you know those NE those shells
+around the red atom kind of relax a lot
+
+ align:start position:0%
+around the red atom kind of relax a lot
+ 
+
+ align:start position:0%
+around the red atom kind of relax a lot
+and then as you sort of go further uh
+
+ align:start position:0%
+and then as you sort of go further uh
+ 
+
+ align:start position:0%
+and then as you sort of go further uh
+this is largely an elastic problem you
+
+ align:start position:0%
+this is largely an elastic problem you
+ 
+
+ align:start position:0%
+this is largely an elastic problem you
+know you've put a ball in a hole that's
+
+ align:start position:0%
+know you've put a ball in a hole that's
+ 
+
+ align:start position:0%
+know you've put a ball in a hole that's
+too small and sort of the system relaxes
+
+ align:start position:0%
+too small and sort of the system relaxes
+ 
+
+ align:start position:0%
+too small and sort of the system relaxes
+around it um you know we tend to sort
+
+ align:start position:0%
+around it um you know we tend to sort
+ 
+
+ align:start position:0%
+around it um you know we tend to sort
+brute force that typically you know we
+
+ align:start position:0%
+brute force that typically you know we
+ 
+
+ align:start position:0%
+brute force that typically you know we
+do quantum mechanics on bigger and
+
+ align:start position:0%
+do quantum mechanics on bigger and
+ 
+
+ align:start position:0%
+do quantum mechanics on bigger and
+bigger unit cells but it's actually
+
+ align:start position:0%
+bigger unit cells but it's actually
+ 
+
+ align:start position:0%
+bigger unit cells but it's actually
+remarkable if you ever plot the
+
+ align:start position:0%
+remarkable if you ever plot the
+ 
+
+ align:start position:0%
+remarkable if you ever plot the
+displacements um this system be you'll
+
+ align:start position:0%
+displacements um this system be you'll
+ 
+
+ align:start position:0%
+displacements um this system be you'll
+find that these systems behaves
+
+ align:start position:0%
+find that these systems behaves
+ 
+
+ align:start position:0%
+find that these systems behaves
+remarkably elastically in very close
+
+ align:start position:0%
+remarkably elastically in very close
+ 
+
+ align:start position:0%
+remarkably elastically in very close
+shells to the defect already you know
+
+ align:start position:0%
+shells to the defect already you know
+ 
+
+ align:start position:0%
+shells to the defect already you know
+often from the second third neighbor you
+
+ align:start position:0%
+often from the second third neighbor you
+ 
+
+ align:start position:0%
+often from the second third neighbor you
+if you were to apply elasticity Theory
+
+ align:start position:0%
+if you were to apply elasticity Theory
+ 
+
+ align:start position:0%
+if you were to apply elasticity Theory
+you'd still get it right it's amazing
+
+ align:start position:0%
+you'd still get it right it's amazing
+ 
+
+ align:start position:0%
+you'd still get it right it's amazing
+how how applicable elasticity theory is
+
+ align:start position:0%
+how how applicable elasticity theory is
+ 
+
+ align:start position:0%
+how how applicable elasticity theory is
+at the atomistic level um so that gave
+
+ align:start position:0%
+at the atomistic level um so that gave
+ 
+
+ align:start position:0%
+at the atomistic level um so that gave
+people the idea that really when they do
+
+ align:start position:0%
+people the idea that really when they do
+ 
+
+ align:start position:0%
+people the idea that really when they do
+uh calculations with broken symmetry so
+
+ align:start position:0%
+uh calculations with broken symmetry so
+ 
+
+ align:start position:0%
+uh calculations with broken symmetry so
+around defects um maybe you really don't
+
+ align:start position:0%
+around defects um maybe you really don't
+ 
+
+ align:start position:0%
+around defects um maybe you really don't
+need all the atoms that we tend to put
+
+ align:start position:0%
+need all the atoms that we tend to put
+ 
+
+ align:start position:0%
+need all the atoms that we tend to put
+in uh
+
+ align:start position:0%
+in uh
+ 
+
+ align:start position:0%
+in uh
+calculations um so the the idea that's
+
+ align:start position:0%
+calculations um so the the idea that's
+ 
+
+ align:start position:0%
+calculations um so the the idea that's
+been kicked around is that um let's say
+
+ align:start position:0%
+been kicked around is that um let's say
+ 
+
+ align:start position:0%
+been kicked around is that um let's say
+that this is a piece of your
+
+ align:start position:0%
+that this is a piece of your
+ 
+
+ align:start position:0%
+that this is a piece of your
+simulation that's far away from whatever
+
+ align:start position:0%
+simulation that's far away from whatever
+ 
+
+ align:start position:0%
+simulation that's far away from whatever
+perturbation you're looking at you know
+
+ align:start position:0%
+perturbation you're looking at you know
+ 
+
+ align:start position:0%
+perturbation you're looking at you know
+maybe it's a grain boundary maybe it's a
+
+ align:start position:0%
+maybe it's a grain boundary maybe it's a
+ 
+
+ align:start position:0%
+maybe it's a grain boundary maybe it's a
+dislocation moving Maybe youve just uh
+
+ align:start position:0%
+dislocation moving Maybe youve just uh
+ 
+
+ align:start position:0%
+dislocation moving Maybe youve just uh
+you know did nuclear fusion somewhere in
+
+ align:start position:0%
+you know did nuclear fusion somewhere in
+ 
+
+ align:start position:0%
+you know did nuclear fusion somewhere in
+the material um but far away you believe
+
+ align:start position:0%
+the material um but far away you believe
+ 
+
+ align:start position:0%
+the material um but far away you believe
+that the system acts almost in a
+
+ align:start position:0%
+that the system acts almost in a
+ 
+
+ align:start position:0%
+that the system acts almost in a
+Continuum mode and so the idea is that
+
+ align:start position:0%
+Continuum mode and so the idea is that
+ 
+
+ align:start position:0%
+Continuum mode and so the idea is that
+what if I kept track only of these red
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atoms if I knew say let's say I'm
+
+ align:start position:0%
+atoms if I knew say let's say I'm
+ 
+
+ align:start position:0%
+atoms if I knew say let's say I'm
+looking at you know at energy of an
+
+ align:start position:0%
+looking at you know at energy of an
+ 
+
+ align:start position:0%
+looking at you know at energy of an
+elastic displacement or even not elastic
+
+ align:start position:0%
+elastic displacement or even not elastic
+ 
+
+ align:start position:0%
+elastic displacement or even not elastic
+um if I knew how these four atoms moved
+
+ align:start position:0%
+um if I knew how these four atoms moved
+ 
+
+ align:start position:0%
+um if I knew how these four atoms moved
+I could probably know something about
+
+ align:start position:0%
+I could probably know something about
+ 
+
+ align:start position:0%
+I could probably know something about
+how the other atoms move
+
+ align:start position:0%
+how the other atoms move
+ 
+
+ align:start position:0%
+how the other atoms move
+okay so I could interpolate say their
+
+ align:start position:0%
+okay so I could interpolate say their
+ 
+
+ align:start position:0%
+okay so I could interpolate say their
+displacement from the displacement of
+
+ align:start position:0%
+displacement from the displacement of
+ 
+
+ align:start position:0%
+displacement from the displacement of
+the corner atoms okay so what one thing
+
+ align:start position:0%
+the corner atoms okay so what one thing
+ 
+
+ align:start position:0%
+the corner atoms okay so what one thing
+you can do is say well if I know how
+
+ align:start position:0%
+you can do is say well if I know how
+ 
+
+ align:start position:0%
+you can do is say well if I know how
+these atoms move I assume that the
+
+ align:start position:0%
+these atoms move I assume that the
+ 
+
+ align:start position:0%
+these atoms move I assume that the
+energy of the atoms in between is
+
+ align:start position:0%
+energy of the atoms in between is
+ 
+
+ align:start position:0%
+energy of the atoms in between is
+essentially the same as an energy of a
+
+ align:start position:0%
+essentially the same as an energy of a
+ 
+
+ align:start position:0%
+essentially the same as an energy of a
+sort of macroscopic solid that I deform
+
+ align:start position:0%
+sort of macroscopic solid that I deform
+ 
+
+ align:start position:0%
+sort of macroscopic solid that I deform
+with that
+
+ align:start position:0%
+with that
+ 
+
+ align:start position:0%
+with that
+displacement uh you can do things in
+
+ align:start position:0%
+displacement uh you can do things in
+ 
+
+ align:start position:0%
+displacement uh you can do things in
+between you can actually sort of
+
+ align:start position:0%
+between you can actually sort of
+ 
+
+ align:start position:0%
+between you can actually sort of
+calculate the energy of that unit cell
+
+ align:start position:0%
+calculate the energy of that unit cell
+ 
+
+ align:start position:0%
+calculate the energy of that unit cell
+as it's displaced
+
+ align:start position:0%
+as it's displaced
+ 
+
+ align:start position:0%
+as it's displaced
+but the whole idea is that essentially
+
+ align:start position:0%
+but the whole idea is that essentially
+ 
+
+ align:start position:0%
+but the whole idea is that essentially
+you only have to keep you start keeping
+
+ align:start position:0%
+you only have to keep you start keeping
+ 
+
+ align:start position:0%
+you only have to keep you start keeping
+only track of a limited number of atoms
+
+ align:start position:0%
+only track of a limited number of atoms
+ 
+
+ align:start position:0%
+only track of a limited number of atoms
+and you can think of these as nodes so
+
+ align:start position:0%
+and you can think of these as nodes so
+ 
+
+ align:start position:0%
+and you can think of these as nodes so
+these are called nodal atoms and what
+
+ align:start position:0%
+these are called nodal atoms and what
+ 
+
+ align:start position:0%
+these are called nodal atoms and what
+happens to all the atoms you removed you
+
+ align:start position:0%
+happens to all the atoms you removed you
+ 
+
+ align:start position:0%
+happens to all the atoms you removed you
+essentially get by interpolation and
+
+ align:start position:0%
+essentially get by interpolation and
+ 
+
+ align:start position:0%
+essentially get by interpolation and
+once you're happy with using elasticity
+
+ align:start position:0%
+once you're happy with using elasticity
+ 
+
+ align:start position:0%
+once you're happy with using elasticity
+Theory then essentially you know what
+
+ align:start position:0%
+Theory then essentially you know what
+ 
+
+ align:start position:0%
+Theory then essentially you know what
+the energy of that Cube how that changes
+
+ align:start position:0%
+the energy of that Cube how that changes
+ 
+
+ align:start position:0%
+the energy of that Cube how that changes
+as you change the Four
+
+ align:start position:0%
+as you change the Four
+ 
+
+ align:start position:0%
+as you change the Four
+Corners um typically people use TR
+
+ align:start position:0%
+Corners um typically people use TR
+ 
+
+ align:start position:0%
+Corners um typically people use TR
+triangles because people will tend to
+
+ align:start position:0%
+triangles because people will tend to
+ 
+
+ align:start position:0%
+triangles because people will tend to
+use triangular meshes but I want to give
+
+ align:start position:0%
+use triangular meshes but I want to give
+ 
+
+ align:start position:0%
+use triangular meshes but I want to give
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the the example with a square since it's
+
+ align:start position:0%
+the the example with a square since it's
+ 
+
+ align:start position:0%
+the the example with a square since it's
+a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simpler so this is essentially the idea
+
+ align:start position:0%
+simpler so this is essentially the idea
+ 
+
+ align:start position:0%
+simpler so this is essentially the idea
+of the Quasi Continuum method that you
+
+ align:start position:0%
+of the Quasi Continuum method that you
+ 
+
+ align:start position:0%
+of the Quasi Continuum method that you
+know let's say add
+
+ align:start position:0%
+know let's say add
+ 
+
+ align:start position:0%
+know let's say add
+here you have some perturbation
+
+ align:start position:0%
+here you have some perturbation
+ 
+
+ align:start position:0%
+here you have some perturbation
+something you want to study at there at
+
+ align:start position:0%
+something you want to study at there at
+ 
+
+ align:start position:0%
+something you want to study at there at
+the Mystic level as you go farther and
+
+ align:start position:0%
+the Mystic level as you go farther and
+ 
+
+ align:start position:0%
+the Mystic level as you go farther and
+farther away you want to cor grain more
+
+ align:start position:0%
+farther away you want to cor grain more
+ 
+
+ align:start position:0%
+farther away you want to cor grain more
+and more so essentially you want to keep
+
+ align:start position:0%
+and more so essentially you want to keep
+ 
+
+ align:start position:0%
+and more so essentially you want to keep
+less and less Nal atoms and get more and
+
+ align:start position:0%
+less and less Nal atoms and get more and
+ 
+
+ align:start position:0%
+less and less Nal atoms and get more and
+more information simply by interpolation
+
+ align:start position:0%
+more information simply by interpolation
+ 
+
+ align:start position:0%
+more information simply by interpolation
+so you could say this is Coors graining
+
+ align:start position:0%
+so you could say this is Coors graining
+ 
+
+ align:start position:0%
+so you could say this is Coors graining
+at the level of one out of four when
+
+ align:start position:0%
+at the level of one out of four when
+ 
+
+ align:start position:0%
+at the level of one out of four when
+you're here okay and then you have a few
+
+ align:start position:0%
+you're here okay and then you have a few
+ 
+
+ align:start position:0%
+you're here okay and then you have a few
+regions of that and then you co grain at
+
+ align:start position:0%
+regions of that and then you co grain at
+ 
+
+ align:start position:0%
+regions of that and then you co grain at
+a higher
+
+ align:start position:0%
+a higher
+ 
+
+ align:start position:0%
+a higher
+level okay so you keep say I should have
+
+ align:start position:0%
+level okay so you keep say I should have
+ 
+
+ align:start position:0%
+level okay so you keep say I should have
+removed so this should not be red this
+
+ align:start position:0%
+removed so this should not be red this
+ 
+
+ align:start position:0%
+removed so this should not be red this
+should be blue sorry so you only keep
+
+ align:start position:0%
+should be blue sorry so you only keep
+ 
+
+ align:start position:0%
+should be blue sorry so you only keep
+these four atoms and you sort of assume
+
+ align:start position:0%
+these four atoms and you sort of assume
+ 
+
+ align:start position:0%
+these four atoms and you sort of assume
+that that solid under goes a homogeneous
+
+ align:start position:0%
+that that solid under goes a homogeneous
+ 
+
+ align:start position:0%
+that that solid under goes a homogeneous
+deformation within that
+
+ align:start position:0%
+deformation within that
+ 
+
+ align:start position:0%
+deformation within that
+box um what you see is that you know
+
+ align:start position:0%
+box um what you see is that you know
+ 
+
+ align:start position:0%
+box um what you see is that you know
+somewhere in this limit you're going to
+
+ align:start position:0%
+somewhere in this limit you're going to
+ 
+
+ align:start position:0%
+somewhere in this limit you're going to
+end up with finite element approaches
+
+ align:start position:0%
+end up with finite element approaches
+ 
+
+ align:start position:0%
+end up with finite element approaches
+where essentially you do Continuum
+
+ align:start position:0%
+where essentially you do Continuum
+ 
+
+ align:start position:0%
+where essentially you do Continuum
+Theory and you essentially say that you
+
+ align:start position:0%
+Theory and you essentially say that you
+ 
+
+ align:start position:0%
+Theory and you essentially say that you
+know if I know some displacements of
+
+ align:start position:0%
+know if I know some displacements of
+ 
+
+ align:start position:0%
+know if I know some displacements of
+elements I know how that of the corner
+
+ align:start position:0%
+elements I know how that of the corner
+ 
+
+ align:start position:0%
+elements I know how that of the corner
+points the vertices of elements I know
+
+ align:start position:0%
+points the vertices of elements I know
+ 
+
+ align:start position:0%
+points the vertices of elements I know
+how that element deforms okay so what
+
+ align:start position:0%
+how that element deforms okay so what
+ 
+
+ align:start position:0%
+how that element deforms okay so what
+you have is essentially a sort of
+
+ align:start position:0%
+you have is essentially a sort of
+ 
+
+ align:start position:0%
+you have is essentially a sort of
+continuous transition here in cor
+
+ align:start position:0%
+continuous transition here in cor
+ 
+
+ align:start position:0%
+continuous transition here in cor
+graining from atomistic Behavior to a
+
+ align:start position:0%
+graining from atomistic Behavior to a
+ 
+
+ align:start position:0%
+graining from atomistic Behavior to a
+finite element approach and people have
+
+ align:start position:0%
+finite element approach and people have
+ 
+
+ align:start position:0%
+finite element approach and people have
+put that together and this is called a
+
+ align:start position:0%
+put that together and this is called a
+ 
+
+ align:start position:0%
+put that together and this is called a
+quasi Continuum approach you know this
+
+ align:start position:0%
+quasi Continuum approach you know this
+ 
+
+ align:start position:0%
+quasi Continuum approach you know this
+is sort of a pictorial version of it
+
+ align:start position:0%
+is sort of a pictorial version of it
+ 
+
+ align:start position:0%
+is sort of a pictorial version of it
+near some let's say this is some
+
+ align:start position:0%
+near some let's say this is some
+ 
+
+ align:start position:0%
+near some let's say this is some
+boundary where you do something uh you
+
+ align:start position:0%
+boundary where you do something uh you
+ 
+
+ align:start position:0%
+boundary where you do something uh you
+have very fine resolution you could say
+
+ align:start position:0%
+have very fine resolution you could say
+ 
+
+ align:start position:0%
+have very fine resolution you could say
+the nodes of your finite element M are
+
+ align:start position:0%
+the nodes of your finite element M are
+ 
+
+ align:start position:0%
+the nodes of your finite element M are
+the atoms and then as you go farther and
+
+ align:start position:0%
+the atoms and then as you go farther and
+ 
+
+ align:start position:0%
+the atoms and then as you go farther and
+farther away you cor graen more and more
+
+ align:start position:0%
+farther away you cor graen more and more
+ 
+
+ align:start position:0%
+farther away you cor graen more and more
+and you keep less and less
+
+ align:start position:0%
+and you keep less and less
+ 
+
+ align:start position:0%
+and you keep less and less
+information um I'll give you a reference
+
+ align:start position:0%
+information um I'll give you a reference
+ 
+
+ align:start position:0%
+information um I'll give you a reference
+at the end but um uh the people
+
+ align:start position:0%
+at the end but um uh the people
+ 
+
+ align:start position:0%
+at the end but um uh the people
+developed this were essentially a fairly
+
+ align:start position:0%
+developed this were essentially a fairly
+ 
+
+ align:start position:0%
+developed this were essentially a fairly
+small group of people shenoi tadmore and
+
+ align:start position:0%
+small group of people shenoi tadmore and
+ 
+
+ align:start position:0%
+small group of people shenoi tadmore and
+Rob Phillips and Michael Ortiz at
+
+ align:start position:0%
+Rob Phillips and Michael Ortiz at
+ 
+
+ align:start position:0%
+Rob Phillips and Michael Ortiz at
+Caltech and there's some excellent
+
+ align:start position:0%
+Caltech and there's some excellent
+ 
+
+ align:start position:0%
+Caltech and there's some excellent
+review papers about this if you like to
+
+ align:start position:0%
+review papers about this if you like to
+ 
+
+ align:start position:0%
+review papers about this if you like to
+read more about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this it's it's now been fairly well
+
+ align:start position:0%
+this it's it's now been fairly well
+ 
+
+ align:start position:0%
+this it's it's now been fairly well
+implemented these kind of approaches
+
+ align:start position:0%
+implemented these kind of approaches
+ 
+
+ align:start position:0%
+implemented these kind of approaches
+mainly with
+
+ align:start position:0%
+mainly with
+ 
+
+ align:start position:0%
+mainly with
+empirical energy methods um people have
+
+ align:start position:0%
+empirical energy methods um people have
+ 
+
+ align:start position:0%
+empirical energy methods um people have
+tried to implement it with quantum
+
+ align:start position:0%
+tried to implement it with quantum
+ 
+
+ align:start position:0%
+tried to implement it with quantum
+mechanics and some people have actually
+
+ align:start position:0%
+mechanics and some people have actually
+ 
+
+ align:start position:0%
+mechanics and some people have actually
+done it but it's not all that effective
+
+ align:start position:0%
+done it but it's not all that effective
+ 
+
+ align:start position:0%
+done it but it's not all that effective
+really because of the the it's extremely
+
+ align:start position:0%
+really because of the the it's extremely
+ 
+
+ align:start position:0%
+really because of the the it's extremely
+hard to couple the atomistic region when
+
+ align:start position:0%
+hard to couple the atomistic region when
+ 
+
+ align:start position:0%
+hard to couple the atomistic region when
+you where you do quantum mechanics to a
+
+ align:start position:0%
+you where you do quantum mechanics to a
+ 
+
+ align:start position:0%
+you where you do quantum mechanics to a
+sort of more coar grained region um but
+
+ align:start position:0%
+sort of more coar grained region um but
+ 
+
+ align:start position:0%
+sort of more coar grained region um but
+with potentials and with things like
+
+ align:start position:0%
+with potentials and with things like
+ 
+
+ align:start position:0%
+with potentials and with things like
+embeded atom method people have coupled
+
+ align:start position:0%
+embeded atom method people have coupled
+ 
+
+ align:start position:0%
+embeded atom method people have coupled
+these things fairly well together uh
+
+ align:start position:0%
+these things fairly well together uh
+ 
+
+ align:start position:0%
+these things fairly well together uh
+this is for example a grain boundary uh
+
+ align:start position:0%
+this is for example a grain boundary uh
+ 
+
+ align:start position:0%
+this is for example a grain boundary uh
+sorry a crack impinging on a grain
+
+ align:start position:0%
+sorry a crack impinging on a grain
+ 
+
+ align:start position:0%
+sorry a crack impinging on a grain
+boundary see this is a symmetric grain
+
+ align:start position:0%
+boundary see this is a symmetric grain
+ 
+
+ align:start position:0%
+boundary see this is a symmetric grain
+boundary and you have the crack in the
+
+ align:start position:0%
+boundary and you have the crack in the
+ 
+
+ align:start position:0%
+boundary and you have the crack in the
+middle there it uh comes in hits the
+
+ align:start position:0%
+middle there it uh comes in hits the
+ 
+
+ align:start position:0%
+middle there it uh comes in hits the
+grain boundary and essentially deflects
+
+ align:start position:0%
+grain boundary and essentially deflects
+ 
+
+ align:start position:0%
+grain boundary and essentially deflects
+in the grain boundary okay so that's a
+
+ align:start position:0%
+in the grain boundary okay so that's a
+ 
+
+ align:start position:0%
+in the grain boundary okay so that's a
+simulation done with quasi
+
+ align:start position:0%
+simulation done with quasi
+ 
+
+ align:start position:0%
+simulation done with quasi
+Continuum you know if you want to think
+
+ align:start position:0%
+Continuum you know if you want to think
+ 
+
+ align:start position:0%
+Continuum you know if you want to think
+about it what it really does for you
+
+ align:start position:0%
+about it what it really does for you
+ 
+
+ align:start position:0%
+about it what it really does for you
+quasi Continuum is that it's a way of
+
+ align:start position:0%
+quasi Continuum is that it's a way of
+ 
+
+ align:start position:0%
+quasi Continuum is that it's a way of
+getting the boundary conditions right on
+
+ align:start position:0%
+getting the boundary conditions right on
+ 
+
+ align:start position:0%
+getting the boundary conditions right on
+your atomistic simulation
+
+ align:start position:0%
+your atomistic simulation
+ 
+
+ align:start position:0%
+your atomistic simulation
+uh by slowly integrating essentially
+
+ align:start position:0%
+uh by slowly integrating essentially
+ 
+
+ align:start position:0%
+uh by slowly integrating essentially
+with a Continuum Theory um you first of
+
+ align:start position:0%
+with a Continuum Theory um you first of
+ 
+
+ align:start position:0%
+with a Continuum Theory um you first of
+all have adaptive your your um uh
+
+ align:start position:0%
+all have adaptive your your um uh
+ 
+
+ align:start position:0%
+all have adaptive your your um uh
+boundary conditions on your atomistic
+
+ align:start position:0%
+boundary conditions on your atomistic
+ 
+
+ align:start position:0%
+boundary conditions on your atomistic
+simulation change during the simulation
+
+ align:start position:0%
+simulation change during the simulation
+ 
+
+ align:start position:0%
+simulation change during the simulation
+and because you have a better embedding
+
+ align:start position:0%
+and because you have a better embedding
+ 
+
+ align:start position:0%
+and because you have a better embedding
+Theory you have a better Continuum
+
+ align:start position:0%
+Theory you have a better Continuum
+ 
+
+ align:start position:0%
+Theory you have a better Continuum
+Theory um they're sort of more
+
+ align:start position:0%
+Theory um they're sort of more
+ 
+
+ align:start position:0%
+Theory um they're sort of more
+appropriate and especially in mechanical
+
+ align:start position:0%
+appropriate and especially in mechanical
+ 
+
+ align:start position:0%
+appropriate and especially in mechanical
+problems that is very important uh to
+
+ align:start position:0%
+problems that is very important uh to
+ 
+
+ align:start position:0%
+problems that is very important uh to
+have the right elastic boundary
+
+ align:start position:0%
+have the right elastic boundary
+ 
+
+ align:start position:0%
+have the right elastic boundary
+conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so let me sort of position this for
+
+ align:start position:0%
+um so let me sort of position this for
+ 
+
+ align:start position:0%
+um so let me sort of position this for
+you uh to show you where we have the
+
+ align:start position:0%
+you uh to show you where we have the
+ 
+
+ align:start position:0%
+you uh to show you where we have the
+solution and where we still have
+
+ align:start position:0%
+solution and where we still have
+ 
+
+ align:start position:0%
+solution and where we still have
+significant problems you know I would
+
+ align:start position:0%
+significant problems you know I would
+ 
+
+ align:start position:0%
+significant problems you know I would
+essentially say when we work purely at a
+
+ align:start position:0%
+essentially say when we work purely at a
+ 
+
+ align:start position:0%
+essentially say when we work purely at a
+microscopic scale we have most things
+
+ align:start position:0%
+microscopic scale we have most things
+ 
+
+ align:start position:0%
+microscopic scale we have most things
+under control um you know we know well
+
+ align:start position:0%
+under control um you know we know well
+ 
+
+ align:start position:0%
+under control um you know we know well
+how to deal with the energetics we know
+
+ align:start position:0%
+how to deal with the energetics we know
+ 
+
+ align:start position:0%
+how to deal with the energetics we know
+fairly well how to deal with the
+
+ align:start position:0%
+fairly well how to deal with the
+ 
+
+ align:start position:0%
+fairly well how to deal with the
+Dynamics because for pretty much
+
+ align:start position:0%
+Dynamics because for pretty much
+ 
+
+ align:start position:0%
+Dynamics because for pretty much
+everything except things like hydrogen
+
+ align:start position:0%
+everything except things like hydrogen
+ 
+
+ align:start position:0%
+everything except things like hydrogen
+you can use Newtonian Dynamics even on
+
+ align:start position:0%
+you can use Newtonian Dynamics even on
+ 
+
+ align:start position:0%
+you can use Newtonian Dynamics even on
+the atomistic scale You could argue we
+
+ align:start position:0%
+the atomistic scale You could argue we
+ 
+
+ align:start position:0%
+the atomistic scale You could argue we
+don't really know how to deal well with
+
+ align:start position:0%
+don't really know how to deal well with
+ 
+
+ align:start position:0%
+don't really know how to deal well with
+electron Dynamics but that's another
+
+ align:start position:0%
+electron Dynamics but that's another
+ 
+
+ align:start position:0%
+electron Dynamics but that's another
+problem if you're willing to go all the
+
+ align:start position:0%
+problem if you're willing to go all the
+ 
+
+ align:start position:0%
+problem if you're willing to go all the
+way to the Continuum scale we also know
+
+ align:start position:0%
+way to the Continuum scale we also know
+ 
+
+ align:start position:0%
+way to the Continuum scale we also know
+the equations that describe matter it's
+
+ align:start position:0%
+the equations that describe matter it's
+ 
+
+ align:start position:0%
+the equations that describe matter it's
+essentially thermodynamics and
+
+ align:start position:0%
+essentially thermodynamics and
+ 
+
+ align:start position:0%
+essentially thermodynamics and
+elasticity you know and you could think
+
+ align:start position:0%
+elasticity you know and you could think
+ 
+
+ align:start position:0%
+elasticity you know and you could think
+of thermodynamics as the integrator of
+
+ align:start position:0%
+of thermodynamics as the integrator of
+ 
+
+ align:start position:0%
+of thermodynamics as the integrator of
+those um it's when we live at this
+
+ align:start position:0%
+those um it's when we live at this
+ 
+
+ align:start position:0%
+those um it's when we live at this
+inhomogeneous Co grain scale that we're
+
+ align:start position:0%
+inhomogeneous Co grain scale that we're
+ 
+
+ align:start position:0%
+inhomogeneous Co grain scale that we're
+really in trouble and I'll give you an
+
+ align:start position:0%
+really in trouble and I'll give you an
+ 
+
+ align:start position:0%
+really in trouble and I'll give you an
+example uh think of
+
+ align:start position:0%
+example uh think of
+ 
+
+ align:start position:0%
+example uh think of
+temperature in Continuum Theory
+
+ align:start position:0%
+temperature in Continuum Theory
+ 
+
+ align:start position:0%
+temperature in Continuum Theory
+temperature is a
+
+ align:start position:0%
+temperature is a
+ 
+
+ align:start position:0%
+temperature is a
+field um in a microscopic simulation
+
+ align:start position:0%
+field um in a microscopic simulation
+ 
+
+ align:start position:0%
+field um in a microscopic simulation
+it's kinetic energy of the
+
+ align:start position:0%
+it's kinetic energy of the
+ 
+
+ align:start position:0%
+it's kinetic energy of the
+atoms you can already see a problem of
+
+ align:start position:0%
+atoms you can already see a problem of
+ 
+
+ align:start position:0%
+atoms you can already see a problem of
+appear
+
+ align:start position:0%
+appear
+ 
+
+ align:start position:0%
+appear
+essentially as you inhomogeneously cor
+
+ align:start position:0%
+essentially as you inhomogeneously cor
+ 
+
+ align:start position:0%
+essentially as you inhomogeneously cor
+grain around an atomistic region that
+
+ align:start position:0%
+grain around an atomistic region that
+ 
+
+ align:start position:0%
+grain around an atomistic region that
+temperature has to evolve from being you
+
+ align:start position:0%
+temperature has to evolve from being you
+ 
+
+ align:start position:0%
+temperature has to evolve from being you
+know the kinetic energy of motion to a
+
+ align:start position:0%
+know the kinetic energy of motion to a
+ 
+
+ align:start position:0%
+know the kinetic energy of motion to a
+field and it's it's non tricky to know
+
+ align:start position:0%
+field and it's it's non tricky to know
+ 
+
+ align:start position:0%
+field and it's it's non tricky to know
+what you do in between I mean I know how
+
+ align:start position:0%
+what you do in between I mean I know how
+ 
+
+ align:start position:0%
+what you do in between I mean I know how
+to deal with temperature as a field I
+
+ align:start position:0%
+to deal with temperature as a field I
+ 
+
+ align:start position:0%
+to deal with temperature as a field I
+know how to deal with this kinetic
+
+ align:start position:0%
+know how to deal with this kinetic
+ 
+
+ align:start position:0%
+know how to deal with this kinetic
+energy but what is it in between what is
+
+ align:start position:0%
+energy but what is it in between what is
+ 
+
+ align:start position:0%
+energy but what is it in between what is
+it when you're say a factor of 10 cor
+
+ align:start position:0%
+it when you're say a factor of 10 cor
+ 
+
+ align:start position:0%
+it when you're say a factor of 10 cor
+grain so you've removed every 10th atom
+
+ align:start position:0%
+grain so you've removed every 10th atom
+ 
+
+ align:start position:0%
+grain so you've removed every 10th atom
+and I'm going to go a little deeper in
+
+ align:start position:0%
+and I'm going to go a little deeper in
+ 
+
+ align:start position:0%
+and I'm going to go a little deeper in
+some of these things but those are some
+
+ align:start position:0%
+some of these things but those are some
+ 
+
+ align:start position:0%
+some of these things but those are some
+of the problems we also don't know what
+
+ align:start position:0%
+of the problems we also don't know what
+ 
+
+ align:start position:0%
+of the problems we also don't know what
+the Dynamics here is at this
+
+ align:start position:0%
+the Dynamics here is at this
+ 
+
+ align:start position:0%
+the Dynamics here is at this
+scale um because think of you know how
+
+ align:start position:0%
+scale um because think of you know how
+ 
+
+ align:start position:0%
+scale um because think of you know how
+do you dissipate energy how do you
+
+ align:start position:0%
+do you dissipate energy how do you
+ 
+
+ align:start position:0%
+do you dissipate energy how do you
+dissipate energy in a microscopic
+
+ align:start position:0%
+dissipate energy in a microscopic
+ 
+
+ align:start position:0%
+dissipate energy in a microscopic
+system okay you dissipate it essentially
+
+ align:start position:0%
+system okay you dissipate it essentially
+ 
+
+ align:start position:0%
+system okay you dissipate it essentially
+by non-harmonic
+
+ align:start position:0%
+by non-harmonic
+ 
+
+ align:start position:0%
+by non-harmonic
+vibrations okay that's how you dissipate
+
+ align:start position:0%
+vibrations okay that's how you dissipate
+ 
+
+ align:start position:0%
+vibrations okay that's how you dissipate
+energy how do you dissipate it here
+
+ align:start position:0%
+energy how do you dissipate it here
+ 
+
+ align:start position:0%
+energy how do you dissipate it here
+actually you don't unless you put it in
+
+ align:start position:0%
+actually you don't unless you put it in
+ 
+
+ align:start position:0%
+actually you don't unless you put it in
+explicitly okay you in a perfectly
+
+ align:start position:0%
+explicitly okay you in a perfectly
+ 
+
+ align:start position:0%
+explicitly okay you in a perfectly
+elasticity Theory you you know you don't
+
+ align:start position:0%
+elasticity Theory you you know you don't
+ 
+
+ align:start position:0%
+elasticity Theory you you know you don't
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+dissipation so again energy dissipation
+
+ align:start position:0%
+dissipation so again energy dissipation
+ 
+
+ align:start position:0%
+dissipation so again energy dissipation
+is a big deal in inhomogeneously cor
+
+ align:start position:0%
+is a big deal in inhomogeneously cor
+ 
+
+ align:start position:0%
+is a big deal in inhomogeneously cor
+grain systems uh because the mechanism
+
+ align:start position:0%
+grain systems uh because the mechanism
+ 
+
+ align:start position:0%
+grain systems uh because the mechanism
+by which it happens at the atomistic and
+
+ align:start position:0%
+by which it happens at the atomistic and
+ 
+
+ align:start position:0%
+by which it happens at the atomistic and
+at the Continuum scale is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different um so quasi Continuum
+
+ align:start position:0%
+different um so quasi Continuum
+ 
+
+ align:start position:0%
+different um so quasi Continuum
+approaches have been extremely
+
+ align:start position:0%
+approaches have been extremely
+ 
+
+ align:start position:0%
+approaches have been extremely
+successful for elastic static properties
+
+ align:start position:0%
+successful for elastic static properties
+ 
+
+ align:start position:0%
+successful for elastic static properties
+and even nonlinear elastic problems um
+
+ align:start position:0%
+and even nonlinear elastic problems um
+ 
+
+ align:start position:0%
+and even nonlinear elastic problems um
+it's when people try to put temperature
+
+ align:start position:0%
+it's when people try to put temperature
+ 
+
+ align:start position:0%
+it's when people try to put temperature
+and Dynamics in that life gets a lot
+
+ align:start position:0%
+and Dynamics in that life gets a lot
+ 
+
+ align:start position:0%
+and Dynamics in that life gets a lot
+more complicated so there are
+
+ align:start position:0%
+more complicated so there are
+ 
+
+ align:start position:0%
+more complicated so there are
+essentially two approaches that have
+
+ align:start position:0%
+essentially two approaches that have
+ 
+
+ align:start position:0%
+essentially two approaches that have
+been suggested tried and both you know
+
+ align:start position:0%
+been suggested tried and both you know
+ 
+
+ align:start position:0%
+been suggested tried and both you know
+sort of seem reasonable but have
+
+ align:start position:0%
+sort of seem reasonable but have
+ 
+
+ align:start position:0%
+sort of seem reasonable but have
+significant failures um one is to Simply
+
+ align:start position:0%
+significant failures um one is to Simply
+ 
+
+ align:start position:0%
+significant failures um one is to Simply
+let's say you how you do how would you
+
+ align:start position:0%
+let's say you how you do how would you
+ 
+
+ align:start position:0%
+let's say you how you do how would you
+do molecular Dynamics on a CO grain
+
+ align:start position:0%
+do molecular Dynamics on a CO grain
+ 
+
+ align:start position:0%
+do molecular Dynamics on a CO grain
+system like this well you remember
+
+ align:start position:0%
+system like this well you remember
+ 
+
+ align:start position:0%
+system like this well you remember
+you've removed these
+
+ align:start position:0%
+you've removed these
+ 
+
+ align:start position:0%
+you've removed these
+atoms uh you could lump their Mass into
+
+ align:start position:0%
+atoms uh you could lump their Mass into
+ 
+
+ align:start position:0%
+atoms uh you could lump their Mass into
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+nodes so essentially the nodes of your
+
+ align:start position:0%
+nodes so essentially the nodes of your
+ 
+
+ align:start position:0%
+nodes so essentially the nodes of your
+mesh now become heavier and then you do
+
+ align:start position:0%
+mesh now become heavier and then you do
+ 
+
+ align:start position:0%
+mesh now become heavier and then you do
+MD on those okay the problem with that
+
+ align:start position:0%
+MD on those okay the problem with that
+ 
+
+ align:start position:0%
+MD on those okay the problem with that
+is that as you cor grade more and more
+
+ align:start position:0%
+is that as you cor grade more and more
+ 
+
+ align:start position:0%
+is that as you cor grade more and more
+you get the heavier and heavier notes
+
+ align:start position:0%
+you get the heavier and heavier notes
+ 
+
+ align:start position:0%
+you get the heavier and heavier notes
+and after a while they don't move
+
+ align:start position:0%
+and after a while they don't move
+ 
+
+ align:start position:0%
+and after a while they don't move
+anymore because if they have the same
+
+ align:start position:0%
+anymore because if they have the same
+ 
+
+ align:start position:0%
+anymore because if they have the same
+temperature okay mv^ s average over two
+
+ align:start position:0%
+temperature okay mv^ s average over two
+ 
+
+ align:start position:0%
+temperature okay mv^ s average over two
+is the temperature so if the same
+
+ align:start position:0%
+is the temperature so if the same
+ 
+
+ align:start position:0%
+is the temperature so if the same
+temperature the V becomes very
+
+ align:start position:0%
+temperature the V becomes very
+ 
+
+ align:start position:0%
+temperature the V becomes very
+small um the other one is a sort of uh
+
+ align:start position:0%
+small um the other one is a sort of uh
+ 
+
+ align:start position:0%
+small um the other one is a sort of uh
+often used approach to use um static
+
+ align:start position:0%
+often used approach to use um static
+ 
+
+ align:start position:0%
+often used approach to use um static
+optimizations but rather than say get
+
+ align:start position:0%
+optimizations but rather than say get
+ 
+
+ align:start position:0%
+optimizations but rather than say get
+all the the positions of these
+
+ align:start position:0%
+all the the positions of these
+ 
+
+ align:start position:0%
+all the the positions of these
+atoms rather than get them from the
+
+ align:start position:0%
+atoms rather than get them from the
+ 
+
+ align:start position:0%
+atoms rather than get them from the
+energy get them from minimizing the free
+
+ align:start position:0%
+energy get them from minimizing the free
+ 
+
+ align:start position:0%
+energy get them from minimizing the free
+energy so use say the force would be now
+
+ align:start position:0%
+energy so use say the force would be now
+ 
+
+ align:start position:0%
+energy so use say the force would be now
+the gradient of something like the free
+
+ align:start position:0%
+the gradient of something like the free
+ 
+
+ align:start position:0%
+the gradient of something like the free
+energy rather than the gradient of the
+
+ align:start position:0%
+energy rather than the gradient of the
+ 
+
+ align:start position:0%
+energy rather than the gradient of the
+energy so you have some amount of
+
+ align:start position:0%
+energy so you have some amount of
+ 
+
+ align:start position:0%
+energy so you have some amount of
+temperature effects in there then um but
+
+ align:start position:0%
+temperature effects in there then um but
+ 
+
+ align:start position:0%
+temperature effects in there then um but
+you don't truly have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dynamics so one thing this would do for
+
+ align:start position:0%
+Dynamics so one thing this would do for
+ 
+
+ align:start position:0%
+Dynamics so one thing this would do for
+you for example is you'd get the right
+
+ align:start position:0%
+you for example is you'd get the right
+ 
+
+ align:start position:0%
+you for example is you'd get the right
+Bond Lings and lce parameters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh I want to show you some other
+
+ align:start position:0%
+okay uh I want to show you some other
+ 
+
+ align:start position:0%
+okay uh I want to show you some other
+ideas that have been out there uh this
+
+ align:start position:0%
+ideas that have been out there uh this
+ 
+
+ align:start position:0%
+ideas that have been out there uh this
+is one that I've worked on for a short
+
+ align:start position:0%
+is one that I've worked on for a short
+ 
+
+ align:start position:0%
+is one that I've worked on for a short
+while um but the generic idea has really
+
+ align:start position:0%
+while um but the generic idea has really
+ 
+
+ align:start position:0%
+while um but the generic idea has really
+been out there in the community a long
+
+ align:start position:0%
+been out there in the community a long
+ 
+
+ align:start position:0%
+been out there in the community a long
+time and it's very similar to what we've
+
+ align:start position:0%
+time and it's very similar to what we've
+ 
+
+ align:start position:0%
+time and it's very similar to what we've
+done in the cor graining of time um the
+
+ align:start position:0%
+done in the cor graining of time um the
+ 
+
+ align:start position:0%
+done in the cor graining of time um the
+idea is essentially you know think of
+
+ align:start position:0%
+idea is essentially you know think of
+ 
+
+ align:start position:0%
+idea is essentially you know think of
+three atoms on a chain one two three
+
+ align:start position:0%
+three atoms on a chain one two three
+ 
+
+ align:start position:0%
+three atoms on a chain one two three
+there um what if you want to remove atom
+
+ align:start position:0%
+there um what if you want to remove atom
+ 
+
+ align:start position:0%
+there um what if you want to remove atom
+two and So Co grain and only keep one
+
+ align:start position:0%
+two and So Co grain and only keep one
+ 
+
+ align:start position:0%
+two and So Co grain and only keep one
+and three as the nodes the question
+
+ align:start position:0%
+and three as the nodes the question
+ 
+
+ align:start position:0%
+and three as the nodes the question
+really is what should your
+
+ align:start position:0%
+really is what should your
+ 
+
+ align:start position:0%
+really is what should your
+potential let's say you do this with
+
+ align:start position:0%
+potential let's say you do this with
+ 
+
+ align:start position:0%
+potential let's say you do this with
+potential don't even worry about quantum
+
+ align:start position:0%
+potential don't even worry about quantum
+ 
+
+ align:start position:0%
+potential don't even worry about quantum
+mechanics what should your potential
+
+ align:start position:0%
+mechanics what should your potential
+ 
+
+ align:start position:0%
+mechanics what should your potential
+between one and
+
+ align:start position:0%
+between one and
+ 
+
+ align:start position:0%
+between one and
+3B um so that they behave the same way
+
+ align:start position:0%
+3B um so that they behave the same way
+ 
+
+ align:start position:0%
+3B um so that they behave the same way
+as if two were there so you're going to
+
+ align:start position:0%
+as if two were there so you're going to
+ 
+
+ align:start position:0%
+as if two were there so you're going to
+take two out but you want to set up a
+
+ align:start position:0%
+take two out but you want to set up a
+ 
+
+ align:start position:0%
+take two out but you want to set up a
+potential between one and three that
+
+ align:start position:0%
+potential between one and three that
+ 
+
+ align:start position:0%
+potential between one and three that
+acts like if two were there well you
+
+ align:start position:0%
+acts like if two were there well you
+ 
+
+ align:start position:0%
+acts like if two were there well you
+could can get the solution again from
+
+ align:start position:0%
+could can get the solution again from
+ 
+
+ align:start position:0%
+could can get the solution again from
+thermodynamics essentially
+
+ align:start position:0%
+thermodynamics essentially
+ 
+
+ align:start position:0%
+thermodynamics essentially
+requiring that the partition function
+
+ align:start position:0%
+requiring that the partition function
+ 
+
+ align:start position:0%
+requiring that the partition function
+for the motion of 1 and three is the
+
+ align:start position:0%
+for the motion of 1 and three is the
+ 
+
+ align:start position:0%
+for the motion of 1 and three is the
+same with or without two there and
+
+ align:start position:0%
+same with or without two there and
+ 
+
+ align:start position:0%
+same with or without two there and
+that's essentially what's written out
+
+ align:start position:0%
+that's essentially what's written out
+ 
+
+ align:start position:0%
+that's essentially what's written out
+out here if you think of uh q's and PS
+
+ align:start position:0%
+out here if you think of uh q's and PS
+ 
+
+ align:start position:0%
+out here if you think of uh q's and PS
+for the coordinates remember Q's are
+
+ align:start position:0%
+for the coordinates remember Q's are
+ 
+
+ align:start position:0%
+for the coordinates remember Q's are
+spatial coordinates PS are um velocities
+
+ align:start position:0%
+spatial coordinates PS are um velocities
+ 
+
+ align:start position:0%
+spatial coordinates PS are um velocities
+essentially they're moment um
+
+ align:start position:0%
+essentially they're moment um
+ 
+
+ align:start position:0%
+essentially they're moment um
+essentially what you're saying is that
+
+ align:start position:0%
+essentially what you're saying is that
+ 
+
+ align:start position:0%
+essentially what you're saying is that
+the free energy of the hamiltonian with
+
+ align:start position:0%
+the free energy of the hamiltonian with
+ 
+
+ align:start position:0%
+the free energy of the hamiltonian with
+only q1 and Q3 so now you keep only the
+
+ align:start position:0%
+only q1 and Q3 so now you keep only the
+ 
+
+ align:start position:0%
+only q1 and Q3 so now you keep only the
+positions of one and three is obtained
+
+ align:start position:0%
+positions of one and three is obtained
+ 
+
+ align:start position:0%
+positions of one and three is obtained
+by integrating away the coordinates of
+
+ align:start position:0%
+by integrating away the coordinates of
+ 
+
+ align:start position:0%
+by integrating away the coordinates of
+two so you integrate over the position
+
+ align:start position:0%
+two so you integrate over the position
+ 
+
+ align:start position:0%
+two so you integrate over the position
+and over the momentum of Two And if the
+
+ align:start position:0%
+and over the momentum of Two And if the
+ 
+
+ align:start position:0%
+and over the momentum of Two And if the
+Motions are classical then the
+
+ align:start position:0%
+Motions are classical then the
+ 
+
+ align:start position:0%
+Motions are classical then the
+integration over the momentum is Trivial
+
+ align:start position:0%
+integration over the momentum is Trivial
+ 
+
+ align:start position:0%
+integration over the momentum is Trivial
+you know you always get the same factors
+
+ align:start position:0%
+you know you always get the same factors
+ 
+
+ align:start position:0%
+you know you always get the same factors
+from the momentum so it's really the
+
+ align:start position:0%
+from the momentum so it's really the
+ 
+
+ align:start position:0%
+from the momentum so it's really the
+integration over um the coordinates and
+
+ align:start position:0%
+integration over um the coordinates and
+ 
+
+ align:start position:0%
+integration over um the coordinates and
+so you know if you integrate this away
+
+ align:start position:0%
+so you know if you integrate this away
+ 
+
+ align:start position:0%
+so you know if you integrate this away
+then formally this integral has no Q2
+
+ align:start position:0%
+then formally this integral has no Q2
+ 
+
+ align:start position:0%
+then formally this integral has no Q2
+dependence by definition you've
+
+ align:start position:0%
+dependence by definition you've
+ 
+
+ align:start position:0%
+dependence by definition you've
+essentially integrated over all possible
+
+ align:start position:0%
+essentially integrated over all possible
+ 
+
+ align:start position:0%
+essentially integrated over all possible
+displacements of two to get the
+
+ align:start position:0%
+displacements of two to get the
+ 
+
+ align:start position:0%
+displacements of two to get the
+interaction between one and
+
+ align:start position:0%
+interaction between one and
+ 
+
+ align:start position:0%
+interaction between one and
+three um and so that then defines a
+
+ align:start position:0%
+three um and so that then defines a
+ 
+
+ align:start position:0%
+three um and so that then defines a
+potential just between one and three
+
+ align:start position:0%
+potential just between one and three
+ 
+
+ align:start position:0%
+potential just between one and three
+okay now there's all kinds of practical
+
+ align:start position:0%
+okay now there's all kinds of practical
+ 
+
+ align:start position:0%
+okay now there's all kinds of practical
+issues you can really only do this
+
+ align:start position:0%
+issues you can really only do this
+ 
+
+ align:start position:0%
+issues you can really only do this
+effectively if you have um interactions
+
+ align:start position:0%
+effectively if you have um interactions
+ 
+
+ align:start position:0%
+effectively if you have um interactions
+that are spatially limited because
+
+ align:start position:0%
+that are spatially limited because
+ 
+
+ align:start position:0%
+that are spatially limited because
+otherwise you really don't know over
+
+ align:start position:0%
+otherwise you really don't know over
+ 
+
+ align:start position:0%
+otherwise you really don't know over
+what you all have to integrate so this
+
+ align:start position:0%
+what you all have to integrate so this
+ 
+
+ align:start position:0%
+what you all have to integrate so this
+works great with pair
+
+ align:start position:0%
+works great with pair
+ 
+
+ align:start position:0%
+works great with pair
+potential okay so you know what does
+
+ align:start position:0%
+potential okay so you know what does
+ 
+
+ align:start position:0%
+potential okay so you know what does
+this physically mean it really means
+
+ align:start position:0%
+this physically mean it really means
+ 
+
+ align:start position:0%
+this physically mean it really means
+that um if you say displace atom three
+
+ align:start position:0%
+that um if you say displace atom three
+ 
+
+ align:start position:0%
+that um if you say displace atom three
+and you look at the force that it
+
+ align:start position:0%
+and you look at the force that it
+ 
+
+ align:start position:0%
+and you look at the force that it
+produces on atom one that you're looking
+
+ align:start position:0%
+produces on atom one that you're looking
+ 
+
+ align:start position:0%
+produces on atom one that you're looking
+at the kind of screening by atom 2 is
+
+ align:start position:0%
+at the kind of screening by atom 2 is
+ 
+
+ align:start position:0%
+at the kind of screening by atom 2 is
+included now you know in the real system
+
+ align:start position:0%
+included now you know in the real system
+ 
+
+ align:start position:0%
+included now you know in the real system
+atom 2 would sort of maybe screen that
+
+ align:start position:0%
+atom 2 would sort of maybe screen that
+ 
+
+ align:start position:0%
+atom 2 would sort of maybe screen that
+displacement away somewhat and that's
+
+ align:start position:0%
+displacement away somewhat and that's
+ 
+
+ align:start position:0%
+displacement away somewhat and that's
+not included and people have done this
+
+ align:start position:0%
+not included and people have done this
+ 
+
+ align:start position:0%
+not included and people have done this
+before like looking at interactions of
+
+ align:start position:0%
+before like looking at interactions of
+ 
+
+ align:start position:0%
+before like looking at interactions of
+you know when you look at interactions
+
+ align:start position:0%
+you know when you look at interactions
+ 
+
+ align:start position:0%
+you know when you look at interactions
+of ions in
+
+ align:start position:0%
+of ions in
+ 
+
+ align:start position:0%
+of ions in
+fluids okay the way to look at the
+
+ align:start position:0%
+fluids okay the way to look at the
+ 
+
+ align:start position:0%
+fluids okay the way to look at the
+interaction between two ions is by
+
+ align:start position:0%
+interaction between two ions is by
+ 
+
+ align:start position:0%
+interaction between two ions is by
+integrating over the possible
+
+ align:start position:0%
+integrating over the possible
+ 
+
+ align:start position:0%
+integrating over the possible
+displacements of all the other ones in
+
+ align:start position:0%
+displacements of all the other ones in
+ 
+
+ align:start position:0%
+displacements of all the other ones in
+between and that's how you end up with
+
+ align:start position:0%
+between and that's how you end up with
+ 
+
+ align:start position:0%
+between and that's how you end up with
+screening so this is sort of the
+
+ align:start position:0%
+screening so this is sort of the
+ 
+
+ align:start position:0%
+screening so this is sort of the
+screening equivalent um in displacement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fields um and what you geta is very much
+
+ align:start position:0%
+Fields um and what you geta is very much
+ 
+
+ align:start position:0%
+Fields um and what you geta is very much
+what you'd expected uh this is the
+
+ align:start position:0%
+what you'd expected uh this is the
+ 
+
+ align:start position:0%
+what you'd expected uh this is the
+potentials for different levels of Co
+
+ align:start position:0%
+potentials for different levels of Co
+ 
+
+ align:start position:0%
+potentials for different levels of Co
+grading in normalized distances so if
+
+ align:start position:0%
+grading in normalized distances so if
+ 
+
+ align:start position:0%
+grading in normalized distances so if
+the the length of the the the bond
+
+ align:start position:0%
+the the length of the the the bond
+ 
+
+ align:start position:0%
+the the length of the the the bond
+length is in is in units of one so this
+
+ align:start position:0%
+length is in is in units of one so this
+ 
+
+ align:start position:0%
+length is in is in units of one so this
+would be the normal potential if you cor
+
+ align:start position:0%
+would be the normal potential if you cor
+ 
+
+ align:start position:0%
+would be the normal potential if you cor
+green one level so you remove every
+
+ align:start position:0%
+green one level so you remove every
+ 
+
+ align:start position:0%
+green one level so you remove every
+other atom you actually end up with a
+
+ align:start position:0%
+other atom you actually end up with a
+ 
+
+ align:start position:0%
+other atom you actually end up with a
+potential that's twice the bond length
+
+ align:start position:0%
+potential that's twice the bond length
+ 
+
+ align:start position:0%
+potential that's twice the bond length
+because you remember you now you have
+
+ align:start position:0%
+because you remember you now you have
+ 
+
+ align:start position:0%
+because you remember you now you have
+one two atom one two three you've
+
+ align:start position:0%
+one two atom one two three you've
+ 
+
+ align:start position:0%
+one two atom one two three you've
+removed two so the equilibrium distance
+
+ align:start position:0%
+removed two so the equilibrium distance
+ 
+
+ align:start position:0%
+removed two so the equilibrium distance
+between one and three is about two times
+
+ align:start position:0%
+between one and three is about two times
+ 
+
+ align:start position:0%
+between one and three is about two times
+the bond
+
+ align:start position:0%
+the bond
+ 
+
+ align:start position:0%
+the bond
+length and you keep on Co graining and
+
+ align:start position:0%
+length and you keep on Co graining and
+ 
+
+ align:start position:0%
+length and you keep on Co graining and
+you end up with a potential that's four
+
+ align:start position:0%
+you end up with a potential that's four
+ 
+
+ align:start position:0%
+you end up with a potential that's four
+times the bond length 8 times the bond
+
+ align:start position:0%
+times the bond length 8 times the bond
+ 
+
+ align:start position:0%
+times the bond length 8 times the bond
+Ling okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it turns out that spatial Co graining
+
+ align:start position:0%
+um it turns out that spatial Co graining
+ 
+
+ align:start position:0%
+um it turns out that spatial Co graining
+um always uh tends to ca some kind of
+
+ align:start position:0%
+um always uh tends to ca some kind of
+ 
+
+ align:start position:0%
+um always uh tends to ca some kind of
+time cor that's a much more difficult
+
+ align:start position:0%
+time cor that's a much more difficult
+ 
+
+ align:start position:0%
+time cor that's a much more difficult
+issue that I want to say much um you
+
+ align:start position:0%
+issue that I want to say much um you
+ 
+
+ align:start position:0%
+issue that I want to say much um you
+know in 1D it's easy to remove atoms uh
+
+ align:start position:0%
+know in 1D it's easy to remove atoms uh
+ 
+
+ align:start position:0%
+know in 1D it's easy to remove atoms uh
+and add up so when you remove atom two
+
+ align:start position:0%
+and add up so when you remove atom two
+ 
+
+ align:start position:0%
+and add up so when you remove atom two
+that's between one and three you
+
+ align:start position:0%
+that's between one and three you
+ 
+
+ align:start position:0%
+that's between one and three you
+essentially that defines the potential
+
+ align:start position:0%
+essentially that defines the potential
+ 
+
+ align:start position:0%
+essentially that defines the potential
+between and three
+
+ align:start position:0%
+between and three
+ 
+
+ align:start position:0%
+between and three
+in 2D it's a little harder how you
+
+ align:start position:0%
+in 2D it's a little harder how you
+ 
+
+ align:start position:0%
+in 2D it's a little harder how you
+partition bonds but you can do all kinds
+
+ align:start position:0%
+partition bonds but you can do all kinds
+ 
+
+ align:start position:0%
+partition bonds but you can do all kinds
+of bond moving approximations this is a
+
+ align:start position:0%
+of bond moving approximations this is a
+ 
+
+ align:start position:0%
+of bond moving approximations this is a
+simple one in a triangular lce where if
+
+ align:start position:0%
+simple one in a triangular lce where if
+ 
+
+ align:start position:0%
+simple one in a triangular lce where if
+you um if you have a
+
+ align:start position:0%
+you um if you have a
+ 
+
+ align:start position:0%
+you um if you have a
+triangle you essentially want to remove
+
+ align:start position:0%
+triangle you essentially want to remove
+ 
+
+ align:start position:0%
+triangle you essentially want to remove
+these guys
+
+ align:start position:0%
+these guys
+ 
+
+ align:start position:0%
+these guys
+here and so you can Define some scheme
+
+ align:start position:0%
+here and so you can Define some scheme
+ 
+
+ align:start position:0%
+here and so you can Define some scheme
+by which you sort of collapse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um collapse the bonds onto these side es
+
+ align:start position:0%
+um collapse the bonds onto these side es
+ 
+
+ align:start position:0%
+um collapse the bonds onto these side es
+um you can also Define other schemes so
+
+ align:start position:0%
+um you can also Define other schemes so
+ 
+
+ align:start position:0%
+um you can also Define other schemes so
+here's an example of an inhomogeneously
+
+ align:start position:0%
+here's an example of an inhomogeneously
+ 
+
+ align:start position:0%
+here's an example of an inhomogeneously
+coar grain system in 2D where in this
+
+ align:start position:0%
+coar grain system in 2D where in this
+ 
+
+ align:start position:0%
+coar grain system in 2D where in this
+case it's fine at the edges and it's
+
+ align:start position:0%
+case it's fine at the edges and it's
+ 
+
+ align:start position:0%
+case it's fine at the edges and it's
+coarse in the middle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay um there are essentially two
+
+ align:start position:0%
+um okay um there are essentially two
+ 
+
+ align:start position:0%
+um okay um there are essentially two
+major problems with almost any Co
+
+ align:start position:0%
+major problems with almost any Co
+ 
+
+ align:start position:0%
+major problems with almost any Co
+graining scheme and the first one is the
+
+ align:start position:0%
+graining scheme and the first one is the
+ 
+
+ align:start position:0%
+graining scheme and the first one is the
+worst
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that um whenever you go from a you
+
+ align:start position:0%
+is that um whenever you go from a you
+ 
+
+ align:start position:0%
+is that um whenever you go from a you
+know let's say you're at the Mystic out
+
+ align:start position:0%
+know let's say you're at the Mystic out
+ 
+
+ align:start position:0%
+know let's say you're at the Mystic out
+here here you've Co grained level four
+
+ align:start position:0%
+here here you've Co grained level four
+ 
+
+ align:start position:0%
+here here you've Co grained level four
+Co grain another factor of four um you
+
+ align:start position:0%
+Co grain another factor of four um you
+ 
+
+ align:start position:0%
+Co grain another factor of four um you
+cannot sustain short wavelength phonons
+
+ align:start position:0%
+cannot sustain short wavelength phonons
+ 
+
+ align:start position:0%
+cannot sustain short wavelength phonons
+in the course regions you know let's say
+
+ align:start position:0%
+in the course regions you know let's say
+ 
+
+ align:start position:0%
+in the course regions you know let's say
+you have a phonon come in here that's
+
+ align:start position:0%
+you have a phonon come in here that's
+ 
+
+ align:start position:0%
+you have a phonon come in here that's
+um say has a wavelength uh like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh since here you only have these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nodes this is essentially the minimum
+
+ align:start position:0%
+nodes this is essentially the minimum
+ 
+
+ align:start position:0%
+nodes this is essentially the minimum
+wavelength you can have okay because the
+
+ align:start position:0%
+wavelength you can have okay because the
+ 
+
+ align:start position:0%
+wavelength you can have okay because the
+minimum bound distance so every time at
+
+ align:start position:0%
+minimum bound distance so every time at
+ 
+
+ align:start position:0%
+minimum bound distance so every time at
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+interface between a fine region and a
+
+ align:start position:0%
+interface between a fine region and a
+ 
+
+ align:start position:0%
+interface between a fine region and a
+corser region what happens is that
+
+ align:start position:0%
+corser region what happens is that
+ 
+
+ align:start position:0%
+corser region what happens is that
+there's a series of phonons the one with
+
+ align:start position:0%
+there's a series of phonons the one with
+ 
+
+ align:start position:0%
+there's a series of phonons the one with
+that have a wavelength that's too short
+
+ align:start position:0%
+that have a wavelength that's too short
+ 
+
+ align:start position:0%
+that have a wavelength that's too short
+get reflected back because they cannot
+
+ align:start position:0%
+get reflected back because they cannot
+ 
+
+ align:start position:0%
+get reflected back because they cannot
+not um go into the cors of
+
+ align:start position:0%
+not um go into the cors of
+ 
+
+ align:start position:0%
+not um go into the cors of
+region and ultimately you hit the
+
+ align:start position:0%
+region and ultimately you hit the
+ 
+
+ align:start position:0%
+region and ultimately you hit the
+Continuum region and you can't have any
+
+ align:start position:0%
+Continuum region and you can't have any
+ 
+
+ align:start position:0%
+Continuum region and you can't have any
+phons okay because there they should all
+
+ align:start position:0%
+phons okay because there they should all
+ 
+
+ align:start position:0%
+phons okay because there they should all
+be dissipated as
+
+ align:start position:0%
+be dissipated as
+ 
+
+ align:start position:0%
+be dissipated as
+temperature um so what does that cause
+
+ align:start position:0%
+temperature um so what does that cause
+ 
+
+ align:start position:0%
+temperature um so what does that cause
+well um if you look at dynamical
+
+ align:start position:0%
+well um if you look at dynamical
+ 
+
+ align:start position:0%
+well um if you look at dynamical
+processes um let's say you have a fine
+
+ align:start position:0%
+processes um let's say you have a fine
+ 
+
+ align:start position:0%
+processes um let's say you have a fine
+region in which you have some reaction
+
+ align:start position:0%
+region in which you have some reaction
+ 
+
+ align:start position:0%
+region in which you have some reaction
+that dissipates energy or that creates
+
+ align:start position:0%
+that dissipates energy or that creates
+ 
+
+ align:start position:0%
+that dissipates energy or that creates
+energy the way that that energy has to
+
+ align:start position:0%
+energy the way that that energy has to
+ 
+
+ align:start position:0%
+energy the way that that energy has to
+get out is by phon transmission okay you
+
+ align:start position:0%
+get out is by phon transmission okay you
+ 
+
+ align:start position:0%
+get out is by phon transmission okay you
+have to send lce vibrations out which
+
+ align:start position:0%
+have to send lce vibrations out which
+ 
+
+ align:start position:0%
+have to send lce vibrations out which
+through their anharmonicity have to get
+
+ align:start position:0%
+through their anharmonicity have to get
+ 
+
+ align:start position:0%
+through their anharmonicity have to get
+dissipated
+
+ align:start position:0%
+dissipated
+ 
+
+ align:start position:0%
+dissipated
+somewhere and so anytime you block phons
+
+ align:start position:0%
+somewhere and so anytime you block phons
+ 
+
+ align:start position:0%
+somewhere and so anytime you block phons
+you're essentially reducing the thermal
+
+ align:start position:0%
+you're essentially reducing the thermal
+ 
+
+ align:start position:0%
+you're essentially reducing the thermal
+conductivity of the system okay so this
+
+ align:start position:0%
+conductivity of the system okay so this
+ 
+
+ align:start position:0%
+conductivity of the system okay so this
+Co graining gives you lower thermal
+
+ align:start position:0%
+Co graining gives you lower thermal
+ 
+
+ align:start position:0%
+Co graining gives you lower thermal
+conductivity and I'll show you some
+
+ align:start position:0%
+conductivity and I'll show you some
+ 
+
+ align:start position:0%
+conductivity and I'll show you some
+examples in a second but you know it
+
+ align:start position:0%
+examples in a second but you know it
+ 
+
+ align:start position:0%
+examples in a second but you know it
+does worse things it's essentially
+
+ align:start position:0%
+does worse things it's essentially
+ 
+
+ align:start position:0%
+does worse things it's essentially
+elastically confining also your system
+
+ align:start position:0%
+elastically confining also your system
+ 
+
+ align:start position:0%
+elastically confining also your system
+somewhat but only in a dynamic sense so
+
+ align:start position:0%
+somewhat but only in a dynamic sense so
+ 
+
+ align:start position:0%
+somewhat but only in a dynamic sense so
+it's like you're having for
+
+ align:start position:0%
+it's like you're having for
+ 
+
+ align:start position:0%
+it's like you're having for
+certain dynamical modes a small unit
+
+ align:start position:0%
+certain dynamical modes a small unit
+ 
+
+ align:start position:0%
+certain dynamical modes a small unit
+cell and so that means that they reflect
+
+ align:start position:0%
+cell and so that means that they reflect
+ 
+
+ align:start position:0%
+cell and so that means that they reflect
+back of the co graining
+
+ align:start position:0%
+back of the co graining
+ 
+
+ align:start position:0%
+back of the co graining
+interface and they hit your your region
+
+ align:start position:0%
+interface and they hit your your region
+ 
+
+ align:start position:0%
+interface and they hit your your region
+of action fairly quickly as soon as
+
+ align:start position:0%
+of action fairly quickly as soon as
+ 
+
+ align:start position:0%
+of action fairly quickly as soon as
+they're reflected back okay um so it's
+
+ align:start position:0%
+they're reflected back okay um so it's
+ 
+
+ align:start position:0%
+they're reflected back okay um so it's
+exactly the same as
+
+ align:start position:0%
+exactly the same as
+ 
+
+ align:start position:0%
+exactly the same as
+putting you know your Dynamics in a very
+
+ align:start position:0%
+putting you know your Dynamics in a very
+ 
+
+ align:start position:0%
+putting you know your Dynamics in a very
+small box except that the size of the
+
+ align:start position:0%
+small box except that the size of the
+ 
+
+ align:start position:0%
+small box except that the size of the
+box that the system feels is different
+
+ align:start position:0%
+box that the system feels is different
+ 
+
+ align:start position:0%
+box that the system feels is different
+for different wavelengths okay but so a
+
+ align:start position:0%
+for different wavelengths okay but so a
+ 
+
+ align:start position:0%
+for different wavelengths okay but so a
+certain amount of elastic Behavior gets
+
+ align:start position:0%
+certain amount of elastic Behavior gets
+ 
+
+ align:start position:0%
+certain amount of elastic Behavior gets
+reflected back um fairly quickly so the
+
+ align:start position:0%
+reflected back um fairly quickly so the
+ 
+
+ align:start position:0%
+reflected back um fairly quickly so the
+phon on transmission prom is a serious
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one um and the phon transmission one is
+
+ align:start position:0%
+one um and the phon transmission one is
+ 
+
+ align:start position:0%
+one um and the phon transmission one is
+usually recognized very well uh there's
+
+ align:start position:0%
+usually recognized very well uh there's
+ 
+
+ align:start position:0%
+usually recognized very well uh there's
+one that's not as well recognized but is
+
+ align:start position:0%
+one that's not as well recognized but is
+ 
+
+ align:start position:0%
+one that's not as well recognized but is
+probably in the long term just a beer
+
+ align:start position:0%
+probably in the long term just a beer
+ 
+
+ align:start position:0%
+probably in the long term just a beer
+it's um anytime you remove degrees of
+
+ align:start position:0%
+it's um anytime you remove degrees of
+ 
+
+ align:start position:0%
+it's um anytime you remove degrees of
+freedom you remove
+
+ align:start position:0%
+freedom you remove
+ 
+
+ align:start position:0%
+freedom you remove
+entropy okay because entropy is
+
+ align:start position:0%
+entropy okay because entropy is
+ 
+
+ align:start position:0%
+entropy okay because entropy is
+essentially a count of your degrees of
+
+ align:start position:0%
+essentially a count of your degrees of
+ 
+
+ align:start position:0%
+essentially a count of your degrees of
+freedom um you may not worry about that
+
+ align:start position:0%
+freedom um you may not worry about that
+ 
+
+ align:start position:0%
+freedom um you may not worry about that
+but the problem is that if you do
+
+ align:start position:0%
+but the problem is that if you do
+ 
+
+ align:start position:0%
+but the problem is that if you do
+Dynamics your system will equilibrate
+
+ align:start position:0%
+Dynamics your system will equilibrate
+ 
+
+ align:start position:0%
+Dynamics your system will equilibrate
+along certain derivatives of the entropy
+
+ align:start position:0%
+along certain derivatives of the entropy
+ 
+
+ align:start position:0%
+along certain derivatives of the entropy
+and you'll get them wrong if you get the
+
+ align:start position:0%
+and you'll get them wrong if you get the
+ 
+
+ align:start position:0%
+and you'll get them wrong if you get the
+entropy wrong you'll get its derivatives
+
+ align:start position:0%
+entropy wrong you'll get its derivatives
+ 
+
+ align:start position:0%
+entropy wrong you'll get its derivatives
+wrong and some of the ones that you may
+
+ align:start position:0%
+wrong and some of the ones that you may
+ 
+
+ align:start position:0%
+wrong and some of the ones that you may
+worry about uh are heat capacity which
+
+ align:start position:0%
+worry about uh are heat capacity which
+ 
+
+ align:start position:0%
+worry about uh are heat capacity which
+is the temperature derivative of the
+
+ align:start position:0%
+is the temperature derivative of the
+ 
+
+ align:start position:0%
+is the temperature derivative of the
+entropy but also this one which you may
+
+ align:start position:0%
+entropy but also this one which you may
+ 
+
+ align:start position:0%
+entropy but also this one which you may
+worry a lot more about if you do
+
+ align:start position:0%
+worry a lot more about if you do
+ 
+
+ align:start position:0%
+worry a lot more about if you do
+mechanical Behavior thermal expansion
+
+ align:start position:0%
+mechanical Behavior thermal expansion
+ 
+
+ align:start position:0%
+mechanical Behavior thermal expansion
+which is the volume derivative of the
+
+ align:start position:0%
+which is the volume derivative of the
+ 
+
+ align:start position:0%
+which is the volume derivative of the
+entropy remember if remember your maxal
+
+ align:start position:0%
+entropy remember if remember your maxal
+ 
+
+ align:start position:0%
+entropy remember if remember your maxal
+relations d s DV is essentially dvdt up
+
+ align:start position:0%
+relations d s DV is essentially dvdt up
+ 
+
+ align:start position:0%
+relations d s DV is essentially dvdt up
+to some factors so how the entropy Chang
+
+ align:start position:0%
+to some factors so how the entropy Chang
+ 
+
+ align:start position:0%
+to some factors so how the entropy Chang
+with volume determines the thermal
+
+ align:start position:0%
+with volume determines the thermal
+ 
+
+ align:start position:0%
+with volume determines the thermal
+expansion and that's why if you actually
+
+ align:start position:0%
+expansion and that's why if you actually
+ 
+
+ align:start position:0%
+expansion and that's why if you actually
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+back the slide I showed
+
+ align:start position:0%
+back the slide I showed
+ 
+
+ align:start position:0%
+back the slide I showed
+you when we Define the effective
+
+ align:start position:0%
+you when we Define the effective
+ 
+
+ align:start position:0%
+you when we Define the effective
+potential between atoms 1 and
+
+ align:start position:0%
+potential between atoms 1 and
+ 
+
+ align:start position:0%
+potential between atoms 1 and
+three there's actually a potential and
+
+ align:start position:0%
+three there's actually a potential and
+ 
+
+ align:start position:0%
+three there's actually a potential and
+then there's a
+
+ align:start position:0%
+then there's a
+ 
+
+ align:start position:0%
+then there's a
+part that doesn't contain the
+
+ align:start position:0%
+part that doesn't contain the
+ 
+
+ align:start position:0%
+part that doesn't contain the
+coordinates of one and
+
+ align:start position:0%
+coordinates of one and
+ 
+
+ align:start position:0%
+coordinates of one and
+three and it's essentially the entropy
+
+ align:start position:0%
+three and it's essentially the entropy
+ 
+
+ align:start position:0%
+three and it's essentially the entropy
+you've lost by removing no too you have
+
+ align:start position:0%
+you've lost by removing no too you have
+ 
+
+ align:start position:0%
+you've lost by removing no too you have
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+actually keep that entropy in the system
+
+ align:start position:0%
+actually keep that entropy in the system
+ 
+
+ align:start position:0%
+actually keep that entropy in the system
+if you want to get the total
+
+ align:start position:0%
+if you want to get the total
+ 
+
+ align:start position:0%
+if you want to get the total
+thermodynamic quantities right okay it's
+
+ align:start position:0%
+thermodynamic quantities right okay it's
+ 
+
+ align:start position:0%
+thermodynamic quantities right okay it's
+sort of like you can think of this of
+
+ align:start position:0%
+sort of like you can think of this of
+ 
+
+ align:start position:0%
+sort of like you can think of this of
+the you you see that this is obvious if
+
+ align:start position:0%
+the you you see that this is obvious if
+ 
+
+ align:start position:0%
+the you you see that this is obvious if
+you take the complete limit of removing
+
+ align:start position:0%
+you take the complete limit of removing
+ 
+
+ align:start position:0%
+you take the complete limit of removing
+all nodes or going to one node then you
+
+ align:start position:0%
+all nodes or going to one node then you
+ 
+
+ align:start position:0%
+all nodes or going to one node then you
+end up with Continuum
+
+ align:start position:0%
+end up with Continuum
+ 
+
+ align:start position:0%
+end up with Continuum
+Behavior and the degrees of freedom of
+
+ align:start position:0%
+Behavior and the degrees of freedom of
+ 
+
+ align:start position:0%
+Behavior and the degrees of freedom of
+Continuum Behavior are not the entropy
+
+ align:start position:0%
+Continuum Behavior are not the entropy
+ 
+
+ align:start position:0%
+Continuum Behavior are not the entropy
+you've actually
+
+ align:start position:0%
+you've actually
+ 
+
+ align:start position:0%
+you've actually
+removed all the dynamic motion when you
+
+ align:start position:0%
+removed all the dynamic motion when you
+ 
+
+ align:start position:0%
+removed all the dynamic motion when you
+go to Continuum Theory so unless you've
+
+ align:start position:0%
+go to Continuum Theory so unless you've
+ 
+
+ align:start position:0%
+go to Continuum Theory so unless you've
+kept track of the degrees of freedom and
+
+ align:start position:0%
+kept track of the degrees of freedom and
+ 
+
+ align:start position:0%
+kept track of the degrees of freedom and
+the entropy that they include um you've
+
+ align:start position:0%
+the entropy that they include um you've
+ 
+
+ align:start position:0%
+the entropy that they include um you've
+lost all your information about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you do something like this
+
+ align:start position:0%
+so when you do something like this
+ 
+
+ align:start position:0%
+so when you do something like this
+here these will actually if you define
+
+ align:start position:0%
+here these will actually if you define
+ 
+
+ align:start position:0%
+here these will actually if you define
+the potentials at a given temperature
+
+ align:start position:0%
+the potentials at a given temperature
+ 
+
+ align:start position:0%
+the potentials at a given temperature
+because the renormalization of potential
+
+ align:start position:0%
+because the renormalization of potential
+ 
+
+ align:start position:0%
+because the renormalization of potential
+depends on temperature um if you define
+
+ align:start position:0%
+depends on temperature um if you define
+ 
+
+ align:start position:0%
+depends on temperature um if you define
+this at a given temperature and you run
+
+ align:start position:0%
+this at a given temperature and you run
+ 
+
+ align:start position:0%
+this at a given temperature and you run
+this at any other temperature these
+
+ align:start position:0%
+this at any other temperature these
+ 
+
+ align:start position:0%
+this at any other temperature these
+regions will have different thermal
+
+ align:start position:0%
+regions will have different thermal
+ 
+
+ align:start position:0%
+regions will have different thermal
+expansions and so you'll build up
+
+ align:start position:0%
+expansions and so you'll build up
+ 
+
+ align:start position:0%
+expansions and so you'll build up
+internal strain in your system without
+
+ align:start position:0%
+internal strain in your system without
+ 
+
+ align:start position:0%
+internal strain in your system without
+knowing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it ah
+
+ align:start position:0%
+it ah
+ 
+
+ align:start position:0%
+it ah
+I get a new color
+
+ align:start position:0%
+I get a new color
+ 
+
+ align:start position:0%
+I get a new color
+scheme there we go so if you take a
+
+ align:start position:0%
+scheme there we go so if you take a
+ 
+
+ align:start position:0%
+scheme there we go so if you take a
+simple pair potential model um these Co
+
+ align:start position:0%
+simple pair potential model um these Co
+ 
+
+ align:start position:0%
+simple pair potential model um these Co
+graining schemes work pretty well here's
+
+ align:start position:0%
+graining schemes work pretty well here's
+ 
+
+ align:start position:0%
+graining schemes work pretty well here's
+essentially a static property even
+
+ align:start position:0%
+essentially a static property even
+ 
+
+ align:start position:0%
+essentially a static property even
+though it has temperature in it but this
+
+ align:start position:0%
+though it has temperature in it but this
+ 
+
+ align:start position:0%
+though it has temperature in it but this
+is the strain in that 2D system versus
+
+ align:start position:0%
+is the strain in that 2D system versus
+ 
+
+ align:start position:0%
+is the strain in that 2D system versus
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+stress um and the the black curve
+
+ align:start position:0%
+stress um and the the black curve
+ 
+
+ align:start position:0%
+stress um and the the black curve
+underlying this is the full system so no
+
+ align:start position:0%
+underlying this is the full system so no
+ 
+
+ align:start position:0%
+underlying this is the full system so no
+Co graining and the red curve is that
+
+ align:start position:0%
+Co graining and the red curve is that
+ 
+
+ align:start position:0%
+Co graining and the red curve is that
+hor grain system that I showed you and
+
+ align:start position:0%
+hor grain system that I showed you and
+ 
+
+ align:start position:0%
+hor grain system that I showed you and
+you'll see even in the nonlinear part
+
+ align:start position:0%
+you'll see even in the nonlinear part
+ 
+
+ align:start position:0%
+you'll see even in the nonlinear part
+this does very well and it makes sense
+
+ align:start position:0%
+this does very well and it makes sense
+ 
+
+ align:start position:0%
+this does very well and it makes sense
+you know this kind of mechanical
+
+ align:start position:0%
+you know this kind of mechanical
+ 
+
+ align:start position:0%
+you know this kind of mechanical
+Behavior you know strain versus stress
+
+ align:start position:0%
+Behavior you know strain versus stress
+ 
+
+ align:start position:0%
+Behavior you know strain versus stress
+is largely dominated by the Potentials
+
+ align:start position:0%
+is largely dominated by the Potentials
+ 
+
+ align:start position:0%
+is largely dominated by the Potentials
+in these kind of solid system there's
+
+ align:start position:0%
+in these kind of solid system there's
+ 
+
+ align:start position:0%
+in these kind of solid system there's
+very little dynamical factors that play
+
+ align:start position:0%
+very little dynamical factors that play
+ 
+
+ align:start position:0%
+very little dynamical factors that play
+a role in it so as long as you normalize
+
+ align:start position:0%
+a role in it so as long as you normalize
+ 
+
+ align:start position:0%
+a role in it so as long as you normalize
+the potentials right you will get the
+
+ align:start position:0%
+the potentials right you will get the
+ 
+
+ align:start position:0%
+the potentials right you will get the
+stress strain relation right even in the
+
+ align:start position:0%
+stress strain relation right even in the
+ 
+
+ align:start position:0%
+stress strain relation right even in the
+nonlinear regime so that's not a big
+
+ align:start position:0%
+nonlinear regime so that's not a big
+ 
+
+ align:start position:0%
+nonlinear regime so that's not a big
+surprise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you keep track of the entropy right
+
+ align:start position:0%
+if you keep track of the entropy right
+ 
+
+ align:start position:0%
+if you keep track of the entropy right
+you'll get uh things like the heat
+
+ align:start position:0%
+you'll get uh things like the heat
+ 
+
+ align:start position:0%
+you'll get uh things like the heat
+capacities right uh this is the ratio
+
+ align:start position:0%
+capacities right uh this is the ratio
+ 
+
+ align:start position:0%
+capacities right uh this is the ratio
+between um the heat capacity in the
+
+ align:start position:0%
+between um the heat capacity in the
+ 
+
+ align:start position:0%
+between um the heat capacity in the
+nonhomogeneous system which is the cor
+
+ align:start position:0%
+nonhomogeneous system which is the cor
+ 
+
+ align:start position:0%
+nonhomogeneous system which is the cor
+grain system divided by the exact result
+
+ align:start position:0%
+grain system divided by the exact result
+ 
+
+ align:start position:0%
+grain system divided by the exact result
+you could say the heat capacity and the
+
+ align:start position:0%
+you could say the heat capacity and the
+ 
+
+ align:start position:0%
+you could say the heat capacity and the
+homogeneous it essentially oscillates
+
+ align:start position:0%
+homogeneous it essentially oscillates
+ 
+
+ align:start position:0%
+homogeneous it essentially oscillates
+around one U as a function of
+
+ align:start position:0%
+around one U as a function of
+ 
+
+ align:start position:0%
+around one U as a function of
+temperature so by construction you
+
+ align:start position:0%
+temperature so by construction you
+ 
+
+ align:start position:0%
+temperature so by construction you
+pretty much have that right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but so here it gets more interesting um
+
+ align:start position:0%
+but so here it gets more interesting um
+ 
+
+ align:start position:0%
+but so here it gets more interesting um
+if you look at heat
+
+ align:start position:0%
+if you look at heat
+ 
+
+ align:start position:0%
+if you look at heat
+conduction through a coar grained
+
+ align:start position:0%
+conduction through a coar grained
+ 
+
+ align:start position:0%
+conduction through a coar grained
+interface so let's say you're fine at
+
+ align:start position:0%
+interface so let's say you're fine at
+ 
+
+ align:start position:0%
+interface so let's say you're fine at
+this side these are let's say these are
+
+ align:start position:0%
+this side these are let's say these are
+ 
+
+ align:start position:0%
+this side these are let's say these are
+atoms and here we've
+
+ align:start position:0%
+atoms and here we've
+ 
+
+ align:start position:0%
+atoms and here we've
+removed uh a bunch of nodes we've Co
+
+ align:start position:0%
+removed uh a bunch of nodes we've Co
+ 
+
+ align:start position:0%
+removed uh a bunch of nodes we've Co
+grained and so you look at the heat
+
+ align:start position:0%
+grained and so you look at the heat
+ 
+
+ align:start position:0%
+grained and so you look at the heat
+conduction through this so you set up a
+
+ align:start position:0%
+conduction through this so you set up a
+ 
+
+ align:start position:0%
+conduction through this so you set up a
+temperature gradient and essentially
+
+ align:start position:0%
+temperature gradient and essentially
+ 
+
+ align:start position:0%
+temperature gradient and essentially
+look at the heat flux when you do
+
+ align:start position:0%
+look at the heat flux when you do
+ 
+
+ align:start position:0%
+look at the heat flux when you do
+Dynamics so what this is showing here is
+
+ align:start position:0%
+Dynamics so what this is showing here is
+ 
+
+ align:start position:0%
+Dynamics so what this is showing here is
+um the heat conduction the the heat
+
+ align:start position:0%
+um the heat conduction the the heat
+ 
+
+ align:start position:0%
+um the heat conduction the the heat
+conduction in the non-homogeneous system
+
+ align:start position:0%
+conduction in the non-homogeneous system
+ 
+
+ align:start position:0%
+conduction in the non-homogeneous system
+divide by the heat conduction in the
+
+ align:start position:0%
+divide by the heat conduction in the
+ 
+
+ align:start position:0%
+divide by the heat conduction in the
+homogeneous system and this is pretty
+
+ align:start position:0%
+homogeneous system and this is pretty
+ 
+
+ align:start position:0%
+homogeneous system and this is pretty
+much always lower than one so the
+
+ align:start position:0%
+much always lower than one so the
+ 
+
+ align:start position:0%
+much always lower than one so the
+non-homogeneous system has less heat
+
+ align:start position:0%
+non-homogeneous system has less heat
+ 
+
+ align:start position:0%
+non-homogeneous system has less heat
+conduction and the reason is you scatter
+
+ align:start position:0%
+conduction and the reason is you scatter
+ 
+
+ align:start position:0%
+conduction and the reason is you scatter
+phonons of this
+
+ align:start position:0%
+phonons of this
+ 
+
+ align:start position:0%
+phonons of this
+interface okay so here there's a certain
+
+ align:start position:0%
+interface okay so here there's a certain
+ 
+
+ align:start position:0%
+interface okay so here there's a certain
+amount of phonons that get reflected
+
+ align:start position:0%
+amount of phonons that get reflected
+ 
+
+ align:start position:0%
+amount of phonons that get reflected
+back but it's
+
+ align:start position:0%
+back but it's
+ 
+
+ align:start position:0%
+back but it's
+interesting if you show this here as a
+
+ align:start position:0%
+interesting if you show this here as a
+ 
+
+ align:start position:0%
+interesting if you show this here as a
+function of the length of the hom genous
+
+ align:start position:0%
+function of the length of the hom genous
+ 
+
+ align:start position:0%
+function of the length of the hom genous
+system okay you do better and better as
+
+ align:start position:0%
+system okay you do better and better as
+ 
+
+ align:start position:0%
+system okay you do better and better as
+this system gets bigger and that makes
+
+ align:start position:0%
+this system gets bigger and that makes
+ 
+
+ align:start position:0%
+this system gets bigger and that makes
+sense because then the interface becomes
+
+ align:start position:0%
+sense because then the interface becomes
+ 
+
+ align:start position:0%
+sense because then the interface becomes
+less and less important but you know
+
+ align:start position:0%
+less and less important but you know
+ 
+
+ align:start position:0%
+less and less important but you know
+look at the size here um you know to get
+
+ align:start position:0%
+look at the size here um you know to get
+ 
+
+ align:start position:0%
+look at the size here um you know to get
+up to sort of about one you need about
+
+ align:start position:0%
+up to sort of about one you need about
+ 
+
+ align:start position:0%
+up to sort of about one you need about
+1,500 atoms in the homogeneous
+
+ align:start position:0%
+1,500 atoms in the homogeneous
+ 
+
+ align:start position:0%
+1,500 atoms in the homogeneous
+region so this is a major problem with
+
+ align:start position:0%
+region so this is a major problem with
+ 
+
+ align:start position:0%
+region so this is a major problem with
+foun in general I think of all any
+
+ align:start position:0%
+foun in general I think of all any
+ 
+
+ align:start position:0%
+foun in general I think of all any
+atomistic level phenomena phonons are
+
+ align:start position:0%
+atomistic level phenomena phonons are
+ 
+
+ align:start position:0%
+atomistic level phenomena phonons are
+probably the ones that have the largest
+
+ align:start position:0%
+probably the ones that have the largest
+ 
+
+ align:start position:0%
+probably the ones that have the largest
+length scale the phonon mean free pad a
+
+ align:start position:0%
+length scale the phonon mean free pad a
+ 
+
+ align:start position:0%
+length scale the phonon mean free pad a
+low temperature is enormous it's can you
+
+ align:start position:0%
+low temperature is enormous it's can you
+ 
+
+ align:start position:0%
+low temperature is enormous it's can you
+know it's thousands of atoms far that
+
+ align:start position:0%
+know it's thousands of atoms far that
+ 
+
+ align:start position:0%
+know it's thousands of atoms far that
+means that phonons are usually the first
+
+ align:start position:0%
+means that phonons are usually the first
+ 
+
+ align:start position:0%
+means that phonons are usually the first
+thing to see something far away there's
+
+ align:start position:0%
+thing to see something far away there's
+ 
+
+ align:start position:0%
+thing to see something far away there's
+they're the first thing to see finite
+
+ align:start position:0%
+they're the first thing to see finite
+ 
+
+ align:start position:0%
+they're the first thing to see finite
+size effects there the first thing to
+
+ align:start position:0%
+size effects there the first thing to
+ 
+
+ align:start position:0%
+size effects there the first thing to
+see scattering of interfaces because you
+
+ align:start position:0%
+see scattering of interfaces because you
+ 
+
+ align:start position:0%
+see scattering of interfaces because you
+know the reason is that a lot of systems
+
+ align:start position:0%
+know the reason is that a lot of systems
+ 
+
+ align:start position:0%
+know the reason is that a lot of systems
+behave at low temperature fairly
+
+ align:start position:0%
+behave at low temperature fairly
+ 
+
+ align:start position:0%
+behave at low temperature fairly
+harmonic
+
+ align:start position:0%
+harmonic
+ 
+
+ align:start position:0%
+harmonic
+that means that these phonons just
+
+ align:start position:0%
+that means that these phonons just
+ 
+
+ align:start position:0%
+that means that these phonons just
+travel and travel and travel and their
+
+ align:start position:0%
+travel and travel and travel and their
+ 
+
+ align:start position:0%
+travel and travel and travel and their
+probability of being scattered is pretty
+
+ align:start position:0%
+probability of being scattered is pretty
+ 
+
+ align:start position:0%
+probability of being scattered is pretty
+low it's only as they start becoming
+
+ align:start position:0%
+low it's only as they start becoming
+ 
+
+ align:start position:0%
+low it's only as they start becoming
+inharmonic that they scatter um of
+
+ align:start position:0%
+inharmonic that they scatter um of
+ 
+
+ align:start position:0%
+inharmonic that they scatter um of
+course they could scatter off Disorder
+
+ align:start position:0%
+course they could scatter off Disorder
+ 
+
+ align:start position:0%
+course they could scatter off Disorder
+so if you have disordered systems that
+
+ align:start position:0%
+so if you have disordered systems that
+ 
+
+ align:start position:0%
+so if you have disordered systems that
+mean free path is a lot lower but phons
+
+ align:start position:0%
+mean free path is a lot lower but phons
+ 
+
+ align:start position:0%
+mean free path is a lot lower but phons
+you know often see hundreds of angstrom
+
+ align:start position:0%
+you know often see hundreds of angstrom
+ 
+
+ align:start position:0%
+you know often see hundreds of angstrom
+far essentially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here's the same result as a
+
+ align:start position:0%
+okay here's the same result as a
+ 
+
+ align:start position:0%
+okay here's the same result as a
+function of
+
+ align:start position:0%
+function of
+ 
+
+ align:start position:0%
+function of
+temperature so the heat capacity versus
+
+ align:start position:0%
+temperature so the heat capacity versus
+ 
+
+ align:start position:0%
+temperature so the heat capacity versus
+the normalized temperature uh this is
+
+ align:start position:0%
+the normalized temperature uh this is
+ 
+
+ align:start position:0%
+the normalized temperature uh this is
+the real system so the these are uh this
+
+ align:start position:0%
+the real system so the these are uh this
+ 
+
+ align:start position:0%
+the real system so the these are uh this
+is a fully atomistic level system and
+
+ align:start position:0%
+is a fully atomistic level system and
+ 
+
+ align:start position:0%
+is a fully atomistic level system and
+this is the um in red here is the
+
+ align:start position:0%
+this is the um in red here is the
+ 
+
+ align:start position:0%
+this is the um in red here is the
+partially coed grain system in this case
+
+ align:start position:0%
+partially coed grain system in this case
+ 
+
+ align:start position:0%
+partially coed grain system in this case
+with two interfaces and what you see is
+
+ align:start position:0%
+with two interfaces and what you see is
+ 
+
+ align:start position:0%
+with two interfaces and what you see is
+the co grain system always has lower
+
+ align:start position:0%
+the co grain system always has lower
+ 
+
+ align:start position:0%
+the co grain system always has lower
+heat conductance um they tend tend to
+
+ align:start position:0%
+heat conductance um they tend tend to
+ 
+
+ align:start position:0%
+heat conductance um they tend tend to
+come a little closer together at higher
+
+ align:start position:0%
+come a little closer together at higher
+ 
+
+ align:start position:0%
+come a little closer together at higher
+temperature and the reason is at higher
+
+ align:start position:0%
+temperature and the reason is at higher
+ 
+
+ align:start position:0%
+temperature and the reason is at higher
+temperature you have more inharmonicity
+
+ align:start position:0%
+temperature you have more inharmonicity
+ 
+
+ align:start position:0%
+temperature you have more inharmonicity
+so the phonons have a shorter mean-free
+
+ align:start position:0%
+so the phonons have a shorter mean-free
+ 
+
+ align:start position:0%
+so the phonons have a shorter mean-free
+PAAD so they tend to see you know they
+
+ align:start position:0%
+PAAD so they tend to see you know they
+ 
+
+ align:start position:0%
+PAAD so they tend to see you know they
+tend to homogenize easier and don't see
+
+ align:start position:0%
+tend to homogenize easier and don't see
+ 
+
+ align:start position:0%
+tend to homogenize easier and don't see
+the interfaces um as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much okay let me skip this okay um so
+
+ align:start position:0%
+much okay let me skip this okay um so
+ 
+
+ align:start position:0%
+much okay let me skip this okay um so
+that's some of the efforts going on in
+
+ align:start position:0%
+that's some of the efforts going on in
+ 
+
+ align:start position:0%
+that's some of the efforts going on in
+um Co graining over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space u you know I think if you if you
+
+ align:start position:0%
+space u you know I think if you if you
+ 
+
+ align:start position:0%
+space u you know I think if you if you
+if there's an area in which you want to
+
+ align:start position:0%
+if there's an area in which you want to
+ 
+
+ align:start position:0%
+if there's an area in which you want to
+work and have high impact this is
+
+ align:start position:0%
+work and have high impact this is
+ 
+
+ align:start position:0%
+work and have high impact this is
+probably one um I haven't seen a single
+
+ align:start position:0%
+probably one um I haven't seen a single
+ 
+
+ align:start position:0%
+probably one um I haven't seen a single
+good idea in this field in the last 10
+
+ align:start position:0%
+good idea in this field in the last 10
+ 
+
+ align:start position:0%
+good idea in this field in the last 10
+years I probably shouldn't say this on
+
+ align:start position:0%
+years I probably shouldn't say this on
+ 
+
+ align:start position:0%
+years I probably shouldn't say this on
+tape but um you know this is a field
+
+ align:start position:0%
+tape but um you know this is a field
+ 
+
+ align:start position:0%
+tape but um you know this is a field
+that where progress is desperately
+
+ align:start position:0%
+that where progress is desperately
+ 
+
+ align:start position:0%
+that where progress is desperately
+needed and it's a really really hard
+
+ align:start position:0%
+needed and it's a really really hard
+ 
+
+ align:start position:0%
+needed and it's a really really hard
+problem uh because you're essentially
+
+ align:start position:0%
+problem uh because you're essentially
+ 
+
+ align:start position:0%
+problem uh because you're essentially
+asking the question what is the Dynamics
+
+ align:start position:0%
+asking the question what is the Dynamics
+ 
+
+ align:start position:0%
+asking the question what is the Dynamics
+of partially Co grain
+
+ align:start position:0%
+of partially Co grain
+ 
+
+ align:start position:0%
+of partially Co grain
+systems and the pro the reason it's so
+
+ align:start position:0%
+systems and the pro the reason it's so
+ 
+
+ align:start position:0%
+systems and the pro the reason it's so
+hard that it's that it's a mixture of
+
+ align:start position:0%
+hard that it's that it's a mixture of
+ 
+
+ align:start position:0%
+hard that it's that it's a mixture of
+sort of Newtonian mechanics which is
+
+ align:start position:0%
+sort of Newtonian mechanics which is
+ 
+
+ align:start position:0%
+sort of Newtonian mechanics which is
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+conserving and dissipative
+
+ align:start position:0%
+conserving and dissipative
+ 
+
+ align:start position:0%
+conserving and dissipative
+Dynamics okay and you have to sort of
+
+ align:start position:0%
+Dynamics okay and you have to sort of
+ 
+
+ align:start position:0%
+Dynamics okay and you have to sort of
+and that how you mix those essentially
+
+ align:start position:0%
+and that how you mix those essentially
+ 
+
+ align:start position:0%
+and that how you mix those essentially
+depends on the frequency of your
+
+ align:start position:0%
+depends on the frequency of your
+ 
+
+ align:start position:0%
+depends on the frequency of your
+motion uh and that's why this is such a
+
+ align:start position:0%
+motion uh and that's why this is such a
+ 
+
+ align:start position:0%
+motion uh and that's why this is such a
+hard problem people have tried things
+
+ align:start position:0%
+hard problem people have tried things
+ 
+
+ align:start position:0%
+hard problem people have tried things
+where you know with boundaries that have
+
+ align:start position:0%
+where you know with boundaries that have
+ 
+
+ align:start position:0%
+where you know with boundaries that have
+complex impedance
+
+ align:start position:0%
+complex impedance
+ 
+
+ align:start position:0%
+complex impedance
+where essentially your transmission
+
+ align:start position:0%
+where essentially your transmission
+ 
+
+ align:start position:0%
+where essentially your transmission
+through the boundary is frequency
+
+ align:start position:0%
+through the boundary is frequency
+ 
+
+ align:start position:0%
+through the boundary is frequency
+dependent and you can see with that way
+
+ align:start position:0%
+dependent and you can see with that way
+ 
+
+ align:start position:0%
+dependent and you can see with that way
+you can definitely sort of tailor better
+
+ align:start position:0%
+you can definitely sort of tailor better
+ 
+
+ align:start position:0%
+you can definitely sort of tailor better
+what the phons do okay because now you
+
+ align:start position:0%
+what the phons do okay because now you
+ 
+
+ align:start position:0%
+what the phons do okay because now you
+have a much more complex interface
+
+ align:start position:0%
+have a much more complex interface
+ 
+
+ align:start position:0%
+have a much more complex interface
+literally to control you know the
+
+ align:start position:0%
+literally to control you know the
+ 
+
+ align:start position:0%
+literally to control you know the
+problem is that some of these things you
+
+ align:start position:0%
+problem is that some of these things you
+ 
+
+ align:start position:0%
+problem is that some of these things you
+can make work but they get so
+
+ align:start position:0%
+can make work but they get so
+ 
+
+ align:start position:0%
+can make work but they get so
+complicated to implement that they're NE
+
+ align:start position:0%
+complicated to implement that they're NE
+ 
+
+ align:start position:0%
+complicated to implement that they're NE
+not necessarily very practical other
+
+ align:start position:0%
+not necessarily very practical other
+ 
+
+ align:start position:0%
+not necessarily very practical other
+people do things with large overlapping
+
+ align:start position:0%
+people do things with large overlapping
+ 
+
+ align:start position:0%
+people do things with large overlapping
+regions you could say you know one way
+
+ align:start position:0%
+regions you could say you know one way
+ 
+
+ align:start position:0%
+regions you could say you know one way
+to Sol this problem is to not have these
+
+ align:start position:0%
+to Sol this problem is to not have these
+ 
+
+ align:start position:0%
+to Sol this problem is to not have these
+sharp boundaries between different
+
+ align:start position:0%
+sharp boundaries between different
+ 
+
+ align:start position:0%
+sharp boundaries between different
+levels of Co graining but overlap the
+
+ align:start position:0%
+levels of Co graining but overlap the
+ 
+
+ align:start position:0%
+levels of Co graining but overlap the
+two regions and slowly force that in the
+
+ align:start position:0%
+two regions and slowly force that in the
+ 
+
+ align:start position:0%
+two regions and slowly force that in the
+overlap region the solution say to the
+
+ align:start position:0%
+overlap region the solution say to the
+ 
+
+ align:start position:0%
+overlap region the solution say to the
+displacement fields are the same
+
+ align:start position:0%
+displacement fields are the same
+ 
+
+ align:start position:0%
+displacement fields are the same
+um okay the the next thing I want to
+
+ align:start position:0%
+um okay the the next thing I want to
+ 
+
+ align:start position:0%
+um okay the the next thing I want to
+talk about is U accelerating time um I
+
+ align:start position:0%
+talk about is U accelerating time um I
+ 
+
+ align:start position:0%
+talk about is U accelerating time um I
+said without Einstein but I think
+
+ align:start position:0%
+said without Einstein but I think
+ 
+
+ align:start position:0%
+said without Einstein but I think
+Einstein only could slow down time isn't
+
+ align:start position:0%
+Einstein only could slow down time isn't
+ 
+
+ align:start position:0%
+Einstein only could slow down time isn't
+that right I'm not sure we can
+
+ align:start position:0%
+that right I'm not sure we can
+ 
+
+ align:start position:0%
+that right I'm not sure we can
+accelerate I don't know
+
+ align:start position:0%
+accelerate I don't know
+ 
+
+ align:start position:0%
+accelerate I don't know
+um I don't know my theory of relativity
+
+ align:start position:0%
+um I don't know my theory of relativity
+ 
+
+ align:start position:0%
+um I don't know my theory of relativity
+too well anymore um I think I don't have
+
+ align:start position:0%
+too well anymore um I think I don't have
+ 
+
+ align:start position:0%
+too well anymore um I think I don't have
+to convince you you've done MD uh why
+
+ align:start position:0%
+to convince you you've done MD uh why
+ 
+
+ align:start position:0%
+to convince you you've done MD uh why
+you need to speed up time sometimes most
+
+ align:start position:0%
+you need to speed up time sometimes most
+ 
+
+ align:start position:0%
+you need to speed up time sometimes most
+of what I'm going to say comes out of
+
+ align:start position:0%
+of what I'm going to say comes out of
+ 
+
+ align:start position:0%
+of what I'm going to say comes out of
+this review article by Art voter uh
+
+ align:start position:0%
+this review article by Art voter uh
+ 
+
+ align:start position:0%
+this review article by Art voter uh
+who's probably been the guy to like work
+
+ align:start position:0%
+who's probably been the guy to like work
+ 
+
+ align:start position:0%
+who's probably been the guy to like work
+on accelerated MD methods uh and I'll
+
+ align:start position:0%
+on accelerated MD methods uh and I'll
+ 
+
+ align:start position:0%
+on accelerated MD methods uh and I'll
+give you the references again at the end
+
+ align:start position:0%
+give you the references again at the end
+ 
+
+ align:start position:0%
+give you the references again at the end
+this is a great review if you want to
+
+ align:start position:0%
+this is a great review if you want to
+ 
+
+ align:start position:0%
+this is a great review if you want to
+read about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this um cuz there's some really clever
+
+ align:start position:0%
+this um cuz there's some really clever
+ 
+
+ align:start position:0%
+this um cuz there's some really clever
+stuff in here that I think even if you
+
+ align:start position:0%
+stuff in here that I think even if you
+ 
+
+ align:start position:0%
+stuff in here that I think even if you
+don't want to do accelerate MD that you
+
+ align:start position:0%
+don't want to do accelerate MD that you
+ 
+
+ align:start position:0%
+don't want to do accelerate MD that you
+could use for for other um things um so
+
+ align:start position:0%
+could use for for other um things um so
+ 
+
+ align:start position:0%
+could use for for other um things um so
+first of all what's the problem um you
+
+ align:start position:0%
+first of all what's the problem um you
+ 
+
+ align:start position:0%
+first of all what's the problem um you
+know the problem is obviously that in
+
+ align:start position:0%
+know the problem is obviously that in
+ 
+
+ align:start position:0%
+know the problem is obviously that in
+most systems that are fairly U
+
+ align:start position:0%
+most systems that are fairly U
+ 
+
+ align:start position:0%
+most systems that are fairly U
+dense uh you have well defined minim in
+
+ align:start position:0%
+dense uh you have well defined minim in
+ 
+
+ align:start position:0%
+dense uh you have well defined minim in
+face space and often the barriers
+
+ align:start position:0%
+face space and often the barriers
+ 
+
+ align:start position:0%
+face space and often the barriers
+between them are pretty high so you
+
+ align:start position:0%
+between them are pretty high so you
+ 
+
+ align:start position:0%
+between them are pretty high so you
+sample the transitions between them at a
+
+ align:start position:0%
+sample the transitions between them at a
+ 
+
+ align:start position:0%
+sample the transitions between them at a
+very low rate uh the rate is essentially
+
+ align:start position:0%
+very low rate uh the rate is essentially
+ 
+
+ align:start position:0%
+very low rate uh the rate is essentially
+proportional to the exponential of the
+
+ align:start position:0%
+proportional to the exponential of the
+ 
+
+ align:start position:0%
+proportional to the exponential of the
+activation barrier between the Min and
+
+ align:start position:0%
+activation barrier between the Min and
+ 
+
+ align:start position:0%
+activation barrier between the Min and
+like I said in a lot of condensed
+
+ align:start position:0%
+like I said in a lot of condensed
+ 
+
+ align:start position:0%
+like I said in a lot of condensed
+systems those activation barriers uh are
+
+ align:start position:0%
+systems those activation barriers uh are
+ 
+
+ align:start position:0%
+systems those activation barriers uh are
+quite high and lead to time scales that
+
+ align:start position:0%
+quite high and lead to time scales that
+ 
+
+ align:start position:0%
+quite high and lead to time scales that
+you can't quite uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sample um so I'm going to talk briefly
+
+ align:start position:0%
+sample um so I'm going to talk briefly
+ 
+
+ align:start position:0%
+sample um so I'm going to talk briefly
+about three different methods to speed
+
+ align:start position:0%
+about three different methods to speed
+ 
+
+ align:start position:0%
+about three different methods to speed
+up time um parallel replica Dynamics
+
+ align:start position:0%
+up time um parallel replica Dynamics
+ 
+
+ align:start position:0%
+up time um parallel replica Dynamics
+hyper dynamics and temperature
+
+ align:start position:0%
+hyper dynamics and temperature
+ 
+
+ align:start position:0%
+hyper dynamics and temperature
+accelerated Dynamics
+
+ align:start position:0%
+accelerated Dynamics
+ 
+
+ align:start position:0%
+accelerated Dynamics
+um okay let me sort of quickly review
+
+ align:start position:0%
+um okay let me sort of quickly review
+ 
+
+ align:start position:0%
+um okay let me sort of quickly review
+what you would do with transition state
+
+ align:start position:0%
+what you would do with transition state
+ 
+
+ align:start position:0%
+what you would do with transition state
+Theory so if you knew the transitions
+
+ align:start position:0%
+Theory so if you knew the transitions
+ 
+
+ align:start position:0%
+Theory so if you knew the transitions
+that a system had to make like in a say
+
+ align:start position:0%
+that a system had to make like in a say
+ 
+
+ align:start position:0%
+that a system had to make like in a say
+a simple molecular reaction uh then you
+
+ align:start position:0%
+a simple molecular reaction uh then you
+ 
+
+ align:start position:0%
+a simple molecular reaction uh then you
+really don't need to do a simulation
+
+ align:start position:0%
+really don't need to do a simulation
+ 
+
+ align:start position:0%
+really don't need to do a simulation
+because if you know the activation
+
+ align:start position:0%
+because if you know the activation
+ 
+
+ align:start position:0%
+because if you know the activation
+barrier this quantity and you have some
+
+ align:start position:0%
+barrier this quantity and you have some
+ 
+
+ align:start position:0%
+barrier this quantity and you have some
+idea of the frequency with which the
+
+ align:start position:0%
+idea of the frequency with which the
+ 
+
+ align:start position:0%
+idea of the frequency with which the
+system tries to cross that barrier you
+
+ align:start position:0%
+system tries to cross that barrier you
+ 
+
+ align:start position:0%
+system tries to cross that barrier you
+know you can do Transition State Theory
+
+ align:start position:0%
+know you can do Transition State Theory
+ 
+
+ align:start position:0%
+know you can do Transition State Theory
+and essentially say that the The
+
+ align:start position:0%
+and essentially say that the The
+ 
+
+ align:start position:0%
+and essentially say that the The
+Crossing rate is going to be something
+
+ align:start position:0%
+Crossing rate is going to be something
+ 
+
+ align:start position:0%
+Crossing rate is going to be something
+like the attempt rate New Times the
+
+ align:start position:0%
+like the attempt rate New Times the
+ 
+
+ align:start position:0%
+like the attempt rate New Times the
+success rate which is this Bol Factor
+
+ align:start position:0%
+success rate which is this Bol Factor
+ 
+
+ align:start position:0%
+success rate which is this Bol Factor
+you know and the chemists among you and
+
+ align:start position:0%
+you know and the chemists among you and
+ 
+
+ align:start position:0%
+you know and the chemists among you and
+chemical Engineers know there's all
+
+ align:start position:0%
+chemical Engineers know there's all
+ 
+
+ align:start position:0%
+chemical Engineers know there's all
+kinds of approximations in there but
+
+ align:start position:0%
+kinds of approximations in there but
+ 
+
+ align:start position:0%
+kinds of approximations in there but
+none of them are particularly severe for
+
+ align:start position:0%
+none of them are particularly severe for
+ 
+
+ align:start position:0%
+none of them are particularly severe for
+most things to study like one
+
+ align:start position:0%
+most things to study like one
+ 
+
+ align:start position:0%
+most things to study like one
+approximation is this assumes you don't
+
+ align:start position:0%
+approximation is this assumes you don't
+ 
+
+ align:start position:0%
+approximation is this assumes you don't
+cross
+
+ align:start position:0%
+cross
+ 
+
+ align:start position:0%
+cross
+back uh often you know when you sit at
+
+ align:start position:0%
+back uh often you know when you sit at
+ 
+
+ align:start position:0%
+back uh often you know when you sit at
+the transition state you're essentially
+
+ align:start position:0%
+the transition state you're essentially
+ 
+
+ align:start position:0%
+the transition state you're essentially
+assuming that you fall over and don't
+
+ align:start position:0%
+assuming that you fall over and don't
+ 
+
+ align:start position:0%
+assuming that you fall over and don't
+cross back the other approximation is
+
+ align:start position:0%
+cross back the other approximation is
+ 
+
+ align:start position:0%
+cross back the other approximation is
+that this assumes that the transitions
+
+ align:start position:0%
+that this assumes that the transitions
+ 
+
+ align:start position:0%
+that this assumes that the transitions
+are infrequent compared to the
+
+ align:start position:0%
+are infrequent compared to the
+ 
+
+ align:start position:0%
+are infrequent compared to the
+vibrations in the minimum so you assume
+
+ align:start position:0%
+vibrations in the minimum so you assume
+ 
+
+ align:start position:0%
+vibrations in the minimum so you assume
+that when the system goes from here to
+
+ align:start position:0%
+that when the system goes from here to
+ 
+
+ align:start position:0%
+that when the system goes from here to
+here it sort of equilibrates here
+
+ align:start position:0%
+here it sort of equilibrates here
+ 
+
+ align:start position:0%
+here it sort of equilibrates here
+vibrates around until it makes a the
+
+ align:start position:0%
+vibrates around until it makes a the
+ 
+
+ align:start position:0%
+vibrates around until it makes a the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+transition and the reason you need to do
+
+ align:start position:0%
+transition and the reason you need to do
+ 
+
+ align:start position:0%
+transition and the reason you need to do
+that is that um you need to equilibrate
+
+ align:start position:0%
+that is that um you need to equilibrate
+ 
+
+ align:start position:0%
+that is that um you need to equilibrate
+First in every potential well before you
+
+ align:start position:0%
+First in every potential well before you
+ 
+
+ align:start position:0%
+First in every potential well before you
+go to the next one because otherwise you
+
+ align:start position:0%
+go to the next one because otherwise you
+ 
+
+ align:start position:0%
+go to the next one because otherwise you
+have dynamical memory left from the
+
+ align:start position:0%
+have dynamical memory left from the
+ 
+
+ align:start position:0%
+have dynamical memory left from the
+previous transition which which
+
+ align:start position:0%
+previous transition which which
+ 
+
+ align:start position:0%
+previous transition which which
+essentially change your statistic would
+
+ align:start position:0%
+essentially change your statistic would
+ 
+
+ align:start position:0%
+essentially change your statistic would
+make your statistical mechanics approach
+
+ align:start position:0%
+make your statistical mechanics approach
+ 
+
+ align:start position:0%
+make your statistical mechanics approach
+invalid um but usually those are um easy
+
+ align:start position:0%
+invalid um but usually those are um easy
+ 
+
+ align:start position:0%
+invalid um but usually those are um easy
+to deal with um it's sort of obvious
+
+ align:start position:0%
+to deal with um it's sort of obvious
+ 
+
+ align:start position:0%
+to deal with um it's sort of obvious
+because if you think about if the system
+
+ align:start position:0%
+because if you think about if the system
+ 
+
+ align:start position:0%
+because if you think about if the system
+crosses very rapidly compared to the
+
+ align:start position:0%
+crosses very rapidly compared to the
+ 
+
+ align:start position:0%
+crosses very rapidly compared to the
+time it vibrates then you just do molec
+
+ align:start position:0%
+time it vibrates then you just do molec
+ 
+
+ align:start position:0%
+time it vibrates then you just do molec
+Dynamics because then you have very fast
+
+ align:start position:0%
+Dynamics because then you have very fast
+ 
+
+ align:start position:0%
+Dynamics because then you have very fast
+transition so who cares about transition
+
+ align:start position:0%
+transition so who cares about transition
+ 
+
+ align:start position:0%
+transition so who cares about transition
+state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory okay
+
+ align:start position:0%
+Theory okay
+ 
+
+ align:start position:0%
+Theory okay
+so the parallel replica method is really
+
+ align:start position:0%
+so the parallel replica method is really
+ 
+
+ align:start position:0%
+so the parallel replica method is really
+kind of elegant in its triviality almost
+
+ align:start position:0%
+kind of elegant in its triviality almost
+ 
+
+ align:start position:0%
+kind of elegant in its triviality almost
+um if you think of you know what is time
+
+ align:start position:0%
+um if you think of you know what is time
+ 
+
+ align:start position:0%
+um if you think of you know what is time
+time is waiting for events to happen um
+
+ align:start position:0%
+time is waiting for events to happen um
+ 
+
+ align:start position:0%
+time is waiting for events to happen um
+and if you think of a really trivial
+
+ align:start position:0%
+and if you think of a really trivial
+ 
+
+ align:start position:0%
+and if you think of a really trivial
+example you know let's say the system
+
+ align:start position:0%
+example you know let's say the system
+ 
+
+ align:start position:0%
+example you know let's say the system
+wants to move from this state to that
+
+ align:start position:0%
+wants to move from this state to that
+ 
+
+ align:start position:0%
+wants to move from this state to that
+state you're just sitting there you know
+
+ align:start position:0%
+state you're just sitting there you know
+ 
+
+ align:start position:0%
+state you're just sitting there you know
+the atoms are vibrating around and
+
+ align:start position:0%
+the atoms are vibrating around and
+ 
+
+ align:start position:0%
+the atoms are vibrating around and
+waiting you're waiting for the system to
+
+ align:start position:0%
+waiting you're waiting for the system to
+ 
+
+ align:start position:0%
+waiting you're waiting for the system to
+to transition why not wait on many
+
+ align:start position:0%
+to transition why not wait on many
+ 
+
+ align:start position:0%
+to transition why not wait on many
+processors at a time
+
+ align:start position:0%
+processors at a time
+ 
+
+ align:start position:0%
+processors at a time
+so the idea is you run this simulation
+
+ align:start position:0%
+so the idea is you run this simulation
+ 
+
+ align:start position:0%
+so the idea is you run this simulation
+on a bunch of
+
+ align:start position:0%
+on a bunch of
+ 
+
+ align:start position:0%
+on a bunch of
+processors and if you run on say 100 you
+
+ align:start position:0%
+processors and if you run on say 100 you
+ 
+
+ align:start position:0%
+processors and if you run on say 100 you
+could say that's kind of like waiting a
+
+ align:start position:0%
+could say that's kind of like waiting a
+ 
+
+ align:start position:0%
+could say that's kind of like waiting a
+100 times the time you wait on One
+
+ align:start position:0%
+100 times the time you wait on One
+ 
+
+ align:start position:0%
+100 times the time you wait on One
+processor and then let's say it happens
+
+ align:start position:0%
+processor and then let's say it happens
+ 
+
+ align:start position:0%
+processor and then let's say it happens
+at on One
+
+ align:start position:0%
+at on One
+ 
+
+ align:start position:0%
+at on One
+processor okay the system transitions
+
+ align:start position:0%
+processor okay the system transitions
+ 
+
+ align:start position:0%
+processor okay the system transitions
+then you essentially add up all the time
+
+ align:start position:0%
+then you essentially add up all the time
+ 
+
+ align:start position:0%
+then you essentially add up all the time
+all the systems have waited and that's
+
+ align:start position:0%
+all the systems have waited and that's
+ 
+
+ align:start position:0%
+all the systems have waited and that's
+your total waiting time and in a
+
+ align:start position:0%
+your total waiting time and in a
+ 
+
+ align:start position:0%
+your total waiting time and in a
+statistical sense that's actually right
+
+ align:start position:0%
+statistical sense that's actually right
+ 
+
+ align:start position:0%
+statistical sense that's actually right
+you know if you do queuing Theory and
+
+ align:start position:0%
+you know if you do queuing Theory and
+ 
+
+ align:start position:0%
+you know if you do queuing Theory and
+things like that you'll find that this
+
+ align:start position:0%
+things like that you'll find that this
+ 
+
+ align:start position:0%
+things like that you'll find that this
+is the solution if you it's actually
+
+ align:start position:0%
+is the solution if you it's actually
+ 
+
+ align:start position:0%
+is the solution if you it's actually
+easy to see if you turn this all into
+
+ align:start position:0%
+easy to see if you turn this all into
+ 
+
+ align:start position:0%
+easy to see if you turn this all into
+probabilities for transfer you know
+
+ align:start position:0%
+probabilities for transfer you know
+ 
+
+ align:start position:0%
+probabilities for transfer you know
+essentially you could say when when you
+
+ align:start position:0%
+essentially you could say when when you
+ 
+
+ align:start position:0%
+essentially you could say when when you
+do it 100 times you've 100 times
+
+ align:start position:0%
+do it 100 times you've 100 times
+ 
+
+ align:start position:0%
+do it 100 times you've 100 times
+attempted or given the system chances in
+
+ align:start position:0%
+attempted or given the system chances in
+ 
+
+ align:start position:0%
+attempted or given the system chances in
+a given time to make a transition so you
+
+ align:start position:0%
+a given time to make a transition so you
+ 
+
+ align:start position:0%
+a given time to make a transition so you
+add up all the time and then you just
+
+ align:start position:0%
+add up all the time and then you just
+ 
+
+ align:start position:0%
+add up all the time and then you just
+restart so you put the system in the
+
+ align:start position:0%
+restart so you put the system in the
+ 
+
+ align:start position:0%
+restart so you put the system in the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+state and you again run all those
+
+ align:start position:0%
+state and you again run all those
+ 
+
+ align:start position:0%
+state and you again run all those
+replicas you do you have to introduce a
+
+ align:start position:0%
+replicas you do you have to introduce a
+ 
+
+ align:start position:0%
+replicas you do you have to introduce a
+little bit of randomization of course
+
+ align:start position:0%
+little bit of randomization of course
+ 
+
+ align:start position:0%
+little bit of randomization of course
+you don't want these to fall exactly the
+
+ align:start position:0%
+you don't want these to fall exactly the
+ 
+
+ align:start position:0%
+you don't want these to fall exactly the
+same trajectory through face space okay
+
+ align:start position:0%
+same trajectory through face space okay
+ 
+
+ align:start position:0%
+same trajectory through face space okay
+so there's a certain amount of
+
+ align:start position:0%
+so there's a certain amount of
+ 
+
+ align:start position:0%
+so there's a certain amount of
+randomization that goes on um so
+
+ align:start position:0%
+randomization that goes on um so
+ 
+
+ align:start position:0%
+randomization that goes on um so
+essentially this is linear time scaling
+
+ align:start position:0%
+essentially this is linear time scaling
+ 
+
+ align:start position:0%
+essentially this is linear time scaling
+you know o overall you pretty much you
+
+ align:start position:0%
+you know o overall you pretty much you
+ 
+
+ align:start position:0%
+you know o overall you pretty much you
+know if you have n processors time is
+
+ align:start position:0%
+know if you have n processors time is
+ 
+
+ align:start position:0%
+know if you have n processors time is
+accelerated by a factor of n you could
+
+ align:start position:0%
+accelerated by a factor of n you could
+ 
+
+ align:start position:0%
+accelerated by a factor of n you could
+say it's a little less because there's
+
+ align:start position:0%
+say it's a little less because there's
+ 
+
+ align:start position:0%
+say it's a little less because there's
+overhead you know you have to first of
+
+ align:start position:0%
+overhead you know you have to first of
+ 
+
+ align:start position:0%
+overhead you know you have to first of
+all do a non-trivial thing which is
+
+ align:start position:0%
+all do a non-trivial thing which is
+ 
+
+ align:start position:0%
+all do a non-trivial thing which is
+detect the transition when you think
+
+ align:start position:0%
+detect the transition when you think
+ 
+
+ align:start position:0%
+detect the transition when you think
+about it this is kind of you know not
+
+ align:start position:0%
+about it this is kind of you know not
+ 
+
+ align:start position:0%
+about it this is kind of you know not
+that trivial you're doing your md
+
+ align:start position:0%
+that trivial you're doing your md
+ 
+
+ align:start position:0%
+that trivial you're doing your md
+simulation and you got to sort of ask
+
+ align:start position:0%
+simulation and you got to sort of ask
+ 
+
+ align:start position:0%
+simulation and you got to sort of ask
+your system oh has something happened
+
+ align:start position:0%
+your system oh has something happened
+ 
+
+ align:start position:0%
+your system oh has something happened
+and you know maybe it's like an atom
+
+ align:start position:0%
+and you know maybe it's like an atom
+ 
+
+ align:start position:0%
+and you know maybe it's like an atom
+diffusing whatever so you got to do
+
+ align:start position:0%
+diffusing whatever so you got to do
+ 
+
+ align:start position:0%
+diffusing whatever so you got to do
+quite a bit of work to sort of check
+
+ align:start position:0%
+quite a bit of work to sort of check
+ 
+
+ align:start position:0%
+quite a bit of work to sort of check
+whether a transition that happen so you
+
+ align:start position:0%
+whether a transition that happen so you
+ 
+
+ align:start position:0%
+whether a transition that happen so you
+got overhead there and then you have
+
+ align:start position:0%
+got overhead there and then you have
+ 
+
+ align:start position:0%
+got overhead there and then you have
+overhead when you sort of copy the the
+
+ align:start position:0%
+overhead when you sort of copy the the
+ 
+
+ align:start position:0%
+overhead when you sort of copy the the
+the trans transition state into all the
+
+ align:start position:0%
+the trans transition state into all the
+ 
+
+ align:start position:0%
+the trans transition state into all the
+other ones you have to do a little bit
+
+ align:start position:0%
+other ones you have to do a little bit
+ 
+
+ align:start position:0%
+other ones you have to do a little bit
+of randomization here so typically you
+
+ align:start position:0%
+of randomization here so typically you
+ 
+
+ align:start position:0%
+of randomization here so typically you
+like you may restart with a different
+
+ align:start position:0%
+like you may restart with a different
+ 
+
+ align:start position:0%
+like you may restart with a different
+uh like with a maxal boltman
+
+ align:start position:0%
+uh like with a maxal boltman
+ 
+
+ align:start position:0%
+uh like with a maxal boltman
+distribution of velocities and so but
+
+ align:start position:0%
+distribution of velocities and so but
+ 
+
+ align:start position:0%
+distribution of velocities and so but
+you have to like initialize that you
+
+ align:start position:0%
+you have to like initialize that you
+ 
+
+ align:start position:0%
+you have to like initialize that you
+have to run that for a very short time
+
+ align:start position:0%
+have to run that for a very short time
+ 
+
+ align:start position:0%
+have to run that for a very short time
+and so so you have a bit of overhead
+
+ align:start position:0%
+and so so you have a bit of overhead
+ 
+
+ align:start position:0%
+and so so you have a bit of overhead
+there so you'll get a little less than
+
+ align:start position:0%
+there so you'll get a little less than
+ 
+
+ align:start position:0%
+there so you'll get a little less than
+uh and scaling um but you know it's not
+
+ align:start position:0%
+uh and scaling um but you know it's not
+ 
+
+ align:start position:0%
+uh and scaling um but you know it's not
+bad it's not great either but like I
+
+ align:start position:0%
+bad it's not great either but like I
+ 
+
+ align:start position:0%
+bad it's not great either but like I
+said with a thousand processors you can
+
+ align:start position:0%
+said with a thousand processors you can
+ 
+
+ align:start position:0%
+said with a thousand processors you can
+go from uh Nan to microsc so yeah that's
+
+ align:start position:0%
+go from uh Nan to microsc so yeah that's
+ 
+
+ align:start position:0%
+go from uh Nan to microsc so yeah that's
+not bad I mean you you can see that
+
+ align:start position:0%
+not bad I mean you you can see that
+ 
+
+ align:start position:0%
+not bad I mean you you can see that
+you're never going to make it to Second
+
+ align:start position:0%
+you're never going to make it to Second
+ 
+
+ align:start position:0%
+you're never going to make it to Second
+some okay because of the linear scale
+
+ align:start position:0%
+some okay because of the linear scale
+ 
+
+ align:start position:0%
+some okay because of the linear scale
+scaling but it is a sort of intermediate
+
+ align:start position:0%
+scaling but it is a sort of intermediate
+ 
+
+ align:start position:0%
+scaling but it is a sort of intermediate
+time scale that can be
+
+ align:start position:0%
+time scale that can be
+ 
+
+ align:start position:0%
+time scale that can be
+useful here's an example this is
+
+ align:start position:0%
+useful here's an example this is
+ 
+
+ align:start position:0%
+useful here's an example this is
+planarization uh of silver on Silver uh
+
+ align:start position:0%
+planarization uh of silver on Silver uh
+ 
+
+ align:start position:0%
+planarization uh of silver on Silver uh
+and this comes straight out of our
+
+ align:start position:0%
+and this comes straight out of our
+ 
+
+ align:start position:0%
+and this comes straight out of our
+voter's article um so essentially this
+
+ align:start position:0%
+voter's article um so essentially this
+ 
+
+ align:start position:0%
+voter's article um so essentially this
+is a a one one layer of silver that's
+
+ align:start position:0%
+is a a one one layer of silver that's
+ 
+
+ align:start position:0%
+is a a one one layer of silver that's
+the white atoms um and then on top of
+
+ align:start position:0%
+the white atoms um and then on top of
+ 
+
+ align:start position:0%
+the white atoms um and then on top of
+that is an a first layer which is the
+
+ align:start position:0%
+that is an a first layer which is the
+ 
+
+ align:start position:0%
+that is an a first layer which is the
+blue atoms and then the yellow atoms is
+
+ align:start position:0%
+blue atoms and then the yellow atoms is
+ 
+
+ align:start position:0%
+blue atoms and then the yellow atoms is
+another layer on top okay so you're
+
+ align:start position:0%
+another layer on top okay so you're
+ 
+
+ align:start position:0%
+another layer on top okay so you're
+seeing three layers and so this studies
+
+ align:start position:0%
+seeing three layers and so this studies
+ 
+
+ align:start position:0%
+seeing three layers and so this studies
+this study um tracks how the system
+
+ align:start position:0%
+this study um tracks how the system
+ 
+
+ align:start position:0%
+this study um tracks how the system
+planarizes to lower its surface energy
+
+ align:start position:0%
+planarizes to lower its surface energy
+ 
+
+ align:start position:0%
+planarizes to lower its surface energy
+so the top atoms should sort of come
+
+ align:start position:0%
+so the top atoms should sort of come
+ 
+
+ align:start position:0%
+so the top atoms should sort of come
+down and form all one
+
+ align:start position:0%
+down and form all one
+ 
+
+ align:start position:0%
+down and form all one
+Island and so this is perfect for
+
+ align:start position:0%
+Island and so this is perfect for
+ 
+
+ align:start position:0%
+Island and so this is perfect for
+Accelerated MD I mean you know
+
+ align:start position:0%
+Accelerated MD I mean you know
+ 
+
+ align:start position:0%
+Accelerated MD I mean you know
+researchers know why they pick problems
+
+ align:start position:0%
+researchers know why they pick problems
+ 
+
+ align:start position:0%
+researchers know why they pick problems
+because they can solve them um because
+
+ align:start position:0%
+because they can solve them um because
+ 
+
+ align:start position:0%
+because they can solve them um because
+this is a set of discrete events you
+
+ align:start position:0%
+this is a set of discrete events you
+ 
+
+ align:start position:0%
+this is a set of discrete events you
+know atoms diffuse and maybe even
+
+ align:start position:0%
+know atoms diffuse and maybe even
+ 
+
+ align:start position:0%
+know atoms diffuse and maybe even
+collectively you see the nice thing
+
+ align:start position:0%
+collectively you see the nice thing
+ 
+
+ align:start position:0%
+collectively you see the nice thing
+about it these that you're not imposing
+
+ align:start position:0%
+about it these that you're not imposing
+ 
+
+ align:start position:0%
+about it these that you're not imposing
+the kinetic mechanism but it's still a
+
+ align:start position:0%
+the kinetic mechanism but it's still a
+ 
+
+ align:start position:0%
+the kinetic mechanism but it's still a
+set of discrete events so you know atoms
+
+ align:start position:0%
+set of discrete events so you know atoms
+ 
+
+ align:start position:0%
+set of discrete events so you know atoms
+May hop a little you can see it in the
+
+ align:start position:0%
+May hop a little you can see it in the
+ 
+
+ align:start position:0%
+May hop a little you can see it in the
+first few slides there and ultimately
+
+ align:start position:0%
+first few slides there and ultimately
+ 
+
+ align:start position:0%
+first few slides there and ultimately
+sort of PL Ariz and you know people got
+
+ align:start position:0%
+sort of PL Ariz and you know people got
+ 
+
+ align:start position:0%
+sort of PL Ariz and you know people got
+all the way up to um one micro second uh
+
+ align:start position:0%
+all the way up to um one micro second uh
+ 
+
+ align:start position:0%
+all the way up to um one micro second uh
+although it was done with empirical
+
+ align:start position:0%
+although it was done with empirical
+ 
+
+ align:start position:0%
+although it was done with empirical
+potential so and according to Art voter
+
+ align:start position:0%
+potential so and according to Art voter
+ 
+
+ align:start position:0%
+potential so and according to Art voter
+this took only about 5 days on 32
+
+ align:start position:0%
+this took only about 5 days on 32
+ 
+
+ align:start position:0%
+this took only about 5 days on 32
+pennium and these are all I mean these
+
+ align:start position:0%
+pennium and these are all I mean these
+ 
+
+ align:start position:0%
+pennium and these are all I mean these
+are 1 GHz pennium so probably do it in
+
+ align:start position:0%
+are 1 GHz pennium so probably do it in
+ 
+
+ align:start position:0%
+are 1 GHz pennium so probably do it in
+maybe you know 1 to two days
+
+ align:start position:0%
+maybe you know 1 to two days
+ 
+
+ align:start position:0%
+maybe you know 1 to two days
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um I think you can already see if I go
+
+ align:start position:0%
+um I think you can already see if I go
+ 
+
+ align:start position:0%
+um I think you can already see if I go
+back um when this will not
+
+ align:start position:0%
+back um when this will not
+ 
+
+ align:start position:0%
+back um when this will not
+work um it this will not work if the
+
+ align:start position:0%
+work um it this will not work if the
+ 
+
+ align:start position:0%
+work um it this will not work if the
+overhead becomes excessive and how is it
+
+ align:start position:0%
+overhead becomes excessive and how is it
+ 
+
+ align:start position:0%
+overhead becomes excessive and how is it
+going to become
+
+ align:start position:0%
+going to become
+ 
+
+ align:start position:0%
+going to become
+excessive
+
+ align:start position:0%
+excessive
+ 
+
+ align:start position:0%
+excessive
+if if you start getting a lot of
+
+ align:start position:0%
+if if you start getting a lot of
+ 
+
+ align:start position:0%
+if if you start getting a lot of
+Transitions okay if only after a little
+
+ align:start position:0%
+Transitions okay if only after a little
+ 
+
+ align:start position:0%
+Transitions okay if only after a little
+bit of simulation you get a transition
+
+ align:start position:0%
+bit of simulation you get a transition
+ 
+
+ align:start position:0%
+bit of simulation you get a transition
+then you're over head starts to weigh
+
+ align:start position:0%
+then you're over head starts to weigh
+ 
+
+ align:start position:0%
+then you're over head starts to weigh
+heavily and when's that going to happen
+
+ align:start position:0%
+heavily and when's that going to happen
+ 
+
+ align:start position:0%
+heavily and when's that going to happen
+well it's going to happen of course when
+
+ align:start position:0%
+well it's going to happen of course when
+ 
+
+ align:start position:0%
+well it's going to happen of course when
+you have low activation barriers but
+
+ align:start position:0%
+you have low activation barriers but
+ 
+
+ align:start position:0%
+you have low activation barriers but
+there's another problem which is a
+
+ align:start position:0%
+there's another problem which is a
+ 
+
+ align:start position:0%
+there's another problem which is a
+little more severe if you make your
+
+ align:start position:0%
+little more severe if you make your
+ 
+
+ align:start position:0%
+little more severe if you make your
+system bigger and bigger see the
+
+ align:start position:0%
+system bigger and bigger see the
+ 
+
+ align:start position:0%
+system bigger and bigger see the
+probability let's say you have a system
+
+ align:start position:0%
+probability let's say you have a system
+ 
+
+ align:start position:0%
+probability let's say you have a system
+that's sort of locally identical if you
+
+ align:start position:0%
+that's sort of locally identical if you
+ 
+
+ align:start position:0%
+that's sort of locally identical if you
+make it bigger and
+
+ align:start position:0%
+make it bigger and
+ 
+
+ align:start position:0%
+make it bigger and
+bigger the the probability that a
+
+ align:start position:0%
+bigger the the probability that a
+ 
+
+ align:start position:0%
+bigger the the probability that a
+transition occurs let's see an atom
+
+ align:start position:0%
+transition occurs let's see an atom
+ 
+
+ align:start position:0%
+transition occurs let's see an atom
+diffuses is proportional to the system
+
+ align:start position:0%
+diffuses is proportional to the system
+ 
+
+ align:start position:0%
+diffuses is proportional to the system
+size the pro the probability that an
+
+ align:start position:0%
+size the pro the probability that an
+ 
+
+ align:start position:0%
+size the pro the probability that an
+event happens is is proportional to the
+
+ align:start position:0%
+event happens is is proportional to the
+ 
+
+ align:start position:0%
+event happens is is proportional to the
+system size so as you make the system
+
+ align:start position:0%
+system size so as you make the system
+ 
+
+ align:start position:0%
+system size so as you make the system
+bigger and bigger this essentially
+
+ align:start position:0%
+bigger and bigger this essentially
+ 
+
+ align:start position:0%
+bigger and bigger this essentially
+becomes less and less efficient okay
+
+ align:start position:0%
+becomes less and less efficient okay
+ 
+
+ align:start position:0%
+becomes less and less efficient okay
+because you get more and more
+
+ align:start position:0%
+because you get more and more
+ 
+
+ align:start position:0%
+because you get more and more
+transitions uh and that's something
+
+ align:start position:0%
+transitions uh and that's something
+ 
+
+ align:start position:0%
+transitions uh and that's something
+you'll see in other versions of
+
+ align:start position:0%
+you'll see in other versions of
+ 
+
+ align:start position:0%
+you'll see in other versions of
+accelerated uh MD as
+
+ align:start position:0%
+accelerated uh MD as
+ 
+
+ align:start position:0%
+accelerated uh MD as
+well okay hyper dynamics I like I like
+
+ align:start position:0%
+well okay hyper dynamics I like I like
+ 
+
+ align:start position:0%
+well okay hyper dynamics I like I like
+the word very much but I'm not going to
+
+ align:start position:0%
+the word very much but I'm not going to
+ 
+
+ align:start position:0%
+the word very much but I'm not going to
+say much about it um hyper dynamics is
+
+ align:start position:0%
+say much about it um hyper dynamics is
+ 
+
+ align:start position:0%
+say much about it um hyper dynamics is
+really a class of methods uh that is
+
+ align:start position:0%
+really a class of methods uh that is
+ 
+
+ align:start position:0%
+really a class of methods uh that is
+getting very popular not just in
+
+ align:start position:0%
+getting very popular not just in
+ 
+
+ align:start position:0%
+getting very popular not just in
+accelerating mdn but the whole idea of
+
+ align:start position:0%
+accelerating mdn but the whole idea of
+ 
+
+ align:start position:0%
+accelerating mdn but the whole idea of
+modifying the potential surface it's
+
+ align:start position:0%
+modifying the potential surface it's
+ 
+
+ align:start position:0%
+modifying the potential surface it's
+it's getting sort of very popular also
+
+ align:start position:0%
+it's getting sort of very popular also
+ 
+
+ align:start position:0%
+it's getting sort of very popular also
+for Pure optimization methods you know
+
+ align:start position:0%
+for Pure optimization methods you know
+ 
+
+ align:start position:0%
+for Pure optimization methods you know
+if you think that this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the surface of the original system
+
+ align:start position:0%
+is the surface of the original system
+ 
+
+ align:start position:0%
+is the surface of the original system
+this is the energy surface you know your
+
+ align:start position:0%
+this is the energy surface you know your
+ 
+
+ align:start position:0%
+this is the energy surface you know your
+problem is that these Wells are too deep
+
+ align:start position:0%
+problem is that these Wells are too deep
+ 
+
+ align:start position:0%
+problem is that these Wells are too deep
+well solve the problem by lifting them
+
+ align:start position:0%
+well solve the problem by lifting them
+ 
+
+ align:start position:0%
+well solve the problem by lifting them
+up so if you can define a potential that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tracks the original potential in most of
+
+ align:start position:0%
+tracks the original potential in most of
+ 
+
+ align:start position:0%
+tracks the original potential in most of
+space especially deactivated pieces but
+
+ align:start position:0%
+space especially deactivated pieces but
+ 
+
+ align:start position:0%
+space especially deactivated pieces but
+then lifts up the minimum of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well if your system moves on the red
+
+ align:start position:0%
+well if your system moves on the red
+ 
+
+ align:start position:0%
+well if your system moves on the red
+potential it's going to transition a lot
+
+ align:start position:0%
+potential it's going to transition a lot
+ 
+
+ align:start position:0%
+potential it's going to transition a lot
+faster okay because the activation barer
+
+ align:start position:0%
+faster okay because the activation barer
+ 
+
+ align:start position:0%
+faster okay because the activation barer
+goes down a lot um and you can actually
+
+ align:start position:0%
+goes down a lot um and you can actually
+ 
+
+ align:start position:0%
+goes down a lot um and you can actually
+run the system on the red curve and
+
+ align:start position:0%
+run the system on the red curve and
+ 
+
+ align:start position:0%
+run the system on the red curve and
+correct for the transition rates cuz see
+
+ align:start position:0%
+correct for the transition rates cuz see
+ 
+
+ align:start position:0%
+correct for the transition rates cuz see
+the cool thing is that once
+
+ align:start position:0%
+the cool thing is that once
+ 
+
+ align:start position:0%
+the cool thing is that once
+the MD finds the
+
+ align:start position:0%
+the MD finds the
+ 
+
+ align:start position:0%
+the MD finds the
+Transitions okay so you know MD is like
+
+ align:start position:0%
+Transitions okay so you know MD is like
+ 
+
+ align:start position:0%
+Transitions okay so you know MD is like
+going back and forth here but once it's
+
+ align:start position:0%
+going back and forth here but once it's
+ 
+
+ align:start position:0%
+going back and forth here but once it's
+found the transition you could calculate
+
+ align:start position:0%
+found the transition you could calculate
+ 
+
+ align:start position:0%
+found the transition you could calculate
+back what the real barrier should have
+
+ align:start position:0%
+back what the real barrier should have
+ 
+
+ align:start position:0%
+back what the real barrier should have
+been okay so you know at what rate the
+
+ align:start position:0%
+been okay so you know at what rate the
+ 
+
+ align:start position:0%
+been okay so you know at what rate the
+system should have
+
+ align:start position:0%
+system should have
+ 
+
+ align:start position:0%
+system should have
+transitioned okay so boosting the
+
+ align:start position:0%
+transitioned okay so boosting the
+ 
+
+ align:start position:0%
+transitioned okay so boosting the
+potential surface with this boost
+
+ align:start position:0%
+potential surface with this boost
+ 
+
+ align:start position:0%
+potential surface with this boost
+potential that's this difference here
+
+ align:start position:0%
+potential that's this difference here
+ 
+
+ align:start position:0%
+potential that's this difference here
+boosting it up is essentially you know
+
+ align:start position:0%
+boosting it up is essentially you know
+ 
+
+ align:start position:0%
+boosting it up is essentially you know
+accelerating the escape from the minimum
+
+ align:start position:0%
+accelerating the escape from the minimum
+ 
+
+ align:start position:0%
+accelerating the escape from the minimum
+okay and you can correct back by this
+
+ align:start position:0%
+okay and you can correct back by this
+ 
+
+ align:start position:0%
+okay and you can correct back by this
+boltzman factor which is essentially the
+
+ align:start position:0%
+boltzman factor which is essentially the
+ 
+
+ align:start position:0%
+boltzman factor which is essentially the
+the comes from the ratio of of the
+
+ align:start position:0%
+the comes from the ratio of of the
+ 
+
+ align:start position:0%
+the comes from the ratio of of the
+proper rate to the rate that you
+
+ align:start position:0%
+proper rate to the rate that you
+ 
+
+ align:start position:0%
+proper rate to the rate that you
+actually had in your ND simulation
+
+ align:start position:0%
+actually had in your ND simulation
+ 
+
+ align:start position:0%
+actually had in your ND simulation
+there's all kinds of Tricks involved
+
+ align:start position:0%
+there's all kinds of Tricks involved
+ 
+
+ align:start position:0%
+there's all kinds of Tricks involved
+this is a simplified version of it um
+
+ align:start position:0%
+this is a simplified version of it um
+ 
+
+ align:start position:0%
+this is a simplified version of it um
+like there's a lot of questions about
+
+ align:start position:0%
+like there's a lot of questions about
+ 
+
+ align:start position:0%
+like there's a lot of questions about
+how you define that boost surface uh for
+
+ align:start position:0%
+how you define that boost surface uh for
+ 
+
+ align:start position:0%
+how you define that boost surface uh for
+example do you want to keep the same
+
+ align:start position:0%
+example do you want to keep the same
+ 
+
+ align:start position:0%
+example do you want to keep the same
+frequencies so then you'd like to keep
+
+ align:start position:0%
+frequencies so then you'd like to keep
+ 
+
+ align:start position:0%
+frequencies so then you'd like to keep
+the curvature the same uh because then
+
+ align:start position:0%
+the curvature the same uh because then
+ 
+
+ align:start position:0%
+the curvature the same uh because then
+you keep the same attempt frequencies
+
+ align:start position:0%
+you keep the same attempt frequencies
+ 
+
+ align:start position:0%
+you keep the same attempt frequencies
+but you're only changing the the success
+
+ align:start position:0%
+but you're only changing the the success
+ 
+
+ align:start position:0%
+but you're only changing the the success
+rate of crossing the barrier that's a
+
+ align:start position:0%
+rate of crossing the barrier that's a
+ 
+
+ align:start position:0%
+rate of crossing the barrier that's a
+very elegant way of doing and people
+
+ align:start position:0%
+very elegant way of doing and people
+ 
+
+ align:start position:0%
+very elegant way of doing and people
+have ways that they can do this um
+
+ align:start position:0%
+have ways that they can do this um
+ 
+
+ align:start position:0%
+have ways that they can do this um
+so doing this in
+
+ align:start position:0%
+so doing this in
+ 
+
+ align:start position:0%
+so doing this in
+practice um often means calculating um
+
+ align:start position:0%
+practice um often means calculating um
+ 
+
+ align:start position:0%
+practice um often means calculating um
+derivatives of potential surfaces in
+
+ align:start position:0%
+derivatives of potential surfaces in
+ 
+
+ align:start position:0%
+derivatives of potential surfaces in
+many cases even H so matrices of second
+
+ align:start position:0%
+many cases even H so matrices of second
+ 
+
+ align:start position:0%
+many cases even H so matrices of second
+derivatives and that's easy to do when
+
+ align:start position:0%
+derivatives and that's easy to do when
+ 
+
+ align:start position:0%
+derivatives and that's easy to do when
+you have potentials it's a lot harder to
+
+ align:start position:0%
+you have potentials it's a lot harder to
+ 
+
+ align:start position:0%
+you have potentials it's a lot harder to
+do when you're doing quantum mechanics
+
+ align:start position:0%
+do when you're doing quantum mechanics
+ 
+
+ align:start position:0%
+do when you're doing quantum mechanics
+and so this again one of these things
+
+ align:start position:0%
+and so this again one of these things
+ 
+
+ align:start position:0%
+and so this again one of these things
+that is usually only done with empirical
+
+ align:start position:0%
+that is usually only done with empirical
+ 
+
+ align:start position:0%
+that is usually only done with empirical
+potentials uh actually I don't know of
+
+ align:start position:0%
+potentials uh actually I don't know of
+ 
+
+ align:start position:0%
+potentials uh actually I don't know of
+any implementation with Quanto mechanics
+
+ align:start position:0%
+any implementation with Quanto mechanics
+ 
+
+ align:start position:0%
+any implementation with Quanto mechanics
+but I it may be something I've just
+
+ align:start position:0%
+but I it may be something I've just
+ 
+
+ align:start position:0%
+but I it may be something I've just
+missed in the literature um this is used
+
+ align:start position:0%
+missed in the literature um this is used
+ 
+
+ align:start position:0%
+missed in the literature um this is used
+for sort of other schemes as well if you
+
+ align:start position:0%
+for sort of other schemes as well if you
+ 
+
+ align:start position:0%
+for sort of other schemes as well if you
+for a second don't care about Dynamics
+
+ align:start position:0%
+for a second don't care about Dynamics
+ 
+
+ align:start position:0%
+for a second don't care about Dynamics
+there are not schemes out there to use
+
+ align:start position:0%
+there are not schemes out there to use
+ 
+
+ align:start position:0%
+there are not schemes out there to use
+this for
+
+ align:start position:0%
+this for
+ 
+
+ align:start position:0%
+this for
+optimization you know if you think of
+
+ align:start position:0%
+optimization you know if you think of
+ 
+
+ align:start position:0%
+optimization you know if you think of
+global optimization of a system is a big
+
+ align:start position:0%
+global optimization of a system is a big
+ 
+
+ align:start position:0%
+global optimization of a system is a big
+problem because there's all kinds of
+
+ align:start position:0%
+problem because there's all kinds of
+ 
+
+ align:start position:0%
+problem because there's all kinds of
+local Wells well what you can do is if
+
+ align:start position:0%
+local Wells well what you can do is if
+ 
+
+ align:start position:0%
+local Wells well what you can do is if
+you fall in a well you essentially start
+
+ align:start position:0%
+you fall in a well you essentially start
+ 
+
+ align:start position:0%
+you fall in a well you essentially start
+filling up the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well until you until it's sort of like
+
+ align:start position:0%
+well until you until it's sort of like
+ 
+
+ align:start position:0%
+well until you until it's sort of like
+water filling up the well until you fall
+
+ align:start position:0%
+water filling up the well until you fall
+ 
+
+ align:start position:0%
+water filling up the well until you fall
+out into the next well okay and then you
+
+ align:start position:0%
+out into the next well okay and then you
+ 
+
+ align:start position:0%
+out into the next well okay and then you
+start filling up that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well till you fall in the next well and
+
+ align:start position:0%
+well till you fall in the next well and
+ 
+
+ align:start position:0%
+well till you fall in the next well and
+it's sort of like water cascading down
+
+ align:start position:0%
+it's sort of like water cascading down
+ 
+
+ align:start position:0%
+it's sort of like water cascading down
+an energy surface and it's a way to do
+
+ align:start position:0%
+an energy surface and it's a way to do
+ 
+
+ align:start position:0%
+an energy surface and it's a way to do
+Global optimization ation in a in a
+
+ align:start position:0%
+Global optimization ation in a in a
+ 
+
+ align:start position:0%
+Global optimization ation in a in a
+landscape of many minim and I think this
+
+ align:start position:0%
+landscape of many minim and I think this
+ 
+
+ align:start position:0%
+landscape of many minim and I think this
+method was developed by uh people at
+
+ align:start position:0%
+method was developed by uh people at
+ 
+
+ align:start position:0%
+method was developed by uh people at
+Princeton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so that's sort of in the category of
+
+ align:start position:0%
+um so that's sort of in the category of
+ 
+
+ align:start position:0%
+um so that's sort of in the category of
+hyper dynamics
+
+ align:start position:0%
+hyper dynamics
+ 
+
+ align:start position:0%
+hyper dynamics
+um the one that's actually very
+
+ align:start position:0%
+um the one that's actually very
+ 
+
+ align:start position:0%
+um the one that's actually very
+practical is the next one um which is
+
+ align:start position:0%
+practical is the next one um which is
+ 
+
+ align:start position:0%
+practical is the next one um which is
+temperature accelerated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dynamics which is again a sort of
+
+ align:start position:0%
+Dynamics which is again a sort of
+ 
+
+ align:start position:0%
+Dynamics which is again a sort of
+obvious idea you know if stuff runs too
+
+ align:start position:0%
+obvious idea you know if stuff runs too
+ 
+
+ align:start position:0%
+obvious idea you know if stuff runs too
+slow at low temperature run it at higher
+
+ align:start position:0%
+slow at low temperature run it at higher
+ 
+
+ align:start position:0%
+slow at low temperature run it at higher
+temperature and will go faster um that's
+
+ align:start position:0%
+temperature and will go faster um that's
+ 
+
+ align:start position:0%
+temperature and will go faster um that's
+actually something people have often
+
+ align:start position:0%
+actually something people have often
+ 
+
+ align:start position:0%
+actually something people have often
+done inmd without much
+
+ align:start position:0%
+done inmd without much
+ 
+
+ align:start position:0%
+done inmd without much
+justification uh what art voters group
+
+ align:start position:0%
+justification uh what art voters group
+ 
+
+ align:start position:0%
+justification uh what art voters group
+did in Los Al is essentially give this a
+
+ align:start position:0%
+did in Los Al is essentially give this a
+ 
+
+ align:start position:0%
+did in Los Al is essentially give this a
+justification and show how you can
+
+ align:start position:0%
+justification and show how you can
+ 
+
+ align:start position:0%
+justification and show how you can
+correct for that temperature difference
+
+ align:start position:0%
+correct for that temperature difference
+ 
+
+ align:start position:0%
+correct for that temperature difference
+between where you would like the result
+
+ align:start position:0%
+between where you would like the result
+ 
+
+ align:start position:0%
+between where you would like the result
+and where you're actually simulating um
+
+ align:start position:0%
+and where you're actually simulating um
+ 
+
+ align:start position:0%
+and where you're actually simulating um
+and so the idea of Tad as it's called is
+
+ align:start position:0%
+and so the idea of Tad as it's called is
+ 
+
+ align:start position:0%
+and so the idea of Tad as it's called is
+to uh use the high temperature to find
+
+ align:start position:0%
+to uh use the high temperature to find
+ 
+
+ align:start position:0%
+to uh use the high temperature to find
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+transitions but then execute them with
+
+ align:start position:0%
+transitions but then execute them with
+ 
+
+ align:start position:0%
+transitions but then execute them with
+the proper rate of the low
+
+ align:start position:0%
+the proper rate of the low
+ 
+
+ align:start position:0%
+the proper rate of the low
+temperature okay so essentially you run
+
+ align:start position:0%
+temperature okay so essentially you run
+ 
+
+ align:start position:0%
+temperature okay so essentially you run
+at high temperature so you sort of
+
+ align:start position:0%
+at high temperature so you sort of
+ 
+
+ align:start position:0%
+at high temperature so you sort of
+fairly quickly scan the potential
+
+ align:start position:0%
+fairly quickly scan the potential
+ 
+
+ align:start position:0%
+fairly quickly scan the potential
+surface and that tells you what the
+
+ align:start position:0%
+surface and that tells you what the
+ 
+
+ align:start position:0%
+surface and that tells you what the
+transitions are and then you go back to
+
+ align:start position:0%
+transitions are and then you go back to
+ 
+
+ align:start position:0%
+transitions are and then you go back to
+the low temperature and you do a sort of
+
+ align:start position:0%
+the low temperature and you do a sort of
+ 
+
+ align:start position:0%
+the low temperature and you do a sort of
+statistical mechanics a kind of kinetic
+
+ align:start position:0%
+statistical mechanics a kind of kinetic
+ 
+
+ align:start position:0%
+statistical mechanics a kind of kinetic
+Monte Carlo scheme or a um a transition
+
+ align:start position:0%
+Monte Carlo scheme or a um a transition
+ 
+
+ align:start position:0%
+Monte Carlo scheme or a um a transition
+state Theory approach and and execute
+
+ align:start position:0%
+state Theory approach and and execute
+ 
+
+ align:start position:0%
+state Theory approach and and execute
+the transitions so uh I'll show you an
+
+ align:start position:0%
+the transitions so uh I'll show you an
+ 
+
+ align:start position:0%
+the transitions so uh I'll show you an
+example um the idea is that you run at
+
+ align:start position:0%
+example um the idea is that you run at
+ 
+
+ align:start position:0%
+example um the idea is that you run at
+high temperature until a transition
+
+ align:start position:0%
+high temperature until a transition
+ 
+
+ align:start position:0%
+high temperature until a transition
+occurs once you find the transition it's
+
+ align:start position:0%
+occurs once you find the transition it's
+ 
+
+ align:start position:0%
+occurs once you find the transition it's
+a trivial matter of finding the
+
+ align:start position:0%
+a trivial matter of finding the
+ 
+
+ align:start position:0%
+a trivial matter of finding the
+activation barrier okay um then you
+
+ align:start position:0%
+activation barrier okay um then you
+ 
+
+ align:start position:0%
+activation barrier okay um then you
+reverse the transition and you run again
+
+ align:start position:0%
+reverse the transition and you run again
+ 
+
+ align:start position:0%
+reverse the transition and you run again
+at high temperature and the idea is that
+
+ align:start position:0%
+at high temperature and the idea is that
+ 
+
+ align:start position:0%
+at high temperature and the idea is that
+you get this catalog of transitions so
+
+ align:start position:0%
+you get this catalog of transitions so
+ 
+
+ align:start position:0%
+you get this catalog of transitions so
+you get this catalog of possible
+
+ align:start position:0%
+you get this catalog of possible
+ 
+
+ align:start position:0%
+you get this catalog of possible
+transitions now why do you need more
+
+ align:start position:0%
+transitions now why do you need more
+ 
+
+ align:start position:0%
+transitions now why do you need more
+than one you say well the reason is that
+
+ align:start position:0%
+than one you say well the reason is that
+ 
+
+ align:start position:0%
+than one you say well the reason is that
+the one you find at high temperature May
+
+ align:start position:0%
+the one you find at high temperature May
+ 
+
+ align:start position:0%
+the one you find at high temperature May
+not be the one that actually gets
+
+ align:start position:0%
+not be the one that actually gets
+ 
+
+ align:start position:0%
+not be the one that actually gets
+executed at low temperature if they have
+
+ align:start position:0%
+executed at low temperature if they have
+ 
+
+ align:start position:0%
+executed at low temperature if they have
+different activation barriers then their
+
+ align:start position:0%
+different activation barriers then their
+ 
+
+ align:start position:0%
+different activation barriers then their
+rates may cross with
+
+ align:start position:0%
+rates may cross with
+ 
+
+ align:start position:0%
+rates may cross with
+temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um here's an example if I show The
+
+ align:start position:0%
+um here's an example if I show The
+ 
+
+ align:start position:0%
+um here's an example if I show The
+Crossing
+
+ align:start position:0%
+Crossing
+ 
+
+ align:start position:0%
+Crossing
+rate okay versus 1 overt let's say you
+
+ align:start position:0%
+rate okay versus 1 overt let's say you
+ 
+
+ align:start position:0%
+rate okay versus 1 overt let's say you
+run at high temperature uh you know if
+
+ align:start position:0%
+run at high temperature uh you know if
+ 
+
+ align:start position:0%
+run at high temperature uh you know if
+these behave arenus then their Crossing
+
+ align:start position:0%
+these behave arenus then their Crossing
+ 
+
+ align:start position:0%
+these behave arenus then their Crossing
+rate which is one one over the time you
+
+ align:start position:0%
+rate which is one one over the time you
+ 
+
+ align:start position:0%
+rate which is one one over the time you
+have to wait goes like 1 over T um you
+
+ align:start position:0%
+have to wait goes like 1 over T um you
+ 
+
+ align:start position:0%
+have to wait goes like 1 over T um you
+may find one that has a high Crossing
+
+ align:start position:0%
+may find one that has a high Crossing
+ 
+
+ align:start position:0%
+may find one that has a high Crossing
+rate at high
+
+ align:start position:0%
+rate at high
+ 
+
+ align:start position:0%
+rate at high
+temperature and one and this one that
+
+ align:start position:0%
+temperature and one and this one that
+ 
+
+ align:start position:0%
+temperature and one and this one that
+has a a lower Crossing rate at high
+
+ align:start position:0%
+has a a lower Crossing rate at high
+ 
+
+ align:start position:0%
+has a a lower Crossing rate at high
+temperature but if they have a different
+
+ align:start position:0%
+temperature but if they have a different
+ 
+
+ align:start position:0%
+temperature but if they have a different
+activation barrier they'll extrapolate
+
+ align:start position:0%
+activation barrier they'll extrapolate
+ 
+
+ align:start position:0%
+activation barrier they'll extrapolate
+differently to low temperature what you
+
+ align:start position:0%
+differently to low temperature what you
+ 
+
+ align:start position:0%
+differently to low temperature what you
+see now at low
+
+ align:start position:0%
+see now at low
+ 
+
+ align:start position:0%
+see now at low
+temperature okay the one with the high
+
+ align:start position:0%
+temperature okay the one with the high
+ 
+
+ align:start position:0%
+temperature okay the one with the high
+rate at high temperature has the lower
+
+ align:start position:0%
+rate at high temperature has the lower
+ 
+
+ align:start position:0%
+rate at high temperature has the lower
+rate at low temperature okay so because
+
+ align:start position:0%
+rate at low temperature okay so because
+ 
+
+ align:start position:0%
+rate at low temperature okay so because
+transition have different activation
+
+ align:start position:0%
+transition have different activation
+ 
+
+ align:start position:0%
+transition have different activation
+barriers they may not be in the same
+
+ align:start position:0%
+barriers they may not be in the same
+ 
+
+ align:start position:0%
+barriers they may not be in the same
+order the sort of same frequency the
+
+ align:start position:0%
+order the sort of same frequency the
+ 
+
+ align:start position:0%
+order the sort of same frequency the
+same rate at different
+
+ align:start position:0%
+same rate at different
+ 
+
+ align:start position:0%
+same rate at different
+temperatures and that's why you need a
+
+ align:start position:0%
+temperatures and that's why you need a
+ 
+
+ align:start position:0%
+temperatures and that's why you need a
+catalog of them you essentially need a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+window
+
+ align:start position:0%
+window
+ 
+
+ align:start position:0%
+window
+okay of rates of transition rates that
+
+ align:start position:0%
+okay of rates of transition rates that
+ 
+
+ align:start position:0%
+okay of rates of transition rates that
+give you a certain certainty that at the
+
+ align:start position:0%
+give you a certain certainty that at the
+ 
+
+ align:start position:0%
+give you a certain certainty that at the
+lower temperature you found the lowest
+
+ align:start position:0%
+lower temperature you found the lowest
+ 
+
+ align:start position:0%
+lower temperature you found the lowest
+one and you can kind of do back of the
+
+ align:start position:0%
+one and you can kind of do back of the
+ 
+
+ align:start position:0%
+one and you can kind of do back of the
+envelope calculation
+
+ align:start position:0%
+envelope calculation
+ 
+
+ align:start position:0%
+envelope calculation
+if you um make some assumptions about
+
+ align:start position:0%
+if you um make some assumptions about
+ 
+
+ align:start position:0%
+if you um make some assumptions about
+the range in which your EAS your
+
+ align:start position:0%
+the range in which your EAS your
+ 
+
+ align:start position:0%
+the range in which your EAS your
+activation barrier can vary then you
+
+ align:start position:0%
+activation barrier can vary then you
+ 
+
+ align:start position:0%
+activation barrier can vary then you
+know the range of slopes of these arous
+
+ align:start position:0%
+know the range of slopes of these arous
+ 
+
+ align:start position:0%
+know the range of slopes of these arous
+walls okay so that can tell you a little
+
+ align:start position:0%
+walls okay so that can tell you a little
+ 
+
+ align:start position:0%
+walls okay so that can tell you a little
+bit about how long you should be running
+
+ align:start position:0%
+bit about how long you should be running
+ 
+
+ align:start position:0%
+bit about how long you should be running
+okay uh at the high temperature to make
+
+ align:start position:0%
+okay uh at the high temperature to make
+ 
+
+ align:start position:0%
+okay uh at the high temperature to make
+sure you you found all the transitions
+
+ align:start position:0%
+sure you you found all the transitions
+ 
+
+ align:start position:0%
+sure you you found all the transitions
+or are likely to have found all the
+
+ align:start position:0%
+or are likely to have found all the
+ 
+
+ align:start position:0%
+or are likely to have found all the
+transitions that get executed at the low
+
+ align:start position:0%
+transitions that get executed at the low
+ 
+
+ align:start position:0%
+transitions that get executed at the low
+temperature so as everybody see the idea
+
+ align:start position:0%
+temperature so as everybody see the idea
+ 
+
+ align:start position:0%
+temperature so as everybody see the idea
+you're essentially using
+
+ align:start position:0%
+you're essentially using
+ 
+
+ align:start position:0%
+you're essentially using
+uh molecular Dynamics as a way of
+
+ align:start position:0%
+uh molecular Dynamics as a way of
+ 
+
+ align:start position:0%
+uh molecular Dynamics as a way of
+finding Transitions okay and that's the
+
+ align:start position:0%
+finding Transitions okay and that's the
+ 
+
+ align:start position:0%
+finding Transitions okay and that's the
+hard problem in any kinetic problem it's
+
+ align:start position:0%
+hard problem in any kinetic problem it's
+ 
+
+ align:start position:0%
+hard problem in any kinetic problem it's
+finding the transitions once you find
+
+ align:start position:0%
+finding the transitions once you find
+ 
+
+ align:start position:0%
+finding the transitions once you find
+them you know you can calculate their
+
+ align:start position:0%
+them you know you can calculate their
+ 
+
+ align:start position:0%
+them you know you can calculate their
+activation barrier and you can execute
+
+ align:start position:0%
+activation barrier and you can execute
+ 
+
+ align:start position:0%
+activation barrier and you can execute
+them with you know standard rate
+
+ align:start position:0%
+them with you know standard rate
+ 
+
+ align:start position:0%
+them with you know standard rate
+constant Theory but it's finding them
+
+ align:start position:0%
+constant Theory but it's finding them
+ 
+
+ align:start position:0%
+constant Theory but it's finding them
+and MD because it's unbiased is great um
+
+ align:start position:0%
+and MD because it's unbiased is great um
+ 
+
+ align:start position:0%
+and MD because it's unbiased is great um
+at doing that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the approximations of the method
+
+ align:start position:0%
+okay so the approximations of the method
+ 
+
+ align:start position:0%
+okay so the approximations of the method
+are fairly obvious um to do this
+
+ align:start position:0%
+are fairly obvious um to do this
+ 
+
+ align:start position:0%
+are fairly obvious um to do this
+extrapolation you assume harmonic
+
+ align:start position:0%
+extrapolation you assume harmonic
+ 
+
+ align:start position:0%
+extrapolation you assume harmonic
+transition state Theory so you
+
+ align:start position:0%
+transition state Theory so you
+ 
+
+ align:start position:0%
+transition state Theory so you
+essentially assume that you have a
+
+ align:start position:0%
+essentially assume that you have a
+ 
+
+ align:start position:0%
+essentially assume that you have a
+simple arenus extrapolation between
+
+ align:start position:0%
+simple arenus extrapolation between
+ 
+
+ align:start position:0%
+simple arenus extrapolation between
+temperature so that the pre-exponential
+
+ align:start position:0%
+temperature so that the pre-exponential
+ 
+
+ align:start position:0%
+temperature so that the pre-exponential
+factor is constant um and well like I
+
+ align:start position:0%
+factor is constant um and well like I
+ 
+
+ align:start position:0%
+factor is constant um and well like I
+said before you have to make sure that
+
+ align:start position:0%
+said before you have to make sure that
+ 
+
+ align:start position:0%
+said before you have to make sure that
+you found all the mechanisms at that you
+
+ align:start position:0%
+you found all the mechanisms at that you
+ 
+
+ align:start position:0%
+you found all the mechanisms at that you
+found enough mechanisms at high
+
+ align:start position:0%
+found enough mechanisms at high
+ 
+
+ align:start position:0%
+found enough mechanisms at high
+temperature show you definitely have the
+
+ align:start position:0%
+temperature show you definitely have the
+ 
+
+ align:start position:0%
+temperature show you definitely have the
+low the fastest one um at low
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature okay you know and here's
+
+ align:start position:0%
+temperature okay you know and here's
+ 
+
+ align:start position:0%
+temperature okay you know and here's
+another application out of uh art
+
+ align:start position:0%
+another application out of uh art
+ 
+
+ align:start position:0%
+another application out of uh art
+voter's work uh this is copper on copper
+
+ align:start position:0%
+voter's work uh this is copper on copper
+ 
+
+ align:start position:0%
+voter's work uh this is copper on copper
+deposition um so they literally I think
+
+ align:start position:0%
+deposition um so they literally I think
+ 
+
+ align:start position:0%
+deposition um so they literally I think
+add atoms to a surface and then
+
+ align:start position:0%
+add atoms to a surface and then
+ 
+
+ align:start position:0%
+add atoms to a surface and then
+equilibrate them um and you know they
+
+ align:start position:0%
+equilibrate them um and you know they
+ 
+
+ align:start position:0%
+equilibrate them um and you know they
+run so they do direct MD for two P
+
+ align:start position:0%
+run so they do direct MD for two P
+ 
+
+ align:start position:0%
+run so they do direct MD for two P
+seconds that's how they deposit the atom
+
+ align:start position:0%
+seconds that's how they deposit the atom
+ 
+
+ align:start position:0%
+seconds that's how they deposit the atom
+but then then uh run you know 3 seconds
+
+ align:start position:0%
+but then then uh run you know 3 seconds
+ 
+
+ align:start position:0%
+but then then uh run you know 3 seconds
+of intervening time with uh Tad uh now
+
+ align:start position:0%
+of intervening time with uh Tad uh now
+ 
+
+ align:start position:0%
+of intervening time with uh Tad uh now
+you may think you know 3 seconds that's
+
+ align:start position:0%
+you may think you know 3 seconds that's
+ 
+
+ align:start position:0%
+you may think you know 3 seconds that's
+a lot well it's not because you're
+
+ align:start position:0%
+a lot well it's not because you're
+ 
+
+ align:start position:0%
+a lot well it's not because you're
+really doing transition state Theory um
+
+ align:start position:0%
+really doing transition state Theory um
+ 
+
+ align:start position:0%
+really doing transition state Theory um
+if I have barriers of one electron volt
+
+ align:start position:0%
+if I have barriers of one electron volt
+ 
+
+ align:start position:0%
+if I have barriers of one electron volt
+okay then pretty much at room
+
+ align:start position:0%
+okay then pretty much at room
+ 
+
+ align:start position:0%
+okay then pretty much at room
+temperature one electron volt that tends
+
+ align:start position:0%
+temperature one electron volt that tends
+ 
+
+ align:start position:0%
+temperature one electron volt that tends
+to give you rates around one per second
+
+ align:start position:0%
+to give you rates around one per second
+ 
+
+ align:start position:0%
+to give you rates around one per second
+that's kind of the time scale so if you
+
+ align:start position:0%
+that's kind of the time scale so if you
+ 
+
+ align:start position:0%
+that's kind of the time scale so if you
+have barriers of one electron volt then
+
+ align:start position:0%
+have barriers of one electron volt then
+ 
+
+ align:start position:0%
+have barriers of one electron volt then
+every time you execute a step you're 1
+
+ align:start position:0%
+every time you execute a step you're 1
+ 
+
+ align:start position:0%
+every time you execute a step you're 1
+second further on average so the 3
+
+ align:start position:0%
+second further on average so the 3
+ 
+
+ align:start position:0%
+second further on average so the 3
+seconds is in that sense not that
+
+ align:start position:0%
+seconds is in that sense not that
+ 
+
+ align:start position:0%
+seconds is in that sense not that
+impressive you know I can do a thousand
+
+ align:start position:0%
+impressive you know I can do a thousand
+ 
+
+ align:start position:0%
+impressive you know I can do a thousand
+seconds with one step just by having a
+
+ align:start position:0%
+seconds with one step just by having a
+ 
+
+ align:start position:0%
+seconds with one step just by having a
+system with a very high activation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+barrier okay um you can look at the
+
+ align:start position:0%
+barrier okay um you can look at the
+ 
+
+ align:start position:0%
+barrier okay um you can look at the
+different events in the simulation and
+
+ align:start position:0%
+different events in the simulation and
+ 
+
+ align:start position:0%
+different events in the simulation and
+one of the nice things is because you're
+
+ align:start position:0%
+one of the nice things is because you're
+ 
+
+ align:start position:0%
+one of the nice things is because you're
+doing MD um your your system is
+
+ align:start position:0%
+doing MD um your your system is
+ 
+
+ align:start position:0%
+doing MD um your your system is
+unbiased and you know one we've learned
+
+ align:start position:0%
+unbiased and you know one we've learned
+ 
+
+ align:start position:0%
+unbiased and you know one we've learned
+more and more by doing MD on surfaces is
+
+ align:start position:0%
+more and more by doing MD on surfaces is
+ 
+
+ align:start position:0%
+more and more by doing MD on surfaces is
+that um the diffusive processes are not
+
+ align:start position:0%
+that um the diffusive processes are not
+ 
+
+ align:start position:0%
+that um the diffusive processes are not
+at all the way people thought they were
+
+ align:start position:0%
+at all the way people thought they were
+ 
+
+ align:start position:0%
+at all the way people thought they were
+people think of atoms hopping by
+
+ align:start position:0%
+people think of atoms hopping by
+ 
+
+ align:start position:0%
+people think of atoms hopping by
+themselves but because surfaces have so
+
+ align:start position:0%
+themselves but because surfaces have so
+ 
+
+ align:start position:0%
+themselves but because surfaces have so
+much open space of such low symmetry you
+
+ align:start position:0%
+much open space of such low symmetry you
+ 
+
+ align:start position:0%
+much open space of such low symmetry you
+see a lot of collectic Behavior Uh for
+
+ align:start position:0%
+see a lot of collectic Behavior Uh for
+ 
+
+ align:start position:0%
+see a lot of collectic Behavior Uh for
+example here's one um this this blue
+
+ align:start position:0%
+example here's one um this this blue
+ 
+
+ align:start position:0%
+example here's one um this this blue
+atom here um pushes in the surface
+
+ align:start position:0%
+atom here um pushes in the surface
+ 
+
+ align:start position:0%
+atom here um pushes in the surface
+pushing that um
+
+ align:start position:0%
+pushing that um
+ 
+
+ align:start position:0%
+pushing that um
+um uh orange at them or kind of what is
+
+ align:start position:0%
+um uh orange at them or kind of what is
+ 
+
+ align:start position:0%
+um uh orange at them or kind of what is
+it brown and that pushes then these two
+
+ align:start position:0%
+it brown and that pushes then these two
+ 
+
+ align:start position:0%
+it brown and that pushes then these two
+out and that's all one Collective event
+
+ align:start position:0%
+out and that's all one Collective event
+ 
+
+ align:start position:0%
+out and that's all one Collective event
+okay so these are not things you would
+
+ align:start position:0%
+okay so these are not things you would
+ 
+
+ align:start position:0%
+okay so these are not things you would
+easily guess
+
+ align:start position:0%
+easily guess
+ 
+
+ align:start position:0%
+easily guess
+at um here's another Collective event of
+
+ align:start position:0%
+at um here's another Collective event of
+ 
+
+ align:start position:0%
+at um here's another Collective event of
+sort of a kind of um row of atoms three
+
+ align:start position:0%
+sort of a kind of um row of atoms three
+ 
+
+ align:start position:0%
+sort of a kind of um row of atoms three
+at a time at a step Edge essentially
+
+ align:start position:0%
+at a time at a step Edge essentially
+ 
+
+ align:start position:0%
+at a time at a step Edge essentially
+kind of moving down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you you you typically need MD methods
+
+ align:start position:0%
+so you you you typically need MD methods
+ 
+
+ align:start position:0%
+so you you you typically need MD methods
+um whenever you don't know or you're not
+
+ align:start position:0%
+um whenever you don't know or you're not
+ 
+
+ align:start position:0%
+um whenever you don't know or you're not
+absolutely sure what the transition
+
+ align:start position:0%
+absolutely sure what the transition
+ 
+
+ align:start position:0%
+absolutely sure what the transition
+mechanisms are if you know what the
+
+ align:start position:0%
+mechanisms are if you know what the
+ 
+
+ align:start position:0%
+mechanisms are if you know what the
+transition mechanisms are then it tends
+
+ align:start position:0%
+transition mechanisms are then it tends
+ 
+
+ align:start position:0%
+transition mechanisms are then it tends
+to be much more efficient to do Mont
+
+ align:start position:0%
+to be much more efficient to do Mont
+ 
+
+ align:start position:0%
+to be much more efficient to do Mont
+Carlo okay you can set up kinetic Monte
+
+ align:start position:0%
+Carlo okay you can set up kinetic Monte
+ 
+
+ align:start position:0%
+Carlo okay you can set up kinetic Monte
+Carlo schemes um that execute
+
+ align:start position:0%
+Carlo schemes um that execute
+ 
+
+ align:start position:0%
+Carlo schemes um that execute
+transitions with the right uh transfer
+
+ align:start position:0%
+transitions with the right uh transfer
+ 
+
+ align:start position:0%
+transitions with the right uh transfer
+it's just that you have to know what
+
+ align:start position:0%
+it's just that you have to know what
+ 
+
+ align:start position:0%
+it's just that you have to know what
+those transitions are so you've already
+
+ align:start position:0%
+those transitions are so you've already
+ 
+
+ align:start position:0%
+those transitions are so you've already
+done Monte Carlo and lce models but we
+
+ align:start position:0%
+done Monte Carlo and lce models but we
+ 
+
+ align:start position:0%
+done Monte Carlo and lce models but we
+saw it as a sampling method um you could
+
+ align:start position:0%
+saw it as a sampling method um you could
+ 
+
+ align:start position:0%
+saw it as a sampling method um you could
+also now see it as a kinetic method you
+
+ align:start position:0%
+also now see it as a kinetic method you
+ 
+
+ align:start position:0%
+also now see it as a kinetic method you
+know let's say you have a latus of
+
+ align:start position:0%
+know let's say you have a latus of
+ 
+
+ align:start position:0%
+know let's say you have a latus of
+atoms let's make it easier even atoms
+
+ align:start position:0%
+atoms let's make it easier even atoms
+ 
+
+ align:start position:0%
+atoms let's make it easier even atoms
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+vacancies you
+
+ align:start position:0%
+vacancies you
+ 
+
+ align:start position:0%
+vacancies you
+know so we've shown you how to do the
+
+ align:start position:0%
+know so we've shown you how to do the
+ 
+
+ align:start position:0%
+know so we've shown you how to do the
+thermodynamics well let's say you want
+
+ align:start position:0%
+thermodynamics well let's say you want
+ 
+
+ align:start position:0%
+thermodynamics well let's say you want
+to study
+
+ align:start position:0%
+to study
+ 
+
+ align:start position:0%
+to study
+diffusion if you know microscopically
+
+ align:start position:0%
+diffusion if you know microscopically
+ 
+
+ align:start position:0%
+diffusion if you know microscopically
+how this atom would migrate to there
+
+ align:start position:0%
+how this atom would migrate to there
+ 
+
+ align:start position:0%
+how this atom would migrate to there
+through which path it would do that then
+
+ align:start position:0%
+through which path it would do that then
+ 
+
+ align:start position:0%
+through which path it would do that then
+you just calculate the energy along that
+
+ align:start position:0%
+you just calculate the energy along that
+ 
+
+ align:start position:0%
+you just calculate the energy along that
+path and you can now do a mon Carlo
+
+ align:start position:0%
+path and you can now do a mon Carlo
+ 
+
+ align:start position:0%
+path and you can now do a mon Carlo
+where the way you travel through face
+
+ align:start position:0%
+where the way you travel through face
+ 
+
+ align:start position:0%
+where the way you travel through face
+space is by a a real kinetic mechanism
+
+ align:start position:0%
+space is by a a real kinetic mechanism
+ 
+
+ align:start position:0%
+space is by a a real kinetic mechanism
+okay so you could not take your exchange
+
+ align:start position:0%
+okay so you could not take your exchange
+ 
+
+ align:start position:0%
+okay so you could not take your exchange
+rate dependent not only on the energy of
+
+ align:start position:0%
+rate dependent not only on the energy of
+ 
+
+ align:start position:0%
+rate dependent not only on the energy of
+the initial and the final state which is
+
+ align:start position:0%
+the initial and the final state which is
+ 
+
+ align:start position:0%
+the initial and the final state which is
+the way we did it in the Metropolis
+
+ align:start position:0%
+the way we did it in the Metropolis
+ 
+
+ align:start position:0%
+the way we did it in the Metropolis
+algorithm but also have a preactor now
+
+ align:start position:0%
+algorithm but also have a preactor now
+ 
+
+ align:start position:0%
+algorithm but also have a preactor now
+that kinetic so that has a frequency
+
+ align:start position:0%
+that kinetic so that has a frequency
+ 
+
+ align:start position:0%
+that kinetic so that has a frequency
+times an activation barrier that's
+
+ align:start position:0%
+times an activation barrier that's
+ 
+
+ align:start position:0%
+times an activation barrier that's
+essentially kinetic mon Carlo okay but
+
+ align:start position:0%
+essentially kinetic mon Carlo okay but
+ 
+
+ align:start position:0%
+essentially kinetic mon Carlo okay but
+you see kinetic mon car implies that you
+
+ align:start position:0%
+you see kinetic mon car implies that you
+ 
+
+ align:start position:0%
+you see kinetic mon car implies that you
+know what your
+
+ align:start position:0%
+know what your
+ 
+
+ align:start position:0%
+know what your
+possible migration mechanisms are
+
+ align:start position:0%
+possible migration mechanisms are
+ 
+
+ align:start position:0%
+possible migration mechanisms are
+between states and usually um you know
+
+ align:start position:0%
+between states and usually um you know
+ 
+
+ align:start position:0%
+between states and usually um you know
+that reasonably well in things like
+
+ align:start position:0%
+that reasonably well in things like
+ 
+
+ align:start position:0%
+that reasonably well in things like
+crystalline solids so there kinetic
+
+ align:start position:0%
+crystalline solids so there kinetic
+ 
+
+ align:start position:0%
+crystalline solids so there kinetic
+monol is very applicable people also use
+
+ align:start position:0%
+monol is very applicable people also use
+ 
+
+ align:start position:0%
+monol is very applicable people also use
+it on surfaces even though it gets a
+
+ align:start position:0%
+it on surfaces even though it gets a
+ 
+
+ align:start position:0%
+it on surfaces even though it gets a
+little more dicey there um but once of
+
+ align:start position:0%
+little more dicey there um but once of
+ 
+
+ align:start position:0%
+little more dicey there um but once of
+course you go to sort of very disorted
+
+ align:start position:0%
+course you go to sort of very disorted
+ 
+
+ align:start position:0%
+course you go to sort of very disorted
+systems it it really gets way out of
+
+ align:start position:0%
+systems it it really gets way out of
+ 
+
+ align:start position:0%
+systems it it really gets way out of
+hand what the kinetic mechanisms are and
+
+ align:start position:0%
+hand what the kinetic mechanisms are and
+ 
+
+ align:start position:0%
+hand what the kinetic mechanisms are and
+this wouldn't work
+
+ align:start position:0%
+this wouldn't work
+ 
+
+ align:start position:0%
+this wouldn't work
+anymore so I was going to show you one
+
+ align:start position:0%
+anymore so I was going to show you one
+ 
+
+ align:start position:0%
+anymore so I was going to show you one
+example to sort of end up and um at a
+
+ align:start position:0%
+example to sort of end up and um at a
+ 
+
+ align:start position:0%
+example to sort of end up and um at a
+continuity I was going to take the same
+
+ align:start position:0%
+continuity I was going to take the same
+ 
+
+ align:start position:0%
+continuity I was going to take the same
+example that we did for the phase
+
+ align:start position:0%
+example that we did for the phase
+ 
+
+ align:start position:0%
+example that we did for the phase
+stability if you remember this uh when
+
+ align:start position:0%
+stability if you remember this uh when
+ 
+
+ align:start position:0%
+stability if you remember this uh when
+we talked about the cluster expansion we
+
+ align:start position:0%
+we talked about the cluster expansion we
+ 
+
+ align:start position:0%
+we talked about the cluster expansion we
+looked at the phase diagram of um
+
+ align:start position:0%
+looked at the phase diagram of um
+ 
+
+ align:start position:0%
+looked at the phase diagram of um
+lithium and lithium vacancies in lithium
+
+ align:start position:0%
+lithium and lithium vacancies in lithium
+ 
+
+ align:start position:0%
+lithium and lithium vacancies in lithium
+Coral oxide so remember the issue is
+
+ align:start position:0%
+Coral oxide so remember the issue is
+ 
+
+ align:start position:0%
+Coral oxide so remember the issue is
+that if you take lithium out
+
+ align:start position:0%
+that if you take lithium out
+ 
+
+ align:start position:0%
+that if you take lithium out
+you create vacancies there and and the
+
+ align:start position:0%
+you create vacancies there and and the
+ 
+
+ align:start position:0%
+you create vacancies there and and the
+issue was how do they organize and I
+
+ align:start position:0%
+issue was how do they organize and I
+ 
+
+ align:start position:0%
+issue was how do they organize and I
+showed you how to use a cluster
+
+ align:start position:0%
+showed you how to use a cluster
+ 
+
+ align:start position:0%
+showed you how to use a cluster
+expansion to do the phase AR and the
+
+ align:start position:0%
+expansion to do the phase AR and the
+ 
+
+ align:start position:0%
+expansion to do the phase AR and the
+thermodynamics of that let's say you
+
+ align:start position:0%
+thermodynamics of that let's say you
+ 
+
+ align:start position:0%
+thermodynamics of that let's say you
+want to worry about the kinetics so
+
+ align:start position:0%
+want to worry about the kinetics so
+ 
+
+ align:start position:0%
+want to worry about the kinetics so
+essentially how fast can you get that
+
+ align:start position:0%
+essentially how fast can you get that
+ 
+
+ align:start position:0%
+essentially how fast can you get that
+lithium in and out so you essentially
+
+ align:start position:0%
+lithium in and out so you essentially
+ 
+
+ align:start position:0%
+lithium in and out so you essentially
+want a diffusion constant in that
+
+ align:start position:0%
+want a diffusion constant in that
+ 
+
+ align:start position:0%
+want a diffusion constant in that
+material um well this is fairly well
+
+ align:start position:0%
+material um well this is fairly well
+ 
+
+ align:start position:0%
+material um well this is fairly well
+suited for kinetic Monte Carlo rather
+
+ align:start position:0%
+suited for kinetic Monte Carlo rather
+ 
+
+ align:start position:0%
+suited for kinetic Monte Carlo rather
+than molecular Dynamics first of all the
+
+ align:start position:0%
+than molecular Dynamics first of all the
+ 
+
+ align:start position:0%
+than molecular Dynamics first of all the
+rates are fairly slow so um doing
+
+ align:start position:0%
+rates are fairly slow so um doing
+ 
+
+ align:start position:0%
+rates are fairly slow so um doing
+anything with transition state theory is
+
+ align:start position:0%
+anything with transition state theory is
+ 
+
+ align:start position:0%
+anything with transition state theory is
+going to help you a lot uh and it's um
+
+ align:start position:0%
+going to help you a lot uh and it's um
+ 
+
+ align:start position:0%
+going to help you a lot uh and it's um
+you you have transitions between
+
+ align:start position:0%
+you you have transitions between
+ 
+
+ align:start position:0%
+you you have transitions between
+welldefined positions you know the atoms
+
+ align:start position:0%
+welldefined positions you know the atoms
+ 
+
+ align:start position:0%
+welldefined positions you know the atoms
+go from one well-defined side to another
+
+ align:start position:0%
+go from one well-defined side to another
+ 
+
+ align:start position:0%
+go from one well-defined side to another
+side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um if you had dute diffusion uh you
+
+ align:start position:0%
+um if you had dute diffusion uh you
+ 
+
+ align:start position:0%
+um if you had dute diffusion uh you
+could just use random walk Theory so in
+
+ align:start position:0%
+could just use random walk Theory so in
+ 
+
+ align:start position:0%
+could just use random walk Theory so in
+that case diffusion is sort of trivial
+
+ align:start position:0%
+that case diffusion is sort of trivial
+ 
+
+ align:start position:0%
+that case diffusion is sort of trivial
+all you need is an activation barrier
+
+ align:start position:0%
+all you need is an activation barrier
+ 
+
+ align:start position:0%
+all you need is an activation barrier
+and a preactor all the rest you know you
+
+ align:start position:0%
+and a preactor all the rest you know you
+ 
+
+ align:start position:0%
+and a preactor all the rest you know you
+have the lce constant which is actually
+
+ align:start position:0%
+have the lce constant which is actually
+ 
+
+ align:start position:0%
+have the lce constant which is actually
+the jump link and you have the geometric
+
+ align:start position:0%
+the jump link and you have the geometric
+ 
+
+ align:start position:0%
+the jump link and you have the geometric
+correlation Factor these are all known
+
+ align:start position:0%
+correlation Factor these are all known
+ 
+
+ align:start position:0%
+correlation Factor these are all known
+the things in green you would have to
+
+ align:start position:0%
+the things in green you would have to
+ 
+
+ align:start position:0%
+the things in green you would have to
+calculate but that's two calculation
+
+ align:start position:0%
+calculate but that's two calculation
+ 
+
+ align:start position:0%
+calculate but that's two calculation
+random walks only apply when you have
+
+ align:start position:0%
+random walks only apply when you have
+ 
+
+ align:start position:0%
+random walks only apply when you have
+dilute diffusion what I mean with dilute
+
+ align:start position:0%
+dilute diffusion what I mean with dilute
+ 
+
+ align:start position:0%
+dilute diffusion what I mean with dilute
+diffusion um it's when the carrier of
+
+ align:start position:0%
+diffusion um it's when the carrier of
+ 
+
+ align:start position:0%
+diffusion um it's when the carrier of
+diffusion is very dilute so it doesn't
+
+ align:start position:0%
+diffusion is very dilute so it doesn't
+ 
+
+ align:start position:0%
+diffusion is very dilute so it doesn't
+interact um uh with itself so if you
+
+ align:start position:0%
+interact um uh with itself so if you
+ 
+
+ align:start position:0%
+interact um uh with itself so if you
+have substitutional diffusion with very
+
+ align:start position:0%
+have substitutional diffusion with very
+ 
+
+ align:start position:0%
+have substitutional diffusion with very
+dilute vacancy concentration then this
+
+ align:start position:0%
+dilute vacancy concentration then this
+ 
+
+ align:start position:0%
+dilute vacancy concentration then this
+would apply um the problem of course
+
+ align:start position:0%
+would apply um the problem of course
+ 
+
+ align:start position:0%
+would apply um the problem of course
+that we're going to look at the lithium
+
+ align:start position:0%
+that we're going to look at the lithium
+ 
+
+ align:start position:0%
+that we're going to look at the lithium
+Cobalt waxin is by definition not dilute
+
+ align:start position:0%
+Cobalt waxin is by definition not dilute
+ 
+
+ align:start position:0%
+Cobalt waxin is by definition not dilute
+you essentially can go all the way from
+
+ align:start position:0%
+you essentially can go all the way from
+ 
+
+ align:start position:0%
+you essentially can go all the way from
+all lithium on the SES to all vacancies
+
+ align:start position:0%
+all lithium on the SES to all vacancies
+ 
+
+ align:start position:0%
+all lithium on the SES to all vacancies
+on the SES okay so you go to very non-
+
+ align:start position:0%
+on the SES okay so you go to very non-
+ 
+
+ align:start position:0%
+on the SES okay so you go to very non-
+dilute regimes um if you want to do that
+
+ align:start position:0%
+dilute regimes um if you want to do that
+ 
+
+ align:start position:0%
+dilute regimes um if you want to do that
+you need to actually simulate the
+
+ align:start position:0%
+you need to actually simulate the
+ 
+
+ align:start position:0%
+you need to actually simulate the
+diffusion and and you may have even done
+
+ align:start position:0%
+diffusion and and you may have even done
+ 
+
+ align:start position:0%
+diffusion and and you may have even done
+that in the MD homework um by doing some
+
+ align:start position:0%
+that in the MD homework um by doing some
+ 
+
+ align:start position:0%
+that in the MD homework um by doing some
+kinetic model and then tracking the root
+
+ align:start position:0%
+kinetic model and then tracking the root
+ 
+
+ align:start position:0%
+kinetic model and then tracking the root
+mean Square displacement um this is sort
+
+ align:start position:0%
+mean Square displacement um this is sort
+ 
+
+ align:start position:0%
+mean Square displacement um this is sort
+of a simple form for the self diffusion
+
+ align:start position:0%
+of a simple form for the self diffusion
+ 
+
+ align:start position:0%
+of a simple form for the self diffusion
+um the chemical diffusion constant which
+
+ align:start position:0%
+um the chemical diffusion constant which
+ 
+
+ align:start position:0%
+um the chemical diffusion constant which
+is the one you would use in macroscopic
+
+ align:start position:0%
+is the one you would use in macroscopic
+ 
+
+ align:start position:0%
+is the one you would use in macroscopic
+theories is the self diffusion times the
+
+ align:start position:0%
+theories is the self diffusion times the
+ 
+
+ align:start position:0%
+theories is the self diffusion times the
+ther thermodynamic Factor but the
+
+ align:start position:0%
+ther thermodynamic Factor but the
+ 
+
+ align:start position:0%
+ther thermodynamic Factor but the
+thermodynamic factor is essentially the
+
+ align:start position:0%
+thermodynamic factor is essentially the
+ 
+
+ align:start position:0%
+thermodynamic factor is essentially the
+derivative of the chemical potential
+
+ align:start position:0%
+derivative of the chemical potential
+ 
+
+ align:start position:0%
+derivative of the chemical potential
+with composition so that you already
+
+ align:start position:0%
+with composition so that you already
+ 
+
+ align:start position:0%
+with composition so that you already
+have from the thermodynamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculation okay
+
+ align:start position:0%
+calculation okay
+ 
+
+ align:start position:0%
+calculation okay
+um so I have a few more slides here that
+
+ align:start position:0%
+um so I have a few more slides here that
+ 
+
+ align:start position:0%
+um so I have a few more slides here that
+I already Ed so I'm going to create to
+
+ align:start position:0%
+I already Ed so I'm going to create to
+ 
+
+ align:start position:0%
+I already Ed so I'm going to create to
+them uh you remember how we did the
+
+ align:start position:0%
+them uh you remember how we did the
+ 
+
+ align:start position:0%
+them uh you remember how we did the
+thermodynamics so we build a latus model
+
+ align:start position:0%
+thermodynamics so we build a latus model
+ 
+
+ align:start position:0%
+thermodynamics so we build a latus model
+uh we calculate a lot of lithium vacancy
+
+ align:start position:0%
+uh we calculate a lot of lithium vacancy
+ 
+
+ align:start position:0%
+uh we calculate a lot of lithium vacancy
+Arrangement build a cluster expansion
+
+ align:start position:0%
+Arrangement build a cluster expansion
+ 
+
+ align:start position:0%
+Arrangement build a cluster expansion
+and do Monte Carlo on that and that
+
+ align:start position:0%
+and do Monte Carlo on that and that
+ 
+
+ align:start position:0%
+and do Monte Carlo on that and that
+gives you the phase
+
+ align:start position:0%
+gives you the phase
+ 
+
+ align:start position:0%
+gives you the phase
+diagram um me skip that since we did
+
+ align:start position:0%
+diagram um me skip that since we did
+ 
+
+ align:start position:0%
+diagram um me skip that since we did
+that already those are the interactions
+
+ align:start position:0%
+that already those are the interactions
+ 
+
+ align:start position:0%
+that already those are the interactions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um how would you do kinetic Monte Carlo
+
+ align:start position:0%
+um how would you do kinetic Monte Carlo
+ 
+
+ align:start position:0%
+um how would you do kinetic Monte Carlo
+I sort of also mentioned that you would
+
+ align:start position:0%
+I sort of also mentioned that you would
+ 
+
+ align:start position:0%
+I sort of also mentioned that you would
+now execute only exchanges in the Monte
+
+ align:start position:0%
+now execute only exchanges in the Monte
+ 
+
+ align:start position:0%
+now execute only exchanges in the Monte
+Carlo that look like diffusive processes
+
+ align:start position:0%
+Carlo that look like diffusive processes
+ 
+
+ align:start position:0%
+Carlo that look like diffusive processes
+and you would execute them with the
+
+ align:start position:0%
+and you would execute them with the
+ 
+
+ align:start position:0%
+and you would execute them with the
+proper rate um so you would have an
+
+ align:start position:0%
+proper rate um so you would have an
+ 
+
+ align:start position:0%
+proper rate um so you would have an
+activation barrier in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay I think I said all this
+
+ align:start position:0%
+there okay I think I said all this
+ 
+
+ align:start position:0%
+there okay I think I said all this
+okay so here's an example of how that
+
+ align:start position:0%
+okay so here's an example of how that
+ 
+
+ align:start position:0%
+okay so here's an example of how that
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+out uh if you calculate barriers in
+
+ align:start position:0%
+out uh if you calculate barriers in
+ 
+
+ align:start position:0%
+out uh if you calculate barriers in
+lithium Coral oxide and you then do a
+
+ align:start position:0%
+lithium Coral oxide and you then do a
+ 
+
+ align:start position:0%
+lithium Coral oxide and you then do a
+kinetic mon caral simulation you keep
+
+ align:start position:0%
+kinetic mon caral simulation you keep
+ 
+
+ align:start position:0%
+kinetic mon caral simulation you keep
+track of the root mean Square
+
+ align:start position:0%
+track of the root mean Square
+ 
+
+ align:start position:0%
+track of the root mean Square
+displacement uh you get the macroscopic
+
+ align:start position:0%
+displacement uh you get the macroscopic
+ 
+
+ align:start position:0%
+displacement uh you get the macroscopic
+diffusivity uh and as you see um it
+
+ align:start position:0%
+diffusivity uh and as you see um it
+ 
+
+ align:start position:0%
+diffusivity uh and as you see um it
+varies by orders of magnitude it's 10- 7
+
+ align:start position:0%
+varies by orders of magnitude it's 10- 7
+ 
+
+ align:start position:0%
+varies by orders of magnitude it's 10- 7
+here C uh cenim s/ Second and it's 10-3
+
+ align:start position:0%
+here C uh cenim s/ Second and it's 10-3
+ 
+
+ align:start position:0%
+here C uh cenim s/ Second and it's 10-3
+here you can already see that you would
+
+ align:start position:0%
+here you can already see that you would
+ 
+
+ align:start position:0%
+here you can already see that you would
+never get to all these time scales uh
+
+ align:start position:0%
+never get to all these time scales uh
+ 
+
+ align:start position:0%
+never get to all these time scales uh
+with a simple Dynamics uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model okay um how you get uh activation
+
+ align:start position:0%
+model okay um how you get uh activation
+ 
+
+ align:start position:0%
+model okay um how you get uh activation
+barriers uh typically we get this with
+
+ align:start position:0%
+barriers uh typically we get this with
+ 
+
+ align:start position:0%
+barriers uh typically we get this with
+what's called a nud nudged elastic band
+
+ align:start position:0%
+what's called a nud nudged elastic band
+ 
+
+ align:start position:0%
+what's called a nud nudged elastic band
+model um you
+
+ align:start position:0%
+model um you
+ 
+
+ align:start position:0%
+model um you
+know what's the issue in finding
+
+ align:start position:0%
+know what's the issue in finding
+ 
+
+ align:start position:0%
+know what's the issue in finding
+activation barriers well you know the
+
+ align:start position:0%
+activation barriers well you know the
+ 
+
+ align:start position:0%
+activation barriers well you know the
+initial State and you know the final
+
+ align:start position:0%
+initial State and you know the final
+ 
+
+ align:start position:0%
+initial State and you know the final
+State this is not necessarily the state
+
+ align:start position:0%
+State this is not necessarily the state
+ 
+
+ align:start position:0%
+State this is not necessarily the state
+of an atom you really should think of
+
+ align:start position:0%
+of an atom you really should think of
+ 
+
+ align:start position:0%
+of an atom you really should think of
+these as two states in face space now if
+
+ align:start position:0%
+these as two states in face space now if
+ 
+
+ align:start position:0%
+these as two states in face space now if
+for Simplicity you can think well only
+
+ align:start position:0%
+for Simplicity you can think well only
+ 
+
+ align:start position:0%
+for Simplicity you can think well only
+one atom moves is different between the
+
+ align:start position:0%
+one atom moves is different between the
+ 
+
+ align:start position:0%
+one atom moves is different between the
+those two states but in reality more
+
+ align:start position:0%
+those two states but in reality more
+ 
+
+ align:start position:0%
+those two states but in reality more
+stuff is different because if the atom
+
+ align:start position:0%
+stuff is different because if the atom
+ 
+
+ align:start position:0%
+stuff is different because if the atom
+has moved the other atoms may have
+
+ align:start position:0%
+has moved the other atoms may have
+ 
+
+ align:start position:0%
+has moved the other atoms may have
+relaxed around it so these are really
+
+ align:start position:0%
+relaxed around it so these are really
+ 
+
+ align:start position:0%
+relaxed around it so these are really
+States in face space um so what you have
+
+ align:start position:0%
+States in face space um so what you have
+ 
+
+ align:start position:0%
+States in face space um so what you have
+to find is the path between the
+
+ align:start position:0%
+to find is the path between the
+ 
+
+ align:start position:0%
+to find is the path between the
+two with the lowest Max Energy maximum
+
+ align:start position:0%
+two with the lowest Max Energy maximum
+ 
+
+ align:start position:0%
+two with the lowest Max Energy maximum
+along that path that's essentially the
+
+ align:start position:0%
+along that path that's essentially the
+ 
+
+ align:start position:0%
+along that path that's essentially the
+activated State um and a very practical
+
+ align:start position:0%
+activated State um and a very practical
+ 
+
+ align:start position:0%
+activated State um and a very practical
+way to find is What's called the nudge
+
+ align:start position:0%
+way to find is What's called the nudge
+ 
+
+ align:start position:0%
+way to find is What's called the nudge
+elastic band model which is essentially
+
+ align:start position:0%
+elastic band model which is essentially
+ 
+
+ align:start position:0%
+elastic band model which is essentially
+that you do a
+
+ align:start position:0%
+that you do a
+ 
+
+ align:start position:0%
+that you do a
+simulation uh on many systems at a time
+
+ align:start position:0%
+simulation uh on many systems at a time
+ 
+
+ align:start position:0%
+simulation uh on many systems at a time
+and all the systems live at intermediate
+
+ align:start position:0%
+and all the systems live at intermediate
+ 
+
+ align:start position:0%
+and all the systems live at intermediate
+States between the inti the final State
+
+ align:start position:0%
+States between the inti the final State
+ 
+
+ align:start position:0%
+States between the inti the final State
+and the initial State and the way you
+
+ align:start position:0%
+and the initial State and the way you
+ 
+
+ align:start position:0%
+and the initial State and the way you
+keep them there is interesting um rather
+
+ align:start position:0%
+keep them there is interesting um rather
+ 
+
+ align:start position:0%
+keep them there is interesting um rather
+than optimizing the energy of each
+
+ align:start position:0%
+than optimizing the energy of each
+ 
+
+ align:start position:0%
+than optimizing the energy of each
+system what you optimize is the sum of
+
+ align:start position:0%
+system what you optimize is the sum of
+ 
+
+ align:start position:0%
+system what you optimize is the sum of
+their energies okay the sum of their
+
+ align:start position:0%
+their energies okay the sum of their
+ 
+
+ align:start position:0%
+their energies okay the sum of their
+hamiltonian values okay plus some spring
+
+ align:start position:0%
+hamiltonian values okay plus some spring
+ 
+
+ align:start position:0%
+hamiltonian values okay plus some spring
+constant okay basically plus some energy
+
+ align:start position:0%
+constant okay basically plus some energy
+ 
+
+ align:start position:0%
+constant okay basically plus some energy
+penalty which is associated with the
+
+ align:start position:0%
+penalty which is associated with the
+ 
+
+ align:start position:0%
+penalty which is associated with the
+difference in coordinate between the two
+
+ align:start position:0%
+difference in coordinate between the two
+ 
+
+ align:start position:0%
+difference in coordinate between the two
+systems and what that tends to do is
+
+ align:start position:0%
+systems and what that tends to do is
+ 
+
+ align:start position:0%
+systems and what that tends to do is
+actually since this is a quadratic in
+
+ align:start position:0%
+actually since this is a quadratic in
+ 
+
+ align:start position:0%
+actually since this is a quadratic in
+the difference in coordinates it tends
+
+ align:start position:0%
+the difference in coordinates it tends
+ 
+
+ align:start position:0%
+the difference in coordinates it tends
+to spread
+
+ align:start position:0%
+to spread
+ 
+
+ align:start position:0%
+to spread
+out the systems along the path between
+
+ align:start position:0%
+out the systems along the path between
+ 
+
+ align:start position:0%
+out the systems along the path between
+the two states I mean think of it if I
+
+ align:start position:0%
+the two states I mean think of it if I
+ 
+
+ align:start position:0%
+the two states I mean think of it if I
+got rid of this so if I set K to zero
+
+ align:start position:0%
+got rid of this so if I set K to zero
+ 
+
+ align:start position:0%
+got rid of this so if I set K to zero
+then you know I'm going to minimize this
+
+ align:start position:0%
+then you know I'm going to minimize this
+ 
+
+ align:start position:0%
+then you know I'm going to minimize this
+so they're all going to go down here but
+
+ align:start position:0%
+so they're all going to go down here but
+ 
+
+ align:start position:0%
+so they're all going to go down here but
+what you actually do is you hold one
+
+ align:start position:0%
+what you actually do is you hold one
+ 
+
+ align:start position:0%
+what you actually do is you hold one
+here you hold one there um and then
+
+ align:start position:0%
+here you hold one there um and then
+ 
+
+ align:start position:0%
+here you hold one there um and then
+because of the harmonic potential
+
+ align:start position:0%
+because of the harmonic potential
+ 
+
+ align:start position:0%
+because of the harmonic potential
+between them you tend to end up with
+
+ align:start position:0%
+between them you tend to end up with
+ 
+
+ align:start position:0%
+between them you tend to end up with
+systems that live in between so it's a
+
+ align:start position:0%
+systems that live in between so it's a
+ 
+
+ align:start position:0%
+systems that live in between so it's a
+very elegant way of finding um minimum
+
+ align:start position:0%
+very elegant way of finding um minimum
+ 
+
+ align:start position:0%
+very elegant way of finding um minimum
+energy paths between states um it's
+
+ align:start position:0%
+energy paths between states um it's
+ 
+
+ align:start position:0%
+energy paths between states um it's
+called the elastic band method or the
+
+ align:start position:0%
+called the elastic band method or the
+ 
+
+ align:start position:0%
+called the elastic band method or the
+nudg elastic band method and there's a
+
+ align:start position:0%
+nudg elastic band method and there's a
+ 
+
+ align:start position:0%
+nudg elastic band method and there's a
+whole bunch of variants of it um as well
+
+ align:start position:0%
+whole bunch of variants of it um as well
+ 
+
+ align:start position:0%
+whole bunch of variants of it um as well
+um it's the perfect parallelization may
+
+ align:start position:0%
+um it's the perfect parallelization may
+ 
+
+ align:start position:0%
+um it's the perfect parallelization may
+have noticed you you can run if you want
+
+ align:start position:0%
+have noticed you you can run if you want
+ 
+
+ align:start position:0%
+have noticed you you can run if you want
+to do say 10 r replicas so you want to
+
+ align:start position:0%
+to do say 10 r replicas so you want to
+ 
+
+ align:start position:0%
+to do say 10 r replicas so you want to
+do 10 points along the path you run on
+
+ align:start position:0%
+do 10 points along the path you run on
+ 
+
+ align:start position:0%
+do 10 points along the path you run on
+10 processors because it's the same
+
+ align:start position:0%
+10 processors because it's the same
+ 
+
+ align:start position:0%
+10 processors because it's the same
+system they pretty much run about the
+
+ align:start position:0%
+system they pretty much run about the
+ 
+
+ align:start position:0%
+system they pretty much run about the
+same amount of time they never have to
+
+ align:start position:0%
+same amount of time they never have to
+ 
+
+ align:start position:0%
+same amount of time they never have to
+talk to each other they have to talk to
+
+ align:start position:0%
+talk to each other they have to talk to
+ 
+
+ align:start position:0%
+talk to each other they have to talk to
+each other on extremely rare occasion
+
+ align:start position:0%
+each other on extremely rare occasion
+ 
+
+ align:start position:0%
+each other on extremely rare occasion
+when they exchange coordinat that's it
+
+ align:start position:0%
+when they exchange coordinat that's it
+ 
+
+ align:start position:0%
+when they exchange coordinat that's it
+so it's perfect paralyzation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tool uh if you do that in lithium cobal
+
+ align:start position:0%
+Tool uh if you do that in lithium cobal
+ 
+
+ align:start position:0%
+Tool uh if you do that in lithium cobal
+oxide you have a
+
+ align:start position:0%
+oxide you have a
+ 
+
+ align:start position:0%
+oxide you have a
+complication um just to show you how the
+
+ align:start position:0%
+complication um just to show you how the
+ 
+
+ align:start position:0%
+complication um just to show you how the
+data for kinetic mon Carlo simulation
+
+ align:start position:0%
+data for kinetic mon Carlo simulation
+ 
+
+ align:start position:0%
+data for kinetic mon Carlo simulation
+was derived um the yellow is the lithium
+
+ align:start position:0%
+was derived um the yellow is the lithium
+ 
+
+ align:start position:0%
+was derived um the yellow is the lithium
+here uh these are oxygens the the big
+
+ align:start position:0%
+here uh these are oxygens the the big
+ 
+
+ align:start position:0%
+here uh these are oxygens the the big
+red balls uh the way you can diffuse
+
+ align:start position:0%
+red balls uh the way you can diffuse
+ 
+
+ align:start position:0%
+red balls uh the way you can diffuse
+from this side to that side is straight
+
+ align:start position:0%
+from this side to that side is straight
+ 
+
+ align:start position:0%
+from this side to that side is straight
+through the oxygen Bond and if you do
+
+ align:start position:0%
+through the oxygen Bond and if you do
+ 
+
+ align:start position:0%
+through the oxygen Bond and if you do
+that this is this is obtained by elastic
+
+ align:start position:0%
+that this is this is obtained by elastic
+ 
+
+ align:start position:0%
+that this is this is obtained by elastic
+band method so these are the replicas so
+
+ align:start position:0%
+band method so these are the replicas so
+ 
+
+ align:start position:0%
+band method so these are the replicas so
+this is initial State this is the final
+
+ align:start position:0%
+this is initial State this is the final
+ 
+
+ align:start position:0%
+this is initial State this is the final
+State and so you get an activation bear
+
+ align:start position:0%
+State and so you get an activation bear
+ 
+
+ align:start position:0%
+State and so you get an activation bear
+of about 085
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so you it's very nice how you get
+
+ align:start position:0%
+um so you it's very nice how you get
+ 
+
+ align:start position:0%
+um so you it's very nice how you get
+these activation curves um but the
+
+ align:start position:0%
+these activation curves um but the
+ 
+
+ align:start position:0%
+these activation curves um but the
+problem is that there's two paths in
+
+ align:start position:0%
+problem is that there's two paths in
+ 
+
+ align:start position:0%
+problem is that there's two paths in
+this material so already you're starting
+
+ align:start position:0%
+this material so already you're starting
+ 
+
+ align:start position:0%
+this material so already you're starting
+to run into a particular problem of
+
+ align:start position:0%
+to run into a particular problem of
+ 
+
+ align:start position:0%
+to run into a particular problem of
+kinetic Monte Carlo that let's say you
+
+ align:start position:0%
+kinetic Monte Carlo that let's say you
+ 
+
+ align:start position:0%
+kinetic Monte Carlo that let's say you
+thought that was the path well you'd be
+
+ align:start position:0%
+thought that was the path well you'd be
+ 
+
+ align:start position:0%
+thought that was the path well you'd be
+very wrong because there's another path
+
+ align:start position:0%
+very wrong because there's another path
+ 
+
+ align:start position:0%
+very wrong because there's another path
+um and that's one when the atom actually
+
+ align:start position:0%
+um and that's one when the atom actually
+ 
+
+ align:start position:0%
+um and that's one when the atom actually
+rather than going straight through this
+
+ align:start position:0%
+rather than going straight through this
+ 
+
+ align:start position:0%
+rather than going straight through this
+Bond it takes a curve into this
+
+ align:start position:0%
+Bond it takes a curve into this
+ 
+
+ align:start position:0%
+Bond it takes a curve into this
+tetrahedron
+
+ align:start position:0%
+tetrahedron
+ 
+
+ align:start position:0%
+tetrahedron
+and comes back out and that's actually a
+
+ align:start position:0%
+and comes back out and that's actually a
+ 
+
+ align:start position:0%
+and comes back out and that's actually a
+pad if you do elastic band that is so
+
+ align:start position:0%
+pad if you do elastic band that is so
+ 
+
+ align:start position:0%
+pad if you do elastic band that is so
+much lower it's only about 200 M
+
+ align:start position:0%
+much lower it's only about 200 M
+ 
+
+ align:start position:0%
+much lower it's only about 200 M
+electron volts and it sort of shows the
+
+ align:start position:0%
+electron volts and it sort of shows the
+ 
+
+ align:start position:0%
+electron volts and it sort of shows the
+real problem you can run into that when
+
+ align:start position:0%
+real problem you can run into that when
+ 
+
+ align:start position:0%
+real problem you can run into that when
+you do kinetic mon Carlo you have to
+
+ align:start position:0%
+you do kinetic mon Carlo you have to
+ 
+
+ align:start position:0%
+you do kinetic mon Carlo you have to
+assume what your paths are for
+
+ align:start position:0%
+assume what your paths are for
+ 
+
+ align:start position:0%
+assume what your paths are for
+Transitions and if you don't get them
+
+ align:start position:0%
+Transitions and if you don't get them
+ 
+
+ align:start position:0%
+Transitions and if you don't get them
+right you can be seriously wrong and
+
+ align:start position:0%
+right you can be seriously wrong and
+ 
+
+ align:start position:0%
+right you can be seriously wrong and
+that's one of the nice things of MD that
+
+ align:start position:0%
+that's one of the nice things of MD that
+ 
+
+ align:start position:0%
+that's one of the nice things of MD that
+it's unbiased so it would find these
+
+ align:start position:0%
+it's unbiased so it would find these
+ 
+
+ align:start position:0%
+it's unbiased so it would find these
+things um for you but these are actually
+
+ align:start position:0%
+things um for you but these are actually
+ 
+
+ align:start position:0%
+things um for you but these are actually
+the only two paths and of course because
+
+ align:start position:0%
+the only two paths and of course because
+ 
+
+ align:start position:0%
+the only two paths and of course because
+the activation barrier of this is so
+
+ align:start position:0%
+the activation barrier of this is so
+ 
+
+ align:start position:0%
+the activation barrier of this is so
+much lower this is pretty much the one
+
+ align:start position:0%
+much lower this is pretty much the one
+ 
+
+ align:start position:0%
+much lower this is pretty much the one
+that gets executed almost all the time
+
+ align:start position:0%
+that gets executed almost all the time
+ 
+
+ align:start position:0%
+that gets executed almost all the time
+you know the difference between 0 2 EV
+
+ align:start position:0%
+you know the difference between 0 2 EV
+ 
+
+ align:start position:0%
+you know the difference between 0 2 EV
+and 08 EV at room temperature is amazing
+
+ align:start position:0%
+and 08 EV at room temperature is amazing
+ 
+
+ align:start position:0%
+and 08 EV at room temperature is amazing
+it's uh you know I think five six orders
+
+ align:start position:0%
+it's uh you know I think five six orders
+ 
+
+ align:start position:0%
+it's uh you know I think five six orders
+of magnitude in in in rate constant you
+
+ align:start position:0%
+of magnitude in in in rate constant you
+ 
+
+ align:start position:0%
+of magnitude in in in rate constant you
+just have to calculate the exponential
+
+ align:start position:0%
+just have to calculate the exponential
+ 
+
+ align:start position:0%
+just have to calculate the exponential
+of each of
+
+ align:start position:0%
+of each of
+ 
+
+ align:start position:0%
+of each of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+um one of the problems you have whenever
+
+ align:start position:0%
+um one of the problems you have whenever
+ 
+
+ align:start position:0%
+um one of the problems you have whenever
+you have two rate constants uh um is
+
+ align:start position:0%
+you have two rate constants uh um is
+ 
+
+ align:start position:0%
+you have two rate constants uh um is
+that when you do your mon Carlo you can
+
+ align:start position:0%
+that when you do your mon Carlo you can
+ 
+
+ align:start position:0%
+that when you do your mon Carlo you can
+only scale the fastest one
+
+ align:start position:0%
+only scale the fastest one
+ 
+
+ align:start position:0%
+only scale the fastest one
+away so you have essentially one scale
+
+ align:start position:0%
+away so you have essentially one scale
+ 
+
+ align:start position:0%
+away so you have essentially one scale
+factor in the time of your mon Carlo
+
+ align:start position:0%
+factor in the time of your mon Carlo
+ 
+
+ align:start position:0%
+factor in the time of your mon Carlo
+simulation so when you do multiple time
+
+ align:start position:0%
+simulation so when you do multiple time
+ 
+
+ align:start position:0%
+simulation so when you do multiple time
+scales uh when you have multiple time
+
+ align:start position:0%
+scales uh when you have multiple time
+ 
+
+ align:start position:0%
+scales uh when you have multiple time
+scales it gets very inefficient to do
+
+ align:start position:0%
+scales it gets very inefficient to do
+ 
+
+ align:start position:0%
+scales it gets very inefficient to do
+kinetic mon
+
+ align:start position:0%
+kinetic mon
+ 
+
+ align:start position:0%
+kinetic mon
+Cara but this works you can get
+
+ align:start position:0%
+Cara but this works you can get
+ 
+
+ align:start position:0%
+Cara but this works you can get
+diffusion constants um this is
+
+ align:start position:0%
+diffusion constants um this is
+ 
+
+ align:start position:0%
+diffusion constants um this is
+with uh elastic band method this is the
+
+ align:start position:0%
+with uh elastic band method this is the
+ 
+
+ align:start position:0%
+with uh elastic band method this is the
+activation for that low energy mechanism
+
+ align:start position:0%
+activation for that low energy mechanism
+ 
+
+ align:start position:0%
+activation for that low energy mechanism
+as a function of lithium concentration
+
+ align:start position:0%
+as a function of lithium concentration
+ 
+
+ align:start position:0%
+as a function of lithium concentration
+so very dependent on concentration so
+
+ align:start position:0%
+so very dependent on concentration so
+ 
+
+ align:start position:0%
+so very dependent on concentration so
+you can do your kinetic Monte Carlo and
+
+ align:start position:0%
+you can do your kinetic Monte Carlo and
+ 
+
+ align:start position:0%
+you can do your kinetic Monte Carlo and
+then you know you have these and you can
+
+ align:start position:0%
+then you know you have these and you can
+ 
+
+ align:start position:0%
+then you know you have these and you can
+go all the way to macroscopic simulation
+
+ align:start position:0%
+go all the way to macroscopic simulation
+ 
+
+ align:start position:0%
+go all the way to macroscopic simulation
+then you can solve fix equation and
+
+ align:start position:0%
+then you can solve fix equation and
+ 
+
+ align:start position:0%
+then you can solve fix equation and
+actually look at you know diffusion on
+
+ align:start position:0%
+actually look at you know diffusion on
+ 
+
+ align:start position:0%
+actually look at you know diffusion on
+the scale of microns so it's a sort of
+
+ align:start position:0%
+the scale of microns so it's a sort of
+ 
+
+ align:start position:0%
+the scale of microns so it's a sort of
+Fairly simplistic way of cor
+
+ align:start position:0%
+Fairly simplistic way of cor
+ 
+
+ align:start position:0%
+Fairly simplistic way of cor
+graining
+
+ align:start position:0%
+graining
+ 
+
+ align:start position:0%
+graining
+um okay so I'm going to end just uh
+
+ align:start position:0%
+um okay so I'm going to end just uh
+ 
+
+ align:start position:0%
+um okay so I'm going to end just uh
+giving you some reference if you want to
+
+ align:start position:0%
+giving you some reference if you want to
+ 
+
+ align:start position:0%
+giving you some reference if you want to
+read more about the Quasi continu method
+
+ align:start position:0%
+read more about the Quasi continu method
+ 
+
+ align:start position:0%
+read more about the Quasi continu method
+uh there's these great papers by Miller
+
+ align:start position:0%
+uh there's these great papers by Miller
+ 
+
+ align:start position:0%
+uh there's these great papers by Miller
+and tadmore these are actually somewhat
+
+ align:start position:0%
+and tadmore these are actually somewhat
+ 
+
+ align:start position:0%
+and tadmore these are actually somewhat
+similar but the 202 version is an update
+
+ align:start position:0%
+similar but the 202 version is an update
+ 
+
+ align:start position:0%
+similar but the 202 version is an update
+uh these are not the original papers but
+
+ align:start position:0%
+uh these are not the original papers but
+ 
+
+ align:start position:0%
+uh these are not the original papers but
+uh they're actually some more
+
+ align:start position:0%
+uh they're actually some more
+ 
+
+ align:start position:0%
+uh they're actually some more
+pedagogical than the original papers you
+
+ align:start position:0%
+pedagogical than the original papers you
+ 
+
+ align:start position:0%
+pedagogical than the original papers you
+but you'll find the references in there
+
+ align:start position:0%
+but you'll find the references in there
+ 
+
+ align:start position:0%
+but you'll find the references in there
+to the original papers um the problem of
+
+ align:start position:0%
+to the original papers um the problem of
+ 
+
+ align:start position:0%
+to the original papers um the problem of
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+Dynamics uh at that scale is my own work
+
+ align:start position:0%
+Dynamics uh at that scale is my own work
+ 
+
+ align:start position:0%
+Dynamics uh at that scale is my own work
+um The Accelerated MD uh there's a
+
+ align:start position:0%
+um The Accelerated MD uh there's a
+ 
+
+ align:start position:0%
+um The Accelerated MD uh there's a
+series of papers by Art voter but uh
+
+ align:start position:0%
+series of papers by Art voter but uh
+ 
+
+ align:start position:0%
+series of papers by Art voter but uh
+this annual review of materials research
+
+ align:start position:0%
+this annual review of materials research
+ 
+
+ align:start position:0%
+this annual review of materials research
+is a I think a great review uh if you
+
+ align:start position:0%
+is a I think a great review uh if you
+ 
+
+ align:start position:0%
+is a I think a great review uh if you
+want to read about it and the lithium
+
+ align:start position:0%
+want to read about it and the lithium
+ 
+
+ align:start position:0%
+want to read about it and the lithium
+Cobalt application um is is in a few
+
+ align:start position:0%
+Cobalt application um is is in a few
+ 
+
+ align:start position:0%
+Cobalt application um is is in a few
+papers but it's quite elaborate the
+
+ align:start position:0%
+papers but it's quite elaborate the
+ 
+
+ align:start position:0%
+papers but it's quite elaborate the
+whole idea of kinetic Monte Carlo and
+
+ align:start position:0%
+whole idea of kinetic Monte Carlo and
+ 
+
+ align:start position:0%
+whole idea of kinetic Monte Carlo and
+parameterizing activation bearers is
+
+ align:start position:0%
+parameterizing activation bearers is
+ 
+
+ align:start position:0%
+parameterizing activation bearers is
+quite elaborately um discussed in this
+
+ align:start position:0%
+quite elaborately um discussed in this
+ 
+
+ align:start position:0%
+quite elaborately um discussed in this
+paper so I think we're done a little
+
+ align:start position:0%
+paper so I think we're done a little
+ 
+
+ align:start position:0%
+paper so I think we're done a little
+early but that's fine so I'm going to
+
+ align:start position:0%
+early but that's fine so I'm going to
+ 
+
+ align:start position:0%
+early but that's fine so I'm going to
+end here and uh I'll see you on Thursday
+
+ align:start position:0%
+end here and uh I'll see you on Thursday
+ 
+
+ align:start position:0%
+end here and uh I'll see you on Thursday
+for uh the lecture from Fort
\ No newline at end of file
diff --git a/SgJo7_4mp6w.txt b/SgJo7_4mp6w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e8930564346f2b1ac793e905f5acd24d6e3ee40b
--- /dev/null
+++ b/SgJo7_4mp6w.txt
@@ -0,0 +1,1376 @@
+align:start position:0%
+ 
+hi welcome back to recitation in lecture
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+ 
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+you've been learning about planes and
+
+ align:start position:0%
+you've been learning about planes and
+ 
+
+ align:start position:0%
+you've been learning about planes and
+their equations and various different
+
+ align:start position:0%
+their equations and various different
+ 
+
+ align:start position:0%
+their equations and various different
+geometric problems relating to them so I
+
+ align:start position:0%
+geometric problems relating to them so I
+ 
+
+ align:start position:0%
+geometric problems relating to them so I
+have an example of such a problem here
+
+ align:start position:0%
+have an example of such a problem here
+ 
+
+ align:start position:0%
+have an example of such a problem here
+so I've got a point which happens to be
+
+ align:start position:0%
+so I've got a point which happens to be
+ 
+
+ align:start position:0%
+so I've got a point which happens to be
+the origin which I'm going to call P
+
+ align:start position:0%
+the origin which I'm going to call P
+ 
+
+ align:start position:0%
+the origin which I'm going to call P
+0000 0 and I've got a plane which has
+
+ align:start position:0%
+0000 0 and I've got a plane which has
+ 
+
+ align:start position:0%
+0000 0 and I've got a plane which has
+the equation 2x + y - 2 Z is Al to four
+
+ align:start position:0%
+the equation 2x + y - 2 Z is Al to four
+ 
+
+ align:start position:0%
+the equation 2x + y - 2 Z is Al to four
+and what I'd like you to do is compute
+
+ align:start position:0%
+and what I'd like you to do is compute
+ 
+
+ align:start position:0%
+and what I'd like you to do is compute
+the distance from that point to that
+
+ align:start position:0%
+the distance from that point to that
+ 
+
+ align:start position:0%
+the distance from that point to that
+plane so um just to to to remind you the
+
+ align:start position:0%
+plane so um just to to to remind you the
+ 
+
+ align:start position:0%
+plane so um just to to to remind you the
+distance so there are lots of points on
+
+ align:start position:0%
+distance so there are lots of points on
+ 
+
+ align:start position:0%
+distance so there are lots of points on
+a plane of course and and our point in
+
+ align:start position:0%
+a plane of course and and our point in
+ 
+
+ align:start position:0%
+a plane of course and and our point in
+question has a distance to each of them
+
+ align:start position:0%
+question has a distance to each of them
+ 
+
+ align:start position:0%
+question has a distance to each of them
+when we talk about the distance between
+
+ align:start position:0%
+when we talk about the distance between
+ 
+
+ align:start position:0%
+when we talk about the distance between
+a point and a plane what we mean is the
+
+ align:start position:0%
+a point and a plane what we mean is the
+ 
+
+ align:start position:0%
+a point and a plane what we mean is the
+shortest distance so the the the
+
+ align:start position:0%
+shortest distance so the the the
+ 
+
+ align:start position:0%
+shortest distance so the the the
+perpendicular distance so if we have if
+
+ align:start position:0%
+perpendicular distance so if we have if
+ 
+
+ align:start position:0%
+perpendicular distance so if we have if
+we have the plane and we have the point
+
+ align:start position:0%
+we have the plane and we have the point
+ 
+
+ align:start position:0%
+we have the plane and we have the point
+so we we want to drop a perpendicular
+
+ align:start position:0%
+so we we want to drop a perpendicular
+ 
+
+ align:start position:0%
+so we we want to drop a perpendicular
+from from the point to the plane and
+
+ align:start position:0%
+from from the point to the plane and
+ 
+
+ align:start position:0%
+from from the point to the plane and
+then we're asking for for for that
+
+ align:start position:0%
+then we're asking for for for that
+ 
+
+ align:start position:0%
+then we're asking for for for that
+length of that segment um so that's
+
+ align:start position:0%
+length of that segment um so that's
+ 
+
+ align:start position:0%
+length of that segment um so that's
+that's the distance between the point
+
+ align:start position:0%
+that's the distance between the point
+ 
+
+ align:start position:0%
+that's the distance between the point
+and the plane so why don't you pause the
+
+ align:start position:0%
+and the plane so why don't you pause the
+ 
+
+ align:start position:0%
+and the plane so why don't you pause the
+video take a little while to uh to
+
+ align:start position:0%
+video take a little while to uh to
+ 
+
+ align:start position:0%
+video take a little while to uh to
+figure this out come back and we can
+
+ align:start position:0%
+figure this out come back and we can
+ 
+
+ align:start position:0%
+figure this out come back and we can
+figure it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together so hopefully you had some luck
+
+ align:start position:0%
+together so hopefully you had some luck
+ 
+
+ align:start position:0%
+together so hopefully you had some luck
+working out this problem let's uh let's
+
+ align:start position:0%
+working out this problem let's uh let's
+ 
+
+ align:start position:0%
+working out this problem let's uh let's
+let's think about it a little bit we
+
+ align:start position:0%
+let's think about it a little bit we
+ 
+
+ align:start position:0%
+let's think about it a little bit we
+have we have a point and we have a plane
+
+ align:start position:0%
+have we have a point and we have a plane
+ 
+
+ align:start position:0%
+have we have a point and we have a plane
+and we want to figure out what the what
+
+ align:start position:0%
+and we want to figure out what the what
+ 
+
+ align:start position:0%
+and we want to figure out what the what
+the perpendicular distance from from the
+
+ align:start position:0%
+the perpendicular distance from from the
+ 
+
+ align:start position:0%
+the perpendicular distance from from the
+point to the plane is um so one thing
+
+ align:start position:0%
+point to the plane is um so one thing
+ 
+
+ align:start position:0%
+point to the plane is um so one thing
+that's going to be important then is
+
+ align:start position:0%
+that's going to be important then is
+ 
+
+ align:start position:0%
+that's going to be important then is
+definitely knowing what what direction
+
+ align:start position:0%
+definitely knowing what what direction
+ 
+
+ align:start position:0%
+definitely knowing what what direction
+that that Vector is right we have the
+
+ align:start position:0%
+that that Vector is right we have the
+ 
+
+ align:start position:0%
+that that Vector is right we have the
+plane and and we and we want to find the
+
+ align:start position:0%
+plane and and we and we want to find the
+ 
+
+ align:start position:0%
+plane and and we and we want to find the
+a perpendicular segment to it um and so
+
+ align:start position:0%
+a perpendicular segment to it um and so
+ 
+
+ align:start position:0%
+a perpendicular segment to it um and so
+in order to do that it's it's useful to
+
+ align:start position:0%
+in order to do that it's it's useful to
+ 
+
+ align:start position:0%
+in order to do that it's it's useful to
+know which what direction is that
+
+ align:start position:0%
+know which what direction is that
+ 
+
+ align:start position:0%
+know which what direction is that
+segment pointing in so luckily we're
+
+ align:start position:0%
+segment pointing in so luckily we're
+ 
+
+ align:start position:0%
+segment pointing in so luckily we're
+given the plane in this in this simple
+
+ align:start position:0%
+given the plane in this in this simple
+ 
+
+ align:start position:0%
+given the plane in this in this simple
+equation form so the normal to the plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when you're given an equation of a
+
+ align:start position:0%
+and when you're given an equation of a
+ 
+
+ align:start position:0%
+and when you're given an equation of a
+plane in this form the the normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector is just given by the the
+
+ align:start position:0%
+Vector is just given by the the
+ 
+
+ align:start position:0%
+Vector is just given by the the
+coefficients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of X Y and Z so in our case the plane is
+
+ align:start position:0%
+of X Y and Z so in our case the plane is
+ 
+
+ align:start position:0%
+of X Y and Z so in our case the plane is
+2x + y - 2 Z = 4 so the normal Vector to
+
+ align:start position:0%
+2x + y - 2 Z = 4 so the normal Vector to
+ 
+
+ align:start position:0%
+2x + y - 2 Z = 4 so the normal Vector to
+this plane is the vector 2 1us 2 so this
+
+ align:start position:0%
+this plane is the vector 2 1us 2 so this
+ 
+
+ align:start position:0%
+this plane is the vector 2 1us 2 so this
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+direction um in in which we need to go
+
+ align:start position:0%
+direction um in in which we need to go
+ 
+
+ align:start position:0%
+direction um in in which we need to go
+from our Point p in order to get to the
+
+ align:start position:0%
+from our Point p in order to get to the
+ 
+
+ align:start position:0%
+from our Point p in order to get to the
+plane by the by the shortest distance so
+
+ align:start position:0%
+plane by the by the shortest distance so
+ 
+
+ align:start position:0%
+plane by the by the shortest distance so
+now what we need is we need to know the
+
+ align:start position:0%
+now what we need is we need to know the
+ 
+
+ align:start position:0%
+now what we need is we need to know the
+component of oh sorry rather we need to
+
+ align:start position:0%
+component of oh sorry rather we need to
+ 
+
+ align:start position:0%
+component of oh sorry rather we need to
+know the the distance the the actual
+
+ align:start position:0%
+know the the distance the the actual
+ 
+
+ align:start position:0%
+know the the distance the the actual
+distance we have to travel in that
+
+ align:start position:0%
+distance we have to travel in that
+ 
+
+ align:start position:0%
+distance we have to travel in that
+direction um so one way to do this is if
+
+ align:start position:0%
+direction um so one way to do this is if
+ 
+
+ align:start position:0%
+direction um so one way to do this is if
+we go back to our little picture here
+
+ align:start position:0%
+we go back to our little picture here
+ 
+
+ align:start position:0%
+we go back to our little picture here
+if we choose we we don't know what this
+
+ align:start position:0%
+if we choose we we don't know what this
+ 
+
+ align:start position:0%
+if we choose we we don't know what this
+point is we don't know when we start
+
+ align:start position:0%
+point is we don't know when we start
+ 
+
+ align:start position:0%
+point is we don't know when we start
+from p and head in a direction
+
+ align:start position:0%
+from p and head in a direction
+ 
+
+ align:start position:0%
+from p and head in a direction
+perpendicular to the plane we don't know
+
+ align:start position:0%
+perpendicular to the plane we don't know
+ 
+
+ align:start position:0%
+perpendicular to the plane we don't know
+what point we're going to land on the
+
+ align:start position:0%
+what point we're going to land on the
+ 
+
+ align:start position:0%
+what point we're going to land on the
+plane at um but what we could do is if
+
+ align:start position:0%
+plane at um but what we could do is if
+ 
+
+ align:start position:0%
+plane at um but what we could do is if
+we knew some other point on the
+
+ align:start position:0%
+we knew some other point on the
+ 
+
+ align:start position:0%
+we knew some other point on the
+plane somewhere we could look at the
+
+ align:start position:0%
+plane somewhere we could look at the
+ 
+
+ align:start position:0%
+plane somewhere we could look at the
+vector connecting P to that other point
+
+ align:start position:0%
+vector connecting P to that other point
+ 
+
+ align:start position:0%
+vector connecting P to that other point
+and then we could project it onto the
+
+ align:start position:0%
+and then we could project it onto the
+ 
+
+ align:start position:0%
+and then we could project it onto the
+normal Direction so we could can take
+
+ align:start position:0%
+normal Direction so we could can take
+ 
+
+ align:start position:0%
+normal Direction so we could can take
+the components let's call this other
+
+ align:start position:0%
+the components let's call this other
+ 
+
+ align:start position:0%
+the components let's call this other
+point Q so if we choose any point Q in
+
+ align:start position:0%
+point Q so if we choose any point Q in
+ 
+
+ align:start position:0%
+point Q so if we choose any point Q in
+the plane that we're looking at we can
+
+ align:start position:0%
+the plane that we're looking at we can
+ 
+
+ align:start position:0%
+the plane that we're looking at we can
+take the vector PQ and we can project it
+
+ align:start position:0%
+take the vector PQ and we can project it
+ 
+
+ align:start position:0%
+take the vector PQ and we can project it
+onto this normal vector and if we take
+
+ align:start position:0%
+onto this normal vector and if we take
+ 
+
+ align:start position:0%
+onto this normal vector and if we take
+the component of of this Vector
+
+ align:start position:0%
+the component of of this Vector
+ 
+
+ align:start position:0%
+the component of of this Vector
+projected onto that normal Vector if we
+
+ align:start position:0%
+projected onto that normal Vector if we
+ 
+
+ align:start position:0%
+projected onto that normal Vector if we
+if we take the component of this Vector
+
+ align:start position:0%
+if we take the component of this Vector
+ 
+
+ align:start position:0%
+if we take the component of this Vector
+in the direction of the normal Vector
+
+ align:start position:0%
+in the direction of the normal Vector
+ 
+
+ align:start position:0%
+in the direction of the normal Vector
+what that'll give us is exactly the the
+
+ align:start position:0%
+what that'll give us is exactly the the
+ 
+
+ align:start position:0%
+what that'll give us is exactly the the
+length of this segment yeah that
+
+ align:start position:0%
+length of this segment yeah that
+ 
+
+ align:start position:0%
+length of this segment yeah that
+projection will be exactly the the
+
+ align:start position:0%
+projection will be exactly the the
+ 
+
+ align:start position:0%
+projection will be exactly the the
+perpendicular ular segment we're looking
+
+ align:start position:0%
+perpendicular ular segment we're looking
+ 
+
+ align:start position:0%
+perpendicular ular segment we're looking
+for and its length the component or the
+
+ align:start position:0%
+for and its length the component or the
+ 
+
+ align:start position:0%
+for and its length the component or the
+absolute value of the component perhaps
+
+ align:start position:0%
+absolute value of the component perhaps
+ 
+
+ align:start position:0%
+absolute value of the component perhaps
+um it's uh will be will be exactly that
+
+ align:start position:0%
+um it's uh will be will be exactly that
+ 
+
+ align:start position:0%
+um it's uh will be will be exactly that
+that distance so
+
+ align:start position:0%
+that distance so
+ 
+
+ align:start position:0%
+that distance so
+um so good so then we just have to
+
+ align:start position:0%
+um so good so then we just have to
+ 
+
+ align:start position:0%
+um so good so then we just have to
+compute well we need to find a point q
+
+ align:start position:0%
+compute well we need to find a point q
+ 
+
+ align:start position:0%
+compute well we need to find a point q
+and we need to compute a component so we
+
+ align:start position:0%
+and we need to compute a component so we
+ 
+
+ align:start position:0%
+and we need to compute a component so we
+need any point on the plane so actually
+
+ align:start position:0%
+need any point on the plane so actually
+ 
+
+ align:start position:0%
+need any point on the plane so actually
+I'm going to walk back over here and and
+
+ align:start position:0%
+I'm going to walk back over here and and
+ 
+
+ align:start position:0%
+I'm going to walk back over here and and
+and to find a point on the the plane we
+
+ align:start position:0%
+and to find a point on the the plane we
+ 
+
+ align:start position:0%
+and to find a point on the the plane we
+we can just do this by looking at the at
+
+ align:start position:0%
+we can just do this by looking at the at
+ 
+
+ align:start position:0%
+we can just do this by looking at the at
+the equation so so one way to go about
+
+ align:start position:0%
+the equation so so one way to go about
+ 
+
+ align:start position:0%
+the equation so so one way to go about
+this for example is that you pick a pick
+
+ align:start position:0%
+this for example is that you pick a pick
+ 
+
+ align:start position:0%
+this for example is that you pick a pick
+a variable that appears in the equation
+
+ align:start position:0%
+a variable that appears in the equation
+ 
+
+ align:start position:0%
+a variable that appears in the equation
+so X appears in the equation and now if
+
+ align:start position:0%
+so X appears in the equation and now if
+ 
+
+ align:start position:0%
+so X appears in the equation and now if
+you you could just set all the other
+
+ align:start position:0%
+you you could just set all the other
+ 
+
+ align:start position:0%
+you you could just set all the other
+variables equal to zero and that'll give
+
+ align:start position:0%
+variables equal to zero and that'll give
+ 
+
+ align:start position:0%
+variables equal to zero and that'll give
+you something you can solve for x so so
+
+ align:start position:0%
+you something you can solve for x so so
+ 
+
+ align:start position:0%
+you something you can solve for x so so
+in particular you know there's a point
+
+ align:start position:0%
+in particular you know there's a point
+ 
+
+ align:start position:0%
+in particular you know there's a point
+on this plane with yal zal 0 that point
+
+ align:start position:0%
+on this plane with yal zal 0 that point
+ 
+
+ align:start position:0%
+on this plane with yal zal 0 that point
+has 2x = 4 so we can take for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example Q to be the point two
+
+ align:start position:0%
+example Q to be the point two
+ 
+
+ align:start position:0%
+example Q to be the point two
+0 0 so this is a point on the plane um
+
+ align:start position:0%
+0 0 so this is a point on the plane um
+ 
+
+ align:start position:0%
+0 0 so this is a point on the plane um
+so this is our point on the plane and so
+
+ align:start position:0%
+so this is our point on the plane and so
+ 
+
+ align:start position:0%
+so this is our point on the plane and so
+we have what we want to do is we want to
+
+ align:start position:0%
+we have what we want to do is we want to
+ 
+
+ align:start position:0%
+we have what we want to do is we want to
+project so
+
+ align:start position:0%
+project so
+ 
+
+ align:start position:0%
+project so
+PQ the vector from P to Q we get by
+
+ align:start position:0%
+PQ the vector from P to Q we get by
+ 
+
+ align:start position:0%
+PQ the vector from P to Q we get by
+subtracting the coordinates of of P from
+
+ align:start position:0%
+subtracting the coordinates of of P from
+ 
+
+ align:start position:0%
+subtracting the coordinates of of P from
+those of q q minus P so this is the
+
+ align:start position:0%
+those of q q minus P so this is the
+ 
+
+ align:start position:0%
+those of q q minus P so this is the
+vector 2 0 Z and we want the component
+
+ align:start position:0%
+vector 2 0 Z and we want the component
+ 
+
+ align:start position:0%
+vector 2 0 Z and we want the component
+of PQ in the direction n so
+
+ align:start position:0%
+of PQ in the direction n so
+ 
+
+ align:start position:0%
+of PQ in the direction n so
+the distance in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the and really when I say component in
+
+ align:start position:0%
+the and really when I say component in
+ 
+
+ align:start position:0%
+the and really when I say component in
+this case I mean the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positive component I want because the
+
+ align:start position:0%
+positive component I want because the
+ 
+
+ align:start position:0%
+positive component I want because the
+distance has to be positive so if I get
+
+ align:start position:0%
+distance has to be positive so if I get
+ 
+
+ align:start position:0%
+distance has to be positive so if I get
+a a negative component I really want its
+
+ align:start position:0%
+a a negative component I really want its
+ 
+
+ align:start position:0%
+a a negative component I really want its
+absolute value here so the distance is
+
+ align:start position:0%
+absolute value here so the distance is
+ 
+
+ align:start position:0%
+absolute value here so the distance is
+the positive component in the direction
+
+ align:start position:0%
+the positive component in the direction
+ 
+
+ align:start position:0%
+the positive component in the direction
+n um so what's that equal to well it's
+
+ align:start position:0%
+n um so what's that equal to well it's
+ 
+
+ align:start position:0%
+n um so what's that equal to well it's
+just equal to the absolute value of so
+
+ align:start position:0%
+just equal to the absolute value of so
+ 
+
+ align:start position:0%
+just equal to the absolute value of so
+we know the component of of PQ in the
+
+ align:start position:0%
+we know the component of of PQ in the
+ 
+
+ align:start position:0%
+we know the component of of PQ in the
+direction n is what we get when we take
+
+ align:start position:0%
+direction n is what we get when we take
+ 
+
+ align:start position:0%
+direction n is what we get when we take
+PQ and we dot it with n divided by the
+
+ align:start position:0%
+PQ and we dot it with n divided by the
+ 
+
+ align:start position:0%
+PQ and we dot it with n divided by the
+length of
+
+ align:start position:0%
+length of
+ 
+
+ align:start position:0%
+length of
+N and then I to make sure it's positive
+
+ align:start position:0%
+N and then I to make sure it's positive
+ 
+
+ align:start position:0%
+N and then I to make sure it's positive
+at the end I want to throw in these
+
+ align:start position:0%
+at the end I want to throw in these
+ 
+
+ align:start position:0%
+at the end I want to throw in these
+absolute value sign
+
+ align:start position:0%
+absolute value sign
+ 
+
+ align:start position:0%
+absolute value sign
+so okay so this is and this is now you
+
+ align:start position:0%
+so okay so this is and this is now you
+ 
+
+ align:start position:0%
+so okay so this is and this is now you
+know we have we have our Vector PQ and
+
+ align:start position:0%
+know we have we have our Vector PQ and
+ 
+
+ align:start position:0%
+know we have we have our Vector PQ and
+we have our Vector n so it should be
+
+ align:start position:0%
+we have our Vector n so it should be
+ 
+
+ align:start position:0%
+we have our Vector n so it should be
+straightforward to to compute this final
+
+ align:start position:0%
+straightforward to to compute this final
+ 
+
+ align:start position:0%
+straightforward to to compute this final
+expression so we know that n is equal to
+
+ align:start position:0%
+expression so we know that n is equal to
+ 
+
+ align:start position:0%
+expression so we know that n is equal to
+21 minus 2 so the length of n which is
+
+ align:start position:0%
+21 minus 2 so the length of n which is
+ 
+
+ align:start position:0%
+21 minus 2 so the length of n which is
+in the denominator here is equal to the
+
+ align:start position:0%
+in the denominator here is equal to the
+ 
+
+ align:start position:0%
+in the denominator here is equal to the
+square < TK of 2^ 2 + 1^ 2 + - 2^
+
+ align:start position:0%
+square < TK of 2^ 2 + 1^ 2 + - 2^
+ 
+
+ align:start position:0%
+square < TK of 2^ 2 + 1^ 2 + - 2^
+2 and in the numerator we have the
+
+ align:start position:0%
+2 and in the numerator we have the
+ 
+
+ align:start position:0%
+2 and in the numerator we have the
+absolute value of PQ
+
+ align:start position:0%
+absolute value of PQ
+ 
+
+ align:start position:0%
+absolute value of PQ
+n so pqn is going to be 2 *
+
+ align:start position:0%
+n so pqn is going to be 2 *
+ 
+
+ align:start position:0%
+n so pqn is going to be 2 *
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+plus 0 * 1 + 0 *
+
+ align:start position:0%
+plus 0 * 1 + 0 *
+ 
+
+ align:start position:0%
+plus 0 * 1 + 0 *
+-2 okay and so if we this is just a
+
+ align:start position:0%
+-2 okay and so if we this is just a
+ 
+
+ align:start position:0%
+-2 okay and so if we this is just a
+fraction bar here and so if we simplify
+
+ align:start position:0%
+fraction bar here and so if we simplify
+ 
+
+ align:start position:0%
+fraction bar here and so if we simplify
+that a little bit so up top we just have
+
+ align:start position:0%
+that a little bit so up top we just have
+ 
+
+ align:start position:0%
+that a little bit so up top we just have
+four plus 0 plus 0 is 4 and on the
+
+ align:start position:0%
+four plus 0 plus 0 is 4 and on the
+ 
+
+ align:start position:0%
+four plus 0 plus 0 is 4 and on the
+bottom we have the square Ro T of 2^ 2 +
+
+ align:start position:0%
+bottom we have the square Ro T of 2^ 2 +
+ 
+
+ align:start position:0%
+bottom we have the square Ro T of 2^ 2 +
+1 2 + 2^ 2 that's uh going to going to
+
+ align:start position:0%
+1 2 + 2^ 2 that's uh going to going to
+ 
+
+ align:start position:0%
+1 2 + 2^ 2 that's uh going to going to
+be < TK of 9 which is 3 so this is just
+
+ align:start position:0%
+be < TK of 9 which is 3 so this is just
+ 
+
+ align:start position:0%
+be < TK of 9 which is 3 so this is just
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+4/3 so there we go the distance in
+
+ align:start position:0%
+4/3 so there we go the distance in
+ 
+
+ align:start position:0%
+4/3 so there we go the distance in
+question is 4/3 the way we got it is we
+
+ align:start position:0%
+question is 4/3 the way we got it is we
+ 
+
+ align:start position:0%
+question is 4/3 the way we got it is we
+realized that that distance is just the
+
+ align:start position:0%
+realized that that distance is just the
+ 
+
+ align:start position:0%
+realized that that distance is just the
+component of any segment any Vector
+
+ align:start position:0%
+component of any segment any Vector
+ 
+
+ align:start position:0%
+component of any segment any Vector
+connecting our Point P to the plane in
+
+ align:start position:0%
+connecting our Point P to the plane in
+ 
+
+ align:start position:0%
+connecting our Point P to the plane in
+the direction of the normal so you
+
+ align:start position:0%
+the direction of the normal so you
+ 
+
+ align:start position:0%
+the direction of the normal so you
+choose any any any Vector PQ so you know
+
+ align:start position:0%
+choose any any any Vector PQ so you know
+ 
+
+ align:start position:0%
+choose any any any Vector PQ so you know
+you just have to come up with a with a
+
+ align:start position:0%
+you just have to come up with a with a
+ 
+
+ align:start position:0%
+you just have to come up with a with a
+point Q on the plane which you can do by
+
+ align:start position:0%
+point Q on the plane which you can do by
+ 
+
+ align:start position:0%
+point Q on the plane which you can do by
+inspection from the equation so that
+
+ align:start position:0%
+inspection from the equation so that
+ 
+
+ align:start position:0%
+inspection from the equation so that
+gives you a vector that gets you from P
+
+ align:start position:0%
+gives you a vector that gets you from P
+ 
+
+ align:start position:0%
+gives you a vector that gets you from P
+to some point on the plane and then you
+
+ align:start position:0%
+to some point on the plane and then you
+ 
+
+ align:start position:0%
+to some point on the plane and then you
+choose the component in the normal
+
+ align:start position:0%
+choose the component in the normal
+ 
+
+ align:start position:0%
+choose the component in the normal
+Direction and so once you do that you
+
+ align:start position:0%
+Direction and so once you do that you
+ 
+
+ align:start position:0%
+Direction and so once you do that you
+get you get this distance your answer so
+
+ align:start position:0%
+get you get this distance your answer so
+ 
+
+ align:start position:0%
+get you get this distance your answer so
+I'll end there
\ No newline at end of file
diff --git a/Siqu0aOOQCM.txt b/Siqu0aOOQCM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cdf898bb206213c82584bcbda6adf136b834503e
--- /dev/null
+++ b/Siqu0aOOQCM.txt
@@ -0,0 +1,7939 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so uh today's lecture is
+
+ align:start position:0%
+ocw.mit.edu so uh today's lecture is
+ 
+
+ align:start position:0%
+ocw.mit.edu so uh today's lecture is
+partly kind of picking up cleaning up
+
+ align:start position:0%
+partly kind of picking up cleaning up
+ 
+
+ align:start position:0%
+partly kind of picking up cleaning up
+some pieces left from uh one D problems
+
+ align:start position:0%
+some pieces left from uh one D problems
+ 
+
+ align:start position:0%
+some pieces left from uh one D problems
+3.1 was second order equations 3.2 was
+
+ align:start position:0%
+3.1 was second order equations 3.2 was
+ 
+
+ align:start position:0%
+3.1 was second order equations 3.2 was
+fourth order equations for beams and
+
+ align:start position:0%
+fourth order equations for beams and
+ 
+
+ align:start position:0%
+fourth order equations for beams and
+just a few more comments to make but
+
+ align:start position:0%
+just a few more comments to make but
+ 
+
+ align:start position:0%
+just a few more comments to make but
+then I do want to say something about
+
+ align:start position:0%
+then I do want to say something about
+ 
+
+ align:start position:0%
+then I do want to say something about
+splines however I I'm not that's that
+
+ align:start position:0%
+splines however I I'm not that's that
+ 
+
+ align:start position:0%
+splines however I I'm not that's that
+topic will really and it I included a a
+
+ align:start position:0%
+topic will really and it I included a a
+ 
+
+ align:start position:0%
+topic will really and it I included a a
+homework question that asked you to use
+
+ align:start position:0%
+homework question that asked you to use
+ 
+
+ align:start position:0%
+homework question that asked you to use
+the spind command and and get a result
+
+ align:start position:0%
+the spind command and and get a result
+ 
+
+ align:start position:0%
+the spind command and and get a result
+uh I'm not planning to make that a major
+
+ align:start position:0%
+uh I'm not planning to make that a major
+ 
+
+ align:start position:0%
+uh I'm not planning to make that a major
+you know a serious Topic in the course
+
+ align:start position:0%
+you know a serious Topic in the course
+ 
+
+ align:start position:0%
+you know a serious Topic in the course
+um in other words you're not like going
+
+ align:start position:0%
+um in other words you're not like going
+ 
+
+ align:start position:0%
+um in other words you're not like going
+to be responsible on exam for the
+
+ align:start position:0%
+to be responsible on exam for the
+ 
+
+ align:start position:0%
+to be responsible on exam for the
+discussion of splines but it's such a
+
+ align:start position:0%
+discussion of splines but it's such a
+ 
+
+ align:start position:0%
+discussion of splines but it's such a
+major uh event in major requirement in
+
+ align:start position:0%
+major uh event in major requirement in
+ 
+
+ align:start position:0%
+major uh event in major requirement in
+scientific Computing if you're given
+
+ align:start position:0%
+scientific Computing if you're given
+ 
+
+ align:start position:0%
+scientific Computing if you're given
+some values put a curve through them
+
+ align:start position:0%
+some values put a curve through them
+ 
+
+ align:start position:0%
+some values put a curve through them
+that I have to say something about that
+
+ align:start position:0%
+that I have to say something about that
+ 
+
+ align:start position:0%
+that I have to say something about that
+so that's interpr ation if I if because
+
+ align:start position:0%
+so that's interpr ation if I if because
+ 
+
+ align:start position:0%
+so that's interpr ation if I if because
+you you I mean you'll have this all the
+
+ align:start position:0%
+you you I mean you'll have this all the
+ 
+
+ align:start position:0%
+you you I mean you'll have this all the
+time if you you you your experiment
+
+ align:start position:0%
+time if you you you your experiment
+ 
+
+ align:start position:0%
+time if you you you your experiment
+produces some values at specific times
+
+ align:start position:0%
+produces some values at specific times
+ 
+
+ align:start position:0%
+produces some values at specific times
+or specific you know a finite number of
+
+ align:start position:0%
+or specific you know a finite number of
+ 
+
+ align:start position:0%
+or specific you know a finite number of
+values and you want to fit a curve
+
+ align:start position:0%
+values and you want to fit a curve
+ 
+
+ align:start position:0%
+values and you want to fit a curve
+through those points how do you do it so
+
+ align:start position:0%
+through those points how do you do it so
+ 
+
+ align:start position:0%
+through those points how do you do it so
+splines give a very very good answer and
+
+ align:start position:0%
+splines give a very very good answer and
+ 
+
+ align:start position:0%
+splines give a very very good answer and
+then with
+
+ align:start position:0%
+then with
+ 
+
+ align:start position:0%
+then with
+the the ne the next and big uh topic of
+
+ align:start position:0%
+the the ne the next and big uh topic of
+ 
+
+ align:start position:0%
+the the ne the next and big uh topic of
+the course uh we'll make a beginning on
+
+ align:start position:0%
+the course uh we'll make a beginning on
+ 
+
+ align:start position:0%
+the course uh we'll make a beginning on
+which is gradient Divergence leading to
+
+ align:start position:0%
+which is gradient Divergence leading to
+ 
+
+ align:start position:0%
+which is gradient Divergence leading to
+thees equation problems in
+
+ align:start position:0%
+thees equation problems in
+ 
+
+ align:start position:0%
+thees equation problems in
+2D so partial differential equations are
+
+ align:start position:0%
+2D so partial differential equations are
+ 
+
+ align:start position:0%
+2D so partial differential equations are
+going to show up okay but let me just so
+
+ align:start position:0%
+going to show up okay but let me just so
+ 
+
+ align:start position:0%
+going to show up okay but let me just so
+I some small points f first point about
+
+ align:start position:0%
+I some small points f first point about
+ 
+
+ align:start position:0%
+I some small points f first point about
+the mat lab homework for for Monday
+
+ align:start position:0%
+the mat lab homework for for Monday
+ 
+
+ align:start position:0%
+the mat lab homework for for Monday
+uh a question came by email uh should we
+
+ align:start position:0%
+uh a question came by email uh should we
+ 
+
+ align:start position:0%
+uh a question came by email uh should we
+really uh so I I put the
+
+ align:start position:0%
+really uh so I I put the
+ 
+
+ align:start position:0%
+really uh so I I put the
+spike at and also the jump in C in the
+
+ align:start position:0%
+spike at and also the jump in C in the
+ 
+
+ align:start position:0%
+spike at and also the jump in C in the
+coefficient at not at mesh point if
+
+ align:start position:0%
+coefficient at not at mesh point if
+ 
+
+ align:start position:0%
+coefficient at not at mesh point if
+you've started on that problem you
+
+ align:start position:0%
+you've started on that problem you
+ 
+
+ align:start position:0%
+you've started on that problem you
+probably noticed that and and
+
+ align:start position:0%
+probably noticed that and and
+ 
+
+ align:start position:0%
+probably noticed that and and
+uh um maybe a little swearing went on
+
+ align:start position:0%
+uh um maybe a little swearing went on
+ 
+
+ align:start position:0%
+uh um maybe a little swearing went on
+but uh cuz it makes it uh not so easy
+
+ align:start position:0%
+but uh cuz it makes it uh not so easy
+ 
+
+ align:start position:0%
+but uh cuz it makes it uh not so easy
+and then um the question came did I
+
+ align:start position:0%
+and then um the question came did I
+ 
+
+ align:start position:0%
+and then um the question came did I
+really expect you to to compute to to
+
+ align:start position:0%
+really expect you to to compute to to
+ 
+
+ align:start position:0%
+really expect you to to compute to to
+use the exact position and figure out
+
+ align:start position:0%
+use the exact position and figure out
+ 
+
+ align:start position:0%
+use the exact position and figure out
+the when you have some interal integrals
+
+ align:start position:0%
+the when you have some interal integrals
+ 
+
+ align:start position:0%
+the when you have some interal integrals
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+do uh they'll change at the place where
+
+ align:start position:0%
+do uh they'll change at the place where
+ 
+
+ align:start position:0%
+do uh they'll change at the place where
+C changes values where we have integrals
+
+ align:start position:0%
+C changes values where we have integrals
+ 
+
+ align:start position:0%
+C changes values where we have integrals
+of C if C has one of those jumps on the
+
+ align:start position:0%
+of C if C has one of those jumps on the
+ 
+
+ align:start position:0%
+of C if C has one of those jumps on the
+quiz the jump came right at a neat point
+
+ align:start position:0%
+quiz the jump came right at a neat point
+ 
+
+ align:start position:0%
+quiz the jump came right at a neat point
+so it was clear see was one on one side
+
+ align:start position:0%
+so it was clear see was one on one side
+ 
+
+ align:start position:0%
+so it was clear see was one on one side
+and two on the other now the jump is
+
+ align:start position:0%
+and two on the other now the jump is
+ 
+
+ align:start position:0%
+and two on the other now the jump is
+going to come at a in between point so
+
+ align:start position:0%
+going to come at a in between point so
+ 
+
+ align:start position:0%
+going to come at a in between point so
+the answer is yes uh I uh well I had a
+
+ align:start position:0%
+the answer is yes uh I uh well I had a
+ 
+
+ align:start position:0%
+the answer is yes uh I uh well I had a
+nice email this morning from somebody
+
+ align:start position:0%
+nice email this morning from somebody
+ 
+
+ align:start position:0%
+nice email this morning from somebody
+who has done that mat lab homework and
+
+ align:start position:0%
+who has done that mat lab homework and
+ 
+
+ align:start position:0%
+who has done that mat lab homework and
+he said
+
+ align:start position:0%
+he said
+ 
+
+ align:start position:0%
+he said
+quote uh it's a good problem I learned
+
+ align:start position:0%
+quote uh it's a good problem I learned
+ 
+
+ align:start position:0%
+quote uh it's a good problem I learned
+more from it than I did from the other
+
+ align:start position:0%
+more from it than I did from the other
+ 
+
+ align:start position:0%
+more from it than I did from the other
+problems in the piece
+
+ align:start position:0%
+problems in the piece
+ 
+
+ align:start position:0%
+problems in the piece
+so I'll blame it on
+
+ align:start position:0%
+so I'll blame it on
+ 
+
+ align:start position:0%
+so I'll blame it on
+him I'll stay with that problem and ask
+
+ align:start position:0%
+him I'll stay with that problem and ask
+ 
+
+ align:start position:0%
+him I'll stay with that problem and ask
+you to do your best to to deal with the
+
+ align:start position:0%
+you to do your best to to deal with the
+ 
+
+ align:start position:0%
+you to do your best to to deal with the
+calculation of the it's second order and
+
+ align:start position:0%
+calculation of the it's second order and
+ 
+
+ align:start position:0%
+calculation of the it's second order and
+I Ed linear elements I didn't want to
+
+ align:start position:0%
+I Ed linear elements I didn't want to
+ 
+
+ align:start position:0%
+I Ed linear elements I didn't want to
+push you up to these cubic elements even
+
+ align:start position:0%
+push you up to these cubic elements even
+ 
+
+ align:start position:0%
+push you up to these cubic elements even
+though those would be give much better
+
+ align:start position:0%
+though those would be give much better
+ 
+
+ align:start position:0%
+though those would be give much better
+accuracy the one reason I didn't put the
+
+ align:start position:0%
+accuracy the one reason I didn't put the
+ 
+
+ align:start position:0%
+accuracy the one reason I didn't put the
+spike and the jump right at the node is
+
+ align:start position:0%
+spike and the jump right at the node is
+ 
+
+ align:start position:0%
+spike and the jump right at the node is
+that if I
+
+ align:start position:0%
+that if I
+ 
+
+ align:start position:0%
+that if I
+did the find out element Sol solution
+
+ align:start position:0%
+did the find out element Sol solution
+ 
+
+ align:start position:0%
+did the find out element Sol solution
+would be exactly right because the
+
+ align:start position:0%
+would be exactly right because the
+ 
+
+ align:start position:0%
+would be exactly right because the
+correct solution is going to be
+
+ align:start position:0%
+correct solution is going to be
+ 
+
+ align:start position:0%
+correct solution is going to be
+piecewise linear and if I put the the
+
+ align:start position:0%
+piecewise linear and if I put the the
+ 
+
+ align:start position:0%
+piecewise linear and if I put the the
+breaks in the in between pieces right at
+
+ align:start position:0%
+breaks in the in between pieces right at
+ 
+
+ align:start position:0%
+breaks in the in between pieces right at
+node points well then I have a function
+
+ align:start position:0%
+node points well then I have a function
+ 
+
+ align:start position:0%
+node points well then I have a function
+that's in my finite element space in my
+
+ align:start position:0%
+that's in my finite element space in my
+ 
+
+ align:start position:0%
+that's in my finite element space in my
+linear space so it'll come out exactly
+
+ align:start position:0%
+linear space so it'll come out exactly
+ 
+
+ align:start position:0%
+linear space so it'll come out exactly
+so I thought well let's at least have
+
+ align:start position:0%
+so I thought well let's at least have
+ 
+
+ align:start position:0%
+so I thought well let's at least have
+some chance to
+
+ align:start position:0%
+some chance to
+ 
+
+ align:start position:0%
+some chance to
+see the error between the finite element
+
+ align:start position:0%
+see the error between the finite element
+ 
+
+ align:start position:0%
+see the error between the finite element
+solution and the exact one do you see
+
+ align:start position:0%
+solution and the exact one do you see
+ 
+
+ align:start position:0%
+solution and the exact one do you see
+what I'm saying I'm just anticipating
+
+ align:start position:0%
+what I'm saying I'm just anticipating
+ 
+
+ align:start position:0%
+what I'm saying I'm just anticipating
+that the result the the exact solution
+
+ align:start position:0%
+that the result the the exact solution
+ 
+
+ align:start position:0%
+that the result the the exact solution
+will let's see there was something
+
+ align:start position:0%
+will let's see there was something
+ 
+
+ align:start position:0%
+will let's see there was something
+happened at 1/3 and something happened
+
+ align:start position:0%
+happened at 1/3 and something happened
+ 
+
+ align:start position:0%
+happened at 1/3 and something happened
+at 2/3 and I I'm afraid I don't remember
+
+ align:start position:0%
+at 2/3 and I I'm afraid I don't remember
+ 
+
+ align:start position:0%
+at 2/3 and I I'm afraid I don't remember
+the boundary conditions does anybody
+
+ align:start position:0%
+the boundary conditions does anybody
+ 
+
+ align:start position:0%
+the boundary conditions does anybody
+remember what I took for boundary
+
+ align:start position:0%
+remember what I took for boundary
+ 
+
+ align:start position:0%
+remember what I took for boundary
+conditions probably free fixed or
+
+ align:start position:0%
+conditions probably free fixed or
+ 
+
+ align:start position:0%
+conditions probably free fixed or
+something so maybe if it was free fixed
+
+ align:start position:0%
+something so maybe if it was free fixed
+ 
+
+ align:start position:0%
+something so maybe if it was free fixed
+probably uh the uh solution would be
+
+ align:start position:0%
+probably uh the uh solution would be
+ 
+
+ align:start position:0%
+probably uh the uh solution would be
+maybe something like that I don't know
+
+ align:start position:0%
+maybe something like that I don't know
+ 
+
+ align:start position:0%
+maybe something like that I don't know
+whatever piecewise linear with brakes
+
+ align:start position:0%
+whatever piecewise linear with brakes
+ 
+
+ align:start position:0%
+whatever piecewise linear with brakes
+where there's a jump in C or where the
+
+ align:start position:0%
+where there's a jump in C or where the
+ 
+
+ align:start position:0%
+where there's a jump in C or where the
+point load is hitting uh oh yeah uh I
+
+ align:start position:0%
+point load is hitting uh oh yeah uh I
+ 
+
+ align:start position:0%
+point load is hitting uh oh yeah uh I
+don't know if that picture is accurate
+
+ align:start position:0%
+don't know if that picture is accurate
+ 
+
+ align:start position:0%
+don't know if that picture is accurate
+but you my point was if I chose those
+
+ align:start position:0%
+but you my point was if I chose those
+ 
+
+ align:start position:0%
+but you my point was if I chose those
+points to be also mesh points then the
+
+ align:start position:0%
+points to be also mesh points then the
+ 
+
+ align:start position:0%
+points to be also mesh points then the
+finite element solution would would be
+
+ align:start position:0%
+finite element solution would would be
+ 
+
+ align:start position:0%
+finite element solution would would be
+exact and we wouldn't learn anything
+
+ align:start position:0%
+exact and we wouldn't learn anything
+ 
+
+ align:start position:0%
+exact and we wouldn't learn anything
+about accuracy okay so anyway for that
+
+ align:start position:0%
+about accuracy okay so anyway for that
+ 
+
+ align:start position:0%
+about accuracy okay so anyway for that
+mat lab problem I'm hoping you can do it
+
+ align:start position:0%
+mat lab problem I'm hoping you can do it
+ 
+
+ align:start position:0%
+mat lab problem I'm hoping you can do it
+uh you can you can do the integrals
+
+ align:start position:0%
+uh you can you can do the integrals
+ 
+
+ align:start position:0%
+uh you can you can do the integrals
+which will mean noticing which
+
+ align:start position:0%
+which will mean noticing which
+ 
+
+ align:start position:0%
+which will mean noticing which
+integral if that doesn't fall if so if
+
+ align:start position:0%
+integral if that doesn't fall if so if
+ 
+
+ align:start position:0%
+integral if that doesn't fall if so if
+the mesh points are like this then you
+
+ align:start position:0%
+the mesh points are like this then you
+ 
+
+ align:start position:0%
+the mesh points are like this then you
+do have in in the integral in the finite
+
+ align:start position:0%
+do have in in the integral in the finite
+ 
+
+ align:start position:0%
+do have in in the integral in the finite
+element integral over that mesh over
+
+ align:start position:0%
+element integral over that mesh over
+ 
+
+ align:start position:0%
+element integral over that mesh over
+that interval you're going to have to
+
+ align:start position:0%
+that interval you're going to have to
+ 
+
+ align:start position:0%
+that interval you're going to have to
+split it into two pieces that's that's
+
+ align:start position:0%
+split it into two pieces that's that's
+ 
+
+ align:start position:0%
+split it into two pieces that's that's
+it yeah just so so see if you can do
+
+ align:start position:0%
+it yeah just so so see if you can do
+ 
+
+ align:start position:0%
+it yeah just so so see if you can do
+that split do the split into two pieces
+
+ align:start position:0%
+that split do the split into two pieces
+ 
+
+ align:start position:0%
+that split do the split into two pieces
+okay so that's a comment on that
+
+ align:start position:0%
+okay so that's a comment on that
+ 
+
+ align:start position:0%
+okay so that's a comment on that
+homework okay what else do I need to
+
+ align:start position:0%
+homework okay what else do I need to
+ 
+
+ align:start position:0%
+homework okay what else do I need to
+comment on when I'm sort of catching up
+
+ align:start position:0%
+comment on when I'm sort of catching up
+ 
+
+ align:start position:0%
+comment on when I'm sort of catching up
+here oh about boundary
+
+ align:start position:0%
+here oh about boundary
+ 
+
+ align:start position:0%
+here oh about boundary
+conditions uh I thought I would just
+
+ align:start position:0%
+conditions uh I thought I would just
+ 
+
+ align:start position:0%
+conditions uh I thought I would just
+repeat clearly on the board uh the
+
+ align:start position:0%
+repeat clearly on the board uh the
+ 
+
+ align:start position:0%
+repeat clearly on the board uh the
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+rules about and the difference between
+
+ align:start position:0%
+rules about and the difference between
+ 
+
+ align:start position:0%
+rules about and the difference between
+fixed and free when we're doing this
+
+ align:start position:0%
+fixed and free when we're doing this
+ 
+
+ align:start position:0%
+fixed and free when we're doing this
+uh uh weak form approach to the uh to
+
+ align:start position:0%
+uh uh weak form approach to the uh to
+ 
+
+ align:start position:0%
+uh uh weak form approach to the uh to
+the problem and and then I gave the
+
+ align:start position:0%
+the problem and and then I gave the
+ 
+
+ align:start position:0%
+the problem and and then I gave the
+other names a fixed condition in in the
+
+ align:start position:0%
+other names a fixed condition in in the
+ 
+
+ align:start position:0%
+other names a fixed condition in in the
+in this Theory it's often called an
+
+ align:start position:0%
+in this Theory it's often called an
+ 
+
+ align:start position:0%
+in this Theory it's often called an
+essential boundary condition but many
+
+ align:start position:0%
+essential boundary condition but many
+ 
+
+ align:start position:0%
+essential boundary condition but many
+people just name d CL as the as the
+
+ align:start position:0%
+people just name d CL as the as the
+ 
+
+ align:start position:0%
+people just name d CL as the as the
+person's name that's associated with
+
+ align:start position:0%
+person's name that's associated with
+ 
+
+ align:start position:0%
+person's name that's associated with
+such conditions like U of 0 equals 0 so
+
+ align:start position:0%
+such conditions like U of 0 equals 0 so
+ 
+
+ align:start position:0%
+such conditions like U of 0 equals 0 so
+right fixed and then free conditions are
+
+ align:start position:0%
+right fixed and then free conditions are
+ 
+
+ align:start position:0%
+right fixed and then free conditions are
+natural conditions in the finite element
+
+ align:start position:0%
+natural conditions in the finite element
+ 
+
+ align:start position:0%
+natural conditions in the finite element
+method and that that means that we don't
+
+ align:start position:0%
+method and that that means that we don't
+ 
+
+ align:start position:0%
+method and that that means that we don't
+have to impose them right I I discussed
+
+ align:start position:0%
+have to impose them right I I discussed
+ 
+
+ align:start position:0%
+have to impose them right I I discussed
+this in the earlier lecture I just
+
+ align:start position:0%
+this in the earlier lecture I just
+ 
+
+ align:start position:0%
+this in the earlier lecture I just
+thought I'd bring it back here because
+
+ align:start position:0%
+thought I'd bring it back here because
+ 
+
+ align:start position:0%
+thought I'd bring it back here because
+uh um it's easy to describe in one line
+
+ align:start position:0%
+uh um it's easy to describe in one line
+ 
+
+ align:start position:0%
+uh um it's easy to describe in one line
+now somebody asked on Wednesday a good
+
+ align:start position:0%
+now somebody asked on Wednesday a good
+ 
+
+ align:start position:0%
+now somebody asked on Wednesday a good
+question suppose the the NOA suppose the
+
+ align:start position:0%
+question suppose the the NOA suppose the
+ 
+
+ align:start position:0%
+question suppose the the NOA suppose the
+suppose U
+
+ align:start position:0%
+suppose U
+ 
+
+ align:start position:0%
+suppose U
+Prime is
+
+ align:start position:0%
+Prime is
+ 
+
+ align:start position:0%
+Prime is
+given but not given a zero so suppose
+
+ align:start position:0%
+given but not given a zero so suppose
+ 
+
+ align:start position:0%
+given but not given a zero so suppose
+there's the the suppose we have have a
+
+ align:start position:0%
+there's the the suppose we have have a
+ 
+
+ align:start position:0%
+there's the the suppose we have have a
+condition like U Prime equals a let's
+
+ align:start position:0%
+condition like U Prime equals a let's
+ 
+
+ align:start position:0%
+condition like U Prime equals a let's
+say what to do so so I'll just put
+
+ align:start position:0%
+say what to do so so I'll just put
+ 
+
+ align:start position:0%
+say what to do so so I'll just put
+question mark there how do I deal with a
+
+ align:start position:0%
+question mark there how do I deal with a
+ 
+
+ align:start position:0%
+question mark there how do I deal with a
+a how does the how do I how does the
+
+ align:start position:0%
+a how does the how do I how does the
+ 
+
+ align:start position:0%
+a how does the how do I how does the
+weak form and the guran approach deal
+
+ align:start position:0%
+weak form and the guran approach deal
+ 
+
+ align:start position:0%
+weak form and the guran approach deal
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+nonzero
+
+ align:start position:0%
+nonzero
+ 
+
+ align:start position:0%
+nonzero
+uh natural condition a nonzero noyman
+
+ align:start position:0%
+uh natural condition a nonzero noyman
+ 
+
+ align:start position:0%
+uh natural condition a nonzero noyman
+condition that would be the natural that
+
+ align:start position:0%
+condition that would be the natural that
+ 
+
+ align:start position:0%
+condition that would be the natural that
+would be the right words so this would
+
+ align:start position:0%
+would be the right words so this would
+ 
+
+ align:start position:0%
+would be the right words so this would
+be in a second order problem this would
+
+ align:start position:0%
+be in a second order problem this would
+ 
+
+ align:start position:0%
+be in a second order problem this would
+be a a noyon condition and I'm thinking
+
+ align:start position:0%
+be a a noyon condition and I'm thinking
+ 
+
+ align:start position:0%
+be a a noyon condition and I'm thinking
+what what do you do if a isn't zero
+
+ align:start position:0%
+what what do you do if a isn't zero
+ 
+
+ align:start position:0%
+what what do you do if a isn't zero
+somehow that has to show up in your
+
+ align:start position:0%
+somehow that has to show up in your
+ 
+
+ align:start position:0%
+somehow that has to show up in your
+finite element equations right so I
+
+ align:start position:0%
+finite element equations right so I
+ 
+
+ align:start position:0%
+finite element equations right so I
+guess the right way is to go back to
+
+ align:start position:0%
+guess the right way is to go back to
+ 
+
+ align:start position:0%
+guess the right way is to go back to
+where they came from so do you remember
+
+ align:start position:0%
+where they came from so do you remember
+ 
+
+ align:start position:0%
+where they came from so do you remember
+how the weak form came I I took the took
+
+ align:start position:0%
+how the weak form came I I took the took
+ 
+
+ align:start position:0%
+how the weak form came I I took the took
+the differential equation I multiplied
+
+ align:start position:0%
+the differential equation I multiplied
+ 
+
+ align:start position:0%
+the differential equation I multiplied
+by any test function and I integrated by
+
+ align:start position:0%
+by any test function and I integrated by
+ 
+
+ align:start position:0%
+by any test function and I integrated by
+parts that's where the weak form started
+
+ align:start position:0%
+parts that's where the weak form started
+ 
+
+ align:start position:0%
+parts that's where the weak form started
+so the integration by parts gave me this
+
+ align:start position:0%
+so the integration by parts gave me this
+ 
+
+ align:start position:0%
+so the integration by parts gave me this
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+symmetric uh uh integral s sort of it's
+
+ align:start position:0%
+symmetric uh uh integral s sort of it's
+ 
+
+ align:start position:0%
+symmetric uh uh integral s sort of it's
+symmetric in u and v it only requires
+
+ align:start position:0%
+symmetric in u and v it only requires
+ 
+
+ align:start position:0%
+symmetric in u and v it only requires
+one derivative of U so that I'm allowed
+
+ align:start position:0%
+one derivative of U so that I'm allowed
+ 
+
+ align:start position:0%
+one derivative of U so that I'm allowed
+to use uh uh hat functions and I'm
+
+ align:start position:0%
+to use uh uh hat functions and I'm
+ 
+
+ align:start position:0%
+to use uh uh hat functions and I'm
+allowed to use hat functions for V
+
+ align:start position:0%
+allowed to use hat functions for V
+ 
+
+ align:start position:0%
+allowed to use hat functions for V
+because their derivatives have just a
+
+ align:start position:0%
+because their derivatives have just a
+ 
+
+ align:start position:0%
+because their derivatives have just a
+jump and a jump function I can integrate
+
+ align:start position:0%
+jump and a jump function I can integrate
+ 
+
+ align:start position:0%
+jump and a jump function I can integrate
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+problem now what about
+
+ align:start position:0%
+problem now what about
+ 
+
+ align:start position:0%
+problem now what about
+this this U Prime equal a and I guess
+
+ align:start position:0%
+this this U Prime equal a and I guess
+ 
+
+ align:start position:0%
+this this U Prime equal a and I guess
+we're seeing it
+
+ align:start position:0%
+we're seeing it
+ 
+
+ align:start position:0%
+we're seeing it
+there if U Prime was Zero if we had a
+
+ align:start position:0%
+there if U Prime was Zero if we had a
+ 
+
+ align:start position:0%
+there if U Prime was Zero if we had a
+totally free n u Prime was Zero nothing
+
+ align:start position:0%
+totally free n u Prime was Zero nothing
+ 
+
+ align:start position:0%
+totally free n u Prime was Zero nothing
+happening there then that term would
+
+ align:start position:0%
+happening there then that term would
+ 
+
+ align:start position:0%
+happening there then that term would
+drop out of the integration by parts and
+
+ align:start position:0%
+drop out of the integration by parts and
+ 
+
+ align:start position:0%
+drop out of the integration by parts and
+you see why I don't have to impose
+
+ align:start position:0%
+you see why I don't have to impose
+ 
+
+ align:start position:0%
+you see why I don't have to impose
+anything on V because that term is
+
+ align:start position:0%
+anything on V because that term is
+ 
+
+ align:start position:0%
+anything on V because that term is
+already accounted for by the U Prime
+
+ align:start position:0%
+already accounted for by the U Prime
+ 
+
+ align:start position:0%
+already accounted for by the U Prime
+going away now what about if U Prime
+
+ align:start position:0%
+going away now what about if U Prime
+ 
+
+ align:start position:0%
+going away now what about if U Prime
+isn't is is is given but not given zero
+
+ align:start position:0%
+isn't is is is given but not given zero
+ 
+
+ align:start position:0%
+isn't is is is given but not given zero
+suppose it's given the value a all I
+
+ align:start position:0%
+suppose it's given the value a all I
+ 
+
+ align:start position:0%
+suppose it's given the value a all I
+want to say
+
+ align:start position:0%
+want to say
+ 
+
+ align:start position:0%
+want to say
+is then I have to I have to This this
+
+ align:start position:0%
+is then I have to I have to This this
+ 
+
+ align:start position:0%
+is then I have to I have to This this
+term is is uh has to stay I have to pay
+
+ align:start position:0%
+term is is uh has to stay I have to pay
+ 
+
+ align:start position:0%
+term is is uh has to stay I have to pay
+attention to it what what happens when
+
+ align:start position:0%
+attention to it what what happens when
+ 
+
+ align:start position:0%
+attention to it what what happens when
+gurin takes over gurin will try will put
+
+ align:start position:0%
+gurin takes over gurin will try will put
+ 
+
+ align:start position:0%
+gurin takes over gurin will try will put
+in one of his test functions maybe I
+
+ align:start position:0%
+in one of his test functions maybe I
+ 
+
+ align:start position:0%
+in one of his test functions maybe I
+just indicate that by changing the V to
+
+ align:start position:0%
+just indicate that by changing the V to
+ 
+
+ align:start position:0%
+just indicate that by changing the V to
+a cap V it'll be one of them there will
+
+ align:start position:0%
+a cap V it'll be one of them there will
+ 
+
+ align:start position:0%
+a cap V it'll be one of them there will
+be n of
+
+ align:start position:0%
+be n of
+ 
+
+ align:start position:0%
+be n of
+them each one of each VI each test guy
+
+ align:start position:0%
+them each one of each VI each test guy
+ 
+
+ align:start position:0%
+them each one of each VI each test guy
+gives me an equation and of course U is
+
+ align:start position:0%
+gives me an equation and of course U is
+ 
+
+ align:start position:0%
+gives me an equation and of course U is
+now going
+
+ align:start position:0%
+now going
+ 
+
+ align:start position:0%
+now going
+to the gurin idea is instead of any U I
+
+ align:start position:0%
+to the gurin idea is instead of any U I
+ 
+
+ align:start position:0%
+to the gurin idea is instead of any U I
+only have Capital U's combinations of
+
+ align:start position:0%
+only have Capital U's combinations of
+ 
+
+ align:start position:0%
+only have Capital U's combinations of
+these Fe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm not going to say anything very big
+
+ align:start position:0%
+I'm not going to say anything very big
+ 
+
+ align:start position:0%
+I'm not going to say anything very big
+here or very clear all I want to say is
+
+ align:start position:0%
+here or very clear all I want to say is
+ 
+
+ align:start position:0%
+here or very clear all I want to say is
+that if U Prime is given at an end point
+
+ align:start position:0%
+that if U Prime is given at an end point
+ 
+
+ align:start position:0%
+that if U Prime is given at an end point
+then and given by a then when then this
+
+ align:start position:0%
+then and given by a then when then this
+ 
+
+ align:start position:0%
+then and given by a then when then this
+is part you know this whole stuff is
+
+ align:start position:0%
+is part you know this whole stuff is
+ 
+
+ align:start position:0%
+is part you know this whole stuff is
+equaling something with an F right FV DX
+
+ align:start position:0%
+equaling something with an F right FV DX
+ 
+
+ align:start position:0%
+equaling something with an F right FV DX
+X I should remember the other side of
+
+ align:start position:0%
+X I should remember the other side of
+ 
+
+ align:start position:0%
+X I should remember the other side of
+the equation If U Prime is given then
+
+ align:start position:0%
+the equation If U Prime is given then
+ 
+
+ align:start position:0%
+the equation If U Prime is given then
+then C at that end point times the given
+
+ align:start position:0%
+then C at that end point times the given
+ 
+
+ align:start position:0%
+then C at that end point times the given
+value of a times the
+
+ align:start position:0%
+value of a times the
+ 
+
+ align:start position:0%
+value of a times the
+V will be whatever value of V that is
+
+ align:start position:0%
+V will be whatever value of V that is
+ 
+
+ align:start position:0%
+V will be whatever value of V that is
+will show up in equation I this will be
+
+ align:start position:0%
+will show up in equation I this will be
+ 
+
+ align:start position:0%
+will show up in equation I this will be
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+term that'll be a term that goes on the
+
+ align:start position:0%
+term that'll be a term that goes on the
+ 
+
+ align:start position:0%
+term that'll be a term that goes on the
+right hand side that's what I all I'm
+
+ align:start position:0%
+right hand side that's what I all I'm
+ 
+
+ align:start position:0%
+right hand side that's what I all I'm
+saying and all you would expect
+
+ align:start position:0%
+saying and all you would expect
+ 
+
+ align:start position:0%
+saying and all you would expect
+that anytime I have a you know I'm I'm
+
+ align:start position:0%
+that anytime I have a you know I'm I'm
+ 
+
+ align:start position:0%
+that anytime I have a you know I'm I'm
+given some data I'm given some nonzero
+
+ align:start position:0%
+given some data I'm given some nonzero
+ 
+
+ align:start position:0%
+given some data I'm given some nonzero
+boundary conditions or I'm given some
+
+ align:start position:0%
+boundary conditions or I'm given some
+ 
+
+ align:start position:0%
+boundary conditions or I'm given some
+nonzero F in the inside that stuff is
+
+ align:start position:0%
+nonzero F in the inside that stuff is
+ 
+
+ align:start position:0%
+nonzero F in the inside that stuff is
+going to show up on the right hand side
+
+ align:start position:0%
+going to show up on the right hand side
+ 
+
+ align:start position:0%
+going to show up on the right hand side
+it'll show up as part of the big of the
+
+ align:start position:0%
+it'll show up as part of the big of the
+ 
+
+ align:start position:0%
+it'll show up as part of the big of the
+of the it'll show up as part of the F
+
+ align:start position:0%
+of the it'll show up as part of the F
+ 
+
+ align:start position:0%
+of the it'll show up as part of the F
+the the vector of these uh uh so up to
+
+ align:start position:0%
+the the vector of these uh uh so up to
+ 
+
+ align:start position:0%
+the the vector of these uh uh so up to
+now F has just come from Little F ofx
+
+ align:start position:0%
+now F has just come from Little F ofx
+ 
+
+ align:start position:0%
+now F has just come from Little F ofx
+integrated against V and all I'm saying
+
+ align:start position:0%
+integrated against V and all I'm saying
+ 
+
+ align:start position:0%
+integrated against V and all I'm saying
+is that uh if we had one of these guys
+
+ align:start position:0%
+is that uh if we had one of these guys
+ 
+
+ align:start position:0%
+is that uh if we had one of these guys
+then that would contribute to Big F
+
+ align:start position:0%
+then that would contribute to Big F
+ 
+
+ align:start position:0%
+then that would contribute to Big F
+also yeah you can see it's not beautiful
+
+ align:start position:0%
+also yeah you can see it's not beautiful
+ 
+
+ align:start position:0%
+also yeah you can see it's not beautiful
+it's it's uh it's uh but we have to
+
+ align:start position:0%
+it's it's uh it's uh but we have to
+ 
+
+ align:start position:0%
+it's it's uh it's uh but we have to
+realize what we would do okay maybe uh
+
+ align:start position:0%
+realize what we would do okay maybe uh
+ 
+
+ align:start position:0%
+realize what we would do okay maybe uh
+that's not my favorite topic but I'll
+
+ align:start position:0%
+that's not my favorite topic but I'll
+ 
+
+ align:start position:0%
+that's not my favorite topic but I'll
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+say quit on that one and uh not
+
+ align:start position:0%
+say quit on that one and uh not
+ 
+
+ align:start position:0%
+say quit on that one and uh not
+expecting you to do problems or anything
+
+ align:start position:0%
+expecting you to do problems or anything
+ 
+
+ align:start position:0%
+expecting you to do problems or anything
+that that involv that possibility just
+
+ align:start position:0%
+that that involv that possibility just
+ 
+
+ align:start position:0%
+that that involv that possibility just
+to see that it could happen okay quit
+
+ align:start position:0%
+to see that it could happen okay quit
+ 
+
+ align:start position:0%
+to see that it could happen okay quit
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+interpolation all
+
+ align:start position:0%
+interpolation all
+ 
+
+ align:start position:0%
+interpolation all
+right so I guess if I had to en list
+
+ align:start position:0%
+right so I guess if I had to en list
+ 
+
+ align:start position:0%
+right so I guess if I had to en list
+problems that people face all the time
+
+ align:start position:0%
+problems that people face all the time
+ 
+
+ align:start position:0%
+problems that people face all the time
+and need numerical guidance on
+
+ align:start position:0%
+and need numerical guidance on
+ 
+
+ align:start position:0%
+and need numerical guidance on
+this is one of them and and so let's say
+
+ align:start position:0%
+this is one of them and and so let's say
+ 
+
+ align:start position:0%
+this is one of them and and so let's say
+we're in
+
+ align:start position:0%
+we're in
+ 
+
+ align:start position:0%
+we're in
+1D 1D is certainly a lot easier so
+
+ align:start position:0%
+1D 1D is certainly a lot easier so
+ 
+
+ align:start position:0%
+1D 1D is certainly a lot easier so
+suppose I have this could be like I'll
+
+ align:start position:0%
+suppose I have this could be like I'll
+ 
+
+ align:start position:0%
+suppose I have this could be like I'll
+call this x just to have a name for the
+
+ align:start position:0%
+call this x just to have a name for the
+ 
+
+ align:start position:0%
+call this x just to have a name for the
+variable suppose I have some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values say six
+
+ align:start position:0%
+values say six
+ 
+
+ align:start position:0%
+values say six
+values and I want to
+
+ align:start position:0%
+values and I want to
+ 
+
+ align:start position:0%
+values and I want to
+put uh and then measured them I've
+
+ align:start position:0%
+put uh and then measured them I've
+ 
+
+ align:start position:0%
+put uh and then measured them I've
+worked hard to find those six values but
+
+ align:start position:0%
+worked hard to find those six values but
+ 
+
+ align:start position:0%
+worked hard to find those six values but
+now you may say well so I'm I'm thinking
+
+ align:start position:0%
+now you may say well so I'm I'm thinking
+ 
+
+ align:start position:0%
+now you may say well so I'm I'm thinking
+I have some function uh F ofx
+
+ align:start position:0%
+I have some function uh F ofx
+ 
+
+ align:start position:0%
+I have some function uh F ofx
+here but right now I don't have a
+
+ align:start position:0%
+here but right now I don't have a
+ 
+
+ align:start position:0%
+here but right now I don't have a
+function right now I just have six
+
+ align:start position:0%
+function right now I just have six
+ 
+
+ align:start position:0%
+function right now I just have six
+values of that function you know what is
+
+ align:start position:0%
+values of that function you know what is
+ 
+
+ align:start position:0%
+values of that function you know what is
+the uh stretching constant what is the
+
+ align:start position:0%
+the uh stretching constant what is the
+ 
+
+ align:start position:0%
+the uh stretching constant what is the
+like the C
+
+ align:start position:0%
+like the C
+ 
+
+ align:start position:0%
+like the C
+ofx if you had if you had a physical
+
+ align:start position:0%
+ofx if you had if you had a physical
+ 
+
+ align:start position:0%
+ofx if you had if you had a physical
+expr experiment with a with a um uh you
+
+ align:start position:0%
+expr experiment with a with a um uh you
+ 
+
+ align:start position:0%
+expr experiment with a with a um uh you
+know an actual spring you might measure
+
+ align:start position:0%
+know an actual spring you might measure
+ 
+
+ align:start position:0%
+know an actual spring you might measure
+you might put on different uh forces and
+
+ align:start position:0%
+you might put on different uh forces and
+ 
+
+ align:start position:0%
+you might put on different uh forces and
+measure the stretching and have six
+
+ align:start position:0%
+measure the stretching and have six
+ 
+
+ align:start position:0%
+measure the stretching and have six
+values of that so this what how how do I
+
+ align:start position:0%
+values of that so this what how how do I
+ 
+
+ align:start position:0%
+values of that so this what how how do I
+fit those with a curve in other words
+
+ align:start position:0%
+fit those with a curve in other words
+ 
+
+ align:start position:0%
+fit those with a curve in other words
+how do I how do I know interpolation
+
+ align:start position:0%
+how do I how do I know interpolation
+ 
+
+ align:start position:0%
+how do I how do I know interpolation
+means inter means is sort of asking what
+
+ align:start position:0%
+means inter means is sort of asking what
+ 
+
+ align:start position:0%
+means inter means is sort of asking what
+about between the
+
+ align:start position:0%
+about between the
+ 
+
+ align:start position:0%
+about between the
+points what about between what value
+
+ align:start position:0%
+points what about between what value
+ 
+
+ align:start position:0%
+points what about between what value
+should it have
+
+ align:start position:0%
+should it have
+ 
+
+ align:start position:0%
+should it have
+there okay well there's a simple one
+
+ align:start position:0%
+there okay well there's a simple one
+ 
+
+ align:start position:0%
+there okay well there's a simple one
+simple rule would be just just uh
+
+ align:start position:0%
+simple rule would be just just uh
+ 
+
+ align:start position:0%
+simple rule would be just just uh
+interpolate linearly
+
+ align:start position:0%
+interpolate linearly
+ 
+
+ align:start position:0%
+interpolate linearly
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's that's certainly pretty stable it
+
+ align:start position:0%
+that's that's certainly pretty stable it
+ 
+
+ align:start position:0%
+that's that's certainly pretty stable it
+will not get out of control but it's not
+
+ align:start position:0%
+will not get out of control but it's not
+ 
+
+ align:start position:0%
+will not get out of control but it's not
+very accurate it's not it's it's has the
+
+ align:start position:0%
+very accurate it's not it's it's has the
+ 
+
+ align:start position:0%
+very accurate it's not it's it's has the
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if there for the function that's
+
+ align:start position:0%
+if there for the function that's
+ 
+
+ align:start position:0%
+if there for the function that's
+probably lying behind this this isn't
+
+ align:start position:0%
+probably lying behind this this isn't
+ 
+
+ align:start position:0%
+probably lying behind this this isn't
+that great a
+
+ align:start position:0%
+that great a
+ 
+
+ align:start position:0%
+that great a
+representation okay you say I want
+
+ align:start position:0%
+representation okay you say I want
+ 
+
+ align:start position:0%
+representation okay you say I want
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+smoother well another idea that
+
+ align:start position:0%
+smoother well another idea that
+ 
+
+ align:start position:0%
+smoother well another idea that
+naturally comes up
+
+ align:start position:0%
+naturally comes up
+ 
+
+ align:start position:0%
+naturally comes up
+is second sort of The Other Extreme
+
+ align:start position:0%
+is second sort of The Other Extreme
+ 
+
+ align:start position:0%
+is second sort of The Other Extreme
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+be so that was completely local just
+
+ align:start position:0%
+be so that was completely local just
+ 
+
+ align:start position:0%
+be so that was completely local just
+every two values determine the broken
+
+ align:start position:0%
+every two values determine the broken
+ 
+
+ align:start position:0%
+every two values determine the broken
+line second idea that's completely
+
+ align:start position:0%
+line second idea that's completely
+ 
+
+ align:start position:0%
+line second idea that's completely
+natural would be fit a
+
+ align:start position:0%
+natural would be fit a
+ 
+
+ align:start position:0%
+natural would be fit a
+polinomial fit a polinomial through
+
+ align:start position:0%
+polinomial fit a polinomial through
+ 
+
+ align:start position:0%
+polinomial fit a polinomial through
+those points and then you have a nice
+
+ align:start position:0%
+those points and then you have a nice
+ 
+
+ align:start position:0%
+those points and then you have a nice
+totally simple function nice curve and
+
+ align:start position:0%
+totally simple function nice curve and
+ 
+
+ align:start position:0%
+totally simple function nice curve and
+uh so what degree polinomial would we be
+
+ align:start position:0%
+uh so what degree polinomial would we be
+ 
+
+ align:start position:0%
+uh so what degree polinomial would we be
+looking for here if I have six points I
+
+ align:start position:0%
+looking for here if I have six points I
+ 
+
+ align:start position:0%
+looking for here if I have six points I
+could fit a polom of
+
+ align:start position:0%
+could fit a polom of
+ 
+
+ align:start position:0%
+could fit a polom of
+degree what do you say I I want I want
+
+ align:start position:0%
+degree what do you say I I want I want
+ 
+
+ align:start position:0%
+degree what do you say I I want I want
+to have six coefficients so I can m get
+
+ align:start position:0%
+to have six coefficients so I can m get
+ 
+
+ align:start position:0%
+to have six coefficients so I can m get
+six equations to make the make the
+
+ align:start position:0%
+six equations to make the make the
+ 
+
+ align:start position:0%
+six equations to make the make the
+polinomial go through those six points
+
+ align:start position:0%
+polinomial go through those six points
+ 
+
+ align:start position:0%
+polinomial go through those six points
+so my polinomial P of X my which
+
+ align:start position:0%
+so my polinomial P of X my which
+ 
+
+ align:start position:0%
+so my polinomial P of X my which
+actually goes through those points would
+
+ align:start position:0%
+actually goes through those points would
+ 
+
+ align:start position:0%
+actually goes through those points would
+be some polinomial of the form it's got
+
+ align:start position:0%
+be some polinomial of the form it's got
+ 
+
+ align:start position:0%
+be some polinomial of the form it's got
+some constant term and it's got some
+
+ align:start position:0%
+some constant term and it's got some
+ 
+
+ align:start position:0%
+some constant term and it's got some
+linear term and how far am I going to
+
+ align:start position:0%
+linear term and how far am I going to
+ 
+
+ align:start position:0%
+linear term and how far am I going to
+go fifth right that'll give me six
+
+ align:start position:0%
+go fifth right that'll give me six
+ 
+
+ align:start position:0%
+go fifth right that'll give me six
+coefficients okay so I could fo put a
+
+ align:start position:0%
+coefficients okay so I could fo put a
+ 
+
+ align:start position:0%
+coefficients okay so I could fo put a
+fifth degree polinomial that gives me a
+
+ align:start position:0%
+fifth degree polinomial that gives me a
+ 
+
+ align:start position:0%
+fifth degree polinomial that gives me a
+A1 up to A5
+
+ align:start position:0%
+A1 up to A5
+ 
+
+ align:start position:0%
+A1 up to A5
+six coefficients through six
+
+ align:start position:0%
+six coefficients through six
+ 
+
+ align:start position:0%
+six coefficients through six
+points well six isn't too
+
+ align:start position:0%
+points well six isn't too
+ 
+
+ align:start position:0%
+points well six isn't too
+bad but if six if six became
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+60 don't do it that's the message don't
+
+ align:start position:0%
+60 don't do it that's the message don't
+ 
+
+ align:start position:0%
+60 don't do it that's the message don't
+do it don't I if if if I'm going on up
+
+ align:start position:0%
+do it don't I if if if I'm going on up
+ 
+
+ align:start position:0%
+do it don't I if if if I'm going on up
+to say I have an a59 x to the
+
+ align:start position:0%
+to say I have an a59 x to the
+ 
+
+ align:start position:0%
+to say I have an a59 x to the
+59th and that and that fits my 60 points
+
+ align:start position:0%
+59th and that and that fits my 60 points
+ 
+
+ align:start position:0%
+59th and that and that fits my 60 points
+and and you say well well look I've got
+
+ align:start position:0%
+and and you say well well look I've got
+ 
+
+ align:start position:0%
+and and you say well well look I've got
+60 values that should be way better than
+
+ align:start position:0%
+60 values that should be way better than
+ 
+
+ align:start position:0%
+60 values that should be way better than
+having only six but the polinomial that
+
+ align:start position:0%
+having only six but the polinomial that
+ 
+
+ align:start position:0%
+having only six but the polinomial that
+would come out of that even if these
+
+ align:start position:0%
+would come out of that even if these
+ 
+
+ align:start position:0%
+would come out of that even if these
+even if these values were on a pretty
+
+ align:start position:0%
+even if these values were on a pretty
+ 
+
+ align:start position:0%
+even if these values were on a pretty
+were pretty smooth the polom that fits
+
+ align:start position:0%
+were pretty smooth the polom that fits
+ 
+
+ align:start position:0%
+were pretty smooth the polom that fits
+well I have to put in a whole lot more
+
+ align:start position:0%
+well I have to put in a whole lot more
+ 
+
+ align:start position:0%
+well I have to put in a whole lot more
+to get 60 and I won't try the polinomial
+
+ align:start position:0%
+to get 60 and I won't try the polinomial
+ 
+
+ align:start position:0%
+to get 60 and I won't try the polinomial
+would go
+
+ align:start position:0%
+would go
+ 
+
+ align:start position:0%
+would go
+crazy right I mean it would just I I
+
+ align:start position:0%
+crazy right I mean it would just I I
+ 
+
+ align:start position:0%
+crazy right I mean it would just I I
+don't can I just draw something crazy I
+
+ align:start position:0%
+don't can I just draw something crazy I
+ 
+
+ align:start position:0%
+don't can I just draw something crazy I
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+whatever it's it's unstable it's it and
+
+ align:start position:0%
+whatever it's it's unstable it's it and
+ 
+
+ align:start position:0%
+whatever it's it's unstable it's it and
+there are classical examples of that in
+
+ align:start position:0%
+there are classical examples of that in
+ 
+
+ align:start position:0%
+there are classical examples of that in
+fact the the famous example is the
+
+ align:start position:0%
+fact the the famous example is the
+ 
+
+ align:start position:0%
+fact the the famous example is the
+function 1 over 1 +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X2 and later in a there's a figure in
+
+ align:start position:0%
+X2 and later in a there's a figure in
+ 
+
+ align:start position:0%
+X2 and later in a there's a figure in
+the book I think it's in section
+
+ align:start position:0%
+the book I think it's in section
+ 
+
+ align:start position:0%
+the book I think it's in section
+5.4 uh which
+
+ align:start position:0%
+5.4 uh which
+ 
+
+ align:start position:0%
+5.4 uh which
+shows uh the result of that's I mean
+
+ align:start position:0%
+shows uh the result of that's I mean
+ 
+
+ align:start position:0%
+shows uh the result of that's I mean
+that's a terrific function it it has no
+
+ align:start position:0%
+that's a terrific function it it has no
+ 
+
+ align:start position:0%
+that's a terrific function it it has no
+no it's infinitely differentiable it's
+
+ align:start position:0%
+no it's infinitely differentiable it's
+ 
+
+ align:start position:0%
+no it's infinitely differentiable it's
+it's I would even call it an analytic
+
+ align:start position:0%
+it's I would even call it an analytic
+ 
+
+ align:start position:0%
+it's I would even call it an analytic
+function it's great but if I try to fit
+
+ align:start position:0%
+function it's great but if I try to fit
+ 
+
+ align:start position:0%
+function it's great but if I try to fit
+it with a high degree polom at at
+
+ align:start position:0%
+it with a high degree polom at at
+ 
+
+ align:start position:0%
+it with a high degree polom at at
+points that polinomial gets out of hand
+
+ align:start position:0%
+points that polinomial gets out of hand
+ 
+
+ align:start position:0%
+points that polinomial gets out of hand
+right and the and a figure is in there's
+
+ align:start position:0%
+right and the and a figure is in there's
+ 
+
+ align:start position:0%
+right and the and a figure is in there's
+a figure there okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+I mean this I mean mat
+
+ align:start position:0%
+I mean this I mean mat
+ 
+
+ align:start position:0%
+I mean this I mean mat
+lab or any Computing system would have a
+
+ align:start position:0%
+lab or any Computing system would have a
+ 
+
+ align:start position:0%
+lab or any Computing system would have a
+would have a a
+
+ align:start position:0%
+would have a a
+ 
+
+ align:start position:0%
+would have a a
+subroutine that does interpolation and
+
+ align:start position:0%
+subroutine that does interpolation and
+ 
+
+ align:start position:0%
+subroutine that does interpolation and
+this is this was named after lron so
+
+ align:start position:0%
+this is this was named after lron so
+ 
+
+ align:start position:0%
+this is this was named after lron so
+this is called lron interpolation
+
+ align:start position:0%
+this is called lron interpolation
+ 
+
+ align:start position:0%
+this is called lron interpolation
+fitting a
+
+ align:start position:0%
+fitting a
+ 
+
+ align:start position:0%
+fitting a
+polom and if the if the degree is small
+
+ align:start position:0%
+polom and if the if the degree is small
+ 
+
+ align:start position:0%
+polom and if the if the degree is small
+and maybe maybe degree five would be
+
+ align:start position:0%
+and maybe maybe degree five would be
+ 
+
+ align:start position:0%
+and maybe maybe degree five would be
+okay then that that's a re that's an
+
+ align:start position:0%
+okay then that that's a re that's an
+ 
+
+ align:start position:0%
+okay then that that's a re that's an
+important uh thing to be able to do and
+
+ align:start position:0%
+important uh thing to be able to do and
+ 
+
+ align:start position:0%
+important uh thing to be able to do and
+and it's uh in other words you're
+
+ align:start position:0%
+and it's uh in other words you're
+ 
+
+ align:start position:0%
+and it's uh in other words you're
+finding these six coefficients from
+
+ align:start position:0%
+finding these six coefficients from
+ 
+
+ align:start position:0%
+finding these six coefficients from
+these six Heights you've got some 6x6
+
+ align:start position:0%
+these six Heights you've got some 6x6
+ 
+
+ align:start position:0%
+these six Heights you've got some 6x6
+Matrix that connects the six Heights to
+
+ align:start position:0%
+Matrix that connects the six Heights to
+ 
+
+ align:start position:0%
+Matrix that connects the six Heights to
+the six
+
+ align:start position:0%
+the six
+ 
+
+ align:start position:0%
+the six
+A's but when you get up to 60 that
+
+ align:start position:0%
+A's but when you get up to 60 that
+ 
+
+ align:start position:0%
+A's but when you get up to 60 that
+Matrix stops behaving well it's uh
+
+ align:start position:0%
+Matrix stops behaving well it's uh
+ 
+
+ align:start position:0%
+Matrix stops behaving well it's uh
+becomes very ill conditioned and you're
+
+ align:start position:0%
+becomes very ill conditioned and you're
+ 
+
+ align:start position:0%
+becomes very ill conditioned and you're
+you're coefficients go all over the
+
+ align:start position:0%
+you're coefficients go all over the
+ 
+
+ align:start position:0%
+you're coefficients go all over the
+place okay so that my question is what
+
+ align:start position:0%
+place okay so that my question is what
+ 
+
+ align:start position:0%
+place okay so that my question is what
+do you do
+
+ align:start position:0%
+do you do
+ 
+
+ align:start position:0%
+do you do
+and one answer one good answer is fit
+
+ align:start position:0%
+and one answer one good answer is fit
+ 
+
+ align:start position:0%
+and one answer one good answer is fit
+those points not with straight lines
+
+ align:start position:0%
+those points not with straight lines
+ 
+
+ align:start position:0%
+those points not with straight lines
+that's too crude not with a single polom
+
+ align:start position:0%
+that's too crude not with a single polom
+ 
+
+ align:start position:0%
+that's too crude not with a single polom
+that's too unstable but fit it with
+
+ align:start position:0%
+that's too unstable but fit it with
+ 
+
+ align:start position:0%
+that's too unstable but fit it with
+splines so so interpolation by
+
+ align:start position:0%
+splines so so interpolation by
+ 
+
+ align:start position:0%
+splines so so interpolation by
+splines okay so that's where it's just
+
+ align:start position:0%
+splines okay so that's where it's just
+ 
+
+ align:start position:0%
+splines okay so that's where it's just
+sort of appearing in in this uh section
+
+ align:start position:0%
+sort of appearing in in this uh section
+ 
+
+ align:start position:0%
+sort of appearing in in this uh section
+3.2 because those
+
+ align:start position:0%
+3.2 because those
+ 
+
+ align:start position:0%
+3.2 because those
+are I'm I have and I mean by that and
+
+ align:start position:0%
+are I'm I have and I mean by that and
+ 
+
+ align:start position:0%
+are I'm I have and I mean by that and
+people often do mean when they say
+
+ align:start position:0%
+people often do mean when they say
+ 
+
+ align:start position:0%
+people often do mean when they say
+spline they mean cubic
+
+ align:start position:0%
+spline they mean cubic
+ 
+
+ align:start position:0%
+spline they mean cubic
+spline so so it's
+
+ align:start position:0%
+spline so so it's
+ 
+
+ align:start position:0%
+spline so so it's
+a you could have splines of other
+
+ align:start position:0%
+a you could have splines of other
+ 
+
+ align:start position:0%
+a you could have splines of other
+degrees but often the sort of the
+
+ align:start position:0%
+degrees but often the sort of the
+ 
+
+ align:start position:0%
+degrees but often the sort of the
+Natural Choice is the cubic so can I
+
+ align:start position:0%
+Natural Choice is the cubic so can I
+ 
+
+ align:start position:0%
+Natural Choice is the cubic so can I
+just briefly describe what uh that does
+
+ align:start position:0%
+just briefly describe what uh that does
+ 
+
+ align:start position:0%
+just briefly describe what uh that does
+what the cub bline would be
+
+ align:start position:0%
+what the cub bline would be
+ 
+
+ align:start position:0%
+what the cub bline would be
+like so let me draw in again these six
+
+ align:start position:0%
+like so let me draw in again these six
+ 
+
+ align:start position:0%
+like so let me draw in again these six
+points that I'm going to
+
+ align:start position:0%
+points that I'm going to
+ 
+
+ align:start position:0%
+points that I'm going to
+fit and just say for these few minutes
+
+ align:start position:0%
+fit and just say for these few minutes
+ 
+
+ align:start position:0%
+fit and just say for these few minutes
+what's a cubic
+
+ align:start position:0%
+what's a cubic
+ 
+
+ align:start position:0%
+what's a cubic
+spot I I got I touched on that uh
+
+ align:start position:0%
+spot I I got I touched on that uh
+ 
+
+ align:start position:0%
+spot I I got I touched on that uh
+Wednesday and now I just want to say a
+
+ align:start position:0%
+Wednesday and now I just want to say a
+ 
+
+ align:start position:0%
+Wednesday and now I just want to say a
+little bit more and then the homework
+
+ align:start position:0%
+little bit more and then the homework
+ 
+
+ align:start position:0%
+little bit more and then the homework
+asked you to
+
+ align:start position:0%
+asked you to
+ 
+
+ align:start position:0%
+asked you to
+actually uh do it with uh a a part
+
+ align:start position:0%
+actually uh do it with uh a a part
+ 
+
+ align:start position:0%
+actually uh do it with uh a a part
+values of a particular function and see
+
+ align:start position:0%
+values of a particular function and see
+ 
+
+ align:start position:0%
+values of a particular function and see
+how close does the cubic spline come to
+
+ align:start position:0%
+how close does the cubic spline come to
+ 
+
+ align:start position:0%
+how close does the cubic spline come to
+the to the uh given function okay so
+
+ align:start position:0%
+the to the uh given function okay so
+ 
+
+ align:start position:0%
+the to the uh given function okay so
+what's a cubic
+
+ align:start position:0%
+what's a cubic
+ 
+
+ align:start position:0%
+what's a cubic
+spline what does that word spline what
+
+ align:start position:0%
+spline what does that word spline what
+ 
+
+ align:start position:0%
+spline what does that word spline what
+should that mean in your mind so a cubic
+
+ align:start position:0%
+should that mean in your mind so a cubic
+ 
+
+ align:start position:0%
+should that mean in your mind so a cubic
+spline is a cubic in each
+
+ align:start position:0%
+spline is a cubic in each
+ 
+
+ align:start position:0%
+spline is a cubic in each
+piece a cubic in each
+
+ align:start position:0%
+piece a cubic in each
+ 
+
+ align:start position:0%
+piece a cubic in each
+piece now we we've met cubics in each
+
+ align:start position:0%
+piece now we we've met cubics in each
+ 
+
+ align:start position:0%
+piece now we we've met cubics in each
+piece as finite elements and and part of
+
+ align:start position:0%
+piece as finite elements and and part of
+ 
+
+ align:start position:0%
+piece as finite elements and and part of
+this short discussion is to keep those
+
+ align:start position:0%
+this short discussion is to keep those
+ 
+
+ align:start position:0%
+this short discussion is to keep those
+two slightly different ideas
+
+ align:start position:0%
+two slightly different ideas
+ 
+
+ align:start position:0%
+two slightly different ideas
+separate the finite element
+
+ align:start position:0%
+separate the finite element
+ 
+
+ align:start position:0%
+separate the finite element
+idea was also peie wise
+
+ align:start position:0%
+idea was also peie wise
+ 
+
+ align:start position:0%
+idea was also peie wise
+cubic and but it used values and
+
+ align:start position:0%
+cubic and but it used values and
+ 
+
+ align:start position:0%
+cubic and but it used values and
+slopes so it was completely local if I
+
+ align:start position:0%
+slopes so it was completely local if I
+ 
+
+ align:start position:0%
+slopes so it was completely local if I
+had a value as I have here six values
+
+ align:start position:0%
+had a value as I have here six values
+ 
+
+ align:start position:0%
+had a value as I have here six values
+and if I also had six slopes if I knew
+
+ align:start position:0%
+and if I also had six slopes if I knew
+ 
+
+ align:start position:0%
+and if I also had six slopes if I knew
+the slopes then I would use those find
+
+ align:start position:0%
+the slopes then I would use those find
+ 
+
+ align:start position:0%
+the slopes then I would use those find
+those cubic elements and I would fit
+
+ align:start position:0%
+those cubic elements and I would fit
+ 
+
+ align:start position:0%
+those cubic elements and I would fit
+a if I knew the height and slope there
+
+ align:start position:0%
+a if I knew the height and slope there
+ 
+
+ align:start position:0%
+a if I knew the height and slope there
+and I knew the height and slope there
+
+ align:start position:0%
+and I knew the height and slope there
+ 
+
+ align:start position:0%
+and I knew the height and slope there
+there would be exactly one cubic because
+
+ align:start position:0%
+there would be exactly one cubic because
+ 
+
+ align:start position:0%
+there would be exactly one cubic because
+I I would have four conditions two
+
+ align:start position:0%
+I I would have four conditions two
+ 
+
+ align:start position:0%
+I I would have four conditions two
+conditions there two conditions there
+
+ align:start position:0%
+conditions there two conditions there
+ 
+
+ align:start position:0%
+conditions there two conditions there
+would be four I could fit a cubic
+
+ align:start position:0%
+would be four I could fit a cubic
+ 
+
+ align:start position:0%
+would be four I could fit a cubic
+between another cubic there another
+
+ align:start position:0%
+between another cubic there another
+ 
+
+ align:start position:0%
+between another cubic there another
+cubic there and
+
+ align:start position:0%
+cubic there and
+ 
+
+ align:start position:0%
+cubic there and
+because I'm using the same slope from
+
+ align:start position:0%
+because I'm using the same slope from
+ 
+
+ align:start position:0%
+because I'm using the same slope from
+the left and from the right the slope
+
+ align:start position:0%
+the left and from the right the slope
+ 
+
+ align:start position:0%
+the left and from the right the slope
+would be good it would be continuous the
+
+ align:start position:0%
+would be good it would be continuous the
+ 
+
+ align:start position:0%
+would be good it would be continuous the
+second derivative the curving the
+
+ align:start position:0%
+second derivative the curving the
+ 
+
+ align:start position:0%
+second derivative the curving the
+curvature would not be continuous with
+
+ align:start position:0%
+curvature would not be continuous with
+ 
+
+ align:start position:0%
+curvature would not be continuous with
+those cubic elements and that's the
+
+ align:start position:0%
+those cubic elements and that's the
+ 
+
+ align:start position:0%
+those cubic elements and that's the
+difference so the difference is splines
+
+ align:start position:0%
+difference so the difference is splines
+ 
+
+ align:start position:0%
+difference so the difference is splines
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+continuous the no jump in let me just
+
+ align:start position:0%
+continuous the no jump in let me just
+ 
+
+ align:start position:0%
+continuous the no jump in let me just
+put it this way no jump
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in in the function I'll use S maybe for
+
+ align:start position:0%
+in in the function I'll use S maybe for
+ 
+
+ align:start position:0%
+in in the function I'll use S maybe for
+spline no jump in its slope and no jump
+
+ align:start position:0%
+spline no jump in its slope and no jump
+ 
+
+ align:start position:0%
+spline no jump in its slope and no jump
+in the second derivative so that's the
+
+ align:start position:0%
+in the second derivative so that's the
+ 
+
+ align:start position:0%
+in the second derivative so that's the
+that's the difference that that the
+
+ align:start position:0%
+that's the difference that that the
+ 
+
+ align:start position:0%
+that's the difference that that the
+spline
+
+ align:start position:0%
+spline
+ 
+
+ align:start position:0%
+spline
+functions the only jumps you see for
+
+ align:start position:0%
+functions the only jumps you see for
+ 
+
+ align:start position:0%
+functions the only jumps you see for
+those are jumps in the third
+
+ align:start position:0%
+those are jumps in the third
+ 
+
+ align:start position:0%
+those are jumps in the third
+derivative and uh so that makes it
+
+ align:start position:0%
+derivative and uh so that makes it
+ 
+
+ align:start position:0%
+derivative and uh so that makes it
+extremely smooth so so if I just try to
+
+ align:start position:0%
+extremely smooth so so if I just try to
+ 
+
+ align:start position:0%
+extremely smooth so so if I just try to
+draw now what a spline would do it'll go
+
+ align:start position:0%
+draw now what a spline would do it'll go
+ 
+
+ align:start position:0%
+draw now what a spline would do it'll go
+through those points coming out of the
+
+ align:start position:0%
+through those points coming out of the
+ 
+
+ align:start position:0%
+through those points coming out of the
+spline fit mat lab command and it will
+
+ align:start position:0%
+spline fit mat lab command and it will
+ 
+
+ align:start position:0%
+spline fit mat lab command and it will
+be well it'll be as smooth as I drew it
+
+ align:start position:0%
+be well it'll be as smooth as I drew it
+ 
+
+ align:start position:0%
+be well it'll be as smooth as I drew it
+uh there there'll be there is a change
+
+ align:start position:0%
+uh there there'll be there is a change
+ 
+
+ align:start position:0%
+uh there there'll be there is a change
+in the third derivative at these
+
+ align:start position:0%
+in the third derivative at these
+ 
+
+ align:start position:0%
+in the third derivative at these
+points and
+
+ align:start position:0%
+points and
+ 
+
+ align:start position:0%
+points and
+um actually do you you have you ever
+
+ align:start position:0%
+um actually do you you have you ever
+ 
+
+ align:start position:0%
+um actually do you you have you ever
+seen this word spine before uh came out
+
+ align:start position:0%
+seen this word spine before uh came out
+ 
+
+ align:start position:0%
+seen this word spine before uh came out
+of Naval
+
+ align:start position:0%
+of Naval
+ 
+
+ align:start position:0%
+of Naval
+engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um when uh people were were designing
+
+ align:start position:0%
+um when uh people were were designing
+ 
+
+ align:start position:0%
+um when uh people were were designing
+the uh the shape of the
+
+ align:start position:0%
+the uh the shape of the
+ 
+
+ align:start position:0%
+the uh the shape of the
+ship uh for a naval architect is fitting
+
+ align:start position:0%
+ship uh for a naval architect is fitting
+ 
+
+ align:start position:0%
+ship uh for a naval architect is fitting
+the proposed shape of a ship by this was
+
+ align:start position:0%
+the proposed shape of a ship by this was
+ 
+
+ align:start position:0%
+the proposed shape of a ship by this was
+before mat lab before uh yeah before
+
+ align:start position:0%
+before mat lab before uh yeah before
+ 
+
+ align:start position:0%
+before mat lab before uh yeah before
+life started uh uh uh they had little uh
+
+ align:start position:0%
+life started uh uh uh they had little uh
+ 
+
+ align:start position:0%
+life started uh uh uh they had little uh
+physical slightly
+
+ align:start position:0%
+physical slightly
+ 
+
+ align:start position:0%
+physical slightly
+bendable uh
+
+ align:start position:0%
+bendable uh
+ 
+
+ align:start position:0%
+bendable uh
+um I'll call them splines I guess that's
+
+ align:start position:0%
+um I'll call them splines I guess that's
+ 
+
+ align:start position:0%
+um I'll call them splines I guess that's
+what they were that that's where the
+
+ align:start position:0%
+what they were that that's where the
+ 
+
+ align:start position:0%
+what they were that that's where the
+word came from some physical thing which
+
+ align:start position:0%
+word came from some physical thing which
+ 
+
+ align:start position:0%
+word came from some physical thing which
+was like a curve that you used I don't
+
+ align:start position:0%
+was like a curve that you used I don't
+ 
+
+ align:start position:0%
+was like a curve that you used I don't
+know if you guys ever did draw like
+
+ align:start position:0%
+know if you guys ever did draw like
+ 
+
+ align:start position:0%
+know if you guys ever did draw like
+mechanical drawing that was a freshman
+
+ align:start position:0%
+mechanical drawing that was a freshman
+ 
+
+ align:start position:0%
+mechanical drawing that was a freshman
+subject when I came to MIT mechanical
+
+ align:start position:0%
+subject when I came to MIT mechanical
+ 
+
+ align:start position:0%
+subject when I came to MIT mechanical
+drawing I was terrible terrible at
+
+ align:start position:0%
+drawing I was terrible terrible at
+ 
+
+ align:start position:0%
+drawing I was terrible terrible at
+mechanical
+
+ align:start position:0%
+mechanical
+ 
+
+ align:start position:0%
+mechanical
+drawing but uh I don't know I I had a
+
+ align:start position:0%
+drawing but uh I don't know I I had a
+ 
+
+ align:start position:0%
+drawing but uh I don't know I I had a
+friend uh who helped I mean just like I
+
+ align:start position:0%
+friend uh who helped I mean just like I
+ 
+
+ align:start position:0%
+friend uh who helped I mean just like I
+I help probably helped him at some other
+
+ align:start position:0%
+I help probably helped him at some other
+ 
+
+ align:start position:0%
+I help probably helped him at some other
+course anyway whatever uh so there were
+
+ align:start position:0%
+course anyway whatever uh so there were
+ 
+
+ align:start position:0%
+course anyway whatever uh so there were
+physical things curves that you used to
+
+ align:start position:0%
+physical things curves that you used to
+ 
+
+ align:start position:0%
+physical things curves that you used to
+use and these spline curves were used
+
+ align:start position:0%
+use and these spline curves were used
+ 
+
+ align:start position:0%
+use and these spline curves were used
+and maybe still are used by Naval
+
+ align:start position:0%
+and maybe still are used by Naval
+ 
+
+ align:start position:0%
+and maybe still are used by Naval
+architects in in in creating a drawing
+
+ align:start position:0%
+architects in in in creating a drawing
+ 
+
+ align:start position:0%
+architects in in in creating a drawing
+but I'm assuming that those things are
+
+ align:start position:0%
+but I'm assuming that those things are
+ 
+
+ align:start position:0%
+but I'm assuming that those things are
+now all computerized and and the spline
+
+ align:start position:0%
+now all computerized and and the spline
+ 
+
+ align:start position:0%
+now all computerized and and the spline
+command is used anyway the result is
+
+ align:start position:0%
+command is used anyway the result is
+ 
+
+ align:start position:0%
+command is used anyway the result is
+that now I have to draw one picture of a
+
+ align:start position:0%
+that now I have to draw one picture of a
+ 
+
+ align:start position:0%
+that now I have to draw one picture of a
+spline of the of the most important
+
+ align:start position:0%
+spline of the of the most important
+ 
+
+ align:start position:0%
+spline of the of the most important
+spine and then I'm done with
+
+ align:start position:0%
+spine and then I'm done with
+ 
+
+ align:start position:0%
+spine and then I'm done with
+splines yeah so
+
+ align:start position:0%
+splines yeah so
+ 
+
+ align:start position:0%
+splines yeah so
+so what I'm going to draw is now a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+splot and and and and and that that's
+
+ align:start position:0%
+splot and and and and and that that's
+ 
+
+ align:start position:0%
+splot and and and and and that that's
+that's a Basics bline that's a it could
+
+ align:start position:0%
+that's a Basics bline that's a it could
+ 
+
+ align:start position:0%
+that's a Basics bline that's a it could
+be it could be one of our functions it
+
+ align:start position:0%
+be it could be one of our functions it
+ 
+
+ align:start position:0%
+be it could be one of our functions it
+could be one of our functions f of x one
+
+ align:start position:0%
+could be one of our functions f of x one
+ 
+
+ align:start position:0%
+could be one of our functions f of x one
+of our one of our trial functions it
+
+ align:start position:0%
+of our one of our trial functions it
+ 
+
+ align:start position:0%
+of our one of our trial functions it
+could be and let me comment on that so
+
+ align:start position:0%
+could be and let me comment on that so
+ 
+
+ align:start position:0%
+could be and let me comment on that so
+so I'll let me remind myself good or bad
+
+ align:start position:0%
+so I'll let me remind myself good or bad
+ 
+
+ align:start position:0%
+so I'll let me remind myself good or bad
+to to with a question and let me try to
+
+ align:start position:0%
+to to with a question and let me try to
+ 
+
+ align:start position:0%
+to to with a question and let me try to
+answer that but let me first draw the
+
+ align:start position:0%
+answer that but let me first draw the
+ 
+
+ align:start position:0%
+answer that but let me first draw the
+the be spine okay
+
+ align:start position:0%
+the be spine okay
+ 
+
+ align:start position:0%
+the be spine okay
+so it's like a hat function that's
+
+ align:start position:0%
+so it's like a hat function that's
+ 
+
+ align:start position:0%
+so it's like a hat function that's
+that's actually that a hat function is
+
+ align:start position:0%
+that's actually that a hat function is
+ 
+
+ align:start position:0%
+that's actually that a hat function is
+a linear spline a hat function is the
+
+ align:start position:0%
+a linear spline a hat function is the
+ 
+
+ align:start position:0%
+a linear spline a hat function is the
+that that lowlevel spline that's linear
+
+ align:start position:0%
+that that lowlevel spline that's linear
+ 
+
+ align:start position:0%
+that that lowlevel spline that's linear
+between pieces now the B
+
+ align:start position:0%
+between pieces now the B
+ 
+
+ align:start position:0%
+between pieces now the B
+spline is going to be is going to have
+
+ align:start position:0%
+spline is going to be is going to have
+ 
+
+ align:start position:0%
+spline is going to be is going to have
+the value one
+
+ align:start position:0%
+the value one
+ 
+
+ align:start position:0%
+the value one
+there it's going to have no jump in the
+
+ align:start position:0%
+there it's going to have no jump in the
+ 
+
+ align:start position:0%
+there it's going to have no jump in the
+function so the function will go through
+
+ align:start position:0%
+function so the function will go through
+ 
+
+ align:start position:0%
+function so the function will go through
+there no jump in the slope no jump in
+
+ align:start position:0%
+there no jump in the slope no jump in
+ 
+
+ align:start position:0%
+there no jump in the slope no jump in
+the second
+
+ align:start position:0%
+the second
+ 
+
+ align:start position:0%
+the second
+derivative and I want to get down to
+
+ align:start position:0%
+derivative and I want to get down to
+ 
+
+ align:start position:0%
+derivative and I want to get down to
+zero I want to get down to zero here and
+
+ align:start position:0%
+zero I want to get down to zero here and
+ 
+
+ align:start position:0%
+zero I want to get down to zero here and
+so it it's it's it's sort of it's just
+
+ align:start position:0%
+so it it's it's it's sort of it's just
+ 
+
+ align:start position:0%
+so it it's it's it's sort of it's just
+it's I want it to be as local as I can
+
+ align:start position:0%
+it's I want it to be as local as I can
+ 
+
+ align:start position:0%
+it's I want it to be as local as I can
+make it so I want it to get to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero here's the
+
+ align:start position:0%
+zero here's the
+ 
+
+ align:start position:0%
+zero here's the
+point I can't get down to with those
+
+ align:start position:0%
+point I can't get down to with those
+ 
+
+ align:start position:0%
+point I can't get down to with those
+with those uh
+
+ align:start position:0%
+with those uh
+ 
+
+ align:start position:0%
+with those uh
+cubic finite elements I got them down to
+
+ align:start position:0%
+cubic finite elements I got them down to
+ 
+
+ align:start position:0%
+cubic finite elements I got them down to
+zero they came in here with zero slope
+
+ align:start position:0%
+zero they came in here with zero slope
+ 
+
+ align:start position:0%
+zero they came in here with zero slope
+and then they continued to zero no
+
+ align:start position:0%
+and then they continued to zero no
+ 
+
+ align:start position:0%
+and then they continued to zero no
+problem with if I'm if I'm wanting the
+
+ align:start position:0%
+problem with if I'm if I'm wanting the
+ 
+
+ align:start position:0%
+problem with if I'm if I'm wanting the
+second derivative
+
+ align:start position:0%
+second derivative
+ 
+
+ align:start position:0%
+second derivative
+also to to to meet it to be zero to be
+
+ align:start position:0%
+also to to to meet it to be zero to be
+ 
+
+ align:start position:0%
+also to to to meet it to be zero to be
+continuous I won't be able to do it in
+
+ align:start position:0%
+continuous I won't be able to do it in
+ 
+
+ align:start position:0%
+continuous I won't be able to do it in
+one interval it's going to take
+
+ align:start position:0%
+one interval it's going to take
+ 
+
+ align:start position:0%
+one interval it's going to take
+me a total of four intervals this one
+
+ align:start position:0%
+me a total of four intervals this one
+ 
+
+ align:start position:0%
+me a total of four intervals this one
+can come down to some point here where
+
+ align:start position:0%
+can come down to some point here where
+ 
+
+ align:start position:0%
+can come down to some point here where
+it meets where another cubic starts and
+
+ align:start position:0%
+it meets where another cubic starts and
+ 
+
+ align:start position:0%
+it meets where another cubic starts and
+this is the Let Me Maybe I should drew
+
+ align:start position:0%
+this is the Let Me Maybe I should drew
+ 
+
+ align:start position:0%
+this is the Let Me Maybe I should drew
+the one here going up you remember the
+
+ align:start position:0%
+the one here going up you remember the
+ 
+
+ align:start position:0%
+the one here going up you remember the
+good the allowed cubic spine would be an
+
+ align:start position:0%
+good the allowed cubic spine would be an
+ 
+
+ align:start position:0%
+good the allowed cubic spine would be an
+a sort of an X Cub over 6 or some some
+
+ align:start position:0%
+a sort of an X Cub over 6 or some some
+ 
+
+ align:start position:0%
+a sort of an X Cub over 6 or some some
+multiple of X Cub I don't know what
+
+ align:start position:0%
+multiple of X Cub I don't know what
+ 
+
+ align:start position:0%
+multiple of X Cub I don't know what
+multiple it'll take maybe X Cub over 6
+
+ align:start position:0%
+multiple it'll take maybe X Cub over 6
+ 
+
+ align:start position:0%
+multiple it'll take maybe X Cub over 6
+is right it'll come up to some point
+
+ align:start position:0%
+is right it'll come up to some point
+ 
+
+ align:start position:0%
+is right it'll come up to some point
+here now I've got to get it I've got to
+
+ align:start position:0%
+here now I've got to get it I've got to
+ 
+
+ align:start position:0%
+here now I've got to get it I've got to
+get it sort
+
+ align:start position:0%
+get it sort
+ 
+
+ align:start position:0%
+get it sort
+of beginning to curve downwards so I'm
+
+ align:start position:0%
+of beginning to curve downwards so I'm
+ 
+
+ align:start position:0%
+of beginning to curve downwards so I'm
+going to have to change the third
+
+ align:start position:0%
+going to have to change the third
+ 
+
+ align:start position:0%
+going to have to change the third
+derivative change to another cubic
+
+ align:start position:0%
+derivative change to another cubic
+ 
+
+ align:start position:0%
+derivative change to another cubic
+there change to another cubic there and
+
+ align:start position:0%
+there change to another cubic there and
+ 
+
+ align:start position:0%
+there change to another cubic there and
+a final cubic here so there is a picture
+
+ align:start position:0%
+a final cubic here so there is a picture
+ 
+
+ align:start position:0%
+a final cubic here so there is a picture
+of a b spline and we could figure
+
+ align:start position:0%
+of a b spline and we could figure
+ 
+
+ align:start position:0%
+of a b spline and we could figure
+out by requiring all these
+
+ align:start position:0%
+out by requiring all these
+ 
+
+ align:start position:0%
+out by requiring all these
+continuity conditions we could figure
+
+ align:start position:0%
+continuity conditions we could figure
+ 
+
+ align:start position:0%
+continuity conditions we could figure
+out the formulas for the cubic in these
+
+ align:start position:0%
+out the formulas for the cubic in these
+ 
+
+ align:start position:0%
+out the formulas for the cubic in these
+four pieces and it would be symetric of
+
+ align:start position:0%
+four pieces and it would be symetric of
+ 
+
+ align:start position:0%
+four pieces and it would be symetric of
+course ac across that center point but
+
+ align:start position:0%
+course ac across that center point but
+ 
+
+ align:start position:0%
+course ac across that center point but
+uh I think I won't try to do it I'll
+
+ align:start position:0%
+uh I think I won't try to do it I'll
+ 
+
+ align:start position:0%
+uh I think I won't try to do it I'll
+just leave that idea then the the the
+
+ align:start position:0%
+just leave that idea then the the the
+ 
+
+ align:start position:0%
+just leave that idea then the the the
+book there's a figure in the book
+
+ align:start position:0%
+book there's a figure in the book
+ 
+
+ align:start position:0%
+book there's a figure in the book
+showing a picture of the beast
+
+ align:start position:0%
+showing a picture of the beast
+ 
+
+ align:start position:0%
+showing a picture of the beast
+bline so so those are
+
+ align:start position:0%
+bline so so those are
+ 
+
+ align:start position:0%
+bline so so those are
+functions extremely valuable in this
+
+ align:start position:0%
+functions extremely valuable in this
+ 
+
+ align:start position:0%
+functions extremely valuable in this
+interpolation problem because all
+
+ align:start position:0%
+interpolation problem because all
+ 
+
+ align:start position:0%
+interpolation problem because all
+splines are combinations of B splines
+
+ align:start position:0%
+splines are combinations of B splines
+ 
+
+ align:start position:0%
+splines are combinations of B splines
+yeah now let me pull this topic together
+
+ align:start position:0%
+yeah now let me pull this topic together
+ 
+
+ align:start position:0%
+yeah now let me pull this topic together
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+spline every spline
+
+ align:start position:0%
+spline every spline
+ 
+
+ align:start position:0%
+spline every spline
+function is some
+
+ align:start position:0%
+function is some
+ 
+
+ align:start position:0%
+function is some
+combination of these Beast
+
+ align:start position:0%
+combination of these Beast
+ 
+
+ align:start position:0%
+combination of these Beast
+spines let bi of X be the one centered
+
+ align:start position:0%
+spines let bi of X be the one centered
+ 
+
+ align:start position:0%
+spines let bi of X be the one centered
+on node I
+
+ align:start position:0%
+on node I
+ 
+
+ align:start position:0%
+on node I
+and then there's a neighbor centered on
+
+ align:start position:0%
+and then there's a neighbor centered on
+ 
+
+ align:start position:0%
+and then there's a neighbor centered on
+node I + one and a a neighbor to the
+
+ align:start position:0%
+node I + one and a a neighbor to the
+ 
+
+ align:start position:0%
+node I + one and a a neighbor to the
+left centered on node I minus one what's
+
+ align:start position:0%
+left centered on node I minus one what's
+ 
+
+ align:start position:0%
+left centered on node I minus one what's
+the point the point is that at node at a
+
+ align:start position:0%
+the point the point is that at node at a
+ 
+
+ align:start position:0%
+the point the point is that at node at a
+typical node i+
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one how three three of these functions
+
+ align:start position:0%
+one how three three of these functions
+ 
+
+ align:start position:0%
+one how three three of these functions
+will will be non zero with these very
+
+ align:start position:0%
+will will be non zero with these very
+ 
+
+ align:start position:0%
+will will be non zero with these very
+local hat functions at that node the
+
+ align:start position:0%
+local hat functions at that node the
+ 
+
+ align:start position:0%
+local hat functions at that node the
+only hat that was the only one of the Fe
+
+ align:start position:0%
+only hat that was the only one of the Fe
+ 
+
+ align:start position:0%
+only hat that was the only one of the Fe
+functions that wasn't zero is the one
+
+ align:start position:0%
+functions that wasn't zero is the one
+ 
+
+ align:start position:0%
+functions that wasn't zero is the one
+I've drawn all the others were were zero
+
+ align:start position:0%
+I've drawn all the others were were zero
+ 
+
+ align:start position:0%
+I've drawn all the others were were zero
+there right all the other
+
+ align:start position:0%
+there right all the other
+ 
+
+ align:start position:0%
+there right all the other
+hats were zero there was just the one
+
+ align:start position:0%
+hats were zero there was just the one
+ 
+
+ align:start position:0%
+hats were zero there was just the one
+but now there'll be a beast blind
+
+ align:start position:0%
+but now there'll be a beast blind
+ 
+
+ align:start position:0%
+but now there'll be a beast blind
+starting from here going up to here
+
+ align:start position:0%
+starting from here going up to here
+ 
+
+ align:start position:0%
+starting from here going up to here
+coming down from here there'll be a be
+
+ align:start position:0%
+coming down from here there'll be a be
+ 
+
+ align:start position:0%
+coming down from here there'll be a be
+there'll be the Beast blind starting
+
+ align:start position:0%
+there'll be the Beast blind starting
+ 
+
+ align:start position:0%
+there'll be the Beast blind starting
+from here going up to here up down so on
+
+ align:start position:0%
+from here going up to here up down so on
+ 
+
+ align:start position:0%
+from here going up to here up down so on
+so at a typical node I'm getting the one
+
+ align:start position:0%
+so at a typical node I'm getting the one
+ 
+
+ align:start position:0%
+so at a typical node I'm getting the one
+centered at that
+
+ align:start position:0%
+centered at that
+ 
+
+ align:start position:0%
+centered at that
+node and also the one to the left which
+
+ align:start position:0%
+node and also the one to the left which
+ 
+
+ align:start position:0%
+node and also the one to the left which
+is on its way down and also the one to
+
+ align:start position:0%
+is on its way down and also the one to
+ 
+
+ align:start position:0%
+is on its way down and also the one to
+the right which is on its way up in
+
+ align:start position:0%
+the right which is on its way up in
+ 
+
+ align:start position:0%
+the right which is on its way up in
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+words it's not as local as the other
+
+ align:start position:0%
+words it's not as local as the other
+ 
+
+ align:start position:0%
+words it's not as local as the other
+construction uh and that's and that's
+
+ align:start position:0%
+construction uh and that's and that's
+ 
+
+ align:start position:0%
+construction uh and that's and that's
+why so good good uh I would say good
+
+ align:start position:0%
+why so good good uh I would say good
+ 
+
+ align:start position:0%
+why so good good uh I would say good
+because it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smooth but bad because it's not fully
+
+ align:start position:0%
+smooth but bad because it's not fully
+ 
+
+ align:start position:0%
+smooth but bad because it's not fully
+local not completely local it it's
+
+ align:start position:0%
+local not completely local it it's
+ 
+
+ align:start position:0%
+local not completely local it it's
+reasonably local in that there are only
+
+ align:start position:0%
+reasonably local in that there are only
+ 
+
+ align:start position:0%
+reasonably local in that there are only
+three functions that are affecting these
+
+ align:start position:0%
+three functions that are affecting these
+ 
+
+ align:start position:0%
+three functions that are affecting these
+points if I used those
+
+ align:start position:0%
+points if I used those
+ 
+
+ align:start position:0%
+points if I used those
+pols they weren't local at all all the
+
+ align:start position:0%
+pols they weren't local at all all the
+ 
+
+ align:start position:0%
+pols they weren't local at all all the
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+uh it was a typical x to the 5ifth is
+
+ align:start position:0%
+uh it was a typical x to the 5ifth is
+ 
+
+ align:start position:0%
+uh it was a typical x to the 5ifth is
+not zero at any of the points these
+
+ align:start position:0%
+not zero at any of the points these
+ 
+
+ align:start position:0%
+not zero at any of the points these
+Beast lines are zero at a lot of points
+
+ align:start position:0%
+Beast lines are zero at a lot of points
+ 
+
+ align:start position:0%
+Beast lines are zero at a lot of points
+but three of them
+
+ align:start position:0%
+but three of them
+ 
+
+ align:start position:0%
+but three of them
+one two and three will be nonzero at a
+
+ align:start position:0%
+one two and three will be nonzero at a
+ 
+
+ align:start position:0%
+one two and three will be nonzero at a
+typical mesh Point
+
+ align:start position:0%
+typical mesh Point
+ 
+
+ align:start position:0%
+typical mesh Point
+okay in so so they're not popular as a
+
+ align:start position:0%
+okay in so so they're not popular as a
+ 
+
+ align:start position:0%
+okay in so so they're not popular as a
+result for finite elements and I'm just
+
+ align:start position:0%
+result for finite elements and I'm just
+ 
+
+ align:start position:0%
+result for finite elements and I'm just
+wanting to be sure you make the
+
+ align:start position:0%
+wanting to be sure you make the
+ 
+
+ align:start position:0%
+wanting to be sure you make the
+distinction they're very popular for the
+
+ align:start position:0%
+distinction they're very popular for the
+ 
+
+ align:start position:0%
+distinction they're very popular for the
+interpolation job they're very popular
+
+ align:start position:0%
+interpolation job they're very popular
+ 
+
+ align:start position:0%
+interpolation job they're very popular
+for the interpolation job I I I just
+
+ align:start position:0%
+for the interpolation job I I I just
+ 
+
+ align:start position:0%
+for the interpolation job I I I just
+I've got some comination of these at at
+
+ align:start position:0%
+I've got some comination of these at at
+ 
+
+ align:start position:0%
+I've got some comination of these at at
+particular mesh points is supposed to
+
+ align:start position:0%
+particular mesh points is supposed to
+ 
+
+ align:start position:0%
+particular mesh points is supposed to
+agree with F at those mesh points this
+
+ align:start position:0%
+agree with F at those mesh points this
+ 
+
+ align:start position:0%
+agree with F at those mesh points this
+is my this is my system to solve I've
+
+ align:start position:0%
+is my this is my system to solve I've
+ 
+
+ align:start position:0%
+is my this is my system to solve I've
+create these functions these be blindes
+
+ align:start position:0%
+create these functions these be blindes
+ 
+
+ align:start position:0%
+create these functions these be blindes
+I given an F at typical points and I
+
+ align:start position:0%
+I given an F at typical points and I
+ 
+
+ align:start position:0%
+I given an F at typical points and I
+choose a combination which matches F at
+
+ align:start position:0%
+choose a combination which matches F at
+ 
+
+ align:start position:0%
+choose a combination which matches F at
+those points yeah
+
+ align:start position:0%
+those points yeah
+ 
+
+ align:start position:0%
+those points yeah
+okay is there a question or a discussion
+
+ align:start position:0%
+okay is there a question or a discussion
+ 
+
+ align:start position:0%
+okay is there a question or a discussion
+on this it's a I always you know I I I
+
+ align:start position:0%
+on this it's a I always you know I I I
+ 
+
+ align:start position:0%
+on this it's a I always you know I I I
+don't like to not say anything about
+
+ align:start position:0%
+don't like to not say anything about
+ 
+
+ align:start position:0%
+don't like to not say anything about
+such an important problem as as putting
+
+ align:start position:0%
+such an important problem as as putting
+ 
+
+ align:start position:0%
+such an important problem as as putting
+points through curves through points but
+
+ align:start position:0%
+points through curves through points but
+ 
+
+ align:start position:0%
+points through curves through points but
+I don't want to make
+
+ align:start position:0%
+I don't want to make
+ 
+
+ align:start position:0%
+I don't want to make
+a make it a course on on
+
+ align:start position:0%
+a make it a course on on
+ 
+
+ align:start position:0%
+a make it a course on on
+splines
+
+ align:start position:0%
+splines
+ 
+
+ align:start position:0%
+splines
+yes yeah
+
+ align:start position:0%
+yes yeah
+ 
+
+ align:start position:0%
+yes yeah
+good okay I don't know that I'll do oh
+
+ align:start position:0%
+good okay I don't know that I'll do oh
+ 
+
+ align:start position:0%
+good okay I don't know that I'll do oh
+okay yes all right yeah two or three
+
+ align:start position:0%
+okay yes all right yeah two or three
+ 
+
+ align:start position:0%
+okay yes all right yeah two or three
+comments and that that that suggests a
+
+ align:start position:0%
+comments and that that that suggests a
+ 
+
+ align:start position:0%
+comments and that that that suggests a
+good question very good
+
+ align:start position:0%
+good question very good
+ 
+
+ align:start position:0%
+good question very good
+question can I make a a a separate
+
+ align:start position:0%
+question can I make a a a separate
+ 
+
+ align:start position:0%
+question can I make a a a separate
+comment that if I go into two
+
+ align:start position:0%
+comment that if I go into two
+ 
+
+ align:start position:0%
+comment that if I go into two
+Dimensions this is gets much tougher
+
+ align:start position:0%
+Dimensions this is gets much tougher
+ 
+
+ align:start position:0%
+Dimensions this is gets much tougher
+what happens if I had a function of X
+
+ align:start position:0%
+what happens if I had a function of X
+ 
+
+ align:start position:0%
+what happens if I had a function of X
+and Y so that I'm I've got points on a
+
+ align:start position:0%
+and Y so that I'm I've got points on a
+ 
+
+ align:start position:0%
+and Y so that I'm I've got points on a
+surface and I'm trying to fit a surface
+
+ align:start position:0%
+surface and I'm trying to fit a surface
+ 
+
+ align:start position:0%
+surface and I'm trying to fit a surface
+to it just just
+
+ align:start position:0%
+to it just just
+ 
+
+ align:start position:0%
+to it just just
+one message first that's not as easy
+
+ align:start position:0%
+one message first that's not as easy
+ 
+
+ align:start position:0%
+one message first that's not as easy
+it's pretty easy if though those points
+
+ align:start position:0%
+it's pretty easy if though those points
+ 
+
+ align:start position:0%
+it's pretty easy if though those points
+are on a rectangular grid so this is
+
+ align:start position:0%
+are on a rectangular grid so this is
+ 
+
+ align:start position:0%
+are on a rectangular grid so this is
+like typical if if I'm and then I'll
+
+ align:start position:0%
+like typical if if I'm and then I'll
+ 
+
+ align:start position:0%
+like typical if if I'm and then I'll
+come to your Nyquist question which is a
+
+ align:start position:0%
+come to your Nyquist question which is a
+ 
+
+ align:start position:0%
+come to your Nyquist question which is a
+very good one can I can I
+
+ align:start position:0%
+very good one can I can I
+ 
+
+ align:start position:0%
+very good one can I can I
+just because we're coming into 2D now
+
+ align:start position:0%
+just because we're coming into 2D now
+ 
+
+ align:start position:0%
+just because we're coming into 2D now
+suppose I there's two Dimensions I have
+
+ align:start position:0%
+suppose I there's two Dimensions I have
+ 
+
+ align:start position:0%
+suppose I there's two Dimensions I have
+a grid let's suppose it's a nice grid
+
+ align:start position:0%
+a grid let's suppose it's a nice grid
+ 
+
+ align:start position:0%
+a grid let's suppose it's a nice grid
+and at every point at every grid
+
+ align:start position:0%
+and at every point at every grid
+ 
+
+ align:start position:0%
+and at every point at every grid
+point I have a height then I'm fitting a
+
+ align:start position:0%
+point I have a height then I'm fitting a
+ 
+
+ align:start position:0%
+point I have a height then I'm fitting a
+surface right through I'm I'm my
+
+ align:start position:0%
+surface right through I'm I'm my
+ 
+
+ align:start position:0%
+surface right through I'm I'm my
+function is now a function of X and
+
+ align:start position:0%
+function is now a function of X and
+ 
+
+ align:start position:0%
+function is now a function of X and
+Y X is here Y is here f is the surface
+
+ align:start position:0%
+Y X is here Y is here f is the surface
+ 
+
+ align:start position:0%
+Y X is here Y is here f is the surface
+coming out of the board in the in the
+
+ align:start position:0%
+coming out of the board in the in the
+ 
+
+ align:start position:0%
+coming out of the board in the in the
+third dimension and fitting those points
+
+ align:start position:0%
+third dimension and fitting those points
+ 
+
+ align:start position:0%
+third dimension and fitting those points
+if they're regularly spaced like that my
+
+ align:start position:0%
+if they're regularly spaced like that my
+ 
+
+ align:start position:0%
+if they're regularly spaced like that my
+life would be okay I could use sort of
+
+ align:start position:0%
+life would be okay I could use sort of
+ 
+
+ align:start position:0%
+life would be okay I could use sort of
+products of splines in 1D X I could use
+
+ align:start position:0%
+products of splines in 1D X I could use
+ 
+
+ align:start position:0%
+products of splines in 1D X I could use
+products of
+
+ align:start position:0%
+products of
+ 
+
+ align:start position:0%
+products of
+of basis of of of uh function of splines
+
+ align:start position:0%
+of basis of of of uh function of splines
+ 
+
+ align:start position:0%
+of basis of of of uh function of splines
+in the X Direction times splines in the
+
+ align:start position:0%
+in the X Direction times splines in the
+ 
+
+ align:start position:0%
+in the X Direction times splines in the
+y direction and it would be pretty
+
+ align:start position:0%
+y direction and it would be pretty
+ 
+
+ align:start position:0%
+y direction and it would be pretty
+successful it's a it would be yeah not
+
+ align:start position:0%
+successful it's a it would be yeah not
+ 
+
+ align:start position:0%
+successful it's a it would be yeah not
+as not quite as nice but almost okay but
+
+ align:start position:0%
+as not quite as nice but almost okay but
+ 
+
+ align:start position:0%
+as not quite as nice but almost okay but
+if I have irregularly spaced points from
+
+ align:start position:0%
+if I have irregularly spaced points from
+ 
+
+ align:start position:0%
+if I have irregularly spaced points from
+a from a general
+
+ align:start position:0%
+a from a general
+ 
+
+ align:start position:0%
+a from a general
+grid uh
+
+ align:start position:0%
+grid uh
+ 
+
+ align:start position:0%
+grid uh
+it's not as easy yeah and I won't so
+
+ align:start position:0%
+it's not as easy yeah and I won't so
+ 
+
+ align:start position:0%
+it's not as easy yeah and I won't so
+people have obviously had to figure out
+
+ align:start position:0%
+people have obviously had to figure out
+ 
+
+ align:start position:0%
+people have obviously had to figure out
+how to do it and that to repeat again
+
+ align:start position:0%
+how to do it and that to repeat again
+ 
+
+ align:start position:0%
+how to do it and that to repeat again
+that's what the cad cam world is having
+
+ align:start position:0%
+that's what the cad cam world is having
+ 
+
+ align:start position:0%
+that's what the cad cam world is having
+to do all the time is fit a curve fit a
+
+ align:start position:0%
+to do all the time is fit a curve fit a
+ 
+
+ align:start position:0%
+to do all the time is fit a curve fit a
+surface through points it's it's
+
+ align:start position:0%
+surface through points it's it's
+ 
+
+ align:start position:0%
+surface through points it's it's
+significant now uh you asked about
+
+ align:start position:0%
+significant now uh you asked about
+ 
+
+ align:start position:0%
+significant now uh you asked about
+Nyquist that's so that's a good question
+
+ align:start position:0%
+Nyquist that's so that's a good question
+ 
+
+ align:start position:0%
+Nyquist that's so that's a good question
+can I just
+
+ align:start position:0%
+can I just
+ 
+
+ align:start position:0%
+can I just
+say um something about I have to say
+
+ align:start position:0%
+say um something about I have to say
+ 
+
+ align:start position:0%
+say um something about I have to say
+what but uh so what's a function called
+
+ align:start position:0%
+what but uh so what's a function called
+ 
+
+ align:start position:0%
+what but uh so what's a function called
+band
+
+ align:start position:0%
+band
+ 
+
+ align:start position:0%
+band
+limited how many have heard Nyquist
+
+ align:start position:0%
+limited how many have heard Nyquist
+ 
+
+ align:start position:0%
+limited how many have heard Nyquist
+name okay and some of you may know a lot
+
+ align:start position:0%
+name okay and some of you may know a lot
+ 
+
+ align:start position:0%
+name okay and some of you may know a lot
+more than I about it but let me
+
+ align:start position:0%
+more than I about it but let me
+ 
+
+ align:start position:0%
+more than I about it but let me
+just get some context for band limited
+
+ align:start position:0%
+just get some context for band limited
+ 
+
+ align:start position:0%
+just get some context for band limited
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+okay this is actually a topic that will
+
+ align:start position:0%
+okay this is actually a topic that will
+ 
+
+ align:start position:0%
+okay this is actually a topic that will
+belong in the third part of our course
+
+ align:start position:0%
+belong in the third part of our course
+ 
+
+ align:start position:0%
+belong in the third part of our course
+in the 48 part so this this is in this
+
+ align:start position:0%
+in the 48 part so this this is in this
+ 
+
+ align:start position:0%
+in the 48 part so this this is in this
+is a forier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea so we'll I'll come back to it
+
+ align:start position:0%
+idea so we'll I'll come back to it
+ 
+
+ align:start position:0%
+idea so we'll I'll come back to it
+actually and so right here I'm just
+
+ align:start position:0%
+actually and so right here I'm just
+ 
+
+ align:start position:0%
+actually and so right here I'm just
+going to say very briefly what uh what
+
+ align:start position:0%
+going to say very briefly what uh what
+ 
+
+ align:start position:0%
+going to say very briefly what uh what
+um uh how it might connect us to uh what
+
+ align:start position:0%
+um uh how it might connect us to uh what
+ 
+
+ align:start position:0%
+um uh how it might connect us to uh what
+I've said today but then let's make a a
+
+ align:start position:0%
+I've said today but then let's make a a
+ 
+
+ align:start position:0%
+I've said today but then let's make a a
+plan to when we're when we
+
+ align:start position:0%
+plan to when we're when we
+ 
+
+ align:start position:0%
+plan to when we're when we
+got the idea of 48
+
+ align:start position:0%
+got the idea of 48
+ 
+
+ align:start position:0%
+got the idea of 48
+coefficients what what is a band limited
+
+ align:start position:0%
+coefficients what what is a band limited
+ 
+
+ align:start position:0%
+coefficients what what is a band limited
+function it's for it's so a f you know
+
+ align:start position:0%
+function it's for it's so a f you know
+ 
+
+ align:start position:0%
+function it's for it's so a f you know
+the F fora idea is to take F ofx and
+
+ align:start position:0%
+the F fora idea is to take F ofx and
+ 
+
+ align:start position:0%
+the F fora idea is to take F ofx and
+write it as some combination of pure
+
+ align:start position:0%
+write it as some combination of pure
+ 
+
+ align:start position:0%
+write it as some combination of pure
+frequencies e to the I KX let me say e
+
+ align:start position:0%
+frequencies e to the I KX let me say e
+ 
+
+ align:start position:0%
+frequencies e to the I KX let me say e
+to the I
+
+ align:start position:0%
+to the I
+ 
+
+ align:start position:0%
+to the I
+KX so this is Fier that's
+
+ align:start position:0%
+KX so this is Fier that's
+ 
+
+ align:start position:0%
+KX so this is Fier that's
+coming I take the function f ofx and I
+
+ align:start position:0%
+coming I take the function f ofx and I
+ 
+
+ align:start position:0%
+coming I take the function f ofx and I
+write it I could think of it as a
+
+ align:start position:0%
+write it I could think of it as a
+ 
+
+ align:start position:0%
+write it I could think of it as a
+combination
+
+ align:start position:0%
+combination
+ 
+
+ align:start position:0%
+combination
+of pure exponentials pure frequencies
+
+ align:start position:0%
+of pure exponentials pure frequencies
+ 
+
+ align:start position:0%
+of pure exponentials pure frequencies
+that would be a Fier
+
+ align:start position:0%
+that would be a Fier
+ 
+
+ align:start position:0%
+that would be a Fier
+Series so that's a for series because
+
+ align:start position:0%
+Series so that's a for series because
+ 
+
+ align:start position:0%
+Series so that's a for series because
+it's I'm using K has integer values the
+
+ align:start position:0%
+it's I'm using K has integer values the
+ 
+
+ align:start position:0%
+it's I'm using K has integer values the
+frequencies are 0 1 two three
+
+ align:start position:0%
+frequencies are 0 1 two three
+ 
+
+ align:start position:0%
+frequencies are 0 1 two three
+whatever now
+
+ align:start position:0%
+whatever now
+ 
+
+ align:start position:0%
+whatever now
+and and that that will'll use so that
+
+ align:start position:0%
+and and that that will'll use so that
+ 
+
+ align:start position:0%
+and and that that will'll use so that
+Fier series comes for functions that are
+
+ align:start position:0%
+Fier series comes for functions that are
+ 
+
+ align:start position:0%
+Fier series comes for functions that are
+periodic they repeat every 2 pi because
+
+ align:start position:0%
+periodic they repeat every 2 pi because
+ 
+
+ align:start position:0%
+periodic they repeat every 2 pi because
+those functions if I increase X by 2 pi
+
+ align:start position:0%
+those functions if I increase X by 2 pi
+ 
+
+ align:start position:0%
+those functions if I increase X by 2 pi
+don't change so I'm repeating every 2 pi
+
+ align:start position:0%
+don't change so I'm repeating every 2 pi
+ 
+
+ align:start position:0%
+don't change so I'm repeating every 2 pi
+now I I have to I have to say a word
+
+ align:start position:0%
+now I I have to I have to say a word
+ 
+
+ align:start position:0%
+now I I have to I have to say a word
+about the other possibility which would
+
+ align:start position:0%
+about the other possibility which would
+ 
+
+ align:start position:0%
+about the other possibility which would
+be to have all frequencies have I'll
+
+ align:start position:0%
+be to have all frequencies have I'll
+ 
+
+ align:start position:0%
+be to have all frequencies have I'll
+I'll integrate now K instead of summing
+
+ align:start position:0%
+I'll integrate now K instead of summing
+ 
+
+ align:start position:0%
+I'll integrate now K instead of summing
+on K I'll integrate on
+
+ align:start position:0%
+on K I'll integrate on
+ 
+
+ align:start position:0%
+on K I'll integrate on
+K what does band limited
+
+ align:start position:0%
+K what does band limited
+ 
+
+ align:start position:0%
+K what does band limited
+mean band limited means that
+
+ align:start position:0%
+mean band limited means that
+ 
+
+ align:start position:0%
+mean band limited means that
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+frequencies in a certain range say a
+
+ align:start position:0%
+frequencies in a certain range say a
+ 
+
+ align:start position:0%
+frequencies in a certain range say a
+range around zero are included so a band
+
+ align:start position:0%
+range around zero are included so a band
+ 
+
+ align:start position:0%
+range around zero are included so a band
+limited function would be a function
+
+ align:start position:0%
+limited function would be a function
+ 
+
+ align:start position:0%
+limited function would be a function
+whose frequencies go from some value say
+
+ align:start position:0%
+whose frequencies go from some value say
+ 
+
+ align:start position:0%
+whose frequencies go from some value say
+minus Omega to Omega instead of going
+
+ align:start position:0%
+minus Omega to Omega instead of going
+ 
+
+ align:start position:0%
+minus Omega to Omega instead of going
+from minus infinity to Infinity this
+
+ align:start position:0%
+from minus infinity to Infinity this
+ 
+
+ align:start position:0%
+from minus infinity to Infinity this
+would be band limited uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequencies between minus
+
+ align:start position:0%
+frequencies between minus
+ 
+
+ align:start position:0%
+frequencies between minus
+Omega and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega so
+
+ align:start position:0%
+Omega so
+ 
+
+ align:start position:0%
+Omega so
+that that that's another kind of smooth
+
+ align:start position:0%
+that that that's another kind of smooth
+ 
+
+ align:start position:0%
+that that that's another kind of smooth
+function that's another way
+
+ align:start position:0%
+function that's another way
+ 
+
+ align:start position:0%
+function that's another way
+to functions that have only low low
+
+ align:start position:0%
+to functions that have only low low
+ 
+
+ align:start position:0%
+to functions that have only low low
+frequencies are associated with
+
+ align:start position:0%
+frequencies are associated with
+ 
+
+ align:start position:0%
+frequencies are associated with
+smoothness
+
+ align:start position:0%
+smoothness
+ 
+
+ align:start position:0%
+smoothness
+high frequencies are associated with
+
+ align:start position:0%
+high frequencies are associated with
+ 
+
+ align:start position:0%
+high frequencies are associated with
+fast
+
+ align:start position:0%
+fast
+ 
+
+ align:start position:0%
+fast
+oscillations so the class of band
+
+ align:start position:0%
+oscillations so the class of band
+ 
+
+ align:start position:0%
+oscillations so the class of band
+limited functions gives me another a
+
+ align:start position:0%
+limited functions gives me another a
+ 
+
+ align:start position:0%
+limited functions gives me another a
+forier way to talk about smoothness so
+
+ align:start position:0%
+forier way to talk about smoothness so
+ 
+
+ align:start position:0%
+forier way to talk about smoothness so
+for us smoothness was something about
+
+ align:start position:0%
+for us smoothness was something about
+ 
+
+ align:start position:0%
+for us smoothness was something about
+how many derivatives were
+
+ align:start position:0%
+how many derivatives were
+ 
+
+ align:start position:0%
+how many derivatives were
+continuous that's the sort of smoothness
+
+ align:start position:0%
+continuous that's the sort of smoothness
+ 
+
+ align:start position:0%
+continuous that's the sort of smoothness
+in the X domain how many
+
+ align:start position:0%
+in the X domain how many
+ 
+
+ align:start position:0%
+in the X domain how many
+derivatives smoothness in the frequency
+
+ align:start position:0%
+derivatives smoothness in the frequency
+ 
+
+ align:start position:0%
+derivatives smoothness in the frequency
+domain is how fast of the frequencies
+
+ align:start position:0%
+domain is how fast of the frequencies
+ 
+
+ align:start position:0%
+domain is how fast of the frequencies
+drop off and here band limited means
+
+ align:start position:0%
+drop off and here band limited means
+ 
+
+ align:start position:0%
+drop off and here band limited means
+they drop like a shot band limited means
+
+ align:start position:0%
+they drop like a shot band limited means
+ 
+
+ align:start position:0%
+they drop like a shot band limited means
+that the frequencies in the
+
+ align:start position:0%
+that the frequencies in the
+ 
+
+ align:start position:0%
+that the frequencies in the
+function that that these e to the I kxs
+
+ align:start position:0%
+function that that these e to the I kxs
+ 
+
+ align:start position:0%
+function that that these e to the I kxs
+are not there for high frequencies high
+
+ align:start position:0%
+are not there for high frequencies high
+ 
+
+ align:start position:0%
+are not there for high frequencies high
+frequencies are are out for a band
+
+ align:start position:0%
+frequencies are are out for a band
+ 
+
+ align:start position:0%
+frequencies are are out for a band
+limited function and then you have uh
+
+ align:start position:0%
+limited function and then you have uh
+ 
+
+ align:start position:0%
+limited function and then you have uh
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+Shannon uh has a formula for the natural
+
+ align:start position:0%
+Shannon uh has a formula for the natural
+ 
+
+ align:start position:0%
+Shannon uh has a formula for the natural
+way to fit
+
+ align:start position:0%
+way to fit
+ 
+
+ align:start position:0%
+way to fit
+uh Val so our same interpolation
+
+ align:start position:0%
+uh Val so our same interpolation
+ 
+
+ align:start position:0%
+uh Val so our same interpolation
+problem so now I'm completing the answer
+
+ align:start position:0%
+problem so now I'm completing the answer
+ 
+
+ align:start position:0%
+problem so now I'm completing the answer
+to your question so I have these
+
+ align:start position:0%
+to your question so I have these
+ 
+
+ align:start position:0%
+to your question so I have these
+points so Shannon could fit a function
+
+ align:start position:0%
+points so Shannon could fit a function
+ 
+
+ align:start position:0%
+points so Shannon could fit a function
+as and it would look smooth through
+
+ align:start position:0%
+as and it would look smooth through
+ 
+
+ align:start position:0%
+as and it would look smooth through
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+points and His function would be band
+
+ align:start position:0%
+points and His function would be band
+ 
+
+ align:start position:0%
+points and His function would be band
+limited so it would be smooth again it
+
+ align:start position:0%
+limited so it would be smooth again it
+ 
+
+ align:start position:0%
+limited so it would be smooth again it
+would be uh yeah it would be smooth in
+
+ align:start position:0%
+would be uh yeah it would be smooth in
+ 
+
+ align:start position:0%
+would be uh yeah it would be smooth in
+some way yeah actually in some way this
+
+ align:start position:0%
+some way yeah actually in some way this
+ 
+
+ align:start position:0%
+some way yeah actually in some way this
+Shannon ban limited stuff is the limit
+
+ align:start position:0%
+Shannon ban limited stuff is the limit
+ 
+
+ align:start position:0%
+Shannon ban limited stuff is the limit
+of splines as the spline degree goes way
+
+ align:start position:0%
+of splines as the spline degree goes way
+ 
+
+ align:start position:0%
+of splines as the spline degree goes way
+up so we did hat functions degree one
+
+ align:start position:0%
+up so we did hat functions degree one
+ 
+
+ align:start position:0%
+up so we did hat functions degree one
+splines cubic splines I recommended as a
+
+ align:start position:0%
+splines cubic splines I recommended as a
+ 
+
+ align:start position:0%
+splines cubic splines I recommended as a
+as a as a pretty reliable construction
+
+ align:start position:0%
+as a as a pretty reliable construction
+ 
+
+ align:start position:0%
+as a as a pretty reliable construction
+but you could do fifth degre splines 7th
+
+ align:start position:0%
+but you could do fifth degre splines 7th
+ 
+
+ align:start position:0%
+but you could do fifth degre splines 7th
+degree Lins all you could keep going and
+
+ align:start position:0%
+degree Lins all you could keep going and
+ 
+
+ align:start position:0%
+degree Lins all you could keep going and
+in the limit you would get this so maybe
+
+ align:start position:0%
+in the limit you would get this so maybe
+ 
+
+ align:start position:0%
+in the limit you would get this so maybe
+that's some half part of partial answer
+
+ align:start position:0%
+that's some half part of partial answer
+ 
+
+ align:start position:0%
+that's some half part of partial answer
+to the connection between splines and
+
+ align:start position:0%
+to the connection between splines and
+ 
+
+ align:start position:0%
+to the connection between splines and
+and uh this Fier world yeah okay thanks
+
+ align:start position:0%
+and uh this Fier world yeah okay thanks
+ 
+
+ align:start position:0%
+and uh this Fier world yeah okay thanks
+yeah so the these are topics now wow
+
+ align:start position:0%
+yeah so the these are topics now wow
+ 
+
+ align:start position:0%
+yeah so the these are topics now wow
+today's lecture is kind of
+
+ align:start position:0%
+today's lecture is kind of
+ 
+
+ align:start position:0%
+today's lecture is kind of
+a can I do one really important thing
+
+ align:start position:0%
+a can I do one really important thing
+ 
+
+ align:start position:0%
+a can I do one really important thing
+now in today's lecture for you to
+
+ align:start position:0%
+now in today's lecture for you to
+ 
+
+ align:start position:0%
+now in today's lecture for you to
+remember gradient and Divergence I I
+
+ align:start position:0%
+remember gradient and Divergence I I
+ 
+
+ align:start position:0%
+remember gradient and Divergence I I
+don't want you to spend the weekend
+
+ align:start position:0%
+don't want you to spend the weekend
+ 
+
+ align:start position:0%
+don't want you to spend the weekend
+without uh thinking about gradient and
+
+ align:start position:0%
+without uh thinking about gradient and
+ 
+
+ align:start position:0%
+without uh thinking about gradient and
+Divergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay here's here's the
+
+ align:start position:0%
+okay here's here's the
+ 
+
+ align:start position:0%
+okay here's here's the
+idea that for lots and lots of
+
+ align:start position:0%
+idea that for lots and lots of
+ 
+
+ align:start position:0%
+idea that for lots and lots of
+applications for function for for region
+
+ align:start position:0%
+applications for function for for region
+ 
+
+ align:start position:0%
+applications for function for for region
+let's say in the
+
+ align:start position:0%
+let's say in the
+ 
+
+ align:start position:0%
+let's say in the
+plane I have the same uh maybe I I have
+
+ align:start position:0%
+plane I have the same uh maybe I I have
+ 
+
+ align:start position:0%
+plane I have the same uh maybe I I have
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+what what physical example shall I pick
+
+ align:start position:0%
+what what physical example shall I pick
+ 
+
+ align:start position:0%
+what what physical example shall I pick
+now maybe I'll I'll let youu be the
+
+ align:start position:0%
+now maybe I'll I'll let youu be the
+ 
+
+ align:start position:0%
+now maybe I'll I'll let youu be the
+temperature so instead of being
+
+ align:start position:0%
+temperature so instead of being
+ 
+
+ align:start position:0%
+temperature so instead of being
+displacement let me make it
+
+ align:start position:0%
+displacement let me make it
+ 
+
+ align:start position:0%
+displacement let me make it
+temperature U okay then I have a
+
+ align:start position:0%
+temperature U okay then I have a
+ 
+
+ align:start position:0%
+temperature U okay then I have a
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+gradient a a slope but now the whole
+
+ align:start position:0%
+gradient a a slope but now the whole
+ 
+
+ align:start position:0%
+gradient a a slope but now the whole
+point is that's a function of X and Y
+
+ align:start position:0%
+point is that's a function of X and Y
+ 
+
+ align:start position:0%
+point is that's a function of X and Y
+then I have a temperature
+
+ align:start position:0%
+then I have a temperature
+ 
+
+ align:start position:0%
+then I have a temperature
+gradient and if I'm consistent with a
+
+ align:start position:0%
+gradient and if I'm consistent with a
+ 
+
+ align:start position:0%
+gradient and if I'm consistent with a
+notation that'll be e of X and
+
+ align:start position:0%
+notation that'll be e of X and
+ 
+
+ align:start position:0%
+notation that'll be e of X and
+Y and then you'll expect that there's
+
+ align:start position:0%
+Y and then you'll expect that there's
+ 
+
+ align:start position:0%
+Y and then you'll expect that there's
+some C of X and
+
+ align:start position:0%
+some C of X and
+ 
+
+ align:start position:0%
+some C of X and
+Y some operator C that makes that tells
+
+ align:start position:0%
+Y some operator C that makes that tells
+ 
+
+ align:start position:0%
+Y some operator C that makes that tells
+me how much heat flows this this will
+
+ align:start position:0%
+me how much heat flows this this will
+ 
+
+ align:start position:0%
+me how much heat flows this this will
+tell me something about the heat the
+
+ align:start position:0%
+tell me something about the heat the
+ 
+
+ align:start position:0%
+tell me something about the heat the
+thermal conductivity right I'm just
+
+ align:start position:0%
+thermal conductivity right I'm just
+ 
+
+ align:start position:0%
+thermal conductivity right I'm just
+really as
+
+ align:start position:0%
+really as
+ 
+
+ align:start position:0%
+really as
+I speak about this uh framework I'm just
+
+ align:start position:0%
+I speak about this uh framework I'm just
+ 
+
+ align:start position:0%
+I speak about this uh framework I'm just
+uttering the sort of the correct words
+
+ align:start position:0%
+uttering the sort of the correct words
+ 
+
+ align:start position:0%
+uttering the sort of the correct words
+having started with temperature this
+
+ align:start position:0%
+having started with temperature this
+ 
+
+ align:start position:0%
+having started with temperature this
+thing should be a temperature gradient
+
+ align:start position:0%
+thing should be a temperature gradient
+ 
+
+ align:start position:0%
+thing should be a temperature gradient
+then I should have some physical thermal
+
+ align:start position:0%
+then I should have some physical thermal
+ 
+
+ align:start position:0%
+then I should have some physical thermal
+conductivity different for different
+
+ align:start position:0%
+conductivity different for different
+ 
+
+ align:start position:0%
+conductivity different for different
+metals or different materials and and
+
+ align:start position:0%
+metals or different materials and and
+ 
+
+ align:start position:0%
+metals or different materials and and
+I'll have a heat
+
+ align:start position:0%
+I'll have a heat
+ 
+
+ align:start position:0%
+I'll have a heat
+flow W of X and Y and everybody knows
+
+ align:start position:0%
+flow W of X and Y and everybody knows
+ 
+
+ align:start position:0%
+flow W of X and Y and everybody knows
+that W will be C * e and then there will
+
+ align:start position:0%
+that W will be C * e and then there will
+ 
+
+ align:start position:0%
+that W will be C * e and then there will
+be some uh a transpose so of
+
+ align:start position:0%
+be some uh a transpose so of
+ 
+
+ align:start position:0%
+be some uh a transpose so of
+course there'll be some a transpose here
+
+ align:start position:0%
+course there'll be some a transpose here
+ 
+
+ align:start position:0%
+course there'll be some a transpose here
+and some a here and up here I'll have a
+
+ align:start position:0%
+and some a here and up here I'll have a
+ 
+
+ align:start position:0%
+and some a here and up here I'll have a
+balance
+
+ align:start position:0%
+balance
+ 
+
+ align:start position:0%
+balance
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it it
+
+ align:start position:0%
+okay so it it
+ 
+
+ align:start position:0%
+okay so it it
+just I just want to think what's the
+
+ align:start position:0%
+just I just want to think what's the
+ 
+
+ align:start position:0%
+just I just want to think what's the
+what's the operator a that's that's the
+
+ align:start position:0%
+what's the operator a that's that's the
+ 
+
+ align:start position:0%
+what's the operator a that's that's the
+if we can focus on
+
+ align:start position:0%
+if we can focus on
+ 
+
+ align:start position:0%
+if we can focus on
+that question then that's what's going
+
+ align:start position:0%
+that question then that's what's going
+ 
+
+ align:start position:0%
+that question then that's what's going
+to occupy us for the certainly the whole
+
+ align:start position:0%
+to occupy us for the certainly the whole
+ 
+
+ align:start position:0%
+to occupy us for the certainly the whole
+of next week what's so I've actually
+
+ align:start position:0%
+of next week what's so I've actually
+ 
+
+ align:start position:0%
+of next week what's so I've actually
+used the word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradient we have functions of two
+
+ align:start position:0%
+gradient we have functions of two
+ 
+
+ align:start position:0%
+gradient we have functions of two
+variables we're looking for the change
+
+ align:start position:0%
+variables we're looking for the change
+ 
+
+ align:start position:0%
+variables we're looking for the change
+the rate of change the steepness of
+
+ align:start position:0%
+the rate of change the steepness of
+ 
+
+ align:start position:0%
+the rate of change the steepness of
+those functions so this a
+
+ align:start position:0%
+those functions so this a
+ 
+
+ align:start position:0%
+those functions so this a
+Au is going to give me two
+
+ align:start position:0%
+Au is going to give me two
+ 
+
+ align:start position:0%
+Au is going to give me two
+derivatives I've got fun I've got two
+
+ align:start position:0%
+derivatives I've got fun I've got two
+ 
+
+ align:start position:0%
+derivatives I've got fun I've got two
+variables there are two first
+
+ align:start position:0%
+variables there are two first
+ 
+
+ align:start position:0%
+variables there are two first
+derivatives both of them are
+
+ align:start position:0%
+derivatives both of them are
+ 
+
+ align:start position:0%
+derivatives both of them are
+important that's the that's what the A
+
+ align:start position:0%
+important that's the that's what the A
+ 
+
+ align:start position:0%
+important that's the that's what the A
+is for for the next big
+
+ align:start position:0%
+is for for the next big
+ 
+
+ align:start position:0%
+is for for the next big
+example in the course like the final
+
+ align:start position:0%
+example in the course like the final
+ 
+
+ align:start position:0%
+example in the course like the final
+major example of the course is when a
+
+ align:start position:0%
+major example of the course is when a
+ 
+
+ align:start position:0%
+major example of the course is when a
+acts on a function of two variables
+
+ align:start position:0%
+acts on a function of two variables
+ 
+
+ align:start position:0%
+acts on a function of two variables
+because I have a I'm in a region in the
+
+ align:start position:0%
+because I have a I'm in a region in the
+ 
+
+ align:start position:0%
+because I have a I'm in a region in the
+plane to find its rate of change and and
+
+ align:start position:0%
+plane to find its rate of change and and
+ 
+
+ align:start position:0%
+plane to find its rate of change and and
+this is called the gradient so this is
+
+ align:start position:0%
+this is called the gradient so this is
+ 
+
+ align:start position:0%
+this is called the gradient so this is
+the GR
+
+ align:start position:0%
+the GR
+ 
+
+ align:start position:0%
+the GR
+shorthand is the gradient of
+
+ align:start position:0%
+shorthand is the gradient of
+ 
+
+ align:start position:0%
+shorthand is the gradient of
+U uh yeah let me just so we have to
+
+ align:start position:0%
+U uh yeah let me just so we have to
+ 
+
+ align:start position:0%
+U uh yeah let me just so we have to
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+that we have to understand what the
+
+ align:start position:0%
+that we have to understand what the
+ 
+
+ align:start position:0%
+that we have to understand what the
+gradient
+
+ align:start position:0%
+gradient
+ 
+
+ align:start position:0%
+gradient
+is and of course we want to know its
+
+ align:start position:0%
+is and of course we want to know its
+ 
+
+ align:start position:0%
+is and of course we want to know its
+transpose so let's can I just like think
+
+ align:start position:0%
+transpose so let's can I just like think
+ 
+
+ align:start position:0%
+transpose so let's can I just like think
+what should be the transpose of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradient uh okay I'll take that picture
+
+ align:start position:0%
+gradient uh okay I'll take that picture
+ 
+
+ align:start position:0%
+gradient uh okay I'll take that picture
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+okay I'm thinking now about the
+
+ align:start position:0%
+okay I'm thinking now about the
+ 
+
+ align:start position:0%
+okay I'm thinking now about the
+transpose of the
+
+ align:start position:0%
+transpose of the
+ 
+
+ align:start position:0%
+transpose of the
+gradient
+
+ align:start position:0%
+gradient
+ 
+
+ align:start position:0%
+gradient
+okay so a itself
+
+ align:start position:0%
+okay so a itself
+ 
+
+ align:start position:0%
+okay so a itself
+is you could say is d by DX and D by Dy
+
+ align:start position:0%
+is you could say is d by DX and D by Dy
+ 
+
+ align:start position:0%
+is you could say is d by DX and D by Dy
+you notice how I'm I'm separating out a
+
+ align:start position:0%
+you notice how I'm I'm separating out a
+ 
+
+ align:start position:0%
+you notice how I'm I'm separating out a
+from Au U this is when this acts on a
+
+ align:start position:0%
+from Au U this is when this acts on a
+ 
+
+ align:start position:0%
+from Au U this is when this acts on a
+function this is the gradient operator
+
+ align:start position:0%
+function this is the gradient operator
+ 
+
+ align:start position:0%
+function this is the gradient operator
+that acts on a function U to produce DX
+
+ align:start position:0%
+that acts on a function U to produce DX
+ 
+
+ align:start position:0%
+that acts on a function U to produce DX
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+duy Okay now what's the transpose of
+
+ align:start position:0%
+duy Okay now what's the transpose of
+ 
+
+ align:start position:0%
+duy Okay now what's the transpose of
+this okay you can figure you can guess
+
+ align:start position:0%
+this okay you can figure you can guess
+ 
+
+ align:start position:0%
+this okay you can figure you can guess
+what it should be and then we'll see
+
+ align:start position:0%
+what it should be and then we'll see
+ 
+
+ align:start position:0%
+what it should be and then we'll see
+that yes that guess is correct so what
+
+ align:start position:0%
+that yes that guess is correct so what
+ 
+
+ align:start position:0%
+that yes that guess is correct so what
+what should a transpose look like if if
+
+ align:start position:0%
+what should a transpose look like if if
+ 
+
+ align:start position:0%
+what should a transpose look like if if
+if there's any
+
+ align:start position:0%
+if there's any
+ 
+
+ align:start position:0%
+if there's any
+justice a a transpose should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be okay this is 2 by one
+
+ align:start position:0%
+be okay this is 2 by one
+ 
+
+ align:start position:0%
+be okay this is 2 by one
+the transpose you would expect to be a a
+
+ align:start position:0%
+the transpose you would expect to be a a
+ 
+
+ align:start position:0%
+the transpose you would expect to be a a
+a row a row Vector of I should have the
+
+ align:start position:0%
+a row a row Vector of I should have the
+ 
+
+ align:start position:0%
+a row a row Vector of I should have the
+transpose of that there and what is the
+
+ align:start position:0%
+transpose of that there and what is the
+ 
+
+ align:start position:0%
+transpose of that there and what is the
+transpose of that yeah just tell me what
+
+ align:start position:0%
+transpose of that yeah just tell me what
+ 
+
+ align:start position:0%
+transpose of that yeah just tell me what
+what because we have an idea of what
+
+ align:start position:0%
+what because we have an idea of what
+ 
+
+ align:start position:0%
+what because we have an idea of what
+what should be the transpose of d by
+
+ align:start position:0%
+what should be the transpose of d by
+ 
+
+ align:start position:0%
+what should be the transpose of d by
+DX negative d by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX and what should be the transpose of d
+
+ align:start position:0%
+DX and what should be the transpose of d
+ 
+
+ align:start position:0%
+DX and what should be the transpose of d
+by Dy should be negative d by Dy those
+
+ align:start position:0%
+by Dy should be negative d by Dy those
+ 
+
+ align:start position:0%
+by Dy should be negative d by Dy those
+are two different pieces this is not run
+
+ align:start position:0%
+are two different pieces this is not run
+ 
+
+ align:start position:0%
+are two different pieces this is not run
+together there's a big space in there
+
+ align:start position:0%
+together there's a big space in there
+ 
+
+ align:start position:0%
+together there's a big space in there
+right that's two pieces and what is so
+
+ align:start position:0%
+right that's two pieces and what is so
+ 
+
+ align:start position:0%
+right that's two pieces and what is so
+what is a transpose applied to a
+
+ align:start position:0%
+what is a transpose applied to a
+ 
+
+ align:start position:0%
+what is a transpose applied to a
+ah so heat flow W I want to say what is
+
+ align:start position:0%
+ah so heat flow W I want to say what is
+ 
+
+ align:start position:0%
+ah so heat flow W I want to say what is
+a transpose applied to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W you're going to see this again
+
+ align:start position:0%
+W you're going to see this again
+ 
+
+ align:start position:0%
+W you're going to see this again
+but would just take these minutes to
+
+ align:start position:0%
+but would just take these minutes to
+ 
+
+ align:start position:0%
+but would just take these minutes to
+show it for the first time so a
+
+ align:start position:0%
+show it for the first time so a
+ 
+
+ align:start position:0%
+show it for the first time so a
+transpose wait a minute what is w a a
+
+ align:start position:0%
+transpose wait a minute what is w a a
+ 
+
+ align:start position:0%
+transpose wait a minute what is w a a
+function or is it a
+
+ align:start position:0%
+function or is it a
+ 
+
+ align:start position:0%
+function or is it a
+vector yeah we've got to get that
+
+ align:start position:0%
+vector yeah we've got to get that
+ 
+
+ align:start position:0%
+vector yeah we've got to get that
+straight before we start here's an
+
+ align:start position:0%
+straight before we start here's an
+ 
+
+ align:start position:0%
+straight before we start here's an
+ordinary function a scalar function just
+
+ align:start position:0%
+ordinary function a scalar function just
+ 
+
+ align:start position:0%
+ordinary function a scalar function just
+whatever X2 +
+
+ align:start position:0%
+whatever X2 +
+ 
+
+ align:start position:0%
+whatever X2 +
+y^2 what what is
+
+ align:start position:0%
+y^2 what what is
+ 
+
+ align:start position:0%
+y^2 what what is
+e suppose this is x^2 + y^2 what would
+
+ align:start position:0%
+e suppose this is x^2 + y^2 what would
+ 
+
+ align:start position:0%
+e suppose this is x^2 + y^2 what would
+just let's let's have a specific ific
+
+ align:start position:0%
+just let's let's have a specific ific
+ 
+
+ align:start position:0%
+just let's let's have a specific ific
+example what would e then
+
+ align:start position:0%
+example what would e then
+ 
+
+ align:start position:0%
+example what would e then
+be it's got two components right it's
+
+ align:start position:0%
+be it's got two components right it's
+ 
+
+ align:start position:0%
+be it's got two components right it's
+got an X derivative and a y derivative e
+
+ align:start position:0%
+got an X derivative and a y derivative e
+ 
+
+ align:start position:0%
+got an X derivative and a y derivative e
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+vector 2X and 2
+
+ align:start position:0%
+vector 2X and 2
+ 
+
+ align:start position:0%
+vector 2X and 2
+y then I multiply by C so this W has two
+
+ align:start position:0%
+y then I multiply by C so this W has two
+ 
+
+ align:start position:0%
+y then I multiply by C so this W has two
+components this has got a W1 of X and Y
+
+ align:start position:0%
+components this has got a W1 of X and Y
+ 
+
+ align:start position:0%
+components this has got a W1 of X and Y
+W2 of X and
+
+ align:start position:0%
+W2 of X and
+ 
+
+ align:start position:0%
+W2 of X and
+Y so just keep things straight so so
+
+ align:start position:0%
+Y so just keep things straight so so
+ 
+
+ align:start position:0%
+Y so just keep things straight so so
+it's that that I want to apply a
+
+ align:start position:0%
+it's that that I want to apply a
+ 
+
+ align:start position:0%
+it's that that I want to apply a
+transpose to so a transpose W is minus d
+
+ align:start position:0%
+transpose to so a transpose W is minus d
+ 
+
+ align:start position:0%
+transpose to so a transpose W is minus d
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+DX minus d by Dy and everything's coming
+
+ align:start position:0%
+DX minus d by Dy and everything's coming
+ 
+
+ align:start position:0%
+DX minus d by Dy and everything's coming
+out right because it's applied to a
+
+ align:start position:0%
+out right because it's applied to a
+ 
+
+ align:start position:0%
+out right because it's applied to a
+function W1 and
+
+ align:start position:0%
+function W1 and
+ 
+
+ align:start position:0%
+function W1 and
+W2 W is a vector field it's not a scalar
+
+ align:start position:0%
+W2 W is a vector field it's not a scalar
+ 
+
+ align:start position:0%
+W2 W is a vector field it's not a scalar
+field it's a vector field and the result
+
+ align:start position:0%
+field it's a vector field and the result
+ 
+
+ align:start position:0%
+field it's a vector field and the result
+is just what it should be minus dw1 DX
+
+ align:start position:0%
+is just what it should be minus dw1 DX
+ 
+
+ align:start position:0%
+is just what it should be minus dw1 DX
+minus dw2
+
+ align:start position:0%
+minus dw2
+ 
+
+ align:start position:0%
+minus dw2
+Dy okay good
+
+ align:start position:0%
+Dy okay good
+ 
+
+ align:start position:0%
+Dy okay good
+that's we're going to this this has got
+
+ align:start position:0%
+that's we're going to this this has got
+ 
+
+ align:start position:0%
+that's we're going to this this has got
+to come out of integration by parts
+
+ align:start position:0%
+to come out of integration by parts
+ 
+
+ align:start position:0%
+to come out of integration by parts
+right so we'll have to think what is
+
+ align:start position:0%
+right so we'll have to think what is
+ 
+
+ align:start position:0%
+right so we'll have to think what is
+integration by parts mean in two
+
+ align:start position:0%
+integration by parts mean in two
+ 
+
+ align:start position:0%
+integration by parts mean in two
+variables and it's a famous formula
+
+ align:start position:0%
+variables and it's a famous formula
+ 
+
+ align:start position:0%
+variables and it's a famous formula
+named after gaus and green the greens
+
+ align:start position:0%
+named after gaus and green the greens
+ 
+
+ align:start position:0%
+named after gaus and green the greens
+formula often but do you recognize what
+
+ align:start position:0%
+formula often but do you recognize what
+ 
+
+ align:start position:0%
+formula often but do you recognize what
+I'm looking at here this is so important
+
+ align:start position:0%
+I'm looking at here this is so important
+ 
+
+ align:start position:0%
+I'm looking at here this is so important
+it has a
+
+ align:start position:0%
+it has a
+ 
+
+ align:start position:0%
+it has a
+name and what's the name and then we're
+
+ align:start position:0%
+name and what's the name and then we're
+ 
+
+ align:start position:0%
+name and what's the name and then we're
+ready to go what's the name of if I take
+
+ align:start position:0%
+ready to go what's the name of if I take
+ 
+
+ align:start position:0%
+ready to go what's the name of if I take
+a vector field like 2x2 y let me take
+
+ align:start position:0%
+a vector field like 2x2 y let me take
+ 
+
+ align:start position:0%
+a vector field like 2x2 y let me take
+2x2 y as a specific
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example suppose W is 2x2
+
+ align:start position:0%
+example suppose W is 2x2
+ 
+
+ align:start position:0%
+example suppose W is 2x2
+y it was multiplied by let me take C to
+
+ align:start position:0%
+y it was multiplied by let me take C to
+ 
+
+ align:start position:0%
+y it was multiplied by let me take C to
+be one then what is a transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W specifically what what what am I
+
+ align:start position:0%
+W specifically what what what am I
+ 
+
+ align:start position:0%
+W specifically what what what am I
+getting out of
+
+ align:start position:0%
+getting out of
+ 
+
+ align:start position:0%
+getting out of
+it I'm getting what do I get from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here that's minus the X derivative of
+
+ align:start position:0%
+here that's minus the X derivative of
+ 
+
+ align:start position:0%
+here that's minus the X derivative of
+the first guy and the X derivative of
+
+ align:start position:0%
+the first guy and the X derivative of
+ 
+
+ align:start position:0%
+the first guy and the X derivative of
+that guy is two so I'm getting a minus
+
+ align:start position:0%
+that guy is two so I'm getting a minus
+ 
+
+ align:start position:0%
+that guy is two so I'm getting a minus
+two and this is minus the Y derivative
+
+ align:start position:0%
+two and this is minus the Y derivative
+ 
+
+ align:start position:0%
+two and this is minus the Y derivative
+of the second guy so that's another
+
+ align:start position:0%
+of the second guy so that's another
+ 
+
+ align:start position:0%
+of the second guy so that's another
+minus two so I'm getting a number it
+
+ align:start position:0%
+minus two so I'm getting a number it
+ 
+
+ align:start position:0%
+minus two so I'm getting a number it
+happens to be a number here I I chose
+
+ align:start position:0%
+happens to be a number here I I chose
+ 
+
+ align:start position:0%
+happens to be a number here I I chose
+such a simple function it came out to be
+
+ align:start position:0%
+such a simple function it came out to be
+ 
+
+ align:start position:0%
+such a simple function it came out to be
+a number uh and what's the name that so
+
+ align:start position:0%
+a number uh and what's the name that so
+ 
+
+ align:start position:0%
+a number uh and what's the name that so
+this is minus the what of w just just
+
+ align:start position:0%
+this is minus the what of w just just
+ 
+
+ align:start position:0%
+this is minus the what of w just just
+tell me what what's the the the name
+
+ align:start position:0%
+tell me what what's the the the name
+ 
+
+ align:start position:0%
+tell me what what's the the the name
+everybody uses for that
+
+ align:start position:0%
+everybody uses for that
+ 
+
+ align:start position:0%
+everybody uses for that
+operation the Divergence it's the minus
+
+ align:start position:0%
+operation the Divergence it's the minus
+ 
+
+ align:start position:0%
+operation the Divergence it's the minus
+the Divergence of w
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I'm saying here is
+
+ align:start position:0%
+so what I'm saying here is
+ 
+
+ align:start position:0%
+so what I'm saying here is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+I I'm saying it because uh somehow I
+
+ align:start position:0%
+I I'm saying it because uh somehow I
+ 
+
+ align:start position:0%
+I I'm saying it because uh somehow I
+remember learn studying Vector calculus
+
+ align:start position:0%
+remember learn studying Vector calculus
+ 
+
+ align:start position:0%
+remember learn studying Vector calculus
+and in that process I learned about the
+
+ align:start position:0%
+and in that process I learned about the
+ 
+
+ align:start position:0%
+and in that process I learned about the
+gradient and I learned about the
+
+ align:start position:0%
+gradient and I learned about the
+ 
+
+ align:start position:0%
+gradient and I learned about the
+Divergent but I never learned that the
+
+ align:start position:0%
+Divergent but I never learned that the
+ 
+
+ align:start position:0%
+Divergent but I never learned that the
+one was the transpose of the other I
+
+ align:start position:0%
+one was the transpose of the other I
+ 
+
+ align:start position:0%
+one was the transpose of the other I
+mean I think
+
+ align:start position:0%
+mean I think
+ 
+
+ align:start position:0%
+mean I think
+what looking back that was criminal uh
+
+ align:start position:0%
+what looking back that was criminal uh
+ 
+
+ align:start position:0%
+what looking back that was criminal uh
+to to to to teach to to describe those
+
+ align:start position:0%
+to to to to teach to to describe those
+ 
+
+ align:start position:0%
+to to to to teach to to describe those
+with a minus sign of course to to I
+
+ align:start position:0%
+with a minus sign of course to to I
+ 
+
+ align:start position:0%
+with a minus sign of course to to I
+learned Green's formula but
+
+ align:start position:0%
+learned Green's formula but
+ 
+
+ align:start position:0%
+learned Green's formula but
+now uh sort of we'll see why it why what
+
+ align:start position:0%
+now uh sort of we'll see why it why what
+ 
+
+ align:start position:0%
+now uh sort of we'll see why it why what
+it means okay that's next week's job
+
+ align:start position:0%
+it means okay that's next week's job
+ 
+
+ align:start position:0%
+it means okay that's next week's job
+have a great weekend and see you Monday
\ No newline at end of file
diff --git a/T8IjB94ka2g.txt b/T8IjB94ka2g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..08b14809b7da8f5ecc82c5978e5e479e1dcc4f3c
--- /dev/null
+++ b/T8IjB94ka2g.txt
@@ -0,0 +1,1403 @@
+align:start position:0%
+ 
+you know so the idea is that if English
+
+ align:start position:0%
+you know so the idea is that if English
+ 
+
+ align:start position:0%
+you know so the idea is that if English
+is more of a Creole in Haitian Creole
+
+ align:start position:0%
+is more of a Creole in Haitian Creole
+ 
+
+ align:start position:0%
+is more of a Creole in Haitian Creole
+then why reserve the term Creole to only
+
+ align:start position:0%
+then why reserve the term Creole to only
+ 
+
+ align:start position:0%
+then why reserve the term Creole to only
+Creole languages right that's that's a
+
+ align:start position:0%
+Creole languages right that's that's a
+ 
+
+ align:start position:0%
+Creole languages right that's that's a
+passive very valid question and and and
+
+ align:start position:0%
+passive very valid question and and and
+ 
+
+ align:start position:0%
+passive very valid question and and and
+nowadays in Haiti and also in Mauritius
+
+ align:start position:0%
+nowadays in Haiti and also in Mauritius
+ 
+
+ align:start position:0%
+nowadays in Haiti and also in Mauritius
+I don't know whether you're aware of
+
+ align:start position:0%
+I don't know whether you're aware of
+ 
+
+ align:start position:0%
+I don't know whether you're aware of
+this debate in Mauritius people ask you
+
+ align:start position:0%
+this debate in Mauritius people ask you
+ 
+
+ align:start position:0%
+this debate in Mauritius people ask you
+know white why do we call you know
+
+ align:start position:0%
+know white why do we call you know
+ 
+
+ align:start position:0%
+know white why do we call you know
+Mauritian Creole Creole although you
+
+ align:start position:0%
+Mauritian Creole Creole although you
+ 
+
+ align:start position:0%
+Mauritian Creole Creole although you
+just call it Mauritian why don't you
+
+ align:start position:0%
+just call it Mauritian why don't you
+ 
+
+ align:start position:0%
+just call it Mauritian why don't you
+just call Asian Creole hey a Haitian and
+
+ align:start position:0%
+just call Asian Creole hey a Haitian and
+ 
+
+ align:start position:0%
+just call Asian Creole hey a Haitian and
+so as a linguist might take when I'm
+
+ align:start position:0%
+so as a linguist might take when I'm
+ 
+
+ align:start position:0%
+so as a linguist might take when I'm
+being asked that question is that well
+
+ align:start position:0%
+being asked that question is that well
+ 
+
+ align:start position:0%
+being asked that question is that well
+the people who speak the language
+
+ align:start position:0%
+the people who speak the language
+ 
+
+ align:start position:0%
+the people who speak the language
+most of them call it Creole so what is a
+
+ align:start position:0%
+most of them call it Creole so what is a
+ 
+
+ align:start position:0%
+most of them call it Creole so what is a
+linguist to say no you won't call it
+
+ align:start position:0%
+linguist to say no you won't call it
+ 
+
+ align:start position:0%
+linguist to say no you won't call it
+Haitian you see because we have a basic
+
+ align:start position:0%
+Haitian you see because we have a basic
+ 
+
+ align:start position:0%
+Haitian you see because we have a basic
+principle in linguistics at least in you
+
+ align:start position:0%
+principle in linguistics at least in you
+ 
+
+ align:start position:0%
+principle in linguistics at least in you
+know when you consider the center
+
+ align:start position:0%
+know when you consider the center
+ 
+
+ align:start position:0%
+know when you consider the center
+linguistics it's supposed to be
+
+ align:start position:0%
+linguistics it's supposed to be
+ 
+
+ align:start position:0%
+linguistics it's supposed to be
+descriptive not supposed to prescribe to
+
+ align:start position:0%
+descriptive not supposed to prescribe to
+ 
+
+ align:start position:0%
+descriptive not supposed to prescribe to
+tell people no this is what you say we
+
+ align:start position:0%
+tell people no this is what you say we
+ 
+
+ align:start position:0%
+tell people no this is what you say we
+supposed to be taught what we say I mean
+
+ align:start position:0%
+supposed to be taught what we say I mean
+ 
+
+ align:start position:0%
+supposed to be taught what we say I mean
+I have a Avila anecdote when it comes to
+
+ align:start position:0%
+I have a Avila anecdote when it comes to
+ 
+
+ align:start position:0%
+I have a Avila anecdote when it comes to
+the because people see that the time is
+
+ align:start position:0%
+the because people see that the time is
+ 
+
+ align:start position:0%
+the because people see that the time is
+negative that the term Creole because
+
+ align:start position:0%
+negative that the term Creole because
+ 
+
+ align:start position:0%
+negative that the term Creole because
+it's been used to refer to lesser
+
+ align:start position:0%
+it's been used to refer to lesser
+ 
+
+ align:start position:0%
+it's been used to refer to lesser
+languages it's basically bit of it and
+
+ align:start position:0%
+languages it's basically bit of it and
+ 
+
+ align:start position:0%
+languages it's basically bit of it and
+now as as someone but who has a question
+
+ align:start position:0%
+now as as someone but who has a question
+ 
+
+ align:start position:0%
+now as as someone but who has a question
+so as someone but up since we know at
+
+ align:start position:0%
+so as someone but up since we know at
+ 
+
+ align:start position:0%
+so as someone but up since we know at
+least we can claim that we have evidence
+
+ align:start position:0%
+least we can claim that we have evidence
+ 
+
+ align:start position:0%
+least we can claim that we have evidence
+that hey image in terms of its
+
+ align:start position:0%
+that hey image in terms of its
+ 
+
+ align:start position:0%
+that hey image in terms of its
+structures instead of its history might
+
+ align:start position:0%
+structures instead of its history might
+ 
+
+ align:start position:0%
+structures instead of its history might
+be more of a Creole than Haitian Creole
+
+ align:start position:0%
+be more of a Creole than Haitian Creole
+ 
+
+ align:start position:0%
+be more of a Creole than Haitian Creole
+so why you know the time curl then
+
+ align:start position:0%
+so why you know the time curl then
+ 
+
+ align:start position:0%
+so why you know the time curl then
+doesn't make sense if you think of
+
+ align:start position:0%
+doesn't make sense if you think of
+ 
+
+ align:start position:0%
+doesn't make sense if you think of
+Creole as a sexual term as but the party
+
+ align:start position:0%
+Creole as a sexual term as but the party
+ 
+
+ align:start position:0%
+Creole as a sexual term as but the party
+is that so the word Creole means
+
+ align:start position:0%
+is that so the word Creole means
+ 
+
+ align:start position:0%
+is that so the word Creole means
+different things different people right
+
+ align:start position:0%
+different things different people right
+ 
+
+ align:start position:0%
+different things different people right
+so in Haiti is someone called a language
+
+ align:start position:0%
+so in Haiti is someone called a language
+ 
+
+ align:start position:0%
+so in Haiti is someone called a language
+Creole they don't think of Bickerton we
+
+ align:start position:0%
+Creole they don't think of Bickerton we
+ 
+
+ align:start position:0%
+Creole they don't think of Bickerton we
+don't care about because I don't even
+
+ align:start position:0%
+don't care about because I don't even
+ 
+
+ align:start position:0%
+don't care about because I don't even
+know who begotten is I do not know who
+
+ align:start position:0%
+know who begotten is I do not know who
+ 
+
+ align:start position:0%
+know who begotten is I do not know who
+my poetry is you don't know who you know
+
+ align:start position:0%
+my poetry is you don't know who you know
+ 
+
+ align:start position:0%
+my poetry is you don't know who you know
+missing either or these other linguist
+
+ align:start position:0%
+missing either or these other linguist
+ 
+
+ align:start position:0%
+missing either or these other linguist
+who said all these ugly things about it
+
+ align:start position:0%
+who said all these ugly things about it
+ 
+
+ align:start position:0%
+who said all these ugly things about it
+about Creole languages I did not care is
+
+ align:start position:0%
+about Creole languages I did not care is
+ 
+
+ align:start position:0%
+about Creole languages I did not care is
+that that's why they call the languages
+
+ align:start position:0%
+that that's why they call the languages
+ 
+
+ align:start position:0%
+that that's why they call the languages
+and and they're happy with the time so
+
+ align:start position:0%
+and and they're happy with the time so
+ 
+
+ align:start position:0%
+and and they're happy with the time so
+for them the term has changed meaning
+
+ align:start position:0%
+for them the term has changed meaning
+ 
+
+ align:start position:0%
+for them the term has changed meaning
+the term means just this is my language
+
+ align:start position:0%
+the term means just this is my language
+ 
+
+ align:start position:0%
+the term means just this is my language
+the same way with words like let's take
+
+ align:start position:0%
+the same way with words like let's take
+ 
+
+ align:start position:0%
+the same way with words like let's take
+the word neg okay so this is the way
+
+ align:start position:0%
+the word neg okay so this is the way
+ 
+
+ align:start position:0%
+the word neg okay so this is the way
+that actually you know
+
+ align:start position:0%
+that actually you know
+ 
+
+ align:start position:0%
+that actually you know
+in Haiti we have this word now
+
+ align:start position:0%
+in Haiti we have this word now
+ 
+
+ align:start position:0%
+in Haiti we have this word now
+what does it come from it comes from the
+
+ align:start position:0%
+what does it come from it comes from the
+ 
+
+ align:start position:0%
+what does it come from it comes from the
+French okay Nick now the French neg you
+
+ align:start position:0%
+French okay Nick now the French neg you
+ 
+
+ align:start position:0%
+French okay Nick now the French neg you
+can speak in a puppy you know
+
+ align:start position:0%
+can speak in a puppy you know
+ 
+
+ align:start position:0%
+can speak in a puppy you know
+solicitation Creole this is French now
+
+ align:start position:0%
+solicitation Creole this is French now
+ 
+
+ align:start position:0%
+solicitation Creole this is French now
+you can tell that well this is connected
+
+ align:start position:0%
+you can tell that well this is connected
+ 
+
+ align:start position:0%
+you can tell that well this is connected
+to Negro right now in the movie that we
+
+ align:start position:0%
+to Negro right now in the movie that we
+ 
+
+ align:start position:0%
+to Negro right now in the movie that we
+talked about many times I'm not a negro
+
+ align:start position:0%
+talked about many times I'm not a negro
+ 
+
+ align:start position:0%
+talked about many times I'm not a negro
+you can see that the term negro can be
+
+ align:start position:0%
+you can see that the term negro can be
+ 
+
+ align:start position:0%
+you can see that the term negro can be
+seen as having some negative rotation
+
+ align:start position:0%
+seen as having some negative rotation
+ 
+
+ align:start position:0%
+seen as having some negative rotation
+it's not positive right but guess what
+
+ align:start position:0%
+it's not positive right but guess what
+ 
+
+ align:start position:0%
+it's not positive right but guess what
+in Haiti the term neg is positive you
+
+ align:start position:0%
+in Haiti the term neg is positive you
+ 
+
+ align:start position:0%
+in Haiti the term neg is positive you
+see like I can call you Michelle with
+
+ align:start position:0%
+see like I can call you Michelle with
+ 
+
+ align:start position:0%
+see like I can call you Michelle with
+the neck down no you may well I wouldn't
+
+ align:start position:0%
+the neck down no you may well I wouldn't
+ 
+
+ align:start position:0%
+the neck down no you may well I wouldn't
+see it well you might exactly my negro
+
+ align:start position:0%
+see it well you might exactly my negro
+ 
+
+ align:start position:0%
+see it well you might exactly my negro
+right but it doesn't mean it is
+
+ align:start position:0%
+right but it doesn't mean it is
+ 
+
+ align:start position:0%
+right but it doesn't mean it is
+something negative about calling someone
+
+ align:start position:0%
+something negative about calling someone
+ 
+
+ align:start position:0%
+something negative about calling someone
+like if you leave it if you live in
+
+ align:start position:0%
+like if you leave it if you live in
+ 
+
+ align:start position:0%
+like if you leave it if you live in
+Haiti yourself you know you're a white
+
+ align:start position:0%
+Haiti yourself you know you're a white
+ 
+
+ align:start position:0%
+Haiti yourself you know you're a white
+person after a couple of years Maxwell
+
+ align:start position:0%
+person after a couple of years Maxwell
+ 
+
+ align:start position:0%
+person after a couple of years Maxwell
+might call you neg you see you become
+
+ align:start position:0%
+might call you neg you see you become
+ 
+
+ align:start position:0%
+might call you neg you see you become
+neg
+
+ align:start position:0%
+neg
+ 
+
+ align:start position:0%
+neg
+and hear the term net just means person
+
+ align:start position:0%
+and hear the term net just means person
+ 
+
+ align:start position:0%
+and hear the term net just means person
+you know human you're human you see so
+
+ align:start position:0%
+you know human you're human you see so
+ 
+
+ align:start position:0%
+you know human you're human you see so
+in Haiti the term neg although it
+
+ align:start position:0%
+in Haiti the term neg although it
+ 
+
+ align:start position:0%
+in Haiti the term neg although it
+derives from neg which can be perceived
+
+ align:start position:0%
+derives from neg which can be perceived
+ 
+
+ align:start position:0%
+derives from neg which can be perceived
+as being negative it's become just now
+
+ align:start position:0%
+as being negative it's become just now
+ 
+
+ align:start position:0%
+as being negative it's become just now
+that refers to human being in fact we
+
+ align:start position:0%
+that refers to human being in fact we
+ 
+
+ align:start position:0%
+that refers to human being in fact we
+saw that in fact we'll go back to that
+
+ align:start position:0%
+saw that in fact we'll go back to that
+ 
+
+ align:start position:0%
+saw that in fact we'll go back to that
+the Italian himself see that you know in
+
+ align:start position:0%
+the Italian himself see that you know in
+ 
+
+ align:start position:0%
+the Italian himself see that you know in
+Haiti now at independence will all make
+
+ align:start position:0%
+Haiti now at independence will all make
+ 
+
+ align:start position:0%
+Haiti now at independence will all make
+with all Negroes even if you have white
+
+ align:start position:0%
+with all Negroes even if you have white
+ 
+
+ align:start position:0%
+with all Negroes even if you have white
+skin you know that's what 1805 right
+
+ align:start position:0%
+skin you know that's what 1805 right
+ 
+
+ align:start position:0%
+skin you know that's what 1805 right
+deciding told alterations that legally
+
+ align:start position:0%
+deciding told alterations that legally
+ 
+
+ align:start position:0%
+deciding told alterations that legally
+if we went in Haiti we independent we've
+
+ align:start position:0%
+if we went in Haiti we independent we've
+ 
+
+ align:start position:0%
+if we went in Haiti we independent we've
+established of freedom of sovereignty if
+
+ align:start position:0%
+established of freedom of sovereignty if
+ 
+
+ align:start position:0%
+established of freedom of sovereignty if
+you want is black
+
+ align:start position:0%
+you want is black
+ 
+
+ align:start position:0%
+you want is black
+whether you white whether you polish
+
+ align:start position:0%
+whether you white whether you polish
+ 
+
+ align:start position:0%
+whether you white whether you polish
+with since you live in Haiti you black
+
+ align:start position:0%
+with since you live in Haiti you black
+ 
+
+ align:start position:0%
+with since you live in Haiti you black
+and that was actually quite forward
+
+ align:start position:0%
+and that was actually quite forward
+ 
+
+ align:start position:0%
+and that was actually quite forward
+right it was postmodern he understood
+
+ align:start position:0%
+right it was postmodern he understood
+ 
+
+ align:start position:0%
+right it was postmodern he understood
+that race was not biological that
+
+ align:start position:0%
+that race was not biological that
+ 
+
+ align:start position:0%
+that race was not biological that
+marriage was a political concept you see
+
+ align:start position:0%
+marriage was a political concept you see
+ 
+
+ align:start position:0%
+marriage was a political concept you see
+so from the same perspective and could
+
+ align:start position:0%
+so from the same perspective and could
+ 
+
+ align:start position:0%
+so from the same perspective and could
+see well Creole in Haiti means language
+
+ align:start position:0%
+see well Creole in Haiti means language
+ 
+
+ align:start position:0%
+see well Creole in Haiti means language
+it's my language so you know and indeed
+
+ align:start position:0%
+it's my language so you know and indeed
+ 
+
+ align:start position:0%
+it's my language so you know and indeed
+there are groups like I'm on Facebook
+
+ align:start position:0%
+there are groups like I'm on Facebook
+ 
+
+ align:start position:0%
+there are groups like I'm on Facebook
+there's a group called Creole Oh funny
+
+ align:start position:0%
+there's a group called Creole Oh funny
+ 
+
+ align:start position:0%
+there's a group called Creole Oh funny
+you know Creole phony they claim that
+
+ align:start position:0%
+you know Creole phony they claim that
+ 
+
+ align:start position:0%
+you know Creole phony they claim that
+you know we can look at them or Creoles
+
+ align:start position:0%
+you know we can look at them or Creoles
+ 
+
+ align:start position:0%
+you know we can look at them or Creoles
+phony
+
+ align:start position:0%
+phony
+ 
+
+ align:start position:0%
+phony
+you know fooled me right
+
+ align:start position:0%
+you know fooled me right
+ 
+
+ align:start position:0%
+you know fooled me right
+so the route here is Creole and then
+
+ align:start position:0%
+so the route here is Creole and then
+ 
+
+ align:start position:0%
+so the route here is Creole and then
+they use it's like Francophonie you know
+
+ align:start position:0%
+they use it's like Francophonie you know
+ 
+
+ align:start position:0%
+they use it's like Francophonie you know
+this French linguistic cultural empires
+
+ align:start position:0%
+this French linguistic cultural empires
+ 
+
+ align:start position:0%
+this French linguistic cultural empires
+well let's do our own and and and talk
+
+ align:start position:0%
+well let's do our own and and and talk
+ 
+
+ align:start position:0%
+well let's do our own and and and talk
+about cool funny because we believe that
+
+ align:start position:0%
+about cool funny because we believe that
+ 
+
+ align:start position:0%
+about cool funny because we believe that
+we from wishes from seashell from heaven
+
+ align:start position:0%
+we from wishes from seashell from heaven
+ 
+
+ align:start position:0%
+we from wishes from seashell from heaven
+or from Martinique from Guadeloupe from
+
+ align:start position:0%
+or from Martinique from Guadeloupe from
+ 
+
+ align:start position:0%
+or from Martinique from Guadeloupe from
+Gyan we all speak that language that we
+
+ align:start position:0%
+Gyan we all speak that language that we
+ 
+
+ align:start position:0%
+Gyan we all speak that language that we
+call Creole and we share historical
+
+ align:start position:0%
+call Creole and we share historical
+ 
+
+ align:start position:0%
+call Creole and we share historical
+concerns interests in common so let's
+
+ align:start position:0%
+concerns interests in common so let's
+ 
+
+ align:start position:0%
+concerns interests in common so let's
+call this creates this clue for me that
+
+ align:start position:0%
+call this creates this clue for me that
+ 
+
+ align:start position:0%
+call this creates this clue for me that
+will make us stronger actually
+
+ align:start position:0%
+will make us stronger actually
+ 
+
+ align:start position:0%
+will make us stronger actually
+interestingly if you go to the web
+
+ align:start position:0%
+interestingly if you go to the web
+ 
+
+ align:start position:0%
+interestingly if you go to the web
+Facebook page do that because we have
+
+ align:start position:0%
+Facebook page do that because we have
+ 
+
+ align:start position:0%
+Facebook page do that because we have
+interesting recording so different like
+
+ align:start position:0%
+interesting recording so different like
+ 
+
+ align:start position:0%
+interesting recording so different like
+God people from God blue people from
+
+ align:start position:0%
+God people from God blue people from
+ 
+
+ align:start position:0%
+God people from God blue people from
+Martinique G Anne Marie she is speaking
+
+ align:start position:0%
+Martinique G Anne Marie she is speaking
+ 
+
+ align:start position:0%
+Martinique G Anne Marie she is speaking
+the Creole they even have Christian to
+
+ align:start position:0%
+the Creole they even have Christian to
+ 
+
+ align:start position:0%
+the Creole they even have Christian to
+be ha which is this famous French
+
+ align:start position:0%
+be ha which is this famous French
+ 
+
+ align:start position:0%
+be ha which is this famous French
+politician we know from beyond you know
+
+ align:start position:0%
+politician we know from beyond you know
+ 
+
+ align:start position:0%
+politician we know from beyond you know
+black woman raised from very eloquent
+
+ align:start position:0%
+black woman raised from very eloquent
+ 
+
+ align:start position:0%
+black woman raised from very eloquent
+they had the Rick Ritter have speaking a
+
+ align:start position:0%
+they had the Rick Ritter have speaking a
+ 
+
+ align:start position:0%
+they had the Rick Ritter have speaking a
+grannies Creole you know DNA you see and
+
+ align:start position:0%
+grannies Creole you know DNA you see and
+ 
+
+ align:start position:0%
+grannies Creole you know DNA you see and
+then you can understand them you know
+
+ align:start position:0%
+then you can understand them you know
+ 
+
+ align:start position:0%
+then you can understand them you know
+academic you know when I went to
+
+ align:start position:0%
+academic you know when I went to
+ 
+
+ align:start position:0%
+academic you know when I went to
+Mauritius I could speak Creole in
+
+ align:start position:0%
+Mauritius I could speak Creole in
+ 
+
+ align:start position:0%
+Mauritius I could speak Creole in
+Mauritius you see and people can
+
+ align:start position:0%
+Mauritius you see and people can
+ 
+
+ align:start position:0%
+Mauritius you see and people can
+understand me I could understand
+
+ align:start position:0%
+understand me I could understand
+ 
+
+ align:start position:0%
+understand me I could understand
+Mauritian speaking Creole so there is
+
+ align:start position:0%
+Mauritian speaking Creole so there is
+ 
+
+ align:start position:0%
+Mauritian speaking Creole so there is
+some evidence to Criollo funny you know
+
+ align:start position:0%
+some evidence to Criollo funny you know
+ 
+
+ align:start position:0%
+some evidence to Criollo funny you know
+that there is certain is the level of
+
+ align:start position:0%
+that there is certain is the level of
+ 
+
+ align:start position:0%
+that there is certain is the level of
+mutual understanding yeah definitely
+
+ align:start position:0%
+mutual understanding yeah definitely
+ 
+
+ align:start position:0%
+mutual understanding yeah definitely
+you're right you're right you know that
+
+ align:start position:0%
+you're right you're right you know that
+ 
+
+ align:start position:0%
+you're right you're right you know that
+that is thanks to the French that we
+
+ align:start position:0%
+that is thanks to the French that we
+ 
+
+ align:start position:0%
+that is thanks to the French that we
+have this solidarity right but you know
+
+ align:start position:0%
+have this solidarity right but you know
+ 
+
+ align:start position:0%
+have this solidarity right but you know
+it's it's it's you know you can either
+
+ align:start position:0%
+it's it's it's you know you can either
+ 
+
+ align:start position:0%
+it's it's it's you know you can either
+use it for your use it against you right
+
+ align:start position:0%
+use it for your use it against you right
+ 
+
+ align:start position:0%
+use it for your use it against you right
+in this case you think well we have this
+
+ align:start position:0%
+in this case you think well we have this
+ 
+
+ align:start position:0%
+in this case you think well we have this
+mutual common interest based on our
+
+ align:start position:0%
+mutual common interest based on our
+ 
+
+ align:start position:0%
+mutual common interest based on our
+similar languages and let's call it
+
+ align:start position:0%
+similar languages and let's call it
+ 
+
+ align:start position:0%
+similar languages and let's call it
+Californian s turn it into a critical
+
+ align:start position:0%
+Californian s turn it into a critical
+ 
+
+ align:start position:0%
+Californian s turn it into a critical
+critical power you know it's very
+
+ align:start position:0%
+critical power you know it's very
+ 
+
+ align:start position:0%
+critical power you know it's very
+idealistic but you know why not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+describing it to like people but what
+
+ align:start position:0%
+describing it to like people but what
+ 
+
+ align:start position:0%
+describing it to like people but what
+about within linguist like using a
+
+ align:start position:0%
+about within linguist like using a
+ 
+
+ align:start position:0%
+about within linguist like using a
+tongue Creole like to classify like
+
+ align:start position:0%
+tongue Creole like to classify like
+ 
+
+ align:start position:0%
+tongue Creole like to classify like
+languages originated stay the same
+
+ align:start position:0%
+languages originated stay the same
+ 
+
+ align:start position:0%
+languages originated stay the same
+well no because now in science you can
+
+ align:start position:0%
+well no because now in science you can
+ 
+
+ align:start position:0%
+well no because now in science you can
+redefine your terms right so this is
+
+ align:start position:0%
+redefine your terms right so this is
+ 
+
+ align:start position:0%
+redefine your terms right so this is
+different so when you're doing science
+
+ align:start position:0%
+different so when you're doing science
+ 
+
+ align:start position:0%
+different so when you're doing science
+you know it's like when you know so h2o
+
+ align:start position:0%
+you know it's like when you know so h2o
+ 
+
+ align:start position:0%
+you know it's like when you know so h2o
+water for a chemist it's not water for
+
+ align:start position:0%
+water for a chemist it's not water for
+ 
+
+ align:start position:0%
+water for a chemist it's not water for
+for a gardener right yes because I know
+
+ align:start position:0%
+for a gardener right yes because I know
+ 
+
+ align:start position:0%
+for a gardener right yes because I know
+we'll use water to to to to sprinkle
+
+ align:start position:0%
+we'll use water to to to to sprinkle
+ 
+
+ align:start position:0%
+we'll use water to to to to sprinkle
+flowers without thinking about this the
+
+ align:start position:0%
+flowers without thinking about this the
+ 
+
+ align:start position:0%
+flowers without thinking about this the
+structure of water but if you chemist
+
+ align:start position:0%
+structure of water but if you chemist
+ 
+
+ align:start position:0%
+structure of water but if you chemist
+the word water as it's a meaning for you
+
+ align:start position:0%
+the word water as it's a meaning for you
+ 
+
+ align:start position:0%
+the word water as it's a meaning for you
+and you might want to define what you
+
+ align:start position:0%
+and you might want to define what you
+ 
+
+ align:start position:0%
+and you might want to define what you
+mean by water in that case I think in
+
+ align:start position:0%
+mean by water in that case I think in
+ 
+
+ align:start position:0%
+mean by water in that case I think in
+system in linguistics I think that you
+
+ align:start position:0%
+system in linguistics I think that you
+ 
+
+ align:start position:0%
+system in linguistics I think that you
+can you can say well I'm going to use
+
+ align:start position:0%
+can you can say well I'm going to use
+ 
+
+ align:start position:0%
+can you can say well I'm going to use
+Creole with that particular sense and
+
+ align:start position:0%
+Creole with that particular sense and
+ 
+
+ align:start position:0%
+Creole with that particular sense and
+for me it's just you know I'm going to
+
+ align:start position:0%
+for me it's just you know I'm going to
+ 
+
+ align:start position:0%
+for me it's just you know I'm going to
+point to these languages you know the
+
+ align:start position:0%
+point to these languages you know the
+ 
+
+ align:start position:0%
+point to these languages you know the
+people call them Creoles who speak them
+
+ align:start position:0%
+people call them Creoles who speak them
+ 
+
+ align:start position:0%
+people call them Creoles who speak them
+and I'm going to use the name that they
+
+ align:start position:0%
+and I'm going to use the name that they
+ 
+
+ align:start position:0%
+and I'm going to use the name that they
+use but I'm not going to assume that it
+
+ align:start position:0%
+use but I'm not going to assume that it
+ 
+
+ align:start position:0%
+use but I'm not going to assume that it
+means something similar for all Creole
+
+ align:start position:0%
+means something similar for all Creole
+ 
+
+ align:start position:0%
+means something similar for all Creole
+languages
\ No newline at end of file
diff --git a/TNDIZI1v4as.txt b/TNDIZI1v4as.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0b523e09a1ef09980f93b6104c6ed1fb1417c084
--- /dev/null
+++ b/TNDIZI1v4as.txt
@@ -0,0 +1,715 @@
+align:start position:0%
+ 
+what we need to understand is at a very
+
+ align:start position:0%
+what we need to understand is at a very
+ 
+
+ align:start position:0%
+what we need to understand is at a very
+basic level how the cells uh are being
+
+ align:start position:0%
+basic level how the cells uh are being
+ 
+
+ align:start position:0%
+basic level how the cells uh are being
+governed by their environment and how we
+
+ align:start position:0%
+governed by their environment and how we
+ 
+
+ align:start position:0%
+governed by their environment and how we
+can in turn engineer the environment of
+
+ align:start position:0%
+can in turn engineer the environment of
+ 
+
+ align:start position:0%
+can in turn engineer the environment of
+the cells to affect an outcome that we
+
+ align:start position:0%
+the cells to affect an outcome that we
+ 
+
+ align:start position:0%
+the cells to affect an outcome that we
+want so there's got to be a very basic
+
+ align:start position:0%
+want so there's got to be a very basic
+ 
+
+ align:start position:0%
+want so there's got to be a very basic
+marriage of biology and Engineering to
+
+ align:start position:0%
+marriage of biology and Engineering to
+ 
+
+ align:start position:0%
+marriage of biology and Engineering to
+go from the molecular level up to a
+
+ align:start position:0%
+go from the molecular level up to a
+ 
+
+ align:start position:0%
+go from the molecular level up to a
+device level that would go into patients
+
+ align:start position:0%
+device level that would go into patients
+ 
+
+ align:start position:0%
+device level that would go into patients
+we work with an orthopedic surgeon at
+
+ align:start position:0%
+we work with an orthopedic surgeon at
+ 
+
+ align:start position:0%
+we work with an orthopedic surgeon at
+the Cleveland Clinic Dr George mushler
+
+ align:start position:0%
+the Cleveland Clinic Dr George mushler
+ 
+
+ align:start position:0%
+the Cleveland Clinic Dr George mushler
+and he treats a lot of patients who get
+
+ align:start position:0%
+and he treats a lot of patients who get
+ 
+
+ align:start position:0%
+and he treats a lot of patients who get
+big tumors in their bones and so they
+
+ align:start position:0%
+big tumors in their bones and so they
+ 
+
+ align:start position:0%
+big tumors in their bones and so they
+have to cut out very large segments of
+
+ align:start position:0%
+have to cut out very large segments of
+ 
+
+ align:start position:0%
+have to cut out very large segments of
+bone and right now there isn't a very
+
+ align:start position:0%
+bone and right now there isn't a very
+ 
+
+ align:start position:0%
+bone and right now there isn't a very
+good replacement for the large defects
+
+ align:start position:0%
+good replacement for the large defects
+ 
+
+ align:start position:0%
+good replacement for the large defects
+that are taken out so right now patients
+
+ align:start position:0%
+that are taken out so right now patients
+ 
+
+ align:start position:0%
+that are taken out so right now patients
+go in and have their knee joint chopped
+
+ align:start position:0%
+go in and have their knee joint chopped
+ 
+
+ align:start position:0%
+go in and have their knee joint chopped
+off and a prosthetic replac you can make
+
+ align:start position:0%
+off and a prosthetic replac you can make
+ 
+
+ align:start position:0%
+off and a prosthetic replac you can make
+a prosthetic knee in fact a metal knee
+
+ align:start position:0%
+a prosthetic knee in fact a metal knee
+ 
+
+ align:start position:0%
+a prosthetic knee in fact a metal knee
+with this mold that was made by
+
+ align:start position:0%
+with this mold that was made by
+ 
+
+ align:start position:0%
+with this mold that was made by
+three-dimensional printing about 10
+
+ align:start position:0%
+three-dimensional printing about 10
+ 
+
+ align:start position:0%
+three-dimensional printing about 10
+years ago but what we want to do is
+
+ align:start position:0%
+years ago but what we want to do is
+ 
+
+ align:start position:0%
+years ago but what we want to do is
+instead of of chopping the knee off and
+
+ align:start position:0%
+instead of of chopping the knee off and
+ 
+
+ align:start position:0%
+instead of of chopping the knee off and
+replacing it we actually want to regrow
+
+ align:start position:0%
+replacing it we actually want to regrow
+ 
+
+ align:start position:0%
+replacing it we actually want to regrow
+the damaged tissue so now we're using
+
+ align:start position:0%
+the damaged tissue so now we're using
+ 
+
+ align:start position:0%
+the damaged tissue so now we're using
+three-dimensional printing to build
+
+ align:start position:0%
+three-dimensional printing to build
+ 
+
+ align:start position:0%
+three-dimensional printing to build
+build very sophisticated scaffolds that
+
+ align:start position:0%
+build very sophisticated scaffolds that
+ 
+
+ align:start position:0%
+build very sophisticated scaffolds that
+give instructions to the cells on how to
+
+ align:start position:0%
+give instructions to the cells on how to
+ 
+
+ align:start position:0%
+give instructions to the cells on how to
+regrow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bone with the three-dimensional printing
+
+ align:start position:0%
+bone with the three-dimensional printing
+ 
+
+ align:start position:0%
+bone with the three-dimensional printing
+process we build complicated objects as
+
+ align:start position:0%
+process we build complicated objects as
+ 
+
+ align:start position:0%
+process we build complicated objects as
+a series of very thin two-dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slices we start by spreading a powder
+
+ align:start position:0%
+slices we start by spreading a powder
+ 
+
+ align:start position:0%
+slices we start by spreading a powder
+into a very thin layer about 100 microns
+
+ align:start position:0%
+into a very thin layer about 100 microns
+ 
+
+ align:start position:0%
+into a very thin layer about 100 microns
+thick this particular powder is made out
+
+ align:start position:0%
+thick this particular powder is made out
+ 
+
+ align:start position:0%
+thick this particular powder is made out
+of a biodegradable surgical polymer then
+
+ align:start position:0%
+of a biodegradable surgical polymer then
+ 
+
+ align:start position:0%
+of a biodegradable surgical polymer then
+we put a stencil over the top that
+
+ align:start position:0%
+we put a stencil over the top that
+ 
+
+ align:start position:0%
+we put a stencil over the top that
+governs where liquid can be printed onto
+
+ align:start position:0%
+governs where liquid can be printed onto
+ 
+
+ align:start position:0%
+governs where liquid can be printed onto
+this layer then a print head rasters
+
+ align:start position:0%
+this layer then a print head rasters
+ 
+
+ align:start position:0%
+this layer then a print head rasters
+across the surface and prints very very
+
+ align:start position:0%
+across the surface and prints very very
+ 
+
+ align:start position:0%
+across the surface and prints very very
+fine tiny droplets of a liquid in this
+
+ align:start position:0%
+fine tiny droplets of a liquid in this
+ 
+
+ align:start position:0%
+fine tiny droplets of a liquid in this
+case chloroform to dissolve the
+
+ align:start position:0%
+case chloroform to dissolve the
+ 
+
+ align:start position:0%
+case chloroform to dissolve the
+particles of powder and bind them
+
+ align:start position:0%
+particles of powder and bind them
+ 
+
+ align:start position:0%
+particles of powder and bind them
+together we can also add lots of other
+
+ align:start position:0%
+together we can also add lots of other
+ 
+
+ align:start position:0%
+together we can also add lots of other
+things that might be growth factors or
+
+ align:start position:0%
+things that might be growth factors or
+ 
+
+ align:start position:0%
+things that might be growth factors or
+things that would mediate the biological
+
+ align:start position:0%
+things that would mediate the biological
+ 
+
+ align:start position:0%
+things that would mediate the biological
+response during this
+
+ align:start position:0%
+response during this
+ 
+
+ align:start position:0%
+response during this
+process in this particular build we have
+
+ align:start position:0%
+process in this particular build we have
+ 
+
+ align:start position:0%
+process in this particular build we have
+77 different layers at the end what we
+
+ align:start position:0%
+77 different layers at the end what we
+ 
+
+ align:start position:0%
+77 different layers at the end what we
+have is a scaffold for bone regeneration
+
+ align:start position:0%
+have is a scaffold for bone regeneration
+ 
+
+ align:start position:0%
+have is a scaffold for bone regeneration
+and we're in the stage right now where
+
+ align:start position:0%
+and we're in the stage right now where
+ 
+
+ align:start position:0%
+and we're in the stage right now where
+we're testing these scaffolds in a dog
+
+ align:start position:0%
+we're testing these scaffolds in a dog
+ 
+
+ align:start position:0%
+we're testing these scaffolds in a dog
+model with an orthopedic surgeon who's
+
+ align:start position:0%
+model with an orthopedic surgeon who's
+ 
+
+ align:start position:0%
+model with an orthopedic surgeon who's
+developing better ways to use marrow in
+
+ align:start position:0%
+developing better ways to use marrow in
+ 
+
+ align:start position:0%
+developing better ways to use marrow in
+his human patients the scaffold has a
+
+ align:start position:0%
+his human patients the scaffold has a
+ 
+
+ align:start position:0%
+his human patients the scaffold has a
+very very precise internal architecture
+
+ align:start position:0%
+very very precise internal architecture
+ 
+
+ align:start position:0%
+very very precise internal architecture
+so we have a design that lets us put the
+
+ align:start position:0%
+so we have a design that lets us put the
+ 
+
+ align:start position:0%
+so we have a design that lets us put the
+marrow in and have it go to very
+
+ align:start position:0%
+marrow in and have it go to very
+ 
+
+ align:start position:0%
+marrow in and have it go to very
+specific places we also can use the
+
+ align:start position:0%
+specific places we also can use the
+ 
+
+ align:start position:0%
+specific places we also can use the
+design to call blood vessels in from the
+
+ align:start position:0%
+design to call blood vessels in from the
+ 
+
+ align:start position:0%
+design to call blood vessels in from the
+surrounding tissue so there was an
+
+ align:start position:0%
+surrounding tissue so there was an
+ 
+
+ align:start position:0%
+surrounding tissue so there was an
+enormous amount of engineering that went
+
+ align:start position:0%
+enormous amount of engineering that went
+ 
+
+ align:start position:0%
+enormous amount of engineering that went
+into making a three-dimensional model
+
+ align:start position:0%
+into making a three-dimensional model
+ 
+
+ align:start position:0%
+into making a three-dimensional model
+before we ever turned on the
+
+ align:start position:0%
+before we ever turned on the
+ 
+
+ align:start position:0%
+before we ever turned on the
+three-dimensional printer and we started
+
+ align:start position:0%
+three-dimensional printer and we started
+ 
+
+ align:start position:0%
+three-dimensional printer and we started
+with thinking about how the bone will
+
+ align:start position:0%
+with thinking about how the bone will
+ 
+
+ align:start position:0%
+with thinking about how the bone will
+grow into this scaffold we're at a very
+
+ align:start position:0%
+grow into this scaffold we're at a very
+ 
+
+ align:start position:0%
+grow into this scaffold we're at a very
+exciting time in the science of biology
+
+ align:start position:0%
+exciting time in the science of biology
+ 
+
+ align:start position:0%
+exciting time in the science of biology
+you read about it almost every day in
+
+ align:start position:0%
+you read about it almost every day in
+ 
+
+ align:start position:0%
+you read about it almost every day in
+the newspaper the Human Genome Project
+
+ align:start position:0%
+the newspaper the Human Genome Project
+ 
+
+ align:start position:0%
+the newspaper the Human Genome Project
+proteomics things that make the front
+
+ align:start position:0%
+proteomics things that make the front
+ 
+
+ align:start position:0%
+proteomics things that make the front
+page make the business page but what it
+
+ align:start position:0%
+page make the business page but what it
+ 
+
+ align:start position:0%
+page make the business page but what it
+takes to translate discoveries and basic
+
+ align:start position:0%
+takes to translate discoveries and basic
+ 
+
+ align:start position:0%
+takes to translate discoveries and basic
+science including biology into things
+
+ align:start position:0%
+science including biology into things
+ 
+
+ align:start position:0%
+science including biology into things
+that people use is engineering so you
+
+ align:start position:0%
+that people use is engineering so you
+ 
+
+ align:start position:0%
+that people use is engineering so you
+have to be able to go from molecular to
+
+ align:start position:0%
+have to be able to go from molecular to
+ 
+
+ align:start position:0%
+have to be able to go from molecular to
+a systems level and understand a huge
+
+ align:start position:0%
+a systems level and understand a huge
+ 
+
+ align:start position:0%
+a systems level and understand a huge
+context of Link scales and time scales
+
+ align:start position:0%
+context of Link scales and time scales
+ 
+
+ align:start position:0%
+context of Link scales and time scales
+you require engineering at the same time
+
+ align:start position:0%
+you require engineering at the same time
+ 
+
+ align:start position:0%
+you require engineering at the same time
+to move a science forward you need new
+
+ align:start position:0%
+to move a science forward you need new
+ 
+
+ align:start position:0%
+to move a science forward you need new
+engineering tools and new ways of
+
+ align:start position:0%
+engineering tools and new ways of
+ 
+
+ align:start position:0%
+engineering tools and new ways of
+engineering analysis in that field and
+
+ align:start position:0%
+engineering analysis in that field and
+ 
+
+ align:start position:0%
+engineering analysis in that field and
+we're at a very exciting time because
+
+ align:start position:0%
+we're at a very exciting time because
+ 
+
+ align:start position:0%
+we're at a very exciting time because
+engineering is starting to both create
+
+ align:start position:0%
+engineering is starting to both create
+ 
+
+ align:start position:0%
+engineering is starting to both create
+products out of biology and feedback
+
+ align:start position:0%
+products out of biology and feedback
+ 
+
+ align:start position:0%
+products out of biology and feedback
+into biology to make postgenomic biology
+
+ align:start position:0%
+into biology to make postgenomic biology
+ 
+
+ align:start position:0%
+into biology to make postgenomic biology
+a much uh more pervasive and exciting
+
+ align:start position:0%
+a much uh more pervasive and exciting
+ 
+
+ align:start position:0%
+a much uh more pervasive and exciting
+discipline so MIT is really the center
+
+ align:start position:0%
+discipline so MIT is really the center
+ 
+
+ align:start position:0%
+discipline so MIT is really the center
+of the universe where this is happening
\ No newline at end of file
diff --git a/TtItFQTNMA4.txt b/TtItFQTNMA4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c8fc2bb16e3dc87576307b0a9f8dbb8ae90d323b
--- /dev/null
+++ b/TtItFQTNMA4.txt
@@ -0,0 +1,9323 @@
+align:start position:0%
+ 
+so you know you've gone through and
+
+ align:start position:0%
+so you know you've gone through and
+ 
+
+ align:start position:0%
+so you know you've gone through and
+you've designed your converter and
+
+ align:start position:0%
+you've designed your converter and
+ 
+
+ align:start position:0%
+you've designed your converter and
+you've worked out the magnetics and the
+
+ align:start position:0%
+you've worked out the magnetics and the
+ 
+
+ align:start position:0%
+you've worked out the magnetics and the
+controls and the circuit topology all
+
+ align:start position:0%
+controls and the circuit topology all
+ 
+
+ align:start position:0%
+controls and the circuit topology all
+that stuff and now it's time to kind of
+
+ align:start position:0%
+that stuff and now it's time to kind of
+ 
+
+ align:start position:0%
+that stuff and now it's time to kind of
+put it on a board or put it in a package
+
+ align:start position:0%
+put it on a board or put it in a package
+ 
+
+ align:start position:0%
+put it on a board or put it in a package
+system and get the performance you want
+
+ align:start position:0%
+system and get the performance you want
+ 
+
+ align:start position:0%
+system and get the performance you want
+and what you'll find is that depending
+
+ align:start position:0%
+and what you'll find is that depending
+ 
+
+ align:start position:0%
+and what you'll find is that depending
+ending upon how you do this the details
+
+ align:start position:0%
+ending upon how you do this the details
+ 
+
+ align:start position:0%
+ending upon how you do this the details
+of how you put your circuit together you
+
+ align:start position:0%
+of how you put your circuit together you
+ 
+
+ align:start position:0%
+of how you put your circuit together you
+can get great performance or terrible
+
+ align:start position:0%
+can get great performance or terrible
+ 
+
+ align:start position:0%
+can get great performance or terrible
+performance and so what I'd like to do
+
+ align:start position:0%
+performance and so what I'd like to do
+ 
+
+ align:start position:0%
+performance and so what I'd like to do
+is spend a little bit of time today just
+
+ align:start position:0%
+is spend a little bit of time today just
+ 
+
+ align:start position:0%
+is spend a little bit of time today just
+talking about pla practical
+
+ align:start position:0%
+talking about pla practical
+ 
+
+ align:start position:0%
+talking about pla practical
+implementation issues and this is
+
+ align:start position:0%
+implementation issues and this is
+ 
+
+ align:start position:0%
+implementation issues and this is
+something that I'm what I'm hoping is
+
+ align:start position:0%
+something that I'm what I'm hoping is
+ 
+
+ align:start position:0%
+something that I'm what I'm hoping is
+you'll keep this in the back of your
+
+ align:start position:0%
+you'll keep this in the back of your
+ 
+
+ align:start position:0%
+you'll keep this in the back of your
+mind until the day you're actually
+
+ align:start position:0%
+mind until the day you're actually
+ 
+
+ align:start position:0%
+mind until the day you're actually
+building one of these things and and
+
+ align:start position:0%
+building one of these things and and
+ 
+
+ align:start position:0%
+building one of these things and and
+maybe the first one you build might
+
+ align:start position:0%
+maybe the first one you build might
+ 
+
+ align:start position:0%
+maybe the first one you build might
+cause you some unhappiness and then
+
+ align:start position:0%
+cause you some unhappiness and then
+ 
+
+ align:start position:0%
+cause you some unhappiness and then
+you'll remember the lecture and look at
+
+ align:start position:0%
+you'll remember the lecture and look at
+ 
+
+ align:start position:0%
+you'll remember the lecture and look at
+it and say what what can I do to fix
+
+ align:start position:0%
+it and say what what can I do to fix
+ 
+
+ align:start position:0%
+it and say what what can I do to fix
+that or you can kind of remember it all
+
+ align:start position:0%
+that or you can kind of remember it all
+ 
+
+ align:start position:0%
+that or you can kind of remember it all
+now and then you'll never have this
+
+ align:start position:0%
+now and then you'll never have this
+ 
+
+ align:start position:0%
+now and then you'll never have this
+problem and I and I certainly found over
+
+ align:start position:0%
+problem and I and I certainly found over
+ 
+
+ align:start position:0%
+problem and I and I certainly found over
+time that the more attention you pay to
+
+ align:start position:0%
+time that the more attention you pay to
+ 
+
+ align:start position:0%
+time that the more attention you pay to
+this kind of thing I'm going to talk
+
+ align:start position:0%
+this kind of thing I'm going to talk
+ 
+
+ align:start position:0%
+this kind of thing I'm going to talk
+about right now in your first design
+
+ align:start position:0%
+about right now in your first design
+ 
+
+ align:start position:0%
+about right now in your first design
+like when you
+
+ align:start position:0%
+like when you
+ 
+
+ align:start position:0%
+like when you
+first build the system the less trouble
+
+ align:start position:0%
+first build the system the less trouble
+ 
+
+ align:start position:0%
+first build the system the less trouble
+you'll have with it getting it across
+
+ align:start position:0%
+you'll have with it getting it across
+ 
+
+ align:start position:0%
+you'll have with it getting it across
+the Finish
+
+ align:start position:0%
+the Finish
+ 
+
+ align:start position:0%
+the Finish
+Line okay so uh let's talk about our
+
+ align:start position:0%
+Line okay so uh let's talk about our
+ 
+
+ align:start position:0%
+Line okay so uh let's talk about our
+friendly neighborhood Hood Buck
+
+ align:start position:0%
+friendly neighborhood Hood Buck
+ 
+
+ align:start position:0%
+friendly neighborhood Hood Buck
+converter okay so suppose I have a buck
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converter and I'll let me assume I'm
+
+ align:start position:0%
+converter and I'll let me assume I'm
+ 
+
+ align:start position:0%
+converter and I'll let me assume I'm
+coming from some Source impedance that
+
+ align:start position:0%
+coming from some Source impedance that
+ 
+
+ align:start position:0%
+coming from some Source impedance that
+we don't have to worry about it but I
+
+ align:start position:0%
+we don't have to worry about it but I
+ 
+
+ align:start position:0%
+we don't have to worry about it but I
+have a capacitor
+
+ align:start position:0%
+have a capacitor
+ 
+
+ align:start position:0%
+have a capacitor
+here to take the high frequency input
+
+ align:start position:0%
+here to take the high frequency input
+ 
+
+ align:start position:0%
+here to take the high frequency input
+Ripple Cur and to hold the voltage
+
+ align:start position:0%
+Ripple Cur and to hold the voltage
+ 
+
+ align:start position:0%
+Ripple Cur and to hold the voltage
+steady and I'll have a switch and I'll
+
+ align:start position:0%
+steady and I'll have a switch and I'll
+ 
+
+ align:start position:0%
+steady and I'll have a switch and I'll
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+diode and my load inductor I mean my
+
+ align:start position:0%
+diode and my load inductor I mean my
+ 
+
+ align:start position:0%
+diode and my load inductor I mean my
+output inductor and my
+
+ align:start position:0%
+output inductor and my
+ 
+
+ align:start position:0%
+output inductor and my
+load okay
+
+ align:start position:0%
+load okay
+ 
+
+ align:start position:0%
+load okay
+as far as the switching of this
+
+ align:start position:0%
+as far as the switching of this
+ 
+
+ align:start position:0%
+as far as the switching of this
+circuit is concerned right when the
+
+ align:start position:0%
+circuit is concerned right when the
+ 
+
+ align:start position:0%
+circuit is concerned right when the
+diode is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the path through the circuits like
+
+ align:start position:0%
+on the path through the circuits like
+ 
+
+ align:start position:0%
+on the path through the circuits like
+this when I turn the diode off and the
+
+ align:start position:0%
+this when I turn the diode off and the
+ 
+
+ align:start position:0%
+this when I turn the diode off and the
+switch turns
+
+ align:start position:0%
+switch turns
+ 
+
+ align:start position:0%
+switch turns
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+essentially I'm commutating to this
+
+ align:start position:0%
+essentially I'm commutating to this
+ 
+
+ align:start position:0%
+essentially I'm commutating to this
+Branch right so I have a commutation
+
+ align:start position:0%
+Branch right so I have a commutation
+ 
+
+ align:start position:0%
+Branch right so I have a commutation
+between this branch and this branch of
+
+ align:start position:0%
+between this branch and this branch of
+ 
+
+ align:start position:0%
+between this branch and this branch of
+the circuit and I'm assuming all the
+
+ align:start position:0%
+the circuit and I'm assuming all the
+ 
+
+ align:start position:0%
+the circuit and I'm assuming all the
+high frequency currents going through
+
+ align:start position:0%
+high frequency currents going through
+ 
+
+ align:start position:0%
+high frequency currents going through
+the input capacitor okay likewise when
+
+ align:start position:0%
+the input capacitor okay likewise when
+ 
+
+ align:start position:0%
+the input capacitor okay likewise when
+the switch is on I'm carrying it this
+
+ align:start position:0%
+the switch is on I'm carrying it this
+ 
+
+ align:start position:0%
+the switch is on I'm carrying it this
+way and when I turn the switch
+
+ align:start position:0%
+way and when I turn the switch
+ 
+
+ align:start position:0%
+way and when I turn the switch
+off I essentially from an AC perspective
+
+ align:start position:0%
+off I essentially from an AC perspective
+ 
+
+ align:start position:0%
+off I essentially from an AC perspective
+I have a loop going this way so
+
+ align:start position:0%
+I have a loop going this way so
+ 
+
+ align:start position:0%
+I have a loop going this way so
+essentially what dominates The High
+
+ align:start position:0%
+essentially what dominates The High
+ 
+
+ align:start position:0%
+essentially what dominates The High
+Frequency behavior in terms of high
+
+ align:start position:0%
+Frequency behavior in terms of high
+ 
+
+ align:start position:0%
+Frequency behavior in terms of high
+currents is this switching Loop here
+
+ align:start position:0%
+currents is this switching Loop here
+ 
+
+ align:start position:0%
+currents is this switching Loop here
+right you can imagine that there's a
+
+ align:start position:0%
+right you can imagine that there's a
+ 
+
+ align:start position:0%
+right you can imagine that there's a
+large AC current running around this
+
+ align:start position:0%
+large AC current running around this
+ 
+
+ align:start position:0%
+large AC current running around this
+switching
+
+ align:start position:0%
+switching
+ 
+
+ align:start position:0%
+switching
+Loop okay this branch has almost
+
+ align:start position:0%
+Loop okay this branch has almost
+ 
+
+ align:start position:0%
+Loop okay this branch has almost
+constant current if you've done a good
+
+ align:start position:0%
+constant current if you've done a good
+ 
+
+ align:start position:0%
+constant current if you've done a good
+job of filtering this input will have an
+
+ align:start position:0%
+job of filtering this input will have an
+ 
+
+ align:start position:0%
+job of filtering this input will have an
+almost constant current but this is
+
+ align:start position:0%
+almost constant current but this is
+ 
+
+ align:start position:0%
+almost constant current but this is
+where the big AC current is so the first
+
+ align:start position:0%
+where the big AC current is so the first
+ 
+
+ align:start position:0%
+where the big AC current is so the first
+thing I think about when I'm putting
+
+ align:start position:0%
+thing I think about when I'm putting
+ 
+
+ align:start position:0%
+thing I think about when I'm putting
+together my circuit is how do I minimize
+
+ align:start position:0%
+together my circuit is how do I minimize
+ 
+
+ align:start position:0%
+together my circuit is how do I minimize
+that Loop in terms of its
+
+ align:start position:0%
+that Loop in terms of its
+ 
+
+ align:start position:0%
+that Loop in terms of its
+inductance
+
+ align:start position:0%
+inductance
+ 
+
+ align:start position:0%
+inductance
+okay and so um one of the things we're
+
+ align:start position:0%
+okay and so um one of the things we're
+ 
+
+ align:start position:0%
+okay and so um one of the things we're
+going to talk about today is
+
+ align:start position:0%
+going to talk about today is
+ 
+
+ align:start position:0%
+going to talk about today is
+minimizing Loop inductance and you got
+
+ align:start position:0%
+minimizing Loop inductance and you got
+ 
+
+ align:start position:0%
+minimizing Loop inductance and you got
+to the first thing you want to do when
+
+ align:start position:0%
+to the first thing you want to do when
+ 
+
+ align:start position:0%
+to the first thing you want to do when
+you look at any converter is which Loops
+
+ align:start position:0%
+you look at any converter is which Loops
+ 
+
+ align:start position:0%
+you look at any converter is which Loops
+do I care about right uh and this is the
+
+ align:start position:0%
+do I care about right uh and this is the
+ 
+
+ align:start position:0%
+do I care about right uh and this is the
+key Loop so the first thing I'm looking
+
+ align:start position:0%
+key Loop so the first thing I'm looking
+ 
+
+ align:start position:0%
+key Loop so the first thing I'm looking
+at when I'm laying out my power stage is
+
+ align:start position:0%
+at when I'm laying out my power stage is
+ 
+
+ align:start position:0%
+at when I'm laying out my power stage is
+you know what's my diode what's my
+
+ align:start position:0%
+you know what's my diode what's my
+ 
+
+ align:start position:0%
+you know what's my diode what's my
+capacitor I sorry what's my diode what's
+
+ align:start position:0%
+capacitor I sorry what's my diode what's
+ 
+
+ align:start position:0%
+capacitor I sorry what's my diode what's
+my switch here's the capacitor how am I
+
+ align:start position:0%
+my switch here's the capacitor how am I
+ 
+
+ align:start position:0%
+my switch here's the capacitor how am I
+going to close this Loop to minimize
+
+ align:start position:0%
+going to close this Loop to minimize
+ 
+
+ align:start position:0%
+going to close this Loop to minimize
+that and we've talked about how
+
+ align:start position:0%
+that and we've talked about how
+ 
+
+ align:start position:0%
+that and we've talked about how
+electromagnetic interference from that
+
+ align:start position:0%
+electromagnetic interference from that
+ 
+
+ align:start position:0%
+electromagnetic interference from that
+Loop can couple into other
+
+ align:start position:0%
+Loop can couple into other
+ 
+
+ align:start position:0%
+Loop can couple into other
+systems we'll talk about that in more
+
+ align:start position:0%
+systems we'll talk about that in more
+ 
+
+ align:start position:0%
+systems we'll talk about that in more
+detail um we should also uh
+
+ align:start position:0%
+detail um we should also uh
+ 
+
+ align:start position:0%
+detail um we should also uh
+recognize that where is the high
+
+ align:start position:0%
+recognize that where is the high
+ 
+
+ align:start position:0%
+recognize that where is the high
+switching node in this
+
+ align:start position:0%
+switching node in this
+ 
+
+ align:start position:0%
+switching node in this
+circuit
+
+ align:start position:0%
+circuit
+ 
+
+ align:start position:0%
+circuit
+okay this
+
+ align:start position:0%
+okay this
+ 
+
+ align:start position:0%
+okay this
+node has a big Square wave on it with
+
+ align:start position:0%
+node has a big Square wave on it with
+ 
+
+ align:start position:0%
+node has a big Square wave on it with
+respect to ground
+
+ align:start position:0%
+respect to ground
+ 
+
+ align:start position:0%
+respect to ground
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so this node flying up and down can
+
+ align:start position:0%
+so this node flying up and down can
+ 
+
+ align:start position:0%
+so this node flying up and down can
+inject charge into other places in the
+
+ align:start position:0%
+inject charge into other places in the
+ 
+
+ align:start position:0%
+inject charge into other places in the
+circuit and cause noise so making this
+
+ align:start position:0%
+circuit and cause noise so making this
+ 
+
+ align:start position:0%
+circuit and cause noise so making this
+node this flying node bigger than I need
+
+ align:start position:0%
+node this flying node bigger than I need
+ 
+
+ align:start position:0%
+node this flying node bigger than I need
+it to be is kind of a bad thing right
+
+ align:start position:0%
+it to be is kind of a bad thing right
+ 
+
+ align:start position:0%
+it to be is kind of a bad thing right
+because that can capacitively inject
+
+ align:start position:0%
+because that can capacitively inject
+ 
+
+ align:start position:0%
+because that can capacitively inject
+noise into other places in the system
+
+ align:start position:0%
+noise into other places in the system
+ 
+
+ align:start position:0%
+noise into other places in the system
+okay so not only going to think about
+
+ align:start position:0%
+okay so not only going to think about
+ 
+
+ align:start position:0%
+okay so not only going to think about
+how to make this tight I also want to
+
+ align:start position:0%
+how to make this tight I also want to
+ 
+
+ align:start position:0%
+how to make this tight I also want to
+think about you know what's the size of
+
+ align:start position:0%
+think about you know what's the size of
+ 
+
+ align:start position:0%
+think about you know what's the size of
+this flying node uh and you know if if I
+
+ align:start position:0%
+this flying node uh and you know if if I
+ 
+
+ align:start position:0%
+this flying node uh and you know if if I
+imag imagine that I you know maybe I
+
+ align:start position:0%
+imag imagine that I you know maybe I
+ 
+
+ align:start position:0%
+imag imagine that I you know maybe I
+could place
+
+ align:start position:0%
+could place
+ 
+
+ align:start position:0%
+could place
+my you know maybe I could place my
+
+ align:start position:0%
+my you know maybe I could place my
+ 
+
+ align:start position:0%
+my you know maybe I could place my
+inductor over to the right and have a
+
+ align:start position:0%
+inductor over to the right and have a
+ 
+
+ align:start position:0%
+inductor over to the right and have a
+long lead going between the the switch
+
+ align:start position:0%
+long lead going between the the switch
+ 
+
+ align:start position:0%
+long lead going between the the switch
+and diode and the inductor or I could
+
+ align:start position:0%
+and diode and the inductor or I could
+ 
+
+ align:start position:0%
+and diode and the inductor or I could
+place you know if if this is my switch
+
+ align:start position:0%
+place you know if if this is my switch
+ 
+
+ align:start position:0%
+place you know if if this is my switch
+and and diode node or I could put the
+
+ align:start position:0%
+and and diode node or I could put the
+ 
+
+ align:start position:0%
+and and diode node or I could put the
+inductor here and then have a long lead
+
+ align:start position:0%
+inductor here and then have a long lead
+ 
+
+ align:start position:0%
+inductor here and then have a long lead
+going to the output
+
+ align:start position:0%
+going to the output
+ 
+
+ align:start position:0%
+going to the output
+capacitor right these two things seem
+
+ align:start position:0%
+capacitor right these two things seem
+ 
+
+ align:start position:0%
+capacitor right these two things seem
+the same because you know the lead's
+
+ align:start position:0%
+the same because you know the lead's
+ 
+
+ align:start position:0%
+the same because you know the lead's
+either in series with the inductor one
+
+ align:start position:0%
+either in series with the inductor one
+ 
+
+ align:start position:0%
+either in series with the inductor one
+side or another but this node is lying
+
+ align:start position:0%
+side or another but this node is lying
+ 
+
+ align:start position:0%
+side or another but this node is lying
+up and down and this node is about fixed
+
+ align:start position:0%
+up and down and this node is about fixed
+ 
+
+ align:start position:0%
+up and down and this node is about fixed
+right so in voltage so to the extent
+
+ align:start position:0%
+right so in voltage so to the extent
+ 
+
+ align:start position:0%
+right so in voltage so to the extent
+that this is forming a
+
+ align:start position:0%
+that this is forming a
+ 
+
+ align:start position:0%
+that this is forming a
+capacitor plate to other stuff and this
+
+ align:start position:0%
+capacitor plate to other stuff and this
+ 
+
+ align:start position:0%
+capacitor plate to other stuff and this
+is forming a capacitor plate to other
+
+ align:start position:0%
+is forming a capacitor plate to other
+ 
+
+ align:start position:0%
+is forming a capacitor plate to other
+stuff this is much worse than this
+
+ align:start position:0%
+stuff this is much worse than this
+ 
+
+ align:start position:0%
+stuff this is much worse than this
+one right so you got to think about both
+
+ align:start position:0%
+one right so you got to think about both
+ 
+
+ align:start position:0%
+one right so you got to think about both
+this Loop and this flying node in the
+
+ align:start position:0%
+this Loop and this flying node in the
+ 
+
+ align:start position:0%
+this Loop and this flying node in the
+buck converter in a boost converter it
+
+ align:start position:0%
+buck converter in a boost converter it
+ 
+
+ align:start position:0%
+buck converter in a boost converter it
+would be a different Loop in node or in
+
+ align:start position:0%
+would be a different Loop in node or in
+ 
+
+ align:start position:0%
+would be a different Loop in node or in
+some other converter would be different
+
+ align:start position:0%
+some other converter would be different
+ 
+
+ align:start position:0%
+some other converter would be different
+but that's the first thing you want to
+
+ align:start position:0%
+but that's the first thing you want to
+ 
+
+ align:start position:0%
+but that's the first thing you want to
+think about and it can really have have
+
+ align:start position:0%
+think about and it can really have have
+ 
+
+ align:start position:0%
+think about and it can really have have
+a big impact on performance and just to
+
+ align:start position:0%
+a big impact on performance and just to
+ 
+
+ align:start position:0%
+a big impact on performance and just to
+illustrate that um Rafa has actually set
+
+ align:start position:0%
+illustrate that um Rafa has actually set
+ 
+
+ align:start position:0%
+illustrate that um Rafa has actually set
+up a buck
+
+ align:start position:0%
+up a buck
+ 
+
+ align:start position:0%
+up a buck
+converter and I'm going to let her show
+
+ align:start position:0%
+converter and I'm going to let her show
+ 
+
+ align:start position:0%
+converter and I'm going to let her show
+you uh s sort of uh four
+
+ align:start position:0%
+you uh s sort of uh four
+ 
+
+ align:start position:0%
+you uh s sort of uh four
+cases okay why don't you tell me and
+
+ align:start position:0%
+cases okay why don't you tell me and
+ 
+
+ align:start position:0%
+cases okay why don't you tell me and
+since I have the mic which which case
+
+ align:start position:0%
+since I have the mic which which case
+ 
+
+ align:start position:0%
+since I have the mic which which case
+you going to do first uh we can start
+
+ align:start position:0%
+you going to do first uh we can start
+ 
+
+ align:start position:0%
+you going to do first uh we can start
+with the war one
+
+ align:start position:0%
+with the war one
+ 
+
+ align:start position:0%
+with the war one
+okay yeah so suppose I did a bad thing
+
+ align:start position:0%
+okay yeah so suppose I did a bad thing
+ 
+
+ align:start position:0%
+okay yeah so suppose I did a bad thing
+in two Dimensions I made this Loop
+
+ align:start position:0%
+in two Dimensions I made this Loop
+ 
+
+ align:start position:0%
+in two Dimensions I made this Loop
+terrible and I have excess area on this
+
+ align:start position:0%
+terrible and I have excess area on this
+ 
+
+ align:start position:0%
+terrible and I have excess area on this
+switching node right so so I'm just
+
+ align:start position:0%
+switching node right so so I'm just
+ 
+
+ align:start position:0%
+switching node right so so I'm just
+doing a bad job of laying out my circuit
+
+ align:start position:0%
+doing a bad job of laying out my circuit
+ 
+
+ align:start position:0%
+doing a bad job of laying out my circuit
+what would that waveform look like okay
+
+ align:start position:0%
+what would that waveform look like okay
+ 
+
+ align:start position:0%
+what would that waveform look like okay
+so we can see the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and what you see is a whole pile of
+
+ align:start position:0%
+one and what you see is a whole pile of
+ 
+
+ align:start position:0%
+one and what you see is a whole pile of
+ringing in this circuit right so what
+
+ align:start position:0%
+ringing in this circuit right so what
+ 
+
+ align:start position:0%
+ringing in this circuit right so what
+she's looking at is you're you're
+
+ align:start position:0%
+she's looking at is you're you're
+ 
+
+ align:start position:0%
+she's looking at is you're you're
+looking at the vol at the switching node
+
+ align:start position:0%
+looking at the vol at the switching node
+ 
+
+ align:start position:0%
+looking at the vol at the switching node
+right that's right yeah so it's this
+
+ align:start position:0%
+right that's right yeah so it's this
+ 
+
+ align:start position:0%
+right that's right yeah so it's this
+voltage we're looking at this switching
+
+ align:start position:0%
+voltage we're looking at this switching
+ 
+
+ align:start position:0%
+voltage we're looking at this switching
+node voltage and what you see is there's
+
+ align:start position:0%
+node voltage and what you see is there's
+ 
+
+ align:start position:0%
+node voltage and what you see is there's
+all kinds of excess ringing there why
+
+ align:start position:0%
+all kinds of excess ringing there why
+ 
+
+ align:start position:0%
+all kinds of excess ringing there why
+because there's this inductance in this
+
+ align:start position:0%
+because there's this inductance in this
+ 
+
+ align:start position:0%
+because there's this inductance in this
+Loop which is ringing with things and
+
+ align:start position:0%
+Loop which is ringing with things and
+ 
+
+ align:start position:0%
+Loop which is ringing with things and
+then it's settling down and you know
+
+ align:start position:0%
+then it's settling down and you know
+ 
+
+ align:start position:0%
+then it's settling down and you know
+that's pretty bad right because that can
+
+ align:start position:0%
+that's pretty bad right because that can
+ 
+
+ align:start position:0%
+that's pretty bad right because that can
+inject noise elsewhere in the circuit it
+
+ align:start position:0%
+inject noise elsewhere in the circuit it
+ 
+
+ align:start position:0%
+inject noise elsewhere in the circuit it
+can even interfere with the circuit
+
+ align:start position:0%
+can even interfere with the circuit
+ 
+
+ align:start position:0%
+can even interfere with the circuit
+itself so you'll see a lot of people
+
+ align:start position:0%
+itself so you'll see a lot of people
+ 
+
+ align:start position:0%
+itself so you'll see a lot of people
+have problems that you know they build
+
+ align:start position:0%
+have problems that you know they build
+ 
+
+ align:start position:0%
+have problems that you know they build
+their circuit and maybe it works at
+
+ align:start position:0%
+their circuit and maybe it works at
+ 
+
+ align:start position:0%
+their circuit and maybe it works at
+super low voltage to the poers and they
+
+ align:start position:0%
+super low voltage to the poers and they
+ 
+
+ align:start position:0%
+super low voltage to the poers and they
+turn it off and everything starts
+
+ align:start position:0%
+turn it off and everything starts
+ 
+
+ align:start position:0%
+turn it off and everything starts
+misoperation and doing funny things it's
+
+ align:start position:0%
+misoperation and doing funny things it's
+ 
+
+ align:start position:0%
+misoperation and doing funny things it's
+because you're having interference with
+
+ align:start position:0%
+because you're having interference with
+ 
+
+ align:start position:0%
+because you're having interference with
+your own circuit right so not only can
+
+ align:start position:0%
+your own circuit right so not only can
+ 
+
+ align:start position:0%
+your own circuit right so not only can
+you interfere with the world you can
+
+ align:start position:0%
+you interfere with the world you can
+ 
+
+ align:start position:0%
+you interfere with the world you can
+interfere with yourself okay now that's
+
+ align:start position:0%
+interfere with yourself okay now that's
+ 
+
+ align:start position:0%
+interfere with yourself okay now that's
+the result of sort of two bad things
+
+ align:start position:0%
+the result of sort of two bad things
+ 
+
+ align:start position:0%
+the result of sort of two bad things
+which which one are we going to look at
+
+ align:start position:0%
+which which one are we going to look at
+ 
+
+ align:start position:0%
+which which one are we going to look at
+next we're going to move the capacitor
+
+ align:start position:0%
+next we're going to move the capacitor
+ 
+
+ align:start position:0%
+next we're going to move the capacitor
+closer to the
+
+ align:start position:0%
+closer to the
+ 
+
+ align:start position:0%
+closer to the
+switch we're going to have a bad
+
+ align:start position:0%
+switch we're going to have a bad
+ 
+
+ align:start position:0%
+switch we're going to have a bad
+switching Loop but small
+
+ align:start position:0%
+switching Loop but small
+ 
+
+ align:start position:0%
+switching Loop but small
+smaller right so we're gonna reduce the
+
+ align:start position:0%
+smaller right so we're gonna reduce the
+ 
+
+ align:start position:0%
+smaller right so we're gonna reduce the
+capacitance here we're going to improve
+
+ align:start position:0%
+capacitance here we're going to improve
+ 
+
+ align:start position:0%
+capacitance here we're going to improve
+one aspect of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's much more pleasant in
+
+ align:start position:0%
+okay so that's much more pleasant in
+ 
+
+ align:start position:0%
+okay so that's much more pleasant in
+terms of the amount of switching it's
+
+ align:start position:0%
+terms of the amount of switching it's
+ 
+
+ align:start position:0%
+terms of the amount of switching it's
+you can still you can see it's still
+
+ align:start position:0%
+you can still you can see it's still
+ 
+
+ align:start position:0%
+you can still you can see it's still
+noisy stuff still going on but not
+
+ align:start position:0%
+noisy stuff still going on but not
+ 
+
+ align:start position:0%
+noisy stuff still going on but not
+nearly as bad as when I was really
+
+ align:start position:0%
+nearly as bad as when I was really
+ 
+
+ align:start position:0%
+nearly as bad as when I was really
+sloppy about about both the loop
+
+ align:start position:0%
+sloppy about about both the loop
+ 
+
+ align:start position:0%
+sloppy about about both the loop
+inductance and the node capacitance now
+
+ align:start position:0%
+inductance and the node capacitance now
+ 
+
+ align:start position:0%
+inductance and the node capacitance now
+we'll do the case where we have um yeah
+
+ align:start position:0%
+we'll do the case where we have um yeah
+ 
+
+ align:start position:0%
+we'll do the case where we have um yeah
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the capacitor is bad but I still have a
+
+ align:start position:0%
+the capacitor is bad but I still have a
+ 
+
+ align:start position:0%
+the capacitor is bad but I still have a
+big switching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Loop and again yeah you got some ring
+
+ align:start position:0%
+Loop and again yeah you got some ring
+ 
+
+ align:start position:0%
+Loop and again yeah you got some ring
+you might not like that you might start
+
+ align:start position:0%
+you might not like that you might start
+ 
+
+ align:start position:0%
+you might not like that you might start
+thinking about putting snubbers in there
+
+ align:start position:0%
+thinking about putting snubbers in there
+ 
+
+ align:start position:0%
+thinking about putting snubbers in there
+but it's not as bad as that first case
+
+ align:start position:0%
+but it's not as bad as that first case
+ 
+
+ align:start position:0%
+but it's not as bad as that first case
+and then the last case is when you know
+
+ align:start position:0%
+and then the last case is when you know
+ 
+
+ align:start position:0%
+and then the last case is when you know
+perhaps better attention was paid to
+
+ align:start position:0%
+perhaps better attention was paid to
+ 
+
+ align:start position:0%
+perhaps better attention was paid to
+everything and this is you know sort of
+
+ align:start position:0%
+everything and this is you know sort of
+ 
+
+ align:start position:0%
+everything and this is you know sort of
+I don't want to say the ideal case but
+
+ align:start position:0%
+I don't want to say the ideal case but
+ 
+
+ align:start position:0%
+I don't want to say the ideal case but
+this is when attention was paid to the
+
+ align:start position:0%
+this is when attention was paid to the
+ 
+
+ align:start position:0%
+this is when attention was paid to the
+layout of the circuit so if you look at
+
+ align:start position:0%
+layout of the circuit so if you look at
+ 
+
+ align:start position:0%
+layout of the circuit so if you look at
+the two ends of that Spectrum you can
+
+ align:start position:0%
+the two ends of that Spectrum you can
+ 
+
+ align:start position:0%
+the two ends of that Spectrum you can
+see there's a pretty darn big difference
+
+ align:start position:0%
+see there's a pretty darn big difference
+ 
+
+ align:start position:0%
+see there's a pretty darn big difference
+between the actual performance of the
+
+ align:start position:0%
+between the actual performance of the
+ 
+
+ align:start position:0%
+between the actual performance of the
+converter right now this isn't a low
+
+ align:start position:0%
+converter right now this isn't a low
+ 
+
+ align:start position:0%
+converter right now this isn't a low
+voltage kind of low power thing that you
+
+ align:start position:0%
+voltage kind of low power thing that you
+ 
+
+ align:start position:0%
+voltage kind of low power thing that you
+know it's not that bad but when you're
+
+ align:start position:0%
+know it's not that bad but when you're
+ 
+
+ align:start position:0%
+know it's not that bad but when you're
+when you're operating at hundreds of
+
+ align:start position:0%
+when you're operating at hundreds of
+ 
+
+ align:start position:0%
+when you're operating at hundreds of
+volts and hundreds of amps
+
+ align:start position:0%
+volts and hundreds of amps
+ 
+
+ align:start position:0%
+volts and hundreds of amps
+these things get really really bad okay
+
+ align:start position:0%
+these things get really really bad okay
+ 
+
+ align:start position:0%
+these things get really really bad okay
+so you really want to think about layout
+
+ align:start position:0%
+so you really want to think about layout
+ 
+
+ align:start position:0%
+so you really want to think about layout
+so thanks very
+
+ align:start position:0%
+so thanks very
+ 
+
+ align:start position:0%
+so thanks very
+much so suppose I want to think
+
+ align:start position:0%
+much so suppose I want to think
+ 
+
+ align:start position:0%
+much so suppose I want to think
+about producing the inductance of my
+
+ align:start position:0%
+about producing the inductance of my
+ 
+
+ align:start position:0%
+about producing the inductance of my
+Loop
+
+ align:start position:0%
+Loop
+ 
+
+ align:start position:0%
+Loop
+okay what does that mean in practice
+
+ align:start position:0%
+okay what does that mean in practice
+ 
+
+ align:start position:0%
+okay what does that mean in practice
+well it means that I certainly want to
+
+ align:start position:0%
+well it means that I certainly want to
+ 
+
+ align:start position:0%
+well it means that I certainly want to
+uh place these three components close
+
+ align:start position:0%
+uh place these three components close
+ 
+
+ align:start position:0%
+uh place these three components close
+together okay okay such that if I think
+
+ align:start position:0%
+together okay okay such that if I think
+ 
+
+ align:start position:0%
+together okay okay such that if I think
+about the current flowing around in this
+
+ align:start position:0%
+about the current flowing around in this
+ 
+
+ align:start position:0%
+about the current flowing around in this
+Loop it forms a very tight area Okay so
+
+ align:start position:0%
+Loop it forms a very tight area Okay so
+ 
+
+ align:start position:0%
+Loop it forms a very tight area Okay so
+that's one way to think about it okay
+
+ align:start position:0%
+that's one way to think about it okay
+ 
+
+ align:start position:0%
+that's one way to think about it okay
+how if I imagine the current AC current
+
+ align:start position:0%
+how if I imagine the current AC current
+ 
+
+ align:start position:0%
+how if I imagine the current AC current
+circulating this Loop how much flux is
+
+ align:start position:0%
+circulating this Loop how much flux is
+ 
+
+ align:start position:0%
+circulating this Loop how much flux is
+it throwing out in the world and that
+
+ align:start position:0%
+it throwing out in the world and that
+ 
+
+ align:start position:0%
+it throwing out in the world and that
+relates to the
+
+ align:start position:0%
+relates to the
+ 
+
+ align:start position:0%
+relates to the
+inductance sometimes of course I have to
+
+ align:start position:0%
+inductance sometimes of course I have to
+ 
+
+ align:start position:0%
+inductance sometimes of course I have to
+put
+
+ align:start position:0%
+put
+ 
+
+ align:start position:0%
+put
+components at a distance there there's
+
+ align:start position:0%
+components at a distance there there's
+ 
+
+ align:start position:0%
+components at a distance there there's
+some inconnect between them that I have
+
+ align:start position:0%
+some inconnect between them that I have
+ 
+
+ align:start position:0%
+some inconnect between them that I have
+to live with right why don't we think
+
+ align:start position:0%
+to live with right why don't we think
+ 
+
+ align:start position:0%
+to live with right why don't we think
+about what is the
+
+ align:start position:0%
+about what is the
+ 
+
+ align:start position:0%
+about what is the
+um what is the parasitic of a pair of
+
+ align:start position:0%
+um what is the parasitic of a pair of
+ 
+
+ align:start position:0%
+um what is the parasitic of a pair of
+wires or a pair of traces
+
+ align:start position:0%
+wires or a pair of traces
+ 
+
+ align:start position:0%
+wires or a pair of traces
+interconnecting something okay so let's
+
+ align:start position:0%
+interconnecting something okay so let's
+ 
+
+ align:start position:0%
+interconnecting something okay so let's
+think about this
+
+ align:start position:0%
+think about this
+ 
+
+ align:start position:0%
+think about this
+example suppose I have two
+
+ align:start position:0%
+example suppose I have two
+ 
+
+ align:start position:0%
+example suppose I have two
+traces
+
+ align:start position:0%
+traces
+ 
+
+ align:start position:0%
+traces
+okay um here's the first
+
+ align:start position:0%
+okay um here's the first
+ 
+
+ align:start position:0%
+okay um here's the first
+trace and I'm going to carry current
+
+ align:start position:0%
+trace and I'm going to carry current
+ 
+
+ align:start position:0%
+trace and I'm going to carry current
+down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and then I'm going to return the
+
+ align:start position:0%
+it and then I'm going to return the
+ 
+
+ align:start position:0%
+it and then I'm going to return the
+current somewhere else so let me return
+
+ align:start position:0%
+current somewhere else so let me return
+ 
+
+ align:start position:0%
+current somewhere else so let me return
+it in a trace that's right under Neath
+
+ align:start position:0%
+it in a trace that's right under Neath
+ 
+
+ align:start position:0%
+it in a trace that's right under Neath
+it like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and um you know I will close off the end
+
+ align:start position:0%
+and um you know I will close off the end
+ 
+
+ align:start position:0%
+and um you know I will close off the end
+I'm going to drive current in one return
+
+ align:start position:0%
+I'm going to drive current in one return
+ 
+
+ align:start position:0%
+I'm going to drive current in one return
+it on the other and let's say it's got a
+
+ align:start position:0%
+it on the other and let's say it's got a
+ 
+
+ align:start position:0%
+it on the other and let's say it's got a
+trace of a width
+
+ align:start position:0%
+trace of a width
+ 
+
+ align:start position:0%
+trace of a width
+w a length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l and a spacing that I'm going to call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta okay
+
+ align:start position:0%
+Delta okay
+ 
+
+ align:start position:0%
+Delta okay
+what would be the inductance of that
+
+ align:start position:0%
+what would be the inductance of that
+ 
+
+ align:start position:0%
+what would be the inductance of that
+Loop where I'm going to carry current
+
+ align:start position:0%
+Loop where I'm going to carry current
+ 
+
+ align:start position:0%
+Loop where I'm going to carry current
+down current down one side and back the
+
+ align:start position:0%
+down current down one side and back the
+ 
+
+ align:start position:0%
+down current down one side and back the
+other okay and if I look at this end
+
+ align:start position:0%
+other okay and if I look at this end
+ 
+
+ align:start position:0%
+other okay and if I look at this end
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+right maybe I'm going to put current in
+
+ align:start position:0%
+right maybe I'm going to put current in
+ 
+
+ align:start position:0%
+right maybe I'm going to put current in
+one end or maybe current will go in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here right goes down the conductor comes
+
+ align:start position:0%
+here right goes down the conductor comes
+ 
+
+ align:start position:0%
+here right goes down the conductor comes
+back the other side coming out
+
+ align:start position:0%
+back the other side coming out
+ 
+
+ align:start position:0%
+back the other side coming out
+here okay and from from that what I'm
+
+ align:start position:0%
+here okay and from from that what I'm
+ 
+
+ align:start position:0%
+here okay and from from that what I'm
+going to get is some magnetic fields and
+
+ align:start position:0%
+going to get is some magnetic fields and
+ 
+
+ align:start position:0%
+going to get is some magnetic fields and
+they're going to be very
+
+ align:start position:0%
+they're going to be very
+ 
+
+ align:start position:0%
+they're going to be very
+concentrated in between the traces I'm
+
+ align:start position:0%
+concentrated in between the traces I'm
+ 
+
+ align:start position:0%
+concentrated in between the traces I'm
+assuming these traces are quite close
+
+ align:start position:0%
+assuming these traces are quite close
+ 
+
+ align:start position:0%
+assuming these traces are quite close
+together right and it's going to look
+
+ align:start position:0%
+together right and it's going to look
+ 
+
+ align:start position:0%
+together right and it's going to look
+something like this here's the magnetic
+
+ align:start position:0%
+something like this here's the magnetic
+ 
+
+ align:start position:0%
+something like this here's the magnetic
+fields right here's the H
+
+ align:start position:0%
+fields right here's the H
+ 
+
+ align:start position:0%
+fields right here's the H
+Fields looks like something like this if
+
+ align:start position:0%
+Fields looks like something like this if
+ 
+
+ align:start position:0%
+Fields looks like something like this if
+I'm being schematic about it does that
+
+ align:start position:0%
+I'm being schematic about it does that
+ 
+
+ align:start position:0%
+I'm being schematic about it does that
+make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody so the question is if these
+
+ align:start position:0%
+everybody so the question is if these
+ 
+
+ align:start position:0%
+everybody so the question is if these
+are the H fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right how might I analyze this thing and
+
+ align:start position:0%
+right how might I analyze this thing and
+ 
+
+ align:start position:0%
+right how might I analyze this thing and
+let me do an
+
+ align:start position:0%
+let me do an
+ 
+
+ align:start position:0%
+let me do an
+analysis a very simple analysis just to
+
+ align:start position:0%
+analysis a very simple analysis just to
+ 
+
+ align:start position:0%
+analysis a very simple analysis just to
+say What are the tradeoffs in the
+
+ align:start position:0%
+say What are the tradeoffs in the
+ 
+
+ align:start position:0%
+say What are the tradeoffs in the
+interconnect so we can say okay the
+
+ align:start position:0%
+interconnect so we can say okay the
+ 
+
+ align:start position:0%
+interconnect so we can say okay the
+integral of h.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DL is equal to the integral of aj. Da
+
+ align:start position:0%
+DL is equal to the integral of aj. Da
+ 
+
+ align:start position:0%
+DL is equal to the integral of aj. Da
+which is just the the which is just the
+
+ align:start position:0%
+which is just the the which is just the
+ 
+
+ align:start position:0%
+which is just the the which is just the
+net current right this a I'm I'm
+
+ align:start position:0%
+net current right this a I'm I'm
+ 
+
+ align:start position:0%
+net current right this a I'm I'm
+ignoring displacement current in this
+
+ align:start position:0%
+ignoring displacement current in this
+ 
+
+ align:start position:0%
+ignoring displacement current in this
+okay so what I'm saying is that if I
+
+ align:start position:0%
+okay so what I'm saying is that if I
+ 
+
+ align:start position:0%
+okay so what I'm saying is that if I
+integrate the H field around any
+
+ align:start position:0%
+integrate the H field around any
+ 
+
+ align:start position:0%
+integrate the H field around any
+Loop okay I'm going to get the net
+
+ align:start position:0%
+Loop okay I'm going to get the net
+ 
+
+ align:start position:0%
+Loop okay I'm going to get the net
+current enclosed so suppose this total
+
+ align:start position:0%
+current enclosed so suppose this total
+ 
+
+ align:start position:0%
+current enclosed so suppose this total
+current here is
+
+ align:start position:0%
+current here is
+ 
+
+ align:start position:0%
+current here is
+I all right well that's
+
+ align:start position:0%
+I all right well that's
+ 
+
+ align:start position:0%
+I all right well that's
+fine the simplest thing for me to think
+
+ align:start position:0%
+fine the simplest thing for me to think
+ 
+
+ align:start position:0%
+fine the simplest thing for me to think
+about might be the fact that the fields
+
+ align:start position:0%
+about might be the fact that the fields
+ 
+
+ align:start position:0%
+about might be the fact that the fields
+are really concentrated in between the
+
+ align:start position:0%
+are really concentrated in between the
+ 
+
+ align:start position:0%
+are really concentrated in between the
+traces and they're kind of very diffuse
+
+ align:start position:0%
+traces and they're kind of very diffuse
+ 
+
+ align:start position:0%
+traces and they're kind of very diffuse
+out here so maybe I can make the
+
+ align:start position:0%
+out here so maybe I can make the
+ 
+
+ align:start position:0%
+out here so maybe I can make the
+approximation and this is purely
+
+ align:start position:0%
+approximation and this is purely
+ 
+
+ align:start position:0%
+approximation and this is purely
+approximation that all the field that I
+
+ align:start position:0%
+approximation that all the field that I
+ 
+
+ align:start position:0%
+approximation that all the field that I
+I'm interested in is in here right so
+
+ align:start position:0%
+I'm interested in is in here right so
+ 
+
+ align:start position:0%
+I'm interested in is in here right so
+then if I took this integral around this
+
+ align:start position:0%
+then if I took this integral around this
+ 
+
+ align:start position:0%
+then if I took this integral around this
+loop I might say the integral of H.L is
+
+ align:start position:0%
+loop I might say the integral of H.L is
+ 
+
+ align:start position:0%
+loop I might say the integral of H.L is
+just H
+
+ align:start position:0%
+just H
+ 
+
+ align:start position:0%
+just H
+subx let me call this the X direction
+
+ align:start position:0%
+subx let me call this the X direction
+ 
+
+ align:start position:0%
+subx let me call this the X direction
+right it's the H inside the inside
+
+ align:start position:0%
+right it's the H inside the inside
+ 
+
+ align:start position:0%
+right it's the H inside the inside
+between here times this is the width of
+
+ align:start position:0%
+between here times this is the width of
+ 
+
+ align:start position:0%
+between here times this is the width of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+winding is equal to I or equivalently I
+
+ align:start position:0%
+winding is equal to I or equivalently I
+ 
+
+ align:start position:0%
+winding is equal to I or equivalently I
+could approximate this H field as H subx
+
+ align:start position:0%
+could approximate this H field as H subx
+ 
+
+ align:start position:0%
+could approximate this H field as H subx
+is equal to I over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right has the right units amps per
+
+ align:start position:0%
+all right has the right units amps per
+ 
+
+ align:start position:0%
+all right has the right units amps per
+meter um how much energy am I storing in
+
+ align:start position:0%
+meter um how much energy am I storing in
+ 
+
+ align:start position:0%
+meter um how much energy am I storing in
+this thing well again I'm only going to
+
+ align:start position:0%
+this thing well again I'm only going to
+ 
+
+ align:start position:0%
+this thing well again I'm only going to
+pay attention to the really the energy
+
+ align:start position:0%
+pay attention to the really the energy
+ 
+
+ align:start position:0%
+pay attention to the really the energy
+I'm storing here but that ought to be
+
+ align:start position:0%
+I'm storing here but that ought to be
+ 
+
+ align:start position:0%
+I'm storing here but that ought to be
+most of the energy I'm going to ignore
+
+ align:start position:0%
+most of the energy I'm going to ignore
+ 
+
+ align:start position:0%
+most of the energy I'm going to ignore
+this sort of the fringing Fields out
+
+ align:start position:0%
+this sort of the fringing Fields out
+ 
+
+ align:start position:0%
+this sort of the fringing Fields out
+here even though I know they exist so
+
+ align:start position:0%
+here even though I know they exist so
+ 
+
+ align:start position:0%
+here even though I know they exist so
+that means I get the
+
+ align:start position:0%
+that means I get the
+ 
+
+ align:start position:0%
+that means I get the
+integral the magnetic energy storage is
+
+ align:start position:0%
+integral the magnetic energy storage is
+ 
+
+ align:start position:0%
+integral the magnetic energy storage is
+equal to the integral of b.h
+
+ align:start position:0%
+equal to the integral of b.h
+ 
+
+ align:start position:0%
+equal to the integral of b.h
+DV okay which is going to give me 12
+
+ align:start position:0%
+DV okay which is going to give me 12
+ 
+
+ align:start position:0%
+DV okay which is going to give me 12
+mu uh H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sared times the volume which in this
+
+ align:start position:0%
+sared times the volume which in this
+ 
+
+ align:start position:0%
+sared times the volume which in this
+case is going to be equal to 12
+
+ align:start position:0%
+case is going to be equal to 12
+ 
+
+ align:start position:0%
+case is going to be equal to 12
+mu I over i^ 2 over w^2 time the volume
+
+ align:start position:0%
+mu I over i^ 2 over w^2 time the volume
+ 
+
+ align:start position:0%
+mu I over i^ 2 over w^2 time the volume
+which is W * L * Delta right so I'm
+
+ align:start position:0%
+which is W * L * Delta right so I'm
+ 
+
+ align:start position:0%
+which is W * L * Delta right so I'm
+finding all the energy stored sort of in
+
+ align:start position:0%
+finding all the energy stored sort of in
+ 
+
+ align:start position:0%
+finding all the energy stored sort of in
+between the plates of this conductor in
+
+ align:start position:0%
+between the plates of this conductor in
+ 
+
+ align:start position:0%
+between the plates of this conductor in
+return any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so this is also equal
+
+ align:start position:0%
+that so this is also equal
+ 
+
+ align:start position:0%
+that so this is also equal
+to li^
+
+ align:start position:0%
+to li^
+ 
+
+ align:start position:0%
+to li^
+2 okay that's the energy I'm storing in
+
+ align:start position:0%
+2 okay that's the energy I'm storing in
+ 
+
+ align:start position:0%
+2 okay that's the energy I'm storing in
+the magnetic field and if I work that
+
+ align:start position:0%
+the magnetic field and if I work that
+ 
+
+ align:start position:0%
+the magnetic field and if I work that
+out right this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cancels right then I get if I just
+
+ align:start position:0%
+cancels right then I get if I just
+ 
+
+ align:start position:0%
+cancels right then I get if I just
+pattern match here what I get is
+
+ align:start position:0%
+pattern match here what I get is
+ 
+
+ align:start position:0%
+pattern match here what I get is
+L is approximately equal to the with
+
+ align:start position:0%
+L is approximately equal to the with
+ 
+
+ align:start position:0%
+L is approximately equal to the with
+these simp simplifications mu
+
+ align:start position:0%
+these simp simplifications mu
+ 
+
+ align:start position:0%
+these simp simplifications mu
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+L over W and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta okay this is sort of the
+
+ align:start position:0%
+Delta okay this is sort of the
+ 
+
+ align:start position:0%
+Delta okay this is sort of the
+equivalent of saying you know
+
+ align:start position:0%
+equivalent of saying you know
+ 
+
+ align:start position:0%
+equivalent of saying you know
+capacitance is Epsilon not a over D I'm
+
+ align:start position:0%
+capacitance is Epsilon not a over D I'm
+ 
+
+ align:start position:0%
+capacitance is Epsilon not a over D I'm
+ignoring fringing between two plates
+
+ align:start position:0%
+ignoring fringing between two plates
+ 
+
+ align:start position:0%
+ignoring fringing between two plates
+this is sort of the magnetic equivalent
+
+ align:start position:0%
+this is sort of the magnetic equivalent
+ 
+
+ align:start position:0%
+this is sort of the magnetic equivalent
+of that okay so the
+
+ align:start position:0%
+of that okay so the
+ 
+
+ align:start position:0%
+of that okay so the
+inductance of this Trace to carry
+
+ align:start position:0%
+inductance of this Trace to carry
+ 
+
+ align:start position:0%
+inductance of this Trace to carry
+current up and back is going to be
+
+ align:start position:0%
+current up and back is going to be
+ 
+
+ align:start position:0%
+current up and back is going to be
+basically mu l w over W
+
+ align:start position:0%
+basically mu l w over W
+ 
+
+ align:start position:0%
+basically mu l w over W
+Delta so if I want a low inductance Loop
+
+ align:start position:0%
+Delta so if I want a low inductance Loop
+ 
+
+ align:start position:0%
+Delta so if I want a low inductance Loop
+what do I want I firstly obviously I
+
+ align:start position:0%
+what do I want I firstly obviously I
+ 
+
+ align:start position:0%
+what do I want I firstly obviously I
+mean I'm assuming there's no magnetic
+
+ align:start position:0%
+mean I'm assuming there's no magnetic
+ 
+
+ align:start position:0%
+mean I'm assuming there's no magnetic
+material in here clearly I don't want
+
+ align:start position:0%
+material in here clearly I don't want
+ 
+
+ align:start position:0%
+material in here clearly I don't want
+magnetic material in there if I want it
+
+ align:start position:0%
+magnetic material in there if I want it
+ 
+
+ align:start position:0%
+magnetic material in there if I want it
+to be low
+
+ align:start position:0%
+to be low
+ 
+
+ align:start position:0%
+to be low
+inductance uh I want it to be short put
+
+ align:start position:0%
+inductance uh I want it to be short put
+ 
+
+ align:start position:0%
+inductance uh I want it to be short put
+everything as close together in terms of
+
+ align:start position:0%
+everything as close together in terms of
+ 
+
+ align:start position:0%
+everything as close together in terms of
+the length I'm carrying the current over
+
+ align:start position:0%
+the length I'm carrying the current over
+ 
+
+ align:start position:0%
+the length I'm carrying the current over
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+possible if I have to carry a current in
+
+ align:start position:0%
+possible if I have to carry a current in
+ 
+
+ align:start position:0%
+possible if I have to carry a current in
+a trace I would like the trace to be
+
+ align:start position:0%
+a trace I would like the trace to be
+ 
+
+ align:start position:0%
+a trace I would like the trace to be
+wide The Wider the trace the more the
+
+ align:start position:0%
+wide The Wider the trace the more the
+ 
+
+ align:start position:0%
+wide The Wider the trace the more the
+current and field spreads out and the
+
+ align:start position:0%
+current and field spreads out and the
+ 
+
+ align:start position:0%
+current and field spreads out and the
+lower net energy
+
+ align:start position:0%
+lower net energy
+ 
+
+ align:start position:0%
+lower net energy
+stored okay because the width you know
+
+ align:start position:0%
+stored okay because the width you know
+ 
+
+ align:start position:0%
+stored okay because the width you know
+the width helps me reduce the field
+
+ align:start position:0%
+the width helps me reduce the field
+ 
+
+ align:start position:0%
+the width helps me reduce the field
+magnitude and even though I'm carrying
+
+ align:start position:0%
+magnitude and even though I'm carrying
+ 
+
+ align:start position:0%
+magnitude and even though I'm carrying
+it over a wider space I have more volume
+
+ align:start position:0%
+it over a wider space I have more volume
+ 
+
+ align:start position:0%
+it over a wider space I have more volume
+I get a lower inductance then the other
+
+ align:start position:0%
+I get a lower inductance then the other
+ 
+
+ align:start position:0%
+I get a lower inductance then the other
+thing I can see is here I want Delta to
+
+ align:start position:0%
+thing I can see is here I want Delta to
+ 
+
+ align:start position:0%
+thing I can see is here I want Delta to
+be small right so if I'm going to carry
+
+ align:start position:0%
+be small right so if I'm going to carry
+ 
+
+ align:start position:0%
+be small right so if I'm going to carry
+current out and return it I want the
+
+ align:start position:0%
+current out and return it I want the
+ 
+
+ align:start position:0%
+current out and return it I want the
+spacing between those traces to be
+
+ align:start position:0%
+spacing between those traces to be
+ 
+
+ align:start position:0%
+spacing between those traces to be
+really low okay so the thing I'm
+
+ align:start position:0%
+really low okay so the thing I'm
+ 
+
+ align:start position:0%
+really low okay so the thing I'm
+thinking about when I'm thinking about
+
+ align:start position:0%
+thinking about when I'm thinking about
+ 
+
+ align:start position:0%
+thinking about when I'm thinking about
+what am I going to make this
+
+ align:start position:0%
+what am I going to make this
+ 
+
+ align:start position:0%
+what am I going to make this
+interconnect Loop do it's not only that
+
+ align:start position:0%
+interconnect Loop do it's not only that
+ 
+
+ align:start position:0%
+interconnect Loop do it's not only that
+I want I can think about I can imagine
+
+ align:start position:0%
+I want I can think about I can imagine
+ 
+
+ align:start position:0%
+I want I can think about I can imagine
+this original thing I
+
+ align:start position:0%
+this original thing I
+ 
+
+ align:start position:0%
+this original thing I
+drew and say yeah I want this Loop to be
+
+ align:start position:0%
+drew and say yeah I want this Loop to be
+ 
+
+ align:start position:0%
+drew and say yeah I want this Loop to be
+tight but that can you know this might
+
+ align:start position:0%
+tight but that can you know this might
+ 
+
+ align:start position:0%
+tight but that can you know this might
+actually be in multiple Dimensions that
+
+ align:start position:0%
+actually be in multiple Dimensions that
+ 
+
+ align:start position:0%
+actually be in multiple Dimensions that
+I have to think about and if I have to
+
+ align:start position:0%
+I have to think about and if I have to
+ 
+
+ align:start position:0%
+I have to think about and if I have to
+carry current over some distance
+
+ align:start position:0%
+carry current over some distance
+ 
+
+ align:start position:0%
+carry current over some distance
+carrying a y trace and putting those
+
+ align:start position:0%
+carrying a y trace and putting those
+ 
+
+ align:start position:0%
+carrying a y trace and putting those
+traces closer together helps me make
+
+ align:start position:0%
+traces closer together helps me make
+ 
+
+ align:start position:0%
+traces closer together helps me make
+that inductance
+
+ align:start position:0%
+that inductance
+ 
+
+ align:start position:0%
+that inductance
+low okay any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so you know if I'm you know an
+
+ align:start position:0%
+that so you know if I'm you know an
+ 
+
+ align:start position:0%
+that so you know if I'm you know an
+example of this would be not only for
+
+ align:start position:0%
+example of this would be not only for
+ 
+
+ align:start position:0%
+example of this would be not only for
+the switching Loop but you know the Gate
+
+ align:start position:0%
+the switching Loop but you know the Gate
+ 
+
+ align:start position:0%
+the switching Loop but you know the Gate
+Drive I got to put the gate drive and I
+
+ align:start position:0%
+Drive I got to put the gate drive and I
+ 
+
+ align:start position:0%
+Drive I got to put the gate drive and I
+want to send current out and bring the
+
+ align:start position:0%
+want to send current out and bring the
+ 
+
+ align:start position:0%
+want to send current out and bring the
+current back right when I'm thinking
+
+ align:start position:0%
+current back right when I'm thinking
+ 
+
+ align:start position:0%
+current back right when I'm thinking
+about that if you want the energy
+
+ align:start position:0%
+about that if you want the energy
+ 
+
+ align:start position:0%
+about that if you want the energy
+storage to be small at least the
+
+ align:start position:0%
+storage to be small at least the
+ 
+
+ align:start position:0%
+storage to be small at least the
+magnetic energy storage to be small use
+
+ align:start position:0%
+magnetic energy storage to be small use
+ 
+
+ align:start position:0%
+magnetic energy storage to be small use
+a wide Trace put the return very
+
+ align:start position:0%
+a wide Trace put the return very
+ 
+
+ align:start position:0%
+a wide Trace put the return very
+close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now what would
+
+ align:start position:0%
+okay now what would
+ 
+
+ align:start position:0%
+okay now what would
+be um the equivalent of that for this
+
+ align:start position:0%
+be um the equivalent of that for this
+ 
+
+ align:start position:0%
+be um the equivalent of that for this
+Loop right what
+
+ align:start position:0%
+Loop right what
+ 
+
+ align:start position:0%
+Loop right what
+happens um the parasitic capacitance
+
+ align:start position:0%
+happens um the parasitic capacitance
+ 
+
+ align:start position:0%
+happens um the parasitic capacitance
+suppose I have some Trace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know this is my switching node and
+
+ align:start position:0%
+you know this is my switching node and
+ 
+
+ align:start position:0%
+you know this is my switching node and
+this is say ground or something or or
+
+ align:start position:0%
+this is say ground or something or or
+ 
+
+ align:start position:0%
+this is say ground or something or or
+some other node and I'm asking what's
+
+ align:start position:0%
+some other node and I'm asking what's
+ 
+
+ align:start position:0%
+some other node and I'm asking what's
+the capacitance between these two pieces
+
+ align:start position:0%
+the capacitance between these two pieces
+ 
+
+ align:start position:0%
+the capacitance between these two pieces
+of metal that are very close to each
+
+ align:start position:0%
+of metal that are very close to each
+ 
+
+ align:start position:0%
+of metal that are very close to each
+other that I think is
+
+ align:start position:0%
+other that I think is
+ 
+
+ align:start position:0%
+other that I think is
+um more familiar to people right people
+
+ align:start position:0%
+um more familiar to people right people
+ 
+
+ align:start position:0%
+um more familiar to people right people
+recall that the
+
+ align:start position:0%
+recall that the
+ 
+
+ align:start position:0%
+recall that the
+capacitance is equal to Epsilon it's the
+
+ align:start position:0%
+capacitance is equal to Epsilon it's the
+ 
+
+ align:start position:0%
+capacitance is equal to Epsilon it's the
+dialectric between my two pieces of
+
+ align:start position:0%
+dialectric between my two pieces of
+ 
+
+ align:start position:0%
+dialectric between my two pieces of
+metal times the a area ided the distance
+
+ align:start position:0%
+metal times the a area ided the distance
+ 
+
+ align:start position:0%
+metal times the a area ided the distance
+Epsilon a over D which in the way I've
+
+ align:start position:0%
+Epsilon a over D which in the way I've
+ 
+
+ align:start position:0%
+Epsilon a over D which in the way I've
+been writing this with these two plate
+
+ align:start position:0%
+been writing this with these two plate
+ 
+
+ align:start position:0%
+been writing this with these two plate
+sizes would be Epsilon times the area
+
+ align:start position:0%
+sizes would be Epsilon times the area
+ 
+
+ align:start position:0%
+sizes would be Epsilon times the area
+would be width time the length
+
+ align:start position:0%
+would be width time the length
+ 
+
+ align:start position:0%
+would be width time the length
+/
+
+ align:start position:0%
+/
+ 
+
+ align:start position:0%
+/
+Delta does that make
+
+ align:start position:0%
+Delta does that make
+ 
+
+ align:start position:0%
+Delta does that make
+sense so what does this say um in this
+
+ align:start position:0%
+sense so what does this say um in this
+ 
+
+ align:start position:0%
+sense so what does this say um in this
+case if I want to make capacitance small
+
+ align:start position:0%
+case if I want to make capacitance small
+ 
+
+ align:start position:0%
+case if I want to make capacitance small
+I also want to make the length of this
+
+ align:start position:0%
+I also want to make the length of this
+ 
+
+ align:start position:0%
+I also want to make the length of this
+thing short
+
+ align:start position:0%
+thing short
+ 
+
+ align:start position:0%
+thing short
+okay but notice that whereas inductance
+
+ align:start position:0%
+okay but notice that whereas inductance
+ 
+
+ align:start position:0%
+okay but notice that whereas inductance
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+as um let's see where do I have it here
+
+ align:start position:0%
+as um let's see where do I have it here
+ 
+
+ align:start position:0%
+as um let's see where do I have it here
+L over Del L over Delta so let me let me
+
+ align:start position:0%
+L over Del L over Delta so let me let me
+ 
+
+ align:start position:0%
+L over Del L over Delta so let me let me
+write c c is equal to
+
+ align:start position:0%
+write c c is equal to
+ 
+
+ align:start position:0%
+write c c is equal to
+Epsilon
+
+ align:start position:0%
+Epsilon
+ 
+
+ align:start position:0%
+Epsilon
+uh uh L * W over Delta
+
+ align:start position:0%
+uh uh L * W over Delta
+ 
+
+ align:start position:0%
+uh uh L * W over Delta
+right if I thought about my inductance
+
+ align:start position:0%
+right if I thought about my inductance
+ 
+
+ align:start position:0%
+right if I thought about my inductance
+per unit
+
+ align:start position:0%
+per unit
+ 
+
+ align:start position:0%
+per unit
+length is
+
+ align:start position:0%
+length is
+ 
+
+ align:start position:0%
+length is
+Mu over
+
+ align:start position:0%
+Mu over
+ 
+
+ align:start position:0%
+Mu over
+W
+
+ align:start position:0%
+W
+ 
+
+ align:start position:0%
+W
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+capacitance what did I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here it should be yes that's completely
+
+ align:start position:0%
+here it should be yes that's completely
+ 
+
+ align:start position:0%
+here it should be yes that's completely
+wrong it's what happens when I skip
+
+ align:start position:0%
+wrong it's what happens when I skip
+ 
+
+ align:start position:0%
+wrong it's what happens when I skip
+boards the inductance needs to
+
+ align:start position:0%
+boards the inductance needs to
+ 
+
+ align:start position:0%
+boards the inductance needs to
+be m not yeah all right that's what I
+
+ align:start position:0%
+be m not yeah all right that's what I
+ 
+
+ align:start position:0%
+be m not yeah all right that's what I
+did Delta over w
+
+ align:start position:0%
+did Delta over w
+ 
+
+ align:start position:0%
+did Delta over w
+right if I want the inductance to low
+
+ align:start position:0%
+right if I want the inductance to low
+ 
+
+ align:start position:0%
+right if I want the inductance to low
+make it make W big and and Delta small
+
+ align:start position:0%
+make it make W big and and Delta small
+ 
+
+ align:start position:0%
+make it make W big and and Delta small
+okay this should be uh W over
+
+ align:start position:0%
+okay this should be uh W over
+ 
+
+ align:start position:0%
+okay this should be uh W over
+Delta right it's the induct I'm sorry
+
+ align:start position:0%
+Delta right it's the induct I'm sorry
+ 
+
+ align:start position:0%
+Delta right it's the induct I'm sorry
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitance right inductance per unit
+
+ align:start position:0%
+capacitance right inductance per unit
+ 
+
+ align:start position:0%
+capacitance right inductance per unit
+length is then Mu Delta over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W right so L Prime because if I I have
+
+ align:start position:0%
+W right so L Prime because if I I have
+ 
+
+ align:start position:0%
+W right so L Prime because if I I have
+to do it over some length then I can say
+
+ align:start position:0%
+to do it over some length then I can say
+ 
+
+ align:start position:0%
+to do it over some length then I can say
+what this is and I want Delta to be
+
+ align:start position:0%
+what this is and I want Delta to be
+ 
+
+ align:start position:0%
+what this is and I want Delta to be
+small and W to be big if I calculated
+
+ align:start position:0%
+small and W to be big if I calculated
+ 
+
+ align:start position:0%
+small and W to be big if I calculated
+the capacitance the capacitance per unit
+
+ align:start position:0%
+the capacitance the capacitance per unit
+ 
+
+ align:start position:0%
+the capacitance the capacitance per unit
+length is Epsilon time W over
+
+ align:start position:0%
+length is Epsilon time W over
+ 
+
+ align:start position:0%
+length is Epsilon time W over
+Delta okay so if I'm thinking about some
+
+ align:start position:0%
+Delta okay so if I'm thinking about some
+ 
+
+ align:start position:0%
+Delta okay so if I'm thinking about some
+Trace in its return or two pieces of
+
+ align:start position:0%
+Trace in its return or two pieces of
+ 
+
+ align:start position:0%
+Trace in its return or two pieces of
+metal close to each other whatever I do
+
+ align:start position:0%
+metal close to each other whatever I do
+ 
+
+ align:start position:0%
+metal close to each other whatever I do
+to reduce the inductance increases the
+
+ align:start position:0%
+to reduce the inductance increases the
+ 
+
+ align:start position:0%
+to reduce the inductance increases the
+capacitance in vice
+
+ align:start position:0%
+capacitance in vice
+ 
+
+ align:start position:0%
+capacitance in vice
+versa Okay so so you know in some in
+
+ align:start position:0%
+versa Okay so so you know in some in
+ 
+
+ align:start position:0%
+versa Okay so so you know in some in
+some cases if I do the best thing I can
+
+ align:start position:0%
+some cases if I do the best thing I can
+ 
+
+ align:start position:0%
+some cases if I do the best thing I can
+do I'm going to be trading capacitance
+
+ align:start position:0%
+do I'm going to be trading capacitance
+ 
+
+ align:start position:0%
+do I'm going to be trading capacitance
+for inductance and I got to decide which
+
+ align:start position:0%
+for inductance and I got to decide which
+ 
+
+ align:start position:0%
+for inductance and I got to decide which
+I want you know which I don't like
+
+ align:start position:0%
+I want you know which I don't like
+ 
+
+ align:start position:0%
+I want you know which I don't like
+less okay now that doesn't mean you
+
+ align:start position:0%
+less okay now that doesn't mean you
+ 
+
+ align:start position:0%
+less okay now that doesn't mean you
+can't you know this tradeoff and I
+
+ align:start position:0%
+can't you know this tradeoff and I
+ 
+
+ align:start position:0%
+can't you know this tradeoff and I
+should say by the way one
+
+ align:start position:0%
+should say by the way one
+ 
+
+ align:start position:0%
+should say by the way one
+over um L Prime C
+
+ align:start position:0%
+over um L Prime C
+ 
+
+ align:start position:0%
+over um L Prime C
+Prime uh ends up being the speed of
+
+ align:start position:0%
+Prime uh ends up being the speed of
+ 
+
+ align:start position:0%
+Prime uh ends up being the speed of
+light squared okay so it's you know it's
+
+ align:start position:0%
+light squared okay so it's you know it's
+ 
+
+ align:start position:0%
+light squared okay so it's you know it's
+a physical constant mu m epon
+
+ align:start position:0%
+a physical constant mu m epon
+ 
+
+ align:start position:0%
+a physical constant mu m epon
+not but um that doesn't mean I can't do
+
+ align:start position:0%
+not but um that doesn't mean I can't do
+ 
+
+ align:start position:0%
+not but um that doesn't mean I can't do
+anything bad here that doesn't help me
+
+ align:start position:0%
+anything bad here that doesn't help me
+ 
+
+ align:start position:0%
+anything bad here that doesn't help me
+right if I thought about you know I'm
+
+ align:start position:0%
+right if I thought about you know I'm
+ 
+
+ align:start position:0%
+right if I thought about you know I'm
+going to carry some
+
+ align:start position:0%
+going to carry some
+ 
+
+ align:start position:0%
+going to carry some
+current over some distance you know I'm
+
+ align:start position:0%
+current over some distance you know I'm
+ 
+
+ align:start position:0%
+current over some distance you know I'm
+going to carry current here and it's
+
+ align:start position:0%
+going to carry current here and it's
+ 
+
+ align:start position:0%
+going to carry current here and it's
+going to return underneath here right if
+
+ align:start position:0%
+going to return underneath here right if
+ 
+
+ align:start position:0%
+going to return underneath here right if
+I put some piece of metal out here that
+
+ align:start position:0%
+I put some piece of metal out here that
+ 
+
+ align:start position:0%
+I put some piece of metal out here that
+doesn't really carry any current he can
+
+ align:start position:0%
+doesn't really carry any current he can
+ 
+
+ align:start position:0%
+doesn't really carry any current he can
+add capacitance without reducing
+
+ align:start position:0%
+add capacitance without reducing
+ 
+
+ align:start position:0%
+add capacitance without reducing
+inductance right so I can certainly do
+
+ align:start position:0%
+inductance right so I can certainly do
+ 
+
+ align:start position:0%
+inductance right so I can certainly do
+things to make both inductance and
+
+ align:start position:0%
+things to make both inductance and
+ 
+
+ align:start position:0%
+things to make both inductance and
+capacit accidents worse or make one of
+
+ align:start position:0%
+capacit accidents worse or make one of
+ 
+
+ align:start position:0%
+capacit accidents worse or make one of
+them worse without helping the other but
+
+ align:start position:0%
+them worse without helping the other but
+ 
+
+ align:start position:0%
+them worse without helping the other but
+when I get it down to the sort of the
+
+ align:start position:0%
+when I get it down to the sort of the
+ 
+
+ align:start position:0%
+when I get it down to the sort of the
+best interconnect strategy at some point
+
+ align:start position:0%
+best interconnect strategy at some point
+ 
+
+ align:start position:0%
+best interconnect strategy at some point
+you know if I put my trace and return
+
+ align:start position:0%
+you know if I put my trace and return
+ 
+
+ align:start position:0%
+you know if I put my trace and return
+close I'm making the inductance low and
+
+ align:start position:0%
+close I'm making the inductance low and
+ 
+
+ align:start position:0%
+close I'm making the inductance low and
+the capacit capacitance high and vice
+
+ align:start position:0%
+the capacit capacitance high and vice
+ 
+
+ align:start position:0%
+the capacit capacitance high and vice
+versa okay and you just got to think
+
+ align:start position:0%
+versa okay and you just got to think
+ 
+
+ align:start position:0%
+versa okay and you just got to think
+about which piece of Trace is it and
+
+ align:start position:0%
+about which piece of Trace is it and
+ 
+
+ align:start position:0%
+about which piece of Trace is it and
+what is it doing for
+
+ align:start position:0%
+what is it doing for
+ 
+
+ align:start position:0%
+what is it doing for
+you any question about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's talk a little bit about more about
+
+ align:start position:0%
+let's talk a little bit about more about
+ 
+
+ align:start position:0%
+let's talk a little bit about more about
+this switching node here
+
+ align:start position:0%
+this switching node here
+ 
+
+ align:start position:0%
+this switching node here
+okay um one thing it does which we saw
+
+ align:start position:0%
+okay um one thing it does which we saw
+ 
+
+ align:start position:0%
+okay um one thing it does which we saw
+in the demo is it'll cause a bunch of
+
+ align:start position:0%
+in the demo is it'll cause a bunch of
+ 
+
+ align:start position:0%
+in the demo is it'll cause a bunch of
+ringing because you have excess
+
+ align:start position:0%
+ringing because you have excess
+ 
+
+ align:start position:0%
+ringing because you have excess
+capacitance at this node that you don't
+
+ align:start position:0%
+capacitance at this node that you don't
+ 
+
+ align:start position:0%
+capacitance at this node that you don't
+like but there are other capacitors is
+
+ align:start position:0%
+like but there are other capacitors is
+ 
+
+ align:start position:0%
+like but there are other capacitors is
+that node like the device capacitors and
+
+ align:start position:0%
+that node like the device capacitors and
+ 
+
+ align:start position:0%
+that node like the device capacitors and
+so forth but what really often hurts you
+
+ align:start position:0%
+so forth but what really often hurts you
+ 
+
+ align:start position:0%
+so forth but what really often hurts you
+is the capacitance of that node not to
+
+ align:start position:0%
+is the capacitance of that node not to
+ 
+
+ align:start position:0%
+is the capacitance of that node not to
+ground but to other stuff in your
+
+ align:start position:0%
+ground but to other stuff in your
+ 
+
+ align:start position:0%
+ground but to other stuff in your
+circuit so let's let's just
+
+ align:start position:0%
+circuit so let's let's just
+ 
+
+ align:start position:0%
+circuit so let's let's just
+imagine um this node is driven by the
+
+ align:start position:0%
+imagine um this node is driven by the
+ 
+
+ align:start position:0%
+imagine um this node is driven by the
+switching so there's a volt there sort
+
+ align:start position:0%
+switching so there's a volt there sort
+ 
+
+ align:start position:0%
+switching so there's a volt there sort
+of a square wave voltage here right so
+
+ align:start position:0%
+of a square wave voltage here right so
+ 
+
+ align:start position:0%
+of a square wave voltage here right so
+if I thought about modeling this I might
+
+ align:start position:0%
+if I thought about modeling this I might
+ 
+
+ align:start position:0%
+if I thought about modeling this I might
+say okay here's my here's my big Square
+
+ align:start position:0%
+say okay here's my here's my big Square
+ 
+
+ align:start position:0%
+say okay here's my here's my big Square
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+voltage right this is going up and down
+
+ align:start position:0%
+voltage right this is going up and down
+ 
+
+ align:start position:0%
+voltage right this is going up and down
+like this okay
+
+ align:start position:0%
+like this okay
+ 
+
+ align:start position:0%
+like this okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this piece of metal here forms one plate
+
+ align:start position:0%
+this piece of metal here forms one plate
+ 
+
+ align:start position:0%
+this piece of metal here forms one plate
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+capacitor okay so maybe I think about
+
+ align:start position:0%
+capacitor okay so maybe I think about
+ 
+
+ align:start position:0%
+capacitor okay so maybe I think about
+that as being one plate here it is he's
+
+ align:start position:0%
+that as being one plate here it is he's
+ 
+
+ align:start position:0%
+that as being one plate here it is he's
+one plate of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitor all right what's the other
+
+ align:start position:0%
+capacitor all right what's the other
+ 
+
+ align:start position:0%
+capacitor all right what's the other
+plate of my capacitor well it depends
+
+ align:start position:0%
+plate of my capacitor well it depends
+ 
+
+ align:start position:0%
+plate of my capacitor well it depends
+what's around it but imagine
+
+ align:start position:0%
+what's around it but imagine
+ 
+
+ align:start position:0%
+what's around it but imagine
+nearby I have in my circuit for example
+
+ align:start position:0%
+nearby I have in my circuit for example
+ 
+
+ align:start position:0%
+nearby I have in my circuit for example
+suppose I have some control circuitry
+
+ align:start position:0%
+suppose I have some control circuitry
+ 
+
+ align:start position:0%
+suppose I have some control circuitry
+down here it's ground
+
+ align:start position:0%
+down here it's ground
+ 
+
+ align:start position:0%
+down here it's ground
+referenced right I have drivers and
+
+ align:start position:0%
+referenced right I have drivers and
+ 
+
+ align:start position:0%
+referenced right I have drivers and
+sensors and comparators are going to do
+
+ align:start position:0%
+sensors and comparators are going to do
+ 
+
+ align:start position:0%
+sensors and comparators are going to do
+all the computation for me right and
+
+ align:start position:0%
+all the computation for me right and
+ 
+
+ align:start position:0%
+all the computation for me right and
+maybe within this there's some very
+
+ align:start position:0%
+maybe within this there's some very
+ 
+
+ align:start position:0%
+maybe within this there's some very
+sensitive node maybe that's the input of
+
+ align:start position:0%
+sensitive node maybe that's the input of
+ 
+
+ align:start position:0%
+sensitive node maybe that's the input of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+comparator or at the you know right
+
+ align:start position:0%
+comparator or at the you know right
+ 
+
+ align:start position:0%
+comparator or at the you know right
+where my error amplifier is my opamp and
+
+ align:start position:0%
+where my error amplifier is my opamp and
+ 
+
+ align:start position:0%
+where my error amplifier is my opamp and
+I can have some very high impedance
+
+ align:start position:0%
+I can have some very high impedance
+ 
+
+ align:start position:0%
+I can have some very high impedance
+nodes right so maybe I have a plate
+
+ align:start position:0%
+nodes right so maybe I have a plate
+ 
+
+ align:start position:0%
+nodes right so maybe I have a plate
+there that plate is just the metal of
+
+ align:start position:0%
+there that plate is just the metal of
+ 
+
+ align:start position:0%
+there that plate is just the metal of
+that node okay and you know it has some
+
+ align:start position:0%
+that node okay and you know it has some
+ 
+
+ align:start position:0%
+that node okay and you know it has some
+resistance too right so maybe my
+
+ align:start position:0%
+resistance too right so maybe my
+ 
+
+ align:start position:0%
+resistance too right so maybe my
+comparator has some resistance to ground
+
+ align:start position:0%
+comparator has some resistance to ground
+ 
+
+ align:start position:0%
+comparator has some resistance to ground
+so this is you know this white could be
+
+ align:start position:0%
+so this is you know this white could be
+ 
+
+ align:start position:0%
+so this is you know this white could be
+inside this box maybe there's a
+
+ align:start position:0%
+inside this box maybe there's a
+ 
+
+ align:start position:0%
+inside this box maybe there's a
+comparator and he has a positive input
+
+ align:start position:0%
+comparator and he has a positive input
+ 
+
+ align:start position:0%
+comparator and he has a positive input
+and there's some metal that I've got
+
+ align:start position:0%
+and there's some metal that I've got
+ 
+
+ align:start position:0%
+and there's some metal that I've got
+sitting right here that's the other
+
+ align:start position:0%
+sitting right here that's the other
+ 
+
+ align:start position:0%
+sitting right here that's the other
+plate of this capacitor okay does that
+
+ align:start position:0%
+plate of this capacitor okay does that
+ 
+
+ align:start position:0%
+plate of this capacitor okay does that
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+sense so if this voltage is here what is
+
+ align:start position:0%
+sense so if this voltage is here what is
+ 
+
+ align:start position:0%
+sense so if this voltage is here what is
+this voltage the induced voltage
+
+ align:start position:0%
+this voltage the induced voltage
+ 
+
+ align:start position:0%
+this voltage the induced voltage
+well simple RC divider what does that
+
+ align:start position:0%
+well simple RC divider what does that
+ 
+
+ align:start position:0%
+well simple RC divider what does that
+tell me it tells me I ought to be doing
+
+ align:start position:0%
+tell me it tells me I ought to be doing
+ 
+
+ align:start position:0%
+tell me it tells me I ought to be doing
+this I ought to be seeing a voltage that
+
+ align:start position:0%
+this I ought to be seeing a voltage that
+ 
+
+ align:start position:0%
+this I ought to be seeing a voltage that
+spikes up and Rings down and then and
+
+ align:start position:0%
+spikes up and Rings down and then and
+ 
+
+ align:start position:0%
+spikes up and Rings down and then and
+then spikes down and Rings up and vice
+
+ align:start position:0%
+then spikes down and Rings up and vice
+ 
+
+ align:start position:0%
+then spikes down and Rings up and vice
+versa right so this is the voltage I'm
+
+ align:start position:0%
+versa right so this is the voltage I'm
+ 
+
+ align:start position:0%
+versa right so this is the voltage I'm
+going to see here does that make sense
+
+ align:start position:0%
+going to see here does that make sense
+ 
+
+ align:start position:0%
+going to see here does that make sense
+everybody and maybe the energy in these
+
+ align:start position:0%
+everybody and maybe the energy in these
+ 
+
+ align:start position:0%
+everybody and maybe the energy in these
+spikes isn't very big but if that's the
+
+ align:start position:0%
+spikes isn't very big but if that's the
+ 
+
+ align:start position:0%
+spikes isn't very big but if that's the
+input to a comparator maybe I'm very
+
+ align:start position:0%
+input to a comparator maybe I'm very
+ 
+
+ align:start position:0%
+input to a comparator maybe I'm very
+unhappy right because if that comparator
+
+ align:start position:0%
+unhappy right because if that comparator
+ 
+
+ align:start position:0%
+unhappy right because if that comparator
+is determining when the switch turns on
+
+ align:start position:0%
+is determining when the switch turns on
+ 
+
+ align:start position:0%
+is determining when the switch turns on
+and off
+
+ align:start position:0%
+and off
+ 
+
+ align:start position:0%
+and off
+and I get a spike on that signal because
+
+ align:start position:0%
+and I get a spike on that signal because
+ 
+
+ align:start position:0%
+and I get a spike on that signal because
+of this capacitive injection I could be
+
+ align:start position:0%
+of this capacitive injection I could be
+ 
+
+ align:start position:0%
+of this capacitive injection I could be
+really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unhappy any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so what can I do about
+
+ align:start position:0%
+that so what can I do about
+ 
+
+ align:start position:0%
+that so what can I do about
+that one thing
+
+ align:start position:0%
+that one thing
+ 
+
+ align:start position:0%
+that one thing
+is we said you know the area the
+
+ align:start position:0%
+is we said you know the area the
+ 
+
+ align:start position:0%
+is we said you know the area the
+capacitance is related to the area I
+
+ align:start position:0%
+capacitance is related to the area I
+ 
+
+ align:start position:0%
+capacitance is related to the area I
+assume the two plate areas were the same
+
+ align:start position:0%
+assume the two plate areas were the same
+ 
+
+ align:start position:0%
+assume the two plate areas were the same
+here this is some small area that's this
+
+ align:start position:0%
+here this is some small area that's this
+ 
+
+ align:start position:0%
+here this is some small area that's this
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+this is some big area that's associated
+
+ align:start position:0%
+this is some big area that's associated
+ 
+
+ align:start position:0%
+this is some big area that's associated
+with carrying currents for my switching
+
+ align:start position:0%
+with carrying currents for my switching
+ 
+
+ align:start position:0%
+with carrying currents for my switching
+node one thing I want to do is make that
+
+ align:start position:0%
+node one thing I want to do is make that
+ 
+
+ align:start position:0%
+node one thing I want to do is make that
+as small as
+
+ align:start position:0%
+as small as
+ 
+
+ align:start position:0%
+as small as
+possible also keep the
+
+ align:start position:0%
+possible also keep the
+ 
+
+ align:start position:0%
+possible also keep the
+distance between this thing and this
+
+ align:start position:0%
+distance between this thing and this
+ 
+
+ align:start position:0%
+distance between this thing and this
+thing bigger so that the capacitance
+
+ align:start position:0%
+thing bigger so that the capacitance
+ 
+
+ align:start position:0%
+thing bigger so that the capacitance
+goes down right so I can kind of put
+
+ align:start position:0%
+goes down right so I can kind of put
+ 
+
+ align:start position:0%
+goes down right so I can kind of put
+them far apart farther as far as I can
+
+ align:start position:0%
+them far apart farther as far as I can
+ 
+
+ align:start position:0%
+them far apart farther as far as I can
+practically do it and reduce the areas
+
+ align:start position:0%
+practically do it and reduce the areas
+ 
+
+ align:start position:0%
+practically do it and reduce the areas
+and that will help me um minimize that
+
+ align:start position:0%
+and that will help me um minimize that
+ 
+
+ align:start position:0%
+and that will help me um minimize that
+capacitance that's causing noise does
+
+ align:start position:0%
+capacitance that's causing noise does
+ 
+
+ align:start position:0%
+capacitance that's causing noise does
+that make sense everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else could I do about that well
+
+ align:start position:0%
+what else could I do about that well
+ 
+
+ align:start position:0%
+what else could I do about that well
+another thing I could do about that is
+
+ align:start position:0%
+another thing I could do about that is
+ 
+
+ align:start position:0%
+another thing I could do about that is
+start to get smart about where those
+
+ align:start position:0%
+start to get smart about where those
+ 
+
+ align:start position:0%
+start to get smart about where those
+components are and what I put in between
+
+ align:start position:0%
+components are and what I put in between
+ 
+
+ align:start position:0%
+components are and what I put in between
+them okay so one thing I could do is put
+
+ align:start position:0%
+them okay so one thing I could do is put
+ 
+
+ align:start position:0%
+them okay so one thing I could do is put
+in what's known as a faraday Shield okay
+
+ align:start position:0%
+in what's known as a faraday Shield okay
+ 
+
+ align:start position:0%
+in what's known as a faraday Shield okay
+or lay out my circuit so I effectively
+
+ align:start position:0%
+or lay out my circuit so I effectively
+ 
+
+ align:start position:0%
+or lay out my circuit so I effectively
+get a faraday Shield what's a faraday
+
+ align:start position:0%
+get a faraday Shield what's a faraday
+ 
+
+ align:start position:0%
+get a faraday Shield what's a faraday
+Shield let me just say you know this is
+
+ align:start position:0%
+Shield let me just say you know this is
+ 
+
+ align:start position:0%
+Shield let me just say you know this is
+a model for what's going on right
+
+ align:start position:0%
+a model for what's going on right
+ 
+
+ align:start position:0%
+a model for what's going on right
+suppose I did this instead I said okay
+
+ align:start position:0%
+suppose I did this instead I said okay
+ 
+
+ align:start position:0%
+suppose I did this instead I said okay
+I have my switching node right it's
+
+ align:start position:0%
+I have my switching node right it's
+ 
+
+ align:start position:0%
+I have my switching node right it's
+switching up and down and I and I still
+
+ align:start position:0%
+switching up and down and I and I still
+ 
+
+ align:start position:0%
+switching up and down and I and I still
+have this you know maybe this is still a
+
+ align:start position:0%
+have this you know maybe this is still a
+ 
+
+ align:start position:0%
+have this you know maybe this is still a
+a i minimized it but I still got a
+
+ align:start position:0%
+a i minimized it but I still got a
+ 
+
+ align:start position:0%
+a i minimized it but I still got a
+certain plate area there and I've still
+
+ align:start position:0%
+certain plate area there and I've still
+ 
+
+ align:start position:0%
+certain plate area there and I've still
+you know I I need some area for
+
+ align:start position:0%
+you know I I need some area for
+ 
+
+ align:start position:0%
+you know I I need some area for
+my um I need some area for my switching
+
+ align:start position:0%
+my um I need some area for my switching
+ 
+
+ align:start position:0%
+my um I need some area for my switching
+node and he's still going to be a high
+
+ align:start position:0%
+node and he's still going to be a high
+ 
+
+ align:start position:0%
+node and he's still going to be a high
+impedance node the other thing I can do
+
+ align:start position:0%
+impedance node the other thing I can do
+ 
+
+ align:start position:0%
+impedance node the other thing I can do
+by the way is if I make this resistor
+
+ align:start position:0%
+by the way is if I make this resistor
+ 
+
+ align:start position:0%
+by the way is if I make this resistor
+smaller that starts to become
+
+ align:start position:0%
+smaller that starts to become
+ 
+
+ align:start position:0%
+smaller that starts to become
+less nasty but you know there's only so
+
+ align:start position:0%
+less nasty but you know there's only so
+ 
+
+ align:start position:0%
+less nasty but you know there's only so
+much I can do about that well what else
+
+ align:start position:0%
+much I can do about that well what else
+ 
+
+ align:start position:0%
+much I can do about that well what else
+could I do maybe I could come in and say
+
+ align:start position:0%
+could I do maybe I could come in and say
+ 
+
+ align:start position:0%
+could I do maybe I could come in and say
+okay let me put some piece of
+
+ align:start position:0%
+okay let me put some piece of
+ 
+
+ align:start position:0%
+okay let me put some piece of
+metal that sits
+
+ align:start position:0%
+metal that sits
+ 
+
+ align:start position:0%
+metal that sits
+between the noisy node and the thing the
+
+ align:start position:0%
+between the noisy node and the thing the
+ 
+
+ align:start position:0%
+between the noisy node and the thing the
+sensitive
+
+ align:start position:0%
+sensitive
+ 
+
+ align:start position:0%
+sensitive
+node and maybe I'll just take that piece
+
+ align:start position:0%
+node and maybe I'll just take that piece
+ 
+
+ align:start position:0%
+node and maybe I'll just take that piece
+of metal and I'll ground
+
+ align:start position:0%
+of metal and I'll ground
+ 
+
+ align:start position:0%
+of metal and I'll ground
+it okay so what would be the circuit
+
+ align:start position:0%
+it okay so what would be the circuit
+ 
+
+ align:start position:0%
+it okay so what would be the circuit
+model for this the circuit model for
+
+ align:start position:0%
+model for this the circuit model for
+ 
+
+ align:start position:0%
+model for this the circuit model for
+this would be the following right I have
+
+ align:start position:0%
+this would be the following right I have
+ 
+
+ align:start position:0%
+this would be the following right I have
+my I this is sort of a circuit model
+
+ align:start position:0%
+my I this is sort of a circuit model
+ 
+
+ align:start position:0%
+my I this is sort of a circuit model
+already but what I have is you know
+
+ align:start position:0%
+already but what I have is you know
+ 
+
+ align:start position:0%
+already but what I have is you know
+essentially one capacitor that's tied to
+
+ align:start position:0%
+essentially one capacitor that's tied to
+ 
+
+ align:start position:0%
+essentially one capacitor that's tied to
+ground right I have the capacitance
+
+ align:start position:0%
+ground right I have the capacitance
+ 
+
+ align:start position:0%
+ground right I have the capacitance
+between pink and green and I'm grounding
+
+ align:start position:0%
+between pink and green and I'm grounding
+ 
+
+ align:start position:0%
+between pink and green and I'm grounding
+green and then I have the capacitance
+
+ align:start position:0%
+green and then I have the capacitance
+ 
+
+ align:start position:0%
+green and then I have the capacitance
+between green and
+
+ align:start position:0%
+between green and
+ 
+
+ align:start position:0%
+between green and
+yellow right so here's my other
+
+ align:start position:0%
+yellow right so here's my other
+ 
+
+ align:start position:0%
+yellow right so here's my other
+capacitance that goes to my sensitive
+
+ align:start position:0%
+capacitance that goes to my sensitive
+ 
+
+ align:start position:0%
+capacitance that goes to my sensitive
+node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here's now the voltage I'm inducing
+
+ align:start position:0%
+and here's now the voltage I'm inducing
+ 
+
+ align:start position:0%
+and here's now the voltage I'm inducing
+on the sensitive node what voltage would
+
+ align:start position:0%
+on the sensitive node what voltage would
+ 
+
+ align:start position:0%
+on the sensitive node what voltage would
+I be inducing due to this Square wave in
+
+ align:start position:0%
+I be inducing due to this Square wave in
+ 
+
+ align:start position:0%
+I be inducing due to this Square wave in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case am I going to see a voltage over
+
+ align:start position:0%
+case am I going to see a voltage over
+ 
+
+ align:start position:0%
+case am I going to see a voltage over
+here in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circuit no right I he's on he's got a
+
+ align:start position:0%
+circuit no right I he's on he's got a
+ 
+
+ align:start position:0%
+circuit no right I he's on he's got a
+grounded capacitor over here okay so
+
+ align:start position:0%
+grounded capacitor over here okay so
+ 
+
+ align:start position:0%
+grounded capacitor over here okay so
+essentially this piece of metal acts as
+
+ align:start position:0%
+essentially this piece of metal acts as
+ 
+
+ align:start position:0%
+essentially this piece of metal acts as
+an electrostatic Shield right if it was
+
+ align:start position:0%
+an electrostatic Shield right if it was
+ 
+
+ align:start position:0%
+an electrostatic Shield right if it was
+all the way around you'd call it a
+
+ align:start position:0%
+all the way around you'd call it a
+ 
+
+ align:start position:0%
+all the way around you'd call it a
+faraday cage okay but it prevents this
+
+ align:start position:0%
+faraday cage okay but it prevents this
+ 
+
+ align:start position:0%
+faraday cage okay but it prevents this
+noisy signal from injecting onto this
+
+ align:start position:0%
+noisy signal from injecting onto this
+ 
+
+ align:start position:0%
+noisy signal from injecting onto this
+well how would I do that one way to do
+
+ align:start position:0%
+well how would I do that one way to do
+ 
+
+ align:start position:0%
+well how would I do that one way to do
+that is maybe I put this switching Noe
+
+ align:start position:0%
+that is maybe I put this switching Noe
+ 
+
+ align:start position:0%
+that is maybe I put this switching Noe
+on one side of my circuit board I have a
+
+ align:start position:0%
+on one side of my circuit board I have a
+ 
+
+ align:start position:0%
+on one side of my circuit board I have a
+ground plane in between them and I put
+
+ align:start position:0%
+ground plane in between them and I put
+ 
+
+ align:start position:0%
+ground plane in between them and I put
+my control circuitry on the other side
+
+ align:start position:0%
+my control circuitry on the other side
+ 
+
+ align:start position:0%
+my control circuitry on the other side
+of the circuit board is sort of shielded
+
+ align:start position:0%
+of the circuit board is sort of shielded
+ 
+
+ align:start position:0%
+of the circuit board is sort of shielded
+or hidden from the high switching
+
+ align:start position:0%
+or hidden from the high switching
+ 
+
+ align:start position:0%
+or hidden from the high switching
+node that make sense
+
+ align:start position:0%
+node that make sense
+ 
+
+ align:start position:0%
+node that make sense
+everybody now you can't always do that
+
+ align:start position:0%
+everybody now you can't always do that
+ 
+
+ align:start position:0%
+everybody now you can't always do that
+what else could you do if you have
+
+ align:start position:0%
+what else could you do if you have
+ 
+
+ align:start position:0%
+what else could you do if you have
+really sensitive stuff so suppose I had
+
+ align:start position:0%
+really sensitive stuff so suppose I had
+ 
+
+ align:start position:0%
+really sensitive stuff so suppose I had
+a radio receiver right next to my
+
+ align:start position:0%
+a radio receiver right next to my
+ 
+
+ align:start position:0%
+a radio receiver right next to my
+switching node circuit
+
+ align:start position:0%
+switching node circuit
+ 
+
+ align:start position:0%
+switching node circuit
+right is that a good thing no but you
+
+ align:start position:0%
+right is that a good thing no but you
+ 
+
+ align:start position:0%
+right is that a good thing no but you
+know some days you don't get a choice
+
+ align:start position:0%
+know some days you don't get a choice
+ 
+
+ align:start position:0%
+know some days you don't get a choice
+right you can actually
+
+ align:start position:0%
+right you can actually
+ 
+
+ align:start position:0%
+right you can actually
+buy for printed circuit board Mount
+
+ align:start position:0%
+buy for printed circuit board Mount
+ 
+
+ align:start position:0%
+buy for printed circuit board Mount
+little shielding cans so basically is
+
+ align:start position:0%
+little shielding cans so basically is
+ 
+
+ align:start position:0%
+little shielding cans so basically is
+like it'll be it'll run around on the
+
+ align:start position:0%
+like it'll be it'll run around on the
+ 
+
+ align:start position:0%
+like it'll be it'll run around on the
+circuit board and provide a side edge
+
+ align:start position:0%
+circuit board and provide a side edge
+ 
+
+ align:start position:0%
+circuit board and provide a side edge
+and then put a little cap on it and you
+
+ align:start position:0%
+and then put a little cap on it and you
+ 
+
+ align:start position:0%
+and then put a little cap on it and you
+can put your whole your radio receiver
+
+ align:start position:0%
+can put your whole your radio receiver
+ 
+
+ align:start position:0%
+can put your whole your radio receiver
+or whatever very sensitive noise noise
+
+ align:start position:0%
+or whatever very sensitive noise noise
+ 
+
+ align:start position:0%
+or whatever very sensitive noise noise
+sensitive element inside of there so
+
+ align:start position:0%
+sensitive element inside of there so
+ 
+
+ align:start position:0%
+sensitive element inside of there so
+actually if you take a w take aart a WI
+
+ align:start position:0%
+actually if you take a w take aart a WI
+ 
+
+ align:start position:0%
+actually if you take a w take aart a WI
+router or something like that you'll
+
+ align:start position:0%
+router or something like that you'll
+ 
+
+ align:start position:0%
+router or something like that you'll
+often see these little kind of metal
+
+ align:start position:0%
+often see these little kind of metal
+ 
+
+ align:start position:0%
+often see these little kind of metal
+boxes at the top will pop off and and
+
+ align:start position:0%
+boxes at the top will pop off and and
+ 
+
+ align:start position:0%
+boxes at the top will pop off and and
+some of the RF stuff will be in there
+
+ align:start position:0%
+some of the RF stuff will be in there
+ 
+
+ align:start position:0%
+some of the RF stuff will be in there
+that's both to keep the RF noise in and
+
+ align:start position:0%
+that's both to keep the RF noise in and
+ 
+
+ align:start position:0%
+that's both to keep the RF noise in and
+to keep the external stuff out but you
+
+ align:start position:0%
+to keep the external stuff out but you
+ 
+
+ align:start position:0%
+to keep the external stuff out but you
+could do that with your control
+
+ align:start position:0%
+could do that with your control
+ 
+
+ align:start position:0%
+could do that with your control
+circuitry too if you had to but mostly
+
+ align:start position:0%
+circuitry too if you had to but mostly
+ 
+
+ align:start position:0%
+circuitry too if you had to but mostly
+what do you do you try to be smart by
+
+ align:start position:0%
+what do you do you try to be smart by
+ 
+
+ align:start position:0%
+what do you do you try to be smart by
+not putting it close or maybe putting it
+
+ align:start position:0%
+not putting it close or maybe putting it
+ 
+
+ align:start position:0%
+not putting it close or maybe putting it
+on the other side of the circuit board
+
+ align:start position:0%
+on the other side of the circuit board
+ 
+
+ align:start position:0%
+on the other side of the circuit board
+and getting yourself an electrostatic
+
+ align:start position:0%
+and getting yourself an electrostatic
+ 
+
+ align:start position:0%
+and getting yourself an electrostatic
+shield in there
+
+ align:start position:0%
+shield in there
+ 
+
+ align:start position:0%
+shield in there
+okay questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I should give
+
+ align:start position:0%
+I should give
+ 
+
+ align:start position:0%
+I should give
+you a little
+
+ align:start position:0%
+you a little
+ 
+
+ align:start position:0%
+you a little
+warning right when I did this
+
+ align:start position:0%
+warning right when I did this
+ 
+
+ align:start position:0%
+warning right when I did this
+approximation and hopefully get the
+
+ align:start position:0%
+approximation and hopefully get the
+ 
+
+ align:start position:0%
+approximation and hopefully get the
+right actual equation here to get the
+
+ align:start position:0%
+right actual equation here to get the
+ 
+
+ align:start position:0%
+right actual equation here to get the
+inductance and the capacitance in both
+
+ align:start position:0%
+inductance and the capacitance in both
+ 
+
+ align:start position:0%
+inductance and the capacitance in both
+cases I was neglecting fringing Fields
+
+ align:start position:0%
+cases I was neglecting fringing Fields
+ 
+
+ align:start position:0%
+cases I was neglecting fringing Fields
+right so when does this inductance
+
+ align:start position:0%
+right so when does this inductance
+ 
+
+ align:start position:0%
+right so when does this inductance
+equation really work well it works well
+
+ align:start position:0%
+equation really work well it works well
+ 
+
+ align:start position:0%
+equation really work well it works well
+when you have two really kind of wide
+
+ align:start position:0%
+when you have two really kind of wide
+ 
+
+ align:start position:0%
+when you have two really kind of wide
+conductors put close together so maybe I
+
+ align:start position:0%
+conductors put close together so maybe I
+ 
+
+ align:start position:0%
+conductors put close together so maybe I
+send my Gate Drive signal out and I
+
+ align:start position:0%
+send my Gate Drive signal out and I
+ 
+
+ align:start position:0%
+send my Gate Drive signal out and I
+return it right underneath that becomes
+
+ align:start position:0%
+return it right underneath that becomes
+ 
+
+ align:start position:0%
+return it right underneath that becomes
+a pretty good approximation to the loop
+
+ align:start position:0%
+a pretty good approximation to the loop
+ 
+
+ align:start position:0%
+a pretty good approximation to the loop
+inductance you're going to get or in a
+
+ align:start position:0%
+inductance you're going to get or in a
+ 
+
+ align:start position:0%
+inductance you're going to get or in a
+capacitance if I have two pieces of
+
+ align:start position:0%
+capacitance if I have two pieces of
+ 
+
+ align:start position:0%
+capacitance if I have two pieces of
+metal that are of the same size and
+
+ align:start position:0%
+metal that are of the same size and
+ 
+
+ align:start position:0%
+metal that are of the same size and
+they're really close together that's a
+
+ align:start position:0%
+they're really close together that's a
+ 
+
+ align:start position:0%
+they're really close together that's a
+pretty good approximation when I start
+
+ align:start position:0%
+pretty good approximation when I start
+ 
+
+ align:start position:0%
+pretty good approximation when I start
+to pull them apart what happens well I
+
+ align:start position:0%
+to pull them apart what happens well I
+ 
+
+ align:start position:0%
+to pull them apart what happens well I
+you know in the capacitance case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right for example this approximation
+
+ align:start position:0%
+right for example this approximation
+ 
+
+ align:start position:0%
+right for example this approximation
+is really just capturing the fields that
+
+ align:start position:0%
+is really just capturing the fields that
+ 
+
+ align:start position:0%
+is really just capturing the fields that
+are directly between these plates that's
+
+ align:start position:0%
+are directly between these plates that's
+ 
+
+ align:start position:0%
+are directly between these plates that's
+how you get to this equation once you
+
+ align:start position:0%
+how you get to this equation once you
+ 
+
+ align:start position:0%
+how you get to this equation once you
+start to have significant fringing
+
+ align:start position:0%
+start to have significant fringing
+ 
+
+ align:start position:0%
+start to have significant fringing
+Fields right the distance between the
+
+ align:start position:0%
+Fields right the distance between the
+ 
+
+ align:start position:0%
+Fields right the distance between the
+plates is long compared to the sort of
+
+ align:start position:0%
+plates is long compared to the sort of
+ 
+
+ align:start position:0%
+plates is long compared to the sort of
+the Coss the areas or the lengths on the
+
+ align:start position:0%
+the Coss the areas or the lengths on the
+ 
+
+ align:start position:0%
+the Coss the areas or the lengths on the
+other dimensions of the plate then these
+
+ align:start position:0%
+other dimensions of the plate then these
+ 
+
+ align:start position:0%
+other dimensions of the plate then these
+fringing Fields start to become
+
+ align:start position:0%
+fringing Fields start to become
+ 
+
+ align:start position:0%
+fringing Fields start to become
+important okay so you can't necessarily
+
+ align:start position:0%
+important okay so you can't necessarily
+ 
+
+ align:start position:0%
+important okay so you can't necessarily
+think of oh jeez you know my Capac is
+
+ align:start position:0%
+think of oh jeez you know my Capac is
+ 
+
+ align:start position:0%
+think of oh jeez you know my Capac is
+going to go exactly as the inverse of
+
+ align:start position:0%
+going to go exactly as the inverse of
+ 
+
+ align:start position:0%
+going to go exactly as the inverse of
+the distance between whatever things I'm
+
+ align:start position:0%
+the distance between whatever things I'm
+ 
+
+ align:start position:0%
+the distance between whatever things I'm
+going to have that's true when they're
+
+ align:start position:0%
+going to have that's true when they're
+ 
+
+ align:start position:0%
+going to have that's true when they're
+really close together but less true as
+
+ align:start position:0%
+really close together but less true as
+ 
+
+ align:start position:0%
+really close together but less true as
+you start to pull them far apart so a
+
+ align:start position:0%
+you start to pull them far apart so a
+ 
+
+ align:start position:0%
+you start to pull them far apart so a
+classic analysis you might look at is
+
+ align:start position:0%
+classic analysis you might look at is
+ 
+
+ align:start position:0%
+classic analysis you might look at is
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this suppose I took a
+
+ align:start position:0%
+this suppose I took a
+ 
+
+ align:start position:0%
+this suppose I took a
+sphere of radius R
+
+ align:start position:0%
+sphere of radius R
+ 
+
+ align:start position:0%
+sphere of radius R
+KN okay and I'm going to put a little
+
+ align:start position:0%
+KN okay and I'm going to put a little
+ 
+
+ align:start position:0%
+KN okay and I'm going to put a little
+charge on that sphere plus
+
+ align:start position:0%
+charge on that sphere plus
+ 
+
+ align:start position:0%
+charge on that sphere plus
+Q right right total net charge on the
+
+ align:start position:0%
+Q right right total net charge on the
+ 
+
+ align:start position:0%
+Q right right total net charge on the
+sphere and let me make the other plate
+
+ align:start position:0%
+sphere and let me make the other plate
+ 
+
+ align:start position:0%
+sphere and let me make the other plate
+of my capacitor a sphere that's around
+
+ align:start position:0%
+of my capacitor a sphere that's around
+ 
+
+ align:start position:0%
+of my capacitor a sphere that's around
+it at some you know Big
+
+ align:start position:0%
+it at some you know Big
+ 
+
+ align:start position:0%
+it at some you know Big
+R okay there's that itself forms a
+
+ align:start position:0%
+R okay there's that itself forms a
+ 
+
+ align:start position:0%
+R okay there's that itself forms a
+capacitance right where I have electric
+
+ align:start position:0%
+capacitance right where I have electric
+ 
+
+ align:start position:0%
+capacitance right where I have electric
+fields that are sort of you know I'm
+
+ align:start position:0%
+fields that are sort of you know I'm
+ 
+
+ align:start position:0%
+fields that are sort of you know I'm
+going to have mirror
+
+ align:start position:0%
+going to have mirror
+ 
+
+ align:start position:0%
+going to have mirror
+charges distributed on my outer plate on
+
+ align:start position:0%
+charges distributed on my outer plate on
+ 
+
+ align:start position:0%
+charges distributed on my outer plate on
+my outer sphere okay and I'm going to
+
+ align:start position:0%
+my outer sphere okay and I'm going to
+ 
+
+ align:start position:0%
+my outer sphere okay and I'm going to
+have electric field pointing outward
+
+ align:start position:0%
+have electric field pointing outward
+ 
+
+ align:start position:0%
+have electric field pointing outward
+here like this does that make sense
+
+ align:start position:0%
+here like this does that make sense
+ 
+
+ align:start position:0%
+here like this does that make sense
+everybody the picture I'm drawing I've
+
+ align:start position:0%
+everybody the picture I'm drawing I've
+ 
+
+ align:start position:0%
+everybody the picture I'm drawing I've
+got an inner sphere and an outer sphere
+
+ align:start position:0%
+got an inner sphere and an outer sphere
+ 
+
+ align:start position:0%
+got an inner sphere and an outer sphere
+and I want to calculate the capacitance
+
+ align:start position:0%
+and I want to calculate the capacitance
+ 
+
+ align:start position:0%
+and I want to calculate the capacitance
+between them and why am I doing spheres
+
+ align:start position:0%
+between them and why am I doing spheres
+ 
+
+ align:start position:0%
+between them and why am I doing spheres
+because I'm lazy and the Math's easy
+
+ align:start position:0%
+because I'm lazy and the Math's easy
+ 
+
+ align:start position:0%
+because I'm lazy and the Math's easy
+okay so think of whatever you got as
+
+ align:start position:0%
+okay so think of whatever you got as
+ 
+
+ align:start position:0%
+okay so think of whatever you got as
+being a little sphere okay but here's
+
+ align:start position:0%
+being a little sphere okay but here's
+ 
+
+ align:start position:0%
+being a little sphere okay but here's
+what I'm going to do let me make the
+
+ align:start position:0%
+what I'm going to do let me make the
+ 
+
+ align:start position:0%
+what I'm going to do let me make the
+outer sphere go off to
+
+ align:start position:0%
+outer sphere go off to
+ 
+
+ align:start position:0%
+outer sphere go off to
+Infinity right so I can say what is the
+
+ align:start position:0%
+Infinity right so I can say what is the
+ 
+
+ align:start position:0%
+Infinity right so I can say what is the
+capacitance of this little sphere of
+
+ align:start position:0%
+capacitance of this little sphere of
+ 
+
+ align:start position:0%
+capacitance of this little sphere of
+metal to the rest of the universe
+
+ align:start position:0%
+metal to the rest of the universe
+ 
+
+ align:start position:0%
+metal to the rest of the universe
+okay well what is that well we can
+
+ align:start position:0%
+okay well what is that well we can
+ 
+
+ align:start position:0%
+okay well what is that well we can
+calculate
+
+ align:start position:0%
+calculate
+ 
+
+ align:start position:0%
+calculate
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um if I take the integral of Epsilon KN
+
+ align:start position:0%
+um if I take the integral of Epsilon KN
+ 
+
+ align:start position:0%
+um if I take the integral of Epsilon KN
+a over uh
+
+ align:start position:0%
+a over uh
+ 
+
+ align:start position:0%
+a over uh
+the the integral of Epsilon e Doda is
+
+ align:start position:0%
+the the integral of Epsilon e Doda is
+ 
+
+ align:start position:0%
+the the integral of Epsilon e Doda is
+equal to the net charge I'm enclosing
+
+ align:start position:0%
+equal to the net charge I'm enclosing
+ 
+
+ align:start position:0%
+equal to the net charge I'm enclosing
+right so um if I then figured this out
+
+ align:start position:0%
+right so um if I then figured this out
+ 
+
+ align:start position:0%
+right so um if I then figured this out
+suppose I took a a sphere around my
+
+ align:start position:0%
+suppose I took a a sphere around my
+ 
+
+ align:start position:0%
+suppose I took a a sphere around my
+inner sphere and I said what's the
+
+ align:start position:0%
+inner sphere and I said what's the
+ 
+
+ align:start position:0%
+inner sphere and I said what's the
+radial electric field what is the E subr
+
+ align:start position:0%
+radial electric field what is the E subr
+ 
+
+ align:start position:0%
+radial electric field what is the E subr
+the radial electric field going to be
+
+ align:start position:0%
+the radial electric field going to be
+ 
+
+ align:start position:0%
+the radial electric field going to be
+you know what is this electric field
+
+ align:start position:0%
+you know what is this electric field
+ 
+
+ align:start position:0%
+you know what is this electric field
+going to be at some distance R from the
+
+ align:start position:0%
+going to be at some distance R from the
+ 
+
+ align:start position:0%
+going to be at some distance R from the
+center right that's going to be equal to
+
+ align:start position:0%
+center right that's going to be equal to
+ 
+
+ align:start position:0%
+center right that's going to be equal to
+e subr is just going to be equal to Q
+
+ align:start position:0%
+e subr is just going to be equal to Q
+ 
+
+ align:start position:0%
+e subr is just going to be equal to Q
+over Epsilon times the area which is 4
+
+ align:start position:0%
+over Epsilon times the area which is 4
+ 
+
+ align:start position:0%
+over Epsilon times the area which is 4
+pi r 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right what's the voltage that's going to
+
+ align:start position:0%
+right what's the voltage that's going to
+ 
+
+ align:start position:0%
+right what's the voltage that's going to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+between the outer sphere and the inner
+
+ align:start position:0%
+between the outer sphere and the inner
+ 
+
+ align:start position:0%
+between the outer sphere and the inner
+sphere well the voltage is going to be
+
+ align:start position:0%
+sphere well the voltage is going to be
+ 
+
+ align:start position:0%
+sphere well the voltage is going to be
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+to minus the integral from of es subar
+
+ align:start position:0%
+to minus the integral from of es subar
+ 
+
+ align:start position:0%
+to minus the integral from of es subar
+Dr or I could write that just to be easy
+
+ align:start position:0%
+Dr or I could write that just to be easy
+ 
+
+ align:start position:0%
+Dr or I could write that just to be easy
+as Infinity to R not the integral from
+
+ align:start position:0%
+as Infinity to R not the integral from
+ 
+
+ align:start position:0%
+as Infinity to R not the integral from
+Infinity out to the surface of my little
+
+ align:start position:0%
+Infinity out to the surface of my little
+ 
+
+ align:start position:0%
+Infinity out to the surface of my little
+piece of metal that's got charge on
+
+ align:start position:0%
+piece of metal that's got charge on
+ 
+
+ align:start position:0%
+piece of metal that's got charge on
+it of uh Q over Epsilon * 4i r^ 2 which
+
+ align:start position:0%
+it of uh Q over Epsilon * 4i r^ 2 which
+ 
+
+ align:start position:0%
+it of uh Q over Epsilon * 4i r^ 2 which
+is just going to be equal to Q
+
+ align:start position:0%
+is just going to be equal to Q
+ 
+
+ align:start position:0%
+is just going to be equal to Q
+/ uh Epsilon over 4 pi r
+
+ align:start position:0%
+/ uh Epsilon over 4 pi r
+ 
+
+ align:start position:0%
+/ uh Epsilon over 4 pi r
+right and that means that Q if I write
+
+ align:start position:0%
+right and that means that Q if I write
+ 
+
+ align:start position:0%
+right and that means that Q if I write
+this Q is just going to be equal to V *
+
+ align:start position:0%
+this Q is just going to be equal to V *
+ 
+
+ align:start position:0%
+this Q is just going to be equal to V *
+Epsilon * 4i r
+
+ align:start position:0%
+Epsilon * 4i r
+ 
+
+ align:start position:0%
+Epsilon * 4i r
+r r KN it's the radius of this little
+
+ align:start position:0%
+r r KN it's the radius of this little
+ 
+
+ align:start position:0%
+r r KN it's the radius of this little
+sphere R KN
+
+ align:start position:0%
+sphere R KN
+ 
+
+ align:start position:0%
+sphere R KN
+okay but we know that Q is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CV right so this must be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitance okay so I'm kind of taking
+
+ align:start position:0%
+capacitance okay so I'm kind of taking
+ 
+
+ align:start position:0%
+capacitance okay so I'm kind of taking
+the other case where all of my field is
+
+ align:start position:0%
+the other case where all of my field is
+ 
+
+ align:start position:0%
+the other case where all of my field is
+fringing field out to the universe
+
+ align:start position:0%
+fringing field out to the universe
+ 
+
+ align:start position:0%
+fringing field out to the universe
+okay and in this case the capacitance to
+
+ align:start position:0%
+okay and in this case the capacitance to
+ 
+
+ align:start position:0%
+okay and in this case the capacitance to
+the universe from some little sphere of
+
+ align:start position:0%
+the universe from some little sphere of
+ 
+
+ align:start position:0%
+the universe from some little sphere of
+metal that I've got sitting here is
+
+ align:start position:0%
+metal that I've got sitting here is
+ 
+
+ align:start position:0%
+metal that I've got sitting here is
+exactly the dialectric which presumably
+
+ align:start position:0%
+exactly the dialectric which presumably
+ 
+
+ align:start position:0%
+exactly the dialectric which presumably
+if it's free space it's Epsilon KN Time
+
+ align:start position:0%
+if it's free space it's Epsilon KN Time
+ 
+
+ align:start position:0%
+if it's free space it's Epsilon KN Time
+4 Pi * the radius of the sphere so it's
+
+ align:start position:0%
+4 Pi * the radius of the sphere so it's
+ 
+
+ align:start position:0%
+4 Pi * the radius of the sphere so it's
+related to the square root of the area
+
+ align:start position:0%
+related to the square root of the area
+ 
+
+ align:start position:0%
+related to the square root of the area
+of the sphere if I increase the area of
+
+ align:start position:0%
+of the sphere if I increase the area of
+ 
+
+ align:start position:0%
+of the sphere if I increase the area of
+this thing the capacitance to the
+
+ align:start position:0%
+this thing the capacitance to the
+ 
+
+ align:start position:0%
+this thing the capacitance to the
+universe is not zero even though the
+
+ align:start position:0%
+universe is not zero even though the
+ 
+
+ align:start position:0%
+universe is not zero even though the
+universe is infinitely far away it's
+
+ align:start position:0%
+universe is infinitely far away it's
+ 
+
+ align:start position:0%
+universe is infinitely far away it's
+some finite amount related to the area
+
+ align:start position:0%
+some finite amount related to the area
+ 
+
+ align:start position:0%
+some finite amount related to the area
+or the radius of the thing I've got okay
+
+ align:start position:0%
+or the radius of the thing I've got okay
+ 
+
+ align:start position:0%
+or the radius of the thing I've got okay
+so that's like this basically a long way
+
+ align:start position:0%
+so that's like this basically a long way
+ 
+
+ align:start position:0%
+so that's like this basically a long way
+of saying when I make things space far
+
+ align:start position:0%
+of saying when I make things space far
+ 
+
+ align:start position:0%
+of saying when I make things space far
+apart fringing becomes very very
+
+ align:start position:0%
+apart fringing becomes very very
+ 
+
+ align:start position:0%
+apart fringing becomes very very
+important and I can get you know nonzero
+
+ align:start position:0%
+important and I can get you know nonzero
+ 
+
+ align:start position:0%
+important and I can get you know nonzero
+capacitances right or significant
+
+ align:start position:0%
+capacitances right or significant
+ 
+
+ align:start position:0%
+capacitances right or significant
+capacitances and in that light the only
+
+ align:start position:0%
+capacitances and in that light the only
+ 
+
+ align:start position:0%
+capacitances and in that light the only
+way you can really make that capacit
+
+ align:start position:0%
+way you can really make that capacit
+ 
+
+ align:start position:0%
+way you can really make that capacit
+smaller is to basically make R KN
+
+ align:start position:0%
+smaller is to basically make R KN
+ 
+
+ align:start position:0%
+smaller is to basically make R KN
+smaller or Mak basically make the area
+
+ align:start position:0%
+smaller or Mak basically make the area
+ 
+
+ align:start position:0%
+smaller or Mak basically make the area
+of the thing that you're worried about
+
+ align:start position:0%
+of the thing that you're worried about
+ 
+
+ align:start position:0%
+of the thing that you're worried about
+spraying field out smaller so its
+
+ align:start position:0%
+spraying field out smaller so its
+ 
+
+ align:start position:0%
+spraying field out smaller so its
+capacitance to other stuff will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smaller questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so this is just sort of a case
+
+ align:start position:0%
+that so this is just sort of a case
+ 
+
+ align:start position:0%
+that so this is just sort of a case
+where you know physics
+
+ align:start position:0%
+where you know physics
+ 
+
+ align:start position:0%
+where you know physics
+101 leads you to some conclusions about
+
+ align:start position:0%
+101 leads you to some conclusions about
+ 
+
+ align:start position:0%
+101 leads you to some conclusions about
+how you should lay your circuits out
+
+ align:start position:0%
+how you should lay your circuits out
+ 
+
+ align:start position:0%
+how you should lay your circuits out
+which comes back to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make your Loops very tight and you I
+
+ align:start position:0%
+make your Loops very tight and you I
+ 
+
+ align:start position:0%
+make your Loops very tight and you I
+could make this I could have done the
+
+ align:start position:0%
+could make this I could have done the
+ 
+
+ align:start position:0%
+could make this I could have done the
+same analysis for finding inductances of
+
+ align:start position:0%
+same analysis for finding inductances of
+ 
+
+ align:start position:0%
+same analysis for finding inductances of
+loops and so so forth right you make
+
+ align:start position:0%
+loops and so so forth right you make
+ 
+
+ align:start position:0%
+loops and so so forth right you make
+your Loop tight you spread the area you
+
+ align:start position:0%
+your Loop tight you spread the area you
+ 
+
+ align:start position:0%
+your Loop tight you spread the area you
+spread the current out to get the
+
+ align:start position:0%
+spread the current out to get the
+ 
+
+ align:start position:0%
+spread the current out to get the
+inductance low so and and make the loop
+
+ align:start position:0%
+inductance low so and and make the loop
+ 
+
+ align:start position:0%
+inductance low so and and make the loop
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+tight don't use excess Loop don't use
+
+ align:start position:0%
+tight don't use excess Loop don't use
+ 
+
+ align:start position:0%
+tight don't use excess Loop don't use
+excess Trace area especially at these
+
+ align:start position:0%
+excess Trace area especially at these
+ 
+
+ align:start position:0%
+excess Trace area especially at these
+this Loop and this node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if you going to go analyze a che
+
+ align:start position:0%
+okay if you going to go analyze a che
+ 
+
+ align:start position:0%
+okay if you going to go analyze a che
+converter or some other kind of
+
+ align:start position:0%
+converter or some other kind of
+ 
+
+ align:start position:0%
+converter or some other kind of
+converter the which Loop you care about
+
+ align:start position:0%
+converter the which Loop you care about
+ 
+
+ align:start position:0%
+converter the which Loop you care about
+is different which nodes you care about
+
+ align:start position:0%
+is different which nodes you care about
+ 
+
+ align:start position:0%
+is different which nodes you care about
+are different but they're usually the
+
+ align:start position:0%
+are different but they're usually the
+ 
+
+ align:start position:0%
+are different but they're usually the
+ones with the square wave currents in
+
+ align:start position:0%
+ones with the square wave currents in
+ 
+
+ align:start position:0%
+ones with the square wave currents in
+them and the square wave voltages on or
+
+ align:start position:0%
+them and the square wave voltages on or
+ 
+
+ align:start position:0%
+them and the square wave voltages on or
+the high dvdt or didt elements on them
+
+ align:start position:0%
+the high dvdt or didt elements on them
+ 
+
+ align:start position:0%
+the high dvdt or didt elements on them
+okay and small changes can make a big
+
+ align:start position:0%
+okay and small changes can make a big
+ 
+
+ align:start position:0%
+okay and small changes can make a big
+difference questions about any of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just talk about a couple of other
+
+ align:start position:0%
+let me just talk about a couple of other
+ 
+
+ align:start position:0%
+let me just talk about a couple of other
+things that I've glossed over or just
+
+ align:start position:0%
+things that I've glossed over or just
+ 
+
+ align:start position:0%
+things that I've glossed over or just
+not it's not that I've glossed over I've
+
+ align:start position:0%
+not it's not that I've glossed over I've
+ 
+
+ align:start position:0%
+not it's not that I've glossed over I've
+just not worried about them uh and these
+
+ align:start position:0%
+just not worried about them uh and these
+ 
+
+ align:start position:0%
+just not worried about them uh and these
+again are practical implementation
+
+ align:start position:0%
+again are practical implementation
+ 
+
+ align:start position:0%
+again are practical implementation
+issues which are important but you know
+
+ align:start position:0%
+issues which are important but you know
+ 
+
+ align:start position:0%
+issues which are important but you know
+you got to worry about them after you
+
+ align:start position:0%
+you got to worry about them after you
+ 
+
+ align:start position:0%
+you got to worry about them after you
+worry about the rest of your
+
+ align:start position:0%
+worry about the rest of your
+ 
+
+ align:start position:0%
+worry about the rest of your
+system let's think about driving the
+
+ align:start position:0%
+system let's think about driving the
+ 
+
+ align:start position:0%
+system let's think about driving the
+gates of our uh
+
+ align:start position:0%
+gates of our uh
+ 
+
+ align:start position:0%
+gates of our uh
+converters a Gates of our transistors
+
+ align:start position:0%
+converters a Gates of our transistors
+ 
+
+ align:start position:0%
+converters a Gates of our transistors
+right so if I think about my mosfet so
+
+ align:start position:0%
+right so if I think about my mosfet so
+ 
+
+ align:start position:0%
+right so if I think about my mosfet so
+suppose I I don't know suppose I make a
+
+ align:start position:0%
+suppose I I don't know suppose I make a
+ 
+
+ align:start position:0%
+suppose I I don't know suppose I make a
+boost converter for example so I've been
+
+ align:start position:0%
+boost converter for example so I've been
+ 
+
+ align:start position:0%
+boost converter for example so I've been
+talking about Buck converters now I'll
+
+ align:start position:0%
+talking about Buck converters now I'll
+ 
+
+ align:start position:0%
+talking about Buck converters now I'll
+talk about boost converters right I'm
+
+ align:start position:0%
+talk about boost converters right I'm
+ 
+
+ align:start position:0%
+talk about boost converters right I'm
+going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have some circuit here and I'm going to
+
+ align:start position:0%
+have some circuit here and I'm going to
+ 
+
+ align:start position:0%
+have some circuit here and I'm going to
+drive him right and usually what's going
+
+ align:start position:0%
+drive him right and usually what's going
+ 
+
+ align:start position:0%
+drive him right and usually what's going
+to be here is there's going to be some
+
+ align:start position:0%
+to be here is there's going to be some
+ 
+
+ align:start position:0%
+to be here is there's going to be some
+circuit which is making switching
+
+ align:start position:0%
+circuit which is making switching
+ 
+
+ align:start position:0%
+circuit which is making switching
+decisions it's powered from some low
+
+ align:start position:0%
+decisions it's powered from some low
+ 
+
+ align:start position:0%
+decisions it's powered from some low
+voltage
+
+ align:start position:0%
+voltage
+ 
+
+ align:start position:0%
+voltage
+Supply and it's you know it's got some
+
+ align:start position:0%
+Supply and it's you know it's got some
+ 
+
+ align:start position:0%
+Supply and it's you know it's got some
+input that's telling me when to switch
+
+ align:start position:0%
+input that's telling me when to switch
+ 
+
+ align:start position:0%
+input that's telling me when to switch
+this transistor
+
+ align:start position:0%
+this transistor
+ 
+
+ align:start position:0%
+this transistor
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um what does the input of that
+
+ align:start position:0%
+um what does the input of that
+ 
+
+ align:start position:0%
+um what does the input of that
+transistor look like well you know this
+
+ align:start position:0%
+transistor look like well you know this
+ 
+
+ align:start position:0%
+transistor look like well you know this
+thing in him the last thing between me
+
+ align:start position:0%
+thing in him the last thing between me
+ 
+
+ align:start position:0%
+thing in him the last thing between me
+and my switch is some sort of gate
+
+ align:start position:0%
+and my switch is some sort of gate
+ 
+
+ align:start position:0%
+and my switch is some sort of gate
+driver right which is going to be
+
+ align:start position:0%
+driver right which is going to be
+ 
+
+ align:start position:0%
+driver right which is going to be
+powered from some voltage and he's got
+
+ align:start position:0%
+powered from some voltage and he's got
+ 
+
+ align:start position:0%
+powered from some voltage and he's got
+some signal coming
+
+ align:start position:0%
+some signal coming
+ 
+
+ align:start position:0%
+some signal coming
+in and he's going to try to turn this
+
+ align:start position:0%
+in and he's going to try to turn this
+ 
+
+ align:start position:0%
+in and he's going to try to turn this
+transistor on and off right so if I I
+
+ align:start position:0%
+transistor on and off right so if I I
+ 
+
+ align:start position:0%
+transistor on and off right so if I I
+thought about my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transistor right here I'm going to I'm
+
+ align:start position:0%
+transistor right here I'm going to I'm
+ 
+
+ align:start position:0%
+transistor right here I'm going to I'm
+going to drive this with some Square
+
+ align:start position:0%
+going to drive this with some Square
+ 
+
+ align:start position:0%
+going to drive this with some Square
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+voltage and I I need to remember that
+
+ align:start position:0%
+voltage and I I need to remember that
+ 
+
+ align:start position:0%
+voltage and I I need to remember that
+this transistor is going to have some
+
+ align:start position:0%
+this transistor is going to have some
+ 
+
+ align:start position:0%
+this transistor is going to have some
+gate Source
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitance he's going to have some
+
+ align:start position:0%
+capacitance he's going to have some
+ 
+
+ align:start position:0%
+capacitance he's going to have some
+drain Source capacitance but he's also
+
+ align:start position:0%
+drain Source capacitance but he's also
+ 
+
+ align:start position:0%
+drain Source capacitance but he's also
+importantly going to have some gate to
+
+ align:start position:0%
+importantly going to have some gate to
+ 
+
+ align:start position:0%
+importantly going to have some gate to
+drain
+
+ align:start position:0%
+drain
+ 
+
+ align:start position:0%
+drain
+capacitance
+
+ align:start position:0%
+capacitance
+ 
+
+ align:start position:0%
+capacitance
+okay and and this gate to drain
+
+ align:start position:0%
+okay and and this gate to drain
+ 
+
+ align:start position:0%
+okay and and this gate to drain
+capacitance actually has a significant
+
+ align:start position:0%
+capacitance actually has a significant
+ 
+
+ align:start position:0%
+capacitance actually has a significant
+influence especially in the case when
+
+ align:start position:0%
+influence especially in the case when
+ 
+
+ align:start position:0%
+influence especially in the case when
+suppose I'm driving this between you
+
+ align:start position:0%
+suppose I'm driving this between you
+ 
+
+ align:start position:0%
+suppose I'm driving this between you
+know 0 and 10 volts or something or 0
+
+ align:start position:0%
+know 0 and 10 volts or something or 0
+ 
+
+ align:start position:0%
+know 0 and 10 volts or something or 0
+and 5 volts if it's a a lower you know a
+
+ align:start position:0%
+and 5 volts if it's a a lower you know a
+ 
+
+ align:start position:0%
+and 5 volts if it's a a lower you know a
+logic level kind of device all right but
+
+ align:start position:0%
+logic level kind of device all right but
+ 
+
+ align:start position:0%
+logic level kind of device all right but
+maybe this drain node is switching by
+
+ align:start position:0%
+maybe this drain node is switching by
+ 
+
+ align:start position:0%
+maybe this drain node is switching by
+hundreds of volts so this capacitance is
+
+ align:start position:0%
+hundreds of volts so this capacitance is
+ 
+
+ align:start position:0%
+hundreds of volts so this capacitance is
+the so-called sort of Miller feedback
+
+ align:start position:0%
+the so-called sort of Miller feedback
+ 
+
+ align:start position:0%
+the so-called sort of Miller feedback
+capacitance this guy right here can have
+
+ align:start position:0%
+capacitance this guy right here can have
+ 
+
+ align:start position:0%
+capacitance this guy right here can have
+a big impact
+
+ align:start position:0%
+a big impact
+ 
+
+ align:start position:0%
+a big impact
+on the switching characteristics here
+
+ align:start position:0%
+on the switching characteristics here
+ 
+
+ align:start position:0%
+on the switching characteristics here
+okay because what happens if I look at
+
+ align:start position:0%
+okay because what happens if I look at
+ 
+
+ align:start position:0%
+okay because what happens if I look at
+sort of the charge I'm sourcing in here
+
+ align:start position:0%
+sort of the charge I'm sourcing in here
+ 
+
+ align:start position:0%
+sort of the charge I'm sourcing in here
+and the voltage vgs I'm getting and this
+
+ align:start position:0%
+and the voltage vgs I'm getting and this
+ 
+
+ align:start position:0%
+and the voltage vgs I'm getting and this
+voltage if this is a end Channel mosfet
+
+ align:start position:0%
+voltage if this is a end Channel mosfet
+ 
+
+ align:start position:0%
+voltage if this is a end Channel mosfet
+it's this voltage that this vgs voltage
+
+ align:start position:0%
+it's this voltage that this vgs voltage
+ 
+
+ align:start position:0%
+it's this voltage that this vgs voltage
+is what's controlling how he switches on
+
+ align:start position:0%
+is what's controlling how he switches on
+ 
+
+ align:start position:0%
+is what's controlling how he switches on
+right if I looked
+
+ align:start position:0%
+right if I looked
+ 
+
+ align:start position:0%
+right if I looked
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+vgs versus
+
+ align:start position:0%
+vgs versus
+ 
+
+ align:start position:0%
+vgs versus
+Q sub Q
+
+ align:start position:0%
+Q sub Q
+ 
+
+ align:start position:0%
+Q sub Q
+subg right the gate charge I'm putting
+
+ align:start position:0%
+subg right the gate charge I'm putting
+ 
+
+ align:start position:0%
+subg right the gate charge I'm putting
+in what would happen well when this
+
+ align:start position:0%
+in what would happen well when this
+ 
+
+ align:start position:0%
+in what would happen well when this
+thing's
+
+ align:start position:0%
+thing's
+ 
+
+ align:start position:0%
+thing's
+off before he turns on I'm going to
+
+ align:start position:0%
+off before he turns on I'm going to
+ 
+
+ align:start position:0%
+off before he turns on I'm going to
+start
+
+ align:start position:0%
+start
+ 
+
+ align:start position:0%
+start
+charging the gate right and this is the
+
+ align:start position:0%
+charging the gate right and this is the
+ 
+
+ align:start position:0%
+charging the gate right and this is the
+capacitance my gate driver is driving
+
+ align:start position:0%
+capacitance my gate driver is driving
+ 
+
+ align:start position:0%
+capacitance my gate driver is driving
+right DQ is
+
+ align:start position:0%
+right DQ is
+ 
+
+ align:start position:0%
+right DQ is
+CDV all right but what happens at some
+
+ align:start position:0%
+CDV all right but what happens at some
+ 
+
+ align:start position:0%
+CDV all right but what happens at some
+point is when vgs gets bigger than the
+
+ align:start position:0%
+point is when vgs gets bigger than the
+ 
+
+ align:start position:0%
+point is when vgs gets bigger than the
+threshold
+
+ align:start position:0%
+threshold
+ 
+
+ align:start position:0%
+threshold
+voltage I'm going to start turning on
+
+ align:start position:0%
+voltage I'm going to start turning on
+ 
+
+ align:start position:0%
+voltage I'm going to start turning on
+this fet which and what what does that
+
+ align:start position:0%
+this fet which and what what does that
+ 
+
+ align:start position:0%
+this fet which and what what does that
+happen this voltage which was up at some
+
+ align:start position:0%
+happen this voltage which was up at some
+ 
+
+ align:start position:0%
+happen this voltage which was up at some
+high voltage this was the output voltage
+
+ align:start position:0%
+high voltage this was the output voltage
+ 
+
+ align:start position:0%
+high voltage this was the output voltage
+maybe that's 200 volts starts to swing
+
+ align:start position:0%
+maybe that's 200 volts starts to swing
+ 
+
+ align:start position:0%
+maybe that's 200 volts starts to swing
+down and when it starts to swing down I
+
+ align:start position:0%
+down and when it starts to swing down I
+ 
+
+ align:start position:0%
+down and when it starts to swing down I
+need to feed charge in from the gate to
+
+ align:start position:0%
+need to feed charge in from the gate to
+ 
+
+ align:start position:0%
+need to feed charge in from the gate to
+to sort of discharge this
+
+ align:start position:0%
+to sort of discharge this
+ 
+
+ align:start position:0%
+to sort of discharge this
+capacitor
+
+ align:start position:0%
+capacitor
+ 
+
+ align:start position:0%
+capacitor
+right and what that means is I'm going
+
+ align:start position:0%
+right and what that means is I'm going
+ 
+
+ align:start position:0%
+right and what that means is I'm going
+to be trying I'm going to be pumping
+
+ align:start position:0%
+to be trying I'm going to be pumping
+ 
+
+ align:start position:0%
+to be trying I'm going to be pumping
+charge in
+
+ align:start position:0%
+charge in
+ 
+
+ align:start position:0%
+charge in
+here but the gate voltage isn't going to
+
+ align:start position:0%
+here but the gate voltage isn't going to
+ 
+
+ align:start position:0%
+here but the gate voltage isn't going to
+be going up appreciatively he's just
+
+ align:start position:0%
+be going up appreciatively he's just
+ 
+
+ align:start position:0%
+be going up appreciatively he's just
+going to sit flat and all the charge I'm
+
+ align:start position:0%
+going to sit flat and all the charge I'm
+ 
+
+ align:start position:0%
+going to sit flat and all the charge I'm
+pumping in here is basically going to
+
+ align:start position:0%
+pumping in here is basically going to
+ 
+
+ align:start position:0%
+pumping in here is basically going to
+drive the drain
+
+ align:start position:0%
+drive the drain
+ 
+
+ align:start position:0%
+drive the drain
+down Okay so this capacitor basically
+
+ align:start position:0%
+down Okay so this capacitor basically
+ 
+
+ align:start position:0%
+down Okay so this capacitor basically
+suddenly makes the equivalent
+
+ align:start position:0%
+suddenly makes the equivalent
+ 
+
+ align:start position:0%
+suddenly makes the equivalent
+capacitance I'm driving at my gate very
+
+ align:start position:0%
+capacitance I'm driving at my gate very
+ 
+
+ align:start position:0%
+capacitance I'm driving at my gate very
+large eventually once I've pumped enough
+
+ align:start position:0%
+large eventually once I've pumped enough
+ 
+
+ align:start position:0%
+large eventually once I've pumped enough
+in this node comes down to close to
+
+ align:start position:0%
+in this node comes down to close to
+ 
+
+ align:start position:0%
+in this node comes down to close to
+ground this voltage ceases changing and
+
+ align:start position:0%
+ground this voltage ceases changing and
+ 
+
+ align:start position:0%
+ground this voltage ceases changing and
+then this goes up like this okay so this
+
+ align:start position:0%
+then this goes up like this okay so this
+ 
+
+ align:start position:0%
+then this goes up like this okay so this
+happens you know somewhere near vth the
+
+ align:start position:0%
+happens you know somewhere near vth the
+ 
+
+ align:start position:0%
+happens you know somewhere near vth the
+threshold voltage of the f
+
+ align:start position:0%
+threshold voltage of the f
+ 
+
+ align:start position:0%
+threshold voltage of the f
+that does that make sense
+
+ align:start position:0%
+that does that make sense
+ 
+
+ align:start position:0%
+that does that make sense
+everybody why am I why am I pointing
+
+ align:start position:0%
+everybody why am I why am I pointing
+ 
+
+ align:start position:0%
+everybody why am I why am I pointing
+this out well two reasons
+
+ align:start position:0%
+this out well two reasons
+ 
+
+ align:start position:0%
+this out well two reasons
+firstly um when I think about the amount
+
+ align:start position:0%
+firstly um when I think about the amount
+ 
+
+ align:start position:0%
+firstly um when I think about the amount
+of charge I need to put in you know
+
+ align:start position:0%
+of charge I need to put in you know
+ 
+
+ align:start position:0%
+of charge I need to put in you know
+maybe this is my this is my threshold
+
+ align:start position:0%
+maybe this is my this is my threshold
+ 
+
+ align:start position:0%
+maybe this is my this is my threshold
+voltage I don't know whatever that is
+
+ align:start position:0%
+voltage I don't know whatever that is
+ 
+
+ align:start position:0%
+voltage I don't know whatever that is
+maybe this is 10 volts and this is 50
+
+ align:start position:0%
+maybe this is 10 volts and this is 50
+ 
+
+ align:start position:0%
+maybe this is 10 volts and this is 50
+nanocs right so what I sort of care
+
+ align:start position:0%
+nanocs right so what I sort of care
+ 
+
+ align:start position:0%
+nanocs right so what I sort of care
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+is I need to Source this total
+
+ align:start position:0%
+is I need to Source this total
+ 
+
+ align:start position:0%
+is I need to Source this total
+charge um to get to 10 volts and if I
+
+ align:start position:0%
+charge um to get to 10 volts and if I
+ 
+
+ align:start position:0%
+charge um to get to 10 volts and if I
+only paid attention to what this
+
+ align:start position:0%
+only paid attention to what this
+ 
+
+ align:start position:0%
+only paid attention to what this
+capacitance was I wouldn't really
+
+ align:start position:0%
+capacitance was I wouldn't really
+ 
+
+ align:start position:0%
+capacitance was I wouldn't really
+calculate the total charge I needed
+
+ align:start position:0%
+calculate the total charge I needed
+ 
+
+ align:start position:0%
+calculate the total charge I needed
+right and how much energy how much do I
+
+ align:start position:0%
+right and how much energy how much do I
+ 
+
+ align:start position:0%
+right and how much energy how much do I
+lose from this Gate Drive power supply
+
+ align:start position:0%
+lose from this Gate Drive power supply
+ 
+
+ align:start position:0%
+lose from this Gate Drive power supply
+well we talked about this when we talked
+
+ align:start position:0%
+well we talked about this when we talked
+ 
+
+ align:start position:0%
+well we talked about this when we talked
+about switch capacitor converters right
+
+ align:start position:0%
+about switch capacitor converters right
+ 
+
+ align:start position:0%
+about switch capacitor converters right
+if I'm supplying you know here's some
+
+ align:start position:0%
+if I'm supplying you know here's some
+ 
+
+ align:start position:0%
+if I'm supplying you know here's some
+value Q
+
+ align:start position:0%
+value Q
+ 
+
+ align:start position:0%
+value Q
+subg total right that Supply is always
+
+ align:start position:0%
+subg total right that Supply is always
+ 
+
+ align:start position:0%
+subg total right that Supply is always
+coming from this you know Gate Drive
+
+ align:start position:0%
+coming from this you know Gate Drive
+ 
+
+ align:start position:0%
+coming from this you know Gate Drive
+power supply voltage 10 volts or
+
+ align:start position:0%
+power supply voltage 10 volts or
+ 
+
+ align:start position:0%
+power supply voltage 10 volts or
+something right so the amount of energy
+
+ align:start position:0%
+something right so the amount of energy
+ 
+
+ align:start position:0%
+something right so the amount of energy
+that comes in to charge up this gate is
+
+ align:start position:0%
+that comes in to charge up this gate is
+ 
+
+ align:start position:0%
+that comes in to charge up this gate is
+going to be equal to
+
+ align:start position:0%
+going to be equal to
+ 
+
+ align:start position:0%
+going to be equal to
+qg times vgs
+
+ align:start position:0%
+qg times vgs
+ 
+
+ align:start position:0%
+qg times vgs
+Max or v v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Supply or this is my Gate Drive power
+
+ align:start position:0%
+Supply or this is my Gate Drive power
+ 
+
+ align:start position:0%
+Supply or this is my Gate Drive power
+supply V
+
+ align:start position:0%
+supply V
+ 
+
+ align:start position:0%
+supply V
+Supply right if I wanted the power
+
+ align:start position:0%
+Supply right if I wanted the power
+ 
+
+ align:start position:0%
+Supply right if I wanted the power
+dissipation that's how much I L you know
+
+ align:start position:0%
+dissipation that's how much I L you know
+ 
+
+ align:start position:0%
+dissipation that's how much I L you know
+some of that energy goes to charging the
+
+ align:start position:0%
+some of that energy goes to charging the
+ 
+
+ align:start position:0%
+some of that energy goes to charging the
+gate some of it goes it gets dissipated
+
+ align:start position:0%
+gate some of it goes it gets dissipated
+ 
+
+ align:start position:0%
+gate some of it goes it gets dissipated
+in the resistors here right we talked
+
+ align:start position:0%
+in the resistors here right we talked
+ 
+
+ align:start position:0%
+in the resistors here right we talked
+about that um when we talked about
+
+ align:start position:0%
+about that um when we talked about
+ 
+
+ align:start position:0%
+about that um when we talked about
+switch capacitor supplies but in the end
+
+ align:start position:0%
+switch capacitor supplies but in the end
+ 
+
+ align:start position:0%
+switch capacitor supplies but in the end
+what happens is I dump all that energy
+
+ align:start position:0%
+what happens is I dump all that energy
+ 
+
+ align:start position:0%
+what happens is I dump all that energy
+anyways when I turn the switch off and
+
+ align:start position:0%
+anyways when I turn the switch off and
+ 
+
+ align:start position:0%
+anyways when I turn the switch off and
+so each cycle I'm going to lose qg time
+
+ align:start position:0%
+so each cycle I'm going to lose qg time
+ 
+
+ align:start position:0%
+so each cycle I'm going to lose qg time
+V Supply or my power is going to be qg V
+
+ align:start position:0%
+V Supply or my power is going to be qg V
+ 
+
+ align:start position:0%
+V Supply or my power is going to be qg V
+Supply times the frequ switching
+
+ align:start position:0%
+Supply times the frequ switching
+ 
+
+ align:start position:0%
+Supply times the frequ switching
+frequency does that make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody the
+
+ align:start position:0%
+everybody the
+ 
+
+ align:start position:0%
+everybody the
+you know so P
+
+ align:start position:0%
+you know so P
+ 
+
+ align:start position:0%
+you know so P
+gate might be equal to q subg v
+
+ align:start position:0%
+gate might be equal to q subg v
+ 
+
+ align:start position:0%
+gate might be equal to q subg v
+Supply times F switch the number of
+
+ align:start position:0%
+Supply times F switch the number of
+ 
+
+ align:start position:0%
+Supply times F switch the number of
+times I'm turning on and off the switch
+
+ align:start position:0%
+times I'm turning on and off the switch
+ 
+
+ align:start position:0%
+times I'm turning on and off the switch
+per second notice that it has nothing to
+
+ align:start position:0%
+per second notice that it has nothing to
+ 
+
+ align:start position:0%
+per second notice that it has nothing to
+do with the necessarily with the Gate
+
+ align:start position:0%
+do with the necessarily with the Gate
+ 
+
+ align:start position:0%
+do with the necessarily with the Gate
+Drive um internal resistances for the
+
+ align:start position:0%
+Drive um internal resistances for the
+ 
+
+ align:start position:0%
+Drive um internal resistances for the
+same reasons we talked about when we
+
+ align:start position:0%
+same reasons we talked about when we
+ 
+
+ align:start position:0%
+same reasons we talked about when we
+talked about switch capacitor
+
+ align:start position:0%
+talked about switch capacitor
+ 
+
+ align:start position:0%
+talked about switch capacitor
+converters any questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's think
+
+ align:start position:0%
+so let's think
+ 
+
+ align:start position:0%
+so let's think
+about so that's one thing I want you to
+
+ align:start position:0%
+about so that's one thing I want you to
+ 
+
+ align:start position:0%
+about so that's one thing I want you to
+pay attention about is you got to really
+
+ align:start position:0%
+pay attention about is you got to really
+ 
+
+ align:start position:0%
+pay attention about is you got to really
+look at these threshold curves to get
+
+ align:start position:0%
+look at these threshold curves to get
+ 
+
+ align:start position:0%
+look at these threshold curves to get
+your total loss okay there's another
+
+ align:start position:0%
+your total loss okay there's another
+ 
+
+ align:start position:0%
+your total loss okay there's another
+thing you might want to think about when
+
+ align:start position:0%
+thing you might want to think about when
+ 
+
+ align:start position:0%
+thing you might want to think about when
+you think about the driver itself and
+
+ align:start position:0%
+you think about the driver itself and
+ 
+
+ align:start position:0%
+you think about the driver itself and
+that's the
+
+ align:start position:0%
+that's the
+ 
+
+ align:start position:0%
+that's the
+following what would this driver this
+
+ align:start position:0%
+following what would this driver this
+ 
+
+ align:start position:0%
+following what would this driver this
+guy look like inside right inside this
+
+ align:start position:0%
+guy look like inside right inside this
+ 
+
+ align:start position:0%
+guy look like inside right inside this
+driver you might model as um you know
+
+ align:start position:0%
+driver you might model as um you know
+ 
+
+ align:start position:0%
+driver you might model as um you know
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+mosfet and another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mosfet and then he's connected to the
+
+ align:start position:0%
+mosfet and then he's connected to the
+ 
+
+ align:start position:0%
+mosfet and then he's connected to the
+gate that he's going to drive right so
+
+ align:start position:0%
+gate that he's going to drive right so
+ 
+
+ align:start position:0%
+gate that he's going to drive right so
+I'm going to either turn on the top you
+
+ align:start position:0%
+I'm going to either turn on the top you
+ 
+
+ align:start position:0%
+I'm going to either turn on the top you
+know so this is my gate driver right I'm
+
+ align:start position:0%
+know so this is my gate driver right I'm
+ 
+
+ align:start position:0%
+know so this is my gate driver right I'm
+going to turn on this is V
+
+ align:start position:0%
+going to turn on this is V
+ 
+
+ align:start position:0%
+going to turn on this is V
+Supply so I'm going to turn on the top
+
+ align:start position:0%
+Supply so I'm going to turn on the top
+ 
+
+ align:start position:0%
+Supply so I'm going to turn on the top
+switch and he's going to charge the gate
+
+ align:start position:0%
+switch and he's going to charge the gate
+ 
+
+ align:start position:0%
+switch and he's going to charge the gate
+and I'm going to turn on the bottom
+
+ align:start position:0%
+and I'm going to turn on the bottom
+ 
+
+ align:start position:0%
+and I'm going to turn on the bottom
+switch and he's going to discharge the
+
+ align:start position:0%
+switch and he's going to discharge the
+ 
+
+ align:start position:0%
+switch and he's going to discharge the
+gate and turn it off does that make
+
+ align:start position:0%
+gate and turn it off does that make
+ 
+
+ align:start position:0%
+gate and turn it off does that make
+sense to everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's think about and by the way
+
+ align:start position:0%
+let's think about and by the way
+ 
+
+ align:start position:0%
+let's think about and by the way
+sometimes let me just think about this
+
+ align:start position:0%
+sometimes let me just think about this
+ 
+
+ align:start position:0%
+sometimes let me just think about this
+I'm going to simplify this as just being
+
+ align:start position:0%
+I'm going to simplify this as just being
+ 
+
+ align:start position:0%
+I'm going to simplify this as just being
+a capacitance a simple linear
+
+ align:start position:0%
+a capacitance a simple linear
+ 
+
+ align:start position:0%
+a capacitance a simple linear
+capacitance but what we know is it's
+
+ align:start position:0%
+capacitance but what we know is it's
+ 
+
+ align:start position:0%
+capacitance but what we know is it's
+anything but a simple linear capacitance
+
+ align:start position:0%
+anything but a simple linear capacitance
+ 
+
+ align:start position:0%
+anything but a simple linear capacitance
+right maybe I'm thinking about this
+
+ align:start position:0%
+right maybe I'm thinking about this
+ 
+
+ align:start position:0%
+right maybe I'm thinking about this
+equivalent capacitance now for
+
+ align:start position:0%
+equivalent capacitance now for
+ 
+
+ align:start position:0%
+equivalent capacitance now for
+Simplicity this cordal
+
+ align:start position:0%
+Simplicity this cordal
+ 
+
+ align:start position:0%
+Simplicity this cordal
+capacitance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let's think about charging this up
+
+ align:start position:0%
+um let's think about charging this up
+ 
+
+ align:start position:0%
+um let's think about charging this up
+and discharging it okay
+
+ align:start position:0%
+and discharging it okay
+ 
+
+ align:start position:0%
+and discharging it okay
+if I turn on you know one of my
+
+ align:start position:0%
+if I turn on you know one of my
+ 
+
+ align:start position:0%
+if I turn on you know one of my
+Tendencies might be to turn this on as
+
+ align:start position:0%
+Tendencies might be to turn this on as
+ 
+
+ align:start position:0%
+Tendencies might be to turn this on as
+fast as possible but maybe let me just
+
+ align:start position:0%
+fast as possible but maybe let me just
+ 
+
+ align:start position:0%
+fast as possible but maybe let me just
+imagine I have some resistance
+
+ align:start position:0%
+imagine I have some resistance
+ 
+
+ align:start position:0%
+imagine I have some resistance
+here sometimes I have resistance in the
+
+ align:start position:0%
+here sometimes I have resistance in the
+ 
+
+ align:start position:0%
+here sometimes I have resistance in the
+driver sometimes I have resistance in
+
+ align:start position:0%
+driver sometimes I have resistance in
+ 
+
+ align:start position:0%
+driver sometimes I have resistance in
+the gate and sometimes I actually add
+
+ align:start position:0%
+the gate and sometimes I actually add
+ 
+
+ align:start position:0%
+the gate and sometimes I actually add
+external resistor why would I add
+
+ align:start position:0%
+external resistor why would I add
+ 
+
+ align:start position:0%
+external resistor why would I add
+external resistor we talked about Emi
+
+ align:start position:0%
+external resistor we talked about Emi
+ 
+
+ align:start position:0%
+external resistor we talked about Emi
+before when I turn this transistor
+
+ align:start position:0%
+before when I turn this transistor
+ 
+
+ align:start position:0%
+before when I turn this transistor
+on I'm discharging this
+
+ align:start position:0%
+on I'm discharging this
+ 
+
+ align:start position:0%
+on I'm discharging this
+capacitance right so I have some
+
+ align:start position:0%
+capacitance right so I have some
+ 
+
+ align:start position:0%
+capacitance right so I have some
+capacitance here and I'm discharging it
+
+ align:start position:0%
+capacitance here and I'm discharging it
+ 
+
+ align:start position:0%
+capacitance here and I'm discharging it
+into the switch capacitance on my diode
+
+ align:start position:0%
+into the switch capacitance on my diode
+ 
+
+ align:start position:0%
+into the switch capacitance on my diode
+I'm discharging or I'm charging it into
+
+ align:start position:0%
+I'm discharging or I'm charging it into
+ 
+
+ align:start position:0%
+I'm discharging or I'm charging it into
+the switch that causes a huge pulse of
+
+ align:start position:0%
+the switch that causes a huge pulse of
+ 
+
+ align:start position:0%
+the switch that causes a huge pulse of
+current in this
+
+ align:start position:0%
+current in this
+ 
+
+ align:start position:0%
+current in this
+Loop which could cause a lot of noise if
+
+ align:start position:0%
+Loop which could cause a lot of noise if
+ 
+
+ align:start position:0%
+Loop which could cause a lot of noise if
+it rings a lot right and yet the amount
+
+ align:start position:0%
+it rings a lot right and yet the amount
+ 
+
+ align:start position:0%
+it rings a lot right and yet the amount
+I lose at least in the capacitive
+
+ align:start position:0%
+I lose at least in the capacitive
+ 
+
+ align:start position:0%
+I lose at least in the capacitive
+portion doesn't depend on how fast I
+
+ align:start position:0%
+portion doesn't depend on how fast I
+ 
+
+ align:start position:0%
+portion doesn't depend on how fast I
+turn it on right so at some level maybe
+
+ align:start position:0%
+turn it on right so at some level maybe
+ 
+
+ align:start position:0%
+turn it on right so at some level maybe
+I'm motivated to turn on my
+
+ align:start position:0%
+I'm motivated to turn on my
+ 
+
+ align:start position:0%
+I'm motivated to turn on my
+switch somewhat slowly so that I don't
+
+ align:start position:0%
+switch somewhat slowly so that I don't
+ 
+
+ align:start position:0%
+switch somewhat slowly so that I don't
+like discharge this capacitors really
+
+ align:start position:0%
+like discharge this capacitors really
+ 
+
+ align:start position:0%
+like discharge this capacitors really
+really fast and cause a lot of noise so
+
+ align:start position:0%
+really fast and cause a lot of noise so
+ 
+
+ align:start position:0%
+really fast and cause a lot of noise so
+a lot of the time we actually put
+
+ align:start position:0%
+a lot of the time we actually put
+ 
+
+ align:start position:0%
+a lot of the time we actually put
+additional resistance in
+
+ align:start position:0%
+additional resistance in
+ 
+
+ align:start position:0%
+additional resistance in
+here to slow up how fast I turn on the
+
+ align:start position:0%
+here to slow up how fast I turn on the
+ 
+
+ align:start position:0%
+here to slow up how fast I turn on the
+device and some gate drivers will tell
+
+ align:start position:0%
+device and some gate drivers will tell
+ 
+
+ align:start position:0%
+device and some gate drivers will tell
+you what that is sometimes you put your
+
+ align:start position:0%
+you what that is sometimes you put your
+ 
+
+ align:start position:0%
+you what that is sometimes you put your
+in a discrete resistor
+
+ align:start position:0%
+in a discrete resistor
+ 
+
+ align:start position:0%
+in a discrete resistor
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+that what about turning off the
+
+ align:start position:0%
+that what about turning off the
+ 
+
+ align:start position:0%
+that what about turning off the
+device when I turn off the device well
+
+ align:start position:0%
+device when I turn off the device well
+ 
+
+ align:start position:0%
+device when I turn off the device well
+he was on so this already has zero
+
+ align:start position:0%
+he was on so this already has zero
+ 
+
+ align:start position:0%
+he was on so this already has zero
+voltage when I turn him off this device
+
+ align:start position:0%
+voltage when I turn him off this device
+ 
+
+ align:start position:0%
+voltage when I turn him off this device
+isn't going to turn on instantly it's
+
+ align:start position:0%
+isn't going to turn on instantly it's
+ 
+
+ align:start position:0%
+isn't going to turn on instantly it's
+not going to turn on until the inductor
+
+ align:start position:0%
+not going to turn on until the inductor
+ 
+
+ align:start position:0%
+not going to turn on until the inductor
+charges up this capacitance again right
+
+ align:start position:0%
+charges up this capacitance again right
+ 
+
+ align:start position:0%
+charges up this capacitance again right
+so in some sense this capacitance it
+
+ align:start position:0%
+so in some sense this capacitance it
+ 
+
+ align:start position:0%
+so in some sense this capacitance it
+hurt me when I turn it on but now that
+
+ align:start position:0%
+hurt me when I turn it on but now that
+ 
+
+ align:start position:0%
+hurt me when I turn it on but now that
+I'm turning them off he's actually
+
+ align:start position:0%
+I'm turning them off he's actually
+ 
+
+ align:start position:0%
+I'm turning them off he's actually
+acting like a little bit like a snubber
+
+ align:start position:0%
+acting like a little bit like a snubber
+ 
+
+ align:start position:0%
+acting like a little bit like a snubber
+and slowing down the rate of Rise of
+
+ align:start position:0%
+and slowing down the rate of Rise of
+ 
+
+ align:start position:0%
+and slowing down the rate of Rise of
+this thing right
+
+ align:start position:0%
+this thing right
+ 
+
+ align:start position:0%
+this thing right
+but the longer I take to turn him off
+
+ align:start position:0%
+but the longer I take to turn him off
+ 
+
+ align:start position:0%
+but the longer I take to turn him off
+the more overlap I get right like the if
+
+ align:start position:0%
+the more overlap I get right like the if
+ 
+
+ align:start position:0%
+the more overlap I get right like the if
+the longer his current takes to fall The
+
+ align:start position:0%
+the longer his current takes to fall The
+ 
+
+ align:start position:0%
+the longer his current takes to fall The
+More Voltage
+
+ align:start position:0%
+More Voltage
+ 
+
+ align:start position:0%
+More Voltage
+I'm I'm building up across this
+
+ align:start position:0%
+I'm I'm building up across this
+ 
+
+ align:start position:0%
+I'm I'm building up across this
+transistor and dissipating them so it
+
+ align:start position:0%
+transistor and dissipating them so it
+ 
+
+ align:start position:0%
+transistor and dissipating them so it
+doesn't cost me anything to turn them
+
+ align:start position:0%
+doesn't cost me anything to turn them
+ 
+
+ align:start position:0%
+doesn't cost me anything to turn them
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+fast whereas it costs me something to
+
+ align:start position:0%
+fast whereas it costs me something to
+ 
+
+ align:start position:0%
+fast whereas it costs me something to
+turn them on fast in terms of noise so
+
+ align:start position:0%
+turn them on fast in terms of noise so
+ 
+
+ align:start position:0%
+turn them on fast in terms of noise so
+very often we would like to turn on the
+
+ align:start position:0%
+very often we would like to turn on the
+ 
+
+ align:start position:0%
+very often we would like to turn on the
+transistor somewhat slow
+
+ align:start position:0%
+transistor somewhat slow
+ 
+
+ align:start position:0%
+transistor somewhat slow
+slowly and turn them off really fast
+
+ align:start position:0%
+slowly and turn them off really fast
+ 
+
+ align:start position:0%
+slowly and turn them off really fast
+right so you don't
+
+ align:start position:0%
+right so you don't
+ 
+
+ align:start position:0%
+right so you don't
+want this resistor if I if I load it all
+
+ align:start position:0%
+want this resistor if I if I load it all
+ 
+
+ align:start position:0%
+want this resistor if I if I load it all
+into this resistor I don't want this
+
+ align:start position:0%
+into this resistor I don't want this
+ 
+
+ align:start position:0%
+into this resistor I don't want this
+resistor to be the same for turn on and
+
+ align:start position:0%
+resistor to be the same for turn on and
+ 
+
+ align:start position:0%
+resistor to be the same for turn on and
+turn off and what you'll see in a lot of
+
+ align:start position:0%
+turn off and what you'll see in a lot of
+ 
+
+ align:start position:0%
+turn off and what you'll see in a lot of
+drivers is that what they'll do is for
+
+ align:start position:0%
+drivers is that what they'll do is for
+ 
+
+ align:start position:0%
+drivers is that what they'll do is for
+turn on this resistance or equivalently
+
+ align:start position:0%
+turn on this resistance or equivalently
+ 
+
+ align:start position:0%
+turn on this resistance or equivalently
+the positive sourcing capability will be
+
+ align:start position:0%
+the positive sourcing capability will be
+ 
+
+ align:start position:0%
+the positive sourcing capability will be
+you know a bigger resistance and the
+
+ align:start position:0%
+you know a bigger resistance and the
+ 
+
+ align:start position:0%
+you know a bigger resistance and the
+resistance for turning off will be a
+
+ align:start position:0%
+resistance for turning off will be a
+ 
+
+ align:start position:0%
+resistance for turning off will be a
+much smaller resistance so you can turn
+
+ align:start position:0%
+much smaller resistance so you can turn
+ 
+
+ align:start position:0%
+much smaller resistance so you can turn
+the transistor off fast but turn them on
+
+ align:start position:0%
+the transistor off fast but turn them on
+ 
+
+ align:start position:0%
+the transistor off fast but turn them on
+only slightly slow and that'll help
+
+ align:start position:0%
+only slightly slow and that'll help
+ 
+
+ align:start position:0%
+only slightly slow and that'll help
+reduce your
+
+ align:start position:0%
+reduce your
+ 
+
+ align:start position:0%
+reduce your
+noise okay if you don't like what that
+
+ align:start position:0%
+noise okay if you don't like what that
+ 
+
+ align:start position:0%
+noise okay if you don't like what that
+looks
+
+ align:start position:0%
+looks
+ 
+
+ align:start position:0%
+looks
+like right you can add your own resistor
+
+ align:start position:0%
+like right you can add your own resistor
+ 
+
+ align:start position:0%
+like right you can add your own resistor
+that'll slow down the turn on maybe you
+
+ align:start position:0%
+that'll slow down the turn on maybe you
+ 
+
+ align:start position:0%
+that'll slow down the turn on maybe you
+don't want to slow down the turn off as
+
+ align:start position:0%
+don't want to slow down the turn off as
+ 
+
+ align:start position:0%
+don't want to slow down the turn off as
+much so for the turn off maybe what you
+
+ align:start position:0%
+much so for the turn off maybe what you
+ 
+
+ align:start position:0%
+much so for the turn off maybe what you
+do is you put a diode in a smaller
+
+ align:start position:0%
+do is you put a diode in a smaller
+ 
+
+ align:start position:0%
+do is you put a diode in a smaller
+resistor or no resistor here so he
+
+ align:start position:0%
+resistor or no resistor here so he
+ 
+
+ align:start position:0%
+resistor or no resistor here so he
+charges slowly through the yellow
+
+ align:start position:0%
+charges slowly through the yellow
+ 
+
+ align:start position:0%
+charges slowly through the yellow
+resistor and he discharges quickly
+
+ align:start position:0%
+resistor and he discharges quickly
+ 
+
+ align:start position:0%
+resistor and he discharges quickly
+through the green diode
+
+ align:start position:0%
+through the green diode
+ 
+
+ align:start position:0%
+through the green diode
+okay so you can control rate of turn on
+
+ align:start position:0%
+okay so you can control rate of turn on
+ 
+
+ align:start position:0%
+okay so you can control rate of turn on
+and turn off to control that switching
+
+ align:start position:0%
+and turn off to control that switching
+ 
+
+ align:start position:0%
+and turn off to control that switching
+and the noise injection elsewhere in
+
+ align:start position:0%
+and the noise injection elsewhere in
+ 
+
+ align:start position:0%
+and the noise injection elsewhere in
+your circuit and you think about that
+
+ align:start position:0%
+your circuit and you think about that
+ 
+
+ align:start position:0%
+your circuit and you think about that
+when you buy your driver and how you
+
+ align:start position:0%
+when you buy your driver and how you
+ 
+
+ align:start position:0%
+when you buy your driver and how you
+drive you connect your driver to your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+switch questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay so I'm sort of out of time to
+
+ align:start position:0%
+that okay so I'm sort of out of time to
+ 
+
+ align:start position:0%
+that okay so I'm sort of out of time to
+talk about these practical
+
+ align:start position:0%
+talk about these practical
+ 
+
+ align:start position:0%
+talk about these practical
+implementation issues there's like you
+
+ align:start position:0%
+implementation issues there's like you
+ 
+
+ align:start position:0%
+implementation issues there's like you
+could spend a whole course on this but
+
+ align:start position:0%
+could spend a whole course on this but
+ 
+
+ align:start position:0%
+could spend a whole course on this but
+um um at least I hope you get a bit of a
+
+ align:start position:0%
+um um at least I hope you get a bit of a
+ 
+
+ align:start position:0%
+um um at least I hope you get a bit of a
+sense of you know how you might do some
+
+ align:start position:0%
+sense of you know how you might do some
+ 
+
+ align:start position:0%
+sense of you know how you might do some
+of these things in laying out your
+
+ align:start position:0%
+of these things in laying out your
+ 
+
+ align:start position:0%
+of these things in laying out your
+circuit and so at least I've attempted
+
+ align:start position:0%
+circuit and so at least I've attempted
+ 
+
+ align:start position:0%
+circuit and so at least I've attempted
+this term to take you from you know
+
+ align:start position:0%
+this term to take you from you know
+ 
+
+ align:start position:0%
+this term to take you from you know
+what's the basic operation of a
+
+ align:start position:0%
+what's the basic operation of a
+ 
+
+ align:start position:0%
+what's the basic operation of a
+switching circuit how do you design all
+
+ align:start position:0%
+switching circuit how do you design all
+ 
+
+ align:start position:0%
+switching circuit how do you design all
+the components how do you control it how
+
+ align:start position:0%
+the components how do you control it how
+ 
+
+ align:start position:0%
+the components how do you control it how
+do you deal with the
+
+ align:start position:0%
+do you deal with the
+ 
+
+ align:start position:0%
+do you deal with the
+filters how do you lay it out and I'm
+
+ align:start position:0%
+filters how do you lay it out and I'm
+ 
+
+ align:start position:0%
+filters how do you lay it out and I'm
+afraid that's all we have time for I
+
+ align:start position:0%
+afraid that's all we have time for I
+ 
+
+ align:start position:0%
+afraid that's all we have time for I
+wish you the best in finishing your
+
+ align:start position:0%
+wish you the best in finishing your
+ 
+
+ align:start position:0%
+wish you the best in finishing your
+projects and a really nice summer so
+
+ align:start position:0%
+projects and a really nice summer so
+ 
+
+ align:start position:0%
+projects and a really nice summer so
+have a great day
\ No newline at end of file
diff --git a/Txidu-5VYfU.txt b/Txidu-5VYfU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..56ff79efa48864d9bd86ea66a4e406d726d52aef
--- /dev/null
+++ b/Txidu-5VYfU.txt
@@ -0,0 +1,8450 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu um so last time we finished
+
+ align:start position:0%
+ocw.mit.edu um so last time we finished
+ 
+
+ align:start position:0%
+ocw.mit.edu um so last time we finished
+talking about tricular bone and what I
+
+ align:start position:0%
+talking about tricular bone and what I
+ 
+
+ align:start position:0%
+talking about tricular bone and what I
+wanted to talk about this week was
+
+ align:start position:0%
+wanted to talk about this week was
+ 
+
+ align:start position:0%
+wanted to talk about this week was
+tissue engineering scaffolds so the idea
+
+ align:start position:0%
+tissue engineering scaffolds so the idea
+ 
+
+ align:start position:0%
+tissue engineering scaffolds so the idea
+with tissue engineering is you want to
+
+ align:start position:0%
+with tissue engineering is you want to
+ 
+
+ align:start position:0%
+with tissue engineering is you want to
+be able to repair damaged or disease
+
+ align:start position:0%
+be able to repair damaged or disease
+ 
+
+ align:start position:0%
+be able to repair damaged or disease
+tissue and typically that's done by
+
+ align:start position:0%
+tissue and typically that's done by
+ 
+
+ align:start position:0%
+tissue and typically that's done by
+regenerating the tissue in some way so
+
+ align:start position:0%
+regenerating the tissue in some way so
+ 
+
+ align:start position:0%
+regenerating the tissue in some way so
+in your body um many types of cells like
+
+ align:start position:0%
+in your body um many types of cells like
+ 
+
+ align:start position:0%
+in your body um many types of cells like
+maybe not blood cells but most types of
+
+ align:start position:0%
+maybe not blood cells but most types of
+ 
+
+ align:start position:0%
+maybe not blood cells but most types of
+cells for sort of structural tissues are
+
+ align:start position:0%
+cells for sort of structural tissues are
+ 
+
+ align:start position:0%
+cells for sort of structural tissues are
+attached to an extracellular Matrix and
+
+ align:start position:0%
+attached to an extracellular Matrix and
+ 
+
+ align:start position:0%
+attached to an extracellular Matrix and
+this is sort of a schematic of the
+
+ align:start position:0%
+this is sort of a schematic of the
+ 
+
+ align:start position:0%
+this is sort of a schematic of the
+extracellular Matrix here and the
+
+ align:start position:0%
+extracellular Matrix here and the
+ 
+
+ align:start position:0%
+extracellular Matrix here and the
+composition depends on the type of
+
+ align:start position:0%
+composition depends on the type of
+ 
+
+ align:start position:0%
+composition depends on the type of
+tissue that's involved so for example in
+
+ align:start position:0%
+tissue that's involved so for example in
+ 
+
+ align:start position:0%
+tissue that's involved so for example in
+skin it would be um collagen and
+
+ align:start position:0%
+skin it would be um collagen and
+ 
+
+ align:start position:0%
+skin it would be um collagen and
+something called glycoaminoglycans and
+
+ align:start position:0%
+something called glycoaminoglycans and
+ 
+
+ align:start position:0%
+something called glycoaminoglycans and
+elastin in bone it would be collagen and
+
+ align:start position:0%
+elastin in bone it would be collagen and
+ 
+
+ align:start position:0%
+elastin in bone it would be collagen and
+a mineral calcium phosphate mineral
+
+ align:start position:0%
+a mineral calcium phosphate mineral
+ 
+
+ align:start position:0%
+a mineral calcium phosphate mineral
+hydroxy appetite so the composition
+
+ align:start position:0%
+hydroxy appetite so the composition
+ 
+
+ align:start position:0%
+hydroxy appetite so the composition
+varies but the idea with the tissue
+
+ align:start position:0%
+varies but the idea with the tissue
+ 
+
+ align:start position:0%
+varies but the idea with the tissue
+engineering scaffold is that you want to
+
+ align:start position:0%
+engineering scaffold is that you want to
+ 
+
+ align:start position:0%
+engineering scaffold is that you want to
+make a material that essentially
+
+ align:start position:0%
+make a material that essentially
+ 
+
+ align:start position:0%
+make a material that essentially
+substitutes for the extracellular Matrix
+
+ align:start position:0%
+substitutes for the extracellular Matrix
+ 
+
+ align:start position:0%
+substitutes for the extracellular Matrix
+and it does so on a sort of temporary
+
+ align:start position:0%
+and it does so on a sort of temporary
+ 
+
+ align:start position:0%
+and it does so on a sort of temporary
+basis so the idea is you put something
+
+ align:start position:0%
+basis so the idea is you put something
+ 
+
+ align:start position:0%
+basis so the idea is you put something
+in the body the cells attached to that
+
+ align:start position:0%
+in the body the cells attached to that
+ 
+
+ align:start position:0%
+in the body the cells attached to that
+whatever scaffold you put in and the
+
+ align:start position:0%
+whatever scaffold you put in and the
+ 
+
+ align:start position:0%
+whatever scaffold you put in and the
+scaffold has to be made in such a way
+
+ align:start position:0%
+scaffold has to be made in such a way
+ 
+
+ align:start position:0%
+scaffold has to be made in such a way
+that the material that the cells can um
+
+ align:start position:0%
+that the material that the cells can um
+ 
+
+ align:start position:0%
+that the material that the cells can um
+they can migrate through it they can
+
+ align:start position:0%
+they can migrate through it they can
+ 
+
+ align:start position:0%
+they can migrate through it they can
+attach to it they can differentiate they
+
+ align:start position:0%
+attach to it they can differentiate they
+ 
+
+ align:start position:0%
+attach to it they can differentiate they
+can proliferate so the cells can do all
+
+ align:start position:0%
+can proliferate so the cells can do all
+ 
+
+ align:start position:0%
+can proliferate so the cells can do all
+their normal function and the idea is is
+
+ align:start position:0%
+their normal function and the idea is is
+ 
+
+ align:start position:0%
+their normal function and the idea is is
+that as the cells are doing their normal
+
+ align:start position:0%
+that as the cells are doing their normal
+ 
+
+ align:start position:0%
+that as the cells are doing their normal
+function they then secrete the natural
+
+ align:start position:0%
+function they then secrete the natural
+ 
+
+ align:start position:0%
+function they then secrete the natural
+extracellular Matrix and the engineered
+
+ align:start position:0%
+extracellular Matrix and the engineered
+ 
+
+ align:start position:0%
+extracellular Matrix and the engineered
+thing that you put in is resorbed so
+
+ align:start position:0%
+thing that you put in is resorbed so
+ 
+
+ align:start position:0%
+thing that you put in is resorbed so
+there has to be a balance between the
+
+ align:start position:0%
+there has to be a balance between the
+ 
+
+ align:start position:0%
+there has to be a balance between the
+rate at which the scaffold you've made
+
+ align:start position:0%
+rate at which the scaffold you've made
+ 
+
+ align:start position:0%
+rate at which the scaffold you've made
+resorbs and the rate at which the cells
+
+ align:start position:0%
+resorbs and the rate at which the cells
+ 
+
+ align:start position:0%
+resorbs and the rate at which the cells
+are depositing the new native
+
+ align:start position:0%
+are depositing the new native
+ 
+
+ align:start position:0%
+are depositing the new native
+extracellular Matrix so that's one of
+
+ align:start position:0%
+extracellular Matrix so that's one of
+ 
+
+ align:start position:0%
+extracellular Matrix so that's one of
+the the key things about this so so this
+
+ align:start position:0%
+the the key things about this so so this
+ 
+
+ align:start position:0%
+the the key things about this so so this
+is just an example of um sort of a
+
+ align:start position:0%
+is just an example of um sort of a
+ 
+
+ align:start position:0%
+is just an example of um sort of a
+schematic of an extracellular Matrix in
+
+ align:start position:0%
+schematic of an extracellular Matrix in
+ 
+
+ align:start position:0%
+schematic of an extracellular Matrix in
+this case here uh there's collagen
+
+ align:start position:0%
+this case here uh there's collagen
+ 
+
+ align:start position:0%
+this case here uh there's collagen
+fibers so these guys here are collagen
+
+ align:start position:0%
+fibers so these guys here are collagen
+ 
+
+ align:start position:0%
+fibers so these guys here are collagen
+fibers and these kind of hairy looking
+
+ align:start position:0%
+fibers and these kind of hairy looking
+ 
+
+ align:start position:0%
+fibers and these kind of hairy looking
+things are
+
+ align:start position:0%
+things are
+ 
+
+ align:start position:0%
+things are
+proteoglycans so they have a core of
+
+ align:start position:0%
+proteoglycans so they have a core of
+ 
+
+ align:start position:0%
+proteoglycans so they have a core of
+protein with sugars kind of hanging off
+
+ align:start position:0%
+protein with sugars kind of hanging off
+ 
+
+ align:start position:0%
+protein with sugars kind of hanging off
+of them and there's different kinds of
+
+ align:start position:0%
+of them and there's different kinds of
+ 
+
+ align:start position:0%
+of them and there's different kinds of
+of uh gags they're called that hang off
+
+ align:start position:0%
+of uh gags they're called that hang off
+ 
+
+ align:start position:0%
+of uh gags they're called that hang off
+of them uh so one's krtin sulfate the Cs
+
+ align:start position:0%
+of them uh so one's krtin sulfate the Cs
+ 
+
+ align:start position:0%
+of them uh so one's krtin sulfate the Cs
+here stands for condroitin sulfate uh
+
+ align:start position:0%
+here stands for condroitin sulfate uh
+ 
+
+ align:start position:0%
+here stands for condroitin sulfate uh
+there's one called there's one called um
+
+ align:start position:0%
+there's one called there's one called um
+ 
+
+ align:start position:0%
+there's one called there's one called um
+dermatin sulfate and there's one called
+
+ align:start position:0%
+dermatin sulfate and there's one called
+ 
+
+ align:start position:0%
+dermatin sulfate and there's one called
+Heparin sulfate so there there's
+
+ align:start position:0%
+Heparin sulfate so there there's
+ 
+
+ align:start position:0%
+Heparin sulfate so there there's
+different of these
+
+ align:start position:0%
+different of these
+ 
+
+ align:start position:0%
+different of these
+glycosaminoglycans so let me write down
+
+ align:start position:0%
+glycosaminoglycans so let me write down
+ 
+
+ align:start position:0%
+glycosaminoglycans so let me write down
+some of this and then we'll we'll kind
+
+ align:start position:0%
+some of this and then we'll we'll kind
+ 
+
+ align:start position:0%
+some of this and then we'll we'll kind
+of get into this so what I wanted to do
+
+ align:start position:0%
+of get into this so what I wanted to do
+ 
+
+ align:start position:0%
+of get into this so what I wanted to do
+today will show you uh some examples of
+
+ align:start position:0%
+today will show you uh some examples of
+ 
+
+ align:start position:0%
+today will show you uh some examples of
+tissue engineering scaffolds show you uh
+
+ align:start position:0%
+tissue engineering scaffolds show you uh
+ 
+
+ align:start position:0%
+tissue engineering scaffolds show you uh
+some of the sort of design requirements
+
+ align:start position:0%
+some of the sort of design requirements
+ 
+
+ align:start position:0%
+some of the sort of design requirements
+so you have to have obviously a material
+
+ align:start position:0%
+so you have to have obviously a material
+ 
+
+ align:start position:0%
+so you have to have obviously a material
+that's porous so the cells can get in
+
+ align:start position:0%
+that's porous so the cells can get in
+ 
+
+ align:start position:0%
+that's porous so the cells can get in
+there and that's where the cellular
+
+ align:start position:0%
+there and that's where the cellular
+ 
+
+ align:start position:0%
+there and that's where the cellular
+solids comes in um so we'll talk about
+
+ align:start position:0%
+solids comes in um so we'll talk about
+ 
+
+ align:start position:0%
+solids comes in um so we'll talk about
+some scaffolds some of the sort of
+
+ align:start position:0%
+some scaffolds some of the sort of
+ 
+
+ align:start position:0%
+some scaffolds some of the sort of
+design requirements for them and also uh
+
+ align:start position:0%
+design requirements for them and also uh
+ 
+
+ align:start position:0%
+design requirements for them and also uh
+we'll talk a little bit about processing
+
+ align:start position:0%
+we'll talk a little bit about processing
+ 
+
+ align:start position:0%
+we'll talk a little bit about processing
+of the scaffolds and mechanical
+
+ align:start position:0%
+of the scaffolds and mechanical
+ 
+
+ align:start position:0%
+of the scaffolds and mechanical
+properties of the scaffolds so I'm
+
+ align:start position:0%
+properties of the scaffolds so I'm
+ 
+
+ align:start position:0%
+properties of the scaffolds so I'm
+hoping I can finish most of that today
+
+ align:start position:0%
+hoping I can finish most of that today
+ 
+
+ align:start position:0%
+hoping I can finish most of that today
+and then next time I have a little case
+
+ align:start position:0%
+and then next time I have a little case
+ 
+
+ align:start position:0%
+and then next time I have a little case
+study on osteochondral scaffolds so
+
+ align:start position:0%
+study on osteochondral scaffolds so
+ 
+
+ align:start position:0%
+study on osteochondral scaffolds so
+Osteo means bone and the condal means
+
+ align:start position:0%
+Osteo means bone and the condal means
+ 
+
+ align:start position:0%
+Osteo means bone and the condal means
+cartilage so this was sort of a
+
+ align:start position:0%
+cartilage so this was sort of a
+ 
+
+ align:start position:0%
+cartilage so this was sort of a
+two-layer scaffold that we developed in
+
+ align:start position:0%
+two-layer scaffold that we developed in
+ 
+
+ align:start position:0%
+two-layer scaffold that we developed in
+collaboration with some other people in
+
+ align:start position:0%
+collaboration with some other people in
+ 
+
+ align:start position:0%
+collaboration with some other people in
+MIT and some people at Cambridge
+
+ align:start position:0%
+MIT and some people at Cambridge
+ 
+
+ align:start position:0%
+MIT and some people at Cambridge
+University um and it went from sort of a
+
+ align:start position:0%
+University um and it went from sort of a
+ 
+
+ align:start position:0%
+University um and it went from sort of a
+research thing to a startup thing and
+
+ align:start position:0%
+research thing to a startup thing and
+ 
+
+ align:start position:0%
+research thing to a startup thing and
+being used clinically so I was going to
+
+ align:start position:0%
+being used clinically so I was going to
+ 
+
+ align:start position:0%
+being used clinically so I was going to
+talk about that uh Wednesday okay so
+
+ align:start position:0%
+talk about that uh Wednesday okay so
+ 
+
+ align:start position:0%
+talk about that uh Wednesday okay so
+oops let me just get started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so the goal of tissue engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is to regenerate diseased or damaged
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tissues and in the body the cells
+
+ align:start position:0%
+tissues and in the body the cells
+ 
+
+ align:start position:0%
+tissues and in the body the cells
+attached to the extracellular Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's sometimes called the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ECM so sometimes the scaffolds are
+
+ align:start position:0%
+ECM so sometimes the scaffolds are
+ 
+
+ align:start position:0%
+ECM so sometimes the scaffolds are
+called scaffolds and sometimes they're
+
+ align:start position:0%
+called scaffolds and sometimes they're
+ 
+
+ align:start position:0%
+called scaffolds and sometimes they're
+called Matrix because the extracellular
+
+ align:start position:0%
+called Matrix because the extracellular
+ 
+
+ align:start position:0%
+called Matrix because the extracellular
+Matrix is called uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix so then the composition of the
+
+ align:start position:0%
+Matrix so then the composition of the
+ 
+
+ align:start position:0%
+Matrix so then the composition of the
+ECM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depends on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tissue but it usually involves some sort
+
+ align:start position:0%
+tissue but it usually involves some sort
+ 
+
+ align:start position:0%
+tissue but it usually involves some sort
+of structural protein so something like
+
+ align:start position:0%
+of structural protein so something like
+ 
+
+ align:start position:0%
+of structural protein so something like
+collagen or elastin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it also typically involves some sort of
+
+ align:start position:0%
+it also typically involves some sort of
+ 
+
+ align:start position:0%
+it also typically involves some sort of
+adhesive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proteins so something like fibron
+
+ align:start position:0%
+proteins so something like fibron
+ 
+
+ align:start position:0%
+proteins so something like fibron
+nectin or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+laminin and it involves these
+
+ align:start position:0%
+laminin and it involves these
+ 
+
+ align:start position:0%
+laminin and it involves these
+proteoglycans which are the core of
+
+ align:start position:0%
+proteoglycans which are the core of
+ 
+
+ align:start position:0%
+proteoglycans which are the core of
+protein with a sugar hanging off them
+
+ align:start position:0%
+protein with a sugar hanging off them
+ 
+
+ align:start position:0%
+protein with a sugar hanging off them
+oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the sugars are typically um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glycosaminoglycans and for short people
+
+ align:start position:0%
+glycosaminoglycans and for short people
+ 
+
+ align:start position:0%
+glycosaminoglycans and for short people
+call them Gags Just because it's easier
+
+ align:start position:0%
+call them Gags Just because it's easier
+ 
+
+ align:start position:0%
+call them Gags Just because it's easier
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say so some examples of the gags are kro
+
+ align:start position:0%
+say so some examples of the gags are kro
+ 
+
+ align:start position:0%
+say so some examples of the gags are kro
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sulfate and we're going to talk more
+
+ align:start position:0%
+sulfate and we're going to talk more
+ 
+
+ align:start position:0%
+sulfate and we're going to talk more
+about that a little later because that's
+
+ align:start position:0%
+about that a little later because that's
+ 
+
+ align:start position:0%
+about that a little later because that's
+that's one that we've used um in making
+
+ align:start position:0%
+that's one that we've used um in making
+ 
+
+ align:start position:0%
+that's one that we've used um in making
+collagen based scaffolds with uh Yanni
+
+ align:start position:0%
+collagen based scaffolds with uh Yanni
+ 
+
+ align:start position:0%
+collagen based scaffolds with uh Yanni
+and ass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example if you look at the
+
+ align:start position:0%
+so for example if you look at the
+ 
+
+ align:start position:0%
+so for example if you look at the
+composition of extracellular Matrix and
+
+ align:start position:0%
+composition of extracellular Matrix and
+ 
+
+ align:start position:0%
+composition of extracellular Matrix and
+something like cartilage it has a
+
+ align:start position:0%
+something like cartilage it has a
+ 
+
+ align:start position:0%
+something like cartilage it has a
+collagen component and um and a h
+
+ align:start position:0%
+collagen component and um and a h
+ 
+
+ align:start position:0%
+collagen component and um and a h
+hyaluronic acid component and some gags
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this hialuronic acid is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proteoglycan if you look at
+
+ align:start position:0%
+proteoglycan if you look at
+ 
+
+ align:start position:0%
+proteoglycan if you look at
+bone extracellular matrix in bone is
+
+ align:start position:0%
+bone extracellular matrix in bone is
+ 
+
+ align:start position:0%
+bone extracellular matrix in bone is
+made up mostly of collagen and hydroxy
+
+ align:start position:0%
+made up mostly of collagen and hydroxy
+ 
+
+ align:start position:0%
+made up mostly of collagen and hydroxy
+appetite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you look at
+
+ align:start position:0%
+and if you look at
+ 
+
+ align:start position:0%
+and if you look at
+skin skin is made up of
+
+ align:start position:0%
+skin skin is made up of
+ 
+
+ align:start position:0%
+skin skin is made up of
+collagen elastin and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proteoglycans and the idea is that the
+
+ align:start position:0%
+proteoglycans and the idea is that the
+ 
+
+ align:start position:0%
+proteoglycans and the idea is that the
+cells have to be attached to this
+
+ align:start position:0%
+cells have to be attached to this
+ 
+
+ align:start position:0%
+cells have to be attached to this
+extracellular Matrix in order to
+
+ align:start position:0%
+extracellular Matrix in order to
+ 
+
+ align:start position:0%
+extracellular Matrix in order to
+function or they have to be attached to
+
+ align:start position:0%
+function or they have to be attached to
+ 
+
+ align:start position:0%
+function or they have to be attached to
+this or to other cells in most cases is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so next week I'm going to talk a bit
+
+ align:start position:0%
+so next week I'm going to talk a bit
+ 
+
+ align:start position:0%
+so next week I'm going to talk a bit
+about cell mechanics and uh we have some
+
+ align:start position:0%
+about cell mechanics and uh we have some
+ 
+
+ align:start position:0%
+about cell mechanics and uh we have some
+video where we watch a cell um deforming
+
+ align:start position:0%
+video where we watch a cell um deforming
+ 
+
+ align:start position:0%
+video where we watch a cell um deforming
+a scaffold and I don't have videos to
+
+ align:start position:0%
+a scaffold and I don't have videos to
+ 
+
+ align:start position:0%
+a scaffold and I don't have videos to
+show you but I had a student who took
+
+ align:start position:0%
+show you but I had a student who took
+ 
+
+ align:start position:0%
+show you but I had a student who took
+videos of cells migrating along the
+
+ align:start position:0%
+videos of cells migrating along the
+ 
+
+ align:start position:0%
+videos of cells migrating along the
+scaffolds um and you can see how we'll
+
+ align:start position:0%
+scaffolds um and you can see how we'll
+ 
+
+ align:start position:0%
+scaffolds um and you can see how we'll
+look at how the stiffness of the
+
+ align:start position:0%
+look at how the stiffness of the
+ 
+
+ align:start position:0%
+look at how the stiffness of the
+scaffold affects how the cells m along
+
+ align:start position:0%
+scaffold affects how the cells m along
+ 
+
+ align:start position:0%
+scaffold affects how the cells m along
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scaffold so that's kind of the the
+
+ align:start position:0%
+scaffold so that's kind of the the
+ 
+
+ align:start position:0%
+scaffold so that's kind of the the
+native ECM in the body and the idea with
+
+ align:start position:0%
+native ECM in the body and the idea with
+ 
+
+ align:start position:0%
+native ECM in the body and the idea with
+tissue engineering is that you want to
+
+ align:start position:0%
+tissue engineering is that you want to
+ 
+
+ align:start position:0%
+tissue engineering is that you want to
+make a scaffold that's porous that mimic
+
+ align:start position:0%
+make a scaffold that's porous that mimic
+ 
+
+ align:start position:0%
+make a scaffold that's porous that mimic
+The extracellular Matrix in the body so
+
+ align:start position:0%
+The extracellular Matrix in the body so
+ 
+
+ align:start position:0%
+The extracellular Matrix in the body so
+that say there's some tissue that's
+
+ align:start position:0%
+that say there's some tissue that's
+ 
+
+ align:start position:0%
+that say there's some tissue that's
+damaged say there's damaged cartilage
+
+ align:start position:0%
+damaged say there's damaged cartilage
+ 
+
+ align:start position:0%
+damaged say there's damaged cartilage
+you want to provide sort of an
+
+ align:start position:0%
+you want to provide sort of an
+ 
+
+ align:start position:0%
+you want to provide sort of an
+extracellular Matrix that's a sort of
+
+ align:start position:0%
+extracellular Matrix that's a sort of
+ 
+
+ align:start position:0%
+extracellular Matrix that's a sort of
+synthetic thing that's going to provide
+
+ align:start position:0%
+synthetic thing that's going to provide
+ 
+
+ align:start position:0%
+synthetic thing that's going to provide
+the same function as the the ECM in the
+
+ align:start position:0%
+the same function as the the ECM in the
+ 
+
+ align:start position:0%
+the same function as the the ECM in the
+native
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tissue so people have been working on
+
+ align:start position:0%
+tissue so people have been working on
+ 
+
+ align:start position:0%
+tissue so people have been working on
+scaffolds for regenerating all sorts of
+
+ align:start position:0%
+scaffolds for regenerating all sorts of
+ 
+
+ align:start position:0%
+scaffolds for regenerating all sorts of
+different tissues and probably the most
+
+ align:start position:0%
+different tissues and probably the most
+ 
+
+ align:start position:0%
+different tissues and probably the most
+successful one has been used to
+
+ align:start position:0%
+successful one has been used to
+ 
+
+ align:start position:0%
+successful one has been used to
+regenerate skin and there's been
+
+ align:start position:0%
+regenerate skin and there's been
+ 
+
+ align:start position:0%
+regenerate skin and there's been
+scaffolds available for regenerating
+
+ align:start position:0%
+scaffolds available for regenerating
+ 
+
+ align:start position:0%
+scaffolds available for regenerating
+skin for probably almost 20 years now
+
+ align:start position:0%
+skin for probably almost 20 years now
+ 
+
+ align:start position:0%
+skin for probably almost 20 years now
+and one of the first ones was developed
+
+ align:start position:0%
+and one of the first ones was developed
+ 
+
+ align:start position:0%
+and one of the first ones was developed
+by professor yanos in mechanical
+
+ align:start position:0%
+by professor yanos in mechanical
+ 
+
+ align:start position:0%
+by professor yanos in mechanical
+engineering here at MIT and it's
+
+ align:start position:0%
+engineering here at MIT and it's
+ 
+
+ align:start position:0%
+engineering here at MIT and it's
+actually still sold by a company called
+
+ align:start position:0%
+actually still sold by a company called
+ 
+
+ align:start position:0%
+actually still sold by a company called
+Integra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there's research to develop
+
+ align:start position:0%
+but there's research to develop
+ 
+
+ align:start position:0%
+but there's research to develop
+scaffolds for lots of different tissues
+
+ align:start position:0%
+scaffolds for lots of different tissues
+ 
+
+ align:start position:0%
+scaffolds for lots of different tissues
+um Orthopedic tissues things like bone
+
+ align:start position:0%
+um Orthopedic tissues things like bone
+ 
+
+ align:start position:0%
+um Orthopedic tissues things like bone
+and cartilage cardiovascular tissues uh
+
+ align:start position:0%
+and cartilage cardiovascular tissues uh
+ 
+
+ align:start position:0%
+and cartilage cardiovascular tissues uh
+nerve like Professor Yos works on
+
+ align:start position:0%
+nerve like Professor Yos works on
+ 
+
+ align:start position:0%
+nerve like Professor Yos works on
+peripheral nerve these days people have
+
+ align:start position:0%
+peripheral nerve these days people have
+ 
+
+ align:start position:0%
+peripheral nerve these days people have
+looked at trying to make scaffolds for
+
+ align:start position:0%
+looked at trying to make scaffolds for
+ 
+
+ align:start position:0%
+looked at trying to make scaffolds for
+gastrointestinal tissues so all sorts of
+
+ align:start position:0%
+gastrointestinal tissues so all sorts of
+ 
+
+ align:start position:0%
+gastrointestinal tissues so all sorts of
+different tissues and MIT there's quite
+
+ align:start position:0%
+different tissues and MIT there's quite
+ 
+
+ align:start position:0%
+different tissues and MIT there's quite
+a lot of interest in this there's a lot
+
+ align:start position:0%
+a lot of interest in this there's a lot
+ 
+
+ align:start position:0%
+a lot of interest in this there's a lot
+of people work on it so Bob Langer works
+
+ align:start position:0%
+of people work on it so Bob Langer works
+ 
+
+ align:start position:0%
+of people work on it so Bob Langer works
+on it Linda Griffith Sita baa there's
+
+ align:start position:0%
+on it Linda Griffith Sita baa there's
+ 
+
+ align:start position:0%
+on it Linda Griffith Sita baa there's
+there's really quite a number of people
+
+ align:start position:0%
+there's really quite a number of people
+ 
+
+ align:start position:0%
+there's really quite a number of people
+at MIT who work on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so those are just some of the people at
+
+ align:start position:0%
+so those are just some of the people at
+ 
+
+ align:start position:0%
+so those are just some of the people at
+MIT so the idea is is in the body the
+
+ align:start position:0%
+MIT so the idea is is in the body the
+ 
+
+ align:start position:0%
+MIT so the idea is is in the body the
+cells are constantly resorbing The
+
+ align:start position:0%
+cells are constantly resorbing The
+ 
+
+ align:start position:0%
+cells are constantly resorbing The
+extracellular Matrix and depositing more
+
+ align:start position:0%
+extracellular Matrix and depositing more
+ 
+
+ align:start position:0%
+extracellular Matrix and depositing more
+so if you think about bone B for example
+
+ align:start position:0%
+so if you think about bone B for example
+ 
+
+ align:start position:0%
+so if you think about bone B for example
+remember we said bone grows in response
+
+ align:start position:0%
+remember we said bone grows in response
+ 
+
+ align:start position:0%
+remember we said bone grows in response
+to load even in healthy bone the bone is
+
+ align:start position:0%
+to load even in healthy bone the bone is
+ 
+
+ align:start position:0%
+to load even in healthy bone the bone is
+constantly being resorbed and deposited
+
+ align:start position:0%
+constantly being resorbed and deposited
+ 
+
+ align:start position:0%
+constantly being resorbed and deposited
+and in normal bone the rate of
+
+ align:start position:0%
+and in normal bone the rate of
+ 
+
+ align:start position:0%
+and in normal bone the rate of
+resorption and the rate of deposition is
+
+ align:start position:0%
+resorption and the rate of deposition is
+ 
+
+ align:start position:0%
+resorption and the rate of deposition is
+roughly the same when people get
+
+ align:start position:0%
+roughly the same when people get
+ 
+
+ align:start position:0%
+roughly the same when people get
+osteoporosis the thing that happens is
+
+ align:start position:0%
+osteoporosis the thing that happens is
+ 
+
+ align:start position:0%
+osteoporosis the thing that happens is
+that that balance gets out of whack and
+
+ align:start position:0%
+that that balance gets out of whack and
+ 
+
+ align:start position:0%
+that that balance gets out of whack and
+so it's not being deposited at the same
+
+ align:start position:0%
+so it's not being deposited at the same
+ 
+
+ align:start position:0%
+so it's not being deposited at the same
+rate it's being resorbed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the idea with the tissue engineering
+
+ align:start position:0%
+and the idea with the tissue engineering
+ 
+
+ align:start position:0%
+and the idea with the tissue engineering
+scaffolds is that that they degrade over
+
+ align:start position:0%
+scaffolds is that that they degrade over
+ 
+
+ align:start position:0%
+scaffolds is that that they degrade over
+time and that the cells that were
+
+ align:start position:0%
+time and that the cells that were
+ 
+
+ align:start position:0%
+time and that the cells that were
+attached to them uh are forming their
+
+ align:start position:0%
+attached to them uh are forming their
+ 
+
+ align:start position:0%
+attached to them uh are forming their
+own extracellular Matrix so there's kind
+
+ align:start position:0%
+own extracellular Matrix so there's kind
+ 
+
+ align:start position:0%
+own extracellular Matrix so there's kind
+of a balancing act between the cells
+
+ align:start position:0%
+of a balancing act between the cells
+ 
+
+ align:start position:0%
+of a balancing act between the cells
+depositing the native ECM and the tissue
+
+ align:start position:0%
+depositing the native ECM and the tissue
+ 
+
+ align:start position:0%
+depositing the native ECM and the tissue
+engineering scaffold that was provided
+
+ align:start position:0%
+engineering scaffold that was provided
+ 
+
+ align:start position:0%
+engineering scaffold that was provided
+Say by the clinician being
+
+ align:start position:0%
+Say by the clinician being
+ 
+
+ align:start position:0%
+Say by the clinician being
+resorbed so the so the scaffolds are
+
+ align:start position:0%
+resorbed so the so the scaffolds are
+ 
+
+ align:start position:0%
+resorbed so the so the scaffolds are
+actually designed to degrade and
+
+ align:start position:0%
+actually designed to degrade and
+ 
+
+ align:start position:0%
+actually designed to degrade and
+controlling that degradation rate is one
+
+ align:start position:0%
+controlling that degradation rate is one
+ 
+
+ align:start position:0%
+controlling that degradation rate is one
+of the design parameters of the
+
+ align:start position:0%
+of the design parameters of the
+ 
+
+ align:start position:0%
+of the design parameters of the
+scaffolds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's kind of the the overall
+
+ align:start position:0%
+okay so that's kind of the the overall
+ 
+
+ align:start position:0%
+okay so that's kind of the the overall
+kind of big picture and what I wanted to
+
+ align:start position:0%
+kind of big picture and what I wanted to
+ 
+
+ align:start position:0%
+kind of big picture and what I wanted to
+talk about next was some design
+
+ align:start position:0%
+talk about next was some design
+ 
+
+ align:start position:0%
+talk about next was some design
+requirements for the scaffolds so if you
+
+ align:start position:0%
+requirements for the scaffolds so if you
+ 
+
+ align:start position:0%
+requirements for the scaffolds so if you
+think about it there's there's different
+
+ align:start position:0%
+think about it there's there's different
+ 
+
+ align:start position:0%
+think about it there's there's different
+sort of um ways you can think about what
+
+ align:start position:0%
+sort of um ways you can think about what
+ 
+
+ align:start position:0%
+sort of um ways you can think about what
+the requirements are so you have to make
+
+ align:start position:0%
+the requirements are so you have to make
+ 
+
+ align:start position:0%
+the requirements are so you have to make
+the scaffold out of Some solid and
+
+ align:start position:0%
+the scaffold out of Some solid and
+ 
+
+ align:start position:0%
+the scaffold out of Some solid and
+there's some requirements for the solid
+
+ align:start position:0%
+there's some requirements for the solid
+ 
+
+ align:start position:0%
+there's some requirements for the solid
+so obviously you want a solid that's
+
+ align:start position:0%
+so obviously you want a solid that's
+ 
+
+ align:start position:0%
+so obviously you want a solid that's
+biocompatible that's one kind of main
+
+ align:start position:0%
+biocompatible that's one kind of main
+ 
+
+ align:start position:0%
+biocompatible that's one kind of main
+requirement another requirement is that
+
+ align:start position:0%
+requirement another requirement is that
+ 
+
+ align:start position:0%
+requirement another requirement is that
+not only the solid has to be
+
+ align:start position:0%
+not only the solid has to be
+ 
+
+ align:start position:0%
+not only the solid has to be
+biocompatible but when the solid
+
+ align:start position:0%
+biocompatible but when the solid
+ 
+
+ align:start position:0%
+biocompatible but when the solid
+decomposes if it decomposes into other
+
+ align:start position:0%
+decomposes if it decomposes into other
+ 
+
+ align:start position:0%
+decomposes if it decomposes into other
+components they have to be biocompatible
+
+ align:start position:0%
+components they have to be biocompatible
+ 
+
+ align:start position:0%
+components they have to be biocompatible
+too so you don't want the the solid to
+
+ align:start position:0%
+too so you don't want the the solid to
+ 
+
+ align:start position:0%
+too so you don't want the the solid to
+degrade during this resorption process
+
+ align:start position:0%
+degrade during this resorption process
+ 
+
+ align:start position:0%
+degrade during this resorption process
+into toxic components that would be a
+
+ align:start position:0%
+into toxic components that would be a
+ 
+
+ align:start position:0%
+into toxic components that would be a
+bad idea and then the other thing is the
+
+ align:start position:0%
+bad idea and then the other thing is the
+ 
+
+ align:start position:0%
+bad idea and then the other thing is the
+solid itself has to promote cell
+
+ align:start position:0%
+solid itself has to promote cell
+ 
+
+ align:start position:0%
+solid itself has to promote cell
+attachment and cell proliferation and uh
+
+ align:start position:0%
+attachment and cell proliferation and uh
+ 
+
+ align:start position:0%
+attachment and cell proliferation and uh
+cell migration all these kinds of things
+
+ align:start position:0%
+cell migration all these kinds of things
+ 
+
+ align:start position:0%
+cell migration all these kinds of things
+so we're going to talk about some
+
+ align:start position:0%
+so we're going to talk about some
+ 
+
+ align:start position:0%
+so we're going to talk about some
+different materials for the scaffolds
+
+ align:start position:0%
+different materials for the scaffolds
+ 
+
+ align:start position:0%
+different materials for the scaffolds
+and some of them are are sort of native
+
+ align:start position:0%
+and some of them are are sort of native
+ 
+
+ align:start position:0%
+and some of them are are sort of native
+proteins so some of them are things like
+
+ align:start position:0%
+proteins so some of them are things like
+ 
+
+ align:start position:0%
+proteins so some of them are things like
+collagen collagen already has binding
+
+ align:start position:0%
+collagen collagen already has binding
+ 
+
+ align:start position:0%
+collagen collagen already has binding
+sites for cells to attach to it
+
+ align:start position:0%
+sites for cells to attach to it
+ 
+
+ align:start position:0%
+sites for cells to attach to it
+obviously it's one of the proteins in in
+
+ align:start position:0%
+obviously it's one of the proteins in in
+ 
+
+ align:start position:0%
+obviously it's one of the proteins in in
+the native ECM there's also a number of
+
+ align:start position:0%
+the native ECM there's also a number of
+ 
+
+ align:start position:0%
+the native ECM there's also a number of
+synthetic polymers you can use and with
+
+ align:start position:0%
+synthetic polymers you can use and with
+ 
+
+ align:start position:0%
+synthetic polymers you can use and with
+the synthetic polymers they don't have
+
+ align:start position:0%
+the synthetic polymers they don't have
+ 
+
+ align:start position:0%
+the synthetic polymers they don't have
+natural binding sites for the cells and
+
+ align:start position:0%
+natural binding sites for the cells and
+ 
+
+ align:start position:0%
+natural binding sites for the cells and
+so you have to coat them with something
+
+ align:start position:0%
+so you have to coat them with something
+ 
+
+ align:start position:0%
+so you have to coat them with something
+else so you have to coat them with say
+
+ align:start position:0%
+else so you have to coat them with say
+ 
+
+ align:start position:0%
+else so you have to coat them with say
+adhesive proteins so that the cells will
+
+ align:start position:0%
+adhesive proteins so that the cells will
+ 
+
+ align:start position:0%
+adhesive proteins so that the cells will
+attach to them so we're going to talk
+
+ align:start position:0%
+attach to them so we're going to talk
+ 
+
+ align:start position:0%
+attach to them so we're going to talk
+about the um requirements for the solid
+
+ align:start position:0%
+about the um requirements for the solid
+ 
+
+ align:start position:0%
+about the um requirements for the solid
+then you make the solid into some sort
+
+ align:start position:0%
+then you make the solid into some sort
+ 
+
+ align:start position:0%
+then you make the solid into some sort
+of porous foamy thing I think I have
+
+ align:start position:0%
+of porous foamy thing I think I have
+ 
+
+ align:start position:0%
+of porous foamy thing I think I have
+some slides here here's an example of a
+
+ align:start position:0%
+some slides here here's an example of a
+ 
+
+ align:start position:0%
+some slides here here's an example of a
+collagen gag scaffold and this is one of
+
+ align:start position:0%
+collagen gag scaffold and this is one of
+ 
+
+ align:start position:0%
+collagen gag scaffold and this is one of
+the ones that um is made in yasis lab
+
+ align:start position:0%
+the ones that um is made in yasis lab
+ 
+
+ align:start position:0%
+the ones that um is made in yasis lab
+and you can see it looks a lot like a
+
+ align:start position:0%
+and you can see it looks a lot like a
+ 
+
+ align:start position:0%
+and you can see it looks a lot like a
+foam it's very very porous and there's
+
+ align:start position:0%
+foam it's very very porous and there's
+ 
+
+ align:start position:0%
+foam it's very very porous and there's
+some requirements for the sort of
+
+ align:start position:0%
+some requirements for the sort of
+ 
+
+ align:start position:0%
+some requirements for the sort of
+cellular structure the foamy structure
+
+ align:start position:0%
+cellular structure the foamy structure
+ 
+
+ align:start position:0%
+cellular structure the foamy structure
+of the scaffold as well so typically you
+
+ align:start position:0%
+of the scaffold as well so typically you
+ 
+
+ align:start position:0%
+of the scaffold as well so typically you
+want interconnected pores so it's easy
+
+ align:start position:0%
+want interconnected pores so it's easy
+ 
+
+ align:start position:0%
+want interconnected pores so it's easy
+for the cells to migrate in you want a
+
+ align:start position:0%
+for the cells to migrate in you want a
+ 
+
+ align:start position:0%
+for the cells to migrate in you want a
+typically you want pores to be within a
+
+ align:start position:0%
+typically you want pores to be within a
+ 
+
+ align:start position:0%
+typically you want pores to be within a
+certain range it turns out if the pores
+
+ align:start position:0%
+certain range it turns out if the pores
+ 
+
+ align:start position:0%
+certain range it turns out if the pores
+are too small it makes difficult for the
+
+ align:start position:0%
+are too small it makes difficult for the
+ 
+
+ align:start position:0%
+are too small it makes difficult for the
+cells to get in I mean sometimes they
+
+ align:start position:0%
+cells to get in I mean sometimes they
+ 
+
+ align:start position:0%
+cells to get in I mean sometimes they
+can by eating away at the material but
+
+ align:start position:0%
+can by eating away at the material but
+ 
+
+ align:start position:0%
+can by eating away at the material but
+um typically the pores want you want
+
+ align:start position:0%
+um typically the pores want you want
+ 
+
+ align:start position:0%
+um typically the pores want you want
+them to be bigger than a certain size
+
+ align:start position:0%
+them to be bigger than a certain size
+ 
+
+ align:start position:0%
+them to be bigger than a certain size
+you Al also want them to be smaller than
+
+ align:start position:0%
+you Al also want them to be smaller than
+ 
+
+ align:start position:0%
+you Al also want them to be smaller than
+a certain size because how much specific
+
+ align:start position:0%
+a certain size because how much specific
+ 
+
+ align:start position:0%
+a certain size because how much specific
+surface area how much surface area per
+
+ align:start position:0%
+surface area how much surface area per
+ 
+
+ align:start position:0%
+surface area how much surface area per
+unit volume you've got depends on the
+
+ align:start position:0%
+unit volume you've got depends on the
+ 
+
+ align:start position:0%
+unit volume you've got depends on the
+pore size the smaller the pores the more
+
+ align:start position:0%
+pore size the smaller the pores the more
+ 
+
+ align:start position:0%
+pore size the smaller the pores the more
+surface area per unit volume you have
+
+ align:start position:0%
+surface area per unit volume you have
+ 
+
+ align:start position:0%
+surface area per unit volume you have
+and then the number of binding sites you
+
+ align:start position:0%
+and then the number of binding sites you
+ 
+
+ align:start position:0%
+and then the number of binding sites you
+have for cells to attach to it depends
+
+ align:start position:0%
+have for cells to attach to it depends
+ 
+
+ align:start position:0%
+have for cells to attach to it depends
+on that specific surface area I'm going
+
+ align:start position:0%
+on that specific surface area I'm going
+ 
+
+ align:start position:0%
+on that specific surface area I'm going
+to write all this down so um I'll do
+
+ align:start position:0%
+to write all this down so um I'll do
+ 
+
+ align:start position:0%
+to write all this down so um I'll do
+that so so there's requirements for sort
+
+ align:start position:0%
+that so so there's requirements for sort
+ 
+
+ align:start position:0%
+that so so there's requirements for sort
+of the pore structure uh and then
+
+ align:start position:0%
+of the pore structure uh and then
+ 
+
+ align:start position:0%
+of the pore structure uh and then
+there's also some requirements for the
+
+ align:start position:0%
+there's also some requirements for the
+ 
+
+ align:start position:0%
+there's also some requirements for the
+whole scaffold itself so for instance
+
+ align:start position:0%
+whole scaffold itself so for instance
+ 
+
+ align:start position:0%
+whole scaffold itself so for instance
+it's got to have some minimum mechanical
+
+ align:start position:0%
+it's got to have some minimum mechanical
+ 
+
+ align:start position:0%
+it's got to have some minimum mechanical
+Integrity so there's sort of some
+
+ align:start position:0%
+Integrity so there's sort of some
+ 
+
+ align:start position:0%
+Integrity so there's sort of some
+requirements for that so there's
+
+ align:start position:0%
+requirements for that so there's
+ 
+
+ align:start position:0%
+requirements for that so there's
+requirements for the solid there's
+
+ align:start position:0%
+requirements for the solid there's
+ 
+
+ align:start position:0%
+requirements for the solid there's
+requirements for the sort of cells
+
+ align:start position:0%
+requirements for the sort of cells
+ 
+
+ align:start position:0%
+requirements for the sort of cells
+cellular structure the porous structure
+
+ align:start position:0%
+cellular structure the porous structure
+ 
+
+ align:start position:0%
+cellular structure the porous structure
+and there requirements for the overall
+
+ align:start position:0%
+and there requirements for the overall
+ 
+
+ align:start position:0%
+and there requirements for the overall
+scaffold so let me um write some of
+
+ align:start position:0%
+scaffold so let me um write some of
+ 
+
+ align:start position:0%
+scaffold so let me um write some of
+these things down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's some requirements for the
+
+ align:start position:0%
+so there's some requirements for the
+ 
+
+ align:start position:0%
+so there's some requirements for the
+solid so it must be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+biocompatible it must also promote cell
+
+ align:start position:0%
+biocompatible it must also promote cell
+ 
+
+ align:start position:0%
+biocompatible it must also promote cell
+attachment and proliferation in the cell
+
+ align:start position:0%
+attachment and proliferation in the cell
+ 
+
+ align:start position:0%
+attachment and proliferation in the cell
+functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then it must degrade into non-toxic
+
+ align:start position:0%
+and then it must degrade into non-toxic
+ 
+
+ align:start position:0%
+and then it must degrade into non-toxic
+components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's some requirements for the
+
+ align:start position:0%
+so there's some requirements for the
+ 
+
+ align:start position:0%
+so there's some requirements for the
+cellular structure too and what you want
+
+ align:start position:0%
+cellular structure too and what you want
+ 
+
+ align:start position:0%
+cellular structure too and what you want
+to have is a large volume fraction
+
+ align:start position:0%
+to have is a large volume fraction
+ 
+
+ align:start position:0%
+to have is a large volume fraction
+interconnected pores and so you want
+
+ align:start position:0%
+interconnected pores and so you want
+ 
+
+ align:start position:0%
+interconnected pores and so you want
+that to facilitate the cell migration
+
+ align:start position:0%
+that to facilitate the cell migration
+ 
+
+ align:start position:0%
+that to facilitate the cell migration
+and also the transport of nutrients into
+
+ align:start position:0%
+and also the transport of nutrients into
+ 
+
+ align:start position:0%
+and also the transport of nutrients into
+the cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you also want the pore size with the
+
+ align:start position:0%
+so you also want the pore size with the
+ 
+
+ align:start position:0%
+so you also want the pore size with the
+pore size to be within a critical range
+
+ align:start position:0%
+pore size to be within a critical range
+ 
+
+ align:start position:0%
+pore size to be within a critical range
+so you need the pores bigger than a
+
+ align:start position:0%
+so you need the pores bigger than a
+ 
+
+ align:start position:0%
+so you need the pores bigger than a
+lower limit so the cells can Mig migrate
+
+ align:start position:0%
+lower limit so the cells can Mig migrate
+ 
+
+ align:start position:0%
+lower limit so the cells can Mig migrate
+through easily can kind of get in there
+
+ align:start position:0%
+through easily can kind of get in there
+ 
+
+ align:start position:0%
+through easily can kind of get in there
+and you want the porees size to be less
+
+ align:start position:0%
+and you want the porees size to be less
+ 
+
+ align:start position:0%
+and you want the porees size to be less
+than an upper limit to have enough
+
+ align:start position:0%
+than an upper limit to have enough
+ 
+
+ align:start position:0%
+than an upper limit to have enough
+surface area to have enough binding SES
+
+ align:start position:0%
+surface area to have enough binding SES
+ 
+
+ align:start position:0%
+surface area to have enough binding SES
+to actually attach cells and for
+
+ align:start position:0%
+to actually attach cells and for
+ 
+
+ align:start position:0%
+to actually attach cells and for
+different tissues there's different
+
+ align:start position:0%
+different tissues there's different
+ 
+
+ align:start position:0%
+different tissues there's different
+critical ranges of the pore size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example for
+
+ align:start position:0%
+so for example for
+ 
+
+ align:start position:0%
+so for example for
+skin they found that you want to have a
+
+ align:start position:0%
+skin they found that you want to have a
+ 
+
+ align:start position:0%
+skin they found that you want to have a
+pore size between about 20
+
+ align:start position:0%
+pore size between about 20
+ 
+
+ align:start position:0%
+pore size between about 20
+microns and about 150
+
+ align:start position:0%
+microns and about 150
+ 
+
+ align:start position:0%
+microns and about 150
+microns and for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bone the pore sizes that people tend to
+
+ align:start position:0%
+bone the pore sizes that people tend to
+ 
+
+ align:start position:0%
+bone the pore sizes that people tend to
+use are between about 100 and
+
+ align:start position:0%
+use are between about 100 and
+ 
+
+ align:start position:0%
+use are between about 100 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+microns so there's the pore size and one
+
+ align:start position:0%
+microns so there's the pore size and one
+ 
+
+ align:start position:0%
+microns so there's the pore size and one
+other feature is that the POR geometry
+
+ align:start position:0%
+other feature is that the POR geometry
+ 
+
+ align:start position:0%
+other feature is that the POR geometry
+should be conducive for the cell type so
+
+ align:start position:0%
+should be conducive for the cell type so
+ 
+
+ align:start position:0%
+should be conducive for the cell type so
+lots of cells are somewhat equiaxed
+
+ align:start position:0%
+lots of cells are somewhat equiaxed
+ 
+
+ align:start position:0%
+lots of cells are somewhat equiaxed
+maybe a little elongated uh but if you
+
+ align:start position:0%
+maybe a little elongated uh but if you
+ 
+
+ align:start position:0%
+maybe a little elongated uh but if you
+look at something like nerve cells like
+
+ align:start position:0%
+look at something like nerve cells like
+ 
+
+ align:start position:0%
+look at something like nerve cells like
+peripheral nerve they're incredibly
+
+ align:start position:0%
+peripheral nerve they're incredibly
+ 
+
+ align:start position:0%
+peripheral nerve they're incredibly
+elongated so you want to have pores in
+
+ align:start position:0%
+elongated so you want to have pores in
+ 
+
+ align:start position:0%
+elongated so you want to have pores in
+the scaffold that are also very
+
+ align:start position:0%
+the scaffold that are also very
+ 
+
+ align:start position:0%
+the scaffold that are also very
+elongated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then for the overall scaffold it
+
+ align:start position:0%
+and then for the overall scaffold it
+ 
+
+ align:start position:0%
+and then for the overall scaffold it
+needs to have some mechanical Integrity
+
+ align:start position:0%
+needs to have some mechanical Integrity
+ 
+
+ align:start position:0%
+needs to have some mechanical Integrity
+you guys okay yeah we're good um oh achy
+
+ align:start position:0%
+you guys okay yeah we're good um oh achy
+ 
+
+ align:start position:0%
+you guys okay yeah we're good um oh achy
+yeah I don't I know
+
+ align:start position:0%
+yeah I don't I know
+ 
+
+ align:start position:0%
+yeah I don't I know
+um uh so you want to have some overall
+
+ align:start position:0%
+um uh so you want to have some overall
+ 
+
+ align:start position:0%
+um uh so you want to have some overall
+mechanical Integrity I mean the thing
+
+ align:start position:0%
+mechanical Integrity I mean the thing
+ 
+
+ align:start position:0%
+mechanical Integrity I mean the thing
+has to be put into the body in surgery
+
+ align:start position:0%
+has to be put into the body in surgery
+ 
+
+ align:start position:0%
+has to be put into the body in surgery
+and people are going to be pushing and
+
+ align:start position:0%
+and people are going to be pushing and
+ 
+
+ align:start position:0%
+and people are going to be pushing and
+poking at it and so there has to have
+
+ align:start position:0%
+poking at it and so there has to have
+ 
+
+ align:start position:0%
+poking at it and so there has to have
+some just overall mechanical Integrity
+
+ align:start position:0%
+some just overall mechanical Integrity
+ 
+
+ align:start position:0%
+some just overall mechanical Integrity
+also it it turns out that if you put
+
+ align:start position:0%
+also it it turns out that if you put
+ 
+
+ align:start position:0%
+also it it turns out that if you put
+stem cells into scaffolds uh the types
+
+ align:start position:0%
+stem cells into scaffolds uh the types
+ 
+
+ align:start position:0%
+stem cells into scaffolds uh the types
+of cells they differentiate into depends
+
+ align:start position:0%
+of cells they differentiate into depends
+ 
+
+ align:start position:0%
+of cells they differentiate into depends
+in part on the stiffness of the scaffold
+
+ align:start position:0%
+in part on the stiffness of the scaffold
+ 
+
+ align:start position:0%
+in part on the stiffness of the scaffold
+so you want to be able to control the
+
+ align:start position:0%
+so you want to be able to control the
+ 
+
+ align:start position:0%
+so you want to be able to control the
+stiffness of the scaffold how they do
+
+ align:start position:0%
+stiffness of the scaffold how they do
+ 
+
+ align:start position:0%
+stiffness of the scaffold how they do
+this research do they use like animals
+
+ align:start position:0%
+this research do they use like animals
+ 
+
+ align:start position:0%
+this research do they use like animals
+or they do yeah so the question is how
+
+ align:start position:0%
+or they do yeah so the question is how
+ 
+
+ align:start position:0%
+or they do yeah so the question is how
+do they do the research so they do a
+
+ align:start position:0%
+do they do the research so they do a
+ 
+
+ align:start position:0%
+do they do the research so they do a
+sort of a series of different things so
+
+ align:start position:0%
+sort of a series of different things so
+ 
+
+ align:start position:0%
+sort of a series of different things so
+uh you know at one level you could have
+
+ align:start position:0%
+uh you know at one level you could have
+ 
+
+ align:start position:0%
+uh you know at one level you could have
+the scaffold and you'd put cells on it
+
+ align:start position:0%
+the scaffold and you'd put cells on it
+ 
+
+ align:start position:0%
+the scaffold and you'd put cells on it
+so you could put you know say you're
+
+ align:start position:0%
+so you could put you know say you're
+ 
+
+ align:start position:0%
+so you could put you know say you're
+making a bone scaffold you'd put
+
+ align:start position:0%
+making a bone scaffold you'd put
+ 
+
+ align:start position:0%
+making a bone scaffold you'd put
+osteocytes onto it so so one level you
+
+ align:start position:0%
+osteocytes onto it so so one level you
+ 
+
+ align:start position:0%
+osteocytes onto it so so one level you
+just put cells onto it
+
+ align:start position:0%
+just put cells onto it
+ 
+
+ align:start position:0%
+just put cells onto it
+and you want to see you know are the
+
+ align:start position:0%
+and you want to see you know are the
+ 
+
+ align:start position:0%
+and you want to see you know are the
+cells attaching are they dying are they
+
+ align:start position:0%
+cells attaching are they dying are they
+ 
+
+ align:start position:0%
+cells attaching are they dying are they
+proliferating so you know sometimes what
+
+ align:start position:0%
+proliferating so you know sometimes what
+ 
+
+ align:start position:0%
+proliferating so you know sometimes what
+people will do is put this they'll see a
+
+ align:start position:0%
+people will do is put this they'll see a
+ 
+
+ align:start position:0%
+people will do is put this they'll see a
+certain number of cells at a certain
+
+ align:start position:0%
+certain number of cells at a certain
+ 
+
+ align:start position:0%
+certain number of cells at a certain
+time say Time Zero then they'll um look
+
+ align:start position:0%
+time say Time Zero then they'll um look
+ 
+
+ align:start position:0%
+time say Time Zero then they'll um look
+at how many cells are attached at 24
+
+ align:start position:0%
+at how many cells are attached at 24
+ 
+
+ align:start position:0%
+at how many cells are attached at 24
+hours or 48 hours and you kind of see um
+
+ align:start position:0%
+hours or 48 hours and you kind of see um
+ 
+
+ align:start position:0%
+hours or 48 hours and you kind of see um
+the cell attachment you can measure
+
+ align:start position:0%
+the cell attachment you can measure
+ 
+
+ align:start position:0%
+the cell attachment you can measure
+relatively easily um another thing
+
+ align:start position:0%
+relatively easily um another thing
+ 
+
+ align:start position:0%
+relatively easily um another thing
+people do is animal studies so for
+
+ align:start position:0%
+people do is animal studies so for
+ 
+
+ align:start position:0%
+people do is animal studies so for
+instance yanos does research on
+
+ align:start position:0%
+instance yanos does research on
+ 
+
+ align:start position:0%
+instance yanos does research on
+peripheral nerves and scaffold for
+
+ align:start position:0%
+peripheral nerves and scaffold for
+ 
+
+ align:start position:0%
+peripheral nerves and scaffold for
+peripheral nerves and they cut a piece
+
+ align:start position:0%
+peripheral nerves and they cut a piece
+ 
+
+ align:start position:0%
+peripheral nerves and they cut a piece
+out of the sciatic nerve of rats so
+
+ align:start position:0%
+out of the sciatic nerve of rats so
+ 
+
+ align:start position:0%
+out of the sciatic nerve of rats so
+obviously they have a surgeon and do a
+
+ align:start position:0%
+obviously they have a surgeon and do a
+ 
+
+ align:start position:0%
+obviously they have a surgeon and do a
+surgery thing with it you can't just
+
+ align:start position:0%
+surgery thing with it you can't just
+ 
+
+ align:start position:0%
+surgery thing with it you can't just
+kind of do this in the lab you've got to
+
+ align:start position:0%
+kind of do this in the lab you've got to
+ 
+
+ align:start position:0%
+kind of do this in the lab you've got to
+get permissions and stuff to do it um
+
+ align:start position:0%
+get permissions and stuff to do it um
+ 
+
+ align:start position:0%
+get permissions and stuff to do it um
+and then they put in the scaffold and
+
+ align:start position:0%
+and then they put in the scaffold and
+ 
+
+ align:start position:0%
+and then they put in the scaffold and
+the scaffold is actually in a tube and
+
+ align:start position:0%
+the scaffold is actually in a tube and
+ 
+
+ align:start position:0%
+the scaffold is actually in a tube and
+so they put the two stumps of the nerve
+
+ align:start position:0%
+so they put the two stumps of the nerve
+ 
+
+ align:start position:0%
+so they put the two stumps of the nerve
+end at either end of the tube and then
+
+ align:start position:0%
+end at either end of the tube and then
+ 
+
+ align:start position:0%
+end at either end of the tube and then
+the tube's filled with the sort of
+
+ align:start position:0%
+the tube's filled with the sort of
+ 
+
+ align:start position:0%
+the tube's filled with the sort of
+porous scaffold that we're talking about
+
+ align:start position:0%
+porous scaffold that we're talking about
+ 
+
+ align:start position:0%
+porous scaffold that we're talking about
+here and then they you know they wait
+
+ align:start position:0%
+here and then they you know they wait
+ 
+
+ align:start position:0%
+here and then they you know they wait
+some period of time um and they you know
+
+ align:start position:0%
+some period of time um and they you know
+ 
+
+ align:start position:0%
+some period of time um and they you know
+they take video of rat running things
+
+ align:start position:0%
+they take video of rat running things
+ 
+
+ align:start position:0%
+they take video of rat running things
+like that they um they then sacrifice
+
+ align:start position:0%
+like that they um they then sacrifice
+ 
+
+ align:start position:0%
+like that they um they then sacrifice
+the rat and they do histology and they
+
+ align:start position:0%
+the rat and they do histology and they
+ 
+
+ align:start position:0%
+the rat and they do histology and they
+look at the the sort of cross-sections
+
+ align:start position:0%
+look at the the sort of cross-sections
+ 
+
+ align:start position:0%
+look at the the sort of cross-sections
+and see what it looks like um and so I'm
+
+ align:start position:0%
+and see what it looks like um and so I'm
+ 
+
+ align:start position:0%
+and see what it looks like um and so I'm
+going to talk next time about this
+
+ align:start position:0%
+going to talk next time about this
+ 
+
+ align:start position:0%
+going to talk next time about this
+osteochondral scaffold we worked on so
+
+ align:start position:0%
+osteochondral scaffold we worked on so
+ 
+
+ align:start position:0%
+osteochondral scaffold we worked on so
+we did cell studies we did goat studies
+
+ align:start position:0%
+we did cell studies we did goat studies
+ 
+
+ align:start position:0%
+we did cell studies we did goat studies
+we put into goat knees there was a
+
+ align:start position:0%
+we put into goat knees there was a
+ 
+
+ align:start position:0%
+we put into goat knees there was a
+longer term sheep study and then uh the
+
+ align:start position:0%
+longer term sheep study and then uh the
+ 
+
+ align:start position:0%
+longer term sheep study and then uh the
+the student who's in Cambridge England
+
+ align:start position:0%
+the student who's in Cambridge England
+ 
+
+ align:start position:0%
+the student who's in Cambridge England
+started up a company and um he ended up
+
+ align:start position:0%
+started up a company and um he ended up
+ 
+
+ align:start position:0%
+started up a company and um he ended up
+getting approval in Europe to start
+
+ align:start position:0%
+getting approval in Europe to start
+ 
+
+ align:start position:0%
+getting approval in Europe to start
+clinical trials and and you know he
+
+ align:start position:0%
+clinical trials and and you know he
+ 
+
+ align:start position:0%
+clinical trials and and you know he
+worked with an orthopedic surgeon who
+
+ align:start position:0%
+worked with an orthopedic surgeon who
+ 
+
+ align:start position:0%
+worked with an orthopedic surgeon who
+started putting in people but typically
+
+ align:start position:0%
+started putting in people but typically
+ 
+
+ align:start position:0%
+started putting in people but typically
+they're sort of looking at cells looking
+
+ align:start position:0%
+they're sort of looking at cells looking
+ 
+
+ align:start position:0%
+they're sort of looking at cells looking
+at animals before you get to the people
+
+ align:start position:0%
+at animals before you get to the people
+ 
+
+ align:start position:0%
+at animals before you get to the people
+stage okay and you know one of the
+
+ align:start position:0%
+stage okay and you know one of the
+ 
+
+ align:start position:0%
+stage okay and you know one of the
+things people do when they're making
+
+ align:start position:0%
+things people do when they're making
+ 
+
+ align:start position:0%
+things people do when they're making
+these scaffolds is you want to use
+
+ align:start position:0%
+these scaffolds is you want to use
+ 
+
+ align:start position:0%
+these scaffolds is you want to use
+materials that already have some sort of
+
+ align:start position:0%
+materials that already have some sort of
+ 
+
+ align:start position:0%
+materials that already have some sort of
+regulatory approval so say FDA approval
+
+ align:start position:0%
+regulatory approval so say FDA approval
+ 
+
+ align:start position:0%
+regulatory approval so say FDA approval
+or approval in Europe so typically
+
+ align:start position:0%
+or approval in Europe so typically
+ 
+
+ align:start position:0%
+or approval in Europe so typically
+people don't start with a brand new
+
+ align:start position:0%
+people don't start with a brand new
+ 
+
+ align:start position:0%
+people don't start with a brand new
+material from scratch because to get
+
+ align:start position:0%
+material from scratch because to get
+ 
+
+ align:start position:0%
+material from scratch because to get
+approval for that would just take a very
+
+ align:start position:0%
+approval for that would just take a very
+ 
+
+ align:start position:0%
+approval for that would just take a very
+long time so so typically people start
+
+ align:start position:0%
+long time so so typically people start
+ 
+
+ align:start position:0%
+long time so so typically people start
+with the solid material is already
+
+ align:start position:0%
+with the solid material is already
+ 
+
+ align:start position:0%
+with the solid material is already
+approved for some other sort of use so
+
+ align:start position:0%
+approved for some other sort of use so
+ 
+
+ align:start position:0%
+approved for some other sort of use so
+okay um so One requirement for the
+
+ align:start position:0%
+okay um so One requirement for the
+ 
+
+ align:start position:0%
+okay um so One requirement for the
+overall scaffold is it has to have
+
+ align:start position:0%
+overall scaffold is it has to have
+ 
+
+ align:start position:0%
+overall scaffold is it has to have
+sufficient mechanical
+
+ align:start position:0%
+sufficient mechanical
+ 
+
+ align:start position:0%
+sufficient mechanical
+Integrity uh sufficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then also as I mentioned the
+
+ align:start position:0%
+and then also as I mentioned the
+ 
+
+ align:start position:0%
+and then also as I mentioned the
+stiffness of the scaffold can affect the
+
+ align:start position:0%
+stiffness of the scaffold can affect the
+ 
+
+ align:start position:0%
+stiffness of the scaffold can affect the
+differentiation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cells and the other thing that is really
+
+ align:start position:0%
+cells and the other thing that is really
+ 
+
+ align:start position:0%
+cells and the other thing that is really
+a factor for the overall SC scaffold is
+
+ align:start position:0%
+a factor for the overall SC scaffold is
+ 
+
+ align:start position:0%
+a factor for the overall SC scaffold is
+you want to control the rate of
+
+ align:start position:0%
+you want to control the rate of
+ 
+
+ align:start position:0%
+you want to control the rate of
+degradation of the overall scaffold so
+
+ align:start position:0%
+degradation of the overall scaffold so
+ 
+
+ align:start position:0%
+degradation of the overall scaffold so
+you want that rate to be matched to the
+
+ align:start position:0%
+you want that rate to be matched to the
+ 
+
+ align:start position:0%
+you want that rate to be matched to the
+rate at which the new tissue is
+
+ align:start position:0%
+rate at which the new tissue is
+ 
+
+ align:start position:0%
+rate at which the new tissue is
+forming so it has to degrade at a
+
+ align:start position:0%
+forming so it has to degrade at a
+ 
+
+ align:start position:0%
+forming so it has to degrade at a
+controllable rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so I wanted to talk about the
+
+ align:start position:0%
+uh so I wanted to talk about the
+ 
+
+ align:start position:0%
+uh so I wanted to talk about the
+materials that people use and you can
+
+ align:start position:0%
+materials that people use and you can
+ 
+
+ align:start position:0%
+materials that people use and you can
+kind of break them down into a few
+
+ align:start position:0%
+kind of break them down into a few
+ 
+
+ align:start position:0%
+kind of break them down into a few
+classes so one class is natural polymers
+
+ align:start position:0%
+classes so one class is natural polymers
+ 
+
+ align:start position:0%
+classes so one class is natural polymers
+so things like collagen so you can get
+
+ align:start position:0%
+so things like collagen so you can get
+ 
+
+ align:start position:0%
+so things like collagen so you can get
+collagen and that's an example up there
+
+ align:start position:0%
+collagen and that's an example up there
+ 
+
+ align:start position:0%
+collagen and that's an example up there
+of a scaffold that's made with collagen
+
+ align:start position:0%
+of a scaffold that's made with collagen
+ 
+
+ align:start position:0%
+of a scaffold that's made with collagen
+another class of materials is synthetic
+
+ align:start position:0%
+another class of materials is synthetic
+ 
+
+ align:start position:0%
+another class of materials is synthetic
+biomaterials and if you've had stitches
+
+ align:start position:0%
+biomaterials and if you've had stitches
+ 
+
+ align:start position:0%
+biomaterials and if you've had stitches
+or surgery uh you may know that some of
+
+ align:start position:0%
+or surgery uh you may know that some of
+ 
+
+ align:start position:0%
+or surgery uh you may know that some of
+the sutures they use are resorbable so
+
+ align:start position:0%
+the sutures they use are resorbable so
+ 
+
+ align:start position:0%
+the sutures they use are resorbable so
+some of those polymers that they use for
+
+ align:start position:0%
+some of those polymers that they use for
+ 
+
+ align:start position:0%
+some of those polymers that they use for
+resorbable sutures are also used for uh
+
+ align:start position:0%
+resorbable sutures are also used for uh
+ 
+
+ align:start position:0%
+resorbable sutures are also used for uh
+tissue engineering scaffold and then
+
+ align:start position:0%
+tissue engineering scaffold and then
+ 
+
+ align:start position:0%
+tissue engineering scaffold and then
+there's also Hydro gels that people use
+
+ align:start position:0%
+there's also Hydro gels that people use
+ 
+
+ align:start position:0%
+there's also Hydro gels that people use
+as well so those are probably the three
+
+ align:start position:0%
+as well so those are probably the three
+ 
+
+ align:start position:0%
+as well so those are probably the three
+main groups are um sort of natural
+
+ align:start position:0%
+main groups are um sort of natural
+ 
+
+ align:start position:0%
+main groups are um sort of natural
+polymers synthetic
+
+ align:start position:0%
+polymers synthetic
+ 
+
+ align:start position:0%
+polymers synthetic
+biopolymers and I guess the hydrogels
+
+ align:start position:0%
+biopolymers and I guess the hydrogels
+ 
+
+ align:start position:0%
+biopolymers and I guess the hydrogels
+are sort of a subset of the synthetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+biopolymers so collagen is probably the
+
+ align:start position:0%
+biopolymers so collagen is probably the
+ 
+
+ align:start position:0%
+biopolymers so collagen is probably the
+most common kind of natural polymer
+
+ align:start position:0%
+most common kind of natural polymer
+ 
+
+ align:start position:0%
+most common kind of natural polymer
+that's used U they also use gags and
+
+ align:start position:0%
+that's used U they also use gags and
+ 
+
+ align:start position:0%
+that's used U they also use gags and
+this scaffold up here is made by making
+
+ align:start position:0%
+this scaffold up here is made by making
+ 
+
+ align:start position:0%
+this scaffold up here is made by making
+a co-precipitate of collagen with a gag
+
+ align:start position:0%
+a co-precipitate of collagen with a gag
+ 
+
+ align:start position:0%
+a co-precipitate of collagen with a gag
+Condren sulfate people also use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alginate I think one of the project
+
+ align:start position:0%
+alginate I think one of the project
+ 
+
+ align:start position:0%
+alginate I think one of the project
+groups you guys are going to make some
+
+ align:start position:0%
+groups you guys are going to make some
+ 
+
+ align:start position:0%
+groups you guys are going to make some
+sort of alate scaffold right no scal
+
+ align:start position:0%
+sort of alate scaffold right no scal
+ 
+
+ align:start position:0%
+sort of alate scaffold right no scal
+foamy thing yeah um and people also use
+
+ align:start position:0%
+foamy thing yeah um and people also use
+ 
+
+ align:start position:0%
+foamy thing yeah um and people also use
+something called
+
+ align:start position:0%
+something called
+ 
+
+ align:start position:0%
+something called
+kosan which is a derivative of kiten
+
+ align:start position:0%
+kosan which is a derivative of kiten
+ 
+
+ align:start position:0%
+kosan which is a derivative of kiten
+which is what's in the exoskeleton of
+
+ align:start position:0%
+which is what's in the exoskeleton of
+ 
+
+ align:start position:0%
+which is what's in the exoskeleton of
+insects and things like lobsters so
+
+ align:start position:0%
+insects and things like lobsters so
+ 
+
+ align:start position:0%
+insects and things like lobsters so
+those would be all examples of natural
+
+ align:start position:0%
+those would be all examples of natural
+ 
+
+ align:start position:0%
+those would be all examples of natural
+polymers that can be used and people
+
+ align:start position:0%
+polymers that can be used and people
+ 
+
+ align:start position:0%
+polymers that can be used and people
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+tried I'm going to talk a bit more about
+
+ align:start position:0%
+tried I'm going to talk a bit more about
+ 
+
+ align:start position:0%
+tried I'm going to talk a bit more about
+collagen just because it's the most
+
+ align:start position:0%
+collagen just because it's the most
+ 
+
+ align:start position:0%
+collagen just because it's the most
+common one so collagen's a major
+
+ align:start position:0%
+common one so collagen's a major
+ 
+
+ align:start position:0%
+common one so collagen's a major
+component in the natural extracellular
+
+ align:start position:0%
+component in the natural extracellular
+ 
+
+ align:start position:0%
+component in the natural extracellular
+Matrix and not surprisingly it has
+
+ align:start position:0%
+Matrix and not surprisingly it has
+ 
+
+ align:start position:0%
+Matrix and not surprisingly it has
+binding sites for cells to attach to it
+
+ align:start position:0%
+binding sites for cells to attach to it
+ 
+
+ align:start position:0%
+binding sites for cells to attach to it
+so if you use that that kind of takes
+
+ align:start position:0%
+so if you use that that kind of takes
+ 
+
+ align:start position:0%
+so if you use that that kind of takes
+care of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+issue down here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so collagen exists in many types of
+
+ align:start position:0%
+so collagen exists in many types of
+ 
+
+ align:start position:0%
+so collagen exists in many types of
+tissues exists in skin exists in bone
+
+ align:start position:0%
+tissues exists in skin exists in bone
+ 
+
+ align:start position:0%
+tissues exists in skin exists in bone
+cartilage ligament tendon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cartilage so it's very common
+
+ align:start position:0%
+cartilage so it's very common
+ 
+
+ align:start position:0%
+cartilage so it's very common
+it has surface binding
+
+ align:start position:0%
+it has surface binding
+ 
+
+ align:start position:0%
+it has surface binding
+sites for cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it has a relatively low young
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modulus so the low Young's modulus is a
+
+ align:start position:0%
+modulus so the low Young's modulus is a
+ 
+
+ align:start position:0%
+modulus so the low Young's modulus is a
+little less than a gigap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pascal uh but you can increase the
+
+ align:start position:0%
+pascal uh but you can increase the
+ 
+
+ align:start position:0%
+pascal uh but you can increase the
+modulus by either cross- linking or by
+
+ align:start position:0%
+modulus by either cross- linking or by
+ 
+
+ align:start position:0%
+modulus by either cross- linking or by
+using it in conjunction with some
+
+ align:start position:0%
+using it in conjunction with some
+ 
+
+ align:start position:0%
+using it in conjunction with some
+synthetic polymers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to talk a little bit about
+
+ align:start position:0%
+and I'm going to talk a little bit about
+ 
+
+ align:start position:0%
+and I'm going to talk a little bit about
+how you make these scaffolds up here and
+
+ align:start position:0%
+how you make these scaffolds up here and
+ 
+
+ align:start position:0%
+how you make these scaffolds up here and
+the first step in doing making those
+
+ align:start position:0%
+the first step in doing making those
+ 
+
+ align:start position:0%
+the first step in doing making those
+scaffolds is you put the collagen in
+
+ align:start position:0%
+scaffolds is you put the collagen in
+ 
+
+ align:start position:0%
+scaffolds is you put the collagen in
+acetic acid and then you add the
+
+ align:start position:0%
+acetic acid and then you add the
+ 
+
+ align:start position:0%
+acetic acid and then you add the
+glycosaminoglycan and it forms a
+
+ align:start position:0%
+glycosaminoglycan and it forms a
+ 
+
+ align:start position:0%
+glycosaminoglycan and it forms a
+co-precipitate and the fact that it
+
+ align:start position:0%
+co-precipitate and the fact that it
+ 
+
+ align:start position:0%
+co-precipitate and the fact that it
+forms a go coprecipitate with the uh
+
+ align:start position:0%
+forms a go coprecipitate with the uh
+ 
+
+ align:start position:0%
+forms a go coprecipitate with the uh
+glycosaminoglycan the gag means that you
+
+ align:start position:0%
+glycosaminoglycan the gag means that you
+ 
+
+ align:start position:0%
+glycosaminoglycan the gag means that you
+can use a freeze drying process and
+
+ align:start position:0%
+can use a freeze drying process and
+ 
+
+ align:start position:0%
+can use a freeze drying process and
+that's how that's made
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's collagen is one option so then
+
+ align:start position:0%
+so that's collagen is one option so then
+ 
+
+ align:start position:0%
+so that's collagen is one option so then
+synthetic biopolymers is another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+option and as I said typically they use
+
+ align:start position:0%
+option and as I said typically they use
+ 
+
+ align:start position:0%
+option and as I said typically they use
+the materials that are used for
+
+ align:start position:0%
+the materials that are used for
+ 
+
+ align:start position:0%
+the materials that are used for
+resorbable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sutures so there's several of those
+
+ align:start position:0%
+sutures so there's several of those
+ 
+
+ align:start position:0%
+sutures so there's several of those
+there's something called
+
+ align:start position:0%
+there's something called
+ 
+
+ align:start position:0%
+there's something called
+PGA that's polyglycolic acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's something called pla that's
+
+ align:start position:0%
+there's something called pla that's
+ 
+
+ align:start position:0%
+there's something called pla that's
+polylactic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid and then you can combine those two
+
+ align:start position:0%
+acid and then you can combine those two
+ 
+
+ align:start position:0%
+acid and then you can combine those two
+and make something called plga
+
+ align:start position:0%
+and make something called plga
+ 
+
+ align:start position:0%
+and make something called plga
+polylactic Co glycolic acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can control the degradation rate
+
+ align:start position:0%
+and you can control the degradation rate
+ 
+
+ align:start position:0%
+and you can control the degradation rate
+of these things by controlling the
+
+ align:start position:0%
+of these things by controlling the
+ 
+
+ align:start position:0%
+of these things by controlling the
+molecular weight and in this case you
+
+ align:start position:0%
+molecular weight and in this case you
+ 
+
+ align:start position:0%
+molecular weight and in this case you
+can also control it by controlling how
+
+ align:start position:0%
+can also control it by controlling how
+ 
+
+ align:start position:0%
+can also control it by controlling how
+much of each of those things you put in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's another one called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polycaprolactone so those are
+
+ align:start position:0%
+polycaprolactone so those are
+ 
+
+ align:start position:0%
+polycaprolactone so those are
+several uh synthetic biop poers that
+
+ align:start position:0%
+several uh synthetic biop poers that
+ 
+
+ align:start position:0%
+several uh synthetic biop poers that
+people use there's lots of different
+
+ align:start position:0%
+people use there's lots of different
+ 
+
+ align:start position:0%
+people use there's lots of different
+materials but these are just some
+
+ align:start position:0%
+materials but these are just some
+ 
+
+ align:start position:0%
+materials but these are just some
+typical ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then another class are hydrogels
+
+ align:start position:0%
+and then another class are hydrogels
+ 
+
+ align:start position:0%
+and then another class are hydrogels
+which are produced by crosslinking water
+
+ align:start position:0%
+which are produced by crosslinking water
+ 
+
+ align:start position:0%
+which are produced by crosslinking water
+soluble polymers to form an insoluble
+
+ align:start position:0%
+soluble polymers to form an insoluble
+ 
+
+ align:start position:0%
+soluble polymers to form an insoluble
+Network
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and those are typically used for soft
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tissues so sometimes they're used for
+
+ align:start position:0%
+tissues so sometimes they're used for
+ 
+
+ align:start position:0%
+tissues so sometimes they're used for
+things like cartilage and this again
+
+ align:start position:0%
+things like cartilage and this again
+ 
+
+ align:start position:0%
+things like cartilage and this again
+there's a few different materials that
+
+ align:start position:0%
+there's a few different materials that
+ 
+
+ align:start position:0%
+there's a few different materials that
+are commonly used one's Peg po
+
+ align:start position:0%
+are commonly used one's Peg po
+ 
+
+ align:start position:0%
+are commonly used one's Peg po
+polyethylene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glycol one's
+
+ align:start position:0%
+glycol one's
+ 
+
+ align:start position:0%
+glycol one's
+PVA polyvinyl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alcohol and another one's
+
+ align:start position:0%
+alcohol and another one's
+ 
+
+ align:start position:0%
+alcohol and another one's
+paa polyacrylic acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for these synthetic polymers there's
+
+ align:start position:0%
+so for these synthetic polymers there's
+ 
+
+ align:start position:0%
+so for these synthetic polymers there's
+many different processing techniques
+
+ align:start position:0%
+many different processing techniques
+ 
+
+ align:start position:0%
+many different processing techniques
+available and I'll talk a little bit
+
+ align:start position:0%
+available and I'll talk a little bit
+ 
+
+ align:start position:0%
+available and I'll talk a little bit
+about some of the processing techniques
+
+ align:start position:0%
+about some of the processing techniques
+ 
+
+ align:start position:0%
+about some of the processing techniques
+but one of the uh limitations is they
+
+ align:start position:0%
+but one of the uh limitations is they
+ 
+
+ align:start position:0%
+but one of the uh limitations is they
+don't have natural binding sites and you
+
+ align:start position:0%
+don't have natural binding sites and you
+ 
+
+ align:start position:0%
+don't have natural binding sites and you
+have to coat them with some sort of um
+
+ align:start position:0%
+have to coat them with some sort of um
+ 
+
+ align:start position:0%
+have to coat them with some sort of um
+binding agent like an adhesive protein
+
+ align:start position:0%
+binding agent like an adhesive protein
+ 
+
+ align:start position:0%
+binding agent like an adhesive protein
+to get the cells to attach to them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then as I mentioned before you have
+
+ align:start position:0%
+and then as I mentioned before you have
+ 
+
+ align:start position:0%
+and then as I mentioned before you have
+to make sure that whatever material you
+
+ align:start position:0%
+to make sure that whatever material you
+ 
+
+ align:start position:0%
+to make sure that whatever material you
+choose if it's a synthetic material but
+
+ align:start position:0%
+choose if it's a synthetic material but
+ 
+
+ align:start position:0%
+choose if it's a synthetic material but
+when it degrades it's not toxic uh to
+
+ align:start position:0%
+when it degrades it's not toxic uh to
+ 
+
+ align:start position:0%
+when it degrades it's not toxic uh to
+the cells because you don't want to have
+
+ align:start position:0%
+the cells because you don't want to have
+ 
+
+ align:start position:0%
+the cells because you don't want to have
+some sort of toxic reaction or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inflammation okay so there's a couple
+
+ align:start position:0%
+inflammation okay so there's a couple
+ 
+
+ align:start position:0%
+inflammation okay so there's a couple
+more things about
+
+ align:start position:0%
+more things about
+ 
+
+ align:start position:0%
+more things about
+materials so those are all sort of
+
+ align:start position:0%
+materials so those are all sort of
+ 
+
+ align:start position:0%
+materials so those are all sort of
+polymer-based materials when people are
+
+ align:start position:0%
+polymer-based materials when people are
+ 
+
+ align:start position:0%
+polymer-based materials when people are
+trying to make scaffolds for bone tissue
+
+ align:start position:0%
+trying to make scaffolds for bone tissue
+ 
+
+ align:start position:0%
+trying to make scaffolds for bone tissue
+engineering they also include a calcium
+
+ align:start position:0%
+engineering they also include a calcium
+ 
+
+ align:start position:0%
+engineering they also include a calcium
+phosphate mineral and there's different
+
+ align:start position:0%
+phosphate mineral and there's different
+ 
+
+ align:start position:0%
+phosphate mineral and there's different
+versions of the calcium phosphate so
+
+ align:start position:0%
+versions of the calcium phosphate so
+ 
+
+ align:start position:0%
+versions of the calcium phosphate so
+they can include you can buy for
+
+ align:start position:0%
+they can include you can buy for
+ 
+
+ align:start position:0%
+they can include you can buy for
+instance hydroxy appetite powders now
+
+ align:start position:0%
+instance hydroxy appetite powders now
+ 
+
+ align:start position:0%
+instance hydroxy appetite powders now
+there's another calcium phosphate called
+
+ align:start position:0%
+there's another calcium phosphate called
+ 
+
+ align:start position:0%
+there's another calcium phosphate called
+octacalcium phosphate which will with
+
+ align:start position:0%
+octacalcium phosphate which will with
+ 
+
+ align:start position:0%
+octacalcium phosphate which will with
+water uh turn into hydroxyapetite so
+
+ align:start position:0%
+water uh turn into hydroxyapetite so
+ 
+
+ align:start position:0%
+water uh turn into hydroxyapetite so
+typically this this mineral some sort of
+
+ align:start position:0%
+typically this this mineral some sort of
+ 
+
+ align:start position:0%
+typically this this mineral some sort of
+calcium phosphate is combined with
+
+ align:start position:0%
+calcium phosphate is combined with
+ 
+
+ align:start position:0%
+calcium phosphate is combined with
+either collagen or with one of these
+
+ align:start position:0%
+either collagen or with one of these
+ 
+
+ align:start position:0%
+either collagen or with one of these
+synthetic biopolymers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one other option is something called
+
+ align:start position:0%
+and one other option is something called
+ 
+
+ align:start position:0%
+and one other option is something called
+an acellular scaffold and what that is
+
+ align:start position:0%
+an acellular scaffold and what that is
+ 
+
+ align:start position:0%
+an acellular scaffold and what that is
+is they take some natural tissue and
+
+ align:start position:0%
+is they take some natural tissue and
+ 
+
+ align:start position:0%
+is they take some natural tissue and
+they remove all the cell material from
+
+ align:start position:0%
+they remove all the cell material from
+ 
+
+ align:start position:0%
+they remove all the cell material from
+it and so when they remove all the cell
+
+ align:start position:0%
+it and so when they remove all the cell
+ 
+
+ align:start position:0%
+it and so when they remove all the cell
+material what they're left with is the
+
+ align:start position:0%
+material what they're left with is the
+ 
+
+ align:start position:0%
+material what they're left with is the
+native ECM and that's called an a
+
+ align:start position:0%
+native ECM and that's called an a
+ 
+
+ align:start position:0%
+native ECM and that's called an a
+cellular
+
+ align:start position:0%
+cellular
+ 
+
+ align:start position:0%
+cellular
+scaffold so it's a a
+
+ align:start position:0%
+scaffold so it's a a
+ 
+
+ align:start position:0%
+scaffold so it's a a
+native ECM with all the cell matter
+
+ align:start position:0%
+native ECM with all the cell matter
+ 
+
+ align:start position:0%
+native ECM with all the cell matter
+removed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they remove the cells by they can
+
+ align:start position:0%
+and they remove the cells by they can
+ 
+
+ align:start position:0%
+and they remove the cells by they can
+use sort of a physical agitation or
+
+ align:start position:0%
+use sort of a physical agitation or
+ 
+
+ align:start position:0%
+use sort of a physical agitation or
+chemical um or or using enzymatic
+
+ align:start position:0%
+chemical um or or using enzymatic
+ 
+
+ align:start position:0%
+chemical um or or using enzymatic
+methods using something like Tron to get
+
+ align:start position:0%
+methods using something like Tron to get
+ 
+
+ align:start position:0%
+methods using something like Tron to get
+rid of the cell so there's ways that
+
+ align:start position:0%
+rid of the cell so there's ways that
+ 
+
+ align:start position:0%
+rid of the cell so there's ways that
+they can get rid of the
+
+ align:start position:0%
+they can get rid of the
+ 
+
+ align:start position:0%
+they can get rid of the
+cells okay so are we good so far so
+
+ align:start position:0%
+cells okay so are we good so far so
+ 
+
+ align:start position:0%
+cells okay so are we good so far so
+there's some requirements for what
+
+ align:start position:0%
+there's some requirements for what
+ 
+
+ align:start position:0%
+there's some requirements for what
+materials we kind of use what the cell
+
+ align:start position:0%
+materials we kind of use what the cell
+ 
+
+ align:start position:0%
+materials we kind of use what the cell
+structure should be and these are some
+
+ align:start position:0%
+structure should be and these are some
+ 
+
+ align:start position:0%
+structure should be and these are some
+examples of typical materials so I want
+
+ align:start position:0%
+examples of typical materials so I want
+ 
+
+ align:start position:0%
+examples of typical materials so I want
+to talk a little bit about the process
+
+ align:start position:0%
+to talk a little bit about the process
+ 
+
+ align:start position:0%
+to talk a little bit about the process
+processing of the
+
+ align:start position:0%
+processing of the
+ 
+
+ align:start position:0%
+processing of the
+materials um Let Me Wait Till people
+
+ align:start position:0%
+materials um Let Me Wait Till people
+ 
+
+ align:start position:0%
+materials um Let Me Wait Till people
+catch up a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+little oh and I have some scaffolds I
+
+ align:start position:0%
+little oh and I have some scaffolds I
+ 
+
+ align:start position:0%
+little oh and I have some scaffolds I
+was going to pass
+
+ align:start position:0%
+was going to pass
+ 
+
+ align:start position:0%
+was going to pass
+around so uh this big sheet is a piece
+
+ align:start position:0%
+around so uh this big sheet is a piece
+ 
+
+ align:start position:0%
+around so uh this big sheet is a piece
+of the collagen gag scaffold that I
+
+ align:start position:0%
+of the collagen gag scaffold that I
+ 
+
+ align:start position:0%
+of the collagen gag scaffold that I
+showed a minute ago and then this little
+
+ align:start position:0%
+showed a minute ago and then this little
+ 
+
+ align:start position:0%
+showed a minute ago and then this little
+piece is a mineralized version of that
+
+ align:start position:0%
+piece is a mineralized version of that
+ 
+
+ align:start position:0%
+piece is a mineralized version of that
+so this has the collagen plus um a
+
+ align:start position:0%
+so this has the collagen plus um a
+ 
+
+ align:start position:0%
+so this has the collagen plus um a
+calcium phosphate plus hydroxy appetite
+
+ align:start position:0%
+calcium phosphate plus hydroxy appetite
+ 
+
+ align:start position:0%
+calcium phosphate plus hydroxy appetite
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay uh so this slide shows some
+
+ align:start position:0%
+it okay uh so this slide shows some
+ 
+
+ align:start position:0%
+it okay uh so this slide shows some
+examples of different uh scaffolds that
+
+ align:start position:0%
+examples of different uh scaffolds that
+ 
+
+ align:start position:0%
+examples of different uh scaffolds that
+people have made and I was going to talk
+
+ align:start position:0%
+people have made and I was going to talk
+ 
+
+ align:start position:0%
+people have made and I was going to talk
+a little bit about some of these methods
+
+ align:start position:0%
+a little bit about some of these methods
+ 
+
+ align:start position:0%
+a little bit about some of these methods
+and I'll why don't I talk about them and
+
+ align:start position:0%
+and I'll why don't I talk about them and
+ 
+
+ align:start position:0%
+and I'll why don't I talk about them and
+then I'll write some notes on the board
+
+ align:start position:0%
+then I'll write some notes on the board
+ 
+
+ align:start position:0%
+then I'll write some notes on the board
+so this top one here on the top left
+
+ align:start position:0%
+so this top one here on the top left
+ 
+
+ align:start position:0%
+so this top one here on the top left
+that's the collagen gag scaffold that's
+
+ align:start position:0%
+that's the collagen gag scaffold that's
+ 
+
+ align:start position:0%
+that's the collagen gag scaffold that's
+made in yanasa group and that's made by
+
+ align:start position:0%
+made in yanasa group and that's made by
+ 
+
+ align:start position:0%
+made in yanasa group and that's made by
+a freeze drying process so you put the
+
+ align:start position:0%
+a freeze drying process so you put the
+ 
+
+ align:start position:0%
+a freeze drying process so you put the
+collagen in acetic acid then you put in
+
+ align:start position:0%
+collagen in acetic acid then you put in
+ 
+
+ align:start position:0%
+collagen in acetic acid then you put in
+the gag the gag the collagen form a
+
+ align:start position:0%
+the gag the gag the collagen form a
+ 
+
+ align:start position:0%
+the gag the gag the collagen form a
+co-precipitate and then you can freeze
+
+ align:start position:0%
+co-precipitate and then you can freeze
+ 
+
+ align:start position:0%
+co-precipitate and then you can freeze
+that and if you freeze it what happens
+
+ align:start position:0%
+that and if you freeze it what happens
+ 
+
+ align:start position:0%
+that and if you freeze it what happens
+is uh you know it's just like if you
+
+ align:start position:0%
+is uh you know it's just like if you
+ 
+
+ align:start position:0%
+is uh you know it's just like if you
+freeze salt water the the water um
+
+ align:start position:0%
+freeze salt water the the water um
+ 
+
+ align:start position:0%
+freeze salt water the the water um
+freezes pure water freezes and you've
+
+ align:start position:0%
+freezes pure water freezes and you've
+ 
+
+ align:start position:0%
+freezes pure water freezes and you've
+got increasingly higher brine content in
+
+ align:start position:0%
+got increasingly higher brine content in
+ 
+
+ align:start position:0%
+got increasingly higher brine content in
+the bit in between the water grains or
+
+ align:start position:0%
+the bit in between the water grains or
+ 
+
+ align:start position:0%
+the bit in between the water grains or
+in in between the ice so you get the
+
+ align:start position:0%
+in in between the ice so you get the
+ 
+
+ align:start position:0%
+in in between the ice so you get the
+sort of solid ice forming and the
+
+ align:start position:0%
+sort of solid ice forming and the
+ 
+
+ align:start position:0%
+sort of solid ice forming and the
+collagen and the gag are kind of swee
+
+ align:start position:0%
+collagen and the gag are kind of swee
+ 
+
+ align:start position:0%
+collagen and the gag are kind of swee
+squeezed into the interstitial bits
+
+ align:start position:0%
+squeezed into the interstitial bits
+ 
+
+ align:start position:0%
+squeezed into the interstitial bits
+between the ice crystals and then if you
+
+ align:start position:0%
+between the ice crystals and then if you
+ 
+
+ align:start position:0%
+between the ice crystals and then if you
+sublimate the ice off you're left with
+
+ align:start position:0%
+sublimate the ice off you're left with
+ 
+
+ align:start position:0%
+sublimate the ice off you're left with
+this porous kind of structure that looks
+
+ align:start position:0%
+this porous kind of structure that looks
+ 
+
+ align:start position:0%
+this porous kind of structure that looks
+like a foam so that's made by a freeze
+
+ align:start position:0%
+like a foam so that's made by a freeze
+ 
+
+ align:start position:0%
+like a foam so that's made by a freeze
+drying process and I I'll go over it in
+
+ align:start position:0%
+drying process and I I'll go over it in
+ 
+
+ align:start position:0%
+drying process and I I'll go over it in
+a bit more detail when I write the notes
+
+ align:start position:0%
+a bit more detail when I write the notes
+ 
+
+ align:start position:0%
+a bit more detail when I write the notes
+on the board you can also foam some of
+
+ align:start position:0%
+on the board you can also foam some of
+ 
+
+ align:start position:0%
+on the board you can also foam some of
+these polymers so just blowing a gas the
+
+ align:start position:0%
+these polymers so just blowing a gas the
+ 
+
+ align:start position:0%
+these polymers so just blowing a gas the
+same way you can blow a gas through you
+
+ align:start position:0%
+same way you can blow a gas through you
+ 
+
+ align:start position:0%
+same way you can blow a gas through you
+know an engineering foam you do the same
+
+ align:start position:0%
+know an engineering foam you do the same
+ 
+
+ align:start position:0%
+know an engineering foam you do the same
+thing with some of these polymers this
+
+ align:start position:0%
+thing with some of these polymers this
+ 
+
+ align:start position:0%
+thing with some of these polymers this
+one's made by foaming you can have a
+
+ align:start position:0%
+one's made by foaming you can have a
+ 
+
+ align:start position:0%
+one's made by foaming you can have a
+fugitive phase process so this is made
+
+ align:start position:0%
+fugitive phase process so this is made
+ 
+
+ align:start position:0%
+fugitive phase process so this is made
+by salt leeching the second row on the
+
+ align:start position:0%
+by salt leeching the second row on the
+ 
+
+ align:start position:0%
+by salt leeching the second row on the
+left there so you could imagine you
+
+ align:start position:0%
+left there so you could imagine you
+ 
+
+ align:start position:0%
+left there so you could imagine you
+could take a polymer powder you could
+
+ align:start position:0%
+could take a polymer powder you could
+ 
+
+ align:start position:0%
+could take a polymer powder you could
+mix it with salt you can sort of mix
+
+ align:start position:0%
+mix it with salt you can sort of mix
+ 
+
+ align:start position:0%
+mix it with salt you can sort of mix
+them up combine them together you heat
+
+ align:start position:0%
+them up combine them together you heat
+ 
+
+ align:start position:0%
+them up combine them together you heat
+it up to get the polymer to melt and to
+
+ align:start position:0%
+it up to get the polymer to melt and to
+ 
+
+ align:start position:0%
+it up to get the polymer to melt and to
+sort of form a a connected mass and then
+
+ align:start position:0%
+sort of form a a connected mass and then
+ 
+
+ align:start position:0%
+sort of form a a connected mass and then
+you Lee out the salt and then you get
+
+ align:start position:0%
+you Lee out the salt and then you get
+ 
+
+ align:start position:0%
+you Lee out the salt and then you get
+pores where the salt was this one here
+
+ align:start position:0%
+pores where the salt was this one here
+ 
+
+ align:start position:0%
+pores where the salt was this one here
+is made by an electri spinning process
+
+ align:start position:0%
+is made by an electri spinning process
+ 
+
+ align:start position:0%
+is made by an electri spinning process
+so you have a nozzle you feed the
+
+ align:start position:0%
+so you have a nozzle you feed the
+ 
+
+ align:start position:0%
+so you have a nozzle you feed the
+polymer through the nozzle then you have
+
+ align:start position:0%
+polymer through the nozzle then you have
+ 
+
+ align:start position:0%
+polymer through the nozzle then you have
+plates that are charged and you get
+
+ align:start position:0%
+plates that are charged and you get
+ 
+
+ align:start position:0%
+plates that are charged and you get
+fibers uh forming and kind of scattered
+
+ align:start position:0%
+fibers uh forming and kind of scattered
+ 
+
+ align:start position:0%
+fibers uh forming and kind of scattered
+in different directions by the electro
+
+ align:start position:0%
+in different directions by the electro
+ 
+
+ align:start position:0%
+in different directions by the electro
+spinning process then this one here
+
+ align:start position:0%
+spinning process then this one here
+ 
+
+ align:start position:0%
+spinning process then this one here
+represents
+
+ align:start position:0%
+represents
+ 
+
+ align:start position:0%
+represents
+um scaffold that are made by
+
+ align:start position:0%
+um scaffold that are made by
+ 
+
+ align:start position:0%
+um scaffold that are made by
+um uh by things like 3D printing
+
+ align:start position:0%
+um uh by things like 3D printing
+ 
+
+ align:start position:0%
+um uh by things like 3D printing
+selective laser centering you can have
+
+ align:start position:0%
+selective laser centering you can have
+ 
+
+ align:start position:0%
+selective laser centering you can have
+um you know laser sensitive sensitive
+
+ align:start position:0%
+um you know laser sensitive sensitive
+ 
+
+ align:start position:0%
+um you know laser sensitive sensitive
+polymer and you can produce uh scaffolds
+
+ align:start position:0%
+polymer and you can produce uh scaffolds
+ 
+
+ align:start position:0%
+polymer and you can produce uh scaffolds
+that way I think the geometry of this
+
+ align:start position:0%
+that way I think the geometry of this
+ 
+
+ align:start position:0%
+that way I think the geometry of this
+one matches I don't know some part in
+
+ align:start position:0%
+one matches I don't know some part in
+ 
+
+ align:start position:0%
+one matches I don't know some part in
+the body I think it was a a knee or
+
+ align:start position:0%
+the body I think it was a a knee or
+ 
+
+ align:start position:0%
+the body I think it was a a knee or
+something like that and then these two
+
+ align:start position:0%
+something like that and then these two
+ 
+
+ align:start position:0%
+something like that and then these two
+examples down here are the acellular
+
+ align:start position:0%
+examples down here are the acellular
+ 
+
+ align:start position:0%
+examples down here are the acellular
+scaffolds that's what I was talking
+
+ align:start position:0%
+scaffolds that's what I was talking
+ 
+
+ align:start position:0%
+scaffolds that's what I was talking
+about at the very end there so those are
+
+ align:start position:0%
+about at the very end there so those are
+ 
+
+ align:start position:0%
+about at the very end there so those are
+from porcine pork heart tissue you know
+
+ align:start position:0%
+from porcine pork heart tissue you know
+ 
+
+ align:start position:0%
+from porcine pork heart tissue you know
+pig heart tissue and those are mostly
+
+ align:start position:0%
+pig heart tissue and those are mostly
+ 
+
+ align:start position:0%
+pig heart tissue and those are mostly
+elastin um and they've had all the cell
+
+ align:start position:0%
+elastin um and they've had all the cell
+ 
+
+ align:start position:0%
+elastin um and they've had all the cell
+matter removed from them okay so you can
+
+ align:start position:0%
+matter removed from them okay so you can
+ 
+
+ align:start position:0%
+matter removed from them okay so you can
+kind of see that these synthetic
+
+ align:start position:0%
+kind of see that these synthetic
+ 
+
+ align:start position:0%
+kind of see that these synthetic
+scaffolds here have a structure that's
+
+ align:start position:0%
+scaffolds here have a structure that's
+ 
+
+ align:start position:0%
+scaffolds here have a structure that's
+not so different from these native ECM
+
+ align:start position:0%
+not so different from these native ECM
+ 
+
+ align:start position:0%
+not so different from these native ECM
+scaffolds down here okay so let me write
+
+ align:start position:0%
+scaffolds down here okay so let me write
+ 
+
+ align:start position:0%
+scaffolds down here okay so let me write
+some of the um things about the
+
+ align:start position:0%
+some of the um things about the
+ 
+
+ align:start position:0%
+some of the um things about the
+processing on the board uh see let me
+
+ align:start position:0%
+processing on the board uh see let me
+ 
+
+ align:start position:0%
+processing on the board uh see let me
+rub this off start over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these freeze Sky freeze dried
+
+ align:start position:0%
+so these freeze Sky freeze dried
+ 
+
+ align:start position:0%
+so these freeze Sky freeze dried
+scaffolds are used for um the skin
+
+ align:start position:0%
+scaffolds are used for um the skin
+ 
+
+ align:start position:0%
+scaffolds are used for um the skin
+regeneration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I think I have some more slides here
+
+ align:start position:0%
+and I think I have some more slides here
+ 
+
+ align:start position:0%
+and I think I have some more slides here
+so there kind of a two-step process in
+
+ align:start position:0%
+so there kind of a two-step process in
+ 
+
+ align:start position:0%
+so there kind of a two-step process in
+the first step you make what they call a
+
+ align:start position:0%
+the first step you make what they call a
+ 
+
+ align:start position:0%
+the first step you make what they call a
+slurry so you make the slurry by taking
+
+ align:start position:0%
+slurry so you make the slurry by taking
+ 
+
+ align:start position:0%
+slurry so you make the slurry by taking
+the collagen and uh for skin I think you
+
+ align:start position:0%
+the collagen and uh for skin I think you
+ 
+
+ align:start position:0%
+the collagen and uh for skin I think you
+want type one collagen yeah skin is type
+
+ align:start position:0%
+want type one collagen yeah skin is type
+ 
+
+ align:start position:0%
+want type one collagen yeah skin is type
+one collagen there's different types you
+
+ align:start position:0%
+one collagen there's different types you
+ 
+
+ align:start position:0%
+one collagen there's different types you
+put it in acidic acid and then you add
+
+ align:start position:0%
+put it in acidic acid and then you add
+ 
+
+ align:start position:0%
+put it in acidic acid and then you add
+the gag and we use kren 6 sulfate as
+
+ align:start position:0%
+the gag and we use kren 6 sulfate as
+ 
+
+ align:start position:0%
+the gag and we use kren 6 sulfate as
+just the particular gag that that we use
+
+ align:start position:0%
+just the particular gag that that we use
+ 
+
+ align:start position:0%
+just the particular gag that that we use
+and the one of the things that the acid
+
+ align:start position:0%
+and the one of the things that the acid
+ 
+
+ align:start position:0%
+and the one of the things that the acid
+does is that it swells the collagen and
+
+ align:start position:0%
+does is that it swells the collagen and
+ 
+
+ align:start position:0%
+does is that it swells the collagen and
+collagen has a sort of periodic
+
+ align:start position:0%
+collagen has a sort of periodic
+ 
+
+ align:start position:0%
+collagen has a sort of periodic
+structure in it sort of a periodic
+
+ align:start position:0%
+structure in it sort of a periodic
+ 
+
+ align:start position:0%
+structure in it sort of a periodic
+banding and the acid destroys that
+
+ align:start position:0%
+banding and the acid destroys that
+ 
+
+ align:start position:0%
+banding and the acid destroys that
+periodic banding structure and that
+
+ align:start position:0%
+periodic banding structure and that
+ 
+
+ align:start position:0%
+periodic banding structure and that
+helps um increase the uh resistance to
+
+ align:start position:0%
+helps um increase the uh resistance to
+ 
+
+ align:start position:0%
+helps um increase the uh resistance to
+having some host immune response so that
+
+ align:start position:0%
+having some host immune response so that
+ 
+
+ align:start position:0%
+having some host immune response so that
+you remove the immunological markers and
+
+ align:start position:0%
+you remove the immunological markers and
+ 
+
+ align:start position:0%
+you remove the immunological markers and
+it makes it less likely that the
+
+ align:start position:0%
+it makes it less likely that the
+ 
+
+ align:start position:0%
+it makes it less likely that the
+scaffold's going to get rejected by the
+
+ align:start position:0%
+scaffold's going to get rejected by the
+ 
+
+ align:start position:0%
+scaffold's going to get rejected by the
+body um so then when you put the gag in
+
+ align:start position:0%
+body um so then when you put the gag in
+ 
+
+ align:start position:0%
+body um so then when you put the gag in
+you form a co-precipitate so this next
+
+ align:start position:0%
+you form a co-precipitate so this next
+ 
+
+ align:start position:0%
+you form a co-precipitate so this next
+step just shows kind of mixing the whole
+
+ align:start position:0%
+step just shows kind of mixing the whole
+ 
+
+ align:start position:0%
+step just shows kind of mixing the whole
+thing up and then you've got kind of a
+
+ align:start position:0%
+thing up and then you've got kind of a
+ 
+
+ align:start position:0%
+thing up and then you've got kind of a
+you know little slurry that you can
+
+ align:start position:0%
+you know little slurry that you can
+ 
+
+ align:start position:0%
+you know little slurry that you can
+store and then this is the freeze drying
+
+ align:start position:0%
+store and then this is the freeze drying
+ 
+
+ align:start position:0%
+store and then this is the freeze drying
+step here so you put the the slurry of
+
+ align:start position:0%
+step here so you put the the slurry of
+ 
+
+ align:start position:0%
+step here so you put the the slurry of
+the suspension into a pan kind of like a
+
+ align:start position:0%
+the suspension into a pan kind of like a
+ 
+
+ align:start position:0%
+the suspension into a pan kind of like a
+just like a cookie sheet really um and
+
+ align:start position:0%
+just like a cookie sheet really um and
+ 
+
+ align:start position:0%
+just like a cookie sheet really um and
+then you freeze it so if you think of
+
+ align:start position:0%
+then you freeze it so if you think of
+ 
+
+ align:start position:0%
+then you freeze it so if you think of
+this phase diagram here we have
+
+ align:start position:0%
+this phase diagram here we have
+ 
+
+ align:start position:0%
+this phase diagram here we have
+temperature and pressure so here we have
+
+ align:start position:0%
+temperature and pressure so here we have
+ 
+
+ align:start position:0%
+temperature and pressure so here we have
+liquid solid and Vapor so if you start
+
+ align:start position:0%
+liquid solid and Vapor so if you start
+ 
+
+ align:start position:0%
+liquid solid and Vapor so if you start
+off at this point here you freeze it so
+
+ align:start position:0%
+off at this point here you freeze it so
+ 
+
+ align:start position:0%
+off at this point here you freeze it so
+you reduce the temperature uh so that
+
+ align:start position:0%
+you reduce the temperature uh so that
+ 
+
+ align:start position:0%
+you reduce the temperature uh so that
+forms the the ice and the ice is
+
+ align:start position:0%
+forms the the ice and the ice is
+ 
+
+ align:start position:0%
+forms the the ice and the ice is
+surrounded by the collagen and the gag
+
+ align:start position:0%
+surrounded by the collagen and the gag
+ 
+
+ align:start position:0%
+surrounded by the collagen and the gag
+fibers and then if you do the
+
+ align:start position:0%
+fibers and then if you do the
+ 
+
+ align:start position:0%
+fibers and then if you do the
+sublimation step you reduce the pressure
+
+ align:start position:0%
+sublimation step you reduce the pressure
+ 
+
+ align:start position:0%
+sublimation step you reduce the pressure
+and increase the temperature a bit and
+
+ align:start position:0%
+and increase the temperature a bit and
+ 
+
+ align:start position:0%
+and increase the temperature a bit and
+then you get over to the vapor end of
+
+ align:start position:0%
+then you get over to the vapor end of
+ 
+
+ align:start position:0%
+then you get over to the vapor end of
+the world and then you're left with this
+
+ align:start position:0%
+the world and then you're left with this
+ 
+
+ align:start position:0%
+the world and then you're left with this
+porous
+
+ align:start position:0%
+porous
+ 
+
+ align:start position:0%
+porous
+scaffold um and then let me see let me
+
+ align:start position:0%
+scaffold um and then let me see let me
+ 
+
+ align:start position:0%
+scaffold um and then let me see let me
+do one more step here and then you can
+
+ align:start position:0%
+do one more step here and then you can
+ 
+
+ align:start position:0%
+do one more step here and then you can
+control the size of the pores by
+
+ align:start position:0%
+control the size of the pores by
+ 
+
+ align:start position:0%
+control the size of the pores by
+controlling the freezing temperature so
+
+ align:start position:0%
+controlling the freezing temperature so
+ 
+
+ align:start position:0%
+controlling the freezing temperature so
+the the size of the pores is exactly
+
+ align:start position:0%
+the the size of the pores is exactly
+ 
+
+ align:start position:0%
+the the size of the pores is exactly
+related to the size of the ice grains
+
+ align:start position:0%
+related to the size of the ice grains
+ 
+
+ align:start position:0%
+related to the size of the ice grains
+that are forming and the fast fter it
+
+ align:start position:0%
+that are forming and the fast fter it
+ 
+
+ align:start position:0%
+that are forming and the fast fter it
+freezes the smaller the grains are going
+
+ align:start position:0%
+freezes the smaller the grains are going
+ 
+
+ align:start position:0%
+freezes the smaller the grains are going
+to be and then the smaller your pore
+
+ align:start position:0%
+to be and then the smaller your pore
+ 
+
+ align:start position:0%
+to be and then the smaller your pore
+size are going to be so you can control
+
+ align:start position:0%
+size are going to be so you can control
+ 
+
+ align:start position:0%
+size are going to be so you can control
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the type one collagen is mixed
+
+ align:start position:0%
+okay so the type one collagen is mixed
+ 
+
+ align:start position:0%
+okay so the type one collagen is mixed
+with acetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid and it then swells the collagen
+
+ align:start position:0%
+acid and it then swells the collagen
+ 
+
+ align:start position:0%
+acid and it then swells the collagen
+and disrupts this periodic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+banding and it removes immunological
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+markers immune
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you add the the gag the krtin 6
+
+ align:start position:0%
+and then you add the the gag the krtin 6
+ 
+
+ align:start position:0%
+and then you add the the gag the krtin 6
+sulfate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then that cross links with the
+
+ align:start position:0%
+and then that cross links with the
+ 
+
+ align:start position:0%
+and then that cross links with the
+collagen and forms a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+co-precipitate and then you can freeze
+
+ align:start position:0%
+co-precipitate and then you can freeze
+ 
+
+ align:start position:0%
+co-precipitate and then you can freeze
+dry that to get the porous scaffold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and typically the relative densities of
+
+ align:start position:0%
+and typically the relative densities of
+ 
+
+ align:start position:0%
+and typically the relative densities of
+these scaffolds is very
+
+ align:start position:0%
+these scaffolds is very
+ 
+
+ align:start position:0%
+these scaffolds is very
+low so typically they're 05% dense the
+
+ align:start position:0%
+low so typically they're 05% dense the
+ 
+
+ align:start position:0%
+low so typically they're 05% dense the
+relative density is 0.05 so they're
+
+ align:start position:0%
+relative density is 0.05 so they're
+ 
+
+ align:start position:0%
+relative density is 0.05 so they're
+99.5% air and the rest of it's the
+
+ align:start position:0%
+99.5% air and the rest of it's the
+ 
+
+ align:start position:0%
+99.5% air and the rest of it's the
+collagen and the gag and the pore sizes
+
+ align:start position:0%
+collagen and the gag and the pore sizes
+ 
+
+ align:start position:0%
+collagen and the gag and the pore sizes
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+typically between about 100 150
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+microns and yanos uses the same
+
+ align:start position:0%
+microns and yanos uses the same
+ 
+
+ align:start position:0%
+microns and yanos uses the same
+scaffolds for the nerve regeneration and
+
+ align:start position:0%
+scaffolds for the nerve regeneration and
+ 
+
+ align:start position:0%
+scaffolds for the nerve regeneration and
+he uses a directional Cooling and that
+
+ align:start position:0%
+he uses a directional Cooling and that
+ 
+
+ align:start position:0%
+he uses a directional Cooling and that
+then elongates the pores so that the the
+
+ align:start position:0%
+then elongates the pores so that the the
+ 
+
+ align:start position:0%
+then elongates the pores so that the the
+ideas that they elongate so the nerves
+
+ align:start position:0%
+ideas that they elongate so the nerves
+ 
+
+ align:start position:0%
+ideas that they elongate so the nerves
+kind of grow along that length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's one way another
+
+ align:start position:0%
+so that's one way another
+ 
+
+ align:start position:0%
+so that's one way another
+way is leeching a f fugitive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase so let's see I
+
+ align:start position:0%
+phase so let's see I
+ 
+
+ align:start position:0%
+phase so let's see I
+think here we go back to there so if you
+
+ align:start position:0%
+think here we go back to there so if you
+ 
+
+ align:start position:0%
+think here we go back to there so if you
+look at the the one on the second row on
+
+ align:start position:0%
+look at the the one on the second row on
+ 
+
+ align:start position:0%
+look at the the one on the second row on
+the left that's done by using salt as
+
+ align:start position:0%
+the left that's done by using salt as
+ 
+
+ align:start position:0%
+the left that's done by using salt as
+The Fugitive phase people use other
+
+ align:start position:0%
+The Fugitive phase people use other
+ 
+
+ align:start position:0%
+The Fugitive phase people use other
+things you can use wax par paraffin wax
+
+ align:start position:0%
+things you can use wax par paraffin wax
+ 
+
+ align:start position:0%
+things you can use wax par paraffin wax
+works as well uh so it doesn't have to
+
+ align:start position:0%
+works as well uh so it doesn't have to
+ 
+
+ align:start position:0%
+works as well uh so it doesn't have to
+be salt there's different things you can
+
+ align:start position:0%
+be salt there's different things you can
+ 
+
+ align:start position:0%
+be salt there's different things you can
+use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you combine a powder of the polymer
+
+ align:start position:0%
+so you combine a powder of the polymer
+ 
+
+ align:start position:0%
+so you combine a powder of the polymer
+with your fugitive phase say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+salt then you heat it up to get the
+
+ align:start position:0%
+salt then you heat it up to get the
+ 
+
+ align:start position:0%
+salt then you heat it up to get the
+polymer to
+
+ align:start position:0%
+polymer to
+ 
+
+ align:start position:0%
+polymer to
+bind and then you leech out the salt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can control the paracity by the
+
+ align:start position:0%
+so you can control the paracity by the
+ 
+
+ align:start position:0%
+so you can control the paracity by the
+volume fraction of the fugitive phase
+
+ align:start position:0%
+volume fraction of the fugitive phase
+ 
+
+ align:start position:0%
+volume fraction of the fugitive phase
+and then the pore size by the size of
+
+ align:start position:0%
+and then the pore size by the size of
+ 
+
+ align:start position:0%
+and then the pore size by the size of
+whatever The Fugitive phase is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so another technique is electr spinning
+
+ align:start position:0%
+so another technique is electr spinning
+ 
+
+ align:start position:0%
+so another technique is electr spinning
+the idea is you produce fibers uh from a
+
+ align:start position:0%
+the idea is you produce fibers uh from a
+ 
+
+ align:start position:0%
+the idea is you produce fibers uh from a
+polymer solution that you extrude
+
+ align:start position:0%
+polymer solution that you extrude
+ 
+
+ align:start position:0%
+polymer solution that you extrude
+through a nozzle and then you apply a
+
+ align:start position:0%
+through a nozzle and then you apply a
+ 
+
+ align:start position:0%
+through a nozzle and then you apply a
+voltage uh across some plates to spin
+
+ align:start position:0%
+voltage uh across some plates to spin
+ 
+
+ align:start position:0%
+voltage uh across some plates to spin
+the fibers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you get a
+
+ align:start position:0%
+and then you get a
+ 
+
+ align:start position:0%
+and then you get a
+network of these fibers and typically
+
+ align:start position:0%
+network of these fibers and typically
+ 
+
+ align:start position:0%
+network of these fibers and typically
+they're Micron scale diameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the last method I'm going to talk
+
+ align:start position:0%
+and the last method I'm going to talk
+ 
+
+ align:start position:0%
+and the last method I'm going to talk
+about is rapid prototyping so you could
+
+ align:start position:0%
+about is rapid prototyping so you could
+ 
+
+ align:start position:0%
+about is rapid prototyping so you could
+think of using 3D printing or you could
+
+ align:start position:0%
+think of using 3D printing or you could
+ 
+
+ align:start position:0%
+think of using 3D printing or you could
+use um selective laser centering or
+
+ align:start position:0%
+use um selective laser centering or
+ 
+
+ align:start position:0%
+use um selective laser centering or
+stereol lithography using a
+
+ align:start position:0%
+stereol lithography using a
+ 
+
+ align:start position:0%
+stereol lithography using a
+photosensitive sensitive polymer so the
+
+ align:start position:0%
+photosensitive sensitive polymer so the
+ 
+
+ align:start position:0%
+photosensitive sensitive polymer so the
+idea is you you know how this works you
+
+ align:start position:0%
+idea is you you know how this works you
+ 
+
+ align:start position:0%
+idea is you you know how this works you
+just build up layers um of solid one
+
+ align:start position:0%
+just build up layers um of solid one
+ 
+
+ align:start position:0%
+just build up layers um of solid one
+layer at a time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you can make complex geometries
+
+ align:start position:0%
+and then you can make complex geometries
+ 
+
+ align:start position:0%
+and then you can make complex geometries
+with that so that's one of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+advantages so if you wanted to make a
+
+ align:start position:0%
+advantages so if you wanted to make a
+ 
+
+ align:start position:0%
+advantages so if you wanted to make a
+part to fit you know a particular place
+
+ align:start position:0%
+part to fit you know a particular place
+ 
+
+ align:start position:0%
+part to fit you know a particular place
+in the tissue then it's it's convenient
+
+ align:start position:0%
+in the tissue then it's it's convenient
+ 
+
+ align:start position:0%
+in the tissue then it's it's convenient
+that you can control the geometry of the
+
+ align:start position:0%
+that you can control the geometry of the
+ 
+
+ align:start position:0%
+that you can control the geometry of the
+whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that just kind of summarizes
+
+ align:start position:0%
+okay so that just kind of summarizes
+ 
+
+ align:start position:0%
+okay so that just kind of summarizes
+very briefly kind of how the tissue
+
+ align:start position:0%
+very briefly kind of how the tissue
+ 
+
+ align:start position:0%
+very briefly kind of how the tissue
+engineering scaffolds are meant to work
+
+ align:start position:0%
+engineering scaffolds are meant to work
+ 
+
+ align:start position:0%
+engineering scaffolds are meant to work
+what kinds of materials people make them
+
+ align:start position:0%
+what kinds of materials people make them
+ 
+
+ align:start position:0%
+what kinds of materials people make them
+from and a few of the processes and
+
+ align:start position:0%
+from and a few of the processes and
+ 
+
+ align:start position:0%
+from and a few of the processes and
+there there's many many processes these
+
+ align:start position:0%
+there there's many many processes these
+ 
+
+ align:start position:0%
+there there's many many processes these
+are just sort of a few common processes
+
+ align:start position:0%
+are just sort of a few common processes
+ 
+
+ align:start position:0%
+are just sort of a few common processes
+I wanted to talk a little bit about the
+
+ align:start position:0%
+I wanted to talk a little bit about the
+ 
+
+ align:start position:0%
+I wanted to talk a little bit about the
+mechanical Behavior because that's kind
+
+ align:start position:0%
+mechanical Behavior because that's kind
+ 
+
+ align:start position:0%
+mechanical Behavior because that's kind
+of what I do uh and so this next plot
+
+ align:start position:0%
+of what I do uh and so this next plot
+ 
+
+ align:start position:0%
+of what I do uh and so this next plot
+just shows a stress strain curve in
+
+ align:start position:0%
+just shows a stress strain curve in
+ 
+
+ align:start position:0%
+just shows a stress strain curve in
+compression for a collagen gag scaffold
+
+ align:start position:0%
+compression for a collagen gag scaffold
+ 
+
+ align:start position:0%
+compression for a collagen gag scaffold
+and I'm hoping that by now you're
+
+ align:start position:0%
+and I'm hoping that by now you're
+ 
+
+ align:start position:0%
+and I'm hoping that by now you're
+getting the idea all of these cellular
+
+ align:start position:0%
+getting the idea all of these cellular
+ 
+
+ align:start position:0%
+getting the idea all of these cellular
+materials have this kind of shape of a
+
+ align:start position:0%
+materials have this kind of shape of a
+ 
+
+ align:start position:0%
+materials have this kind of shape of a
+curve so there's the same kind of linear
+
+ align:start position:0%
+curve so there's the same kind of linear
+ 
+
+ align:start position:0%
+curve so there's the same kind of linear
+elastic regime and then a collapsed
+
+ align:start position:0%
+elastic regime and then a collapsed
+ 
+
+ align:start position:0%
+elastic regime and then a collapsed
+Plateau these collagen things as you can
+
+ align:start position:0%
+Plateau these collagen things as you can
+ 
+
+ align:start position:0%
+Plateau these collagen things as you can
+imagine just pressing them in your hand
+
+ align:start position:0%
+imagine just pressing them in your hand
+ 
+
+ align:start position:0%
+imagine just pressing them in your hand
+they fail by buckling by an elastic
+
+ align:start position:0%
+they fail by buckling by an elastic
+ 
+
+ align:start position:0%
+they fail by buckling by an elastic
+buckling and then there's a
+
+ align:start position:0%
+buckling and then there's a
+ 
+
+ align:start position:0%
+buckling and then there's a
+densification regime so they look like
+
+ align:start position:0%
+densification regime so they look like
+ 
+
+ align:start position:0%
+densification regime so they look like
+all the other kinds of curves that we've
+
+ align:start position:0%
+all the other kinds of curves that we've
+ 
+
+ align:start position:0%
+all the other kinds of curves that we've
+got um one of the things we've done in
+
+ align:start position:0%
+got um one of the things we've done in
+ 
+
+ align:start position:0%
+got um one of the things we've done in
+the modeling is typically in the model
+
+ align:start position:0%
+the modeling is typically in the model
+ 
+
+ align:start position:0%
+the modeling is typically in the model
+we want to be able to calculate or
+
+ align:start position:0%
+we want to be able to calculate or
+ 
+
+ align:start position:0%
+we want to be able to calculate or
+measure the uh modulus of the solid or
+
+ align:start position:0%
+measure the uh modulus of the solid or
+ 
+
+ align:start position:0%
+measure the uh modulus of the solid or
+the strength of the solid from which the
+
+ align:start position:0%
+the strength of the solid from which the
+ 
+
+ align:start position:0%
+the strength of the solid from which the
+things made so Brendan Harley was one of
+
+ align:start position:0%
+things made so Brendan Harley was one of
+ 
+
+ align:start position:0%
+things made so Brendan Harley was one of
+my PhD students uh and he took a little
+
+ align:start position:0%
+my PhD students uh and he took a little
+ 
+
+ align:start position:0%
+my PhD students uh and he took a little
+microscope cut a little strut the struts
+
+ align:start position:0%
+microscope cut a little strut the struts
+ 
+
+ align:start position:0%
+microscope cut a little strut the struts
+are very small right the pore size is
+
+ align:start position:0%
+are very small right the pore size is
+ 
+
+ align:start position:0%
+are very small right the pore size is
+100 Micron so the struts are you know on
+
+ align:start position:0%
+100 Micron so the struts are you know on
+ 
+
+ align:start position:0%
+100 Micron so the struts are you know on
+that order uh he glued one end of the
+
+ align:start position:0%
+that order uh he glued one end of the
+ 
+
+ align:start position:0%
+that order uh he glued one end of the
+strut to a glass slide and then he used
+
+ align:start position:0%
+strut to a glass slide and then he used
+ 
+
+ align:start position:0%
+strut to a glass slide and then he used
+an AFM probe to do a little bending test
+
+ align:start position:0%
+an AFM probe to do a little bending test
+ 
+
+ align:start position:0%
+an AFM probe to do a little bending test
+on that little strut and so he could
+
+ align:start position:0%
+on that little strut and so he could
+ 
+
+ align:start position:0%
+on that little strut and so he could
+measure you know if he could measure the
+
+ align:start position:0%
+measure you know if he could measure the
+ 
+
+ align:start position:0%
+measure you know if he could measure the
+deflection he knew the length he knew
+
+ align:start position:0%
+deflection he knew the length he knew
+ 
+
+ align:start position:0%
+deflection he knew the length he knew
+the geometry of the strut he could
+
+ align:start position:0%
+the geometry of the strut he could
+ 
+
+ align:start position:0%
+the geometry of the strut he could
+figure out what the modulus was for the
+
+ align:start position:0%
+figure out what the modulus was for the
+ 
+
+ align:start position:0%
+figure out what the modulus was for the
+solid so he backs out what the modulus
+
+ align:start position:0%
+solid so he backs out what the modulus
+ 
+
+ align:start position:0%
+solid so he backs out what the modulus
+is so he did these measurements on a dry
+
+ align:start position:0%
+is so he did these measurements on a dry
+ 
+
+ align:start position:0%
+is so he did these measurements on a dry
+strut and then by comparing the um
+
+ align:start position:0%
+strut and then by comparing the um
+ 
+
+ align:start position:0%
+strut and then by comparing the um
+overall modulus of a dry scaffold with a
+
+ align:start position:0%
+overall modulus of a dry scaffold with a
+ 
+
+ align:start position:0%
+overall modulus of a dry scaffold with a
+wet scaffold he estimated what the
+
+ align:start position:0%
+wet scaffold he estimated what the
+ 
+
+ align:start position:0%
+wet scaffold he estimated what the
+modulus of the wet scaffold or the wet
+
+ align:start position:0%
+modulus of the wet scaffold or the wet
+ 
+
+ align:start position:0%
+modulus of the wet scaffold or the wet
+strut would be so the modulus of the dry
+
+ align:start position:0%
+strut would be so the modulus of the dry
+ 
+
+ align:start position:0%
+strut would be so the modulus of the dry
+collagen gag was 672 megap Pascal it's a
+
+ align:start position:0%
+collagen gag was 672 megap Pascal it's a
+ 
+
+ align:start position:0%
+collagen gag was 672 megap Pascal it's a
+little less than a gigap pascal and wet
+
+ align:start position:0%
+little less than a gigap pascal and wet
+ 
+
+ align:start position:0%
+little less than a gigap pascal and wet
+it was about five so it's there's a huge
+
+ align:start position:0%
+it was about five so it's there's a huge
+ 
+
+ align:start position:0%
+it was about five so it's there's a huge
+difference between the wet and the
+
+ align:start position:0%
+difference between the wet and the
+ 
+
+ align:start position:0%
+difference between the wet and the
+dry okay so let me uh let me just write
+
+ align:start position:0%
+dry okay so let me uh let me just write
+ 
+
+ align:start position:0%
+dry okay so let me uh let me just write
+a few notes about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in compression there's the three
+
+ align:start position:0%
+so in compression there's the three
+ 
+
+ align:start position:0%
+so in compression there's the three
+regimes that we see for all these
+
+ align:start position:0%
+regimes that we see for all these
+ 
+
+ align:start position:0%
+regimes that we see for all these
+cellular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+materials and so you can estimate the
+
+ align:start position:0%
+materials and so you can estimate the
+ 
+
+ align:start position:0%
+materials and so you can estimate the
+modulus by using the model we have for
+
+ align:start position:0%
+modulus by using the model we have for
+ 
+
+ align:start position:0%
+modulus by using the model we have for
+the foam for the modulus the modulus of
+
+ align:start position:0%
+the foam for the modulus the modulus of
+ 
+
+ align:start position:0%
+the foam for the modulus the modulus of
+the foam divided by the modulus of the
+
+ align:start position:0%
+the foam divided by the modulus of the
+ 
+
+ align:start position:0%
+the foam divided by the modulus of the
+solid goes as the relative density
+
+ align:start position:0%
+solid goes as the relative density
+ 
+
+ align:start position:0%
+solid goes as the relative density
+squared and that's related to bending in
+
+ align:start position:0%
+squared and that's related to bending in
+ 
+
+ align:start position:0%
+squared and that's related to bending in
+the cell
+
+ align:start position:0%
+the cell
+ 
+
+ align:start position:0%
+the cell
+wall and then the collapse Plateau is
+
+ align:start position:0%
+wall and then the collapse Plateau is
+ 
+
+ align:start position:0%
+wall and then the collapse Plateau is
+related to elastic buckling and so
+
+ align:start position:0%
+related to elastic buckling and so
+ 
+
+ align:start position:0%
+related to elastic buckling and so
+that's equal to some constant * e of the
+
+ align:start position:0%
+that's equal to some constant * e of the
+ 
+
+ align:start position:0%
+that's equal to some constant * e of the
+solid time the relative density squared
+
+ align:start position:0%
+solid time the relative density squared
+ 
+
+ align:start position:0%
+solid time the relative density squared
+and that's related to elastic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+buckling and then we measured e of the
+
+ align:start position:0%
+buckling and then we measured e of the
+ 
+
+ align:start position:0%
+buckling and then we measured e of the
+solid doing this little AFM uh beam
+
+ align:start position:0%
+solid doing this little AFM uh beam
+ 
+
+ align:start position:0%
+solid doing this little AFM uh beam
+bending test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and for one of these low density
+
+ align:start position:0%
+okay and for one of these low density
+ 
+
+ align:start position:0%
+okay and for one of these low density
+scaffold folds uh we measured the
+
+ align:start position:0%
+scaffold folds uh we measured the
+ 
+
+ align:start position:0%
+scaffold folds uh we measured the
+modulus we measured the buckling
+
+ align:start position:0%
+modulus we measured the buckling
+ 
+
+ align:start position:0%
+modulus we measured the buckling
+strength and we got pretty good
+
+ align:start position:0%
+strength and we got pretty good
+ 
+
+ align:start position:0%
+strength and we got pretty good
+agreement by using these equations here
+
+ align:start position:0%
+agreement by using these equations here
+ 
+
+ align:start position:0%
+agreement by using these equations here
+and uh the good
+
+ align:start position:0%
+and uh the good
+ 
+
+ align:start position:0%
+and uh the good
+agreement was if this constant was 0 2
+
+ align:start position:0%
+agreement was if this constant was 0 2
+ 
+
+ align:start position:0%
+agreement was if this constant was 0 2
+that was the strain at buckling yeah so
+
+ align:start position:0%
+that was the strain at buckling yeah so
+ 
+
+ align:start position:0%
+that was the strain at buckling yeah so
+what does it mean to be like wet here
+
+ align:start position:0%
+what does it mean to be like wet here
+ 
+
+ align:start position:0%
+what does it mean to be like wet here
+and and uh like why is it so much lower
+
+ align:start position:0%
+and and uh like why is it so much lower
+ 
+
+ align:start position:0%
+and and uh like why is it so much lower
+um well we can you know we make the
+
+ align:start position:0%
+um well we can you know we make the
+ 
+
+ align:start position:0%
+um well we can you know we make the
+scaffolds by this freeze drying thing
+
+ align:start position:0%
+scaffolds by this freeze drying thing
+ 
+
+ align:start position:0%
+scaffolds by this freeze drying thing
+and like this thing I passed around that
+
+ align:start position:0%
+and like this thing I passed around that
+ 
+
+ align:start position:0%
+and like this thing I passed around that
+was dry right we just immerse it in
+
+ align:start position:0%
+was dry right we just immerse it in
+ 
+
+ align:start position:0%
+was dry right we just immerse it in
+water we just put it in water and then
+
+ align:start position:0%
+water we just put it in water and then
+ 
+
+ align:start position:0%
+water we just put it in water and then
+we he does the test um you know so he
+
+ align:start position:0%
+we he does the test um you know so he
+ 
+
+ align:start position:0%
+we he does the test um you know so he
+does the test on the whole scaffold dry
+
+ align:start position:0%
+does the test on the whole scaffold dry
+ 
+
+ align:start position:0%
+does the test on the whole scaffold dry
+and then he does the test on the whole
+
+ align:start position:0%
+and then he does the test on the whole
+ 
+
+ align:start position:0%
+and then he does the test on the whole
+scaffold wet and I assume there's some
+
+ align:start position:0%
+scaffold wet and I assume there's some
+ 
+
+ align:start position:0%
+scaffold wet and I assume there's some
+sort of bonding that gets disrupted by
+
+ align:start position:0%
+sort of bonding that gets disrupted by
+ 
+
+ align:start position:0%
+sort of bonding that gets disrupted by
+having the water I don't know the
+
+ align:start position:0%
+having the water I don't know the
+ 
+
+ align:start position:0%
+having the water I don't know the
+details of how that works but there must
+
+ align:start position:0%
+details of how that works but there must
+ 
+
+ align:start position:0%
+details of how that works but there must
+be some change in the bonding to make
+
+ align:start position:0%
+be some change in the bonding to make
+ 
+
+ align:start position:0%
+be some change in the bonding to make
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+happen um so let's see I'm trying to see
+
+ align:start position:0%
+happen um so let's see I'm trying to see
+ 
+
+ align:start position:0%
+happen um so let's see I'm trying to see
+what else should we do today oh yeah
+
+ align:start position:0%
+what else should we do today oh yeah
+ 
+
+ align:start position:0%
+what else should we do today oh yeah
+so um so we get pretty good agreement
+
+ align:start position:0%
+so um so we get pretty good agreement
+ 
+
+ align:start position:0%
+so um so we get pretty good agreement
+with this sort of simple foamy model one
+
+ align:start position:0%
+with this sort of simple foamy model one
+ 
+
+ align:start position:0%
+with this sort of simple foamy model one
+of the things we did find was that when
+
+ align:start position:0%
+of the things we did find was that when
+ 
+
+ align:start position:0%
+of the things we did find was that when
+we tested higher density scaffolds the
+
+ align:start position:0%
+we tested higher density scaffolds the
+ 
+
+ align:start position:0%
+we tested higher density scaffolds the
+agreement wasn't so good and I think
+
+ align:start position:0%
+agreement wasn't so good and I think
+ 
+
+ align:start position:0%
+agreement wasn't so good and I think
+this was because when you get higher
+
+ align:start position:0%
+this was because when you get higher
+ 
+
+ align:start position:0%
+this was because when you get higher
+density it's just hard to get the
+
+ align:start position:0%
+density it's just hard to get the
+ 
+
+ align:start position:0%
+density it's just hard to get the
+collagen gag mixture to mix in with the
+
+ align:start position:0%
+collagen gag mixture to mix in with the
+ 
+
+ align:start position:0%
+collagen gag mixture to mix in with the
+acetic acid so we ended up getting
+
+ align:start position:0%
+acetic acid so we ended up getting
+ 
+
+ align:start position:0%
+acetic acid so we ended up getting
+inhomogeneous scaffolds with sort of
+
+ align:start position:0%
+inhomogeneous scaffolds with sort of
+ 
+
+ align:start position:0%
+inhomogeneous scaffolds with sort of
+large voids in them so in order for the
+
+ align:start position:0%
+large voids in them so in order for the
+ 
+
+ align:start position:0%
+large voids in them so in order for the
+modeling to work you have to have a
+
+ align:start position:0%
+modeling to work you have to have a
+ 
+
+ align:start position:0%
+modeling to work you have to have a
+scaffold that's relatively homogeneous
+
+ align:start position:0%
+scaffold that's relatively homogeneous
+ 
+
+ align:start position:0%
+scaffold that's relatively homogeneous
+you don't have kind of big defects in it
+
+ align:start position:0%
+you don't have kind of big defects in it
+ 
+
+ align:start position:0%
+you don't have kind of big defects in it
+um so I think that's all I'm going to
+
+ align:start position:0%
+um so I think that's all I'm going to
+ 
+
+ align:start position:0%
+um so I think that's all I'm going to
+say about that
+
+ align:start position:0%
+say about that
+ 
+
+ align:start position:0%
+say about that
+I have one more slide
+
+ align:start position:0%
+I have one more slide
+ 
+
+ align:start position:0%
+I have one more slide
+here um so those are sort of
+
+ align:start position:0%
+here um so those are sort of
+ 
+
+ align:start position:0%
+here um so those are sort of
+three-dimensional scaffolds we've been
+
+ align:start position:0%
+three-dimensional scaffolds we've been
+ 
+
+ align:start position:0%
+three-dimensional scaffolds we've been
+talking about sort of foam like
+
+ align:start position:0%
+talking about sort of foam like
+ 
+
+ align:start position:0%
+talking about sort of foam like
+scaffolds people have also made
+
+ align:start position:0%
+scaffolds people have also made
+ 
+
+ align:start position:0%
+scaffolds people have also made
+honeycomb like scaffolds as well and
+
+ align:start position:0%
+honeycomb like scaffolds as well and
+ 
+
+ align:start position:0%
+honeycomb like scaffolds as well and
+this just shows some examples of some
+
+ align:start position:0%
+this just shows some examples of some
+ 
+
+ align:start position:0%
+this just shows some examples of some
+honeycomb type
+
+ align:start position:0%
+honeycomb type
+ 
+
+ align:start position:0%
+honeycomb type
+scaffolds so uh this one here I think
+
+ align:start position:0%
+scaffolds so uh this one here I think
+ 
+
+ align:start position:0%
+scaffolds so uh this one here I think
+was made in s bia's lab it's sort of you
+
+ align:start position:0%
+was made in s bia's lab it's sort of you
+ 
+
+ align:start position:0%
+was made in s bia's lab it's sort of you
+can sort of think of it as a hexagon but
+
+ align:start position:0%
+can sort of think of it as a hexagon but
+ 
+
+ align:start position:0%
+can sort of think of it as a hexagon but
+it's also kind of triangulated as well
+
+ align:start position:0%
+it's also kind of triangulated as well
+ 
+
+ align:start position:0%
+it's also kind of triangulated as well
+uh these two here were made by George
+
+ align:start position:0%
+uh these two here were made by George
+ 
+
+ align:start position:0%
+uh these two here were made by George
+Angel he worked with Bob Langer at one
+
+ align:start position:0%
+Angel he worked with Bob Langer at one
+ 
+
+ align:start position:0%
+Angel he worked with Bob Langer at one
+point and they were these two scaffolds
+
+ align:start position:0%
+point and they were these two scaffolds
+ 
+
+ align:start position:0%
+point and they were these two scaffolds
+here you know they're both sort of
+
+ align:start position:0%
+here you know they're both sort of
+ 
+
+ align:start position:0%
+here you know they're both sort of
+rectangular cells uh and they were
+
+ align:start position:0%
+rectangular cells uh and they were
+ 
+
+ align:start position:0%
+rectangular cells uh and they were
+designed to look at how the cell
+
+ align:start position:0%
+designed to look at how the cell
+ 
+
+ align:start position:0%
+designed to look at how the cell
+geometry or the pore geometry affected
+
+ align:start position:0%
+geometry or the pore geometry affected
+ 
+
+ align:start position:0%
+geometry or the pore geometry affected
+the sort of morphology of the cells that
+
+ align:start position:0%
+the sort of morphology of the cells that
+ 
+
+ align:start position:0%
+the sort of morphology of the cells that
+attached so if you have different shaped
+
+ align:start position:0%
+attached so if you have different shaped
+ 
+
+ align:start position:0%
+attached so if you have different shaped
+porest you get different morphology in
+
+ align:start position:0%
+porest you get different morphology in
+ 
+
+ align:start position:0%
+porest you get different morphology in
+the cells that you're trying to attach
+
+ align:start position:0%
+the cells that you're trying to attach
+ 
+
+ align:start position:0%
+the cells that you're trying to attach
+and then George engelm also made these
+
+ align:start position:0%
+and then George engelm also made these
+ 
+
+ align:start position:0%
+and then George engelm also made these
+scaffolds here uh and those were
+
+ align:start position:0%
+scaffolds here uh and those were
+ 
+
+ align:start position:0%
+scaffolds here uh and those were
+designed to be anisotropic and have
+
+ align:start position:0%
+designed to be anisotropic and have
+ 
+
+ align:start position:0%
+designed to be anisotropic and have
+different mechanical properties in
+
+ align:start position:0%
+different mechanical properties in
+ 
+
+ align:start position:0%
+different mechanical properties in
+different directions
+
+ align:start position:0%
+different directions
+ 
+
+ align:start position:0%
+different directions
+and I think what they had done was try
+
+ align:start position:0%
+and I think what they had done was try
+ 
+
+ align:start position:0%
+and I think what they had done was try
+to match the anisotropy and the
+
+ align:start position:0%
+to match the anisotropy and the
+ 
+
+ align:start position:0%
+to match the anisotropy and the
+mechanical properties to anisotropy and
+
+ align:start position:0%
+mechanical properties to anisotropy and
+ 
+
+ align:start position:0%
+mechanical properties to anisotropy and
+heart tissue and cardiac tissue so these
+
+ align:start position:0%
+heart tissue and cardiac tissue so these
+ 
+
+ align:start position:0%
+heart tissue and cardiac tissue so these
+are some examples of honeycomb type
+
+ align:start position:0%
+are some examples of honeycomb type
+ 
+
+ align:start position:0%
+are some examples of honeycomb type
+scaffolds so let me just write down a
+
+ align:start position:0%
+scaffolds so let me just write down a
+ 
+
+ align:start position:0%
+scaffolds so let me just write down a
+few things about those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I think these were
+
+ align:start position:0%
+so I think these were
+ 
+
+ align:start position:0%
+so I think these were
+more sometimes you know obviously the
+
+ align:start position:0%
+more sometimes you know obviously the
+ 
+
+ align:start position:0%
+more sometimes you know obviously the
+scaffolds are used the ultimate goal is
+
+ align:start position:0%
+scaffolds are used the ultimate goal is
+ 
+
+ align:start position:0%
+scaffolds are used the ultimate goal is
+to use them clinically but sometimes
+
+ align:start position:0%
+to use them clinically but sometimes
+ 
+
+ align:start position:0%
+to use them clinically but sometimes
+people make scaffolds just to study cell
+
+ align:start position:0%
+people make scaffolds just to study cell
+ 
+
+ align:start position:0%
+people make scaffolds just to study cell
+behavior and some of these I think were
+
+ align:start position:0%
+behavior and some of these I think were
+ 
+
+ align:start position:0%
+behavior and some of these I think were
+made just to study how the cells would
+
+ align:start position:0%
+made just to study how the cells would
+ 
+
+ align:start position:0%
+made just to study how the cells would
+behave on them so they're sort of IDE
+
+ align:start position:0%
+behave on them so they're sort of IDE
+ 
+
+ align:start position:0%
+behave on them so they're sort of IDE
+realized to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so that triangulated kind of looks
+
+ align:start position:0%
+that so that triangulated kind of looks
+ 
+
+ align:start position:0%
+that so that triangulated kind of looks
+like a hexagon but there also sort of
+
+ align:start position:0%
+like a hexagon but there also sort of
+ 
+
+ align:start position:0%
+like a hexagon but there also sort of
+triangles in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there I think the thing they were
+
+ align:start position:0%
+there I think the thing they were
+ 
+
+ align:start position:0%
+there I think the thing they were
+looking at with that was the uh was
+
+ align:start position:0%
+looking at with that was the uh was
+ 
+
+ align:start position:0%
+looking at with that was the uh was
+transport of nutrients to cells um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and from a mechanical point of view if
+
+ align:start position:0%
+and from a mechanical point of view if
+ 
+
+ align:start position:0%
+and from a mechanical point of view if
+it's triangulated you'd expect say the
+
+ align:start position:0%
+it's triangulated you'd expect say the
+ 
+
+ align:start position:0%
+it's triangulated you'd expect say the
+modulus of that to go
+
+ align:start position:0%
+modulus of that to go
+ 
+
+ align:start position:0%
+modulus of that to go
+linearly with how much solid there is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there so the rectangular honeycomb and
+
+ align:start position:0%
+there so the rectangular honeycomb and
+ 
+
+ align:start position:0%
+there so the rectangular honeycomb and
+the diamond shaped pores they were used
+
+ align:start position:0%
+the diamond shaped pores they were used
+ 
+
+ align:start position:0%
+the diamond shaped pores they were used
+to study the effect of pore geometry on
+
+ align:start position:0%
+to study the effect of pore geometry on
+ 
+
+ align:start position:0%
+to study the effect of pore geometry on
+the cell orientation they used fiber
+
+ align:start position:0%
+the cell orientation they used fiber
+ 
+
+ align:start position:0%
+the cell orientation they used fiber
+blasts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that I'm going to call it the
+
+ align:start position:0%
+and that I'm going to call it the
+ 
+
+ align:start position:0%
+and that I'm going to call it the
+accordion like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+honeycomb that's mechanically
+
+ align:start position:0%
+honeycomb that's mechanically
+ 
+
+ align:start position:0%
+honeycomb that's mechanically
+anisotropic and the mechanical an
+
+ align:start position:0%
+anisotropic and the mechanical an
+ 
+
+ align:start position:0%
+anisotropic and the mechanical an
+anisotropy is matched to the cardiac
+
+ align:start position:0%
+anisotropy is matched to the cardiac
+ 
+
+ align:start position:0%
+anisotropy is matched to the cardiac
+tissue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I think I'm going to stop there
+
+ align:start position:0%
+okay so I think I'm going to stop there
+ 
+
+ align:start position:0%
+okay so I think I'm going to stop there
+for today um that's sort of the end of
+
+ align:start position:0%
+for today um that's sort of the end of
+ 
+
+ align:start position:0%
+for today um that's sort of the end of
+this part of it and next time I'm going
+
+ align:start position:0%
+this part of it and next time I'm going
+ 
+
+ align:start position:0%
+this part of it and next time I'm going
+to talk about the osteochondral scaffold
+
+ align:start position:0%
+to talk about the osteochondral scaffold
+ 
+
+ align:start position:0%
+to talk about the osteochondral scaffold
+so I don't think it really makes sense
+
+ align:start position:0%
+so I don't think it really makes sense
+ 
+
+ align:start position:0%
+so I don't think it really makes sense
+to start it for two or three minutes so
+
+ align:start position:0%
+to start it for two or three minutes so
+ 
+
+ align:start position:0%
+to start it for two or three minutes so
+I'll start that tomorrow our wedding day
+
+ align:start position:0%
+I'll start that tomorrow our wedding day
+ 
+
+ align:start position:0%
+I'll start that tomorrow our wedding day
+and we should be able to finish that on
+
+ align:start position:0%
+and we should be able to finish that on
+ 
+
+ align:start position:0%
+and we should be able to finish that on
+weding day so one of the things that the
+
+ align:start position:0%
+weding day so one of the things that the
+ 
+
+ align:start position:0%
+weding day so one of the things that the
+these honeycomb type scaffolds kind of
+
+ align:start position:0%
+these honeycomb type scaffolds kind of
+ 
+
+ align:start position:0%
+these honeycomb type scaffolds kind of
+suggests is that the scaffolds are used
+
+ align:start position:0%
+suggests is that the scaffolds are used
+ 
+
+ align:start position:0%
+suggests is that the scaffolds are used
+both to try to regenerate tissue in the
+
+ align:start position:0%
+both to try to regenerate tissue in the
+ 
+
+ align:start position:0%
+both to try to regenerate tissue in the
+body and clinical applications but
+
+ align:start position:0%
+body and clinical applications but
+ 
+
+ align:start position:0%
+body and clinical applications but
+they're also used as sort of an
+
+ align:start position:0%
+they're also used as sort of an
+ 
+
+ align:start position:0%
+they're also used as sort of an
+environment for cells in order to study
+
+ align:start position:0%
+environment for cells in order to study
+ 
+
+ align:start position:0%
+environment for cells in order to study
+cell Behavior so next time I'm going to
+
+ align:start position:0%
+cell Behavior so next time I'm going to
+ 
+
+ align:start position:0%
+cell Behavior so next time I'm going to
+talk about an osteochondral scaffold and
+
+ align:start position:0%
+talk about an osteochondral scaffold and
+ 
+
+ align:start position:0%
+talk about an osteochondral scaffold and
+the idea with that was to try to use it
+
+ align:start position:0%
+the idea with that was to try to use it
+ 
+
+ align:start position:0%
+the idea with that was to try to use it
+clinically but next week I'm going to
+
+ align:start position:0%
+clinically but next week I'm going to
+ 
+
+ align:start position:0%
+clinically but next week I'm going to
+talk about cell mechanics a bit and when
+
+ align:start position:0%
+talk about cell mechanics a bit and when
+ 
+
+ align:start position:0%
+talk about cell mechanics a bit and when
+people study cell mechanics so we're
+
+ align:start position:0%
+people study cell mechanics so we're
+ 
+
+ align:start position:0%
+people study cell mechanics so we're
+looking at this the mechanics of
+
+ align:start position:0%
+looking at this the mechanics of
+ 
+
+ align:start position:0%
+looking at this the mechanics of
+biological cells not the not the
+
+ align:start position:0%
+biological cells not the not the
+ 
+
+ align:start position:0%
+biological cells not the not the
+cellular structures so when people look
+
+ align:start position:0%
+cellular structures so when people look
+ 
+
+ align:start position:0%
+cellular structures so when people look
+at trying to study how cells behave they
+
+ align:start position:0%
+at trying to study how cells behave they
+ 
+
+ align:start position:0%
+at trying to study how cells behave they
+need some environment to put them on
+
+ align:start position:0%
+need some environment to put them on
+ 
+
+ align:start position:0%
+need some environment to put them on
+typically people started by just using
+
+ align:start position:0%
+typically people started by just using
+ 
+
+ align:start position:0%
+typically people started by just using
+flat 2D substrates but the flat 2D
+
+ align:start position:0%
+flat 2D substrates but the flat 2D
+ 
+
+ align:start position:0%
+flat 2D substrates but the flat 2D
+substrates are kind of easy to study but
+
+ align:start position:0%
+substrates are kind of easy to study but
+ 
+
+ align:start position:0%
+substrates are kind of easy to study but
+they don't really represent the tissue
+
+ align:start position:0%
+they don't really represent the tissue
+ 
+
+ align:start position:0%
+they don't really represent the tissue
+in the body and so people are now using
+
+ align:start position:0%
+in the body and so people are now using
+ 
+
+ align:start position:0%
+in the body and so people are now using
+tissue engineering scaffolds as an
+
+ align:start position:0%
+tissue engineering scaffolds as an
+ 
+
+ align:start position:0%
+tissue engineering scaffolds as an
+environment that they can control to
+
+ align:start position:0%
+environment that they can control to
+ 
+
+ align:start position:0%
+environment that they can control to
+study how cells behave so they study
+
+ align:start position:0%
+study how cells behave so they study
+ 
+
+ align:start position:0%
+study how cells behave so they study
+cell attachment cell proliferation cell
+
+ align:start position:0%
+cell attachment cell proliferation cell
+ 
+
+ align:start position:0%
+cell attachment cell proliferation cell
+migration and cell differentiation all
+
+ align:start position:0%
+migration and cell differentiation all
+ 
+
+ align:start position:0%
+migration and cell differentiation all
+by using the scaffolds as kind of a
+
+ align:start position:0%
+by using the scaffolds as kind of a
+ 
+
+ align:start position:0%
+by using the scaffolds as kind of a
+controlled environment so we'll talk
+
+ align:start position:0%
+controlled environment so we'll talk
+ 
+
+ align:start position:0%
+controlled environment so we'll talk
+talk about that probably not I don't
+
+ align:start position:0%
+talk about that probably not I don't
+ 
+
+ align:start position:0%
+talk about that probably not I don't
+know if we'll get to it on Wednesday but
+
+ align:start position:0%
+know if we'll get to it on Wednesday but
+ 
+
+ align:start position:0%
+know if we'll get to it on Wednesday but
+we'll we might start it on Wednesday and
+
+ align:start position:0%
+we'll we might start it on Wednesday and
+ 
+
+ align:start position:0%
+we'll we might start it on Wednesday and
+finish it next week okay
\ No newline at end of file
diff --git a/U_sZrNjbj1I.txt b/U_sZrNjbj1I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f47c48ead8b6801c8c25b46c3a12321f4f214b81
--- /dev/null
+++ b/U_sZrNjbj1I.txt
@@ -0,0 +1,1411 @@
+align:start position:0%
+ 
+good morning Board of Directors as all
+
+ align:start position:0%
+good morning Board of Directors as all
+ 
+
+ align:start position:0%
+good morning Board of Directors as all
+of you know from 2002 to 2007 the u.s.
+
+ align:start position:0%
+of you know from 2002 to 2007 the u.s.
+ 
+
+ align:start position:0%
+of you know from 2002 to 2007 the u.s.
+lost 4 million acres agricultural land
+
+ align:start position:0%
+lost 4 million acres agricultural land
+ 
+
+ align:start position:0%
+lost 4 million acres agricultural land
+development and area nearly the size of
+
+ align:start position:0%
+development and area nearly the size of
+ 
+
+ align:start position:0%
+development and area nearly the size of
+Massachusetts and although there are
+
+ align:start position:0%
+Massachusetts and although there are
+ 
+
+ align:start position:0%
+Massachusetts and although there are
+federal policies targeted to combat this
+
+ align:start position:0%
+federal policies targeted to combat this
+ 
+
+ align:start position:0%
+federal policies targeted to combat this
+loss of farmland they are not nearly
+
+ align:start position:0%
+loss of farmland they are not nearly
+ 
+
+ align:start position:0%
+loss of farmland they are not nearly
+enough to deal with this problem we have
+
+ align:start position:0%
+enough to deal with this problem we have
+ 
+
+ align:start position:0%
+enough to deal with this problem we have
+here at home and so I'll speak about
+
+ align:start position:0%
+here at home and so I'll speak about
+ 
+
+ align:start position:0%
+here at home and so I'll speak about
+three things today firstly what I intend
+
+ align:start position:0%
+three things today firstly what I intend
+ 
+
+ align:start position:0%
+three things today firstly what I intend
+to find out for my upcoming trips to
+
+ align:start position:0%
+to find out for my upcoming trips to
+ 
+
+ align:start position:0%
+to find out for my upcoming trips to
+yield Japan Australia who I intend to
+
+ align:start position:0%
+yield Japan Australia who I intend to
+ 
+
+ align:start position:0%
+yield Japan Australia who I intend to
+find out this information from secondly
+
+ align:start position:0%
+find out this information from secondly
+ 
+
+ align:start position:0%
+find out this information from secondly
+what opportunities I see in these strips
+
+ align:start position:0%
+what opportunities I see in these strips
+ 
+
+ align:start position:0%
+what opportunities I see in these strips
+for cross contextual learning and
+
+ align:start position:0%
+for cross contextual learning and
+ 
+
+ align:start position:0%
+for cross contextual learning and
+thirdly what challenges anticipate
+
+ align:start position:0%
+thirdly what challenges anticipate
+ 
+
+ align:start position:0%
+thirdly what challenges anticipate
+translating this learning to ideas and
+
+ align:start position:0%
+translating this learning to ideas and
+ 
+
+ align:start position:0%
+translating this learning to ideas and
+strategies that are really useful for us
+
+ align:start position:0%
+strategies that are really useful for us
+ 
+
+ align:start position:0%
+strategies that are really useful for us
+here in the US so firstly in these
+
+ align:start position:0%
+here in the US so firstly in these
+ 
+
+ align:start position:0%
+here in the US so firstly in these
+regions we intend to focus on three
+
+ align:start position:0%
+regions we intend to focus on three
+ 
+
+ align:start position:0%
+regions we intend to focus on three
+critical issues drawn from the problems
+
+ align:start position:0%
+critical issues drawn from the problems
+ 
+
+ align:start position:0%
+critical issues drawn from the problems
+here at home we term them the three P's
+
+ align:start position:0%
+here at home we term them the three P's
+ 
+
+ align:start position:0%
+here at home we term them the three P's
+place policies and people so firstly
+
+ align:start position:0%
+place policies and people so firstly
+ 
+
+ align:start position:0%
+place policies and people so firstly
+this very strong geographical notion of
+
+ align:start position:0%
+this very strong geographical notion of
+ 
+
+ align:start position:0%
+this very strong geographical notion of
+place and a better for it the u.s. is
+
+ align:start position:0%
+place and a better for it the u.s. is
+ 
+
+ align:start position:0%
+place and a better for it the u.s. is
+losing its finest land to development
+
+ align:start position:0%
+losing its finest land to development
+ 
+
+ align:start position:0%
+losing its finest land to development
+and we want to find out in these regions
+
+ align:start position:0%
+and we want to find out in these regions
+ 
+
+ align:start position:0%
+and we want to find out in these regions
+how they view the trade-off between
+
+ align:start position:0%
+how they view the trade-off between
+ 
+
+ align:start position:0%
+how they view the trade-off between
+development and found land protection or
+
+ align:start position:0%
+development and found land protection or
+ 
+
+ align:start position:0%
+development and found land protection or
+if it even exists for them in the first
+
+ align:start position:0%
+if it even exists for them in the first
+ 
+
+ align:start position:0%
+if it even exists for them in the first
+place secondly we want to find out what
+
+ align:start position:0%
+place secondly we want to find out what
+ 
+
+ align:start position:0%
+place secondly we want to find out what
+policies these regions have to combat
+
+ align:start position:0%
+policies these regions have to combat
+ 
+
+ align:start position:0%
+policies these regions have to combat
+the development of farmland into other
+
+ align:start position:0%
+the development of farmland into other
+ 
+
+ align:start position:0%
+the development of farmland into other
+users and the impact of the format's and
+
+ align:start position:0%
+users and the impact of the format's and
+ 
+
+ align:start position:0%
+users and the impact of the format's and
+thirdly the people we want to find out
+
+ align:start position:0%
+thirdly the people we want to find out
+ 
+
+ align:start position:0%
+thirdly the people we want to find out
+the cultural institutions and cultural
+
+ align:start position:0%
+the cultural institutions and cultural
+ 
+
+ align:start position:0%
+the cultural institutions and cultural
+mindset stamp addressing places and
+
+ align:start position:0%
+mindset stamp addressing places and
+ 
+
+ align:start position:0%
+mindset stamp addressing places and
+policies essentially what the
+
+ align:start position:0%
+policies essentially what the
+ 
+
+ align:start position:0%
+policies essentially what the
+stakeholders of these farming
+
+ align:start position:0%
+stakeholders of these farming
+ 
+
+ align:start position:0%
+stakeholders of these farming
+communities are responding to the
+
+ align:start position:0%
+communities are responding to the
+ 
+
+ align:start position:0%
+communities are responding to the
+policies that have been developed so who
+
+ align:start position:0%
+policies that have been developed so who
+ 
+
+ align:start position:0%
+policies that have been developed so who
+do we intend to find out this
+
+ align:start position:0%
+do we intend to find out this
+ 
+
+ align:start position:0%
+do we intend to find out this
+information from we intend to look for
+
+ align:start position:0%
+information from we intend to look for
+ 
+
+ align:start position:0%
+information from we intend to look for
+stakeholders and business industry that
+
+ align:start position:0%
+stakeholders and business industry that
+ 
+
+ align:start position:0%
+stakeholders and business industry that
+are driving the interaction between farm
+
+ align:start position:0%
+are driving the interaction between farm
+ 
+
+ align:start position:0%
+are driving the interaction between farm
+land and development and they were
+
+ align:start position:0%
+land and development and they were
+ 
+
+ align:start position:0%
+land and development and they were
+inform us most about the issues of
+
+ align:start position:0%
+inform us most about the issues of
+ 
+
+ align:start position:0%
+inform us most about the issues of
+please we also intend to look to talk to
+
+ align:start position:0%
+please we also intend to look to talk to
+ 
+
+ align:start position:0%
+please we also intend to look to talk to
+the chairpersons of agriculture
+
+ align:start position:0%
+the chairpersons of agriculture
+ 
+
+ align:start position:0%
+the chairpersons of agriculture
+committees in EU member states as long
+
+ align:start position:0%
+committees in EU member states as long
+ 
+
+ align:start position:0%
+committees in EU member states as long
+as officials and apartments of
+
+ align:start position:0%
+as officials and apartments of
+ 
+
+ align:start position:0%
+as officials and apartments of
+agriculture in Japan Australia
+
+ align:start position:0%
+agriculture in Japan Australia
+ 
+
+ align:start position:0%
+agriculture in Japan Australia
+define our experiences that challenges
+
+ align:start position:0%
+define our experiences that challenges
+ 
+
+ align:start position:0%
+define our experiences that challenges
+and their successes we are dealing with
+
+ align:start position:0%
+and their successes we are dealing with
+ 
+
+ align:start position:0%
+and their successes we are dealing with
+farmland protection policies we also
+
+ align:start position:0%
+farmland protection policies we also
+ 
+
+ align:start position:0%
+farmland protection policies we also
+plan to look at the people to whom these
+
+ align:start position:0%
+plan to look at the people to whom these
+ 
+
+ align:start position:0%
+plan to look at the people to whom these
+effects of policies are filtering down
+
+ align:start position:0%
+effects of policies are filtering down
+ 
+
+ align:start position:0%
+effects of policies are filtering down
+to the members of farming community who
+
+ align:start position:0%
+to the members of farming community who
+ 
+
+ align:start position:0%
+to the members of farming community who
+through that individually unique stories
+
+ align:start position:0%
+through that individually unique stories
+ 
+
+ align:start position:0%
+through that individually unique stories
+are supposed to just policy man was a
+
+ align:start position:0%
+are supposed to just policy man was a
+ 
+
+ align:start position:0%
+are supposed to just policy man was a
+big day
+
+ align:start position:0%
+big day
+ 
+
+ align:start position:0%
+big day
+inform us most about issues of people we
+
+ align:start position:0%
+inform us most about issues of people we
+ 
+
+ align:start position:0%
+inform us most about issues of people we
+need these three piece together to find
+
+ align:start position:0%
+need these three piece together to find
+ 
+
+ align:start position:0%
+need these three piece together to find
+out what was intended what is happening
+
+ align:start position:0%
+out what was intended what is happening
+ 
+
+ align:start position:0%
+out what was intended what is happening
+and what it really should be so the next
+
+ align:start position:0%
+and what it really should be so the next
+ 
+
+ align:start position:0%
+and what it really should be so the next
+idea I would like to talk about would be
+
+ align:start position:0%
+idea I would like to talk about would be
+ 
+
+ align:start position:0%
+idea I would like to talk about would be
+the why you know I want to visit these
+
+ align:start position:0%
+the why you know I want to visit these
+ 
+
+ align:start position:0%
+the why you know I want to visit these
+three countries my opportunities there
+
+ align:start position:0%
+three countries my opportunities there
+ 
+
+ align:start position:0%
+three countries my opportunities there
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+is it really unnecessary available and
+
+ align:start position:0%
+is it really unnecessary available and
+ 
+
+ align:start position:0%
+is it really unnecessary available and
+ever and I would say yes because these
+
+ align:start position:0%
+ever and I would say yes because these
+ 
+
+ align:start position:0%
+ever and I would say yes because these
+three regions are similar enough to the
+
+ align:start position:0%
+three regions are similar enough to the
+ 
+
+ align:start position:0%
+three regions are similar enough to the
+US to raise the possibility of
+
+ align:start position:0%
+US to raise the possibility of
+ 
+
+ align:start position:0%
+US to raise the possibility of
+opportunities for learning and yet
+
+ align:start position:0%
+opportunities for learning and yet
+ 
+
+ align:start position:0%
+opportunities for learning and yet
+different enough to guarantee these
+
+ align:start position:0%
+different enough to guarantee these
+ 
+
+ align:start position:0%
+different enough to guarantee these
+opportunities for learning so the EU the
+
+ align:start position:0%
+opportunities for learning so the EU the
+ 
+
+ align:start position:0%
+opportunities for learning so the EU the
+US the EU Japan Australia they are and
+
+ align:start position:0%
+US the EU Japan Australia they are and
+ 
+
+ align:start position:0%
+US the EU Japan Australia they are and
+the u.s. large industrialized nations
+
+ align:start position:0%
+the u.s. large industrialized nations
+ 
+
+ align:start position:0%
+the u.s. large industrialized nations
+nobody we look beyond the blocks
+
+ align:start position:0%
+nobody we look beyond the blocks
+ 
+
+ align:start position:0%
+nobody we look beyond the blocks
+tonalities of wealth power development
+
+ align:start position:0%
+tonalities of wealth power development
+ 
+
+ align:start position:0%
+tonalities of wealth power development
+levels influence a whole host of
+
+ align:start position:0%
+levels influence a whole host of
+ 
+
+ align:start position:0%
+levels influence a whole host of
+differences appear the unlocated in
+
+ align:start position:0%
+differences appear the unlocated in
+ 
+
+ align:start position:0%
+differences appear the unlocated in
+different parts of the world in the
+
+ align:start position:0%
+different parts of the world in the
+ 
+
+ align:start position:0%
+different parts of the world in the
+Western Hemisphere in Asia and the
+
+ align:start position:0%
+Western Hemisphere in Asia and the
+ 
+
+ align:start position:0%
+Western Hemisphere in Asia and the
+southern hemisphere
+
+ align:start position:0%
+southern hemisphere
+ 
+
+ align:start position:0%
+southern hemisphere
+they have different geographies
+
+ align:start position:0%
+they have different geographies
+ 
+
+ align:start position:0%
+they have different geographies
+histories neighborhoods contexts and
+
+ align:start position:0%
+histories neighborhoods contexts and
+ 
+
+ align:start position:0%
+histories neighborhoods contexts and
+ideologies and in these differences
+
+ align:start position:0%
+ideologies and in these differences
+ 
+
+ align:start position:0%
+ideologies and in these differences
+drive cross context online for two
+
+ align:start position:0%
+drive cross context online for two
+ 
+
+ align:start position:0%
+drive cross context online for two
+reasons firstly they greatly reduce the
+
+ align:start position:0%
+reasons firstly they greatly reduce the
+ 
+
+ align:start position:0%
+reasons firstly they greatly reduce the
+learning curve for looking at the
+
+ align:start position:0%
+learning curve for looking at the
+ 
+
+ align:start position:0%
+learning curve for looking at the
+effects of different policies by
+
+ align:start position:0%
+effects of different policies by
+ 
+
+ align:start position:0%
+effects of different policies by
+providing a test build with exposed
+
+ align:start position:0%
+providing a test build with exposed
+ 
+
+ align:start position:0%
+providing a test build with exposed
+results as well
+
+ align:start position:0%
+results as well
+ 
+
+ align:start position:0%
+results as well
+so instead of sitting up live up with
+
+ align:start position:0%
+so instead of sitting up live up with
+ 
+
+ align:start position:0%
+so instead of sitting up live up with
+all of us debating the merits and
+
+ align:start position:0%
+all of us debating the merits and
+ 
+
+ align:start position:0%
+all of us debating the merits and
+demerits of increased intervention of
+
+ align:start position:0%
+demerits of increased intervention of
+ 
+
+ align:start position:0%
+demerits of increased intervention of
+online policies we need only look at
+
+ align:start position:0%
+online policies we need only look at
+ 
+
+ align:start position:0%
+online policies we need only look at
+Japan highest producer support levels
+
+ align:start position:0%
+Japan highest producer support levels
+ 
+
+ align:start position:0%
+Japan highest producer support levels
+among OECD countries with overly
+
+ align:start position:0%
+among OECD countries with overly
+ 
+
+ align:start position:0%
+among OECD countries with overly
+protected subsidies they have driven
+
+ align:start position:0%
+protected subsidies they have driven
+ 
+
+ align:start position:0%
+protected subsidies they have driven
+average annual Fung house who income
+
+ align:start position:0%
+average annual Fung house who income
+ 
+
+ align:start position:0%
+average annual Fung house who income
+levels 25 to 30 percent higher than the
+
+ align:start position:0%
+levels 25 to 30 percent higher than the
+ 
+
+ align:start position:0%
+levels 25 to 30 percent higher than the
+national average and Australia the
+
+ align:start position:0%
+national average and Australia the
+ 
+
+ align:start position:0%
+national average and Australia the
+second lowest produces support levels
+
+ align:start position:0%
+second lowest produces support levels
+ 
+
+ align:start position:0%
+second lowest produces support levels
+among OECD countries and whereas strong
+
+ align:start position:0%
+among OECD countries and whereas strong
+ 
+
+ align:start position:0%
+among OECD countries and whereas strong
+adherence to macro oriented policies has
+
+ align:start position:0%
+adherence to macro oriented policies has
+ 
+
+ align:start position:0%
+adherence to macro oriented policies has
+actually created a different result of
+
+ align:start position:0%
+actually created a different result of
+ 
+
+ align:start position:0%
+actually created a different result of
+Japan and secondly these are countries
+
+ align:start position:0%
+Japan and secondly these are countries
+ 
+
+ align:start position:0%
+Japan and secondly these are countries
+also provide us with different ideas
+
+ align:start position:0%
+also provide us with different ideas
+ 
+
+ align:start position:0%
+also provide us with different ideas
+that we might not have considered before
+
+ align:start position:0%
+that we might not have considered before
+ 
+
+ align:start position:0%
+that we might not have considered before
+for example the European Union's Common
+
+ align:start position:0%
+for example the European Union's Common
+ 
+
+ align:start position:0%
+for example the European Union's Common
+Agricultural Policy contracts with
+
+ align:start position:0%
+Agricultural Policy contracts with
+ 
+
+ align:start position:0%
+Agricultural Policy contracts with
+farmers for the development of a for the
+
+ align:start position:0%
+farmers for the development of a for the
+ 
+
+ align:start position:0%
+farmers for the development of a for the
+provision of act of ecological services
+
+ align:start position:0%
+provision of act of ecological services
+ 
+
+ align:start position:0%
+provision of act of ecological services
+which is kind of alternative to the
+
+ align:start position:0%
+which is kind of alternative to the
+ 
+
+ align:start position:0%
+which is kind of alternative to the
+traditional notion here in u.s. when
+
+ align:start position:0%
+traditional notion here in u.s. when
+ 
+
+ align:start position:0%
+traditional notion here in u.s. when
+farm land policy is essentially meant to
+
+ align:start position:0%
+farm land policy is essentially meant to
+ 
+
+ align:start position:0%
+farm land policy is essentially meant to
+product to the protect land for
+
+ align:start position:0%
+product to the protect land for
+ 
+
+ align:start position:0%
+product to the protect land for
+productive purposes
+
+ align:start position:0%
+productive purposes
+ 
+
+ align:start position:0%
+productive purposes
+so essentially exposure to these new
+
+ align:start position:0%
+so essentially exposure to these new
+ 
+
+ align:start position:0%
+so essentially exposure to these new
+ideas would provide us with a bigger
+
+ align:start position:0%
+ideas would provide us with a bigger
+ 
+
+ align:start position:0%
+ideas would provide us with a bigger
+toolkit to develop more robust
+
+ align:start position:0%
+toolkit to develop more robust
+ 
+
+ align:start position:0%
+toolkit to develop more robust
+strategies for my protection
+
+ align:start position:0%
+strategies for my protection
+ 
+
+ align:start position:0%
+strategies for my protection
+u.s. might with these great
+
+ align:start position:0%
+u.s. might with these great
+ 
+
+ align:start position:0%
+u.s. might with these great
+opportunities also come great challenges
+
+ align:start position:0%
+opportunities also come great challenges
+ 
+
+ align:start position:0%
+opportunities also come great challenges
+in the form of two in two forms
+
+ align:start position:0%
+in the form of two in two forms
+ 
+
+ align:start position:0%
+in the form of two in two forms
+essentially you differences in
+
+ align:start position:0%
+essentially you differences in
+ 
+
+ align:start position:0%
+essentially you differences in
+institutions and differences in culture
+
+ align:start position:0%
+institutions and differences in culture
+ 
+
+ align:start position:0%
+institutions and differences in culture
+so differences institutions like
+
+ align:start position:0%
+so differences institutions like
+ 
+
+ align:start position:0%
+so differences institutions like
+political systems laws they essentially
+
+ align:start position:0%
+political systems laws they essentially
+ 
+
+ align:start position:0%
+political systems laws they essentially
+make policies nor body relevance in the
+
+ align:start position:0%
+make policies nor body relevance in the
+ 
+
+ align:start position:0%
+make policies nor body relevance in the
+United States in certain way so in a
+
+ align:start position:0%
+United States in certain way so in a
+ 
+
+ align:start position:0%
+United States in certain way so in a
+European Union they have a greater
+
+ align:start position:0%
+European Union they have a greater
+ 
+
+ align:start position:0%
+European Union they have a greater
+acceptance of regional international
+
+ align:start position:0%
+acceptance of regional international
+ 
+
+ align:start position:0%
+acceptance of regional international
+treaties and conventions and this is
+
+ align:start position:0%
+treaties and conventions and this is
+ 
+
+ align:start position:0%
+treaties and conventions and this is
+implications for trying to transplant
+
+ align:start position:0%
+implications for trying to transplant
+ 
+
+ align:start position:0%
+implications for trying to transplant
+policies across their latitude and
+
+ align:start position:0%
+policies across their latitude and
+ 
+
+ align:start position:0%
+policies across their latitude and
+culture we cannot underestimate the
+
+ align:start position:0%
+culture we cannot underestimate the
+ 
+
+ align:start position:0%
+culture we cannot underestimate the
+influence of culture history and
+
+ align:start position:0%
+influence of culture history and
+ 
+
+ align:start position:0%
+influence of culture history and
+policies for example after all in Japan
+
+ align:start position:0%
+policies for example after all in Japan
+ 
+
+ align:start position:0%
+policies for example after all in Japan
+that the reason for the high levels of
+
+ align:start position:0%
+that the reason for the high levels of
+ 
+
+ align:start position:0%
+that the reason for the high levels of
+produces the pot and essentially do can
+
+ align:start position:0%
+produces the pot and essentially do can
+ 
+
+ align:start position:0%
+produces the pot and essentially do can
+be traced back to the memories of food
+
+ align:start position:0%
+be traced back to the memories of food
+ 
+
+ align:start position:0%
+be traced back to the memories of food
+shortage that occurred after World War
+
+ align:start position:0%
+shortage that occurred after World War
+ 
+
+ align:start position:0%
+shortage that occurred after World War
+two something that cannot be said of the
+
+ align:start position:0%
+two something that cannot be said of the
+ 
+
+ align:start position:0%
+two something that cannot be said of the
+US so what may be popular in one country
+
+ align:start position:0%
+US so what may be popular in one country
+ 
+
+ align:start position:0%
+US so what may be popular in one country
+may be very unpopular in another so what
+
+ align:start position:0%
+may be very unpopular in another so what
+ 
+
+ align:start position:0%
+may be very unpopular in another so what
+we intend to do on outfits is not to be
+
+ align:start position:0%
+we intend to do on outfits is not to be
+ 
+
+ align:start position:0%
+we intend to do on outfits is not to be
+transplanted of these policies back to
+
+ align:start position:0%
+transplanted of these policies back to
+ 
+
+ align:start position:0%
+transplanted of these policies back to
+the u.s. we intend to be translators
+
+ align:start position:0%
+the u.s. we intend to be translators
+ 
+
+ align:start position:0%
+the u.s. we intend to be translators
+where we take the spirit and not the
+
+ align:start position:0%
+where we take the spirit and not the
+ 
+
+ align:start position:0%
+where we take the spirit and not the
+letter of these policies and combine it
+
+ align:start position:0%
+letter of these policies and combine it
+ 
+
+ align:start position:0%
+letter of these policies and combine it
+with our understanding of the realities
+
+ align:start position:0%
+with our understanding of the realities
+ 
+
+ align:start position:0%
+with our understanding of the realities
+here in the u.s. to develop a selection
+
+ align:start position:0%
+here in the u.s. to develop a selection
+ 
+
+ align:start position:0%
+here in the u.s. to develop a selection
+of ideas that circumvent differences
+
+ align:start position:0%
+of ideas that circumvent differences
+ 
+
+ align:start position:0%
+of ideas that circumvent differences
+institutions and account for differences
+
+ align:start position:0%
+institutions and account for differences
+ 
+
+ align:start position:0%
+institutions and account for differences
+in culture that's it even in the u.s.
+
+ align:start position:0%
+in culture that's it even in the u.s.
+ 
+
+ align:start position:0%
+in culture that's it even in the u.s.
+that institutions do change and cultures
+
+ align:start position:0%
+that institutions do change and cultures
+ 
+
+ align:start position:0%
+that institutions do change and cultures
+do evolve or be it at a much lower rate
+
+ align:start position:0%
+do evolve or be it at a much lower rate
+ 
+
+ align:start position:0%
+do evolve or be it at a much lower rate
+and even in within the country country
+
+ align:start position:0%
+and even in within the country country
+ 
+
+ align:start position:0%
+and even in within the country country
+cultures will vary widely
+
+ align:start position:0%
+cultures will vary widely
+ 
+
+ align:start position:0%
+cultures will vary widely
+so even ideas that seem improbable for
+
+ align:start position:0%
+so even ideas that seem improbable for
+ 
+
+ align:start position:0%
+so even ideas that seem improbable for
+now should not be discarded but kept for
+
+ align:start position:0%
+now should not be discarded but kept for
+ 
+
+ align:start position:0%
+now should not be discarded but kept for
+future reference so whenever the time
+
+ align:start position:0%
+future reference so whenever the time
+ 
+
+ align:start position:0%
+future reference so whenever the time
+comes we are ready to defend them so in
+
+ align:start position:0%
+comes we are ready to defend them so in
+ 
+
+ align:start position:0%
+comes we are ready to defend them so in
+conclusion my trips will have great a
+
+ align:start position:0%
+conclusion my trips will have great a
+ 
+
+ align:start position:0%
+conclusion my trips will have great a
+deep and benamber
+
+ align:start position:0%
+deep and benamber
+ 
+
+ align:start position:0%
+deep and benamber
+opportunities that also are fraught with
+
+ align:start position:0%
+opportunities that also are fraught with
+ 
+
+ align:start position:0%
+opportunities that also are fraught with
+challenges but an appreciation that
+
+ align:start position:0%
+challenges but an appreciation that
+ 
+
+ align:start position:0%
+challenges but an appreciation that
+promise the differences in countries are
+
+ align:start position:0%
+promise the differences in countries are
+ 
+
+ align:start position:0%
+promise the differences in countries are
+the drivers of learning and not
+
+ align:start position:0%
+the drivers of learning and not
+ 
+
+ align:start position:0%
+the drivers of learning and not
+similarities and also an appreciation
+
+ align:start position:0%
+similarities and also an appreciation
+ 
+
+ align:start position:0%
+similarities and also an appreciation
+that policy learning observations are
+
+ align:start position:0%
+that policy learning observations are
+ 
+
+ align:start position:0%
+that policy learning observations are
+just start to a greater translation
+
+ align:start position:0%
+just start to a greater translation
+ 
+
+ align:start position:0%
+just start to a greater translation
+efforts should allow us to reap the full
+
+ align:start position:0%
+efforts should allow us to reap the full
+ 
+
+ align:start position:0%
+efforts should allow us to reap the full
+benefits of our trips of thank you for
\ No newline at end of file
diff --git a/UdEX0E9lIQM.txt b/UdEX0E9lIQM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f81e516dab2b0f97141a846720e45e665799bf71
--- /dev/null
+++ b/UdEX0E9lIQM.txt
@@ -0,0 +1,14643 @@
+align:start position:0%
+ 
+so let's start today's lecture we're
+
+ align:start position:0%
+so let's start today's lecture we're
+ 
+
+ align:start position:0%
+so let's start today's lecture we're
+going to be looking at sort of three
+
+ align:start position:0%
+going to be looking at sort of three
+ 
+
+ align:start position:0%
+going to be looking at sort of three
+different topics the first is we're
+
+ align:start position:0%
+different topics the first is we're
+ 
+
+ align:start position:0%
+different topics the first is we're
+going to look at a new object type
+
+ align:start position:0%
+going to look at a new object type
+ 
+
+ align:start position:0%
+going to look at a new object type
+called a string we briefly mentioned
+
+ align:start position:0%
+called a string we briefly mentioned
+ 
+
+ align:start position:0%
+called a string we briefly mentioned
+this word last lecture then we're going
+
+ align:start position:0%
+this word last lecture then we're going
+ 
+
+ align:start position:0%
+this word last lecture then we're going
+to see how we can write programs that
+
+ align:start position:0%
+to see how we can write programs that
+ 
+
+ align:start position:0%
+to see how we can write programs that
+start to get input from the user and
+
+ align:start position:0%
+start to get input from the user and
+ 
+
+ align:start position:0%
+start to get input from the user and
+show the user
+
+ align:start position:0%
+show the user
+ 
+
+ align:start position:0%
+show the user
+output and finally we're going to go
+
+ align:start position:0%
+output and finally we're going to go
+ 
+
+ align:start position:0%
+output and finally we're going to go
+into writing a little bit more
+
+ align:start position:0%
+into writing a little bit more
+ 
+
+ align:start position:0%
+into writing a little bit more
+interesting programs that uh that make
+
+ align:start position:0%
+interesting programs that uh that make
+ 
+
+ align:start position:0%
+interesting programs that uh that make
+decisions based on decisions that we
+
+ align:start position:0%
+decisions based on decisions that we
+ 
+
+ align:start position:0%
+decisions based on decisions that we
+actually input in the code so not
+
+ align:start position:0%
+actually input in the code so not
+ 
+
+ align:start position:0%
+actually input in the code so not
+decisions spontaneously but things that
+
+ align:start position:0%
+decisions spontaneously but things that
+ 
+
+ align:start position:0%
+decisions spontaneously but things that
+we will code within our programs but
+
+ align:start position:0%
+we will code within our programs but
+ 
+
+ align:start position:0%
+we will code within our programs but
+before we go on to these topics I just
+
+ align:start position:0%
+before we go on to these topics I just
+ 
+
+ align:start position:0%
+before we go on to these topics I just
+wanted to do a quick recap of what we
+
+ align:start position:0%
+wanted to do a quick recap of what we
+ 
+
+ align:start position:0%
+wanted to do a quick recap of what we
+learned last lecture just to make sure
+
+ align:start position:0%
+learned last lecture just to make sure
+ 
+
+ align:start position:0%
+learned last lecture just to make sure
+we're all on the same page so we
+
+ align:start position:0%
+we're all on the same page so we
+ 
+
+ align:start position:0%
+we're all on the same page so we
+introduced the idea of an object and
+
+ align:start position:0%
+introduced the idea of an object and
+ 
+
+ align:start position:0%
+introduced the idea of an object and
+every object in python has a specific
+
+ align:start position:0%
+every object in python has a specific
+ 
+
+ align:start position:0%
+every object in python has a specific
+type and the type tells python the kinds
+
+ align:start position:0%
+type and the type tells python the kinds
+ 
+
+ align:start position:0%
+type and the type tells python the kinds
+of things you're allowed to do with that
+
+ align:start position:0%
+of things you're allowed to do with that
+ 
+
+ align:start position:0%
+of things you're allowed to do with that
+object okay um we talked about once you
+
+ align:start position:0%
+object okay um we talked about once you
+ 
+
+ align:start position:0%
+object okay um we talked about once you
+have objects you can actually assign
+
+ align:start position:0%
+have objects you can actually assign
+ 
+
+ align:start position:0%
+have objects you can actually assign
+these objects to variables and these
+
+ align:start position:0%
+these objects to variables and these
+ 
+
+ align:start position:0%
+these objects to variables and these
+variables basically bind a name to the
+
+ align:start position:0%
+variables basically bind a name to the
+ 
+
+ align:start position:0%
+variables basically bind a name to the
+object in memory with objects you can
+
+ align:start position:0%
+object in memory with objects you can
+ 
+
+ align:start position:0%
+object in memory with objects you can
+also create Expressions by combining
+
+ align:start position:0%
+also create Expressions by combining
+ 
+
+ align:start position:0%
+also create Expressions by combining
+objects together and the Expressions can
+
+ align:start position:0%
+objects together and the Expressions can
+ 
+
+ align:start position:0%
+objects together and the Expressions can
+either be things that we've seen in math
+
+ align:start position:0%
+either be things that we've seen in math
+ 
+
+ align:start position:0%
+either be things that we've seen in math
+like with parentheses and with operator
+
+ align:start position:0%
+like with parentheses and with operator
+ 
+
+ align:start position:0%
+like with parentheses and with operator
+like object operator object or they can
+
+ align:start position:0%
+like object operator object or they can
+ 
+
+ align:start position:0%
+like object operator object or they can
+be things like this which we which was
+
+ align:start position:0%
+be things like this which we which was
+ 
+
+ align:start position:0%
+be things like this which we which was
+kind of introduced in programming it's
+
+ align:start position:0%
+kind of introduced in programming it's
+ 
+
+ align:start position:0%
+kind of introduced in programming it's
+an expression but it's kind of a
+
+ align:start position:0%
+an expression but it's kind of a
+ 
+
+ align:start position:0%
+an expression but it's kind of a
+different one it's uh more like a
+
+ align:start position:0%
+different one it's uh more like a
+ 
+
+ align:start position:0%
+different one it's uh more like a
+command or I'm asking python to do this
+
+ align:start position:0%
+command or I'm asking python to do this
+ 
+
+ align:start position:0%
+command or I'm asking python to do this
+operation for me what is the object that
+
+ align:start position:0%
+operation for me what is the object that
+ 
+
+ align:start position:0%
+operation for me what is the object that
+comes back from this
+
+ align:start position:0%
+comes back from this
+ 
+
+ align:start position:0%
+comes back from this
+operation so today um I'm going to go
+
+ align:start position:0%
+operation so today um I'm going to go
+ 
+
+ align:start position:0%
+operation so today um I'm going to go
+over this little uh sort of memory
+
+ align:start position:0%
+over this little uh sort of memory
+ 
+
+ align:start position:0%
+over this little uh sort of memory
+diagram we started drawing last lecture
+
+ align:start position:0%
+diagram we started drawing last lecture
+ 
+
+ align:start position:0%
+diagram we started drawing last lecture
+and I'm going to use this memory diagram
+
+ align:start position:0%
+and I'm going to use this memory diagram
+ 
+
+ align:start position:0%
+and I'm going to use this memory diagram
+today as well um here's some lines of
+
+ align:start position:0%
+today as well um here's some lines of
+ 
+
+ align:start position:0%
+today as well um here's some lines of
+code that we wrote last lecture so we
+
+ align:start position:0%
+code that we wrote last lecture so we
+ 
+
+ align:start position:0%
+code that we wrote last lecture so we
+created uh we we wrote a line in Python
+
+ align:start position:0%
+created uh we we wrote a line in Python
+ 
+
+ align:start position:0%
+created uh we we wrote a line in Python
+that created an object its value is 3.14
+
+ align:start position:0%
+that created an object its value is 3.14
+ 
+
+ align:start position:0%
+that created an object its value is 3.14
+a float in memory and the name we gave
+
+ align:start position:0%
+a float in memory and the name we gave
+ 
+
+ align:start position:0%
+a float in memory and the name we gave
+this object was Pi so just the the name
+
+ align:start position:0%
+this object was Pi so just the the name
+ 
+
+ align:start position:0%
+this object was Pi so just the the name
+Pi
+
+ align:start position:0%
+Pi
+ 
+
+ align:start position:0%
+Pi
+Pi radius equals 2.2 is another
+
+ align:start position:0%
+Pi radius equals 2.2 is another
+ 
+
+ align:start position:0%
+Pi radius equals 2.2 is another
+assignment uh statement in Python and it
+
+ align:start position:0%
+assignment uh statement in Python and it
+ 
+
+ align:start position:0%
+assignment uh statement in Python and it
+binds the name radius to the value 2.2
+
+ align:start position:0%
+binds the name radius to the value 2.2
+ 
+
+ align:start position:0%
+binds the name radius to the value 2.2
+in memory and once we've created these
+
+ align:start position:0%
+in memory and once we've created these
+ 
+
+ align:start position:0%
+in memory and once we've created these
+variables we can just invoke their names
+
+ align:start position:0%
+variables we can just invoke their names
+ 
+
+ align:start position:0%
+variables we can just invoke their names
+we can use their names to tell python to
+
+ align:start position:0%
+we can use their names to tell python to
+ 
+
+ align:start position:0%
+we can use their names to tell python to
+grab for me the values from memory so
+
+ align:start position:0%
+grab for me the values from memory so
+ 
+
+ align:start position:0%
+grab for me the values from memory so
+when python sees Pi * radius star star 2
+
+ align:start position:0%
+when python sees Pi * radius star star 2
+ 
+
+ align:start position:0%
+when python sees Pi * radius star star 2
+that means take Pi multiply it with the
+
+ align:start position:0%
+that means take Pi multiply it with the
+ 
+
+ align:start position:0%
+that means take Pi multiply it with the
+radius squared so behind the scenes
+
+ align:start position:0%
+radius squared so behind the scenes
+ 
+
+ align:start position:0%
+radius squared so behind the scenes
+python goes grabs the value 3.14 from
+
+ align:start position:0%
+python goes grabs the value 3.14 from
+ 
+
+ align:start position:0%
+python goes grabs the value 3.14 from
+memory replaces Pi with that value grabs
+
+ align:start position:0%
+memory replaces Pi with that value grabs
+ 
+
+ align:start position:0%
+memory replaces Pi with that value grabs
+2.2 from memory replaces radius with
+
+ align:start position:0%
+2.2 from memory replaces radius with
+ 
+
+ align:start position:0%
+2.2 from memory replaces radius with
+that value does the operation according
+
+ align:start position:0%
+that value does the operation according
+ 
+
+ align:start position:0%
+that value does the operation according
+to the precedent rules and then that
+
+ align:start position:0%
+to the precedent rules and then that
+ 
+
+ align:start position:0%
+to the precedent rules and then that
+expression the thing on the right hand
+
+ align:start position:0%
+expression the thing on the right hand
+ 
+
+ align:start position:0%
+expression the thing on the right hand
+side of this equal sign becomes a value
+
+ align:start position:0%
+side of this equal sign becomes a value
+ 
+
+ align:start position:0%
+side of this equal sign becomes a value
+that value is then created as a new
+
+ align:start position:0%
+that value is then created as a new
+ 
+
+ align:start position:0%
+that value is then created as a new
+object in memory right here and that
+
+ align:start position:0%
+object in memory right here and that
+ 
+
+ align:start position:0%
+object in memory right here and that
+object in memory is then bound to the
+
+ align:start position:0%
+object in memory is then bound to the
+ 
+
+ align:start position:0%
+object in memory is then bound to the
+name area that's exactly what this
+
+ align:start position:0%
+name area that's exactly what this
+ 
+
+ align:start position:0%
+name area that's exactly what this
+assignment statement said okay and we
+
+ align:start position:0%
+assignment statement said okay and we
+ 
+
+ align:start position:0%
+assignment statement said okay and we
+can do something like this in Python
+
+ align:start position:0%
+can do something like this in Python
+ 
+
+ align:start position:0%
+can do something like this in Python
+which we can't actually do in math right
+
+ align:start position:0%
+which we can't actually do in math right
+ 
+
+ align:start position:0%
+which we can't actually do in math right
+if we did this in math the expression
+
+ align:start position:0%
+if we did this in math the expression
+ 
+
+ align:start position:0%
+if we did this in math the expression
+would basically say 0 equals 1 but in
+
+ align:start position:0%
+would basically say 0 equals 1 but in
+ 
+
+ align:start position:0%
+would basically say 0 equals 1 but in
+Python it's totally fine because again
+
+ align:start position:0%
+Python it's totally fine because again
+ 
+
+ align:start position:0%
+Python it's totally fine because again
+we evaluate the thing on the right hand
+
+ align:start position:0%
+we evaluate the thing on the right hand
+ 
+
+ align:start position:0%
+we evaluate the thing on the right hand
+side of the equal sign so on the right
+
+ align:start position:0%
+side of the equal sign so on the right
+ 
+
+ align:start position:0%
+side of the equal sign so on the right
+hand side of the equal sign we say I
+
+ align:start position:0%
+hand side of the equal sign we say I
+ 
+
+ align:start position:0%
+hand side of the equal sign we say I
+want to grab the value of radius so 2.2
+
+ align:start position:0%
+want to grab the value of radius so 2.2
+ 
+
+ align:start position:0%
+want to grab the value of radius so 2.2
+add one to it 3.2 create this object in
+
+ align:start position:0%
+add one to it 3.2 create this object in
+ 
+
+ align:start position:0%
+add one to it 3.2 create this object in
+memory here I have a whole new object in
+
+ align:start position:0%
+memory here I have a whole new object in
+ 
+
+ align:start position:0%
+memory here I have a whole new object in
+memory 3.2 and then assign it to the
+
+ align:start position:0%
+memory 3.2 and then assign it to the
+ 
+
+ align:start position:0%
+memory 3.2 and then assign it to the
+name radius so I've lost The Binding
+
+ align:start position:0%
+name radius so I've lost The Binding
+ 
+
+ align:start position:0%
+name radius so I've lost The Binding
+from the original 2.2 and rebound the
+
+ align:start position:0%
+from the original 2.2 and rebound the
+ 
+
+ align:start position:0%
+from the original 2.2 and rebound the
+name to 3.2 okay so we're not modifying
+
+ align:start position:0%
+name to 3.2 okay so we're not modifying
+ 
+
+ align:start position:0%
+name to 3.2 okay so we're not modifying
+objects in memory we're creating new
+
+ align:start position:0%
+objects in memory we're creating new
+ 
+
+ align:start position:0%
+objects in memory we're creating new
+objects in memory whenever we uh do such
+
+ align:start position:0%
+objects in memory whenever we uh do such
+ 
+
+ align:start position:0%
+objects in memory whenever we uh do such
+operations we're going to see how we can
+
+ align:start position:0%
+operations we're going to see how we can
+ 
+
+ align:start position:0%
+operations we're going to see how we can
+modify objects way into the
+
+ align:start position:0%
+modify objects way into the
+ 
+
+ align:start position:0%
+modify objects way into the
+future and uh just sort of for
+
+ align:start position:0%
+future and uh just sort of for
+ 
+
+ align:start position:0%
+future and uh just sort of for
+completion when we have a line that says
+
+ align:start position:0%
+completion when we have a line that says
+ 
+
+ align:start position:0%
+completion when we have a line that says
+VAR is equal type five multiplied by
+
+ align:start position:0%
+VAR is equal type five multiplied by
+ 
+
+ align:start position:0%
+VAR is equal type five multiplied by
+four python also sees this as an
+
+ align:start position:0%
+four python also sees this as an
+ 
+
+ align:start position:0%
+four python also sees this as an
+expression and so as an expression it
+
+ align:start position:0%
+expression and so as an expression it
+ 
+
+ align:start position:0%
+expression and so as an expression it
+has a value so the right hand side of
+
+ align:start position:0%
+has a value so the right hand side of
+ 
+
+ align:start position:0%
+has a value so the right hand side of
+this equal sign says well I'm going to
+
+ align:start position:0%
+this equal sign says well I'm going to
+ 
+
+ align:start position:0%
+this equal sign says well I'm going to
+sort of systematically evaluate this and
+
+ align:start position:0%
+sort of systematically evaluate this and
+ 
+
+ align:start position:0%
+sort of systematically evaluate this and
+say what's 5 * 4 it's
+
+ align:start position:0%
+say what's 5 * 4 it's
+ 
+
+ align:start position:0%
+say what's 5 * 4 it's
+20 what's the type of 20 it's an integer
+
+ align:start position:0%
+20 what's the type of 20 it's an integer
+ 
+
+ align:start position:0%
+20 what's the type of 20 it's an integer
+and so that's what the right hand side
+
+ align:start position:0%
+and so that's what the right hand side
+ 
+
+ align:start position:0%
+and so that's what the right hand side
+evaluates to an integer and I'm going to
+
+ align:start position:0%
+evaluates to an integer and I'm going to
+ 
+
+ align:start position:0%
+evaluates to an integer and I'm going to
+bom find that value int to the name VAR
+
+ align:start position:0%
+bom find that value int to the name VAR
+ 
+
+ align:start position:0%
+bom find that value int to the name VAR
+okay so VAR is another variable name and
+
+ align:start position:0%
+okay so VAR is another variable name and
+ 
+
+ align:start position:0%
+okay so VAR is another variable name and
+its value is int right the type of my
+
+ align:start position:0%
+its value is int right the type of my
+ 
+
+ align:start position:0%
+its value is int right the type of my
+object which is a little strange right
+
+ align:start position:0%
+object which is a little strange right
+ 
+
+ align:start position:0%
+object which is a little strange right
+so far we've kind of just put numbers in
+
+ align:start position:0%
+so far we've kind of just put numbers in
+ 
+
+ align:start position:0%
+so far we've kind of just put numbers in
+our memory but we can put any object
+
+ align:start position:0%
+our memory but we can put any object
+ 
+
+ align:start position:0%
+our memory but we can put any object
+type in
+
+ align:start position:0%
+type in
+ 
+
+ align:start position:0%
+type in
+memory okay so let's move on a little
+
+ align:start position:0%
+memory okay so let's move on a little
+ 
+
+ align:start position:0%
+memory okay so let's move on a little
+bit uh in onto the new object type
+
+ align:start position:0%
+bit uh in onto the new object type
+ 
+
+ align:start position:0%
+bit uh in onto the new object type
+called a string so a string is actually
+
+ align:start position:0%
+called a string so a string is actually
+ 
+
+ align:start position:0%
+called a string so a string is actually
+a sequence of K sensitive
+
+ align:start position:0%
+a sequence of K sensitive
+ 
+
+ align:start position:0%
+a sequence of K sensitive
+characters um the characters can be
+
+ align:start position:0%
+characters um the characters can be
+ 
+
+ align:start position:0%
+characters um the characters can be
+anything uh we have lowercase letters
+
+ align:start position:0%
+anything uh we have lowercase letters
+ 
+
+ align:start position:0%
+anything uh we have lowercase letters
+uppercase letters the numbers on your
+
+ align:start position:0%
+uppercase letters the numbers on your
+ 
+
+ align:start position:0%
+uppercase letters the numbers on your
+keyboard the special characters you see
+
+ align:start position:0%
+keyboard the special characters you see
+ 
+
+ align:start position:0%
+keyboard the special characters you see
+on the keyboard even the enter when you
+
+ align:start position:0%
+on the keyboard even the enter when you
+ 
+
+ align:start position:0%
+on the keyboard even the enter when you
+do a new line or a tab has a special
+
+ align:start position:0%
+do a new line or a tab has a special
+ 
+
+ align:start position:0%
+do a new line or a tab has a special
+character associated with it and the way
+
+ align:start position:0%
+character associated with it and the way
+ 
+
+ align:start position:0%
+character associated with it and the way
+we tell python we're creating an object
+
+ align:start position:0%
+we tell python we're creating an object
+ 
+
+ align:start position:0%
+we tell python we're creating an object
+of type string is by enclosing the the
+
+ align:start position:0%
+of type string is by enclosing the the
+ 
+
+ align:start position:0%
+of type string is by enclosing the the
+characters we want to be part of that
+
+ align:start position:0%
+characters we want to be part of that
+ 
+
+ align:start position:0%
+characters we want to be part of that
+object in these quotation marks so when
+
+ align:start position:0%
+object in these quotation marks so when
+ 
+
+ align:start position:0%
+object in these quotation marks so when
+python sees the quotation mark it knows
+
+ align:start position:0%
+python sees the quotation mark it knows
+ 
+
+ align:start position:0%
+python sees the quotation mark it knows
+you're creating a string object so here
+
+ align:start position:0%
+you're creating a string object so here
+ 
+
+ align:start position:0%
+you're creating a string object so here
+I'm creating the string object uh which
+
+ align:start position:0%
+I'm creating the string object uh which
+ 
+
+ align:start position:0%
+I'm creating the string object uh which
+has the lowercase letter M lowercase
+
+ align:start position:0%
+has the lowercase letter M lowercase
+ 
+
+ align:start position:0%
+has the lowercase letter M lowercase
+letter e and here I'm creating the uh
+
+ align:start position:0%
+letter e and here I'm creating the uh
+ 
+
+ align:start position:0%
+letter e and here I'm creating the uh
+string object which has the lowercase y
+
+ align:start position:0%
+string object which has the lowercase y
+ 
+
+ align:start position:0%
+string object which has the lowercase y
+lowercase o and lowercase U letters and
+
+ align:start position:0%
+lowercase o and lowercase U letters and
+ 
+
+ align:start position:0%
+lowercase o and lowercase U letters and
+these objects are things in Python and
+
+ align:start position:0%
+these objects are things in Python and
+ 
+
+ align:start position:0%
+these objects are things in Python and
+we're just going to give them a handle a
+
+ align:start position:0%
+we're just going to give them a handle a
+ 
+
+ align:start position:0%
+we're just going to give them a handle a
+binding with some more convenient
+
+ align:start position:0%
+binding with some more convenient
+ 
+
+ align:start position:0%
+binding with some more convenient
+variable names A and Z so in memory the
+
+ align:start position:0%
+variable names A and Z so in memory the
+ 
+
+ align:start position:0%
+variable names A and Z so in memory the
+way this would look in a little me
+
+ align:start position:0%
+way this would look in a little me
+ 
+
+ align:start position:0%
+way this would look in a little me
+memory diagram is we would have the
+
+ align:start position:0%
+memory diagram is we would have the
+ 
+
+ align:start position:0%
+memory diagram is we would have the
+string uh characters me bound to the
+
+ align:start position:0%
+string uh characters me bound to the
+ 
+
+ align:start position:0%
+string uh characters me bound to the
+variable a right so basically what we've
+
+ align:start position:0%
+variable a right so basically what we've
+ 
+
+ align:start position:0%
+variable a right so basically what we've
+seen
+
+ align:start position:0%
+seen
+ 
+
+ align:start position:0%
+seen
+before all right so now what are some
+
+ align:start position:0%
+before all right so now what are some
+ 
+
+ align:start position:0%
+before all right so now what are some
+things we can do with strings well some
+
+ align:start position:0%
+things we can do with strings well some
+ 
+
+ align:start position:0%
+things we can do with strings well some
+really common operations is are that we
+
+ align:start position:0%
+really common operations is are that we
+ 
+
+ align:start position:0%
+really common operations is are that we
+can concatenate strings or we can repeat
+
+ align:start position:0%
+can concatenate strings or we can repeat
+ 
+
+ align:start position:0%
+can concatenate strings or we can repeat
+strings so here I'm not going to put the
+
+ align:start position:0%
+strings so here I'm not going to put the
+ 
+
+ align:start position:0%
+strings so here I'm not going to put the
+Z in memory you can kind of imagine how
+
+ align:start position:0%
+Z in memory you can kind of imagine how
+ 
+
+ align:start position:0%
+Z in memory you can kind of imagine how
+that would look like but let's say I
+
+ align:start position:0%
+that would look like but let's say I
+ 
+
+ align:start position:0%
+that would look like but let's say I
+create now a variable b equals the
+
+ align:start position:0%
+create now a variable b equals the
+ 
+
+ align:start position:0%
+create now a variable b equals the
+letters uh my y c
+
+ align:start position:0%
+letters uh my y c
+ 
+
+ align:start position:0%
+letters uh my y c
+LF what if I do a plus operator between
+
+ align:start position:0%
+LF what if I do a plus operator between
+ 
+
+ align:start position:0%
+LF what if I do a plus operator between
+these two strings the plus operator
+
+ align:start position:0%
+these two strings the plus operator
+ 
+
+ align:start position:0%
+these two strings the plus operator
+tells python that I'm going to take
+
+ align:start position:0%
+tells python that I'm going to take
+ 
+
+ align:start position:0%
+tells python that I'm going to take
+these two strings the individual
+
+ align:start position:0%
+these two strings the individual
+ 
+
+ align:start position:0%
+these two strings the individual
+characters in each string and kind of
+
+ align:start position:0%
+characters in each string and kind of
+ 
+
+ align:start position:0%
+characters in each string and kind of
+just put them together to make one new
+
+ align:start position:0%
+just put them together to make one new
+ 
+
+ align:start position:0%
+just put them together to make one new
+object that is all of these letters put
+
+ align:start position:0%
+object that is all of these letters put
+ 
+
+ align:start position:0%
+object that is all of these letters put
+together so C is equal to a plus b is
+
+ align:start position:0%
+together so C is equal to a plus b is
+ 
+
+ align:start position:0%
+together so C is equal to a plus b is
+another uh uh assignment operator and on
+
+ align:start position:0%
+another uh uh assignment operator and on
+ 
+
+ align:start position:0%
+another uh uh assignment operator and on
+the right hand side we have an
+
+ align:start position:0%
+the right hand side we have an
+ 
+
+ align:start position:0%
+the right hand side we have an
+expression plus operator between two
+
+ align:start position:0%
+expression plus operator between two
+ 
+
+ align:start position:0%
+expression plus operator between two
+objects it's going to put me which is
+
+ align:start position:0%
+objects it's going to put me which is
+ 
+
+ align:start position:0%
+objects it's going to put me which is
+the uh the c letters and the my LF the
+
+ align:start position:0%
+the uh the c letters and the my LF the
+ 
+
+ align:start position:0%
+the uh the c letters and the my LF the
+uh B letters Al together to create a new
+
+ align:start position:0%
+uh B letters Al together to create a new
+ 
+
+ align:start position:0%
+uh B letters Al together to create a new
+object which I then give a handle a
+
+ align:start position:0%
+object which I then give a handle a
+ 
+
+ align:start position:0%
+object which I then give a handle a
+binding C so from now on anytime I want
+
+ align:start position:0%
+binding C so from now on anytime I want
+ 
+
+ align:start position:0%
+binding C so from now on anytime I want
+this particular uh string of characters
+
+ align:start position:0%
+this particular uh string of characters
+ 
+
+ align:start position:0%
+this particular uh string of characters
+M me m
+
+ align:start position:0%
+M me m
+ 
+
+ align:start position:0%
+M me m
+ysf I can just invoke the name c in my
+
+ align:start position:0%
+ysf I can just invoke the name c in my
+ 
+
+ align:start position:0%
+ysf I can just invoke the name c in my
+program that's just the variable name
+
+ align:start position:0%
+program that's just the variable name
+ 
+
+ align:start position:0%
+program that's just the variable name
+that I gave
+
+ align:start position:0%
+that I gave
+ 
+
+ align:start position:0%
+that I gave
+it now notice it didn't insert a space
+
+ align:start position:0%
+it now notice it didn't insert a space
+ 
+
+ align:start position:0%
+it now notice it didn't insert a space
+right it didn't do me space myself
+
+ align:start position:0%
+right it didn't do me space myself
+ 
+
+ align:start position:0%
+right it didn't do me space myself
+because we didn't tell it to do a space
+
+ align:start position:0%
+because we didn't tell it to do a space
+ 
+
+ align:start position:0%
+because we didn't tell it to do a space
+so if we want it to do a space we'd have
+
+ align:start position:0%
+so if we want it to do a space we'd have
+ 
+
+ align:start position:0%
+so if we want it to do a space we'd have
+to put it in ourselves so we can
+
+ align:start position:0%
+to put it in ourselves so we can
+ 
+
+ align:start position:0%
+to put it in ourselves so we can
+concatenate so we can have a larger
+
+ align:start position:0%
+concatenate so we can have a larger
+ 
+
+ align:start position:0%
+concatenate so we can have a larger
+expression where we concatenate a with a
+
+ align:start position:0%
+expression where we concatenate a with a
+ 
+
+ align:start position:0%
+expression where we concatenate a with a
+space and with B together so that will
+
+ align:start position:0%
+space and with B together so that will
+ 
+
+ align:start position:0%
+space and with B together so that will
+give me an entirely new object in memory
+
+ align:start position:0%
+give me an entirely new object in memory
+ 
+
+ align:start position:0%
+give me an entirely new object in memory
+the string me space m y s e LF this new
+
+ align:start position:0%
+the string me space m y s e LF this new
+ 
+
+ align:start position:0%
+the string me space m y s e LF this new
+object is bound to the name
+
+ align:start position:0%
+object is bound to the name
+ 
+
+ align:start position:0%
+object is bound to the name
+d is that okay so far does that make
+
+ align:start position:0%
+d is that okay so far does that make
+ 
+
+ align:start position:0%
+d is that okay so far does that make
+sense okay all right so that's
+
+ align:start position:0%
+sense okay all right so that's
+ 
+
+ align:start position:0%
+sense okay all right so that's
+concatenation basically takes these two
+
+ align:start position:0%
+concatenation basically takes these two
+ 
+
+ align:start position:0%
+concatenation basically takes these two
+string characters puts them together in
+
+ align:start position:0%
+string characters puts them together in
+ 
+
+ align:start position:0%
+string characters puts them together in
+a new object what about the star I kind
+
+ align:start position:0%
+a new object what about the star I kind
+ 
+
+ align:start position:0%
+a new object what about the star I kind
+of briefly talked about this as
+
+ align:start position:0%
+of briefly talked about this as
+ 
+
+ align:start position:0%
+of briefly talked about this as
+repeating something last lecture well
+
+ align:start position:0%
+repeating something last lecture well
+ 
+
+ align:start position:0%
+repeating something last lecture well
+the star operator Works between a string
+
+ align:start position:0%
+the star operator Works between a string
+ 
+
+ align:start position:0%
+the star operator Works between a string
+and a number it doesn't work between a
+
+ align:start position:0%
+and a number it doesn't work between a
+ 
+
+ align:start position:0%
+and a number it doesn't work between a
+string and a string it doesn't work
+
+ align:start position:0%
+string and a string it doesn't work
+ 
+
+ align:start position:0%
+string and a string it doesn't work
+between uh you know things like that it
+
+ align:start position:0%
+between uh you know things like that it
+ 
+
+ align:start position:0%
+between uh you know things like that it
+works between a string and a number in
+
+ align:start position:0%
+works between a string and a number in
+ 
+
+ align:start position:0%
+works between a string and a number in
+either order so a number string or
+
+ align:start position:0%
+either order so a number string or
+ 
+
+ align:start position:0%
+either order so a number string or
+string times
+
+ align:start position:0%
+string times
+ 
+
+ align:start position:0%
+string times
+number so here again it's an assignment
+
+ align:start position:0%
+number so here again it's an assignment
+ 
+
+ align:start position:0%
+number so here again it's an assignment
+operator the right hand side we're going
+
+ align:start position:0%
+operator the right hand side we're going
+ 
+
+ align:start position:0%
+operator the right hand side we're going
+to figure out what it what it evaluates
+
+ align:start position:0%
+to figure out what it what it evaluates
+ 
+
+ align:start position:0%
+to figure out what it what it evaluates
+to first so a * 3 means I'm going to
+
+ align:start position:0%
+to first so a * 3 means I'm going to
+ 
+
+ align:start position:0%
+to first so a * 3 means I'm going to
+repeat this particular sequence of
+
+ align:start position:0%
+repeat this particular sequence of
+ 
+
+ align:start position:0%
+repeat this particular sequence of
+characters me because that's what a is
+
+ align:start position:0%
+characters me because that's what a is
+ 
+
+ align:start position:0%
+characters me because that's what a is
+it's me three times
+
+ align:start position:0%
+it's me three times
+ 
+
+ align:start position:0%
+it's me three times
+so this line of code here is going to
+
+ align:start position:0%
+so this line of code here is going to
+ 
+
+ align:start position:0%
+so this line of code here is going to
+create me me me as a new object and the
+
+ align:start position:0%
+create me me me as a new object and the
+ 
+
+ align:start position:0%
+create me me me as a new object and the
+equal sign tells it to bind it to the
+
+ align:start position:0%
+equal sign tells it to bind it to the
+ 
+
+ align:start position:0%
+equal sign tells it to bind it to the
+name silly so anytime I want to grab
+
+ align:start position:0%
+name silly so anytime I want to grab
+ 
+
+ align:start position:0%
+name silly so anytime I want to grab
+this particular string of characters for
+
+ align:start position:0%
+this particular string of characters for
+ 
+
+ align:start position:0%
+this particular string of characters for
+memory I can just type in silly in my
+
+ align:start position:0%
+memory I can just type in silly in my
+ 
+
+ align:start position:0%
+memory I can just type in silly in my
+program and that will automatically grab
+
+ align:start position:0%
+program and that will automatically grab
+ 
+
+ align:start position:0%
+program and that will automatically grab
+that particular sequence of characters
+
+ align:start position:0%
+that particular sequence of characters
+ 
+
+ align:start position:0%
+that particular sequence of characters
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+memory all right let's do a quick
+
+ align:start position:0%
+memory all right let's do a quick
+ 
+
+ align:start position:0%
+memory all right let's do a quick
+exercise to make sure that you all have
+
+ align:start position:0%
+exercise to make sure that you all have
+ 
+
+ align:start position:0%
+exercise to make sure that you all have
+this and um as you're thinking about
+
+ align:start position:0%
+this and um as you're thinking about
+ 
+
+ align:start position:0%
+this and um as you're thinking about
+what this does I can can start typing it
+
+ align:start position:0%
+what this does I can can start typing it
+ 
+
+ align:start position:0%
+what this does I can can start typing it
+in uh to the um to the console um or you
+
+ align:start position:0%
+in uh to the um to the console um or you
+ 
+
+ align:start position:0%
+in uh to the um to the console um or you
+can either even type it in to check uh
+
+ align:start position:0%
+can either even type it in to check uh
+ 
+
+ align:start position:0%
+can either even type it in to check uh
+yourself so B is going to be colon and C
+
+ align:start position:0%
+yourself so B is going to be colon and C
+ 
+
+ align:start position:0%
+yourself so B is going to be colon and C
+is going to be the closed
+
+ align:start position:0%
+is going to be the closed
+ 
+
+ align:start position:0%
+is going to be the closed
+parenthesis so if we go here right we
+
+ align:start position:0%
+parenthesis so if we go here right we
+ 
+
+ align:start position:0%
+parenthesis so if we go here right we
+have B is equal to just this
+
+ align:start position:0%
+have B is equal to just this
+ 
+
+ align:start position:0%
+have B is equal to just this
+colon and C is equal to the Clos
+
+ align:start position:0%
+colon and C is equal to the Clos
+ 
+
+ align:start position:0%
+colon and C is equal to the Clos
+parenthesis and we don't have to do all
+
+ align:start position:0%
+parenthesis and we don't have to do all
+ 
+
+ align:start position:0%
+parenthesis and we don't have to do all
+the operations at once right we can just
+
+ align:start position:0%
+the operations at once right we can just
+ 
+
+ align:start position:0%
+the operations at once right we can just
+do something like 2 * C and figure out
+
+ align:start position:0%
+do something like 2 * C and figure out
+ 
+
+ align:start position:0%
+do something like 2 * C and figure out
+what that is right it's just repeating
+
+ align:start position:0%
+what that is right it's just repeating
+ 
+
+ align:start position:0%
+what that is right it's just repeating
+the closed parenthesis twice and then we
+
+ align:start position:0%
+the closed parenthesis twice and then we
+ 
+
+ align:start position:0%
+the closed parenthesis twice and then we
+can do B + 2 *
+
+ align:start position:0%
+can do B + 2 *
+ 
+
+ align:start position:0%
+can do B + 2 *
+C to give us closed parenthesis or colon
+
+ align:start position:0%
+C to give us closed parenthesis or colon
+ 
+
+ align:start position:0%
+C to give us closed parenthesis or colon
+closed parenthesis Clos parenthesis
+
+ align:start position:0%
+closed parenthesis Clos parenthesis
+ 
+
+ align:start position:0%
+closed parenthesis Clos parenthesis
+right so super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happy what about the next one f is
+
+ align:start position:0%
+happy what about the next one f is
+ 
+
+ align:start position:0%
+happy what about the next one f is
+a g is actually the
+
+ align:start position:0%
+a g is actually the
+ 
+
+ align:start position:0%
+a g is actually the
+space b right so there's a space
+
+ align:start position:0%
+space b right so there's a space
+ 
+
+ align:start position:0%
+space b right so there's a space
+character in there little trick
+
+ align:start position:0%
+character in there little trick
+ 
+
+ align:start position:0%
+character in there little trick
+and H is
+
+ align:start position:0%
+and H is
+ 
+
+ align:start position:0%
+and H is
+three is this the number three or the
+
+ align:start position:0%
+three is this the number three or the
+ 
+
+ align:start position:0%
+three is this the number three or the
+string three for
+
+ align:start position:0%
+string three for
+ 
+
+ align:start position:0%
+string three for
+H yeah exactly it's the string
+
+ align:start position:0%
+H yeah exactly it's the string
+ 
+
+ align:start position:0%
+H yeah exactly it's the string
+three so what is f plus G again we can
+
+ align:start position:0%
+three so what is f plus G again we can
+ 
+
+ align:start position:0%
+three so what is f plus G again we can
+do it in pieces what is f plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+g a space b exactly right a is uh um a
+
+ align:start position:0%
+g a space b exactly right a is uh um a
+ 
+
+ align:start position:0%
+g a space b exactly right a is uh um a
+is by itself and G is a space b what is
+
+ align:start position:0%
+is by itself and G is a space b what is
+ 
+
+ align:start position:0%
+is by itself and G is a space b what is
+int
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H yes yeah it's just three what's the
+
+ align:start position:0%
+H yes yeah it's just three what's the
+ 
+
+ align:start position:0%
+H yes yeah it's just three what's the
+type of
+
+ align:start position:0%
+type of
+ 
+
+ align:start position:0%
+type of
+three int exactly I just cast it to an
+
+ align:start position:0%
+three int exactly I just cast it to an
+ 
+
+ align:start position:0%
+three int exactly I just cast it to an
+INT right so if I have f is equal to a g
+
+ align:start position:0%
+INT right so if I have f is equal to a g
+ 
+
+ align:start position:0%
+INT right so if I have f is equal to a g
+is equal to space
+
+ align:start position:0%
+is equal to space
+ 
+
+ align:start position:0%
+is equal to space
+B and H is equal to the string
+
+ align:start position:0%
+B and H is equal to the string
+ 
+
+ align:start position:0%
+B and H is equal to the string
+three um f+ G we're doing it in uh a
+
+ align:start position:0%
+three um f+ G we're doing it in uh a
+ 
+
+ align:start position:0%
+three um f+ G we're doing it in uh a
+little bit at a time right is a space B
+
+ align:start position:0%
+little bit at a time right is a space B
+ 
+
+ align:start position:0%
+little bit at a time right is a space B
+and H is just see this string three here
+
+ align:start position:0%
+and H is just see this string three here
+ 
+
+ align:start position:0%
+and H is just see this string three here
+so if I cast it to
+
+ align:start position:0%
+so if I cast it to
+ 
+
+ align:start position:0%
+so if I cast it to
+an integer it gives me just the number
+
+ align:start position:0%
+an integer it gives me just the number
+ 
+
+ align:start position:0%
+an integer it gives me just the number
+three right and we can wrap each of
+
+ align:start position:0%
+three right and we can wrap each of
+ 
+
+ align:start position:0%
+three right and we can wrap each of
+these in a type command to see the Act
+
+ align:start position:0%
+these in a type command to see the Act
+ 
+
+ align:start position:0%
+these in a type command to see the Act
+exact type but we can tell right
+
+ align:start position:0%
+exact type but we can tell right
+ 
+
+ align:start position:0%
+exact type but we can tell right
+away so if we do f+ G multiplied by int
+
+ align:start position:0%
+away so if we do f+ G multiplied by int
+ 
+
+ align:start position:0%
+away so if we do f+ G multiplied by int
+of three or sorry oops int of H right
+
+ align:start position:0%
+of three or sorry oops int of H right
+ 
+
+ align:start position:0%
+of three or sorry oops int of H right
+which is just a three it's going to
+
+ align:start position:0%
+which is just a three it's going to
+ 
+
+ align:start position:0%
+which is just a three it's going to
+repeat a space b three times right so
+
+ align:start position:0%
+repeat a space b three times right so
+ 
+
+ align:start position:0%
+repeat a space b three times right so
+there's one there's two and there's
+
+ align:start position:0%
+there's one there's two and there's
+ 
+
+ align:start position:0%
+there's one there's two and there's
+three what would have happened if I
+
+ align:start position:0%
+three what would have happened if I
+ 
+
+ align:start position:0%
+three what would have happened if I
+forgot to cast it to an integer what do
+
+ align:start position:0%
+forgot to cast it to an integer what do
+ 
+
+ align:start position:0%
+forgot to cast it to an integer what do
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+think if I just did H an error yeah
+
+ align:start position:0%
+think if I just did H an error yeah
+ 
+
+ align:start position:0%
+think if I just did H an error yeah
+exactly they're not scary they're kind
+
+ align:start position:0%
+exactly they're not scary they're kind
+ 
+
+ align:start position:0%
+exactly they're not scary they're kind
+of informative once you get to know them
+
+ align:start position:0%
+of informative once you get to know them
+ 
+
+ align:start position:0%
+of informative once you get to know them
+so it's a type error yeah something's
+
+ align:start position:0%
+so it's a type error yeah something's
+ 
+
+ align:start position:0%
+so it's a type error yeah something's
+wrong with our types can't multiply a
+
+ align:start position:0%
+wrong with our types can't multiply a
+ 
+
+ align:start position:0%
+wrong with our types can't multiply a
+sequence so an integer or a string uh a
+
+ align:start position:0%
+sequence so an integer or a string uh a
+ 
+
+ align:start position:0%
+sequence so an integer or a string uh a
+sequence by a non-
+
+ align:start position:0%
+sequence by a non-
+ 
+
+ align:start position:0%
+sequence by a non-
+integer right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what are some other operations
+
+ align:start position:0%
+okay so what are some other operations
+ 
+
+ align:start position:0%
+okay so what are some other operations
+we can do with strings there's some
+
+ align:start position:0%
+we can do with strings there's some
+ 
+
+ align:start position:0%
+we can do with strings there's some
+different things we can do with strings
+
+ align:start position:0%
+different things we can do with strings
+ 
+
+ align:start position:0%
+different things we can do with strings
+that we actually haven't seen uh with uh
+
+ align:start position:0%
+that we actually haven't seen uh with uh
+ 
+
+ align:start position:0%
+that we actually haven't seen uh with uh
+with numbers uh in last lecture one of
+
+ align:start position:0%
+with numbers uh in last lecture one of
+ 
+
+ align:start position:0%
+with numbers uh in last lecture one of
+the more common operations is to get the
+
+ align:start position:0%
+the more common operations is to get the
+ 
+
+ align:start position:0%
+the more common operations is to get the
+length of a string so this tells us how
+
+ align:start position:0%
+length of a string so this tells us how
+ 
+
+ align:start position:0%
+length of a string so this tells us how
+many characters are in the string so if
+
+ align:start position:0%
+many characters are in the string so if
+ 
+
+ align:start position:0%
+many characters are in the string so if
+we say s is equal to ABC here I'm
+
+ align:start position:0%
+we say s is equal to ABC here I'm
+ 
+
+ align:start position:0%
+we say s is equal to ABC here I'm
+creating a string uh with characters a b
+
+ align:start position:0%
+creating a string uh with characters a b
+ 
+
+ align:start position:0%
+creating a string uh with characters a b
+and c and I'm giving it the name s now
+
+ align:start position:0%
+and c and I'm giving it the name s now
+ 
+
+ align:start position:0%
+and c and I'm giving it the name s now
+anytime in my program when I say s
+
+ align:start position:0%
+anytime in my program when I say s
+ 
+
+ align:start position:0%
+anytime in my program when I say s
+python will replace that with this
+
+ align:start position:0%
+python will replace that with this
+ 
+
+ align:start position:0%
+python will replace that with this
+string of characters ABC I can wrap s in
+
+ align:start position:0%
+string of characters ABC I can wrap s in
+ 
+
+ align:start position:0%
+string of characters ABC I can wrap s in
+this Len command and this Len command is
+
+ align:start position:0%
+this Len command and this Len command is
+ 
+
+ align:start position:0%
+this Len command and this Len command is
+is an expression basically python reads
+
+ align:start position:0%
+is an expression basically python reads
+ 
+
+ align:start position:0%
+is an expression basically python reads
+this and it evaluates it to one value so
+
+ align:start position:0%
+this and it evaluates it to one value so
+ 
+
+ align:start position:0%
+this and it evaluates it to one value so
+replaces this expression with one value
+
+ align:start position:0%
+replaces this expression with one value
+ 
+
+ align:start position:0%
+replaces this expression with one value
+how many characters are in my string so
+
+ align:start position:0%
+how many characters are in my string so
+ 
+
+ align:start position:0%
+how many characters are in my string so
+Len s will basically become the number
+
+ align:start position:0%
+Len s will basically become the number
+ 
+
+ align:start position:0%
+Len s will basically become the number
+three so in my program I can say
+
+ align:start position:0%
+three so in my program I can say
+ 
+
+ align:start position:0%
+three so in my program I can say
+something like another assignment
+
+ align:start position:0%
+something like another assignment
+ 
+
+ align:start position:0%
+something like another assignment
+statement down here right chariz is is
+
+ align:start position:0%
+statement down here right chariz is is
+ 
+
+ align:start position:0%
+statement down here right chariz is is
+equal to lens s this is an expression
+
+ align:start position:0%
+equal to lens s this is an expression
+ 
+
+ align:start position:0%
+equal to lens s this is an expression
+right like in the previous line that
+
+ align:start position:0%
+right like in the previous line that
+ 
+
+ align:start position:0%
+right like in the previous line that
+evaluates to three so basically this
+
+ align:start position:0%
+evaluates to three so basically this
+ 
+
+ align:start position:0%
+evaluates to three so basically this
+line says chars is equal to
+
+ align:start position:0%
+line says chars is equal to
+ 
+
+ align:start position:0%
+line says chars is equal to
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+right okay that's a pretty simple
+
+ align:start position:0%
+right okay that's a pretty simple
+ 
+
+ align:start position:0%
+right okay that's a pretty simple
+operation with strings now we're going
+
+ align:start position:0%
+operation with strings now we're going
+ 
+
+ align:start position:0%
+operation with strings now we're going
+to get into a little bit more uh uh
+
+ align:start position:0%
+to get into a little bit more uh uh
+ 
+
+ align:start position:0%
+to get into a little bit more uh uh
+detailed ones that requires you to kind
+
+ align:start position:0%
+detailed ones that requires you to kind
+ 
+
+ align:start position:0%
+detailed ones that requires you to kind
+of remember this python syntax so one
+
+ align:start position:0%
+of remember this python syntax so one
+ 
+
+ align:start position:0%
+of remember this python syntax so one
+thing we can do with strings is we can
+
+ align:start position:0%
+thing we can do with strings is we can
+ 
+
+ align:start position:0%
+thing we can do with strings is we can
+grab individual characters at different
+
+ align:start position:0%
+grab individual characters at different
+ 
+
+ align:start position:0%
+grab individual characters at different
+positions so that's called
+
+ align:start position:0%
+positions so that's called
+ 
+
+ align:start position:0%
+positions so that's called
+slicing the syntax or the way that we
+
+ align:start position:0%
+slicing the syntax or the way that we
+ 
+
+ align:start position:0%
+slicing the syntax or the way that we
+actually do this in Python is using
+
+ align:start position:0%
+actually do this in Python is using
+ 
+
+ align:start position:0%
+actually do this in Python is using
+square brackets so you can see this here
+
+ align:start position:0%
+square brackets so you can see this here
+ 
+
+ align:start position:0%
+square brackets so you can see this here
+right we have some square bracket
+
+ align:start position:0%
+right we have some square bracket
+ 
+
+ align:start position:0%
+right we have some square bracket
+notation and this is just how python
+
+ align:start position:0%
+notation and this is just how python
+ 
+
+ align:start position:0%
+notation and this is just how python
+does it so if we have string s is equal
+
+ align:start position:0%
+does it so if we have string s is equal
+ 
+
+ align:start position:0%
+does it so if we have string s is equal
+to the characters
+
+ align:start position:0%
+to the characters
+ 
+
+ align:start position:0%
+to the characters
+ABC The Way We Tell python we'd like to
+
+ align:start position:0%
+ABC The Way We Tell python we'd like to
+ 
+
+ align:start position:0%
+ABC The Way We Tell python we'd like to
+extract a character at a particular
+
+ align:start position:0%
+extract a character at a particular
+ 
+
+ align:start position:0%
+extract a character at a particular
+position is by indexing into that
+
+ align:start position:0%
+position is by indexing into that
+ 
+
+ align:start position:0%
+position is by indexing into that
+string now in Python and modern
+
+ align:start position:0%
+string now in Python and modern
+ 
+
+ align:start position:0%
+string now in Python and modern
+programming languages indexing happens
+
+ align:start position:0%
+programming languages indexing happens
+ 
+
+ align:start position:0%
+programming languages indexing happens
+from zero we count from zero in
+
+ align:start position:0%
+from zero we count from zero in
+ 
+
+ align:start position:0%
+from zero we count from zero in
+programming okay in computer science so
+
+ align:start position:0%
+programming okay in computer science so
+ 
+
+ align:start position:0%
+programming okay in computer science so
+what that means is the
+
+ align:start position:0%
+what that means is the
+ 
+
+ align:start position:0%
+what that means is the
+index of the first character the index
+
+ align:start position:0%
+index of the first character the index
+ 
+
+ align:start position:0%
+index of the first character the index
+of a is zero the index of B is one and
+
+ align:start position:0%
+of a is zero the index of B is one and
+ 
+
+ align:start position:0%
+of a is zero the index of B is one and
+the index of C is two right so we can
+
+ align:start position:0%
+the index of C is two right so we can
+ 
+
+ align:start position:0%
+the index of C is two right so we can
+say the what's the character at the
+
+ align:start position:0%
+say the what's the character at the
+ 
+
+ align:start position:0%
+say the what's the character at the
+first position or the first location but
+
+ align:start position:0%
+first position or the first location but
+ 
+
+ align:start position:0%
+first position or the first location but
+in computer science speak we say that's
+
+ align:start position:0%
+in computer science speak we say that's
+ 
+
+ align:start position:0%
+in computer science speak we say that's
+the character at index zero the
+
+ align:start position:0%
+the character at index zero the
+ 
+
+ align:start position:0%
+the character at index zero the
+character at index one is the is the
+
+ align:start position:0%
+character at index one is the is the
+ 
+
+ align:start position:0%
+character at index one is the is the
+character location to and so on right so
+
+ align:start position:0%
+character location to and so on right so
+ 
+
+ align:start position:0%
+character location to and so on right so
+when we're indexing into a string we're
+
+ align:start position:0%
+when we're indexing into a string we're
+ 
+
+ align:start position:0%
+when we're indexing into a string we're
+always starting to count from
+
+ align:start position:0%
+always starting to count from
+ 
+
+ align:start position:0%
+always starting to count from
+zero so s at index zero uh that's how we
+
+ align:start position:0%
+zero so s at index zero uh that's how we
+ 
+
+ align:start position:0%
+zero so s at index zero uh that's how we
+call this line here is another python
+
+ align:start position:0%
+call this line here is another python
+ 
+
+ align:start position:0%
+call this line here is another python
+expression it just has uh it just looks
+
+ align:start position:0%
+expression it just has uh it just looks
+ 
+
+ align:start position:0%
+expression it just has uh it just looks
+different than the Expressions we've
+
+ align:start position:0%
+different than the Expressions we've
+ 
+
+ align:start position:0%
+different than the Expressions we've
+seen so far but this entire expression
+
+ align:start position:0%
+seen so far but this entire expression
+ 
+
+ align:start position:0%
+seen so far but this entire expression
+python evaluates to a particular value
+
+ align:start position:0%
+python evaluates to a particular value
+ 
+
+ align:start position:0%
+python evaluates to a particular value
+and the value it evaluates it to is the
+
+ align:start position:0%
+and the value it evaluates it to is the
+ 
+
+ align:start position:0%
+and the value it evaluates it to is the
+character at that index so just to show
+
+ align:start position:0%
+character at that index so just to show
+ 
+
+ align:start position:0%
+character at that index so just to show
+you kind of what that looks like in here
+
+ align:start position:0%
+you kind of what that looks like in here
+ 
+
+ align:start position:0%
+you kind of what that looks like in here
+if s is equal to ABC all we would type
+
+ align:start position:0%
+if s is equal to ABC all we would type
+ 
+
+ align:start position:0%
+if s is equal to ABC all we would type
+is this s at index zero and this
+
+ align:start position:0%
+is this s at index zero and this
+ 
+
+ align:start position:0%
+is this s at index zero and this
+expression evaluates to that Single
+
+ align:start position:0%
+expression evaluates to that Single
+ 
+
+ align:start position:0%
+expression evaluates to that Single
+Character a okay s at index one b s at
+
+ align:start position:0%
+Character a okay s at index one b s at
+ 
+
+ align:start position:0%
+Character a okay s at index one b s at
+index 2 c s set index
+
+ align:start position:0%
+index 2 c s set index
+ 
+
+ align:start position:0%
+index 2 c s set index
+3 basically says what is the character
+
+ align:start position:0%
+3 basically says what is the character
+ 
+
+ align:start position:0%
+3 basically says what is the character
+at the fourth position well ABC only has
+
+ align:start position:0%
+at the fourth position well ABC only has
+ 
+
+ align:start position:0%
+at the fourth position well ABC only has
+three positions so this will actually
+
+ align:start position:0%
+three positions so this will actually
+ 
+
+ align:start position:0%
+three positions so this will actually
+give us our second error of the class an
+
+ align:start position:0%
+give us our second error of the class an
+ 
+
+ align:start position:0%
+give us our second error of the class an
+index error this is a pretty common
+
+ align:start position:0%
+index error this is a pretty common
+ 
+
+ align:start position:0%
+index error this is a pretty common
+error as we start working with more
+
+ align:start position:0%
+error as we start working with more
+ 
+
+ align:start position:0%
+error as we start working with more
+complex programs it basically means
+
+ align:start position:0%
+complex programs it basically means
+ 
+
+ align:start position:0%
+complex programs it basically means
+you've indexed too far into the list
+
+ align:start position:0%
+you've indexed too far into the list
+ 
+
+ align:start position:0%
+you've indexed too far into the list
+either to the right or to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left you can index into a list with
+
+ align:start position:0%
+left you can index into a list with
+ 
+
+ align:start position:0%
+left you can index into a list with
+negative indices as well so if you ever
+
+ align:start position:0%
+negative indices as well so if you ever
+ 
+
+ align:start position:0%
+negative indices as well so if you ever
+want to grab the character at the last
+
+ align:start position:0%
+want to grab the character at the last
+ 
+
+ align:start position:0%
+want to grab the character at the last
+position so at the rightmost place
+
+ align:start position:0%
+position so at the rightmost place
+ 
+
+ align:start position:0%
+position so at the rightmost place
+that's the character at index negative 1
+
+ align:start position:0%
+that's the character at index negative 1
+ 
+
+ align:start position:0%
+that's the character at index negative 1
+it's a really convenient way to grab
+
+ align:start position:0%
+it's a really convenient way to grab
+ 
+
+ align:start position:0%
+it's a really convenient way to grab
+that last character you basically ask
+
+ align:start position:0%
+that last character you basically ask
+ 
+
+ align:start position:0%
+that last character you basically ask
+what's s at1 and python automatically
+
+ align:start position:0%
+what's s at1 and python automatically
+ 
+
+ align:start position:0%
+what's s at1 and python automatically
+grabs for us that last character so we
+
+ align:start position:0%
+grabs for us that last character so we
+ 
+
+ align:start position:0%
+grabs for us that last character so we
+don't have to use an expression sort of
+
+ align:start position:0%
+don't have to use an expression sort of
+ 
+
+ align:start position:0%
+don't have to use an expression sort of
+like Len of
+
+ align:start position:0%
+like Len of
+ 
+
+ align:start position:0%
+like Len of
+S1 right that would be c as well and
+
+ align:start position:0%
+S1 right that would be c as well and
+ 
+
+ align:start position:0%
+S1 right that would be c as well and
+here I've inserted an expression lens s
+
+ align:start position:0%
+here I've inserted an expression lens s
+ 
+
+ align:start position:0%
+here I've inserted an expression lens s
+minus one directly in that index and
+
+ align:start position:0%
+minus one directly in that index and
+ 
+
+ align:start position:0%
+minus one directly in that index and
+that's totally fine again python
+
+ align:start position:0%
+that's totally fine again python
+ 
+
+ align:start position:0%
+that's totally fine again python
+evaluates things in to out left to right
+
+ align:start position:0%
+evaluates things in to out left to right
+ 
+
+ align:start position:0%
+evaluates things in to out left to right
+it evaluated Len s minus one to be two
+
+ align:start position:0%
+it evaluated Len s minus one to be two
+ 
+
+ align:start position:0%
+it evaluated Len s minus one to be two
+and basically this line became what s at
+
+ align:start position:0%
+and basically this line became what s at
+ 
+
+ align:start position:0%
+and basically this line became what s at
+index 2 which we knew was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c c uh because when you index into
+
+ align:start position:0%
+c c uh because when you index into
+ 
+
+ align:start position:0%
+c c uh because when you index into
+negative numbers the we start counting
+
+ align:start position:0%
+negative numbers the we start counting
+ 
+
+ align:start position:0%
+negative numbers the we start counting
+from the right hand side just python
+
+ align:start position:0%
+from the right hand side just python
+ 
+
+ align:start position:0%
+from the right hand side just python
+convention
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and so s at -4 will give us an
+
+ align:start position:0%
+yeah and so s at -4 will give us an
+ 
+
+ align:start position:0%
+yeah and so s at -4 will give us an
+error as well because now we're indexing
+
+ align:start position:0%
+error as well because now we're indexing
+ 
+
+ align:start position:0%
+error as well because now we're indexing
+too far to the left there's nothing
+
+ align:start position:0%
+too far to the left there's nothing
+ 
+
+ align:start position:0%
+too far to the left there's nothing
+there okay so we can index to get single
+
+ align:start position:0%
+there okay so we can index to get single
+ 
+
+ align:start position:0%
+there okay so we can index to get single
+characters that's fine we just use
+
+ align:start position:0%
+characters that's fine we just use
+ 
+
+ align:start position:0%
+characters that's fine we just use
+square bracket and say the index that
+
+ align:start position:0%
+square bracket and say the index that
+ 
+
+ align:start position:0%
+square bracket and say the index that
+we'd like to get the character at we can
+
+ align:start position:0%
+we'd like to get the character at we can
+ 
+
+ align:start position:0%
+we'd like to get the character at we can
+also slice to get substrings so instead
+
+ align:start position:0%
+also slice to get substrings so instead
+ 
+
+ align:start position:0%
+also slice to get substrings so instead
+of getting single characters we can ask
+
+ align:start position:0%
+of getting single characters we can ask
+ 
+
+ align:start position:0%
+of getting single characters we can ask
+python to get us a substring starting
+
+ align:start position:0%
+python to get us a substring starting
+ 
+
+ align:start position:0%
+python to get us a substring starting
+from one index going up to some other
+
+ align:start position:0%
+from one index going up to some other
+ 
+
+ align:start position:0%
+from one index going up to some other
+index and potentially skipping
+
+ align:start position:0%
+index and potentially skipping
+ 
+
+ align:start position:0%
+index and potentially skipping
+characters you can take every character
+
+ align:start position:0%
+characters you can take every character
+ 
+
+ align:start position:0%
+characters you can take every character
+along the way you can skip every other
+
+ align:start position:0%
+along the way you can skip every other
+ 
+
+ align:start position:0%
+along the way you can skip every other
+character or some other um you know some
+
+ align:start position:0%
+character or some other um you know some
+ 
+
+ align:start position:0%
+character or some other um you know some
+other uh pattern like
+
+ align:start position:0%
+other uh pattern like
+ 
+
+ align:start position:0%
+other uh pattern like
+that the syntax for that is similar to
+
+ align:start position:0%
+that the syntax for that is similar to
+ 
+
+ align:start position:0%
+that the syntax for that is similar to
+slicing to get a A Single Character
+
+ align:start position:0%
+slicing to get a A Single Character
+ 
+
+ align:start position:0%
+slicing to get a A Single Character
+slightly different though it's similar
+
+ align:start position:0%
+slightly different though it's similar
+ 
+
+ align:start position:0%
+slightly different though it's similar
+in that we have square brackets
+
+ align:start position:0%
+in that we have square brackets
+ 
+
+ align:start position:0%
+in that we have square brackets
+involved slightly different because now
+
+ align:start position:0%
+involved slightly different because now
+ 
+
+ align:start position:0%
+involved slightly different because now
+we have to give three numbers within
+
+ align:start position:0%
+we have to give three numbers within
+ 
+
+ align:start position:0%
+we have to give three numbers within
+those square
+
+ align:start position:0%
+those square
+ 
+
+ align:start position:0%
+those square
+brackets separated by
+
+ align:start position:0%
+brackets separated by
+ 
+
+ align:start position:0%
+brackets separated by
+colons the first number number will
+
+ align:start position:0%
+colons the first number number will
+ 
+
+ align:start position:0%
+colons the first number number will
+represent what's the start index so
+
+ align:start position:0%
+represent what's the start index so
+ 
+
+ align:start position:0%
+represent what's the start index so
+where do you want to start your
+
+ align:start position:0%
+where do you want to start your
+ 
+
+ align:start position:0%
+where do you want to start your
+substring from the second is what's the
+
+ align:start position:0%
+substring from the second is what's the
+ 
+
+ align:start position:0%
+substring from the second is what's the
+stop index so we're going to take every
+
+ align:start position:0%
+stop index so we're going to take every
+ 
+
+ align:start position:0%
+stop index so we're going to take every
+character from that start index going
+
+ align:start position:0%
+character from that start index going
+ 
+
+ align:start position:0%
+character from that start index going
+all the way up to but not including the
+
+ align:start position:0%
+all the way up to but not including the
+ 
+
+ align:start position:0%
+all the way up to but not including the
+stop okay and the step means how many
+
+ align:start position:0%
+stop okay and the step means how many
+ 
+
+ align:start position:0%
+stop okay and the step means how many
+characters do we skip so if the step is
+
+ align:start position:0%
+characters do we skip so if the step is
+ 
+
+ align:start position:0%
+characters do we skip so if the step is
+one we're taking every character if the
+
+ align:start position:0%
+one we're taking every character if the
+ 
+
+ align:start position:0%
+one we're taking every character if the
+step is two we'll take every other
+
+ align:start position:0%
+step is two we'll take every other
+ 
+
+ align:start position:0%
+step is two we'll take every other
+character the step is three we skip
+
+ align:start position:0%
+character the step is three we skip
+ 
+
+ align:start position:0%
+character the step is three we skip
+every uh every two characters and so on
+
+ align:start position:0%
+every uh every two characters and so on
+ 
+
+ align:start position:0%
+every uh every two characters and so on
+now there's a bunch of combinations we
+
+ align:start position:0%
+now there's a bunch of combinations we
+ 
+
+ align:start position:0%
+now there's a bunch of combinations we
+can do within these uh with these three
+
+ align:start position:0%
+can do within these uh with these three
+ 
+
+ align:start position:0%
+can do within these uh with these three
+um three numbers within the square
+
+ align:start position:0%
+um three numbers within the square
+ 
+
+ align:start position:0%
+um three numbers within the square
+brackets uh that you'll you know as you
+
+ align:start position:0%
+brackets uh that you'll you know as you
+ 
+
+ align:start position:0%
+brackets uh that you'll you know as you
+work with these with these exercises um
+
+ align:start position:0%
+work with these with these exercises um
+ 
+
+ align:start position:0%
+work with these with these exercises um
+you'll sort of get the hang of for now
+
+ align:start position:0%
+you'll sort of get the hang of for now
+ 
+
+ align:start position:0%
+you'll sort of get the hang of for now
+it won't hurt to always give it a start
+
+ align:start position:0%
+it won't hurt to always give it a start
+ 
+
+ align:start position:0%
+it won't hurt to always give it a start
+a stop and a step that's perfectly fine
+
+ align:start position:0%
+a stop and a step that's perfectly fine
+ 
+
+ align:start position:0%
+a stop and a step that's perfectly fine
+but something that's really common if
+
+ align:start position:0%
+but something that's really common if
+ 
+
+ align:start position:0%
+but something that's really common if
+you're always going to take every single
+
+ align:start position:0%
+you're always going to take every single
+ 
+
+ align:start position:0%
+you're always going to take every single
+character is to just omit the step part
+
+ align:start position:0%
+character is to just omit the step part
+ 
+
+ align:start position:0%
+character is to just omit the step part
+so if you just give it two numbers
+
+ align:start position:0%
+so if you just give it two numbers
+ 
+
+ align:start position:0%
+so if you just give it two numbers
+number colon number python automatically
+
+ align:start position:0%
+number colon number python automatically
+ 
+
+ align:start position:0%
+number colon number python automatically
+knows that your step will be one by
+
+ align:start position:0%
+knows that your step will be one by
+ 
+
+ align:start position:0%
+knows that your step will be one by
+default so you're not skipping anything
+
+ align:start position:0%
+default so you're not skipping anything
+ 
+
+ align:start position:0%
+default so you're not skipping anything
+okay if you're just giving it one number
+
+ align:start position:0%
+okay if you're just giving it one number
+ 
+
+ align:start position:0%
+okay if you're just giving it one number
+no colons we back to the previous slide
+
+ align:start position:0%
+no colons we back to the previous slide
+ 
+
+ align:start position:0%
+no colons we back to the previous slide
+right where we're just grabbing one
+
+ align:start position:0%
+right where we're just grabbing one
+ 
+
+ align:start position:0%
+right where we're just grabbing one
+element and I know this is going to be a
+
+ align:start position:0%
+element and I know this is going to be a
+ 
+
+ align:start position:0%
+element and I know this is going to be a
+little confusing we're going to look at
+
+ align:start position:0%
+little confusing we're going to look at
+ 
+
+ align:start position:0%
+little confusing we're going to look at
+an example on the next slide but this is
+
+ align:start position:0%
+an example on the next slide but this is
+ 
+
+ align:start position:0%
+an example on the next slide but this is
+something you'll just have to practice a
+
+ align:start position:0%
+something you'll just have to practice a
+ 
+
+ align:start position:0%
+something you'll just have to practice a
+little bit on the shell um with the
+
+ align:start position:0%
+little bit on the shell um with the
+ 
+
+ align:start position:0%
+little bit on the shell um with the
+following example hopefully just you
+
+ align:start position:0%
+following example hopefully just you
+ 
+
+ align:start position:0%
+following example hopefully just you
+know just when you go home um just to
+
+ align:start position:0%
+know just when you go home um just to
+ 
+
+ align:start position:0%
+know just when you go home um just to
+kind of make sure that you understand
+
+ align:start position:0%
+kind of make sure that you understand
+ 
+
+ align:start position:0%
+kind of make sure that you understand
+what it's doing if you're have a
+
+ align:start position:0%
+what it's doing if you're have a
+ 
+
+ align:start position:0%
+what it's doing if you're have a
+question like what if I put in this
+
+ align:start position:0%
+question like what if I put in this
+ 
+
+ align:start position:0%
+question like what if I put in this
+number or this number just put it in the
+
+ align:start position:0%
+number or this number just put it in the
+ 
+
+ align:start position:0%
+number or this number just put it in the
+shell and see what happens
+
+ align:start position:0%
+shell and see what happens
+ 
+
+ align:start position:0%
+shell and see what happens
+so let's take a look at a couple of
+
+ align:start position:0%
+so let's take a look at a couple of
+ 
+
+ align:start position:0%
+so let's take a look at a couple of
+examples so how do we slice to get
+
+ align:start position:0%
+examples so how do we slice to get
+ 
+
+ align:start position:0%
+examples so how do we slice to get
+substrings let's say our string is this
+
+ align:start position:0%
+substrings let's say our string is this
+ 
+
+ align:start position:0%
+substrings let's say our string is this
+longer thing a b CDE E F G H when we
+
+ align:start position:0%
+longer thing a b CDE E F G H when we
+ 
+
+ align:start position:0%
+longer thing a b CDE E F G H when we
+slice the first thing we want to look at
+
+ align:start position:0%
+slice the first thing we want to look at
+ 
+
+ align:start position:0%
+slice the first thing we want to look at
+is the step is it positive or negative
+
+ align:start position:0%
+is the step is it positive or negative
+ 
+
+ align:start position:0%
+is the step is it positive or negative
+if it's positive and remember if you
+
+ align:start position:0%
+if it's positive and remember if you
+ 
+
+ align:start position:0%
+if it's positive and remember if you
+omit it by default it's plus one so if
+
+ align:start position:0%
+omit it by default it's plus one so if
+ 
+
+ align:start position:0%
+omit it by default it's plus one so if
+it's positive we're going to work our
+
+ align:start position:0%
+it's positive we're going to work our
+ 
+
+ align:start position:0%
+it's positive we're going to work our
+way left to right right the way we read
+
+ align:start position:0%
+way left to right right the way we read
+ 
+
+ align:start position:0%
+way left to right right the way we read
+if it's negative we're going to work our
+
+ align:start position:0%
+if it's negative we're going to work our
+ 
+
+ align:start position:0%
+if it's negative we're going to work our
+way right to left
+
+ align:start position:0%
+way right to left
+ 
+
+ align:start position:0%
+way right to left
+so what if we index s from 3 colum 6 the
+
+ align:start position:0%
+so what if we index s from 3 colum 6 the
+ 
+
+ align:start position:0%
+so what if we index s from 3 colum 6 the
+step is positive one so we're going to
+
+ align:start position:0%
+step is positive one so we're going to
+ 
+
+ align:start position:0%
+step is positive one so we're going to
+work our way left to right so that means
+
+ align:start position:0%
+work our way left to right so that means
+ 
+
+ align:start position:0%
+work our way left to right so that means
+we're going to start at index three so
+
+ align:start position:0%
+we're going to start at index three so
+ 
+
+ align:start position:0%
+we're going to start at index three so
+that's the D so we're going to grab the
+
+ align:start position:0%
+that's the D so we're going to grab the
+ 
+
+ align:start position:0%
+that's the D so we're going to grab the
+D and we're going to go up to get the
+
+ align:start position:0%
+D and we're going to go up to get the
+ 
+
+ align:start position:0%
+D and we're going to go up to get the
+substring from D up to but not including
+
+ align:start position:0%
+substring from D up to but not including
+ 
+
+ align:start position:0%
+substring from D up to but not including
+the character at index
+
+ align:start position:0%
+the character at index
+ 
+
+ align:start position:0%
+the character at index
+six the H the G sorry the g okay so the
+
+ align:start position:0%
+six the H the G sorry the g okay so the
+ 
+
+ align:start position:0%
+six the H the G sorry the g okay so the
+characters we're going to grab are the D
+
+ align:start position:0%
+characters we're going to grab are the D
+ 
+
+ align:start position:0%
+characters we're going to grab are the D
+the E and the F right we started step
+
+ align:start position:0%
+the E and the F right we started step
+ 
+
+ align:start position:0%
+the E and the F right we started step
+three we go up to but not including six
+
+ align:start position:0%
+three we go up to but not including six
+ 
+
+ align:start position:0%
+three we go up to but not including six
+taking every character because the step
+
+ align:start position:0%
+taking every character because the step
+ 
+
+ align:start position:0%
+taking every character because the step
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+one what if the step was two so same
+
+ align:start position:0%
+one what if the step was two so same
+ 
+
+ align:start position:0%
+one what if the step was two so same
+thing as we just did except the step is
+
+ align:start position:0%
+thing as we just did except the step is
+ 
+
+ align:start position:0%
+thing as we just did except the step is
+two again the step is positive so we're
+
+ align:start position:0%
+two again the step is positive so we're
+ 
+
+ align:start position:0%
+two again the step is positive so we're
+going to work work our way left to right
+
+ align:start position:0%
+going to work work our way left to right
+ 
+
+ align:start position:0%
+going to work work our way left to right
+we're going to start at index three so
+
+ align:start position:0%
+we're going to start at index three so
+ 
+
+ align:start position:0%
+we're going to start at index three so
+we're going to grab the D and we're
+
+ align:start position:0%
+we're going to grab the D and we're
+ 
+
+ align:start position:0%
+we're going to grab the D and we're
+going to create a new object which is
+
+ align:start position:0%
+going to create a new object which is
+ 
+
+ align:start position:0%
+going to create a new object which is
+going to be the the characters D we're
+
+ align:start position:0%
+going to be the the characters D we're
+ 
+
+ align:start position:0%
+going to be the the characters D we're
+going to skip the E because the step is
+
+ align:start position:0%
+going to skip the E because the step is
+ 
+
+ align:start position:0%
+going to skip the E because the step is
+two take the
+
+ align:start position:0%
+two take the
+ 
+
+ align:start position:0%
+two take the
+F and that's it we've worked our way up
+
+ align:start position:0%
+F and that's it we've worked our way up
+ 
+
+ align:start position:0%
+F and that's it we've worked our way up
+to but not not including the element at
+
+ align:start position:0%
+to but not not including the element at
+ 
+
+ align:start position:0%
+to but not not including the element at
+index
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+six there are some other things uh uh I
+
+ align:start position:0%
+six there are some other things uh uh I
+ 
+
+ align:start position:0%
+six there are some other things uh uh I
+guess tricks or you might want to call
+
+ align:start position:0%
+guess tricks or you might want to call
+ 
+
+ align:start position:0%
+guess tricks or you might want to call
+them that you can do so if we just put
+
+ align:start position:0%
+them that you can do so if we just put
+ 
+
+ align:start position:0%
+them that you can do so if we just put
+an empty colon here that says just make
+
+ align:start position:0%
+an empty colon here that says just make
+ 
+
+ align:start position:0%
+an empty colon here that says just make
+the same object again so that will
+
+ align:start position:0%
+the same object again so that will
+ 
+
+ align:start position:0%
+the same object again so that will
+evaluate to just ABCD E F G
+
+ align:start position:0%
+evaluate to just ABCD E F G
+ 
+
+ align:start position:0%
+evaluate to just ABCD E F G
+again if we do colon
+
+ align:start position:0%
+again if we do colon
+ 
+
+ align:start position:0%
+again if we do colon
+colon1 this is shorthand notation for
+
+ align:start position:0%
+colon1 this is shorthand notation for
+ 
+
+ align:start position:0%
+colon1 this is shorthand notation for
+basically grabbing for me the string
+
+ align:start position:0%
+basically grabbing for me the string
+ 
+
+ align:start position:0%
+basically grabbing for me the string
+backward so h g f e d c b a right just
+
+ align:start position:0%
+backward so h g f e d c b a right just
+ 
+
+ align:start position:0%
+backward so h g f e d c b a right just
+make the same string as the original one
+
+ align:start position:0%
+make the same string as the original one
+ 
+
+ align:start position:0%
+make the same string as the original one
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+backward and we can do something like
+
+ align:start position:0%
+backward and we can do something like
+ 
+
+ align:start position:0%
+backward and we can do something like
+this for one with a step
+
+ align:start position:0%
+this for one with a step
+ 
+
+ align:start position:0%
+this for one with a step
+-2 now the step is negative right so
+
+ align:start position:0%
+-2 now the step is negative right so
+ 
+
+ align:start position:0%
+-2 now the step is negative right so
+that means we're going to work our way
+
+ align:start position:0%
+that means we're going to work our way
+ 
+
+ align:start position:0%
+that means we're going to work our way
+right to left we're going to start at
+
+ align:start position:0%
+right to left we're going to start at
+ 
+
+ align:start position:0%
+right to left we're going to start at
+index 4 so we're going to grab the
+
+ align:start position:0%
+index 4 so we're going to grab the
+ 
+
+ align:start position:0%
+index 4 so we're going to grab the
+E we're going to skip every other
+
+ align:start position:0%
+E we're going to skip every other
+ 
+
+ align:start position:0%
+E we're going to skip every other
+character so we're not going to take the
+
+ align:start position:0%
+character so we're not going to take the
+ 
+
+ align:start position:0%
+character so we're not going to take the
+d but we will take the C and we're going
+
+ align:start position:0%
+d but we will take the C and we're going
+ 
+
+ align:start position:0%
+d but we will take the C and we're going
+to go down to but not including the
+
+ align:start position:0%
+to go down to but not including the
+ 
+
+ align:start position:0%
+to go down to but not including the
+character at index one so we're going to
+
+ align:start position:0%
+character at index one so we're going to
+ 
+
+ align:start position:0%
+character at index one so we're going to
+stop right here so the characters we
+
+ align:start position:0%
+stop right here so the characters we
+ 
+
+ align:start position:0%
+stop right here so the characters we
+took in this order were e and then C so
+
+ align:start position:0%
+took in this order were e and then C so
+ 
+
+ align:start position:0%
+took in this order were e and then C so
+this entire expression evaluates to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+EC yes question we D why did we skip D
+
+ align:start position:0%
+EC yes question we D why did we skip D
+ 
+
+ align:start position:0%
+EC yes question we D why did we skip D
+because the step is two so when the step
+
+ align:start position:0%
+because the step is two so when the step
+ 
+
+ align:start position:0%
+because the step is two so when the step
+is one we take every character the step
+
+ align:start position:0%
+is one we take every character the step
+ 
+
+ align:start position:0%
+is one we take every character the step
+is two skip every other one yeah for the
+
+ align:start position:0%
+is two skip every other one yeah for the
+ 
+
+ align:start position:0%
+is two skip every other one yeah for the
+first one S3 to why is G not included G
+
+ align:start position:0%
+first one S3 to why is G not included G
+ 
+
+ align:start position:0%
+first one S3 to why is G not included G
+is not included just by definition we go
+
+ align:start position:0%
+is not included just by definition we go
+ 
+
+ align:start position:0%
+is not included just by definition we go
+up to but not including the stop so
+
+ align:start position:0%
+up to but not including the stop so
+ 
+
+ align:start position:0%
+up to but not including the stop so
+we'll go up to but not including the the
+
+ align:start position:0%
+we'll go up to but not including the the
+ 
+
+ align:start position:0%
+we'll go up to but not including the the
+character at index
+
+ align:start position:0%
+character at index
+ 
+
+ align:start position:0%
+character at index
+six that's just the definition of
+
+ align:start position:0%
+six that's just the definition of
+ 
+
+ align:start position:0%
+six that's just the definition of
+slicing in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Python so up to an including stop minus
+
+ align:start position:0%
+Python so up to an including stop minus
+ 
+
+ align:start position:0%
+Python so up to an including stop minus
+one means we go up to an including five
+
+ align:start position:0%
+one means we go up to an including five
+ 
+
+ align:start position:0%
+one means we go up to an including five
+right yeah exactly yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so again if you're unsure what a
+
+ align:start position:0%
+okay so again if you're unsure what a
+ 
+
+ align:start position:0%
+okay so again if you're unsure what a
+com a command does always try you can
+
+ align:start position:0%
+com a command does always try you can
+ 
+
+ align:start position:0%
+com a command does always try you can
+always try it in your console right the
+
+ align:start position:0%
+always try it in your console right the
+ 
+
+ align:start position:0%
+always try it in your console right the
+shell and um here's an opportunity to do
+
+ align:start position:0%
+shell and um here's an opportunity to do
+ 
+
+ align:start position:0%
+shell and um here's an opportunity to do
+that so here's a string s
+
+ align:start position:0%
+that so here's a string s
+ 
+
+ align:start position:0%
+that so here's a string s
+ABC d3f and I'm actually going to write
+
+ align:start position:0%
+ABC d3f and I'm actually going to write
+ 
+
+ align:start position:0%
+ABC d3f and I'm actually going to write
+this one down just ABC space right
+
+ align:start position:0%
+this one down just ABC space right
+ 
+
+ align:start position:0%
+this one down just ABC space right
+there's a space here 3D what I do or d3f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then another space and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ghi so what do you guys think the first
+
+ align:start position:0%
+ghi so what do you guys think the first
+ 
+
+ align:start position:0%
+ghi so what do you guys think the first
+one will be three colon Len s minus one
+
+ align:start position:0%
+one will be three colon Len s minus one
+ 
+
+ align:start position:0%
+one will be three colon Len s minus one
+I'll even do the indices here for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start yeah the space exactly so it's
+
+ align:start position:0%
+start yeah the space exactly so it's
+ 
+
+ align:start position:0%
+start yeah the space exactly so it's
+going to be a little space
+
+ align:start position:0%
+going to be a little space
+ 
+
+ align:start position:0%
+going to be a little space
+what is len s minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one 10 yeah what's the length how many
+
+ align:start position:0%
+one 10 yeah what's the length how many
+ 
+
+ align:start position:0%
+one 10 yeah what's the length how many
+characters are in here 11 yep and - one
+
+ align:start position:0%
+characters are in here 11 yep and - one
+ 
+
+ align:start position:0%
+characters are in here 11 yep and - one
+is 10 so when we do this when the stop
+
+ align:start position:0%
+is 10 so when we do this when the stop
+ 
+
+ align:start position:0%
+is 10 so when we do this when the stop
+is 10 that means we're going to go up to
+
+ align:start position:0%
+is 10 that means we're going to go up to
+ 
+
+ align:start position:0%
+is 10 that means we're going to go up to
+but not including the character at 10 so
+
+ align:start position:0%
+but not including the character at 10 so
+ 
+
+ align:start position:0%
+but not including the character at 10 so
+we're going to go up to this H right so
+
+ align:start position:0%
+we're going to go up to this H right so
+ 
+
+ align:start position:0%
+we're going to go up to this H right so
+we're going to take the space d 3 f
+
+ align:start position:0%
+we're going to take the space d 3 f
+ 
+
+ align:start position:0%
+we're going to take the space d 3 f
+space g h and we
+
+ align:start position:0%
+space g h and we
+ 
+
+ align:start position:0%
+space g h and we
+stop yeah why do we start at zero again
+
+ align:start position:0%
+stop yeah why do we start at zero again
+ 
+
+ align:start position:0%
+stop yeah why do we start at zero again
+convention computer science
+
+ align:start position:0%
+convention computer science
+ 
+
+ align:start position:0%
+convention computer science
+programming except for mat lab I think
+
+ align:start position:0%
+programming except for mat lab I think
+ 
+
+ align:start position:0%
+programming except for mat lab I think
+they still start indexing it
+
+ align:start position:0%
+they still start indexing it
+ 
+
+ align:start position:0%
+they still start indexing it
+one other questions about this one is
+
+ align:start position:0%
+one other questions about this one is
+ 
+
+ align:start position:0%
+one other questions about this one is
+that all
+
+ align:start position:0%
+that all
+ 
+
+ align:start position:0%
+that all
+right okay how about the next one S4
+
+ align:start position:0%
+right okay how about the next one S4
+ 
+
+ align:start position:0%
+right okay how about the next one S4
+colon Z colon negative 1 what's the
+
+ align:start position:0%
+colon Z colon negative 1 what's the
+ 
+
+ align:start position:0%
+colon Z colon negative 1 what's the
+element at index four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the D yep so we're going to grab the
+
+ align:start position:0%
+the D yep so we're going to grab the
+ 
+
+ align:start position:0%
+the D yep so we're going to grab the
+D are we working our way right or to the
+
+ align:start position:0%
+D are we working our way right or to the
+ 
+
+ align:start position:0%
+D are we working our way right or to the
+right or to the left yeah exactly so
+
+ align:start position:0%
+right or to the left yeah exactly so
+ 
+
+ align:start position:0%
+right or to the left yeah exactly so
+we're going to go up to but not
+
+ align:start position:0%
+we're going to go up to but not
+ 
+
+ align:start position:0%
+we're going to go up to but not
+including the character index zero so
+
+ align:start position:0%
+including the character index zero so
+ 
+
+ align:start position:0%
+including the character index zero so
+we're going to get the D the space it's
+
+ align:start position:0%
+we're going to get the D the space it's
+ 
+
+ align:start position:0%
+we're going to get the D the space it's
+the C the
+
+ align:start position:0%
+the C the
+ 
+
+ align:start position:0%
+the C the
+B am I taking the a no exactly so that's
+
+ align:start position:0%
+B am I taking the a no exactly so that's
+ 
+
+ align:start position:0%
+B am I taking the a no exactly so that's
+it d space
+
+ align:start position:0%
+it d space
+ 
+
+ align:start position:0%
+it d space
+CB yes want to include the a would uh
+
+ align:start position:0%
+CB yes want to include the a would uh
+ 
+
+ align:start position:0%
+CB yes want to include the a would uh
+the second value
+
+ align:start position:0%
+the second value
+ 
+
+ align:start position:0%
+the second value
+if you did want to include the a
+
+ align:start position:0%
+if you did want to include the a
+ 
+
+ align:start position:0%
+if you did want to include the a
+actually you would want to do something
+
+ align:start position:0%
+actually you would want to do something
+ 
+
+ align:start position:0%
+actually you would want to do something
+different I think it you can't go to
+
+ align:start position:0%
+different I think it you can't go to
+ 
+
+ align:start position:0%
+different I think it you can't go to
+negative one because negative one is
+
+ align:start position:0%
+negative one because negative one is
+ 
+
+ align:start position:0%
+negative one because negative one is
+actually this right here that's a good
+
+ align:start position:0%
+actually this right here that's a good
+ 
+
+ align:start position:0%
+actually this right here that's a good
+question I'd have to try it out um play
+
+ align:start position:0%
+question I'd have to try it out um play
+ 
+
+ align:start position:0%
+question I'd have to try it out um play
+around with it but if you want to
+
+ align:start position:0%
+around with it but if you want to
+ 
+
+ align:start position:0%
+around with it but if you want to
+include it I think maybe you would just
+
+ align:start position:0%
+include it I think maybe you would just
+ 
+
+ align:start position:0%
+include it I think maybe you would just
+do an empty sorry go
+
+ align:start position:0%
+do an empty sorry go
+ 
+
+ align:start position:0%
+do an empty sorry go
+ahead you just probably do an empty
+
+ align:start position:0%
+ahead you just probably do an empty
+ 
+
+ align:start position:0%
+ahead you just probably do an empty
+colon and by default that means the
+
+ align:start position:0%
+colon and by default that means the
+ 
+
+ align:start position:0%
+colon and by default that means the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+but I'd have to try it out
+
+ align:start position:0%
+but I'd have to try it out
+ 
+
+ align:start position:0%
+but I'd have to try it out
+yeah how about the last one uh six colon
+
+ align:start position:0%
+yeah how about the last one uh six colon
+ 
+
+ align:start position:0%
+yeah how about the last one uh six colon
+3 what's the element at index six the
+
+ align:start position:0%
+3 what's the element at index six the
+ 
+
+ align:start position:0%
+3 what's the element at index six the
+empty work empty Colon work okay perfect
+
+ align:start position:0%
+empty work empty Colon work okay perfect
+ 
+
+ align:start position:0%
+empty work empty Colon work okay perfect
+thanks for trying it out the empty colon
+
+ align:start position:0%
+thanks for trying it out the empty colon
+ 
+
+ align:start position:0%
+thanks for trying it out the empty colon
+works yeah if you wanted to grab the a
+
+ align:start position:0%
+works yeah if you wanted to grab the a
+ 
+
+ align:start position:0%
+works yeah if you wanted to grab the a
+all right so S6 colon 3 what's the
+
+ align:start position:0%
+all right so S6 colon 3 what's the
+ 
+
+ align:start position:0%
+all right so S6 colon 3 what's the
+element at index six F the F okay great
+
+ align:start position:0%
+element at index six F the F okay great
+ 
+
+ align:start position:0%
+element at index six F the F okay great
+and we're working our way to the right
+
+ align:start position:0%
+and we're working our way to the right
+ 
+
+ align:start position:0%
+and we're working our way to the right
+or to the
+
+ align:start position:0%
+or to the
+ 
+
+ align:start position:0%
+or to the
+left to the right okay so we're going to
+
+ align:start position:0%
+left to the right okay so we're going to
+ 
+
+ align:start position:0%
+left to the right okay so we're going to
+start here but we need to go this way
+
+ align:start position:0%
+start here but we need to go this way
+ 
+
+ align:start position:0%
+start here but we need to go this way
+but what's the stop
+
+ align:start position:0%
+but what's the stop
+ 
+
+ align:start position:0%
+but what's the stop
+index yeah it's not there it's behind
+
+ align:start position:0%
+index yeah it's not there it's behind
+ 
+
+ align:start position:0%
+index yeah it's not there it's behind
+us so this last one is actually an empty
+
+ align:start position:0%
+us so this last one is actually an empty
+ 
+
+ align:start position:0%
+us so this last one is actually an empty
+string and I'll even we can even we can
+
+ align:start position:0%
+string and I'll even we can even we can
+ 
+
+ align:start position:0%
+string and I'll even we can even we can
+try it with something else too um so if
+
+ align:start position:0%
+try it with something else too um so if
+ 
+
+ align:start position:0%
+try it with something else too um so if
+we have this ABC right if I'm indexing
+
+ align:start position:0%
+we have this ABC right if I'm indexing
+ 
+
+ align:start position:0%
+we have this ABC right if I'm indexing
+starting from Two and I'm going backward
+
+ align:start position:0%
+starting from Two and I'm going backward
+ 
+
+ align:start position:0%
+starting from Two and I'm going backward
+to zero then that gives me the empty
+
+ align:start position:0%
+to zero then that gives me the empty
+ 
+
+ align:start position:0%
+to zero then that gives me the empty
+string and the empty string is just
+
+ align:start position:0%
+string and the empty string is just
+ 
+
+ align:start position:0%
+string and the empty string is just
+quote quote with nothing
+
+ align:start position:0%
+quote quote with nothing
+ 
+
+ align:start position:0%
+quote quote with nothing
+inside so that means we didn't take any
+
+ align:start position:0%
+inside so that means we didn't take any
+ 
+
+ align:start position:0%
+inside so that means we didn't take any
+characters in that particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case is that right it's invalid it's
+
+ align:start position:0%
+case is that right it's invalid it's
+ 
+
+ align:start position:0%
+case is that right it's invalid it's
+valid we just there are no characters in
+
+ align:start position:0%
+valid we just there are no characters in
+ 
+
+ align:start position:0%
+valid we just there are no characters in
+between the F and behind the F
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so I'll mention the strings
+
+ align:start position:0%
+yeah okay so I'll mention the strings
+ 
+
+ align:start position:0%
+yeah okay so I'll mention the strings
+are actually immutable objects and
+
+ align:start position:0%
+are actually immutable objects and
+ 
+
+ align:start position:0%
+are actually immutable objects and
+really a lot of the objects we've seen
+
+ align:start position:0%
+really a lot of the objects we've seen
+ 
+
+ align:start position:0%
+really a lot of the objects we've seen
+so far are immutable that means they
+
+ align:start position:0%
+so far are immutable that means they
+ 
+
+ align:start position:0%
+so far are immutable that means they
+can't be modified once they're created
+
+ align:start position:0%
+can't be modified once they're created
+ 
+
+ align:start position:0%
+can't be modified once they're created
+we've kind of seen this already right
+
+ align:start position:0%
+we've kind of seen this already right
+ 
+
+ align:start position:0%
+we've kind of seen this already right
+when I draw the memory diagrams when I
+
+ align:start position:0%
+when I draw the memory diagrams when I
+ 
+
+ align:start position:0%
+when I draw the memory diagrams when I
+create a new object which is you know
+
+ align:start position:0%
+create a new object which is you know
+ 
+
+ align:start position:0%
+create a new object which is you know
+for example what's the string version of
+
+ align:start position:0%
+for example what's the string version of
+ 
+
+ align:start position:0%
+for example what's the string version of
+this integer or you know when I cast a
+
+ align:start position:0%
+this integer or you know when I cast a
+ 
+
+ align:start position:0%
+this integer or you know when I cast a
+float to an in things like that I'm not
+
+ align:start position:0%
+float to an in things like that I'm not
+ 
+
+ align:start position:0%
+float to an in things like that I'm not
+changing those original objects I've
+
+ align:start position:0%
+changing those original objects I've
+ 
+
+ align:start position:0%
+changing those original objects I've
+created I'm just making a new little
+
+ align:start position:0%
+created I'm just making a new little
+ 
+
+ align:start position:0%
+created I'm just making a new little
+green box in my memory and reassigning
+
+ align:start position:0%
+green box in my memory and reassigning
+ 
+
+ align:start position:0%
+green box in my memory and reassigning
+the name and we're going to see later on
+
+ align:start position:0%
+the name and we're going to see later on
+ 
+
+ align:start position:0%
+the name and we're going to see later on
+in this course mutable objects which
+
+ align:start position:0%
+in this course mutable objects which
+ 
+
+ align:start position:0%
+in this course mutable objects which
+means that once you create them in
+
+ align:start position:0%
+means that once you create them in
+ 
+
+ align:start position:0%
+means that once you create them in
+memory you can modify them but for now
+
+ align:start position:0%
+memory you can modify them but for now
+ 
+
+ align:start position:0%
+memory you can modify them but for now
+anytime you make a change to such an
+
+ align:start position:0%
+anytime you make a change to such an
+ 
+
+ align:start position:0%
+anytime you make a change to such an
+object well you can't change the object
+
+ align:start position:0%
+object well you can't change the object
+ 
+
+ align:start position:0%
+object well you can't change the object
+right if you want to get a different
+
+ align:start position:0%
+right if you want to get a different
+ 
+
+ align:start position:0%
+right if you want to get a different
+version of the object python will create
+
+ align:start position:0%
+version of the object python will create
+ 
+
+ align:start position:0%
+version of the object python will create
+a new object in memory and you can
+
+ align:start position:0%
+a new object in memory and you can
+ 
+
+ align:start position:0%
+a new object in memory and you can
+reassign the variable to that new object
+
+ align:start position:0%
+reassign the variable to that new object
+ 
+
+ align:start position:0%
+reassign the variable to that new object
+so in this example if I want to grab uh
+
+ align:start position:0%
+so in this example if I want to grab uh
+ 
+
+ align:start position:0%
+so in this example if I want to grab uh
+if I have the uh the string C in memory
+
+ align:start position:0%
+if I have the uh the string C in memory
+ 
+
+ align:start position:0%
+if I have the uh the string C in memory
+like this and it's bound to variable s
+
+ align:start position:0%
+like this and it's bound to variable s
+ 
+
+ align:start position:0%
+like this and it's bound to variable s
+and I want to change the first letter to
+
+ align:start position:0%
+and I want to change the first letter to
+ 
+
+ align:start position:0%
+and I want to change the first letter to
+a b I'm not allowed to python won't let
+
+ align:start position:0%
+a b I'm not allowed to python won't let
+ 
+
+ align:start position:0%
+a b I'm not allowed to python won't let
+me do something like I want to change
+
+ align:start position:0%
+me do something like I want to change
+ 
+
+ align:start position:0%
+me do something like I want to change
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh the letter at index zero to B that's
+
+ align:start position:0%
+uh the letter at index zero to B that's
+ 
+
+ align:start position:0%
+uh the letter at index zero to B that's
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+allowed you can get new versions of that
+
+ align:start position:0%
+allowed you can get new versions of that
+ 
+
+ align:start position:0%
+allowed you can get new versions of that
+particular string so you can do some you
+
+ align:start position:0%
+particular string so you can do some you
+ 
+
+ align:start position:0%
+particular string so you can do some you
+know random uh expression to create the
+
+ align:start position:0%
+know random uh expression to create the
+ 
+
+ align:start position:0%
+know random uh expression to create the
+bar that you might want but then the C
+
+ align:start position:0%
+bar that you might want but then the C
+ 
+
+ align:start position:0%
+bar that you might want but then the C
+remains in memory right so the C will
+
+ align:start position:0%
+remains in memory right so the C will
+ 
+
+ align:start position:0%
+remains in memory right so the C will
+still be there we're just losing The
+
+ align:start position:0%
+still be there we're just losing The
+ 
+
+ align:start position:0%
+still be there we're just losing The
+Binding from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so uh any questions so far
+
+ align:start position:0%
+it so uh any questions so far
+ 
+
+ align:start position:0%
+it so uh any questions so far
+on these
+
+ align:start position:0%
+on these
+ 
+
+ align:start position:0%
+on these
+strings mostly they're a new data type
+
+ align:start position:0%
+strings mostly they're a new data type
+ 
+
+ align:start position:0%
+strings mostly they're a new data type
+right you haven't worked with them like
+
+ align:start position:0%
+right you haven't worked with them like
+ 
+
+ align:start position:0%
+right you haven't worked with them like
+you have with numbers so it's a little
+
+ align:start position:0%
+you have with numbers so it's a little
+ 
+
+ align:start position:0%
+you have with numbers so it's a little
+bit different again you know someone had
+
+ align:start position:0%
+bit different again you know someone had
+ 
+
+ align:start position:0%
+bit different again you know someone had
+a question how do you get the a right
+
+ align:start position:0%
+a question how do you get the a right
+ 
+
+ align:start position:0%
+a question how do you get the a right
+backward try it out in the console um
+
+ align:start position:0%
+backward try it out in the console um
+ 
+
+ align:start position:0%
+backward try it out in the console um
+I'm happy to answer questions help you
+
+ align:start position:0%
+I'm happy to answer questions help you
+ 
+
+ align:start position:0%
+I'm happy to answer questions help you
+try it try it along with you um but
+
+ align:start position:0%
+try it try it along with you um but
+ 
+
+ align:start position:0%
+try it try it along with you um but
+that's what the console is there for
+
+ align:start position:0%
+that's what the console is there for
+ 
+
+ align:start position:0%
+that's what the console is there for
+right the shell here that's what it's
+
+ align:start position:0%
+right the shell here that's what it's
+ 
+
+ align:start position:0%
+right the shell here that's what it's
+there for it's just to try quick little
+
+ align:start position:0%
+there for it's just to try quick little
+ 
+
+ align:start position:0%
+there for it's just to try quick little
+things if you ever have a question you
+
+ align:start position:0%
+things if you ever have a question you
+ 
+
+ align:start position:0%
+things if you ever have a question you
+know what if this or this and you get to
+
+ align:start position:0%
+know what if this or this and you get to
+ 
+
+ align:start position:0%
+know what if this or this and you get to
+try it out
+
+ align:start position:0%
+try it out
+ 
+
+ align:start position:0%
+try it out
+now let's move on to some input output
+
+ align:start position:0%
+now let's move on to some input output
+ 
+
+ align:start position:0%
+now let's move on to some input output
+right so far the programs that we can
+
+ align:start position:0%
+right so far the programs that we can
+ 
+
+ align:start position:0%
+right so far the programs that we can
+write are pretty stagnant right there
+
+ align:start position:0%
+write are pretty stagnant right there
+ 
+
+ align:start position:0%
+write are pretty stagnant right there
+isn't much interesting uh things that we
+
+ align:start position:0%
+isn't much interesting uh things that we
+ 
+
+ align:start position:0%
+isn't much interesting uh things that we
+can do with them there's no interaction
+
+ align:start position:0%
+can do with them there's no interaction
+ 
+
+ align:start position:0%
+can do with them there's no interaction
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+user so so far when we've tried to
+
+ align:start position:0%
+user so so far when we've tried to
+ 
+
+ align:start position:0%
+user so so far when we've tried to
+Output things well we you might think we
+
+ align:start position:0%
+Output things well we you might think we
+ 
+
+ align:start position:0%
+Output things well we you might think we
+have been outputting things right so
+
+ align:start position:0%
+have been outputting things right so
+ 
+
+ align:start position:0%
+have been outputting things right so
+when we write in our console something
+
+ align:start position:0%
+when we write in our console something
+ 
+
+ align:start position:0%
+when we write in our console something
+like 3+ two python does show something
+
+ align:start position:0%
+like 3+ two python does show something
+ 
+
+ align:start position:0%
+like 3+ two python does show something
+in the Shell right this is maybe how we
+
+ align:start position:0%
+in the Shell right this is maybe how we
+ 
+
+ align:start position:0%
+in the Shell right this is maybe how we
+interact with the user user but this is
+
+ align:start position:0%
+interact with the user user but this is
+ 
+
+ align:start position:0%
+interact with the user user but this is
+not actual true output this is I I call
+
+ align:start position:0%
+not actual true output this is I I call
+ 
+
+ align:start position:0%
+not actual true output this is I I call
+this kind of like peeking into the value
+
+ align:start position:0%
+this kind of like peeking into the value
+ 
+
+ align:start position:0%
+this kind of like peeking into the value
+of the expression but if you were to
+
+ align:start position:0%
+of the expression but if you were to
+ 
+
+ align:start position:0%
+of the expression but if you were to
+write some uh some expression like this
+
+ align:start position:0%
+write some uh some expression like this
+ 
+
+ align:start position:0%
+write some uh some expression like this
+in a file editor python wouldn't
+
+ align:start position:0%
+in a file editor python wouldn't
+ 
+
+ align:start position:0%
+in a file editor python wouldn't
+actually print it out and so here's all
+
+ align:start position:0%
+actually print it out and so here's all
+ 
+
+ align:start position:0%
+actually print it out and so here's all
+the things that we've already tried
+
+ align:start position:0%
+the things that we've already tried
+ 
+
+ align:start position:0%
+the things that we've already tried
+today right we've created all these
+
+ align:start position:0%
+today right we've created all these
+ 
+
+ align:start position:0%
+today right we've created all these
+strings we've got the length of s right
+
+ align:start position:0%
+strings we've got the length of s right
+ 
+
+ align:start position:0%
+strings we've got the length of s right
+we indexed anytime we typed these
+
+ align:start position:0%
+we indexed anytime we typed these
+ 
+
+ align:start position:0%
+we indexed anytime we typed these
+expressions in the Shell python
+
+ align:start position:0%
+expressions in the Shell python
+ 
+
+ align:start position:0%
+expressions in the Shell python
+automatically gave us our value right
+
+ align:start position:0%
+automatically gave us our value right
+ 
+
+ align:start position:0%
+automatically gave us our value right
+but if I were to type those exact
+
+ align:start position:0%
+but if I were to type those exact
+ 
+
+ align:start position:0%
+but if I were to type those exact
+expressions in a file editor on the left
+
+ align:start position:0%
+expressions in a file editor on the left
+ 
+
+ align:start position:0%
+expressions in a file editor on the left
+here Python's not actually going to
+
+ align:start position:0%
+here Python's not actually going to
+ 
+
+ align:start position:0%
+here Python's not actually going to
+print these out so this is the file
+
+ align:start position:0%
+print these out so this is the file
+ 
+
+ align:start position:0%
+print these out so this is the file
+editor from now on we're just going to
+
+ align:start position:0%
+editor from now on we're just going to
+ 
+
+ align:start position:0%
+editor from now on we're just going to
+work with files I'm going to run it by
+
+ align:start position:0%
+work with files I'm going to run it by
+ 
+
+ align:start position:0%
+work with files I'm going to run it by
+hitting this little green run button or
+
+ align:start position:0%
+hitting this little green run button or
+ 
+
+ align:start position:0%
+hitting this little green run button or
+hitting
+
+ align:start position:0%
+hitting
+ 
+
+ align:start position:0%
+hitting
+F5 something happened in the Shell my
+
+ align:start position:0%
+F5 something happened in the Shell my
+ 
+
+ align:start position:0%
+F5 something happened in the Shell my
+program
+
+ align:start position:0%
+program
+ 
+
+ align:start position:0%
+program
+ran right it says here it ran this file
+
+ align:start position:0%
+ran right it says here it ran this file
+ 
+
+ align:start position:0%
+ran right it says here it ran this file
+but there's no output right where was
+
+ align:start position:0%
+but there's no output right where was
+ 
+
+ align:start position:0%
+but there's no output right where was
+the length of s where were all these
+
+ align:start position:0%
+the length of s where were all these
+ 
+
+ align:start position:0%
+the length of s where were all these
+indices we've done before and that's
+
+ align:start position:0%
+indices we've done before and that's
+ 
+
+ align:start position:0%
+indices we've done before and that's
+because these aren't actual outputs
+
+ align:start position:0%
+because these aren't actual outputs
+ 
+
+ align:start position:0%
+because these aren't actual outputs
+right when we typed them into the shell
+
+ align:start position:0%
+right when we typed them into the shell
+ 
+
+ align:start position:0%
+right when we typed them into the shell
+that was just us doing quick little
+
+ align:start position:0%
+that was just us doing quick little
+ 
+
+ align:start position:0%
+that was just us doing quick little
+expressions in the Shell giving us quick
+
+ align:start position:0%
+expressions in the Shell giving us quick
+ 
+
+ align:start position:0%
+expressions in the Shell giving us quick
+you know I that's why I call it peeking
+
+ align:start position:0%
+you know I that's why I call it peeking
+ 
+
+ align:start position:0%
+you know I that's why I call it peeking
+into the value because it's not true
+
+ align:start position:0%
+into the value because it's not true
+ 
+
+ align:start position:0%
+into the value because it's not true
+output if you want the user to see
+
+ align:start position:0%
+output if you want the user to see
+ 
+
+ align:start position:0%
+output if you want the user to see
+output and the shell is how we're going
+
+ align:start position:0%
+output and the shell is how we're going
+ 
+
+ align:start position:0%
+output and the shell is how we're going
+to show the user output from running a
+
+ align:start position:0%
+to show the user output from running a
+ 
+
+ align:start position:0%
+to show the user output from running a
+file we have to explicitly tell python
+
+ align:start position:0%
+file we have to explicitly tell python
+ 
+
+ align:start position:0%
+file we have to explicitly tell python
+hey I want you to show the output from
+
+ align:start position:0%
+hey I want you to show the output from
+ 
+
+ align:start position:0%
+hey I want you to show the output from
+this expression or I want you to show
+
+ align:start position:0%
+this expression or I want you to show
+ 
+
+ align:start position:0%
+this expression or I want you to show
+the out output from this command okay
+
+ align:start position:0%
+the out output from this command okay
+ 
+
+ align:start position:0%
+the out output from this command okay
+and we do this using the print command
+
+ align:start position:0%
+and we do this using the print command
+ 
+
+ align:start position:0%
+and we do this using the print command
+so if we take our expression that we
+
+ align:start position:0%
+so if we take our expression that we
+ 
+
+ align:start position:0%
+so if we take our expression that we
+want to show the output from and wrap it
+
+ align:start position:0%
+want to show the output from and wrap it
+ 
+
+ align:start position:0%
+want to show the output from and wrap it
+in a print command python will then show
+
+ align:start position:0%
+in a print command python will then show
+ 
+
+ align:start position:0%
+in a print command python will then show
+that output and only that output right
+
+ align:start position:0%
+that output and only that output right
+ 
+
+ align:start position:0%
+that output and only that output right
+can you imagine if we wrote a file that
+
+ align:start position:0%
+can you imagine if we wrote a file that
+ 
+
+ align:start position:0%
+can you imagine if we wrote a file that
+did all these operations and all these
+
+ align:start position:0%
+did all these operations and all these
+ 
+
+ align:start position:0%
+did all these operations and all these
+intermediary outputs were being shown
+
+ align:start position:0%
+intermediary outputs were being shown
+ 
+
+ align:start position:0%
+intermediary outputs were being shown
+that would lead to a really messy file
+
+ align:start position:0%
+that would lead to a really messy file
+ 
+
+ align:start position:0%
+that would lead to a really messy file
+or a messy program right and so that's
+
+ align:start position:0%
+or a messy program right and so that's
+ 
+
+ align:start position:0%
+or a messy program right and so that's
+why we have a command where you can
+
+ align:start position:0%
+why we have a command where you can
+ 
+
+ align:start position:0%
+why we have a command where you can
+explicitly tell python just the things
+
+ align:start position:0%
+explicitly tell python just the things
+ 
+
+ align:start position:0%
+explicitly tell python just the things
+you want to show to the user
+
+ align:start position:0%
+you want to show to the user
+ 
+
+ align:start position:0%
+you want to show to the user
+so here if you want to print the length
+
+ align:start position:0%
+so here if you want to print the length
+ 
+
+ align:start position:0%
+so here if you want to print the length
+of s we can wrap the length of s in a
+
+ align:start position:0%
+of s we can wrap the length of s in a
+ 
+
+ align:start position:0%
+of s we can wrap the length of s in a
+print statement and then run the file
+
+ align:start position:0%
+print statement and then run the file
+ 
+
+ align:start position:0%
+print statement and then run the file
+and now the only thing that gets shown
+
+ align:start position:0%
+and now the only thing that gets shown
+ 
+
+ align:start position:0%
+and now the only thing that gets shown
+to the user is the thing I explicitly
+
+ align:start position:0%
+to the user is the thing I explicitly
+ 
+
+ align:start position:0%
+to the user is the thing I explicitly
+printed out the
+
+ align:start position:0%
+printed out the
+ 
+
+ align:start position:0%
+printed out the
+three right and then down here if I want
+
+ align:start position:0%
+three right and then down here if I want
+ 
+
+ align:start position:0%
+three right and then down here if I want
+to print this other result this the
+
+ align:start position:0%
+to print this other result this the
+ 
+
+ align:start position:0%
+to print this other result this the
+result of this other expression I can
+
+ align:start position:0%
+result of this other expression I can
+ 
+
+ align:start position:0%
+result of this other expression I can
+wrap that around a print statement and
+
+ align:start position:0%
+wrap that around a print statement and
+ 
+
+ align:start position:0%
+wrap that around a print statement and
+python will then print that one as well
+
+ align:start position:0%
+python will then print that one as well
+ 
+
+ align:start position:0%
+python will then print that one as well
+but now I'm in charge of showing the
+
+ align:start position:0%
+but now I'm in charge of showing the
+ 
+
+ align:start position:0%
+but now I'm in charge of showing the
+user the things that I want to show show
+
+ align:start position:0%
+user the things that I want to show show
+ 
+
+ align:start position:0%
+user the things that I want to show show
+them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay so whenever you have a print
+
+ align:start position:0%
+okay so whenever you have a print
+ 
+
+ align:start position:0%
+okay so whenever you have a print
+statement python will print that
+
+ align:start position:0%
+statement python will print that
+ 
+
+ align:start position:0%
+statement python will print that
+resulting expression and then enter a
+
+ align:start position:0%
+resulting expression and then enter a
+ 
+
+ align:start position:0%
+resulting expression and then enter a
+new line so as you saw here we had two
+
+ align:start position:0%
+new line so as you saw here we had two
+ 
+
+ align:start position:0%
+new line so as you saw here we had two
+print statements one around Len and one
+
+ align:start position:0%
+print statements one around Len and one
+ 
+
+ align:start position:0%
+print statements one around Len and one
+around s atg -3 and python put the
+
+ align:start position:0%
+around s atg -3 and python put the
+ 
+
+ align:start position:0%
+around s atg -3 and python put the
+result of these um uh Expressions each
+
+ align:start position:0%
+result of these um uh Expressions each
+ 
+
+ align:start position:0%
+result of these um uh Expressions each
+one on a different line sometimes you
+
+ align:start position:0%
+one on a different line sometimes you
+ 
+
+ align:start position:0%
+one on a different line sometimes you
+might want to have Expressions on the
+
+ align:start position:0%
+might want to have Expressions on the
+ 
+
+ align:start position:0%
+might want to have Expressions on the
+same line or uh the results of
+
+ align:start position:0%
+same line or uh the results of
+ 
+
+ align:start position:0%
+same line or uh the results of
+Expressions all on the the same line so
+
+ align:start position:0%
+Expressions all on the the same line so
+ 
+
+ align:start position:0%
+Expressions all on the the same line so
+we can do that we can put all of these
+
+ align:start position:0%
+we can do that we can put all of these
+ 
+
+ align:start position:0%
+we can do that we can put all of these
+different objects within the same print
+
+ align:start position:0%
+different objects within the same print
+ 
+
+ align:start position:0%
+different objects within the same print
+statement okay we separate them by a
+
+ align:start position:0%
+statement okay we separate them by a
+ 
+
+ align:start position:0%
+statement okay we separate them by a
+comma within the print statement that's
+
+ align:start position:0%
+comma within the print statement that's
+ 
+
+ align:start position:0%
+comma within the print statement that's
+down here python will print all of our
+
+ align:start position:0%
+down here python will print all of our
+ 
+
+ align:start position:0%
+down here python will print all of our
+objects no matter what types they are
+
+ align:start position:0%
+objects no matter what types they are
+ 
+
+ align:start position:0%
+objects no matter what types they are
+and it'll separate each object by a
+
+ align:start position:0%
+and it'll separate each object by a
+ 
+
+ align:start position:0%
+and it'll separate each object by a
+space so there's my object the there's
+
+ align:start position:0%
+space so there's my object the there's
+ 
+
+ align:start position:0%
+space so there's my object the there's
+my object the number three and there's
+
+ align:start position:0%
+my object the number three and there's
+ 
+
+ align:start position:0%
+my object the number three and there's
+my object the string Musketeers and it
+
+ align:start position:0%
+my object the string Musketeers and it
+ 
+
+ align:start position:0%
+my object the string Musketeers and it
+printed it all on one line with the
+
+ align:start position:0%
+printed it all on one line with the
+ 
+
+ align:start position:0%
+printed it all on one line with the
+space in between them and that's what
+
+ align:start position:0%
+space in between them and that's what
+ 
+
+ align:start position:0%
+space in between them and that's what
+this comma does it automatically inserts
+
+ align:start position:0%
+this comma does it automatically inserts
+ 
+
+ align:start position:0%
+this comma does it automatically inserts
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+space now let's say you don't want a
+
+ align:start position:0%
+space now let's say you don't want a
+ 
+
+ align:start position:0%
+space now let's say you don't want a
+space for whatever
+
+ align:start position:0%
+space for whatever
+ 
+
+ align:start position:0%
+space for whatever
+reason what if we try concatenating
+
+ align:start position:0%
+reason what if we try concatenating
+ 
+
+ align:start position:0%
+reason what if we try concatenating
+these objects together right remember we
+
+ align:start position:0%
+these objects together right remember we
+ 
+
+ align:start position:0%
+these objects together right remember we
+saw concatenation we said it doesn't
+
+ align:start position:0%
+saw concatenation we said it doesn't
+ 
+
+ align:start position:0%
+saw concatenation we said it doesn't
+automatically insert spaces it just kind
+
+ align:start position:0%
+automatically insert spaces it just kind
+ 
+
+ align:start position:0%
+automatically insert spaces it just kind
+of merges the strings together and we
+
+ align:start position:0%
+of merges the strings together and we
+ 
+
+ align:start position:0%
+of merges the strings together and we
+run it well I kind of already gave it
+
+ align:start position:0%
+run it well I kind of already gave it
+ 
+
+ align:start position:0%
+run it well I kind of already gave it
+away it's going to be an error but let's
+
+ align:start position:0%
+away it's going to be an error but let's
+ 
+
+ align:start position:0%
+away it's going to be an error but let's
+see the error it's a type error it says
+
+ align:start position:0%
+see the error it's a type error it says
+ 
+
+ align:start position:0%
+see the error it's a type error it says
+can only concatenate strings not
+
+ align:start position:0%
+can only concatenate strings not
+ 
+
+ align:start position:0%
+can only concatenate strings not
+integers to
+
+ align:start position:0%
+integers to
+ 
+
+ align:start position:0%
+integers to
+strings all right makes sense this is a
+
+ align:start position:0%
+strings all right makes sense this is a
+ 
+
+ align:start position:0%
+strings all right makes sense this is a
+string this is not a string so that's
+
+ align:start position:0%
+string this is not a string so that's
+ 
+
+ align:start position:0%
+string this is not a string so that's
+not okay and this is a
+
+ align:start position:0%
+not okay and this is a
+ 
+
+ align:start position:0%
+not okay and this is a
+string so instead of
+
+ align:start position:0%
+string so instead of
+ 
+
+ align:start position:0%
+string so instead of
+concatenating different objects together
+
+ align:start position:0%
+concatenating different objects together
+ 
+
+ align:start position:0%
+concatenating different objects together
+we now have to remember to cast every
+
+ align:start position:0%
+we now have to remember to cast every
+ 
+
+ align:start position:0%
+we now have to remember to cast every
+object that's not a string to a string
+
+ align:start position:0%
+object that's not a string to a string
+ 
+
+ align:start position:0%
+object that's not a string to a string
+so this line is exactly the same as the
+
+ align:start position:0%
+so this line is exactly the same as the
+ 
+
+ align:start position:0%
+so this line is exactly the same as the
+previous one except that b which was the
+
+ align:start position:0%
+previous one except that b which was the
+ 
+
+ align:start position:0%
+previous one except that b which was the
+number the integer three is now being
+
+ align:start position:0%
+number the integer three is now being
+ 
+
+ align:start position:0%
+number the integer three is now being
+cast to a string so I'm wrapping the B
+
+ align:start position:0%
+cast to a string so I'm wrapping the B
+ 
+
+ align:start position:0%
+cast to a string so I'm wrapping the B
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+the Str Str and that casts my integer to
+
+ align:start position:0%
+the Str Str and that casts my integer to
+ 
+
+ align:start position:0%
+the Str Str and that casts my integer to
+the string and now python is happy to
+
+ align:start position:0%
+the string and now python is happy to
+ 
+
+ align:start position:0%
+the string and now python is happy to
+concatenate these three strings for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me okay that's basically what I said so
+
+ align:start position:0%
+me okay that's basically what I said so
+ 
+
+ align:start position:0%
+me okay that's basically what I said so
+that's output using the print statement
+
+ align:start position:0%
+that's output using the print statement
+ 
+
+ align:start position:0%
+that's output using the print statement
+now how about
+
+ align:start position:0%
+now how about
+ 
+
+ align:start position:0%
+now how about
+input we can get input from the user not
+
+ align:start position:0%
+input we can get input from the user not
+ 
+
+ align:start position:0%
+input we can get input from the user not
+surprisingly with a command called input
+
+ align:start position:0%
+surprisingly with a command called input
+ 
+
+ align:start position:0%
+surprisingly with a command called input
+the format of input is usually like this
+
+ align:start position:0%
+the format of input is usually like this
+ 
+
+ align:start position:0%
+the format of input is usually like this
+so we have the input command in the
+
+ align:start position:0%
+so we have the input command in the
+ 
+
+ align:start position:0%
+so we have the input command in the
+parentheses we give it a string and then
+
+ align:start position:0%
+parentheses we give it a string and then
+ 
+
+ align:start position:0%
+parentheses we give it a string and then
+we usually want to save the input to a
+
+ align:start position:0%
+we usually want to save the input to a
+ 
+
+ align:start position:0%
+we usually want to save the input to a
+variable so the next few slides are
+
+ align:start position:0%
+variable so the next few slides are
+ 
+
+ align:start position:0%
+variable so the next few slides are
+going to go through step by step what
+
+ align:start position:0%
+going to go through step by step what
+ 
+
+ align:start position:0%
+going to go through step by step what
+happens when I have these two lines of
+
+ align:start position:0%
+happens when I have these two lines of
+ 
+
+ align:start position:0%
+happens when I have these two lines of
+code text equals input type anything and
+
+ align:start position:0%
+code text equals input type anything and
+ 
+
+ align:start position:0%
+code text equals input type anything and
+then I'm going to print five times
+
+ align:start position:0%
+then I'm going to print five times
+ 
+
+ align:start position:0%
+then I'm going to print five times
+text so when python sees a line that
+
+ align:start position:0%
+text so when python sees a line that
+ 
+
+ align:start position:0%
+text so when python sees a line that
+says you know input and then some string
+
+ align:start position:0%
+says you know input and then some string
+ 
+
+ align:start position:0%
+says you know input and then some string
+python will automatically take the
+
+ align:start position:0%
+python will automatically take the
+ 
+
+ align:start position:0%
+python will automatically take the
+string within the input right so in this
+
+ align:start position:0%
+string within the input right so in this
+ 
+
+ align:start position:0%
+string within the input right so in this
+particular case here's my input command
+
+ align:start position:0%
+particular case here's my input command
+ 
+
+ align:start position:0%
+particular case here's my input command
+the string inside the input is type
+
+ align:start position:0%
+the string inside the input is type
+ 
+
+ align:start position:0%
+the string inside the input is type
+anything colon space on the shell python
+
+ align:start position:0%
+anything colon space on the shell python
+ 
+
+ align:start position:0%
+anything colon space on the shell python
+will put that string for you and then it
+
+ align:start position:0%
+will put that string for you and then it
+ 
+
+ align:start position:0%
+will put that string for you and then it
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+wait it waits for the user to type some
+
+ align:start position:0%
+wait it waits for the user to type some
+ 
+
+ align:start position:0%
+wait it waits for the user to type some
+stuff in and hit
+
+ align:start position:0%
+stuff in and hit
+ 
+
+ align:start position:0%
+stuff in and hit
+enter as soon as the user hits enter
+
+ align:start position:0%
+enter as soon as the user hits enter
+ 
+
+ align:start position:0%
+enter as soon as the user hits enter
+whatever the user typed in so let's say
+
+ align:start position:0%
+whatever the user typed in so let's say
+ 
+
+ align:start position:0%
+whatever the user typed in so let's say
+the user typed in howdy whatever the
+
+ align:start position:0%
+the user typed in howdy whatever the
+ 
+
+ align:start position:0%
+the user typed in howdy whatever the
+user types in will be saved as a
+
+ align:start position:0%
+user types in will be saved as a
+ 
+
+ align:start position:0%
+user types in will be saved as a
+string sort of
+
+ align:start position:0%
+string sort of
+ 
+
+ align:start position:0%
+string sort of
+replacing this input statement so you
+
+ align:start position:0%
+replacing this input statement so you
+ 
+
+ align:start position:0%
+replacing this input statement so you
+can think of the input kind of like an
+
+ align:start position:0%
+can think of the input kind of like an
+ 
+
+ align:start position:0%
+can think of the input kind of like an
+expression it's a weird one because it's
+
+ align:start position:0%
+expression it's a weird one because it's
+ 
+
+ align:start position:0%
+expression it's a weird one because it's
+waiting for the user to give us
+
+ align:start position:0%
+waiting for the user to give us
+ 
+
+ align:start position:0%
+waiting for the user to give us
+something right but in the end the input
+
+ align:start position:0%
+something right but in the end the input
+ 
+
+ align:start position:0%
+something right but in the end the input
+gets replaced by the string version of
+
+ align:start position:0%
+gets replaced by the string version of
+ 
+
+ align:start position:0%
+gets replaced by the string version of
+whatever the user typed in so the user
+
+ align:start position:0%
+whatever the user typed in so the user
+ 
+
+ align:start position:0%
+whatever the user typed in so the user
+can type in something you know numbers
+
+ align:start position:0%
+can type in something you know numbers
+ 
+
+ align:start position:0%
+can type in something you know numbers
+letters characters anything as as soon
+
+ align:start position:0%
+letters characters anything as as soon
+ 
+
+ align:start position:0%
+letters characters anything as as soon
+as the user hits enter whatever the user
+
+ align:start position:0%
+as the user hits enter whatever the user
+ 
+
+ align:start position:0%
+as the user hits enter whatever the user
+typed in will be saved as a string
+
+ align:start position:0%
+typed in will be saved as a string
+ 
+
+ align:start position:0%
+typed in will be saved as a string
+replacing this
+
+ align:start position:0%
+replacing this
+ 
+
+ align:start position:0%
+replacing this
+input so in memory the way this looks
+
+ align:start position:0%
+input so in memory the way this looks
+ 
+
+ align:start position:0%
+input so in memory the way this looks
+like is this is our you know memory
+
+ align:start position:0%
+like is this is our you know memory
+ 
+
+ align:start position:0%
+like is this is our you know memory
+Cloud here is this very here is this
+
+ align:start position:0%
+Cloud here is this very here is this
+ 
+
+ align:start position:0%
+Cloud here is this very here is this
+object that I've created which is the
+
+ align:start position:0%
+object that I've created which is the
+ 
+
+ align:start position:0%
+object that I've created which is the
+exact characters the user typed
+
+ align:start position:0%
+exact characters the user typed
+ 
+
+ align:start position:0%
+exact characters the user typed
+in okay well if the user typed in howdy
+
+ align:start position:0%
+in okay well if the user typed in howdy
+ 
+
+ align:start position:0%
+in okay well if the user typed in howdy
+then what does this line end up being
+
+ align:start position:0%
+then what does this line end up being
+ 
+
+ align:start position:0%
+then what does this line end up being
+text is equal to the string
+
+ align:start position:0%
+text is equal to the string
+ 
+
+ align:start position:0%
+text is equal to the string
+howdy and that basically is what we've
+
+ align:start position:0%
+howdy and that basically is what we've
+ 
+
+ align:start position:0%
+howdy and that basically is what we've
+seen on the previous two slides right
+
+ align:start position:0%
+seen on the previous two slides right
+ 
+
+ align:start position:0%
+seen on the previous two slides right
+when we've worked with strings we're
+
+ align:start position:0%
+when we've worked with strings we're
+ 
+
+ align:start position:0%
+when we've worked with strings we're
+going to assign uh this variable and
+
+ align:start position:0%
+going to assign uh this variable and
+ 
+
+ align:start position:0%
+going to assign uh this variable and
+bind it to this particular string of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+characters now the next line is easy
+
+ align:start position:0%
+characters now the next line is easy
+ 
+
+ align:start position:0%
+characters now the next line is easy
+right we're going to print whatever the
+
+ align:start position:0%
+right we're going to print whatever the
+ 
+
+ align:start position:0%
+right we're going to print whatever the
+result of repeating text is five
+
+ align:start position:0%
+result of repeating text is five
+ 
+
+ align:start position:0%
+result of repeating text is five
+times so the print will uh show on the
+
+ align:start position:0%
+times so the print will uh show on the
+ 
+
+ align:start position:0%
+times so the print will uh show on the
+shell howdy howdy howdy howdy howdy
+
+ align:start position:0%
+shell howdy howdy howdy howdy howdy
+ 
+
+ align:start position:0%
+shell howdy howdy howdy howdy howdy
+right five that whatever the user typed
+
+ align:start position:0%
+right five that whatever the user typed
+ 
+
+ align:start position:0%
+right five that whatever the user typed
+in five times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's look at another example in
+
+ align:start position:0%
+okay let's look at another example in
+ 
+
+ align:start position:0%
+okay let's look at another example in
+this particular one we're going to ask
+
+ align:start position:0%
+this particular one we're going to ask
+ 
+
+ align:start position:0%
+this particular one we're going to ask
+the user for a number and I want to
+
+ align:start position:0%
+the user for a number and I want to
+ 
+
+ align:start position:0%
+the user for a number and I want to
+print five times whatever the user types
+
+ align:start position:0%
+print five times whatever the user types
+ 
+
+ align:start position:0%
+print five times whatever the user types
+in so num one we again grab input so
+
+ align:start position:0%
+in so num one we again grab input so
+ 
+
+ align:start position:0%
+in so num one we again grab input so
+what we're asking the user to do is to
+
+ align:start position:0%
+what we're asking the user to do is to
+ 
+
+ align:start position:0%
+what we're asking the user to do is to
+uh type in a number right so when the
+
+ align:start position:0%
+uh type in a number right so when the
+ 
+
+ align:start position:0%
+uh type in a number right so when the
+python sees this it uh prints type a
+
+ align:start position:0%
+python sees this it uh prints type a
+ 
+
+ align:start position:0%
+python sees this it uh prints type a
+number and then waits for user input
+
+ align:start position:0%
+number and then waits for user input
+ 
+
+ align:start position:0%
+number and then waits for user input
+let's say the user types in the number
+
+ align:start position:0%
+let's say the user types in the number
+ 
+
+ align:start position:0%
+let's say the user types in the number
+three that gets saved as the string
+
+ align:start position:0%
+three that gets saved as the string
+ 
+
+ align:start position:0%
+three that gets saved as the string
+three again so no matter what the user
+
+ align:start position:0%
+three again so no matter what the user
+ 
+
+ align:start position:0%
+three again so no matter what the user
+types in it's being saved as a string
+
+ align:start position:0%
+types in it's being saved as a string
+ 
+
+ align:start position:0%
+types in it's being saved as a string
+even if it's a number it's being saved
+
+ align:start position:0%
+even if it's a number it's being saved
+ 
+
+ align:start position:0%
+even if it's a number it's being saved
+as the string that number right so to
+
+ align:start position:0%
+as the string that number right so to
+ 
+
+ align:start position:0%
+as the string that number right so to
+python it's a character to us it's a
+
+ align:start position:0%
+python it's a character to us it's a
+ 
+
+ align:start position:0%
+python it's a character to us it's a
+number but to python it's still a
+
+ align:start position:0%
+number but to python it's still a
+ 
+
+ align:start position:0%
+number but to python it's still a
+character so num one in memory basically
+
+ align:start position:0%
+character so num one in memory basically
+ 
+
+ align:start position:0%
+character so num one in memory basically
+becomes the string three just one single
+
+ align:start position:0%
+becomes the string three just one single
+ 
+
+ align:start position:0%
+becomes the string three just one single
+character
+
+ align:start position:0%
+character
+ 
+
+ align:start position:0%
+character
+three when I print five times num one
+
+ align:start position:0%
+three when I print five times num one
+ 
+
+ align:start position:0%
+three when I print five times num one
+what is that going to look like you guys
+
+ align:start position:0%
+what is that going to look like you guys
+ 
+
+ align:start position:0%
+what is that going to look like you guys
+tell me
+
+ align:start position:0%
+tell me
+ 
+
+ align:start position:0%
+tell me
+exactly right 3 3 3 3 three right
+
+ align:start position:0%
+exactly right 3 3 3 3 three right
+ 
+
+ align:start position:0%
+exactly right 3 3 3 3 three right
+because we're not we're working with a
+
+ align:start position:0%
+because we're not we're working with a
+ 
+
+ align:start position:0%
+because we're not we're working with a
+string here not an
+
+ align:start position:0%
+string here not an
+ 
+
+ align:start position:0%
+string here not an
+integer if we want to work with an
+
+ align:start position:0%
+integer if we want to work with an
+ 
+
+ align:start position:0%
+integer if we want to work with an
+integer we have to wrap our input
+
+ align:start position:0%
+integer we have to wrap our input
+ 
+
+ align:start position:0%
+integer we have to wrap our input
+statement with a cast statement right so
+
+ align:start position:0%
+statement with a cast statement right so
+ 
+
+ align:start position:0%
+statement with a cast statement right so
+again this is what python does we can
+
+ align:start position:0%
+again this is what python does we can
+ 
+
+ align:start position:0%
+again this is what python does we can
+combine Expressions together in this
+
+ align:start position:0%
+combine Expressions together in this
+ 
+
+ align:start position:0%
+combine Expressions together in this
+particular case we're going to combine
+
+ align:start position:0%
+particular case we're going to combine
+ 
+
+ align:start position:0%
+particular case we're going to combine
+the uh casting the input with the input
+
+ align:start position:0%
+the uh casting the input with the input
+ 
+
+ align:start position:0%
+the uh casting the input with the input
+statement so now the user can type in
+
+ align:start position:0%
+statement so now the user can type in
+ 
+
+ align:start position:0%
+statement so now the user can type in
+for me three again the input itself is
+
+ align:start position:0%
+for me three again the input itself is
+ 
+
+ align:start position:0%
+for me three again the input itself is
+going to be the string three but that
+
+ align:start position:0%
+going to be the string three but that
+ 
+
+ align:start position:0%
+going to be the string three but that
+line becomes num two equals int
+
+ align:start position:0%
+line becomes num two equals int
+ 
+
+ align:start position:0%
+line becomes num two equals int
+parentheses string three right and that
+
+ align:start position:0%
+parentheses string three right and that
+ 
+
+ align:start position:0%
+parentheses string three right and that
+we've I did it on the shell a little
+
+ align:start position:0%
+we've I did it on the shell a little
+ 
+
+ align:start position:0%
+we've I did it on the shell a little
+earlier today right we when we cast a
+
+ align:start position:0%
+earlier today right we when we cast a
+ 
+
+ align:start position:0%
+earlier today right we when we cast a
+number a string to an INT it becomes the
+
+ align:start position:0%
+number a string to an INT it becomes the
+ 
+
+ align:start position:0%
+number a string to an INT it becomes the
+number that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+int so num two is then going to be
+
+ align:start position:0%
+int so num two is then going to be
+ 
+
+ align:start position:0%
+int so num two is then going to be
+three in memory num two is not the
+
+ align:start position:0%
+three in memory num two is not the
+ 
+
+ align:start position:0%
+three in memory num two is not the
+string anymore because we've cast it to
+
+ align:start position:0%
+string anymore because we've cast it to
+ 
+
+ align:start position:0%
+string anymore because we've cast it to
+three so when we print 5 * 3 we're doing
+
+ align:start position:0%
+three so when we print 5 * 3 we're doing
+ 
+
+ align:start position:0%
+three so when we print 5 * 3 we're doing
+the mathematical operation 5 * 3 right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+15 okay let's have you code so I'm going
+
+ align:start position:0%
+15 okay let's have you code so I'm going
+ 
+
+ align:start position:0%
+15 okay let's have you code so I'm going
+to give you a couple
+
+ align:start position:0%
+to give you a couple
+ 
+
+ align:start position:0%
+to give you a couple
+minutes I'm going to have you write a
+
+ align:start position:0%
+minutes I'm going to have you write a
+ 
+
+ align:start position:0%
+minutes I'm going to have you write a
+program that is interactive so it's
+
+ align:start position:0%
+program that is interactive so it's
+ 
+
+ align:start position:0%
+program that is interactive so it's
+going to ask the user for something and
+
+ align:start position:0%
+going to ask the user for something and
+ 
+
+ align:start position:0%
+going to ask the user for something and
+it's going to print the something uh
+
+ align:start position:0%
+it's going to print the something uh
+ 
+
+ align:start position:0%
+it's going to print the something uh
+back to the user so we're going to ask
+
+ align:start position:0%
+back to the user so we're going to ask
+ 
+
+ align:start position:0%
+back to the user so we're going to ask
+the user for a verb and then I want you
+
+ align:start position:0%
+the user for a verb and then I want you
+ 
+
+ align:start position:0%
+the user for a verb and then I want you
+to print two things for me the first is
+
+ align:start position:0%
+to print two things for me the first is
+ 
+
+ align:start position:0%
+to print two things for me the first is
+whatever the verb that user typed in
+
+ align:start position:0%
+whatever the verb that user typed in
+ 
+
+ align:start position:0%
+whatever the verb that user typed in
+you're going to write I can whatever
+
+ align:start position:0%
+you're going to write I can whatever
+ 
+
+ align:start position:0%
+you're going to write I can whatever
+better than you on one line and then on
+
+ align:start position:0%
+better than you on one line and then on
+ 
+
+ align:start position:0%
+better than you on one line and then on
+the next line so with another print
+
+ align:start position:0%
+the next line so with another print
+ 
+
+ align:start position:0%
+the next line so with another print
+statement I want you to print that verb
+
+ align:start position:0%
+statement I want you to print that verb
+ 
+
+ align:start position:0%
+statement I want you to print that verb
+five times so if the user types in run
+
+ align:start position:0%
+five times so if the user types in run
+ 
+
+ align:start position:0%
+five times so if the user types in run
+you're going to write I can run better
+
+ align:start position:0%
+you're going to write I can run better
+ 
+
+ align:start position:0%
+you're going to write I can run better
+than you and then on the next line run
+
+ align:start position:0%
+than you and then on the next line run
+ 
+
+ align:start position:0%
+than you and then on the next line run
+run run run run so the way these try it
+
+ align:start position:0%
+run run run run so the way these try it
+ 
+
+ align:start position:0%
+run run run run so the way these try it
+you try it work is I actually have some
+
+ align:start position:0%
+you try it work is I actually have some
+ 
+
+ align:start position:0%
+you try it work is I actually have some
+space here I've already pre-written the
+
+ align:start position:0%
+space here I've already pre-written the
+ 
+
+ align:start position:0%
+space here I've already pre-written the
+instructions for you and all you have to
+
+ align:start position:0%
+instructions for you and all you have to
+ 
+
+ align:start position:0%
+instructions for you and all you have to
+do is fill in the code okay so I'll give
+
+ align:start position:0%
+do is fill in the code okay so I'll give
+ 
+
+ align:start position:0%
+do is fill in the code okay so I'll give
+you a couple minutes and then we'll
+
+ align:start position:0%
+you a couple minutes and then we'll
+ 
+
+ align:start position:0%
+you a couple minutes and then we'll
+write it together with suggestions from
+
+ align:start position:0%
+write it together with suggestions from
+ 
+
+ align:start position:0%
+write it together with suggestions from
+you and uh we'll see how how far we can
+
+ align:start position:0%
+you and uh we'll see how how far we can
+ 
+
+ align:start position:0%
+you and uh we'll see how how far we can
+get and we'll
+
+ align:start position:0%
+get and we'll
+ 
+
+ align:start position:0%
+get and we'll
+definitely we'll definitely finish it
+
+ align:start position:0%
+definitely we'll definitely finish it
+ 
+
+ align:start position:0%
+definitely we'll definitely finish it
+together so you don't have to finish it
+
+ align:start position:0%
+together so you don't have to finish it
+ 
+
+ align:start position:0%
+together so you don't have to finish it
+on your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+own yeah suppos
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to um you should have this file it's
+
+ align:start position:0%
+to um you should have this file it's
+ 
+
+ align:start position:0%
+to um you should have this file it's
+part of the zip file you downloaded for
+
+ align:start position:0%
+part of the zip file you downloaded for
+ 
+
+ align:start position:0%
+part of the zip file you downloaded for
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+uh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right does anyone have a start for
+
+ align:start position:0%
+all right does anyone have a start for
+ 
+
+ align:start position:0%
+all right does anyone have a start for
+me so how can I ask the user for
+
+ align:start position:0%
+me so how can I ask the user for
+ 
+
+ align:start position:0%
+me so how can I ask the user for
+input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yep that works for me and I'm
+
+ align:start position:0%
+yeah yep that works for me and I'm
+ 
+
+ align:start position:0%
+yeah yep that works for me and I'm
+adding a little extra space here between
+
+ align:start position:0%
+adding a little extra space here between
+ 
+
+ align:start position:0%
+adding a little extra space here between
+the colon or whatever prompt you have
+
+ align:start position:0%
+the colon or whatever prompt you have
+ 
+
+ align:start position:0%
+the colon or whatever prompt you have
+just so that when the user types it in
+
+ align:start position:0%
+just so that when the user types it in
+ 
+
+ align:start position:0%
+just so that when the user types it in
+isn't it isn't right beside the colon or
+
+ align:start position:0%
+isn't it isn't right beside the colon or
+ 
+
+ align:start position:0%
+isn't it isn't right beside the colon or
+the end of your uh uh the end of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string so as soon as we do this the user
+
+ align:start position:0%
+string so as soon as we do this the user
+ 
+
+ align:start position:0%
+string so as soon as we do this the user
+will uh the program will wait and the
+
+ align:start position:0%
+will uh the program will wait and the
+ 
+
+ align:start position:0%
+will uh the program will wait and the
+user will get to type something in
+
+ align:start position:0%
+user will get to type something in
+ 
+
+ align:start position:0%
+user will get to type something in
+what's the next
+
+ align:start position:0%
+what's the next
+ 
+
+ align:start position:0%
+what's the next
+step what's the first how can you how
+
+ align:start position:0%
+step what's the first how can you how
+ 
+
+ align:start position:0%
+step what's the first how can you how
+can you use this
+
+ align:start position:0%
+can you use this
+ 
+
+ align:start position:0%
+can you use this
+um this input to uh print yep let's
+
+ align:start position:0%
+um this input to uh print yep let's
+ 
+
+ align:start position:0%
+um this input to uh print yep let's
+print something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can in quotes yep I can would you
+
+ align:start position:0%
+I can in quotes yep I can would you
+ 
+
+ align:start position:0%
+I can in quotes yep I can would you
+outside of the quotes put the
+
+ align:start position:0%
+outside of the quotes put the
+ 
+
+ align:start position:0%
+outside of the quotes put the
+question yep we can put put question yep
+
+ align:start position:0%
+question yep we can put put question yep
+ 
+
+ align:start position:0%
+question yep we can put put question yep
+exactly I can question comma because
+
+ align:start position:0%
+exactly I can question comma because
+ 
+
+ align:start position:0%
+exactly I can question comma because
+it's another object and I'm happy to put
+
+ align:start position:0%
+it's another object and I'm happy to put
+ 
+
+ align:start position:0%
+it's another object and I'm happy to put
+a space in between it I can question add
+
+ align:start position:0%
+a space in between it I can question add
+ 
+
+ align:start position:0%
+a space in between it I can question add
+another string better than you oops
+
+ align:start position:0%
+another string better than you oops
+ 
+
+ align:start position:0%
+another string better than you oops
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there and we don't need to write the
+
+ align:start position:0%
+there and we don't need to write the
+ 
+
+ align:start position:0%
+there and we don't need to write the
+full program right away we can just test
+
+ align:start position:0%
+full program right away we can just test
+ 
+
+ align:start position:0%
+full program right away we can just test
+this little bit out um so choose a verb
+
+ align:start position:0%
+this little bit out um so choose a verb
+ 
+
+ align:start position:0%
+this little bit out um so choose a verb
+run the one I gave you is fine that
+
+ align:start position:0%
+run the one I gave you is fine that
+ 
+
+ align:start position:0%
+run the one I gave you is fine that
+looks good so far all right so then then
+
+ align:start position:0%
+looks good so far all right so then then
+ 
+
+ align:start position:0%
+looks good so far all right so then then
+we can work keep working on the second
+
+ align:start position:0%
+we can work keep working on the second
+ 
+
+ align:start position:0%
+we can work keep working on the second
+part how can I print that
+
+ align:start position:0%
+part how can I print that
+ 
+
+ align:start position:0%
+part how can I print that
+verb five
+
+ align:start position:0%
+verb five
+ 
+
+ align:start position:0%
+verb five
+times yeah print and then Question Time
+
+ align:start position:0%
+times yeah print and then Question Time
+ 
+
+ align:start position:0%
+times yeah print and then Question Time
+5 print Question Time 5 okay let's run
+
+ align:start position:0%
+5 print Question Time 5 okay let's run
+ 
+
+ align:start position:0%
+5 print Question Time 5 okay let's run
+it and see what
+
+ align:start position:0%
+it and see what
+ 
+
+ align:start position:0%
+it and see what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+run not quite I'm missing spaces but
+
+ align:start position:0%
+run not quite I'm missing spaces but
+ 
+
+ align:start position:0%
+run not quite I'm missing spaces but
+this is an aome start how can I add the
+
+ align:start position:0%
+this is an aome start how can I add the
+ 
+
+ align:start position:0%
+this is an aome start how can I add the
+spaces in
+
+ align:start position:0%
+spaces in
+ 
+
+ align:start position:0%
+spaces in
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+put like with a space in parentheses yep
+
+ align:start position:0%
+put like with a space in parentheses yep
+ 
+
+ align:start position:0%
+put like with a space in parentheses yep
+we can uh concatenate it with a space
+
+ align:start position:0%
+we can uh concatenate it with a space
+ 
+
+ align:start position:0%
+we can uh concatenate it with a space
+exactly times on all that times five
+
+ align:start position:0%
+exactly times on all that times five
+ 
+
+ align:start position:0%
+exactly times on all that times five
+yeah let's try
+
+ align:start position:0%
+yeah let's try
+ 
+
+ align:start position:0%
+yeah let's try
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+run yep that looks pretty
+
+ align:start position:0%
+run yep that looks pretty
+ 
+
+ align:start position:0%
+run yep that looks pretty
+good I do want to mention one thing
+
+ align:start position:0%
+good I do want to mention one thing
+ 
+
+ align:start position:0%
+good I do want to mention one thing
+there is one Improvement we can make to
+
+ align:start position:0%
+there is one Improvement we can make to
+ 
+
+ align:start position:0%
+there is one Improvement we can make to
+this program if we look at the output
+
+ align:start position:0%
+this program if we look at the output
+ 
+
+ align:start position:0%
+this program if we look at the output
+here the thing that we're actually run
+
+ align:start position:0%
+here the thing that we're actually run
+ 
+
+ align:start position:0%
+here the thing that we're actually run
+uh printing out is this verb space right
+
+ align:start position:0%
+uh printing out is this verb space right
+ 
+
+ align:start position:0%
+uh printing out is this verb space right
+there's one two three four and the last
+
+ align:start position:0%
+there's one two three four and the last
+ 
+
+ align:start position:0%
+there's one two three four and the last
+one actually prints it with a space at
+
+ align:start position:0%
+one actually prints it with a space at
+ 
+
+ align:start position:0%
+one actually prints it with a space at
+the end so a challenge for you and the
+
+ align:start position:0%
+the end so a challenge for you and the
+ 
+
+ align:start position:0%
+the end so a challenge for you and the
+answer is a little bit lower I provide
+
+ align:start position:0%
+answer is a little bit lower I provide
+ 
+
+ align:start position:0%
+answer is a little bit lower I provide
+you guys with answers to these but a
+
+ align:start position:0%
+you guys with answers to these but a
+ 
+
+ align:start position:0%
+you guys with answers to these but a
+challenge for you is think about how you
+
+ align:start position:0%
+challenge for you is think about how you
+ 
+
+ align:start position:0%
+challenge for you is think about how you
+can change it change this last print
+
+ align:start position:0%
+can change it change this last print
+ 
+
+ align:start position:0%
+can change it change this last print
+statement so that this last run doesn't
+
+ align:start position:0%
+statement so that this last run doesn't
+ 
+
+ align:start position:0%
+statement so that this last run doesn't
+actually have that extra space just you
+
+ align:start position:0%
+actually have that extra space just you
+ 
+
+ align:start position:0%
+actually have that extra space just you
+know think about it
+
+ align:start position:0%
+know think about it
+ 
+
+ align:start position:0%
+know think about it
+um you don't have to do it right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now okay so with what we know so far we
+
+ align:start position:0%
+now okay so with what we know so far we
+ 
+
+ align:start position:0%
+now okay so with what we know so far we
+can actually apply some of these ideas
+
+ align:start position:0%
+can actually apply some of these ideas
+ 
+
+ align:start position:0%
+can actually apply some of these ideas
+to a more numerical example um so
+
+ align:start position:0%
+to a more numerical example um so
+ 
+
+ align:start position:0%
+to a more numerical example um so
+Newton's method is a way to actually
+
+ align:start position:0%
+Newton's method is a way to actually
+ 
+
+ align:start position:0%
+Newton's method is a way to actually
+grab the uh the roots of a polinomial
+
+ align:start position:0%
+grab the uh the roots of a polinomial
+ 
+
+ align:start position:0%
+grab the uh the roots of a polinomial
+numerically using this idea called
+
+ align:start position:0%
+numerically using this idea called
+ 
+
+ align:start position:0%
+numerically using this idea called
+successive
+
+ align:start position:0%
+successive
+ 
+
+ align:start position:0%
+successive
+approximation we can't actually write
+
+ align:start position:0%
+approximation we can't actually write
+ 
+
+ align:start position:0%
+approximation we can't actually write
+the full algorithm with what we know so
+
+ align:start position:0%
+the full algorithm with what we know so
+ 
+
+ align:start position:0%
+the full algorithm with what we know so
+far but we can write a really important
+
+ align:start position:0%
+far but we can write a really important
+ 
+
+ align:start position:0%
+far but we can write a really important
+part of it the part is the the part that
+
+ align:start position:0%
+part of it the part is the the part that
+ 
+
+ align:start position:0%
+part of it the part is the the part that
+we can write is the one that gets a next
+
+ align:start position:0%
+we can write is the one that gets a next
+ 
+
+ align:start position:0%
+we can write is the one that gets a next
+guess based on an initial
+
+ align:start position:0%
+guess based on an initial
+ 
+
+ align:start position:0%
+guess based on an initial
+guess so you don't need to understand
+
+ align:start position:0%
+guess so you don't need to understand
+ 
+
+ align:start position:0%
+guess so you don't need to understand
+how the algorithm works but basically
+
+ align:start position:0%
+how the algorithm works but basically
+ 
+
+ align:start position:0%
+how the algorithm works but basically
+the next guess based on an original
+
+ align:start position:0%
+the next guess based on an original
+ 
+
+ align:start position:0%
+the next guess based on an original
+guess looks like this this is the
+
+ align:start position:0%
+guess looks like this this is the
+ 
+
+ align:start position:0%
+guess looks like this this is the
+formula so the next guess is the
+
+ align:start position:0%
+formula so the next guess is the
+ 
+
+ align:start position:0%
+formula so the next guess is the
+original guess minus and we evaluate the
+
+ align:start position:0%
+original guess minus and we evaluate the
+ 
+
+ align:start position:0%
+original guess minus and we evaluate the
+formula for whatever uh uh you know
+
+ align:start position:0%
+formula for whatever uh uh you know
+ 
+
+ align:start position:0%
+formula for whatever uh uh you know
+polinomial we want to find at the
+
+ align:start position:0%
+polinomial we want to find at the
+ 
+
+ align:start position:0%
+polinomial we want to find at the
+original guess divided by the derivative
+
+ align:start position:0%
+original guess divided by the derivative
+ 
+
+ align:start position:0%
+original guess divided by the derivative
+of that uh of that function at the same
+
+ align:start position:0%
+of that uh of that function at the same
+ 
+
+ align:start position:0%
+of that uh of that function at the same
+guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's just some code we've got
+
+ align:start position:0%
+so here's just some code we've got
+ 
+
+ align:start position:0%
+so here's just some code we've got
+uh asking the user for input what x do
+
+ align:start position:0%
+uh asking the user for input what x do
+ 
+
+ align:start position:0%
+uh asking the user for input what x do
+we want to find the cube root of then we
+
+ align:start position:0%
+we want to find the cube root of then we
+ 
+
+ align:start position:0%
+we want to find the cube root of then we
+ask the user for input what guest do you
+
+ align:start position:0%
+ask the user for input what guest do you
+ 
+
+ align:start position:0%
+ask the user for input what guest do you
+want to start with and then we can just
+
+ align:start position:0%
+want to start with and then we can just
+ 
+
+ align:start position:0%
+want to start with and then we can just
+print the current estimate cubed so we
+
+ align:start position:0%
+print the current estimate cubed so we
+ 
+
+ align:start position:0%
+print the current estimate cubed so we
+just guess
+
+ align:start position:0%
+just guess
+ 
+
+ align:start position:0%
+just guess
+cubed and then the next guess is just
+
+ align:start position:0%
+cubed and then the next guess is just
+ 
+
+ align:start position:0%
+cubed and then the next guess is just
+following the formula up here right the
+
+ align:start position:0%
+following the formula up here right the
+ 
+
+ align:start position:0%
+following the formula up here right the
+next guess is going to say it's my
+
+ align:start position:0%
+next guess is going to say it's my
+ 
+
+ align:start position:0%
+next guess is going to say it's my
+original guess so the G that I read in
+
+ align:start position:0%
+original guess so the G that I read in
+ 
+
+ align:start position:0%
+original guess so the G that I read in
+from the student or from the input minus
+
+ align:start position:0%
+from the student or from the input minus
+ 
+
+ align:start position:0%
+from the student or from the input minus
+and now I have a division the top of it
+
+ align:start position:0%
+and now I have a division the top of it
+ 
+
+ align:start position:0%
+and now I have a division the top of it
+is going to be F at
+
+ align:start position:0%
+is going to be F at
+ 
+
+ align:start position:0%
+is going to be F at
+G right and the computer is not
+
+ align:start position:0%
+G right and the computer is not
+ 
+
+ align:start position:0%
+G right and the computer is not
+evaluating F right we have to give we
+
+ align:start position:0%
+evaluating F right we have to give we
+ 
+
+ align:start position:0%
+evaluating F right we have to give we
+have to actually write down what the
+
+ align:start position:0%
+have to actually write down what the
+ 
+
+ align:start position:0%
+have to actually write down what the
+formula is uh the function is we want to
+
+ align:start position:0%
+formula is uh the function is we want to
+ 
+
+ align:start position:0%
+formula is uh the function is we want to
+evaluate at G so it's G Cub minus X
+
+ align:start position:0%
+evaluate at G so it's G Cub minus X
+ 
+
+ align:start position:0%
+evaluate at G so it's G Cub minus X
+that's our function up there divided by
+
+ align:start position:0%
+that's our function up there divided by
+ 
+
+ align:start position:0%
+that's our function up there divided by
+the derivative and again the program is
+
+ align:start position:0%
+the derivative and again the program is
+ 
+
+ align:start position:0%
+the derivative and again the program is
+not going to evaluate the derivative
+
+ align:start position:0%
+not going to evaluate the derivative
+ 
+
+ align:start position:0%
+not going to evaluate the derivative
+automatically we're going to tell it
+
+ align:start position:0%
+automatically we're going to tell it
+ 
+
+ align:start position:0%
+automatically we're going to tell it
+what the derivative is manually so you
+
+ align:start position:0%
+what the derivative is manually so you
+ 
+
+ align:start position:0%
+what the derivative is manually so you
+know the derivative G Cub - x is just 3
+
+ align:start position:0%
+know the derivative G Cub - x is just 3
+ 
+
+ align:start position:0%
+know the derivative G Cub - x is just 3
+G ^2 so then we just kind of hardcode
+
+ align:start position:0%
+G ^2 so then we just kind of hardcode
+ 
+
+ align:start position:0%
+G ^2 so then we just kind of hardcode
+that in and the next guess to try is
+
+ align:start position:0%
+that in and the next guess to try is
+ 
+
+ align:start position:0%
+that in and the next guess to try is
+just going to be that particular
+
+ align:start position:0%
+just going to be that particular
+ 
+
+ align:start position:0%
+just going to be that particular
+Division and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subtraction I'm sorry Sor there's no
+
+ align:start position:0%
+subtraction I'm sorry Sor there's no
+ 
+
+ align:start position:0%
+subtraction I'm sorry Sor there's no
+function there are there uh there are
+
+ align:start position:0%
+function there are there uh there are
+ 
+
+ align:start position:0%
+function there are there uh there are
+python packages that allow you to do
+
+ align:start position:0%
+python packages that allow you to do
+ 
+
+ align:start position:0%
+python packages that allow you to do
+that but for our purposes we we're just
+
+ align:start position:0%
+that but for our purposes we we're just
+ 
+
+ align:start position:0%
+that but for our purposes we we're just
+going to hard hard code it in this case
+
+ align:start position:0%
+going to hard hard code it in this case
+ 
+
+ align:start position:0%
+going to hard hard code it in this case
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+yeah so the way this
+
+ align:start position:0%
+yeah so the way this
+ 
+
+ align:start position:0%
+yeah so the way this
+looks um and code is as follows right
+
+ align:start position:0%
+looks um and code is as follows right
+ 
+
+ align:start position:0%
+looks um and code is as follows right
+that's exactly what we had in there and
+
+ align:start position:0%
+that's exactly what we had in there and
+ 
+
+ align:start position:0%
+that's exactly what we had in there and
+if we run this program all it does is
+
+ align:start position:0%
+if we run this program all it does is
+ 
+
+ align:start position:0%
+if we run this program all it does is
+let's say we want to find the cube root
+
+ align:start position:0%
+let's say we want to find the cube root
+ 
+
+ align:start position:0%
+let's say we want to find the cube root
+of say 27 let's start with I don't know
+
+ align:start position:0%
+of say 27 let's start with I don't know
+ 
+
+ align:start position:0%
+of say 27 let's start with I don't know
+five right it tells me that 5 cubed is
+
+ align:start position:0%
+five right it tells me that 5 cubed is
+ 
+
+ align:start position:0%
+five right it tells me that 5 cubed is
+125 way too big obviously so the next
+
+ align:start position:0%
+125 way too big obviously so the next
+ 
+
+ align:start position:0%
+125 way too big obviously so the next
+guess to try is
+
+ align:start position:0%
+guess to try is
+ 
+
+ align:start position:0%
+guess to try is
+3.69 right and that's all the program
+
+ align:start position:0%
+3.69 right and that's all the program
+ 
+
+ align:start position:0%
+3.69 right and that's all the program
+does it doesn't take this next guess and
+
+ align:start position:0%
+does it doesn't take this next guess and
+ 
+
+ align:start position:0%
+does it doesn't take this next guess and
+do another guess we haven't learned how
+
+ align:start position:0%
+do another guess we haven't learned how
+ 
+
+ align:start position:0%
+do another guess we haven't learned how
+to do such a thing yet but we will in
+
+ align:start position:0%
+to do such a thing yet but we will in
+ 
+
+ align:start position:0%
+to do such a thing yet but we will in
+the next couple lectures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one other thing I want to mention is
+
+ align:start position:0%
+one other thing I want to mention is
+ 
+
+ align:start position:0%
+one other thing I want to mention is
+this thing called an F string um it's
+
+ align:start position:0%
+this thing called an F string um it's
+ 
+
+ align:start position:0%
+this thing called an F string um it's
+something that became available I think
+
+ align:start position:0%
+something that became available I think
+ 
+
+ align:start position:0%
+something that became available I think
+a couple years ago in Python with python
+
+ align:start position:0%
+a couple years ago in Python with python
+ 
+
+ align:start position:0%
+a couple years ago in Python with python
+3.6 it's a way more convenient way for
+
+ align:start position:0%
+3.6 it's a way more convenient way for
+ 
+
+ align:start position:0%
+3.6 it's a way more convenient way for
+us to print out mixtures of literal
+
+ align:start position:0%
+us to print out mixtures of literal
+ 
+
+ align:start position:0%
+us to print out mixtures of literal
+text and resulting Expressions so if you
+
+ align:start position:0%
+text and resulting Expressions so if you
+ 
+
+ align:start position:0%
+text and resulting Expressions so if you
+have a bunch of complicated Expressions
+
+ align:start position:0%
+have a bunch of complicated Expressions
+ 
+
+ align:start position:0%
+have a bunch of complicated Expressions
+you you want to print out an FST string
+
+ align:start position:0%
+you you want to print out an FST string
+ 
+
+ align:start position:0%
+you you want to print out an FST string
+is the way to do it these days um what
+
+ align:start position:0%
+is the way to do it these days um what
+ 
+
+ align:start position:0%
+is the way to do it these days um what
+we know is these first two lines this is
+
+ align:start position:0%
+we know is these first two lines this is
+ 
+
+ align:start position:0%
+we know is these first two lines this is
+what we've learned in the past couple
+
+ align:start position:0%
+what we've learned in the past couple
+ 
+
+ align:start position:0%
+what we've learned in the past couple
+slides so if you wanted to have you know
+
+ align:start position:0%
+slides so if you wanted to have you know
+ 
+
+ align:start position:0%
+slides so if you wanted to have you know
+these two values and print uh you know
+
+ align:start position:0%
+these two values and print uh you know
+ 
+
+ align:start position:0%
+these two values and print uh you know
+this big number is whatever fraction
+
+ align:start position:0%
+this big number is whatever fraction
+ 
+
+ align:start position:0%
+this big number is whatever fraction
+percent out of the original
+
+ align:start position:0%
+percent out of the original
+ 
+
+ align:start position:0%
+percent out of the original
+number if you actually run this in the
+
+ align:start position:0%
+number if you actually run this in the
+ 
+
+ align:start position:0%
+number if you actually run this in the
+in the python file you'll see that this
+
+ align:start position:0%
+in the python file you'll see that this
+ 
+
+ align:start position:0%
+in the python file you'll see that this
+comma here puts an extra space between
+
+ align:start position:0%
+comma here puts an extra space between
+ 
+
+ align:start position:0%
+comma here puts an extra space between
+my number and the percent right and that
+
+ align:start position:0%
+my number and the percent right and that
+ 
+
+ align:start position:0%
+my number and the percent right and that
+doesn't look very good when you have 3%
+
+ align:start position:0%
+doesn't look very good when you have 3%
+ 
+
+ align:start position:0%
+doesn't look very good when you have 3%
+You're Expecting the percent sign to be
+
+ align:start position:0%
+You're Expecting the percent sign to be
+ 
+
+ align:start position:0%
+You're Expecting the percent sign to be
+right by the three
+
+ align:start position:0%
+right by the three
+ 
+
+ align:start position:0%
+right by the three
+but this comma adds for me an extra
+
+ align:start position:0%
+but this comma adds for me an extra
+ 
+
+ align:start position:0%
+but this comma adds for me an extra
+space so it looks a little bit weird
+
+ align:start position:0%
+space so it looks a little bit weird
+ 
+
+ align:start position:0%
+space so it looks a little bit weird
+which means that our solution was to
+
+ align:start position:0%
+which means that our solution was to
+ 
+
+ align:start position:0%
+which means that our solution was to
+cast things to Strings so if we wanted
+
+ align:start position:0%
+cast things to Strings so if we wanted
+ 
+
+ align:start position:0%
+cast things to Strings so if we wanted
+to have that percent sign be right
+
+ align:start position:0%
+to have that percent sign be right
+ 
+
+ align:start position:0%
+to have that percent sign be right
+beside the number we'd
+
+ align:start position:0%
+beside the number we'd
+ 
+
+ align:start position:0%
+beside the number we'd
+concatenate this cast with a
+
+ align:start position:0%
+concatenate this cast with a
+ 
+
+ align:start position:0%
+concatenate this cast with a
+percent but F strings allow us to do
+
+ align:start position:0%
+percent but F strings allow us to do
+ 
+
+ align:start position:0%
+percent but F strings allow us to do
+this all in one so there's no
+
+ align:start position:0%
+this all in one so there's no
+ 
+
+ align:start position:0%
+this all in one so there's no
+concatenation to think about there's no
+
+ align:start position:0%
+concatenation to think about there's no
+ 
+
+ align:start position:0%
+concatenation to think about there's no
+casting to think about F strings
+
+ align:start position:0%
+casting to think about F strings
+ 
+
+ align:start position:0%
+casting to think about F strings
+basically are this F and then a long
+
+ align:start position:0%
+basically are this F and then a long
+ 
+
+ align:start position:0%
+basically are this F and then a long
+string and it's a mixture of expressions
+
+ align:start position:0%
+string and it's a mixture of expressions
+ 
+
+ align:start position:0%
+string and it's a mixture of expressions
+and things that I want to print
+
+ align:start position:0%
+and things that I want to print
+ 
+
+ align:start position:0%
+and things that I want to print
+literally to the screen so the thing
+
+ align:start position:0%
+literally to the screen so the thing
+ 
+
+ align:start position:0%
+literally to the screen so the thing
+that's not inside a curly bracket are
+
+ align:start position:0%
+that's not inside a curly bracket are
+ 
+
+ align:start position:0%
+that's not inside a curly bracket are
+all things I'm going to print literally
+
+ align:start position:0%
+all things I'm going to print literally
+ 
+
+ align:start position:0%
+all things I'm going to print literally
+to the screen so the space is space and
+
+ align:start position:0%
+to the screen so the space is space and
+ 
+
+ align:start position:0%
+to the screen so the space is space and
+then later on percent space of percent
+
+ align:start position:0%
+then later on percent space of percent
+ 
+
+ align:start position:0%
+then later on percent space of percent
+those are all things that will literally
+
+ align:start position:0%
+those are all things that will literally
+ 
+
+ align:start position:0%
+those are all things that will literally
+be printed to the screen anything that's
+
+ align:start position:0%
+be printed to the screen anything that's
+ 
+
+ align:start position:0%
+be printed to the screen anything that's
+within a curly bracket is considered an
+
+ align:start position:0%
+within a curly bracket is considered an
+ 
+
+ align:start position:0%
+within a curly bracket is considered an
+expression in Python and so before
+
+ align:start position:0%
+expression in Python and so before
+ 
+
+ align:start position:0%
+expression in Python and so before
+python prints out the thing to the
+
+ align:start position:0%
+python prints out the thing to the
+ 
+
+ align:start position:0%
+python prints out the thing to the
+screen it's actually going to evaluate
+
+ align:start position:0%
+screen it's actually going to evaluate
+ 
+
+ align:start position:0%
+screen it's actually going to evaluate
+whatever num times fraction is and it
+
+ align:start position:0%
+whatever num times fraction is and it
+ 
+
+ align:start position:0%
+whatever num times fraction is and it
+knows these are going to be variables
+
+ align:start position:0%
+knows these are going to be variables
+ 
+
+ align:start position:0%
+knows these are going to be variables
+and then later on fraction time 100 and
+
+ align:start position:0%
+and then later on fraction time 100 and
+ 
+
+ align:start position:0%
+and then later on fraction time 100 and
+then later on N these are all variables
+
+ align:start position:0%
+then later on N these are all variables
+ 
+
+ align:start position:0%
+then later on N these are all variables
+or Expressions that it will evaluate
+
+ align:start position:0%
+or Expressions that it will evaluate
+ 
+
+ align:start position:0%
+or Expressions that it will evaluate
+before actually putting them on the
+
+ align:start position:0%
+before actually putting them on the
+ 
+
+ align:start position:0%
+before actually putting them on the
+screen and now notice these these these
+
+ align:start position:0%
+screen and now notice these these these
+ 
+
+ align:start position:0%
+screen and now notice these these these
+Expressions we might have had to cast to
+
+ align:start position:0%
+Expressions we might have had to cast to
+ 
+
+ align:start position:0%
+Expressions we might have had to cast to
+Strings beforehand if we wanted to
+
+ align:start position:0%
+Strings beforehand if we wanted to
+ 
+
+ align:start position:0%
+Strings beforehand if we wanted to
+concatenate them but now we don't
+
+ align:start position:0%
+concatenate them but now we don't
+ 
+
+ align:start position:0%
+concatenate them but now we don't
+because they're in this special format
+
+ align:start position:0%
+because they're in this special format
+ 
+
+ align:start position:0%
+because they're in this special format
+with the curly brackets of the FST
+
+ align:start position:0%
+with the curly brackets of the FST
+ 
+
+ align:start position:0%
+with the curly brackets of the FST
+string so just something to practice uh
+
+ align:start position:0%
+string so just something to practice uh
+ 
+
+ align:start position:0%
+string so just something to practice uh
+I'll interchange change I'll I'll use
+
+ align:start position:0%
+I'll interchange change I'll I'll use
+ 
+
+ align:start position:0%
+I'll interchange change I'll I'll use
+sometimes this I'll use sometimes
+
+ align:start position:0%
+sometimes this I'll use sometimes
+ 
+
+ align:start position:0%
+sometimes this I'll use sometimes
+casting I'll use sometimes FST strings
+
+ align:start position:0%
+casting I'll use sometimes FST strings
+ 
+
+ align:start position:0%
+casting I'll use sometimes FST strings
+but um you know if you can use FST
+
+ align:start position:0%
+but um you know if you can use FST
+ 
+
+ align:start position:0%
+but um you know if you can use FST
+strings whenever you can that's really
+
+ align:start position:0%
+strings whenever you can that's really
+ 
+
+ align:start position:0%
+strings whenever you can that's really
+the way to go um uh in Python uh you
+
+ align:start position:0%
+the way to go um uh in Python uh you
+ 
+
+ align:start position:0%
+the way to go um uh in Python uh you
+know these
+
+ align:start position:0%
+know these
+ 
+
+ align:start position:0%
+know these
+days so the big idea actually even with
+
+ align:start position:0%
+days so the big idea actually even with
+ 
+
+ align:start position:0%
+days so the big idea actually even with
+FST strings is that you can place
+
+ align:start position:0%
+FST strings is that you can place
+ 
+
+ align:start position:0%
+FST strings is that you can place
+Expressions anywhere right we saw we
+
+ align:start position:0%
+Expressions anywhere right we saw we
+ 
+
+ align:start position:0%
+Expressions anywhere right we saw we
+placed expression I forget here where we
+
+ align:start position:0%
+placed expression I forget here where we
+ 
+
+ align:start position:0%
+placed expression I forget here where we
+where we indexed we placed an expression
+
+ align:start position:0%
+where we indexed we placed an expression
+ 
+
+ align:start position:0%
+where we indexed we placed an expression
+in the index right now we're placing
+
+ align:start position:0%
+in the index right now we're placing
+ 
+
+ align:start position:0%
+in the index right now we're placing
+expressions in uh inside print
+
+ align:start position:0%
+expressions in uh inside print
+ 
+
+ align:start position:0%
+expressions in uh inside print
+statements and now we're placing
+
+ align:start position:0%
+statements and now we're placing
+ 
+
+ align:start position:0%
+statements and now we're placing
+expressions inside F string so
+
+ align:start position:0%
+expressions inside F string so
+ 
+
+ align:start position:0%
+expressions inside F string so
+Expressions can be placed really
+
+ align:start position:0%
+Expressions can be placed really
+ 
+
+ align:start position:0%
+Expressions can be placed really
+anywhere which is pretty awesome very
+
+ align:start position:0%
+anywhere which is pretty awesome very
+ 
+
+ align:start position:0%
+anywhere which is pretty awesome very
+versatile python will just evaluate them
+
+ align:start position:0%
+versatile python will just evaluate them
+ 
+
+ align:start position:0%
+versatile python will just evaluate them
+and then just you know move on to the
+
+ align:start position:0%
+and then just you know move on to the
+ 
+
+ align:start position:0%
+and then just you know move on to the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+lines okay so the last topic of sorry
+
+ align:start position:0%
+lines okay so the last topic of sorry
+ 
+
+ align:start position:0%
+lines okay so the last topic of sorry
+any other questions about the inputs and
+
+ align:start position:0%
+any other questions about the inputs and
+ 
+
+ align:start position:0%
+any other questions about the inputs and
+outputs or is that
+
+ align:start position:0%
+outputs or is that
+ 
+
+ align:start position:0%
+outputs or is that
+right okay so the last thing that uh
+
+ align:start position:0%
+right okay so the last thing that uh
+ 
+
+ align:start position:0%
+right okay so the last thing that uh
+we'll talk about today and we will maybe
+
+ align:start position:0%
+we'll talk about today and we will maybe
+ 
+
+ align:start position:0%
+we'll talk about today and we will maybe
+talk a little bit about it next time is
+
+ align:start position:0%
+talk a little bit about it next time is
+ 
+
+ align:start position:0%
+talk a little bit about it next time is
+conditions for branching
+
+ align:start position:0%
+conditions for branching
+ 
+
+ align:start position:0%
+conditions for branching
+so right now the kinds of programs we
+
+ align:start position:0%
+so right now the kinds of programs we
+ 
+
+ align:start position:0%
+so right now the kinds of programs we
+can write are basically very linear we
+
+ align:start position:0%
+can write are basically very linear we
+ 
+
+ align:start position:0%
+can write are basically very linear we
+have a bunch of lines of code and they
+
+ align:start position:0%
+have a bunch of lines of code and they
+ 
+
+ align:start position:0%
+have a bunch of lines of code and they
+get evaluated one by one there's no way
+
+ align:start position:0%
+get evaluated one by one there's no way
+ 
+
+ align:start position:0%
+get evaluated one by one there's no way
+to skip around there's no way to repeat
+
+ align:start position:0%
+to skip around there's no way to repeat
+ 
+
+ align:start position:0%
+to skip around there's no way to repeat
+things there's no decision points in the
+
+ align:start position:0%
+things there's no decision points in the
+ 
+
+ align:start position:0%
+things there's no decision points in the
+programs you know the values that you
+
+ align:start position:0%
+programs you know the values that you
+ 
+
+ align:start position:0%
+programs you know the values that you
+get are just the values that are in the
+
+ align:start position:0%
+get are just the values that are in the
+ 
+
+ align:start position:0%
+get are just the values that are in the
+program now we're going to look at ways
+
+ align:start position:0%
+program now we're going to look at ways
+ 
+
+ align:start position:0%
+program now we're going to look at ways
+that we can add decision points in our
+
+ align:start position:0%
+that we can add decision points in our
+ 
+
+ align:start position:0%
+that we can add decision points in our
+program so if some uh value if some
+
+ align:start position:0%
+program so if some uh value if some
+ 
+
+ align:start position:0%
+program so if some uh value if some
+variable value is less than some other
+
+ align:start position:0%
+variable value is less than some other
+ 
+
+ align:start position:0%
+variable value is less than some other
+variable value we want to valate some
+
+ align:start position:0%
+variable value we want to valate some
+ 
+
+ align:start position:0%
+variable value we want to valate some
+codee and otherwise we'll do some other
+
+ align:start position:0%
+codee and otherwise we'll do some other
+ 
+
+ align:start position:0%
+codee and otherwise we'll do some other
+code right so some code can now be
+
+ align:start position:0%
+code right so some code can now be
+ 
+
+ align:start position:0%
+code right so some code can now be
+skipped in programs with this new uh
+
+ align:start position:0%
+skipped in programs with this new uh
+ 
+
+ align:start position:0%
+skipped in programs with this new uh
+with this new
+
+ align:start position:0%
+with this new
+ 
+
+ align:start position:0%
+with this new
+idea before we go on to showing you
+
+ align:start position:0%
+idea before we go on to showing you
+ 
+
+ align:start position:0%
+idea before we go on to showing you
+exactly how to do that I'm going to talk
+
+ align:start position:0%
+exactly how to do that I'm going to talk
+ 
+
+ align:start position:0%
+exactly how to do that I'm going to talk
+about another notion of equal in
+
+ align:start position:0%
+about another notion of equal in
+ 
+
+ align:start position:0%
+about another notion of equal in
+programming and this might be more the
+
+ align:start position:0%
+programming and this might be more the
+ 
+
+ align:start position:0%
+programming and this might be more the
+notion of equal you might be used to in
+
+ align:start position:0%
+notion of equal you might be used to in
+ 
+
+ align:start position:0%
+notion of equal you might be used to in
+uh in math so the first notion of equal
+
+ align:start position:0%
+uh in math so the first notion of equal
+ 
+
+ align:start position:0%
+uh in math so the first notion of equal
+is the one we've already seen it's
+
+ align:start position:0%
+is the one we've already seen it's
+ 
+
+ align:start position:0%
+is the one we've already seen it's
+assignment it's done with one equal sign
+
+ align:start position:0%
+assignment it's done with one equal sign
+ 
+
+ align:start position:0%
+assignment it's done with one equal sign
+the value on the right hand side is
+
+ align:start position:0%
+the value on the right hand side is
+ 
+
+ align:start position:0%
+the value on the right hand side is
+bound to the variable on the left hand
+
+ align:start position:0%
+bound to the variable on the left hand
+ 
+
+ align:start position:0%
+bound to the variable on the left hand
+side right that we've
+
+ align:start position:0%
+side right that we've
+ 
+
+ align:start position:0%
+side right that we've
+known double equal in in Python is how
+
+ align:start position:0%
+known double equal in in Python is how
+ 
+
+ align:start position:0%
+known double equal in in Python is how
+we tell python that we'd like to know
+
+ align:start position:0%
+we tell python that we'd like to know
+ 
+
+ align:start position:0%
+we tell python that we'd like to know
+whether these two expressions are equal
+
+ align:start position:0%
+whether these two expressions are equal
+ 
+
+ align:start position:0%
+whether these two expressions are equal
+or equivalent sorry
+
+ align:start position:0%
+or equivalent sorry
+ 
+
+ align:start position:0%
+or equivalent sorry
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+so if we're going to be looking at
+
+ align:start position:0%
+so if we're going to be looking at
+ 
+
+ align:start position:0%
+so if we're going to be looking at
+equivalency how do we how so how do we
+
+ align:start position:0%
+equivalency how do we how so how do we
+ 
+
+ align:start position:0%
+equivalency how do we how so how do we
+express equivalency well if something is
+
+ align:start position:0%
+express equivalency well if something is
+ 
+
+ align:start position:0%
+express equivalency well if something is
+equal to something else we can say yes
+
+ align:start position:0%
+equal to something else we can say yes
+ 
+
+ align:start position:0%
+equal to something else we can say yes
+or no we can say true or false right
+
+ align:start position:0%
+or no we can say true or false right
+ 
+
+ align:start position:0%
+or no we can say true or false right
+true or false should ring a bell it's
+
+ align:start position:0%
+true or false should ring a bell it's
+ 
+
+ align:start position:0%
+true or false should ring a bell it's
+the Boolean data type that we saw last
+
+ align:start position:0%
+the Boolean data type that we saw last
+ 
+
+ align:start position:0%
+the Boolean data type that we saw last
+lecture and so now that we're going to
+
+ align:start position:0%
+lecture and so now that we're going to
+ 
+
+ align:start position:0%
+lecture and so now that we're going to
+show you equality or conditionals in
+
+ align:start position:0%
+show you equality or conditionals in
+ 
+
+ align:start position:0%
+show you equality or conditionals in
+programming we're going to start talking
+
+ align:start position:0%
+programming we're going to start talking
+ 
+
+ align:start position:0%
+programming we're going to start talking
+about booleans a little bit
+
+ align:start position:0%
+about booleans a little bit
+ 
+
+ align:start position:0%
+about booleans a little bit
+more so Expressions don't just have to
+
+ align:start position:0%
+more so Expressions don't just have to
+ 
+
+ align:start position:0%
+more so Expressions don't just have to
+be numerical expressions can actually
+
+ align:start position:0%
+be numerical expressions can actually
+ 
+
+ align:start position:0%
+be numerical expressions can actually
+give us Boolean results so for example
+
+ align:start position:0%
+give us Boolean results so for example
+ 
+
+ align:start position:0%
+give us Boolean results so for example
+an expression like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 less than
+
+ align:start position:0%
+2 less than
+ 
+
+ align:start position:0%
+2 less than
+three is okay in Python and this
+
+ align:start position:0%
+three is okay in Python and this
+ 
+
+ align:start position:0%
+three is okay in Python and this
+expression actually evaluates to a
+
+ align:start position:0%
+expression actually evaluates to a
+ 
+
+ align:start position:0%
+expression actually evaluates to a
+certain value it's not a number it
+
+ align:start position:0%
+certain value it's not a number it
+ 
+
+ align:start position:0%
+certain value it's not a number it
+evaluates to true the Boolean value true
+
+ align:start position:0%
+evaluates to true the Boolean value true
+ 
+
+ align:start position:0%
+evaluates to true the Boolean value true
+because yes two is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three the equal sign here this
+
+ align:start position:0%
+three the equal sign here this
+ 
+
+ align:start position:0%
+three the equal sign here this
+notion with a double equal is how we ask
+
+ align:start position:0%
+notion with a double equal is how we ask
+ 
+
+ align:start position:0%
+notion with a double equal is how we ask
+python to tell us whether two things are
+
+ align:start position:0%
+python to tell us whether two things are
+ 
+
+ align:start position:0%
+python to tell us whether two things are
+equivalent and this will be the Boolean
+
+ align:start position:0%
+equivalent and this will be the Boolean
+ 
+
+ align:start position:0%
+equivalent and this will be the Boolean
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+false
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's a bunch of other
+
+ align:start position:0%
+okay so here's a bunch of other
+ 
+
+ align:start position:0%
+okay so here's a bunch of other
+operators that we can run on any type
+
+ align:start position:0%
+operators that we can run on any type
+ 
+
+ align:start position:0%
+operators that we can run on any type
+really in Python uh most of the most of
+
+ align:start position:0%
+really in Python uh most of the most of
+ 
+
+ align:start position:0%
+really in Python uh most of the most of
+the time we're going to run them on
+
+ align:start position:0%
+the time we're going to run them on
+ 
+
+ align:start position:0%
+the time we're going to run them on
+numbers but they can be run on strings
+
+ align:start position:0%
+numbers but they can be run on strings
+ 
+
+ align:start position:0%
+numbers but they can be run on strings
+and and things like that as well so
+
+ align:start position:0%
+and and things like that as well so
+ 
+
+ align:start position:0%
+and and things like that as well so
+obviously the double equal sign checks
+
+ align:start position:0%
+obviously the double equal sign checks
+ 
+
+ align:start position:0%
+obviously the double equal sign checks
+for equality so if I is the same as J
+
+ align:start position:0%
+for equality so if I is the same as J
+ 
+
+ align:start position:0%
+for equality so if I is the same as J
+this entire expression is replaced with
+
+ align:start position:0%
+this entire expression is replaced with
+ 
+
+ align:start position:0%
+this entire expression is replaced with
+true and if they're not equivalent this
+
+ align:start position:0%
+true and if they're not equivalent this
+ 
+
+ align:start position:0%
+true and if they're not equivalent this
+entire expression is replaced with false
+
+ align:start position:0%
+entire expression is replaced with false
+ 
+
+ align:start position:0%
+entire expression is replaced with false
+okay if we want to check for inequality
+
+ align:start position:0%
+okay if we want to check for inequality
+ 
+
+ align:start position:0%
+okay if we want to check for inequality
+we use uh not equal so exclamation mark
+
+ align:start position:0%
+we use uh not equal so exclamation mark
+ 
+
+ align:start position:0%
+we use uh not equal so exclamation mark
+equal is uh means not equal so if the
+
+ align:start position:0%
+equal is uh means not equal so if the
+ 
+
+ align:start position:0%
+equal is uh means not equal so if the
+number I or whatever V object I is not
+
+ align:start position:0%
+number I or whatever V object I is not
+ 
+
+ align:start position:0%
+number I or whatever V object I is not
+equal to object
+
+ align:start position:0%
+equal to object
+ 
+
+ align:start position:0%
+equal to object
+J then this entire expression is true if
+
+ align:start position:0%
+J then this entire expression is true if
+ 
+
+ align:start position:0%
+J then this entire expression is true if
+they are equal then theti entire
+
+ align:start position:0%
+they are equal then theti entire
+ 
+
+ align:start position:0%
+they are equal then theti entire
+expression is
+
+ align:start position:0%
+expression is
+ 
+
+ align:start position:0%
+expression is
+false and then of course we've got the
+
+ align:start position:0%
+false and then of course we've got the
+ 
+
+ align:start position:0%
+false and then of course we've got the
+uh the less than less than or equal to
+
+ align:start position:0%
+uh the less than less than or equal to
+ 
+
+ align:start position:0%
+uh the less than less than or equal to
+greater greater than or equal to um to
+
+ align:start position:0%
+greater greater than or equal to um to
+ 
+
+ align:start position:0%
+greater greater than or equal to um to
+work with this well
+
+ align:start position:0%
+work with this well
+ 
+
+ align:start position:0%
+work with this well
+we can apply these to
+
+ align:start position:0%
+we can apply these to
+ 
+
+ align:start position:0%
+we can apply these to
+Strings and uh with strings it's
+
+ align:start position:0%
+Strings and uh with strings it's
+ 
+
+ align:start position:0%
+Strings and uh with strings it's
+important to be careful about case so
+
+ align:start position:0%
+important to be careful about case so
+ 
+
+ align:start position:0%
+important to be careful about case so
+for example lower case a equivalent to
+
+ align:start position:0%
+for example lower case a equivalent to
+ 
+
+ align:start position:0%
+for example lower case a equivalent to
+uppercase a is false right because they
+
+ align:start position:0%
+uppercase a is false right because they
+ 
+
+ align:start position:0%
+uppercase a is false right because they
+are not the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+character now that we're talking about
+
+ align:start position:0%
+character now that we're talking about
+ 
+
+ align:start position:0%
+character now that we're talking about
+Boolean operators we can actually start
+
+ align:start position:0%
+Boolean operators we can actually start
+ 
+
+ align:start position:0%
+Boolean operators we can actually start
+to combine them together so if I have
+
+ align:start position:0%
+to combine them together so if I have
+ 
+
+ align:start position:0%
+to combine them together so if I have
+the expression for example 2 less than
+
+ align:start position:0%
+the expression for example 2 less than
+ 
+
+ align:start position:0%
+the expression for example 2 less than
+three right like I wrote on the board
+
+ align:start position:0%
+three right like I wrote on the board
+ 
+
+ align:start position:0%
+three right like I wrote on the board
+that's true
+
+ align:start position:0%
+that's true
+ 
+
+ align:start position:0%
+that's true
+but I can combine that expression with
+
+ align:start position:0%
+but I can combine that expression with
+ 
+
+ align:start position:0%
+but I can combine that expression with
+another one actually by itself I can say
+
+ align:start position:0%
+another one actually by itself I can say
+ 
+
+ align:start position:0%
+another one actually by itself I can say
+what is not two less than three and that
+
+ align:start position:0%
+what is not two less than three and that
+ 
+
+ align:start position:0%
+what is not two less than three and that
+will be false right it's the opposite of
+
+ align:start position:0%
+will be false right it's the opposite of
+ 
+
+ align:start position:0%
+will be false right it's the opposite of
+it but I can also combine Boolean
+
+ align:start position:0%
+it but I can also combine Boolean
+ 
+
+ align:start position:0%
+it but I can also combine Boolean
+Expressions together so I can say what's
+
+ align:start position:0%
+Expressions together so I can say what's
+ 
+
+ align:start position:0%
+Expressions together so I can say what's
+two less than three and uh three less
+
+ align:start position:0%
+two less than three and uh three less
+ 
+
+ align:start position:0%
+two less than three and uh three less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+four so two less than three is true
+
+ align:start position:0%
+four so two less than three is true
+ 
+
+ align:start position:0%
+four so two less than three is true
+right and three less than four is also
+
+ align:start position:0%
+right and three less than four is also
+ 
+
+ align:start position:0%
+right and three less than four is also
+true so the combination of these two
+
+ align:start position:0%
+true so the combination of these two
+ 
+
+ align:start position:0%
+true so the combination of these two
+expression of these two ring Expressions
+
+ align:start position:0%
+expression of these two ring Expressions
+ 
+
+ align:start position:0%
+expression of these two ring Expressions
+is what is true and true
+
+ align:start position:0%
+is what is true and true
+ 
+
+ align:start position:0%
+is what is true and true
+true right so if one is true and the
+
+ align:start position:0%
+true right so if one is true and the
+ 
+
+ align:start position:0%
+true right so if one is true and the
+other one is true then both of them and
+
+ align:start position:0%
+other one is true then both of them and
+ 
+
+ align:start position:0%
+other one is true then both of them and
+both of them together are going to be
+
+ align:start position:0%
+both of them together are going to be
+ 
+
+ align:start position:0%
+both of them together are going to be
+true if one of these is false so is uh
+
+ align:start position:0%
+true if one of these is false so is uh
+ 
+
+ align:start position:0%
+true if one of these is false so is uh
+three greater than four is false well
+
+ align:start position:0%
+three greater than four is false well
+ 
+
+ align:start position:0%
+three greater than four is false well
+what's false and true it's going to be
+
+ align:start position:0%
+what's false and true it's going to be
+ 
+
+ align:start position:0%
+what's false and true it's going to be
+false so if one of these operators is
+
+ align:start position:0%
+false so if one of these operators is
+ 
+
+ align:start position:0%
+false so if one of these operators is
+false then the entire expression is
+
+ align:start position:0%
+false then the entire expression is
+ 
+
+ align:start position:0%
+false then the entire expression is
+false and you don't have have to
+
+ align:start position:0%
+false and you don't have have to
+ 
+
+ align:start position:0%
+false and you don't have have to
+remember this truth table um you can
+
+ align:start position:0%
+remember this truth table um you can
+ 
+
+ align:start position:0%
+remember this truth table um you can
+always check it like I just did right
+
+ align:start position:0%
+always check it like I just did right
+ 
+
+ align:start position:0%
+always check it like I just did right
+here in the
+
+ align:start position:0%
+here in the
+ 
+
+ align:start position:0%
+here in the
+console but at a high level right when
+
+ align:start position:0%
+console but at a high level right when
+ 
+
+ align:start position:0%
+console but at a high level right when
+we're doing the and operator between two
+
+ align:start position:0%
+we're doing the and operator between two
+ 
+
+ align:start position:0%
+we're doing the and operator between two
+Boolean Expressions we need both of the
+
+ align:start position:0%
+Boolean Expressions we need both of the
+ 
+
+ align:start position:0%
+Boolean Expressions we need both of the
+Expressions to be
+
+ align:start position:0%
+Expressions to be
+ 
+
+ align:start position:0%
+Expressions to be
+true for the result and to be true the
+
+ align:start position:0%
+true for the result and to be true the
+ 
+
+ align:start position:0%
+true for the result and to be true the
+or is the other one we usually uh we we
+
+ align:start position:0%
+or is the other one we usually uh we we
+ 
+
+ align:start position:0%
+or is the other one we usually uh we we
+can usually do the or is always true
+
+ align:start position:0%
+can usually do the or is always true
+ 
+
+ align:start position:0%
+can usually do the or is always true
+except for when both of the operators
+
+ align:start position:0%
+except for when both of the operators
+ 
+
+ align:start position:0%
+except for when both of the operators
+are false right and it kind of makes
+
+ align:start position:0%
+are false right and it kind of makes
+ 
+
+ align:start position:0%
+are false right and it kind of makes
+makes sense in English too
+
+ align:start position:0%
+makes sense in English too
+ 
+
+ align:start position:0%
+makes sense in English too
+right if either operator is true then
+
+ align:start position:0%
+right if either operator is true then
+ 
+
+ align:start position:0%
+right if either operator is true then
+the entire result is true but when both
+
+ align:start position:0%
+the entire result is true but when both
+ 
+
+ align:start position:0%
+the entire result is true but when both
+are false the or of both of them is
+
+ align:start position:0%
+are false the or of both of them is
+ 
+
+ align:start position:0%
+are false the or of both of them is
+false as
+
+ align:start position:0%
+false as
+ 
+
+ align:start position:0%
+false as
+well so here's a little example uh where
+
+ align:start position:0%
+well so here's a little example uh where
+ 
+
+ align:start position:0%
+well so here's a little example uh where
+we can use these operators in Python so
+
+ align:start position:0%
+we can use these operators in Python so
+ 
+
+ align:start position:0%
+we can use these operators in Python so
+we can draw the little memory diagram as
+
+ align:start position:0%
+we can draw the little memory diagram as
+ 
+
+ align:start position:0%
+we can draw the little memory diagram as
+well so P set time is 15 there's my
+
+ align:start position:0%
+well so P set time is 15 there's my
+ 
+
+ align:start position:0%
+well so P set time is 15 there's my
+variable sleep time is eight there's my
+
+ align:start position:0%
+variable sleep time is eight there's my
+ 
+
+ align:start position:0%
+variable sleep time is eight there's my
+other variable I'm going to print sleep
+
+ align:start position:0%
+other variable I'm going to print sleep
+ 
+
+ align:start position:0%
+other variable I'm going to print sleep
+time is greater than PE at time so here
+
+ align:start position:0%
+time is greater than PE at time so here
+ 
+
+ align:start position:0%
+time is greater than PE at time so here
+my print statement is going to grab that
+
+ align:start position:0%
+my print statement is going to grab that
+ 
+
+ align:start position:0%
+my print statement is going to grab that
+expression which evaluates
+
+ align:start position:0%
+expression which evaluates
+ 
+
+ align:start position:0%
+expression which evaluates
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+to false 8 is is less than 15 is false
+
+ align:start position:0%
+to false 8 is is less than 15 is false
+ 
+
+ align:start position:0%
+to false 8 is is less than 15 is false
+so that's going to print false and then
+
+ align:start position:0%
+so that's going to print false and then
+ 
+
+ align:start position:0%
+so that's going to print false and then
+I have two more variables these ones
+
+ align:start position:0%
+I have two more variables these ones
+ 
+
+ align:start position:0%
+I have two more variables these ones
+just happen to be booleans derive is
+
+ align:start position:0%
+just happen to be booleans derive is
+ 
+
+ align:start position:0%
+just happen to be booleans derive is
+true drink is false so drink and derive
+
+ align:start position:0%
+true drink is false so drink and derive
+ 
+
+ align:start position:0%
+true drink is false so drink and derive
+is going to be false because one of them
+
+ align:start position:0%
+is going to be false because one of them
+ 
+
+ align:start position:0%
+is going to be false because one of them
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+false and so here I've got this other
+
+ align:start position:0%
+false and so here I've got this other
+ 
+
+ align:start position:0%
+false and so here I've got this other
+variable both and then I'm going to
+
+ align:start position:0%
+variable both and then I'm going to
+ 
+
+ align:start position:0%
+variable both and then I'm going to
+print false to the console
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay quick you try it for you guys so
+
+ align:start position:0%
+okay quick you try it for you guys so
+ 
+
+ align:start position:0%
+okay quick you try it for you guys so
+let's have you write a program that
+
+ align:start position:0%
+let's have you write a program that
+ 
+
+ align:start position:0%
+let's have you write a program that
+saves a secret number in a
+
+ align:start position:0%
+saves a secret number in a
+ 
+
+ align:start position:0%
+saves a secret number in a
+variable okay so that's going to be your
+
+ align:start position:0%
+variable okay so that's going to be your
+ 
+
+ align:start position:0%
+variable okay so that's going to be your
+program's Secrets presumably people uh
+
+ align:start position:0%
+program's Secrets presumably people uh
+ 
+
+ align:start position:0%
+program's Secrets presumably people uh
+using your program won't be looking at
+
+ align:start position:0%
+using your program won't be looking at
+ 
+
+ align:start position:0%
+using your program won't be looking at
+the program itself they'll just be
+
+ align:start position:0%
+the program itself they'll just be
+ 
+
+ align:start position:0%
+the program itself they'll just be
+interacting with the program in the
+
+ align:start position:0%
+interacting with the program in the
+ 
+
+ align:start position:0%
+interacting with the program in the
+Shell so save a secret number in a
+
+ align:start position:0%
+Shell so save a secret number in a
+ 
+
+ align:start position:0%
+Shell so save a secret number in a
+variable ask the user to guess a number
+
+ align:start position:0%
+variable ask the user to guess a number
+ 
+
+ align:start position:0%
+variable ask the user to guess a number
+and then print either true or false if
+
+ align:start position:0%
+and then print either true or false if
+ 
+
+ align:start position:0%
+and then print either true or false if
+it's the same as your secret or not so
+
+ align:start position:0%
+it's the same as your secret or not so
+ 
+
+ align:start position:0%
+it's the same as your secret or not so
+it's here in this you try it down here
+
+ align:start position:0%
+it's here in this you try it down here
+ 
+
+ align:start position:0%
+it's here in this you try it down here
+so you can start with something like
+
+ align:start position:0%
+so you can start with something like
+ 
+
+ align:start position:0%
+so you can start with something like
+secret equals and then put your favorite
+
+ align:start position:0%
+secret equals and then put your favorite
+ 
+
+ align:start position:0%
+secret equals and then put your favorite
+number there five whatever and then
+
+ align:start position:0%
+number there five whatever and then
+ 
+
+ align:start position:0%
+number there five whatever and then
+write the rest of the code so ask the
+
+ align:start position:0%
+write the rest of the code so ask the
+ 
+
+ align:start position:0%
+write the rest of the code so ask the
+user to guess a number print a Boolean
+
+ align:start position:0%
+user to guess a number print a Boolean
+ 
+
+ align:start position:0%
+user to guess a number print a Boolean
+depending on whether the guess equals
+
+ align:start position:0%
+depending on whether the guess equals
+ 
+
+ align:start position:0%
+depending on whether the guess equals
+this secret or not so I'll give you a
+
+ align:start position:0%
+this secret or not so I'll give you a
+ 
+
+ align:start position:0%
+this secret or not so I'll give you a
+couple minutes to write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah
+
+ align:start position:0%
+that yeah
+ 
+
+ align:start position:0%
+that yeah
+sorry the symbol and simar
+
+ align:start position:0%
+sorry the symbol and simar
+ 
+
+ align:start position:0%
+sorry the symbol and simar
+to if you use the symbol and it's not
+
+ align:start position:0%
+to if you use the symbol and it's not
+ 
+
+ align:start position:0%
+to if you use the symbol and it's not
+the same have to actually type out A and
+
+ align:start position:0%
+the same have to actually type out A and
+ 
+
+ align:start position:0%
+the same have to actually type out A and
+D in Python the and means something else
+
+ align:start position:0%
+D in Python the and means something else
+ 
+
+ align:start position:0%
+D in Python the and means something else
+it's like a it's an operator with the
+
+ align:start position:0%
+it's like a it's an operator with the
+ 
+
+ align:start position:0%
+it's like a it's an operator with the
+bits of the number so something it's not
+
+ align:start position:0%
+bits of the number so something it's not
+ 
+
+ align:start position:0%
+bits of the number so something it's not
+going to give the same answers
+
+ align:start position:0%
+going to give the same answers
+ 
+
+ align:start position:0%
+going to give the same answers
+yeah right you're thinking about Java or
+
+ align:start position:0%
+yeah right you're thinking about Java or
+ 
+
+ align:start position:0%
+yeah right you're thinking about Java or
+C++ or something right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah all right does anyone have a start
+
+ align:start position:0%
+yeah all right does anyone have a start
+ 
+
+ align:start position:0%
+yeah all right does anyone have a start
+for me for this program how do I get
+
+ align:start position:0%
+for me for this program how do I get
+ 
+
+ align:start position:0%
+for me for this program how do I get
+grab the user input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+input yeah we can be nice please guess a
+
+ align:start position:0%
+input yeah we can be nice please guess a
+ 
+
+ align:start position:0%
+input yeah we can be nice please guess a
+number what's
+
+ align:start position:0%
+number what's
+ 
+
+ align:start position:0%
+number what's
+that we want the user to give us an
+
+ align:start position:0%
+that we want the user to give us an
+ 
+
+ align:start position:0%
+that we want the user to give us an
+integer yeah a number exactly
+
+ align:start position:0%
+integer yeah a number exactly
+ 
+
+ align:start position:0%
+integer yeah a number exactly
+so okay yeah if we leave it like
+
+ align:start position:0%
+so okay yeah if we leave it like
+ 
+
+ align:start position:0%
+so okay yeah if we leave it like
+that then we're just grabbing the string
+
+ align:start position:0%
+that then we're just grabbing the string
+ 
+
+ align:start position:0%
+that then we're just grabbing the string
+so we have to cast it to an integer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly now
+
+ align:start position:0%
+exactly now
+ 
+
+ align:start position:0%
+exactly now
+what how do I check for equivalency
+
+ align:start position:0%
+what how do I check for equivalency
+ 
+
+ align:start position:0%
+what how do I check for equivalency
+between my secret and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guests
+
+ align:start position:0%
+guests
+ 
+
+ align:start position:0%
+guests
+secret equal equal
+
+ align:start position:0%
+secret equal equal
+ 
+
+ align:start position:0%
+secret equal equal
+guess and do you want to print this yeah
+
+ align:start position:0%
+guess and do you want to print this yeah
+ 
+
+ align:start position:0%
+guess and do you want to print this yeah
+let's print
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay run it
+
+ align:start position:0%
+that okay run it
+ 
+
+ align:start position:0%
+that okay run it
+let's guess something that's not the
+
+ align:start position:0%
+let's guess something that's not the
+ 
+
+ align:start position:0%
+let's guess something that's not the
+same false run it again let's guess
+
+ align:start position:0%
+same false run it again let's guess
+ 
+
+ align:start position:0%
+same false run it again let's guess
+something that's the same true and we
+
+ align:start position:0%
+something that's the same true and we
+ 
+
+ align:start position:0%
+something that's the same true and we
+can guess something that's lower too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just is everyone yeah you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assign secret equal
+
+ align:start position:0%
+assign secret equal
+ 
+
+ align:start position:0%
+assign secret equal
+yes con yep yep exactly equal equals
+
+ align:start position:0%
+yes con yep yep exactly equal equals
+ 
+
+ align:start position:0%
+yes con yep yep exactly equal equals
+this thing yep and then you can you know
+
+ align:start position:0%
+this thing yep and then you can you know
+ 
+
+ align:start position:0%
+this thing yep and then you can you know
+do whatever you want with that print
+
+ align:start position:0%
+do whatever you want with that print
+ 
+
+ align:start position:0%
+do whatever you want with that print
+equals or something that's the same but
+
+ align:start position:0%
+equals or something that's the same but
+ 
+
+ align:start position:0%
+equals or something that's the same but
+yeah you can do other things with this
+
+ align:start position:0%
+yeah you can do other things with this
+ 
+
+ align:start position:0%
+yeah you can do other things with this
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+yeah exactly five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah if you want at home try to see what
+
+ align:start position:0%
+yeah if you want at home try to see what
+ 
+
+ align:start position:0%
+yeah if you want at home try to see what
+would have happened if you didn't cast
+
+ align:start position:0%
+would have happened if you didn't cast
+ 
+
+ align:start position:0%
+would have happened if you didn't cast
+it to an
+
+ align:start position:0%
+it to an
+ 
+
+ align:start position:0%
+it to an
+integer uh see if the program would have
+
+ align:start position:0%
+integer uh see if the program would have
+ 
+
+ align:start position:0%
+integer uh see if the program would have
+crashed or not or if it would have just
+
+ align:start position:0%
+crashed or not or if it would have just
+ 
+
+ align:start position:0%
+crashed or not or if it would have just
+you know worked but given a wrong answer
+
+ align:start position:0%
+you know worked but given a wrong answer
+ 
+
+ align:start position:0%
+you know worked but given a wrong answer
+so why do we do booleans right booleans
+
+ align:start position:0%
+so why do we do booleans right booleans
+ 
+
+ align:start position:0%
+so why do we do booleans right booleans
+are important variables because they
+
+ align:start position:0%
+are important variables because they
+ 
+
+ align:start position:0%
+are important variables because they
+allow us to start thinking about writing
+
+ align:start position:0%
+allow us to start thinking about writing
+ 
+
+ align:start position:0%
+allow us to start thinking about writing
+programs that make decisions right the
+
+ align:start position:0%
+programs that make decisions right the
+ 
+
+ align:start position:0%
+programs that make decisions right the
+way we talk is you know we can say
+
+ align:start position:0%
+way we talk is you know we can say
+ 
+
+ align:start position:0%
+way we talk is you know we can say
+something like if this is true do this
+
+ align:start position:0%
+something like if this is true do this
+ 
+
+ align:start position:0%
+something like if this is true do this
+otherwise do this the Boolean part is if
+
+ align:start position:0%
+otherwise do this the Boolean part is if
+ 
+
+ align:start position:0%
+otherwise do this the Boolean part is if
+that something is true right so the
+
+ align:start position:0%
+that something is true right so the
+ 
+
+ align:start position:0%
+that something is true right so the
+something is true is going to be the the
+
+ align:start position:0%
+something is true is going to be the the
+ 
+
+ align:start position:0%
+something is true is going to be the the
+Boolean that we can create in our
+
+ align:start position:0%
+Boolean that we can create in our
+ 
+
+ align:start position:0%
+Boolean that we can create in our
+programs and then the do this is some
+
+ align:start position:0%
+programs and then the do this is some
+ 
+
+ align:start position:0%
+programs and then the do this is some
+sort of commands and then the otherwise
+
+ align:start position:0%
+sort of commands and then the otherwise
+ 
+
+ align:start position:0%
+sort of commands and then the otherwise
+do that is going to be some other set of
+
+ align:start position:0%
+do that is going to be some other set of
+ 
+
+ align:start position:0%
+do that is going to be some other set of
+commands Okay so a really simple uh you
+
+ align:start position:0%
+commands Okay so a really simple uh you
+ 
+
+ align:start position:0%
+commands Okay so a really simple uh you
+know Boolean expression could be it's
+
+ align:start position:0%
+know Boolean expression could be it's
+ 
+
+ align:start position:0%
+know Boolean expression could be it's
+midnight you get a free food email do
+
+ align:start position:0%
+midnight you get a free food email do
+ 
+
+ align:start position:0%
+midnight you get a free food email do
+you go get the free food or do you sleep
+
+ align:start position:0%
+you go get the free food or do you sleep
+ 
+
+ align:start position:0%
+you go get the free food or do you sleep
+right that's the very simplest kind of
+
+ align:start position:0%
+right that's the very simplest kind of
+ 
+
+ align:start position:0%
+right that's the very simplest kind of
+decision point you can make but with
+
+ align:start position:0%
+decision point you can make but with
+ 
+
+ align:start position:0%
+decision point you can make but with
+conditionals you can actually write a
+
+ align:start position:0%
+conditionals you can actually write a
+ 
+
+ align:start position:0%
+conditionals you can actually write a
+pretty cool program that gets you to
+
+ align:start position:0%
+pretty cool program that gets you to
+ 
+
+ align:start position:0%
+pretty cool program that gets you to
+that free food right so let's say this
+
+ align:start position:0%
+that free food right so let's say this
+ 
+
+ align:start position:0%
+that free food right so let's say this
+is a map of MIT this is where you are
+
+ align:start position:0%
+is a map of MIT this is where you are
+ 
+
+ align:start position:0%
+is a map of MIT this is where you are
+that's where the free food is okay we
+
+ align:start position:0%
+that's where the free food is okay we
+ 
+
+ align:start position:0%
+that's where the free food is okay we
+can write a really simple algorithm
+
+ align:start position:0%
+can write a really simple algorithm
+ 
+
+ align:start position:0%
+can write a really simple algorithm
+using just conditionals that takes you
+
+ align:start position:0%
+using just conditionals that takes you
+ 
+
+ align:start position:0%
+using just conditionals that takes you
+to that free food so the algorithm goes
+
+ align:start position:0%
+to that free food so the algorithm goes
+ 
+
+ align:start position:0%
+to that free food so the algorithm goes
+like this so I'm going to say I'm going
+
+ align:start position:0%
+like this so I'm going to say I'm going
+ 
+
+ align:start position:0%
+like this so I'm going to say I'm going
+to walk always you know in this
+
+ align:start position:0%
+to walk always you know in this
+ 
+
+ align:start position:0%
+to walk always you know in this
+direction so I'm either going forward
+
+ align:start position:0%
+direction so I'm either going forward
+ 
+
+ align:start position:0%
+direction so I'm either going forward
+backward left and right I'm not turning
+
+ align:start position:0%
+backward left and right I'm not turning
+ 
+
+ align:start position:0%
+backward left and right I'm not turning
+and I'm going to say the algorithm is
+
+ align:start position:0%
+and I'm going to say the algorithm is
+ 
+
+ align:start position:0%
+and I'm going to say the algorithm is
+always going to have my right hand be on
+
+ align:start position:0%
+always going to have my right hand be on
+ 
+
+ align:start position:0%
+always going to have my right hand be on
+a wall so if the right is clear so
+
+ align:start position:0%
+a wall so if the right is clear so
+ 
+
+ align:start position:0%
+a wall so if the right is clear so
+standing here my right is clear so I'm
+
+ align:start position:0%
+standing here my right is clear so I'm
+ 
+
+ align:start position:0%
+standing here my right is clear so I'm
+just going to keep shimming until I
+
+ align:start position:0%
+just going to keep shimming until I
+ 
+
+ align:start position:0%
+just going to keep shimming until I
+reach a wall if my right is blocked but
+
+ align:start position:0%
+reach a wall if my right is blocked but
+ 
+
+ align:start position:0%
+reach a wall if my right is blocked but
+my forward is clear I'm going to keep
+
+ align:start position:0%
+my forward is clear I'm going to keep
+ 
+
+ align:start position:0%
+my forward is clear I'm going to keep
+going like this all the way to the end
+
+ align:start position:0%
+going like this all the way to the end
+ 
+
+ align:start position:0%
+going like this all the way to the end
+of this uh the the um the the the um the
+
+ align:start position:0%
+of this uh the the um the the the um the
+ 
+
+ align:start position:0%
+of this uh the the um the the the um the
+room if my right is blocked and my
+
+ align:start position:0%
+room if my right is blocked and my
+ 
+
+ align:start position:0%
+room if my right is blocked and my
+forward is blocked right as if I would
+
+ align:start position:0%
+forward is blocked right as if I would
+ 
+
+ align:start position:0%
+forward is blocked right as if I would
+have reached the end of the room I would
+
+ align:start position:0%
+have reached the end of the room I would
+ 
+
+ align:start position:0%
+have reached the end of the room I would
+have gone to the left and if my right
+
+ align:start position:0%
+have gone to the left and if my right
+ 
+
+ align:start position:0%
+have gone to the left and if my right
+forward and left is blocked if I'm over
+
+ align:start position:0%
+forward and left is blocked if I'm over
+ 
+
+ align:start position:0%
+forward and left is blocked if I'm over
+there I would go backward right so I'd
+
+ align:start position:0%
+there I would go backward right so I'd
+ 
+
+ align:start position:0%
+there I would go backward right so I'd
+go backward so basically starting from
+
+ align:start position:0%
+go backward so basically starting from
+ 
+
+ align:start position:0%
+go backward so basically starting from
+here I've made my way all the way around
+
+ align:start position:0%
+here I've made my way all the way around
+ 
+
+ align:start position:0%
+here I've made my way all the way around
+this room and I would go out the door
+
+ align:start position:0%
+this room and I would go out the door
+ 
+
+ align:start position:0%
+this room and I would go out the door
+down the hallway right and if the map of
+
+ align:start position:0%
+down the hallway right and if the map of
+ 
+
+ align:start position:0%
+down the hallway right and if the map of
+MIT doesn't have Islands so if the free
+
+ align:start position:0%
+MIT doesn't have Islands so if the free
+ 
+
+ align:start position:0%
+MIT doesn't have Islands so if the free
+food isn't somewhere sort of in an
+
+ align:start position:0%
+food isn't somewhere sort of in an
+ 
+
+ align:start position:0%
+food isn't somewhere sort of in an
+island in the middle here if it's just a
+
+ align:start position:0%
+island in the middle here if it's just a
+ 
+
+ align:start position:0%
+island in the middle here if it's just a
+a regular old maze I would eventually
+
+ align:start position:0%
+a regular old maze I would eventually
+ 
+
+ align:start position:0%
+a regular old maze I would eventually
+make my way to the free food following
+
+ align:start position:0%
+make my way to the free food following
+ 
+
+ align:start position:0%
+make my way to the free food following
+this really simple conditional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm so how do we actually do
+
+ align:start position:0%
+algorithm so how do we actually do
+ 
+
+ align:start position:0%
+algorithm so how do we actually do
+conditionals in Python how do we tell
+
+ align:start position:0%
+conditionals in Python how do we tell
+ 
+
+ align:start position:0%
+conditionals in Python how do we tell
+python hey I want to create I want to
+
+ align:start position:0%
+python hey I want to create I want to
+ 
+
+ align:start position:0%
+python hey I want to create I want to
+insert a decision point right here we do
+
+ align:start position:0%
+insert a decision point right here we do
+ 
+
+ align:start position:0%
+insert a decision point right here we do
+that using the keyword if and the if
+
+ align:start position:0%
+that using the keyword if and the if
+ 
+
+ align:start position:0%
+that using the keyword if and the if
+starts a decision
+
+ align:start position:0%
+starts a decision
+ 
+
+ align:start position:0%
+starts a decision
+block now the simplest decision block is
+
+ align:start position:0%
+block now the simplest decision block is
+ 
+
+ align:start position:0%
+block now the simplest decision block is
+just an if by itself so if python sees
+
+ align:start position:0%
+just an if by itself so if python sees
+ 
+
+ align:start position:0%
+just an if by itself so if python sees
+that if so there's some code that it's
+
+ align:start position:0%
+that if so there's some code that it's
+ 
+
+ align:start position:0%
+that if so there's some code that it's
+following and then at some point it
+
+ align:start position:0%
+following and then at some point it
+ 
+
+ align:start position:0%
+following and then at some point it
+reaches the if the condition tells
+
+ align:start position:0%
+reaches the if the condition tells
+ 
+
+ align:start position:0%
+reaches the if the condition tells
+python uh to to check whether that
+
+ align:start position:0%
+python uh to to check whether that
+ 
+
+ align:start position:0%
+python uh to to check whether that
+condition is true if the condition is
+
+ align:start position:0%
+condition is true if the condition is
+ 
+
+ align:start position:0%
+condition is true if the condition is
+true so this is our decision point then
+
+ align:start position:0%
+true so this is our decision point then
+ 
+
+ align:start position:0%
+true so this is our decision point then
+I'm going to deviate from my main
+
+ align:start position:0%
+I'm going to deviate from my main
+ 
+
+ align:start position:0%
+I'm going to deviate from my main
+program and potential and and do the
+
+ align:start position:0%
+program and potential and and do the
+ 
+
+ align:start position:0%
+program and potential and and do the
+code that's part of that
+
+ align:start position:0%
+code that's part of that
+ 
+
+ align:start position:0%
+code that's part of that
+condition those I guess two lines dot
+
+ align:start position:0%
+condition those I guess two lines dot
+ 
+
+ align:start position:0%
+condition those I guess two lines dot
+dot dot inside there if the condition is
+
+ align:start position:0%
+dot dot inside there if the condition is
+ 
+
+ align:start position:0%
+dot dot inside there if the condition is
+not false I'm not going to go that route
+
+ align:start position:0%
+not false I'm not going to go that route
+ 
+
+ align:start position:0%
+not false I'm not going to go that route
+and I'll just keep following the rest of
+
+ align:start position:0%
+and I'll just keep following the rest of
+ 
+
+ align:start position:0%
+and I'll just keep following the rest of
+main
+
+ align:start position:0%
+main
+ 
+
+ align:start position:0%
+main
+program how does python know how many
+
+ align:start position:0%
+program how does python know how many
+ 
+
+ align:start position:0%
+program how does python know how many
+code code lines to execute that's part
+
+ align:start position:0%
+code code lines to execute that's part
+ 
+
+ align:start position:0%
+code code lines to execute that's part
+of that condition well it looks at the
+
+ align:start position:0%
+of that condition well it looks at the
+ 
+
+ align:start position:0%
+of that condition well it looks at the
+indentation so notice here I've kind of
+
+ align:start position:0%
+indentation so notice here I've kind of
+ 
+
+ align:start position:0%
+indentation so notice here I've kind of
+put a few spaces and for these two and
+
+ align:start position:0%
+put a few spaces and for these two and
+ 
+
+ align:start position:0%
+put a few spaces and for these two and
+dot dot dot code blocks here anything
+
+ align:start position:0%
+dot dot dot code blocks here anything
+ 
+
+ align:start position:0%
+dot dot dot code blocks here anything
+that's indented right after that if
+
+ align:start position:0%
+that's indented right after that if
+ 
+
+ align:start position:0%
+that's indented right after that if
+statement and that colon there is a a
+
+ align:start position:0%
+statement and that colon there is a a
+ 
+
+ align:start position:0%
+statement and that colon there is a a
+set of commands that are part of that
+
+ align:start position:0%
+set of commands that are part of that
+ 
+
+ align:start position:0%
+set of commands that are part of that
+block so anything here will get executed
+
+ align:start position:0%
+block so anything here will get executed
+ 
+
+ align:start position:0%
+block so anything here will get executed
+all at
+
+ align:start position:0%
+all at
+ 
+
+ align:start position:0%
+all at
+once and that's a really simple if
+
+ align:start position:0%
+once and that's a really simple if
+ 
+
+ align:start position:0%
+once and that's a really simple if
+either you do this set of commands extra
+
+ align:start position:0%
+either you do this set of commands extra
+ 
+
+ align:start position:0%
+either you do this set of commands extra
+commands if the condition is true or you
+
+ align:start position:0%
+commands if the condition is true or you
+ 
+
+ align:start position:0%
+commands if the condition is true or you
+don't now you can add an exception to
+
+ align:start position:0%
+don't now you can add an exception to
+ 
+
+ align:start position:0%
+don't now you can add an exception to
+that so if the condition is true again
+
+ align:start position:0%
+that so if the condition is true again
+ 
+
+ align:start position:0%
+that so if the condition is true again
+we're following the program we reach
+
+ align:start position:0%
+we're following the program we reach
+ 
+
+ align:start position:0%
+we're following the program we reach
+this if conditional here if the
+
+ align:start position:0%
+this if conditional here if the
+ 
+
+ align:start position:0%
+this if conditional here if the
+condition is true again we're going to
+
+ align:start position:0%
+condition is true again we're going to
+ 
+
+ align:start position:0%
+condition is true again we're going to
+deviate from the program and execute
+
+ align:start position:0%
+deviate from the program and execute
+ 
+
+ align:start position:0%
+deviate from the program and execute
+this other set of commands right
+
+ align:start position:0%
+this other set of commands right
+ 
+
+ align:start position:0%
+this other set of commands right
+here otherwise the condition is not true
+
+ align:start position:0%
+here otherwise the condition is not true
+ 
+
+ align:start position:0%
+here otherwise the condition is not true
+and we're going to execute this other
+
+ align:start position:0%
+and we're going to execute this other
+ 
+
+ align:start position:0%
+and we're going to execute this other
+set of commands over here so these guys
+
+ align:start position:0%
+set of commands over here so these guys
+ 
+
+ align:start position:0%
+set of commands over here so these guys
+over here so either we do this set of
+
+ align:start position:0%
+over here so either we do this set of
+ 
+
+ align:start position:0%
+over here so either we do this set of
+commands or the other set of commands
+
+ align:start position:0%
+commands or the other set of commands
+ 
+
+ align:start position:0%
+commands or the other set of commands
+but we never do both and we never skip
+
+ align:start position:0%
+but we never do both and we never skip
+ 
+
+ align:start position:0%
+but we never do both and we never skip
+both of them so either we do one set or
+
+ align:start position:0%
+both of them so either we do one set or
+ 
+
+ align:start position:0%
+both of them so either we do one set or
+the other when we're done executing all
+
+ align:start position:0%
+the other when we're done executing all
+ 
+
+ align:start position:0%
+the other when we're done executing all
+the indented Blocks part of the
+
+ align:start position:0%
+the indented Blocks part of the
+ 
+
+ align:start position:0%
+the indented Blocks part of the
+condition or the other one that's that
+
+ align:start position:0%
+condition or the other one that's that
+ 
+
+ align:start position:0%
+condition or the other one that's that
+if the condition wasn't true then we
+
+ align:start position:0%
+if the condition wasn't true then we
+ 
+
+ align:start position:0%
+if the condition wasn't true then we
+rejoin the rest of the program and
+
+ align:start position:0%
+rejoin the rest of the program and
+ 
+
+ align:start position:0%
+rejoin the rest of the program and
+continue executing so this is all the
+
+ align:start position:0%
+continue executing so this is all the
+ 
+
+ align:start position:0%
+continue executing so this is all the
+rest of the program is at the same
+
+ align:start position:0%
+rest of the program is at the same
+ 
+
+ align:start position:0%
+rest of the program is at the same
+indentation level as our original if and
+
+ align:start position:0%
+indentation level as our original if and
+ 
+
+ align:start position:0%
+indentation level as our original if and
+else we can add a whole bunch of
+
+ align:start position:0%
+else we can add a whole bunch of
+ 
+
+ align:start position:0%
+else we can add a whole bunch of
+conditions right not just an if do this
+
+ align:start position:0%
+conditions right not just an if do this
+ 
+
+ align:start position:0%
+conditions right not just an if do this
+otherwise do this we can actually
+
+ align:start position:0%
+otherwise do this we can actually
+ 
+
+ align:start position:0%
+otherwise do this we can actually
+add a bunch of things to check using L
+
+ align:start position:0%
+add a bunch of things to check using L
+ 
+
+ align:start position:0%
+add a bunch of things to check using L
+if which basically stands for else if
+
+ align:start position:0%
+if which basically stands for else if
+ 
+
+ align:start position:0%
+if which basically stands for else if
+another condition do this so here's our
+
+ align:start position:0%
+another condition do this so here's our
+ 
+
+ align:start position:0%
+another condition do this so here's our
+program we reach a decision point if the
+
+ align:start position:0%
+program we reach a decision point if the
+ 
+
+ align:start position:0%
+program we reach a decision point if the
+condition is true like before we'll
+
+ align:start position:0%
+condition is true like before we'll
+ 
+
+ align:start position:0%
+condition is true like before we'll
+execute the set of commands but
+
+ align:start position:0%
+execute the set of commands but
+ 
+
+ align:start position:0%
+execute the set of commands but
+otherwise the condition is not
+
+ align:start position:0%
+otherwise the condition is not
+ 
+
+ align:start position:0%
+otherwise the condition is not
+true we're going to check another
+
+ align:start position:0%
+true we're going to check another
+ 
+
+ align:start position:0%
+true we're going to check another
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+else if this other condition is is true
+
+ align:start position:0%
+else if this other condition is is true
+ 
+
+ align:start position:0%
+else if this other condition is is true
+we'll execute this other set of commands
+
+ align:start position:0%
+we'll execute this other set of commands
+ 
+
+ align:start position:0%
+we'll execute this other set of commands
+otherwise here's another elsf we'll
+
+ align:start position:0%
+otherwise here's another elsf we'll
+ 
+
+ align:start position:0%
+otherwise here's another elsf we'll
+check another condition if it's true
+
+ align:start position:0%
+check another condition if it's true
+ 
+
+ align:start position:0%
+check another condition if it's true
+we'll execute some other set of commands
+
+ align:start position:0%
+we'll execute some other set of commands
+ 
+
+ align:start position:0%
+we'll execute some other set of commands
+otherwise there can be more L ifs and at
+
+ align:start position:0%
+otherwise there can be more L ifs and at
+ 
+
+ align:start position:0%
+otherwise there can be more L ifs and at
+some point we're going to rejoin the
+
+ align:start position:0%
+some point we're going to rejoin the
+ 
+
+ align:start position:0%
+some point we're going to rejoin the
+rest of the
+
+ align:start position:0%
+rest of the
+ 
+
+ align:start position:0%
+rest of the
+program now these L ifs are going to be
+
+ align:start position:0%
+program now these L ifs are going to be
+ 
+
+ align:start position:0%
+program now these L ifs are going to be
+each condition is checked one at a time
+
+ align:start position:0%
+each condition is checked one at a time
+ 
+
+ align:start position:0%
+each condition is checked one at a time
+the very first one that's true is the
+
+ align:start position:0%
+the very first one that's true is the
+ 
+
+ align:start position:0%
+the very first one that's true is the
+one that gets executed we're never going
+
+ align:start position:0%
+one that gets executed we're never going
+ 
+
+ align:start position:0%
+one that gets executed we're never going
+to execute more than one right because
+
+ align:start position:0%
+to execute more than one right because
+ 
+
+ align:start position:0%
+to execute more than one right because
+this is an if else if else if else if so
+
+ align:start position:0%
+this is an if else if else if else if so
+ 
+
+ align:start position:0%
+this is an if else if else if else if so
+even in English you're only going to do
+
+ align:start position:0%
+even in English you're only going to do
+ 
+
+ align:start position:0%
+even in English you're only going to do
+one of these right you're never going to
+
+ align:start position:0%
+one of these right you're never going to
+ 
+
+ align:start position:0%
+one of these right you're never going to
+do all of them it is possible to skip
+
+ align:start position:0%
+do all of them it is possible to skip
+ 
+
+ align:start position:0%
+do all of them it is possible to skip
+all of them though because if none of
+
+ align:start position:0%
+all of them though because if none of
+ 
+
+ align:start position:0%
+all of them though because if none of
+those conditions are true you just don't
+
+ align:start position:0%
+those conditions are true you just don't
+ 
+
+ align:start position:0%
+those conditions are true you just don't
+do any of them if more than one is true
+
+ align:start position:0%
+do any of them if more than one is true
+ 
+
+ align:start position:0%
+do any of them if more than one is true
+you do the first one that is
+
+ align:start position:0%
+you do the first one that is
+ 
+
+ align:start position:0%
+you do the first one that is
+true if you want to have sort of a
+
+ align:start position:0%
+true if you want to have sort of a
+ 
+
+ align:start position:0%
+true if you want to have sort of a
+catchall kind of version of the middle L
+
+ align:start position:0%
+catchall kind of version of the middle L
+ 
+
+ align:start position:0%
+catchall kind of version of the middle L
+if L if L if L if you just add an else
+
+ align:start position:0%
+if L if L if L if you just add an else
+ 
+
+ align:start position:0%
+if L if L if L if you just add an else
+at the end so if none of those condition
+
+ align:start position:0%
+at the end so if none of those condition
+ 
+
+ align:start position:0%
+at the end so if none of those condition
+are true you can add an else which says
+
+ align:start position:0%
+are true you can add an else which says
+ 
+
+ align:start position:0%
+are true you can add an else which says
+you just do this if nothing is
+
+ align:start position:0%
+you just do this if nothing is
+ 
+
+ align:start position:0%
+you just do this if nothing is
+true okay kind of like what we had over
+
+ align:start position:0%
+true okay kind of like what we had over
+ 
+
+ align:start position:0%
+true okay kind of like what we had over
+here if this one otherwise do this well
+
+ align:start position:0%
+here if this one otherwise do this well
+ 
+
+ align:start position:0%
+here if this one otherwise do this well
+if any of these conditions are true do
+
+ align:start position:0%
+if any of these conditions are true do
+ 
+
+ align:start position:0%
+if any of these conditions are true do
+one of them otherwise do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing so here's an example we've got
+
+ align:start position:0%
+thing so here's an example we've got
+ 
+
+ align:start position:0%
+thing so here's an example we've got
+piece at time we'll just put some
+
+ align:start position:0%
+piece at time we'll just put some
+ 
+
+ align:start position:0%
+piece at time we'll just put some
+variables in there sleep time we'll put
+
+ align:start position:0%
+variables in there sleep time we'll put
+ 
+
+ align:start position:0%
+variables in there sleep time we'll put
+some variables in there and run it see
+
+ align:start position:0%
+some variables in there and run it see
+ 
+
+ align:start position:0%
+some variables in there and run it see
+what we get I've got one code block here
+
+ align:start position:0%
+what we get I've got one code block here
+ 
+
+ align:start position:0%
+what we get I've got one code block here
+and if if and an else so the first code
+
+ align:start position:0%
+and if if and an else so the first code
+ 
+
+ align:start position:0%
+and if if and an else so the first code
+block the condition is it checks that
+
+ align:start position:0%
+block the condition is it checks that
+ 
+
+ align:start position:0%
+block the condition is it checks that
+the the sum of those two is greater than
+
+ align:start position:0%
+the the sum of those two is greater than
+ 
+
+ align:start position:0%
+the the sum of those two is greater than
+24 and it does something this is the
+
+ align:start position:0%
+24 and it does something this is the
+ 
+
+ align:start position:0%
+24 and it does something this is the
+block that's part of that condition
+
+ align:start position:0%
+block that's part of that condition
+ 
+
+ align:start position:0%
+block that's part of that condition
+notice it's indented by usually four
+
+ align:start position:0%
+notice it's indented by usually four
+ 
+
+ align:start position:0%
+notice it's indented by usually four
+spaces L if so if this one was not true
+
+ align:start position:0%
+spaces L if so if this one was not true
+ 
+
+ align:start position:0%
+spaces L if so if this one was not true
+then I'm going to go ahead and check the
+
+ align:start position:0%
+then I'm going to go ahead and check the
+ 
+
+ align:start position:0%
+then I'm going to go ahead and check the
+next one uh the next condition is that
+
+ align:start position:0%
+next one uh the next condition is that
+ 
+
+ align:start position:0%
+next one uh the next condition is that
+the addition is greater than or equal to
+
+ align:start position:0%
+the addition is greater than or equal to
+ 
+
+ align:start position:0%
+the addition is greater than or equal to
+24 and then we're going to do this print
+
+ align:start position:0%
+24 and then we're going to do this print
+ 
+
+ align:start position:0%
+24 and then we're going to do this print
+statement
+
+ align:start position:0%
+statement
+ 
+
+ align:start position:0%
+statement
+here and if neither of those are true
+
+ align:start position:0%
+here and if neither of those are true
+ 
+
+ align:start position:0%
+here and if neither of those are true
+I'm going to do whatever is in in this
+
+ align:start position:0%
+I'm going to do whatever is in in this
+ 
+
+ align:start position:0%
+I'm going to do whatever is in in this
+code block here I'm going to do these
+
+ align:start position:0%
+code block here I'm going to do these
+ 
+
+ align:start position:0%
+code block here I'm going to do these
+two lines okay so this is my sort of I
+
+ align:start position:0%
+two lines okay so this is my sort of I
+ 
+
+ align:start position:0%
+two lines okay so this is my sort of I
+call it a catchall because none of those
+
+ align:start position:0%
+call it a catchall because none of those
+ 
+
+ align:start position:0%
+call it a catchall because none of those
+other conditions were true so we're
+
+ align:start position:0%
+other conditions were true so we're
+ 
+
+ align:start position:0%
+other conditions were true so we're
+going to catch ourselves and do this PR
+
+ align:start position:0%
+going to catch ourselves and do this PR
+ 
+
+ align:start position:0%
+going to catch ourselves and do this PR
+uh do these commands here and otherwise
+
+ align:start position:0%
+uh do these commands here and otherwise
+ 
+
+ align:start position:0%
+uh do these commands here and otherwise
+uh once we finish doing either this one
+
+ align:start position:0%
+uh once we finish doing either this one
+ 
+
+ align:start position:0%
+uh once we finish doing either this one
+or this one or catching whatever is left
+
+ align:start position:0%
+or this one or catching whatever is left
+ 
+
+ align:start position:0%
+or this one or catching whatever is left
+over in here we're going to evaluate the
+
+ align:start position:0%
+over in here we're going to evaluate the
+ 
+
+ align:start position:0%
+over in here we're going to evaluate the
+print statement here and I'm going to
+
+ align:start position:0%
+print statement here and I'm going to
+ 
+
+ align:start position:0%
+print statement here and I'm going to
+print end of day because this is the
+
+ align:start position:0%
+print end of day because this is the
+ 
+
+ align:start position:0%
+print end of day because this is the
+rest of my program notice it's at the
+
+ align:start position:0%
+rest of my program notice it's at the
+ 
+
+ align:start position:0%
+rest of my program notice it's at the
+same indentation level as my original
+
+ align:start position:0%
+same indentation level as my original
+ 
+
+ align:start position:0%
+same indentation level as my original
+program
+
+ align:start position:0%
+program
+ 
+
+ align:start position:0%
+program
+so here
+
+ align:start position:0%
+so here
+ 
+
+ align:start position:0%
+so here
+is this oops this
+
+ align:start position:0%
+is this oops this
+ 
+
+ align:start position:0%
+is this oops this
+program so if uh piece at time and sleep
+
+ align:start position:0%
+program so if uh piece at time and sleep
+ 
+
+ align:start position:0%
+program so if uh piece at time and sleep
+time is uh 22 and 8 right the addition
+
+ align:start position:0%
+time is uh 22 and 8 right the addition
+ 
+
+ align:start position:0%
+time is uh 22 and 8 right the addition
+is more than 24 so this is going to
+
+ align:start position:0%
+is more than 24 so this is going to
+ 
+
+ align:start position:0%
+is more than 24 so this is going to
+enter this code block here and print
+
+ align:start position:0%
+enter this code block here and print
+ 
+
+ align:start position:0%
+enter this code block here and print
+impossible if it's exactly equal to 24
+
+ align:start position:0%
+impossible if it's exactly equal to 24
+ 
+
+ align:start position:0%
+impossible if it's exactly equal to 24
+right so 22 and two we're not going to
+
+ align:start position:0%
+right so 22 and two we're not going to
+ 
+
+ align:start position:0%
+right so 22 and two we're not going to
+enter this one but we will will enter
+
+ align:start position:0%
+enter this one but we will will enter
+ 
+
+ align:start position:0%
+enter this one but we will will enter
+this one right because it's exactly
+
+ align:start position:0%
+this one right because it's exactly
+ 
+
+ align:start position:0%
+this one right because it's exactly
+equal to it's not greater than so then
+
+ align:start position:0%
+equal to it's not greater than so then
+ 
+
+ align:start position:0%
+equal to it's not greater than so then
+we're going to print full schedule and
+
+ align:start position:0%
+we're going to print full schedule and
+ 
+
+ align:start position:0%
+we're going to print full schedule and
+then rejoin the rest of the program here
+
+ align:start position:0%
+then rejoin the rest of the program here
+ 
+
+ align:start position:0%
+then rejoin the rest of the program here
+and print end of
+
+ align:start position:0%
+and print end of
+ 
+
+ align:start position:0%
+and print end of
+day and otherwise if this is something
+
+ align:start position:0%
+day and otherwise if this is something
+ 
+
+ align:start position:0%
+day and otherwise if this is something
+low right less than 24 and not equal to
+
+ align:start position:0%
+low right less than 24 and not equal to
+ 
+
+ align:start position:0%
+low right less than 24 and not equal to
+24 right so neither of these conditions
+
+ align:start position:0%
+24 right so neither of these conditions
+ 
+
+ align:start position:0%
+24 right so neither of these conditions
+are true then we're going to enter the
+
+ align:start position:0%
+are true then we're going to enter the
+ 
+
+ align:start position:0%
+are true then we're going to enter the
+else and we're going to evaluate uh or
+
+ align:start position:0%
+else and we're going to evaluate uh or
+ 
+
+ align:start position:0%
+else and we're going to evaluate uh or
+run these two lines of code here so the
+
+ align:start position:0%
+run these two lines of code here so the
+ 
+
+ align:start position:0%
+run these two lines of code here so the
+two lines of code here are going to grab
+
+ align:start position:0%
+two lines of code here are going to grab
+ 
+
+ align:start position:0%
+two lines of code here are going to grab
+the absolute value of 24 minus the P set
+
+ align:start position:0%
+the absolute value of 24 minus the P set
+ 
+
+ align:start position:0%
+the absolute value of 24 minus the P set
+time minus the sleep time figuring out
+
+ align:start position:0%
+time minus the sleep time figuring out
+ 
+
+ align:start position:0%
+time minus the sleep time figuring out
+how much time we have left in the day
+
+ align:start position:0%
+how much time we have left in the day
+ 
+
+ align:start position:0%
+how much time we have left in the day
+it's also going to print this line here
+
+ align:start position:0%
+it's also going to print this line here
+ 
+
+ align:start position:0%
+it's also going to print this line here
+and then rejoin the rest of the program
+
+ align:start position:0%
+and then rejoin the rest of the program
+ 
+
+ align:start position:0%
+and then rejoin the rest of the program
+to print end of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+day okay Quick Check nothing to run
+
+ align:start position:0%
+day okay Quick Check nothing to run
+ 
+
+ align:start position:0%
+day okay Quick Check nothing to run
+nothing to write here nothing to run
+
+ align:start position:0%
+nothing to write here nothing to run
+ 
+
+ align:start position:0%
+nothing to write here nothing to run
+think about this program what is wrong
+
+ align:start position:0%
+think about this program what is wrong
+ 
+
+ align:start position:0%
+think about this program what is wrong
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so I'm grabbing a number for x a
+
+ align:start position:0%
+it so I'm grabbing a number for x a
+ 
+
+ align:start position:0%
+it so I'm grabbing a number for x a
+number for y and I'm checking if x is
+
+ align:start position:0%
+number for y and I'm checking if x is
+ 
+
+ align:start position:0%
+number for y and I'm checking if x is
+the same as y I'm printing X is the same
+
+ align:start position:0%
+the same as y I'm printing X is the same
+ 
+
+ align:start position:0%
+the same as y I'm printing X is the same
+as y so if I give it five and five I'm
+
+ align:start position:0%
+as y so if I give it five and five I'm
+ 
+
+ align:start position:0%
+as y so if I give it five and five I'm
+going to print five is the same as five
+
+ align:start position:0%
+going to print five is the same as five
+ 
+
+ align:start position:0%
+going to print five is the same as five
+and then I'd also like to print these
+
+ align:start position:0%
+and then I'd also like to print these
+ 
+
+ align:start position:0%
+and then I'd also like to print these
+are equal what's the problem with this
+
+ align:start position:0%
+are equal what's the problem with this
+ 
+
+ align:start position:0%
+are equal what's the problem with this
+program yeah if X is not equal to Y it's
+
+ align:start position:0%
+program yeah if X is not equal to Y it's
+ 
+
+ align:start position:0%
+program yeah if X is not equal to Y it's
+still going to print these are equal
+
+ align:start position:0%
+still going to print these are equal
+ 
+
+ align:start position:0%
+still going to print these are equal
+it's not ined exactly if X is not the
+
+ align:start position:0%
+it's not ined exactly if X is not the
+ 
+
+ align:start position:0%
+it's not ined exactly if X is not the
+same as y we rejoin the rest of a
+
+ align:start position:0%
+same as y we rejoin the rest of a
+ 
+
+ align:start position:0%
+same as y we rejoin the rest of a
+program because the indentation level of
+
+ align:start position:0%
+program because the indentation level of
+ 
+
+ align:start position:0%
+program because the indentation level of
+this print statement is the same as the
+
+ align:start position:0%
+this print statement is the same as the
+ 
+
+ align:start position:0%
+this print statement is the same as the
+rest of our program so how do we fix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it indent yep we'll just indent that
+
+ align:start position:0%
+it indent yep we'll just indent that
+ 
+
+ align:start position:0%
+it indent yep we'll just indent that
+print statement in to be at the same
+
+ align:start position:0%
+print statement in to be at the same
+ 
+
+ align:start position:0%
+print statement in to be at the same
+level as the if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statement so we can actually Nest
+
+ align:start position:0%
+statement so we can actually Nest
+ 
+
+ align:start position:0%
+statement so we can actually Nest
+indentation statement uh we can Nest uh
+
+ align:start position:0%
+indentation statement uh we can Nest uh
+ 
+
+ align:start position:0%
+indentation statement uh we can Nest uh
+conditionals right because once we've
+
+ align:start position:0%
+conditionals right because once we've
+ 
+
+ align:start position:0%
+conditionals right because once we've
+created a conditional it's just a code
+
+ align:start position:0%
+created a conditional it's just a code
+ 
+
+ align:start position:0%
+created a conditional it's just a code
+block so here I've got an if statement
+
+ align:start position:0%
+block so here I've got an if statement
+ 
+
+ align:start position:0%
+block so here I've got an if statement
+with its own code block and inside that
+
+ align:start position:0%
+with its own code block and inside that
+ 
+
+ align:start position:0%
+with its own code block and inside that
+code block I can actually have more if
+
+ align:start position:0%
+code block I can actually have more if
+ 
+
+ align:start position:0%
+code block I can actually have more if
+statements that are just going to be
+
+ align:start position:0%
+statements that are just going to be
+ 
+
+ align:start position:0%
+statements that are just going to be
+executed whenever this condition is
+
+ align:start position:0%
+executed whenever this condition is
+ 
+
+ align:start position:0%
+executed whenever this condition is
+true so this is the insided code block
+
+ align:start position:0%
+true so this is the insided code block
+ 
+
+ align:start position:0%
+true so this is the insided code block
+so for example the the the place where
+
+ align:start position:0%
+so for example the the the place where
+ 
+
+ align:start position:0%
+so for example the the the place where
+we would execute this inner code block
+
+ align:start position:0%
+we would execute this inner code block
+ 
+
+ align:start position:0%
+we would execute this inner code block
+is when X and Y are equivalent right
+
+ align:start position:0%
+is when X and Y are equivalent right
+ 
+
+ align:start position:0%
+is when X and Y are equivalent right
+because then I'm going to enter this
+
+ align:start position:0%
+because then I'm going to enter this
+ 
+
+ align:start position:0%
+because then I'm going to enter this
+code block here this is true I'm going
+
+ align:start position:0%
+code block here this is true I'm going
+ 
+
+ align:start position:0%
+code block here this is true I'm going
+to print X and Y are equal and then this
+
+ align:start position:0%
+to print X and Y are equal and then this
+ 
+
+ align:start position:0%
+to print X and Y are equal and then this
+second co uh conditional here Y is not
+
+ align:start position:0%
+second co uh conditional here Y is not
+ 
+
+ align:start position:0%
+second co uh conditional here Y is not
+equal to zero is also
+
+ align:start position:0%
+equal to zero is also
+ 
+
+ align:start position:0%
+equal to zero is also
+true and then I'm going to print this
+
+ align:start position:0%
+true and then I'm going to print this
+ 
+
+ align:start position:0%
+true and then I'm going to print this
+one as
+
+ align:start position:0%
+one as
+ 
+
+ align:start position:0%
+one as
+well right I've already done one of the
+
+ align:start position:0%
+well right I've already done one of the
+ 
+
+ align:start position:0%
+well right I've already done one of the
+conditionals they're true so I'm going
+
+ align:start position:0%
+conditionals they're true so I'm going
+ 
+
+ align:start position:0%
+conditionals they're true so I'm going
+to skip the L if and skip the else and
+
+ align:start position:0%
+to skip the L if and skip the else and
+ 
+
+ align:start position:0%
+to skip the L if and skip the else and
+I'm going to rejoin the rest of the
+
+ align:start position:0%
+I'm going to rejoin the rest of the
+ 
+
+ align:start position:0%
+I'm going to rejoin the rest of the
+program all the other cases right when
+
+ align:start position:0%
+program all the other cases right when
+ 
+
+ align:start position:0%
+program all the other cases right when
+one uh value is different than the other
+
+ align:start position:0%
+one uh value is different than the other
+ 
+
+ align:start position:0%
+one uh value is different than the other
+will either take me here in the
+
+ align:start position:0%
+will either take me here in the
+ 
+
+ align:start position:0%
+will either take me here in the
+else and then rejoin the rest of the
+
+ align:start position:0%
+else and then rejoin the rest of the
+ 
+
+ align:start position:0%
+else and then rejoin the rest of the
+program or when they're equivalent I'm
+
+ align:start position:0%
+program or when they're equivalent I'm
+ 
+
+ align:start position:0%
+program or when they're equivalent I'm
+going or you know here I don't have I
+
+ align:start position:0%
+going or you know here I don't have I
+ 
+
+ align:start position:0%
+going or you know here I don't have I
+don't actually have a case for that on
+
+ align:start position:0%
+don't actually have a case for that on
+ 
+
+ align:start position:0%
+don't actually have a case for that on
+on the slides but when they're
+
+ align:start position:0%
+on the slides but when they're
+ 
+
+ align:start position:0%
+on the slides but when they're
+equivalent and one and Y is equal to
+
+ align:start position:0%
+equivalent and one and Y is equal to
+ 
+
+ align:start position:0%
+equivalent and one and Y is equal to
+zero I'm not actually going to enter
+
+ align:start position:0%
+zero I'm not actually going to enter
+ 
+
+ align:start position:0%
+zero I'm not actually going to enter
+this inner conditional right because y
+
+ align:start position:0%
+this inner conditional right because y
+ 
+
+ align:start position:0%
+this inner conditional right because y
+while X and Y were true were equivalent
+
+ align:start position:0%
+while X and Y were true were equivalent
+ 
+
+ align:start position:0%
+while X and Y were true were equivalent
+which is true y was equal to zero so
+
+ align:start position:0%
+which is true y was equal to zero so
+ 
+
+ align:start position:0%
+which is true y was equal to zero so
+that not equal to zero is
+
+ align:start position:0%
+that not equal to zero is
+ 
+
+ align:start position:0%
+that not equal to zero is
+false just that
+
+ align:start position:0%
+false just that
+ 
+
+ align:start position:0%
+false just that
+word and then we rejoin the rest of the
+
+ align:start position:0%
+word and then we rejoin the rest of the
+ 
+
+ align:start position:0%
+word and then we rejoin the rest of the
+program yeah what did you do the flo
+
+ align:start position:0%
+program yeah what did you do the flo
+ 
+
+ align:start position:0%
+program yeah what did you do the flo
+for oh I'm casting the numbers to floats
+
+ align:start position:0%
+for oh I'm casting the numbers to floats
+ 
+
+ align:start position:0%
+for oh I'm casting the numbers to floats
+I could cast them to ins as well yeah
+
+ align:start position:0%
+I could cast them to ins as well yeah
+ 
+
+ align:start position:0%
+I could cast them to ins as well yeah
+yeah just so I'm not comparing strings
+
+ align:start position:0%
+yeah just so I'm not comparing strings
+ 
+
+ align:start position:0%
+yeah just so I'm not comparing strings
+yeah so now that I've introduced
+
+ align:start position:0%
+yeah so now that I've introduced
+ 
+
+ align:start position:0%
+yeah so now that I've introduced
+conditionals it's important to do a
+
+ align:start position:0%
+conditionals it's important to do a
+ 
+
+ align:start position:0%
+conditionals it's important to do a
+little bit more practice to get a mental
+
+ align:start position:0%
+little bit more practice to get a mental
+ 
+
+ align:start position:0%
+little bit more practice to get a mental
+model oops a mental model of how to
+
+ align:start position:0%
+model oops a mental model of how to
+ 
+
+ align:start position:0%
+model oops a mental model of how to
+trace the code right and the the visual
+
+ align:start position:0%
+trace the code right and the the visual
+ 
+
+ align:start position:0%
+trace the code right and the the visual
+structure of the code actually helps a
+
+ align:start position:0%
+structure of the code actually helps a
+ 
+
+ align:start position:0%
+structure of the code actually helps a
+lot and python is unique in the sense
+
+ align:start position:0%
+lot and python is unique in the sense
+ 
+
+ align:start position:0%
+lot and python is unique in the sense
+there's no other languages that actually
+
+ align:start position:0%
+there's no other languages that actually
+ 
+
+ align:start position:0%
+there's no other languages that actually
+force you to indent things so the other
+
+ align:start position:0%
+force you to indent things so the other
+ 
+
+ align:start position:0%
+force you to indent things so the other
+anges don't really force you to have
+
+ align:start position:0%
+anges don't really force you to have
+ 
+
+ align:start position:0%
+anges don't really force you to have
+this visual structure to match exactly
+
+ align:start position:0%
+this visual structure to match exactly
+ 
+
+ align:start position:0%
+this visual structure to match exactly
+what's going on but it's actually really
+
+ align:start position:0%
+what's going on but it's actually really
+ 
+
+ align:start position:0%
+what's going on but it's actually really
+useful in Python it that's what I like
+
+ align:start position:0%
+useful in Python it that's what I like
+ 
+
+ align:start position:0%
+useful in Python it that's what I like
+about python it's just helps you see
+
+ align:start position:0%
+about python it's just helps you see
+ 
+
+ align:start position:0%
+about python it's just helps you see
+things that are going on immediately
+
+ align:start position:0%
+things that are going on immediately
+ 
+
+ align:start position:0%
+things that are going on immediately
+like you know this this set of code is
+
+ align:start position:0%
+like you know this this set of code is
+ 
+
+ align:start position:0%
+like you know this this set of code is
+part of this code block and so it it
+
+ align:start position:0%
+part of this code block and so it it
+ 
+
+ align:start position:0%
+part of this code block and so it it
+helps you kind of debug a little bit
+
+ align:start position:0%
+helps you kind of debug a little bit
+ 
+
+ align:start position:0%
+helps you kind of debug a little bit
+more efficiently but the more practice
+
+ align:start position:0%
+more efficiently but the more practice
+ 
+
+ align:start position:0%
+more efficiently but the more practice
+you get the more you'll get used to kind
+
+ align:start position:0%
+you get the more you'll get used to kind
+ 
+
+ align:start position:0%
+you get the more you'll get used to kind
+of tracing the code and knowing exactly
+
+ align:start position:0%
+of tracing the code and knowing exactly
+ 
+
+ align:start position:0%
+of tracing the code and knowing exactly
+you know if these variables have this
+
+ align:start position:0%
+you know if these variables have this
+ 
+
+ align:start position:0%
+you know if these variables have this
+value exactly where your code is going
+
+ align:start position:0%
+value exactly where your code is going
+ 
+
+ align:start position:0%
+value exactly where your code is going
+to go so I'm going to skip this you triy
+
+ align:start position:0%
+to go so I'm going to skip this you triy
+ 
+
+ align:start position:0%
+to go so I'm going to skip this you triy
+it because it's just kind of you tra ing
+
+ align:start position:0%
+it because it's just kind of you tra ing
+ 
+
+ align:start position:0%
+it because it's just kind of you tra ing
+the code and I'm going to uh have you do
+
+ align:start position:0%
+the code and I'm going to uh have you do
+ 
+
+ align:start position:0%
+the code and I'm going to uh have you do
+this one or we can write it real quick
+
+ align:start position:0%
+this one or we can write it real quick
+ 
+
+ align:start position:0%
+this one or we can write it real quick
+or you can start and then we can write
+
+ align:start position:0%
+or you can start and then we can write
+ 
+
+ align:start position:0%
+or you can start and then we can write
+it together it's a variation of the
+
+ align:start position:0%
+it together it's a variation of the
+ 
+
+ align:start position:0%
+it together it's a variation of the
+program you just wrote instead of
+
+ align:start position:0%
+program you just wrote instead of
+ 
+
+ align:start position:0%
+program you just wrote instead of
+telling me whether the guess is true or
+
+ align:start position:0%
+telling me whether the guess is true or
+ 
+
+ align:start position:0%
+telling me whether the guess is true or
+F is the same as the secret number I
+
+ align:start position:0%
+F is the same as the secret number I
+ 
+
+ align:start position:0%
+F is the same as the secret number I
+just want you to print whether the guest
+
+ align:start position:0%
+just want you to print whether the guest
+ 
+
+ align:start position:0%
+just want you to print whether the guest
+is too low too high or the same as the
+
+ align:start position:0%
+is too low too high or the same as the
+ 
+
+ align:start position:0%
+is too low too high or the same as the
+secret number okay so we're going to
+
+ align:start position:0%
+secret number okay so we're going to
+ 
+
+ align:start position:0%
+secret number okay so we're going to
+need to put a conditional in there if
+
+ align:start position:0%
+need to put a conditional in there if
+ 
+
+ align:start position:0%
+need to put a conditional in there if
+some conditional you know we're going to
+
+ align:start position:0%
+some conditional you know we're going to
+ 
+
+ align:start position:0%
+some conditional you know we're going to
+print something and yeah so I'll give
+
+ align:start position:0%
+print something and yeah so I'll give
+ 
+
+ align:start position:0%
+print something and yeah so I'll give
+you about a minute and then we can write
+
+ align:start position:0%
+you about a minute and then we can write
+ 
+
+ align:start position:0%
+you about a minute and then we can write
+it together and then we can be
+
+ align:start position:0%
+it together and then we can be
+ 
+
+ align:start position:0%
+it together and then we can be
+done oh yeah have do if statements in
+
+ align:start position:0%
+done oh yeah have do if statements in
+ 
+
+ align:start position:0%
+done oh yeah have do if statements in
+the programs you can have two if
+
+ align:start position:0%
+the programs you can have two if
+ 
+
+ align:start position:0%
+the programs you can have two if
+statements in the program yeah and
+
+ align:start position:0%
+statements in the program yeah and
+ 
+
+ align:start position:0%
+statements in the program yeah and
+there's actually some exercises I have
+
+ align:start position:0%
+there's actually some exercises I have
+ 
+
+ align:start position:0%
+there's actually some exercises I have
+for you guys to try at home here where
+
+ align:start position:0%
+for you guys to try at home here where
+ 
+
+ align:start position:0%
+for you guys to try at home here where
+there are two if statements in the
+
+ align:start position:0%
+there are two if statements in the
+ 
+
+ align:start position:0%
+there are two if statements in the
+program and just to see what happens
+
+ align:start position:0%
+program and just to see what happens
+ 
+
+ align:start position:0%
+program and just to see what happens
+that starts two conditionals so if you
+
+ align:start position:0%
+that starts two conditionals so if you
+ 
+
+ align:start position:0%
+that starts two conditionals so if you
+have if some conditional that one can be
+
+ align:start position:0%
+have if some conditional that one can be
+ 
+
+ align:start position:0%
+have if some conditional that one can be
+true and if some other conditional that
+
+ align:start position:0%
+true and if some other conditional that
+ 
+
+ align:start position:0%
+true and if some other conditional that
+one can also be true and then both will
+
+ align:start position:0%
+one can also be true and then both will
+ 
+
+ align:start position:0%
+one can also be true and then both will
+be evaluated it's not an lse situation
+
+ align:start position:0%
+be evaluated it's not an lse situation
+ 
+
+ align:start position:0%
+be evaluated it's not an lse situation
+right yeah that's a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question so I'm just going to copy the
+
+ align:start position:0%
+question so I'm just going to copy the
+ 
+
+ align:start position:0%
+question so I'm just going to copy the
+in input from
+
+ align:start position:0%
+in input from
+ 
+
+ align:start position:0%
+in input from
+before does anyone have a start to my
+
+ align:start position:0%
+before does anyone have a start to my
+ 
+
+ align:start position:0%
+before does anyone have a start to my
+conditional I just copied what we had
+
+ align:start position:0%
+conditional I just copied what we had
+ 
+
+ align:start position:0%
+conditional I just copied what we had
+before for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+input yeah so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if text
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+print yep ju High
+
+ align:start position:0%
+print yep ju High
+ 
+
+ align:start position:0%
+print yep ju High
+good yep that's a great start so we can
+
+ align:start position:0%
+good yep that's a great start so we can
+ 
+
+ align:start position:0%
+good yep that's a great start so we can
+even run it and you know guess something
+
+ align:start position:0%
+even run it and you know guess something
+ 
+
+ align:start position:0%
+even run it and you know guess something
+that's we know is too high perfect too
+
+ align:start position:0%
+that's we know is too high perfect too
+ 
+
+ align:start position:0%
+that's we know is too high perfect too
+high yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next do you want to do an else or an L
+
+ align:start position:0%
+next do you want to do an else or an L
+ 
+
+ align:start position:0%
+next do you want to do an else or an L
+if yeah actually I would get rid of the
+
+ align:start position:0%
+if yeah actually I would get rid of the
+ 
+
+ align:start position:0%
+if yeah actually I would get rid of the
+uh equal sign because if we put in a
+
+ align:start position:0%
+uh equal sign because if we put in a
+ 
+
+ align:start position:0%
+uh equal sign because if we put in a
+five now it would still say too high
+
+ align:start position:0%
+five now it would still say too high
+ 
+
+ align:start position:0%
+five now it would still say too high
+that's a good point so if we run it now
+
+ align:start position:0%
+that's a good point so if we run it now
+ 
+
+ align:start position:0%
+that's a good point so if we run it now
+let's run it with a
+
+ align:start position:0%
+let's run it with a
+ 
+
+ align:start position:0%
+let's run it with a
+five it says too high exactly yeah so
+
+ align:start position:0%
+five it says too high exactly yeah so
+ 
+
+ align:start position:0%
+five it says too high exactly yeah so
+let's remove the equal sign it's a good
+
+ align:start position:0%
+let's remove the equal sign it's a good
+ 
+
+ align:start position:0%
+let's remove the equal sign it's a good
+thing we debugged that
+
+ align:start position:0%
+thing we debugged that
+ 
+
+ align:start position:0%
+thing we debugged that
+um so we can do an L if the guess is
+
+ align:start position:0%
+um so we can do an L if the guess is
+ 
+
+ align:start position:0%
+um so we can do an L if the guess is
+equivalent to the
+
+ align:start position:0%
+equivalent to the
+ 
+
+ align:start position:0%
+equivalent to the
+secret and then we can
+
+ align:start position:0%
+secret and then we can
+ 
+
+ align:start position:0%
+secret and then we can
+print uh equal right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops does everyone understand why we
+
+ align:start position:0%
+oops does everyone understand why we
+ 
+
+ align:start position:0%
+oops does everyone understand why we
+remove that equal sign from the greater
+
+ align:start position:0%
+remove that equal sign from the greater
+ 
+
+ align:start position:0%
+remove that equal sign from the greater
+than yeah because we would have Mist
+
+ align:start position:0%
+than yeah because we would have Mist
+ 
+
+ align:start position:0%
+than yeah because we would have Mist
+yeah we would have mistakenly gone into
+
+ align:start position:0%
+yeah we would have mistakenly gone into
+ 
+
+ align:start position:0%
+yeah we would have mistakenly gone into
+that first path but L if we can have a
+
+ align:start position:0%
+that first path but L if we can have a
+ 
+
+ align:start position:0%
+that first path but L if we can have a
+case where the guess is equivalent to
+
+ align:start position:0%
+case where the guess is equivalent to
+ 
+
+ align:start position:0%
+case where the guess is equivalent to
+secret sure and then we'll print equal
+
+ align:start position:0%
+secret sure and then we'll print equal
+ 
+
+ align:start position:0%
+secret sure and then we'll print equal
+and then the last one can either be an
+
+ align:start position:0%
+and then the last one can either be an
+ 
+
+ align:start position:0%
+and then the last one can either be an
+else because we know the only other
+
+ align:start position:0%
+else because we know the only other
+ 
+
+ align:start position:0%
+else because we know the only other
+option is guess is less than or we can
+
+ align:start position:0%
+option is guess is less than or we can
+ 
+
+ align:start position:0%
+option is guess is less than or we can
+do another LF if we want to but we can
+
+ align:start position:0%
+do another LF if we want to but we can
+ 
+
+ align:start position:0%
+do another LF if we want to but we can
+leave it as an else and then we can
+
+ align:start position:0%
+leave it as an else and then we can
+ 
+
+ align:start position:0%
+leave it as an else and then we can
+print um to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+low and then we can run it and we can
+
+ align:start position:0%
+low and then we can run it and we can
+ 
+
+ align:start position:0%
+low and then we can run it and we can
+guess all the variations so something
+
+ align:start position:0%
+guess all the variations so something
+ 
+
+ align:start position:0%
+guess all the variations so something
+that's too high something that's the
+
+ align:start position:0%
+that's too high something that's the
+ 
+
+ align:start position:0%
+that's too high something that's the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm not sure what I did
+
+ align:start position:0%
+and I'm not sure what I did
+ 
+
+ align:start position:0%
+and I'm not sure what I did
+there I should restart my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cal so we did something that's too high
+
+ align:start position:0%
+Cal so we did something that's too high
+ 
+
+ align:start position:0%
+Cal so we did something that's too high
+something that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is uh equivalent and then we can do
+
+ align:start position:0%
+is uh equivalent and then we can do
+ 
+
+ align:start position:0%
+is uh equivalent and then we can do
+something that's too low
+
+ align:start position:0%
+something that's too low
+ 
+
+ align:start position:0%
+something that's too low
+okay yeah what's the difference between
+
+ align:start position:0%
+okay yeah what's the difference between
+ 
+
+ align:start position:0%
+okay yeah what's the difference between
+having El and El as a so there is no
+
+ align:start position:0%
+having El and El as a so there is no
+ 
+
+ align:start position:0%
+having El and El as a so there is no
+difference we can do an L if guess is
+
+ align:start position:0%
+difference we can do an L if guess is
+ 
+
+ align:start position:0%
+difference we can do an L if guess is
+less than secret that would the the
+
+ align:start position:0%
+less than secret that would the the
+ 
+
+ align:start position:0%
+less than secret that would the the
+program would work just the same the
+
+ align:start position:0%
+program would work just the same the
+ 
+
+ align:start position:0%
+program would work just the same the
+else is just quicker because we know
+
+ align:start position:0%
+else is just quicker because we know
+ 
+
+ align:start position:0%
+else is just quicker because we know
+there are no other options uh here why
+
+ align:start position:0%
+there are no other options uh here why
+ 
+
+ align:start position:0%
+there are no other options uh here why
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+a we could also in this particular case
+
+ align:start position:0%
+a we could also in this particular case
+ 
+
+ align:start position:0%
+a we could also in this particular case
+we could also put a bunch of if
+
+ align:start position:0%
+we could also put a bunch of if
+ 
+
+ align:start position:0%
+we could also put a bunch of if
+statements in a row but then we'd have
+
+ align:start position:0%
+statements in a row but then we'd have
+ 
+
+ align:start position:0%
+statements in a row but then we'd have
+to be careful that they are mutually
+
+ align:start position:0%
+to be careful that they are mutually
+ 
+
+ align:start position:0%
+to be careful that they are mutually
+exclusive so like in the pre in the
+
+ align:start position:0%
+exclusive so like in the pre in the
+ 
+
+ align:start position:0%
+exclusive so like in the pre in the
+previous example right if we have a
+
+ align:start position:0%
+previous example right if we have a
+ 
+
+ align:start position:0%
+previous example right if we have a
+bunch of conditions that might all all
+
+ align:start position:0%
+bunch of conditions that might all all
+ 
+
+ align:start position:0%
+bunch of conditions that might all all
+be true all those ifs will
+
+ align:start position:0%
+be true all those ifs will
+ 
+
+ align:start position:0%
+be true all those ifs will
+execute right that's the thing because
+
+ align:start position:0%
+execute right that's the thing because
+ 
+
+ align:start position:0%
+execute right that's the thing because
+the if starts a block the L if is just
+
+ align:start position:0%
+the if starts a block the L if is just
+ 
+
+ align:start position:0%
+the if starts a block the L if is just
+associated with that block so either you
+
+ align:start position:0%
+associated with that block so either you
+ 
+
+ align:start position:0%
+associated with that block so either you
+do one or the other or the other but if
+
+ align:start position:0%
+do one or the other or the other but if
+ 
+
+ align:start position:0%
+do one or the other or the other but if
+you have a whole bunch of ifs then they
+
+ align:start position:0%
+you have a whole bunch of ifs then they
+ 
+
+ align:start position:0%
+you have a whole bunch of ifs then they
+might all be true and they'll all be
+
+ align:start position:0%
+might all be true and they'll all be
+ 
+
+ align:start position:0%
+might all be true and they'll all be
+executed
+
+ align:start position:0%
+executed
+ 
+
+ align:start position:0%
+executed
+yeah yeah why don't we use parentheses
+
+ align:start position:0%
+yeah yeah why don't we use parentheses
+ 
+
+ align:start position:0%
+yeah yeah why don't we use parentheses
+with an oh we could use parentheses in
+
+ align:start position:0%
+with an oh we could use parentheses in
+ 
+
+ align:start position:0%
+with an oh we could use parentheses in
+the if El statements you mean like this
+
+ align:start position:0%
+the if El statements you mean like this
+ 
+
+ align:start position:0%
+the if El statements you mean like this
+yeah we can do that especially if we
+
+ align:start position:0%
+yeah we can do that especially if we
+ 
+
+ align:start position:0%
+yeah we can do that especially if we
+have a whole bunch of Expressions
+
+ align:start position:0%
+have a whole bunch of Expressions
+ 
+
+ align:start position:0%
+have a whole bunch of Expressions
+together but if there's just one python
+
+ align:start position:0%
+together but if there's just one python
+ 
+
+ align:start position:0%
+together but if there's just one python
+will automatically know to do the
+
+ align:start position:0%
+will automatically know to do the
+ 
+
+ align:start position:0%
+will automatically know to do the
+expression first and then do the if yeah
+
+ align:start position:0%
+expression first and then do the if yeah
+ 
+
+ align:start position:0%
+expression first and then do the if yeah
+these are all wonderful questions by the
+
+ align:start position:0%
+these are all wonderful questions by the
+ 
+
+ align:start position:0%
+these are all wonderful questions by the
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+okay so um as we saw there was a little
+
+ align:start position:0%
+okay so um as we saw there was a little
+ 
+
+ align:start position:0%
+okay so um as we saw there was a little
+bug in our code it's a good thing we ran
+
+ align:start position:0%
+bug in our code it's a good thing we ran
+ 
+
+ align:start position:0%
+bug in our code it's a good thing we ran
+it I should have run it with a bunch of
+
+ align:start position:0%
+it I should have run it with a bunch of
+ 
+
+ align:start position:0%
+it I should have run it with a bunch of
+different options but it's important to
+
+ align:start position:0%
+different options but it's important to
+ 
+
+ align:start position:0%
+different options but it's important to
+debug early and debug often just to make
+
+ align:start position:0%
+debug early and debug often just to make
+ 
+
+ align:start position:0%
+debug early and debug often just to make
+sure that you don't introduce a bug that
+
+ align:start position:0%
+sure that you don't introduce a bug that
+ 
+
+ align:start position:0%
+sure that you don't introduce a bug that
+will kind of carry on throughout the
+
+ align:start position:0%
+will kind of carry on throughout the
+ 
+
+ align:start position:0%
+will kind of carry on throughout the
+code um that's another big idea and then
+
+ align:start position:0%
+code um that's another big idea and then
+ 
+
+ align:start position:0%
+code um that's another big idea and then
+a quick summary of what we've learned
+
+ align:start position:0%
+a quick summary of what we've learned
+ 
+
+ align:start position:0%
+a quick summary of what we've learned
+input and outputs obviously make our
+
+ align:start position:0%
+input and outputs obviously make our
+ 
+
+ align:start position:0%
+input and outputs obviously make our
+programs interactive we uh added
+
+ align:start position:0%
+programs interactive we uh added
+ 
+
+ align:start position:0%
+programs interactive we uh added
+branching as a way to introduce decision
+
+ align:start position:0%
+branching as a way to introduce decision
+ 
+
+ align:start position:0%
+branching as a way to introduce decision
+points in our program and next time
+
+ align:start position:0%
+points in our program and next time
+ 
+
+ align:start position:0%
+points in our program and next time
+we're going to do a little bit more
+
+ align:start position:0%
+we're going to do a little bit more
+ 
+
+ align:start position:0%
+we're going to do a little bit more
+branching and then introduce looping so
+
+ align:start position:0%
+branching and then introduce looping so
+ 
+
+ align:start position:0%
+branching and then introduce looping so
+ways to repeat uh commands in our
+
+ align:start position:0%
+ways to repeat uh commands in our
+ 
+
+ align:start position:0%
+ways to repeat uh commands in our
+programs sorry I went a little bit over
+
+ align:start position:0%
+programs sorry I went a little bit over
+ 
+
+ align:start position:0%
+programs sorry I went a little bit over
+time uh I won't do that again
\ No newline at end of file
diff --git a/Ug6DYV6za-k.txt b/Ug6DYV6za-k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3c812b0aa72d0ed6a6f898875ff1060de81e39cb
--- /dev/null
+++ b/Ug6DYV6za-k.txt
@@ -0,0 +1,387 @@
+align:start position:0%
+ 
+first problem is right here uh I'm going
+
+ align:start position:0%
+first problem is right here uh I'm going
+ 
+
+ align:start position:0%
+first problem is right here uh I'm going
+to give you a chance to practice doing a
+
+ align:start position:0%
+to give you a chance to practice doing a
+ 
+
+ align:start position:0%
+to give you a chance to practice doing a
+proportional derivative
+
+ align:start position:0%
+proportional derivative
+ 
+
+ align:start position:0%
+proportional derivative
+controller and I've actually written the
+
+ align:start position:0%
+controller and I've actually written the
+ 
+
+ align:start position:0%
+controller and I've actually written the
+specifications directly in terms of
+
+ align:start position:0%
+specifications directly in terms of
+ 
+
+ align:start position:0%
+specifications directly in terms of
+phase margin and crossover frequency
+
+ align:start position:0%
+phase margin and crossover frequency
+ 
+
+ align:start position:0%
+phase margin and crossover frequency
+so you can either imagine that that's
+
+ align:start position:0%
+so you can either imagine that that's
+ 
+
+ align:start position:0%
+so you can either imagine that that's
+the way the the specifications are given
+
+ align:start position:0%
+the way the the specifications are given
+ 
+
+ align:start position:0%
+the way the the specifications are given
+or that we started with a rise time uh
+
+ align:start position:0%
+or that we started with a rise time uh
+ 
+
+ align:start position:0%
+or that we started with a rise time uh
+and Peak overshoot and and derive these
+
+ align:start position:0%
+and Peak overshoot and and derive these
+ 
+
+ align:start position:0%
+and Peak overshoot and and derive these
+so your goal is to design a kfs that
+
+ align:start position:0%
+so your goal is to design a kfs that
+ 
+
+ align:start position:0%
+so your goal is to design a kfs that
+meets these um specifications so if
+
+ align:start position:0%
+meets these um specifications so if
+ 
+
+ align:start position:0%
+meets these um specifications so if
+everyone could please uh form up in
+
+ align:start position:0%
+everyone could please uh form up in
+ 
+
+ align:start position:0%
+everyone could please uh form up in
+groups of two around the room as usual
+
+ align:start position:0%
+groups of two around the room as usual
+ 
+
+ align:start position:0%
+groups of two around the room as usual
+I'm Steve Hall I'm the instructor of
+
+ align:start position:0%
+I'm Steve Hall I'm the instructor of
+ 
+
+ align:start position:0%
+I'm Steve Hall I'm the instructor of
+16006 which is principles of automatic
+
+ align:start position:0%
+16006 which is principles of automatic
+ 
+
+ align:start position:0%
+16006 which is principles of automatic
+control uh it's a junior level
+
+ align:start position:0%
+control uh it's a junior level
+ 
+
+ align:start position:0%
+control uh it's a junior level
+uh classical control class which I've
+
+ align:start position:0%
+uh classical control class which I've
+ 
+
+ align:start position:0%
+uh classical control class which I've
+been teaching for about six years so
+
+ align:start position:0%
+been teaching for about six years so
+ 
+
+ align:start position:0%
+been teaching for about six years so
+recitations in 16006 are a little
+
+ align:start position:0%
+recitations in 16006 are a little
+ 
+
+ align:start position:0%
+recitations in 16006 are a little
+different than most recitations at MIT
+
+ align:start position:0%
+different than most recitations at MIT
+ 
+
+ align:start position:0%
+different than most recitations at MIT
+it in in most recitations uh the
+
+ align:start position:0%
+it in in most recitations uh the
+ 
+
+ align:start position:0%
+it in in most recitations uh the
+instructor would uh present a series of
+
+ align:start position:0%
+instructor would uh present a series of
+ 
+
+ align:start position:0%
+instructor would uh present a series of
+problems uh maybe related to the
+
+ align:start position:0%
+problems uh maybe related to the
+ 
+
+ align:start position:0%
+problems uh maybe related to the
+homework uh just to give examples of how
+
+ align:start position:0%
+homework uh just to give examples of how
+ 
+
+ align:start position:0%
+homework uh just to give examples of how
+uh the problem should be worked uh
+
+ align:start position:0%
+uh the problem should be worked uh
+ 
+
+ align:start position:0%
+uh the problem should be worked uh
+sometimes they might have students uh
+
+ align:start position:0%
+sometimes they might have students uh
+ 
+
+ align:start position:0%
+sometimes they might have students uh
+try some themselves uh in my recitations
+
+ align:start position:0%
+try some themselves uh in my recitations
+ 
+
+ align:start position:0%
+try some themselves uh in my recitations
+it's much more active students are are
+
+ align:start position:0%
+it's much more active students are are
+ 
+
+ align:start position:0%
+it's much more active students are are
+um always standing up uh we work at the
+
+ align:start position:0%
+um always standing up uh we work at the
+ 
+
+ align:start position:0%
+um always standing up uh we work at the
+board uh usually in in groups of two so
+
+ align:start position:0%
+board uh usually in in groups of two so
+ 
+
+ align:start position:0%
+board uh usually in in groups of two so
+uh there might be 10 groups of two
+
+ align:start position:0%
+uh there might be 10 groups of two
+ 
+
+ align:start position:0%
+uh there might be 10 groups of two
+spread around the room uh each group of
+
+ align:start position:0%
+spread around the room uh each group of
+ 
+
+ align:start position:0%
+spread around the room uh each group of
+two working at a board uh a Blackboard a
+
+ align:start position:0%
+two working at a board uh a Blackboard a
+ 
+
+ align:start position:0%
+two working at a board uh a Blackboard a
+whiteboard could be a a a poster board
+
+ align:start position:0%
+whiteboard could be a a a poster board
+ 
+
+ align:start position:0%
+whiteboard could be a a a poster board
+uh they're working
+
+ align:start position:0%
+uh they're working
+ 
+
+ align:start position:0%
+uh they're working
+problems uh and the TA and I are walking
+
+ align:start position:0%
+problems uh and the TA and I are walking
+ 
+
+ align:start position:0%
+problems uh and the TA and I are walking
+around and um helping when we can
+
+ align:start position:0%
+around and um helping when we can
+ 
+
+ align:start position:0%
+around and um helping when we can
+answering questions when uh students
+
+ align:start position:0%
+answering questions when uh students
+ 
+
+ align:start position:0%
+answering questions when uh students
+have them uh in generally just coaching
+
+ align:start position:0%
+have them uh in generally just coaching
+ 
+
+ align:start position:0%
+have them uh in generally just coaching
+trying to help the students uh
+
+ align:start position:0%
+trying to help the students uh
+ 
+
+ align:start position:0%
+trying to help the students uh
+understand what they're doing and solve
+
+ align:start position:0%
+understand what they're doing and solve
+ 
+
+ align:start position:0%
+understand what they're doing and solve
+the problems really is a chance for
+
+ align:start position:0%
+the problems really is a chance for
+ 
+
+ align:start position:0%
+the problems really is a chance for
+students to understand uh what they know
+
+ align:start position:0%
+students to understand uh what they know
+ 
+
+ align:start position:0%
+students to understand uh what they know
+and what they don't know and to exercise
+
+ align:start position:0%
+and what they don't know and to exercise
+ 
+
+ align:start position:0%
+and what they don't know and to exercise
+the skills that they've learned in the
+
+ align:start position:0%
+the skills that they've learned in the
+ 
+
+ align:start position:0%
+the skills that they've learned in the
+class uh and if they have problems with
+
+ align:start position:0%
+class uh and if they have problems with
+ 
+
+ align:start position:0%
+class uh and if they have problems with
+those skills it's a chance for me to
+
+ align:start position:0%
+those skills it's a chance for me to
+ 
+
+ align:start position:0%
+those skills it's a chance for me to
+help them uh learn them better
\ No newline at end of file
diff --git a/WK5o1nGwTdU.txt b/WK5o1nGwTdU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c38b7aaeb14beb6e251c95bf2c1a4601551a5116
--- /dev/null
+++ b/WK5o1nGwTdU.txt
@@ -0,0 +1,155 @@
+align:start position:0%
+ 
+My name is Luis Perez Breva and I teach
+
+ align:start position:0%
+My name is Luis Perez Breva and I teach
+ 
+
+ align:start position:0%
+My name is Luis Perez Breva and I teach
+the MIT class on how to move
+
+ align:start position:0%
+the MIT class on how to move
+ 
+
+ align:start position:0%
+the MIT class on how to move
+technologies from lab to impact. It is
+
+ align:start position:0%
+technologies from lab to impact. It is
+ 
+
+ align:start position:0%
+technologies from lab to impact. It is
+called innovation teams and it's the
+
+ align:start position:0%
+called innovation teams and it's the
+ 
+
+ align:start position:0%
+called innovation teams and it's the
+longest running course at MIT in
+
+ align:start position:0%
+longest running course at MIT in
+ 
+
+ align:start position:0%
+longest running course at MIT in
+technology innovation. In it, students
+
+ align:start position:0%
+technology innovation. In it, students
+ 
+
+ align:start position:0%
+technology innovation. In it, students
+learn to solve problems with technology.
+
+ align:start position:0%
+learn to solve problems with technology.
+ 
+
+ align:start position:0%
+learn to solve problems with technology.
+This series of videos is an introduction
+
+ align:start position:0%
+This series of videos is an introduction
+ 
+
+ align:start position:0%
+This series of videos is an introduction
+to a whole new mindset for innovation.
+
+ align:start position:0%
+to a whole new mindset for innovation.
+ 
+
+ align:start position:0%
+to a whole new mindset for innovation.
+We can help you think the way the most
+
+ align:start position:0%
+We can help you think the way the most
+ 
+
+ align:start position:0%
+We can help you think the way the most
+creative engineers do. There's 40 years
+
+ align:start position:0%
+creative engineers do. There's 40 years
+ 
+
+ align:start position:0%
+creative engineers do. There's 40 years
+worth of technology sitting and awaiting
+
+ align:start position:0%
+worth of technology sitting and awaiting
+ 
+
+ align:start position:0%
+worth of technology sitting and awaiting
+for individuals with a new kind of
+
+ align:start position:0%
+for individuals with a new kind of
+ 
+
+ align:start position:0%
+for individuals with a new kind of
+problem solving skill. I will share with
+
+ align:start position:0%
+problem solving skill. I will share with
+ 
+
+ align:start position:0%
+problem solving skill. I will share with
+you the MIT way to solve problems with
+
+ align:start position:0%
+you the MIT way to solve problems with
+ 
+
+ align:start position:0%
+you the MIT way to solve problems with
+technology. Many of the ideas I will
+
+ align:start position:0%
+technology. Many of the ideas I will
+ 
+
+ align:start position:0%
+technology. Many of the ideas I will
+share with you in these videos and more
+
+ align:start position:0%
+share with you in these videos and more
+ 
+
+ align:start position:0%
+share with you in these videos and more
+can be found in my book, Innovating AR's
+
+ align:start position:0%
+can be found in my book, Innovating AR's
+ 
+
+ align:start position:0%
+can be found in my book, Innovating AR's
+Manifesto.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/XMVoIzP6Kpo.txt b/XMVoIzP6Kpo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f6b6a222a62bd6c38ea3c0e7910669bf4e8515b6
--- /dev/null
+++ b/XMVoIzP6Kpo.txt
@@ -0,0 +1,14523 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu let's March ahead into
+
+ align:start position:0%
+ocw.mit.edu let's March ahead into
+ 
+
+ align:start position:0%
+ocw.mit.edu let's March ahead into
+Upstate New York and do for Malahide
+
+ align:start position:0%
+Upstate New York and do for Malahide
+ 
+
+ align:start position:0%
+Upstate New York and do for Malahide
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+first there's a what should business do
+
+ align:start position:0%
+first there's a what should business do
+ 
+
+ align:start position:0%
+first there's a what should business do
+issue that I should have brought up last
+
+ align:start position:0%
+issue that I should have brought up last
+ 
+
+ align:start position:0%
+issue that I should have brought up last
+time so I'll bring it up now because I
+
+ align:start position:0%
+time so I'll bring it up now because I
+ 
+
+ align:start position:0%
+time so I'll bring it up now because I
+didn't this is super
+
+ align:start position:0%
+didn't this is super
+ 
+
+ align:start position:0%
+didn't this is super
+Pacs how many people know what the
+
+ align:start position:0%
+Pacs how many people know what the
+ 
+
+ align:start position:0%
+Pacs how many people know what the
+citizens united decision is or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was so well it's more than that yep a
+
+ align:start position:0%
+was so well it's more than that yep a
+ 
+
+ align:start position:0%
+was so well it's more than that yep a
+few let me just walk through it a little
+
+ align:start position:0%
+few let me just walk through it a little
+ 
+
+ align:start position:0%
+few let me just walk through it a little
+bit so before
+
+ align:start position:0%
+bit so before
+ 
+
+ align:start position:0%
+bit so before
+2010 basically corporations and unions
+
+ align:start position:0%
+2010 basically corporations and unions
+ 
+
+ align:start position:0%
+2010 basically corporations and unions
+well they still can't make direct
+
+ align:start position:0%
+well they still can't make direct
+ 
+
+ align:start position:0%
+well they still can't make direct
+contributions to
+
+ align:start position:0%
+contributions to
+ 
+
+ align:start position:0%
+contributions to
+candidates um they could fund
+
+ align:start position:0%
+candidates um they could fund
+ 
+
+ align:start position:0%
+candidates um they could fund
+independent organizations that put up
+
+ align:start position:0%
+independent organizations that put up
+ 
+
+ align:start position:0%
+independent organizations that put up
+political ads but the political ads
+
+ align:start position:0%
+political ads but the political ads
+ 
+
+ align:start position:0%
+political ads but the political ads
+couldn't be near
+
+ align:start position:0%
+couldn't be near
+ 
+
+ align:start position:0%
+couldn't be near
+elections etc etc now after this
+
+ align:start position:0%
+elections etc etc now after this
+ 
+
+ align:start position:0%
+elections etc etc now after this
+decision they can do essentially
+
+ align:start position:0%
+decision they can do essentially
+ 
+
+ align:start position:0%
+decision they can do essentially
+anything as long as it's not formally
+
+ align:start position:0%
+anything as long as it's not formally
+ 
+
+ align:start position:0%
+anything as long as it's not formally
+part of a
+
+ align:start position:0%
+part of a
+ 
+
+ align:start position:0%
+part of a
+campaign so if you've been
+
+ align:start position:0%
+campaign so if you've been
+ 
+
+ align:start position:0%
+campaign so if you've been
+following this year's Republican primary
+
+ align:start position:0%
+following this year's Republican primary
+ 
+
+ align:start position:0%
+following this year's Republican primary
+season there a lot of super pack ads
+
+ align:start position:0%
+season there a lot of super pack ads
+ 
+
+ align:start position:0%
+season there a lot of super pack ads
+targeting one candidate or another most
+
+ align:start position:0%
+targeting one candidate or another most
+ 
+
+ align:start position:0%
+targeting one candidate or another most
+of it's negative and there's a lot of
+
+ align:start position:0%
+of it's negative and there's a lot of
+ 
+
+ align:start position:0%
+of it's negative and there's a lot of
+money the question is you're the head of
+
+ align:start position:0%
+money the question is you're the head of
+ 
+
+ align:start position:0%
+money the question is you're the head of
+a publicly traded Corporation you can
+
+ align:start position:0%
+a publicly traded Corporation you can
+ 
+
+ align:start position:0%
+a publicly traded Corporation you can
+now make major political
+
+ align:start position:0%
+now make major political
+ 
+
+ align:start position:0%
+now make major political
+contributions the corporation can now
+
+ align:start position:0%
+contributions the corporation can now
+ 
+
+ align:start position:0%
+contributions the corporation can now
+make major
+
+ align:start position:0%
+make major
+ 
+
+ align:start position:0%
+make major
+political contributions should
+
+ align:start position:0%
+political contributions should
+ 
+
+ align:start position:0%
+political contributions should
+you should you or when should
+
+ align:start position:0%
+you should you or when should
+ 
+
+ align:start position:0%
+you should you or when should
+you Stephen what do you
+
+ align:start position:0%
+you Stephen what do you
+ 
+
+ align:start position:0%
+you Stephen what do you
+think um I think they should be able to
+
+ align:start position:0%
+think um I think they should be able to
+ 
+
+ align:start position:0%
+think um I think they should be able to
+able to I'm not talking about that
+
+ align:start position:0%
+able to I'm not talking about that
+ 
+
+ align:start position:0%
+able to I'm not talking about that
+should they you're the you're the CEO of
+
+ align:start position:0%
+should they you're the you're the CEO of
+ 
+
+ align:start position:0%
+should they you're the you're the CEO of
+oh pick your fa you're the CEO of
+
+ align:start position:0%
+oh pick your fa you're the CEO of
+ 
+
+ align:start position:0%
+oh pick your fa you're the CEO of
+Apple should you and Apple's got a lot
+
+ align:start position:0%
+Apple should you and Apple's got a lot
+ 
+
+ align:start position:0%
+Apple should you and Apple's got a lot
+of cash should you spend some of it uh
+
+ align:start position:0%
+of cash should you spend some of it uh
+ 
+
+ align:start position:0%
+of cash should you spend some of it uh
+to give some of it to a Super PAC which
+
+ align:start position:0%
+to give some of it to a Super PAC which
+ 
+
+ align:start position:0%
+to give some of it to a Super PAC which
+has a political
+
+ align:start position:0%
+has a political
+ 
+
+ align:start position:0%
+has a political
+agenda that you know that's all um at
+
+ align:start position:0%
+agenda that you know that's all um at
+ 
+
+ align:start position:0%
+agenda that you know that's all um at
+the end of the day I think there is no
+
+ align:start position:0%
+the end of the day I think there is no
+ 
+
+ align:start position:0%
+the end of the day I think there is no
+harm in doing so so I would recommend or
+
+ align:start position:0%
+harm in doing so so I would recommend or
+ 
+
+ align:start position:0%
+harm in doing so so I would recommend or
+I would eventally do that just because
+
+ align:start position:0%
+I would eventally do that just because
+ 
+
+ align:start position:0%
+I would eventally do that just because
+um when you have all these different
+
+ align:start position:0%
+um when you have all these different
+ 
+
+ align:start position:0%
+um when you have all these different
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+candidates that could potentially move
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+
+ align:start position:0%
+candidates that could potentially move
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+ align:start position:0%
+things in different directions
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+ align:start position:0%
+things in different directions
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+ align:start position:0%
+especially for a company that like apple
+ 
+
+ align:start position:0%
+especially for a company that like apple
+that relies heavily on foreign countries
+
+ align:start position:0%
+that relies heavily on foreign countries
+ 
+
+ align:start position:0%
+that relies heavily on foreign countries
+to do some of their manufacturing or
+
+ align:start position:0%
+to do some of their manufacturing or
+ 
+
+ align:start position:0%
+to do some of their manufacturing or
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+
+ align:start position:0%
+some of their new products coming out
+ 
+
+ align:start position:0%
+some of their new products coming out
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+
+ align:start position:0%
+and other related patents it could be
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+
+ align:start position:0%
+and other related patents it could be
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+ align:start position:0%
+very favorable for them to see a certain
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+ align:start position:0%
+very favorable for them to see a certain
+type of political candidate in office
+
+ align:start position:0%
+type of political candidate in office
+ 
+
+ align:start position:0%
+type of political candidate in office
+rather than someone else so you would do
+
+ align:start position:0%
+rather than someone else so you would do
+ 
+
+ align:start position:0%
+rather than someone else so you would do
+it where the corporations interests were
+
+ align:start position:0%
+it where the corporations interests were
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+
+ align:start position:0%
+it where the corporations interests were
+direct likely to be directly affected
+
+ align:start position:0%
+direct likely to be directly affected
+ 
+
+ align:start position:0%
+direct likely to be directly affected
+yes any any other reason you might Do It
+
+ align:start position:0%
+yes any any other reason you might Do It
+ 
+
+ align:start position:0%
+yes any any other reason you might Do It
+um I would also do it as could also do
+
+ align:start position:0%
+um I would also do it as could also do
+ 
+
+ align:start position:0%
+um I would also do it as could also do
+it more of a publicity type of thing
+
+ align:start position:0%
+it more of a publicity type of thing
+ 
+
+ align:start position:0%
+it more of a publicity type of thing
+where it's saying that um we're in favor
+
+ align:start position:0%
+where it's saying that um we're in favor
+ 
+
+ align:start position:0%
+where it's saying that um we're in favor
+of this screen energy initiative and we
+
+ align:start position:0%
+of this screen energy initiative and we
+ 
+
+ align:start position:0%
+of this screen energy initiative and we
+would like to see um our candidates
+
+ align:start position:0%
+would like to see um our candidates
+ 
+
+ align:start position:0%
+would like to see um our candidates
+supported in that
+
+ align:start position:0%
+supported in that
+ 
+
+ align:start position:0%
+supported in that
+area okay David you with him um yeah I
+
+ align:start position:0%
+area okay David you with him um yeah I
+ 
+
+ align:start position:0%
+area okay David you with him um yeah I
+agree that um I mean the the overall
+
+ align:start position:0%
+agree that um I mean the the overall
+ 
+
+ align:start position:0%
+agree that um I mean the the overall
+like morality dist as a CEO I would
+
+ align:start position:0%
+like morality dist as a CEO I would
+ 
+
+ align:start position:0%
+like morality dist as a CEO I would
+probably um donate some money if there
+
+ align:start position:0%
+probably um donate some money if there
+ 
+
+ align:start position:0%
+probably um donate some money if there
+was a direct impact so again from a PR
+
+ align:start position:0%
+was a direct impact so again from a PR
+ 
+
+ align:start position:0%
+was a direct impact so again from a PR
+whatever I'm trying to accomplish as far
+
+ align:start position:0%
+whatever I'm trying to accomplish as far
+ 
+
+ align:start position:0%
+whatever I'm trying to accomplish as far
+as the company know I think Apple gave
+
+ align:start position:0%
+as the company know I think Apple gave
+ 
+
+ align:start position:0%
+as the company know I think Apple gave
+money to a political action campaign
+
+ align:start position:0%
+money to a political action campaign
+ 
+
+ align:start position:0%
+money to a political action campaign
+opposing the gay marriage m in
+
+ align:start position:0%
+opposing the gay marriage m in
+ 
+
+ align:start position:0%
+opposing the gay marriage m in
+California so that's you know part of
+
+ align:start position:0%
+California so that's you know part of
+ 
+
+ align:start position:0%
+California so that's you know part of
+the image that they push forward I think
+
+ align:start position:0%
+the image that they push forward I think
+ 
+
+ align:start position:0%
+the image that they push forward I think
+that might have been Apple's Regular
+
+ align:start position:0%
+that might have been Apple's Regular
+ 
+
+ align:start position:0%
+that might have been Apple's Regular
+Pack I don't think it was a super Maybe
+
+ align:start position:0%
+Pack I don't think it was a super Maybe
+ 
+
+ align:start position:0%
+Pack I don't think it was a super Maybe
+I'm Wrong I think it was the regular the
+
+ align:start position:0%
+I'm Wrong I think it was the regular the
+ 
+
+ align:start position:0%
+I'm Wrong I think it was the regular the
+regular packs let me describe it they've
+
+ align:start position:0%
+regular packs let me describe it they've
+ 
+
+ align:start position:0%
+regular packs let me describe it they've
+existed for a long time the regular
+
+ align:start position:0%
+existed for a long time the regular
+ 
+
+ align:start position:0%
+existed for a long time the regular
+packs where the executives of the
+
+ align:start position:0%
+packs where the executives of the
+ 
+
+ align:start position:0%
+packs where the executives of the
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+
+ align:start position:0%
+company contribute money
+ 
+
+ align:start position:0%
+company contribute money
+the Super PAC is where the company
+
+ align:start position:0%
+the Super PAC is where the company
+ 
+
+ align:start position:0%
+the Super PAC is where the company
+contributes money there's a big
+
+ align:start position:0%
+contributes money there's a big
+ 
+
+ align:start position:0%
+contributes money there's a big
+difference right one is one is the
+
+ align:start position:0%
+difference right one is one is the
+ 
+
+ align:start position:0%
+difference right one is one is the
+executives own money Executives or board
+
+ align:start position:0%
+executives own money Executives or board
+ 
+
+ align:start position:0%
+executives own money Executives or board
+members and the other is my money as a
+
+ align:start position:0%
+members and the other is my money as a
+ 
+
+ align:start position:0%
+members and the other is my money as a
+shareholder of
+
+ align:start position:0%
+shareholder of
+ 
+
+ align:start position:0%
+shareholder of
+Apple but if it directly affects the
+
+ align:start position:0%
+Apple but if it directly affects the
+ 
+
+ align:start position:0%
+Apple but if it directly affects the
+corporation I take the point but you do
+
+ align:start position:0%
+corporation I take the point but you do
+ 
+
+ align:start position:0%
+corporation I take the point but you do
+it for publicity and you do it for a
+
+ align:start position:0%
+it for publicity and you do it for a
+ 
+
+ align:start position:0%
+it for publicity and you do it for a
+variety of causes so I'm a right-wing
+
+ align:start position:0%
+variety of causes so I'm a right-wing
+ 
+
+ align:start position:0%
+variety of causes so I'm a right-wing
+Republican who owns Apple stock do I
+
+ align:start position:0%
+Republican who owns Apple stock do I
+ 
+
+ align:start position:0%
+Republican who owns Apple stock do I
+like you you giving to a green
+
+ align:start position:0%
+like you you giving to a green
+ 
+
+ align:start position:0%
+like you you giving to a green
+pack you don't care
+
+ align:start position:0%
+pack you don't care
+ 
+
+ align:start position:0%
+pack you don't care
+okay app shares the you know have
+
+ align:start position:0%
+okay app shares the you know have
+ 
+
+ align:start position:0%
+okay app shares the you know have
+distaste in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+political okay stance that we're taking
+
+ align:start position:0%
+political okay stance that we're taking
+ 
+
+ align:start position:0%
+political okay stance that we're taking
+is really that offensive to you anybody
+
+ align:start position:0%
+is really that offensive to you anybody
+ 
+
+ align:start position:0%
+is really that offensive to you anybody
+from the other side of the room Vivian
+
+ align:start position:0%
+from the other side of the room Vivian
+ 
+
+ align:start position:0%
+from the other side of the room Vivian
+what do you think sorry i w a little B I
+
+ align:start position:0%
+what do you think sorry i w a little B I
+ 
+
+ align:start position:0%
+what do you think sorry i w a little B I
+don't really know where we're at the the
+
+ align:start position:0%
+don't really know where we're at the the
+ 
+
+ align:start position:0%
+don't really know where we're at the the
+question is uh should a corporation
+
+ align:start position:0%
+question is uh should a corporation
+ 
+
+ align:start position:0%
+question is uh should a corporation
+let's say take a big corporation that
+
+ align:start position:0%
+let's say take a big corporation that
+ 
+
+ align:start position:0%
+let's say take a big corporation that
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+
+ align:start position:0%
+has cash make contributions not the
+ 
+
+ align:start position:0%
+has cash make contributions not the
+executives but should the CEO cause the
+
+ align:start position:0%
+executives but should the CEO cause the
+ 
+
+ align:start position:0%
+executives but should the CEO cause the
+company to make political
+
+ align:start position:0%
+company to make political
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+
+ align:start position:0%
+company to make political
+contributions and if so when and if not
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+ align:start position:0%
+contributions and if so when and if not
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+
+ align:start position:0%
+contributions and if so when and if not
+why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not contri should I go for the reform
+
+ align:start position:0%
+not contri should I go for the reform
+ 
+
+ align:start position:0%
+not contri should I go for the reform
+America pack that favors Ron Paul or the
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+ align:start position:0%
+America pack that favors Ron Paul or the
+ 
+
+ align:start position:0%
+America pack that favors Ron Paul or the
+I forget what it's called pack that
+
+ align:start position:0%
+I forget what it's called pack that
+ 
+
+ align:start position:0%
+I forget what it's called pack that
+favors Romney or one of the Obama
+
+ align:start position:0%
+favors Romney or one of the Obama
+ 
+
+ align:start position:0%
+favors Romney or one of the Obama
+leaning packs
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+ align:start position:0%
+leaning packs
+ 
+
+ align:start position:0%
+leaning packs
+or I think that's a really risky
+
+ align:start position:0%
+or I think that's a really risky
+ 
+
+ align:start position:0%
+or I think that's a really risky
+decision to make as of like different
+
+ align:start position:0%
+decision to make as of like different
+ 
+
+ align:start position:0%
+decision to make as of like different
+interest of your
+
+ align:start position:0%
+interest of your
+ 
+
+ align:start position:0%
+interest of your
+shareholders so sh shareholders might
+
+ align:start position:0%
+shareholders so sh shareholders might
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+
+ align:start position:0%
+shareholders so sh shareholders might
+not all agree right yeah FY you were in
+
+ align:start position:0%
+not all agree right yeah FY you were in
+ 
+
+ align:start position:0%
+not all agree right yeah FY you were in
+the interest of the company like in
+
+ align:start position:0%
+the interest of the company like in
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+
+ align:start position:0%
+the interest of the company like in
+regards to like apple with exports from
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+ align:start position:0%
+regards to like apple with exports from
+ 
+
+ align:start position:0%
+regards to like apple with exports from
+or imports from other countries in terms
+
+ align:start position:0%
+or imports from other countries in terms
+ 
+
+ align:start position:0%
+or imports from other countries in terms
+of manufacturing like it's in the
+
+ align:start position:0%
+of manufacturing like it's in the
+ 
+
+ align:start position:0%
+of manufacturing like it's in the
+benefit it's beneficial to the company
+
+ align:start position:0%
+benefit it's beneficial to the company
+ 
+
+ align:start position:0%
+benefit it's beneficial to the company
+and to the shareholders to maximize
+
+ align:start position:0%
+and to the shareholders to maximize
+ 
+
+ align:start position:0%
+and to the shareholders to maximize
+value in that way
+
+ align:start position:0%
+value in that way
+ 
+
+ align:start position:0%
+value in that way
+so I think I think it's favorable if
+
+ align:start position:0%
+so I think I think it's favorable if
+ 
+
+ align:start position:0%
+so I think I think it's favorable if
+they're doing it for the compan so if
+
+ align:start position:0%
+they're doing it for the compan so if
+ 
+
+ align:start position:0%
+they're doing it for the compan so if
+it's if it's somebody particularly
+
+ align:start position:0%
+it's if it's somebody particularly
+ 
+
+ align:start position:0%
+it's if it's somebody particularly
+focused on on them Ariana I agree um I
+
+ align:start position:0%
+focused on on them Ariana I agree um I
+ 
+
+ align:start position:0%
+focused on on them Ariana I agree um I
+think that like even if like uh the the
+
+ align:start position:0%
+think that like even if like uh the the
+ 
+
+ align:start position:0%
+think that like even if like uh the the
+company ends up giving money to a cause
+
+ align:start position:0%
+company ends up giving money to a cause
+ 
+
+ align:start position:0%
+company ends up giving money to a cause
+that you don't necessarily personally
+
+ align:start position:0%
+that you don't necessarily personally
+ 
+
+ align:start position:0%
+that you don't necessarily personally
+support like as a shareholder you like I
+
+ align:start position:0%
+support like as a shareholder you like I
+ 
+
+ align:start position:0%
+support like as a shareholder you like I
+think you should think of your interest
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+ align:start position:0%
+think you should think of your interest
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+ align:start position:0%
+think you should think of your interest
+separately so like you have interest in
+
+ align:start position:0%
+separately so like you have interest in
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+
+ align:start position:0%
+separately so like you have interest in
+this uh corporation like as pertains to
+
+ align:start position:0%
+this uh corporation like as pertains to
+ 
+
+ align:start position:0%
+this uh corporation like as pertains to
+making a profit and you might also have
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+ align:start position:0%
+making a profit and you might also have
+ 
+
+ align:start position:0%
+making a profit and you might also have
+separate person interest and so like if
+
+ align:start position:0%
+separate person interest and so like if
+ 
+
+ align:start position:0%
+separate person interest and so like if
+you personally you want to donate to
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+ align:start position:0%
+you personally you want to donate to
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+
+ align:start position:0%
+you personally you want to donate to
+like whoever you think has the right
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+ align:start position:0%
+like whoever you think has the right
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+
+ align:start position:0%
+like whoever you think has the right
+position on gay marriage I think that's
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+ align:start position:0%
+position on gay marriage I think that's
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+
+ align:start position:0%
+position on gay marriage I think that's
+that that's fine but you should know
+
+ align:start position:0%
+that that's fine but you should know
+ 
+
+ align:start position:0%
+that that's fine but you should know
+that the interest in the corporation is
+
+ align:start position:0%
+that the interest in the corporation is
+ 
+
+ align:start position:0%
+that the interest in the corporation is
+purely about making a profit so if the
+
+ align:start position:0%
+purely about making a profit so if the
+ 
+
+ align:start position:0%
+purely about making a profit so if the
+corporation is supporting um is
+
+ align:start position:0%
+corporation is supporting um is
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+
+ align:start position:0%
+corporation is supporting um is
+supporting a cause that that furthers
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+supporting a cause that that furthers
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+
+ align:start position:0%
+supporting a cause that that furthers
+that goal then that's fine but gab
+
+ align:start position:0%
+that goal then that's fine but gab
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+
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+that goal then that's fine but gab
+marriage probably doesn't have a lot to
+
+ align:start position:0%
+marriage probably doesn't have a lot to
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+
+ align:start position:0%
+marriage probably doesn't have a lot to
+do with my my earnings as a shareholder
+
+ align:start position:0%
+do with my my earnings as a shareholder
+ 
+
+ align:start position:0%
+do with my my earnings as a shareholder
+you you shouldn't be worried about the
+
+ align:start position:0%
+you you shouldn't be worried about the
+ 
+
+ align:start position:0%
+you you shouldn't be worried about the
+corporation getting involved in that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Andrew so uh one thing about like this
+
+ align:start position:0%
+Andrew so uh one thing about like this
+ 
+
+ align:start position:0%
+Andrew so uh one thing about like this
+sort of uh uh allowing companies to do
+
+ align:start position:0%
+sort of uh uh allowing companies to do
+ 
+
+ align:start position:0%
+sort of uh uh allowing companies to do
+these sort of things I think is that
+
+ align:start position:0%
+these sort of things I think is that
+ 
+
+ align:start position:0%
+these sort of things I think is that
+whereas in some situations you can see
+
+ align:start position:0%
+whereas in some situations you can see
+ 
+
+ align:start position:0%
+whereas in some situations you can see
+the Merit like directly say if I'm bank
+
+ align:start position:0%
+the Merit like directly say if I'm bank
+ 
+
+ align:start position:0%
+the Merit like directly say if I'm bank
+and there's this uh there's this uh
+
+ align:start position:0%
+and there's this uh there's this uh
+ 
+
+ align:start position:0%
+and there's this uh there's this uh
+candidate that I know is going to like
+
+ align:start position:0%
+candidate that I know is going to like
+ 
+
+ align:start position:0%
+candidate that I know is going to like
+force me to have like higher standards
+
+ align:start position:0%
+force me to have like higher standards
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+
+ align:start position:0%
+force me to have like higher standards
+and all that stuff I might might want to
+
+ align:start position:0%
+and all that stuff I might might want to
+ 
+
+ align:start position:0%
+and all that stuff I might might want to
+like uh go for the other candidate but I
+
+ align:start position:0%
+like uh go for the other candidate but I
+ 
+
+ align:start position:0%
+like uh go for the other candidate but I
+think that having these sort of rules
+
+ align:start position:0%
+think that having these sort of rules
+ 
+
+ align:start position:0%
+think that having these sort of rules
+like allows for companies to to go like
+
+ align:start position:0%
+like allows for companies to to go like
+ 
+
+ align:start position:0%
+like allows for companies to to go like
+in these like murky territory where
+
+ align:start position:0%
+in these like murky territory where
+ 
+
+ align:start position:0%
+in these like murky territory where
+you're kind of influencing things you
+
+ align:start position:0%
+you're kind of influencing things you
+ 
+
+ align:start position:0%
+you're kind of influencing things you
+may shouldn't you probably shouldn't and
+
+ align:start position:0%
+may shouldn't you probably shouldn't and
+ 
+
+ align:start position:0%
+may shouldn't you probably shouldn't and
+like your uh you increase your uh in
+
+ align:start position:0%
+like your uh you increase your uh in
+ 
+
+ align:start position:0%
+like your uh you increase your uh in
+terms of like you're arguing you don't
+
+ align:start position:0%
+terms of like you're arguing you don't
+ 
+
+ align:start position:0%
+terms of like you're arguing you don't
+like the decision sorry you don't like
+
+ align:start position:0%
+like the decision sorry you don't like
+ 
+
+ align:start position:0%
+like the decision sorry you don't like
+the decision you don't like what I'm
+
+ align:start position:0%
+the decision you don't like what I'm
+ 
+
+ align:start position:0%
+the decision you don't like what I'm
+trying to say the decision's there what
+
+ align:start position:0%
+trying to say the decision's there what
+ 
+
+ align:start position:0%
+trying to say the decision's there what
+I'm trying to say is that like as a as a
+
+ align:start position:0%
+I'm trying to say is that like as a as a
+ 
+
+ align:start position:0%
+I'm trying to say is that like as a as a
+CEO doing something is uh supposedly to
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+ align:start position:0%
+CEO doing something is uh supposedly to
+ 
+
+ align:start position:0%
+CEO doing something is uh supposedly to
+improve like the the company's position
+
+ align:start position:0%
+improve like the the company's position
+ 
+
+ align:start position:0%
+improve like the the company's position
+is is like completely subjective because
+
+ align:start position:0%
+is is like completely subjective because
+ 
+
+ align:start position:0%
+is is like completely subjective because
+they're M like doing the giving money to
+
+ align:start position:0%
+they're M like doing the giving money to
+ 
+
+ align:start position:0%
+they're M like doing the giving money to
+cand X might be interpreted okay I'm I'm
+
+ align:start position:0%
+cand X might be interpreted okay I'm I'm
+ 
+
+ align:start position:0%
+cand X might be interpreted okay I'm I'm
+doing it because I want him to support
+
+ align:start position:0%
+doing it because I want him to support
+ 
+
+ align:start position:0%
+doing it because I want him to support
+this which is good for my company but
+
+ align:start position:0%
+this which is good for my company but
+ 
+
+ align:start position:0%
+this which is good for my company but
+then there are whole other things that
+
+ align:start position:0%
+then there are whole other things that
+ 
+
+ align:start position:0%
+then there are whole other things that
+you're doing by doing so this I think is
+
+ align:start position:0%
+you're doing by doing so this I think is
+ 
+
+ align:start position:0%
+you're doing by doing so this I think is
+more of a negative publicity than
+
+ align:start position:0%
+more of a negative publicity than
+ 
+
+ align:start position:0%
+more of a negative publicity than
+positive publicity in the sense that
+
+ align:start position:0%
+positive publicity in the sense that
+ 
+
+ align:start position:0%
+positive publicity in the sense that
+you're influencing uh decision making
+
+ align:start position:0%
+you're influencing uh decision making
+ 
+
+ align:start position:0%
+you're influencing uh decision making
+because it might be that you're doing it
+
+ align:start position:0%
+because it might be that you're doing it
+ 
+
+ align:start position:0%
+because it might be that you're doing it
+for him uh to support action a but for
+
+ align:start position:0%
+for him uh to support action a but for
+ 
+
+ align:start position:0%
+for him uh to support action a but for
+action B you also have influence on him
+
+ align:start position:0%
+action B you also have influence on him
+ 
+
+ align:start position:0%
+action B you also have influence on him
+and then that might be that you don't
+
+ align:start position:0%
+and then that might be that you don't
+ 
+
+ align:start position:0%
+and then that might be that you don't
+want have apple to have influence on he
+
+ align:start position:0%
+want have apple to have influence on he
+ 
+
+ align:start position:0%
+want have apple to have influence on he
+decides on something else I've been on
+
+ align:start position:0%
+decides on something else I've been on
+ 
+
+ align:start position:0%
+decides on something else I've been on
+the board of a company that had one of
+
+ align:start position:0%
+the board of a company that had one of
+ 
+
+ align:start position:0%
+the board of a company that had one of
+these ordinary
+
+ align:start position:0%
+these ordinary
+ 
+
+ align:start position:0%
+these ordinary
+packs uh and the directors and the
+
+ align:start position:0%
+packs uh and the directors and the
+ 
+
+ align:start position:0%
+packs uh and the directors and the
+officers chipped
+
+ align:start position:0%
+officers chipped
+ 
+
+ align:start position:0%
+officers chipped
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+and we made contributions this was a
+
+ align:start position:0%
+and we made contributions this was a
+ 
+
+ align:start position:0%
+and we made contributions this was a
+company located on Wall Street and we
+
+ align:start position:0%
+company located on Wall Street and we
+ 
+
+ align:start position:0%
+company located on Wall Street and we
+made and we were a regulated company a
+
+ align:start position:0%
+made and we were a regulated company a
+ 
+
+ align:start position:0%
+made and we were a regulated company a
+Securities Exchange and we made
+
+ align:start position:0%
+Securities Exchange and we made
+ 
+
+ align:start position:0%
+Securities Exchange and we made
+contributions to both New York senators
+
+ align:start position:0%
+contributions to both New York senators
+ 
+
+ align:start position:0%
+contributions to both New York senators
+and to the congressman from Wall Street
+
+ align:start position:0%
+and to the congressman from Wall Street
+ 
+
+ align:start position:0%
+and to the congressman from Wall Street
+so that they'd return our phone calls
+
+ align:start position:0%
+so that they'd return our phone calls
+ 
+
+ align:start position:0%
+so that they'd return our phone calls
+basically we're not going to buy
+
+ align:start position:0%
+basically we're not going to buy
+ 
+
+ align:start position:0%
+basically we're not going to buy
+influence if they're not concerned about
+
+ align:start position:0%
+influence if they're not concerned about
+ 
+
+ align:start position:0%
+influence if they're not concerned about
+the fate of uh companies on Wall Street
+
+ align:start position:0%
+the fate of uh companies on Wall Street
+ 
+
+ align:start position:0%
+the fate of uh companies on Wall Street
+then they're in a a lot of trouble but
+
+ align:start position:0%
+then they're in a a lot of trouble but
+ 
+
+ align:start position:0%
+then they're in a a lot of trouble but
+to basically get your phone call
+
+ align:start position:0%
+to basically get your phone call
+ 
+
+ align:start position:0%
+to basically get your phone call
+returned you make a few thousand
+
+ align:start position:0%
+returned you make a few thousand
+ 
+
+ align:start position:0%
+returned you make a few thousand
+contribution that's a that's different
+
+ align:start position:0%
+contribution that's a that's different
+ 
+
+ align:start position:0%
+contribution that's a that's different
+from giving $10 million to support n
+
+ align:start position:0%
+from giving $10 million to support n
+ 
+
+ align:start position:0%
+from giving $10 million to support n
+Gingrich um but so Marie you had a point
+
+ align:start position:0%
+Gingrich um but so Marie you had a point
+ 
+
+ align:start position:0%
+Gingrich um but so Marie you had a point
+or you were you were waving no sorry
+
+ align:start position:0%
+or you were you were waving no sorry
+ 
+
+ align:start position:0%
+or you were you were waving no sorry
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+Jacob kind a question is it Poss for an
+
+ align:start position:0%
+Jacob kind a question is it Poss for an
+ 
+
+ align:start position:0%
+Jacob kind a question is it Poss for an
+international corporation to contribute
+
+ align:start position:0%
+international corporation to contribute
+ 
+
+ align:start position:0%
+international corporation to contribute
+to an American politician or like if
+
+ align:start position:0%
+to an American politician or like if
+ 
+
+ align:start position:0%
+to an American politician or like if
+it's an American company with say
+
+ align:start position:0%
+it's an American company with say
+ 
+
+ align:start position:0%
+it's an American company with say
+foreign Executives who are making the
+
+ align:start position:0%
+foreign Executives who are making the
+ 
+
+ align:start position:0%
+foreign Executives who are making the
+decision whether appropriation Don any
+
+ align:start position:0%
+decision whether appropriation Don any
+ 
+
+ align:start position:0%
+decision whether appropriation Don any
+Mone
+
+ align:start position:0%
+Mone
+ 
+
+ align:start position:0%
+Mone
+to well if if they have a if they have a
+
+ align:start position:0%
+to well if if they have a if they have a
+ 
+
+ align:start position:0%
+to well if if they have a if they have a
+subsidiary that is a US person okay so
+
+ align:start position:0%
+subsidiary that is a US person okay so
+ 
+
+ align:start position:0%
+subsidiary that is a US person okay so
+if you have a a subsidiary that has a US
+
+ align:start position:0%
+if you have a a subsidiary that has a US
+ 
+
+ align:start position:0%
+if you have a a subsidiary that has a US
+Charter then presumably that entity can
+
+ align:start position:0%
+Charter then presumably that entity can
+ 
+
+ align:start position:0%
+Charter then presumably that entity can
+you can't you can't make direct
+
+ align:start position:0%
+you can't you can't make direct
+ 
+
+ align:start position:0%
+you can't you can't make direct
+contributions in well sorry they can't
+
+ align:start position:0%
+contributions in well sorry they can't
+ 
+
+ align:start position:0%
+contributions in well sorry they can't
+make Direct contributions to the
+
+ align:start position:0%
+make Direct contributions to the
+ 
+
+ align:start position:0%
+make Direct contributions to the
+candidate in any case the question is
+
+ align:start position:0%
+candidate in any case the question is
+ 
+
+ align:start position:0%
+candidate in any case the question is
+can you contribute to a Super PAC I I
+
+ align:start position:0%
+can you contribute to a Super PAC I I
+ 
+
+ align:start position:0%
+can you contribute to a Super PAC I I
+doubt a foreign corporation doesn't have
+
+ align:start position:0%
+doubt a foreign corporation doesn't have
+ 
+
+ align:start position:0%
+doubt a foreign corporation doesn't have
+us rights of free speech so I've never
+
+ align:start position:0%
+us rights of free speech so I've never
+ 
+
+ align:start position:0%
+us rights of free speech so I've never
+heard it brought up but I don't think I
+
+ align:start position:0%
+heard it brought up but I don't think I
+ 
+
+ align:start position:0%
+heard it brought up but I don't think I
+think it could be barred question
+
+ align:start position:0%
+think it could be barred question
+ 
+
+ align:start position:0%
+think it could be barred question
+whether it should be done but I just set
+
+ align:start position:0%
+whether it should be done but I just set
+ 
+
+ align:start position:0%
+whether it should be done but I just set
+up I just set up a us company if I
+
+ align:start position:0%
+up I just set up a us company if I
+ 
+
+ align:start position:0%
+up I just set up a us company if I
+wanted to do that well could yeah in
+
+ align:start position:0%
+wanted to do that well could yeah in
+ 
+
+ align:start position:0%
+wanted to do that well could yeah in
+which case could there be anti-American
+
+ align:start position:0%
+which case could there be anti-American
+ 
+
+ align:start position:0%
+which case could there be anti-American
+interests like influencing our politi so
+
+ align:start position:0%
+interests like influencing our politi so
+ 
+
+ align:start position:0%
+interests like influencing our politi so
+I actually found it found it interesting
+
+ align:start position:0%
+I actually found it found it interesting
+ 
+
+ align:start position:0%
+I actually found it found it interesting
+I looked
+
+ align:start position:0%
+I looked
+ 
+
+ align:start position:0%
+I looked
+at uh there's a foundation called
+
+ align:start position:0%
+at uh there's a foundation called
+ 
+
+ align:start position:0%
+at uh there's a foundation called
+sunlight Foundation you can find them on
+
+ align:start position:0%
+sunlight Foundation you can find them on
+ 
+
+ align:start position:0%
+sunlight Foundation you can find them on
+the web and they looked at who's making
+
+ align:start position:0%
+the web and they looked at who's making
+ 
+
+ align:start position:0%
+the web and they looked at who's making
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+contributions and in fact you don't find
+
+ align:start position:0%
+contributions and in fact you don't find
+ 
+
+ align:start position:0%
+contributions and in fact you don't find
+any publicly held contrib uh I couldn't
+
+ align:start position:0%
+any publicly held contrib uh I couldn't
+ 
+
+ align:start position:0%
+any publicly held contrib uh I couldn't
+find any um certainly no company I'd
+
+ align:start position:0%
+find any um certainly no company I'd
+ 
+
+ align:start position:0%
+find any um certainly no company I'd
+ever heard of is on the list for
+
+ align:start position:0%
+ever heard of is on the list for
+ 
+
+ align:start position:0%
+ever heard of is on the list for
+contributions above 25 20,000 actually
+
+ align:start position:0%
+contributions above 25 20,000 actually
+ 
+
+ align:start position:0%
+contributions above 25 20,000 actually
+was their cut lots of private
+
+ align:start position:0%
+was their cut lots of private
+ 
+
+ align:start position:0%
+was their cut lots of private
+corporations
+
+ align:start position:0%
+corporations
+ 
+
+ align:start position:0%
+corporations
+individuals unions Partnerships the only
+
+ align:start position:0%
+individuals unions Partnerships the only
+ 
+
+ align:start position:0%
+individuals unions Partnerships the only
+publicly traded company I could find is
+
+ align:start position:0%
+publicly traded company I could find is
+ 
+
+ align:start position:0%
+publicly traded company I could find is
+console which is a Coal Company as far
+
+ align:start position:0%
+console which is a Coal Company as far
+ 
+
+ align:start position:0%
+console which is a Coal Company as far
+as I can tell I don't know them well
+
+ align:start position:0%
+as I can tell I don't know them well
+ 
+
+ align:start position:0%
+as I can tell I don't know them well
+they gave
+
+ align:start position:0%
+they gave
+ 
+
+ align:start position:0%
+they gave
+$125,000 to a Romney
+
+ align:start position:0%
+$125,000 to a Romney
+ 
+
+ align:start position:0%
+$125,000 to a Romney
+pack and you have to ask
+
+ align:start position:0%
+pack and you have to ask
+ 
+
+ align:start position:0%
+pack and you have to ask
+yourself
+
+ align:start position:0%
+yourself
+ 
+
+ align:start position:0%
+yourself
+why I assume that's a CEO who leans
+
+ align:start position:0%
+why I assume that's a CEO who leans
+ 
+
+ align:start position:0%
+why I assume that's a CEO who leans
+Romney and whose board is
+
+ align:start position:0%
+Romney and whose board is
+ 
+
+ align:start position:0%
+Romney and whose board is
+captive which is not unheard of that the
+
+ align:start position:0%
+captive which is not unheard of that the
+ 
+
+ align:start position:0%
+captive which is not unheard of that the
+board is opposed of his friends or her
+
+ align:start position:0%
+board is opposed of his friends or her
+ 
+
+ align:start position:0%
+board is opposed of his friends or her
+friends I don't know who the CEO is um
+
+ align:start position:0%
+friends I don't know who the CEO is um
+ 
+
+ align:start position:0%
+friends I don't know who the CEO is um
+so it's interesting that most
+
+ align:start position:0%
+so it's interesting that most
+ 
+
+ align:start position:0%
+so it's interesting that most
+corporations most large corporations
+
+ align:start position:0%
+corporations most large corporations
+ 
+
+ align:start position:0%
+corporations most large corporations
+Apple Etc are not playing this
+
+ align:start position:0%
+Apple Etc are not playing this
+ 
+
+ align:start position:0%
+Apple Etc are not playing this
+game even though by law they
+
+ align:start position:0%
+game even though by law they
+ 
+
+ align:start position:0%
+game even though by law they
+can I just find that interesting and it
+
+ align:start position:0%
+can I just find that interesting and it
+ 
+
+ align:start position:0%
+can I just find that interesting and it
+has to do with what they think their
+
+ align:start position:0%
+has to do with what they think their
+ 
+
+ align:start position:0%
+has to do with what they think their
+role as CEO is and how they should
+
+ align:start position:0%
+role as CEO is and how they should
+ 
+
+ align:start position:0%
+role as CEO is and how they should
+behave as I said I can only find one
+
+ align:start position:0%
+behave as I said I can only find one
+ 
+
+ align:start position:0%
+behave as I said I can only find one
+publicly traded company there are a lot
+
+ align:start position:0%
+publicly traded company there are a lot
+ 
+
+ align:start position:0%
+publicly traded company there are a lot
+of you know so and so family company
+
+ align:start position:0%
+of you know so and so family company
+ 
+
+ align:start position:0%
+of you know so and so family company
+contributes and you know that's a family
+
+ align:start position:0%
+contributes and you know that's a family
+ 
+
+ align:start position:0%
+contributes and you know that's a family
+company it's effectively a
+
+ align:start position:0%
+company it's effectively a
+ 
+
+ align:start position:0%
+company it's effectively a
+partnership so not publicly
+
+ align:start position:0%
+partnership so not publicly
+ 
+
+ align:start position:0%
+partnership so not publicly
+traded so
+
+ align:start position:0%
+traded so
+ 
+
+ align:start position:0%
+traded so
+it which
+
+ align:start position:0%
+it which
+ 
+
+ align:start position:0%
+it which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+yeah yeah yeah oh yeah oh yeah AR that
+
+ align:start position:0%
+yeah yeah yeah oh yeah oh yeah AR that
+ 
+
+ align:start position:0%
+yeah yeah yeah oh yeah oh yeah AR that
+maybe all the companies don't think
+
+ align:start position:0%
+maybe all the companies don't think
+ 
+
+ align:start position:0%
+maybe all the companies don't think
+Romney is going to win so nobody's
+
+ align:start position:0%
+Romney is going to win so nobody's
+ 
+
+ align:start position:0%
+Romney is going to win so nobody's
+putting any money into
+
+ align:start position:0%
+putting any money into
+ 
+
+ align:start position:0%
+putting any money into
+it there's a lot of money going in and
+
+ align:start position:0%
+it there's a lot of money going in and
+ 
+
+ align:start position:0%
+it there's a lot of money going in and
+what we don't
+
+ align:start position:0%
+what we don't
+ 
+
+ align:start position:0%
+what we don't
+see um if you look at what finance's
+
+ align:start position:0%
+see um if you look at what finance's
+ 
+
+ align:start position:0%
+see um if you look at what finance's
+senatorial and Congressional
+
+ align:start position:0%
+senatorial and Congressional
+ 
+
+ align:start position:0%
+senatorial and Congressional
+campaigns you will see plain old
+
+ align:start position:0%
+campaigns you will see plain old
+ 
+
+ align:start position:0%
+campaigns you will see plain old
+ordinary packs contributing uh like the
+
+ align:start position:0%
+ordinary packs contributing uh like the
+ 
+
+ align:start position:0%
+ordinary packs contributing uh like the
+one I described where I want to make
+
+ align:start position:0%
+one I described where I want to make
+ 
+
+ align:start position:0%
+one I described where I want to make
+sure my phone call gets returned uh and
+
+ align:start position:0%
+sure my phone call gets returned uh and
+ 
+
+ align:start position:0%
+sure my phone call gets returned uh and
+I want you to be sure that you worry
+
+ align:start position:0%
+I want you to be sure that you worry
+ 
+
+ align:start position:0%
+I want you to be sure that you worry
+about wheat Farmers so the wheat Farmers
+
+ align:start position:0%
+about wheat Farmers so the wheat Farmers
+ 
+
+ align:start position:0%
+about wheat Farmers so the wheat Farmers
+Association well but
+
+ align:start position:0%
+Association well but
+ 
+
+ align:start position:0%
+Association well but
+um it is interesting Obama has a pack
+
+ align:start position:0%
+um it is interesting Obama has a pack
+ 
+
+ align:start position:0%
+um it is interesting Obama has a pack
+but they're not sure he's going to win
+
+ align:start position:0%
+but they're not sure he's going to win
+ 
+
+ align:start position:0%
+but they're not sure he's going to win
+either
+
+ align:start position:0%
+either
+ 
+
+ align:start position:0%
+either
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+anyway we'll come back to to lobbying
+
+ align:start position:0%
+anyway we'll come back to to lobbying
+ 
+
+ align:start position:0%
+anyway we'll come back to to lobbying
+and and contributions it's more for
+
+ align:start position:0%
+and and contributions it's more for
+ 
+
+ align:start position:0%
+and and contributions it's more for
+Access than for votes I think but okay
+
+ align:start position:0%
+Access than for votes I think but okay
+ 
+
+ align:start position:0%
+Access than for votes I think but okay
+yes Stephen uh just a quick question for
+
+ align:start position:0%
+yes Stephen uh just a quick question for
+ 
+
+ align:start position:0%
+yes Stephen uh just a quick question for
+the you mentioned that there were
+
+ align:start position:0%
+the you mentioned that there were
+ 
+
+ align:start position:0%
+the you mentioned that there were
+private companies that were still doing
+
+ align:start position:0%
+private companies that were still doing
+ 
+
+ align:start position:0%
+private companies that were still doing
+this type of stuff could it be that some
+
+ align:start position:0%
+this type of stuff could it be that some
+ 
+
+ align:start position:0%
+this type of stuff could it be that some
+of the public companies are going
+
+ align:start position:0%
+of the public companies are going
+ 
+
+ align:start position:0%
+of the public companies are going
+through those means to make their
+
+ align:start position:0%
+through those means to make their
+ 
+
+ align:start position:0%
+through those means to make their
+donations I I think and they've talked
+
+ align:start position:0%
+donations I I think and they've talked
+ 
+
+ align:start position:0%
+donations I I think and they've talked
+about it that there are some companies
+
+ align:start position:0%
+about it that there are some companies
+ 
+
+ align:start position:0%
+about it that there are some companies
+that are dummy companies that get set up
+
+ align:start position:0%
+that are dummy companies that get set up
+ 
+
+ align:start position:0%
+that are dummy companies that get set up
+um uh but mostly it hides Rich
+
+ align:start position:0%
+um uh but mostly it hides Rich
+ 
+
+ align:start position:0%
+um uh but mostly it hides Rich
+individuals
+
+ align:start position:0%
+individuals
+ 
+
+ align:start position:0%
+individuals
+ual so I you can't follow through from
+
+ align:start position:0%
+ual so I you can't follow through from
+ 
+
+ align:start position:0%
+ual so I you can't follow through from
+this website but if you read in the
+
+ align:start position:0%
+this website but if you read in the
+ 
+
+ align:start position:0%
+this website but if you read in the
+paper they talk about trying to track
+
+ align:start position:0%
+paper they talk about trying to track
+ 
+
+ align:start position:0%
+paper they talk about trying to track
+down donors and getting a post office
+
+ align:start position:0%
+down donors and getting a post office
+ 
+
+ align:start position:0%
+down donors and getting a post office
+box so it's a company it has a post
+
+ align:start position:0%
+box so it's a company it has a post
+ 
+
+ align:start position:0%
+box so it's a company it has a post
+office box it's legally
+
+ align:start position:0%
+office box it's legally
+ 
+
+ align:start position:0%
+office box it's legally
+Incorporated uh it's documents aren't
+
+ align:start position:0%
+Incorporated uh it's documents aren't
+ 
+
+ align:start position:0%
+Incorporated uh it's documents aren't
+public because it's closely held so
+
+ align:start position:0%
+public because it's closely held so
+ 
+
+ align:start position:0%
+public because it's closely held so
+that's a that's a mask behind which some
+
+ align:start position:0%
+that's a that's a mask behind which some
+ 
+
+ align:start position:0%
+that's a that's a mask behind which some
+rich person is hiding I don't think it
+
+ align:start position:0%
+rich person is hiding I don't think it
+ 
+
+ align:start position:0%
+rich person is hiding I don't think it
+would be a sane thing for a big publicly
+
+ align:start position:0%
+would be a sane thing for a big publicly
+ 
+
+ align:start position:0%
+would be a sane thing for a big publicly
+traded company to hide that way because
+
+ align:start position:0%
+traded company to hide that way because
+ 
+
+ align:start position:0%
+traded company to hide that way because
+if there were enough money somebody will
+
+ align:start position:0%
+if there were enough money somebody will
+ 
+
+ align:start position:0%
+if there were enough money somebody will
+find it out I mean there's a lot there's
+
+ align:start position:0%
+find it out I mean there's a lot there's
+ 
+
+ align:start position:0%
+find it out I mean there's a lot there's
+a lot somebody gives a million dollars
+
+ align:start position:0%
+a lot somebody gives a million dollars
+ 
+
+ align:start position:0%
+a lot somebody gives a million dollars
+and they're hiding it's a good story if
+
+ align:start position:0%
+and they're hiding it's a good story if
+ 
+
+ align:start position:0%
+and they're hiding it's a good story if
+you can figure out who it is if it turns
+
+ align:start position:0%
+you can figure out who it is if it turns
+ 
+
+ align:start position:0%
+you can figure out who it is if it turns
+out to be apple it's a scandal so that's
+
+ align:start position:0%
+out to be apple it's a scandal so that's
+ 
+
+ align:start position:0%
+out to be apple it's a scandal so that's
+too risky David um could it be possible
+
+ align:start position:0%
+too risky David um could it be possible
+ 
+
+ align:start position:0%
+too risky David um could it be possible
+that some of the larger companies whose
+
+ align:start position:0%
+that some of the larger companies whose
+ 
+
+ align:start position:0%
+that some of the larger companies whose
+um Financial contributions would make a
+
+ align:start position:0%
+um Financial contributions would make a
+ 
+
+ align:start position:0%
+um Financial contributions would make a
+significant impact in the campaign are
+
+ align:start position:0%
+significant impact in the campaign are
+ 
+
+ align:start position:0%
+significant impact in the campaign are
+companies that would already have access
+
+ align:start position:0%
+companies that would already have access
+ 
+
+ align:start position:0%
+companies that would already have access
+anyways if D called up you know the
+
+ align:start position:0%
+anyways if D called up you know the
+ 
+
+ align:start position:0%
+anyways if D called up you know the
+White House and said if you really need
+
+ align:start position:0%
+White House and said if you really need
+ 
+
+ align:start position:0%
+White House and said if you really need
+to talk to someone in treasury or
+
+ align:start position:0%
+to talk to someone in treasury or
+ 
+
+ align:start position:0%
+to talk to someone in treasury or
+something they could probably get
+
+ align:start position:0%
+something they could probably get
+ 
+
+ align:start position:0%
+something they could probably get
+a yeah apple doesn't need to buy access
+
+ align:start position:0%
+a yeah apple doesn't need to buy access
+ 
+
+ align:start position:0%
+a yeah apple doesn't need to buy access
+um this Mining Company May backing
+
+ align:start position:0%
+um this Mining Company May backing
+ 
+
+ align:start position:0%
+um this Mining Company May backing
+Romney is not the most obvious way to do
+
+ align:start position:0%
+Romney is not the most obvious way to do
+ 
+
+ align:start position:0%
+Romney is not the most obvious way to do
+it so I assume that this is just a
+
+ align:start position:0%
+it so I assume that this is just a
+ 
+
+ align:start position:0%
+it so I assume that this is just a
+personal preference of somebody and a
+
+ align:start position:0%
+personal preference of somebody and a
+ 
+
+ align:start position:0%
+personal preference of somebody and a
+board that says yeah sure it's 125,000
+
+ align:start position:0%
+board that says yeah sure it's 125,000
+ 
+
+ align:start position:0%
+board that says yeah sure it's 125,000
+who cares we'll just cut your bonus okay
+
+ align:start position:0%
+who cares we'll just cut your bonus okay
+ 
+
+ align:start position:0%
+who cares we'll just cut your bonus okay
+um I it's it's an interesting
+
+ align:start position:0%
+um I it's it's an interesting
+ 
+
+ align:start position:0%
+um I it's it's an interesting
+an interesting issue of the role of the
+
+ align:start position:0%
+an interesting issue of the role of the
+ 
+
+ align:start position:0%
+an interesting issue of the role of the
+the role of the of the corporation but
+
+ align:start position:0%
+the role of the of the corporation but
+ 
+
+ align:start position:0%
+the role of the of the corporation but
+it's also interesting what most of them
+
+ align:start position:0%
+it's also interesting what most of them
+ 
+
+ align:start position:0%
+it's also interesting what most of them
+choose to do let's go to Upstate New
+
+ align:start position:0%
+choose to do let's go to Upstate New
+ 
+
+ align:start position:0%
+choose to do let's go to Upstate New
+York and do F Malahide uh I just told
+
+ align:start position:0%
+York and do F Malahide uh I just told
+ 
+
+ align:start position:0%
+York and do F Malahide uh I just told
+you what it I just answered that
+
+ align:start position:0%
+you what it I just answered that
+ 
+
+ align:start position:0%
+you what it I just answered that
+question so we've lost that one uh
+
+ align:start position:0%
+question so we've lost that one uh
+ 
+
+ align:start position:0%
+question so we've lost that one uh
+what's Darren's issue in the case
+
+ align:start position:0%
+what's Darren's issue in the case
+ 
+
+ align:start position:0%
+what's Darren's issue in the case
+Matthew uh he's in of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the but what what problem is he
+
+ align:start position:0%
+the but what what problem is he
+ 
+
+ align:start position:0%
+the but what what problem is he
+addressing or what opportunity is he
+
+ align:start position:0%
+addressing or what opportunity is he
+ 
+
+ align:start position:0%
+addressing or what opportunity is he
+addressing what's the wasted heat a lot
+
+ align:start position:0%
+addressing what's the wasted heat a lot
+ 
+
+ align:start position:0%
+addressing what's the wasted heat a lot
+of wasted heat they're venting a lot of
+
+ align:start position:0%
+of wasted heat they're venting a lot of
+ 
+
+ align:start position:0%
+of wasted heat they're venting a lot of
+a lot of steam and anything else it does
+
+ align:start position:0%
+a lot of steam and anything else it does
+ 
+
+ align:start position:0%
+a lot of steam and anything else it does
+Scott also the steam causes damage to
+
+ align:start position:0%
+Scott also the steam causes damage to
+ 
+
+ align:start position:0%
+Scott also the steam causes damage to
+the building it uh corrodes the
+
+ align:start position:0%
+the building it uh corrodes the
+ 
+
+ align:start position:0%
+the building it uh corrodes the
+materials in the building and also
+
+ align:start position:0%
+materials in the building and also
+ 
+
+ align:start position:0%
+materials in the building and also
+causes an ice sheet on the ground which
+
+ align:start position:0%
+causes an ice sheet on the ground which
+ 
+
+ align:start position:0%
+causes an ice sheet on the ground which
+is dangerous for the lovely stuff lovely
+
+ align:start position:0%
+is dangerous for the lovely stuff lovely
+ 
+
+ align:start position:0%
+is dangerous for the lovely stuff lovely
+stuff okay that's what he's got
+
+ align:start position:0%
+stuff okay that's what he's got
+ 
+
+ align:start position:0%
+stuff okay that's what he's got
+he has three options to to deal with
+
+ align:start position:0%
+he has three options to to deal with
+ 
+
+ align:start position:0%
+he has three options to to deal with
+these that he considers first of all do
+
+ align:start position:0%
+these that he considers first of all do
+ 
+
+ align:start position:0%
+these that he considers first of all do
+you call what they are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rachel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep lithium bromine Romine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah anybody got anybody got the third
+
+ align:start position:0%
+yeah anybody got anybody got the third
+ 
+
+ align:start position:0%
+yeah anybody got anybody got the third
+one W third one is to uh speed theow of
+
+ align:start position:0%
+one W third one is to uh speed theow of
+ 
+
+ align:start position:0%
+one W third one is to uh speed theow of
+water speed the flow of water through so
+
+ align:start position:0%
+water speed the flow of water through so
+ 
+
+ align:start position:0%
+water speed the flow of water through so
+it just comes out hot it doesn't come
+
+ align:start position:0%
+it just comes out hot it doesn't come
+ 
+
+ align:start position:0%
+it just comes out hot it doesn't come
+out as
+
+ align:start position:0%
+out as
+ 
+
+ align:start position:0%
+out as
+Steam um
+
+ align:start position:0%
+Steam um
+ 
+
+ align:start position:0%
+Steam um
+okay why is he focused on combined heat
+
+ align:start position:0%
+okay why is he focused on combined heat
+ 
+
+ align:start position:0%
+okay why is he focused on combined heat
+and power why is he focused on cenation
+
+ align:start position:0%
+and power why is he focused on cenation
+ 
+
+ align:start position:0%
+and power why is he focused on cenation
+what are the issues with the others or
+
+ align:start position:0%
+what are the issues with the others or
+ 
+
+ align:start position:0%
+what are the issues with the others or
+the advantage of this in Broad
+
+ align:start position:0%
+the advantage of this in Broad
+ 
+
+ align:start position:0%
+the advantage of this in Broad
+terms Kirsten oh um the disadvantage for
+
+ align:start position:0%
+terms Kirsten oh um the disadvantage for
+ 
+
+ align:start position:0%
+terms Kirsten oh um the disadvantage for
+the speeding up the process in producing
+
+ align:start position:0%
+the speeding up the process in producing
+ 
+
+ align:start position:0%
+the speeding up the process in producing
+hot water was that they didn't have a
+
+ align:start position:0%
+hot water was that they didn't have a
+ 
+
+ align:start position:0%
+hot water was that they didn't have a
+good place to put the hot water
+
+ align:start position:0%
+good place to put the hot water
+ 
+
+ align:start position:0%
+good place to put the hot water
+especially in the summer they didn't
+
+ align:start position:0%
+especially in the summer they didn't
+ 
+
+ align:start position:0%
+especially in the summer they didn't
+want to just dump it into the
+
+ align:start position:0%
+want to just dump it into the
+ 
+
+ align:start position:0%
+want to just dump it into the
+environment because that might have a
+
+ align:start position:0%
+environment because that might have a
+ 
+
+ align:start position:0%
+environment because that might have a
+detrimental effect to the environment
+
+ align:start position:0%
+detrimental effect to the environment
+ 
+
+ align:start position:0%
+detrimental effect to the environment
+right and theage they had to just dump
+
+ align:start position:0%
+right and theage they had to just dump
+ 
+
+ align:start position:0%
+right and theage they had to just dump
+it in a cool stream y yeah they in the
+
+ align:start position:0%
+it in a cool stream y yeah they in the
+ 
+
+ align:start position:0%
+it in a cool stream y yeah they in the
+win it would be good they could keep the
+
+ align:start position:0%
+win it would be good they could keep the
+ 
+
+ align:start position:0%
+win it would be good they could keep the
+buildings without using too much other
+
+ align:start position:0%
+buildings without using too much other
+ 
+
+ align:start position:0%
+buildings without using too much other
+electricity but Su be problem and the
+
+ align:start position:0%
+electricity but Su be problem and the
+ 
+
+ align:start position:0%
+electricity but Su be problem and the
+disadvantage of lium gr was that it
+
+ align:start position:0%
+disadvantage of lium gr was that it
+ 
+
+ align:start position:0%
+disadvantage of lium gr was that it
+would require a lot more um
+
+ align:start position:0%
+would require a lot more um
+ 
+
+ align:start position:0%
+would require a lot more um
+infrastructure
+
+ align:start position:0%
+infrastructure
+ 
+
+ align:start position:0%
+infrastructure
+changes okay so we focused on combined
+
+ align:start position:0%
+changes okay so we focused on combined
+ 
+
+ align:start position:0%
+changes okay so we focused on combined
+heat and power
+
+ align:start position:0%
+heat and power
+ 
+
+ align:start position:0%
+heat and power
+um did anybody look at this is this
+
+ align:start position:0%
+um did anybody look at this is this
+ 
+
+ align:start position:0%
+um did anybody look at this is this
+a if it saves money does it save much
+
+ align:start position:0%
+a if it saves money does it save much
+ 
+
+ align:start position:0%
+a if it saves money does it save much
+money relative to the firm's Revenue to
+
+ align:start position:0%
+money relative to the firm's Revenue to
+ 
+
+ align:start position:0%
+money relative to the firm's Revenue to
+that plant's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Revenue not really um in terms of uh I
+
+ align:start position:0%
+Revenue not really um in terms of uh I
+ 
+
+ align:start position:0%
+Revenue not really um in terms of uh I
+think power SA
+
+ align:start position:0%
+think power SA
+ 
+
+ align:start position:0%
+think power SA
+or cleaning the water or treating the
+
+ align:start position:0%
+or cleaning the water or treating the
+ 
+
+ align:start position:0%
+or cleaning the water or treating the
+water so that they can making it soft
+
+ align:start position:0%
+water so that they can making it soft
+ 
+
+ align:start position:0%
+water so that they can making it soft
+because it's usually typically hard um
+
+ align:start position:0%
+because it's usually typically hard um
+ 
+
+ align:start position:0%
+because it's usually typically hard um
+you save 75% but that's only like 10,000
+
+ align:start position:0%
+you save 75% but that's only like 10,000
+ 
+
+ align:start position:0%
+you save 75% but that's only like 10,000
+or $8,000 but this is they make millions
+
+ align:start position:0%
+or $8,000 but this is they make millions
+ 
+
+ align:start position:0%
+or $8,000 but this is they make millions
+upon millions of dollars and savings are
+
+ align:start position:0%
+upon millions of dollars and savings are
+ 
+
+ align:start position:0%
+upon millions of dollars and savings are
+in the low hundreds thousand low
+
+ align:start position:0%
+in the low hundreds thousand low
+ 
+
+ align:start position:0%
+in the low hundreds thousand low
+hundreds thousands right if you
+
+ align:start position:0%
+hundreds thousands right if you
+ 
+
+ align:start position:0%
+hundreds thousands right if you
+calculate
+
+ align:start position:0%
+calculate
+ 
+
+ align:start position:0%
+calculate
+there's a there's a typo in the case
+
+ align:start position:0%
+there's a there's a typo in the case
+ 
+
+ align:start position:0%
+there's a there's a typo in the case
+where it says it talks about 5 days
+
+ align:start position:0%
+where it says it talks about 5 days
+ 
+
+ align:start position:0%
+where it says it talks about 5 days
+absence being
+
+ align:start position:0%
+absence being
+ 
+
+ align:start position:0%
+absence being
+.01% it's in fact 1% and if you use the
+
+ align:start position:0%
+.01% it's in fact 1% and if you use the
+ 
+
+ align:start position:0%
+.01% it's in fact 1% and if you use the
+other numbers that plant has an annual
+
+ align:start position:0%
+other numbers that plant has an annual
+ 
+
+ align:start position:0%
+other numbers that plant has an annual
+revenue of about $5.1 million based on
+
+ align:start position:0%
+revenue of about $5.1 million based on
+ 
+
+ align:start position:0%
+revenue of about $5.1 million based on
+the production numbers they give you
+
+ align:start position:0%
+the production numbers they give you
+ 
+
+ align:start position:0%
+the production numbers they give you
+work the numbers Veronica
+
+ align:start position:0%
+work the numbers Veronica
+ 
+
+ align:start position:0%
+work the numbers Veronica
+good so what I get is that that the
+
+ align:start position:0%
+good so what I get is that that the
+ 
+
+ align:start position:0%
+good so what I get is that that the
+savings would be maybe 2% of Revenue the
+
+ align:start position:0%
+savings would be maybe 2% of Revenue the
+ 
+
+ align:start position:0%
+savings would be maybe 2% of Revenue the
+pre-tax savings to compare pre-tax to
+
+ align:start position:0%
+pre-tax savings to compare pre-tax to
+ 
+
+ align:start position:0%
+pre-tax savings to compare pre-tax to
+pre-tax
+
+ align:start position:0%
+pre-tax
+ 
+
+ align:start position:0%
+pre-tax
+okay so not a big deal we're going to
+
+ align:start position:0%
+okay so not a big deal we're going to
+ 
+
+ align:start position:0%
+okay so not a big deal we're going to
+talk about whether it's a good deal and
+
+ align:start position:0%
+talk about whether it's a good deal and
+ 
+
+ align:start position:0%
+talk about whether it's a good deal and
+we're going to talk about whether
+
+ align:start position:0%
+we're going to talk about whether
+ 
+
+ align:start position:0%
+we're going to talk about whether
+they'll do it let me just do a short
+
+ align:start position:0%
+they'll do it let me just do a short
+ 
+
+ align:start position:0%
+they'll do it let me just do a short
+Riff
+
+ align:start position:0%
+Riff
+ 
+
+ align:start position:0%
+Riff
+on uh combine heat and power and waste
+
+ align:start position:0%
+on uh combine heat and power and waste
+ 
+
+ align:start position:0%
+on uh combine heat and power and waste
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+um it's interesting if you if you look
+
+ align:start position:0%
+um it's interesting if you if you look
+ 
+
+ align:start position:0%
+um it's interesting if you if you look
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+the rejected energy versus usable energy
+
+ align:start position:0%
+the rejected energy versus usable energy
+ 
+
+ align:start position:0%
+the rejected energy versus usable energy
+B sector right so this is
+
+ align:start position:0%
+B sector right so this is
+ 
+
+ align:start position:0%
+B sector right so this is
+waste Transportation 75% of what goes in
+
+ align:start position:0%
+waste Transportation 75% of what goes in
+ 
+
+ align:start position:0%
+waste Transportation 75% of what goes in
+comes out as waste
+
+ align:start position:0%
+comes out as waste
+ 
+
+ align:start position:0%
+comes out as waste
+energy uh electric generation just about
+
+ align:start position:0%
+energy uh electric generation just about
+ 
+
+ align:start position:0%
+energy uh electric generation just about
+a third and every place else about
+
+ align:start position:0%
+a third and every place else about
+ 
+
+ align:start position:0%
+a third and every place else about
+20%
+
+ align:start position:0%
+20%
+ 
+
+ align:start position:0%
+20%
+um and you all know the answer to that
+
+ align:start position:0%
+um and you all know the answer to that
+ 
+
+ align:start position:0%
+um and you all know the answer to that
+what form the waste takes yes waste
+
+ align:start position:0%
+what form the waste takes yes waste
+ 
+
+ align:start position:0%
+what form the waste takes yes waste
+energy is
+
+ align:start position:0%
+energy is
+ 
+
+ align:start position:0%
+energy is
+usually heat yeah yep so I mean oops
+
+ align:start position:0%
+usually heat yeah yep so I mean oops
+ 
+
+ align:start position:0%
+usually heat yeah yep so I mean oops
+backwards this
+
+ align:start position:0%
+backwards this
+ 
+
+ align:start position:0%
+backwards this
+one transportation's tough cuz cars are
+
+ align:start position:0%
+one transportation's tough cuz cars are
+ 
+
+ align:start position:0%
+one transportation's tough cuz cars are
+not all that that efficient really um
+
+ align:start position:0%
+not all that that efficient really um
+ 
+
+ align:start position:0%
+not all that that efficient really um
+and uh but for public transportation
+
+ align:start position:0%
+and uh but for public transportation
+ 
+
+ align:start position:0%
+and uh but for public transportation
+this is a tough one uh residential and
+
+ align:start position:0%
+this is a tough one uh residential and
+ 
+
+ align:start position:0%
+this is a tough one uh residential and
+Commercial an awful lot of the energy is
+
+ align:start position:0%
+Commercial an awful lot of the energy is
+ 
+
+ align:start position:0%
+Commercial an awful lot of the energy is
+going into heating and cooling you can
+
+ align:start position:0%
+going into heating and cooling you can
+ 
+
+ align:start position:0%
+going into heating and cooling you can
+make it more efficient of course um but
+
+ align:start position:0%
+make it more efficient of course um but
+ 
+
+ align:start position:0%
+make it more efficient of course um but
+it's hard to capture what's attractive
+
+ align:start position:0%
+it's hard to capture what's attractive
+ 
+
+ align:start position:0%
+it's hard to capture what's attractive
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+industrial and
+
+ align:start position:0%
+industrial and
+ 
+
+ align:start position:0%
+industrial and
+electricity is you have high heat you
+
+ align:start position:0%
+electricity is you have high heat you
+ 
+
+ align:start position:0%
+electricity is you have high heat you
+have large delta T you have the ability
+
+ align:start position:0%
+have large delta T you have the ability
+ 
+
+ align:start position:0%
+have large delta T you have the ability
+to use a big temperature
+
+ align:start position:0%
+to use a big temperature
+ 
+
+ align:start position:0%
+to use a big temperature
+differential uh and that's the whole
+
+ align:start position:0%
+differential uh and that's the whole
+ 
+
+ align:start position:0%
+differential uh and that's the whole
+combined heat and power
+
+ align:start position:0%
+combined heat and power
+ 
+
+ align:start position:0%
+combined heat and power
+story that there really are two basic
+
+ align:start position:0%
+story that there really are two basic
+ 
+
+ align:start position:0%
+story that there really are two basic
+forms and the case kind of mentions it
+
+ align:start position:0%
+forms and the case kind of mentions it
+ 
+
+ align:start position:0%
+forms and the case kind of mentions it
+the first is called District heating
+
+ align:start position:0%
+the first is called District heating
+ 
+
+ align:start position:0%
+the first is called District heating
+where you
+
+ align:start position:0%
+where you
+ 
+
+ align:start position:0%
+where you
+take waste heat relatively low
+
+ align:start position:0%
+take waste heat relatively low
+ 
+
+ align:start position:0%
+take waste heat relatively low
+temperature from Electric generation and
+
+ align:start position:0%
+temperature from Electric generation and
+ 
+
+ align:start position:0%
+temperature from Electric generation and
+you pipe it around to heat
+
+ align:start position:0%
+you pipe it around to heat
+ 
+
+ align:start position:0%
+you pipe it around to heat
+buildings uh the Danes uh did a lot of
+
+ align:start position:0%
+buildings uh the Danes uh did a lot of
+ 
+
+ align:start position:0%
+buildings uh the Danes uh did a lot of
+this one of the readings mentioned that
+
+ align:start position:0%
+this one of the readings mentioned that
+ 
+
+ align:start position:0%
+this one of the readings mentioned that
+it's also interesting the Soviets did a
+
+ align:start position:0%
+it's also interesting the Soviets did a
+ 
+
+ align:start position:0%
+it's also interesting the Soviets did a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+it um it requires you to have power
+
+ align:start position:0%
+it um it requires you to have power
+ 
+
+ align:start position:0%
+it um it requires you to have power
+plants relatively close to offices or
+
+ align:start position:0%
+plants relatively close to offices or
+ 
+
+ align:start position:0%
+plants relatively close to offices or
+factories or homes so it's not the
+
+ align:start position:0%
+factories or homes so it's not the
+ 
+
+ align:start position:0%
+factories or homes so it's not the
+greatest thing and of course it makes
+
+ align:start position:0%
+greatest thing and of course it makes
+ 
+
+ align:start position:0%
+greatest thing and of course it makes
+more sense in a cold
+
+ align:start position:0%
+more sense in a cold
+ 
+
+ align:start position:0%
+more sense in a cold
+climate using waste heat to heat
+
+ align:start position:0%
+climate using waste heat to heat
+ 
+
+ align:start position:0%
+climate using waste heat to heat
+buildings in Arizona is not
+
+ align:start position:0%
+buildings in Arizona is not
+ 
+
+ align:start position:0%
+buildings in Arizona is not
+necessarily a great a great uh a great
+
+ align:start position:0%
+necessarily a great a great uh a great
+ 
+
+ align:start position:0%
+necessarily a great a great uh a great
+deal we put in subsidies in
+
+ align:start position:0%
+deal we put in subsidies in
+ 
+
+ align:start position:0%
+deal we put in subsidies in
+1978 we'll talk a little bit about Pera
+
+ align:start position:0%
+1978 we'll talk a little bit about Pera
+ 
+
+ align:start position:0%
+1978 we'll talk a little bit about Pera
+some point that we supposed to
+
+ align:start position:0%
+some point that we supposed to
+ 
+
+ align:start position:0%
+some point that we supposed to
+encourage District
+
+ align:start position:0%
+encourage District
+ 
+
+ align:start position:0%
+encourage District
+heating uh it it didn't do much for a
+
+ align:start position:0%
+heating uh it it didn't do much for a
+ 
+
+ align:start position:0%
+heating uh it it didn't do much for a
+variety of complicated reasons it's
+
+ align:start position:0%
+variety of complicated reasons it's
+ 
+
+ align:start position:0%
+variety of complicated reasons it's
+generally acknowledged as a good thing
+
+ align:start position:0%
+generally acknowledged as a good thing
+ 
+
+ align:start position:0%
+generally acknowledged as a good thing
+in lots of places but we don't do very
+
+ align:start position:0%
+in lots of places but we don't do very
+ 
+
+ align:start position:0%
+in lots of places but we don't do very
+much of it in this country for a variety
+
+ align:start position:0%
+much of it in this country for a variety
+ 
+
+ align:start position:0%
+much of it in this country for a variety
+of reasons the
+
+ align:start position:0%
+of reasons the
+ 
+
+ align:start position:0%
+of reasons the
+other is electricity generation and
+
+ align:start position:0%
+other is electricity generation and
+ 
+
+ align:start position:0%
+other is electricity generation and
+there are sort of two versions the first
+
+ align:start position:0%
+there are sort of two versions the first
+ 
+
+ align:start position:0%
+there are sort of two versions the first
+is basic combined cycle gas turbine
+
+ align:start position:0%
+is basic combined cycle gas turbine
+ 
+
+ align:start position:0%
+is basic combined cycle gas turbine
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+a relatively recent I I should be able
+
+ align:start position:0%
+a relatively recent I I should be able
+ 
+
+ align:start position:0%
+a relatively recent I I should be able
+to date it but I can't maybe the 70s
+
+ align:start position:0%
+to date it but I can't maybe the 70s
+ 
+
+ align:start position:0%
+to date it but I can't maybe the 70s
+maybe the 80s generation technology
+
+ align:start position:0%
+maybe the 80s generation technology
+ 
+
+ align:start position:0%
+maybe the 80s generation technology
+that's sort of how people are building
+
+ align:start position:0%
+that's sort of how people are building
+ 
+
+ align:start position:0%
+that's sort of how people are building
+efficient gas plants these days right
+
+ align:start position:0%
+efficient gas plants these days right
+ 
+
+ align:start position:0%
+efficient gas plants these days right
+you you run a combustion
+
+ align:start position:0%
+you you run a combustion
+ 
+
+ align:start position:0%
+you you run a combustion
+turbine which has a hot exhaust you
+
+ align:start position:0%
+turbine which has a hot exhaust you
+ 
+
+ align:start position:0%
+turbine which has a hot exhaust you
+recover the heat from the hot exhaust
+
+ align:start position:0%
+recover the heat from the hot exhaust
+ 
+
+ align:start position:0%
+recover the heat from the hot exhaust
+which makes steam which drives a steam
+
+ align:start position:0%
+which makes steam which drives a steam
+ 
+
+ align:start position:0%
+which makes steam which drives a steam
+turbine combined cycle CC so you got two
+
+ align:start position:0%
+turbine combined cycle CC so you got two
+ 
+
+ align:start position:0%
+turbine combined cycle CC so you got two
+cycles working and basically New
+
+ align:start position:0%
+cycles working and basically New
+ 
+
+ align:start position:0%
+cycles working and basically New
+Generation units this this can be a very
+
+ align:start position:0%
+Generation units this this can be a very
+ 
+
+ align:start position:0%
+Generation units this this can be a very
+this is pulled off a Seaman's website
+
+ align:start position:0%
+this is pulled off a Seaman's website
+ 
+
+ align:start position:0%
+this is pulled off a Seaman's website
+this can be a very efficient a very
+
+ align:start position:0%
+this can be a very efficient a very
+ 
+
+ align:start position:0%
+this can be a very efficient a very
+efficient technology and it's the same
+
+ align:start position:0%
+efficient technology and it's the same
+ 
+
+ align:start position:0%
+efficient technology and it's the same
+notion of capturing waste
+
+ align:start position:0%
+notion of capturing waste
+ 
+
+ align:start position:0%
+notion of capturing waste
+heat um the all you mechanical engineers
+
+ align:start position:0%
+heat um the all you mechanical engineers
+ 
+
+ align:start position:0%
+heat um the all you mechanical engineers
+know more about this than I do
+
+ align:start position:0%
+know more about this than I do
+ 
+
+ align:start position:0%
+know more about this than I do
+but others may not uh and this is the
+
+ align:start position:0%
+but others may not uh and this is the
+ 
+
+ align:start position:0%
+but others may not uh and this is the
+proposal this is the kind of proposal
+
+ align:start position:0%
+proposal this is the kind of proposal
+ 
+
+ align:start position:0%
+proposal this is the kind of proposal
+this is pulled from the case this is the
+
+ align:start position:0%
+this is pulled from the case this is the
+ 
+
+ align:start position:0%
+this is pulled from the case this is the
+kind of proposal that our friend Darren
+
+ align:start position:0%
+kind of proposal that our friend Darren
+ 
+
+ align:start position:0%
+kind of proposal that our friend Darren
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+considering uh it has to do this shows a
+
+ align:start position:0%
+considering uh it has to do this shows a
+ 
+
+ align:start position:0%
+considering uh it has to do this shows a
+boiler but it has to do as you know with
+
+ align:start position:0%
+boiler but it has to do as you know with
+ 
+
+ align:start position:0%
+boiler but it has to do as you know with
+the heat from that exothermic reaction
+
+ align:start position:0%
+the heat from that exothermic reaction
+ 
+
+ align:start position:0%
+the heat from that exothermic reaction
+that makes from Malahide so this is what
+
+ align:start position:0%
+that makes from Malahide so this is what
+ 
+
+ align:start position:0%
+that makes from Malahide so this is what
+he's considering he's considering a
+
+ align:start position:0%
+he's considering he's considering a
+ 
+
+ align:start position:0%
+he's considering he's considering a
+simple system that uh take steam to
+
+ align:start position:0%
+simple system that uh take steam to
+ 
+
+ align:start position:0%
+simple system that uh take steam to
+drive a turbine generate electricity for
+
+ align:start position:0%
+drive a turbine generate electricity for
+ 
+
+ align:start position:0%
+drive a turbine generate electricity for
+internal use maybe for sale you cool it
+
+ align:start position:0%
+internal use maybe for sale you cool it
+ 
+
+ align:start position:0%
+internal use maybe for sale you cool it
+down you recycle it you pump it through
+
+ align:start position:0%
+down you recycle it you pump it through
+ 
+
+ align:start position:0%
+down you recycle it you pump it through
+you don't re you will you will have to
+
+ align:start position:0%
+you don't re you will you will have to
+ 
+
+ align:start position:0%
+you don't re you will you will have to
+use some water but you'll pull a lot of
+
+ align:start position:0%
+use some water but you'll pull a lot of
+ 
+
+ align:start position:0%
+use some water but you'll pull a lot of
+the water a lot of the water through and
+
+ align:start position:0%
+the water a lot of the water through and
+ 
+
+ align:start position:0%
+the water a lot of the water through and
+the stuff that comes out will be
+
+ align:start position:0%
+the stuff that comes out will be
+ 
+
+ align:start position:0%
+the stuff that comes out will be
+basically cooling the uh cooling the
+
+ align:start position:0%
+basically cooling the uh cooling the
+ 
+
+ align:start position:0%
+basically cooling the uh cooling the
+condenser so this is what he's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got there are a lot of benefits of this
+
+ align:start position:0%
+got there are a lot of benefits of this
+ 
+
+ align:start position:0%
+got there are a lot of benefits of this
+kind of system in general terms you can
+
+ align:start position:0%
+kind of system in general terms you can
+ 
+
+ align:start position:0%
+kind of system in general terms you can
+reduce energy expenses you can worry it
+
+ align:start position:0%
+reduce energy expenses you can worry it
+ 
+
+ align:start position:0%
+reduce energy expenses you can worry it
+it could avoid the risk of um uh varying
+
+ align:start position:0%
+it could avoid the risk of um uh varying
+ 
+
+ align:start position:0%
+it could avoid the risk of um uh varying
+Energy prices a lot of security good
+
+ align:start position:0%
+Energy prices a lot of security good
+ 
+
+ align:start position:0%
+Energy prices a lot of security good
+environmental benefits mom and Apple
+
+ align:start position:0%
+environmental benefits mom and Apple
+ 
+
+ align:start position:0%
+environmental benefits mom and Apple
+Pi but the
+
+ align:start position:0%
+Pi but the
+ 
+
+ align:start position:0%
+Pi but the
+question that Darren faces is is it a
+
+ align:start position:0%
+question that Darren faces is is it a
+ 
+
+ align:start position:0%
+question that Darren faces is is it a
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+deal I want to mention
+
+ align:start position:0%
+deal I want to mention
+ 
+
+ align:start position:0%
+deal I want to mention
+two concepts that the case kind of puts
+
+ align:start position:0%
+two concepts that the case kind of puts
+ 
+
+ align:start position:0%
+two concepts that the case kind of puts
+forward and the spreadsheet puts forward
+
+ align:start position:0%
+forward and the spreadsheet puts forward
+ 
+
+ align:start position:0%
+forward and the spreadsheet puts forward
+without defining them and I'll talk
+
+ align:start position:0%
+without defining them and I'll talk
+ 
+
+ align:start position:0%
+without defining them and I'll talk
+about them briefly so if you've got a
+
+ align:start position:0%
+about them briefly so if you've got a
+ 
+
+ align:start position:0%
+about them briefly so if you've got a
+vector of cash flows
+
+ align:start position:0%
+vector of cash flows
+ 
+
+ align:start position:0%
+vector of cash flows
+CT that's the Net Present Value right
+
+ align:start position:0%
+CT that's the Net Present Value right
+ 
+
+ align:start position:0%
+CT that's the Net Present Value right
+you just discount all the cash flows the
+
+ align:start position:0%
+you just discount all the cash flows the
+ 
+
+ align:start position:0%
+you just discount all the cash flows the
+case talks about the payback
+
+ align:start position:0%
+case talks about the payback
+ 
+
+ align:start position:0%
+case talks about the payback
+period and the payback period right is
+
+ align:start position:0%
+period and the payback period right is
+ 
+
+ align:start position:0%
+period and the payback period right is
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smallest time such that basically you
+
+ align:start position:0%
+smallest time such that basically you
+ 
+
+ align:start position:0%
+smallest time such that basically you
+get your initial investment back
+
+ align:start position:0%
+get your initial investment back
+ 
+
+ align:start position:0%
+get your initial investment back
+assuming there's an initial investment
+
+ align:start position:0%
+assuming there's an initial investment
+ 
+
+ align:start position:0%
+assuming there's an initial investment
+up front and
+
+ align:start position:0%
+up front and
+ 
+
+ align:start position:0%
+up front and
+then uh returns in subsequent periods
+
+ align:start position:0%
+then uh returns in subsequent periods
+ 
+
+ align:start position:0%
+then uh returns in subsequent periods
+you go out as far as um uh you need to
+
+ align:start position:0%
+you go out as far as um uh you need to
+ 
+
+ align:start position:0%
+you go out as far as um uh you need to
+to recover the initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+investment this is kind of an old a very
+
+ align:start position:0%
+investment this is kind of an old a very
+ 
+
+ align:start position:0%
+investment this is kind of an old a very
+oldfashioned way of making investment
+
+ align:start position:0%
+oldfashioned way of making investment
+ 
+
+ align:start position:0%
+oldfashioned way of making investment
+decisions and the problem with it is
+
+ align:start position:0%
+decisions and the problem with it is
+ 
+
+ align:start position:0%
+decisions and the problem with it is
+stated there because it matters what
+
+ align:start position:0%
+stated there because it matters what
+ 
+
+ align:start position:0%
+stated there because it matters what
+happens after that
+
+ align:start position:0%
+happens after that
+ 
+
+ align:start position:0%
+happens after that
+time you know I tell you that you invest
+
+ align:start position:0%
+time you know I tell you that you invest
+ 
+
+ align:start position:0%
+time you know I tell you that you invest
+$100 today you get $50 a year from now
+
+ align:start position:0%
+$100 today you get $50 a year from now
+ 
+
+ align:start position:0%
+$100 today you get $50 a year from now
+$50 two years from now the payback
+
+ align:start position:0%
+$50 two years from now the payback
+ 
+
+ align:start position:0%
+$50 two years from now the payback
+period is two years if that's all you
+
+ align:start position:0%
+period is two years if that's all you
+ 
+
+ align:start position:0%
+period is two years if that's all you
+know that's a terrible
+
+ align:start position:0%
+know that's a terrible
+ 
+
+ align:start position:0%
+know that's a terrible
+investment right you've just given me
+
+ align:start position:0%
+investment right you've just given me
+ 
+
+ align:start position:0%
+investment right you've just given me
+your money for two
+
+ align:start position:0%
+your money for two
+ 
+
+ align:start position:0%
+your money for two
+years what really matters is okay what
+
+ align:start position:0%
+years what really matters is okay what
+ 
+
+ align:start position:0%
+years what really matters is okay what
+happens after after
+
+ align:start position:0%
+happens after after
+ 
+
+ align:start position:0%
+happens after after
+that what happens after and the longer
+
+ align:start position:0%
+that what happens after and the longer
+ 
+
+ align:start position:0%
+that what happens after and the longer
+the payback all else equal it may be the
+
+ align:start position:0%
+the payback all else equal it may be the
+ 
+
+ align:start position:0%
+the payback all else equal it may be the
+worse the investment but you you can
+
+ align:start position:0%
+worse the investment but you you can
+ 
+
+ align:start position:0%
+worse the investment but you you can
+have a really
+
+ align:start position:0%
+have a really
+ 
+
+ align:start position:0%
+have a really
+terrible investment with a short payback
+
+ align:start position:0%
+terrible investment with a short payback
+ 
+
+ align:start position:0%
+terrible investment with a short payback
+period because it
+
+ align:start position:0%
+period because it
+ 
+
+ align:start position:0%
+period because it
+dies so the case talks about it I just
+
+ align:start position:0%
+dies so the case talks about it I just
+ 
+
+ align:start position:0%
+dies so the case talks about it I just
+want to caution you that by any sort of
+
+ align:start position:0%
+want to caution you that by any sort of
+ 
+
+ align:start position:0%
+want to caution you that by any sort of
+reasonable standard that's not something
+
+ align:start position:0%
+reasonable standard that's not something
+ 
+
+ align:start position:0%
+reasonable standard that's not something
+you want it's something you want to look
+
+ align:start position:0%
+you want it's something you want to look
+ 
+
+ align:start position:0%
+you want it's something you want to look
+at perhaps because it it may be a
+
+ align:start position:0%
+at perhaps because it it may be a
+ 
+
+ align:start position:0%
+at perhaps because it it may be a
+horseback way of thinking about
+
+ align:start position:0%
+horseback way of thinking about
+ 
+
+ align:start position:0%
+horseback way of thinking about
+risk right right after two years we're
+
+ align:start position:0%
+risk right right after two years we're
+ 
+
+ align:start position:0%
+risk right right after two years we're
+playing with house money because we've
+
+ align:start position:0%
+playing with house money because we've
+ 
+
+ align:start position:0%
+playing with house money because we've
+gotten our money back Andrew you have a
+
+ align:start position:0%
+gotten our money back Andrew you have a
+ 
+
+ align:start position:0%
+gotten our money back Andrew you have a
+comment I was going to ask I mean that I
+
+ align:start position:0%
+comment I was going to ask I mean that I
+ 
+
+ align:start position:0%
+comment I was going to ask I mean that I
+assume that even though it's not like
+
+ align:start position:0%
+assume that even though it's not like
+ 
+
+ align:start position:0%
+assume that even though it's not like
+the best metric to make the decision it
+
+ align:start position:0%
+the best metric to make the decision it
+ 
+
+ align:start position:0%
+the best metric to make the decision it
+could be a good metric to see like when
+
+ align:start position:0%
+could be a good metric to see like when
+ 
+
+ align:start position:0%
+could be a good metric to see like when
+your cash flows are coming in terms of
+
+ align:start position:0%
+your cash flows are coming in terms of
+ 
+
+ align:start position:0%
+your cash flows are coming in terms of
+like if I have something that has a
+
+ align:start position:0%
+like if I have something that has a
+ 
+
+ align:start position:0%
+like if I have something that has a
+payback period of Two and a payback de
+
+ align:start position:0%
+payback period of Two and a payback de
+ 
+
+ align:start position:0%
+payback period of Two and a payback de
+of 15 years I just know that uh like my
+
+ align:start position:0%
+of 15 years I just know that uh like my
+ 
+
+ align:start position:0%
+of 15 years I just know that uh like my
+risk is uh I have higher risk in terms
+
+ align:start position:0%
+risk is uh I have higher risk in terms
+ 
+
+ align:start position:0%
+risk is uh I have higher risk in terms
+of uh like when I get my money back with
+
+ align:start position:0%
+of uh like when I get my money back with
+ 
+
+ align:start position:0%
+of uh like when I get my money back with
+the second one no I think that's right
+
+ align:start position:0%
+the second one no I think that's right
+ 
+
+ align:start position:0%
+the second one no I think that's right
+but you you also want to just look at
+
+ align:start position:0%
+but you you also want to just look at
+ 
+
+ align:start position:0%
+but you you also want to just look at
+the nature of the risks if I tell you
+
+ align:start position:0%
+the nature of the risks if I tell you
+ 
+
+ align:start position:0%
+the nature of the risks if I tell you
+it's a
+
+ align:start position:0%
+it's a
+ 
+
+ align:start position:0%
+it's a
+bond and you don't worry about it if I
+
+ align:start position:0%
+bond and you don't worry about it if I
+ 
+
+ align:start position:0%
+bond and you don't worry about it if I
+tell you it's a nuclear plant okay the
+
+ align:start position:0%
+tell you it's a nuclear plant okay the
+ 
+
+ align:start position:0%
+tell you it's a nuclear plant okay the
+nuclear plant has a 20-year
+
+ align:start position:0%
+nuclear plant has a 20-year
+ 
+
+ align:start position:0%
+nuclear plant has a 20-year
+payback but if it runs for 40 years it's
+
+ align:start position:0%
+payback but if it runs for 40 years it's
+ 
+
+ align:start position:0%
+payback but if it runs for 40 years it's
+got a high Net Present Value you're
+
+ align:start position:0%
+got a high Net Present Value you're
+ 
+
+ align:start position:0%
+got a high Net Present Value you're
+right to say wait a minute an awful lot
+
+ align:start position:0%
+right to say wait a minute an awful lot
+ 
+
+ align:start position:0%
+right to say wait a minute an awful lot
+can happen see Germany see
+
+ align:start position:0%
+can happen see Germany see
+ 
+
+ align:start position:0%
+can happen see Germany see
+Japan uh so maybe I maybe I don't want
+
+ align:start position:0%
+Japan uh so maybe I maybe I don't want
+ 
+
+ align:start position:0%
+Japan uh so maybe I maybe I don't want
+to do that but that's that's sort of the
+
+ align:start position:0%
+to do that but that's that's sort of the
+ 
+
+ align:start position:0%
+to do that but that's that's sort of the
+main the main argument the internal rate
+
+ align:start position:0%
+main the main argument the internal rate
+ 
+
+ align:start position:0%
+main the main argument the internal rate
+of return turn is also sort of
+
+ align:start position:0%
+of return turn is also sort of
+ 
+
+ align:start position:0%
+of return turn is also sort of
+interesting okay you can think about the
+
+ align:start position:0%
+interesting okay you can think about the
+ 
+
+ align:start position:0%
+interesting okay you can think about the
+Net Present Value as a as a polom well
+
+ align:start position:0%
+Net Present Value as a as a polom well
+ 
+
+ align:start position:0%
+Net Present Value as a as a polom well
+it's a polinomial in 1 over 1+
+
+ align:start position:0%
+it's a polinomial in 1 over 1+
+ 
+
+ align:start position:0%
+it's a polinomial in 1 over 1+
+R uh and you can say well
+
+ align:start position:0%
+R uh and you can say well
+ 
+
+ align:start position:0%
+R uh and you can say well
+suppose we doing this
+
+ align:start position:0%
+suppose we doing this
+ 
+
+ align:start position:0%
+suppose we doing this
+chocas suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this is the net present
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value and this is the discount rate then
+
+ align:start position:0%
+value and this is the discount rate then
+ 
+
+ align:start position:0%
+value and this is the discount rate then
+what you might expect is that as you if
+
+ align:start position:0%
+what you might expect is that as you if
+ 
+
+ align:start position:0%
+what you might expect is that as you if
+you if you make an upfront investment
+
+ align:start position:0%
+you if you make an upfront investment
+ 
+
+ align:start position:0%
+you if you make an upfront investment
+you get returns over time the higher the
+
+ align:start position:0%
+you get returns over time the higher the
+ 
+
+ align:start position:0%
+you get returns over time the higher the
+discount rate the lower the Net Present
+
+ align:start position:0%
+discount rate the lower the Net Present
+ 
+
+ align:start position:0%
+discount rate the lower the Net Present
+Value this point would
+
+ align:start position:0%
+Value this point would
+ 
+
+ align:start position:0%
+Value this point would
+be the internal rate of
+
+ align:start position:0%
+be the internal rate of
+ 
+
+ align:start position:0%
+be the internal rate of
+return now what's interesting about
+
+ align:start position:0%
+return now what's interesting about
+ 
+
+ align:start position:0%
+return now what's interesting about
+that is that when the picture looks like
+
+ align:start position:0%
+that is that when the picture looks like
+ 
+
+ align:start position:0%
+that is that when the picture looks like
+that you don't have to get too fussy
+
+ align:start position:0%
+that you don't have to get too fussy
+ 
+
+ align:start position:0%
+that you don't have to get too fussy
+about the discount rate as long as you
+
+ align:start position:0%
+about the discount rate as long as you
+ 
+
+ align:start position:0%
+about the discount rate as long as you
+know it's below our star right that's
+
+ align:start position:0%
+know it's below our star right that's
+ 
+
+ align:start position:0%
+know it's below our star right that's
+what it's good for it says well I know
+
+ align:start position:0%
+what it's good for it says well I know
+ 
+
+ align:start position:0%
+what it's good for it says well I know
+it's got a positive Net Present Value
+
+ align:start position:0%
+it's got a positive Net Present Value
+ 
+
+ align:start position:0%
+it's got a positive Net Present Value
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+but so if if the discount rate somewhere
+
+ align:start position:0%
+but so if if the discount rate somewhere
+ 
+
+ align:start position:0%
+but so if if the discount rate somewhere
+in this range but I'm not sure which
+
+ align:start position:0%
+in this range but I'm not sure which
+ 
+
+ align:start position:0%
+in this range but I'm not sure which
+where it is I know enough to know the
+
+ align:start position:0%
+where it is I know enough to know the
+ 
+
+ align:start position:0%
+where it is I know enough to know the
+net present value is
+
+ align:start position:0%
+net present value is
+ 
+
+ align:start position:0%
+net present value is
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+but you can have the graph could look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it could look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that it could look like that if you know
+
+ align:start position:0%
+that it could look like that if you know
+ 
+
+ align:start position:0%
+that it could look like that if you know
+at the end of the period it is a nuclear
+
+ align:start position:0%
+at the end of the period it is a nuclear
+ 
+
+ align:start position:0%
+at the end of the period it is a nuclear
+reactor and we've got to clean it
+
+ align:start position:0%
+reactor and we've got to clean it
+ 
+
+ align:start position:0%
+reactor and we've got to clean it
+up okay then High discount rates make
+
+ align:start position:0%
+up okay then High discount rates make
+ 
+
+ align:start position:0%
+up okay then High discount rates make
+that cleanup cost smaller in present
+
+ align:start position:0%
+that cleanup cost smaller in present
+ 
+
+ align:start position:0%
+that cleanup cost smaller in present
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+terms right it's a polinomial so the
+
+ align:start position:0%
+terms right it's a polinomial so the
+ 
+
+ align:start position:0%
+terms right it's a polinomial so the
+number of sign changes is related in
+
+ align:start position:0%
+number of sign changes is related in
+ 
+
+ align:start position:0%
+number of sign changes is related in
+ways I've long since forgotten to the
+
+ align:start position:0%
+ways I've long since forgotten to the
+ 
+
+ align:start position:0%
+ways I've long since forgotten to the
+number of real
+
+ align:start position:0%
+number of real
+ 
+
+ align:start position:0%
+number of real
+Roots um
+
+ align:start position:0%
+Roots um
+ 
+
+ align:start position:0%
+Roots um
+if you have a if there's only one sign
+
+ align:start position:0%
+if you have a if there's only one sign
+ 
+
+ align:start position:0%
+if you have a if there's only one sign
+change you're only going to get one real
+
+ align:start position:0%
+change you're only going to get one real
+ 
+
+ align:start position:0%
+change you're only going to get one real
+root but if you have negative n negative
+
+ align:start position:0%
+root but if you have negative n negative
+ 
+
+ align:start position:0%
+root but if you have negative n negative
+returns at the end you can get two I
+
+ align:start position:0%
+returns at the end you can get two I
+ 
+
+ align:start position:0%
+returns at the end you can get two I
+suppose you can get more than two the
+
+ align:start position:0%
+suppose you can get more than two the
+ 
+
+ align:start position:0%
+suppose you can get more than two the
+normal thing and that's what the slide
+
+ align:start position:0%
+normal thing and that's what the slide
+ 
+
+ align:start position:0%
+normal thing and that's what the slide
+says is to call the smallest one R star
+
+ align:start position:0%
+says is to call the smallest one R star
+ 
+
+ align:start position:0%
+says is to call the smallest one R star
+and think that's a little
+
+ align:start position:0%
+and think that's a little
+ 
+
+ align:start position:0%
+and think that's a little
+weird the other thing to keep in
+
+ align:start position:0%
+weird the other thing to keep in
+ 
+
+ align:start position:0%
+weird the other thing to keep in
+mind again if you just graph these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+say here's project
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a here's Project
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B A has a higher internal rate of return
+
+ align:start position:0%
+B A has a higher internal rate of return
+ 
+
+ align:start position:0%
+B A has a higher internal rate of return
+than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b but for discount rates back here you'd
+
+ align:start position:0%
+b but for discount rates back here you'd
+ 
+
+ align:start position:0%
+b but for discount rates back here you'd
+prefer
+
+ align:start position:0%
+prefer
+ 
+
+ align:start position:0%
+prefer
+B if you have to
+
+ align:start position:0%
+B if you have to
+ 
+
+ align:start position:0%
+B if you have to
+choose if you have limited funds they
+
+ align:start position:0%
+choose if you have limited funds they
+ 
+
+ align:start position:0%
+choose if you have limited funds they
+have the same upfront cost your discount
+
+ align:start position:0%
+have the same upfront cost your discount
+ 
+
+ align:start position:0%
+have the same upfront cost your discount
+rate is in here B has the higher Net
+
+ align:start position:0%
+rate is in here B has the higher Net
+ 
+
+ align:start position:0%
+rate is in here B has the higher Net
+Present Value you'd pick
+
+ align:start position:0%
+Present Value you'd pick
+ 
+
+ align:start position:0%
+Present Value you'd pick
+it so ranking by internal rate of return
+
+ align:start position:0%
+it so ranking by internal rate of return
+ 
+
+ align:start position:0%
+it so ranking by internal rate of return
+doesn't give you a desirability measure
+
+ align:start position:0%
+doesn't give you a desirability measure
+ 
+
+ align:start position:0%
+doesn't give you a desirability measure
+it just gives you some confidence
+
+ align:start position:0%
+it just gives you some confidence
+ 
+
+ align:start position:0%
+it just gives you some confidence
+about um
+
+ align:start position:0%
+about um
+ 
+
+ align:start position:0%
+about um
+uh it it allows you to be uncertain
+
+ align:start position:0%
+uh it it allows you to be uncertain
+ 
+
+ align:start position:0%
+uh it it allows you to be uncertain
+about the discount rate and still make a
+
+ align:start position:0%
+about the discount rate and still make a
+ 
+
+ align:start position:0%
+about the discount rate and still make a
+judgment about present
+
+ align:start position:0%
+judgment about present
+ 
+
+ align:start position:0%
+judgment about present
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+okay questions about those David
+
+ align:start position:0%
+okay questions about those David
+ 
+
+ align:start position:0%
+okay questions about those David
+so you just for
+
+ align:start position:0%
+so you just for
+ 
+
+ align:start position:0%
+so you just for
+Value
+
+ align:start position:0%
+Value
+ 
+
+ align:start position:0%
+Value
+no normally that's not that's how they
+
+ align:start position:0%
+no normally that's not that's how they
+ 
+
+ align:start position:0%
+no normally that's not that's how they
+do it this I don't worry about interest
+
+ align:start position:0%
+do it this I don't worry about interest
+ 
+
+ align:start position:0%
+do it this I don't worry about interest
+rates don't give me any of that fancy
+
+ align:start position:0%
+rates don't give me any of that fancy
+ 
+
+ align:start position:0%
+rates don't give me any of that fancy
+stuff when do I get my money
+
+ align:start position:0%
+stuff when do I get my money
+ 
+
+ align:start position:0%
+stuff when do I get my money
+out right and you could see the problem
+
+ align:start position:0%
+out right and you could see the problem
+ 
+
+ align:start position:0%
+out right and you could see the problem
+as I say I could give it to I can give
+
+ align:start position:0%
+as I say I could give it to I can give
+ 
+
+ align:start position:0%
+as I say I could give it to I can give
+you a one-year payback period That's a
+
+ align:start position:0%
+you a one-year payback period That's a
+ 
+
+ align:start position:0%
+you a one-year payback period That's a
+lousy investment that's pretty easy give
+
+ align:start position:0%
+lousy investment that's pretty easy give
+ 
+
+ align:start position:0%
+lousy investment that's pretty easy give
+me $100 today I'll give it back to you
+
+ align:start position:0%
+me $100 today I'll give it back to you
+ 
+
+ align:start position:0%
+me $100 today I'll give it back to you
+in a year one year payback fabulous H
+
+ align:start position:0%
+in a year one year payback fabulous H
+ 
+
+ align:start position:0%
+in a year one year payback fabulous H
+not a good idea so it's a uh
+
+ align:start position:0%
+not a good idea so it's a uh
+ 
+
+ align:start position:0%
+not a good idea so it's a uh
+I it's hard to imagine but but you can
+
+ align:start position:0%
+I it's hard to imagine but but you can
+ 
+
+ align:start position:0%
+I it's hard to imagine but but you can
+read texts in the 50s that are debating
+
+ align:start position:0%
+read texts in the 50s that are debating
+ 
+
+ align:start position:0%
+read texts in the 50s that are debating
+the merits of payback versus Net Present
+
+ align:start position:0%
+the merits of payback versus Net Present
+ 
+
+ align:start position:0%
+the merits of payback versus Net Present
+Value and you say wait what how anyway
+
+ align:start position:0%
+Value and you say wait what how anyway
+ 
+
+ align:start position:0%
+Value and you say wait what how anyway
+okay what I want to do unless there are
+
+ align:start position:0%
+okay what I want to do unless there are
+ 
+
+ align:start position:0%
+okay what I want to do unless there are
+questions about any of this or general
+
+ align:start position:0%
+questions about any of this or general
+ 
+
+ align:start position:0%
+questions about any of this or general
+questions about combined heat and power
+
+ align:start position:0%
+questions about combined heat and power
+ 
+
+ align:start position:0%
+questions about combined heat and power
+I want to go to the
+
+ align:start position:0%
+I want to go to the
+ 
+
+ align:start position:0%
+I want to go to the
+spreadsheet um H it I it didn't occur to
+
+ align:start position:0%
+spreadsheet um H it I it didn't occur to
+ 
+
+ align:start position:0%
+spreadsheet um H it I it didn't occur to
+me to ask because of course this is MIT
+
+ align:start position:0%
+me to ask because of course this is MIT
+ 
+
+ align:start position:0%
+me to ask because of course this is MIT
+but how many of you have played with e
+
+ align:start position:0%
+but how many of you have played with e
+ 
+
+ align:start position:0%
+but how many of you have played with e
+Excel
+
+ align:start position:0%
+Excel
+ 
+
+ align:start position:0%
+Excel
+before oh good that's what I thought
+
+ align:start position:0%
+before oh good that's what I thought
+ 
+
+ align:start position:0%
+before oh good that's what I thought
+I feel so much better all right let's go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there that Accords with my priors
+
+ align:start position:0%
+there that Accords with my priors
+ 
+
+ align:start position:0%
+there that Accords with my priors
+but all right so there we have there we
+
+ align:start position:0%
+but all right so there we have there we
+ 
+
+ align:start position:0%
+but all right so there we have there we
+have the spreadsheet is that readable
+
+ align:start position:0%
+have the spreadsheet is that readable
+ 
+
+ align:start position:0%
+have the spreadsheet is that readable
+more or less in the
+
+ align:start position:0%
+more or less in the
+ 
+
+ align:start position:0%
+more or less in the
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+okay and let's let's walk through a set
+
+ align:start position:0%
+okay and let's let's walk through a set
+ 
+
+ align:start position:0%
+okay and let's let's walk through a set
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+questions let's figure out how to walk
+
+ align:start position:0%
+questions let's figure out how to walk
+ 
+
+ align:start position:0%
+questions let's figure out how to walk
+through a set of questions irum What's
+
+ align:start position:0%
+through a set of questions irum What's
+ 
+
+ align:start position:0%
+through a set of questions irum What's
+Happening Here turn the side screen
+
+ align:start position:0%
+Happening Here turn the side screen
+ 
+
+ align:start position:0%
+Happening Here turn the side screen
+on that's what you got to do turn the
+
+ align:start position:0%
+on that's what you got to do turn the
+ 
+
+ align:start position:0%
+on that's what you got to do turn the
+side screen
+
+ align:start position:0%
+side screen
+ 
+
+ align:start position:0%
+side screen
+on all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+Tada all right this works Let Die thank
+
+ align:start position:0%
+Tada all right this works Let Die thank
+ 
+
+ align:start position:0%
+Tada all right this works Let Die thank
+you um if you walk through
+
+ align:start position:0%
+you um if you walk through
+ 
+
+ align:start position:0%
+you um if you walk through
+this this this illustrates my point
+
+ align:start position:0%
+this this this illustrates my point
+ 
+
+ align:start position:0%
+this this this illustrates my point
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depreciation you get total
+
+ align:start position:0%
+depreciation you get total
+ 
+
+ align:start position:0%
+depreciation you get total
+savings total expenses gross margin that
+
+ align:start position:0%
+savings total expenses gross margin that
+ 
+
+ align:start position:0%
+savings total expenses gross margin that
+is to say what does this thing throw off
+
+ align:start position:0%
+is to say what does this thing throw off
+ 
+
+ align:start position:0%
+is to say what does this thing throw off
+in terms of total savings per
+
+ align:start position:0%
+in terms of total savings per
+ 
+
+ align:start position:0%
+in terms of total savings per
+year you can subtract depreciation and
+
+ align:start position:0%
+year you can subtract depreciation and
+ 
+
+ align:start position:0%
+year you can subtract depreciation and
+get earnings before taxes if you want to
+
+ align:start position:0%
+get earnings before taxes if you want to
+ 
+
+ align:start position:0%
+get earnings before taxes if you want to
+but then you'll notice what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens they compute taxes and they add
+
+ align:start position:0%
+happens they compute taxes and they add
+ 
+
+ align:start position:0%
+happens they compute taxes and they add
+back depreciation right it appears here
+
+ align:start position:0%
+back depreciation right it appears here
+ 
+
+ align:start position:0%
+back depreciation right it appears here
+and it appears
+
+ align:start position:0%
+and it appears
+ 
+
+ align:start position:0%
+and it appears
+there depreciation is a game you and
+
+ align:start position:0%
+there depreciation is a game you and
+ 
+
+ align:start position:0%
+there depreciation is a game you and
+your accountant play with the tax
+
+ align:start position:0%
+your accountant play with the tax
+ 
+
+ align:start position:0%
+your accountant play with the tax
+people so when calculating the after tax
+
+ align:start position:0%
+people so when calculating the after tax
+ 
+
+ align:start position:0%
+people so when calculating the after tax
+in your pocket savings you have to say
+
+ align:start position:0%
+in your pocket savings you have to say
+ 
+
+ align:start position:0%
+in your pocket savings you have to say
+what depreciation do I get to take how
+
+ align:start position:0%
+what depreciation do I get to take how
+ 
+
+ align:start position:0%
+what depreciation do I get to take how
+does that affect my
+
+ align:start position:0%
+does that affect my
+ 
+
+ align:start position:0%
+does that affect my
+taxes that's it that's it if you get
+
+ align:start position:0%
+taxes that's it that's it if you get
+ 
+
+ align:start position:0%
+taxes that's it that's it if you get
+faster depreciation your income is lower
+
+ align:start position:0%
+faster depreciation your income is lower
+ 
+
+ align:start position:0%
+faster depreciation your income is lower
+and your taxes are lower your income
+
+ align:start position:0%
+and your taxes are lower your income
+ 
+
+ align:start position:0%
+and your taxes are lower your income
+being lower doesn't matter your taxes
+
+ align:start position:0%
+being lower doesn't matter your taxes
+ 
+
+ align:start position:0%
+being lower doesn't matter your taxes
+being lower
+
+ align:start position:0%
+being lower
+ 
+
+ align:start position:0%
+being lower
+does is that reasonably straightforward
+
+ align:start position:0%
+does is that reasonably straightforward
+ 
+
+ align:start position:0%
+does is that reasonably straightforward
+because you're going to see this in
+
+ align:start position:0%
+because you're going to see this in
+ 
+
+ align:start position:0%
+because you're going to see this in
+later life I'll guarantee you and it
+
+ align:start position:0%
+later life I'll guarantee you and it
+ 
+
+ align:start position:0%
+later life I'll guarantee you and it
+shouldn't be mysterious it really is and
+
+ align:start position:0%
+shouldn't be mysterious it really is and
+ 
+
+ align:start position:0%
+shouldn't be mysterious it really is and
+it's it's an accounting entity you
+
+ align:start position:0%
+it's it's an accounting entity you
+ 
+
+ align:start position:0%
+it's it's an accounting entity you
+report it on taxes some companies use
+
+ align:start position:0%
+report it on taxes some companies use
+ 
+
+ align:start position:0%
+report it on taxes some companies use
+different depreciation schedules for
+
+ align:start position:0%
+different depreciation schedules for
+ 
+
+ align:start position:0%
+different depreciation schedules for
+taxes than for financial
+
+ align:start position:0%
+taxes than for financial
+ 
+
+ align:start position:0%
+taxes than for financial
+reporting which you're allowed to do to
+
+ align:start position:0%
+reporting which you're allowed to do to
+ 
+
+ align:start position:0%
+reporting which you're allowed to do to
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+extent okay
+
+ align:start position:0%
+extent okay
+ 
+
+ align:start position:0%
+extent okay
+question I talked before about the
+
+ align:start position:0%
+question I talked before about the
+ 
+
+ align:start position:0%
+question I talked before about the
+difference between doing things in real
+
+ align:start position:0%
+difference between doing things in real
+ 
+
+ align:start position:0%
+difference between doing things in real
+terms and doing things in nominal
+
+ align:start position:0%
+terms and doing things in nominal
+ 
+
+ align:start position:0%
+terms and doing things in nominal
+terms which is Dar assuming this is
+
+ align:start position:0%
+terms which is Dar assuming this is
+ 
+
+ align:start position:0%
+terms which is Dar assuming this is
+Darren and not not some um Sloan student
+
+ align:start position:0%
+Darren and not not some um Sloan student
+ 
+
+ align:start position:0%
+Darren and not not some um Sloan student
+who wrote up the case um what's Darren
+
+ align:start position:0%
+who wrote up the case um what's Darren
+ 
+
+ align:start position:0%
+who wrote up the case um what's Darren
+doing is this a real analysis a nominal
+
+ align:start position:0%
+doing is this a real analysis a nominal
+ 
+
+ align:start position:0%
+doing is this a real analysis a nominal
+analysis is he
+
+ align:start position:0%
+analysis is he
+ 
+
+ align:start position:0%
+analysis is he
+confused G what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think I'm confused huh I'm confused
+
+ align:start position:0%
+think I'm confused huh I'm confused
+ 
+
+ align:start position:0%
+think I'm confused huh I'm confused
+you're confused okay okay say
+
+ align:start position:0%
+you're confused okay okay say
+ 
+
+ align:start position:0%
+you're confused okay okay say
+why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I don't exactly understand like
+
+ align:start position:0%
+um I don't exactly understand like
+ 
+
+ align:start position:0%
+um I don't exactly understand like
+how like I would characterize
+
+ align:start position:0%
+how like I would characterize
+ 
+
+ align:start position:0%
+how like I would characterize
+depreciation as nomal real oh what I
+
+ align:start position:0%
+depreciation as nomal real oh what I
+ 
+
+ align:start position:0%
+depreciation as nomal real oh what I
+don't understand how I will like
+
+ align:start position:0%
+don't understand how I will like
+ 
+
+ align:start position:0%
+don't understand how I will like
+characterize it as either nominal real
+
+ align:start position:0%
+characterize it as either nominal real
+ 
+
+ align:start position:0%
+characterize it as either nominal real
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+inconsistent like is this the nominal
+
+ align:start position:0%
+inconsistent like is this the nominal
+ 
+
+ align:start position:0%
+inconsistent like is this the nominal
+like what things should be or nominal
+
+ align:start position:0%
+like what things should be or nominal
+ 
+
+ align:start position:0%
+like what things should be or nominal
+like like interest rate well what I said
+
+ align:start position:0%
+like like interest rate well what I said
+ 
+
+ align:start position:0%
+like like interest rate well what I said
+last time was if you want to assume that
+
+ align:start position:0%
+last time was if you want to assume that
+ 
+
+ align:start position:0%
+last time was if you want to assume that
+prices don't change in this
+
+ align:start position:0%
+prices don't change in this
+ 
+
+ align:start position:0%
+prices don't change in this
+world um where prices do change then
+
+ align:start position:0%
+world um where prices do change then
+ 
+
+ align:start position:0%
+world um where prices do change then
+you'd better use a real discount rate
+
+ align:start position:0%
+you'd better use a real discount rate
+ 
+
+ align:start position:0%
+you'd better use a real discount rate
+that measures purchasing power if you
+
+ align:start position:0%
+that measures purchasing power if you
+ 
+
+ align:start position:0%
+that measures purchasing power if you
+want to use the kind of rates you see in
+
+ align:start position:0%
+want to use the kind of rates you see in
+ 
+
+ align:start position:0%
+want to use the kind of rates you see in
+the market those rates are based on
+
+ align:start position:0%
+the market those rates are based on
+ 
+
+ align:start position:0%
+the market those rates are based on
+people's expectations about inflation so
+
+ align:start position:0%
+people's expectations about inflation so
+ 
+
+ align:start position:0%
+people's expectations about inflation so
+you'd better build in expectations about
+
+ align:start position:0%
+you'd better build in expectations about
+ 
+
+ align:start position:0%
+you'd better build in expectations about
+inflation what people often do and it's
+
+ align:start position:0%
+inflation what people often do and it's
+ 
+
+ align:start position:0%
+inflation what people often do and it's
+a mistake is to use discount rates or
+
+ align:start position:0%
+a mistake is to use discount rates or
+ 
+
+ align:start position:0%
+a mistake is to use discount rates or
+interest rates from the market and
+
+ align:start position:0%
+interest rates from the market and
+ 
+
+ align:start position:0%
+interest rates from the market and
+assume prices don't
+
+ align:start position:0%
+assume prices don't
+ 
+
+ align:start position:0%
+assume prices don't
+change so is he inconsistent like that
+
+ align:start position:0%
+change so is he inconsistent like that
+ 
+
+ align:start position:0%
+change so is he inconsistent like that
+or is he
+
+ align:start position:0%
+or is he
+ 
+
+ align:start position:0%
+or is he
+consistent I give you a hint a 10% real
+
+ align:start position:0%
+consistent I give you a hint a 10% real
+ 
+
+ align:start position:0%
+consistent I give you a hint a 10% real
+rate would be
+
+ align:start position:0%
+rate would be
+ 
+
+ align:start position:0%
+rate would be
+amazing that would be very very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+high not amazing it would be
+
+ align:start position:0%
+high not amazing it would be
+ 
+
+ align:start position:0%
+high not amazing it would be
+High
+
+ align:start position:0%
+High
+ 
+
+ align:start position:0%
+High
+maora um I mean from what you just said
+
+ align:start position:0%
+maora um I mean from what you just said
+ 
+
+ align:start position:0%
+maora um I mean from what you just said
+she's doing nominal analysis doing a
+
+ align:start position:0%
+she's doing nominal analysis doing a
+ 
+
+ align:start position:0%
+she's doing nominal analysis doing a
+nominal analysis yeah cuz he he builds
+
+ align:start position:0%
+nominal analysis yeah cuz he he builds
+ 
+
+ align:start position:0%
+nominal analysis yeah cuz he he builds
+in he has
+
+ align:start position:0%
+in he has
+ 
+
+ align:start position:0%
+in he has
+explicit
+
+ align:start position:0%
+explicit
+ 
+
+ align:start position:0%
+explicit
+assumptions about it about
+
+ align:start position:0%
+assumptions about it about
+ 
+
+ align:start position:0%
+assumptions about it about
+inflation and he's got an interest rate
+
+ align:start position:0%
+inflation and he's got an interest rate
+ 
+
+ align:start position:0%
+inflation and he's got an interest rate
+that's 2003 that's a pretty that's a
+
+ align:start position:0%
+that's 2003 that's a pretty that's a
+ 
+
+ align:start position:0%
+that's 2003 that's a pretty that's a
+market rate in 2003 no reason you would
+
+ align:start position:0%
+market rate in 2003 no reason you would
+ 
+
+ align:start position:0%
+market rate in 2003 no reason you would
+know that but you see the you see the
+
+ align:start position:0%
+know that but you see the you see the
+ 
+
+ align:start position:0%
+know that but you see the you see the
+explicit inflation numbers and a fairly
+
+ align:start position:0%
+explicit inflation numbers and a fairly
+ 
+
+ align:start position:0%
+explicit inflation numbers and a fairly
+High interest rate so he's doing a
+
+ align:start position:0%
+High interest rate so he's doing a
+ 
+
+ align:start position:0%
+High interest rate so he's doing a
+nominal analysis it looks consistent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um is there any defense in the
+
+ align:start position:0%
+um is there any defense in the
+ 
+
+ align:start position:0%
+um is there any defense in the
+spreadsheet or in the case as to the
+
+ align:start position:0%
+spreadsheet or in the case as to the
+ 
+
+ align:start position:0%
+spreadsheet or in the case as to the
+choice of discount
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate Sarah I don't remember there being
+
+ align:start position:0%
+rate Sarah I don't remember there being
+ 
+
+ align:start position:0%
+rate Sarah I don't remember there being
+a very specific one but I would assume
+
+ align:start position:0%
+a very specific one but I would assume
+ 
+
+ align:start position:0%
+a very specific one but I would assume
+comparable risky assets on the market
+
+ align:start position:0%
+comparable risky assets on the market
+ 
+
+ align:start position:0%
+comparable risky assets on the market
+yeah he didn't say it though there's no
+
+ align:start position:0%
+yeah he didn't say it though there's no
+ 
+
+ align:start position:0%
+yeah he didn't say it though there's no
+discussion of where that 10% came from
+
+ align:start position:0%
+discussion of where that 10% came from
+ 
+
+ align:start position:0%
+discussion of where that 10% came from
+after all of that in comprehensible
+
+ align:start position:0%
+after all of that in comprehensible
+ 
+
+ align:start position:0%
+after all of that in comprehensible
+nonsense last time about beta uh I was
+
+ align:start position:0%
+nonsense last time about beta uh I was
+ 
+
+ align:start position:0%
+nonsense last time about beta uh I was
+giving you what you ought to do not what
+
+ align:start position:0%
+giving you what you ought to do not what
+ 
+
+ align:start position:0%
+giving you what you ought to do not what
+people often do and clearly what he did
+
+ align:start position:0%
+people often do and clearly what he did
+ 
+
+ align:start position:0%
+people often do and clearly what he did
+here was to take kind of a horseback
+
+ align:start position:0%
+here was to take kind of a horseback
+ 
+
+ align:start position:0%
+here was to take kind of a horseback
+reasonable rate and say at 10% that's
+
+ align:start position:0%
+reasonable rate and say at 10% that's
+ 
+
+ align:start position:0%
+reasonable rate and say at 10% that's
+pretty pretty much in line with cost of
+
+ align:start position:0%
+pretty pretty much in line with cost of
+ 
+
+ align:start position:0%
+pretty pretty much in line with cost of
+capital you see and discount rates you
+
+ align:start position:0%
+capital you see and discount rates you
+ 
+
+ align:start position:0%
+capital you see and discount rates you
+see you would like him to have done more
+
+ align:start position:0%
+see you would like him to have done more
+ 
+
+ align:start position:0%
+see you would like him to have done more
+this is not necessarily an ideal
+
+ align:start position:0%
+this is not necessarily an ideal
+ 
+
+ align:start position:0%
+this is not necessarily an ideal
+are the inflation assumptions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reasonable anybody react to those what
+
+ align:start position:0%
+reasonable anybody react to those what
+ 
+
+ align:start position:0%
+reasonable anybody react to those what
+do you think 2% electricity 2%
+
+ align:start position:0%
+do you think 2% electricity 2%
+ 
+
+ align:start position:0%
+do you think 2% electricity 2%
+maintenance 2% chemicals to be added to
+
+ align:start position:0%
+maintenance 2% chemicals to be added to
+ 
+
+ align:start position:0%
+maintenance 2% chemicals to be added to
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+water I haven't been looking at interest
+
+ align:start position:0%
+water I haven't been looking at interest
+ 
+
+ align:start position:0%
+water I haven't been looking at interest
+rates on a yearly basis so I don't know
+
+ align:start position:0%
+rates on a yearly basis so I don't know
+ 
+
+ align:start position:0%
+rates on a yearly basis so I don't know
+what to compare it to I'm
+
+ align:start position:0%
+what to compare it to I'm
+ 
+
+ align:start position:0%
+what to compare it to I'm
+shocked shocked I that's what people
+
+ align:start position:0%
+shocked shocked I that's what people
+ 
+
+ align:start position:0%
+shocked shocked I that's what people
+around here did I certainly do
+
+ align:start position:0%
+around here did I certainly do
+ 
+
+ align:start position:0%
+around here did I certainly do
+um I
+
+ align:start position:0%
+um I
+ 
+
+ align:start position:0%
+um I
+mean these are not implausible numbers
+
+ align:start position:0%
+mean these are not implausible numbers
+ 
+
+ align:start position:0%
+mean these are not implausible numbers
+right I mean if you look historically at
+
+ align:start position:0%
+right I mean if you look historically at
+ 
+
+ align:start position:0%
+right I mean if you look historically at
+inflation rates they run in this country
+
+ align:start position:0%
+inflation rates they run in this country
+ 
+
+ align:start position:0%
+inflation rates they run in this country
+one one two two and a half percent so 2%
+
+ align:start position:0%
+one one two two and a half percent so 2%
+ 
+
+ align:start position:0%
+one one two two and a half percent so 2%
+is reasonable what you don't see in this
+
+ align:start position:0%
+is reasonable what you don't see in this
+ 
+
+ align:start position:0%
+is reasonable what you don't see in this
+spreadsheet what you might like to see
+
+ align:start position:0%
+spreadsheet what you might like to see
+ 
+
+ align:start position:0%
+spreadsheet what you might like to see
+in life is you might like to see well
+
+ align:start position:0%
+in life is you might like to see well
+ 
+
+ align:start position:0%
+in life is you might like to see well
+does the choice of discount rate matter
+
+ align:start position:0%
+does the choice of discount rate matter
+ 
+
+ align:start position:0%
+does the choice of discount rate matter
+you could check easily enough we could
+
+ align:start position:0%
+you could check easily enough we could
+ 
+
+ align:start position:0%
+you could check easily enough we could
+put another rate in uh do the inflation
+
+ align:start position:0%
+put another rate in uh do the inflation
+ 
+
+ align:start position:0%
+put another rate in uh do the inflation
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+matter uh are these is the outcome
+
+ align:start position:0%
+matter uh are these is the outcome
+ 
+
+ align:start position:0%
+matter uh are these is the outcome
+sensitive to these things that don't get
+
+ align:start position:0%
+sensitive to these things that don't get
+ 
+
+ align:start position:0%
+sensitive to these things that don't get
+defended
+
+ align:start position:0%
+defended
+ 
+
+ align:start position:0%
+defended
+much that would be if you were doing
+
+ align:start position:0%
+much that would be if you were doing
+ 
+
+ align:start position:0%
+much that would be if you were doing
+this for real and it was your money
+
+ align:start position:0%
+this for real and it was your money
+ 
+
+ align:start position:0%
+this for real and it was your money
+you'd want to do that you'd want to say
+
+ align:start position:0%
+you'd want to do that you'd want to say
+ 
+
+ align:start position:0%
+you'd want to do that you'd want to say
+okay I'm not too sure about those
+
+ align:start position:0%
+okay I'm not too sure about those
+ 
+
+ align:start position:0%
+okay I'm not too sure about those
+assumptions are they critical do they
+
+ align:start position:0%
+assumptions are they critical do they
+ 
+
+ align:start position:0%
+assumptions are they critical do they
+drive the answer if they do you'd want
+
+ align:start position:0%
+drive the answer if they do you'd want
+ 
+
+ align:start position:0%
+drive the answer if they do you'd want
+to look harder we don't see any of that
+
+ align:start position:0%
+to look harder we don't see any of that
+ 
+
+ align:start position:0%
+to look harder we don't see any of that
+we may be missing a dozen spreadsheets
+
+ align:start position:0%
+we may be missing a dozen spreadsheets
+ 
+
+ align:start position:0%
+we may be missing a dozen spreadsheets
+in the background but we don't see it
+
+ align:start position:0%
+in the background but we don't see it
+ 
+
+ align:start position:0%
+in the background but we don't see it
+here okay as you read the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case where are there risks on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sheet
+
+ align:start position:0%
+sheet
+ 
+
+ align:start position:0%
+sheet
+Jorge anything here that's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+certain you think it's all pretty Rock
+
+ align:start position:0%
+certain you think it's all pretty Rock
+ 
+
+ align:start position:0%
+certain you think it's all pretty Rock
+solid Matthew I think something that we
+
+ align:start position:0%
+solid Matthew I think something that we
+ 
+
+ align:start position:0%
+solid Matthew I think something that we
+didn't really bring it up he said that
+
+ align:start position:0%
+didn't really bring it up he said that
+ 
+
+ align:start position:0%
+didn't really bring it up he said that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+company that time took much longer or
+
+ align:start position:0%
+company that time took much longer or
+ 
+
+ align:start position:0%
+company that time took much longer or
+even like a day longer production would
+
+ align:start position:0%
+even like a day longer production would
+ 
+
+ align:start position:0%
+even like a day longer production would
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+back offset of the cost year yeah we
+
+ align:start position:0%
+back offset of the cost year yeah we
+ 
+
+ align:start position:0%
+back offset of the cost year yeah we
+don't see the Lost production here uh
+
+ align:start position:0%
+don't see the Lost production here uh
+ 
+
+ align:start position:0%
+don't see the Lost production here uh
+and there is presumably some risk
+
+ align:start position:0%
+and there is presumably some risk
+ 
+
+ align:start position:0%
+and there is presumably some risk
+there what about and that's related to
+
+ align:start position:0%
+there what about and that's related to
+ 
+
+ align:start position:0%
+there what about and that's related to
+the installation
+
+ align:start position:0%
+the installation
+ 
+
+ align:start position:0%
+the installation
+cost for which we have only an estimate
+
+ align:start position:0%
+cost for which we have only an estimate
+ 
+
+ align:start position:0%
+cost for which we have only an estimate
+right we don't have a guarantee
+
+ align:start position:0%
+right we don't have a guarantee
+ 
+
+ align:start position:0%
+right we don't have a guarantee
+Rachel I guess the thing that kind jump
+
+ align:start position:0%
+Rachel I guess the thing that kind jump
+ 
+
+ align:start position:0%
+Rachel I guess the thing that kind jump
+out to me was assuming that they could
+
+ align:start position:0%
+out to me was assuming that they could
+ 
+
+ align:start position:0%
+out to me was assuming that they could
+get that yeah because a lot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of yeah I thought that was that was
+
+ align:start position:0%
+of yeah I thought that was that was
+ 
+
+ align:start position:0%
+of yeah I thought that was that was
+pretty bold to say well I know the the
+
+ align:start position:0%
+pretty bold to say well I know the the
+ 
+
+ align:start position:0%
+pretty bold to say well I know the the
+text says we're pretty sure we can get
+
+ align:start position:0%
+text says we're pretty sure we can get
+ 
+
+ align:start position:0%
+text says we're pretty sure we can get
+this match in Grant for
+
+ align:start position:0%
+this match in Grant for
+ 
+
+ align:start position:0%
+this match in Grant for
+1725 so we'll just assume we get
+
+ align:start position:0%
+1725 so we'll just assume we get
+ 
+
+ align:start position:0%
+1725 so we'll just assume we get
+it and there's no lost production in
+
+ align:start position:0%
+it and there's no lost production in
+ 
+
+ align:start position:0%
+it and there's no lost production in
+here sharing I think during during that
+
+ align:start position:0%
+here sharing I think during during that
+ 
+
+ align:start position:0%
+here sharing I think during during that
+time was much more reasonable inorder to
+
+ align:start position:0%
+time was much more reasonable inorder to
+ 
+
+ align:start position:0%
+time was much more reasonable inorder to
+get the CR I think nowaday might be much
+
+ align:start position:0%
+get the CR I think nowaday might be much
+ 
+
+ align:start position:0%
+get the CR I think nowaday might be much
+more difficult after the financial
+
+ align:start position:0%
+more difficult after the financial
+ 
+
+ align:start position:0%
+more difficult after the financial
+crisis but before then the period kind
+
+ align:start position:0%
+crisis but before then the period kind
+ 
+
+ align:start position:0%
+crisis but before then the period kind
+of leading up to 2007 it wasn't very
+
+ align:start position:0%
+of leading up to 2007 it wasn't very
+ 
+
+ align:start position:0%
+of leading up to 2007 it wasn't very
+difficult for like
+
+ align:start position:0%
+difficult for like
+ 
+
+ align:start position:0%
+difficult for like
+that's I mean comparably if you I think
+
+ align:start position:0%
+that's I mean comparably if you I think
+ 
+
+ align:start position:0%
+that's I mean comparably if you I think
+sure that it's probably fair for
+
+ align:start position:0%
+sure that it's probably fair for
+ 
+
+ align:start position:0%
+sure that it's probably fair for
+nowadays but not necessarily the case
+
+ align:start position:0%
+nowadays but not necessarily the case
+ 
+
+ align:start position:0%
+nowadays but not necessarily the case
+back then if I were a naysayer I'd say
+
+ align:start position:0%
+back then if I were a naysayer I'd say
+ 
+
+ align:start position:0%
+back then if I were a naysayer I'd say
+do you have that in
+
+ align:start position:0%
+do you have that in
+ 
+
+ align:start position:0%
+do you have that in
+writing do you have that Grant that's
+
+ align:start position:0%
+writing do you have that Grant that's
+ 
+
+ align:start position:0%
+writing do you have that Grant that's
+that's that's big relative to the to the
+
+ align:start position:0%
+that's that's big relative to the to the
+ 
+
+ align:start position:0%
+that's that's big relative to the to the
+whole upfront cost and he didn't he
+
+ align:start position:0%
+whole upfront cost and he didn't he
+ 
+
+ align:start position:0%
+whole upfront cost and he didn't he
+didn't quite mention that yeah really I
+
+ align:start position:0%
+didn't quite mention that yeah really I
+ 
+
+ align:start position:0%
+didn't quite mention that yeah really I
+mean companies like Tesla and viscar
+
+ align:start position:0%
+mean companies like Tesla and viscar
+ 
+
+ align:start position:0%
+mean companies like Tesla and viscar
+Karma got like half a billion dollar
+
+ align:start position:0%
+Karma got like half a billion dollar
+ 
+
+ align:start position:0%
+Karma got like half a billion dollar
+loans for their
+
+ align:start position:0%
+loans for their
+ 
+
+ align:start position:0%
+loans for their
+projects yeah but he this is a New York
+
+ align:start position:0%
+projects yeah but he this is a New York
+ 
+
+ align:start position:0%
+projects yeah but he this is a New York
+state I don't know this program or I
+
+ align:start position:0%
+state I don't know this program or I
+ 
+
+ align:start position:0%
+state I don't know this program or I
+certainly don't what this program looked
+
+ align:start position:0%
+certainly don't what this program looked
+ 
+
+ align:start position:0%
+certainly don't what this program looked
+like in 2003 all I know is that the case
+
+ align:start position:0%
+like in 2003 all I know is that the case
+ 
+
+ align:start position:0%
+like in 2003 all I know is that the case
+said can probably get the
+
+ align:start position:0%
+said can probably get the
+ 
+
+ align:start position:0%
+said can probably get the
+Grant I I I would say gee I'd really
+
+ align:start position:0%
+Grant I I I would say gee I'd really
+ 
+
+ align:start position:0%
+Grant I I I would say gee I'd really
+like to know how does this look without
+
+ align:start position:0%
+like to know how does this look without
+ 
+
+ align:start position:0%
+like to know how does this look without
+getting the
+
+ align:start position:0%
+getting the
+ 
+
+ align:start position:0%
+getting the
+grant um I mean do we know we're going
+
+ align:start position:0%
+grant um I mean do we know we're going
+ 
+
+ align:start position:0%
+grant um I mean do we know we're going
+to get it
+
+ align:start position:0%
+to get it
+ 
+
+ align:start position:0%
+to get it
+suppose installation in fact the
+
+ align:start position:0%
+suppose installation in fact the
+ 
+
+ align:start position:0%
+suppose installation in fact the
+installation
+
+ align:start position:0%
+installation
+ 
+
+ align:start position:0%
+installation
+cost didn't they say 120 125 and he said
+
+ align:start position:0%
+cost didn't they say 120 125 and he said
+ 
+
+ align:start position:0%
+cost didn't they say 120 125 and he said
+I think we can get it down to
+
+ align:start position:0%
+I think we can get it down to
+ 
+
+ align:start position:0%
+I think we can get it down to
+100 isn't that right yeah thank you I
+
+ align:start position:0%
+100 isn't that right yeah thank you I
+ 
+
+ align:start position:0%
+100 isn't that right yeah thank you I
+need support
+
+ align:start position:0%
+need support
+ 
+
+ align:start position:0%
+need support
+um so this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is so we I anything else that's
+
+ align:start position:0%
+is so we I anything else that's
+ 
+
+ align:start position:0%
+is so we I anything else that's
+uncertain here that you might want to
+
+ align:start position:0%
+uncertain here that you might want to
+ 
+
+ align:start position:0%
+uncertain here that you might want to
+focus on
+
+ align:start position:0%
+focus on
+ 
+
+ align:start position:0%
+focus on
+Julian I don't see any removal cost on
+
+ align:start position:0%
+Julian I don't see any removal cost on
+ 
+
+ align:start position:0%
+Julian I don't see any removal cost on
+there like removal cost you mean when
+
+ align:start position:0%
+there like removal cost you mean when
+ 
+
+ align:start position:0%
+there like removal cost you mean when
+when you scrap it at the end yeah uh
+
+ align:start position:0%
+when you scrap it at the end yeah uh
+ 
+
+ align:start position:0%
+when you scrap it at the end yeah uh
+that's a good good point that's a good
+
+ align:start position:0%
+that's a good good point that's a good
+ 
+
+ align:start position:0%
+that's a good good point that's a good
+point he doesn't talk about he runs it
+
+ align:start position:0%
+point he doesn't talk about he runs it
+ 
+
+ align:start position:0%
+point he doesn't talk about he runs it
+out for I forget how long this
+
+ align:start position:0%
+out for I forget how long this
+ 
+
+ align:start position:0%
+out for I forget how long this
+spreadsheet runs uh but he
+
+ align:start position:0%
+spreadsheet runs uh but he
+ 
+
+ align:start position:0%
+spreadsheet runs uh but he
+doesn't he didn't talk about what you
+
+ align:start position:0%
+doesn't he didn't talk about what you
+ 
+
+ align:start position:0%
+doesn't he didn't talk about what you
+presumably you
+
+ align:start position:0%
+presumably you
+ 
+
+ align:start position:0%
+presumably you
+wouldn't presumably you wouldn't throw
+
+ align:start position:0%
+wouldn't presumably you wouldn't throw
+ 
+
+ align:start position:0%
+wouldn't presumably you wouldn't throw
+it all away since some of it's pipe well
+
+ align:start position:0%
+it all away since some of it's pipe well
+ 
+
+ align:start position:0%
+it all away since some of it's pipe well
+maybe you would I mean it's pipe with
+
+ align:start position:0%
+maybe you would I mean it's pipe with
+ 
+
+ align:start position:0%
+maybe you would I mean it's pipe with
+water so it shouldn't be it should last
+
+ align:start position:0%
+water so it shouldn't be it should last
+ 
+
+ align:start position:0%
+water so it shouldn't be it should last
+pretty well but you but the generator
+
+ align:start position:0%
+pretty well but you but the generator
+ 
+
+ align:start position:0%
+pretty well but you but the generator
+you'd have to replace and the turbine
+
+ align:start position:0%
+you'd have to replace and the turbine
+ 
+
+ align:start position:0%
+you'd have to replace and the turbine
+you'd have to replace after a while
+
+ align:start position:0%
+you'd have to replace after a while
+ 
+
+ align:start position:0%
+you'd have to replace after a while
+you're right there's none of that but I
+
+ align:start position:0%
+you're right there's none of that but I
+ 
+
+ align:start position:0%
+you're right there's none of that but I
+guess you could think about
+
+ align:start position:0%
+guess you could think about
+ 
+
+ align:start position:0%
+guess you could think about
+well the question is is there a disposal
+
+ align:start position:0%
+well the question is is there a disposal
+ 
+
+ align:start position:0%
+well the question is is there a disposal
+cost yeah the question isn't would you
+
+ align:start position:0%
+cost yeah the question isn't would you
+ 
+
+ align:start position:0%
+cost yeah the question isn't would you
+have to replace it because you probably
+
+ align:start position:0%
+have to replace it because you probably
+ 
+
+ align:start position:0%
+have to replace it because you probably
+would the question is should there be a
+
+ align:start position:0%
+would the question is should there be a
+ 
+
+ align:start position:0%
+would the question is should there be a
+negative number at the end or could you
+
+ align:start position:0%
+negative number at the end or could you
+ 
+
+ align:start position:0%
+negative number at the end or could you
+sell it for
+
+ align:start position:0%
+sell it for
+ 
+
+ align:start position:0%
+sell it for
+scrap and he didn't mention that
+
+ align:start position:0%
+scrap and he didn't mention that
+ 
+
+ align:start position:0%
+scrap and he didn't mention that
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+okay do you like his treatment of these
+
+ align:start position:0%
+okay do you like his treatment of these
+ 
+
+ align:start position:0%
+okay do you like his treatment of these
+risks Darren is not our favorite person
+
+ align:start position:0%
+risks Darren is not our favorite person
+ 
+
+ align:start position:0%
+risks Darren is not our favorite person
+here yes well the the thing is we since
+
+ align:start position:0%
+here yes well the the thing is we since
+ 
+
+ align:start position:0%
+here yes well the the thing is we since
+we don't know exactly how he came up
+
+ align:start position:0%
+we don't know exactly how he came up
+ 
+
+ align:start position:0%
+we don't know exactly how he came up
+with that discount rate uh there's a
+
+ align:start position:0%
+with that discount rate uh there's a
+ 
+
+ align:start position:0%
+with that discount rate uh there's a
+possibility that he's not really
+
+ align:start position:0%
+possibility that he's not really
+ 
+
+ align:start position:0%
+possibility that he's not really
+accounting for the risk and the cash
+
+ align:start position:0%
+accounting for the risk and the cash
+ 
+
+ align:start position:0%
+accounting for the risk and the cash
+flows he might just I mean the discount
+
+ align:start position:0%
+flows he might just I mean the discount
+ 
+
+ align:start position:0%
+flows he might just I mean the discount
+rate is barely it's not it's kind of low
+
+ align:start position:0%
+rate is barely it's not it's kind of low
+ 
+
+ align:start position:0%
+rate is barely it's not it's kind of low
+but maybe he he's he took that into
+
+ align:start position:0%
+but maybe he he's he took that into
+ 
+
+ align:start position:0%
+but maybe he he's he took that into
+account when calculating the the you
+
+ align:start position:0%
+account when calculating the the you
+ 
+
+ align:start position:0%
+account when calculating the the you
+know risk premium uh associated with uh
+
+ align:start position:0%
+know risk premium uh associated with uh
+ 
+
+ align:start position:0%
+know risk premium uh associated with uh
+his discount rate so
+
+ align:start position:0%
+his discount rate so
+ 
+
+ align:start position:0%
+his discount rate so
+maybe but is this my next question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes did he use pessimistic figures
+
+ align:start position:0%
+yes did he use pessimistic figures
+ 
+
+ align:start position:0%
+yes did he use pessimistic figures
+optimistic figures or more or less
+
+ align:start position:0%
+optimistic figures or more or less
+ 
+
+ align:start position:0%
+optimistic figures or more or less
+middle of the road
+
+ align:start position:0%
+middle of the road
+ 
+
+ align:start position:0%
+middle of the road
+figures pretty optimistic huh yeah Chad
+
+ align:start position:0%
+figures pretty optimistic huh yeah Chad
+ 
+
+ align:start position:0%
+figures pretty optimistic huh yeah Chad
+you agree optimistic
+
+ align:start position:0%
+you agree optimistic
+ 
+
+ align:start position:0%
+you agree optimistic
+okay uh that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a it's an
+
+ align:start position:0%
+a it's an
+ 
+
+ align:start position:0%
+a it's an
+interesting it's an interesting
+
+ align:start position:0%
+interesting it's an interesting
+ 
+
+ align:start position:0%
+interesting it's an interesting
+presentational choice right cuz Darren
+
+ align:start position:0%
+presentational choice right cuz Darren
+ 
+
+ align:start position:0%
+presentational choice right cuz Darren
+knows all of
+
+ align:start position:0%
+knows all of
+ 
+
+ align:start position:0%
+knows all of
+this and Darren could just say well yeah
+
+ align:start position:0%
+this and Darren could just say well yeah
+ 
+
+ align:start position:0%
+this and Darren could just say well yeah
+I've been a little optimistic but the
+
+ align:start position:0%
+I've been a little optimistic but the
+ 
+
+ align:start position:0%
+I've been a little optimistic but the
+10% is
+
+ align:start position:0%
+10% is
+ 
+
+ align:start position:0%
+10% is
+High
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this project looks so good on his
+
+ align:start position:0%
+um this project looks so good on his
+ 
+
+ align:start position:0%
+um this project looks so good on his
+numbers that the better strategy would
+
+ align:start position:0%
+numbers that the better strategy would
+ 
+
+ align:start position:0%
+numbers that the better strategy would
+be to be
+
+ align:start position:0%
+be to be
+ 
+
+ align:start position:0%
+be to be
+pessimistic so you can say look I mean I
+
+ align:start position:0%
+pessimistic so you can say look I mean I
+ 
+
+ align:start position:0%
+pessimistic so you can say look I mean I
+was very pessimistic and it still looked
+
+ align:start position:0%
+was very pessimistic and it still looked
+ 
+
+ align:start position:0%
+was very pessimistic and it still looked
+good he didn't do that uh or he didn't
+
+ align:start position:0%
+good he didn't do that uh or he didn't
+ 
+
+ align:start position:0%
+good he didn't do that uh or he didn't
+explore again if somebody shows you one
+
+ align:start position:0%
+explore again if somebody shows you one
+ 
+
+ align:start position:0%
+explore again if somebody shows you one
+of these spreadsheets in later life uh
+
+ align:start position:0%
+of these spreadsheets in later life uh
+ 
+
+ align:start position:0%
+of these spreadsheets in later life uh
+or if when you're working for McKenzie
+
+ align:start position:0%
+or if when you're working for McKenzie
+ 
+
+ align:start position:0%
+or if when you're working for McKenzie
+they ask you to make one for heaven's
+
+ align:start position:0%
+they ask you to make one for heaven's
+ 
+
+ align:start position:0%
+they ask you to make one for heaven's
+sakes think about the central case think
+
+ align:start position:0%
+sakes think about the central case think
+ 
+
+ align:start position:0%
+sakes think about the central case think
+about variations around it he didn't do
+
+ align:start position:0%
+about variations around it he didn't do
+ 
+
+ align:start position:0%
+about variations around it he didn't do
+that he took the optimistic
+
+ align:start position:0%
+that he took the optimistic
+ 
+
+ align:start position:0%
+that he took the optimistic
+case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um kind of a surprise I think what he
+
+ align:start position:0%
+um kind of a surprise I think what he
+ 
+
+ align:start position:0%
+um kind of a surprise I think what he
+should have done is um oops let's get it
+
+ align:start position:0%
+should have done is um oops let's get it
+ 
+
+ align:start position:0%
+should have done is um oops let's get it
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+there yep he should have been a kind of
+
+ align:start position:0%
+there yep he should have been a kind of
+ 
+
+ align:start position:0%
+there yep he should have been a kind of
+central of the road
+
+ align:start position:0%
+central of the road
+ 
+
+ align:start position:0%
+central of the road
+uh here's a beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question so the discounting applies to
+
+ align:start position:0%
+question so the discounting applies to
+ 
+
+ align:start position:0%
+question so the discounting applies to
+how do we value Energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+savings those Energy savings going to
+
+ align:start position:0%
+savings those Energy savings going to
+ 
+
+ align:start position:0%
+savings those Energy savings going to
+tend to be correlated with the
+
+ align:start position:0%
+tend to be correlated with the
+ 
+
+ align:start position:0%
+tend to be correlated with the
+economy against the economy not at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all the energy
+
+ align:start position:0%
+all the energy
+ 
+
+ align:start position:0%
+all the energy
+savings probably two components one
+
+ align:start position:0%
+savings probably two components one
+ 
+
+ align:start position:0%
+savings probably two components one
+what's the production volume
+
+ align:start position:0%
+what's the production volume
+ 
+
+ align:start position:0%
+what's the production volume
+and let's take that as fixed for the
+
+ align:start position:0%
+and let's take that as fixed for the
+ 
+
+ align:start position:0%
+and let's take that as fixed for the
+moment because they sort of do you tend
+
+ align:start position:0%
+moment because they sort of do you tend
+ 
+
+ align:start position:0%
+moment because they sort of do you tend
+to run the thing flat out unless things
+
+ align:start position:0%
+to run the thing flat out unless things
+ 
+
+ align:start position:0%
+to run the thing flat out unless things
+are terrible and the electricity
+
+ align:start position:0%
+are terrible and the electricity
+ 
+
+ align:start position:0%
+are terrible and the electricity
+price which way does the electricity
+
+ align:start position:0%
+price which way does the electricity
+ 
+
+ align:start position:0%
+price which way does the electricity
+price go with the economy Brendan it
+
+ align:start position:0%
+price go with the economy Brendan it
+ 
+
+ align:start position:0%
+price go with the economy Brendan it
+doesn't vary too much with the economy
+
+ align:start position:0%
+doesn't vary too much with the economy
+ 
+
+ align:start position:0%
+doesn't vary too much with the economy
+I'd say that's more you know energy in
+
+ align:start position:0%
+I'd say that's more you know energy in
+ 
+
+ align:start position:0%
+I'd say that's more you know energy in
+terms of gasoline and stuff that's more
+
+ align:start position:0%
+terms of gasoline and stuff that's more
+ 
+
+ align:start position:0%
+terms of gasoline and stuff that's more
+of that varies a lot more with the eony
+
+ align:start position:0%
+of that varies a lot more with the eony
+ 
+
+ align:start position:0%
+of that varies a lot more with the eony
+but vares a lot more but if you have
+
+ align:start position:0%
+but vares a lot more but if you have
+ 
+
+ align:start position:0%
+but vares a lot more but if you have
+high demand there's going to be a supply
+
+ align:start position:0%
+high demand there's going to be a supply
+ 
+
+ align:start position:0%
+high demand there's going to be a supply
+curve particularly in New York which is
+
+ align:start position:0%
+curve particularly in New York which is
+ 
+
+ align:start position:0%
+curve particularly in New York which is
+a market driven electricity system
+
+ align:start position:0%
+a market driven electricity system
+ 
+
+ align:start position:0%
+a market driven electricity system
+you'll be running up a supply curve so a
+
+ align:start position:0%
+you'll be running up a supply curve so a
+ 
+
+ align:start position:0%
+you'll be running up a supply curve so a
+little bit with the economy I wouldn't
+
+ align:start position:0%
+little bit with the economy I wouldn't
+ 
+
+ align:start position:0%
+little bit with the economy I wouldn't
+say like a very high beta no no no not a
+
+ align:start position:0%
+say like a very high beta no no no not a
+ 
+
+ align:start position:0%
+say like a very high beta no no no not a
+very high beta but a positive beta yeah
+
+ align:start position:0%
+very high beta but a positive beta yeah
+ 
+
+ align:start position:0%
+very high beta but a positive beta yeah
+so maybe yeah the thing is if he was
+
+ align:start position:0%
+so maybe yeah the thing is if he was
+ 
+
+ align:start position:0%
+so maybe yeah the thing is if he was
+using the the whatever the heat that he
+
+ align:start position:0%
+using the the whatever the heat that he
+ 
+
+ align:start position:0%
+using the the whatever the heat that he
+recovers for uh generating more
+
+ align:start position:0%
+recovers for uh generating more
+ 
+
+ align:start position:0%
+recovers for uh generating more
+electricity then maybe that's the case
+
+ align:start position:0%
+electricity then maybe that's the case
+ 
+
+ align:start position:0%
+electricity then maybe that's the case
+but he if he's using heat uh to sell to
+
+ align:start position:0%
+but he if he's using heat uh to sell to
+ 
+
+ align:start position:0%
+but he if he's using heat uh to sell to
+people then you can say that that's
+
+ align:start position:0%
+people then you can say that that's
+ 
+
+ align:start position:0%
+people then you can say that that's
+something that's fairly you know that
+
+ align:start position:0%
+something that's fairly you know that
+ 
+
+ align:start position:0%
+something that's fairly you know that
+people wouldn't be very like Priceless
+
+ align:start position:0%
+people wouldn't be very like Priceless
+ 
+
+ align:start position:0%
+people wouldn't be very like Priceless
+that maybe the E like people will need
+
+ align:start position:0%
+that maybe the E like people will need
+ 
+
+ align:start position:0%
+that maybe the E like people will need
+the heat regardless but what's on the
+
+ align:start position:0%
+the heat regardless but what's on the
+ 
+
+ align:start position:0%
+the heat regardless but what's on the
+what's on the table here is
+
+ align:start position:0%
+what's on the table here is
+ 
+
+ align:start position:0%
+what's on the table here is
+Generation what's on the table is
+
+ align:start position:0%
+Generation what's on the table is
+ 
+
+ align:start position:0%
+Generation what's on the table is
+Generation not heat he doesn't have a he
+
+ align:start position:0%
+Generation not heat he doesn't have a he
+ 
+
+ align:start position:0%
+Generation not heat he doesn't have a he
+doesn't have a scheme to pipe the heat
+
+ align:start position:0%
+doesn't have a scheme to pipe the heat
+ 
+
+ align:start position:0%
+doesn't have a scheme to pipe the heat
+away he has a scheme to use the heat to
+
+ align:start position:0%
+away he has a scheme to use the heat to
+ 
+
+ align:start position:0%
+away he has a scheme to use the heat to
+R use the steam to run a
+
+ align:start position:0%
+R use the steam to run a
+ 
+
+ align:start position:0%
+R use the steam to run a
+turbine so Point good point it's it's
+
+ align:start position:0%
+turbine so Point good point it's it's
+ 
+
+ align:start position:0%
+turbine so Point good point it's it's
+cold in New York even in in good years
+
+ align:start position:0%
+cold in New York even in in good years
+ 
+
+ align:start position:0%
+cold in New York even in in good years
+and bad but but the electricity price is
+
+ align:start position:0%
+and bad but but the electricity price is
+ 
+
+ align:start position:0%
+and bad but but the electricity price is
+what's an issue here you'd value the
+
+ align:start position:0%
+what's an issue here you'd value the
+ 
+
+ align:start position:0%
+what's an issue here you'd value the
+savings so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he you you could
+
+ align:start position:0%
+he you you could
+ 
+
+ align:start position:0%
+he you you could
+argue well you could make it you could
+
+ align:start position:0%
+argue well you could make it you could
+ 
+
+ align:start position:0%
+argue well you could make it you could
+argue you should use a somewhat higher
+
+ align:start position:0%
+argue you should use a somewhat higher
+ 
+
+ align:start position:0%
+argue you should use a somewhat higher
+discount rate uh than the firms over
+
+ align:start position:0%
+discount rate uh than the firms over
+ 
+
+ align:start position:0%
+discount rate uh than the firms over
+than the C cost of capital to the firm
+
+ align:start position:0%
+than the C cost of capital to the firm
+ 
+
+ align:start position:0%
+than the C cost of capital to the firm
+as a whole just because there's a a
+
+ align:start position:0%
+as a whole just because there's a a
+ 
+
+ align:start position:0%
+as a whole just because there's a a
+positive beta we'd have to look at the
+
+ align:start position:0%
+positive beta we'd have to look at the
+ 
+
+ align:start position:0%
+positive beta we'd have to look at the
+firm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I have no idea yeah does anybody
+
+ align:start position:0%
+now I have no idea yeah does anybody
+ 
+
+ align:start position:0%
+now I have no idea yeah does anybody
+know anything about F the felhide
+
+ align:start position:0%
+know anything about F the felhide
+ 
+
+ align:start position:0%
+know anything about F the felhide
+business it's a very diverse group no
+
+ align:start position:0%
+business it's a very diverse group no
+ 
+
+ align:start position:0%
+business it's a very diverse group no
+one does fahid at
+
+ align:start position:0%
+one does fahid at
+ 
+
+ align:start position:0%
+one does fahid at
+Okay Okay I uh I I don't have a clue
+
+ align:start position:0%
+Okay Okay I uh I I don't have a clue
+ 
+
+ align:start position:0%
+Okay Okay I uh I I don't have a clue
+they wrote the case as if you just ran
+
+ align:start position:0%
+they wrote the case as if you just ran
+ 
+
+ align:start position:0%
+they wrote the case as if you just ran
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+factory uh they didn't talk about it
+
+ align:start position:0%
+factory uh they didn't talk about it
+ 
+
+ align:start position:0%
+factory uh they didn't talk about it
+being cyclical uh and nobody talked
+
+ align:start position:0%
+being cyclical uh and nobody talked
+ 
+
+ align:start position:0%
+being cyclical uh and nobody talked
+about none of none of the naysayers
+
+ align:start position:0%
+about none of none of the naysayers
+ 
+
+ align:start position:0%
+about none of none of the naysayers
+talked about much cyclicality but I
+
+ align:start position:0%
+talked about much cyclicality but I
+ 
+
+ align:start position:0%
+talked about much cyclicality but I
+don't know Brandon yeah I mean I think
+
+ align:start position:0%
+don't know Brandon yeah I mean I think
+ 
+
+ align:start position:0%
+don't know Brandon yeah I mean I think
+people are still going to die
+
+ align:start position:0%
+people are still going to die
+ 
+
+ align:start position:0%
+people are still going to die
+so it has other uses but it does have
+
+ align:start position:0%
+so it has other uses but it does have
+ 
+
+ align:start position:0%
+so it has other uses but it does have
+other uses which the case discussed and
+
+ align:start position:0%
+other uses which the case discussed and
+ 
+
+ align:start position:0%
+other uses which the case discussed and
+I don't remember but uh okay what are
+
+ align:start position:0%
+I don't remember but uh okay what are
+ 
+
+ align:start position:0%
+I don't remember but uh okay what are
+the most what do you think are the most
+
+ align:start position:0%
+the most what do you think are the most
+ 
+
+ align:start position:0%
+the most what do you think are the most
+important assumptions in this in this uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spreadsheet Rachel what do you think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tough call just staring at it yes you'd
+
+ align:start position:0%
+tough call just staring at it yes you'd
+ 
+
+ align:start position:0%
+tough call just staring at it yes you'd
+have to go and and look at you'd have to
+
+ align:start position:0%
+have to go and and look at you'd have to
+ 
+
+ align:start position:0%
+have to go and and look at you'd have to
+do to answer that question and I raise
+
+ align:start position:0%
+do to answer that question and I raise
+ 
+
+ align:start position:0%
+do to answer that question and I raise
+it because that is really the key
+
+ align:start position:0%
+it because that is really the key
+ 
+
+ align:start position:0%
+it because that is really the key
+question if I'm a naysayer and he gives
+
+ align:start position:0%
+question if I'm a naysayer and he gives
+ 
+
+ align:start position:0%
+question if I'm a naysayer and he gives
+me this
+
+ align:start position:0%
+me this
+ 
+
+ align:start position:0%
+me this
+spreadsheet um I say well what did you
+
+ align:start position:0%
+spreadsheet um I say well what did you
+ 
+
+ align:start position:0%
+spreadsheet um I say well what did you
+check how sensitive is this to the
+
+ align:start position:0%
+check how sensitive is this to the
+ 
+
+ align:start position:0%
+check how sensitive is this to the
+discount rate to the electricity price
+
+ align:start position:0%
+discount rate to the electricity price
+ 
+
+ align:start position:0%
+discount rate to the electricity price
+to the electricity inflation how
+
+ align:start position:0%
+to the electricity inflation how
+ 
+
+ align:start position:0%
+to the electricity inflation how
+sensitive is it to variations in the
+
+ align:start position:0%
+sensitive is it to variations in the
+ 
+
+ align:start position:0%
+sensitive is it to variations in the
+installation cost does it matter whether
+
+ align:start position:0%
+installation cost does it matter whether
+ 
+
+ align:start position:0%
+installation cost does it matter whether
+you not whether or not you get the grant
+
+ align:start position:0%
+you not whether or not you get the grant
+ 
+
+ align:start position:0%
+you not whether or not you get the grant
+I can't tell here which are the key
+
+ align:start position:0%
+I can't tell here which are the key
+ 
+
+ align:start position:0%
+I can't tell here which are the key
+assumptions uh but a little fiddling
+
+ align:start position:0%
+assumptions uh but a little fiddling
+ 
+
+ align:start position:0%
+assumptions uh but a little fiddling
+with this can Alex wouldn't the grant be
+
+ align:start position:0%
+with this can Alex wouldn't the grant be
+ 
+
+ align:start position:0%
+with this can Alex wouldn't the grant be
+like the most important assumtion
+
+ align:start position:0%
+like the most important assumtion
+ 
+
+ align:start position:0%
+like the most important assumtion
+because it's like half of your it's half
+
+ align:start position:0%
+because it's like half of your it's half
+ 
+
+ align:start position:0%
+because it's like half of your it's half
+the capital cost if you go down though
+
+ align:start position:0%
+the capital cost if you go down though
+ 
+
+ align:start position:0%
+the capital cost if you go down though
+to his net present value you say well
+
+ align:start position:0%
+to his net present value you say well
+ 
+
+ align:start position:0%
+to his net present value you say well
+that doesn't matter because it's 1725
+
+ align:start position:0%
+that doesn't matter because it's 1725
+ 
+
+ align:start position:0%
+that doesn't matter because it's 1725
+and the net present value is ginormous
+
+ align:start position:0%
+and the net present value is ginormous
+ 
+
+ align:start position:0%
+and the net present value is ginormous
+so lose the grant the qu the the the
+
+ align:start position:0%
+so lose the grant the qu the the the
+ 
+
+ align:start position:0%
+so lose the grant the qu the the the
+question is what is
+
+ align:start position:0%
+question is what is
+ 
+
+ align:start position:0%
+question is what is
+assumptions would turn it
+
+ align:start position:0%
+assumptions would turn it
+ 
+
+ align:start position:0%
+assumptions would turn it
+negative and he didn't answer that I uh
+
+ align:start position:0%
+negative and he didn't answer that I uh
+ 
+
+ align:start position:0%
+negative and he didn't answer that I uh
+if if it saved less than you assumed it
+
+ align:start position:0%
+if if it saved less than you assumed it
+ 
+
+ align:start position:0%
+if if it saved less than you assumed it
+would save well there are a lot of
+
+ align:start position:0%
+would save well there are a lot of
+ 
+
+ align:start position:0%
+would save well there are a lot of
+things that'll do it the question is
+
+ align:start position:0%
+things that'll do it the question is
+ 
+
+ align:start position:0%
+things that'll do it the question is
+which are uncertain that s the technical
+
+ align:start position:0%
+which are uncertain that s the technical
+ 
+
+ align:start position:0%
+which are uncertain that s the technical
+they they describ the technology as
+
+ align:start position:0%
+they they describ the technology as
+ 
+
+ align:start position:0%
+they they describ the technology as
+pretty vanilla so I assume that was
+
+ align:start position:0%
+pretty vanilla so I assume that was
+ 
+
+ align:start position:0%
+pretty vanilla so I assume that was
+you're right that would do it um if you
+
+ align:start position:0%
+you're right that would do it um if you
+ 
+
+ align:start position:0%
+you're right that would do it um if you
+saved less
+
+ align:start position:0%
+saved less
+ 
+
+ align:start position:0%
+saved less
+if if the electricity price collapsed
+
+ align:start position:0%
+if if the electricity price collapsed
+ 
+
+ align:start position:0%
+if if the electricity price collapsed
+if the discount rate were much higher in
+
+ align:start position:0%
+if the discount rate were much higher in
+ 
+
+ align:start position:0%
+if the discount rate were much higher in
+fact for one reason or another if it
+
+ align:start position:0%
+fact for one reason or another if it
+ 
+
+ align:start position:0%
+fact for one reason or another if it
+couldn't do the I mean you could you
+
+ align:start position:0%
+couldn't do the I mean you could you
+ 
+
+ align:start position:0%
+couldn't do the I mean you could you
+could add them
+
+ align:start position:0%
+could add them
+ 
+
+ align:start position:0%
+could add them
+up what you I asked this questions not
+
+ align:start position:0%
+up what you I asked this questions not
+ 
+
+ align:start position:0%
+up what you I asked this questions not
+because I expect you to be able to
+
+ align:start position:0%
+because I expect you to be able to
+ 
+
+ align:start position:0%
+because I expect you to be able to
+answer it but because you always have to
+
+ align:start position:0%
+answer it but because you always have to
+ 
+
+ align:start position:0%
+answer it but because you always have to
+ask that
+
+ align:start position:0%
+ask that
+ 
+
+ align:start position:0%
+ask that
+question uh what's what what's driving
+
+ align:start position:0%
+question uh what's what what's driving
+ 
+
+ align:start position:0%
+question uh what's what what's driving
+this answer what's driving this answer
+
+ align:start position:0%
+this answer what's driving this answer
+ 
+
+ align:start position:0%
+this answer what's driving this answer
+finally did anybody see the mistake in
+
+ align:start position:0%
+finally did anybody see the mistake in
+ 
+
+ align:start position:0%
+finally did anybody see the mistake in
+Computing that present
+
+ align:start position:0%
+Computing that present
+ 
+
+ align:start position:0%
+Computing that present
+value Sarah he started in colum C
+
+ align:start position:0%
+value Sarah he started in colum C
+ 
+
+ align:start position:0%
+value Sarah he started in colum C
+instead ofum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bingoing to if you go here he takes the
+
+ align:start position:0%
+bingoing to if you go here he takes the
+ 
+
+ align:start position:0%
+bingoing to if you go here he takes the
+net present value of it's
+
+ align:start position:0%
+net present value of it's
+ 
+
+ align:start position:0%
+net present value of it's
+c45 uh no the net yeah c45 which is here
+
+ align:start position:0%
+c45 uh no the net yeah c45 which is here
+ 
+
+ align:start position:0%
+c45 uh no the net yeah c45 which is here
+D dot do dot dot c45 which is the after
+
+ align:start position:0%
+D dot do dot dot c45 which is the after
+ 
+
+ align:start position:0%
+D dot do dot dot c45 which is the after
+tax net cash flow that's the right thing
+
+ align:start position:0%
+tax net cash flow that's the right thing
+ 
+
+ align:start position:0%
+tax net cash flow that's the right thing
+all the way
+
+ align:start position:0%
+all the way
+ 
+
+ align:start position:0%
+all the way
+out but he forgot the initial cost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's one of the most bizarre mistakes
+
+ align:start position:0%
+that's one of the most bizarre mistakes
+ 
+
+ align:start position:0%
+that's one of the most bizarre mistakes
+I've ever
+
+ align:start position:0%
+I've ever
+ 
+
+ align:start position:0%
+I've ever
+seen if you look at there's the formula
+
+ align:start position:0%
+seen if you look at there's the formula
+ 
+
+ align:start position:0%
+seen if you look at there's the formula
+that present value of all the
+
+ align:start position:0%
+that present value of all the
+ 
+
+ align:start position:0%
+that present value of all the
+savings well what what needs to happen
+
+ align:start position:0%
+savings well what what needs to happen
+ 
+
+ align:start position:0%
+savings well what what needs to happen
+here it's got a not available in
+
+ align:start position:0%
+here it's got a not available in
+ 
+
+ align:start position:0%
+here it's got a not available in
+protected
+
+ align:start position:0%
+protected
+ 
+
+ align:start position:0%
+protected
+view do I trust the contents of the file
+
+ align:start position:0%
+view do I trust the contents of the file
+ 
+
+ align:start position:0%
+view do I trust the contents of the file
+of course I trust the contents of the
+
+ align:start position:0%
+of course I trust the contents of the
+ 
+
+ align:start position:0%
+of course I trust the contents of the
+file we're all friends here uh what he
+
+ align:start position:0%
+file we're all friends here uh what he
+ 
+
+ align:start position:0%
+file we're all friends here uh what he
+needs to oh I see cuz I I erased uh what
+
+ align:start position:0%
+needs to oh I see cuz I I erased uh what
+ 
+
+ align:start position:0%
+needs to oh I see cuz I I erased uh what
+I need to do
+
+ align:start position:0%
+I need to do
+ 
+
+ align:start position:0%
+I need to do
+here is I need to
+
+ align:start position:0%
+here is I need to
+ 
+
+ align:start position:0%
+here is I need to
+subtract the initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cost that doesn't turn it negative but
+
+ align:start position:0%
+cost that doesn't turn it negative but
+ 
+
+ align:start position:0%
+cost that doesn't turn it negative but
+it did make a significant
+
+ align:start position:0%
+it did make a significant
+ 
+
+ align:start position:0%
+it did make a significant
+difference right you see what he did I
+
+ align:start position:0%
+difference right you see what he did I
+ 
+
+ align:start position:0%
+difference right you see what he did I
+just it's one of these you say
+
+ align:start position:0%
+just it's one of these you say
+ 
+
+ align:start position:0%
+just it's one of these you say
+Okay um he took the after tax net cash
+
+ align:start position:0%
+Okay um he took the after tax net cash
+ 
+
+ align:start position:0%
+Okay um he took the after tax net cash
+flow so he went down added the saving
+
+ align:start position:0%
+flow so he went down added the saving
+ 
+
+ align:start position:0%
+flow so he went down added the saving
+added uh that that that's maintenance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+savings you got savings on electricity
+
+ align:start position:0%
+savings you got savings on electricity
+ 
+
+ align:start position:0%
+savings you got savings on electricity
+maintenance and chemicals which gets
+
+ align:start position:0%
+maintenance and chemicals which gets
+ 
+
+ align:start position:0%
+maintenance and chemicals which gets
+inflated
+
+ align:start position:0%
+inflated
+ 
+
+ align:start position:0%
+inflated
+um all these get inflated you'll see the
+
+ align:start position:0%
+um all these get inflated you'll see the
+ 
+
+ align:start position:0%
+um all these get inflated you'll see the
+inflation rate coming in
+
+ align:start position:0%
+inflation rate coming in
+ 
+
+ align:start position:0%
+inflation rate coming in
+here coming in coming in adds them up
+
+ align:start position:0%
+here coming in coming in adds them up
+ 
+
+ align:start position:0%
+here coming in coming in adds them up
+subtracts the required maintenance gets
+
+ align:start position:0%
+subtracts the required maintenance gets
+ 
+
+ align:start position:0%
+subtracts the required maintenance gets
+the net gets the gross margin so to
+
+ align:start position:0%
+the net gets the gross margin so to
+ 
+
+ align:start position:0%
+the net gets the gross margin so to
+speak subtracts depreciation to get the
+
+ align:start position:0%
+speak subtracts depreciation to get the
+ 
+
+ align:start position:0%
+speak subtracts depreciation to get the
+impact on earnings that'd be the
+
+ align:start position:0%
+impact on earnings that'd be the
+ 
+
+ align:start position:0%
+impact on earnings that'd be the
+increase in
+
+ align:start position:0%
+increase in
+ 
+
+ align:start position:0%
+increase in
+earnings gets the taxes adds back
+
+ align:start position:0%
+earnings gets the taxes adds back
+ 
+
+ align:start position:0%
+earnings gets the taxes adds back
+depreciation uh does all
+
+ align:start position:0%
+depreciation uh does all
+ 
+
+ align:start position:0%
+depreciation uh does all
+that row 45 is the right row Net Present
+
+ align:start position:0%
+that row 45 is the right row Net Present
+ 
+
+ align:start position:0%
+that row 45 is the right row Net Present
+Value forgot the initial investment
+
+ align:start position:0%
+Value forgot the initial investment
+ 
+
+ align:start position:0%
+Value forgot the initial investment
+cost that's a bad move that's a bad move
+
+ align:start position:0%
+cost that's a bad move that's a bad move
+ 
+
+ align:start position:0%
+cost that's a bad move that's a bad move
+okay Darren is not doing real well here
+
+ align:start position:0%
+okay Darren is not doing real well here
+ 
+
+ align:start position:0%
+okay Darren is not doing real well here
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+did anybody see anybody look at the
+
+ align:start position:0%
+did anybody see anybody look at the
+ 
+
+ align:start position:0%
+did anybody see anybody look at the
+payback or the internal rate of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return I just want to go back to the
+
+ align:start position:0%
+return I just want to go back to the
+ 
+
+ align:start position:0%
+return I just want to go back to the
+Assumption you're also assuming that for
+
+ align:start position:0%
+Assumption you're also assuming that for
+ 
+
+ align:start position:0%
+Assumption you're also assuming that for
+10 years your production of form Al do
+
+ align:start position:0%
+10 years your production of form Al do
+ 
+
+ align:start position:0%
+10 years your production of form Al do
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+same he's making that assumption
+
+ align:start position:0%
+same he's making that assumption
+ 
+
+ align:start position:0%
+same he's making that assumption
+um and we don't know how sensible it is
+
+ align:start position:0%
+um and we don't know how sensible it is
+ 
+
+ align:start position:0%
+um and we don't know how sensible it is
+because we don't know much about the
+
+ align:start position:0%
+because we don't know much about the
+ 
+
+ align:start position:0%
+because we don't know much about the
+faldy market
+
+ align:start position:0%
+faldy market
+ 
+
+ align:start position:0%
+faldy market
+um they say that they run the plant 24
+
+ align:start position:0%
+um they say that they run the plant 24
+ 
+
+ align:start position:0%
+um they say that they run the plant 24
+hours a day 365 days a year and it's a
+
+ align:start position:0%
+hours a day 365 days a year and it's a
+ 
+
+ align:start position:0%
+hours a day 365 days a year and it's a
+highly automated
+
+ align:start position:0%
+highly automated
+ 
+
+ align:start position:0%
+highly automated
+facility and he's assuming that'll
+
+ align:start position:0%
+facility and he's assuming that'll
+ 
+
+ align:start position:0%
+facility and he's assuming that'll
+continue um it's not clear what other
+
+ align:start position:0%
+continue um it's not clear what other
+ 
+
+ align:start position:0%
+continue um it's not clear what other
+assumption you ought to make but you're
+
+ align:start position:0%
+assumption you ought to make but you're
+ 
+
+ align:start position:0%
+assumption you ought to make but you're
+right that's a key
+
+ align:start position:0%
+right that's a key
+ 
+
+ align:start position:0%
+right that's a key
+assumption if the plant shuts down or
+
+ align:start position:0%
+assumption if the plant shuts down or
+ 
+
+ align:start position:0%
+assumption if the plant shuts down or
+goes to one shift those savings figures
+
+ align:start position:0%
+goes to one shift those savings figures
+ 
+
+ align:start position:0%
+goes to one shift those savings figures
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+cut uh actual sign I mean the science
+
+ align:start position:0%
+cut uh actual sign I mean the science
+ 
+
+ align:start position:0%
+cut uh actual sign I mean the science
+like if if your Delta e is less and
+
+ align:start position:0%
+like if if your Delta e is less and
+ 
+
+ align:start position:0%
+like if if your Delta e is less and
+stuff like that like if you is less
+
+ align:start position:0%
+stuff like that like if you is less
+ 
+
+ align:start position:0%
+stuff like that like if you is less
+make develop Catalyst well you could you
+
+ align:start position:0%
+make develop Catalyst well you could you
+ 
+
+ align:start position:0%
+make develop Catalyst well you could you
+could do it right I mean if it's
+
+ align:start position:0%
+could do it right I mean if it's
+ 
+
+ align:start position:0%
+could do it right I mean if it's
+proportional to
+
+ align:start position:0%
+proportional to
+ 
+
+ align:start position:0%
+proportional to
+throughput the case explicitly states
+
+ align:start position:0%
+throughput the case explicitly states
+ 
+
+ align:start position:0%
+throughput the case explicitly states
+that the board mainly cares about
+
+ align:start position:0%
+that the board mainly cares about
+ 
+
+ align:start position:0%
+that the board mainly cares about
+production of form alide is y use of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electricity uh I'm not sure I get it
+
+ align:start position:0%
+electricity uh I'm not sure I get it
+ 
+
+ align:start position:0%
+electricity uh I'm not sure I get it
+what you're they mainly care about form
+
+ align:start position:0%
+what you're they mainly care about form
+ 
+
+ align:start position:0%
+what you're they mainly care about form
+aldhy and he's
+
+ align:start position:0%
+aldhy and he's
+ 
+
+ align:start position:0%
+aldhy and he's
+assuming that we're just going to keep
+
+ align:start position:0%
+assuming that we're just going to keep
+ 
+
+ align:start position:0%
+assuming that we're just going to keep
+running it flat out because the board
+
+ align:start position:0%
+running it flat out because the board
+ 
+
+ align:start position:0%
+running it flat out because the board
+cares about production I mean if the
+
+ align:start position:0%
+cares about production I mean if the
+ 
+
+ align:start position:0%
+cares about production I mean if the
+market dies or if there's a plant
+
+ align:start position:0%
+market dies or if there's a plant
+ 
+
+ align:start position:0%
+market dies or if there's a plant
+problem that won't happen and you just
+
+ align:start position:0%
+problem that won't happen and you just
+ 
+
+ align:start position:0%
+problem that won't happen and you just
+cut the savings proportionately well
+
+ align:start position:0%
+cut the savings proportionately well
+ 
+
+ align:start position:0%
+cut the savings proportionately well
+you'd cut the savings on electricity and
+
+ align:start position:0%
+you'd cut the savings on electricity and
+ 
+
+ align:start position:0%
+you'd cut the savings on electricity and
+chemicals proportionately I'd have to
+
+ align:start position:0%
+chemicals proportionately I'd have to
+ 
+
+ align:start position:0%
+chemicals proportionately I'd have to
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+maintenance yeah okay
+
+ align:start position:0%
+maintenance yeah okay
+ 
+
+ align:start position:0%
+maintenance yeah okay
+um internal rate of return how did he do
+
+ align:start position:0%
+um internal rate of return how did he do
+ 
+
+ align:start position:0%
+um internal rate of return how did he do
+that it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Roa um and the formula is up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there you can tell it's an internal rate
+
+ align:start position:0%
+there you can tell it's an internal rate
+ 
+
+ align:start position:0%
+there you can tell it's an internal rate
+of return because that's what Excel
+
+ align:start position:0%
+of return because that's what Excel
+ 
+
+ align:start position:0%
+of return because that's what Excel
+calls the
+
+ align:start position:0%
+calls the
+ 
+
+ align:start position:0%
+calls the
+formula uh and if you look at it it's um
+
+ align:start position:0%
+formula uh and if you look at it it's um
+ 
+
+ align:start position:0%
+formula uh and if you look at it it's um
+and 15% is an initial guess it's a it's
+
+ align:start position:0%
+and 15% is an initial guess it's a it's
+ 
+
+ align:start position:0%
+and 15% is an initial guess it's a it's
+an iterative procedure um it's b49 to
+
+ align:start position:0%
+an iterative procedure um it's b49 to
+ 
+
+ align:start position:0%
+an iterative procedure um it's b49 to
+r49 so it's the pre-tax it's the
+
+ align:start position:0%
+r49 so it's the pre-tax it's the
+ 
+
+ align:start position:0%
+r49 so it's the pre-tax it's the
+internal rate of return on the pre-tax
+
+ align:start position:0%
+internal rate of return on the pre-tax
+ 
+
+ align:start position:0%
+internal rate of return on the pre-tax
+cash
+
+ align:start position:0%
+cash
+ 
+
+ align:start position:0%
+cash
+flow
+
+ align:start position:0%
+flow
+ 
+
+ align:start position:0%
+flow
+which why would you do
+
+ align:start position:0%
+which why would you do
+ 
+
+ align:start position:0%
+which why would you do
+that why wouldn't you take into account
+
+ align:start position:0%
+that why wouldn't you take into account
+ 
+
+ align:start position:0%
+that why wouldn't you take into account
+the effect effect of
+
+ align:start position:0%
+the effect effect of
+ 
+
+ align:start position:0%
+the effect effect of
+taxes if you looked at that that's weird
+
+ align:start position:0%
+taxes if you looked at that that's weird
+ 
+
+ align:start position:0%
+taxes if you looked at that that's weird
+you should do it up
+
+ align:start position:0%
+you should do it up
+ 
+
+ align:start position:0%
+you should do it up
+here um and we could do it I haven't
+
+ align:start position:0%
+here um and we could do it I haven't
+ 
+
+ align:start position:0%
+here um and we could do it I haven't
+it's going to be significant but um
+
+ align:start position:0%
+it's going to be significant but um
+ 
+
+ align:start position:0%
+it's going to be significant but um
+that's just
+
+ align:start position:0%
+that's just
+ 
+
+ align:start position:0%
+that's just
+strange that's just
+
+ align:start position:0%
+strange that's just
+ 
+
+ align:start position:0%
+strange that's just
+strange and just for humor you really
+
+ align:start position:0%
+strange and just for humor you really
+ 
+
+ align:start position:0%
+strange and just for humor you really
+have to look at the formulas in a
+
+ align:start position:0%
+have to look at the formulas in a
+ 
+
+ align:start position:0%
+have to look at the formulas in a
+spreadsheet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's he didn't actually compute the
+
+ align:start position:0%
+that's he didn't actually compute the
+ 
+
+ align:start position:0%
+that's he didn't actually compute the
+payback
+
+ align:start position:0%
+payback
+ 
+
+ align:start position:0%
+payback
+per that slide I did he didn't actually
+
+ align:start position:0%
+per that slide I did he didn't actually
+ 
+
+ align:start position:0%
+per that slide I did he didn't actually
+see when you get your money back he may
+
+ align:start position:0%
+see when you get your money back he may
+ 
+
+ align:start position:0%
+see when you get your money back he may
+he he went up here and took
+
+ align:start position:0%
+he he went up here and took
+ 
+
+ align:start position:0%
+he he went up here and took
+the installed cost divided it by
+
+ align:start position:0%
+the installed cost divided it by
+ 
+
+ align:start position:0%
+the installed cost divided it by
+the c21 minus
+
+ align:start position:0%
+the c21 minus
+ 
+
+ align:start position:0%
+the c21 minus
+c29
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah divided it by what amounts to G3
+
+ align:start position:0%
+yeah divided it by what amounts to G3
+ 
+
+ align:start position:0%
+yeah divided it by what amounts to G3
+the C32 divided by the annual Savings in
+
+ align:start position:0%
+the C32 divided by the annual Savings in
+ 
+
+ align:start position:0%
+the C32 divided by the annual Savings in
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+year but the savings differ Year
+
+ align:start position:0%
+year but the savings differ Year
+ 
+
+ align:start position:0%
+year but the savings differ Year
+bye so it's just a very and he doesn't
+
+ align:start position:0%
+bye so it's just a very and he doesn't
+ 
+
+ align:start position:0%
+bye so it's just a very and he doesn't
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+taxes so this is a good-looking
+
+ align:start position:0%
+taxes so this is a good-looking
+ 
+
+ align:start position:0%
+taxes so this is a good-looking
+spreadsheet and what astonished me when
+
+ align:start position:0%
+spreadsheet and what astonished me when
+ 
+
+ align:start position:0%
+spreadsheet and what astonished me when
+I looked at it was wait a minute that's
+
+ align:start position:0%
+I looked at it was wait a minute that's
+ 
+
+ align:start position:0%
+I looked at it was wait a minute that's
+wrong that's wrong that's wrong
+
+ align:start position:0%
+wrong that's wrong that's wrong
+ 
+
+ align:start position:0%
+wrong that's wrong that's wrong
+otherwise pretty good otherwise pretty
+
+ align:start position:0%
+otherwise pretty good otherwise pretty
+ 
+
+ align:start position:0%
+otherwise pretty good otherwise pretty
+good any questions about the spreadsheet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's leave this no I
+
+ align:start position:0%
+okay let's leave this no I
+ 
+
+ align:start position:0%
+okay let's leave this no I
+don't let's go away and let's go back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I just put the spreadsheet with the
+
+ align:start position:0%
+so I just put the spreadsheet with the
+ 
+
+ align:start position:0%
+so I just put the spreadsheet with the
+formulas in the notes those are the
+
+ align:start position:0%
+formulas in the notes those are the
+ 
+
+ align:start position:0%
+formulas in the notes those are the
+issues we've talked
+
+ align:start position:0%
+issues we've talked
+ 
+
+ align:start position:0%
+issues we've talked
+about now let's talk about let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's talk about the naysayers so I'm
+
+ align:start position:0%
+let's talk about the naysayers so I'm
+ 
+
+ align:start position:0%
+let's talk about the naysayers so I'm
+guessing I haven't spent my life doing
+
+ align:start position:0%
+guessing I haven't spent my life doing
+ 
+
+ align:start position:0%
+guessing I haven't spent my life doing
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+spreadsheet uh but I'm guessing if you
+
+ align:start position:0%
+spreadsheet uh but I'm guessing if you
+ 
+
+ align:start position:0%
+spreadsheet uh but I'm guessing if you
+run through all of the things that we've
+
+ align:start position:0%
+run through all of the things that we've
+ 
+
+ align:start position:0%
+run through all of the things that we've
+talked about you know the basic
+
+ align:start position:0%
+talked about you know the basic
+ 
+
+ align:start position:0%
+talked about you know the basic
+assumptions look
+
+ align:start position:0%
+assumptions look
+ 
+
+ align:start position:0%
+assumptions look
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um the
+
+ align:start position:0%
+um the
+ 
+
+ align:start position:0%
+um the
+um numbers he's too optimistic but his
+
+ align:start position:0%
+um numbers he's too optimistic but his
+ 
+
+ align:start position:0%
+um numbers he's too optimistic but his
+his discount rat's probably a little
+
+ align:start position:0%
+his discount rat's probably a little
+ 
+
+ align:start position:0%
+his discount rat's probably a little
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+so I'm guessing that if you fiddle and
+
+ align:start position:0%
+so I'm guessing that if you fiddle and
+ 
+
+ align:start position:0%
+so I'm guessing that if you fiddle and
+didd you will come to the conclusion
+
+ align:start position:0%
+didd you will come to the conclusion
+ 
+
+ align:start position:0%
+didd you will come to the conclusion
+that it does have a positive Net Present
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Value First
+
+ align:start position:0%
+Value First
+ 
+
+ align:start position:0%
+Value First
+objection you were now Darren folks
+
+ align:start position:0%
+objection you were now Darren folks
+ 
+
+ align:start position:0%
+objection you were now Darren folks
+first objection if it's such a great
+
+ align:start position:0%
+first objection if it's such a great
+ 
+
+ align:start position:0%
+first objection if it's such a great
+idea how come nobody else is doing
+
+ align:start position:0%
+idea how come nobody else is doing
+ 
+
+ align:start position:0%
+idea how come nobody else is doing
+it and your answer
+
+ align:start position:0%
+it and your answer
+ 
+
+ align:start position:0%
+it and your answer
+is obadia what do you say you're going
+
+ align:start position:0%
+is obadia what do you say you're going
+ 
+
+ align:start position:0%
+is obadia what do you say you're going
+to just take that you're not going to
+
+ align:start position:0%
+to just take that you're not going to
+ 
+
+ align:start position:0%
+to just take that you're not going to
+just take that what's your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer nobody
+
+ align:start position:0%
+answer nobody
+ 
+
+ align:start position:0%
+answer nobody
+has might be we're
+
+ align:start position:0%
+has might be we're
+ 
+
+ align:start position:0%
+has might be we're
+smart might be this is a chance to take
+
+ align:start position:0%
+smart might be this is a chance to take
+ 
+
+ align:start position:0%
+smart might be this is a chance to take
+a leadership position Charlotte it could
+
+ align:start position:0%
+a leadership position Charlotte it could
+ 
+
+ align:start position:0%
+a leadership position Charlotte it could
+be that like the reason they're
+
+ align:start position:0%
+be that like the reason they're
+ 
+
+ align:start position:0%
+be that like the reason they're
+considering this is because they do have
+
+ align:start position:0%
+considering this is because they do have
+ 
+
+ align:start position:0%
+considering this is because they do have
+all that excess heat and steam that's
+
+ align:start position:0%
+all that excess heat and steam that's
+ 
+
+ align:start position:0%
+all that excess heat and steam that's
+cting their plant and maybe other
+
+ align:start position:0%
+cting their plant and maybe other
+ 
+
+ align:start position:0%
+cting their plant and maybe other
+people's plants are designed in a way
+
+ align:start position:0%
+people's plants are designed in a way
+ 
+
+ align:start position:0%
+people's plants are designed in a way
+that they never had that problem before
+
+ align:start position:0%
+that they never had that problem before
+ 
+
+ align:start position:0%
+that they never had that problem before
+so have I considered
+
+ align:start position:0%
+so have I considered
+ 
+
+ align:start position:0%
+so have I considered
+it could be although it sounds like a
+
+ align:start position:0%
+it could be although it sounds like a
+ 
+
+ align:start position:0%
+it could be although it sounds like a
+standard problem the way they describe
+
+ align:start position:0%
+standard problem the way they describe
+ 
+
+ align:start position:0%
+standard problem the way they describe
+the basic reaction you just dump this
+
+ align:start position:0%
+the basic reaction you just dump this
+ 
+
+ align:start position:0%
+the basic reaction you just dump this
+stuff in a vat and you get it gets hot
+
+ align:start position:0%
+stuff in a vat and you get it gets hot
+ 
+
+ align:start position:0%
+stuff in a vat and you get it gets hot
+Martha in warmer areas don't the same
+
+ align:start position:0%
+Martha in warmer areas don't the same
+ 
+
+ align:start position:0%
+Martha in warmer areas don't the same
+issue with ice of yor they might not
+
+ align:start position:0%
+issue with ice of yor they might not
+ 
+
+ align:start position:0%
+issue with ice of yor they might not
+have the same issue with ice they might
+
+ align:start position:0%
+have the same issue with ice they might
+ 
+
+ align:start position:0%
+have the same issue with ice they might
+all yeah the ice is kind of a big deal
+
+ align:start position:0%
+all yeah the ice is kind of a big deal
+ 
+
+ align:start position:0%
+all yeah the ice is kind of a big deal
+you're right if you're if you're in the
+
+ align:start position:0%
+you're right if you're if you're in the
+ 
+
+ align:start position:0%
+you're right if you're if you're in the
+middle of the desert and nobody can see
+
+ align:start position:0%
+middle of the desert and nobody can see
+ 
+
+ align:start position:0%
+middle of the desert and nobody can see
+you venting a lot of steam you might
+
+ align:start position:0%
+you venting a lot of steam you might
+ 
+
+ align:start position:0%
+you venting a lot of steam you might
+just say of course if you're in the
+
+ align:start position:0%
+just say of course if you're in the
+ 
+
+ align:start position:0%
+just say of course if you're in the
+middle of the desert you may have a
+
+ align:start position:0%
+middle of the desert you may have a
+ 
+
+ align:start position:0%
+middle of the desert you may have a
+water problem
+
+ align:start position:0%
+water problem
+ 
+
+ align:start position:0%
+water problem
+but uh actually I think my my response
+
+ align:start position:0%
+but uh actually I think my my response
+ 
+
+ align:start position:0%
+but uh actually I think my my response
+would be this is an opportunity to show
+
+ align:start position:0%
+would be this is an opportunity to show
+ 
+
+ align:start position:0%
+would be this is an opportunity to show
+leadership uh uh I I but let's try the
+
+ align:start position:0%
+leadership uh uh I I but let's try the
+ 
+
+ align:start position:0%
+leadership uh uh I I but let's try the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+one what's your answer to that one this
+
+ align:start position:0%
+one what's your answer to that one this
+ 
+
+ align:start position:0%
+one what's your answer to that one this
+is what I what what I got is I estimated
+
+ align:start position:0%
+is what I what what I got is I estimated
+ 
+
+ align:start position:0%
+is what I what what I got is I estimated
+the the the
+
+ align:start position:0%
+the the the
+ 
+
+ align:start position:0%
+the the the
+revenue yeah yeah I love your I love
+
+ align:start position:0%
+revenue yeah yeah I love your I love
+ 
+
+ align:start position:0%
+revenue yeah yeah I love your I love
+your Net Present Value that's just swell
+
+ align:start position:0%
+your Net Present Value that's just swell
+ 
+
+ align:start position:0%
+your Net Present Value that's just swell
+but there's a risk here there's always a
+
+ align:start position:0%
+but there's a risk here there's always a
+ 
+
+ align:start position:0%
+but there's a risk here there's always a
+risk here um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes there's always a risk talked about
+
+ align:start position:0%
+yes there's always a risk talked about
+ 
+
+ align:start position:0%
+yes there's always a risk talked about
+outage we'll come back to outage but I
+
+ align:start position:0%
+outage we'll come back to outage but I
+ 
+
+ align:start position:0%
+outage we'll come back to outage but I
+mean it's 2% of Revenue you're going to
+
+ align:start position:0%
+mean it's 2% of Revenue you're going to
+ 
+
+ align:start position:0%
+mean it's 2% of Revenue you're going to
+make the plant more complicated and if
+
+ align:start position:0%
+make the plant more complicated and if
+ 
+
+ align:start position:0%
+make the plant more complicated and if
+you're lucky we'll save 2% of Revenue
+
+ align:start position:0%
+you're lucky we'll save 2% of Revenue
+ 
+
+ align:start position:0%
+you're lucky we'll save 2% of Revenue
+why should we do that it's going to be
+
+ align:start position:0%
+why should we do that it's going to be
+ 
+
+ align:start position:0%
+why should we do that it's going to be
+lost in the noise as production varies
+
+ align:start position:0%
+lost in the noise as production varies
+ 
+
+ align:start position:0%
+lost in the noise as production varies
+as price varies as everything varies why
+
+ align:start position:0%
+as price varies as everything varies why
+ 
+
+ align:start position:0%
+as price varies as everything varies why
+should we complicate our
+
+ align:start position:0%
+should we complicate our
+ 
+
+ align:start position:0%
+should we complicate our
+lives now these kinds of things come up
+
+ align:start position:0%
+lives now these kinds of things come up
+ 
+
+ align:start position:0%
+lives now these kinds of things come up
+Sam one you could say the whole you put
+
+ align:start position:0%
+Sam one you could say the whole you put
+ 
+
+ align:start position:0%
+Sam one you could say the whole you put
+the whole green angle like it's a good
+
+ align:start position:0%
+the whole green angle like it's a good
+ 
+
+ align:start position:0%
+the whole green angle like it's a good
+way to make the environment better but
+
+ align:start position:0%
+way to make the environment better but
+ 
+
+ align:start position:0%
+way to make the environment better but
+also you can say about like in the
+
+ align:start position:0%
+also you can say about like in the
+ 
+
+ align:start position:0%
+also you can say about like in the
+future we don't know what's going to
+
+ align:start position:0%
+future we don't know what's going to
+ 
+
+ align:start position:0%
+future we don't know what's going to
+happen to the rice of electricity and if
+
+ align:start position:0%
+happen to the rice of electricity and if
+ 
+
+ align:start position:0%
+happen to the rice of electricity and if
+it rises it's a good insurance policy we
+
+ align:start position:0%
+it rises it's a good insurance policy we
+ 
+
+ align:start position:0%
+it rises it's a good insurance policy we
+have and also you can say that you know
+
+ align:start position:0%
+have and also you can say that you know
+ 
+
+ align:start position:0%
+have and also you can say that you know
+the technology that we're adding has a
+
+ align:start position:0%
+the technology that we're adding has a
+ 
+
+ align:start position:0%
+the technology that we're adding has a
+pretty good track record like it's not
+
+ align:start position:0%
+pretty good track record like it's not
+ 
+
+ align:start position:0%
+pretty good track record like it's not
+that complex yeah I mean this is this is
+
+ align:start position:0%
+that complex yeah I mean this is this is
+ 
+
+ align:start position:0%
+that complex yeah I mean this is this is
+not the first time this contractor's
+
+ align:start position:0%
+not the first time this contractor's
+ 
+
+ align:start position:0%
+not the first time this contractor's
+ever done it so the risk is doesn't
+
+ align:start position:0%
+ever done it so the risk is doesn't
+ 
+
+ align:start position:0%
+ever done it so the risk is doesn't
+sound to doesn't sound like it's that
+
+ align:start position:0%
+sound to doesn't sound like it's that
+ 
+
+ align:start position:0%
+sound to doesn't sound like it's that
+high 2% is
+
+ align:start position:0%
+high 2% is
+ 
+
+ align:start position:0%
+high 2% is
+2% not bad anybody else wrong
+
+ align:start position:0%
+2% not bad anybody else wrong
+ 
+
+ align:start position:0%
+2% not bad anybody else wrong
+it's not actually changing the formal
+
+ align:start position:0%
+it's not actually changing the formal
+ 
+
+ align:start position:0%
+it's not actually changing the formal
+process so it's not complicating it in
+
+ align:start position:0%
+process so it's not complicating it in
+ 
+
+ align:start position:0%
+process so it's not complicating it in
+that respect there's also the safety
+
+ align:start position:0%
+that respect there's also the safety
+ 
+
+ align:start position:0%
+that respect there's also the safety
+issue and like you said the uh green
+
+ align:start position:0%
+issue and like you said the uh green
+ 
+
+ align:start position:0%
+issue and like you said the uh green
+issue safety issue being like the ice
+
+ align:start position:0%
+issue safety issue being like the ice
+ 
+
+ align:start position:0%
+issue safety issue being like the ice
+yeah got the safety issue that's a risk
+
+ align:start position:0%
+yeah got the safety issue that's a risk
+ 
+
+ align:start position:0%
+yeah got the safety issue that's a risk
+boy somebody slips and falls on that ice
+
+ align:start position:0%
+boy somebody slips and falls on that ice
+ 
+
+ align:start position:0%
+boy somebody slips and falls on that ice
+and uh we get we get stuck with uh nice
+
+ align:start position:0%
+and uh we get we get stuck with uh nice
+ 
+
+ align:start position:0%
+and uh we get we get stuck with uh nice
+negligence big medical bills sympathetic
+
+ align:start position:0%
+negligence big medical bills sympathetic
+ 
+
+ align:start position:0%
+negligence big medical bills sympathetic
+plaintive it's really depressing Scott
+
+ align:start position:0%
+plaintive it's really depressing Scott
+ 
+
+ align:start position:0%
+plaintive it's really depressing Scott
+so I think if you look at it in terms of
+
+ align:start position:0%
+so I think if you look at it in terms of
+ 
+
+ align:start position:0%
+so I think if you look at it in terms of
+the percentage it does doesn't sound
+
+ align:start position:0%
+the percentage it does doesn't sound
+ 
+
+ align:start position:0%
+the percentage it does doesn't sound
+like very much like saying like oh it's
+
+ align:start position:0%
+like very much like saying like oh it's
+ 
+
+ align:start position:0%
+like very much like saying like oh it's
+only 2% of our Revenue that doesn't
+
+ align:start position:0%
+only 2% of our Revenue that doesn't
+ 
+
+ align:start position:0%
+only 2% of our Revenue that doesn't
+sound like very much at all but if you
+
+ align:start position:0%
+sound like very much at all but if you
+ 
+
+ align:start position:0%
+sound like very much at all but if you
+say oh it's $300,000 we're saving then
+
+ align:start position:0%
+say oh it's $300,000 we're saving then
+ 
+
+ align:start position:0%
+say oh it's $300,000 we're saving then
+that's like while it may be only a small
+
+ align:start position:0%
+that's like while it may be only a small
+ 
+
+ align:start position:0%
+that's like while it may be only a small
+portion of the revenue $3,000 is a large
+
+ align:start position:0%
+portion of the revenue $3,000 is a large
+ 
+
+ align:start position:0%
+portion of the revenue $3,000 is a large
+amount of money to pretty much
+
+ align:start position:0%
+amount of money to pretty much
+ 
+
+ align:start position:0%
+amount of money to pretty much
+any to a $5 million operation I don't
+
+ align:start position:0%
+any to a $5 million operation I don't
+ 
+
+ align:start position:0%
+any to a $5 million operation I don't
+know maybe yeah yeah it's not trivial in
+
+ align:start position:0%
+know maybe yeah yeah it's not trivial in
+ 
+
+ align:start position:0%
+know maybe yeah yeah it's not trivial in
+the absolute anybody else uh um they're
+
+ align:start position:0%
+the absolute anybody else uh um they're
+ 
+
+ align:start position:0%
+the absolute anybody else uh um they're
+also going to use current employees to
+
+ align:start position:0%
+also going to use current employees to
+ 
+
+ align:start position:0%
+also going to use current employees to
+run the same thing so I presume their
+
+ align:start position:0%
+run the same thing so I presume their
+ 
+
+ align:start position:0%
+run the same thing so I presume their
+their um salary would increase I
+
+ align:start position:0%
+their um salary would increase I
+ 
+
+ align:start position:0%
+their um salary would increase I
+wouldn't want to presume that I want I
+
+ align:start position:0%
+wouldn't want to presume that I want I
+ 
+
+ align:start position:0%
+wouldn't want to presume that I want I
+I'd say their job satisfaction would
+
+ align:start position:0%
+I'd say their job satisfaction would
+ 
+
+ align:start position:0%
+I'd say their job satisfaction would
+increase because it would make their
+
+ align:start position:0%
+increase because it would make their
+ 
+
+ align:start position:0%
+increase because it would make their
+jobs more interesting that's that's the
+
+ align:start position:0%
+jobs more interesting that's that's the
+ 
+
+ align:start position:0%
+jobs more interesting that's that's the
+that's the pitch I'd use and it's a good
+
+ align:start position:0%
+that's the pitch I'd use and it's a good
+ 
+
+ align:start position:0%
+that's the pitch I'd use and it's a good
+point you might want to see if you can
+
+ align:start position:0%
+point you might want to see if you can
+ 
+
+ align:start position:0%
+point you might want to see if you can
+get them behind
+
+ align:start position:0%
+get them behind
+ 
+
+ align:start position:0%
+get them behind
+it you might want to you might want to
+
+ align:start position:0%
+it you might want to you might want to
+ 
+
+ align:start position:0%
+it you might want to you might want to
+talk it up so you can say well I've
+
+ align:start position:0%
+talk it up so you can say well I've
+ 
+
+ align:start position:0%
+talk it up so you can say well I've
+talked it with talked up with the folks
+
+ align:start position:0%
+talked it with talked up with the folks
+ 
+
+ align:start position:0%
+talked it with talked up with the folks
+in the factory and they actually like
+
+ align:start position:0%
+in the factory and they actually like
+ 
+
+ align:start position:0%
+in the factory and they actually like
+the idea everon
+
+ align:start position:0%
+the idea everon
+ 
+
+ align:start position:0%
+the idea everon
+having those same people who are work in
+
+ align:start position:0%
+having those same people who are work in
+ 
+
+ align:start position:0%
+having those same people who are work in
+the factory doing extra things I think
+
+ align:start position:0%
+the factory doing extra things I think
+ 
+
+ align:start position:0%
+the factory doing extra things I think
+it eliminates some risk because um more
+
+ align:start position:0%
+it eliminates some risk because um more
+ 
+
+ align:start position:0%
+it eliminates some risk because um more
+familiar with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process that helps yeah these people
+
+ align:start position:0%
+process that helps yeah these people
+ 
+
+ align:start position:0%
+process that helps yeah these people
+know it they they want to keep the plant
+
+ align:start position:0%
+know it they they want to keep the plant
+ 
+
+ align:start position:0%
+know it they they want to keep the plant
+running we all want to keep the plant
+
+ align:start position:0%
+running we all want to keep the plant
+ 
+
+ align:start position:0%
+running we all want to keep the plant
+running um this actually is a common I
+
+ align:start position:0%
+running um this actually is a common I
+ 
+
+ align:start position:0%
+running um this actually is a common I
+mean these paraphrase the the objections
+
+ align:start position:0%
+mean these paraphrase the the objections
+ 
+
+ align:start position:0%
+mean these paraphrase the the objections
+in the case I've added a little bit of
+
+ align:start position:0%
+in the case I've added a little bit of
+ 
+
+ align:start position:0%
+in the case I've added a little bit of
+what you always hear this this is
+
+ align:start position:0%
+what you always hear this this is
+ 
+
+ align:start position:0%
+what you always hear this this is
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+one we can invest and grow
+
+ align:start position:0%
+one we can invest and grow
+ 
+
+ align:start position:0%
+one we can invest and grow
+capacity as opposed to this complicating
+
+ align:start position:0%
+capacity as opposed to this complicating
+ 
+
+ align:start position:0%
+capacity as opposed to this complicating
+investment and we want to grow the
+
+ align:start position:0%
+investment and we want to grow the
+ 
+
+ align:start position:0%
+investment and we want to grow the
+business you're not growing the
+
+ align:start position:0%
+business you're not growing the
+ 
+
+ align:start position:0%
+business you're not growing the
+business you know if we didn't have
+
+ align:start position:0%
+business you know if we didn't have
+ 
+
+ align:start position:0%
+business you know if we didn't have
+money well then we wouldn't invest but
+
+ align:start position:0%
+money well then we wouldn't invest but
+ 
+
+ align:start position:0%
+money well then we wouldn't invest but
+if times are good and we're selling this
+
+ align:start position:0%
+if times are good and we're selling this
+ 
+
+ align:start position:0%
+if times are good and we're selling this
+stuff we want to make more of it because
+
+ align:start position:0%
+stuff we want to make more of it because
+ 
+
+ align:start position:0%
+stuff we want to make more of it because
+that's how we grow and your investment
+
+ align:start position:0%
+that's how we grow and your investment
+ 
+
+ align:start position:0%
+that's how we grow and your investment
+isn't a growth
+
+ align:start position:0%
+isn't a growth
+ 
+
+ align:start position:0%
+isn't a growth
+investment James well maybe by selling
+
+ align:start position:0%
+investment James well maybe by selling
+ 
+
+ align:start position:0%
+investment James well maybe by selling
+electricity you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diversify a little safer even though
+
+ align:start position:0%
+diversify a little safer even though
+ 
+
+ align:start position:0%
+diversify a little safer even though
+it's not
+
+ align:start position:0%
+it's not
+ 
+
+ align:start position:0%
+it's not
+much so yeah we're we're we're reducing
+
+ align:start position:0%
+much so yeah we're we're we're reducing
+ 
+
+ align:start position:0%
+much so yeah we're we're we're reducing
+the risk of our operation overall
+
+ align:start position:0%
+the risk of our operation overall
+ 
+
+ align:start position:0%
+the risk of our operation overall
+because of this electricity hedge and
+
+ align:start position:0%
+because of this electricity hedge and
+ 
+
+ align:start position:0%
+because of this electricity hedge and
+that means growth is safer you might try
+
+ align:start position:0%
+that means growth is safer you might try
+ 
+
+ align:start position:0%
+that means growth is safer you might try
+that yes arue that it gives you
+
+ align:start position:0%
+that yes arue that it gives you
+ 
+
+ align:start position:0%
+that yes arue that it gives you
+experience the technology that's more PR
+
+ align:start position:0%
+experience the technology that's more PR
+ 
+
+ align:start position:0%
+experience the technology that's more PR
+friendly in the sense that you have less
+
+ align:start position:0%
+friendly in the sense that you have less
+ 
+
+ align:start position:0%
+friendly in the sense that you have less
+Flume gas putting out it's easier to
+
+ align:start position:0%
+Flume gas putting out it's easier to
+ 
+
+ align:start position:0%
+Flume gas putting out it's easier to
+build things wherever you want CU you
+
+ align:start position:0%
+build things wherever you want CU you
+ 
+
+ align:start position:0%
+build things wherever you want CU you
+get less public out and so that the
+
+ align:start position:0%
+get less public out and so that the
+ 
+
+ align:start position:0%
+get less public out and so that the
+ability to grow more in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+future yeah of course except I mean we
+
+ align:start position:0%
+future yeah of course except I mean we
+ 
+
+ align:start position:0%
+future yeah of course except I mean we
+are making from Malahide we you know we
+
+ align:start position:0%
+are making from Malahide we you know we
+ 
+
+ align:start position:0%
+are making from Malahide we you know we
+can't make it into into flowers
+
+ align:start position:0%
+can't make it into into flowers
+ 
+
+ align:start position:0%
+can't make it into into flowers
+chimo yeah um I think maybe finding like
+
+ align:start position:0%
+chimo yeah um I think maybe finding like
+ 
+
+ align:start position:0%
+chimo yeah um I think maybe finding like
+a better solution to get rid of the
+
+ align:start position:0%
+a better solution to get rid of the
+ 
+
+ align:start position:0%
+a better solution to get rid of the
+steam could allow you to I increased
+
+ align:start position:0%
+steam could allow you to I increased
+ 
+
+ align:start position:0%
+steam could allow you to I increased
+capacity cuz like if it's just like
+
+ align:start position:0%
+capacity cuz like if it's just like
+ 
+
+ align:start position:0%
+capacity cuz like if it's just like
+lying around there's probably a maximum
+
+ align:start position:0%
+lying around there's probably a maximum
+ 
+
+ align:start position:0%
+lying around there's probably a maximum
+amount of that you can produce and have
+
+ align:start position:0%
+amount of that you can produce and have
+ 
+
+ align:start position:0%
+amount of that you can produce and have
+the theme creating ice or that's an
+
+ align:start position:0%
+the theme creating ice or that's an
+ 
+
+ align:start position:0%
+the theme creating ice or that's an
+interesting thought so you're you're
+
+ align:start position:0%
+interesting thought so you're you're
+ 
+
+ align:start position:0%
+interesting thought so you're you're
+saying we can only do so much of this
+
+ align:start position:0%
+saying we can only do so much of this
+ 
+
+ align:start position:0%
+saying we can only do so much of this
+venting and ice and so on and this that
+
+ align:start position:0%
+venting and ice and so on and this that
+ 
+
+ align:start position:0%
+venting and ice and so on and this that
+may someday be a constraint on us yes
+
+ align:start position:0%
+may someday be a constraint on us yes
+ 
+
+ align:start position:0%
+may someday be a constraint on us yes
+and finding like a better solution like
+
+ align:start position:0%
+and finding like a better solution like
+ 
+
+ align:start position:0%
+and finding like a better solution like
+that maybe might make them enable them
+
+ align:start position:0%
+that maybe might make them enable them
+ 
+
+ align:start position:0%
+that maybe might make them enable them
+to expand it even more okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thanks year that get your initial
+
+ align:start position:0%
+thanks year that get your initial
+ 
+
+ align:start position:0%
+thanks year that get your initial
+investment back you're going have extra
+
+ align:start position:0%
+investment back you're going have extra
+ 
+
+ align:start position:0%
+investment back you're going have extra
+money roughly year three yeah extra
+
+ align:start position:0%
+money roughly year three yeah extra
+ 
+
+ align:start position:0%
+money roughly year three yeah extra
+money extra money you
+
+ align:start position:0%
+money extra money you
+ 
+
+ align:start position:0%
+money extra money you
+invest every year after that oh that's
+
+ align:start position:0%
+invest every year after that oh that's
+ 
+
+ align:start position:0%
+invest every year after that oh that's
+nice that's nice if we play it right I
+
+ align:start position:0%
+nice that's nice if we play it right I
+ 
+
+ align:start position:0%
+nice that's nice if we play it right I
+mean this is presumably you get this
+
+ align:start position:0%
+mean this is presumably you get this
+ 
+
+ align:start position:0%
+mean this is presumably you get this
+stuff you're getting this um they don't
+
+ align:start position:0%
+stuff you're getting this um they don't
+ 
+
+ align:start position:0%
+stuff you're getting this um they don't
+specify in the case who he's talking to
+
+ align:start position:0%
+specify in the case who he's talking to
+ 
+
+ align:start position:0%
+specify in the case who he's talking to
+but presumably this is is a middle
+
+ align:start position:0%
+but presumably this is is a middle
+ 
+
+ align:start position:0%
+but presumably this is is a middle
+management group that passes on Capital
+
+ align:start position:0%
+management group that passes on Capital
+ 
+
+ align:start position:0%
+management group that passes on Capital
+spending requests so your response would
+
+ align:start position:0%
+spending requests so your response would
+ 
+
+ align:start position:0%
+spending requests so your response would
+be look
+
+ align:start position:0%
+be look
+ 
+
+ align:start position:0%
+be look
+folks if this plant is more profitable
+
+ align:start position:0%
+folks if this plant is more profitable
+ 
+
+ align:start position:0%
+folks if this plant is more profitable
+which it will be we're going to be able
+
+ align:start position:0%
+which it will be we're going to be able
+ 
+
+ align:start position:0%
+which it will be we're going to be able
+to use that to generate to get more
+
+ align:start position:0%
+to use that to generate to get more
+ 
+
+ align:start position:0%
+to use that to generate to get more
+investment money to to
+
+ align:start position:0%
+investment money to to
+ 
+
+ align:start position:0%
+investment money to to
+expand uh we don't necessarily get to
+
+ align:start position:0%
+expand uh we don't necessarily get to
+ 
+
+ align:start position:0%
+expand uh we don't necessarily get to
+put it in our pocket because it's all
+
+ align:start position:0%
+put it in our pocket because it's all
+ 
+
+ align:start position:0%
+put it in our pocket because it's all
+part of the corporation but it'll be a
+
+ align:start position:0%
+part of the corporation but it'll be a
+ 
+
+ align:start position:0%
+part of the corporation but it'll be a
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+justification Andrew uh what we could be
+
+ align:start position:0%
+justification Andrew uh what we could be
+ 
+
+ align:start position:0%
+justification Andrew uh what we could be
+doing with the uh I it's kind of a
+
+ align:start position:0%
+doing with the uh I it's kind of a
+ 
+
+ align:start position:0%
+doing with the uh I it's kind of a
+question but what you could be doing
+
+ align:start position:0%
+question but what you could be doing
+ 
+
+ align:start position:0%
+question but what you could be doing
+with the money you're using to do this
+
+ align:start position:0%
+with the money you're using to do this
+ 
+
+ align:start position:0%
+with the money you're using to do this
+like isn't that captured by your
+
+ align:start position:0%
+like isn't that captured by your
+ 
+
+ align:start position:0%
+like isn't that captured by your
+discount rate essentially like so can
+
+ align:start position:0%
+discount rate essentially like so can
+ 
+
+ align:start position:0%
+discount rate essentially like so can
+you just argue that uh I mean because
+
+ align:start position:0%
+you just argue that uh I mean because
+ 
+
+ align:start position:0%
+you just argue that uh I mean because
+this kind of an opportunity cost that
+
+ align:start position:0%
+this kind of an opportunity cost that
+ 
+
+ align:start position:0%
+this kind of an opportunity cost that
+they're mentioning right I mean instead
+
+ align:start position:0%
+they're mentioning right I mean instead
+ 
+
+ align:start position:0%
+they're mentioning right I mean instead
+of spending the money to do this you
+
+ align:start position:0%
+of spending the money to do this you
+ 
+
+ align:start position:0%
+of spending the money to do this you
+could spend it to grow the business but
+
+ align:start position:0%
+could spend it to grow the business but
+ 
+
+ align:start position:0%
+could spend it to grow the business but
+then you can answer like but that's why
+
+ align:start position:0%
+then you can answer like but that's why
+ 
+
+ align:start position:0%
+then you can answer like but that's why
+I'm using it is except it in in most
+
+ align:start position:0%
+I'm using it is except it in in most
+ 
+
+ align:start position:0%
+I'm using it is except it in in most
+companies of any size you basically do a
+
+ align:start position:0%
+companies of any size you basically do a
+ 
+
+ align:start position:0%
+companies of any size you basically do a
+capital budgeting process we're going to
+
+ align:start position:0%
+capital budgeting process we're going to
+ 
+
+ align:start position:0%
+capital budgeting process we're going to
+invest X I
+
+ align:start position:0%
+invest X I
+ 
+
+ align:start position:0%
+invest X I
+mean you shouldn't but you do we're
+
+ align:start position:0%
+mean you shouldn't but you do we're
+ 
+
+ align:start position:0%
+mean you shouldn't but you do we're
+going to invest X this year your job is
+
+ align:start position:0%
+going to invest X this year your job is
+ 
+
+ align:start position:0%
+going to invest X this year your job is
+to figure out how best to invest it as
+
+ align:start position:0%
+to figure out how best to invest it as
+ 
+
+ align:start position:0%
+to figure out how best to invest it as
+opposed to saying anything that makes
+
+ align:start position:0%
+opposed to saying anything that makes
+ 
+
+ align:start position:0%
+opposed to saying anything that makes
+that that clears the uh uh has a
+
+ align:start position:0%
+that that clears the uh uh has a
+ 
+
+ align:start position:0%
+that that clears the uh uh has a
+positive net presentence value we'll
+
+ align:start position:0%
+positive net presentence value we'll
+ 
+
+ align:start position:0%
+positive net presentence value we'll
+figure out how to fund I mean if you
+
+ align:start position:0%
+figure out how to fund I mean if you
+ 
+
+ align:start position:0%
+figure out how to fund I mean if you
+have a great
+
+ align:start position:0%
+have a great
+ 
+
+ align:start position:0%
+have a great
+project and it and this is a way of just
+
+ align:start position:0%
+project and it and this is a way of just
+ 
+
+ align:start position:0%
+project and it and this is a way of just
+kind of doing a regular systematic
+
+ align:start position:0%
+kind of doing a regular systematic
+ 
+
+ align:start position:0%
+kind of doing a regular systematic
+budgeting process if you come up with a
+
+ align:start position:0%
+budgeting process if you come up with a
+ 
+
+ align:start position:0%
+budgeting process if you come up with a
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+big great comma big project then you go
+
+ align:start position:0%
+big great comma big project then you go
+ 
+
+ align:start position:0%
+big great comma big project then you go
+to top management and you say I know
+
+ align:start position:0%
+to top management and you say I know
+ 
+
+ align:start position:0%
+to top management and you say I know
+this is over the capital budget but but
+
+ align:start position:0%
+this is over the capital budget but but
+ 
+
+ align:start position:0%
+this is over the capital budget but but
+for little things like this and for this
+
+ align:start position:0%
+for little things like this and for this
+ 
+
+ align:start position:0%
+for little things like this and for this
+company this is probably a relatively
+
+ align:start position:0%
+company this is probably a relatively
+ 
+
+ align:start position:0%
+company this is probably a relatively
+small project Darren doesn't have the
+
+ align:start position:0%
+small project Darren doesn't have the
+ 
+
+ align:start position:0%
+small project Darren doesn't have the
+discretion to do it
+
+ align:start position:0%
+discretion to do it
+ 
+
+ align:start position:0%
+discretion to do it
+himself routine things he probably has a
+
+ align:start position:0%
+himself routine things he probably has a
+ 
+
+ align:start position:0%
+himself routine things he probably has a
+limit you can you can you have a
+
+ align:start position:0%
+limit you can you can you have a
+ 
+
+ align:start position:0%
+limit you can you can you have a
+spending limit without authorization of
+
+ align:start position:0%
+spending limit without authorization of
+ 
+
+ align:start position:0%
+spending limit without authorization of
+without approval of 20,000 maybe maybe
+
+ align:start position:0%
+without approval of 20,000 maybe maybe
+ 
+
+ align:start position:0%
+without approval of 20,000 maybe maybe
+more um
+
+ align:start position:0%
+more um
+ 
+
+ align:start position:0%
+more um
+for anything above that up to some
+
+ align:start position:0%
+for anything above that up to some
+ 
+
+ align:start position:0%
+for anything above that up to some
+ceiling you got to clear it with
+
+ align:start position:0%
+ceiling you got to clear it with
+ 
+
+ align:start position:0%
+ceiling you got to clear it with
+whatever this group is that is full of
+
+ align:start position:0%
+whatever this group is that is full of
+ 
+
+ align:start position:0%
+whatever this group is that is full of
+Skeptics beyond that the group has to go
+
+ align:start position:0%
+Skeptics beyond that the group has to go
+ 
+
+ align:start position:0%
+Skeptics beyond that the group has to go
+and say to top management I know you
+
+ align:start position:0%
+and say to top management I know you
+ 
+
+ align:start position:0%
+and say to top management I know you
+only gave us $800,000 for the fahid
+
+ align:start position:0%
+only gave us $800,000 for the fahid
+ 
+
+ align:start position:0%
+only gave us $800,000 for the fahid
+division but we have this great idea and
+
+ align:start position:0%
+division but we have this great idea and
+ 
+
+ align:start position:0%
+division but we have this great idea and
+we'd like to present it
+
+ align:start position:0%
+we'd like to present it
+ 
+
+ align:start position:0%
+we'd like to present it
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it's it economizes on top management
+
+ align:start position:0%
+it's it economizes on top management
+ 
+
+ align:start position:0%
+it's it economizes on top management
+time to some extent
+
+ align:start position:0%
+time to some extent
+ 
+
+ align:start position:0%
+time to some extent
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+um gives you an orderly budgeting
+
+ align:start position:0%
+um gives you an orderly budgeting
+ 
+
+ align:start position:0%
+um gives you an orderly budgeting
+process so you can kind of predict cash
+
+ align:start position:0%
+process so you can kind of predict cash
+ 
+
+ align:start position:0%
+process so you can kind of predict cash
+flows but it imposes this kind of
+
+ align:start position:0%
+flows but it imposes this kind of
+ 
+
+ align:start position:0%
+flows but it imposes this kind of
+constraint I mean Capital budgeting
+
+ align:start position:0%
+constraint I mean Capital budgeting
+ 
+
+ align:start position:0%
+constraint I mean Capital budgeting
+processes do at some point somebody sits
+
+ align:start position:0%
+processes do at some point somebody sits
+ 
+
+ align:start position:0%
+processes do at some point somebody sits
+in the room you know you got a good
+
+ align:start position:0%
+in the room you know you got a good
+ 
+
+ align:start position:0%
+in the room you know you got a good
+project I got a good project we don't
+
+ align:start position:0%
+project I got a good project we don't
+ 
+
+ align:start position:0%
+project I got a good project we don't
+have money for both and they're not so
+
+ align:start position:0%
+have money for both and they're not so
+ 
+
+ align:start position:0%
+have money for both and they're not so
+good that we can get money for both we
+
+ align:start position:0%
+good that we can get money for both we
+ 
+
+ align:start position:0%
+good that we can get money for both we
+need to choose um and there is a
+
+ align:start position:0%
+need to choose um and there is a
+ 
+
+ align:start position:0%
+need to choose um and there is a
+tendency to say
+
+ align:start position:0%
+tendency to say
+ 
+
+ align:start position:0%
+tendency to say
+we want to grow we want to grow that is
+
+ align:start position:0%
+we want to grow we want to grow that is
+ 
+
+ align:start position:0%
+we want to grow we want to grow that is
+an issue faced that the that investments
+
+ align:start position:0%
+an issue faced that the that investments
+ 
+
+ align:start position:0%
+an issue faced that the that investments
+in efficiency and
+
+ align:start position:0%
+in efficiency and
+ 
+
+ align:start position:0%
+in efficiency and
+conservation traditionally face because
+
+ align:start position:0%
+conservation traditionally face because
+ 
+
+ align:start position:0%
+conservation traditionally face because
+they're not growth Investments and
+
+ align:start position:0%
+they're not growth Investments and
+ 
+
+ align:start position:0%
+they're not growth Investments and
+people like growth obina I don't know if
+
+ align:start position:0%
+people like growth obina I don't know if
+ 
+
+ align:start position:0%
+people like growth obina I don't know if
+someone mention this about the second
+
+ align:start position:0%
+someone mention this about the second
+ 
+
+ align:start position:0%
+someone mention this about the second
+Point um but you know it might be 2% of
+
+ align:start position:0%
+Point um but you know it might be 2% of
+ 
+
+ align:start position:0%
+Point um but you know it might be 2% of
+revenue for one plant but what if you
+
+ align:start position:0%
+revenue for one plant but what if you
+ 
+
+ align:start position:0%
+revenue for one plant but what if you
+have several plants they're like this
+
+ align:start position:0%
+have several plants they're like this
+ 
+
+ align:start position:0%
+have several plants they're like this
+plant it's 2% of revenue for all plants
+
+ align:start position:0%
+plant it's 2% of revenue for all plants
+ 
+
+ align:start position:0%
+plant it's 2% of revenue for all plants
+right if if you if you install the
+
+ align:start position:0%
+right if if you if you install the
+ 
+
+ align:start position:0%
+right if if you if you install the
+system at a number of plants you could
+
+ align:start position:0%
+system at a number of plants you could
+ 
+
+ align:start position:0%
+system at a number of plants you could
+easily end up Revenue Savings in in the
+
+ align:start position:0%
+easily end up Revenue Savings in in the
+ 
+
+ align:start position:0%
+easily end up Revenue Savings in in the
+millions you could end up with with a
+
+ align:start position:0%
+millions you could end up with with a
+ 
+
+ align:start position:0%
+millions you could end up with with a
+good number it would still be 2% of
+
+ align:start position:0%
+good number it would still be 2% of
+ 
+
+ align:start position:0%
+good number it would still be 2% of
+Revenue probably on that order okay yep
+
+ align:start position:0%
+Revenue probably on that order okay yep
+ 
+
+ align:start position:0%
+Revenue probably on that order okay yep
+no I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I another way to do that argument and
+
+ align:start position:0%
+I another way to do that argument and
+ 
+
+ align:start position:0%
+I another way to do that argument and
+it's sort of a little variation on the
+
+ align:start position:0%
+it's sort of a little variation on the
+ 
+
+ align:start position:0%
+it's sort of a little variation on the
+first one would be um look guys we can
+
+ align:start position:0%
+first one would be um look guys we can
+ 
+
+ align:start position:0%
+first one would be um look guys we can
+lead the way for the company whatever
+
+ align:start position:0%
+lead the way for the company whatever
+ 
+
+ align:start position:0%
+lead the way for the company whatever
+this group is that's approving the
+
+ align:start position:0%
+this group is that's approving the
+ 
+
+ align:start position:0%
+this group is that's approving the
+budget if this works here and we're very
+
+ align:start position:0%
+budget if this works here and we're very
+ 
+
+ align:start position:0%
+budget if this works here and we're very
+confident it it works we're going to get
+
+ align:start position:0%
+confident it it works we're going to get
+ 
+
+ align:start position:0%
+confident it it works we're going to get
+a lot of points with the company because
+
+ align:start position:0%
+a lot of points with the company because
+ 
+
+ align:start position:0%
+a lot of points with the company because
+we led the way to 2% of Revenue Savings
+
+ align:start position:0%
+we led the way to 2% of Revenue Savings
+ 
+
+ align:start position:0%
+we led the way to 2% of Revenue Savings
+in all of our form alahh operations now
+
+ align:start position:0%
+in all of our form alahh operations now
+ 
+
+ align:start position:0%
+in all of our form alahh operations now
+maybe it's not 2% everywhere we got to
+
+ align:start position:0%
+maybe it's not 2% everywhere we got to
+ 
+
+ align:start position:0%
+maybe it's not 2% everywhere we got to
+run the
+
+ align:start position:0%
+run the
+ 
+
+ align:start position:0%
+run the
+numbers um electricity is probably
+
+ align:start position:0%
+numbers um electricity is probably
+ 
+
+ align:start position:0%
+numbers um electricity is probably
+particularly expensive in Upstate New
+
+ align:start position:0%
+particularly expensive in Upstate New
+ 
+
+ align:start position:0%
+particularly expensive in Upstate New
+York would be cheaper in Ohio but that's
+
+ align:start position:0%
+York would be cheaper in Ohio but that's
+ 
+
+ align:start position:0%
+York would be cheaper in Ohio but that's
+where that's where I'd go with that I
+
+ align:start position:0%
+where that's where I'd go with that I
+ 
+
+ align:start position:0%
+where that's where I'd go with that I
+wouldn't say 2% is 2% is um 2% is big if
+
+ align:start position:0%
+wouldn't say 2% is 2% is um 2% is big if
+ 
+
+ align:start position:0%
+wouldn't say 2% is 2% is um 2% is big if
+I If I multiply it by a large number I
+
+ align:start position:0%
+I If I multiply it by a large number I
+ 
+
+ align:start position:0%
+I If I multiply it by a large number I
+would say it's in our interest as the
+
+ align:start position:0%
+would say it's in our interest as the
+ 
+
+ align:start position:0%
+would say it's in our interest as the
+group sitting around the table to
+
+ align:start position:0%
+group sitting around the table to
+ 
+
+ align:start position:0%
+group sitting around the table to
+demonstrate to the guys up
+
+ align:start position:0%
+demonstrate to the guys up
+ 
+
+ align:start position:0%
+demonstrate to the guys up
+above that that we can we can do this
+
+ align:start position:0%
+above that that we can we can do this
+ 
+
+ align:start position:0%
+above that that we can we can do this
+okay here's another one this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+killer our bonuses depend on
+
+ align:start position:0%
+killer our bonuses depend on
+ 
+
+ align:start position:0%
+killer our bonuses depend on
+compensation or on production that's how
+
+ align:start position:0%
+compensation or on production that's how
+ 
+
+ align:start position:0%
+compensation or on production that's how
+we do it and you're telling me it's 5
+
+ align:start position:0%
+we do it and you're telling me it's 5
+ 
+
+ align:start position:0%
+we do it and you're telling me it's 5
+days of downtime and we can recover for
+
+ align:start position:0%
+days of downtime and we can recover for
+ 
+
+ align:start position:0%
+days of downtime and we can recover for
+it recover from it but we don't know we
+
+ align:start position:0%
+it recover from it but we don't know we
+ 
+
+ align:start position:0%
+it recover from it but we don't know we
+can recover from it
+
+ align:start position:0%
+can recover from it
+ 
+
+ align:start position:0%
+can recover from it
+you're putting my trip to the Caribbean
+
+ align:start position:0%
+you're putting my trip to the Caribbean
+ 
+
+ align:start position:0%
+you're putting my trip to the Caribbean
+at risk and it's very cold in Upstate
+
+ align:start position:0%
+at risk and it's very cold in Upstate
+ 
+
+ align:start position:0%
+at risk and it's very cold in Upstate
+New York in the winter I need that
+
+ align:start position:0%
+New York in the winter I need that
+ 
+
+ align:start position:0%
+New York in the winter I need that
+bonus this is a
+
+ align:start position:0%
+bonus this is a
+ 
+
+ align:start position:0%
+bonus this is a
+risk what's your response Casey you look
+
+ align:start position:0%
+risk what's your response Casey you look
+ 
+
+ align:start position:0%
+risk what's your response Casey you look
+ready you're ready on this one am I
+
+ align:start position:0%
+ready you're ready on this one am I
+ 
+
+ align:start position:0%
+ready you're ready on this one am I
+right well um first they might be able
+
+ align:start position:0%
+right well um first they might be able
+ 
+
+ align:start position:0%
+right well um first they might be able
+to switch their production schedule to
+
+ align:start position:0%
+to switch their production schedule to
+ 
+
+ align:start position:0%
+to switch their production schedule to
+kind of account for taking those days
+
+ align:start position:0%
+kind of account for taking those days
+ 
+
+ align:start position:0%
+kind of account for taking those days
+off because they're not running at full
+
+ align:start position:0%
+off because they're not running at full
+ 
+
+ align:start position:0%
+off because they're not running at full
+capacity all the time anyway the case
+
+ align:start position:0%
+capacity all the time anyway the case
+ 
+
+ align:start position:0%
+capacity all the time anyway the case
+the case leads you to some optimism yes
+
+ align:start position:0%
+the case leads you to some optimism yes
+ 
+
+ align:start position:0%
+the case leads you to some optimism yes
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+then I mean additionally you can just go
+
+ align:start position:0%
+then I mean additionally you can just go
+ 
+
+ align:start position:0%
+then I mean additionally you can just go
+back to the handy argument that
+
+ align:start position:0%
+back to the handy argument that
+ 
+
+ align:start position:0%
+back to the handy argument that
+businesses need to produce money but
+
+ align:start position:0%
+businesses need to produce money but
+ 
+
+ align:start position:0%
+businesses need to produce money but
+they don't necessarily need to maximize
+
+ align:start position:0%
+they don't necessarily need to maximize
+ 
+
+ align:start position:0%
+they don't necessarily need to maximize
+their funding we can do this because but
+
+ align:start position:0%
+their funding we can do this because but
+ 
+
+ align:start position:0%
+their funding we can do this because but
+this isn't about this this last point
+
+ align:start position:0%
+this isn't about this this last point
+ 
+
+ align:start position:0%
+this isn't about this this last point
+isn't about the business it's about my
+
+ align:start position:0%
+isn't about the business it's about my
+ 
+
+ align:start position:0%
+isn't about the business it's about my
+trip to the Caribbean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+care about
+
+ align:start position:0%
+care about
+ 
+
+ align:start position:0%
+care about
+that this one's tough I don't mean to
+
+ align:start position:0%
+that this one's tough I don't mean to
+ 
+
+ align:start position:0%
+that this one's tough I don't mean to
+put you particularly on the spot but
+
+ align:start position:0%
+put you particularly on the spot but
+ 
+
+ align:start position:0%
+put you particularly on the spot but
+this one's tough if you've got the
+
+ align:start position:0%
+this one's tough if you've got the
+ 
+
+ align:start position:0%
+this one's tough if you've got the
+compensation structure set in such a way
+
+ align:start position:0%
+compensation structure set in such a way
+ 
+
+ align:start position:0%
+compensation structure set in such a way
+that it biases toward growth and towards
+
+ align:start position:0%
+that it biases toward growth and towards
+ 
+
+ align:start position:0%
+that it biases toward growth and towards
+Revenue this is a tough one Charlotte
+
+ align:start position:0%
+Revenue this is a tough one Charlotte
+ 
+
+ align:start position:0%
+Revenue this is a tough one Charlotte
+you could go back to the point that we
+
+ align:start position:0%
+you could go back to the point that we
+ 
+
+ align:start position:0%
+you could go back to the point that we
+made on the the last objection where if
+
+ align:start position:0%
+made on the the last objection where if
+ 
+
+ align:start position:0%
+made on the the last objection where if
+you know you're the first plant to start
+
+ align:start position:0%
+you know you're the first plant to start
+ 
+
+ align:start position:0%
+you know you're the first plant to start
+uh something that saves your company 2%
+
+ align:start position:0%
+uh something that saves your company 2%
+ 
+
+ align:start position:0%
+uh something that saves your company 2%
+in revenue and it happens to other
+
+ align:start position:0%
+in revenue and it happens to other
+ 
+
+ align:start position:0%
+in revenue and it happens to other
+plants in
+
+ align:start position:0%
+plants in
+ 
+
+ align:start position:0%
+plants in
+organ the heads of organization will
+
+ align:start position:0%
+organ the heads of organization will
+ 
+
+ align:start position:0%
+organ the heads of organization will
+look favly on you and in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later we can get a bigger bonus if we
+
+ align:start position:0%
+later we can get a bigger bonus if we
+ 
+
+ align:start position:0%
+later we can get a bigger bonus if we
+can sell
+
+ align:start position:0%
+can sell
+ 
+
+ align:start position:0%
+can sell
+this tough argument it's one you'd try
+
+ align:start position:0%
+this tough argument it's one you'd try
+ 
+
+ align:start position:0%
+this tough argument it's one you'd try
+though David you also get a promotion if
+
+ align:start position:0%
+though David you also get a promotion if
+ 
+
+ align:start position:0%
+though David you also get a promotion if
+you can demonstrate initiative and
+
+ align:start position:0%
+you can demonstrate initiative and
+ 
+
+ align:start position:0%
+you can demonstrate initiative and
+larger scale thinking and if you don't
+
+ align:start position:0%
+larger scale thinking and if you don't
+ 
+
+ align:start position:0%
+larger scale thinking and if you don't
+do it and someone else implements it
+
+ align:start position:0%
+do it and someone else implements it
+ 
+
+ align:start position:0%
+do it and someone else implements it
+they might displace
+
+ align:start position:0%
+they might displace
+ 
+
+ align:start position:0%
+they might displace
+you it works for Dar it might not work
+
+ align:start position:0%
+you it works for Dar it might not work
+ 
+
+ align:start position:0%
+you it works for Dar it might not work
+for the guys one notch above Darren it
+
+ align:start position:0%
+for the guys one notch above Darren it
+ 
+
+ align:start position:0%
+for the guys one notch above Darren it
+might though it might look if you guys
+
+ align:start position:0%
+might though it might look if you guys
+ 
+
+ align:start position:0%
+might though it might look if you guys
+all get behind this we'll all ride up
+
+ align:start position:0%
+all get behind this we'll all ride up
+ 
+
+ align:start position:0%
+all get behind this we'll all ride up
+right up the ladder together Martha um
+
+ align:start position:0%
+right up the ladder together Martha um
+ 
+
+ align:start position:0%
+right up the ladder together Martha um
+going back to what was said about how
+
+ align:start position:0%
+going back to what was said about how
+ 
+
+ align:start position:0%
+going back to what was said about how
+after your investment was returned
+
+ align:start position:0%
+after your investment was returned
+ 
+
+ align:start position:0%
+after your investment was returned
+you'll be continuing to save money so
+
+ align:start position:0%
+you'll be continuing to save money so
+ 
+
+ align:start position:0%
+you'll be continuing to save money so
+youron us may be less this year but it
+
+ align:start position:0%
+youron us may be less this year but it
+ 
+
+ align:start position:0%
+youron us may be less this year but it
+may be much greater in future years when
+
+ align:start position:0%
+may be much greater in future years when
+ 
+
+ align:start position:0%
+may be much greater in future years when
+we're able to start expanding that grow
+
+ align:start position:0%
+we're able to start expanding that grow
+ 
+
+ align:start position:0%
+we're able to start expanding that grow
+we're able to start so maybe instead of
+
+ align:start position:0%
+we're able to start so maybe instead of
+ 
+
+ align:start position:0%
+we're able to start so maybe instead of
+going to the Caribbean this year you go
+
+ align:start position:0%
+going to the Caribbean this year you go
+ 
+
+ align:start position:0%
+going to the Caribbean this year you go
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+bail or
+
+ align:start position:0%
+bail or
+ 
+
+ align:start position:0%
+bail or
+something but five years down the road
+
+ align:start position:0%
+something but five years down the road
+ 
+
+ align:start position:0%
+something but five years down the road
+you could go to Jurassic Park I don't
+
+ align:start position:0%
+you could go to Jurassic Park I don't
+ 
+
+ align:start position:0%
+you could go to Jurassic Park I don't
+know they ski in the adx instead of
+
+ align:start position:0%
+know they ski in the adx instead of
+ 
+
+ align:start position:0%
+know they ski in the adx instead of
+skiing in Vermont I don't know okay um
+
+ align:start position:0%
+skiing in Vermont I don't know okay um
+ 
+
+ align:start position:0%
+skiing in Vermont I don't know okay um
+anybody
+
+ align:start position:0%
+anybody
+ 
+
+ align:start position:0%
+anybody
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um how about that the case talks about
+
+ align:start position:0%
+um how about that the case talks about
+ 
+
+ align:start position:0%
+um how about that the case talks about
+all these policies there's this kill
+
+ align:start position:0%
+all these policies there's this kill
+ 
+
+ align:start position:0%
+all these policies there's this kill
+switch
+
+ align:start position:0%
+switch
+ 
+
+ align:start position:0%
+switch
+problem uh there are other polic I about
+
+ align:start position:0%
+problem uh there are other polic I about
+ 
+
+ align:start position:0%
+problem uh there are other polic I about
+interconnection they're still in flux
+
+ align:start position:0%
+interconnection they're still in flux
+ 
+
+ align:start position:0%
+interconnection they're still in flux
+maybe what we ought to do it's good idea
+
+ align:start position:0%
+maybe what we ought to do it's good idea
+ 
+
+ align:start position:0%
+maybe what we ought to do it's good idea
+okay you've sold me it's a good idea why
+
+ align:start position:0%
+okay you've sold me it's a good idea why
+ 
+
+ align:start position:0%
+okay you've sold me it's a good idea why
+don't we just
+
+ align:start position:0%
+don't we just
+ 
+
+ align:start position:0%
+don't we just
+wait let's just let this stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+settle you know maybe they'll maybe if
+
+ align:start position:0%
+settle you know maybe they'll maybe if
+ 
+
+ align:start position:0%
+settle you know maybe they'll maybe if
+we do it now we'll have to take
+
+ align:start position:0%
+we do it now we'll have to take
+ 
+
+ align:start position:0%
+we do it now we'll have to take
+precautions we wouldn't have to take if
+
+ align:start position:0%
+precautions we wouldn't have to take if
+ 
+
+ align:start position:0%
+precautions we wouldn't have to take if
+they apply more sensible policies down
+
+ align:start position:0%
+they apply more sensible policies down
+ 
+
+ align:start position:0%
+they apply more sensible policies down
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+road David you none of the competitors
+
+ align:start position:0%
+road David you none of the competitors
+ 
+
+ align:start position:0%
+road David you none of the competitors
+are doing it now so doing it now us a
+
+ align:start position:0%
+are doing it now so doing it now us a
+ 
+
+ align:start position:0%
+are doing it now so doing it now us a
+competitive Advantage versus in the
+
+ align:start position:0%
+competitive Advantage versus in the
+ 
+
+ align:start position:0%
+competitive Advantage versus in the
+future compe have already introduced
+
+ align:start position:0%
+future compe have already introduced
+ 
+
+ align:start position:0%
+future compe have already introduced
+itat well we are but suppose the policy
+
+ align:start position:0%
+itat well we are but suppose the policy
+ 
+
+ align:start position:0%
+itat well we are but suppose the policy
+goes against us suppose instead of
+
+ align:start position:0%
+goes against us suppose instead of
+ 
+
+ align:start position:0%
+goes against us suppose instead of
+making it easier to interconnect that
+
+ align:start position:0%
+making it easier to interconnect that
+ 
+
+ align:start position:0%
+making it easier to interconnect that
+the policy change makes it harder
+
+ align:start position:0%
+the policy change makes it harder
+ 
+
+ align:start position:0%
+the policy change makes it harder
+requires us to put on more protective
+
+ align:start position:0%
+requires us to put on more protective
+ 
+
+ align:start position:0%
+requires us to put on more protective
+devices or let's say $200,000 worth uh
+
+ align:start position:0%
+devices or let's say $200,000 worth uh
+ 
+
+ align:start position:0%
+devices or let's say $200,000 worth uh
+and then all of a sudden it's that's
+
+ align:start position:0%
+and then all of a sudden it's that's
+ 
+
+ align:start position:0%
+and then all of a sudden it's that's
+that's extreme but
+
+ align:start position:0%
+that's extreme but
+ 
+
+ align:start position:0%
+that's extreme but
+but uh all of a sudden the policies we
+
+ align:start position:0%
+but uh all of a sudden the policies we
+ 
+
+ align:start position:0%
+but uh all of a sudden the policies we
+were counting on the ability to sell
+
+ align:start position:0%
+were counting on the ability to sell
+ 
+
+ align:start position:0%
+were counting on the ability to sell
+Excess power which is still in flux at
+
+ align:start position:0%
+Excess power which is still in flux at
+ 
+
+ align:start position:0%
+Excess power which is still in flux at
+this point um turns out we can't sell it
+
+ align:start position:0%
+this point um turns out we can't sell it
+ 
+
+ align:start position:0%
+this point um turns out we can't sell it
+turns out we need to have more
+
+ align:start position:0%
+turns out we need to have more
+ 
+
+ align:start position:0%
+turns out we need to have more
+protection maybe we should
+
+ align:start position:0%
+protection maybe we should
+ 
+
+ align:start position:0%
+protection maybe we should
+wait Claudia what do you
+
+ align:start position:0%
+wait Claudia what do you
+ 
+
+ align:start position:0%
+wait Claudia what do you
+say you sold you sold with the Skeptics
+
+ align:start position:0%
+say you sold you sold with the Skeptics
+ 
+
+ align:start position:0%
+say you sold you sold with the Skeptics
+I mean that's not a crazy point
+
+ align:start position:0%
+I mean that's not a crazy point
+ 
+
+ align:start position:0%
+I mean that's not a crazy point
+no is it is there a chance to like
+
+ align:start position:0%
+no is it is there a chance to like
+ 
+
+ align:start position:0%
+no is it is there a chance to like
+approach local Regulators directly and
+
+ align:start position:0%
+approach local Regulators directly and
+ 
+
+ align:start position:0%
+approach local Regulators directly and
+just make
+
+ align:start position:0%
+just make
+ 
+
+ align:start position:0%
+just make
+it well one thing Darren might have done
+
+ align:start position:0%
+it well one thing Darren might have done
+ 
+
+ align:start position:0%
+it well one thing Darren might have done
+is he might have not necessarily
+
+ align:start position:0%
+is he might have not necessarily
+ 
+
+ align:start position:0%
+is he might have not necessarily
+approached them but he might try to get
+
+ align:start position:0%
+approached them but he might try to get
+ 
+
+ align:start position:0%
+approached them but he might try to get
+a feel from say his local representative
+
+ align:start position:0%
+a feel from say his local representative
+ 
+
+ align:start position:0%
+a feel from say his local representative
+a lot of this stuff is going on at the
+
+ align:start position:0%
+a lot of this stuff is going on at the
+ 
+
+ align:start position:0%
+a lot of this stuff is going on at the
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+level he's running a pretty big pretty
+
+ align:start position:0%
+level he's running a pretty big pretty
+ 
+
+ align:start position:0%
+level he's running a pretty big pretty
+big operation he's one of the great
+
+ align:start position:0%
+big operation he's one of the great
+ 
+
+ align:start position:0%
+big operation he's one of the great
+polluters no one of the great great
+
+ align:start position:0%
+polluters no one of the great great
+ 
+
+ align:start position:0%
+polluters no one of the great great
+operations in the area might make a
+
+ align:start position:0%
+operations in the area might make a
+ 
+
+ align:start position:0%
+operations in the area might make a
+phone call and say look can you tell me
+
+ align:start position:0%
+phone call and say look can you tell me
+ 
+
+ align:start position:0%
+phone call and say look can you tell me
+where this stuff stands I mean are we
+
+ align:start position:0%
+where this stuff stands I mean are we
+ 
+
+ align:start position:0%
+where this stuff stands I mean are we
+going to get we going to is it going to
+
+ align:start position:0%
+going to get we going to is it going to
+ 
+
+ align:start position:0%
+going to get we going to is it going to
+get resolved in 6 months or is this a
+
+ align:start position:0%
+get resolved in 6 months or is this a
+ 
+
+ align:start position:0%
+get resolved in 6 months or is this a
+5year marathon and it'll get changed
+
+ align:start position:0%
+5year marathon and it'll get changed
+ 
+
+ align:start position:0%
+5year marathon and it'll get changed
+every so often that matters if it's
+
+ align:start position:0%
+every so often that matters if it's
+ 
+
+ align:start position:0%
+every so often that matters if it's
+going to get resolved in six months
+
+ align:start position:0%
+going to get resolved in six months
+ 
+
+ align:start position:0%
+going to get resolved in six months
+let's wait if it's if it's going to be
+
+ align:start position:0%
+let's wait if it's if it's going to be
+ 
+
+ align:start position:0%
+let's wait if it's if it's going to be
+debated for the next 10 years why wait
+
+ align:start position:0%
+debated for the next 10 years why wait
+ 
+
+ align:start position:0%
+debated for the next 10 years why wait
+Ariana I think this is where it would
+
+ align:start position:0%
+Ariana I think this is where it would
+ 
+
+ align:start position:0%
+Ariana I think this is where it would
+have come in useful for him to have made
+
+ align:start position:0%
+have come in useful for him to have made
+ 
+
+ align:start position:0%
+have come in useful for him to have made
+a more pessimistic analysis um and so
+
+ align:start position:0%
+a more pessimistic analysis um and so
+ 
+
+ align:start position:0%
+a more pessimistic analysis um and so
+maybe you know you do that first and
+
+ align:start position:0%
+maybe you know you do that first and
+ 
+
+ align:start position:0%
+maybe you know you do that first and
+then you say like okay well um because I
+
+ align:start position:0%
+then you say like okay well um because I
+ 
+
+ align:start position:0%
+then you say like okay well um because I
+mean when we looked at it it looked like
+
+ align:start position:0%
+mean when we looked at it it looked like
+ 
+
+ align:start position:0%
+mean when we looked at it it looked like
+even if some of the um estimates were a
+
+ align:start position:0%
+even if some of the um estimates were a
+ 
+
+ align:start position:0%
+even if some of the um estimates were a
+little bit more pessimistic or you
+
+ align:start position:0%
+little bit more pessimistic or you
+ 
+
+ align:start position:0%
+little bit more pessimistic or you
+couldn't get the grant that you wanted
+
+ align:start position:0%
+couldn't get the grant that you wanted
+ 
+
+ align:start position:0%
+couldn't get the grant that you wanted
+maybe um or you like estimated it with
+
+ align:start position:0%
+maybe um or you like estimated it with
+ 
+
+ align:start position:0%
+maybe um or you like estimated it with
+some of the policies not falling your
+
+ align:start position:0%
+some of the policies not falling your
+ 
+
+ align:start position:0%
+some of the policies not falling your
+way and you could still maybe like the
+
+ align:start position:0%
+way and you could still maybe like the
+ 
+
+ align:start position:0%
+way and you could still maybe like the
+profit wouldn't be as large but in the
+
+ align:start position:0%
+profit wouldn't be as large but in the
+ 
+
+ align:start position:0%
+profit wouldn't be as large but in the
+long run it's still worth it then you
+
+ align:start position:0%
+long run it's still worth it then you
+ 
+
+ align:start position:0%
+long run it's still worth it then you
+could come and say like look this is
+
+ align:start position:0%
+could come and say like look this is
+ 
+
+ align:start position:0%
+could come and say like look this is
+what I think is going to happen but even
+
+ align:start position:0%
+what I think is going to happen but even
+ 
+
+ align:start position:0%
+what I think is going to happen but even
+if I mean you never really know and even
+
+ align:start position:0%
+if I mean you never really know and even
+ 
+
+ align:start position:0%
+if I mean you never really know and even
+if it goes a little bit sour like we
+
+ align:start position:0%
+if it goes a little bit sour like we
+ 
+
+ align:start position:0%
+if it goes a little bit sour like we
+still are making some kind of profit so
+
+ align:start position:0%
+still are making some kind of profit so
+ 
+
+ align:start position:0%
+still are making some kind of profit so
+like it's it's worth it
+
+ align:start position:0%
+like it's it's worth it
+ 
+
+ align:start position:0%
+like it's it's worth it
+anyway okay let me go to one last one
+
+ align:start position:0%
+anyway okay let me go to one last one
+ 
+
+ align:start position:0%
+anyway okay let me go to one last one
+who'd like to make the elevator
+
+ align:start position:0%
+who'd like to make the elevator
+ 
+
+ align:start position:0%
+who'd like to make the elevator
+pitch is there a spin he can put on this
+
+ align:start position:0%
+pitch is there a spin he can put on this
+ 
+
+ align:start position:0%
+pitch is there a spin he can put on this
+so so he's he walked in with his
+
+ align:start position:0%
+so so he's he walked in with his
+ 
+
+ align:start position:0%
+so so he's he walked in with his
+spreadsheet he got all these arguments
+
+ align:start position:0%
+spreadsheet he got all these arguments
+ 
+
+ align:start position:0%
+spreadsheet he got all these arguments
+all these naysaying
+
+ align:start position:0%
+all these naysaying
+ 
+
+ align:start position:0%
+all these naysaying
+nitpickers what do you stand up and
+
+ align:start position:0%
+nitpickers what do you stand up and
+ 
+
+ align:start position:0%
+nitpickers what do you stand up and
+say what do you stand up and say
+
+ align:start position:0%
+say what do you stand up and say
+ 
+
+ align:start position:0%
+say what do you stand up and say
+Caroline are you ready with an elevator
+
+ align:start position:0%
+Caroline are you ready with an elevator
+ 
+
+ align:start position:0%
+Caroline are you ready with an elevator
+pitch here you ready with a one minute
+
+ align:start position:0%
+pitch here you ready with a one minute
+ 
+
+ align:start position:0%
+pitch here you ready with a one minute
+speech to to make the committee turn
+
+ align:start position:0%
+speech to to make the committee turn
+ 
+
+ align:start position:0%
+speech to to make the committee turn
+around and charge out the door and go to
+
+ align:start position:0%
+around and charge out the door and go to
+ 
+
+ align:start position:0%
+around and charge out the door and go to
+the CEO and do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it not quite ready okay anybody AA
+
+ align:start position:0%
+it not quite ready okay anybody AA
+ 
+
+ align:start position:0%
+it not quite ready okay anybody AA
+you're ready today okay that's good so
+
+ align:start position:0%
+you're ready today okay that's good so
+ 
+
+ align:start position:0%
+you're ready today okay that's good so
+uh sorry to disappoint you I don't have
+
+ align:start position:0%
+uh sorry to disappoint you I don't have
+ 
+
+ align:start position:0%
+uh sorry to disappoint you I don't have
+an elevator pitch but I'm I'm curious as
+
+ align:start position:0%
+an elevator pitch but I'm I'm curious as
+ 
+
+ align:start position:0%
+an elevator pitch but I'm I'm curious as
+to what the outcome was of this case
+
+ align:start position:0%
+to what the outcome was of this case
+ 
+
+ align:start position:0%
+to what the outcome was of this case
+because it's just not these AR let me
+
+ align:start position:0%
+because it's just not these AR let me
+ 
+
+ align:start position:0%
+because it's just not these AR let me
+fish one more time for an elevator pitch
+
+ align:start position:0%
+fish one more time for an elevator pitch
+ 
+
+ align:start position:0%
+fish one more time for an elevator pitch
+and then I'll and then I'll tell you
+
+ align:start position:0%
+and then I'll and then I'll tell you
+ 
+
+ align:start position:0%
+and then I'll and then I'll tell you
+what I think happened which is not
+
+ align:start position:0%
+what I think happened which is not
+ 
+
+ align:start position:0%
+what I think happened which is not
+unrelated to that question Max um you
+
+ align:start position:0%
+unrelated to that question Max um you
+ 
+
+ align:start position:0%
+unrelated to that question Max um you
+want to appeal to the interest of the
+
+ align:start position:0%
+want to appeal to the interest of the
+ 
+
+ align:start position:0%
+want to appeal to the interest of the
+board and their interest is obviously
+
+ align:start position:0%
+board and their interest is obviously
+ 
+
+ align:start position:0%
+board and their interest is obviously
+production and maximizing profit so
+
+ align:start position:0%
+production and maximizing profit so
+ 
+
+ align:start position:0%
+production and maximizing profit so
+emphasizing the fact that this
+
+ align:start position:0%
+emphasizing the fact that this
+ 
+
+ align:start position:0%
+emphasizing the fact that this
+short-term investment will save a lot of
+
+ align:start position:0%
+short-term investment will save a lot of
+ 
+
+ align:start position:0%
+short-term investment will save a lot of
+money in the long run which you can in
+
+ align:start position:0%
+money in the long run which you can in
+ 
+
+ align:start position:0%
+money in the long run which you can in
+turn invest in Creer production in the
+
+ align:start position:0%
+turn invest in Creer production in the
+ 
+
+ align:start position:0%
+turn invest in Creer production in the
+future which will give them bigger
+
+ align:start position:0%
+future which will give them bigger
+ 
+
+ align:start position:0%
+future which will give them bigger
+bonuses you could also appeal I think
+
+ align:start position:0%
+bonuses you could also appeal I think
+ 
+
+ align:start position:0%
+bonuses you could also appeal I think
+for it deals with a couple of points to
+
+ align:start position:0%
+for it deals with a couple of points to
+ 
+
+ align:start position:0%
+for it deals with a couple of points to
+the safety of the workers and to the
+
+ align:start position:0%
+the safety of the workers and to the
+ 
+
+ align:start position:0%
+the safety of the workers and to the
+Integrity of the whole plan so know in
+
+ align:start position:0%
+Integrity of the whole plan so know in
+ 
+
+ align:start position:0%
+Integrity of the whole plan so know in
+the article it talked about the ice
+
+ align:start position:0%
+the article it talked about the ice
+ 
+
+ align:start position:0%
+the article it talked about the ice
+being a hazard for the workers and the
+
+ align:start position:0%
+being a hazard for the workers and the
+ 
+
+ align:start position:0%
+being a hazard for the workers and the
+corosion of some of the uh structure of
+
+ align:start position:0%
+corosion of some of the uh structure of
+ 
+
+ align:start position:0%
+corosion of some of the uh structure of
+the building spin it that way as well
+
+ align:start position:0%
+the building spin it that way as well
+ 
+
+ align:start position:0%
+the building spin it that way as well
+what I think happened and it's not
+
+ align:start position:0%
+what I think happened and it's not
+ 
+
+ align:start position:0%
+what I think happened and it's not
+unrelated to that my my understanding
+
+ align:start position:0%
+unrelated to that my my understanding
+ 
+
+ align:start position:0%
+unrelated to that my my understanding
+and I've tried to verify it and I'll see
+
+ align:start position:0%
+and I've tried to verify it and I'll see
+ 
+
+ align:start position:0%
+and I've tried to verify it and I'll see
+if I can do it next time um is that in
+
+ align:start position:0%
+if I can do it next time um is that in
+ 
+
+ align:start position:0%
+if I can do it next time um is that in
+fact when he presented it to the review
+
+ align:start position:0%
+fact when he presented it to the review
+ 
+
+ align:start position:0%
+fact when he presented it to the review
+operation it was turned down for sort of
+
+ align:start position:0%
+operation it was turned down for sort of
+ 
+
+ align:start position:0%
+operation it was turned down for sort of
+all of those
+
+ align:start position:0%
+all of those
+ 
+
+ align:start position:0%
+all of those
+reasons uh and he
+
+ align:start position:0%
+reasons uh and he
+ 
+
+ align:start position:0%
+reasons uh and he
+managed uh to get the ear one way or
+
+ align:start position:0%
+managed uh to get the ear one way or
+ 
+
+ align:start position:0%
+managed uh to get the ear one way or
+another of the CEO when he pitched it as
+
+ align:start position:0%
+another of the CEO when he pitched it as
+ 
+
+ align:start position:0%
+another of the CEO when he pitched it as
+industry
+
+ align:start position:0%
+industry
+ 
+
+ align:start position:0%
+industry
+leadership green public relations
+
+ align:start position:0%
+leadership green public relations
+ 
+
+ align:start position:0%
+leadership green public relations
+economics are okay economics are pretty
+
+ align:start position:0%
+economics are okay economics are pretty
+ 
+
+ align:start position:0%
+economics are okay economics are pretty
+good uh so you don't we're not going to
+
+ align:start position:0%
+good uh so you don't we're not going to
+ 
+
+ align:start position:0%
+good uh so you don't we're not going to
+lose money on this investment but
+
+ align:start position:0%
+lose money on this investment but
+ 
+
+ align:start position:0%
+lose money on this investment but
+moreover think about what we can say to
+
+ align:start position:0%
+moreover think about what we can say to
+ 
+
+ align:start position:0%
+moreover think about what we can say to
+the community think about what we can
+
+ align:start position:0%
+the community think about what we can
+ 
+
+ align:start position:0%
+the community think about what we can
+say to the workers think about what you
+
+ align:start position:0%
+say to the workers think about what you
+ 
+
+ align:start position:0%
+say to the workers think about what you
+can say at the next industry convention
+
+ align:start position:0%
+can say at the next industry convention
+ 
+
+ align:start position:0%
+can say at the next industry convention
+when you stand up and give your
+
+ align:start position:0%
+when you stand up and give your
+ 
+
+ align:start position:0%
+when you stand up and give your
+leadership
+
+ align:start position:0%
+leadership
+ 
+
+ align:start position:0%
+leadership
+speech um we'll get benefits I mean
+
+ align:start position:0%
+speech um we'll get benefits I mean
+ 
+
+ align:start position:0%
+speech um we'll get benefits I mean
+we're vetting steam it's not hurting
+
+ align:start position:0%
+we're vetting steam it's not hurting
+ 
+
+ align:start position:0%
+we're vetting steam it's not hurting
+anybody but it doesn't look good it's
+
+ align:start position:0%
+anybody but it doesn't look good it's
+ 
+
+ align:start position:0%
+anybody but it doesn't look good it's
+going to look better so he went around
+
+ align:start position:0%
+going to look better so he went around
+ 
+
+ align:start position:0%
+going to look better so he went around
+these guys is my understanding and
+
+ align:start position:0%
+these guys is my understanding and
+ 
+
+ align:start position:0%
+these guys is my understanding and
+pitched it as an
+
+ align:start position:0%
+pitched it as an
+ 
+
+ align:start position:0%
+pitched it as an
+opportunity as an and not just an
+
+ align:start position:0%
+opportunity as an and not just an
+ 
+
+ align:start position:0%
+opportunity as an and not just an
+Economic Opportunity he he overstated
+
+ align:start position:0%
+Economic Opportunity he he overstated
+ 
+
+ align:start position:0%
+Economic Opportunity he he overstated
+the economics economics are
+
+ align:start position:0%
+the economics economics are
+ 
+
+ align:start position:0%
+the economics economics are
+okay but he pitched it as an opportunity
+
+ align:start position:0%
+okay but he pitched it as an opportunity
+ 
+
+ align:start position:0%
+okay but he pitched it as an opportunity
+and we'll see next week and we will see
+
+ align:start position:0%
+and we'll see next week and we will see
+ 
+
+ align:start position:0%
+and we'll see next week and we will see
+after the vacation that whether you view
+
+ align:start position:0%
+after the vacation that whether you view
+ 
+
+ align:start position:0%
+after the vacation that whether you view
+something as a threat or an oper
+
+ align:start position:0%
+something as a threat or an oper
+ 
+
+ align:start position:0%
+something as a threat or an oper
+opportunity makes a lot of difference as
+
+ align:start position:0%
+opportunity makes a lot of difference as
+ 
+
+ align:start position:0%
+opportunity makes a lot of difference as
+to how you act on it thank you very much
\ No newline at end of file
diff --git a/YD7QG4G7WVg.txt b/YD7QG4G7WVg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4de88593620a2805bafc80eb7a2679328ab908a9
--- /dev/null
+++ b/YD7QG4G7WVg.txt
@@ -0,0 +1,16368 @@
+align:start position:0%
+ 
+all right 1105 let's get started so the
+
+ align:start position:0%
+all right 1105 let's get started so the
+ 
+
+ align:start position:0%
+all right 1105 let's get started so the
+agenda for today we're doing this whole
+
+ align:start position:0%
+agenda for today we're doing this whole
+ 
+
+ align:start position:0%
+agenda for today we're doing this whole
+thing on the methods in human cognitive
+
+ align:start position:0%
+thing on the methods in human cognitive
+ 
+
+ align:start position:0%
+thing on the methods in human cognitive
+neuroscience and i'm illustrating those
+
+ align:start position:0%
+neuroscience and i'm illustrating those
+ 
+
+ align:start position:0%
+neuroscience and i'm illustrating those
+methods with the case of face perception
+
+ align:start position:0%
+methods with the case of face perception
+ 
+
+ align:start position:0%
+methods with the case of face perception
+not just because i'm into face
+
+ align:start position:0%
+not just because i'm into face
+ 
+
+ align:start position:0%
+not just because i'm into face
+perception but it's like a particularly
+
+ align:start position:0%
+perception but it's like a particularly
+ 
+
+ align:start position:0%
+perception but it's like a particularly
+rich
+
+ align:start position:0%
+rich
+ 
+
+ align:start position:0%
+rich
+domain of research where there's lots
+
+ align:start position:0%
+domain of research where there's lots
+ 
+
+ align:start position:0%
+domain of research where there's lots
+lots to say about it from all these
+
+ align:start position:0%
+lots to say about it from all these
+ 
+
+ align:start position:0%
+lots to say about it from all these
+different methods and so last time we
+
+ align:start position:0%
+different methods and so last time we
+ 
+
+ align:start position:0%
+different methods and so last time we
+talked a bit about applying mars
+
+ align:start position:0%
+talked a bit about applying mars
+ 
+
+ align:start position:0%
+talked a bit about applying mars
+computational theory level to face
+
+ align:start position:0%
+computational theory level to face
+ 
+
+ align:start position:0%
+computational theory level to face
+perception we talked a teeny bit about
+
+ align:start position:0%
+perception we talked a teeny bit about
+ 
+
+ align:start position:0%
+perception we talked a teeny bit about
+some behavioral data and a little bit
+
+ align:start position:0%
+some behavioral data and a little bit
+ 
+
+ align:start position:0%
+some behavioral data and a little bit
+about functional mri what i'm going to
+
+ align:start position:0%
+about functional mri what i'm going to
+ 
+
+ align:start position:0%
+about functional mri what i'm going to
+do today is quickly zoom through
+
+ align:start position:0%
+do today is quickly zoom through
+ 
+
+ align:start position:0%
+do today is quickly zoom through
+speed speeded-up review of those things
+
+ align:start position:0%
+speed speeded-up review of those things
+ 
+
+ align:start position:0%
+speed speeded-up review of those things
+and then we're going to get to some of
+
+ align:start position:0%
+and then we're going to get to some of
+ 
+
+ align:start position:0%
+and then we're going to get to some of
+these other methods and there's a quiz
+
+ align:start position:0%
+these other methods and there's a quiz
+ 
+
+ align:start position:0%
+these other methods and there's a quiz
+at the end all right
+
+ align:start position:0%
+at the end all right
+ 
+
+ align:start position:0%
+at the end all right
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+methods in
+
+ align:start position:0%
+methods in
+ 
+
+ align:start position:0%
+methods in
+in any field of science are just there
+
+ align:start position:0%
+in any field of science are just there
+ 
+
+ align:start position:0%
+in any field of science are just there
+to enable us to answer scientific
+
+ align:start position:0%
+to enable us to answer scientific
+ 
+
+ align:start position:0%
+to enable us to answer scientific
+questions they're not to you know
+
+ align:start position:0%
+questions they're not to you know
+ 
+
+ align:start position:0%
+questions they're not to you know
+impress our friends with all the fancy
+
+ align:start position:0%
+impress our friends with all the fancy
+ 
+
+ align:start position:0%
+impress our friends with all the fancy
+things we know how to do or our
+
+ align:start position:0%
+things we know how to do or our
+ 
+
+ align:start position:0%
+things we know how to do or our
+colleagues
+
+ align:start position:0%
+colleagues
+ 
+
+ align:start position:0%
+colleagues
+they're just to answer questions and so
+
+ align:start position:0%
+they're just to answer questions and so
+ 
+
+ align:start position:0%
+they're just to answer questions and so
+you always have to start with the
+
+ align:start position:0%
+you always have to start with the
+ 
+
+ align:start position:0%
+you always have to start with the
+questions and so last time i listed a
+
+ align:start position:0%
+questions and so last time i listed a
+ 
+
+ align:start position:0%
+questions and so last time i listed a
+bunch of questions not all of them but a
+
+ align:start position:0%
+bunch of questions not all of them but a
+ 
+
+ align:start position:0%
+bunch of questions not all of them but a
+bunch of questions one would really want
+
+ align:start position:0%
+bunch of questions one would really want
+ 
+
+ align:start position:0%
+bunch of questions one would really want
+to know about face perception if we were
+
+ align:start position:0%
+to know about face perception if we were
+ 
+
+ align:start position:0%
+to know about face perception if we were
+to understand how it works in the brain
+
+ align:start position:0%
+to understand how it works in the brain
+ 
+
+ align:start position:0%
+to understand how it works in the brain
+and last time we focused on these first
+
+ align:start position:0%
+and last time we focused on these first
+ 
+
+ align:start position:0%
+and last time we focused on these first
+three so let me just do super quick
+
+ align:start position:0%
+three so let me just do super quick
+ 
+
+ align:start position:0%
+three so let me just do super quick
+review
+
+ align:start position:0%
+review
+ 
+
+ align:start position:0%
+review
+questions at the level of mars
+
+ align:start position:0%
+questions at the level of mars
+ 
+
+ align:start position:0%
+questions at the level of mars
+computational theory we ask
+
+ align:start position:0%
+computational theory we ask
+ 
+
+ align:start position:0%
+computational theory we ask
+what is the problem that's being solved
+
+ align:start position:0%
+what is the problem that's being solved
+ 
+
+ align:start position:0%
+what is the problem that's being solved
+and why is that important to the
+
+ align:start position:0%
+and why is that important to the
+ 
+
+ align:start position:0%
+and why is that important to the
+organism
+
+ align:start position:0%
+organism
+ 
+
+ align:start position:0%
+organism
+what is the input what is the output how
+
+ align:start position:0%
+what is the input what is the output how
+ 
+
+ align:start position:0%
+what is the input what is the output how
+much you get from that input to that
+
+ align:start position:0%
+much you get from that input to that
+ 
+
+ align:start position:0%
+much you get from that input to that
+output right so for the case of face
+
+ align:start position:0%
+output right so for the case of face
+ 
+
+ align:start position:0%
+output right so for the case of face
+perception here's a very simple version
+
+ align:start position:0%
+perception here's a very simple version
+ 
+
+ align:start position:0%
+perception here's a very simple version
+of it here's an example of the input
+
+ align:start position:0%
+of it here's an example of the input
+ 
+
+ align:start position:0%
+of it here's an example of the input
+goes in hits the retina
+
+ align:start position:0%
+goes in hits the retina
+ 
+
+ align:start position:0%
+goes in hits the retina
+the stuff that we want to understand
+
+ align:start position:0%
+the stuff that we want to understand
+ 
+
+ align:start position:0%
+the stuff that we want to understand
+happens in here and you have an output
+
+ align:start position:0%
+happens in here and you have an output
+ 
+
+ align:start position:0%
+happens in here and you have an output
+okay so just even thinking about it that
+
+ align:start position:0%
+okay so just even thinking about it that
+ 
+
+ align:start position:0%
+okay so just even thinking about it that
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+we can already just see with common
+
+ align:start position:0%
+we can already just see with common
+ 
+
+ align:start position:0%
+we can already just see with common
+sense that one of the big challenges in
+
+ align:start position:0%
+sense that one of the big challenges in
+ 
+
+ align:start position:0%
+sense that one of the big challenges in
+solving this problem
+
+ align:start position:0%
+solving this problem
+ 
+
+ align:start position:0%
+solving this problem
+is that faces look different every time
+
+ align:start position:0%
+is that faces look different every time
+ 
+
+ align:start position:0%
+is that faces look different every time
+you see them
+
+ align:start position:0%
+you see them
+ 
+
+ align:start position:0%
+you see them
+the lighting changes the orientation of
+
+ align:start position:0%
+the lighting changes the orientation of
+ 
+
+ align:start position:0%
+the lighting changes the orientation of
+the face changes the hair changes the
+
+ align:start position:0%
+the face changes the hair changes the
+ 
+
+ align:start position:0%
+the face changes the hair changes the
+mood changes all this stuff happens
+
+ align:start position:0%
+mood changes all this stuff happens
+ 
+
+ align:start position:0%
+mood changes all this stuff happens
+people put on makeup they shave off
+
+ align:start position:0%
+people put on makeup they shave off
+ 
+
+ align:start position:0%
+people put on makeup they shave off
+their facial hair they do all these
+
+ align:start position:0%
+their facial hair they do all these
+ 
+
+ align:start position:0%
+their facial hair they do all these
+things to make it a real a big challenge
+
+ align:start position:0%
+things to make it a real a big challenge
+ 
+
+ align:start position:0%
+things to make it a real a big challenge
+to recognize faces and yet we manage
+
+ align:start position:0%
+to recognize faces and yet we manage
+ 
+
+ align:start position:0%
+to recognize faces and yet we manage
+really well so how do we do that
+
+ align:start position:0%
+really well so how do we do that
+ 
+
+ align:start position:0%
+really well so how do we do that
+well our field has many methods to
+
+ align:start position:0%
+well our field has many methods to
+ 
+
+ align:start position:0%
+well our field has many methods to
+address this question
+
+ align:start position:0%
+address this question
+ 
+
+ align:start position:0%
+address this question
+last time i talked about one little
+
+ align:start position:0%
+last time i talked about one little
+ 
+
+ align:start position:0%
+last time i talked about one little
+example of a behavioral study simple
+
+ align:start position:0%
+example of a behavioral study simple
+ 
+
+ align:start position:0%
+example of a behavioral study simple
+cognitive psychology study measuring
+
+ align:start position:0%
+cognitive psychology study measuring
+ 
+
+ align:start position:0%
+cognitive psychology study measuring
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+where we showed that
+
+ align:start position:0%
+where we showed that
+ 
+
+ align:start position:0%
+where we showed that
+that the way people solve this problem
+
+ align:start position:0%
+that the way people solve this problem
+ 
+
+ align:start position:0%
+that the way people solve this problem
+is fundamentally different with people
+
+ align:start position:0%
+is fundamentally different with people
+ 
+
+ align:start position:0%
+is fundamentally different with people
+they know well and people they don't
+
+ align:start position:0%
+they know well and people they don't
+ 
+
+ align:start position:0%
+they know well and people they don't
+know well
+
+ align:start position:0%
+know well
+ 
+
+ align:start position:0%
+know well
+so i showed an example that you know all
+
+ align:start position:0%
+so i showed an example that you know all
+ 
+
+ align:start position:0%
+so i showed an example that you know all
+of you presumably would have no trouble
+
+ align:start position:0%
+of you presumably would have no trouble
+ 
+
+ align:start position:0%
+of you presumably would have no trouble
+saying determining that those are all
+
+ align:start position:0%
+saying determining that those are all
+ 
+
+ align:start position:0%
+saying determining that those are all
+pictures of the same person even though
+
+ align:start position:0%
+pictures of the same person even though
+ 
+
+ align:start position:0%
+pictures of the same person even though
+the pics at the pixel level they're
+
+ align:start position:0%
+the pics at the pixel level they're
+ 
+
+ align:start position:0%
+the pics at the pixel level they're
+wildly different
+
+ align:start position:0%
+wildly different
+ 
+
+ align:start position:0%
+wildly different
+and yet you have a hell of a time saying
+
+ align:start position:0%
+and yet you have a hell of a time saying
+ 
+
+ align:start position:0%
+and yet you have a hell of a time saying
+which of those images are of the same
+
+ align:start position:0%
+which of those images are of the same
+ 
+
+ align:start position:0%
+which of those images are of the same
+people and which aren't and so the point
+
+ align:start position:0%
+people and which aren't and so the point
+ 
+
+ align:start position:0%
+people and which aren't and so the point
+is that our ability to extract this
+
+ align:start position:0%
+is that our ability to extract this
+ 
+
+ align:start position:0%
+is that our ability to extract this
+invariant representation that is to
+
+ align:start position:0%
+invariant representation that is to
+ 
+
+ align:start position:0%
+invariant representation that is to
+figure out abstractly who is that
+
+ align:start position:0%
+figure out abstractly who is that
+ 
+
+ align:start position:0%
+figure out abstractly who is that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh is really well to figure out that any
+
+ align:start position:0%
+uh is really well to figure out that any
+ 
+
+ align:start position:0%
+uh is really well to figure out that any
+any of these images are the same as each
+
+ align:start position:0%
+any of these images are the same as each
+ 
+
+ align:start position:0%
+any of these images are the same as each
+other is much better for familiar than
+
+ align:start position:0%
+other is much better for familiar than
+ 
+
+ align:start position:0%
+other is much better for familiar than
+unfamiliar faces and that means we don't
+
+ align:start position:0%
+unfamiliar faces and that means we don't
+ 
+
+ align:start position:0%
+unfamiliar faces and that means we don't
+have a perfectly general ability to take
+
+ align:start position:0%
+have a perfectly general ability to take
+ 
+
+ align:start position:0%
+have a perfectly general ability to take
+any face and abstract out this
+
+ align:start position:0%
+any face and abstract out this
+ 
+
+ align:start position:0%
+any face and abstract out this
+completely of
+
+ align:start position:0%
+completely of
+ 
+
+ align:start position:0%
+completely of
+image independent version of it that's
+
+ align:start position:0%
+image independent version of it that's
+ 
+
+ align:start position:0%
+image independent version of it that's
+what invariant representation is yeah
+
+ align:start position:0%
+what invariant representation is yeah
+ 
+
+ align:start position:0%
+what invariant representation is yeah
+for the case of the dutch politicians
+
+ align:start position:0%
+for the case of the dutch politicians
+ 
+
+ align:start position:0%
+for the case of the dutch politicians
+did they like ever do this study on
+
+ align:start position:0%
+did they like ever do this study on
+ 
+
+ align:start position:0%
+did they like ever do this study on
+people who are like super
+
+ align:start position:0%
+people who are like super
+ 
+
+ align:start position:0%
+people who are like super
+recognizers uh i don't know about that
+
+ align:start position:0%
+recognizers uh i don't know about that
+ 
+
+ align:start position:0%
+recognizers uh i don't know about that
+but they did do it on um
+
+ align:start position:0%
+but they did do it on um
+ 
+
+ align:start position:0%
+but they did do it on um
+uh people who are professional
+
+ align:start position:0%
+uh people who are professional
+ 
+
+ align:start position:0%
+uh people who are professional
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh you know tsa type people
+
+ align:start position:0%
+uh you know tsa type people
+ 
+
+ align:start position:0%
+uh you know tsa type people
+right and i'll tell you guys about that
+
+ align:start position:0%
+right and i'll tell you guys about that
+ 
+
+ align:start position:0%
+right and i'll tell you guys about that
+later but you could think about you know
+
+ align:start position:0%
+later but you could think about you know
+ 
+
+ align:start position:0%
+later but you could think about you know
+you could think about whether you think
+
+ align:start position:0%
+you could think about whether you think
+ 
+
+ align:start position:0%
+you could think about whether you think
+it might work better with those people
+
+ align:start position:0%
+it might work better with those people
+ 
+
+ align:start position:0%
+it might work better with those people
+or not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay everybody get this general point
+
+ align:start position:0%
+okay everybody get this general point
+ 
+
+ align:start position:0%
+okay everybody get this general point
+here all right
+
+ align:start position:0%
+here all right
+ 
+
+ align:start position:0%
+here all right
+so i i skipped over another simple
+
+ align:start position:0%
+so i i skipped over another simple
+ 
+
+ align:start position:0%
+so i i skipped over another simple
+behavioral finding last time that i want
+
+ align:start position:0%
+behavioral finding last time that i want
+ 
+
+ align:start position:0%
+behavioral finding last time that i want
+to mention now
+
+ align:start position:0%
+to mention now
+ 
+
+ align:start position:0%
+to mention now
+and that is an extremely low-tech
+
+ align:start position:0%
+and that is an extremely low-tech
+ 
+
+ align:start position:0%
+and that is an extremely low-tech
+charmingly low-tech and yet i think very
+
+ align:start position:0%
+charmingly low-tech and yet i think very
+ 
+
+ align:start position:0%
+charmingly low-tech and yet i think very
+powerful discovery about face perception
+
+ align:start position:0%
+powerful discovery about face perception
+ 
+
+ align:start position:0%
+powerful discovery about face perception
+one of the most important original
+
+ align:start position:0%
+one of the most important original
+ 
+
+ align:start position:0%
+one of the most important original
+bits of evidence that face perception
+
+ align:start position:0%
+bits of evidence that face perception
+ 
+
+ align:start position:0%
+bits of evidence that face perception
+might be a different thing in the brain
+
+ align:start position:0%
+might be a different thing in the brain
+ 
+
+ align:start position:0%
+might be a different thing in the brain
+came from a phd thesis in this
+
+ align:start position:0%
+came from a phd thesis in this
+ 
+
+ align:start position:0%
+came from a phd thesis in this
+department by a guy named robert yin
+
+ align:start position:0%
+department by a guy named robert yin
+ 
+
+ align:start position:0%
+department by a guy named robert yin
+and he used the extremely high tech
+
+ align:start position:0%
+and he used the extremely high tech
+ 
+
+ align:start position:0%
+and he used the extremely high tech
+equipment of
+
+ align:start position:0%
+equipment of
+ 
+
+ align:start position:0%
+equipment of
+a stopwatch and paper
+
+ align:start position:0%
+a stopwatch and paper
+ 
+
+ align:start position:0%
+a stopwatch and paper
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what did he do he presented faces to
+
+ align:start position:0%
+so what did he do he presented faces to
+ 
+
+ align:start position:0%
+so what did he do he presented faces to
+people upright and he said study these
+
+ align:start position:0%
+people upright and he said study these
+ 
+
+ align:start position:0%
+people upright and he said study these
+20 faces and then he tested them later
+
+ align:start position:0%
+20 faces and then he tested them later
+ 
+
+ align:start position:0%
+20 faces and then he tested them later
+did you see this face did you see this
+
+ align:start position:0%
+did you see this face did you see this
+ 
+
+ align:start position:0%
+did you see this face did you see this
+face did you see this face
+
+ align:start position:0%
+face did you see this face
+ 
+
+ align:start position:0%
+face did you see this face
+and then he did the exact same
+
+ align:start position:0%
+and then he did the exact same
+ 
+
+ align:start position:0%
+and then he did the exact same
+experiment on a different set of phases
+
+ align:start position:0%
+experiment on a different set of phases
+ 
+
+ align:start position:0%
+experiment on a different set of phases
+but they were all upside down studied
+
+ align:start position:0%
+but they were all upside down studied
+ 
+
+ align:start position:0%
+but they were all upside down studied
+upside down and tested upside down
+
+ align:start position:0%
+upside down and tested upside down
+ 
+
+ align:start position:0%
+upside down and tested upside down
+okay and what did he find
+
+ align:start position:0%
+okay and what did he find
+ 
+
+ align:start position:0%
+okay and what did he find
+he found what's known as the face
+
+ align:start position:0%
+he found what's known as the face
+ 
+
+ align:start position:0%
+he found what's known as the face
+inversion effect
+
+ align:start position:0%
+inversion effect
+ 
+
+ align:start position:0%
+inversion effect
+namely people do much worse at this task
+
+ align:start position:0%
+namely people do much worse at this task
+ 
+
+ align:start position:0%
+namely people do much worse at this task
+when the faces are upside down here's
+
+ align:start position:0%
+when the faces are upside down here's
+ 
+
+ align:start position:0%
+when the faces are upside down here's
+errors for inverted upside down errors
+
+ align:start position:0%
+errors for inverted upside down errors
+ 
+
+ align:start position:0%
+errors for inverted upside down errors
+for upright at this task
+
+ align:start position:0%
+for upright at this task
+ 
+
+ align:start position:0%
+for upright at this task
+even though importantly they were
+
+ align:start position:0%
+even though importantly they were
+ 
+
+ align:start position:0%
+even though importantly they were
+studied and tested upside down or
+
+ align:start position:0%
+studied and tested upside down or
+ 
+
+ align:start position:0%
+studied and tested upside down or
+studied and tested inverted
+
+ align:start position:0%
+studied and tested inverted
+ 
+
+ align:start position:0%
+studied and tested inverted
+upright
+
+ align:start position:0%
+upright
+ 
+
+ align:start position:0%
+upright
+okay everybody got what this shows okay
+
+ align:start position:0%
+okay everybody got what this shows okay
+ 
+
+ align:start position:0%
+okay everybody got what this shows okay
+so that's cool um that this face
+
+ align:start position:0%
+so that's cool um that this face
+ 
+
+ align:start position:0%
+so that's cool um that this face
+inversion um so but the further cool
+
+ align:start position:0%
+inversion um so but the further cool
+ 
+
+ align:start position:0%
+inversion um so but the further cool
+thing is he showed that this face
+
+ align:start position:0%
+thing is he showed that this face
+ 
+
+ align:start position:0%
+thing is he showed that this face
+inversion effect is greater for faces
+
+ align:start position:0%
+inversion effect is greater for faces
+ 
+
+ align:start position:0%
+inversion effect is greater for faces
+than for other kinds of stimuli so he
+
+ align:start position:0%
+than for other kinds of stimuli so he
+ 
+
+ align:start position:0%
+than for other kinds of stimuli so he
+tested lots of other things including
+
+ align:start position:0%
+tested lots of other things including
+ 
+
+ align:start position:0%
+tested lots of other things including
+houses and stick figures
+
+ align:start position:0%
+houses and stick figures
+ 
+
+ align:start position:0%
+houses and stick figures
+and he showed that that cost when you
+
+ align:start position:0%
+and he showed that that cost when you
+ 
+
+ align:start position:0%
+and he showed that that cost when you
+turn the stimuli upside down is greater
+
+ align:start position:0%
+turn the stimuli upside down is greater
+ 
+
+ align:start position:0%
+turn the stimuli upside down is greater
+that difference is greater for faces
+
+ align:start position:0%
+that difference is greater for faces
+ 
+
+ align:start position:0%
+that difference is greater for faces
+than for other classes of stimuli
+
+ align:start position:0%
+than for other classes of stimuli
+ 
+
+ align:start position:0%
+than for other classes of stimuli
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what that suggests
+
+ align:start position:0%
+so what that suggests
+ 
+
+ align:start position:0%
+so what that suggests
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+face recognition may just work
+
+ align:start position:0%
+face recognition may just work
+ 
+
+ align:start position:0%
+face recognition may just work
+differently in some deep way from
+
+ align:start position:0%
+differently in some deep way from
+ 
+
+ align:start position:0%
+differently in some deep way from
+recognition of other classes of stimuli
+
+ align:start position:0%
+recognition of other classes of stimuli
+ 
+
+ align:start position:0%
+recognition of other classes of stimuli
+and robert yin actually inferred in his
+
+ align:start position:0%
+and robert yin actually inferred in his
+ 
+
+ align:start position:0%
+and robert yin actually inferred in his
+phd thesis way way back before any
+
+ align:start position:0%
+phd thesis way way back before any
+ 
+
+ align:start position:0%
+phd thesis way way back before any
+imaging method that maybe there are
+
+ align:start position:0%
+imaging method that maybe there are
+ 
+
+ align:start position:0%
+imaging method that maybe there are
+special parts of the brain for face
+
+ align:start position:0%
+special parts of the brain for face
+ 
+
+ align:start position:0%
+special parts of the brain for face
+recognition and maybe face recognition
+
+ align:start position:0%
+recognition and maybe face recognition
+ 
+
+ align:start position:0%
+recognition and maybe face recognition
+is just a totally different thing that's
+
+ align:start position:0%
+is just a totally different thing that's
+ 
+
+ align:start position:0%
+is just a totally different thing that's
+why it is more affected by inversion
+
+ align:start position:0%
+why it is more affected by inversion
+ 
+
+ align:start position:0%
+why it is more affected by inversion
+than recognition of other kinds of
+
+ align:start position:0%
+than recognition of other kinds of
+ 
+
+ align:start position:0%
+than recognition of other kinds of
+things was there a question back there
+
+ align:start position:0%
+things was there a question back there
+ 
+
+ align:start position:0%
+things was there a question back there
+yeah i was going to ask is that just
+
+ align:start position:0%
+yeah i was going to ask is that just
+ 
+
+ align:start position:0%
+yeah i was going to ask is that just
+could that just be because spaces are
+
+ align:start position:0%
+could that just be because spaces are
+ 
+
+ align:start position:0%
+could that just be because spaces are
+much more complex than houses or stick
+
+ align:start position:0%
+much more complex than houses or stick
+ 
+
+ align:start position:0%
+much more complex than houses or stick
+figures in that
+
+ align:start position:0%
+figures in that
+ 
+
+ align:start position:0%
+figures in that
+good question hang on to
+
+ align:start position:0%
+good question hang on to
+ 
+
+ align:start position:0%
+good question hang on to
+good question that's that's a very good
+
+ align:start position:0%
+good question that's that's a very good
+ 
+
+ align:start position:0%
+good question that's that's a very good
+question and many people have tried to
+
+ align:start position:0%
+question and many people have tried to
+ 
+
+ align:start position:0%
+question and many people have tried to
+grapple with that um and actually about
+
+ align:start position:0%
+grapple with that um and actually about
+ 
+
+ align:start position:0%
+grapple with that um and actually about
+10 years ago the idea that this
+
+ align:start position:0%
+10 years ago the idea that this
+ 
+
+ align:start position:0%
+10 years ago the idea that this
+disproportionate effect for faces was
+
+ align:start position:0%
+disproportionate effect for faces was
+ 
+
+ align:start position:0%
+disproportionate effect for faces was
+like you know standard textbook
+
+ align:start position:0%
+like you know standard textbook
+ 
+
+ align:start position:0%
+like you know standard textbook
+completely accepted and now there's like
+
+ align:start position:0%
+completely accepted and now there's like
+ 
+
+ align:start position:0%
+completely accepted and now there's like
+another round of people doubting it with
+
+ align:start position:0%
+another round of people doubting it with
+ 
+
+ align:start position:0%
+another round of people doubting it with
+other kinds of stimuli so it's kind of
+
+ align:start position:0%
+other kinds of stimuli so it's kind of
+ 
+
+ align:start position:0%
+other kinds of stimuli so it's kind of
+ongoing it's a very robust difference
+
+ align:start position:0%
+ongoing it's a very robust difference
+ 
+
+ align:start position:0%
+ongoing it's a very robust difference
+but to say exactly what it is about face
+
+ align:start position:0%
+but to say exactly what it is about face
+ 
+
+ align:start position:0%
+but to say exactly what it is about face
+stimuli versus other kinds of things
+
+ align:start position:0%
+stimuli versus other kinds of things
+ 
+
+ align:start position:0%
+stimuli versus other kinds of things
+that is responsible for that difference
+
+ align:start position:0%
+that is responsible for that difference
+ 
+
+ align:start position:0%
+that is responsible for that difference
+you can imagine
+
+ align:start position:0%
+you can imagine
+ 
+
+ align:start position:0%
+you can imagine
+it's um it's subtle for the for the
+
+ align:start position:0%
+it's um it's subtle for the for the
+ 
+
+ align:start position:0%
+it's um it's subtle for the for the
+purposes of this this course i'm trying
+
+ align:start position:0%
+purposes of this this course i'm trying
+ 
+
+ align:start position:0%
+purposes of this this course i'm trying
+to like not quite lie to you guys but
+
+ align:start position:0%
+to like not quite lie to you guys but
+ 
+
+ align:start position:0%
+to like not quite lie to you guys but
+give you the most standard view without
+
+ align:start position:0%
+give you the most standard view without
+ 
+
+ align:start position:0%
+give you the most standard view without
+freighting you with every possible
+
+ align:start position:0%
+freighting you with every possible
+ 
+
+ align:start position:0%
+freighting you with every possible
+objection to every little thing because
+
+ align:start position:0%
+objection to every little thing because
+ 
+
+ align:start position:0%
+objection to every little thing because
+pretty much every finding there's
+
+ align:start position:0%
+pretty much every finding there's
+ 
+
+ align:start position:0%
+pretty much every finding there's
+somebody who has a beef with it you know
+
+ align:start position:0%
+somebody who has a beef with it you know
+ 
+
+ align:start position:0%
+somebody who has a beef with it you know
+and we'll tell you that's not really
+
+ align:start position:0%
+and we'll tell you that's not really
+ 
+
+ align:start position:0%
+and we'll tell you that's not really
+true because bloody blood okay so yes
+
+ align:start position:0%
+true because bloody blood okay so yes
+ 
+
+ align:start position:0%
+true because bloody blood okay so yes
+there are there's a little bit of uh
+
+ align:start position:0%
+there are there's a little bit of uh
+ 
+
+ align:start position:0%
+there are there's a little bit of uh
+debate going on about this right now but
+
+ align:start position:0%
+debate going on about this right now but
+ 
+
+ align:start position:0%
+debate going on about this right now but
+for the purposes of this course it's
+
+ align:start position:0%
+for the purposes of this course it's
+ 
+
+ align:start position:0%
+for the purposes of this course it's
+pretty damn rock solid at least as an
+
+ align:start position:0%
+pretty damn rock solid at least as an
+ 
+
+ align:start position:0%
+pretty damn rock solid at least as an
+empirical result okay
+
+ align:start position:0%
+empirical result okay
+ 
+
+ align:start position:0%
+empirical result okay
+all right um so there's in fact lots of
+
+ align:start position:0%
+all right um so there's in fact lots of
+ 
+
+ align:start position:0%
+all right um so there's in fact lots of
+versions of the um of the face inversion
+
+ align:start position:0%
+versions of the um of the face inversion
+ 
+
+ align:start position:0%
+versions of the um of the face inversion
+effect one you may have seen before but
+
+ align:start position:0%
+effect one you may have seen before but
+ 
+
+ align:start position:0%
+effect one you may have seen before but
+which is very amusing if you look at
+
+ align:start position:0%
+which is very amusing if you look at
+ 
+
+ align:start position:0%
+which is very amusing if you look at
+faces like this that are upside down
+
+ align:start position:0%
+faces like this that are upside down
+ 
+
+ align:start position:0%
+faces like this that are upside down
+they look
+
+ align:start position:0%
+they look
+ 
+
+ align:start position:0%
+they look
+you know sort of normal
+
+ align:start position:0%
+you know sort of normal
+ 
+
+ align:start position:0%
+you know sort of normal
+uh but then if you rotate them you
+
+ align:start position:0%
+uh but then if you rotate them you
+ 
+
+ align:start position:0%
+uh but then if you rotate them you
+realize there's something deeply weird
+
+ align:start position:0%
+realize there's something deeply weird
+ 
+
+ align:start position:0%
+realize there's something deeply weird
+going on okay so the point is you're
+
+ align:start position:0%
+going on okay so the point is you're
+ 
+
+ align:start position:0%
+going on okay so the point is you're
+much more sensitive to those grotesquely
+
+ align:start position:0%
+much more sensitive to those grotesquely
+ 
+
+ align:start position:0%
+much more sensitive to those grotesquely
+distorted faces when you see them right
+
+ align:start position:0%
+distorted faces when you see them right
+ 
+
+ align:start position:0%
+distorted faces when you see them right
+side up than when you see them upside
+
+ align:start position:0%
+side up than when you see them upside
+ 
+
+ align:start position:0%
+side up than when you see them upside
+down so that's another version of the
+
+ align:start position:0%
+down so that's another version of the
+ 
+
+ align:start position:0%
+down so that's another version of the
+face inversion effect and there are many
+
+ align:start position:0%
+face inversion effect and there are many
+ 
+
+ align:start position:0%
+face inversion effect and there are many
+many incarnations of this effect you'll
+
+ align:start position:0%
+many incarnations of this effect you'll
+ 
+
+ align:start position:0%
+many incarnations of this effect you'll
+see another one later in the
+
+ align:start position:0%
+see another one later in the
+ 
+
+ align:start position:0%
+see another one later in the
+in the lecture so um so where did we get
+
+ align:start position:0%
+in the lecture so um so where did we get
+ 
+
+ align:start position:0%
+in the lecture so um so where did we get
+last time with these questions we got
+
+ align:start position:0%
+last time with these questions we got
+ 
+
+ align:start position:0%
+last time with these questions we got
+that one of the major if not the major
+
+ align:start position:0%
+that one of the major if not the major
+ 
+
+ align:start position:0%
+that one of the major if not the major
+central challenge in face recognition at
+
+ align:start position:0%
+central challenge in face recognition at
+ 
+
+ align:start position:0%
+central challenge in face recognition at
+a computational level
+
+ align:start position:0%
+a computational level
+ 
+
+ align:start position:0%
+a computational level
+is the fact that we deal with a huge
+
+ align:start position:0%
+is the fact that we deal with a huge
+ 
+
+ align:start position:0%
+is the fact that we deal with a huge
+image variation each time we see a face
+
+ align:start position:0%
+image variation each time we see a face
+ 
+
+ align:start position:0%
+image variation each time we see a face
+and yet somehow we're able to grapple
+
+ align:start position:0%
+and yet somehow we're able to grapple
+ 
+
+ align:start position:0%
+and yet somehow we're able to grapple
+with it so to understand how face
+
+ align:start position:0%
+with it so to understand how face
+ 
+
+ align:start position:0%
+with it so to understand how face
+recognition works would be to understand
+
+ align:start position:0%
+recognition works would be to understand
+ 
+
+ align:start position:0%
+recognition works would be to understand
+what is the code ultimately nobody knows
+
+ align:start position:0%
+what is the code ultimately nobody knows
+ 
+
+ align:start position:0%
+what is the code ultimately nobody knows
+right now but what is the code running
+
+ align:start position:0%
+right now but what is the code running
+ 
+
+ align:start position:0%
+right now but what is the code running
+in our heads that enables us to do that
+
+ align:start position:0%
+in our heads that enables us to do that
+ 
+
+ align:start position:0%
+in our heads that enables us to do that
+what is our mental representation of the
+
+ align:start position:0%
+what is our mental representation of the
+ 
+
+ align:start position:0%
+what is our mental representation of the
+face that enables us to deal with this
+
+ align:start position:0%
+face that enables us to deal with this
+ 
+
+ align:start position:0%
+face that enables us to deal with this
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+by looking at behavioral data
+
+ align:start position:0%
+by looking at behavioral data
+ 
+
+ align:start position:0%
+by looking at behavioral data
+we got some evidence from the dutch
+
+ align:start position:0%
+we got some evidence from the dutch
+ 
+
+ align:start position:0%
+we got some evidence from the dutch
+politician study that
+
+ align:start position:0%
+politician study that
+ 
+
+ align:start position:0%
+politician study that
+whatever that representation is that we
+
+ align:start position:0%
+whatever that representation is that we
+ 
+
+ align:start position:0%
+whatever that representation is that we
+extract from faces it's not independent
+
+ align:start position:0%
+extract from faces it's not independent
+ 
+
+ align:start position:0%
+extract from faces it's not independent
+of the particular image it's not that we
+
+ align:start position:0%
+of the particular image it's not that we
+ 
+
+ align:start position:0%
+of the particular image it's not that we
+have some you know platonic ideal of the
+
+ align:start position:0%
+have some you know platonic ideal of the
+ 
+
+ align:start position:0%
+have some you know platonic ideal of the
+face that we can extract from any face
+
+ align:start position:0%
+face that we can extract from any face
+ 
+
+ align:start position:0%
+face that we can extract from any face
+that lands on our retina a planet
+
+ align:start position:0%
+that lands on our retina a planet
+ 
+
+ align:start position:0%
+that lands on our retina a planet
+platonic ideal of that person's face
+
+ align:start position:0%
+platonic ideal of that person's face
+ 
+
+ align:start position:0%
+platonic ideal of that person's face
+right so whatever we're doing it's not
+
+ align:start position:0%
+right so whatever we're doing it's not
+ 
+
+ align:start position:0%
+right so whatever we're doing it's not
+completely invariant um because we can't
+
+ align:start position:0%
+completely invariant um because we can't
+ 
+
+ align:start position:0%
+completely invariant um because we can't
+do that so well with
+
+ align:start position:0%
+do that so well with
+ 
+
+ align:start position:0%
+do that so well with
+unfamiliar faces okay
+
+ align:start position:0%
+unfamiliar faces okay
+ 
+
+ align:start position:0%
+unfamiliar faces okay
+also as i just showed you related but
+
+ align:start position:0%
+also as i just showed you related but
+ 
+
+ align:start position:0%
+also as i just showed you related but
+not exactly the same point
+
+ align:start position:0%
+not exactly the same point
+ 
+
+ align:start position:0%
+not exactly the same point
+our mental representations of faces are
+
+ align:start position:0%
+our mental representations of faces are
+ 
+
+ align:start position:0%
+our mental representations of faces are
+very sensitive to the orientation of the
+
+ align:start position:0%
+very sensitive to the orientation of the
+ 
+
+ align:start position:0%
+very sensitive to the orientation of the
+face
+
+ align:start position:0%
+face
+ 
+
+ align:start position:0%
+face
+more than our mental representations of
+
+ align:start position:0%
+more than our mental representations of
+ 
+
+ align:start position:0%
+more than our mental representations of
+other classes of stimuli
+
+ align:start position:0%
+other classes of stimuli
+ 
+
+ align:start position:0%
+other classes of stimuli
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so those are just very simple uh
+
+ align:start position:0%
+so those are just very simple uh
+ 
+
+ align:start position:0%
+so those are just very simple uh
+insights about the whatever whatever our
+
+ align:start position:0%
+insights about the whatever whatever our
+ 
+
+ align:start position:0%
+insights about the whatever whatever our
+representations of faces are in our
+
+ align:start position:0%
+representations of faces are in our
+ 
+
+ align:start position:0%
+representations of faces are in our
+heads just from simple behavioral data
+
+ align:start position:0%
+heads just from simple behavioral data
+ 
+
+ align:start position:0%
+heads just from simple behavioral data
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so let me just review some of the
+
+ align:start position:0%
+um so let me just review some of the
+ 
+
+ align:start position:0%
+um so let me just review some of the
+strengths and weaknesses of
+
+ align:start position:0%
+strengths and weaknesses of
+ 
+
+ align:start position:0%
+strengths and weaknesses of
+simple behavioral methods strengths are
+
+ align:start position:0%
+simple behavioral methods strengths are
+ 
+
+ align:start position:0%
+simple behavioral methods strengths are
+they're good for characterizing the
+
+ align:start position:0%
+they're good for characterizing the
+ 
+
+ align:start position:0%
+they're good for characterizing the
+internal representation right not with
+
+ align:start position:0%
+internal representation right not with
+ 
+
+ align:start position:0%
+internal representation right not with
+huge computational precision they're
+
+ align:start position:0%
+huge computational precision they're
+ 
+
+ align:start position:0%
+huge computational precision they're
+more like with gisty kind of ideas like
+
+ align:start position:0%
+more like with gisty kind of ideas like
+ 
+
+ align:start position:0%
+more like with gisty kind of ideas like
+okay they're not very invariant they
+
+ align:start position:0%
+okay they're not very invariant they
+ 
+
+ align:start position:0%
+okay they're not very invariant they
+depend on the orientation right that's
+
+ align:start position:0%
+depend on the orientation right that's
+ 
+
+ align:start position:0%
+depend on the orientation right that's
+not very precise but it's a whole lot
+
+ align:start position:0%
+not very precise but it's a whole lot
+ 
+
+ align:start position:0%
+not very precise but it's a whole lot
+better than nothing okay
+
+ align:start position:0%
+better than nothing okay
+ 
+
+ align:start position:0%
+better than nothing okay
+that's what i mean by at least
+
+ align:start position:0%
+that's what i mean by at least
+ 
+
+ align:start position:0%
+that's what i mean by at least
+qualitatively
+
+ align:start position:0%
+qualitatively
+ 
+
+ align:start position:0%
+qualitatively
+they're good for dissociating mental
+
+ align:start position:0%
+they're good for dissociating mental
+ 
+
+ align:start position:0%
+they're good for dissociating mental
+phenomena so you've already seen that in
+
+ align:start position:0%
+phenomena so you've already seen that in
+ 
+
+ align:start position:0%
+phenomena so you've already seen that in
+the inversion effect it happens more for
+
+ align:start position:0%
+the inversion effect it happens more for
+ 
+
+ align:start position:0%
+the inversion effect it happens more for
+faces than other things so that already
+
+ align:start position:0%
+faces than other things so that already
+ 
+
+ align:start position:0%
+faces than other things so that already
+starts to tell us okay maybe however
+
+ align:start position:0%
+starts to tell us okay maybe however
+ 
+
+ align:start position:0%
+starts to tell us okay maybe however
+whatever the code in our head is that we
+
+ align:start position:0%
+whatever the code in our head is that we
+ 
+
+ align:start position:0%
+whatever the code in our head is that we
+use for face recognition maybe it's
+
+ align:start position:0%
+use for face recognition maybe it's
+ 
+
+ align:start position:0%
+use for face recognition maybe it's
+pretty different than the code that we
+
+ align:start position:0%
+pretty different than the code that we
+ 
+
+ align:start position:0%
+pretty different than the code that we
+use in our head to recognize objects
+
+ align:start position:0%
+use in our head to recognize objects
+ 
+
+ align:start position:0%
+use in our head to recognize objects
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay it's also cheap it's really cheap
+
+ align:start position:0%
+okay it's also cheap it's really cheap
+ 
+
+ align:start position:0%
+okay it's also cheap it's really cheap
+much cheaper than all the other methods
+
+ align:start position:0%
+much cheaper than all the other methods
+ 
+
+ align:start position:0%
+much cheaper than all the other methods
+okay weaknesses
+
+ align:start position:0%
+okay weaknesses
+ 
+
+ align:start position:0%
+okay weaknesses
+it doesn't behavioral methods alone
+
+ align:start position:0%
+it doesn't behavioral methods alone
+ 
+
+ align:start position:0%
+it doesn't behavioral methods alone
+don't have any relationship to the brain
+
+ align:start position:0%
+don't have any relationship to the brain
+ 
+
+ align:start position:0%
+don't have any relationship to the brain
+at least without doing extra work okay
+
+ align:start position:0%
+at least without doing extra work okay
+ 
+
+ align:start position:0%
+at least without doing extra work okay
+and it it
+
+ align:start position:0%
+and it it
+ 
+
+ align:start position:0%
+and it it
+it's not that they are useless until you
+
+ align:start position:0%
+it's not that they are useless until you
+ 
+
+ align:start position:0%
+it's not that they are useless until you
+link them to the brain it's just that
+
+ align:start position:0%
+link them to the brain it's just that
+ 
+
+ align:start position:0%
+link them to the brain it's just that
+the brain is a whole source of other
+
+ align:start position:0%
+the brain is a whole source of other
+ 
+
+ align:start position:0%
+the brain is a whole source of other
+data and it's nice to link them because
+
+ align:start position:0%
+data and it's nice to link them because
+ 
+
+ align:start position:0%
+data and it's nice to link them because
+then you can connect with all those
+
+ align:start position:0%
+then you can connect with all those
+ 
+
+ align:start position:0%
+then you can connect with all those
+other data
+
+ align:start position:0%
+other data
+ 
+
+ align:start position:0%
+other data
+also behavioral data are pretty sparse
+
+ align:start position:0%
+also behavioral data are pretty sparse
+ 
+
+ align:start position:0%
+also behavioral data are pretty sparse
+like for the most part you have accuracy
+
+ align:start position:0%
+like for the most part you have accuracy
+ 
+
+ align:start position:0%
+like for the most part you have accuracy
+and reaction time and that's it
+
+ align:start position:0%
+and reaction time and that's it
+ 
+
+ align:start position:0%
+and reaction time and that's it
+and that's just not a whole lot of data
+
+ align:start position:0%
+and that's just not a whole lot of data
+ 
+
+ align:start position:0%
+and that's just not a whole lot of data
+to work with you have to actually be
+
+ align:start position:0%
+to work with you have to actually be
+ 
+
+ align:start position:0%
+to work with you have to actually be
+much smarter to be a behavioral
+
+ align:start position:0%
+much smarter to be a behavioral
+ 
+
+ align:start position:0%
+much smarter to be a behavioral
+cognitive psychologist and you have to
+
+ align:start position:0%
+cognitive psychologist and you have to
+ 
+
+ align:start position:0%
+cognitive psychologist and you have to
+be to be to to be a cognitive
+
+ align:start position:0%
+be to be to to be a cognitive
+ 
+
+ align:start position:0%
+be to be to to be a cognitive
+neuroscientist where you have much
+
+ align:start position:0%
+neuroscientist where you have much
+ 
+
+ align:start position:0%
+neuroscientist where you have much
+richer data to reason from like
+
+ align:start position:0%
+richer data to reason from like
+ 
+
+ align:start position:0%
+richer data to reason from like
+cognitive psychologists really have very
+
+ align:start position:0%
+cognitive psychologists really have very
+ 
+
+ align:start position:0%
+cognitive psychologists really have very
+very clever designs because they're
+
+ align:start position:0%
+very clever designs because they're
+ 
+
+ align:start position:0%
+very clever designs because they're
+taking this extremely limited data and
+
+ align:start position:0%
+taking this extremely limited data and
+ 
+
+ align:start position:0%
+taking this extremely limited data and
+trying to pull out interesting insights
+
+ align:start position:0%
+trying to pull out interesting insights
+ 
+
+ align:start position:0%
+trying to pull out interesting insights
+about mental function
+
+ align:start position:0%
+about mental function
+ 
+
+ align:start position:0%
+about mental function
+another way of looking at that is
+
+ align:start position:0%
+another way of looking at that is
+ 
+
+ align:start position:0%
+another way of looking at that is
+here's you know an eyeball and a bunch
+
+ align:start position:0%
+here's you know an eyeball and a bunch
+ 
+
+ align:start position:0%
+here's you know an eyeball and a bunch
+of processing going over stages and a
+
+ align:start position:0%
+of processing going over stages and a
+ 
+
+ align:start position:0%
+of processing going over stages and a
+response right
+
+ align:start position:0%
+response right
+ 
+
+ align:start position:0%
+response right
+with behavioral data all you have is
+
+ align:start position:0%
+with behavioral data all you have is
+ 
+
+ align:start position:0%
+with behavioral data all you have is
+that response
+
+ align:start position:0%
+that response
+ 
+
+ align:start position:0%
+that response
+but presumably for most of the mental
+
+ align:start position:0%
+but presumably for most of the mental
+ 
+
+ align:start position:0%
+but presumably for most of the mental
+processes that go on in our heads there
+
+ align:start position:0%
+processes that go on in our heads there
+ 
+
+ align:start position:0%
+processes that go on in our heads there
+are many different stages of processing
+
+ align:start position:0%
+are many different stages of processing
+ 
+
+ align:start position:0%
+are many different stages of processing
+where different things are going on
+
+ align:start position:0%
+where different things are going on
+ 
+
+ align:start position:0%
+where different things are going on
+computations tend to have multiple
+
+ align:start position:0%
+computations tend to have multiple
+ 
+
+ align:start position:0%
+computations tend to have multiple
+stages and unfold over time and all we
+
+ align:start position:0%
+stages and unfold over time and all we
+ 
+
+ align:start position:0%
+stages and unfold over time and all we
+have is output
+
+ align:start position:0%
+have is output
+ 
+
+ align:start position:0%
+have is output
+so really what we want to be able to do
+
+ align:start position:0%
+so really what we want to be able to do
+ 
+
+ align:start position:0%
+so really what we want to be able to do
+is characterize the whole sequence of
+
+ align:start position:0%
+is characterize the whole sequence of
+ 
+
+ align:start position:0%
+is characterize the whole sequence of
+processes
+
+ align:start position:0%
+processes
+ 
+
+ align:start position:0%
+processes
+and it's not that you can't get insights
+
+ align:start position:0%
+and it's not that you can't get insights
+ 
+
+ align:start position:0%
+and it's not that you can't get insights
+about some of those intermediates from
+
+ align:start position:0%
+about some of those intermediates from
+ 
+
+ align:start position:0%
+about some of those intermediates from
+behavioral data it's just much more
+
+ align:start position:0%
+behavioral data it's just much more
+ 
+
+ align:start position:0%
+behavioral data it's just much more
+challenging
+
+ align:start position:0%
+challenging
+ 
+
+ align:start position:0%
+challenging
+so if we had a way to look at those
+
+ align:start position:0%
+so if we had a way to look at those
+ 
+
+ align:start position:0%
+so if we had a way to look at those
+things independently wouldn't that be
+
+ align:start position:0%
+things independently wouldn't that be
+ 
+
+ align:start position:0%
+things independently wouldn't that be
+awesome
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there's lots of ways to do that
+
+ align:start position:0%
+okay so there's lots of ways to do that
+ 
+
+ align:start position:0%
+okay so there's lots of ways to do that
+and a particularly good one is
+
+ align:start position:0%
+and a particularly good one is
+ 
+
+ align:start position:0%
+and a particularly good one is
+functional mri so as i mentioned before
+
+ align:start position:0%
+functional mri so as i mentioned before
+ 
+
+ align:start position:0%
+functional mri so as i mentioned before
+i mentioned this very of
+
+ align:start position:0%
+i mentioned this very of
+ 
+
+ align:start position:0%
+i mentioned this very of
+brief very briefly this very early
+
+ align:start position:0%
+brief very briefly this very early
+ 
+
+ align:start position:0%
+brief very briefly this very early
+experiment that i did way back
+
+ align:start position:0%
+experiment that i did way back
+ 
+
+ align:start position:0%
+experiment that i did way back
+asking whether there is a region of the
+
+ align:start position:0%
+asking whether there is a region of the
+ 
+
+ align:start position:0%
+asking whether there is a region of the
+brain that's selectively involved in
+
+ align:start position:0%
+brain that's selectively involved in
+ 
+
+ align:start position:0%
+brain that's selectively involved in
+processing faces
+
+ align:start position:0%
+processing faces
+ 
+
+ align:start position:0%
+processing faces
+and i'm going to put a slightly
+
+ align:start position:0%
+and i'm going to put a slightly
+ 
+
+ align:start position:0%
+and i'm going to put a slightly
+different spin on it from what i put
+
+ align:start position:0%
+different spin on it from what i put
+ 
+
+ align:start position:0%
+different spin on it from what i put
+before it's the same experiment same
+
+ align:start position:0%
+before it's the same experiment same
+ 
+
+ align:start position:0%
+before it's the same experiment same
+data but i want to emphasize more the
+
+ align:start position:0%
+data but i want to emphasize more the
+ 
+
+ align:start position:0%
+data but i want to emphasize more the
+logic of the experimental design because
+
+ align:start position:0%
+logic of the experimental design because
+ 
+
+ align:start position:0%
+logic of the experimental design because
+you guys will be designing an experiment
+
+ align:start position:0%
+you guys will be designing an experiment
+ 
+
+ align:start position:0%
+you guys will be designing an experiment
+on a different topic um
+
+ align:start position:0%
+on a different topic um
+ 
+
+ align:start position:0%
+on a different topic um
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+a due monday night okay that we're gonna
+
+ align:start position:0%
+a due monday night okay that we're gonna
+ 
+
+ align:start position:0%
+a due monday night okay that we're gonna
+discuss in uh sunday night that we're
+
+ align:start position:0%
+discuss in uh sunday night that we're
+ 
+
+ align:start position:0%
+discuss in uh sunday night that we're
+gonna discuss in class on monday okay
+
+ align:start position:0%
+gonna discuss in class on monday okay
+ 
+
+ align:start position:0%
+gonna discuss in class on monday okay
+so we start with a hypothesis that
+
+ align:start position:0%
+so we start with a hypothesis that
+ 
+
+ align:start position:0%
+so we start with a hypothesis that
+there's a special um there's a a region
+
+ align:start position:0%
+there's a special um there's a a region
+ 
+
+ align:start position:0%
+there's a special um there's a a region
+of the brain that's selectively
+
+ align:start position:0%
+of the brain that's selectively
+ 
+
+ align:start position:0%
+of the brain that's selectively
+responsive to faces that's the
+
+ align:start position:0%
+responsive to faces that's the
+ 
+
+ align:start position:0%
+responsive to faces that's the
+hypothesis the way we test it is to pop
+
+ align:start position:0%
+hypothesis the way we test it is to pop
+ 
+
+ align:start position:0%
+hypothesis the way we test it is to pop
+people in a scanner and show them faces
+
+ align:start position:0%
+people in a scanner and show them faces
+ 
+
+ align:start position:0%
+people in a scanner and show them faces
+and objects the data that i showed you
+
+ align:start position:0%
+and objects the data that i showed you
+ 
+
+ align:start position:0%
+and objects the data that i showed you
+before is that this little patch of the
+
+ align:start position:0%
+before is that this little patch of the
+ 
+
+ align:start position:0%
+before is that this little patch of the
+brain remember this is a horizontal
+
+ align:start position:0%
+brain remember this is a horizontal
+ 
+
+ align:start position:0%
+brain remember this is a horizontal
+slice back of the head left and right
+
+ align:start position:0%
+slice back of the head left and right
+ 
+
+ align:start position:0%
+slice back of the head left and right
+are flipped so that little region in me
+
+ align:start position:0%
+are flipped so that little region in me
+ 
+
+ align:start position:0%
+are flipped so that little region in me
+is right about in there everybody
+
+ align:start position:0%
+is right about in there everybody
+ 
+
+ align:start position:0%
+is right about in there everybody
+oriented okay
+
+ align:start position:0%
+oriented okay
+ 
+
+ align:start position:0%
+oriented okay
+that region responds much more to faces
+
+ align:start position:0%
+that region responds much more to faces
+ 
+
+ align:start position:0%
+that region responds much more to faces
+than objects is that clear to everybody
+
+ align:start position:0%
+than objects is that clear to everybody
+ 
+
+ align:start position:0%
+than objects is that clear to everybody
+what that is okay
+
+ align:start position:0%
+what that is okay
+ 
+
+ align:start position:0%
+what that is okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um yes there's and you see that in most
+
+ align:start position:0%
+um yes there's and you see that in most
+ 
+
+ align:start position:0%
+um yes there's and you see that in most
+subjects so yes there's a bit that
+
+ align:start position:0%
+subjects so yes there's a bit that
+ 
+
+ align:start position:0%
+subjects so yes there's a bit that
+responds more to faces and objects
+
+ align:start position:0%
+responds more to faces and objects
+ 
+
+ align:start position:0%
+responds more to faces and objects
+um but now let's consider the hypothesis
+
+ align:start position:0%
+um but now let's consider the hypothesis
+ 
+
+ align:start position:0%
+um but now let's consider the hypothesis
+that that region is really selective to
+
+ align:start position:0%
+that that region is really selective to
+ 
+
+ align:start position:0%
+that that region is really selective to
+faces per se
+
+ align:start position:0%
+faces per se
+ 
+
+ align:start position:0%
+faces per se
+and the way you evaluate whether these
+
+ align:start position:0%
+and the way you evaluate whether these
+ 
+
+ align:start position:0%
+and the way you evaluate whether these
+data so how strongly these data support
+
+ align:start position:0%
+data so how strongly these data support
+ 
+
+ align:start position:0%
+data so how strongly these data support
+that hypothesis they're certainly
+
+ align:start position:0%
+that hypothesis they're certainly
+ 
+
+ align:start position:0%
+that hypothesis they're certainly
+consistent with it but do they nail that
+
+ align:start position:0%
+consistent with it but do they nail that
+ 
+
+ align:start position:0%
+consistent with it but do they nail that
+hypothesis fully
+
+ align:start position:0%
+hypothesis fully
+ 
+
+ align:start position:0%
+hypothesis fully
+is to consider are there any other
+
+ align:start position:0%
+is to consider are there any other
+ 
+
+ align:start position:0%
+is to consider are there any other
+alternative accounts we can think of
+
+ align:start position:0%
+alternative accounts we can think of
+ 
+
+ align:start position:0%
+alternative accounts we can think of
+that are consistent with these data and
+
+ align:start position:0%
+that are consistent with these data and
+ 
+
+ align:start position:0%
+that are consistent with these data and
+different from that hypothesis
+
+ align:start position:0%
+different from that hypothesis
+ 
+
+ align:start position:0%
+different from that hypothesis
+is that clear it's really important
+
+ align:start position:0%
+is that clear it's really important
+ 
+
+ align:start position:0%
+is that clear it's really important
+that's just the whole
+
+ align:start position:0%
+that's just the whole
+ 
+
+ align:start position:0%
+that's just the whole
+kernel of scientific thinking
+
+ align:start position:0%
+kernel of scientific thinking
+ 
+
+ align:start position:0%
+kernel of scientific thinking
+and evaluating evidence is asking
+
+ align:start position:0%
+and evaluating evidence is asking
+ 
+
+ align:start position:0%
+and evaluating evidence is asking
+yourself that question is there any
+
+ align:start position:0%
+yourself that question is there any
+ 
+
+ align:start position:0%
+yourself that question is there any
+other way we could get those data where
+
+ align:start position:0%
+other way we could get those data where
+ 
+
+ align:start position:0%
+other way we could get those data where
+that hypothesis was wasn't true and if
+
+ align:start position:0%
+that hypothesis was wasn't true and if
+ 
+
+ align:start position:0%
+that hypothesis was wasn't true and if
+so you got to grapple with it
+
+ align:start position:0%
+so you got to grapple with it
+ 
+
+ align:start position:0%
+so you got to grapple with it
+so what you do next is you think about
+
+ align:start position:0%
+so what you do next is you think about
+ 
+
+ align:start position:0%
+so what you do next is you think about
+our alternative hypotheses
+
+ align:start position:0%
+our alternative hypotheses
+ 
+
+ align:start position:0%
+our alternative hypotheses
+to the one you started with
+
+ align:start position:0%
+to the one you started with
+ 
+
+ align:start position:0%
+to the one you started with
+that is different accounts of the same
+
+ align:start position:0%
+that is different accounts of the same
+ 
+
+ align:start position:0%
+that is different accounts of the same
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+and so in in our case you guys suggested
+
+ align:start position:0%
+and so in in our case you guys suggested
+ 
+
+ align:start position:0%
+and so in in our case you guys suggested
+a whole bunch i suggested a bunch
+
+ align:start position:0%
+a whole bunch i suggested a bunch
+ 
+
+ align:start position:0%
+a whole bunch i suggested a bunch
+and though then the next thing i showed
+
+ align:start position:0%
+and though then the next thing i showed
+ 
+
+ align:start position:0%
+and though then the next thing i showed
+you is that we can test those
+
+ align:start position:0%
+you is that we can test those
+ 
+
+ align:start position:0%
+you is that we can test those
+alternative hypotheses at least these
+
+ align:start position:0%
+alternative hypotheses at least these
+ 
+
+ align:start position:0%
+alternative hypotheses at least these
+ones here
+
+ align:start position:0%
+ones here
+ 
+
+ align:start position:0%
+ones here
+by um first
+
+ align:start position:0%
+by um first
+ 
+
+ align:start position:0%
+by um first
+what we did was i didn't really
+
+ align:start position:0%
+what we did was i didn't really
+ 
+
+ align:start position:0%
+what we did was i didn't really
+emphasize this before but we re-ran that
+
+ align:start position:0%
+emphasize this before but we re-ran that
+ 
+
+ align:start position:0%
+emphasize this before but we re-ran that
+experiment in a new bunch of subjects
+
+ align:start position:0%
+experiment in a new bunch of subjects
+ 
+
+ align:start position:0%
+experiment in a new bunch of subjects
+each subject individually we found in
+
+ align:start position:0%
+each subject individually we found in
+ 
+
+ align:start position:0%
+each subject individually we found in
+each subject the little bit that does
+
+ align:start position:0%
+each subject the little bit that does
+ 
+
+ align:start position:0%
+each subject the little bit that does
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+we write down exactly where that is in
+
+ align:start position:0%
+we write down exactly where that is in
+ 
+
+ align:start position:0%
+we write down exactly where that is in
+the br in that person's brain okay now
+
+ align:start position:0%
+the br in that person's brain okay now
+ 
+
+ align:start position:0%
+the br in that person's brain okay now
+that we've found that region that's
+
+ align:start position:0%
+that we've found that region that's
+ 
+
+ align:start position:0%
+that we've found that region that's
+called a localizer run because we're
+
+ align:start position:0%
+called a localizer run because we're
+ 
+
+ align:start position:0%
+called a localizer run because we're
+finding that region in each subject
+
+ align:start position:0%
+finding that region in each subject
+ 
+
+ align:start position:0%
+finding that region in each subject
+individually
+
+ align:start position:0%
+individually
+ 
+
+ align:start position:0%
+individually
+now we can ask it new questions
+
+ align:start position:0%
+now we can ask it new questions
+ 
+
+ align:start position:0%
+now we can ask it new questions
+okay and so the new questions we asked
+
+ align:start position:0%
+okay and so the new questions we asked
+ 
+
+ align:start position:0%
+okay and so the new questions we asked
+it last time
+
+ align:start position:0%
+it last time
+ 
+
+ align:start position:0%
+it last time
+was to present faces and hands and we
+
+ align:start position:0%
+was to present faces and hands and we
+ 
+
+ align:start position:0%
+was to present faces and hands and we
+found oh that region right there
+
+ align:start position:0%
+found oh that region right there
+ 
+
+ align:start position:0%
+found oh that region right there
+responds like this
+
+ align:start position:0%
+responds like this
+ 
+
+ align:start position:0%
+responds like this
+okay so the key ideas here is that we
+
+ align:start position:0%
+okay so the key ideas here is that we
+ 
+
+ align:start position:0%
+okay so the key ideas here is that we
+can we can identify that region in each
+
+ align:start position:0%
+can we can identify that region in each
+ 
+
+ align:start position:0%
+can we can identify that region in each
+subject individually with a functional
+
+ align:start position:0%
+subject individually with a functional
+ 
+
+ align:start position:0%
+subject individually with a functional
+scan the reason that's important which
+
+ align:start position:0%
+scan the reason that's important which
+ 
+
+ align:start position:0%
+scan the reason that's important which
+i'll carry on about in more detail later
+
+ align:start position:0%
+i'll carry on about in more detail later
+ 
+
+ align:start position:0%
+i'll carry on about in more detail later
+is that the exact location of that
+
+ align:start position:0%
+is that the exact location of that
+ 
+
+ align:start position:0%
+is that the exact location of that
+region varies from one subject to the
+
+ align:start position:0%
+region varies from one subject to the
+ 
+
+ align:start position:0%
+region varies from one subject to the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+so if we just grab
+
+ align:start position:0%
+so if we just grab
+ 
+
+ align:start position:0%
+so if we just grab
+you know the whole fusiform gyrus or the
+
+ align:start position:0%
+you know the whole fusiform gyrus or the
+ 
+
+ align:start position:0%
+you know the whole fusiform gyrus or the
+whole lateral side of the fusiform gyrus
+
+ align:start position:0%
+whole lateral side of the fusiform gyrus
+ 
+
+ align:start position:0%
+whole lateral side of the fusiform gyrus
+and each subject we'll get lots of stuff
+
+ align:start position:0%
+and each subject we'll get lots of stuff
+ 
+
+ align:start position:0%
+and each subject we'll get lots of stuff
+that is that region and lots of cortical
+
+ align:start position:0%
+that is that region and lots of cortical
+ 
+
+ align:start position:0%
+that is that region and lots of cortical
+neighbors it's something else okay
+
+ align:start position:0%
+neighbors it's something else okay
+ 
+
+ align:start position:0%
+neighbors it's something else okay
+and if we grab you know if we took the
+
+ align:start position:0%
+and if we grab you know if we took the
+ 
+
+ align:start position:0%
+and if we grab you know if we took the
+exact location of that region to my
+
+ align:start position:0%
+exact location of that region to my
+ 
+
+ align:start position:0%
+exact location of that region to my
+brain and registered it to any of your
+
+ align:start position:0%
+brain and registered it to any of your
+ 
+
+ align:start position:0%
+brain and registered it to any of your
+brains and said okay let's take the part
+
+ align:start position:0%
+brains and said okay let's take the part
+ 
+
+ align:start position:0%
+brains and said okay let's take the part
+of your brain that registers spatially
+
+ align:start position:0%
+of your brain that registers spatially
+ 
+
+ align:start position:0%
+of your brain that registers spatially
+as well as we can with mine
+
+ align:start position:0%
+as well as we can with mine
+ 
+
+ align:start position:0%
+as well as we can with mine
+we're not going to exactly get the right
+
+ align:start position:0%
+we're not going to exactly get the right
+ 
+
+ align:start position:0%
+we're not going to exactly get the right
+bit
+
+ align:start position:0%
+bit
+ 
+
+ align:start position:0%
+bit
+so to study that thing we got to first
+
+ align:start position:0%
+so to study that thing we got to first
+ 
+
+ align:start position:0%
+so to study that thing we got to first
+find it functionally and then we can ask
+
+ align:start position:0%
+find it functionally and then we can ask
+ 
+
+ align:start position:0%
+find it functionally and then we can ask
+it new questions does that make sense
+
+ align:start position:0%
+it new questions does that make sense
+ 
+
+ align:start position:0%
+it new questions does that make sense
+okay if anybody's unclear about that i
+
+ align:start position:0%
+okay if anybody's unclear about that i
+ 
+
+ align:start position:0%
+okay if anybody's unclear about that i
+have actually online talks that go
+
+ align:start position:0%
+have actually online talks that go
+ 
+
+ align:start position:0%
+have actually online talks that go
+through the whole logic of this in
+
+ align:start position:0%
+through the whole logic of this in
+ 
+
+ align:start position:0%
+through the whole logic of this in
+painful detail and i'm happy to answer
+
+ align:start position:0%
+painful detail and i'm happy to answer
+ 
+
+ align:start position:0%
+painful detail and i'm happy to answer
+other questions about it later
+
+ align:start position:0%
+other questions about it later
+ 
+
+ align:start position:0%
+other questions about it later
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um i put the word conditions in red
+
+ align:start position:0%
+so um i put the word conditions in red
+ 
+
+ align:start position:0%
+so um i put the word conditions in red
+because somebody asked one of the tas
+
+ align:start position:0%
+because somebody asked one of the tas
+ 
+
+ align:start position:0%
+because somebody asked one of the tas
+what a condition was
+
+ align:start position:0%
+what a condition was
+ 
+
+ align:start position:0%
+what a condition was
+and that's not stupid i should have made
+
+ align:start position:0%
+and that's not stupid i should have made
+ 
+
+ align:start position:0%
+and that's not stupid i should have made
+that clear
+
+ align:start position:0%
+that clear
+ 
+
+ align:start position:0%
+that clear
+this is just experimental design
+
+ align:start position:0%
+this is just experimental design
+ 
+
+ align:start position:0%
+this is just experimental design
+gobbledygook that means
+
+ align:start position:0%
+gobbledygook that means
+ 
+
+ align:start position:0%
+gobbledygook that means
+any any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what is the definition of condition
+
+ align:start position:0%
+okay what is the definition of condition
+ 
+
+ align:start position:0%
+okay what is the definition of condition
+in an experimental design you have
+
+ align:start position:0%
+in an experimental design you have
+ 
+
+ align:start position:0%
+in an experimental design you have
+things that you are manipulating and
+
+ align:start position:0%
+things that you are manipulating and
+ 
+
+ align:start position:0%
+things that you are manipulating and
+measuring
+
+ align:start position:0%
+measuring
+ 
+
+ align:start position:0%
+measuring
+okay so in this case we're manipulating
+
+ align:start position:0%
+okay so in this case we're manipulating
+ 
+
+ align:start position:0%
+okay so in this case we're manipulating
+the stimulus
+
+ align:start position:0%
+the stimulus
+ 
+
+ align:start position:0%
+the stimulus
+and we're measuring the magnitude of
+
+ align:start position:0%
+and we're measuring the magnitude of
+ 
+
+ align:start position:0%
+and we're measuring the magnitude of
+response in the fusiform face area okay
+
+ align:start position:0%
+response in the fusiform face area okay
+ 
+
+ align:start position:0%
+response in the fusiform face area okay
+or in the brain
+
+ align:start position:0%
+or in the brain
+ 
+
+ align:start position:0%
+or in the brain
+so what we're manipulating in this case
+
+ align:start position:0%
+so what we're manipulating in this case
+ 
+
+ align:start position:0%
+so what we're manipulating in this case
+is this the stimulus condition so that
+
+ align:start position:0%
+is this the stimulus condition so that
+ 
+
+ align:start position:0%
+is this the stimulus condition so that
+will be one condition that's another
+
+ align:start position:0%
+will be one condition that's another
+ 
+
+ align:start position:0%
+will be one condition that's another
+condition that's another condition does
+
+ align:start position:0%
+condition that's another condition does
+ 
+
+ align:start position:0%
+condition that's another condition does
+that make sense
+
+ align:start position:0%
+that make sense
+ 
+
+ align:start position:0%
+that make sense
+okay so for your experimental design
+
+ align:start position:0%
+okay so for your experimental design
+ 
+
+ align:start position:0%
+okay so for your experimental design
+assignment for uh monday night
+
+ align:start position:0%
+assignment for uh monday night
+ 
+
+ align:start position:0%
+assignment for uh monday night
+you'll be designing one or more
+
+ align:start position:0%
+you'll be designing one or more
+ 
+
+ align:start position:0%
+you'll be designing one or more
+experiments
+
+ align:start position:0%
+experiments
+ 
+
+ align:start position:0%
+experiments
+uh and you will be describing exactly
+
+ align:start position:0%
+uh and you will be describing exactly
+ 
+
+ align:start position:0%
+uh and you will be describing exactly
+what conditions you are going to test
+
+ align:start position:0%
+what conditions you are going to test
+ 
+
+ align:start position:0%
+what conditions you are going to test
+everybody clear on that
+
+ align:start position:0%
+everybody clear on that
+ 
+
+ align:start position:0%
+everybody clear on that
+okay all right um so these data enable
+
+ align:start position:0%
+okay all right um so these data enable
+ 
+
+ align:start position:0%
+okay all right um so these data enable
+us to rule out those hypotheses
+
+ align:start position:0%
+us to rule out those hypotheses
+ 
+
+ align:start position:0%
+us to rule out those hypotheses
+and now you could ask okay
+
+ align:start position:0%
+and now you could ask okay
+ 
+
+ align:start position:0%
+and now you could ask okay
+once you get more data like this have
+
+ align:start position:0%
+once you get more data like this have
+ 
+
+ align:start position:0%
+once you get more data like this have
+you completely nailed that hypothesis is
+
+ align:start position:0%
+you completely nailed that hypothesis is
+ 
+
+ align:start position:0%
+you completely nailed that hypothesis is
+there just no way that hypothesis could
+
+ align:start position:0%
+there just no way that hypothesis could
+ 
+
+ align:start position:0%
+there just no way that hypothesis could
+be wrong now given these data and those
+
+ align:start position:0%
+be wrong now given these data and those
+ 
+
+ align:start position:0%
+be wrong now given these data and those
+data and i'll let you percolate on that
+
+ align:start position:0%
+data and i'll let you percolate on that
+ 
+
+ align:start position:0%
+data and i'll let you percolate on that
+there are ways it could be wrong
+
+ align:start position:0%
+there are ways it could be wrong
+ 
+
+ align:start position:0%
+there are ways it could be wrong
+but they're you know you have to work
+
+ align:start position:0%
+but they're you know you have to work
+ 
+
+ align:start position:0%
+but they're you know you have to work
+harder to come up with them okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um skipping ahead just to give you the
+
+ align:start position:0%
+um skipping ahead just to give you the
+ 
+
+ align:start position:0%
+um skipping ahead just to give you the
+gist this this field has been going on
+
+ align:start position:0%
+gist this this field has been going on
+ 
+
+ align:start position:0%
+gist this this field has been going on
+for a long time uh and there are now
+
+ align:start position:0%
+for a long time uh and there are now
+ 
+
+ align:start position:0%
+for a long time uh and there are now
+many many studies hundreds maybe even i
+
+ align:start position:0%
+many many studies hundreds maybe even i
+ 
+
+ align:start position:0%
+many many studies hundreds maybe even i
+don't know god maybe even thousands i
+
+ align:start position:0%
+don't know god maybe even thousands i
+ 
+
+ align:start position:0%
+don't know god maybe even thousands i
+don't know
+
+ align:start position:0%
+don't know
+ 
+
+ align:start position:0%
+don't know
+uh studies of this region um in which
+
+ align:start position:0%
+uh studies of this region um in which
+ 
+
+ align:start position:0%
+uh studies of this region um in which
+and so sort of a summary statement from
+
+ align:start position:0%
+and so sort of a summary statement from
+ 
+
+ align:start position:0%
+and so sort of a summary statement from
+a long time ago in my lab we've tested
+
+ align:start position:0%
+a long time ago in my lab we've tested
+ 
+
+ align:start position:0%
+a long time ago in my lab we've tested
+the response of this region to lots of
+
+ align:start position:0%
+the response of this region to lots of
+ 
+
+ align:start position:0%
+the response of this region to lots of
+different kinds of stimuli with that
+
+ align:start position:0%
+different kinds of stimuli with that
+ 
+
+ align:start position:0%
+different kinds of stimuli with that
+same method localize it in each subject
+
+ align:start position:0%
+same method localize it in each subject
+ 
+
+ align:start position:0%
+same method localize it in each subject
+measure its response when people look at
+
+ align:start position:0%
+measure its response when people look at
+ 
+
+ align:start position:0%
+measure its response when people look at
+that kind of stimulus okay
+
+ align:start position:0%
+that kind of stimulus okay
+ 
+
+ align:start position:0%
+that kind of stimulus okay
+and so what we know now was that this
+
+ align:start position:0%
+and so what we know now was that this
+ 
+
+ align:start position:0%
+and so what we know now was that this
+region is found in roughly the same
+
+ align:start position:0%
+region is found in roughly the same
+ 
+
+ align:start position:0%
+region is found in roughly the same
+location
+
+ align:start position:0%
+location
+ 
+
+ align:start position:0%
+location
+in pretty much every normal subject it
+
+ align:start position:0%
+in pretty much every normal subject it
+ 
+
+ align:start position:0%
+in pretty much every normal subject it
+responds more to faces than to any other
+
+ align:start position:0%
+responds more to faces than to any other
+ 
+
+ align:start position:0%
+responds more to faces than to any other
+kind of stimuli anyone has ever tested
+
+ align:start position:0%
+kind of stimuli anyone has ever tested
+ 
+
+ align:start position:0%
+kind of stimuli anyone has ever tested
+let me just give you
+
+ align:start position:0%
+let me just give you
+ 
+
+ align:start position:0%
+let me just give you
+one example here if you haven't seen
+
+ align:start position:0%
+one example here if you haven't seen
+ 
+
+ align:start position:0%
+one example here if you haven't seen
+this stimulus before raise your hand if
+
+ align:start position:0%
+this stimulus before raise your hand if
+ 
+
+ align:start position:0%
+this stimulus before raise your hand if
+you can tell what it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+raise your hand if you can tell what
+
+ align:start position:0%
+raise your hand if you can tell what
+ 
+
+ align:start position:0%
+raise your hand if you can tell what
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+okay some of you didn't quite get it yet
+
+ align:start position:0%
+okay some of you didn't quite get it yet
+ 
+
+ align:start position:0%
+okay some of you didn't quite get it yet
+if you don't see it don't worry there's
+
+ align:start position:0%
+if you don't see it don't worry there's
+ 
+
+ align:start position:0%
+if you don't see it don't worry there's
+nothing wrong with you it's a little
+
+ align:start position:0%
+nothing wrong with you it's a little
+ 
+
+ align:start position:0%
+nothing wrong with you it's a little
+subtle
+
+ align:start position:0%
+subtle
+ 
+
+ align:start position:0%
+subtle
+it's a face in profile eyes nose mouth
+
+ align:start position:0%
+it's a face in profile eyes nose mouth
+ 
+
+ align:start position:0%
+it's a face in profile eyes nose mouth
+everyone got it
+
+ align:start position:0%
+everyone got it
+ 
+
+ align:start position:0%
+everyone got it
+okay so here's the thing that's the same
+
+ align:start position:0%
+okay so here's the thing that's the same
+ 
+
+ align:start position:0%
+okay so here's the thing that's the same
+stimulus it's just upside down another
+
+ align:start position:0%
+stimulus it's just upside down another
+ 
+
+ align:start position:0%
+stimulus it's just upside down another
+version of the face inversion effect
+
+ align:start position:0%
+version of the face inversion effect
+ 
+
+ align:start position:0%
+version of the face inversion effect
+in this case you can't even make
+
+ align:start position:0%
+in this case you can't even make
+ 
+
+ align:start position:0%
+in this case you can't even make
+yourself see the face when it's upside
+
+ align:start position:0%
+yourself see the face when it's upside
+ 
+
+ align:start position:0%
+yourself see the face when it's upside
+down if you think you see the the upside
+
+ align:start position:0%
+down if you think you see the the upside
+ 
+
+ align:start position:0%
+down if you think you see the the upside
+down version of the face you probably
+
+ align:start position:0%
+down version of the face you probably
+ 
+
+ align:start position:0%
+down version of the face you probably
+have the wrong bits the thing you think
+
+ align:start position:0%
+have the wrong bits the thing you think
+ 
+
+ align:start position:0%
+have the wrong bits the thing you think
+is the nose probably isn't etc okay so
+
+ align:start position:0%
+is the nose probably isn't etc okay so
+ 
+
+ align:start position:0%
+is the nose probably isn't etc okay so
+this is an extreme version of the face
+
+ align:start position:0%
+this is an extreme version of the face
+ 
+
+ align:start position:0%
+this is an extreme version of the face
+inversion effect and it's a gift to an
+
+ align:start position:0%
+inversion effect and it's a gift to an
+ 
+
+ align:start position:0%
+inversion effect and it's a gift to an
+experimental psychologist
+
+ align:start position:0%
+experimental psychologist
+ 
+
+ align:start position:0%
+experimental psychologist
+why is that such a gift
+
+ align:start position:0%
+why is that such a gift
+ 
+
+ align:start position:0%
+why is that such a gift
+because it's the same damn stimulus but
+
+ align:start position:0%
+because it's the same damn stimulus but
+ 
+
+ align:start position:0%
+because it's the same damn stimulus but
+in one case you see a face and another
+
+ align:start position:0%
+in one case you see a face and another
+ 
+
+ align:start position:0%
+in one case you see a face and another
+case you don't all we did was tip it
+
+ align:start position:0%
+case you don't all we did was tip it
+ 
+
+ align:start position:0%
+case you don't all we did was tip it
+upside down
+
+ align:start position:0%
+upside down
+ 
+
+ align:start position:0%
+upside down
+and the response of the fusiform face
+
+ align:start position:0%
+and the response of the fusiform face
+ 
+
+ align:start position:0%
+and the response of the fusiform face
+area is much stronger
+
+ align:start position:0%
+area is much stronger
+ 
+
+ align:start position:0%
+area is much stronger
+to the upright version when you see the
+
+ align:start position:0%
+to the upright version when you see the
+ 
+
+ align:start position:0%
+to the upright version when you see the
+face than to the inverted version when
+
+ align:start position:0%
+face than to the inverted version when
+ 
+
+ align:start position:0%
+face than to the inverted version when
+you don't
+
+ align:start position:0%
+you don't
+ 
+
+ align:start position:0%
+you don't
+so that enables us to
+
+ align:start position:0%
+so that enables us to
+ 
+
+ align:start position:0%
+so that enables us to
+stifle a whole line of attack from all
+
+ align:start position:0%
+stifle a whole line of attack from all
+ 
+
+ align:start position:0%
+stifle a whole line of attack from all
+of these hardcore vision people
+
+ align:start position:0%
+of these hardcore vision people
+ 
+
+ align:start position:0%
+of these hardcore vision people
+who early on said cowisher your face
+
+ align:start position:0%
+who early on said cowisher your face
+ 
+
+ align:start position:0%
+who early on said cowisher your face
+area isn't really selective for faces
+
+ align:start position:0%
+area isn't really selective for faces
+ 
+
+ align:start position:0%
+area isn't really selective for faces
+it's respect it's selective for these uh
+
+ align:start position:0%
+it's respect it's selective for these uh
+ 
+
+ align:start position:0%
+it's respect it's selective for these uh
+spatial frequencies or those that kind
+
+ align:start position:0%
+spatial frequencies or those that kind
+ 
+
+ align:start position:0%
+spatial frequencies or those that kind
+of contrast or this kind of shading
+
+ align:start position:0%
+of contrast or this kind of shading
+ 
+
+ align:start position:0%
+of contrast or this kind of shading
+information it's like no same stimulus
+
+ align:start position:0%
+information it's like no same stimulus
+ 
+
+ align:start position:0%
+information it's like no same stimulus
+it's just upside down it makes all the
+
+ align:start position:0%
+it's just upside down it makes all the
+ 
+
+ align:start position:0%
+it's just upside down it makes all the
+difference it's really whether you see a
+
+ align:start position:0%
+difference it's really whether you see a
+ 
+
+ align:start position:0%
+difference it's really whether you see a
+face or not yeah when you're measuring
+
+ align:start position:0%
+face or not yeah when you're measuring
+ 
+
+ align:start position:0%
+face or not yeah when you're measuring
+the response of that example
+
+ align:start position:0%
+the response of that example
+ 
+
+ align:start position:0%
+the response of that example
+did you like did you have it so that at
+
+ align:start position:0%
+did you like did you have it so that at
+ 
+
+ align:start position:0%
+did you like did you have it so that at
+first when people that the first time
+
+ align:start position:0%
+first when people that the first time
+ 
+
+ align:start position:0%
+first when people that the first time
+didn't recognize it and then you told
+
+ align:start position:0%
+didn't recognize it and then you told
+ 
+
+ align:start position:0%
+didn't recognize it and then you told
+them we did that later not in this
+
+ align:start position:0%
+them we did that later not in this
+ 
+
+ align:start position:0%
+them we did that later not in this
+experiment but we did that later and
+
+ align:start position:0%
+experiment but we did that later and
+ 
+
+ align:start position:0%
+experiment but we did that later and
+then look to see like what
+
+ align:start position:0%
+then look to see like what
+ 
+
+ align:start position:0%
+then look to see like what
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so uh it's a great question and
+
+ align:start position:0%
+okay so uh it's a great question and
+ 
+
+ align:start position:0%
+okay so uh it's a great question and
+there's a lot you could do with that and
+
+ align:start position:0%
+there's a lot you could do with that and
+ 
+
+ align:start position:0%
+there's a lot you could do with that and
+actually i think other people have
+
+ align:start position:0%
+actually i think other people have
+ 
+
+ align:start position:0%
+actually i think other people have
+published studies like that since i
+
+ align:start position:0%
+published studies like that since i
+ 
+
+ align:start position:0%
+published studies like that since i
+can't quite remember who all has done it
+
+ align:start position:0%
+can't quite remember who all has done it
+ 
+
+ align:start position:0%
+can't quite remember who all has done it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but what we did was most of our subjects
+
+ align:start position:0%
+but what we did was most of our subjects
+ 
+
+ align:start position:0%
+but what we did was most of our subjects
+especially in the context of a whole
+
+ align:start position:0%
+especially in the context of a whole
+ 
+
+ align:start position:0%
+especially in the context of a whole
+experiment we chose stimuli so that most
+
+ align:start position:0%
+experiment we chose stimuli so that most
+ 
+
+ align:start position:0%
+experiment we chose stimuli so that most
+people could see the face in most of the
+
+ align:start position:0%
+people could see the face in most of the
+ 
+
+ align:start position:0%
+people could see the face in most of the
+upright stimuli and most people could
+
+ align:start position:0%
+upright stimuli and most people could
+ 
+
+ align:start position:0%
+upright stimuli and most people could
+not see the face in most of the inverted
+
+ align:start position:0%
+not see the face in most of the inverted
+ 
+
+ align:start position:0%
+not see the face in most of the inverted
+stimuli it wasn't perfect at all they
+
+ align:start position:0%
+stimuli it wasn't perfect at all they
+ 
+
+ align:start position:0%
+stimuli it wasn't perfect at all they
+didn't see faces in all of the upright
+
+ align:start position:0%
+didn't see faces in all of the upright
+ 
+
+ align:start position:0%
+didn't see faces in all of the upright
+ones and they didn't fail to see them in
+
+ align:start position:0%
+ones and they didn't fail to see them in
+ 
+
+ align:start position:0%
+ones and they didn't fail to see them in
+all of the inverted ones
+
+ align:start position:0%
+all of the inverted ones
+ 
+
+ align:start position:0%
+all of the inverted ones
+and that's probably why this difference
+
+ align:start position:0%
+and that's probably why this difference
+ 
+
+ align:start position:0%
+and that's probably why this difference
+in response is not you know two to one
+
+ align:start position:0%
+in response is not you know two to one
+ 
+
+ align:start position:0%
+in response is not you know two to one
+it's but it's close
+
+ align:start position:0%
+it's but it's close
+ 
+
+ align:start position:0%
+it's but it's close
+but you could do lots of other
+
+ align:start position:0%
+but you could do lots of other
+ 
+
+ align:start position:0%
+but you could do lots of other
+experiments like that and you should
+
+ align:start position:0%
+experiments like that and you should
+ 
+
+ align:start position:0%
+experiments like that and you should
+think about what kinds of designs would
+
+ align:start position:0%
+think about what kinds of designs would
+ 
+
+ align:start position:0%
+think about what kinds of designs would
+be good ones to do
+
+ align:start position:0%
+be good ones to do
+ 
+
+ align:start position:0%
+be good ones to do
+and what it would enable you to test
+
+ align:start position:0%
+and what it would enable you to test
+ 
+
+ align:start position:0%
+and what it would enable you to test
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so okay i'm as usual taking too long to
+
+ align:start position:0%
+so okay i'm as usual taking too long to
+ 
+
+ align:start position:0%
+so okay i'm as usual taking too long to
+do things so i'm just going to throw out
+
+ align:start position:0%
+do things so i'm just going to throw out
+ 
+
+ align:start position:0%
+do things so i'm just going to throw out
+some questions for you to percolate on
+
+ align:start position:0%
+some questions for you to percolate on
+ 
+
+ align:start position:0%
+some questions for you to percolate on
+and we will come back to them later in
+
+ align:start position:0%
+and we will come back to them later in
+ 
+
+ align:start position:0%
+and we will come back to them later in
+the course
+
+ align:start position:0%
+the course
+ 
+
+ align:start position:0%
+the course
+do these data the fact that you can see
+
+ align:start position:0%
+do these data the fact that you can see
+ 
+
+ align:start position:0%
+do these data the fact that you can see
+this so robustly in all subjects and
+
+ align:start position:0%
+this so robustly in all subjects and
+ 
+
+ align:start position:0%
+this so robustly in all subjects and
+that all this evidence suggests it's
+
+ align:start position:0%
+that all this evidence suggests it's
+ 
+
+ align:start position:0%
+that all this evidence suggests it's
+really very selective for faces
+
+ align:start position:0%
+really very selective for faces
+ 
+
+ align:start position:0%
+really very selective for faces
+does that tell us that this region is
+
+ align:start position:0%
+does that tell us that this region is
+ 
+
+ align:start position:0%
+does that tell us that this region is
+innate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's in the same place more or less than
+
+ align:start position:0%
+it's in the same place more or less than
+ 
+
+ align:start position:0%
+it's in the same place more or less than
+pretty much everyone
+
+ align:start position:0%
+pretty much everyone
+ 
+
+ align:start position:0%
+pretty much everyone
+does that mean it's innate
+
+ align:start position:0%
+does that mean it's innate
+ 
+
+ align:start position:0%
+does that mean it's innate
+think about it
+
+ align:start position:0%
+think about it
+ 
+
+ align:start position:0%
+think about it
+okay it's not immediately obvious
+
+ align:start position:0%
+okay it's not immediately obvious
+ 
+
+ align:start position:0%
+okay it's not immediately obvious
+another question
+
+ align:start position:0%
+another question
+ 
+
+ align:start position:0%
+another question
+does the fact that this thing responds
+
+ align:start position:0%
+does the fact that this thing responds
+ 
+
+ align:start position:0%
+does the fact that this thing responds
+so selectively to faces in pretty much
+
+ align:start position:0%
+so selectively to faces in pretty much
+ 
+
+ align:start position:0%
+so selectively to faces in pretty much
+everyone
+
+ align:start position:0%
+everyone
+ 
+
+ align:start position:0%
+everyone
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+mean that it's necessary for face
+
+ align:start position:0%
+mean that it's necessary for face
+ 
+
+ align:start position:0%
+mean that it's necessary for face
+recognition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you guys think about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the sense of like does that
+
+ align:start position:0%
+in the sense of like does that
+ 
+
+ align:start position:0%
+in the sense of like does that
+necessarily mean that if you lost that
+
+ align:start position:0%
+necessarily mean that if you lost that
+ 
+
+ align:start position:0%
+necessarily mean that if you lost that
+thing you wouldn't be able to recognize
+
+ align:start position:0%
+thing you wouldn't be able to recognize
+ 
+
+ align:start position:0%
+thing you wouldn't be able to recognize
+faces isabelle is that isabelle yes um
+
+ align:start position:0%
+faces isabelle is that isabelle yes um
+ 
+
+ align:start position:0%
+faces isabelle is that isabelle yes um
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+i would think would you really test that
+
+ align:start position:0%
+i would think would you really test that
+ 
+
+ align:start position:0%
+i would think would you really test that
+i promise you
+
+ align:start position:0%
+i promise you
+ 
+
+ align:start position:0%
+i promise you
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+exactly and we'll talk more about that
+
+ align:start position:0%
+exactly and we'll talk more about that
+ 
+
+ align:start position:0%
+exactly and we'll talk more about that
+in a moment the critical thing is that
+
+ align:start position:0%
+in a moment the critical thing is that
+ 
+
+ align:start position:0%
+in a moment the critical thing is that
+it's fabulous and powerful and cool to
+
+ align:start position:0%
+it's fabulous and powerful and cool to
+ 
+
+ align:start position:0%
+it's fabulous and powerful and cool to
+be able to find this thing in everybody
+
+ align:start position:0%
+be able to find this thing in everybody
+ 
+
+ align:start position:0%
+be able to find this thing in everybody
+measure its response it's taken us very
+
+ align:start position:0%
+measure its response it's taken us very
+ 
+
+ align:start position:0%
+measure its response it's taken us very
+far but
+
+ align:start position:0%
+far but
+ 
+
+ align:start position:0%
+far but
+just the fact that people have that
+
+ align:start position:0%
+just the fact that people have that
+ 
+
+ align:start position:0%
+just the fact that people have that
+thing doesn't tell us that you need it
+
+ align:start position:0%
+thing doesn't tell us that you need it
+ 
+
+ align:start position:0%
+thing doesn't tell us that you need it
+for face recognition it just tells you
+
+ align:start position:0%
+for face recognition it just tells you
+ 
+
+ align:start position:0%
+for face recognition it just tells you
+what turns on when you recognize faces
+
+ align:start position:0%
+what turns on when you recognize faces
+ 
+
+ align:start position:0%
+what turns on when you recognize faces
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this is really important we'll
+
+ align:start position:0%
+this is really important we'll
+ 
+
+ align:start position:0%
+this is really important we'll
+keep coming around to this
+
+ align:start position:0%
+keep coming around to this
+ 
+
+ align:start position:0%
+keep coming around to this
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+does this tell us how face recognition
+
+ align:start position:0%
+does this tell us how face recognition
+ 
+
+ align:start position:0%
+does this tell us how face recognition
+actually works in the human brain
+
+ align:start position:0%
+actually works in the human brain
+ 
+
+ align:start position:0%
+actually works in the human brain
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+i mean it's important but it's like
+
+ align:start position:0%
+i mean it's important but it's like
+ 
+
+ align:start position:0%
+i mean it's important but it's like
+barely step zero unfortunately the field
+
+ align:start position:0%
+barely step zero unfortunately the field
+ 
+
+ align:start position:0%
+barely step zero unfortunately the field
+is kind of still at step zero for most
+
+ align:start position:0%
+is kind of still at step zero for most
+ 
+
+ align:start position:0%
+is kind of still at step zero for most
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+uh step zero is better than i guess i
+
+ align:start position:0%
+uh step zero is better than i guess i
+ 
+
+ align:start position:0%
+uh step zero is better than i guess i
+don't know maybe i should call it step
+
+ align:start position:0%
+don't know maybe i should call it step
+ 
+
+ align:start position:0%
+don't know maybe i should call it step
+one uh anyway it's something but we
+
+ align:start position:0%
+one uh anyway it's something but we
+ 
+
+ align:start position:0%
+one uh anyway it's something but we
+doesn't tell us how it works
+
+ align:start position:0%
+doesn't tell us how it works
+ 
+
+ align:start position:0%
+doesn't tell us how it works
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so advantages and
+
+ align:start position:0%
+all right so advantages and
+ 
+
+ align:start position:0%
+all right so advantages and
+disadvantages of functional mri
+
+ align:start position:0%
+disadvantages of functional mri
+ 
+
+ align:start position:0%
+disadvantages of functional mri
+advantages it is as i mentioned last
+
+ align:start position:0%
+advantages it is as i mentioned last
+ 
+
+ align:start position:0%
+advantages it is as i mentioned last
+time the best spatial resolution
+
+ align:start position:0%
+time the best spatial resolution
+ 
+
+ align:start position:0%
+time the best spatial resolution
+available for studies on normal subjects
+
+ align:start position:0%
+available for studies on normal subjects
+ 
+
+ align:start position:0%
+available for studies on normal subjects
+without opening their heads okay
+
+ align:start position:0%
+without opening their heads okay
+ 
+
+ align:start position:0%
+without opening their heads okay
+that's what it means to say non-invasive
+
+ align:start position:0%
+that's what it means to say non-invasive
+ 
+
+ align:start position:0%
+that's what it means to say non-invasive
+disadvantages
+
+ align:start position:0%
+disadvantages
+ 
+
+ align:start position:0%
+disadvantages
+as i just said we don't know just
+
+ align:start position:0%
+as i just said we don't know just
+ 
+
+ align:start position:0%
+as i just said we don't know just
+because we see a response there doesn't
+
+ align:start position:0%
+because we see a response there doesn't
+ 
+
+ align:start position:0%
+because we see a response there doesn't
+mean that that region is causally
+
+ align:start position:0%
+mean that that region is causally
+ 
+
+ align:start position:0%
+mean that that region is causally
+involved in perception or cognition or
+
+ align:start position:0%
+involved in perception or cognition or
+ 
+
+ align:start position:0%
+involved in perception or cognition or
+experience
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we don't know exactly what is going on
+
+ align:start position:0%
+we don't know exactly what is going on
+ 
+
+ align:start position:0%
+we don't know exactly what is going on
+at a neural level underlying that bold
+
+ align:start position:0%
+at a neural level underlying that bold
+ 
+
+ align:start position:0%
+at a neural level underlying that bold
+response that blood flow change it could
+
+ align:start position:0%
+response that blood flow change it could
+ 
+
+ align:start position:0%
+response that blood flow change it could
+be any metabolic change not necessarily
+
+ align:start position:0%
+be any metabolic change not necessarily
+ 
+
+ align:start position:0%
+be any metabolic change not necessarily
+neuronal spiking okay so it's a little
+
+ align:start position:0%
+neuronal spiking okay so it's a little
+ 
+
+ align:start position:0%
+neuronal spiking okay so it's a little
+bit it's very indirect and a little
+
+ align:start position:0%
+bit it's very indirect and a little
+ 
+
+ align:start position:0%
+bit it's very indirect and a little
+imprecise
+
+ align:start position:0%
+imprecise
+ 
+
+ align:start position:0%
+imprecise
+spatial resolution is much better than
+
+ align:start position:0%
+spatial resolution is much better than
+ 
+
+ align:start position:0%
+spatial resolution is much better than
+anything else in humans but it's
+
+ align:start position:0%
+anything else in humans but it's
+ 
+
+ align:start position:0%
+anything else in humans but it's
+appallingly bad compared to
+
+ align:start position:0%
+appallingly bad compared to
+ 
+
+ align:start position:0%
+appallingly bad compared to
+anything that people who work on animals
+
+ align:start position:0%
+anything that people who work on animals
+ 
+
+ align:start position:0%
+anything that people who work on animals
+can do or they routinely record from
+
+ align:start position:0%
+can do or they routinely record from
+ 
+
+ align:start position:0%
+can do or they routinely record from
+individual neurons or you know even
+
+ align:start position:0%
+individual neurons or you know even
+ 
+
+ align:start position:0%
+individual neurons or you know even
+dendrites on a
+
+ align:start position:0%
+dendrites on a
+ 
+
+ align:start position:0%
+dendrites on a
+on a neuron
+
+ align:start position:0%
+on a neuron
+ 
+
+ align:start position:0%
+on a neuron
+we are summing over
+
+ align:start position:0%
+we are summing over
+ 
+
+ align:start position:0%
+we are summing over
+hundreds of thousands of neurons in each
+
+ align:start position:0%
+hundreds of thousands of neurons in each
+ 
+
+ align:start position:0%
+hundreds of thousands of neurons in each
+pixel or voxel that we measure with
+
+ align:start position:0%
+pixel or voxel that we measure with
+ 
+
+ align:start position:0%
+pixel or voxel that we measure with
+functional mri
+
+ align:start position:0%
+functional mri
+ 
+
+ align:start position:0%
+functional mri
+it's very expensive
+
+ align:start position:0%
+it's very expensive
+ 
+
+ align:start position:0%
+it's very expensive
+it's a little cheaper than that here but
+
+ align:start position:0%
+it's a little cheaper than that here but
+ 
+
+ align:start position:0%
+it's a little cheaper than that here but
+in most places it's more than 600 bucks
+
+ align:start position:0%
+in most places it's more than 600 bucks
+ 
+
+ align:start position:0%
+in most places it's more than 600 bucks
+an hour that is a lot
+
+ align:start position:0%
+an hour that is a lot
+ 
+
+ align:start position:0%
+an hour that is a lot
+um there are other
+
+ align:start position:0%
+um there are other
+ 
+
+ align:start position:0%
+um there are other
+they're parts of the brain where it's
+
+ align:start position:0%
+they're parts of the brain where it's
+ 
+
+ align:start position:0%
+they're parts of the brain where it's
+really hard to get any signal for
+
+ align:start position:0%
+really hard to get any signal for
+ 
+
+ align:start position:0%
+really hard to get any signal for
+various physics he
+
+ align:start position:0%
+various physics he
+ 
+
+ align:start position:0%
+various physics he
+reasons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it makes a loud noise which is not
+
+ align:start position:0%
+and it makes a loud noise which is not
+ 
+
+ align:start position:0%
+and it makes a loud noise which is not
+always a problem but it's a problem for
+
+ align:start position:0%
+always a problem but it's a problem for
+ 
+
+ align:start position:0%
+always a problem but it's a problem for
+some things like scanning infants or
+
+ align:start position:0%
+some things like scanning infants or
+ 
+
+ align:start position:0%
+some things like scanning infants or
+like doing auditory experiments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the temporal resolution
+
+ align:start position:0%
+the temporal resolution
+ 
+
+ align:start position:0%
+the temporal resolution
+is not even close to the time scale on
+
+ align:start position:0%
+is not even close to the time scale on
+ 
+
+ align:start position:0%
+is not even close to the time scale on
+which vision happens okay so vision is
+
+ align:start position:0%
+which vision happens okay so vision is
+ 
+
+ align:start position:0%
+which vision happens okay so vision is
+really fast
+
+ align:start position:0%
+really fast
+ 
+
+ align:start position:0%
+really fast
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+functional mri is really slow
+
+ align:start position:0%
+functional mri is really slow
+ 
+
+ align:start position:0%
+functional mri is really slow
+right it's slow why is it slow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah blood levels take time to change
+
+ align:start position:0%
+yeah blood levels take time to change
+ 
+
+ align:start position:0%
+yeah blood levels take time to change
+yeah just takes a long time for blood
+
+ align:start position:0%
+yeah just takes a long time for blood
+ 
+
+ align:start position:0%
+yeah just takes a long time for blood
+blood flow to change after the increase
+
+ align:start position:0%
+blood flow to change after the increase
+ 
+
+ align:start position:0%
+blood flow to change after the increase
+in neural activity
+
+ align:start position:0%
+in neural activity
+ 
+
+ align:start position:0%
+in neural activity
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+okay so back to our questions that we're
+
+ align:start position:0%
+okay so back to our questions that we're
+ 
+
+ align:start position:0%
+okay so back to our questions that we're
+asking about face perception where did
+
+ align:start position:0%
+asking about face perception where did
+ 
+
+ align:start position:0%
+asking about face perception where did
+we get with functional mri well actually
+
+ align:start position:0%
+we get with functional mri well actually
+ 
+
+ align:start position:0%
+we get with functional mri well actually
+from both behavior and functional mri it
+
+ align:start position:0%
+from both behavior and functional mri it
+ 
+
+ align:start position:0%
+from both behavior and functional mri it
+kind of looks like we have a distinct
+
+ align:start position:0%
+kind of looks like we have a distinct
+ 
+
+ align:start position:0%
+kind of looks like we have a distinct
+system for recognizing faces than for
+
+ align:start position:0%
+system for recognizing faces than for
+ 
+
+ align:start position:0%
+system for recognizing faces than for
+for recognizing everything else
+
+ align:start position:0%
+for recognizing everything else
+ 
+
+ align:start position:0%
+for recognizing everything else
+i don't think we've totally nailed it
+
+ align:start position:0%
+i don't think we've totally nailed it
+ 
+
+ align:start position:0%
+i don't think we've totally nailed it
+yes quick question regardless
+
+ align:start position:0%
+yes quick question regardless
+ 
+
+ align:start position:0%
+yes quick question regardless
+so it's uh the resolution is the order
+
+ align:start position:0%
+so it's uh the resolution is the order
+ 
+
+ align:start position:0%
+so it's uh the resolution is the order
+of like a couple of seconds
+
+ align:start position:0%
+of like a couple of seconds
+ 
+
+ align:start position:0%
+of like a couple of seconds
+yeah some people would say you could get
+
+ align:start position:0%
+yeah some people would say you could get
+ 
+
+ align:start position:0%
+yeah some people would say you could get
+it down to a couple hundred milliseconds
+
+ align:start position:0%
+it down to a couple hundred milliseconds
+ 
+
+ align:start position:0%
+it down to a couple hundred milliseconds
+but that's debated you have you have to
+
+ align:start position:0%
+but that's debated you have you have to
+ 
+
+ align:start position:0%
+but that's debated you have you have to
+go to great lengths to do that normal
+
+ align:start position:0%
+go to great lengths to do that normal
+ 
+
+ align:start position:0%
+go to great lengths to do that normal
+functional mri a couple seconds at best
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so let's let's consider this next
+
+ align:start position:0%
+so let's let's consider this next
+ 
+
+ align:start position:0%
+so let's let's consider this next
+question how fast does face recognition
+
+ align:start position:0%
+question how fast does face recognition
+ 
+
+ align:start position:0%
+question how fast does face recognition
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+now that may seem like a completely
+
+ align:start position:0%
+now that may seem like a completely
+ 
+
+ align:start position:0%
+now that may seem like a completely
+arbitrary question to ask but it's not
+
+ align:start position:0%
+arbitrary question to ask but it's not
+ 
+
+ align:start position:0%
+arbitrary question to ask but it's not
+remember we're trying to understand the
+
+ align:start position:0%
+remember we're trying to understand the
+ 
+
+ align:start position:0%
+remember we're trying to understand the
+computations that are running in your
+
+ align:start position:0%
+computations that are running in your
+ 
+
+ align:start position:0%
+computations that are running in your
+head when you recognize faces
+
+ align:start position:0%
+head when you recognize faces
+ 
+
+ align:start position:0%
+head when you recognize faces
+and you might imagine some computations
+
+ align:start position:0%
+and you might imagine some computations
+ 
+
+ align:start position:0%
+and you might imagine some computations
+that are iterative that involve
+
+ align:start position:0%
+that are iterative that involve
+ 
+
+ align:start position:0%
+that are iterative that involve
+multiple repeated
+
+ align:start position:0%
+multiple repeated
+ 
+
+ align:start position:0%
+multiple repeated
+testing of hypotheses generative models
+
+ align:start position:0%
+testing of hypotheses generative models
+ 
+
+ align:start position:0%
+testing of hypotheses generative models
+whatever things that involve lots of
+
+ align:start position:0%
+whatever things that involve lots of
+ 
+
+ align:start position:0%
+whatever things that involve lots of
+iterated feedback versus things where
+
+ align:start position:0%
+iterated feedback versus things where
+ 
+
+ align:start position:0%
+iterated feedback versus things where
+you just have a feed-forward sweep of
+
+ align:start position:0%
+you just have a feed-forward sweep of
+ 
+
+ align:start position:0%
+you just have a feed-forward sweep of
+the visual system and so there might be
+
+ align:start position:0%
+the visual system and so there might be
+ 
+
+ align:start position:0%
+the visual system and so there might be
+very different time scales for those
+
+ align:start position:0%
+very different time scales for those
+ 
+
+ align:start position:0%
+very different time scales for those
+different kinds of
+
+ align:start position:0%
+different kinds of
+ 
+
+ align:start position:0%
+different kinds of
+mental processes
+
+ align:start position:0%
+mental processes
+ 
+
+ align:start position:0%
+mental processes
+uh so we just went through this
+
+ align:start position:0%
+uh so we just went through this
+ 
+
+ align:start position:0%
+uh so we just went through this
+functional mri is not going to answer
+
+ align:start position:0%
+functional mri is not going to answer
+ 
+
+ align:start position:0%
+functional mri is not going to answer
+this question it's just not it's a
+
+ align:start position:0%
+this question it's just not it's a
+ 
+
+ align:start position:0%
+this question it's just not it's a
+bummer but that's life we're adults
+
+ align:start position:0%
+bummer but that's life we're adults
+ 
+
+ align:start position:0%
+bummer but that's life we're adults
+we're going to just move on and use a
+
+ align:start position:0%
+we're going to just move on and use a
+ 
+
+ align:start position:0%
+we're going to just move on and use a
+different method
+
+ align:start position:0%
+different method
+ 
+
+ align:start position:0%
+different method
+okay so there's a bunch of different
+
+ align:start position:0%
+okay so there's a bunch of different
+ 
+
+ align:start position:0%
+okay so there's a bunch of different
+methods one is i kind of been around
+
+ align:start position:0%
+methods one is i kind of been around
+ 
+
+ align:start position:0%
+methods one is i kind of been around
+forever you glue electrodes on the head
+
+ align:start position:0%
+forever you glue electrodes on the head
+ 
+
+ align:start position:0%
+forever you glue electrodes on the head
+right sometimes you push the hair apart
+
+ align:start position:0%
+right sometimes you push the hair apart
+ 
+
+ align:start position:0%
+right sometimes you push the hair apart
+or try to find bald people and glue
+
+ align:start position:0%
+or try to find bald people and glue
+ 
+
+ align:start position:0%
+or try to find bald people and glue
+electrodes right on there and you can
+
+ align:start position:0%
+electrodes right on there and you can
+ 
+
+ align:start position:0%
+electrodes right on there and you can
+use in the old days you know about 10
+
+ align:start position:0%
+use in the old days you know about 10
+ 
+
+ align:start position:0%
+use in the old days you know about 10
+electrodes or you can use in more modern
+
+ align:start position:0%
+electrodes or you can use in more modern
+ 
+
+ align:start position:0%
+electrodes or you can use in more modern
+devices these nets with you know a few
+
+ align:start position:0%
+devices these nets with you know a few
+ 
+
+ align:start position:0%
+devices these nets with you know a few
+hundred
+
+ align:start position:0%
+hundred
+ 
+
+ align:start position:0%
+hundred
+electrodes that you settle onto the head
+
+ align:start position:0%
+electrodes that you settle onto the head
+ 
+
+ align:start position:0%
+electrodes that you settle onto the head
+and so then you just measure directly
+
+ align:start position:0%
+and so then you just measure directly
+ 
+
+ align:start position:0%
+and so then you just measure directly
+electrical potentials right on the scalp
+
+ align:start position:0%
+electrical potentials right on the scalp
+ 
+
+ align:start position:0%
+electrical potentials right on the scalp
+okay so what's cool about that is it's
+
+ align:start position:0%
+okay so what's cool about that is it's
+ 
+
+ align:start position:0%
+okay so what's cool about that is it's
+totally non-invasive and it gives you a
+
+ align:start position:0%
+totally non-invasive and it gives you a
+ 
+
+ align:start position:0%
+totally non-invasive and it gives you a
+beautiful online temporal measure of
+
+ align:start position:0%
+beautiful online temporal measure of
+ 
+
+ align:start position:0%
+beautiful online temporal measure of
+underlying neural activity
+
+ align:start position:0%
+underlying neural activity
+ 
+
+ align:start position:0%
+underlying neural activity
+what's not so cool about it is that
+
+ align:start position:0%
+what's not so cool about it is that
+ 
+
+ align:start position:0%
+what's not so cool about it is that
+electrical potentials blur all over the
+
+ align:start position:0%
+electrical potentials blur all over the
+ 
+
+ align:start position:0%
+electrical potentials blur all over the
+scalp and the spatial resolution is
+
+ align:start position:0%
+scalp and the spatial resolution is
+ 
+
+ align:start position:0%
+scalp and the spatial resolution is
+really awful
+
+ align:start position:0%
+really awful
+ 
+
+ align:start position:0%
+really awful
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the analogy has been made
+
+ align:start position:0%
+so the analogy has been made
+ 
+
+ align:start position:0%
+so the analogy has been made
+that it will be like sticking a
+
+ align:start position:0%
+that it will be like sticking a
+ 
+
+ align:start position:0%
+that it will be like sticking a
+microphone on the um inside of the top
+
+ align:start position:0%
+microphone on the um inside of the top
+ 
+
+ align:start position:0%
+microphone on the um inside of the top
+of a football stadium
+
+ align:start position:0%
+of a football stadium
+ 
+
+ align:start position:0%
+of a football stadium
+and collecting audio there like you
+
+ align:start position:0%
+and collecting audio there like you
+ 
+
+ align:start position:0%
+and collecting audio there like you
+would know
+
+ align:start position:0%
+would know
+ 
+
+ align:start position:0%
+would know
+when a touchdown was scored there's a
+
+ align:start position:0%
+when a touchdown was scored there's a
+ 
+
+ align:start position:0%
+when a touchdown was scored there's a
+lot of noise all over it's like okay
+
+ align:start position:0%
+lot of noise all over it's like okay
+ 
+
+ align:start position:0%
+lot of noise all over it's like okay
+there's an event we detected that event
+
+ align:start position:0%
+there's an event we detected that event
+ 
+
+ align:start position:0%
+there's an event we detected that event
+right you might be able to tell a touch
+
+ align:start position:0%
+right you might be able to tell a touch
+ 
+
+ align:start position:0%
+right you might be able to tell a touch
+ball from a touchdown from something
+
+ align:start position:0%
+ball from a touchdown from something
+ 
+
+ align:start position:0%
+ball from a touchdown from something
+else i don't know about football so i
+
+ align:start position:0%
+else i don't know about football so i
+ 
+
+ align:start position:0%
+else i don't know about football so i
+can't tell you what else anyway
+
+ align:start position:0%
+can't tell you what else anyway
+ 
+
+ align:start position:0%
+can't tell you what else anyway
+something else some other event that
+
+ align:start position:0%
+something else some other event that
+ 
+
+ align:start position:0%
+something else some other event that
+could happen okay
+
+ align:start position:0%
+could happen okay
+ 
+
+ align:start position:0%
+could happen okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so that will be useful for some things
+
+ align:start position:0%
+so that will be useful for some things
+ 
+
+ align:start position:0%
+so that will be useful for some things
+but kind of crude
+
+ align:start position:0%
+but kind of crude
+ 
+
+ align:start position:0%
+but kind of crude
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but you'd have a hell of a time telling
+
+ align:start position:0%
+but you'd have a hell of a time telling
+ 
+
+ align:start position:0%
+but you'd have a hell of a time telling
+anything else like what one person is
+
+ align:start position:0%
+anything else like what one person is
+ 
+
+ align:start position:0%
+anything else like what one person is
+saying to another person in the
+
+ align:start position:0%
+saying to another person in the
+ 
+
+ align:start position:0%
+saying to another person in the
+bleachers okay
+
+ align:start position:0%
+bleachers okay
+ 
+
+ align:start position:0%
+bleachers okay
+so that's the old analogy this is
+
+ align:start position:0%
+so that's the old analogy this is
+ 
+
+ align:start position:0%
+so that's the old analogy this is
+changing slightly
+
+ align:start position:0%
+changing slightly
+ 
+
+ align:start position:0%
+changing slightly
+um and i will get to that later
+
+ align:start position:0%
+um and i will get to that later
+ 
+
+ align:start position:0%
+um and i will get to that later
+but first i want to briefly mention the
+
+ align:start position:0%
+but first i want to briefly mention the
+ 
+
+ align:start position:0%
+but first i want to briefly mention the
+one of the assigned readings that i just
+
+ align:start position:0%
+one of the assigned readings that i just
+ 
+
+ align:start position:0%
+one of the assigned readings that i just
+hoped you guys could figure out on your
+
+ align:start position:0%
+hoped you guys could figure out on your
+ 
+
+ align:start position:0%
+hoped you guys could figure out on your
+own but just in case you were confused
+
+ align:start position:0%
+own but just in case you were confused
+ 
+
+ align:start position:0%
+own but just in case you were confused
+about it the point i wanted you to get
+
+ align:start position:0%
+about it the point i wanted you to get
+ 
+
+ align:start position:0%
+about it the point i wanted you to get
+from the thorpe reading
+
+ align:start position:0%
+from the thorpe reading
+ 
+
+ align:start position:0%
+from the thorpe reading
+is he's asking how how quickly can we
+
+ align:start position:0%
+is he's asking how how quickly can we
+ 
+
+ align:start position:0%
+is he's asking how how quickly can we
+tell if an image contains an animal or
+
+ align:start position:0%
+tell if an image contains an animal or
+ 
+
+ align:start position:0%
+tell if an image contains an animal or
+not it's a kind of way to say how fast
+
+ align:start position:0%
+not it's a kind of way to say how fast
+ 
+
+ align:start position:0%
+not it's a kind of way to say how fast
+is object recognition okay
+
+ align:start position:0%
+is object recognition okay
+ 
+
+ align:start position:0%
+is object recognition okay
+so what does he do he has people look at
+
+ align:start position:0%
+so what does he do he has people look at
+ 
+
+ align:start position:0%
+so what does he do he has people look at
+a bunch of images and they press a
+
+ align:start position:0%
+a bunch of images and they press a
+ 
+
+ align:start position:0%
+a bunch of images and they press a
+button if this button if it's an has an
+
+ align:start position:0%
+button if this button if it's an has an
+ 
+
+ align:start position:0%
+button if this button if it's an has an
+animal and this button if it doesn't
+
+ align:start position:0%
+animal and this button if it doesn't
+ 
+
+ align:start position:0%
+animal and this button if it doesn't
+really simple task
+
+ align:start position:0%
+really simple task
+ 
+
+ align:start position:0%
+really simple task
+so first question is why not just use
+
+ align:start position:0%
+so first question is why not just use
+ 
+
+ align:start position:0%
+so first question is why not just use
+those reaction times we can measure how
+
+ align:start position:0%
+those reaction times we can measure how
+ 
+
+ align:start position:0%
+those reaction times we can measure how
+fast it takes for people to press a
+
+ align:start position:0%
+fast it takes for people to press a
+ 
+
+ align:start position:0%
+fast it takes for people to press a
+button after the image comes on why not
+
+ align:start position:0%
+button after the image comes on why not
+ 
+
+ align:start position:0%
+button after the image comes on why not
+just use that
+
+ align:start position:0%
+just use that
+ 
+
+ align:start position:0%
+just use that
+does that tell us how fast object
+
+ align:start position:0%
+does that tell us how fast object
+ 
+
+ align:start position:0%
+does that tell us how fast object
+recognition occurs
+
+ align:start position:0%
+recognition occurs
+ 
+
+ align:start position:0%
+recognition occurs
+yeah jimmy it doesn't because if you
+
+ align:start position:0%
+yeah jimmy it doesn't because if you
+ 
+
+ align:start position:0%
+yeah jimmy it doesn't because if you
+perceive it and then you it also
+
+ align:start position:0%
+perceive it and then you it also
+ 
+
+ align:start position:0%
+perceive it and then you it also
+activates the motor neurons
+
+ align:start position:0%
+activates the motor neurons
+ 
+
+ align:start position:0%
+activates the motor neurons
+yeah i have to take all that time to
+
+ align:start position:0%
+yeah i have to take all that time to
+ 
+
+ align:start position:0%
+yeah i have to take all that time to
+figure out okay i see the animal okay
+
+ align:start position:0%
+figure out okay i see the animal okay
+ 
+
+ align:start position:0%
+figure out okay i see the animal okay
+which button is that and then like which
+
+ align:start position:0%
+which button is that and then like which
+ 
+
+ align:start position:0%
+which button is that and then like which
+finger do i push and then you got to
+
+ align:start position:0%
+finger do i push and then you got to
+ 
+
+ align:start position:0%
+finger do i push and then you got to
+send a signal all the way down here
+
+ align:start position:0%
+send a signal all the way down here
+ 
+
+ align:start position:0%
+send a signal all the way down here
+conduction velocity all the way out down
+
+ align:start position:0%
+conduction velocity all the way out down
+ 
+
+ align:start position:0%
+conduction velocity all the way out down
+to your finger that takes a long time
+
+ align:start position:0%
+to your finger that takes a long time
+ 
+
+ align:start position:0%
+to your finger that takes a long time
+and so it includes all that motor stuff
+
+ align:start position:0%
+and so it includes all that motor stuff
+ 
+
+ align:start position:0%
+and so it includes all that motor stuff
+in with the perceptual stuff we can make
+
+ align:start position:0%
+in with the perceptual stuff we can make
+ 
+
+ align:start position:0%
+in with the perceptual stuff we can make
+some guesses about how long that
+
+ align:start position:0%
+some guesses about how long that
+ 
+
+ align:start position:0%
+some guesses about how long that
+motor stuff takes but it's still not
+
+ align:start position:0%
+motor stuff takes but it's still not
+ 
+
+ align:start position:0%
+motor stuff takes but it's still not
+very precise
+
+ align:start position:0%
+very precise
+ 
+
+ align:start position:0%
+very precise
+so the point of the thorpe paper is
+
+ align:start position:0%
+so the point of the thorpe paper is
+ 
+
+ align:start position:0%
+so the point of the thorpe paper is
+they're basically trying to collect a
+
+ align:start position:0%
+they're basically trying to collect a
+ 
+
+ align:start position:0%
+they're basically trying to collect a
+reaction time out of the neurons in the
+
+ align:start position:0%
+reaction time out of the neurons in the
+ 
+
+ align:start position:0%
+reaction time out of the neurons in the
+head right
+
+ align:start position:0%
+head right
+ 
+
+ align:start position:0%
+head right
+so they're trying to actually collect
+
+ align:start position:0%
+so they're trying to actually collect
+ 
+
+ align:start position:0%
+so they're trying to actually collect
+it's essentially what they're collecting
+
+ align:start position:0%
+it's essentially what they're collecting
+ 
+
+ align:start position:0%
+it's essentially what they're collecting
+in this case is more the motor response
+
+ align:start position:0%
+in this case is more the motor response
+ 
+
+ align:start position:0%
+in this case is more the motor response
+because they're collecting responses
+
+ align:start position:0%
+because they're collecting responses
+ 
+
+ align:start position:0%
+because they're collecting responses
+over frontal lobes right and we haven't
+
+ align:start position:0%
+over frontal lobes right and we haven't
+ 
+
+ align:start position:0%
+over frontal lobes right and we haven't
+talked about this much but all of the
+
+ align:start position:0%
+talked about this much but all of the
+ 
+
+ align:start position:0%
+talked about this much but all of the
+visual stuff we've been talking about
+
+ align:start position:0%
+visual stuff we've been talking about
+ 
+
+ align:start position:0%
+visual stuff we've been talking about
+all happens in the back of the head okay
+
+ align:start position:0%
+all happens in the back of the head okay
+ 
+
+ align:start position:0%
+all happens in the back of the head okay
+more motor planning stuff mostly happens
+
+ align:start position:0%
+more motor planning stuff mostly happens
+ 
+
+ align:start position:0%
+more motor planning stuff mostly happens
+in the front of the head and so they're
+
+ align:start position:0%
+in the front of the head and so they're
+ 
+
+ align:start position:0%
+in the front of the head and so they're
+collecting responses out of here
+
+ align:start position:0%
+collecting responses out of here
+ 
+
+ align:start position:0%
+collecting responses out of here
+averaging over a bunch of frontal
+
+ align:start position:0%
+averaging over a bunch of frontal
+ 
+
+ align:start position:0%
+averaging over a bunch of frontal
+responses and they see the average
+
+ align:start position:0%
+responses and they see the average
+ 
+
+ align:start position:0%
+responses and they see the average
+response when there's an animal this is
+
+ align:start position:0%
+response when there's an animal this is
+ 
+
+ align:start position:0%
+response when there's an animal this is
+just potential average over those
+
+ align:start position:0%
+just potential average over those
+ 
+
+ align:start position:0%
+just potential average over those
+frontal electrodes is like this and when
+
+ align:start position:0%
+frontal electrodes is like this and when
+ 
+
+ align:start position:0%
+frontal electrodes is like this and when
+there's no animal it's like that
+
+ align:start position:0%
+there's no animal it's like that
+ 
+
+ align:start position:0%
+there's no animal it's like that
+and so what does that tell us
+
+ align:start position:0%
+and so what does that tell us
+ 
+
+ align:start position:0%
+and so what does that tell us
+about how fast people can distinguish
+
+ align:start position:0%
+about how fast people can distinguish
+ 
+
+ align:start position:0%
+about how fast people can distinguish
+whether an image has an animal or not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah it's less than that number
+
+ align:start position:0%
+yes yeah it's less than that number
+ 
+
+ align:start position:0%
+yes yeah it's less than that number
+less than
+
+ align:start position:0%
+less than
+ 
+
+ align:start position:0%
+less than
+1 516. okay why less than 150
+
+ align:start position:0%
+1 516. okay why less than 150
+ 
+
+ align:start position:0%
+1 516. okay why less than 150
+i i've read the paper so it's kind of
+
+ align:start position:0%
+i i've read the paper so it's kind of
+ 
+
+ align:start position:0%
+i i've read the paper so it's kind of
+cheating that's okay that's good that's
+
+ align:start position:0%
+cheating that's okay that's good that's
+ 
+
+ align:start position:0%
+cheating that's okay that's good that's
+fine
+
+ align:start position:0%
+fine
+ 
+
+ align:start position:0%
+fine
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it gives you like a bound
+
+ align:start position:0%
+it gives you like a bound
+ 
+
+ align:start position:0%
+it gives you like a bound
+uh the 150 second news giving you a
+
+ align:start position:0%
+uh the 150 second news giving you a
+ 
+
+ align:start position:0%
+uh the 150 second news giving you a
+bounce saying
+
+ align:start position:0%
+bounce saying
+ 
+
+ align:start position:0%
+bounce saying
+some process has been registered and now
+
+ align:start position:0%
+some process has been registered and now
+ 
+
+ align:start position:0%
+some process has been registered and now
+you're trying to do something else
+
+ align:start position:0%
+you're trying to do something else
+ 
+
+ align:start position:0%
+you're trying to do something else
+uh in the case of non-admins right
+
+ align:start position:0%
+uh in the case of non-admins right
+ 
+
+ align:start position:0%
+uh in the case of non-admins right
+so that's the deviation starts telling
+
+ align:start position:0%
+so that's the deviation starts telling
+ 
+
+ align:start position:0%
+so that's the deviation starts telling
+you that okay two different actions have
+
+ align:start position:0%
+you that okay two different actions have
+ 
+
+ align:start position:0%
+you that okay two different actions have
+started taking place yep so by that time
+
+ align:start position:0%
+started taking place yep so by that time
+ 
+
+ align:start position:0%
+started taking place yep so by that time
+the image ought to have been sort of
+
+ align:start position:0%
+the image ought to have been sort of
+ 
+
+ align:start position:0%
+the image ought to have been sort of
+fully processed so
+
+ align:start position:0%
+fully processed so
+ 
+
+ align:start position:0%
+fully processed so
+that should be something less than that
+
+ align:start position:0%
+that should be something less than that
+ 
+
+ align:start position:0%
+that should be something less than that
+number one yeah yeah i did everybody get
+
+ align:start position:0%
+number one yeah yeah i did everybody get
+ 
+
+ align:start position:0%
+number one yeah yeah i did everybody get
+that there's it's it's actually quite
+
+ align:start position:0%
+that there's it's it's actually quite
+ 
+
+ align:start position:0%
+that there's it's it's actually quite
+subtle so
+
+ align:start position:0%
+subtle so
+ 
+
+ align:start position:0%
+subtle so
+so the key thing is the these curves
+
+ align:start position:0%
+so the key thing is the these curves
+ 
+
+ align:start position:0%
+so the key thing is the these curves
+diverge right there at 150. so that
+
+ align:start position:0%
+diverge right there at 150. so that
+ 
+
+ align:start position:0%
+diverge right there at 150. so that
+tells you that by 150 milliseconds
+
+ align:start position:0%
+tells you that by 150 milliseconds
+ 
+
+ align:start position:0%
+tells you that by 150 milliseconds
+something in your brain is happening
+
+ align:start position:0%
+something in your brain is happening
+ 
+
+ align:start position:0%
+something in your brain is happening
+different if there's an animal and not
+
+ align:start position:0%
+different if there's an animal and not
+ 
+
+ align:start position:0%
+different if there's an animal and not
+an animal
+
+ align:start position:0%
+an animal
+ 
+
+ align:start position:0%
+an animal
+okay that's the key question but what is
+
+ align:start position:0%
+okay that's the key question but what is
+ 
+
+ align:start position:0%
+okay that's the key question but what is
+that something
+
+ align:start position:0%
+that something
+ 
+
+ align:start position:0%
+that something
+it may be your motor preparation of the
+
+ align:start position:0%
+it may be your motor preparation of the
+ 
+
+ align:start position:0%
+it may be your motor preparation of the
+response in that case the actual visual
+
+ align:start position:0%
+response in that case the actual visual
+ 
+
+ align:start position:0%
+response in that case the actual visual
+part happened before because you
+
+ align:start position:0%
+part happened before because you
+ 
+
+ align:start position:0%
+part happened before because you
+wouldn't know which button to press if
+
+ align:start position:0%
+wouldn't know which button to press if
+ 
+
+ align:start position:0%
+wouldn't know which button to press if
+you hadn't already recognized it okay
+
+ align:start position:0%
+you hadn't already recognized it okay
+ 
+
+ align:start position:0%
+you hadn't already recognized it okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+an upper bound for when that process
+
+ align:start position:0%
+an upper bound for when that process
+ 
+
+ align:start position:0%
+an upper bound for when that process
+happened because maybe it happened
+
+ align:start position:0%
+happened because maybe it happened
+ 
+
+ align:start position:0%
+happened because maybe it happened
+before and we're looking at a later
+
+ align:start position:0%
+before and we're looking at a later
+ 
+
+ align:start position:0%
+before and we're looking at a later
+stage
+
+ align:start position:0%
+stage
+ 
+
+ align:start position:0%
+stage
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+um but also it's an upper bound
+
+ align:start position:0%
+um but also it's an upper bound
+ 
+
+ align:start position:0%
+um but also it's an upper bound
+for the beginning of that process
+
+ align:start position:0%
+for the beginning of that process
+ 
+
+ align:start position:0%
+for the beginning of that process
+because the fact that those electrode
+
+ align:start position:0%
+because the fact that those electrode
+ 
+
+ align:start position:0%
+because the fact that those electrode
+responses have diverged doesn't mean
+
+ align:start position:0%
+responses have diverged doesn't mean
+ 
+
+ align:start position:0%
+responses have diverged doesn't mean
+you've finished processing whether it's
+
+ align:start position:0%
+you've finished processing whether it's
+ 
+
+ align:start position:0%
+you've finished processing whether it's
+an animal or not
+
+ align:start position:0%
+an animal or not
+ 
+
+ align:start position:0%
+an animal or not
+okay so it's kind of a subtle business
+
+ align:start position:0%
+okay so it's kind of a subtle business
+ 
+
+ align:start position:0%
+okay so it's kind of a subtle business
+reasoning from this
+
+ align:start position:0%
+reasoning from this
+ 
+
+ align:start position:0%
+reasoning from this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um that's all that
+
+ align:start position:0%
+um that's all that
+ 
+
+ align:start position:0%
+um that's all that
+so um that's a case with detecting
+
+ align:start position:0%
+so um that's a case with detecting
+ 
+
+ align:start position:0%
+so um that's a case with detecting
+animals what about faces to get back to
+
+ align:start position:0%
+animals what about faces to get back to
+ 
+
+ align:start position:0%
+animals what about faces to get back to
+our theme for today
+
+ align:start position:0%
+our theme for today
+ 
+
+ align:start position:0%
+our theme for today
+um yes you can learn about the speed of
+
+ align:start position:0%
+um yes you can learn about the speed of
+ 
+
+ align:start position:0%
+um yes you can learn about the speed of
+face detection at least with erps and so
+
+ align:start position:0%
+face detection at least with erps and so
+ 
+
+ align:start position:0%
+face detection at least with erps and so
+here's the first paper that did that
+
+ align:start position:0%
+here's the first paper that did that
+ 
+
+ align:start position:0%
+here's the first paper that did that
+back in 1996 they had electrodes over
+
+ align:start position:0%
+back in 1996 they had electrodes over
+ 
+
+ align:start position:0%
+back in 1996 they had electrodes over
+where's where are these just right
+
+ align:start position:0%
+where's where are these just right
+ 
+
+ align:start position:0%
+where's where are these just right
+around here and here i actually have
+
+ align:start position:0%
+around here and here i actually have
+ 
+
+ align:start position:0%
+around here and here i actually have
+those electrode locations tattooed and
+
+ align:start position:0%
+those electrode locations tattooed and
+ 
+
+ align:start position:0%
+those electrode locations tattooed and
+my on my scalp
+
+ align:start position:0%
+my on my scalp
+ 
+
+ align:start position:0%
+my on my scalp
+color coded anyway yes is erp just
+
+ align:start position:0%
+color coded anyway yes is erp just
+ 
+
+ align:start position:0%
+color coded anyway yes is erp just
+the same as an eeg just specifically yes
+
+ align:start position:0%
+the same as an eeg just specifically yes
+ 
+
+ align:start position:0%
+the same as an eeg just specifically yes
+exactly um it is
+
+ align:start position:0%
+exactly um it is
+ 
+
+ align:start position:0%
+exactly um it is
+it's the same as an eeg except what you
+
+ align:start position:0%
+it's the same as an eeg except what you
+ 
+
+ align:start position:0%
+it's the same as an eeg except what you
+do is you
+
+ align:start position:0%
+do is you
+ 
+
+ align:start position:0%
+do is you
+time lock the data collection to
+
+ align:start position:0%
+time lock the data collection to
+ 
+
+ align:start position:0%
+time lock the data collection to
+stimulus onset so it actually stands for
+
+ align:start position:0%
+stimulus onset so it actually stands for
+ 
+
+ align:start position:0%
+stimulus onset so it actually stands for
+event related potential and the reason
+
+ align:start position:0%
+event related potential and the reason
+ 
+
+ align:start position:0%
+event related potential and the reason
+it's event related is you collect all
+
+ align:start position:0%
+it's event related is you collect all
+ 
+
+ align:start position:0%
+it's event related is you collect all
+those trials and you time lock to
+
+ align:start position:0%
+those trials and you time lock to
+ 
+
+ align:start position:0%
+those trials and you time lock to
+stimulus onset and then you signal
+
+ align:start position:0%
+stimulus onset and then you signal
+ 
+
+ align:start position:0%
+stimulus onset and then you signal
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i had a slide on that but i took it out
+
+ align:start position:0%
+i had a slide on that but i took it out
+ 
+
+ align:start position:0%
+i had a slide on that but i took it out
+as to detail but that's exactly the idea
+
+ align:start position:0%
+as to detail but that's exactly the idea
+ 
+
+ align:start position:0%
+as to detail but that's exactly the idea
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so here stimulus onset is you know right
+
+ align:start position:0%
+so here stimulus onset is you know right
+ 
+
+ align:start position:0%
+so here stimulus onset is you know right
+around here this is time going this way
+
+ align:start position:0%
+around here this is time going this way
+ 
+
+ align:start position:0%
+around here this is time going this way
+and what you see it's hard to see here
+
+ align:start position:0%
+and what you see it's hard to see here
+ 
+
+ align:start position:0%
+and what you see it's hard to see here
+but the faces are right there and at 170
+
+ align:start position:0%
+but the faces are right there and at 170
+ 
+
+ align:start position:0%
+but the faces are right there and at 170
+milliseconds after stimulus onset
+
+ align:start position:0%
+milliseconds after stimulus onset
+ 
+
+ align:start position:0%
+milliseconds after stimulus onset
+there's a bigger bump
+
+ align:start position:0%
+there's a bigger bump
+ 
+
+ align:start position:0%
+there's a bigger bump
+for faces at you know an electrode
+
+ align:start position:0%
+for faces at you know an electrode
+ 
+
+ align:start position:0%
+for faces at you know an electrode
+approximately here
+
+ align:start position:0%
+approximately here
+ 
+
+ align:start position:0%
+approximately here
+uh and even more so actually even more
+
+ align:start position:0%
+uh and even more so actually even more
+ 
+
+ align:start position:0%
+uh and even more so actually even more
+so over the right hemisphere right there
+
+ align:start position:0%
+so over the right hemisphere right there
+ 
+
+ align:start position:0%
+so over the right hemisphere right there
+okay compared to cars and scrambled
+
+ align:start position:0%
+okay compared to cars and scrambled
+ 
+
+ align:start position:0%
+okay compared to cars and scrambled
+faces and stuff like that yeah what is
+
+ align:start position:0%
+faces and stuff like that yeah what is
+ 
+
+ align:start position:0%
+faces and stuff like that yeah what is
+your exactly measuring is it just like
+
+ align:start position:0%
+your exactly measuring is it just like
+ 
+
+ align:start position:0%
+your exactly measuring is it just like
+activity yeah so again it's it's
+
+ align:start position:0%
+activity yeah so again it's it's
+ 
+
+ align:start position:0%
+activity yeah so again it's it's
+electrodes glued on your scalp okay
+
+ align:start position:0%
+electrodes glued on your scalp okay
+ 
+
+ align:start position:0%
+electrodes glued on your scalp okay
+or just stuck there with some kind of
+
+ align:start position:0%
+or just stuck there with some kind of
+ 
+
+ align:start position:0%
+or just stuck there with some kind of
+icky gel okay
+
+ align:start position:0%
+icky gel okay
+ 
+
+ align:start position:0%
+icky gel okay
+and so they're just measuring potentials
+
+ align:start position:0%
+and so they're just measuring potentials
+ 
+
+ align:start position:0%
+and so they're just measuring potentials
+and so the idea is it's neural activity
+
+ align:start position:0%
+and so the idea is it's neural activity
+ 
+
+ align:start position:0%
+and so the idea is it's neural activity
+somewhere underneath those electrodes
+
+ align:start position:0%
+somewhere underneath those electrodes
+ 
+
+ align:start position:0%
+somewhere underneath those electrodes
+but maybe like anywhere within
+
+ align:start position:0%
+but maybe like anywhere within
+ 
+
+ align:start position:0%
+but maybe like anywhere within
+you know in you know inches like along
+
+ align:start position:0%
+you know in you know inches like along
+ 
+
+ align:start position:0%
+you know in you know inches like along
+probably averages over much of the whole
+
+ align:start position:0%
+probably averages over much of the whole
+ 
+
+ align:start position:0%
+probably averages over much of the whole
+lobe underneath so it's very spatially
+
+ align:start position:0%
+lobe underneath so it's very spatially
+ 
+
+ align:start position:0%
+lobe underneath so it's very spatially
+blurry
+
+ align:start position:0%
+blurry
+ 
+
+ align:start position:0%
+blurry
+it's giving you some kind of summed idea
+
+ align:start position:0%
+it's giving you some kind of summed idea
+ 
+
+ align:start position:0%
+it's giving you some kind of summed idea
+of activity under that electrode makes
+
+ align:start position:0%
+of activity under that electrode makes
+ 
+
+ align:start position:0%
+of activity under that electrode makes
+sense electrical activity because it's
+
+ align:start position:0%
+sense electrical activity because it's
+ 
+
+ align:start position:0%
+sense electrical activity because it's
+the direct electrical consequence of
+
+ align:start position:0%
+the direct electrical consequence of
+ 
+
+ align:start position:0%
+the direct electrical consequence of
+neural activity it's very precisely time
+
+ align:start position:0%
+neural activity it's very precisely time
+ 
+
+ align:start position:0%
+neural activity it's very precisely time
+locked
+
+ align:start position:0%
+locked
+ 
+
+ align:start position:0%
+locked
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+unlike functional mri which is going by
+
+ align:start position:0%
+unlike functional mri which is going by
+ 
+
+ align:start position:0%
+unlike functional mri which is going by
+way of blood flow
+
+ align:start position:0%
+way of blood flow
+ 
+
+ align:start position:0%
+way of blood flow
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that tells us that we have a phase
+
+ align:start position:0%
+so that tells us that we have a phase
+ 
+
+ align:start position:0%
+so that tells us that we have a phase
+specific response at 170 milliseconds
+
+ align:start position:0%
+specific response at 170 milliseconds
+ 
+
+ align:start position:0%
+specific response at 170 milliseconds
+and that's
+
+ align:start position:0%
+and that's
+ 
+
+ align:start position:0%
+and that's
+sort of more evidence that there might
+
+ align:start position:0%
+sort of more evidence that there might
+ 
+
+ align:start position:0%
+sort of more evidence that there might
+be something special in the brain for
+
+ align:start position:0%
+be something special in the brain for
+ 
+
+ align:start position:0%
+be something special in the brain for
+face recognition that's useful
+
+ align:start position:0%
+face recognition that's useful
+ 
+
+ align:start position:0%
+face recognition that's useful
+it tells us that faces are discriminated
+
+ align:start position:0%
+it tells us that faces are discriminated
+ 
+
+ align:start position:0%
+it tells us that faces are discriminated
+from non-faces
+
+ align:start position:0%
+from non-faces
+ 
+
+ align:start position:0%
+from non-faces
+they've begun to be discriminated from
+
+ align:start position:0%
+they've begun to be discriminated from
+ 
+
+ align:start position:0%
+they've begun to be discriminated from
+non-faces by 170 milliseconds after the
+
+ align:start position:0%
+non-faces by 170 milliseconds after the
+ 
+
+ align:start position:0%
+non-faces by 170 milliseconds after the
+stimulus comes on
+
+ align:start position:0%
+stimulus comes on
+ 
+
+ align:start position:0%
+stimulus comes on
+make sense
+
+ align:start position:0%
+make sense
+ 
+
+ align:start position:0%
+make sense
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now do we know whether the signal is
+
+ align:start position:0%
+now do we know whether the signal is
+ 
+
+ align:start position:0%
+now do we know whether the signal is
+coming from the fusiform face area
+
+ align:start position:0%
+coming from the fusiform face area
+ 
+
+ align:start position:0%
+coming from the fusiform face area
+no we have no idea it's like probably
+
+ align:start position:0%
+no we have no idea it's like probably
+ 
+
+ align:start position:0%
+no we have no idea it's like probably
+somewhere in the back of the head
+
+ align:start position:0%
+somewhere in the back of the head
+ 
+
+ align:start position:0%
+somewhere in the back of the head
+because you get it better with
+
+ align:start position:0%
+because you get it better with
+ 
+
+ align:start position:0%
+because you get it better with
+electrodes back here than electrodes up
+
+ align:start position:0%
+electrodes back here than electrodes up
+ 
+
+ align:start position:0%
+electrodes back here than electrodes up
+here but that's about it that's all you
+
+ align:start position:0%
+here but that's about it that's all you
+ 
+
+ align:start position:0%
+here but that's about it that's all you
+can tell
+
+ align:start position:0%
+can tell
+ 
+
+ align:start position:0%
+can tell
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so can we do a little bit better
+
+ align:start position:0%
+so can we do a little bit better
+ 
+
+ align:start position:0%
+so can we do a little bit better
+localizing the source of that signal
+
+ align:start position:0%
+localizing the source of that signal
+ 
+
+ align:start position:0%
+localizing the source of that signal
+well maybe a hair better using a very
+
+ align:start position:0%
+well maybe a hair better using a very
+ 
+
+ align:start position:0%
+well maybe a hair better using a very
+similar method called
+
+ align:start position:0%
+similar method called
+ 
+
+ align:start position:0%
+similar method called
+magnetoencephalography
+
+ align:start position:0%
+magnetoencephalography
+ 
+
+ align:start position:0%
+magnetoencephalography
+so this is a picture that chris brewer
+
+ align:start position:0%
+so this is a picture that chris brewer
+ 
+
+ align:start position:0%
+so this is a picture that chris brewer
+took
+
+ align:start position:0%
+took
+ 
+
+ align:start position:0%
+took
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+laila ishik postdoc in my lab and me in
+
+ align:start position:0%
+laila ishik postdoc in my lab and me in
+ 
+
+ align:start position:0%
+laila ishik postdoc in my lab and me in
+the meg system this is in
+
+ align:start position:0%
+the meg system this is in
+ 
+
+ align:start position:0%
+the meg system this is in
+on the other side of the building
+
+ align:start position:0%
+on the other side of the building
+ 
+
+ align:start position:0%
+on the other side of the building
+so meg is a lot like um eeg and erps
+
+ align:start position:0%
+so meg is a lot like um eeg and erps
+ 
+
+ align:start position:0%
+so meg is a lot like um eeg and erps
+except it detects magnetic fields not
+
+ align:start position:0%
+except it detects magnetic fields not
+ 
+
+ align:start position:0%
+except it detects magnetic fields not
+electric fields okay and it does this by
+
+ align:start position:0%
+electric fields okay and it does this by
+ 
+
+ align:start position:0%
+electric fields okay and it does this by
+having these um several hundred um
+
+ align:start position:0%
+having these um several hundred um
+ 
+
+ align:start position:0%
+having these um several hundred um
+devices that are placed right next to
+
+ align:start position:0%
+devices that are placed right next to
+ 
+
+ align:start position:0%
+devices that are placed right next to
+your head in this big hairdryer thing
+
+ align:start position:0%
+your head in this big hairdryer thing
+ 
+
+ align:start position:0%
+your head in this big hairdryer thing
+there's like 300 devices in there that
+
+ align:start position:0%
+there's like 300 devices in there that
+ 
+
+ align:start position:0%
+there's like 300 devices in there that
+measure
+
+ align:start position:0%
+measure
+ 
+
+ align:start position:0%
+measure
+teeny tiny magnetic field changes that
+
+ align:start position:0%
+teeny tiny magnetic field changes that
+ 
+
+ align:start position:0%
+teeny tiny magnetic field changes that
+happen with neural activity
+
+ align:start position:0%
+happen with neural activity
+ 
+
+ align:start position:0%
+happen with neural activity
+the crux of the idea is
+
+ align:start position:0%
+the crux of the idea is
+ 
+
+ align:start position:0%
+the crux of the idea is
+this is a cross section through the
+
+ align:start position:0%
+this is a cross section through the
+ 
+
+ align:start position:0%
+this is a cross section through the
+brain so remember from uh angry bill's
+
+ align:start position:0%
+brain so remember from uh angry bill's
+ 
+
+ align:start position:0%
+brain so remember from uh angry bill's
+dissection right this is cortex here and
+
+ align:start position:0%
+dissection right this is cortex here and
+ 
+
+ align:start position:0%
+dissection right this is cortex here and
+this is underlying what is this stuff
+
+ align:start position:0%
+this is underlying what is this stuff
+ 
+
+ align:start position:0%
+this is underlying what is this stuff
+underneath underneath it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+white matter yeah well those are all the
+
+ align:start position:0%
+white matter yeah well those are all the
+ 
+
+ align:start position:0%
+white matter yeah well those are all the
+fibers okay so
+
+ align:start position:0%
+fibers okay so
+ 
+
+ align:start position:0%
+fibers okay so
+the activity that underlies perception
+
+ align:start position:0%
+the activity that underlies perception
+ 
+
+ align:start position:0%
+the activity that underlies perception
+and and cognition mostly happens in the
+
+ align:start position:0%
+and and cognition mostly happens in the
+ 
+
+ align:start position:0%
+and and cognition mostly happens in the
+gray matter where the cell bodies are
+
+ align:start position:0%
+gray matter where the cell bodies are
+ 
+
+ align:start position:0%
+gray matter where the cell bodies are
+um and so a lot of that activity goes in
+
+ align:start position:0%
+um and so a lot of that activity goes in
+ 
+
+ align:start position:0%
+um and so a lot of that activity goes in
+a direction perpendicular to the
+
+ align:start position:0%
+a direction perpendicular to the
+ 
+
+ align:start position:0%
+a direction perpendicular to the
+cortical orientation with these cells
+
+ align:start position:0%
+cortical orientation with these cells
+ 
+
+ align:start position:0%
+cortical orientation with these cells
+that cross the cortical surface like
+
+ align:start position:0%
+that cross the cortical surface like
+ 
+
+ align:start position:0%
+that cross the cortical surface like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so if you remember 802
+
+ align:start position:0%
+so if you remember 802
+ 
+
+ align:start position:0%
+so if you remember 802
+if you have activity that's going
+
+ align:start position:0%
+if you have activity that's going
+ 
+
+ align:start position:0%
+if you have activity that's going
+through the cortex like this
+
+ align:start position:0%
+through the cortex like this
+ 
+
+ align:start position:0%
+through the cortex like this
+right hand rule
+
+ align:start position:0%
+right hand rule
+ 
+
+ align:start position:0%
+right hand rule
+the magnetic field here
+
+ align:start position:0%
+the magnetic field here
+ 
+
+ align:start position:0%
+the magnetic field here
+is going to be that's a consequence of
+
+ align:start position:0%
+is going to be that's a consequence of
+ 
+
+ align:start position:0%
+is going to be that's a consequence of
+that electrical activity in this
+
+ align:start position:0%
+that electrical activity in this
+ 
+
+ align:start position:0%
+that electrical activity in this
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+is going to mostly stay within the
+
+ align:start position:0%
+is going to mostly stay within the
+ 
+
+ align:start position:0%
+is going to mostly stay within the
+cortex everybody see how that's true
+
+ align:start position:0%
+cortex everybody see how that's true
+ 
+
+ align:start position:0%
+cortex everybody see how that's true
+that's not so great because our
+
+ align:start position:0%
+that's not so great because our
+ 
+
+ align:start position:0%
+that's not so great because our
+detectors are out there outside the
+
+ align:start position:0%
+detectors are out there outside the
+ 
+
+ align:start position:0%
+detectors are out there outside the
+cortex
+
+ align:start position:0%
+cortex
+ 
+
+ align:start position:0%
+cortex
+however consider the activity that's in
+
+ align:start position:0%
+however consider the activity that's in
+ 
+
+ align:start position:0%
+however consider the activity that's in
+the sulcus in here in this fold of the
+
+ align:start position:0%
+the sulcus in here in this fold of the
+ 
+
+ align:start position:0%
+the sulcus in here in this fold of the
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+electrical activity in this direction
+
+ align:start position:0%
+electrical activity in this direction
+ 
+
+ align:start position:0%
+electrical activity in this direction
+right hand rule
+
+ align:start position:0%
+right hand rule
+ 
+
+ align:start position:0%
+right hand rule
+will stick outside the brain and we can
+
+ align:start position:0%
+will stick outside the brain and we can
+ 
+
+ align:start position:0%
+will stick outside the brain and we can
+detect it with our magnetic sensors does
+
+ align:start position:0%
+detect it with our magnetic sensors does
+ 
+
+ align:start position:0%
+detect it with our magnetic sensors does
+that make sense
+
+ align:start position:0%
+that make sense
+ 
+
+ align:start position:0%
+that make sense
+so you can sort of see
+
+ align:start position:0%
+so you can sort of see
+ 
+
+ align:start position:0%
+so you can sort of see
+um the most cortical activity better if
+
+ align:start position:0%
+um the most cortical activity better if
+ 
+
+ align:start position:0%
+um the most cortical activity better if
+it's in a sulcus or at least
+
+ align:start position:0%
+it's in a sulcus or at least
+ 
+
+ align:start position:0%
+it's in a sulcus or at least
+in part of the cortical surface that's
+
+ align:start position:0%
+in part of the cortical surface that's
+ 
+
+ align:start position:0%
+in part of the cortical surface that's
+perpendicular to the scalp where the
+
+ align:start position:0%
+perpendicular to the scalp where the
+ 
+
+ align:start position:0%
+perpendicular to the scalp where the
+detectors are just because of the
+
+ align:start position:0%
+detectors are just because of the
+ 
+
+ align:start position:0%
+detectors are just because of the
+orientation in the right hand rule
+
+ align:start position:0%
+orientation in the right hand rule
+ 
+
+ align:start position:0%
+orientation in the right hand rule
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so it primarily sees
+
+ align:start position:0%
+so it primarily sees
+ 
+
+ align:start position:0%
+so it primarily sees
+activity in the in the folds or soul
+
+ align:start position:0%
+activity in the in the folds or soul
+ 
+
+ align:start position:0%
+activity in the in the folds or soul
+site not in the outer bumps or right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field strengths are minuscule as a
+
+ align:start position:0%
+field strengths are minuscule as a
+ 
+
+ align:start position:0%
+field strengths are minuscule as a
+consequence of neural activity so the
+
+ align:start position:0%
+consequence of neural activity so the
+ 
+
+ align:start position:0%
+consequence of neural activity so the
+fields we measure are 10 to the minus
+
+ align:start position:0%
+fields we measure are 10 to the minus
+ 
+
+ align:start position:0%
+fields we measure are 10 to the minus
+13th tesla
+
+ align:start position:0%
+13th tesla
+ 
+
+ align:start position:0%
+13th tesla
+a million times weaker than the earth's
+
+ align:start position:0%
+a million times weaker than the earth's
+ 
+
+ align:start position:0%
+a million times weaker than the earth's
+magnetic field
+
+ align:start position:0%
+magnetic field
+ 
+
+ align:start position:0%
+magnetic field
+so you can imagine that if you set up an
+
+ align:start position:0%
+so you can imagine that if you set up an
+ 
+
+ align:start position:0%
+so you can imagine that if you set up an
+meg system
+
+ align:start position:0%
+meg system
+ 
+
+ align:start position:0%
+meg system
+you need a lot of shielding we had a
+
+ align:start position:0%
+you need a lot of shielding we had a
+ 
+
+ align:start position:0%
+you need a lot of shielding we had a
+whole rigmarole when the
+
+ align:start position:0%
+whole rigmarole when the
+ 
+
+ align:start position:0%
+whole rigmarole when the
+meg system was set up in this building
+
+ align:start position:0%
+meg system was set up in this building
+ 
+
+ align:start position:0%
+meg system was set up in this building
+because it's right near the um the
+
+ align:start position:0%
+because it's right near the um the
+ 
+
+ align:start position:0%
+because it's right near the um the
+subway and the train
+
+ align:start position:0%
+subway and the train
+ 
+
+ align:start position:0%
+subway and the train
+and so there are many many layers of
+
+ align:start position:0%
+and so there are many many layers of
+ 
+
+ align:start position:0%
+and so there are many many layers of
+copper shielding to protect it so we can
+
+ align:start position:0%
+copper shielding to protect it so we can
+ 
+
+ align:start position:0%
+copper shielding to protect it so we can
+detect these teeny tiny
+
+ align:start position:0%
+detect these teeny tiny
+ 
+
+ align:start position:0%
+detect these teeny tiny
+magnetic fields from the brain's
+
+ align:start position:0%
+magnetic fields from the brain's
+ 
+
+ align:start position:0%
+magnetic fields from the brain's
+activity with
+
+ align:start position:0%
+activity with
+ 
+
+ align:start position:0%
+activity with
+separated from the noise of the outside
+
+ align:start position:0%
+separated from the noise of the outside
+ 
+
+ align:start position:0%
+separated from the noise of the outside
+world which is much greater in magnitude
+
+ align:start position:0%
+world which is much greater in magnitude
+ 
+
+ align:start position:0%
+world which is much greater in magnitude
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um all right so actually meg was
+
+ align:start position:0%
+so um all right so actually meg was
+ 
+
+ align:start position:0%
+so um all right so actually meg was
+invented here at mit by this guy david
+
+ align:start position:0%
+invented here at mit by this guy david
+ 
+
+ align:start position:0%
+invented here at mit by this guy david
+cohen
+
+ align:start position:0%
+cohen
+ 
+
+ align:start position:0%
+cohen
+and this is the first mg device ever
+
+ align:start position:0%
+and this is the first mg device ever
+ 
+
+ align:start position:0%
+and this is the first mg device ever
+built very cool
+
+ align:start position:0%
+built very cool
+ 
+
+ align:start position:0%
+built very cool
+way back in
+
+ align:start position:0%
+way back in
+ 
+
+ align:start position:0%
+way back in
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+what can it tell us about face
+
+ align:start position:0%
+what can it tell us about face
+ 
+
+ align:start position:0%
+what can it tell us about face
+perception well a lot i'll give you just
+
+ align:start position:0%
+perception well a lot i'll give you just
+ 
+
+ align:start position:0%
+perception well a lot i'll give you just
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+rudimentary example
+
+ align:start position:0%
+rudimentary example
+ 
+
+ align:start position:0%
+rudimentary example
+that n170 that you can detect with scalp
+
+ align:start position:0%
+that n170 that you can detect with scalp
+ 
+
+ align:start position:0%
+that n170 that you can detect with scalp
+electrodes you can also detect with
+
+ align:start position:0%
+electrodes you can also detect with
+ 
+
+ align:start position:0%
+electrodes you can also detect with
+magnetic sensors on the head so here's
+
+ align:start position:0%
+magnetic sensors on the head so here's
+ 
+
+ align:start position:0%
+magnetic sensors on the head so here's
+some of our data from a long time ago
+
+ align:start position:0%
+some of our data from a long time ago
+ 
+
+ align:start position:0%
+some of our data from a long time ago
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+strength of the magnetic field at sites
+
+ align:start position:0%
+strength of the magnetic field at sites
+ 
+
+ align:start position:0%
+strength of the magnetic field at sites
+right about you know out here
+
+ align:start position:0%
+right about you know out here
+ 
+
+ align:start position:0%
+right about you know out here
+and you can see a face selective
+
+ align:start position:0%
+and you can see a face selective
+ 
+
+ align:start position:0%
+and you can see a face selective
+response also at 170 milliseconds just
+
+ align:start position:0%
+response also at 170 milliseconds just
+ 
+
+ align:start position:0%
+response also at 170 milliseconds just
+like you can
+
+ align:start position:0%
+like you can
+ 
+
+ align:start position:0%
+like you can
+uh with scalp with scalp electrodes
+
+ align:start position:0%
+uh with scalp with scalp electrodes
+ 
+
+ align:start position:0%
+uh with scalp with scalp electrodes
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so that tells us that at least you've
+
+ align:start position:0%
+so that tells us that at least you've
+ 
+
+ align:start position:0%
+so that tells us that at least you've
+you've started to detect faces by 170
+
+ align:start position:0%
+you've started to detect faces by 170
+ 
+
+ align:start position:0%
+you've started to detect faces by 170
+milliseconds that's pretty fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again it's more evidence that
+
+ align:start position:0%
+and again it's more evidence that
+ 
+
+ align:start position:0%
+and again it's more evidence that
+there's specialized machinery these data
+
+ align:start position:0%
+there's specialized machinery these data
+ 
+
+ align:start position:0%
+there's specialized machinery these data
+don't yet go beyond the eeg data the erp
+
+ align:start position:0%
+don't yet go beyond the eeg data the erp
+ 
+
+ align:start position:0%
+don't yet go beyond the eeg data the erp
+data from electrical potentials
+
+ align:start position:0%
+data from electrical potentials
+ 
+
+ align:start position:0%
+data from electrical potentials
+but they might in principle and there's
+
+ align:start position:0%
+but they might in principle and there's
+ 
+
+ align:start position:0%
+but they might in principle and there's
+lots of ongoing work trying to do that
+
+ align:start position:0%
+lots of ongoing work trying to do that
+ 
+
+ align:start position:0%
+lots of ongoing work trying to do that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+overview advantages of these these
+
+ align:start position:0%
+overview advantages of these these
+ 
+
+ align:start position:0%
+overview advantages of these these
+methods both eeg and and meg they're
+
+ align:start position:0%
+methods both eeg and and meg they're
+ 
+
+ align:start position:0%
+methods both eeg and and meg they're
+non-invasive that means you don't need
+
+ align:start position:0%
+non-invasive that means you don't need
+ 
+
+ align:start position:0%
+non-invasive that means you don't need
+to open the head a very good thing
+
+ align:start position:0%
+to open the head a very good thing
+ 
+
+ align:start position:0%
+to open the head a very good thing
+especially if you're the subject
+
+ align:start position:0%
+especially if you're the subject
+ 
+
+ align:start position:0%
+especially if you're the subject
+they have very good temporal resolution
+
+ align:start position:0%
+they have very good temporal resolution
+ 
+
+ align:start position:0%
+they have very good temporal resolution
+and if we want to see computations
+
+ align:start position:0%
+and if we want to see computations
+ 
+
+ align:start position:0%
+and if we want to see computations
+unfolding over time in the brain this is
+
+ align:start position:0%
+unfolding over time in the brain this is
+ 
+
+ align:start position:0%
+unfolding over time in the brain this is
+a good way
+
+ align:start position:0%
+a good way
+ 
+
+ align:start position:0%
+a good way
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i just said why would care about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so far well never mind i'm going to skip
+
+ align:start position:0%
+so far well never mind i'm going to skip
+ 
+
+ align:start position:0%
+so far well never mind i'm going to skip
+this point not that important we will
+
+ align:start position:0%
+this point not that important we will
+ 
+
+ align:start position:0%
+this point not that important we will
+get back and do more sophisticated
+
+ align:start position:0%
+get back and do more sophisticated
+ 
+
+ align:start position:0%
+get back and do more sophisticated
+things with eeg and meg and subsequent
+
+ align:start position:0%
+things with eeg and meg and subsequent
+ 
+
+ align:start position:0%
+things with eeg and meg and subsequent
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+disadvantages
+
+ align:start position:0%
+disadvantages
+ 
+
+ align:start position:0%
+disadvantages
+spatial resolution is terrible
+
+ align:start position:0%
+spatial resolution is terrible
+ 
+
+ align:start position:0%
+spatial resolution is terrible
+and this is another kind of ill-posed
+
+ align:start position:0%
+and this is another kind of ill-posed
+ 
+
+ align:start position:0%
+and this is another kind of ill-posed
+problem so just as the brain is facing
+
+ align:start position:0%
+problem so just as the brain is facing
+ 
+
+ align:start position:0%
+problem so just as the brain is facing
+lots of ill-posed problems in perception
+
+ align:start position:0%
+lots of ill-posed problems in perception
+ 
+
+ align:start position:0%
+lots of ill-posed problems in perception
+and cognition
+
+ align:start position:0%
+and cognition
+ 
+
+ align:start position:0%
+and cognition
+we scientists are facing ill pose
+
+ align:start position:0%
+we scientists are facing ill pose
+ 
+
+ align:start position:0%
+we scientists are facing ill pose
+problems when we collect
+
+ align:start position:0%
+problems when we collect
+ 
+
+ align:start position:0%
+problems when we collect
+electrical or magnetic activity at the
+
+ align:start position:0%
+electrical or magnetic activity at the
+ 
+
+ align:start position:0%
+electrical or magnetic activity at the
+scalp and try to infer the exact
+
+ align:start position:0%
+scalp and try to infer the exact
+ 
+
+ align:start position:0%
+scalp and try to infer the exact
+location in the brain where it's coming
+
+ align:start position:0%
+location in the brain where it's coming
+ 
+
+ align:start position:0%
+location in the brain where it's coming
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+it's a similar problem to the problem of
+
+ align:start position:0%
+it's a similar problem to the problem of
+ 
+
+ align:start position:0%
+it's a similar problem to the problem of
+invariant object recognition there are
+
+ align:start position:0%
+invariant object recognition there are
+ 
+
+ align:start position:0%
+invariant object recognition there are
+many possible configurations of sources
+
+ align:start position:0%
+many possible configurations of sources
+ 
+
+ align:start position:0%
+many possible configurations of sources
+in the brain
+
+ align:start position:0%
+in the brain
+ 
+
+ align:start position:0%
+in the brain
+that could give rise to the same set of
+
+ align:start position:0%
+that could give rise to the same set of
+ 
+
+ align:start position:0%
+that could give rise to the same set of
+electrical and magnetic fields out of
+
+ align:start position:0%
+electrical and magnetic fields out of
+ 
+
+ align:start position:0%
+electrical and magnetic fields out of
+the scalp
+
+ align:start position:0%
+the scalp
+ 
+
+ align:start position:0%
+the scalp
+and that means it's ill-posed we don't
+
+ align:start position:0%
+and that means it's ill-posed we don't
+ 
+
+ align:start position:0%
+and that means it's ill-posed we don't
+have a way to get a unique solution okay
+
+ align:start position:0%
+have a way to get a unique solution okay
+ 
+
+ align:start position:0%
+have a way to get a unique solution okay
+so all that to say
+
+ align:start position:0%
+so all that to say
+ 
+
+ align:start position:0%
+so all that to say
+we can't figure out the exact sources we
+
+ align:start position:0%
+we can't figure out the exact sources we
+ 
+
+ align:start position:0%
+we can't figure out the exact sources we
+can make some guesses that's not very
+
+ align:start position:0%
+can make some guesses that's not very
+ 
+
+ align:start position:0%
+can make some guesses that's not very
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so what do we do just give up
+
+ align:start position:0%
+so what do we do just give up
+ 
+
+ align:start position:0%
+so what do we do just give up
+no we use another method
+
+ align:start position:0%
+no we use another method
+ 
+
+ align:start position:0%
+no we use another method
+um so here's an amazing method
+
+ align:start position:0%
+um so here's an amazing method
+ 
+
+ align:start position:0%
+um so here's an amazing method
+this is the one method in humans that
+
+ align:start position:0%
+this is the one method in humans that
+ 
+
+ align:start position:0%
+this is the one method in humans that
+gives us high resolution in both space
+
+ align:start position:0%
+gives us high resolution in both space
+ 
+
+ align:start position:0%
+gives us high resolution in both space
+and time and that's when we have the
+
+ align:start position:0%
+and time and that's when we have the
+ 
+
+ align:start position:0%
+and time and that's when we have the
+very rare opportunity to record directly
+
+ align:start position:0%
+very rare opportunity to record directly
+ 
+
+ align:start position:0%
+very rare opportunity to record directly
+from inside the human brain this happens
+
+ align:start position:0%
+from inside the human brain this happens
+ 
+
+ align:start position:0%
+from inside the human brain this happens
+only in the context of neurosurgery
+
+ align:start position:0%
+only in the context of neurosurgery
+ 
+
+ align:start position:0%
+only in the context of neurosurgery
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+neurosurgical patients like this guy
+
+ align:start position:0%
+neurosurgical patients like this guy
+ 
+
+ align:start position:0%
+neurosurgical patients like this guy
+here we'll meet in a little bit
+
+ align:start position:0%
+here we'll meet in a little bit
+ 
+
+ align:start position:0%
+here we'll meet in a little bit
+this guy had intractable epilepsy
+
+ align:start position:0%
+this guy had intractable epilepsy
+ 
+
+ align:start position:0%
+this guy had intractable epilepsy
+and most people with epilepsy are
+
+ align:start position:0%
+and most people with epilepsy are
+ 
+
+ align:start position:0%
+and most people with epilepsy are
+treated well by drugs that suppress
+
+ align:start position:0%
+treated well by drugs that suppress
+ 
+
+ align:start position:0%
+treated well by drugs that suppress
+seizures
+
+ align:start position:0%
+seizures
+ 
+
+ align:start position:0%
+seizures
+but some people are just not responsive
+
+ align:start position:0%
+but some people are just not responsive
+ 
+
+ align:start position:0%
+but some people are just not responsive
+to drugs and if the seizures are bad
+
+ align:start position:0%
+to drugs and if the seizures are bad
+ 
+
+ align:start position:0%
+to drugs and if the seizures are bad
+enough they can be you know totally life
+
+ align:start position:0%
+enough they can be you know totally life
+ 
+
+ align:start position:0%
+enough they can be you know totally life
+disrupting if they happen
+
+ align:start position:0%
+disrupting if they happen
+ 
+
+ align:start position:0%
+disrupting if they happen
+dozens of times a day you just can't
+
+ align:start position:0%
+dozens of times a day you just can't
+ 
+
+ align:start position:0%
+dozens of times a day you just can't
+live a normal life and under those
+
+ align:start position:0%
+live a normal life and under those
+ 
+
+ align:start position:0%
+live a normal life and under those
+rather extreme circumstances
+
+ align:start position:0%
+rather extreme circumstances
+ 
+
+ align:start position:0%
+rather extreme circumstances
+sometimes the best option is
+
+ align:start position:0%
+sometimes the best option is
+ 
+
+ align:start position:0%
+sometimes the best option is
+neurosurgery that is trying to find the
+
+ align:start position:0%
+neurosurgery that is trying to find the
+ 
+
+ align:start position:0%
+neurosurgery that is trying to find the
+the source of that of those seizures and
+
+ align:start position:0%
+the source of that of those seizures and
+ 
+
+ align:start position:0%
+the source of that of those seizures and
+trying to remove it surgically
+
+ align:start position:0%
+trying to remove it surgically
+ 
+
+ align:start position:0%
+trying to remove it surgically
+okay so you hope you never have to go
+
+ align:start position:0%
+okay so you hope you never have to go
+ 
+
+ align:start position:0%
+okay so you hope you never have to go
+through this or anyone you care about
+
+ align:start position:0%
+through this or anyone you care about
+ 
+
+ align:start position:0%
+through this or anyone you care about
+has to go through it it's no picnic
+
+ align:start position:0%
+has to go through it it's no picnic
+ 
+
+ align:start position:0%
+has to go through it it's no picnic
+but actually this surgical treatment is
+
+ align:start position:0%
+but actually this surgical treatment is
+ 
+
+ align:start position:0%
+but actually this surgical treatment is
+often very effective okay
+
+ align:start position:0%
+often very effective okay
+ 
+
+ align:start position:0%
+often very effective okay
+so when neurosurgeons
+
+ align:start position:0%
+so when neurosurgeons
+ 
+
+ align:start position:0%
+so when neurosurgeons
+decide to do this they have to remove a
+
+ align:start position:0%
+decide to do this they have to remove a
+ 
+
+ align:start position:0%
+decide to do this they have to remove a
+whole piece of
+
+ align:start position:0%
+whole piece of
+ 
+
+ align:start position:0%
+whole piece of
+of skull bone to get access to the brain
+
+ align:start position:0%
+of skull bone to get access to the brain
+ 
+
+ align:start position:0%
+of skull bone to get access to the brain
+they have to go through what structure
+
+ align:start position:0%
+they have to go through what structure
+ 
+
+ align:start position:0%
+they have to go through what structure
+that ann treesman and treesman and
+
+ align:start position:0%
+that ann treesman and treesman and
+ 
+
+ align:start position:0%
+that ann treesman and treesman and
+graybill showed you in her dissection
+
+ align:start position:0%
+graybill showed you in her dissection
+ 
+
+ align:start position:0%
+graybill showed you in her dissection
+the other day
+
+ align:start position:0%
+the other day
+ 
+
+ align:start position:0%
+the other day
+what do you have to after you take off
+
+ align:start position:0%
+what do you have to after you take off
+ 
+
+ align:start position:0%
+what do you have to after you take off
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+a skull patch yes
+
+ align:start position:0%
+a skull patch yes
+ 
+
+ align:start position:0%
+a skull patch yes
+dura mater exactly that nice big piece
+
+ align:start position:0%
+dura mater exactly that nice big piece
+ 
+
+ align:start position:0%
+dura mater exactly that nice big piece
+of white leathery stuff that was sitting
+
+ align:start position:0%
+of white leathery stuff that was sitting
+ 
+
+ align:start position:0%
+of white leathery stuff that was sitting
+over the surface of the brain so you
+
+ align:start position:0%
+over the surface of the brain so you
+ 
+
+ align:start position:0%
+over the surface of the brain so you
+need to take off a skull piece of skull
+
+ align:start position:0%
+need to take off a skull piece of skull
+ 
+
+ align:start position:0%
+need to take off a skull piece of skull
+then you need to like you know cut
+
+ align:start position:0%
+then you need to like you know cut
+ 
+
+ align:start position:0%
+then you need to like you know cut
+through and push apart the dura and then
+
+ align:start position:0%
+through and push apart the dura and then
+ 
+
+ align:start position:0%
+through and push apart the dura and then
+what they sometimes do is stick
+
+ align:start position:0%
+what they sometimes do is stick
+ 
+
+ align:start position:0%
+what they sometimes do is stick
+electrodes straight on the surface of
+
+ align:start position:0%
+electrodes straight on the surface of
+ 
+
+ align:start position:0%
+electrodes straight on the surface of
+the brain
+
+ align:start position:0%
+the brain
+ 
+
+ align:start position:0%
+the brain
+okay and they do that for two reasons
+
+ align:start position:0%
+okay and they do that for two reasons
+ 
+
+ align:start position:0%
+okay and they do that for two reasons
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+if they have enough of them sampled far
+
+ align:start position:0%
+if they have enough of them sampled far
+ 
+
+ align:start position:0%
+if they have enough of them sampled far
+enough apart they can kind of
+
+ align:start position:0%
+enough apart they can kind of
+ 
+
+ align:start position:0%
+enough apart they can kind of
+triangulate and figure out where is the
+
+ align:start position:0%
+triangulate and figure out where is the
+ 
+
+ align:start position:0%
+triangulate and figure out where is the
+source of the seizure so the patient
+
+ align:start position:0%
+source of the seizure so the patient
+ 
+
+ align:start position:0%
+source of the seizure so the patient
+hangs out in the hospital for a week or
+
+ align:start position:0%
+hangs out in the hospital for a week or
+ 
+
+ align:start position:0%
+hangs out in the hospital for a week or
+so with these electrodes in their head
+
+ align:start position:0%
+so with these electrodes in their head
+ 
+
+ align:start position:0%
+so with these electrodes in their head
+waiting to have seizures and then when
+
+ align:start position:0%
+waiting to have seizures and then when
+ 
+
+ align:start position:0%
+waiting to have seizures and then when
+they have a seizure the clinicians can
+
+ align:start position:0%
+they have a seizure the clinicians can
+ 
+
+ align:start position:0%
+they have a seizure the clinicians can
+figure out where the source is so they
+
+ align:start position:0%
+figure out where the source is so they
+ 
+
+ align:start position:0%
+figure out where the source is so they
+know what bit to cut out
+
+ align:start position:0%
+know what bit to cut out
+ 
+
+ align:start position:0%
+know what bit to cut out
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the other reason to do this is to map
+
+ align:start position:0%
+the other reason to do this is to map
+ 
+
+ align:start position:0%
+the other reason to do this is to map
+functions because once the surgeons
+
+ align:start position:0%
+functions because once the surgeons
+ 
+
+ align:start position:0%
+functions because once the surgeons
+decide they have to go in and cut
+
+ align:start position:0%
+decide they have to go in and cut
+ 
+
+ align:start position:0%
+decide they have to go in and cut
+they want to try to not cut out any of
+
+ align:start position:0%
+they want to try to not cut out any of
+ 
+
+ align:start position:0%
+they want to try to not cut out any of
+the most important parts i don't know
+
+ align:start position:0%
+the most important parts i don't know
+ 
+
+ align:start position:0%
+the most important parts i don't know
+what it means to have unimportant parts
+
+ align:start position:0%
+what it means to have unimportant parts
+ 
+
+ align:start position:0%
+what it means to have unimportant parts
+of the brain but you know they try to
+
+ align:start position:0%
+of the brain but you know they try to
+ 
+
+ align:start position:0%
+of the brain but you know they try to
+they try to avoid language regions and
+
+ align:start position:0%
+they try to avoid language regions and
+ 
+
+ align:start position:0%
+they try to avoid language regions and
+stuff like that because then you know
+
+ align:start position:0%
+stuff like that because then you know
+ 
+
+ align:start position:0%
+stuff like that because then you know
+patients really notice if they lose
+
+ align:start position:0%
+patients really notice if they lose
+ 
+
+ align:start position:0%
+patients really notice if they lose
+those things
+
+ align:start position:0%
+those things
+ 
+
+ align:start position:0%
+those things
+right or motor control regions okay so
+
+ align:start position:0%
+right or motor control regions okay so
+ 
+
+ align:start position:0%
+right or motor control regions okay so
+they map out functions where they might
+
+ align:start position:0%
+they map out functions where they might
+ 
+
+ align:start position:0%
+they map out functions where they might
+be planning their route okay make sense
+
+ align:start position:0%
+be planning their route okay make sense
+ 
+
+ align:start position:0%
+be planning their route okay make sense
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+some of these patients are very kind and
+
+ align:start position:0%
+some of these patients are very kind and
+ 
+
+ align:start position:0%
+some of these patients are very kind and
+generous to the world and say
+
+ align:start position:0%
+generous to the world and say
+ 
+
+ align:start position:0%
+generous to the world and say
+yes you scientists can measure responses
+
+ align:start position:0%
+yes you scientists can measure responses
+ 
+
+ align:start position:0%
+yes you scientists can measure responses
+in my brain while i look at your damn
+
+ align:start position:0%
+in my brain while i look at your damn
+ 
+
+ align:start position:0%
+in my brain while i look at your damn
+stimuli
+
+ align:start position:0%
+stimuli
+ 
+
+ align:start position:0%
+stimuli
+and so whenever we can we ask them
+
+ align:start position:0%
+and so whenever we can we ask them
+ 
+
+ align:start position:0%
+and so whenever we can we ask them
+please please please can we show you
+
+ align:start position:0%
+please please please can we show you
+ 
+
+ align:start position:0%
+please please please can we show you
+some pictures or play you some towns or
+
+ align:start position:0%
+some pictures or play you some towns or
+ 
+
+ align:start position:0%
+some pictures or play you some towns or
+have you read some sentences while we
+
+ align:start position:0%
+have you read some sentences while we
+ 
+
+ align:start position:0%
+have you read some sentences while we
+record from your brain
+
+ align:start position:0%
+record from your brain
+ 
+
+ align:start position:0%
+record from your brain
+and some of those patients very kindly
+
+ align:start position:0%
+and some of those patients very kindly
+ 
+
+ align:start position:0%
+and some of those patients very kindly
+let us do that
+
+ align:start position:0%
+let us do that
+ 
+
+ align:start position:0%
+let us do that
+and that gives us the most amazing data
+
+ align:start position:0%
+and that gives us the most amazing data
+ 
+
+ align:start position:0%
+and that gives us the most amazing data
+you can get from human brains
+
+ align:start position:0%
+you can get from human brains
+ 
+
+ align:start position:0%
+you can get from human brains
+so for example i had a rare opportunity
+
+ align:start position:0%
+so for example i had a rare opportunity
+ 
+
+ align:start position:0%
+so for example i had a rare opportunity
+to do this a few years ago from this
+
+ align:start position:0%
+to do this a few years ago from this
+ 
+
+ align:start position:0%
+to do this a few years ago from this
+lovely guy who was undergoing
+
+ align:start position:0%
+lovely guy who was undergoing
+ 
+
+ align:start position:0%
+lovely guy who was undergoing
+neurosurgery in japan and while he had
+
+ align:start position:0%
+neurosurgery in japan and while he had
+ 
+
+ align:start position:0%
+neurosurgery in japan and while he had
+electrodes in his brain a colleague of
+
+ align:start position:0%
+electrodes in his brain a colleague of
+ 
+
+ align:start position:0%
+electrodes in his brain a colleague of
+mine was there and emailed me and said
+
+ align:start position:0%
+mine was there and emailed me and said
+ 
+
+ align:start position:0%
+mine was there and emailed me and said
+look where these electrodes are right
+
+ align:start position:0%
+look where these electrodes are right
+ 
+
+ align:start position:0%
+look where these electrodes are right
+near regions i care about do you want to
+
+ align:start position:0%
+near regions i care about do you want to
+ 
+
+ align:start position:0%
+near regions i care about do you want to
+show us some stimuli and we can we'll
+
+ align:start position:0%
+show us some stimuli and we can we'll
+ 
+
+ align:start position:0%
+show us some stimuli and we can we'll
+record responses from those electrodes
+
+ align:start position:0%
+record responses from those electrodes
+ 
+
+ align:start position:0%
+record responses from those electrodes
+and i said damn straight i want to send
+
+ align:start position:0%
+and i said damn straight i want to send
+ 
+
+ align:start position:0%
+and i said damn straight i want to send
+you some stimuli
+
+ align:start position:0%
+you some stimuli
+ 
+
+ align:start position:0%
+you some stimuli
+so my students and i stayed up for a
+
+ align:start position:0%
+so my students and i stayed up for a
+ 
+
+ align:start position:0%
+so my students and i stayed up for a
+couple days and made some stimuli and
+
+ align:start position:0%
+couple days and made some stimuli and
+ 
+
+ align:start position:0%
+couple days and made some stimuli and
+shot them to japan and got some
+
+ align:start position:0%
+shot them to japan and got some
+ 
+
+ align:start position:0%
+shot them to japan and got some
+responses from those very electrodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here they are
+
+ align:start position:0%
+and here they are
+ 
+
+ align:start position:0%
+and here they are
+so this is a strip of
+
+ align:start position:0%
+so this is a strip of
+ 
+
+ align:start position:0%
+so this is a strip of
+a pair of two parallel strips of
+
+ align:start position:0%
+a pair of two parallel strips of
+ 
+
+ align:start position:0%
+a pair of two parallel strips of
+electrodes right along the fusiform
+
+ align:start position:0%
+electrodes right along the fusiform
+ 
+
+ align:start position:0%
+electrodes right along the fusiform
+gyrus right where the fusiform face area
+
+ align:start position:0%
+gyrus right where the fusiform face area
+ 
+
+ align:start position:0%
+gyrus right where the fusiform face area
+should be in most people
+
+ align:start position:0%
+should be in most people
+ 
+
+ align:start position:0%
+should be in most people
+and here are the responses of each of
+
+ align:start position:0%
+and here are the responses of each of
+ 
+
+ align:start position:0%
+and here are the responses of each of
+those electrodes like 174 is here what's
+
+ align:start position:0%
+those electrodes like 174 is here what's
+ 
+
+ align:start position:0%
+those electrodes like 174 is here what's
+173 and so forth and what you see is
+
+ align:start position:0%
+173 and so forth and what you see is
+ 
+
+ align:start position:0%
+173 and so forth and what you see is
+this batch of electrodes right here this
+
+ align:start position:0%
+this batch of electrodes right here this
+ 
+
+ align:start position:0%
+this batch of electrodes right here this
+is the response when the patient was
+
+ align:start position:0%
+is the response when the patient was
+ 
+
+ align:start position:0%
+is the response when the patient was
+looking at faces and these are the
+
+ align:start position:0%
+looking at faces and these are the
+ 
+
+ align:start position:0%
+looking at faces and these are the
+responses when they looked at a whole
+
+ align:start position:0%
+responses when they looked at a whole
+ 
+
+ align:start position:0%
+responses when they looked at a whole
+bunch of different kinds of stimuli
+
+ align:start position:0%
+bunch of different kinds of stimuli
+ 
+
+ align:start position:0%
+bunch of different kinds of stimuli
+objects and this guy's japanese so we
+
+ align:start position:0%
+objects and this guy's japanese so we
+ 
+
+ align:start position:0%
+objects and this guy's japanese so we
+showed him kana and kanji and digit
+
+ align:start position:0%
+showed him kana and kanji and digit
+ 
+
+ align:start position:0%
+showed him kana and kanji and digit
+strings and other kinds of stuff
+
+ align:start position:0%
+strings and other kinds of stuff
+ 
+
+ align:start position:0%
+strings and other kinds of stuff
+very low response to those other things
+
+ align:start position:0%
+very low response to those other things
+ 
+
+ align:start position:0%
+very low response to those other things
+this is a extremely selective response
+
+ align:start position:0%
+this is a extremely selective response
+ 
+
+ align:start position:0%
+this is a extremely selective response
+right it's much more selective than you
+
+ align:start position:0%
+right it's much more selective than you
+ 
+
+ align:start position:0%
+right it's much more selective than you
+see with functional mri because we are
+
+ align:start position:0%
+see with functional mri because we are
+ 
+
+ align:start position:0%
+see with functional mri because we are
+recording directly from the surface of
+
+ align:start position:0%
+recording directly from the surface of
+ 
+
+ align:start position:0%
+recording directly from the surface of
+the brain
+
+ align:start position:0%
+the brain
+ 
+
+ align:start position:0%
+the brain
+further we have time information this
+
+ align:start position:0%
+further we have time information this
+ 
+
+ align:start position:0%
+further we have time information this
+axis here is time and you can see that
+
+ align:start position:0%
+axis here is time and you can see that
+ 
+
+ align:start position:0%
+axis here is time and you can see that
+that response well you can't see the
+
+ align:start position:0%
+that response well you can't see the
+ 
+
+ align:start position:0%
+that response well you can't see the
+axis but that response starts up at
+
+ align:start position:0%
+axis but that response starts up at
+ 
+
+ align:start position:0%
+axis but that response starts up at
+around 130 milliseconds and peaks up
+
+ align:start position:0%
+around 130 milliseconds and peaks up
+ 
+
+ align:start position:0%
+around 130 milliseconds and peaks up
+there at around 170. everybody clear
+
+ align:start position:0%
+there at around 170. everybody clear
+ 
+
+ align:start position:0%
+there at around 170. everybody clear
+what we're seeing here
+
+ align:start position:0%
+what we're seeing here
+ 
+
+ align:start position:0%
+what we're seeing here
+and why this is so vastly better than
+
+ align:start position:0%
+and why this is so vastly better than
+ 
+
+ align:start position:0%
+and why this is so vastly better than
+either functional mri or mg or erps or
+
+ align:start position:0%
+either functional mri or mg or erps or
+ 
+
+ align:start position:0%
+either functional mri or mg or erps or
+anything else
+
+ align:start position:0%
+anything else
+ 
+
+ align:start position:0%
+anything else
+makes sense
+
+ align:start position:0%
+makes sense
+ 
+
+ align:start position:0%
+makes sense
+okay so these are very very precious
+
+ align:start position:0%
+okay so these are very very precious
+ 
+
+ align:start position:0%
+okay so these are very very precious
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+nonetheless the electrodes in this in
+
+ align:start position:0%
+nonetheless the electrodes in this in
+ 
+
+ align:start position:0%
+nonetheless the electrodes in this in
+this case
+
+ align:start position:0%
+this case
+ 
+
+ align:start position:0%
+this case
+are about two millimeters across
+
+ align:start position:0%
+are about two millimeters across
+ 
+
+ align:start position:0%
+are about two millimeters across
+each electrode
+
+ align:start position:0%
+each electrode
+ 
+
+ align:start position:0%
+each electrode
+and that is about the size of a
+
+ align:start position:0%
+and that is about the size of a
+ 
+
+ align:start position:0%
+and that is about the size of a
+functional mri pixel or voxel
+
+ align:start position:0%
+functional mri pixel or voxel
+ 
+
+ align:start position:0%
+functional mri pixel or voxel
+okay a little bit smaller
+
+ align:start position:0%
+okay a little bit smaller
+ 
+
+ align:start position:0%
+okay a little bit smaller
+it has less blurring because functional
+
+ align:start position:0%
+it has less blurring because functional
+ 
+
+ align:start position:0%
+it has less blurring because functional
+mri blurs spatially because it's looking
+
+ align:start position:0%
+mri blurs spatially because it's looking
+ 
+
+ align:start position:0%
+mri blurs spatially because it's looking
+at blood flow so this is a more precise
+
+ align:start position:0%
+at blood flow so this is a more precise
+ 
+
+ align:start position:0%
+at blood flow so this is a more precise
+spatial measurement than functional mri
+
+ align:start position:0%
+spatial measurement than functional mri
+ 
+
+ align:start position:0%
+spatial measurement than functional mri
+but it is still averaging over probably
+
+ align:start position:0%
+but it is still averaging over probably
+ 
+
+ align:start position:0%
+but it is still averaging over probably
+tens of thousands of neurons down from
+
+ align:start position:0%
+tens of thousands of neurons down from
+ 
+
+ align:start position:0%
+tens of thousands of neurons down from
+hundreds of thousands of neurons with
+
+ align:start position:0%
+hundreds of thousands of neurons with
+ 
+
+ align:start position:0%
+hundreds of thousands of neurons with
+functional mri okay
+
+ align:start position:0%
+functional mri okay
+ 
+
+ align:start position:0%
+functional mri okay
+so can we ever get responses from
+
+ align:start position:0%
+so can we ever get responses from
+ 
+
+ align:start position:0%
+so can we ever get responses from
+individual neurons in the human brain
+
+ align:start position:0%
+individual neurons in the human brain
+ 
+
+ align:start position:0%
+individual neurons in the human brain
+yes occasionally
+
+ align:start position:0%
+yes occasionally
+ 
+
+ align:start position:0%
+yes occasionally
+in fact a paper came out on the bio
+
+ align:start position:0%
+in fact a paper came out on the bio
+ 
+
+ align:start position:0%
+in fact a paper came out on the bio
+archive a couple months ago i was on
+
+ align:start position:0%
+archive a couple months ago i was on
+ 
+
+ align:start position:0%
+archive a couple months ago i was on
+this guy's phd thesis defense and this
+
+ align:start position:0%
+this guy's phd thesis defense and this
+ 
+
+ align:start position:0%
+this guy's phd thesis defense and this
+is a guy who works with a neurosurgeon
+
+ align:start position:0%
+is a guy who works with a neurosurgeon
+ 
+
+ align:start position:0%
+is a guy who works with a neurosurgeon
+on long island and this neurosurgeon
+
+ align:start position:0%
+on long island and this neurosurgeon
+ 
+
+ align:start position:0%
+on long island and this neurosurgeon
+specializes in epilepsy
+
+ align:start position:0%
+specializes in epilepsy
+ 
+
+ align:start position:0%
+specializes in epilepsy
+neurosurgery and he's very interested in
+
+ align:start position:0%
+neurosurgery and he's very interested in
+ 
+
+ align:start position:0%
+neurosurgery and he's very interested in
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+damaging people's ability to recognize
+
+ align:start position:0%
+damaging people's ability to recognize
+ 
+
+ align:start position:0%
+damaging people's ability to recognize
+faces
+
+ align:start position:0%
+faces
+ 
+
+ align:start position:0%
+faces
+and so he sticks electrodes to map out
+
+ align:start position:0%
+and so he sticks electrodes to map out
+ 
+
+ align:start position:0%
+and so he sticks electrodes to map out
+neural activity and to discover seizure
+
+ align:start position:0%
+neural activity and to discover seizure
+ 
+
+ align:start position:0%
+neural activity and to discover seizure
+foci before the neurosurgery he sticks
+
+ align:start position:0%
+foci before the neurosurgery he sticks
+ 
+
+ align:start position:0%
+foci before the neurosurgery he sticks
+electrodes in
+
+ align:start position:0%
+electrodes in
+ 
+
+ align:start position:0%
+electrodes in
+parts of the brain near the fusiform
+
+ align:start position:0%
+parts of the brain near the fusiform
+ 
+
+ align:start position:0%
+parts of the brain near the fusiform
+face area
+
+ align:start position:0%
+face area
+ 
+
+ align:start position:0%
+face area
+so this is a slice like this through the
+
+ align:start position:0%
+so this is a slice like this through the
+ 
+
+ align:start position:0%
+so this is a slice like this through the
+brain i should do before horizontal
+
+ align:start position:0%
+brain i should do before horizontal
+ 
+
+ align:start position:0%
+brain i should do before horizontal
+slices okay so left and right are
+
+ align:start position:0%
+slices okay so left and right are
+ 
+
+ align:start position:0%
+slices okay so left and right are
+flipped that region is like you know
+
+ align:start position:0%
+flipped that region is like you know
+ 
+
+ align:start position:0%
+flipped that region is like you know
+right in there everybody oriented with
+
+ align:start position:0%
+right in there everybody oriented with
+ 
+
+ align:start position:0%
+right in there everybody oriented with
+this picture here so that this is an mri
+
+ align:start position:0%
+this picture here so that this is an mri
+ 
+
+ align:start position:0%
+this picture here so that this is an mri
+image of this person was it was scanned
+
+ align:start position:0%
+image of this person was it was scanned
+ 
+
+ align:start position:0%
+image of this person was it was scanned
+with functional mri before the
+
+ align:start position:0%
+with functional mri before the
+ 
+
+ align:start position:0%
+with functional mri before the
+electrodes were put in and that shows
+
+ align:start position:0%
+electrodes were put in and that shows
+ 
+
+ align:start position:0%
+electrodes were put in and that shows
+you their fusiform face area right there
+
+ align:start position:0%
+you their fusiform face area right there
+ 
+
+ align:start position:0%
+you their fusiform face area right there
+okay so now the neurosurgeons put in
+
+ align:start position:0%
+okay so now the neurosurgeons put in
+ 
+
+ align:start position:0%
+okay so now the neurosurgeons put in
+electrodes for clinical reasons but the
+
+ align:start position:0%
+electrodes for clinical reasons but the
+ 
+
+ align:start position:0%
+electrodes for clinical reasons but the
+electrodes this surgeon uses have these
+
+ align:start position:0%
+electrodes this surgeon uses have these
+ 
+
+ align:start position:0%
+electrodes this surgeon uses have these
+little tiny micro wires that come out of
+
+ align:start position:0%
+little tiny micro wires that come out of
+ 
+
+ align:start position:0%
+little tiny micro wires that come out of
+the tip of the electrode that enable him
+
+ align:start position:0%
+the tip of the electrode that enable him
+ 
+
+ align:start position:0%
+the tip of the electrode that enable him
+to record from individual neurons
+
+ align:start position:0%
+to record from individual neurons
+ 
+
+ align:start position:0%
+to record from individual neurons
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+these guys for the first time have
+
+ align:start position:0%
+these guys for the first time have
+ 
+
+ align:start position:0%
+these guys for the first time have
+recorded from individual neurons in the
+
+ align:start position:0%
+recorded from individual neurons in the
+ 
+
+ align:start position:0%
+recorded from individual neurons in the
+fusiform face area in humans
+
+ align:start position:0%
+fusiform face area in humans
+ 
+
+ align:start position:0%
+fusiform face area in humans
+and here's an example of one of these
+
+ align:start position:0%
+and here's an example of one of these
+ 
+
+ align:start position:0%
+and here's an example of one of these
+neurons
+
+ align:start position:0%
+neurons
+ 
+
+ align:start position:0%
+neurons
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here different stimuli here a bunch of
+
+ align:start position:0%
+here different stimuli here a bunch of
+ 
+
+ align:start position:0%
+here different stimuli here a bunch of
+different face stimuli body stimuli
+
+ align:start position:0%
+different face stimuli body stimuli
+ 
+
+ align:start position:0%
+different face stimuli body stimuli
+houses patterns and tools
+
+ align:start position:0%
+houses patterns and tools
+ 
+
+ align:start position:0%
+houses patterns and tools
+and this shows you
+
+ align:start position:0%
+and this shows you
+ 
+
+ align:start position:0%
+and this shows you
+time across here each one of those dots
+
+ align:start position:0%
+time across here each one of those dots
+ 
+
+ align:start position:0%
+time across here each one of those dots
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+this is all the response of a single
+
+ align:start position:0%
+this is all the response of a single
+ 
+
+ align:start position:0%
+this is all the response of a single
+neuron that's been identified in a human
+
+ align:start position:0%
+neuron that's been identified in a human
+ 
+
+ align:start position:0%
+neuron that's been identified in a human
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+each dot is an action potential is a
+
+ align:start position:0%
+each dot is an action potential is a
+ 
+
+ align:start position:0%
+each dot is an action potential is a
+spike out of that neuron so you can see
+
+ align:start position:0%
+spike out of that neuron so you can see
+ 
+
+ align:start position:0%
+spike out of that neuron so you can see
+them happening over time here to all the
+
+ align:start position:0%
+them happening over time here to all the
+ 
+
+ align:start position:0%
+them happening over time here to all the
+faces this is an average amount of
+
+ align:start position:0%
+faces this is an average amount of
+ 
+
+ align:start position:0%
+faces this is an average amount of
+activity to all of the faces and average
+
+ align:start position:0%
+activity to all of the faces and average
+ 
+
+ align:start position:0%
+activity to all of the faces and average
+amount of activity to all the other
+
+ align:start position:0%
+amount of activity to all the other
+ 
+
+ align:start position:0%
+amount of activity to all the other
+stimuli
+
+ align:start position:0%
+stimuli
+ 
+
+ align:start position:0%
+stimuli
+okay makes sense
+
+ align:start position:0%
+okay makes sense
+ 
+
+ align:start position:0%
+okay makes sense
+so that's pretty breathtaking to me
+
+ align:start position:0%
+so that's pretty breathtaking to me
+ 
+
+ align:start position:0%
+so that's pretty breathtaking to me
+because i've been using these very
+
+ align:start position:0%
+because i've been using these very
+ 
+
+ align:start position:0%
+because i've been using these very
+indirect methods for a long time
+
+ align:start position:0%
+indirect methods for a long time
+ 
+
+ align:start position:0%
+indirect methods for a long time
+inferring that they must result from the
+
+ align:start position:0%
+inferring that they must result from the
+ 
+
+ align:start position:0%
+inferring that they must result from the
+average across a lot of neurons doing
+
+ align:start position:0%
+average across a lot of neurons doing
+ 
+
+ align:start position:0%
+average across a lot of neurons doing
+that but it's pretty awesome to actually
+
+ align:start position:0%
+that but it's pretty awesome to actually
+ 
+
+ align:start position:0%
+that but it's pretty awesome to actually
+see individual neurons doing that
+
+ align:start position:0%
+see individual neurons doing that
+ 
+
+ align:start position:0%
+see individual neurons doing that
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+here's the time course of responses just
+
+ align:start position:0%
+here's the time course of responses just
+ 
+
+ align:start position:0%
+here's the time course of responses just
+averaging over this raster over time
+
+ align:start position:0%
+averaging over this raster over time
+ 
+
+ align:start position:0%
+averaging over this raster over time
+showing you a similar time course to
+
+ align:start position:0%
+showing you a similar time course to
+ 
+
+ align:start position:0%
+showing you a similar time course to
+what i've shown before
+
+ align:start position:0%
+what i've shown before
+ 
+
+ align:start position:0%
+what i've shown before
+uh and in this guy's thesis he found
+
+ align:start position:0%
+uh and in this guy's thesis he found
+ 
+
+ align:start position:0%
+uh and in this guy's thesis he found
+three other
+
+ align:start position:0%
+three other
+ 
+
+ align:start position:0%
+three other
+phase selective neurons in the ffa
+
+ align:start position:0%
+phase selective neurons in the ffa
+ 
+
+ align:start position:0%
+phase selective neurons in the ffa
+but the electors are so rarely in the
+
+ align:start position:0%
+but the electors are so rarely in the
+ 
+
+ align:start position:0%
+but the electors are so rarely in the
+right location that they only have a few
+
+ align:start position:0%
+right location that they only have a few
+ 
+
+ align:start position:0%
+right location that they only have a few
+in this whole thesis and there they are
+
+ align:start position:0%
+in this whole thesis and there they are
+ 
+
+ align:start position:0%
+in this whole thesis and there they are
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+well even if we can measure individual
+
+ align:start position:0%
+well even if we can measure individual
+ 
+
+ align:start position:0%
+well even if we can measure individual
+neurons we don't really know like which
+
+ align:start position:0%
+neurons we don't really know like which
+ 
+
+ align:start position:0%
+neurons we don't really know like which
+neuron it is right if i wanted to go
+
+ align:start position:0%
+neuron it is right if i wanted to go
+ 
+
+ align:start position:0%
+neuron it is right if i wanted to go
+back and find the same neuron again
+
+ align:start position:0%
+back and find the same neuron again
+ 
+
+ align:start position:0%
+back and find the same neuron again
+that's pretty much impossible forget it
+
+ align:start position:0%
+that's pretty much impossible forget it
+ 
+
+ align:start position:0%
+that's pretty much impossible forget it
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+yep so
+
+ align:start position:0%
+yep so
+ 
+
+ align:start position:0%
+yep so
+people like me who almost never get to
+
+ align:start position:0%
+people like me who almost never get to
+ 
+
+ align:start position:0%
+people like me who almost never get to
+see responses from individual neurons
+
+ align:start position:0%
+see responses from individual neurons
+ 
+
+ align:start position:0%
+see responses from individual neurons
+and human brains have kind of neuron
+
+ align:start position:0%
+and human brains have kind of neuron
+ 
+
+ align:start position:0%
+and human brains have kind of neuron
+envy you know it's like everyone else in
+
+ align:start position:0%
+envy you know it's like everyone else in
+ 
+
+ align:start position:0%
+envy you know it's like everyone else in
+this building has they can measure stuff
+
+ align:start position:0%
+this building has they can measure stuff
+ 
+
+ align:start position:0%
+this building has they can measure stuff
+from like dendrites or ion channels or
+
+ align:start position:0%
+from like dendrites or ion channels or
+ 
+
+ align:start position:0%
+from like dendrites or ion channels or
+individual neurons they can do all this
+
+ align:start position:0%
+individual neurons they can do all this
+ 
+
+ align:start position:0%
+individual neurons they can do all this
+amazing stuff but actually there are a
+
+ align:start position:0%
+amazing stuff but actually there are a
+ 
+
+ align:start position:0%
+amazing stuff but actually there are a
+lot of limits in those limitations in
+
+ align:start position:0%
+lot of limits in those limitations in
+ 
+
+ align:start position:0%
+lot of limits in those limitations in
+those methods too and you just put your
+
+ align:start position:0%
+those methods too and you just put your
+ 
+
+ align:start position:0%
+those methods too and you just put your
+finger on one of them so there's like
+
+ align:start position:0%
+finger on one of them so there's like
+ 
+
+ align:start position:0%
+finger on one of them so there's like
+okay they found those neurons they're
+
+ align:start position:0%
+okay they found those neurons they're
+ 
+
+ align:start position:0%
+okay they found those neurons they're
+four neurons we can't go back and find
+
+ align:start position:0%
+four neurons we can't go back and find
+ 
+
+ align:start position:0%
+four neurons we can't go back and find
+those neurons again that's that right
+
+ align:start position:0%
+those neurons again that's that right
+ 
+
+ align:start position:0%
+those neurons again that's that right
+and they're probably
+
+ align:start position:0%
+and they're probably
+ 
+
+ align:start position:0%
+and they're probably
+subtly different in different brains
+
+ align:start position:0%
+subtly different in different brains
+ 
+
+ align:start position:0%
+subtly different in different brains
+right so they're it's it's cool and
+
+ align:start position:0%
+right so they're it's it's cool and
+ 
+
+ align:start position:0%
+right so they're it's it's cool and
+powerful but has still has many
+
+ align:start position:0%
+powerful but has still has many
+ 
+
+ align:start position:0%
+powerful but has still has many
+limitations
+
+ align:start position:0%
+limitations
+ 
+
+ align:start position:0%
+limitations
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+does this tell us that these neurons are
+
+ align:start position:0%
+does this tell us that these neurons are
+ 
+
+ align:start position:0%
+does this tell us that these neurons are
+involved in discriminating one face from
+
+ align:start position:0%
+involved in discriminating one face from
+ 
+
+ align:start position:0%
+involved in discriminating one face from
+another or just detecting faces can we
+
+ align:start position:0%
+another or just detecting faces can we
+ 
+
+ align:start position:0%
+another or just detecting faces can we
+tell from these data
+
+ align:start position:0%
+tell from these data
+ 
+
+ align:start position:0%
+tell from these data
+are they just saying here's a face
+
+ align:start position:0%
+are they just saying here's a face
+ 
+
+ align:start position:0%
+are they just saying here's a face
+are they saying that's joe
+
+ align:start position:0%
+are they saying that's joe
+ 
+
+ align:start position:0%
+are they saying that's joe
+did they
+
+ align:start position:0%
+did they
+ 
+
+ align:start position:0%
+did they
+have different conditions for different
+
+ align:start position:0%
+have different conditions for different
+ 
+
+ align:start position:0%
+have different conditions for different
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+these are different faces here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you think what are these neurons
+
+ align:start position:0%
+what do you think what are these neurons
+ 
+
+ align:start position:0%
+what do you think what are these neurons
+doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah just right from that
+
+ align:start position:0%
+yeah just right from that
+ 
+
+ align:start position:0%
+yeah just right from that
+you can see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you mean just detecting
+
+ align:start position:0%
+you mean just detecting
+ 
+
+ align:start position:0%
+you mean just detecting
+no just say more what do you think
+
+ align:start position:0%
+no just say more what do you think
+ 
+
+ align:start position:0%
+no just say more what do you think
+they're doing uh like they're just
+
+ align:start position:0%
+they're doing uh like they're just
+ 
+
+ align:start position:0%
+they're doing uh like they're just
+selected from faces
+
+ align:start position:0%
+selected from faces
+ 
+
+ align:start position:0%
+selected from faces
+there's no evidence to show them and
+
+ align:start position:0%
+there's no evidence to show them and
+ 
+
+ align:start position:0%
+there's no evidence to show them and
+distinguish different places
+
+ align:start position:0%
+distinguish different places
+ 
+
+ align:start position:0%
+distinguish different places
+well how about this these are different
+
+ align:start position:0%
+well how about this these are different
+ 
+
+ align:start position:0%
+well how about this these are different
+faces here
+
+ align:start position:0%
+faces here
+ 
+
+ align:start position:0%
+faces here
+these are different faces here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was the task did the task involve them
+
+ align:start position:0%
+was the task did the task involve them
+ 
+
+ align:start position:0%
+was the task did the task involve them
+sort of acknowledging what phrases what
+
+ align:start position:0%
+sort of acknowledging what phrases what
+ 
+
+ align:start position:0%
+sort of acknowledging what phrases what
+did they have to put into their face
+
+ align:start position:0%
+did they have to put into their face
+ 
+
+ align:start position:0%
+did they have to put into their face
+nope they do they're just sitting there
+
+ align:start position:0%
+nope they do they're just sitting there
+ 
+
+ align:start position:0%
+nope they do they're just sitting there
+looking at stuff
+
+ align:start position:0%
+looking at stuff
+ 
+
+ align:start position:0%
+looking at stuff
+okay so bottom line is we don't know
+
+ align:start position:0%
+okay so bottom line is we don't know
+ 
+
+ align:start position:0%
+okay so bottom line is we don't know
+from this it could be just responding
+
+ align:start position:0%
+from this it could be just responding
+ 
+
+ align:start position:0%
+from this it could be just responding
+and saying essentially there's a face
+
+ align:start position:0%
+and saying essentially there's a face
+ 
+
+ align:start position:0%
+and saying essentially there's a face
+but the fact that there's different
+
+ align:start position:0%
+but the fact that there's different
+ 
+
+ align:start position:0%
+but the fact that there's different
+responses to different faces
+
+ align:start position:0%
+responses to different faces
+ 
+
+ align:start position:0%
+responses to different faces
+suggests that maybe there's some
+
+ align:start position:0%
+suggests that maybe there's some
+ 
+
+ align:start position:0%
+suggests that maybe there's some
+information in there
+
+ align:start position:0%
+information in there
+ 
+
+ align:start position:0%
+information in there
+like if you ran some machine learning
+
+ align:start position:0%
+like if you ran some machine learning
+ 
+
+ align:start position:0%
+like if you ran some machine learning
+code on this
+
+ align:start position:0%
+code on this
+ 
+
+ align:start position:0%
+code on this
+you could tell a little bit which face
+
+ align:start position:0%
+you could tell a little bit which face
+ 
+
+ align:start position:0%
+you could tell a little bit which face
+was being presented because those
+
+ align:start position:0%
+was being presented because those
+ 
+
+ align:start position:0%
+was being presented because those
+neurons are responding differently to
+
+ align:start position:0%
+neurons are responding differently to
+ 
+
+ align:start position:0%
+neurons are responding differently to
+different faces
+
+ align:start position:0%
+different faces
+ 
+
+ align:start position:0%
+different faces
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+is it really like if they just show the
+
+ align:start position:0%
+is it really like if they just show the
+ 
+
+ align:start position:0%
+is it really like if they just show the
+same face repeat that you wouldn't just
+
+ align:start position:0%
+same face repeat that you wouldn't just
+ 
+
+ align:start position:0%
+same face repeat that you wouldn't just
+feel like
+
+ align:start position:0%
+feel like
+ 
+
+ align:start position:0%
+feel like
+okay very good question very good
+
+ align:start position:0%
+okay very good question very good
+ 
+
+ align:start position:0%
+okay very good question very good
+question that's why i said suggests
+
+ align:start position:0%
+question that's why i said suggests
+ 
+
+ align:start position:0%
+question that's why i said suggests
+right you're absolutely right that could
+
+ align:start position:0%
+right you're absolutely right that could
+ 
+
+ align:start position:0%
+right you're absolutely right that could
+be just noise it could be that if you
+
+ align:start position:0%
+be just noise it could be that if you
+ 
+
+ align:start position:0%
+be just noise it could be that if you
+presented the same face every time you
+
+ align:start position:0%
+presented the same face every time you
+ 
+
+ align:start position:0%
+presented the same face every time you
+get that same distribution you're
+
+ align:start position:0%
+get that same distribution you're
+ 
+
+ align:start position:0%
+get that same distribution you're
+exactly right
+
+ align:start position:0%
+exactly right
+ 
+
+ align:start position:0%
+exactly right
+and so we will talk not next time i
+
+ align:start position:0%
+and so we will talk not next time i
+ 
+
+ align:start position:0%
+and so we will talk not next time i
+think wednesday next week but anyways
+
+ align:start position:0%
+think wednesday next week but anyways
+ 
+
+ align:start position:0%
+think wednesday next week but anyways
+very soon we'll talk about methods that
+
+ align:start position:0%
+very soon we'll talk about methods that
+ 
+
+ align:start position:0%
+very soon we'll talk about methods that
+enable us to exactly deal with that
+
+ align:start position:0%
+enable us to exactly deal with that
+ 
+
+ align:start position:0%
+enable us to exactly deal with that
+question and ask is there actually
+
+ align:start position:0%
+question and ask is there actually
+ 
+
+ align:start position:0%
+question and ask is there actually
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+in this pattern of response across
+
+ align:start position:0%
+in this pattern of response across
+ 
+
+ align:start position:0%
+in this pattern of response across
+neurons or voxels or whatever it is
+
+ align:start position:0%
+neurons or voxels or whatever it is
+ 
+
+ align:start position:0%
+neurons or voxels or whatever it is
+or is that just the noise of variation
+
+ align:start position:0%
+or is that just the noise of variation
+ 
+
+ align:start position:0%
+or is that just the noise of variation
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+well how many neurons are in the
+
+ align:start position:0%
+well how many neurons are in the
+ 
+
+ align:start position:0%
+well how many neurons are in the
+epidemic
+
+ align:start position:0%
+epidemic
+ 
+
+ align:start position:0%
+epidemic
+oh good question um
+
+ align:start position:0%
+oh good question um
+ 
+
+ align:start position:0%
+oh good question um
+let's see uh
+
+ align:start position:0%
+let's see uh
+ 
+
+ align:start position:0%
+let's see uh
+i would say um
+
+ align:start position:0%
+i would say um
+ 
+
+ align:start position:0%
+i would say um
+i think a few million so let's think
+
+ align:start position:0%
+i think a few million so let's think
+ 
+
+ align:start position:0%
+i think a few million so let's think
+about it each each voxel is about um
+
+ align:start position:0%
+about it each each voxel is about um
+ 
+
+ align:start position:0%
+about it each each voxel is about um
+a half a
+
+ align:start position:0%
+a half a
+ 
+
+ align:start position:0%
+a half a
+half a million and they're typically
+
+ align:start position:0%
+half a million and they're typically
+ 
+
+ align:start position:0%
+half a million and they're typically
+maybe like
+
+ align:start position:0%
+maybe like
+ 
+
+ align:start position:0%
+maybe like
+30 voxels something like that somewhere
+
+ align:start position:0%
+30 voxels something like that somewhere
+ 
+
+ align:start position:0%
+30 voxels something like that somewhere
+on the order of 20 million something
+
+ align:start position:0%
+on the order of 20 million something
+ 
+
+ align:start position:0%
+on the order of 20 million something
+like that i mean with huge error bars
+
+ align:start position:0%
+like that i mean with huge error bars
+ 
+
+ align:start position:0%
+like that i mean with huge error bars
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+this is cool and tantalizing but it
+
+ align:start position:0%
+this is cool and tantalizing but it
+ 
+
+ align:start position:0%
+this is cool and tantalizing but it
+doesn't even tell us what these neurons
+
+ align:start position:0%
+doesn't even tell us what these neurons
+ 
+
+ align:start position:0%
+doesn't even tell us what these neurons
+what exactly they're participating in it
+
+ align:start position:0%
+what exactly they're participating in it
+ 
+
+ align:start position:0%
+what exactly they're participating in it
+doesn't tell us if those neurons are
+
+ align:start position:0%
+doesn't tell us if those neurons are
+ 
+
+ align:start position:0%
+doesn't tell us if those neurons are
+telling that person which face is there
+
+ align:start position:0%
+telling that person which face is there
+ 
+
+ align:start position:0%
+telling that person which face is there
+or maybe what facial expression the
+
+ align:start position:0%
+or maybe what facial expression the
+ 
+
+ align:start position:0%
+or maybe what facial expression the
+person has or how old they are or
+
+ align:start position:0%
+person has or how old they are or
+ 
+
+ align:start position:0%
+person has or how old they are or
+whether they're male or female or god
+
+ align:start position:0%
+whether they're male or female or god
+ 
+
+ align:start position:0%
+whether they're male or female or god
+knows what else right
+
+ align:start position:0%
+knows what else right
+ 
+
+ align:start position:0%
+knows what else right
+and it certainly doesn't tell us how
+
+ align:start position:0%
+and it certainly doesn't tell us how
+ 
+
+ align:start position:0%
+and it certainly doesn't tell us how
+those neurons get that information okay
+
+ align:start position:0%
+those neurons get that information okay
+ 
+
+ align:start position:0%
+those neurons get that information okay
+still it's cool
+
+ align:start position:0%
+still it's cool
+ 
+
+ align:start position:0%
+still it's cool
+okay so intracranial recording
+
+ align:start position:0%
+okay so intracranial recording
+ 
+
+ align:start position:0%
+okay so intracranial recording
+both with the um the grids that i showed
+
+ align:start position:0%
+both with the um the grids that i showed
+ 
+
+ align:start position:0%
+both with the um the grids that i showed
+you and the single unit version
+
+ align:start position:0%
+you and the single unit version
+ 
+
+ align:start position:0%
+you and the single unit version
+advantages are this is the only method
+
+ align:start position:0%
+advantages are this is the only method
+ 
+
+ align:start position:0%
+advantages are this is the only method
+in humans that has both pretty good
+
+ align:start position:0%
+in humans that has both pretty good
+ 
+
+ align:start position:0%
+in humans that has both pretty good
+spatial resolution and temporal
+
+ align:start position:0%
+spatial resolution and temporal
+ 
+
+ align:start position:0%
+spatial resolution and temporal
+resolution at the same time
+
+ align:start position:0%
+resolution at the same time
+ 
+
+ align:start position:0%
+resolution at the same time
+um disadvantage well you need to have a
+
+ align:start position:0%
+um disadvantage well you need to have a
+ 
+
+ align:start position:0%
+um disadvantage well you need to have a
+craniotomy which is no picnic to put it
+
+ align:start position:0%
+craniotomy which is no picnic to put it
+ 
+
+ align:start position:0%
+craniotomy which is no picnic to put it
+mildly you need to have a huge piece of
+
+ align:start position:0%
+mildly you need to have a huge piece of
+ 
+
+ align:start position:0%
+mildly you need to have a huge piece of
+your skull removed and
+
+ align:start position:0%
+your skull removed and
+ 
+
+ align:start position:0%
+your skull removed and
+neurosurgery and that means that the
+
+ align:start position:0%
+neurosurgery and that means that the
+ 
+
+ align:start position:0%
+neurosurgery and that means that the
+only times we get to do this are when
+
+ align:start position:0%
+only times we get to do this are when
+ 
+
+ align:start position:0%
+only times we get to do this are when
+it's required clinically
+
+ align:start position:0%
+it's required clinically
+ 
+
+ align:start position:0%
+it's required clinically
+and everything is under control of the
+
+ align:start position:0%
+and everything is under control of the
+ 
+
+ align:start position:0%
+and everything is under control of the
+doctors as it should be right so the
+
+ align:start position:0%
+doctors as it should be right so the
+ 
+
+ align:start position:0%
+doctors as it should be right so the
+doctors make all the choices about where
+
+ align:start position:0%
+doctors make all the choices about where
+ 
+
+ align:start position:0%
+doctors make all the choices about where
+the electrodes go
+
+ align:start position:0%
+the electrodes go
+ 
+
+ align:start position:0%
+the electrodes go
+and we just get to sit in the background
+
+ align:start position:0%
+and we just get to sit in the background
+ 
+
+ align:start position:0%
+and we just get to sit in the background
+and say please please please look at
+
+ align:start position:0%
+and say please please please look at
+ 
+
+ align:start position:0%
+and say please please please look at
+these stimuli
+
+ align:start position:0%
+these stimuli
+ 
+
+ align:start position:0%
+these stimuli
+but try not to hassle the patients too
+
+ align:start position:0%
+but try not to hassle the patients too
+ 
+
+ align:start position:0%
+but try not to hassle the patients too
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+right now there's a patient in albany
+
+ align:start position:0%
+right now there's a patient in albany
+ 
+
+ align:start position:0%
+right now there's a patient in albany
+new york who has electrodes right over a
+
+ align:start position:0%
+new york who has electrodes right over a
+ 
+
+ align:start position:0%
+new york who has electrodes right over a
+really exciting part of the brain to us
+
+ align:start position:0%
+really exciting part of the brain to us
+ 
+
+ align:start position:0%
+really exciting part of the brain to us
+that i'll talk about in a few months
+
+ align:start position:0%
+that i'll talk about in a few months
+ 
+
+ align:start position:0%
+that i'll talk about in a few months
+this patient has electrodes that respond
+
+ align:start position:0%
+this patient has electrodes that respond
+ 
+
+ align:start position:0%
+this patient has electrodes that respond
+specifically to music we will talk about
+
+ align:start position:0%
+specifically to music we will talk about
+ 
+
+ align:start position:0%
+specifically to music we will talk about
+that later it's pretty amazing
+
+ align:start position:0%
+that later it's pretty amazing
+ 
+
+ align:start position:0%
+that later it's pretty amazing
+and for the last couple days dana and i
+
+ align:start position:0%
+and for the last couple days dana and i
+ 
+
+ align:start position:0%
+and for the last couple days dana and i
+have been mostly dana has been
+
+ align:start position:0%
+have been mostly dana has been
+ 
+
+ align:start position:0%
+have been mostly dana has been
+collecting stimuli because we really
+
+ align:start position:0%
+collecting stimuli because we really
+ 
+
+ align:start position:0%
+collecting stimuli because we really
+want to ask questions about the response
+
+ align:start position:0%
+want to ask questions about the response
+ 
+
+ align:start position:0%
+want to ask questions about the response
+of those electrodes and this patient is
+
+ align:start position:0%
+of those electrodes and this patient is
+ 
+
+ align:start position:0%
+of those electrodes and this patient is
+not too thrilled listening to our
+
+ align:start position:0%
+not too thrilled listening to our
+ 
+
+ align:start position:0%
+not too thrilled listening to our
+stimuli so we finally said oh you okay
+
+ align:start position:0%
+stimuli so we finally said oh you okay
+ 
+
+ align:start position:0%
+stimuli so we finally said oh you okay
+you can watch tell the patient they can
+
+ align:start position:0%
+you can watch tell the patient they can
+ 
+
+ align:start position:0%
+you can watch tell the patient they can
+just do instagram on their phone and
+
+ align:start position:0%
+just do instagram on their phone and
+ 
+
+ align:start position:0%
+just do instagram on their phone and
+we'll play the stimuli in the background
+
+ align:start position:0%
+we'll play the stimuli in the background
+ 
+
+ align:start position:0%
+we'll play the stimuli in the background
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+hopefully we'll have cool data from that
+
+ align:start position:0%
+hopefully we'll have cool data from that
+ 
+
+ align:start position:0%
+hopefully we'll have cool data from that
+soon
+
+ align:start position:0%
+soon
+ 
+
+ align:start position:0%
+soon
+okay so to say that these data are
+
+ align:start position:0%
+okay so to say that these data are
+ 
+
+ align:start position:0%
+okay so to say that these data are
+limited and hard to control is an
+
+ align:start position:0%
+limited and hard to control is an
+ 
+
+ align:start position:0%
+limited and hard to control is an
+understatement like we basically can't
+
+ align:start position:0%
+understatement like we basically can't
+ 
+
+ align:start position:0%
+understatement like we basically can't
+control it at all all we can control
+
+ align:start position:0%
+control it at all all we can control
+ 
+
+ align:start position:0%
+control it at all all we can control
+occasionally is the stimuli
+
+ align:start position:0%
+occasionally is the stimuli
+ 
+
+ align:start position:0%
+occasionally is the stimuli
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and it also like functional mri just
+
+ align:start position:0%
+and it also like functional mri just
+ 
+
+ align:start position:0%
+and it also like functional mri just
+because we see those beautiful responses
+
+ align:start position:0%
+because we see those beautiful responses
+ 
+
+ align:start position:0%
+because we see those beautiful responses
+it doesn't tell us
+
+ align:start position:0%
+it doesn't tell us
+ 
+
+ align:start position:0%
+it doesn't tell us
+how how those responses are connected to
+
+ align:start position:0%
+how how those responses are connected to
+ 
+
+ align:start position:0%
+how how those responses are connected to
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so that's a that's a real challenge
+
+ align:start position:0%
+so that's a that's a real challenge
+ 
+
+ align:start position:0%
+so that's a that's a real challenge
+so that won't do
+
+ align:start position:0%
+so that won't do
+ 
+
+ align:start position:0%
+so that won't do
+uh we need to get beyond this problem i
+
+ align:start position:0%
+uh we need to get beyond this problem i
+ 
+
+ align:start position:0%
+uh we need to get beyond this problem i
+keep saying this method is great but it
+
+ align:start position:0%
+keep saying this method is great but it
+ 
+
+ align:start position:0%
+keep saying this method is great but it
+doesn't tell us the causal role of that
+
+ align:start position:0%
+doesn't tell us the causal role of that
+ 
+
+ align:start position:0%
+doesn't tell us the causal role of that
+neural phenomenon in in cognition and
+
+ align:start position:0%
+neural phenomenon in in cognition and
+ 
+
+ align:start position:0%
+neural phenomenon in in cognition and
+behavior as scientists science is all
+
+ align:start position:0%
+behavior as scientists science is all
+ 
+
+ align:start position:0%
+behavior as scientists science is all
+about discovering causal mechanisms
+
+ align:start position:0%
+about discovering causal mechanisms
+ 
+
+ align:start position:0%
+about discovering causal mechanisms
+right we're not just interested in what
+
+ align:start position:0%
+right we're not just interested in what
+ 
+
+ align:start position:0%
+right we're not just interested in what
+is correlated with what we want to know
+
+ align:start position:0%
+is correlated with what we want to know
+ 
+
+ align:start position:0%
+is correlated with what we want to know
+what's causing what that's really of the
+
+ align:start position:0%
+what's causing what that's really of the
+ 
+
+ align:start position:0%
+what's causing what that's really of the
+essence and so we need to do better here
+
+ align:start position:0%
+essence and so we need to do better here
+ 
+
+ align:start position:0%
+essence and so we need to do better here
+uh so what are we gonna do somebody
+
+ align:start position:0%
+uh so what are we gonna do somebody
+ 
+
+ align:start position:0%
+uh so what are we gonna do somebody
+mentioned a while ago maybe it was
+
+ align:start position:0%
+mentioned a while ago maybe it was
+ 
+
+ align:start position:0%
+mentioned a while ago maybe it was
+isabelle that one of the ways to do that
+
+ align:start position:0%
+isabelle that one of the ways to do that
+ 
+
+ align:start position:0%
+isabelle that one of the ways to do that
+and ask whether the face area is
+
+ align:start position:0%
+and ask whether the face area is
+ 
+
+ align:start position:0%
+and ask whether the face area is
+causally involved in face perception
+
+ align:start position:0%
+causally involved in face perception
+ 
+
+ align:start position:0%
+causally involved in face perception
+is to look at a case where the face area
+
+ align:start position:0%
+is to look at a case where the face area
+ 
+
+ align:start position:0%
+is to look at a case where the face area
+is altered okay so there's a bunch of
+
+ align:start position:0%
+is altered okay so there's a bunch of
+ 
+
+ align:start position:0%
+is altered okay so there's a bunch of
+ways to do that
+
+ align:start position:0%
+ways to do that
+ 
+
+ align:start position:0%
+ways to do that
+and one of them
+
+ align:start position:0%
+and one of them
+ 
+
+ align:start position:0%
+and one of them
+okay that's just a review we said faces
+
+ align:start position:0%
+okay that's just a review we said faces
+ 
+
+ align:start position:0%
+okay that's just a review we said faces
+are recognized fast but we haven't
+
+ align:start position:0%
+are recognized fast but we haven't
+ 
+
+ align:start position:0%
+are recognized fast but we haven't
+learned much more
+
+ align:start position:0%
+learned much more
+ 
+
+ align:start position:0%
+learned much more
+how do we
+
+ align:start position:0%
+how do we
+ 
+
+ align:start position:0%
+how do we
+test causality okay patients with vocal
+
+ align:start position:0%
+test causality okay patients with vocal
+ 
+
+ align:start position:0%
+test causality okay patients with vocal
+brain damage
+
+ align:start position:0%
+brain damage
+ 
+
+ align:start position:0%
+brain damage
+here is a patient these are vertical
+
+ align:start position:0%
+here is a patient these are vertical
+ 
+
+ align:start position:0%
+here is a patient these are vertical
+slices through the back back of this
+
+ align:start position:0%
+slices through the back back of this
+ 
+
+ align:start position:0%
+slices through the back back of this
+patient's head okay let me get oriented
+
+ align:start position:0%
+patient's head okay let me get oriented
+ 
+
+ align:start position:0%
+patient's head okay let me get oriented
+this slice is maybe like this here and
+
+ align:start position:0%
+this slice is maybe like this here and
+ 
+
+ align:start position:0%
+this slice is maybe like this here and
+as you go rightward you're marching back
+
+ align:start position:0%
+as you go rightward you're marching back
+ 
+
+ align:start position:0%
+as you go rightward you're marching back
+in the brain like that everybody
+
+ align:start position:0%
+in the brain like that everybody
+ 
+
+ align:start position:0%
+in the brain like that everybody
+oriented
+
+ align:start position:0%
+oriented
+ 
+
+ align:start position:0%
+oriented
+what's this thing right there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah cerebellum right
+
+ align:start position:0%
+yeah cerebellum right
+ 
+
+ align:start position:0%
+yeah cerebellum right
+that thing right there is this patient's
+
+ align:start position:0%
+that thing right there is this patient's
+ 
+
+ align:start position:0%
+that thing right there is this patient's
+lesion that spans several slices going
+
+ align:start position:0%
+lesion that spans several slices going
+ 
+
+ align:start position:0%
+lesion that spans several slices going
+back like that
+
+ align:start position:0%
+back like that
+ 
+
+ align:start position:0%
+back like that
+and this patient's lesion
+
+ align:start position:0%
+and this patient's lesion
+ 
+
+ align:start position:0%
+and this patient's lesion
+looks a whole lot like my ffa there's my
+
+ align:start position:0%
+looks a whole lot like my ffa there's my
+ 
+
+ align:start position:0%
+looks a whole lot like my ffa there's my
+ffa
+
+ align:start position:0%
+ffa
+ 
+
+ align:start position:0%
+ffa
+greater response to faces and objects on
+
+ align:start position:0%
+greater response to faces and objects on
+ 
+
+ align:start position:0%
+greater response to faces and objects on
+similar slices
+
+ align:start position:0%
+similar slices
+ 
+
+ align:start position:0%
+similar slices
+we don't have functional mri from this
+
+ align:start position:0%
+we don't have functional mri from this
+ 
+
+ align:start position:0%
+we don't have functional mri from this
+patient so we don't know exactly where
+
+ align:start position:0%
+patient so we don't know exactly where
+ 
+
+ align:start position:0%
+patient so we don't know exactly where
+this guy's ffa was but there's a good
+
+ align:start position:0%
+this guy's ffa was but there's a good
+ 
+
+ align:start position:0%
+this guy's ffa was but there's a good
+bet that it was blitzed by that lesion
+
+ align:start position:0%
+bet that it was blitzed by that lesion
+ 
+
+ align:start position:0%
+bet that it was blitzed by that lesion
+okay because it's right in the zone
+
+ align:start position:0%
+okay because it's right in the zone
+ 
+
+ align:start position:0%
+okay because it's right in the zone
+where it usually lands
+
+ align:start position:0%
+where it usually lands
+ 
+
+ align:start position:0%
+where it usually lands
+and this patient
+
+ align:start position:0%
+and this patient
+ 
+
+ align:start position:0%
+and this patient
+can't recognize faces at all
+
+ align:start position:0%
+can't recognize faces at all
+ 
+
+ align:start position:0%
+can't recognize faces at all
+and importantly
+
+ align:start position:0%
+and importantly
+ 
+
+ align:start position:0%
+and importantly
+patient is absolutely normal at
+
+ align:start position:0%
+patient is absolutely normal at
+ 
+
+ align:start position:0%
+patient is absolutely normal at
+recognizing objects
+
+ align:start position:0%
+recognizing objects
+ 
+
+ align:start position:0%
+recognizing objects
+no problem whatsoever at recognizing
+
+ align:start position:0%
+no problem whatsoever at recognizing
+ 
+
+ align:start position:0%
+no problem whatsoever at recognizing
+objects
+
+ align:start position:0%
+objects
+ 
+
+ align:start position:0%
+objects
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+how does this take us beyond functional
+
+ align:start position:0%
+how does this take us beyond functional
+ 
+
+ align:start position:0%
+how does this take us beyond functional
+mri
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speak up
+
+ align:start position:0%
+speak up
+ 
+
+ align:start position:0%
+speak up
+yeah say more what what is it what does
+
+ align:start position:0%
+yeah say more what what is it what does
+ 
+
+ align:start position:0%
+yeah say more what what is it what does
+it tell us so because the because of the
+
+ align:start position:0%
+it tell us so because the because of the
+ 
+
+ align:start position:0%
+it tell us so because the because of the
+fact that like that theory is damaged
+
+ align:start position:0%
+fact that like that theory is damaged
+ 
+
+ align:start position:0%
+fact that like that theory is damaged
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+it makes it to like not being recognized
+
+ align:start position:0%
+it makes it to like not being recognized
+ 
+
+ align:start position:0%
+it makes it to like not being recognized
+because i could see how there's
+
+ align:start position:0%
+because i could see how there's
+ 
+
+ align:start position:0%
+because i could see how there's
+something to do with that period exactly
+
+ align:start position:0%
+something to do with that period exactly
+ 
+
+ align:start position:0%
+something to do with that period exactly
+exactly it says you need that bit to
+
+ align:start position:0%
+exactly it says you need that bit to
+ 
+
+ align:start position:0%
+exactly it says you need that bit to
+recognize faces but also says something
+
+ align:start position:0%
+recognize faces but also says something
+ 
+
+ align:start position:0%
+recognize faces but also says something
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+what else does it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you don't need it for recognizing
+
+ align:start position:0%
+you don't need it for recognizing
+ 
+
+ align:start position:0%
+you don't need it for recognizing
+objects so this is actually really
+
+ align:start position:0%
+objects so this is actually really
+ 
+
+ align:start position:0%
+objects so this is actually really
+strong evidence that that bit of brain
+
+ align:start position:0%
+strong evidence that that bit of brain
+ 
+
+ align:start position:0%
+strong evidence that that bit of brain
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+very specialized for face recognition
+
+ align:start position:0%
+very specialized for face recognition
+ 
+
+ align:start position:0%
+very specialized for face recognition
+specialized and necessary for face
+
+ align:start position:0%
+specialized and necessary for face
+ 
+
+ align:start position:0%
+specialized and necessary for face
+recognition
+
+ align:start position:0%
+recognition
+ 
+
+ align:start position:0%
+recognition
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so person still attacked faces
+
+ align:start position:0%
+so person still attacked faces
+ 
+
+ align:start position:0%
+so person still attacked faces
+oh yes good question absolutely like
+
+ align:start position:0%
+oh yes good question absolutely like
+ 
+
+ align:start position:0%
+oh yes good question absolutely like
+okay so let me just distinguish this
+
+ align:start position:0%
+okay so let me just distinguish this
+ 
+
+ align:start position:0%
+okay so let me just distinguish this
+person here
+
+ align:start position:0%
+person here
+ 
+
+ align:start position:0%
+person here
+um who has prosopagnosia that means a
+
+ align:start position:0%
+um who has prosopagnosia that means a
+ 
+
+ align:start position:0%
+um who has prosopagnosia that means a
+selective deficit and face recognition
+
+ align:start position:0%
+selective deficit and face recognition
+ 
+
+ align:start position:0%
+selective deficit and face recognition
+like jacob hodes who i described
+
+ align:start position:0%
+like jacob hodes who i described
+ 
+
+ align:start position:0%
+like jacob hodes who i described
+yesterday who has no brain damage
+
+ align:start position:0%
+yesterday who has no brain damage
+ 
+
+ align:start position:0%
+yesterday who has no brain damage
+whatsoever but has just never been able
+
+ align:start position:0%
+whatsoever but has just never been able
+ 
+
+ align:start position:0%
+whatsoever but has just never been able
+to recognize faces at any point in his
+
+ align:start position:0%
+to recognize faces at any point in his
+ 
+
+ align:start position:0%
+to recognize faces at any point in his
+life
+
+ align:start position:0%
+life
+ 
+
+ align:start position:0%
+life
+so this syndrome can arise just from
+
+ align:start position:0%
+so this syndrome can arise just from
+ 
+
+ align:start position:0%
+so this syndrome can arise just from
+some weird developmental thing where
+
+ align:start position:0%
+some weird developmental thing where
+ 
+
+ align:start position:0%
+some weird developmental thing where
+you're atypical and you're just really
+
+ align:start position:0%
+you're atypical and you're just really
+ 
+
+ align:start position:0%
+you're atypical and you're just really
+bad at it or it can result from damage
+
+ align:start position:0%
+bad at it or it can result from damage
+ 
+
+ align:start position:0%
+bad at it or it can result from damage
+to that part of the brain okay so now
+
+ align:start position:0%
+to that part of the brain okay so now
+ 
+
+ align:start position:0%
+to that part of the brain okay so now
+we're talking about the case of damage
+
+ align:start position:0%
+we're talking about the case of damage
+ 
+
+ align:start position:0%
+we're talking about the case of damage
+but in both cases
+
+ align:start position:0%
+but in both cases
+ 
+
+ align:start position:0%
+but in both cases
+people with prosopagnosia have no
+
+ align:start position:0%
+people with prosopagnosia have no
+ 
+
+ align:start position:0%
+people with prosopagnosia have no
+problem knowing that a face is a face
+
+ align:start position:0%
+problem knowing that a face is a face
+ 
+
+ align:start position:0%
+problem knowing that a face is a face
+they just don't know who it is
+
+ align:start position:0%
+they just don't know who it is
+ 
+
+ align:start position:0%
+they just don't know who it is
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+has there ever been a case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of people who can't recognize spaces who
+
+ align:start position:0%
+of people who can't recognize spaces who
+ 
+
+ align:start position:0%
+of people who can't recognize spaces who
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indeed
+
+ align:start position:0%
+indeed
+ 
+
+ align:start position:0%
+indeed
+indeed jacob hodes who i talked about
+
+ align:start position:0%
+indeed jacob hodes who i talked about
+ 
+
+ align:start position:0%
+indeed jacob hodes who i talked about
+last time who is just absolutely awful
+
+ align:start position:0%
+last time who is just absolutely awful
+ 
+
+ align:start position:0%
+last time who is just absolutely awful
+at face recognition including family
+
+ align:start position:0%
+at face recognition including family
+ 
+
+ align:start position:0%
+at face recognition including family
+members close friends can't do it like
+
+ align:start position:0%
+members close friends can't do it like
+ 
+
+ align:start position:0%
+members close friends can't do it like
+not at all
+
+ align:start position:0%
+not at all
+ 
+
+ align:start position:0%
+not at all
+he has a very normal looking fusiform
+
+ align:start position:0%
+he has a very normal looking fusiform
+ 
+
+ align:start position:0%
+he has a very normal looking fusiform
+face area
+
+ align:start position:0%
+face area
+ 
+
+ align:start position:0%
+face area
+so after i told you that i had that
+
+ align:start position:0%
+so after i told you that i had that
+ 
+
+ align:start position:0%
+so after i told you that i had that
+conversation with him
+
+ align:start position:0%
+conversation with him
+ 
+
+ align:start position:0%
+conversation with him
+a dozen years ago or something like that
+
+ align:start position:0%
+a dozen years ago or something like that
+ 
+
+ align:start position:0%
+a dozen years ago or something like that
+i scanned him
+
+ align:start position:0%
+i scanned him
+ 
+
+ align:start position:0%
+i scanned him
+and he had a beautiful fusiform face
+
+ align:start position:0%
+and he had a beautiful fusiform face
+ 
+
+ align:start position:0%
+and he had a beautiful fusiform face
+area like textbook it looked
+
+ align:start position:0%
+area like textbook it looked
+ 
+
+ align:start position:0%
+area like textbook it looked
+well looked like mine which is a damn
+
+ align:start position:0%
+well looked like mine which is a damn
+ 
+
+ align:start position:0%
+well looked like mine which is a damn
+fine one if i if i do say so myself
+
+ align:start position:0%
+fine one if i if i do say so myself
+ 
+
+ align:start position:0%
+fine one if i if i do say so myself
+um and um
+
+ align:start position:0%
+um and um
+ 
+
+ align:start position:0%
+um and um
+i looked at that and i went oh
+
+ align:start position:0%
+i looked at that and i went oh
+ 
+
+ align:start position:0%
+i looked at that and i went oh
+i better publish this before someone
+
+ align:start position:0%
+i better publish this before someone
+ 
+
+ align:start position:0%
+i better publish this before someone
+else does and i didn't get my act
+
+ align:start position:0%
+else does and i didn't get my act
+ 
+
+ align:start position:0%
+else does and i didn't get my act
+together and then a whole bunch of
+
+ align:start position:0%
+together and then a whole bunch of
+ 
+
+ align:start position:0%
+together and then a whole bunch of
+papers came out saying oh people with
+
+ align:start position:0%
+papers came out saying oh people with
+ 
+
+ align:start position:0%
+papers came out saying oh people with
+developmental prosopagnosia have normal
+
+ align:start position:0%
+developmental prosopagnosia have normal
+ 
+
+ align:start position:0%
+developmental prosopagnosia have normal
+looking face areas take that canvasser
+
+ align:start position:0%
+looking face areas take that canvasser
+ 
+
+ align:start position:0%
+looking face areas take that canvasser
+what do you say about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it was a little shocking
+
+ align:start position:0%
+and it was a little shocking
+ 
+
+ align:start position:0%
+and it was a little shocking
+but upon further reflection it's not
+
+ align:start position:0%
+but upon further reflection it's not
+ 
+
+ align:start position:0%
+but upon further reflection it's not
+really devastating right i mean it's
+
+ align:start position:0%
+really devastating right i mean it's
+ 
+
+ align:start position:0%
+really devastating right i mean it's
+bracing it's informative
+
+ align:start position:0%
+bracing it's informative
+ 
+
+ align:start position:0%
+bracing it's informative
+but it tells you
+
+ align:start position:0%
+but it tells you
+ 
+
+ align:start position:0%
+but it tells you
+that having a face area that is a region
+
+ align:start position:0%
+that having a face area that is a region
+ 
+
+ align:start position:0%
+that having a face area that is a region
+that responds more to faces and objects
+
+ align:start position:0%
+that responds more to faces and objects
+ 
+
+ align:start position:0%
+that responds more to faces and objects
+isn't sufficient
+
+ align:start position:0%
+isn't sufficient
+ 
+
+ align:start position:0%
+isn't sufficient
+for normal face recognition
+
+ align:start position:0%
+for normal face recognition
+ 
+
+ align:start position:0%
+for normal face recognition
+right you need other stuff
+
+ align:start position:0%
+right you need other stuff
+ 
+
+ align:start position:0%
+right you need other stuff
+what might that other stuff be well the
+
+ align:start position:0%
+what might that other stuff be well the
+ 
+
+ align:start position:0%
+what might that other stuff be well the
+circuits in there need to work right
+
+ align:start position:0%
+circuits in there need to work right
+ 
+
+ align:start position:0%
+circuits in there need to work right
+it's not enough to just respond more to
+
+ align:start position:0%
+it's not enough to just respond more to
+ 
+
+ align:start position:0%
+it's not enough to just respond more to
+faces and objects to recognize faces
+
+ align:start position:0%
+faces and objects to recognize faces
+ 
+
+ align:start position:0%
+faces and objects to recognize faces
+they need to be able to distinguish
+
+ align:start position:0%
+they need to be able to distinguish
+ 
+
+ align:start position:0%
+they need to be able to distinguish
+faces from objects we don't know if
+
+ align:start position:0%
+faces from objects we don't know if
+ 
+
+ align:start position:0%
+faces from objects we don't know if
+that's working right
+
+ align:start position:0%
+that's working right
+ 
+
+ align:start position:0%
+that's working right
+what else do you need
+
+ align:start position:0%
+what else do you need
+ 
+
+ align:start position:0%
+what else do you need
+memory absolutely
+
+ align:start position:0%
+memory absolutely
+ 
+
+ align:start position:0%
+memory absolutely
+yes you need to remember faces what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+could be but in jacob's case it was like
+
+ align:start position:0%
+could be but in jacob's case it was like
+ 
+
+ align:start position:0%
+could be but in jacob's case it was like
+close friends he couldn't recognize
+
+ align:start position:0%
+close friends he couldn't recognize
+ 
+
+ align:start position:0%
+close friends he couldn't recognize
+so what's another possible account of
+
+ align:start position:0%
+so what's another possible account of
+ 
+
+ align:start position:0%
+so what's another possible account of
+how could he have a normal face area and
+
+ align:start position:0%
+how could he have a normal face area and
+ 
+
+ align:start position:0%
+how could he have a normal face area and
+yeah david it might be a
+
+ align:start position:0%
+yeah david it might be a
+ 
+
+ align:start position:0%
+yeah david it might be a
+gap between
+
+ align:start position:0%
+gap between
+ 
+
+ align:start position:0%
+gap between
+recognizing on face and connecting that
+
+ align:start position:0%
+recognizing on face and connecting that
+ 
+
+ align:start position:0%
+recognizing on face and connecting that
+to recognizing a person
+
+ align:start position:0%
+to recognizing a person
+ 
+
+ align:start position:0%
+to recognizing a person
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah or to put that neuroanatomically
+
+ align:start position:0%
+yeah or to put that neuroanatomically
+ 
+
+ align:start position:0%
+yeah or to put that neuroanatomically
+you got to get the information out of
+
+ align:start position:0%
+you got to get the information out of
+ 
+
+ align:start position:0%
+you got to get the information out of
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+like maybe for all we know
+
+ align:start position:0%
+like maybe for all we know
+ 
+
+ align:start position:0%
+like maybe for all we know
+that little face area is working
+
+ align:start position:0%
+that little face area is working
+ 
+
+ align:start position:0%
+that little face area is working
+perfectly maybe that face area knows who
+
+ align:start position:0%
+perfectly maybe that face area knows who
+ 
+
+ align:start position:0%
+perfectly maybe that face area knows who
+that person is in a sense
+
+ align:start position:0%
+that person is in a sense
+ 
+
+ align:start position:0%
+that person is in a sense
+but if the connections out of that brain
+
+ align:start position:0%
+but if the connections out of that brain
+ 
+
+ align:start position:0%
+but if the connections out of that brain
+region to the rest of the brain
+
+ align:start position:0%
+region to the rest of the brain
+ 
+
+ align:start position:0%
+region to the rest of the brain
+are messed up it doesn't do you any good
+
+ align:start position:0%
+are messed up it doesn't do you any good
+ 
+
+ align:start position:0%
+are messed up it doesn't do you any good
+right you need to be able to read that
+
+ align:start position:0%
+right you need to be able to read that
+ 
+
+ align:start position:0%
+right you need to be able to read that
+information out and act on the basis of
+
+ align:start position:0%
+information out and act on the basis of
+ 
+
+ align:start position:0%
+information out and act on the basis of
+it right
+
+ align:start position:0%
+it right
+ 
+
+ align:start position:0%
+it right
+anyway that's a big sidebar
+
+ align:start position:0%
+anyway that's a big sidebar
+ 
+
+ align:start position:0%
+anyway that's a big sidebar
+point is you can have prosopagnosia
+
+ align:start position:0%
+point is you can have prosopagnosia
+ 
+
+ align:start position:0%
+point is you can have prosopagnosia
+either as just a developmental disorder
+
+ align:start position:0%
+either as just a developmental disorder
+ 
+
+ align:start position:0%
+either as just a developmental disorder
+or as a result of brain damage oh god i
+
+ align:start position:0%
+or as a result of brain damage oh god i
+ 
+
+ align:start position:0%
+or as a result of brain damage oh god i
+knew that was going to happen all right
+
+ align:start position:0%
+knew that was going to happen all right
+ 
+
+ align:start position:0%
+knew that was going to happen all right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so okay so very briefly um it s it
+
+ align:start position:0%
+so okay so very briefly um it s it
+ 
+
+ align:start position:0%
+so okay so very briefly um it s it
+messes up ability to discriminate and
+
+ align:start position:0%
+messes up ability to discriminate and
+ 
+
+ align:start position:0%
+messes up ability to discriminate and
+recognize faces not your ability to
+
+ align:start position:0%
+recognize faces not your ability to
+ 
+
+ align:start position:0%
+recognize faces not your ability to
+detect a face right so spurted ass it's
+
+ align:start position:0%
+detect a face right so spurted ass it's
+ 
+
+ align:start position:0%
+detect a face right so spurted ass it's
+not just you can't uh tell the thing as
+
+ align:start position:0%
+not just you can't uh tell the thing as
+ 
+
+ align:start position:0%
+not just you can't uh tell the thing as
+a face they're fine with that
+
+ align:start position:0%
+a face they're fine with that
+ 
+
+ align:start position:0%
+a face they're fine with that
+importantly they're normal at voice
+
+ align:start position:0%
+importantly they're normal at voice
+ 
+
+ align:start position:0%
+importantly they're normal at voice
+recognition okay so it's not that
+
+ align:start position:0%
+recognition okay so it's not that
+ 
+
+ align:start position:0%
+recognition okay so it's not that
+they're confused about distinguishing
+
+ align:start position:0%
+they're confused about distinguishing
+ 
+
+ align:start position:0%
+they're confused about distinguishing
+one person from another they can do it
+
+ align:start position:0%
+one person from another they can do it
+ 
+
+ align:start position:0%
+one person from another they can do it
+fine
+
+ align:start position:0%
+fine
+ 
+
+ align:start position:0%
+fine
+from audition just not from vision
+
+ align:start position:0%
+from audition just not from vision
+ 
+
+ align:start position:0%
+from audition just not from vision
+um when the in the rare cases where the
+
+ align:start position:0%
+um when the in the rare cases where the
+ 
+
+ align:start position:0%
+um when the in the rare cases where the
+lesion is small it can be very specific
+
+ align:start position:0%
+lesion is small it can be very specific
+ 
+
+ align:start position:0%
+lesion is small it can be very specific
+leaving object recognition intact more
+
+ align:start position:0%
+leaving object recognition intact more
+ 
+
+ align:start position:0%
+leaving object recognition intact more
+often there's kind of a blurry mess you
+
+ align:start position:0%
+often there's kind of a blurry mess you
+ 
+
+ align:start position:0%
+often there's kind of a blurry mess you
+have a big lesion and a bunch of things
+
+ align:start position:0%
+have a big lesion and a bunch of things
+ 
+
+ align:start position:0%
+have a big lesion and a bunch of things
+are affected
+
+ align:start position:0%
+are affected
+ 
+
+ align:start position:0%
+are affected
+okay so we've talked about that okay now
+
+ align:start position:0%
+okay so we've talked about that okay now
+ 
+
+ align:start position:0%
+okay so we've talked about that okay now
+it's very important in neuropsychology
+
+ align:start position:0%
+it's very important in neuropsychology
+ 
+
+ align:start position:0%
+it's very important in neuropsychology
+reasoning like we want to say okay
+
+ align:start position:0%
+reasoning like we want to say okay
+ 
+
+ align:start position:0%
+reasoning like we want to say okay
+that's really powerful the case of
+
+ align:start position:0%
+that's really powerful the case of
+ 
+
+ align:start position:0%
+that's really powerful the case of
+prosopagnosia you lose that bit you
+
+ align:start position:0%
+prosopagnosia you lose that bit you
+ 
+
+ align:start position:0%
+prosopagnosia you lose that bit you
+can't recognize faces
+
+ align:start position:0%
+can't recognize faces
+ 
+
+ align:start position:0%
+can't recognize faces
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and and that that establishes a kind of
+
+ align:start position:0%
+and and that that establishes a kind of
+ 
+
+ align:start position:0%
+and and that that establishes a kind of
+causality that we didn't have before
+
+ align:start position:0%
+causality that we didn't have before
+ 
+
+ align:start position:0%
+causality that we didn't have before
+okay with just functional mri
+
+ align:start position:0%
+okay with just functional mri
+ 
+
+ align:start position:0%
+okay with just functional mri
+but is that sufficient to say that that
+
+ align:start position:0%
+but is that sufficient to say that that
+ 
+
+ align:start position:0%
+but is that sufficient to say that that
+region is specialized for face
+
+ align:start position:0%
+region is specialized for face
+ 
+
+ align:start position:0%
+region is specialized for face
+recognition only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's not whenever i ask this the answer
+
+ align:start position:0%
+it's not whenever i ask this the answer
+ 
+
+ align:start position:0%
+it's not whenever i ask this the answer
+is no your task is to say why
+
+ align:start position:0%
+is no your task is to say why
+ 
+
+ align:start position:0%
+is no your task is to say why
+how could you have
+
+ align:start position:0%
+how could you have
+ 
+
+ align:start position:0%
+how could you have
+great difficulty recognizing faces and
+
+ align:start position:0%
+great difficulty recognizing faces and
+ 
+
+ align:start position:0%
+great difficulty recognizing faces and
+be okay at object recognition and yet
+
+ align:start position:0%
+be okay at object recognition and yet
+ 
+
+ align:start position:0%
+be okay at object recognition and yet
+not have a deficit that's specific to
+
+ align:start position:0%
+not have a deficit that's specific to
+ 
+
+ align:start position:0%
+not have a deficit that's specific to
+faces
+
+ align:start position:0%
+faces
+ 
+
+ align:start position:0%
+faces
+what what are how how might that arise
+
+ align:start position:0%
+what what are how how might that arise
+ 
+
+ align:start position:0%
+what what are how how might that arise
+you guys have suggested this hypothesis
+
+ align:start position:0%
+you guys have suggested this hypothesis
+ 
+
+ align:start position:0%
+you guys have suggested this hypothesis
+in different contexts before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes you look like you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+sort of um but the question here is
+
+ align:start position:0%
+sort of um but the question here is
+ 
+
+ align:start position:0%
+sort of um but the question here is
+how if you if you
+
+ align:start position:0%
+how if you if you
+ 
+
+ align:start position:0%
+how if you if you
+okay let's just start bare bones you
+
+ align:start position:0%
+okay let's just start bare bones you
+ 
+
+ align:start position:0%
+okay let's just start bare bones you
+have a lesion
+
+ align:start position:0%
+have a lesion
+ 
+
+ align:start position:0%
+have a lesion
+you get around fine in the world you can
+
+ align:start position:0%
+you get around fine in the world you can
+ 
+
+ align:start position:0%
+you get around fine in the world you can
+do everything else but you have a real
+
+ align:start position:0%
+do everything else but you have a real
+ 
+
+ align:start position:0%
+do everything else but you have a real
+problem recognizing faces
+
+ align:start position:0%
+problem recognizing faces
+ 
+
+ align:start position:0%
+problem recognizing faces
+does that mean that the region lesioned
+
+ align:start position:0%
+does that mean that the region lesioned
+ 
+
+ align:start position:0%
+does that mean that the region lesioned
+is necessary for face recognition per se
+
+ align:start position:0%
+is necessary for face recognition per se
+ 
+
+ align:start position:0%
+is necessary for face recognition per se
+there might be
+
+ align:start position:0%
+there might be
+ 
+
+ align:start position:0%
+there might be
+like other ancients
+
+ align:start position:0%
+like other ancients
+ 
+
+ align:start position:0%
+like other ancients
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+that's true there could be other things
+
+ align:start position:0%
+that's true there could be other things
+ 
+
+ align:start position:0%
+that's true there could be other things
+going on absolutely but let's suppose
+
+ align:start position:0%
+going on absolutely but let's suppose
+ 
+
+ align:start position:0%
+going on absolutely but let's suppose
+they're not let's suppose you had good
+
+ align:start position:0%
+they're not let's suppose you had good
+ 
+
+ align:start position:0%
+they're not let's suppose you had good
+reason to think there weren't yeah it
+
+ align:start position:0%
+reason to think there weren't yeah it
+ 
+
+ align:start position:0%
+reason to think there weren't yeah it
+could be like uh
+
+ align:start position:0%
+could be like uh
+ 
+
+ align:start position:0%
+could be like uh
+like could be a path it could be like
+
+ align:start position:0%
+like could be a path it could be like
+ 
+
+ align:start position:0%
+like could be a path it could be like
+one point in a pathway that's true it
+
+ align:start position:0%
+one point in a pathway that's true it
+ 
+
+ align:start position:0%
+one point in a pathway that's true it
+could be totally a point in a pathway
+
+ align:start position:0%
+could be totally a point in a pathway
+ 
+
+ align:start position:0%
+could be totally a point in a pathway
+absolutely that's another account what
+
+ align:start position:0%
+absolutely that's another account what
+ 
+
+ align:start position:0%
+absolutely that's another account what
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+oh i i couldn't give lots of comments he
+
+ align:start position:0%
+oh i i couldn't give lots of comments he
+ 
+
+ align:start position:0%
+oh i i couldn't give lots of comments he
+said like maybe you damage a pathway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+maybe there's some other function we
+
+ align:start position:0%
+maybe there's some other function we
+ 
+
+ align:start position:0%
+maybe there's some other function we
+haven't tested
+
+ align:start position:0%
+haven't tested
+ 
+
+ align:start position:0%
+haven't tested
+let's all these are very good
+
+ align:start position:0%
+let's all these are very good
+ 
+
+ align:start position:0%
+let's all these are very good
+alternative hypotheses you guys are very
+
+ align:start position:0%
+alternative hypotheses you guys are very
+ 
+
+ align:start position:0%
+alternative hypotheses you guys are very
+good at this the one i'm fishing for is
+
+ align:start position:0%
+good at this the one i'm fishing for is
+ 
+
+ align:start position:0%
+good at this the one i'm fishing for is
+maybe face recognition is just harder
+
+ align:start position:0%
+maybe face recognition is just harder
+ 
+
+ align:start position:0%
+maybe face recognition is just harder
+than object recognition
+
+ align:start position:0%
+than object recognition
+ 
+
+ align:start position:0%
+than object recognition
+maybe the part that's damaged is just
+
+ align:start position:0%
+maybe the part that's damaged is just
+ 
+
+ align:start position:0%
+maybe the part that's damaged is just
+generically involved in object
+
+ align:start position:0%
+generically involved in object
+ 
+
+ align:start position:0%
+generically involved in object
+recognition
+
+ align:start position:0%
+recognition
+ 
+
+ align:start position:0%
+recognition
+but you damage part of the object
+
+ align:start position:0%
+but you damage part of the object
+ 
+
+ align:start position:0%
+but you damage part of the object
+recognition system and face recognition
+
+ align:start position:0%
+recognition system and face recognition
+ 
+
+ align:start position:0%
+recognition system and face recognition
+takes a bigger hit because it's harder
+
+ align:start position:0%
+takes a bigger hit because it's harder
+ 
+
+ align:start position:0%
+takes a bigger hit because it's harder
+right does that make sense
+
+ align:start position:0%
+right does that make sense
+ 
+
+ align:start position:0%
+right does that make sense
+do you see how the case of prosopagnosia
+
+ align:start position:0%
+do you see how the case of prosopagnosia
+ 
+
+ align:start position:0%
+do you see how the case of prosopagnosia
+is consistent with that so that means we
+
+ align:start position:0%
+is consistent with that so that means we
+ 
+
+ align:start position:0%
+is consistent with that so that means we
+cannot infer from these data alone that
+
+ align:start position:0%
+cannot infer from these data alone that
+ 
+
+ align:start position:0%
+cannot infer from these data alone that
+that region is specialized for face
+
+ align:start position:0%
+that region is specialized for face
+ 
+
+ align:start position:0%
+that region is specialized for face
+recognition
+
+ align:start position:0%
+recognition
+ 
+
+ align:start position:0%
+recognition
+now we can do various things like test
+
+ align:start position:0%
+now we can do various things like test
+ 
+
+ align:start position:0%
+now we can do various things like test
+them on really hard versions of object
+
+ align:start position:0%
+them on really hard versions of object
+ 
+
+ align:start position:0%
+them on really hard versions of object
+recognition and people have done that
+
+ align:start position:0%
+recognition and people have done that
+ 
+
+ align:start position:0%
+recognition and people have done that
+but there's another kind of data that
+
+ align:start position:0%
+but there's another kind of data that
+ 
+
+ align:start position:0%
+but there's another kind of data that
+are really powerful here
+
+ align:start position:0%
+are really powerful here
+ 
+
+ align:start position:0%
+are really powerful here
+and that's when we have the opposite
+
+ align:start position:0%
+and that's when we have the opposite
+ 
+
+ align:start position:0%
+and that's when we have the opposite
+syndrome
+
+ align:start position:0%
+syndrome
+ 
+
+ align:start position:0%
+syndrome
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so there's a only a couple cases of this
+
+ align:start position:0%
+so there's a only a couple cases of this
+ 
+
+ align:start position:0%
+so there's a only a couple cases of this
+the best one is called ck published in a
+
+ align:start position:0%
+the best one is called ck published in a
+ 
+
+ align:start position:0%
+the best one is called ck published in a
+paper in 1997. you don't need to
+
+ align:start position:0%
+paper in 1997. you don't need to
+ 
+
+ align:start position:0%
+paper in 1997. you don't need to
+remember that the point about this is
+
+ align:start position:0%
+remember that the point about this is
+ 
+
+ align:start position:0%
+remember that the point about this is
+that this guy has the opposite syndrome
+
+ align:start position:0%
+that this guy has the opposite syndrome
+ 
+
+ align:start position:0%
+that this guy has the opposite syndrome
+he's severely impaired at object
+
+ align:start position:0%
+he's severely impaired at object
+ 
+
+ align:start position:0%
+he's severely impaired at object
+recognition he can't tell a chair from a
+
+ align:start position:0%
+recognition he can't tell a chair from a
+ 
+
+ align:start position:0%
+recognition he can't tell a chair from a
+table from a car from a toaster
+
+ align:start position:0%
+table from a car from a toaster
+ 
+
+ align:start position:0%
+table from a car from a toaster
+but he's a hundred percent normal at
+
+ align:start position:0%
+but he's a hundred percent normal at
+ 
+
+ align:start position:0%
+but he's a hundred percent normal at
+face recognition
+
+ align:start position:0%
+face recognition
+ 
+
+ align:start position:0%
+face recognition
+totally normal at face recognition in
+
+ align:start position:0%
+totally normal at face recognition in
+ 
+
+ align:start position:0%
+totally normal at face recognition in
+fact better than average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you see how that's in some ways even
+
+ align:start position:0%
+do you see how that's in some ways even
+ 
+
+ align:start position:0%
+do you see how that's in some ways even
+more powerful evidence
+
+ align:start position:0%
+more powerful evidence
+ 
+
+ align:start position:0%
+more powerful evidence
+that face recognition goes on in
+
+ align:start position:0%
+that face recognition goes on in
+ 
+
+ align:start position:0%
+that face recognition goes on in
+specialized brain machinery than the
+
+ align:start position:0%
+specialized brain machinery than the
+ 
+
+ align:start position:0%
+specialized brain machinery than the
+case of prostagnosia
+
+ align:start position:0%
+case of prostagnosia
+ 
+
+ align:start position:0%
+case of prostagnosia
+like face recognition isn't even like a
+
+ align:start position:0%
+like face recognition isn't even like a
+ 
+
+ align:start position:0%
+like face recognition isn't even like a
+special thing that sits on top of normal
+
+ align:start position:0%
+special thing that sits on top of normal
+ 
+
+ align:start position:0%
+special thing that sits on top of normal
+object recognition it's a totally
+
+ align:start position:0%
+object recognition it's a totally
+ 
+
+ align:start position:0%
+object recognition it's a totally
+different pathway you can have no
+
+ align:start position:0%
+different pathway you can have no
+ 
+
+ align:start position:0%
+different pathway you can have no
+ability to recognize objects and you're
+
+ align:start position:0%
+ability to recognize objects and you're
+ 
+
+ align:start position:0%
+ability to recognize objects and you're
+okay at face recognition does everybody
+
+ align:start position:0%
+okay at face recognition does everybody
+ 
+
+ align:start position:0%
+okay at face recognition does everybody
+see how that's really powerful
+
+ align:start position:0%
+see how that's really powerful
+ 
+
+ align:start position:0%
+see how that's really powerful
+and how those two kinds of evidence
+
+ align:start position:0%
+and how those two kinds of evidence
+ 
+
+ align:start position:0%
+and how those two kinds of evidence
+together are vastly more powerful than
+
+ align:start position:0%
+together are vastly more powerful than
+ 
+
+ align:start position:0%
+together are vastly more powerful than
+either one alone okay
+
+ align:start position:0%
+either one alone okay
+ 
+
+ align:start position:0%
+either one alone okay
+well that's called a doubled association
+
+ align:start position:0%
+well that's called a doubled association
+ 
+
+ align:start position:0%
+well that's called a doubled association
+um we'll skip all of that for now double
+
+ align:start position:0%
+um we'll skip all of that for now double
+ 
+
+ align:start position:0%
+um we'll skip all of that for now double
+dissociations are particularly powerful
+
+ align:start position:0%
+dissociations are particularly powerful
+ 
+
+ align:start position:0%
+dissociations are particularly powerful
+examples uh powerful forms of evidence
+
+ align:start position:0%
+examples uh powerful forms of evidence
+ 
+
+ align:start position:0%
+examples uh powerful forms of evidence
+in cognitive neuroscience where we have
+
+ align:start position:0%
+in cognitive neuroscience where we have
+ 
+
+ align:start position:0%
+in cognitive neuroscience where we have
+opposite syndromes that collectively
+
+ align:start position:0%
+opposite syndromes that collectively
+ 
+
+ align:start position:0%
+opposite syndromes that collectively
+make it really hard to wiggle out and
+
+ align:start position:0%
+make it really hard to wiggle out and
+ 
+
+ align:start position:0%
+make it really hard to wiggle out and
+come up with alternative accounts other
+
+ align:start position:0%
+come up with alternative accounts other
+ 
+
+ align:start position:0%
+come up with alternative accounts other
+than that
+
+ align:start position:0%
+than that
+ 
+
+ align:start position:0%
+than that
+there's a there's a bit of brain that's
+
+ align:start position:0%
+there's a there's a bit of brain that's
+ 
+
+ align:start position:0%
+there's a there's a bit of brain that's
+really specialized for face recognition
+
+ align:start position:0%
+really specialized for face recognition
+ 
+
+ align:start position:0%
+really specialized for face recognition
+it's not just that face recognition is
+
+ align:start position:0%
+it's not just that face recognition is
+ 
+
+ align:start position:0%
+it's not just that face recognition is
+harder or else you'd never get this
+
+ align:start position:0%
+harder or else you'd never get this
+ 
+
+ align:start position:0%
+harder or else you'd never get this
+syndrome
+
+ align:start position:0%
+syndrome
+ 
+
+ align:start position:0%
+syndrome
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right i just wanted to finish that
+
+ align:start position:0%
+all right i just wanted to finish that
+ 
+
+ align:start position:0%
+all right i just wanted to finish that
+point okay now how much time do i have
+
+ align:start position:0%
+point okay now how much time do i have
+ 
+
+ align:start position:0%
+point okay now how much time do i have
+until the quiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50 minutes okay good um okay good we're
+
+ align:start position:0%
+50 minutes okay good um okay good we're
+ 
+
+ align:start position:0%
+50 minutes okay good um okay good we're
+going to skip over tms i'm sorry about
+
+ align:start position:0%
+going to skip over tms i'm sorry about
+ 
+
+ align:start position:0%
+going to skip over tms i'm sorry about
+that guys someday i'll learn to time
+
+ align:start position:0%
+that guys someday i'll learn to time
+ 
+
+ align:start position:0%
+that guys someday i'll learn to time
+things in a lecture actually i knew this
+
+ align:start position:0%
+things in a lecture actually i knew this
+ 
+
+ align:start position:0%
+things in a lecture actually i knew this
+was going to happen just
+
+ align:start position:0%
+was going to happen just
+ 
+
+ align:start position:0%
+was going to happen just
+we'll get back to tms later
+
+ align:start position:0%
+we'll get back to tms later
+ 
+
+ align:start position:0%
+we'll get back to tms later
+and we will skip to
+
+ align:start position:0%
+and we will skip to
+ 
+
+ align:start position:0%
+and we will skip to
+the most amazing method in all of
+
+ align:start position:0%
+the most amazing method in all of
+ 
+
+ align:start position:0%
+the most amazing method in all of
+cognitive neuroscience
+
+ align:start position:0%
+cognitive neuroscience
+ 
+
+ align:start position:0%
+cognitive neuroscience
+for which we're going to come back to
+
+ align:start position:0%
+for which we're going to come back to
+ 
+
+ align:start position:0%
+for which we're going to come back to
+this dude who you met before who has the
+
+ align:start position:0%
+this dude who you met before who has the
+ 
+
+ align:start position:0%
+this dude who you met before who has the
+face selective responses in that part of
+
+ align:start position:0%
+face selective responses in that part of
+ 
+
+ align:start position:0%
+face selective responses in that part of
+his brain
+
+ align:start position:0%
+his brain
+ 
+
+ align:start position:0%
+his brain
+okay remember how i said that even
+
+ align:start position:0%
+okay remember how i said that even
+ 
+
+ align:start position:0%
+okay remember how i said that even
+though these data are gorgeous and
+
+ align:start position:0%
+though these data are gorgeous and
+ 
+
+ align:start position:0%
+though these data are gorgeous and
+spectacular and the only way we can get
+
+ align:start position:0%
+spectacular and the only way we can get
+ 
+
+ align:start position:0%
+spectacular and the only way we can get
+high spatial and temporal resolution
+
+ align:start position:0%
+high spatial and temporal resolution
+ 
+
+ align:start position:0%
+high spatial and temporal resolution
+together but they don't tell us
+
+ align:start position:0%
+together but they don't tell us
+ 
+
+ align:start position:0%
+together but they don't tell us
+causality
+
+ align:start position:0%
+causality
+ 
+
+ align:start position:0%
+causality
+right that's true here
+
+ align:start position:0%
+right that's true here
+ 
+
+ align:start position:0%
+right that's true here
+resolution doesn't get you causality to
+
+ align:start position:0%
+resolution doesn't get you causality to
+ 
+
+ align:start position:0%
+resolution doesn't get you causality to
+test the causal role of something you
+
+ align:start position:0%
+test the causal role of something you
+ 
+
+ align:start position:0%
+test the causal role of something you
+need to mess with it
+
+ align:start position:0%
+need to mess with it
+ 
+
+ align:start position:0%
+need to mess with it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so it turns out that sometimes the
+
+ align:start position:0%
+so it turns out that sometimes the
+ 
+
+ align:start position:0%
+so it turns out that sometimes the
+neurosurgeons electrically stimulate
+
+ align:start position:0%
+neurosurgeons electrically stimulate
+ 
+
+ align:start position:0%
+neurosurgeons electrically stimulate
+through those same electrodes
+
+ align:start position:0%
+through those same electrodes
+ 
+
+ align:start position:0%
+through those same electrodes
+and they do that to test the function of
+
+ align:start position:0%
+and they do that to test the function of
+ 
+
+ align:start position:0%
+and they do that to test the function of
+those regions causally
+
+ align:start position:0%
+those regions causally
+ 
+
+ align:start position:0%
+those regions causally
+they also do it to test their hypotheses
+
+ align:start position:0%
+they also do it to test their hypotheses
+ 
+
+ align:start position:0%
+they also do it to test their hypotheses
+about the location of the seizure foci
+
+ align:start position:0%
+about the location of the seizure foci
+ 
+
+ align:start position:0%
+about the location of the seizure foci
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so in those rare cases where you have a
+
+ align:start position:0%
+so in those rare cases where you have a
+ 
+
+ align:start position:0%
+so in those rare cases where you have a
+patient like this with selective
+
+ align:start position:0%
+patient like this with selective
+ 
+
+ align:start position:0%
+patient like this with selective
+electrodes like that
+
+ align:start position:0%
+electrodes like that
+ 
+
+ align:start position:0%
+electrodes like that
+where the clinicians decide that they
+
+ align:start position:0%
+where the clinicians decide that they
+ 
+
+ align:start position:0%
+where the clinicians decide that they
+are going to electrically stimulate
+
+ align:start position:0%
+are going to electrically stimulate
+ 
+
+ align:start position:0%
+are going to electrically stimulate
+through some of those electrodes then
+
+ align:start position:0%
+through some of those electrodes then
+ 
+
+ align:start position:0%
+through some of those electrodes then
+we're in a position to kind of have it
+
+ align:start position:0%
+we're in a position to kind of have it
+ 
+
+ align:start position:0%
+we're in a position to kind of have it
+all scientifically right i don't mean to
+
+ align:start position:0%
+all scientifically right i don't mean to
+ 
+
+ align:start position:0%
+all scientifically right i don't mean to
+be so crude this is a horrible situation
+
+ align:start position:0%
+be so crude this is a horrible situation
+ 
+
+ align:start position:0%
+be so crude this is a horrible situation
+for that lovely guy to be in but
+
+ align:start position:0%
+for that lovely guy to be in but
+ 
+
+ align:start position:0%
+for that lovely guy to be in but
+scientifically it's extremely powerful
+
+ align:start position:0%
+scientifically it's extremely powerful
+ 
+
+ align:start position:0%
+scientifically it's extremely powerful
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i'm going to show you um we did in fact
+
+ align:start position:0%
+i'm going to show you um we did in fact
+ 
+
+ align:start position:0%
+i'm going to show you um we did in fact
+have an opportunity the same guys in
+
+ align:start position:0%
+have an opportunity the same guys in
+ 
+
+ align:start position:0%
+have an opportunity the same guys in
+japan
+
+ align:start position:0%
+japan
+ 
+
+ align:start position:0%
+japan
+emailed me and said okay we're going to
+
+ align:start position:0%
+emailed me and said okay we're going to
+ 
+
+ align:start position:0%
+emailed me and said okay we're going to
+be stimulating that electrode
+
+ align:start position:0%
+be stimulating that electrode
+ 
+
+ align:start position:0%
+be stimulating that electrode
+what do we do
+
+ align:start position:0%
+what do we do
+ 
+
+ align:start position:0%
+what do we do
+and i said okay have him look at faces
+
+ align:start position:0%
+and i said okay have him look at faces
+ 
+
+ align:start position:0%
+and i said okay have him look at faces
+and have him look at other objects and
+
+ align:start position:0%
+and have him look at other objects and
+ 
+
+ align:start position:0%
+and have him look at other objects and
+ask him if anything changes and i'm
+
+ align:start position:0%
+ask him if anything changes and i'm
+ 
+
+ align:start position:0%
+ask him if anything changes and i'm
+going to show you a video of what
+
+ align:start position:0%
+going to show you a video of what
+ 
+
+ align:start position:0%
+going to show you a video of what
+happens when that goes on
+
+ align:start position:0%
+happens when that goes on
+ 
+
+ align:start position:0%
+happens when that goes on
+okay there we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh and i need to turn on the audio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here this is getting stimulated
+
+ align:start position:0%
+okay here this is getting stimulated
+ 
+
+ align:start position:0%
+okay here this is getting stimulated
+right there and he says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he's such a good subject this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that tells us that that region is
+
+ align:start position:0%
+okay that tells us that that region is
+ 
+
+ align:start position:0%
+okay that tells us that that region is
+causally involved in face perception is
+
+ align:start position:0%
+causally involved in face perception is
+ 
+
+ align:start position:0%
+causally involved in face perception is
+it causally involved in perception of
+
+ align:start position:0%
+it causally involved in perception of
+ 
+
+ align:start position:0%
+it causally involved in perception of
+things that aren't faces he's getting
+
+ align:start position:0%
+things that aren't faces he's getting
+ 
+
+ align:start position:0%
+things that aren't faces he's getting
+stimulated in the same electrode he
+
+ align:start position:0%
+stimulated in the same electrode he
+ 
+
+ align:start position:0%
+stimulated in the same electrode he
+doesn't know that there's a face area
+
+ align:start position:0%
+doesn't know that there's a face area
+ 
+
+ align:start position:0%
+doesn't know that there's a face area
+he doesn't know what which electrode is
+
+ align:start position:0%
+he doesn't know what which electrode is
+ 
+
+ align:start position:0%
+he doesn't know what which electrode is
+being stimulated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a kanji character on a card here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one more time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+awesome huh what did we just learn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can trigger it yeah
+
+ align:start position:0%
+you can trigger it yeah
+ 
+
+ align:start position:0%
+you can trigger it yeah
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so what does that tell us about the
+
+ align:start position:0%
+so what does that tell us about the
+ 
+
+ align:start position:0%
+so what does that tell us about the
+function of that region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why is this i mean it's amazing to see
+
+ align:start position:0%
+why is this i mean it's amazing to see
+ 
+
+ align:start position:0%
+why is this i mean it's amazing to see
+no question but what does it tell us
+
+ align:start position:0%
+no question but what does it tell us
+ 
+
+ align:start position:0%
+no question but what does it tell us
+scientifically
+
+ align:start position:0%
+scientifically
+ 
+
+ align:start position:0%
+scientifically
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+how does it tell us that it's specific
+
+ align:start position:0%
+how does it tell us that it's specific
+ 
+
+ align:start position:0%
+how does it tell us that it's specific
+because when you stimulate it like
+
+ align:start position:0%
+because when you stimulate it like
+ 
+
+ align:start position:0%
+because when you stimulate it like
+it particularly sees a face
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and what happens when he's looking at
+
+ align:start position:0%
+and what happens when he's looking at
+ 
+
+ align:start position:0%
+and what happens when he's looking at
+things that aren't faces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so you know if that region was causally
+
+ align:start position:0%
+so you know if that region was causally
+ 
+
+ align:start position:0%
+so you know if that region was causally
+involved in perception of things that
+
+ align:start position:0%
+involved in perception of things that
+ 
+
+ align:start position:0%
+involved in perception of things that
+aren't faces
+
+ align:start position:0%
+aren't faces
+ 
+
+ align:start position:0%
+aren't faces
+you might think that um that it would
+
+ align:start position:0%
+you might think that um that it would
+ 
+
+ align:start position:0%
+you might think that um that it would
+distort the box would look different or
+
+ align:start position:0%
+distort the box would look different or
+ 
+
+ align:start position:0%
+distort the box would look different or
+the ball would look different or the
+
+ align:start position:0%
+the ball would look different or the
+ 
+
+ align:start position:0%
+the ball would look different or the
+kanji would look different it doesn't
+
+ align:start position:0%
+kanji would look different it doesn't
+ 
+
+ align:start position:0%
+kanji would look different it doesn't
+there's just a face on top
+
+ align:start position:0%
+there's just a face on top
+ 
+
+ align:start position:0%
+there's just a face on top
+so i think that's very strong evidence
+
+ align:start position:0%
+so i think that's very strong evidence
+ 
+
+ align:start position:0%
+so i think that's very strong evidence
+that that region is not only causally
+
+ align:start position:0%
+that that region is not only causally
+ 
+
+ align:start position:0%
+that that region is not only causally
+involved in face perception
+
+ align:start position:0%
+involved in face perception
+ 
+
+ align:start position:0%
+involved in face perception
+but very specifically causally involved
+
+ align:start position:0%
+but very specifically causally involved
+ 
+
+ align:start position:0%
+but very specifically causally involved
+in face perception only anybody get that
+
+ align:start position:0%
+in face perception only anybody get that
+ 
+
+ align:start position:0%
+in face perception only anybody get that
+do i have to stop
+
+ align:start position:0%
+do i have to stop
+ 
+
+ align:start position:0%
+do i have to stop
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um okay i have another video consider
+
+ align:start position:0%
+um okay i have another video consider
+ 
+
+ align:start position:0%
+um okay i have another video consider
+and we'll get back to this later
+
+ align:start position:0%
+and we'll get back to this later
+ 
+
+ align:start position:0%
+and we'll get back to this later
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+other alternative hypotheses to this
+
+ align:start position:0%
+other alternative hypotheses to this
+ 
+
+ align:start position:0%
+other alternative hypotheses to this
+this is this is pretty powerful like
+
+ align:start position:0%
+this is this is pretty powerful like
+ 
+
+ align:start position:0%
+this is this is pretty powerful like
+this is more powerful than most of the
+
+ align:start position:0%
+this is more powerful than most of the
+ 
+
+ align:start position:0%
+this is more powerful than most of the
+other things i showed you but there's
+
+ align:start position:0%
+other things i showed you but there's
+ 
+
+ align:start position:0%
+other things i showed you but there's
+always ways to come up with alternative
+
+ align:start position:0%
+always ways to come up with alternative
+ 
+
+ align:start position:0%
+always ways to come up with alternative
+hypotheses and that's the business we're
+
+ align:start position:0%
+hypotheses and that's the business we're
+ 
+
+ align:start position:0%
+hypotheses and that's the business we're
+in here so be percolating on what other
+
+ align:start position:0%
+in here so be percolating on what other
+ 
+
+ align:start position:0%
+in here so be percolating on what other
+control conditions you'd want from this
+
+ align:start position:0%
+control conditions you'd want from this
+ 
+
+ align:start position:0%
+control conditions you'd want from this
+guy
+
+ align:start position:0%
+guy
+ 
+
+ align:start position:0%
+guy
+to really believe these data
\ No newline at end of file
diff --git a/YEZUywtDJQ4.txt b/YEZUywtDJQ4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..912d487692e707c8b8b3bc56d0d7084cd46bfcad
--- /dev/null
+++ b/YEZUywtDJQ4.txt
@@ -0,0 +1,608 @@
+In order to understand how procedures are
+implemented on the beta, we will take a look
+
+at a mystery function and its translation
+into beta assembly code.
+
+The mystery function is shown here:
+The function f takes an argument x as an input.
+
+It then performs a logical AND operation on
+the input x and the constant 5 to produce
+
+the variable a.
+After that, it checks if the input x is equal
+
+to 0, and if so returns the value 0, otherwise
+it returns an unknown value which we need
+
+to determine.
+We are provided with the translation of this
+
+C code into beta assembly as shown here.
+We take a closer look at the various parts
+
+of this code to understand how this function
+as well as procedures in general work on the
+
+beta.
+The code that calls the procedure is responsible
+
+for pushing any arguments onto the stack.
+This is shown in pink in the code and on the
+
+stack.
+If there are multiple arguments then they
+
+are pushed in reverse order so that the first
+argument is always in the same location relative
+
+to the BP, or base pointer, register which
+we will see in a moment.
+
+The BR instruction branches to label f after
+storing the return address, which is b, into
+
+the LP, or linkage pointer, register.
+In yellow, we see the entry sequence for the
+
+procedure.
+The structure of this entry sequence is identical
+
+for all procedures.
+The first thing it does is PUSH(LP) which
+
+pushes the LP register onto the stack immediately
+after the arguments that were pushed onto
+
+the stack by the caller.
+Next it pushes the BP onto the stack in order
+
+to save the most recent value of the BP register
+before updating it.
+
+Now, a MOVE(SP, BP) is performed.
+SP is the stack pointer which always points
+
+to the next empty location on the stack.
+At the time that this MOVE operation is executed,
+
+the SP, points to the location immediately
+following the saved BP.
+
+This move instruction makes the BP point to
+the same location that the SP is currently
+
+pointing to, which is the location that is
+immediately following the saved BP.
+
+Note, that once the BP register is set up,
+one can always find the first argument at
+
+location BP – 12 (or in other words, 3 words
+before the current BP register).
+
+If there was a second argument, it could be
+found in location BP – 16, and so on.
+
+Next, we allocate space on the stack for any
+local variables.
+
+This procedure allocates space for one local
+variable.
+
+Finally, we push all registers that are going
+to be modified by our procedure onto the stack.
+
+Doing this makes it possible to recover the
+registers' original values once the procedure
+
+completes execution.
+In this example, register R1 is saved onto
+
+the stack.
+Once the entry sequence is complete, the BP
+
+register still points to the location immediately
+following the saved BP.
+
+The SP, however, now points to the location
+immediately following the saved R1 register.
+
+So for this procedure, after executing the
+entry sequence, the stack has been modified
+
+as shown here.
+The procedure return, or exit, sequence for
+
+all beta procedures follows the same structure.
+It is assumed that the return value for the
+
+procedure has already been placed into register
+R0.
+
+Next, all registers that were used in the
+procedure body, are restored to their original
+
+values.
+This is followed by deallocating all of the
+
+local variables from the stack.
+We then restore the BP, followed by the LP
+
+register.
+Finally, we jump to LP which contains the
+
+return address of our procedure.
+In this case, LP contains the address b which
+
+is the address of the next instruction that
+should be executed following the execution
+
+of the f procedure.
+Taking a closer look at the details for our
+
+example, we see that we begin our exit sequence
+with POP(R1) in order to restore the original
+
+value of register R1.
+Note that this also frees up the location
+
+on the stack that was used to store the value
+of R1.
+
+Next, we get rid of the local variables we
+stored on the stack.
+
+This is achieved using the MOVE(BP, SP) instruction
+which makes the SP point to the same location
+
+as the BP thus specifying that all the locations
+following the updated SP are now considered
+
+unused.
+Next, we restore the BP register.
+
+Restoring the BP register is particularly
+important for nested procedure calls.
+
+If we did not restore the BP register, then
+upon return to the calling procedure, the
+
+calling procedure would no longer have a correct
+BP, so it would not be able to rely on the
+
+fact that it's first argument is located at
+location BP-12, for example.
+
+Finally, we restore the LP register and JMP
+to the location of the restored LP register.
+
+This is the return address, so by jumping
+to LP, we return from our procedure call and
+
+are now ready to execute the next instruction
+at label b.
+
+Now let's get back to our original procedure
+and its translation to beta assembly.
+
+We will now try to understand what this mystery
+function is actually doing by examining the
+
+remaining sections of our assembly code highlighted
+here.
+
+Let's zoom into the highlighted code.
+The LD instruction loads the first argument
+
+into register R0.
+Recall that the first argument can always
+
+be found at location BP – 12, or in other
+words, 3 words before the current BP register.
+
+This means that the value x is loaded into
+R0.
+
+Next we perform a binary AND operation between
+R0 and the constant 5, and store the result
+
+of that operation into register R1.
+Note that its okay to overwrite R1 because
+
+the entry sequence already saved a copy of
+the original R1 onto the stack.
+
+Also, note that overwriting R0 is considered
+fine because we ultimately expect the result
+
+to be returned in R0, so there is no expectation
+of maintaining the original value of R0.
+
+Looking back at the c code of our function,
+we see that the bitwise AND of x and 5 is
+
+stored into a local variable named a.
+In our entry sequence, we allocated 1 word
+
+on the stack for our local variables.
+That is where we want to store this intermediate
+
+result.
+The address of this location is equal to the
+
+contents of the BP register.
+Since the destination of a store operation
+
+is determined by adding the contents of the
+last register in the instruction to the constant,
+
+the destination of this store operation is
+the value of BP + 0.
+
+So as expected, variable a is stored at the
+location pointed to by the BP register.
+
+Now we check if x equals 0 and if so we want
+to return the value 0.
+
+This is achieved in beta assembly by checking
+if R0 is equal to 0 since R0 was loaded with
+
+the value of x by the LD operation.
+The BEQ operation checks whether or not this
+
+condition holds and if so, it branches to
+label bye which is our exit sequence.
+
+In that situation, we just saw that R0 = 0,
+so R0 already contains the correct return
+
+value and we are ready to execute our return
+sequence.
+
+If x is not equal to 0, then we perform the
+instructions after label xx.
+
+By figuring out what these instructions do,
+we can identify the value of our mystery function
+
+labeled ?????.
+We begin by decrementing R0 by 1.
+
+This means that R0 will be updated to hold
+x-1.
+
+We then push this value onto the stack and
+make a recursive call to procedure f.
+
+In other words, we call f again with a new
+argument which is equal to x-1.
+
+So far we know that our mystery function will
+contain the term f(x-1).
+
+We also see that LP gets updated with the
+new return address which is yy + 4.
+
+So just before our recursive call to f with
+the new argument x-1, our stack looks like
+
+this.
+After the procedure entry sequence is executed
+
+in the first recursive call, our stack looks
+like this.
+
+Note that this time the saved LP is yy + 4
+because that is our return address for the
+
+recursive procedure call.
+The previous BP points to where the BP was
+
+pointing to in the original call to f.
+Another term for this group of stack elements
+
+is the activation record.
+In this example, each activation record consists
+
+of 5 elements.
+These are the argument to f, the saved LP,
+
+the saved BP, the local variable, and the
+saved R1.
+
+Each time that f is called recursively another
+activation record will be added to the stack.
+
+When we finally return from all of these recursive
+calls, we are back to a stack that looks like
+
+this with a single activation record left
+on the stack plus the first argument with
+
+which the recursive call was made.
+The DEALLOCATE(1) instruction then removes
+
+this argument from the stack.
+So the SP is now pointing to the location
+
+where we previously pushed the argument x-1.
+R0 holds the return value from the recursive
+
+call to f which is the value of f(x-1).
+Now, we execute a LD into register R1 of the
+
+address that is the contents of register BP
++ 0.
+
+This value is a.
+We then ADD R1 to R0 to produce our final
+
+result in R0.
+R0 is now equal to a + f(x-1), so we have
+
+discovered that our mystery function is a
++ f(x-1).
+
+Before we continue with analyzing a stack
+trace from this problem, let's answer a few
+
+simpler questions.
+The first question is whether or not variable
+
+a, from the statement a = x & 5, is stored
+on the stack and if so where is it stored
+
+relative to the BP register.
+Earlier we saw that our assembly program allocates
+
+space for one local variable on the stack.
+It then stores R1, which holds the result
+
+of performing a binary ANDC between x and
+the constant 5, into the location pointed
+
+to by the BP register, as shown here.
+Next, we want to translate the instruction
+
+at label yy into its binary representation.
+The instruction at label yy is BR(f, LP).
+
+This instruction is actually a macro that
+translates to a BEQ(R31, f, LP).
+
+Note that because R31 always equals 0, this
+branch is always taken.
+
+The format of the binary representation for
+this instruction is a 6-bit opcode, followed
+
+by a 5 bit Rc identifier, followed by another
+5 bits which specify Ra, and then followed
+
+by a 16 bit literal.
+The opcode for BEQ is 011100.
+
+Rc = LP which is register R28.
+The 5-bit encoding of 28 is 11100.
+
+Ra is R31 whose encoding is 11111.
+Now, we need to determine the value of the
+
+literal in this instruction.
+The literal in a branch instruction stores
+
+the offset measured in words from the instruction
+immediately following the branch, to the destination
+
+address.
+Looking at our assembly code for this function,
+
+we see that we want to count the number of
+words from the DEALLOCATE(1) instruction back
+
+to label f.
+Recall that the PUSH and POP macros are actually
+
+each made of up two instructions so each of
+those counts as 2 words.
+
+Counting back, and accounting for the two
+instructions per push and pop, we see that
+
+we have to go back 16 instructions, so our
+literal is -16 expressed as a 16 bit binary
+
+number.
+Positive 16 is 0000 0000 0001 0000, so -16
+
+is 1111 1111 1111 0000.
+Now, suppose that the function f is called
+
+from an external main program, and the machine
+is halted when a recursive call to f is about
+
+to execute the BEQ instruction tagged xx.
+The BP register of the halted machine contains
+
+0x174, and the hex contents of a region of
+memory are shown here.
+
+The values on the left of the stack are the
+addresses of each location on the stack.
+
+We first want to determine the current value
+of the SP, or stack pointer, register.
+
+We were told that the machine is halted when
+a recursive call to f is about to execute
+
+the BEQ instruction tagged xx.
+And that the BP register was 0x174 at that
+
+point.
+We see that after the BP was updated to be
+
+equal to the SP in the MOVE operation, two
+additional entries were made on the stack.
+
+The first was an ALLOCATE instruction which
+allocated space for one local variable, thus
+
+making the SP point to location 0x178, and
+then PUSH(R1), which saves a copy of R1 on
+
+the stack, thus moving the SP register one
+further location down to 0x17C.
+
+We now want to answer some questions about
+the stack trace itself to help us better understand
+
+its structure.
+We first want to determine the value of local
+
+variable a in the current stack frame.
+We know that a is stored at location BP +
+
+0.
+So a is the variable stored at address 0x174,
+
+and that value is 5.
+From here, we can label all the entries in
+
+the stack trace as follows.
+We saw earlier, that each activation record
+
+consists of 5 words, the argument x followed
+by the saved LP, the saved BP, the local variable,
+
+and the saved register R1.
+We can apply this structure to label our stack
+
+trace.
+Now that our stack trace is fully labeled
+
+we can take a closer look at the details of
+implementing procedures on the beta.
+
+We begin by looking at the multiple LP values
+that were stored on the stack.
+
+Note that the first one at address 0x144 has
+a value of 0x5C whereas the following two
+
+have a value of 0xA4.
+This occurs because the LP value stored at
+
+address 0x144 is the return address from the
+main procedure that originally called procedure
+
+f, whereas the following two LP values are
+the return addresses from recursive calls
+
+to f made from within the f function itself.
+Using this information you can now answer
+
+the question: What is the address of the BR
+instruction that made the original call to
+
+f from the external main program?
+Recall that the value stored in the LP register
+
+is actually the return address which is the
+address of the instruction immediately following
+
+the branch instruction.
+So if the original LP value was 0x5C, that
+
+means that the address of the branch instruction
+was 0x58.
+
+We can also answer the question, what is the
+value of the PC when the program is halted.
+
+We know that the program was halted just before
+executing the instruction at label xx.
+
+We also know, that the instruction at label
+yy makes a recursive call to f.
+
+We know that the LP value from the recursive
+calls is 0xA4.
+
+This means that the address of the DEALLOCATE(1)
+instruction is 0xA4.
+
+Counting backwards by 4 bytes, and accounting
+for the fact that a PUSH operation consists
+
+of two instructions, we see that label xx
+= 0x90 and that is the value of the PC when
+
+the program is halted.
+As our last question, we want to consider
+
+the following: Suppose that you are told that
+you could delete 4 instructions from your
+
+program without affecting the behavior of
+the program.
+
+The 4 instructions to be removed are a LD,
+a ST, an ALLOCATE, and a MOVE instruction.
+
+Removing these instructions would make our
+program shorter and faster.
+
+So, our goal is to determine whether or not
+this is possible without affecting the behavior
+
+of the program.
+Let's first consider removing the ALLOCATE
+
+instruction.
+If this instruction is removed, that means
+
+that we will not be saving space on the stack
+for local variable a.
+
+However, if we take a closer look at the 3
+lines of code highlighted in yellow, we see
+
+that the actual value of a is first computed
+in R1 before storing it in local variable
+
+a.
+Since R1 is going to be saved on the stack
+
+during each recursive call, we could get away
+without saving a on the stack because we can
+
+find its value in the stored R1 of the next
+activation record as shown in the highlighted
+
+pairs of a and R1 on the stack.
+This means that we could safely remove the
+
+ALLOCATE instruction.
+As a result, this also means that we don't
+
+need the ST operation that stores a on the
+stack or the LD operation that reloads a into
+
+register R1.
+Finally, because there are no longer any local
+
+variables stored on the stack, then the instruction
+MOVE(BP,SP) which is normally used to deallocate
+
+all local variables, can be skipped because
+after popping R1, the BP and SP registers
+
+will already point to the same location.
+So, in conclusion the 4 operations can be
+
+removed from the program without changing
+the behavior of the code.
\ No newline at end of file
diff --git a/YPAbQU7NUZQ.txt b/YPAbQU7NUZQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c61a265be41113333c9ce3925fb5cb211cf56d67
--- /dev/null
+++ b/YPAbQU7NUZQ.txt
@@ -0,0 +1,3851 @@
+PROFESSOR: Chapter six, problem
+set three, problem set
+
+two solutions.
+
+OK.
+
+Good morning.
+
+Nice to see you all again
+on this mild day.
+
+I want to start off by thanking
+Ashish greatly for
+
+giving the last three
+lectures.
+
+I have very high confidence in
+Ashish, and I'm sure he give
+
+you excellent lectures and was
+able to answer all your
+
+questions, right?
+
+But if you feel dissatisfied at
+any point, you'll have an
+
+opportunity to ask the
+question again today.
+
+We will continue now
+in chapter six.
+
+I understand Ashish got up to
+section six point one already,
+
+so that makes my life
+a little easier.
+
+And we'll just continue to plow
+ahead through the notes.
+
+You have as handouts today
+chapter six, the outgoing
+
+problem set, the solutions to
+the incoming problem set.
+
+So does anyone have any comments
+or questions or
+
+suggestions as we go forward
+at this point?
+
+Let's say I'll do a very quick
+review of everything so far,
+
+at least what we need to
+proceed, so you'll have a
+
+chance to ask questions along
+there if you like.
+
+Anyone have anything to say?
+
+Anyone want to say
+thanks to Ashish?
+
+All right.
+
+Great.
+
+OK.
+
+So a very quick review.
+
+We first said we were going to
+work with a continuous time
+
+Additive White Gaussian noise
+channel, but we quickly
+
+reduced it to a discrete
+time additive white
+
+Gaussian noise model.
+
+Vector model, Y equals X plus N,
+where the vectors may go on
+
+as long as you like.
+
+And implicit in here is we
+have some kind of power
+
+limitation expressed
+by various --
+
+I know I've probably introduced
+too many parameters
+
+in the early part
+of the course.
+
+But you'll see them all in the
+literature, and I thought you
+
+might as well see the relation
+between them all at once.
+
+The noise.
+
+The main thing about this
+is it's an independent,
+
+identically distributed noise,
+also independent of X, and
+
+it's characterized simply by
+its variance per symbol, or
+
+average power.
+
+Again, there are various
+notations that we
+
+can use for its power.
+
+OK.
+
+However you express the power
+of the signal of the noise,
+
+you're going to get some
+signal-to-noise ratio out of
+
+that, as long as you use
+consistent the same units for
+
+signal and noise.
+
+And so the key parameters
+of this channel turn
+
+out to be just two.
+
+One is the signal-to-noise
+ratio.
+
+And the other is something which
+in the discrete time
+
+domain we might think of as a
+data rate, rho, the number of
+
+bits per two dimensions.
+
+But we were at pains
+to show --
+
+and the reason we measure it in
+bits per two dimensions is
+
+that it converts directly to the
+spectral efficiency, or we
+
+sometimes say, the nominal
+spectral efficiency, or the
+
+Nyquist spectral efficiency.
+
+Basically, this is the spectral
+efficiency if you
+
+assume that you only use the
+nominal Nyquist bandwidth.
+
+And both in 450 and here it was
+shown that you can really
+
+get as close to the nominal
+bandwidth as you like, its
+
+sharp or roll off as you
+like, by using filters.
+
+Very sharp filters or very sharp
+digital filters that
+
+today we can really
+realistically get effectively
+
+to the Nyquist bandwidth.
+
+So this is a good measure of
+nominal spectral efficiency,
+
+which is an extremely important
+parameter, the
+
+spectral efficiency in
+continuous time.
+
+And then the Shannon limit is
+expressed in this very simple
+
+form that we can never do better
+in data rate or nominal
+
+spectral efficiency than
+log of 1 plus SNR.
+
+And the units are bits
+per two dimensions.
+
+So there's an awful lot about
+parameters and units in the
+
+first part of the course, and
+sometimes it's a little
+
+overwhelming and confusing.
+
+But in my experience in
+engineering is, it's extremely
+
+important to get the
+units right.
+
+It helps you in thinking
+clearly.
+
+It helps you to focus
+on the right things.
+
+And so in the first couple of
+chapters, there's a lot of
+
+emphasis on getting
+the units right.
+
+For instance, bits per
+two dimensions.
+
+I could simply assert to you
+that things are always to come
+
+out better if you do things
+per two dimensions.
+
+This basically has to do with
+Gaussian distributions being
+
+simpler in two dimensions than
+they are in one dimension.
+
+So you know you can get closed
+form integrals in two and four
+
+and so forth dimensions that you
+can't get in one and three
+
+and so forth dimensions.
+
+So you know, the geometrical
+formulas for the volume of the
+
+sphere and so forth are much
+simpler in even dimensions
+
+than they are in
+odd dimensions.
+
+This all, I think, has to do
+with the fact that really a
+
+one-dimensional complex Gaussian
+variable, or in
+
+general, complex Gaussian
+variables, are in some sense
+
+mathematically simpler than
+real Gaussian variables.
+
+For instance, the Q function
+is a very ugly thing.
+
+In two dimensions, you can
+closed-form integrals with
+
+probability of error.
+
+So there's a lot of clues that
+we really want to think in
+
+terms of pairs of
+real dimensions.
+
+All right.
+
+And then we introduced a
+couple more parameters.
+
+And I understand Ashish
+got the questions
+
+that I get every year.
+
+Why do we introduce both
+of these things?
+
+SNR norm, which is SNR
+normalized by 2 to the rho
+
+minus 1, that's motivated
+directly by the
+
+Shannon limit formula.
+
+Or Eb over N_0, which is
+SNR divided by rho.
+
+You know, these are
+both more or less
+
+equivalent to each other.
+
+From this Eb over N_0 is just 2
+to the rho minus 1 over rho
+
+times SNR norm, so why do we
+introduce both of them?
+
+And there's not an
+intellectually very strong
+
+argument to introduce
+both of them.
+
+Because one is easily translated
+into the other.
+
+For fixed nominal spectral
+efficiency rho, there clearly
+
+is just a one-to-one
+translation.
+
+We could use either one.
+
+If you graph something versus
+Eb over N_0 or versus SNR
+
+norm, it's just a matter of
+shifting it by this factor.
+
+They're going to be exactly the
+same graph with the 0 dB
+
+point in a different place,
+according to where 0 dB is.
+
+Philosophically, of course, SNR
+norm, which is sometimes
+
+called the gap to capacity, is
+exactly a measure of how many
+
+dBs away are we from
+the Shannon limit.
+
+Measuring things on
+a log scale in dB.
+
+And so 0 dB is always the
+Shannon limit point with SNR
+
+norm, because this statement
+translates into SNR norm is
+
+greater than 1, which is 0 dB.
+
+So here the focus is always, how
+far are you from capacity?
+
+How far are you from
+the Shannon limit?
+
+And that really is
+the modern view.
+
+In the early days of coding, the
+view was, well, how much
+
+coding gain can we get
+over no coding?
+
+And as we'll see, Eb over N_0
+is often a very convenient
+
+parameter to use when we're
+focusing on coding gain.
+
+In fact, for binary linear block
+codes, which is what
+
+we're talking about in chapter
+six, we get an extremely
+
+simple expression that Eb over
+N_0 it's just kd over N, where
+
+N, k, d are the basic parameters
+of a block code.
+
+If you don't know those
+yet, you will by
+
+the end of this lecture.
+
+And Eb over N_0 is what was put
+forward in the early days,
+
+when the principal coding
+application was coding for
+
+deep space communications.
+
+It makes sense in the
+power-limited regime.
+
+In the power-limited regime,
+we showed that this
+
+essentially goes -- this is rho
+log2 over rho, so up to a
+
+factor of natural logarithm of
+two, these are the same,
+
+almost independent of the
+spectral efficiency, as well.
+
+And so this is a very natural
+thing to use, especially in
+
+the power-limited regime.
+
+In the bandwidth-limited regime,
+as rho gets large,
+
+then these things become
+very different.
+
+SNR norm always keeps us in
+the neighborhood of 0 dB.
+
+This thing goes up to 10 dB,
+20 dB, 30 dB, and so forth.
+
+Nonetheless, you'll see in
+some literature, people
+
+continue to measure against Eb
+over N_0 maybe I would say,
+
+just because they don't
+know any better.
+
+Anyway, since I started writing
+these notes about
+
+eight or nine years ago, I've
+been advocating SNR norm.
+
+It's more and more widely
+used in our business,
+
+in the coding business.
+
+Or equivalently, one always
+shows nowadays how far are you
+
+from capacity, and that's
+what SNR norm is about.
+
+And you can always translate
+this into this and this into
+
+this by this simple formula.
+
+So that's why we introduce
+them both.
+
+Eb over N_0 is traditional.
+
+SNR norm is more of the modern
+gap to capacity viewpoint.
+
+Any questions about that?
+
+Because I understood that
+Ashish got a number of
+
+questions about that.
+
+Yes?
+
+AUDIENCE: And the probability
+of error you mentioned
+
+[UNINTELLIGIBLE] is natural
+with SNR model.
+
+PROFESSOR: Well, this
+is a slightly
+
+different point, actually.
+
+So we go on from this to talk
+about the power-limited
+
+regime, which we defined more
+or less arbitrarily as the
+
+regime where rho is less than
+or equal to two bits per two
+
+dimensions, and the
+bandwidth-limited regime,
+
+which is where rho is larger.
+
+And at this point, I simply
+assert that it's better to do
+
+everything per two dimensions
+in the bandwidth-limited
+
+regime and to do everything
+per bit in the
+
+power-limited regime.
+
+And the reason for this is
+basically long practice and
+
+intuition and experience that
+things do work out better, and
+
+this is the proper
+normalization.
+
+But I think at this point
+in the course, with your
+
+background, this is only an
+assertion, all right?
+
+So I simply say, this is the way
+we're going to do things
+
+in bandwidth-limited
+and power-limited.
+
+For most of the rest of the
+course, we're going to be in
+
+the power-limited regime.
+
+Then we'll come back to the
+bandwidth-limited very late in
+
+the course.
+
+So you can now forget this
+assertion for a while.
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Well, I'm trying
+to focus on that here.
+
+That if two systems have
+different rhos, then you
+
+should take that into account
+in their comparison.
+
+And when you see charts of a
+rate 7/8 system, or a rho 7/4
+
+system versus one that's rate
+1/8, those are very different
+
+regimes, and it probably isn't
+fair to compare two systems,
+
+just in terms of their
+probability of error versus Eb
+
+over N_0 at two different
+spectral efficiencies.
+
+What is more fair is to compare
+them in terms of their
+
+gap to capacity.
+
+You can get more powerful
+codes with more
+
+error-correcting capability the
+lower in rate that you go.
+
+And so you should start from
+the point of view that two
+
+systems with different rho are
+incomparable, and then using
+
+this you can say, but, you know,
+if we can get within 1
+
+dB of the Shannon limit with
+both of them, then they're
+
+both approximately
+equally powerful.
+
+That would be the modern
+point of view.
+
+But it's really apples and
+oranges if they have different
+
+rates, different rhos.
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]
+
+If [UNINTELLIGIBLE]
+
+systems modulation
+[INAUDIBLE].
+
+Then is it fair --
+
+because if one of them
+has coding --
+
+PROFESSOR: If none of them
+have coding, well --
+
+AUDIENCE: No, just modulation.
+
+PROFESSOR: So what shall
+I say to that.
+
+In the power-limited regime,
+an uncoded system is simply
+
+binary modulation or 4-QAM,
+and there aren't different
+
+systems to compare, really.
+
+There's only one baseline
+system.
+
+As you go up into the
+bandwidth-limited regime, then
+
+it is fair to compare
+systems of the same
+
+class, like M by M QAM.
+
+That's a simple uncoded
+system.
+
+Now there, rho keeps changing.
+
+rho equals 2, rho equals 4, rho
+equals 6, rho equals 8.
+
+Or you can easily find
+intermediate
+
+rates that are uncoded.
+
+And there you find that this
+normalization makes all these
+
+systems comparable.
+
+In fact, we saw that we got a
+universal baseline curve for
+
+the bandwidth-limited regime,
+which was independent of rho,
+
+for, say, the class of 4 by
+4, by the class of M by M
+
+bandwidth-limited QAM systems.
+
+I'm sorry.
+
+I got off a plane at nine
+o'clock last night, so I may
+
+not be totally coherent today.
+
+But all of these systems have
+exactly the same baseline
+
+curve up to the approximations
+we've made that their exactly
+
+four nearest neighbors
+and so forth.
+
+But on a curve of probability
+of error per two dimensions,
+
+per QAM symbol, versus
+SNR norm, we
+
+get a universal curve.
+
+So that indicates they really
+are comparable.
+
+They form a class where the
+performance of the class is
+
+independent of rho.
+
+And that's sort of typical of
+the bandwidth-limited regime.
+
+Two systems that differ, that
+basically use the same code
+
+with smaller constellation
+or a larger-based uncoded
+
+constellation are going to be
+directly comparable, and are
+
+probably going to have the
+same gap to capacity.
+
+Going to be just as far away
+from the Shannon limit.
+
+But we don't have that
+phenomenon in the
+
+power-limited case.
+
+Other questions, or
+shall I proceed?
+
+OK.
+
+Again continuing what I hope
+will be a quick review, but I
+
+don't want to go any faster than
+you're comfortable with.
+
+We get this baseline curve
+for 2-PAM or 2
+
+by 2 QAM, same thing.
+
+So this is the baseline of Pb of
+E on a log scale, where we
+
+typically go down to ten to
+the minus six, ten to the
+
+minus five.
+
+Here's 0 dB.
+
+This goes down through
+about 9.6 dB here or
+
+about 10.5 dB here.
+
+And the ultimate Shannon
+limit is over here.
+
+The ultimate Shannon limit for
+very low rho, as rho goes to
+
+0, is about minus 1.6 dB.
+
+And we get expressions.
+
+0 dB is the Shannon limit
+at rho equals 1.
+
+At rho equals 2, it's
+up about 1.8 dB.
+
+Shannon limit for rho equals
+2, and so forth.
+
+And anyway, so we see as a
+function of rho, we can
+
+measure the gap to capacity at
+different probabilities of
+
+error and see how much
+coding gain is,
+
+in principle, possible.
+
+And then for a coded system,
+we can put that on here.
+
+The effective coding gain
+is the distance
+
+between here and here.
+
+At some target probability
+of error.
+
+It's going to differ according
+to probably of error.
+
+You found a way of getting a
+good, rough-cut estimate, at
+
+least for not very complicated
+codes called the union bound
+
+estimate for any signal
+constellation in any number of
+
+dimensions.
+
+So if we have a signal
+constellation A, which
+
+consists of M points in N
+dimensions, so forth,
+
+basically found that we could,
+in the power-limited regime,
+
+get an approximate expression
+from considering pairwise
+
+error probabilities that's
+very simple.
+
+And I used this notation.
+
+Q of the square root of some
+coding gain of the
+
+constellation times
+2 Eb over N_0.
+
+If it's just 2-PAM then the
+coding gain becomes 1.
+
+This is the average number
+of nearest neighbors per
+
+transmitted bit.
+
+And so the whole thing reduces
+to this expression in terms of
+
+couple of parameters.
+
+the principal parameter is the
+nominal coding gain, which is
+
+the minimum squared distance of
+A over 4 times the energy
+
+per bit of this constellation
+A. So we really only need to
+
+know this kind of normalized
+measure of goodness of the
+
+constellation.
+
+And K_b of A Is the average
+number of nearest neighbors.
+
+I forget what we call it.
+
+What is the numerator here?
+
+K_min of A, which itself is an
+average, over the number of
+
+bits that we're actually
+sending, which is log2 of the
+
+size of A.
+
+So basically we only need to
+know a couple of parameters of
+
+this signal constellation.
+
+Its minimum square distance
+is very important.
+
+Energy parameter, which we
+choose to make the energy per
+
+bit, or so that we get
+this expression.
+
+And the average number of
+nearest neighbors per bit that
+
+we transmit.
+
+OK.
+
+And our best example so far is
+the tetrahedral constellation,
+
+where we basically
+pick every other
+
+point from the 4 simplex.
+
+Maybe I should do that
+in a different color.
+
+I don't think that's
+a different color.
+
+Nope.
+
+Anyway.
+
+You know this quite
+well by now.
+
+And if we do that, we find that
+normalizing everything,
+
+this is 4/3 or 1.25 dB.
+
+And every point has three
+nearest neighbors, and we're
+
+sending 2 bits, so
+this is 3/2.
+
+So then we get this handy dandy
+engineering rule to make
+
+a quick plot of the union
+bound estimate.
+
+Given that we decided to put
+this on a log-log scale to
+
+start with, all we have to do
+to plot this expression --
+
+if we're given, as we always
+are, the baseline curve, which
+
+is simply Q to the square
+root of 2 Eb over N_0.
+
+How do you convert this
+curve to this curve
+
+on a log-log plot?
+
+Well, you simply move it to the
+left by the coding gain.
+
+And you move it up by the
+log of whatever K_b is.
+
+So if the dominant effect is
+moving it left, in this case,
+
+by 1.25 dB --
+
+I'm going to wind up getting
+about this curve, so I won't
+
+draw it again --
+
+then we move it up by a factor
+of 3/2, we developed a rule of
+
+thumb that said a factor of two
+is basically going to cost
+
+you about 0.2 dB.
+
+Around ten to the minus five.
+
+This is just based on the slope
+of this baseline curve,
+
+as long as we're somewhat
+in that region.
+
+So this will cost us about 1/10
+of a dB, so we'll get an
+
+effective coding gain
+of about 1.15 dB.
+
+So graphically, we take
+this curve bodily.
+
+We move it over 1.25 dB,
+and we move it up
+
+by a factor of 3/2.
+
+And what we'll find is the
+effective coding gain is
+
+thereby reduced to, I estimate,
+about 1.15 dB.
+
+And this is all just engineering
+rules of thumb.
+
+Nice template.
+
+I sometimes say you should
+fill out a copy of this
+
+baseline curve, cut it out, put
+it in your wallet for the
+
+duration of this course,
+because you'll have the
+
+opportunity to make
+this kind of
+
+calculation again and again.
+
+All right.
+
+So that's union bound SNR.
+
+For simple constellations,
+the union bound
+
+estimate is very accurate.
+
+So this is a very good way to
+proceed, from an engineering
+
+point of view.
+
+We want to write a paper?
+
+You know, it's a little late
+to write a paper on the
+
+performance of the four simplex
+signal constellations,
+
+but if you wanted to, and you
+wanted to have one graph in
+
+that paper, you would
+have the graph of --
+
+well, you would actually
+probably compute the exact
+
+error of probability, either by
+analysis or by Monte Carlo
+
+simulation, you would
+put that in there.
+
+But in your first draft of the
+paper, you would put in union
+
+bound estimate and you would
+find that wasn't far off.
+
+OK.
+
+Any questions on that?
+
+This has basically got
+us up to chapter six.
+
+So in chapter six now, which
+Ashish got into last time.
+
+This is basically about binary
+linear block codes.
+
+And well, we first just
+start talking about
+
+binary block codes.
+
+That's what Ashish
+did last time.
+
+We basically take 0 and 1
+as our binary alphabet.
+
+We take a blocks of length n.
+
+Sorry.
+
+Are we using little
+n or big N?
+
+Little n, where n is called
+the block plank.
+
+So we take the set of all binary
+symbols of length n,
+
+and we're going to convert
+this to real n space.
+
+How do we convert it?
+
+Component-wise, by the
+standard 2-PAM map.
+
+We map 0 into plus alpha,
+1 into minus alpha.
+
+So this maps into plus or
+minus alpha to the n.
+
+So the entire universe of
+possible code words that we
+
+have is this set of 2 to the
+n real n-tuples, which are
+
+simply the vertices of an
+n cube of size 2 alpha,
+
+obviously, right?
+
+Just like this.
+
+We have eight possible
+vertices in 3-space.
+
+They obviously all have
+the same power.
+
+They all lie on the surface of
+a sphere of squared radius n
+
+alpha squared.
+
+So they're not only the vertices
+of a cube, they're
+
+vertices that are spread on
+an equal energy sphere.
+
+And the whole idea is that our
+code is going to be some
+
+subset of this, and the code
+will map under the same map,
+
+which we call S, into
+some subset of the
+
+vertices of the n-cube.
+
+OK?
+
+And again, our favorite example
+is the tetrahedron.
+
+For instance, if we take the
+code as being 0, 0, 0, 0, 1,
+
+1, 1, 0, 1 1, 1, 0, those for
+binary three-tuples, this maps
+
+into T, the tetrahedron.
+
+OK?
+
+Well, we get this signal
+structure, which we've already
+
+found the coding gain.
+
+It has a little bit
+of coding gain.
+
+We actually accomplished
+something.
+
+All right.
+
+So that's the basic idea that
+we go through in 6.1.
+
+That's our favorite example.
+
+And Ashish also shows you that,
+you know, you might
+
+think this is an awfully
+restricted way of designing
+
+constellations.
+
+But when we're talking about low
+spectral efficiencies, by
+
+going through the capacity
+calculation, we can assure
+
+ourselves that in principle,
+this is not going to be very
+
+sub-optimal for it.
+
+Capacity is about the regime
+where n gets very large for
+
+very long block codes.
+
+We don't lose much in potential
+coding gain, or in
+
+the Shannon limit, equivalently,
+by restricting
+
+the input output input alphabet
+to be just these two
+
+numbers, plus or minus alpha,
+I should say, rather than
+
+using the whole real line as
+an input, as long as the
+
+nominal spectral efficiency is
+less than or equal to one bit
+
+per two dimensions.
+
+And the exact numbers --
+
+at rho equals 1, you lose about
+0.2 dB, in principle,
+
+using the Shannon limit
+as your guide.
+
+And for lower rho, it
+just goes to 0.
+
+And you did this last time.
+
+OK.
+
+So it's a very reasonable, and
+obviously attractive from an
+
+implementation point of view,
+way of designing signal
+
+constellations.
+
+And again, this is basically all
+we're going to be talking
+
+about for the majority of
+the course, is signal
+
+constellations like this.
+
+But of course as we get to codes
+that are thousands of
+
+bits long, or perhaps even
+infinitely long, as in the
+
+case of convolutional codes and
+trellis codes, sometimes
+
+you forget that we're really
+talking about just putting
+
+points in Euclidian
+signal space.
+
+Because we're going to be very
+abstracted back into the
+
+binary domain.
+
+But in this course, we're always
+thinking of codes as
+
+means of designing signal
+constellations.
+
+Of course, codes are used far
+more widely than just for
+
+signaling over the additive
+white Gaussian noise channel.
+
+I've sort of packaged this
+course as a search to get to
+
+capacity, we have added
+the additive white
+
+Gaussian noise channel.
+
+First of all because
+this corresponds
+
+very closely to history.
+
+Within this package, we can
+talk about all of the
+
+principal classes of codes that
+have been developed to
+
+date, and we can compare them
+in some performance terms.
+
+How close do they get to
+capacity on the additive white
+
+Gaussian noise channel.
+
+So you get most of what you
+would get if you took a
+
+communications-free view
+of coding theory.
+
+You know, people are interested
+in codes for
+
+computer memories, for
+God knows what,
+
+lots of other things.
+
+And for many of these other
+applications, you are going to
+
+be interested in the same
+class of codes.
+
+Basically, you're going to want
+to maximize the distance
+
+between code words for a given
+rate, which has to do with the
+
+size of the code.
+
+And so you're going to be
+interested in the same codes.
+
+Putting it in the framework of
+getting to capacity on the
+
+additive white Gaussian noise
+channel gives a motivation,
+
+gives a very nice story, because
+over 50 years, we were
+
+able to get to capacity,
+and gives it a real
+
+communications flavor.
+
+Some of you, I'm sure, are here
+without any interest in
+
+communications whatsoever.
+
+You simply want to know
+about coding.
+
+You will still get that story,
+but you'll get it
+
+in this nice package.
+
+That's why I do it this way.
+
+OK.
+
+I'm about to get
+into new stuff.
+
+End of review.
+
+Any questions?
+
+So you must have done
+a great job.
+
+Everyone understands
+perfectly.
+
+All right.
+
+So now let's talk about,
+as I said, binary
+
+linear block codes.
+
+When you see the word "linear,"
+that's a signal that
+
+there's some algebra ahead.
+
+And so this is the very first
+point at which we get into
+
+what's called algebraic
+coding theory.
+
+The algebra will be extremely
+simple at this
+
+point, not to worry.
+
+And what are we doing here?
+
+First thing we do is to identify
+0 and 1 with the
+
+binary field, which I'm always
+going to write as F2.
+
+The older way of writing this
+is GF(2), for Galois field
+
+with two elements.
+
+They mean exactly
+the same thing.
+
+Nowadays most people
+write just F2.
+
+Now we have [UNINTELLIGIBLE],
+we can write this blackboard
+
+F.
+
+And OK.
+
+Step one.
+
+We've identified our alphabet
+with a field.
+
+So algebraically,
+this is a field.
+
+Some of you know exactly
+what I mean by that.
+
+Others don't.
+
+We'll come back to this again.
+
+Informally, I would say a field
+is simply something
+
+where you can add, subtract,
+multiply, or divide.
+
+Our best examples of that before
+now have been the real
+
+and complex fields.
+
+There is a more formal
+definition of that.
+
+In this case, we have
+only two elements.
+
+So let me just write down the
+tables, which you all know,
+
+regardless of your background.
+
+What's the addition table
+for this field?
+
+Well, 0 is the additive
+identity.
+
+So we know that 0 added to
+anything gives itself, so that
+
+gives us three of the entries
+of this table.
+
+What do we put down here?
+
+There's really only one choice
+to satisfy one of the axioms
+
+of the field, which is that
+under addition, the field must
+
+form a group.
+
+In particular, that means that
+all elements are invertible.
+
+That means that each row or
+column has to be a permutation
+
+of the group elements.
+
+And so the only possibility
+here is to put in a 0.
+
+And well, we are forced, if
+we're going to make 0 and 1
+
+into a field to find an addition
+table which is the
+
+table of mod2 addition.
+
+You've had this stated
+as an axiom before.
+
+You can derive it just from the
+fact that 0 needs to be
+
+the additive identity, and then
+we need to put a 0 in
+
+here in order to get
+invertibility.
+
+Under multiplication.
+
+What is the multiplication
+table?
+
+Well, the additive identity
+is also a nullifier under
+
+multiplication in any field.
+
+So 0 times anything
+is equal to 0.
+
+1 times anything is
+equal to itself.
+
+So that completely determines
+the multiplication table.
+
+Again, just the table of
+mod2 multiplication.
+
+So if I'd done this
+axiomatically, I would have
+
+given you the axioms of field.
+
+Then I would show that under
+this binary addition
+
+operation, this multiplication
+operation,
+
+we satisfy the axioms.
+
+I'll do that as we get
+into chapter seven.
+
+OK.
+
+So now we have 0 1 to the n,
+n-tuples, binary n-tuples, we
+
+will now regard as n-tuples
+of field elements, F2.
+
+And these will be regarded as
+vectors in a vector space.
+
+Well, I'll just say that F2 to
+the n is a vector space, which
+
+clearly has 2 to
+the n elements.
+
+Now again, informally.
+
+What's a vector space?
+
+A vector space is always
+over a given field.
+
+In this case, it's going
+to be over the
+
+binary field, of course.
+
+F2.
+
+The given field is
+called a scalar.
+
+Just like vector space over
+the reals, the scalars are
+
+real numbers.
+
+Here the scalars are
+elements of F2.
+
+And what do we have to have to
+make something algebraically a
+
+vector space?
+
+We have to have that the
+addition of two vectors is
+
+well-defined and gives another
+vector, and that the
+
+multiplication of a vector by
+a scalar is well-defined and
+
+gives another vector in
+our vector space.
+
+All right?
+
+OK.
+
+So how are we going to define
+that to addition?
+
+If we want to add
+two n-tuples --
+
+again, you aren't going to see
+anything here that you haven't
+
+already seen in some
+other context.
+
+What do we do?
+
+We add them component-wise,
+using the component-wise rules
+
+of field addition.
+
+OK.
+
+So we just add two
+vector n-tuples,
+
+component by component.
+
+We obviously get some result,
+which is itself a binary
+
+vector or an F2 vector.
+
+No problem there.
+
+Except that --
+
+well, all right.
+
+As long as we're talking about
+all possible n-tuples, the
+
+result is certainly in the
+vector space, right?
+
+We add two binary n-tuples,
+we get a binary n-tuple.
+
+So the result is
+in F2 to the n.
+
+This is going to be the key test
+when we get to subspaces
+
+of F2 to the n.
+
+OK.
+
+And multiplication
+is even easier.
+
+How do we define multiplication
+by scalars?
+
+Well, we only have
+two scalars --
+
+0 and 1.
+
+So 0 times any vector is going
+to equal the all 0 vector.
+
+Again, you can view that
+as just component-wise
+
+multiplication of everything
+by 0, and since 0 times
+
+anything equals 0, we're
+always going
+
+to get the 0 vector.
+
+All right?
+
+So is the 0 vector in
+the vector space?
+
+Well, yes.
+
+If we're talking about several
+n-tuples, it of
+
+course always is.
+
+And one times anything, again,
+we can just do this
+
+component-wise, and it
+just gives itself.
+
+Trivially.
+
+So since this was a vector in
+the vector space, this is
+
+certainly a vector in
+the vector space.
+
+OK.
+
+This seems pretty
+trivial so far.
+
+But what's a binary
+linear block code?
+
+Again, focusing on the
+linear, is a --
+
+now I'll give a formal
+definition.
+
+it's a subspace of F2
+to the n for some n
+
+called the block length.
+
+All right.
+
+What do I mean when
+I say a subspace?
+
+I mean subsets of the elements
+of a vector space that itself
+
+forms a vector space.
+
+So in this case when I
+say subset, I mean a
+
+set of binary n-tuples.
+
+OK?
+
+That itself forms
+a vector space.
+
+OK.
+
+What are the components
+of that?
+
+To check that it forms a vector
+space, let's see.
+
+Multiplication by scalars is,
+again, easy to check.
+
+If it's going to be a subspace,
+then the all 0 --
+
+so it has to contain the all 0
+vector in order that when I
+
+multiply by the scalar
+0, I get another
+
+element of this subspace.
+
+Multiplication by 1 is always
+trivially satisfied.
+
+If I start off with a set, I
+multiply by 1, I'm going to
+
+get the same set.
+
+So let's check whether the
+elements of a subspace are
+
+closed under vector addition.
+
+What do I mean by that?
+
+I mean if you add two elements
+of the of the subspace
+
+together, you get another
+element of the subspace.
+
+That's the key property
+to check.
+
+Key property -- we can
+write that as closure
+
+under vector addition.
+
+Which is also called
+the group property.
+
+It means that just under
+addition, under vector
+
+addition, the set of elements
+that you have forms a group.
+
+You add any two elements,
+you get another
+
+element of the subset.
+
+The example is our favorite
+example so far.
+
+Let's take this little code,
+and I'm going to ask.
+
+Is that a subspace of
+F2 to the three?
+
+So does this equal subspace
+of the set of all binary
+
+three-tuples?
+
+Anyone care to hazard a guess
+whether it is or isn't?
+
+AUDIENCE: It is.
+
+PROFESSOR: It is?
+
+Why?
+
+AUDIENCE: It has the
+all 0 vector.
+
+PROFESSOR: It has the all
+0 vector, first of all.
+
+Good.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: And it's closed
+under addition.
+
+Now how might we see that?
+
+You could, of course, just
+take all pair-wise --
+
+you could form the addition
+table of these four elements,
+
+and you would find that you
+always get another one of
+
+these elements.
+
+For instance, 0, 1, 1 plus 1,
+0, 1, is equal to 1, 1, 0.
+
+In fact, you easily see that you
+take any two of these, add
+
+them together, you get
+the third one.
+
+If you call this a, b, and c,
+a plus b plus c equals 0,
+
+addition is the same as
+subtraction, because we're in
+
+a binary field.
+
+So that means that a plus b
+equals c, a equals b plus c, c
+
+equals b plus a, whatever
+you like.
+
+And of course, if you add 0 to
+anything, it's trivially
+
+closed under that.
+
+All right.
+
+So it is.
+
+It satisfies --
+
+it's all you've got to check.
+
+A more abstract proof of this
+would be, this is the set of
+
+all even-weight three-tuples.
+
+If I add even to even, I'm
+going to get even.
+
+So of course my result is
+going to be another
+
+even-weight three-tuple,
+therefore in the set.
+
+That's the more algebraic
+proof.
+
+All right.
+
+Suppose I just add 0, 0, 1
+to all of these things.
+
+I'll get the set of all
+odd-weight n-tuples.
+
+Add any odd-weight
+n-tuple to this.
+
+Let me take the C prime,
+which is the set of
+
+all odd-weight n-tuples.
+
+Is that a vector space?
+
+It doesn't have 0, and in fact,
+it's not even closed
+
+under vector addition.
+
+All right.
+
+If I take in C double prime is
+equal to 0, 0, 0 0, 1, 1, 1,
+
+0, 1 and I stop there,
+is that a subspace?
+
+No.
+
+Because?
+
+Not closed.
+
+For instance, if I add these
+two together, I would get
+
+that, and that's missing.
+
+OK.
+
+So actually, everything is
+much simpler when we're
+
+talking about finite fields.
+
+All the finite dimensional
+vector spaces consist of a
+
+finite number of elements.
+
+It's easier than real and
+complex vector spaces.
+
+There's no analysis involved.
+
+So forth.
+
+All right.
+
+So a binary linear block
+code is in a subspace
+
+of F2 to the n.
+
+What are some of the key
+algebraic facts we know about
+
+vector spaces from our study
+of linear algebra, which I
+
+assume all of you have had
+in some form or another?
+
+What's a key algebraic property
+of a vector space?
+
+What's the very first
+property?
+
+All vector spaces have a --
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Norm?
+
+No.
+
+Dimension.
+
+Dimension, that's
+where I'm going.
+
+What's the significance
+of dimension?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: The definition of
+dimension is the number of
+
+generators in any basis.
+
+So we're talking about
+generators of the vector
+
+space, or a set of generators
+which form a basis.
+
+If you think we have the same
+properties here in the case of
+
+vector spaces over finite
+fields, well, we probably do.
+
+But let's see how
+it works out.
+
+So we're talking about
+things like
+
+generators, basis, dimension.
+
+These are all closely
+interlinked properties.
+
+Again, the fact that everything
+is finite here
+
+gives us very elementary
+ways of addressing
+
+all of these concepts.
+
+We don't have any
+geometry yet.
+
+We don't have norms.
+
+We don't have distances.
+
+We don't have angles.
+
+We'll talk about that
+in a minute.
+
+Here we just have a set that
+basically has these two
+
+properties.
+
+It contains the all-0 vector,
+and it's closed
+
+as the group property.
+
+It's closed under
+vector addition.
+
+All right.
+
+So the first property is that
+the all-0 vector is always in
+
+the subspace, which I'll
+represent by C, meaning code.
+
+So when I talk about a code
+now, I'm talking about a
+
+binary linear block code,
+which by definition is a
+
+vector space, a subspace
+of F2 to the n, where
+
+n is the code length.
+
+All right.
+
+Let me try to find a set of
+generators for the code.
+
+All right?
+
+If somebody gives me a code,
+they say, this is a binary
+
+linear block code.
+
+Let me see if I can find a
+set of generators for it.
+
+If I find three generators,
+then I'll know the
+
+dimension is three.
+
+That's basically where
+I'm going.
+
+I'll state this a little bit
+more formally as we go ahead.
+
+So suppose I'm given a code.
+
+I know it's a binary linear
+block code, so I know it has
+
+the all-0 element.
+
+So how might I go about finding
+a set of generators?
+
+Let's just take a greedy
+algorithm.
+
+All right?
+
+Suppose the code contains
+only the all-0 vector.
+
+Is that a subspace?
+
+What's its dimension?
+
+0.
+
+All right?
+
+So that's a very trivial vector
+space, but it's a
+
+vector space.
+
+Satisfies the axioms.
+
+Suppose it is not the
+trivial code.
+
+That means it has more than
+the all-0 vector.
+
+So I take as my first generator
+any non-zero vector.
+
+OK?
+
+I can always do that.
+
+Don't have the axiom of choice
+involved here, because
+
+everything is finite.
+
+So I'm going to take g1 to
+be any non-zero vector.
+
+Now I've got a generator.
+
+And how many code words
+does it generate?
+
+I want to take the set of all
+binary linear combinations of
+
+all the generators that
+I have so far.
+
+At this point, the binary linear
+combinations are 0
+
+times g1 and 1 times g1 And that
+just gives me this word
+
+and this word.
+
+So now I have counted for two
+words with one generator.
+
+Could it be that that's
+the whole code?
+
+Sure.
+
+The all-0 vector and any
+non-zero vector together form
+
+a one-dimensional subspace.
+
+That's all you can get
+from one dimension.
+
+So I could be finished
+here now.
+
+But if I'm not finished, there's
+still more code words
+
+that I haven't accounted for.
+
+Then I greedily pick
+a second generator.
+
+So this is now, let's say, any
+vector not generated by g1.
+
+So I have a branch here.
+
+Either I've finished or I can
+pick another generator g2.
+
+Now with g1 and g-two, how many
+vectors can I generate?
+
+Let me take all binary
+linear combinations.
+
+So a binary linear combination
+is any vector of the form
+
+alpha1 g1 plus alpha2 g2 where
+these are both scalars.
+
+And therefore this can be 0 or
+1, this could be 0 or 1.
+
+So what have I got now?
+
+I've got 0, g1 g2 and g1 plus g2
+I've got four binary linear
+
+combinations of two
+generators.
+
+Could that be the whole code?
+
+Certainly.
+
+At this point, again, consider
+our standing example.
+
+I start out what I take
+as my first generator.
+
+Let me take g1 equal 1 0, 1, g2
+equals whatever, 0, 1, 1.
+
+Then if I take all binary linear
+combinations of these
+
+two generators, I'm going to
+get the whole code, right?
+
+These four code words.
+
+They can all be expressed
+in this form.
+
+Or I'm not done, and then
+I have to pick g3.
+
+And how many binary linear
+combinations are there of g1,
+
+g2, and g3?
+
+Eight.
+
+Are they all necessarily
+in my subspace?
+
+Yes, by the fact that the
+subspace is closed under
+
+scalar multiplication.
+
+Alpha g1.
+
+Alpha1 g1, alpha2 g2 alpha3 g3
+are all in the subspace.
+
+Any vector addition of any of
+these scalar multiples is in
+
+the subspace.
+
+So I get now eight possible
+elements of the subspace, and
+
+I either may be done or not.
+
+Continuing in this way, I get
+some number gk of generators,
+
+just by picking greedily the
+next one until I'm done.
+
+All right?
+
+When I'm done --
+
+so I have to stop.
+
+Why do I have to stop?
+
+All right.
+
+Let's look at the size.
+
+At each point here, this
+accounts for two code words,
+
+this for four, this for eight,
+this for 2 to the k.
+
+How many binary n-tuples
+are there?
+
+2 to the n.
+
+All right?
+
+So I clearly can't find more
+than n generators.
+
+More more than n independent
+generators, in the sense that
+
+the set of all the
+binary linear
+
+combinations are distinct.
+
+All right.
+
+So k is, at most,
+going to be n.
+
+So I will stop in a finite
+number of steps.
+
+I'll stop at some number k.
+
+When I've stopped, that's
+because the code consists of
+
+all binary linear combinations
+of these k generators, and
+
+therefore has size 2 to the k.
+
+So the only possible size of a
+subspace is 2 to the k for k
+
+less than n.
+
+A power of 2 where the
+power is, at most, n.
+
+So any subspace besides
+the subspace --
+
+I'm repeating myself.
+
+OK.
+
+So this means I found a basis.
+
+Does this mean that all possible
+bases of any subspace
+
+have the same size?
+
+Well yeah, it must.
+
+I mean, I've proved now that any
+subspace has to have this
+
+size 2 to the k for some k.
+
+So obviously, if I go through
+this process, no matter how I
+
+choose my generators, I could
+choose any pair of these
+
+non-zero n-tuples as
+my generators.
+
+So that would be a
+legitimate basis.
+
+Take any two out
+of these three.
+
+But it's always going to take
+exactly two of them, right?
+
+Why?
+
+Because the size of this
+subspace is four.
+
+Two to the two.
+
+So if I go through this process,
+I'm always going to
+
+come up with k generators, where
+k is the log to the base
+
+2 of the size of this code that
+I was given, which I was
+
+told was a linear code, meaning
+it's a subspace.
+
+So I'm somewhat free to choose
+the generators, but I'm always
+
+going to come up with k of
+them if the code has
+
+size 2 to the k.
+
+So a basis is a set of k
+linearly independent k-tuples,
+
+where linear independence has
+the same meaning here as
+
+you're accustomed to, meaning
+that all linear combinations
+
+of the k generators
+are distinct.
+
+So I get 2 to the k distinct
+elements of the code.
+
+And I say the dimension
+of the code is k.
+
+In this case, basically it's the
+size of the code is 2 to
+
+the k, then its dimension
+is k.
+
+Has to be.
+
+And all basis have k
+generators in them.
+
+And there are, in general,
+many ways to pick them.
+
+All right?
+
+So just by considering this
+greedy basis construction
+
+algorithm, I basically find the
+size of any subspace is a
+
+power of two, and the power
+is equal to the dimension.
+
+And any basis is going to
+have that cardinality.
+
+Are you with me?
+
+This is a pretty simple proof.
+
+And I call this an n, k binary
+linear block code.
+
+n being the length.
+
+That just means that every code
+word is an n-tuple over
+
+the binary field.
+
+And k is the dimension.
+
+So an n, k binary linear block
+code has size 2 to the k.
+
+That's 2 to the k distinct
+code words.
+
+Main example is this guy.
+
+Easy?
+
+Any questions?
+
+I think this is clear.
+
+AUDIENCE: Can n use the number
+of code word, I take
+
+like 2 to the k?
+
+PROFESSOR: n is something I
+specify a priori as the length
+
+of every vector in the code.
+
+In other words, it has size 2 to
+the k, and it's a subset of
+
+the set of all binary
+n-tuples, which
+
+I write like that.
+
+In other words, the
+elements of the
+
+code are binary n-tuples.
+
+If I write them out, each
+one has length n.
+
+OK?
+
+We're good?
+
+What are some other examples?
+
+The simplest codes you can
+think of is, first of
+
+all, an n, 0 code.
+
+That means a code with dimension
+zero, has size what?
+
+1.
+
+And what does it consist of?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah.
+
+So this is the so-called trivial
+code, just containing
+
+the all-0 word.
+
+Has to mention 0.
+
+It is a binary linear block
+code, but it's not much use
+
+for communication.
+
+So but nonetheless, we include
+that in this family.
+
+Another trivial one is n, n.
+
+What's that?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: F2 to the n, right.
+
+What's its size?
+
+2 to the n.
+
+That means it has to contain all
+distinct binary n-tuples.
+
+So this is called the
+trivial code.
+
+This is called the
+universe code.
+
+Contains the entire universe
+of binary n-tuples.
+
+Let's get some slightly
+less trivial ones.
+
+n, 1.
+
+What would that be?
+
+An n, 1 code.
+
+What's its size?
+
+2.
+
+What does it consist of?
+
+The 0 word, and?
+
+Any other non-zero generator.
+
+And that's correct.
+
+This can be 0 and any generator,
+two words.
+
+In communications, where we want
+to maximize the distance,
+
+in some sense, between the
+two code words, what is g
+
+always taken as?
+
+0,1's, right.
+
+So if it's in particular the
+all-0 and the all-1 word,
+
+which I might write as a vector
+of 0's and a vector of
+
+1's, this is called the
+repetition code.
+
+The binary repetition
+code of length n.
+
+It either gives me a 0 and I
+repeat it n times, or gives me
+
+a 1 and I repeat it n times.
+
+So whenever you see n,1, you
+can pretty well assume it's
+
+the repetition code, though
+it might be any pair 0, g.
+
+And n, minus 1.
+
+This is an interesting one.
+
+Again, while this could
+be a lot of things, in
+
+communications, whenever you see
+this, this will always be
+
+the set of all even-weight
+n-tuples.
+
+In other words, the set of all
+n-tuples with even parity such
+
+that if you sum up all of
+the components of any
+
+vector, mod2 equals 0.
+
+OK?
+
+So this I will call the single
+parity check, or more briefly,
+
+the SPC code, or the
+even-weight code.
+
+That's equally good.
+
+And here we maybe should do
+a little bit more work.
+
+Say, is this in fact
+a subspace?
+
+Does it include the all-zero
+code word?
+
+Yes, all-zero has even weight.
+
+The sum of any two even-weight
+code words, an even-weight
+
+code word, an even-weight
+n-tuple.
+
+Yes.
+
+As here.
+
+This is an example.
+
+This is the three,
+two SPC code.
+
+OK.
+
+Why is this dimension
+n minus one?
+
+AUDIENCE: [INAUDIBLE]
+
+Is every code word orthogonal
+to the one-vector?
+
+PROFESSOR: OK.
+
+That's an excellent answer.
+
+It's a little advanced
+for us right now.
+
+I'm looking for an elementary
+argument.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: OK.
+
+So you're saying we have
+a set of generators
+
+that looks like this.
+
+Is that what you're saying?
+
+You are correct.
+
+And how many such generators
+are there?
+
+There are n minus 1 of them.
+
+I always like to find the most
+elementary argument possible.
+
+I think the most elementary
+argument here is that the
+
+number of even-weight n-tuples
+is equal to the number of
+
+odd-weight n-tuples, and
+together they form the set of
+
+all n-tuples.
+
+So exactly half of the n-tuples
+are even weight.
+
+That means there are 2 to the n
+minus 1 of them, 2 to the n
+
+over 2, and therefore, the
+dimension must be n minus 1.
+
+But perhaps this is just
+as elementary a proof.
+
+Well, however you do it, you'll
+find that there are 2
+
+to the n minus 1 of them, or
+that here is clearly a set of
+
+generators.
+
+It might take a few more lines
+to show that every even-weight
+
+code word is a linear
+combination of this particular
+
+set of generators, but
+it's certainly true.
+
+All right.
+
+So these four classes of codes,
+these two entirely
+
+trivial ones, these two which
+are actually somewhat more
+
+interesting for coding
+purposes --
+
+we've already seen, we can get a
+coding game with this length
+
+three, dimension two code --
+
+are basically the simplest
+codes we can think of.
+
+The simplest binary linear
+block codes.
+
+Now we'll see them
+again and again.
+
+They turn up.
+
+All right?
+
+So the whole course is
+going to be about
+
+finding 1's in between.
+
+More complicated ones.
+
+There's clearly more
+room to play.
+
+For instance, if k is equal to
+half of n, which means that
+
+rho is equal to one bit per two
+dimensions, there's a lot
+
+of possibilities.
+
+And so we're going to explore
+those possibilities.
+
+AUDIENCE: [INAUDIBLE]
+
+[UNINTELLIGIBLE]
+
+PROFESSOR: Sure.
+
+Let's take the 6,5 code
+generated by these five
+
+generators.
+
+Well, it contains some
+
+odd-weight code words, obviously.
+
+But it's not as interesting from
+a coding point of view.
+
+It's not the only one,
+but it's the only one
+
+you'll ever see here.
+
+All right.
+
+Let's see.
+
+One thing I didn't point out
+in the notes but probably
+
+should have here is, what is rho
+for an n, k binary linear
+
+block code?
+
+How many bits can we send?
+
+Suppose we take the Euclidean
+image of this.
+
+It is going to have 2 to the k
+points, 2 to the k vertices of
+
+the n-cube, and so
+what is rho?
+
+What is the rate in bits
+per two dimensions?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Right.
+
+The rate is basically k over n
+over 2, if you like, or 2 k
+
+over n bits per two
+dimensions.
+
+You can send k bits in n
+dimensions, or 2 k over n bits
+
+per two dimensions.
+
+And since k can't be larger than
+n, this is going to be
+
+less than or equal to two
+bits per two dimensions.
+
+So again, we see we're
+definitely in the
+
+power-limited regime, and that
+we can really get any nominal
+
+spectral efficiency between 0
+and 2 by choosing k and n
+
+appropriately.
+
+All right.
+
+So n and k determine the rate,
+determine the nominal spectral
+
+efficiency.
+
+All right.
+
+Let's now talk about things that
+I think are also very old
+
+hat to you.
+
+I mean weight and distance.
+
+But we begin to get into areas
+that show us that these vector
+
+spaces are very different from
+the real and complex vector
+
+spaces that we're
+accustomed to.
+
+So what are we doing now?
+
+We're starting to get into the
+geometry of this vector space.
+
+The geometry is not Euclidean
+geometry, but
+
+it's Hamming geometry.
+
+We define the Hamming weight
+of a vector as simply the
+
+number of 1's in v. So the
+Hamming weight of the all-0
+
+vector is 0, the Hamming weight
+of the all-1 vector is
+
+n, and in general, the Hamming
+weight is somewhere
+
+between 0 and n.
+
+Just the number of 1's.
+
+Pretty simple.
+
+And given two vectors x and
+y, what is their distance?
+
+The Hamming distance between x
+and y is equal to the Hamming
+
+weight of x minus y.
+
+This is the standard way of
+converting a weight metric
+
+into a distance metric.
+
+Or because addition is the
+same as subtraction in a
+
+binary vector space, we might
+equally well write this is as
+
+the Hamming weight
+of x plus y.
+
+And more informally, this is
+simply the number of places in
+
+which they differ.
+
+OK.
+
+So if x and y are identical,
+then x plus y is equal to 0
+
+and the distance is 0.
+
+If they are complementary, y is
+the complement of x, then
+
+they differ in every place.
+
+The sum will then be the all-1
+vector, and the weight, the
+
+Hamming distance, will be n.
+
+And so again, the Hamming
+distance is somewhere between
+
+0 and n, measures how
+different they are.
+
+Clearly going to be important
+for coding.
+
+It's going to translate directly
+into Euclidean
+
+distance under this standard
+2-PAM map.
+
+OK.
+
+Again, let's check that it
+satisfies the distance axioms.
+
+I don't know how many of you
+have seen this, but let's see.
+
+What are the distance axioms?
+
+Strict non-negativity.
+
+In other words, the Hamming
+distance between x and y --
+
+that's a single comma --
+
+is greater than or equal to
+0, and equality if and
+
+only if x equals y.
+
+That's what strict means.
+
+So if we find the Hamming
+distance is 0, we can assert
+
+that x equals y.
+
+We have, of course, symmetry.
+
+The Hamming distance between
+x and y is the same as the
+
+Hamming distance between
+y and x.
+
+Order doesn't matter.
+
+And finally we have the triangle
+inequality, that the
+
+Hamming distance between x and z
+certainly can't be more than
+
+the Hamming distance between
+x and y plus the Hamming
+
+distance between y and z.
+
+If x differs from y in only n1
+places, and y differs from z
+
+in only n2 places, then clearly
+z can't differ from x
+
+in more than n1 plus
+n2 places.
+
+So check, check, check.
+
+This is a legitimate metric for
+defining a geometry on the
+
+space, and this is the one that
+we use on the space of
+
+all n-tuples.
+
+But notice it's not all like
+the Euclidean Distance.
+
+Now when we have a
+linear code --
+
+let's combine these things.
+
+When we have a linear code, we
+have a group property which
+
+is, let me write it this way.
+
+If we take any code word and add
+it to any other code word,
+
+that's in the code.
+
+And furthermore, c plus c prime
+is not equal to c prime
+
+plus c single prime, c
+plus c single prime,
+
+because we can --
+
+well, I'll finish it.
+
+Unless c prime equals
+c double prime.
+
+Why is that?
+
+We can do subtraction,
+cancellation.
+
+Cancel c out from each side.
+
+So if we add c to c double
+prime, we're going to get a
+
+different result from adding c
+to c prime, if c prime and c
+
+double prime are different.
+
+So this implies that
+c plus C --
+
+I write that as an abbreviation
+for the set of
+
+all c plus c prime, as a c prime
+runs through the code C.
+
+So this is the 2 to the k sums
+of the code plus any code word
+
+in the code.
+
+Sorry if I don't write
+down all steps.
+
+What is that going to be?
+
+C. How did we conclude that?
+
+AUDIENCE: [INAUDIBLE]
+
+[UNINTELLIGIBLE]
+
+PROFESSOR: Perfect.
+
+Did you all hear that?
+
+By the group property,
+each one of these
+
+things is in the code.
+
+By this argument, no two
+of them are the same.
+
+That means I get 2 to the k
+distinct elements all in the
+
+code, that's got to be the code,
+because the code only
+
+has 2 to the k elements.
+
+All right.
+
+So if I add a code word --
+
+in other words, if I write
+down the code --
+
+0, 0, 0, 0, 1, 1, 1 0 1, 1 1 0-
+and I add any code word to
+
+it -- say I add 0
+1 1 to the code.
+
+So let me just do one column
+of the addition table.
+
+I get 0, 1, 1, 0, 0, 0,
+1, 1, 0, 1, 0, 1.
+
+I'll get the code
+itself again.
+
+This has a very important
+property.
+
+The set of Hamming distances C
+and c prime, as c prime runs
+
+through c, from any given code
+word C, it is independent of
+
+C. So I can start from any code
+word, measure the Hamming
+
+distances, the 2 to the k
+Hamming distances to all other
+
+code words, including
+C itself --
+
+let c prime run through the
+entire code, I'm going to get
+
+a set of 2 to the k distances
+called the distance
+
+profile of the code.
+
+And I claim that it doesn't
+matter which code
+
+word I start from.
+
+I'm going to get the same
+distance profile regardless of
+
+where I start.
+
+In other words, the set of all
+distances from the all-0 word
+
+here, which is 0, 2, 2, 2, is
+the same as the set of all
+
+distances from the 0,
+1, 1, code word,
+
+which is 2, 0, 2, 2.
+
+And the proof is basically
+that this is simply the
+
+Hamming weight of C plus c prime
+as c prime runs through
+
+C. What is this equal to?
+
+So the proof is that this is
+equal to the Hamming weight of
+
+c prime as c prime
+runs through C.
+
+So the distance profile from any
+code word is simply equal
+
+to the weight profile
+of the code itself.
+
+The weight profile of this code
+is 0, 2, 2, 2, Start from
+
+any code word, measure the
+distances to other code words,
+
+I'm always going to get
+0, 2, 2, 2, 0, to
+
+itself, and the others.
+
+Sounds sort of like the
+tetrahedron, doesn't it?
+
+It's zero distance from a code
+word to itself and equal
+
+distance to all the other
+code words, in
+
+that particular case.
+
+OK.
+
+So again, everything is
+very elementary here.
+
+The distance profile is
+independent of C and equal to
+
+the weight profile.
+
+So this has an extremely
+important corollary.
+
+What's the minimum Hamming
+distance of the code?
+
+You might expect this
+is going to be an
+
+important code parameter.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: The minimum Hamming
+distance between any two code
+
+words is going to
+be equal to --
+
+I think you said it.
+
+AUDIENCE: The 0
+[UNINTELLIGIBLE].
+
+PROFESSOR: Non-zero
+is important here.
+
+If the distance profile is equal
+to the weight profile,
+
+one of the weights is always
+going to be zero.
+
+And that corresponds to the
+distance between a code word
+
+and itself.
+
+All right.
+
+If I go through all the other 2
+to the k minus 1 distances,
+
+they're going to be weights.
+
+They're going to be the
+distances from a code to all
+
+other code words.
+
+And the minimum distance is
+simply going to be the minimum
+
+non-zero weight of the code.
+
+For example, in this code, the
+minimum Hamming distance
+
+between any two distinct code
+words is going to be equal to
+
+the minimum distance from
+the 0 code word --
+
+that's another way
+of doing it.
+
+Since it's independent of C, we
+may as well take the base
+
+code word C to be zero.
+
+And then what's the minimum
+distance to 0?
+
+To the 0-code word?
+
+It's the minimum weight.
+
+From the 0 code word, distance
+equals weight.
+
+So the minimum distance is the
+minimum weight of any non-zero
+
+code word, which for
+this code is two.
+
+Now here the weight profile
+is 0, 2, 2, 2, 0.
+
+The distance profile from any
+code word to all the others is
+
+0, 2, 2,2 2.
+
+This is always the distance
+to itself.
+
+So minimum distance to
+other code words is
+
+always going to be two.
+
+Furthermore, the number of
+nearest neighbors --
+
+to go back and use chapter
+five terminology --
+
+the number of nearest neighbors
+is going to be the
+
+number of code words that have
+that minimum weight --
+
+in this case, three.
+
+Still sounding a lot like
+a tetrahedron, isn't it?
+
+This easy map between Hamming
+distance and Euclidean
+
+distance for this case and in
+general for all of our cases.
+
+So corollary.
+
+The minimum Hamming distance,
+which implicitly means between
+
+two distinct code words of C,
+is equal to the minimum
+
+non-zero weight of C, and the
+number of minimum weight code
+
+words is independent --
+
+I'm doing this backwards.
+
+From any code word, the number
+of code words that distance,
+
+let's call this d, is equal
+to the number of
+
+weight d code words.
+
+Sorry, you probably
+can't see that.
+
+All right.
+
+So we get this symmetry property
+for codes that
+
+follows from the group property
+of the code that if
+
+we stand on any code word and
+look out, we're always going
+
+to see the same thing.
+
+We have this constant.
+
+It's actually easiest to see
+this when we make the map from
+
+the code to the Euclidean
+image of the code.
+
+So the Euclidean image S of C
+of the code word is going to
+
+be some set of 2 to the
+k vertices of an
+
+n-cube of side alpha.
+
+Let's talk about the Euclidean
+image of these properties.
+
+If the minimum Hamming distance
+of the code is d,
+
+what's the minimum squared
+Euclidean distance between
+
+elements of S of
+C going to be?
+
+Well, let's do it coordinate
+by coordinates.
+
+Let's take two code words,
+C and c prime, let's say.
+
+And let's suppose we have
+some Hamming distance
+
+between C and c prime.
+
+That means that c and c prime
+differ in the Hamming
+
+distance, number of places.
+
+So if we map this into the
+corresponding pair of vertices
+
+of the n-cube in Euclidean
+space, S of C and S of c
+
+prime, how many coordinates are
+these going to differ in?
+
+It's going to differ in same
+number of coordinates, D_h.
+
+If they don't differ, what's
+Euclidean squared distance in
+
+those coordinates?
+
+0.
+
+If they do differ, the Euclidean
+squared distance is
+
+4 alpha squared.
+
+So the Euclidean distance D_e
+between S of C and S of c
+
+prime is simply going to be
+4 alpha squared times the
+
+Hamming distance between
+C and c prime, yes?
+
+So I should say this is the
+squared Euclidean distance.
+
+Why do we always talk about the
+
+squared Euclidean distance?
+
+Because it's additive,
+coordinate-wise.
+
+And the Hamming distance is
+additive, coordinate-wise.
+
+So there's a nice
+easy map here.
+
+So what does this mean d_min
+squared is going to be?
+
+d_min squared of, let's say, S
+of C. This constellation that
+
+we've formed by taking the
+Euclidean image of c.
+
+The minimum square distance
+between points in S of C is
+
+just going to be 4 alpha squared
+times d, where I don't
+
+think I ever --
+
+d equals min Hamming distance.
+
+And we're always going to talk
+about n, k, d as the three key
+
+parameters of a binary
+linear block code.
+
+n is the code length, F2 to the
+n, k is the dimension, d
+
+is the minimum Hamming
+distance.
+
+So by going into this Hamming
+geometry, we've got a third
+
+key property of the code.
+
+And we see it's key, because we
+can get the minimum squared
+
+distance between this Euclidean
+image constellation,
+
+just 4 alpha squared d.
+
+AUDIENCE: nd makes
+a probability of
+
+[UNINTELLIGIBLE] that is
+dependent on [UNINTELLIGIBLE]
+
+then.
+
+PROFESSOR: Correct.
+
+This is all we need to know to
+get the union bound estimate.
+
+Well, a few more things.
+
+We need to know what K_min
+average of S of C. And what is
+
+that going to be?
+
+This is simply going to be the
+number of words in the code.
+
+To get this minimum squared
+distance, we need a Hamming
+
+distance of d.
+
+So the number of words in the
+code of distance d, which is
+
+given by the parameter n sub d,
+is simply going to be the
+
+number of nearest neighbors.
+
+Not just the average distance,
+but I want to emphasize this
+
+symmetry property.
+
+If we stand on any point, on
+any vertex of this cube in
+
+n-space, which is the code
+vertex, and we look at all the
+
+other points in the
+constellation, no matter which
+
+point we stand on, we
+will always see the
+
+same profile of distances.
+
+We'll see precisely nd code
+words at Euclidean distance 4
+
+alpha squared d.
+
+We'll see nd plus 1 at Euclidean
+squared distance 4
+
+alpha squared d plus 1, and so
+forth, right up the profile.
+
+So there's complete symmetry
+in the constellation.
+
+In that universe, you don't know
+which code point you're
+
+standing on just by looking out,
+because the world looks
+
+the same to you.
+
+Is that clear?
+
+OK.
+
+So from a communications point
+of view, this is important,
+
+because it means it doesn't
+matter what code word we send.
+
+The probability of error from
+any code word is going to be
+
+the same as the probability of
+error from any other code
+
+word, because the geometry
+is exactly the same.
+
+The Voronoi regions are
+all the same shape.
+
+So given the exact probability
+of error, not just the
+
+union-bound estimate, is going
+to be independent of which
+
+code word was sent.
+
+This all follows from the fact
+that it's a linear code and
+
+therefore has the group
+property, which translates
+
+into this very strong
+geometrical uniformity
+
+property in Euclidean space.
+
+Or actually in Hamming space
+too, but it's more striking in
+
+Euclidean space.
+
+OK?
+
+So we have everything we
+need to write down
+
+the union bound estimate.
+
+Union bound estimate was just
+the probably of error per bit
+
+is well approximated by K_b of
+constellation, in this case, S
+
+of C, times Q of the square root
+of the coding gain of the
+
+constellation times
+2 Eb over N_0.
\ No newline at end of file
diff --git a/YUjdyKhWt6E.txt b/YUjdyKhWt6E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4fe1f840b3325aa099071e64d3b899f0a913b7ab
--- /dev/null
+++ b/YUjdyKhWt6E.txt
@@ -0,0 +1,1179 @@
+align:start position:0%
+ 
+welcome back so in this session we're
+
+ align:start position:0%
+welcome back so in this session we're
+ 
+
+ align:start position:0%
+welcome back so in this session we're
+going to use the Matrix method to solve
+
+ align:start position:0%
+going to use the Matrix method to solve
+ 
+
+ align:start position:0%
+going to use the Matrix method to solve
+this linear system of differential
+
+ align:start position:0%
+this linear system of differential
+ 
+
+ align:start position:0%
+this linear system of differential
+equations these are X doal 6x + 5 Y and
+
+ align:start position:0%
+equations these are X doal 6x + 5 Y and
+ 
+
+ align:start position:0%
+equations these are X doal 6x + 5 Y and
+Y dot equal x + 2 y so why don't you
+
+ align:start position:0%
+Y dot equal x + 2 y so why don't you
+ 
+
+ align:start position:0%
+Y dot equal x + 2 y so why don't you
+take a few minutes to write down a
+
+ align:start position:0%
+take a few minutes to write down a
+ 
+
+ align:start position:0%
+take a few minutes to write down a
+system in Matrix form and go through the
+
+ align:start position:0%
+system in Matrix form and go through the
+ 
+
+ align:start position:0%
+system in Matrix form and go through the
+method of the M The Matrix method to
+
+ align:start position:0%
+method of the M The Matrix method to
+ 
+
+ align:start position:0%
+method of the M The Matrix method to
+solve it and I'll be right back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+welcome back so let's write down this
+
+ align:start position:0%
+welcome back so let's write down this
+ 
+
+ align:start position:0%
+welcome back so let's write down this
+system in Matrix
+
+ align:start position:0%
+system in Matrix
+ 
+
+ align:start position:0%
+system in Matrix
+form we would have a vector with entries
+
+ align:start position:0%
+form we would have a vector with entries
+ 
+
+ align:start position:0%
+form we would have a vector with entries
+X and Y Prime equals a matrix with entry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+65 one two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiplying the colum Vector X Y so now
+
+ align:start position:0%
+multiplying the colum Vector X Y so now
+ 
+
+ align:start position:0%
+multiplying the colum Vector X Y so now
+we did big part of the work the Matrix
+
+ align:start position:0%
+we did big part of the work the Matrix
+ 
+
+ align:start position:0%
+we did big part of the work the Matrix
+method tells us that we need to find the
+
+ align:start position:0%
+method tells us that we need to find the
+ 
+
+ align:start position:0%
+method tells us that we need to find the
+aen values of this Matrix to be able to
+
+ align:start position:0%
+aen values of this Matrix to be able to
+ 
+
+ align:start position:0%
+aen values of this Matrix to be able to
+basically diagonalize it and seek aen
+
+ align:start position:0%
+basically diagonalize it and seek aen
+ 
+
+ align:start position:0%
+basically diagonalize it and seek aen
+vectors so that then we can just read
+
+ align:start position:0%
+vectors so that then we can just read
+ 
+
+ align:start position:0%
+vectors so that then we can just read
+off the solutions and write the solution
+
+ align:start position:0%
+off the solutions and write the solution
+ 
+
+ align:start position:0%
+off the solutions and write the solution
+of the system as a linear combination of
+
+ align:start position:0%
+of the system as a linear combination of
+ 
+
+ align:start position:0%
+of the system as a linear combination of
+the aen vectors that we found so let's
+
+ align:start position:0%
+the aen vectors that we found so let's
+ 
+
+ align:start position:0%
+the aen vectors that we found so let's
+look for The Egan values first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the aen values would be computed by
+
+ align:start position:0%
+the aen values would be computed by
+ 
+
+ align:start position:0%
+the aen values would be computed by
+seeking the determinant of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix in this
+
+ align:start position:0%
+Matrix in this
+ 
+
+ align:start position:0%
+Matrix in this
+form 6 minus lamba 5 1 2 minus Lambda
+
+ align:start position:0%
+form 6 minus lamba 5 1 2 minus Lambda
+ 
+
+ align:start position:0%
+form 6 minus lamba 5 1 2 minus Lambda
+we're going to have an equation on
+
+ align:start position:0%
+we're going to have an equation on
+ 
+
+ align:start position:0%
+we're going to have an equation on
+Lambda solve for Lambda and the
+
+ align:start position:0%
+Lambda solve for Lambda and the
+ 
+
+ align:start position:0%
+Lambda solve for Lambda and the
+solutions will be out a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values so the determinant would be 6
+
+ align:start position:0%
+values so the determinant would be 6
+ 
+
+ align:start position:0%
+values so the determinant would be 6
+minus Lambda multiplying 2us LDA minus 5
+
+ align:start position:0%
+minus Lambda multiplying 2us LDA minus 5
+ 
+
+ align:start position:0%
+minus Lambda multiplying 2us LDA minus 5
+1. 5 = to0 so here the Landa Landa gives
+
+ align:start position:0%
+1. 5 = to0 so here the Landa Landa gives
+ 
+
+ align:start position:0%
+1. 5 = to0 so here the Landa Landa gives
+us a land Square we have Min - 6 L minus
+
+ align:start position:0%
+us a land Square we have Min - 6 L minus
+ 
+
+ align:start position:0%
+us a land Square we have Min - 6 L minus
+2 land which would be minus 8 Landa and
+
+ align:start position:0%
+2 land which would be minus 8 Landa and
+ 
+
+ align:start position:0%
+2 land which would be minus 8 Landa and
+then we would have 2. 6 which is 12
+
+ align:start position:0%
+then we would have 2. 6 which is 12
+ 
+
+ align:start position:0%
+then we would have 2. 6 which is 12
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+5 which gives us a seven so quadratic
+
+ align:start position:0%
+5 which gives us a seven so quadratic
+ 
+
+ align:start position:0%
+5 which gives us a seven so quadratic
+equation on in Landa and you can
+
+ align:start position:0%
+equation on in Landa and you can
+ 
+
+ align:start position:0%
+equation on in Landa and you can
+factorize it and find the solutions
+
+ align:start position:0%
+factorize it and find the solutions
+ 
+
+ align:start position:0%
+factorize it and find the solutions
+which as Lambda 1 = 2 1 Lambda 2 equal 2
+
+ align:start position:0%
+which as Lambda 1 = 2 1 Lambda 2 equal 2
+ 
+
+ align:start position:0%
+which as Lambda 1 = 2 1 Lambda 2 equal 2
+7 okay so we're done with the first part
+
+ align:start position:0%
+7 okay so we're done with the first part
+ 
+
+ align:start position:0%
+7 okay so we're done with the first part
+first part these are aen values they're
+
+ align:start position:0%
+first part these are aen values they're
+ 
+
+ align:start position:0%
+first part these are aen values they're
+not repeated they're just completely
+
+ align:start position:0%
+not repeated they're just completely
+ 
+
+ align:start position:0%
+not repeated they're just completely
+different and real valued so now we're
+
+ align:start position:0%
+different and real valued so now we're
+ 
+
+ align:start position:0%
+different and real valued so now we're
+going to look at the aen vectors
+
+ align:start position:0%
+going to look at the aen vectors
+ 
+
+ align:start position:0%
+going to look at the aen vectors
+Associated to each aen
+
+ align:start position:0%
+Associated to each aen
+ 
+
+ align:start position:0%
+Associated to each aen
+value um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so first aen
+
+ align:start position:0%
+so so first aen
+ 
+
+ align:start position:0%
+so so first aen
+Vector would be associated with Lambda 1
+
+ align:start position:0%
+Vector would be associated with Lambda 1
+ 
+
+ align:start position:0%
+Vector would be associated with Lambda 1
+equals to 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we would be solving the
+
+ align:start position:0%
+okay so we would be solving the
+ 
+
+ align:start position:0%
+okay so we would be solving the
+system uh we would be solving the system
+
+ align:start position:0%
+system uh we would be solving the system
+ 
+
+ align:start position:0%
+system uh we would be solving the system
+with the new Matrix 6 minus one I'm
+
+ align:start position:0%
+with the new Matrix 6 minus one I'm
+ 
+
+ align:start position:0%
+with the new Matrix 6 minus one I'm
+going to spell out this one so
+
+ align:start position:0%
+going to spell out this one so
+ 
+
+ align:start position:0%
+going to spell out this one so
+that 2 - one so this is just our land
+
+ align:start position:0%
+that 2 - one so this is just our land
+ 
+
+ align:start position:0%
+that 2 - one so this is just our land
+multiplying an unknown Vector with
+
+ align:start position:0%
+multiplying an unknown Vector with
+ 
+
+ align:start position:0%
+multiplying an unknown Vector with
+composant and 1 and
+
+ align:start position:0%
+composant and 1 and
+ 
+
+ align:start position:0%
+composant and 1 and
+A2 equals to zero
+
+ align:start position:0%
+A2 equals to zero
+ 
+
+ align:start position:0%
+A2 equals to zero
+vector and basically here the unknowns
+
+ align:start position:0%
+vector and basically here the unknowns
+ 
+
+ align:start position:0%
+vector and basically here the unknowns
+are A1 and A2 okay so this is
+
+ align:start position:0%
+are A1 and A2 okay so this is
+ 
+
+ align:start position:0%
+are A1 and A2 okay so this is
+simply five five 1 and
+
+ align:start position:0%
+simply five five 1 and
+ 
+
+ align:start position:0%
+simply five five 1 and
+one A1 A2 equal to 0 0 so as you saw
+
+ align:start position:0%
+one A1 A2 equal to 0 0 so as you saw
+ 
+
+ align:start position:0%
+one A1 A2 equal to 0 0 so as you saw
+before here basically we can read off
+
+ align:start position:0%
+before here basically we can read off
+ 
+
+ align:start position:0%
+before here basically we can read off
+the equation as being 5 A1 + 5 A2 equal
+
+ align:start position:0%
+the equation as being 5 A1 + 5 A2 equal
+ 
+
+ align:start position:0%
+the equation as being 5 A1 + 5 A2 equal
+to0 and another one which is A1 + A2
+
+ align:start position:0%
+to0 and another one which is A1 + A2
+ 
+
+ align:start position:0%
+to0 and another one which is A1 + A2
+equal to Z they are the same equations
+
+ align:start position:0%
+equal to Z they are the same equations
+ 
+
+ align:start position:0%
+equal to Z they are the same equations
+so really we just have A1 + A2 equal to
+
+ align:start position:0%
+so really we just have A1 + A2 equal to
+ 
+
+ align:start position:0%
+so really we just have A1 + A2 equal to
+zero and so our Vector
+
+ align:start position:0%
+zero and so our Vector
+ 
+
+ align:start position:0%
+zero and so our Vector
+V1 could be picked to just have compon
+
+ align:start position:0%
+V1 could be picked to just have compon
+ 
+
+ align:start position:0%
+V1 could be picked to just have compon
+component one for example A1 equals to
+
+ align:start position:0%
+component one for example A1 equals to
+ 
+
+ align:start position:0%
+component one for example A1 equals to
+one and its second component would just
+
+ align:start position:0%
+one and its second component would just
+ 
+
+ align:start position:0%
+one and its second component would just
+be minus one that would be one pick for
+
+ align:start position:0%
+be minus one that would be one pick for
+ 
+
+ align:start position:0%
+be minus one that would be one pick for
+our V1 okay we could normalize this
+
+ align:start position:0%
+our V1 okay we could normalize this
+ 
+
+ align:start position:0%
+our V1 okay we could normalize this
+Vector if we wanted to I'm just going to
+
+ align:start position:0%
+Vector if we wanted to I'm just going to
+ 
+
+ align:start position:0%
+Vector if we wanted to I'm just going to
+keep it like this for now so if we look
+
+ align:start position:0%
+keep it like this for now so if we look
+ 
+
+ align:start position:0%
+keep it like this for now so if we look
+now for the second negative vector
+
+ align:start position:0%
+now for the second negative vector
+ 
+
+ align:start position:0%
+now for the second negative vector
+corresponding to the second angle value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S I would be looking for the components
+
+ align:start position:0%
+S I would be looking for the components
+ 
+
+ align:start position:0%
+S I would be looking for the components
+of this vector by doing the
+
+ align:start position:0%
+of this vector by doing the
+ 
+
+ align:start position:0%
+of this vector by doing the
+similar solving for the same thing and
+
+ align:start position:0%
+similar solving for the same thing and
+ 
+
+ align:start position:0%
+similar solving for the same thing and
+I'm going to spell it out again so that
+
+ align:start position:0%
+I'm going to spell it out again so that
+ 
+
+ align:start position:0%
+I'm going to spell it out again so that
+you see where the terms are coming from
+
+ align:start position:0%
+you see where the terms are coming from
+ 
+
+ align:start position:0%
+you see where the terms are coming from
+it's just six minus the value of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LDA 0 Z so here we have 6 - 7 which is 1
+
+ align:start position:0%
+LDA 0 Z so here we have 6 - 7 which is 1
+ 
+
+ align:start position:0%
+LDA 0 Z so here we have 6 - 7 which is 1
+five and then we have 1 and 2 - 7 which
+
+ align:start position:0%
+five and then we have 1 and 2 - 7 which
+ 
+
+ align:start position:0%
+five and then we have 1 and 2 - 7 which
+is minus 5 so really what do we have is
+
+ align:start position:0%
+is minus 5 so really what do we have is
+ 
+
+ align:start position:0%
+is minus 5 so really what do we have is
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+min-1 + 5 A2 in both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cases so we can pick a value for V1 for
+
+ align:start position:0%
+cases so we can pick a value for V1 for
+ 
+
+ align:start position:0%
+cases so we can pick a value for V1 for
+A1 or
+
+ align:start position:0%
+A1 or
+ 
+
+ align:start position:0%
+A1 or
+A2 and write down a vector
+
+ align:start position:0%
+A2 and write down a vector
+ 
+
+ align:start position:0%
+A2 and write down a vector
+V2 in for example the form of A1 equals
+
+ align:start position:0%
+V2 in for example the form of A1 equals
+ 
+
+ align:start position:0%
+V2 in for example the form of A1 equals
+to Let's Pi A2 equals to 1 and we would
+
+ align:start position:0%
+to Let's Pi A2 equals to 1 and we would
+ 
+
+ align:start position:0%
+to Let's Pi A2 equals to 1 and we would
+have A1 equal to 5 for example again if
+
+ align:start position:0%
+have A1 equal to 5 for example again if
+ 
+
+ align:start position:0%
+have A1 equal to 5 for example again if
+you wanted an auton normal uh basis
+
+ align:start position:0%
+you wanted an auton normal uh basis
+ 
+
+ align:start position:0%
+you wanted an auton normal uh basis
+formed by your V1 V2 you would just
+
+ align:start position:0%
+formed by your V1 V2 you would just
+ 
+
+ align:start position:0%
+formed by your V1 V2 you would just
+normalize these two
+
+ align:start position:0%
+normalize these two
+ 
+
+ align:start position:0%
+normalize these two
+vectors so here basically we can then
+
+ align:start position:0%
+vectors so here basically we can then
+ 
+
+ align:start position:0%
+vectors so here basically we can then
+rewrite the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution to the original system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as being a linear combinations
+
+ align:start position:0%
+as being a linear combinations
+ 
+
+ align:start position:0%
+as being a linear combinations
+of so I'm just going to write it in
+
+ align:start position:0%
+of so I'm just going to write it in
+ 
+
+ align:start position:0%
+of so I'm just going to write it in
+Vector
+
+ align:start position:0%
+Vector
+ 
+
+ align:start position:0%
+Vector
+form the first
+
+ align:start position:0%
+form the first
+ 
+
+ align:start position:0%
+form the first
+Vector one I keep it in V1 V2 that way
+
+ align:start position:0%
+Vector one I keep it in V1 V2 that way
+ 
+
+ align:start position:0%
+Vector one I keep it in V1 V2 that way
+you see it and then I'll go into the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components we we have V1
+
+ align:start position:0%
+components we we have V1
+ 
+
+ align:start position:0%
+components we we have V1
+exponential of the value of Lambda we
+
+ align:start position:0%
+exponential of the value of Lambda we
+ 
+
+ align:start position:0%
+exponential of the value of Lambda we
+found that corresponds to V1 so it would
+
+ align:start position:0%
+found that corresponds to V1 so it would
+ 
+
+ align:start position:0%
+found that corresponds to V1 so it would
+be 1. T and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V2 exponential of the Lambda value that
+
+ align:start position:0%
+V2 exponential of the Lambda value that
+ 
+
+ align:start position:0%
+V2 exponential of the Lambda value that
+corresponds to
+
+ align:start position:0%
+corresponds to
+ 
+
+ align:start position:0%
+corresponds to
+V2 okay and then uh basically we would
+
+ align:start position:0%
+V2 okay and then uh basically we would
+ 
+
+ align:start position:0%
+V2 okay and then uh basically we would
+just have constants of
+
+ align:start position:0%
+just have constants of
+ 
+
+ align:start position:0%
+just have constants of
+integration here and so the solution to
+
+ align:start position:0%
+integration here and so the solution to
+ 
+
+ align:start position:0%
+integration here and so the solution to
+this problem would be linear combination
+
+ align:start position:0%
+this problem would be linear combination
+ 
+
+ align:start position:0%
+this problem would be linear combination
+of the vectors form by our the bases of
+
+ align:start position:0%
+of the vectors form by our the bases of
+ 
+
+ align:start position:0%
+of the vectors form by our the bases of
+our aen vectors and multiply by the
+
+ align:start position:0%
+our aen vectors and multiply by the
+ 
+
+ align:start position:0%
+our aen vectors and multiply by the
+exponentials assign the values of the a
+
+ align:start position:0%
+exponentials assign the values of the a
+ 
+
+ align:start position:0%
+exponentials assign the values of the a
+values that we found when we looked for
+
+ align:start position:0%
+values that we found when we looked for
+ 
+
+ align:start position:0%
+values that we found when we looked for
+uh the Ang values of the Matrix of the
+
+ align:start position:0%
+uh the Ang values of the Matrix of the
+ 
+
+ align:start position:0%
+uh the Ang values of the Matrix of the
+system so here just note that like for
+
+ align:start position:0%
+system so here just note that like for
+ 
+
+ align:start position:0%
+system so here just note that like for
+the linear like for the 1D problem that
+
+ align:start position:0%
+the linear like for the 1D problem that
+ 
+
+ align:start position:0%
+the linear like for the 1D problem that
+we saw before we're building a solution
+
+ align:start position:0%
+we saw before we're building a solution
+ 
+
+ align:start position:0%
+we saw before we're building a solution
+based on linear combination of of lucky
+
+ align:start position:0%
+based on linear combination of of lucky
+ 
+
+ align:start position:0%
+based on linear combination of of lucky
+guesses that we used and in the one
+
+ align:start position:0%
+guesses that we used and in the one
+ 
+
+ align:start position:0%
+guesses that we used and in the one
+equation case we used a guess of e to
+
+ align:start position:0%
+equation case we used a guess of e to
+ 
+
+ align:start position:0%
+equation case we used a guess of e to
+lamb T in a
+
+ align:start position:0%
+lamb T in a
+ 
+
+ align:start position:0%
+lamb T in a
+1D here in this case we had a g a guess
+
+ align:start position:0%
+1D here in this case we had a g a guess
+ 
+
+ align:start position:0%
+1D here in this case we had a g a guess
+of a vector v in the form of LDA T that
+
+ align:start position:0%
+of a vector v in the form of LDA T that
+ 
+
+ align:start position:0%
+of a vector v in the form of LDA T that
+we used and then basically we just solve
+
+ align:start position:0%
+we used and then basically we just solve
+ 
+
+ align:start position:0%
+we used and then basically we just solve
+for the lendas and solve for the v's and
+
+ align:start position:0%
+for the lendas and solve for the v's and
+ 
+
+ align:start position:0%
+for the lendas and solve for the v's and
+did a linear combination of all those
+
+ align:start position:0%
+did a linear combination of all those
+ 
+
+ align:start position:0%
+did a linear combination of all those
+Solutions like we did before in the 1D
+
+ align:start position:0%
+Solutions like we did before in the 1D
+ 
+
+ align:start position:0%
+Solutions like we did before in the 1D
+case we softed out the lenda we had
+
+ align:start position:0%
+case we softed out the lenda we had
+ 
+
+ align:start position:0%
+case we softed out the lenda we had
+different values of lenda we did linear
+
+ align:start position:0%
+different values of lenda we did linear
+ 
+
+ align:start position:0%
+different values of lenda we did linear
+combinations of those exponentials so
+
+ align:start position:0%
+combinations of those exponentials so
+ 
+
+ align:start position:0%
+combinations of those exponentials so
+that ends this problem and here the key
+
+ align:start position:0%
+that ends this problem and here the key
+ 
+
+ align:start position:0%
+that ends this problem and here the key
+is just to go through the method of
+
+ align:start position:0%
+is just to go through the method of
+ 
+
+ align:start position:0%
+is just to go through the method of
+diagonalizing your Matrix basically it's
+
+ align:start position:0%
+diagonalizing your Matrix basically it's
+ 
+
+ align:start position:0%
+diagonalizing your Matrix basically it's
+finding the aen values and then
+
+ align:start position:0%
+finding the aen values and then
+ 
+
+ align:start position:0%
+finding the aen values and then
+Computing the aen vectors associated
+
+ align:start position:0%
+Computing the aen vectors associated
+ 
+
+ align:start position:0%
+Computing the aen vectors associated
+with that and writing your Solutions in
+
+ align:start position:0%
+with that and writing your Solutions in
+ 
+
+ align:start position:0%
+with that and writing your Solutions in
+terms of linear combination of the
+
+ align:start position:0%
+terms of linear combination of the
+ 
+
+ align:start position:0%
+terms of linear combination of the
+solution that you found
\ No newline at end of file
diff --git a/Yarwp7TNTL4.txt b/Yarwp7TNTL4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f143b75511c0945c7d3d9137bfb106efdfa27cef
--- /dev/null
+++ b/Yarwp7TNTL4.txt
@@ -0,0 +1,13344 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right welcome to my last
+
+ align:start position:0%
+ocw.mit.edu all right welcome to my last
+ 
+
+ align:start position:0%
+ocw.mit.edu all right welcome to my last
+lecture for the semester um we finish
+
+ align:start position:0%
+lecture for the semester um we finish
+ 
+
+ align:start position:0%
+lecture for the semester um we finish
+our coverage of dynamic graphs and also
+
+ align:start position:0%
+our coverage of dynamic graphs and also
+ 
+
+ align:start position:0%
+our coverage of dynamic graphs and also
+our coverage of lower bounds we saw one
+
+ align:start position:0%
+our coverage of lower bounds we saw one
+ 
+
+ align:start position:0%
+our coverage of lower bounds we saw one
+big lower Bound in this class uh in the
+
+ align:start position:0%
+big lower Bound in this class uh in the
+ 
+
+ align:start position:0%
+big lower Bound in this class uh in the
+cell probe model you may recall cell
+
+ align:start position:0%
+cell probe model you may recall cell
+ 
+
+ align:start position:0%
+cell probe model you may recall cell
+probe model you just count how many
+
+ align:start position:0%
+probe model you just count how many
+ 
+
+ align:start position:0%
+probe model you just count how many
+cells of memory do you
+
+ align:start position:0%
+cells of memory do you
+ 
+
+ align:start position:0%
+cells of memory do you
+touch uh you want to prove a lower bound
+
+ align:start position:0%
+touch uh you want to prove a lower bound
+ 
+
+ align:start position:0%
+touch uh you want to prove a lower bound
+on that uh and today we're going to
+
+ align:start position:0%
+on that uh and today we're going to
+ 
+
+ align:start position:0%
+on that uh and today we're going to
+prove a cell prob lower bound on Dynamic
+
+ align:start position:0%
+prove a cell prob lower bound on Dynamic
+ 
+
+ align:start position:0%
+prove a cell prob lower bound on Dynamic
+connectivity uh which is a problem we've
+
+ align:start position:0%
+connectivity uh which is a problem we've
+ 
+
+ align:start position:0%
+connectivity uh which is a problem we've
+solved a few different times our lower
+
+ align:start position:0%
+solved a few different times our lower
+ 
+
+ align:start position:0%
+solved a few different times our lower
+bound will apply even when each of the
+
+ align:start position:0%
+bound will apply even when each of the
+ 
+
+ align:start position:0%
+bound will apply even when each of the
+connected compon components of your
+
+ align:start position:0%
+connected compon components of your
+ 
+
+ align:start position:0%
+connected compon components of your
+graph are just a
+
+ align:start position:0%
+graph are just a
+ 
+
+ align:start position:0%
+graph are just a
+path and so in particular they imply
+
+ align:start position:0%
+path and so in particular they imply
+ 
+
+ align:start position:0%
+path and so in particular they imply
+matching lower bounds for dynamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees so here's the theorem we'll be
+
+ align:start position:0%
+trees so here's the theorem we'll be
+ 
+
+ align:start position:0%
+trees so here's the theorem we'll be
+proving today uh you want to
+
+ align:start position:0%
+proving today uh you want to
+ 
+
+ align:start position:0%
+proving today uh you want to
+insert and delete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges and do connectivity queries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh between Pairs of vertices
+
+ align:start position:0%
+uh between Pairs of vertices
+ 
+
+ align:start position:0%
+uh between Pairs of vertices
+VW I want to know is there a path from V
+
+ align:start position:0%
+VW I want to know is there a path from V
+ 
+
+ align:start position:0%
+VW I want to know is there a path from V
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+W just like we've been
+
+ align:start position:0%
+W just like we've been
+ 
+
+ align:start position:0%
+W just like we've been
+considering
+
+ align:start position:0%
+considering
+ 
+
+ align:start position:0%
+considering
+um these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+require Omega log n uh time per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operation this is the max of update and
+
+ align:start position:0%
+operation this is the max of update and
+ 
+
+ align:start position:0%
+operation this is the max of update and
+query times has to be at least log n
+
+ align:start position:0%
+query times has to be at least log n
+ 
+
+ align:start position:0%
+query times has to be at least log n
+time proper
+
+ align:start position:0%
+time proper
+ 
+
+ align:start position:0%
+time proper
+operation uh
+
+ align:start position:0%
+operation uh
+ 
+
+ align:start position:0%
+operation uh
+even if the connected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paths and even amortized and even
+
+ align:start position:0%
+paths and even amortized and even
+ 
+
+ align:start position:0%
+paths and even amortized and even
+randomized although I'm not going to
+
+ align:start position:0%
+randomized although I'm not going to
+ 
+
+ align:start position:0%
+randomized although I'm not going to
+prove all of these versions I I won't
+
+ align:start position:0%
+prove all of these versions I I won't
+ 
+
+ align:start position:0%
+prove all of these versions I I won't
+prove the amortized version I'm going to
+
+ align:start position:0%
+prove the amortized version I'm going to
+ 
+
+ align:start position:0%
+prove the amortized version I'm going to
+prove a worst case log and lower bound
+
+ align:start position:0%
+prove a worst case log and lower bound
+ 
+
+ align:start position:0%
+prove a worst case log and lower bound
+it's just a little more work to prove an
+
+ align:start position:0%
+it's just a little more work to prove an
+ 
+
+ align:start position:0%
+it's just a little more work to prove an
+amortized lower bound uh but same same
+
+ align:start position:0%
+amortized lower bound uh but same same
+ 
+
+ align:start position:0%
+amortized lower bound uh but same same
+principles and so that's going to
+
+ align:start position:0%
+principles and so that's going to
+ 
+
+ align:start position:0%
+principles and so that's going to
+be today is proving this theorem uh it's
+
+ align:start position:0%
+be today is proving this theorem uh it's
+ 
+
+ align:start position:0%
+be today is proving this theorem uh it's
+not short proof but it combines a bunch
+
+ align:start position:0%
+not short proof but it combines a bunch
+ 
+
+ align:start position:0%
+not short proof but it combines a bunch
+of relatively simple ideas uh and ends
+
+ align:start position:0%
+of relatively simple ideas uh and ends
+ 
+
+ align:start position:0%
+of relatively simple ideas uh and ends
+up being pretty clean overall piece by
+
+ align:start position:0%
+up being pretty clean overall piece by
+ 
+
+ align:start position:0%
+up being pretty clean overall piece by
+piece but there's just a bunch of pieces
+
+ align:start position:0%
+piece but there's just a bunch of pieces
+ 
+
+ align:start position:0%
+piece but there's just a bunch of pieces
+as we will get to key concept is an idea
+
+ align:start position:0%
+as we will get to key concept is an idea
+ 
+
+ align:start position:0%
+as we will get to key concept is an idea
+uh introduced in this paper which is uh
+
+ align:start position:0%
+uh introduced in this paper which is uh
+ 
+
+ align:start position:0%
+uh introduced in this paper which is uh
+to build build a balance binary tree
+
+ align:start position:0%
+to build build a balance binary tree
+ 
+
+ align:start position:0%
+to build build a balance binary tree
+over time over your access sequence and
+
+ align:start position:0%
+over time over your access sequence and
+ 
+
+ align:start position:0%
+over time over your access sequence and
+argue about different sub trees within
+
+ align:start position:0%
+argue about different sub trees within
+ 
+
+ align:start position:0%
+argue about different sub trees within
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+tree uh this is a
+
+ align:start position:0%
+tree uh this is a
+ 
+
+ align:start position:0%
+tree uh this is a
+paper uh that maybe came out of this
+
+ align:start position:0%
+paper uh that maybe came out of this
+ 
+
+ align:start position:0%
+paper uh that maybe came out of this
+class in some sense it was uh by Mii
+
+ align:start position:0%
+class in some sense it was uh by Mii
+ 
+
+ align:start position:0%
+class in some sense it was uh by Mii
+patashu and myself uh back when Mii was
+
+ align:start position:0%
+patashu and myself uh back when Mii was
+ 
+
+ align:start position:0%
+patashu and myself uh back when Mii was
+an undergrad I think he'd just taken
+
+ align:start position:0%
+an undergrad I think he'd just taken
+ 
+
+ align:start position:0%
+an undergrad I think he'd just taken
+this class uh but at that point the
+
+ align:start position:0%
+this class uh but at that point the
+ 
+
+ align:start position:0%
+this class uh but at that point the
+class didn't even cover Dynamic
+
+ align:start position:0%
+class didn't even cover Dynamic
+ 
+
+ align:start position:0%
+class didn't even cover Dynamic
+connectivity
+
+ align:start position:0%
+connectivity
+ 
+
+ align:start position:0%
+connectivity
+so uh uh and time here is cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probes so this is a very strong model uh
+
+ align:start position:0%
+probes so this is a very strong model uh
+ 
+
+ align:start position:0%
+probes so this is a very strong model uh
+it implies a lower bound on RAM it
+
+ align:start position:0%
+it implies a lower bound on RAM it
+ 
+
+ align:start position:0%
+it implies a lower bound on RAM it
+implies lower bound on pointer machine
+
+ align:start position:0%
+implies lower bound on pointer machine
+ 
+
+ align:start position:0%
+implies lower bound on pointer machine
+we know matching upper bounds for trees
+
+ align:start position:0%
+we know matching upper bounds for trees
+ 
+
+ align:start position:0%
+we know matching upper bounds for trees
+on a pointer machine uh link cut trees
+
+ align:start position:0%
+on a pointer machine uh link cut trees
+ 
+
+ align:start position:0%
+on a pointer machine uh link cut trees
+and Oiler tour trees it's kind of fun
+
+ align:start position:0%
+and Oiler tour trees it's kind of fun
+ 
+
+ align:start position:0%
+and Oiler tour trees it's kind of fun
+that this lower bound even applies to
+
+ align:start position:0%
+that this lower bound even applies to
+ 
+
+ align:start position:0%
+that this lower bound even applies to
+paths because most of the work in link
+
+ align:start position:0%
+paths because most of the work in link
+ 
+
+ align:start position:0%
+paths because most of the work in link
+cut trees is about decomposing your tree
+
+ align:start position:0%
+cut trees is about decomposing your tree
+ 
+
+ align:start position:0%
+cut trees is about decomposing your tree
+into paths and so what this is saying is
+
+ align:start position:0%
+into paths and so what this is saying is
+ 
+
+ align:start position:0%
+into paths and so what this is saying is
+even if that's done for you and you just
+
+ align:start position:0%
+even if that's done for you and you just
+ 
+
+ align:start position:0%
+even if that's done for you and you just
+need to be able to take paths and
+
+ align:start position:0%
+need to be able to take paths and
+ 
+
+ align:start position:0%
+need to be able to take paths and
+concatenate them together by adding
+
+ align:start position:0%
+concatenate them together by adding
+ 
+
+ align:start position:0%
+concatenate them together by adding
+edges uh then maintaining the find root
+
+ align:start position:0%
+edges uh then maintaining the find root
+ 
+
+ align:start position:0%
+edges uh then maintaining the find root
+property so that you can do connectivity
+
+ align:start position:0%
+property so that you can do connectivity
+ 
+
+ align:start position:0%
+property so that you can do connectivity
+queries even that requires log and time
+
+ align:start position:0%
+queries even that requires log and time
+ 
+
+ align:start position:0%
+queries even that requires log and time
+so the converting a tree into a path is
+
+ align:start position:0%
+so the converting a tree into a path is
+ 
+
+ align:start position:0%
+so the converting a tree into a path is
+basically free uh the hard part is
+
+ align:start position:0%
+basically free uh the hard part is
+ 
+
+ align:start position:0%
+basically free uh the hard part is
+maintaining the
+
+ align:start position:0%
+maintaining the
+ 
+
+ align:start position:0%
+maintaining the
+paths
+
+ align:start position:0%
+paths
+ 
+
+ align:start position:0%
+paths
+so let's prove the
+
+ align:start position:0%
+so let's prove the
+ 
+
+ align:start position:0%
+so let's prove the
+theorem uh the lower bound we get to
+
+ align:start position:0%
+theorem uh the lower bound we get to
+ 
+
+ align:start position:0%
+theorem uh the lower bound we get to
+choose what access sequence we think is
+
+ align:start position:0%
+choose what access sequence we think is
+ 
+
+ align:start position:0%
+choose what access sequence we think is
+bad and so we're going to uh come up
+
+ align:start position:0%
+bad and so we're going to uh come up
+ 
+
+ align:start position:0%
+bad and so we're going to uh come up
+with a particular style of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph which looks like the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following graph is going to be the
+
+ align:start position:0%
+following graph is going to be the
+ 
+
+ align:start position:0%
+following graph is going to be the
+vertices are going to be a root n by
+
+ align:start position:0%
+vertices are going to be a root n by
+ 
+
+ align:start position:0%
+vertices are going to be a root n by
+root n
+
+ align:start position:0%
+root n
+ 
+
+ align:start position:0%
+root n
+grid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh we're going to these guys are in
+
+ align:start position:0%
+and uh we're going to these guys are in
+ 
+
+ align:start position:0%
+and uh we're going to these guys are in
+what do I call them groups columns
+
+ align:start position:0%
+what do I call them groups columns
+ 
+
+ align:start position:0%
+what do I call them groups columns
+columns is good name these are columns
+
+ align:start position:0%
+columns is good name these are columns
+ 
+
+ align:start position:0%
+columns is good name these are columns
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+Matrix or vertices and what I'd like to
+
+ align:start position:0%
+Matrix or vertices and what I'd like to
+ 
+
+ align:start position:0%
+Matrix or vertices and what I'd like to
+have is between consecutive columns I
+
+ align:start position:0%
+have is between consecutive columns I
+ 
+
+ align:start position:0%
+have is between consecutive columns I
+want to have a perfect matching between
+
+ align:start position:0%
+want to have a perfect matching between
+ 
+
+ align:start position:0%
+want to have a perfect matching between
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+vertices so could be I don't know this
+
+ align:start position:0%
+vertices so could be I don't know this
+ 
+
+ align:start position:0%
+vertices so could be I don't know this
+Edge this Edge this Edge and that edge
+
+ align:start position:0%
+Edge this Edge this Edge and that edge
+ 
+
+ align:start position:0%
+Edge this Edge this Edge and that edge
+and I also want a perfect matching
+
+ align:start position:0%
+and I also want a perfect matching
+ 
+
+ align:start position:0%
+and I also want a perfect matching
+between these two columns so maybe this
+
+ align:start position:0%
+between these two columns so maybe this
+ 
+
+ align:start position:0%
+between these two columns so maybe this
+one this
+
+ align:start position:0%
+one this
+ 
+
+ align:start position:0%
+one this
+one uh this one this
+
+ align:start position:0%
+one uh this one this
+ 
+
+ align:start position:0%
+one uh this one this
+one and I know you can have some boring
+
+ align:start position:0%
+one and I know you can have some boring
+ 
+
+ align:start position:0%
+one and I know you can have some boring
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+too something like that so between every
+
+ align:start position:0%
+too something like that so between every
+ 
+
+ align:start position:0%
+too something like that so between every
+pair of columns is a perfect
+
+ align:start position:0%
+pair of columns is a perfect
+ 
+
+ align:start position:0%
+pair of columns is a perfect
+matching meaning perfect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pairing okay this of course results in a
+
+ align:start position:0%
+pairing okay this of course results in a
+ 
+
+ align:start position:0%
+pairing okay this of course results in a
+collection of paths square root of n
+
+ align:start position:0%
+collection of paths square root of n
+ 
+
+ align:start position:0%
+collection of paths square root of n
+paths you can start at any vertex on the
+
+ align:start position:0%
+paths you can start at any vertex on the
+ 
+
+ align:start position:0%
+paths you can start at any vertex on the
+left and you'll have a unique way to go
+
+ align:start position:0%
+left and you'll have a unique way to go
+ 
+
+ align:start position:0%
+left and you'll have a unique way to go
+to the right and so that's your that's
+
+ align:start position:0%
+to the right and so that's your that's
+ 
+
+ align:start position:0%
+to the right and so that's your that's
+path one this is path two this is path
+
+ align:start position:0%
+path one this is path two this is path
+ 
+
+ align:start position:0%
+path one this is path two this is path
+three and this is path
+
+ align:start position:0%
+three and this is path
+ 
+
+ align:start position:0%
+three and this is path
+four and so if I an interesting
+
+ align:start position:0%
+four and so if I an interesting
+ 
+
+ align:start position:0%
+four and so if I an interesting
+query well I mean interesting query is
+
+ align:start position:0%
+query well I mean interesting query is
+ 
+
+ align:start position:0%
+query well I mean interesting query is
+something like I want to know is this
+
+ align:start position:0%
+something like I want to know is this
+ 
+
+ align:start position:0%
+something like I want to know is this
+vertex connected to this one uh it's not
+
+ align:start position:0%
+vertex connected to this one uh it's not
+ 
+
+ align:start position:0%
+vertex connected to this one uh it's not
+so easy to figure it out because you
+
+ align:start position:0%
+so easy to figure it out because you
+ 
+
+ align:start position:0%
+so easy to figure it out because you
+have to sort of walk through this path
+
+ align:start position:0%
+have to sort of walk through this path
+ 
+
+ align:start position:0%
+have to sort of walk through this path
+to to figure that out we're going to
+
+ align:start position:0%
+to to figure that out we're going to
+ 
+
+ align:start position:0%
+to to figure that out we're going to
+think of each of these perfect matchings
+
+ align:start position:0%
+think of each of these perfect matchings
+ 
+
+ align:start position:0%
+think of each of these perfect matchings
+as defining a
+
+ align:start position:0%
+as defining a
+ 
+
+ align:start position:0%
+as defining a
+permutation on the vertices on the
+
+ align:start position:0%
+permutation on the vertices on the
+ 
+
+ align:start position:0%
+permutation on the vertices on the
+column really so you start with the
+
+ align:start position:0%
+column really so you start with the
+ 
+
+ align:start position:0%
+column really so you start with the
+identity permutation and then some
+
+ align:start position:0%
+identity permutation and then some
+ 
+
+ align:start position:0%
+identity permutation and then some
+things get swapped around that's Pi 1
+
+ align:start position:0%
+things get swapped around that's Pi 1
+ 
+
+ align:start position:0%
+things get swapped around that's Pi 1
+some things get swapped around again
+
+ align:start position:0%
+some things get swapped around again
+ 
+
+ align:start position:0%
+some things get swapped around again
+that's Pi 2 some things get swapped
+
+ align:start position:0%
+that's Pi 2 some things get swapped
+ 
+
+ align:start position:0%
+that's Pi 2 some things get swapped
+around here that's Pi 3 and then this
+
+ align:start position:0%
+around here that's Pi 3 and then this
+ 
+
+ align:start position:0%
+around here that's Pi 3 and then this
+position would be uh Pi 3 of Pi 2 of Pi
+
+ align:start position:0%
+position would be uh Pi 3 of Pi 2 of Pi
+ 
+
+ align:start position:0%
+position would be uh Pi 3 of Pi 2 of Pi
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+of Vertex
+
+ align:start position:0%
+of Vertex
+ 
+
+ align:start position:0%
+of Vertex
+4 we call this Vertex
+
+ align:start position:0%
+4 we call this Vertex
+ 
+
+ align:start position:0%
+4 we call this Vertex
+4 or Row Row
+
+ align:start position:0%
+4 or Row Row
+ 
+
+ align:start position:0%
+4 or Row Row
+4 so in some sense we have to compose
+
+ align:start position:0%
+4 so in some sense we have to compose
+ 
+
+ align:start position:0%
+4 so in some sense we have to compose
+permutations I'll call this Pi 1 circle
+
+ align:start position:0%
+permutations I'll call this Pi 1 circle
+ 
+
+ align:start position:0%
+permutations I'll call this Pi 1 circle
+Pi 2 Circle
+
+ align:start position:0%
+Pi 2 Circle
+ 
+
+ align:start position:0%
+Pi 2 Circle
+pi3 uh of
+
+ align:start position:0%
+pi3 uh of
+ 
+
+ align:start position:0%
+pi3 uh of
+four and we're going to show basically
+
+ align:start position:0%
+four and we're going to show basically
+ 
+
+ align:start position:0%
+four and we're going to show basically
+composing permutations is tough when you
+
+ align:start position:0%
+composing permutations is tough when you
+ 
+
+ align:start position:0%
+composing permutations is tough when you
+can change those permutations
+
+ align:start position:0%
+can change those permutations
+ 
+
+ align:start position:0%
+can change those permutations
+dynamically so what we're going to do is
+
+ align:start position:0%
+dynamically so what we're going to do is
+ 
+
+ align:start position:0%
+dynamically so what we're going to do is
+a series of block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operations which uh change or query
+
+ align:start position:0%
+operations which uh change or query
+ 
+
+ align:start position:0%
+operations which uh change or query
+entire
+
+ align:start position:0%
+entire
+ 
+
+ align:start position:0%
+entire
+permutations so here an
+
+ align:start position:0%
+permutations so here an
+ 
+
+ align:start position:0%
+permutations so here an
+update is going to be a whole bunch of
+
+ align:start position:0%
+update is going to be a whole bunch of
+ 
+
+ align:start position:0%
+update is going to be a whole bunch of
+uh insertions and deletions of
+
+ align:start position:0%
+uh insertions and deletions of
+ 
+
+ align:start position:0%
+uh insertions and deletions of
+edges basically what we want to do is
+
+ align:start position:0%
+edges basically what we want to do is
+ 
+
+ align:start position:0%
+edges basically what we want to do is
+set Pi I equal to
+
+ align:start position:0%
+set Pi I equal to
+ 
+
+ align:start position:0%
+set Pi I equal to
+Pi so that's what update of I comma Pi
+
+ align:start position:0%
+Pi so that's what update of I comma Pi
+ 
+
+ align:start position:0%
+Pi so that's what update of I comma Pi
+does it changes an entire perfect
+
+ align:start position:0%
+does it changes an entire perfect
+ 
+
+ align:start position:0%
+does it changes an entire perfect
+matching to be a specified permutation
+
+ align:start position:0%
+matching to be a specified permutation
+ 
+
+ align:start position:0%
+matching to be a specified permutation
+so how do you do that well you delete
+
+ align:start position:0%
+so how do you do that well you delete
+ 
+
+ align:start position:0%
+so how do you do that well you delete
+all the edges that are in the existing
+
+ align:start position:0%
+all the edges that are in the existing
+ 
+
+ align:start position:0%
+all the edges that are in the existing
+permutation and then you insert all the
+
+ align:start position:0%
+permutation and then you insert all the
+ 
+
+ align:start position:0%
+permutation and then you insert all the
+new edges so this can be done in
+
+ align:start position:0%
+new edges so this can be done in
+ 
+
+ align:start position:0%
+new edges so this can be done in
+uh square root of n Edge deletions and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+insertions so it's a bulk update of
+
+ align:start position:0%
+insertions so it's a bulk update of
+ 
+
+ align:start position:0%
+insertions so it's a bulk update of
+square of V operations and so this could
+
+ align:start position:0%
+square of V operations and so this could
+ 
+
+ align:start position:0%
+square of V operations and so this could
+only make our problem easier because
+
+ align:start position:0%
+only make our problem easier because
+ 
+
+ align:start position:0%
+only make our problem easier because
+we're given Square event updates that we
+
+ align:start position:0%
+we're given Square event updates that we
+ 
+
+ align:start position:0%
+we're given Square event updates that we
+all need to do at once uh so you could
+
+ align:start position:0%
+all need to do at once uh so you could
+ 
+
+ align:start position:0%
+all need to do at once uh so you could
+amortise over them you could do lots of
+
+ align:start position:0%
+amortise over them you could do lots of
+ 
+
+ align:start position:0%
+amortise over them you could do lots of
+different things uh but we're sure that
+
+ align:start position:0%
+different things uh but we're sure that
+ 
+
+ align:start position:0%
+different things uh but we're sure that
+won't won't
+
+ align:start position:0%
+won't won't
+ 
+
+ align:start position:0%
+won't won't
+help and then we have a
+
+ align:start position:0%
+help and then we have a
+ 
+
+ align:start position:0%
+help and then we have a
+query and the query is going to it's
+
+ align:start position:0%
+query and the query is going to it's
+ 
+
+ align:start position:0%
+query and the query is going to it's
+going to be a little bit
+
+ align:start position:0%
+going to be a little bit
+ 
+
+ align:start position:0%
+going to be a little bit
+weird and it's also going to make the
+
+ align:start position:0%
+weird and it's also going to make the
+ 
+
+ align:start position:0%
+weird and it's also going to make the
+proof a little bit more
+
+ align:start position:0%
+proof a little bit more
+ 
+
+ align:start position:0%
+proof a little bit more
+awkward but what it asks
+
+ align:start position:0%
+awkward but what it asks
+ 
+
+ align:start position:0%
+awkward but what it asks
+is if I look at the
+
+ align:start position:0%
+is if I look at the
+ 
+
+ align:start position:0%
+is if I look at the
+composition of Pi J from one up to
+
+ align:start position:0%
+composition of Pi J from one up to
+ 
+
+ align:start position:0%
+composition of Pi J from one up to
+I this is
+
+ align:start position:0%
+I this is
+ 
+
+ align:start position:0%
+I this is
+one to I I want to know is that
+
+ align:start position:0%
+one to I I want to know is that
+ 
+
+ align:start position:0%
+one to I I want to know is that
+composition equal to
+
+ align:start position:0%
+composition equal to
+ 
+
+ align:start position:0%
+composition equal to
+Pi yes or no this is what I'll call
+
+ align:start position:0%
+Pi yes or no this is what I'll call
+ 
+
+ align:start position:0%
+Pi yes or no this is what I'll call
+verify sum sum meaning composition uh
+
+ align:start position:0%
+verify sum sum meaning composition uh
+ 
+
+ align:start position:0%
+verify sum sum meaning composition uh
+but the sum terminology comes from a
+
+ align:start position:0%
+but the sum terminology comes from a
+ 
+
+ align:start position:0%
+but the sum terminology comes from a
+different problem which we won't talk
+
+ align:start position:0%
+different problem which we won't talk
+ 
+
+ align:start position:0%
+different problem which we won't talk
+about directly here called partial sums
+
+ align:start position:0%
+about directly here called partial sums
+ 
+
+ align:start position:0%
+about directly here called partial sums
+this partial sums is basically this
+
+ align:start position:0%
+this partial sums is basically this
+ 
+
+ align:start position:0%
+this partial sums is basically this
+problem you can change numbers in an
+
+ align:start position:0%
+problem you can change numbers in an
+ 
+
+ align:start position:0%
+problem you can change numbers in an
+array
+
+ align:start position:0%
+array
+ 
+
+ align:start position:0%
+array
+and you can compute the prefix sum from
+
+ align:start position:0%
+and you can compute the prefix sum from
+ 
+
+ align:start position:0%
+and you can compute the prefix sum from
+one up to I here we're not Computing it
+
+ align:start position:0%
+one up to I here we're not Computing it
+ 
+
+ align:start position:0%
+one up to I here we're not Computing it
+uh why are we not Computing it because
+
+ align:start position:0%
+uh why are we not Computing it because
+ 
+
+ align:start position:0%
+uh why are we not Computing it because
+actually figuring out what pi 3 of Pi 2
+
+ align:start position:0%
+actually figuring out what pi 3 of Pi 2
+ 
+
+ align:start position:0%
+actually figuring out what pi 3 of Pi 2
+of Pi 1 is of something is tricky in
+
+ align:start position:0%
+of Pi 1 is of something is tricky in
+ 
+
+ align:start position:0%
+of Pi 1 is of something is tricky in
+this setting what we the operations
+
+ align:start position:0%
+this setting what we the operations
+ 
+
+ align:start position:0%
+this setting what we the operations
+we're given are given two vertices are
+
+ align:start position:0%
+we're given are given two vertices are
+ 
+
+ align:start position:0%
+we're given are given two vertices are
+they connected by a
+
+ align:start position:0%
+they connected by a
+ 
+
+ align:start position:0%
+they connected by a
+path uh so to figure out where the other
+
+ align:start position:0%
+path uh so to figure out where the other
+ 
+
+ align:start position:0%
+path uh so to figure out where the other
+end of this path that
+
+ align:start position:0%
+end of this path that
+ 
+
+ align:start position:0%
+end of this path that
+requires I mean it's hard to figure out
+
+ align:start position:0%
+requires I mean it's hard to figure out
+ 
+
+ align:start position:0%
+requires I mean it's hard to figure out
+where the other end is if I told you is
+
+ align:start position:0%
+where the other end is if I told you is
+ 
+
+ align:start position:0%
+where the other end is if I told you is
+it is it this one then I can answer that
+
+ align:start position:0%
+it is it this one then I can answer that
+ 
+
+ align:start position:0%
+it is it this one then I can answer that
+question with just a connectivity query
+
+ align:start position:0%
+question with just a connectivity query
+ 
+
+ align:start position:0%
+question with just a connectivity query
+so verify sum can be done with order
+
+ align:start position:0%
+so verify sum can be done with order
+ 
+
+ align:start position:0%
+so verify sum can be done with order
+square root of
+
+ align:start position:0%
+square root of
+ 
+
+ align:start position:0%
+square root of
+n uh connectivity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+queries whereas Computing the sum could
+
+ align:start position:0%
+queries whereas Computing the sum could
+ 
+
+ align:start position:0%
+queries whereas Computing the sum could
+not be as far as we know uh if I tell
+
+ align:start position:0%
+not be as far as we know uh if I tell
+ 
+
+ align:start position:0%
+not be as far as we know uh if I tell
+you what the what that composition is
+
+ align:start position:0%
+you what the what that composition is
+ 
+
+ align:start position:0%
+you what the what that composition is
+supposed to be I can check oh does four
+
+ align:start position:0%
+supposed to be I can check oh does four
+ 
+
+ align:start position:0%
+supposed to be I can check oh does four
+go to one yes or no does three go to
+
+ align:start position:0%
+go to one yes or no does three go to
+ 
+
+ align:start position:0%
+go to one yes or no does three go to
+three yes or no does two go to four yes
+
+ align:start position:0%
+three yes or no does two go to four yes
+ 
+
+ align:start position:0%
+three yes or no does two go to four yes
+or no does one go to two yes or no so
+
+ align:start position:0%
+or no does one go to two yes or no so
+ 
+
+ align:start position:0%
+or no does one go to two yes or no so
+with four queries I can check whether
+
+ align:start position:0%
+with four queries I can check whether
+ 
+
+ align:start position:0%
+with four queries I can check whether
+the permutation is what it
+
+ align:start position:0%
+the permutation is what it
+ 
+
+ align:start position:0%
+the permutation is what it
+is uh if any of those fail then I return
+
+ align:start position:0%
+is uh if any of those fail then I return
+ 
+
+ align:start position:0%
+is uh if any of those fail then I return
+no um so I mean the way this proceed is
+
+ align:start position:0%
+no um so I mean the way this proceed is
+ 
+
+ align:start position:0%
+no um so I mean the way this proceed is
+first we proved a lower bound on partial
+
+ align:start position:0%
+first we proved a lower bound on partial
+ 
+
+ align:start position:0%
+first we proved a lower bound on partial
+sums uh which is Computing this value
+
+ align:start position:0%
+sums uh which is Computing this value
+ 
+
+ align:start position:0%
+sums uh which is Computing this value
+when you're not not told what the answer
+
+ align:start position:0%
+when you're not not told what the answer
+ 
+
+ align:start position:0%
+when you're not not told what the answer
+is and then we extended that Pro and
+
+ align:start position:0%
+is and then we extended that Pro and
+ 
+
+ align:start position:0%
+is and then we extended that Pro and
+we'll we'll do such a proof here today
+
+ align:start position:0%
+we'll we'll do such a proof here today
+ 
+
+ align:start position:0%
+we'll we'll do such a proof here today
+first we're going to prove a lower bound
+
+ align:start position:0%
+first we're going to prove a lower bound
+ 
+
+ align:start position:0%
+first we're going to prove a lower bound
+on the sum operation which is Computing
+
+ align:start position:0%
+on the sum operation which is Computing
+ 
+
+ align:start position:0%
+on the sum operation which is Computing
+this value that's on our outline over
+
+ align:start position:0%
+this value that's on our outline over
+ 
+
+ align:start position:0%
+this value that's on our outline over
+here sum lower
+
+ align:start position:0%
+here sum lower
+ 
+
+ align:start position:0%
+here sum lower
+bounds uh and then we'll extend that
+
+ align:start position:0%
+bounds uh and then we'll extend that
+ 
+
+ align:start position:0%
+bounds uh and then we'll extend that
+make the argument a little bit more
+
+ align:start position:0%
+make the argument a little bit more
+ 
+
+ align:start position:0%
+make the argument a little bit more
+complicated then we'll get an actual
+
+ align:start position:0%
+complicated then we'll get an actual
+ 
+
+ align:start position:0%
+complicated then we'll get an actual
+connectivity lower bound a lower bound
+
+ align:start position:0%
+connectivity lower bound a lower bound
+ 
+
+ align:start position:0%
+connectivity lower bound a lower bound
+on verify
+
+ align:start position:0%
+on verify
+ 
+
+ align:start position:0%
+on verify
+sum okay but obviously if we can prove
+
+ align:start position:0%
+sum okay but obviously if we can prove
+ 
+
+ align:start position:0%
+sum okay but obviously if we can prove
+uh that these operations take a long
+
+ align:start position:0%
+uh that these operations take a long
+ 
+
+ align:start position:0%
+uh that these operations take a long
+time to do
+
+ align:start position:0%
+time to do
+ 
+
+ align:start position:0%
+time to do
+we can prove that these original
+
+ align:start position:0%
+we can prove that these original
+ 
+
+ align:start position:0%
+we can prove that these original
+operations take a long time to do
+
+ align:start position:0%
+operations take a long time to do
+ 
+
+ align:start position:0%
+operations take a long time to do
+so what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claim is that uh square root of n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+updates these uh block updates plus
+
+ align:start position:0%
+updates these uh block updates plus
+ 
+
+ align:start position:0%
+updates these uh block updates plus
+square root of n uh verify sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+queries uh require
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+root n * root n log
+
+ align:start position:0%
+root n * root n log
+ 
+
+ align:start position:0%
+root n * root n log
+n cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probes I guess this is the amortised
+
+ align:start position:0%
+probes I guess this is the amortised
+ 
+
+ align:start position:0%
+probes I guess this is the amortised
+claim so if I want to do Ruden updates
+
+ align:start position:0%
+claim so if I want to do Ruden updates
+ 
+
+ align:start position:0%
+claim so if I want to do Ruden updates
+and roten queries and I take rud * roten
+
+ align:start position:0%
+and roten queries and I take rud * roten
+ 
+
+ align:start position:0%
+and roten queries and I take rud * roten
+time log n funny way of writing n logn
+
+ align:start position:0%
+time log n funny way of writing n logn
+ 
+
+ align:start position:0%
+time log n funny way of writing n logn
+uh cell probes then uh if I divide
+
+ align:start position:0%
+uh cell probes then uh if I divide
+ 
+
+ align:start position:0%
+uh cell probes then uh if I divide
+through I want the amortized lower bound
+
+ align:start position:0%
+through I want the amortized lower bound
+ 
+
+ align:start position:0%
+through I want the amortized lower bound
+I I lose one of these root ends because
+
+ align:start position:0%
+I I lose one of these root ends because
+ 
+
+ align:start position:0%
+I I lose one of these root ends because
+I'm doing different operations I lose
+
+ align:start position:0%
+I'm doing different operations I lose
+ 
+
+ align:start position:0%
+I'm doing different operations I lose
+another root n because each of these
+
+ align:start position:0%
+another root n because each of these
+ 
+
+ align:start position:0%
+another root n because each of these
+updates corresponds to root n operations
+
+ align:start position:0%
+updates corresponds to root n operations
+ 
+
+ align:start position:0%
+updates corresponds to root n operations
+each of the verify sums corresponds to
+
+ align:start position:0%
+each of the verify sums corresponds to
+ 
+
+ align:start position:0%
+each of the verify sums corresponds to
+root n operations so overall per
+
+ align:start position:0%
+root n operations so overall per
+ 
+
+ align:start position:0%
+root n operations so overall per
+operation per original operation of edge
+
+ align:start position:0%
+operation per original operation of edge
+ 
+
+ align:start position:0%
+operation per original operation of edge
+deletion insertion or connectivity query
+
+ align:start position:0%
+deletion insertion or connectivity query
+ 
+
+ align:start position:0%
+deletion insertion or connectivity query
+I'm paying log n per operation so if I
+
+ align:start position:0%
+I'm paying log n per operation so if I
+ 
+
+ align:start position:0%
+I'm paying log n per operation so if I
+can prove this claim then I get this
+
+ align:start position:0%
+can prove this claim then I get this
+ 
+
+ align:start position:0%
+can prove this claim then I get this
+theorem all clear so now we've reduced
+
+ align:start position:0%
+theorem all clear so now we've reduced
+ 
+
+ align:start position:0%
+theorem all clear so now we've reduced
+the problem to these bulk operations
+
+ align:start position:0%
+the problem to these bulk operations
+ 
+
+ align:start position:0%
+the problem to these bulk operations
+we'll just be thinking about the bulk
+
+ align:start position:0%
+we'll just be thinking about the bulk
+ 
+
+ align:start position:0%
+we'll just be thinking about the bulk
+operations update verify some we won't
+
+ align:start position:0%
+operations update verify some we won't
+ 
+
+ align:start position:0%
+operations update verify some we won't
+think about Edge deletions insertions
+
+ align:start position:0%
+think about Edge deletions insertions
+ 
+
+ align:start position:0%
+think about Edge deletions insertions
+and connectivity queries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anymore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is just sort of the general
+
+ align:start position:0%
+okay so this is just sort of the general
+ 
+
+ align:start position:0%
+okay so this is just sort of the general
+setup of what the graph's going to look
+
+ align:start position:0%
+setup of what the graph's going to look
+ 
+
+ align:start position:0%
+setup of what the graph's going to look
+like and now I'm going to tell you what
+
+ align:start position:0%
+like and now I'm going to tell you what
+ 
+
+ align:start position:0%
+like and now I'm going to tell you what
+sequence of updates and verify sums
+
+ align:start position:0%
+sequence of updates and verify sums
+ 
+
+ align:start position:0%
+sequence of updates and verify sums
+we're actually going to do that are bad
+
+ align:start position:0%
+we're actually going to do that are bad
+ 
+
+ align:start position:0%
+we're actually going to do that are bad
+this is the bad access
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence and this is actually something
+
+ align:start position:0%
+sequence and this is actually something
+ 
+
+ align:start position:0%
+sequence and this is actually something
+we've seen before in lecture six I think
+
+ align:start position:0%
+we've seen before in lecture six I think
+ 
+
+ align:start position:0%
+we've seen before in lecture six I think
+the binary search tree
+
+ align:start position:0%
+the binary search tree
+ 
+
+ align:start position:0%
+the binary search tree
+stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we're going to look at the bit
+
+ align:start position:0%
+uh we're going to look at the bit
+ 
+
+ align:start position:0%
+uh we're going to look at the bit
+reversal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+so you may recall a bit reversal
+
+ align:start position:0%
+so you may recall a bit reversal
+ 
+
+ align:start position:0%
+so you may recall a bit reversal
+sequence you take binary
+
+ align:start position:0%
+sequence you take binary
+ 
+
+ align:start position:0%
+sequence you take binary
+numbers in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order uh reverse the bits so this
+
+ align:start position:0%
+order uh reverse the bits so this
+ 
+
+ align:start position:0%
+order uh reverse the bits so this
+becomes 0 0 0 1 0 0 0 1 0 1 1 0 0 0
+
+ align:start position:0%
+becomes 0 0 0 1 0 0 0 1 0 1 1 0 0 0
+ 
+
+ align:start position:0%
+becomes 0 0 0 1 0 0 0 1 0 1 1 0 0 0
+1 one 1 0 1 1 and 11 one1 so those are
+
+ align:start position:0%
+1 one 1 0 1 1 and 11 one1 so those are
+ 
+
+ align:start position:0%
+1 one 1 0 1 1 and 11 one1 so those are
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Reversed
+
+ align:start position:0%
+Reversed
+ 
+
+ align:start position:0%
+Reversed
+strings and then you reinterpret those
+
+ align:start position:0%
+strings and then you reinterpret those
+ 
+
+ align:start position:0%
+strings and then you reinterpret those
+as regular numbers so this is 0 4 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+6 and then it should be the same thing
+
+ align:start position:0%
+6 and then it should be the same thing
+ 
+
+ align:start position:0%
+6 and then it should be the same thing
+but the odd version so we'll have 1 5 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+7 okay we uh I claimed I think probably
+
+ align:start position:0%
+7 okay we uh I claimed I think probably
+ 
+
+ align:start position:0%
+7 okay we uh I claimed I think probably
+didn't prove that this bit reversal
+
+ align:start position:0%
+didn't prove that this bit reversal
+ 
+
+ align:start position:0%
+didn't prove that this bit reversal
+sequence has a high Wilbur lower bound
+
+ align:start position:0%
+sequence has a high Wilbur lower bound
+ 
+
+ align:start position:0%
+sequence has a high Wilbur lower bound
+uh and so any binary search tree
+
+ align:start position:0%
+uh and so any binary search tree
+ 
+
+ align:start position:0%
+uh and so any binary search tree
+accessing items in this order requires
+
+ align:start position:0%
+accessing items in this order requires
+ 
+
+ align:start position:0%
+accessing items in this order requires
+log and per operation and we want log in
+
+ align:start position:0%
+log and per operation and we want log in
+ 
+
+ align:start position:0%
+log and per operation and we want log in
+prop operation here so it seems like a
+
+ align:start position:0%
+prop operation here so it seems like a
+ 
+
+ align:start position:0%
+prop operation here so it seems like a
+good choice why not so we're going to
+
+ align:start position:0%
+good choice why not so we're going to
+ 
+
+ align:start position:0%
+good choice why not so we're going to
+follow this access sequence and sorry
+
+ align:start position:0%
+follow this access sequence and sorry
+ 
+
+ align:start position:0%
+follow this access sequence and sorry
+I've changed notation here we're going
+
+ align:start position:0%
+I've changed notation here we're going
+ 
+
+ align:start position:0%
+I've changed notation here we're going
+to number the permutations from zero to
+
+ align:start position:0%
+to number the permutations from zero to
+ 
+
+ align:start position:0%
+to number the permutations from zero to
+root n minus one
+
+ align:start position:0%
+root n minus one
+ 
+
+ align:start position:0%
+root n minus one
+now and assume root N is a power of two
+
+ align:start position:0%
+now and assume root N is a power of two
+ 
+
+ align:start position:0%
+now and assume root N is a power of two
+so the bit reversal sequence is well
+
+ align:start position:0%
+so the bit reversal sequence is well
+ 
+
+ align:start position:0%
+so the bit reversal sequence is well
+defined and then we are going to do two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things for each such I we're going to do
+
+ align:start position:0%
+things for each such I we're going to do
+ 
+
+ align:start position:0%
+things for each such I we're going to do
+a verify sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh actually maybe it is starting at one
+
+ align:start position:0%
+uh actually maybe it is starting at one
+ 
+
+ align:start position:0%
+uh actually maybe it is starting at one
+I don't know doesn't
+
+ align:start position:0%
+I don't know doesn't
+ 
+
+ align:start position:0%
+I don't know doesn't
+matter and then we'll do an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+update
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's see this Pi random is just a
+
+ align:start position:0%
+so let's see this Pi random is just a
+ 
+
+ align:start position:0%
+so let's see this Pi random is just a
+uniform random permutation it's computed
+
+ align:start position:0%
+uniform random permutation it's computed
+ 
+
+ align:start position:0%
+uniform random permutation it's computed
+fresh every time so we're just
+
+ align:start position:0%
+fresh every time so we're just
+ 
+
+ align:start position:0%
+fresh every time so we're just
+randomizing Pi
+
+ align:start position:0%
+randomizing Pi
+ 
+
+ align:start position:0%
+randomizing Pi
+I in this operation before we do that
+
+ align:start position:0%
+I in this operation before we do that
+ 
+
+ align:start position:0%
+I in this operation before we do that
+we're checking that this the sum the
+
+ align:start position:0%
+we're checking that this the sum the
+ 
+
+ align:start position:0%
+we're checking that this the sum the
+composition of all the permutations up
+
+ align:start position:0%
+composition of all the permutations up
+ 
+
+ align:start position:0%
+composition of all the permutations up
+to position I is what it is so this is
+
+ align:start position:0%
+to position I is what it is so this is
+ 
+
+ align:start position:0%
+to position I is what it is so this is
+the actual value here and we're
+
+ align:start position:0%
+the actual value here and we're
+ 
+
+ align:start position:0%
+the actual value here and we're
+verifying uh that that is the indeed the
+
+ align:start position:0%
+verifying uh that that is the indeed the
+ 
+
+ align:start position:0%
+verifying uh that that is the indeed the
+sum so this will always return
+
+ align:start position:0%
+sum so this will always return
+ 
+
+ align:start position:0%
+sum so this will always return
+Yes but data structure has to be correct
+
+ align:start position:0%
+Yes but data structure has to be correct
+ 
+
+ align:start position:0%
+Yes but data structure has to be correct
+so it needs to really verify that that
+
+ align:start position:0%
+so it needs to really verify that that
+ 
+
+ align:start position:0%
+so it needs to really verify that that
+is the case uh there's the threat that
+
+ align:start position:0%
+is the case uh there's the threat that
+ 
+
+ align:start position:0%
+is the case uh there's the threat that
+maybe we gave the wrong answer here and
+
+ align:start position:0%
+maybe we gave the wrong answer here and
+ 
+
+ align:start position:0%
+maybe we gave the wrong answer here and
+it needs to double check that that is
+
+ align:start position:0%
+it needs to double check that that is
+ 
+
+ align:start position:0%
+it needs to double check that that is
+indeed the right answer it may seem a
+
+ align:start position:0%
+indeed the right answer it may seem a
+ 
+
+ align:start position:0%
+indeed the right answer it may seem a
+little weird but we'll see why it works
+
+ align:start position:0%
+little weird but we'll see why it works
+ 
+
+ align:start position:0%
+little weird but we'll see why it works
+so this is the bad access sequence just
+
+ align:start position:0%
+so this is the bad access sequence just
+ 
+
+ align:start position:0%
+so this is the bad access sequence just
+do a query do an update in this weird
+
+ align:start position:0%
+do a query do an update in this weird
+ 
+
+ align:start position:0%
+do a query do an update in this weird
+order in
+
+ align:start position:0%
+order in
+ 
+
+ align:start position:0%
+order in
+I okay and big idea is
+
+ align:start position:0%
+I okay and big idea is
+ 
+
+ align:start position:0%
+I okay and big idea is
+to uh build a nice balanced binary
+
+ align:start position:0%
+to uh build a nice balanced binary
+ 
+
+ align:start position:0%
+to uh build a nice balanced binary
+tree over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time so we have on the ground here 0 4 2
+
+ align:start position:0%
+time so we have on the ground here 0 4 2
+ 
+
+ align:start position:0%
+time so we have on the ground here 0 4 2
+6 1 5 3 7 and when I write five mean
+
+ align:start position:0%
+6 1 5 3 7 and when I write five mean
+ 
+
+ align:start position:0%
+6 1 5 3 7 and when I write five mean
+verify sum of five and update
+
+ align:start position:0%
+verify sum of five and update
+ 
+
+ align:start position:0%
+verify sum of five and update
+permutation five and then we can build a
+
+ align:start position:0%
+permutation five and then we can build a
+ 
+
+ align:start position:0%
+permutation five and then we can build a
+binary tree on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and for each node in this tree we
+
+ align:start position:0%
+that and for each node in this tree we
+ 
+
+ align:start position:0%
+that and for each node in this tree we
+have the notion of a left sub tree and
+
+ align:start position:0%
+have the notion of a left sub tree and
+ 
+
+ align:start position:0%
+have the notion of a left sub tree and
+we have the notion of a right sub tree
+
+ align:start position:0%
+we have the notion of a right sub tree
+ 
+
+ align:start position:0%
+we have the notion of a right sub tree
+and cool thing about bit reversal
+
+ align:start position:0%
+and cool thing about bit reversal
+ 
+
+ align:start position:0%
+and cool thing about bit reversal
+sequence is kind of this nice
+
+ align:start position:0%
+sequence is kind of this nice
+ 
+
+ align:start position:0%
+sequence is kind of this nice
+self-similarity if you look at the left
+
+ align:start position:0%
+self-similarity if you look at the left
+ 
+
+ align:start position:0%
+self-similarity if you look at the left
+sub tree of any node and the right sub
+
+ align:start position:0%
+sub tree of any node and the right sub
+ 
+
+ align:start position:0%
+sub tree of any node and the right sub
+tree of any node those items inter leave
+
+ align:start position:0%
+tree of any node those items inter leave
+ 
+
+ align:start position:0%
+tree of any node those items inter leave
+if you look at the sorted order it's one
+
+ align:start position:0%
+if you look at the sorted order it's one
+ 
+
+ align:start position:0%
+if you look at the sorted order it's one
+on the left three on the right five on
+
+ align:start position:0%
+on the left three on the right five on
+ 
+
+ align:start position:0%
+on the left three on the right five on
+the left seven on the right they always
+
+ align:start position:0%
+the left seven on the right they always
+ 
+
+ align:start position:0%
+the left seven on the right they always
+perfectly interl because this thing is
+
+ align:start position:0%
+perfectly interl because this thing is
+ 
+
+ align:start position:0%
+perfectly interl because this thing is
+designed to interl at every possible
+
+ align:start position:0%
+designed to interl at every possible
+ 
+
+ align:start position:0%
+designed to interl at every possible
+level so that's the fact we're going to
+
+ align:start position:0%
+level so that's the fact we're going to
+ 
+
+ align:start position:0%
+level so that's the fact we're going to
+use we're going to analyze each node
+
+ align:start position:0%
+use we're going to analyze each node
+ 
+
+ align:start position:0%
+use we're going to analyze each node
+separately and talk about uh what
+
+ align:start position:0%
+separately and talk about uh what
+ 
+
+ align:start position:0%
+separately and talk about uh what
+information has to be carried from the
+
+ align:start position:0%
+information has to be carried from the
+ 
+
+ align:start position:0%
+information has to be carried from the
+left sub tree to the right sub Tree in
+
+ align:start position:0%
+left sub tree to the right sub Tree in
+ 
+
+ align:start position:0%
+left sub tree to the right sub Tree in
+particular we're interested on the in
+
+ align:start position:0%
+particular we're interested on the in
+ 
+
+ align:start position:0%
+particular we're interested on the in
+the updates being done on the left sub
+
+ align:start position:0%
+the updates being done on the left sub
+ 
+
+ align:start position:0%
+the updates being done on the left sub
+tree cuz we change Pi 1 we change Pi 5
+
+ align:start position:0%
+tree cuz we change Pi 1 we change Pi 5
+ 
+
+ align:start position:0%
+tree cuz we change Pi 1 we change Pi 5
+and the quer is being done on the right
+
+ align:start position:0%
+and the quer is being done on the right
+ 
+
+ align:start position:0%
+and the quer is being done on the right
+subt tree because here we query uh three
+
+ align:start position:0%
+subt tree because here we query uh three
+ 
+
+ align:start position:0%
+subt tree because here we query uh three
+we query 7even when we query three that
+
+ align:start position:0%
+we query 7even when we query three that
+ 
+
+ align:start position:0%
+we query 7even when we query three that
+queries everything all the permutations
+
+ align:start position:0%
+queries everything all the permutations
+ 
+
+ align:start position:0%
+queries everything all the permutations
+up to three it's the composition of all
+
+ align:start position:0%
+up to three it's the composition of all
+ 
+
+ align:start position:0%
+up to three it's the composition of all
+permutations up to three so in
+
+ align:start position:0%
+permutations up to three so in
+ 
+
+ align:start position:0%
+permutations up to three so in
+particular it involves one so the claim
+
+ align:start position:0%
+particular it involves one so the claim
+ 
+
+ align:start position:0%
+particular it involves one so the claim
+is going to be that the permutation that
+
+ align:start position:0%
+is going to be that the permutation that
+ 
+
+ align:start position:0%
+is going to be that the permutation that
+we set in one has to be carried over to
+
+ align:start position:0%
+we set in one has to be carried over to
+ 
+
+ align:start position:0%
+we set in one has to be carried over to
+this query and similarly five a changing
+
+ align:start position:0%
+this query and similarly five a changing
+ 
+
+ align:start position:0%
+this query and similarly five a changing
+permutation five will affect the query
+
+ align:start position:0%
+permutation five will affect the query
+ 
+
+ align:start position:0%
+permutation five will affect the query
+for seven also query the update for one
+
+ align:start position:0%
+for seven also query the update for one
+ 
+
+ align:start position:0%
+for seven also query the update for one
+will affect the query for
+
+ align:start position:0%
+will affect the query for
+ 
+
+ align:start position:0%
+will affect the query for
+seven so uh we need to formalize that a
+
+ align:start position:0%
+seven so uh we need to formalize that a
+ 
+
+ align:start position:0%
+seven so uh we need to formalize that a
+little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit so here is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claim for every node in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree uh say it has L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leaves in its sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+uh this should be a comma this should be
+
+ align:start position:0%
+uh this should be a comma this should be
+ 
+
+ align:start position:0%
+uh this should be a comma this should be
+a colon
+
+ align:start position:0%
+a colon
+ 
+
+ align:start position:0%
+a colon
+whatever here's we
+
+ align:start position:0%
+whatever here's we
+ 
+
+ align:start position:0%
+whatever here's we
+say during the right sub tree of V of
+
+ align:start position:0%
+say during the right sub tree of V of
+ 
+
+ align:start position:0%
+say during the right sub tree of V of
+course the right sub tree corresponds to
+
+ align:start position:0%
+course the right sub tree corresponds to
+ 
+
+ align:start position:0%
+course the right sub tree corresponds to
+an interval of time so we're talking
+
+ align:start position:0%
+an interval of time so we're talking
+ 
+
+ align:start position:0%
+an interval of time so we're talking
+talking about those operations done
+
+ align:start position:0%
+talking about those operations done
+ 
+
+ align:start position:0%
+talking about those operations done
+during the right sub tree of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V claim is we must
+
+ align:start position:0%
+V claim is we must
+ 
+
+ align:start position:0%
+V claim is we must
+do Omega L root n cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probes sorry expected cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probes we are using some Randomness here
+
+ align:start position:0%
+probes we are using some Randomness here
+ 
+
+ align:start position:0%
+probes we are using some Randomness here
+right we said we're going to update each
+
+ align:start position:0%
+right we said we're going to update each
+ 
+
+ align:start position:0%
+right we said we're going to update each
+permutation to a random value so we can
+
+ align:start position:0%
+permutation to a random value so we can
+ 
+
+ align:start position:0%
+permutation to a random value so we can
+only make claims about the expected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+performance uh fine but that's actually
+
+ align:start position:0%
+performance uh fine but that's actually
+ 
+
+ align:start position:0%
+performance uh fine but that's actually
+a stronger thing it implies a lower
+
+ align:start position:0%
+a stronger thing it implies a lower
+ 
+
+ align:start position:0%
+a stronger thing it implies a lower
+bound even for randomized algorithms if
+
+ align:start position:0%
+bound even for randomized algorithms if
+ 
+
+ align:start position:0%
+bound even for randomized algorithms if
+you can randomize your input
+
+ align:start position:0%
+you can randomize your input
+ 
+
+ align:start position:0%
+you can randomize your input
+Set uh and
+
+ align:start position:0%
+Set uh and
+ 
+
+ align:start position:0%
+Set uh and
+then not just any cell probes but
+
+ align:start position:0%
+then not just any cell probes but
+ 
+
+ align:start position:0%
+then not just any cell probes but
+they're cell probes that read cells last
+
+ align:start position:0%
+they're cell probes that read cells last
+ 
+
+ align:start position:0%
+they're cell probes that read cells last
+written during the left
+
+ align:start position:0%
+written during the left
+ 
+
+ align:start position:0%
+written during the left
+subtree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is what I
+
+ align:start position:0%
+okay so this is what I
+ 
+
+ align:start position:0%
+okay so this is what I
+was saying at a high level before we're
+
+ align:start position:0%
+was saying at a high level before we're
+ 
+
+ align:start position:0%
+was saying at a high level before we're
+looking at reads over
+
+ align:start position:0%
+looking at reads over
+ 
+
+ align:start position:0%
+looking at reads over
+here to cells that are written over here
+
+ align:start position:0%
+here to cells that are written over here
+ 
+
+ align:start position:0%
+here to cells that are written over here
+because we claim the updates over here
+
+ align:start position:0%
+because we claim the updates over here
+ 
+
+ align:start position:0%
+because we claim the updates over here
+have to store some information that is I
+
+ align:start position:0%
+have to store some information that is I
+ 
+
+ align:start position:0%
+have to store some information that is I
+mean whatever the updates that happen
+
+ align:start position:0%
+mean whatever the updates that happen
+ 
+
+ align:start position:0%
+mean whatever the updates that happen
+over here influence the queries that
+
+ align:start position:0%
+over here influence the queries that
+ 
+
+ align:start position:0%
+over here influence the queries that
+happen over here so these queries have
+
+ align:start position:0%
+happen over here so these queries have
+ 
+
+ align:start position:0%
+happen over here so these queries have
+to read the data that was written over
+
+ align:start position:0%
+to read the data that was written over
+ 
+
+ align:start position:0%
+to read the data that was written over
+here and specifically we're claiming at
+
+ align:start position:0%
+here and specifically we're claiming at
+ 
+
+ align:start position:0%
+here and specifically we're claiming at
+least L root n cell probes have to be
+
+ align:start position:0%
+least L root n cell probes have to be
+ 
+
+ align:start position:0%
+least L root n cell probes have to be
+read over here uh from cells that were
+
+ align:start position:0%
+read over here uh from cells that were
+ 
+
+ align:start position:0%
+read over here uh from cells that were
+written that were basically just written
+
+ align:start position:0%
+written that were basically just written
+ 
+
+ align:start position:0%
+written that were basically just written
+in the left sub tree if we could prove
+
+ align:start position:0%
+in the left sub tree if we could prove
+ 
+
+ align:start position:0%
+in the left sub tree if we could prove
+this then we get our other claim this
+
+ align:start position:0%
+this then we get our other claim this
+ 
+
+ align:start position:0%
+this then we get our other claim this
+one over here that root n updates and
+
+ align:start position:0%
+one over here that root n updates and
+ 
+
+ align:start position:0%
+one over here that root n updates and
+root n verify sums require this much
+
+ align:start position:0%
+root n verify sums require this much
+ 
+
+ align:start position:0%
+root n verify sums require this much
+time uh the difference
+
+ align:start position:0%
+time uh the difference
+ 
+
+ align:start position:0%
+time uh the difference
+is well here we have an L for an L leaf
+
+ align:start position:0%
+is well here we have an L for an L leaf
+ 
+
+ align:start position:0%
+is well here we have an L for an L leaf
+tree and so uh what I'd like to do is
+
+ align:start position:0%
+tree and so uh what I'd like to do is
+ 
+
+ align:start position:0%
+tree and so uh what I'd like to do is
+sum this lower bound over every node in
+
+ align:start position:0%
+sum this lower bound over every node in
+ 
+
+ align:start position:0%
+sum this lower bound over every node in
+the tree need to check that that is
+
+ align:start position:0%
+the tree need to check that that is
+ 
+
+ align:start position:0%
+the tree need to check that that is
+valid to do so let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay for for every node V we
+
+ align:start position:0%
+that okay for for every node V we
+ 
+
+ align:start position:0%
+that okay for for every node V we
+claiming there's a certain number of
+
+ align:start position:0%
+claiming there's a certain number of
+ 
+
+ align:start position:0%
+claiming there's a certain number of
+reads that happen over here that
+
+ align:start position:0%
+reads that happen over here that
+ 
+
+ align:start position:0%
+reads that happen over here that
+corresponder writes over here uh but you
+
+ align:start position:0%
+corresponder writes over here uh but you
+ 
+
+ align:start position:0%
+corresponder writes over here uh but you
+know uh let's say you look at the parent
+
+ align:start position:0%
+know uh let's say you look at the parent
+ 
+
+ align:start position:0%
+know uh let's say you look at the parent
+of e which is over here this thing is
+
+ align:start position:0%
+of e which is over here this thing is
+ 
+
+ align:start position:0%
+of e which is over here this thing is
+also in the right sub tree and we're
+
+ align:start position:0%
+also in the right sub tree and we're
+ 
+
+ align:start position:0%
+also in the right sub tree and we're
+claiming there's some number of reads on
+
+ align:start position:0%
+claiming there's some number of reads on
+ 
+
+ align:start position:0%
+claiming there's some number of reads on
+the right sub tree that read things that
+
+ align:start position:0%
+the right sub tree that read things that
+ 
+
+ align:start position:0%
+the right sub tree that read things that
+written over on the left the worry would
+
+ align:start position:0%
+written over on the left the worry would
+ 
+
+ align:start position:0%
+written over on the left the worry would
+be that the reads we counted here we
+
+ align:start position:0%
+be that the reads we counted here we
+ 
+
+ align:start position:0%
+be that the reads we counted here we
+also count at the next level up we don't
+
+ align:start position:0%
+also count at the next level up we don't
+ 
+
+ align:start position:0%
+also count at the next level up we don't
+want to double count in our lower bounds
+
+ align:start position:0%
+want to double count in our lower bounds
+ 
+
+ align:start position:0%
+want to double count in our lower bounds
+if we're able to sum them up we can't be
+
+ align:start position:0%
+if we're able to sum them up we can't be
+ 
+
+ align:start position:0%
+if we're able to sum them up we can't be
+double counting uh but the claim is
+
+ align:start position:0%
+double counting uh but the claim is
+ 
+
+ align:start position:0%
+double counting uh but the claim is
+we're not double counting because if you
+
+ align:start position:0%
+we're not double counting because if you
+ 
+
+ align:start position:0%
+we're not double counting because if you
+look at any particular any read so you
+
+ align:start position:0%
+look at any particular any read so you
+ 
+
+ align:start position:0%
+look at any particular any read so you
+here's time and suppose you do a read
+
+ align:start position:0%
+here's time and suppose you do a read
+ 
+
+ align:start position:0%
+here's time and suppose you do a read
+here you're reading a cell that was
+
+ align:start position:0%
+here you're reading a cell that was
+ 
+
+ align:start position:0%
+here you're reading a cell that was
+written sometime in the past if it was
+
+ align:start position:0%
+written sometime in the past if it was
+ 
+
+ align:start position:0%
+written sometime in the past if it was
+never written it's not very interesting
+
+ align:start position:0%
+never written it's not very interesting
+ 
+
+ align:start position:0%
+never written it's not very interesting
+read communicates no information so
+
+ align:start position:0%
+read communicates no information so
+ 
+
+ align:start position:0%
+read communicates no information so
+there's some right in the past that uh
+
+ align:start position:0%
+there's some right in the past that uh
+ 
+
+ align:start position:0%
+there's some right in the past that uh
+changed the the cell is just red and
+
+ align:start position:0%
+changed the the cell is just red and
+ 
+
+ align:start position:0%
+changed the the cell is just red and
+we're going to count this read at a
+
+ align:start position:0%
+we're going to count this read at a
+ 
+
+ align:start position:0%
+we're going to count this read at a
+particular node namely the LCA of those
+
+ align:start position:0%
+particular node namely the LCA of those
+ 
+
+ align:start position:0%
+particular node namely the LCA of those
+two times so if you look at the LCA of
+
+ align:start position:0%
+two times so if you look at the LCA of
+ 
+
+ align:start position:0%
+two times so if you look at the LCA of
+the times the reads and the wrs that is
+
+ align:start position:0%
+the times the reads and the wrs that is
+ 
+
+ align:start position:0%
+the times the reads and the wrs that is
+the single node we'll think about that
+
+ align:start position:0%
+the single node we'll think about that
+ 
+
+ align:start position:0%
+the single node we'll think about that
+read uh that happened in the right sub
+
+ align:start position:0%
+read uh that happened in the right sub
+ 
+
+ align:start position:0%
+read uh that happened in the right sub
+tree that was written in the left sub
+
+ align:start position:0%
+tree that was written in the left sub
+ 
+
+ align:start position:0%
+tree that was written in the left sub
+tree okay so no double
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+counting
+
+ align:start position:0%
+counting
+ 
+
+ align:start position:0%
+counting
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh we only count at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LCA uh the other thing we need to be
+
+ align:start position:0%
+LCA uh the other thing we need to be
+ 
+
+ align:start position:0%
+LCA uh the other thing we need to be
+able to do is because this is an
+
+ align:start position:0%
+able to do is because this is an
+ 
+
+ align:start position:0%
+able to do is because this is an
+expected lower bound we need linearity
+
+ align:start position:0%
+expected lower bound we need linearity
+ 
+
+ align:start position:0%
+expected lower bound we need linearity
+of expectation but expectation is indeed
+
+ align:start position:0%
+of expectation but expectation is indeed
+ 
+
+ align:start position:0%
+of expectation but expectation is indeed
+linear so we're we're all set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so all this left is a little bit of
+
+ align:start position:0%
+okay so all this left is a little bit of
+ 
+
+ align:start position:0%
+okay so all this left is a little bit of
+combinatorics if we take L root n where
+
+ align:start position:0%
+combinatorics if we take L root n where
+ 
+
+ align:start position:0%
+combinatorics if we take L root n where
+L is the size of the sub tree below a
+
+ align:start position:0%
+L is the size of the sub tree below a
+ 
+
+ align:start position:0%
+L is the size of the sub tree below a
+given node uh and we sum that up over
+
+ align:start position:0%
+given node uh and we sum that up over
+ 
+
+ align:start position:0%
+given node uh and we sum that up over
+all nodes and it's a balanced binary
+
+ align:start position:0%
+all nodes and it's a balanced binary
+ 
+
+ align:start position:0%
+all nodes and it's a balanced binary
+search tree uh or a balanced binary tree
+
+ align:start position:0%
+search tree uh or a balanced binary tree
+ 
+
+ align:start position:0%
+search tree uh or a balanced binary tree
+I should say not a search tree uh what
+
+ align:start position:0%
+I should say not a search tree uh what
+ 
+
+ align:start position:0%
+I should say not a search tree uh what
+do we get well every leaf appears in log
+
+ align:start position:0%
+do we get well every leaf appears in log
+ 
+
+ align:start position:0%
+do we get well every leaf appears in log
+and sub trees so we get the total size
+
+ align:start position:0%
+and sub trees so we get the total size
+ 
+
+ align:start position:0%
+and sub trees so we get the total size
+of the tree time log n for this and we
+
+ align:start position:0%
+of the tree time log n for this and we
+ 
+
+ align:start position:0%
+of the tree time log n for this and we
+get another root n over here the total
+
+ align:start position:0%
+get another root n over here the total
+ 
+
+ align:start position:0%
+get another root n over here the total
+size of the sub tree of the tree is root
+
+ align:start position:0%
+size of the sub tree of the tree is root
+ 
+
+ align:start position:0%
+size of the sub tree of the tree is root
+n so we get
+
+ align:start position:0%
+n so we get
+ 
+
+ align:start position:0%
+n so we get
+uh this root n log n that's when you sum
+
+ align:start position:0%
+uh this root n log n that's when you sum
+ 
+
+ align:start position:0%
+uh this root n log n that's when you sum
+up the L part then everything gets
+
+ align:start position:0%
+up the L part then everything gets
+ 
+
+ align:start position:0%
+up the L part then everything gets
+multiplied by root
+
+ align:start position:0%
+multiplied by root
+ 
+
+ align:start position:0%
+multiplied by root
+n and that becomes our lower bound and
+
+ align:start position:0%
+n and that becomes our lower bound and
+ 
+
+ align:start position:0%
+n and that becomes our lower bound and
+that's exactly what we need over
+
+ align:start position:0%
+that's exactly what we need over
+ 
+
+ align:start position:0%
+that's exactly what we need over
+here so now uh this claim is
+
+ align:start position:0%
+here so now uh this claim is
+ 
+
+ align:start position:0%
+here so now uh this claim is
+done uh maybe I should do a check mark
+
+ align:start position:0%
+done uh maybe I should do a check mark
+ 
+
+ align:start position:0%
+done uh maybe I should do a check mark
+provided we can prove this claim so now
+
+ align:start position:0%
+provided we can prove this claim so now
+ 
+
+ align:start position:0%
+provided we can prove this claim so now
+our goal is to prove this thing and now
+
+ align:start position:0%
+our goal is to prove this thing and now
+ 
+
+ align:start position:0%
+our goal is to prove this thing and now
+we're in a sort of more local world
+
+ align:start position:0%
+we're in a sort of more local world
+ 
+
+ align:start position:0%
+we're in a sort of more local world
+looking at a single node counting reads
+
+ align:start position:0%
+looking at a single node counting reads
+ 
+
+ align:start position:0%
+looking at a single node counting reads
+over here the correspondent writes over
+
+ align:start position:0%
+over here the correspondent writes over
+ 
+
+ align:start position:0%
+over here the correspondent writes over
+there and then you just add up those
+
+ align:start position:0%
+there and then you just add up those
+ 
+
+ align:start position:0%
+there and then you just add up those
+lower bounds you get what you want so
+
+ align:start position:0%
+lower bounds you get what you want so
+ 
+
+ align:start position:0%
+lower bounds you get what you want so
+this is where the log comes from because
+
+ align:start position:0%
+this is where the log comes from because
+ 
+
+ align:start position:0%
+this is where the log comes from because
+it's a balanced tree and there's log end
+
+ align:start position:0%
+it's a balanced tree and there's log end
+ 
+
+ align:start position:0%
+it's a balanced tree and there's log end
+levels in a balance tree that's where
+
+ align:start position:0%
+levels in a balance tree that's where
+ 
+
+ align:start position:0%
+levels in a balance tree that's where
+we're getting our lower bound the root
+
+ align:start position:0%
+we're getting our lower bound the root
+ 
+
+ align:start position:0%
+we're getting our lower bound the root
+ends are just you know keeping track of
+
+ align:start position:0%
+ends are just you know keeping track of
+ 
+
+ align:start position:0%
+ends are just you know keeping track of
+the size of the things we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+manipulating all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it remains to prove this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claim we prove that claim we get that
+
+ align:start position:0%
+claim we prove that claim we get that
+ 
+
+ align:start position:0%
+claim we prove that claim we get that
+claim and then we get this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so proof of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claim uh we're going to do an
+
+ align:start position:0%
+claim uh we're going to do an
+ 
+
+ align:start position:0%
+claim uh we're going to do an
+information theoretic argument uh so let
+
+ align:start position:0%
+information theoretic argument uh so let
+ 
+
+ align:start position:0%
+information theoretic argument uh so let
+me set it up it's again it's making this
+
+ align:start position:0%
+me set it up it's again it's making this
+ 
+
+ align:start position:0%
+me set it up it's again it's making this
+claim that I said before that the
+
+ align:start position:0%
+claim that I said before that the
+ 
+
+ align:start position:0%
+claim that I said before that the
+permutations that get written over here
+
+ align:start position:0%
+permutations that get written over here
+ 
+
+ align:start position:0%
+permutations that get written over here
+somehow have to be communicated to the
+
+ align:start position:0%
+somehow have to be communicated to the
+ 
+
+ align:start position:0%
+somehow have to be communicated to the
+queries over here because uh they matter
+
+ align:start position:0%
+queries over here because uh they matter
+ 
+
+ align:start position:0%
+queries over here because uh they matter
+because the the permutations that get
+
+ align:start position:0%
+because the the permutations that get
+ 
+
+ align:start position:0%
+because the the permutations that get
+set over here in change the answers to
+
+ align:start position:0%
+set over here in change the answers to
+ 
+
+ align:start position:0%
+set over here in change the answers to
+all the queries over here because they
+
+ align:start position:0%
+all the queries over here because they
+ 
+
+ align:start position:0%
+all the queries over here because they
+because of the interleaving between left
+
+ align:start position:0%
+because of the interleaving between left
+ 
+
+ align:start position:0%
+because of the interleaving between left
+and right so how we going to formalize
+
+ align:start position:0%
+and right so how we going to formalize
+ 
+
+ align:start position:0%
+and right so how we going to formalize
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well left sub
+
+ align:start position:0%
+well left sub
+ 
+
+ align:start position:0%
+well left sub
+tree uh does L over2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+updates uh uh with L over2 random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+permutations uniform random permutations
+
+ align:start position:0%
+permutations uniform random permutations
+ 
+
+ align:start position:0%
+permutations uniform random permutations
+because every node does an
+
+ align:start position:0%
+because every node does an
+ 
+
+ align:start position:0%
+because every node does an
+update um and so the information
+
+ align:start position:0%
+update um and so the information
+ 
+
+ align:start position:0%
+update um and so the information
+theoretic idea is that if we were to
+
+ align:start position:0%
+theoretic idea is that if we were to
+ 
+
+ align:start position:0%
+theoretic idea is that if we were to
+somehow encode those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+permutations that
+
+ align:start position:0%
+permutations that
+ 
+
+ align:start position:0%
+permutations that
+encoding um must
+
+ align:start position:0%
+encoding um must
+ 
+
+ align:start position:0%
+encoding um must
+use Omega L log l l no sorry that's not
+
+ align:start position:0%
+use Omega L log l l no sorry that's not
+ 
+
+ align:start position:0%
+use Omega L log l l no sorry that's not
+right off by some root n factors here L
+
+ align:start position:0%
+right off by some root n factors here L
+ 
+
+ align:start position:0%
+right off by some root n factors here L
+root n log
+
+ align:start position:0%
+root n log
+ 
+
+ align:start position:0%
+root n log
+n okay each permutation must take root n
+
+ align:start position:0%
+n okay each permutation must take root n
+ 
+
+ align:start position:0%
+n okay each permutation must take root n
+log root n Bits to encode uh if you have
+
+ align:start position:0%
+log root n Bits to encode uh if you have
+ 
+
+ align:start position:0%
+log root n Bits to encode uh if you have
+a random permutation expected number of
+
+ align:start position:0%
+a random permutation expected number of
+ 
+
+ align:start position:0%
+a random permutation expected number of
+bits effect with very high probability
+
+ align:start position:0%
+bits effect with very high probability
+ 
+
+ align:start position:0%
+bits effect with very high probability
+almost every permutation requires root n
+
+ align:start position:0%
+almost every permutation requires root n
+ 
+
+ align:start position:0%
+almost every permutation requires root n
+log root n Bits I'm not going to worry
+
+ align:start position:0%
+log root n Bits I'm not going to worry
+ 
+
+ align:start position:0%
+log root n Bits I'm not going to worry
+about constant factors put an Omega here
+
+ align:start position:0%
+about constant factors put an Omega here
+ 
+
+ align:start position:0%
+about constant factors put an Omega here
+so the root n turns into an n and then
+
+ align:start position:0%
+so the root n turns into an n and then
+ 
+
+ align:start position:0%
+so the root n turns into an n and then
+we've got L over2 of them so again
+
+ align:start position:0%
+we've got L over2 of them so again
+ 
+
+ align:start position:0%
+we've got L over2 of them so again
+ignoring constant factors that's L root
+
+ align:start position:0%
+ignoring constant factors that's L root
+ 
+
+ align:start position:0%
+ignoring constant factors that's L root
+n log n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bits okay this is just information
+
+ align:start position:0%
+Bits okay this is just information
+ 
+
+ align:start position:0%
+Bits okay this is just information
+theoretic
+
+ align:start position:0%
+theoretic
+ 
+
+ align:start position:0%
+theoretic
+fact uh or kagor Theory fact and
+
+ align:start position:0%
+fact uh or kagor Theory fact and
+ 
+
+ align:start position:0%
+fact uh or kagor Theory fact and
+uh once we know that the idea is let's
+
+ align:start position:0%
+uh once we know that the idea is let's
+ 
+
+ align:start position:0%
+uh once we know that the idea is let's
+find an encoding that's better than this
+
+ align:start position:0%
+find an encoding that's better than this
+ 
+
+ align:start position:0%
+find an encoding that's better than this
+and get a
+
+ align:start position:0%
+and get a
+ 
+
+ align:start position:0%
+and get a
+contradiction of course we shouldn't get
+
+ align:start position:0%
+contradiction of course we shouldn't get
+ 
+
+ align:start position:0%
+contradiction of course we shouldn't get
+a contradiction unless this claim is
+
+ align:start position:0%
+a contradiction unless this claim is
+ 
+
+ align:start position:0%
+a contradiction unless this claim is
+false so either this claim is true and
+
+ align:start position:0%
+false so either this claim is true and
+ 
+
+ align:start position:0%
+false so either this claim is true and
+we're happy but if somehow there were
+
+ align:start position:0%
+we're happy but if somehow there were
+ 
+
+ align:start position:0%
+we're happy but if somehow there were
+not enough cell reads on the right that
+
+ align:start position:0%
+not enough cell reads on the right that
+ 
+
+ align:start position:0%
+not enough cell reads on the right that
+did things that were written on the left
+
+ align:start position:0%
+did things that were written on the left
+ 
+
+ align:start position:0%
+did things that were written on the left
+then we will from that get a smaller
+
+ align:start position:0%
+then we will from that get a smaller
+ 
+
+ align:start position:0%
+then we will from that get a smaller
+encoding of the uh update permutations
+
+ align:start position:0%
+encoding of the uh update permutations
+ 
+
+ align:start position:0%
+encoding of the uh update permutations
+that happen on the left if we could
+
+ align:start position:0%
+that happen on the left if we could
+ 
+
+ align:start position:0%
+that happen on the left if we could
+somehow do that then we get a
+
+ align:start position:0%
+somehow do that then we get a
+ 
+
+ align:start position:0%
+somehow do that then we get a
+contradiction and therefore conclude uh
+
+ align:start position:0%
+contradiction and therefore conclude uh
+ 
+
+ align:start position:0%
+contradiction and therefore conclude uh
+the claim is in fact
+
+ align:start position:0%
+the claim is in fact
+ 
+
+ align:start position:0%
+the claim is in fact
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so if the claim
+
+ align:start position:0%
+uh so if the claim
+ 
+
+ align:start position:0%
+uh so if the claim
+fails uh we'll find a smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+encoding which will give us a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contradiction all
+
+ align:start position:0%
+contradiction all
+ 
+
+ align:start position:0%
+contradiction all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+set up this problem a little bit
+
+ align:start position:0%
+set up this problem a little bit
+ 
+
+ align:start position:0%
+set up this problem a little bit
+more uh I'm going
+
+ align:start position:0%
+more uh I'm going
+ 
+
+ align:start position:0%
+more uh I'm going
+to because we're really just interested
+
+ align:start position:0%
+to because we're really just interested
+ 
+
+ align:start position:0%
+to because we're really just interested
+in this sub tree V stuff on the left
+
+ align:start position:0%
+in this sub tree V stuff on the left
+ 
+
+ align:start position:0%
+in this sub tree V stuff on the left
+stuff on the right but this of course
+
+ align:start position:0%
+stuff on the right but this of course
+ 
+
+ align:start position:0%
+stuff on the right but this of course
+lives in a much bigger tree there's
+
+ align:start position:0%
+lives in a much bigger tree there's
+ 
+
+ align:start position:0%
+lives in a much bigger tree there's
+stuff that happens over here this I will
+
+ align:start position:0%
+stuff that happens over here this I will
+ 
+
+ align:start position:0%
+stuff that happens over here this I will
+call the past I'm just going to assum
+
+ align:start position:0%
+call the past I'm just going to assum
+ 
+
+ align:start position:0%
+call the past I'm just going to assum
+assume we know everything about the
+
+ align:start position:0%
+assume we know everything about the
+ 
+
+ align:start position:0%
+assume we know everything about the
+past everything to the left of V
+
+ align:start position:0%
+past everything to the left of V
+ 
+
+ align:start position:0%
+past everything to the left of V
+subtree we know we can assume that we
+
+ align:start position:0%
+subtree we know we can assume that we
+ 
+
+ align:start position:0%
+subtree we know we can assume that we
+know when I say we know
+
+ align:start position:0%
+know when I say we know
+ 
+
+ align:start position:0%
+know when I say we know
+uh what what do we know we know all the
+
+ align:start position:0%
+uh what what do we know we know all the
+ 
+
+ align:start position:0%
+uh what what do we know we know all the
+updates we know all the queries that
+
+ align:start position:0%
+updates we know all the queries that
+ 
+
+ align:start position:0%
+updates we know all the queries that
+happen and we know at this moment in
+
+ align:start position:0%
+happen and we know at this moment in
+ 
+
+ align:start position:0%
+happen and we know at this moment in
+particular what is the state of the data
+
+ align:start position:0%
+particular what is the state of the data
+ 
+
+ align:start position:0%
+particular what is the state of the data
+structure because this claim has nothing
+
+ align:start position:0%
+structure because this claim has nothing
+ 
+
+ align:start position:0%
+structure because this claim has nothing
+to do with this stuff it's all about
+
+ align:start position:0%
+to do with this stuff it's all about
+ 
+
+ align:start position:0%
+to do with this stuff it's all about
+reads here that correspond to writes
+
+ align:start position:0%
+reads here that correspond to writes
+ 
+
+ align:start position:0%
+reads here that correspond to writes
+here so we can just assume we know
+
+ align:start position:0%
+here so we can just assume we know
+ 
+
+ align:start position:0%
+here so we can just assume we know
+everything up to this point in our
+
+ align:start position:0%
+everything up to this point in our
+ 
+
+ align:start position:0%
+everything up to this point in our
+encoding this is a key point one way to
+
+ align:start position:0%
+encoding this is a key point one way to
+ 
+
+ align:start position:0%
+encoding this is a key point one way to
+say this in a probabilistic sense is
+
+ align:start position:0%
+say this in a probabilistic sense is
+ 
+
+ align:start position:0%
+say this in a probabilistic sense is
+we're conditioning on what this what
+
+ align:start position:0%
+we're conditioning on what this what
+ 
+
+ align:start position:0%
+we're conditioning on what this what
+happened over here on the left what
+
+ align:start position:0%
+happened over here on the left what
+ 
+
+ align:start position:0%
+happened over here on the left what
+updates happened and if we can prove
+
+ align:start position:0%
+updates happened and if we can prove
+ 
+
+ align:start position:0%
+updates happened and if we can prove
+that whatever we need to happen here
+
+ align:start position:0%
+that whatever we need to happen here
+ 
+
+ align:start position:0%
+that whatever we need to happen here
+holds no matter what the condition is
+
+ align:start position:0%
+holds no matter what the condition is
+ 
+
+ align:start position:0%
+holds no matter what the condition is
+then it will hold overall so that's how
+
+ align:start position:0%
+then it will hold overall so that's how
+ 
+
+ align:start position:0%
+then it will hold overall so that's how
+we uh that's probabilistic justification
+
+ align:start position:0%
+we uh that's probabilistic justification
+ 
+
+ align:start position:0%
+we uh that's probabilistic justification
+for why we can assume we know the
+
+ align:start position:0%
+for why we can assume we know the
+ 
+
+ align:start position:0%
+for why we can assume we know the
+past okay uh so then our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goal is
+
+ align:start position:0%
+goal is
+ 
+
+ align:start position:0%
+goal is
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+encode this is a little bit different
+
+ align:start position:0%
+encode this is a little bit different
+ 
+
+ align:start position:0%
+encode this is a little bit different
+from this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what we really want to do is encode
+
+ align:start position:0%
+okay what we really want to do is encode
+ 
+
+ align:start position:0%
+okay what we really want to do is encode
+the update permutations on the
+
+ align:start position:0%
+the update permutations on the
+ 
+
+ align:start position:0%
+the update permutations on the
+left that's a little awkward to think
+
+ align:start position:0%
+left that's a little awkward to think
+ 
+
+ align:start position:0%
+left that's a little awkward to think
+about because this is a claim about how
+
+ align:start position:0%
+about because this is a claim about how
+ 
+
+ align:start position:0%
+about because this is a claim about how
+many probes happen on the right so
+
+ align:start position:0%
+many probes happen on the right so
+ 
+
+ align:start position:0%
+many probes happen on the right so
+instead what we're going to do is encode
+
+ align:start position:0%
+instead what we're going to do is encode
+ 
+
+ align:start position:0%
+instead what we're going to do is encode
+the query permutations on the right so
+
+ align:start position:0%
+the query permutations on the right so
+ 
+
+ align:start position:0%
+the query permutations on the right so
+there are updates over here that's what
+
+ align:start position:0%
+there are updates over here that's what
+ 
+
+ align:start position:0%
+there are updates over here that's what
+we want to encode but we're instead
+
+ align:start position:0%
+we want to encode but we're instead
+ 
+
+ align:start position:0%
+we want to encode but we're instead
+going to encode the queries over here I
+
+ align:start position:0%
+going to encode the queries over here I
+ 
+
+ align:start position:0%
+going to encode the queries over here I
+claim if you know what the results of
+
+ align:start position:0%
+claim if you know what the results of
+ 
+
+ align:start position:0%
+claim if you know what the results of
+the queries were over here then uh you
+
+ align:start position:0%
+the queries were over here then uh you
+ 
+
+ align:start position:0%
+the queries were over here then uh you
+know what the updates were over
+
+ align:start position:0%
+know what the updates were over
+ 
+
+ align:start position:0%
+know what the updates were over
+there basically because of this
+
+ align:start position:0%
+there basically because of this
+ 
+
+ align:start position:0%
+there basically because of this
+interleaving property so I can write
+
+ align:start position:0%
+interleaving property so I can write
+ 
+
+ align:start position:0%
+interleaving property so I can write
+that down a little more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formally so if we look at time here over
+
+ align:start position:0%
+formally so if we look at time here over
+ 
+
+ align:start position:0%
+formally so if we look at time here over
+let's say this is V's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subtree then what we have are sequence
+
+ align:start position:0%
+subtree then what we have are sequence
+ 
+
+ align:start position:0%
+subtree then what we have are sequence
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+updates and a sequence of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+queries these are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+queries and these are
+
+ align:start position:0%
+queries and these are
+ 
+
+ align:start position:0%
+queries and these are
+Updates this is what the sequence looks
+
+ align:start position:0%
+Updates this is what the sequence looks
+ 
+
+ align:start position:0%
+Updates this is what the sequence looks
+like uh sorry this is V sub this is the
+
+ align:start position:0%
+like uh sorry this is V sub this is the
+ 
+
+ align:start position:0%
+like uh sorry this is V sub this is the
+pi eyes I should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say I mean these operations are all
+
+ align:start position:0%
+say I mean these operations are all
+ 
+
+ align:start position:0%
+say I mean these operations are all
+happen during time but now I'm sorting
+
+ align:start position:0%
+happen during time but now I'm sorting
+ 
+
+ align:start position:0%
+happen during time but now I'm sorting
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+I a little
+
+ align:start position:0%
+I a little
+ 
+
+ align:start position:0%
+I a little
+confusing there's two orders to think
+
+ align:start position:0%
+confusing there's two orders to think
+ 
+
+ align:start position:0%
+confusing there's two orders to think
+about right there's the the sequence
+
+ align:start position:0%
+about right there's the the sequence
+ 
+
+ align:start position:0%
+about right there's the the sequence
+over time we're now looking at such a
+
+ align:start position:0%
+over time we're now looking at such a
+ 
+
+ align:start position:0%
+over time we're now looking at such a
+left sub tree where we do say 15 and
+
+ align:start position:0%
+left sub tree where we do say 15 and
+ 
+
+ align:start position:0%
+left sub tree where we do say 15 and
+37 what that means so you're imagining
+
+ align:start position:0%
+37 what that means so you're imagining
+ 
+
+ align:start position:0%
+37 what that means so you're imagining
+here this is one this is five this is
+
+ align:start position:0%
+here this is one this is five this is
+ 
+
+ align:start position:0%
+here this is one this is five this is
+three this is seven here we've sorted by
+
+ align:start position:0%
+three this is seven here we've sorted by
+ 
+
+ align:start position:0%
+three this is seven here we've sorted by
+the the value written down there sorting
+
+ align:start position:0%
+the the value written down there sorting
+ 
+
+ align:start position:0%
+the the value written down there sorting
+by the I the pi I that you're changing
+
+ align:start position:0%
+by the I the pi I that you're changing
+ 
+
+ align:start position:0%
+by the I the pi I that you're changing
+or querying and so all the red things
+
+ align:start position:0%
+or querying and so all the red things
+ 
+
+ align:start position:0%
+or querying and so all the red things
+are on in the right sub tree of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v and all the
+
+ align:start position:0%
+v and all the
+ 
+
+ align:start position:0%
+v and all the
+updates are in the left sub tree of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V this is the interleaving property that
+
+ align:start position:0%
+V this is the interleaving property that
+ 
+
+ align:start position:0%
+V this is the interleaving property that
+I mentioned
+
+ align:start position:0%
+I mentioned
+ 
+
+ align:start position:0%
+I mentioned
+earlier uh so I claim that if I encode
+
+ align:start position:0%
+earlier uh so I claim that if I encode
+ 
+
+ align:start position:0%
+earlier uh so I claim that if I encode
+the results of the queries namely I
+
+ align:start position:0%
+the results of the queries namely I
+ 
+
+ align:start position:0%
+the results of the queries namely I
+encode these
+
+ align:start position:0%
+encode these
+ 
+
+ align:start position:0%
+encode these
+permutations these are like summary
+
+ align:start position:0%
+permutations these are like summary
+ 
+
+ align:start position:0%
+permutations these are like summary
+partial sums these are prefix sums of
+
+ align:start position:0%
+partial sums these are prefix sums of
+ 
+
+ align:start position:0%
+partial sums these are prefix sums of
+the permutation lists then I can figure
+
+ align:start position:0%
+the permutation lists then I can figure
+ 
+
+ align:start position:0%
+the permutation lists then I can figure
+out what the updates were why because if
+
+ align:start position:0%
+out what the updates were why because if
+ 
+
+ align:start position:0%
+out what the updates were why because if
+I if I figure out what this query what
+
+ align:start position:0%
+I if I figure out what this query what
+ 
+
+ align:start position:0%
+I if I figure out what this query what
+its permutation is that's the sum of all
+
+ align:start position:0%
+its permutation is that's the sum of all
+ 
+
+ align:start position:0%
+its permutation is that's the sum of all
+of these
+
+ align:start position:0%
+of these
+ 
+
+ align:start position:0%
+of these
+permutations now only one of them
+
+ align:start position:0%
+permutations now only one of them
+ 
+
+ align:start position:0%
+permutations now only one of them
+changed in the left sub tree the rest
+
+ align:start position:0%
+changed in the left sub tree the rest
+ 
+
+ align:start position:0%
+changed in the left sub tree the rest
+all are in the past they were all set
+
+ align:start position:0%
+all are in the past they were all set
+ 
+
+ align:start position:0%
+all are in the past they were all set
+before this time over here and I know
+
+ align:start position:0%
+before this time over here and I know
+ 
+
+ align:start position:0%
+before this time over here and I know
+everything about the past I'm assuming
+
+ align:start position:0%
+everything about the past I'm assuming
+ 
+
+ align:start position:0%
+everything about the past I'm assuming
+so most of these I already know the one
+
+ align:start position:0%
+so most of these I already know the one
+ 
+
+ align:start position:0%
+so most of these I already know the one
+thing I don't know is this one but I
+
+ align:start position:0%
+thing I don't know is this one but I
+ 
+
+ align:start position:0%
+thing I don't know is this one but I
+claim if I know this
+
+ align:start position:0%
+claim if I know this
+ 
+
+ align:start position:0%
+claim if I know this
+sum and I know uh and I know all the
+
+ align:start position:0%
+sum and I know uh and I know all the
+ 
+
+ align:start position:0%
+sum and I know uh and I know all the
+others then I can figure out what this
+
+ align:start position:0%
+others then I can figure out what this
+ 
+
+ align:start position:0%
+others then I can figure out what this
+one is right it's slightly awkward to do
+
+ align:start position:0%
+one is right it's slightly awkward to do
+ 
+
+ align:start position:0%
+one is right it's slightly awkward to do
+if I give you this uh I give you the sum
+
+ align:start position:0%
+if I give you this uh I give you the sum
+ 
+
+ align:start position:0%
+if I give you this uh I give you the sum
+of Pi J from J equal 0 I or
+
+ align:start position:0%
+of Pi J from J equal 0 I or
+ 
+
+ align:start position:0%
+of Pi J from J equal 0 I or
+something uh I've got
+
+ align:start position:0%
+something uh I've got
+ 
+
+ align:start position:0%
+something uh I've got
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+to I want to strip away all these strip
+
+ align:start position:0%
+to I want to strip away all these strip
+ 
+
+ align:start position:0%
+to I want to strip away all these strip
+away all these so I'm going to multiply
+
+ align:start position:0%
+away all these so I'm going to multiply
+ 
+
+ align:start position:0%
+away all these so I'm going to multiply
+by some sum of Pi J inverses over here
+
+ align:start position:0%
+by some sum of Pi J inverses over here
+ 
+
+ align:start position:0%
+by some sum of Pi J inverses over here
+and multiply by su Pi J or I say
+
+ align:start position:0%
+and multiply by su Pi J or I say
+ 
+
+ align:start position:0%
+and multiply by su Pi J or I say
+multiply I mean
+
+ align:start position:0%
+multiply I mean
+ 
+
+ align:start position:0%
+multiply I mean
+compose some PJ inverses here maybe
+
+ align:start position:0%
+compose some PJ inverses here maybe
+ 
+
+ align:start position:0%
+compose some PJ inverses here maybe
+let's not worry about the exact indices
+
+ align:start position:0%
+let's not worry about the exact indices
+ 
+
+ align:start position:0%
+let's not worry about the exact indices
+here but the point is this is all in the
+
+ align:start position:0%
+here but the point is this is all in the
+ 
+
+ align:start position:0%
+here but the point is this is all in the
+past
+
+ align:start position:0%
+past
+ 
+
+ align:start position:0%
+past
+and this is all in the past so I know
+
+ align:start position:0%
+and this is all in the past so I know
+ 
+
+ align:start position:0%
+and this is all in the past so I know
+all these Pi JS I know they're
+
+ align:start position:0%
+all these Pi JS I know they're
+ 
+
+ align:start position:0%
+all these Pi JS I know they're
+inverses so if I have this total sum and
+
+ align:start position:0%
+inverses so if I have this total sum and
+ 
+
+ align:start position:0%
+inverses so if I have this total sum and
+I right multiply with these inverses
+
+ align:start position:0%
+I right multiply with these inverses
+ 
+
+ align:start position:0%
+I right multiply with these inverses
+left multiply with these inverses I get
+
+ align:start position:0%
+left multiply with these inverses I get
+ 
+
+ align:start position:0%
+left multiply with these inverses I get
+the one that I want this gives me uh
+
+ align:start position:0%
+the one that I want this gives me uh
+ 
+
+ align:start position:0%
+the one that I want this gives me uh
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+particular uh Pi
+
+ align:start position:0%
+particular uh Pi
+ 
+
+ align:start position:0%
+particular uh Pi
+K if I set the indices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so if I know this query I
+
+ align:start position:0%
+right okay so if I know this query I
+ 
+
+ align:start position:0%
+right okay so if I know this query I
+figure out what this update is now once
+
+ align:start position:0%
+figure out what this update is now once
+ 
+
+ align:start position:0%
+figure out what this update is now once
+I know what this update is and I know
+
+ align:start position:0%
+I know what this update is and I know
+ 
+
+ align:start position:0%
+I know what this update is and I know
+this query then in this sum I know
+
+ align:start position:0%
+this query then in this sum I know
+ 
+
+ align:start position:0%
+this query then in this sum I know
+everything except this one thing and so
+
+ align:start position:0%
+everything except this one thing and so
+ 
+
+ align:start position:0%
+everything except this one thing and so
+uh using the same trick I can figure out
+
+ align:start position:0%
+uh using the same trick I can figure out
+ 
+
+ align:start position:0%
+uh using the same trick I can figure out
+what this update is that so now I know
+
+ align:start position:0%
+what this update is that so now I know
+ 
+
+ align:start position:0%
+what this update is that so now I know
+the first two updates if I then know the
+
+ align:start position:0%
+the first two updates if I then know the
+ 
+
+ align:start position:0%
+the first two updates if I then know the
+answer to this query I can figure out
+
+ align:start position:0%
+answer to this query I can figure out
+ 
+
+ align:start position:0%
+answer to this query I can figure out
+what this update is if I know the answer
+
+ align:start position:0%
+what this update is if I know the answer
+ 
+
+ align:start position:0%
+what this update is if I know the answer
+to this query I can figure out this
+
+ align:start position:0%
+to this query I can figure out this
+ 
+
+ align:start position:0%
+to this query I can figure out this
+update because they're perfectly
+
+ align:start position:0%
+update because they're perfectly
+ 
+
+ align:start position:0%
+update because they're perfectly
+interleaved I only need to reconstruct
+
+ align:start position:0%
+interleaved I only need to reconstruct
+ 
+
+ align:start position:0%
+interleaved I only need to reconstruct
+One update at a time so if I'm given if
+
+ align:start position:0%
+One update at a time so if I'm given if
+ 
+
+ align:start position:0%
+One update at a time so if I'm given if
+I've somehow encoded all of the queries
+
+ align:start position:0%
+I've somehow encoded all of the queries
+ 
+
+ align:start position:0%
+I've somehow encoded all of the queries
+results all of these prefix sums and I'm
+
+ align:start position:0%
+results all of these prefix sums and I'm
+ 
+
+ align:start position:0%
+results all of these prefix sums and I'm
+given the past then I can reconstruct
+
+ align:start position:0%
+given the past then I can reconstruct
+ 
+
+ align:start position:0%
+given the past then I can reconstruct
+what all the updates were so that's
+
+ align:start position:0%
+what all the updates were so that's
+ 
+
+ align:start position:0%
+what all the updates were so that's
+basically saying these two are the same
+
+ align:start position:0%
+basically saying these two are the same
+ 
+
+ align:start position:0%
+basically saying these two are the same
+issue if I can encode the verified sums
+
+ align:start position:0%
+issue if I can encode the verified sums
+ 
+
+ align:start position:0%
+issue if I can encode the verified sums
+in the right subtree using less than L
+
+ align:start position:0%
+in the right subtree using less than L
+ 
+
+ align:start position:0%
+in the right subtree using less than L
+root n log n Bits then I'll get a
+
+ align:start position:0%
+root n log n Bits then I'll get a
+ 
+
+ align:start position:0%
+root n log n Bits then I'll get a
+contradiction because it implies from
+
+ align:start position:0%
+contradiction because it implies from
+ 
+
+ align:start position:0%
+contradiction because it implies from
+that same encoding you can also decode
+
+ align:start position:0%
+that same encoding you can also decode
+ 
+
+ align:start position:0%
+that same encoding you can also decode
+the update permutations in the left sub
+
+ align:start position:0%
+the update permutations in the left sub
+ 
+
+ align:start position:0%
+the update permutations in the left sub
+tree so that's our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goal okay uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'd like to prove this for verify
+
+ align:start position:0%
+so we'd like to prove this for verify
+ 
+
+ align:start position:0%
+so we'd like to prove this for verify
+sum but the first thing I'm going to do
+
+ align:start position:0%
+sum but the first thing I'm going to do
+ 
+
+ align:start position:0%
+sum but the first thing I'm going to do
+is consider an easier problem which is
+
+ align:start position:0%
+is consider an easier problem which is
+ 
+
+ align:start position:0%
+is consider an easier problem which is
+sum so suppose basically this was not an
+
+ align:start position:0%
+sum so suppose basically this was not an
+ 
+
+ align:start position:0%
+sum so suppose basically this was not an
+input to the query suppose the query was
+
+ align:start position:0%
+input to the query suppose the query was
+ 
+
+ align:start position:0%
+input to the query suppose the query was
+what is the sum of
+
+ align:start position:0%
+what is the sum of
+ 
+
+ align:start position:0%
+what is the sum of
+I it's like this I just want to I want
+
+ align:start position:0%
+I it's like this I just want to I want
+ 
+
+ align:start position:0%
+I it's like this I just want to I want
+this is the partial sum problem and
+
+ align:start position:0%
+this is the partial sum problem and
+ 
+
+ align:start position:0%
+this is the partial sum problem and
+given an index I I want to know what is
+
+ align:start position:0%
+given an index I I want to know what is
+ 
+
+ align:start position:0%
+given an index I I want to know what is
+the permutation from PI 0 up to Pi I now
+
+ align:start position:0%
+the permutation from PI 0 up to Pi I now
+ 
+
+ align:start position:0%
+the permutation from PI 0 up to Pi I now
+that is not that doesn't correspond to
+
+ align:start position:0%
+that is not that doesn't correspond to
+ 
+
+ align:start position:0%
+that is not that doesn't correspond to
+Dynamic connectivity it's a new problem
+
+ align:start position:0%
+Dynamic connectivity it's a new problem
+ 
+
+ align:start position:0%
+Dynamic connectivity it's a new problem
+we'll first prove a lower Bound for that
+
+ align:start position:0%
+we'll first prove a lower Bound for that
+ 
+
+ align:start position:0%
+we'll first prove a lower Bound for that
+problem and then we'll put the verify
+
+ align:start position:0%
+problem and then we'll put the verify
+ 
+
+ align:start position:0%
+problem and then we'll put the verify
+word back
+
+ align:start position:0%
+word back
+ 
+
+ align:start position:0%
+word back
+in okay that's uh we're now
+
+ align:start position:0%
+in okay that's uh we're now
+ 
+
+ align:start position:0%
+in okay that's uh we're now
+here some lower bound and where should I
+
+ align:start position:0%
+here some lower bound and where should I
+ 
+
+ align:start position:0%
+here some lower bound and where should I
+go different so this is a lower bound on
+
+ align:start position:0%
+go different so this is a lower bound on
+ 
+
+ align:start position:0%
+go different so this is a lower bound on
+the operation sum as opposed to here
+
+ align:start position:0%
+the operation sum as opposed to here
+ 
+
+ align:start position:0%
+the operation sum as opposed to here
+where we were adding up lower bounds
+
+ align:start position:0%
+where we were adding up lower bounds
+ 
+
+ align:start position:0%
+where we were adding up lower bounds
+sorry for the conflation of terms
+
+ align:start position:0%
+sorry for the conflation of terms
+ 
+
+ align:start position:0%
+sorry for the conflation of terms
+uh let's
+
+ align:start position:0%
+uh let's
+ 
+
+ align:start position:0%
+uh let's
+go up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so I'll call this a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+warm-up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose the query is sum of I which is
+
+ align:start position:0%
+suppose the query is sum of I which is
+ 
+
+ align:start position:0%
+suppose the query is sum of I which is
+supposed to give
+
+ align:start position:0%
+supposed to give
+ 
+
+ align:start position:0%
+supposed to give
+you this prefix sum of Pi JS again sum
+
+ align:start position:0%
+you this prefix sum of Pi JS again sum
+ 
+
+ align:start position:0%
+you this prefix sum of Pi JS again sum
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+composition uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is going to be relatively easy
+
+ align:start position:0%
+so this is going to be relatively easy
+ 
+
+ align:start position:0%
+so this is going to be relatively easy
+to prove but it's not the problem we
+
+ align:start position:0%
+to prove but it's not the problem we
+ 
+
+ align:start position:0%
+to prove but it's not the problem we
+actually want to solve we'll use it to
+
+ align:start position:0%
+actually want to solve we'll use it to
+ 
+
+ align:start position:0%
+actually want to solve we'll use it to
+then solve the the real problem and this
+
+ align:start position:0%
+then solve the the real problem and this
+ 
+
+ align:start position:0%
+then solve the the real problem and this
+is the order in which we actually solve
+
+ align:start position:0%
+is the order in which we actually solve
+ 
+
+ align:start position:0%
+is the order in which we actually solve
+things first prove a lower bound on
+
+ align:start position:0%
+things first prove a lower bound on
+ 
+
+ align:start position:0%
+things first prove a lower bound on
+partial sums uh okay so let me give you
+
+ align:start position:0%
+partial sums uh okay so let me give you
+ 
+
+ align:start position:0%
+partial sums uh okay so let me give you
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+notation so we can really get at uh this
+
+ align:start position:0%
+notation so we can really get at uh this
+ 
+
+ align:start position:0%
+notation so we can really get at uh this
+claim reading on the
+
+ align:start position:0%
+claim reading on the
+ 
+
+ align:start position:0%
+claim reading on the
+right writing on the left so let R be
+
+ align:start position:0%
+right writing on the left so let R be
+ 
+
+ align:start position:0%
+right writing on the left so let R be
+all the cells that are read
+
+ align:start position:0%
+all the cells that are read
+ 
+
+ align:start position:0%
+all the cells that are read
+during the right sub tree which is an
+
+ align:start position:0%
+during the right sub tree which is an
+ 
+
+ align:start position:0%
+during the right sub tree which is an
+interval of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time and let
+
+ align:start position:0%
+time and let
+ 
+
+ align:start position:0%
+time and let
+W be the cells written in the left sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree okay so what we're talking about
+
+ align:start position:0%
+tree okay so what we're talking about
+ 
+
+ align:start position:0%
+tree okay so what we're talking about
+over here is that R intersect W those
+
+ align:start position:0%
+over here is that R intersect W those
+ 
+
+ align:start position:0%
+over here is that R intersect W those
+are cells that are read during the right
+
+ align:start position:0%
+are cells that are read during the right
+ 
+
+ align:start position:0%
+are cells that are read during the right
+C Tre that were at some point written
+
+ align:start position:0%
+C Tre that were at some point written
+ 
+
+ align:start position:0%
+C Tre that were at some point written
+during the left sub tree uh should be
+
+ align:start position:0%
+during the left sub tree uh should be
+ 
+
+ align:start position:0%
+during the left sub tree uh should be
+large so we want to prove a lower bound
+
+ align:start position:0%
+large so we want to prove a lower bound
+ 
+
+ align:start position:0%
+large so we want to prove a lower bound
+on the size of R intersect w
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if the lower bound doesn't hold that
+
+ align:start position:0%
+so if the lower bound doesn't hold that
+ 
+
+ align:start position:0%
+so if the lower bound doesn't hold that
+means that R intersect W is relatively
+
+ align:start position:0%
+means that R intersect W is relatively
+ 
+
+ align:start position:0%
+means that R intersect W is relatively
+small so imagine a situation where R
+
+ align:start position:0%
+small so imagine a situation where R
+ 
+
+ align:start position:0%
+small so imagine a situation where R
+intersect W is very small there's not
+
+ align:start position:0%
+intersect W is very small there's not
+ 
+
+ align:start position:0%
+intersect W is very small there's not
+very much information passed on the left
+
+ align:start position:0%
+very much information passed on the left
+ 
+
+ align:start position:0%
+very much information passed on the left
+sub tree to the right sub tree if R
+
+ align:start position:0%
+sub tree to the right sub tree if R
+ 
+
+ align:start position:0%
+sub tree to the right sub tree if R
+intersect W is small then presumably I
+
+ align:start position:0%
+intersect W is small then presumably I
+ 
+
+ align:start position:0%
+intersect W is small then presumably I
+can afford to write it down I can encode
+
+ align:start position:0%
+can afford to write it down I can encode
+ 
+
+ align:start position:0%
+can afford to write it down I can encode
+it so that's what we're going to do and
+
+ align:start position:0%
+it so that's what we're going to do and
+ 
+
+ align:start position:0%
+it so that's what we're going to do and
+we'll compute we'll figure out that this
+
+ align:start position:0%
+we'll compute we'll figure out that this
+ 
+
+ align:start position:0%
+we'll compute we'll figure out that this
+is indeed something we can afford I'm
+
+ align:start position:0%
+is indeed something we can afford I'm
+ 
+
+ align:start position:0%
+is indeed something we can afford I'm
+going to encode R intersect W explicitly
+
+ align:start position:0%
+going to encode R intersect W explicitly
+ 
+
+ align:start position:0%
+going to encode R intersect W explicitly
+meaning this is a a set of cells in
+
+ align:start position:0%
+meaning this is a a set of cells in
+ 
+
+ align:start position:0%
+meaning this is a a set of cells in
+memory so for every cell I'm going to
+
+ align:start position:0%
+memory so for every cell I'm going to
+ 
+
+ align:start position:0%
+memory so for every cell I'm going to
+write down what its address is and what
+
+ align:start position:0%
+write down what its address is and what
+ 
+
+ align:start position:0%
+write down what its address is and what
+the contents of the cell are
+
+ align:start position:0%
+the contents of the cell are
+ 
+
+ align:start position:0%
+the contents of the cell are
+so write down the
+
+ align:start position:0%
+so write down the
+ 
+
+ align:start position:0%
+so write down the
+addresses and the
+
+ align:start position:0%
+addresses and the
+ 
+
+ align:start position:0%
+addresses and the
+contents for every such cell so how many
+
+ align:start position:0%
+contents for every such cell so how many
+ 
+
+ align:start position:0%
+contents for every such cell so how many
+bits does that take uh I'm going to say
+
+ align:start position:0%
+bits does that take uh I'm going to say
+ 
+
+ align:start position:0%
+bits does that take uh I'm going to say
+that it's R inter
+
+ align:start position:0%
+that it's R inter
+ 
+
+ align:start position:0%
+that it's R inter
+W time log n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bits uh here's where I need to mention
+
+ align:start position:0%
+Bits uh here's where I need to mention
+ 
+
+ align:start position:0%
+Bits uh here's where I need to mention
+an assumption uh I'm assuming that the
+
+ align:start position:0%
+an assumption uh I'm assuming that the
+ 
+
+ align:start position:0%
+an assumption uh I'm assuming that the
+address space is order log n Bits long
+
+ align:start position:0%
+address space is order log n Bits long
+ 
+
+ align:start position:0%
+address space is order log n Bits long
+that's like saying that the space of
+
+ align:start position:0%
+that's like saying that the space of
+ 
+
+ align:start position:0%
+that's like saying that the space of
+your data structure is order uh is
+
+ align:start position:0%
+your data structure is order uh is
+ 
+
+ align:start position:0%
+your data structure is order uh is
+polinomial In N and if you want any hope
+
+ align:start position:0%
+polinomial In N and if you want any hope
+ 
+
+ align:start position:0%
+polinomial In N and if you want any hope
+of having a reasonable update time you
+
+ align:start position:0%
+of having a reasonable update time you
+ 
+
+ align:start position:0%
+of having a reasonable update time you
+need to have polinomial space at most so
+
+ align:start position:0%
+need to have polinomial space at most so
+ 
+
+ align:start position:0%
+need to have polinomial space at most so
+assuming polinomial space each of those
+
+ align:start position:0%
+assuming polinomial space each of those
+ 
+
+ align:start position:0%
+assuming polinomial space each of those
+addresses only takes order log n Bits to
+
+ align:start position:0%
+addresses only takes order log n Bits to
+ 
+
+ align:start position:0%
+addresses only takes order log n Bits to
+write down the contents uh let's say
+
+ align:start position:0%
+write down the contents uh let's say
+ 
+
+ align:start position:0%
+write down the contents uh let's say
+also take order log n Bits to write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down okay so
+
+ align:start position:0%
+down okay so
+ 
+
+ align:start position:0%
+down okay so
+fine uh
+
+ align:start position:0%
+fine uh
+ 
+
+ align:start position:0%
+fine uh
+that's uh I mean yeah we don't really
+
+ align:start position:0%
+that's uh I mean yeah we don't really
+ 
+
+ align:start position:0%
+that's uh I mean yeah we don't really
+need to make those assumptions I don't
+
+ align:start position:0%
+need to make those assumptions I don't
+ 
+
+ align:start position:0%
+need to make those assumptions I don't
+think but uh we will for here to keep
+
+ align:start position:0%
+think but uh we will for here to keep
+ 
+
+ align:start position:0%
+think but uh we will for here to keep
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+simple so if R intersect W is small
+
+ align:start position:0%
+simple so if R intersect W is small
+ 
+
+ align:start position:0%
+simple so if R intersect W is small
+meaning smaller than this thing then
+
+ align:start position:0%
+meaning smaller than this thing then
+ 
+
+ align:start position:0%
+meaning smaller than this thing then
+this will be small smaller than L root n
+
+ align:start position:0%
+this will be small smaller than L root n
+ 
+
+ align:start position:0%
+this will be small smaller than L root n
+log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh on the other hand we know that
+
+ align:start position:0%
+so uh on the other hand we know that
+ 
+
+ align:start position:0%
+so uh on the other hand we know that
+every encoding should take L root n log
+
+ align:start position:0%
+every encoding should take L root n log
+ 
+
+ align:start position:0%
+every encoding should take L root n log
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+Bits right so this will be a
+
+ align:start position:0%
+Bits right so this will be a
+ 
+
+ align:start position:0%
+Bits right so this will be a
+contradiction although we're not we
+
+ align:start position:0%
+contradiction although we're not we
+ 
+
+ align:start position:0%
+contradiction although we're not we
+haven't quite encoded what we need yet
+
+ align:start position:0%
+haven't quite encoded what we need yet
+ 
+
+ align:start position:0%
+haven't quite encoded what we need yet
+uh or we haven't proved that but we're
+
+ align:start position:0%
+uh or we haven't proved that but we're
+ 
+
+ align:start position:0%
+uh or we haven't proved that but we're
+we're getting to be the right point
+
+ align:start position:0%
+we're getting to be the right point
+ 
+
+ align:start position:0%
+we're getting to be the right point
+there these log ends are going to cancel
+
+ align:start position:0%
+there these log ends are going to cancel
+ 
+
+ align:start position:0%
+there these log ends are going to cancel
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+moment so what what we need to do is I
+
+ align:start position:0%
+moment so what what we need to do is I
+ 
+
+ align:start position:0%
+moment so what what we need to do is I
+claim this is actually enough to encode
+
+ align:start position:0%
+claim this is actually enough to encode
+ 
+
+ align:start position:0%
+claim this is actually enough to encode
+what we need and so all that's left is a
+
+ align:start position:0%
+what we need and so all that's left is a
+ 
+
+ align:start position:0%
+what we need and so all that's left is a
+decoding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm uh for the sum
+
+ align:start position:0%
+algorithm uh for the sum
+ 
+
+ align:start position:0%
+algorithm uh for the sum
+queries in the right sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree so how we going to do that uh so
+
+ align:start position:0%
+tree so how we going to do that uh so
+ 
+
+ align:start position:0%
+tree so how we going to do that uh so
+this is my encoding these are the bits
+
+ align:start position:0%
+this is my encoding these are the bits
+ 
+
+ align:start position:0%
+this is my encoding these are the bits
+that I have written down so now what I
+
+ align:start position:0%
+that I have written down so now what I
+ 
+
+ align:start position:0%
+that I have written down so now what I
+know as a decoder is I know everything
+
+ align:start position:0%
+know as a decoder is I know everything
+ 
+
+ align:start position:0%
+know as a decoder is I know everything
+about the past I don't know what these
+
+ align:start position:0%
+about the past I don't know what these
+ 
+
+ align:start position:0%
+about the past I don't know what these
+updates are that's my whole goal is to
+
+ align:start position:0%
+updates are that's my whole goal is to
+ 
+
+ align:start position:0%
+updates are that's my whole goal is to
+figure out what they are I don't know
+
+ align:start position:0%
+figure out what they are I don't know
+ 
+
+ align:start position:0%
+figure out what they are I don't know
+what the results of the queries are but
+
+ align:start position:0%
+what the results of the queries are but
+ 
+
+ align:start position:0%
+what the results of the queries are but
+magically I know R intersect W well not
+
+ align:start position:0%
+magically I know R intersect W well not
+ 
+
+ align:start position:0%
+magically I know R intersect W well not
+magically I wrote it down kept on a
+
+ align:start position:0%
+magically I wrote it down kept on a
+ 
+
+ align:start position:0%
+magically I wrote it down kept on a
+piece of paper so that's what I know and
+
+ align:start position:0%
+piece of paper so that's what I know and
+ 
+
+ align:start position:0%
+piece of paper so that's what I know and
+so the idea is well um we somebody gave
+
+ align:start position:0%
+so the idea is well um we somebody gave
+ 
+
+ align:start position:0%
+so the idea is well um we somebody gave
+us a data structure to tells you how to
+
+ align:start position:0%
+us a data structure to tells you how to
+ 
+
+ align:start position:0%
+us a data structure to tells you how to
+do an update tells you how to do a query
+
+ align:start position:0%
+do an update tells you how to do a query
+ 
+
+ align:start position:0%
+do an update tells you how to do a query
+let's run the query algorithm over
+
+ align:start position:0%
+let's run the query algorithm over
+ 
+
+ align:start position:0%
+let's run the query algorithm over
+here run that query run that query
+
+ align:start position:0%
+here run that query run that query
+ 
+
+ align:start position:0%
+here run that query run that query
+whatever uh it's a little hard to run
+
+ align:start position:0%
+whatever uh it's a little hard to run
+ 
+
+ align:start position:0%
+whatever uh it's a little hard to run
+them because we don't know what happened
+
+ align:start position:0%
+them because we don't know what happened
+ 
+
+ align:start position:0%
+them because we don't know what happened
+in this intermediate part but I claim R
+
+ align:start position:0%
+in this intermediate part but I claim R
+ 
+
+ align:start position:0%
+in this intermediate part but I claim R
+intersect W tells us everything we need
+
+ align:start position:0%
+intersect W tells us everything we need
+ 
+
+ align:start position:0%
+intersect W tells us everything we need
+to know so decoding algorithm is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simulate uh some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+queries simulate that
+
+ align:start position:0%
+queries simulate that
+ 
+
+ align:start position:0%
+queries simulate that
+algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and let's go up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here how do we simulate that algorithm
+
+ align:start position:0%
+here how do we simulate that algorithm
+ 
+
+ align:start position:0%
+here how do we simulate that algorithm
+well this the algorithm makes a series
+
+ align:start position:0%
+well this the algorithm makes a series
+ 
+
+ align:start position:0%
+well this the algorithm makes a series
+of cell reads and maybe wres but really
+
+ align:start position:0%
+of cell reads and maybe wres but really
+ 
+
+ align:start position:0%
+of cell reads and maybe wres but really
+we care about the
+
+ align:start position:0%
+we care about the
+ 
+
+ align:start position:0%
+we care about the
+reads wres are pretty easy to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simulate there are three cases for reads
+
+ align:start position:0%
+simulate there are three cases for reads
+ 
+
+ align:start position:0%
+simulate there are three cases for reads
+it could be that the thing you're trying
+
+ align:start position:0%
+it could be that the thing you're trying
+ 
+
+ align:start position:0%
+it could be that the thing you're trying
+to read was written in the right sub
+
+ align:start position:0%
+to read was written in the right sub
+ 
+
+ align:start position:0%
+to read was written in the right sub
+tree it could be that it was written in
+
+ align:start position:0%
+tree it could be that it was written in
+ 
+
+ align:start position:0%
+tree it could be that it was written in
+the left sub tree or it could be it was
+
+ align:start position:0%
+the left sub tree or it could be it was
+ 
+
+ align:start position:0%
+the left sub tree or it could be it was
+written in the past before we got to V's
+
+ align:start position:0%
+written in the past before we got to V's
+ 
+
+ align:start position:0%
+written in the past before we got to V's
+sub
+
+ align:start position:0%
+sub
+ 
+
+ align:start position:0%
+sub
+tree now we don't necessarily know which
+
+ align:start position:0%
+tree now we don't necessarily know which
+ 
+
+ align:start position:0%
+tree now we don't necessarily know which
+case we're in but I claim we'll be able
+
+ align:start position:0%
+case we're in but I claim we'll be able
+ 
+
+ align:start position:0%
+case we're in but I claim we'll be able
+to figure it out because any cells that
+
+ align:start position:0%
+to figure it out because any cells that
+ 
+
+ align:start position:0%
+to figure it out because any cells that
+are written in the right subtree well we
+
+ align:start position:0%
+are written in the right subtree well we
+ 
+
+ align:start position:0%
+are written in the right subtree well we
+we've just been running the simulation
+
+ align:start position:0%
+we've just been running the simulation
+ 
+
+ align:start position:0%
+we've just been running the simulation
+algorithm so every time we do a right we
+
+ align:start position:0%
+algorithm so every time we do a right we
+ 
+
+ align:start position:0%
+algorithm so every time we do a right we
+just we can store it off to the side so
+
+ align:start position:0%
+just we can store it off to the side so
+ 
+
+ align:start position:0%
+just we can store it off to the side so
+as when we're doing simulations we don't
+
+ align:start position:0%
+as when we're doing simulations we don't
+ 
+
+ align:start position:0%
+as when we're doing simulations we don't
+need that the simulation takes low speed
+
+ align:start position:0%
+need that the simulation takes low speed
+ 
+
+ align:start position:0%
+need that the simulation takes low speed
+space we just need that the input I this
+
+ align:start position:0%
+space we just need that the input I this
+ 
+
+ align:start position:0%
+space we just need that the input I this
+decoding algorithm doesn't have to be
+
+ align:start position:0%
+decoding algorithm doesn't have to be
+ 
+
+ align:start position:0%
+decoding algorithm doesn't have to be
+low space we just need that the encoding
+
+ align:start position:0%
+low space we just need that the encoding
+ 
+
+ align:start position:0%
+low space we just need that the encoding
+was small we've already made the
+
+ align:start position:0%
+was small we've already made the
+ 
+
+ align:start position:0%
+was small we've already made the
+encoding small and so the decoding
+
+ align:start position:0%
+encoding small and so the decoding
+ 
+
+ align:start position:0%
+encoding small and so the decoding
+algorithm can spend lots of time and
+
+ align:start position:0%
+algorithm can spend lots of time and
+ 
+
+ align:start position:0%
+algorithm can spend lots of time and
+space we just need to show the decoding
+
+ align:start position:0%
+space we just need to show the decoding
+ 
+
+ align:start position:0%
+space we just need to show the decoding
+algorithm can recover what it's supposed
+
+ align:start position:0%
+algorithm can recover what it's supposed
+ 
+
+ align:start position:0%
+algorithm can recover what it's supposed
+to recover this is like a compression
+
+ align:start position:0%
+to recover this is like a compression
+ 
+
+ align:start position:0%
+to recover this is like a compression
+algorithm to show there's some way to
+
+ align:start position:0%
+algorithm to show there's some way to
+ 
+
+ align:start position:0%
+algorithm to show there's some way to
+decompress could take arbitrarily amount
+
+ align:start position:0%
+decompress could take arbitrarily amount
+ 
+
+ align:start position:0%
+decompress could take arbitrarily amount
+of time and space so uh when we're
+
+ align:start position:0%
+of time and space so uh when we're
+ 
+
+ align:start position:0%
+of time and space so uh when we're
+simulating the right subtree I mean we
+
+ align:start position:0%
+simulating the right subtree I mean we
+ 
+
+ align:start position:0%
+simulating the right subtree I mean we
+simulate not only the sum the sum
+
+ align:start position:0%
+simulate not only the sum the sum
+ 
+
+ align:start position:0%
+simulate not only the sum the sum
+queries but also the
+
+ align:start position:0%
+queries but also the
+ 
+
+ align:start position:0%
+queries but also the
+updates
+
+ align:start position:0%
+updates
+ 
+
+ align:start position:0%
+updates
+so whatever gets written during that
+
+ align:start position:0%
+so whatever gets written during that
+ 
+
+ align:start position:0%
+so whatever gets written during that
+simulation we just store it and so easy
+
+ align:start position:0%
+simulation we just store it and so easy
+ 
+
+ align:start position:0%
+simulation we just store it and so easy
+to reread it if it was store if it was
+
+ align:start position:0%
+to reread it if it was store if it was
+ 
+
+ align:start position:0%
+to reread it if it was store if it was
+written in the left sub tree well that
+
+ align:start position:0%
+written in the left sub tree well that
+ 
+
+ align:start position:0%
+written in the left sub tree well that
+is R intersect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W and we've written down our intersect W
+
+ align:start position:0%
+W and we've written down our intersect W
+ 
+
+ align:start position:0%
+W and we've written down our intersect W
+so we can detect that this happened
+
+ align:start position:0%
+so we can detect that this happened
+ 
+
+ align:start position:0%
+so we can detect that this happened
+because we look at uh our intersect w we
+
+ align:start position:0%
+because we look at uh our intersect w we
+ 
+
+ align:start position:0%
+because we look at uh our intersect w we
+see oh that word was in there that
+
+ align:start position:0%
+see oh that word was in there that
+ 
+
+ align:start position:0%
+see oh that word was in there that
+address was in there and so we read the
+
+ align:start position:0%
+address was in there and so we read the
+ 
+
+ align:start position:0%
+address was in there and so we read the
+contents from the
+
+ align:start position:0%
+contents from the
+ 
+
+ align:start position:0%
+contents from the
+encoding if it was in the past
+
+ align:start position:0%
+encoding if it was in the past
+ 
+
+ align:start position:0%
+encoding if it was in the past
+uh it's also
+
+ align:start position:0%
+uh it's also
+ 
+
+ align:start position:0%
+uh it's also
+easy we already knew
+
+ align:start position:0%
+easy we already knew
+ 
+
+ align:start position:0%
+easy we already knew
+it okay so basically what we
+
+ align:start position:0%
+it okay so basically what we
+ 
+
+ align:start position:0%
+it okay so basically what we
+do what the simulation algorithm is
+
+ align:start position:0%
+do what the simulation algorithm is
+ 
+
+ align:start position:0%
+do what the simulation algorithm is
+doing is it says okay let's assume that
+
+ align:start position:0%
+doing is it says okay let's assume that
+ 
+
+ align:start position:0%
+doing is it says okay let's assume that
+main memory was whatever it was at this
+
+ align:start position:0%
+main memory was whatever it was at this
+ 
+
+ align:start position:0%
+main memory was whatever it was at this
+point the data structure I mean we know
+
+ align:start position:0%
+point the data structure I mean we know
+ 
+
+ align:start position:0%
+point the data structure I mean we know
+everything about the past so we know
+
+ align:start position:0%
+everything about the past so we know
+ 
+
+ align:start position:0%
+everything about the past so we know
+what the data structure looked like at
+
+ align:start position:0%
+what the data structure looked like at
+ 
+
+ align:start position:0%
+what the data structure looked like at
+this moment store that uh update all of
+
+ align:start position:0%
+this moment store that uh update all of
+ 
+
+ align:start position:0%
+this moment store that uh update all of
+the cells that are in R intersect W
+
+ align:start position:0%
+the cells that are in R intersect W
+ 
+
+ align:start position:0%
+the cells that are in R intersect W
+given by our encoding and then just run
+
+ align:start position:0%
+given by our encoding and then just run
+ 
+
+ align:start position:0%
+given by our encoding and then just run
+the algorithm so we're sort of jumping
+
+ align:start position:0%
+the algorithm so we're sort of jumping
+ 
+
+ align:start position:0%
+the algorithm so we're sort of jumping
+into this moment in time with a slightly
+
+ align:start position:0%
+into this moment in time with a slightly
+ 
+
+ align:start position:0%
+into this moment in time with a slightly
+weird data structure it's not the
+
+ align:start position:0%
+weird data structure it's not the
+ 
+
+ align:start position:0%
+weird data structure it's not the
+correct data
+
+ align:start position:0%
+correct data
+ 
+
+ align:start position:0%
+correct data
+structure uh it's not what the data
+
+ align:start position:0%
+structure uh it's not what the data
+ 
+
+ align:start position:0%
+structure uh it's not what the data
+structure will actually look like at
+
+ align:start position:0%
+structure will actually look like at
+ 
+
+ align:start position:0%
+structure will actually look like at
+this point but it's close enough because
+
+ align:start position:0%
+this point but it's close enough because
+ 
+
+ align:start position:0%
+this point but it's close enough because
+anything that's read here uh either was
+
+ align:start position:0%
+anything that's read here uh either was
+ 
+
+ align:start position:0%
+anything that's read here uh either was
+written here which case it's correct or
+
+ align:start position:0%
+written here which case it's correct or
+ 
+
+ align:start position:0%
+written here which case it's correct or
+was written here in which case it's
+
+ align:start position:0%
+was written here in which case it's
+ 
+
+ align:start position:0%
+was written here in which case it's
+correct because R intersect W had it um
+
+ align:start position:0%
+correct because R intersect W had it um
+ 
+
+ align:start position:0%
+correct because R intersect W had it um
+or is written here in which case maybe
+
+ align:start position:0%
+or is written here in which case maybe
+ 
+
+ align:start position:0%
+or is written here in which case maybe
+it's always
+
+ align:start position:0%
+it's always
+ 
+
+ align:start position:0%
+it's always
+correct no no see there could be some
+
+ align:start position:0%
+correct no no see there could be some
+ 
+
+ align:start position:0%
+correct no no see there could be some
+rights that happened here where there's
+
+ align:start position:0%
+rights that happened here where there's
+ 
+
+ align:start position:0%
+rights that happened here where there's
+no corresponding read over here so the
+
+ align:start position:0%
+no corresponding read over here so the
+ 
+
+ align:start position:0%
+no corresponding read over here so the
+data structure may have been changed in
+
+ align:start position:0%
+data structure may have been changed in
+ 
+
+ align:start position:0%
+data structure may have been changed in
+ways here that don't matter for this R
+
+ align:start position:0%
+ways here that don't matter for this R
+ 
+
+ align:start position:0%
+ways here that don't matter for this R
+execution of the right sub tree because
+
+ align:start position:0%
+execution of the right sub tree because
+ 
+
+ align:start position:0%
+execution of the right sub tree because
+any rights that happen here to some cell
+
+ align:start position:0%
+any rights that happen here to some cell
+ 
+
+ align:start position:0%
+any rights that happen here to some cell
+probe to some cell where that cell is
+
+ align:start position:0%
+probe to some cell where that cell is
+ 
+
+ align:start position:0%
+probe to some cell where that cell is
+not red over here we don't care about
+
+ align:start position:0%
+not red over here we don't care about
+ 
+
+ align:start position:0%
+not red over here we don't care about
+because they don't affect the simulation
+
+ align:start position:0%
+because they don't affect the simulation
+ 
+
+ align:start position:0%
+because they don't affect the simulation
+so we have a good enough data structure
+
+ align:start position:0%
+so we have a good enough data structure
+ 
+
+ align:start position:0%
+so we have a good enough data structure
+over here may not be completely accurate
+
+ align:start position:0%
+over here may not be completely accurate
+ 
+
+ align:start position:0%
+over here may not be completely accurate
+but it's accurate enough to run these
+
+ align:start position:0%
+but it's accurate enough to run these
+ 
+
+ align:start position:0%
+but it's accurate enough to run these
+queries once we run the queries the
+
+ align:start position:0%
+queries once we run the queries the
+ 
+
+ align:start position:0%
+queries once we run the queries the
+queries output the sums that's what
+
+ align:start position:0%
+queries output the sums that's what
+ 
+
+ align:start position:0%
+queries output the sums that's what
+we're assuming in this warmup We Run The
+
+ align:start position:0%
+we're assuming in this warmup We Run The
+ 
+
+ align:start position:0%
+we're assuming in this warmup We Run The
+query we get the sum once I have that
+
+ align:start position:0%
+query we get the sum once I have that
+ 
+
+ align:start position:0%
+query we get the sum once I have that
+sum as I argued before once you know
+
+ align:start position:0%
+sum as I argued before once you know
+ 
+
+ align:start position:0%
+sum as I argued before once you know
+what the results of these queries were I
+
+ align:start position:0%
+what the results of these queries were I
+ 
+
+ align:start position:0%
+what the results of these queries were I
+can figure out what the arguments to the
+
+ align:start position:0%
+can figure out what the arguments to the
+ 
+
+ align:start position:0%
+can figure out what the arguments to the
+updates were by doing that inverse
+
+ align:start position:0%
+updates were by doing that inverse
+ 
+
+ align:start position:0%
+updates were by doing that inverse
+multiplication stuff okay so that's
+
+ align:start position:0%
+multiplication stuff okay so that's
+ 
+
+ align:start position:0%
+multiplication stuff okay so that's
+actually it what this
+
+ align:start position:0%
+actually it what this
+ 
+
+ align:start position:0%
+actually it what this
+implies is that this is a correct
+
+ align:start position:0%
+implies is that this is a correct
+ 
+
+ align:start position:0%
+implies is that this is a correct
+encoding which means that this uh order
+
+ align:start position:0%
+encoding which means that this uh order
+ 
+
+ align:start position:0%
+encoding which means that this uh order
+R intersect w time log n Bits that we
+
+ align:start position:0%
+R intersect w time log n Bits that we
+ 
+
+ align:start position:0%
+R intersect w time log n Bits that we
+use to encode must be at least this big
+
+ align:start position:0%
+use to encode must be at least this big
+ 
+
+ align:start position:0%
+use to encode must be at least this big
+because we know and any encoding is
+
+ align:start position:0%
+because we know and any encoding is
+ 
+
+ align:start position:0%
+because we know and any encoding is
+going to require at least that many
+
+ align:start position:0%
+going to require at least that many
+ 
+
+ align:start position:0%
+going to require at least that many
+bits L root n log
+
+ align:start position:0%
+bits L root n log
+ 
+
+ align:start position:0%
+bits L root n log
+n and so the log n's
+
+ align:start position:0%
+n and so the log n's
+ 
+
+ align:start position:0%
+n and so the log n's
+cancel and we're left with r intersect W
+
+ align:start position:0%
+cancel and we're left with r intersect W
+ 
+
+ align:start position:0%
+cancel and we're left with r intersect W
+is at least L root n and this is exactly
+
+ align:start position:0%
+is at least L root n and this is exactly
+ 
+
+ align:start position:0%
+is at least L root n and this is exactly
+the quantity we cared about for this
+
+ align:start position:0%
+the quantity we cared about for this
+ 
+
+ align:start position:0%
+the quantity we cared about for this
+claim so same thing R intersect is at
+
+ align:start position:0%
+claim so same thing R intersect is at
+ 
+
+ align:start position:0%
+claim so same thing R intersect is at
+least lot
+
+ align:start position:0%
+least lot
+ 
+
+ align:start position:0%
+least lot
+n okay so warmup done any questions
+
+ align:start position:0%
+n okay so warmup done any questions
+ 
+
+ align:start position:0%
+n okay so warmup done any questions
+about the
+
+ align:start position:0%
+about the
+ 
+
+ align:start position:0%
+about the
+warmup so in this weird problem which
+
+ align:start position:0%
+warmup so in this weird problem which
+ 
+
+ align:start position:0%
+warmup so in this weird problem which
+does not correspond to Dynamic
+
+ align:start position:0%
+does not correspond to Dynamic
+ 
+
+ align:start position:0%
+does not correspond to Dynamic
+connectivity it's this other problem
+
+ align:start position:0%
+connectivity it's this other problem
+ 
+
+ align:start position:0%
+connectivity it's this other problem
+prefix sums computation uh we get the
+
+ align:start position:0%
+prefix sums computation uh we get the
+ 
+
+ align:start position:0%
+prefix sums computation uh we get the
+intended lower bound you need log n per
+
+ align:start position:0%
+intended lower bound you need log n per
+ 
+
+ align:start position:0%
+intended lower bound you need log n per
+operation or need root n log n per block
+
+ align:start position:0%
+operation or need root n log n per block
+ 
+
+ align:start position:0%
+operation or need root n log n per block
+operation okay but this is not what we
+
+ align:start position:0%
+operation okay but this is not what we
+ 
+
+ align:start position:0%
+operation okay but this is not what we
+really want we really want a lower bound
+
+ align:start position:0%
+really want we really want a lower bound
+ 
+
+ align:start position:0%
+really want we really want a lower bound
+on verify sum well you're given as an
+
+ align:start position:0%
+on verify sum well you're given as an
+ 
+
+ align:start position:0%
+on verify sum well you're given as an
+argument the permutation that we're
+
+ align:start position:0%
+argument the permutation that we're
+ 
+
+ align:start position:0%
+argument the permutation that we're
+talking about over here so it's uh this
+
+ align:start position:0%
+talking about over here so it's uh this
+ 
+
+ align:start position:0%
+talking about over here so it's uh this
+goal is not the right goal for verify
+
+ align:start position:0%
+goal is not the right goal for verify
+ 
+
+ align:start position:0%
+goal is not the right goal for verify
+sum in some sense well sort of the right
+
+ align:start position:0%
+sum in some sense well sort of the right
+ 
+
+ align:start position:0%
+sum in some sense well sort of the right
+goal it's a little awkward though
+
+ align:start position:0%
+goal it's a little awkward though
+ 
+
+ align:start position:0%
+goal it's a little awkward though
+because they're given as inputs to the
+
+ align:start position:0%
+because they're given as inputs to the
+ 
+
+ align:start position:0%
+because they're given as inputs to the
+queries so what is there to
+
+ align:start position:0%
+queries so what is there to
+ 
+
+ align:start position:0%
+queries so what is there to
+encode well we can still set it up in a
+
+ align:start position:0%
+encode well we can still set it up in a
+ 
+
+ align:start position:0%
+encode well we can still set it up in a
+useful way same goal slightly
+
+ align:start position:0%
+useful way same goal slightly
+ 
+
+ align:start position:0%
+useful way same goal slightly
+restated
+
+ align:start position:0%
+restated
+ 
+
+ align:start position:0%
+restated
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the the last step to verify
+
+ align:start position:0%
+so this is the the last step to verify
+ 
+
+ align:start position:0%
+so this is the the last step to verify
+some lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+setup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's a slightly different setup
+
+ align:start position:0%
+okay it's a slightly different setup
+ 
+
+ align:start position:0%
+okay it's a slightly different setup
+here here I assume that we just knew the
+
+ align:start position:0%
+here here I assume that we just knew the
+ 
+
+ align:start position:0%
+here here I assume that we just knew the
+past uh I also basically assumed these
+
+ align:start position:0%
+past uh I also basically assumed these
+ 
+
+ align:start position:0%
+past uh I also basically assumed these
+two things that we don't we didn't know
+
+ align:start position:0%
+two things that we don't we didn't know
+ 
+
+ align:start position:0%
+two things that we don't we didn't know
+what the update permutations were in the
+
+ align:start position:0%
+what the update permutations were in the
+ 
+
+ align:start position:0%
+what the update permutations were in the
+left sub tree and we didn't know what
+
+ align:start position:0%
+left sub tree and we didn't know what
+ 
+
+ align:start position:0%
+left sub tree and we didn't know what
+the answers to the queries were in the
+
+ align:start position:0%
+the answers to the queries were in the
+ 
+
+ align:start position:0%
+the answers to the queries were in the
+right sub tree now I'm going to assume
+
+ align:start position:0%
+right sub tree now I'm going to assume
+ 
+
+ align:start position:0%
+right sub tree now I'm going to assume
+we don't even know what we're passing
+
+ align:start position:0%
+we don't even know what we're passing
+ 
+
+ align:start position:0%
+we don't even know what we're passing
+into the queries because is the
+
+ align:start position:0%
+into the queries because is the
+ 
+
+ align:start position:0%
+into the queries because is the
+information we're trying to figure out
+
+ align:start position:0%
+information we're trying to figure out
+ 
+
+ align:start position:0%
+information we're trying to figure out
+or these two things are basically the
+
+ align:start position:0%
+or these two things are basically the
+ 
+
+ align:start position:0%
+or these two things are basically the
+same if if you knew all the update
+
+ align:start position:0%
+same if if you knew all the update
+ 
+
+ align:start position:0%
+same if if you knew all the update
+permutations you could figure out all
+
+ align:start position:0%
+permutations you could figure out all
+ 
+
+ align:start position:0%
+permutations you could figure out all
+the query permutations if you knew all
+
+ align:start position:0%
+the query permutations if you knew all
+ 
+
+ align:start position:0%
+the query permutations if you knew all
+the query permutations you could figure
+
+ align:start position:0%
+the query permutations you could figure
+ 
+
+ align:start position:0%
+the query permutations you could figure
+out all the update permutations that's
+
+ align:start position:0%
+out all the update permutations that's
+ 
+
+ align:start position:0%
+out all the update permutations that's
+what we argued over here it was enough
+
+ align:start position:0%
+what we argued over here it was enough
+ 
+
+ align:start position:0%
+what we argued over here it was enough
+to figure out uh query permutations that
+
+ align:start position:0%
+to figure out uh query permutations that
+ 
+
+ align:start position:0%
+to figure out uh query permutations that
+we could figure out the update
+
+ align:start position:0%
+we could figure out the update
+ 
+
+ align:start position:0%
+we could figure out the update
+permutations uh it's just a little more
+
+ align:start position:0%
+permutations uh it's just a little more
+ 
+
+ align:start position:0%
+permutations uh it's just a little more
+Awkward because now they're arguments to
+
+ align:start position:0%
+Awkward because now they're arguments to
+ 
+
+ align:start position:0%
+Awkward because now they're arguments to
+queries and so if we did this simulation
+
+ align:start position:0%
+queries and so if we did this simulation
+ 
+
+ align:start position:0%
+queries and so if we did this simulation
+right we' simulate we don't know how to
+
+ align:start position:0%
+right we' simulate we don't know how to
+ 
+
+ align:start position:0%
+right we' simulate we don't know how to
+simulate the quer query algorithm
+
+ align:start position:0%
+simulate the quer query algorithm
+ 
+
+ align:start position:0%
+simulate the quer query algorithm
+because it's supposed to be given the
+
+ align:start position:0%
+because it's supposed to be given the
+ 
+
+ align:start position:0%
+because it's supposed to be given the
+argument which is what we're trying to
+
+ align:start position:0%
+argument which is what we're trying to
+ 
+
+ align:start position:0%
+argument which is what we're trying to
+figure out so we can't simulate the
+
+ align:start position:0%
+figure out so we can't simulate the
+ 
+
+ align:start position:0%
+figure out so we can't simulate the
+query
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm it's kind of annoying but
+
+ align:start position:0%
+algorithm it's kind of annoying but
+ 
+
+ align:start position:0%
+algorithm it's kind of annoying but
+otherwise the setup is roughly the same
+
+ align:start position:0%
+otherwise the setup is roughly the same
+ 
+
+ align:start position:0%
+otherwise the setup is roughly the same
+uh the one thing we know is that the
+
+ align:start position:0%
+uh the one thing we know is that the
+ 
+
+ align:start position:0%
+uh the one thing we know is that the
+query is supposed to return Yes because
+
+ align:start position:0%
+query is supposed to return Yes because
+ 
+
+ align:start position:0%
+query is supposed to return Yes because
+if you look at uh this bad access
+
+ align:start position:0%
+if you look at uh this bad access
+ 
+
+ align:start position:0%
+if you look at uh this bad access
+sequence it is designed to always return
+
+ align:start position:0%
+sequence it is designed to always return
+ 
+
+ align:start position:0%
+sequence it is designed to always return
+yes so that is a a thing we know um but
+
+ align:start position:0%
+yes so that is a a thing we know um but
+ 
+
+ align:start position:0%
+yes so that is a a thing we know um but
+we don't know the arguments to the
+
+ align:start position:0%
+we don't know the arguments to the
+ 
+
+ align:start position:0%
+we don't know the arguments to the
+updates on the left we don't know
+
+ align:start position:0%
+updates on the left we don't know
+ 
+
+ align:start position:0%
+updates on the left we don't know
+arguments the updates on the right we'll
+
+ align:start position:0%
+arguments the updates on the right we'll
+ 
+
+ align:start position:0%
+arguments the updates on the right we'll
+assume we know everything else basically
+
+ align:start position:0%
+assume we know everything else basically
+ 
+
+ align:start position:0%
+assume we know everything else basically
+up to this time again this is a a
+
+ align:start position:0%
+up to this time again this is a a
+ 
+
+ align:start position:0%
+up to this time again this is a a
+probabilistic statement that uh
+
+ align:start position:0%
+probabilistic statement that uh
+ 
+
+ align:start position:0%
+probabilistic statement that uh
+conditioned on the past conditioned on
+
+ align:start position:0%
+conditioned on the past conditioned on
+ 
+
+ align:start position:0%
+conditioned on the past conditioned on
+the queries on the left which probably
+
+ align:start position:0%
+the queries on the left which probably
+ 
+
+ align:start position:0%
+the queries on the left which probably
+don't matter conditioned on the updates
+
+ align:start position:0%
+don't matter conditioned on the updates
+ 
+
+ align:start position:0%
+don't matter conditioned on the updates
+on the right which do matter but they're
+
+ align:start position:0%
+on the right which do matter but they're
+ 
+
+ align:start position:0%
+on the right which do matter but they're
+sort of irrelevant to this R intersect W
+
+ align:start position:0%
+sort of irrelevant to this R intersect W
+ 
+
+ align:start position:0%
+sort of irrelevant to this R intersect W
+issue uh conditioned on all those things
+
+ align:start position:0%
+issue uh conditioned on all those things
+ 
+
+ align:start position:0%
+issue uh conditioned on all those things
+will prove that the expected number of
+
+ align:start position:0%
+will prove that the expected number of
+ 
+
+ align:start position:0%
+will prove that the expected number of
+operations you need to or expected
+
+ align:start position:0%
+operations you need to or expected
+ 
+
+ align:start position:0%
+operations you need to or expected
+encoding size for this problem is at
+
+ align:start position:0%
+encoding size for this problem is at
+ 
+
+ align:start position:0%
+encoding size for this problem is at
+least what it is L root n log n Bits And
+
+ align:start position:0%
+least what it is L root n log n Bits And
+ 
+
+ align:start position:0%
+least what it is L root n log n Bits And
+from that lower bound you can then uh
+
+ align:start position:0%
+from that lower bound you can then uh
+ 
+
+ align:start position:0%
+from that lower bound you can then uh
+take the sum over all possible setups
+
+ align:start position:0%
+take the sum over all possible setups
+ 
+
+ align:start position:0%
+take the sum over all possible setups
+overall
+
+ align:start position:0%
+overall
+ 
+
+ align:start position:0%
+overall
+conditions and that implies a lower
+
+ align:start position:0%
+conditions and that implies a lower
+ 
+
+ align:start position:0%
+conditions and that implies a lower
+bound on the overall setting without
+
+ align:start position:0%
+bound on the overall setting without
+ 
+
+ align:start position:0%
+bound on the overall setting without
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+okay so all I'm saying is in this setup
+
+ align:start position:0%
+okay so all I'm saying is in this setup
+ 
+
+ align:start position:0%
+okay so all I'm saying is in this setup
+it still takes a lot of bits to encode
+
+ align:start position:0%
+it still takes a lot of bits to encode
+ 
+
+ align:start position:0%
+it still takes a lot of bits to encode
+these updates because we don't have the
+
+ align:start position:0%
+these updates because we don't have the
+ 
+
+ align:start position:0%
+these updates because we don't have the
+queries which would tell us the answers
+
+ align:start position:0%
+queries which would tell us the answers
+ 
+
+ align:start position:0%
+queries which would tell us the answers
+so we get a lower bound on encoding
+
+ align:start position:0%
+so we get a lower bound on encoding
+ 
+
+ align:start position:0%
+so we get a lower bound on encoding
+these updates or a lower bound encoding
+
+ align:start position:0%
+these updates or a lower bound encoding
+ 
+
+ align:start position:0%
+these updates or a lower bound encoding
+these queries because we assume we don't
+
+ align:start position:0%
+these queries because we assume we don't
+ 
+
+ align:start position:0%
+these queries because we assume we don't
+know them the rest of the all the
+
+ align:start position:0%
+know them the rest of the all the
+ 
+
+ align:start position:0%
+know them the rest of the all the
+remaining operations don't tell us
+
+ align:start position:0%
+remaining operations don't tell us
+ 
+
+ align:start position:0%
+remaining operations don't tell us
+enough about
+
+ align:start position:0%
+enough about
+ 
+
+ align:start position:0%
+enough about
+this okay so how the heck are we going
+
+ align:start position:0%
+this okay so how the heck are we going
+ 
+
+ align:start position:0%
+this okay so how the heck are we going
+to do prove a lower Bound in this
+
+ align:start position:0%
+to do prove a lower Bound in this
+ 
+
+ align:start position:0%
+to do prove a lower Bound in this
+setting when we can't simulate the query
+
+ align:start position:0%
+setting when we can't simulate the query
+ 
+
+ align:start position:0%
+setting when we can't simulate the query
+algorithm it's one cool idea to make
+
+ align:start position:0%
+algorithm it's one cool idea to make
+ 
+
+ align:start position:0%
+algorithm it's one cool idea to make
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work you may recall our last uh Cell Pro
+
+ align:start position:0%
+work you may recall our last uh Cell Pro
+ 
+
+ align:start position:0%
+work you may recall our last uh Cell Pro
+blower
+
+ align:start position:0%
+blower
+ 
+
+ align:start position:0%
+blower
+Bound for the the predecessor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem uh use this idea of round
+
+ align:start position:0%
+problem uh use this idea of round
+ 
+
+ align:start position:0%
+problem uh use this idea of round
+elimination the idea with round
+
+ align:start position:0%
+elimination the idea with round
+ 
+
+ align:start position:0%
+elimination the idea with round
+elimination was uh Alice was sending a
+
+ align:start position:0%
+elimination was uh Alice was sending a
+ 
+
+ align:start position:0%
+elimination was uh Alice was sending a
+message Bob was sending a response but
+
+ align:start position:0%
+message Bob was sending a response but
+ 
+
+ align:start position:0%
+message Bob was sending a response but
+that first me we set things up we set up
+
+ align:start position:0%
+that first me we set things up we set up
+ 
+
+ align:start position:0%
+that first me we set things up we set up
+the problem so the first message sent by
+
+ align:start position:0%
+the problem so the first message sent by
+ 
+
+ align:start position:0%
+the problem so the first message sent by
+Alice had on average less than one bit
+
+ align:start position:0%
+Alice had on average less than one bit
+ 
+
+ align:start position:0%
+Alice had on average less than one bit
+of information to Bob or very little
+
+ align:start position:0%
+of information to Bob or very little
+ 
+
+ align:start position:0%
+of information to Bob or very little
+information to Bob and so what Bob could
+
+ align:start position:0%
+information to Bob and so what Bob could
+ 
+
+ align:start position:0%
+information to Bob and so what Bob could
+do is basically guess what that message
+
+ align:start position:0%
+do is basically guess what that message
+ 
+
+ align:start position:0%
+do is basically guess what that message
+was and that would be accurate with some
+
+ align:start position:0%
+was and that would be accurate with some
+ 
+
+ align:start position:0%
+was and that would be accurate with some
+probability now here we're not quite
+
+ align:start position:0%
+probability now here we're not quite
+ 
+
+ align:start position:0%
+probability now here we're not quite
+allowed to do that we're not allowed to
+
+ align:start position:0%
+allowed to do that we're not allowed to
+ 
+
+ align:start position:0%
+allowed to do that we're not allowed to
+change the accuracy of our results
+
+ align:start position:0%
+change the accuracy of our results
+ 
+
+ align:start position:0%
+change the accuracy of our results
+because of our particular setting uh so
+
+ align:start position:0%
+because of our particular setting uh so
+ 
+
+ align:start position:0%
+because of our particular setting uh so
+we can't afford to just guess by like
+
+ align:start position:0%
+we can't afford to just guess by like
+ 
+
+ align:start position:0%
+we can't afford to just guess by like
+flipping coins what we were supposed to
+
+ align:start position:0%
+flipping coins what we were supposed to
+ 
+
+ align:start position:0%
+flipping coins what we were supposed to
+know uh what we supposed to know here is
+
+ align:start position:0%
+know uh what we supposed to know here is
+ 
+
+ align:start position:0%
+know uh what we supposed to know here is
+we're trying to simulate a query
+
+ align:start position:0%
+we're trying to simulate a query
+ 
+
+ align:start position:0%
+we're trying to simulate a query
+operation and so we need to know the
+
+ align:start position:0%
+operation and so we need to know the
+ 
+
+ align:start position:0%
+operation and so we need to know the
+argument that whole permutation to the
+
+ align:start position:0%
+argument that whole permutation to the
+ 
+
+ align:start position:0%
+argument that whole permutation to the
+query it's hard to run it without that
+
+ align:start position:0%
+query it's hard to run it without that
+ 
+
+ align:start position:0%
+query it's hard to run it without that
+permutation so instead of guessing by
+
+ align:start position:0%
+permutation so instead of guessing by
+ 
+
+ align:start position:0%
+permutation so instead of guessing by
+flipping coins we're going to guess in
+
+ align:start position:0%
+flipping coins we're going to guess in
+ 
+
+ align:start position:0%
+flipping coins we're going to guess in
+the dynamic programming sense which is
+
+ align:start position:0%
+the dynamic programming sense which is
+ 
+
+ align:start position:0%
+the dynamic programming sense which is
+going to try all the
+
+ align:start position:0%
+going to try all the
+ 
+
+ align:start position:0%
+going to try all the
+possibilities run this simulation over
+
+ align:start position:0%
+possibilities run this simulation over
+ 
+
+ align:start position:0%
+possibilities run this simulation over
+all possible queries all possible second
+
+ align:start position:0%
+all possible queries all possible second
+ 
+
+ align:start position:0%
+all possible queries all possible second
+arguments to the query we don't know
+
+ align:start position:0%
+arguments to the query we don't know
+ 
+
+ align:start position:0%
+arguments to the query we don't know
+what the permutation is so just try them
+
+ align:start position:0%
+what the permutation is so just try them
+ 
+
+ align:start position:0%
+what the permutation is so just try them
+all cool thing is only one argument here
+
+ align:start position:0%
+all cool thing is only one argument here
+ 
+
+ align:start position:0%
+all cool thing is only one argument here
+should return yes that's the one we're
+
+ align:start position:0%
+should return yes that's the one we're
+ 
+
+ align:start position:0%
+should return yes that's the one we're
+looking for so if we try them all find
+
+ align:start position:0%
+looking for so if we try them all find
+ 
+
+ align:start position:0%
+looking for so if we try them all find
+which one says yes we'll be
+
+ align:start position:0%
+which one says yes we'll be
+ 
+
+ align:start position:0%
+which one says yes we'll be
+done so this is called the decod
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simulate uh verify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum of I comma Pi for all
+
+ align:start position:0%
+sum of I comma Pi for all
+ 
+
+ align:start position:0%
+sum of I comma Pi for all
+pi and take the one that returns yes
+
+ align:start position:0%
+pi and take the one that returns yes
+ 
+
+ align:start position:0%
+pi and take the one that returns yes
+that is our permutation and so if we
+
+ align:start position:0%
+that is our permutation and so if we
+ 
+
+ align:start position:0%
+that is our permutation and so if we
+figure out what those query permutations
+
+ align:start position:0%
+figure out what those query permutations
+ 
+
+ align:start position:0%
+figure out what those query permutations
+are then we figure out what the update
+
+ align:start position:0%
+are then we figure out what the update
+ 
+
+ align:start position:0%
+are then we figure out what the update
+permutations are and we get our lower
+
+ align:start position:0%
+permutations are and we get our lower
+ 
+
+ align:start position:0%
+permutations are and we get our lower
+balce just like
+
+ align:start position:0%
+balce just like
+ 
+
+ align:start position:0%
+balce just like
+before okay uh this is easier said than
+
+ align:start position:0%
+before okay uh this is easier said than
+ 
+
+ align:start position:0%
+before okay uh this is easier said than
+done unfortunately um we'd like to run
+
+ align:start position:0%
+done unfortunately um we'd like to run
+ 
+
+ align:start position:0%
+done unfortunately um we'd like to run
+the simulation just
+
+ align:start position:0%
+the simulation just
+ 
+
+ align:start position:0%
+the simulation just
+like here so simulating query algorith
+
+ align:start position:0%
+like here so simulating query algorith
+ 
+
+ align:start position:0%
+like here so simulating query algorith
+we said okay still the case that if
+
+ align:start position:0%
+we said okay still the case that if
+ 
+
+ align:start position:0%
+we said okay still the case that if
+you're reading a Cell It's either in the
+
+ align:start position:0%
+you're reading a Cell It's either in the
+ 
+
+ align:start position:0%
+you're reading a Cell It's either in the
+left sub tree in the right sub tree or
+
+ align:start position:0%
+left sub tree in the right sub tree or
+ 
+
+ align:start position:0%
+left sub tree in the right sub tree or
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+past uh and we said this was easy this
+
+ align:start position:0%
+past uh and we said this was easy this
+ 
+
+ align:start position:0%
+past uh and we said this was easy this
+was known and the hard part is this case
+
+ align:start position:0%
+was known and the hard part is this case
+ 
+
+ align:start position:0%
+was known and the hard part is this case
+because if we're running this
+
+ align:start position:0%
+because if we're running this
+ 
+
+ align:start position:0%
+because if we're running this
+query and it reads something that was
+
+ align:start position:0%
+query and it reads something that was
+ 
+
+ align:start position:0%
+query and it reads something that was
+written in the left subtree it may not
+
+ align:start position:0%
+written in the left subtree it may not
+ 
+
+ align:start position:0%
+written in the left subtree it may not
+be in R intersect
+
+ align:start position:0%
+be in R intersect
+ 
+
+ align:start position:0%
+be in R intersect
+w why is
+
+ align:start position:0%
+w why is
+ 
+
+ align:start position:0%
+w why is
+that little puzzle for
+
+ align:start position:0%
+that little puzzle for
+ 
+
+ align:start position:0%
+that little puzzle for
+you so we're running one of these
+
+ align:start position:0%
+you so we're running one of these
+ 
+
+ align:start position:0%
+you so we're running one of these
+queries for some pi and I claim that
+
+ align:start position:0%
+queries for some pi and I claim that
+ 
+
+ align:start position:0%
+queries for some pi and I claim that
+when we read something left sub tree we
+
+ align:start position:0%
+when we read something left sub tree we
+ 
+
+ align:start position:0%
+when we read something left sub tree we
+don't know if it's an R intersect W
+
+ align:start position:0%
+don't know if it's an R intersect W
+ 
+
+ align:start position:0%
+don't know if it's an R intersect W
+might not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see if we're on the same page so
+
+ align:start position:0%
+see if we're on the same page so
+ 
+
+ align:start position:0%
+see if we're on the same page so
+r r is a set of cells read during the
+
+ align:start position:0%
+r r is a set of cells read during the
+ 
+
+ align:start position:0%
+r r is a set of cells read during the
+right subtree when executing these
+
+ align:start position:0%
+right subtree when executing these
+ 
+
+ align:start position:0%
+right subtree when executing these
+operations okay but what we're doing now
+
+ align:start position:0%
+operations okay but what we're doing now
+ 
+
+ align:start position:0%
+operations okay but what we're doing now
+is simulating some executions that
+
+ align:start position:0%
+is simulating some executions that
+ 
+
+ align:start position:0%
+is simulating some executions that
+didn't necessarily happen we're doing
+
+ align:start position:0%
+didn't necessarily happen we're doing
+ 
+
+ align:start position:0%
+didn't necessarily happen we're doing
+verify sum of I comma Pi but in the bad
+
+ align:start position:0%
+verify sum of I comma Pi but in the bad
+ 
+
+ align:start position:0%
+verify sum of I comma Pi but in the bad
+access sequence we did verify sum of I
+
+ align:start position:0%
+access sequence we did verify sum of I
+ 
+
+ align:start position:0%
+access sequence we did verify sum of I
+comma something specific not any PI but
+
+ align:start position:0%
+comma something specific not any PI but
+ 
+
+ align:start position:0%
+comma something specific not any PI but
+the correct Pi so we only ran the yes
+
+ align:start position:0%
+the correct Pi so we only ran the yes
+ 
+
+ align:start position:0%
+the correct Pi so we only ran the yes
+verify sums and that's what R is defined
+
+ align:start position:0%
+verify sums and that's what R is defined
+ 
+
+ align:start position:0%
+verify sums and that's what R is defined
+with respect to R is a set of things to
+
+ align:start position:0%
+with respect to R is a set of things to
+ 
+
+ align:start position:0%
+with respect to R is a set of things to
+get read during these operations where
+
+ align:start position:0%
+get read during these operations where
+ 
+
+ align:start position:0%
+get read during these operations where
+the verify sums always output yes if you
+
+ align:start position:0%
+the verify sums always output yes if you
+ 
+
+ align:start position:0%
+the verify sums always output yes if you
+now run a verify sum where the answer is
+
+ align:start position:0%
+now run a verify sum where the answer is
+ 
+
+ align:start position:0%
+now run a verify sum where the answer is
+no it may read stuff that the other
+
+ align:start position:0%
+no it may read stuff that the other
+ 
+
+ align:start position:0%
+no it may read stuff that the other
+verify sum didn't read maybe shouldn't
+
+ align:start position:0%
+verify sum didn't read maybe shouldn't
+ 
+
+ align:start position:0%
+verify sum didn't read maybe shouldn't
+matter but it's awkward because now it's
+
+ align:start position:0%
+matter but it's awkward because now it's
+ 
+
+ align:start position:0%
+matter but it's awkward because now it's
+not just R intersect w we need to encode
+
+ align:start position:0%
+not just R intersect w we need to encode
+ 
+
+ align:start position:0%
+not just R intersect w we need to encode
+we need to encode some more stuff
+
+ align:start position:0%
+we need to encode some more stuff
+ 
+
+ align:start position:0%
+we need to encode some more stuff
+it's basically a new RP Prime that may
+
+ align:start position:0%
+it's basically a new RP Prime that may
+ 
+
+ align:start position:0%
+it's basically a new RP Prime that may
+happen during these reads and we just
+
+ align:start position:0%
+happen during these reads and we just
+ 
+
+ align:start position:0%
+happen during these reads and we just
+can't afford to encode that RP Prime
+
+ align:start position:0%
+can't afford to encode that RP Prime
+ 
+
+ align:start position:0%
+can't afford to encode that RP Prime
+because it's not the thing we care about
+
+ align:start position:0%
+because it's not the thing we care about
+ 
+
+ align:start position:0%
+because it's not the thing we care about
+we care about what happens in the actual
+
+ align:start position:0%
+we care about what happens in the actual
+ 
+
+ align:start position:0%
+we care about what happens in the actual
+AIS sequence not in this arbitrary
+
+ align:start position:0%
+AIS sequence not in this arbitrary
+ 
+
+ align:start position:0%
+AIS sequence not in this arbitrary
+simulation so
+
+ align:start position:0%
+simulation so
+ 
+
+ align:start position:0%
+simulation so
+uh This Is The Annoying Thing uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trouble if you look at an incorrect
+
+ align:start position:0%
+trouble if you look at an incorrect
+ 
+
+ align:start position:0%
+trouble if you look at an incorrect
+query
+
+ align:start position:0%
+query
+ 
+
+ align:start position:0%
+query
+meaning the the wrong
+
+ align:start position:0%
+meaning the the wrong
+ 
+
+ align:start position:0%
+meaning the the wrong
+Pi so this is like a no query the
+
+ align:start position:0%
+Pi so this is like a no query the
+ 
+
+ align:start position:0%
+Pi so this is like a no query the
+output's
+
+ align:start position:0%
+output's
+ 
+
+ align:start position:0%
+output's
+no uh reads some different set of
+
+ align:start position:0%
+no uh reads some different set of
+ 
+
+ align:start position:0%
+no uh reads some different set of
+cells R Prime which isn't the same thing
+
+ align:start position:0%
+cells R Prime which isn't the same thing
+ 
+
+ align:start position:0%
+cells R Prime which isn't the same thing
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+R and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we have some good news which is if we
+
+ align:start position:0%
+if we have some good news which is if we
+ 
+
+ align:start position:0%
+if we have some good news which is if we
+could somehow detect that this happened
+
+ align:start position:0%
+could somehow detect that this happened
+ 
+
+ align:start position:0%
+could somehow detect that this happened
+that we read something that is in our
+
+ align:start position:0%
+that we read something that is in our
+ 
+
+ align:start position:0%
+that we read something that is in our
+Prime but not
+
+ align:start position:0%
+Prime but not
+ 
+
+ align:start position:0%
+Prime but not
+R uh then the answer must be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no so that's our our Saving Hope is that
+
+ align:start position:0%
+no so that's our our Saving Hope is that
+ 
+
+ align:start position:0%
+no so that's our our Saving Hope is that
+either uh we're reading something in R
+
+ align:start position:0%
+either uh we're reading something in R
+ 
+
+ align:start position:0%
+either uh we're reading something in R
+intersect W in which case it's been
+
+ align:start position:0%
+intersect W in which case it's been
+ 
+
+ align:start position:0%
+intersect W in which case it's been
+written down we know how to do it or
+
+ align:start position:0%
+written down we know how to do it or
+ 
+
+ align:start position:0%
+written down we know how to do it or
+it's not written
+
+ align:start position:0%
+it's not written
+ 
+
+ align:start position:0%
+it's not written
+there and if it's not written there then
+
+ align:start position:0%
+there and if it's not written there then
+ 
+
+ align:start position:0%
+there and if it's not written there then
+it should be hopefully in R Prime minus
+
+ align:start position:0%
+it should be hopefully in R Prime minus
+ 
+
+ align:start position:0%
+it should be hopefully in R Prime minus
+r and so the answer should be
+
+ align:start position:0%
+r and so the answer should be
+ 
+
+ align:start position:0%
+r and so the answer should be
+no maybe maybe slight problem though
+
+ align:start position:0%
+no maybe maybe slight problem though
+ 
+
+ align:start position:0%
+no maybe maybe slight problem though
+because we used R intersect W to detect
+
+ align:start position:0%
+because we used R intersect W to detect
+ 
+
+ align:start position:0%
+because we used R intersect W to detect
+what case we were in if we were in our
+
+ align:start position:0%
+what case we were in if we were in our
+ 
+
+ align:start position:0%
+what case we were in if we were in our
+our intersect W then we knew we should
+
+ align:start position:0%
+our intersect W then we knew we should
+ 
+
+ align:start position:0%
+our intersect W then we knew we should
+read from those encoded cells if we
+
+ align:start position:0%
+read from those encoded cells if we
+ 
+
+ align:start position:0%
+read from those encoded cells if we
+weren't uh we were either in the past or
+
+ align:start position:0%
+weren't uh we were either in the past or
+ 
+
+ align:start position:0%
+weren't uh we were either in the past or
+in the right sub tree these things we
+
+ align:start position:0%
+in the right sub tree these things we
+ 
+
+ align:start position:0%
+in the right sub tree these things we
+are easy to detect because they got
+
+ align:start position:0%
+are easy to detect because they got
+ 
+
+ align:start position:0%
+are easy to detect because they got
+written during the simulation but we
+
+ align:start position:0%
+written during the simulation but we
+ 
+
+ align:start position:0%
+written during the simulation but we
+need to distinguish between did we read
+
+ align:start position:0%
+need to distinguish between did we read
+ 
+
+ align:start position:0%
+need to distinguish between did we read
+something that was in the left sub tree
+
+ align:start position:0%
+something that was in the left sub tree
+ 
+
+ align:start position:0%
+something that was in the left sub tree
+or did we read something that was known
+
+ align:start position:0%
+or did we read something that was known
+ 
+
+ align:start position:0%
+or did we read something that was known
+this is a little tricky because this
+
+ align:start position:0%
+this is a little tricky because this
+ 
+
+ align:start position:0%
+this is a little tricky because this
+gets it exactly the issue left sub tree
+
+ align:start position:0%
+gets it exactly the issue left sub tree
+ 
+
+ align:start position:0%
+gets it exactly the issue left sub tree
+might write some stuff that didn't get
+
+ align:start position:0%
+might write some stuff that didn't get
+ 
+
+ align:start position:0%
+might write some stuff that didn't get
+re read by verify sum so now you go to
+
+ align:start position:0%
+re read by verify sum so now you go to
+ 
+
+ align:start position:0%
+re read by verify sum so now you go to
+read it you need to know am I reading
+
+ align:start position:0%
+read it you need to know am I reading
+ 
+
+ align:start position:0%
+read it you need to know am I reading
+something that was not in our intersect
+
+ align:start position:0%
+something that was not in our intersect
+ 
+
+ align:start position:0%
+something that was not in our intersect
+W and therefore uh
+
+ align:start position:0%
+W and therefore uh
+ 
+
+ align:start position:0%
+W and therefore uh
+yeah basically the issue is is it in
+
+ align:start position:0%
+yeah basically the issue is is it in
+ 
+
+ align:start position:0%
+yeah basically the issue is is it in
+W if it's in W but not in R intersect W
+
+ align:start position:0%
+W if it's in W but not in R intersect W
+ 
+
+ align:start position:0%
+W if it's in W but not in R intersect W
+then I know the answer is no should stop
+
+ align:start position:0%
+then I know the answer is no should stop
+ 
+
+ align:start position:0%
+then I know the answer is no should stop
+if it's not in W though that means it
+
+ align:start position:0%
+if it's not in W though that means it
+ 
+
+ align:start position:0%
+if it's not in W though that means it
+was in the known past and then I should
+
+ align:start position:0%
+was in the known past and then I should
+ 
+
+ align:start position:0%
+was in the known past and then I should
+continue how do I know whether I should
+
+ align:start position:0%
+continue how do I know whether I should
+ 
+
+ align:start position:0%
+continue how do I know whether I should
+stop or continue
+
+ align:start position:0%
+stop or continue
+ 
+
+ align:start position:0%
+stop or continue
+so uh this is the tricky
+
+ align:start position:0%
+so uh this is the tricky
+ 
+
+ align:start position:0%
+so uh this is the tricky
+part we can't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tell whether here's the weird
+
+ align:start position:0%
+tell whether here's the weird
+ 
+
+ align:start position:0%
+tell whether here's the weird
+notation we want to know whether R is in
+
+ align:start position:0%
+notation we want to know whether R is in
+ 
+
+ align:start position:0%
+notation we want to know whether R is in
+wus
+
+ align:start position:0%
+wus
+ 
+
+ align:start position:0%
+wus
+r or
+
+ align:start position:0%
+r or
+ 
+
+ align:start position:0%
+r or
+past minus r inter
+
+ align:start position:0%
+past minus r inter
+ 
+
+ align:start position:0%
+past minus r inter
+W okay we know we can tell whether it's
+
+ align:start position:0%
+W okay we know we can tell whether it's
+ 
+
+ align:start position:0%
+W okay we know we can tell whether it's
+in R intersect W if it is we're happy if
+
+ align:start position:0%
+in R intersect W if it is we're happy if
+ 
+
+ align:start position:0%
+in R intersect W if it is we're happy if
+it's not in R intersect W it could be
+
+ align:start position:0%
+it's not in R intersect W it could be
+ 
+
+ align:start position:0%
+it's not in R intersect W it could be
+that's because it was just in some past
+
+ align:start position:0%
+that's because it was just in some past
+ 
+
+ align:start position:0%
+that's because it was just in some past
+thing we were reading uh that didn't get
+
+ align:start position:0%
+thing we were reading uh that didn't get
+ 
+
+ align:start position:0%
+thing we were reading uh that didn't get
+read other read otherwise or it could be
+
+ align:start position:0%
+read other read otherwise or it could be
+ 
+
+ align:start position:0%
+read other read otherwise or it could be
+something we're reading something that
+
+ align:start position:0%
+something we're reading something that
+ 
+
+ align:start position:0%
+something we're reading something that
+was written in the left subtree but not
+
+ align:start position:0%
+was written in the left subtree but not
+ 
+
+ align:start position:0%
+was written in the left subtree but not
+read in the right subtree so in this
+
+ align:start position:0%
+read in the right subtree so in this
+ 
+
+ align:start position:0%
+read in the right subtree so in this
+case we want to
+
+ align:start position:0%
+case we want to
+ 
+
+ align:start position:0%
+case we want to
+abort and in this case uh it's known and
+
+ align:start position:0%
+abort and in this case uh it's known and
+ 
+
+ align:start position:0%
+abort and in this case uh it's known and
+so we just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continue so that's what the simulation
+
+ align:start position:0%
+continue so that's what the simulation
+ 
+
+ align:start position:0%
+continue so that's what the simulation
+would like to do if we could distinguish
+
+ align:start position:0%
+would like to do if we could distinguish
+ 
+
+ align:start position:0%
+would like to do if we could distinguish
+between these two
+
+ align:start position:0%
+between these two
+ 
+
+ align:start position:0%
+between these two
+cases but right now we can't distinguish
+
+ align:start position:0%
+cases but right now we can't distinguish
+ 
+
+ align:start position:0%
+cases but right now we can't distinguish
+between these two cases because we don't
+
+ align:start position:0%
+between these two cases because we don't
+ 
+
+ align:start position:0%
+between these two cases because we don't
+have enough information so we're going
+
+ align:start position:0%
+have enough information so we're going
+ 
+
+ align:start position:0%
+have enough information so we're going
+to make our encoding a little bit
+
+ align:start position:0%
+to make our encoding a little bit
+ 
+
+ align:start position:0%
+to make our encoding a little bit
+bigger what we're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do this is over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is in code a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+separator for Rus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W and wus
+
+ align:start position:0%
+W and wus
+ 
+
+ align:start position:0%
+W and wus
+R so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's go over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does this mean separator is going
+
+ align:start position:0%
+what does this mean separator is going
+ 
+
+ align:start position:0%
+what does this mean separator is going
+to call called the
+
+ align:start position:0%
+to call called the
+ 
+
+ align:start position:0%
+to call called the
+S so I want this picture R minus
+
+ align:start position:0%
+S so I want this picture R minus
+ 
+
+ align:start position:0%
+S so I want this picture R minus
+W sits inside
+
+ align:start position:0%
+W sits inside
+ 
+
+ align:start position:0%
+W sits inside
+S and wus R sits outside s so this is my
+
+ align:start position:0%
+S and wus R sits outside s so this is my
+ 
+
+ align:start position:0%
+S and wus R sits outside s so this is my
+universe of
+
+ align:start position:0%
+universe of
+ 
+
+ align:start position:0%
+universe of
+cells these are the things that are read
+
+ align:start position:0%
+cells these are the things that are read
+ 
+
+ align:start position:0%
+cells these are the things that are read
+in the right sub tree but not written in
+
+ align:start position:0%
+in the right sub tree but not written in
+ 
+
+ align:start position:0%
+in the right sub tree but not written in
+the left sub tree those are the things I
+
+ align:start position:0%
+the left sub tree those are the things I
+ 
+
+ align:start position:0%
+the left sub tree those are the things I
+care
+
+ align:start position:0%
+care
+ 
+
+ align:start position:0%
+care
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+uh well not quite this the other ones so
+
+ align:start position:0%
+uh well not quite this the other ones so
+ 
+
+ align:start position:0%
+uh well not quite this the other ones so
+things that are read in the right sub
+
+ align:start position:0%
+things that are read in the right sub
+ 
+
+ align:start position:0%
+things that are read in the right sub
+tree and that are not written in the
+
+ align:start position:0%
+tree and that are not written in the
+ 
+
+ align:start position:0%
+tree and that are not written in the
+left sub tree this is the past
+
+ align:start position:0%
+left sub tree this is the past
+ 
+
+ align:start position:0%
+left sub tree this is the past
+essentially that that's useful over
+
+ align:start position:0%
+essentially that that's useful over
+ 
+
+ align:start position:0%
+essentially that that's useful over
+there over here I have uh wus R these
+
+ align:start position:0%
+there over here I have uh wus R these
+ 
+
+ align:start position:0%
+there over here I have uh wus R these
+are things that are written in the left
+
+ align:start position:0%
+are things that are written in the left
+ 
+
+ align:start position:0%
+are things that are written in the left
+sub tree but not read in the right sub
+
+ align:start position:0%
+sub tree but not read in the right sub
+ 
+
+ align:start position:0%
+sub tree but not read in the right sub
+tree these are the things that I worry
+
+ align:start position:0%
+tree these are the things that I worry
+ 
+
+ align:start position:0%
+tree these are the things that I worry
+about because those ones I need to
+
+ align:start position:0%
+about because those ones I need to
+ 
+
+ align:start position:0%
+about because those ones I need to
+detect that that was changed and say
+
+ align:start position:0%
+detect that that was changed and say
+ 
+
+ align:start position:0%
+detect that that was changed and say
+whoops um you must have an answer of
+
+ align:start position:0%
+whoops um you must have an answer of
+ 
+
+ align:start position:0%
+whoops um you must have an answer of
+no okay so I can't afford to store these
+
+ align:start position:0%
+no okay so I can't afford to store these
+ 
+
+ align:start position:0%
+no okay so I can't afford to store these
+sets exactly so I'm going to approximate
+
+ align:start position:0%
+sets exactly so I'm going to approximate
+ 
+
+ align:start position:0%
+sets exactly so I'm going to approximate
+them by saying well let's store this
+
+ align:start position:0%
+them by saying well let's store this
+ 
+
+ align:start position:0%
+them by saying well let's store this
+separator out
+
+ align:start position:0%
+separator out
+ 
+
+ align:start position:0%
+separator out
+here uh and if you're in s then you're
+
+ align:start position:0%
+here uh and if you're in s then you're
+ 
+
+ align:start position:0%
+here uh and if you're in s then you're
+definitely not in wus R if you're
+
+ align:start position:0%
+definitely not in wus R if you're
+ 
+
+ align:start position:0%
+definitely not in wus R if you're
+definitely not in wus R then you can run
+
+ align:start position:0%
+definitely not in wus R then you can run
+ 
+
+ align:start position:0%
+definitely not in wus R then you can run
+you can treat it as if if it was
+
+ align:start position:0%
+you can treat it as if if it was
+ 
+
+ align:start position:0%
+you can treat it as if if it was
+known okay so if you're in s this will
+
+ align:start position:0%
+known okay so if you're in s this will
+ 
+
+ align:start position:0%
+known okay so if you're in s this will
+be well why don't I write it
+
+ align:start position:0%
+be well why don't I write it
+ 
+
+ align:start position:0%
+be well why don't I write it
+here uh for the decoding algorithm if
+
+ align:start position:0%
+here uh for the decoding algorithm if
+ 
+
+ align:start position:0%
+here uh for the decoding algorithm if
+you want to read a
+
+ align:start position:0%
+you want to read a
+ 
+
+ align:start position:0%
+you want to read a
+cell that
+
+ align:start position:0%
+cell that
+ 
+
+ align:start position:0%
+cell that
+is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+written or last written
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subtree in the past the these are the
+
+ align:start position:0%
+subtree in the past the these are the
+ 
+
+ align:start position:0%
+subtree in the past the these are the
+two easy
+
+ align:start position:0%
+two easy
+ 
+
+ align:start position:0%
+two easy
+cases um sorry in I don't want to write
+
+ align:start position:0%
+cases um sorry in I don't want to write
+ 
+
+ align:start position:0%
+cases um sorry in I don't want to write
+in the past because the whole point is
+
+ align:start position:0%
+in the past because the whole point is
+ 
+
+ align:start position:0%
+in the past because the whole point is
+to figure out what's in the past uh the
+
+ align:start position:0%
+to figure out what's in the past uh the
+ 
+
+ align:start position:0%
+to figure out what's in the past uh the
+other easy case is if it's in R
+
+ align:start position:0%
+other easy case is if it's in R
+ 
+
+ align:start position:0%
+other easy case is if it's in R
+intersect W then it's written down for
+
+ align:start position:0%
+intersect W then it's written down for
+ 
+
+ align:start position:0%
+intersect W then it's written down for
+us so this is
+
+ align:start position:0%
+us so this is
+ 
+
+ align:start position:0%
+us so this is
+encoded uh this is easy because during
+
+ align:start position:0%
+encoded uh this is easy because during
+ 
+
+ align:start position:0%
+encoded uh this is easy because during
+the simulation we did those rights and
+
+ align:start position:0%
+the simulation we did those rights and
+ 
+
+ align:start position:0%
+the simulation we did those rights and
+so we know what they were uh R intersect
+
+ align:start position:0%
+so we know what they were uh R intersect
+ 
+
+ align:start position:0%
+so we know what they were uh R intersect
+W we've written down so it's easy to
+
+ align:start position:0%
+W we've written down so it's easy to
+ 
+
+ align:start position:0%
+W we've written down so it's easy to
+know then the other cases are either
+
+ align:start position:0%
+know then the other cases are either
+ 
+
+ align:start position:0%
+know then the other cases are either
+you're in s or you're not in s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I claim if you're in s you must be
+
+ align:start position:0%
+okay I claim if you're in s you must be
+ 
+
+ align:start position:0%
+okay I claim if you're in s you must be
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+past that cell must have been written in
+
+ align:start position:0%
+past that cell must have been written in
+ 
+
+ align:start position:0%
+past that cell must have been written in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+past and so you know what the value
+
+ align:start position:0%
+past and so you know what the value
+ 
+
+ align:start position:0%
+past and so you know what the value
+was and so you can continue running the
+
+ align:start position:0%
+was and so you can continue running the
+ 
+
+ align:start position:0%
+was and so you can continue running the
+simulation just like in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+situation the other situation is you're
+
+ align:start position:0%
+situation the other situation is you're
+ 
+
+ align:start position:0%
+situation the other situation is you're
+not in s then you don't know it could
+
+ align:start position:0%
+not in s then you don't know it could
+ 
+
+ align:start position:0%
+not in s then you don't know it could
+have been written or it might not have
+
+ align:start position:0%
+have been written or it might not have
+ 
+
+ align:start position:0%
+have been written or it might not have
+been
+
+ align:start position:0%
+been
+ 
+
+ align:start position:0%
+been
+but what you know is that you're
+
+ align:start position:0%
+but what you know is that you're
+ 
+
+ align:start position:0%
+but what you know is that you're
+definitely not in
+
+ align:start position:0%
+definitely not in
+ 
+
+ align:start position:0%
+definitely not in
+R because if you're not in R minus W and
+
+ align:start position:0%
+R because if you're not in R minus W and
+ 
+
+ align:start position:0%
+R because if you're not in R minus W and
+you're not in R intersect W then you're
+
+ align:start position:0%
+you're not in R intersect W then you're
+ 
+
+ align:start position:0%
+you're not in R intersect W then you're
+not in R if you're not in R then we're
+
+ align:start position:0%
+not in R if you're not in R then we're
+ 
+
+ align:start position:0%
+not in R if you're not in R then we're
+in this situation if you read something
+
+ align:start position:0%
+in this situation if you read something
+ 
+
+ align:start position:0%
+in this situation if you read something
+not an r that means you're running the
+
+ align:start position:0%
+not an r that means you're running the
+ 
+
+ align:start position:0%
+not an r that means you're running the
+wrong query because the correct query
+
+ align:start position:0%
+wrong query because the correct query
+ 
+
+ align:start position:0%
+wrong query because the correct query
+does r only reads from R so if you're
+
+ align:start position:0%
+does r only reads from R so if you're
+ 
+
+ align:start position:0%
+does r only reads from R so if you're
+not an S you must not be in
+
+ align:start position:0%
+not an S you must not be in
+ 
+
+ align:start position:0%
+not an S you must not be in
+R and so in this case you know you can
+
+ align:start position:0%
+R and so in this case you know you can
+ 
+
+ align:start position:0%
+R and so in this case you know you can
+abort and try the next Pi so we're going
+
+ align:start position:0%
+abort and try the next Pi so we're going
+ 
+
+ align:start position:0%
+abort and try the next Pi so we're going
+to do this for all Pi run the simulation
+
+ align:start position:0%
+to do this for all Pi run the simulation
+ 
+
+ align:start position:0%
+to do this for all Pi run the simulation
+according to this way of reading
+
+ align:start position:0%
+according to this way of reading
+ 
+
+ align:start position:0%
+according to this way of reading
+cells at the end the query is either
+
+ align:start position:0%
+cells at the end the query is either
+ 
+
+ align:start position:0%
+cells at the end the query is either
+going to say yes or no or it may uh
+
+ align:start position:0%
+going to say yes or no or it may uh
+ 
+
+ align:start position:0%
+going to say yes or no or it may uh
+abort
+
+ align:start position:0%
+abort
+ 
+
+ align:start position:0%
+abort
+early so if it says no or it aborts
+
+ align:start position:0%
+early so if it says no or it aborts
+ 
+
+ align:start position:0%
+early so if it says no or it aborts
+early then we know that was not the
+
+ align:start position:0%
+early then we know that was not the
+ 
+
+ align:start position:0%
+early then we know that was not the
+right P only one of them can say yes
+
+ align:start position:0%
+right P only one of them can say yes
+ 
+
+ align:start position:0%
+right P only one of them can say yes
+that tells what the pi is that tells us
+
+ align:start position:0%
+that tells what the pi is that tells us
+ 
+
+ align:start position:0%
+that tells what the pi is that tells us
+what the queries were once we know what
+
+ align:start position:0%
+what the queries were once we know what
+ 
+
+ align:start position:0%
+what the queries were once we know what
+the queries were in the right sube we
+
+ align:start position:0%
+the queries were in the right sube we
+ 
+
+ align:start position:0%
+the queries were in the right sube we
+can use the same multiplying by inverses
+
+ align:start position:0%
+can use the same multiplying by inverses
+ 
+
+ align:start position:0%
+can use the same multiplying by inverses
+trick figure out what the updates were
+
+ align:start position:0%
+trick figure out what the updates were
+ 
+
+ align:start position:0%
+trick figure out what the updates were
+in the left sub tree but the those
+
+ align:start position:0%
+in the left sub tree but the those
+ 
+
+ align:start position:0%
+in the left sub tree but the those
+permutations require L root n log n Bits
+
+ align:start position:0%
+permutations require L root n log n Bits
+ 
+
+ align:start position:0%
+permutations require L root n log n Bits
+which used to be on this board an erase
+
+ align:start position:0%
+which used to be on this board an erase
+ 
+
+ align:start position:0%
+which used to be on this board an erase
+now that's what we use for this
+
+ align:start position:0%
+now that's what we use for this
+ 
+
+ align:start position:0%
+now that's what we use for this
+argument and so what we get is overall
+
+ align:start position:0%
+argument and so what we get is overall
+ 
+
+ align:start position:0%
+argument and so what we get is overall
+encoding must use l root n log n
+
+ align:start position:0%
+encoding must use l root n log n
+ 
+
+ align:start position:0%
+encoding must use l root n log n
+Bits okay but our encodings a little bit
+
+ align:start position:0%
+Bits okay but our encodings a little bit
+ 
+
+ align:start position:0%
+Bits okay but our encodings a little bit
+bigger now the big issue is how do we
+
+ align:start position:0%
+bigger now the big issue is how do we
+ 
+
+ align:start position:0%
+bigger now the big issue is how do we
+store this separator we need to do store
+
+ align:start position:0%
+store this separator we need to do store
+ 
+
+ align:start position:0%
+store this separator we need to do store
+the separator with very few bits
+
+ align:start position:0%
+the separator with very few bits
+ 
+
+ align:start position:0%
+the separator with very few bits
+otherwise uh doesn't we don't haven't
+
+ align:start position:0%
+otherwise uh doesn't we don't haven't
+ 
+
+ align:start position:0%
+otherwise uh doesn't we don't haven't
+really proved anything we want the
+
+ align:start position:0%
+really proved anything we want the
+ 
+
+ align:start position:0%
+really proved anything we want the
+encoding to be
+
+ align:start position:0%
+encoding to be
+ 
+
+ align:start position:0%
+encoding to be
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+so uh so we get that the
+
+ align:start position:0%
+so uh so we get that the
+ 
+
+ align:start position:0%
+so uh so we get that the
+encoding must
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use Omega L root n log n Bits in
+
+ align:start position:0%
+use Omega L root n log n Bits in
+ 
+
+ align:start position:0%
+use Omega L root n log n Bits in
+expectation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because this is a valid decoding
+
+ align:start position:0%
+because this is a valid decoding
+ 
+
+ align:start position:0%
+because this is a valid decoding
+algorithm it will figure out what the
+
+ align:start position:0%
+algorithm it will figure out what the
+ 
+
+ align:start position:0%
+algorithm it will figure out what the
+permutations were so and they require at
+
+ align:start position:0%
+permutations were so and they require at
+ 
+
+ align:start position:0%
+permutations were so and they require at
+least this many bits so encoding must
+
+ align:start position:0%
+least this many bits so encoding must
+ 
+
+ align:start position:0%
+least this many bits so encoding must
+use this many bits in expectation now
+
+ align:start position:0%
+use this many bits in expectation now
+ 
+
+ align:start position:0%
+use this many bits in expectation now
+the question is how many bits does the
+
+ align:start position:0%
+the question is how many bits does the
+ 
+
+ align:start position:0%
+the question is how many bits does the
+encoding use then we'll get either a
+
+ align:start position:0%
+encoding use then we'll get either a
+ 
+
+ align:start position:0%
+encoding use then we'll get either a
+contradiction or we'll prove the prove
+
+ align:start position:0%
+contradiction or we'll prove the prove
+ 
+
+ align:start position:0%
+contradiction or we'll prove the prove
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+claim so let's go over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's a fun fact about separators
+
+ align:start position:0%
+so here's a fun fact about separators
+ 
+
+ align:start position:0%
+so here's a fun fact about separators
+I'm not going to prove it fully but I'm
+
+ align:start position:0%
+I'm not going to prove it fully but I'm
+ 
+
+ align:start position:0%
+I'm not going to prove it fully but I'm
+going to rely on some hashing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ability so given some Universe u in this
+
+ align:start position:0%
+ability so given some Universe u in this
+ 
+
+ align:start position:0%
+ability so given some Universe u in this
+case it's going to be the cells in our
+
+ align:start position:0%
+case it's going to be the cells in our
+ 
+
+ align:start position:0%
+case it's going to be the cells in our
+data structure but speak a little bit
+
+ align:start position:0%
+data structure but speak a little bit
+ 
+
+ align:start position:0%
+data structure but speak a little bit
+more generally of universe U we have
+
+ align:start position:0%
+more generally of universe U we have
+ 
+
+ align:start position:0%
+more generally of universe U we have
+some number M which is our set size and
+
+ align:start position:0%
+some number M which is our set size and
+ 
+
+ align:start position:0%
+some number M which is our set size and
+what we're interested is in defining we
+
+ align:start position:0%
+what we're interested is in defining we
+ 
+
+ align:start position:0%
+what we're interested is in defining we
+call a separator family
+
+ align:start position:0%
+call a separator family
+ 
+
+ align:start position:0%
+call a separator family
+kind of like a family of hash
+
+ align:start position:0%
+kind of like a family of hash
+ 
+
+ align:start position:0%
+kind of like a family of hash
+functions closely related in fact call
+
+ align:start position:0%
+functions closely related in fact call
+ 
+
+ align:start position:0%
+functions closely related in fact call
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+uh and it's going to work for size M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sets uh and so s is a separator family
+
+ align:start position:0%
+sets uh and so s is a separator family
+ 
+
+ align:start position:0%
+sets uh and so s is a separator family
+if uh for any two sets A and
+
+ align:start position:0%
+if uh for any two sets A and
+ 
+
+ align:start position:0%
+if uh for any two sets A and
+B in the
+
+ align:start position:0%
+B in the
+ 
+
+ align:start position:0%
+B in the
+universe of size at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M uh and
+
+ align:start position:0%
+M uh and
+ 
+
+ align:start position:0%
+M uh and
+disjoint so a intersect B is the empty
+
+ align:start position:0%
+disjoint so a intersect B is the empty
+ 
+
+ align:start position:0%
+disjoint so a intersect B is the empty
+set so of course what we're thinking
+
+ align:start position:0%
+set so of course what we're thinking
+ 
+
+ align:start position:0%
+set so of course what we're thinking
+about here is R minus W and wus R these
+
+ align:start position:0%
+about here is R minus W and wus R these
+ 
+
+ align:start position:0%
+about here is R minus W and wus R these
+are two subsets of the universe
+
+ align:start position:0%
+are two subsets of the universe
+ 
+
+ align:start position:0%
+are two subsets of the universe
+hopefully they're not too big because if
+
+ align:start position:0%
+hopefully they're not too big because if
+ 
+
+ align:start position:0%
+hopefully they're not too big because if
+this one's huge that means you read a
+
+ align:start position:0%
+this one's huge that means you read a
+ 
+
+ align:start position:0%
+this one's huge that means you read a
+huge amount of data in the right sub
+
+ align:start position:0%
+huge amount of data in the right sub
+ 
+
+ align:start position:0%
+huge amount of data in the right sub
+tree if this one is huge it meant you
+
+ align:start position:0%
+tree if this one is huge it meant you
+ 
+
+ align:start position:0%
+tree if this one is huge it meant you
+wrote a huge amount of data on the left
+
+ align:start position:0%
+wrote a huge amount of data on the left
+ 
+
+ align:start position:0%
+wrote a huge amount of data on the left
+sub tree and then we get lower bounds in
+
+ align:start position:0%
+sub tree and then we get lower bounds in
+ 
+
+ align:start position:0%
+sub tree and then we get lower bounds in
+an easier way or or they're not so big
+
+ align:start position:0%
+an easier way or or they're not so big
+ 
+
+ align:start position:0%
+an easier way or or they're not so big
+it's say their size at most M they're
+
+ align:start position:0%
+it's say their size at most M they're
+ 
+
+ align:start position:0%
+it's say their size at most M they're
+disjoint for sure by definition Rus W is
+
+ align:start position:0%
+disjoint for sure by definition Rus W is
+ 
+
+ align:start position:0%
+disjoint for sure by definition Rus W is
+disjoint from wus R you removes the
+
+ align:start position:0%
+disjoint from wus R you removes the
+ 
+
+ align:start position:0%
+disjoint from wus R you removes the
+intersection
+
+ align:start position:0%
+intersection
+ 
+
+ align:start position:0%
+intersection
+uh so that's our
+
+ align:start position:0%
+uh so that's our
+ 
+
+ align:start position:0%
+uh so that's our
+setup then what we want is that there is
+
+ align:start position:0%
+setup then what we want is that there is
+ 
+
+ align:start position:0%
+setup then what we want is that there is
+some set C in the separator
+
+ align:start position:0%
+some set C in the separator
+ 
+
+ align:start position:0%
+some set C in the separator
+family such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh a is contained in C and B is outside
+
+ align:start position:0%
+uh a is contained in C and B is outside
+ 
+
+ align:start position:0%
+uh a is contained in C and B is outside
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C so B is in the universe minus C so
+
+ align:start position:0%
+C so B is in the universe minus C so
+ 
+
+ align:start position:0%
+C so B is in the universe minus C so
+this is exactly our picture from before
+
+ align:start position:0%
+this is exactly our picture from before
+ 
+
+ align:start position:0%
+this is exactly our picture from before
+we have a a contains C and we have B
+
+ align:start position:0%
+we have a a contains C and we have B
+ 
+
+ align:start position:0%
+we have a a contains C and we have B
+over on the right and this is the whole
+
+ align:start position:0%
+over on the right and this is the whole
+ 
+
+ align:start position:0%
+over on the right and this is the whole
+universe U and so B is outside of c a is
+
+ align:start position:0%
+universe U and so B is outside of c a is
+ 
+
+ align:start position:0%
+universe U and so B is outside of c a is
+entirely inside
+
+ align:start position:0%
+entirely inside
+ 
+
+ align:start position:0%
+entirely inside
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+okay this is what we want to exist cuz
+
+ align:start position:0%
+okay this is what we want to exist cuz
+ 
+
+ align:start position:0%
+okay this is what we want to exist cuz
+if a separator family exists then we
+
+ align:start position:0%
+if a separator family exists then we
+ 
+
+ align:start position:0%
+if a separator family exists then we
+know whatever our Rus W and wus R sets
+
+ align:start position:0%
+know whatever our Rus W and wus R sets
+ 
+
+ align:start position:0%
+know whatever our Rus W and wus R sets
+were as long as they're not too big
+
+ align:start position:0%
+were as long as they're not too big
+ 
+
+ align:start position:0%
+were as long as they're not too big
+they're definitely disjoint we can find
+
+ align:start position:0%
+they're definitely disjoint we can find
+ 
+
+ align:start position:0%
+they're definitely disjoint we can find
+one of these separators that encodes
+
+ align:start position:0%
+one of these separators that encodes
+ 
+
+ align:start position:0%
+one of these separators that encodes
+what we need to encode which is this set
+
+ align:start position:0%
+what we need to encode which is this set
+ 
+
+ align:start position:0%
+what we need to encode which is this set
+C which is called uh s over
+
+ align:start position:0%
+C which is called uh s over
+ 
+
+ align:start position:0%
+C which is called uh s over
+there cool uh how do we encode it well
+
+ align:start position:0%
+there cool uh how do we encode it well
+ 
+
+ align:start position:0%
+there cool uh how do we encode it well
+if this if the number if the
+
+ align:start position:0%
+if this if the number if the
+ 
+
+ align:start position:0%
+if this if the number if the
+size of the separator family is
+
+ align:start position:0%
+size of the separator family is
+ 
+
+ align:start position:0%
+size of the separator family is
+something then we need log of that bits
+
+ align:start position:0%
+something then we need log of that bits
+ 
+
+ align:start position:0%
+something then we need log of that bits
+to write down the separator said so as
+
+ align:start position:0%
+to write down the separator said so as
+ 
+
+ align:start position:0%
+to write down the separator said so as
+long as this is small we're
+
+ align:start position:0%
+long as this is small we're
+ 
+
+ align:start position:0%
+long as this is small we're
+happy so uh let me tell you what's not
+
+ align:start position:0%
+happy so uh let me tell you what's not
+ 
+
+ align:start position:0%
+happy so uh let me tell you what's not
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+separators uh there exists a separator
+
+ align:start position:0%
+separators uh there exists a separator
+ 
+
+ align:start position:0%
+separators uh there exists a separator
+family
+
+ align:start position:0%
+family
+ 
+
+ align:start position:0%
+family
+s with size of
+
+ align:start position:0%
+s with size of
+ 
+
+ align:start position:0%
+s with size of
+s at most 2 to the order m + log log
+
+ align:start position:0%
+s at most 2 to the order m + log log
+ 
+
+ align:start position:0%
+s at most 2 to the order m + log log
+U now this is getting into an area that
+
+ align:start position:0%
+U now this is getting into an area that
+ 
+
+ align:start position:0%
+U now this is getting into an area that
+we haven't spent a lot of time on uh but
+
+ align:start position:0%
+we haven't spent a lot of time on uh but
+ 
+
+ align:start position:0%
+we haven't spent a lot of time on uh but
+so I'm going to give you a sketch of a
+
+ align:start position:0%
+so I'm going to give you a sketch of a
+ 
+
+ align:start position:0%
+so I'm going to give you a sketch of a
+proof of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claim relying on perfect hash
+
+ align:start position:0%
+claim relying on perfect hash
+ 
+
+ align:start position:0%
+claim relying on perfect hash
+functions so
+
+ align:start position:0%
+functions so
+ 
+
+ align:start position:0%
+functions so
+the idea is the following we want to
+
+ align:start position:0%
+the idea is the following we want to
+ 
+
+ align:start position:0%
+the idea is the following we want to
+know basically which elements are in a
+
+ align:start position:0%
+know basically which elements are in a
+ 
+
+ align:start position:0%
+know basically which elements are in a
+which elements are in B but it's kind of
+
+ align:start position:0%
+which elements are in B but it's kind of
+ 
+
+ align:start position:0%
+which elements are in B but it's kind of
+annoying to do that you can't store that
+
+ align:start position:0%
+annoying to do that you can't store that
+ 
+
+ align:start position:0%
+annoying to do that you can't store that
+for all Universe elements so if we could
+
+ align:start position:0%
+for all Universe elements so if we could
+ 
+
+ align:start position:0%
+for all Universe elements so if we could
+just find a nice perfect hash function
+
+ align:start position:0%
+just find a nice perfect hash function
+ 
+
+ align:start position:0%
+just find a nice perfect hash function
+that mapped the elements of a and the
+
+ align:start position:0%
+that mapped the elements of a and the
+ 
+
+ align:start position:0%
+that mapped the elements of a and the
+elements of B to different slots in some
+
+ align:start position:0%
+elements of B to different slots in some
+ 
+
+ align:start position:0%
+elements of B to different slots in some
+hash table then for every slot in the
+
+ align:start position:0%
+hash table then for every slot in the
+ 
+
+ align:start position:0%
+hash table then for every slot in the
+hash table we could say is it in a or is
+
+ align:start position:0%
+hash table we could say is it in a or is
+ 
+
+ align:start position:0%
+hash table we could say is it in a or is
+it in B now if you not in a union B and
+
+ align:start position:0%
+it in B now if you not in a union B and
+ 
+
+ align:start position:0%
+it in B now if you not in a union B and
+you hash somewhere I mean you'll get
+
+ align:start position:0%
+you hash somewhere I mean you'll get
+ 
+
+ align:start position:0%
+you hash somewhere I mean you'll get
+some bit who knows what that bit stores
+
+ align:start position:0%
+some bit who knows what that bit stores
+ 
+
+ align:start position:0%
+some bit who knows what that bit stores
+I don't care I don't for for the things
+
+ align:start position:0%
+I don't care I don't for for the things
+ 
+
+ align:start position:0%
+I don't care I don't for for the things
+outside of a union B they could be in C
+
+ align:start position:0%
+outside of a union B they could be in C
+ 
+
+ align:start position:0%
+outside of a union B they could be in C
+or not in C I don't really care and so
+
+ align:start position:0%
+or not in C I don't really care and so
+ 
+
+ align:start position:0%
+or not in C I don't really care and so
+uh all I care about is that a and b have
+
+ align:start position:0%
+uh all I care about is that a and b have
+ 
+
+ align:start position:0%
+uh all I care about is that a and b have
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+collisions between each other I don't
+
+ align:start position:0%
+collisions between each other I don't
+ 
+
+ align:start position:0%
+collisions between each other I don't
+want any a thing to Hash to a b thing
+
+ align:start position:0%
+want any a thing to Hash to a b thing
+ 
+
+ align:start position:0%
+want any a thing to Hash to a b thing
+then I can store a bit in every cell in
+
+ align:start position:0%
+then I can store a bit in every cell in
+ 
+
+ align:start position:0%
+then I can store a bit in every cell in
+the hash table and that will tell me in
+
+ align:start position:0%
+the hash table and that will tell me in
+ 
+
+ align:start position:0%
+the hash table and that will tell me in
+particular a versus B and then the rest
+
+ align:start position:0%
+particular a versus B and then the rest
+ 
+
+ align:start position:0%
+particular a versus B and then the rest
+of the items are somehow categorized but
+
+ align:start position:0%
+of the items are somehow categorized but
+ 
+
+ align:start position:0%
+of the items are somehow categorized but
+I don't care how they're
+
+ align:start position:0%
+I don't care how they're
+ 
+
+ align:start position:0%
+I don't care how they're
+categorized so going to use this fact
+
+ align:start position:0%
+categorized so going to use this fact
+ 
+
+ align:start position:0%
+categorized so going to use this fact
+that there is a set of perfect hash
+
+ align:start position:0%
+that there is a set of perfect hash
+ 
+
+ align:start position:0%
+that there is a set of perfect hash
+functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the same
+
+ align:start position:0%
+of the same
+ 
+
+ align:start position:0%
+of the same
+size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh sorry that should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H this is what's really
+
+ align:start position:0%
+H this is what's really
+ 
+
+ align:start position:0%
+H this is what's really
+true size of H is 2 to the order m+ log
+
+ align:start position:0%
+true size of H is 2 to the order m+ log
+ 
+
+ align:start position:0%
+true size of H is 2 to the order m+ log
+log
+
+ align:start position:0%
+log
+ 
+
+ align:start position:0%
+log
+U okay I'm not going to prove this but
+
+ align:start position:0%
+U okay I'm not going to prove this but
+ 
+
+ align:start position:0%
+U okay I'm not going to prove this but
+this is about succinct hash functions
+
+ align:start position:0%
+this is about succinct hash functions
+ 
+
+ align:start position:0%
+this is about succinct hash functions
+may be hard to find such a hash family
+
+ align:start position:0%
+may be hard to find such a hash family
+ 
+
+ align:start position:0%
+may be hard to find such a hash family
+but the claim is there they exist or
+
+ align:start position:0%
+but the claim is there they exist or
+ 
+
+ align:start position:0%
+but the claim is there they exist or
+it's hard to find the hash function in
+
+ align:start position:0%
+it's hard to find the hash function in
+ 
+
+ align:start position:0%
+it's hard to find the hash function in
+the family that has no collisions but
+
+ align:start position:0%
+the family that has no collisions but
+ 
+
+ align:start position:0%
+the family that has no collisions but
+the guarantee is as long as you have uh
+
+ align:start position:0%
+the guarantee is as long as you have uh
+ 
+
+ align:start position:0%
+the guarantee is as long as you have uh
+I guess in total 2 m items out of your
+
+ align:start position:0%
+I guess in total 2 m items out of your
+ 
+
+ align:start position:0%
+I guess in total 2 m items out of your
+univers of size U uh you can get a
+
+ align:start position:0%
+univers of size U uh you can get a
+ 
+
+ align:start position:0%
+univers of size U uh you can get a
+collision free hash function 2 to the
+
+ align:start position:0%
+collision free hash function 2 to the
+ 
+
+ align:start position:0%
+collision free hash function 2 to the
+order M plus log log
+
+ align:start position:0%
+order M plus log log
+ 
+
+ align:start position:0%
+order M plus log log
+U okay so this is going to um
+
+ align:start position:0%
+U okay so this is going to um
+ 
+
+ align:start position:0%
+U okay so this is going to um
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+Maps say a union B to an order M size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+table and here there are no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collisions so then what we also
+
+ align:start position:0%
+collisions so then what we also
+ 
+
+ align:start position:0%
+collisions so then what we also
+store is an A or B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit uh for each table
+
+ align:start position:0%
+bit uh for each table
+ 
+
+ align:start position:0%
+bit uh for each table
+entry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so that's our encoding we store a
+
+ align:start position:0%
+uh so that's our encoding we store a
+ 
+
+ align:start position:0%
+uh so that's our encoding we store a
+hash fun perfect hash function uh that's
+
+ align:start position:0%
+hash fun perfect hash function uh that's
+ 
+
+ align:start position:0%
+hash fun perfect hash function uh that's
+going to cost you know log H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bits for this part and log of H is just
+
+ align:start position:0%
+bits for this part and log of H is just
+ 
+
+ align:start position:0%
+bits for this part and log of H is just
+M plus log log U and then we're going to
+
+ align:start position:0%
+M plus log log U and then we're going to
+ 
+
+ align:start position:0%
+M plus log log U and then we're going to
+store this A or B uh B for every table
+
+ align:start position:0%
+store this A or B uh B for every table
+ 
+
+ align:start position:0%
+store this A or B uh B for every table
+entry the number of table entries is
+
+ align:start position:0%
+entry the number of table entries is
+ 
+
+ align:start position:0%
+entry the number of table entries is
+order M so this is going to take 2 to
+
+ align:start position:0%
+order M so this is going to take 2 to
+ 
+
+ align:start position:0%
+order M so this is going to take 2 to
+the order
+
+ align:start position:0%
+the order
+ 
+
+ align:start position:0%
+the order
+M bits or sorry not uh sorry terms of
+
+ align:start position:0%
+M bits or sorry not uh sorry terms of
+ 
+
+ align:start position:0%
+M bits or sorry not uh sorry terms of
+bits it's order M bits I should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say in terms of functions it's uh you
+
+ align:start position:0%
+say in terms of functions it's uh you
+ 
+
+ align:start position:0%
+say in terms of functions it's uh you
+know two to the order M possible choices
+
+ align:start position:0%
+know two to the order M possible choices
+ 
+
+ align:start position:0%
+know two to the order M possible choices
+for this bit vector and so uh the easy
+
+ align:start position:0%
+for this bit vector and so uh the easy
+ 
+
+ align:start position:0%
+for this bit vector and so uh the easy
+way is to just sum up these bits you use
+
+ align:start position:0%
+way is to just sum up these bits you use
+ 
+
+ align:start position:0%
+way is to just sum up these bits you use
+log of H bits plus order M bits this
+
+ align:start position:0%
+log of H bits plus order M bits this
+ 
+
+ align:start position:0%
+log of H bits plus order M bits this
+already had an order M term and so you
+
+ align:start position:0%
+already had an order M term and so you
+ 
+
+ align:start position:0%
+already had an order M term and so you
+get this that log of s is order M plus
+
+ align:start position:0%
+get this that log of s is order M plus
+ 
+
+ align:start position:0%
+get this that log of s is order M plus
+log log
+
+ align:start position:0%
+log log
+ 
+
+ align:start position:0%
+log log
+U okay so that's the end of proof sketch
+
+ align:start position:0%
+U okay so that's the end of proof sketch
+ 
+
+ align:start position:0%
+U okay so that's the end of proof sketch
+of the claim if you believe perfect hash
+
+ align:start position:0%
+of the claim if you believe perfect hash
+ 
+
+ align:start position:0%
+of the claim if you believe perfect hash
+functions can be written down in small
+
+ align:start position:0%
+functions can be written down in small
+ 
+
+ align:start position:0%
+functions can be written down in small
+way then we're done now for with
+
+ align:start position:0%
+way then we're done now for with
+ 
+
+ align:start position:0%
+way then we're done now for with
+separators now let's apply this
+
+ align:start position:0%
+separators now let's apply this
+ 
+
+ align:start position:0%
+separators now let's apply this
+separator theorem claim to this
+
+ align:start position:0%
+separator theorem claim to this
+ 
+
+ align:start position:0%
+separator theorem claim to this
+setting so now we can compute the size
+
+ align:start position:0%
+setting so now we can compute the size
+ 
+
+ align:start position:0%
+setting so now we can compute the size
+of our en coding our encoding involves
+
+ align:start position:0%
+of our en coding our encoding involves
+ 
+
+ align:start position:0%
+of our en coding our encoding involves
+writing down R intersect W that takes R
+
+ align:start position:0%
+writing down R intersect W that takes R
+ 
+
+ align:start position:0%
+writing down R intersect W that takes R
+intersect W * log n just like
+
+ align:start position:0%
+intersect W * log n just like
+ 
+
+ align:start position:0%
+intersect W * log n just like
+before uh it also
+
+ align:start position:0%
+before uh it also
+ 
+
+ align:start position:0%
+before uh it also
+involves uh writing down the separator
+
+ align:start position:0%
+involves uh writing down the separator
+ 
+
+ align:start position:0%
+involves uh writing down the separator
+separator takes order M bits m is r+
+
+ align:start position:0%
+separator takes order M bits m is r+
+ 
+
+ align:start position:0%
+separator takes order M bits m is r+
+W things that are its order R plus W
+
+ align:start position:0%
+W things that are its order R plus W
+ 
+
+ align:start position:0%
+W things that are its order R plus W
+these are all the things trying to write
+
+ align:start position:0%
+these are all the things trying to write
+ 
+
+ align:start position:0%
+these are all the things trying to write
+down Rus W and wus R so that you add up
+
+ align:start position:0%
+down Rus W and wus R so that you add up
+ 
+
+ align:start position:0%
+down Rus W and wus R so that you add up
+those sizes basically R plus W plus log
+
+ align:start position:0%
+those sizes basically R plus W plus log
+ 
+
+ align:start position:0%
+those sizes basically R plus W plus log
+log u u
+
+ align:start position:0%
+log u u
+ 
+
+ align:start position:0%
+log u u
+is some small thing uh size of memory
+
+ align:start position:0%
+is some small thing uh size of memory
+ 
+
+ align:start position:0%
+is some small thing uh size of memory
+number of cells in memory we're assuming
+
+ align:start position:0%
+number of cells in memory we're assuming
+ 
+
+ align:start position:0%
+number of cells in memory we're assuming
+that's polinomial so you take log log of
+
+ align:start position:0%
+that's polinomial so you take log log of
+ 
+
+ align:start position:0%
+that's polinomial so you take log log of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+polinomial uh that's like log log
+
+ align:start position:0%
+polinomial uh that's like log log
+ 
+
+ align:start position:0%
+polinomial uh that's like log log
+n so let's finish this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before before this was our equation R
+
+ align:start position:0%
+before before this was our equation R
+ 
+
+ align:start position:0%
+before before this was our equation R
+inter W * log n that was the size of our
+
+ align:start position:0%
+inter W * log n that was the size of our
+ 
+
+ align:start position:0%
+inter W * log n that was the size of our
+encoding we still have that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term sorry R inter W size of
+
+ align:start position:0%
+term sorry R inter W size of
+ 
+
+ align:start position:0%
+term sorry R inter W size of
+that uh Times log n so we still do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that now we also pay for this separator
+
+ align:start position:0%
+that now we also pay for this separator
+ 
+
+ align:start position:0%
+that now we also pay for this separator
+we're going to pay r plus
+
+ align:start position:0%
+we're going to pay r plus
+ 
+
+ align:start position:0%
+we're going to pay r plus
+W that's the M part plus log log
+
+ align:start position:0%
+W that's the M part plus log log
+ 
+
+ align:start position:0%
+W that's the M part plus log log
+n this is the number of bits in our
+
+ align:start position:0%
+n this is the number of bits in our
+ 
+
+ align:start position:0%
+n this is the number of bits in our
+encoding okay and I claim or what we
+
+ align:start position:0%
+encoding okay and I claim or what we
+ 
+
+ align:start position:0%
+encoding okay and I claim or what we
+proved over here is that any encoding
+
+ align:start position:0%
+proved over here is that any encoding
+ 
+
+ align:start position:0%
+proved over here is that any encoding
+must use l root n log n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bits so this thing must be at least this
+
+ align:start position:0%
+Bits so this thing must be at least this
+ 
+
+ align:start position:0%
+Bits so this thing must be at least this
+thing so we have a little bit more work
+
+ align:start position:0%
+thing so we have a little bit more work
+ 
+
+ align:start position:0%
+thing so we have a little bit more work
+to prove there are now two cases it
+
+ align:start position:0%
+to prove there are now two cases it
+ 
+
+ align:start position:0%
+to prove there are now two cases it
+depends there's basically log log n is
+
+ align:start position:0%
+depends there's basically log log n is
+ 
+
+ align:start position:0%
+depends there's basically log log n is
+unlikely to dominate we're doing a block
+
+ align:start position:0%
+unlikely to dominate we're doing a block
+ 
+
+ align:start position:0%
+unlikely to dominate we're doing a block
+operation on root N Things probably need
+
+ align:start position:0%
+operation on root N Things probably need
+ 
+
+ align:start position:0%
+operation on root N Things probably need
+to use at least log log and steps so
+
+ align:start position:0%
+to use at least log log and steps so
+ 
+
+ align:start position:0%
+to use at least log log and steps so
+that's not really relevant what will
+
+ align:start position:0%
+that's not really relevant what will
+ 
+
+ align:start position:0%
+that's not really relevant what will
+dominate is either this term as it used
+
+ align:start position:0%
+dominate is either this term as it used
+ 
+
+ align:start position:0%
+dominate is either this term as it used
+to or this term these are two different
+
+ align:start position:0%
+to or this term these are two different
+ 
+
+ align:start position:0%
+to or this term these are two different
+cases call them case one case two in
+
+ align:start position:0%
+cases call them case one case two in
+ 
+
+ align:start position:0%
+cases call them case one case two in
+case two r+ w is at least L root n log
+
+ align:start position:0%
+case two r+ w is at least L root n log
+ 
+
+ align:start position:0%
+case two r+ w is at least L root n log
+n that's the lower bound we want if we
+
+ align:start position:0%
+n that's the lower bound we want if we
+ 
+
+ align:start position:0%
+n that's the lower bound we want if we
+can in case two uh r +
+
+ align:start position:0%
+can in case two uh r +
+ 
+
+ align:start position:0%
+can in case two uh r +
+W is Omega L root n log n what that
+
+ align:start position:0%
+W is Omega L root n log n what that
+ 
+
+ align:start position:0%
+W is Omega L root n log n what that
+means is in this sub tree the amount of
+
+ align:start position:0%
+means is in this sub tree the amount of
+ 
+
+ align:start position:0%
+means is in this sub tree the amount of
+reading we did in the right sub tree
+
+ align:start position:0%
+reading we did in the right sub tree
+ 
+
+ align:start position:0%
+reading we did in the right sub tree
+plus the amount of writing we did in the
+
+ align:start position:0%
+plus the amount of writing we did in the
+ 
+
+ align:start position:0%
+plus the amount of writing we did in the
+left sub tree is at least L root n log n
+
+ align:start position:0%
+left sub tree is at least L root n log n
+ 
+
+ align:start position:0%
+left sub tree is at least L root n log n
+that's our goal over here we want to
+
+ align:start position:0%
+that's our goal over here we want to
+ 
+
+ align:start position:0%
+that's our goal over here we want to
+prove uh sorry it's a previous claim
+
+ align:start position:0%
+prove uh sorry it's a previous claim
+ 
+
+ align:start position:0%
+prove uh sorry it's a previous claim
+that's Now by now erased it's the easier
+
+ align:start position:0%
+that's Now by now erased it's the easier
+ 
+
+ align:start position:0%
+that's Now by now erased it's the easier
+claim we just want to show that the
+
+ align:start position:0%
+claim we just want to show that the
+ 
+
+ align:start position:0%
+claim we just want to show that the
+total amount of time spent in V sub
+
+ align:start position:0%
+total amount of time spent in V sub
+ 
+
+ align:start position:0%
+total amount of time spent in V sub
+is at least log n per operation we're
+
+ align:start position:0%
+is at least log n per operation we're
+ 
+
+ align:start position:0%
+is at least log n per operation we're
+doing L root N Things here so this is a
+
+ align:start position:0%
+doing L root N Things here so this is a
+ 
+
+ align:start position:0%
+doing L root N Things here so this is a
+ton of reading and writing so in that
+
+ align:start position:0%
+ton of reading and writing so in that
+ 
+
+ align:start position:0%
+ton of reading and writing so in that
+case we are happy because we get an
+
+ align:start position:0%
+case we are happy because we get an
+ 
+
+ align:start position:0%
+case we are happy because we get an
+actual lower bound on time
+
+ align:start position:0%
+actual lower bound on time
+ 
+
+ align:start position:0%
+actual lower bound on time
+otherwise uh we don't I mean these are
+
+ align:start position:0%
+otherwise uh we don't I mean these are
+ 
+
+ align:start position:0%
+otherwise uh we don't I mean these are
+actual reads and wrs or total number of
+
+ align:start position:0%
+actual reads and wrs or total number of
+ 
+
+ align:start position:0%
+actual reads and wrs or total number of
+reads and wrs here we're getting uh in
+
+ align:start position:0%
+reads and wrs here we're getting uh in
+ 
+
+ align:start position:0%
+reads and wrs here we're getting uh in
+the other case we get our intersect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W as log n is at least L root n log n
+
+ align:start position:0%
+W as log n is at least L root n log n
+ 
+
+ align:start position:0%
+W as log n is at least L root n log n
+just like before so again the log n's
+
+ align:start position:0%
+just like before so again the log n's
+ 
+
+ align:start position:0%
+just like before so again the log n's
+cancel so here we lose a log n Factor
+
+ align:start position:0%
+cancel so here we lose a log n Factor
+ 
+
+ align:start position:0%
+cancel so here we lose a log n Factor
+but it's okay uh because this is only
+
+ align:start position:0%
+but it's okay uh because this is only
+ 
+
+ align:start position:0%
+but it's okay uh because this is only
+talking about R intersect W this we use
+
+ align:start position:0%
+talking about R intersect W this we use
+ 
+
+ align:start position:0%
+talking about R intersect W this we use
+the LCA charging say well if you look at
+
+ align:start position:0%
+the LCA charging say well if you look at
+ 
+
+ align:start position:0%
+the LCA charging say well if you look at
+a particular read it's only gets charged
+
+ align:start position:0%
+a particular read it's only gets charged
+ 
+
+ align:start position:0%
+a particular read it's only gets charged
+by the LCA so then we can afford to sum
+
+ align:start position:0%
+by the LCA so then we can afford to sum
+ 
+
+ align:start position:0%
+by the LCA so then we can afford to sum
+up lower bounds so there it's a little
+
+ align:start position:0%
+up lower bounds so there it's a little
+ 
+
+ align:start position:0%
+up lower bounds so there it's a little
+bit weird in this situation we add up
+
+ align:start position:0%
+bit weird in this situation we add up
+ 
+
+ align:start position:0%
+bit weird in this situation we add up
+all the lower bounds each of them
+
+ align:start position:0%
+all the lower bounds each of them
+ 
+
+ align:start position:0%
+all the lower bounds each of them
+doesn't give us a log n but in aggregate
+
+ align:start position:0%
+doesn't give us a log n but in aggregate
+ 
+
+ align:start position:0%
+doesn't give us a log n but in aggregate
+we get a log n because every leaf
+
+ align:start position:0%
+we get a log n because every leaf
+ 
+
+ align:start position:0%
+we get a log n because every leaf
+appears in log n levels in this case we
+
+ align:start position:0%
+appears in log n levels in this case we
+ 
+
+ align:start position:0%
+appears in log n levels in this case we
+don't need to aggregate because we just
+
+ align:start position:0%
+don't need to aggregate because we just
+ 
+
+ align:start position:0%
+don't need to aggregate because we just
+say well the number of operations in the
+
+ align:start position:0%
+say well the number of operations in the
+ 
+
+ align:start position:0%
+say well the number of operations in the
+subtree is at least log n per operation
+
+ align:start position:0%
+subtree is at least log n per operation
+ 
+
+ align:start position:0%
+subtree is at least log n per operation
+number this time spent cell probes done
+
+ align:start position:0%
+number this time spent cell probes done
+ 
+
+ align:start position:0%
+number this time spent cell probes done
+is at least log n per operation so in
+
+ align:start position:0%
+is at least log n per operation so in
+ 
+
+ align:start position:0%
+is at least log n per operation so in
+that case we don't need to sum the lower
+
+ align:start position:0%
+that case we don't need to sum the lower
+ 
+
+ align:start position:0%
+that case we don't need to sum the lower
+bounds which're is dumb so in either
+
+ align:start position:0%
+bounds which're is dumb so in either
+ 
+
+ align:start position:0%
+bounds which're is dumb so in either
+case we're happy little weird because
+
+ align:start position:0%
+case we're happy little weird because
+ 
+
+ align:start position:0%
+case we're happy little weird because
+you kind of have a mix of cases you know
+
+ align:start position:0%
+you kind of have a mix of cases you know
+ 
+
+ align:start position:0%
+you kind of have a mix of cases you know
+one vertex V could be in case two then
+
+ align:start position:0%
+one vertex V could be in case two then
+ 
+
+ align:start position:0%
+one vertex V could be in case two then
+you just ignore all the things below it
+
+ align:start position:0%
+you just ignore all the things below it
+ 
+
+ align:start position:0%
+you just ignore all the things below it
+some other the rest of the tree might be
+
+ align:start position:0%
+some other the rest of the tree might be
+ 
+
+ align:start position:0%
+some other the rest of the tree might be
+in case one but you can mix and match
+
+ align:start position:0%
+in case one but you can mix and match
+ 
+
+ align:start position:0%
+in case one but you can mix and match
+one and two as long as you uh you don't
+
+ align:start position:0%
+one and two as long as you uh you don't
+ 
+
+ align:start position:0%
+one and two as long as you uh you don't
+use a one below a two you're okay you
+
+ align:start position:0%
+use a one below a two you're okay you
+ 
+
+ align:start position:0%
+use a one below a two you're okay you
+won't double count and so in either case
+
+ align:start position:0%
+won't double count and so in either case
+ 
+
+ align:start position:0%
+won't double count and so in either case
+we're happy we get a log n lower bound
+
+ align:start position:0%
+we're happy we get a log n lower bound
+ 
+
+ align:start position:0%
+we're happy we get a log n lower bound
+either on time per operation or on this
+
+ align:start position:0%
+either on time per operation or on this
+ 
+
+ align:start position:0%
+either on time per operation or on this
+kind of time per
+
+ align:start position:0%
+kind of time per
+ 
+
+ align:start position:0%
+kind of time per
+operation add up all those lower bounds
+
+ align:start position:0%
+operation add up all those lower bounds
+ 
+
+ align:start position:0%
+operation add up all those lower bounds
+get log n per
+
+ align:start position:0%
+get log n per
+ 
+
+ align:start position:0%
+get log n per
+operation uh we get root n log n per
+
+ align:start position:0%
+operation uh we get root n log n per
+ 
+
+ align:start position:0%
+operation uh we get root n log n per
+block operation which implies log n per
+
+ align:start position:0%
+block operation which implies log n per
+ 
+
+ align:start position:0%
+block operation which implies log n per
+insert delete Edge or connectivity
+
+ align:start position:0%
+insert delete Edge or connectivity
+ 
+
+ align:start position:0%
+insert delete Edge or connectivity
+query and that proves our
+
+ align:start position:0%
+query and that proves our
+ 
+
+ align:start position:0%
+query and that proves our
+theorem more or less on time you can use
+
+ align:start position:0%
+theorem more or less on time you can use
+ 
+
+ align:start position:0%
+theorem more or less on time you can use
+the same technique to do a trade-off
+
+ align:start position:0%
+the same technique to do a trade-off
+ 
+
+ align:start position:0%
+the same technique to do a trade-off
+between updates and queries this is just
+
+ align:start position:0%
+between updates and queries this is just
+ 
+
+ align:start position:0%
+between updates and queries this is just
+log in worst case of the two I mentioned
+
+ align:start position:0%
+log in worst case of the two I mentioned
+ 
+
+ align:start position:0%
+log in worst case of the two I mentioned
+what the bound was last time same trick
+
+ align:start position:0%
+what the bound was last time same trick
+ 
+
+ align:start position:0%
+what the bound was last time same trick
+works you just do more updates than
+
+ align:start position:0%
+works you just do more updates than
+ 
+
+ align:start position:0%
+works you just do more updates than
+queries or more queries than updates so
+
+ align:start position:0%
+queries or more queries than updates so
+ 
+
+ align:start position:0%
+queries or more queries than updates so
+we get link cut trees are optimal or
+
+ align:start position:0%
+we get link cut trees are optimal or
+ 
+
+ align:start position:0%
+we get link cut trees are optimal or
+tour trees are optimal and we got lots
+
+ align:start position:0%
+tour trees are optimal and we got lots
+ 
+
+ align:start position:0%
+tour trees are optimal and we got lots
+of other points on the trade-off curve
+
+ align:start position:0%
+of other points on the trade-off curve
+ 
+
+ align:start position:0%
+of other points on the trade-off curve
+as you may recall last class like our
+
+ align:start position:0%
+as you may recall last class like our
+ 
+
+ align:start position:0%
+as you may recall last class like our
+log squared up update is optimal for a
+
+ align:start position:0%
+log squared up update is optimal for a
+ 
+
+ align:start position:0%
+log squared up update is optimal for a
+log over log log
+
+ align:start position:0%
+log over log log
+ 
+
+ align:start position:0%
+log over log log
+query and that's the end of that dynamic
+
+ align:start position:0%
+query and that's the end of that dynamic
+ 
+
+ align:start position:0%
+query and that's the end of that dynamic
+graphs in the end of advanced data
+
+ align:start position:0%
+graphs in the end of advanced data
+ 
+
+ align:start position:0%
+graphs in the end of advanced data
+structures um hope you had a fun time we
+
+ align:start position:0%
+structures um hope you had a fun time we
+ 
+
+ align:start position:0%
+structures um hope you had a fun time we
+got to see lots of different topics and
+
+ align:start position:0%
+got to see lots of different topics and
+ 
+
+ align:start position:0%
+got to see lots of different topics and
+I hope you all enjoy watching on the
+
+ align:start position:0%
+I hope you all enjoy watching on the
+ 
+
+ align:start position:0%
+I hope you all enjoy watching on the
+videos and let me know if you have any
+
+ align:start position:0%
+videos and let me know if you have any
+ 
+
+ align:start position:0%
+videos and let me know if you have any
+comments send email or
+
+ align:start position:0%
+comments send email or
+ 
+
+ align:start position:0%
+comments send email or
+whatever
+
+ align:start position:0%
+whatever
+ 
+
+ align:start position:0%
+whatever
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yay
\ No newline at end of file
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new file mode 100644
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+++ b/YegKLHb9TOU.txt
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+[WRITING ON CHALKBOARD]
+
+PROFESSOR: Good morning.
+
+I think I'll start even though
+people are not quite all here,
+
+because it's time.
+
+Sorry, I'd hoped to start
+Chapter 10 last time, but
+
+we'll start it this time.
+
+When Ashish comes, we'll have
+handouts for Chapter 10, the
+
+new problem set and the
+old problem set
+
+solutions as usual.
+
+This chapter is about trellis
+diagrams for block codes.
+
+Binary linear block codes of
+the kind that we've seen
+
+before, it's actually a much
+more general notion that
+
+applies to --
+
+well, linearity is important,
+although we don't see it very
+
+specifically in the
+trellis diagram.
+
+But we'll see that for
+constructing a unique minimal
+
+trellis, linearity is
+an important aspect.
+
+Or more generally, it's just
+the group property of codes
+
+that allows us to
+construct unique
+
+minimal trellis diagrams.
+
+And I think it's best
+to motivate this
+
+chapter by an example.
+
+Here's a nice example of a code
+that we know very well.
+
+It has a nice trellis diagram.
+
+It's the 8, 4, 4 Reed-Muller
+code.
+
+Just to remind you of how we
+construct this code, or one of
+
+the methods.
+
+We have many methods.
+
+We take this kind of universal
+eight by eight --
+
+well, it's a list
+of eight tuples.
+
+And it's the tensor product
+of this little
+
+matrix three times.
+
+And if we create this, we get a
+matrix that looks like that.
+
+And we just pick the rows that
+have weight four or greater,
+
+and they are the generators of
+the 8, 4, 4 Reed-Muller code.
+
+So we'll take those as our
+set of generators.
+
+It's the 16 code words generated
+by these four
+
+generators here.
+
+This goes back to the first part
+of the term, but I hope
+
+you recall that fairly
+quickly.
+
+Now I'd like to draw a trellis
+diagram for this code.
+
+I don't particularly
+know why yet.
+
+One idea I might have in mind
+is to do a Viterbi algorithm
+
+decoding as a maximum likelihood
+decoding algorithm
+
+for this code.
+
+So let's see if I can
+come up with an
+
+efficient trellis diagram.
+
+That means one that first
+of all has really
+
+few states in it.
+
+Relatively few branches would be
+efficient as a decoding map
+
+for the Viterbi algorithm.
+
+And here's a very nice one.
+
+This looks sort of
+like a rate 1/2
+
+four-state trellis diagram.
+
+Of course, it's not
+time-invariant, doesn't go on
+
+forever like for a convolutional
+code, for a
+
+block code.
+
+Block code only exists
+over a finite time.
+
+So we're going to get a block
+trellis that starts at a
+
+particular time, that
+ends at a particular
+
+time in a single state.
+
+But we want the basic
+property that the --
+
+the paths in this trellis are
+in one-to-one correspondence
+
+with the words in the code.
+
+So, how many words are
+there in the code?
+
+There are 16 in this code.
+
+How many paths are there
+through this trellis?
+
+Well, again it has a very
+regular structure.
+
+There is a four-way
+branch here.
+
+Wherever you get to, you have
+a two-way branch here.
+
+You have a two-way
+branch here.
+
+You have no choice here.
+
+So there are 16 possible ways
+to get through this trellis,
+
+16 trajectories if you like.
+
+And next let's check if they
+correspond to all the possible
+
+code words.
+
+Here is the all 0 code
+word up here.
+
+What's next?
+
+Let's check for the
+generators.
+
+Here is one of the generators,
+1, 1, 1, 1, 0, 0, 0, 0.
+
+And it's a 1, 1, 0, 0.
+
+This is 1, 1 also.
+
+1, 1 --
+
+no, I'm sorry.
+
+1, 1, 0, 0, 1, 1, 0, 0.
+
+That's right.
+
+That's this one going
+through here.
+
+And 1, 0, 1, 0, 1, 0, 1, 0.
+
+That's here.
+
+And what's the last one?
+
+All ones.
+
+Well, that's up here too.
+
+The all one path.
+
+Yeah.
+
+AUDIENCE: How did you know
+whether to make the
+
+[INAUDIBLE] procedure?
+
+PROFESSOR: I had side
+information.
+
+A genie told me.
+
+I know that this is an
+efficient trellis.
+
+Where we'll get to, and I hope
+today in this lecture, is a
+
+turn-the-crank method of
+constructing not only a
+
+trellis, but the minimal
+possible trellis.
+
+So you'll be able to see how
+starting from a set of four
+
+generators like this, turn the
+crank, and I'll produce a
+
+trellis for you.
+
+But of course you don't
+see that yet.
+
+I just know that this
+is a trellis,
+
+and it's a nice trellis.
+
+It has nice, regular
+structure.
+
+You could decode this with a
+Viterbi algorithm, and you
+
+could see the complexity would
+be comparable to the
+
+complexity of decoding
+a rate 1/2 four-state
+
+convolutional code.
+
+And in fact, you remember I
+compared our example rate 1/2
+
+four-state convolutional code
+which had a coding gain of 4
+
+dB with this code saying they
+roughly have the same
+
+complexity.
+
+And when I said that, this is
+what I had in mind, that I
+
+could decode each of them with
+a Viterbi algorithm with
+
+approximately the same
+amount of complexity.
+
+And unfortunately this only has
+a nominal coding gain of 3
+
+dB, and an effective
+coding gain of
+
+slightly less than that.
+
+So it's not quite as good as
+the convolutional code.
+
+And at the end of the day, we're
+going to find out that
+
+that's kind of typical of a
+comparison between block and
+
+convolutional codes of the
+same trellis complexity.
+
+But on the other hand, this is
+certainly a better way to
+
+decode this code, recursive by
+the Viterbi algorithm, than to
+
+do a full maximum likelihood
+decoding of all 16 code words,
+
+which involves just brute force
+computing the distance
+
+to 16 code words.
+
+This is if you like a more
+organized way of performing
+
+the computation of how far is
+the receive sequence from each
+
+of the 16 code words.
+
+So the reason we look for
+trellises of block codes is
+
+first of all, it's better
+than exhaustive
+
+maximum likelihood decoding.
+
+It is a maximum likelihood
+decoding algorithm since we're
+
+going to find that we can
+construct a trellis for any
+
+linear block code, which at
+worst, it's never going to be
+
+more complicated than just
+enumerating all the code words
+
+and doing exhaustive maximum
+likelihood decoding.
+
+And usually, as in this case,
+it's going to be a more
+
+efficient method of doing
+maximum likelihood decoding.
+
+So we will have a general method
+of maximum likelihood
+
+decoding that is more
+efficient than
+
+the exhaustive method.
+
+Secondly, there's
+an interesting
+
+link to system theory.
+
+I won't make a great deal
+of this in this course.
+
+But what are we really
+doing here?
+
+We're representing a block code
+as a finite state system.
+
+In fact, a linear block code
+is a finite state linear
+
+system, although again the
+linearity is not terribly
+
+transparent from this picture.
+
+So we have a linear finite state
+system, just as we did
+
+for the convolutional code.
+
+However, it's necessarily
+time varying.
+
+It couldn't possibly be shift
+invariant because we only have
+
+a finite time axis,
+if you like.
+
+Time axis only goes over four
+time units in this particular
+
+picture, where I've grouped
+two outputs at a time.
+
+So that's interesting, and for
+our purposes an interesting
+
+aspect of this is that we now
+get a notion of how complex is
+
+a block code.
+
+So far we've been focused on
+parameters like n, k, d, which
+
+are all algebraic parameters
+of the code itself.
+
+But we really want to know
+about performance versus
+
+complexity.
+
+So how complex is
+the 8 4 4 code?
+
+Well, now we have a little
+bit of a handle on it.
+
+We can say its complexity is
+that of a four-state machine.
+
+So trellis complexity gives us a
+measure of the complexity of
+
+a block code so that we can,
+for instance, say the
+
+Reed-Muller codes tend to be
+less complex than PCH codes.
+
+And I'll try to give
+some substance to
+
+that as we go along.
+
+So we get additional parameters
+that have more to
+
+do with what we really care
+about, which is decoding
+
+complexity.
+
+And finally, I introduce this
+subject because it's a
+
+stepping stone to where we're
+really going, is this notion
+
+of codes on graphs, which is the
+underlying concept for the
+
+capacity-approaching codes
+that is our goal point.
+
+Our whole goal in this course
+is to get to capacity,
+
+specifically on the additive
+white Gaussian noise channel.
+
+And the way that people have
+found they get to capacity
+
+turbo codes, low-density
+parity check codes, the
+
+underlying concept that I'm
+going to be framing that in is
+
+codes on graphs.
+
+And this is kind of a code on
+a very elementary graph.
+
+So it's a good way from
+here to there.
+
+So that's why we're taking
+a little time to
+
+look at this subject.
+
+Even though as I say, at the
+end of the day, even though
+
+there's a better way of decoding
+block codes than the
+
+ways we've had previously, and a
+better non-algebraic way, it
+
+still is not going to turn out
+to be as good as convolutional
+
+codes, which we already
+know about.
+
+Any questions on what
+we're doing,
+
+motivation and so forth?
+
+Yeah.
+
+AUDIENCE: [INAUDIBLE]
+convolutional codes is that
+
+each node doesn't have two
+things coming on to it?
+
+PROFESSOR: That's right, it's
+a little bit more irregular,
+
+and this trellis section
+doesn't look the same.
+
+We had a completely mixing
+trellis section for the
+
+convolutional code.
+
+This kind of divides it into two
+halves which don't meet.
+
+This basically expresses the
+code as a certain subcode, and
+
+its coset is down here.
+
+So, it's not quite the same.
+
+Looks different.
+
+Maybe this will turn out
+to be interesting.
+
+Good observation.
+
+Anything else at this point?
+
+AUDIENCE: You just said
+that this is not a
+
+convolutional code.
+
+Or maybe we can have more than
+one states, and it is a
+
+convolutional code.
+
+PROFESSOR: Let's see, it's
+not a convolutional code.
+
+It's not even a terminated
+convolutional code, because it
+
+doesn't have the simple
+shift register
+
+type of trellis diagram.
+
+At least it's not the kind
+of convolutional
+
+code we know about.
+
+But why should it be?
+
+Let's open up our minds
+to more possibilities.
+
+We don't really care.
+
+The objective that we have in
+mind here is we're just going
+
+to try to come up with the most
+efficient trellis picture
+
+that we can for block code.
+
+And we're going to use the
+linearity, and we're going to
+
+basically try to find
+as few states as
+
+possible at each time.
+
+That's going to be our measure
+of efficiency.
+
+That's not the only one you
+could think of, but it'll turn
+
+out that any notion of efficient
+representation comes
+
+down to the same thing.
+
+So we'll focus on a minimal
+state representation of a
+
+block code, and you can think
+of this as an exercise in
+
+system theory and minimal
+
+realizations of a linear system.
+
+This you can view.
+
+A set of all 16 code words you
+can view is the set of
+
+possible trajectories of a
+linear system on a time axis
+
+of length 8, and we want to find
+a minimal realization,
+
+minimal state realization
+of that linear system.
+
+So that'll make sense to some
+of you, and it won't make an
+
+awful lot of sense to
+the rest of you.
+
+So we're after a minimal, in the
+state sense, minimal state
+
+complexity, let's say.
+
+And let's continue to focus on
+this example, and let's focus
+
+on a particular time.
+
+Let's focus on the halfway
+point here.
+
+Where do the state times
+occur, by the way?
+
+They occur between
+the symbol tags.
+
+You can think of a state as
+being associated with a cut
+
+between a certain set of symbols
+which we call the past
+
+and another set of symbols
+which we call the future,
+
+again using just some theoretic
+temporal language.
+
+So if we make a cut --
+
+let's say I do it over here.
+
+States are based on cuts between
+a past and a future,
+
+so the state actually occurs
+between the fourth and the
+
+fifth symbol here, not at either
+of them, if you want to
+
+draw where is the stated time.
+
+And let's start with
+this example.
+
+And let's ask if we could find
+any simpler trellis for this.
+
+In other words, let's see if
+we can have fewer than four
+
+states at this midpoint.
+
+Could we possibly have
+fewer than four
+
+states at the midpoint?
+
+What's the key property
+of states?
+
+The key property of states is
+that once you get to a state,
+
+that then becomes a summary of
+all the history that you know
+
+about the past, and any past
+sequence or partial sequence
+
+that gets you to this state has
+to have the same set of
+
+possible continuations over here
+in the future in order
+
+for this to be a valid trellis
+representation.
+
+So maybe it will help if I draw
+this just focusing on the
+
+central time.
+
+There are two ways to get
+to this central time.
+
+One is to get to what
+we call the 0 state.
+
+We can get there by 0, 0,
+0, 0 or 1, 1, 1, 1.
+
+There's a second state which
+we can get to again by two
+
+paths, which are 0, 0,
+1, 1 or 1, 1, 0, 0.
+
+There's a third one, which we
+can get to by 1, 0, 1, 0 or
+
+its complement, 0, 1, 0, 1.
+
+We'll see that each of these
+involves a four-tuple and its
+
+complement.
+
+And this is 1, 0, 0,
+1 or 0, 1, 1, 0.
+
+Those are the set of possible
+past sequences that can get to
+
+any of these four states.
+
+There are two of them.
+
+Now what this trellis says
+is that from this state,
+
+regardless of how we got here,
+either of these two things,
+
+there are two possible
+continuations, which happen to
+
+be the same thing.
+
+And the property state has to
+be that either of these
+
+continuations is a legitimate
+continuation of either of the
+
+paths that it takes
+to get there.
+
+So we now have four possible
+code words that go through
+
+this particular state, that
+pass through this state.
+
+And down here, similarly, I
+think what we have is the same
+
+set of code words.
+
+There's complete symmetry
+and so forth.
+
+Let's ask, could we combine
+these two states, somehow
+
+smush them together into
+a single state?
+
+And the answer is obviously no,
+because 0, 0, 1, 1 is not
+
+a continuation of the
+all 0 sequence, or
+
+of the all 1 sequence.
+
+And 0, 0, 0, 0 is not a
+continuation of the 0, 0, 1, 1
+
+sequence or the 1,
+1, 0, 0 sequence.
+
+The property of the state
+is the Markov property.
+
+And there are many ways of
+phrasing this, but this is the
+
+defining property of states, is
+that if two past paths have
+
+a future continuation --
+
+I hope you understand this
+language as I introduce it --
+
+in common, then all
+their future
+
+continuations are in common.
+
+So I have two past
+paths, let's say.
+
+This is the definition
+of states.
+
+If we can find such a situation,
+then we can say
+
+that these two past paths go
+through the same state at the
+
+cut time, because then we
+can smush them together.
+
+You can think of this as our
+starting from, but suppose we
+
+drew all 16 code words,
+and we drew a --
+
+here would be a 16 state
+trellis, and the first two
+
+elements of it might be 0, 0,
+0, 1, 1, 1, 1, 1, 1, 1, 1.
+
+And we'd ask, can we smush these
+two states together?
+
+And the answer is yes because
+of this property, because 0,
+
+0, 0 can also be followed
+by 1, 1, 1, 1.
+
+There are actually four
+states that we're
+
+smushing together here.
+
+1, 1, 1, 1 and 0, 0, 0.
+
+These are all legitimate code
+words, and because they're all
+
+legitimate, we can basically
+break this up into a Cartesian
+
+product of two paths with two
+futures, and represent all
+
+four of them by a
+single state.
+
+So that's what states do.
+
+If we want a minimal state
+diagram, we should do this as
+
+much as possible.
+
+It's not very well-defined right
+now, but we should merge
+
+states wherever this
+property holds.
+
+So this implies they go through
+a common state, and
+
+it's if and only if.
+
+So you could see it
+very concretely
+
+from the trellis diagram.
+
+This is the property
+that we need.
+
+You can see that for this
+particular code, we do have
+
+the possibility of combining
+all 16 possible states here
+
+into 4, because we can
+combine them all
+
+pair-wise in this way.
+
+This is going to come from the
+linear property of the code.
+
+That's why everything
+is so symmetric.
+
+But we can't go any
+further than that.
+
+So we can conclude from this is
+that for the 8, 4, 4 code,
+
+the minimal state space
+at the center has four
+
+states, has size four.
+
+For simple code like this, you
+can simply see what all the
+
+possibilities are, and this
+is the best we can do.
+
+So do you get that?
+
+This is fundamental
+system theory
+
+state realization theory.
+
+I don't know where
+in the curriculum
+
+one gets this nowadays.
+
+Probably somewhere over towards
+the control side,
+
+maybe in digital signal
+processing, but maybe not.
+
+But we're doing system
+theory here.
+
+We all get that?
+
+Yeah.
+
+AUDIENCE: [INAUDIBLE]
+
+properties basically defined, I
+have two possible paths, and
+
+they have one common
+[INAUDIBLE]
+
+data, they have [INAUDIBLE]
+
+PROFESSOR: Yeah, if they go
+through a common state, that
+
+implies this statement.
+
+Conversely, if we have a set of
+past paths and future paths
+
+that have this property, then
+we can define a state.
+
+In other words, states are
+always going to look something
+
+like this, with a set
+of past paths.
+
+We have a set of future paths,
+and the state is simply a node
+
+that they go through such that
+you can combine any of these
+
+paths with any of
+these futures.
+
+If it's symmetric, you could
+say the same thing.
+
+If two futures have a past in
+common, then they have all
+
+their paths in common.
+
+But whenever you have a state
+representation --
+
+let's suppose we have
+three states there.
+
+Then this is what, just looking
+at those states and
+
+the initial and final states,
+this is what the code is going
+
+to have to look like.
+
+Because property of state is
+that however you got there,
+
+you have to be able to take
+any of these over here.
+
+Otherwise the trellis
+is invalid.
+
+If not all of these nine
+sequences are code words, then
+
+it's not a valid trellis
+representation, or
+
+equivalently, it's not a valid
+state representation.
+
+So if, and only if, we
+can draw the thing in
+
+this way, we get it.
+
+So for a small code, you can
+just see how much combining
+
+you can do.
+
+In particular, you can ask,
+what can the 0, 0 state --
+
+0, 0 path sequence -- what can
+that be combined with?
+
+Well, it can only be combined
+with sequences that have a 0
+
+first part.
+
+So let me introduce now
+the idea of subcodes.
+
+We have a linear code C. Let's
+define an interval on the time
+
+axis: k, k prime, whatever.
+
+The subcode C on that interval
+is the set of all code words.
+
+Elegant way to say it is whose
+support is in k, k prime.
+
+In other words, which are all
+0 outside, which have all 0
+
+symbols outside of this
+interval that we've
+
+identified.
+
+So that's just notation.
+
+So specifically, let's say the
+past code with respect to a
+
+certain time, like the
+midpoint there.
+
+Well, we can define that as the
+set of all code words that
+
+are 0 outside the past, the
+first four symbols, and we
+
+define the future subcode as the
+set of all code words that
+
+are 0 outside the future.
+
+For this code, what is that?
+
+We list the 16 code words.
+
+We make this the past.
+
+We make this the future.
+
+What is the past subcode here?
+
+In this particular case, the
+past subcode is, of course,
+
+the all 0 sequence.
+
+It was always in this code
+or this sequence,
+
+1, 1, 1, 0, 0, 0.
+
+It's a linear code of dimension
+one, and it consists
+
+of these two code words.
+
+It is precisely the set of all
+code words that can be
+
+followed by the all
+0 sequence.
+
+So I can read it directly off of
+this trellis picture here.
+
+So everybody with me?
+
+The past subcode just consists
+of those two words.
+
+The future subcode consists
+similarly.
+
+Looking at the trellis, it's the
+1's that are all 0 outside
+
+the future.
+
+In other words, can follow
+a past which is all 0.
+
+In other words, it's these
+two code words.
+
+So here are two little
+subcodes with a code.
+
+So by definition, this is
+subcode of C. If C is linear,
+
+you can quickly convince
+yourself this is a linear
+
+subcode, so it's going to have
+a certain dimension.
+
+It's going to have size equal
+to a power of two.
+
+It's even going to have a
+minimum distance that is at
+
+least as great as the minimum
+distance of C, because it
+
+consists of code words of C, so
+its minimum non-zero weight
+
+is going to be at least as great
+as that of C. So it has
+
+some properties immediately.
+
+These past and future codes seem
+to have a lot to do with
+
+the structure of the
+trellis up here.
+
+In fact, the zero state consists
+of precisely --
+
+the sequences that go through
+the zero state here are not
+
+coincidentally the set of all
+past code words in Cp followed
+
+by the set of all future
+code words in Cf.
+
+And why is that?
+
+It's because the set of all
+ways of getting to here,
+
+getting to this state, have
+to be the set of all code
+
+sequences that can be followed
+by the all 0 sequence.
+
+Similarly, the set of all
+continuations from this state
+
+have to be the set of
+all continuations
+
+of the all 0 sequence.
+
+So the zero state is always
+going to be a little
+
+sub-trellis that is going to
+represent in effect --
+
+you can draw it as a sum, or
+a product, of the past and
+
+future subcodes.
+
+In other words, there's a
+two-dimensional code that has
+
+these two generators.
+
+g1, g2 generates a little
+two-dimensional code.
+
+Here's the fourth code word in
+it, the all 1 code sequence.
+
+And every element in that
+two-dimensional code goes
+
+through the zero state.
+
+AUDIENCE: [INAUDIBLE]
+
+code word.
+
+So then you know --
+
+PROFESSOR: It's whatever
+it happens to be.
+
+AUDIENCE: Then you have a
+separate state just for --
+
+you could combine them.
+
+PROFESSOR: It doesn't matter.
+
+Suppose that Cp has
+dimension one.
+
+Cf has dimension one.
+
+That means Cp is going to
+be something like this.
+
+Cf is going to be something
+like this.
+
+Whatever, what way.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: It just follows
+from linearity.
+
+And clearly, since C itself was
+linear, we're allowed to
+
+add x, x, x, x all 0's
+to y, y, y, y.
+
+That's a code word, because
+these were both code words in
+
+C. So the linearity allows you
+to fill in this fourth corner
+
+of the rectangle, if you like.
+
+So Cp plus Cf is always going
+to look like this.
+
+And we'll always call this the
+zero state, the state that you
+
+get to by the all 0 sequence.
+
+And that can be followed
+by the all 0 sequence.
+
+That's always going to be
+called the zero state.
+
+By linearity, it's always
+going to look like that.
+
+It might not be dimension one.
+
+It could have any
+dimension here.
+
+So we're really beginning
+to get somewhere now.
+
+What do all these other states
+look like, grouped
+
+theoretically?
+
+Cosets.
+
+Somebody -- who said cosets?
+
+Good, that's right.
+
+So Cp plus Cf is itself
+a subcode of C, a
+
+two-dimensional subcode.
+
+So there are four cosets of Cp
+plus Cf in C, and we'll see if
+
+they correspond to
+the four states.
+
+So how do we do this
+algebraically?
+
+Let's draw a generator matrix
+for C in a certain form.
+
+Again, I'll draw the
+past, the future.
+
+So that's the only division I'm
+concerned with right now.
+
+And let me draw it in
+general form first.
+
+I've defined this past subcode,
+Cp, at a certain
+
+dimension, so it has a certain
+number of generators.
+
+So we're going to put up here a
+set of generators for Cp, g
+
+of Cp, however many there
+happen to be.
+
+And what's their common
+characteristic?
+
+They all are all 0
+in the future.
+
+So they're all going
+to look like that.
+
+Then I'm going to take a set
+of generators of Cf, and
+
+similarly I'm going to use
+them up over there.
+
+These are all code words, and
+they're clearly linear and
+
+independent of those.
+
+So I'm on my way to constructing
+a generator
+
+matrix for C.
+
+But obviously I'm going
+to need some more.
+
+We can call this the number of
+generators in the past, the
+
+number of generators
+in the future.
+
+This is the dimension of Cp.
+
+This is the dimension of Cf.
+
+And now I need some more
+generators, which by
+
+definition are going to have to
+span both past and future.
+
+Let's see.
+
+Since I've already introduced
+the coset language, let me
+
+just mysteriously put that
+as the generators
+
+of a quotient group.
+
+C mod Cp and Cf is what that
+means, and it's a quotient
+
+group, if you know or recall
+what a quotient group is.
+
+But anyway, there are k minus
+kp minus kf of these.
+
+And I don't particularly care
+what I put down in here.
+
+Their property is that
+they have to span
+
+both past and future.
+
+So for our particular example,
+here's the generator for the
+
+8, 4, 4 code.
+
+What we're talking about is
+a generator that looks
+
+like 1, 1, 1, 1.
+
+That's k past is 1.
+
+0, 0, 0, 1, 1, 1, 1.
+
+k future is 1.
+
+They're both one-dimensional
+codes.
+
+Now I need two other generators,
+which must span
+
+past and future.
+
+So what'll I take?
+
+Let me just take two more.
+
+1, 1, 0, 0, 1, 1, 0, 0, 1,
+0, 1, 0, 1, 0, 1, 0.
+
+That would be one
+possible choice.
+
+And so this is k minus kp
+minus kf, which is 2.
+
+What I'm going to claim is that
+I'm going to need a state
+
+for every possible linear
+combination of these
+
+generators.
+
+So claim --
+
+well, let me break it down into
+more logical sequence.
+
+Every code word in C can be
+written as some linear
+
+combination of the generators.
+
+What does that amount to?
+
+It amounts to a certain code
+word in the past code plus a
+
+certain component in the future
+code, either all 0 or
+
+they're all one, plus --
+
+let me call this the state code,
+S, as I do in the notes.
+
+So in this case we have a
+two-dimensional state code.
+
+Its elements are eight-tuples.
+
+It's just a subcode of the code
+we started with, so it's
+
+not quite clear how it
+corresponds to states yet.
+
+Well, let me just call that
+S for state sequence.
+
+And I claim I can break this up
+because the proof is that
+
+for every c in C is equal
+to a sum of --
+
+it's a linear combination
+of the generators.
+
+So I just break that up into
+the three possible parts.
+
+So I get one part that's in the
+past subcode, one part's
+
+in the future subcode, and
+one is in the state.
+
+So this is the past, this is the
+future, this is the state.
+
+So I just break it up
+according to this.
+
+So the 16 code words can all be
+written in this way in our
+
+particular example.
+
+So let's project this code
+word on the past.
+
+What does projection mean?
+
+It means you just don't
+look at the part
+
+that's in the future.
+
+So we're looking at
+four-tuples now.
+
+So C projected on to the
+past, this is the part
+
+that lives over here.
+
+It is equal to -- well, if I
+project the past code word on
+
+the past, I basically get the
+past code word again.
+
+Let me write it like that, but
+it's a little bit redundant.
+
+Incidental comment: I can regard
+this past subcode as
+
+either an 8 1 4 code, but
+what is it really?
+
+It doesn't live out here.
+
+It's support is on these four.
+
+It's really a 4 1 4 repetition
+code that lives on the past.
+
+It's support is the past.
+
+Similarly, the support here
+is the future, and it's
+
+effectively a 4 1 4 repetition
+code for our example.
+
+But formally, if we project
+this on the past, it's a
+
+one-to-one projection.
+
+What happens to the
+future part?
+
+This disappears, because the
+projection of anything in the
+
+future code on the past is
+all 0 by definition.
+
+Plus, it's the projection
+of the state
+
+sequence on the past.
+
+Could the projection of
+the state sequence on
+
+the past be all 0?
+
+This is actually an
+important point.
+
+Could the the projection of
+any linear combination of
+
+these generators down here
+be all 0 in the past?
+
+The answer is no by
+the definition
+
+of the future subcode.
+
+If I found a linear combination
+of this that was
+
+all 0 in the past, I should add
+that to the generators of
+
+the future subcode.
+
+So by defining this in this way,
+I've forced this to be
+
+nonzero, unless, of
+course, the state
+
+sequence itself was 0.
+
+The all 0 sequence is
+in the state code.
+
+So this is nonzero
+if S is nonzero.
+
+And similarly, if I project
+a code word on the
+
+future, I get --
+
+this becomes all 0.
+
+I get the element of the future
+code projected on the
+
+future, plus the state on the
+future, the state projected on
+
+the future.
+
+And now I claim further that
+this means I can draw a
+
+trellis as follows.
+
+Start from here.
+
+For the all 0 sequence, I'll
+have a bunch of parallel paths
+
+going to the zero state
+that together add
+
+up to the past subcode.
+
+These are precise.
+
+One of these is going to be all
+0, and these are precisely
+
+the ones over here that can be
+followed by all 0, as I've
+
+already claimed.
+
+So these are the ones that
+can be followed by 0, and
+
+similarly over here I'm going to
+put all the future subcode.
+
+I will say these correspond
+to the state sequence 0.
+
+These are the ones where if I
+put 0 coefficients down here,
+
+I just get linear combinations
+of the past subcode and the
+
+future subcode.
+
+I'm going to write those
+as going through
+
+all one trellis state.
+
+And I believe I've already made
+the argument that this
+
+state at least is legitimate,
+that every combination of
+
+something in the past subcode
+with something in the future
+
+subcode is a code word.
+
+This is simply just Cp plus
+Cf, what I wrote before.
+
+So I've got one state that
+represents all of Cp plus Cf.
+
+And now let's take another
+typical state down here.
+
+We'll say this state corresponds
+to the state
+
+sequence S, or S is a general
+state sequence.
+
+Think of it as being nonzero.
+
+And what am I going
+to put on that?
+
+I'm going to put Cp plus
+this state sequence
+
+projected on the past.
+
+And that way I'll get all past
+projections that are of this
+
+form for a specific S projected
+on the past,
+
+allowing this to vary through
+the past subcode.
+
+And similarly over here, I will
+let the set of all these
+
+trellis branches be
+Cf plus the state
+
+projected on the future.
+
+So all the things that go
+through this state here will
+
+be Cp plus Cf plus this
+particular state sequence.
+
+So for each of the state
+sequences, I claim I can
+
+define a state.
+
+So it's the set of all past
+continuations of anything that
+
+projects on the past as anything
+in the past subcode
+
+plus a past projection of the
+state sequence can be combined
+
+with anything in the future,
+Cf plus the future
+
+continuation of the
+state sequence.
+
+One of these is simply the past
+projection of the state
+
+sequence plus the future
+projection
+
+of the state sequence.
+
+And this is S, and by
+construction this is a code
+
+word in the code.
+
+Now by linearity I can add any
+past code word to this past
+
+projection.
+
+And that's a code word, so any
+of these elements plus Sf,
+
+continued by Sf, the future
+projection is a code word.
+
+See, there we're taking
+something generated by Cp and
+
+the state code.
+
+And similarly, anything by
+here comes out here.
+
+So I think I've left one or two
+details undone, but are
+
+you convinced that I can define
+a state in this way
+
+such that all of these pasts can
+be followed by all these
+
+futures, and they're
+code words?
+
+In fact, they correspond
+to this subset of
+
+elements of the code.
+
+We have examples
+of it up here.
+
+For instance, 0, 0, 1, 1.
+
+Or let's see.
+
+Let's take a past protection,
+1, 1, 0, 0.
+
+Here's a typical state
+sequence, 1, 1,
+
+0, 0, 1, 1, 0, 0.
+
+And I can add to this anything
+in the past, so I get 0, 0, 1,
+
+1, 1, 1, 0, 0.
+
+I can add to it any of these
+two, anything in the future.
+
+So I get 1, 1, 0, 0, 0, 0, 1, 1
+and 0, 0, 1, 1, 0, 0, 1, 1.
+
+And I claim that all four of
+these have the state projected
+
+on the past equals 1, 1, 0, 0.
+
+The state projected on the
+future is 1, 1, 0, 0.
+
+And that any of these pasts
+can be followed by any of
+
+these futures.
+
+So this is C past plus
+C future plus 1, 1,
+
+0, 0, 1, 1, 0, 0.
+
+That is the claim.
+
+And furthermore, if I go through
+this, dot dot dot, I'm
+
+going to generate everything in
+C. So this is the partition
+
+of C -- into what?
+
+S cosets of Cp plus Cf,
+subcode of C. So
+
+algebraically, that's
+what's going on.
+
+But having done this partition,
+at least with
+
+respect to this state space, I
+can create something which has
+
+S states the size of
+S, which is --
+
+what is this?
+
+The dimension of S is the
+dimension of C minus the
+
+dimension of Cp minus
+the dimension of Cf.
+
+So I've argued that
+I can get a state
+
+space with this dimension.
+
+It's a linear state space, and
+it has a certain dimension,
+
+which is just the dimension of
+C minus the dimension of the
+
+past subcode minus
+the dimension
+
+of the future subcode.
+
+It's the number of generators
+that I need for S. So in the
+
+example, I need two generators
+for S, so I get a state space
+
+of dimension two,
+or size four.
+
+It's just a vector space
+over F2 in this case.
+
+You all with me?
+
+I think you are.
+
+I don't see any great puzzles.
+
+So I can get at least
+these few states.
+
+Could I get any fewer?
+
+Can I possibly merge any
+two of these states?
+
+Could I draw a trellis in which,
+say, I've mushed the
+
+zero state together with one
+of these nonzero states?
+
+And the answer to that is
+clearly no by the definition
+
+of the past and the
+future subcodes.
+
+These are all of the future
+sequences that can follow the
+
+all 0 past sequence.
+
+There can't be any more down
+here, so we can't possibly
+
+mush them together.
+
+And similarly, just by going
+through this, if you can't
+
+take the past part of one state
+and combine it with a
+
+future part of another state
+sequence, because that clearly
+
+is not in the code.
+
+And I don't have a slick proof
+of that in mind at the moment,
+
+but there is one in the notes.
+
+The conclusion from this
+is what I call
+
+the state space theorem.
+
+Given code C, any partition of
+the time axis, the total index
+
+set, into past and future,
+I can do this
+
+not just at the midpoint.
+
+I can do this any point along
+the code that I want to, any
+
+partition into past
+and future.
+
+The minimal --
+
+we get a linear state space, in
+other words a vector space,
+
+S. And the dimension of S is
+equal to the dimension of C
+
+minus the dimension of this
+past subcode minus the
+
+dimension of the
+future subcode.
+
+So we can simply calculate what
+the minimal dimension of
+
+a state space is at any
+point along here.
+
+So for instance, at this point
+here, what's the minimal size
+
+of a state space?
+
+What's the past subcode here?
+
+What's the set of all code
+sequences that are all 0 in
+
+the future, as we have
+all 0's out here?
+
+This point, Cp, is just 0, 0.
+
+It just has dimension 0.
+
+Yeah, 0
+
+What's the future subcode?
+
+This is the subcode which has
+support all out here.
+
+This is anything that
+starts with 0, 0.
+
+This is 0, 0, 0, 0, 0,
+0, 0, 1, 1, 1, 1.
+
+Let me just write
+down generators.
+
+1, 1, 1, 1, 0, 0.
+
+So there is -- this is dimension
+Cp equals 0.
+
+Dimension Cf equals 2.
+
+And so the minimum size of the
+state space is 4 minus 2.
+
+That's again 2.
+
+AUDIENCE: Does this mean
+that [INAUDIBLE]
+
+each state's the number
+of states is the same?
+
+PROFESSOR: Certainly not
+true in general.
+
+Let me ask about time three.
+
+Can certainly do that.
+
+Time three, what's
+the past subcode?
+
+This is the code words that
+have support on the first
+
+three symbols.
+
+Again, that has to have
+dimension 0, because the
+
+minimum weight of
+this code is 4.
+
+So there can't be anything that
+just looks like 1,1,1 and
+
+then five 0's
+
+What is the future
+subcode for that?
+
+Now the only generator
+of the future subcode
+
+is 0, 1, 1, 1, 1.
+
+We have to go this far, and then
+it's what futures can we
+
+get from here?
+
+There are only two words
+that are in the future.
+
+So in that case we have
+dimension past is 0.
+
+Dimension future is 1.
+
+So if we drew a state space
+here, we would have to have
+
+eight states.
+
+In fact, I can do that if I just
+draw a little state in
+
+the middle of each
+of these lines.
+
+I get now a trellis picture
+which has an explicit state at
+
+this third time here, but
+it has eight states.
+
+Oo ugly, so I've masked that.
+
+I've suppressed that
+by this nice
+
+little four-state trellis.
+
+But yeah, if you insisted on
+drawing a state space at time
+
+three, it would have
+eight states in it.
+
+We'll get back to that when I
+get to this turn-the-crank
+
+procedure, if I do, of getting
+to minimal trellises.
+
+So what have we done?
+
+We've established that there is
+a uniquely defined minimal
+
+state space size for
+any partition
+
+between past and future.
+
+In other words, if there's any
+time where you want to make a
+
+cut in the time axis between
+past and future, you can
+
+define what the minimal
+state space size is.
+
+And now you might ask
+the question, can we
+
+simultaneously achieve minimal
+state spaces at all times?
+
+In other words, can we draw a
+single trellis which gets the
+
+minimal state space
+at each time?
+
+We haven't proved
+that there is.
+
+It might be that if you push
+in the state space at one
+
+time, it forces the state
+space to balloon out at
+
+another time.
+
+And in fact, for nonlinear
+codes, that is
+
+typically what happens.
+
+But for linear codes, a
+minor miracle occurs.
+
+And the answer is yes.
+
+So how am I going
+to prove that?
+
+I'm going to prove it via this
+very handy tool, which is also
+
+a construction tool which is
+called a trellis-oriented, or
+
+a little bit more formally, a
+minimum span generator matrix.
+
+The idea here is, given a
+generator matrix, reduce to
+
+trellis-oriented form.
+
+We're going to prove that this
+is unique, or effectively
+
+unique, and specifies minimal
+trellis at all times in a
+
+certain way.
+
+Let's start again.
+
+So loosely, what is a
+
+trellis-oriented generator matrix?
+
+Well, if we have a generator,
+say 0, 0, 1, 1, 1, 1, 0, 0,
+
+its span is this interval from
+its starting time to its
+
+ending time.
+
+It's this.
+
+We say it starts at time 3, it
+ends at time 6, the span is
+
+the interval 3 to
+6 in this case.
+
+So we think of this as not being
+active before time 3.
+
+At time 3 we get the first
+interesting thing happens.
+
+A 1 comes up, but then goes
+through something.
+
+These don't have
+to all be ones.
+
+It could be 1, 1, 0, 1.
+
+Then there's a last 1 at some
+point, and then it quiets
+
+down, and it's dead again.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yes.
+
+Except I'm not sure.
+
+Would you say the support of
+this was 3, 4, and 6, or would
+
+you say it was the interval
+from 3 to 6?
+
+I don't know.
+
+What's the definition
+of support?
+
+AUDIENCE: I don't know it.
+
+PROFESSOR: I'm not
+sure I know.
+
+It's probably been defined
+both ways in different
+
+literatures.
+
+So I'll call it a span, but it's
+roughly the support of
+
+the interesting part.
+
+So that's the definition
+of span.
+
+And what a trellis-oriented
+general matrix is, a
+
+minimal-span matrix, meaning all
+generators have a short a
+
+span as possible.
+
+I'll just say, are as
+short as possible.
+
+This is a lecture.
+
+I can be loose.
+
+Now it's not even clear that's
+well-defined yet.
+
+But let me again give you an
+example, and show you how to
+
+find a trellis-oriented
+generating
+
+matrix just by example.
+
+Let me take our example here, 1,
+1, 0, 0, 1, 1, 0, 0, 1, 0,
+
+1, 0, 1, 0, 1, 0, 1,
+1, 1, 1, 1, 1, 1.
+
+So there is a generator
+matrix that's not in
+
+trellis-oriented form.
+
+In particular, I can see that by
+adding this to this, I can
+
+make this generator
+have shorter span.
+
+I can replace it by one, which
+is four 0's and then four 1's,
+
+which we've already
+found useful in
+
+constructing a trellis.
+
+But let me proceed through
+it more systematically.
+
+How can I make --
+
+this generator generates
+all words in the code.
+
+So how can I find a set of
+linearly independent
+
+generators that has
+shorter span?
+
+There's the sort of greedy
+way of proceeding.
+
+Let's take the first
+two generators.
+
+Can I combine these to find
+anything that has a shorter
+
+span, that I can replace one
+of the generators with?
+
+Anybody?
+
+AUDIENCE: No.
+
+PROFESSOR: No, I can't.
+
+That's not the answer
+I expected to hear.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Let's identify what
+the spans of these are.
+
+That has a span of four.
+
+That has a span of six.
+
+That has a span of seven.
+
+This has a span of eight.
+
+What I'm trying to do
+is to reduce that.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: So if I add the first
+two, that seems like a
+
+good thing to do, because then
+I get 0, 0, 1, 1, and I've
+
+reduced the span of
+that generator.
+
+Any way I can combine these
+two to reduce the span?
+
+Obviously not, because the span
+of this is completely
+
+included in the span of this.
+
+If I add these two together,
+then I'll get something which
+
+still starts here
+and ends here.
+
+Why was I able to reduce
+the span here?
+
+Because the spans had the same
+starting time, so I got a
+
+cancellation of the first bit.
+
+I got a 0 up here.
+
+That's what I wanted.
+
+So that's the key
+to proceeding.
+
+If I see any place, any two that
+have the same starting
+
+time, then I can add them
+together, and the result will
+
+be something that has a
+shorter span than at
+
+least one of them.
+
+So let me do that.
+
+I see two here that have the
+same starting time, and so I
+
+add that to that, and
+I get 0 1 0 1.
+
+So I've got the span
+down to here.
+
+I can do that down here.
+
+And I get this, which is a very
+nice reduction in span.
+
+Can I go any further?
+
+I can clearly look for the same
+thing in ending times, if
+
+I could find two ending times
+that were the same.
+
+I could do the same trick, add
+those two generators together,
+
+and the result would be
+something that was shorter
+
+than at least one of the
+component generators.
+
+But here are my starting
+times, here,
+
+here, here, and here.
+
+They're all different.
+
+So I have no possibility for
+combining two and getting a
+
+better starting time.
+
+Similarly, the ending times
+are here, here, and here.
+
+They're all different.
+
+So I'm done.
+
+So, that's how you find a
+
+trellis-oriented generator matrix.
+
+And there's a closely associated
+theorem, which is
+
+that a generator matrix g is
+trellis-oriented if, and only
+
+if, all starting times differ,
+all ending terms differ.
+
+Yeah?
+
+AUDIENCE: What's the definition
+of all generators
+
+as short as possible?
+
+PROFESSOR: I'm now making it.
+
+This is really just
+motivation.
+
+So this can be my actual
+definition of a
+
+trellis-oriented generator
+matrix, which
+
+I've proved this theorem.
+
+It's a matrix in which all the
+starting times are different,
+
+and all the ending times
+are different.
+
+And what I've achieved is
+that all generators
+
+are as short as possible.
+
+How would I go about proving
+the theorem?
+
+Suppose I have a matrix that's
+not in this form.
+
+And I've already proved that I
+can shorten the generators.
+
+So if it's not in this form,
+it's not trellis-oriented.
+
+The generators are not
+as short as possible.
+
+So all I need to do is
+prove the other side.
+
+Suppose it is in this form.
+
+Then could I possibly find
+shorter generators?
+
+And the proof of that is
+basically the following lemma,
+
+that the subcode C, take
+any interval kk prime.
+
+So given a trellis-oriented
+generating matrix, namely one
+
+that satisfies these conditions,
+then the subcode
+
+consisting of all the code words
+who have support on this
+
+interval is generated by
+the gj in G that have
+
+support in kk prime.
+
+And that's kind of intuitive
+and obvious.
+
+On the one hand, it's clear that
+any linear combination of
+
+these generators is a code
+word in the subcode.
+
+Obviously they all have support
+in this interval.
+
+I can't generate anything that
+has support outside that
+
+interval by linear
+combinations.
+
+So the only question is, can I
+possibly get anything that's
+
+in the subcode by combining
+with a generator that is
+
+outside this interval?
+
+And again, it's clear that say I
+take kk prime to be here, if
+
+all the starting times are
+different, and all the ending
+
+times are different, and I start
+to add generators that
+
+are outside here, I can't
+possibly get cancellation of
+
+the starting time, or I can't
+possibly get cancellation of
+
+the ending time.
+
+So I'm going to wind up with a
+code word which has support
+
+outside the interval.
+
+So, it really is
+a simple lemma.
+
+AUDIENCE: [INAUDIBLE]
+
+have the all 0 code word?
+
+PROFESSOR: Excuse me?
+
+AUDIENCE: The all 0 word will
+be part of the subcode.
+
+PROFESSOR: The all 0 word is
+always part of the subcode.
+
+AUDIENCE: [INAUDIBLE]
+
+who has something outside
+this interval.
+
+Then when you add that with the
+all 0 one, you would get
+
+something that does not belong
+to the subcode, [INAUDIBLE]
+
+PROFESSOR: Right, but
+I have to ask if
+
+there's any code word.
+
+So I have to consider all
+the code words, really.
+
+But I'm saying if I have a code
+word C that is sum of the
+
+generators, and I have a nonzero
+coefficient here on
+
+any generator that has starting
+time outside this
+
+interval or ending time outside
+this interval, then I
+
+can't possibly get
+cancellation of
+
+that nonzero thing.
+
+And so if it really requires
+this to be nonzero, and then
+
+I'm going to say that
+I get a code word
+
+that's not in this subcode.
+
+So that's very quick, intuitive
+
+sketch of that proof.
+
+Again, for writing it
+out, see the notes.
+
+But this lemma then proves this
+theorem, because it now
+
+says I can't --
+
+if all the starting times are
+different, and all the ending
+
+times are different, then I
+can't possibly get shorter
+
+support for any of
+the generators.
+
+And I don't think so in a
+totally convincing way, but
+
+that basically is
+the point here.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Well, now
+I'm defining this.
+
+So, meaning that all the
+starting times are different,
+
+and all the ending times
+are different.
+
+From now on that's going to
+be my definition of a
+
+trellis-oriented generator
+matrix.
+
+So, saying that this property
+implies this property.
+
+But now this lemma has an
+interesting consequence.
+
+This implies for any past and
+future, Cp is generated by the
+
+generators in a trellis-oriented
+generating
+
+matrix with support in p.
+
+And similarly, Cf is generated
+by the generators
+
+with support in f.
+
+So for any p and f, I get a
+picture that looks like this.
+
+I can draw now this boundary
+anywhere I want, and if the
+
+matrix was trellis-oriented,
+then I'm going to get a
+
+certain subset of generators
+that live in the past, and
+
+they'll be the generators
+in fact of Cp.
+
+The dimension of them will
+simply be the number of
+
+generators that live in
+the past for that
+
+definition of the past.
+
+There will be some other
+set that live
+
+entirely in the future.
+
+Those will be the ones that
+generate the future.
+
+And the ones that are neither
+wholly in the past or in the
+
+future will generate
+the state code.
+
+So that says I can read off the
+dimensions of the state
+
+spaces just by looking at this
+single trellis-oriented
+
+generator matrix.
+
+So now let me very quickly go
+through the calculation that I
+
+went through a little bit
+laboriously over here.
+
+Suppose I make the whole
+thing the future.
+
+In other words, I draw
+a cut before time 0.
+
+Then the state space
+has dimension 0.
+
+All four generators live
+on the future.
+
+If I make the cut here, the
+state space has dimension 1,
+
+because three of the generators
+live on the future.
+
+One is active at time 1.
+
+So that means I'm going to get a
+two-state trellis at time 1.
+
+If I make the cut here between
+past and future, I see two
+
+generators live on the future
+and are inactive, haven't
+
+started yet.
+
+But two of the generators
+have already started.
+
+At this time we have three
+active generators.
+
+Only one is still completely
+on the future.
+
+At this time in the middle I
+have two generators which --
+
+past subcode, future subcode,
+and two that aren't.
+
+So I get this form that we
+looked at over there.
+
+And I get a state space here
+generated by these two
+
+generators of size two.
+
+So just by looking at this I go
+right through the picture,
+
+and I find the size of the
+state space at each time.
+
+So this is an algebraic way of
+finding the minimal state.
+
+So now I can draw from this a
+trellis just by writing down
+
+these state spaces.
+
+Let me leave these
+trellises here.
+
+Let me draw now a full
+trellis, or an
+
+eight-section trellis.
+
+I'm only going to put one
+bit on each trellis.
+
+Here is the starting
+state, dimension 0.
+
+One state.
+
+From that I can go
+out to 0 or 1.
+
+I won't label the
+state spaces.
+
+Next time, I'm still
+just branching.
+
+Actually, to make it look like
+that, I'm going to want to
+
+come down here, 0,
+1, 1, 1, 1, 0.
+
+I basically just have four
+states at time two
+
+corresponding to whatever
+the first two bits are.
+
+They all go to different states,
+because all these have
+
+possible future continuations.
+
+Then I have eight
+states at this
+
+time, still just branching.
+
+Sorry, this is going to take
+some time to do correctly.
+
+Add this time, then
+I come in here.
+
+0, 1.
+
+Anyway, and it's symmetrical
+on the other side.
+
+So that's what a full trellis
+will look like.
+
+And how did I do this trellis
+in principle?
+
+I wrote down all
+16 code words.
+
+I wrote down what linear
+combinations they were up
+
+here, and I therefore found what
+states they went through
+
+at each time.
+
+And then I just drew the graph
+that goes through that
+
+describes those trajectories.
+
+So I wrote down all
+the code words.
+
+I wrote down all these state
+codes at all these times.
+
+I could have written them
+down in any order.
+
+And then I just connected
+the dots according
+
+to which state --
+
+I make this calculation as to
+which state they go through.
+
+That's a good place to stop.
+
+Let me summarize.
+
+We now have a method, given a
+generator matrix for a binary
+
+linear block code, of reducing
+that generator matrix to
+
+trellis-oriented form.
+
+Just by inspection of the
+trellis-oriented generator
+
+matrix, we can determine what
+the state space dimensions are
+
+at each instant of time, at
+each possible state cut.
+
+And we can then draw a trellis
+which achieves that minimal
+
+state space dimension, or
+minimal state space size, for
+
+every moment of time
+simultaneously.
+
+And I assert that this trellis
+is the minimal trellis in
+
+every respect, whether you're
+trying to minimize state
+
+complexity, or if you're using
+the Viterbi algorithm.
+
+Really what you want to minimize
+is the number of
+
+branches, but there's a
+calculation about branch
+
+spaces in the notes that shows
+that this also achieves the
+
+minimal branch space size at
+every time, regardless of how
+
+you draw the trellis.
+
+More elaborate calculations with
+a more refined notion of
+
+Viterbi algorithm complexities
+still come up
+
+with the same result.
+
+The result is there is
+essentially a unique minimal
+
+trellis, where it's minimal
+in every way.
+
+And this comes from the linear,
+or more broadly, the
+
+group property of the code.
+
+So for any linear group code,
+there's a well-defined,
+
+essentially unique up to
+re-labeling, minimal trellis
+
+that achieves the minimum of
+whatever complexity quantity
+
+you want to define.
+
+So in this sense, the trellis
+complexity of a group or
+
+linear code is very
+well-defined.
+
+It's defined by this minimal
+trellis, or by its parameters,
+
+and we can use that as a measure
+of the complexity of
+
+the corresponding group code.
+
+And from an engineering point
+of view, once we've got this
+
+minimal trellis, we can use the
+Viterbi algorithm to do
+
+maximum likelihood decoding.
+
+Just in the same way we did for
+convolutional codes, sweep
+
+from the starting node
+to the ending node.
+
+Digest that, and we'll come back
+and talk about it again.
+
+Do a few more details
+on Monday, but
+
+that's the basic idea.
\ No newline at end of file
diff --git a/Z2ENBilJWN0.txt b/Z2ENBilJWN0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..38bbfa1353868ce7cc75e8fd23b68fd083abd323
--- /dev/null
+++ b/Z2ENBilJWN0.txt
@@ -0,0 +1,10483 @@
+align:start position:0%
+ 
+So today we're going to continue our
+
+ align:start position:0%
+So today we're going to continue our
+ 
+
+ align:start position:0%
+So today we're going to continue our
+discussion of networking we're going to
+
+ align:start position:0%
+discussion of networking we're going to
+ 
+
+ align:start position:0%
+discussion of networking we're going to
+if you remember from the last two times
+
+ align:start position:0%
+if you remember from the last two times
+ 
+
+ align:start position:0%
+if you remember from the last two times
+we've talked about these three different
+
+ align:start position:0%
+we've talked about these three different
+ 
+
+ align:start position:0%
+we've talked about these three different
+network two different network two
+
+ align:start position:0%
+network two different network two
+ 
+
+ align:start position:0%
+network two different network two
+different layers of the network stack so
+
+ align:start position:0%
+different layers of the network stack so
+ 
+
+ align:start position:0%
+different layers of the network stack so
+far we talked about the link layer and
+
+ align:start position:0%
+far we talked about the link layer and
+ 
+
+ align:start position:0%
+far we talked about the link layer and
+we talked about the network layer and
+
+ align:start position:0%
+we talked about the network layer and
+ 
+
+ align:start position:0%
+we talked about the network layer and
+today we're going to talk about the end
+
+ align:start position:0%
+today we're going to talk about the end
+ 
+
+ align:start position:0%
+today we're going to talk about the end
+to end layer um and what we so what
+
+ align:start position:0%
+to end layer um and what we so what
+ 
+
+ align:start position:0%
+to end layer um and what we so what
+we've talked about so far has been a
+
+ align:start position:0%
+we've talked about so far has been a
+ 
+
+ align:start position:0%
+we've talked about so far has been a
+network stack that provides this
+
+ align:start position:0%
+network stack that provides this
+ 
+
+ align:start position:0%
+network stack that provides this
+abstraction of being able to send a
+
+ align:start position:0%
+abstraction of being able to send a
+ 
+
+ align:start position:0%
+abstraction of being able to send a
+message from one machine to another
+
+ align:start position:0%
+message from one machine to another
+ 
+
+ align:start position:0%
+message from one machine to another
+machine across a number of links on a
+
+ align:start position:0%
+machine across a number of links on a
+ 
+
+ align:start position:0%
+machine across a number of links on a
+network and this network stack that
+
+ align:start position:0%
+network and this network stack that
+ 
+
+ align:start position:0%
+network and this network stack that
+we've talked about is if you'll remember
+
+ align:start position:0%
+we've talked about is if you'll remember
+ 
+
+ align:start position:0%
+we've talked about is if you'll remember
+a best effort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Network so best effort Network
+
+ align:start position:0%
+Network so best effort Network
+ 
+
+ align:start position:0%
+Network so best effort Network
+as you'll remember is a network that is
+
+ align:start position:0%
+as you'll remember is a network that is
+ 
+
+ align:start position:0%
+as you'll remember is a network that is
+subject to
+
+ align:start position:0%
+subject to
+ 
+
+ align:start position:0%
+subject to
+losses so some messages may not be
+
+ align:start position:0%
+losses so some messages may not be
+ 
+
+ align:start position:0%
+losses so some messages may not be
+properly transmitted from one point to
+
+ align:start position:0%
+properly transmitted from one point to
+ 
+
+ align:start position:0%
+properly transmitted from one point to
+the other point it's subject to the
+
+ align:start position:0%
+the other point it's subject to the
+ 
+
+ align:start position:0%
+the other point it's subject to the
+possibility of reordering of
+
+ align:start position:0%
+possibility of reordering of
+ 
+
+ align:start position:0%
+possibility of reordering of
+messages as messages may take say for
+
+ align:start position:0%
+messages as messages may take say for
+ 
+
+ align:start position:0%
+messages as messages may take say for
+example different routes through the
+
+ align:start position:0%
+example different routes through the
+ 
+
+ align:start position:0%
+example different routes through the
+network and it's subject to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delays and congestion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+typically due to queuing within the
+
+ align:start position:0%
+typically due to queuing within the
+ 
+
+ align:start position:0%
+typically due to queuing within the
+network so today what we're going to
+
+ align:start position:0%
+network so today what we're going to
+ 
+
+ align:start position:0%
+network so today what we're going to
+talk about our is the end to- end layer
+
+ align:start position:0%
+talk about our is the end to- end layer
+ 
+
+ align:start position:0%
+talk about our is the end to- end layer
+and the end to end layer is going to be
+
+ align:start position:0%
+and the end to end layer is going to be
+ 
+
+ align:start position:0%
+and the end to end layer is going to be
+the way that we're going to get at
+
+ align:start position:0%
+the way that we're going to get at
+ 
+
+ align:start position:0%
+the way that we're going to get at
+finally addressing some of these best
+
+ align:start position:0%
+finally addressing some of these best
+ 
+
+ align:start position:0%
+finally addressing some of these best
+effort Network properties we've been
+
+ align:start position:0%
+effort Network properties we've been
+ 
+
+ align:start position:0%
+effort Network properties we've been
+kind of skirting around for the last few
+
+ align:start position:0%
+kind of skirting around for the last few
+ 
+
+ align:start position:0%
+kind of skirting around for the last few
+lectures particular today we're going to
+
+ align:start position:0%
+lectures particular today we're going to
+ 
+
+ align:start position:0%
+lectures particular today we're going to
+focus on the issue of loss how do we
+
+ align:start position:0%
+focus on the issue of loss how do we
+ 
+
+ align:start position:0%
+focus on the issue of loss how do we
+mitigate how do we avoid losses within
+
+ align:start position:0%
+mitigate how do we avoid losses within
+ 
+
+ align:start position:0%
+mitigate how do we avoid losses within
+the network and we'll talk a little bit
+
+ align:start position:0%
+the network and we'll talk a little bit
+ 
+
+ align:start position:0%
+the network and we'll talk a little bit
+about this problem of reordering uh
+
+ align:start position:0%
+about this problem of reordering uh
+ 
+
+ align:start position:0%
+about this problem of reordering uh
+we're going to save the discussion of
+
+ align:start position:0%
+we're going to save the discussion of
+ 
+
+ align:start position:0%
+we're going to save the discussion of
+delays in congestion for next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+so the endand layer in addition to
+
+ align:start position:0%
+so the endand layer in addition to
+ 
+
+ align:start position:0%
+so the endand layer in addition to
+helping us deal with these limitations
+
+ align:start position:0%
+helping us deal with these limitations
+ 
+
+ align:start position:0%
+helping us deal with these limitations
+of a best effort Network provides a few
+
+ align:start position:0%
+of a best effort Network provides a few
+ 
+
+ align:start position:0%
+of a best effort Network provides a few
+other features that we need to mention
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first thing that the end to-end
+
+ align:start position:0%
+so the first thing that the end to-end
+ 
+
+ align:start position:0%
+so the first thing that the end to-end
+layer does is it provides the ability to
+
+ align:start position:0%
+layer does is it provides the ability to
+ 
+
+ align:start position:0%
+layer does is it provides the ability to
+Multiplex multi applications on top of
+
+ align:start position:0%
+Multiplex multi applications on top of
+ 
+
+ align:start position:0%
+Multiplex multi applications on top of
+the network so the network that we've
+
+ align:start position:0%
+the network so the network that we've
+ 
+
+ align:start position:0%
+the network so the network that we've
+talked about so far is one in which
+
+ align:start position:0%
+talked about so far is one in which
+ 
+
+ align:start position:0%
+talked about so far is one in which
+there are these two end points two
+
+ align:start position:0%
+there are these two end points two
+ 
+
+ align:start position:0%
+there are these two end points two
+computers that are connected to each
+
+ align:start position:0%
+computers that are connected to each
+ 
+
+ align:start position:0%
+computers that are connected to each
+other and they're transmitting a
+
+ align:start position:0%
+other and they're transmitting a
+ 
+
+ align:start position:0%
+other and they're transmitting a
+sequence of messages but we haven't
+
+ align:start position:0%
+sequence of messages but we haven't
+ 
+
+ align:start position:0%
+sequence of messages but we haven't
+really said anything about how those
+
+ align:start position:0%
+really said anything about how those
+ 
+
+ align:start position:0%
+really said anything about how those
+messages get dispatched to different
+
+ align:start position:0%
+messages get dispatched to different
+ 
+
+ align:start position:0%
+messages get dispatched to different
+applications that are running above the
+
+ align:start position:0%
+applications that are running above the
+ 
+
+ align:start position:0%
+applications that are running above the
+network
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+layer the other thing the end to end
+
+ align:start position:0%
+layer the other thing the end to end
+ 
+
+ align:start position:0%
+layer the other thing the end to end
+layer provides for us is the ability to
+
+ align:start position:0%
+layer provides for us is the ability to
+ 
+
+ align:start position:0%
+layer provides for us is the ability to
+is is
+
+ align:start position:0%
+is is
+ 
+
+ align:start position:0%
+is is
+fragmentation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+messages okay and fragmentation is
+
+ align:start position:0%
+messages okay and fragmentation is
+ 
+
+ align:start position:0%
+messages okay and fragmentation is
+really about is the the fact that these
+
+ align:start position:0%
+really about is the the fact that these
+ 
+
+ align:start position:0%
+really about is the the fact that these
+link layer the link itself may have some
+
+ align:start position:0%
+link layer the link itself may have some
+ 
+
+ align:start position:0%
+link layer the link itself may have some
+maximum size message that it can
+
+ align:start position:0%
+maximum size message that it can
+ 
+
+ align:start position:0%
+maximum size message that it can
+physically transmit because that's the
+
+ align:start position:0%
+physically transmit because that's the
+ 
+
+ align:start position:0%
+physically transmit because that's the
+say for example the maximum size message
+
+ align:start position:0%
+say for example the maximum size message
+ 
+
+ align:start position:0%
+say for example the maximum size message
+is how long the sender and receiver can
+
+ align:start position:0%
+is how long the sender and receiver can
+ 
+
+ align:start position:0%
+is how long the sender and receiver can
+remain synchronized with each other so
+
+ align:start position:0%
+remain synchronized with each other so
+ 
+
+ align:start position:0%
+remain synchronized with each other so
+what the end end layer often does is it
+
+ align:start position:0%
+what the end end layer often does is it
+ 
+
+ align:start position:0%
+what the end end layer often does is it
+provides the ability to take a longer
+
+ align:start position:0%
+provides the ability to take a longer
+ 
+
+ align:start position:0%
+provides the ability to take a longer
+message and fragment it up into smaller
+
+ align:start position:0%
+message and fragment it up into smaller
+ 
+
+ align:start position:0%
+message and fragment it up into smaller
+chunks or fragments that it transmit and
+
+ align:start position:0%
+chunks or fragments that it transmit and
+ 
+
+ align:start position:0%
+chunks or fragments that it transmit and
+it transmits each of those fragments
+
+ align:start position:0%
+it transmits each of those fragments
+ 
+
+ align:start position:0%
+it transmits each of those fragments
+independently as a as a separate message
+
+ align:start position:0%
+independently as a as a separate message
+ 
+
+ align:start position:0%
+independently as a as a separate message
+across the
+
+ align:start position:0%
+across the
+ 
+
+ align:start position:0%
+across the
+network so just to sort of illustrate
+
+ align:start position:0%
+network so just to sort of illustrate
+ 
+
+ align:start position:0%
+network so just to sort of illustrate
+how these things are dealt with within
+
+ align:start position:0%
+how these things are dealt with within
+ 
+
+ align:start position:0%
+how these things are dealt with within
+the end to end layer let's look at a
+
+ align:start position:0%
+the end to end layer let's look at a
+ 
+
+ align:start position:0%
+the end to end layer let's look at a
+little illustration so suppose we have
+
+ align:start position:0%
+little illustration so suppose we have
+ 
+
+ align:start position:0%
+little illustration so suppose we have
+some set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+applications that are connected up to
+
+ align:start position:0%
+applications that are connected up to
+ 
+
+ align:start position:0%
+applications that are connected up to
+the end to end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+layer okay so these applications the
+
+ align:start position:0%
+layer okay so these applications the
+ 
+
+ align:start position:0%
+layer okay so these applications the
+idea is going to be that when a message
+
+ align:start position:0%
+idea is going to be that when a message
+ 
+
+ align:start position:0%
+idea is going to be that when a message
+arrives over the end to end layer it's
+
+ align:start position:0%
+arrives over the end to end layer it's
+ 
+
+ align:start position:0%
+arrives over the end to end layer it's
+going to be dispatched to one of these
+
+ align:start position:0%
+going to be dispatched to one of these
+ 
+
+ align:start position:0%
+going to be dispatched to one of these
+applications by looking at a special
+
+ align:start position:0%
+applications by looking at a special
+ 
+
+ align:start position:0%
+applications by looking at a special
+number that's in the header of this
+
+ align:start position:0%
+number that's in the header of this
+ 
+
+ align:start position:0%
+number that's in the header of this
+message that comes in so this number is
+
+ align:start position:0%
+message that comes in so this number is
+ 
+
+ align:start position:0%
+message that comes in so this number is
+often referred to as a port
+
+ align:start position:0%
+often referred to as a port
+ 
+
+ align:start position:0%
+often referred to as a port
+number and each application is going to
+
+ align:start position:0%
+number and each application is going to
+ 
+
+ align:start position:0%
+number and each application is going to
+be running on one of these ports so
+
+ align:start position:0%
+be running on one of these ports so
+ 
+
+ align:start position:0%
+be running on one of these ports so
+often times these ports are sort of
+
+ align:start position:0%
+often times these ports are sort of
+ 
+
+ align:start position:0%
+often times these ports are sort of
+running at well-known addresses so we
+
+ align:start position:0%
+running at well-known addresses so we
+ 
+
+ align:start position:0%
+running at well-known addresses so we
+talk about a little we talk about this
+
+ align:start position:0%
+talk about a little we talk about this
+ 
+
+ align:start position:0%
+talk about a little we talk about this
+numbers very briefly earlier for example
+
+ align:start position:0%
+numbers very briefly earlier for example
+ 
+
+ align:start position:0%
+numbers very briefly earlier for example
+web servers run at Port number 80 on uh
+
+ align:start position:0%
+web servers run at Port number 80 on uh
+ 
+
+ align:start position:0%
+web servers run at Port number 80 on uh
+in the tcpip in the TCP protocol so uh
+
+ align:start position:0%
+in the tcpip in the TCP protocol so uh
+ 
+
+ align:start position:0%
+in the tcpip in the TCP protocol so uh
+web Ser if you want to contact a web
+
+ align:start position:0%
+web Ser if you want to contact a web
+ 
+
+ align:start position:0%
+web Ser if you want to contact a web
+server at a particular machine you talk
+
+ align:start position:0%
+server at a particular machine you talk
+ 
+
+ align:start position:0%
+server at a particular machine you talk
+to Port 80 other times applications will
+
+ align:start position:0%
+to Port 80 other times applications will
+ 
+
+ align:start position:0%
+to Port 80 other times applications will
+send the port number that they're
+
+ align:start position:0%
+send the port number that they're
+ 
+
+ align:start position:0%
+send the port number that they're
+listening at in the message that they in
+
+ align:start position:0%
+listening at in the message that they in
+ 
+
+ align:start position:0%
+listening at in the message that they in
+in a message or two people will exchange
+
+ align:start position:0%
+in a message or two people will exchange
+ 
+
+ align:start position:0%
+in a message or two people will exchange
+the port numbers through some out ofand
+
+ align:start position:0%
+the port numbers through some out ofand
+ 
+
+ align:start position:0%
+the port numbers through some out ofand
+protocol Say by you know telling telling
+
+ align:start position:0%
+protocol Say by you know telling telling
+ 
+
+ align:start position:0%
+protocol Say by you know telling telling
+some telling your friend in an email
+
+ align:start position:0%
+some telling your friend in an email
+ 
+
+ align:start position:0%
+some telling your friend in an email
+that he should connect your server
+
+ align:start position:0%
+that he should connect your server
+ 
+
+ align:start position:0%
+that he should connect your server
+because it's running on Port
+
+ align:start position:0%
+because it's running on Port
+ 
+
+ align:start position:0%
+because it's running on Port
+X so this is the way that so messages
+
+ align:start position:0%
+X so this is the way that so messages
+ 
+
+ align:start position:0%
+X so this is the way that so messages
+now are going to arrive into the end to
+
+ align:start position:0%
+now are going to arrive into the end to
+ 
+
+ align:start position:0%
+now are going to arrive into the end to
+endend layer from the network layer and
+
+ align:start position:0%
+endend layer from the network layer and
+ 
+
+ align:start position:0%
+endend layer from the network layer and
+these messages are going to have in
+
+ align:start position:0%
+these messages are going to have in
+ 
+
+ align:start position:0%
+these messages are going to have in
+their Header information about which
+
+ align:start position:0%
+their Header information about which
+ 
+
+ align:start position:0%
+their Header information about which
+Port they should be dispatched to so the
+
+ align:start position:0%
+Port they should be dispatched to so the
+ 
+
+ align:start position:0%
+Port they should be dispatched to so the
+other functionality the end to end layer
+
+ align:start position:0%
+other functionality the end to end layer
+ 
+
+ align:start position:0%
+other functionality the end to end layer
+I said is this is fragmentation and
+
+ align:start position:0%
+I said is this is fragmentation and
+ 
+
+ align:start position:0%
+I said is this is fragmentation and
+fragmentation is about taking a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+message that's being sent down from one
+
+ align:start position:0%
+message that's being sent down from one
+ 
+
+ align:start position:0%
+message that's being sent down from one
+of these applications into the end
+
+ align:start position:0%
+of these applications into the end
+ 
+
+ align:start position:0%
+of these applications into the end
+to-end layer and then that message on
+
+ align:start position:0%
+to-end layer and then that message on
+ 
+
+ align:start position:0%
+to-end layer and then that message on
+its
+
+ align:start position:0%
+its
+ 
+
+ align:start position:0%
+its
+way to the network
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+layer gets fragmented up into a number
+
+ align:start position:0%
+layer gets fragmented up into a number
+ 
+
+ align:start position:0%
+layer gets fragmented up into a number
+of chunks so these are each each of
+
+ align:start position:0%
+of chunks so these are each each of
+ 
+
+ align:start position:0%
+of chunks so these are each each of
+these little chunks in this message is a
+
+ align:start position:0%
+these little chunks in this message is a
+ 
+
+ align:start position:0%
+these little chunks in this message is a
+it's called a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fragment so these are sort of two uh and
+
+ align:start position:0%
+fragment so these are sort of two uh and
+ 
+
+ align:start position:0%
+fragment so these are sort of two uh and
+the so often times we talk about what
+
+ align:start position:0%
+the so often times we talk about what
+ 
+
+ align:start position:0%
+the so often times we talk about what
+the end one common end to end layer is
+
+ align:start position:0%
+the end one common end to end layer is
+ 
+
+ align:start position:0%
+the end one common end to end layer is
+one that provides an abstraction that's
+
+ align:start position:0%
+one that provides an abstraction that's
+ 
+
+ align:start position:0%
+one that provides an abstraction that's
+called a stream so a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stream is simply a uh flow of messages
+
+ align:start position:0%
+stream is simply a uh flow of messages
+ 
+
+ align:start position:0%
+stream is simply a uh flow of messages
+or data from one endpoint to the other
+
+ align:start position:0%
+or data from one endpoint to the other
+ 
+
+ align:start position:0%
+or data from one endpoint to the other
+one application to the the other um and
+
+ align:start position:0%
+one application to the the other um and
+ 
+
+ align:start position:0%
+one application to the the other um and
+where the where the the segments in that
+
+ align:start position:0%
+where the where the the segments in that
+ 
+
+ align:start position:0%
+where the where the the segments in that
+stream are guaranteed to be delivered uh
+
+ align:start position:0%
+stream are guaranteed to be delivered uh
+ 
+
+ align:start position:0%
+stream are guaranteed to be delivered uh
+Lo are are loss free so there are no
+
+ align:start position:0%
+Lo are are loss free so there are no
+ 
+
+ align:start position:0%
+Lo are are loss free so there are no
+missing segments or missing messages uh
+
+ align:start position:0%
+missing segments or missing messages uh
+ 
+
+ align:start position:0%
+missing segments or missing messages uh
+and they're in order so the
+
+ align:start position:0%
+and they're in order so the
+ 
+
+ align:start position:0%
+and they're in order so the
+application knows that the data that it
+
+ align:start position:0%
+application knows that the data that it
+ 
+
+ align:start position:0%
+application knows that the data that it
+receives is going to be in the order
+
+ align:start position:0%
+receives is going to be in the order
+ 
+
+ align:start position:0%
+receives is going to be in the order
+that the the receiver knows the
+
+ align:start position:0%
+that the the receiver knows the
+ 
+
+ align:start position:0%
+that the the receiver knows the
+application it rece the data it receives
+
+ align:start position:0%
+application it rece the data it receives
+ 
+
+ align:start position:0%
+application it rece the data it receives
+is going to be in the order that the
+
+ align:start position:0%
+is going to be in the order that the
+ 
+
+ align:start position:0%
+is going to be in the order that the
+sender sent it out on the channel and
+
+ align:start position:0%
+sender sent it out on the channel and
+ 
+
+ align:start position:0%
+sender sent it out on the channel and
+there won't be any missing messages so
+
+ align:start position:0%
+there won't be any missing messages so
+ 
+
+ align:start position:0%
+there won't be any missing messages so
+this sounds like a pretty convenient
+
+ align:start position:0%
+this sounds like a pretty convenient
+ 
+
+ align:start position:0%
+this sounds like a pretty convenient
+abstraction and it's one that is often
+
+ align:start position:0%
+abstraction and it's one that is often
+ 
+
+ align:start position:0%
+abstraction and it's one that is often
+used in applications and in fact the
+
+ align:start position:0%
+used in applications and in fact the
+ 
+
+ align:start position:0%
+used in applications and in fact the
+stream the stream abstraction is the
+
+ align:start position:0%
+stream the stream abstraction is the
+ 
+
+ align:start position:0%
+stream the stream abstraction is the
+abstraction that the TCP protocol
+
+ align:start position:0%
+abstraction that the TCP protocol
+ 
+
+ align:start position:0%
+abstraction that the TCP protocol
+provides
+
+ align:start position:0%
+provides
+ 
+
+ align:start position:0%
+provides
+okay so um just to sort of make it
+
+ align:start position:0%
+okay so um just to sort of make it
+ 
+
+ align:start position:0%
+okay so um just to sort of make it
+clear I just want to look quickly the at
+
+ align:start position:0%
+clear I just want to look quickly the at
+ 
+
+ align:start position:0%
+clear I just want to look quickly the at
+a simplified endtoend header format so
+
+ align:start position:0%
+a simplified endtoend header format so
+ 
+
+ align:start position:0%
+a simplified endtoend header format so
+we looked at the header formats for uh
+
+ align:start position:0%
+we looked at the header formats for uh
+ 
+
+ align:start position:0%
+we looked at the header formats for uh
+other at the other layers last time and
+
+ align:start position:0%
+other at the other layers last time and
+ 
+
+ align:start position:0%
+other at the other layers last time and
+this is just showing some of the things
+
+ align:start position:0%
+this is just showing some of the things
+ 
+
+ align:start position:0%
+this is just showing some of the things
+that you might expect to see in an end
+
+ align:start position:0%
+that you might expect to see in an end
+ 
+
+ align:start position:0%
+that you might expect to see in an end
+to- end header there of course could be
+
+ align:start position:0%
+to- end header there of course could be
+ 
+
+ align:start position:0%
+to- end header there of course could be
+there are additional things if you go
+
+ align:start position:0%
+there are additional things if you go
+ 
+
+ align:start position:0%
+there are additional things if you go
+look at the TCP header but these are the
+
+ align:start position:0%
+look at the TCP header but these are the
+ 
+
+ align:start position:0%
+look at the TCP header but these are the
+ones that mostly matter from the point
+
+ align:start position:0%
+ones that mostly matter from the point
+ 
+
+ align:start position:0%
+ones that mostly matter from the point
+of view of this class so there's a
+
+ align:start position:0%
+of view of this class so there's a
+ 
+
+ align:start position:0%
+of view of this class so there's a
+source Port which allows the which
+
+ align:start position:0%
+source Port which allows the which
+ 
+
+ align:start position:0%
+source Port which allows the which
+specifies which Port the sender of the
+
+ align:start position:0%
+specifies which Port the sender of the
+ 
+
+ align:start position:0%
+specifies which Port the sender of the
+message is listening at on the other
+
+ align:start position:0%
+message is listening at on the other
+ 
+
+ align:start position:0%
+message is listening at on the other
+side there's a destination Port which
+
+ align:start position:0%
+side there's a destination Port which
+ 
+
+ align:start position:0%
+side there's a destination Port which
+specifies which port number uh this
+
+ align:start position:0%
+specifies which port number uh this
+ 
+
+ align:start position:0%
+specifies which port number uh this
+message should be sent to on the
+
+ align:start position:0%
+message should be sent to on the
+ 
+
+ align:start position:0%
+message should be sent to on the
+receiver side um there's something
+
+ align:start position:0%
+receiver side um there's something
+ 
+
+ align:start position:0%
+receiver side um there's something
+called the nons the non is just a unique
+
+ align:start position:0%
+called the nons the non is just a unique
+ 
+
+ align:start position:0%
+called the nons the non is just a unique
+identifier it's just a thing that
+
+ align:start position:0%
+identifier it's just a thing that
+ 
+
+ align:start position:0%
+identifier it's just a thing that
+uniquely identifies this message as far
+
+ align:start position:0%
+uniquely identifies this message as far
+ 
+
+ align:start position:0%
+uniquely identifies this message as far
+as the two as as far as the conversation
+
+ align:start position:0%
+as the two as as far as the conversation
+ 
+
+ align:start position:0%
+as the two as as far as the conversation
+between the two endpoints is concerned
+
+ align:start position:0%
+between the two endpoints is concerned
+ 
+
+ align:start position:0%
+between the two endpoints is concerned
+for the purposes a common kind of anoun
+
+ align:start position:0%
+for the purposes a common kind of anoun
+ 
+
+ align:start position:0%
+for the purposes a common kind of anoun
+to use is just a sequence number that
+
+ align:start position:0%
+to use is just a sequence number that
+ 
+
+ align:start position:0%
+to use is just a sequence number that
+gets incremented by one every time an
+
+ align:start position:0%
+gets incremented by one every time an
+ 
+
+ align:start position:0%
+gets incremented by one every time an
+additional message is sent and then
+
+ align:start position:0%
+additional message is sent and then
+ 
+
+ align:start position:0%
+additional message is sent and then
+oftentimes in the end to end layer
+
+ align:start position:0%
+oftentimes in the end to end layer
+ 
+
+ align:start position:0%
+oftentimes in the end to end layer
+there's also some check check sum
+
+ align:start position:0%
+there's also some check check sum
+ 
+
+ align:start position:0%
+there's also some check check sum
+information something that allows you to
+
+ align:start position:0%
+information something that allows you to
+ 
+
+ align:start position:0%
+information something that allows you to
+verify the Integrity of the messages
+
+ align:start position:0%
+verify the Integrity of the messages
+ 
+
+ align:start position:0%
+verify the Integrity of the messages
+that are transmitted out over the
+
+ align:start position:0%
+that are transmitted out over the
+ 
+
+ align:start position:0%
+that are transmitted out over the
+network and we do this at the end to end
+
+ align:start position:0%
+network and we do this at the end to end
+ 
+
+ align:start position:0%
+network and we do this at the end to end
+layer we we we saw that the check sums
+
+ align:start position:0%
+layer we we we saw that the check sums
+ 
+
+ align:start position:0%
+layer we we we saw that the check sums
+sometimes appeared in the link layer
+
+ align:start position:0%
+sometimes appeared in the link layer
+ 
+
+ align:start position:0%
+sometimes appeared in the link layer
+before they also appear at the end to
+
+ align:start position:0%
+before they also appear at the end to
+ 
+
+ align:start position:0%
+before they also appear at the end to
+end layer because it's uh important it's
+
+ align:start position:0%
+end layer because it's uh important it's
+ 
+
+ align:start position:0%
+end layer because it's uh important it's
+it's possible that as you guys read in
+
+ align:start position:0%
+it's possible that as you guys read in
+ 
+
+ align:start position:0%
+it's possible that as you guys read in
+the in the paper about end to end
+
+ align:start position:0%
+the in the paper about end to end
+ 
+
+ align:start position:0%
+the in the paper about end to end
+arguments the end to end argument often
+
+ align:start position:0%
+arguments the end to end argument often
+ 
+
+ align:start position:0%
+arguments the end to end argument often
+times we want to verify that a message
+
+ align:start position:0%
+times we want to verify that a message
+ 
+
+ align:start position:0%
+times we want to verify that a message
+is correct uh at the at the end to end
+
+ align:start position:0%
+is correct uh at the at the end to end
+ 
+
+ align:start position:0%
+is correct uh at the at the end to end
+layer or at the application layer even
+
+ align:start position:0%
+layer or at the application layer even
+ 
+
+ align:start position:0%
+layer or at the application layer even
+if we have already maybe verified that
+
+ align:start position:0%
+if we have already maybe verified that
+ 
+
+ align:start position:0%
+if we have already maybe verified that
+that was the case at the link layer
+
+ align:start position:0%
+that was the case at the link layer
+ 
+
+ align:start position:0%
+that was the case at the link layer
+because the message could have been
+
+ align:start position:0%
+because the message could have been
+ 
+
+ align:start position:0%
+because the message could have been
+corrupted somewhere above just the link
+
+ align:start position:0%
+corrupted somewhere above just the link
+ 
+
+ align:start position:0%
+corrupted somewhere above just the link
+layer right so um this is sort of the
+
+ align:start position:0%
+layer right so um this is sort of the
+ 
+
+ align:start position:0%
+layer right so um this is sort of the
+abstraction that the end to end layer
+
+ align:start position:0%
+abstraction that the end to end layer
+ 
+
+ align:start position:0%
+abstraction that the end to end layer
+provides notice that the the header
+
+ align:start position:0%
+provides notice that the the header
+ 
+
+ align:start position:0%
+provides notice that the the header
+format here doesn't actually include not
+
+ align:start position:0%
+format here doesn't actually include not
+ 
+
+ align:start position:0%
+format here doesn't actually include not
+it doesn't include for example the
+
+ align:start position:0%
+it doesn't include for example the
+ 
+
+ align:start position:0%
+it doesn't include for example the
+addresses of the endpoints the IP
+
+ align:start position:0%
+addresses of the endpoints the IP
+ 
+
+ align:start position:0%
+addresses of the endpoints the IP
+addresses that's because the IP address
+
+ align:start position:0%
+addresses that's because the IP address
+ 
+
+ align:start position:0%
+addresses that's because the IP address
+are in the IP header so remember this is
+
+ align:start position:0%
+are in the IP header so remember this is
+ 
+
+ align:start position:0%
+are in the IP header so remember this is
+just the additional information that's
+
+ align:start position:0%
+just the additional information that's
+ 
+
+ align:start position:0%
+just the additional information that's
+added by the end to end layer and is
+
+ align:start position:0%
+added by the end to end layer and is
+ 
+
+ align:start position:0%
+added by the end to end layer and is
+used to dispatch from the end to end
+
+ align:start position:0%
+used to dispatch from the end to end
+ 
+
+ align:start position:0%
+used to dispatch from the end to end
+layer to the applications that are
+
+ align:start position:0%
+layer to the applications that are
+ 
+
+ align:start position:0%
+layer to the applications that are
+running above it the once the we're
+
+ align:start position:0%
+running above it the once the we're
+ 
+
+ align:start position:0%
+running above it the once the we're
+we're dealing with the endtoend header
+
+ align:start position:0%
+we're dealing with the endtoend header
+ 
+
+ align:start position:0%
+we're dealing with the endtoend header
+all the network the packets have already
+
+ align:start position:0%
+all the network the packets have already
+ 
+
+ align:start position:0%
+all the network the packets have already
+been transmitted across the network and
+
+ align:start position:0%
+been transmitted across the network and
+ 
+
+ align:start position:0%
+been transmitted across the network and
+in fact we don't necessarily we don't
+
+ align:start position:0%
+in fact we don't necessarily we don't
+ 
+
+ align:start position:0%
+in fact we don't necessarily we don't
+need to know what the IP address is
+
+ align:start position:0%
+need to know what the IP address is
+ 
+
+ align:start position:0%
+need to know what the IP address is
+anymore because this is happening on the
+
+ align:start position:0%
+anymore because this is happening on the
+ 
+
+ align:start position:0%
+anymore because this is happening on the
+local machine and the IP all the
+
+ align:start position:0%
+local machine and the IP all the
+ 
+
+ align:start position:0%
+local machine and the IP all the
+applications are running at the same IP
+
+ align:start position:0%
+applications are running at the same IP
+ 
+
+ align:start position:0%
+applications are running at the same IP
+address okay so um but the other things
+
+ align:start position:0%
+address okay so um but the other things
+ 
+
+ align:start position:0%
+address okay so um but the other things
+that we said the end so I said today
+
+ align:start position:0%
+that we said the end so I said today
+ 
+
+ align:start position:0%
+that we said the end so I said today
+we're going to focus mostly on the
+
+ align:start position:0%
+we're going to focus mostly on the
+ 
+
+ align:start position:0%
+we're going to focus mostly on the
+ability of the end to-end layer to
+
+ align:start position:0%
+ability of the end to-end layer to
+ 
+
+ align:start position:0%
+ability of the end to-end layer to
+mitigate these problems of losses so
+
+ align:start position:0%
+mitigate these problems of losses so
+ 
+
+ align:start position:0%
+mitigate these problems of losses so
+this is sort of the abstraction that the
+
+ align:start position:0%
+this is sort of the abstraction that the
+ 
+
+ align:start position:0%
+this is sort of the abstraction that the
+end to- end layer provides but what we
+
+ align:start position:0%
+end to- end layer provides but what we
+ 
+
+ align:start position:0%
+end to- end layer provides but what we
+want to look at now is how does the end
+
+ align:start position:0%
+want to look at now is how does the end
+ 
+
+ align:start position:0%
+want to look at now is how does the end
+to-end layer actually deal with loss and
+
+ align:start position:0%
+to-end layer actually deal with loss and
+ 
+
+ align:start position:0%
+to-end layer actually deal with loss and
+we're going to talk about two different
+
+ align:start position:0%
+we're going to talk about two different
+ 
+
+ align:start position:0%
+we're going to talk about two different
+uh techniques or there's two different
+
+ align:start position:0%
+uh techniques or there's two different
+ 
+
+ align:start position:0%
+uh techniques or there's two different
+components to uh dealing with loss so
+
+ align:start position:0%
+components to uh dealing with loss so
+ 
+
+ align:start position:0%
+components to uh dealing with loss so
+the first thing we want to do is we want
+
+ align:start position:0%
+the first thing we want to do is we want
+ 
+
+ align:start position:0%
+the first thing we want to do is we want
+to make sure that no packets get lost
+
+ align:start position:0%
+to make sure that no packets get lost
+ 
+
+ align:start position:0%
+to make sure that no packets get lost
+during transmission and the way we're
+
+ align:start position:0%
+during transmission and the way we're
+ 
+
+ align:start position:0%
+during transmission and the way we're
+going to do that is providing we call
+
+ align:start position:0%
+going to do that is providing we call
+ 
+
+ align:start position:0%
+going to do that is providing we call
+at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delivery the reason I put at least once
+
+ align:start position:0%
+delivery the reason I put at least once
+ 
+
+ align:start position:0%
+delivery the reason I put at least once
+in quotes here is that I'm going to talk
+
+ align:start position:0%
+in quotes here is that I'm going to talk
+ 
+
+ align:start position:0%
+in quotes here is that I'm going to talk
+you through a protocol but and this
+
+ align:start position:0%
+you through a protocol but and this
+ 
+
+ align:start position:0%
+you through a protocol but and this
+protocol is going to guarantee that a
+
+ align:start position:0%
+protocol is going to guarantee that a
+ 
+
+ align:start position:0%
+protocol is going to guarantee that a
+message gets received by the receiver as
+
+ align:start position:0%
+message gets received by the receiver as
+ 
+
+ align:start position:0%
+message gets received by the receiver as
+long as for example the receiver doesn't
+
+ align:start position:0%
+long as for example the receiver doesn't
+ 
+
+ align:start position:0%
+long as for example the receiver doesn't
+completely fail or the network doesn't
+
+ align:start position:0%
+completely fail or the network doesn't
+ 
+
+ align:start position:0%
+completely fail or the network doesn't
+completely explode so it's always
+
+ align:start position:0%
+completely explode so it's always
+ 
+
+ align:start position:0%
+completely explode so it's always
+possible that messages can be lost
+
+ align:start position:0%
+possible that messages can be lost
+ 
+
+ align:start position:0%
+possible that messages can be lost
+because there can be some physical
+
+ align:start position:0%
+because there can be some physical
+ 
+
+ align:start position:0%
+because there can be some physical
+failure that makes it impossible for the
+
+ align:start position:0%
+failure that makes it impossible for the
+ 
+
+ align:start position:0%
+failure that makes it impossible for the
+messages to get through but as long as
+
+ align:start position:0%
+messages to get through but as long as
+ 
+
+ align:start position:0%
+messages to get through but as long as
+it is possible for the message to get
+
+ align:start position:0%
+it is possible for the message to get
+ 
+
+ align:start position:0%
+it is possible for the message to get
+through uh there there there's a a very
+
+ align:start position:0%
+through uh there there there's a a very
+ 
+
+ align:start position:0%
+through uh there there there's a a very
+high probability the message will in
+
+ align:start position:0%
+high probability the message will in
+ 
+
+ align:start position:0%
+high probability the message will in
+fact get through and if the message
+
+ align:start position:0%
+fact get through and if the message
+ 
+
+ align:start position:0%
+fact get through and if the message
+doesn't get through what this is this at
+
+ align:start position:0%
+doesn't get through what this is this at
+ 
+
+ align:start position:0%
+doesn't get through what this is this at
+least once delivery protocol is going to
+
+ align:start position:0%
+least once delivery protocol is going to
+ 
+
+ align:start position:0%
+least once delivery protocol is going to
+guarantee is that the receiver knows
+
+ align:start position:0%
+guarantee is that the receiver knows
+ 
+
+ align:start position:0%
+guarantee is that the receiver knows
+that the sender may not have actually
+
+ align:start position:0%
+that the sender may not have actually
+ 
+
+ align:start position:0%
+that the sender may not have actually
+received the message okay so um now once
+
+ align:start position:0%
+received the message okay so um now once
+ 
+
+ align:start position:0%
+received the message okay so um now once
+we talk about at least once we're going
+
+ align:start position:0%
+we talk about at least once we're going
+ 
+
+ align:start position:0%
+we talk about at least once we're going
+to talk about something we call at most
+
+ align:start position:0%
+to talk about something we call at most
+ 
+
+ align:start position:0%
+to talk about something we call at most
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+delivery um and the issue with it most
+
+ align:start position:0%
+delivery um and the issue with it most
+ 
+
+ align:start position:0%
+delivery um and the issue with it most
+once delivery is that the at least once
+
+ align:start position:0%
+once delivery is that the at least once
+ 
+
+ align:start position:0%
+once delivery is that the at least once
+protocol that I'm going to sketch out is
+
+ align:start position:0%
+protocol that I'm going to sketch out is
+ 
+
+ align:start position:0%
+protocol that I'm going to sketch out is
+going to generate duplicates and we're
+
+ align:start position:0%
+going to generate duplicates and we're
+ 
+
+ align:start position:0%
+going to generate duplicates and we're
+going to need to make sure that we can
+
+ align:start position:0%
+going to need to make sure that we can
+ 
+
+ align:start position:0%
+going to need to make sure that we can
+get rid of some of the
+
+ align:start position:0%
+get rid of some of the
+ 
+
+ align:start position:0%
+get rid of some of the
+duplicates um and these two things
+
+ align:start position:0%
+duplicates um and these two things
+ 
+
+ align:start position:0%
+duplicates um and these two things
+together are going to provide what's
+
+ align:start position:0%
+together are going to provide what's
+ 
+
+ align:start position:0%
+together are going to provide what's
+known as exactly once delivery of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+messages
+
+ align:start position:0%
+messages
+ 
+
+ align:start position:0%
+messages
+okay so let's start off by talking about
+
+ align:start position:0%
+okay so let's start off by talking about
+ 
+
+ align:start position:0%
+okay so let's start off by talking about
+our at least once
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protocol this protocol is going to
+
+ align:start position:0%
+protocol this protocol is going to
+ 
+
+ align:start position:0%
+protocol this protocol is going to
+guarantee that uh if at all possible the
+
+ align:start position:0%
+guarantee that uh if at all possible the
+ 
+
+ align:start position:0%
+guarantee that uh if at all possible the
+message will be received a message will
+
+ align:start position:0%
+message will be received a message will
+ 
+
+ align:start position:0%
+message will be received a message will
+be received by the receiver and the way
+
+ align:start position:0%
+be received by the receiver and the way
+ 
+
+ align:start position:0%
+be received by the receiver and the way
+that we're going to do this is really
+
+ align:start position:0%
+that we're going to do this is really
+ 
+
+ align:start position:0%
+that we're going to do this is really
+very straightforward we're just going to
+
+ align:start position:0%
+very straightforward we're just going to
+ 
+
+ align:start position:0%
+very straightforward we're just going to
+have the receiver send a message back to
+
+ align:start position:0%
+have the receiver send a message back to
+ 
+
+ align:start position:0%
+have the receiver send a message back to
+the sender that says I got the message
+
+ align:start position:0%
+the sender that says I got the message
+ 
+
+ align:start position:0%
+the sender that says I got the message
+so the receiver when it gets the message
+
+ align:start position:0%
+so the receiver when it gets the message
+ 
+
+ align:start position:0%
+so the receiver when it gets the message
+sends this what's called an
+
+ align:start position:0%
+sends this what's called an
+ 
+
+ align:start position:0%
+sends this what's called an
+acknowledgement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back sometimes abbreviated
+
+ align:start position:0%
+back sometimes abbreviated
+ 
+
+ align:start position:0%
+back sometimes abbreviated
+act
+
+ align:start position:0%
+act
+ 
+
+ align:start position:0%
+act
+uh indicating that the message was
+
+ align:start position:0%
+uh indicating that the message was
+ 
+
+ align:start position:0%
+uh indicating that the message was
+received at the other end okay this is
+
+ align:start position:0%
+received at the other end okay this is
+ 
+
+ align:start position:0%
+received at the other end okay this is
+just going to be uh this just going to
+
+ align:start position:0%
+just going to be uh this just going to
+ 
+
+ align:start position:0%
+just going to be uh this just going to
+be sent back to the receiver directly so
+
+ align:start position:0%
+be sent back to the receiver directly so
+ 
+
+ align:start position:0%
+be sent back to the receiver directly so
+um in order to send this acknowledgement
+
+ align:start position:0%
+um in order to send this acknowledgement
+ 
+
+ align:start position:0%
+um in order to send this acknowledgement
+though we're going to need a way for the
+
+ align:start position:0%
+though we're going to need a way for the
+ 
+
+ align:start position:0%
+though we're going to need a way for the
+receiver to refer to the message that
+
+ align:start position:0%
+receiver to refer to the message that
+ 
+
+ align:start position:0%
+receiver to refer to the message that
+the sender sent right so we want the
+
+ align:start position:0%
+the sender sent right so we want the
+ 
+
+ align:start position:0%
+the sender sent right so we want the
+receiver to be able to say I received
+
+ align:start position:0%
+receiver to be able to say I received
+ 
+
+ align:start position:0%
+receiver to be able to say I received
+this message that you that you sent to
+
+ align:start position:0%
+this message that you that you sent to
+ 
+
+ align:start position:0%
+this message that you that you sent to
+me and one way that you so and the
+
+ align:start position:0%
+me and one way that you so and the
+ 
+
+ align:start position:0%
+me and one way that you so and the
+simplest way to be able to do that is to
+
+ align:start position:0%
+simplest way to be able to do that is to
+ 
+
+ align:start position:0%
+simplest way to be able to do that is to
+just use this nons information that's in
+
+ align:start position:0%
+just use this nons information that's in
+ 
+
+ align:start position:0%
+just use this nons information that's in
+the packets we said the nons is a unique
+
+ align:start position:0%
+the packets we said the nons is a unique
+ 
+
+ align:start position:0%
+the packets we said the nons is a unique
+identifier as far as the two end points
+
+ align:start position:0%
+identifier as far as the two end points
+ 
+
+ align:start position:0%
+identifier as far as the two end points
+of the conversation are Ur are are
+
+ align:start position:0%
+of the conversation are Ur are are
+ 
+
+ align:start position:0%
+of the conversation are Ur are are
+concerned so the the acknowledgement is
+
+ align:start position:0%
+concerned so the the acknowledgement is
+ 
+
+ align:start position:0%
+concerned so the the acknowledgement is
+basically just going to be the knots of
+
+ align:start position:0%
+basically just going to be the knots of
+ 
+
+ align:start position:0%
+basically just going to be the knots of
+the message
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's look at how this works in
+
+ align:start position:0%
+okay so let's look at how this works in
+ 
+
+ align:start position:0%
+okay so let's look at how this works in
+a simple
+
+ align:start position:0%
+a simple
+ 
+
+ align:start position:0%
+a simple
+example so the idea is that the sender
+
+ align:start position:0%
+example so the idea is that the sender
+ 
+
+ align:start position:0%
+example so the idea is that the sender
+at some
+
+ align:start position:0%
+at some
+ 
+
+ align:start position:0%
+at some
+point is going to send a message to the
+
+ align:start position:0%
+point is going to send a message to the
+ 
+
+ align:start position:0%
+point is going to send a message to the
+receiver and this message is going to
+
+ align:start position:0%
+receiver and this message is going to
+ 
+
+ align:start position:0%
+receiver and this message is going to
+contain information like uh well it's
+
+ align:start position:0%
+contain information like uh well it's
+ 
+
+ align:start position:0%
+contain information like uh well it's
+going to have the uh address of the
+
+ align:start position:0%
+going to have the uh address of the
+ 
+
+ align:start position:0%
+going to have the uh address of the
+sender the address of the receiver the
+
+ align:start position:0%
+sender the address of the receiver the
+ 
+
+ align:start position:0%
+sender the address of the receiver the
+ports on both ends the message is
+
+ align:start position:0%
+ports on both ends the message is
+ 
+
+ align:start position:0%
+ports on both ends the message is
+supposed to be sent to this knots
+
+ align:start position:0%
+supposed to be sent to this knots
+ 
+
+ align:start position:0%
+supposed to be sent to this knots
+information that uniquely identifies the
+
+ align:start position:0%
+information that uniquely identifies the
+ 
+
+ align:start position:0%
+information that uniquely identifies the
+message and then whatever the data that
+
+ align:start position:0%
+message and then whatever the data that
+ 
+
+ align:start position:0%
+message and then whatever the data that
+needs to go in the message now uh when
+
+ align:start position:0%
+needs to go in the message now uh when
+ 
+
+ align:start position:0%
+needs to go in the message now uh when
+it sends this message what's going to
+
+ align:start position:0%
+it sends this message what's going to
+ 
+
+ align:start position:0%
+it sends this message what's going to
+happen is that the the sender is going
+
+ align:start position:0%
+happen is that the the sender is going
+ 
+
+ align:start position:0%
+happen is that the the sender is going
+to keep this table of pending messages
+
+ align:start position:0%
+to keep this table of pending messages
+ 
+
+ align:start position:0%
+to keep this table of pending messages
+so the sender is going to keep a list of
+
+ align:start position:0%
+so the sender is going to keep a list of
+ 
+
+ align:start position:0%
+so the sender is going to keep a list of
+all the messages that it hasn't yet
+
+ align:start position:0%
+all the messages that it hasn't yet
+ 
+
+ align:start position:0%
+all the messages that it hasn't yet
+heard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acknowledged and then at some point and
+
+ align:start position:0%
+acknowledged and then at some point and
+ 
+
+ align:start position:0%
+acknowledged and then at some point and
+it's going to keep for example if this
+
+ align:start position:0%
+it's going to keep for example if this
+ 
+
+ align:start position:0%
+it's going to keep for example if this
+message is message say that the the name
+
+ align:start position:0%
+message is message say that the the name
+ 
+
+ align:start position:0%
+message is message say that the the name
+of this message is what
+
+ align:start position:0%
+of this message is what
+ 
+
+ align:start position:0%
+of this message is what
+and the knots for this message is X is
+
+ align:start position:0%
+and the knots for this message is X is
+ 
+
+ align:start position:0%
+and the knots for this message is X is
+going to add that information into its
+
+ align:start position:0%
+going to add that information into its
+ 
+
+ align:start position:0%
+going to add that information into its
+table now at some point later the
+
+ align:start position:0%
+table now at some point later the
+ 
+
+ align:start position:0%
+table now at some point later the
+receiver is going to send an
+
+ align:start position:0%
+receiver is going to send an
+ 
+
+ align:start position:0%
+receiver is going to send an
+acknowledgement for this message one
+
+ align:start position:0%
+acknowledgement for this message one
+ 
+
+ align:start position:0%
+acknowledgement for this message one
+back uh and it's just going to have this
+
+ align:start position:0%
+back uh and it's just going to have this
+ 
+
+ align:start position:0%
+back uh and it's just going to have this
+the sender and the receiver IP address
+
+ align:start position:0%
+the sender and the receiver IP address
+ 
+
+ align:start position:0%
+the sender and the receiver IP address
+the port number that of uh of the
+
+ align:start position:0%
+the port number that of uh of the
+ 
+
+ align:start position:0%
+the port number that of uh of the
+receiver and the knots um which the
+
+ align:start position:0%
+receiver and the knots um which the
+ 
+
+ align:start position:0%
+receiver and the knots um which the
+sender is going to use in order to
+
+ align:start position:0%
+sender is going to use in order to
+ 
+
+ align:start position:0%
+sender is going to use in order to
+remove this entry from its table so once
+
+ align:start position:0%
+remove this entry from its table so once
+ 
+
+ align:start position:0%
+remove this entry from its table so once
+the sender receives an acknowledgement
+
+ align:start position:0%
+the sender receives an acknowledgement
+ 
+
+ align:start position:0%
+the sender receives an acknowledgement
+for a message it no longer needs to keep
+
+ align:start position:0%
+for a message it no longer needs to keep
+ 
+
+ align:start position:0%
+for a message it no longer needs to keep
+any state about it because it knows that
+
+ align:start position:0%
+any state about it because it knows that
+ 
+
+ align:start position:0%
+any state about it because it knows that
+the receiver has received it okay okay
+
+ align:start position:0%
+the receiver has received it okay okay
+ 
+
+ align:start position:0%
+the receiver has received it okay okay
+so how does this do us any good how is
+
+ align:start position:0%
+so how does this do us any good how is
+ 
+
+ align:start position:0%
+so how does this do us any good how is
+this at least once well let's see what
+
+ align:start position:0%
+this at least once well let's see what
+ 
+
+ align:start position:0%
+this at least once well let's see what
+happens when there's loss that occurs
+
+ align:start position:0%
+happens when there's loss that occurs
+ 
+
+ align:start position:0%
+happens when there's loss that occurs
+within the network so the idea is is
+
+ align:start position:0%
+within the network so the idea is is
+ 
+
+ align:start position:0%
+within the network so the idea is is
+very simple suppose we suppose that the
+
+ align:start position:0%
+very simple suppose we suppose that the
+ 
+
+ align:start position:0%
+very simple suppose we suppose that the
+sender sends out a message message two
+
+ align:start position:0%
+sender sends out a message message two
+ 
+
+ align:start position:0%
+sender sends out a message message two
+this this time and that message somehow
+
+ align:start position:0%
+this this time and that message somehow
+ 
+
+ align:start position:0%
+this this time and that message somehow
+gets lost in in transit through the
+
+ align:start position:0%
+gets lost in in transit through the
+ 
+
+ align:start position:0%
+gets lost in in transit through the
+network so the network uh drops the
+
+ align:start position:0%
+network so the network uh drops the
+ 
+
+ align:start position:0%
+network so the network uh drops the
+message either because of congestion or
+
+ align:start position:0%
+message either because of congestion or
+ 
+
+ align:start position:0%
+message either because of congestion or
+because some link failed and it doesn't
+
+ align:start position:0%
+because some link failed and it doesn't
+ 
+
+ align:start position:0%
+because some link failed and it doesn't
+get through the idea is that the sender
+
+ align:start position:0%
+get through the idea is that the sender
+ 
+
+ align:start position:0%
+get through the idea is that the sender
+is going to keep a timer associated with
+
+ align:start position:0%
+is going to keep a timer associated with
+ 
+
+ align:start position:0%
+is going to keep a timer associated with
+every message that it sends
+
+ align:start position:0%
+every message that it sends
+ 
+
+ align:start position:0%
+every message that it sends
+and this timer is going to be a timeout
+
+ align:start position:0%
+and this timer is going to be a timeout
+ 
+
+ align:start position:0%
+and this timer is going to be a timeout
+value that's going to tell the sender
+
+ align:start position:0%
+value that's going to tell the sender
+ 
+
+ align:start position:0%
+value that's going to tell the sender
+when it should retry transmitting this
+
+ align:start position:0%
+when it should retry transmitting this
+ 
+
+ align:start position:0%
+when it should retry transmitting this
+message and the sender is just going to
+
+ align:start position:0%
+message and the sender is just going to
+ 
+
+ align:start position:0%
+message and the sender is just going to
+retry transmitting messages over and
+
+ align:start position:0%
+retry transmitting messages over and
+ 
+
+ align:start position:0%
+retry transmitting messages over and
+over and over again until the message
+
+ align:start position:0%
+over and over again until the message
+ 
+
+ align:start position:0%
+over and over again until the message
+actually gets through so in this case uh
+
+ align:start position:0%
+actually gets through so in this case uh
+ 
+
+ align:start position:0%
+actually gets through so in this case uh
+it sets this timer for time
+
+ align:start position:0%
+it sets this timer for time
+ 
+
+ align:start position:0%
+it sets this timer for time
+tr1 uh at the same instant that it sends
+
+ align:start position:0%
+tr1 uh at the same instant that it sends
+ 
+
+ align:start position:0%
+tr1 uh at the same instant that it sends
+out this message and then when time tr1
+
+ align:start position:0%
+out this message and then when time tr1
+ 
+
+ align:start position:0%
+out this message and then when time tr1
+arrives and the message hasn't yet been
+
+ align:start position:0%
+arrives and the message hasn't yet been
+ 
+
+ align:start position:0%
+arrives and the message hasn't yet been
+acknowledged the sender is so after this
+
+ align:start position:0%
+acknowledged the sender is so after this
+ 
+
+ align:start position:0%
+acknowledged the sender is so after this
+this retry interval time the sender is
+
+ align:start position:0%
+this retry interval time the sender is
+ 
+
+ align:start position:0%
+this retry interval time the sender is
+just going to try and retransmit the
+
+ align:start position:0%
+just going to try and retransmit the
+ 
+
+ align:start position:0%
+just going to try and retransmit the
+message so now in this case the receiver
+
+ align:start position:0%
+message so now in this case the receiver
+ 
+
+ align:start position:0%
+message so now in this case the receiver
+has successfully received the message
+
+ align:start position:0%
+has successfully received the message
+ 
+
+ align:start position:0%
+has successfully received the message
+but notice that the sender doesn't
+
+ align:start position:0%
+but notice that the sender doesn't
+ 
+
+ align:start position:0%
+but notice that the sender doesn't
+actually know that the receiver has
+
+ align:start position:0%
+actually know that the receiver has
+ 
+
+ align:start position:0%
+actually know that the receiver has
+received it it's we can see it from the
+
+ align:start position:0%
+received it it's we can see it from the
+ 
+
+ align:start position:0%
+received it it's we can see it from the
+diagram but there's been no feedback
+
+ align:start position:0%
+diagram but there's been no feedback
+ 
+
+ align:start position:0%
+diagram but there's been no feedback
+that has come from the receiver yet and
+
+ align:start position:0%
+that has come from the receiver yet and
+ 
+
+ align:start position:0%
+that has come from the receiver yet and
+now suppose that the receiver sends its
+
+ align:start position:0%
+now suppose that the receiver sends its
+ 
+
+ align:start position:0%
+now suppose that the receiver sends its
+acknowledgement for this message and
+
+ align:start position:0%
+acknowledgement for this message and
+ 
+
+ align:start position:0%
+acknowledgement for this message and
+along the way the acknowledgement gets
+
+ align:start position:0%
+along the way the acknowledgement gets
+ 
+
+ align:start position:0%
+along the way the acknowledgement gets
+lost right so this could happen just as
+
+ align:start position:0%
+lost right so this could happen just as
+ 
+
+ align:start position:0%
+lost right so this could happen just as
+easily as the original message being
+
+ align:start position:0%
+easily as the original message being
+ 
+
+ align:start position:0%
+easily as the original message being
+sent out um so now in this case our
+
+ align:start position:0%
+sent out um so now in this case our
+ 
+
+ align:start position:0%
+sent out um so now in this case our
+retry mechanism continues to
+
+ align:start position:0%
+retry mechanism continues to
+ 
+
+ align:start position:0%
+retry mechanism continues to
+work and after this retry interval and
+
+ align:start position:0%
+work and after this retry interval and
+ 
+
+ align:start position:0%
+work and after this retry interval and
+time tr2 is reached the message gets
+
+ align:start position:0%
+time tr2 is reached the message gets
+ 
+
+ align:start position:0%
+time tr2 is reached the message gets
+resent and then in this case finally the
+
+ align:start position:0%
+resent and then in this case finally the
+ 
+
+ align:start position:0%
+resent and then in this case finally the
+message is actually received and we can
+
+ align:start position:0%
+message is actually received and we can
+ 
+
+ align:start position:0%
+message is actually received and we can
+go ahead and remove it from the pending
+
+ align:start position:0%
+go ahead and remove it from the pending
+ 
+
+ align:start position:0%
+go ahead and remove it from the pending
+message list so this process the
+
+ align:start position:0%
+message list so this process the
+ 
+
+ align:start position:0%
+message list so this process the
+receiver the sender is just going to
+
+ align:start position:0%
+receiver the sender is just going to
+ 
+
+ align:start position:0%
+receiver the sender is just going to
+continually try retry transmitting these
+
+ align:start position:0%
+continually try retry transmitting these
+ 
+
+ align:start position:0%
+continually try retry transmitting these
+messages until it gets an
+
+ align:start position:0%
+messages until it gets an
+ 
+
+ align:start position:0%
+messages until it gets an
+acknowledgement from the receiver it's
+
+ align:start position:0%
+acknowledgement from the receiver it's
+ 
+
+ align:start position:0%
+acknowledgement from the receiver it's
+actually in practice it's the case that
+
+ align:start position:0%
+actually in practice it's the case that
+ 
+
+ align:start position:0%
+actually in practice it's the case that
+the receiver will only retry a fixed
+
+ align:start position:0%
+the receiver will only retry a fixed
+ 
+
+ align:start position:0%
+the receiver will only retry a fixed
+number of times because as we said it is
+
+ align:start position:0%
+number of times because as we said it is
+ 
+
+ align:start position:0%
+number of times because as we said it is
+there are certain situations in which
+
+ align:start position:0%
+there are certain situations in which
+ 
+
+ align:start position:0%
+there are certain situations in which
+the network can just be simply
+
+ align:start position:0%
+the network can just be simply
+ 
+
+ align:start position:0%
+the network can just be simply
+unavailable suppose there's no network
+
+ align:start position:0%
+unavailable suppose there's no network
+ 
+
+ align:start position:0%
+unavailable suppose there's no network
+connection ail aailable to the to the
+
+ align:start position:0%
+connection ail aailable to the to the
+ 
+
+ align:start position:0%
+connection ail aailable to the to the
+transmitter to the sender of course at
+
+ align:start position:0%
+transmitter to the sender of course at
+ 
+
+ align:start position:0%
+transmitter to the sender of course at
+some point it's going to make sense for
+
+ align:start position:0%
+some point it's going to make sense for
+ 
+
+ align:start position:0%
+some point it's going to make sense for
+it to give up and stop trying and then
+
+ align:start position:0%
+it to give up and stop trying and then
+ 
+
+ align:start position:0%
+it to give up and stop trying and then
+it will report an error to the user the
+
+ align:start position:0%
+it will report an error to the user the
+ 
+
+ align:start position:0%
+it will report an error to the user the
+other thing to notice about this
+
+ align:start position:0%
+other thing to notice about this
+ 
+
+ align:start position:0%
+other thing to notice about this
+protocol that we've described here is
+
+ align:start position:0%
+protocol that we've described here is
+ 
+
+ align:start position:0%
+protocol that we've described here is
+that the receiver has received two
+
+ align:start position:0%
+that the receiver has received two
+ 
+
+ align:start position:0%
+that the receiver has received two
+copies of this
+
+ align:start position:0%
+copies of this
+ 
+
+ align:start position:0%
+copies of this
+message so that seems a little bit
+
+ align:start position:0%
+message so that seems a little bit
+ 
+
+ align:start position:0%
+message so that seems a little bit
+problematic right the rece if if this is
+
+ align:start position:0%
+problematic right the rece if if this is
+ 
+
+ align:start position:0%
+problematic right the rece if if this is
+a message that says withdraw $10,000
+
+ align:start position:0%
+a message that says withdraw $10,000
+ 
+
+ align:start position:0%
+a message that says withdraw $10,000
+from your bank account we don't probably
+
+ align:start position:0%
+from your bank account we don't probably
+ 
+
+ align:start position:0%
+from your bank account we don't probably
+want to process that message twice right
+
+ align:start position:0%
+want to process that message twice right
+ 
+
+ align:start position:0%
+want to process that message twice right
+that might be problematic so
+
+ align:start position:0%
+that might be problematic so
+ 
+
+ align:start position:0%
+that might be problematic so
+uh that that's the so we're going to
+
+ align:start position:0%
+uh that that's the so we're going to
+ 
+
+ align:start position:0%
+uh that that's the so we're going to
+address that issue when we get to
+
+ align:start position:0%
+address that issue when we get to
+ 
+
+ align:start position:0%
+address that issue when we get to
+talking about at most once delivery but
+
+ align:start position:0%
+talking about at most once delivery but
+ 
+
+ align:start position:0%
+talking about at most once delivery but
+just bear in mind for now that these
+
+ align:start position:0%
+just bear in mind for now that these
+ 
+
+ align:start position:0%
+just bear in mind for now that these
+duplicates can occur there's another
+
+ align:start position:0%
+duplicates can occur there's another
+ 
+
+ align:start position:0%
+duplicates can occur there's another
+subtlety with this protocol that I've
+
+ align:start position:0%
+subtlety with this protocol that I've
+ 
+
+ align:start position:0%
+subtlety with this protocol that I've
+described here though um does anybody
+
+ align:start position:0%
+described here though um does anybody
+ 
+
+ align:start position:0%
+described here though um does anybody
+see does anybody see something that's a
+
+ align:start position:0%
+see does anybody see something that's a
+ 
+
+ align:start position:0%
+see does anybody see something that's a
+little bit suspicious about this diagram
+
+ align:start position:0%
+little bit suspicious about this diagram
+ 
+
+ align:start position:0%
+little bit suspicious about this diagram
+that I've shown here a little bit a
+
+ align:start position:0%
+that I've shown here a little bit a
+ 
+
+ align:start position:0%
+that I've shown here a little bit a
+little bit weird about the way I've
+
+ align:start position:0%
+little bit weird about the way I've
+ 
+
+ align:start position:0%
+little bit weird about the way I've
+shown it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay right good so there's this
+
+ align:start position:0%
+yeah okay right good so there's this
+ 
+
+ align:start position:0%
+yeah okay right good so there's this
+question about how are you going to set
+
+ align:start position:0%
+question about how are you going to set
+ 
+
+ align:start position:0%
+question about how are you going to set
+the retry interval for these messag
+
+ align:start position:0%
+the retry interval for these messag
+ 
+
+ align:start position:0%
+the retry interval for these messag
+mesages right so what I've shown here is
+
+ align:start position:0%
+mesages right so what I've shown here is
+ 
+
+ align:start position:0%
+mesages right so what I've shown here is
+that the retry interval is short and the
+
+ align:start position:0%
+that the retry interval is short and the
+ 
+
+ align:start position:0%
+that the retry interval is short and the
+first time we sent and received this
+
+ align:start position:0%
+first time we sent and received this
+ 
+
+ align:start position:0%
+first time we sent and received this
+message in fact the time that it took us
+
+ align:start position:0%
+message in fact the time that it took us
+ 
+
+ align:start position:0%
+message in fact the time that it took us
+to do that appeared to be quite quite
+
+ align:start position:0%
+to do that appeared to be quite quite
+ 
+
+ align:start position:0%
+to do that appeared to be quite quite
+long on this diagram right and so in in
+
+ align:start position:0%
+long on this diagram right and so in in
+ 
+
+ align:start position:0%
+long on this diagram right and so in in
+fact what would have happened if we had
+
+ align:start position:0%
+fact what would have happened if we had
+ 
+
+ align:start position:0%
+fact what would have happened if we had
+if we had done this is that the sender
+
+ align:start position:0%
+if we had done this is that the sender
+ 
+
+ align:start position:0%
+if we had done this is that the sender
+would have retransmitted this message
+
+ align:start position:0%
+would have retransmitted this message
+ 
+
+ align:start position:0%
+would have retransmitted this message
+several times even though the receiver
+
+ align:start position:0%
+several times even though the receiver
+ 
+
+ align:start position:0%
+several times even though the receiver
+had actually received the message and
+
+ align:start position:0%
+had actually received the message and
+ 
+
+ align:start position:0%
+had actually received the message and
+and the the acknowledgement was on the
+
+ align:start position:0%
+and the the acknowledgement was on the
+ 
+
+ align:start position:0%
+and the the acknowledgement was on the
+way back to way back to us correctly
+
+ align:start position:0%
+way back to way back to us correctly
+ 
+
+ align:start position:0%
+way back to way back to us correctly
+it's just that we uh didn't wait long
+
+ align:start position:0%
+it's just that we uh didn't wait long
+ 
+
+ align:start position:0%
+it's just that we uh didn't wait long
+enough for that acknowledgement to come
+
+ align:start position:0%
+enough for that acknowledgement to come
+ 
+
+ align:start position:0%
+enough for that acknowledgement to come
+back to us so there's this question
+
+ align:start position:0%
+back to us so there's this question
+ 
+
+ align:start position:0%
+back to us so there's this question
+about well how are we going to pick this
+
+ align:start position:0%
+about well how are we going to pick this
+ 
+
+ align:start position:0%
+about well how are we going to pick this
+timer interval so that it's appropriate
+
+ align:start position:0%
+timer interval so that it's appropriate
+ 
+
+ align:start position:0%
+timer interval so that it's appropriate
+for the network that we're running
+
+ align:start position:0%
+for the network that we're running
+ 
+
+ align:start position:0%
+for the network that we're running
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+and this this turns out to be kind of an
+
+ align:start position:0%
+and this this turns out to be kind of an
+ 
+
+ align:start position:0%
+and this this turns out to be kind of an
+interesting and challenging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+so there's this question about how long
+
+ align:start position:0%
+so there's this question about how long
+ 
+
+ align:start position:0%
+so there's this question about how long
+do we wait before retry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a simple answer for how long we
+
+ align:start position:0%
+so a simple answer for how long we
+ 
+
+ align:start position:0%
+so a simple answer for how long we
+should wait is well however whatever the
+
+ align:start position:0%
+should wait is well however whatever the
+ 
+
+ align:start position:0%
+should wait is well however whatever the
+roundtrip time of the network is however
+
+ align:start position:0%
+roundtrip time of the network is however
+ 
+
+ align:start position:0%
+roundtrip time of the network is however
+long it takes for a message to reach the
+
+ align:start position:0%
+long it takes for a message to reach the
+ 
+
+ align:start position:0%
+long it takes for a message to reach the
+receiver and then uh for the
+
+ align:start position:0%
+receiver and then uh for the
+ 
+
+ align:start position:0%
+receiver and then uh for the
+acknowledgement to be sent back to the
+
+ align:start position:0%
+acknowledgement to be sent back to the
+ 
+
+ align:start position:0%
+acknowledgement to be sent back to the
+sender so we call that the round trip
+
+ align:start position:0%
+sender so we call that the round trip
+ 
+
+ align:start position:0%
+sender so we call that the round trip
+time or the rtt um so we'd like to wait
+
+ align:start position:0%
+time or the rtt um so we'd like to wait
+ 
+
+ align:start position:0%
+time or the rtt um so we'd like to wait
+at least rtt
+
+ align:start position:0%
+at least rtt
+ 
+
+ align:start position:0%
+at least rtt
+right but the problem is that rtt is uh
+
+ align:start position:0%
+right but the problem is that rtt is uh
+ 
+
+ align:start position:0%
+right but the problem is that rtt is uh
+this round trip time is not necessarily
+
+ align:start position:0%
+this round trip time is not necessarily
+ 
+
+ align:start position:0%
+this round trip time is not necessarily
+going to be constant over the whole
+
+ align:start position:0%
+going to be constant over the whole
+ 
+
+ align:start position:0%
+going to be constant over the whole
+lifetime of the network so let me show
+
+ align:start position:0%
+lifetime of the network so let me show
+ 
+
+ align:start position:0%
+lifetime of the network so let me show
+you you what I mean this is a a plot of
+
+ align:start position:0%
+you you what I mean this is a a plot of
+ 
+
+ align:start position:0%
+you you what I mean this is a a plot of
+round of some round trip time
+
+ align:start position:0%
+round of some round trip time
+ 
+
+ align:start position:0%
+round of some round trip time
+information from a wide area wireless
+
+ align:start position:0%
+information from a wide area wireless
+ 
+
+ align:start position:0%
+information from a wide area wireless
+link so these uh transit times are very
+
+ align:start position:0%
+link so these uh transit times are very
+ 
+
+ align:start position:0%
+link so these uh transit times are very
+long here over this link they're sort of
+
+ align:start position:0%
+long here over this link they're sort of
+ 
+
+ align:start position:0%
+long here over this link they're sort of
+order of thousands of Mill thousands of
+
+ align:start position:0%
+order of thousands of Mill thousands of
+ 
+
+ align:start position:0%
+order of thousands of Mill thousands of
+milliseconds um so the long so the
+
+ align:start position:0%
+milliseconds um so the long so the
+ 
+
+ align:start position:0%
+milliseconds um so the long so the
+average transmission time is 2.4 seconds
+
+ align:start position:0%
+average transmission time is 2.4 seconds
+ 
+
+ align:start position:0%
+average transmission time is 2.4 seconds
+here the standard deviation the sort of
+
+ align:start position:0%
+here the standard deviation the sort of
+ 
+
+ align:start position:0%
+here the standard deviation the sort of
+which is a measure of the variance
+
+ align:start position:0%
+which is a measure of the variance
+ 
+
+ align:start position:0%
+which is a measure of the variance
+between these different samples um is is
+
+ align:start position:0%
+between these different samples um is is
+ 
+
+ align:start position:0%
+between these different samples um is is
+1.5 seconds so there's a lot of sort of
+
+ align:start position:0%
+1.5 seconds so there's a lot of sort of
+ 
+
+ align:start position:0%
+1.5 seconds so there's a lot of sort of
+bouncing around of this signal and it's
+
+ align:start position:0%
+bouncing around of this signal and it's
+ 
+
+ align:start position:0%
+bouncing around of this signal and it's
+not so it's not as though the roundtrip
+
+ align:start position:0%
+not so it's not as though the roundtrip
+ 
+
+ align:start position:0%
+not so it's not as though the roundtrip
+time is just a it's saying that the
+
+ align:start position:0%
+time is just a it's saying that the
+ 
+
+ align:start position:0%
+time is just a it's saying that the
+round expecting the roundtrip time to
+
+ align:start position:0%
+round expecting the roundtrip time to
+ 
+
+ align:start position:0%
+round expecting the roundtrip time to
+simply be a single constant value isn't
+
+ align:start position:0%
+simply be a single constant value isn't
+ 
+
+ align:start position:0%
+simply be a single constant value isn't
+a very good idea so if we want to set
+
+ align:start position:0%
+a very good idea so if we want to set
+ 
+
+ align:start position:0%
+a very good idea so if we want to set
+the timeout just to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rtt that's going to cause us you know if
+
+ align:start position:0%
+rtt that's going to cause us you know if
+ 
+
+ align:start position:0%
+rtt that's going to cause us you know if
+you think about this for a minute if we
+
+ align:start position:0%
+you think about this for a minute if we
+ 
+
+ align:start position:0%
+you think about this for a minute if we
+said it just to be rtt uh which is say
+
+ align:start position:0%
+said it just to be rtt uh which is say
+ 
+
+ align:start position:0%
+said it just to be rtt uh which is say
+for example maybe the average uh the the
+
+ align:start position:0%
+for example maybe the average uh the the
+ 
+
+ align:start position:0%
+for example maybe the average uh the the
+the average roundtrip time that we've
+
+ align:start position:0%
+the average roundtrip time that we've
+ 
+
+ align:start position:0%
+the average roundtrip time that we've
+measured in a signal like this well half
+
+ align:start position:0%
+measured in a signal like this well half
+ 
+
+ align:start position:0%
+measured in a signal like this well half
+the time we're going to be uh well uh
+
+ align:start position:0%
+the time we're going to be uh well uh
+ 
+
+ align:start position:0%
+the time we're going to be uh well uh
+you know some significant proportion of
+
+ align:start position:0%
+you know some significant proportion of
+ 
+
+ align:start position:0%
+you know some significant proportion of
+the time we're going to be above the the
+
+ align:start position:0%
+the time we're going to be above the the
+ 
+
+ align:start position:0%
+the time we're going to be above the the
+rtt right um because you know if just
+
+ align:start position:0%
+rtt right um because you know if just
+ 
+
+ align:start position:0%
+rtt right um because you know if just
+just picking the average there's going
+
+ align:start position:0%
+just picking the average there's going
+ 
+
+ align:start position:0%
+just picking the average there's going
+to be many samples that are above the
+
+ align:start position:0%
+to be many samples that are above the
+ 
+
+ align:start position:0%
+to be many samples that are above the
+rtt um so instead we want to do rtt plus
+
+ align:start position:0%
+rtt um so instead we want to do rtt plus
+ 
+
+ align:start position:0%
+rtt um so instead we want to do rtt plus
+some slop value something that's sort of
+
+ align:start position:0%
+some slop value something that's sort of
+ 
+
+ align:start position:0%
+some slop value something that's sort of
+some adjustment factor that uh gets us a
+
+ align:start position:0%
+some adjustment factor that uh gets us a
+ 
+
+ align:start position:0%
+some adjustment factor that uh gets us a
+little bit gives us a little bit of
+
+ align:start position:0%
+little bit gives us a little bit of
+ 
+
+ align:start position:0%
+little bit gives us a little bit of
+extra sort of leeway in how long we wait
+
+ align:start position:0%
+extra sort of leeway in how long we wait
+ 
+
+ align:start position:0%
+extra sort of leeway in how long we wait
+but of course we don't want to wait too
+
+ align:start position:0%
+but of course we don't want to wait too
+ 
+
+ align:start position:0%
+but of course we don't want to wait too
+long because if we wait too long then
+
+ align:start position:0%
+long because if we wait too long then
+ 
+
+ align:start position:0%
+long because if we wait too long then
+we're not going to actually retransmit
+
+ align:start position:0%
+we're not going to actually retransmit
+ 
+
+ align:start position:0%
+we're not going to actually retransmit
+messages that were in fact
+
+ align:start position:0%
+messages that were in fact
+ 
+
+ align:start position:0%
+messages that were in fact
+lost okay so let's look at how so that's
+
+ align:start position:0%
+lost okay so let's look at how so that's
+ 
+
+ align:start position:0%
+lost okay so let's look at how so that's
+sort of a simple intuitive argument for
+
+ align:start position:0%
+sort of a simple intuitive argument for
+ 
+
+ align:start position:0%
+sort of a simple intuitive argument for
+how we should do this um what I want to
+
+ align:start position:0%
+how we should do this um what I want to
+ 
+
+ align:start position:0%
+how we should do this um what I want to
+do now is just quickly take you through
+
+ align:start position:0%
+do now is just quickly take you through
+ 
+
+ align:start position:0%
+do now is just quickly take you through
+the way that these round trip times are
+
+ align:start position:0%
+the way that these round trip times are
+ 
+
+ align:start position:0%
+the way that these round trip times are
+done uh actually are the these roundt
+
+ align:start position:0%
+done uh actually are the these roundt
+ 
+
+ align:start position:0%
+done uh actually are the these roundt
+trip times are estimated in the TCP
+
+ align:start position:0%
+trip times are estimated in the TCP
+ 
+
+ align:start position:0%
+trip times are estimated in the TCP
+protocol um and the way this is done is
+
+ align:start position:0%
+protocol um and the way this is done is
+ 
+
+ align:start position:0%
+protocol um and the way this is done is
+really pretty pretty
+
+ align:start position:0%
+really pretty pretty
+ 
+
+ align:start position:0%
+really pretty pretty
+straightforward the idea is that we want
+
+ align:start position:0%
+straightforward the idea is that we want
+ 
+
+ align:start position:0%
+straightforward the idea is that we want
+to estimate the um the the average rtt
+
+ align:start position:0%
+to estimate the um the the average rtt
+ 
+
+ align:start position:0%
+to estimate the um the the average rtt
+so one way that we could and then we
+
+ align:start position:0%
+so one way that we could and then we
+ 
+
+ align:start position:0%
+so one way that we could and then we
+also want to estimate the sort of
+
+ align:start position:0%
+also want to estimate the sort of
+ 
+
+ align:start position:0%
+also want to estimate the sort of
+variance which is going to be our slop
+
+ align:start position:0%
+variance which is going to be our slop
+ 
+
+ align:start position:0%
+variance which is going to be our slop
+number okay the way that we want we we
+
+ align:start position:0%
+number okay the way that we want we we
+ 
+
+ align:start position:0%
+number okay the way that we want we we
+so one way we could compute the average
+
+ align:start position:0%
+so one way we could compute the average
+ 
+
+ align:start position:0%
+so one way we could compute the average
+rtt is to keep this sort of set of
+
+ align:start position:0%
+rtt is to keep this sort of set of
+ 
+
+ align:start position:0%
+rtt is to keep this sort of set of
+samples of all the roundtrip time so I
+
+ align:start position:0%
+samples of all the roundtrip time so I
+ 
+
+ align:start position:0%
+samples of all the roundtrip time so I
+have maybe 20 points I have whatever it
+
+ align:start position:0%
+have maybe 20 points I have whatever it
+ 
+
+ align:start position:0%
+have maybe 20 points I have whatever it
+is 20 points here they're samples of the
+
+ align:start position:0%
+is 20 points here they're samples of the
+ 
+
+ align:start position:0%
+is 20 points here they're samples of the
+round trip time so I could take this uh
+
+ align:start position:0%
+round trip time so I could take this uh
+ 
+
+ align:start position:0%
+round trip time so I could take this uh
+set of 20 numbers and compute the
+
+ align:start position:0%
+set of 20 numbers and compute the
+ 
+
+ align:start position:0%
+set of 20 numbers and compute the
+average of them and I could recompute
+
+ align:start position:0%
+average of them and I could recompute
+ 
+
+ align:start position:0%
+average of them and I could recompute
+the average every time a new number
+
+ align:start position:0%
+the average every time a new number
+ 
+
+ align:start position:0%
+the average every time a new number
+comes in the problem with that is that I
+
+ align:start position:0%
+comes in the problem with that is that I
+ 
+
+ align:start position:0%
+comes in the problem with that is that I
+have to keep this window of all the
+
+ align:start position:0%
+have to keep this window of all the
+ 
+
+ align:start position:0%
+have to keep this window of all the
+averages around so instead what we want
+
+ align:start position:0%
+averages around so instead what we want
+ 
+
+ align:start position:0%
+averages around so instead what we want
+to do is to have some way of sort of
+
+ align:start position:0%
+to do is to have some way of sort of
+ 
+
+ align:start position:0%
+to do is to have some way of sort of
+updating the average without having to
+
+ align:start position:0%
+updating the average without having to
+ 
+
+ align:start position:0%
+updating the average without having to
+keep all the previous values around and
+
+ align:start position:0%
+keep all the previous values around and
+ 
+
+ align:start position:0%
+keep all the previous values around and
+there's a simple technique that's
+
+ align:start position:0%
+there's a simple technique that's
+ 
+
+ align:start position:0%
+there's a simple technique that's
+commonly used uh in computer systems
+
+ align:start position:0%
+commonly used uh in computer systems
+ 
+
+ align:start position:0%
+commonly used uh in computer systems
+called an exponentially weighted moving
+
+ align:start position:0%
+called an exponentially weighted moving
+ 
+
+ align:start position:0%
+called an exponentially weighted moving
+average which is a way that we can keep
+
+ align:start position:0%
+average which is a way that we can keep
+ 
+
+ align:start position:0%
+average which is a way that we can keep
+track of this average with just a single
+
+ align:start position:0%
+track of this average with just a single
+ 
+
+ align:start position:0%
+track of this average with just a single
+number so this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ewma what the ewma does is it given a
+
+ align:start position:0%
+ewma what the ewma does is it given a
+ 
+
+ align:start position:0%
+ewma what the ewma does is it given a
+set of samples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say S1 up to some most recent sample s
+
+ align:start position:0%
+say S1 up to some most recent sample s
+ 
+
+ align:start position:0%
+say S1 up to some most recent sample s
+new what the ewma does is computes the
+
+ align:start position:0%
+new what the ewma does is computes the
+ 
+
+ align:start position:0%
+new what the ewma does is computes the
+RT uh uh incrementally adjusts the rtt
+
+ align:start position:0%
+RT uh uh incrementally adjusts the rtt
+ 
+
+ align:start position:0%
+RT uh uh incrementally adjusts the rtt
+according to the following formula says
+
+ align:start position:0%
+according to the following formula says
+ 
+
+ align:start position:0%
+according to the following formula says
+the new rtt is going to be equal to 1
+
+ align:start position:0%
+the new rtt is going to be equal to 1
+ 
+
+ align:start position:0%
+the new rtt is going to be equal to 1
+minus Alpha so these samples are samples
+
+ align:start position:0%
+minus Alpha so these samples are samples
+ 
+
+ align:start position:0%
+minus Alpha so these samples are samples
+uh of round trip times okay like this
+
+ align:start position:0%
+uh of round trip times okay like this
+ 
+
+ align:start position:0%
+uh of round trip times okay like this
+number here so these are numbers the
+
+ align:start position:0%
+number here so these are numbers the
+ 
+
+ align:start position:0%
+number here so these are numbers the
+numbers that we've observed over time as
+
+ align:start position:0%
+numbers that we've observed over time as
+ 
+
+ align:start position:0%
+numbers that we've observed over time as
+messages have been trans committed back
+
+ align:start position:0%
+messages have been trans committed back
+ 
+
+ align:start position:0%
+messages have been trans committed back
+and forth we're going to take some
+
+ align:start position:0%
+and forth we're going to take some
+ 
+
+ align:start position:0%
+and forth we're going to take some
+number 1us Alpha time uh s new our our
+
+ align:start position:0%
+number 1us Alpha time uh s new our our
+ 
+
+ align:start position:0%
+number 1us Alpha time uh s new our our
+newly observed roundtrip time and we're
+
+ align:start position:0%
+newly observed roundtrip time and we're
+ 
+
+ align:start position:0%
+newly observed roundtrip time and we're
+going to add to that some Alpha times
+
+ align:start position:0%
+going to add to that some Alpha times
+ 
+
+ align:start position:0%
+going to add to that some Alpha times
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+old roundtrip
+
+ align:start position:0%
+old roundtrip
+ 
+
+ align:start position:0%
+old roundtrip
+time okay so what this does is basically
+
+ align:start position:0%
+time okay so what this does is basically
+ 
+
+ align:start position:0%
+time okay so what this does is basically
+it adds into the it it computes the rtt
+
+ align:start position:0%
+it adds into the it it computes the rtt
+ 
+
+ align:start position:0%
+it adds into the it it computes the rtt
+as some weighted combination of the old
+
+ align:start position:0%
+as some weighted combination of the old
+ 
+
+ align:start position:0%
+as some weighted combination of the old
+roundtrip time and the newly observed
+
+ align:start position:0%
+roundtrip time and the newly observed
+ 
+
+ align:start position:0%
+roundtrip time and the newly observed
+roundtrip time and if you think about
+
+ align:start position:0%
+roundtrip time and if you think about
+ 
+
+ align:start position:0%
+roundtrip time and if you think about
+this for a minute if we make alpha if so
+
+ align:start position:0%
+this for a minute if we make alpha if so
+ 
+
+ align:start position:0%
+this for a minute if we make alpha if so
+Alpha is in this case is going to be
+
+ align:start position:0%
+Alpha is in this case is going to be
+ 
+
+ align:start position:0%
+Alpha is in this case is going to be
+some number between zero and
+
+ align:start position:0%
+some number between zero and
+ 
+
+ align:start position:0%
+some number between zero and
+one um and if you think about Alpha
+
+ align:start position:0%
+one um and if you think about Alpha
+ 
+
+ align:start position:0%
+one um and if you think about Alpha
+being zero if Alpha is zero then the new
+
+ align:start position:0%
+being zero if Alpha is zero then the new
+ 
+
+ align:start position:0%
+being zero if Alpha is zero then the new
+art roundtrip the newly computed
+
+ align:start position:0%
+art roundtrip the newly computed
+ 
+
+ align:start position:0%
+art roundtrip the newly computed
+roundtrip time is just equal to s new
+
+ align:start position:0%
+roundtrip time is just equal to s new
+ 
+
+ align:start position:0%
+roundtrip time is just equal to s new
+right and if Alpha is one then the newly
+
+ align:start position:0%
+right and if Alpha is one then the newly
+ 
+
+ align:start position:0%
+right and if Alpha is one then the newly
+uh the newly computed roundtrip time is
+
+ align:start position:0%
+uh the newly computed roundtrip time is
+ 
+
+ align:start position:0%
+uh the newly computed roundtrip time is
+just equal to whatever the old round
+
+ align:start position:0%
+just equal to whatever the old round
+ 
+
+ align:start position:0%
+just equal to whatever the old round
+trip time was right so the new sample
+
+ align:start position:0%
+trip time was right so the new sample
+ 
+
+ align:start position:0%
+trip time was right so the new sample
+has no effect so as we move veryy Alpha
+
+ align:start position:0%
+has no effect so as we move veryy Alpha
+ 
+
+ align:start position:0%
+has no effect so as we move veryy Alpha
+between these two extremes we're going
+
+ align:start position:0%
+between these two extremes we're going
+ 
+
+ align:start position:0%
+between these two extremes we're going
+to wait the new roundtrip time more or
+
+ align:start position:0%
+to wait the new roundtrip time more or
+ 
+
+ align:start position:0%
+to wait the new roundtrip time more or
+less heavily okay so this is not going
+
+ align:start position:0%
+less heavily okay so this is not going
+ 
+
+ align:start position:0%
+less heavily okay so this is not going
+to perfectly compute the average of the
+
+ align:start position:0%
+to perfectly compute the average of the
+ 
+
+ align:start position:0%
+to perfectly compute the average of the
+samples over time but it's going to give
+
+ align:start position:0%
+samples over time but it's going to give
+ 
+
+ align:start position:0%
+samples over time but it's going to give
+us some estimate that sort of varies
+
+ align:start position:0%
+us some estimate that sort of varies
+ 
+
+ align:start position:0%
+us some estimate that sort of varies
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+time the other thing we said we wanted
+
+ align:start position:0%
+time the other thing we said we wanted
+ 
+
+ align:start position:0%
+time the other thing we said we wanted
+to is compute what this slop factor is
+
+ align:start position:0%
+to is compute what this slop factor is
+ 
+
+ align:start position:0%
+to is compute what this slop factor is
+and this slop factor is just going to be
+
+ align:start position:0%
+and this slop factor is just going to be
+ 
+
+ align:start position:0%
+and this slop factor is just going to be
+we just want this to be some measure of
+
+ align:start position:0%
+we just want this to be some measure of
+ 
+
+ align:start position:0%
+we just want this to be some measure of
+the variance of this signal so in
+
+ align:start position:0%
+the variance of this signal so in
+ 
+
+ align:start position:0%
+the variance of this signal so in
+particular what we want it to meet is
+
+ align:start position:0%
+particular what we want it to meet is
+ 
+
+ align:start position:0%
+particular what we want it to meet is
+uh just going to push this up so can
+
+ align:start position:0%
+uh just going to push this up so can
+ 
+
+ align:start position:0%
+uh just going to push this up so can
+write slop is going to be equal to uh
+
+ align:start position:0%
+write slop is going to be equal to uh
+ 
+
+ align:start position:0%
+write slop is going to be equal to uh
+some Factor beta times some variance of
+
+ align:start position:0%
+some Factor beta times some variance of
+ 
+
+ align:start position:0%
+some Factor beta times some variance of
+this some some some number that's the
+
+ align:start position:0%
+this some some some number that's the
+ 
+
+ align:start position:0%
+this some some some number that's the
+variance and what I mean by variance is
+
+ align:start position:0%
+variance and what I mean by variance is
+ 
+
+ align:start position:0%
+variance and what I mean by variance is
+simply the
+
+ align:start position:0%
+simply the
+ 
+
+ align:start position:0%
+simply the
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+between the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+predicted and actual roundt trip
+
+ align:start position:0%
+predicted and actual roundt trip
+ 
+
+ align:start position:0%
+predicted and actual roundt trip
+times so if our formula says that this
+
+ align:start position:0%
+times so if our formula says that this
+ 
+
+ align:start position:0%
+times so if our formula says that this
+round trip time given a sample uh the
+
+ align:start position:0%
+round trip time given a sample uh the
+ 
+
+ align:start position:0%
+round trip time given a sample uh the
+the round trip time uh should be you
+
+ align:start position:0%
+the round trip time uh should be you
+ 
+
+ align:start position:0%
+the round trip time uh should be you
+know 10 milliseconds and the next sample
+
+ align:start position:0%
+know 10 milliseconds and the next sample
+ 
+
+ align:start position:0%
+know 10 milliseconds and the next sample
+comes in and it says the you know actual
+
+ align:start position:0%
+comes in and it says the you know actual
+ 
+
+ align:start position:0%
+comes in and it says the you know actual
+roundtrip time was 20 milliseconds then
+
+ align:start position:0%
+roundtrip time was 20 milliseconds then
+ 
+
+ align:start position:0%
+roundtrip time was 20 milliseconds then
+the variance we would we would say that
+
+ align:start position:0%
+the variance we would we would say that
+ 
+
+ align:start position:0%
+the variance we would we would say that
+the sort of this deviation the
+
+ align:start position:0%
+the sort of this deviation the
+ 
+
+ align:start position:0%
+the sort of this deviation the
+difference between those two things
+
+ align:start position:0%
+difference between those two things
+ 
+
+ align:start position:0%
+difference between those two things
+would be 10 milliseconds okay so let's
+
+ align:start position:0%
+would be 10 milliseconds okay so let's
+ 
+
+ align:start position:0%
+would be 10 milliseconds okay so let's
+see how this works I'll show you now the
+
+ align:start position:0%
+see how this works I'll show you now the
+ 
+
+ align:start position:0%
+see how this works I'll show you now the
+pseudo code for how this actually works
+
+ align:start position:0%
+pseudo code for how this actually works
+ 
+
+ align:start position:0%
+pseudo code for how this actually works
+in the internet um and it should be
+
+ align:start position:0%
+in the internet um and it should be
+ 
+
+ align:start position:0%
+in the internet um and it should be
+pretty clear what's going on so what
+
+ align:start position:0%
+pretty clear what's going on so what
+ 
+
+ align:start position:0%
+pretty clear what's going on so what
+we're going to do is we're going to keep
+
+ align:start position:0%
+we're going to do is we're going to keep
+ 
+
+ align:start position:0%
+we're going to do is we're going to keep
+a set of variables called one of which
+
+ align:start position:0%
+a set of variables called one of which
+ 
+
+ align:start position:0%
+a set of variables called one of which
+is called SRT so this is this is ex
+
+ align:start position:0%
+is called SRT so this is this is ex
+ 
+
+ align:start position:0%
+is called SRT so this is this is ex
+almost exactly what the TCP protocol
+
+ align:start position:0%
+almost exactly what the TCP protocol
+ 
+
+ align:start position:0%
+almost exactly what the TCP protocol
+does so we're going to have srtt which
+
+ align:start position:0%
+does so we're going to have srtt which
+ 
+
+ align:start position:0%
+does so we're going to have srtt which
+is the current roundtrip the roundt trip
+
+ align:start position:0%
+is the current roundtrip the roundt trip
+ 
+
+ align:start position:0%
+is the current roundtrip the roundt trip
+time estimate and then we're going to
+
+ align:start position:0%
+time estimate and then we're going to
+ 
+
+ align:start position:0%
+time estimate and then we're going to
+have this thing we're call RTD which is
+
+ align:start position:0%
+have this thing we're call RTD which is
+ 
+
+ align:start position:0%
+have this thing we're call RTD which is
+the deviation the current estimate of
+
+ align:start position:0%
+the deviation the current estimate of
+ 
+
+ align:start position:0%
+the deviation the current estimate of
+the sort of variance of this uh round
+
+ align:start position:0%
+the sort of variance of this uh round
+ 
+
+ align:start position:0%
+the sort of variance of this uh round
+trip time and we're going to initialize
+
+ align:start position:0%
+trip time and we're going to initialize
+ 
+
+ align:start position:0%
+trip time and we're going to initialize
+these two numbers to be something that
+
+ align:start position:0%
+these two numbers to be something that
+ 
+
+ align:start position:0%
+these two numbers to be something that
+seems reasonable we might say the
+
+ align:start position:0%
+seems reasonable we might say the
+ 
+
+ align:start position:0%
+seems reasonable we might say the
+roundtrip time is 100 milliseconds and
+
+ align:start position:0%
+roundtrip time is 100 milliseconds and
+ 
+
+ align:start position:0%
+roundtrip time is 100 milliseconds and
+this rtt D is 50
+
+ align:start position:0%
+this rtt D is 50
+ 
+
+ align:start position:0%
+this rtt D is 50
+milliseconds and now what we're going to
+
+ align:start position:0%
+milliseconds and now what we're going to
+ 
+
+ align:start position:0%
+milliseconds and now what we're going to
+do is we're going to just every time new
+
+ align:start position:0%
+do is we're going to just every time new
+ 
+
+ align:start position:0%
+do is we're going to just every time new
+one of these samples of the roundtrip
+
+ align:start position:0%
+one of these samples of the roundtrip
+ 
+
+ align:start position:0%
+one of these samples of the roundtrip
+time comes in we're going to call this
+
+ align:start position:0%
+time comes in we're going to call this
+ 
+
+ align:start position:0%
+time comes in we're going to call this
+Cal rtt function what the Cal rtt
+
+ align:start position:0%
+Cal rtt function what the Cal rtt
+ 
+
+ align:start position:0%
+Cal rtt function what the Cal rtt
+function is going to do it's going to
+
+ align:start position:0%
+function is going to do it's going to
+ 
+
+ align:start position:0%
+function is going to do it's going to
+update the old uh update the the round
+
+ align:start position:0%
+update the old uh update the the round
+ 
+
+ align:start position:0%
+update the old uh update the the round
+trip time using this formula that we've
+
+ align:start position:0%
+trip time using this formula that we've
+ 
+
+ align:start position:0%
+trip time using this formula that we've
+seen here and in the case of TCP people
+
+ align:start position:0%
+seen here and in the case of TCP people
+ 
+
+ align:start position:0%
+seen here and in the case of TCP people
+have sort of experimented with different
+
+ align:start position:0%
+have sort of experimented with different
+ 
+
+ align:start position:0%
+have sort of experimented with different
+values and you know there the sort of
+
+ align:start position:0%
+values and you know there the sort of
+ 
+
+ align:start position:0%
+values and you know there the sort of
+the number that is typically used is
+
+ align:start position:0%
+the number that is typically used is
+ 
+
+ align:start position:0%
+the number that is typically used is
+that you sort of 18 uh a number that is
+
+ align:start position:0%
+that you sort of 18 uh a number that is
+ 
+
+ align:start position:0%
+that you sort of 18 uh a number that is
+commonly used is that uh sort of use
+
+ align:start position:0%
+commonly used is that uh sort of use
+ 
+
+ align:start position:0%
+commonly used is that uh sort of use
+Alpha you set Alpha to be 7 es so that
+
+ align:start position:0%
+Alpha you set Alpha to be 7 es so that
+ 
+
+ align:start position:0%
+Alpha you set Alpha to be 7 es so that
+means that you sort of add in 1/8 of the
+
+ align:start position:0%
+means that you sort of add in 1/8 of the
+ 
+
+ align:start position:0%
+means that you sort of add in 1/8 of the
+uh new number and use 78 of the old
+
+ align:start position:0%
+uh new number and use 78 of the old
+ 
+
+ align:start position:0%
+uh new number and use 78 of the old
+number so this is not going to the a new
+
+ align:start position:0%
+number so this is not going to the a new
+ 
+
+ align:start position:0%
+number so this is not going to the a new
+number that varies a lot isn't going to
+
+ align:start position:0%
+number that varies a lot isn't going to
+ 
+
+ align:start position:0%
+number that varies a lot isn't going to
+change the overall uh the overall round
+
+ align:start position:0%
+change the overall uh the overall round
+ 
+
+ align:start position:0%
+change the overall uh the overall round
+trip time estimate of the round time
+
+ align:start position:0%
+trip time estimate of the round time
+ 
+
+ align:start position:0%
+trip time estimate of the round time
+trip time terribly dramatically and
+
+ align:start position:0%
+trip time terribly dramatically and
+ 
+
+ align:start position:0%
+trip time terribly dramatically and
+we're going to compute the deviation as
+
+ align:start position:0%
+we're going to compute the deviation as
+ 
+
+ align:start position:0%
+we're going to compute the deviation as
+I've shown here we're going to take the
+
+ align:start position:0%
+I've shown here we're going to take the
+ 
+
+ align:start position:0%
+I've shown here we're going to take the
+absolute value of it um and then we're
+
+ align:start position:0%
+absolute value of it um and then we're
+ 
+
+ align:start position:0%
+absolute value of it um and then we're
+going to keep some running estimate of
+
+ align:start position:0%
+going to keep some running estimate of
+ 
+
+ align:start position:0%
+going to keep some running estimate of
+the roundtrip time again using one of
+
+ align:start position:0%
+the roundtrip time again using one of
+ 
+
+ align:start position:0%
+the roundtrip time again using one of
+these sort of exponentially weighted
+
+ align:start position:0%
+these sort of exponentially weighted
+ 
+
+ align:start position:0%
+these sort of exponentially weighted
+things so in this case we're going to
+
+ align:start position:0%
+things so in this case we're going to
+ 
+
+ align:start position:0%
+things so in this case we're going to
+wait with
+
+ align:start position:0%
+wait with
+ 
+
+ align:start position:0%
+wait with
+with this uh setting the the value of
+
+ align:start position:0%
+with this uh setting the the value of
+ 
+
+ align:start position:0%
+with this uh setting the the value of
+the weight here to
+
+ align:start position:0%
+the weight here to
+ 
+
+ align:start position:0%
+the weight here to
+3/4 okay so that's a simple way to
+
+ align:start position:0%
+3/4 okay so that's a simple way to
+ 
+
+ align:start position:0%
+3/4 okay so that's a simple way to
+compute the round trip time and now
+
+ align:start position:0%
+compute the round trip time and now
+ 
+
+ align:start position:0%
+compute the round trip time and now
+given the the computation of the round
+
+ align:start position:0%
+given the the computation of the round
+ 
+
+ align:start position:0%
+given the the computation of the round
+trip time what we need to do is to
+
+ align:start position:0%
+trip time what we need to do is to
+ 
+
+ align:start position:0%
+trip time what we need to do is to
+compute the timeout value that we should
+
+ align:start position:0%
+compute the timeout value that we should
+ 
+
+ align:start position:0%
+compute the timeout value that we should
+use so in uh what we said is the the
+
+ align:start position:0%
+use so in uh what we said is the the
+ 
+
+ align:start position:0%
+use so in uh what we said is the the
+timeout value we want to use is rtt plus
+
+ align:start position:0%
+timeout value we want to use is rtt plus
+ 
+
+ align:start position:0%
+timeout value we want to use is rtt plus
+some slop and uh in the case of TCP a
+
+ align:start position:0%
+some slop and uh in the case of TCP a
+ 
+
+ align:start position:0%
+some slop and uh in the case of TCP a
+commonly used slop value might be four
+
+ align:start position:0%
+commonly used slop value might be four
+ 
+
+ align:start position:0%
+commonly used slop value might be four
+times the estimate of the deviation so
+
+ align:start position:0%
+times the estimate of the deviation so
+ 
+
+ align:start position:0%
+times the estimate of the deviation so
+the idea is that we want the slot value
+
+ align:start position:0%
+the idea is that we want the slot value
+ 
+
+ align:start position:0%
+the idea is that we want the slot value
+to be larger if this if the round trip
+
+ align:start position:0%
+to be larger if this if the round trip
+ 
+
+ align:start position:0%
+to be larger if this if the round trip
+time varies more if the roundtrip time
+
+ align:start position:0%
+time varies more if the roundtrip time
+ 
+
+ align:start position:0%
+time varies more if the roundtrip time
+is practically constant we don't want it
+
+ align:start position:0%
+is practically constant we don't want it
+ 
+
+ align:start position:0%
+is practically constant we don't want it
+to vary much we we we're sort of happy
+
+ align:start position:0%
+to vary much we we we're sort of happy
+ 
+
+ align:start position:0%
+to vary much we we we're sort of happy
+if we're um we don't want we we if the
+
+ align:start position:0%
+if we're um we don't want we we if the
+ 
+
+ align:start position:0%
+if we're um we don't want we we if the
+roundtrip time is is practically
+
+ align:start position:0%
+roundtrip time is is practically
+ 
+
+ align:start position:0%
+roundtrip time is is practically
+constant then we uh don't the timeout
+
+ align:start position:0%
+constant then we uh don't the timeout
+ 
+
+ align:start position:0%
+constant then we uh don't the timeout
+shouldn't be very much longer than that
+
+ align:start position:0%
+shouldn't be very much longer than that
+ 
+
+ align:start position:0%
+shouldn't be very much longer than that
+roundt trip time because that's going to
+
+ align:start position:0%
+roundt trip time because that's going to
+ 
+
+ align:start position:0%
+roundt trip time because that's going to
+suggest that we're going to be waiting
+
+ align:start position:0%
+suggest that we're going to be waiting
+ 
+
+ align:start position:0%
+suggest that we're going to be waiting
+longer than we need to to time out if
+
+ align:start position:0%
+longer than we need to to time out if
+ 
+
+ align:start position:0%
+longer than we need to to time out if
+the roundtrip time varies very
+
+ align:start position:0%
+the roundtrip time varies very
+ 
+
+ align:start position:0%
+the roundtrip time varies very
+dramatically we need to wait a
+
+ align:start position:0%
+dramatically we need to wait a
+ 
+
+ align:start position:0%
+dramatically we need to wait a
+relatively long time in order to be sure
+
+ align:start position:0%
+relatively long time in order to be sure
+ 
+
+ align:start position:0%
+relatively long time in order to be sure
+that the message uh in fact has has been
+
+ align:start position:0%
+that the message uh in fact has has been
+ 
+
+ align:start position:0%
+that the message uh in fact has has been
+lost as a oos to Simply uh taking a long
+
+ align:start position:0%
+lost as a oos to Simply uh taking a long
+ 
+
+ align:start position:0%
+lost as a oos to Simply uh taking a long
+time for the acknowledgement to get back
+
+ align:start position:0%
+time for the acknowledgement to get back
+ 
+
+ align:start position:0%
+time for the acknowledgement to get back
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us okay so this is what we've seen so
+
+ align:start position:0%
+us okay so this is what we've seen so
+ 
+
+ align:start position:0%
+us okay so this is what we've seen so
+far now is we've seen how we can uh do
+
+ align:start position:0%
+far now is we've seen how we can uh do
+ 
+
+ align:start position:0%
+far now is we've seen how we can uh do
+build up this at at least once semantics
+
+ align:start position:0%
+build up this at at least once semantics
+ 
+
+ align:start position:0%
+build up this at at least once semantics
+using acknowledgements and we've talked
+
+ align:start position:0%
+using acknowledgements and we've talked
+ 
+
+ align:start position:0%
+using acknowledgements and we've talked
+about how we can go ahead and set these
+
+ align:start position:0%
+about how we can go ahead and set these
+ 
+
+ align:start position:0%
+about how we can go ahead and set these
+timers in order to uh allow us to
+
+ align:start position:0%
+timers in order to uh allow us to
+ 
+
+ align:start position:0%
+timers in order to uh allow us to
+calculate the roundtrip time for a
+
+ align:start position:0%
+calculate the roundtrip time for a
+ 
+
+ align:start position:0%
+calculate the roundtrip time for a
+message uh and these timers are going to
+
+ align:start position:0%
+message uh and these timers are going to
+ 
+
+ align:start position:0%
+message uh and these timers are going to
+allow us to sort of decide when we
+
+ align:start position:0%
+allow us to sort of decide when we
+ 
+
+ align:start position:0%
+allow us to sort of decide when we
+should ask when we should retransmit a
+
+ align:start position:0%
+should ask when we should retransmit a
+ 
+
+ align:start position:0%
+should ask when we should retransmit a
+message but we also saw how we have a
+
+ align:start position:0%
+message but we also saw how we have a
+ 
+
+ align:start position:0%
+message but we also saw how we have a
+little bit of a
+
+ align:start position:0%
+little bit of a
+ 
+
+ align:start position:0%
+little bit of a
+problem in the uh at least once protocol
+
+ align:start position:0%
+problem in the uh at least once protocol
+ 
+
+ align:start position:0%
+problem in the uh at least once protocol
+and the problem is that we can generate
+
+ align:start position:0%
+and the problem is that we can generate
+ 
+
+ align:start position:0%
+and the problem is that we can generate
+duplicates so in order to avoid
+
+ align:start position:0%
+duplicates so in order to avoid
+ 
+
+ align:start position:0%
+duplicates so in order to avoid
+duplicates we need to introduce this
+
+ align:start position:0%
+duplicates we need to introduce this
+ 
+
+ align:start position:0%
+duplicates we need to introduce this
+notion of atmost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once okay so the idea with the at most
+
+ align:start position:0%
+once okay so the idea with the at most
+ 
+
+ align:start position:0%
+once okay so the idea with the at most
+wants is that we want to suppress
+
+ align:start position:0%
+wants is that we want to suppress
+ 
+
+ align:start position:0%
+wants is that we want to suppress
+duplicates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and duplicate suppression it turns out
+
+ align:start position:0%
+and duplicate suppression it turns out
+ 
+
+ align:start position:0%
+and duplicate suppression it turns out
+it works a lot like the way that uh
+
+ align:start position:0%
+it works a lot like the way that uh
+ 
+
+ align:start position:0%
+it works a lot like the way that uh
+acknowledgements work on the on the
+
+ align:start position:0%
+acknowledgements work on the on the
+ 
+
+ align:start position:0%
+acknowledgements work on the on the
+receiver side uh or on the sender side
+
+ align:start position:0%
+receiver side uh or on the sender side
+ 
+
+ align:start position:0%
+receiver side uh or on the sender side
+so on the receiver side we're going to
+
+ align:start position:0%
+so on the receiver side we're going to
+ 
+
+ align:start position:0%
+so on the receiver side we're going to
+keep a table of all the of the nonces of
+
+ align:start position:0%
+keep a table of all the of the nonces of
+ 
+
+ align:start position:0%
+keep a table of all the of the nonces of
+all the messages that we've heard and
+
+ align:start position:0%
+all the messages that we've heard and
+ 
+
+ align:start position:0%
+all the messages that we've heard and
+we're only going to process a message
+
+ align:start position:0%
+we're only going to process a message
+ 
+
+ align:start position:0%
+we're only going to process a message
+when we receive when when we haven't
+
+ align:start position:0%
+when we receive when when we haven't
+ 
+
+ align:start position:0%
+when we receive when when we haven't
+already processed that message and we're
+
+ align:start position:0%
+already processed that message and we're
+ 
+
+ align:start position:0%
+already processed that message and we're
+going to tell whether we've already
+
+ align:start position:0%
+going to tell whether we've already
+ 
+
+ align:start position:0%
+going to tell whether we've already
+processed it by looking in this table of
+
+ align:start position:0%
+processed it by looking in this table of
+ 
+
+ align:start position:0%
+processed it by looking in this table of
+Anis so let's look at an example so here
+
+ align:start position:0%
+Anis so let's look at an example so here
+ 
+
+ align:start position:0%
+Anis so let's look at an example so here
+we are at this is sort of I'm showing
+
+ align:start position:0%
+we are at this is sort of I'm showing
+ 
+
+ align:start position:0%
+we are at this is sort of I'm showing
+you the protocol a stage in the uh at
+
+ align:start position:0%
+you the protocol a stage in the uh at
+ 
+
+ align:start position:0%
+you the protocol a stage in the uh at
+least once protocol that we were in
+
+ align:start position:0%
+least once protocol that we were in
+ 
+
+ align:start position:0%
+least once protocol that we were in
+before so we've already sent message one
+
+ align:start position:0%
+before so we've already sent message one
+ 
+
+ align:start position:0%
+before so we've already sent message one
+it's been successfully acknowledged um
+
+ align:start position:0%
+it's been successfully acknowledged um
+ 
+
+ align:start position:0%
+it's been successfully acknowledged um
+and you notice that we have this table
+
+ align:start position:0%
+and you notice that we have this table
+ 
+
+ align:start position:0%
+and you notice that we have this table
+of non's received messages that is at
+
+ align:start position:0%
+of non's received messages that is at
+ 
+
+ align:start position:0%
+of non's received messages that is at
+the receiver and in this table we have
+
+ align:start position:0%
+the receiver and in this table we have
+ 
+
+ align:start position:0%
+the receiver and in this table we have
+received uh this message with knot
+
+ align:start position:0%
+received uh this message with knot
+ 
+
+ align:start position:0%
+received uh this message with knot
+X Okay so now when the sender starts to
+
+ align:start position:0%
+X Okay so now when the sender starts to
+ 
+
+ align:start position:0%
+X Okay so now when the sender starts to
+decides to send message to with knots y
+
+ align:start position:0%
+decides to send message to with knots y
+ 
+
+ align:start position:0%
+decides to send message to with knots y
+it sends it out the message doesn't
+
+ align:start position:0%
+it sends it out the message doesn't
+ 
+
+ align:start position:0%
+it sends it out the message doesn't
+arrive uh we time out we
+
+ align:start position:0%
+arrive uh we time out we
+ 
+
+ align:start position:0%
+arrive uh we time out we
+retry um and this time the message is
+
+ align:start position:0%
+retry um and this time the message is
+ 
+
+ align:start position:0%
+retry um and this time the message is
+successfully received so what we do is
+
+ align:start position:0%
+successfully received so what we do is
+ 
+
+ align:start position:0%
+successfully received so what we do is
+we go ahead and add the nons for this
+
+ align:start position:0%
+we go ahead and add the nons for this
+ 
+
+ align:start position:0%
+we go ahead and add the nons for this
+message into the table on the
+
+ align:start position:0%
+message into the table on the
+ 
+
+ align:start position:0%
+message into the table on the
+receiver and then the receiver goes
+
+ align:start position:0%
+receiver and then the receiver goes
+ 
+
+ align:start position:0%
+receiver and then the receiver goes
+ahead and sends the acknowledgement but
+
+ align:start position:0%
+ahead and sends the acknowledgement but
+ 
+
+ align:start position:0%
+ahead and sends the acknowledgement but
+the acknowledgement is lost so again the
+
+ align:start position:0%
+the acknowledgement is lost so again the
+ 
+
+ align:start position:0%
+the acknowledgement is lost so again the
+sender times out sends the message and
+
+ align:start position:0%
+sender times out sends the message and
+ 
+
+ align:start position:0%
+sender times out sends the message and
+this time when the receiver receives
+
+ align:start position:0%
+this time when the receiver receives
+ 
+
+ align:start position:0%
+this time when the receiver receives
+this message it's going to look it up in
+
+ align:start position:0%
+this message it's going to look it up in
+ 
+
+ align:start position:0%
+this message it's going to look it up in
+the Reed messages table and it's going
+
+ align:start position:0%
+the Reed messages table and it's going
+ 
+
+ align:start position:0%
+the Reed messages table and it's going
+to see that this is a duplicate it
+
+ align:start position:0%
+to see that this is a duplicate it
+ 
+
+ align:start position:0%
+to see that this is a duplicate it
+already has seen a message with nony so
+
+ align:start position:0%
+already has seen a message with nony so
+ 
+
+ align:start position:0%
+already has seen a message with nony so
+it's not going to process this but it
+
+ align:start position:0%
+it's not going to process this but it
+ 
+
+ align:start position:0%
+it's not going to process this but it
+needs to still be sure that it sends the
+
+ align:start position:0%
+needs to still be sure that it sends the
+ 
+
+ align:start position:0%
+needs to still be sure that it sends the
+acknowledgement for the message so it
+
+ align:start position:0%
+acknowledgement for the message so it
+ 
+
+ align:start position:0%
+acknowledgement for the message so it
+doesn't actually do anything it doesn't
+
+ align:start position:0%
+doesn't actually do anything it doesn't
+ 
+
+ align:start position:0%
+doesn't actually do anything it doesn't
+actually process this message it doesn't
+
+ align:start position:0%
+actually process this message it doesn't
+ 
+
+ align:start position:0%
+actually process this message it doesn't
+pass it up to the application so the
+
+ align:start position:0%
+pass it up to the application so the
+ 
+
+ align:start position:0%
+pass it up to the application so the
+application can look at it but it still
+
+ align:start position:0%
+application can look at it but it still
+ 
+
+ align:start position:0%
+application can look at it but it still
+sends the acknowledgement so that the
+
+ align:start position:0%
+sends the acknowledgement so that the
+ 
+
+ align:start position:0%
+sends the acknowledgement so that the
+receiver knows that the message has been
+
+ align:start position:0%
+receiver knows that the message has been
+ 
+
+ align:start position:0%
+receiver knows that the message has been
+received okay
+
+ align:start position:0%
+received okay
+ 
+
+ align:start position:0%
+received okay
+so this is fine but if you think about
+
+ align:start position:0%
+so this is fine but if you think about
+ 
+
+ align:start position:0%
+so this is fine but if you think about
+this for a second this table of received
+
+ align:start position:0%
+this for a second this table of received
+ 
+
+ align:start position:0%
+this for a second this table of received
+messages is now just going to be kind of
+
+ align:start position:0%
+messages is now just going to be kind of
+ 
+
+ align:start position:0%
+messages is now just going to be kind of
+growing without bound right because
+
+ align:start position:0%
+growing without bound right because
+ 
+
+ align:start position:0%
+growing without bound right because
+every time we receive a message we're
+
+ align:start position:0%
+every time we receive a message we're
+ 
+
+ align:start position:0%
+every time we receive a message we're
+going to add a new message to this table
+
+ align:start position:0%
+going to add a new message to this table
+ 
+
+ align:start position:0%
+going to add a new message to this table
+of nonas right and this is a problem I
+
+ align:start position:0%
+of nonas right and this is a problem I
+ 
+
+ align:start position:0%
+of nonas right and this is a problem I
+mean if we're sending you know thousands
+
+ align:start position:0%
+mean if we're sending you know thousands
+ 
+
+ align:start position:0%
+mean if we're sending you know thousands
+of messages out over the out over the
+
+ align:start position:0%
+of messages out over the out over the
+ 
+
+ align:start position:0%
+of messages out over the out over the
+network then this table is going to
+
+ align:start position:0%
+network then this table is going to
+ 
+
+ align:start position:0%
+network then this table is going to
+become very very
+
+ align:start position:0%
+become very very
+ 
+
+ align:start position:0%
+become very very
+large so what are we going to do about
+
+ align:start position:0%
+large so what are we going to do about
+ 
+
+ align:start position:0%
+large so what are we going to do about
+it well uh we're going to do sort of
+
+ align:start position:0%
+it well uh we're going to do sort of
+ 
+
+ align:start position:0%
+it well uh we're going to do sort of
+again uh the obvious thing we're going
+
+ align:start position:0%
+again uh the obvious thing we're going
+ 
+
+ align:start position:0%
+again uh the obvious thing we're going
+to have the the sender send some
+
+ align:start position:0%
+to have the the sender send some
+ 
+
+ align:start position:0%
+to have the the sender send some
+additional information that lets the
+
+ align:start position:0%
+additional information that lets the
+ 
+
+ align:start position:0%
+additional information that lets the
+receiver know when the receiver when
+
+ align:start position:0%
+receiver know when the receiver when
+ 
+
+ align:start position:0%
+receiver know when the receiver when
+which messages the receiver has actually
+
+ align:start position:0%
+which messages the receiver has actually
+ 
+
+ align:start position:0%
+which messages the receiver has actually
+heard so a common way that this might be
+
+ align:start position:0%
+heard so a common way that this might be
+ 
+
+ align:start position:0%
+heard so a common way that this might be
+done is to Simply along with each
+
+ align:start position:0%
+done is to Simply along with each
+ 
+
+ align:start position:0%
+done is to Simply along with each
+message that gets sent piggy back a
+
+ align:start position:0%
+message that gets sent piggy back a
+ 
+
+ align:start position:0%
+message that gets sent piggy back a
+little bit of information for example
+
+ align:start position:0%
+little bit of information for example
+ 
+
+ align:start position:0%
+little bit of information for example
+that contains the list of messages that
+
+ align:start position:0%
+that contains the list of messages that
+ 
+
+ align:start position:0%
+that contains the list of messages that
+the uh sender knows that the receiver
+
+ align:start position:0%
+the uh sender knows that the receiver
+ 
+
+ align:start position:0%
+the uh sender knows that the receiver
+has actually received right so when a
+
+ align:start position:0%
+has actually received right so when a
+ 
+
+ align:start position:0%
+has actually received right so when a
+sender receives an acknowledgement for a
+
+ align:start position:0%
+sender receives an acknowledgement for a
+ 
+
+ align:start position:0%
+sender receives an acknowledgement for a
+message um it knows that it's never
+
+ align:start position:0%
+message um it knows that it's never
+ 
+
+ align:start position:0%
+message um it knows that it's never
+going to have to request that the uh
+
+ align:start position:0%
+going to have to request that the uh
+ 
+
+ align:start position:0%
+going to have to request that the uh
+it's never going to resend that message
+
+ align:start position:0%
+it's never going to resend that message
+ 
+
+ align:start position:0%
+it's never going to resend that message
+anymore and so there's no reason for the
+
+ align:start position:0%
+anymore and so there's no reason for the
+ 
+
+ align:start position:0%
+anymore and so there's no reason for the
+receiver to keep that message in its
+
+ align:start position:0%
+receiver to keep that message in its
+ 
+
+ align:start position:0%
+receiver to keep that message in its
+table of received messages because it's
+
+ align:start position:0%
+table of received messages because it's
+ 
+
+ align:start position:0%
+table of received messages because it's
+never going to be asked to acknowledge
+
+ align:start position:0%
+never going to be asked to acknowledge
+ 
+
+ align:start position:0%
+never going to be asked to acknowledge
+that message again so we can attach a
+
+ align:start position:0%
+that message again so we can attach a
+ 
+
+ align:start position:0%
+that message again so we can attach a
+little bit of information to the
+
+ align:start position:0%
+little bit of information to the
+ 
+
+ align:start position:0%
+little bit of information to the
+messages that we send that indicates
+
+ align:start position:0%
+messages that we send that indicates
+ 
+
+ align:start position:0%
+messages that we send that indicates
+sort of which messages we' have
+
+ align:start position:0%
+sort of which messages we' have
+ 
+
+ align:start position:0%
+sort of which messages we' have
+definitely we've completed up to this
+
+ align:start position:0%
+definitely we've completed up to this
+ 
+
+ align:start position:0%
+definitely we've completed up to this
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um so this is a simple way in which
+
+ align:start position:0%
+okay um so this is a simple way in which
+ 
+
+ align:start position:0%
+okay um so this is a simple way in which
+we can sort of eliminate these uh
+
+ align:start position:0%
+we can sort of eliminate these uh
+ 
+
+ align:start position:0%
+we can sort of eliminate these uh
+messages that are hanging around um
+
+ align:start position:0%
+messages that are hanging around um
+ 
+
+ align:start position:0%
+messages that are hanging around um
+these messages that are sort of left in
+
+ align:start position:0%
+these messages that are sort of left in
+ 
+
+ align:start position:0%
+these messages that are sort of left in
+the uh in our table of uh received
+
+ align:start position:0%
+the uh in our table of uh received
+ 
+
+ align:start position:0%
+the uh in our table of uh received
+messages are sometimes referred to as
+
+ align:start position:0%
+messages are sometimes referred to as
+ 
+
+ align:start position:0%
+messages are sometimes referred to as
+tombstones which is kind of a funny name
+
+ align:start position:0%
+tombstones which is kind of a funny name
+ 
+
+ align:start position:0%
+tombstones which is kind of a funny name
+but uh the idea is that there these
+
+ align:start position:0%
+but uh the idea is that there these
+ 
+
+ align:start position:0%
+but uh the idea is that there these
+messages that are kind of hanging the
+
+ align:start position:0%
+messages that are kind of hanging the
+ 
+
+ align:start position:0%
+messages that are kind of hanging the
+they're these the sort of remnants of a
+
+ align:start position:0%
+they're these the sort of remnants of a
+ 
+
+ align:start position:0%
+they're these the sort of remnants of a
+dead message that's hanging around that
+
+ align:start position:0%
+dead message that's hanging around that
+ 
+
+ align:start position:0%
+dead message that's hanging around that
+we're never going to need to process
+
+ align:start position:0%
+we're never going to need to process
+ 
+
+ align:start position:0%
+we're never going to need to process
+again but uh it might just be sitting in
+
+ align:start position:0%
+again but uh it might just be sitting in
+ 
+
+ align:start position:0%
+again but uh it might just be sitting in
+this table and we're able to get rid of
+
+ align:start position:0%
+this table and we're able to get rid of
+ 
+
+ align:start position:0%
+this table and we're able to get rid of
+some of the tombstones by piggybacking
+
+ align:start position:0%
+some of the tombstones by piggybacking
+ 
+
+ align:start position:0%
+some of the tombstones by piggybacking
+this information onto the ends of the
+
+ align:start position:0%
+this information onto the ends of the
+ 
+
+ align:start position:0%
+this information onto the ends of the
+messages that we retransmit but uh you
+
+ align:start position:0%
+messages that we retransmit but uh you
+ 
+
+ align:start position:0%
+messages that we retransmit but uh you
+have to you have to realize that there's
+
+ align:start position:0%
+have to you have to realize that there's
+ 
+
+ align:start position:0%
+have to you have to realize that there's
+always going to be a few messages left
+
+ align:start position:0%
+always going to be a few messages left
+ 
+
+ align:start position:0%
+always going to be a few messages left
+over in this received messages table
+
+ align:start position:0%
+over in this received messages table
+ 
+
+ align:start position:0%
+over in this received messages table
+because if we use this piggybacking
+
+ align:start position:0%
+because if we use this piggybacking
+ 
+
+ align:start position:0%
+because if we use this piggybacking
+technique because we're piggybacking
+
+ align:start position:0%
+technique because we're piggybacking
+ 
+
+ align:start position:0%
+technique because we're piggybacking
+messages uh piggybacking the list of
+
+ align:start position:0%
+messages uh piggybacking the list of
+ 
+
+ align:start position:0%
+messages uh piggybacking the list of
+done messages uh onto messages that are
+
+ align:start position:0%
+done messages uh onto messages that are
+ 
+
+ align:start position:0%
+done messages uh onto messages that are
+sent so if me if the sender never sends
+
+ align:start position:0%
+sent so if me if the sender never sends
+ 
+
+ align:start position:0%
+sent so if me if the sender never sends
+any more messages then the receiver is
+
+ align:start position:0%
+any more messages then the receiver is
+ 
+
+ align:start position:0%
+any more messages then the receiver is
+never going to be able to eliminate any
+
+ align:start position:0%
+never going to be able to eliminate any
+ 
+
+ align:start position:0%
+never going to be able to eliminate any
+of the Tombstones from its list of
+
+ align:start position:0%
+of the Tombstones from its list of
+ 
+
+ align:start position:0%
+of the Tombstones from its list of
+received messages
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now what we've seen is a simple way
+
+ align:start position:0%
+so now what we've seen is a simple way
+ 
+
+ align:start position:0%
+so now what we've seen is a simple way
+to provide this sort of notion of at
+
+ align:start position:0%
+to provide this sort of notion of at
+ 
+
+ align:start position:0%
+to provide this sort of notion of at
+least once and at most once delivery um
+
+ align:start position:0%
+least once and at most once delivery um
+ 
+
+ align:start position:0%
+least once and at most once delivery um
+and so as I said before taken together
+
+ align:start position:0%
+and so as I said before taken together
+ 
+
+ align:start position:0%
+and so as I said before taken together
+this is of is sometimes called exactly
+
+ align:start position:0%
+this is of is sometimes called exactly
+ 
+
+ align:start position:0%
+this is of is sometimes called exactly
+once an exactly once protocol um and
+
+ align:start position:0%
+once an exactly once protocol um and
+ 
+
+ align:start position:0%
+once an exactly once protocol um and
+this variant of this protocol that we've
+
+ align:start position:0%
+this variant of this protocol that we've
+ 
+
+ align:start position:0%
+this variant of this protocol that we've
+seen uh is is called a lock step
+
+ align:start position:0%
+seen uh is is called a lock step
+ 
+
+ align:start position:0%
+seen uh is is called a lock step
+protocol
+
+ align:start position:0%
+protocol
+ 
+
+ align:start position:0%
+protocol
+okay so it's called lock step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because the sender and receiver are
+
+ align:start position:0%
+because the sender and receiver are
+ 
+
+ align:start position:0%
+because the sender and receiver are
+operating in lockstep the sender is the
+
+ align:start position:0%
+operating in lockstep the sender is the
+ 
+
+ align:start position:0%
+operating in lockstep the sender is the
+receiver sends a message and then it
+
+ align:start position:0%
+receiver sends a message and then it
+ 
+
+ align:start position:0%
+receiver sends a message and then it
+waits for the the sender sends a message
+
+ align:start position:0%
+waits for the the sender sends a message
+ 
+
+ align:start position:0%
+waits for the the sender sends a message
+and then it waits for the receiver to
+
+ align:start position:0%
+and then it waits for the receiver to
+ 
+
+ align:start position:0%
+and then it waits for the receiver to
+send an acknowledgement before it sends
+
+ align:start position:0%
+send an acknowledgement before it sends
+ 
+
+ align:start position:0%
+send an acknowledgement before it sends
+any additional messages right so we're
+
+ align:start position:0%
+any additional messages right so we're
+ 
+
+ align:start position:0%
+any additional messages right so we're
+always sort of sitting here uh waiting
+
+ align:start position:0%
+always sort of sitting here uh waiting
+ 
+
+ align:start position:0%
+always sort of sitting here uh waiting
+for the the the sender is sort of
+
+ align:start position:0%
+for the the the sender is sort of
+ 
+
+ align:start position:0%
+for the the the sender is sort of
+basically spending a lot of time idle
+
+ align:start position:0%
+basically spending a lot of time idle
+ 
+
+ align:start position:0%
+basically spending a lot of time idle
+waiting to receive an acknowledgement
+
+ align:start position:0%
+waiting to receive an acknowledgement
+ 
+
+ align:start position:0%
+waiting to receive an acknowledgement
+and if you think about what this
+
+ align:start position:0%
+and if you think about what this
+ 
+
+ align:start position:0%
+and if you think about what this
+means in terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the in terms of the throughput of the
+
+ align:start position:0%
+the in terms of the throughput of the
+ 
+
+ align:start position:0%
+the in terms of the throughput of the
+network it's kind of a limitation so
+
+ align:start position:0%
+network it's kind of a limitation so
+ 
+
+ align:start position:0%
+network it's kind of a limitation so
+let's do a simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculation so suppose that we said that
+
+ align:start position:0%
+calculation so suppose that we said that
+ 
+
+ align:start position:0%
+calculation so suppose that we said that
+uh packets that the the segments that
+
+ align:start position:0%
+uh packets that the the segments that
+ 
+
+ align:start position:0%
+uh packets that the the segments that
+are being sent in this network that are
+
+ align:start position:0%
+are being sent in this network that are
+ 
+
+ align:start position:0%
+are being sent in this network that are
+being these things that are being sent
+
+ align:start position:0%
+being these things that are being sent
+ 
+
+ align:start position:0%
+being these things that are being sent
+back and forth and being acknowledged
+
+ align:start position:0%
+back and forth and being acknowledged
+ 
+
+ align:start position:0%
+back and forth and being acknowledged
+are say 512 bytes large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and suppose we said that it takes the
+
+ align:start position:0%
+and suppose we said that it takes the
+ 
+
+ align:start position:0%
+and suppose we said that it takes the
+roundtrip time in the network is say 100
+
+ align:start position:0%
+roundtrip time in the network is say 100
+ 
+
+ align:start position:0%
+roundtrip time in the network is say 100
+milliseconds which might be a common
+
+ align:start position:0%
+milliseconds which might be a common
+ 
+
+ align:start position:0%
+milliseconds which might be a common
+roundtrip time uh in a traditional
+
+ align:start position:0%
+roundtrip time uh in a traditional
+ 
+
+ align:start position:0%
+roundtrip time uh in a traditional
+Network well the throughput of this
+
+ align:start position:0%
+Network well the throughput of this
+ 
+
+ align:start position:0%
+Network well the throughput of this
+network is going to be the maximum
+
+ align:start position:0%
+network is going to be the maximum
+ 
+
+ align:start position:0%
+network is going to be the maximum
+throughput of this network is going to
+
+ align:start position:0%
+throughput of this network is going to
+ 
+
+ align:start position:0%
+throughput of this network is going to
+be limited by this number 512 bytes
+
+ align:start position:0%
+be limited by this number 512 bytes
+ 
+
+ align:start position:0%
+be limited by this number 512 bytes
+divided by 100 milliseconds right the
+
+ align:start position:0%
+divided by 100 milliseconds right the
+ 
+
+ align:start position:0%
+divided by 100 milliseconds right the
+roundt trip time is 100 milliseconds um
+
+ align:start position:0%
+roundt trip time is 100 milliseconds um
+ 
+
+ align:start position:0%
+roundt trip time is 100 milliseconds um
+and so we have to wait 100 milliseconds
+
+ align:start position:0%
+and so we have to wait 100 milliseconds
+ 
+
+ align:start position:0%
+and so we have to wait 100 milliseconds
+between each transmission of messages
+
+ align:start position:0%
+between each transmission of messages
+ 
+
+ align:start position:0%
+between each transmission of messages
+and the sort of size of a message is uh
+
+ align:start position:0%
+and the sort of size of a message is uh
+ 
+
+ align:start position:0%
+and the sort of size of a message is uh
+if the size of a message is 512 bytes
+
+ align:start position:0%
+if the size of a message is 512 bytes
+ 
+
+ align:start position:0%
+if the size of a message is 512 bytes
+then we're going to be able to send 10
+
+ align:start position:0%
+then we're going to be able to send 10
+ 
+
+ align:start position:0%
+then we're going to be able to send 10
+of these messages per second so we're
+
+ align:start position:0%
+of these messages per second so we're
+ 
+
+ align:start position:0%
+of these messages per second so we're
+going to send sort of uh approximately
+
+ align:start position:0%
+going to send sort of uh approximately
+ 
+
+ align:start position:0%
+going to send sort of uh approximately
+50 kilobits per
+
+ align:start position:0%
+50 kilobits per
+ 
+
+ align:start position:0%
+50 kilobits per
+second okay that's not very fast right
+
+ align:start position:0%
+second okay that's not very fast right
+ 
+
+ align:start position:0%
+second okay that's not very fast right
+if we want to send you know to modern
+
+ align:start position:0%
+if we want to send you know to modern
+ 
+
+ align:start position:0%
+if we want to send you know to modern
+modern networks are often capable of
+
+ align:start position:0%
+modern networks are often capable of
+ 
+
+ align:start position:0%
+modern networks are often capable of
+sending uh you know tens or hundreds of
+
+ align:start position:0%
+sending uh you know tens or hundreds of
+ 
+
+ align:start position:0%
+sending uh you know tens or hundreds of
+megabytes a second so megabits a second
+
+ align:start position:0%
+megabytes a second so megabits a second
+ 
+
+ align:start position:0%
+megabytes a second so megabits a second
+so we would like to be able to make this
+
+ align:start position:0%
+so we would like to be able to make this
+ 
+
+ align:start position:0%
+so we would like to be able to make this
+number higher
+
+ align:start position:0%
+number higher
+ 
+
+ align:start position:0%
+number higher
+um so this is a this is a bit of a
+
+ align:start position:0%
+um so this is a this is a bit of a
+ 
+
+ align:start position:0%
+um so this is a this is a bit of a
+performance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem and the way we're going to do
+
+ align:start position:0%
+problem and the way we're going to do
+ 
+
+ align:start position:0%
+problem and the way we're going to do
+this is by making it so that the rece
+
+ align:start position:0%
+this is by making it so that the rece
+ 
+
+ align:start position:0%
+this is by making it so that the rece
+the sender doesn't wait uh to receive
+
+ align:start position:0%
+the sender doesn't wait uh to receive
+ 
+
+ align:start position:0%
+the sender doesn't wait uh to receive
+its acknowledgements before it goes and
+
+ align:start position:0%
+its acknowledgements before it goes and
+ 
+
+ align:start position:0%
+its acknowledgements before it goes and
+sends the next message so the sender is
+
+ align:start position:0%
+sends the next message so the sender is
+ 
+
+ align:start position:0%
+sends the next message so the sender is
+going to start sending the next message
+
+ align:start position:0%
+going to start sending the next message
+ 
+
+ align:start position:0%
+going to start sending the next message
+before it's even heard the first message
+
+ align:start position:0%
+before it's even heard the first message
+ 
+
+ align:start position:0%
+before it's even heard the first message
+being acknowledged so we're going to
+
+ align:start position:0%
+being acknowledged so we're going to
+ 
+
+ align:start position:0%
+being acknowledged so we're going to
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiple overlapping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Transmissions
+
+ align:start position:0%
+Transmissions
+ 
+
+ align:start position:0%
+Transmissions
+okay so let's see a really simple
+
+ align:start position:0%
+okay so let's see a really simple
+ 
+
+ align:start position:0%
+okay so let's see a really simple
+example of how this
+
+ align:start position:0%
+example of how this
+ 
+
+ align:start position:0%
+example of how this
+works so the idea is now that the sender
+
+ align:start position:0%
+works so the idea is now that the sender
+ 
+
+ align:start position:0%
+works so the idea is now that the sender
+is it's going to send a message and then
+
+ align:start position:0%
+is it's going to send a message and then
+ 
+
+ align:start position:0%
+is it's going to send a message and then
+before the receiver before it's even
+
+ align:start position:0%
+before the receiver before it's even
+ 
+
+ align:start position:0%
+before the receiver before it's even
+heard the acknowledgement from the
+
+ align:start position:0%
+heard the acknowledgement from the
+ 
+
+ align:start position:0%
+heard the acknowledgement from the
+receiver it's going to go ahead and
+
+ align:start position:0%
+receiver it's going to go ahead and
+ 
+
+ align:start position:0%
+receiver it's going to go ahead and
+start sending the message at the same
+
+ align:start position:0%
+start sending the message at the same
+ 
+
+ align:start position:0%
+start sending the message at the same
+time the receiver can go ahead and
+
+ align:start position:0%
+time the receiver can go ahead and
+ 
+
+ align:start position:0%
+time the receiver can go ahead and
+acknowledge the messages that have
+
+ align:start position:0%
+acknowledge the messages that have
+ 
+
+ align:start position:0%
+acknowledge the messages that have
+already been sent so you sort of see
+
+ align:start position:0%
+already been sent so you sort of see
+ 
+
+ align:start position:0%
+already been sent so you sort of see
+what's happening here is that as time
+
+ align:start position:0%
+what's happening here is that as time
+ 
+
+ align:start position:0%
+what's happening here is that as time
+passes the additional messages are being
+
+ align:start position:0%
+passes the additional messages are being
+ 
+
+ align:start position:0%
+passes the additional messages are being
+sent and the acknowledgement for those
+
+ align:start position:0%
+sent and the acknowledgement for those
+ 
+
+ align:start position:0%
+sent and the acknowledgement for those
+messages start getting being sent as
+
+ align:start position:0%
+messages start getting being sent as
+ 
+
+ align:start position:0%
+messages start getting being sent as
+soon as possible so we have a whole
+
+ align:start position:0%
+soon as possible so we have a whole
+ 
+
+ align:start position:0%
+soon as possible so we have a whole
+bunch of messages that are kind of
+
+ align:start position:0%
+bunch of messages that are kind of
+ 
+
+ align:start position:0%
+bunch of messages that are kind of
+flying back and forth within this
+
+ align:start position:0%
+flying back and forth within this
+ 
+
+ align:start position:0%
+flying back and forth within this
+network um and these I've only shown the
+
+ align:start position:0%
+network um and these I've only shown the
+ 
+
+ align:start position:0%
+network um and these I've only shown the
+sort of yellow red and blue messages
+
+ align:start position:0%
+sort of yellow red and blue messages
+ 
+
+ align:start position:0%
+sort of yellow red and blue messages
+actually being acknowledged here the
+
+ align:start position:0%
+actually being acknowledged here the
+ 
+
+ align:start position:0%
+actually being acknowledged here the
+white messages aren't being acknowledged
+
+ align:start position:0%
+white messages aren't being acknowledged
+ 
+
+ align:start position:0%
+white messages aren't being acknowledged
+but of course there would be
+
+ align:start position:0%
+but of course there would be
+ 
+
+ align:start position:0%
+but of course there would be
+acknowledgements flowing for those as
+
+ align:start position:0%
+acknowledgements flowing for those as
+ 
+
+ align:start position:0%
+acknowledgements flowing for those as
+well um so this is this seems really
+
+ align:start position:0%
+well um so this is this seems really
+ 
+
+ align:start position:0%
+well um so this is this seems really
+good right now we can send messages
+
+ align:start position:0%
+good right now we can send messages
+ 
+
+ align:start position:0%
+good right now we can send messages
+basically as fast as we can cram them
+
+ align:start position:0%
+basically as fast as we can cram them
+ 
+
+ align:start position:0%
+basically as fast as we can cram them
+onto the network work um and we sort of
+
+ align:start position:0%
+onto the network work um and we sort of
+ 
+
+ align:start position:0%
+onto the network work um and we sort of
+don't have to wait for the
+
+ align:start position:0%
+don't have to wait for the
+ 
+
+ align:start position:0%
+don't have to wait for the
+acknowledgements to come back
+
+ align:start position:0%
+acknowledgements to come back
+ 
+
+ align:start position:0%
+acknowledgements to come back
+anymore um so in in effect what we've
+
+ align:start position:0%
+anymore um so in in effect what we've
+ 
+
+ align:start position:0%
+anymore um so in in effect what we've
+said is now the throughput is simply
+
+ align:start position:0%
+said is now the throughput is simply
+ 
+
+ align:start position:0%
+said is now the throughput is simply
+constrained by how fast we can cram the
+
+ align:start position:0%
+constrained by how fast we can cram the
+ 
+
+ align:start position:0%
+constrained by how fast we can cram the
+bites onto the
+
+ align:start position:0%
+bites onto the
+ 
+
+ align:start position:0%
+bites onto the
+network but this is a little bit of an
+
+ align:start position:0%
+network but this is a little bit of an
+ 
+
+ align:start position:0%
+network but this is a little bit of an
+oversimplification right because this is
+
+ align:start position:0%
+oversimplification right because this is
+ 
+
+ align:start position:0%
+oversimplification right because this is
+sort of uh
+
+ align:start position:0%
+sort of uh
+ 
+
+ align:start position:0%
+sort of uh
+ignoring what it is that the receiver
+
+ align:start position:0%
+ignoring what it is that the receiver
+ 
+
+ align:start position:0%
+ignoring what it is that the receiver
+suppose the sender is just sending data
+
+ align:start position:0%
+suppose the sender is just sending data
+ 
+
+ align:start position:0%
+suppose the sender is just sending data
+as fast as it can well the receiver has
+
+ align:start position:0%
+as fast as it can well the receiver has
+ 
+
+ align:start position:0%
+as fast as it can well the receiver has
+to receive that data has to do something
+
+ align:start position:0%
+to receive that data has to do something
+ 
+
+ align:start position:0%
+to receive that data has to do something
+with it it has to process it has to take
+
+ align:start position:0%
+with it it has to process it has to take
+ 
+
+ align:start position:0%
+with it it has to process it has to take
+some action on it right and so it's very
+
+ align:start position:0%
+some action on it right and so it's very
+ 
+
+ align:start position:0%
+some action on it right and so it's very
+possible or very likely in fact that uh
+
+ align:start position:0%
+possible or very likely in fact that uh
+ 
+
+ align:start position:0%
+possible or very likely in fact that uh
+if we send if we if we cram data at the
+
+ align:start position:0%
+if we send if we if we cram data at the
+ 
+
+ align:start position:0%
+if we send if we if we cram data at the
+receiver in this way that the receiver
+
+ align:start position:0%
+receiver in this way that the receiver
+ 
+
+ align:start position:0%
+receiver in this way that the receiver
+is going to become overloaded right the
+
+ align:start position:0%
+is going to become overloaded right the
+ 
+
+ align:start position:0%
+is going to become overloaded right the
+receiver has some limited SI limited
+
+ align:start position:0%
+receiver has some limited SI limited
+ 
+
+ align:start position:0%
+receiver has some limited SI limited
+amount of data that it can buffer or
+
+ align:start position:0%
+amount of data that it can buffer or
+ 
+
+ align:start position:0%
+amount of data that it can buffer or
+that it can hold on to um and it's going
+
+ align:start position:0%
+that it can hold on to um and it's going
+ 
+
+ align:start position:0%
+that it can hold on to um and it's going
+to you're going we're going to overflow
+
+ align:start position:0%
+to you're going we're going to overflow
+ 
+
+ align:start position:0%
+to you're going we're going to overflow
+those buffers and we're going to create
+
+ align:start position:0%
+those buffers and we're going to create
+ 
+
+ align:start position:0%
+those buffers and we're going to create
+a problem so what we want to do is to
+
+ align:start position:0%
+a problem so what we want to do is to
+ 
+
+ align:start position:0%
+a problem so what we want to do is to
+have some way to allow the receiver to
+
+ align:start position:0%
+have some way to allow the receiver to
+ 
+
+ align:start position:0%
+have some way to allow the receiver to
+kind of throttle the transmission of the
+
+ align:start position:0%
+kind of throttle the transmission of the
+ 
+
+ align:start position:0%
+kind of throttle the transmission of the
+sender to ask the sender to back off a
+
+ align:start position:0%
+sender to ask the sender to back off a
+ 
+
+ align:start position:0%
+sender to ask the sender to back off a
+little bit and not send so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aggressively okay so we call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this the the technique that we're going
+
+ align:start position:0%
+this the the technique that we're going
+ 
+
+ align:start position:0%
+this the the technique that we're going
+to use is called flow control and it's
+
+ align:start position:0%
+to use is called flow control and it's
+ 
+
+ align:start position:0%
+to use is called flow control and it's
+basically just a way in which the
+
+ align:start position:0%
+basically just a way in which the
+ 
+
+ align:start position:0%
+basically just a way in which the
+receiver can tell the sender what rate
+
+ align:start position:0%
+receiver can tell the sender what rate
+ 
+
+ align:start position:0%
+receiver can tell the sender what rate
+it would like to receive data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at okay so this is going to be sort of
+
+ align:start position:0%
+at okay so this is going to be sort of
+ 
+
+ align:start position:0%
+at okay so this is going to be sort of
+receiver driven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+feedback um and we're going to look
+
+ align:start position:0%
+feedback um and we're going to look
+ 
+
+ align:start position:0%
+feedback um and we're going to look
+at two techniques basically for doing
+
+ align:start position:0%
+at two techniques basically for doing
+ 
+
+ align:start position:0%
+at two techniques basically for doing
+this the first one is a technique called
+
+ align:start position:0%
+this the first one is a technique called
+ 
+
+ align:start position:0%
+this the first one is a technique called
+fixed
+
+ align:start position:0%
+fixed
+ 
+
+ align:start position:0%
+fixed
+windows and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the other technique is a technique
+
+ align:start position:0%
+the other technique is a technique
+ 
+
+ align:start position:0%
+the other technique is a technique
+called sliding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Windows okay and what we mean by wind
+
+ align:start position:0%
+Windows okay and what we mean by wind
+ 
+
+ align:start position:0%
+Windows okay and what we mean by wind
+here this is simply a window is simply a
+
+ align:start position:0%
+here this is simply a window is simply a
+ 
+
+ align:start position:0%
+here this is simply a window is simply a
+the the the size of the data that the
+
+ align:start position:0%
+the the the size of the data that the
+ 
+
+ align:start position:0%
+the the the size of the data that the
+receiver uh can accept the amount the
+
+ align:start position:0%
+receiver uh can accept the amount the
+ 
+
+ align:start position:0%
+receiver uh can accept the amount the
+number of messages that the receiver can
+
+ align:start position:0%
+number of messages that the receiver can
+ 
+
+ align:start position:0%
+number of messages that the receiver can
+accept so this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is can accept at one time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea is we're going to send a
+
+ align:start position:0%
+so the idea is we're going to send a
+ 
+
+ align:start position:0%
+so the idea is we're going to send a
+Windows worth of data uh all
+
+ align:start position:0%
+Windows worth of data uh all
+ 
+
+ align:start position:0%
+Windows worth of data uh all
+continuously and then once the receiver
+
+ align:start position:0%
+continuously and then once the receiver
+ 
+
+ align:start position:0%
+continuously and then once the receiver
+says that it's done processing that
+
+ align:start position:0%
+says that it's done processing that
+ 
+
+ align:start position:0%
+says that it's done processing that
+window we're going to be able to go
+
+ align:start position:0%
+window we're going to be able to go
+ 
+
+ align:start position:0%
+window we're going to be able to go
+ahead and uh send uh send send a next
+
+ align:start position:0%
+ahead and uh send uh send send a next
+ 
+
+ align:start position:0%
+ahead and uh send uh send send a next
+window to it so this first scheme that
+
+ align:start position:0%
+window to it so this first scheme that
+ 
+
+ align:start position:0%
+window to it so this first scheme that
+we're going to look at um is called
+
+ align:start position:0%
+we're going to look at um is called
+ 
+
+ align:start position:0%
+we're going to look at um is called
+fixed is called the fixed wind is called
+
+ align:start position:0%
+fixed is called the fixed wind is called
+ 
+
+ align:start position:0%
+fixed is called the fixed wind is called
+the fixed window scheme um and the idea
+
+ align:start position:0%
+the fixed window scheme um and the idea
+ 
+
+ align:start position:0%
+the fixed window scheme um and the idea
+is really very straightforward the
+
+ align:start position:0%
+is really very straightforward the
+ 
+
+ align:start position:0%
+is really very straightforward the
+sender and the receiver at the beginning
+
+ align:start position:0%
+sender and the receiver at the beginning
+ 
+
+ align:start position:0%
+sender and the receiver at the beginning
+of communication are going to negotiate
+
+ align:start position:0%
+of communication are going to negotiate
+ 
+
+ align:start position:0%
+of communication are going to negotiate
+they're going to exchange some
+
+ align:start position:0%
+they're going to exchange some
+ 
+
+ align:start position:0%
+they're going to exchange some
+information about what the window size
+
+ align:start position:0%
+information about what the window size
+ 
+
+ align:start position:0%
+information about what the window size
+is so the receiver is gonna so the
+
+ align:start position:0%
+is so the receiver is gonna so the
+ 
+
+ align:start position:0%
+is so the receiver is gonna so the
+sender is going to request the
+
+ align:start position:0%
+sender is going to request the
+ 
+
+ align:start position:0%
+sender is going to request the
+connection be opened and then the
+
+ align:start position:0%
+connection be opened and then the
+ 
+
+ align:start position:0%
+connection be opened and then the
+receiver is going to say for example
+
+ align:start position:0%
+receiver is going to say for example
+ 
+
+ align:start position:0%
+receiver is going to say for example
+okay uh I'm let's go ahead and start
+
+ align:start position:0%
+okay uh I'm let's go ahead and start
+ 
+
+ align:start position:0%
+okay uh I'm let's go ahead and start
+having this conversation and by the way
+
+ align:start position:0%
+having this conversation and by the way
+ 
+
+ align:start position:0%
+having this conversation and by the way
+my window size is four
+
+ align:start position:0%
+my window size is four
+ 
+
+ align:start position:0%
+my window size is four
+segments so now the sender can send four
+
+ align:start position:0%
+segments so now the sender can send four
+ 
+
+ align:start position:0%
+segments so now the sender can send four
+segments all at once and the receiver
+
+ align:start position:0%
+segments all at once and the receiver
+ 
+
+ align:start position:0%
+segments all at once and the receiver
+can go ahead and acknowledge them so we
+
+ align:start position:0%
+can go ahead and acknowledge them so we
+ 
+
+ align:start position:0%
+can go ahead and acknowledge them so we
+can have four segments that are sort of
+
+ align:start position:0%
+can have four segments that are sort of
+ 
+
+ align:start position:0%
+can have four segments that are sort of
+uh inflight at any one time and then
+
+ align:start position:0%
+uh inflight at any one time and then
+ 
+
+ align:start position:0%
+uh inflight at any one time and then
+after those messages have all been
+
+ align:start position:0%
+after those messages have all been
+ 
+
+ align:start position:0%
+after those messages have all been
+acknowledged um
+
+ align:start position:0%
+acknowledged um
+ 
+
+ align:start position:0%
+acknowledged um
+the receiver is going to have to sort of
+
+ align:start position:0%
+the receiver is going to have to sort of
+ 
+
+ align:start position:0%
+the receiver is going to have to sort of
+chew on those messages and process them
+
+ align:start position:0%
+chew on those messages and process them
+ 
+
+ align:start position:0%
+chew on those messages and process them
+for a little
+
+ align:start position:0%
+for a little
+ 
+
+ align:start position:0%
+for a little
+while after which during which time
+
+ align:start position:0%
+while after which during which time
+ 
+
+ align:start position:0%
+while after which during which time
+basically the sender is simply waiting
+
+ align:start position:0%
+basically the sender is simply waiting
+ 
+
+ align:start position:0%
+basically the sender is simply waiting
+it's simply sitting there waiting but
+
+ align:start position:0%
+it's simply sitting there waiting but
+ 
+
+ align:start position:0%
+it's simply sitting there waiting but
+notice that we were at least able to uh
+
+ align:start position:0%
+notice that we were at least able to uh
+ 
+
+ align:start position:0%
+notice that we were at least able to uh
+the sender was able to do a little bit
+
+ align:start position:0%
+the sender was able to do a little bit
+ 
+
+ align:start position:0%
+the sender was able to do a little bit
+of extra work it was able to send all
+
+ align:start position:0%
+of extra work it was able to send all
+ 
+
+ align:start position:0%
+of extra work it was able to send all
+four of these messages
+
+ align:start position:0%
+four of these messages
+ 
+
+ align:start position:0%
+four of these messages
+simultaneously and then when this
+
+ align:start position:0%
+simultaneously and then when this
+ 
+
+ align:start position:0%
+simultaneously and then when this
+receiver has finished processing these
+
+ align:start position:0%
+receiver has finished processing these
+ 
+
+ align:start position:0%
+receiver has finished processing these
+messages it's going to go ahead and uh
+
+ align:start position:0%
+messages it's going to go ahead and uh
+ 
+
+ align:start position:0%
+messages it's going to go ahead and uh
+ask for some additional set of messages
+
+ align:start position:0%
+ask for some additional set of messages
+ 
+
+ align:start position:0%
+ask for some additional set of messages
+to be transmitted out over the Network
+
+ align:start position:0%
+to be transmitted out over the Network
+ 
+
+ align:start position:0%
+to be transmitted out over the Network
+so notice that there's uh a s a little
+
+ align:start position:0%
+so notice that there's uh a s a little
+ 
+
+ align:start position:0%
+so notice that there's uh a s a little
+assumption here which is that
+
+ align:start position:0%
+assumption here which is that
+ 
+
+ align:start position:0%
+assumption here which is that
+acknowledgements uh are being sent
+
+ align:start position:0%
+acknowledgements uh are being sent
+ 
+
+ align:start position:0%
+acknowledgements uh are being sent
+before the sort of receiver has actually
+
+ align:start position:0%
+before the sort of receiver has actually
+ 
+
+ align:start position:0%
+before the sort of receiver has actually
+finished processing the messages so that
+
+ align:start position:0%
+finished processing the messages so that
+ 
+
+ align:start position:0%
+finished processing the messages so that
+we're it's sort of what the protocol
+
+ align:start position:0%
+we're it's sort of what the protocol
+ 
+
+ align:start position:0%
+we're it's sort of what the protocol
+that I'm showing here is that the
+
+ align:start position:0%
+that I'm showing here is that the
+ 
+
+ align:start position:0%
+that I'm showing here is that the
+receiver receives a message and it
+
+ align:start position:0%
+receiver receives a message and it
+ 
+
+ align:start position:0%
+receiver receives a message and it
+immediately acknowledges it uh without
+
+ align:start position:0%
+immediately acknowledges it uh without
+ 
+
+ align:start position:0%
+immediately acknowledges it uh without
+even though it hasn't actually the
+
+ align:start position:0%
+even though it hasn't actually the
+ 
+
+ align:start position:0%
+even though it hasn't actually the
+application hasn't necessarily processed
+
+ align:start position:0%
+application hasn't necessarily processed
+ 
+
+ align:start position:0%
+application hasn't necessarily processed
+this message yet the reason we want to
+
+ align:start position:0%
+this message yet the reason we want to
+ 
+
+ align:start position:0%
+this message yet the reason we want to
+do this is that application process
+
+ align:start position:0%
+do this is that application process
+ 
+
+ align:start position:0%
+do this is that application process
+remember we're it's already hard enough
+
+ align:start position:0%
+remember we're it's already hard enough
+ 
+
+ align:start position:0%
+remember we're it's already hard enough
+for us to estimate this roundtrip time
+
+ align:start position:0%
+for us to estimate this roundtrip time
+ 
+
+ align:start position:0%
+for us to estimate this roundtrip time
+using this estimated this this ewma uh
+
+ align:start position:0%
+using this estimated this this ewma uh
+ 
+
+ align:start position:0%
+using this estimated this this ewma uh
+approach and so trying to sort of also
+
+ align:start position:0%
+approach and so trying to sort of also
+ 
+
+ align:start position:0%
+approach and so trying to sort of also
+estimate how long it would take the
+
+ align:start position:0%
+estimate how long it would take the
+ 
+
+ align:start position:0%
+estimate how long it would take the
+application to process the data would
+
+ align:start position:0%
+application to process the data would
+ 
+
+ align:start position:0%
+application to process the data would
+further complicate this process of
+
+ align:start position:0%
+further complicate this process of
+ 
+
+ align:start position:0%
+further complicate this process of
+setting timers so we usually just send
+
+ align:start position:0%
+setting timers so we usually just send
+ 
+
+ align:start position:0%
+setting timers so we usually just send
+acknowledgements right
+
+ align:start position:0%
+acknowledgements right
+ 
+
+ align:start position:0%
+acknowledgements right
+away okay so this is the fix size window
+
+ align:start position:0%
+away okay so this is the fix size window
+ 
+
+ align:start position:0%
+away okay so this is the fix size window
+scheme and it's nice because now uh
+
+ align:start position:0%
+scheme and it's nice because now uh
+ 
+
+ align:start position:0%
+scheme and it's nice because now uh
+basically we've set this thing up so
+
+ align:start position:0%
+basically we've set this thing up so
+ 
+
+ align:start position:0%
+basically we've set this thing up so
+that uh the the sender can send more me
+
+ align:start position:0%
+that uh the the sender can send more me
+ 
+
+ align:start position:0%
+that uh the the sender can send more me
+can can sort of send more messages
+
+ align:start position:0%
+can can sort of send more messages
+ 
+
+ align:start position:0%
+can can sort of send more messages
+without waiting for the acknowledgements
+
+ align:start position:0%
+without waiting for the acknowledgements
+ 
+
+ align:start position:0%
+without waiting for the acknowledgements
+but the receiver has a way that it can
+
+ align:start position:0%
+but the receiver has a way that it can
+ 
+
+ align:start position:0%
+but the receiver has a way that it can
+kind of throttle how fast the sender
+
+ align:start position:0%
+kind of throttle how fast the sender
+ 
+
+ align:start position:0%
+kind of throttle how fast the sender
+sends it knows that it only has buffers
+
+ align:start position:0%
+sends it knows that it only has buffers
+ 
+
+ align:start position:0%
+sends it knows that it only has buffers
+for four messages so it says my window
+
+ align:start position:0%
+for four messages so it says my window
+ 
+
+ align:start position:0%
+for four messages so it says my window
+size is
+
+ align:start position:0%
+size is
+ 
+
+ align:start position:0%
+size is
+four but we would like to do a little
+
+ align:start position:0%
+four but we would like to do a little
+ 
+
+ align:start position:0%
+four but we would like to do a little
+bit better right in particular we would
+
+ align:start position:0%
+bit better right in particular we would
+ 
+
+ align:start position:0%
+bit better right in particular we would
+like to avoid this sort of situation
+
+ align:start position:0%
+like to avoid this sort of situation
+ 
+
+ align:start position:0%
+like to avoid this sort of situation
+where uh the sender both so so in this
+
+ align:start position:0%
+where uh the sender both so so in this
+ 
+
+ align:start position:0%
+where uh the sender both so so in this
+case we sort of have long periods where
+
+ align:start position:0%
+case we sort of have long periods where
+ 
+
+ align:start position:0%
+case we sort of have long periods where
+the network is kind of sitting idle
+
+ align:start position:0%
+the network is kind of sitting idle
+ 
+
+ align:start position:0%
+the network is kind of sitting idle
+where we're not using available
+
+ align:start position:0%
+where we're not using available
+ 
+
+ align:start position:0%
+where we're not using available
+bandwidth within the network um because
+
+ align:start position:0%
+bandwidth within the network um because
+ 
+
+ align:start position:0%
+bandwidth within the network um because
+we're sort of waiting the the the sender
+
+ align:start position:0%
+we're sort of waiting the the the sender
+ 
+
+ align:start position:0%
+we're sort of waiting the the the sender
+has perhaps has data to send but it
+
+ align:start position:0%
+has perhaps has data to send but it
+ 
+
+ align:start position:0%
+has perhaps has data to send but it
+hasn't received the message to send more
+
+ align:start position:0%
+hasn't received the message to send more
+ 
+
+ align:start position:0%
+hasn't received the message to send more
+that the it could the receiver can
+
+ align:start position:0%
+that the it could the receiver can
+ 
+
+ align:start position:0%
+that the it could the receiver can
+accept more messages and the receiver
+
+ align:start position:0%
+accept more messages and the receiver
+ 
+
+ align:start position:0%
+accept more messages and the receiver
+maybe has processed some of the messages
+
+ align:start position:0%
+maybe has processed some of the messages
+ 
+
+ align:start position:0%
+maybe has processed some of the messages
+that it's received but it hasn't yet
+
+ align:start position:0%
+that it's received but it hasn't yet
+ 
+
+ align:start position:0%
+that it's received but it hasn't yet
+sent this message uh over to it hasn't
+
+ align:start position:0%
+sent this message uh over to it hasn't
+ 
+
+ align:start position:0%
+sent this message uh over to it hasn't
+yet asked the sender to go ahead and
+
+ align:start position:0%
+yet asked the sender to go ahead and
+ 
+
+ align:start position:0%
+yet asked the sender to go ahead and
+send any additional data so the way that
+
+ align:start position:0%
+send any additional data so the way that
+ 
+
+ align:start position:0%
+send any additional data so the way that
+we're going to fix this um is to use
+
+ align:start position:0%
+we're going to fix this um is to use
+ 
+
+ align:start position:0%
+we're going to fix this um is to use
+something called a sliding window
+
+ align:start position:0%
+something called a sliding window
+ 
+
+ align:start position:0%
+something called a sliding window
+technique and the idea is that when the
+
+ align:start position:0%
+technique and the idea is that when the
+ 
+
+ align:start position:0%
+technique and the idea is that when the
+receiver rather than the receiver
+
+ align:start position:0%
+receiver rather than the receiver
+ 
+
+ align:start position:0%
+receiver rather than the receiver
+waiting until it has processed the whole
+
+ align:start position:0%
+waiting until it has processed the whole
+ 
+
+ align:start position:0%
+waiting until it has processed the whole
+Windows worth of data when the receiver
+
+ align:start position:0%
+Windows worth of data when the receiver
+ 
+
+ align:start position:0%
+Windows worth of data when the receiver
+processes one or it processes each
+
+ align:start position:0%
+processes one or it processes each
+ 
+
+ align:start position:0%
+processes one or it processes each
+message within its window so if this
+
+ align:start position:0%
+message within its window so if this
+ 
+
+ align:start position:0%
+message within its window so if this
+window is four messages big once it's
+
+ align:start position:0%
+window is four messages big once it's
+ 
+
+ align:start position:0%
+window is four messages big once it's
+processed the first message it's going
+
+ align:start position:0%
+processed the first message it's going
+ 
+
+ align:start position:0%
+processed the first message it's going
+to go ahead and indicate that to the
+
+ align:start position:0%
+to go ahead and indicate that to the
+ 
+
+ align:start position:0%
+to go ahead and indicate that to the
+sender so that the sender can then go
+
+ align:start position:0%
+sender so that the sender can then go
+ 
+
+ align:start position:0%
+sender so that the sender can then go
+ahead and send additional messages so
+
+ align:start position:0%
+ahead and send additional messages so
+ 
+
+ align:start position:0%
+ahead and send additional messages so
+rather than this window sort of moving
+
+ align:start position:0%
+rather than this window sort of moving
+ 
+
+ align:start position:0%
+rather than this window sort of moving
+rather than sort of getting four new
+
+ align:start position:0%
+rather than sort of getting four new
+ 
+
+ align:start position:0%
+rather than sort of getting four new
+messages at a time what we're going to
+
+ align:start position:0%
+messages at a time what we're going to
+ 
+
+ align:start position:0%
+messages at a time what we're going to
+do is we're going to send our first four
+
+ align:start position:0%
+do is we're going to send our first four
+ 
+
+ align:start position:0%
+do is we're going to send our first four
+messages and then we're going to just
+
+ align:start position:0%
+messages and then we're going to just
+ 
+
+ align:start position:0%
+messages and then we're going to just
+send one additional message at a time so
+
+ align:start position:0%
+send one additional message at a time so
+ 
+
+ align:start position:0%
+send one additional message at a time so
+that's why we call the window we say the
+
+ align:start position:0%
+that's why we call the window we say the
+ 
+
+ align:start position:0%
+that's why we call the window we say the
+window is sliding because we're going to
+
+ align:start position:0%
+window is sliding because we're going to
+ 
+
+ align:start position:0%
+window is sliding because we're going to
+sort of allow the sender to send an
+
+ align:start position:0%
+sort of allow the sender to send an
+ 
+
+ align:start position:0%
+sort of allow the sender to send an
+additional message whenever it is that
+
+ align:start position:0%
+additional message whenever it is that
+ 
+
+ align:start position:0%
+additional message whenever it is that
+the receiver has Pro finished processing
+
+ align:start position:0%
+the receiver has Pro finished processing
+ 
+
+ align:start position:0%
+the receiver has Pro finished processing
+just one message and the way we're going
+
+ align:start position:0%
+just one message and the way we're going
+ 
+
+ align:start position:0%
+just one message and the way we're going
+to do this again um we're going to
+
+ align:start position:0%
+to do this again um we're going to
+ 
+
+ align:start position:0%
+to do this again um we're going to
+initially negotiate a window
+
+ align:start position:0%
+initially negotiate a window
+ 
+
+ align:start position:0%
+initially negotiate a window
+size um and then when the sender starts
+
+ align:start position:0%
+size um and then when the sender starts
+ 
+
+ align:start position:0%
+size um and then when the sender starts
+sending it's going to do the same thing
+
+ align:start position:0%
+sending it's going to do the same thing
+ 
+
+ align:start position:0%
+sending it's going to do the same thing
+it's going to send all four of these
+
+ align:start position:0%
+it's going to send all four of these
+ 
+
+ align:start position:0%
+it's going to send all four of these
+messages um I've sort of halted this
+
+ align:start position:0%
+messages um I've sort of halted this
+ 
+
+ align:start position:0%
+messages um I've sort of halted this
+animation in the middle of it so I can
+
+ align:start position:0%
+animation in the middle of it so I can
+ 
+
+ align:start position:0%
+animation in the middle of it so I can
+show you an intermediate step but what
+
+ align:start position:0%
+show you an intermediate step but what
+ 
+
+ align:start position:0%
+show you an intermediate step but what
+would really be happening here is the
+
+ align:start position:0%
+would really be happening here is the
+ 
+
+ align:start position:0%
+would really be happening here is the
+sender would sort of send all the
+
+ align:start position:0%
+sender would sort of send all the
+ 
+
+ align:start position:0%
+sender would sort of send all the
+messages that were in the window um and
+
+ align:start position:0%
+messages that were in the window um and
+ 
+
+ align:start position:0%
+messages that were in the window um and
+then the receiver would begin processing
+
+ align:start position:0%
+then the receiver would begin processing
+ 
+
+ align:start position:0%
+then the receiver would begin processing
+them so now the the receiver begins
+
+ align:start position:0%
+them so now the the receiver begins
+ 
+
+ align:start position:0%
+them so now the the receiver begins
+processing this message and suppose the
+
+ align:start position:0%
+processing this message and suppose the
+ 
+
+ align:start position:0%
+processing this message and suppose the
+the first message so suppose it finishes
+
+ align:start position:0%
+the first message so suppose it finishes
+ 
+
+ align:start position:0%
+the first message so suppose it finishes
+processing segment one um before it
+
+ align:start position:0%
+processing segment one um before it
+ 
+
+ align:start position:0%
+processing segment one um before it
+receives uh the the segment two from the
+
+ align:start position:0%
+receives uh the the segment two from the
+ 
+
+ align:start position:0%
+receives uh the the segment two from the
+from the cender so now what it can do is
+
+ align:start position:0%
+from the cender so now what it can do is
+ 
+
+ align:start position:0%
+from the cender so now what it can do is
+in its acknowledgement for Segment two
+
+ align:start position:0%
+in its acknowledgement for Segment two
+ 
+
+ align:start position:0%
+in its acknowledgement for Segment two
+it can piggyback again using this idea
+
+ align:start position:0%
+it can piggyback again using this idea
+ 
+
+ align:start position:0%
+it can piggyback again using this idea
+can stick a little bit of information
+
+ align:start position:0%
+can stick a little bit of information
+ 
+
+ align:start position:0%
+can stick a little bit of information
+onto the acknowledgement that says oh
+
+ align:start position:0%
+onto the acknowledgement that says oh
+ 
+
+ align:start position:0%
+onto the acknowledgement that says oh
+and by the way I have finished
+
+ align:start position:0%
+and by the way I have finished
+ 
+
+ align:start position:0%
+and by the way I have finished
+processing one of these messages you can
+
+ align:start position:0%
+processing one of these messages you can
+ 
+
+ align:start position:0%
+processing one of these messages you can
+go ahead and send one more additional
+
+ align:start position:0%
+go ahead and send one more additional
+ 
+
+ align:start position:0%
+go ahead and send one more additional
+message you can slide the window by one
+
+ align:start position:0%
+message you can slide the window by one
+ 
+
+ align:start position:0%
+message you can slide the window by one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so I'm going to hit the next step of
+
+ align:start position:0%
+um so I'm going to hit the next step of
+ 
+
+ align:start position:0%
+um so I'm going to hit the next step of
+this animation and it's going to zip by
+
+ align:start position:0%
+this animation and it's going to zip by
+ 
+
+ align:start position:0%
+this animation and it's going to zip by
+really fast um don't I I'll explain what
+
+ align:start position:0%
+really fast um don't I I'll explain what
+ 
+
+ align:start position:0%
+really fast um don't I I'll explain what
+what's what's happening but don't try
+
+ align:start position:0%
+what's what's happening but don't try
+ 
+
+ align:start position:0%
+what's what's happening but don't try
+and worry too much about exactly
+
+ align:start position:0%
+and worry too much about exactly
+ 
+
+ align:start position:0%
+and worry too much about exactly
+following the details um okay so what
+
+ align:start position:0%
+following the details um okay so what
+ 
+
+ align:start position:0%
+following the details um okay so what
+happened here is now so now what what uh
+
+ align:start position:0%
+happened here is now so now what what uh
+ 
+
+ align:start position:0%
+happened here is now so now what what uh
+what happens is that the receiver sort
+
+ align:start position:0%
+what happens is that the receiver sort
+ 
+
+ align:start position:0%
+what happens is that the receiver sort
+of continues to process these messages
+
+ align:start position:0%
+of continues to process these messages
+ 
+
+ align:start position:0%
+of continues to process these messages
+as it arrives and then it continues to
+
+ align:start position:0%
+as it arrives and then it continues to
+ 
+
+ align:start position:0%
+as it arrives and then it continues to
+uh piggyback this acknow this
+
+ align:start position:0%
+uh piggyback this acknow this
+ 
+
+ align:start position:0%
+uh piggyback this acknow this
+information about the fact that it has
+
+ align:start position:0%
+information about the fact that it has
+ 
+
+ align:start position:0%
+information about the fact that it has
+finished sending
+
+ align:start position:0%
+finished sending
+ 
+
+ align:start position:0%
+finished sending
+uh some some messages onto the
+
+ align:start position:0%
+uh some some messages onto the
+ 
+
+ align:start position:0%
+uh some some messages onto the
+acknowledgements finished processing
+
+ align:start position:0%
+acknowledgements finished processing
+ 
+
+ align:start position:0%
+acknowledgements finished processing
+some messages onto the acknowledgements
+
+ align:start position:0%
+some messages onto the acknowledgements
+ 
+
+ align:start position:0%
+some messages onto the acknowledgements
+um if their sender if the receiver
+
+ align:start position:0%
+um if their sender if the receiver
+ 
+
+ align:start position:0%
+um if their sender if the receiver
+doesn't have any acknowledgements to
+
+ align:start position:0%
+doesn't have any acknowledgements to
+ 
+
+ align:start position:0%
+doesn't have any acknowledgements to
+send which was the case for these last
+
+ align:start position:0%
+send which was the case for these last
+ 
+
+ align:start position:0%
+send which was the case for these last
+two messages that it sent out here that
+
+ align:start position:0%
+two messages that it sent out here that
+ 
+
+ align:start position:0%
+two messages that it sent out here that
+I have labeled send more it may need to
+
+ align:start position:0%
+I have labeled send more it may need to
+ 
+
+ align:start position:0%
+I have labeled send more it may need to
+send these sort of uh Slide the window
+
+ align:start position:0%
+send these sort of uh Slide the window
+ 
+
+ align:start position:0%
+send these sort of uh Slide the window
+messages out by itself with without
+
+ align:start position:0%
+messages out by itself with without
+ 
+
+ align:start position:0%
+messages out by itself with without
+acknowledgement so here it sends a
+
+ align:start position:0%
+acknowledgement so here it sends a
+ 
+
+ align:start position:0%
+acknowledgement so here it sends a
+couple of additional messages that say
+
+ align:start position:0%
+couple of additional messages that say
+ 
+
+ align:start position:0%
+couple of additional messages that say
+go ahead and uh send me some more
+
+ align:start position:0%
+go ahead and uh send me some more
+ 
+
+ align:start position:0%
+go ahead and uh send me some more
+data okay so in this way now what we've
+
+ align:start position:0%
+data okay so in this way now what we've
+ 
+
+ align:start position:0%
+data okay so in this way now what we've
+done is we've managed to make it so that
+
+ align:start position:0%
+done is we've managed to make it so that
+ 
+
+ align:start position:0%
+done is we've managed to make it so that
+the uh send
+
+ align:start position:0%
+the uh send
+ 
+
+ align:start position:0%
+the uh send
+so so that the sender can send
+
+ align:start position:0%
+so so that the sender can send
+ 
+
+ align:start position:0%
+so so that the sender can send
+additional information before all of the
+
+ align:start position:0%
+additional information before all of the
+ 
+
+ align:start position:0%
+additional information before all of the
+uh sort of messages in the initial in
+
+ align:start position:0%
+uh sort of messages in the initial in
+ 
+
+ align:start position:0%
+uh sort of messages in the initial in
+the initial window were processed by the
+
+ align:start position:0%
+the initial window were processed by the
+ 
+
+ align:start position:0%
+the initial window were processed by the
+receiver so you see that uh
+
+ align:start position:0%
+receiver so you see that uh
+ 
+
+ align:start position:0%
+receiver so you see that uh
+the before the sender sends excuse me
+
+ align:start position:0%
+the before the sender sends excuse me
+ 
+
+ align:start position:0%
+the before the sender sends excuse me
+before the receiver actually requests
+
+ align:start position:0%
+before the receiver actually requests
+ 
+
+ align:start position:0%
+before the receiver actually requests
+you know sends a message requesting a
+
+ align:start position:0%
+you know sends a message requesting a
+ 
+
+ align:start position:0%
+you know sends a message requesting a
+whole new window SI window worth of data
+
+ align:start position:0%
+whole new window SI window worth of data
+ 
+
+ align:start position:0%
+whole new window SI window worth of data
+so you see now that some of the uh sort
+
+ align:start position:0%
+so you see now that some of the uh sort
+ 
+
+ align:start position:0%
+so you see now that some of the uh sort
+of go ahead and send more messages from
+
+ align:start position:0%
+of go ahead and send more messages from
+ 
+
+ align:start position:0%
+of go ahead and send more messages from
+the receiver arrive at the sender after
+
+ align:start position:0%
+the receiver arrive at the sender after
+ 
+
+ align:start position:0%
+the receiver arrive at the sender after
+the time that the
+
+ align:start position:0%
+the time that the
+ 
+
+ align:start position:0%
+the time that the
+um a after the time that the the sender
+
+ align:start position:0%
+um a after the time that the the sender
+ 
+
+ align:start position:0%
+um a after the time that the the sender
+starts Pro sending messages this fifth
+
+ align:start position:0%
+starts Pro sending messages this fifth
+ 
+
+ align:start position:0%
+starts Pro sending messages this fifth
+and sixth meage message to be go ahead
+
+ align:start position:0%
+and sixth meage message to be go ahead
+ 
+
+ align:start position:0%
+and sixth meage message to be go ahead
+and process so we managed to sort of
+
+ align:start position:0%
+and process so we managed to sort of
+ 
+
+ align:start position:0%
+and process so we managed to sort of
+increase the amount of concurrent
+
+ align:start position:0%
+increase the amount of concurrent
+ 
+
+ align:start position:0%
+increase the amount of concurrent
+processing that we can do in this
+
+ align:start position:0%
+processing that we can do in this
+ 
+
+ align:start position:0%
+processing that we can do in this
+network um but there's still are periods
+
+ align:start position:0%
+network um but there's still are periods
+ 
+
+ align:start position:0%
+network um but there's still are periods
+where the network is sort of idle where
+
+ align:start position:0%
+where the network is sort of idle where
+ 
+
+ align:start position:0%
+where the network is sort of idle where
+we're not actually where the sender and
+
+ align:start position:0%
+we're not actually where the sender and
+ 
+
+ align:start position:0%
+we're not actually where the sender and
+receiver are sort of not not
+
+ align:start position:0%
+receiver are sort of not not
+ 
+
+ align:start position:0%
+receiver are sort of not not
+transmitting data so we haven't done
+
+ align:start position:0%
+transmitting data so we haven't done
+ 
+
+ align:start position:0%
+transmitting data so we haven't done
+quite as good a job as maybe we would
+
+ align:start position:0%
+quite as good a job as maybe we would
+ 
+
+ align:start position:0%
+quite as good a job as maybe we would
+like um and the reason we haven't done
+
+ align:start position:0%
+like um and the reason we haven't done
+ 
+
+ align:start position:0%
+like um and the reason we haven't done
+quite as good a job as maybe we would
+
+ align:start position:0%
+quite as good a job as maybe we would
+ 
+
+ align:start position:0%
+quite as good a job as maybe we would
+like is that the sender that that when
+
+ align:start position:0%
+like is that the sender that that when
+ 
+
+ align:start position:0%
+like is that the sender that that when
+the receiver so so the property that we
+
+ align:start position:0%
+the receiver so so the property that we
+ 
+
+ align:start position:0%
+the receiver so so the property that we
+would like to enforce is that when the
+
+ align:start position:0%
+would like to enforce is that when the
+ 
+
+ align:start position:0%
+would like to enforce is that when the
+receiver says go ahead and uh go ahead
+
+ align:start position:0%
+receiver says go ahead and uh go ahead
+ 
+
+ align:start position:0%
+receiver says go ahead and uh go ahead
+and send me a new message when the
+
+ align:start position:0%
+and send me a new message when the
+ 
+
+ align:start position:0%
+and send me a new message when the
+receiver says Slide the window by one by
+
+ align:start position:0%
+receiver says Slide the window by one by
+ 
+
+ align:start position:0%
+receiver says Slide the window by one by
+the time that that the message the next
+
+ align:start position:0%
+the time that that the message the next
+ 
+
+ align:start position:0%
+the time that that the message the next
+message to process arrives from the
+
+ align:start position:0%
+message to process arrives from the
+ 
+
+ align:start position:0%
+message to process arrives from the
+sender we would like uh the receiver to
+
+ align:start position:0%
+sender we would like uh the receiver to
+ 
+
+ align:start position:0%
+sender we would like uh the receiver to
+uh still to not have uh reached the
+
+ align:start position:0%
+uh still to not have uh reached the
+ 
+
+ align:start position:0%
+uh still to not have uh reached the
+point where it's idle where it has to
+
+ align:start position:0%
+point where it's idle where it has to
+ 
+
+ align:start position:0%
+point where it's idle where it has to
+wait so we'd like the receiver's buffer
+
+ align:start position:0%
+wait so we'd like the receiver's buffer
+ 
+
+ align:start position:0%
+wait so we'd like the receiver's buffer
+to be big enough such that uh By the
+
+ align:start position:0%
+to be big enough such that uh By the
+ 
+
+ align:start position:0%
+to be big enough such that uh By the
+time its request for more data reaches
+
+ align:start position:0%
+time its request for more data reaches
+ 
+
+ align:start position:0%
+time its request for more data reaches
+the receiver and by the time the
+
+ align:start position:0%
+the receiver and by the time the
+ 
+
+ align:start position:0%
+the receiver and by the time the
+receiver's uh the sender and by the time
+
+ align:start position:0%
+receiver's uh the sender and by the time
+ 
+
+ align:start position:0%
+receiver's uh the sender and by the time
+the sender's uh uh response comes back
+
+ align:start position:0%
+the sender's uh uh response comes back
+ 
+
+ align:start position:0%
+the sender's uh uh response comes back
+we would like the receiver to still have
+
+ align:start position:0%
+we would like the receiver to still have
+ 
+
+ align:start position:0%
+we would like the receiver to still have
+some data to process whereas what's
+
+ align:start position:0%
+some data to process whereas what's
+ 
+
+ align:start position:0%
+some data to process whereas what's
+happened here is that the receiver
+
+ align:start position:0%
+happened here is that the receiver
+ 
+
+ align:start position:0%
+happened here is that the receiver
+finished processing all four messages in
+
+ align:start position:0%
+finished processing all four messages in
+ 
+
+ align:start position:0%
+finished processing all four messages in
+its buffer before this next message came
+
+ align:start position:0%
+its buffer before this next message came
+ 
+
+ align:start position:0%
+its buffer before this next message came
+back that with additional data for the
+
+ align:start position:0%
+back that with additional data for the
+ 
+
+ align:start position:0%
+back that with additional data for the
+receiver to process from the sender
+
+ align:start position:0%
+receiver to process from the sender
+ 
+
+ align:start position:0%
+receiver to process from the sender
+right so basically the problem was that
+
+ align:start position:0%
+right so basically the problem was that
+ 
+
+ align:start position:0%
+right so basically the problem was that
+the receiver's buffer wasn't quite large
+
+ align:start position:0%
+the receiver's buffer wasn't quite large
+ 
+
+ align:start position:0%
+the receiver's buffer wasn't quite large
+enough for it to it to uh be able to
+
+ align:start position:0%
+enough for it to it to uh be able to
+ 
+
+ align:start position:0%
+enough for it to it to uh be able to
+continuously process data uh while it uh
+
+ align:start position:0%
+continuously process data uh while it uh
+ 
+
+ align:start position:0%
+continuously process data uh while it uh
+for it to be able to it didn't have
+
+ align:start position:0%
+for it to be able to it didn't have
+ 
+
+ align:start position:0%
+for it to be able to it didn't have
+quite enough data for it to be able to
+
+ align:start position:0%
+quite enough data for it to be able to
+ 
+
+ align:start position:0%
+quite enough data for it to be able to
+continuously process while it waited for
+
+ align:start position:0%
+continuously process while it waited for
+ 
+
+ align:start position:0%
+continuously process while it waited for
+the sort of additional data to arrive
+
+ align:start position:0%
+the sort of additional data to arrive
+ 
+
+ align:start position:0%
+the sort of additional data to arrive
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+sender so what we want is what this
+
+ align:start position:0%
+sender so what we want is what this
+ 
+
+ align:start position:0%
+sender so what we want is what this
+suggests that we want is to set this
+
+ align:start position:0%
+suggests that we want is to set this
+ 
+
+ align:start position:0%
+suggests that we want is to set this
+buffer size to set the size of the
+
+ align:start position:0%
+buffer size to set the size of the
+ 
+
+ align:start position:0%
+buffer size to set the size of the
+window to be uh the the appropriate size
+
+ align:start position:0%
+window to be uh the the appropriate size
+ 
+
+ align:start position:0%
+window to be uh the the appropriate size
+in order for the receiver to be able to
+
+ align:start position:0%
+in order for the receiver to be able to
+ 
+
+ align:start position:0%
+in order for the receiver to be able to
+sort of continuously process information
+
+ align:start position:0%
+sort of continuously process information
+ 
+
+ align:start position:0%
+sort of continuously process information
+um if at all
+
+ align:start position:0%
+um if at all
+ 
+
+ align:start position:0%
+um if at all
+possible so there's this question about
+
+ align:start position:0%
+possible so there's this question about
+ 
+
+ align:start position:0%
+possible so there's this question about
+how do we pick the window
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size so let's assume so the the problem
+
+ align:start position:0%
+size so let's assume so the the problem
+ 
+
+ align:start position:0%
+size so let's assume so the the problem
+we have is that small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Windows imply uh underutilization of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+network okay because we have both the
+
+ align:start position:0%
+network okay because we have both the
+ 
+
+ align:start position:0%
+network okay because we have both the
+cender and receiver are sort of Sitting
+
+ align:start position:0%
+cender and receiver are sort of Sitting
+ 
+
+ align:start position:0%
+cender and receiver are sort of Sitting
+Waiting there's times when there's no
+
+ align:start position:0%
+Waiting there's times when there's no
+ 
+
+ align:start position:0%
+Waiting there's times when there's no
+data that's actually trans that's being
+
+ align:start position:0%
+data that's actually trans that's being
+ 
+
+ align:start position:0%
+data that's actually trans that's being
+transferred across the
+
+ align:start position:0%
+transferred across the
+ 
+
+ align:start position:0%
+transferred across the
+network
+
+ align:start position:0%
+network
+ 
+
+ align:start position:0%
+network
+um so the question is then how big
+
+ align:start position:0%
+um so the question is then how big
+ 
+
+ align:start position:0%
+um so the question is then how big
+should we make the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+window what we said is we want the uh
+
+ align:start position:0%
+window what we said is we want the uh
+ 
+
+ align:start position:0%
+window what we said is we want the uh
+window size to be greater than the
+
+ align:start position:0%
+window size to be greater than the
+ 
+
+ align:start position:0%
+window size to be greater than the
+amount of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want it to be long enough so that the
+
+ align:start position:0%
+we want it to be long enough so that the
+ 
+
+ align:start position:0%
+we want it to be long enough so that the
+receiver which say for example if the
+
+ align:start position:0%
+receiver which say for example if the
+ 
+
+ align:start position:0%
+receiver which say for example if the
+receiver can process some number of
+
+ align:start position:0%
+receiver can process some number of
+ 
+
+ align:start position:0%
+receiver can process some number of
+messages rate messages per second okay
+
+ align:start position:0%
+messages rate messages per second okay
+ 
+
+ align:start position:0%
+messages rate messages per second okay
+the receiver can process this many
+
+ align:start position:0%
+the receiver can process this many
+ 
+
+ align:start position:0%
+the receiver can process this many
+messages uh we want the its buffer uh to
+
+ align:start position:0%
+messages uh we want the its buffer uh to
+ 
+
+ align:start position:0%
+messages uh we want the its buffer uh to
+be large enough that uh the it if it
+
+ align:start position:0%
+be large enough that uh the it if it
+ 
+
+ align:start position:0%
+be large enough that uh the it if it
+processes that many messages per second
+
+ align:start position:0%
+processes that many messages per second
+ 
+
+ align:start position:0%
+processes that many messages per second
+that the amount of time for an
+
+ align:start position:0%
+that the amount of time for an
+ 
+
+ align:start position:0%
+that the amount of time for an
+additional additional messages for it to
+
+ align:start position:0%
+additional additional messages for it to
+ 
+
+ align:start position:0%
+additional additional messages for it to
+process that that it will still have
+
+ align:start position:0%
+process that that it will still have
+ 
+
+ align:start position:0%
+process that that it will still have
+messages to process by the time
+
+ align:start position:0%
+messages to process by the time
+ 
+
+ align:start position:0%
+messages to process by the time
+additional messages arrive from the
+
+ align:start position:0%
+additional messages arrive from the
+ 
+
+ align:start position:0%
+additional messages arrive from the
+sender so
+
+ align:start position:0%
+sender so
+ 
+
+ align:start position:0%
+sender so
+um the amount of time that it takes for
+
+ align:start position:0%
+um the amount of time that it takes for
+ 
+
+ align:start position:0%
+um the amount of time that it takes for
+a message to arrive additional messages
+
+ align:start position:0%
+a message to arrive additional messages
+ 
+
+ align:start position:0%
+a message to arrive additional messages
+to arrive from the sender from the time
+
+ align:start position:0%
+to arrive from the sender from the time
+ 
+
+ align:start position:0%
+to arrive from the sender from the time
+that this guy first sends this uh okay
+
+ align:start position:0%
+that this guy first sends this uh okay
+ 
+
+ align:start position:0%
+that this guy first sends this uh okay
+to send more message right is one
+
+ align:start position:0%
+to send more message right is one
+ 
+
+ align:start position:0%
+to send more message right is one
+roundtrip time of the network so it
+
+ align:start position:0%
+roundtrip time of the network so it
+ 
+
+ align:start position:0%
+roundtrip time of the network so it
+takes one roundtrip time of the network
+
+ align:start position:0%
+takes one roundtrip time of the network
+ 
+
+ align:start position:0%
+takes one roundtrip time of the network
+for the the sender for the for the
+
+ align:start position:0%
+for the the sender for the for the
+ 
+
+ align:start position:0%
+for the the sender for the for the
+receiver to receive additional messages
+
+ align:start position:0%
+receiver to receive additional messages
+ 
+
+ align:start position:0%
+receiver to receive additional messages
+to process from the sender um and the
+
+ align:start position:0%
+to process from the sender um and the
+ 
+
+ align:start position:0%
+to process from the sender um and the
+number of messages that it will process
+
+ align:start position:0%
+number of messages that it will process
+ 
+
+ align:start position:0%
+number of messages that it will process
+during that round trip time is whatever
+
+ align:start position:0%
+during that round trip time is whatever
+ 
+
+ align:start position:0%
+during that round trip time is whatever
+it message processing rate is times the
+
+ align:start position:0%
+it message processing rate is times the
+ 
+
+ align:start position:0%
+it message processing rate is times the
+roundtrip time of the network um and so
+
+ align:start position:0%
+roundtrip time of the network um and so
+ 
+
+ align:start position:0%
+roundtrip time of the network um and so
+therefore this is sort of ideally how we
+
+ align:start position:0%
+therefore this is sort of ideally how we
+ 
+
+ align:start position:0%
+therefore this is sort of ideally how we
+would set the window size in this
+
+ align:start position:0%
+would set the window size in this
+ 
+
+ align:start position:0%
+would set the window size in this
+network of course we talked about before
+
+ align:start position:0%
+network of course we talked about before
+ 
+
+ align:start position:0%
+network of course we talked about before
+How It's tricky to estimate this sort of
+
+ align:start position:0%
+How It's tricky to estimate this sort of
+ 
+
+ align:start position:0%
+How It's tricky to estimate this sort of
+ewma thing that we do to estimate the
+
+ align:start position:0%
+ewma thing that we do to estimate the
+ 
+
+ align:start position:0%
+ewma thing that we do to estimate the
+window size is not a perfect estimator
+
+ align:start position:0%
+window size is not a perfect estimator
+ 
+
+ align:start position:0%
+window size is not a perfect estimator
+um but we're going to try and sort of
+
+ align:start position:0%
+um but we're going to try and sort of
+ 
+
+ align:start position:0%
+um but we're going to try and sort of
+set this we're we're going to this is
+
+ align:start position:0%
+set this we're we're going to this is
+ 
+
+ align:start position:0%
+set this we're we're going to this is
+this is going to be a sort of good
+
+ align:start position:0%
+this is going to be a sort of good
+ 
+
+ align:start position:0%
+this is going to be a sort of good
+choice for a window size to use um and
+
+ align:start position:0%
+choice for a window size to use um and
+ 
+
+ align:start position:0%
+choice for a window size to use um and
+so typically the the receiver is the
+
+ align:start position:0%
+so typically the the receiver is the
+ 
+
+ align:start position:0%
+so typically the the receiver is the
+receiver is going to try and sort of use
+
+ align:start position:0%
+receiver is going to try and sort of use
+ 
+
+ align:start position:0%
+receiver is going to try and sort of use
+some rough estimate of what it thinks
+
+ align:start position:0%
+some rough estimate of what it thinks
+ 
+
+ align:start position:0%
+some rough estimate of what it thinks
+the round trip time is and the rate
+
+ align:start position:0%
+the round trip time is and the rate
+ 
+
+ align:start position:0%
+the round trip time is and the rate
+process the rate at which it can process
+
+ align:start position:0%
+process the rate at which it can process
+ 
+
+ align:start position:0%
+process the rate at which it can process
+messages when it informs the cender of
+
+ align:start position:0%
+messages when it informs the cender of
+ 
+
+ align:start position:0%
+messages when it informs the cender of
+the uh sort of the window size at the
+
+ align:start position:0%
+the uh sort of the window size at the
+ 
+
+ align:start position:0%
+the uh sort of the window size at the
+initiation of the
+
+ align:start position:0%
+initiation of the
+ 
+
+ align:start position:0%
+initiation of the
+connection okay so this basically um is
+
+ align:start position:0%
+connection okay so this basically um is
+ 
+
+ align:start position:0%
+connection okay so this basically um is
+going to wrap up our discussion of the
+
+ align:start position:0%
+going to wrap up our discussion of the
+ 
+
+ align:start position:0%
+going to wrap up our discussion of the
+end to-end layer or of this the the sort
+
+ align:start position:0%
+end to-end layer or of this the the sort
+ 
+
+ align:start position:0%
+end to-end layer or of this the the sort
+of the loss recovery issues in the end
+
+ align:start position:0%
+of the loss recovery issues in the end
+ 
+
+ align:start position:0%
+of the loss recovery issues in the end
+to-end layer what we're going to talk
+
+ align:start position:0%
+to-end layer what we're going to talk
+ 
+
+ align:start position:0%
+to-end layer what we're going to talk
+about next time um is this issue of how
+
+ align:start position:0%
+about next time um is this issue of how
+ 
+
+ align:start position:0%
+about next time um is this issue of how
+we deal with congestion right so we said
+
+ align:start position:0%
+we deal with congestion right so we said
+ 
+
+ align:start position:0%
+we deal with congestion right so we said
+that in one of these networks there be
+
+ align:start position:0%
+that in one of these networks there be
+ 
+
+ align:start position:0%
+that in one of these networks there be
+uh in one of these networks there can be
+
+ align:start position:0%
+uh in one of these networks there can be
+ 
+
+ align:start position:0%
+uh in one of these networks there can be
+all these delays due to queuing um and
+
+ align:start position:0%
+all these delays due to queuing um and
+ 
+
+ align:start position:0%
+all these delays due to queuing um and
+that these delays can introduce
+
+ align:start position:0%
+that these delays can introduce
+ 
+
+ align:start position:0%
+that these delays can introduce
+additional loss and we call these delays
+
+ align:start position:0%
+additional loss and we call these delays
+ 
+
+ align:start position:0%
+additional loss and we call these delays
+congestion and so the what we're going
+
+ align:start position:0%
+congestion and so the what we're going
+ 
+
+ align:start position:0%
+congestion and so the what we're going
+to talk about next time is how we
+
+ align:start position:0%
+to talk about next time is how we
+ 
+
+ align:start position:0%
+to talk about next time is how we
+actually deal with congestion how we
+
+ align:start position:0%
+actually deal with congestion how we
+ 
+
+ align:start position:0%
+actually deal with congestion how we
+respond to congestion okay so we'll see
+
+ align:start position:0%
+respond to congestion okay so we'll see
+ 
+
+ align:start position:0%
+respond to congestion okay so we'll see
+you on Wednesday
\ No newline at end of file
diff --git a/ZDQk45NQbEo.txt b/ZDQk45NQbEo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..190bcd1b6e89d7534abb4dcdac7b07bd3db82f2f
--- /dev/null
+++ b/ZDQk45NQbEo.txt
@@ -0,0 +1,2200 @@
+align:start position:0%
+ 
+we've considered arithmetic sums where
+
+ align:start position:0%
+we've considered arithmetic sums where
+ 
+
+ align:start position:0%
+we've considered arithmetic sums where
+each term is a fixed amount larger than
+
+ align:start position:0%
+each term is a fixed amount larger than
+ 
+
+ align:start position:0%
+each term is a fixed amount larger than
+the previous term by an additive amount
+
+ align:start position:0%
+the previous term by an additive amount
+ 
+
+ align:start position:0%
+the previous term by an additive amount
+another kind of sum called geometric
+
+ align:start position:0%
+another kind of sum called geometric
+ 
+
+ align:start position:0%
+another kind of sum called geometric
+sums which we're going to look at now
+
+ align:start position:0%
+sums which we're going to look at now
+ 
+
+ align:start position:0%
+sums which we're going to look at now
+come about where each sum is a fixed
+
+ align:start position:0%
+come about where each sum is a fixed
+ 
+
+ align:start position:0%
+come about where each sum is a fixed
+multiple of the previous sum and
+
+ align:start position:0%
+multiple of the previous sum and
+ 
+
+ align:start position:0%
+multiple of the previous sum and
+these come up all the time in lots of
+
+ align:start position:0%
+these come up all the time in lots of
+ 
+
+ align:start position:0%
+these come up all the time in lots of
+different settings in this particular
+
+ align:start position:0%
+different settings in this particular
+ 
+
+ align:start position:0%
+different settings in this particular
+case we're going to look at an example
+
+ align:start position:0%
+case we're going to look at an example
+ 
+
+ align:start position:0%
+case we're going to look at an example
+of how it applies to
+
+ align:start position:0%
+of how it applies to
+ 
+
+ align:start position:0%
+of how it applies to
+analyzing the value of money in the
+
+ align:start position:0%
+analyzing the value of money in the
+ 
+
+ align:start position:0%
+analyzing the value of money in the
+future so let's begin with a geometric
+
+ align:start position:0%
+future so let's begin with a geometric
+ 
+
+ align:start position:0%
+future so let's begin with a geometric
+sum and there's the standard form of it
+
+ align:start position:0%
+sum and there's the standard form of it
+ 
+
+ align:start position:0%
+sum and there's the standard form of it
+geometric sum is of the form uh 1 plus x
+
+ align:start position:0%
+geometric sum is of the form uh 1 plus x
+ 
+
+ align:start position:0%
+geometric sum is of the form uh 1 plus x
+plus x squared up through the nth power
+
+ align:start position:0%
+plus x squared up through the nth power
+ 
+
+ align:start position:0%
+plus x squared up through the nth power
+of x and for uniformly notice that 1 is
+
+ align:start position:0%
+of x and for uniformly notice that 1 is
+ 
+
+ align:start position:0%
+of x and for uniformly notice that 1 is
+actually x to the zero so we're taking
+
+ align:start position:0%
+actually x to the zero so we're taking
+ 
+
+ align:start position:0%
+actually x to the zero so we're taking
+the sum from and from k equals 0 to n of
+
+ align:start position:0%
+the sum from and from k equals 0 to n of
+ 
+
+ align:start position:0%
+the sum from and from k equals 0 to n of
+x to the k
+
+ align:start position:0%
+x to the k
+ 
+
+ align:start position:0%
+x to the k
+now what i'd like to do is find a nice
+
+ align:start position:0%
+now what i'd like to do is find a nice
+ 
+
+ align:start position:0%
+now what i'd like to do is find a nice
+closed form for this without those
+
+ align:start position:0%
+closed form for this without those
+ 
+
+ align:start position:0%
+closed form for this without those
+ellipses uh and and having a growing
+
+ align:start position:0%
+ellipses uh and and having a growing
+ 
+
+ align:start position:0%
+ellipses uh and and having a growing
+number of terms n and there's a simple
+
+ align:start position:0%
+number of terms n and there's a simple
+ 
+
+ align:start position:0%
+number of terms n and there's a simple
+trick with the arithmetic sum the way
+
+ align:start position:0%
+trick with the arithmetic sum the way
+ 
+
+ align:start position:0%
+trick with the arithmetic sum the way
+gauss got it and the way we got it was
+
+ align:start position:0%
+gauss got it and the way we got it was
+ 
+
+ align:start position:0%
+gauss got it and the way we got it was
+by reversing the summonating the things
+
+ align:start position:0%
+by reversing the summonating the things
+ 
+
+ align:start position:0%
+by reversing the summonating the things
+together this time the trick is to
+
+ align:start position:0%
+together this time the trick is to
+ 
+
+ align:start position:0%
+together this time the trick is to
+multiply gn by x
+
+ align:start position:0%
+multiply gn by x
+ 
+
+ align:start position:0%
+multiply gn by x
+now what's that going to do is it's
+
+ align:start position:0%
+now what's that going to do is it's
+ 
+
+ align:start position:0%
+now what's that going to do is it's
+going to increase the power of x in each
+
+ align:start position:0%
+going to increase the power of x in each
+ 
+
+ align:start position:0%
+going to increase the power of x in each
+term by one
+
+ align:start position:0%
+term by one
+ 
+
+ align:start position:0%
+term by one
+which is tantamount to a right shift
+
+ align:start position:0%
+which is tantamount to a right shift
+ 
+
+ align:start position:0%
+which is tantamount to a right shift
+let's look at that there's x g of n so
+
+ align:start position:0%
+let's look at that there's x g of n so
+ 
+
+ align:start position:0%
+let's look at that there's x g of n so
+uh uh one times x of course i'm
+
+ align:start position:0%
+uh uh one times x of course i'm
+ 
+
+ align:start position:0%
+uh uh one times x of course i'm
+subtracting looking ahead so one times x
+
+ align:start position:0%
+subtracting looking ahead so one times x
+ 
+
+ align:start position:0%
+subtracting looking ahead so one times x
+is minus l minus x um
+
+ align:start position:0%
+is minus l minus x um
+ 
+
+ align:start position:0%
+is minus l minus x um
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+x times
+
+ align:start position:0%
+x times
+ 
+
+ align:start position:0%
+x times
+x is x squared i'm going to subtract it
+
+ align:start position:0%
+x is x squared i'm going to subtract it
+ 
+
+ align:start position:0%
+x is x squared i'm going to subtract it
+down through
+
+ align:start position:0%
+down through
+ 
+
+ align:start position:0%
+down through
+x to the n minus 1 times x gives me the
+
+ align:start position:0%
+x to the n minus 1 times x gives me the
+ 
+
+ align:start position:0%
+x to the n minus 1 times x gives me the
+x to the n term and finally i have an
+
+ align:start position:0%
+x to the n term and finally i have an
+ 
+
+ align:start position:0%
+x to the n term and finally i have an
+extra term from right shifting x to the
+
+ align:start position:0%
+extra term from right shifting x to the
+ 
+
+ align:start position:0%
+extra term from right shifting x to the
+n to be x to the n plus 1. now let's do
+
+ align:start position:0%
+n to be x to the n plus 1. now let's do
+ 
+
+ align:start position:0%
+n to be x to the n plus 1. now let's do
+this subtraction
+
+ align:start position:0%
+this subtraction
+ 
+
+ align:start position:0%
+this subtraction
+but of course i'm going to line the
+
+ align:start position:0%
+but of course i'm going to line the
+ 
+
+ align:start position:0%
+but of course i'm going to line the
+terms up so that they're easy to
+
+ align:start position:0%
+terms up so that they're easy to
+ 
+
+ align:start position:0%
+terms up so that they're easy to
+subtract and now all the terms in the
+
+ align:start position:0%
+subtract and now all the terms in the
+ 
+
+ align:start position:0%
+subtract and now all the terms in the
+middle cancel which is very cool because
+
+ align:start position:0%
+middle cancel which is very cool because
+ 
+
+ align:start position:0%
+middle cancel which is very cool because
+we've just figured out that gn minus xgn
+
+ align:start position:0%
+we've just figured out that gn minus xgn
+ 
+
+ align:start position:0%
+we've just figured out that gn minus xgn
+is 1 minus
+
+ align:start position:0%
+is 1 minus
+ 
+
+ align:start position:0%
+is 1 minus
+x to the n plus 1. so we have this nice
+
+ align:start position:0%
+x to the n plus 1. so we have this nice
+ 
+
+ align:start position:0%
+x to the n plus 1. so we have this nice
+elegant formula now i can factor out gn
+
+ align:start position:0%
+elegant formula now i can factor out gn
+ 
+
+ align:start position:0%
+elegant formula now i can factor out gn
+and i get a gn times 1 minus x on the
+
+ align:start position:0%
+and i get a gn times 1 minus x on the
+ 
+
+ align:start position:0%
+and i get a gn times 1 minus x on the
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+and the result is that i get the gn is 1
+
+ align:start position:0%
+and the result is that i get the gn is 1
+ 
+
+ align:start position:0%
+and the result is that i get the gn is 1
+minus x to the n plus 1 over 1 minus x
+
+ align:start position:0%
+minus x to the n plus 1 over 1 minus x
+ 
+
+ align:start position:0%
+minus x to the n plus 1 over 1 minus x
+this is actually a formula that we
+
+ align:start position:0%
+this is actually a formula that we
+ 
+
+ align:start position:0%
+this is actually a formula that we
+proved before by induction but when we
+
+ align:start position:0%
+proved before by induction but when we
+ 
+
+ align:start position:0%
+proved before by induction but when we
+did it by induction there was no clue
+
+ align:start position:0%
+did it by induction there was no clue
+ 
+
+ align:start position:0%
+did it by induction there was no clue
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+who was the clever person to think of
+
+ align:start position:0%
+who was the clever person to think of
+ 
+
+ align:start position:0%
+who was the clever person to think of
+this formula now you know how that
+
+ align:start position:0%
+this formula now you know how that
+ 
+
+ align:start position:0%
+this formula now you know how that
+clever person uh found it and that's
+
+ align:start position:0%
+clever person uh found it and that's
+ 
+
+ align:start position:0%
+clever person uh found it and that's
+kind of a standard trick that we'll see
+
+ align:start position:0%
+kind of a standard trick that we'll see
+ 
+
+ align:start position:0%
+kind of a standard trick that we'll see
+more of when we look at generating
+
+ align:start position:0%
+more of when we look at generating
+ 
+
+ align:start position:0%
+more of when we look at generating
+functions but for now um it's a simple
+
+ align:start position:0%
+functions but for now um it's a simple
+ 
+
+ align:start position:0%
+functions but for now um it's a simple
+trick for getting a nice closed form for
+
+ align:start position:0%
+trick for getting a nice closed form for
+ 
+
+ align:start position:0%
+trick for getting a nice closed form for
+a sum we refer to as the perturbation
+
+ align:start position:0%
+a sum we refer to as the perturbation
+ 
+
+ align:start position:0%
+a sum we refer to as the perturbation
+method you take the sum you perturb it a
+
+ align:start position:0%
+method you take the sum you perturb it a
+ 
+
+ align:start position:0%
+method you take the sum you perturb it a
+little see how it relates to itself get
+
+ align:start position:0%
+little see how it relates to itself get
+ 
+
+ align:start position:0%
+little see how it relates to itself get
+an arithmetic relation and solve for a
+
+ align:start position:0%
+an arithmetic relation and solve for a
+ 
+
+ align:start position:0%
+an arithmetic relation and solve for a
+formula for the sum
+
+ align:start position:0%
+formula for the sum
+ 
+
+ align:start position:0%
+formula for the sum
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+a geometric series i use the word sum
+
+ align:start position:0%
+a geometric series i use the word sum
+ 
+
+ align:start position:0%
+a geometric series i use the word sum
+for a finite sum geometric series is
+
+ align:start position:0%
+for a finite sum geometric series is
+ 
+
+ align:start position:0%
+for a finite sum geometric series is
+when you take an infinite sum so the
+
+ align:start position:0%
+when you take an infinite sum so the
+ 
+
+ align:start position:0%
+when you take an infinite sum so the
+infinite geometric sum is the sum 1 plus
+
+ align:start position:0%
+infinite geometric sum is the sum 1 plus
+ 
+
+ align:start position:0%
+infinite geometric sum is the sum 1 plus
+x plus x squared x to the n and it keeps
+
+ align:start position:0%
+x plus x squared x to the n and it keeps
+ 
+
+ align:start position:0%
+x plus x squared x to the n and it keeps
+going it's the sum from i equals 0 to
+
+ align:start position:0%
+going it's the sum from i equals 0 to
+ 
+
+ align:start position:0%
+going it's the sum from i equals 0 to
+infinity of x to the i
+
+ align:start position:0%
+infinity of x to the i
+ 
+
+ align:start position:0%
+infinity of x to the i
+and there's a simple formula for that
+
+ align:start position:0%
+and there's a simple formula for that
+ 
+
+ align:start position:0%
+and there's a simple formula for that
+too it's even simpler actually because
+
+ align:start position:0%
+too it's even simpler actually because
+ 
+
+ align:start position:0%
+too it's even simpler actually because
+the definition of
+
+ align:start position:0%
+the definition of
+ 
+
+ align:start position:0%
+the definition of
+an infinite sum is it's the limit of the
+
+ align:start position:0%
+an infinite sum is it's the limit of the
+ 
+
+ align:start position:0%
+an infinite sum is it's the limit of the
+truncated sums it's the limit of the sum
+
+ align:start position:0%
+truncated sums it's the limit of the sum
+ 
+
+ align:start position:0%
+truncated sums it's the limit of the sum
+of the first n terms as n goes to
+
+ align:start position:0%
+of the first n terms as n goes to
+ 
+
+ align:start position:0%
+of the first n terms as n goes to
+infinity assuming that limit exists and
+
+ align:start position:0%
+infinity assuming that limit exists and
+ 
+
+ align:start position:0%
+infinity assuming that limit exists and
+so for uh the value of o of this
+
+ align:start position:0%
+so for uh the value of o of this
+ 
+
+ align:start position:0%
+so for uh the value of o of this
+infinite series is the limit of g n
+
+ align:start position:0%
+infinite series is the limit of g n
+ 
+
+ align:start position:0%
+infinite series is the limit of g n
+which is the sum up to n
+
+ align:start position:0%
+which is the sum up to n
+ 
+
+ align:start position:0%
+which is the sum up to n
+um and let's look at that well it's uh
+
+ align:start position:0%
+um and let's look at that well it's uh
+ 
+
+ align:start position:0%
+um and let's look at that well it's uh
+why it's g n is one minus x to the n
+
+ align:start position:0%
+why it's g n is one minus x to the n
+ 
+
+ align:start position:0%
+why it's g n is one minus x to the n
+plus one over one minus x so the limit
+
+ align:start position:0%
+plus one over one minus x so the limit
+ 
+
+ align:start position:0%
+plus one over one minus x so the limit
+of that the limits distribute past the
+
+ align:start position:0%
+of that the limits distribute past the
+ 
+
+ align:start position:0%
+of that the limits distribute past the
+one uh down to
+
+ align:start position:0%
+one uh down to
+ 
+
+ align:start position:0%
+one uh down to
+um and the x doesn't have an n in it so
+
+ align:start position:0%
+um and the x doesn't have an n in it so
+ 
+
+ align:start position:0%
+um and the x doesn't have an n in it so
+it winds up being um one minus the limit
+
+ align:start position:0%
+it winds up being um one minus the limit
+ 
+
+ align:start position:0%
+it winds up being um one minus the limit
+as n approaches infinity of x to the n
+
+ align:start position:0%
+as n approaches infinity of x to the n
+ 
+
+ align:start position:0%
+as n approaches infinity of x to the n
+plus one divided by one minus x and as
+
+ align:start position:0%
+plus one divided by one minus x and as
+ 
+
+ align:start position:0%
+plus one divided by one minus x and as
+long as x is less than one
+
+ align:start position:0%
+long as x is less than one
+ 
+
+ align:start position:0%
+long as x is less than one
+x to the n plus one is going to go to
+
+ align:start position:0%
+x to the n plus one is going to go to
+ 
+
+ align:start position:0%
+x to the n plus one is going to go to
+zero and i wind up with this nice simple
+
+ align:start position:0%
+zero and i wind up with this nice simple
+ 
+
+ align:start position:0%
+zero and i wind up with this nice simple
+formula that the uh infinite series uh
+
+ align:start position:0%
+formula that the uh infinite series uh
+ 
+
+ align:start position:0%
+formula that the uh infinite series uh
+the sum from i equals zero to infinity
+
+ align:start position:0%
+the sum from i equals zero to infinity
+ 
+
+ align:start position:0%
+the sum from i equals zero to infinity
+of x to the i is equal to one over one
+
+ align:start position:0%
+of x to the i is equal to one over one
+ 
+
+ align:start position:0%
+of x to the i is equal to one over one
+minus x
+
+ align:start position:0%
+minus x
+ 
+
+ align:start position:0%
+minus x
+providing that the magnitude of x is
+
+ align:start position:0%
+providing that the magnitude of x is
+ 
+
+ align:start position:0%
+providing that the magnitude of x is
+less than one okay that's the uh basics
+
+ align:start position:0%
+less than one okay that's the uh basics
+ 
+
+ align:start position:0%
+less than one okay that's the uh basics
+mathematical preliminaries of uh of
+
+ align:start position:0%
+mathematical preliminaries of uh of
+ 
+
+ align:start position:0%
+mathematical preliminaries of uh of
+geometric sums and geometric series now
+
+ align:start position:0%
+geometric sums and geometric series now
+ 
+
+ align:start position:0%
+geometric sums and geometric series now
+let's look at a typical application
+
+ align:start position:0%
+let's look at a typical application
+ 
+
+ align:start position:0%
+let's look at a typical application
+having to do with the future value of
+
+ align:start position:0%
+having to do with the future value of
+ 
+
+ align:start position:0%
+having to do with the future value of
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+suppose we want to make the following
+
+ align:start position:0%
+suppose we want to make the following
+ 
+
+ align:start position:0%
+suppose we want to make the following
+deal i promise i will pay you 100 in one
+
+ align:start position:0%
+deal i promise i will pay you 100 in one
+ 
+
+ align:start position:0%
+deal i promise i will pay you 100 in one
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+if you will pay me a fixed amount now
+
+ align:start position:0%
+if you will pay me a fixed amount now
+ 
+
+ align:start position:0%
+if you will pay me a fixed amount now
+so let's call it x dollars and the
+
+ align:start position:0%
+so let's call it x dollars and the
+ 
+
+ align:start position:0%
+so let's call it x dollars and the
+puzzle is
+
+ align:start position:0%
+puzzle is
+ 
+
+ align:start position:0%
+puzzle is
+how much money is a hundred dollars
+
+ align:start position:0%
+how much money is a hundred dollars
+ 
+
+ align:start position:0%
+how much money is a hundred dollars
+worth if you can't have it now you can
+
+ align:start position:0%
+worth if you can't have it now you can
+ 
+
+ align:start position:0%
+worth if you can't have it now you can
+only have it in one year it's worth x
+
+ align:start position:0%
+only have it in one year it's worth x
+ 
+
+ align:start position:0%
+only have it in one year it's worth x
+dollars how are we going to figure out
+
+ align:start position:0%
+dollars how are we going to figure out
+ 
+
+ align:start position:0%
+dollars how are we going to figure out
+what x should be what would be a fair
+
+ align:start position:0%
+what x should be what would be a fair
+ 
+
+ align:start position:0%
+what x should be what would be a fair
+amount for you to pay me so that i'm
+
+ align:start position:0%
+amount for you to pay me so that i'm
+ 
+
+ align:start position:0%
+amount for you to pay me so that i'm
+willing to pay you a hundred dollars in
+
+ align:start position:0%
+willing to pay you a hundred dollars in
+ 
+
+ align:start position:0%
+willing to pay you a hundred dollars in
+one year and it's fair nobody loses okay
+
+ align:start position:0%
+one year and it's fair nobody loses okay
+ 
+
+ align:start position:0%
+one year and it's fair nobody loses okay
+well here's the basic fact that is the
+
+ align:start position:0%
+well here's the basic fact that is the
+ 
+
+ align:start position:0%
+well here's the basic fact that is the
+basis for
+
+ align:start position:0%
+basis for
+ 
+
+ align:start position:0%
+basis for
+evaluating what the value of money in
+
+ align:start position:0%
+evaluating what the value of money in
+ 
+
+ align:start position:0%
+evaluating what the value of money in
+the future is is i'm going to assume
+
+ align:start position:0%
+the future is is i'm going to assume
+ 
+
+ align:start position:0%
+the future is is i'm going to assume
+that my bank will pay me 3 interest this
+
+ align:start position:0%
+that my bank will pay me 3 interest this
+ 
+
+ align:start position:0%
+that my bank will pay me 3 interest this
+is a generous bank in today's uh economy
+
+ align:start position:0%
+is a generous bank in today's uh economy
+ 
+
+ align:start position:0%
+is a generous bank in today's uh economy
+but it used to be a a stingy offer
+
+ align:start position:0%
+but it used to be a a stingy offer
+ 
+
+ align:start position:0%
+but it used to be a a stingy offer
+interest rates in my lifetime have
+
+ align:start position:0%
+interest rates in my lifetime have
+ 
+
+ align:start position:0%
+interest rates in my lifetime have
+ranged between about 17 a year down to
+
+ align:start position:0%
+ranged between about 17 a year down to
+ 
+
+ align:start position:0%
+ranged between about 17 a year down to
+uh less than one percent a year
+
+ align:start position:0%
+uh less than one percent a year
+ 
+
+ align:start position:0%
+uh less than one percent a year
+uh three percent a reasonable number to
+
+ align:start position:0%
+uh three percent a reasonable number to
+ 
+
+ align:start position:0%
+uh three percent a reasonable number to
+play with so let's suppose that my bank
+
+ align:start position:0%
+play with so let's suppose that my bank
+ 
+
+ align:start position:0%
+play with so let's suppose that my bank
+commits to paying me three percent
+
+ align:start position:0%
+commits to paying me three percent
+ 
+
+ align:start position:0%
+commits to paying me three percent
+interest uh on a deposit now that is to
+
+ align:start position:0%
+interest uh on a deposit now that is to
+ 
+
+ align:start position:0%
+interest uh on a deposit now that is to
+say uh let's define the bank rate b to
+
+ align:start position:0%
+say uh let's define the bank rate b to
+ 
+
+ align:start position:0%
+say uh let's define the bank rate b to
+be 1.03 and the deal is that the bank
+
+ align:start position:0%
+be 1.03 and the deal is that the bank
+ 
+
+ align:start position:0%
+be 1.03 and the deal is that the bank
+will increase the money that i have now
+
+ align:start position:0%
+will increase the money that i have now
+ 
+
+ align:start position:0%
+will increase the money that i have now
+by a factor of b in one year
+
+ align:start position:0%
+by a factor of b in one year
+ 
+
+ align:start position:0%
+by a factor of b in one year
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well so if i deposit your x dollars now
+
+ align:start position:0%
+well so if i deposit your x dollars now
+ 
+
+ align:start position:0%
+well so if i deposit your x dollars now
+i means i will have b times x dollars in
+
+ align:start position:0%
+i means i will have b times x dollars in
+ 
+
+ align:start position:0%
+i means i will have b times x dollars in
+one year
+
+ align:start position:0%
+one year
+ 
+
+ align:start position:0%
+one year
+okay assuming that the bank is
+
+ align:start position:0%
+okay assuming that the bank is
+ 
+
+ align:start position:0%
+okay assuming that the bank is
+completely reliable there's no risk
+
+ align:start position:0%
+completely reliable there's no risk
+ 
+
+ align:start position:0%
+completely reliable there's no risk
+there and it's and i get exactly b times
+
+ align:start position:0%
+there and it's and i get exactly b times
+ 
+
+ align:start position:0%
+there and it's and i get exactly b times
+x in one year then i won't lose any
+
+ align:start position:0%
+x in one year then i won't lose any
+ 
+
+ align:start position:0%
+x in one year then i won't lose any
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+providing that b times x is greater than
+
+ align:start position:0%
+providing that b times x is greater than
+ 
+
+ align:start position:0%
+providing that b times x is greater than
+or equal to 100. i need the x dollars
+
+ align:start position:0%
+or equal to 100. i need the x dollars
+ 
+
+ align:start position:0%
+or equal to 100. i need the x dollars
+you give me now to be worth the hundred
+
+ align:start position:0%
+you give me now to be worth the hundred
+ 
+
+ align:start position:0%
+you give me now to be worth the hundred
+dollars i'm supposed to pay you i'll
+
+ align:start position:0%
+dollars i'm supposed to pay you i'll
+ 
+
+ align:start position:0%
+dollars i'm supposed to pay you i'll
+come out ahead if bx is greater than or
+
+ align:start position:0%
+come out ahead if bx is greater than or
+ 
+
+ align:start position:0%
+come out ahead if bx is greater than or
+equal to 100. um
+
+ align:start position:0%
+equal to 100. um
+ 
+
+ align:start position:0%
+equal to 100. um
+i'll lose if it's less than 100 and it's
+
+ align:start position:0%
+i'll lose if it's less than 100 and it's
+ 
+
+ align:start position:0%
+i'll lose if it's less than 100 and it's
+a completely fair if bx is equal to 100.
+
+ align:start position:0%
+a completely fair if bx is equal to 100.
+ 
+
+ align:start position:0%
+a completely fair if bx is equal to 100.
+all right well that means that x is
+
+ align:start position:0%
+all right well that means that x is
+ 
+
+ align:start position:0%
+all right well that means that x is
+simply uh 100 over b which we decided
+
+ align:start position:0%
+simply uh 100 over b which we decided
+ 
+
+ align:start position:0%
+simply uh 100 over b which we decided
+was 1.03 9709 so a hundred dollars in
+
+ align:start position:0%
+was 1.03 9709 so a hundred dollars in
+ 
+
+ align:start position:0%
+was 1.03 9709 so a hundred dollars in
+one year
+
+ align:start position:0%
+one year
+ 
+
+ align:start position:0%
+one year
+is worth um
+
+ align:start position:0%
+is worth um
+ 
+
+ align:start position:0%
+is worth um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+97.
+
+ align:start position:0%
+97.
+ 
+
+ align:start position:0%
+97.
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+nine cents or normalizing to one dollar
+
+ align:start position:0%
+nine cents or normalizing to one dollar
+ 
+
+ align:start position:0%
+nine cents or normalizing to one dollar
+one dollar in one year is worth 97 cents
+
+ align:start position:0%
+one dollar in one year is worth 97 cents
+ 
+
+ align:start position:0%
+one dollar in one year is worth 97 cents
+essentially now
+
+ align:start position:0%
+essentially now
+ 
+
+ align:start position:0%
+essentially now
+well now we can shift perspective a
+
+ align:start position:0%
+well now we can shift perspective a
+ 
+
+ align:start position:0%
+well now we can shift perspective a
+little bit and think back a year
+
+ align:start position:0%
+little bit and think back a year
+ 
+
+ align:start position:0%
+little bit and think back a year
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+how much money did i need last year in
+
+ align:start position:0%
+how much money did i need last year in
+ 
+
+ align:start position:0%
+how much money did i need last year in
+order to be worth a dollar today well by
+
+ align:start position:0%
+order to be worth a dollar today well by
+ 
+
+ align:start position:0%
+order to be worth a dollar today well by
+the same reasoning the bank is going to
+
+ align:start position:0%
+the same reasoning the bank is going to
+ 
+
+ align:start position:0%
+the same reasoning the bank is going to
+pay me
+
+ align:start position:0%
+pay me
+ 
+
+ align:start position:0%
+pay me
+b times r today so i need b times r to
+
+ align:start position:0%
+b times r today so i need b times r to
+ 
+
+ align:start position:0%
+b times r today so i need b times r to
+equal a dollar in other words i r has
+
+ align:start position:0%
+equal a dollar in other words i r has
+ 
+
+ align:start position:0%
+equal a dollar in other words i r has
+got to be 1 over b r is one over the
+
+ align:start position:0%
+got to be 1 over b r is one over the
+ 
+
+ align:start position:0%
+got to be 1 over b r is one over the
+bank rate so a dollar a year ago is
+
+ align:start position:0%
+bank rate so a dollar a year ago is
+ 
+
+ align:start position:0%
+bank rate so a dollar a year ago is
+worth our dollars a year ago is worth a
+
+ align:start position:0%
+worth our dollars a year ago is worth a
+ 
+
+ align:start position:0%
+worth our dollars a year ago is worth a
+dollar today
+
+ align:start position:0%
+dollar today
+ 
+
+ align:start position:0%
+dollar today
+and by the same reasoning um
+
+ align:start position:0%
+and by the same reasoning um
+ 
+
+ align:start position:0%
+and by the same reasoning um
+uh n dollars paid in two years is worth
+
+ align:start position:0%
+uh n dollars paid in two years is worth
+ 
+
+ align:start position:0%
+uh n dollars paid in two years is worth
+n times r
+
+ align:start position:0%
+n times r
+ 
+
+ align:start position:0%
+n times r
+paid in one year which is worth n times
+
+ align:start position:0%
+paid in one year which is worth n times
+ 
+
+ align:start position:0%
+paid in one year which is worth n times
+r squared paid today paid today
+
+ align:start position:0%
+r squared paid today paid today
+ 
+
+ align:start position:0%
+r squared paid today paid today
+so i can iterate
+
+ align:start position:0%
+so i can iterate
+ 
+
+ align:start position:0%
+so i can iterate
+this bank of this one over bank rate
+
+ align:start position:0%
+this bank of this one over bank rate
+ 
+
+ align:start position:0%
+this bank of this one over bank rate
+factor and as time goes on uh k years
+
+ align:start position:0%
+factor and as time goes on uh k years
+ 
+
+ align:start position:0%
+factor and as time goes on uh k years
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+a value of n dollars paid in k years is
+
+ align:start position:0%
+a value of n dollars paid in k years is
+ 
+
+ align:start position:0%
+a value of n dollars paid in k years is
+worth
+
+ align:start position:0%
+worth
+ 
+
+ align:start position:0%
+worth
+n times r to the k today where r is one
+
+ align:start position:0%
+n times r to the k today where r is one
+ 
+
+ align:start position:0%
+n times r to the k today where r is one
+over the bank rate
+
+ align:start position:0%
+over the bank rate
+ 
+
+ align:start position:0%
+over the bank rate
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's good to know
+
+ align:start position:0%
+that's good to know
+ 
+
+ align:start position:0%
+that's good to know
+um let's think about annuities now an
+
+ align:start position:0%
+um let's think about annuities now an
+ 
+
+ align:start position:0%
+um let's think about annuities now an
+annuity is a contract that people buy
+
+ align:start position:0%
+annuity is a contract that people buy
+ 
+
+ align:start position:0%
+annuity is a contract that people buy
+to provide income for themselves without
+
+ align:start position:0%
+to provide income for themselves without
+ 
+
+ align:start position:0%
+to provide income for themselves without
+risk so they will make a deal typically
+
+ align:start position:0%
+risk so they will make a deal typically
+ 
+
+ align:start position:0%
+risk so they will make a deal typically
+with insurance company where they will
+
+ align:start position:0%
+with insurance company where they will
+ 
+
+ align:start position:0%
+with insurance company where they will
+pay a certain amount of money now to the
+
+ align:start position:0%
+pay a certain amount of money now to the
+ 
+
+ align:start position:0%
+pay a certain amount of money now to the
+insurance company and the insurance
+
+ align:start position:0%
+insurance company and the insurance
+ 
+
+ align:start position:0%
+insurance company and the insurance
+company promises to provide them a
+
+ align:start position:0%
+company promises to provide them a
+ 
+
+ align:start position:0%
+company promises to provide them a
+regular income sometimes for life or
+
+ align:start position:0%
+regular income sometimes for life or
+ 
+
+ align:start position:0%
+regular income sometimes for life or
+sometimes for a fixed period so let's
+
+ align:start position:0%
+sometimes for a fixed period so let's
+ 
+
+ align:start position:0%
+sometimes for a fixed period so let's
+look at an example i will pay you one
+
+ align:start position:0%
+look at an example i will pay you one
+ 
+
+ align:start position:0%
+look at an example i will pay you one
+hundred dollars a year for ten years
+
+ align:start position:0%
+hundred dollars a year for ten years
+ 
+
+ align:start position:0%
+hundred dollars a year for ten years
+if you will pay me a fixed premium what
+
+ align:start position:0%
+if you will pay me a fixed premium what
+ 
+
+ align:start position:0%
+if you will pay me a fixed premium what
+should it be so i'm i'm gonna promise as
+
+ align:start position:0%
+should it be so i'm i'm gonna promise as
+ 
+
+ align:start position:0%
+should it be so i'm i'm gonna promise as
+the insurance company to pay you one
+
+ align:start position:0%
+the insurance company to pay you one
+ 
+
+ align:start position:0%
+the insurance company to pay you one
+hundred dollars a year for ten years i
+
+ align:start position:0%
+hundred dollars a year for ten years i
+ 
+
+ align:start position:0%
+hundred dollars a year for ten years i
+want you to pay me a a premium of why
+
+ align:start position:0%
+want you to pay me a a premium of why
+ 
+
+ align:start position:0%
+want you to pay me a a premium of why
+dollars now how much should you pay
+
+ align:start position:0%
+dollars now how much should you pay
+ 
+
+ align:start position:0%
+dollars now how much should you pay
+well let's think about it
+
+ align:start position:0%
+well let's think about it
+ 
+
+ align:start position:0%
+well let's think about it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+one hundred dollars in one year is worth
+
+ align:start position:0%
+one hundred dollars in one year is worth
+ 
+
+ align:start position:0%
+one hundred dollars in one year is worth
+a hundred times r
+
+ align:start position:0%
+a hundred times r
+ 
+
+ align:start position:0%
+a hundred times r
+and one hundred dollars in two years is
+
+ align:start position:0%
+and one hundred dollars in two years is
+ 
+
+ align:start position:0%
+and one hundred dollars in two years is
+worth 100 times r squared and finally
+
+ align:start position:0%
+worth 100 times r squared and finally
+ 
+
+ align:start position:0%
+worth 100 times r squared and finally
+100 in 10 years is worth 100 times r to
+
+ align:start position:0%
+100 in 10 years is worth 100 times r to
+ 
+
+ align:start position:0%
+100 in 10 years is worth 100 times r to
+the 10th
+
+ align:start position:0%
+the 10th
+ 
+
+ align:start position:0%
+the 10th
+so this is the amount that i will have
+
+ align:start position:0%
+so this is the amount that i will have
+ 
+
+ align:start position:0%
+so this is the amount that i will have
+to pay you in today's dollars
+
+ align:start position:0%
+to pay you in today's dollars
+ 
+
+ align:start position:0%
+to pay you in today's dollars
+i need in order to be paying you 100 a
+
+ align:start position:0%
+i need in order to be paying you 100 a
+ 
+
+ align:start position:0%
+i need in order to be paying you 100 a
+year for ten years i need a total of
+
+ align:start position:0%
+year for ten years i need a total of
+ 
+
+ align:start position:0%
+year for ten years i need a total of
+this amount much amount of money now
+
+ align:start position:0%
+this amount much amount of money now
+ 
+
+ align:start position:0%
+this amount much amount of money now
+because each of these terms is the
+
+ align:start position:0%
+because each of these terms is the
+ 
+
+ align:start position:0%
+because each of these terms is the
+amount of money that the hundred dollars
+
+ align:start position:0%
+amount of money that the hundred dollars
+ 
+
+ align:start position:0%
+amount of money that the hundred dollars
+will be worth paid to you that many
+
+ align:start position:0%
+will be worth paid to you that many
+ 
+
+ align:start position:0%
+will be worth paid to you that many
+years out well look at this
+
+ align:start position:0%
+years out well look at this
+ 
+
+ align:start position:0%
+years out well look at this
+some if i factor out a hundred r
+
+ align:start position:0%
+some if i factor out a hundred r
+ 
+
+ align:start position:0%
+some if i factor out a hundred r
+i'm left with a hundred r times the
+
+ align:start position:0%
+i'm left with a hundred r times the
+ 
+
+ align:start position:0%
+i'm left with a hundred r times the
+geometric sum from one to r to the ninth
+
+ align:start position:0%
+geometric sum from one to r to the ninth
+ 
+
+ align:start position:0%
+geometric sum from one to r to the ninth
+where the base of the sum is r the
+
+ align:start position:0%
+where the base of the sum is r the
+ 
+
+ align:start position:0%
+where the base of the sum is r the
+factor is r well we have a nice formula
+
+ align:start position:0%
+factor is r well we have a nice formula
+ 
+
+ align:start position:0%
+factor is r well we have a nice formula
+for that
+
+ align:start position:0%
+for that
+ 
+
+ align:start position:0%
+for that
+it's simply 1 minus r to the 10th over 1
+
+ align:start position:0%
+it's simply 1 minus r to the 10th over 1
+ 
+
+ align:start position:0%
+it's simply 1 minus r to the 10th over 1
+minus r
+
+ align:start position:0%
+minus r
+ 
+
+ align:start position:0%
+minus r
+and now plugging in r equals 1 over 1.03
+
+ align:start position:0%
+and now plugging in r equals 1 over 1.03
+ 
+
+ align:start position:0%
+and now plugging in r equals 1 over 1.03
+i wind up with the conclusion that this
+
+ align:start position:0%
+i wind up with the conclusion that this
+ 
+
+ align:start position:0%
+i wind up with the conclusion that this
+annuity
+
+ align:start position:0%
+annuity
+ 
+
+ align:start position:0%
+annuity
+is worth
+
+ align:start position:0%
+is worth
+ 
+
+ align:start position:0%
+is worth
+dollars and 853.00 cents today
+
+ align:start position:0%
+dollars and 853.00 cents today
+ 
+
+ align:start position:0%
+dollars and 853.00 cents today
+my promise to pay you a thousand dollars
+
+ align:start position:0%
+my promise to pay you a thousand dollars
+ 
+
+ align:start position:0%
+my promise to pay you a thousand dollars
+but spread out over the next 11 years is
+
+ align:start position:0%
+but spread out over the next 11 years is
+ 
+
+ align:start position:0%
+but spread out over the next 11 years is
+worth
+
+ align:start position:0%
+worth
+ 
+
+ align:start position:0%
+worth
+853.2 cents today assuming that the bank
+
+ align:start position:0%
+853.2 cents today assuming that the bank
+ 
+
+ align:start position:0%
+853.2 cents today assuming that the bank
+rate is three percent a year
+
+ align:start position:0%
+rate is three percent a year
+ 
+
+ align:start position:0%
+rate is three percent a year
+and that's a typical case where um
+
+ align:start position:0%
+and that's a typical case where um
+ 
+
+ align:start position:0%
+and that's a typical case where um
+geometric series come up and you'll see
+
+ align:start position:0%
+geometric series come up and you'll see
+ 
+
+ align:start position:0%
+geometric series come up and you'll see
+other examples uh in problems just a
+
+ align:start position:0%
+other examples uh in problems just a
+ 
+
+ align:start position:0%
+other examples uh in problems just a
+quick thing to think about suppose that
+
+ align:start position:0%
+quick thing to think about suppose that
+ 
+
+ align:start position:0%
+quick thing to think about suppose that
+the bank rates uh rapidly increase
+
+ align:start position:0%
+the bank rates uh rapidly increase
+ 
+
+ align:start position:0%
+the bank rates uh rapidly increase
+unexpectedly increase the fed finally
+
+ align:start position:0%
+unexpectedly increase the fed finally
+ 
+
+ align:start position:0%
+unexpectedly increase the fed finally
+gets the economy moving and interest
+
+ align:start position:0%
+gets the economy moving and interest
+ 
+
+ align:start position:0%
+gets the economy moving and interest
+rates run up to five percent say
+
+ align:start position:0%
+rates run up to five percent say
+ 
+
+ align:start position:0%
+rates run up to five percent say
+what happens
+
+ align:start position:0%
+what happens
+ 
+
+ align:start position:0%
+what happens
+on this annuity you've already paid me
+
+ align:start position:0%
+on this annuity you've already paid me
+ 
+
+ align:start position:0%
+on this annuity you've already paid me
+the 853 and i've already committed to
+
+ align:start position:0%
+the 853 and i've already committed to
+ 
+
+ align:start position:0%
+the 853 and i've already committed to
+paying you 100 a year for the next 10
+
+ align:start position:0%
+paying you 100 a year for the next 10
+ 
+
+ align:start position:0%
+paying you 100 a year for the next 10
+years uh starting in a year who comes
+
+ align:start position:0%
+years uh starting in a year who comes
+ 
+
+ align:start position:0%
+years uh starting in a year who comes
+out ahead if bank if
+
+ align:start position:0%
+out ahead if bank if
+ 
+
+ align:start position:0%
+out ahead if bank if
+uh bank rates increase you come out
+
+ align:start position:0%
+uh bank rates increase you come out
+ 
+
+ align:start position:0%
+uh bank rates increase you come out
+ahead the deal stays fair or i come out
+
+ align:start position:0%
+ahead the deal stays fair or i come out
+ 
+
+ align:start position:0%
+ahead the deal stays fair or i come out
+ahead and i'll close by letting you
+
+ align:start position:0%
+ahead and i'll close by letting you
+ 
+
+ align:start position:0%
+ahead and i'll close by letting you
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+that question
\ No newline at end of file
diff --git a/ZQQiquqm7Ro.txt b/ZQQiquqm7Ro.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f2f974779d32ded03b05b4cb5f020494f734cd22
--- /dev/null
+++ b/ZQQiquqm7Ro.txt
@@ -0,0 +1,16939 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So today we're talking about uh the
+
+ align:start position:0%
+So today we're talking about uh the
+ 
+
+ align:start position:0%
+So today we're talking about uh the
+reception of Einstein's work from 1905
+
+ align:start position:0%
+reception of Einstein's work from 1905
+ 
+
+ align:start position:0%
+reception of Einstein's work from 1905
+on the electrodynamics moving body so
+
+ align:start position:0%
+on the electrodynamics moving body so
+ 
+
+ align:start position:0%
+on the electrodynamics moving body so
+we'll talk about the reception of what
+
+ align:start position:0%
+we'll talk about the reception of what
+ 
+
+ align:start position:0%
+we'll talk about the reception of what
+we have come to call the special theory
+
+ align:start position:0%
+we have come to call the special theory
+ 
+
+ align:start position:0%
+we have come to call the special theory
+of relativity
+
+ align:start position:0%
+of relativity
+ 
+
+ align:start position:0%
+of relativity
+so as a quick uh reminder we're gonna um
+
+ align:start position:0%
+so as a quick uh reminder we're gonna um
+ 
+
+ align:start position:0%
+so as a quick uh reminder we're gonna um
+sorry so excuse me the the class today
+
+ align:start position:0%
+sorry so excuse me the the class today
+ 
+
+ align:start position:0%
+sorry so excuse me the the class today
+has three main parts like they usually
+
+ align:start position:0%
+has three main parts like they usually
+ 
+
+ align:start position:0%
+has three main parts like they usually
+do we'll talk about some of the early
+
+ align:start position:0%
+do we'll talk about some of the early
+ 
+
+ align:start position:0%
+do we'll talk about some of the early
+reactions to Einstein himself and to
+
+ align:start position:0%
+reactions to Einstein himself and to
+ 
+
+ align:start position:0%
+reactions to Einstein himself and to
+this body of work and then we'll look at
+
+ align:start position:0%
+this body of work and then we'll look at
+ 
+
+ align:start position:0%
+this body of work and then we'll look at
+two specific examples of those reactions
+
+ align:start position:0%
+two specific examples of those reactions
+ 
+
+ align:start position:0%
+two specific examples of those reactions
+in a bit more detail get more of a sense
+
+ align:start position:0%
+in a bit more detail get more of a sense
+ 
+
+ align:start position:0%
+in a bit more detail get more of a sense
+of what ways where people could have
+
+ align:start position:0%
+of what ways where people could have
+ 
+
+ align:start position:0%
+of what ways where people could have
+engaging with Einstein's paper from 1905
+
+ align:start position:0%
+engaging with Einstein's paper from 1905
+ 
+
+ align:start position:0%
+engaging with Einstein's paper from 1905
+what did they think it was really about
+
+ align:start position:0%
+what did they think it was really about
+ 
+
+ align:start position:0%
+what did they think it was really about
+what do they get excited about what do
+
+ align:start position:0%
+what do they get excited about what do
+ 
+
+ align:start position:0%
+what do they get excited about what do
+they ignore that otherwise seem to have
+
+ align:start position:0%
+they ignore that otherwise seem to have
+ 
+
+ align:start position:0%
+they ignore that otherwise seem to have
+been really important to Einstein
+
+ align:start position:0%
+been really important to Einstein
+ 
+
+ align:start position:0%
+been really important to Einstein
+himself so we're going to talk about not
+
+ align:start position:0%
+himself so we're going to talk about not
+ 
+
+ align:start position:0%
+himself so we're going to talk about not
+just did people read the paper and make
+
+ align:start position:0%
+just did people read the paper and make
+ 
+
+ align:start position:0%
+just did people read the paper and make
+use of it but in what specific ways how
+
+ align:start position:0%
+use of it but in what specific ways how
+ 
+
+ align:start position:0%
+use of it but in what specific ways how
+would they kind of creatively making
+
+ align:start position:0%
+would they kind of creatively making
+ 
+
+ align:start position:0%
+would they kind of creatively making
+this work uh relevant from where they
+
+ align:start position:0%
+this work uh relevant from where they
+ 
+
+ align:start position:0%
+this work uh relevant from where they
+sat intellectually and institutionally
+
+ align:start position:0%
+sat intellectually and institutionally
+ 
+
+ align:start position:0%
+sat intellectually and institutionally
+and we'll see that sometimes that
+
+ align:start position:0%
+and we'll see that sometimes that
+ 
+
+ align:start position:0%
+and we'll see that sometimes that
+diverged sometimes in dramatic ways from
+
+ align:start position:0%
+diverged sometimes in dramatic ways from
+ 
+
+ align:start position:0%
+diverged sometimes in dramatic ways from
+what Einstein himself thought was most
+
+ align:start position:0%
+what Einstein himself thought was most
+ 
+
+ align:start position:0%
+what Einstein himself thought was most
+relevant or most interesting or most
+
+ align:start position:0%
+relevant or most interesting or most
+ 
+
+ align:start position:0%
+relevant or most interesting or most
+important about his own work and that's
+
+ align:start position:0%
+important about his own work and that's
+ 
+
+ align:start position:0%
+important about his own work and that's
+a theme again we've seen already a few
+
+ align:start position:0%
+a theme again we've seen already a few
+ 
+
+ align:start position:0%
+a theme again we've seen already a few
+times so far in this class different
+
+ align:start position:0%
+times so far in this class different
+ 
+
+ align:start position:0%
+times so far in this class different
+people engaging with Maxwell's equations
+
+ align:start position:0%
+people engaging with Maxwell's equations
+ 
+
+ align:start position:0%
+people engaging with Maxwell's equations
+in different ways
+
+ align:start position:0%
+in different ways
+ 
+
+ align:start position:0%
+in different ways
+it's a theme that we'll see really
+
+ align:start position:0%
+it's a theme that we'll see really
+ 
+
+ align:start position:0%
+it's a theme that we'll see really
+throughout the entire semester and
+
+ align:start position:0%
+throughout the entire semester and
+ 
+
+ align:start position:0%
+throughout the entire semester and
+here's a class I like I this is pretty
+
+ align:start position:0%
+here's a class I like I this is pretty
+ 
+
+ align:start position:0%
+here's a class I like I this is pretty
+fun material because I think we get to
+
+ align:start position:0%
+fun material because I think we get to
+ 
+
+ align:start position:0%
+fun material because I think we get to
+really sit with some examples in some
+
+ align:start position:0%
+really sit with some examples in some
+ 
+
+ align:start position:0%
+really sit with some examples in some
+detail and really watch people kind of
+
+ align:start position:0%
+detail and really watch people kind of
+ 
+
+ align:start position:0%
+detail and really watch people kind of
+wrestle with what was a fairly new
+
+ align:start position:0%
+wrestle with what was a fairly new
+ 
+
+ align:start position:0%
+wrestle with what was a fairly new
+material Einstein's paper from 1905.
+
+ align:start position:0%
+material Einstein's paper from 1905.
+ 
+
+ align:start position:0%
+material Einstein's paper from 1905.
+so just a reminder where what we cover
+
+ align:start position:0%
+so just a reminder where what we cover
+ 
+
+ align:start position:0%
+so just a reminder where what we cover
+in our previous discussion just on
+
+ align:start position:0%
+in our previous discussion just on
+ 
+
+ align:start position:0%
+in our previous discussion just on
+Monday
+
+ align:start position:0%
+Monday
+ 
+
+ align:start position:0%
+Monday
+Einstein had many different kind of
+
+ align:start position:0%
+Einstein had many different kind of
+ 
+
+ align:start position:0%
+Einstein had many different kind of
+threads that he brought together in this
+
+ align:start position:0%
+threads that he brought together in this
+ 
+
+ align:start position:0%
+threads that he brought together in this
+paper from 1905 entitled on the
+
+ align:start position:0%
+paper from 1905 entitled on the
+ 
+
+ align:start position:0%
+paper from 1905 entitled on the
+electronomics of moving bodies he was a
+
+ align:start position:0%
+electronomics of moving bodies he was a
+ 
+
+ align:start position:0%
+electronomics of moving bodies he was a
+recent college graduate he was working
+
+ align:start position:0%
+recent college graduate he was working
+ 
+
+ align:start position:0%
+recent college graduate he was working
+kind of off hours on his PhD thesis he
+
+ align:start position:0%
+kind of off hours on his PhD thesis he
+ 
+
+ align:start position:0%
+kind of off hours on his PhD thesis he
+had a full-time day job working at the
+
+ align:start position:0%
+had a full-time day job working at the
+ 
+
+ align:start position:0%
+had a full-time day job working at the
+patent office in Barron Switzerland at
+
+ align:start position:0%
+patent office in Barron Switzerland at
+ 
+
+ align:start position:0%
+patent office in Barron Switzerland at
+the lowest level entry-level job of
+
+ align:start position:0%
+the lowest level entry-level job of
+ 
+
+ align:start position:0%
+the lowest level entry-level job of
+patent office with third class and in
+
+ align:start position:0%
+patent office with third class and in
+ 
+
+ align:start position:0%
+patent office with third class and in
+the evenings he would hang out with his
+
+ align:start position:0%
+the evenings he would hang out with his
+ 
+
+ align:start position:0%
+the evenings he would hang out with his
+friends like um Laurie Sullivan and
+
+ align:start position:0%
+friends like um Laurie Sullivan and
+ 
+
+ align:start position:0%
+friends like um Laurie Sullivan and
+comrade had peaked and another friend uh
+
+ align:start position:0%
+comrade had peaked and another friend uh
+ 
+
+ align:start position:0%
+comrade had peaked and another friend uh
+Michelangelo besso and a small circle
+
+ align:start position:0%
+Michelangelo besso and a small circle
+ 
+
+ align:start position:0%
+Michelangelo besso and a small circle
+and they would read physics and
+
+ align:start position:0%
+and they would read physics and
+ 
+
+ align:start position:0%
+and they would read physics and
+philosophy together and they call
+
+ align:start position:0%
+philosophy together and they call
+ 
+
+ align:start position:0%
+philosophy together and they call
+themselves The Olympia Academy even
+
+ align:start position:0%
+themselves The Olympia Academy even
+ 
+
+ align:start position:0%
+themselves The Olympia Academy even
+though it was really just three recent
+
+ align:start position:0%
+though it was really just three recent
+ 
+
+ align:start position:0%
+though it was really just three recent
+graduates drinking beer in the in the
+
+ align:start position:0%
+graduates drinking beer in the in the
+ 
+
+ align:start position:0%
+graduates drinking beer in the in the
+pub talking about things like the work
+
+ align:start position:0%
+pub talking about things like the work
+ 
+
+ align:start position:0%
+pub talking about things like the work
+of Aaron's mock not a bad way to spend
+
+ align:start position:0%
+of Aaron's mock not a bad way to spend
+ 
+
+ align:start position:0%
+of Aaron's mock not a bad way to spend
+your time after college
+
+ align:start position:0%
+your time after college
+ 
+
+ align:start position:0%
+your time after college
+so one of the people that we're really
+
+ align:start position:0%
+so one of the people that we're really
+ 
+
+ align:start position:0%
+so one of the people that we're really
+interested in was Aaron's Mock and again
+
+ align:start position:0%
+interested in was Aaron's Mock and again
+ 
+
+ align:start position:0%
+interested in was Aaron's Mock and again
+we have this great reading um that was
+
+ align:start position:0%
+we have this great reading um that was
+ 
+
+ align:start position:0%
+we have this great reading um that was
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+um the canvas site I think designed for
+
+ align:start position:0%
+um the canvas site I think designed for
+ 
+
+ align:start position:0%
+um the canvas site I think designed for
+this for Mondays this past Monday's
+
+ align:start position:0%
+this for Mondays this past Monday's
+ 
+
+ align:start position:0%
+this for Mondays this past Monday's
+class by our own Amanda gafter one of
+
+ align:start position:0%
+class by our own Amanda gafter one of
+ 
+
+ align:start position:0%
+class by our own Amanda gafter one of
+our Tas who helps us really even more
+
+ align:start position:0%
+our Tas who helps us really even more
+ 
+
+ align:start position:0%
+our Tas who helps us really even more
+understand what was mock all about what
+
+ align:start position:0%
+understand what was mock all about what
+ 
+
+ align:start position:0%
+understand what was mock all about what
+did Einstein take from Mock's work and
+
+ align:start position:0%
+did Einstein take from Mock's work and
+ 
+
+ align:start position:0%
+did Einstein take from Mock's work and
+so I encourage you to go back and reread
+
+ align:start position:0%
+so I encourage you to go back and reread
+ 
+
+ align:start position:0%
+so I encourage you to go back and reread
+Amanda's piece as well
+
+ align:start position:0%
+Amanda's piece as well
+ 
+
+ align:start position:0%
+Amanda's piece as well
+so Aaron's mock was his Viennese
+
+ align:start position:0%
+so Aaron's mock was his Viennese
+ 
+
+ align:start position:0%
+so Aaron's mock was his Viennese
+polymath who introduced this philosophy
+
+ align:start position:0%
+polymath who introduced this philosophy
+ 
+
+ align:start position:0%
+polymath who introduced this philosophy
+of science in the later years of the
+
+ align:start position:0%
+of science in the later years of the
+ 
+
+ align:start position:0%
+of science in the later years of the
+19th century uh really during kind of
+
+ align:start position:0%
+19th century uh really during kind of
+ 
+
+ align:start position:0%
+19th century uh really during kind of
+Einstein's childhood
+
+ align:start position:0%
+Einstein's childhood
+ 
+
+ align:start position:0%
+Einstein's childhood
+they came to be called positivism as far
+
+ align:start position:0%
+they came to be called positivism as far
+ 
+
+ align:start position:0%
+they came to be called positivism as far
+as ants Mark was concerned the only the
+
+ align:start position:0%
+as ants Mark was concerned the only the
+ 
+
+ align:start position:0%
+as ants Mark was concerned the only the
+best way to make progress scientifically
+
+ align:start position:0%
+best way to make progress scientifically
+ 
+
+ align:start position:0%
+best way to make progress scientifically
+was to focus on objects of positive
+
+ align:start position:0%
+was to focus on objects of positive
+ 
+
+ align:start position:0%
+was to focus on objects of positive
+experience that's where the positivism
+
+ align:start position:0%
+experience that's where the positivism
+ 
+
+ align:start position:0%
+experience that's where the positivism
+comes from things we could really
+
+ align:start position:0%
+comes from things we could really
+ 
+
+ align:start position:0%
+comes from things we could really
+concretely observe or measure and not
+
+ align:start position:0%
+concretely observe or measure and not
+ 
+
+ align:start position:0%
+concretely observe or measure and not
+focus on things that could never even in
+
+ align:start position:0%
+focus on things that could never even in
+ 
+
+ align:start position:0%
+focus on things that could never even in
+principle be subject to these kind of
+
+ align:start position:0%
+principle be subject to these kind of
+ 
+
+ align:start position:0%
+principle be subject to these kind of
+empirical inputs so we have this
+
+ align:start position:0%
+empirical inputs so we have this
+ 
+
+ align:start position:0%
+empirical inputs so we have this
+extensive often very biting very very uh
+
+ align:start position:0%
+extensive often very biting very very uh
+ 
+
+ align:start position:0%
+extensive often very biting very very uh
+very you know uh
+
+ align:start position:0%
+very you know uh
+ 
+
+ align:start position:0%
+very you know uh
+significant critique of Newtonian
+
+ align:start position:0%
+significant critique of Newtonian
+ 
+
+ align:start position:0%
+significant critique of Newtonian
+physics which Mark was as far as Mark
+
+ align:start position:0%
+physics which Mark was as far as Mark
+ 
+
+ align:start position:0%
+physics which Mark was as far as Mark
+was concerned was like riddled with
+
+ align:start position:0%
+was concerned was like riddled with
+ 
+
+ align:start position:0%
+was concerned was like riddled with
+these things that could never ever
+
+ align:start position:0%
+these things that could never ever
+ 
+
+ align:start position:0%
+these things that could never ever
+become objects of positive experience
+
+ align:start position:0%
+become objects of positive experience
+ 
+
+ align:start position:0%
+become objects of positive experience
+and that really was very very inspiring
+
+ align:start position:0%
+and that really was very very inspiring
+ 
+
+ align:start position:0%
+and that really was very very inspiring
+for Young Einstein and his circle of
+
+ align:start position:0%
+for Young Einstein and his circle of
+ 
+
+ align:start position:0%
+for Young Einstein and his circle of
+friends so one of the lessons that
+
+ align:start position:0%
+friends so one of the lessons that
+ 
+
+ align:start position:0%
+friends so one of the lessons that
+Einstein took from that among several
+
+ align:start position:0%
+Einstein took from that among several
+ 
+
+ align:start position:0%
+Einstein took from that among several
+in these years leading up to around 1905
+
+ align:start position:0%
+in these years leading up to around 1905
+ 
+
+ align:start position:0%
+in these years leading up to around 1905
+was that it would make sense to focus on
+
+ align:start position:0%
+was that it would make sense to focus on
+ 
+
+ align:start position:0%
+was that it would make sense to focus on
+kinematics the the motion of objects
+
+ align:start position:0%
+kinematics the the motion of objects
+ 
+
+ align:start position:0%
+kinematics the the motion of objects
+through space and time things we could
+
+ align:start position:0%
+through space and time things we could
+ 
+
+ align:start position:0%
+through space and time things we could
+at least in principle really measure and
+
+ align:start position:0%
+at least in principle really measure and
+ 
+
+ align:start position:0%
+at least in principle really measure and
+observe rather than starting our inquiry
+
+ align:start position:0%
+observe rather than starting our inquiry
+ 
+
+ align:start position:0%
+observe rather than starting our inquiry
+with Dynamics the study of forces that
+
+ align:start position:0%
+with Dynamics the study of forces that
+ 
+
+ align:start position:0%
+with Dynamics the study of forces that
+was really turning on its head would
+
+ align:start position:0%
+was really turning on its head would
+ 
+
+ align:start position:0%
+was really turning on its head would
+have become quite a standard way to
+
+ align:start position:0%
+have become quite a standard way to
+ 
+
+ align:start position:0%
+have become quite a standard way to
+approach topics like electrodynamics we
+
+ align:start position:0%
+approach topics like electrodynamics we
+ 
+
+ align:start position:0%
+approach topics like electrodynamics we
+saw when Hendrick Lorenz considered
+
+ align:start position:0%
+saw when Hendrick Lorenz considered
+ 
+
+ align:start position:0%
+saw when Hendrick Lorenz considered
+electronomics he would start with the
+
+ align:start position:0%
+electronomics he would start with the
+ 
+
+ align:start position:0%
+electronomics he would start with the
+forces exerted by The Ether on objects
+
+ align:start position:0%
+forces exerted by The Ether on objects
+ 
+
+ align:start position:0%
+forces exerted by The Ether on objects
+and so on Einstein said let's start with
+
+ align:start position:0%
+and so on Einstein said let's start with
+ 
+
+ align:start position:0%
+and so on Einstein said let's start with
+kinematics first it was that kind of
+
+ align:start position:0%
+kinematics first it was that kind of
+ 
+
+ align:start position:0%
+kinematics first it was that kind of
+thinking that led him to postulate these
+
+ align:start position:0%
+thinking that led him to postulate these
+ 
+
+ align:start position:0%
+thinking that led him to postulate these
+opening postulates in his 1905 paper
+
+ align:start position:0%
+opening postulates in his 1905 paper
+ 
+
+ align:start position:0%
+opening postulates in his 1905 paper
+which hopefully is now quite familiar to
+
+ align:start position:0%
+which hopefully is now quite familiar to
+ 
+
+ align:start position:0%
+which hopefully is now quite familiar to
+you in these opening few pages this is
+
+ align:start position:0%
+you in these opening few pages this is
+ 
+
+ align:start position:0%
+you in these opening few pages this is
+the subject for your first paper
+
+ align:start position:0%
+the subject for your first paper
+ 
+
+ align:start position:0%
+the subject for your first paper
+assignment
+
+ align:start position:0%
+assignment
+ 
+
+ align:start position:0%
+assignment
+and to to paraphrase these two passwords
+
+ align:start position:0%
+and to to paraphrase these two passwords
+ 
+
+ align:start position:0%
+and to to paraphrase these two passwords
+that Einstein elevates in those opening
+
+ align:start position:0%
+that Einstein elevates in those opening
+ 
+
+ align:start position:0%
+that Einstein elevates in those opening
+paragraphs the first is a kind of
+
+ align:start position:0%
+paragraphs the first is a kind of
+ 
+
+ align:start position:0%
+paragraphs the first is a kind of
+extension or generalization of an idea
+
+ align:start position:0%
+extension or generalization of an idea
+ 
+
+ align:start position:0%
+extension or generalization of an idea
+that was actually centuries old by this
+
+ align:start position:0%
+that was actually centuries old by this
+ 
+
+ align:start position:0%
+that was actually centuries old by this
+point he was really building on
+
+ align:start position:0%
+point he was really building on
+ 
+
+ align:start position:0%
+point he was really building on
+Galileo's work and Einstein says not
+
+ align:start position:0%
+Galileo's work and Einstein says not
+ 
+
+ align:start position:0%
+Galileo's work and Einstein says not
+only should the laws of mechanics be
+
+ align:start position:0%
+only should the laws of mechanics be
+ 
+
+ align:start position:0%
+only should the laws of mechanics be
+valid for any Observer who's moving at a
+
+ align:start position:0%
+valid for any Observer who's moving at a
+ 
+
+ align:start position:0%
+valid for any Observer who's moving at a
+constant speed as long as they're not
+
+ align:start position:0%
+constant speed as long as they're not
+ 
+
+ align:start position:0%
+constant speed as long as they're not
+speeding up or slowing down they're not
+
+ align:start position:0%
+speeding up or slowing down they're not
+ 
+
+ align:start position:0%
+speeding up or slowing down they're not
+accelerating then all the laws and
+
+ align:start position:0%
+accelerating then all the laws and
+ 
+
+ align:start position:0%
+accelerating then all the laws and
+mechanics or ballistics of you know a a
+
+ align:start position:0%
+mechanics or ballistics of you know a a
+ 
+
+ align:start position:0%
+mechanics or ballistics of you know a a
+ball you might toss and play catch all
+
+ align:start position:0%
+ball you might toss and play catch all
+ 
+
+ align:start position:0%
+ball you might toss and play catch all
+those laws are valid whether you're on a
+
+ align:start position:0%
+those laws are valid whether you're on a
+ 
+
+ align:start position:0%
+those laws are valid whether you're on a
+boat moving at a constant speed down the
+
+ align:start position:0%
+boat moving at a constant speed down the
+ 
+
+ align:start position:0%
+boat moving at a constant speed down the
+river or standing still on the on the
+
+ align:start position:0%
+river or standing still on the on the
+ 
+
+ align:start position:0%
+river or standing still on the on the
+shore Einstein says that's true that
+
+ align:start position:0%
+shore Einstein says that's true that
+ 
+
+ align:start position:0%
+shore Einstein says that's true that
+should be true for all of physics for
+
+ align:start position:0%
+should be true for all of physics for
+ 
+
+ align:start position:0%
+should be true for all of physics for
+electricity for magnesium for optics for
+
+ align:start position:0%
+electricity for magnesium for optics for
+ 
+
+ align:start position:0%
+electricity for magnesium for optics for
+thermodynamics so part one is kind of
+
+ align:start position:0%
+thermodynamics so part one is kind of
+ 
+
+ align:start position:0%
+thermodynamics so part one is kind of
+elevating or generalizing what was
+
+ align:start position:0%
+elevating or generalizing what was
+ 
+
+ align:start position:0%
+elevating or generalizing what was
+already a fairly familiar notion to many
+
+ align:start position:0%
+already a fairly familiar notion to many
+ 
+
+ align:start position:0%
+already a fairly familiar notion to many
+many physicists and part two at least at
+
+ align:start position:0%
+many physicists and part two at least at
+ 
+
+ align:start position:0%
+many physicists and part two at least at
+first he says looks apparently
+
+ align:start position:0%
+first he says looks apparently
+ 
+
+ align:start position:0%
+first he says looks apparently
+irreconcilable with the first the second
+
+ align:start position:0%
+irreconcilable with the first the second
+ 
+
+ align:start position:0%
+irreconcilable with the first the second
+postulate according to Einstein is that
+
+ align:start position:0%
+postulate according to Einstein is that
+ 
+
+ align:start position:0%
+postulate according to Einstein is that
+the speed of light C is a con constant
+
+ align:start position:0%
+the speed of light C is a con constant
+ 
+
+ align:start position:0%
+the speed of light C is a con constant
+independent of the motion of the source
+
+ align:start position:0%
+independent of the motion of the source
+ 
+
+ align:start position:0%
+independent of the motion of the source
+and he had we now know he came to that
+
+ align:start position:0%
+and he had we now know he came to that
+ 
+
+ align:start position:0%
+and he had we now know he came to that
+in his own kind of private thinking or
+
+ align:start position:0%
+in his own kind of private thinking or
+ 
+
+ align:start position:0%
+in his own kind of private thinking or
+in talking with a small circle of
+
+ align:start position:0%
+in talking with a small circle of
+ 
+
+ align:start position:0%
+in talking with a small circle of
+friends by a series of these thought
+
+ align:start position:0%
+friends by a series of these thought
+ 
+
+ align:start position:0%
+friends by a series of these thought
+experiments like what would it be like
+
+ align:start position:0%
+experiments like what would it be like
+ 
+
+ align:start position:0%
+experiments like what would it be like
+if you could catch up to a light wave
+
+ align:start position:0%
+if you could catch up to a light wave
+ 
+
+ align:start position:0%
+if you could catch up to a light wave
+like this Surfer riding at the same
+
+ align:start position:0%
+like this Surfer riding at the same
+ 
+
+ align:start position:0%
+like this Surfer riding at the same
+speed as the ocean wave you would see
+
+ align:start position:0%
+speed as the ocean wave you would see
+ 
+
+ align:start position:0%
+speed as the ocean wave you would see
+this frozen field configuration which
+
+ align:start position:0%
+this frozen field configuration which
+ 
+
+ align:start position:0%
+this frozen field configuration which
+Einstein was convinced could never
+
+ align:start position:0%
+Einstein was convinced could never
+ 
+
+ align:start position:0%
+Einstein was convinced could never
+really happen so how do you make sure no
+
+ align:start position:0%
+really happen so how do you make sure no
+ 
+
+ align:start position:0%
+really happen so how do you make sure no
+one gets caught in that absurdity make
+
+ align:start position:0%
+one gets caught in that absurdity make
+ 
+
+ align:start position:0%
+one gets caught in that absurdity make
+sure no one can ever catch up to a light
+
+ align:start position:0%
+sure no one can ever catch up to a light
+ 
+
+ align:start position:0%
+sure no one can ever catch up to a light
+wave who have lights always going to
+
+ align:start position:0%
+wave who have lights always going to
+ 
+
+ align:start position:0%
+wave who have lights always going to
+travel at a fixed speed no matter how
+
+ align:start position:0%
+travel at a fixed speed no matter how
+ 
+
+ align:start position:0%
+travel at a fixed speed no matter how
+fast you're chasing after it if I'm on a
+
+ align:start position:0%
+fast you're chasing after it if I'm on a
+ 
+
+ align:start position:0%
+fast you're chasing after it if I'm on a
+supersonic Jet Plane
+
+ align:start position:0%
+supersonic Jet Plane
+ 
+
+ align:start position:0%
+supersonic Jet Plane
+I'm still going to see the light wave
+
+ align:start position:0%
+I'm still going to see the light wave
+ 
+
+ align:start position:0%
+I'm still going to see the light wave
+travel past me at this fixed speed of
+
+ align:start position:0%
+travel past me at this fixed speed of
+ 
+
+ align:start position:0%
+travel past me at this fixed speed of
+light that no matter what you know fancy
+
+ align:start position:0%
+light that no matter what you know fancy
+ 
+
+ align:start position:0%
+light that no matter what you know fancy
+engines I soup up on my on my means of
+
+ align:start position:0%
+engines I soup up on my on my means of
+ 
+
+ align:start position:0%
+engines I soup up on my on my means of
+transportation I will never ever be like
+
+ align:start position:0%
+transportation I will never ever be like
+ 
+
+ align:start position:0%
+transportation I will never ever be like
+this Surfer I will never catch up to and
+
+ align:start position:0%
+this Surfer I will never catch up to and
+ 
+
+ align:start position:0%
+this Surfer I will never catch up to and
+move at the same speed as that light
+
+ align:start position:0%
+move at the same speed as that light
+ 
+
+ align:start position:0%
+move at the same speed as that light
+wave and that was Einstein considered
+
+ align:start position:0%
+wave and that was Einstein considered
+ 
+
+ align:start position:0%
+wave and that was Einstein considered
+really Central as a posture he doesn't
+
+ align:start position:0%
+really Central as a posture he doesn't
+ 
+
+ align:start position:0%
+really Central as a posture he doesn't
+prove it he doesn't even really motivate
+
+ align:start position:0%
+prove it he doesn't even really motivate
+ 
+
+ align:start position:0%
+prove it he doesn't even really motivate
+it in this paper very strongly he
+
+ align:start position:0%
+it in this paper very strongly he
+ 
+
+ align:start position:0%
+it in this paper very strongly he
+elevates it to an assumption and sees
+
+ align:start position:0%
+elevates it to an assumption and sees
+ 
+
+ align:start position:0%
+elevates it to an assumption and sees
+what will follow
+
+ align:start position:0%
+what will follow
+ 
+
+ align:start position:0%
+what will follow
+and then it's from those starting
+
+ align:start position:0%
+and then it's from those starting
+ 
+
+ align:start position:0%
+and then it's from those starting
+postulates where again just in the
+
+ align:start position:0%
+postulates where again just in the
+ 
+
+ align:start position:0%
+postulates where again just in the
+opening few pages of this article where
+
+ align:start position:0%
+opening few pages of this article where
+ 
+
+ align:start position:0%
+opening few pages of this article where
+he comes to what he calls the relativity
+
+ align:start position:0%
+he comes to what he calls the relativity
+ 
+
+ align:start position:0%
+he comes to what he calls the relativity
+of simultaneity that events that that we
+
+ align:start position:0%
+of simultaneity that events that that we
+ 
+
+ align:start position:0%
+of simultaneity that events that that we
+might consider to have happened at the
+
+ align:start position:0%
+might consider to have happened at the
+ 
+
+ align:start position:0%
+might consider to have happened at the
+same time to have been simultaneous will
+
+ align:start position:0%
+same time to have been simultaneous will
+ 
+
+ align:start position:0%
+same time to have been simultaneous will
+not appear to have been simultaneous to
+
+ align:start position:0%
+not appear to have been simultaneous to
+ 
+
+ align:start position:0%
+not appear to have been simultaneous to
+emotion to an observer who is otherwise
+
+ align:start position:0%
+emotion to an observer who is otherwise
+ 
+
+ align:start position:0%
+emotion to an observer who is otherwise
+fully legitimate meaning all the laws of
+
+ align:start position:0%
+fully legitimate meaning all the laws of
+ 
+
+ align:start position:0%
+fully legitimate meaning all the laws of
+physics should hold perfectly valid for
+
+ align:start position:0%
+physics should hold perfectly valid for
+ 
+
+ align:start position:0%
+physics should hold perfectly valid for
+her she just happens to be moving at
+
+ align:start position:0%
+her she just happens to be moving at
+ 
+
+ align:start position:0%
+her she just happens to be moving at
+some constant speed with respect to us
+
+ align:start position:0%
+some constant speed with respect to us
+ 
+
+ align:start position:0%
+some constant speed with respect to us
+we will disagree on what counts as
+
+ align:start position:0%
+we will disagree on what counts as
+ 
+
+ align:start position:0%
+we will disagree on what counts as
+simultaneous
+
+ align:start position:0%
+simultaneous
+ 
+
+ align:start position:0%
+simultaneous
+and from that from that Einstein was
+
+ align:start position:0%
+and from that from that Einstein was
+ 
+
+ align:start position:0%
+and from that from that Einstein was
+convinced would lead uh these other
+
+ align:start position:0%
+convinced would lead uh these other
+ 
+
+ align:start position:0%
+convinced would lead uh these other
+phenomena like length contraction and
+
+ align:start position:0%
+phenomena like length contraction and
+ 
+
+ align:start position:0%
+phenomena like length contraction and
+time dilation not because of forces
+
+ align:start position:0%
+time dilation not because of forces
+ 
+
+ align:start position:0%
+time dilation not because of forces
+exerted by an ether but because we
+
+ align:start position:0%
+exerted by an ether but because we
+ 
+
+ align:start position:0%
+exerted by an ether but because we
+disagree on when to implement our
+
+ align:start position:0%
+disagree on when to implement our
+ 
+
+ align:start position:0%
+disagree on when to implement our
+measurements because we disagree on what
+
+ align:start position:0%
+measurements because we disagree on what
+ 
+
+ align:start position:0%
+measurements because we disagree on what
+counts as simultaneous events and that
+
+ align:start position:0%
+counts as simultaneous events and that
+ 
+
+ align:start position:0%
+counts as simultaneous events and that
+comes for him come from starting with
+
+ align:start position:0%
+comes for him come from starting with
+ 
+
+ align:start position:0%
+comes for him come from starting with
+kinematics not Dynamics and again that's
+
+ align:start position:0%
+kinematics not Dynamics and again that's
+ 
+
+ align:start position:0%
+kinematics not Dynamics and again that's
+the the form of reasoning that Einstein
+
+ align:start position:0%
+the the form of reasoning that Einstein
+ 
+
+ align:start position:0%
+the the form of reasoning that Einstein
+puts in those uh those opening pages of
+
+ align:start position:0%
+puts in those uh those opening pages of
+ 
+
+ align:start position:0%
+puts in those uh those opening pages of
+his paper from 1905. okay
+
+ align:start position:0%
+his paper from 1905. okay
+ 
+
+ align:start position:0%
+his paper from 1905. okay
+so what were the early reactions to that
+
+ align:start position:0%
+so what were the early reactions to that
+ 
+
+ align:start position:0%
+so what were the early reactions to that
+body of work remember it was published
+
+ align:start position:0%
+body of work remember it was published
+ 
+
+ align:start position:0%
+body of work remember it was published
+in really the leading or certainly one
+
+ align:start position:0%
+in really the leading or certainly one
+ 
+
+ align:start position:0%
+in really the leading or certainly one
+of the leading journals in Western
+
+ align:start position:0%
+of the leading journals in Western
+ 
+
+ align:start position:0%
+of the leading journals in Western
+Europe for professional physicists it
+
+ align:start position:0%
+Europe for professional physicists it
+ 
+
+ align:start position:0%
+Europe for professional physicists it
+was it was a perfect uh venue to try to
+
+ align:start position:0%
+was it was a perfect uh venue to try to
+ 
+
+ align:start position:0%
+was it was a perfect uh venue to try to
+get some attention and yet we now know
+
+ align:start position:0%
+get some attention and yet we now know
+ 
+
+ align:start position:0%
+get some attention and yet we now know
+historically the first reaction was no
+
+ align:start position:0%
+historically the first reaction was no
+ 
+
+ align:start position:0%
+historically the first reaction was no
+reaction at all the kind of Baseline
+
+ align:start position:0%
+reaction at all the kind of Baseline
+ 
+
+ align:start position:0%
+reaction at all the kind of Baseline
+summary for today's class is no one paid
+
+ align:start position:0%
+summary for today's class is no one paid
+ 
+
+ align:start position:0%
+summary for today's class is no one paid
+attention to very few people paid
+
+ align:start position:0%
+attention to very few people paid
+ 
+
+ align:start position:0%
+attention to very few people paid
+attention we now know Einstein's name we
+
+ align:start position:0%
+attention we now know Einstein's name we
+ 
+
+ align:start position:0%
+attention we now know Einstein's name we
+might own Einstein's swag you know
+
+ align:start position:0%
+might own Einstein's swag you know
+ 
+
+ align:start position:0%
+might own Einstein's swag you know
+t-shirts and coffee mugs bumper stickers
+
+ align:start position:0%
+t-shirts and coffee mugs bumper stickers
+ 
+
+ align:start position:0%
+t-shirts and coffee mugs bumper stickers
+uh that simply was not the case in 1905
+
+ align:start position:0%
+uh that simply was not the case in 1905
+ 
+
+ align:start position:0%
+uh that simply was not the case in 1905
+or 1906 or 1907 it really was quite a
+
+ align:start position:0%
+or 1906 or 1907 it really was quite a
+ 
+
+ align:start position:0%
+or 1906 or 1907 it really was quite a
+delay so at the time Einstein as we saw
+
+ align:start position:0%
+delay so at the time Einstein as we saw
+ 
+
+ align:start position:0%
+delay so at the time Einstein as we saw
+was this really little-known patent
+
+ align:start position:0%
+was this really little-known patent
+ 
+
+ align:start position:0%
+was this really little-known patent
+clerk he was not employed as a research
+
+ align:start position:0%
+clerk he was not employed as a research
+ 
+
+ align:start position:0%
+clerk he was not employed as a research
+scientist he was not teaching in a
+
+ align:start position:0%
+scientist he was not teaching in a
+ 
+
+ align:start position:0%
+scientist he was not teaching in a
+university that that had been his
+
+ align:start position:0%
+university that that had been his
+ 
+
+ align:start position:0%
+university that that had been his
+ambition he just was not able to get
+
+ align:start position:0%
+ambition he just was not able to get
+ 
+
+ align:start position:0%
+ambition he just was not able to get
+that kind of job at first
+
+ align:start position:0%
+that kind of job at first
+ 
+
+ align:start position:0%
+that kind of job at first
+he was publishing before then perfectly
+
+ align:start position:0%
+he was publishing before then perfectly
+ 
+
+ align:start position:0%
+he was publishing before then perfectly
+adequate not very special articles on
+
+ align:start position:0%
+adequate not very special articles on
+ 
+
+ align:start position:0%
+adequate not very special articles on
+other topics in the main Journal he was
+
+ align:start position:0%
+other topics in the main Journal he was
+ 
+
+ align:start position:0%
+other topics in the main Journal he was
+building up a kind of portfolio of
+
+ align:start position:0%
+building up a kind of portfolio of
+ 
+
+ align:start position:0%
+building up a kind of portfolio of
+perfectly competent not very
+
+ align:start position:0%
+perfectly competent not very
+ 
+
+ align:start position:0%
+perfectly competent not very
+earth-shattering work so no one was like
+
+ align:start position:0%
+earth-shattering work so no one was like
+ 
+
+ align:start position:0%
+earth-shattering work so no one was like
+hanging on you know waiting at their
+
+ align:start position:0%
+hanging on you know waiting at their
+ 
+
+ align:start position:0%
+hanging on you know waiting at their
+mailbox to get the latest issue of the
+
+ align:start position:0%
+mailbox to get the latest issue of the
+ 
+
+ align:start position:0%
+mailbox to get the latest issue of the
+journal to see what Einstein had done
+
+ align:start position:0%
+journal to see what Einstein had done
+ 
+
+ align:start position:0%
+journal to see what Einstein had done
+lately very few people noticed anything
+
+ align:start position:0%
+lately very few people noticed anything
+ 
+
+ align:start position:0%
+lately very few people noticed anything
+at all
+
+ align:start position:0%
+at all
+ 
+
+ align:start position:0%
+at all
+so what I this next point I I is one of
+
+ align:start position:0%
+so what I this next point I I is one of
+ 
+
+ align:start position:0%
+so what I this next point I I is one of
+my favorites not only did Einstein still
+
+ align:start position:0%
+my favorites not only did Einstein still
+ 
+
+ align:start position:0%
+my favorites not only did Einstein still
+not get the kind of job he had most
+
+ align:start position:0%
+not get the kind of job he had most
+ 
+
+ align:start position:0%
+not get the kind of job he had most
+wanted an academic position he didn't
+
+ align:start position:0%
+wanted an academic position he didn't
+ 
+
+ align:start position:0%
+wanted an academic position he didn't
+even get a raise or promotion at his
+
+ align:start position:0%
+even get a raise or promotion at his
+ 
+
+ align:start position:0%
+even get a raise or promotion at his
+current job he was he remained a patent
+
+ align:start position:0%
+current job he was he remained a patent
+ 
+
+ align:start position:0%
+current job he was he remained a patent
+clerk third class even after publishing
+
+ align:start position:0%
+clerk third class even after publishing
+ 
+
+ align:start position:0%
+clerk third class even after publishing
+all of these articles even in the space
+
+ align:start position:0%
+all of these articles even in the space
+ 
+
+ align:start position:0%
+all of these articles even in the space
+of just one year within the leading
+
+ align:start position:0%
+of just one year within the leading
+ 
+
+ align:start position:0%
+of just one year within the leading
+physics journal not just the one we've
+
+ align:start position:0%
+physics journal not just the one we've
+ 
+
+ align:start position:0%
+physics journal not just the one we've
+looked at so far even others will look
+
+ align:start position:0%
+looked at so far even others will look
+ 
+
+ align:start position:0%
+looked at so far even others will look
+at soon he didn't even become patent
+
+ align:start position:0%
+at soon he didn't even become patent
+ 
+
+ align:start position:0%
+at soon he didn't even become patent
+Clerk's second class this was really
+
+ align:start position:0%
+Clerk's second class this was really
+ 
+
+ align:start position:0%
+Clerk's second class this was really
+really a complete you know shattering
+
+ align:start position:0%
+really a complete you know shattering
+ 
+
+ align:start position:0%
+really a complete you know shattering
+silence
+
+ align:start position:0%
+silence
+ 
+
+ align:start position:0%
+silence
+in response to his work so one of his
+
+ align:start position:0%
+in response to his work so one of his
+ 
+
+ align:start position:0%
+in response to his work so one of his
+close friends an exact contemporary of
+
+ align:start position:0%
+close friends an exact contemporary of
+ 
+
+ align:start position:0%
+close friends an exact contemporary of
+his max funlawa whom he happened to me
+
+ align:start position:0%
+his max funlawa whom he happened to me
+ 
+
+ align:start position:0%
+his max funlawa whom he happened to me
+uh who was following a more traditional
+
+ align:start position:0%
+uh who was following a more traditional
+ 
+
+ align:start position:0%
+uh who was following a more traditional
+uh physics research and academic career
+
+ align:start position:0%
+uh physics research and academic career
+ 
+
+ align:start position:0%
+uh physics research and academic career
+so now he was the same age as Einstein
+
+ align:start position:0%
+so now he was the same age as Einstein
+ 
+
+ align:start position:0%
+so now he was the same age as Einstein
+but was making advances of the sore nice
+
+ align:start position:0%
+but was making advances of the sore nice
+ 
+
+ align:start position:0%
+but was making advances of the sore nice
+I had hoped to make but it was not yet
+
+ align:start position:0%
+I had hoped to make but it was not yet
+ 
+
+ align:start position:0%
+I had hoped to make but it was not yet
+making for now what did his PhD quickly
+
+ align:start position:0%
+making for now what did his PhD quickly
+ 
+
+ align:start position:0%
+making for now what did his PhD quickly
+he got a very prestigious post-doctoral
+
+ align:start position:0%
+he got a very prestigious post-doctoral
+ 
+
+ align:start position:0%
+he got a very prestigious post-doctoral
+position he was soon teaching at a
+
+ align:start position:0%
+position he was soon teaching at a
+ 
+
+ align:start position:0%
+position he was soon teaching at a
+central uh Research Institute funlawy
+
+ align:start position:0%
+central uh Research Institute funlawy
+ 
+
+ align:start position:0%
+central uh Research Institute funlawy
+had befriended Einstein they would talk
+
+ align:start position:0%
+had befriended Einstein they would talk
+ 
+
+ align:start position:0%
+had befriended Einstein they would talk
+and because of this kind of direct
+
+ align:start position:0%
+and because of this kind of direct
+ 
+
+ align:start position:0%
+and because of this kind of direct
+connection Max funlawy and a very small
+
+ align:start position:0%
+connection Max funlawy and a very small
+ 
+
+ align:start position:0%
+connection Max funlawy and a very small
+number of others began trying to get a
+
+ align:start position:0%
+number of others began trying to get a
+ 
+
+ align:start position:0%
+number of others began trying to get a
+little more attention to Einstein's work
+
+ align:start position:0%
+little more attention to Einstein's work
+ 
+
+ align:start position:0%
+little more attention to Einstein's work
+on on what we would Now call special
+
+ align:start position:0%
+on on what we would Now call special
+ 
+
+ align:start position:0%
+on on what we would Now call special
+relativity so for example
+
+ align:start position:0%
+relativity so for example
+ 
+
+ align:start position:0%
+relativity so for example
+from his sort of better established uh
+
+ align:start position:0%
+from his sort of better established uh
+ 
+
+ align:start position:0%
+from his sort of better established uh
+academic position for now I wrote a
+
+ align:start position:0%
+academic position for now I wrote a
+ 
+
+ align:start position:0%
+academic position for now I wrote a
+review article that people did pay
+
+ align:start position:0%
+review article that people did pay
+ 
+
+ align:start position:0%
+review article that people did pay
+attention to he was kind of seen as a
+
+ align:start position:0%
+attention to he was kind of seen as a
+ 
+
+ align:start position:0%
+attention to he was kind of seen as a
+rising person to follow he wrote an
+
+ align:start position:0%
+rising person to follow he wrote an
+ 
+
+ align:start position:0%
+rising person to follow he wrote an
+article fully four years later in 1909
+
+ align:start position:0%
+article fully four years later in 1909
+ 
+
+ align:start position:0%
+article fully four years later in 1909
+which helped to bring Einstein's work to
+
+ align:start position:0%
+which helped to bring Einstein's work to
+ 
+
+ align:start position:0%
+which helped to bring Einstein's work to
+others attention Isis work and that work
+
+ align:start position:0%
+others attention Isis work and that work
+ 
+
+ align:start position:0%
+others attention Isis work and that work
+of others as well so a few years later
+
+ align:start position:0%
+of others as well so a few years later
+ 
+
+ align:start position:0%
+of others as well so a few years later
+um some more people began to pay
+
+ align:start position:0%
+um some more people began to pay
+ 
+
+ align:start position:0%
+um some more people began to pay
+attention not because they were
+
+ align:start position:0%
+attention not because they were
+ 
+
+ align:start position:0%
+attention not because they were
+following Einstein per se but a little
+
+ align:start position:0%
+following Einstein per se but a little
+ 
+
+ align:start position:0%
+following Einstein per se but a little
+bit of a kind of percolation starts
+
+ align:start position:0%
+bit of a kind of percolation starts
+ 
+
+ align:start position:0%
+bit of a kind of percolation starts
+so reaction one is really no reaction at
+
+ align:start position:0%
+so reaction one is really no reaction at
+ 
+
+ align:start position:0%
+so reaction one is really no reaction at
+all the second reaction didn't make
+
+ align:start position:0%
+all the second reaction didn't make
+ 
+
+ align:start position:0%
+all the second reaction didn't make
+Einstein much happier so when people did
+
+ align:start position:0%
+Einstein much happier so when people did
+ 
+
+ align:start position:0%
+Einstein much happier so when people did
+notice the work the minority the
+
+ align:start position:0%
+notice the work the minority the
+ 
+
+ align:start position:0%
+notice the work the minority the
+exceptions to that rule who paid any
+
+ align:start position:0%
+exceptions to that rule who paid any
+ 
+
+ align:start position:0%
+exceptions to that rule who paid any
+attention at all they tended to read
+
+ align:start position:0%
+attention at all they tended to read
+ 
+
+ align:start position:0%
+attention at all they tended to read
+Einstein's paper the one that we're all
+
+ align:start position:0%
+Einstein's paper the one that we're all
+ 
+
+ align:start position:0%
+Einstein's paper the one that we're all
+immersed in now as kind of a clever
+
+ align:start position:0%
+immersed in now as kind of a clever
+ 
+
+ align:start position:0%
+immersed in now as kind of a clever
+rederivation of what was by then kind of
+
+ align:start position:0%
+rederivation of what was by then kind of
+ 
+
+ align:start position:0%
+rederivation of what was by then kind of
+old news they saw this as a really kind
+
+ align:start position:0%
+old news they saw this as a really kind
+ 
+
+ align:start position:0%
+old news they saw this as a really kind
+of smart way to get back to the results
+
+ align:start position:0%
+of smart way to get back to the results
+ 
+
+ align:start position:0%
+of smart way to get back to the results
+that leading physicists like Hedrick
+
+ align:start position:0%
+that leading physicists like Hedrick
+ 
+
+ align:start position:0%
+that leading physicists like Hedrick
+Lorenz and Henri pankarai in Paris and
+
+ align:start position:0%
+Lorenz and Henri pankarai in Paris and
+ 
+
+ align:start position:0%
+Lorenz and Henri pankarai in Paris and
+others had been fighting for a decade
+
+ align:start position:0%
+others had been fighting for a decade
+ 
+
+ align:start position:0%
+others had been fighting for a decade
+since the 1890s remember we even we saw
+
+ align:start position:0%
+since the 1890s remember we even we saw
+ 
+
+ align:start position:0%
+since the 1890s remember we even we saw
+this in our own class discussions a few
+
+ align:start position:0%
+this in our own class discussions a few
+ 
+
+ align:start position:0%
+this in our own class discussions a few
+sessions ago
+
+ align:start position:0%
+sessions ago
+ 
+
+ align:start position:0%
+sessions ago
+Hendrick Lorenz had already published on
+
+ align:start position:0%
+Hendrick Lorenz had already published on
+ 
+
+ align:start position:0%
+Hendrick Lorenz had already published on
+length contraction he was directly
+
+ align:start position:0%
+length contraction he was directly
+ 
+
+ align:start position:0%
+length contraction he was directly
+responding to the Michaelson model
+
+ align:start position:0%
+responding to the Michaelson model
+ 
+
+ align:start position:0%
+responding to the Michaelson model
+experiment in Lorenzo's case he hadn't
+
+ align:start position:0%
+experiment in Lorenzo's case he hadn't
+ 
+
+ align:start position:0%
+experiment in Lorenzo's case he hadn't
+only argued about there should be a
+
+ align:start position:0%
+only argued about there should be a
+ 
+
+ align:start position:0%
+only argued about there should be a
+contraction he had derived
+
+ align:start position:0%
+contraction he had derived
+ 
+
+ align:start position:0%
+contraction he had derived
+quantitatively an expression involving
+
+ align:start position:0%
+quantitatively an expression involving
+ 
+
+ align:start position:0%
+quantitatively an expression involving
+this Factor gamma that we've already
+
+ align:start position:0%
+this Factor gamma that we've already
+ 
+
+ align:start position:0%
+this Factor gamma that we've already
+seen many times one over the square root
+
+ align:start position:0%
+seen many times one over the square root
+ 
+
+ align:start position:0%
+seen many times one over the square root
+of one minus V over c squared that was
+
+ align:start position:0%
+of one minus V over c squared that was
+ 
+
+ align:start position:0%
+of one minus V over c squared that was
+the exact same quantitative result to
+
+ align:start position:0%
+the exact same quantitative result to
+ 
+
+ align:start position:0%
+the exact same quantitative result to
+which Einstein had arrived by very
+
+ align:start position:0%
+which Einstein had arrived by very
+ 
+
+ align:start position:0%
+which Einstein had arrived by very
+different forms of reasoning lorentz was
+
+ align:start position:0%
+different forms of reasoning lorentz was
+ 
+
+ align:start position:0%
+different forms of reasoning lorentz was
+a very senior very established very
+
+ align:start position:0%
+a very senior very established very
+ 
+
+ align:start position:0%
+a very senior very established very
+productive mathematical physicist people
+
+ align:start position:0%
+productive mathematical physicist people
+ 
+
+ align:start position:0%
+productive mathematical physicist people
+really did want to see what was
+
+ align:start position:0%
+really did want to see what was
+ 
+
+ align:start position:0%
+really did want to see what was
+Lorenzo's latest work they really would
+
+ align:start position:0%
+Lorenzo's latest work they really would
+ 
+
+ align:start position:0%
+Lorenzo's latest work they really would
+you know hang on his latest articles so
+
+ align:start position:0%
+you know hang on his latest articles so
+ 
+
+ align:start position:0%
+you know hang on his latest articles so
+the small number the exceptions who
+
+ align:start position:0%
+the small number the exceptions who
+ 
+
+ align:start position:0%
+the small number the exceptions who
+noticed Einstein's work in 1905 so I've
+
+ align:start position:0%
+noticed Einstein's work in 1905 so I've
+ 
+
+ align:start position:0%
+noticed Einstein's work in 1905 so I've
+sort of seen that before that's it's a
+
+ align:start position:0%
+sort of seen that before that's it's a
+ 
+
+ align:start position:0%
+sort of seen that before that's it's a
+clever way of getting back to what was
+
+ align:start position:0%
+clever way of getting back to what was
+ 
+
+ align:start position:0%
+clever way of getting back to what was
+by then kind of 10 year old results and
+
+ align:start position:0%
+by then kind of 10 year old results and
+ 
+
+ align:start position:0%
+by then kind of 10 year old results and
+so if anyone gave Einstein credit
+
+ align:start position:0%
+so if anyone gave Einstein credit
+ 
+
+ align:start position:0%
+so if anyone gave Einstein credit
+in his early years it was a as kind of
+
+ align:start position:0%
+in his early years it was a as kind of
+ 
+
+ align:start position:0%
+in his early years it was a as kind of
+like second fiddle they would refer
+
+ align:start position:0%
+like second fiddle they would refer
+ 
+
+ align:start position:0%
+like second fiddle they would refer
+sometimes to lorentz Theory Lawrence's
+
+ align:start position:0%
+sometimes to lorentz Theory Lawrence's
+ 
+
+ align:start position:0%
+sometimes to lorentz Theory Lawrence's
+electronamics or a few of them would
+
+ align:start position:0%
+electronamics or a few of them would
+ 
+
+ align:start position:0%
+electronamics or a few of them would
+refer to the lorentz Einstein theory no
+
+ align:start position:0%
+refer to the lorentz Einstein theory no
+ 
+
+ align:start position:0%
+refer to the lorentz Einstein theory no
+one referred to the Einstein Lorenz
+
+ align:start position:0%
+one referred to the Einstein Lorenz
+ 
+
+ align:start position:0%
+one referred to the Einstein Lorenz
+Theory so the second reaction didn't
+
+ align:start position:0%
+Theory so the second reaction didn't
+ 
+
+ align:start position:0%
+Theory so the second reaction didn't
+make Einstein much happier either people
+
+ align:start position:0%
+make Einstein much happier either people
+ 
+
+ align:start position:0%
+make Einstein much happier either people
+ignored it or they somehow as far as he
+
+ align:start position:0%
+ignored it or they somehow as far as he
+ 
+
+ align:start position:0%
+ignored it or they somehow as far as he
+was concerned misunderstood this as a
+
+ align:start position:0%
+was concerned misunderstood this as a
+ 
+
+ align:start position:0%
+was concerned misunderstood this as a
+kind of trivial reworking of more
+
+ align:start position:0%
+kind of trivial reworking of more
+ 
+
+ align:start position:0%
+kind of trivial reworking of more
+established results
+
+ align:start position:0%
+established results
+ 
+
+ align:start position:0%
+established results
+so even when people gave Einstein's work
+
+ align:start position:0%
+so even when people gave Einstein's work
+ 
+
+ align:start position:0%
+so even when people gave Einstein's work
+any attention within this kind of rubric
+
+ align:start position:0%
+any attention within this kind of rubric
+ 
+
+ align:start position:0%
+any attention within this kind of rubric
+of the of the framework that Lorenz had
+
+ align:start position:0%
+of the of the framework that Lorenz had
+ 
+
+ align:start position:0%
+of the of the framework that Lorenz had
+been establishing throughout the 1890s
+
+ align:start position:0%
+been establishing throughout the 1890s
+ 
+
+ align:start position:0%
+been establishing throughout the 1890s
+few people seem to notice that the
+
+ align:start position:0%
+few people seem to notice that the
+ 
+
+ align:start position:0%
+few people seem to notice that the
+conceptual underpinning was really quite
+
+ align:start position:0%
+conceptual underpinning was really quite
+ 
+
+ align:start position:0%
+conceptual underpinning was really quite
+distinct some of the equations were
+
+ align:start position:0%
+distinct some of the equations were
+ 
+
+ align:start position:0%
+distinct some of the equations were
+identical the same factor of gamma the
+
+ align:start position:0%
+identical the same factor of gamma the
+ 
+
+ align:start position:0%
+identical the same factor of gamma the
+same coordinate Transformations and so
+
+ align:start position:0%
+same coordinate Transformations and so
+ 
+
+ align:start position:0%
+same coordinate Transformations and so
+on and yet they seem to be based as we
+
+ align:start position:0%
+on and yet they seem to be based as we
+ 
+
+ align:start position:0%
+on and yet they seem to be based as we
+would now see with with hindsight on
+
+ align:start position:0%
+would now see with with hindsight on
+ 
+
+ align:start position:0%
+would now see with with hindsight on
+very very different con uh starting
+
+ align:start position:0%
+very very different con uh starting
+ 
+
+ align:start position:0%
+very very different con uh starting
+assumptions Lorenzo's work was all about
+
+ align:start position:0%
+assumptions Lorenzo's work was all about
+ 
+
+ align:start position:0%
+assumptions Lorenzo's work was all about
+The Ether the either wasn't only Central
+
+ align:start position:0%
+The Ether the either wasn't only Central
+ 
+
+ align:start position:0%
+The Ether the either wasn't only Central
+it was exerting forces these Dynamics
+
+ align:start position:0%
+it was exerting forces these Dynamics
+ 
+
+ align:start position:0%
+it was exerting forces these Dynamics
+according to Lorenzo's view it was
+
+ align:start position:0%
+according to Lorenzo's view it was
+ 
+
+ align:start position:0%
+according to Lorenzo's view it was
+literally squeezing the atoms and
+
+ align:start position:0%
+literally squeezing the atoms and
+ 
+
+ align:start position:0%
+literally squeezing the atoms and
+molecules in the arm of michelson's
+
+ align:start position:0%
+molecules in the arm of michelson's
+ 
+
+ align:start position:0%
+molecules in the arm of michelson's
+device right it was all about the
+
+ align:start position:0%
+device right it was all about the
+ 
+
+ align:start position:0%
+device right it was all about the
+elasticity and the forces exerted by a
+
+ align:start position:0%
+elasticity and the forces exerted by a
+ 
+
+ align:start position:0%
+elasticity and the forces exerted by a
+physical ether
+
+ align:start position:0%
+physical ether
+ 
+
+ align:start position:0%
+physical ether
+and as we've seen in Einstein's case in
+
+ align:start position:0%
+and as we've seen in Einstein's case in
+ 
+
+ align:start position:0%
+and as we've seen in Einstein's case in
+the opening few paragraphs he's
+
+ align:start position:0%
+the opening few paragraphs he's
+ 
+
+ align:start position:0%
+the opening few paragraphs he's
+dismissed The Ether is Superfluous his
+
+ align:start position:0%
+dismissed The Ether is Superfluous his
+ 
+
+ align:start position:0%
+dismissed The Ether is Superfluous his
+work is not about The Ether he says The
+
+ align:start position:0%
+work is not about The Ether he says The
+ 
+
+ align:start position:0%
+work is not about The Ether he says The
+Ether was a century-long distraction
+
+ align:start position:0%
+Ether was a century-long distraction
+ 
+
+ align:start position:0%
+Ether was a century-long distraction
+which is a very different starting point
+
+ align:start position:0%
+which is a very different starting point
+ 
+
+ align:start position:0%
+which is a very different starting point
+even though they both arrive at some
+
+ align:start position:0%
+even though they both arrive at some
+ 
+
+ align:start position:0%
+even though they both arrive at some
+very similar equations so even when
+
+ align:start position:0%
+very similar equations so even when
+ 
+
+ align:start position:0%
+very similar equations so even when
+people gave it attention they they sort
+
+ align:start position:0%
+people gave it attention they they sort
+ 
+
+ align:start position:0%
+people gave it attention they they sort
+of misread it or they read it in ways
+
+ align:start position:0%
+of misread it or they read it in ways
+ 
+
+ align:start position:0%
+of misread it or they read it in ways
+different from how Einstein uh probably
+
+ align:start position:0%
+different from how Einstein uh probably
+ 
+
+ align:start position:0%
+different from how Einstein uh probably
+had hoped
+
+ align:start position:0%
+had hoped
+ 
+
+ align:start position:0%
+had hoped
+and again this lasts not just until 1906
+
+ align:start position:0%
+and again this lasts not just until 1906
+ 
+
+ align:start position:0%
+and again this lasts not just until 1906
+or seven even after 1909 review articles
+
+ align:start position:0%
+or seven even after 1909 review articles
+ 
+
+ align:start position:0%
+or seven even after 1909 review articles
+by people like Max funlawy here's a
+
+ align:start position:0%
+by people like Max funlawy here's a
+ 
+
+ align:start position:0%
+by people like Max funlawy here's a
+great example that I take from uh Andy
+
+ align:start position:0%
+great example that I take from uh Andy
+ 
+
+ align:start position:0%
+great example that I take from uh Andy
+Warwick's work we had some more of
+
+ align:start position:0%
+Warwick's work we had some more of
+ 
+
+ align:start position:0%
+Warwick's work we had some more of
+Andy's work to read for today and and
+
+ align:start position:0%
+Andy's work to read for today and and
+ 
+
+ align:start position:0%
+Andy's work to read for today and and
+I'll talk about that later in today's
+
+ align:start position:0%
+I'll talk about that later in today's
+ 
+
+ align:start position:0%
+I'll talk about that later in today's
+class but he has this great example in
+
+ align:start position:0%
+class but he has this great example in
+ 
+
+ align:start position:0%
+class but he has this great example in
+his article that even as late as 1913
+
+ align:start position:0%
+his article that even as late as 1913
+ 
+
+ align:start position:0%
+his article that even as late as 1913
+now we're talking nearly a decade later
+
+ align:start position:0%
+now we're talking nearly a decade later
+ 
+
+ align:start position:0%
+now we're talking nearly a decade later
+right eight so fully eight years later a
+
+ align:start position:0%
+right eight so fully eight years later a
+ 
+
+ align:start position:0%
+right eight so fully eight years later a
+leading British physicist had written
+
+ align:start position:0%
+leading British physicist had written
+ 
+
+ align:start position:0%
+leading British physicist had written
+about what he called the abstruse
+
+ align:start position:0%
+about what he called the abstruse
+ 
+
+ align:start position:0%
+about what he called the abstruse
+conceptions of Einstein's knights in the
+
+ align:start position:0%
+conceptions of Einstein's knights in the
+ 
+
+ align:start position:0%
+conceptions of Einstein's knights in the
+five paper which were quote most foreign
+
+ align:start position:0%
+five paper which were quote most foreign
+ 
+
+ align:start position:0%
+five paper which were quote most foreign
+to our habits of thought and as yet
+
+ align:start position:0%
+to our habits of thought and as yet
+ 
+
+ align:start position:0%
+to our habits of thought and as yet
+scarcely anyone in this country by which
+
+ align:start position:0%
+scarcely anyone in this country by which
+ 
+
+ align:start position:0%
+scarcely anyone in this country by which
+he means Britain professed to understand
+
+ align:start position:0%
+he means Britain professed to understand
+ 
+
+ align:start position:0%
+he means Britain professed to understand
+or at least to appreciate so even the
+
+ align:start position:0%
+or at least to appreciate so even the
+ 
+
+ align:start position:0%
+or at least to appreciate so even the
+people who knew there was this person in
+
+ align:start position:0%
+people who knew there was this person in
+ 
+
+ align:start position:0%
+people who knew there was this person in
+Einstein who worked on the electronamics
+
+ align:start position:0%
+Einstein who worked on the electronamics
+ 
+
+ align:start position:0%
+Einstein who worked on the electronamics
+of moving bodies this was not kind of
+
+ align:start position:0%
+of moving bodies this was not kind of
+ 
+
+ align:start position:0%
+of moving bodies this was not kind of
+commanding attention in the way that we
+
+ align:start position:0%
+commanding attention in the way that we
+ 
+
+ align:start position:0%
+commanding attention in the way that we
+might expect because so we know how the
+
+ align:start position:0%
+might expect because so we know how the
+ 
+
+ align:start position:0%
+might expect because so we know how the
+story ends we know what Einstein would
+
+ align:start position:0%
+story ends we know what Einstein would
+ 
+
+ align:start position:0%
+story ends we know what Einstein would
+go on to to be recognized for it was a
+
+ align:start position:0%
+go on to to be recognized for it was a
+ 
+
+ align:start position:0%
+go on to to be recognized for it was a
+pretty slow uh transformation
+
+ align:start position:0%
+pretty slow uh transformation
+ 
+
+ align:start position:0%
+pretty slow uh transformation
+and we see this reflected in Einstein's
+
+ align:start position:0%
+and we see this reflected in Einstein's
+ 
+
+ align:start position:0%
+and we see this reflected in Einstein's
+own career as well so as I mentioned my
+
+ align:start position:0%
+own career as well so as I mentioned my
+ 
+
+ align:start position:0%
+own career as well so as I mentioned my
+one of my favorite factoids for the
+
+ align:start position:0%
+one of my favorite factoids for the
+ 
+
+ align:start position:0%
+one of my favorite factoids for the
+entire class today Einstein didn't not
+
+ align:start position:0%
+entire class today Einstein didn't not
+ 
+
+ align:start position:0%
+entire class today Einstein didn't not
+only didn't leave the patent office he
+
+ align:start position:0%
+only didn't leave the patent office he
+ 
+
+ align:start position:0%
+only didn't leave the patent office he
+didn't even get promoted within the
+
+ align:start position:0%
+didn't even get promoted within the
+ 
+
+ align:start position:0%
+didn't even get promoted within the
+patent office in the light of this quite
+
+ align:start position:0%
+patent office in the light of this quite
+ 
+
+ align:start position:0%
+patent office in the light of this quite
+extraordinary work his first break the
+
+ align:start position:0%
+extraordinary work his first break the
+ 
+
+ align:start position:0%
+extraordinary work his first break the
+first opportunity for the kind of career
+
+ align:start position:0%
+first opportunity for the kind of career
+ 
+
+ align:start position:0%
+first opportunity for the kind of career
+we know that he really wanted we know
+
+ align:start position:0%
+we know that he really wanted we know
+ 
+
+ align:start position:0%
+we know that he really wanted we know
+from his personal letters that had
+
+ align:start position:0%
+from his personal letters that had
+ 
+
+ align:start position:0%
+from his personal letters that had
+survived and uh are available he had
+
+ align:start position:0%
+survived and uh are available he had
+ 
+
+ align:start position:0%
+survived and uh are available he had
+been hoping for an academic position
+
+ align:start position:0%
+been hoping for an academic position
+ 
+
+ align:start position:0%
+been hoping for an academic position
+from his early early days his first big
+
+ align:start position:0%
+from his early early days his first big
+ 
+
+ align:start position:0%
+from his early early days his first big
+break along that new career path comes
+
+ align:start position:0%
+break along that new career path comes
+ 
+
+ align:start position:0%
+break along that new career path comes
+actually in 1909
+
+ align:start position:0%
+actually in 1909
+ 
+
+ align:start position:0%
+actually in 1909
+around the time that fun Lowry was
+
+ align:start position:0%
+around the time that fun Lowry was
+ 
+
+ align:start position:0%
+around the time that fun Lowry was
+writing that review article on others
+
+ align:start position:0%
+writing that review article on others
+ 
+
+ align:start position:0%
+writing that review article on others
+where he was offered an assistant
+
+ align:start position:0%
+where he was offered an assistant
+ 
+
+ align:start position:0%
+where he was offered an assistant
+professor position in Zurich which was
+
+ align:start position:0%
+professor position in Zurich which was
+ 
+
+ align:start position:0%
+professor position in Zurich which was
+actually very exciting it's where he had
+
+ align:start position:0%
+actually very exciting it's where he had
+ 
+
+ align:start position:0%
+actually very exciting it's where he had
+done his own School his own University
+
+ align:start position:0%
+done his own School his own University
+ 
+
+ align:start position:0%
+done his own School his own University
+training then two years later he's given
+
+ align:start position:0%
+training then two years later he's given
+ 
+
+ align:start position:0%
+training then two years later he's given
+a kind of promotion an offer to move uh
+
+ align:start position:0%
+a kind of promotion an offer to move uh
+ 
+
+ align:start position:0%
+a kind of promotion an offer to move uh
+now to Prague he spends about one year
+
+ align:start position:0%
+now to Prague he spends about one year
+ 
+
+ align:start position:0%
+now to Prague he spends about one year
+there that is hired back at a different
+
+ align:start position:0%
+there that is hired back at a different
+ 
+
+ align:start position:0%
+there that is hired back at a different
+institution back in Zurich and then
+
+ align:start position:0%
+institution back in Zurich and then
+ 
+
+ align:start position:0%
+institution back in Zurich and then
+finally uh in the spring of 1914 in
+
+ align:start position:0%
+finally uh in the spring of 1914 in
+ 
+
+ align:start position:0%
+finally uh in the spring of 1914 in
+April or May he's invited to join the
+
+ align:start position:0%
+April or May he's invited to join the
+ 
+
+ align:start position:0%
+April or May he's invited to join the
+very very prestigious oppression Academy
+
+ align:start position:0%
+very very prestigious oppression Academy
+ 
+
+ align:start position:0%
+very very prestigious oppression Academy
+of Sciences in Berlin so roughly a
+
+ align:start position:0%
+of Sciences in Berlin so roughly a
+ 
+
+ align:start position:0%
+of Sciences in Berlin so roughly a
+decade later he's kind of promoted to
+
+ align:start position:0%
+decade later he's kind of promoted to
+ 
+
+ align:start position:0%
+decade later he's kind of promoted to
+the kind of position he'd been um really
+
+ align:start position:0%
+the kind of position he'd been um really
+ 
+
+ align:start position:0%
+the kind of position he'd been um really
+angling for all along and it comes not
+
+ align:start position:0%
+angling for all along and it comes not
+ 
+
+ align:start position:0%
+angling for all along and it comes not
+one year not two year not three years
+
+ align:start position:0%
+one year not two year not three years
+ 
+
+ align:start position:0%
+one year not two year not three years
+later but nearly a decade later and and
+
+ align:start position:0%
+later but nearly a decade later and and
+ 
+
+ align:start position:0%
+later but nearly a decade later and and
+after a lot more work has come out not
+
+ align:start position:0%
+after a lot more work has come out not
+ 
+
+ align:start position:0%
+after a lot more work has come out not
+just on the basis of this 1905 work so
+
+ align:start position:0%
+just on the basis of this 1905 work so
+ 
+
+ align:start position:0%
+just on the basis of this 1905 work so
+he's a kind of slowly kind of
+
+ align:start position:0%
+he's a kind of slowly kind of
+ 
+
+ align:start position:0%
+he's a kind of slowly kind of
+accelerating academic career starting
+
+ align:start position:0%
+accelerating academic career starting
+ 
+
+ align:start position:0%
+accelerating academic career starting
+from these very uh unusual starting
+
+ align:start position:0%
+from these very uh unusual starting
+ 
+
+ align:start position:0%
+from these very uh unusual starting
+points so I'll pause there any questions
+
+ align:start position:0%
+points so I'll pause there any questions
+ 
+
+ align:start position:0%
+points so I'll pause there any questions
+on that early uh discussion of the
+
+ align:start position:0%
+on that early uh discussion of the
+ 
+
+ align:start position:0%
+on that early uh discussion of the
+reception of Einstein's work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a good moment to remind you try not
+
+ align:start position:0%
+is a good moment to remind you try not
+ 
+
+ align:start position:0%
+is a good moment to remind you try not
+to annoy all your professors in college
+
+ align:start position:0%
+to annoy all your professors in college
+ 
+
+ align:start position:0%
+to annoy all your professors in college
+you'll get better letters of
+
+ align:start position:0%
+you'll get better letters of
+ 
+
+ align:start position:0%
+you'll get better letters of
+recommendation that will help you on the
+
+ align:start position:0%
+recommendation that will help you on the
+ 
+
+ align:start position:0%
+recommendation that will help you on the
+job market that was one of one of many
+
+ align:start position:0%
+job market that was one of one of many
+ 
+
+ align:start position:0%
+job market that was one of one of many
+things Einstein had done so poorly
+
+ align:start position:0%
+things Einstein had done so poorly
+ 
+
+ align:start position:0%
+things Einstein had done so poorly
+because he was kind of a dummy Einstein
+
+ align:start position:0%
+because he was kind of a dummy Einstein
+ 
+
+ align:start position:0%
+because he was kind of a dummy Einstein
+as I'd like to say was no Einstein when
+
+ align:start position:0%
+as I'd like to say was no Einstein when
+ 
+
+ align:start position:0%
+as I'd like to say was no Einstein when
+it came to his own schooling so that's
+
+ align:start position:0%
+it came to his own schooling so that's
+ 
+
+ align:start position:0%
+it came to his own schooling so that's
+life lesson number one from 8225 write
+
+ align:start position:0%
+life lesson number one from 8225 write
+ 
+
+ align:start position:0%
+life lesson number one from 8225 write
+that down any other questions about
+
+ align:start position:0%
+that down any other questions about
+ 
+
+ align:start position:0%
+that down any other questions about
+Einstein's uh or the early reception of
+
+ align:start position:0%
+Einstein's uh or the early reception of
+ 
+
+ align:start position:0%
+Einstein's uh or the early reception of
+either his own career or this body of
+
+ align:start position:0%
+either his own career or this body of
+ 
+
+ align:start position:0%
+either his own career or this body of
+work if not I'll gladly uh Press On
+
+ align:start position:0%
+work if not I'll gladly uh Press On
+ 
+
+ align:start position:0%
+work if not I'll gladly uh Press On
+okay if questions come up put them in
+
+ align:start position:0%
+okay if questions come up put them in
+ 
+
+ align:start position:0%
+okay if questions come up put them in
+the chat we'll we'll have more time to
+
+ align:start position:0%
+the chat we'll we'll have more time to
+ 
+
+ align:start position:0%
+the chat we'll we'll have more time to
+uh to talk about them but I'll go back
+
+ align:start position:0%
+uh to talk about them but I'll go back
+ 
+
+ align:start position:0%
+uh to talk about them but I'll go back
+to the slides we'll talk about now this
+
+ align:start position:0%
+to the slides we'll talk about now this
+ 
+
+ align:start position:0%
+to the slides we'll talk about now this
+next part we can dig in a bit more to to
+
+ align:start position:0%
+next part we can dig in a bit more to to
+ 
+
+ align:start position:0%
+next part we can dig in a bit more to to
+an example of a bit more significant
+
+ align:start position:0%
+an example of a bit more significant
+ 
+
+ align:start position:0%
+an example of a bit more significant
+engagement of stronger reaction and
+
+ align:start position:0%
+engagement of stronger reaction and
+ 
+
+ align:start position:0%
+engagement of stronger reaction and
+response to Einstein's work and that
+
+ align:start position:0%
+response to Einstein's work and that
+ 
+
+ align:start position:0%
+response to Einstein's work and that
+came actually somewhat surprisingly from
+
+ align:start position:0%
+came actually somewhat surprisingly from
+ 
+
+ align:start position:0%
+came actually somewhat surprisingly from
+one of Einstein's former mathematics
+
+ align:start position:0%
+one of Einstein's former mathematics
+ 
+
+ align:start position:0%
+one of Einstein's former mathematics
+teachers Herman minkowski so mikowski
+
+ align:start position:0%
+teachers Herman minkowski so mikowski
+ 
+
+ align:start position:0%
+teachers Herman minkowski so mikowski
+was a very um Elite established
+
+ align:start position:0%
+was a very um Elite established
+ 
+
+ align:start position:0%
+was a very um Elite established
+professional mathematician he was in he
+
+ align:start position:0%
+professional mathematician he was in he
+ 
+
+ align:start position:0%
+professional mathematician he was in he
+was a professor at the eth that's that
+
+ align:start position:0%
+was a professor at the eth that's that
+ 
+
+ align:start position:0%
+was a professor at the eth that's that
+uh the University of Einstein had worked
+
+ align:start position:0%
+uh the University of Einstein had worked
+ 
+
+ align:start position:0%
+uh the University of Einstein had worked
+so hard to get into the idea
+
+ align:start position:0%
+so hard to get into the idea
+ 
+
+ align:start position:0%
+so hard to get into the idea
+which I never Tire of trying to
+
+ align:start position:0%
+which I never Tire of trying to
+ 
+
+ align:start position:0%
+which I never Tire of trying to
+pronounce we can just call it eth that
+
+ align:start position:0%
+pronounce we can just call it eth that
+ 
+
+ align:start position:0%
+pronounce we can just call it eth that
+was the sort of Swiss Federal Polytech
+
+ align:start position:0%
+was the sort of Swiss Federal Polytech
+ 
+
+ align:start position:0%
+was the sort of Swiss Federal Polytech
+Institute in Zurich kind of like MIT
+
+ align:start position:0%
+Institute in Zurich kind of like MIT
+ 
+
+ align:start position:0%
+Institute in Zurich kind of like MIT
+was a mathematics professor not a
+
+ align:start position:0%
+was a mathematics professor not a
+ 
+
+ align:start position:0%
+was a mathematics professor not a
+physicist uh and through a kind of
+
+ align:start position:0%
+physicist uh and through a kind of
+ 
+
+ align:start position:0%
+physicist uh and through a kind of
+roundabout way Einstein's work was
+
+ align:start position:0%
+roundabout way Einstein's work was
+ 
+
+ align:start position:0%
+roundabout way Einstein's work was
+brought back to minkowski's attention a
+
+ align:start position:0%
+brought back to minkowski's attention a
+ 
+
+ align:start position:0%
+brought back to minkowski's attention a
+few a few years later at
+
+ align:start position:0%
+few a few years later at
+ 
+
+ align:start position:0%
+few a few years later at
+post-publication
+
+ align:start position:0%
+post-publication
+ 
+
+ align:start position:0%
+post-publication
+so it turns out minkowski was certainly
+
+ align:start position:0%
+so it turns out minkowski was certainly
+ 
+
+ align:start position:0%
+so it turns out minkowski was certainly
+not looking for Einstein's work and we
+
+ align:start position:0%
+not looking for Einstein's work and we
+ 
+
+ align:start position:0%
+not looking for Einstein's work and we
+have again some wonderful juicy colorful
+
+ align:start position:0%
+have again some wonderful juicy colorful
+ 
+
+ align:start position:0%
+have again some wonderful juicy colorful
+letters that survive of minkowski
+
+ align:start position:0%
+letters that survive of minkowski
+ 
+
+ align:start position:0%
+letters that survive of minkowski
+basically talking behind Einstein his
+
+ align:start position:0%
+basically talking behind Einstein his
+ 
+
+ align:start position:0%
+basically talking behind Einstein his
+back and vice versa so we know that when
+
+ align:start position:0%
+back and vice versa so we know that when
+ 
+
+ align:start position:0%
+back and vice versa so we know that when
+Einstein was a university student he
+
+ align:start position:0%
+Einstein was a university student he
+ 
+
+ align:start position:0%
+Einstein was a university student he
+worked so hard to get into the eth what
+
+ align:start position:0%
+worked so hard to get into the eth what
+ 
+
+ align:start position:0%
+worked so hard to get into the eth what
+did he do he began cutting classes
+
+ align:start position:0%
+did he do he began cutting classes
+ 
+
+ align:start position:0%
+did he do he began cutting classes
+especially classes of Faculty for whom
+
+ align:start position:0%
+especially classes of Faculty for whom
+ 
+
+ align:start position:0%
+especially classes of Faculty for whom
+he had little respect
+
+ align:start position:0%
+he had little respect
+ 
+
+ align:start position:0%
+he had little respect
+and that happens to include Hammond
+
+ align:start position:0%
+and that happens to include Hammond
+ 
+
+ align:start position:0%
+and that happens to include Hammond
+nikowski so even though he was
+
+ align:start position:0%
+nikowski so even though he was
+ 
+
+ align:start position:0%
+nikowski so even though he was
+registered and took classes for credit
+
+ align:start position:0%
+registered and took classes for credit
+ 
+
+ align:start position:0%
+registered and took classes for credit
+from minkowski in the math department he
+
+ align:start position:0%
+from minkowski in the math department he
+ 
+
+ align:start position:0%
+from minkowski in the math department he
+rarely showed up and minkowski noticed
+
+ align:start position:0%
+rarely showed up and minkowski noticed
+ 
+
+ align:start position:0%
+rarely showed up and minkowski noticed
+that so Einstein used to borrow notes
+
+ align:start position:0%
+that so Einstein used to borrow notes
+ 
+
+ align:start position:0%
+that so Einstein used to borrow notes
+from several friends from his at the
+
+ align:start position:0%
+from several friends from his at the
+ 
+
+ align:start position:0%
+from several friends from his at the
+time girlfriend who became his first
+
+ align:start position:0%
+time girlfriend who became his first
+ 
+
+ align:start position:0%
+time girlfriend who became his first
+wife maleva marriage she was also a
+
+ align:start position:0%
+wife maleva marriage she was also a
+ 
+
+ align:start position:0%
+wife maleva marriage she was also a
+physics student at the eth and doing
+
+ align:start position:0%
+physics student at the eth and doing
+ 
+
+ align:start position:0%
+physics student at the eth and doing
+actually quite well in her mathematics
+
+ align:start position:0%
+actually quite well in her mathematics
+ 
+
+ align:start position:0%
+actually quite well in her mathematics
+classes she would very dutifully attend
+
+ align:start position:0%
+classes she would very dutifully attend
+ 
+
+ align:start position:0%
+classes she would very dutifully attend
+take very careful notes share them with
+
+ align:start position:0%
+take very careful notes share them with
+ 
+
+ align:start position:0%
+take very careful notes share them with
+her good for nothing boyfriend Albert
+
+ align:start position:0%
+her good for nothing boyfriend Albert
+ 
+
+ align:start position:0%
+her good for nothing boyfriend Albert
+Einstein he would cram before the exam
+
+ align:start position:0%
+Einstein he would cram before the exam
+ 
+
+ align:start position:0%
+Einstein he would cram before the exam
+and kind of do it okay another one of
+
+ align:start position:0%
+and kind of do it okay another one of
+ 
+
+ align:start position:0%
+and kind of do it okay another one of
+Einstein's close buddies from
+
+ align:start position:0%
+Einstein's close buddies from
+ 
+
+ align:start position:0%
+Einstein's close buddies from
+undergraduate days Marcel Grossman did
+
+ align:start position:0%
+undergraduate days Marcel Grossman did
+ 
+
+ align:start position:0%
+undergraduate days Marcel Grossman did
+the same thing Grossman went on to a
+
+ align:start position:0%
+the same thing Grossman went on to a
+ 
+
+ align:start position:0%
+the same thing Grossman went on to a
+career as a mathematician himself so
+
+ align:start position:0%
+career as a mathematician himself so
+ 
+
+ align:start position:0%
+career as a mathematician himself so
+would basically cut classes from people
+
+ align:start position:0%
+would basically cut classes from people
+ 
+
+ align:start position:0%
+would basically cut classes from people
+like minkowski
+
+ align:start position:0%
+like minkowski
+ 
+
+ align:start position:0%
+like minkowski
+and then catch up and like just skate
+
+ align:start position:0%
+and then catch up and like just skate
+ 
+
+ align:start position:0%
+and then catch up and like just skate
+through he would just like barely pass
+
+ align:start position:0%
+through he would just like barely pass
+ 
+
+ align:start position:0%
+through he would just like barely pass
+by cramming the night before don't do
+
+ align:start position:0%
+by cramming the night before don't do
+ 
+
+ align:start position:0%
+by cramming the night before don't do
+that on paper one please
+
+ align:start position:0%
+that on paper one please
+ 
+
+ align:start position:0%
+that on paper one please
+so um a friend of Einstein's encouraged
+
+ align:start position:0%
+so um a friend of Einstein's encouraged
+ 
+
+ align:start position:0%
+so um a friend of Einstein's encouraged
+the professor minkowski to read this
+
+ align:start position:0%
+the professor minkowski to read this
+ 
+
+ align:start position:0%
+the professor minkowski to read this
+1905 paper a few years after to come out
+
+ align:start position:0%
+1905 paper a few years after to come out
+ 
+
+ align:start position:0%
+1905 paper a few years after to come out
+and minkowski wrote back I really
+
+ align:start position:0%
+and minkowski wrote back I really
+ 
+
+ align:start position:0%
+and minkowski wrote back I really
+wouldn't have thought Einstein capable
+
+ align:start position:0%
+wouldn't have thought Einstein capable
+ 
+
+ align:start position:0%
+wouldn't have thought Einstein capable
+of that he wrote mankowster wrote to
+
+ align:start position:0%
+of that he wrote mankowster wrote to
+ 
+
+ align:start position:0%
+of that he wrote mankowster wrote to
+another colleague Einstein's paper came
+
+ align:start position:0%
+another colleague Einstein's paper came
+ 
+
+ align:start position:0%
+another colleague Einstein's paper came
+as a tremendous surprise because in his
+
+ align:start position:0%
+as a tremendous surprise because in his
+ 
+
+ align:start position:0%
+as a tremendous surprise because in his
+student days Einstein had been a lazy
+
+ align:start position:0%
+student days Einstein had been a lazy
+ 
+
+ align:start position:0%
+student days Einstein had been a lazy
+dog he never bothered about mathematics
+
+ align:start position:0%
+dog he never bothered about mathematics
+ 
+
+ align:start position:0%
+dog he never bothered about mathematics
+at all so much for minkowski having a
+
+ align:start position:0%
+at all so much for minkowski having a
+ 
+
+ align:start position:0%
+at all so much for minkowski having a
+high opinion of young Albert Einstein
+
+ align:start position:0%
+high opinion of young Albert Einstein
+ 
+
+ align:start position:0%
+high opinion of young Albert Einstein
+so once minkowski was convinced even
+
+ align:start position:0%
+so once minkowski was convinced even
+ 
+
+ align:start position:0%
+so once minkowski was convinced even
+look at this again a few years post
+
+ align:start position:0%
+look at this again a few years post
+ 
+
+ align:start position:0%
+look at this again a few years post
+publication he quickly became convinced
+
+ align:start position:0%
+publication he quickly became convinced
+ 
+
+ align:start position:0%
+publication he quickly became convinced
+that Einstein was still a lazy dog or at
+
+ align:start position:0%
+that Einstein was still a lazy dog or at
+ 
+
+ align:start position:0%
+that Einstein was still a lazy dog or at
+least was still making things
+
+ align:start position:0%
+least was still making things
+ 
+
+ align:start position:0%
+least was still making things
+unnecessarily complicated so minkowski
+
+ align:start position:0%
+unnecessarily complicated so minkowski
+ 
+
+ align:start position:0%
+unnecessarily complicated so minkowski
+thought Einstein had a few interesting
+
+ align:start position:0%
+thought Einstein had a few interesting
+ 
+
+ align:start position:0%
+thought Einstein had a few interesting
+ideas in this paper from 1905 but it
+
+ align:start position:0%
+ideas in this paper from 1905 but it
+ 
+
+ align:start position:0%
+ideas in this paper from 1905 but it
+really kind of messed things up as far
+
+ align:start position:0%
+really kind of messed things up as far
+ 
+
+ align:start position:0%
+really kind of messed things up as far
+as minkowski was concerned but he really
+
+ align:start position:0%
+as minkowski was concerned but he really
+ 
+
+ align:start position:0%
+as minkowski was concerned but he really
+missed the the main point of his own
+
+ align:start position:0%
+missed the the main point of his own
+ 
+
+ align:start position:0%
+missed the the main point of his own
+work Mankowski was convinced that
+
+ align:start position:0%
+work Mankowski was convinced that
+ 
+
+ align:start position:0%
+work Mankowski was convinced that
+Einstein's understanding of Einstein's
+
+ align:start position:0%
+Einstein's understanding of Einstein's
+ 
+
+ align:start position:0%
+Einstein's understanding of Einstein's
+work was not the best understanding at
+
+ align:start position:0%
+work was not the best understanding at
+ 
+
+ align:start position:0%
+work was not the best understanding at
+all so in fact minkowski said about
+
+ align:start position:0%
+all so in fact minkowski said about
+ 
+
+ align:start position:0%
+all so in fact minkowski said about
+reformulating this work in his own way
+
+ align:start position:0%
+reformulating this work in his own way
+ 
+
+ align:start position:0%
+reformulating this work in his own way
+in around 1907 it was actually published
+
+ align:start position:0%
+in around 1907 it was actually published
+ 
+
+ align:start position:0%
+in around 1907 it was actually published
+posthumously in 1908. minkowski died
+
+ align:start position:0%
+posthumously in 1908. minkowski died
+ 
+
+ align:start position:0%
+posthumously in 1908. minkowski died
+rather young so he gave this famous
+
+ align:start position:0%
+rather young so he gave this famous
+ 
+
+ align:start position:0%
+rather young so he gave this famous
+lecture and uh and it was published soon
+
+ align:start position:0%
+lecture and uh and it was published soon
+ 
+
+ align:start position:0%
+lecture and uh and it was published soon
+after he passed away
+
+ align:start position:0%
+after he passed away
+ 
+
+ align:start position:0%
+after he passed away
+who was this person Herman minkowski he
+
+ align:start position:0%
+who was this person Herman minkowski he
+ 
+
+ align:start position:0%
+who was this person Herman minkowski he
+wasn't only a mathematician at the eth
+
+ align:start position:0%
+wasn't only a mathematician at the eth
+ 
+
+ align:start position:0%
+wasn't only a mathematician at the eth
+in Zurich he was in particular a
+
+ align:start position:0%
+in Zurich he was in particular a
+ 
+
+ align:start position:0%
+in Zurich he was in particular a
+geometry his specialty within
+
+ align:start position:0%
+geometry his specialty within
+ 
+
+ align:start position:0%
+geometry his specialty within
+mathematics was kind of pure geometry in
+
+ align:start position:0%
+mathematics was kind of pure geometry in
+ 
+
+ align:start position:0%
+mathematics was kind of pure geometry in
+fact he was he was kind of like an
+
+ align:start position:0%
+fact he was he was kind of like an
+ 
+
+ align:start position:0%
+fact he was he was kind of like an
+evangelist for geometry he'd written a
+
+ align:start position:0%
+evangelist for geometry he'd written a
+ 
+
+ align:start position:0%
+evangelist for geometry he'd written a
+book uh first published in 1896 the
+
+ align:start position:0%
+book uh first published in 1896 the
+ 
+
+ align:start position:0%
+book uh first published in 1896 the
+cover here is from a later Edition
+
+ align:start position:0%
+cover here is from a later Edition
+ 
+
+ align:start position:0%
+cover here is from a later Edition
+called the geometry of numbers he
+
+ align:start position:0%
+called the geometry of numbers he
+ 
+
+ align:start position:0%
+called the geometry of numbers he
+actually wanted to remake abstract
+
+ align:start position:0%
+actually wanted to remake abstract
+ 
+
+ align:start position:0%
+actually wanted to remake abstract
+fields of pure mathematics like number
+
+ align:start position:0%
+fields of pure mathematics like number
+ 
+
+ align:start position:0%
+fields of pure mathematics like number
+Theory make those part of geometry as
+
+ align:start position:0%
+Theory make those part of geometry as
+ 
+
+ align:start position:0%
+Theory make those part of geometry as
+well so he wasn't only kind of an expert
+
+ align:start position:0%
+well so he wasn't only kind of an expert
+ 
+
+ align:start position:0%
+well so he wasn't only kind of an expert
+in Geometry he thought geometry was
+
+ align:start position:0%
+in Geometry he thought geometry was
+ 
+
+ align:start position:0%
+in Geometry he thought geometry was
+would unlock the secrets for like all of
+
+ align:start position:0%
+would unlock the secrets for like all of
+ 
+
+ align:start position:0%
+would unlock the secrets for like all of
+math and and that's all he cared about
+
+ align:start position:0%
+math and and that's all he cared about
+ 
+
+ align:start position:0%
+math and and that's all he cared about
+like that was the key to everything so
+
+ align:start position:0%
+like that was the key to everything so
+ 
+
+ align:start position:0%
+like that was the key to everything so
+he really was a geometer all the way
+
+ align:start position:0%
+he really was a geometer all the way
+ 
+
+ align:start position:0%
+he really was a geometer all the way
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+so when he then later turned to
+
+ align:start position:0%
+so when he then later turned to
+ 
+
+ align:start position:0%
+so when he then later turned to
+Einstein's work about two years after it
+
+ align:start position:0%
+Einstein's work about two years after it
+ 
+
+ align:start position:0%
+Einstein's work about two years after it
+had been published he did so as a
+
+ align:start position:0%
+had been published he did so as a
+ 
+
+ align:start position:0%
+had been published he did so as a
+geometer not as a physicist not as a
+
+ align:start position:0%
+geometer not as a physicist not as a
+ 
+
+ align:start position:0%
+geometer not as a physicist not as a
+philosopher interested in mock or
+
+ align:start position:0%
+philosopher interested in mock or
+ 
+
+ align:start position:0%
+philosopher interested in mock or
+positive positivism to mikowski
+
+ align:start position:0%
+positive positivism to mikowski
+ 
+
+ align:start position:0%
+positive positivism to mikowski
+Einstein's work held lessons that were
+
+ align:start position:0%
+Einstein's work held lessons that were
+ 
+
+ align:start position:0%
+Einstein's work held lessons that were
+best understood uh through using the
+
+ align:start position:0%
+best understood uh through using the
+ 
+
+ align:start position:0%
+best understood uh through using the
+tools of geometry
+
+ align:start position:0%
+tools of geometry
+ 
+
+ align:start position:0%
+tools of geometry
+so one of the first things minkowski did
+
+ align:start position:0%
+so one of the first things minkowski did
+ 
+
+ align:start position:0%
+so one of the first things minkowski did
+is something we all take for granted
+
+ align:start position:0%
+is something we all take for granted
+ 
+
+ align:start position:0%
+is something we all take for granted
+today you many of you have probably seen
+
+ align:start position:0%
+today you many of you have probably seen
+ 
+
+ align:start position:0%
+today you many of you have probably seen
+this before we now will call these
+
+ align:start position:0%
+this before we now will call these
+ 
+
+ align:start position:0%
+this before we now will call these
+things space-time diagrams or often
+
+ align:start position:0%
+things space-time diagrams or often
+ 
+
+ align:start position:0%
+things space-time diagrams or often
+we'll call them minkowski diagrams these
+
+ align:start position:0%
+we'll call them minkowski diagrams these
+ 
+
+ align:start position:0%
+we'll call them minkowski diagrams these
+were one of the things that Hermann
+
+ align:start position:0%
+were one of the things that Hermann
+ 
+
+ align:start position:0%
+were one of the things that Hermann
+minkowski introduced once he kind of
+
+ align:start position:0%
+minkowski introduced once he kind of
+ 
+
+ align:start position:0%
+minkowski introduced once he kind of
+grudgingly began to pay attention to
+
+ align:start position:0%
+grudgingly began to pay attention to
+ 
+
+ align:start position:0%
+grudgingly began to pay attention to
+this paper of Albert Einstein
+
+ align:start position:0%
+this paper of Albert Einstein
+ 
+
+ align:start position:0%
+this paper of Albert Einstein
+so what are we going to do with these
+
+ align:start position:0%
+so what are we going to do with these
+ 
+
+ align:start position:0%
+so what are we going to do with these
+with these space-time diagrams to make
+
+ align:start position:0%
+with these space-time diagrams to make
+ 
+
+ align:start position:0%
+with these space-time diagrams to make
+things simple we'll consider Motion in
+
+ align:start position:0%
+things simple we'll consider Motion in
+ 
+
+ align:start position:0%
+things simple we'll consider Motion in
+only one direction of space let's say
+
+ align:start position:0%
+only one direction of space let's say
+ 
+
+ align:start position:0%
+only one direction of space let's say
+the x-axis so quite typically the
+
+ align:start position:0%
+the x-axis so quite typically the
+ 
+
+ align:start position:0%
+the x-axis so quite typically the
+convention very quickly became it will
+
+ align:start position:0%
+convention very quickly became it will
+ 
+
+ align:start position:0%
+convention very quickly became it will
+will measure uh locations of space along
+
+ align:start position:0%
+will measure uh locations of space along
+ 
+
+ align:start position:0%
+will measure uh locations of space along
+the horizontal axis or the x-axis and
+
+ align:start position:0%
+the horizontal axis or the x-axis and
+ 
+
+ align:start position:0%
+the horizontal axis or the x-axis and
+we'll measure changes in time
+
+ align:start position:0%
+we'll measure changes in time
+ 
+
+ align:start position:0%
+we'll measure changes in time
+along the vertical axis okay so now we
+
+ align:start position:0%
+along the vertical axis okay so now we
+ 
+
+ align:start position:0%
+along the vertical axis okay so now we
+have a two-dimensional plot to measure
+
+ align:start position:0%
+have a two-dimensional plot to measure
+ 
+
+ align:start position:0%
+have a two-dimensional plot to measure
+to with which to to make sense of motion
+
+ align:start position:0%
+to with which to to make sense of motion
+ 
+
+ align:start position:0%
+to with which to to make sense of motion
+in space and time these are space time
+
+ align:start position:0%
+in space and time these are space time
+ 
+
+ align:start position:0%
+in space and time these are space time
+diagrams one of the next things that
+
+ align:start position:0%
+diagrams one of the next things that
+ 
+
+ align:start position:0%
+diagrams one of the next things that
+became very very common very quickly
+
+ align:start position:0%
+became very very common very quickly
+ 
+
+ align:start position:0%
+became very very common very quickly
+with these uh kinds of graphs was to use
+
+ align:start position:0%
+with these uh kinds of graphs was to use
+ 
+
+ align:start position:0%
+with these uh kinds of graphs was to use
+very convenient coordinates coordinates
+
+ align:start position:0%
+very convenient coordinates coordinates
+ 
+
+ align:start position:0%
+very convenient coordinates coordinates
+in which light waves would travel one
+
+ align:start position:0%
+in which light waves would travel one
+ 
+
+ align:start position:0%
+in which light waves would travel one
+unit of space one tick along the x-axis
+
+ align:start position:0%
+unit of space one tick along the x-axis
+ 
+
+ align:start position:0%
+unit of space one tick along the x-axis
+for every one tick for every one unit of
+
+ align:start position:0%
+for every one tick for every one unit of
+ 
+
+ align:start position:0%
+for every one tick for every one unit of
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+so for example if we're going to measure
+
+ align:start position:0%
+so for example if we're going to measure
+ 
+
+ align:start position:0%
+so for example if we're going to measure
+time in seconds a very common unit of uh
+
+ align:start position:0%
+time in seconds a very common unit of uh
+ 
+
+ align:start position:0%
+time in seconds a very common unit of uh
+with which to measure time then we
+
+ align:start position:0%
+with which to measure time then we
+ 
+
+ align:start position:0%
+with which to measure time then we
+better not measure the spatial distances
+
+ align:start position:0%
+better not measure the spatial distances
+ 
+
+ align:start position:0%
+better not measure the spatial distances
+in either meters or feet or kilometers
+
+ align:start position:0%
+in either meters or feet or kilometers
+ 
+
+ align:start position:0%
+in either meters or feet or kilometers
+or even parsecs we're going to measure
+
+ align:start position:0%
+or even parsecs we're going to measure
+ 
+
+ align:start position:0%
+or even parsecs we're going to measure
+them in light seconds which is the
+
+ align:start position:0%
+them in light seconds which is the
+ 
+
+ align:start position:0%
+them in light seconds which is the
+distance light will travel in one second
+
+ align:start position:0%
+distance light will travel in one second
+ 
+
+ align:start position:0%
+distance light will travel in one second
+so we're going to measure the distances
+
+ align:start position:0%
+so we're going to measure the distances
+ 
+
+ align:start position:0%
+so we're going to measure the distances
+in units such that light will travel to
+
+ align:start position:0%
+in units such that light will travel to
+ 
+
+ align:start position:0%
+in units such that light will travel to
+one of those spatial units in one unit
+
+ align:start position:0%
+one of those spatial units in one unit
+ 
+
+ align:start position:0%
+one of those spatial units in one unit
+of time for example seconds and light
+
+ align:start position:0%
+of time for example seconds and light
+ 
+
+ align:start position:0%
+of time for example seconds and light
+seconds so what we're really doing in
+
+ align:start position:0%
+seconds so what we're really doing in
+ 
+
+ align:start position:0%
+seconds so what we're really doing in
+effect is scaling the speed of light to
+
+ align:start position:0%
+effect is scaling the speed of light to
+ 
+
+ align:start position:0%
+effect is scaling the speed of light to
+be what and therefore when we go to plot
+
+ align:start position:0%
+be what and therefore when we go to plot
+ 
+
+ align:start position:0%
+be what and therefore when we go to plot
+the motion of light rays or light waves
+
+ align:start position:0%
+the motion of light rays or light waves
+ 
+
+ align:start position:0%
+the motion of light rays or light waves
+on these space-time diagrams
+
+ align:start position:0%
+on these space-time diagrams
+ 
+
+ align:start position:0%
+on these space-time diagrams
+they'll follow these very simple 45
+
+ align:start position:0%
+they'll follow these very simple 45
+ 
+
+ align:start position:0%
+they'll follow these very simple 45
+degree diagonals their slope is fixed to
+
+ align:start position:0%
+degree diagonals their slope is fixed to
+ 
+
+ align:start position:0%
+degree diagonals their slope is fixed to
+be always inclined at 45 degrees because
+
+ align:start position:0%
+be always inclined at 45 degrees because
+ 
+
+ align:start position:0%
+be always inclined at 45 degrees because
+we've chosen our coordinates such that
+
+ align:start position:0%
+we've chosen our coordinates such that
+ 
+
+ align:start position:0%
+we've chosen our coordinates such that
+they will always Traverse one unit of
+
+ align:start position:0%
+they will always Traverse one unit of
+ 
+
+ align:start position:0%
+they will always Traverse one unit of
+space in one area of time now why will
+
+ align:start position:0%
+space in one area of time now why will
+ 
+
+ align:start position:0%
+space in one area of time now why will
+they always travel at that slope because
+
+ align:start position:0%
+they always travel at that slope because
+ 
+
+ align:start position:0%
+they always travel at that slope because
+if we take Einstein's second postulate
+
+ align:start position:0%
+if we take Einstein's second postulate
+ 
+
+ align:start position:0%
+if we take Einstein's second postulate
+seriously light will always be traveling
+
+ align:start position:0%
+seriously light will always be traveling
+ 
+
+ align:start position:0%
+seriously light will always be traveling
+at that single Universal speed the speed
+
+ align:start position:0%
+at that single Universal speed the speed
+ 
+
+ align:start position:0%
+at that single Universal speed the speed
+of light therefore they'll have a single
+
+ align:start position:0%
+of light therefore they'll have a single
+ 
+
+ align:start position:0%
+of light therefore they'll have a single
+fixed slope they could travel off to the
+
+ align:start position:0%
+fixed slope they could travel off to the
+ 
+
+ align:start position:0%
+fixed slope they could travel off to the
+left and therefore we then we'd have a
+
+ align:start position:0%
+left and therefore we then we'd have a
+ 
+
+ align:start position:0%
+left and therefore we then we'd have a
+world line like this inclined at 45
+
+ align:start position:0%
+world line like this inclined at 45
+ 
+
+ align:start position:0%
+world line like this inclined at 45
+degrees pointing off to the left they
+
+ align:start position:0%
+degrees pointing off to the left they
+ 
+
+ align:start position:0%
+degrees pointing off to the left they
+can travel to the right but they can't
+
+ align:start position:0%
+can travel to the right but they can't
+ 
+
+ align:start position:0%
+can travel to the right but they can't
+change the slope that's the Imp that's
+
+ align:start position:0%
+change the slope that's the Imp that's
+ 
+
+ align:start position:0%
+change the slope that's the Imp that's
+the the impact of Einstein's second
+
+ align:start position:0%
+the the impact of Einstein's second
+ 
+
+ align:start position:0%
+the the impact of Einstein's second
+posture okay so far so good we can do
+
+ align:start position:0%
+posture okay so far so good we can do
+ 
+
+ align:start position:0%
+posture okay so far so good we can do
+things like we can plot more than just
+
+ align:start position:0%
+things like we can plot more than just
+ 
+
+ align:start position:0%
+things like we can plot more than just
+the path of light
+
+ align:start position:0%
+the path of light
+ 
+
+ align:start position:0%
+the path of light
+here's this is actually this is real
+
+ align:start position:0%
+here's this is actually this is real
+ 
+
+ align:start position:0%
+here's this is actually this is real
+data this is how I spend my time these
+
+ align:start position:0%
+data this is how I spend my time these
+ 
+
+ align:start position:0%
+data this is how I spend my time these
+days in quarantine I don't go anywhere
+
+ align:start position:0%
+days in quarantine I don't go anywhere
+ 
+
+ align:start position:0%
+days in quarantine I don't go anywhere
+right so my my uh position my my the
+
+ align:start position:0%
+right so my my uh position my my the
+ 
+
+ align:start position:0%
+right so my my uh position my my the
+plot of my motion through space and time
+
+ align:start position:0%
+plot of my motion through space and time
+ 
+
+ align:start position:0%
+plot of my motion through space and time
+is really easy now uh I just sit in one
+
+ align:start position:0%
+is really easy now uh I just sit in one
+ 
+
+ align:start position:0%
+is really easy now uh I just sit in one
+location of space like this chair and I
+
+ align:start position:0%
+location of space like this chair and I
+ 
+
+ align:start position:0%
+location of space like this chair and I
+don't move so all that happens is time
+
+ align:start position:0%
+don't move so all that happens is time
+ 
+
+ align:start position:0%
+don't move so all that happens is time
+Ticks inexorably by I just get older and
+
+ align:start position:0%
+Ticks inexorably by I just get older and
+ 
+
+ align:start position:0%
+Ticks inexorably by I just get older and
+older and older but I'm not moving
+
+ align:start position:0%
+older and older but I'm not moving
+ 
+
+ align:start position:0%
+older and older but I'm not moving
+around or barely so we can plot what's
+
+ align:start position:0%
+around or barely so we can plot what's
+ 
+
+ align:start position:0%
+around or barely so we can plot what's
+called my world line that's the
+
+ align:start position:0%
+called my world line that's the
+ 
+
+ align:start position:0%
+called my world line that's the
+vocabulary that gets used now with these
+
+ align:start position:0%
+vocabulary that gets used now with these
+ 
+
+ align:start position:0%
+vocabulary that gets used now with these
+space-time diagrams dating really back
+
+ align:start position:0%
+space-time diagrams dating really back
+ 
+
+ align:start position:0%
+space-time diagrams dating really back
+to the era of Herman minkowski
+
+ align:start position:0%
+to the era of Herman minkowski
+ 
+
+ align:start position:0%
+to the era of Herman minkowski
+so for any object we can chart its
+
+ align:start position:0%
+so for any object we can chart its
+ 
+
+ align:start position:0%
+so for any object we can chart its
+motion through space and time in one of
+
+ align:start position:0%
+motion through space and time in one of
+ 
+
+ align:start position:0%
+motion through space and time in one of
+these plots if it's not changing its
+
+ align:start position:0%
+these plots if it's not changing its
+ 
+
+ align:start position:0%
+these plots if it's not changing its
+location but only moving through time
+
+ align:start position:0%
+location but only moving through time
+ 
+
+ align:start position:0%
+location but only moving through time
+it'll have a straight line heading
+
+ align:start position:0%
+it'll have a straight line heading
+ 
+
+ align:start position:0%
+it'll have a straight line heading
+straight up the page it will move if
+
+ align:start position:0%
+straight up the page it will move if
+ 
+
+ align:start position:0%
+straight up the page it will move if
+it's light it's going to move at this
+
+ align:start position:0%
+it's light it's going to move at this
+ 
+
+ align:start position:0%
+it's light it's going to move at this
+fixed uh inclination or slope and of
+
+ align:start position:0%
+fixed uh inclination or slope and of
+ 
+
+ align:start position:0%
+fixed uh inclination or slope and of
+course if my family forces me to get off
+
+ align:start position:0%
+course if my family forces me to get off
+ 
+
+ align:start position:0%
+course if my family forces me to get off
+the chair and go out for a jog then I'll
+
+ align:start position:0%
+the chair and go out for a jog then I'll
+ 
+
+ align:start position:0%
+the chair and go out for a jog then I'll
+have a more complicated World line I'll
+
+ align:start position:0%
+have a more complicated World line I'll
+ 
+
+ align:start position:0%
+have a more complicated World line I'll
+be moving I'll be changing my location
+
+ align:start position:0%
+be moving I'll be changing my location
+ 
+
+ align:start position:0%
+be moving I'll be changing my location
+over time not nearly as fast as light
+
+ align:start position:0%
+over time not nearly as fast as light
+ 
+
+ align:start position:0%
+over time not nearly as fast as light
+not really as fast as shown here this is
+
+ align:start position:0%
+not really as fast as shown here this is
+ 
+
+ align:start position:0%
+not really as fast as shown here this is
+like supersonic jet pack but I will
+
+ align:start position:0%
+like supersonic jet pack but I will
+ 
+
+ align:start position:0%
+like supersonic jet pack but I will
+sometimes be moving to the right at some
+
+ align:start position:0%
+sometimes be moving to the right at some
+ 
+
+ align:start position:0%
+sometimes be moving to the right at some
+speed I might change directions later
+
+ align:start position:0%
+speed I might change directions later
+ 
+
+ align:start position:0%
+speed I might change directions later
+and move to the left but whatever I do
+
+ align:start position:0%
+and move to the left but whatever I do
+ 
+
+ align:start position:0%
+and move to the left but whatever I do
+I'll be moving at a speed slower than
+
+ align:start position:0%
+I'll be moving at a speed slower than
+ 
+
+ align:start position:0%
+I'll be moving at a speed slower than
+light that's for sure and therefore the
+
+ align:start position:0%
+light that's for sure and therefore the
+ 
+
+ align:start position:0%
+light that's for sure and therefore the
+slope of my world line is limited to
+
+ align:start position:0%
+slope of my world line is limited to
+ 
+
+ align:start position:0%
+slope of my world line is limited to
+never be as sharp as inclined as a 45
+
+ align:start position:0%
+never be as sharp as inclined as a 45
+ 
+
+ align:start position:0%
+never be as sharp as inclined as a 45
+degree line so I might have a
+
+ align:start position:0%
+degree line so I might have a
+ 
+
+ align:start position:0%
+degree line so I might have a
+non-trivial world line but it's a way
+
+ align:start position:0%
+non-trivial world line but it's a way
+ 
+
+ align:start position:0%
+non-trivial world line but it's a way
+nonetheless to chart my motion to space
+
+ align:start position:0%
+nonetheless to chart my motion to space
+ 
+
+ align:start position:0%
+nonetheless to chart my motion to space
+and time
+
+ align:start position:0%
+and time
+ 
+
+ align:start position:0%
+and time
+many of you probably seen that before
+
+ align:start position:0%
+many of you probably seen that before
+ 
+
+ align:start position:0%
+many of you probably seen that before
+this comes from the geometer Hammond
+
+ align:start position:0%
+this comes from the geometer Hammond
+ 
+
+ align:start position:0%
+this comes from the geometer Hammond
+minkowski trying to make sense of
+
+ align:start position:0%
+minkowski trying to make sense of
+ 
+
+ align:start position:0%
+minkowski trying to make sense of
+Einstein's work okay now let's go back
+
+ align:start position:0%
+Einstein's work okay now let's go back
+ 
+
+ align:start position:0%
+Einstein's work okay now let's go back
+to one of the scenarios that Einstein
+
+ align:start position:0%
+to one of the scenarios that Einstein
+ 
+
+ align:start position:0%
+to one of the scenarios that Einstein
+introduced in those opening Pages the
+
+ align:start position:0%
+introduced in those opening Pages the
+ 
+
+ align:start position:0%
+introduced in those opening Pages the
+part that you have for your assignment I
+
+ align:start position:0%
+part that you have for your assignment I
+ 
+
+ align:start position:0%
+part that you have for your assignment I
+was a 1905 paper let's imagine that I'm
+
+ align:start position:0%
+was a 1905 paper let's imagine that I'm
+ 
+
+ align:start position:0%
+was a 1905 paper let's imagine that I'm
+standing still so I'm back to my very
+
+ align:start position:0%
+standing still so I'm back to my very
+ 
+
+ align:start position:0%
+standing still so I'm back to my very
+trivial straight up the page World line
+
+ align:start position:0%
+trivial straight up the page World line
+ 
+
+ align:start position:0%
+trivial straight up the page World line
+I'm back in my chair
+
+ align:start position:0%
+I'm back in my chair
+ 
+
+ align:start position:0%
+I'm back in my chair
+and I'm standing exactly equal distance
+
+ align:start position:0%
+and I'm standing exactly equal distance
+ 
+
+ align:start position:0%
+and I'm standing exactly equal distance
+from two colleagues who are at locations
+
+ align:start position:0%
+from two colleagues who are at locations
+ 
+
+ align:start position:0%
+from two colleagues who are at locations
+A and B so I'm in equal distance along
+
+ align:start position:0%
+A and B so I'm in equal distance along
+ 
+
+ align:start position:0%
+A and B so I'm in equal distance along
+the x-axis
+
+ align:start position:0%
+the x-axis
+ 
+
+ align:start position:0%
+the x-axis
+from each of my colleagues I've asked
+
+ align:start position:0%
+from each of my colleagues I've asked
+ 
+
+ align:start position:0%
+from each of my colleagues I've asked
+them to please shine their lanterns at
+
+ align:start position:0%
+them to please shine their lanterns at
+ 
+
+ align:start position:0%
+them to please shine their lanterns at
+me at the same time if they've really
+
+ align:start position:0%
+me at the same time if they've really
+ 
+
+ align:start position:0%
+me at the same time if they've really
+done that then I'll receive the light
+
+ align:start position:0%
+done that then I'll receive the light
+ 
+
+ align:start position:0%
+done that then I'll receive the light
+waves from each of them at the same time
+
+ align:start position:0%
+waves from each of them at the same time
+ 
+
+ align:start position:0%
+waves from each of them at the same time
+the light wave traveling from B toward
+
+ align:start position:0%
+the light wave traveling from B toward
+ 
+
+ align:start position:0%
+the light wave traveling from B toward
+me and the light wave traveling from a
+
+ align:start position:0%
+me and the light wave traveling from a
+ 
+
+ align:start position:0%
+me and the light wave traveling from a
+toward me will arrive at my location at
+
+ align:start position:0%
+toward me will arrive at my location at
+ 
+
+ align:start position:0%
+toward me will arrive at my location at
+the same time sorry
+
+ align:start position:0%
+the same time sorry
+ 
+
+ align:start position:0%
+the same time sorry
+and if so then I know that A and B
+
+ align:start position:0%
+and if so then I know that A and B
+ 
+
+ align:start position:0%
+and if so then I know that A and B
+emitted their light waves simultaneously
+
+ align:start position:0%
+emitted their light waves simultaneously
+ 
+
+ align:start position:0%
+emitted their light waves simultaneously
+because the speed of light is fixed so
+
+ align:start position:0%
+because the speed of light is fixed so
+ 
+
+ align:start position:0%
+because the speed of light is fixed so
+the light wave from say the lantern held
+
+ align:start position:0%
+the light wave from say the lantern held
+ 
+
+ align:start position:0%
+the light wave from say the lantern held
+by person B couldn't have either sped up
+
+ align:start position:0%
+by person B couldn't have either sped up
+ 
+
+ align:start position:0%
+by person B couldn't have either sped up
+or slowed down it had no choice but to
+
+ align:start position:0%
+or slowed down it had no choice but to
+ 
+
+ align:start position:0%
+or slowed down it had no choice but to
+travel along this world line at exactly
+
+ align:start position:0%
+travel along this world line at exactly
+ 
+
+ align:start position:0%
+travel along this world line at exactly
+45 degrees likewise for the light wave
+
+ align:start position:0%
+45 degrees likewise for the light wave
+ 
+
+ align:start position:0%
+45 degrees likewise for the light wave
+from my friend at position a so if I
+
+ align:start position:0%
+from my friend at position a so if I
+ 
+
+ align:start position:0%
+from my friend at position a so if I
+know I'm equal distances along the
+
+ align:start position:0%
+know I'm equal distances along the
+ 
+
+ align:start position:0%
+know I'm equal distances along the
+x-axis from A and B and I receive both
+
+ align:start position:0%
+x-axis from A and B and I receive both
+ 
+
+ align:start position:0%
+x-axis from A and B and I receive both
+light waves at the same time here then
+
+ align:start position:0%
+light waves at the same time here then
+ 
+
+ align:start position:0%
+light waves at the same time here then
+they must have been emitted
+
+ align:start position:0%
+they must have been emitted
+ 
+
+ align:start position:0%
+they must have been emitted
+simultaneously there so now I can
+
+ align:start position:0%
+simultaneously there so now I can
+ 
+
+ align:start position:0%
+simultaneously there so now I can
+establish lines of simultaneity
+
+ align:start position:0%
+establish lines of simultaneity
+ 
+
+ align:start position:0%
+establish lines of simultaneity
+every point along this x-axis would have
+
+ align:start position:0%
+every point along this x-axis would have
+ 
+
+ align:start position:0%
+every point along this x-axis would have
+the same value of time in my coordinate
+
+ align:start position:0%
+the same value of time in my coordinate
+ 
+
+ align:start position:0%
+the same value of time in my coordinate
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+the value of t on my T axis is the same
+
+ align:start position:0%
+the value of t on my T axis is the same
+ 
+
+ align:start position:0%
+the value of t on my T axis is the same
+so the way I've set things up here event
+
+ align:start position:0%
+so the way I've set things up here event
+ 
+
+ align:start position:0%
+so the way I've set things up here event
+a corresponds to the time T equals zero
+
+ align:start position:0%
+a corresponds to the time T equals zero
+ 
+
+ align:start position:0%
+a corresponds to the time T equals zero
+event B corresponds to time equals zero
+
+ align:start position:0%
+event B corresponds to time equals zero
+ 
+
+ align:start position:0%
+event B corresponds to time equals zero
+at time equals zero sitting here on my
+
+ align:start position:0%
+at time equals zero sitting here on my
+ 
+
+ align:start position:0%
+at time equals zero sitting here on my
+chair
+
+ align:start position:0%
+chair
+ 
+
+ align:start position:0%
+chair
+likewise uh every other sort of moment
+
+ align:start position:0%
+likewise uh every other sort of moment
+ 
+
+ align:start position:0%
+likewise uh every other sort of moment
+line of simultaneity is parallel to the
+
+ align:start position:0%
+line of simultaneity is parallel to the
+ 
+
+ align:start position:0%
+line of simultaneity is parallel to the
+x-axis they're all parallel to the line
+
+ align:start position:0%
+x-axis they're all parallel to the line
+ 
+
+ align:start position:0%
+x-axis they're all parallel to the line
+T equals zero so I can imagine every
+
+ align:start position:0%
+T equals zero so I can imagine every
+ 
+
+ align:start position:0%
+T equals zero so I can imagine every
+event in my set of coordinates that have
+
+ align:start position:0%
+event in my set of coordinates that have
+ 
+
+ align:start position:0%
+event in my set of coordinates that have
+the assignment T equals one instead of T
+
+ align:start position:0%
+the assignment T equals one instead of T
+ 
+
+ align:start position:0%
+the assignment T equals one instead of T
+equals zero all of these were
+
+ align:start position:0%
+equals zero all of these were
+ 
+
+ align:start position:0%
+equals zero all of these were
+simultaneous with each other not
+
+ align:start position:0%
+simultaneous with each other not
+ 
+
+ align:start position:0%
+simultaneous with each other not
+simultaneous with events A and B or
+
+ align:start position:0%
+simultaneous with events A and B or
+ 
+
+ align:start position:0%
+simultaneous with events A and B or
+every point along the line T equals two
+
+ align:start position:0%
+every point along the line T equals two
+ 
+
+ align:start position:0%
+every point along the line T equals two
+and so on this is I'm sure very very
+
+ align:start position:0%
+and so on this is I'm sure very very
+ 
+
+ align:start position:0%
+and so on this is I'm sure very very
+familiar this is how we use graphs all
+
+ align:start position:0%
+familiar this is how we use graphs all
+ 
+
+ align:start position:0%
+familiar this is how we use graphs all
+the time when calcium try to just kind
+
+ align:start position:0%
+the time when calcium try to just kind
+ 
+
+ align:start position:0%
+the time when calcium try to just kind
+of give us a more straightforward
+
+ align:start position:0%
+of give us a more straightforward
+ 
+
+ align:start position:0%
+of give us a more straightforward
+geometrical interpretation Ford Einstein
+
+ align:start position:0%
+geometrical interpretation Ford Einstein
+ 
+
+ align:start position:0%
+geometrical interpretation Ford Einstein
+kind of belabors in those opening pages
+
+ align:start position:0%
+kind of belabors in those opening pages
+ 
+
+ align:start position:0%
+kind of belabors in those opening pages
+about what do we mean by simultaneous
+
+ align:start position:0%
+about what do we mean by simultaneous
+ 
+
+ align:start position:0%
+about what do we mean by simultaneous
+events in our frame of reference
+
+ align:start position:0%
+events in our frame of reference
+ 
+
+ align:start position:0%
+events in our frame of reference
+these are events that occur along a line
+
+ align:start position:0%
+these are events that occur along a line
+ 
+
+ align:start position:0%
+these are events that occur along a line
+of simultaneity well now we can use our
+
+ align:start position:0%
+of simultaneity well now we can use our
+ 
+
+ align:start position:0%
+of simultaneity well now we can use our
+set of coordinates our x and t and and
+
+ align:start position:0%
+set of coordinates our x and t and and
+ 
+
+ align:start position:0%
+set of coordinates our x and t and and
+map the motion of some other object
+
+ align:start position:0%
+map the motion of some other object
+ 
+
+ align:start position:0%
+map the motion of some other object
+that's moving with respect to us for
+
+ align:start position:0%
+that's moving with respect to us for
+ 
+
+ align:start position:0%
+that's moving with respect to us for
+example Einstein's favorite object a
+
+ align:start position:0%
+example Einstein's favorite object a
+ 
+
+ align:start position:0%
+example Einstein's favorite object a
+train
+
+ align:start position:0%
+train
+ 
+
+ align:start position:0%
+train
+so now we can chart the world lines of
+
+ align:start position:0%
+so now we can chart the world lines of
+ 
+
+ align:start position:0%
+so now we can chart the world lines of
+the back of the Train the middle of the
+
+ align:start position:0%
+the back of the Train the middle of the
+ 
+
+ align:start position:0%
+the back of the Train the middle of the
+train and the front of the train as the
+
+ align:start position:0%
+train and the front of the train as the
+ 
+
+ align:start position:0%
+train and the front of the train as the
+entire assembly moves past us while we
+
+ align:start position:0%
+entire assembly moves past us while we
+ 
+
+ align:start position:0%
+entire assembly moves past us while we
+stand still on the train platform so
+
+ align:start position:0%
+stand still on the train platform so
+ 
+
+ align:start position:0%
+stand still on the train platform so
+this is our Mo our mapping of the moving
+
+ align:start position:0%
+this is our Mo our mapping of the moving
+ 
+
+ align:start position:0%
+this is our Mo our mapping of the moving
+object's motion from within our set of
+
+ align:start position:0%
+object's motion from within our set of
+ 
+
+ align:start position:0%
+object's motion from within our set of
+coordinates with respect to the
+
+ align:start position:0%
+coordinates with respect to the
+ 
+
+ align:start position:0%
+coordinates with respect to the
+coordinates of Mark our frame of rest
+
+ align:start position:0%
+coordinates of Mark our frame of rest
+ 
+
+ align:start position:0%
+coordinates of Mark our frame of rest
+and we're going to watch this moving
+
+ align:start position:0%
+and we're going to watch this moving
+ 
+
+ align:start position:0%
+and we're going to watch this moving
+train move through our coordinates okay
+
+ align:start position:0%
+train move through our coordinates okay
+ 
+
+ align:start position:0%
+train move through our coordinates okay
+now remember we have a partner who rides
+
+ align:start position:0%
+now remember we have a partner who rides
+ 
+
+ align:start position:0%
+now remember we have a partner who rides
+in the middle of the train again very
+
+ align:start position:0%
+in the middle of the train again very
+ 
+
+ align:start position:0%
+in the middle of the train again very
+much like what Einstein was describing
+
+ align:start position:0%
+much like what Einstein was describing
+ 
+
+ align:start position:0%
+much like what Einstein was describing
+so we have a colleague who's sitting in
+
+ align:start position:0%
+so we have a colleague who's sitting in
+ 
+
+ align:start position:0%
+so we have a colleague who's sitting in
+the middle of the train she knows she's
+
+ align:start position:0%
+the middle of the train she knows she's
+ 
+
+ align:start position:0%
+the middle of the train she knows she's
+exactly equal distance from the front to
+
+ align:start position:0%
+exactly equal distance from the front to
+ 
+
+ align:start position:0%
+exactly equal distance from the front to
+the back of the train
+
+ align:start position:0%
+the back of the train
+ 
+
+ align:start position:0%
+the back of the train
+she's asked friends on the train to
+
+ align:start position:0%
+she's asked friends on the train to
+ 
+
+ align:start position:0%
+she's asked friends on the train to
+shine their lanterns toward her and
+
+ align:start position:0%
+shine their lanterns toward her and
+ 
+
+ align:start position:0%
+shine their lanterns toward her and
+she'll uh she'll be able to determine
+
+ align:start position:0%
+she'll uh she'll be able to determine
+ 
+
+ align:start position:0%
+she'll uh she'll be able to determine
+whether or not her colleagues A and B
+
+ align:start position:0%
+whether or not her colleagues A and B
+ 
+
+ align:start position:0%
+whether or not her colleagues A and B
+shine their lanterns toward her
+
+ align:start position:0%
+shine their lanterns toward her
+ 
+
+ align:start position:0%
+shine their lanterns toward her
+simultaneously well light can only
+
+ align:start position:0%
+simultaneously well light can only
+ 
+
+ align:start position:0%
+simultaneously well light can only
+travel along 45 degrees on these
+
+ align:start position:0%
+travel along 45 degrees on these
+ 
+
+ align:start position:0%
+travel along 45 degrees on these
+diagrams for me or for her even on the
+
+ align:start position:0%
+diagrams for me or for her even on the
+ 
+
+ align:start position:0%
+diagrams for me or for her even on the
+moving train the light wave that's
+
+ align:start position:0%
+moving train the light wave that's
+ 
+
+ align:start position:0%
+moving train the light wave that's
+emitted from point B doesn't speed up it
+
+ align:start position:0%
+emitted from point B doesn't speed up it
+ 
+
+ align:start position:0%
+emitted from point B doesn't speed up it
+go it can only but go along a 45 degree
+
+ align:start position:0%
+go it can only but go along a 45 degree
+ 
+
+ align:start position:0%
+go it can only but go along a 45 degree
+angle that's the that's the real force
+
+ align:start position:0%
+angle that's the that's the real force
+ 
+
+ align:start position:0%
+angle that's the that's the real force
+of Einstein's second postulate likewise
+
+ align:start position:0%
+of Einstein's second postulate likewise
+ 
+
+ align:start position:0%
+of Einstein's second postulate likewise
+the light wave that's emitted from point
+
+ align:start position:0%
+the light wave that's emitted from point
+ 
+
+ align:start position:0%
+the light wave that's emitted from point
+B can only travel at the speed of light
+
+ align:start position:0%
+B can only travel at the speed of light
+ 
+
+ align:start position:0%
+B can only travel at the speed of light
+so in my coordinates as much as in my
+
+ align:start position:0%
+so in my coordinates as much as in my
+ 
+
+ align:start position:0%
+so in my coordinates as much as in my
+colleague's coordinates on the train
+
+ align:start position:0%
+colleague's coordinates on the train
+ 
+
+ align:start position:0%
+colleague's coordinates on the train
+those light waves must travel at 45
+
+ align:start position:0%
+those light waves must travel at 45
+ 
+
+ align:start position:0%
+those light waves must travel at 45
+degree lines at the constant speed of
+
+ align:start position:0%
+degree lines at the constant speed of
+ 
+
+ align:start position:0%
+degree lines at the constant speed of
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+so our colleague who's moving on this
+
+ align:start position:0%
+so our colleague who's moving on this
+ 
+
+ align:start position:0%
+so our colleague who's moving on this
+train sitting in the middle she receives
+
+ align:start position:0%
+train sitting in the middle she receives
+ 
+
+ align:start position:0%
+train sitting in the middle she receives
+the light beams from point A and point B
+
+ align:start position:0%
+the light beams from point A and point B
+ 
+
+ align:start position:0%
+the light beams from point A and point B
+at the same time so now she knows those
+
+ align:start position:0%
+at the same time so now she knows those
+ 
+
+ align:start position:0%
+at the same time so now she knows those
+in Mission events must have been
+
+ align:start position:0%
+in Mission events must have been
+ 
+
+ align:start position:0%
+in Mission events must have been
+simultaneous how could they not have
+
+ align:start position:0%
+simultaneous how could they not have
+ 
+
+ align:start position:0%
+simultaneous how could they not have
+been she's in equal distance the light
+
+ align:start position:0%
+been she's in equal distance the light
+ 
+
+ align:start position:0%
+been she's in equal distance the light
+waves couldn't have either sped up or
+
+ align:start position:0%
+waves couldn't have either sped up or
+ 
+
+ align:start position:0%
+waves couldn't have either sped up or
+slowed down so therefore all the points
+
+ align:start position:0%
+slowed down so therefore all the points
+ 
+
+ align:start position:0%
+slowed down so therefore all the points
+along this new lie we can call the X
+
+ align:start position:0%
+along this new lie we can call the X
+ 
+
+ align:start position:0%
+along this new lie we can call the X
+Prime axis all those events were occur
+
+ align:start position:0%
+Prime axis all those events were occur
+ 
+
+ align:start position:0%
+Prime axis all those events were occur
+along a line of simultaneity for her in
+
+ align:start position:0%
+along a line of simultaneity for her in
+ 
+
+ align:start position:0%
+along a line of simultaneity for her in
+the moving train she knows exactly how
+
+ align:start position:0%
+the moving train she knows exactly how
+ 
+
+ align:start position:0%
+the moving train she knows exactly how
+to establish which events are
+
+ align:start position:0%
+to establish which events are
+ 
+
+ align:start position:0%
+to establish which events are
+simultaneous she can take advantage of
+
+ align:start position:0%
+simultaneous she can take advantage of
+ 
+
+ align:start position:0%
+simultaneous she can take advantage of
+light waves they travel at a universal
+
+ align:start position:0%
+light waves they travel at a universal
+ 
+
+ align:start position:0%
+light waves they travel at a universal
+speed
+
+ align:start position:0%
+speed
+ 
+
+ align:start position:0%
+speed
+it just turns out that what events are
+
+ align:start position:0%
+it just turns out that what events are
+ 
+
+ align:start position:0%
+it just turns out that what events are
+simultaneous for her no longer Maps the
+
+ align:start position:0%
+simultaneous for her no longer Maps the
+ 
+
+ align:start position:0%
+simultaneous for her no longer Maps the
+set of events that are simultaneous for
+
+ align:start position:0%
+set of events that are simultaneous for
+ 
+
+ align:start position:0%
+set of events that are simultaneous for
+us she has a different set of lines of
+
+ align:start position:0%
+us she has a different set of lines of
+ 
+
+ align:start position:0%
+us she has a different set of lines of
+simultaneity and minkowski was saying in
+
+ align:start position:0%
+simultaneity and minkowski was saying in
+ 
+
+ align:start position:0%
+simultaneity and minkowski was saying in
+effect you idiot Einstein it's just a
+
+ align:start position:0%
+effect you idiot Einstein it's just a
+ 
+
+ align:start position:0%
+effect you idiot Einstein it's just a
+coordinate rotation you're just
+
+ align:start position:0%
+coordinate rotation you're just
+ 
+
+ align:start position:0%
+coordinate rotation you're just
+establishing a new set of coordinates
+
+ align:start position:0%
+establishing a new set of coordinates
+ 
+
+ align:start position:0%
+establishing a new set of coordinates
+like any student of geometry should be
+
+ align:start position:0%
+like any student of geometry should be
+ 
+
+ align:start position:0%
+like any student of geometry should be
+able to do he said it only slightly more
+
+ align:start position:0%
+able to do he said it only slightly more
+ 
+
+ align:start position:0%
+able to do he said it only slightly more
+nicely in his published article
+
+ align:start position:0%
+nicely in his published article
+ 
+
+ align:start position:0%
+nicely in his published article
+meanwhile the T Prime axis is nothing
+
+ align:start position:0%
+meanwhile the T Prime axis is nothing
+ 
+
+ align:start position:0%
+meanwhile the T Prime axis is nothing
+other than the world line of the zero
+
+ align:start position:0%
+other than the world line of the zero
+ 
+
+ align:start position:0%
+other than the world line of the zero
+point of space for the moving uh moving
+
+ align:start position:0%
+point of space for the moving uh moving
+ 
+
+ align:start position:0%
+point of space for the moving uh moving
+Observer that is to say it's the world
+
+ align:start position:0%
+Observer that is to say it's the world
+ 
+
+ align:start position:0%
+Observer that is to say it's the world
+line of the back of the Train the origin
+
+ align:start position:0%
+line of the back of the Train the origin
+ 
+
+ align:start position:0%
+line of the back of the Train the origin
+point of her coordinates is say the back
+
+ align:start position:0%
+point of her coordinates is say the back
+ 
+
+ align:start position:0%
+point of her coordinates is say the back
+of the train X Prime equals zero she can
+
+ align:start position:0%
+of the train X Prime equals zero she can
+ 
+
+ align:start position:0%
+of the train X Prime equals zero she can
+measure any distance she wants with
+
+ align:start position:0%
+measure any distance she wants with
+ 
+
+ align:start position:0%
+measure any distance she wants with
+reference to the back of the train right
+
+ align:start position:0%
+reference to the back of the train right
+ 
+
+ align:start position:0%
+reference to the back of the train right
+she's moving with the train she can
+
+ align:start position:0%
+she's moving with the train she can
+ 
+
+ align:start position:0%
+she's moving with the train she can
+always lay out meter sticks and measure
+
+ align:start position:0%
+always lay out meter sticks and measure
+ 
+
+ align:start position:0%
+always lay out meter sticks and measure
+how far the front of the train is from
+
+ align:start position:0%
+how far the front of the train is from
+ 
+
+ align:start position:0%
+how far the front of the train is from
+the back so the origin the spatial
+
+ align:start position:0%
+the back so the origin the spatial
+ 
+
+ align:start position:0%
+the back so the origin the spatial
+origin of her coordinates is the back of
+
+ align:start position:0%
+origin of her coordinates is the back of
+ 
+
+ align:start position:0%
+origin of her coordinates is the back of
+the train how does that move through
+
+ align:start position:0%
+the train how does that move through
+ 
+
+ align:start position:0%
+the train how does that move through
+space and time that just put that just
+
+ align:start position:0%
+space and time that just put that just
+ 
+
+ align:start position:0%
+space and time that just put that just
+Becomes Her T Prime axis much as our
+
+ align:start position:0%
+Becomes Her T Prime axis much as our
+ 
+
+ align:start position:0%
+Becomes Her T Prime axis much as our
+location of the point x equals zero as
+
+ align:start position:0%
+location of the point x equals zero as
+ 
+
+ align:start position:0%
+location of the point x equals zero as
+it just sits still and moves through
+
+ align:start position:0%
+it just sits still and moves through
+ 
+
+ align:start position:0%
+it just sits still and moves through
+time that Maps out for us the t-axis
+
+ align:start position:0%
+time that Maps out for us the t-axis
+ 
+
+ align:start position:0%
+time that Maps out for us the t-axis
+the next thing minkowski showed very
+
+ align:start position:0%
+the next thing minkowski showed very
+ 
+
+ align:start position:0%
+the next thing minkowski showed very
+very uh very easily for him as a
+
+ align:start position:0%
+very uh very easily for him as a
+ 
+
+ align:start position:0%
+very uh very easily for him as a
+geometer is that the angle between the X
+
+ align:start position:0%
+geometer is that the angle between the X
+ 
+
+ align:start position:0%
+geometer is that the angle between the X
+and the X Prime axis some angle Theta is
+
+ align:start position:0%
+and the X Prime axis some angle Theta is
+ 
+
+ align:start position:0%
+and the X Prime axis some angle Theta is
+exactly the same angle as that between
+
+ align:start position:0%
+exactly the same angle as that between
+ 
+
+ align:start position:0%
+exactly the same angle as that between
+the T and the T Prime axis in fact that
+
+ align:start position:0%
+the T and the T Prime axis in fact that
+ 
+
+ align:start position:0%
+the T and the T Prime axis in fact that
+angle is directly related to this ratio
+
+ align:start position:0%
+angle is directly related to this ratio
+ 
+
+ align:start position:0%
+angle is directly related to this ratio
+V over C So the faster the relative
+
+ align:start position:0%
+V over C So the faster the relative
+ 
+
+ align:start position:0%
+V over C So the faster the relative
+motion between us and the Train the more
+
+ align:start position:0%
+motion between us and the Train the more
+ 
+
+ align:start position:0%
+motion between us and the Train the more
+steeply these lines are inclined the
+
+ align:start position:0%
+steeply these lines are inclined the
+ 
+
+ align:start position:0%
+steeply these lines are inclined the
+larger the angle as the relative speed V
+
+ align:start position:0%
+larger the angle as the relative speed V
+ 
+
+ align:start position:0%
+larger the angle as the relative speed V
+Rises with respect to that constant
+
+ align:start position:0%
+Rises with respect to that constant
+ 
+
+ align:start position:0%
+Rises with respect to that constant
+Universal speed the speed of light this
+
+ align:start position:0%
+Universal speed the speed of light this
+ 
+
+ align:start position:0%
+Universal speed the speed of light this
+angle becomes larger the X Prime axis
+
+ align:start position:0%
+angle becomes larger the X Prime axis
+ 
+
+ align:start position:0%
+angle becomes larger the X Prime axis
+becomes tilted even more far away from X
+
+ align:start position:0%
+becomes tilted even more far away from X
+ 
+
+ align:start position:0%
+becomes tilted even more far away from X
+the T Prime axis gets tilted even more
+
+ align:start position:0%
+the T Prime axis gets tilted even more
+ 
+
+ align:start position:0%
+the T Prime axis gets tilted even more
+inward away from T but all we're doing
+
+ align:start position:0%
+inward away from T but all we're doing
+ 
+
+ align:start position:0%
+inward away from T but all we're doing
+is establishing a new set of axes with
+
+ align:start position:0%
+is establishing a new set of axes with
+ 
+
+ align:start position:0%
+is establishing a new set of axes with
+respect to which we can mark the motion
+
+ align:start position:0%
+respect to which we can mark the motion
+ 
+
+ align:start position:0%
+respect to which we can mark the motion
+of objects through space and time
+
+ align:start position:0%
+of objects through space and time
+ 
+
+ align:start position:0%
+of objects through space and time
+according to the geometer hermannkowski
+
+ align:start position:0%
+according to the geometer hermannkowski
+ 
+
+ align:start position:0%
+according to the geometer hermannkowski
+so now we come to some of these strange
+
+ align:start position:0%
+so now we come to some of these strange
+ 
+
+ align:start position:0%
+so now we come to some of these strange
+sounding ideas that Einstein again had
+
+ align:start position:0%
+sounding ideas that Einstein again had
+ 
+
+ align:start position:0%
+sounding ideas that Einstein again had
+kind of belabored as far as minkowski is
+
+ align:start position:0%
+kind of belabored as far as minkowski is
+ 
+
+ align:start position:0%
+kind of belabored as far as minkowski is
+concerned Einstein belabored with all
+
+ align:start position:0%
+concerned Einstein belabored with all
+ 
+
+ align:start position:0%
+concerned Einstein belabored with all
+this kind of lengthy discussion of kind
+
+ align:start position:0%
+this kind of lengthy discussion of kind
+ 
+
+ align:start position:0%
+this kind of lengthy discussion of kind
+of Eric's mock inspired you know uh
+
+ align:start position:0%
+of Eric's mock inspired you know uh
+ 
+
+ align:start position:0%
+of Eric's mock inspired you know uh
+measurement procedures Mankowski says
+
+ align:start position:0%
+measurement procedures Mankowski says
+ 
+
+ align:start position:0%
+measurement procedures Mankowski says
+it's just more geometry let's take the
+
+ align:start position:0%
+it's just more geometry let's take the
+ 
+
+ align:start position:0%
+it's just more geometry let's take the
+example of length contraction we all
+
+ align:start position:0%
+example of length contraction we all
+ 
+
+ align:start position:0%
+example of length contraction we all
+agree the procedure for measuring
+
+ align:start position:0%
+agree the procedure for measuring
+ 
+
+ align:start position:0%
+agree the procedure for measuring
+lengths is to measure the location of
+
+ align:start position:0%
+lengths is to measure the location of
+ 
+
+ align:start position:0%
+lengths is to measure the location of
+the front of the object and the back of
+
+ align:start position:0%
+the front of the object and the back of
+ 
+
+ align:start position:0%
+the front of the object and the back of
+the object at the same time and then
+
+ align:start position:0%
+the object at the same time and then
+ 
+
+ align:start position:0%
+the object at the same time and then
+take the difference okay
+
+ align:start position:0%
+take the difference okay
+ 
+
+ align:start position:0%
+take the difference okay
+so we measure the length of the train to
+
+ align:start position:0%
+so we measure the length of the train to
+ 
+
+ align:start position:0%
+so we measure the length of the train to
+be this length I've called L Prime we
+
+ align:start position:0%
+be this length I've called L Prime we
+ 
+
+ align:start position:0%
+be this length I've called L Prime we
+have our friend at the back of the train
+
+ align:start position:0%
+have our friend at the back of the train
+ 
+
+ align:start position:0%
+have our friend at the back of the train
+at position a we have our friend at the
+
+ align:start position:0%
+at position a we have our friend at the
+ 
+
+ align:start position:0%
+at position a we have our friend at the
+front of the train at position B Prime
+
+ align:start position:0%
+front of the train at position B Prime
+ 
+
+ align:start position:0%
+front of the train at position B Prime
+we know those are simultaneous because
+
+ align:start position:0%
+we know those are simultaneous because
+ 
+
+ align:start position:0%
+we know those are simultaneous because
+they lie along a line of simultaneous
+
+ align:start position:0%
+they lie along a line of simultaneous
+ 
+
+ align:start position:0%
+they lie along a line of simultaneous
+for us or a little bit more kind of uh
+
+ align:start position:0%
+for us or a little bit more kind of uh
+ 
+
+ align:start position:0%
+for us or a little bit more kind of uh
+concretely both the event a and the
+
+ align:start position:0%
+concretely both the event a and the
+ 
+
+ align:start position:0%
+concretely both the event a and the
+event B Prime share the coordinate T
+
+ align:start position:0%
+event B Prime share the coordinate T
+ 
+
+ align:start position:0%
+event B Prime share the coordinate T
+equals zero they have the same time
+
+ align:start position:0%
+equals zero they have the same time
+ 
+
+ align:start position:0%
+equals zero they have the same time
+coordinate in our coordinate system in
+
+ align:start position:0%
+coordinate in our coordinate system in
+ 
+
+ align:start position:0%
+coordinate in our coordinate system in
+our reference frame they lie along a
+
+ align:start position:0%
+our reference frame they lie along a
+ 
+
+ align:start position:0%
+our reference frame they lie along a
+line of simultaneity so we've therefore
+
+ align:start position:0%
+line of simultaneity so we've therefore
+ 
+
+ align:start position:0%
+line of simultaneity so we've therefore
+marked the position along the x-axis of
+
+ align:start position:0%
+marked the position along the x-axis of
+ 
+
+ align:start position:0%
+marked the position along the x-axis of
+the front of the train and the back of
+
+ align:start position:0%
+the front of the train and the back of
+ 
+
+ align:start position:0%
+the front of the train and the back of
+the train at the same time in our
+
+ align:start position:0%
+the train at the same time in our
+ 
+
+ align:start position:0%
+the train at the same time in our
+reference frame now we can just take the
+
+ align:start position:0%
+reference frame now we can just take the
+ 
+
+ align:start position:0%
+reference frame now we can just take the
+difference subtract the location of this
+
+ align:start position:0%
+difference subtract the location of this
+ 
+
+ align:start position:0%
+difference subtract the location of this
+point B Prime along the x-axis subtract
+
+ align:start position:0%
+point B Prime along the x-axis subtract
+ 
+
+ align:start position:0%
+point B Prime along the x-axis subtract
+it from the origin of a that's our
+
+ align:start position:0%
+it from the origin of a that's our
+ 
+
+ align:start position:0%
+it from the origin of a that's our
+length of trade front and back same time
+
+ align:start position:0%
+length of trade front and back same time
+ 
+
+ align:start position:0%
+length of trade front and back same time
+length L Prime meanwhile for our friend
+
+ align:start position:0%
+length L Prime meanwhile for our friend
+ 
+
+ align:start position:0%
+length L Prime meanwhile for our friend
+who's riding along the train
+
+ align:start position:0%
+who's riding along the train
+ 
+
+ align:start position:0%
+who's riding along the train
+she knows exactly which events are
+
+ align:start position:0%
+she knows exactly which events are
+ 
+
+ align:start position:0%
+she knows exactly which events are
+simultaneous because she can have her
+
+ align:start position:0%
+simultaneous because she can have her
+ 
+
+ align:start position:0%
+simultaneous because she can have her
+friends test this with the exchange of
+
+ align:start position:0%
+friends test this with the exchange of
+ 
+
+ align:start position:0%
+friends test this with the exchange of
+light signals and she knows very very
+
+ align:start position:0%
+light signals and she knows very very
+ 
+
+ align:start position:0%
+light signals and she knows very very
+clearly that the events A and B are
+
+ align:start position:0%
+clearly that the events A and B are
+ 
+
+ align:start position:0%
+clearly that the events A and B are
+simultaneous for her reference frame A
+
+ align:start position:0%
+simultaneous for her reference frame A
+ 
+
+ align:start position:0%
+simultaneous for her reference frame A
+and B lie along a shared line of
+
+ align:start position:0%
+and B lie along a shared line of
+ 
+
+ align:start position:0%
+and B lie along a shared line of
+simultaneous just not our line of
+
+ align:start position:0%
+simultaneous just not our line of
+ 
+
+ align:start position:0%
+simultaneous just not our line of
+simultaneity so her friend of the front
+
+ align:start position:0%
+simultaneity so her friend of the front
+ 
+
+ align:start position:0%
+simultaneity so her friend of the front
+of the train can mark that location her
+
+ align:start position:0%
+of the train can mark that location her
+ 
+
+ align:start position:0%
+of the train can mark that location her
+friend at the back of the train can mark
+
+ align:start position:0%
+friend at the back of the train can mark
+ 
+
+ align:start position:0%
+friend at the back of the train can mark
+that location we know they're doing it
+
+ align:start position:0%
+that location we know they're doing it
+ 
+
+ align:start position:0%
+that location we know they're doing it
+at the same time in the moving reference
+
+ align:start position:0%
+at the same time in the moving reference
+ 
+
+ align:start position:0%
+at the same time in the moving reference
+frame take the difference is the
+
+ align:start position:0%
+frame take the difference is the
+ 
+
+ align:start position:0%
+frame take the difference is the
+difference l which as you can see now
+
+ align:start position:0%
+difference l which as you can see now
+ 
+
+ align:start position:0%
+difference l which as you can see now
+just trivially is longer than L Prime
+
+ align:start position:0%
+just trivially is longer than L Prime
+ 
+
+ align:start position:0%
+just trivially is longer than L Prime
+so what Einstein called Edward Frank for
+
+ align:start position:0%
+so what Einstein called Edward Frank for
+ 
+
+ align:start position:0%
+so what Einstein called Edward Frank for
+that matter Lorenzo called length
+
+ align:start position:0%
+that matter Lorenzo called length
+ 
+
+ align:start position:0%
+that matter Lorenzo called length
+contraction our measurement of the
+
+ align:start position:0%
+contraction our measurement of the
+ 
+
+ align:start position:0%
+contraction our measurement of the
+moving object is short compared to the
+
+ align:start position:0%
+moving object is short compared to the
+ 
+
+ align:start position:0%
+moving object is short compared to the
+measurement conducted by someone moving
+
+ align:start position:0%
+measurement conducted by someone moving
+ 
+
+ align:start position:0%
+measurement conducted by someone moving
+with that object L Prime is demonstrably
+
+ align:start position:0%
+with that object L Prime is demonstrably
+ 
+
+ align:start position:0%
+with that object L Prime is demonstrably
+shorter than L and minkowski's has an
+
+ align:start position:0%
+shorter than L and minkowski's has an
+ 
+
+ align:start position:0%
+shorter than L and minkowski's has an
+effect of course it is we're just
+
+ align:start position:0%
+effect of course it is we're just
+ 
+
+ align:start position:0%
+effect of course it is we're just
+projecting our measurements onto
+
+ align:start position:0%
+projecting our measurements onto
+ 
+
+ align:start position:0%
+projecting our measurements onto
+different sets of axes we are geometers
+
+ align:start position:0%
+different sets of axes we are geometers
+ 
+
+ align:start position:0%
+different sets of axes we are geometers
+we reckon objects with certain sets of
+
+ align:start position:0%
+we reckon objects with certain sets of
+ 
+
+ align:start position:0%
+we reckon objects with certain sets of
+coordinates and we just happen to have
+
+ align:start position:0%
+coordinates and we just happen to have
+ 
+
+ align:start position:0%
+coordinates and we just happen to have
+different coordinates that we with which
+
+ align:start position:0%
+different coordinates that we with which
+ 
+
+ align:start position:0%
+different coordinates that we with which
+we're making sense of the world
+
+ align:start position:0%
+we're making sense of the world
+ 
+
+ align:start position:0%
+we're making sense of the world
+it doesn't just derive the qualitative
+
+ align:start position:0%
+it doesn't just derive the qualitative
+ 
+
+ align:start position:0%
+it doesn't just derive the qualitative
+phenomenon of length contraction he gets
+
+ align:start position:0%
+phenomenon of length contraction he gets
+ 
+
+ align:start position:0%
+phenomenon of length contraction he gets
+exactly the answer that both Einstein
+
+ align:start position:0%
+exactly the answer that both Einstein
+ 
+
+ align:start position:0%
+exactly the answer that both Einstein
+and Lorenzo gotten even though they had
+
+ align:start position:0%
+and Lorenzo gotten even though they had
+ 
+
+ align:start position:0%
+and Lorenzo gotten even though they had
+had very different forms of argument he
+
+ align:start position:0%
+had very different forms of argument he
+ 
+
+ align:start position:0%
+had very different forms of argument he
+even gets the exact form of this gamma
+
+ align:start position:0%
+even gets the exact form of this gamma
+ 
+
+ align:start position:0%
+even gets the exact form of this gamma
+because as you may remember the angle
+
+ align:start position:0%
+because as you may remember the angle
+ 
+
+ align:start position:0%
+because as you may remember the angle
+here between x and x Prime is directly
+
+ align:start position:0%
+here between x and x Prime is directly
+ 
+
+ align:start position:0%
+here between x and x Prime is directly
+related to V over c as is the factored
+
+ align:start position:0%
+related to V over c as is the factored
+ 
+
+ align:start position:0%
+related to V over c as is the factored
+gamma a few lines of algebra not very
+
+ align:start position:0%
+gamma a few lines of algebra not very
+ 
+
+ align:start position:0%
+gamma a few lines of algebra not very
+hard to see the relationship between
+
+ align:start position:0%
+hard to see the relationship between
+ 
+
+ align:start position:0%
+hard to see the relationship between
+this line segment and that line segment
+
+ align:start position:0%
+this line segment and that line segment
+ 
+
+ align:start position:0%
+this line segment and that line segment
+what's important again to underscore is
+
+ align:start position:0%
+what's important again to underscore is
+ 
+
+ align:start position:0%
+what's important again to underscore is
+not the algebra I'm confident we can all
+
+ align:start position:0%
+not the algebra I'm confident we can all
+ 
+
+ align:start position:0%
+not the algebra I'm confident we can all
+do that is to say that for minkowski
+
+ align:start position:0%
+do that is to say that for minkowski
+ 
+
+ align:start position:0%
+do that is to say that for minkowski
+this is not about The Ether it's not
+
+ align:start position:0%
+this is not about The Ether it's not
+ 
+
+ align:start position:0%
+this is not about The Ether it's not
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um Mahi and observations that are
+
+ align:start position:0%
+um Mahi and observations that are
+ 
+
+ align:start position:0%
+um Mahi and observations that are
+subject to positive experience this is
+
+ align:start position:0%
+subject to positive experience this is
+ 
+
+ align:start position:0%
+subject to positive experience this is
+just geometry as we transform between
+
+ align:start position:0%
+just geometry as we transform between
+ 
+
+ align:start position:0%
+just geometry as we transform between
+different coordinate systems and you can
+
+ align:start position:0%
+different coordinate systems and you can
+ 
+
+ align:start position:0%
+different coordinate systems and you can
+almost hear him saying no da to Einstein
+
+ align:start position:0%
+almost hear him saying no da to Einstein
+ 
+
+ align:start position:0%
+almost hear him saying no da to Einstein
+who'd cut all his classes
+
+ align:start position:0%
+who'd cut all his classes
+ 
+
+ align:start position:0%
+who'd cut all his classes
+Mankowski goes on in this article uh
+
+ align:start position:0%
+Mankowski goes on in this article uh
+ 
+
+ align:start position:0%
+Mankowski goes on in this article uh
+first worked out in 1907. using these
+
+ align:start position:0%
+first worked out in 1907. using these
+ 
+
+ align:start position:0%
+first worked out in 1907. using these
+space-time diagrams he then shows that
+
+ align:start position:0%
+space-time diagrams he then shows that
+ 
+
+ align:start position:0%
+space-time diagrams he then shows that
+the full lorentz transformation was
+
+ align:start position:0%
+the full lorentz transformation was
+ 
+
+ align:start position:0%
+the full lorentz transformation was
+nothing but geometry remember to
+
+ align:start position:0%
+nothing but geometry remember to
+ 
+
+ align:start position:0%
+nothing but geometry remember to
+Mankowski everything was geometry this
+
+ align:start position:0%
+Mankowski everything was geometry this
+ 
+
+ align:start position:0%
+Mankowski everything was geometry this
+was just a rotation in space-time now to
+
+ align:start position:0%
+was just a rotation in space-time now to
+ 
+
+ align:start position:0%
+was just a rotation in space-time now to
+warm up for that again we'll do
+
+ align:start position:0%
+warm up for that again we'll do
+ 
+
+ align:start position:0%
+warm up for that again we'll do
+something probably a little bit familiar
+
+ align:start position:0%
+something probably a little bit familiar
+ 
+
+ align:start position:0%
+something probably a little bit familiar
+to start we'll talk about just an
+
+ align:start position:0%
+to start we'll talk about just an
+ 
+
+ align:start position:0%
+to start we'll talk about just an
+ordinary uh X Y plane two directions of
+
+ align:start position:0%
+ordinary uh X Y plane two directions of
+ 
+
+ align:start position:0%
+ordinary uh X Y plane two directions of
+space that are perpendicular to each
+
+ align:start position:0%
+space that are perpendicular to each
+ 
+
+ align:start position:0%
+space that are perpendicular to each
+other the Cartesian plane or if you like
+
+ align:start position:0%
+other the Cartesian plane or if you like
+ 
+
+ align:start position:0%
+other the Cartesian plane or if you like
+the euclidean plane we can lay out our
+
+ align:start position:0%
+the euclidean plane we can lay out our
+ 
+
+ align:start position:0%
+the euclidean plane we can lay out our
+coordinates X will be our horizontal
+
+ align:start position:0%
+coordinates X will be our horizontal
+ 
+
+ align:start position:0%
+coordinates X will be our horizontal
+axis y is at right angles heading up the
+
+ align:start position:0%
+axis y is at right angles heading up the
+ 
+
+ align:start position:0%
+axis y is at right angles heading up the
+page these are two directions of space
+
+ align:start position:0%
+page these are two directions of space
+ 
+
+ align:start position:0%
+page these are two directions of space
+we can identify some points in the plane
+
+ align:start position:0%
+we can identify some points in the plane
+ 
+
+ align:start position:0%
+we can identify some points in the plane
+we'll call it Point P we can label the
+
+ align:start position:0%
+we'll call it Point P we can label the
+ 
+
+ align:start position:0%
+we'll call it Point P we can label the
+location of that point in our coordinate
+
+ align:start position:0%
+location of that point in our coordinate
+ 
+
+ align:start position:0%
+location of that point in our coordinate
+system we'll project what that means
+
+ align:start position:0%
+system we'll project what that means
+ 
+
+ align:start position:0%
+system we'll project what that means
+really is we're projecting the location
+
+ align:start position:0%
+really is we're projecting the location
+ 
+
+ align:start position:0%
+really is we're projecting the location
+of Point P onto our perpendicular axes
+
+ align:start position:0%
+of Point P onto our perpendicular axes
+ 
+
+ align:start position:0%
+of Point P onto our perpendicular axes
+so we label the x coordinate of Point p
+
+ align:start position:0%
+so we label the x coordinate of Point p
+ 
+
+ align:start position:0%
+so we label the x coordinate of Point p
+as its projection along the P excuse me
+
+ align:start position:0%
+as its projection along the P excuse me
+ 
+
+ align:start position:0%
+as its projection along the P excuse me
+along the x-axis it has some value X1 we
+
+ align:start position:0%
+along the x-axis it has some value X1 we
+ 
+
+ align:start position:0%
+along the x-axis it has some value X1 we
+identified the location of Point P the
+
+ align:start position:0%
+identified the location of Point P the
+ 
+
+ align:start position:0%
+identified the location of Point P the
+projection along the y-axis that's it's
+
+ align:start position:0%
+projection along the y-axis that's it's
+ 
+
+ align:start position:0%
+projection along the y-axis that's it's
+a y coordinate y one fine
+
+ align:start position:0%
+a y coordinate y one fine
+ 
+
+ align:start position:0%
+a y coordinate y one fine
+now we all know even Einstein knew we're
+
+ align:start position:0%
+now we all know even Einstein knew we're
+ 
+
+ align:start position:0%
+now we all know even Einstein knew we're
+allowed to rotate our coordinate systems
+
+ align:start position:0%
+allowed to rotate our coordinate systems
+ 
+
+ align:start position:0%
+allowed to rotate our coordinate systems
+in the X Y plane what if a friend of
+
+ align:start position:0%
+in the X Y plane what if a friend of
+ 
+
+ align:start position:0%
+in the X Y plane what if a friend of
+ours had used an inclined set of
+
+ align:start position:0%
+ours had used an inclined set of
+ 
+
+ align:start position:0%
+ours had used an inclined set of
+coordinates X Prime and Y Prime that are
+
+ align:start position:0%
+coordinates X Prime and Y Prime that are
+ 
+
+ align:start position:0%
+coordinates X Prime and Y Prime that are
+rotated by some fixed angle away from
+
+ align:start position:0%
+rotated by some fixed angle away from
+ 
+
+ align:start position:0%
+rotated by some fixed angle away from
+our original coordinates
+
+ align:start position:0%
+our original coordinates
+ 
+
+ align:start position:0%
+our original coordinates
+the point P hasn't moved all we've done
+
+ align:start position:0%
+the point P hasn't moved all we've done
+ 
+
+ align:start position:0%
+the point P hasn't moved all we've done
+is change the labels we assign to the
+
+ align:start position:0%
+is change the labels we assign to the
+ 
+
+ align:start position:0%
+is change the labels we assign to the
+coordinates in our new coordinate system
+
+ align:start position:0%
+coordinates in our new coordinate system
+ 
+
+ align:start position:0%
+coordinates in our new coordinate system
+in the rotated coordinates the same
+
+ align:start position:0%
+in the rotated coordinates the same
+ 
+
+ align:start position:0%
+in the rotated coordinates the same
+point P which itself hasn't moved is
+
+ align:start position:0%
+point P which itself hasn't moved is
+ 
+
+ align:start position:0%
+point P which itself hasn't moved is
+assigned a different value of its X
+
+ align:start position:0%
+assigned a different value of its X
+ 
+
+ align:start position:0%
+assigned a different value of its X
+Prime coordinate projecting now to the
+
+ align:start position:0%
+Prime coordinate projecting now to the
+ 
+
+ align:start position:0%
+Prime coordinate projecting now to the
+new axis and a different value is y
+
+ align:start position:0%
+new axis and a different value is y
+ 
+
+ align:start position:0%
+new axis and a different value is y
+Prime coordinate projecting to the new y
+
+ align:start position:0%
+Prime coordinate projecting to the new y
+ 
+
+ align:start position:0%
+Prime coordinate projecting to the new y
+axis
+
+ align:start position:0%
+axis
+ 
+
+ align:start position:0%
+axis
+these are related quite
+
+ align:start position:0%
+these are related quite
+ 
+
+ align:start position:0%
+these are related quite
+straightforwardly by a rotation matrix
+
+ align:start position:0%
+straightforwardly by a rotation matrix
+ 
+
+ align:start position:0%
+straightforwardly by a rotation matrix
+by uh if we want to do little fancy
+
+ align:start position:0%
+by uh if we want to do little fancy
+ 
+
+ align:start position:0%
+by uh if we want to do little fancy
+paths we could say it's a a one
+
+ align:start position:0%
+paths we could say it's a a one
+ 
+
+ align:start position:0%
+paths we could say it's a a one
+parameter group
+
+ align:start position:0%
+parameter group
+ 
+
+ align:start position:0%
+parameter group
+the rotation in two Dimensions but it's
+
+ align:start position:0%
+the rotation in two Dimensions but it's
+ 
+
+ align:start position:0%
+the rotation in two Dimensions but it's
+just a set of Sines and cosines to take
+
+ align:start position:0%
+just a set of Sines and cosines to take
+ 
+
+ align:start position:0%
+just a set of Sines and cosines to take
+into account how the X and X Prime axes
+
+ align:start position:0%
+into account how the X and X Prime axes
+ 
+
+ align:start position:0%
+into account how the X and X Prime axes
+are related to each other by this angle
+
+ align:start position:0%
+are related to each other by this angle
+ 
+
+ align:start position:0%
+are related to each other by this angle
+Theta and the Y and Y Prime axis so it's
+
+ align:start position:0%
+Theta and the Y and Y Prime axis so it's
+ 
+
+ align:start position:0%
+Theta and the Y and Y Prime axis so it's
+actually very straightforward to relate
+
+ align:start position:0%
+actually very straightforward to relate
+ 
+
+ align:start position:0%
+actually very straightforward to relate
+the coordinate labels in one set of
+
+ align:start position:0%
+the coordinate labels in one set of
+ 
+
+ align:start position:0%
+the coordinate labels in one set of
+coordinates to those in the other
+
+ align:start position:0%
+coordinates to those in the other
+ 
+
+ align:start position:0%
+coordinates to those in the other
+nothing magic has happened we can see
+
+ align:start position:0%
+nothing magic has happened we can see
+ 
+
+ align:start position:0%
+nothing magic has happened we can see
+that what I had called X Prime was
+
+ align:start position:0%
+that what I had called X Prime was
+ 
+
+ align:start position:0%
+that what I had called X Prime was
+related to X in this very
+
+ align:start position:0%
+related to X in this very
+ 
+
+ align:start position:0%
+related to X in this very
+straightforward fashion taking into
+
+ align:start position:0%
+straightforward fashion taking into
+ 
+
+ align:start position:0%
+straightforward fashion taking into
+account
+
+ align:start position:0%
+account
+ 
+
+ align:start position:0%
+account
+um the different coordinate systems in
+
+ align:start position:0%
+um the different coordinate systems in
+ 
+
+ align:start position:0%
+um the different coordinate systems in
+their angle between them and likewise y
+
+ align:start position:0%
+their angle between them and likewise y
+ 
+
+ align:start position:0%
+their angle between them and likewise y
+Prime in terms of X and Y
+
+ align:start position:0%
+Prime in terms of X and Y
+ 
+
+ align:start position:0%
+Prime in terms of X and Y
+so Makowski says that's all that's
+
+ align:start position:0%
+so Makowski says that's all that's
+ 
+
+ align:start position:0%
+so Makowski says that's all that's
+happening with space-time diagrams as
+
+ align:start position:0%
+happening with space-time diagrams as
+ 
+
+ align:start position:0%
+happening with space-time diagrams as
+well now let's imagine some event in
+
+ align:start position:0%
+well now let's imagine some event in
+ 
+
+ align:start position:0%
+well now let's imagine some event in
+space time so now we're going back to
+
+ align:start position:0%
+space time so now we're going back to
+ 
+
+ align:start position:0%
+space time so now we're going back to
+these minkowski diagrams the spatial
+
+ align:start position:0%
+these minkowski diagrams the spatial
+ 
+
+ align:start position:0%
+these minkowski diagrams the spatial
+Direction runs along the horizontal axis
+
+ align:start position:0%
+Direction runs along the horizontal axis
+ 
+
+ align:start position:0%
+Direction runs along the horizontal axis
+the time Direction runs vertically we
+
+ align:start position:0%
+the time Direction runs vertically we
+ 
+
+ align:start position:0%
+the time Direction runs vertically we
+have some event that happens in space
+
+ align:start position:0%
+have some event that happens in space
+ 
+
+ align:start position:0%
+have some event that happens in space
+and time let's say we assigned to it a
+
+ align:start position:0%
+and time let's say we assigned to it a
+ 
+
+ align:start position:0%
+and time let's say we assigned to it a
+time that happened at 12 noon uh at my
+
+ align:start position:0%
+time that happened at 12 noon uh at my
+ 
+
+ align:start position:0%
+time that happened at 12 noon uh at my
+house right a spatial location okay
+
+ align:start position:0%
+house right a spatial location okay
+ 
+
+ align:start position:0%
+house right a spatial location okay
+there's some point
+
+ align:start position:0%
+there's some point
+ 
+
+ align:start position:0%
+there's some point
+Now The Observer on the train is going
+
+ align:start position:0%
+Now The Observer on the train is going
+ 
+
+ align:start position:0%
+Now The Observer on the train is going
+to label that exact same event
+
+ align:start position:0%
+to label that exact same event
+ 
+
+ align:start position:0%
+to label that exact same event
+but give it different coordinate values
+
+ align:start position:0%
+but give it different coordinate values
+ 
+
+ align:start position:0%
+but give it different coordinate values
+because her coordinate system is
+
+ align:start position:0%
+because her coordinate system is
+ 
+
+ align:start position:0%
+because her coordinate system is
+different the lines of simultaneity for
+
+ align:start position:0%
+different the lines of simultaneity for
+ 
+
+ align:start position:0%
+different the lines of simultaneity for
+her frame are different
+
+ align:start position:0%
+her frame are different
+ 
+
+ align:start position:0%
+her frame are different
+the world line of x equals zero for her
+
+ align:start position:0%
+the world line of x equals zero for her
+ 
+
+ align:start position:0%
+the world line of x equals zero for her
+is different so she has the X Prime T
+
+ align:start position:0%
+is different so she has the X Prime T
+ 
+
+ align:start position:0%
+is different so she has the X Prime T
+Prime coordinates she's still perfectly
+
+ align:start position:0%
+Prime coordinates she's still perfectly
+ 
+
+ align:start position:0%
+Prime coordinates she's still perfectly
+capable of labeling uh the event p and
+
+ align:start position:0%
+capable of labeling uh the event p and
+ 
+
+ align:start position:0%
+capable of labeling uh the event p and
+assigning to it values in her
+
+ align:start position:0%
+assigning to it values in her
+ 
+
+ align:start position:0%
+assigning to it values in her
+coordinates X1 Prime and T1 Prime and
+
+ align:start position:0%
+coordinates X1 Prime and T1 Prime and
+ 
+
+ align:start position:0%
+coordinates X1 Prime and T1 Prime and
+again remember the angle of inclination
+
+ align:start position:0%
+again remember the angle of inclination
+ 
+
+ align:start position:0%
+again remember the angle of inclination
+here is directly related to the relative
+
+ align:start position:0%
+here is directly related to the relative
+ 
+
+ align:start position:0%
+here is directly related to the relative
+speed between these two sets of chords
+
+ align:start position:0%
+speed between these two sets of chords
+ 
+
+ align:start position:0%
+speed between these two sets of chords
+these two reference frames
+
+ align:start position:0%
+these two reference frames
+ 
+
+ align:start position:0%
+these two reference frames
+moreover what Lorenz had had derived
+
+ align:start position:0%
+moreover what Lorenz had had derived
+ 
+
+ align:start position:0%
+moreover what Lorenz had had derived
+because of the kind of what he assumed
+
+ align:start position:0%
+because of the kind of what he assumed
+ 
+
+ align:start position:0%
+because of the kind of what he assumed
+to be the elastic forces of an ether
+
+ align:start position:0%
+to be the elastic forces of an ether
+ 
+
+ align:start position:0%
+to be the elastic forces of an ether
+acting on the molecules what Einstein
+
+ align:start position:0%
+acting on the molecules what Einstein
+ 
+
+ align:start position:0%
+acting on the molecules what Einstein
+had derived quite differently by
+
+ align:start position:0%
+had derived quite differently by
+ 
+
+ align:start position:0%
+had derived quite differently by
+thinking about uh the relative
+
+ align:start position:0%
+thinking about uh the relative
+ 
+
+ align:start position:0%
+thinking about uh the relative
+relativity of simultaneity minkowski
+
+ align:start position:0%
+relativity of simultaneity minkowski
+ 
+
+ align:start position:0%
+relativity of simultaneity minkowski
+says is just the set of rules for making
+
+ align:start position:0%
+says is just the set of rules for making
+ 
+
+ align:start position:0%
+says is just the set of rules for making
+rotations in this only slightly more
+
+ align:start position:0%
+rotations in this only slightly more
+ 
+
+ align:start position:0%
+rotations in this only slightly more
+complicated geometrical space it's still
+
+ align:start position:0%
+complicated geometrical space it's still
+ 
+
+ align:start position:0%
+complicated geometrical space it's still
+basically like making rotations in the X
+
+ align:start position:0%
+basically like making rotations in the X
+ 
+
+ align:start position:0%
+basically like making rotations in the X
+Y plane we have again to be fancy pants
+
+ align:start position:0%
+Y plane we have again to be fancy pants
+ 
+
+ align:start position:0%
+Y plane we have again to be fancy pants
+a one parameter family of rotations the
+
+ align:start position:0%
+a one parameter family of rotations the
+ 
+
+ align:start position:0%
+a one parameter family of rotations the
+one parameter that changes now is the
+
+ align:start position:0%
+one parameter that changes now is the
+ 
+
+ align:start position:0%
+one parameter that changes now is the
+relative speed V or if you like the
+
+ align:start position:0%
+relative speed V or if you like the
+ 
+
+ align:start position:0%
+relative speed V or if you like the
+ratio of V over C but of course C is a
+
+ align:start position:0%
+ratio of V over C but of course C is a
+ 
+
+ align:start position:0%
+ratio of V over C but of course C is a
+universal constant the only thing that
+
+ align:start position:0%
+universal constant the only thing that
+ 
+
+ align:start position:0%
+universal constant the only thing that
+really varies here is there is a speed
+
+ align:start position:0%
+really varies here is there is a speed
+ 
+
+ align:start position:0%
+really varies here is there is a speed
+Little V we have some other set of rules
+
+ align:start position:0%
+Little V we have some other set of rules
+ 
+
+ align:start position:0%
+Little V we have some other set of rules
+these take the place of our kind of
+
+ align:start position:0%
+these take the place of our kind of
+ 
+
+ align:start position:0%
+these take the place of our kind of
+Sines and cosines of the relative angle
+
+ align:start position:0%
+Sines and cosines of the relative angle
+ 
+
+ align:start position:0%
+Sines and cosines of the relative angle
+so once again we can now trivially
+
+ align:start position:0%
+so once again we can now trivially
+ 
+
+ align:start position:0%
+so once again we can now trivially
+geometrically relate the labels that the
+
+ align:start position:0%
+geometrically relate the labels that the
+ 
+
+ align:start position:0%
+geometrically relate the labels that the
+moving uh the person on the moving train
+
+ align:start position:0%
+moving uh the person on the moving train
+ 
+
+ align:start position:0%
+moving uh the person on the moving train
+had assigned to the same event P relate
+
+ align:start position:0%
+had assigned to the same event P relate
+ 
+
+ align:start position:0%
+had assigned to the same event P relate
+those to the labels that we assigned
+
+ align:start position:0%
+those to the labels that we assigned
+ 
+
+ align:start position:0%
+those to the labels that we assigned
+standing still on the station platform
+
+ align:start position:0%
+standing still on the station platform
+ 
+
+ align:start position:0%
+standing still on the station platform
+he gets precisely the Lorenz
+
+ align:start position:0%
+he gets precisely the Lorenz
+ 
+
+ align:start position:0%
+he gets precisely the Lorenz
+transformation not because of the ether
+
+ align:start position:0%
+transformation not because of the ether
+ 
+
+ align:start position:0%
+transformation not because of the ether
+not because of Einstein's um uh
+
+ align:start position:0%
+not because of Einstein's um uh
+ 
+
+ align:start position:0%
+not because of Einstein's um uh
+arguments about sort of how we perform
+
+ align:start position:0%
+arguments about sort of how we perform
+ 
+
+ align:start position:0%
+arguments about sort of how we perform
+measurements but because he's just a
+
+ align:start position:0%
+measurements but because he's just a
+ 
+
+ align:start position:0%
+measurements but because he's just a
+geometer making
+
+ align:start position:0%
+geometer making
+ 
+
+ align:start position:0%
+geometer making
+um rotations in a particular kind of
+
+ align:start position:0%
+um rotations in a particular kind of
+ 
+
+ align:start position:0%
+um rotations in a particular kind of
+two-dimensional space
+
+ align:start position:0%
+two-dimensional space
+ 
+
+ align:start position:0%
+two-dimensional space
+so to minkowski the Lorenz
+
+ align:start position:0%
+so to minkowski the Lorenz
+ 
+
+ align:start position:0%
+so to minkowski the Lorenz
+transformation itself was nothing but
+
+ align:start position:0%
+transformation itself was nothing but
+ 
+
+ align:start position:0%
+transformation itself was nothing but
+geometric rotations and space-time again
+
+ align:start position:0%
+geometric rotations and space-time again
+ 
+
+ align:start position:0%
+geometric rotations and space-time again
+so not surprising since we know
+
+ align:start position:0%
+so not surprising since we know
+ 
+
+ align:start position:0%
+so not surprising since we know
+minkowski is a geometer above all okay
+
+ align:start position:0%
+minkowski is a geometer above all okay
+ 
+
+ align:start position:0%
+minkowski is a geometer above all okay
+now this gives them something that's
+
+ align:start position:0%
+now this gives them something that's
+ 
+
+ align:start position:0%
+now this gives them something that's
+actually new he's no longer just
+
+ align:start position:0%
+actually new he's no longer just
+ 
+
+ align:start position:0%
+actually new he's no longer just
+rederiding stuff in a new way now we get
+
+ align:start position:0%
+rederiding stuff in a new way now we get
+ 
+
+ align:start position:0%
+rederiding stuff in a new way now we get
+stuff that neither lorentz nor Einstein
+
+ align:start position:0%
+stuff that neither lorentz nor Einstein
+ 
+
+ align:start position:0%
+stuff that neither lorentz nor Einstein
+had actually recognized or realized this
+
+ align:start position:0%
+had actually recognized or realized this
+ 
+
+ align:start position:0%
+had actually recognized or realized this
+next part comes really from minkowski
+
+ align:start position:0%
+next part comes really from minkowski
+ 
+
+ align:start position:0%
+next part comes really from minkowski
+taking geometry very seriously as he
+
+ align:start position:0%
+taking geometry very seriously as he
+ 
+
+ align:start position:0%
+taking geometry very seriously as he
+knew as a geometer even in ordinary X Y
+
+ align:start position:0%
+knew as a geometer even in ordinary X Y
+ 
+
+ align:start position:0%
+knew as a geometer even in ordinary X Y
+plane type of geometry when we we can
+
+ align:start position:0%
+plane type of geometry when we we can
+ 
+
+ align:start position:0%
+plane type of geometry when we we can
+perform rotations the coordinate labels
+
+ align:start position:0%
+perform rotations the coordinate labels
+ 
+
+ align:start position:0%
+perform rotations the coordinate labels
+of a given point will change but some
+
+ align:start position:0%
+of a given point will change but some
+ 
+
+ align:start position:0%
+of a given point will change but some
+quantities remain unchanged even under
+
+ align:start position:0%
+quantities remain unchanged even under
+ 
+
+ align:start position:0%
+quantities remain unchanged even under
+rotations for example the distance
+
+ align:start position:0%
+rotations for example the distance
+ 
+
+ align:start position:0%
+rotations for example the distance
+so what's the distance between the
+
+ align:start position:0%
+so what's the distance between the
+ 
+
+ align:start position:0%
+so what's the distance between the
+origin and my coordinates and the point
+
+ align:start position:0%
+origin and my coordinates and the point
+ 
+
+ align:start position:0%
+origin and my coordinates and the point
+P we'll call that distance D that
+
+ align:start position:0%
+P we'll call that distance D that
+ 
+
+ align:start position:0%
+P we'll call that distance D that
+doesn't change even if I change the
+
+ align:start position:0%
+doesn't change even if I change the
+ 
+
+ align:start position:0%
+doesn't change even if I change the
+labeling of my coordinates so when I
+
+ align:start position:0%
+labeling of my coordinates so when I
+ 
+
+ align:start position:0%
+labeling of my coordinates so when I
+rotate my some angle Theta
+
+ align:start position:0%
+rotate my some angle Theta
+ 
+
+ align:start position:0%
+rotate my some angle Theta
+I change the labeling the description of
+
+ align:start position:0%
+I change the labeling the description of
+ 
+
+ align:start position:0%
+I change the labeling the description of
+X and Y versus X Prime and Y Prime I
+
+ align:start position:0%
+X and Y versus X Prime and Y Prime I
+ 
+
+ align:start position:0%
+X and Y versus X Prime and Y Prime I
+didn't pick up the point p and move it
+
+ align:start position:0%
+didn't pick up the point p and move it
+ 
+
+ align:start position:0%
+didn't pick up the point p and move it
+further from the origin the distance
+
+ align:start position:0%
+further from the origin the distance
+ 
+
+ align:start position:0%
+further from the origin the distance
+between say the origin and point p is
+
+ align:start position:0%
+between say the origin and point p is
+ 
+
+ align:start position:0%
+between say the origin and point p is
+invariant under those rotations and
+
+ align:start position:0%
+invariant under those rotations and
+ 
+
+ align:start position:0%
+invariant under those rotations and
+again it'll take you about
+
+ align:start position:0%
+again it'll take you about
+ 
+
+ align:start position:0%
+again it'll take you about
+28 milliseconds to figure that out for
+
+ align:start position:0%
+28 milliseconds to figure that out for
+ 
+
+ align:start position:0%
+28 milliseconds to figure that out for
+the geometrical case just using you know
+
+ align:start position:0%
+the geometrical case just using you know
+ 
+
+ align:start position:0%
+the geometrical case just using you know
+sine squared theta plus cosine squared
+
+ align:start position:0%
+sine squared theta plus cosine squared
+ 
+
+ align:start position:0%
+sine squared theta plus cosine squared
+theta equals one use the usual
+
+ align:start position:0%
+theta equals one use the usual
+ 
+
+ align:start position:0%
+theta equals one use the usual
+trigonometric identity between these
+
+ align:start position:0%
+trigonometric identity between these
+ 
+
+ align:start position:0%
+trigonometric identity between these
+trigonometric functions and then it's
+
+ align:start position:0%
+trigonometric functions and then it's
+ 
+
+ align:start position:0%
+trigonometric functions and then it's
+very straightforward to see the distance
+
+ align:start position:0%
+very straightforward to see the distance
+ 
+
+ align:start position:0%
+very straightforward to see the distance
+is invariant even though the coordinate
+
+ align:start position:0%
+is invariant even though the coordinate
+ 
+
+ align:start position:0%
+is invariant even though the coordinate
+labels have changed under rotation
+
+ align:start position:0%
+labels have changed under rotation
+ 
+
+ align:start position:0%
+labels have changed under rotation
+that's what now becomes really new that
+
+ align:start position:0%
+that's what now becomes really new that
+ 
+
+ align:start position:0%
+that's what now becomes really new that
+minkowski pushes forward
+
+ align:start position:0%
+minkowski pushes forward
+ 
+
+ align:start position:0%
+minkowski pushes forward
+as as with the first real concrete
+
+ align:start position:0%
+as as with the first real concrete
+ 
+
+ align:start position:0%
+as as with the first real concrete
+Advantage as far as he's concerned of
+
+ align:start position:0%
+Advantage as far as he's concerned of
+ 
+
+ align:start position:0%
+Advantage as far as he's concerned of
+this geometrical approach there's a
+
+ align:start position:0%
+this geometrical approach there's a
+ 
+
+ align:start position:0%
+this geometrical approach there's a
+generalization of distance that
+
+ align:start position:0%
+generalization of distance that
+ 
+
+ align:start position:0%
+generalization of distance that
+minkowski introduces it comes to be
+
+ align:start position:0%
+minkowski introduces it comes to be
+ 
+
+ align:start position:0%
+minkowski introduces it comes to be
+called the space-time interval often
+
+ align:start position:0%
+called the space-time interval often
+ 
+
+ align:start position:0%
+called the space-time interval often
+abbreviated by the letter s it's like a
+
+ align:start position:0%
+abbreviated by the letter s it's like a
+ 
+
+ align:start position:0%
+abbreviated by the letter s it's like a
+version of distance for space time
+
+ align:start position:0%
+version of distance for space time
+ 
+
+ align:start position:0%
+version of distance for space time
+instead of only uh a spatial problem
+
+ align:start position:0%
+instead of only uh a spatial problem
+ 
+
+ align:start position:0%
+instead of only uh a spatial problem
+only space space so what is this space
+
+ align:start position:0%
+only space space so what is this space
+ 
+
+ align:start position:0%
+only space space so what is this space
+time interval that remains unchanged
+
+ align:start position:0%
+time interval that remains unchanged
+ 
+
+ align:start position:0%
+time interval that remains unchanged
+even though the coordinate labels might
+
+ align:start position:0%
+even though the coordinate labels might
+ 
+
+ align:start position:0%
+even though the coordinate labels might
+be switched onto these coordinate
+
+ align:start position:0%
+be switched onto these coordinate
+ 
+
+ align:start position:0%
+be switched onto these coordinate
+lorentz transformations so again we come
+
+ align:start position:0%
+lorentz transformations so again we come
+ 
+
+ align:start position:0%
+lorentz transformations so again we come
+back to this way to relate our x and t
+
+ align:start position:0%
+back to this way to relate our x and t
+ 
+
+ align:start position:0%
+back to this way to relate our x and t
+coordinate store X Prime and T Prime
+
+ align:start position:0%
+coordinate store X Prime and T Prime
+ 
+
+ align:start position:0%
+coordinate store X Prime and T Prime
+that's what mankowski's rederived from
+
+ align:start position:0%
+that's what mankowski's rederived from
+ 
+
+ align:start position:0%
+that's what mankowski's rederived from
+his rotation and now he shows using the
+
+ align:start position:0%
+his rotation and now he shows using the
+ 
+
+ align:start position:0%
+his rotation and now he shows using the
+definition of gamma that just for the
+
+ align:start position:0%
+definition of gamma that just for the
+ 
+
+ align:start position:0%
+definition of gamma that just for the
+exact same reason that
+
+ align:start position:0%
+exact same reason that
+ 
+
+ align:start position:0%
+exact same reason that
+the euclidean distance Little D in the
+
+ align:start position:0%
+the euclidean distance Little D in the
+ 
+
+ align:start position:0%
+the euclidean distance Little D in the
+previous example remains unchanged just
+
+ align:start position:0%
+previous example remains unchanged just
+ 
+
+ align:start position:0%
+previous example remains unchanged just
+because of the definitions of sine and
+
+ align:start position:0%
+because of the definitions of sine and
+ 
+
+ align:start position:0%
+because of the definitions of sine and
+cosine of a given angle given the
+
+ align:start position:0%
+cosine of a given angle given the
+ 
+
+ align:start position:0%
+cosine of a given angle given the
+definition of gamma that way of relating
+
+ align:start position:0%
+definition of gamma that way of relating
+ 
+
+ align:start position:0%
+definition of gamma that way of relating
+the kind of rotation the degree to which
+
+ align:start position:0%
+the kind of rotation the degree to which
+ 
+
+ align:start position:0%
+the kind of rotation the degree to which
+X Prime is inclined with respect to X we
+
+ align:start position:0%
+X Prime is inclined with respect to X we
+ 
+
+ align:start position:0%
+X Prime is inclined with respect to X we
+get an unavoidable um outcome that
+
+ align:start position:0%
+get an unavoidable um outcome that
+ 
+
+ align:start position:0%
+get an unavoidable um outcome that
+whether we had chosen to label the event
+
+ align:start position:0%
+whether we had chosen to label the event
+ 
+
+ align:start position:0%
+whether we had chosen to label the event
+p in our x and t coordinates or X Prime
+
+ align:start position:0%
+p in our x and t coordinates or X Prime
+ 
+
+ align:start position:0%
+p in our x and t coordinates or X Prime
+and T Prime coordinates the space time
+
+ align:start position:0%
+and T Prime coordinates the space time
+ 
+
+ align:start position:0%
+and T Prime coordinates the space time
+interval little s has remained unchanged
+
+ align:start position:0%
+interval little s has remained unchanged
+ 
+
+ align:start position:0%
+interval little s has remained unchanged
+there's a something that remains
+
+ align:start position:0%
+there's a something that remains
+ 
+
+ align:start position:0%
+there's a something that remains
+invariant even though our different
+
+ align:start position:0%
+invariant even though our different
+ 
+
+ align:start position:0%
+invariant even though our different
+descriptions of spatial spatial
+
+ align:start position:0%
+descriptions of spatial spatial
+ 
+
+ align:start position:0%
+descriptions of spatial spatial
+distances and temporal durations have
+
+ align:start position:0%
+distances and temporal durations have
+ 
+
+ align:start position:0%
+distances and temporal durations have
+changed
+
+ align:start position:0%
+changed
+ 
+
+ align:start position:0%
+changed
+so to minkowski this shows that really
+
+ align:start position:0%
+so to minkowski this shows that really
+ 
+
+ align:start position:0%
+so to minkowski this shows that really
+geometry in particular the geometry of
+
+ align:start position:0%
+geometry in particular the geometry of
+ 
+
+ align:start position:0%
+geometry in particular the geometry of
+space-time that dominkowski becomes the
+
+ align:start position:0%
+space-time that dominkowski becomes the
+ 
+
+ align:start position:0%
+space-time that dominkowski becomes the
+only thing that matters not The Ether
+
+ align:start position:0%
+only thing that matters not The Ether
+ 
+
+ align:start position:0%
+only thing that matters not The Ether
+not this kind of mock-like show me how I
+
+ align:start position:0%
+not this kind of mock-like show me how I
+ 
+
+ align:start position:0%
+not this kind of mock-like show me how I
+can uh you know taste it or measure or
+
+ align:start position:0%
+can uh you know taste it or measure or
+ 
+
+ align:start position:0%
+can uh you know taste it or measure or
+make it subject of positive experience
+
+ align:start position:0%
+make it subject of positive experience
+ 
+
+ align:start position:0%
+make it subject of positive experience
+it's this geometrical feature of
+
+ align:start position:0%
+it's this geometrical feature of
+ 
+
+ align:start position:0%
+it's this geometrical feature of
+space-time and in particular not space
+
+ align:start position:0%
+space-time and in particular not space
+ 
+
+ align:start position:0%
+space-time and in particular not space
+and time separately it's actually
+
+ align:start position:0%
+and time separately it's actually
+ 
+
+ align:start position:0%
+and time separately it's actually
+minkowski's work not Einstein's at first
+
+ align:start position:0%
+minkowski's work not Einstein's at first
+ 
+
+ align:start position:0%
+minkowski's work not Einstein's at first
+then really introduces this notion of a
+
+ align:start position:0%
+then really introduces this notion of a
+ 
+
+ align:start position:0%
+then really introduces this notion of a
+union of space and time that very
+
+ align:start position:0%
+union of space and time that very
+ 
+
+ align:start position:0%
+union of space and time that very
+quickly becomes called by a single name
+
+ align:start position:0%
+quickly becomes called by a single name
+ 
+
+ align:start position:0%
+quickly becomes called by a single name
+space time so that's what minkowski is
+
+ align:start position:0%
+space time so that's what minkowski is
+ 
+
+ align:start position:0%
+space time so that's what minkowski is
+convinced is the only really important
+
+ align:start position:0%
+convinced is the only really important
+ 
+
+ align:start position:0%
+convinced is the only really important
+Insight or or outcome of Einstein's work
+
+ align:start position:0%
+Insight or or outcome of Einstein's work
+ 
+
+ align:start position:0%
+Insight or or outcome of Einstein's work
+it is geometrical so as he famously
+
+ align:start position:0%
+it is geometrical so as he famously
+ 
+
+ align:start position:0%
+it is geometrical so as he famously
+concludes in this article it was
+
+ align:start position:0%
+concludes in this article it was
+ 
+
+ align:start position:0%
+concludes in this article it was
+published soon after he passed away
+
+ align:start position:0%
+published soon after he passed away
+ 
+
+ align:start position:0%
+published soon after he passed away
+laying out all this work on space-time
+
+ align:start position:0%
+laying out all this work on space-time
+ 
+
+ align:start position:0%
+laying out all this work on space-time
+diagrams the invariant space-time
+
+ align:start position:0%
+diagrams the invariant space-time
+ 
+
+ align:start position:0%
+diagrams the invariant space-time
+interval and so on he says henceforth
+
+ align:start position:0%
+interval and so on he says henceforth
+ 
+
+ align:start position:0%
+interval and so on he says henceforth
+Space by itself and Time by itself are
+
+ align:start position:0%
+Space by itself and Time by itself are
+ 
+
+ align:start position:0%
+Space by itself and Time by itself are
+doomed to fade away into mere Shadows
+
+ align:start position:0%
+doomed to fade away into mere Shadows
+ 
+
+ align:start position:0%
+doomed to fade away into mere Shadows
+these are really just the projections on
+
+ align:start position:0%
+these are really just the projections on
+ 
+
+ align:start position:0%
+these are really just the projections on
+a on a idiosyncratic choice of
+
+ align:start position:0%
+a on a idiosyncratic choice of
+ 
+
+ align:start position:0%
+a on a idiosyncratic choice of
+coordinate axes these are mere shadows
+
+ align:start position:0%
+coordinate axes these are mere shadows
+ 
+
+ align:start position:0%
+coordinate axes these are mere shadows
+and only a kind of Union of the two a
+
+ align:start position:0%
+and only a kind of Union of the two a
+ 
+
+ align:start position:0%
+and only a kind of Union of the two a
+single Union of space-time will preserve
+
+ align:start position:0%
+single Union of space-time will preserve
+ 
+
+ align:start position:0%
+single Union of space-time will preserve
+Independence
+
+ align:start position:0%
+Independence
+ 
+
+ align:start position:0%
+Independence
+so let me pause there again and ask for
+
+ align:start position:0%
+so let me pause there again and ask for
+ 
+
+ align:start position:0%
+so let me pause there again and ask for
+any questions
+
+ align:start position:0%
+any questions
+ 
+
+ align:start position:0%
+any questions
+any questions on the minkowski stuff on
+
+ align:start position:0%
+any questions on the minkowski stuff on
+ 
+
+ align:start position:0%
+any questions on the minkowski stuff on
+where he was coming from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh so Sulu asks what rhinestones are
+
+ align:start position:0%
+so uh so Sulu asks what rhinestones are
+ 
+
+ align:start position:0%
+so uh so Sulu asks what rhinestones are
+this reaction to mikowski good very good
+
+ align:start position:0%
+this reaction to mikowski good very good
+ 
+
+ align:start position:0%
+this reaction to mikowski good very good
+so the first reaction of Einstein to
+
+ align:start position:0%
+so the first reaction of Einstein to
+ 
+
+ align:start position:0%
+so the first reaction of Einstein to
+minkowski was also thoroughly
+
+ align:start position:0%
+minkowski was also thoroughly
+ 
+
+ align:start position:0%
+minkowski was also thoroughly
+predictable he hated it he never liked
+
+ align:start position:0%
+predictable he hated it he never liked
+ 
+
+ align:start position:0%
+predictable he hated it he never liked
+Mankowski as a person he cut his classes
+
+ align:start position:0%
+Mankowski as a person he cut his classes
+ 
+
+ align:start position:0%
+Mankowski as a person he cut his classes
+he was like oh look this guy still
+
+ align:start position:0%
+he was like oh look this guy still
+ 
+
+ align:start position:0%
+he was like oh look this guy still
+understands nothing important the
+
+ align:start position:0%
+understands nothing important the
+ 
+
+ align:start position:0%
+understands nothing important the
+feeling was totally
+
+ align:start position:0%
+feeling was totally
+ 
+
+ align:start position:0%
+feeling was totally
+um you know Mutual so minkowski thought
+
+ align:start position:0%
+um you know Mutual so minkowski thought
+ 
+
+ align:start position:0%
+um you know Mutual so minkowski thought
+Einstein had made a mess of things and
+
+ align:start position:0%
+Einstein had made a mess of things and
+ 
+
+ align:start position:0%
+Einstein had made a mess of things and
+only grudgingly paid attention Einstein
+
+ align:start position:0%
+only grudgingly paid attention Einstein
+ 
+
+ align:start position:0%
+only grudgingly paid attention Einstein
+read this paper said oh this guy
+
+ align:start position:0%
+read this paper said oh this guy
+ 
+
+ align:start position:0%
+read this paper said oh this guy
+understands nothing he's not reading
+
+ align:start position:0%
+understands nothing he's not reading
+ 
+
+ align:start position:0%
+understands nothing he's not reading
+Mark he missed the real conceptual
+
+ align:start position:0%
+Mark he missed the real conceptual
+ 
+
+ align:start position:0%
+Mark he missed the real conceptual
+Innovation he's just playing with axes
+
+ align:start position:0%
+Innovation he's just playing with axes
+ 
+
+ align:start position:0%
+Innovation he's just playing with axes
+now the difference was minkowski died
+
+ align:start position:0%
+now the difference was minkowski died
+ 
+
+ align:start position:0%
+now the difference was minkowski died
+and Einstein didn't in 1908 so Einstein
+
+ align:start position:0%
+and Einstein didn't in 1908 so Einstein
+ 
+
+ align:start position:0%
+and Einstein didn't in 1908 so Einstein
+later over and if I go look at this in
+
+ align:start position:0%
+later over and if I go look at this in
+ 
+
+ align:start position:0%
+later over and if I go look at this in
+our upcoming class session
+
+ align:start position:0%
+our upcoming class session
+ 
+
+ align:start position:0%
+our upcoming class session
+over the next several years again about
+
+ align:start position:0%
+over the next several years again about
+ 
+
+ align:start position:0%
+over the next several years again about
+four years after minkowski's work was
+
+ align:start position:0%
+four years after minkowski's work was
+ 
+
+ align:start position:0%
+four years after minkowski's work was
+published did Einstein slowly grudgingly
+
+ align:start position:0%
+published did Einstein slowly grudgingly
+ 
+
+ align:start position:0%
+published did Einstein slowly grudgingly
+with other kind of inputs and nudges
+
+ align:start position:0%
+with other kind of inputs and nudges
+ 
+
+ align:start position:0%
+with other kind of inputs and nudges
+begin to appreciate the geometrical view
+
+ align:start position:0%
+begin to appreciate the geometrical view
+ 
+
+ align:start position:0%
+begin to appreciate the geometrical view
+that minkowski was putting forward
+
+ align:start position:0%
+that minkowski was putting forward
+ 
+
+ align:start position:0%
+that minkowski was putting forward
+Einstein's original reaction was this
+
+ align:start position:0%
+Einstein's original reaction was this
+ 
+
+ align:start position:0%
+Einstein's original reaction was this
+guy still doesn't get it I would cut his
+
+ align:start position:0%
+guy still doesn't get it I would cut his
+ 
+
+ align:start position:0%
+guy still doesn't get it I would cut his
+classes again if I were still there I
+
+ align:start position:0%
+classes again if I were still there I
+ 
+
+ align:start position:0%
+classes again if I were still there I
+mean really was just less Mutual like
+
+ align:start position:0%
+mean really was just less Mutual like
+ 
+
+ align:start position:0%
+mean really was just less Mutual like
+and it's really about four years later
+
+ align:start position:0%
+and it's really about four years later
+ 
+
+ align:start position:0%
+and it's really about four years later
+as we'll talk a bit about uh in the next
+
+ align:start position:0%
+as we'll talk a bit about uh in the next
+ 
+
+ align:start position:0%
+as we'll talk a bit about uh in the next
+class that Einstein kind of grudgingly
+
+ align:start position:0%
+class that Einstein kind of grudgingly
+ 
+
+ align:start position:0%
+class that Einstein kind of grudgingly
+comes along to say geometry is really
+
+ align:start position:0%
+comes along to say geometry is really
+ 
+
+ align:start position:0%
+comes along to say geometry is really
+cool space time as a unified notion
+
+ align:start position:0%
+cool space time as a unified notion
+ 
+
+ align:start position:0%
+cool space time as a unified notion
+actually seems important and then he
+
+ align:start position:0%
+actually seems important and then he
+ 
+
+ align:start position:0%
+actually seems important and then he
+says oh I wish I had cited all that math
+
+ align:start position:0%
+says oh I wish I had cited all that math
+ 
+
+ align:start position:0%
+says oh I wish I had cited all that math
+after all and it goes back to one of his
+
+ align:start position:0%
+after all and it goes back to one of his
+ 
+
+ align:start position:0%
+after all and it goes back to one of his
+friends Marcel Grossman says oh not only
+
+ align:start position:0%
+friends Marcel Grossman says oh not only
+ 
+
+ align:start position:0%
+friends Marcel Grossman says oh not only
+can I borrow your notes can you teach me
+
+ align:start position:0%
+can I borrow your notes can you teach me
+ 
+
+ align:start position:0%
+can I borrow your notes can you teach me
+all the stuff I should have learned when
+
+ align:start position:0%
+all the stuff I should have learned when
+ 
+
+ align:start position:0%
+all the stuff I should have learned when
+I was in college lesson number three if
+
+ align:start position:0%
+I was in college lesson number three if
+ 
+
+ align:start position:0%
+I was in college lesson number three if
+don't act like Einstein
+
+ align:start position:0%
+don't act like Einstein
+ 
+
+ align:start position:0%
+don't act like Einstein
+so Gary asks if minkowski had lived who
+
+ align:start position:0%
+so Gary asks if minkowski had lived who
+ 
+
+ align:start position:0%
+so Gary asks if minkowski had lived who
+would have been deem the greater genius
+
+ align:start position:0%
+would have been deem the greater genius
+ 
+
+ align:start position:0%
+would have been deem the greater genius
+well that's that's an interesting
+
+ align:start position:0%
+well that's that's an interesting
+ 
+
+ align:start position:0%
+well that's that's an interesting
+question I don't know uh we could that's
+
+ align:start position:0%
+question I don't know uh we could that's
+ 
+
+ align:start position:0%
+question I don't know uh we could that's
+a Time varying question in 1909 still
+
+ align:start position:0%
+a Time varying question in 1909 still
+ 
+
+ align:start position:0%
+a Time varying question in 1909 still
+minkowski in 1915 I'm not sure in 1945 I
+
+ align:start position:0%
+minkowski in 1915 I'm not sure in 1945 I
+ 
+
+ align:start position:0%
+minkowski in 1915 I'm not sure in 1945 I
+don't know right it's interesting to see
+
+ align:start position:0%
+don't know right it's interesting to see
+ 
+
+ align:start position:0%
+don't know right it's interesting to see
+and I imagine the mathematicians then is
+
+ align:start position:0%
+and I imagine the mathematicians then is
+ 
+
+ align:start position:0%
+and I imagine the mathematicians then is
+now would Harold minkowski's work for a
+
+ align:start position:0%
+now would Harold minkowski's work for a
+ 
+
+ align:start position:0%
+now would Harold minkowski's work for a
+lot longer we'd see I'm sure some
+
+ align:start position:0%
+lot longer we'd see I'm sure some
+ 
+
+ align:start position:0%
+lot longer we'd see I'm sure some
+different opinions continue to vary
+
+ align:start position:0%
+different opinions continue to vary
+ 
+
+ align:start position:0%
+different opinions continue to vary
+uh Jesus writes it's scary to realize
+
+ align:start position:0%
+uh Jesus writes it's scary to realize
+ 
+
+ align:start position:0%
+uh Jesus writes it's scary to realize
+that nobody cared too much about these
+
+ align:start position:0%
+that nobody cared too much about these
+ 
+
+ align:start position:0%
+that nobody cared too much about these
+Grand breaking results for so long makes
+
+ align:start position:0%
+Grand breaking results for so long makes
+ 
+
+ align:start position:0%
+Grand breaking results for so long makes
+me wonder what kind of groundbreaking
+
+ align:start position:0%
+me wonder what kind of groundbreaking
+ 
+
+ align:start position:0%
+me wonder what kind of groundbreaking
+work may have actually fallen through
+
+ align:start position:0%
+work may have actually fallen through
+ 
+
+ align:start position:0%
+work may have actually fallen through
+the cracks and never gotten a full
+
+ align:start position:0%
+the cracks and never gotten a full
+ 
+
+ align:start position:0%
+the cracks and never gotten a full
+exploration but yes that's a fair point
+
+ align:start position:0%
+exploration but yes that's a fair point
+ 
+
+ align:start position:0%
+exploration but yes that's a fair point
+uh you know that's something we can keep
+
+ align:start position:0%
+uh you know that's something we can keep
+ 
+
+ align:start position:0%
+uh you know that's something we can keep
+in mind throughout this whole semester
+
+ align:start position:0%
+in mind throughout this whole semester
+ 
+
+ align:start position:0%
+in mind throughout this whole semester
+um not only uh
+
+ align:start position:0%
+um not only uh
+ 
+
+ align:start position:0%
+um not only uh
+you know there's all kinds of
+
+ align:start position:0%
+you know there's all kinds of
+ 
+
+ align:start position:0%
+you know there's all kinds of
+gatekeeping about who determines at what
+
+ align:start position:0%
+gatekeeping about who determines at what
+ 
+
+ align:start position:0%
+gatekeeping about who determines at what
+time what what work is worth paying
+
+ align:start position:0%
+time what what work is worth paying
+ 
+
+ align:start position:0%
+time what what work is worth paying
+attention to
+
+ align:start position:0%
+attention to
+ 
+
+ align:start position:0%
+attention to
+institutions play a role individual
+
+ align:start position:0%
+institutions play a role individual
+ 
+
+ align:start position:0%
+institutions play a role individual
+rivalries play a role soon we'll come to
+
+ align:start position:0%
+rivalries play a role soon we'll come to
+ 
+
+ align:start position:0%
+rivalries play a role soon we'll come to
+examples where worldly events play a
+
+ align:start position:0%
+examples where worldly events play a
+ 
+
+ align:start position:0%
+examples where worldly events play a
+role well beyond the control of Any
+
+ align:start position:0%
+role well beyond the control of Any
+ 
+
+ align:start position:0%
+role well beyond the control of Any
+Given individual or institution uh
+
+ align:start position:0%
+Given individual or institution uh
+ 
+
+ align:start position:0%
+Given individual or institution uh
+sexism plays a role racism plays a role
+
+ align:start position:0%
+sexism plays a role racism plays a role
+ 
+
+ align:start position:0%
+sexism plays a role racism plays a role
+I mean there's all kinds of things that
+
+ align:start position:0%
+I mean there's all kinds of things that
+ 
+
+ align:start position:0%
+I mean there's all kinds of things that
+factor into who who determines this is
+
+ align:start position:0%
+factor into who who determines this is
+ 
+
+ align:start position:0%
+factor into who who determines this is
+of value and worth paying attention to
+
+ align:start position:0%
+of value and worth paying attention to
+ 
+
+ align:start position:0%
+of value and worth paying attention to
+at any given time and that's a kind of
+
+ align:start position:0%
+at any given time and that's a kind of
+ 
+
+ align:start position:0%
+at any given time and that's a kind of
+General historical lesson we grapple
+
+ align:start position:0%
+General historical lesson we grapple
+ 
+
+ align:start position:0%
+General historical lesson we grapple
+with you all the time not just in the
+
+ align:start position:0%
+with you all the time not just in the
+ 
+
+ align:start position:0%
+with you all the time not just in the
+history of science but but much more
+
+ align:start position:0%
+history of science but but much more
+ 
+
+ align:start position:0%
+history of science but but much more
+generally and we'll have a lot of
+
+ align:start position:0%
+generally and we'll have a lot of
+ 
+
+ align:start position:0%
+generally and we'll have a lot of
+examples of that really actually more
+
+ align:start position:0%
+examples of that really actually more
+ 
+
+ align:start position:0%
+examples of that really actually more
+examples even pretty soon in in our own
+
+ align:start position:0%
+examples even pretty soon in in our own
+ 
+
+ align:start position:0%
+examples even pretty soon in in our own
+class The Zone examples we might think
+
+ align:start position:0%
+class The Zone examples we might think
+ 
+
+ align:start position:0%
+class The Zone examples we might think
+of from from other uh instances
+
+ align:start position:0%
+of from from other uh instances
+ 
+
+ align:start position:0%
+of from from other uh instances
+uh here's an example where to to his
+
+ align:start position:0%
+uh here's an example where to to his
+ 
+
+ align:start position:0%
+uh here's an example where to to his
+credit Einstein later grudgingly came
+
+ align:start position:0%
+credit Einstein later grudgingly came
+ 
+
+ align:start position:0%
+credit Einstein later grudgingly came
+around to say oh that stuff is important
+
+ align:start position:0%
+around to say oh that stuff is important
+ 
+
+ align:start position:0%
+around to say oh that stuff is important
+minkowski does deserve credit I now see
+
+ align:start position:0%
+minkowski does deserve credit I now see
+ 
+
+ align:start position:0%
+minkowski does deserve credit I now see
+it was really valuable but it took Eisen
+
+ align:start position:0%
+it was really valuable but it took Eisen
+ 
+
+ align:start position:0%
+it was really valuable but it took Eisen
+himself quite a few years to get there
+
+ align:start position:0%
+himself quite a few years to get there
+ 
+
+ align:start position:0%
+himself quite a few years to get there
+doesn't always happen uh or there can be
+
+ align:start position:0%
+doesn't always happen uh or there can be
+ 
+
+ align:start position:0%
+doesn't always happen uh or there can be
+a much longer delay
+
+ align:start position:0%
+a much longer delay
+ 
+
+ align:start position:0%
+a much longer delay
+any other questions on on minkowski's
+
+ align:start position:0%
+any other questions on on minkowski's
+ 
+
+ align:start position:0%
+any other questions on on minkowski's
+um kind of reaction to or remaking of of
+
+ align:start position:0%
+um kind of reaction to or remaking of of
+ 
+
+ align:start position:0%
+um kind of reaction to or remaking of of
+Einstein's work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so minkowski actually thought this was
+
+ align:start position:0%
+so minkowski actually thought this was
+ 
+
+ align:start position:0%
+so minkowski actually thought this was
+really a big deal minkowsey thought his
+
+ align:start position:0%
+really a big deal minkowsey thought his
+ 
+
+ align:start position:0%
+really a big deal minkowsey thought his
+own work was a big deal which is not
+
+ align:start position:0%
+own work was a big deal which is not
+ 
+
+ align:start position:0%
+own work was a big deal which is not
+shocking it's also not unique in the
+
+ align:start position:0%
+shocking it's also not unique in the
+ 
+
+ align:start position:0%
+shocking it's also not unique in the
+history science and in particular he
+
+ align:start position:0%
+history science and in particular he
+ 
+
+ align:start position:0%
+history science and in particular he
+thought it wasn't actually only about
+
+ align:start position:0%
+thought it wasn't actually only about
+ 
+
+ align:start position:0%
+thought it wasn't actually only about
+coordinate Transformations rotations of
+
+ align:start position:0%
+coordinate Transformations rotations of
+ 
+
+ align:start position:0%
+coordinate Transformations rotations of
+axes he thought that was the most
+
+ align:start position:0%
+axes he thought that was the most
+ 
+
+ align:start position:0%
+axes he thought that was the most
+obvious thing to do and anyone who
+
+ align:start position:0%
+obvious thing to do and anyone who
+ 
+
+ align:start position:0%
+obvious thing to do and anyone who
+doesn't do that is a dummy right he had
+
+ align:start position:0%
+doesn't do that is a dummy right he had
+ 
+
+ align:start position:0%
+doesn't do that is a dummy right he had
+very clear ideas about the proper tools
+
+ align:start position:0%
+very clear ideas about the proper tools
+ 
+
+ align:start position:0%
+very clear ideas about the proper tools
+of research but even in that first
+
+ align:start position:0%
+of research but even in that first
+ 
+
+ align:start position:0%
+of research but even in that first
+article that gets published soon after
+
+ align:start position:0%
+article that gets published soon after
+ 
+
+ align:start position:0%
+article that gets published soon after
+he passed away he develops in the later
+
+ align:start position:0%
+he passed away he develops in the later
+ 
+
+ align:start position:0%
+he passed away he develops in the later
+sections a larger kind of world view
+
+ align:start position:0%
+sections a larger kind of world view
+ 
+
+ align:start position:0%
+sections a larger kind of world view
+literally a view of the world that's
+
+ align:start position:0%
+literally a view of the world that's
+ 
+
+ align:start position:0%
+literally a view of the world that's
+based on this Union space-time notion it
+
+ align:start position:0%
+based on this Union space-time notion it
+ 
+
+ align:start position:0%
+based on this Union space-time notion it
+gets very wrapped up with certain Trends
+
+ align:start position:0%
+gets very wrapped up with certain Trends
+ 
+
+ align:start position:0%
+gets very wrapped up with certain Trends
+in in idealist German philosophy he's
+
+ align:start position:0%
+in in idealist German philosophy he's
+ 
+
+ align:start position:0%
+in in idealist German philosophy he's
+very inspired by the work of Emmanuel
+
+ align:start position:0%
+very inspired by the work of Emmanuel
+ 
+
+ align:start position:0%
+very inspired by the work of Emmanuel
+Kant for example
+
+ align:start position:0%
+Kant for example
+ 
+
+ align:start position:0%
+Kant for example
+as I was too but in different ways and
+
+ align:start position:0%
+as I was too but in different ways and
+ 
+
+ align:start position:0%
+as I was too but in different ways and
+so as far as Mankowski is concerned he
+
+ align:start position:0%
+so as far as Mankowski is concerned he
+ 
+
+ align:start position:0%
+so as far as Mankowski is concerned he
+thought he found like a new deep level
+
+ align:start position:0%
+thought he found like a new deep level
+ 
+
+ align:start position:0%
+thought he found like a new deep level
+of reality the reality wasn't The Ether
+
+ align:start position:0%
+of reality the reality wasn't The Ether
+ 
+
+ align:start position:0%
+of reality the reality wasn't The Ether
+it was aptitude minkowski the reality
+
+ align:start position:0%
+it was aptitude minkowski the reality
+ 
+
+ align:start position:0%
+it was aptitude minkowski the reality
+was there's this single thing space time
+
+ align:start position:0%
+was there's this single thing space time
+ 
+
+ align:start position:0%
+was there's this single thing space time
+and there are certain things on which
+
+ align:start position:0%
+and there are certain things on which
+ 
+
+ align:start position:0%
+and there are certain things on which
+all people will agree these invariances
+
+ align:start position:0%
+all people will agree these invariances
+ 
+
+ align:start position:0%
+all people will agree these invariances
+even as we disagree separately on on
+
+ align:start position:0%
+even as we disagree separately on on
+ 
+
+ align:start position:0%
+even as we disagree separately on on
+measurements of length and measurements
+
+ align:start position:0%
+measurements of length and measurements
+ 
+
+ align:start position:0%
+measurements of length and measurements
+of time
+
+ align:start position:0%
+of time
+ 
+
+ align:start position:0%
+of time
+and so that for him and reintroduce a
+
+ align:start position:0%
+and so that for him and reintroduce a
+ 
+
+ align:start position:0%
+and so that for him and reintroduce a
+kind of absolute an absolutism not
+
+ align:start position:0%
+kind of absolute an absolutism not
+ 
+
+ align:start position:0%
+kind of absolute an absolutism not
+absolute rest like in Newton not
+
+ align:start position:0%
+absolute rest like in Newton not
+ 
+
+ align:start position:0%
+absolute rest like in Newton not
+absolute space because space and time he
+
+ align:start position:0%
+absolute space because space and time he
+ 
+
+ align:start position:0%
+absolute space because space and time he
+says are now just mere Shadows but there
+
+ align:start position:0%
+says are now just mere Shadows but there
+ 
+
+ align:start position:0%
+says are now just mere Shadows but there
+is an absolute um past and an absolute
+
+ align:start position:0%
+is an absolute um past and an absolute
+ 
+
+ align:start position:0%
+is an absolute um past and an absolute
+future there's an absolute away the
+
+ align:start position:0%
+future there's an absolute away the
+ 
+
+ align:start position:0%
+future there's an absolute away the
+things that we would now call if you've
+
+ align:start position:0%
+things that we would now call if you've
+ 
+
+ align:start position:0%
+things that we would now call if you've
+had some more coursework in this area
+
+ align:start position:0%
+had some more coursework in this area
+ 
+
+ align:start position:0%
+had some more coursework in this area
+you'd recognize as things like um space
+
+ align:start position:0%
+you'd recognize as things like um space
+ 
+
+ align:start position:0%
+you'd recognize as things like um space
+like separated and so on he starts
+
+ align:start position:0%
+like separated and so on he starts
+ 
+
+ align:start position:0%
+like separated and so on he starts
+mapping sets of events that could not
+
+ align:start position:0%
+mapping sets of events that could not
+ 
+
+ align:start position:0%
+mapping sets of events that could not
+possibly have exchanged even a single
+
+ align:start position:0%
+possibly have exchanged even a single
+ 
+
+ align:start position:0%
+possibly have exchanged even a single
+light signal yet those are absolutely
+
+ align:start position:0%
+light signal yet those are absolutely
+ 
+
+ align:start position:0%
+light signal yet those are absolutely
+separated from each other and he gives
+
+ align:start position:0%
+separated from each other and he gives
+ 
+
+ align:start position:0%
+separated from each other and he gives
+these very absolutist language to them
+
+ align:start position:0%
+these very absolutist language to them
+ 
+
+ align:start position:0%
+these very absolutist language to them
+so he's actually mapping what he
+
+ align:start position:0%
+so he's actually mapping what he
+ 
+
+ align:start position:0%
+so he's actually mapping what he
+considers like the ultimate absolute
+
+ align:start position:0%
+considers like the ultimate absolute
+ 
+
+ align:start position:0%
+considers like the ultimate absolute
+structure of space-time and as far as
+
+ align:start position:0%
+structure of space-time and as far as
+ 
+
+ align:start position:0%
+structure of space-time and as far as
+he's concerned that's the real lesson
+
+ align:start position:0%
+he's concerned that's the real lesson
+ 
+
+ align:start position:0%
+he's concerned that's the real lesson
+that the geometry leads us to so he
+
+ align:start position:0%
+that the geometry leads us to so he
+ 
+
+ align:start position:0%
+that the geometry leads us to so he
+actually thinks it's not a theory of
+
+ align:start position:0%
+actually thinks it's not a theory of
+ 
+
+ align:start position:0%
+actually thinks it's not a theory of
+relativity at all relativity is like an
+
+ align:start position:0%
+relativity at all relativity is like an
+ 
+
+ align:start position:0%
+relativity at all relativity is like an
+accident and boring and trivial and the
+
+ align:start position:0%
+accident and boring and trivial and the
+ 
+
+ align:start position:0%
+accident and boring and trivial and the
+stupid thing that no one should pay
+
+ align:start position:0%
+stupid thing that no one should pay
+ 
+
+ align:start position:0%
+stupid thing that no one should pay
+attention to right relativity all we
+
+ align:start position:0%
+attention to right relativity all we
+ 
+
+ align:start position:0%
+attention to right relativity all we
+differ the person that trains says this
+
+ align:start position:0%
+differ the person that trains says this
+ 
+
+ align:start position:0%
+differ the person that trains says this
+wasn't the same says that's just
+
+ align:start position:0%
+wasn't the same says that's just
+ 
+
+ align:start position:0%
+wasn't the same says that's just
+accidents who cares what's actually
+
+ align:start position:0%
+accidents who cares what's actually
+ 
+
+ align:start position:0%
+accidents who cares what's actually
+important are these underlying
+
+ align:start position:0%
+important are these underlying
+ 
+
+ align:start position:0%
+important are these underlying
+invariances or absolutes we all agree on
+
+ align:start position:0%
+invariances or absolutes we all agree on
+ 
+
+ align:start position:0%
+invariances or absolutes we all agree on
+certain combinations of things and
+
+ align:start position:0%
+certain combinations of things and
+ 
+
+ align:start position:0%
+certain combinations of things and
+that's the real lesson so for him this
+
+ align:start position:0%
+that's the real lesson so for him this
+ 
+
+ align:start position:0%
+that's the real lesson so for him this
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+a kind of re-injection of the absolute
+
+ align:start position:0%
+a kind of re-injection of the absolute
+ 
+
+ align:start position:0%
+a kind of re-injection of the absolute
+not because we're all sitting in a
+
+ align:start position:0%
+not because we're all sitting in a
+ 
+
+ align:start position:0%
+not because we're all sitting in a
+physical ether he couldn't care less
+
+ align:start position:0%
+physical ether he couldn't care less
+ 
+
+ align:start position:0%
+physical ether he couldn't care less
+he's a geometer because there is a kind
+
+ align:start position:0%
+he's a geometer because there is a kind
+ 
+
+ align:start position:0%
+he's a geometer because there is a kind
+of a unique structure to space-time that
+
+ align:start position:0%
+of a unique structure to space-time that
+ 
+
+ align:start position:0%
+of a unique structure to space-time that
+the tools of geometry are uniquely well
+
+ align:start position:0%
+the tools of geometry are uniquely well
+ 
+
+ align:start position:0%
+the tools of geometry are uniquely well
+um well adapted to help us understand so
+
+ align:start position:0%
+um well adapted to help us understand so
+ 
+
+ align:start position:0%
+um well adapted to help us understand so
+that that
+
+ align:start position:0%
+that that
+ 
+
+ align:start position:0%
+that that
+makes sense does it make address your
+
+ align:start position:0%
+makes sense does it make address your
+ 
+
+ align:start position:0%
+makes sense does it make address your
+question okay cool thank you so let's
+
+ align:start position:0%
+question okay cool thank you so let's
+ 
+
+ align:start position:0%
+question okay cool thank you so let's
+see Fisher asks the question to chat we
+
+ align:start position:0%
+see Fisher asks the question to chat we
+ 
+
+ align:start position:0%
+see Fisher asks the question to chat we
+now think of space-time as something as
+
+ align:start position:0%
+now think of space-time as something as
+ 
+
+ align:start position:0%
+now think of space-time as something as
+deformable hey that's cheating who
+
+ align:start position:0%
+deformable hey that's cheating who
+ 
+
+ align:start position:0%
+deformable hey that's cheating who
+that's we're going to get there next
+
+ align:start position:0%
+that's we're going to get there next
+ 
+
+ align:start position:0%
+that's we're going to get there next
+week you don't know that yet it's 1905
+
+ align:start position:0%
+week you don't know that yet it's 1905
+ 
+
+ align:start position:0%
+week you don't know that yet it's 1905
+it's 1908. but you're right certainly as
+
+ align:start position:0%
+it's 1908. but you're right certainly as
+ 
+
+ align:start position:0%
+it's 1908. but you're right certainly as
+we'll talk about quite a lot uh starting
+
+ align:start position:0%
+we'll talk about quite a lot uh starting
+ 
+
+ align:start position:0%
+we'll talk about quite a lot uh starting
+uh in this coming the next class session
+
+ align:start position:0%
+uh in this coming the next class session
+ 
+
+ align:start position:0%
+uh in this coming the next class session
+where eyesight himself gets to is to
+
+ align:start position:0%
+where eyesight himself gets to is to
+ 
+
+ align:start position:0%
+where eyesight himself gets to is to
+begin thinking about space-time as one
+
+ align:start position:0%
+begin thinking about space-time as one
+ 
+
+ align:start position:0%
+begin thinking about space-time as one
+thing that also can respond to be
+
+ align:start position:0%
+thing that also can respond to be
+ 
+
+ align:start position:0%
+thing that also can respond to be
+deformable
+
+ align:start position:0%
+deformable
+ 
+
+ align:start position:0%
+deformable
+Andrew originally introduced as a
+
+ align:start position:0%
+Andrew originally introduced as a
+ 
+
+ align:start position:0%
+Andrew originally introduced as a
+mathematical artifact was a point where
+
+ align:start position:0%
+mathematical artifact was a point where
+ 
+
+ align:start position:0%
+mathematical artifact was a point where
+we moved from thinking about it as a
+
+ align:start position:0%
+we moved from thinking about it as a
+ 
+
+ align:start position:0%
+we moved from thinking about it as a
+mathematical concept what generally was
+
+ align:start position:0%
+mathematical concept what generally was
+ 
+
+ align:start position:0%
+mathematical concept what generally was
+published yes very good okay so fishery
+
+ align:start position:0%
+published yes very good okay so fishery
+ 
+
+ align:start position:0%
+published yes very good okay so fishery
+um it's a great question thank you for
+
+ align:start position:0%
+um it's a great question thank you for
+ 
+
+ align:start position:0%
+um it's a great question thank you for
+that and we're going to come we're going
+
+ align:start position:0%
+that and we're going to come we're going
+ 
+
+ align:start position:0%
+that and we're going to come we're going
+to sit with that actually quite directly
+
+ align:start position:0%
+to sit with that actually quite directly
+ 
+
+ align:start position:0%
+to sit with that actually quite directly
+on our next class so I'm going to punt
+
+ align:start position:0%
+on our next class so I'm going to punt
+ 
+
+ align:start position:0%
+on our next class so I'm going to punt
+on that for now the short answer is if
+
+ align:start position:0%
+on that for now the short answer is if
+ 
+
+ align:start position:0%
+on that for now the short answer is if
+it's not it doesn't come only when
+
+ align:start position:0%
+it's not it doesn't come only when
+ 
+
+ align:start position:0%
+it's not it doesn't come only when
+Einstein publishes gender relativity
+
+ align:start position:0%
+Einstein publishes gender relativity
+ 
+
+ align:start position:0%
+Einstein publishes gender relativity
+that comes a very late 1915 but it's an
+
+ align:start position:0%
+that comes a very late 1915 but it's an
+ 
+
+ align:start position:0%
+that comes a very late 1915 but it's an
+evolution in Einstein's own thinking
+
+ align:start position:0%
+evolution in Einstein's own thinking
+ 
+
+ align:start position:0%
+evolution in Einstein's own thinking
+with some colleagues like Marcel
+
+ align:start position:0%
+with some colleagues like Marcel
+ 
+
+ align:start position:0%
+with some colleagues like Marcel
+Grossman in a small circle over the over
+
+ align:start position:0%
+Grossman in a small circle over the over
+ 
+
+ align:start position:0%
+Grossman in a small circle over the over
+the intermediate decade so starting
+
+ align:start position:0%
+the intermediate decade so starting
+ 
+
+ align:start position:0%
+the intermediate decade so starting
+around 19 11 12 13 he has a lot of
+
+ align:start position:0%
+around 19 11 12 13 he has a lot of
+ 
+
+ align:start position:0%
+around 19 11 12 13 he has a lot of
+mistakes a lot of blind alleys he starts
+
+ align:start position:0%
+mistakes a lot of blind alleys he starts
+ 
+
+ align:start position:0%
+mistakes a lot of blind alleys he starts
+wondering about that more in the terms
+
+ align:start position:0%
+wondering about that more in the terms
+ 
+
+ align:start position:0%
+wondering about that more in the terms
+as you describe it
+
+ align:start position:0%
+as you describe it
+ 
+
+ align:start position:0%
+as you describe it
+um starting
+
+ align:start position:0%
+um starting
+ 
+
+ align:start position:0%
+um starting
+well Downstream both from his own work
+
+ align:start position:0%
+well Downstream both from his own work
+ 
+
+ align:start position:0%
+well Downstream both from his own work
+in 1905 Downstream by four years even
+
+ align:start position:0%
+in 1905 Downstream by four years even
+ 
+
+ align:start position:0%
+in 1905 Downstream by four years even
+from minkowski's work it's a real kind
+
+ align:start position:0%
+from minkowski's work it's a real kind
+ 
+
+ align:start position:0%
+from minkowski's work it's a real kind
+of intellectual Journey so that's that's
+
+ align:start position:0%
+of intellectual Journey so that's that's
+ 
+
+ align:start position:0%
+of intellectual Journey so that's that's
+a preview we'll get there next time
+
+ align:start position:0%
+a preview we'll get there next time
+ 
+
+ align:start position:0%
+a preview we'll get there next time
+great Gary asks how did folks react to
+
+ align:start position:0%
+great Gary asks how did folks react to
+ 
+
+ align:start position:0%
+great Gary asks how did folks react to
+mikowski's work again I think maybe
+
+ align:start position:0%
+mikowski's work again I think maybe
+ 
+
+ align:start position:0%
+mikowski's work again I think maybe
+sorry maybe I mentioned that or you had
+
+ align:start position:0%
+sorry maybe I mentioned that or you had
+ 
+
+ align:start position:0%
+sorry maybe I mentioned that or you had
+asked earlier who was it who made the
+
+ align:start position:0%
+asked earlier who was it who made the
+ 
+
+ align:start position:0%
+asked earlier who was it who made the
+greater contribution yominkowski was on
+
+ align:start position:0%
+greater contribution yominkowski was on
+ 
+
+ align:start position:0%
+greater contribution yominkowski was on
+people's radar screen he was a big fancy
+
+ align:start position:0%
+people's radar screen he was a big fancy
+ 
+
+ align:start position:0%
+people's radar screen he was a big fancy
+senior mathematician very widely
+
+ align:start position:0%
+senior mathematician very widely
+ 
+
+ align:start position:0%
+senior mathematician very widely
+published very influential at a central
+
+ align:start position:0%
+published very influential at a central
+ 
+
+ align:start position:0%
+published very influential at a central
+you know center of learning in Western
+
+ align:start position:0%
+you know center of learning in Western
+ 
+
+ align:start position:0%
+you know center of learning in Western
+Europe so his work was paid attention to
+
+ align:start position:0%
+Europe so his work was paid attention to
+ 
+
+ align:start position:0%
+Europe so his work was paid attention to
+mostly by other mathematicians and by
+
+ align:start position:0%
+mostly by other mathematicians and by
+ 
+
+ align:start position:0%
+mostly by other mathematicians and by
+some sort of mathematical physicists uh
+
+ align:start position:0%
+some sort of mathematical physicists uh
+ 
+
+ align:start position:0%
+some sort of mathematical physicists uh
+like uh Hedrick Lorenz
+
+ align:start position:0%
+like uh Hedrick Lorenz
+ 
+
+ align:start position:0%
+like uh Hedrick Lorenz
+uh not every single physicist it's not
+
+ align:start position:0%
+uh not every single physicist it's not
+ 
+
+ align:start position:0%
+uh not every single physicist it's not
+every experimental physicist but it was
+
+ align:start position:0%
+every experimental physicist but it was
+ 
+
+ align:start position:0%
+every experimental physicist but it was
+not kind of buried and forgotten for
+
+ align:start position:0%
+not kind of buried and forgotten for
+ 
+
+ align:start position:0%
+not kind of buried and forgotten for
+years and years it was appreciated in
+
+ align:start position:0%
+years and years it was appreciated in
+ 
+
+ align:start position:0%
+years and years it was appreciated in
+certain specialist communities right
+
+ align:start position:0%
+certain specialist communities right
+ 
+
+ align:start position:0%
+certain specialist communities right
+away and then as we'll talk about uh
+
+ align:start position:0%
+away and then as we'll talk about uh
+ 
+
+ align:start position:0%
+away and then as we'll talk about uh
+later even other people like Einstein
+
+ align:start position:0%
+later even other people like Einstein
+ 
+
+ align:start position:0%
+later even other people like Einstein
+belatedly come to admire it as well so
+
+ align:start position:0%
+belatedly come to admire it as well so
+ 
+
+ align:start position:0%
+belatedly come to admire it as well so
+it becomes very very well known partly I
+
+ align:start position:0%
+it becomes very very well known partly I
+ 
+
+ align:start position:0%
+it becomes very very well known partly I
+think because Einstein goes back to it
+
+ align:start position:0%
+think because Einstein goes back to it
+ 
+
+ align:start position:0%
+think because Einstein goes back to it
+and Eisen herself becomes then
+
+ align:start position:0%
+and Eisen herself becomes then
+ 
+
+ align:start position:0%
+and Eisen herself becomes then
+eventually someone that everyone pays
+
+ align:start position:0%
+eventually someone that everyone pays
+ 
+
+ align:start position:0%
+eventually someone that everyone pays
+attention to many people so it has a
+
+ align:start position:0%
+attention to many people so it has a
+ 
+
+ align:start position:0%
+attention to many people so it has a
+kind of bumpy few years but it was not
+
+ align:start position:0%
+kind of bumpy few years but it was not
+ 
+
+ align:start position:0%
+kind of bumpy few years but it was not
+launched Into Obscurity because
+
+ align:start position:0%
+launched Into Obscurity because
+ 
+
+ align:start position:0%
+launched Into Obscurity because
+minkowski himself was actually already
+
+ align:start position:0%
+minkowski himself was actually already
+ 
+
+ align:start position:0%
+minkowski himself was actually already
+quite well established and well known
+
+ align:start position:0%
+quite well established and well known
+ 
+
+ align:start position:0%
+quite well established and well known
+asks what was Lorenzo's stats with
+
+ align:start position:0%
+asks what was Lorenzo's stats with
+ 
+
+ align:start position:0%
+asks what was Lorenzo's stats with
+regard to this good did he jump on the
+
+ align:start position:0%
+regard to this good did he jump on the
+ 
+
+ align:start position:0%
+regard to this good did he jump on the
+space-time wagon great so the short
+
+ align:start position:0%
+space-time wagon great so the short
+ 
+
+ align:start position:0%
+space-time wagon great so the short
+answer is we'll see an example of the
+
+ align:start position:0%
+answer is we'll see an example of the
+ 
+
+ align:start position:0%
+answer is we'll see an example of the
+kind of reaction action the next part of
+
+ align:start position:0%
+kind of reaction action the next part of
+ 
+
+ align:start position:0%
+kind of reaction action the next part of
+today's class not Lorenz per se but an
+
+ align:start position:0%
+today's class not Lorenz per se but an
+ 
+
+ align:start position:0%
+today's class not Lorenz per se but an
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+Lorenz really for for the rest of his
+
+ align:start position:0%
+Lorenz really for for the rest of his
+ 
+
+ align:start position:0%
+Lorenz really for for the rest of his
+career was still pretty convinced The
+
+ align:start position:0%
+career was still pretty convinced The
+ 
+
+ align:start position:0%
+career was still pretty convinced The
+Ether exists and he had a great
+
+ align:start position:0%
+Ether exists and he had a great
+ 
+
+ align:start position:0%
+Ether exists and he had a great
+appreciation for some of these very
+
+ align:start position:0%
+appreciation for some of these very
+ 
+
+ align:start position:0%
+appreciation for some of these very
+clever mathematical techniques he
+
+ align:start position:0%
+clever mathematical techniques he
+ 
+
+ align:start position:0%
+clever mathematical techniques he
+certainly liked it that Einsteins and
+
+ align:start position:0%
+certainly liked it that Einsteins and
+ 
+
+ align:start position:0%
+certainly liked it that Einsteins and
+now minkowski's work LED back to
+
+ align:start position:0%
+now minkowski's work LED back to
+ 
+
+ align:start position:0%
+now minkowski's work LED back to
+equations that he himself had derived
+
+ align:start position:0%
+equations that he himself had derived
+ 
+
+ align:start position:0%
+equations that he himself had derived
+from his own
+
+ align:start position:0%
+from his own
+ 
+
+ align:start position:0%
+from his own
+set of of arguments but he really was
+
+ align:start position:0%
+set of of arguments but he really was
+ 
+
+ align:start position:0%
+set of of arguments but he really was
+convinced that you know there's
+
+ align:start position:0%
+convinced that you know there's
+ 
+
+ align:start position:0%
+convinced that you know there's
+something physical about this elastic
+
+ align:start position:0%
+something physical about this elastic
+ 
+
+ align:start position:0%
+something physical about this elastic
+medium in which we're all immersed for a
+
+ align:start position:0%
+medium in which we're all immersed for a
+ 
+
+ align:start position:0%
+medium in which we're all immersed for a
+long long time so he thought these were
+
+ align:start position:0%
+long long time so he thought these were
+ 
+
+ align:start position:0%
+long long time so he thought these were
+more Cool Tools more mathematical tools
+
+ align:start position:0%
+more Cool Tools more mathematical tools
+ 
+
+ align:start position:0%
+more Cool Tools more mathematical tools
+with which to keep asking questions you
+
+ align:start position:0%
+with which to keep asking questions you
+ 
+
+ align:start position:0%
+with which to keep asking questions you
+already considered important those
+
+ align:start position:0%
+already considered important those
+ 
+
+ align:start position:0%
+already considered important those
+warrant as we've seen the same set of
+
+ align:start position:0%
+warrant as we've seen the same set of
+ 
+
+ align:start position:0%
+warrant as we've seen the same set of
+questions that Einstein thought were
+
+ align:start position:0%
+questions that Einstein thought were
+ 
+
+ align:start position:0%
+questions that Einstein thought were
+important or the minkowski file report
+
+ align:start position:0%
+important or the minkowski file report
+ 
+
+ align:start position:0%
+important or the minkowski file report
+and in that sense it's a lot like the
+
+ align:start position:0%
+and in that sense it's a lot like the
+ 
+
+ align:start position:0%
+and in that sense it's a lot like the
+example we look at now from Cambridge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah very good so again we'll look at
+
+ align:start position:0%
+yeah very good so again we'll look at
+ 
+
+ align:start position:0%
+yeah very good so again we'll look at
+this much more directly in the upcoming
+
+ align:start position:0%
+this much more directly in the upcoming
+ 
+
+ align:start position:0%
+this much more directly in the upcoming
+class session next week the short answer
+
+ align:start position:0%
+class session next week the short answer
+ 
+
+ align:start position:0%
+class session next week the short answer
+was it wasn't really minkowski per se
+
+ align:start position:0%
+was it wasn't really minkowski per se
+ 
+
+ align:start position:0%
+was it wasn't really minkowski per se
+because he just had no respect for
+
+ align:start position:0%
+because he just had no respect for
+ 
+
+ align:start position:0%
+because he just had no respect for
+McAlister cutting his mask
+
+ align:start position:0%
+McAlister cutting his mask
+ 
+
+ align:start position:0%
+McAlister cutting his mask
+um it was actually an independent series
+
+ align:start position:0%
+um it was actually an independent series
+ 
+
+ align:start position:0%
+um it was actually an independent series
+of thought experiments and and
+
+ align:start position:0%
+of thought experiments and and
+ 
+
+ align:start position:0%
+of thought experiments and and
+conceptual puzzles and calculations that
+
+ align:start position:0%
+conceptual puzzles and calculations that
+ 
+
+ align:start position:0%
+conceptual puzzles and calculations that
+Einstein got immersed in and he kept
+
+ align:start position:0%
+Einstein got immersed in and he kept
+ 
+
+ align:start position:0%
+Einstein got immersed in and he kept
+getting stuck and he let that led him
+
+ align:start position:0%
+getting stuck and he let that led him
+ 
+
+ align:start position:0%
+getting stuck and he let that led him
+back to realizing geometry might be
+
+ align:start position:0%
+back to realizing geometry might be
+ 
+
+ align:start position:0%
+back to realizing geometry might be
+really important by which point
+
+ align:start position:0%
+really important by which point
+ 
+
+ align:start position:0%
+really important by which point
+minkowski had died he went to his former
+
+ align:start position:0%
+minkowski had died he went to his former
+ 
+
+ align:start position:0%
+minkowski had died he went to his former
+classmate his buddy um Marcel Grossman
+
+ align:start position:0%
+classmate his buddy um Marcel Grossman
+ 
+
+ align:start position:0%
+classmate his buddy um Marcel Grossman
+and had to do like a crash course on the
+
+ align:start position:0%
+and had to do like a crash course on the
+ 
+
+ align:start position:0%
+and had to do like a crash course on the
+stuff that he kind of should have
+
+ align:start position:0%
+stuff that he kind of should have
+ 
+
+ align:start position:0%
+stuff that he kind of should have
+learned uh when he was an undergraduate
+
+ align:start position:0%
+learned uh when he was an undergraduate
+ 
+
+ align:start position:0%
+learned uh when he was an undergraduate
+so it was he came to an appreciation of
+
+ align:start position:0%
+so it was he came to an appreciation of
+ 
+
+ align:start position:0%
+so it was he came to an appreciation of
+the geometrical approach of minkowski's
+
+ align:start position:0%
+the geometrical approach of minkowski's
+ 
+
+ align:start position:0%
+the geometrical approach of minkowski's
+work in particular thinking about a
+
+ align:start position:0%
+work in particular thinking about a
+ 
+
+ align:start position:0%
+work in particular thinking about a
+single object called space time he gets
+
+ align:start position:0%
+single object called space time he gets
+ 
+
+ align:start position:0%
+single object called space time he gets
+there but not because he reads
+
+ align:start position:0%
+there but not because he reads
+ 
+
+ align:start position:0%
+there but not because he reads
+minkowski's paper says oh my great
+
+ align:start position:0%
+minkowski's paper says oh my great
+ 
+
+ align:start position:0%
+minkowski's paper says oh my great
+Professor I'm totally convinced he's
+
+ align:start position:0%
+Professor I'm totally convinced he's
+ 
+
+ align:start position:0%
+Professor I'm totally convinced he's
+like that's dumb it's wrong it's boring
+
+ align:start position:0%
+like that's dumb it's wrong it's boring
+ 
+
+ align:start position:0%
+like that's dumb it's wrong it's boring
+he's still irrelevant I would cut his
+
+ align:start position:0%
+he's still irrelevant I would cut his
+ 
+
+ align:start position:0%
+he's still irrelevant I would cut his
+classes again if that's the reaction for
+
+ align:start position:0%
+classes again if that's the reaction for
+ 
+
+ align:start position:0%
+classes again if that's the reaction for
+like four years three or four years
+
+ align:start position:0%
+like four years three or four years
+ 
+
+ align:start position:0%
+like four years three or four years
+and it's a separate set of of
+
+ align:start position:0%
+and it's a separate set of of
+ 
+
+ align:start position:0%
+and it's a separate set of of
+um lines of thought that kind of and
+
+ align:start position:0%
+um lines of thought that kind of and
+ 
+
+ align:start position:0%
+um lines of thought that kind of and
+interactions with other people including
+
+ align:start position:0%
+interactions with other people including
+ 
+
+ align:start position:0%
+interactions with other people including
+friends who were more a better verse in
+
+ align:start position:0%
+friends who were more a better verse in
+ 
+
+ align:start position:0%
+friends who were more a better verse in
+mathematics that bring him his own
+
+ align:start position:0%
+mathematics that bring him his own
+ 
+
+ align:start position:0%
+mathematics that bring him his own
+thinking back uh or bring it presenting
+
+ align:start position:0%
+thinking back uh or bring it presenting
+ 
+
+ align:start position:0%
+thinking back uh or bring it presenting
+towards a more thoroughly geometrical
+
+ align:start position:0%
+towards a more thoroughly geometrical
+ 
+
+ align:start position:0%
+towards a more thoroughly geometrical
+approach and then he never leaves then
+
+ align:start position:0%
+approach and then he never leaves then
+ 
+
+ align:start position:0%
+approach and then he never leaves then
+he becomes a kind of card-carrying
+
+ align:start position:0%
+he becomes a kind of card-carrying
+ 
+
+ align:start position:0%
+he becomes a kind of card-carrying
+geometer himself once he gets a crash
+
+ align:start position:0%
+geometer himself once he gets a crash
+ 
+
+ align:start position:0%
+geometer himself once he gets a crash
+course from real geometers and gets a
+
+ align:start position:0%
+course from real geometers and gets a
+ 
+
+ align:start position:0%
+course from real geometers and gets a
+kind of Newfound appreciation because of
+
+ align:start position:0%
+kind of Newfound appreciation because of
+ 
+
+ align:start position:0%
+kind of Newfound appreciation because of
+his own questions have led him there so
+
+ align:start position:0%
+his own questions have led him there so
+ 
+
+ align:start position:0%
+his own questions have led him there so
+it's it's he he comes to greatly admire
+
+ align:start position:0%
+it's it's he he comes to greatly admire
+ 
+
+ align:start position:0%
+it's it's he he comes to greatly admire
+minkowski's work and indeed to try to
+
+ align:start position:0%
+minkowski's work and indeed to try to
+ 
+
+ align:start position:0%
+minkowski's work and indeed to try to
+build upon it as we'll see next time but
+
+ align:start position:0%
+build upon it as we'll see next time but
+ 
+
+ align:start position:0%
+build upon it as we'll see next time but
+not because he thought oh this is a cool
+
+ align:start position:0%
+not because he thought oh this is a cool
+ 
+
+ align:start position:0%
+not because he thought oh this is a cool
+work by smart person it was again a kind
+
+ align:start position:0%
+work by smart person it was again a kind
+ 
+
+ align:start position:0%
+work by smart person it was again a kind
+of roundabout thing
+
+ align:start position:0%
+of roundabout thing
+ 
+
+ align:start position:0%
+of roundabout thing
+um and so we'll look at that in a bit
+
+ align:start position:0%
+um and so we'll look at that in a bit
+ 
+
+ align:start position:0%
+um and so we'll look at that in a bit
+more detail in the coming class
+
+ align:start position:0%
+more detail in the coming class
+ 
+
+ align:start position:0%
+more detail in the coming class
+another question on this stuff if not
+
+ align:start position:0%
+another question on this stuff if not
+ 
+
+ align:start position:0%
+another question on this stuff if not
+I'll go to this last part of the lecture
+
+ align:start position:0%
+I'll go to this last part of the lecture
+ 
+
+ align:start position:0%
+I'll go to this last part of the lecture
+on some of the pretty wacky work that
+
+ align:start position:0%
+on some of the pretty wacky work that
+ 
+
+ align:start position:0%
+on some of the pretty wacky work that
+the Cambridge gang
+
+ align:start position:0%
+the Cambridge gang
+ 
+
+ align:start position:0%
+the Cambridge gang
+so I started with us as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah thank you Fisher so so as far as
+
+ align:start position:0%
+yeah thank you Fisher so so as far as
+ 
+
+ align:start position:0%
+yeah thank you Fisher so so as far as
+minkowski is concerned Einstein's paper
+
+ align:start position:0%
+minkowski is concerned Einstein's paper
+ 
+
+ align:start position:0%
+minkowski is concerned Einstein's paper
+especially the first few pages which you
+
+ align:start position:0%
+especially the first few pages which you
+ 
+
+ align:start position:0%
+especially the first few pages which you
+are all dutifully reviewing and maybe
+
+ align:start position:0%
+are all dutifully reviewing and maybe
+ 
+
+ align:start position:0%
+are all dutifully reviewing and maybe
+even rejecting
+
+ align:start position:0%
+even rejecting
+ 
+
+ align:start position:0%
+even rejecting
+um or not or ask me at least for
+
+ align:start position:0%
+um or not or ask me at least for
+ 
+
+ align:start position:0%
+um or not or ask me at least for
+revisions the first few pages at least
+
+ align:start position:0%
+revisions the first few pages at least
+ 
+
+ align:start position:0%
+revisions the first few pages at least
+are really to to someone like Ben Cassie
+
+ align:start position:0%
+are really to to someone like Ben Cassie
+ 
+
+ align:start position:0%
+are really to to someone like Ben Cassie
+a kind of jumble word salad this is like
+
+ align:start position:0%
+a kind of jumble word salad this is like
+ 
+
+ align:start position:0%
+a kind of jumble word salad this is like
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+of course you know I know how to
+
+ align:start position:0%
+of course you know I know how to
+ 
+
+ align:start position:0%
+of course you know I know how to
+calculate distance traveled if the
+
+ align:start position:0%
+calculate distance traveled if the
+ 
+
+ align:start position:0%
+calculate distance traveled if the
+person's traveling at constant speed
+
+ align:start position:0%
+person's traveling at constant speed
+ 
+
+ align:start position:0%
+person's traveling at constant speed
+that's like Middle School right this is
+
+ align:start position:0%
+that's like Middle School right this is
+ 
+
+ align:start position:0%
+that's like Middle School right this is
+not like why you belaboring this
+
+ align:start position:0%
+not like why you belaboring this
+ 
+
+ align:start position:0%
+not like why you belaboring this
+paragraph after paragraph why are you
+
+ align:start position:0%
+paragraph after paragraph why are you
+ 
+
+ align:start position:0%
+paragraph after paragraph why are you
+using this kind of mock inspired
+
+ align:start position:0%
+using this kind of mock inspired
+ 
+
+ align:start position:0%
+using this kind of mock inspired
+language without even citing as Mark
+
+ align:start position:0%
+language without even citing as Mark
+ 
+
+ align:start position:0%
+language without even citing as Mark
+about how objects should be um subject
+
+ align:start position:0%
+about how objects should be um subject
+ 
+
+ align:start position:0%
+about how objects should be um subject
+to uh empirical measurement why are you
+
+ align:start position:0%
+to uh empirical measurement why are you
+ 
+
+ align:start position:0%
+to uh empirical measurement why are you
+telling me how to have my friend shine a
+
+ align:start position:0%
+telling me how to have my friend shine a
+ 
+
+ align:start position:0%
+telling me how to have my friend shine a
+lantern in my face it's like get to the
+
+ align:start position:0%
+lantern in my face it's like get to the
+ 
+
+ align:start position:0%
+lantern in my face it's like get to the
+point right show me equations show me
+
+ align:start position:0%
+point right show me equations show me
+ 
+
+ align:start position:0%
+point right show me equations show me
+what you're doing show me the
+
+ align:start position:0%
+what you're doing show me the
+ 
+
+ align:start position:0%
+what you're doing show me the
+measurements you've performed in your
+
+ align:start position:0%
+measurements you've performed in your
+ 
+
+ align:start position:0%
+measurements you've performed in your
+laboratory show me the missing factor of
+
+ align:start position:0%
+laboratory show me the missing factor of
+ 
+
+ align:start position:0%
+laboratory show me the missing factor of
+2 pi and maximum equations like do
+
+ align:start position:0%
+2 pi and maximum equations like do
+ 
+
+ align:start position:0%
+2 pi and maximum equations like do
+something right calculate something you
+
+ align:start position:0%
+something right calculate something you
+ 
+
+ align:start position:0%
+something right calculate something you
+lazy dog right I think what minkowski
+
+ align:start position:0%
+lazy dog right I think what minkowski
+ 
+
+ align:start position:0%
+lazy dog right I think what minkowski
+was reacting to was this kind of not
+
+ align:start position:0%
+was reacting to was this kind of not
+ 
+
+ align:start position:0%
+was reacting to was this kind of not
+just a kind of everything's in a
+
+ align:start position:0%
+just a kind of everything's in a
+ 
+
+ align:start position:0%
+just a kind of everything's in a
+specific coordinate basis it's not very
+
+ align:start position:0%
+specific coordinate basis it's not very
+ 
+
+ align:start position:0%
+specific coordinate basis it's not very
+unified or we would we would learn fancy
+
+ align:start position:0%
+unified or we would we would learn fancy
+ 
+
+ align:start position:0%
+unified or we would we would learn fancy
+techniques later it's not just that he
+
+ align:start position:0%
+techniques later it's not just that he
+ 
+
+ align:start position:0%
+techniques later it's not just that he
+doesn't that Einstein
+
+ align:start position:0%
+doesn't that Einstein
+ 
+
+ align:start position:0%
+doesn't that Einstein
+doesn't scale out the speed of light to
+
+ align:start position:0%
+doesn't scale out the speed of light to
+ 
+
+ align:start position:0%
+doesn't scale out the speed of light to
+make things more um you know
+
+ align:start position:0%
+make things more um you know
+ 
+
+ align:start position:0%
+make things more um you know
+dimensionless these are all things that
+
+ align:start position:0%
+dimensionless these are all things that
+ 
+
+ align:start position:0%
+dimensionless these are all things that
+we would admire or come to take to to
+
+ align:start position:0%
+we would admire or come to take to to
+ 
+
+ align:start position:0%
+we would admire or come to take to to
+consider a natural move to make because
+
+ align:start position:0%
+consider a natural move to make because
+ 
+
+ align:start position:0%
+consider a natural move to make because
+on the benefit of work by people like
+
+ align:start position:0%
+on the benefit of work by people like
+ 
+
+ align:start position:0%
+on the benefit of work by people like
+mkowski I think to Mankowski this was
+
+ align:start position:0%
+mkowski I think to Mankowski this was
+ 
+
+ align:start position:0%
+mkowski I think to Mankowski this was
+just a lot of philosophical blah blah
+
+ align:start position:0%
+just a lot of philosophical blah blah
+ 
+
+ align:start position:0%
+just a lot of philosophical blah blah
+blah that wasn't advancing any new
+
+ align:start position:0%
+blah that wasn't advancing any new
+ 
+
+ align:start position:0%
+blah that wasn't advancing any new
+mathematics it wasn't analyzing you know
+
+ align:start position:0%
+mathematics it wasn't analyzing you know
+ 
+
+ align:start position:0%
+mathematics it wasn't analyzing you know
+concrete experiments in a new detail it
+
+ align:start position:0%
+concrete experiments in a new detail it
+ 
+
+ align:start position:0%
+concrete experiments in a new detail it
+wasn't telling us anything new about
+
+ align:start position:0%
+wasn't telling us anything new about
+ 
+
+ align:start position:0%
+wasn't telling us anything new about
+things that other researchers had done
+
+ align:start position:0%
+things that other researchers had done
+ 
+
+ align:start position:0%
+things that other researchers had done
+it was like Hey I read some stuff and I
+
+ align:start position:0%
+it was like Hey I read some stuff and I
+ 
+
+ align:start position:0%
+it was like Hey I read some stuff and I
+think it's confusing the way people talk
+
+ align:start position:0%
+think it's confusing the way people talk
+ 
+
+ align:start position:0%
+think it's confusing the way people talk
+about it I think that was the kind of
+
+ align:start position:0%
+about it I think that was the kind of
+ 
+
+ align:start position:0%
+about it I think that was the kind of
+response from from many readers which is
+
+ align:start position:0%
+response from from many readers which is
+ 
+
+ align:start position:0%
+response from from many readers which is
+why many people ignored it those who
+
+ align:start position:0%
+why many people ignored it those who
+ 
+
+ align:start position:0%
+why many people ignored it those who
+bothered reading past page five said oh
+
+ align:start position:0%
+bothered reading past page five said oh
+ 
+
+ align:start position:0%
+bothered reading past page five said oh
+I've seen that equation before that's
+
+ align:start position:0%
+I've seen that equation before that's
+ 
+
+ align:start position:0%
+I've seen that equation before that's
+just lorenz's stuff oh it's the I it's
+
+ align:start position:0%
+just lorenz's stuff oh it's the I it's
+ 
+
+ align:start position:0%
+just lorenz's stuff oh it's the I it's
+Lorenz Einstein theory right it's I
+
+ align:start position:0%
+Lorenz Einstein theory right it's I
+ 
+
+ align:start position:0%
+Lorenz Einstein theory right it's I
+think it's that kind of response and for
+
+ align:start position:0%
+think it's that kind of response and for
+ 
+
+ align:start position:0%
+think it's that kind of response and for
+Mankowski I think he would have seen an
+
+ align:start position:0%
+Mankowski I think he would have seen an
+ 
+
+ align:start position:0%
+Mankowski I think he would have seen an
+insufficient
+
+ align:start position:0%
+insufficient
+ 
+
+ align:start position:0%
+insufficient
+um precision and Clarity right and now
+
+ align:start position:0%
+um precision and Clarity right and now
+ 
+
+ align:start position:0%
+um precision and Clarity right and now
+that's a that's a value judgment and
+
+ align:start position:0%
+that's a that's a value judgment and
+ 
+
+ align:start position:0%
+that's a that's a value judgment and
+that depends on our own personality but
+
+ align:start position:0%
+that depends on our own personality but
+ 
+
+ align:start position:0%
+that depends on our own personality but
+our own training our own toolkit so for
+
+ align:start position:0%
+our own training our own toolkit so for
+ 
+
+ align:start position:0%
+our own training our own toolkit so for
+minkowski if you're not talking about
+
+ align:start position:0%
+minkowski if you're not talking about
+ 
+
+ align:start position:0%
+minkowski if you're not talking about
+what happens when you perform rotations
+
+ align:start position:0%
+what happens when you perform rotations
+ 
+
+ align:start position:0%
+what happens when you perform rotations
+there should be something invariant like
+
+ align:start position:0%
+there should be something invariant like
+ 
+
+ align:start position:0%
+there should be something invariant like
+that should be Lesson Zero in Geometry
+
+ align:start position:0%
+that should be Lesson Zero in Geometry
+ 
+
+ align:start position:0%
+that should be Lesson Zero in Geometry
+the distance between my house and the
+
+ align:start position:0%
+the distance between my house and the
+ 
+
+ align:start position:0%
+the distance between my house and the
+Town Square hasn't changed even if I
+
+ align:start position:0%
+Town Square hasn't changed even if I
+ 
+
+ align:start position:0%
+Town Square hasn't changed even if I
+rotate you know the street map like who
+
+ align:start position:0%
+rotate you know the street map like who
+ 
+
+ align:start position:0%
+rotate you know the street map like who
+doesn't think of that I think would have
+
+ align:start position:0%
+doesn't think of that I think would have
+ 
+
+ align:start position:0%
+doesn't think of that I think would have
+been minkowski's kind of response
+
+ align:start position:0%
+been minkowski's kind of response
+ 
+
+ align:start position:0%
+been minkowski's kind of response
+there's a you know once you think in a
+
+ align:start position:0%
+there's a you know once you think in a
+ 
+
+ align:start position:0%
+there's a you know once you think in a
+geometrical way according to minkowski
+
+ align:start position:0%
+geometrical way according to minkowski
+ 
+
+ align:start position:0%
+geometrical way according to minkowski
+there should be unavoidable follow-up
+
+ align:start position:0%
+there should be unavoidable follow-up
+ 
+
+ align:start position:0%
+there should be unavoidable follow-up
+questions and this Lazy Dog is too busy
+
+ align:start position:0%
+questions and this Lazy Dog is too busy
+ 
+
+ align:start position:0%
+questions and this Lazy Dog is too busy
+talking about you know he doesn't like
+
+ align:start position:0%
+talking about you know he doesn't like
+ 
+
+ align:start position:0%
+talking about you know he doesn't like
+the way textbooks describe Maxwell like
+
+ align:start position:0%
+the way textbooks describe Maxwell like
+ 
+
+ align:start position:0%
+the way textbooks describe Maxwell like
+I got no time for this I think that
+
+ align:start position:0%
+I got no time for this I think that
+ 
+
+ align:start position:0%
+I got no time for this I think that
+would have been a pretty reasonable
+
+ align:start position:0%
+would have been a pretty reasonable
+ 
+
+ align:start position:0%
+would have been a pretty reasonable
+approximation to his first reaction and
+
+ align:start position:0%
+approximation to his first reaction and
+ 
+
+ align:start position:0%
+approximation to his first reaction and
+then he's like oh actually okay the
+
+ align:start position:0%
+then he's like oh actually okay the
+ 
+
+ align:start position:0%
+then he's like oh actually okay the
+speedway is constant that I can perform
+
+ align:start position:0%
+speedway is constant that I can perform
+ 
+
+ align:start position:0%
+speedway is constant that I can perform
+these very clever sets of rotations and
+
+ align:start position:0%
+these very clever sets of rotations and
+ 
+
+ align:start position:0%
+these very clever sets of rotations and
+of course therefore there's an
+
+ align:start position:0%
+of course therefore there's an
+ 
+
+ align:start position:0%
+of course therefore there's an
+invariance and of course there's an
+
+ align:start position:0%
+invariance and of course there's an
+ 
+
+ align:start position:0%
+invariance and of course there's an
+absolute way right so he he has his own
+
+ align:start position:0%
+absolute way right so he he has his own
+ 
+
+ align:start position:0%
+absolute way right so he he has his own
+he's on his own trade right he's on a
+
+ align:start position:0%
+he's on his own trade right he's on a
+ 
+
+ align:start position:0%
+he's on his own trade right he's on a
+different kind of reference frame so to
+
+ align:start position:0%
+different kind of reference frame so to
+ 
+
+ align:start position:0%
+different kind of reference frame so to
+speak and certain questions are the
+
+ align:start position:0%
+speak and certain questions are the
+ 
+
+ align:start position:0%
+speak and certain questions are the
+obvious next ones to ask because he has
+
+ align:start position:0%
+obvious next ones to ask because he has
+ 
+
+ align:start position:0%
+obvious next ones to ask because he has
+a certain kind of set of tools and
+
+ align:start position:0%
+a certain kind of set of tools and
+ 
+
+ align:start position:0%
+a certain kind of set of tools and
+starting point and that's true of I
+
+ align:start position:0%
+starting point and that's true of I
+ 
+
+ align:start position:0%
+starting point and that's true of I
+think of all of us and we'll see another
+
+ align:start position:0%
+think of all of us and we'll see another
+ 
+
+ align:start position:0%
+think of all of us and we'll see another
+a contrasting example in this next part
+
+ align:start position:0%
+a contrasting example in this next part
+ 
+
+ align:start position:0%
+a contrasting example in this next part
+of today's class we'll see that over and
+
+ align:start position:0%
+of today's class we'll see that over and
+ 
+
+ align:start position:0%
+of today's class we'll see that over and
+over again throughout the turn
+
+ align:start position:0%
+over again throughout the turn
+ 
+
+ align:start position:0%
+over again throughout the turn
+not only about relativity but quantum
+
+ align:start position:0%
+not only about relativity but quantum
+ 
+
+ align:start position:0%
+not only about relativity but quantum
+theory about cosmology about particle
+
+ align:start position:0%
+theory about cosmology about particle
+ 
+
+ align:start position:0%
+theory about cosmology about particle
+physics and here's a kind of early
+
+ align:start position:0%
+physics and here's a kind of early
+ 
+
+ align:start position:0%
+physics and here's a kind of early
+example where you can sink our teeth
+
+ align:start position:0%
+example where you can sink our teeth
+ 
+
+ align:start position:0%
+example where you can sink our teeth
+into it say these people weren't just
+
+ align:start position:0%
+into it say these people weren't just
+ 
+
+ align:start position:0%
+into it say these people weren't just
+like misreading it they were doing
+
+ align:start position:0%
+like misreading it they were doing
+ 
+
+ align:start position:0%
+like misreading it they were doing
+really cool productive stuff some of
+
+ align:start position:0%
+really cool productive stuff some of
+ 
+
+ align:start position:0%
+really cool productive stuff some of
+which we still take advantage of today
+
+ align:start position:0%
+which we still take advantage of today
+ 
+
+ align:start position:0%
+which we still take advantage of today
+uh and yet what they thought they were
+
+ align:start position:0%
+uh and yet what they thought they were
+ 
+
+ align:start position:0%
+uh and yet what they thought they were
+doing is neither what we think we do nor
+
+ align:start position:0%
+doing is neither what we think we do nor
+ 
+
+ align:start position:0%
+doing is neither what we think we do nor
+what you know the original authors
+
+ align:start position:0%
+what you know the original authors
+ 
+
+ align:start position:0%
+what you know the original authors
+thought they were doing so we have this
+
+ align:start position:0%
+thought they were doing so we have this
+ 
+
+ align:start position:0%
+thought they were doing so we have this
+the kind of plasticity of meaning and
+
+ align:start position:0%
+the kind of plasticity of meaning and
+ 
+
+ align:start position:0%
+the kind of plasticity of meaning and
+interpretation even when our equation
+
+ align:start position:0%
+interpretation even when our equation
+ 
+
+ align:start position:0%
+interpretation even when our equation
+when our equations agree perfectly let
+
+ align:start position:0%
+when our equations agree perfectly let
+ 
+
+ align:start position:0%
+when our equations agree perfectly let
+alone when we come up with different
+
+ align:start position:0%
+alone when we come up with different
+ 
+
+ align:start position:0%
+alone when we come up with different
+equations I find that wonderful I love
+
+ align:start position:0%
+equations I find that wonderful I love
+ 
+
+ align:start position:0%
+equations I find that wonderful I love
+that exactly all writing down the same
+
+ align:start position:0%
+that exactly all writing down the same
+ 
+
+ align:start position:0%
+that exactly all writing down the same
+factor gamma that's fantastic right
+
+ align:start position:0%
+factor gamma that's fantastic right
+ 
+
+ align:start position:0%
+factor gamma that's fantastic right
+because then we can really map you know
+
+ align:start position:0%
+because then we can really map you know
+ 
+
+ align:start position:0%
+because then we can really map you know
+what is the same and what's not the same
+
+ align:start position:0%
+what is the same and what's not the same
+ 
+
+ align:start position:0%
+what is the same and what's not the same
+conceptually let alone in the exchange
+
+ align:start position:0%
+conceptually let alone in the exchange
+ 
+
+ align:start position:0%
+conceptually let alone in the exchange
+of light signals so keep that kind of
+
+ align:start position:0%
+of light signals so keep that kind of
+ 
+
+ align:start position:0%
+of light signals so keep that kind of
+question in mind we'll come back to that
+
+ align:start position:0%
+question in mind we'll come back to that
+ 
+
+ align:start position:0%
+question in mind we'll come back to that
+theme really over and over this semester
+
+ align:start position:0%
+theme really over and over this semester
+ 
+
+ align:start position:0%
+theme really over and over this semester
+it's a great question
+
+ align:start position:0%
+it's a great question
+ 
+
+ align:start position:0%
+it's a great question
+let me go on to the last part uh and
+
+ align:start position:0%
+let me go on to the last part uh and
+ 
+
+ align:start position:0%
+let me go on to the last part uh and
+look at our favorite Cambridge Wranglers
+
+ align:start position:0%
+look at our favorite Cambridge Wranglers
+ 
+
+ align:start position:0%
+look at our favorite Cambridge Wranglers
+or at least my favorite camera
+
+ align:start position:0%
+or at least my favorite camera
+ 
+
+ align:start position:0%
+or at least my favorite camera
+so minkowski wasn't the only person who
+
+ align:start position:0%
+so minkowski wasn't the only person who
+ 
+
+ align:start position:0%
+so minkowski wasn't the only person who
+slowly sometimes kind of grudgingly
+
+ align:start position:0%
+slowly sometimes kind of grudgingly
+ 
+
+ align:start position:0%
+slowly sometimes kind of grudgingly
+began to to read Einstein's work on the
+
+ align:start position:0%
+began to to read Einstein's work on the
+ 
+
+ align:start position:0%
+began to to read Einstein's work on the
+electronamics of moving bodies another
+
+ align:start position:0%
+electronamics of moving bodies another
+ 
+
+ align:start position:0%
+electronamics of moving bodies another
+group that really did dig in in pretty
+
+ align:start position:0%
+group that really did dig in in pretty
+ 
+
+ align:start position:0%
+group that really did dig in in pretty
+substantive ways was a subset of these
+
+ align:start position:0%
+substantive ways was a subset of these
+ 
+
+ align:start position:0%
+substantive ways was a subset of these
+Cambridge Wranglers the folks that now
+
+ align:start position:0%
+Cambridge Wranglers the folks that now
+ 
+
+ align:start position:0%
+Cambridge Wranglers the folks that now
+we've talked about a few times at
+
+ align:start position:0%
+we've talked about a few times at
+ 
+
+ align:start position:0%
+we've talked about a few times at
+Cambridge University
+
+ align:start position:0%
+Cambridge University
+ 
+
+ align:start position:0%
+Cambridge University
+for them much like for minkowski there
+
+ align:start position:0%
+for them much like for minkowski there
+ 
+
+ align:start position:0%
+for them much like for minkowski there
+were elements of real value in
+
+ align:start position:0%
+were elements of real value in
+ 
+
+ align:start position:0%
+were elements of real value in
+Einstein's work they just weren't the
+
+ align:start position:0%
+Einstein's work they just weren't the
+ 
+
+ align:start position:0%
+Einstein's work they just weren't the
+same elements that minkowski considered
+
+ align:start position:0%
+same elements that minkowski considered
+ 
+
+ align:start position:0%
+same elements that minkowski considered
+valuable or they're not inside
+
+ align:start position:0%
+valuable or they're not inside
+ 
+
+ align:start position:0%
+valuable or they're not inside
+considered valuable so let's take a
+
+ align:start position:0%
+considered valuable so let's take a
+ 
+
+ align:start position:0%
+considered valuable so let's take a
+little look at the kinds of things that
+
+ align:start position:0%
+little look at the kinds of things that
+ 
+
+ align:start position:0%
+little look at the kinds of things that
+they did with Einstein's paper
+
+ align:start position:0%
+they did with Einstein's paper
+ 
+
+ align:start position:0%
+they did with Einstein's paper
+as a warm-up to make sense of this and
+
+ align:start position:0%
+as a warm-up to make sense of this and
+ 
+
+ align:start position:0%
+as a warm-up to make sense of this and
+by the way for this part of course I'm
+
+ align:start position:0%
+by the way for this part of course I'm
+ 
+
+ align:start position:0%
+by the way for this part of course I'm
+drawing very heavily on the article in
+
+ align:start position:0%
+drawing very heavily on the article in
+ 
+
+ align:start position:0%
+drawing very heavily on the article in
+in the reading for today from uh Andy
+
+ align:start position:0%
+in the reading for today from uh Andy
+ 
+
+ align:start position:0%
+in the reading for today from uh Andy
+Warwick and I'll talk through some of
+
+ align:start position:0%
+Warwick and I'll talk through some of
+ 
+
+ align:start position:0%
+Warwick and I'll talk through some of
+the specifics some of the some of the
+
+ align:start position:0%
+the specifics some of the some of the
+ 
+
+ align:start position:0%
+the specifics some of the some of the
+details of the article might be pretty
+
+ align:start position:0%
+details of the article might be pretty
+ 
+
+ align:start position:0%
+details of the article might be pretty
+confusing so we'll talk through what
+
+ align:start position:0%
+confusing so we'll talk through what
+ 
+
+ align:start position:0%
+confusing so we'll talk through what
+what were they doing at least a little
+
+ align:start position:0%
+what were they doing at least a little
+ 
+
+ align:start position:0%
+what were they doing at least a little
+bit more the historical point I want to
+
+ align:start position:0%
+bit more the historical point I want to
+ 
+
+ align:start position:0%
+bit more the historical point I want to
+clarify is really just like minkowski in
+
+ align:start position:0%
+clarify is really just like minkowski in
+ 
+
+ align:start position:0%
+clarify is really just like minkowski in
+the sense that very smart professional
+
+ align:start position:0%
+the sense that very smart professional
+ 
+
+ align:start position:0%
+the sense that very smart professional
+researchers were making sense of
+
+ align:start position:0%
+researchers were making sense of
+ 
+
+ align:start position:0%
+researchers were making sense of
+Einstein's work differently than
+
+ align:start position:0%
+Einstein's work differently than
+ 
+
+ align:start position:0%
+Einstein's work differently than
+Einstein did and that didn't make them
+
+ align:start position:0%
+Einstein did and that didn't make them
+ 
+
+ align:start position:0%
+Einstein did and that didn't make them
+wrong and made them it indicates that
+
+ align:start position:0%
+wrong and made them it indicates that
+ 
+
+ align:start position:0%
+wrong and made them it indicates that
+they were finding elements of value out
+
+ align:start position:0%
+they were finding elements of value out
+ 
+
+ align:start position:0%
+they were finding elements of value out
+of interest in Einstein's work different
+
+ align:start position:0%
+of interest in Einstein's work different
+ 
+
+ align:start position:0%
+of interest in Einstein's work different
+from Einstein's own and sometimes
+
+ align:start position:0%
+from Einstein's own and sometimes
+ 
+
+ align:start position:0%
+from Einstein's own and sometimes
+different from ARA that's the historical
+
+ align:start position:0%
+different from ARA that's the historical
+ 
+
+ align:start position:0%
+different from ARA that's the historical
+lesson and if you get a little bit lost
+
+ align:start position:0%
+lesson and if you get a little bit lost
+ 
+
+ align:start position:0%
+lesson and if you get a little bit lost
+with image charges and conformal
+
+ align:start position:0%
+with image charges and conformal
+ 
+
+ align:start position:0%
+with image charges and conformal
+Transformations that's okay in this
+
+ align:start position:0%
+Transformations that's okay in this
+ 
+
+ align:start position:0%
+Transformations that's okay in this
+class especially that's okay but I
+
+ align:start position:0%
+class especially that's okay but I
+ 
+
+ align:start position:0%
+class especially that's okay but I
+figure it's still fun to see what were
+
+ align:start position:0%
+figure it's still fun to see what were
+ 
+
+ align:start position:0%
+figure it's still fun to see what were
+they really doing because that's what
+
+ align:start position:0%
+they really doing because that's what
+ 
+
+ align:start position:0%
+they really doing because that's what
+we're going to talk about
+
+ align:start position:0%
+we're going to talk about
+ 
+
+ align:start position:0%
+we're going to talk about
+a little bit here so many of you again
+
+ align:start position:0%
+a little bit here so many of you again
+ 
+
+ align:start position:0%
+a little bit here so many of you again
+might have seen in even maybe in high
+
+ align:start position:0%
+might have seen in even maybe in high
+ 
+
+ align:start position:0%
+might have seen in even maybe in high
+school classes on electricity to
+
+ align:start position:0%
+school classes on electricity to
+ 
+
+ align:start position:0%
+school classes on electricity to
+magnetism there are all these really
+
+ align:start position:0%
+magnetism there are all these really
+ 
+
+ align:start position:0%
+magnetism there are all these really
+clever tricks uh that we that we still
+
+ align:start position:0%
+clever tricks uh that we that we still
+ 
+
+ align:start position:0%
+clever tricks uh that we that we still
+take advantage of to try to make pretty
+
+ align:start position:0%
+take advantage of to try to make pretty
+ 
+
+ align:start position:0%
+take advantage of to try to make pretty
+complicated problems simpler and yet can
+
+ align:start position:0%
+complicated problems simpler and yet can
+ 
+
+ align:start position:0%
+complicated problems simpler and yet can
+still get Exact Solutions one of those
+
+ align:start position:0%
+still get Exact Solutions one of those
+ 
+
+ align:start position:0%
+still get Exact Solutions one of those
+that we learned pretty early on
+
+ align:start position:0%
+that we learned pretty early on
+ 
+
+ align:start position:0%
+that we learned pretty early on
+is called the message the method of
+
+ align:start position:0%
+is called the message the method of
+ 
+
+ align:start position:0%
+is called the message the method of
+image charges and electrostatics so
+
+ align:start position:0%
+image charges and electrostatics so
+ 
+
+ align:start position:0%
+image charges and electrostatics so
+let's say some Nene some one of my mean
+
+ align:start position:0%
+let's say some Nene some one of my mean
+ 
+
+ align:start position:0%
+let's say some Nene some one of my mean
+old colleagues in the department of
+
+ align:start position:0%
+old colleagues in the department of
+ 
+
+ align:start position:0%
+old colleagues in the department of
+physics assigned to you the problem to
+
+ align:start position:0%
+physics assigned to you the problem to
+ 
+
+ align:start position:0%
+physics assigned to you the problem to
+solve for the the state of the electric
+
+ align:start position:0%
+solve for the the state of the electric
+ 
+
+ align:start position:0%
+solve for the the state of the electric
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+between a stationary uh Point charge
+
+ align:start position:0%
+between a stationary uh Point charge
+ 
+
+ align:start position:0%
+between a stationary uh Point charge
+with a positive charge some charge plus
+
+ align:start position:0%
+with a positive charge some charge plus
+ 
+
+ align:start position:0%
+with a positive charge some charge plus
+q and some infinite an extent some
+
+ align:start position:0%
+q and some infinite an extent some
+ 
+
+ align:start position:0%
+q and some infinite an extent some
+infinitely long perfectly flat
+
+ align:start position:0%
+infinitely long perfectly flat
+ 
+
+ align:start position:0%
+infinitely long perfectly flat
+conducting plate that's sort of grounded
+
+ align:start position:0%
+conducting plate that's sort of grounded
+ 
+
+ align:start position:0%
+conducting plate that's sort of grounded
+that's kind of a pain in the neck to
+
+ align:start position:0%
+that's kind of a pain in the neck to
+ 
+
+ align:start position:0%
+that's kind of a pain in the neck to
+find the exact uh value of the electric
+
+ align:start position:0%
+find the exact uh value of the electric
+ 
+
+ align:start position:0%
+find the exact uh value of the electric
+field that it's a vector quantity if the
+
+ align:start position:0%
+field that it's a vector quantity if the
+ 
+
+ align:start position:0%
+field that it's a vector quantity if the
+you know worry about how it's changing
+
+ align:start position:0%
+you know worry about how it's changing
+ 
+
+ align:start position:0%
+you know worry about how it's changing
+through space so one thing that you may
+
+ align:start position:0%
+through space so one thing that you may
+ 
+
+ align:start position:0%
+through space so one thing that you may
+remember from studying Max's equations
+
+ align:start position:0%
+remember from studying Max's equations
+ 
+
+ align:start position:0%
+remember from studying Max's equations
+is that for this kind of scenario the
+
+ align:start position:0%
+is that for this kind of scenario the
+ 
+
+ align:start position:0%
+is that for this kind of scenario the
+field lines of the electric field almost
+
+ align:start position:0%
+field lines of the electric field almost
+ 
+
+ align:start position:0%
+field lines of the electric field almost
+intersect the plate at right angles
+
+ align:start position:0%
+intersect the plate at right angles
+ 
+
+ align:start position:0%
+intersect the plate at right angles
+that's that's to remain consistent with
+
+ align:start position:0%
+that's that's to remain consistent with
+ 
+
+ align:start position:0%
+that's that's to remain consistent with
+the fact this is a grounded conducting
+
+ align:start position:0%
+the fact this is a grounded conducting
+ 
+
+ align:start position:0%
+the fact this is a grounded conducting
+plate if they didn't all intersect at
+
+ align:start position:0%
+plate if they didn't all intersect at
+ 
+
+ align:start position:0%
+plate if they didn't all intersect at
+right angles you actually build up a
+
+ align:start position:0%
+right angles you actually build up a
+ 
+
+ align:start position:0%
+right angles you actually build up a
+voltage difference it would not satisfy
+
+ align:start position:0%
+voltage difference it would not satisfy
+ 
+
+ align:start position:0%
+voltage difference it would not satisfy
+the boundary conditions of the problem
+
+ align:start position:0%
+the boundary conditions of the problem
+ 
+
+ align:start position:0%
+the boundary conditions of the problem
+it's kind of a pain in the neck meanies
+
+ align:start position:0%
+it's kind of a pain in the neck meanies
+ 
+
+ align:start position:0%
+it's kind of a pain in the neck meanies
+so there's a pretty clever trick we can
+
+ align:start position:0%
+so there's a pretty clever trick we can
+ 
+
+ align:start position:0%
+so there's a pretty clever trick we can
+solve a much much simpler mathematical
+
+ align:start position:0%
+solve a much much simpler mathematical
+ 
+
+ align:start position:0%
+solve a much much simpler mathematical
+setup to get the exact solution for the
+
+ align:start position:0%
+setup to get the exact solution for the
+ 
+
+ align:start position:0%
+setup to get the exact solution for the
+original problem
+
+ align:start position:0%
+original problem
+ 
+
+ align:start position:0%
+original problem
+forget about the plate throw the plate
+
+ align:start position:0%
+forget about the plate throw the plate
+ 
+
+ align:start position:0%
+forget about the plate throw the plate
+away right in it for a few steps and
+
+ align:start position:0%
+away right in it for a few steps and
+ 
+
+ align:start position:0%
+away right in it for a few steps and
+instead insert a second Point charge of
+
+ align:start position:0%
+instead insert a second Point charge of
+ 
+
+ align:start position:0%
+instead insert a second Point charge of
+equal but opposite sign people equal
+
+ align:start position:0%
+equal but opposite sign people equal
+ 
+
+ align:start position:0%
+equal but opposite sign people equal
+magnitude but opposite sign so now in
+
+ align:start position:0%
+magnitude but opposite sign so now in
+ 
+
+ align:start position:0%
+magnitude but opposite sign so now in
+this new scenario we pretend there's no
+
+ align:start position:0%
+this new scenario we pretend there's no
+ 
+
+ align:start position:0%
+this new scenario we pretend there's no
+nothing physical here but we have an
+
+ align:start position:0%
+nothing physical here but we have an
+ 
+
+ align:start position:0%
+nothing physical here but we have an
+equal distance away from that where the
+
+ align:start position:0%
+equal distance away from that where the
+ 
+
+ align:start position:0%
+equal distance away from that where the
+plate had been in the original problem
+
+ align:start position:0%
+plate had been in the original problem
+ 
+
+ align:start position:0%
+plate had been in the original problem
+we put down an imaginary image charge
+
+ align:start position:0%
+we put down an imaginary image charge
+ 
+
+ align:start position:0%
+we put down an imaginary image charge
+that has a negative uh charge but the
+
+ align:start position:0%
+that has a negative uh charge but the
+ 
+
+ align:start position:0%
+that has a negative uh charge but the
+same magnitude as the original uh
+
+ align:start position:0%
+same magnitude as the original uh
+ 
+
+ align:start position:0%
+same magnitude as the original uh
+positive charge now we can easily solve
+
+ align:start position:0%
+positive charge now we can easily solve
+ 
+
+ align:start position:0%
+positive charge now we can easily solve
+for a much more easily solved for the
+
+ align:start position:0%
+for a much more easily solved for the
+ 
+
+ align:start position:0%
+for a much more easily solved for the
+value of the electrostatic potential
+
+ align:start position:0%
+value of the electrostatic potential
+ 
+
+ align:start position:0%
+value of the electrostatic potential
+it's just two bodies it just uh you know
+
+ align:start position:0%
+it's just two bodies it just uh you know
+ 
+
+ align:start position:0%
+it's just two bodies it just uh you know
+goes like a one over R between them we
+
+ align:start position:0%
+goes like a one over R between them we
+ 
+
+ align:start position:0%
+goes like a one over R between them we
+can take the gradient see how that
+
+ align:start position:0%
+can take the gradient see how that
+ 
+
+ align:start position:0%
+can take the gradient see how that
+changes through space we can do
+
+ align:start position:0%
+changes through space we can do
+ 
+
+ align:start position:0%
+changes through space we can do
+everything we was asked to do to solve
+
+ align:start position:0%
+everything we was asked to do to solve
+ 
+
+ align:start position:0%
+everything we was asked to do to solve
+for the exact behavior of the electric
+
+ align:start position:0%
+for the exact behavior of the electric
+ 
+
+ align:start position:0%
+for the exact behavior of the electric
+field by replacing one problem with a
+
+ align:start position:0%
+field by replacing one problem with a
+ 
+
+ align:start position:0%
+field by replacing one problem with a
+simpler but equivalent one okay that's
+
+ align:start position:0%
+simpler but equivalent one okay that's
+ 
+
+ align:start position:0%
+simpler but equivalent one okay that's
+the method of image charges you can
+
+ align:start position:0%
+the method of image charges you can
+ 
+
+ align:start position:0%
+the method of image charges you can
+learn about that on Wikipedia or on any
+
+ align:start position:0%
+learn about that on Wikipedia or on any
+ 
+
+ align:start position:0%
+learn about that on Wikipedia or on any
+e m textbook it's a standard technique
+
+ align:start position:0%
+e m textbook it's a standard technique
+ 
+
+ align:start position:0%
+e m textbook it's a standard technique
+that goes back really century it's
+
+ align:start position:0%
+that goes back really century it's
+ 
+
+ align:start position:0%
+that goes back really century it's
+pretty powerful well that's baby stuff
+
+ align:start position:0%
+pretty powerful well that's baby stuff
+ 
+
+ align:start position:0%
+pretty powerful well that's baby stuff
+right we're talking about Cambridge
+
+ align:start position:0%
+right we're talking about Cambridge
+ 
+
+ align:start position:0%
+right we're talking about Cambridge
+Wranglers here or for that matter MIT
+
+ align:start position:0%
+Wranglers here or for that matter MIT
+ 
+
+ align:start position:0%
+Wranglers here or for that matter MIT
+students we don't have to do one single
+
+ align:start position:0%
+students we don't have to do one single
+ 
+
+ align:start position:0%
+students we don't have to do one single
+point charge behind what would have been
+
+ align:start position:0%
+point charge behind what would have been
+ 
+
+ align:start position:0%
+point charge behind what would have been
+an infinite unbending conducting plate
+
+ align:start position:0%
+an infinite unbending conducting plate
+ 
+
+ align:start position:0%
+an infinite unbending conducting plate
+that is boring let's do some crazy stuff
+
+ align:start position:0%
+that is boring let's do some crazy stuff
+ 
+
+ align:start position:0%
+that is boring let's do some crazy stuff
+and that's what the Wranglers got very
+
+ align:start position:0%
+and that's what the Wranglers got very
+ 
+
+ align:start position:0%
+and that's what the Wranglers got very
+good at doing with their personal tutors
+
+ align:start position:0%
+good at doing with their personal tutors
+ 
+
+ align:start position:0%
+good at doing with their personal tutors
+for the tripods exam so a very similar
+
+ align:start position:0%
+for the tripods exam so a very similar
+ 
+
+ align:start position:0%
+for the tripods exam so a very similar
+related technique became known as the
+
+ align:start position:0%
+related technique became known as the
+ 
+
+ align:start position:0%
+related technique became known as the
+method of inversion and that's again
+
+ align:start position:0%
+method of inversion and that's again
+ 
+
+ align:start position:0%
+method of inversion and that's again
+really just mapping a difficult problem
+
+ align:start position:0%
+really just mapping a difficult problem
+ 
+
+ align:start position:0%
+really just mapping a difficult problem
+into a simpler one and again this this
+
+ align:start position:0%
+into a simpler one and again this this
+ 
+
+ align:start position:0%
+into a simpler one and again this this
+illustration is taken from Andy
+
+ align:start position:0%
+illustration is taken from Andy
+ 
+
+ align:start position:0%
+illustration is taken from Andy
+Warwick's article uh which that is
+
+ align:start position:0%
+Warwick's article uh which that is
+ 
+
+ align:start position:0%
+Warwick's article uh which that is
+elaborate upon in in this book of his
+
+ align:start position:0%
+elaborate upon in in this book of his
+ 
+
+ align:start position:0%
+elaborate upon in in this book of his
+that I really can't recommend strongly
+
+ align:start position:0%
+that I really can't recommend strongly
+ 
+
+ align:start position:0%
+that I really can't recommend strongly
+enough I love this book masters of
+
+ align:start position:0%
+enough I love this book masters of
+ 
+
+ align:start position:0%
+enough I love this book masters of
+theory but the article itself really
+
+ align:start position:0%
+theory but the article itself really
+ 
+
+ align:start position:0%
+theory but the article itself really
+gets this this part this part across
+
+ align:start position:0%
+gets this this part this part across
+ 
+
+ align:start position:0%
+gets this this part this part across
+let's first do a little geometry a
+
+ align:start position:0%
+let's first do a little geometry a
+ 
+
+ align:start position:0%
+let's first do a little geometry a
+little mapping exercise which is what
+
+ align:start position:0%
+little mapping exercise which is what
+ 
+
+ align:start position:0%
+little mapping exercise which is what
+the Wranglers would have learned to do
+
+ align:start position:0%
+the Wranglers would have learned to do
+ 
+
+ align:start position:0%
+the Wranglers would have learned to do
+very early with their coaches take any
+
+ align:start position:0%
+very early with their coaches take any
+ 
+
+ align:start position:0%
+very early with their coaches take any
+single point a here's the point a for
+
+ align:start position:0%
+single point a here's the point a for
+ 
+
+ align:start position:0%
+single point a here's the point a for
+our case any point that happens to be
+
+ align:start position:0%
+our case any point that happens to be
+ 
+
+ align:start position:0%
+our case any point that happens to be
+inside a circle of radius K so the point
+
+ align:start position:0%
+inside a circle of radius K so the point
+ 
+
+ align:start position:0%
+inside a circle of radius K so the point
+a is clearly contained within that
+
+ align:start position:0%
+a is clearly contained within that
+ 
+
+ align:start position:0%
+a is clearly contained within that
+Circle
+
+ align:start position:0%
+Circle
+ 
+
+ align:start position:0%
+Circle
+we can then do a unique mapping to an
+
+ align:start position:0%
+we can then do a unique mapping to an
+ 
+
+ align:start position:0%
+we can then do a unique mapping to an
+inverse Point kind of like that where we
+
+ align:start position:0%
+inverse Point kind of like that where we
+ 
+
+ align:start position:0%
+inverse Point kind of like that where we
+place our image charge from the past
+
+ align:start position:0%
+place our image charge from the past
+ 
+
+ align:start position:0%
+place our image charge from the past
+example there's a one-to-one map for a
+
+ align:start position:0%
+example there's a one-to-one map for a
+ 
+
+ align:start position:0%
+example there's a one-to-one map for a
+point corresponding uniquely to that
+
+ align:start position:0%
+point corresponding uniquely to that
+ 
+
+ align:start position:0%
+point corresponding uniquely to that
+point a that's now outside the circle
+
+ align:start position:0%
+point a that's now outside the circle
+ 
+
+ align:start position:0%
+point a that's now outside the circle
+and so the way we determine where that
+
+ align:start position:0%
+and so the way we determine where that
+ 
+
+ align:start position:0%
+and so the way we determine where that
+point would be is by requiring the
+
+ align:start position:0%
+point would be is by requiring the
+ 
+
+ align:start position:0%
+point would be is by requiring the
+distance from the center of the circle
+
+ align:start position:0%
+distance from the center of the circle
+ 
+
+ align:start position:0%
+distance from the center of the circle
+to our original point that distance o a
+
+ align:start position:0%
+to our original point that distance o a
+ 
+
+ align:start position:0%
+to our original point that distance o a
+times the distance between uh the center
+
+ align:start position:0%
+times the distance between uh the center
+ 
+
+ align:start position:0%
+times the distance between uh the center
+of the circle and the new point the
+
+ align:start position:0%
+of the circle and the new point the
+ 
+
+ align:start position:0%
+of the circle and the new point the
+inverse point the product of those
+
+ align:start position:0%
+inverse point the product of those
+ 
+
+ align:start position:0%
+inverse point the product of those
+distances must equal the square of this
+
+ align:start position:0%
+distances must equal the square of this
+ 
+
+ align:start position:0%
+distances must equal the square of this
+radius that's enough to do this mapping
+
+ align:start position:0%
+radius that's enough to do this mapping
+ 
+
+ align:start position:0%
+radius that's enough to do this mapping
+this is actually called a conformal map
+
+ align:start position:0%
+this is actually called a conformal map
+ 
+
+ align:start position:0%
+this is actually called a conformal map
+now what if there was some point uh the
+
+ align:start position:0%
+now what if there was some point uh the
+ 
+
+ align:start position:0%
+now what if there was some point uh the
+point a is actually moving along this
+
+ align:start position:0%
+point a is actually moving along this
+ 
+
+ align:start position:0%
+point a is actually moving along this
+curve this orange curve between points p
+
+ align:start position:0%
+curve this orange curve between points p
+ 
+
+ align:start position:0%
+curve this orange curve between points p
+and Q we can imagine it knows a whole
+
+ align:start position:0%
+and Q we can imagine it knows a whole
+ 
+
+ align:start position:0%
+and Q we can imagine it knows a whole
+set of points Each of which lies
+
+ align:start position:0%
+set of points Each of which lies
+ 
+
+ align:start position:0%
+set of points Each of which lies
+entirely within this original Circle
+
+ align:start position:0%
+entirely within this original Circle
+ 
+
+ align:start position:0%
+entirely within this original Circle
+for each of these points along the
+
+ align:start position:0%
+for each of these points along the
+ 
+
+ align:start position:0%
+for each of these points along the
+orange curve between p and Q we can do
+
+ align:start position:0%
+orange curve between p and Q we can do
+ 
+
+ align:start position:0%
+orange curve between p and Q we can do
+the same trick we can map them to each
+
+ align:start position:0%
+the same trick we can map them to each
+ 
+
+ align:start position:0%
+the same trick we can map them to each
+of their corresponding inverse points
+
+ align:start position:0%
+of their corresponding inverse points
+ 
+
+ align:start position:0%
+of their corresponding inverse points
+for every single point along this orange
+
+ align:start position:0%
+for every single point along this orange
+ 
+
+ align:start position:0%
+for every single point along this orange
+curve we we require this relationship to
+
+ align:start position:0%
+curve we we require this relationship to
+ 
+
+ align:start position:0%
+curve we we require this relationship to
+hold and we map them to an inverse Arc a
+
+ align:start position:0%
+hold and we map them to an inverse Arc a
+ 
+
+ align:start position:0%
+hold and we map them to an inverse Arc a
+collection of inverse points that are
+
+ align:start position:0%
+collection of inverse points that are
+ 
+
+ align:start position:0%
+collection of inverse points that are
+entirely outside the circle so if we
+
+ align:start position:0%
+entirely outside the circle so if we
+ 
+
+ align:start position:0%
+entirely outside the circle so if we
+imagine swooping from P from point P to
+
+ align:start position:0%
+imagine swooping from P from point P to
+ 
+
+ align:start position:0%
+imagine swooping from P from point P to
+Q within that Circle the mapped motion
+
+ align:start position:0%
+Q within that Circle the mapped motion
+ 
+
+ align:start position:0%
+Q within that Circle the mapped motion
+the uniquely corresponding motion would
+
+ align:start position:0%
+the uniquely corresponding motion would
+ 
+
+ align:start position:0%
+the uniquely corresponding motion would
+swoop from point P Prime to Q Prime
+
+ align:start position:0%
+swoop from point P Prime to Q Prime
+ 
+
+ align:start position:0%
+swoop from point P Prime to Q Prime
+now this transformation is called a
+
+ align:start position:0%
+now this transformation is called a
+ 
+
+ align:start position:0%
+now this transformation is called a
+conformal transformation we use this all
+
+ align:start position:0%
+conformal transformation we use this all
+ 
+
+ align:start position:0%
+conformal transformation we use this all
+the time I use these all the time even
+
+ align:start position:0%
+the time I use these all the time even
+ 
+
+ align:start position:0%
+the time I use these all the time even
+to this day in my own physical search
+
+ align:start position:0%
+to this day in my own physical search
+ 
+
+ align:start position:0%
+to this day in my own physical search
+they're really really helpful in topics
+
+ align:start position:0%
+they're really really helpful in topics
+ 
+
+ align:start position:0%
+they're really really helpful in topics
+like general relativity and cosmology
+
+ align:start position:0%
+like general relativity and cosmology
+ 
+
+ align:start position:0%
+like general relativity and cosmology
+the Wranglers were doing this for
+
+ align:start position:0%
+the Wranglers were doing this for
+ 
+
+ align:start position:0%
+the Wranglers were doing this for
+electrostatics uh to get ready for their
+
+ align:start position:0%
+electrostatics uh to get ready for their
+ 
+
+ align:start position:0%
+electrostatics uh to get ready for their
+for their exam so this transformation
+
+ align:start position:0%
+for their exam so this transformation
+ 
+
+ align:start position:0%
+for their exam so this transformation
+preserves angles the angles between any
+
+ align:start position:0%
+preserves angles the angles between any
+ 
+
+ align:start position:0%
+preserves angles the angles between any
+of these arcs any of these line segments
+
+ align:start position:0%
+of these arcs any of these line segments
+ 
+
+ align:start position:0%
+of these arcs any of these line segments
+this angle marks W here those angles are
+
+ align:start position:0%
+this angle marks W here those angles are
+ 
+
+ align:start position:0%
+this angle marks W here those angles are
+preserved the lengths are not you can
+
+ align:start position:0%
+preserved the lengths are not you can
+ 
+
+ align:start position:0%
+preserved the lengths are not you can
+see the line segment PQ is clearly a
+
+ align:start position:0%
+see the line segment PQ is clearly a
+ 
+
+ align:start position:0%
+see the line segment PQ is clearly a
+shorter overall length the distance
+
+ align:start position:0%
+shorter overall length the distance
+ 
+
+ align:start position:0%
+shorter overall length the distance
+between points p and Q is shorter than
+
+ align:start position:0%
+between points p and Q is shorter than
+ 
+
+ align:start position:0%
+between points p and Q is shorter than
+the distance between the corresponding
+
+ align:start position:0%
+the distance between the corresponding
+ 
+
+ align:start position:0%
+the distance between the corresponding
+inverse points P Prime and Q Prime so
+
+ align:start position:0%
+inverse points P Prime and Q Prime so
+ 
+
+ align:start position:0%
+inverse points P Prime and Q Prime so
+very generally conformal Transformations
+
+ align:start position:0%
+very generally conformal Transformations
+ 
+
+ align:start position:0%
+very generally conformal Transformations
+preserve angles but not lengths if that
+
+ align:start position:0%
+preserve angles but not lengths if that
+ 
+
+ align:start position:0%
+preserve angles but not lengths if that
+sounds confusing to you you're in good
+
+ align:start position:0%
+sounds confusing to you you're in good
+ 
+
+ align:start position:0%
+sounds confusing to you you're in good
+company the point is that's the kind of
+
+ align:start position:0%
+company the point is that's the kind of
+ 
+
+ align:start position:0%
+company the point is that's the kind of
+stuff these Wranglers would have learned
+
+ align:start position:0%
+stuff these Wranglers would have learned
+ 
+
+ align:start position:0%
+stuff these Wranglers would have learned
+with their coaches pretty early there
+
+ align:start position:0%
+with their coaches pretty early there
+ 
+
+ align:start position:0%
+with their coaches pretty early there
+are properties of these geometrical
+
+ align:start position:0%
+are properties of these geometrical
+ 
+
+ align:start position:0%
+are properties of these geometrical
+Transformations the upshot of which is
+
+ align:start position:0%
+Transformations the upshot of which is
+ 
+
+ align:start position:0%
+Transformations the upshot of which is
+to make complicated problems uh easier
+
+ align:start position:0%
+to make complicated problems uh easier
+ 
+
+ align:start position:0%
+to make complicated problems uh easier
+so now let's get to an actual tripos
+
+ align:start position:0%
+so now let's get to an actual tripos
+ 
+
+ align:start position:0%
+so now let's get to an actual tripos
+type problem now let's say because
+
+ align:start position:0%
+type problem now let's say because
+ 
+
+ align:start position:0%
+type problem now let's say because
+you're at Cambridge in you know 1880 or
+
+ align:start position:0%
+you're at Cambridge in you know 1880 or
+ 
+
+ align:start position:0%
+you're at Cambridge in you know 1880 or
+1890 they don't ask you to solve for the
+
+ align:start position:0%
+1890 they don't ask you to solve for the
+ 
+
+ align:start position:0%
+1890 they don't ask you to solve for the
+field between a static positive charge
+
+ align:start position:0%
+field between a static positive charge
+ 
+
+ align:start position:0%
+field between a static positive charge
+and an infinite conducting plate come on
+
+ align:start position:0%
+and an infinite conducting plate come on
+ 
+
+ align:start position:0%
+and an infinite conducting plate come on
+we're wrinkles instead we want to solve
+
+ align:start position:0%
+we're wrinkles instead we want to solve
+ 
+
+ align:start position:0%
+we're wrinkles instead we want to solve
+for the electric field lines or or let's
+
+ align:start position:0%
+for the electric field lines or or let's
+ 
+
+ align:start position:0%
+for the electric field lines or or let's
+say the equipotential surfaces where the
+
+ align:start position:0%
+say the equipotential surfaces where the
+ 
+
+ align:start position:0%
+say the equipotential surfaces where the
+electrostatic potential is equal so
+
+ align:start position:0%
+electrostatic potential is equal so
+ 
+
+ align:start position:0%
+electrostatic potential is equal so
+equivalential surface due to a single
+
+ align:start position:0%
+equivalential surface due to a single
+ 
+
+ align:start position:0%
+equivalential surface due to a single
+charge at
+
+ align:start position:0%
+charge at
+ 
+
+ align:start position:0%
+charge at
+um at location o
+
+ align:start position:0%
+um at location o
+ 
+
+ align:start position:0%
+um at location o
+that's near a grounded conducting sphere
+
+ align:start position:0%
+that's near a grounded conducting sphere
+ 
+
+ align:start position:0%
+that's near a grounded conducting sphere
+of centered at B so here is an actual
+
+ align:start position:0%
+of centered at B so here is an actual
+ 
+
+ align:start position:0%
+of centered at B so here is an actual
+physical parts of our problem some
+
+ align:start position:0%
+physical parts of our problem some
+ 
+
+ align:start position:0%
+physical parts of our problem some
+charge here sitting at rest
+
+ align:start position:0%
+charge here sitting at rest
+ 
+
+ align:start position:0%
+charge here sitting at rest
+electrostatics some electric charge at
+
+ align:start position:0%
+electrostatics some electric charge at
+ 
+
+ align:start position:0%
+electrostatics some electric charge at
+Point O that's near some spherical
+
+ align:start position:0%
+Point O that's near some spherical
+ 
+
+ align:start position:0%
+Point O that's near some spherical
+grounded conducting sphere there's a
+
+ align:start position:0%
+grounded conducting sphere there's a
+ 
+
+ align:start position:0%
+grounded conducting sphere there's a
+harder version than our infinite plane
+
+ align:start position:0%
+harder version than our infinite plane
+ 
+
+ align:start position:0%
+harder version than our infinite plane
+well let's use this method of inversion
+
+ align:start position:0%
+well let's use this method of inversion
+ 
+
+ align:start position:0%
+well let's use this method of inversion
+to treat what turns out to be a much
+
+ align:start position:0%
+to treat what turns out to be a much
+ 
+
+ align:start position:0%
+to treat what turns out to be a much
+simpler problem so we have to map the
+
+ align:start position:0%
+simpler problem so we have to map the
+ 
+
+ align:start position:0%
+simpler problem so we have to map the
+simpler version First
+
+ align:start position:0%
+simpler version First
+ 
+
+ align:start position:0%
+simpler version First
+instead of considering either Point O or
+
+ align:start position:0%
+instead of considering either Point O or
+ 
+
+ align:start position:0%
+instead of considering either Point O or
+this conducting sphere B we introduce
+
+ align:start position:0%
+this conducting sphere B we introduce
+ 
+
+ align:start position:0%
+this conducting sphere B we introduce
+the equivalent of a kind of image charge
+
+ align:start position:0%
+the equivalent of a kind of image charge
+ 
+
+ align:start position:0%
+the equivalent of a kind of image charge
+we consider a Charged conducting sphere
+
+ align:start position:0%
+we consider a Charged conducting sphere
+ 
+
+ align:start position:0%
+we consider a Charged conducting sphere
+set you to point a we put in this in
+
+ align:start position:0%
+set you to point a we put in this in
+ 
+
+ align:start position:0%
+set you to point a we put in this in
+this like our image charge our new
+
+ align:start position:0%
+this like our image charge our new
+ 
+
+ align:start position:0%
+this like our image charge our new
+geometrical simplified system some
+
+ align:start position:0%
+geometrical simplified system some
+ 
+
+ align:start position:0%
+geometrical simplified system some
+positive charge and a sphere at a then
+
+ align:start position:0%
+positive charge and a sphere at a then
+ 
+
+ align:start position:0%
+positive charge and a sphere at a then
+we draw the field lines and the
+
+ align:start position:0%
+we draw the field lines and the
+ 
+
+ align:start position:0%
+we draw the field lines and the
+equipotential surfaces for that now
+
+ align:start position:0%
+equipotential surfaces for that now
+ 
+
+ align:start position:0%
+equipotential surfaces for that now
+that's very easy it's just a sphere
+
+ align:start position:0%
+that's very easy it's just a sphere
+ 
+
+ align:start position:0%
+that's very easy it's just a sphere
+they're just going to be sort of
+
+ align:start position:0%
+they're just going to be sort of
+ 
+
+ align:start position:0%
+they're just going to be sort of
+concentric circles around it for the
+
+ align:start position:0%
+concentric circles around it for the
+ 
+
+ align:start position:0%
+concentric circles around it for the
+equipotential surfaces the field is just
+
+ align:start position:0%
+equipotential surfaces the field is just
+ 
+
+ align:start position:0%
+equipotential surfaces the field is just
+you know radial it goes back to like
+
+ align:start position:0%
+you know radial it goes back to like
+ 
+
+ align:start position:0%
+you know radial it goes back to like
+like Faraday's lines of force it
+
+ align:start position:0%
+like Faraday's lines of force it
+ 
+
+ align:start position:0%
+like Faraday's lines of force it
+couldn't be easier for these Wranglers
+
+ align:start position:0%
+couldn't be easier for these Wranglers
+ 
+
+ align:start position:0%
+couldn't be easier for these Wranglers
+now we use that method of inversion to
+
+ align:start position:0%
+now we use that method of inversion to
+ 
+
+ align:start position:0%
+now we use that method of inversion to
+map it back to the original problem
+
+ align:start position:0%
+map it back to the original problem
+ 
+
+ align:start position:0%
+map it back to the original problem
+we're going to close this imaginary
+
+ align:start position:0%
+we're going to close this imaginary
+ 
+
+ align:start position:0%
+we're going to close this imaginary
+object a in a sphere of radius k
+
+ align:start position:0%
+object a in a sphere of radius k
+ 
+
+ align:start position:0%
+object a in a sphere of radius k
+and then we'll map every point along
+
+ align:start position:0%
+and then we'll map every point along
+ 
+
+ align:start position:0%
+and then we'll map every point along
+this orange curve to the corresponding
+
+ align:start position:0%
+this orange curve to the corresponding
+ 
+
+ align:start position:0%
+this orange curve to the corresponding
+uh image points outside of our Circle
+
+ align:start position:0%
+uh image points outside of our Circle
+ 
+
+ align:start position:0%
+uh image points outside of our Circle
+and now we've mapped the equipotential
+
+ align:start position:0%
+and now we've mapped the equipotential
+ 
+
+ align:start position:0%
+and now we've mapped the equipotential
+surfaces for the original problem based
+
+ align:start position:0%
+surfaces for the original problem based
+ 
+
+ align:start position:0%
+surfaces for the original problem based
+on this much simplified problem if
+
+ align:start position:0%
+on this much simplified problem if
+ 
+
+ align:start position:0%
+on this much simplified problem if
+that's confusing to you first of all
+
+ align:start position:0%
+that's confusing to you first of all
+ 
+
+ align:start position:0%
+that's confusing to you first of all
+good you've led a healthy life
+
+ align:start position:0%
+good you've led a healthy life
+ 
+
+ align:start position:0%
+good you've led a healthy life
+um it is not on the exam this is just
+
+ align:start position:0%
+um it is not on the exam this is just
+ 
+
+ align:start position:0%
+um it is not on the exam this is just
+meant to be an example to make sure that
+
+ align:start position:0%
+meant to be an example to make sure that
+ 
+
+ align:start position:0%
+meant to be an example to make sure that
+the kind of reasoning that these that
+
+ align:start position:0%
+the kind of reasoning that these that
+ 
+
+ align:start position:0%
+the kind of reasoning that these that
+these Wranglers would have been immersed
+
+ align:start position:0%
+these Wranglers would have been immersed
+ 
+
+ align:start position:0%
+these Wranglers would have been immersed
+in of the sort we've seen a few times
+
+ align:start position:0%
+in of the sort we've seen a few times
+ 
+
+ align:start position:0%
+in of the sort we've seen a few times
+this is like standard tripod stuff
+
+ align:start position:0%
+this is like standard tripod stuff
+ 
+
+ align:start position:0%
+this is like standard tripod stuff
+I remember unlike um us here at MIT the
+
+ align:start position:0%
+I remember unlike um us here at MIT the
+ 
+
+ align:start position:0%
+I remember unlike um us here at MIT the
+undergraduates of Cambridge in the 1880s
+
+ align:start position:0%
+undergraduates of Cambridge in the 1880s
+ 
+
+ align:start position:0%
+undergraduates of Cambridge in the 1880s
+would have done all this on a timed exam
+
+ align:start position:0%
+would have done all this on a timed exam
+ 
+
+ align:start position:0%
+would have done all this on a timed exam
+that determined the graduation Rank and
+
+ align:start position:0%
+that determined the graduation Rank and
+ 
+
+ align:start position:0%
+that determined the graduation Rank and
+would be published in the National
+
+ align:start position:0%
+would be published in the National
+ 
+
+ align:start position:0%
+would be published in the National
+newspaper so we won't ask them so now
+
+ align:start position:0%
+newspaper so we won't ask them so now
+ 
+
+ align:start position:0%
+newspaper so we won't ask them so now
+let's come back to what Andy's writing
+
+ align:start position:0%
+let's come back to what Andy's writing
+ 
+
+ align:start position:0%
+let's come back to what Andy's writing
+about uh in this article this method of
+
+ align:start position:0%
+about uh in this article this method of
+ 
+
+ align:start position:0%
+about uh in this article this method of
+inversion and these geometrical
+
+ align:start position:0%
+inversion and these geometrical
+ 
+
+ align:start position:0%
+inversion and these geometrical
+techniques like informal Transformations
+
+ align:start position:0%
+techniques like informal Transformations
+ 
+
+ align:start position:0%
+techniques like informal Transformations
+that was like daily stuff for these
+
+ align:start position:0%
+that was like daily stuff for these
+ 
+
+ align:start position:0%
+that was like daily stuff for these
+Kings Wranglers uh by 1900.
+
+ align:start position:0%
+Kings Wranglers uh by 1900.
+ 
+
+ align:start position:0%
+Kings Wranglers uh by 1900.
+these techniques apply to electrostatics
+
+ align:start position:0%
+these techniques apply to electrostatics
+ 
+
+ align:start position:0%
+these techniques apply to electrostatics
+right imagine you have a fixed charge
+
+ align:start position:0%
+right imagine you have a fixed charge
+ 
+
+ align:start position:0%
+right imagine you have a fixed charge
+sitting still at Point o a a fixed
+
+ align:start position:0%
+sitting still at Point o a a fixed
+ 
+
+ align:start position:0%
+sitting still at Point o a a fixed
+grounded sphere nothing changes over
+
+ align:start position:0%
+grounded sphere nothing changes over
+ 
+
+ align:start position:0%
+grounded sphere nothing changes over
+time and that is to say a little more
+
+ align:start position:0%
+time and that is to say a little more
+ 
+
+ align:start position:0%
+time and that is to say a little more
+quantitatively you're always solving for
+
+ align:start position:0%
+quantitatively you're always solving for
+ 
+
+ align:start position:0%
+quantitatively you're always solving for
+situations in which the electric
+
+ align:start position:0%
+situations in which the electric
+ 
+
+ align:start position:0%
+situations in which the electric
+potential is not varying it's a problem
+
+ align:start position:0%
+potential is not varying it's a problem
+ 
+
+ align:start position:0%
+potential is not varying it's a problem
+in electrostatics not varying over time
+
+ align:start position:0%
+in electrostatics not varying over time
+ 
+
+ align:start position:0%
+in electrostatics not varying over time
+even though it varies over space
+
+ align:start position:0%
+even though it varies over space
+ 
+
+ align:start position:0%
+even though it varies over space
+so what these young recent Wranglers
+
+ align:start position:0%
+so what these young recent Wranglers
+ 
+
+ align:start position:0%
+so what these young recent Wranglers
+wanted to do Ebenezer Cunningham and
+
+ align:start position:0%
+wanted to do Ebenezer Cunningham and
+ 
+
+ align:start position:0%
+wanted to do Ebenezer Cunningham and
+Harry Bateman was to actually use
+
+ align:start position:0%
+Harry Bateman was to actually use
+ 
+
+ align:start position:0%
+Harry Bateman was to actually use
+Einstein's work to tackle a problem they
+
+ align:start position:0%
+Einstein's work to tackle a problem they
+ 
+
+ align:start position:0%
+Einstein's work to tackle a problem they
+cared about
+
+ align:start position:0%
+cared about
+ 
+
+ align:start position:0%
+cared about
+which is to generalize these inversion
+
+ align:start position:0%
+which is to generalize these inversion
+ 
+
+ align:start position:0%
+which is to generalize these inversion
+problems and conformal transformations
+
+ align:start position:0%
+problems and conformal transformations
+ 
+
+ align:start position:0%
+problems and conformal transformations
+to situations where objects might be
+
+ align:start position:0%
+to situations where objects might be
+ 
+
+ align:start position:0%
+to situations where objects might be
+moving around to electrodynamics of
+
+ align:start position:0%
+moving around to electrodynamics of
+ 
+
+ align:start position:0%
+moving around to electrodynamics of
+moving bodies not to electrostatics you
+
+ align:start position:0%
+moving bodies not to electrostatics you
+ 
+
+ align:start position:0%
+moving bodies not to electrostatics you
+can see why Einstein that the title of
+
+ align:start position:0%
+can see why Einstein that the title of
+ 
+
+ align:start position:0%
+can see why Einstein that the title of
+Einstein's paper would have caught their
+
+ align:start position:0%
+Einstein's paper would have caught their
+ 
+
+ align:start position:0%
+Einstein's paper would have caught their
+attention they wanted to understand how
+
+ align:start position:0%
+attention they wanted to understand how
+ 
+
+ align:start position:0%
+attention they wanted to understand how
+to generalize these randomly-like
+
+ align:start position:0%
+to generalize these randomly-like
+ 
+
+ align:start position:0%
+to generalize these randomly-like
+techniques to the question of the
+
+ align:start position:0%
+techniques to the question of the
+ 
+
+ align:start position:0%
+techniques to the question of the
+electrodynamics of moving bodies and
+
+ align:start position:0%
+electrodynamics of moving bodies and
+ 
+
+ align:start position:0%
+electrodynamics of moving bodies and
+they thought Einstein's paper had some
+
+ align:start position:0%
+they thought Einstein's paper had some
+ 
+
+ align:start position:0%
+they thought Einstein's paper had some
+pretty clever Tools in there to do that
+
+ align:start position:0%
+pretty clever Tools in there to do that
+ 
+
+ align:start position:0%
+pretty clever Tools in there to do that
+so they could identify using Einstein's
+
+ align:start position:0%
+so they could identify using Einstein's
+ 
+
+ align:start position:0%
+so they could identify using Einstein's
+work all the Transformations which we
+
+ align:start position:0%
+work all the Transformations which we
+ 
+
+ align:start position:0%
+work all the Transformations which we
+would Now call the lorentz
+
+ align:start position:0%
+would Now call the lorentz
+ 
+
+ align:start position:0%
+would Now call the lorentz
+Transformations Lambda eiside had
+
+ align:start position:0%
+Transformations Lambda eiside had
+ 
+
+ align:start position:0%
+Transformations Lambda eiside had
+separately rederived those in a later
+
+ align:start position:0%
+separately rederived those in a later
+ 
+
+ align:start position:0%
+separately rederived those in a later
+part of the paper that I didn't decide
+
+ align:start position:0%
+part of the paper that I didn't decide
+ 
+
+ align:start position:0%
+part of the paper that I didn't decide
+for our class but it's in Hisense paper
+
+ align:start position:0%
+for our class but it's in Hisense paper
+ 
+
+ align:start position:0%
+for our class but it's in Hisense paper
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+these are the Transformations that would
+
+ align:start position:0%
+these are the Transformations that would
+ 
+
+ align:start position:0%
+these are the Transformations that would
+leave the original wave equation
+
+ align:start position:0%
+leave the original wave equation
+ 
+
+ align:start position:0%
+leave the original wave equation
+invariant so then they could use these
+
+ align:start position:0%
+invariant so then they could use these
+ 
+
+ align:start position:0%
+invariant so then they could use these
+inversion these sort of mapping
+
+ align:start position:0%
+inversion these sort of mapping
+ 
+
+ align:start position:0%
+inversion these sort of mapping
+techniques the kind of characteristic
+
+ align:start position:0%
+techniques the kind of characteristic
+ 
+
+ align:start position:0%
+techniques the kind of characteristic
+Wrangler techniques to map into new
+
+ align:start position:0%
+Wrangler techniques to map into new
+ 
+
+ align:start position:0%
+Wrangler techniques to map into new
+dynamical solutions that could vary in
+
+ align:start position:0%
+dynamical solutions that could vary in
+ 
+
+ align:start position:0%
+dynamical solutions that could vary in
+time and not just space keeping in mind
+
+ align:start position:0%
+time and not just space keeping in mind
+ 
+
+ align:start position:0%
+time and not just space keeping in mind
+that now the time coordinate as well as
+
+ align:start position:0%
+that now the time coordinate as well as
+ 
+
+ align:start position:0%
+that now the time coordinate as well as
+the spatial coordinates might need to be
+
+ align:start position:0%
+the spatial coordinates might need to be
+ 
+
+ align:start position:0%
+the spatial coordinates might need to be
+shifted thanks to this lorentz
+
+ align:start position:0%
+shifted thanks to this lorentz
+ 
+
+ align:start position:0%
+shifted thanks to this lorentz
+transformation so they wanted to use
+
+ align:start position:0%
+transformation so they wanted to use
+ 
+
+ align:start position:0%
+transformation so they wanted to use
+Einstein's paper to find the most
+
+ align:start position:0%
+Einstein's paper to find the most
+ 
+
+ align:start position:0%
+Einstein's paper to find the most
+General class of Transformations Lambda
+
+ align:start position:0%
+General class of Transformations Lambda
+ 
+
+ align:start position:0%
+General class of Transformations Lambda
+that would leave this little this harder
+
+ align:start position:0%
+that would leave this little this harder
+ 
+
+ align:start position:0%
+that would leave this little this harder
+problem invariant to do for
+
+ align:start position:0%
+problem invariant to do for
+ 
+
+ align:start position:0%
+problem invariant to do for
+electrodynamics what they had already
+
+ align:start position:0%
+electrodynamics what they had already
+ 
+
+ align:start position:0%
+electrodynamics what they had already
+learned with their uh with their coaches
+
+ align:start position:0%
+learned with their uh with their coaches
+ 
+
+ align:start position:0%
+learned with their uh with their coaches
+to do for electrostatics that's what
+
+ align:start position:0%
+to do for electrostatics that's what
+ 
+
+ align:start position:0%
+to do for electrostatics that's what
+relativity was all about for these folks
+
+ align:start position:0%
+relativity was all about for these folks
+ 
+
+ align:start position:0%
+relativity was all about for these folks
+they were reading Einstein's work very
+
+ align:start position:0%
+they were reading Einstein's work very
+ 
+
+ align:start position:0%
+they were reading Einstein's work very
+carefully they were doing extremely
+
+ align:start position:0%
+carefully they were doing extremely
+ 
+
+ align:start position:0%
+carefully they were doing extremely
+productive hard original work they just
+
+ align:start position:0%
+productive hard original work they just
+ 
+
+ align:start position:0%
+productive hard original work they just
+were doing things that Einstein didn't
+
+ align:start position:0%
+were doing things that Einstein didn't
+ 
+
+ align:start position:0%
+were doing things that Einstein didn't
+notice or care or think was important
+
+ align:start position:0%
+notice or care or think was important
+ 
+
+ align:start position:0%
+notice or care or think was important
+or that minkowski did so they weren't
+
+ align:start position:0%
+or that minkowski did so they weren't
+ 
+
+ align:start position:0%
+or that minkowski did so they weren't
+trying to understand the ether per se
+
+ align:start position:0%
+trying to understand the ether per se
+ 
+
+ align:start position:0%
+trying to understand the ether per se
+again they weren't trying to understand
+
+ align:start position:0%
+again they weren't trying to understand
+ 
+
+ align:start position:0%
+again they weren't trying to understand
+mocking positivism they weren't even
+
+ align:start position:0%
+mocking positivism they weren't even
+ 
+
+ align:start position:0%
+mocking positivism they weren't even
+really that concerned about minkowski's
+
+ align:start position:0%
+really that concerned about minkowski's
+ 
+
+ align:start position:0%
+really that concerned about minkowski's
+space-time for them it's about kind of
+
+ align:start position:0%
+space-time for them it's about kind of
+ 
+
+ align:start position:0%
+space-time for them it's about kind of
+wranglerist manipulations uh of mapping
+
+ align:start position:0%
+wranglerist manipulations uh of mapping
+ 
+
+ align:start position:0%
+wranglerist manipulations uh of mapping
+complicated problems into simpler ones
+
+ align:start position:0%
+complicated problems into simpler ones
+ 
+
+ align:start position:0%
+complicated problems into simpler ones
+and Einstein's paper to them gave them
+
+ align:start position:0%
+and Einstein's paper to them gave them
+ 
+
+ align:start position:0%
+and Einstein's paper to them gave them
+additional tools with which to do their
+
+ align:start position:0%
+additional tools with which to do their
+ 
+
+ align:start position:0%
+additional tools with which to do their
+problem so they weren't ignoring
+
+ align:start position:0%
+problem so they weren't ignoring
+ 
+
+ align:start position:0%
+problem so they weren't ignoring
+Einstein's work but they also weren't
+
+ align:start position:0%
+Einstein's work but they also weren't
+ 
+
+ align:start position:0%
+Einstein's work but they also weren't
+kind of card carrying einsteinians so
+
+ align:start position:0%
+kind of card carrying einsteinians so
+ 
+
+ align:start position:0%
+kind of card carrying einsteinians so
+that's what I want to go through just to
+
+ align:start position:0%
+that's what I want to go through just to
+ 
+
+ align:start position:0%
+that's what I want to go through just to
+make sure the real historical point of
+
+ align:start position:0%
+make sure the real historical point of
+ 
+
+ align:start position:0%
+make sure the real historical point of
+Andy's paper would be clear it gets
+
+ align:start position:0%
+Andy's paper would be clear it gets
+ 
+
+ align:start position:0%
+Andy's paper would be clear it gets
+pretty complicated the details of these
+
+ align:start position:0%
+pretty complicated the details of these
+ 
+
+ align:start position:0%
+pretty complicated the details of these
+inversions all that I'd be glad to chat
+
+ align:start position:0%
+inversions all that I'd be glad to chat
+ 
+
+ align:start position:0%
+inversions all that I'd be glad to chat
+more about that but the main point the
+
+ align:start position:0%
+more about that but the main point the
+ 
+
+ align:start position:0%
+more about that but the main point the
+main lesson for us is really that
+
+ align:start position:0%
+main lesson for us is really that
+ 
+
+ align:start position:0%
+main lesson for us is really that
+they're also doing real work with
+
+ align:start position:0%
+they're also doing real work with
+ 
+
+ align:start position:0%
+they're also doing real work with
+Einstein's paper just different work
+
+ align:start position:0%
+Einstein's paper just different work
+ 
+
+ align:start position:0%
+Einstein's paper just different work
+than Einstein so let me wrap up for
+
+ align:start position:0%
+than Einstein so let me wrap up for
+ 
+
+ align:start position:0%
+than Einstein so let me wrap up for
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+researchers didn't just read Einstein's
+
+ align:start position:0%
+researchers didn't just read Einstein's
+ 
+
+ align:start position:0%
+researchers didn't just read Einstein's
+paper and sort of become convinced they
+
+ align:start position:0%
+paper and sort of become convinced they
+ 
+
+ align:start position:0%
+paper and sort of become convinced they
+didn't become like a converted
+
+ align:start position:0%
+didn't become like a converted
+ 
+
+ align:start position:0%
+didn't become like a converted
+Einstein's for a long long time most
+
+ align:start position:0%
+Einstein's for a long long time most
+ 
+
+ align:start position:0%
+Einstein's for a long long time most
+people ignored the paper altogether uh
+
+ align:start position:0%
+people ignored the paper altogether uh
+ 
+
+ align:start position:0%
+people ignored the paper altogether uh
+those few who paid attention often
+
+ align:start position:0%
+those few who paid attention often
+ 
+
+ align:start position:0%
+those few who paid attention often
+thought it was just a kind of minor
+
+ align:start position:0%
+thought it was just a kind of minor
+ 
+
+ align:start position:0%
+thought it was just a kind of minor
+elaboration of previous work the few who
+
+ align:start position:0%
+elaboration of previous work the few who
+ 
+
+ align:start position:0%
+elaboration of previous work the few who
+really did pay attention to it much more
+
+ align:start position:0%
+really did pay attention to it much more
+ 
+
+ align:start position:0%
+really did pay attention to it much more
+squarely did so from within their own
+
+ align:start position:0%
+squarely did so from within their own
+ 
+
+ align:start position:0%
+squarely did so from within their own
+context we could even kind of jokingly
+
+ align:start position:0%
+context we could even kind of jokingly
+ 
+
+ align:start position:0%
+context we could even kind of jokingly
+say within their own frames of reference
+
+ align:start position:0%
+say within their own frames of reference
+ 
+
+ align:start position:0%
+say within their own frames of reference
+much like you know Einstein's favorite
+
+ align:start position:0%
+much like you know Einstein's favorite
+ 
+
+ align:start position:0%
+much like you know Einstein's favorite
+example of the observers on the platform
+
+ align:start position:0%
+example of the observers on the platform
+ 
+
+ align:start position:0%
+example of the observers on the platform
+are on the train they do different stuff
+
+ align:start position:0%
+are on the train they do different stuff
+ 
+
+ align:start position:0%
+are on the train they do different stuff
+with it different parts of the paper are
+
+ align:start position:0%
+with it different parts of the paper are
+ 
+
+ align:start position:0%
+with it different parts of the paper are
+relevant to them enough value they're
+
+ align:start position:0%
+relevant to them enough value they're
+ 
+
+ align:start position:0%
+relevant to them enough value they're
+not misunderstanding Einstein's work
+
+ align:start position:0%
+not misunderstanding Einstein's work
+ 
+
+ align:start position:0%
+not misunderstanding Einstein's work
+they're like utterly understanding
+
+ align:start position:0%
+they're like utterly understanding
+ 
+
+ align:start position:0%
+they're like utterly understanding
+they're doing real stuff with it which
+
+ align:start position:0%
+they're doing real stuff with it which
+ 
+
+ align:start position:0%
+they're doing real stuff with it which
+is not what Einstein had first intended
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in terms of a certain kind of
+
+ align:start position:0%
+in terms of a certain kind of
+ 
+
+ align:start position:0%
+in terms of a certain kind of
+geometrical uh vision of the Cambridge
+
+ align:start position:0%
+geometrical uh vision of the Cambridge
+ 
+
+ align:start position:0%
+geometrical uh vision of the Cambridge
+gang Cunningham Bateman and some of
+
+ align:start position:0%
+gang Cunningham Bateman and some of
+ 
+
+ align:start position:0%
+gang Cunningham Bateman and some of
+their immediate circles they do other
+
+ align:start position:0%
+their immediate circles they do other
+ 
+
+ align:start position:0%
+their immediate circles they do other
+kinds of geometrical things with it
+
+ align:start position:0%
+kinds of geometrical things with it
+ 
+
+ align:start position:0%
+kinds of geometrical things with it
+because they have other concerns more
+
+ align:start position:0%
+because they have other concerns more
+ 
+
+ align:start position:0%
+because they have other concerns more
+related to the properties uh and and
+
+ align:start position:0%
+related to the properties uh and and
+ 
+
+ align:start position:0%
+related to the properties uh and and
+transformation properties of
+
+ align:start position:0%
+transformation properties of
+ 
+
+ align:start position:0%
+transformation properties of
+differential equations
+
+ align:start position:0%
+differential equations
+ 
+
+ align:start position:0%
+differential equations
+the point is none of these readers seem
+
+ align:start position:0%
+the point is none of these readers seem
+ 
+
+ align:start position:0%
+the point is none of these readers seem
+to care much about what was most
+
+ align:start position:0%
+to care much about what was most
+ 
+
+ align:start position:0%
+to care much about what was most
+important to Einstein as far as
+
+ align:start position:0%
+important to Einstein as far as
+ 
+
+ align:start position:0%
+important to Einstein as far as
+Einstein's concerned none of them were
+
+ align:start position:0%
+Einstein's concerned none of them were
+ 
+
+ align:start position:0%
+Einstein's concerned none of them were
+getting the point of his article even
+
+ align:start position:0%
+getting the point of his article even
+ 
+
+ align:start position:0%
+getting the point of his article even
+though these were among the people who
+
+ align:start position:0%
+though these were among the people who
+ 
+
+ align:start position:0%
+though these were among the people who
+paid any attention at all Einstein had
+
+ align:start position:0%
+paid any attention at all Einstein had
+ 
+
+ align:start position:0%
+paid any attention at all Einstein had
+argued in those opening paragraphs but
+
+ align:start position:0%
+argued in those opening paragraphs but
+ 
+
+ align:start position:0%
+argued in those opening paragraphs but
+the ether was merely Superfluous who
+
+ align:start position:0%
+the ether was merely Superfluous who
+ 
+
+ align:start position:0%
+the ether was merely Superfluous who
+cared that's you know they didn't that
+
+ align:start position:0%
+cared that's you know they didn't that
+ 
+
+ align:start position:0%
+cared that's you know they didn't that
+wasn't the part that landed them
+
+ align:start position:0%
+wasn't the part that landed them
+ 
+
+ align:start position:0%
+wasn't the part that landed them
+moreover Einstein had insisted that we
+
+ align:start position:0%
+moreover Einstein had insisted that we
+ 
+
+ align:start position:0%
+moreover Einstein had insisted that we
+start with kinematics instead of
+
+ align:start position:0%
+start with kinematics instead of
+ 
+
+ align:start position:0%
+start with kinematics instead of
+Dynamics forget that that sort of didn't
+
+ align:start position:0%
+Dynamics forget that that sort of didn't
+ 
+
+ align:start position:0%
+Dynamics forget that that sort of didn't
+wash that didn't register instead as
+
+ align:start position:0%
+wash that didn't register instead as
+ 
+
+ align:start position:0%
+wash that didn't register instead as
+we've seen before and we'll see again
+
+ align:start position:0%
+we've seen before and we'll see again
+ 
+
+ align:start position:0%
+we've seen before and we'll see again
+even the exact same equations could
+
+ align:start position:0%
+even the exact same equations could
+ 
+
+ align:start position:0%
+even the exact same equations could
+Inspire quite different interpretations
+
+ align:start position:0%
+Inspire quite different interpretations
+ 
+
+ align:start position:0%
+Inspire quite different interpretations
+for different meanings so I'll stop
+
+ align:start position:0%
+for different meanings so I'll stop
+ 
+
+ align:start position:0%
+for different meanings so I'll stop
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+any other questions on that last part
+
+ align:start position:0%
+any other questions on that last part
+ 
+
+ align:start position:0%
+any other questions on that last part
+about the Cambridge gang
+
+ align:start position:0%
+about the Cambridge gang
+ 
+
+ align:start position:0%
+about the Cambridge gang
+and again if the particulars of
+
+ align:start position:0%
+and again if the particulars of
+ 
+
+ align:start position:0%
+and again if the particulars of
+conformal Transformations or inversion
+
+ align:start position:0%
+conformal Transformations or inversion
+ 
+
+ align:start position:0%
+conformal Transformations or inversion
+uh went by too quickly or Andy's paper
+
+ align:start position:0%
+uh went by too quickly or Andy's paper
+ 
+
+ align:start position:0%
+uh went by too quickly or Andy's paper
+was confusing please don't worry I'd be
+
+ align:start position:0%
+was confusing please don't worry I'd be
+ 
+
+ align:start position:0%
+was confusing please don't worry I'd be
+glad to chat more if it's of interest
+
+ align:start position:0%
+glad to chat more if it's of interest
+ 
+
+ align:start position:0%
+glad to chat more if it's of interest
+for you but but the historical point is
+
+ align:start position:0%
+for you but but the historical point is
+ 
+
+ align:start position:0%
+for you but but the historical point is
+just to say they were they were doing
+
+ align:start position:0%
+just to say they were they were doing
+ 
+
+ align:start position:0%
+just to say they were they were doing
+real work it's still in our textbooks it
+
+ align:start position:0%
+real work it's still in our textbooks it
+ 
+
+ align:start position:0%
+real work it's still in our textbooks it
+was valuable work it was just different
+
+ align:start position:0%
+was valuable work it was just different
+ 
+
+ align:start position:0%
+was valuable work it was just different
+work than than Einstein's or minkowski's
+
+ align:start position:0%
+work than than Einstein's or minkowski's
+ 
+
+ align:start position:0%
+work than than Einstein's or minkowski's
+or you know lorenzes and so on that's
+
+ align:start position:0%
+or you know lorenzes and so on that's
+ 
+
+ align:start position:0%
+or you know lorenzes and so on that's
+that's really the point I think we can
+
+ align:start position:0%
+that's really the point I think we can
+ 
+
+ align:start position:0%
+that's really the point I think we can
+hold on to in this class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other questions on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone want to volunteer to do more uh
+
+ align:start position:0%
+anyone want to volunteer to do more uh
+ 
+
+ align:start position:0%
+anyone want to volunteer to do more uh
+inversion problems for conducting
+
+ align:start position:0%
+inversion problems for conducting
+ 
+
+ align:start position:0%
+inversion problems for conducting
+spheres and I hate that stuff that's
+
+ align:start position:0%
+spheres and I hate that stuff that's
+ 
+
+ align:start position:0%
+spheres and I hate that stuff that's
+done yeah Julia says no I'm with Julie
+
+ align:start position:0%
+done yeah Julia says no I'm with Julie
+ 
+
+ align:start position:0%
+done yeah Julia says no I'm with Julie
+on this that stuff makes me that really
+
+ align:start position:0%
+on this that stuff makes me that really
+ 
+
+ align:start position:0%
+on this that stuff makes me that really
+makes my head hurt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I didn't want to do that for five hours
+
+ align:start position:0%
+I didn't want to do that for five hours
+ 
+
+ align:start position:0%
+I didn't want to do that for five hours
+before lunch like a good Wrangler that's
+
+ align:start position:0%
+before lunch like a good Wrangler that's
+ 
+
+ align:start position:0%
+before lunch like a good Wrangler that's
+another question your math homework
+
+ align:start position:0%
+another question your math homework
+ 
+
+ align:start position:0%
+another question your math homework
+before lunchtime
+
+ align:start position:0%
+before lunchtime
+ 
+
+ align:start position:0%
+before lunchtime
+okay if there's no more questions uh for
+
+ align:start position:0%
+okay if there's no more questions uh for
+ 
+
+ align:start position:0%
+okay if there's no more questions uh for
+now then I'll I'll pause there uh we'll
+
+ align:start position:0%
+now then I'll I'll pause there uh we'll
+ 
+
+ align:start position:0%
+now then I'll I'll pause there uh we'll
+pick it up uh early next week and we'll
+
+ align:start position:0%
+pick it up uh early next week and we'll
+ 
+
+ align:start position:0%
+pick it up uh early next week and we'll
+and we'll get into many of the questions
+
+ align:start position:0%
+and we'll get into many of the questions
+ 
+
+ align:start position:0%
+and we'll get into many of the questions
+that were raised even um for today what
+
+ align:start position:0%
+that were raised even um for today what
+ 
+
+ align:start position:0%
+that were raised even um for today what
+does Einstein himself do with all this
+
+ align:start position:0%
+does Einstein himself do with all this
+ 
+
+ align:start position:0%
+does Einstein himself do with all this
+work in what in his march to work what
+
+ align:start position:0%
+work in what in his march to work what
+ 
+
+ align:start position:0%
+work in what in his march to work what
+we would eventually call the general
+
+ align:start position:0%
+we would eventually call the general
+ 
+
+ align:start position:0%
+we would eventually call the general
+theory of relativity so we'll come to
+
+ align:start position:0%
+theory of relativity so we'll come to
+ 
+
+ align:start position:0%
+theory of relativity so we'll come to
+that that will occupy us then for for
+
+ align:start position:0%
+that that will occupy us then for for
+ 
+
+ align:start position:0%
+that that will occupy us then for for
+our next class
\ No newline at end of file
diff --git a/ZSv_gYLBi8E.txt b/ZSv_gYLBi8E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3a6834a5dfe6b3fd77d3eaa04ea88a42b4719190
--- /dev/null
+++ b/ZSv_gYLBi8E.txt
@@ -0,0 +1,9427 @@
+align:start position:0%
+ 
+we're gonna
+
+ align:start position:0%
+we're gonna
+ 
+
+ align:start position:0%
+we're gonna
+pick up where we left off on monday
+
+ align:start position:0%
+pick up where we left off on monday
+ 
+
+ align:start position:0%
+pick up where we left off on monday
+and where we left off was we were
+
+ align:start position:0%
+and where we left off was we were
+ 
+
+ align:start position:0%
+and where we left off was we were
+dissolving stuff we talked about how
+
+ align:start position:0%
+dissolving stuff we talked about how
+ 
+
+ align:start position:0%
+dissolving stuff we talked about how
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+dissolve why does something dissolve
+
+ align:start position:0%
+dissolve why does something dissolve
+ 
+
+ align:start position:0%
+dissolve why does something dissolve
+maybe in this solvent versus that and
+
+ align:start position:0%
+maybe in this solvent versus that and
+ 
+
+ align:start position:0%
+maybe in this solvent versus that and
+how does it dissolve and what makes them
+
+ align:start position:0%
+how does it dissolve and what makes them
+ 
+
+ align:start position:0%
+how does it dissolve and what makes them
+and then we say well what if we had
+
+ align:start position:0%
+and then we say well what if we had
+ 
+
+ align:start position:0%
+and then we say well what if we had
+something and we wanted it to dissolve
+
+ align:start position:0%
+something and we wanted it to dissolve
+ 
+
+ align:start position:0%
+something and we wanted it to dissolve
+all the way until it couldn't dissolve
+
+ align:start position:0%
+all the way until it couldn't dissolve
+ 
+
+ align:start position:0%
+all the way until it couldn't dissolve
+anymore well that's called
+
+ align:start position:0%
+anymore well that's called
+ 
+
+ align:start position:0%
+anymore well that's called
+saturation right
+
+ align:start position:0%
+saturation right
+ 
+
+ align:start position:0%
+saturation right
+and and we talked about that we talked
+
+ align:start position:0%
+and and we talked about that we talked
+ 
+
+ align:start position:0%
+and and we talked about that we talked
+about how if you had a general reaction
+
+ align:start position:0%
+about how if you had a general reaction
+ 
+
+ align:start position:0%
+about how if you had a general reaction
+you know maybe we had something like
+
+ align:start position:0%
+you know maybe we had something like
+ 
+
+ align:start position:0%
+you know maybe we had something like
+this right a
+
+ align:start position:0%
+this right a
+ 
+
+ align:start position:0%
+this right a
+a plus b b
+
+ align:start position:0%
+a plus b b
+ 
+
+ align:start position:0%
+a plus b b
+goes to and comes back from
+
+ align:start position:0%
+goes to and comes back from
+ 
+
+ align:start position:0%
+goes to and comes back from
+c c plus dd then
+
+ align:start position:0%
+c c plus dd then
+ 
+
+ align:start position:0%
+c c plus dd then
+this reaction can happen in both ways
+
+ align:start position:0%
+this reaction can happen in both ways
+ 
+
+ align:start position:0%
+this reaction can happen in both ways
+right and so the general
+
+ align:start position:0%
+right and so the general
+ 
+
+ align:start position:0%
+right and so the general
+concept that we called a reaction
+
+ align:start position:0%
+concept that we called a reaction
+ 
+
+ align:start position:0%
+concept that we called a reaction
+quotient
+
+ align:start position:0%
+quotient
+ 
+
+ align:start position:0%
+quotient
+reaction q
+
+ align:start position:0%
+reaction q
+ 
+
+ align:start position:0%
+reaction q
+is equal to remember it's equal to the
+
+ align:start position:0%
+is equal to remember it's equal to the
+ 
+
+ align:start position:0%
+is equal to remember it's equal to the
+concentrations
+
+ align:start position:0%
+concentrations
+ 
+
+ align:start position:0%
+concentrations
+raised to those stoichiometric
+
+ align:start position:0%
+raised to those stoichiometric
+ 
+
+ align:start position:0%
+raised to those stoichiometric
+coefficients
+
+ align:start position:0%
+coefficients
+ 
+
+ align:start position:0%
+coefficients
+and it's the products over
+
+ align:start position:0%
+and it's the products over
+ 
+
+ align:start position:0%
+and it's the products over
+the reactants okay so that's what we now
+
+ align:start position:0%
+the reactants okay so that's what we now
+ 
+
+ align:start position:0%
+the reactants okay so that's what we now
+then we
+
+ align:start position:0%
+then we
+ 
+
+ align:start position:0%
+then we
+we say well okay that's just okay that's
+
+ align:start position:0%
+we say well okay that's just okay that's
+ 
+
+ align:start position:0%
+we say well okay that's just okay that's
+a thing that that has to do with sort of
+
+ align:start position:0%
+a thing that that has to do with sort of
+ 
+
+ align:start position:0%
+a thing that that has to do with sort of
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+you know where's that reaction going
+
+ align:start position:0%
+you know where's that reaction going
+ 
+
+ align:start position:0%
+you know where's that reaction going
+what's dominating
+
+ align:start position:0%
+what's dominating
+ 
+
+ align:start position:0%
+what's dominating
+uh it and these came remember these are
+
+ align:start position:0%
+uh it and these came remember these are
+ 
+
+ align:start position:0%
+uh it and these came remember these are
+the stoichiometric coefficients and
+
+ align:start position:0%
+the stoichiometric coefficients and
+ 
+
+ align:start position:0%
+the stoichiometric coefficients and
+they're related to
+
+ align:start position:0%
+they're related to
+ 
+
+ align:start position:0%
+they're related to
+literally like the probability that that
+
+ align:start position:0%
+literally like the probability that that
+ 
+
+ align:start position:0%
+literally like the probability that that
+reaction can happen
+
+ align:start position:0%
+reaction can happen
+ 
+
+ align:start position:0%
+reaction can happen
+okay um and so if you want an intuitive
+
+ align:start position:0%
+okay um and so if you want an intuitive
+ 
+
+ align:start position:0%
+okay um and so if you want an intuitive
+reason for the exponents you can think
+
+ align:start position:0%
+reason for the exponents you can think
+ 
+
+ align:start position:0%
+reason for the exponents you can think
+about this as well if these all have to
+
+ align:start position:0%
+about this as well if these all have to
+ 
+
+ align:start position:0%
+about this as well if these all have to
+get close enough in a given volume
+
+ align:start position:0%
+get close enough in a given volume
+ 
+
+ align:start position:0%
+get close enough in a given volume
+to react then that's where those
+
+ align:start position:0%
+to react then that's where those
+ 
+
+ align:start position:0%
+to react then that's where those
+exponents come from
+
+ align:start position:0%
+exponents come from
+ 
+
+ align:start position:0%
+exponents come from
+but they don't but unlike the rate law
+
+ align:start position:0%
+but they don't but unlike the rate law
+ 
+
+ align:start position:0%
+but they don't but unlike the rate law
+when i said this money i'm saying it
+
+ align:start position:0%
+when i said this money i'm saying it
+ 
+
+ align:start position:0%
+when i said this money i'm saying it
+again say they are not things that are
+
+ align:start position:0%
+again say they are not things that are
+ 
+
+ align:start position:0%
+again say they are not things that are
+experimentally measured instead they
+
+ align:start position:0%
+experimentally measured instead they
+ 
+
+ align:start position:0%
+experimentally measured instead they
+just come
+
+ align:start position:0%
+just come
+ 
+
+ align:start position:0%
+just come
+from the reaction itself okay now uh so
+
+ align:start position:0%
+from the reaction itself okay now uh so
+ 
+
+ align:start position:0%
+from the reaction itself okay now uh so
+we're just getting back into the right
+
+ align:start position:0%
+we're just getting back into the right
+ 
+
+ align:start position:0%
+we're just getting back into the right
+mood here but then we said well but look
+
+ align:start position:0%
+mood here but then we said well but look
+ 
+
+ align:start position:0%
+mood here but then we said well but look
+okay this thing is reacting it's going
+
+ align:start position:0%
+okay this thing is reacting it's going
+ 
+
+ align:start position:0%
+okay this thing is reacting it's going
+back and forth
+
+ align:start position:0%
+back and forth
+ 
+
+ align:start position:0%
+back and forth
+whatever but what about once it reaches
+
+ align:start position:0%
+whatever but what about once it reaches
+ 
+
+ align:start position:0%
+whatever but what about once it reaches
+equilibrium right equilibrium and and
+
+ align:start position:0%
+equilibrium right equilibrium and and
+ 
+
+ align:start position:0%
+equilibrium right equilibrium and and
+when it reaches equilibrium
+
+ align:start position:0%
+when it reaches equilibrium
+ 
+
+ align:start position:0%
+when it reaches equilibrium
+it's the same thing but we call it k
+
+ align:start position:0%
+it's the same thing but we call it k
+ 
+
+ align:start position:0%
+it's the same thing but we call it k
+eq in
+
+ align:start position:0%
+eq in
+ 
+
+ align:start position:0%
+eq in
+equilibrium equal m
+
+ align:start position:0%
+equilibrium equal m
+ 
+
+ align:start position:0%
+equilibrium equal m
+equilibrium right so so that reaction
+
+ align:start position:0%
+equilibrium right so so that reaction
+ 
+
+ align:start position:0%
+equilibrium right so so that reaction
+quotient
+
+ align:start position:0%
+quotient
+ 
+
+ align:start position:0%
+quotient
+has a very specific value a constant
+
+ align:start position:0%
+has a very specific value a constant
+ 
+
+ align:start position:0%
+has a very specific value a constant
+a constant once this way
+
+ align:start position:0%
+a constant once this way
+ 
+
+ align:start position:0%
+a constant once this way
+is happening in the same amount as that
+
+ align:start position:0%
+is happening in the same amount as that
+ 
+
+ align:start position:0%
+is happening in the same amount as that
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+right that's the saturation point
+
+ align:start position:0%
+right that's the saturation point
+ 
+
+ align:start position:0%
+right that's the saturation point
+well if you're dissolving something
+
+ align:start position:0%
+well if you're dissolving something
+ 
+
+ align:start position:0%
+well if you're dissolving something
+that's the saturation point
+
+ align:start position:0%
+that's the saturation point
+ 
+
+ align:start position:0%
+that's the saturation point
+okay so it's where it's where the
+
+ align:start position:0%
+okay so it's where it's where the
+ 
+
+ align:start position:0%
+okay so it's where it's where the
+precipitation remember we wrote this as
+
+ align:start position:0%
+precipitation remember we wrote this as
+ 
+
+ align:start position:0%
+precipitation remember we wrote this as
+dissolution and precipitation when we
+
+ align:start position:0%
+dissolution and precipitation when we
+ 
+
+ align:start position:0%
+dissolution and precipitation when we
+were putting stuff in solution and
+
+ align:start position:0%
+were putting stuff in solution and
+ 
+
+ align:start position:0%
+were putting stuff in solution and
+that's kind of where we got to
+
+ align:start position:0%
+that's kind of where we got to
+ 
+
+ align:start position:0%
+that's kind of where we got to
+we went a little bit further and we had
+
+ align:start position:0%
+we went a little bit further and we had
+ 
+
+ align:start position:0%
+we went a little bit further and we had
+a specific example and that's where i
+
+ align:start position:0%
+a specific example and that's where i
+ 
+
+ align:start position:0%
+a specific example and that's where i
+want to start today
+
+ align:start position:0%
+want to start today
+ 
+
+ align:start position:0%
+want to start today
+and that's silver chloride okay so here
+
+ align:start position:0%
+and that's silver chloride okay so here
+ 
+
+ align:start position:0%
+and that's silver chloride okay so here
+we go so we have
+
+ align:start position:0%
+we go so we have
+ 
+
+ align:start position:0%
+we go so we have
+silver chloride and if i write this all
+
+ align:start position:0%
+silver chloride and if i write this all
+ 
+
+ align:start position:0%
+silver chloride and if i write this all
+out for silver chloride i've got
+
+ align:start position:0%
+out for silver chloride i've got
+ 
+
+ align:start position:0%
+out for silver chloride i've got
+a g cl and i've got a little pinch of it
+
+ align:start position:0%
+a g cl and i've got a little pinch of it
+ 
+
+ align:start position:0%
+a g cl and i've got a little pinch of it
+you know like a little speck of silver
+
+ align:start position:0%
+you know like a little speck of silver
+ 
+
+ align:start position:0%
+you know like a little speck of silver
+chloride i'm putting it into
+
+ align:start position:0%
+chloride i'm putting it into
+ 
+
+ align:start position:0%
+chloride i'm putting it into
+a beaker so it starts out as a solid and
+
+ align:start position:0%
+a beaker so it starts out as a solid and
+ 
+
+ align:start position:0%
+a beaker so it starts out as a solid and
+i add some water to it
+
+ align:start position:0%
+i add some water to it
+ 
+
+ align:start position:0%
+i add some water to it
+and the water is l because it's
+
+ align:start position:0%
+and the water is l because it's
+ 
+
+ align:start position:0%
+and the water is l because it's
+everywhere it's the liquid it's the
+
+ align:start position:0%
+everywhere it's the liquid it's the
+ 
+
+ align:start position:0%
+everywhere it's the liquid it's the
+solvent
+
+ align:start position:0%
+solvent
+ 
+
+ align:start position:0%
+solvent
+okay it's the liquid that i'm dissolving
+
+ align:start position:0%
+okay it's the liquid that i'm dissolving
+ 
+
+ align:start position:0%
+okay it's the liquid that i'm dissolving
+it in and we say well okay
+
+ align:start position:0%
+it in and we say well okay
+ 
+
+ align:start position:0%
+it in and we say well okay
+that's going to go like this so that
+
+ align:start position:0%
+that's going to go like this so that
+ 
+
+ align:start position:0%
+that's going to go like this so that
+reaction it's going to give us
+
+ align:start position:0%
+reaction it's going to give us
+ 
+
+ align:start position:0%
+reaction it's going to give us
+silver ions remember salts we did salts
+
+ align:start position:0%
+silver ions remember salts we did salts
+ 
+
+ align:start position:0%
+silver ions remember salts we did salts
+and chlorine ions and
+
+ align:start position:0%
+and chlorine ions and
+ 
+
+ align:start position:0%
+and chlorine ions and
+back to some more water
+
+ align:start position:0%
+back to some more water
+ 
+
+ align:start position:0%
+back to some more water
+okay that's h2o now the aq means aqueous
+
+ align:start position:0%
+okay that's h2o now the aq means aqueous
+ 
+
+ align:start position:0%
+okay that's h2o now the aq means aqueous
+these are now
+
+ align:start position:0%
+these are now
+ 
+
+ align:start position:0%
+these are now
+because it's a salt right these are now
+
+ align:start position:0%
+because it's a salt right these are now
+ 
+
+ align:start position:0%
+because it's a salt right these are now
+dissolved ions because it's a salt so we
+
+ align:start position:0%
+dissolved ions because it's a salt so we
+ 
+
+ align:start position:0%
+dissolved ions because it's a salt so we
+write them like that
+
+ align:start position:0%
+write them like that
+ 
+
+ align:start position:0%
+write them like that
+and we know we got water everywhere and
+
+ align:start position:0%
+and we know we got water everywhere and
+ 
+
+ align:start position:0%
+and we know we got water everywhere and
+so oftentimes we leave the water out
+
+ align:start position:0%
+so oftentimes we leave the water out
+ 
+
+ align:start position:0%
+so oftentimes we leave the water out
+oftentimes we don't really write the
+
+ align:start position:0%
+oftentimes we don't really write the
+ 
+
+ align:start position:0%
+oftentimes we don't really write the
+water because it's on both sides
+
+ align:start position:0%
+water because it's on both sides
+ 
+
+ align:start position:0%
+water because it's on both sides
+and anyway we don't the water the water
+
+ align:start position:0%
+and anyway we don't the water the water
+ 
+
+ align:start position:0%
+and anyway we don't the water the water
+is just surrounding stuff it's not
+
+ align:start position:0%
+is just surrounding stuff it's not
+ 
+
+ align:start position:0%
+is just surrounding stuff it's not
+necessarily been consumed
+
+ align:start position:0%
+necessarily been consumed
+ 
+
+ align:start position:0%
+necessarily been consumed
+the concentration of the water isn't
+
+ align:start position:0%
+the concentration of the water isn't
+ 
+
+ align:start position:0%
+the concentration of the water isn't
+changing
+
+ align:start position:0%
+changing
+ 
+
+ align:start position:0%
+changing
+the water is the water in the liquid
+
+ align:start position:0%
+the water is the water in the liquid
+ 
+
+ align:start position:0%
+the water is the water in the liquid
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+well okay then we went even further you
+
+ align:start position:0%
+well okay then we went even further you
+ 
+
+ align:start position:0%
+well okay then we went even further you
+said well if you write a keq for this
+
+ align:start position:0%
+said well if you write a keq for this
+ 
+
+ align:start position:0%
+said well if you write a keq for this
+then it would uh i would look like
+
+ align:start position:0%
+then it would uh i would look like
+ 
+
+ align:start position:0%
+then it would uh i would look like
+something like okay it's the
+
+ align:start position:0%
+something like okay it's the
+ 
+
+ align:start position:0%
+something like okay it's the
+concentration of silver plus
+
+ align:start position:0%
+concentration of silver plus
+ 
+
+ align:start position:0%
+concentration of silver plus
+in solution times the concentration of
+
+ align:start position:0%
+in solution times the concentration of
+ 
+
+ align:start position:0%
+in solution times the concentration of
+chlorine
+
+ align:start position:0%
+chlorine
+ 
+
+ align:start position:0%
+chlorine
+minus in solution and that would be
+
+ align:start position:0%
+minus in solution and that would be
+ 
+
+ align:start position:0%
+minus in solution and that would be
+divided by
+
+ align:start position:0%
+divided by
+ 
+
+ align:start position:0%
+divided by
+the concentration of silver chloride
+
+ align:start position:0%
+the concentration of silver chloride
+ 
+
+ align:start position:0%
+the concentration of silver chloride
+as a solid and then we said
+
+ align:start position:0%
+as a solid and then we said
+ 
+
+ align:start position:0%
+as a solid and then we said
+but hold on no but hold on
+
+ align:start position:0%
+but hold on no but hold on
+ 
+
+ align:start position:0%
+but hold on no but hold on
+in the solid phase the concentration
+
+ align:start position:0%
+in the solid phase the concentration
+ 
+
+ align:start position:0%
+in the solid phase the concentration
+isn't changing
+
+ align:start position:0%
+isn't changing
+ 
+
+ align:start position:0%
+isn't changing
+right as a solid silver chloride the
+
+ align:start position:0%
+right as a solid silver chloride the
+ 
+
+ align:start position:0%
+right as a solid silver chloride the
+concentration of silver chloride is
+
+ align:start position:0%
+concentration of silver chloride is
+ 
+
+ align:start position:0%
+concentration of silver chloride is
+silver chloride it's a constant
+
+ align:start position:0%
+silver chloride it's a constant
+ 
+
+ align:start position:0%
+silver chloride it's a constant
+and so then we say well okay if this
+
+ align:start position:0%
+and so then we say well okay if this
+ 
+
+ align:start position:0%
+and so then we say well okay if this
+is a constant this is a constant
+
+ align:start position:0%
+is a constant this is a constant
+ 
+
+ align:start position:0%
+is a constant this is a constant
+then we can also absorb it into the
+
+ align:start position:0%
+then we can also absorb it into the
+ 
+
+ align:start position:0%
+then we can also absorb it into the
+equilibrium constant
+
+ align:start position:0%
+equilibrium constant
+ 
+
+ align:start position:0%
+equilibrium constant
+and i somewhat confusingly wrote it as
+
+ align:start position:0%
+and i somewhat confusingly wrote it as
+ 
+
+ align:start position:0%
+and i somewhat confusingly wrote it as
+ksp in both
+
+ align:start position:0%
+ksp in both
+ 
+
+ align:start position:0%
+ksp in both
+this form and the form that
+
+ align:start position:0%
+this form and the form that
+ 
+
+ align:start position:0%
+this form and the form that
+we know and love for ksp which is simply
+
+ align:start position:0%
+we know and love for ksp which is simply
+ 
+
+ align:start position:0%
+we know and love for ksp which is simply
+literally the solubilities of these
+
+ align:start position:0%
+literally the solubilities of these
+ 
+
+ align:start position:0%
+literally the solubilities of these
+times each other right and that is ksp
+
+ align:start position:0%
+times each other right and that is ksp
+ 
+
+ align:start position:0%
+times each other right and that is ksp
+so i wanted just to clarify this
+
+ align:start position:0%
+so i wanted just to clarify this
+ 
+
+ align:start position:0%
+so i wanted just to clarify this
+because the student asked a very good
+
+ align:start position:0%
+because the student asked a very good
+ 
+
+ align:start position:0%
+because the student asked a very good
+question which is
+
+ align:start position:0%
+question which is
+ 
+
+ align:start position:0%
+question which is
+which is which is it now is this in ks
+
+ align:start position:0%
+which is which is it now is this in ks
+ 
+
+ align:start position:0%
+which is which is it now is this in ks
+p or is this in keq well the the the big
+
+ align:start position:0%
+p or is this in keq well the the the big
+ 
+
+ align:start position:0%
+p or is this in keq well the the the big
+full picture for keq
+
+ align:start position:0%
+full picture for keq
+ 
+
+ align:start position:0%
+full picture for keq
+you know you'd write it all in but the
+
+ align:start position:0%
+you know you'd write it all in but the
+ 
+
+ align:start position:0%
+you know you'd write it all in but the
+solubility product
+
+ align:start position:0%
+solubility product
+ 
+
+ align:start position:0%
+solubility product
+is focusing in right on on the the
+
+ align:start position:0%
+is focusing in right on on the the
+ 
+
+ align:start position:0%
+is focusing in right on on the the
+dissolution
+
+ align:start position:0%
+dissolution
+ 
+
+ align:start position:0%
+dissolution
+of these ions and and so you wrap this
+
+ align:start position:0%
+of these ions and and so you wrap this
+ 
+
+ align:start position:0%
+of these ions and and so you wrap this
+into the equilibrium constant because
+
+ align:start position:0%
+into the equilibrium constant because
+ 
+
+ align:start position:0%
+into the equilibrium constant because
+it's another constant so that's the
+
+ align:start position:0%
+it's another constant so that's the
+ 
+
+ align:start position:0%
+it's another constant so that's the
+solubility product and that's where we
+
+ align:start position:0%
+solubility product and that's where we
+ 
+
+ align:start position:0%
+solubility product and that's where we
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+to on monday the solubility product is a
+
+ align:start position:0%
+to on monday the solubility product is a
+ 
+
+ align:start position:0%
+to on monday the solubility product is a
+special equilibrium constant
+
+ align:start position:0%
+special equilibrium constant
+ 
+
+ align:start position:0%
+special equilibrium constant
+where what we're talking about right
+
+ align:start position:0%
+where what we're talking about right
+ 
+
+ align:start position:0%
+where what we're talking about right
+is is you know what what are the
+
+ align:start position:0%
+is is you know what what are the
+ 
+
+ align:start position:0%
+is is you know what what are the
+concentrations when you've reached
+
+ align:start position:0%
+concentrations when you've reached
+ 
+
+ align:start position:0%
+concentrations when you've reached
+saturation of this dissolution
+
+ align:start position:0%
+saturation of this dissolution
+ 
+
+ align:start position:0%
+saturation of this dissolution
+precipitation reaction
+
+ align:start position:0%
+precipitation reaction
+ 
+
+ align:start position:0%
+precipitation reaction
+okay that's the solubility product
+
+ align:start position:0%
+okay that's the solubility product
+ 
+
+ align:start position:0%
+okay that's the solubility product
+that's ksp
+
+ align:start position:0%
+that's ksp
+ 
+
+ align:start position:0%
+that's ksp
+so you wrap this in and you get you get
+
+ align:start position:0%
+so you wrap this in and you get you get
+ 
+
+ align:start position:0%
+so you wrap this in and you get you get
+your ksp
+
+ align:start position:0%
+your ksp
+ 
+
+ align:start position:0%
+your ksp
+uh you can think about it as well maybe
+
+ align:start position:0%
+uh you can think about it as well maybe
+ 
+
+ align:start position:0%
+uh you can think about it as well maybe
+you could have called this some ksp
+
+ align:start position:0%
+you could have called this some ksp
+ 
+
+ align:start position:0%
+you could have called this some ksp
+in you know uh uh pre-ksp and then you
+
+ align:start position:0%
+in you know uh uh pre-ksp and then you
+ 
+
+ align:start position:0%
+in you know uh uh pre-ksp and then you
+wrap this in and then it's still just
+
+ align:start position:0%
+wrap this in and then it's still just
+ 
+
+ align:start position:0%
+wrap this in and then it's still just
+kidding
+
+ align:start position:0%
+kidding
+ 
+
+ align:start position:0%
+kidding
+because it's still just a constant
+
+ align:start position:0%
+because it's still just a constant
+ 
+
+ align:start position:0%
+because it's still just a constant
+representing this reaction okay i just
+
+ align:start position:0%
+representing this reaction okay i just
+ 
+
+ align:start position:0%
+representing this reaction okay i just
+wanted to make this super clear because
+
+ align:start position:0%
+wanted to make this super clear because
+ 
+
+ align:start position:0%
+wanted to make this super clear because
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+part leads to confusion often that this
+
+ align:start position:0%
+part leads to confusion often that this
+ 
+
+ align:start position:0%
+part leads to confusion often that this
+gets left
+
+ align:start position:0%
+gets left
+ 
+
+ align:start position:0%
+gets left
+out because it's constant doesn't change
+
+ align:start position:0%
+out because it's constant doesn't change
+ 
+
+ align:start position:0%
+out because it's constant doesn't change
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good now we get to that because
+
+ align:start position:0%
+good now we get to that because
+ 
+
+ align:start position:0%
+good now we get to that because
+this is a constant okay so what does
+
+ align:start position:0%
+this is a constant okay so what does
+ 
+
+ align:start position:0%
+this is a constant okay so what does
+that mean
+
+ align:start position:0%
+that mean
+ 
+
+ align:start position:0%
+that mean
+well it means that if i dissolve this
+
+ align:start position:0%
+well it means that if i dissolve this
+ 
+
+ align:start position:0%
+well it means that if i dissolve this
+thing in water
+
+ align:start position:0%
+thing in water
+ 
+
+ align:start position:0%
+thing in water
+right then then the equilibrium the
+
+ align:start position:0%
+right then then the equilibrium the
+ 
+
+ align:start position:0%
+right then then the equilibrium the
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+is is a fixed number this equilibrium
+
+ align:start position:0%
+is is a fixed number this equilibrium
+ 
+
+ align:start position:0%
+is is a fixed number this equilibrium
+product is fixed
+
+ align:start position:0%
+product is fixed
+ 
+
+ align:start position:0%
+product is fixed
+and that has a very important meaning
+
+ align:start position:0%
+and that has a very important meaning
+ 
+
+ align:start position:0%
+and that has a very important meaning
+it's the green curve
+
+ align:start position:0%
+it's the green curve
+ 
+
+ align:start position:0%
+it's the green curve
+you see it says equilibrium right and
+
+ align:start position:0%
+you see it says equilibrium right and
+ 
+
+ align:start position:0%
+you see it says equilibrium right and
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+that what that means is that if i you
+
+ align:start position:0%
+that what that means is that if i you
+ 
+
+ align:start position:0%
+that what that means is that if i you
+know if i'm at point b well there i go
+
+ align:start position:0%
+know if i'm at point b well there i go
+ 
+
+ align:start position:0%
+know if i'm at point b well there i go
+i've got my we we said ksp
+
+ align:start position:0%
+i've got my we we said ksp
+ 
+
+ align:start position:0%
+i've got my we we said ksp
+ksp for this one equals
+
+ align:start position:0%
+ksp for this one equals
+ 
+
+ align:start position:0%
+ksp for this one equals
+uh what was it 1.7
+
+ align:start position:0%
+uh what was it 1.7
+ 
+
+ align:start position:0%
+uh what was it 1.7
+times 10 to the minus 10th
+
+ align:start position:0%
+times 10 to the minus 10th
+ 
+
+ align:start position:0%
+times 10 to the minus 10th
+units are coming and so now so that's
+
+ align:start position:0%
+units are coming and so now so that's
+ 
+
+ align:start position:0%
+units are coming and so now so that's
+the ksp
+
+ align:start position:0%
+the ksp
+ 
+
+ align:start position:0%
+the ksp
+for uh for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+silver chloride
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in h2o oh and you have to say
+
+ align:start position:0%
+in h2o oh and you have to say
+ 
+
+ align:start position:0%
+in h2o oh and you have to say
+at some temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it will depend on temperature often you
+
+ align:start position:0%
+it will depend on temperature often you
+ 
+
+ align:start position:0%
+it will depend on temperature often you
+often will just
+
+ align:start position:0%
+often will just
+ 
+
+ align:start position:0%
+often will just
+be at room temperature 25 c for example
+
+ align:start position:0%
+be at room temperature 25 c for example
+ 
+
+ align:start position:0%
+be at room temperature 25 c for example
+so often these get quoted just at room
+
+ align:start position:0%
+so often these get quoted just at room
+ 
+
+ align:start position:0%
+so often these get quoted just at room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+okay now okay so once i know that then i
+
+ align:start position:0%
+okay now okay so once i know that then i
+ 
+
+ align:start position:0%
+okay now okay so once i know that then i
+know that that's equilibrium no matter
+
+ align:start position:0%
+know that that's equilibrium no matter
+ 
+
+ align:start position:0%
+know that that's equilibrium no matter
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+right and so that means that if like you
+
+ align:start position:0%
+right and so that means that if like you
+ 
+
+ align:start position:0%
+right and so that means that if like you
+know and then we solve this we said well
+
+ align:start position:0%
+know and then we solve this we said well
+ 
+
+ align:start position:0%
+know and then we solve this we said well
+okay if i dissolve silver chloride
+
+ align:start position:0%
+okay if i dissolve silver chloride
+ 
+
+ align:start position:0%
+okay if i dissolve silver chloride
+and i didn't and i had nothing else then
+
+ align:start position:0%
+and i didn't and i had nothing else then
+ 
+
+ align:start position:0%
+and i didn't and i had nothing else then
+you know the ksp would equal
+
+ align:start position:0%
+you know the ksp would equal
+ 
+
+ align:start position:0%
+you know the ksp would equal
+the concentration of silver times the
+
+ align:start position:0%
+the concentration of silver times the
+ 
+
+ align:start position:0%
+the concentration of silver times the
+concentration of chlorine ions
+
+ align:start position:0%
+concentration of chlorine ions
+ 
+
+ align:start position:0%
+concentration of chlorine ions
+and so if we let each one but those are
+
+ align:start position:0%
+and so if we let each one but those are
+ 
+
+ align:start position:0%
+and so if we let each one but those are
+equal and so if we let each one of them
+
+ align:start position:0%
+equal and so if we let each one of them
+ 
+
+ align:start position:0%
+equal and so if we let each one of them
+be x then it's equal to x squared
+
+ align:start position:0%
+be x then it's equal to x squared
+ 
+
+ align:start position:0%
+be x then it's equal to x squared
+and so we know that the concentration of
+
+ align:start position:0%
+and so we know that the concentration of
+ 
+
+ align:start position:0%
+and so we know that the concentration of
+each of them
+
+ align:start position:0%
+each of them
+ 
+
+ align:start position:0%
+each of them
+is 10 to the minus
+
+ align:start position:0%
+is 10 to the minus
+ 
+
+ align:start position:0%
+is 10 to the minus
+let me write it exactly 1.3 times 10
+
+ align:start position:0%
+let me write it exactly 1.3 times 10
+ 
+
+ align:start position:0%
+let me write it exactly 1.3 times 10
+to the minus fifth now it's a
+
+ align:start position:0%
+to the minus fifth now it's a
+ 
+
+ align:start position:0%
+to the minus fifth now it's a
+concentration so you know
+
+ align:start position:0%
+concentration so you know
+ 
+
+ align:start position:0%
+concentration so you know
+that it's got to be capital m moles per
+
+ align:start position:0%
+that it's got to be capital m moles per
+ 
+
+ align:start position:0%
+that it's got to be capital m moles per
+liter
+
+ align:start position:0%
+liter
+ 
+
+ align:start position:0%
+liter
+and and since that's the case since
+
+ align:start position:0%
+and and since that's the case since
+ 
+
+ align:start position:0%
+and and since that's the case since
+that's where you know
+
+ align:start position:0%
+that's where you know
+ 
+
+ align:start position:0%
+that's where you know
+what it is then now you can back up
+
+ align:start position:0%
+what it is then now you can back up
+ 
+
+ align:start position:0%
+what it is then now you can back up
+because this is the concentration
+
+ align:start position:0%
+because this is the concentration
+ 
+
+ align:start position:0%
+because this is the concentration
+of ag ions and it's also the
+
+ align:start position:0%
+of ag ions and it's also the
+ 
+
+ align:start position:0%
+of ag ions and it's also the
+concentration of chlorine ions
+
+ align:start position:0%
+concentration of chlorine ions
+ 
+
+ align:start position:0%
+concentration of chlorine ions
+then you know that the the units of ksp
+
+ align:start position:0%
+then you know that the the units of ksp
+ 
+
+ align:start position:0%
+then you know that the the units of ksp
+must be m squared right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+units in this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moles per liter square must be because
+
+ align:start position:0%
+moles per liter square must be because
+ 
+
+ align:start position:0%
+moles per liter square must be because
+otherwise the concentration isn't right
+
+ align:start position:0%
+otherwise the concentration isn't right
+ 
+
+ align:start position:0%
+otherwise the concentration isn't right
+the units are concentration okay now now
+
+ align:start position:0%
+the units are concentration okay now now
+ 
+
+ align:start position:0%
+the units are concentration okay now now
+okay now we're going to play with this
+
+ align:start position:0%
+okay now we're going to play with this
+ 
+
+ align:start position:0%
+okay now we're going to play with this
+so okay so i'm at b i'm at point b
+
+ align:start position:0%
+so okay so i'm at b i'm at point b
+ 
+
+ align:start position:0%
+so okay so i'm at b i'm at point b
+you see that there i am and i've got my
+
+ align:start position:0%
+you see that there i am and i've got my
+ 
+
+ align:start position:0%
+you see that there i am and i've got my
+concentration of chlorine
+
+ align:start position:0%
+concentration of chlorine
+ 
+
+ align:start position:0%
+concentration of chlorine
+concentration of silver and i'm here and
+
+ align:start position:0%
+concentration of silver and i'm here and
+ 
+
+ align:start position:0%
+concentration of silver and i'm here and
+and so that's 1.3 times 10 to minus 5th
+
+ align:start position:0%
+and so that's 1.3 times 10 to minus 5th
+ 
+
+ align:start position:0%
+and so that's 1.3 times 10 to minus 5th
+okay now if i if i didn't have as much
+
+ align:start position:0%
+okay now if i if i didn't have as much
+ 
+
+ align:start position:0%
+okay now if i if i didn't have as much
+if i didn't if i weren't at the
+
+ align:start position:0%
+if i didn't if i weren't at the
+ 
+
+ align:start position:0%
+if i didn't if i weren't at the
+saturation point
+
+ align:start position:0%
+saturation point
+ 
+
+ align:start position:0%
+saturation point
+right then i could add more i'd be here
+
+ align:start position:0%
+right then i could add more i'd be here
+ 
+
+ align:start position:0%
+right then i could add more i'd be here
+and i could add more solid silver
+
+ align:start position:0%
+and i could add more solid silver
+ 
+
+ align:start position:0%
+and i could add more solid silver
+chloride and i didn't you know and
+
+ align:start position:0%
+chloride and i didn't you know and
+ 
+
+ align:start position:0%
+chloride and i didn't you know and
+eventually i'd reach this uh
+
+ align:start position:0%
+eventually i'd reach this uh
+ 
+
+ align:start position:0%
+eventually i'd reach this uh
+i'd reach this this equilibrium but if i
+
+ align:start position:0%
+i'd reach this this equilibrium but if i
+ 
+
+ align:start position:0%
+i'd reach this this equilibrium but if i
+added more than that
+
+ align:start position:0%
+added more than that
+ 
+
+ align:start position:0%
+added more than that
+so now i'm adding way more than i can
+
+ align:start position:0%
+so now i'm adding way more than i can
+ 
+
+ align:start position:0%
+so now i'm adding way more than i can
+then it's just going to be a solid
+
+ align:start position:0%
+then it's just going to be a solid
+ 
+
+ align:start position:0%
+then it's just going to be a solid
+and that's kind of boring so now i'm up
+
+ align:start position:0%
+and that's kind of boring so now i'm up
+ 
+
+ align:start position:0%
+and that's kind of boring so now i'm up
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+but maybe i had ions in so these are the
+
+ align:start position:0%
+but maybe i had ions in so these are the
+ 
+
+ align:start position:0%
+but maybe i had ions in so these are the
+ions so maybe i add a whole bunch of
+
+ align:start position:0%
+ions so maybe i add a whole bunch of
+ 
+
+ align:start position:0%
+ions so maybe i add a whole bunch of
+ions well they're just going to
+
+ align:start position:0%
+ions well they're just going to
+ 
+
+ align:start position:0%
+ions well they're just going to
+precipitate i can't be here
+
+ align:start position:0%
+precipitate i can't be here
+ 
+
+ align:start position:0%
+precipitate i can't be here
+and be in equilibrium that's the point
+
+ align:start position:0%
+and be in equilibrium that's the point
+ 
+
+ align:start position:0%
+and be in equilibrium that's the point
+of the green curve this k
+
+ align:start position:0%
+of the green curve this k
+ 
+
+ align:start position:0%
+of the green curve this k
+doesn't change this k is is this k
+
+ align:start position:0%
+doesn't change this k is is this k
+ 
+
+ align:start position:0%
+doesn't change this k is is this k
+that's what the green curve is it is
+
+ align:start position:0%
+that's what the green curve is it is
+ 
+
+ align:start position:0%
+that's what the green curve is it is
+that being constant
+
+ align:start position:0%
+that being constant
+ 
+
+ align:start position:0%
+that being constant
+that's very important that is
+
+ align:start position:0%
+that's very important that is
+ 
+
+ align:start position:0%
+that's very important that is
+equilibrium now
+
+ align:start position:0%
+equilibrium now
+ 
+
+ align:start position:0%
+equilibrium now
+there is a way though to move around on
+
+ align:start position:0%
+there is a way though to move around on
+ 
+
+ align:start position:0%
+there is a way though to move around on
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+yeah because if i did imagine now look
+
+ align:start position:0%
+yeah because if i did imagine now look
+ 
+
+ align:start position:0%
+yeah because if i did imagine now look
+at point c
+
+ align:start position:0%
+at point c
+ 
+
+ align:start position:0%
+at point c
+now imagine now that i've i've found
+
+ align:start position:0%
+now imagine now that i've i've found
+ 
+
+ align:start position:0%
+now imagine now that i've i've found
+some source of chlorine ions
+
+ align:start position:0%
+some source of chlorine ions
+ 
+
+ align:start position:0%
+some source of chlorine ions
+and i add a whole bunch of them
+
+ align:start position:0%
+and i add a whole bunch of them
+ 
+
+ align:start position:0%
+and i add a whole bunch of them
+right a whole bunch of them into this
+
+ align:start position:0%
+right a whole bunch of them into this
+ 
+
+ align:start position:0%
+right a whole bunch of them into this
+solution i don't add silver
+
+ align:start position:0%
+solution i don't add silver
+ 
+
+ align:start position:0%
+solution i don't add silver
+and chlorine together i just add
+
+ align:start position:0%
+and chlorine together i just add
+ 
+
+ align:start position:0%
+and chlorine together i just add
+chlorine well you can see what's going
+
+ align:start position:0%
+chlorine well you can see what's going
+ 
+
+ align:start position:0%
+chlorine well you can see what's going
+to happen
+
+ align:start position:0%
+to happen
+ 
+
+ align:start position:0%
+to happen
+i have to get to equilibrium and so in
+
+ align:start position:0%
+i have to get to equilibrium and so in
+ 
+
+ align:start position:0%
+i have to get to equilibrium and so in
+order to stay
+
+ align:start position:0%
+order to stay
+ 
+
+ align:start position:0%
+order to stay
+in equilibrium for silver chloride in
+
+ align:start position:0%
+in equilibrium for silver chloride in
+ 
+
+ align:start position:0%
+in equilibrium for silver chloride in
+solution then
+
+ align:start position:0%
+solution then
+ 
+
+ align:start position:0%
+solution then
+i must lower my concentration of silver
+
+ align:start position:0%
+i must lower my concentration of silver
+ 
+
+ align:start position:0%
+i must lower my concentration of silver
+because i added all this chlorine right
+
+ align:start position:0%
+because i added all this chlorine right
+ 
+
+ align:start position:0%
+because i added all this chlorine right
+well the only way to do that
+
+ align:start position:0%
+well the only way to do that
+ 
+
+ align:start position:0%
+well the only way to do that
+is to eat up some silver and precipitate
+
+ align:start position:0%
+is to eat up some silver and precipitate
+ 
+
+ align:start position:0%
+is to eat up some silver and precipitate
+that's the only way to do that and that
+
+ align:start position:0%
+that's the only way to do that and that
+ 
+
+ align:start position:0%
+that's the only way to do that and that
+has a name
+
+ align:start position:0%
+has a name
+ 
+
+ align:start position:0%
+has a name
+and that's what i want to talk about
+
+ align:start position:0%
+and that's what i want to talk about
+ 
+
+ align:start position:0%
+and that's what i want to talk about
+next that is called
+
+ align:start position:0%
+next that is called
+ 
+
+ align:start position:0%
+next that is called
+the common ion effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is an example this
+
+ align:start position:0%
+now this is an example this
+ 
+
+ align:start position:0%
+now this is an example this
+is an example of a broader principle
+
+ align:start position:0%
+is an example of a broader principle
+ 
+
+ align:start position:0%
+is an example of a broader principle
+which is which i mentioned monday which
+
+ align:start position:0%
+which is which i mentioned monday which
+ 
+
+ align:start position:0%
+which is which i mentioned monday which
+is le chatelier's principle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is that position of
+
+ align:start position:0%
+and that is that position of
+ 
+
+ align:start position:0%
+and that is that position of
+position of equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will move it's still equilibrium but
+
+ align:start position:0%
+will move it's still equilibrium but
+ 
+
+ align:start position:0%
+will move it's still equilibrium but
+it's moving
+
+ align:start position:0%
+it's moving
+ 
+
+ align:start position:0%
+it's moving
+on that green curve right to counteract
+
+ align:start position:0%
+on that green curve right to counteract
+ 
+
+ align:start position:0%
+on that green curve right to counteract
+change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a very uh
+
+ align:start position:0%
+this is a very uh
+ 
+
+ align:start position:0%
+this is a very uh
+general principle it applies to many
+
+ align:start position:0%
+general principle it applies to many
+ 
+
+ align:start position:0%
+general principle it applies to many
+many things it's
+
+ align:start position:0%
+many things it's
+ 
+
+ align:start position:0%
+many things it's
+done not just concentrations it applies
+
+ align:start position:0%
+done not just concentrations it applies
+ 
+
+ align:start position:0%
+done not just concentrations it applies
+to changes in pressure
+
+ align:start position:0%
+to changes in pressure
+ 
+
+ align:start position:0%
+to changes in pressure
+and other changes that you can make in a
+
+ align:start position:0%
+and other changes that you can make in a
+ 
+
+ align:start position:0%
+and other changes that you can make in a
+system here we care about concentration
+
+ align:start position:0%
+system here we care about concentration
+ 
+
+ align:start position:0%
+system here we care about concentration
+and in this particular case we're going
+
+ align:start position:0%
+and in this particular case we're going
+ 
+
+ align:start position:0%
+and in this particular case we're going
+to see it for what happens when you add
+
+ align:start position:0%
+to see it for what happens when you add
+ 
+
+ align:start position:0%
+to see it for what happens when you add
+ions right of one particular type
+
+ align:start position:0%
+ions right of one particular type
+ 
+
+ align:start position:0%
+ions right of one particular type
+and not the other that's the common ion
+
+ align:start position:0%
+and not the other that's the common ion
+ 
+
+ align:start position:0%
+and not the other that's the common ion
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+but it's a very general effect that it
+
+ align:start position:0%
+but it's a very general effect that it
+ 
+
+ align:start position:0%
+but it's a very general effect that it
+resists the change
+
+ align:start position:0%
+resists the change
+ 
+
+ align:start position:0%
+resists the change
+now let's see how that works
+
+ align:start position:0%
+now let's see how that works
+ 
+
+ align:start position:0%
+now let's see how that works
+my if i um if i want a source of ions
+
+ align:start position:0%
+my if i um if i want a source of ions
+ 
+
+ align:start position:0%
+my if i um if i want a source of ions
+let's say i want a source of chlorine
+
+ align:start position:0%
+let's say i want a source of chlorine
+ 
+
+ align:start position:0%
+let's say i want a source of chlorine
+one way would be to add a whole bunch of
+
+ align:start position:0%
+one way would be to add a whole bunch of
+ 
+
+ align:start position:0%
+one way would be to add a whole bunch of
+sodium chloride
+
+ align:start position:0%
+sodium chloride
+ 
+
+ align:start position:0%
+sodium chloride
+right so let's suppose that i have
+
+ align:start position:0%
+right so let's suppose that i have
+ 
+
+ align:start position:0%
+right so let's suppose that i have
+um okay so i'm going to add
+
+ align:start position:0%
+um okay so i'm going to add
+ 
+
+ align:start position:0%
+um okay so i'm going to add
+as an example i'm going to add
+
+ align:start position:0%
+as an example i'm going to add
+ 
+
+ align:start position:0%
+as an example i'm going to add
+to this nice equilibrium that i reached
+
+ align:start position:0%
+to this nice equilibrium that i reached
+ 
+
+ align:start position:0%
+to this nice equilibrium that i reached
+here so i'm at point b
+
+ align:start position:0%
+here so i'm at point b
+ 
+
+ align:start position:0%
+here so i'm at point b
+okay and i'm going to add
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.1 mol
+
+ align:start position:0%
+0.1 mol
+ 
+
+ align:start position:0%
+0.1 mol
+moles per liter of sodium chloride
+
+ align:start position:0%
+moles per liter of sodium chloride
+ 
+
+ align:start position:0%
+moles per liter of sodium chloride
+and this nearly
+
+ align:start position:0%
+and this nearly
+ 
+
+ align:start position:0%
+and this nearly
+and so we're going to say it does it
+
+ align:start position:0%
+and so we're going to say it does it
+ 
+
+ align:start position:0%
+and so we're going to say it does it
+nearly fully dissociates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll be talking about that later
+
+ align:start position:0%
+and we'll be talking about that later
+ 
+
+ align:start position:0%
+and we'll be talking about that later
+today and so that means that that this
+
+ align:start position:0%
+today and so that means that that this
+ 
+
+ align:start position:0%
+today and so that means that that this
+goes nacl
+
+ align:start position:0%
+goes nacl
+ 
+
+ align:start position:0%
+goes nacl
+basically goes to na plus plus cl minus
+
+ align:start position:0%
+basically goes to na plus plus cl minus
+ 
+
+ align:start position:0%
+basically goes to na plus plus cl minus
+both in solution so if i put point
+
+ align:start position:0%
+both in solution so if i put point
+ 
+
+ align:start position:0%
+both in solution so if i put point
+if i put 0.1 moles per liter of sodium
+
+ align:start position:0%
+if i put 0.1 moles per liter of sodium
+ 
+
+ align:start position:0%
+if i put 0.1 moles per liter of sodium
+chloride into this
+
+ align:start position:0%
+chloride into this
+ 
+
+ align:start position:0%
+chloride into this
+into this uh container of the silver
+
+ align:start position:0%
+into this uh container of the silver
+ 
+
+ align:start position:0%
+into this uh container of the silver
+chloride
+
+ align:start position:0%
+chloride
+ 
+
+ align:start position:0%
+chloride
+i'm basically going to get point one
+
+ align:start position:0%
+i'm basically going to get point one
+ 
+
+ align:start position:0%
+i'm basically going to get point one
+because of the stoichiometric
+
+ align:start position:0%
+because of the stoichiometric
+ 
+
+ align:start position:0%
+because of the stoichiometric
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+one one one right yeah so if i put .1
+
+ align:start position:0%
+one one one right yeah so if i put .1
+ 
+
+ align:start position:0%
+one one one right yeah so if i put .1
+moles per liter of this i'm going to
+
+ align:start position:0%
+moles per liter of this i'm going to
+ 
+
+ align:start position:0%
+moles per liter of this i'm going to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+0.1 moles per liter of chlorine ions
+
+ align:start position:0%
+0.1 moles per liter of chlorine ions
+ 
+
+ align:start position:0%
+0.1 moles per liter of chlorine ions
+that i just dumped into the container
+
+ align:start position:0%
+that i just dumped into the container
+ 
+
+ align:start position:0%
+that i just dumped into the container
+but the sodium doesn't it the sodium is
+
+ align:start position:0%
+but the sodium doesn't it the sodium is
+ 
+
+ align:start position:0%
+but the sodium doesn't it the sodium is
+not going to do anything
+
+ align:start position:0%
+not going to do anything
+ 
+
+ align:start position:0%
+not going to do anything
+but it's just look at the chlorine
+
+ align:start position:0%
+but it's just look at the chlorine
+ 
+
+ align:start position:0%
+but it's just look at the chlorine
+that's going to mess
+
+ align:start position:0%
+that's going to mess
+ 
+
+ align:start position:0%
+that's going to mess
+with my equilibrium but k
+
+ align:start position:0%
+with my equilibrium but k
+ 
+
+ align:start position:0%
+with my equilibrium but k
+is a constant so let's see what happens
+
+ align:start position:0%
+is a constant so let's see what happens
+ 
+
+ align:start position:0%
+is a constant so let's see what happens
+we can do it
+
+ align:start position:0%
+we can do it
+ 
+
+ align:start position:0%
+we can do it
+we can do it visually but we can also do
+
+ align:start position:0%
+we can do it visually but we can also do
+ 
+
+ align:start position:0%
+we can do it visually but we can also do
+it back when we use the ice table
+
+ align:start position:0%
+it back when we use the ice table
+ 
+
+ align:start position:0%
+it back when we use the ice table
+right so so now we're going to go ice
+
+ align:start position:0%
+right so so now we're going to go ice
+ 
+
+ align:start position:0%
+right so so now we're going to go ice
+again a g
+
+ align:start position:0%
+again a g
+ 
+
+ align:start position:0%
+again a g
+c l and here's uh
+
+ align:start position:0%
+c l and here's uh
+ 
+
+ align:start position:0%
+c l and here's uh
+a g plus okay and here's
+
+ align:start position:0%
+a g plus okay and here's
+ 
+
+ align:start position:0%
+a g plus okay and here's
+c l minus so now i've added the okay so
+
+ align:start position:0%
+c l minus so now i've added the okay so
+ 
+
+ align:start position:0%
+c l minus so now i've added the okay so
+my initial
+
+ align:start position:0%
+my initial
+ 
+
+ align:start position:0%
+my initial
+is that this is solid remember it's it's
+
+ align:start position:0%
+is that this is solid remember it's it's
+ 
+
+ align:start position:0%
+is that this is solid remember it's it's
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+the solid of the that i'm putting in
+
+ align:start position:0%
+the solid of the that i'm putting in
+ 
+
+ align:start position:0%
+the solid of the that i'm putting in
+there and then i
+
+ align:start position:0%
+there and then i
+ 
+
+ align:start position:0%
+there and then i
+i started my initial is that i started
+
+ align:start position:0%
+i started my initial is that i started
+ 
+
+ align:start position:0%
+i started my initial is that i started
+in that nice equilibrium at point b
+
+ align:start position:0%
+in that nice equilibrium at point b
+ 
+
+ align:start position:0%
+in that nice equilibrium at point b
+so i've got 1.3 times 10 to the minus
+
+ align:start position:0%
+so i've got 1.3 times 10 to the minus
+ 
+
+ align:start position:0%
+so i've got 1.3 times 10 to the minus
+fifth
+
+ align:start position:0%
+fifth
+ 
+
+ align:start position:0%
+fifth
+and over here i've got the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now the change now the change
+
+ align:start position:0%
+but now the change now the change
+ 
+
+ align:start position:0%
+but now the change now the change
+we're gonna add okay so we're gonna add
+
+ align:start position:0%
+we're gonna add okay so we're gonna add
+ 
+
+ align:start position:0%
+we're gonna add okay so we're gonna add
+some chlorine ions 0.1
+
+ align:start position:0%
+some chlorine ions 0.1
+ 
+
+ align:start position:0%
+some chlorine ions 0.1
+so i've added 0.1 moles per liter of
+
+ align:start position:0%
+so i've added 0.1 moles per liter of
+ 
+
+ align:start position:0%
+so i've added 0.1 moles per liter of
+chlorine ions from the salt
+
+ align:start position:0%
+chlorine ions from the salt
+ 
+
+ align:start position:0%
+chlorine ions from the salt
+from sodium chloride yeah but now some
+
+ align:start position:0%
+from sodium chloride yeah but now some
+ 
+
+ align:start position:0%
+from sodium chloride yeah but now some
+of that is going to
+
+ align:start position:0%
+of that is going to
+ 
+
+ align:start position:0%
+of that is going to
+react because as i just said le
+
+ align:start position:0%
+react because as i just said le
+ 
+
+ align:start position:0%
+react because as i just said le
+chatelier's principle tells me that now
+
+ align:start position:0%
+chatelier's principle tells me that now
+ 
+
+ align:start position:0%
+chatelier's principle tells me that now
+there's it's got to counter that and you
+
+ align:start position:0%
+there's it's got to counter that and you
+ 
+
+ align:start position:0%
+there's it's got to counter that and you
+can see it right here too
+
+ align:start position:0%
+can see it right here too
+ 
+
+ align:start position:0%
+can see it right here too
+i'm adding a whole bunch of chlorine so
+
+ align:start position:0%
+i'm adding a whole bunch of chlorine so
+ 
+
+ align:start position:0%
+i'm adding a whole bunch of chlorine so
+i'm going look at how far i'm going out
+
+ align:start position:0%
+i'm going look at how far i'm going out
+ 
+
+ align:start position:0%
+i'm going look at how far i'm going out
+point one that's like literally all the
+
+ align:start position:0%
+point one that's like literally all the
+ 
+
+ align:start position:0%
+point one that's like literally all the
+way out to here
+
+ align:start position:0%
+way out to here
+ 
+
+ align:start position:0%
+way out to here
+and so and so the amount of silver has
+
+ align:start position:0%
+and so and so the amount of silver has
+ 
+
+ align:start position:0%
+and so and so the amount of silver has
+got to go down
+
+ align:start position:0%
+got to go down
+ 
+
+ align:start position:0%
+got to go down
+and what's going to happen is it's going
+
+ align:start position:0%
+and what's going to happen is it's going
+ 
+
+ align:start position:0%
+and what's going to happen is it's going
+to consume
+
+ align:start position:0%
+to consume
+ 
+
+ align:start position:0%
+to consume
+some of the silver and form precipitate
+
+ align:start position:0%
+some of the silver and form precipitate
+ 
+
+ align:start position:0%
+some of the silver and form precipitate
+to counter
+
+ align:start position:0%
+to counter
+ 
+
+ align:start position:0%
+to counter
+all this addition it's going to run the
+
+ align:start position:0%
+all this addition it's going to run the
+ 
+
+ align:start position:0%
+all this addition it's going to run the
+reaction the other way
+
+ align:start position:0%
+reaction the other way
+ 
+
+ align:start position:0%
+reaction the other way
+so it's going to lose a little bit there
+
+ align:start position:0%
+so it's going to lose a little bit there
+ 
+
+ align:start position:0%
+so it's going to lose a little bit there
+from the point 1 that's going to react
+
+ align:start position:0%
+from the point 1 that's going to react
+ 
+
+ align:start position:0%
+from the point 1 that's going to react
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+the silver ions so that's going to also
+
+ align:start position:0%
+the silver ions so that's going to also
+ 
+
+ align:start position:0%
+the silver ions so that's going to also
+lose and this is going to gain
+
+ align:start position:0%
+lose and this is going to gain
+ 
+
+ align:start position:0%
+lose and this is going to gain
+that's how much that's going to get so
+
+ align:start position:0%
+that's how much that's going to get so
+ 
+
+ align:start position:0%
+that's how much that's going to get so
+those are the variables right this is
+
+ align:start position:0%
+those are the variables right this is
+ 
+
+ align:start position:0%
+those are the variables right this is
+the ice table
+
+ align:start position:0%
+the ice table
+ 
+
+ align:start position:0%
+the ice table
+that's how much how much it's going to
+
+ align:start position:0%
+that's how much how much it's going to
+ 
+
+ align:start position:0%
+that's how much how much it's going to
+look these are going to react
+
+ align:start position:0%
+look these are going to react
+ 
+
+ align:start position:0%
+look these are going to react
+to give me some precipitate and so the
+
+ align:start position:0%
+to give me some precipitate and so the
+ 
+
+ align:start position:0%
+to give me some precipitate and so the
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+is more okay more solid
+
+ align:start position:0%
+is more okay more solid
+ 
+
+ align:start position:0%
+is more okay more solid
+forms that's not a good e
+
+ align:start position:0%
+forms that's not a good e
+ 
+
+ align:start position:0%
+forms that's not a good e
+more solid forms and over here it's 1.3
+
+ align:start position:0%
+more solid forms and over here it's 1.3
+ 
+
+ align:start position:0%
+more solid forms and over here it's 1.3
+times 10 to the minus fifth minus x
+
+ align:start position:0%
+times 10 to the minus fifth minus x
+ 
+
+ align:start position:0%
+times 10 to the minus fifth minus x
+and over here it's 0.1 minus x
+
+ align:start position:0%
+and over here it's 0.1 minus x
+ 
+
+ align:start position:0%
+and over here it's 0.1 minus x
+that's the equilibrium condition i've
+
+ align:start position:0%
+that's the equilibrium condition i've
+ 
+
+ align:start position:0%
+that's the equilibrium condition i've
+added in a common ion this is the common
+
+ align:start position:0%
+added in a common ion this is the common
+ 
+
+ align:start position:0%
+added in a common ion this is the common
+ion effect
+
+ align:start position:0%
+ion effect
+ 
+
+ align:start position:0%
+ion effect
+and so now if you do the math
+
+ align:start position:0%
+and so now if you do the math
+ 
+
+ align:start position:0%
+and so now if you do the math
+then what happens
+
+ align:start position:0%
+then what happens
+ 
+
+ align:start position:0%
+then what happens
+well again ksp
+
+ align:start position:0%
+well again ksp
+ 
+
+ align:start position:0%
+well again ksp
+is the same it's the equilibrium
+
+ align:start position:0%
+is the same it's the equilibrium
+ 
+
+ align:start position:0%
+is the same it's the equilibrium
+constant so it's the constant
+
+ align:start position:0%
+constant so it's the constant
+ 
+
+ align:start position:0%
+constant so it's the constant
+so that is going to be the same value
+
+ align:start position:0%
+so that is going to be the same value
+ 
+
+ align:start position:0%
+so that is going to be the same value
+it's going to be 1.7
+
+ align:start position:0%
+it's going to be 1.7
+ 
+
+ align:start position:0%
+it's going to be 1.7
+times 10 to the minus 10th but you see
+
+ align:start position:0%
+times 10 to the minus 10th but you see
+ 
+
+ align:start position:0%
+times 10 to the minus 10th but you see
+ksp
+
+ align:start position:0%
+ksp
+ 
+
+ align:start position:0%
+ksp
+is also equal to the concentration in
+
+ align:start position:0%
+is also equal to the concentration in
+ 
+
+ align:start position:0%
+is also equal to the concentration in
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+of the silver ions times the
+
+ align:start position:0%
+of the silver ions times the
+ 
+
+ align:start position:0%
+of the silver ions times the
+concentration of the chlorine ion so
+
+ align:start position:0%
+concentration of the chlorine ion so
+ 
+
+ align:start position:0%
+concentration of the chlorine ion so
+it's going to be
+
+ align:start position:0%
+it's going to be
+ 
+
+ align:start position:0%
+it's going to be
+0.1 minus x times 1.3
+
+ align:start position:0%
+0.1 minus x times 1.3
+ 
+
+ align:start position:0%
+0.1 minus x times 1.3
+times 10 to the fifth minus x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we don't like doing all this
+
+ align:start position:0%
+and then we don't like doing all this
+ 
+
+ align:start position:0%
+and then we don't like doing all this
+math and so we simplify
+
+ align:start position:0%
+math and so we simplify
+ 
+
+ align:start position:0%
+math and so we simplify
+then we can simplify because look
+
+ align:start position:0%
+then we can simplify because look
+ 
+
+ align:start position:0%
+then we can simplify because look
+you started with silver ions in a very
+
+ align:start position:0%
+you started with silver ions in a very
+ 
+
+ align:start position:0%
+you started with silver ions in a very
+small concentration
+
+ align:start position:0%
+small concentration
+ 
+
+ align:start position:0%
+small concentration
+x can't be you can't take away something
+
+ align:start position:0%
+x can't be you can't take away something
+ 
+
+ align:start position:0%
+x can't be you can't take away something
+you don't have
+
+ align:start position:0%
+you don't have
+ 
+
+ align:start position:0%
+you don't have
+right and and so x has got to be somehow
+
+ align:start position:0%
+right and and so x has got to be somehow
+ 
+
+ align:start position:0%
+right and and so x has got to be somehow
+this or less right and so x is a small
+
+ align:start position:0%
+this or less right and so x is a small
+ 
+
+ align:start position:0%
+this or less right and so x is a small
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+and this is a really big number in
+
+ align:start position:0%
+and this is a really big number in
+ 
+
+ align:start position:0%
+and this is a really big number in
+comparison
+
+ align:start position:0%
+comparison
+ 
+
+ align:start position:0%
+comparison
+and so we like simplifying our lives
+
+ align:start position:0%
+and so we like simplifying our lives
+ 
+
+ align:start position:0%
+and so we like simplifying our lives
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so we we like saying that that's
+
+ align:start position:0%
+and so we we like saying that that's
+ 
+
+ align:start position:0%
+and so we we like saying that that's
+like point one
+
+ align:start position:0%
+like point one
+ 
+
+ align:start position:0%
+like point one
+we know that that'll make the math a lot
+
+ align:start position:0%
+we know that that'll make the math a lot
+ 
+
+ align:start position:0%
+we know that that'll make the math a lot
+easier right
+
+ align:start position:0%
+easier right
+ 
+
+ align:start position:0%
+easier right
+that'll make the math a lot easier and
+
+ align:start position:0%
+that'll make the math a lot easier and
+ 
+
+ align:start position:0%
+that'll make the math a lot easier and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now we can say that this is equal to
+
+ align:start position:0%
+now we can say that this is equal to
+ 
+
+ align:start position:0%
+now we can say that this is equal to
+uh okay 0.1
+
+ align:start position:0%
+uh okay 0.1
+ 
+
+ align:start position:0%
+uh okay 0.1
+times 1.3 times 10 to the minus fifth
+
+ align:start position:0%
+times 1.3 times 10 to the minus fifth
+ 
+
+ align:start position:0%
+times 1.3 times 10 to the minus fifth
+minus x and then we get that x
+
+ align:start position:0%
+minus x and then we get that x
+ 
+
+ align:start position:0%
+minus x and then we get that x
+equals 1.7 times 10 to the minus ninth
+
+ align:start position:0%
+equals 1.7 times 10 to the minus ninth
+ 
+
+ align:start position:0%
+equals 1.7 times 10 to the minus ninth
+that is the common ion effect what i've
+
+ align:start position:0%
+that is the common ion effect what i've
+ 
+
+ align:start position:0%
+that is the common ion effect what i've
+done i've taken this thing in
+
+ align:start position:0%
+done i've taken this thing in
+ 
+
+ align:start position:0%
+done i've taken this thing in
+equilibrium and i've added one of the
+
+ align:start position:0%
+equilibrium and i've added one of the
+ 
+
+ align:start position:0%
+equilibrium and i've added one of the
+ions
+
+ align:start position:0%
+ions
+ 
+
+ align:start position:0%
+ions
+right and and and it changes the
+
+ align:start position:0%
+right and and and it changes the
+ 
+
+ align:start position:0%
+right and and and it changes the
+solubility remember the solubility is
+
+ align:start position:0%
+solubility remember the solubility is
+ 
+
+ align:start position:0%
+solubility remember the solubility is
+what we care about
+
+ align:start position:0%
+what we care about
+ 
+
+ align:start position:0%
+what we care about
+that's what the solubility product the
+
+ align:start position:0%
+that's what the solubility product the
+ 
+
+ align:start position:0%
+that's what the solubility product the
+solubility constant helps us determine
+
+ align:start position:0%
+solubility constant helps us determine
+ 
+
+ align:start position:0%
+solubility constant helps us determine
+and i've literally just changed it by
+
+ align:start position:0%
+and i've literally just changed it by
+ 
+
+ align:start position:0%
+and i've literally just changed it by
+orders of magnitude
+
+ align:start position:0%
+orders of magnitude
+ 
+
+ align:start position:0%
+orders of magnitude
+right because now the the amount that
+
+ align:start position:0%
+right because now the the amount that
+ 
+
+ align:start position:0%
+right because now the the amount that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so this thing precipitates like crazy i
+
+ align:start position:0%
+so this thing precipitates like crazy i
+ 
+
+ align:start position:0%
+so this thing precipitates like crazy i
+added in a little bit of some other ion
+
+ align:start position:0%
+added in a little bit of some other ion
+ 
+
+ align:start position:0%
+added in a little bit of some other ion
+that some other salt that had
+
+ align:start position:0%
+that some other salt that had
+ 
+
+ align:start position:0%
+that some other salt that had
+chlorinitis and all of a sudden silver
+
+ align:start position:0%
+chlorinitis and all of a sudden silver
+ 
+
+ align:start position:0%
+chlorinitis and all of a sudden silver
+chloride precipitates out
+
+ align:start position:0%
+chloride precipitates out
+ 
+
+ align:start position:0%
+chloride precipitates out
+right so here's a video of that so this
+
+ align:start position:0%
+right so here's a video of that so this
+ 
+
+ align:start position:0%
+right so here's a video of that so this
+is kind of cool so watch this is a
+
+ align:start position:0%
+is kind of cool so watch this is a
+ 
+
+ align:start position:0%
+is kind of cool so watch this is a
+an equilibrium container and what i'm
+
+ align:start position:0%
+an equilibrium container and what i'm
+ 
+
+ align:start position:0%
+an equilibrium container and what i'm
+adding is salt
+
+ align:start position:0%
+adding is salt
+ 
+
+ align:start position:0%
+adding is salt
+and look at that what is that that's
+
+ align:start position:0%
+and look at that what is that that's
+ 
+
+ align:start position:0%
+and look at that what is that that's
+silver chloride precipitate
+
+ align:start position:0%
+silver chloride precipitate
+ 
+
+ align:start position:0%
+silver chloride precipitate
+right because the thing has to reach
+
+ align:start position:0%
+right because the thing has to reach
+ 
+
+ align:start position:0%
+right because the thing has to reach
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+and so in order to do so what you do is
+
+ align:start position:0%
+and so in order to do so what you do is
+ 
+
+ align:start position:0%
+and so in order to do so what you do is
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+you suppress the solubility you
+
+ align:start position:0%
+you suppress the solubility you
+ 
+
+ align:start position:0%
+you suppress the solubility you
+literally by adding chlorine the common
+
+ align:start position:0%
+literally by adding chlorine the common
+ 
+
+ align:start position:0%
+literally by adding chlorine the common
+ion effect
+
+ align:start position:0%
+ion effect
+ 
+
+ align:start position:0%
+ion effect
+you suppress the solubility of the
+
+ align:start position:0%
+you suppress the solubility of the
+ 
+
+ align:start position:0%
+you suppress the solubility of the
+silver chloride right
+
+ align:start position:0%
+silver chloride right
+ 
+
+ align:start position:0%
+silver chloride right
+it's pretty cool stuff that is the
+
+ align:start position:0%
+it's pretty cool stuff that is the
+ 
+
+ align:start position:0%
+it's pretty cool stuff that is the
+common ion effect now why does this
+
+ align:start position:0%
+common ion effect now why does this
+ 
+
+ align:start position:0%
+common ion effect now why does this
+matter
+
+ align:start position:0%
+matter
+ 
+
+ align:start position:0%
+matter
+oh let me give you one i'll get to why
+
+ align:start position:0%
+oh let me give you one i'll get to why
+ 
+
+ align:start position:0%
+oh let me give you one i'll get to why
+this matters in a second
+
+ align:start position:0%
+this matters in a second
+ 
+
+ align:start position:0%
+this matters in a second
+one more question so you can now without
+
+ align:start position:0%
+one more question so you can now without
+ 
+
+ align:start position:0%
+one more question so you can now without
+even doing the math
+
+ align:start position:0%
+even doing the math
+ 
+
+ align:start position:0%
+even doing the math
+check this one out this is cool without
+
+ align:start position:0%
+check this one out this is cool without
+ 
+
+ align:start position:0%
+check this one out this is cool without
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+without even doing the math i can take
+
+ align:start position:0%
+without even doing the math i can take
+ 
+
+ align:start position:0%
+without even doing the math i can take
+barium sulfate
+
+ align:start position:0%
+barium sulfate
+ 
+
+ align:start position:0%
+barium sulfate
+okay and from this from the common ion
+
+ align:start position:0%
+okay and from this from the common ion
+ 
+
+ align:start position:0%
+okay and from this from the common ion
+effect so barium sulfate
+
+ align:start position:0%
+effect so barium sulfate
+ 
+
+ align:start position:0%
+effect so barium sulfate
+is going to go so what does that one
+
+ align:start position:0%
+is going to go so what does that one
+ 
+
+ align:start position:0%
+is going to go so what does that one
+look like well it's going to go to be a
+
+ align:start position:0%
+look like well it's going to go to be a
+ 
+
+ align:start position:0%
+look like well it's going to go to be a
+two plus plus so4
+
+ align:start position:0%
+two plus plus so4
+ 
+
+ align:start position:0%
+two plus plus so4
+two minus both in solution in solution
+
+ align:start position:0%
+two minus both in solution in solution
+ 
+
+ align:start position:0%
+two minus both in solution in solution
+dissolved ions this is a solid
+
+ align:start position:0%
+dissolved ions this is a solid
+ 
+
+ align:start position:0%
+dissolved ions this is a solid
+now which here's the question
+
+ align:start position:0%
+now which here's the question
+ 
+
+ align:start position:0%
+now which here's the question
+which of the following will be required
+
+ align:start position:0%
+which of the following will be required
+ 
+
+ align:start position:0%
+which of the following will be required
+in the least amount to dissolve
+
+ align:start position:0%
+in the least amount to dissolve
+ 
+
+ align:start position:0%
+in the least amount to dissolve
+the same amount of ba so4
+
+ align:start position:0%
+the same amount of ba so4
+ 
+
+ align:start position:0%
+the same amount of ba so4
+i don't need any constants or math i can
+
+ align:start position:0%
+i don't need any constants or math i can
+ 
+
+ align:start position:0%
+i don't need any constants or math i can
+use the same principle because
+
+ align:start position:0%
+use the same principle because
+ 
+
+ align:start position:0%
+use the same principle because
+if i had some 0.1 molar or 0.01
+
+ align:start position:0%
+if i had some 0.1 molar or 0.01
+ 
+
+ align:start position:0%
+if i had some 0.1 molar or 0.01
+moles per liter of either of these what
+
+ align:start position:0%
+moles per liter of either of these what
+ 
+
+ align:start position:0%
+moles per liter of either of these what
+are they doing
+
+ align:start position:0%
+are they doing
+ 
+
+ align:start position:0%
+are they doing
+they're serving up ions right in the one
+
+ align:start position:0%
+they're serving up ions right in the one
+ 
+
+ align:start position:0%
+they're serving up ions right in the one
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+you're serving up in one case you're
+
+ align:start position:0%
+you're serving up in one case you're
+ 
+
+ align:start position:0%
+you're serving up in one case you're
+serving up
+
+ align:start position:0%
+serving up
+ 
+
+ align:start position:0%
+serving up
+so in case a you're going to give me
+
+ align:start position:0%
+so in case a you're going to give me
+ 
+
+ align:start position:0%
+so in case a you're going to give me
+what do i have there h2so4
+
+ align:start position:0%
+what do i have there h2so4
+ 
+
+ align:start position:0%
+what do i have there h2so4
+so let's do a first h2so4
+
+ align:start position:0%
+so let's do a first h2so4
+ 
+
+ align:start position:0%
+so let's do a first h2so4
+is going to give me a whole bunch of h
+
+ align:start position:0%
+is going to give me a whole bunch of h
+ 
+
+ align:start position:0%
+is going to give me a whole bunch of h
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+but also so4 2 minus and
+
+ align:start position:0%
+but also so4 2 minus and
+ 
+
+ align:start position:0%
+but also so4 2 minus and
+in case b you have
+
+ align:start position:0%
+in case b you have
+ 
+
+ align:start position:0%
+in case b you have
+uh bacl okay so you have ba
+
+ align:start position:0%
+uh bacl okay so you have ba
+ 
+
+ align:start position:0%
+uh bacl okay so you have ba
+cl2 and if i put that in i've got this
+
+ align:start position:0%
+cl2 and if i put that in i've got this
+ 
+
+ align:start position:0%
+cl2 and if i put that in i've got this
+in water
+
+ align:start position:0%
+in water
+ 
+
+ align:start position:0%
+in water
+right but if i put but if this dissolves
+
+ align:start position:0%
+right but if i put but if this dissolves
+ 
+
+ align:start position:0%
+right but if i put but if this dissolves
+in water a little bit then it's going to
+
+ align:start position:0%
+in water a little bit then it's going to
+ 
+
+ align:start position:0%
+in water a little bit then it's going to
+serve up
+
+ align:start position:0%
+serve up
+ 
+
+ align:start position:0%
+serve up
+some ba 2 plus plus
+
+ align:start position:0%
+some ba 2 plus plus
+ 
+
+ align:start position:0%
+some ba 2 plus plus
+2 cl minus
+
+ align:start position:0%
+2 cl minus
+ 
+
+ align:start position:0%
+2 cl minus
+either way now you know what's going to
+
+ align:start position:0%
+either way now you know what's going to
+ 
+
+ align:start position:0%
+either way now you know what's going to
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+because if i'm trying to dissolve
+
+ align:start position:0%
+because if i'm trying to dissolve
+ 
+
+ align:start position:0%
+because if i'm trying to dissolve
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+and i add any of the ions
+
+ align:start position:0%
+and i add any of the ions
+ 
+
+ align:start position:0%
+and i add any of the ions
+that it's dissolving into from some
+
+ align:start position:0%
+that it's dissolving into from some
+ 
+
+ align:start position:0%
+that it's dissolving into from some
+external source
+
+ align:start position:0%
+external source
+ 
+
+ align:start position:0%
+external source
+it's going to drive it this way it's
+
+ align:start position:0%
+it's going to drive it this way it's
+ 
+
+ align:start position:0%
+it's going to drive it this way it's
+going to precipitate
+
+ align:start position:0%
+going to precipitate
+ 
+
+ align:start position:0%
+going to precipitate
+right so the answer has to be just water
+
+ align:start position:0%
+right so the answer has to be just water
+ 
+
+ align:start position:0%
+right so the answer has to be just water
+stick with pure water in this case
+
+ align:start position:0%
+stick with pure water in this case
+ 
+
+ align:start position:0%
+stick with pure water in this case
+otherwise you're gonna
+
+ align:start position:0%
+otherwise you're gonna
+ 
+
+ align:start position:0%
+otherwise you're gonna
+you're gonna have more trouble
+
+ align:start position:0%
+you're gonna have more trouble
+ 
+
+ align:start position:0%
+you're gonna have more trouble
+dissolving just like we just showed
+
+ align:start position:0%
+dissolving just like we just showed
+ 
+
+ align:start position:0%
+dissolving just like we just showed
+you're gonna have more trouble
+
+ align:start position:0%
+you're gonna have more trouble
+ 
+
+ align:start position:0%
+you're gonna have more trouble
+dissolving not less that's the common
+
+ align:start position:0%
+dissolving not less that's the common
+ 
+
+ align:start position:0%
+dissolving not less that's the common
+ion effect
+
+ align:start position:0%
+ion effect
+ 
+
+ align:start position:0%
+ion effect
+all right now why okay so now why does
+
+ align:start position:0%
+all right now why okay so now why does
+ 
+
+ align:start position:0%
+all right now why okay so now why does
+this matter
+
+ align:start position:0%
+this matter
+ 
+
+ align:start position:0%
+this matter
+why does this matter oh we go back to
+
+ align:start position:0%
+why does this matter oh we go back to
+ 
+
+ align:start position:0%
+why does this matter oh we go back to
+the terror pot
+
+ align:start position:0%
+the terror pot
+ 
+
+ align:start position:0%
+the terror pot
+and by the way i didn't have this link
+
+ align:start position:0%
+and by the way i didn't have this link
+ 
+
+ align:start position:0%
+and by the way i didn't have this link
+and i should have when i showed you the
+
+ align:start position:0%
+and i should have when i showed you the
+ 
+
+ align:start position:0%
+and i should have when i showed you the
+the and this is your goody bag etc right
+
+ align:start position:0%
+the and this is your goody bag etc right
+ 
+
+ align:start position:0%
+the and this is your goody bag etc right
+there's some really nice uh articles
+
+ align:start position:0%
+there's some really nice uh articles
+ 
+
+ align:start position:0%
+there's some really nice uh articles
+here that you can find related to these
+
+ align:start position:0%
+here that you can find related to these
+ 
+
+ align:start position:0%
+here that you can find related to these
+experiments and other things about ocean
+
+ align:start position:0%
+experiments and other things about ocean
+ 
+
+ align:start position:0%
+experiments and other things about ocean
+acidity
+
+ align:start position:0%
+acidity
+ 
+
+ align:start position:0%
+acidity
+and uh in case you're interested um but
+
+ align:start position:0%
+and uh in case you're interested um but
+ 
+
+ align:start position:0%
+and uh in case you're interested um but
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+what we what i did is was that this was
+
+ align:start position:0%
+what we what i did is was that this was
+ 
+
+ align:start position:0%
+what we what i did is was that this was
+my why this matters on monday
+
+ align:start position:0%
+my why this matters on monday
+ 
+
+ align:start position:0%
+my why this matters on monday
+and i wanted to tell you about the
+
+ align:start position:0%
+and i wanted to tell you about the
+ 
+
+ align:start position:0%
+and i wanted to tell you about the
+goodie bag and about
+
+ align:start position:0%
+goodie bag and about
+ 
+
+ align:start position:0%
+goodie bag and about
+the how things dissolve because monday
+
+ align:start position:0%
+the how things dissolve because monday
+ 
+
+ align:start position:0%
+the how things dissolve because monday
+was about
+
+ align:start position:0%
+was about
+ 
+
+ align:start position:0%
+was about
+dissolving right and finding a
+
+ align:start position:0%
+dissolving right and finding a
+ 
+
+ align:start position:0%
+dissolving right and finding a
+saturation point
+
+ align:start position:0%
+saturation point
+ 
+
+ align:start position:0%
+saturation point
+now we can we can get to the next place
+
+ align:start position:0%
+now we can we can get to the next place
+ 
+
+ align:start position:0%
+now we can we can get to the next place
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+why does that matter for the terrapot
+
+ align:start position:0%
+why does that matter for the terrapot
+ 
+
+ align:start position:0%
+why does that matter for the terrapot
+shell
+
+ align:start position:0%
+shell
+ 
+
+ align:start position:0%
+shell
+what is the chemistry that that matters
+
+ align:start position:0%
+what is the chemistry that that matters
+ 
+
+ align:start position:0%
+what is the chemistry that that matters
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay so i made the ocean a little more
+
+ align:start position:0%
+okay so i made the ocean a little more
+ 
+
+ align:start position:0%
+okay so i made the ocean a little more
+acidic
+
+ align:start position:0%
+acidic
+ 
+
+ align:start position:0%
+acidic
+why does that matter but you see now
+
+ align:start position:0%
+why does that matter but you see now
+ 
+
+ align:start position:0%
+why does that matter but you see now
+we're armed with the knowledge we need
+
+ align:start position:0%
+we're armed with the knowledge we need
+ 
+
+ align:start position:0%
+we're armed with the knowledge we need
+to answer that question
+
+ align:start position:0%
+to answer that question
+ 
+
+ align:start position:0%
+to answer that question
+now we're armed with it all we need to
+
+ align:start position:0%
+now we're armed with it all we need to
+ 
+
+ align:start position:0%
+now we're armed with it all we need to
+do as always with everything in life
+
+ align:start position:0%
+do as always with everything in life
+ 
+
+ align:start position:0%
+do as always with everything in life
+is look at the chemistry that's it
+
+ align:start position:0%
+is look at the chemistry that's it
+ 
+
+ align:start position:0%
+is look at the chemistry that's it
+say that at the thanksgiving table
+
+ align:start position:0%
+say that at the thanksgiving table
+ 
+
+ align:start position:0%
+say that at the thanksgiving table
+you'll be very popular
+
+ align:start position:0%
+you'll be very popular
+ 
+
+ align:start position:0%
+you'll be very popular
+we said co2 plus h2o
+
+ align:start position:0%
+we said co2 plus h2o
+ 
+
+ align:start position:0%
+we said co2 plus h2o
+this goes oh
+
+ align:start position:0%
+this goes oh
+ 
+
+ align:start position:0%
+this goes oh
+it finds some equilibrium 2h2
+
+ align:start position:0%
+it finds some equilibrium 2h2
+ 
+
+ align:start position:0%
+it finds some equilibrium 2h2
+co3 now this is called carbonic acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is called carbonic acid there's the
+
+ align:start position:0%
+this is called carbonic acid there's the
+ 
+
+ align:start position:0%
+this is called carbonic acid there's the
+pteropod up there
+
+ align:start position:0%
+pteropod up there
+ 
+
+ align:start position:0%
+pteropod up there
+and there's a reaction that's that's
+
+ align:start position:0%
+and there's a reaction that's that's
+ 
+
+ align:start position:0%
+and there's a reaction that's that's
+really relevant that you'll see from the
+
+ align:start position:0%
+really relevant that you'll see from the
+ 
+
+ align:start position:0%
+really relevant that you'll see from the
+ones we're about to write down why
+
+ align:start position:0%
+ones we're about to write down why
+ 
+
+ align:start position:0%
+ones we're about to write down why
+because the thing is that why what
+
+ align:start position:0%
+because the thing is that why what
+ 
+
+ align:start position:0%
+because the thing is that why what
+happens to carbonic acid
+
+ align:start position:0%
+happens to carbonic acid
+ 
+
+ align:start position:0%
+happens to carbonic acid
+that well carbonic acid also goes
+
+ align:start position:0%
+that well carbonic acid also goes
+ 
+
+ align:start position:0%
+that well carbonic acid also goes
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+a dissolution reaction so carbonic acid
+
+ align:start position:0%
+a dissolution reaction so carbonic acid
+ 
+
+ align:start position:0%
+a dissolution reaction so carbonic acid
+so this is co2
+
+ align:start position:0%
+so this is co2
+ 
+
+ align:start position:0%
+so this is co2
+dissolving in water now we make carbon
+
+ align:start position:0%
+dissolving in water now we make carbon
+ 
+
+ align:start position:0%
+dissolving in water now we make carbon
+so carbonic acid
+
+ align:start position:0%
+so carbonic acid
+ 
+
+ align:start position:0%
+so carbonic acid
+uh goes like this okay
+
+ align:start position:0%
+uh goes like this okay
+ 
+
+ align:start position:0%
+uh goes like this okay
+it goes into h co three minus
+
+ align:start position:0%
+it goes into h co three minus
+ 
+
+ align:start position:0%
+it goes into h co three minus
+plus h plus
+
+ align:start position:0%
+plus h plus
+ 
+
+ align:start position:0%
+plus h plus
+now here's the thing okay what is the
+
+ align:start position:0%
+now here's the thing okay what is the
+ 
+
+ align:start position:0%
+now here's the thing okay what is the
+shell made of
+
+ align:start position:0%
+shell made of
+ 
+
+ align:start position:0%
+shell made of
+well the shell that's dissolving in
+
+ align:start position:0%
+well the shell that's dissolving in
+ 
+
+ align:start position:0%
+well the shell that's dissolving in
+in its you know kind of like the core
+
+ align:start position:0%
+in its you know kind of like the core
+ 
+
+ align:start position:0%
+in its you know kind of like the core
+material is calcium carbonate
+
+ align:start position:0%
+material is calcium carbonate
+ 
+
+ align:start position:0%
+material is calcium carbonate
+so that's caco3
+
+ align:start position:0%
+so that's caco3
+ 
+
+ align:start position:0%
+so that's caco3
+that's the shell and the shell also has
+
+ align:start position:0%
+that's the shell and the shell also has
+ 
+
+ align:start position:0%
+that's the shell and the shell also has
+an equilibrium reaction that happens
+
+ align:start position:0%
+an equilibrium reaction that happens
+ 
+
+ align:start position:0%
+an equilibrium reaction that happens
+the shell of of of a c a creature is in
+
+ align:start position:0%
+the shell of of of a c a creature is in
+ 
+
+ align:start position:0%
+the shell of of of a c a creature is in
+dynamic equilibrium with the ocean
+
+ align:start position:0%
+dynamic equilibrium with the ocean
+ 
+
+ align:start position:0%
+dynamic equilibrium with the ocean
+and and so it's going like this it's
+
+ align:start position:0%
+and and so it's going like this it's
+ 
+
+ align:start position:0%
+and and so it's going like this it's
+going to uh well okay
+
+ align:start position:0%
+going to uh well okay
+ 
+
+ align:start position:0%
+going to uh well okay
+c a two plus and
+
+ align:start position:0%
+c a two plus and
+ 
+
+ align:start position:0%
+c a two plus and
+c o three two minus and
+
+ align:start position:0%
+c o three two minus and
+ 
+
+ align:start position:0%
+c o three two minus and
+and and okay but the thing is it has an
+
+ align:start position:0%
+and and okay but the thing is it has an
+ 
+
+ align:start position:0%
+and and okay but the thing is it has an
+equilibrium constant all these have
+
+ align:start position:0%
+equilibrium constant all these have
+ 
+
+ align:start position:0%
+equilibrium constant all these have
+equilibrium constants
+
+ align:start position:0%
+equilibrium constants
+ 
+
+ align:start position:0%
+equilibrium constants
+so like for example for this one the k
+
+ align:start position:0%
+so like for example for this one the k
+ 
+
+ align:start position:0%
+so like for example for this one the k
+sp
+
+ align:start position:0%
+sp
+ 
+
+ align:start position:0%
+sp
+the solubility product constant because
+
+ align:start position:0%
+the solubility product constant because
+ 
+
+ align:start position:0%
+the solubility product constant because
+this is a solid this is a solid shell
+
+ align:start position:0%
+this is a solid this is a solid shell
+ 
+
+ align:start position:0%
+this is a solid this is a solid shell
+solid going to ions in aqueous solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but so the ksp for that is somewhere
+
+ align:start position:0%
+but so the ksp for that is somewhere
+ 
+
+ align:start position:0%
+but so the ksp for that is somewhere
+around 5
+
+ align:start position:0%
+around 5
+ 
+
+ align:start position:0%
+around 5
+times 10 to the minus 9.
+
+ align:start position:0%
+times 10 to the minus 9.
+ 
+
+ align:start position:0%
+times 10 to the minus 9.
+5 times 10 to the minus 9. yeah but
+
+ align:start position:0%
+5 times 10 to the minus 9. yeah but
+ 
+
+ align:start position:0%
+5 times 10 to the minus 9. yeah but
+here's the thing we just went through
+
+ align:start position:0%
+here's the thing we just went through
+ 
+
+ align:start position:0%
+here's the thing we just went through
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+if i consume one of these or change the
+
+ align:start position:0%
+if i consume one of these or change the
+ 
+
+ align:start position:0%
+if i consume one of these or change the
+concentration of
+
+ align:start position:0%
+concentration of
+ 
+
+ align:start position:0%
+concentration of
+one of these and not the other
+
+ align:start position:0%
+one of these and not the other
+ 
+
+ align:start position:0%
+one of these and not the other
+we just did this if i if i change the
+
+ align:start position:0%
+we just did this if i if i change the
+ 
+
+ align:start position:0%
+we just did this if i if i change the
+concentration if i consume
+
+ align:start position:0%
+concentration if i consume
+ 
+
+ align:start position:0%
+concentration if i consume
+any of these then i might drive the
+
+ align:start position:0%
+any of these then i might drive the
+ 
+
+ align:start position:0%
+any of these then i might drive the
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+consume or produce if i change any of
+
+ align:start position:0%
+consume or produce if i change any of
+ 
+
+ align:start position:0%
+consume or produce if i change any of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+independently i'm going to drive the
+
+ align:start position:0%
+independently i'm going to drive the
+ 
+
+ align:start position:0%
+independently i'm going to drive the
+reaction because that's
+
+ align:start position:0%
+reaction because that's
+ 
+
+ align:start position:0%
+reaction because that's
+how we keep to our k that's what le
+
+ align:start position:0%
+how we keep to our k that's what le
+ 
+
+ align:start position:0%
+how we keep to our k that's what le
+chatelier's principle tells us
+
+ align:start position:0%
+chatelier's principle tells us
+ 
+
+ align:start position:0%
+chatelier's principle tells us
+and so what ends up happening is you've
+
+ align:start position:0%
+and so what ends up happening is you've
+ 
+
+ align:start position:0%
+and so what ends up happening is you've
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+the extra h
+
+ align:start position:0%
+the extra h
+ 
+
+ align:start position:0%
+the extra h
+plus ions so these are ions in solution
+
+ align:start position:0%
+plus ions so these are ions in solution
+ 
+
+ align:start position:0%
+plus ions so these are ions in solution
+where did they come from they came from
+
+ align:start position:0%
+where did they come from they came from
+ 
+
+ align:start position:0%
+where did they come from they came from
+the co2 giving us
+
+ align:start position:0%
+the co2 giving us
+ 
+
+ align:start position:0%
+the co2 giving us
+carbonic acid which then gave us h plus
+
+ align:start position:0%
+carbonic acid which then gave us h plus
+ 
+
+ align:start position:0%
+carbonic acid which then gave us h plus
+those are what i'm talking about
+
+ align:start position:0%
+those are what i'm talking about
+ 
+
+ align:start position:0%
+those are what i'm talking about
+well they react
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the co3 minus
+
+ align:start position:0%
+with the co3 minus
+ 
+
+ align:start position:0%
+with the co3 minus
+3032 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this lowers the co32 minus concentration
+
+ align:start position:0%
+this lowers the co32 minus concentration
+ 
+
+ align:start position:0%
+this lowers the co32 minus concentration
+near the shell right because then tight
+
+ align:start position:0%
+near the shell right because then tight
+ 
+
+ align:start position:0%
+near the shell right because then tight
+and if i lower this because i've taken
+
+ align:start position:0%
+and if i lower this because i've taken
+ 
+
+ align:start position:0%
+and if i lower this because i've taken
+some of this now and i've reacted it
+
+ align:start position:0%
+some of this now and i've reacted it
+ 
+
+ align:start position:0%
+some of this now and i've reacted it
+so now i've got less of it and because
+
+ align:start position:0%
+so now i've got less of it and because
+ 
+
+ align:start position:0%
+so now i've got less of it and because
+of what we just saw if i've got less of
+
+ align:start position:0%
+of what we just saw if i've got less of
+ 
+
+ align:start position:0%
+of what we just saw if i've got less of
+this you're going to drive
+
+ align:start position:0%
+this you're going to drive
+ 
+
+ align:start position:0%
+this you're going to drive
+this way which is going to dissolve
+
+ align:start position:0%
+this way which is going to dissolve
+ 
+
+ align:start position:0%
+this way which is going to dissolve
+more of the shell right that's why this
+
+ align:start position:0%
+more of the shell right that's why this
+ 
+
+ align:start position:0%
+more of the shell right that's why this
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+that's why this this happens
+
+ align:start position:0%
+that's why this this happens
+ 
+
+ align:start position:0%
+that's why this this happens
+works sounds like a positive thing right
+
+ align:start position:0%
+works sounds like a positive thing right
+ 
+
+ align:start position:0%
+works sounds like a positive thing right
+so this lowers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the concentration of co32 minus
+
+ align:start position:0%
+the concentration of co32 minus
+ 
+
+ align:start position:0%
+the concentration of co32 minus
+and that drives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more dissolution
+
+ align:start position:0%
+more dissolution
+ 
+
+ align:start position:0%
+more dissolution
+that is what's happening and we now can
+
+ align:start position:0%
+that is what's happening and we now can
+ 
+
+ align:start position:0%
+that is what's happening and we now can
+understand it in terms of the concepts
+
+ align:start position:0%
+understand it in terms of the concepts
+ 
+
+ align:start position:0%
+understand it in terms of the concepts
+that we've just learned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+historically i mentioned 50 million
+
+ align:start position:0%
+historically i mentioned 50 million
+ 
+
+ align:start position:0%
+historically i mentioned 50 million
+years actually by some accounts it's 300
+
+ align:start position:0%
+years actually by some accounts it's 300
+ 
+
+ align:start position:0%
+years actually by some accounts it's 300
+million
+
+ align:start position:0%
+million
+ 
+
+ align:start position:0%
+million
+it depends on which studies you read
+
+ align:start position:0%
+it depends on which studies you read
+ 
+
+ align:start position:0%
+it depends on which studies you read
+but but for at least 50 and maybe as
+
+ align:start position:0%
+but but for at least 50 and maybe as
+ 
+
+ align:start position:0%
+but but for at least 50 and maybe as
+much as 300 million years the ocean
+
+ align:start position:0%
+much as 300 million years the ocean
+ 
+
+ align:start position:0%
+much as 300 million years the ocean
+uh has had a ph of 8.18
+
+ align:start position:0%
+uh has had a ph of 8.18
+ 
+
+ align:start position:0%
+uh has had a ph of 8.18
+now where's the oh yeah right
+
+ align:start position:0%
+now where's the oh yeah right
+ 
+
+ align:start position:0%
+now where's the oh yeah right
+so let's just say you know
+
+ align:start position:0%
+so let's just say you know
+ 
+
+ align:start position:0%
+so let's just say you know
+last 0 50 to 300 million
+
+ align:start position:0%
+last 0 50 to 300 million
+ 
+
+ align:start position:0%
+last 0 50 to 300 million
+ish years
+
+ align:start position:0%
+ish years
+ 
+
+ align:start position:0%
+ish years
+the ocean ph
+
+ align:start position:0%
+the ocean ph
+ 
+
+ align:start position:0%
+the ocean ph
+was 8.18 and today
+
+ align:start position:0%
+was 8.18 and today
+ 
+
+ align:start position:0%
+was 8.18 and today
+it's 8.07
+
+ align:start position:0%
+it's 8.07
+ 
+
+ align:start position:0%
+it's 8.07
+and the prediction is that in 2100
+
+ align:start position:0%
+and the prediction is that in 2100
+ 
+
+ align:start position:0%
+and the prediction is that in 2100
+it will be 7.8
+
+ align:start position:0%
+it will be 7.8
+ 
+
+ align:start position:0%
+it will be 7.8
+now as we will see in a little bit and
+
+ align:start position:0%
+now as we will see in a little bit and
+ 
+
+ align:start position:0%
+now as we will see in a little bit and
+he said what's ph
+
+ align:start position:0%
+he said what's ph
+ 
+
+ align:start position:0%
+he said what's ph
+well many of you probably already know
+
+ align:start position:0%
+well many of you probably already know
+ 
+
+ align:start position:0%
+well many of you probably already know
+but we i will tell you what it is in a
+
+ align:start position:0%
+but we i will tell you what it is in a
+ 
+
+ align:start position:0%
+but we i will tell you what it is in a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+but because this is a logarithmic thing
+
+ align:start position:0%
+but because this is a logarithmic thing
+ 
+
+ align:start position:0%
+but because this is a logarithmic thing
+this is a lot
+
+ align:start position:0%
+this is a lot
+ 
+
+ align:start position:0%
+this is a lot
+right today the ocean is 25 percent more
+
+ align:start position:0%
+right today the ocean is 25 percent more
+ 
+
+ align:start position:0%
+right today the ocean is 25 percent more
+acidic than it's been in 300 million
+
+ align:start position:0%
+acidic than it's been in 300 million
+ 
+
+ align:start position:0%
+acidic than it's been in 300 million
+ish years and in 2100 it will be 126
+
+ align:start position:0%
+ish years and in 2100 it will be 126
+ 
+
+ align:start position:0%
+ish years and in 2100 it will be 126
+percent
+
+ align:start position:0%
+percent
+ 
+
+ align:start position:0%
+percent
+more acidic that's why they used 7.8 in
+
+ align:start position:0%
+more acidic that's why they used 7.8 in
+ 
+
+ align:start position:0%
+more acidic that's why they used 7.8 in
+in the experiments of the pteropots okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay right
+
+ align:start position:0%
+okay right
+ 
+
+ align:start position:0%
+okay right
+why does this happen why is this
+
+ align:start position:0%
+why does this happen why is this
+ 
+
+ align:start position:0%
+why does this happen why is this
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+an acid we're talking about
+
+ align:start position:0%
+an acid we're talking about
+ 
+
+ align:start position:0%
+an acid we're talking about
+acidification of oceans
+
+ align:start position:0%
+acidification of oceans
+ 
+
+ align:start position:0%
+acidification of oceans
+why is this an acid in the first place
+
+ align:start position:0%
+why is this an acid in the first place
+ 
+
+ align:start position:0%
+why is this an acid in the first place
+what does it mean to be an acid and that
+
+ align:start position:0%
+what does it mean to be an acid and that
+ 
+
+ align:start position:0%
+what does it mean to be an acid and that
+is the next topic
+
+ align:start position:0%
+is the next topic
+ 
+
+ align:start position:0%
+is the next topic
+that is what i want to talk about next
+
+ align:start position:0%
+that is what i want to talk about next
+ 
+
+ align:start position:0%
+that is what i want to talk about next
+why what is an acid
+
+ align:start position:0%
+why what is an acid
+ 
+
+ align:start position:0%
+why what is an acid
+and an acid is something that is very
+
+ align:start position:0%
+and an acid is something that is very
+ 
+
+ align:start position:0%
+and an acid is something that is very
+specific it has a very definite
+
+ align:start position:0%
+specific it has a very definite
+ 
+
+ align:start position:0%
+specific it has a very definite
+meaning to it and i want to talk about
+
+ align:start position:0%
+meaning to it and i want to talk about
+ 
+
+ align:start position:0%
+meaning to it and i want to talk about
+that today
+
+ align:start position:0%
+that today
+ 
+
+ align:start position:0%
+that today
+and then we'll continue after the break
+
+ align:start position:0%
+and then we'll continue after the break
+ 
+
+ align:start position:0%
+and then we'll continue after the break
+right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this molecule carbonic acid is called an
+
+ align:start position:0%
+this molecule carbonic acid is called an
+ 
+
+ align:start position:0%
+this molecule carbonic acid is called an
+acid
+
+ align:start position:0%
+acid
+ 
+
+ align:start position:0%
+acid
+because of that proton and you could
+
+ align:start position:0%
+because of that proton and you could
+ 
+
+ align:start position:0%
+because of that proton and you could
+feel it
+
+ align:start position:0%
+feel it
+ 
+
+ align:start position:0%
+feel it
+right you could feel it in this in this
+
+ align:start position:0%
+right you could feel it in this in this
+ 
+
+ align:start position:0%
+right you could feel it in this in this
+whole thing the proton is the part is
+
+ align:start position:0%
+whole thing the proton is the part is
+ 
+
+ align:start position:0%
+whole thing the proton is the part is
+the thing that did the
+
+ align:start position:0%
+the thing that did the
+ 
+
+ align:start position:0%
+the thing that did the
+cause the problem right an acid
+
+ align:start position:0%
+cause the problem right an acid
+ 
+
+ align:start position:0%
+cause the problem right an acid
+this is an acid because of the proton so
+
+ align:start position:0%
+this is an acid because of the proton so
+ 
+
+ align:start position:0%
+this is an acid because of the proton so
+an acid is it's it's a dissolution
+
+ align:start position:0%
+an acid is it's it's a dissolution
+ 
+
+ align:start position:0%
+an acid is it's it's a dissolution
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+dissolution it's what we've been talking
+
+ align:start position:0%
+dissolution it's what we've been talking
+ 
+
+ align:start position:0%
+dissolution it's what we've been talking
+about it's a dissolution
+
+ align:start position:0%
+about it's a dissolution
+ 
+
+ align:start position:0%
+about it's a dissolution
+reaction that
+
+ align:start position:0%
+reaction that
+ 
+
+ align:start position:0%
+reaction that
+gives an h plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so now if i think about it as kind
+
+ align:start position:0%
+and so now if i think about it as kind
+ 
+
+ align:start position:0%
+and so now if i think about it as kind
+of a generic case
+
+ align:start position:0%
+of a generic case
+ 
+
+ align:start position:0%
+of a generic case
+generic acid a
+
+ align:start position:0%
+generic acid a
+ 
+
+ align:start position:0%
+generic acid a
+then the reaction looks something like
+
+ align:start position:0%
+then the reaction looks something like
+ 
+
+ align:start position:0%
+then the reaction looks something like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+i'm going to call out the acid and the
+
+ align:start position:0%
+i'm going to call out the acid and the
+ 
+
+ align:start position:0%
+i'm going to call out the acid and the
+proton that it gives
+
+ align:start position:0%
+proton that it gives
+ 
+
+ align:start position:0%
+proton that it gives
+separately right okay so this is h a so
+
+ align:start position:0%
+separately right okay so this is h a so
+ 
+
+ align:start position:0%
+separately right okay so this is h a so
+we do this because it highlights
+
+ align:start position:0%
+we do this because it highlights
+ 
+
+ align:start position:0%
+we do this because it highlights
+that it's an acid h plus
+
+ align:start position:0%
+that it's an acid h plus
+ 
+
+ align:start position:0%
+that it's an acid h plus
+in solution and these can all be in
+
+ align:start position:0%
+in solution and these can all be in
+ 
+
+ align:start position:0%
+in solution and these can all be in
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+plus a minus in solution
+
+ align:start position:0%
+plus a minus in solution
+ 
+
+ align:start position:0%
+plus a minus in solution
+right h plus a minus
+
+ align:start position:0%
+right h plus a minus
+ 
+
+ align:start position:0%
+right h plus a minus
+right so i've taken a proton off you see
+
+ align:start position:0%
+right so i've taken a proton off you see
+ 
+
+ align:start position:0%
+right so i've taken a proton off you see
+it's right there
+
+ align:start position:0%
+it's right there
+ 
+
+ align:start position:0%
+it's right there
+that's that's h a h a where a
+
+ align:start position:0%
+that's that's h a h a where a
+ 
+
+ align:start position:0%
+that's that's h a h a where a
+is hco3 and h is h and then what i've
+
+ align:start position:0%
+is hco3 and h is h and then what i've
+ 
+
+ align:start position:0%
+is hco3 and h is h and then what i've
+done is i've transferred
+
+ align:start position:0%
+done is i've transferred
+ 
+
+ align:start position:0%
+done is i've transferred
+the proton into solution that's an acid
+
+ align:start position:0%
+the proton into solution that's an acid
+ 
+
+ align:start position:0%
+the proton into solution that's an acid
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um the thing is one of the things now
+
+ align:start position:0%
+um the thing is one of the things now
+ 
+
+ align:start position:0%
+um the thing is one of the things now
+you will see
+
+ align:start position:0%
+you will see
+ 
+
+ align:start position:0%
+you will see
+a lot of of places and people writing h
+
+ align:start position:0%
+a lot of of places and people writing h
+ 
+
+ align:start position:0%
+a lot of of places and people writing h
+plus and we will do that too because so
+
+ align:start position:0%
+plus and we will do that too because so
+ 
+
+ align:start position:0%
+plus and we will do that too because so
+many textbooks use h plus
+
+ align:start position:0%
+many textbooks use h plus
+ 
+
+ align:start position:0%
+many textbooks use h plus
+but the thing is that h plus what i want
+
+ align:start position:0%
+but the thing is that h plus what i want
+ 
+
+ align:start position:0%
+but the thing is that h plus what i want
+you to know
+
+ align:start position:0%
+you to know
+ 
+
+ align:start position:0%
+you to know
+is that h plus is never a thing
+
+ align:start position:0%
+is that h plus is never a thing
+ 
+
+ align:start position:0%
+is that h plus is never a thing
+we just write it that way h plus is not
+
+ align:start position:0%
+we just write it that way h plus is not
+ 
+
+ align:start position:0%
+we just write it that way h plus is not
+stable in water
+
+ align:start position:0%
+stable in water
+ 
+
+ align:start position:0%
+stable in water
+so the the proper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the proper way to write this general
+
+ align:start position:0%
+the proper way to write this general
+ 
+
+ align:start position:0%
+the proper way to write this general
+reaction would be h
+
+ align:start position:0%
+reaction would be h
+ 
+
+ align:start position:0%
+reaction would be h
+a plus h2o
+
+ align:start position:0%
+a plus h2o
+ 
+
+ align:start position:0%
+a plus h2o
+okay is going to go to and now i'm going
+
+ align:start position:0%
+okay is going to go to and now i'm going
+ 
+
+ align:start position:0%
+okay is going to go to and now i'm going
+to write the full
+
+ align:start position:0%
+to write the full
+ 
+
+ align:start position:0%
+to write the full
+right so the fold goes both ways is
+
+ align:start position:0%
+right so the fold goes both ways is
+ 
+
+ align:start position:0%
+right so the fold goes both ways is
+going to go to h3
+
+ align:start position:0%
+going to go to h3
+ 
+
+ align:start position:0%
+going to go to h3
+o plus plus a minus goes in tight
+
+ align:start position:0%
+o plus plus a minus goes in tight
+ 
+
+ align:start position:0%
+o plus plus a minus goes in tight
+this is what happens because h plus is
+
+ align:start position:0%
+this is what happens because h plus is
+ 
+
+ align:start position:0%
+this is what happens because h plus is
+not stable in water but you will see h
+
+ align:start position:0%
+not stable in water but you will see h
+ 
+
+ align:start position:0%
+not stable in water but you will see h
+plus written all over the place
+
+ align:start position:0%
+plus written all over the place
+ 
+
+ align:start position:0%
+plus written all over the place
+when you see h plus and if it's in water
+
+ align:start position:0%
+when you see h plus and if it's in water
+ 
+
+ align:start position:0%
+when you see h plus and if it's in water
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+that it's h3o plus that is what is
+
+ align:start position:0%
+that it's h3o plus that is what is
+ 
+
+ align:start position:0%
+that it's h3o plus that is what is
+stable
+
+ align:start position:0%
+stable
+ 
+
+ align:start position:0%
+stable
+okay h plus in water is not
+
+ align:start position:0%
+okay h plus in water is not
+ 
+
+ align:start position:0%
+okay h plus in water is not
+now there's something here that's
+
+ align:start position:0%
+now there's something here that's
+ 
+
+ align:start position:0%
+now there's something here that's
+important in terms of terminology
+
+ align:start position:0%
+important in terms of terminology
+ 
+
+ align:start position:0%
+important in terms of terminology
+and that is that these are notice that
+
+ align:start position:0%
+and that is that these are notice that
+ 
+
+ align:start position:0%
+and that is that these are notice that
+these are related
+
+ align:start position:0%
+these are related
+ 
+
+ align:start position:0%
+these are related
+right the h a and the a minus seem very
+
+ align:start position:0%
+right the h a and the a minus seem very
+ 
+
+ align:start position:0%
+right the h a and the a minus seem very
+related and the h2o and the h2o
+
+ align:start position:0%
+related and the h2o and the h2o
+ 
+
+ align:start position:0%
+related and the h2o and the h2o
+h3o plus seem very related well they are
+
+ align:start position:0%
+h3o plus seem very related well they are
+ 
+
+ align:start position:0%
+h3o plus seem very related well they are
+because they're just
+
+ align:start position:0%
+because they're just
+ 
+
+ align:start position:0%
+because they're just
+a proton is the only difference between
+
+ align:start position:0%
+a proton is the only difference between
+ 
+
+ align:start position:0%
+a proton is the only difference between
+them and so those are called conjugate
+
+ align:start position:0%
+them and so those are called conjugate
+ 
+
+ align:start position:0%
+them and so those are called conjugate
+pairs
+
+ align:start position:0%
+pairs
+ 
+
+ align:start position:0%
+pairs
+conjugate related conjugate pairs
+
+ align:start position:0%
+conjugate related conjugate pairs
+ 
+
+ align:start position:0%
+conjugate related conjugate pairs
+okay those are called conjugate pairs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now back in the day there was a lot of
+
+ align:start position:0%
+now back in the day there was a lot of
+ 
+
+ align:start position:0%
+now back in the day there was a lot of
+interest people knew about
+
+ align:start position:0%
+interest people knew about
+ 
+
+ align:start position:0%
+interest people knew about
+these kind of liquids
+
+ align:start position:0%
+these kind of liquids
+ 
+
+ align:start position:0%
+these kind of liquids
+mostly liquids for a long time and there
+
+ align:start position:0%
+mostly liquids for a long time and there
+ 
+
+ align:start position:0%
+mostly liquids for a long time and there
+was a lot of experimentation before this
+
+ align:start position:0%
+was a lot of experimentation before this
+ 
+
+ align:start position:0%
+was a lot of experimentation before this
+let's say well there's these general
+
+ align:start position:0%
+let's say well there's these general
+ 
+
+ align:start position:0%
+let's say well there's these general
+classes of materials
+
+ align:start position:0%
+classes of materials
+ 
+
+ align:start position:0%
+classes of materials
+we're going to call them a and b well a
+
+ align:start position:0%
+we're going to call them a and b well a
+ 
+
+ align:start position:0%
+we're going to call them a and b well a
+seems to always taste kind of sour
+
+ align:start position:0%
+seems to always taste kind of sour
+ 
+
+ align:start position:0%
+seems to always taste kind of sour
+b is bitter a reacts with carbonates
+
+ align:start position:0%
+b is bitter a reacts with carbonates
+ 
+
+ align:start position:0%
+b is bitter a reacts with carbonates
+to make co2 b reacts with fats and soap
+
+ align:start position:0%
+to make co2 b reacts with fats and soap
+ 
+
+ align:start position:0%
+to make co2 b reacts with fats and soap
+to make soaps
+
+ align:start position:0%
+to make soaps
+ 
+
+ align:start position:0%
+to make soaps
+all right one reacts with metals the
+
+ align:start position:0%
+all right one reacts with metals the
+ 
+
+ align:start position:0%
+all right one reacts with metals the
+other doesn't and by the way if we mix
+
+ align:start position:0%
+other doesn't and by the way if we mix
+ 
+
+ align:start position:0%
+other doesn't and by the way if we mix
+them together we seem to always get salt
+
+ align:start position:0%
+them together we seem to always get salt
+ 
+
+ align:start position:0%
+them together we seem to always get salt
+and water
+
+ align:start position:0%
+and water
+ 
+
+ align:start position:0%
+and water
+this had been going on for centuries
+
+ align:start position:0%
+this had been going on for centuries
+ 
+
+ align:start position:0%
+this had been going on for centuries
+this investigation
+
+ align:start position:0%
+this investigation
+ 
+
+ align:start position:0%
+this investigation
+into properties of acids and bases
+
+ align:start position:0%
+into properties of acids and bases
+ 
+
+ align:start position:0%
+into properties of acids and bases
+but who was it that came along who was
+
+ align:start position:0%
+but who was it that came along who was
+ 
+
+ align:start position:0%
+but who was it that came along who was
+it that came along
+
+ align:start position:0%
+it that came along
+ 
+
+ align:start position:0%
+it that came along
+svante is there anything you can't do
+
+ align:start position:0%
+svante is there anything you can't do
+ 
+
+ align:start position:0%
+svante is there anything you can't do
+svonte
+
+ align:start position:0%
+svonte
+ 
+
+ align:start position:0%
+svonte
+i ask you again in the late 1800s
+
+ align:start position:0%
+i ask you again in the late 1800s
+ 
+
+ align:start position:0%
+i ask you again in the late 1800s
+it was svonte to the rescue
+
+ align:start position:0%
+it was svonte to the rescue
+ 
+
+ align:start position:0%
+it was svonte to the rescue
+who first proposed that what is
+
+ align:start position:0%
+who first proposed that what is
+ 
+
+ align:start position:0%
+who first proposed that what is
+happening here
+
+ align:start position:0%
+happening here
+ 
+
+ align:start position:0%
+happening here
+is a dissolution reaction that is what
+
+ align:start position:0%
+is a dissolution reaction that is what
+ 
+
+ align:start position:0%
+is a dissolution reaction that is what
+an acid or base is
+
+ align:start position:0%
+an acid or base is
+ 
+
+ align:start position:0%
+an acid or base is
+it is that in on the one hand you're
+
+ align:start position:0%
+it is that in on the one hand you're
+ 
+
+ align:start position:0%
+it is that in on the one hand you're
+given an h plus
+
+ align:start position:0%
+given an h plus
+ 
+
+ align:start position:0%
+given an h plus
+which is what i just said
+
+ align:start position:0%
+which is what i just said
+ 
+
+ align:start position:0%
+which is what i just said
+but on the other hand
+
+ align:start position:0%
+but on the other hand
+ 
+
+ align:start position:0%
+but on the other hand
+for a base you're given an oh minus and
+
+ align:start position:0%
+for a base you're given an oh minus and
+ 
+
+ align:start position:0%
+for a base you're given an oh minus and
+it was fonte arenas
+
+ align:start position:0%
+it was fonte arenas
+ 
+
+ align:start position:0%
+it was fonte arenas
+who first put that down and first
+
+ align:start position:0%
+who first put that down and first
+ 
+
+ align:start position:0%
+who first put that down and first
+conceived of acids and
+
+ align:start position:0%
+conceived of acids and
+ 
+
+ align:start position:0%
+conceived of acids and
+are we snapping are we quiet snapping
+
+ align:start position:0%
+are we snapping are we quiet snapping
+ 
+
+ align:start position:0%
+are we snapping are we quiet snapping
+for sponte i love it
+
+ align:start position:0%
+for sponte i love it
+ 
+
+ align:start position:0%
+for sponte i love it
+i've just recently learned what that
+
+ align:start position:0%
+i've just recently learned what that
+ 
+
+ align:start position:0%
+i've just recently learned what that
+means it makes me happy
+
+ align:start position:0%
+means it makes me happy
+ 
+
+ align:start position:0%
+means it makes me happy
+quiet snapping it's instead of clapping
+
+ align:start position:0%
+quiet snapping it's instead of clapping
+ 
+
+ align:start position:0%
+quiet snapping it's instead of clapping
+but you don't want to make noise but you
+
+ align:start position:0%
+but you don't want to make noise but you
+ 
+
+ align:start position:0%
+but you don't want to make noise but you
+still want to give props i got it
+
+ align:start position:0%
+still want to give props i got it
+ 
+
+ align:start position:0%
+still want to give props i got it
+i'm there i'm right there now okay so uh
+
+ align:start position:0%
+i'm there i'm right there now okay so uh
+ 
+
+ align:start position:0%
+i'm there i'm right there now okay so uh
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now here's the thing so we'll talk about
+
+ align:start position:0%
+now here's the thing so we'll talk about
+ 
+
+ align:start position:0%
+now here's the thing so we'll talk about
+so uh okay arrhenius says
+
+ align:start position:0%
+so uh okay arrhenius says
+ 
+
+ align:start position:0%
+so uh okay arrhenius says
+bases give oh ions in solution and
+
+ align:start position:0%
+bases give oh ions in solution and
+ 
+
+ align:start position:0%
+bases give oh ions in solution and
+oh acids give h plus but we know that
+
+ align:start position:0%
+oh acids give h plus but we know that
+ 
+
+ align:start position:0%
+oh acids give h plus but we know that
+that's h3o plus
+
+ align:start position:0%
+that's h3o plus
+ 
+
+ align:start position:0%
+that's h3o plus
+okay we know that okay
+
+ align:start position:0%
+okay we know that okay
+ 
+
+ align:start position:0%
+okay we know that okay
+yeah but the thing is there's a
+
+ align:start position:0%
+yeah but the thing is there's a
+ 
+
+ align:start position:0%
+yeah but the thing is there's a
+dissolution reactions
+
+ align:start position:0%
+dissolution reactions
+ 
+
+ align:start position:0%
+dissolution reactions
+these things lead to really small
+
+ align:start position:0%
+these things lead to really small
+ 
+
+ align:start position:0%
+these things lead to really small
+concentrations
+
+ align:start position:0%
+concentrations
+ 
+
+ align:start position:0%
+concentrations
+and so soren sorensen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is a beer bottle by the way his
+
+ align:start position:0%
+that is a beer bottle by the way his
+ 
+
+ align:start position:0%
+that is a beer bottle by the way his
+research was funded by a beer company
+
+ align:start position:0%
+research was funded by a beer company
+ 
+
+ align:start position:0%
+research was funded by a beer company
+yeah and it was all about the taste of
+
+ align:start position:0%
+yeah and it was all about the taste of
+ 
+
+ align:start position:0%
+yeah and it was all about the taste of
+beer
+
+ align:start position:0%
+beer
+ 
+
+ align:start position:0%
+beer
+he called it looking at proteins
+
+ align:start position:0%
+he called it looking at proteins
+ 
+
+ align:start position:0%
+he called it looking at proteins
+but it was about beer and what he
+
+ align:start position:0%
+but it was about beer and what he
+ 
+
+ align:start position:0%
+but it was about beer and what he
+realized he's
+
+ align:start position:0%
+realized he's
+ 
+
+ align:start position:0%
+realized he's
+doing all these dissolution reactions of
+
+ align:start position:0%
+doing all these dissolution reactions of
+ 
+
+ align:start position:0%
+doing all these dissolution reactions of
+ions i think iranians was right yeah
+
+ align:start position:0%
+ions i think iranians was right yeah
+ 
+
+ align:start position:0%
+ions i think iranians was right yeah
+ions are really important
+
+ align:start position:0%
+ions are really important
+ 
+
+ align:start position:0%
+ions are really important
+uh and we're trying to measure these
+
+ align:start position:0%
+uh and we're trying to measure these
+ 
+
+ align:start position:0%
+uh and we're trying to measure these
+things and but i'm sick of all these
+
+ align:start position:0%
+things and but i'm sick of all these
+ 
+
+ align:start position:0%
+things and but i'm sick of all these
+zeroes
+
+ align:start position:0%
+zeroes
+ 
+
+ align:start position:0%
+zeroes
+i don't like writing .0001 or whatever
+
+ align:start position:0%
+i don't like writing .0001 or whatever
+ 
+
+ align:start position:0%
+i don't like writing .0001 or whatever
+all the time and and so look at that
+
+ align:start position:0%
+all the time and and so look at that
+ 
+
+ align:start position:0%
+all the time and and so look at that
+1.3 times 10 to the minus fifth that's
+
+ align:start position:0%
+1.3 times 10 to the minus fifth that's
+ 
+
+ align:start position:0%
+1.3 times 10 to the minus fifth that's
+not efficient
+
+ align:start position:0%
+not efficient
+ 
+
+ align:start position:0%
+not efficient
+and so what sorensen did is he talked
+
+ align:start position:0%
+and so what sorensen did is he talked
+ 
+
+ align:start position:0%
+and so what sorensen did is he talked
+about how
+
+ align:start position:0%
+about how
+ 
+
+ align:start position:0%
+about how
+you've got the power now what do i mean
+
+ align:start position:0%
+you've got the power now what do i mean
+ 
+
+ align:start position:0%
+you've got the power now what do i mean
+by power
+
+ align:start position:0%
+by power
+ 
+
+ align:start position:0%
+by power
+so many things right but if i look at h
+
+ align:start position:0%
+so many things right but if i look at h
+ 
+
+ align:start position:0%
+so many things right but if i look at h
+plus okay h3o plus
+
+ align:start position:0%
+plus okay h3o plus
+ 
+
+ align:start position:0%
+plus okay h3o plus
+and i say let's suppose the
+
+ align:start position:0%
+and i say let's suppose the
+ 
+
+ align:start position:0%
+and i say let's suppose the
+concentration is 0.0
+
+ align:start position:0%
+concentration is 0.0
+ 
+
+ align:start position:0%
+concentration is 0.0
+oh boy zero zero zero zero one
+
+ align:start position:0%
+oh boy zero zero zero zero one
+ 
+
+ align:start position:0%
+oh boy zero zero zero zero one
+that's ten to the minus seventh
+
+ align:start position:0%
+that's ten to the minus seventh
+ 
+
+ align:start position:0%
+that's ten to the minus seventh
+because but but sorensen wasn't happy
+
+ align:start position:0%
+because but but sorensen wasn't happy
+ 
+
+ align:start position:0%
+because but but sorensen wasn't happy
+with that that's still
+
+ align:start position:0%
+with that that's still
+ 
+
+ align:start position:0%
+with that that's still
+you simplified it wait two four no it's
+
+ align:start position:0%
+you simplified it wait two four no it's
+ 
+
+ align:start position:0%
+you simplified it wait two four no it's
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+okay maybe it is now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he said well i ten to the minus
+
+ align:start position:0%
+and he said well i ten to the minus
+ 
+
+ align:start position:0%
+and he said well i ten to the minus
+seven there's still four characters i
+
+ align:start position:0%
+seven there's still four characters i
+ 
+
+ align:start position:0%
+seven there's still four characters i
+gotta write
+
+ align:start position:0%
+gotta write
+ 
+
+ align:start position:0%
+gotta write
+four so he went to the math department
+
+ align:start position:0%
+four so he went to the math department
+ 
+
+ align:start position:0%
+four so he went to the math department
+at his place and he said how do you what
+
+ align:start position:0%
+at his place and he said how do you what
+ 
+
+ align:start position:0%
+at his place and he said how do you what
+else could me
+
+ align:start position:0%
+else could me
+ 
+
+ align:start position:0%
+else could me
+i want to talk about the power of these
+
+ align:start position:0%
+i want to talk about the power of these
+ 
+
+ align:start position:0%
+i want to talk about the power of these
+ions and they're like
+
+ align:start position:0%
+ions and they're like
+ 
+
+ align:start position:0%
+ions and they're like
+power well that's the logarithm
+
+ align:start position:0%
+power well that's the logarithm
+ 
+
+ align:start position:0%
+power well that's the logarithm
+and and so if you take the log it's the
+
+ align:start position:0%
+and and so if you take the log it's the
+ 
+
+ align:start position:0%
+and and so if you take the log it's the
+power of hydrogen
+
+ align:start position:0%
+power of hydrogen
+ 
+
+ align:start position:0%
+power of hydrogen
+power of hydrogen
+
+ align:start position:0%
+power of hydrogen
+ 
+
+ align:start position:0%
+power of hydrogen
+is the ph and that's simply minus the
+
+ align:start position:0%
+is the ph and that's simply minus the
+ 
+
+ align:start position:0%
+is the ph and that's simply minus the
+law
+
+ align:start position:0%
+law
+ 
+
+ align:start position:0%
+law
+they didn't want negative numbers either
+
+ align:start position:0%
+they didn't want negative numbers either
+ 
+
+ align:start position:0%
+they didn't want negative numbers either
+oh but you can't have negative ph
+
+ align:start position:0%
+oh but you can't have negative ph
+ 
+
+ align:start position:0%
+oh but you can't have negative ph
+you can why because this is the
+
+ align:start position:0%
+you can why because this is the
+ 
+
+ align:start position:0%
+you can why because this is the
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+of ph right or you could do poh since
+
+ align:start position:0%
+of ph right or you could do poh since
+ 
+
+ align:start position:0%
+of ph right or you could do poh since
+if you're going with arrhenius right so
+
+ align:start position:0%
+if you're going with arrhenius right so
+ 
+
+ align:start position:0%
+if you're going with arrhenius right so
+the power of
+
+ align:start position:0%
+the power of
+ 
+
+ align:start position:0%
+the power of
+hydrogen is the ph the poh would be
+
+ align:start position:0%
+hydrogen is the ph the poh would be
+ 
+
+ align:start position:0%
+hydrogen is the ph the poh would be
+minus log
+
+ align:start position:0%
+minus log
+ 
+
+ align:start position:0%
+minus log
+of the concentration of o h minus
+
+ align:start position:0%
+of the concentration of o h minus
+ 
+
+ align:start position:0%
+of the concentration of o h minus
+that's the poh but ph is the one that we
+
+ align:start position:0%
+that's the poh but ph is the one that we
+ 
+
+ align:start position:0%
+that's the poh but ph is the one that we
+most
+
+ align:start position:0%
+most
+ 
+
+ align:start position:0%
+most
+often see to describe
+
+ align:start position:0%
+often see to describe
+ 
+
+ align:start position:0%
+often see to describe
+whether something is acidic or basic
+
+ align:start position:0%
+whether something is acidic or basic
+ 
+
+ align:start position:0%
+whether something is acidic or basic
+right and so now you see well if the you
+
+ align:start position:0%
+right and so now you see well if the you
+ 
+
+ align:start position:0%
+right and so now you see well if the you
+know okay well this is a ph
+
+ align:start position:0%
+know okay well this is a ph
+ 
+
+ align:start position:0%
+know okay well this is a ph
+now this is easy right it's a ph of
+
+ align:start position:0%
+now this is easy right it's a ph of
+ 
+
+ align:start position:0%
+now this is easy right it's a ph of
+seven and and if the concentration were
+
+ align:start position:0%
+seven and and if the concentration were
+ 
+
+ align:start position:0%
+seven and and if the concentration were
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+point one it'd be a ph of one right
+
+ align:start position:0%
+point one it'd be a ph of one right
+ 
+
+ align:start position:0%
+point one it'd be a ph of one right
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+log the power of hydrogen the law
+
+ align:start position:0%
+log the power of hydrogen the law
+ 
+
+ align:start position:0%
+log the power of hydrogen the law
+literally the log
+
+ align:start position:0%
+literally the log
+ 
+
+ align:start position:0%
+literally the log
+okay now if you look at scales of ph and
+
+ align:start position:0%
+okay now if you look at scales of ph and
+ 
+
+ align:start position:0%
+okay now if you look at scales of ph and
+it's a really fun thing to do
+
+ align:start position:0%
+it's a really fun thing to do
+ 
+
+ align:start position:0%
+it's a really fun thing to do
+then what you find is that usually
+
+ align:start position:0%
+then what you find is that usually
+ 
+
+ align:start position:0%
+then what you find is that usually
+almost always actually you'll see the
+
+ align:start position:0%
+almost always actually you'll see the
+ 
+
+ align:start position:0%
+almost always actually you'll see the
+scale ranging from 0 to 14.
+
+ align:start position:0%
+scale ranging from 0 to 14.
+ 
+
+ align:start position:0%
+scale ranging from 0 to 14.
+that's what sorensen originally decided
+
+ align:start position:0%
+that's what sorensen originally decided
+ 
+
+ align:start position:0%
+that's what sorensen originally decided
+i'm going to talk about these ions in
+
+ align:start position:0%
+i'm going to talk about these ions in
+ 
+
+ align:start position:0%
+i'm going to talk about these ions in
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+i don't want to write it out every time
+
+ align:start position:0%
+i don't want to write it out every time
+ 
+
+ align:start position:0%
+i don't want to write it out every time
+i'm just going to have a simple scale
+
+ align:start position:0%
+i'm just going to have a simple scale
+ 
+
+ align:start position:0%
+i'm just going to have a simple scale
+we'll take the minus log and there you
+
+ align:start position:0%
+we'll take the minus log and there you
+ 
+
+ align:start position:0%
+we'll take the minus log and there you
+go yeah but
+
+ align:start position:0%
+go yeah but
+ 
+
+ align:start position:0%
+go yeah but
+you can see that if the if the
+
+ align:start position:0%
+you can see that if the if the
+ 
+
+ align:start position:0%
+you can see that if the if the
+concentration is more than one here
+
+ align:start position:0%
+concentration is more than one here
+ 
+
+ align:start position:0%
+concentration is more than one here
+then you could have negative ph's
+
+ align:start position:0%
+then you could have negative ph's
+ 
+
+ align:start position:0%
+then you could have negative ph's
+there's nothing special about zero here
+
+ align:start position:0%
+there's nothing special about zero here
+ 
+
+ align:start position:0%
+there's nothing special about zero here
+it just so happens that most things
+
+ align:start position:0%
+it just so happens that most things
+ 
+
+ align:start position:0%
+it just so happens that most things
+certainly that he was playing with at
+
+ align:start position:0%
+certainly that he was playing with at
+ 
+
+ align:start position:0%
+certainly that he was playing with at
+the time
+
+ align:start position:0%
+the time
+ 
+
+ align:start position:0%
+the time
+were in this scale and here's a few
+
+ align:start position:0%
+were in this scale and here's a few
+ 
+
+ align:start position:0%
+were in this scale and here's a few
+things that we know
+
+ align:start position:0%
+things that we know
+ 
+
+ align:start position:0%
+things that we know
+there it is right okay don't play with
+
+ align:start position:0%
+there it is right okay don't play with
+ 
+
+ align:start position:0%
+there it is right okay don't play with
+that one but play with lemon juice
+
+ align:start position:0%
+that one but play with lemon juice
+ 
+
+ align:start position:0%
+that one but play with lemon juice
+vinegar
+
+ align:start position:0%
+vinegar
+ 
+
+ align:start position:0%
+vinegar
+by the way vinegar okay wine is around
+
+ align:start position:0%
+by the way vinegar okay wine is around
+ 
+
+ align:start position:0%
+by the way vinegar okay wine is around
+three and a half
+
+ align:start position:0%
+three and a half
+ 
+
+ align:start position:0%
+three and a half
+vinegar is around two you know
+
+ align:start position:0%
+vinegar is around two you know
+ 
+
+ align:start position:0%
+vinegar is around two you know
+then the the word vinegar is
+
+ align:start position:0%
+then the the word vinegar is
+ 
+
+ align:start position:0%
+then the the word vinegar is
+von egar it's eager wine
+
+ align:start position:0%
+von egar it's eager wine
+ 
+
+ align:start position:0%
+von egar it's eager wine
+that's it right and but and it comes
+
+ align:start position:0%
+that's it right and but and it comes
+ 
+
+ align:start position:0%
+that's it right and but and it comes
+it's because of the the acidity
+
+ align:start position:0%
+it's because of the the acidity
+ 
+
+ align:start position:0%
+it's because of the the acidity
+the acidity well it's more than that but
+
+ align:start position:0%
+the acidity well it's more than that but
+ 
+
+ align:start position:0%
+the acidity well it's more than that but
+it's the acidity is changing
+
+ align:start position:0%
+it's the acidity is changing
+ 
+
+ align:start position:0%
+it's the acidity is changing
+by orders of magnitude power
+
+ align:start position:0%
+by orders of magnitude power
+ 
+
+ align:start position:0%
+by orders of magnitude power
+right and then you can go back and you
+
+ align:start position:0%
+right and then you can go back and you
+ 
+
+ align:start position:0%
+right and then you can go back and you
+say okay there's coffee i like that a
+
+ align:start position:0%
+say okay there's coffee i like that a
+ 
+
+ align:start position:0%
+say okay there's coffee i like that a
+lot and
+
+ align:start position:0%
+lot and
+ 
+
+ align:start position:0%
+lot and
+and blood
+
+ align:start position:0%
+and blood
+ 
+
+ align:start position:0%
+and blood
+by the way by the way talk about ocean
+
+ align:start position:0%
+by the way by the way talk about ocean
+ 
+
+ align:start position:0%
+by the way by the way talk about ocean
+acidity
+
+ align:start position:0%
+acidity
+ 
+
+ align:start position:0%
+acidity
+blood has a very narrow range of ph
+
+ align:start position:0%
+blood has a very narrow range of ph
+ 
+
+ align:start position:0%
+blood has a very narrow range of ph
+and if you change the ph of your blood
+
+ align:start position:0%
+and if you change the ph of your blood
+ 
+
+ align:start position:0%
+and if you change the ph of your blood
+by more than 0.2
+
+ align:start position:0%
+by more than 0.2
+ 
+
+ align:start position:0%
+by more than 0.2
+it is very likely to lead to death right
+
+ align:start position:0%
+it is very likely to lead to death right
+ 
+
+ align:start position:0%
+it is very likely to lead to death right
+so just think about that's what we're
+
+ align:start position:0%
+so just think about that's what we're
+ 
+
+ align:start position:0%
+so just think about that's what we're
+doing to the ocean
+
+ align:start position:0%
+doing to the ocean
+ 
+
+ align:start position:0%
+doing to the ocean
+okay anyway that was an aside
+
+ align:start position:0%
+okay anyway that was an aside
+ 
+
+ align:start position:0%
+okay anyway that was an aside
+seawater oh ph 8.07 currently and
+
+ align:start position:0%
+seawater oh ph 8.07 currently and
+ 
+
+ align:start position:0%
+seawater oh ph 8.07 currently and
+dropping
+
+ align:start position:0%
+dropping
+ 
+
+ align:start position:0%
+dropping
+right uh okay baking soda so this is a
+
+ align:start position:0%
+right uh okay baking soda so this is a
+ 
+
+ align:start position:0%
+right uh okay baking soda so this is a
+very powerful no pun intended actually
+
+ align:start position:0%
+very powerful no pun intended actually
+ 
+
+ align:start position:0%
+very powerful no pun intended actually
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh now these are dissociation reactions
+
+ align:start position:0%
+uh now these are dissociation reactions
+ 
+
+ align:start position:0%
+uh now these are dissociation reactions
+these are dissolution reactions i'm
+
+ align:start position:0%
+these are dissolution reactions i'm
+ 
+
+ align:start position:0%
+these are dissolution reactions i'm
+taking an acid
+
+ align:start position:0%
+taking an acid
+ 
+
+ align:start position:0%
+taking an acid
+and i'm dissociating it in water
+
+ align:start position:0%
+and i'm dissociating it in water
+ 
+
+ align:start position:0%
+and i'm dissociating it in water
+and so you have equilibrium constants
+
+ align:start position:0%
+and so you have equilibrium constants
+ 
+
+ align:start position:0%
+and so you have equilibrium constants
+for that dissociation
+
+ align:start position:0%
+for that dissociation
+ 
+
+ align:start position:0%
+for that dissociation
+right and so and so if you if you go
+
+ align:start position:0%
+right and so and so if you if you go
+ 
+
+ align:start position:0%
+right and so and so if you if you go
+back to
+
+ align:start position:0%
+back to
+ 
+
+ align:start position:0%
+back to
+to that you know that's still going to
+
+ align:start position:0%
+to that you know that's still going to
+ 
+
+ align:start position:0%
+to that you know that's still going to
+matter here and that's
+
+ align:start position:0%
+matter here and that's
+ 
+
+ align:start position:0%
+matter here and that's
+going to be important in thinking about
+
+ align:start position:0%
+going to be important in thinking about
+ 
+
+ align:start position:0%
+going to be important in thinking about
+what an acid is because again why is it
+
+ align:start position:0%
+what an acid is because again why is it
+ 
+
+ align:start position:0%
+what an acid is because again why is it
+sick well because there's these protons
+
+ align:start position:0%
+sick well because there's these protons
+ 
+
+ align:start position:0%
+sick well because there's these protons
+well how many of them are there
+
+ align:start position:0%
+well how many of them are there
+ 
+
+ align:start position:0%
+well how many of them are there
+it depends on how it dissolved where did
+
+ align:start position:0%
+it depends on how it dissolved where did
+ 
+
+ align:start position:0%
+it depends on how it dissolved where did
+it find
+
+ align:start position:0%
+it find
+ 
+
+ align:start position:0%
+it find
+its equilibrium right and so for some of
+
+ align:start position:0%
+its equilibrium right and so for some of
+ 
+
+ align:start position:0%
+its equilibrium right and so for some of
+them like i just wrote
+
+ align:start position:0%
+them like i just wrote
+ 
+
+ align:start position:0%
+them like i just wrote
+you know we we just talked about
+
+ align:start position:0%
+you know we we just talked about
+ 
+
+ align:start position:0%
+you know we we just talked about
+hcl plus uh
+
+ align:start position:0%
+hcl plus uh
+ 
+
+ align:start position:0%
+hcl plus uh
+h2o that went to uh
+
+ align:start position:0%
+h2o that went to uh
+ 
+
+ align:start position:0%
+h2o that went to uh
+h3o plus plus
+
+ align:start position:0%
+h3o plus plus
+ 
+
+ align:start position:0%
+h3o plus plus
+uh cl minus okay now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the thing is if i had if i had 0.1
+
+ align:start position:0%
+the thing is if i had if i had 0.1
+ 
+
+ align:start position:0%
+the thing is if i had if i had 0.1
+moles per liter of hcl then
+
+ align:start position:0%
+moles per liter of hcl then
+ 
+
+ align:start position:0%
+moles per liter of hcl then
+it's going to lead to a concentration of
+
+ align:start position:0%
+it's going to lead to a concentration of
+ 
+
+ align:start position:0%
+it's going to lead to a concentration of
+h3o plus
+
+ align:start position:0%
+h3o plus
+ 
+
+ align:start position:0%
+h3o plus
+of around 0.1 moles per liter because
+
+ align:start position:0%
+of around 0.1 moles per liter because
+ 
+
+ align:start position:0%
+of around 0.1 moles per liter because
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+nearly full nearly
+
+ align:start position:0%
+nearly full nearly
+ 
+
+ align:start position:0%
+nearly full nearly
+full dissociation
+
+ align:start position:0%
+full dissociation
+ 
+
+ align:start position:0%
+full dissociation
+what is what do i mean by that well i
+
+ align:start position:0%
+what is what do i mean by that well i
+ 
+
+ align:start position:0%
+what is what do i mean by that well i
+mean that yeah okay you know so you'll
+
+ align:start position:0%
+mean that yeah okay you know so you'll
+ 
+
+ align:start position:0%
+mean that yeah okay you know so you'll
+often see for
+
+ align:start position:0%
+often see for
+ 
+
+ align:start position:0%
+often see for
+like an acid like that one arrow
+
+ align:start position:0%
+like an acid like that one arrow
+ 
+
+ align:start position:0%
+like an acid like that one arrow
+well we know that in reality there's
+
+ align:start position:0%
+well we know that in reality there's
+ 
+
+ align:start position:0%
+well we know that in reality there's
+another arrow there
+
+ align:start position:0%
+another arrow there
+ 
+
+ align:start position:0%
+another arrow there
+but see here the acid dissociation
+
+ align:start position:0%
+but see here the acid dissociation
+ 
+
+ align:start position:0%
+but see here the acid dissociation
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+is huge right so now we have a thing for
+
+ align:start position:0%
+is huge right so now we have a thing for
+ 
+
+ align:start position:0%
+is huge right so now we have a thing for
+the equilibrium
+
+ align:start position:0%
+the equilibrium
+ 
+
+ align:start position:0%
+the equilibrium
+of an acid which forms by dissociating
+
+ align:start position:0%
+of an acid which forms by dissociating
+ 
+
+ align:start position:0%
+of an acid which forms by dissociating
+the acid
+
+ align:start position:0%
+the acid
+ 
+
+ align:start position:0%
+the acid
+into its you know ions right and this
+
+ align:start position:0%
+into its you know ions right and this
+ 
+
+ align:start position:0%
+into its you know ions right and this
+is well for in this case it's 10 to the
+
+ align:start position:0%
+is well for in this case it's 10 to the
+ 
+
+ align:start position:0%
+is well for in this case it's 10 to the
+sixth
+
+ align:start position:0%
+sixth
+ 
+
+ align:start position:0%
+sixth
+it's enormous which means that the
+
+ align:start position:0%
+it's enormous which means that the
+ 
+
+ align:start position:0%
+it's enormous which means that the
+equilibrium lies
+
+ align:start position:0%
+equilibrium lies
+ 
+
+ align:start position:0%
+equilibrium lies
+very very very very far over and so
+
+ align:start position:0%
+very very very very far over and so
+ 
+
+ align:start position:0%
+very very very very far over and so
+oftentimes you'll see
+
+ align:start position:0%
+oftentimes you'll see
+ 
+
+ align:start position:0%
+oftentimes you'll see
+if it's going to strongly dissociate
+
+ align:start position:0%
+if it's going to strongly dissociate
+ 
+
+ align:start position:0%
+if it's going to strongly dissociate
+like sodium chloride did
+
+ align:start position:0%
+like sodium chloride did
+ 
+
+ align:start position:0%
+like sodium chloride did
+right then you'll sometimes see it
+
+ align:start position:0%
+right then you'll sometimes see it
+ 
+
+ align:start position:0%
+right then you'll sometimes see it
+written as just one arrow
+
+ align:start position:0%
+written as just one arrow
+ 
+
+ align:start position:0%
+written as just one arrow
+but there's a little bit going back as
+
+ align:start position:0%
+but there's a little bit going back as
+ 
+
+ align:start position:0%
+but there's a little bit going back as
+well right
+
+ align:start position:0%
+well right
+ 
+
+ align:start position:0%
+well right
+that is another equilibrium constant and
+
+ align:start position:0%
+that is another equilibrium constant and
+ 
+
+ align:start position:0%
+that is another equilibrium constant and
+we will talk about ka
+
+ align:start position:0%
+we will talk about ka
+ 
+
+ align:start position:0%
+we will talk about ka
+a little later and probably pick up on
+
+ align:start position:0%
+a little later and probably pick up on
+ 
+
+ align:start position:0%
+a little later and probably pick up on
+it next week
+
+ align:start position:0%
+it next week
+ 
+
+ align:start position:0%
+it next week
+okay now so near fold associated now
+
+ align:start position:0%
+okay now so near fold associated now
+ 
+
+ align:start position:0%
+okay now so near fold associated now
+the other thing that can happen that's
+
+ align:start position:0%
+the other thing that can happen that's
+ 
+
+ align:start position:0%
+the other thing that can happen that's
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+is water can do both and so there's
+
+ align:start position:0%
+is water can do both and so there's
+ 
+
+ align:start position:0%
+is water can do both and so there's
+there's uh let's see where should i go
+
+ align:start position:0%
+there's uh let's see where should i go
+ 
+
+ align:start position:0%
+there's uh let's see where should i go
+i'll go back over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see that picture there they got it wrong
+
+ align:start position:0%
+see that picture there they got it wrong
+ 
+
+ align:start position:0%
+see that picture there they got it wrong
+but it's okay they got it right because
+
+ align:start position:0%
+but it's okay they got it right because
+ 
+
+ align:start position:0%
+but it's okay they got it right because
+we all get along
+
+ align:start position:0%
+we all get along
+ 
+
+ align:start position:0%
+we all get along
+if you want to put h plus fine but you
+
+ align:start position:0%
+if you want to put h plus fine but you
+ 
+
+ align:start position:0%
+if you want to put h plus fine but you
+know that it's actually h3o plus okay
+
+ align:start position:0%
+know that it's actually h3o plus okay
+ 
+
+ align:start position:0%
+know that it's actually h3o plus okay
+good but you can put h plus no problem
+
+ align:start position:0%
+good but you can put h plus no problem
+ 
+
+ align:start position:0%
+good but you can put h plus no problem
+okay um now there it
+
+ align:start position:0%
+okay um now there it
+ 
+
+ align:start position:0%
+okay um now there it
+is and you can see that what water can
+
+ align:start position:0%
+is and you can see that what water can
+ 
+
+ align:start position:0%
+is and you can see that what water can
+do is it can do both
+
+ align:start position:0%
+do is it can do both
+ 
+
+ align:start position:0%
+do is it can do both
+and that turns out to be extremely
+
+ align:start position:0%
+and that turns out to be extremely
+ 
+
+ align:start position:0%
+and that turns out to be extremely
+important so if i take water
+
+ align:start position:0%
+important so if i take water
+ 
+
+ align:start position:0%
+important so if i take water
+and i mix it with water
+
+ align:start position:0%
+and i mix it with water
+ 
+
+ align:start position:0%
+and i mix it with water
+then you can get a combination of
+
+ align:start position:0%
+then you can get a combination of
+ 
+
+ align:start position:0%
+then you can get a combination of
+these ions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh plus a whole bunch of water
+
+ align:start position:0%
+oh plus a whole bunch of water
+ 
+
+ align:start position:0%
+oh plus a whole bunch of water
+so this would be like dissociation now
+
+ align:start position:0%
+so this would be like dissociation now
+ 
+
+ align:start position:0%
+so this would be like dissociation now
+there's a word for this
+
+ align:start position:0%
+there's a word for this
+ 
+
+ align:start position:0%
+there's a word for this
+water can turn into either
+
+ align:start position:0%
+water can turn into either
+ 
+
+ align:start position:0%
+water can turn into either
+it can it can be basic or acidic it can
+
+ align:start position:0%
+it can it can be basic or acidic it can
+ 
+
+ align:start position:0%
+it can it can be basic or acidic it can
+it can deliver o h minus
+
+ align:start position:0%
+it can deliver o h minus
+ 
+
+ align:start position:0%
+it can deliver o h minus
+or h3o plus right that's called auto
+
+ align:start position:0%
+or h3o plus right that's called auto
+ 
+
+ align:start position:0%
+or h3o plus right that's called auto
+ionization
+
+ align:start position:0%
+ionization
+ 
+
+ align:start position:0%
+ionization
+and it also has a special word water is
+
+ align:start position:0%
+and it also has a special word water is
+ 
+
+ align:start position:0%
+and it also has a special word water is
+called amphoteric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amphoteric now that means
+
+ align:start position:0%
+amphoteric now that means
+ 
+
+ align:start position:0%
+amphoteric now that means
+that the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can be both
+
+ align:start position:0%
+can be both
+ 
+
+ align:start position:0%
+can be both
+both acid
+
+ align:start position:0%
+both acid
+ 
+
+ align:start position:0%
+both acid
+or a base
+
+ align:start position:0%
+or a base
+ 
+
+ align:start position:0%
+or a base
+it can act as either now so if you take
+
+ align:start position:0%
+it can act as either now so if you take
+ 
+
+ align:start position:0%
+it can act as either now so if you take
+pure water so let's see
+
+ align:start position:0%
+pure water so let's see
+ 
+
+ align:start position:0%
+pure water so let's see
+if i take pure water and
+
+ align:start position:0%
+if i take pure water and
+ 
+
+ align:start position:0%
+if i take pure water and
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i look at the concentrations of
+
+ align:start position:0%
+and i look at the concentrations of
+ 
+
+ align:start position:0%
+and i look at the concentrations of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+uh so atrial plus it's all happening
+
+ align:start position:0%
+uh so atrial plus it's all happening
+ 
+
+ align:start position:0%
+uh so atrial plus it's all happening
+from the water there's nothing in it i
+
+ align:start position:0%
+from the water there's nothing in it i
+ 
+
+ align:start position:0%
+from the water there's nothing in it i
+didn't add anything to it
+
+ align:start position:0%
+didn't add anything to it
+ 
+
+ align:start position:0%
+didn't add anything to it
+it's just pure water acetyl plus so that
+
+ align:start position:0%
+it's just pure water acetyl plus so that
+ 
+
+ align:start position:0%
+it's just pure water acetyl plus so that
+means that
+
+ align:start position:0%
+means that
+ 
+
+ align:start position:0%
+means that
+you know if that reaction happens it's
+
+ align:start position:0%
+you know if that reaction happens it's
+ 
+
+ align:start position:0%
+you know if that reaction happens it's
+going to generate
+
+ align:start position:0%
+going to generate
+ 
+
+ align:start position:0%
+going to generate
+you know the same number so the h3o plus
+
+ align:start position:0%
+you know the same number so the h3o plus
+ 
+
+ align:start position:0%
+you know the same number so the h3o plus
+would equal the concentration of the o h
+
+ align:start position:0%
+would equal the concentration of the o h
+ 
+
+ align:start position:0%
+would equal the concentration of the o h
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+and in pure water that is a value
+
+ align:start position:0%
+and in pure water that is a value
+ 
+
+ align:start position:0%
+and in pure water that is a value
+that is equal to 1 times 10 to the minus
+
+ align:start position:0%
+that is equal to 1 times 10 to the minus
+ 
+
+ align:start position:0%
+that is equal to 1 times 10 to the minus
+7th
+
+ align:start position:0%
+7th
+ 
+
+ align:start position:0%
+7th
+moles per liter at
+
+ align:start position:0%
+moles per liter at
+ 
+
+ align:start position:0%
+moles per liter at
+25c okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at 25c and so now we have yet another
+
+ align:start position:0%
+at 25c and so now we have yet another
+ 
+
+ align:start position:0%
+at 25c and so now we have yet another
+that's neutral you can understand that
+
+ align:start position:0%
+that's neutral you can understand that
+ 
+
+ align:start position:0%
+that's neutral you can understand that
+that's neutral
+
+ align:start position:0%
+that's neutral
+ 
+
+ align:start position:0%
+that's neutral
+because because it you have the
+
+ align:start position:0%
+because because it you have the
+ 
+
+ align:start position:0%
+because because it you have the
+same you know if an acid is h plus or
+
+ align:start position:0%
+same you know if an acid is h plus or
+ 
+
+ align:start position:0%
+same you know if an acid is h plus or
+h3o plus in solution and a base is o h
+
+ align:start position:0%
+h3o plus in solution and a base is o h
+ 
+
+ align:start position:0%
+h3o plus in solution and a base is o h
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+and i've made the same number right
+
+ align:start position:0%
+and i've made the same number right
+ 
+
+ align:start position:0%
+and i've made the same number right
+uh then they neutralize the acidity and
+
+ align:start position:0%
+uh then they neutralize the acidity and
+ 
+
+ align:start position:0%
+uh then they neutralize the acidity and
+basicity are neutralizing one another so
+
+ align:start position:0%
+basicity are neutralizing one another so
+ 
+
+ align:start position:0%
+basicity are neutralizing one another so
+that's neutral
+
+ align:start position:0%
+that's neutral
+ 
+
+ align:start position:0%
+that's neutral
+and in fact you can see that that's uh
+
+ align:start position:0%
+and in fact you can see that that's uh
+ 
+
+ align:start position:0%
+and in fact you can see that that's uh
+ph
+
+ align:start position:0%
+ph
+ 
+
+ align:start position:0%
+ph
+is seven oh and we can even write the
+
+ align:start position:0%
+is seven oh and we can even write the
+ 
+
+ align:start position:0%
+is seven oh and we can even write the
+equilibrium constant for water
+
+ align:start position:0%
+equilibrium constant for water
+ 
+
+ align:start position:0%
+equilibrium constant for water
+which is going to be those guys h3o
+
+ align:start position:0%
+which is going to be those guys h3o
+ 
+
+ align:start position:0%
+which is going to be those guys h3o
+minus times uh atrial plus times oh
+
+ align:start position:0%
+minus times uh atrial plus times oh
+ 
+
+ align:start position:0%
+minus times uh atrial plus times oh
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+which is equal to 10 to the negative
+
+ align:start position:0%
+which is equal to 10 to the negative
+ 
+
+ align:start position:0%
+which is equal to 10 to the negative
+14th
+
+ align:start position:0%
+14th
+ 
+
+ align:start position:0%
+14th
+right because that's the dissociation
+
+ align:start position:0%
+right because that's the dissociation
+ 
+
+ align:start position:0%
+right because that's the dissociation
+reaction for water water plus water goes
+
+ align:start position:0%
+reaction for water water plus water goes
+ 
+
+ align:start position:0%
+reaction for water water plus water goes
+to those ions in solution
+
+ align:start position:0%
+to those ions in solution
+ 
+
+ align:start position:0%
+to those ions in solution
+we ignore the water right and then we're
+
+ align:start position:0%
+we ignore the water right and then we're
+ 
+
+ align:start position:0%
+we ignore the water right and then we're
+left with this
+
+ align:start position:0%
+left with this
+ 
+
+ align:start position:0%
+left with this
+same thing we've been doing okay 10 to
+
+ align:start position:0%
+same thing we've been doing okay 10 to
+ 
+
+ align:start position:0%
+same thing we've been doing okay 10 to
+the minus 14.
+
+ align:start position:0%
+the minus 14.
+ 
+
+ align:start position:0%
+the minus 14.
+now that takes us we neutral you know
+
+ align:start position:0%
+now that takes us we neutral you know
+ 
+
+ align:start position:0%
+now that takes us we neutral you know
+those are neutral
+
+ align:start position:0%
+those are neutral
+ 
+
+ align:start position:0%
+those are neutral
+and and and so speaking of of neutral
+
+ align:start position:0%
+and and and so speaking of of neutral
+ 
+
+ align:start position:0%
+and and and so speaking of of neutral
+that's where we're going to go next and
+
+ align:start position:0%
+that's where we're going to go next and
+ 
+
+ align:start position:0%
+that's where we're going to go next and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i think what i want to do now is you
+
+ align:start position:0%
+i think what i want to do now is you
+ 
+
+ align:start position:0%
+i think what i want to do now is you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+so we're going to go next into
+
+ align:start position:0%
+so we're going to go next into
+ 
+
+ align:start position:0%
+so we're going to go next into
+neutralizing things
+
+ align:start position:0%
+neutralizing things
+ 
+
+ align:start position:0%
+neutralizing things
+so like if you add an acid to a base or
+
+ align:start position:0%
+so like if you add an acid to a base or
+ 
+
+ align:start position:0%
+so like if you add an acid to a base or
+if you had a bastion acid
+
+ align:start position:0%
+if you had a bastion acid
+ 
+
+ align:start position:0%
+if you had a bastion acid
+and and we already said on monday you
+
+ align:start position:0%
+and and we already said on monday you
+ 
+
+ align:start position:0%
+and and we already said on monday you
+get salt and water um
+
+ align:start position:0%
+get salt and water um
+ 
+
+ align:start position:0%
+get salt and water um
+but see to understand that you need a
+
+ align:start position:0%
+but see to understand that you need a
+ 
+
+ align:start position:0%
+but see to understand that you need a
+different you need a broader definition
+
+ align:start position:0%
+different you need a broader definition
+ 
+
+ align:start position:0%
+different you need a broader definition
+cevante is amazing
+
+ align:start position:0%
+cevante is amazing
+ 
+
+ align:start position:0%
+cevante is amazing
+but zevante missed something and and so
+
+ align:start position:0%
+but zevante missed something and and so
+ 
+
+ align:start position:0%
+but zevante missed something and and so
+we need
+
+ align:start position:0%
+we need
+ 
+
+ align:start position:0%
+we need
+a different definition of acids and
+
+ align:start position:0%
+a different definition of acids and
+ 
+
+ align:start position:0%
+a different definition of acids and
+bases that's more general
+
+ align:start position:0%
+bases that's more general
+ 
+
+ align:start position:0%
+bases that's more general
+and that's what we're going to start
+
+ align:start position:0%
+and that's what we're going to start
+ 
+
+ align:start position:0%
+and that's what we're going to start
+with on monday but wait because
+
+ align:start position:0%
+with on monday but wait because
+ 
+
+ align:start position:0%
+with on monday but wait because
+this is a great place for me to work on
+
+ align:start position:0%
+this is a great place for me to work on
+ 
+
+ align:start position:0%
+this is a great place for me to work on
+my arm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i gotta hit okay
+
+ align:start position:0%
+i gotta hit okay
+ 
+
+ align:start position:0%
+i gotta hit okay
+we're gonna go all the way up there and
+
+ align:start position:0%
+we're gonna go all the way up there and
+ 
+
+ align:start position:0%
+we're gonna go all the way up there and
+all the way up there
+
+ align:start position:0%
+all the way up there
+ 
+
+ align:start position:0%
+all the way up there
+and right there and right there and
+
+ align:start position:0%
+and right there and right there and
+ 
+
+ align:start position:0%
+and right there and right there and
+oh there and there and there
+
+ align:start position:0%
+oh there and there and there
+ 
+
+ align:start position:0%
+oh there and there and there
+and there oh that was excitement
+
+ align:start position:0%
+and there oh that was excitement
+ 
+
+ align:start position:0%
+and there oh that was excitement
+let's go back there in there okay
+
+ align:start position:0%
+let's go back there in there okay
+ 
+
+ align:start position:0%
+let's go back there in there okay
+and there oh that was the same direction
+
+ align:start position:0%
+and there oh that was the same direction
+ 
+
+ align:start position:0%
+and there oh that was the same direction
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and there and there in the middle
+
+ align:start position:0%
+and there and there in the middle
+ 
+
+ align:start position:0%
+and there and there in the middle
+and there and there oh
+
+ align:start position:0%
+and there and there oh
+ 
+
+ align:start position:0%
+and there and there oh
+that was there and there
+
+ align:start position:0%
+that was there and there
+ 
+
+ align:start position:0%
+that was there and there
+and there and
+
+ align:start position:0%
+and there and
+ 
+
+ align:start position:0%
+and there and
+you guys are seeing i need i need a
+
+ align:start position:0%
+you guys are seeing i need i need a
+ 
+
+ align:start position:0%
+you guys are seeing i need i need a
+stronger arm here
+
+ align:start position:0%
+stronger arm here
+ 
+
+ align:start position:0%
+stronger arm here
+i can't really get too far and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and oh that side is all in there
+
+ align:start position:0%
+and oh that side is all in there
+ 
+
+ align:start position:0%
+and oh that side is all in there
+and there and there
+
+ align:start position:0%
+and there and there
+ 
+
+ align:start position:0%
+and there and there
+and one more i'm going deep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have a great thanksgiving everyone
+
+ align:start position:0%
+have a great thanksgiving everyone
+ 
+
+ align:start position:0%
+have a great thanksgiving everyone
+see you guys on monday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/Zg6wQdMFO2c.txt b/Zg6wQdMFO2c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1371ee1dd140fc9c836790f04637013ae5bc56f7
--- /dev/null
+++ b/Zg6wQdMFO2c.txt
@@ -0,0 +1,2491 @@
+align:start position:0%
+ 
+how do you design test and build a small
+
+ align:start position:0%
+how do you design test and build a small
+ 
+
+ align:start position:0%
+how do you design test and build a small
+and completely edible boat that propels
+
+ align:start position:0%
+and completely edible boat that propels
+ 
+
+ align:start position:0%
+and completely edible boat that propels
+itself through your cocktail this is a
+
+ align:start position:0%
+itself through your cocktail this is a
+ 
+
+ align:start position:0%
+itself through your cocktail this is a
+complicated problem but it and many
+
+ align:start position:0%
+complicated problem but it and many
+ 
+
+ align:start position:0%
+complicated problem but it and many
+other problems like it can be solved by
+
+ align:start position:0%
+other problems like it can be solved by
+ 
+
+ align:start position:0%
+other problems like it can be solved by
+systematically breaking those problems
+
+ align:start position:0%
+systematically breaking those problems
+ 
+
+ align:start position:0%
+systematically breaking those problems
+down in this video we'll explore how to
+
+ align:start position:0%
+down in this video we'll explore how to
+ 
+
+ align:start position:0%
+down in this video we'll explore how to
+MIT graduate students created these
+
+ align:start position:0%
+MIT graduate students created these
+ 
+
+ align:start position:0%
+MIT graduate students created these
+cocktail cruisers
+
+ align:start position:0%
+cocktail cruisers
+ 
+
+ align:start position:0%
+cocktail cruisers
+this video is part of the
+
+ align:start position:0%
+this video is part of the
+ 
+
+ align:start position:0%
+this video is part of the
+problem-solving video series
+
+ align:start position:0%
+problem-solving video series
+ 
+
+ align:start position:0%
+problem-solving video series
+problem-solving skills in combination
+
+ align:start position:0%
+problem-solving skills in combination
+ 
+
+ align:start position:0%
+problem-solving skills in combination
+with an understanding of the natural and
+
+ align:start position:0%
+with an understanding of the natural and
+ 
+
+ align:start position:0%
+with an understanding of the natural and
+human-made world are critical to the
+
+ align:start position:0%
+human-made world are critical to the
+ 
+
+ align:start position:0%
+human-made world are critical to the
+design and optimization of systems and
+
+ align:start position:0%
+design and optimization of systems and
+ 
+
+ align:start position:0%
+design and optimization of systems and
+processes hi my name is Lisa Burton and
+
+ align:start position:0%
+processes hi my name is Lisa Burton and
+ 
+
+ align:start position:0%
+processes hi my name is Lisa Burton and
+I'm Nadia Chang we are graduate students
+
+ align:start position:0%
+I'm Nadia Chang we are graduate students
+ 
+
+ align:start position:0%
+I'm Nadia Chang we are graduate students
+in Pecola's soy's lab in the department
+
+ align:start position:0%
+in Pecola's soy's lab in the department
+ 
+
+ align:start position:0%
+in Pecola's soy's lab in the department
+of mechanical engineering at MIT today
+
+ align:start position:0%
+of mechanical engineering at MIT today
+ 
+
+ align:start position:0%
+of mechanical engineering at MIT today
+we're going to tell you about a class
+
+ align:start position:0%
+we're going to tell you about a class
+ 
+
+ align:start position:0%
+we're going to tell you about a class
+project that we worked on that turn into
+
+ align:start position:0%
+project that we worked on that turn into
+ 
+
+ align:start position:0%
+project that we worked on that turn into
+a product called cocktail cruisers after
+
+ align:start position:0%
+a product called cocktail cruisers after
+ 
+
+ align:start position:0%
+a product called cocktail cruisers after
+watching this video you should be able
+
+ align:start position:0%
+watching this video you should be able
+ 
+
+ align:start position:0%
+watching this video you should be able
+to identify the steps of the
+
+ align:start position:0%
+to identify the steps of the
+ 
+
+ align:start position:0%
+to identify the steps of the
+problem-solving process and recognize
+
+ align:start position:0%
+problem-solving process and recognize
+ 
+
+ align:start position:0%
+problem-solving process and recognize
+that the problem-solving process is
+
+ align:start position:0%
+that the problem-solving process is
+ 
+
+ align:start position:0%
+that the problem-solving process is
+iterative take a moment to think about
+
+ align:start position:0%
+iterative take a moment to think about
+ 
+
+ align:start position:0%
+iterative take a moment to think about
+your approach to problem-solving what
+
+ align:start position:0%
+your approach to problem-solving what
+ 
+
+ align:start position:0%
+your approach to problem-solving what
+steps do you generally go through please
+
+ align:start position:0%
+steps do you generally go through please
+ 
+
+ align:start position:0%
+steps do you generally go through please
+pause the video and take a moment to
+
+ align:start position:0%
+pause the video and take a moment to
+ 
+
+ align:start position:0%
+pause the video and take a moment to
+think about it then continue playing the
+
+ align:start position:0%
+think about it then continue playing the
+ 
+
+ align:start position:0%
+think about it then continue playing the
+video to hear about one approach while
+
+ align:start position:0%
+video to hear about one approach while
+ 
+
+ align:start position:0%
+video to hear about one approach while
+different people might approach a
+
+ align:start position:0%
+different people might approach a
+ 
+
+ align:start position:0%
+different people might approach a
+problem in different ways using an
+
+ align:start position:0%
+problem in different ways using an
+ 
+
+ align:start position:0%
+problem in different ways using an
+explicit strategy for problem-solving
+
+ align:start position:0%
+explicit strategy for problem-solving
+ 
+
+ align:start position:0%
+explicit strategy for problem-solving
+can be very helpful you can find
+
+ align:start position:0%
+can be very helpful you can find
+ 
+
+ align:start position:0%
+can be very helpful you can find
+different problem-solving strategies in
+
+ align:start position:0%
+different problem-solving strategies in
+ 
+
+ align:start position:0%
+different problem-solving strategies in
+the literature the strategy that we will
+
+ align:start position:0%
+the literature the strategy that we will
+ 
+
+ align:start position:0%
+the literature the strategy that we will
+present in this video is adapted from
+
+ align:start position:0%
+present in this video is adapted from
+ 
+
+ align:start position:0%
+present in this video is adapted from
+dawn Woods and Phil Blanc at the first
+
+ align:start position:0%
+dawn Woods and Phil Blanc at the first
+ 
+
+ align:start position:0%
+dawn Woods and Phil Blanc at the first
+step is to define the problem what are
+
+ align:start position:0%
+step is to define the problem what are
+ 
+
+ align:start position:0%
+step is to define the problem what are
+the criteria what are the constraints
+
+ align:start position:0%
+the criteria what are the constraints
+ 
+
+ align:start position:0%
+the criteria what are the constraints
+after defining the problem you need to
+
+ align:start position:0%
+after defining the problem you need to
+ 
+
+ align:start position:0%
+after defining the problem you need to
+gather information what are the knowns
+
+ align:start position:0%
+gather information what are the knowns
+ 
+
+ align:start position:0%
+gather information what are the knowns
+and unknowns what content knowledge is
+
+ align:start position:0%
+and unknowns what content knowledge is
+ 
+
+ align:start position:0%
+and unknowns what content knowledge is
+needed to solve the problem have others
+
+ align:start position:0%
+needed to solve the problem have others
+ 
+
+ align:start position:0%
+needed to solve the problem have others
+worked on a similar problem before the
+
+ align:start position:0%
+worked on a similar problem before the
+ 
+
+ align:start position:0%
+worked on a similar problem before the
+next step is to explore look at the
+
+ align:start position:0%
+next step is to explore look at the
+ 
+
+ align:start position:0%
+next step is to explore look at the
+problem in different ways brainstorm
+
+ align:start position:0%
+problem in different ways brainstorm
+ 
+
+ align:start position:0%
+problem in different ways brainstorm
+different approaches to meeting the
+
+ align:start position:0%
+different approaches to meeting the
+ 
+
+ align:start position:0%
+different approaches to meeting the
+criteria given the constraints after
+
+ align:start position:0%
+criteria given the constraints after
+ 
+
+ align:start position:0%
+criteria given the constraints after
+exploring you need to pick one approach
+
+ align:start position:0%
+exploring you need to pick one approach
+ 
+
+ align:start position:0%
+exploring you need to pick one approach
+to solving your problem and plan your
+
+ align:start position:0%
+to solving your problem and plan your
+ 
+
+ align:start position:0%
+to solving your problem and plan your
+strategy determine the resources needed
+
+ align:start position:0%
+strategy determine the resources needed
+ 
+
+ align:start position:0%
+strategy determine the resources needed
+to carry out your plan a flowchart
+
+ align:start position:0%
+to carry out your plan a flowchart
+ 
+
+ align:start position:0%
+to carry out your plan a flowchart
+outline or schematic might be useful
+
+ align:start position:0%
+outline or schematic might be useful
+ 
+
+ align:start position:0%
+outline or schematic might be useful
+after the planning phase it is time to
+
+ align:start position:0%
+after the planning phase it is time to
+ 
+
+ align:start position:0%
+after the planning phase it is time to
+act in this step you follow your plan to
+
+ align:start position:0%
+act in this step you follow your plan to
+ 
+
+ align:start position:0%
+act in this step you follow your plan to
+create your solution
+
+ align:start position:0%
+create your solution
+ 
+
+ align:start position:0%
+create your solution
+once you have a solution you need to
+
+ align:start position:0%
+once you have a solution you need to
+ 
+
+ align:start position:0%
+once you have a solution you need to
+check it does it make sense does it meet
+
+ align:start position:0%
+check it does it make sense does it meet
+ 
+
+ align:start position:0%
+check it does it make sense does it meet
+the criteria where does it fall short is
+
+ align:start position:0%
+the criteria where does it fall short is
+ 
+
+ align:start position:0%
+the criteria where does it fall short is
+any troubleshooting required if the
+
+ align:start position:0%
+any troubleshooting required if the
+ 
+
+ align:start position:0%
+any troubleshooting required if the
+solution isn't satisfactory it might be
+
+ align:start position:0%
+solution isn't satisfactory it might be
+ 
+
+ align:start position:0%
+solution isn't satisfactory it might be
+necessary to explore some more and
+
+ align:start position:0%
+necessary to explore some more and
+ 
+
+ align:start position:0%
+necessary to explore some more and
+create a new plan once you have your
+
+ align:start position:0%
+create a new plan once you have your
+ 
+
+ align:start position:0%
+create a new plan once you have your
+final solution what have you learned
+
+ align:start position:0%
+final solution what have you learned
+ 
+
+ align:start position:0%
+final solution what have you learned
+that can be generalized to other
+
+ align:start position:0%
+that can be generalized to other
+ 
+
+ align:start position:0%
+that can be generalized to other
+contexts finally disseminate your
+
+ align:start position:0%
+contexts finally disseminate your
+ 
+
+ align:start position:0%
+contexts finally disseminate your
+results so that others can learn from
+
+ align:start position:0%
+results so that others can learn from
+ 
+
+ align:start position:0%
+results so that others can learn from
+your solution this could be through a
+
+ align:start position:0%
+your solution this could be through a
+ 
+
+ align:start position:0%
+your solution this could be through a
+class discussion a formal presentation
+
+ align:start position:0%
+class discussion a formal presentation
+ 
+
+ align:start position:0%
+class discussion a formal presentation
+or a scientific paper now that you are
+
+ align:start position:0%
+or a scientific paper now that you are
+ 
+
+ align:start position:0%
+or a scientific paper now that you are
+familiar with the problem-solving
+
+ align:start position:0%
+familiar with the problem-solving
+ 
+
+ align:start position:0%
+familiar with the problem-solving
+process see if you can identify where I
+
+ align:start position:0%
+process see if you can identify where I
+ 
+
+ align:start position:0%
+process see if you can identify where I
+use these steps as I worked on a class
+
+ align:start position:0%
+use these steps as I worked on a class
+ 
+
+ align:start position:0%
+use these steps as I worked on a class
+project this project began in my fluid
+
+ align:start position:0%
+project this project began in my fluid
+ 
+
+ align:start position:0%
+project this project began in my fluid
+dynamics class which focused on
+
+ align:start position:0%
+dynamics class which focused on
+ 
+
+ align:start position:0%
+dynamics class which focused on
+interfacial phenomena and was taught by
+
+ align:start position:0%
+interfacial phenomena and was taught by
+ 
+
+ align:start position:0%
+interfacial phenomena and was taught by
+my other adviser professor John Bush the
+
+ align:start position:0%
+my other adviser professor John Bush the
+ 
+
+ align:start position:0%
+my other adviser professor John Bush the
+main criterion or requirement for the
+
+ align:start position:0%
+main criterion or requirement for the
+ 
+
+ align:start position:0%
+main criterion or requirement for the
+project was to conduct an experiment
+
+ align:start position:0%
+project was to conduct an experiment
+ 
+
+ align:start position:0%
+project was to conduct an experiment
+perform a simulation or design a product
+
+ align:start position:0%
+perform a simulation or design a product
+ 
+
+ align:start position:0%
+perform a simulation or design a product
+fundamentally based on a topic covered
+
+ align:start position:0%
+fundamentally based on a topic covered
+ 
+
+ align:start position:0%
+fundamentally based on a topic covered
+in class there were also some
+
+ align:start position:0%
+in class there were also some
+ 
+
+ align:start position:0%
+in class there were also some
+constraints placed on the project we
+
+ align:start position:0%
+constraints placed on the project we
+ 
+
+ align:start position:0%
+constraints placed on the project we
+only had three months to work on it in a
+
+ align:start position:0%
+only had three months to work on it in a
+ 
+
+ align:start position:0%
+only had three months to work on it in a
+limited budget other than that it was
+
+ align:start position:0%
+limited budget other than that it was
+ 
+
+ align:start position:0%
+limited budget other than that it was
+very open-ended it was really up to me
+
+ align:start position:0%
+very open-ended it was really up to me
+ 
+
+ align:start position:0%
+very open-ended it was really up to me
+to define the problem from there
+
+ align:start position:0%
+to define the problem from there
+ 
+
+ align:start position:0%
+to define the problem from there
+learning about the Marangoni effect
+
+ align:start position:0%
+learning about the Marangoni effect
+ 
+
+ align:start position:0%
+learning about the Marangoni effect
+inspired my design
+
+ align:start position:0%
+inspired my design
+ 
+
+ align:start position:0%
+inspired my design
+the Marangoni effect arises from a
+
+ align:start position:0%
+the Marangoni effect arises from a
+ 
+
+ align:start position:0%
+the Marangoni effect arises from a
+gradient or difference in surface
+
+ align:start position:0%
+gradient or difference in surface
+ 
+
+ align:start position:0%
+gradient or difference in surface
+tension we can see the Marangoni effect
+
+ align:start position:0%
+tension we can see the Marangoni effect
+ 
+
+ align:start position:0%
+tension we can see the Marangoni effect
+by adding a drop of soap solution to a
+
+ align:start position:0%
+by adding a drop of soap solution to a
+ 
+
+ align:start position:0%
+by adding a drop of soap solution to a
+container of water the soap solution
+
+ align:start position:0%
+container of water the soap solution
+ 
+
+ align:start position:0%
+container of water the soap solution
+reduces the surface tension of the water
+
+ align:start position:0%
+reduces the surface tension of the water
+ 
+
+ align:start position:0%
+reduces the surface tension of the water
+locally causing flow using black pepper
+
+ align:start position:0%
+locally causing flow using black pepper
+ 
+
+ align:start position:0%
+locally causing flow using black pepper
+flakes as a tracer we can visualize the
+
+ align:start position:0%
+flakes as a tracer we can visualize the
+ 
+
+ align:start position:0%
+flakes as a tracer we can visualize the
+flow away from the area of low surface
+
+ align:start position:0%
+flow away from the area of low surface
+ 
+
+ align:start position:0%
+flow away from the area of low surface
+tension surface tension is simply a
+
+ align:start position:0%
+tension surface tension is simply a
+ 
+
+ align:start position:0%
+tension surface tension is simply a
+property of liquid that results from
+
+ align:start position:0%
+property of liquid that results from
+ 
+
+ align:start position:0%
+property of liquid that results from
+intermolecular forces in the bulk of a
+
+ align:start position:0%
+intermolecular forces in the bulk of a
+ 
+
+ align:start position:0%
+intermolecular forces in the bulk of a
+uniform liquid each molecule experience
+
+ align:start position:0%
+uniform liquid each molecule experience
+ 
+
+ align:start position:0%
+uniform liquid each molecule experience
+is a zero net force because molecules
+
+ align:start position:0%
+is a zero net force because molecules
+ 
+
+ align:start position:0%
+is a zero net force because molecules
+that exert equivalent force on each
+
+ align:start position:0%
+that exert equivalent force on each
+ 
+
+ align:start position:0%
+that exert equivalent force on each
+other surrounded at the surface of a
+
+ align:start position:0%
+other surrounded at the surface of a
+ 
+
+ align:start position:0%
+other surrounded at the surface of a
+liquid molecules from the liquid
+
+ align:start position:0%
+liquid molecules from the liquid
+ 
+
+ align:start position:0%
+liquid molecules from the liquid
+experience a nonzero net force pulling
+
+ align:start position:0%
+experience a nonzero net force pulling
+ 
+
+ align:start position:0%
+experience a nonzero net force pulling
+them toward the bulk of the fluid
+
+ align:start position:0%
+them toward the bulk of the fluid
+ 
+
+ align:start position:0%
+them toward the bulk of the fluid
+because they are not completely
+
+ align:start position:0%
+because they are not completely
+ 
+
+ align:start position:0%
+because they are not completely
+surrounded by like molecules this causes
+
+ align:start position:0%
+surrounded by like molecules this causes
+ 
+
+ align:start position:0%
+surrounded by like molecules this causes
+the surface to minimize its area the
+
+ align:start position:0%
+the surface to minimize its area the
+ 
+
+ align:start position:0%
+the surface to minimize its area the
+high surface tension of water allows
+
+ align:start position:0%
+high surface tension of water allows
+ 
+
+ align:start position:0%
+high surface tension of water allows
+objects denser than water such as a
+
+ align:start position:0%
+objects denser than water such as a
+ 
+
+ align:start position:0%
+objects denser than water such as a
+paper clip or
+
+ align:start position:0%
+paper clip or
+ 
+
+ align:start position:0%
+paper clip or
+water Strider to float on the surface if
+
+ align:start position:0%
+water Strider to float on the surface if
+ 
+
+ align:start position:0%
+water Strider to float on the surface if
+an object has a high surface tension
+
+ align:start position:0%
+an object has a high surface tension
+ 
+
+ align:start position:0%
+an object has a high surface tension
+liquid on one side of it and a low
+
+ align:start position:0%
+liquid on one side of it and a low
+ 
+
+ align:start position:0%
+liquid on one side of it and a low
+surface tension liquid on the other side
+
+ align:start position:0%
+surface tension liquid on the other side
+ 
+
+ align:start position:0%
+surface tension liquid on the other side
+the difference in surface tension will
+
+ align:start position:0%
+the difference in surface tension will
+ 
+
+ align:start position:0%
+the difference in surface tension will
+cause the object to move toward the high
+
+ align:start position:0%
+cause the object to move toward the high
+ 
+
+ align:start position:0%
+cause the object to move toward the high
+surface tension liquid we can see that
+
+ align:start position:0%
+surface tension liquid we can see that
+ 
+
+ align:start position:0%
+surface tension liquid we can see that
+happen in this demonstration of a
+
+ align:start position:0%
+happen in this demonstration of a
+ 
+
+ align:start position:0%
+happen in this demonstration of a
+toothpick floating on water if we add a
+
+ align:start position:0%
+toothpick floating on water if we add a
+ 
+
+ align:start position:0%
+toothpick floating on water if we add a
+few drops of soapy water to one side of
+
+ align:start position:0%
+few drops of soapy water to one side of
+ 
+
+ align:start position:0%
+few drops of soapy water to one side of
+the toothpick the toothpick moves away I
+
+ align:start position:0%
+the toothpick the toothpick moves away I
+ 
+
+ align:start position:0%
+the toothpick the toothpick moves away I
+decided that I wanted to make a
+
+ align:start position:0%
+decided that I wanted to make a
+ 
+
+ align:start position:0%
+decided that I wanted to make a
+miniature boat that would be propelled
+
+ align:start position:0%
+miniature boat that would be propelled
+ 
+
+ align:start position:0%
+miniature boat that would be propelled
+by a surface tension gradient I wanted
+
+ align:start position:0%
+by a surface tension gradient I wanted
+ 
+
+ align:start position:0%
+by a surface tension gradient I wanted
+to propel the boat in a water-based
+
+ align:start position:0%
+to propel the boat in a water-based
+ 
+
+ align:start position:0%
+to propel the boat in a water-based
+environment with the ultimate goal of
+
+ align:start position:0%
+environment with the ultimate goal of
+ 
+
+ align:start position:0%
+environment with the ultimate goal of
+using it in a food setting this required
+
+ align:start position:0%
+using it in a food setting this required
+ 
+
+ align:start position:0%
+using it in a food setting this required
+that the second liquid be safe to eat
+
+ align:start position:0%
+that the second liquid be safe to eat
+ 
+
+ align:start position:0%
+that the second liquid be safe to eat
+since it would mix with the water at
+
+ align:start position:0%
+since it would mix with the water at
+ 
+
+ align:start position:0%
+since it would mix with the water at
+this point I wasn't concerned with
+
+ align:start position:0%
+this point I wasn't concerned with
+ 
+
+ align:start position:0%
+this point I wasn't concerned with
+making the boat edible because it could
+
+ align:start position:0%
+making the boat edible because it could
+ 
+
+ align:start position:0%
+making the boat edible because it could
+simply be removed by hand from the food
+
+ align:start position:0%
+simply be removed by hand from the food
+ 
+
+ align:start position:0%
+simply be removed by hand from the food
+therefore the problem we needed to solve
+
+ align:start position:0%
+therefore the problem we needed to solve
+ 
+
+ align:start position:0%
+therefore the problem we needed to solve
+was how to design a boat that could be
+
+ align:start position:0%
+was how to design a boat that could be
+ 
+
+ align:start position:0%
+was how to design a boat that could be
+propelled by the Marangoni effect
+
+ align:start position:0%
+propelled by the Marangoni effect
+ 
+
+ align:start position:0%
+propelled by the Marangoni effect
+this included the identification of a
+
+ align:start position:0%
+this included the identification of a
+ 
+
+ align:start position:0%
+this included the identification of a
+liquid that was edible and had the
+
+ align:start position:0%
+liquid that was edible and had the
+ 
+
+ align:start position:0%
+liquid that was edible and had the
+appropriate surface tension for use as
+
+ align:start position:0%
+appropriate surface tension for use as
+ 
+
+ align:start position:0%
+appropriate surface tension for use as
+the propellant I started gathering
+
+ align:start position:0%
+the propellant I started gathering
+ 
+
+ align:start position:0%
+the propellant I started gathering
+information about different fluids that
+
+ align:start position:0%
+information about different fluids that
+ 
+
+ align:start position:0%
+information about different fluids that
+had a lower surface tension than water I
+
+ align:start position:0%
+had a lower surface tension than water I
+ 
+
+ align:start position:0%
+had a lower surface tension than water I
+also looked at the existing designs of
+
+ align:start position:0%
+also looked at the existing designs of
+ 
+
+ align:start position:0%
+also looked at the existing designs of
+other boats noting what propellants they
+
+ align:start position:0%
+other boats noting what propellants they
+ 
+
+ align:start position:0%
+other boats noting what propellants they
+used in their method for releasing the
+
+ align:start position:0%
+used in their method for releasing the
+ 
+
+ align:start position:0%
+used in their method for releasing the
+propellant into the surrounding water to
+
+ align:start position:0%
+propellant into the surrounding water to
+ 
+
+ align:start position:0%
+propellant into the surrounding water to
+identify important physical features of
+
+ align:start position:0%
+identify important physical features of
+ 
+
+ align:start position:0%
+identify important physical features of
+the boat I did some calculations
+
+ align:start position:0%
+the boat I did some calculations
+ 
+
+ align:start position:0%
+the boat I did some calculations
+starting with a simple force balance
+
+ align:start position:0%
+starting with a simple force balance
+ 
+
+ align:start position:0%
+starting with a simple force balance
+diagram we can represent the boat as a
+
+ align:start position:0%
+diagram we can represent the boat as a
+ 
+
+ align:start position:0%
+diagram we can represent the boat as a
+rectangular prism for now viewing the
+
+ align:start position:0%
+rectangular prism for now viewing the
+ 
+
+ align:start position:0%
+rectangular prism for now viewing the
+boat from the side we see just a
+
+ align:start position:0%
+boat from the side we see just a
+ 
+
+ align:start position:0%
+boat from the side we see just a
+rectangle in the vertical direction the
+
+ align:start position:0%
+rectangle in the vertical direction the
+ 
+
+ align:start position:0%
+rectangle in the vertical direction the
+forces acting on the boat are the force
+
+ align:start position:0%
+forces acting on the boat are the force
+ 
+
+ align:start position:0%
+forces acting on the boat are the force
+due to gravity or the weight of the boat
+
+ align:start position:0%
+due to gravity or the weight of the boat
+ 
+
+ align:start position:0%
+due to gravity or the weight of the boat
+and the buoyancy force which is
+
+ align:start position:0%
+and the buoyancy force which is
+ 
+
+ align:start position:0%
+and the buoyancy force which is
+equivalent to the weight of the water
+
+ align:start position:0%
+equivalent to the weight of the water
+ 
+
+ align:start position:0%
+equivalent to the weight of the water
+displaced by the boat and the meniscus
+
+ align:start position:0%
+displaced by the boat and the meniscus
+ 
+
+ align:start position:0%
+displaced by the boat and the meniscus
+you've probably noticed that water in
+
+ align:start position:0%
+you've probably noticed that water in
+ 
+
+ align:start position:0%
+you've probably noticed that water in
+your drinking glass slightly climbs up
+
+ align:start position:0%
+your drinking glass slightly climbs up
+ 
+
+ align:start position:0%
+your drinking glass slightly climbs up
+the wall of the glass this is the
+
+ align:start position:0%
+the wall of the glass this is the
+ 
+
+ align:start position:0%
+the wall of the glass this is the
+meniscus then it depends on the material
+
+ align:start position:0%
+meniscus then it depends on the material
+ 
+
+ align:start position:0%
+meniscus then it depends on the material
+of the object for instance the boat or
+
+ align:start position:0%
+of the object for instance the boat or
+ 
+
+ align:start position:0%
+of the object for instance the boat or
+the glass the liquid and the gas in our
+
+ align:start position:0%
+the glass the liquid and the gas in our
+ 
+
+ align:start position:0%
+the glass the liquid and the gas in our
+case air therefore to make the boat
+
+ align:start position:0%
+case air therefore to make the boat
+ 
+
+ align:start position:0%
+case air therefore to make the boat
+float we must ensure that the weight of
+
+ align:start position:0%
+float we must ensure that the weight of
+ 
+
+ align:start position:0%
+float we must ensure that the weight of
+the water displaced balances the weight
+
+ align:start position:0%
+the water displaced balances the weight
+ 
+
+ align:start position:0%
+the water displaced balances the weight
+of the boat this is Archimedes principle
+
+ align:start position:0%
+of the boat this is Archimedes principle
+ 
+
+ align:start position:0%
+of the boat this is Archimedes principle
+in the horizontal direction we have the
+
+ align:start position:0%
+in the horizontal direction we have the
+ 
+
+ align:start position:0%
+in the horizontal direction we have the
+force of surface tension of the fuel on
+
+ align:start position:0%
+force of surface tension of the fuel on
+ 
+
+ align:start position:0%
+force of surface tension of the fuel on
+the left side and the force of surface
+
+ align:start position:0%
+the left side and the force of surface
+ 
+
+ align:start position:0%
+the left side and the force of surface
+tension of the surrounding fluid which
+
+ align:start position:0%
+tension of the surrounding fluid which
+ 
+
+ align:start position:0%
+tension of the surrounding fluid which
+we will assume as
+
+ align:start position:0%
+we will assume as
+ 
+
+ align:start position:0%
+we will assume as
+if the forces aren't equal the boat must
+
+ align:start position:0%
+if the forces aren't equal the boat must
+ 
+
+ align:start position:0%
+if the forces aren't equal the boat must
+accelerate according to Newton's laws
+
+ align:start position:0%
+accelerate according to Newton's laws
+ 
+
+ align:start position:0%
+accelerate according to Newton's laws
+therefore to make the boat move faster
+
+ align:start position:0%
+therefore to make the boat move faster
+ 
+
+ align:start position:0%
+therefore to make the boat move faster
+we want the difference in surface
+
+ align:start position:0%
+we want the difference in surface
+ 
+
+ align:start position:0%
+we want the difference in surface
+stitching to be as great as possible
+
+ align:start position:0%
+stitching to be as great as possible
+ 
+
+ align:start position:0%
+stitching to be as great as possible
+once the boat is moving drag becomes
+
+ align:start position:0%
+once the boat is moving drag becomes
+ 
+
+ align:start position:0%
+once the boat is moving drag becomes
+important drag opposes the direction of
+
+ align:start position:0%
+important drag opposes the direction of
+ 
+
+ align:start position:0%
+important drag opposes the direction of
+motion and increase with velocity and
+
+ align:start position:0%
+motion and increase with velocity and
+ 
+
+ align:start position:0%
+motion and increase with velocity and
+the cross sectional area of the boat a
+
+ align:start position:0%
+the cross sectional area of the boat a
+ 
+
+ align:start position:0%
+the cross sectional area of the boat a
+smaller cross-sectional area will allow
+
+ align:start position:0%
+smaller cross-sectional area will allow
+ 
+
+ align:start position:0%
+smaller cross-sectional area will allow
+the boat to move faster to ensure that
+
+ align:start position:0%
+the boat to move faster to ensure that
+ 
+
+ align:start position:0%
+the boat to move faster to ensure that
+the boat remains stable the center of
+
+ align:start position:0%
+the boat remains stable the center of
+ 
+
+ align:start position:0%
+the boat remains stable the center of
+mass must be below the center of
+
+ align:start position:0%
+mass must be below the center of
+ 
+
+ align:start position:0%
+mass must be below the center of
+buoyancy otherwise the boat will tip
+
+ align:start position:0%
+buoyancy otherwise the boat will tip
+ 
+
+ align:start position:0%
+buoyancy otherwise the boat will tip
+over and sink as I explore different
+
+ align:start position:0%
+over and sink as I explore different
+ 
+
+ align:start position:0%
+over and sink as I explore different
+ideas it became clear that I needed to
+
+ align:start position:0%
+ideas it became clear that I needed to
+ 
+
+ align:start position:0%
+ideas it became clear that I needed to
+do some testing to find an edible low
+
+ align:start position:0%
+do some testing to find an edible low
+ 
+
+ align:start position:0%
+do some testing to find an edible low
+surface tension liquid to act as the
+
+ align:start position:0%
+surface tension liquid to act as the
+ 
+
+ align:start position:0%
+surface tension liquid to act as the
+boats fuel I tested different liquids I
+
+ align:start position:0%
+boats fuel I tested different liquids I
+ 
+
+ align:start position:0%
+boats fuel I tested different liquids I
+found in my kitchen from hot sauce to
+
+ align:start position:0%
+found in my kitchen from hot sauce to
+ 
+
+ align:start position:0%
+found in my kitchen from hot sauce to
+sugar water to vinegar from these tests
+
+ align:start position:0%
+sugar water to vinegar from these tests
+ 
+
+ align:start position:0%
+sugar water to vinegar from these tests
+I decided that I needed a low surface
+
+ align:start position:0%
+I decided that I needed a low surface
+ 
+
+ align:start position:0%
+I decided that I needed a low surface
+tension liquid that was also volatile or
+
+ align:start position:0%
+tension liquid that was also volatile or
+ 
+
+ align:start position:0%
+tension liquid that was also volatile or
+evaporative this is necessary for the
+
+ align:start position:0%
+evaporative this is necessary for the
+ 
+
+ align:start position:0%
+evaporative this is necessary for the
+boat to continue to move otherwise the
+
+ align:start position:0%
+boat to continue to move otherwise the
+ 
+
+ align:start position:0%
+boat to continue to move otherwise the
+fuel surrounds the boat equally on all
+
+ align:start position:0%
+fuel surrounds the boat equally on all
+ 
+
+ align:start position:0%
+fuel surrounds the boat equally on all
+sides so that no surface tension
+
+ align:start position:0%
+sides so that no surface tension
+ 
+
+ align:start position:0%
+sides so that no surface tension
+gradient exists and therefore the boat
+
+ align:start position:0%
+gradient exists and therefore the boat
+ 
+
+ align:start position:0%
+gradient exists and therefore the boat
+does not move the best fuel I found was
+
+ align:start position:0%
+does not move the best fuel I found was
+ 
+
+ align:start position:0%
+does not move the best fuel I found was
+liquor the alcohol content of liquor and
+
+ align:start position:0%
+liquor the alcohol content of liquor and
+ 
+
+ align:start position:0%
+liquor the alcohol content of liquor and
+the surface tension are inversely
+
+ align:start position:0%
+the surface tension are inversely
+ 
+
+ align:start position:0%
+the surface tension are inversely
+related
+
+ align:start position:0%
+related
+ 
+
+ align:start position:0%
+related
+therefore using a very high alcohol
+
+ align:start position:0%
+therefore using a very high alcohol
+ 
+
+ align:start position:0%
+therefore using a very high alcohol
+content liquor will result in a faster
+
+ align:start position:0%
+content liquor will result in a faster
+ 
+
+ align:start position:0%
+content liquor will result in a faster
+boat I started sketching ideas for what
+
+ align:start position:0%
+boat I started sketching ideas for what
+ 
+
+ align:start position:0%
+boat I started sketching ideas for what
+the boats might look like drawing on
+
+ align:start position:0%
+the boats might look like drawing on
+ 
+
+ align:start position:0%
+the boats might look like drawing on
+previous research the initial design had
+
+ align:start position:0%
+previous research the initial design had
+ 
+
+ align:start position:0%
+previous research the initial design had
+an open fuel reservoir in the middle of
+
+ align:start position:0%
+an open fuel reservoir in the middle of
+ 
+
+ align:start position:0%
+an open fuel reservoir in the middle of
+the boat with a small slit that allows
+
+ align:start position:0%
+the boat with a small slit that allows
+ 
+
+ align:start position:0%
+the boat with a small slit that allows
+the liquid to leave the reservoir the
+
+ align:start position:0%
+the liquid to leave the reservoir the
+ 
+
+ align:start position:0%
+the liquid to leave the reservoir the
+overall shape was a very simple boat
+
+ align:start position:0%
+overall shape was a very simple boat
+ 
+
+ align:start position:0%
+overall shape was a very simple boat
+shape after testing materials for a
+
+ align:start position:0%
+shape after testing materials for a
+ 
+
+ align:start position:0%
+shape after testing materials for a
+while it was time to come up with a plan
+
+ align:start position:0%
+while it was time to come up with a plan
+ 
+
+ align:start position:0%
+while it was time to come up with a plan
+I decided that I needed to create a
+
+ align:start position:0%
+I decided that I needed to create a
+ 
+
+ align:start position:0%
+I decided that I needed to create a
+prototype so I enlisted the help of my
+
+ align:start position:0%
+prototype so I enlisted the help of my
+ 
+
+ align:start position:0%
+prototype so I enlisted the help of my
+lab mate Nadia she suggested using a 3d
+
+ align:start position:0%
+lab mate Nadia she suggested using a 3d
+ 
+
+ align:start position:0%
+lab mate Nadia she suggested using a 3d
+printer to create the boat in the
+
+ align:start position:0%
+printer to create the boat in the
+ 
+
+ align:start position:0%
+printer to create the boat in the
+Edgerton Center student shop the only
+
+ align:start position:0%
+Edgerton Center student shop the only
+ 
+
+ align:start position:0%
+Edgerton Center student shop the only
+way we were really going to know if the
+
+ align:start position:0%
+way we were really going to know if the
+ 
+
+ align:start position:0%
+way we were really going to know if the
+boat design was going to work was to
+
+ align:start position:0%
+boat design was going to work was to
+ 
+
+ align:start position:0%
+boat design was going to work was to
+actually try it it was time to act and
+
+ align:start position:0%
+actually try it it was time to act and
+ 
+
+ align:start position:0%
+actually try it it was time to act and
+having a rapid prototyping technology
+
+ align:start position:0%
+having a rapid prototyping technology
+ 
+
+ align:start position:0%
+having a rapid prototyping technology
+such as 3d printers available
+
+ align:start position:0%
+such as 3d printers available
+ 
+
+ align:start position:0%
+such as 3d printers available
+significantly expedites the testing and
+
+ align:start position:0%
+significantly expedites the testing and
+ 
+
+ align:start position:0%
+significantly expedites the testing and
+iteration process the 3d printer
+
+ align:start position:0%
+iteration process the 3d printer
+ 
+
+ align:start position:0%
+iteration process the 3d printer
+requires that we develop 3d
+
+ align:start position:0%
+requires that we develop 3d
+ 
+
+ align:start position:0%
+requires that we develop 3d
+representations of our boat design and
+
+ align:start position:0%
+representations of our boat design and
+ 
+
+ align:start position:0%
+representations of our boat design and
+there are various types of 3d printing
+
+ align:start position:0%
+there are various types of 3d printing
+ 
+
+ align:start position:0%
+there are various types of 3d printing
+technologies the one we used utilizes
+
+ align:start position:0%
+technologies the one we used utilizes
+ 
+
+ align:start position:0%
+technologies the one we used utilizes
+fused deposition modeling or FDM the way
+
+ align:start position:0%
+fused deposition modeling or FDM the way
+ 
+
+ align:start position:0%
+fused deposition modeling or FDM the way
+it works is that there is a spool of
+
+ align:start position:0%
+it works is that there is a spool of
+ 
+
+ align:start position:0%
+it works is that there is a spool of
+thin plastic thread that is fed through
+
+ align:start position:0%
+thin plastic thread that is fed through
+ 
+
+ align:start position:0%
+thin plastic thread that is fed through
+a nozzle the nozzle heats the plastic to
+
+ align:start position:0%
+a nozzle the nozzle heats the plastic to
+ 
+
+ align:start position:0%
+a nozzle the nozzle heats the plastic to
+soften it so that the plastic can be
+
+ align:start position:0%
+soften it so that the plastic can be
+ 
+
+ align:start position:0%
+soften it so that the plastic can be
+laid out to build a 3d object basically
+
+ align:start position:0%
+laid out to build a 3d object basically
+ 
+
+ align:start position:0%
+laid out to build a 3d object basically
+it is like piling a piece of string on
+
+ align:start position:0%
+it is like piling a piece of string on
+ 
+
+ align:start position:0%
+it is like piling a piece of string on
+top of itself to make a 3d shape because
+
+ align:start position:0%
+top of itself to make a 3d shape because
+ 
+
+ align:start position:0%
+top of itself to make a 3d shape because
+the votes needed to be less dense than
+
+ align:start position:0%
+the votes needed to be less dense than
+ 
+
+ align:start position:0%
+the votes needed to be less dense than
+the liquids they were to float on we
+
+ align:start position:0%
+the liquids they were to float on we
+ 
+
+ align:start position:0%
+the liquids they were to float on we
+specify that the votes were to be
+
+ align:start position:0%
+specify that the votes were to be
+ 
+
+ align:start position:0%
+specify that the votes were to be
+printed sparsely such that the plastic
+
+ align:start position:0%
+printed sparsely such that the plastic
+ 
+
+ align:start position:0%
+printed sparsely such that the plastic
+thread was to be laid out loosely
+
+ align:start position:0%
+thread was to be laid out loosely
+ 
+
+ align:start position:0%
+thread was to be laid out loosely
+whenever possible in the interior of the
+
+ align:start position:0%
+whenever possible in the interior of the
+ 
+
+ align:start position:0%
+whenever possible in the interior of the
+boats once we had our boat it was time
+
+ align:start position:0%
+boats once we had our boat it was time
+ 
+
+ align:start position:0%
+boats once we had our boat it was time
+to check and see if it did what we
+
+ align:start position:0%
+to check and see if it did what we
+ 
+
+ align:start position:0%
+to check and see if it did what we
+wanted it to of course our very first
+
+ align:start position:0%
+wanted it to of course our very first
+ 
+
+ align:start position:0%
+wanted it to of course our very first
+boat wasn't the ideal solution the
+
+ align:start position:0%
+boat wasn't the ideal solution the
+ 
+
+ align:start position:0%
+boat wasn't the ideal solution the
+reservoir was too small and the boat was
+
+ align:start position:0%
+reservoir was too small and the boat was
+ 
+
+ align:start position:0%
+reservoir was too small and the boat was
+too large it didn't hold enough fuel and
+
+ align:start position:0%
+too large it didn't hold enough fuel and
+ 
+
+ align:start position:0%
+too large it didn't hold enough fuel and
+move slowly because of the mass but it
+
+ align:start position:0%
+move slowly because of the mass but it
+ 
+
+ align:start position:0%
+move slowly because of the mass but it
+gave us insight into what we needed to
+
+ align:start position:0%
+gave us insight into what we needed to
+ 
+
+ align:start position:0%
+gave us insight into what we needed to
+change we modified our plan created a
+
+ align:start position:0%
+change we modified our plan created a
+ 
+
+ align:start position:0%
+change we modified our plan created a
+new design and tested it again after
+
+ align:start position:0%
+new design and tested it again after
+ 
+
+ align:start position:0%
+new design and tested it again after
+some troubleshooting we went through
+
+ align:start position:0%
+some troubleshooting we went through
+ 
+
+ align:start position:0%
+some troubleshooting we went through
+several design iterations we examined
+
+ align:start position:0%
+several design iterations we examined
+ 
+
+ align:start position:0%
+several design iterations we examined
+many different boat designs and liqueurs
+
+ align:start position:0%
+many different boat designs and liqueurs
+ 
+
+ align:start position:0%
+many different boat designs and liqueurs
+to use as fuel until we had a design we
+
+ align:start position:0%
+to use as fuel until we had a design we
+ 
+
+ align:start position:0%
+to use as fuel until we had a design we
+were happy with I presented my project
+
+ align:start position:0%
+were happy with I presented my project
+ 
+
+ align:start position:0%
+were happy with I presented my project
+to the class at the end of the course I
+
+ align:start position:0%
+to the class at the end of the course I
+ 
+
+ align:start position:0%
+to the class at the end of the course I
+successfully stayed within the design
+
+ align:start position:0%
+successfully stayed within the design
+ 
+
+ align:start position:0%
+successfully stayed within the design
+and project constraints I created a boat
+
+ align:start position:0%
+and project constraints I created a boat
+ 
+
+ align:start position:0%
+and project constraints I created a boat
+that used edible materials for
+
+ align:start position:0%
+that used edible materials for
+ 
+
+ align:start position:0%
+that used edible materials for
+propulsion through the Marangoni effect
+
+ align:start position:0%
+propulsion through the Marangoni effect
+ 
+
+ align:start position:0%
+propulsion through the Marangoni effect
+after completing the course project we
+
+ align:start position:0%
+after completing the course project we
+ 
+
+ align:start position:0%
+after completing the course project we
+continued to pursue this idea we wanted
+
+ align:start position:0%
+continued to pursue this idea we wanted
+ 
+
+ align:start position:0%
+continued to pursue this idea we wanted
+to improve our design and also make the
+
+ align:start position:0%
+to improve our design and also make the
+ 
+
+ align:start position:0%
+to improve our design and also make the
+boat out of edible material so that they
+
+ align:start position:0%
+boat out of edible material so that they
+ 
+
+ align:start position:0%
+boat out of edible material so that they
+could be used as a fun garnish for
+
+ align:start position:0%
+could be used as a fun garnish for
+ 
+
+ align:start position:0%
+could be used as a fun garnish for
+drinks this required us to generalize
+
+ align:start position:0%
+drinks this required us to generalize
+ 
+
+ align:start position:0%
+drinks this required us to generalize
+our solution to a new situation we
+
+ align:start position:0%
+our solution to a new situation we
+ 
+
+ align:start position:0%
+our solution to a new situation we
+constructed soft flexible molds out of
+
+ align:start position:0%
+constructed soft flexible molds out of
+ 
+
+ align:start position:0%
+constructed soft flexible molds out of
+silicone by 3d printing rigid plastic
+
+ align:start position:0%
+silicone by 3d printing rigid plastic
+ 
+
+ align:start position:0%
+silicone by 3d printing rigid plastic
+molds that the silicone molds could be
+
+ align:start position:0%
+molds that the silicone molds could be
+ 
+
+ align:start position:0%
+molds that the silicone molds could be
+made from after creating the molds we
+
+ align:start position:0%
+made from after creating the molds we
+ 
+
+ align:start position:0%
+made from after creating the molds we
+tried several edible materials for the
+
+ align:start position:0%
+tried several edible materials for the
+ 
+
+ align:start position:0%
+tried several edible materials for the
+boat including candy chocolate and marsh
+
+ align:start position:0%
+boat including candy chocolate and marsh
+ 
+
+ align:start position:0%
+boat including candy chocolate and marsh
+Mallos we quickly discovered that the
+
+ align:start position:0%
+Mallos we quickly discovered that the
+ 
+
+ align:start position:0%
+Mallos we quickly discovered that the
+density of the material is a common
+
+ align:start position:0%
+density of the material is a common
+ 
+
+ align:start position:0%
+density of the material is a common
+limiting factor after further testing we
+
+ align:start position:0%
+limiting factor after further testing we
+ 
+
+ align:start position:0%
+limiting factor after further testing we
+found two materials that worked edible
+
+ align:start position:0%
+found two materials that worked edible
+ 
+
+ align:start position:0%
+found two materials that worked edible
+wax and gelatin which we foam as it sets
+
+ align:start position:0%
+wax and gelatin which we foam as it sets
+ 
+
+ align:start position:0%
+wax and gelatin which we foam as it sets
+to reduce the density of the boat we've
+
+ align:start position:0%
+to reduce the density of the boat we've
+ 
+
+ align:start position:0%
+to reduce the density of the boat we've
+since disseminated our product I want to
+
+ align:start position:0%
+since disseminated our product I want to
+ 
+
+ align:start position:0%
+since disseminated our product I want to
+design award at a competition at MIT and
+
+ align:start position:0%
+design award at a competition at MIT and
+ 
+
+ align:start position:0%
+design award at a competition at MIT and
+we're currently working with chef Jose
+
+ align:start position:0%
+we're currently working with chef Jose
+ 
+
+ align:start position:0%
+we're currently working with chef Jose
+Andres to incorporate our design into
+
+ align:start position:0%
+Andres to incorporate our design into
+ 
+
+ align:start position:0%
+Andres to incorporate our design into
+his restaurant additionally an article
+
+ align:start position:0%
+his restaurant additionally an article
+ 
+
+ align:start position:0%
+his restaurant additionally an article
+in the American Society for engineering
+
+ align:start position:0%
+in the American Society for engineering
+ 
+
+ align:start position:0%
+in the American Society for engineering
+education prism magazine helped spread
+
+ align:start position:0%
+education prism magazine helped spread
+ 
+
+ align:start position:0%
+education prism magazine helped spread
+our ideas and product to a broader
+
+ align:start position:0%
+our ideas and product to a broader
+ 
+
+ align:start position:0%
+our ideas and product to a broader
+audience to review in order to solve
+
+ align:start position:0%
+audience to review in order to solve
+ 
+
+ align:start position:0%
+audience to review in order to solve
+this problem we had to define the
+
+ align:start position:0%
+this problem we had to define the
+ 
+
+ align:start position:0%
+this problem we had to define the
+problem gather information explore plan
+
+ align:start position:0%
+problem gather information explore plan
+ 
+
+ align:start position:0%
+problem gather information explore plan
+act and then check our solution we were
+
+ align:start position:0%
+act and then check our solution we were
+ 
+
+ align:start position:0%
+act and then check our solution we were
+able to generalize our solution to a new
+
+ align:start position:0%
+able to generalize our solution to a new
+ 
+
+ align:start position:0%
+able to generalize our solution to a new
+context and then disseminate our results
+
+ align:start position:0%
+context and then disseminate our results
+ 
+
+ align:start position:0%
+context and then disseminate our results
+the problem-solving process really
+
+ align:start position:0%
+the problem-solving process really
+ 
+
+ align:start position:0%
+the problem-solving process really
+helped us approach this problem and
+
+ align:start position:0%
+helped us approach this problem and
+ 
+
+ align:start position:0%
+helped us approach this problem and
+break it down by consciously using a
+
+ align:start position:0%
+break it down by consciously using a
+ 
+
+ align:start position:0%
+break it down by consciously using a
+problem-solving process you will find
+
+ align:start position:0%
+problem-solving process you will find
+ 
+
+ align:start position:0%
+problem-solving process you will find
+that you'll become a more confident and
+
+ align:start position:0%
+that you'll become a more confident and
+ 
+
+ align:start position:0%
+that you'll become a more confident and
+better problem solver best of luck
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/ZjjpLMKs7Tc.txt b/ZjjpLMKs7Tc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c5d4cab715873d9679fcacf80d622f27d4a007aa
--- /dev/null
+++ b/ZjjpLMKs7Tc.txt
@@ -0,0 +1,9858 @@
+align:start position:0%
+ 
+okay so let's uh continue our discussion
+
+ align:start position:0%
+okay so let's uh continue our discussion
+ 
+
+ align:start position:0%
+okay so let's uh continue our discussion
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+series so last time
+
+ align:start position:0%
+series so last time
+ 
+
+ align:start position:0%
+series so last time
+we proved the comparison test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or the end of last time
+
+ align:start position:0%
+or the end of last time
+ 
+
+ align:start position:0%
+or the end of last time
+so this was a comparison test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so which
+
+ align:start position:0%
+so which
+ 
+
+ align:start position:0%
+so which
+is a statement about
+
+ align:start position:0%
+is a statement about
+ 
+
+ align:start position:0%
+is a statement about
+series with non-negative terms with one
+
+ align:start position:0%
+series with non-negative terms with one
+ 
+
+ align:start position:0%
+series with non-negative terms with one
+being smaller than the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of two things
+
+ align:start position:0%
+and one of two things
+ 
+
+ align:start position:0%
+and one of two things
+or two things are true
+
+ align:start position:0%
+or two things are true
+ 
+
+ align:start position:0%
+or two things are true
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+i have x in and y and non-negative with
+
+ align:start position:0%
+i have x in and y and non-negative with
+ 
+
+ align:start position:0%
+i have x in and y and non-negative with
+y n bigger than or equal to x in
+
+ align:start position:0%
+y n bigger than or equal to x in
+ 
+
+ align:start position:0%
+y n bigger than or equal to x in
+then the conclusion is if the bigger
+
+ align:start position:0%
+then the conclusion is if the bigger
+ 
+
+ align:start position:0%
+then the conclusion is if the bigger
+series converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this implies that the smaller series
+
+ align:start position:0%
+this implies that the smaller series
+ 
+
+ align:start position:0%
+this implies that the smaller series
+converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the second statement is if
+
+ align:start position:0%
+and the second statement is if
+ 
+
+ align:start position:0%
+and the second statement is if
+the smaller
+
+ align:start position:0%
+the smaller
+ 
+
+ align:start position:0%
+the smaller
+series diverges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the larger series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diverges
+
+ align:start position:0%
+diverges
+ 
+
+ align:start position:0%
+diverges
+and we also proved not using the
+
+ align:start position:0%
+and we also proved not using the
+ 
+
+ align:start position:0%
+and we also proved not using the
+comparison test but
+
+ align:start position:0%
+comparison test but
+ 
+
+ align:start position:0%
+comparison test but
+for p series that uh
+
+ align:start position:0%
+for p series that uh
+ 
+
+ align:start position:0%
+for p series that uh
+the series 1
+
+ align:start position:0%
+the series 1
+ 
+
+ align:start position:0%
+the series 1
+sum from n equals 1 to infinity of 1
+
+ align:start position:0%
+sum from n equals 1 to infinity of 1
+ 
+
+ align:start position:0%
+sum from n equals 1 to infinity of 1
+over n to the p
+
+ align:start position:0%
+over n to the p
+ 
+
+ align:start position:0%
+over n to the p
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges well i mean we did use a
+
+ align:start position:0%
+converges well i mean we did use a
+ 
+
+ align:start position:0%
+converges well i mean we did use a
+comparison test
+
+ align:start position:0%
+comparison test
+ 
+
+ align:start position:0%
+comparison test
+for one direction i guess so 1 over n to
+
+ align:start position:0%
+for one direction i guess so 1 over n to
+ 
+
+ align:start position:0%
+for one direction i guess so 1 over n to
+the p converges if and only if p is
+
+ align:start position:0%
+the p converges if and only if p is
+ 
+
+ align:start position:0%
+the p converges if and only if p is
+bigger than one so
+
+ align:start position:0%
+bigger than one so
+ 
+
+ align:start position:0%
+bigger than one so
+this converging implied p has to be
+
+ align:start position:0%
+this converging implied p has to be
+ 
+
+ align:start position:0%
+this converging implied p has to be
+bigger than one by the comparison test
+
+ align:start position:0%
+bigger than one by the comparison test
+ 
+
+ align:start position:0%
+bigger than one by the comparison test
+and what we know about
+
+ align:start position:0%
+and what we know about
+ 
+
+ align:start position:0%
+and what we know about
+the harmonic series one over n
+
+ align:start position:0%
+the harmonic series one over n
+ 
+
+ align:start position:0%
+the harmonic series one over n
+sum of one over n
+
+ align:start position:0%
+sum of one over n
+ 
+
+ align:start position:0%
+sum of one over n
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+you know typically in applications you
+
+ align:start position:0%
+you know typically in applications you
+ 
+
+ align:start position:0%
+you know typically in applications you
+use these two theorems together
+
+ align:start position:0%
+use these two theorems together
+ 
+
+ align:start position:0%
+use these two theorems together
+to say something about series that don't
+
+ align:start position:0%
+to say something about series that don't
+ 
+
+ align:start position:0%
+to say something about series that don't
+look so
+
+ align:start position:0%
+look so
+ 
+
+ align:start position:0%
+look so
+simple so for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um if i look at
+
+ align:start position:0%
+um if i look at
+ 
+
+ align:start position:0%
+um if i look at
+the series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 over n squared plus 20
+
+ align:start position:0%
+1 over n squared plus 20
+ 
+
+ align:start position:0%
+1 over n squared plus 20
+20 n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n equals
+
+ align:start position:0%
+n equals
+ 
+
+ align:start position:0%
+n equals
+1 to infinity
+
+ align:start position:0%
+1 to infinity
+ 
+
+ align:start position:0%
+1 to infinity
+so one could ask oh does this converge
+
+ align:start position:0%
+so one could ask oh does this converge
+ 
+
+ align:start position:0%
+so one could ask oh does this converge
+diverge
+
+ align:start position:0%
+diverge
+ 
+
+ align:start position:0%
+diverge
+well this is a
+
+ align:start position:0%
+well this is a
+ 
+
+ align:start position:0%
+well this is a
+series with non-negative terms and
+
+ align:start position:0%
+series with non-negative terms and
+ 
+
+ align:start position:0%
+series with non-negative terms and
+remember i mean the bigger thing has to
+
+ align:start position:0%
+remember i mean the bigger thing has to
+ 
+
+ align:start position:0%
+remember i mean the bigger thing has to
+converge
+
+ align:start position:0%
+converge
+ 
+
+ align:start position:0%
+converge
+to give you
+
+ align:start position:0%
+to give you
+ 
+
+ align:start position:0%
+to give you
+to imply that the smaller thing
+
+ align:start position:0%
+to imply that the smaller thing
+ 
+
+ align:start position:0%
+to imply that the smaller thing
+converges and if the smaller thing
+
+ align:start position:0%
+converges and if the smaller thing
+ 
+
+ align:start position:0%
+converges and if the smaller thing
+diverges then the bigger thing diverges
+
+ align:start position:0%
+diverges then the bigger thing diverges
+ 
+
+ align:start position:0%
+diverges then the bigger thing diverges
+so don't get the inequalities mixed up
+
+ align:start position:0%
+so don't get the inequalities mixed up
+ 
+
+ align:start position:0%
+so don't get the inequalities mixed up
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i have
+
+ align:start position:0%
+i have
+ 
+
+ align:start position:0%
+i have
+1 over n squared plus 20
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+this 20 20 times n is just making things
+
+ align:start position:0%
+this 20 20 times n is just making things
+ 
+
+ align:start position:0%
+this 20 20 times n is just making things
+bigger on the bottom and therefore
+
+ align:start position:0%
+bigger on the bottom and therefore
+ 
+
+ align:start position:0%
+bigger on the bottom and therefore
+smaller overall so this is less than or
+
+ align:start position:0%
+smaller overall so this is less than or
+ 
+
+ align:start position:0%
+smaller overall so this is less than or
+equal to one over n squared
+
+ align:start position:0%
+equal to one over n squared
+ 
+
+ align:start position:0%
+equal to one over n squared
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since this converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this implies by the comparison test that
+
+ align:start position:0%
+this implies by the comparison test that
+ 
+
+ align:start position:0%
+this implies by the comparison test that
+the sum from n equals 1 to infinity of 1
+
+ align:start position:0%
+the sum from n equals 1 to infinity of 1
+ 
+
+ align:start position:0%
+the sum from n equals 1 to infinity of 1
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+n squared plus 20 20
+
+ align:start position:0%
+n squared plus 20 20
+ 
+
+ align:start position:0%
+n squared plus 20 20
+n also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges
+
+ align:start position:0%
+converges
+ 
+
+ align:start position:0%
+converges
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now um
+
+ align:start position:0%
+now um
+ 
+
+ align:start position:0%
+now um
+you know a mistake i'm sure we've all
+
+ align:start position:0%
+you know a mistake i'm sure we've all
+ 
+
+ align:start position:0%
+you know a mistake i'm sure we've all
+made at some point is mixing up the
+
+ align:start position:0%
+made at some point is mixing up the
+ 
+
+ align:start position:0%
+made at some point is mixing up the
+inequality
+
+ align:start position:0%
+inequality
+ 
+
+ align:start position:0%
+inequality
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+not getting quite
+
+ align:start position:0%
+not getting quite
+ 
+
+ align:start position:0%
+not getting quite
+the right answer so for example
+
+ align:start position:0%
+the right answer so for example
+ 
+
+ align:start position:0%
+the right answer so for example
+it is also true that 1 over n squared
+
+ align:start position:0%
+it is also true that 1 over n squared
+ 
+
+ align:start position:0%
+it is also true that 1 over n squared
+plus 20
+
+ align:start position:0%
+plus 20
+ 
+
+ align:start position:0%
+plus 20
+20 n is certainly less than or equal to
+
+ align:start position:0%
+20 n is certainly less than or equal to
+ 
+
+ align:start position:0%
+20 n is certainly less than or equal to
+1 over 20
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 over 20 20 times n which is also less
+
+ align:start position:0%
+1 over 20 20 times n which is also less
+ 
+
+ align:start position:0%
+1 over 20 20 times n which is also less
+than or equal to 1 over n
+
+ align:start position:0%
+than or equal to 1 over n
+ 
+
+ align:start position:0%
+than or equal to 1 over n
+and so you're tempted to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since this diverges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+series diverges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+this is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not right okay because the inequality is
+
+ align:start position:0%
+not right okay because the inequality is
+ 
+
+ align:start position:0%
+not right okay because the inequality is
+wrong remember if you want to apply the
+
+ align:start position:0%
+wrong remember if you want to apply the
+ 
+
+ align:start position:0%
+wrong remember if you want to apply the
+comparison test
+
+ align:start position:0%
+comparison test
+ 
+
+ align:start position:0%
+comparison test
+you either have to have a bigger series
+
+ align:start position:0%
+you either have to have a bigger series
+ 
+
+ align:start position:0%
+you either have to have a bigger series
+which converges
+
+ align:start position:0%
+which converges
+ 
+
+ align:start position:0%
+which converges
+or a smaller series which diverges okay
+
+ align:start position:0%
+or a smaller series which diverges okay
+ 
+
+ align:start position:0%
+or a smaller series which diverges okay
+here we came up with a bigger series
+
+ align:start position:0%
+here we came up with a bigger series
+ 
+
+ align:start position:0%
+here we came up with a bigger series
+which diverges which gives us no
+
+ align:start position:0%
+which diverges which gives us no
+ 
+
+ align:start position:0%
+which diverges which gives us no
+information at all
+
+ align:start position:0%
+information at all
+ 
+
+ align:start position:0%
+information at all
+okay it's if we have a bigger series
+
+ align:start position:0%
+okay it's if we have a bigger series
+ 
+
+ align:start position:0%
+okay it's if we have a bigger series
+like one over n squared that we know
+
+ align:start position:0%
+like one over n squared that we know
+ 
+
+ align:start position:0%
+like one over n squared that we know
+converges
+
+ align:start position:0%
+converges
+ 
+
+ align:start position:0%
+converges
+then do we get information about the
+
+ align:start position:0%
+then do we get information about the
+ 
+
+ align:start position:0%
+then do we get information about the
+original series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's do
+
+ align:start position:0%
+okay so let's do
+ 
+
+ align:start position:0%
+okay so let's do
+um let's do another well-known test or
+
+ align:start position:0%
+um let's do another well-known test or
+ 
+
+ align:start position:0%
+um let's do another well-known test or
+at least
+
+ align:start position:0%
+at least
+ 
+
+ align:start position:0%
+at least
+test you should remember from
+
+ align:start position:0%
+test you should remember from
+ 
+
+ align:start position:0%
+test you should remember from
+calculus so-called ratio tests
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is the statement of this so
+
+ align:start position:0%
+so what is the statement of this so
+ 
+
+ align:start position:0%
+so what is the statement of this so
+suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xn does not equal 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this limit
+
+ align:start position:0%
+and this limit
+ 
+
+ align:start position:0%
+and this limit
+l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals the limit as n goes to infinity
+
+ align:start position:0%
+equals the limit as n goes to infinity
+ 
+
+ align:start position:0%
+equals the limit as n goes to infinity
+of x to the n plus 1
+
+ align:start position:0%
+of x to the n plus 1
+ 
+
+ align:start position:0%
+of x to the n plus 1
+over x to the n and absolute value
+
+ align:start position:0%
+over x to the n and absolute value
+ 
+
+ align:start position:0%
+over x to the n and absolute value
+exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if l is less than 1
+
+ align:start position:0%
+if l is less than 1
+ 
+
+ align:start position:0%
+if l is less than 1
+this implies that
+
+ align:start position:0%
+this implies that
+ 
+
+ align:start position:0%
+this implies that
+the series
+
+ align:start position:0%
+the series
+ 
+
+ align:start position:0%
+the series
+x n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges absolutely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if l
+
+ align:start position:0%
+and if l
+ 
+
+ align:start position:0%
+and if l
+is bigger than one
+
+ align:start position:0%
+is bigger than one
+ 
+
+ align:start position:0%
+is bigger than one
+then the series
+
+ align:start position:0%
+then the series
+ 
+
+ align:start position:0%
+then the series
+diverges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what about l equals one there's no
+
+ align:start position:0%
+now what about l equals one there's no
+ 
+
+ align:start position:0%
+now what about l equals one there's no
+information for l equals one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meaning
+
+ align:start position:0%
+meaning
+ 
+
+ align:start position:0%
+meaning
+you could have
+
+ align:start position:0%
+you could have
+ 
+
+ align:start position:0%
+you could have
+a series so that this l equals one
+
+ align:start position:0%
+a series so that this l equals one
+ 
+
+ align:start position:0%
+a series so that this l equals one
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know you could have a series where
+
+ align:start position:0%
+you know you could have a series where
+ 
+
+ align:start position:0%
+you know you could have a series where
+it diverges and you could also have a
+
+ align:start position:0%
+it diverges and you could also have a
+ 
+
+ align:start position:0%
+it diverges and you could also have a
+series where l equals one in the series
+
+ align:start position:0%
+series where l equals one in the series
+ 
+
+ align:start position:0%
+series where l equals one in the series
+converges so for
+
+ align:start position:0%
+converges so for
+ 
+
+ align:start position:0%
+converges so for
+example um
+
+ align:start position:0%
+example um
+ 
+
+ align:start position:0%
+example um
+x n equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+one over n
+
+ align:start position:0%
+one over n
+ 
+
+ align:start position:0%
+one over n
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+or i mean even worse
+
+ align:start position:0%
+or i mean even worse
+ 
+
+ align:start position:0%
+or i mean even worse
+let's say one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay for all in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we know that the series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one diverges because the individual
+
+ align:start position:0%
+one diverges because the individual
+ 
+
+ align:start position:0%
+one diverges because the individual
+terms do not convert to zero they're
+
+ align:start position:0%
+terms do not convert to zero they're
+ 
+
+ align:start position:0%
+terms do not convert to zero they're
+just one the whole time
+
+ align:start position:0%
+just one the whole time
+ 
+
+ align:start position:0%
+just one the whole time
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+for x n equals let's say one over
+
+ align:start position:0%
+for x n equals let's say one over
+ 
+
+ align:start position:0%
+for x n equals let's say one over
+n squared so the one we just saw a
+
+ align:start position:0%
+n squared so the one we just saw a
+ 
+
+ align:start position:0%
+n squared so the one we just saw a
+minute ago
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implies l which is the limit as n goes
+
+ align:start position:0%
+implies l which is the limit as n goes
+ 
+
+ align:start position:0%
+implies l which is the limit as n goes
+to infinity
+
+ align:start position:0%
+to infinity
+ 
+
+ align:start position:0%
+to infinity
+of n plus 1
+
+ align:start position:0%
+of n plus 1
+ 
+
+ align:start position:0%
+of n plus 1
+squared over n squared
+
+ align:start position:0%
+squared over n squared
+ 
+
+ align:start position:0%
+squared over n squared
+equals the limit
+
+ align:start position:0%
+equals the limit
+ 
+
+ align:start position:0%
+equals the limit
+as n goes to infinity dividing through
+
+ align:start position:0%
+as n goes to infinity dividing through
+ 
+
+ align:start position:0%
+as n goes to infinity dividing through
+1 plus 1 over n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared and this equals 1 plus 0
+
+ align:start position:0%
+squared and this equals 1 plus 0
+ 
+
+ align:start position:0%
+squared and this equals 1 plus 0
+squared equals 1.
+
+ align:start position:0%
+squared equals 1.
+ 
+
+ align:start position:0%
+squared equals 1.
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+the root or the ratio
+
+ align:start position:0%
+the root or the ratio
+ 
+
+ align:start position:0%
+the root or the ratio
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+gives
+
+ align:start position:0%
+gives
+ 
+
+ align:start position:0%
+gives
+this l is one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this series converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+again for the case that l equals one we
+
+ align:start position:0%
+again for the case that l equals one we
+ 
+
+ align:start position:0%
+again for the case that l equals one we
+have no information we can't say
+
+ align:start position:0%
+have no information we can't say
+ 
+
+ align:start position:0%
+have no information we can't say
+anything uh based on
+
+ align:start position:0%
+anything uh based on
+ 
+
+ align:start position:0%
+anything uh based on
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+this theorem gives us no information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+all right we're going to prove this
+
+ align:start position:0%
+all right we're going to prove this
+ 
+
+ align:start position:0%
+all right we're going to prove this
+theorem um
+
+ align:start position:0%
+theorem um
+ 
+
+ align:start position:0%
+theorem um
+basically by um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're not exactly going to use a
+
+ align:start position:0%
+so we're not exactly going to use a
+ 
+
+ align:start position:0%
+so we're not exactly going to use a
+comparison test but we are still going
+
+ align:start position:0%
+comparison test but we are still going
+ 
+
+ align:start position:0%
+comparison test but we are still going
+to compare
+
+ align:start position:0%
+to compare
+ 
+
+ align:start position:0%
+to compare
+this series satisfying
+
+ align:start position:0%
+this series satisfying
+ 
+
+ align:start position:0%
+this series satisfying
+you know one of these two assumptions to
+
+ align:start position:0%
+you know one of these two assumptions to
+ 
+
+ align:start position:0%
+you know one of these two assumptions to
+a series we know which is uh namely the
+
+ align:start position:0%
+a series we know which is uh namely the
+ 
+
+ align:start position:0%
+a series we know which is uh namely the
+the ratio test for number one so first
+
+ align:start position:0%
+the ratio test for number one so first
+ 
+
+ align:start position:0%
+the ratio test for number one so first
+off let's get um
+
+ align:start position:0%
+off let's get um
+ 
+
+ align:start position:0%
+off let's get um
+let's get number
+
+ align:start position:0%
+let's get number
+ 
+
+ align:start position:0%
+let's get number
+two out of the way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l is bigger than one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be a number between one
+
+ align:start position:0%
+be a number between one
+ 
+
+ align:start position:0%
+be a number between one
+and l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually we don't even need to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's one here's l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since
+
+ align:start position:0%
+so since
+ 
+
+ align:start position:0%
+so since
+xn plus 1 over
+
+ align:start position:0%
+xn plus 1 over
+ 
+
+ align:start position:0%
+xn plus 1 over
+xn absolute value converges to l
+
+ align:start position:0%
+xn absolute value converges to l
+ 
+
+ align:start position:0%
+xn absolute value converges to l
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+an integer m0
+
+ align:start position:0%
+an integer m0
+ 
+
+ align:start position:0%
+an integer m0
+so it's a natural
+
+ align:start position:0%
+so it's a natural
+ 
+
+ align:start position:0%
+so it's a natural
+number so that
+
+ align:start position:0%
+number so that
+ 
+
+ align:start position:0%
+number so that
+for all n bigger than or equal to m zero
+
+ align:start position:0%
+for all n bigger than or equal to m zero
+ 
+
+ align:start position:0%
+for all n bigger than or equal to m zero
+x n plus one over x n
+
+ align:start position:0%
+x n plus one over x n
+ 
+
+ align:start position:0%
+x n plus one over x n
+absolute value is bigger than or equal
+
+ align:start position:0%
+absolute value is bigger than or equal
+ 
+
+ align:start position:0%
+absolute value is bigger than or equal
+to so
+
+ align:start position:0%
+to so
+ 
+
+ align:start position:0%
+to so
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+you could write 1 as this is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l plus
+
+ align:start position:0%
+l plus
+ 
+
+ align:start position:0%
+l plus
+say minus
+
+ align:start position:0%
+say minus
+ 
+
+ align:start position:0%
+say minus
+l minus 1.
+
+ align:start position:0%
+l minus 1.
+ 
+
+ align:start position:0%
+l minus 1.
+so think of this as being epsilon in the
+
+ align:start position:0%
+so think of this as being epsilon in the
+ 
+
+ align:start position:0%
+so think of this as being epsilon in the
+definition of convergence
+
+ align:start position:0%
+definition of convergence
+ 
+
+ align:start position:0%
+definition of convergence
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is over here l plus
+
+ align:start position:0%
+this is over here l plus
+ 
+
+ align:start position:0%
+this is over here l plus
+l minus 1.
+
+ align:start position:0%
+l minus 1.
+ 
+
+ align:start position:0%
+l minus 1.
+so by the definition of convergence uh
+
+ align:start position:0%
+so by the definition of convergence uh
+ 
+
+ align:start position:0%
+so by the definition of convergence uh
+for all n sufficiently large x n plus
+
+ align:start position:0%
+for all n sufficiently large x n plus
+ 
+
+ align:start position:0%
+for all n sufficiently large x n plus
+one over x n an absolute value has to be
+
+ align:start position:0%
+one over x n an absolute value has to be
+ 
+
+ align:start position:0%
+one over x n an absolute value has to be
+in this interval so it has to be bigger
+
+ align:start position:0%
+in this interval so it has to be bigger
+ 
+
+ align:start position:0%
+in this interval so it has to be bigger
+than or equal to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which implies that for all
+
+ align:start position:0%
+which implies that for all
+ 
+
+ align:start position:0%
+which implies that for all
+n bigger than or equal to m 0
+
+ align:start position:0%
+n bigger than or equal to m 0
+ 
+
+ align:start position:0%
+n bigger than or equal to m 0
+x n plus 1 is bigger than or equal to
+
+ align:start position:0%
+x n plus 1 is bigger than or equal to
+ 
+
+ align:start position:0%
+x n plus 1 is bigger than or equal to
+xn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so i could write this as saying that x
+
+ align:start position:0%
+so i could write this as saying that x
+ 
+
+ align:start position:0%
+so i could write this as saying that x
+m0 is less than or equal to x
+
+ align:start position:0%
+m0 is less than or equal to x
+ 
+
+ align:start position:0%
+m0 is less than or equal to x
+and 0 plus 1 is less than or equal to
+
+ align:start position:0%
+and 0 plus 1 is less than or equal to
+ 
+
+ align:start position:0%
+and 0 plus 1 is less than or equal to
+x m0 plus 2
+
+ align:start position:0%
+x m0 plus 2
+ 
+
+ align:start position:0%
+x m0 plus 2
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but this implies that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that these x ends cannot converge to
+
+ align:start position:0%
+that these x ends cannot converge to
+ 
+
+ align:start position:0%
+that these x ends cannot converge to
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as n goes to infinity because
+
+ align:start position:0%
+as n goes to infinity because
+ 
+
+ align:start position:0%
+as n goes to infinity because
+for all n bigger than or equal to m0
+
+ align:start position:0%
+for all n bigger than or equal to m0
+ 
+
+ align:start position:0%
+for all n bigger than or equal to m0
+they're increasing
+
+ align:start position:0%
+they're increasing
+ 
+
+ align:start position:0%
+they're increasing
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the only way for an increasing
+
+ align:start position:0%
+and the only way for an increasing
+ 
+
+ align:start position:0%
+and the only way for an increasing
+sequence which is not negative to
+
+ align:start position:0%
+sequence which is not negative to
+ 
+
+ align:start position:0%
+sequence which is not negative to
+converge to zero is for them all to be
+
+ align:start position:0%
+converge to zero is for them all to be
+ 
+
+ align:start position:0%
+converge to zero is for them all to be
+nuns for them all to be zero and we're
+
+ align:start position:0%
+nuns for them all to be zero and we're
+ 
+
+ align:start position:0%
+nuns for them all to be zero and we're
+assuming they're not zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so that proves two
+
+ align:start position:0%
+okay so that proves two
+ 
+
+ align:start position:0%
+okay so that proves two
+let's prove one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose l is now less than one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+now let
+
+ align:start position:0%
+now let
+ 
+
+ align:start position:0%
+now let
+alpha be a number uh
+
+ align:start position:0%
+alpha be a number uh
+ 
+
+ align:start position:0%
+alpha be a number uh
+between l and one so i just want to give
+
+ align:start position:0%
+between l and one so i just want to give
+ 
+
+ align:start position:0%
+between l and one so i just want to give
+myself a little bit of room
+
+ align:start position:0%
+myself a little bit of room
+ 
+
+ align:start position:0%
+myself a little bit of room
+to work as you'll see in just a second
+
+ align:start position:0%
+to work as you'll see in just a second
+ 
+
+ align:start position:0%
+to work as you'll see in just a second
+so by the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reasoning as before
+
+ align:start position:0%
+reasoning as before
+ 
+
+ align:start position:0%
+reasoning as before
+so here's
+
+ align:start position:0%
+so here's
+ 
+
+ align:start position:0%
+so here's
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+alpha
+
+ align:start position:0%
+alpha
+ 
+
+ align:start position:0%
+alpha
+1 alpha i can write
+
+ align:start position:0%
+1 alpha i can write
+ 
+
+ align:start position:0%
+1 alpha i can write
+as l
+
+ align:start position:0%
+as l
+ 
+
+ align:start position:0%
+as l
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+alpha minus l so i should think of this
+
+ align:start position:0%
+alpha minus l so i should think of this
+ 
+
+ align:start position:0%
+alpha minus l so i should think of this
+so think of this as kind of an epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since x n plus 1
+
+ align:start position:0%
+since x n plus 1
+ 
+
+ align:start position:0%
+since x n plus 1
+over x in an absolute value converges to
+
+ align:start position:0%
+over x in an absolute value converges to
+ 
+
+ align:start position:0%
+over x in an absolute value converges to
+l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is less than alpha there exists an
+
+ align:start position:0%
+which is less than alpha there exists an
+ 
+
+ align:start position:0%
+which is less than alpha there exists an
+m naught
+
+ align:start position:0%
+m naught
+ 
+
+ align:start position:0%
+m naught
+natural number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+while n bigger than or equal to m 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x n plus 1 over x in an absolute value
+
+ align:start position:0%
+x n plus 1 over x in an absolute value
+ 
+
+ align:start position:0%
+x n plus 1 over x in an absolute value
+is less than or equal to alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here i have alpha just a little
+
+ align:start position:0%
+okay so here i have alpha just a little
+ 
+
+ align:start position:0%
+okay so here i have alpha just a little
+bit bigger than l
+
+ align:start position:0%
+bit bigger than l
+ 
+
+ align:start position:0%
+bit bigger than l
+and if i draw
+
+ align:start position:0%
+and if i draw
+ 
+
+ align:start position:0%
+and if i draw
+so this is l
+
+ align:start position:0%
+so this is l
+ 
+
+ align:start position:0%
+so this is l
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+alpha minus l
+
+ align:start position:0%
+alpha minus l
+ 
+
+ align:start position:0%
+alpha minus l
+so since i have um this sequence here
+
+ align:start position:0%
+so since i have um this sequence here
+ 
+
+ align:start position:0%
+so since i have um this sequence here
+converging to l for all
+
+ align:start position:0%
+converging to l for all
+ 
+
+ align:start position:0%
+converging to l for all
+insufficiently large
+
+ align:start position:0%
+insufficiently large
+ 
+
+ align:start position:0%
+insufficiently large
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+should be in this interval meaning
+
+ align:start position:0%
+should be in this interval meaning
+ 
+
+ align:start position:0%
+should be in this interval meaning
+this should be less than or equal to
+
+ align:start position:0%
+this should be less than or equal to
+ 
+
+ align:start position:0%
+this should be less than or equal to
+alpha
+
+ align:start position:0%
+alpha
+ 
+
+ align:start position:0%
+alpha
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then for all n bigger than or equal to
+
+ align:start position:0%
+then for all n bigger than or equal to
+ 
+
+ align:start position:0%
+then for all n bigger than or equal to
+m0 so let me just write this uh
+
+ align:start position:0%
+m0 so let me just write this uh
+ 
+
+ align:start position:0%
+m0 so let me just write this uh
+slightly differently x
+
+ align:start position:0%
+slightly differently x
+ 
+
+ align:start position:0%
+slightly differently x
+sub n plus 1
+
+ align:start position:0%
+sub n plus 1
+ 
+
+ align:start position:0%
+sub n plus 1
+is less than or equal to alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times the absolute value of x of n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see what this means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all n bigger than or equal to m sub
+
+ align:start position:0%
+for all n bigger than or equal to m sub
+ 
+
+ align:start position:0%
+for all n bigger than or equal to m sub
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+let's say i look at the absolute value
+
+ align:start position:0%
+let's say i look at the absolute value
+ 
+
+ align:start position:0%
+let's say i look at the absolute value
+of x sub n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now this n has nothing to do with
+
+ align:start position:0%
+so now this n has nothing to do with
+ 
+
+ align:start position:0%
+so now this n has nothing to do with
+these end it's just that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then the absolute value of x sub n is
+
+ align:start position:0%
+so then the absolute value of x sub n is
+ 
+
+ align:start position:0%
+so then the absolute value of x sub n is
+less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so maybe i'm off by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's let's
+
+ align:start position:0%
+okay so let's let's
+ 
+
+ align:start position:0%
+okay so let's let's
+increase that by one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay so let's not
+
+ align:start position:0%
+well okay so let's not
+ 
+
+ align:start position:0%
+well okay so let's not
+let's not be confusing here
+
+ align:start position:0%
+let's not be confusing here
+ 
+
+ align:start position:0%
+let's not be confusing here
+let's make this
+
+ align:start position:0%
+let's make this
+ 
+
+ align:start position:0%
+let's make this
+let's make this l
+
+ align:start position:0%
+let's make this l
+ 
+
+ align:start position:0%
+let's make this l
+let's make that l
+
+ align:start position:0%
+let's make that l
+ 
+
+ align:start position:0%
+let's make that l
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+l bigger than or equal to m zero plus
+
+ align:start position:0%
+l bigger than or equal to m zero plus
+ 
+
+ align:start position:0%
+l bigger than or equal to m zero plus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+um so think of l as playing the role of
+
+ align:start position:0%
+um so think of l as playing the role of
+ 
+
+ align:start position:0%
+um so think of l as playing the role of
+being n plus one
+
+ align:start position:0%
+being n plus one
+ 
+
+ align:start position:0%
+being n plus one
+this is less than or equal to l
+
+ align:start position:0%
+this is less than or equal to l
+ 
+
+ align:start position:0%
+this is less than or equal to l
+x to the l minus one
+
+ align:start position:0%
+x to the l minus one
+ 
+
+ align:start position:0%
+x to the l minus one
+which is less than or equal to x to the
+
+ align:start position:0%
+which is less than or equal to x to the
+ 
+
+ align:start position:0%
+which is less than or equal to x to the
+l minus two
+
+ align:start position:0%
+l minus two
+ 
+
+ align:start position:0%
+l minus two
+now with a square so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what i have here is now f times alpha
+
+ align:start position:0%
+what i have here is now f times alpha
+ 
+
+ align:start position:0%
+what i have here is now f times alpha
+x to the l minus two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+now let's drop again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by 1 and i can do this
+
+ align:start position:0%
+by 1 and i can do this
+ 
+
+ align:start position:0%
+by 1 and i can do this
+as long as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this quantity here is bigger than or
+
+ align:start position:0%
+this quantity here is bigger than or
+ 
+
+ align:start position:0%
+this quantity here is bigger than or
+equal to m
+
+ align:start position:0%
+equal to m
+ 
+
+ align:start position:0%
+equal to m
+so i get this is
+
+ align:start position:0%
+so i get this is
+ 
+
+ align:start position:0%
+so i get this is
+if i keep doing that this is less than
+
+ align:start position:0%
+if i keep doing that this is less than
+ 
+
+ align:start position:0%
+if i keep doing that this is less than
+or equal to alpha
+
+ align:start position:0%
+or equal to alpha
+ 
+
+ align:start position:0%
+or equal to alpha
+to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l minus m naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x to the m naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so actually let's
+
+ align:start position:0%
+and so actually let's
+ 
+
+ align:start position:0%
+and so actually let's
+since we shifted things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now we're going to use this to bound the
+
+ align:start position:0%
+now we're going to use this to bound the
+ 
+
+ align:start position:0%
+now we're going to use this to bound the
+partial sums of the x of n
+
+ align:start position:0%
+partial sums of the x of n
+ 
+
+ align:start position:0%
+partial sums of the x of n
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me be a natural number
+
+ align:start position:0%
+let me be a natural number
+ 
+
+ align:start position:0%
+let me be a natural number
+and if we look at
+
+ align:start position:0%
+and if we look at
+ 
+
+ align:start position:0%
+and if we look at
+partial sum sum from n equals 1 to m
+
+ align:start position:0%
+partial sum sum from n equals 1 to m
+ 
+
+ align:start position:0%
+partial sum sum from n equals 1 to m
+of x sub n this is equal to
+
+ align:start position:0%
+of x sub n this is equal to
+ 
+
+ align:start position:0%
+of x sub n this is equal to
+some n equals 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to m naught
+
+ align:start position:0%
+to m naught
+ 
+
+ align:start position:0%
+to m naught
+x n plus
+
+ align:start position:0%
+x n plus
+ 
+
+ align:start position:0%
+x n plus
+sum from n equals m naught plus 1
+
+ align:start position:0%
+sum from n equals m naught plus 1
+ 
+
+ align:start position:0%
+sum from n equals m naught plus 1
+to m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+sub
+
+ align:start position:0%
+sub
+ 
+
+ align:start position:0%
+sub
+now let me
+
+ align:start position:0%
+now let me
+ 
+
+ align:start position:0%
+now let me
+just change dummy variables for for
+
+ align:start position:0%
+just change dummy variables for for
+ 
+
+ align:start position:0%
+just change dummy variables for for
+signing for the
+
+ align:start position:0%
+signing for the
+ 
+
+ align:start position:0%
+signing for the
+indexing this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is equal to the sum from n
+
+ align:start position:0%
+so this is equal to the sum from n
+ 
+
+ align:start position:0%
+so this is equal to the sum from n
+equals 1 to m naught of
+
+ align:start position:0%
+equals 1 to m naught of
+ 
+
+ align:start position:0%
+equals 1 to m naught of
+x n
+
+ align:start position:0%
+x n
+ 
+
+ align:start position:0%
+x n
+and now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this i'm going to use this inequality
+
+ align:start position:0%
+this i'm going to use this inequality
+ 
+
+ align:start position:0%
+this i'm going to use this inequality
+here so
+
+ align:start position:0%
+here so
+ 
+
+ align:start position:0%
+here so
+okay this is kind of a mess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the inequality
+
+ align:start position:0%
+so this is the inequality
+ 
+
+ align:start position:0%
+so this is the inequality
+that i get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from this
+
+ align:start position:0%
+from this
+ 
+
+ align:start position:0%
+from this
+remember alpha is less than one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+l equals
+
+ align:start position:0%
+l equals
+ 
+
+ align:start position:0%
+l equals
+and not plus 1
+
+ align:start position:0%
+and not plus 1
+ 
+
+ align:start position:0%
+and not plus 1
+to m okay everything's fine
+
+ align:start position:0%
+to m okay everything's fine
+ 
+
+ align:start position:0%
+to m okay everything's fine
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+alpha to the l minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m not plus 1. okay so all i did here was
+
+ align:start position:0%
+m not plus 1. okay so all i did here was
+ 
+
+ align:start position:0%
+m not plus 1. okay so all i did here was
+replace
+
+ align:start position:0%
+replace
+ 
+
+ align:start position:0%
+replace
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+absolute value of x to the of x sub l l
+
+ align:start position:0%
+absolute value of x to the of x sub l l
+ 
+
+ align:start position:0%
+absolute value of x to the of x sub l l
+is just a dummy variable for indexing
+
+ align:start position:0%
+is just a dummy variable for indexing
+ 
+
+ align:start position:0%
+is just a dummy variable for indexing
+these guys but using this uh inequality
+
+ align:start position:0%
+these guys but using this uh inequality
+ 
+
+ align:start position:0%
+these guys but using this uh inequality
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+all right so sorry i kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mess that up a little bit but the
+
+ align:start position:0%
+mess that up a little bit but the
+ 
+
+ align:start position:0%
+mess that up a little bit but the
+important thing is that we have this
+
+ align:start position:0%
+important thing is that we have this
+ 
+
+ align:start position:0%
+important thing is that we have this
+inequality which somehow
+
+ align:start position:0%
+inequality which somehow
+ 
+
+ align:start position:0%
+inequality which somehow
+tells you this
+
+ align:start position:0%
+tells you this
+ 
+
+ align:start position:0%
+tells you this
+um series is not that far from being a
+
+ align:start position:0%
+um series is not that far from being a
+ 
+
+ align:start position:0%
+um series is not that far from being a
+geometric series at least when l is big
+
+ align:start position:0%
+geometric series at least when l is big
+ 
+
+ align:start position:0%
+geometric series at least when l is big
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so then when we take an arbitrary
+
+ align:start position:0%
+so then when we take an arbitrary
+ 
+
+ align:start position:0%
+so then when we take an arbitrary
+partial sums we split it up into two
+
+ align:start position:0%
+partial sums we split it up into two
+ 
+
+ align:start position:0%
+partial sums we split it up into two
+parts uh the stuff that comes up to this
+
+ align:start position:0%
+parts uh the stuff that comes up to this
+ 
+
+ align:start position:0%
+parts uh the stuff that comes up to this
+integer m sub zero which we don't care
+
+ align:start position:0%
+integer m sub zero which we don't care
+ 
+
+ align:start position:0%
+integer m sub zero which we don't care
+about that's just a fixed number
+
+ align:start position:0%
+about that's just a fixed number
+ 
+
+ align:start position:0%
+about that's just a fixed number
+plus this
+
+ align:start position:0%
+plus this
+ 
+
+ align:start position:0%
+plus this
+uh part that we care about which is
+
+ align:start position:0%
+uh part that we care about which is
+ 
+
+ align:start position:0%
+uh part that we care about which is
+after
+
+ align:start position:0%
+after
+ 
+
+ align:start position:0%
+after
+uh this fixed number m0
+
+ align:start position:0%
+uh this fixed number m0
+ 
+
+ align:start position:0%
+uh this fixed number m0
+and we use this inequality to replace
+
+ align:start position:0%
+and we use this inequality to replace
+ 
+
+ align:start position:0%
+and we use this inequality to replace
+this by x sub m0 plus one alpha to the l
+
+ align:start position:0%
+this by x sub m0 plus one alpha to the l
+ 
+
+ align:start position:0%
+this by x sub m0 plus one alpha to the l
+minus m0 plus one okay the thing to
+
+ align:start position:0%
+minus m0 plus one okay the thing to
+ 
+
+ align:start position:0%
+minus m0 plus one okay the thing to
+remember is that little m
+
+ align:start position:0%
+remember is that little m
+ 
+
+ align:start position:0%
+remember is that little m
+is the thing that's changing okay so
+
+ align:start position:0%
+is the thing that's changing okay so
+ 
+
+ align:start position:0%
+is the thing that's changing okay so
+we're trying to bound this
+
+ align:start position:0%
+we're trying to bound this
+ 
+
+ align:start position:0%
+we're trying to bound this
+independent of little m
+
+ align:start position:0%
+independent of little m
+ 
+
+ align:start position:0%
+independent of little m
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+capital m sub zero that's just something
+
+ align:start position:0%
+capital m sub zero that's just something
+ 
+
+ align:start position:0%
+capital m sub zero that's just something
+fixed that could be a thousand all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is equal to sum from n equals 1
+
+ align:start position:0%
+so this is equal to sum from n equals 1
+ 
+
+ align:start position:0%
+so this is equal to sum from n equals 1
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+m 0
+
+ align:start position:0%
+m 0
+ 
+
+ align:start position:0%
+m 0
+x n plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x sub m0 plus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now if i change
+
+ align:start position:0%
+and now if i change
+ 
+
+ align:start position:0%
+and now if i change
+the variable again so
+
+ align:start position:0%
+the variable again so
+ 
+
+ align:start position:0%
+the variable again so
+l starts at m 0 plus 1 and ends at m
+
+ align:start position:0%
+l starts at m 0 plus 1 and ends at m
+ 
+
+ align:start position:0%
+l starts at m 0 plus 1 and ends at m
+so this is now a sum if i go
+
+ align:start position:0%
+so this is now a sum if i go
+ 
+
+ align:start position:0%
+so this is now a sum if i go
+so now for the second sum
+
+ align:start position:0%
+so now for the second sum
+ 
+
+ align:start position:0%
+so now for the second sum
+n is equal to l minus m zero
+
+ align:start position:0%
+n is equal to l minus m zero
+ 
+
+ align:start position:0%
+n is equal to l minus m zero
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+so now n starts at zero and ends at m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus uh
+
+ align:start position:0%
+minus uh
+ 
+
+ align:start position:0%
+minus uh
+0 plus 1
+
+ align:start position:0%
+0 plus 1
+ 
+
+ align:start position:0%
+0 plus 1
+alpha to the n
+
+ align:start position:0%
+alpha to the n
+ 
+
+ align:start position:0%
+alpha to the n
+okay again m is the little is the thing
+
+ align:start position:0%
+okay again m is the little is the thing
+ 
+
+ align:start position:0%
+okay again m is the little is the thing
+that's changing here and we're trying to
+
+ align:start position:0%
+that's changing here and we're trying to
+ 
+
+ align:start position:0%
+that's changing here and we're trying to
+bound this independently of little m but
+
+ align:start position:0%
+bound this independently of little m but
+ 
+
+ align:start position:0%
+bound this independently of little m but
+now we're in good shape because this
+
+ align:start position:0%
+now we're in good shape because this
+ 
+
+ align:start position:0%
+now we're in good shape because this
+looks like a geometric series
+
+ align:start position:0%
+looks like a geometric series
+ 
+
+ align:start position:0%
+looks like a geometric series
+alpha remember is less than one
+
+ align:start position:0%
+alpha remember is less than one
+ 
+
+ align:start position:0%
+alpha remember is less than one
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is less than or equal to sum from n
+
+ align:start position:0%
+this is less than or equal to sum from n
+ 
+
+ align:start position:0%
+this is less than or equal to sum from n
+equals one to m zero
+
+ align:start position:0%
+equals one to m zero
+ 
+
+ align:start position:0%
+equals one to m zero
+x sub n
+
+ align:start position:0%
+x sub n
+ 
+
+ align:start position:0%
+x sub n
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+x of m 0 plus 1 times
+
+ align:start position:0%
+x of m 0 plus 1 times
+ 
+
+ align:start position:0%
+x of m 0 plus 1 times
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+instead of just being
+
+ align:start position:0%
+instead of just being
+ 
+
+ align:start position:0%
+instead of just being
+a sum from 0 up to m minus m 0 plus 1
+
+ align:start position:0%
+a sum from 0 up to m minus m 0 plus 1
+ 
+
+ align:start position:0%
+a sum from 0 up to m minus m 0 plus 1
+why not throw
+
+ align:start position:0%
+why not throw
+ 
+
+ align:start position:0%
+why not throw
+all of it in there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is equal to
+
+ align:start position:0%
+and this is equal to
+ 
+
+ align:start position:0%
+and this is equal to
+n equals 0
+
+ align:start position:0%
+n equals 0
+ 
+
+ align:start position:0%
+n equals 0
+x n
+
+ align:start position:0%
+x n
+ 
+
+ align:start position:0%
+x n
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+x sub m0 plus 1
+
+ align:start position:0%
+x sub m0 plus 1
+ 
+
+ align:start position:0%
+x sub m0 plus 1
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+1 over 1 minus alpha remember alpha is a
+
+ align:start position:0%
+1 over 1 minus alpha remember alpha is a
+ 
+
+ align:start position:0%
+1 over 1 minus alpha remember alpha is a
+number that we fixed to be less than one
+
+ align:start position:0%
+number that we fixed to be less than one
+ 
+
+ align:start position:0%
+number that we fixed to be less than one
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+if you try to do
+
+ align:start position:0%
+if you try to do
+ 
+
+ align:start position:0%
+if you try to do
+what we did before and not kind of fix
+
+ align:start position:0%
+what we did before and not kind of fix
+ 
+
+ align:start position:0%
+what we did before and not kind of fix
+the alpha just a little bit to the left
+
+ align:start position:0%
+the alpha just a little bit to the left
+ 
+
+ align:start position:0%
+the alpha just a little bit to the left
+of one and try to do everything with one
+
+ align:start position:0%
+of one and try to do everything with one
+ 
+
+ align:start position:0%
+of one and try to do everything with one
+you would have wound up
+
+ align:start position:0%
+you would have wound up
+ 
+
+ align:start position:0%
+you would have wound up
+with one to the n here and that that
+
+ align:start position:0%
+with one to the n here and that that
+ 
+
+ align:start position:0%
+with one to the n here and that that
+wouldn't have
+
+ align:start position:0%
+wouldn't have
+ 
+
+ align:start position:0%
+wouldn't have
+finished the proof that wouldn't have
+
+ align:start position:0%
+finished the proof that wouldn't have
+ 
+
+ align:start position:0%
+finished the proof that wouldn't have
+closed the proof but giving yourself a
+
+ align:start position:0%
+closed the proof but giving yourself a
+ 
+
+ align:start position:0%
+closed the proof but giving yourself a
+little bit of room which is why we fixed
+
+ align:start position:0%
+little bit of room which is why we fixed
+ 
+
+ align:start position:0%
+little bit of room which is why we fixed
+this alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now this number here is independent
+
+ align:start position:0%
+okay now this number here is independent
+ 
+
+ align:start position:0%
+okay now this number here is independent
+of little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m that's the whole point okay
+
+ align:start position:0%
+m that's the whole point okay
+ 
+
+ align:start position:0%
+m that's the whole point okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have we
+
+ align:start position:0%
+have we
+ 
+
+ align:start position:0%
+have we
+proven that for all natural numbers
+
+ align:start position:0%
+proven that for all natural numbers
+ 
+
+ align:start position:0%
+proven that for all natural numbers
+little m
+
+ align:start position:0%
+little m
+ 
+
+ align:start position:0%
+little m
+the nth
+
+ align:start position:0%
+the nth
+ 
+
+ align:start position:0%
+the nth
+partial sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is less than or equal to a fixed number
+
+ align:start position:0%
+is less than or equal to a fixed number
+ 
+
+ align:start position:0%
+is less than or equal to a fixed number
+given by
+
+ align:start position:0%
+given by
+ 
+
+ align:start position:0%
+given by
+some from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+this sequence of partial sums is bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so kind of the simplest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+application of this is um
+
+ align:start position:0%
+application of this is um
+ 
+
+ align:start position:0%
+application of this is um
+maybe a series that
+
+ align:start position:0%
+maybe a series that
+ 
+
+ align:start position:0%
+maybe a series that
+looks familiar so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all x so this is i guess a theorem
+
+ align:start position:0%
+for all x so this is i guess a theorem
+ 
+
+ align:start position:0%
+for all x so this is i guess a theorem
+slash example but for all x and r the
+
+ align:start position:0%
+slash example but for all x and r the
+ 
+
+ align:start position:0%
+slash example but for all x and r the
+series x to the n
+
+ align:start position:0%
+series x to the n
+ 
+
+ align:start position:0%
+series x to the n
+over n factorial
+
+ align:start position:0%
+over n factorial
+ 
+
+ align:start position:0%
+over n factorial
+n equals zero to infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges absolutely here um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero factorial is of course one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and you just use the the ratio test
+
+ align:start position:0%
+okay and you just use the the ratio test
+ 
+
+ align:start position:0%
+okay and you just use the the ratio test
+right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the x to the n plus 1
+
+ align:start position:0%
+of the x to the n plus 1
+ 
+
+ align:start position:0%
+of the x to the n plus 1
+or the n plus first term over x to the n
+
+ align:start position:0%
+or the n plus first term over x to the n
+ 
+
+ align:start position:0%
+or the n plus first term over x to the n
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+absolute value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this equals the limit as
+
+ align:start position:0%
+this equals the limit as
+ 
+
+ align:start position:0%
+this equals the limit as
+n goes to infinity of
+
+ align:start position:0%
+n goes to infinity of
+ 
+
+ align:start position:0%
+n goes to infinity of
+n plus 1 factorial is equal to n plus 1
+
+ align:start position:0%
+n plus 1 factorial is equal to n plus 1
+ 
+
+ align:start position:0%
+n plus 1 factorial is equal to n plus 1
+times n factorial so this cancels with
+
+ align:start position:0%
+times n factorial so this cancels with
+ 
+
+ align:start position:0%
+times n factorial so this cancels with
+that n factorial and i get x
+
+ align:start position:0%
+that n factorial and i get x
+ 
+
+ align:start position:0%
+that n factorial and i get x
+over n
+
+ align:start position:0%
+over n
+ 
+
+ align:start position:0%
+over n
+plus 1.
+
+ align:start position:0%
+plus 1.
+ 
+
+ align:start position:0%
+plus 1.
+limit as n goes to infinity of just this
+
+ align:start position:0%
+limit as n goes to infinity of just this
+ 
+
+ align:start position:0%
+limit as n goes to infinity of just this
+fixed number over n plus one equals zero
+
+ align:start position:0%
+fixed number over n plus one equals zero
+ 
+
+ align:start position:0%
+fixed number over n plus one equals zero
+and this is certainly less than
+
+ align:start position:0%
+and this is certainly less than
+ 
+
+ align:start position:0%
+and this is certainly less than
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore by the ratio test
+
+ align:start position:0%
+and therefore by the ratio test
+ 
+
+ align:start position:0%
+and therefore by the ratio test
+this series converges absolutely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+i got a little hung up on exactly uh
+
+ align:start position:0%
+i got a little hung up on exactly uh
+ 
+
+ align:start position:0%
+i got a little hung up on exactly uh
+the indexes and matching them up uh
+
+ align:start position:0%
+the indexes and matching them up uh
+ 
+
+ align:start position:0%
+the indexes and matching them up uh
+precisely but
+
+ align:start position:0%
+precisely but
+ 
+
+ align:start position:0%
+precisely but
+the important thing to
+
+ align:start position:0%
+the important thing to
+ 
+
+ align:start position:0%
+the important thing to
+to take home from this proof was that
+
+ align:start position:0%
+to take home from this proof was that
+ 
+
+ align:start position:0%
+to take home from this proof was that
+when this
+
+ align:start position:0%
+when this
+ 
+
+ align:start position:0%
+when this
+ratio is less than one then
+
+ align:start position:0%
+ratio is less than one then
+ 
+
+ align:start position:0%
+ratio is less than one then
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+series behaves very much like um
+
+ align:start position:0%
+series behaves very much like um
+ 
+
+ align:start position:0%
+series behaves very much like um
+a geometric series for
+
+ align:start position:0%
+a geometric series for
+ 
+
+ align:start position:0%
+a geometric series for
+as the terms get very as you go far
+
+ align:start position:0%
+as the terms get very as you go far
+ 
+
+ align:start position:0%
+as the terms get very as you go far
+enough out
+
+ align:start position:0%
+enough out
+ 
+
+ align:start position:0%
+enough out
+in the terms
+
+ align:start position:0%
+in the terms
+ 
+
+ align:start position:0%
+in the terms
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this idea of just
+
+ align:start position:0%
+this idea of just
+ 
+
+ align:start position:0%
+this idea of just
+trying to relate the series to a simple
+
+ align:start position:0%
+trying to relate the series to a simple
+ 
+
+ align:start position:0%
+trying to relate the series to a simple
+series that you know a lot about name i
+
+ align:start position:0%
+series that you know a lot about name i
+ 
+
+ align:start position:0%
+series that you know a lot about name i
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+basically the only series that you know
+
+ align:start position:0%
+basically the only series that you know
+ 
+
+ align:start position:0%
+basically the only series that you know
+everything about
+
+ align:start position:0%
+everything about
+ 
+
+ align:start position:0%
+everything about
+namely even how to sum it
+
+ align:start position:0%
+namely even how to sum it
+ 
+
+ align:start position:0%
+namely even how to sum it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this is how you get
+
+ align:start position:0%
+this is how you get
+ 
+
+ align:start position:0%
+this is how you get
+you know this test and this is also even
+
+ align:start position:0%
+you know this test and this is also even
+ 
+
+ align:start position:0%
+you know this test and this is also even
+simpler how you get the next test which
+
+ align:start position:0%
+simpler how you get the next test which
+ 
+
+ align:start position:0%
+simpler how you get the next test which
+is the root test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's a root test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take a series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this l
+
+ align:start position:0%
+this l
+ 
+
+ align:start position:0%
+this l
+this limit
+
+ align:start position:0%
+this limit
+ 
+
+ align:start position:0%
+this limit
+l equals the limit as
+
+ align:start position:0%
+l equals the limit as
+ 
+
+ align:start position:0%
+l equals the limit as
+n goes to infinity
+
+ align:start position:0%
+n goes to infinity
+ 
+
+ align:start position:0%
+n goes to infinity
+of x sub n to the 1 over n
+
+ align:start position:0%
+of x sub n to the 1 over n
+ 
+
+ align:start position:0%
+of x sub n to the 1 over n
+exists
+
+ align:start position:0%
+exists
+ 
+
+ align:start position:0%
+exists
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+two conclusions just kind of just like
+
+ align:start position:0%
+two conclusions just kind of just like
+ 
+
+ align:start position:0%
+two conclusions just kind of just like
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+ratio tests
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+l is less than one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this implies that
+
+ align:start position:0%
+and this implies that
+ 
+
+ align:start position:0%
+and this implies that
+the series converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolutely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if l is bigger than one
+
+ align:start position:0%
+and if l is bigger than one
+ 
+
+ align:start position:0%
+and if l is bigger than one
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this series converges um
+
+ align:start position:0%
+this series converges um
+ 
+
+ align:start position:0%
+this series converges um
+no the series diverges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and again just like in the ratio
+
+ align:start position:0%
+okay and again just like in the ratio
+ 
+
+ align:start position:0%
+okay and again just like in the ratio
+test um no
+
+ align:start position:0%
+test um no
+ 
+
+ align:start position:0%
+test um no
+no information for l equals one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you take the same series that we looked
+
+ align:start position:0%
+you take the same series that we looked
+ 
+
+ align:start position:0%
+you take the same series that we looked
+at before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see did i leave it up there yes
+
+ align:start position:0%
+let's see did i leave it up there yes
+ 
+
+ align:start position:0%
+let's see did i leave it up there yes
+so xn x sub n equals 1 for all in
+
+ align:start position:0%
+so xn x sub n equals 1 for all in
+ 
+
+ align:start position:0%
+so xn x sub n equals 1 for all in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+limit here l exists it's equal to 1 and
+
+ align:start position:0%
+limit here l exists it's equal to 1 and
+ 
+
+ align:start position:0%
+limit here l exists it's equal to 1 and
+that series diverges
+
+ align:start position:0%
+that series diverges
+ 
+
+ align:start position:0%
+that series diverges
+if you look at one over n squared
+
+ align:start position:0%
+if you look at one over n squared
+ 
+
+ align:start position:0%
+if you look at one over n squared
+and i take
+
+ align:start position:0%
+and i take
+ 
+
+ align:start position:0%
+and i take
+this limit
+
+ align:start position:0%
+this limit
+ 
+
+ align:start position:0%
+this limit
+i again get one but that series
+
+ align:start position:0%
+i again get one but that series
+ 
+
+ align:start position:0%
+i again get one but that series
+converges okay so for
+
+ align:start position:0%
+converges okay so for
+ 
+
+ align:start position:0%
+converges okay so for
+capital l equals one
+
+ align:start position:0%
+capital l equals one
+ 
+
+ align:start position:0%
+capital l equals one
+we get no information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so let's uh
+
+ align:start position:0%
+so let's uh
+ 
+
+ align:start position:0%
+so let's uh
+and and in this case
+
+ align:start position:0%
+and and in this case
+ 
+
+ align:start position:0%
+and and in this case
+it's even clearer how
+
+ align:start position:0%
+it's even clearer how
+ 
+
+ align:start position:0%
+it's even clearer how
+you know we're relating
+
+ align:start position:0%
+you know we're relating
+ 
+
+ align:start position:0%
+you know we're relating
+um the series
+
+ align:start position:0%
+um the series
+ 
+
+ align:start position:0%
+um the series
+to a geometric series so
+
+ align:start position:0%
+to a geometric series so
+ 
+
+ align:start position:0%
+to a geometric series so
+let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in my notes i proved two first both
+
+ align:start position:0%
+in my notes i proved two first both
+ 
+
+ align:start position:0%
+in my notes i proved two first both
+times so perhaps i should have written
+
+ align:start position:0%
+times so perhaps i should have written
+ 
+
+ align:start position:0%
+times so perhaps i should have written
+it one two
+
+ align:start position:0%
+it one two
+ 
+
+ align:start position:0%
+it one two
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i'll know for the future
+
+ align:start position:0%
+i'll know for the future
+ 
+
+ align:start position:0%
+i'll know for the future
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose l is bigger than one
+
+ align:start position:0%
+suppose l is bigger than one
+ 
+
+ align:start position:0%
+suppose l is bigger than one
+okay and now we're going to show that
+
+ align:start position:0%
+okay and now we're going to show that
+ 
+
+ align:start position:0%
+okay and now we're going to show that
+this series diverges again by showing
+
+ align:start position:0%
+this series diverges again by showing
+ 
+
+ align:start position:0%
+this series diverges again by showing
+that the terms do not converge to zero
+
+ align:start position:0%
+that the terms do not converge to zero
+ 
+
+ align:start position:0%
+that the terms do not converge to zero
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it's the same idea as before
+
+ align:start position:0%
+it's the same idea as before
+ 
+
+ align:start position:0%
+it's the same idea as before
+here's l
+
+ align:start position:0%
+here's l
+ 
+
+ align:start position:0%
+here's l
+here's one
+
+ align:start position:0%
+here's one
+ 
+
+ align:start position:0%
+here's one
+so for all n sufficiently large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x to the n to the one over n
+
+ align:start position:0%
+x to the n to the one over n
+ 
+
+ align:start position:0%
+x to the n to the one over n
+has to be inside this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interval and since
+
+ align:start position:0%
+interval and since
+ 
+
+ align:start position:0%
+interval and since
+x to the n
+
+ align:start position:0%
+x to the n
+ 
+
+ align:start position:0%
+x to the n
+x sub n to the one over n
+
+ align:start position:0%
+x sub n to the one over n
+ 
+
+ align:start position:0%
+x sub n to the one over n
+converges to l which is bigger than one
+
+ align:start position:0%
+converges to l which is bigger than one
+ 
+
+ align:start position:0%
+converges to l which is bigger than one
+this implies there exists
+
+ align:start position:0%
+this implies there exists
+ 
+
+ align:start position:0%
+this implies there exists
+an integer
+
+ align:start position:0%
+an integer
+ 
+
+ align:start position:0%
+an integer
+and zero such that
+
+ align:start position:0%
+and zero such that
+ 
+
+ align:start position:0%
+and zero such that
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+n bigger than or equal to m 0
+
+ align:start position:0%
+n bigger than or equal to m 0
+ 
+
+ align:start position:0%
+n bigger than or equal to m 0
+x sub n to the 1 over n
+
+ align:start position:0%
+x sub n to the 1 over n
+ 
+
+ align:start position:0%
+x sub n to the 1 over n
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+bigger than 1
+
+ align:start position:0%
+bigger than 1
+ 
+
+ align:start position:0%
+bigger than 1
+which implies
+
+ align:start position:0%
+which implies
+ 
+
+ align:start position:0%
+which implies
+well n bigger than or equal to m0 x sub
+
+ align:start position:0%
+well n bigger than or equal to m0 x sub
+ 
+
+ align:start position:0%
+well n bigger than or equal to m0 x sub
+n an absolute value
+
+ align:start position:0%
+n an absolute value
+ 
+
+ align:start position:0%
+n an absolute value
+is bigger than by just taking n powers
+
+ align:start position:0%
+is bigger than by just taking n powers
+ 
+
+ align:start position:0%
+is bigger than by just taking n powers
+of both sides is bigger than one
+
+ align:start position:0%
+of both sides is bigger than one
+ 
+
+ align:start position:0%
+of both sides is bigger than one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now since all of the absolute values of
+
+ align:start position:0%
+now since all of the absolute values of
+ 
+
+ align:start position:0%
+now since all of the absolute values of
+x of n's is bigger than one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this implies that this cannot converge
+
+ align:start position:0%
+this implies that this cannot converge
+ 
+
+ align:start position:0%
+this implies that this cannot converge
+to zero all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so remember i mean uh
+
+ align:start position:0%
+so remember i mean uh
+ 
+
+ align:start position:0%
+so remember i mean uh
+let me remove this absolute value
+
+ align:start position:0%
+let me remove this absolute value
+ 
+
+ align:start position:0%
+let me remove this absolute value
+x sub n cannot converge to zero why i
+
+ align:start position:0%
+x sub n cannot converge to zero why i
+ 
+
+ align:start position:0%
+x sub n cannot converge to zero why i
+mean we could
+
+ align:start position:0%
+mean we could
+ 
+
+ align:start position:0%
+mean we could
+go back to the basic definition of
+
+ align:start position:0%
+go back to the basic definition of
+ 
+
+ align:start position:0%
+go back to the basic definition of
+convergence
+
+ align:start position:0%
+convergence
+ 
+
+ align:start position:0%
+convergence
+of what it means for a sequence to
+
+ align:start position:0%
+of what it means for a sequence to
+ 
+
+ align:start position:0%
+of what it means for a sequence to
+converge to a real number x
+
+ align:start position:0%
+converge to a real number x
+ 
+
+ align:start position:0%
+converge to a real number x
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and what it doesn't mean or what it
+
+ align:start position:0%
+and what it doesn't mean or what it
+ 
+
+ align:start position:0%
+and what it doesn't mean or what it
+means for it to not converge to x so xn
+
+ align:start position:0%
+means for it to not converge to x so xn
+ 
+
+ align:start position:0%
+means for it to not converge to x so xn
+does not converge to 0 if there exists
+
+ align:start position:0%
+does not converge to 0 if there exists
+ 
+
+ align:start position:0%
+does not converge to 0 if there exists
+a bad epsilon so that x sub n is
+
+ align:start position:0%
+a bad epsilon so that x sub n is
+ 
+
+ align:start position:0%
+a bad epsilon so that x sub n is
+outside of that interval
+
+ align:start position:0%
+outside of that interval
+ 
+
+ align:start position:0%
+outside of that interval
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+as long uh
+
+ align:start position:0%
+as long uh
+ 
+
+ align:start position:0%
+as long uh
+is outside of that interval
+
+ align:start position:0%
+is outside of that interval
+ 
+
+ align:start position:0%
+is outside of that interval
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if i go far enough out okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we certainly have that here okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or you know you could use
+
+ align:start position:0%
+or you know you could use
+ 
+
+ align:start position:0%
+or you know you could use
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+bigger than one in fact implies
+
+ align:start position:0%
+bigger than one in fact implies
+ 
+
+ align:start position:0%
+bigger than one in fact implies
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the limb soup
+
+ align:start position:0%
+the limb soup
+ 
+
+ align:start position:0%
+the limb soup
+of x of n is bigger than one because if
+
+ align:start position:0%
+of x of n is bigger than one because if
+ 
+
+ align:start position:0%
+of x of n is bigger than one because if
+i have two sequences one bigger than the
+
+ align:start position:0%
+i have two sequences one bigger than the
+ 
+
+ align:start position:0%
+i have two sequences one bigger than the
+other then the limb soup of the bigger
+
+ align:start position:0%
+other then the limb soup of the bigger
+ 
+
+ align:start position:0%
+other then the limb soup of the bigger
+one is bigger than or equal to the limb
+
+ align:start position:0%
+one is bigger than or equal to the limb
+ 
+
+ align:start position:0%
+one is bigger than or equal to the limb
+soup of the other one which is one
+
+ align:start position:0%
+soup of the other one which is one
+ 
+
+ align:start position:0%
+soup of the other one which is one
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're doing in this week's assignment
+
+ align:start position:0%
+you're doing in this week's assignment
+ 
+
+ align:start position:0%
+you're doing in this week's assignment
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this converges that xn converges to zero
+
+ align:start position:0%
+this converges that xn converges to zero
+ 
+
+ align:start position:0%
+this converges that xn converges to zero
+if and only if the limb soup of the
+
+ align:start position:0%
+if and only if the limb soup of the
+ 
+
+ align:start position:0%
+if and only if the limb soup of the
+absolute values of x ends converge to
+
+ align:start position:0%
+absolute values of x ends converge to
+ 
+
+ align:start position:0%
+absolute values of x ends converge to
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+this is not it's bigger than or equal to
+
+ align:start position:0%
+this is not it's bigger than or equal to
+ 
+
+ align:start position:0%
+this is not it's bigger than or equal to
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'll leave that there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now for
+
+ align:start position:0%
+okay so now for
+ 
+
+ align:start position:0%
+okay so now for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+other case that
+
+ align:start position:0%
+other case that
+ 
+
+ align:start position:0%
+other case that
+l is less than one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose l is less than one then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let alpha be
+
+ align:start position:0%
+let alpha be
+ 
+
+ align:start position:0%
+let alpha be
+a number between l and one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again since this converges to
+
+ align:start position:0%
+again since this converges to
+ 
+
+ align:start position:0%
+again since this converges to
+uh l which is less than alpha
+
+ align:start position:0%
+uh l which is less than alpha
+ 
+
+ align:start position:0%
+uh l which is less than alpha
+for all n sufficiently large this has to
+
+ align:start position:0%
+for all n sufficiently large this has to
+ 
+
+ align:start position:0%
+for all n sufficiently large this has to
+be less than alpha
+
+ align:start position:0%
+be less than alpha
+ 
+
+ align:start position:0%
+be less than alpha
+so there exists a integer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i have
+
+ align:start position:0%
+i have
+ 
+
+ align:start position:0%
+i have
+x to the n to the 1 over n
+
+ align:start position:0%
+x to the n to the 1 over n
+ 
+
+ align:start position:0%
+x to the n to the 1 over n
+is less than
+
+ align:start position:0%
+is less than
+ 
+
+ align:start position:0%
+is less than
+alpha
+
+ align:start position:0%
+alpha
+ 
+
+ align:start position:0%
+alpha
+which implies that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all n
+
+ align:start position:0%
+for all n
+ 
+
+ align:start position:0%
+for all n
+bigger than or equal to m0
+
+ align:start position:0%
+bigger than or equal to m0
+ 
+
+ align:start position:0%
+bigger than or equal to m0
+x to the n and absolute value is less
+
+ align:start position:0%
+x to the n and absolute value is less
+ 
+
+ align:start position:0%
+x to the n and absolute value is less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+alpha to the n okay so here again we're
+
+ align:start position:0%
+alpha to the n okay so here again we're
+ 
+
+ align:start position:0%
+alpha to the n okay so here again we're
+seeing
+
+ align:start position:0%
+seeing
+ 
+
+ align:start position:0%
+seeing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this series if it satisfies these
+
+ align:start position:0%
+this series if it satisfies these
+ 
+
+ align:start position:0%
+this series if it satisfies these
+hypotheses
+
+ align:start position:0%
+hypotheses
+ 
+
+ align:start position:0%
+hypotheses
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+very much acting like a geometric series
+
+ align:start position:0%
+very much acting like a geometric series
+ 
+
+ align:start position:0%
+very much acting like a geometric series
+remember alpha is less than one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then for every
+
+ align:start position:0%
+then for every
+ 
+
+ align:start position:0%
+then for every
+natural number little m if we look at
+
+ align:start position:0%
+natural number little m if we look at
+ 
+
+ align:start position:0%
+natural number little m if we look at
+the nth partial sum
+
+ align:start position:0%
+the nth partial sum
+ 
+
+ align:start position:0%
+the nth partial sum
+of the absolute value
+
+ align:start position:0%
+of the absolute value
+ 
+
+ align:start position:0%
+of the absolute value
+say n equals 1.
+
+ align:start position:0%
+say n equals 1.
+ 
+
+ align:start position:0%
+say n equals 1.
+this is we split it up again into the
+
+ align:start position:0%
+this is we split it up again into the
+ 
+
+ align:start position:0%
+this is we split it up again into the
+part into a part that we don't really
+
+ align:start position:0%
+part into a part that we don't really
+ 
+
+ align:start position:0%
+part into a part that we don't really
+care about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus a
+
+ align:start position:0%
+plus a
+ 
+
+ align:start position:0%
+plus a
+interesting part remember little m is
+
+ align:start position:0%
+interesting part remember little m is
+ 
+
+ align:start position:0%
+interesting part remember little m is
+the thing that's changing
+
+ align:start position:0%
+the thing that's changing
+ 
+
+ align:start position:0%
+the thing that's changing
+this should look like a little m
+
+ align:start position:0%
+this should look like a little m
+ 
+
+ align:start position:0%
+this should look like a little m
+compared to capital m 0.
+
+ align:start position:0%
+compared to capital m 0.
+ 
+
+ align:start position:0%
+compared to capital m 0.
+and this is less than or equal to sum
+
+ align:start position:0%
+and this is less than or equal to sum
+ 
+
+ align:start position:0%
+and this is less than or equal to sum
+from n equals 1 to m 0
+
+ align:start position:0%
+from n equals 1 to m 0
+ 
+
+ align:start position:0%
+from n equals 1 to m 0
+x sub n again this is just a fixed
+
+ align:start position:0%
+x sub n again this is just a fixed
+ 
+
+ align:start position:0%
+x sub n again this is just a fixed
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+now we input this inequality
+
+ align:start position:0%
+now we input this inequality
+ 
+
+ align:start position:0%
+now we input this inequality
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+n equals m0
+
+ align:start position:0%
+n equals m0
+ 
+
+ align:start position:0%
+n equals m0
+plus 1
+
+ align:start position:0%
+plus 1
+ 
+
+ align:start position:0%
+plus 1
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+alpha to the n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is less than or equal to
+
+ align:start position:0%
+this is less than or equal to
+ 
+
+ align:start position:0%
+this is less than or equal to
+sum from n equals m zero
+
+ align:start position:0%
+sum from n equals m zero
+ 
+
+ align:start position:0%
+sum from n equals m zero
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i'm gonna go
+
+ align:start position:0%
+i'm gonna go
+ 
+
+ align:start position:0%
+i'm gonna go
+kind of fast here because i'm running
+
+ align:start position:0%
+kind of fast here because i'm running
+ 
+
+ align:start position:0%
+kind of fast here because i'm running
+out of space on the board here
+
+ align:start position:0%
+out of space on the board here
+ 
+
+ align:start position:0%
+out of space on the board here
+um maybe i'll write this out in just a
+
+ align:start position:0%
+um maybe i'll write this out in just a
+ 
+
+ align:start position:0%
+um maybe i'll write this out in just a
+minute but
+
+ align:start position:0%
+minute but
+ 
+
+ align:start position:0%
+minute but
+why this is true and
+
+ align:start position:0%
+why this is true and
+ 
+
+ align:start position:0%
+why this is true and
+this part here is less than or equal to
+
+ align:start position:0%
+this part here is less than or equal to
+ 
+
+ align:start position:0%
+this part here is less than or equal to
+one over one minus alpha
+
+ align:start position:0%
+one over one minus alpha
+ 
+
+ align:start position:0%
+one over one minus alpha
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+because what do i do this sum is a
+
+ align:start position:0%
+because what do i do this sum is a
+ 
+
+ align:start position:0%
+because what do i do this sum is a
+finite sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's certainly bigger than if i
+
+ align:start position:0%
+and it's certainly bigger than if i
+ 
+
+ align:start position:0%
+and it's certainly bigger than if i
+make the lower bound smaller and the
+
+ align:start position:0%
+make the lower bound smaller and the
+ 
+
+ align:start position:0%
+make the lower bound smaller and the
+upper bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+larger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is just the imp partial sum
+
+ align:start position:0%
+and this is just the imp partial sum
+ 
+
+ align:start position:0%
+and this is just the imp partial sum
+corresponding to a geometric series with
+
+ align:start position:0%
+corresponding to a geometric series with
+ 
+
+ align:start position:0%
+corresponding to a geometric series with
+non-negative terms the alpha to the n
+
+ align:start position:0%
+non-negative terms the alpha to the n
+ 
+
+ align:start position:0%
+non-negative terms the alpha to the n
+and so that's less than or equal to sum
+
+ align:start position:0%
+and so that's less than or equal to sum
+ 
+
+ align:start position:0%
+and so that's less than or equal to sum
+from n equals 0 to infinity of alpha to
+
+ align:start position:0%
+from n equals 0 to infinity of alpha to
+ 
+
+ align:start position:0%
+from n equals 0 to infinity of alpha to
+the n which equals 1 over
+
+ align:start position:0%
+the n which equals 1 over
+ 
+
+ align:start position:0%
+the n which equals 1 over
+1 minus alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's how we got this term and
+
+ align:start position:0%
+so that's how we got this term and
+ 
+
+ align:start position:0%
+so that's how we got this term and
+therefore the partial sums corresponding
+
+ align:start position:0%
+therefore the partial sums corresponding
+ 
+
+ align:start position:0%
+therefore the partial sums corresponding
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the absolute the series with absolute
+
+ align:start position:0%
+the absolute the series with absolute
+ 
+
+ align:start position:0%
+the absolute the series with absolute
+values is bounded
+
+ align:start position:0%
+values is bounded
+ 
+
+ align:start position:0%
+values is bounded
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+that series
+
+ align:start position:0%
+that series
+ 
+
+ align:start position:0%
+that series
+with the absolute values converges and
+
+ align:start position:0%
+with the absolute values converges and
+ 
+
+ align:start position:0%
+with the absolute values converges and
+we have absolute convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let me state a theorem about
+
+ align:start position:0%
+now let me state a theorem about
+ 
+
+ align:start position:0%
+now let me state a theorem about
+alternating series it is not
+
+ align:start position:0%
+alternating series it is not
+ 
+
+ align:start position:0%
+alternating series it is not
+i prefer not to call it an alternating
+
+ align:start position:0%
+i prefer not to call it an alternating
+ 
+
+ align:start position:0%
+i prefer not to call it an alternating
+series test
+
+ align:start position:0%
+series test
+ 
+
+ align:start position:0%
+series test
+because there's nothing really to test
+
+ align:start position:0%
+because there's nothing really to test
+ 
+
+ align:start position:0%
+because there's nothing really to test
+i mean at least with the ratio and root
+
+ align:start position:0%
+i mean at least with the ratio and root
+ 
+
+ align:start position:0%
+i mean at least with the ratio and root
+test you have to compute a limit
+
+ align:start position:0%
+test you have to compute a limit
+ 
+
+ align:start position:0%
+test you have to compute a limit
+which might require some work to do
+
+ align:start position:0%
+which might require some work to do
+ 
+
+ align:start position:0%
+which might require some work to do
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore at least to me that's kind
+
+ align:start position:0%
+and therefore at least to me that's kind
+ 
+
+ align:start position:0%
+and therefore at least to me that's kind
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+real thing that you have to
+
+ align:start position:0%
+real thing that you have to
+ 
+
+ align:start position:0%
+real thing that you have to
+do a little work
+
+ align:start position:0%
+do a little work
+ 
+
+ align:start position:0%
+do a little work
+to test whether a series converges
+
+ align:start position:0%
+to test whether a series converges
+ 
+
+ align:start position:0%
+to test whether a series converges
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+for alternating series the test is you
+
+ align:start position:0%
+for alternating series the test is you
+ 
+
+ align:start position:0%
+for alternating series the test is you
+look at it
+
+ align:start position:0%
+look at it
+ 
+
+ align:start position:0%
+look at it
+and that's it
+
+ align:start position:0%
+and that's it
+ 
+
+ align:start position:0%
+and that's it
+you don't compute anything
+
+ align:start position:0%
+you don't compute anything
+ 
+
+ align:start position:0%
+you don't compute anything
+you look at it
+
+ align:start position:0%
+you look at it
+ 
+
+ align:start position:0%
+you look at it
+so i prefer not to call
+
+ align:start position:0%
+so i prefer not to call
+ 
+
+ align:start position:0%
+so i prefer not to call
+this theorem about alternating series
+
+ align:start position:0%
+this theorem about alternating series
+ 
+
+ align:start position:0%
+this theorem about alternating series
+and alternating series test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the theorem is for alternating series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and statement is the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let x sub n
+
+ align:start position:0%
+let x sub n
+ 
+
+ align:start position:0%
+let x sub n
+be a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monotone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decreasing sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converging to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so because this thing is monotone and
+
+ align:start position:0%
+so because this thing is monotone and
+ 
+
+ align:start position:0%
+so because this thing is monotone and
+conv monotone decreasing and converging
+
+ align:start position:0%
+conv monotone decreasing and converging
+ 
+
+ align:start position:0%
+conv monotone decreasing and converging
+to zero um
+
+ align:start position:0%
+to zero um
+ 
+
+ align:start position:0%
+to zero um
+it's all
+
+ align:start position:0%
+it's all
+ 
+
+ align:start position:0%
+it's all
+so let me
+
+ align:start position:0%
+so let me
+ 
+
+ align:start position:0%
+so let me
+put this in parentheses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before xn is bigger than or equal to 0
+
+ align:start position:0%
+before xn is bigger than or equal to 0
+ 
+
+ align:start position:0%
+before xn is bigger than or equal to 0
+for all n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i cannot have a monotone decreasing
+
+ align:start position:0%
+i cannot have a monotone decreasing
+ 
+
+ align:start position:0%
+i cannot have a monotone decreasing
+sequence converging to zero if one of
+
+ align:start position:0%
+sequence converging to zero if one of
+ 
+
+ align:start position:0%
+sequence converging to zero if one of
+the x ends is less than zero because
+
+ align:start position:0%
+the x ends is less than zero because
+ 
+
+ align:start position:0%
+the x ends is less than zero because
+they keep getting smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is uh this is it this is not
+
+ align:start position:0%
+this is uh this is it this is not
+ 
+
+ align:start position:0%
+this is uh this is it this is not
+this is all of the hypotheses you don't
+
+ align:start position:0%
+this is all of the hypotheses you don't
+ 
+
+ align:start position:0%
+this is all of the hypotheses you don't
+have to compute anything
+
+ align:start position:0%
+have to compute anything
+ 
+
+ align:start position:0%
+have to compute anything
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the series
+
+ align:start position:0%
+the series
+ 
+
+ align:start position:0%
+the series
+minus 1 to the n
+
+ align:start position:0%
+minus 1 to the n
+ 
+
+ align:start position:0%
+minus 1 to the n
+x n
+
+ align:start position:0%
+x n
+ 
+
+ align:start position:0%
+x n
+n equals
+
+ align:start position:0%
+n equals
+ 
+
+ align:start position:0%
+n equals
+let's uh
+
+ align:start position:0%
+let's uh
+ 
+
+ align:start position:0%
+let's uh
+of course
+
+ align:start position:0%
+of course
+ 
+
+ align:start position:0%
+of course
+you know we don't have to start at one
+
+ align:start position:0%
+you know we don't have to start at one
+ 
+
+ align:start position:0%
+you know we don't have to start at one
+in particular but
+
+ align:start position:0%
+in particular but
+ 
+
+ align:start position:0%
+in particular but
+at least for this statement let's make
+
+ align:start position:0%
+at least for this statement let's make
+ 
+
+ align:start position:0%
+at least for this statement let's make
+it precise
+
+ align:start position:0%
+it precise
+ 
+
+ align:start position:0%
+it precise
+sum from n equals 1 to infinity of minus
+
+ align:start position:0%
+sum from n equals 1 to infinity of minus
+ 
+
+ align:start position:0%
+sum from n equals 1 to infinity of minus
+1 to the n x to the n x sub n
+
+ align:start position:0%
+1 to the n x to the n x sub n
+ 
+
+ align:start position:0%
+1 to the n x to the n x sub n
+converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and we can just say
+
+ align:start position:0%
+all right and we can just say
+ 
+
+ align:start position:0%
+all right and we can just say
+convergence not necessarily absolute
+
+ align:start position:0%
+convergence not necessarily absolute
+ 
+
+ align:start position:0%
+convergence not necessarily absolute
+convergence because again if we look at
+
+ align:start position:0%
+convergence because again if we look at
+ 
+
+ align:start position:0%
+convergence because again if we look at
+minus one to the n one over n which is
+
+ align:start position:0%
+minus one to the n one over n which is
+ 
+
+ align:start position:0%
+minus one to the n one over n which is
+one over n is a monotone decreasing
+
+ align:start position:0%
+one over n is a monotone decreasing
+ 
+
+ align:start position:0%
+one over n is a monotone decreasing
+sequence converging to zero that
+
+ align:start position:0%
+sequence converging to zero that
+ 
+
+ align:start position:0%
+sequence converging to zero that
+converges but not absolutely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and if we have x sub n equal one
+
+ align:start position:0%
+okay and if we have x sub n equal one
+ 
+
+ align:start position:0%
+okay and if we have x sub n equal one
+over n squared again one over n squared
+
+ align:start position:0%
+over n squared again one over n squared
+ 
+
+ align:start position:0%
+over n squared again one over n squared
+is a monotone decreasing sequence
+
+ align:start position:0%
+is a monotone decreasing sequence
+ 
+
+ align:start position:0%
+is a monotone decreasing sequence
+converging to zero that would converge
+
+ align:start position:0%
+converging to zero that would converge
+ 
+
+ align:start position:0%
+converging to zero that would converge
+absolutely so we just have a statement
+
+ align:start position:0%
+absolutely so we just have a statement
+ 
+
+ align:start position:0%
+absolutely so we just have a statement
+about convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how we're going to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we are
+
+ align:start position:0%
+we are
+ 
+
+ align:start position:0%
+we are
+it's kind of like how we um proved
+
+ align:start position:0%
+it's kind of like how we um proved
+ 
+
+ align:start position:0%
+it's kind of like how we um proved
+convergence for
+
+ align:start position:0%
+convergence for
+ 
+
+ align:start position:0%
+convergence for
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+p series in that we're going to show
+
+ align:start position:0%
+p series in that we're going to show
+ 
+
+ align:start position:0%
+p series in that we're going to show
+that a
+
+ align:start position:0%
+that a
+ 
+
+ align:start position:0%
+that a
+certain subsequence of partial sums
+
+ align:start position:0%
+certain subsequence of partial sums
+ 
+
+ align:start position:0%
+certain subsequence of partial sums
+converges and then we're going to use
+
+ align:start position:0%
+converges and then we're going to use
+ 
+
+ align:start position:0%
+converges and then we're going to use
+that to show
+
+ align:start position:0%
+that to show
+ 
+
+ align:start position:0%
+that to show
+that the full sequence of partial sums
+
+ align:start position:0%
+that the full sequence of partial sums
+ 
+
+ align:start position:0%
+that the full sequence of partial sums
+converge okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me state this as claim one
+
+ align:start position:0%
+let me state this as claim one
+ 
+
+ align:start position:0%
+let me state this as claim one
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequence
+
+ align:start position:0%
+subsequence
+ 
+
+ align:start position:0%
+subsequence
+of partial sums s sub 2k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is just the sum from n equals 1
+
+ align:start position:0%
+so this is just the sum from n equals 1
+ 
+
+ align:start position:0%
+so this is just the sum from n equals 1
+to 2k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to show this converges
+
+ align:start position:0%
+we're going to show this converges
+ 
+
+ align:start position:0%
+we're going to show this converges
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so again um
+
+ align:start position:0%
+so again um
+ 
+
+ align:start position:0%
+so again um
+just to become
+
+ align:start position:0%
+just to become
+ 
+
+ align:start position:0%
+just to become
+complete s of m this is the nth partial
+
+ align:start position:0%
+complete s of m this is the nth partial
+ 
+
+ align:start position:0%
+complete s of m this is the nth partial
+sum is the sum from n equals 1
+
+ align:start position:0%
+sum is the sum from n equals 1
+ 
+
+ align:start position:0%
+sum is the sum from n equals 1
+to m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so how we're going to do this
+
+ align:start position:0%
+all right so how we're going to do this
+ 
+
+ align:start position:0%
+all right so how we're going to do this
+is we're going to show that this uh
+
+ align:start position:0%
+is we're going to show that this uh
+ 
+
+ align:start position:0%
+is we're going to show that this uh
+these partial sums are in fact monotone
+
+ align:start position:0%
+these partial sums are in fact monotone
+ 
+
+ align:start position:0%
+these partial sums are in fact monotone
+decreasing
+
+ align:start position:0%
+decreasing
+ 
+
+ align:start position:0%
+decreasing
+and bounded from below monotone
+
+ align:start position:0%
+and bounded from below monotone
+ 
+
+ align:start position:0%
+and bounded from below monotone
+decreasing
+
+ align:start position:0%
+decreasing
+ 
+
+ align:start position:0%
+decreasing
+basically because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these guys are monotone decreasing
+
+ align:start position:0%
+these guys are monotone decreasing
+ 
+
+ align:start position:0%
+these guys are monotone decreasing
+and bounded from below
+
+ align:start position:0%
+and bounded from below
+ 
+
+ align:start position:0%
+and bounded from below
+by the same
+
+ align:start position:0%
+by the same
+ 
+
+ align:start position:0%
+by the same
+same reasoning okay
+
+ align:start position:0%
+same reasoning okay
+ 
+
+ align:start position:0%
+same reasoning okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's show that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for k a natural number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i look at
+
+ align:start position:0%
+if i look at
+ 
+
+ align:start position:0%
+if i look at
+s 2 k
+
+ align:start position:0%
+s 2 k
+ 
+
+ align:start position:0%
+s 2 k
+so this is the sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n equals 1 2 k
+
+ align:start position:0%
+n equals 1 2 k
+ 
+
+ align:start position:0%
+n equals 1 2 k
+minus 1 to the n
+
+ align:start position:0%
+minus 1 to the n
+ 
+
+ align:start position:0%
+minus 1 to the n
+x sub n
+
+ align:start position:0%
+x sub n
+ 
+
+ align:start position:0%
+x sub n
+now i have the n equals 1 term which i
+
+ align:start position:0%
+now i have the n equals 1 term which i
+ 
+
+ align:start position:0%
+now i have the n equals 1 term which i
+can write as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus x so just
+
+ align:start position:0%
+minus x so just
+ 
+
+ align:start position:0%
+minus x so just
+writing this out in a certain way so
+
+ align:start position:0%
+writing this out in a certain way so
+ 
+
+ align:start position:0%
+writing this out in a certain way so
+this is minus x1
+
+ align:start position:0%
+this is minus x1
+ 
+
+ align:start position:0%
+this is minus x1
+plus x2
+
+ align:start position:0%
+plus x2
+ 
+
+ align:start position:0%
+plus x2
+minus x3 plus
+
+ align:start position:0%
+minus x3 plus
+ 
+
+ align:start position:0%
+minus x3 plus
+and then n equals 2k is even so then i
+
+ align:start position:0%
+and then n equals 2k is even so then i
+ 
+
+ align:start position:0%
+and then n equals 2k is even so then i
+get plus x
+
+ align:start position:0%
+get plus x
+ 
+
+ align:start position:0%
+get plus x
+2k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is equal to x sub 2 minus x sub 1
+
+ align:start position:0%
+this is equal to x sub 2 minus x sub 1
+ 
+
+ align:start position:0%
+this is equal to x sub 2 minus x sub 1
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+x sub 4 minus x sub 3 plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all the way to
+
+ align:start position:0%
+all the way to
+ 
+
+ align:start position:0%
+all the way to
+x sub 2 k minus x sub 2 k minus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this sequence is monotone decreasing
+
+ align:start position:0%
+this sequence is monotone decreasing
+ 
+
+ align:start position:0%
+this sequence is monotone decreasing
+right so x sub 2
+
+ align:start position:0%
+right so x sub 2
+ 
+
+ align:start position:0%
+right so x sub 2
+is going to be smaller than x sub 1 all
+
+ align:start position:0%
+is going to be smaller than x sub 1 all
+ 
+
+ align:start position:0%
+is going to be smaller than x sub 1 all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+x sub 4 is going to be less than x sub
+
+ align:start position:0%
+x sub 4 is going to be less than x sub
+ 
+
+ align:start position:0%
+x sub 4 is going to be less than x sub
+3.
+
+ align:start position:0%
+3.
+ 
+
+ align:start position:0%
+3.
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+x sub 2 k
+
+ align:start position:0%
+x sub 2 k
+ 
+
+ align:start position:0%
+x sub 2 k
+minus x sub 2 k minus 1 is less than
+
+ align:start position:0%
+minus x sub 2 k minus 1 is less than
+ 
+
+ align:start position:0%
+minus x sub 2 k minus 1 is less than
+zero so since uh
+
+ align:start position:0%
+zero so since uh
+ 
+
+ align:start position:0%
+zero so since uh
+this is monotone decreasing this is
+
+ align:start position:0%
+this is monotone decreasing this is
+ 
+
+ align:start position:0%
+this is monotone decreasing this is
+bigger than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what i just said has nothing to do with
+
+ align:start position:0%
+what i just said has nothing to do with
+ 
+
+ align:start position:0%
+what i just said has nothing to do with
+this inequality i'm writing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i kept everything here and now i add
+
+ align:start position:0%
+so i kept everything here and now i add
+ 
+
+ align:start position:0%
+so i kept everything here and now i add
+uh x
+
+ align:start position:0%
+uh x
+ 
+
+ align:start position:0%
+uh x
+sub
+
+ align:start position:0%
+sub
+ 
+
+ align:start position:0%
+sub
+2k plus 2 minus x of
+
+ align:start position:0%
+2k plus 2 minus x of
+ 
+
+ align:start position:0%
+2k plus 2 minus x of
+2k plus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what i was saying was that
+
+ align:start position:0%
+okay so what i was saying was that
+ 
+
+ align:start position:0%
+okay so what i was saying was that
+the x of n's are monotone decreasing
+
+ align:start position:0%
+the x of n's are monotone decreasing
+ 
+
+ align:start position:0%
+the x of n's are monotone decreasing
+this term is right after this term
+
+ align:start position:0%
+this term is right after this term
+ 
+
+ align:start position:0%
+this term is right after this term
+so it's smaller
+
+ align:start position:0%
+so it's smaller
+ 
+
+ align:start position:0%
+so it's smaller
+than this term so this term here
+
+ align:start position:0%
+than this term so this term here
+ 
+
+ align:start position:0%
+than this term so this term here
+is less than or equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and therefore this thing plus itself
+
+ align:start position:0%
+and therefore this thing plus itself
+ 
+
+ align:start position:0%
+and therefore this thing plus itself
+plus something that's negative is less
+
+ align:start position:0%
+plus something that's negative is less
+ 
+
+ align:start position:0%
+plus something that's negative is less
+than or equal to this thing
+
+ align:start position:0%
+than or equal to this thing
+ 
+
+ align:start position:0%
+than or equal to this thing
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what is this thing on the right hand
+
+ align:start position:0%
+now what is this thing on the right hand
+ 
+
+ align:start position:0%
+now what is this thing on the right hand
+side this is just uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+2 k minus
+
+ align:start position:0%
+2 k minus
+ 
+
+ align:start position:0%
+2 k minus
+plus x 2 k minus x 2 k plus 1 plus x sub
+
+ align:start position:0%
+plus x 2 k minus x 2 k plus 1 plus x sub
+ 
+
+ align:start position:0%
+plus x 2 k minus x 2 k plus 1 plus x sub
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+k plus 1 and this is the k plus 1
+
+ align:start position:0%
+k plus 1 and this is the k plus 1
+ 
+
+ align:start position:0%
+k plus 1 and this is the k plus 1
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+k plus 1 partial sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus
+
+ align:start position:0%
+thus
+ 
+
+ align:start position:0%
+thus
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is monotone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decreasing
+
+ align:start position:0%
+decreasing
+ 
+
+ align:start position:0%
+decreasing
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to show that this subsequence of
+
+ align:start position:0%
+so to show that this subsequence of
+ 
+
+ align:start position:0%
+so to show that this subsequence of
+partial sums converges we just have to
+
+ align:start position:0%
+partial sums converges we just have to
+ 
+
+ align:start position:0%
+partial sums converges we just have to
+show that um this subsequence is bounded
+
+ align:start position:0%
+show that um this subsequence is bounded
+ 
+
+ align:start position:0%
+show that um this subsequence is bounded
+right or bounded below
+
+ align:start position:0%
+right or bounded below
+ 
+
+ align:start position:0%
+right or bounded below
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if it's monotone decreasing it's already
+
+ align:start position:0%
+if it's monotone decreasing it's already
+ 
+
+ align:start position:0%
+if it's monotone decreasing it's already
+bounded
+
+ align:start position:0%
+bounded
+ 
+
+ align:start position:0%
+bounded
+above by something so we just need to
+
+ align:start position:0%
+above by something so we just need to
+ 
+
+ align:start position:0%
+above by something so we just need to
+show it's bounded from below
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all k a natural number
+
+ align:start position:0%
+for all k a natural number
+ 
+
+ align:start position:0%
+for all k a natural number
+let's look at s sub 2 k
+
+ align:start position:0%
+let's look at s sub 2 k
+ 
+
+ align:start position:0%
+let's look at s sub 2 k
+and group terms slightly differently
+
+ align:start position:0%
+and group terms slightly differently
+ 
+
+ align:start position:0%
+and group terms slightly differently
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is equal now to i'm going to
+
+ align:start position:0%
+so this is equal now to i'm going to
+ 
+
+ align:start position:0%
+so this is equal now to i'm going to
+write it as minus x1 plus
+
+ align:start position:0%
+write it as minus x1 plus
+ 
+
+ align:start position:0%
+write it as minus x1 plus
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+sub 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x sub 2 minus x sub 3 plus
+
+ align:start position:0%
+x sub 2 minus x sub 3 plus
+ 
+
+ align:start position:0%
+x sub 2 minus x sub 3 plus
+x sub 4 minus x sub 5 plus
+
+ align:start position:0%
+x sub 4 minus x sub 5 plus
+ 
+
+ align:start position:0%
+x sub 4 minus x sub 5 plus
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+x 2 k minus x 2 k minus 1.
+
+ align:start position:0%
+x 2 k minus x 2 k minus 1.
+ 
+
+ align:start position:0%
+x 2 k minus x 2 k minus 1.
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah
+
+ align:start position:0%
+ah
+ 
+
+ align:start position:0%
+ah
+no that's not right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is
+
+ align:start position:0%
+okay so this is
+ 
+
+ align:start position:0%
+okay so this is
+minus 2
+
+ align:start position:0%
+minus 2
+ 
+
+ align:start position:0%
+minus 2
+plus x of
+
+ align:start position:0%
+plus x of
+ 
+
+ align:start position:0%
+plus x of
+2k all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now this is right
+
+ align:start position:0%
+now this is right
+ 
+
+ align:start position:0%
+now this is right
+okay so this is equal to minus so
+
+ align:start position:0%
+okay so this is equal to minus so
+ 
+
+ align:start position:0%
+okay so this is equal to minus so
+again the x of n's are monotone
+
+ align:start position:0%
+again the x of n's are monotone
+ 
+
+ align:start position:0%
+again the x of n's are monotone
+decreasing
+
+ align:start position:0%
+decreasing
+ 
+
+ align:start position:0%
+decreasing
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+um x sub 3 is smaller than x sub 2 so
+
+ align:start position:0%
+um x sub 3 is smaller than x sub 2 so
+ 
+
+ align:start position:0%
+um x sub 3 is smaller than x sub 2 so
+this is non-negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is also non-negative
+
+ align:start position:0%
+this is also non-negative
+ 
+
+ align:start position:0%
+this is also non-negative
+because x sub 5 is smaller than x sub 4
+
+ align:start position:0%
+because x sub 5 is smaller than x sub 4
+ 
+
+ align:start position:0%
+because x sub 5 is smaller than x sub 4
+so on and so on so this is also
+
+ align:start position:0%
+so on and so on so this is also
+ 
+
+ align:start position:0%
+so on and so on so this is also
+non-negative so
+
+ align:start position:0%
+non-negative so
+ 
+
+ align:start position:0%
+non-negative so
+s sub 2 k is bigger than or equal to
+
+ align:start position:0%
+s sub 2 k is bigger than or equal to
+ 
+
+ align:start position:0%
+s sub 2 k is bigger than or equal to
+minus x sub 1
+
+ align:start position:0%
+minus x sub 1
+ 
+
+ align:start position:0%
+minus x sub 1
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+non-negative terms so
+
+ align:start position:0%
+non-negative terms so
+ 
+
+ align:start position:0%
+non-negative terms so
+2k and
+
+ align:start position:0%
+2k and
+ 
+
+ align:start position:0%
+2k and
+remember x sub
+
+ align:start position:0%
+remember x sub
+ 
+
+ align:start position:0%
+remember x sub
+ends these are monotone decreasing
+
+ align:start position:0%
+ends these are monotone decreasing
+ 
+
+ align:start position:0%
+ends these are monotone decreasing
+converging to zero and therefore that
+
+ align:start position:0%
+converging to zero and therefore that
+ 
+
+ align:start position:0%
+converging to zero and therefore that
+they're all non-negative so this is
+
+ align:start position:0%
+they're all non-negative so this is
+ 
+
+ align:start position:0%
+they're all non-negative so this is
+bigger than or equal to
+
+ align:start position:0%
+bigger than or equal to
+ 
+
+ align:start position:0%
+bigger than or equal to
+minus x sub one
+
+ align:start position:0%
+minus x sub one
+ 
+
+ align:start position:0%
+minus x sub one
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus
+
+ align:start position:0%
+thus
+ 
+
+ align:start position:0%
+thus
+what do we get so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all natural numbers k
+
+ align:start position:0%
+for all natural numbers k
+ 
+
+ align:start position:0%
+for all natural numbers k
+i have minus x1 is less than or equal to
+
+ align:start position:0%
+i have minus x1 is less than or equal to
+ 
+
+ align:start position:0%
+i have minus x1 is less than or equal to
+s of 2k and because these are monotone
+
+ align:start position:0%
+s of 2k and because these are monotone
+ 
+
+ align:start position:0%
+s of 2k and because these are monotone
+decreasing this is always less than or
+
+ align:start position:0%
+decreasing this is always less than or
+ 
+
+ align:start position:0%
+decreasing this is always less than or
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+k equals 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and this is uh so if you like s sub 2 is
+
+ align:start position:0%
+and this is uh so if you like s sub 2 is
+ 
+
+ align:start position:0%
+and this is uh so if you like s sub 2 is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+minus x sub 1 plus x sub 2.
+
+ align:start position:0%
+minus x sub 1 plus x sub 2.
+ 
+
+ align:start position:0%
+minus x sub 1 plus x sub 2.
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this sequence of numbers is bounded
+
+ align:start position:0%
+this sequence of numbers is bounded
+ 
+
+ align:start position:0%
+this sequence of numbers is bounded
+between this real number and this real
+
+ align:start position:0%
+between this real number and this real
+ 
+
+ align:start position:0%
+between this real number and this real
+number and therefore it's bounded
+
+ align:start position:0%
+number and therefore it's bounded
+ 
+
+ align:start position:0%
+number and therefore it's bounded
+and since it's monotone decreasing it
+
+ align:start position:0%
+and since it's monotone decreasing it
+ 
+
+ align:start position:0%
+and since it's monotone decreasing it
+has to have a limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so s of 2k
+
+ align:start position:0%
+so s of 2k
+ 
+
+ align:start position:0%
+so s of 2k
+converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's call this limit something
+
+ align:start position:0%
+let's call this limit something
+ 
+
+ align:start position:0%
+let's call this limit something
+let's call it s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right we'll show that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sequence of partial sums converge to
+
+ align:start position:0%
+the sequence of partial sums converge to
+ 
+
+ align:start position:0%
+the sequence of partial sums converge to
+s now we just showed this for along a
+
+ align:start position:0%
+s now we just showed this for along a
+ 
+
+ align:start position:0%
+s now we just showed this for along a
+sequence of
+
+ align:start position:0%
+sequence of
+ 
+
+ align:start position:0%
+sequence of
+along a subsequence of partial sums
+
+ align:start position:0%
+along a subsequence of partial sums
+ 
+
+ align:start position:0%
+along a subsequence of partial sums
+let's show it converges to s along the
+
+ align:start position:0%
+let's show it converges to s along the
+ 
+
+ align:start position:0%
+let's show it converges to s along the
+full sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is if you like claim two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the full sequence of partial sums
+
+ align:start position:0%
+the full sequence of partial sums
+ 
+
+ align:start position:0%
+the full sequence of partial sums
+converges to s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and we're going to do this
+
+ align:start position:0%
+all right and we're going to do this
+ 
+
+ align:start position:0%
+all right and we're going to do this
+by brute force using epsilon m
+
+ align:start position:0%
+by brute force using epsilon m
+ 
+
+ align:start position:0%
+by brute force using epsilon m
+argument
+
+ align:start position:0%
+argument
+ 
+
+ align:start position:0%
+argument
+so remember to show something
+
+ align:start position:0%
+so remember to show something
+ 
+
+ align:start position:0%
+so remember to show something
+a limit
+
+ align:start position:0%
+a limit
+ 
+
+ align:start position:0%
+a limit
+of something equals s means for all
+
+ align:start position:0%
+of something equals s means for all
+ 
+
+ align:start position:0%
+of something equals s means for all
+epsilon there exists a capital m so that
+
+ align:start position:0%
+epsilon there exists a capital m so that
+ 
+
+ align:start position:0%
+epsilon there exists a capital m so that
+for all n bigger than or equal to
+
+ align:start position:0%
+for all n bigger than or equal to
+ 
+
+ align:start position:0%
+for all n bigger than or equal to
+capital m s of m minus s an absolute
+
+ align:start position:0%
+capital m s of m minus s an absolute
+ 
+
+ align:start position:0%
+capital m s of m minus s an absolute
+value is less than epsilon okay so let
+
+ align:start position:0%
+value is less than epsilon okay so let
+ 
+
+ align:start position:0%
+value is less than epsilon okay so let
+epsilon be positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since s
+
+ align:start position:0%
+since s
+ 
+
+ align:start position:0%
+since s
+sub 2k converges to s there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an m0 natural number so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all k bigger than or equal to m0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s of 2k minus s an absolute value is
+
+ align:start position:0%
+s of 2k minus s an absolute value is
+ 
+
+ align:start position:0%
+s of 2k minus s an absolute value is
+less than epsilon right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+we haven't used it all in this proof uh
+
+ align:start position:0%
+we haven't used it all in this proof uh
+ 
+
+ align:start position:0%
+we haven't used it all in this proof uh
+that the xns really converge to zero we
+
+ align:start position:0%
+that the xns really converge to zero we
+ 
+
+ align:start position:0%
+that the xns really converge to zero we
+did use that they were non-negative at
+
+ align:start position:0%
+did use that they were non-negative at
+ 
+
+ align:start position:0%
+did use that they were non-negative at
+one point
+
+ align:start position:0%
+one point
+ 
+
+ align:start position:0%
+one point
+but now this is where we'll use a
+
+ align:start position:0%
+but now this is where we'll use a
+ 
+
+ align:start position:0%
+but now this is where we'll use a
+conversion zero because
+
+ align:start position:0%
+conversion zero because
+ 
+
+ align:start position:0%
+conversion zero because
+you know here's here's the intuition
+
+ align:start position:0%
+you know here's here's the intuition
+ 
+
+ align:start position:0%
+you know here's here's the intuition
+the s sub two k's
+
+ align:start position:0%
+the s sub two k's
+ 
+
+ align:start position:0%
+the s sub two k's
+are converging to something
+
+ align:start position:0%
+are converging to something
+ 
+
+ align:start position:0%
+are converging to something
+so now i just kind of have to look at
+
+ align:start position:0%
+so now i just kind of have to look at
+ 
+
+ align:start position:0%
+so now i just kind of have to look at
+the odd ones i've shown all the even
+
+ align:start position:0%
+the odd ones i've shown all the even
+ 
+
+ align:start position:0%
+the odd ones i've shown all the even
+partial sums converge to s so
+
+ align:start position:0%
+partial sums converge to s so
+ 
+
+ align:start position:0%
+partial sums converge to s so
+if i can show the odd partial sums also
+
+ align:start position:0%
+if i can show the odd partial sums also
+ 
+
+ align:start position:0%
+if i can show the odd partial sums also
+converge to s then essentially i'm done
+
+ align:start position:0%
+converge to s then essentially i'm done
+ 
+
+ align:start position:0%
+converge to s then essentially i'm done
+what's the difference between an even
+
+ align:start position:0%
+what's the difference between an even
+ 
+
+ align:start position:0%
+what's the difference between an even
+partial sum and an odd partial sum
+
+ align:start position:0%
+partial sum and an odd partial sum
+ 
+
+ align:start position:0%
+partial sum and an odd partial sum
+well it's just x to the 2k plus x sub 2k
+
+ align:start position:0%
+well it's just x to the 2k plus x sub 2k
+ 
+
+ align:start position:0%
+well it's just x to the 2k plus x sub 2k
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+which is converging to zero so
+
+ align:start position:0%
+which is converging to zero so
+ 
+
+ align:start position:0%
+which is converging to zero so
+um they don't differ by much
+
+ align:start position:0%
+um they don't differ by much
+ 
+
+ align:start position:0%
+um they don't differ by much
+and that's essentially um
+
+ align:start position:0%
+and that's essentially um
+ 
+
+ align:start position:0%
+and that's essentially um
+that's essentially the whole argument
+
+ align:start position:0%
+that's essentially the whole argument
+ 
+
+ align:start position:0%
+that's essentially the whole argument
+right there
+
+ align:start position:0%
+right there
+ 
+
+ align:start position:0%
+right there
+so since
+
+ align:start position:0%
+so since
+ 
+
+ align:start position:0%
+so since
+x ends converge to zero
+
+ align:start position:0%
+x ends converge to zero
+ 
+
+ align:start position:0%
+x ends converge to zero
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+natural number m sub
+
+ align:start position:0%
+natural number m sub
+ 
+
+ align:start position:0%
+natural number m sub
+one so that for all n bigger than or
+
+ align:start position:0%
+one so that for all n bigger than or
+ 
+
+ align:start position:0%
+one so that for all n bigger than or
+equal to m sub 1
+
+ align:start position:0%
+equal to m sub 1
+ 
+
+ align:start position:0%
+equal to m sub 1
+x of n is less than
+
+ align:start position:0%
+x of n is less than
+ 
+
+ align:start position:0%
+x of n is less than
+epsilon over 2. i should prevent epsilon
+
+ align:start position:0%
+epsilon over 2. i should prevent epsilon
+ 
+
+ align:start position:0%
+epsilon over 2. i should prevent epsilon
+over 2 here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choose m to be
+
+ align:start position:0%
+choose m to be
+ 
+
+ align:start position:0%
+choose m to be
+the maximum of two numbers
+
+ align:start position:0%
+the maximum of two numbers
+ 
+
+ align:start position:0%
+the maximum of two numbers
+two m zero plus one
+
+ align:start position:0%
+two m zero plus one
+ 
+
+ align:start position:0%
+two m zero plus one
+and m one so you'll see why i made these
+
+ align:start position:0%
+and m one so you'll see why i made these
+ 
+
+ align:start position:0%
+and m one so you'll see why i made these
+choices in just a minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+suppose m is bigger than or equal to m
+
+ align:start position:0%
+suppose m is bigger than or equal to m
+ 
+
+ align:start position:0%
+suppose m is bigger than or equal to m
+we now want to show that s sub m minus s
+
+ align:start position:0%
+we now want to show that s sub m minus s
+ 
+
+ align:start position:0%
+we now want to show that s sub m minus s
+is less than epsilon in absolute value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's two cases if m is even
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+m over 2 is bigger than or equal to
+
+ align:start position:0%
+m over 2 is bigger than or equal to
+ 
+
+ align:start position:0%
+m over 2 is bigger than or equal to
+capital m over 2 which is
+
+ align:start position:0%
+capital m over 2 which is
+ 
+
+ align:start position:0%
+capital m over 2 which is
+the max of these if i divide by 2 that's
+
+ align:start position:0%
+the max of these if i divide by 2 that's
+ 
+
+ align:start position:0%
+the max of these if i divide by 2 that's
+certainly bigger than or equal to m0
+
+ align:start position:0%
+certainly bigger than or equal to m0
+ 
+
+ align:start position:0%
+certainly bigger than or equal to m0
+all right and therefore
+
+ align:start position:0%
+all right and therefore
+ 
+
+ align:start position:0%
+all right and therefore
+i use this first inequality s sub m
+
+ align:start position:0%
+i use this first inequality s sub m
+ 
+
+ align:start position:0%
+i use this first inequality s sub m
+minus s
+
+ align:start position:0%
+minus s
+ 
+
+ align:start position:0%
+minus s
+which is equal to s 2 times m over 2
+
+ align:start position:0%
+which is equal to s 2 times m over 2
+ 
+
+ align:start position:0%
+which is equal to s 2 times m over 2
+minus s now m over 2
+
+ align:start position:0%
+minus s now m over 2
+ 
+
+ align:start position:0%
+minus s now m over 2
+is an integer bigger than or equal to m
+
+ align:start position:0%
+is an integer bigger than or equal to m
+ 
+
+ align:start position:0%
+is an integer bigger than or equal to m
+sub 0.
+
+ align:start position:0%
+sub 0.
+ 
+
+ align:start position:0%
+sub 0.
+so i can use this inequality it's less
+
+ align:start position:0%
+so i can use this inequality it's less
+ 
+
+ align:start position:0%
+so i can use this inequality it's less
+than epsilon over two which is less than
+
+ align:start position:0%
+than epsilon over two which is less than
+ 
+
+ align:start position:0%
+than epsilon over two which is less than
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we do odd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again m is bigger than or equal to
+
+ align:start position:0%
+so again m is bigger than or equal to
+ 
+
+ align:start position:0%
+so again m is bigger than or equal to
+capital m and there's two cases m even
+
+ align:start position:0%
+capital m and there's two cases m even
+ 
+
+ align:start position:0%
+capital m and there's two cases m even
+and m odd if m is odd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let k be this integer now since m is odd
+
+ align:start position:0%
+let k be this integer now since m is odd
+ 
+
+ align:start position:0%
+let k be this integer now since m is odd
+m minus one is even divided by two
+
+ align:start position:0%
+m minus one is even divided by two
+ 
+
+ align:start position:0%
+m minus one is even divided by two
+that's an integer okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so m
+
+ align:start position:0%
+so m
+ 
+
+ align:start position:0%
+so m
+equals 2k
+
+ align:start position:0%
+equals 2k
+ 
+
+ align:start position:0%
+equals 2k
+plus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and since m is bigger than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m0
+
+ align:start position:0%
+m0
+ 
+
+ align:start position:0%
+m0
+this implies a couple of things
+
+ align:start position:0%
+this implies a couple of things
+ 
+
+ align:start position:0%
+this implies a couple of things
+this implies that this integer so
+
+ align:start position:0%
+this implies that this integer so
+ 
+
+ align:start position:0%
+this implies that this integer so
+our m
+
+ align:start position:0%
+our m
+ 
+
+ align:start position:0%
+our m
+this implies that
+
+ align:start position:0%
+this implies that
+ 
+
+ align:start position:0%
+this implies that
+2k plus 1 is bigger than or equal to 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so m is just equal to two k plus one so
+
+ align:start position:0%
+so m is just equal to two k plus one so
+ 
+
+ align:start position:0%
+so m is just equal to two k plus one so
+that's bigger than or equal to m which
+
+ align:start position:0%
+that's bigger than or equal to m which
+ 
+
+ align:start position:0%
+that's bigger than or equal to m which
+is bigger than or equal to two m sub
+
+ align:start position:0%
+is bigger than or equal to two m sub
+ 
+
+ align:start position:0%
+is bigger than or equal to two m sub
+zero plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore k
+
+ align:start position:0%
+and therefore k
+ 
+
+ align:start position:0%
+and therefore k
+this integer here is bigger than m zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m is bigger than or equal to
+
+ align:start position:0%
+m is bigger than or equal to
+ 
+
+ align:start position:0%
+m is bigger than or equal to
+m sub 1 as well i mean m is bigger than
+
+ align:start position:0%
+m sub 1 as well i mean m is bigger than
+ 
+
+ align:start position:0%
+m sub 1 as well i mean m is bigger than
+or equal to m and m is bigger than or
+
+ align:start position:0%
+or equal to m and m is bigger than or
+ 
+
+ align:start position:0%
+or equal to m and m is bigger than or
+equal to the max of these two things so
+
+ align:start position:0%
+equal to the max of these two things so
+ 
+
+ align:start position:0%
+equal to the max of these two things so
+it's bigger than or equal to m1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then if i look at s of m
+
+ align:start position:0%
+then if i look at s of m
+ 
+
+ align:start position:0%
+then if i look at s of m
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+s this is equal to
+
+ align:start position:0%
+s this is equal to
+ 
+
+ align:start position:0%
+s this is equal to
+s sub m so
+
+ align:start position:0%
+s sub m so
+ 
+
+ align:start position:0%
+s sub m so
+the nth partial sum
+
+ align:start position:0%
+the nth partial sum
+ 
+
+ align:start position:0%
+the nth partial sum
+is equal to the m minus first partial
+
+ align:start position:0%
+is equal to the m minus first partial
+ 
+
+ align:start position:0%
+is equal to the m minus first partial
+sum plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the next term
+
+ align:start position:0%
+the next term
+ 
+
+ align:start position:0%
+the next term
+minus s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now m minus 1 in terms of the integer k
+
+ align:start position:0%
+now m minus 1 in terms of the integer k
+ 
+
+ align:start position:0%
+now m minus 1 in terms of the integer k
+is equal to 2
+
+ align:start position:0%
+is equal to 2
+ 
+
+ align:start position:0%
+is equal to 2
+times k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now i'm going to take this s
+
+ align:start position:0%
+and now i'm going to take this s
+ 
+
+ align:start position:0%
+and now i'm going to take this s
+and group it with this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since k
+
+ align:start position:0%
+so since k
+ 
+
+ align:start position:0%
+so since k
+is bigger than or equal to m sub 0 we
+
+ align:start position:0%
+is bigger than or equal to m sub 0 we
+ 
+
+ align:start position:0%
+is bigger than or equal to m sub 0 we
+can use this inequality here
+
+ align:start position:0%
+can use this inequality here
+ 
+
+ align:start position:0%
+can use this inequality here
+after we do the triangle inequality so
+
+ align:start position:0%
+after we do the triangle inequality so
+ 
+
+ align:start position:0%
+after we do the triangle inequality so
+this is less than or equal to s2k minus
+
+ align:start position:0%
+this is less than or equal to s2k minus
+ 
+
+ align:start position:0%
+this is less than or equal to s2k minus
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+plus the absolute value of this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again since k is bigger than or equal
+
+ align:start position:0%
+so again since k is bigger than or equal
+ 
+
+ align:start position:0%
+so again since k is bigger than or equal
+to m sub 0 i can use this
+
+ align:start position:0%
+to m sub 0 i can use this
+ 
+
+ align:start position:0%
+to m sub 0 i can use this
+inequality
+
+ align:start position:0%
+inequality
+ 
+
+ align:start position:0%
+inequality
+to get this is less than epsilon over 2
+
+ align:start position:0%
+to get this is less than epsilon over 2
+ 
+
+ align:start position:0%
+to get this is less than epsilon over 2
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+this guy and since m is bigger than or
+
+ align:start position:0%
+this guy and since m is bigger than or
+ 
+
+ align:start position:0%
+this guy and since m is bigger than or
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+capital m which is bigger than or equal
+
+ align:start position:0%
+capital m which is bigger than or equal
+ 
+
+ align:start position:0%
+capital m which is bigger than or equal
+to capital m sub 1.
+
+ align:start position:0%
+to capital m sub 1.
+ 
+
+ align:start position:0%
+to capital m sub 1.
+i can use this inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is less than epsilon
+
+ align:start position:0%
+and this is less than epsilon
+ 
+
+ align:start position:0%
+and this is less than epsilon
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+we've done the case of m even or m odd
+
+ align:start position:0%
+we've done the case of m even or m odd
+ 
+
+ align:start position:0%
+we've done the case of m even or m odd
+and bigger than or equal to m so in
+
+ align:start position:0%
+and bigger than or equal to m so in
+ 
+
+ align:start position:0%
+and bigger than or equal to m so in
+summary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've shown that if m is bigger than or
+
+ align:start position:0%
+we've shown that if m is bigger than or
+ 
+
+ align:start position:0%
+we've shown that if m is bigger than or
+equal to m
+
+ align:start position:0%
+equal to m
+ 
+
+ align:start position:0%
+equal to m
+s of m minus s is less than epsilon and
+
+ align:start position:0%
+s of m minus s is less than epsilon and
+ 
+
+ align:start position:0%
+s of m minus s is less than epsilon and
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+the s of n's converge
+
+ align:start position:0%
+the s of n's converge
+ 
+
+ align:start position:0%
+the s of n's converge
+to s and
+
+ align:start position:0%
+to s and
+ 
+
+ align:start position:0%
+to s and
+i don't think i have enough time to do
+
+ align:start position:0%
+i don't think i have enough time to do
+ 
+
+ align:start position:0%
+i don't think i have enough time to do
+this next theorem
+
+ align:start position:0%
+this next theorem
+ 
+
+ align:start position:0%
+this next theorem
+so we'll stop there
\ No newline at end of file
diff --git a/ZzMdrYTCPO4.txt b/ZzMdrYTCPO4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..011c7d64beb4b474e4b627a5f88cf0d11fb52792
--- /dev/null
+++ b/ZzMdrYTCPO4.txt
@@ -0,0 +1,7272 @@
+align:start position:0%
+ 
+all right so by last Friday we
+
+ align:start position:0%
+all right so by last Friday we
+ 
+
+ align:start position:0%
+all right so by last Friday we
+discovered the electron discovered the
+
+ align:start position:0%
+discovered the electron discovered the
+ 
+
+ align:start position:0%
+discovered the electron discovered the
+nucleus and um the problem then was how
+
+ align:start position:0%
+nucleus and um the problem then was how
+ 
+
+ align:start position:0%
+nucleus and um the problem then was how
+to describe the structure of the atom
+
+ align:start position:0%
+to describe the structure of the atom
+ 
+
+ align:start position:0%
+to describe the structure of the atom
+they knew there was an electron they
+
+ align:start position:0%
+they knew there was an electron they
+ 
+
+ align:start position:0%
+they knew there was an electron they
+knew there was a
+
+ align:start position:0%
+knew there was a
+ 
+
+ align:start position:0%
+knew there was a
+nucleus but exactly how did the electron
+
+ align:start position:0%
+nucleus but exactly how did the electron
+ 
+
+ align:start position:0%
+nucleus but exactly how did the electron
+and the nucleus uh hang
+
+ align:start position:0%
+and the nucleus uh hang
+ 
+
+ align:start position:0%
+and the nucleus uh hang
+together and we talked about
+
+ align:start position:0%
+together and we talked about
+ 
+
+ align:start position:0%
+together and we talked about
+how uh the scientists at that time
+
+ align:start position:0%
+how uh the scientists at that time
+ 
+
+ align:start position:0%
+how uh the scientists at that time
+proposed a classical model where the
+
+ align:start position:0%
+proposed a classical model where the
+ 
+
+ align:start position:0%
+proposed a classical model where the
+interaction between the electron the
+
+ align:start position:0%
+interaction between the electron the
+ 
+
+ align:start position:0%
+interaction between the electron the
+nucleus was of course the kulum
+
+ align:start position:0%
+nucleus was of course the kulum
+ 
+
+ align:start position:0%
+nucleus was of course the kulum
+interaction but where the equations of
+
+ align:start position:0%
+interaction but where the equations of
+ 
+
+ align:start position:0%
+interaction but where the equations of
+motion were Newton's equations of motion
+
+ align:start position:0%
+motion were Newton's equations of motion
+ 
+
+ align:start position:0%
+motion were Newton's equations of motion
+to describe this electron going around
+
+ align:start position:0%
+to describe this electron going around
+ 
+
+ align:start position:0%
+to describe this electron going around
+the nucleus F equal
+
+ align:start position:0%
+the nucleus F equal
+ 
+
+ align:start position:0%
+the nucleus F equal
+Ma and although we didn't show it what
+
+ align:start position:0%
+Ma and although we didn't show it what
+ 
+
+ align:start position:0%
+Ma and although we didn't show it what
+we said was that if we used that Force
+
+ align:start position:0%
+we said was that if we used that Force
+ 
+
+ align:start position:0%
+we said was that if we used that Force
+field the kulon force coupled with
+
+ align:start position:0%
+field the kulon force coupled with
+ 
+
+ align:start position:0%
+field the kulon force coupled with
+Newton's equations of motion and
+
+ align:start position:0%
+Newton's equations of motion and
+ 
+
+ align:start position:0%
+Newton's equations of motion and
+actually you also have to couple them
+
+ align:start position:0%
+actually you also have to couple them
+ 
+
+ align:start position:0%
+actually you also have to couple them
+with some classical electromagnetism
+
+ align:start position:0%
+with some classical electromagnetism
+ 
+
+ align:start position:0%
+with some classical electromagnetism
+which I may not have said but which
+
+ align:start position:0%
+which I may not have said but which
+ 
+
+ align:start position:0%
+which I may not have said but which
+isn't important but if you use those
+
+ align:start position:0%
+isn't important but if you use those
+ 
+
+ align:start position:0%
+isn't important but if you use those
+classical
+
+ align:start position:0%
+classical
+ 
+
+ align:start position:0%
+classical
+ideas to describe how that electron goes
+
+ align:start position:0%
+ideas to describe how that electron goes
+ 
+
+ align:start position:0%
+ideas to describe how that electron goes
+around that nucleus well you would find
+
+ align:start position:0%
+around that nucleus well you would find
+ 
+
+ align:start position:0%
+around that nucleus well you would find
+that in 10 Theus 10 seconds that
+
+ align:start position:0%
+that in 10 Theus 10 seconds that
+ 
+
+ align:start position:0%
+that in 10 Theus 10 seconds that
+electron would be on top of the nucleus
+
+ align:start position:0%
+electron would be on top of the nucleus
+ 
+
+ align:start position:0%
+electron would be on top of the nucleus
+and youd no longer have what we know to
+
+ align:start position:0%
+and youd no longer have what we know to
+ 
+
+ align:start position:0%
+and youd no longer have what we know to
+be the structure of the atom in the
+
+ align:start position:0%
+be the structure of the atom in the
+ 
+
+ align:start position:0%
+be the structure of the atom in the
+sense that you'd no longer have some
+
+ align:start position:0%
+sense that you'd no longer have some
+ 
+
+ align:start position:0%
+sense that you'd no longer have some
+volume where the diameter of that volume
+
+ align:start position:0%
+volume where the diameter of that volume
+ 
+
+ align:start position:0%
+volume where the diameter of that volume
+is on the order of an angstrom or so so
+
+ align:start position:0%
+is on the order of an angstrom or so so
+ 
+
+ align:start position:0%
+is on the order of an angstrom or so so
+the bottom line is that these classical
+
+ align:start position:0%
+the bottom line is that these classical
+ 
+
+ align:start position:0%
+the bottom line is that these classical
+ideas classical mechanics and classical
+
+ align:start position:0%
+ideas classical mechanics and classical
+ 
+
+ align:start position:0%
+ideas classical mechanics and classical
+electromagnetism they just totally fail
+
+ align:start position:0%
+electromagnetism they just totally fail
+ 
+
+ align:start position:0%
+electromagnetism they just totally fail
+to explain the structure of the atom and
+
+ align:start position:0%
+to explain the structure of the atom and
+ 
+
+ align:start position:0%
+to explain the structure of the atom and
+that was the conundrum that the
+
+ align:start position:0%
+that was the conundrum that the
+ 
+
+ align:start position:0%
+that was the conundrum that the
+scientists fac in 1911 this was quite a
+
+ align:start position:0%
+scientists fac in 1911 this was quite a
+ 
+
+ align:start position:0%
+scientists fac in 1911 this was quite a
+a a big problem for the scientific
+
+ align:start position:0%
+a a big problem for the scientific
+ 
+
+ align:start position:0%
+a a big problem for the scientific
+community and was so for about 10 12 13
+
+ align:start position:0%
+community and was so for about 10 12 13
+ 
+
+ align:start position:0%
+community and was so for about 10 12 13
+years all right and of course what fails
+
+ align:start position:0%
+years all right and of course what fails
+ 
+
+ align:start position:0%
+years all right and of course what fails
+are the classical equations of motion
+
+ align:start position:0%
+are the classical equations of motion
+ 
+
+ align:start position:0%
+are the classical equations of motion
+Newton's equations a new kind of
+
+ align:start position:0%
+Newton's equations a new kind of
+ 
+
+ align:start position:0%
+Newton's equations a new kind of
+mechanics is going to have to be
+
+ align:start position:0%
+mechanics is going to have to be
+ 
+
+ align:start position:0%
+mechanics is going to have to be
+invented in order to understand how that
+
+ align:start position:0%
+invented in order to understand how that
+ 
+
+ align:start position:0%
+invented in order to understand how that
+atom is bound or how the electron in the
+
+ align:start position:0%
+atom is bound or how the electron in the
+ 
+
+ align:start position:0%
+atom is bound or how the electron in the
+nucleus are bound how it's stable
+
+ align:start position:0%
+nucleus are bound how it's stable
+ 
+
+ align:start position:0%
+nucleus are bound how it's stable
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+historically the actual clues for why
+
+ align:start position:0%
+historically the actual clues for why
+ 
+
+ align:start position:0%
+historically the actual clues for why
+the electron didn't collapse into the
+
+ align:start position:0%
+the electron didn't collapse into the
+ 
+
+ align:start position:0%
+the electron didn't collapse into the
+nucleus those Clues actually came from a
+
+ align:start position:0%
+nucleus those Clues actually came from a
+ 
+
+ align:start position:0%
+nucleus those Clues actually came from a
+very different area of discussion and
+
+ align:start position:0%
+very different area of discussion and
+ 
+
+ align:start position:0%
+very different area of discussion and
+that area of discussion is this wave
+
+ align:start position:0%
+that area of discussion is this wave
+ 
+
+ align:start position:0%
+that area of discussion is this wave
+particle duality of light and
+
+ align:start position:0%
+particle duality of light and
+ 
+
+ align:start position:0%
+particle duality of light and
+matter it was certainly long believed
+
+ align:start position:0%
+matter it was certainly long believed
+ 
+
+ align:start position:0%
+matter it was certainly long believed
+that matter with its particle like
+
+ align:start position:0%
+that matter with its particle like
+ 
+
+ align:start position:0%
+that matter with its particle like
+Behavior was distinct from Light which
+
+ align:start position:0%
+Behavior was distinct from Light which
+ 
+
+ align:start position:0%
+Behavior was distinct from Light which
+was this kind of transmission of energy
+
+ align:start position:0%
+was this kind of transmission of energy
+ 
+
+ align:start position:0%
+was this kind of transmission of energy
+uh through
+
+ align:start position:0%
+uh through
+ 
+
+ align:start position:0%
+uh through
+space but in the late 1800s in early
+
+ align:start position:0%
+space but in the late 1800s in early
+ 
+
+ align:start position:0%
+space but in the late 1800s in early
+1900s there began to be made some
+
+ align:start position:0%
+1900s there began to be made some
+ 
+
+ align:start position:0%
+1900s there began to be made some
+observations that seemed to suggest that
+
+ align:start position:0%
+observations that seemed to suggest that
+ 
+
+ align:start position:0%
+observations that seemed to suggest that
+well you know maybe this boundary
+
+ align:start position:0%
+well you know maybe this boundary
+ 
+
+ align:start position:0%
+well you know maybe this boundary
+between matter and Its particle-like
+
+ align:start position:0%
+between matter and Its particle-like
+ 
+
+ align:start position:0%
+between matter and Its particle-like
+Behavior and light and its wav likee
+
+ align:start position:0%
+Behavior and light and its wav likee
+ 
+
+ align:start position:0%
+Behavior and light and its wav likee
+Behavior well maybe that boundary wasn't
+
+ align:start position:0%
+Behavior well maybe that boundary wasn't
+ 
+
+ align:start position:0%
+Behavior well maybe that boundary wasn't
+so rigid after
+
+ align:start position:0%
+so rigid after
+ 
+
+ align:start position:0%
+so rigid after
+all and in fact what we're going to see
+
+ align:start position:0%
+all and in fact what we're going to see
+ 
+
+ align:start position:0%
+all and in fact what we're going to see
+is that radiation or light exhibits both
+
+ align:start position:0%
+is that radiation or light exhibits both
+ 
+
+ align:start position:0%
+is that radiation or light exhibits both
+wav like behavior and particle like
+
+ align:start position:0%
+wav like behavior and particle like
+ 
+
+ align:start position:0%
+wav like behavior and particle like
+behavior and it depends on the kind of
+
+ align:start position:0%
+behavior and it depends on the kind of
+ 
+
+ align:start position:0%
+behavior and it depends on the kind of
+experiment that you do which one of
+
+ align:start position:0%
+experiment that you do which one of
+ 
+
+ align:start position:0%
+experiment that you do which one of
+those properties you
+
+ align:start position:0%
+those properties you
+ 
+
+ align:start position:0%
+those properties you
+see and then consequently matter matter
+
+ align:start position:0%
+see and then consequently matter matter
+ 
+
+ align:start position:0%
+see and then consequently matter matter
+it also exhibits both particle like
+
+ align:start position:0%
+it also exhibits both particle like
+ 
+
+ align:start position:0%
+it also exhibits both particle like
+behavior and wav like behavior and again
+
+ align:start position:0%
+behavior and wav like behavior and again
+ 
+
+ align:start position:0%
+behavior and wav like behavior and again
+it depends depends on the particular
+
+ align:start position:0%
+it depends depends on the particular
+ 
+
+ align:start position:0%
+it depends depends on the particular
+experiment you do as to which one of
+
+ align:start position:0%
+experiment you do as to which one of
+ 
+
+ align:start position:0%
+experiment you do as to which one of
+those properties you actually
+
+ align:start position:0%
+those properties you actually
+ 
+
+ align:start position:0%
+those properties you actually
+observe all right so what we're going to
+
+ align:start position:0%
+observe all right so what we're going to
+ 
+
+ align:start position:0%
+observe all right so what we're going to
+do right now is we're actually going to
+
+ align:start position:0%
+do right now is we're actually going to
+ 
+
+ align:start position:0%
+do right now is we're actually going to
+set aside the discussion of the
+
+ align:start position:0%
+set aside the discussion of the
+ 
+
+ align:start position:0%
+set aside the discussion of the
+structure of the atom how the electron
+
+ align:start position:0%
+structure of the atom how the electron
+ 
+
+ align:start position:0%
+structure of the atom how the electron
+and the nucleus are bound together how
+
+ align:start position:0%
+and the nucleus are bound together how
+ 
+
+ align:start position:0%
+and the nucleus are bound together how
+in the world do they remain stable we're
+
+ align:start position:0%
+in the world do they remain stable we're
+ 
+
+ align:start position:0%
+in the world do they remain stable we're
+going to set that discussion
+
+ align:start position:0%
+going to set that discussion
+ 
+
+ align:start position:0%
+going to set that discussion
+aside and we're not going to pick it up
+
+ align:start position:0%
+aside and we're not going to pick it up
+ 
+
+ align:start position:0%
+aside and we're not going to pick it up
+until next Monday and and the reason for
+
+ align:start position:0%
+until next Monday and and the reason for
+ 
+
+ align:start position:0%
+until next Monday and and the reason for
+it is because in order to proceed with
+
+ align:start position:0%
+it is because in order to proceed with
+ 
+
+ align:start position:0%
+it is because in order to proceed with
+that discussion we actually have to go
+
+ align:start position:0%
+that discussion we actually have to go
+ 
+
+ align:start position:0%
+that discussion we actually have to go
+through this other set of
+
+ align:start position:0%
+through this other set of
+ 
+
+ align:start position:0%
+through this other set of
+observations sorry this other set of
+
+ align:start position:0%
+observations sorry this other set of
+ 
+
+ align:start position:0%
+observations sorry this other set of
+observ that was my my my pointer I was
+
+ align:start position:0%
+observ that was my my my pointer I was
+ 
+
+ align:start position:0%
+observ that was my my my pointer I was
+zapping some of you here sorry um we
+
+ align:start position:0%
+zapping some of you here sorry um we
+ 
+
+ align:start position:0%
+zapping some of you here sorry um we
+have to go and look at these other
+
+ align:start position:0%
+have to go and look at these other
+ 
+
+ align:start position:0%
+have to go and look at these other
+observations this discussion about the
+
+ align:start position:0%
+observations this discussion about the
+ 
+
+ align:start position:0%
+observations this discussion about the
+wave particle duality of light and
+
+ align:start position:0%
+wave particle duality of light and
+ 
+
+ align:start position:0%
+wave particle duality of light and
+matter in order to get the clues in
+
+ align:start position:0%
+matter in order to get the clues in
+ 
+
+ align:start position:0%
+matter in order to get the clues in
+order for us to make progress about
+
+ align:start position:0%
+order for us to make progress about
+ 
+
+ align:start position:0%
+order for us to make progress about
+about what next big leap we got to make
+
+ align:start position:0%
+about what next big leap we got to make
+ 
+
+ align:start position:0%
+about what next big leap we got to make
+right in order to talk about the
+
+ align:start position:0%
+right in order to talk about the
+ 
+
+ align:start position:0%
+right in order to talk about the
+structure of the atom all right so we're
+
+ align:start position:0%
+structure of the atom all right so we're
+ 
+
+ align:start position:0%
+structure of the atom all right so we're
+going to change subjects or it's going
+
+ align:start position:0%
+going to change subjects or it's going
+ 
+
+ align:start position:0%
+going to change subjects or it's going
+to look like we're changing subjects but
+
+ align:start position:0%
+to look like we're changing subjects but
+ 
+
+ align:start position:0%
+to look like we're changing subjects but
+we're going to use the results of our
+
+ align:start position:0%
+we're going to use the results of our
+ 
+
+ align:start position:0%
+we're going to use the results of our
+discussions in the next three days to
+
+ align:start position:0%
+discussions in the next three days to
+ 
+
+ align:start position:0%
+discussions in the next three days to
+come back to talk about the structure of
+
+ align:start position:0%
+come back to talk about the structure of
+ 
+
+ align:start position:0%
+come back to talk about the structure of
+the atom all right okay so then the
+
+ align:start position:0%
+the atom all right okay so then the
+ 
+
+ align:start position:0%
+the atom all right okay so then the
+first thing we got to talk about is
+
+ align:start position:0%
+first thing we got to talk about is
+ 
+
+ align:start position:0%
+first thing we got to talk about is
+we're going to talk about light and
+
+ align:start position:0%
+we're going to talk about light and
+ 
+
+ align:start position:0%
+we're going to talk about light and
+we're going to talk about the wave like
+
+ align:start position:0%
+we're going to talk about the wave like
+ 
+
+ align:start position:0%
+we're going to talk about the wave like
+nature to uh
+
+ align:start position:0%
+nature to uh
+ 
+
+ align:start position:0%
+nature to uh
+radiation and uh since that's really uh
+
+ align:start position:0%
+radiation and uh since that's really uh
+ 
+
+ align:start position:0%
+radiation and uh since that's really uh
+probably most intuitive so let's let's
+
+ align:start position:0%
+probably most intuitive so let's let's
+ 
+
+ align:start position:0%
+probably most intuitive so let's let's
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+okay so uh can we uh dim the front
+
+ align:start position:0%
+okay so uh can we uh dim the front
+ 
+
+ align:start position:0%
+okay so uh can we uh dim the front
+lights here oh okay uh I could do that
+
+ align:start position:0%
+lights here oh okay uh I could do that
+ 
+
+ align:start position:0%
+lights here oh okay uh I could do that
+too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe got it all right I got it
+
+ align:start position:0%
+maybe got it all right I got it
+ 
+
+ align:start position:0%
+maybe got it all right I got it
+Christine thank you all all right so um
+
+ align:start position:0%
+Christine thank you all all right so um
+ 
+
+ align:start position:0%
+Christine thank you all all right so um
+properties of waves well what are waves
+
+ align:start position:0%
+properties of waves well what are waves
+ 
+
+ align:start position:0%
+properties of waves well what are waves
+well you are familiar with that right
+
+ align:start position:0%
+well you are familiar with that right
+ 
+
+ align:start position:0%
+well you are familiar with that right
+waves are a periodic variation of some
+
+ align:start position:0%
+waves are a periodic variation of some
+ 
+
+ align:start position:0%
+waves are a periodic variation of some
+uh quantity in the case of water waves
+
+ align:start position:0%
+uh quantity in the case of water waves
+ 
+
+ align:start position:0%
+uh quantity in the case of water waves
+right we have the periodic variation of
+
+ align:start position:0%
+right we have the periodic variation of
+ 
+
+ align:start position:0%
+right we have the periodic variation of
+the height of water so at some points in
+
+ align:start position:0%
+the height of water so at some points in
+ 
+
+ align:start position:0%
+the height of water so at some points in
+space here the height of the water is
+
+ align:start position:0%
+space here the height of the water is
+ 
+
+ align:start position:0%
+space here the height of the water is
+high at some point the height of the
+
+ align:start position:0%
+high at some point the height of the
+ 
+
+ align:start position:0%
+high at some point the height of the
+water is low and there's some average
+
+ align:start position:0%
+water is low and there's some average
+ 
+
+ align:start position:0%
+water is low and there's some average
+level here all right a uh sound wve well
+
+ align:start position:0%
+level here all right a uh sound wve well
+ 
+
+ align:start position:0%
+level here all right a uh sound wve well
+Soundwave is a periodic variation of the
+
+ align:start position:0%
+Soundwave is a periodic variation of the
+ 
+
+ align:start position:0%
+Soundwave is a periodic variation of the
+density of air at some points in Space
+
+ align:start position:0%
+density of air at some points in Space
+ 
+
+ align:start position:0%
+density of air at some points in Space
+the air is very dense at other points in
+
+ align:start position:0%
+the air is very dense at other points in
+ 
+
+ align:start position:0%
+the air is very dense at other points in
+Space the air is is not so dense and
+
+ align:start position:0%
+Space the air is is not so dense and
+ 
+
+ align:start position:0%
+Space the air is is not so dense and
+then there's an average level
+
+ align:start position:0%
+then there's an average level
+ 
+
+ align:start position:0%
+then there's an average level
+here well what we're going to do is
+
+ align:start position:0%
+here well what we're going to do is
+ 
+
+ align:start position:0%
+here well what we're going to do is
+we're going to set this average level
+
+ align:start position:0%
+we're going to set this average level
+ 
+
+ align:start position:0%
+we're going to set this average level
+here to a
+
+ align:start position:0%
+here to a
+ 
+
+ align:start position:0%
+here to a
+zero and then consequently our
+
+ align:start position:0%
+zero and then consequently our
+ 
+
+ align:start position:0%
+zero and then consequently our
+waves are going to have a positive
+
+ align:start position:0%
+waves are going to have a positive
+ 
+
+ align:start position:0%
+waves are going to have a positive
+amplitude that is measured from this
+
+ align:start position:0%
+amplitude that is measured from this
+ 
+
+ align:start position:0%
+amplitude that is measured from this
+zero level up that's a positive
+
+ align:start position:0%
+zero level up that's a positive
+ 
+
+ align:start position:0%
+zero level up that's a positive
+amplitude and measured from the zero
+
+ align:start position:0%
+amplitude and measured from the zero
+ 
+
+ align:start position:0%
+amplitude and measured from the zero
+level down that's our negative amplitude
+
+ align:start position:0%
+level down that's our negative amplitude
+ 
+
+ align:start position:0%
+level down that's our negative amplitude
+all right so these waves are going to
+
+ align:start position:0%
+all right so these waves are going to
+ 
+
+ align:start position:0%
+all right so these waves are going to
+have positive and negative amplitude
+
+ align:start position:0%
+have positive and negative amplitude
+ 
+
+ align:start position:0%
+have positive and negative amplitude
+that's going to be very important in how
+
+ align:start position:0%
+that's going to be very important in how
+ 
+
+ align:start position:0%
+that's going to be very important in how
+they actually
+
+ align:start position:0%
+they actually
+ 
+
+ align:start position:0%
+they actually
+behave now what we're going to do oh
+
+ align:start position:0%
+behave now what we're going to do oh
+ 
+
+ align:start position:0%
+behave now what we're going to do oh
+okay and so what is light well light is
+
+ align:start position:0%
+okay and so what is light well light is
+ 
+
+ align:start position:0%
+okay and so what is light well light is
+a periodic
+
+ align:start position:0%
+a periodic
+ 
+
+ align:start position:0%
+a periodic
+variation of an electric field and
+
+ align:start position:0%
+variation of an electric field and
+ 
+
+ align:start position:0%
+variation of an electric field and
+that's what I plot here Electric El
+
+ align:start position:0%
+that's what I plot here Electric El
+ 
+
+ align:start position:0%
+that's what I plot here Electric El
+field versus distance and you can see
+
+ align:start position:0%
+field versus distance and you can see
+ 
+
+ align:start position:0%
+field versus distance and you can see
+it's varying in
+
+ align:start position:0%
+it's varying in
+ 
+
+ align:start position:0%
+it's varying in
+intensity but uh what exactly is an
+
+ align:start position:0%
+intensity but uh what exactly is an
+ 
+
+ align:start position:0%
+intensity but uh what exactly is an
+electric
+
+ align:start position:0%
+electric
+ 
+
+ align:start position:0%
+electric
+field let's just think about that for a
+
+ align:start position:0%
+field let's just think about that for a
+ 
+
+ align:start position:0%
+field let's just think about that for a
+moment suppose I take a uh paral two
+
+ align:start position:0%
+moment suppose I take a uh paral two
+ 
+
+ align:start position:0%
+moment suppose I take a uh paral two
+parallel plates so here's one here's
+
+ align:start position:0%
+parallel plates so here's one here's
+ 
+
+ align:start position:0%
+parallel plates so here's one here's
+another and I'm going to put a uh
+
+ align:start position:0%
+another and I'm going to put a uh
+ 
+
+ align:start position:0%
+another and I'm going to put a uh
+negative potential on that top plate and
+
+ align:start position:0%
+negative potential on that top plate and
+ 
+
+ align:start position:0%
+negative potential on that top plate and
+a positive potential on the bottom plate
+
+ align:start position:0%
+a positive potential on the bottom plate
+ 
+
+ align:start position:0%
+a positive potential on the bottom plate
+and what is operating then between this
+
+ align:start position:0%
+and what is operating then between this
+ 
+
+ align:start position:0%
+and what is operating then between this
+negatively charged plate and the
+
+ align:start position:0%
+negatively charged plate and the
+ 
+
+ align:start position:0%
+negatively charged plate and the
+positively charged plate is the kulum
+
+ align:start position:0%
+positively charged plate is the kulum
+ 
+
+ align:start position:0%
+positively charged plate is the kulum
+interaction and the electric field then
+
+ align:start position:0%
+interaction and the electric field then
+ 
+
+ align:start position:0%
+interaction and the electric field then
+is the space through which that kolum
+
+ align:start position:0%
+is the space through which that kolum
+ 
+
+ align:start position:0%
+is the space through which that kolum
+Force operates so that electric field
+
+ align:start position:0%
+Force operates so that electric field
+ 
+
+ align:start position:0%
+Force operates so that electric field
+here is this space through which this
+
+ align:start position:0%
+here is this space through which this
+ 
+
+ align:start position:0%
+here is this space through which this
+kulum force is operating and by
+
+ align:start position:0%
+kulum force is operating and by
+ 
+
+ align:start position:0%
+kulum force is operating and by
+convention we're going to say that it's
+
+ align:start position:0%
+convention we're going to say that it's
+ 
+
+ align:start position:0%
+convention we're going to say that it's
+operating here in this uh in this
+
+ align:start position:0%
+operating here in this uh in this
+ 
+
+ align:start position:0%
+operating here in this uh in this
+orientation so in other words if I put a
+
+ align:start position:0%
+orientation so in other words if I put a
+ 
+
+ align:start position:0%
+orientation so in other words if I put a
+positive charge in between these two
+
+ align:start position:0%
+positive charge in between these two
+ 
+
+ align:start position:0%
+positive charge in between these two
+plates in this electric field this space
+
+ align:start position:0%
+plates in this electric field this space
+ 
+
+ align:start position:0%
+plates in this electric field this space
+through which the kolon force is
+
+ align:start position:0%
+through which the kolon force is
+ 
+
+ align:start position:0%
+through which the kolon force is
+operating well what's going to happen is
+
+ align:start position:0%
+operating well what's going to happen is
+ 
+
+ align:start position:0%
+operating well what's going to happen is
+that this positive charge is going to
+
+ align:start position:0%
+that this positive charge is going to
+ 
+
+ align:start position:0%
+that this positive charge is going to
+drift to the negatively charged
+
+ align:start position:0%
+drift to the negatively charged
+ 
+
+ align:start position:0%
+drift to the negatively charged
+plate but if I turn the geometry around
+
+ align:start position:0%
+plate but if I turn the geometry around
+ 
+
+ align:start position:0%
+plate but if I turn the geometry around
+right if I put the negatively charged
+
+ align:start position:0%
+right if I put the negatively charged
+ 
+
+ align:start position:0%
+right if I put the negatively charged
+plate on the the bottom using this
+
+ align:start position:0%
+plate on the the bottom using this
+ 
+
+ align:start position:0%
+plate on the the bottom using this
+coordinate system and I now put that
+
+ align:start position:0%
+coordinate system and I now put that
+ 
+
+ align:start position:0%
+coordinate system and I now put that
+positive charge in that electric field
+
+ align:start position:0%
+positive charge in that electric field
+ 
+
+ align:start position:0%
+positive charge in that electric field
+it's going to drift to the negatively
+
+ align:start position:0%
+it's going to drift to the negatively
+ 
+
+ align:start position:0%
+it's going to drift to the negatively
+charged plate again but it's going to
+
+ align:start position:0%
+charged plate again but it's going to
+ 
+
+ align:start position:0%
+charged plate again but it's going to
+move in this coordinate system
+
+ align:start position:0%
+move in this coordinate system
+ 
+
+ align:start position:0%
+move in this coordinate system
+down so this electric field has not
+
+ align:start position:0%
+down so this electric field has not
+ 
+
+ align:start position:0%
+down so this electric field has not
+only magnitude because you can imagine
+
+ align:start position:0%
+only magnitude because you can imagine
+ 
+
+ align:start position:0%
+only magnitude because you can imagine
+the larger the potential difference
+
+ align:start position:0%
+the larger the potential difference
+ 
+
+ align:start position:0%
+the larger the potential difference
+between these two plates the larger the
+
+ align:start position:0%
+between these two plates the larger the
+ 
+
+ align:start position:0%
+between these two plates the larger the
+magnitude of the electric field but that
+
+ align:start position:0%
+magnitude of the electric field but that
+ 
+
+ align:start position:0%
+magnitude of the electric field but that
+electric field also has Direction it's
+
+ align:start position:0%
+electric field also has Direction it's
+ 
+
+ align:start position:0%
+electric field also has Direction it's
+pointed in one way or the other and
+
+ align:start position:0%
+pointed in one way or the other and
+ 
+
+ align:start position:0%
+pointed in one way or the other and
+that's what's represented here on my
+
+ align:start position:0%
+that's what's represented here on my
+ 
+
+ align:start position:0%
+that's what's represented here on my
+diagram of the electric field versus
+
+ align:start position:0%
+diagram of the electric field versus
+ 
+
+ align:start position:0%
+diagram of the electric field versus
+distance you can see that right here the
+
+ align:start position:0%
+distance you can see that right here the
+ 
+
+ align:start position:0%
+distance you can see that right here the
+electric field the magnitude of it
+
+ align:start position:0%
+electric field the magnitude of it
+ 
+
+ align:start position:0%
+electric field the magnitude of it
+starts out small it increases continues
+
+ align:start position:0%
+starts out small it increases continues
+ 
+
+ align:start position:0%
+starts out small it increases continues
+to increase till we get a maximum and
+
+ align:start position:0%
+to increase till we get a maximum and
+ 
+
+ align:start position:0%
+to increase till we get a maximum and
+then it starts getting smaller it getss
+
+ align:start position:0%
+then it starts getting smaller it getss
+ 
+
+ align:start position:0%
+then it starts getting smaller it getss
+smaller and goes all the way to zero at
+
+ align:start position:0%
+smaller and goes all the way to zero at
+ 
+
+ align:start position:0%
+smaller and goes all the way to zero at
+which point then it turns around and the
+
+ align:start position:0%
+which point then it turns around and the
+ 
+
+ align:start position:0%
+which point then it turns around and the
+magnitude begins to increase in the
+
+ align:start position:0%
+magnitude begins to increase in the
+ 
+
+ align:start position:0%
+magnitude begins to increase in the
+opposite direction and again it becomes
+
+ align:start position:0%
+opposite direction and again it becomes
+ 
+
+ align:start position:0%
+opposite direction and again it becomes
+a maximum in the opposite direction and
+
+ align:start position:0%
+a maximum in the opposite direction and
+ 
+
+ align:start position:0%
+a maximum in the opposite direction and
+then turns around goes to zero and
+
+ align:start position:0%
+then turns around goes to zero and
+ 
+
+ align:start position:0%
+then turns around goes to zero and
+continues so it's a periodic variation
+
+ align:start position:0%
+continues so it's a periodic variation
+ 
+
+ align:start position:0%
+continues so it's a periodic variation
+here of an electric
+
+ align:start position:0%
+here of an electric
+ 
+
+ align:start position:0%
+here of an electric
+field and so what that means is that if
+
+ align:start position:0%
+field and so what that means is that if
+ 
+
+ align:start position:0%
+field and so what that means is that if
+we put some charge say at this point in
+
+ align:start position:0%
+we put some charge say at this point in
+ 
+
+ align:start position:0%
+we put some charge say at this point in
+space it would be pulled one way and if
+
+ align:start position:0%
+space it would be pulled one way and if
+ 
+
+ align:start position:0%
+space it would be pulled one way and if
+we put it at this point in space it
+
+ align:start position:0%
+we put it at this point in space it
+ 
+
+ align:start position:0%
+we put it at this point in space it
+would be pulled in another way and if we
+
+ align:start position:0%
+would be pulled in another way and if we
+ 
+
+ align:start position:0%
+would be pulled in another way and if we
+put it right here at zero it's not going
+
+ align:start position:0%
+put it right here at zero it's not going
+ 
+
+ align:start position:0%
+put it right here at zero it's not going
+anywhere
+
+ align:start position:0%
+anywhere
+ 
+
+ align:start position:0%
+anywhere
+okay okay now what I've showed you here
+
+ align:start position:0%
+okay okay now what I've showed you here
+ 
+
+ align:start position:0%
+okay okay now what I've showed you here
+is a periodic variation of an electric
+
+ align:start position:0%
+is a periodic variation of an electric
+ 
+
+ align:start position:0%
+is a periodic variation of an electric
+field it is also the case that whenever
+
+ align:start position:0%
+field it is also the case that whenever
+ 
+
+ align:start position:0%
+field it is also the case that whenever
+we have an electric field we also have a
+
+ align:start position:0%
+we have an electric field we also have a
+ 
+
+ align:start position:0%
+we have an electric field we also have a
+magnetic field that is actually
+
+ align:start position:0%
+magnetic field that is actually
+ 
+
+ align:start position:0%
+magnetic field that is actually
+perpendicular to this electric field
+
+ align:start position:0%
+perpendicular to this electric field
+ 
+
+ align:start position:0%
+perpendicular to this electric field
+here but since that magnetic field is
+
+ align:start position:0%
+here but since that magnetic field is
+ 
+
+ align:start position:0%
+here but since that magnetic field is
+going to have all the same
+
+ align:start position:0%
+going to have all the same
+ 
+
+ align:start position:0%
+going to have all the same
+characteristics as the electric field
+
+ align:start position:0%
+characteristics as the electric field
+ 
+
+ align:start position:0%
+characteristics as the electric field
+for from our point of discussion here
+
+ align:start position:0%
+for from our point of discussion here
+ 
+
+ align:start position:0%
+for from our point of discussion here
+I'm not going to talk about it but
+
+ align:start position:0%
+I'm not going to talk about it but
+ 
+
+ align:start position:0%
+I'm not going to talk about it but
+you're going to see this a lot next
+
+ align:start position:0%
+you're going to see this a lot next
+ 
+
+ align:start position:0%
+you're going to see this a lot next
+semester in 802 all right so we're just
+
+ align:start position:0%
+semester in 802 all right so we're just
+ 
+
+ align:start position:0%
+semester in 802 all right so we're just
+going to characterize here the electric
+
+ align:start position:0%
+going to characterize here the electric
+ 
+
+ align:start position:0%
+going to characterize here the electric
+field all right
+
+ align:start position:0%
+field all right
+ 
+
+ align:start position:0%
+field all right
+and the way we're going to characterize
+
+ align:start position:0%
+and the way we're going to characterize
+ 
+
+ align:start position:0%
+and the way we're going to characterize
+it is to put a functional form to
+
+ align:start position:0%
+it is to put a functional form to
+ 
+
+ align:start position:0%
+it is to put a functional form to
+it so I'm plotting the electric field
+
+ align:start position:0%
+it so I'm plotting the electric field
+ 
+
+ align:start position:0%
+it so I'm plotting the electric field
+here as a function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and the functional form that we're
+
+ align:start position:0%
+X and the functional form that we're
+ 
+
+ align:start position:0%
+X and the functional form that we're
+going to use to characterize it is a *
+
+ align:start position:0%
+going to use to characterize it is a *
+ 
+
+ align:start position:0%
+going to use to characterize it is a *
+cine 2 pix over Lambda a cosine
+
+ align:start position:0%
+cine 2 pix over Lambda a cosine
+ 
+
+ align:start position:0%
+cine 2 pix over Lambda a cosine
+function now what I want you to
+
+ align:start position:0%
+function now what I want you to
+ 
+
+ align:start position:0%
+function now what I want you to
+notice is that this field
+
+ align:start position:0%
+notice is that this field
+ 
+
+ align:start position:0%
+notice is that this field
+oscillates between a positive amplitude
+
+ align:start position:0%
+oscillates between a positive amplitude
+ 
+
+ align:start position:0%
+oscillates between a positive amplitude
+a and a negative amplitude a or a minus
+
+ align:start position:0%
+a and a negative amplitude a or a minus
+ 
+
+ align:start position:0%
+a and a negative amplitude a or a minus
+a right so this coefficient right out in
+
+ align:start position:0%
+a right so this coefficient right out in
+ 
+
+ align:start position:0%
+a right so this coefficient right out in
+front right here that
+
+ align:start position:0%
+front right here that
+ 
+
+ align:start position:0%
+front right here that
+coefficient physically is the maximum
+
+ align:start position:0%
+coefficient physically is the maximum
+ 
+
+ align:start position:0%
+coefficient physically is the maximum
+amplitude so if you were to be given a
+
+ align:start position:0%
+amplitude so if you were to be given a
+ 
+
+ align:start position:0%
+amplitude so if you were to be given a
+waveform that has a number out here in
+
+ align:start position:0%
+waveform that has a number out here in
+ 
+
+ align:start position:0%
+waveform that has a number out here in
+front of a cosine X hey that number
+
+ align:start position:0%
+front of a cosine X hey that number
+ 
+
+ align:start position:0%
+front of a cosine X hey that number
+immediately the physical significance of
+
+ align:start position:0%
+immediately the physical significance of
+ 
+
+ align:start position:0%
+immediately the physical significance of
+it is that it's the maximum
+
+ align:start position:0%
+it is that it's the maximum
+ 
+
+ align:start position:0%
+it is that it's the maximum
+amplitude the other parameter beside the
+
+ align:start position:0%
+amplitude the other parameter beside the
+ 
+
+ align:start position:0%
+amplitude the other parameter beside the
+amplitude here the maximum amplitude
+
+ align:start position:0%
+amplitude here the maximum amplitude
+ 
+
+ align:start position:0%
+amplitude here the maximum amplitude
+that we use to characterize this cosine
+
+ align:start position:0%
+that we use to characterize this cosine
+ 
+
+ align:start position:0%
+that we use to characterize this cosine
+function is the
+
+ align:start position:0%
+function is the
+ 
+
+ align:start position:0%
+function is the
+wavelength the wavelength is the
+
+ align:start position:0%
+wavelength the wavelength is the
+ 
+
+ align:start position:0%
+wavelength the wavelength is the
+distance between two successive Maxima
+
+ align:start position:0%
+distance between two successive Maxima
+ 
+
+ align:start position:0%
+distance between two successive Maxima
+or two successive minimum right and that
+
+ align:start position:0%
+or two successive minimum right and that
+ 
+
+ align:start position:0%
+or two successive minimum right and that
+wavelength here comes in the argument of
+
+ align:start position:0%
+wavelength here comes in the argument of
+ 
+
+ align:start position:0%
+wavelength here comes in the argument of
+that Co sign function so again if you
+
+ align:start position:0%
+that Co sign function so again if you
+ 
+
+ align:start position:0%
+that Co sign function so again if you
+were to be given a form that had a
+
+ align:start position:0%
+were to be given a form that had a
+ 
+
+ align:start position:0%
+were to be given a form that had a
+number time cosine time a number time x
+
+ align:start position:0%
+number time cosine time a number time x
+ 
+
+ align:start position:0%
+number time cosine time a number time x
+well that number is equal to 2 pi over
+
+ align:start position:0%
+well that number is equal to 2 pi over
+ 
+
+ align:start position:0%
+well that number is equal to 2 pi over
+Lambda and so almost by inspection you
+
+ align:start position:0%
+Lambda and so almost by inspection you
+ 
+
+ align:start position:0%
+Lambda and so almost by inspection you
+can figure out what the wavelength is
+
+ align:start position:0%
+can figure out what the wavelength is
+ 
+
+ align:start position:0%
+can figure out what the wavelength is
+just from the functional form of that
+
+ align:start position:0%
+just from the functional form of that
+ 
+
+ align:start position:0%
+just from the functional form of that
+cosine
+
+ align:start position:0%
+cosine
+ 
+
+ align:start position:0%
+cosine
+function all right and because the
+
+ align:start position:0%
+function all right and because the
+ 
+
+ align:start position:0%
+function all right and because the
+argument is 2 pix over
+
+ align:start position:0%
+argument is 2 pix over
+ 
+
+ align:start position:0%
+argument is 2 pix over
+Lambda well you can easily see that you
+
+ align:start position:0%
+Lambda well you can easily see that you
+ 
+
+ align:start position:0%
+Lambda well you can easily see that you
+get the maximum amplitude a here
+
+ align:start position:0%
+get the maximum amplitude a here
+ 
+
+ align:start position:0%
+get the maximum amplitude a here
+whenever X is an integral multiple of
+
+ align:start position:0%
+whenever X is an integral multiple of
+ 
+
+ align:start position:0%
+whenever X is an integral multiple of
+Lambda so when X is Lambda 2 Lambda 3
+
+ align:start position:0%
+Lambda so when X is Lambda 2 Lambda 3
+ 
+
+ align:start position:0%
+Lambda so when X is Lambda 2 Lambda 3
+Lambda or minus Lambda minus 2 Lambda or
+
+ align:start position:0%
+Lambda or minus Lambda minus 2 Lambda or
+ 
+
+ align:start position:0%
+Lambda or minus Lambda minus 2 Lambda or
+zero all right so most of that I think
+
+ align:start position:0%
+zero all right so most of that I think
+ 
+
+ align:start position:0%
+zero all right so most of that I think
+you're familiar
+
+ align:start position:0%
+you're familiar
+ 
+
+ align:start position:0%
+you're familiar
+with all right but not only is light or
+
+ align:start position:0%
+with all right but not only is light or
+ 
+
+ align:start position:0%
+with all right but not only is light or
+formally electromagnetic radiation not
+
+ align:start position:0%
+formally electromagnetic radiation not
+ 
+
+ align:start position:0%
+formally electromagnetic radiation not
+only is that simply a periodic variation
+
+ align:start position:0%
+only is that simply a periodic variation
+ 
+
+ align:start position:0%
+only is that simply a periodic variation
+of the electric or magnetic
+
+ align:start position:0%
+of the electric or magnetic
+ 
+
+ align:start position:0%
+of the electric or magnetic
+field but light is
+
+ align:start position:0%
+field but light is
+ 
+
+ align:start position:0%
+field but light is
+also a um periodic variation in
+
+ align:start position:0%
+also a um periodic variation in
+ 
+
+ align:start position:0%
+also a um periodic variation in
+time that is light propagates it moves
+
+ align:start position:0%
+time that is light propagates it moves
+ 
+
+ align:start position:0%
+time that is light propagates it moves
+so for
+
+ align:start position:0%
+so for
+ 
+
+ align:start position:0%
+so for
+example here's a uh cosine functional
+
+ align:start position:0%
+example here's a uh cosine functional
+ 
+
+ align:start position:0%
+example here's a uh cosine functional
+form at some snapshot in T equals z and
+
+ align:start position:0%
+form at some snapshot in T equals z and
+ 
+
+ align:start position:0%
+form at some snapshot in T equals z and
+I put a star here on the maximum of uh
+
+ align:start position:0%
+I put a star here on the maximum of uh
+ 
+
+ align:start position:0%
+I put a star here on the maximum of uh
+one of these U Maxima all
+
+ align:start position:0%
+one of these U Maxima all
+ 
+
+ align:start position:0%
+one of these U Maxima all
+right now what happens is that this wave
+
+ align:start position:0%
+right now what happens is that this wave
+ 
+
+ align:start position:0%
+right now what happens is that this wave
+moves it
+
+ align:start position:0%
+moves it
+ 
+
+ align:start position:0%
+moves it
+propagates and the time it takes that
+
+ align:start position:0%
+propagates and the time it takes that
+ 
+
+ align:start position:0%
+propagates and the time it takes that
+wave to move one wavelength just like it
+
+ align:start position:0%
+wave to move one wavelength just like it
+ 
+
+ align:start position:0%
+wave to move one wavelength just like it
+did in that very short clip the time it
+
+ align:start position:0%
+did in that very short clip the time it
+ 
+
+ align:start position:0%
+did in that very short clip the time it
+takes to move
+
+ align:start position:0%
+takes to move
+ 
+
+ align:start position:0%
+takes to move
+one wavelength so that this Maxima that
+
+ align:start position:0%
+one wavelength so that this Maxima that
+ 
+
+ align:start position:0%
+one wavelength so that this Maxima that
+was here is now there is what we call a
+
+ align:start position:0%
+was here is now there is what we call a
+ 
+
+ align:start position:0%
+was here is now there is what we call a
+period one period is the time it takes
+
+ align:start position:0%
+period one period is the time it takes
+ 
+
+ align:start position:0%
+period one period is the time it takes
+the wave to move one
+
+ align:start position:0%
+the wave to move one
+ 
+
+ align:start position:0%
+the wave to move one
+wavelength and we can also characterize
+
+ align:start position:0%
+wavelength and we can also characterize
+ 
+
+ align:start position:0%
+wavelength and we can also characterize
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+period by the frequency of the
+
+ align:start position:0%
+period by the frequency of the
+ 
+
+ align:start position:0%
+period by the frequency of the
+wave that frequency is is new here and
+
+ align:start position:0%
+wave that frequency is is new here and
+ 
+
+ align:start position:0%
+wave that frequency is is new here and
+the period is one over new and the
+
+ align:start position:0%
+the period is one over new and the
+ 
+
+ align:start position:0%
+the period is one over new and the
+frequency then is the number of cycles
+
+ align:start position:0%
+frequency then is the number of cycles
+ 
+
+ align:start position:0%
+frequency then is the number of cycles
+per second so another words if I were
+
+ align:start position:0%
+per second so another words if I were
+ 
+
+ align:start position:0%
+per second so another words if I were
+sitting right here at x equals z okay
+
+ align:start position:0%
+sitting right here at x equals z okay
+ 
+
+ align:start position:0%
+sitting right here at x equals z okay
+and I'm just watching the wave come by
+
+ align:start position:0%
+and I'm just watching the wave come by
+ 
+
+ align:start position:0%
+and I'm just watching the wave come by
+me the frequency is the number of
+
+ align:start position:0%
+me the frequency is the number of
+ 
+
+ align:start position:0%
+me the frequency is the number of
+times that a Maxima passes by me per
+
+ align:start position:0%
+times that a Maxima passes by me per
+ 
+
+ align:start position:0%
+times that a Maxima passes by me per
+second or the number of times a minim
+
+ align:start position:0%
+second or the number of times a minim
+ 
+
+ align:start position:0%
+second or the number of times a minim
+passes by me per second that's the
+
+ align:start position:0%
+passes by me per second that's the
+ 
+
+ align:start position:0%
+passes by me per second that's the
+frequency okay I'll make that a little
+
+ align:start position:0%
+frequency okay I'll make that a little
+ 
+
+ align:start position:0%
+frequency okay I'll make that a little
+bit more obvious in just a
+
+ align:start position:0%
+bit more obvious in just a
+ 
+
+ align:start position:0%
+bit more obvious in just a
+moment
+
+ align:start position:0%
+moment
+ 
+
+ align:start position:0%
+moment
+frequency I said is a number of cycles
+
+ align:start position:0%
+frequency I said is a number of cycles
+ 
+
+ align:start position:0%
+frequency I said is a number of cycles
+per second but the unit that we use to
+
+ align:start position:0%
+per second but the unit that we use to
+ 
+
+ align:start position:0%
+per second but the unit that we use to
+uh convey frequency something called the
+
+ align:start position:0%
+uh convey frequency something called the
+ 
+
+ align:start position:0%
+uh convey frequency something called the
+Hertz HZ Hertz and formally it is just
+
+ align:start position:0%
+Hertz HZ Hertz and formally it is just
+ 
+
+ align:start position:0%
+Hertz HZ Hertz and formally it is just
+inverse seconds right we drop the number
+
+ align:start position:0%
+inverse seconds right we drop the number
+ 
+
+ align:start position:0%
+inverse seconds right we drop the number
+of Cycles but the number of Cycles in
+
+ align:start position:0%
+of Cycles but the number of Cycles in
+ 
+
+ align:start position:0%
+of Cycles but the number of Cycles in
+that unit is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implied all right so now suppose the
+
+ align:start position:0%
+implied all right so now suppose the
+ 
+
+ align:start position:0%
+implied all right so now suppose the
+following I said that this electric
+
+ align:start position:0%
+following I said that this electric
+ 
+
+ align:start position:0%
+following I said that this electric
+field has uh magnitude and it also has
+
+ align:start position:0%
+field has uh magnitude and it also has
+ 
+
+ align:start position:0%
+field has uh magnitude and it also has
+direction right so suppose I take an
+
+ align:start position:0%
+direction right so suppose I take an
+ 
+
+ align:start position:0%
+direction right so suppose I take an
+electric field or an electromagnetic
+
+ align:start position:0%
+electric field or an electromagnetic
+ 
+
+ align:start position:0%
+electric field or an electromagnetic
+radiation that has a frequency of one
+
+ align:start position:0%
+radiation that has a frequency of one
+ 
+
+ align:start position:0%
+radiation that has a frequency of one
+Hertz one cycle per second
+
+ align:start position:0%
+Hertz one cycle per second
+ 
+
+ align:start position:0%
+Hertz one cycle per second
+and right here at x equals 0 I stick
+
+ align:start position:0%
+and right here at x equals 0 I stick
+ 
+
+ align:start position:0%
+and right here at x equals 0 I stick
+somehow I pin an elect uh an electron
+
+ align:start position:0%
+somehow I pin an elect uh an electron
+ 
+
+ align:start position:0%
+somehow I pin an elect uh an electron
+right there okay it can't move anywhere
+
+ align:start position:0%
+right there okay it can't move anywhere
+ 
+
+ align:start position:0%
+right there okay it can't move anywhere
+it's just
+
+ align:start position:0%
+it's just
+ 
+
+ align:start position:0%
+it's just
+stuck what's going to happen to that
+
+ align:start position:0%
+stuck what's going to happen to that
+ 
+
+ align:start position:0%
+stuck what's going to happen to that
+electron as this radiation of one Hertz
+
+ align:start position:0%
+electron as this radiation of one Hertz
+ 
+
+ align:start position:0%
+electron as this radiation of one Hertz
+passes by well what's going to happen is
+
+ align:start position:0%
+passes by well what's going to happen is
+ 
+
+ align:start position:0%
+passes by well what's going to happen is
+that that electron is going to be now
+
+ align:start position:0%
+that that electron is going to be now
+ 
+
+ align:start position:0%
+that that electron is going to be now
+since it start at the top it's going to
+
+ align:start position:0%
+since it start at the top it's going to
+ 
+
+ align:start position:0%
+since it start at the top it's going to
+be pulled down and then it's going to be
+
+ align:start position:0%
+be pulled down and then it's going to be
+ 
+
+ align:start position:0%
+be pulled down and then it's going to be
+pushed back up to its original position
+
+ align:start position:0%
+pushed back up to its original position
+ 
+
+ align:start position:0%
+pushed back up to its original position
+every 1 second because this frequency
+
+ align:start position:0%
+every 1 second because this frequency
+ 
+
+ align:start position:0%
+every 1 second because this frequency
+here is 1 Hertz and because this
+
+ align:start position:0%
+here is 1 Hertz and because this
+ 
+
+ align:start position:0%
+here is 1 Hertz and because this
+electric field has both magnitude and it
+
+ align:start position:0%
+electric field has both magnitude and it
+ 
+
+ align:start position:0%
+electric field has both magnitude and it
+has Direction all right so now we're
+
+ align:start position:0%
+has Direction all right so now we're
+ 
+
+ align:start position:0%
+has Direction all right so now we're
+going to let this electric field go by
+
+ align:start position:0%
+going to let this electric field go by
+ 
+
+ align:start position:0%
+going to let this electric field go by
+the electron gets pushed down and pulled
+
+ align:start position:0%
+the electron gets pushed down and pulled
+ 
+
+ align:start position:0%
+the electron gets pushed down and pulled
+back up once every second all right so
+
+ align:start position:0%
+back up once every second all right so
+ 
+
+ align:start position:0%
+back up once every second all right so
+hopefully that makes the idea of
+
+ align:start position:0%
+hopefully that makes the idea of
+ 
+
+ align:start position:0%
+hopefully that makes the idea of
+frequency a little bit more uh real to
+
+ align:start position:0%
+frequency a little bit more uh real to
+ 
+
+ align:start position:0%
+frequency a little bit more uh real to
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+okay but not only do we have this
+
+ align:start position:0%
+okay but not only do we have this
+ 
+
+ align:start position:0%
+okay but not only do we have this
+periodic variation in
+
+ align:start position:0%
+periodic variation in
+ 
+
+ align:start position:0%
+periodic variation in
+time but we also have the wave propagate
+
+ align:start position:0%
+time but we also have the wave propagate
+ 
+
+ align:start position:0%
+time but we also have the wave propagate
+here in space you know that wave moves
+
+ align:start position:0%
+here in space you know that wave moves
+ 
+
+ align:start position:0%
+here in space you know that wave moves
+this way or this way or this way
+
+ align:start position:0%
+this way or this way or this way
+ 
+
+ align:start position:0%
+this way or this way or this way
+okay and so what we want to know is the
+
+ align:start position:0%
+okay and so what we want to know is the
+ 
+
+ align:start position:0%
+okay and so what we want to know is the
+speed of that
+
+ align:start position:0%
+speed of that
+ 
+
+ align:start position:0%
+speed of that
+propagation now speed is always distance
+
+ align:start position:0%
+propagation now speed is always distance
+ 
+
+ align:start position:0%
+propagation now speed is always distance
+traveled over the time
+
+ align:start position:0%
+traveled over the time
+ 
+
+ align:start position:0%
+traveled over the time
+elapsed and um what we've already seen
+
+ align:start position:0%
+elapsed and um what we've already seen
+ 
+
+ align:start position:0%
+elapsed and um what we've already seen
+is that this wave will move by one
+
+ align:start position:0%
+is that this wave will move by one
+ 
+
+ align:start position:0%
+is that this wave will move by one
+wavelength in the time period of a
+
+ align:start position:0%
+wavelength in the time period of a
+ 
+
+ align:start position:0%
+wavelength in the time period of a
+period okay that is we already saw that
+
+ align:start position:0%
+period okay that is we already saw that
+ 
+
+ align:start position:0%
+period okay that is we already saw that
+this wave will move here one wavelength
+
+ align:start position:0%
+this wave will move here one wavelength
+ 
+
+ align:start position:0%
+this wave will move here one wavelength
+from here to
+
+ align:start position:0%
+from here to
+ 
+
+ align:start position:0%
+from here to
+here in the time period of a period or
+
+ align:start position:0%
+here in the time period of a period or
+ 
+
+ align:start position:0%
+here in the time period of a period or
+one over new okay that's the time elapse
+
+ align:start position:0%
+one over new okay that's the time elapse
+ 
+
+ align:start position:0%
+one over new okay that's the time elapse
+so the speed of this propagation the
+
+ align:start position:0%
+so the speed of this propagation the
+ 
+
+ align:start position:0%
+so the speed of this propagation the
+speed with which it's moving is the
+
+ align:start position:0%
+speed with which it's moving is the
+ 
+
+ align:start position:0%
+speed with which it's moving is the
+distance traveled which is Lambda right
+
+ align:start position:0%
+distance traveled which is Lambda right
+ 
+
+ align:start position:0%
+distance traveled which is Lambda right
+divided by the time
+
+ align:start position:0%
+divided by the time
+ 
+
+ align:start position:0%
+divided by the time
+elapsed which is one over new and
+
+ align:start position:0%
+elapsed which is one over new and
+ 
+
+ align:start position:0%
+elapsed which is one over new and
+therefore the speed of that propagation
+
+ align:start position:0%
+therefore the speed of that propagation
+ 
+
+ align:start position:0%
+therefore the speed of that propagation
+is Lambda time
+
+ align:start position:0%
+is Lambda time
+ 
+
+ align:start position:0%
+is Lambda time
+U all right so these are the important
+
+ align:start position:0%
+U all right so these are the important
+ 
+
+ align:start position:0%
+U all right so these are the important
+Concepts here we have the speed of the
+
+ align:start position:0%
+Concepts here we have the speed of the
+ 
+
+ align:start position:0%
+Concepts here we have the speed of the
+propagation Lambda Time new we
+
+ align:start position:0%
+propagation Lambda Time new we
+ 
+
+ align:start position:0%
+propagation Lambda Time new we
+characterized our wave in terms of
+
+ align:start position:0%
+characterized our wave in terms of
+ 
+
+ align:start position:0%
+characterized our wave in terms of
+amplitudes in terms of wavelengths and
+
+ align:start position:0%
+amplitudes in terms of wavelengths and
+ 
+
+ align:start position:0%
+amplitudes in terms of wavelengths and
+in terms of frequency those are the
+
+ align:start position:0%
+in terms of frequency those are the
+ 
+
+ align:start position:0%
+in terms of frequency those are the
+quantities that are important that you
+
+ align:start position:0%
+quantities that are important that you
+ 
+
+ align:start position:0%
+quantities that are important that you
+really do have to understand very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay
+
+ align:start position:0%
+well okay
+ 
+
+ align:start position:0%
+well okay
+now I think that you're all familiar
+
+ align:start position:0%
+now I think that you're all familiar
+ 
+
+ align:start position:0%
+now I think that you're all familiar
+with the fact that all electromagnetic
+
+ align:start position:0%
+with the fact that all electromagnetic
+ 
+
+ align:start position:0%
+with the fact that all electromagnetic
+radiation has a constant speed right
+
+ align:start position:0%
+radiation has a constant speed right
+ 
+
+ align:start position:0%
+radiation has a constant speed right
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+wavelength of electromagnetic radiation
+
+ align:start position:0%
+wavelength of electromagnetic radiation
+ 
+
+ align:start position:0%
+wavelength of electromagnetic radiation
+times its
+
+ align:start position:0%
+times its
+ 
+
+ align:start position:0%
+times its
+frequency is always equal to this number
+
+ align:start position:0%
+frequency is always equal to this number
+ 
+
+ align:start position:0%
+frequency is always equal to this number
+it's about 3 * 10 8
+
+ align:start position:0%
+it's about 3 * 10 8
+ 
+
+ align:start position:0%
+it's about 3 * 10 8
+m/s and we call it we abbreviate it C
+
+ align:start position:0%
+m/s and we call it we abbreviate it C
+ 
+
+ align:start position:0%
+m/s and we call it we abbreviate it C
+the speed of light so no matter what
+
+ align:start position:0%
+the speed of light so no matter what
+ 
+
+ align:start position:0%
+the speed of light so no matter what
+frequency you have of
+
+ align:start position:0%
+frequency you have of
+ 
+
+ align:start position:0%
+frequency you have of
+radiation the
+
+ align:start position:0%
+radiation the
+ 
+
+ align:start position:0%
+radiation the
+corresponding wavelength is such that
+
+ align:start position:0%
+corresponding wavelength is such that
+ 
+
+ align:start position:0%
+corresponding wavelength is such that
+the wavelength times the frequency is as
+
+ align:start position:0%
+the wavelength times the frequency is as
+ 
+
+ align:start position:0%
+the wavelength times the frequency is as
+constant is this value of
+
+ align:start position:0%
+constant is this value of
+ 
+
+ align:start position:0%
+constant is this value of
+c and of course it is the differ
+
+ align:start position:0%
+c and of course it is the differ
+ 
+
+ align:start position:0%
+c and of course it is the differ
+different frequencies or the different
+
+ align:start position:0%
+different frequencies or the different
+ 
+
+ align:start position:0%
+different frequencies or the different
+wavelengths of electromagnetic radiation
+
+ align:start position:0%
+wavelengths of electromagnetic radiation
+ 
+
+ align:start position:0%
+wavelengths of electromagnetic radiation
+that gives it its different characters
+
+ align:start position:0%
+that gives it its different characters
+ 
+
+ align:start position:0%
+that gives it its different characters
+even though it all has the same speed of
+
+ align:start position:0%
+even though it all has the same speed of
+ 
+
+ align:start position:0%
+even though it all has the same speed of
+propagation right and that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um those different kinds of uh
+
+ align:start position:0%
+um those different kinds of uh
+ 
+
+ align:start position:0%
+um those different kinds of uh
+properties so to
+
+ align:start position:0%
+properties so to
+ 
+
+ align:start position:0%
+properties so to
+speak is this um spectrum of
+
+ align:start position:0%
+speak is this um spectrum of
+ 
+
+ align:start position:0%
+speak is this um spectrum of
+electromagnetic
+
+ align:start position:0%
+electromagnetic
+ 
+
+ align:start position:0%
+electromagnetic
+radiation okay so electromagnetic
+
+ align:start position:0%
+radiation okay so electromagnetic
+ 
+
+ align:start position:0%
+radiation okay so electromagnetic
+radiation is an infinitely wide
+
+ align:start position:0%
+radiation is an infinitely wide
+ 
+
+ align:start position:0%
+radiation is an infinitely wide
+spectrum it's
+
+ align:start position:0%
+spectrum it's
+ 
+
+ align:start position:0%
+spectrum it's
+uh very long wavelengths right we have
+
+ align:start position:0%
+uh very long wavelengths right we have
+ 
+
+ align:start position:0%
+uh very long wavelengths right we have
+what are known as radial
+
+ align:start position:0%
+what are known as radial
+ 
+
+ align:start position:0%
+what are known as radial
+waves at very short wavelengths we have
+
+ align:start position:0%
+waves at very short wavelengths we have
+ 
+
+ align:start position:0%
+waves at very short wavelengths we have
+what we know are known as gamma rays or
+
+ align:start position:0%
+what we know are known as gamma rays or
+ 
+
+ align:start position:0%
+what we know are known as gamma rays or
+cosmic rays
+
+ align:start position:0%
+cosmic rays
+ 
+
+ align:start position:0%
+cosmic rays
+right the long wavelengths the radial
+
+ align:start position:0%
+right the long wavelengths the radial
+ 
+
+ align:start position:0%
+right the long wavelengths the radial
+waves are going to have a relatively low
+
+ align:start position:0%
+waves are going to have a relatively low
+ 
+
+ align:start position:0%
+waves are going to have a relatively low
+frequency the high W the short
+
+ align:start position:0%
+frequency the high W the short
+ 
+
+ align:start position:0%
+frequency the high W the short
+wavelengths are going to have a
+
+ align:start position:0%
+wavelengths are going to have a
+ 
+
+ align:start position:0%
+wavelengths are going to have a
+relatively high
+
+ align:start position:0%
+relatively high
+ 
+
+ align:start position:0%
+relatively high
+frequency why because the product of
+
+ align:start position:0%
+frequency why because the product of
+ 
+
+ align:start position:0%
+frequency why because the product of
+Lambda times new always has to be
+
+ align:start position:0%
+Lambda times new always has to be
+ 
+
+ align:start position:0%
+Lambda times new always has to be
+C all
+
+ align:start position:0%
+C all
+ 
+
+ align:start position:0%
+C all
+right okay well we're not going to go
+
+ align:start position:0%
+right okay well we're not going to go
+ 
+
+ align:start position:0%
+right okay well we're not going to go
+very much in detail here all right
+
+ align:start position:0%
+very much in detail here all right
+ 
+
+ align:start position:0%
+very much in detail here all right
+except maybe to tell you the following
+
+ align:start position:0%
+except maybe to tell you the following
+ 
+
+ align:start position:0%
+except maybe to tell you the following
+see this microwave range here well
+
+ align:start position:0%
+see this microwave range here well
+ 
+
+ align:start position:0%
+see this microwave range here well
+molecules when they absorb microwave
+
+ align:start position:0%
+molecules when they absorb microwave
+ 
+
+ align:start position:0%
+molecules when they absorb microwave
+radiation they
+
+ align:start position:0%
+radiation they
+ 
+
+ align:start position:0%
+radiation they
+rotate right see infrared radiation when
+
+ align:start position:0%
+rotate right see infrared radiation when
+ 
+
+ align:start position:0%
+rotate right see infrared radiation when
+molecules absorb infrared radiation they
+
+ align:start position:0%
+molecules absorb infrared radiation they
+ 
+
+ align:start position:0%
+molecules absorb infrared radiation they
+vibrate see the visible and UltraViolet
+
+ align:start position:0%
+vibrate see the visible and UltraViolet
+ 
+
+ align:start position:0%
+vibrate see the visible and UltraViolet
+range when molecules absorb visible or
+
+ align:start position:0%
+range when molecules absorb visible or
+ 
+
+ align:start position:0%
+range when molecules absorb visible or
+UV radiation they put an electron into a
+
+ align:start position:0%
+UV radiation they put an electron into a
+ 
+
+ align:start position:0%
+UV radiation they put an electron into a
+higher energy
+
+ align:start position:0%
+higher energy
+ 
+
+ align:start position:0%
+higher energy
+State and often times once you do that
+
+ align:start position:0%
+State and often times once you do that
+ 
+
+ align:start position:0%
+State and often times once you do that
+of course the electron wants to relax to
+
+ align:start position:0%
+of course the electron wants to relax to
+ 
+
+ align:start position:0%
+of course the electron wants to relax to
+a lower energy State and so it relaxes
+
+ align:start position:0%
+a lower energy State and so it relaxes
+ 
+
+ align:start position:0%
+a lower energy State and so it relaxes
+by emitting a photon and that's how you
+
+ align:start position:0%
+by emitting a photon and that's how you
+ 
+
+ align:start position:0%
+by emitting a photon and that's how you
+see fluorescents or
+
+ align:start position:0%
+see fluorescents or
+ 
+
+ align:start position:0%
+see fluorescents or
+phosphorescence but it's usually a
+
+ align:start position:0%
+phosphorescence but it's usually a
+ 
+
+ align:start position:0%
+phosphorescence but it's usually a
+result of the absorption of visible or
+
+ align:start position:0%
+result of the absorption of visible or
+ 
+
+ align:start position:0%
+result of the absorption of visible or
+UV
+
+ align:start position:0%
+UV
+ 
+
+ align:start position:0%
+UV
+radiation although it is also possible
+
+ align:start position:0%
+radiation although it is also possible
+ 
+
+ align:start position:0%
+radiation although it is also possible
+for a molecule to absorb some x-ray
+
+ align:start position:0%
+for a molecule to absorb some x-ray
+ 
+
+ align:start position:0%
+for a molecule to absorb some x-ray
+radiation and see that kind of
+
+ align:start position:0%
+radiation and see that kind of
+ 
+
+ align:start position:0%
+radiation and see that kind of
+fluorescence too and we'll talk about it
+
+ align:start position:0%
+fluorescence too and we'll talk about it
+ 
+
+ align:start position:0%
+fluorescence too and we'll talk about it
+but a little bit later on we're going to
+
+ align:start position:0%
+but a little bit later on we're going to
+ 
+
+ align:start position:0%
+but a little bit later on we're going to
+talk about molecules absorbing x-ray
+
+ align:start position:0%
+talk about molecules absorbing x-ray
+ 
+
+ align:start position:0%
+talk about molecules absorbing x-ray
+radiation and kicking out an electron
+
+ align:start position:0%
+radiation and kicking out an electron
+ 
+
+ align:start position:0%
+radiation and kicking out an electron
+and we're going to use that to figure
+
+ align:start position:0%
+and we're going to use that to figure
+ 
+
+ align:start position:0%
+and we're going to use that to figure
+out how strongly bound electrons are to
+
+ align:start position:0%
+out how strongly bound electrons are to
+ 
+
+ align:start position:0%
+out how strongly bound electrons are to
+uh in atoms or how strongly bound they
+
+ align:start position:0%
+uh in atoms or how strongly bound they
+ 
+
+ align:start position:0%
+uh in atoms or how strongly bound they
+are in molecules all right okay but
+
+ align:start position:0%
+are in molecules all right okay but
+ 
+
+ align:start position:0%
+are in molecules all right okay but
+that's all I'll say about that right now
+
+ align:start position:0%
+that's all I'll say about that right now
+ 
+
+ align:start position:0%
+that's all I'll say about that right now
+what you're responsible for is you're
+
+ align:start position:0%
+what you're responsible for is you're
+ 
+
+ align:start position:0%
+what you're responsible for is you're
+responsible in knowing that microwaves
+
+ align:start position:0%
+responsible in knowing that microwaves
+ 
+
+ align:start position:0%
+responsible in knowing that microwaves
+have longer wavelengths than gamma rays
+
+ align:start position:0%
+have longer wavelengths than gamma rays
+ 
+
+ align:start position:0%
+have longer wavelengths than gamma rays
+or cosmic rays all right you are
+
+ align:start position:0%
+or cosmic rays all right you are
+ 
+
+ align:start position:0%
+or cosmic rays all right you are
+responsible for knowing the relative
+
+ align:start position:0%
+responsible for knowing the relative
+ 
+
+ align:start position:0%
+responsible for knowing the relative
+wavelengths here of uh these different
+
+ align:start position:0%
+wavelengths here of uh these different
+ 
+
+ align:start position:0%
+wavelengths here of uh these different
+kinds of radiation every MIT uh student
+
+ align:start position:0%
+kinds of radiation every MIT uh student
+ 
+
+ align:start position:0%
+kinds of radiation every MIT uh student
+should know that all right of course
+
+ align:start position:0%
+should know that all right of course
+ 
+
+ align:start position:0%
+should know that all right of course
+there's a very narrow range here a
+
+ align:start position:0%
+there's a very narrow range here a
+ 
+
+ align:start position:0%
+there's a very narrow range here a
+visible
+
+ align:start position:0%
+visible
+ 
+
+ align:start position:0%
+visible
+radiation that our I is sensitive
+
+ align:start position:0%
+radiation that our I is sensitive
+ 
+
+ align:start position:0%
+radiation that our I is sensitive
+to at the very long wavelengths is red
+
+ align:start position:0%
+to at the very long wavelengths is red
+ 
+
+ align:start position:0%
+to at the very long wavelengths is red
+at the very short wavelengths is blue
+
+ align:start position:0%
+at the very short wavelengths is blue
+ 
+
+ align:start position:0%
+at the very short wavelengths is blue
+and purple again you need to know that
+
+ align:start position:0%
+and purple again you need to know that
+ 
+
+ align:start position:0%
+and purple again you need to know that
+red has a longer wavelength than blue or
+
+ align:start position:0%
+red has a longer wavelength than blue or
+ 
+
+ align:start position:0%
+red has a longer wavelength than blue or
+purple all
+
+ align:start position:0%
+purple all
+ 
+
+ align:start position:0%
+purple all
+right all right so what I've done right
+
+ align:start position:0%
+right all right so what I've done right
+ 
+
+ align:start position:0%
+right all right so what I've done right
+now is really just to
+
+ align:start position:0%
+now is really just to
+ 
+
+ align:start position:0%
+now is really just to
+um tell you that light is an
+
+ align:start position:0%
+um tell you that light is an
+ 
+
+ align:start position:0%
+um tell you that light is an
+electromagnetic radiation characterize
+
+ align:start position:0%
+electromagnetic radiation characterize
+ 
+
+ align:start position:0%
+electromagnetic radiation characterize
+it the way I put a functional form to a
+
+ align:start position:0%
+it the way I put a functional form to a
+ 
+
+ align:start position:0%
+it the way I put a functional form to a
+cosine characterize it by frequency
+
+ align:start position:0%
+cosine characterize it by frequency
+ 
+
+ align:start position:0%
+cosine characterize it by frequency
+wavelength we talked about speed of
+
+ align:start position:0%
+wavelength we talked about speed of
+ 
+
+ align:start position:0%
+wavelength we talked about speed of
+propagation what I haven't done yet is I
+
+ align:start position:0%
+propagation what I haven't done yet is I
+ 
+
+ align:start position:0%
+propagation what I haven't done yet is I
+haven't proved to you that light is in
+
+ align:start position:0%
+haven't proved to you that light is in
+ 
+
+ align:start position:0%
+haven't proved to you that light is in
+fact or light behaves like a wave and
+
+ align:start position:0%
+fact or light behaves like a wave and
+ 
+
+ align:start position:0%
+fact or light behaves like a wave and
+that's what we're going to do now and
+
+ align:start position:0%
+that's what we're going to do now and
+ 
+
+ align:start position:0%
+that's what we're going to do now and
+the experiment we're going to do is the
+
+ align:start position:0%
+the experiment we're going to do is the
+ 
+
+ align:start position:0%
+the experiment we're going to do is the
+same experiment that a gentleman called
+
+ align:start position:0%
+same experiment that a gentleman called
+ 
+
+ align:start position:0%
+same experiment that a gentleman called
+young did in the late 1800s
+
+ align:start position:0%
+young did in the late 1800s
+ 
+
+ align:start position:0%
+young did in the late 1800s
+that seem to really demonstrate without
+
+ align:start position:0%
+that seem to really demonstrate without
+ 
+
+ align:start position:0%
+that seem to really demonstrate without
+a question that light is a wave or light
+
+ align:start position:0%
+a question that light is a wave or light
+ 
+
+ align:start position:0%
+a question that light is a wave or light
+behaves like a
+
+ align:start position:0%
+behaves like a
+ 
+
+ align:start position:0%
+behaves like a
+wave we're going to do what's called the
+
+ align:start position:0%
+wave we're going to do what's called the
+ 
+
+ align:start position:0%
+wave we're going to do what's called the
+two slit
+
+ align:start position:0%
+two slit
+ 
+
+ align:start position:0%
+two slit
+experiment and in this experiment I'm
+
+ align:start position:0%
+experiment and in this experiment I'm
+ 
+
+ align:start position:0%
+experiment and in this experiment I'm
+going to take radiation of a single
+
+ align:start position:0%
+going to take radiation of a single
+ 
+
+ align:start position:0%
+going to take radiation of a single
+wavelength so we're going to make the
+
+ align:start position:0%
+wavelength so we're going to make the
+ 
+
+ align:start position:0%
+wavelength so we're going to make the
+radiation
+
+ align:start position:0%
+radiation
+ 
+
+ align:start position:0%
+radiation
+monochromatic and uh that wavelength
+
+ align:start position:0%
+monochromatic and uh that wavelength
+ 
+
+ align:start position:0%
+monochromatic and uh that wavelength
+that we're going to use is 600 6,000 330
+
+ align:start position:0%
+that we're going to use is 600 6,000 330
+ 
+
+ align:start position:0%
+that we're going to use is 600 6,000 330
+angstroms or 633
+
+ align:start position:0%
+angstroms or 633
+ 
+
+ align:start position:0%
+angstroms or 633
+nanometers and we're going to put in
+
+ align:start position:0%
+nanometers and we're going to put in
+ 
+
+ align:start position:0%
+nanometers and we're going to put in
+front of that Source we're going to put
+
+ align:start position:0%
+front of that Source we're going to put
+ 
+
+ align:start position:0%
+front of that Source we're going to put
+a piece of uh it's going to be a thin uh
+
+ align:start position:0%
+a piece of uh it's going to be a thin uh
+ 
+
+ align:start position:0%
+a piece of uh it's going to be a thin uh
+piece of metal or the could be any
+
+ align:start position:0%
+piece of metal or the could be any
+ 
+
+ align:start position:0%
+piece of metal or the could be any
+material but we're going to poke two
+
+ align:start position:0%
+material but we're going to poke two
+ 
+
+ align:start position:0%
+material but we're going to poke two
+holes in it we're going to make two
+
+ align:start position:0%
+holes in it we're going to make two
+ 
+
+ align:start position:0%
+holes in it we're going to make two
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+slits and
+
+ align:start position:0%
+slits and
+ 
+
+ align:start position:0%
+slits and
+naively what you might expect is that if
+
+ align:start position:0%
+naively what you might expect is that if
+ 
+
+ align:start position:0%
+naively what you might expect is that if
+you have a screen back here that kind of
+
+ align:start position:0%
+you have a screen back here that kind of
+ 
+
+ align:start position:0%
+you have a screen back here that kind of
+uh images this radiat
+
+ align:start position:0%
+uh images this radiat
+ 
+
+ align:start position:0%
+uh images this radiat
+what you might expect is that the the
+
+ align:start position:0%
+what you might expect is that the the
+ 
+
+ align:start position:0%
+what you might expect is that the the
+spots on the screen right directly
+
+ align:start position:0%
+spots on the screen right directly
+ 
+
+ align:start position:0%
+spots on the screen right directly
+opposite these two slits well these are
+
+ align:start position:0%
+opposite these two slits well these are
+ 
+
+ align:start position:0%
+opposite these two slits well these are
+the two spots that are going to light up
+
+ align:start position:0%
+the two spots that are going to light up
+ 
+
+ align:start position:0%
+the two spots that are going to light up
+on the screen that's where you're going
+
+ align:start position:0%
+on the screen that's where you're going
+ 
+
+ align:start position:0%
+on the screen that's where you're going
+to see the image because after all light
+
+ align:start position:0%
+to see the image because after all light
+ 
+
+ align:start position:0%
+to see the image because after all light
+travels in straight lines that's where
+
+ align:start position:0%
+travels in straight lines that's where
+ 
+
+ align:start position:0%
+travels in straight lines that's where
+you should see those two spots so the
+
+ align:start position:0%
+you should see those two spots so the
+ 
+
+ align:start position:0%
+you should see those two spots so the
+slits here are 0.02 in from each other
+
+ align:start position:0%
+slits here are 0.02 in from each other
+ 
+
+ align:start position:0%
+slits here are 0.02 in from each other
+these two spots ought to be .02 in 0.02
+
+ align:start position:0%
+these two spots ought to be .02 in 0.02
+ 
+
+ align:start position:0%
+these two spots ought to be .02 in 0.02
+in separated from each
+
+ align:start position:0%
+in separated from each
+ 
+
+ align:start position:0%
+in separated from each
+other but of course uh when you do that
+
+ align:start position:0%
+other but of course uh when you do that
+ 
+
+ align:start position:0%
+other but of course uh when you do that
+experiment and Christine is actually
+
+ align:start position:0%
+experiment and Christine is actually
+ 
+
+ align:start position:0%
+experiment and Christine is actually
+going to do that experiment right right
+
+ align:start position:0%
+going to do that experiment right right
+ 
+
+ align:start position:0%
+going to do that experiment right right
+now for us I think there it is on the
+
+ align:start position:0%
+now for us I think there it is on the
+ 
+
+ align:start position:0%
+now for us I think there it is on the
+sideboard you can sort of see
+
+ align:start position:0%
+sideboard you can sort of see
+ 
+
+ align:start position:0%
+sideboard you can sort of see
+it okay she's holding
+
+ align:start position:0%
+it okay she's holding
+ 
+
+ align:start position:0%
+it okay she's holding
+it all right well what you can see
+
+ align:start position:0%
+it all right well what you can see
+ 
+
+ align:start position:0%
+it all right well what you can see
+here is that we don't see just two
+
+ align:start position:0%
+here is that we don't see just two
+ 
+
+ align:start position:0%
+here is that we don't see just two
+bright spots but what we see are a bunch
+
+ align:start position:0%
+bright spots but what we see are a bunch
+ 
+
+ align:start position:0%
+bright spots but what we see are a bunch
+of spots here the brightest one happens
+
+ align:start position:0%
+of spots here the brightest one happens
+ 
+
+ align:start position:0%
+of spots here the brightest one happens
+to be right in the center of these two
+
+ align:start position:0%
+to be right in the center of these two
+ 
+
+ align:start position:0%
+to be right in the center of these two
+slits and then there's darkness and then
+
+ align:start position:0%
+slits and then there's darkness and then
+ 
+
+ align:start position:0%
+slits and then there's darkness and then
+there's a bright spot and darkness and a
+
+ align:start position:0%
+there's a bright spot and darkness and a
+ 
+
+ align:start position:0%
+there's a bright spot and darkness and a
+bright spot etc etc we see lots of
+
+ align:start position:0%
+bright spot etc etc we see lots of
+ 
+
+ align:start position:0%
+bright spot etc etc we see lots of
+different bright spots on the screen not
+
+ align:start position:0%
+different bright spots on the screen not
+ 
+
+ align:start position:0%
+different bright spots on the screen not
+just two directly opposite
+
+ align:start position:0%
+just two directly opposite
+ 
+
+ align:start position:0%
+just two directly opposite
+the openings of the slits all
+
+ align:start position:0%
+the openings of the slits all
+ 
+
+ align:start position:0%
+the openings of the slits all
+right okay so and this is just then a
+
+ align:start position:0%
+right okay so and this is just then a
+ 
+
+ align:start position:0%
+right okay so and this is just then a
+cartoon of uh approximately what it is
+
+ align:start position:0%
+cartoon of uh approximately what it is
+ 
+
+ align:start position:0%
+cartoon of uh approximately what it is
+we see with um in real life so CH
+
+ align:start position:0%
+we see with um in real life so CH
+ 
+
+ align:start position:0%
+we see with um in real life so CH
+Christine's up there in the projection
+
+ align:start position:0%
+Christine's up there in the projection
+ 
+
+ align:start position:0%
+Christine's up there in the projection
+booth holding a helium neon laser uh
+
+ align:start position:0%
+booth holding a helium neon laser uh
+ 
+
+ align:start position:0%
+booth holding a helium neon laser uh
+Behind These two slits separated by
+
+ align:start position:0%
+Behind These two slits separated by
+ 
+
+ align:start position:0%
+Behind These two slits separated by
+point2 Ines
+
+ align:start position:0%
+point2 Ines
+ 
+
+ align:start position:0%
+point2 Ines
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay well so what's going on here
+
+ align:start position:0%
+okay well so what's going on here
+ 
+
+ align:start position:0%
+okay well so what's going on here
+can we can we understand uh what's the
+
+ align:start position:0%
+can we can we understand uh what's the
+ 
+
+ align:start position:0%
+can we can we understand uh what's the
+origin of these lots of different bright
+
+ align:start position:0%
+origin of these lots of different bright
+ 
+
+ align:start position:0%
+origin of these lots of different bright
+spots in this two slit
+
+ align:start position:0%
+spots in this two slit
+ 
+
+ align:start position:0%
+spots in this two slit
+experiment and actually if we were to
+
+ align:start position:0%
+experiment and actually if we were to
+ 
+
+ align:start position:0%
+experiment and actually if we were to
+measure that uh the distance here should
+
+ align:start position:0%
+measure that uh the distance here should
+ 
+
+ align:start position:0%
+measure that uh the distance here should
+be about 3 cmers between those bright
+
+ align:start position:0%
+be about 3 cmers between those bright
+ 
+
+ align:start position:0%
+be about 3 cmers between those bright
+spots okay well what's going on well
+
+ align:start position:0%
+spots okay well what's going on well
+ 
+
+ align:start position:0%
+spots okay well what's going on well
+what's going on is this
+
+ align:start position:0%
+what's going on is this
+ 
+
+ align:start position:0%
+what's going on is this
+waves waves have the property called
+
+ align:start position:0%
+waves waves have the property called
+ 
+
+ align:start position:0%
+waves waves have the property called
+superposition that is if I take one
+
+ align:start position:0%
+superposition that is if I take one
+ 
+
+ align:start position:0%
+superposition that is if I take one
+wave but then I take a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wave and I put that second
+
+ align:start position:0%
+wave and I put that second
+ 
+
+ align:start position:0%
+wave and I put that second
+wave in the same space the actual same
+
+ align:start position:0%
+wave in the same space the actual same
+ 
+
+ align:start position:0%
+wave in the same space the actual same
+space as the first wave and I arranged
+
+ align:start position:0%
+space as the first wave and I arranged
+ 
+
+ align:start position:0%
+space as the first wave and I arranged
+the two waves such that the maximum of
+
+ align:start position:0%
+the two waves such that the maximum of
+ 
+
+ align:start position:0%
+the two waves such that the maximum of
+both waves or the minimum of both waves
+
+ align:start position:0%
+both waves or the minimum of both waves
+ 
+
+ align:start position:0%
+both waves or the minimum of both waves
+is at the same position well the prop
+
+ align:start position:0%
+is at the same position well the prop
+ 
+
+ align:start position:0%
+is at the same position well the prop
+property of waves is that these two
+
+ align:start position:0%
+property of waves is that these two
+ 
+
+ align:start position:0%
+property of waves is that these two
+waves add up they
+
+ align:start position:0%
+waves add up they
+ 
+
+ align:start position:0%
+waves add up they
+superimpose they superimpose to make a
+
+ align:start position:0%
+superimpose they superimpose to make a
+ 
+
+ align:start position:0%
+superimpose they superimpose to make a
+wave that now has the amplitude of twice
+
+ align:start position:0%
+wave that now has the amplitude of twice
+ 
+
+ align:start position:0%
+wave that now has the amplitude of twice
+the amplitude of each of those
+
+ align:start position:0%
+the amplitude of each of those
+ 
+
+ align:start position:0%
+the amplitude of each of those
+waves and that's the condition that we
+
+ align:start position:0%
+waves and that's the condition that we
+ 
+
+ align:start position:0%
+waves and that's the condition that we
+call constructive interference but we
+
+ align:start position:0%
+call constructive interference but we
+ 
+
+ align:start position:0%
+call constructive interference but we
+have to have the two waves at the same
+
+ align:start position:0%
+have to have the two waves at the same
+ 
+
+ align:start position:0%
+have to have the two waves at the same
+place and space and the two Maxima have
+
+ align:start position:0%
+place and space and the two Maxima have
+ 
+
+ align:start position:0%
+place and space and the two Maxima have
+to be in the exact same place in space
+
+ align:start position:0%
+to be in the exact same place in space
+ 
+
+ align:start position:0%
+to be in the exact same place in space
+but conversely we can also take the
+
+ align:start position:0%
+but conversely we can also take the
+ 
+
+ align:start position:0%
+but conversely we can also take the
+wave and um bring in another wave but we
+
+ align:start position:0%
+wave and um bring in another wave but we
+ 
+
+ align:start position:0%
+wave and um bring in another wave but we
+can move that other wave
+
+ align:start position:0%
+can move that other wave
+ 
+
+ align:start position:0%
+can move that other wave
+over such that the maximum of one of the
+
+ align:start position:0%
+over such that the maximum of one of the
+ 
+
+ align:start position:0%
+over such that the maximum of one of the
+waves is at the same place in space as
+
+ align:start position:0%
+waves is at the same place in space as
+ 
+
+ align:start position:0%
+waves is at the same place in space as
+the minimum of the other wave in this
+
+ align:start position:0%
+the minimum of the other wave in this
+ 
+
+ align:start position:0%
+the minimum of the other wave in this
+case these two waves are out of phase
+
+ align:start position:0%
+case these two waves are out of phase
+ 
+
+ align:start position:0%
+case these two waves are out of phase
+and when we add them up hey there'll be
+
+ align:start position:0%
+and when we add them up hey there'll be
+ 
+
+ align:start position:0%
+and when we add them up hey there'll be
+nothing this is destructive interference
+
+ align:start position:0%
+nothing this is destructive interference
+ 
+
+ align:start position:0%
+nothing this is destructive interference
+why well because we have positive
+
+ align:start position:0%
+why well because we have positive
+ 
+
+ align:start position:0%
+why well because we have positive
+amplitudes and negative amplitudes they
+
+ align:start position:0%
+amplitudes and negative amplitudes they
+ 
+
+ align:start position:0%
+amplitudes and negative amplitudes they
+cancel to give us nothing destructive
+
+ align:start position:0%
+cancel to give us nothing destructive
+ 
+
+ align:start position:0%
+cancel to give us nothing destructive
+interference okay and um there's a
+
+ align:start position:0%
+interference okay and um there's a
+ 
+
+ align:start position:0%
+interference okay and um there's a
+website here in the University of
+
+ align:start position:0%
+website here in the University of
+ 
+
+ align:start position:0%
+website here in the University of
+Colorado that
+
+ align:start position:0%
+Colorado that
+ 
+
+ align:start position:0%
+Colorado that
+uh lets you um take uh two waves and
+
+ align:start position:0%
+uh lets you um take uh two waves and
+ 
+
+ align:start position:0%
+uh lets you um take uh two waves and
+superimpose them could I uh I need to I
+
+ align:start position:0%
+superimpose them could I uh I need to I
+ 
+
+ align:start position:0%
+superimpose them could I uh I need to I
+need to play with it okay um
+
+ align:start position:0%
+need to play with it okay um
+ 
+
+ align:start position:0%
+need to play with it okay um
+that's all right I'm down here all right
+
+ align:start position:0%
+that's all right I'm down here all right
+ 
+
+ align:start position:0%
+that's all right I'm down here all right
+what I'm going to do is I'm going to um
+
+ align:start position:0%
+what I'm going to do is I'm going to um
+ 
+
+ align:start position:0%
+what I'm going to do is I'm going to um
+make it so that uh these two waves have
+
+ align:start position:0%
+make it so that uh these two waves have
+ 
+
+ align:start position:0%
+make it so that uh these two waves have
+the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequency and uh or the same wavelength
+
+ align:start position:0%
+frequency and uh or the same wavelength
+ 
+
+ align:start position:0%
+frequency and uh or the same wavelength
+and the same amplitude right so it's
+
+ align:start position:0%
+and the same amplitude right so it's
+ 
+
+ align:start position:0%
+and the same amplitude right so it's
+what I'm doing here is I'm adding this
+
+ align:start position:0%
+what I'm doing here is I'm adding this
+ 
+
+ align:start position:0%
+what I'm doing here is I'm adding this
+wave I'm adding this wave right here to
+
+ align:start position:0%
+wave I'm adding this wave right here to
+ 
+
+ align:start position:0%
+wave I'm adding this wave right here to
+this wave and the result is shown here
+
+ align:start position:0%
+this wave and the result is shown here
+ 
+
+ align:start position:0%
+this wave and the result is shown here
+and what you can't see is that the
+
+ align:start position:0%
+and what you can't see is that the
+ 
+
+ align:start position:0%
+and what you can't see is that the
+amplitude down here that amplitude is
+
+ align:start position:0%
+amplitude down here that amplitude is
+ 
+
+ align:start position:0%
+amplitude down here that amplitude is
+twice that of these two all right
+
+ align:start position:0%
+twice that of these two all right
+ 
+
+ align:start position:0%
+twice that of these two all right
+there's a two there but of course what I
+
+ align:start position:0%
+there's a two there but of course what I
+ 
+
+ align:start position:0%
+there's a two there but of course what I
+can do is I can move this wave
+
+ align:start position:0%
+can do is I can move this wave
+ 
+
+ align:start position:0%
+can do is I can move this wave
+over such that the two waves are now at
+
+ align:start position:0%
+over such that the two waves are now at
+ 
+
+ align:start position:0%
+over such that the two waves are now at
+the same place in space sort
+
+ align:start position:0%
+the same place in space sort
+ 
+
+ align:start position:0%
+the same place in space sort
+of uh where the maximum and the
+
+ align:start position:0%
+of uh where the maximum and the
+ 
+
+ align:start position:0%
+of uh where the maximum and the
+Minima are at the same place in space
+
+ align:start position:0%
+Minima are at the same place in space
+ 
+
+ align:start position:0%
+Minima are at the same place in space
+and exactly cancel them and I'm not
+
+ align:start position:0%
+and exactly cancel them and I'm not
+ 
+
+ align:start position:0%
+and exactly cancel them and I'm not
+having such a great time doing this here
+
+ align:start position:0%
+having such a great time doing this here
+ 
+
+ align:start position:0%
+having such a great time doing this here
+but I know you can do it because I've
+
+ align:start position:0%
+but I know you can do it because I've
+ 
+
+ align:start position:0%
+but I know you can do it because I've
+done it
+
+ align:start position:0%
+done it
+ 
+
+ align:start position:0%
+done it
+before okay and you can see that that
+
+ align:start position:0%
+before okay and you can see that that
+ 
+
+ align:start position:0%
+before okay and you can see that that
+the resulting amplitude is zero and of
+
+ align:start position:0%
+the resulting amplitude is zero and of
+ 
+
+ align:start position:0%
+the resulting amplitude is zero and of
+course then you can go home and you can
+
+ align:start position:0%
+course then you can go home and you can
+ 
+
+ align:start position:0%
+course then you can go home and you can
+play all you want with this make all
+
+ align:start position:0%
+play all you want with this make all
+ 
+
+ align:start position:0%
+play all you want with this make all
+kinds of different
+
+ align:start position:0%
+kinds of different
+ 
+
+ align:start position:0%
+kinds of different
+waveforms I'm trying to change the
+
+ align:start position:0%
+waveforms I'm trying to change the
+ 
+
+ align:start position:0%
+waveforms I'm trying to change the
+amplitude here it's I've done before but
+
+ align:start position:0%
+amplitude here it's I've done before but
+ 
+
+ align:start position:0%
+amplitude here it's I've done before but
+I can't right now grab the red grab the
+
+ align:start position:0%
+I can't right now grab the red grab the
+ 
+
+ align:start position:0%
+I can't right now grab the red grab the
+red ball Maybe
+
+ align:start position:0%
+red ball Maybe
+ 
+
+ align:start position:0%
+red ball Maybe
+all right but
+
+ align:start position:0%
+all right but
+ 
+
+ align:start position:0%
+all right but
+uh all right so you can do whatever
+
+ align:start position:0%
+uh all right so you can do whatever
+ 
+
+ align:start position:0%
+uh all right so you can do whatever
+waveform you want
+
+ align:start position:0%
+waveform you want
+ 
+
+ align:start position:0%
+waveform you want
+to all right so you get the idea here
+
+ align:start position:0%
+to all right so you get the idea here
+ 
+
+ align:start position:0%
+to all right so you get the idea here
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+superposition all right well let's uh so
+
+ align:start position:0%
+superposition all right well let's uh so
+ 
+
+ align:start position:0%
+superposition all right well let's uh so
+that's a characteristic of waves they
+
+ align:start position:0%
+that's a characteristic of waves they
+ 
+
+ align:start position:0%
+that's a characteristic of waves they
+have positive negative amplitudes they
+
+ align:start position:0%
+have positive negative amplitudes they
+ 
+
+ align:start position:0%
+have positive negative amplitudes they
+add and they cancel depending on the
+
+ align:start position:0%
+add and they cancel depending on the
+ 
+
+ align:start position:0%
+add and they cancel depending on the
+relative positions in
+
+ align:start position:0%
+relative positions in
+ 
+
+ align:start position:0%
+relative positions in
+space but now let's talk a little bit
+
+ align:start position:0%
+space but now let's talk a little bit
+ 
+
+ align:start position:0%
+space but now let's talk a little bit
+more about this uh pattern that we saw
+
+ align:start position:0%
+more about this uh pattern that we saw
+ 
+
+ align:start position:0%
+more about this uh pattern that we saw
+in the two slit experiment this kind of
+
+ align:start position:0%
+in the two slit experiment this kind of
+ 
+
+ align:start position:0%
+in the two slit experiment this kind of
+row of bright
+
+ align:start position:0%
+row of bright
+ 
+
+ align:start position:0%
+row of bright
+spots and to talk about it what we're
+
+ align:start position:0%
+spots and to talk about it what we're
+ 
+
+ align:start position:0%
+spots and to talk about it what we're
+going to do is we're going to use water
+
+ align:start position:0%
+going to do is we're going to use water
+ 
+
+ align:start position:0%
+going to do is we're going to use water
+waves to try to explain
+
+ align:start position:0%
+waves to try to explain
+ 
+
+ align:start position:0%
+waves to try to explain
+it so here's a picture of the
+
+ align:start position:0%
+it so here's a picture of the
+ 
+
+ align:start position:0%
+it so here's a picture of the
+beach here's the uh here's the water
+
+ align:start position:0%
+beach here's the uh here's the water
+ 
+
+ align:start position:0%
+beach here's the uh here's the water
+right here's the
+
+ align:start position:0%
+right here's the
+ 
+
+ align:start position:0%
+right here's the
+sand and here is where I wanted to be
+
+ align:start position:0%
+sand and here is where I wanted to be
+ 
+
+ align:start position:0%
+sand and here is where I wanted to be
+all weekend okay and the way waves are
+
+ align:start position:0%
+all weekend okay and the way waves are
+ 
+
+ align:start position:0%
+all weekend okay and the way waves are
+coming in here to the beach right these
+
+ align:start position:0%
+coming in here to the beach right these
+ 
+
+ align:start position:0%
+coming in here to the beach right these
+straight blue lines are the crests of
+
+ align:start position:0%
+straight blue lines are the crests of
+ 
+
+ align:start position:0%
+straight blue lines are the crests of
+the Waves rolling into the
+
+ align:start position:0%
+the Waves rolling into the
+ 
+
+ align:start position:0%
+the Waves rolling into the
+beach and suppose I get
+
+ align:start position:0%
+beach and suppose I get
+ 
+
+ align:start position:0%
+beach and suppose I get
+ambitious and I erect a barrier right
+
+ align:start position:0%
+ambitious and I erect a barrier right
+ 
+
+ align:start position:0%
+ambitious and I erect a barrier right
+here at the shore the sand
+
+ align:start position:0%
+here at the shore the sand
+ 
+
+ align:start position:0%
+here at the shore the sand
+barrier but for whatever perverse reason
+
+ align:start position:0%
+barrier but for whatever perverse reason
+ 
+
+ align:start position:0%
+barrier but for whatever perverse reason
+I poke two holes in that sand barrier
+
+ align:start position:0%
+I poke two holes in that sand barrier
+ 
+
+ align:start position:0%
+I poke two holes in that sand barrier
+okay well what's going to happen as the
+
+ align:start position:0%
+okay well what's going to happen as the
+ 
+
+ align:start position:0%
+okay well what's going to happen as the
+w waves roll up
+
+ align:start position:0%
+w waves roll up
+ 
+
+ align:start position:0%
+w waves roll up
+well what's going to happen is that a
+
+ align:start position:0%
+well what's going to happen is that a
+ 
+
+ align:start position:0%
+well what's going to happen is that a
+little bit of the wave here this is kind
+
+ align:start position:0%
+little bit of the wave here this is kind
+ 
+
+ align:start position:0%
+little bit of the wave here this is kind
+of like a pinhole a little bit of this
+
+ align:start position:0%
+of like a pinhole a little bit of this
+ 
+
+ align:start position:0%
+of like a pinhole a little bit of this
+wave is going to leak through when it
+
+ align:start position:0%
+wave is going to leak through when it
+ 
+
+ align:start position:0%
+wave is going to leak through when it
+leaks through it's going to spread out
+
+ align:start position:0%
+leaks through it's going to spread out
+ 
+
+ align:start position:0%
+leaks through it's going to spread out
+equally in all
+
+ align:start position:0%
+equally in all
+ 
+
+ align:start position:0%
+equally in all
+directions and so the wavefront is going
+
+ align:start position:0%
+directions and so the wavefront is going
+ 
+
+ align:start position:0%
+directions and so the wavefront is going
+to look like this semicircle here right
+
+ align:start position:0%
+to look like this semicircle here right
+ 
+
+ align:start position:0%
+to look like this semicircle here right
+that's the wave Crest it's going to look
+
+ align:start position:0%
+that's the wave Crest it's going to look
+ 
+
+ align:start position:0%
+that's the wave Crest it's going to look
+like a semicircle and that's going to
+
+ align:start position:0%
+like a semicircle and that's going to
+ 
+
+ align:start position:0%
+like a semicircle and that's going to
+propagate
+
+ align:start position:0%
+propagate
+ 
+
+ align:start position:0%
+propagate
+out and when it propagates out to a
+
+ align:start position:0%
+out and when it propagates out to a
+ 
+
+ align:start position:0%
+out and when it propagates out to a
+distance of two Lambda well then another
+
+ align:start position:0%
+distance of two Lambda well then another
+ 
+
+ align:start position:0%
+distance of two Lambda well then another
+wave has snuck in here through this hole
+
+ align:start position:0%
+wave has snuck in here through this hole
+ 
+
+ align:start position:0%
+wave has snuck in here through this hole
+and it propagates out and again the
+
+ align:start position:0%
+and it propagates out and again the
+ 
+
+ align:start position:0%
+and it propagates out and again the
+distance between these two semicircles
+
+ align:start position:0%
+distance between these two semicircles
+ 
+
+ align:start position:0%
+distance between these two semicircles
+is a Lambda is the wavelength because
+
+ align:start position:0%
+is a Lambda is the wavelength because
+ 
+
+ align:start position:0%
+is a Lambda is the wavelength because
+these are the Maxima of the two
+
+ align:start position:0%
+these are the Maxima of the two
+ 
+
+ align:start position:0%
+these are the Maxima of the two
+waves and as time goes on that
+
+ align:start position:0%
+waves and as time goes on that
+ 
+
+ align:start position:0%
+waves and as time goes on that
+propagates further and another wave
+
+ align:start position:0%
+propagates further and another wave
+ 
+
+ align:start position:0%
+propagates further and another wave
+sneaks through that hole and another
+
+ align:start position:0%
+sneaks through that hole and another
+ 
+
+ align:start position:0%
+sneaks through that hole and another
+wave sneaks through and the whole thing
+
+ align:start position:0%
+wave sneaks through and the whole thing
+ 
+
+ align:start position:0%
+wave sneaks through and the whole thing
+propagates all right and meanwhile while
+
+ align:start position:0%
+propagates all right and meanwhile while
+ 
+
+ align:start position:0%
+propagates all right and meanwhile while
+that is happening there's also a part of
+
+ align:start position:0%
+that is happening there's also a part of
+ 
+
+ align:start position:0%
+that is happening there's also a part of
+the wave sneaking through this hole and
+
+ align:start position:0%
+the wave sneaking through this hole and
+ 
+
+ align:start position:0%
+the wave sneaking through this hole and
+it emanates out in all directions and
+
+ align:start position:0%
+it emanates out in all directions and
+ 
+
+ align:start position:0%
+it emanates out in all directions and
+propagates out right in all
+
+ align:start position:0%
+propagates out right in all
+ 
+
+ align:start position:0%
+propagates out right in all
+directions and uh again all right and
+
+ align:start position:0%
+directions and uh again all right and
+ 
+
+ align:start position:0%
+directions and uh again all right and
+propagates out in all
+
+ align:start position:0%
+propagates out in all
+ 
+
+ align:start position:0%
+propagates out in all
+directions and let me for the purpose of
+
+ align:start position:0%
+directions and let me for the purpose of
+ 
+
+ align:start position:0%
+directions and let me for the purpose of
+uh talking about this let me call this
+
+ align:start position:0%
+uh talking about this let me call this
+ 
+
+ align:start position:0%
+uh talking about this let me call this
+slit slit one
+
+ align:start position:0%
+slit slit one
+ 
+
+ align:start position:0%
+slit slit one
+so all the green
+
+ align:start position:0%
+so all the green
+ 
+
+ align:start position:0%
+so all the green
+waves are the waves that came through
+
+ align:start position:0%
+waves are the waves that came through
+ 
+
+ align:start position:0%
+waves are the waves that came through
+slit one and I'm going to call this slit
+
+ align:start position:0%
+slit one and I'm going to call this slit
+ 
+
+ align:start position:0%
+slit one and I'm going to call this slit
+two and all the blue waves are the waves
+
+ align:start position:0%
+two and all the blue waves are the waves
+ 
+
+ align:start position:0%
+two and all the blue waves are the waves
+that came out slit two and
+
+ align:start position:0%
+that came out slit two and
+ 
+
+ align:start position:0%
+that came out slit two and
+again the uh distance between any of
+
+ align:start position:0%
+again the uh distance between any of
+ 
+
+ align:start position:0%
+again the uh distance between any of
+these two crests is the wavelength and
+
+ align:start position:0%
+these two crests is the wavelength and
+ 
+
+ align:start position:0%
+these two crests is the wavelength and
+the wavelength is the same for the waves
+
+ align:start position:0%
+the wavelength is the same for the waves
+ 
+
+ align:start position:0%
+the wavelength is the same for the waves
+coming from slit one and slit
+
+ align:start position:0%
+coming from slit one and slit
+ 
+
+ align:start position:0%
+coming from slit one and slit
+two now what I want you to do is I want
+
+ align:start position:0%
+two now what I want you to do is I want
+ 
+
+ align:start position:0%
+two now what I want you to do is I want
+you to look at this point right here see
+
+ align:start position:0%
+you to look at this point right here see
+ 
+
+ align:start position:0%
+you to look at this point right here see
+that point
+
+ align:start position:0%
+that point
+ 
+
+ align:start position:0%
+that point
+Point well right at that point what we
+
+ align:start position:0%
+Point well right at that point what we
+ 
+
+ align:start position:0%
+Point well right at that point what we
+have is we've got the wave Crest the
+
+ align:start position:0%
+have is we've got the wave Crest the
+ 
+
+ align:start position:0%
+have is we've got the wave Crest the
+wave maximum from slit two at the same
+
+ align:start position:0%
+wave maximum from slit two at the same
+ 
+
+ align:start position:0%
+wave maximum from slit two at the same
+point in space as the wave Maxima from
+
+ align:start position:0%
+point in space as the wave Maxima from
+ 
+
+ align:start position:0%
+point in space as the wave Maxima from
+slit one so if we've got two Maxima at
+
+ align:start position:0%
+slit one so if we've got two Maxima at
+ 
+
+ align:start position:0%
+slit one so if we've got two Maxima at
+the same point in space hey we got
+
+ align:start position:0%
+the same point in space hey we got
+ 
+
+ align:start position:0%
+the same point in space hey we got
+constructive interference right there
+
+ align:start position:0%
+constructive interference right there
+ 
+
+ align:start position:0%
+constructive interference right there
+right because those amplitudes are going
+
+ align:start position:0%
+right because those amplitudes are going
+ 
+
+ align:start position:0%
+right because those amplitudes are going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+add look at this point well again we got
+
+ align:start position:0%
+add look at this point well again we got
+ 
+
+ align:start position:0%
+add look at this point well again we got
+the wave Maxima from this Blue Wave
+
+ align:start position:0%
+the wave Maxima from this Blue Wave
+ 
+
+ align:start position:0%
+the wave Maxima from this Blue Wave
+coming through slit 2 at the same point
+
+ align:start position:0%
+coming through slit 2 at the same point
+ 
+
+ align:start position:0%
+coming through slit 2 at the same point
+in space as the wave Maxima from the
+
+ align:start position:0%
+in space as the wave Maxima from the
+ 
+
+ align:start position:0%
+in space as the wave Maxima from the
+wave coming from slit one again this is
+
+ align:start position:0%
+wave coming from slit one again this is
+ 
+
+ align:start position:0%
+wave coming from slit one again this is
+a point of constructive
+
+ align:start position:0%
+a point of constructive
+ 
+
+ align:start position:0%
+a point of constructive
+interference and we can keep going again
+
+ align:start position:0%
+interference and we can keep going again
+ 
+
+ align:start position:0%
+interference and we can keep going again
+we have two Maxima right here a point of
+
+ align:start position:0%
+we have two Maxima right here a point of
+ 
+
+ align:start position:0%
+we have two Maxima right here a point of
+constructive interference and you know
+
+ align:start position:0%
+constructive interference and you know
+ 
+
+ align:start position:0%
+constructive interference and you know
+what everywhere along this line we're
+
+ align:start position:0%
+what everywhere along this line we're
+ 
+
+ align:start position:0%
+what everywhere along this line we're
+going to have constructive interference
+
+ align:start position:0%
+going to have constructive interference
+ 
+
+ align:start position:0%
+going to have constructive interference
+we're going to have a resultant wave a
+
+ align:start position:0%
+we're going to have a resultant wave a
+ 
+
+ align:start position:0%
+we're going to have a resultant wave a
+water wave that's going to be twice as
+
+ align:start position:0%
+water wave that's going to be twice as
+ 
+
+ align:start position:0%
+water wave that's going to be twice as
+high right
+
+ align:start position:0%
+high right
+ 
+
+ align:start position:0%
+high right
+as each of the individual
+
+ align:start position:0%
+as each of the individual
+ 
+
+ align:start position:0%
+as each of the individual
+waves look at this okay and what I want
+
+ align:start position:0%
+waves look at this okay and what I want
+ 
+
+ align:start position:0%
+waves look at this okay and what I want
+you to notice here for this point all
+
+ align:start position:0%
+you to notice here for this point all
+ 
+
+ align:start position:0%
+you to notice here for this point all
+right for this point the wave that is
+
+ align:start position:0%
+right for this point the wave that is
+ 
+
+ align:start position:0%
+right for this point the wave that is
+constructively
+
+ align:start position:0%
+constructively
+ 
+
+ align:start position:0%
+constructively
+interfering that has traveled from the
+
+ align:start position:0%
+interfering that has traveled from the
+ 
+
+ align:start position:0%
+interfering that has traveled from the
+slit a distance R2 because this is slit
+
+ align:start position:0%
+slit a distance R2 because this is slit
+ 
+
+ align:start position:0%
+slit a distance R2 because this is slit
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+but the distance from here to here is
+
+ align:start position:0%
+but the distance from here to here is
+ 
+
+ align:start position:0%
+but the distance from here to here is
+four Lambda right it's one Lambda 2
+
+ align:start position:0%
+four Lambda right it's one Lambda 2
+ 
+
+ align:start position:0%
+four Lambda right it's one Lambda 2
+Lambda 3 Lambda 4 Lambda right the
+
+ align:start position:0%
+Lambda 3 Lambda 4 Lambda right the
+ 
+
+ align:start position:0%
+Lambda 3 Lambda 4 Lambda right the
+radius R2 of this circle is four
+
+ align:start position:0%
+radius R2 of this circle is four
+ 
+
+ align:start position:0%
+radius R2 of this circle is four
+Lambda and it is interfering with this
+
+ align:start position:0%
+Lambda and it is interfering with this
+ 
+
+ align:start position:0%
+Lambda and it is interfering with this
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+Crest and the distance that that wave
+
+ align:start position:0%
+Crest and the distance that that wave
+ 
+
+ align:start position:0%
+Crest and the distance that that wave
+traveled from slit one I'm going to call
+
+ align:start position:0%
+traveled from slit one I'm going to call
+ 
+
+ align:start position:0%
+traveled from slit one I'm going to call
+R1 and that's equal to three Lambda 1 2
+
+ align:start position:0%
+R1 and that's equal to three Lambda 1 2
+ 
+
+ align:start position:0%
+R1 and that's equal to three Lambda 1 2
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay so the this interference here is
+
+ align:start position:0%
+okay so the this interference here is
+ 
+
+ align:start position:0%
+okay so the this interference here is
+between this wave that's traveled out a
+
+ align:start position:0%
+between this wave that's traveled out a
+ 
+
+ align:start position:0%
+between this wave that's traveled out a
+distance for Lambda and this wave that's
+
+ align:start position:0%
+distance for Lambda and this wave that's
+ 
+
+ align:start position:0%
+distance for Lambda and this wave that's
+traveled out a distance three Lambda and
+
+ align:start position:0%
+traveled out a distance three Lambda and
+ 
+
+ align:start position:0%
+traveled out a distance three Lambda and
+the difference in the distance traveled
+
+ align:start position:0%
+the difference in the distance traveled
+ 
+
+ align:start position:0%
+the difference in the distance traveled
+by those two waves that are
+
+ align:start position:0%
+by those two waves that are
+ 
+
+ align:start position:0%
+by those two waves that are
+constructively interfering is 4 Lambda
+
+ align:start position:0%
+constructively interfering is 4 Lambda
+ 
+
+ align:start position:0%
+constructively interfering is 4 Lambda
+minus 3 Lambda = 1
+
+ align:start position:0%
+minus 3 Lambda = 1
+ 
+
+ align:start position:0%
+minus 3 Lambda = 1
+Lambda okay is there a question over
+
+ align:start position:0%
+Lambda okay is there a question over
+ 
+
+ align:start position:0%
+Lambda okay is there a question over
+here yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay H I think I'm coming to that that's
+
+ align:start position:0%
+okay H I think I'm coming to that that's
+ 
+
+ align:start position:0%
+okay H I think I'm coming to that that's
+was a snapshot of the next slide okay
+
+ align:start position:0%
+was a snapshot of the next slide okay
+ 
+
+ align:start position:0%
+was a snapshot of the next slide okay
+sorry all right yes how do you know the
+
+ align:start position:0%
+sorry all right yes how do you know the
+ 
+
+ align:start position:0%
+sorry all right yes how do you know the
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+one because um we are treating these as
+
+ align:start position:0%
+one because um we are treating these as
+ 
+
+ align:start position:0%
+one because um we are treating these as
+regular waves okay ordered waves real
+
+ align:start position:0%
+regular waves okay ordered waves real
+ 
+
+ align:start position:0%
+regular waves okay ordered waves real
+waves on an ocean aren't like that okay
+
+ align:start position:0%
+waves on an ocean aren't like that okay
+ 
+
+ align:start position:0%
+waves on an ocean aren't like that okay
+and then you won't see this defraction
+
+ align:start position:0%
+and then you won't see this defraction
+ 
+
+ align:start position:0%
+and then you won't see this defraction
+pattern that uh I'm ere ing here but if
+
+ align:start position:0%
+pattern that uh I'm ere ing here but if
+ 
+
+ align:start position:0%
+pattern that uh I'm ere ing here but if
+you had pretty regular waves coming in
+
+ align:start position:0%
+you had pretty regular waves coming in
+ 
+
+ align:start position:0%
+you had pretty regular waves coming in
+in principle you could see it and I'm
+
+ align:start position:0%
+in principle you could see it and I'm
+ 
+
+ align:start position:0%
+in principle you could see it and I'm
+going to show you a a a um a uh in a in
+
+ align:start position:0%
+going to show you a a a um a uh in a in
+ 
+
+ align:start position:0%
+going to show you a a a um a uh in a in
+a tank some water waves that do just
+
+ align:start position:0%
+a tank some water waves that do just
+ 
+
+ align:start position:0%
+a tank some water waves that do just
+this okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right now I want you to look at
+
+ align:start position:0%
+okay all right now I want you to look at
+ 
+
+ align:start position:0%
+okay all right now I want you to look at
+this point right here all right right
+
+ align:start position:0%
+this point right here all right right
+ 
+
+ align:start position:0%
+this point right here all right right
+here we have a point of constructive
+
+ align:start position:0%
+here we have a point of constructive
+ 
+
+ align:start position:0%
+here we have a point of constructive
+interference because we have two Maxima
+
+ align:start position:0%
+interference because we have two Maxima
+ 
+
+ align:start position:0%
+interference because we have two Maxima
+at the same point in space
+
+ align:start position:0%
+at the same point in space
+ 
+
+ align:start position:0%
+at the same point in space
+and at this point we've got constructive
+
+ align:start position:0%
+and at this point we've got constructive
+ 
+
+ align:start position:0%
+and at this point we've got constructive
+interference so everywhere along this
+
+ align:start position:0%
+interference so everywhere along this
+ 
+
+ align:start position:0%
+interference so everywhere along this
+line here we're going to have
+
+ align:start position:0%
+line here we're going to have
+ 
+
+ align:start position:0%
+line here we're going to have
+constructive
+
+ align:start position:0%
+constructive
+ 
+
+ align:start position:0%
+constructive
+interference and now I want you to look
+
+ align:start position:0%
+interference and now I want you to look
+ 
+
+ align:start position:0%
+interference and now I want you to look
+at the difference in the distance of the
+
+ align:start position:0%
+at the difference in the distance of the
+ 
+
+ align:start position:0%
+at the difference in the distance of the
+waves that yield this constructive
+
+ align:start position:0%
+waves that yield this constructive
+ 
+
+ align:start position:0%
+waves that yield this constructive
+interference along this line
+
+ align:start position:0%
+interference along this line
+ 
+
+ align:start position:0%
+interference along this line
+okay I want you to look at this Green
+
+ align:start position:0%
+okay I want you to look at this Green
+ 
+
+ align:start position:0%
+okay I want you to look at this Green
+Wave this Green Wave
+
+ align:start position:0%
+Wave this Green Wave
+ 
+
+ align:start position:0%
+Wave this Green Wave
+that's constructively interfering with
+
+ align:start position:0%
+that's constructively interfering with
+ 
+
+ align:start position:0%
+that's constructively interfering with
+this Blue Wave this Green Wave has
+
+ align:start position:0%
+this Blue Wave this Green Wave has
+ 
+
+ align:start position:0%
+this Blue Wave this Green Wave has
+traveled out a distance R1 or 2
+
+ align:start position:0%
+traveled out a distance R1 or 2
+ 
+
+ align:start position:0%
+traveled out a distance R1 or 2
+Lambda and it is interfering with this
+
+ align:start position:0%
+Lambda and it is interfering with this
+ 
+
+ align:start position:0%
+Lambda and it is interfering with this
+uh Blue Wave here that has traveled out
+
+ align:start position:0%
+uh Blue Wave here that has traveled out
+ 
+
+ align:start position:0%
+uh Blue Wave here that has traveled out
+a distance for Lambda R2 equal 4
+
+ align:start position:0%
+a distance for Lambda R2 equal 4
+ 
+
+ align:start position:0%
+a distance for Lambda R2 equal 4
+Lambda so the difference in the distance
+
+ align:start position:0%
+Lambda so the difference in the distance
+ 
+
+ align:start position:0%
+Lambda so the difference in the distance
+travel for all of these points that lead
+
+ align:start position:0%
+travel for all of these points that lead
+ 
+
+ align:start position:0%
+travel for all of these points that lead
+to constructive interference the
+
+ align:start position:0%
+to constructive interference the
+ 
+
+ align:start position:0%
+to constructive interference the
+difference in the distance traveled here
+
+ align:start position:0%
+difference in the distance traveled here
+ 
+
+ align:start position:0%
+difference in the distance traveled here
+is is R2 -
+
+ align:start position:0%
+is is R2 -
+ 
+
+ align:start position:0%
+is is R2 -
+R1 or 4 Lambda minus 2 Lambda equal 2
+
+ align:start position:0%
+R1 or 4 Lambda minus 2 Lambda equal 2
+ 
+
+ align:start position:0%
+R1 or 4 Lambda minus 2 Lambda equal 2
+Lambda does that agree with the snapshot
+
+ align:start position:0%
+Lambda does that agree with the snapshot
+ 
+
+ align:start position:0%
+Lambda does that agree with the snapshot
+in your
+
+ align:start position:0%
+in your
+ 
+
+ align:start position:0%
+in your
+picture yes okay I just didn't show you
+
+ align:start position:0%
+picture yes okay I just didn't show you
+ 
+
+ align:start position:0%
+picture yes okay I just didn't show you
+the U uh other one
+
+ align:start position:0%
+the U uh other one
+ 
+
+ align:start position:0%
+the U uh other one
+okay all
+
+ align:start position:0%
+okay all
+ 
+
+ align:start position:0%
+okay all
+right now I want you to look here here's
+
+ align:start position:0%
+right now I want you to look here here's
+ 
+
+ align:start position:0%
+right now I want you to look here here's
+a point of constructive
+
+ align:start position:0%
+a point of constructive
+ 
+
+ align:start position:0%
+a point of constructive
+interference here's another point of
+
+ align:start position:0%
+interference here's another point of
+ 
+
+ align:start position:0%
+interference here's another point of
+constructive
+
+ align:start position:0%
+constructive
+ 
+
+ align:start position:0%
+constructive
+interference everywhere along this line
+
+ align:start position:0%
+interference everywhere along this line
+ 
+
+ align:start position:0%
+interference everywhere along this line
+we're going to have constructive
+
+ align:start position:0%
+we're going to have constructive
+ 
+
+ align:start position:0%
+we're going to have constructive
+interference and if we check out what
+
+ align:start position:0%
+interference and if we check out what
+ 
+
+ align:start position:0%
+interference and if we check out what
+the difference in the distance traveled
+
+ align:start position:0%
+the difference in the distance traveled
+ 
+
+ align:start position:0%
+the difference in the distance traveled
+is between the waves that are
+
+ align:start position:0%
+is between the waves that are
+ 
+
+ align:start position:0%
+is between the waves that are
+constructively interfering there you're
+
+ align:start position:0%
+constructively interfering there you're
+ 
+
+ align:start position:0%
+constructively interfering there you're
+going to see that R2 minus R1 is equal
+
+ align:start position:0%
+going to see that R2 minus R1 is equal
+ 
+
+ align:start position:0%
+going to see that R2 minus R1 is equal
+to zero all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right all right now so what you would
+
+ align:start position:0%
+right all right now so what you would
+ 
+
+ align:start position:0%
+right all right now so what you would
+predict is we'd have along this angle
+
+ align:start position:0%
+predict is we'd have along this angle
+ 
+
+ align:start position:0%
+predict is we'd have along this angle
+some very bright spots along this angle
+
+ align:start position:0%
+some very bright spots along this angle
+ 
+
+ align:start position:0%
+some very bright spots along this angle
+some very bright spots and along this
+
+ align:start position:0%
+some very bright spots and along this
+ 
+
+ align:start position:0%
+some very bright spots and along this
+angle some very bright spots and you
+
+ align:start position:0%
+angle some very bright spots and you
+ 
+
+ align:start position:0%
+angle some very bright spots and you
+also can see that there is going to be
+
+ align:start position:0%
+also can see that there is going to be
+ 
+
+ align:start position:0%
+also can see that there is going to be
+symmetric about the center so you would
+
+ align:start position:0%
+symmetric about the center so you would
+ 
+
+ align:start position:0%
+symmetric about the center so you would
+have bright spots here bright spots
+
+ align:start position:0%
+have bright spots here bright spots
+ 
+
+ align:start position:0%
+have bright spots here bright spots
+there well let's look at this uh in real
+
+ align:start position:0%
+there well let's look at this uh in real
+ 
+
+ align:start position:0%
+there well let's look at this uh in real
+life in a water tank where we have waves
+
+ align:start position:0%
+life in a water tank where we have waves
+ 
+
+ align:start position:0%
+life in a water tank where we have waves
+uh there you go where we have waves
+
+ align:start position:0%
+uh there you go where we have waves
+ 
+
+ align:start position:0%
+uh there you go where we have waves
+plane waves coming in to a barrier and
+
+ align:start position:0%
+plane waves coming in to a barrier and
+ 
+
+ align:start position:0%
+plane waves coming in to a barrier and
+then we have two little slits like right
+
+ align:start position:0%
+then we have two little slits like right
+ 
+
+ align:start position:0%
+then we have two little slits like right
+there and right there and what you can
+
+ align:start position:0%
+there and right there and what you can
+ 
+
+ align:start position:0%
+there and right there and what you can
+see is that these bright semi circles
+
+ align:start position:0%
+see is that these bright semi circles
+ 
+
+ align:start position:0%
+see is that these bright semi circles
+well well those are in fact the crests
+
+ align:start position:0%
+well well those are in fact the crests
+ 
+
+ align:start position:0%
+well well those are in fact the crests
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+waves but what I want you to see is
+
+ align:start position:0%
+waves but what I want you to see is
+ 
+
+ align:start position:0%
+waves but what I want you to see is
+right here whoops what happened oh okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all
+
+ align:start position:0%
+okay all
+ 
+
+ align:start position:0%
+okay all
+right there you go okay what I want you
+
+ align:start position:0%
+right there you go okay what I want you
+ 
+
+ align:start position:0%
+right there you go okay what I want you
+to see is right here these are the
+
+ align:start position:0%
+to see is right here these are the
+ 
+
+ align:start position:0%
+to see is right here these are the
+bright this bright row here's a bright
+
+ align:start position:0%
+bright this bright row here's a bright
+ 
+
+ align:start position:0%
+bright this bright row here's a bright
+row here's a bright row and in between
+
+ align:start position:0%
+row here's a bright row and in between
+ 
+
+ align:start position:0%
+row here's a bright row and in between
+there's kind of just a muddy a diffuse
+
+ align:start position:0%
+there's kind of just a muddy a diffuse
+ 
+
+ align:start position:0%
+there's kind of just a muddy a diffuse
+pattern well this diffuse pattern is
+
+ align:start position:0%
+pattern well this diffuse pattern is
+ 
+
+ align:start position:0%
+pattern well this diffuse pattern is
+nothing this is a bright row
+
+ align:start position:0%
+nothing this is a bright row
+ 
+
+ align:start position:0%
+nothing this is a bright row
+okay okay that's all
+
+ align:start position:0%
+okay okay that's all
+ 
+
+ align:start position:0%
+okay okay that's all
+right all right but you get the idea
+
+ align:start position:0%
+right all right but you get the idea
+ 
+
+ align:start position:0%
+right all right but you get the idea
+right you're going to have an angle
+
+ align:start position:0%
+right you're going to have an angle
+ 
+
+ align:start position:0%
+right you're going to have an angle
+which there's going to be constructive
+
+ align:start position:0%
+which there's going to be constructive
+ 
+
+ align:start position:0%
+which there's going to be constructive
+interference several angles of which
+
+ align:start position:0%
+interference several angles of which
+ 
+
+ align:start position:0%
+interference several angles of which
+they're going to be constructive
+
+ align:start position:0%
+they're going to be constructive
+ 
+
+ align:start position:0%
+they're going to be constructive
+interference and in between those places
+
+ align:start position:0%
+interference and in between those places
+ 
+
+ align:start position:0%
+interference and in between those places
+where there's constructive interference
+
+ align:start position:0%
+where there's constructive interference
+ 
+
+ align:start position:0%
+where there's constructive interference
+there's destructive interference and
+
+ align:start position:0%
+there's destructive interference and
+ 
+
+ align:start position:0%
+there's destructive interference and
+you're not going to have any
+
+ align:start position:0%
+you're not going to have any
+ 
+
+ align:start position:0%
+you're not going to have any
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+okay so how does
+
+ align:start position:0%
+okay so how does
+ 
+
+ align:start position:0%
+okay so how does
+that how does that relate to what we saw
+
+ align:start position:0%
+that how does that relate to what we saw
+ 
+
+ align:start position:0%
+that how does that relate to what we saw
+in the two slit defraction
+
+ align:start position:0%
+in the two slit defraction
+ 
+
+ align:start position:0%
+in the two slit defraction
+experiment well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+along this
+
+ align:start position:0%
+along this
+ 
+
+ align:start position:0%
+along this
+line we have waves that have
+
+ align:start position:0%
+line we have waves that have
+ 
+
+ align:start position:0%
+line we have waves that have
+constructively
+
+ align:start position:0%
+constructively
+ 
+
+ align:start position:0%
+constructively
+interfered and they constructively
+
+ align:start position:0%
+interfered and they constructively
+ 
+
+ align:start position:0%
+interfered and they constructively
+interfere so that on the screen right
+
+ align:start position:0%
+interfere so that on the screen right
+ 
+
+ align:start position:0%
+interfere so that on the screen right
+there you have a bright
+
+ align:start position:0%
+there you have a bright
+ 
+
+ align:start position:0%
+there you have a bright
+spot and along this line the difference
+
+ align:start position:0%
+spot and along this line the difference
+ 
+
+ align:start position:0%
+spot and along this line the difference
+in the distance traveled by the waves
+
+ align:start position:0%
+in the distance traveled by the waves
+ 
+
+ align:start position:0%
+in the distance traveled by the waves
+that it constructively interfere is one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda and then we've got another row or
+
+ align:start position:0%
+Lambda and then we've got another row or
+ 
+
+ align:start position:0%
+Lambda and then we've got another row or
+another line
+
+ align:start position:0%
+another line
+ 
+
+ align:start position:0%
+another line
+points of constructive interference
+
+ align:start position:0%
+points of constructive interference
+ 
+
+ align:start position:0%
+points of constructive interference
+that's going to image as a bright
+
+ align:start position:0%
+that's going to image as a bright
+ 
+
+ align:start position:0%
+that's going to image as a bright
+spot and if you analyze that the
+
+ align:start position:0%
+spot and if you analyze that the
+ 
+
+ align:start position:0%
+spot and if you analyze that the
+difference in the distance traveled by
+
+ align:start position:0%
+difference in the distance traveled by
+ 
+
+ align:start position:0%
+difference in the distance traveled by
+these two waves is 2
+
+ align:start position:0%
+these two waves is 2
+ 
+
+ align:start position:0%
+these two waves is 2
+Lambda and then we're going to have
+
+ align:start position:0%
+Lambda and then we're going to have
+ 
+
+ align:start position:0%
+Lambda and then we're going to have
+another bright spot here right for all
+
+ align:start position:0%
+another bright spot here right for all
+ 
+
+ align:start position:0%
+another bright spot here right for all
+the constructive interference along this
+
+ align:start position:0%
+the constructive interference along this
+ 
+
+ align:start position:0%
+the constructive interference along this
+line the difference in the distance
+
+ align:start position:0%
+line the difference in the distance
+ 
+
+ align:start position:0%
+line the difference in the distance
+traveled is zero and of course I said
+
+ align:start position:0%
+traveled is zero and of course I said
+ 
+
+ align:start position:0%
+traveled is zero and of course I said
+before this was symmetric around the
+
+ align:start position:0%
+before this was symmetric around the
+ 
+
+ align:start position:0%
+before this was symmetric around the
+center and so this is what gives rise to
+
+ align:start position:0%
+center and so this is what gives rise to
+ 
+
+ align:start position:0%
+center and so this is what gives rise to
+the different bright spots on the screen
+
+ align:start position:0%
+the different bright spots on the screen
+ 
+
+ align:start position:0%
+the different bright spots on the screen
+when we did the two slit experiment
+
+ align:start position:0%
+when we did the two slit experiment
+ 
+
+ align:start position:0%
+when we did the two slit experiment
+bright
+
+ align:start position:0%
+bright
+ 
+
+ align:start position:0%
+bright
+spot dark spot bright spot dark
+
+ align:start position:0%
+spot dark spot bright spot dark
+ 
+
+ align:start position:0%
+spot dark spot bright spot dark
+spot okay the bright spots are
+
+ align:start position:0%
+spot okay the bright spots are
+ 
+
+ align:start position:0%
+spot okay the bright spots are
+constructive
+
+ align:start position:0%
+constructive
+ 
+
+ align:start position:0%
+constructive
+interference the dark spots here are
+
+ align:start position:0%
+interference the dark spots here are
+ 
+
+ align:start position:0%
+interference the dark spots here are
+destructive
+
+ align:start position:0%
+destructive
+ 
+
+ align:start position:0%
+destructive
+interference
+
+ align:start position:0%
+interference
+ 
+
+ align:start position:0%
+interference
+okay now let me just tell you you that
+
+ align:start position:0%
+okay now let me just tell you you that
+ 
+
+ align:start position:0%
+okay now let me just tell you you that
+the general condition for having these
+
+ align:start position:0%
+the general condition for having these
+ 
+
+ align:start position:0%
+the general condition for having these
+bright
+
+ align:start position:0%
+bright
+ 
+
+ align:start position:0%
+bright
+spots the general condition that has to
+
+ align:start position:0%
+spots the general condition that has to
+ 
+
+ align:start position:0%
+spots the general condition that has to
+obtain is that the difference in the
+
+ align:start position:0%
+obtain is that the difference in the
+ 
+
+ align:start position:0%
+obtain is that the difference in the
+distance traveled has to be equal to n
+
+ align:start position:0%
+distance traveled has to be equal to n
+ 
+
+ align:start position:0%
+distance traveled has to be equal to n
+in integer times Lambda right this
+
+ align:start position:0%
+in integer times Lambda right this
+ 
+
+ align:start position:0%
+in integer times Lambda right this
+Bright Spot the Difference in the
+
+ align:start position:0%
+Bright Spot the Difference in the
+ 
+
+ align:start position:0%
+Bright Spot the Difference in the
+distance traveled then is zero we call
+
+ align:start position:0%
+distance traveled then is zero we call
+ 
+
+ align:start position:0%
+distance traveled then is zero we call
+that the zero order spot this Bright
+
+ align:start position:0%
+that the zero order spot this Bright
+ 
+
+ align:start position:0%
+that the zero order spot this Bright
+Spot the Difference in the distance
+
+ align:start position:0%
+Spot the Difference in the distance
+ 
+
+ align:start position:0%
+Spot the Difference in the distance
+traveled is land lamb or n * Lambda
+
+ align:start position:0%
+traveled is land lamb or n * Lambda
+ 
+
+ align:start position:0%
+traveled is land lamb or n * Lambda
+where n is one first order interference
+
+ align:start position:0%
+where n is one first order interference
+ 
+
+ align:start position:0%
+where n is one first order interference
+feature here the difference in the
+
+ align:start position:0%
+feature here the difference in the
+ 
+
+ align:start position:0%
+feature here the difference in the
+distance traveled is 2 Lambda n * 2
+
+ align:start position:0%
+distance traveled is 2 Lambda n * 2
+ 
+
+ align:start position:0%
+distance traveled is 2 Lambda n * 2
+called the second order interference
+
+ align:start position:0%
+called the second order interference
+ 
+
+ align:start position:0%
+called the second order interference
+feature and the condition for that is
+
+ align:start position:0%
+feature and the condition for that is
+ 
+
+ align:start position:0%
+feature and the condition for that is
+this R2 - R1 equal n *
+
+ align:start position:0%
+this R2 - R1 equal n *
+ 
+
+ align:start position:0%
+this R2 - R1 equal n *
+Lambda there is also a condition for
+
+ align:start position:0%
+Lambda there is also a condition for
+ 
+
+ align:start position:0%
+Lambda there is also a condition for
+destructive
+
+ align:start position:0%
+destructive
+ 
+
+ align:start position:0%
+destructive
+interference which I ask you to think
+
+ align:start position:0%
+interference which I ask you to think
+ 
+
+ align:start position:0%
+interference which I ask you to think
+about and we'll talk just briefly about
+
+ align:start position:0%
+about and we'll talk just briefly about
+ 
+
+ align:start position:0%
+about and we'll talk just briefly about
+its origin next time all right see you
+
+ align:start position:0%
+its origin next time all right see you
+ 
+
+ align:start position:0%
+its origin next time all right see you
+on Wednesday
\ No newline at end of file
diff --git a/_SxMjq1_RrI.txt b/_SxMjq1_RrI.txt
new file mode 100644
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+
+PROFESSOR: OK, so let's move
+into are our topic for the day.
+
+So we've got a couple of things.
+
+We're going to talk a little
+bit about In a Silent Way.
+
+And then I want to
+have us have a chance
+
+to present what
+you have created.
+
+And we'll see how this goes.
+
+So this is pretty much, at least
+in the second part, unknown.
+
+We don't know what's
+going to happen.
+
+So it should be interesting.
+
+But in terms of In
+a Silent Way, did
+
+everybody get to listen to that?
+
+And what do you make of
+that composition, called
+
+In a Silent Way by Miles Davis?
+
+What do you make of that?
+
+What did you hear happening?
+
+AUDIENCE: It seemed modal, so it
+didn't have any definite chord
+
+changes, which I think
+gave it sort of like a,
+
+like, spacey
+ambiguous feel to it.
+
+PROFESSOR: OK.
+
+Good.
+
+Modal, spacey, ambiguous.
+
+Anybody else?
+
+AUDIENCE: A lot of the melody
+and things were also ambiguous.
+
+There were a few clear
+themes that would repeat,
+
+but there was a
+lot of just sounds.
+
+That was cool.
+
+PROFESSOR: Sounds, OK.
+
+AUDIENCE: The instrumentation
+was just very different
+
+from the other Miles Davis
+pieces we'd listened to,
+
+and the style and
+everything, like it being
+
+so like a slow, laid-back,
+almost free-flowing piece,
+
+with a more I guess like
+electronic feel to it.
+
+But that was interesting.
+
+PROFESSOR: Right.
+
+And because, what were
+some of the accompanying
+
+instruments in this?
+
+AUDIENCE: It sounded maybe
+like a synth, I want to say.
+
+Was that a synth?
+
+PROFESSOR: Fender Rhodes.
+
+Actually, two
+Fender Rhodes piano,
+
+which is sort of old school.
+
+But you see these around a lot.
+
+In fact, we have
+one at MIT, which
+
+the current pianist
+with the FJE likes
+
+to call it out and play it.
+
+So that's great.
+
+And somebody playing the
+organ, as well as that.
+
+What else?
+
+What else did you
+hear, instruments?
+
+AUDIENCE: How prominent
+the instruments
+
+were to one another was more
+uniform than the recordings
+
+we've listened to.
+
+PROFESSOR: Meaning?
+
+AUDIENCE: Like, it's not like
+that obviously the trumpet
+
+had the lead the whole time.
+
+PROFESSOR: Right.
+
+So a lot more diversity
+of who is sort of
+
+in the lead and
+that kind of thing.
+
+Was it only that sort of
+ambiguous free floating sound?
+
+Was it only that, are
+did it do something else?
+
+AUDIENCE: Well, after a
+few minutes [INAUDIBLE]
+
+PROFESSOR: OK, a regular beat.
+
+And what was the
+rhythmic feel there?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: But I mean,
+was it jazz, was it--
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Percussive.
+
+OK.
+
+Anybody else have
+a term that could
+
+characterize what it went into?
+
+We all heard the piece, right?
+
+And it was a fairly
+long piece, right,
+
+like about 20 minute piece?
+
+OK.
+
+I was sure you would catch this.
+
+It goes into essentially
+a rock kind of a feel.
+
+It's a more subtle
+rock feel than what
+
+you would have heard from
+a rock band in that period.
+
+But nonetheless, that's
+what it's going to.
+
+This became sort of
+the signature piece
+
+that moved jazz into what was
+called jazz rock or fusion.
+
+In 1969 is when this came out.
+
+And in fact, this middle
+part is the longest part
+
+of the whole piece.
+
+It's where most of
+the soloing happens.
+
+And then it returns to this sort
+of quieter, more lyrical thing
+
+at the end.
+
+And I put these
+names of the board,
+
+because it turns out
+that this is actually
+
+a piece that was put
+together in the studio.
+
+It's a studio realization,
+you could say.
+
+And the first part is
+called In a Silent Way.
+
+That's composed by
+Joe Zawinul, who
+
+was one of the three
+keyboard players.
+
+That shows up at the
+beginning and at the end.
+
+And in the middle is a piece
+that both Zawinul and Miles
+
+Davis co-composed, called
+It's About That Time, which
+
+is the more funky,
+rock type of piece.
+
+And so they decided to
+essentially blend these pieces.
+
+And the further
+thing about this is
+
+this was an early
+attempt by people
+
+in the studio, one guy in
+particular, Teo Macero, who
+
+worked with Miles Davis a
+lot, to essentially sort
+
+of you could say cut
+and paste, because they
+
+used to have to splice tape
+to make cuts and paste them
+
+back together.
+
+It's before digital editing.
+
+And so there's
+some of that that's
+
+going on in the middle section.
+
+And in fact, the last
+section is exactly what
+
+was played for the
+first four minutes.
+
+It's just a replica.
+
+It's a replication.
+
+It's the same exact music
+just pasted in at the end.
+
+So it sort of calls
+into a new perspective
+
+what is improvisation and what
+is jazz composition, really.
+
+And you're going
+to have a chance
+
+to talk with Neil
+Leonard when he comes
+
+in about another month about
+exactly that, electronic usage,
+
+computer usage, and
+improvisation stuff.
+
+But this is sort of
+an early attempt.
+
+The other thing that I wanted
+us to listen to this for
+
+is that this basically is a
+jazz version of the format
+
+that we're going to hear on
+Sunday at the Indian concert.
+
+Because how many people have
+had the Music of India course?
+
+Anybody have that course?
+
+You've had that.
+
+Anybody else?
+
+And so you know that the way
+that the music in the Raga
+
+tradition works is there's a
+very slow presentation, as it's
+
+called, of the raga,
+the main melody.
+
+And then after that is
+allowed to be stated
+
+in a very lyrical,
+free floating way,
+
+then you get this rhythmic
+sense with a particular cycle
+
+or a tala that comes in.
+
+And so it's hard to believe that
+Miles Davis was not influenced
+
+by John Coltrane,
+who had previously
+
+been part of Miles' band.
+
+But Coltrane, as
+many of you know,
+
+had explored the music of India.
+
+And so it's sort of
+like a cross influence
+
+coming back from what
+somebody had originally
+
+been a player in Miles' band
+coming back to inform him.
+
+And this piece really has a very
+Indian at least pattern to it,
+
+if not Indian music.
+
+It's not a raga, but it is
+its own particular mode,
+
+as people have said.
+
+Anybody know what mode
+it was, or did you
+
+try to figure that out?
+
+AUDIENCE: Was it,
+could it be in Dorian?
+
+Because it began with a flat
+[INAUDIBLE] 7th, I think.
+
+PROFESSOR: OK.
+
+Anybody have a
+different take on it?
+
+AUDIENCE: I figured out
+which notes were in the mode,
+
+but I don't know if I
+could remember them.
+
+I was playing along
+to it, but I didn't
+
+think about what
+the actual mode was.
+
+PROFESSOR: OK, but you
+tried to play along with it.
+
+That's good.
+
+AUDIENCE: Yeah.
+
+I feel like I figured out
+which notes that actually fit.
+
+AUDIENCE: Anybody remember what
+was going on at the same time
+
+that the melody
+was being played?
+
+So obviously I'm
+going to suggest
+
+you go listen to it again, so
+we can hear more deeply inside
+
+of what's going on.
+
+Let me just come over to
+the piano for a second.
+
+I made a brief transcription
+of this melody.
+
+And what's going on
+is-- if I can just
+
+get over there-- the
+first thing that we
+
+have with this is a drone.
+
+A drone is just a long
+note underneath the melody.
+
+And we've done that with
+some of our exercises,
+
+right, where we've just
+had a basic tonal center.
+
+I didn't call it that,
+but that's what it is.
+
+Same thing in Indian music.
+
+There's a drone established
+by one of the instruments.
+
+And then the melody
+works off that.
+
+So in this case, it's
+an E. [PIANO PLAYING]
+
+So you're always hearing this
+E, and then it's actually,
+
+this is the melody.
+
+[PIANO PLAYING] It
+starts on the third.
+
+If you were in E and
+you had E major chord,
+
+it's actually the third of the
+E major chord. [PIANO PLAYING]
+
+But you never get that chord.
+
+You just get this.
+
+[PIANO PLAYING]
+
+PROFESSOR: And that's
+a big interval.
+
+That's a minor seventh jump.
+
+And here's where you get the
+tip off of what the mode is.
+
+[PIANO PLAYING]
+
+PROFESSOR: And what that
+is is E to D natural, which
+
+means that it's E essentially
+mixolydian, because if you had
+
+come on that same phrase
+and gone [PIANO PLAYING]
+
+it's totally different.
+[PIANO PLAYING]
+
+And it winds up on
+the fifth, which
+
+is the B, which is
+again an open sound.
+
+So except for occasionally
+getting a major third of what
+
+might have been the
+chord, it's really
+
+ambiguous, which a
+number of you said.
+
+Yeah, Jamie, you had a point.
+
+AUDIENCE: Yeah, it's
+funny because the piece
+
+that I wrote, which I wrote
+after I listened to the song,
+
+was in E mixolydian.
+
+So obviously that
+transferred over.
+
+PROFESSOR: Deeply
+influenced by this piece.
+
+And that's great.
+
+AUDIENCE: So I
+knew as soon as you
+
+played that, that
+was E mixolydian.
+
+PROFESSOR: That's OK.
+
+That's how we learn.
+
+And that's a great homage
+to this particular piece.
+
+So what we've got here, in other
+words, is a pretty simple mode.
+
+It's just one.
+
+And it almost sounds
+like it's major,
+
+except for that little trick
+note that I pointed out.
+
+But that's a very
+distinctive note.
+
+And so when you
+listen to this again,
+
+pay attention to that,
+because it really
+
+is the thing that
+sets this piece off
+
+apart from many others.
+
+Now the interesting
+thing about this
+
+is according to
+people who have really
+
+studied this and
+interviewed people
+
+who were on the recording
+session, when Joe Zawinul, who
+
+wrote this tune, the one we just
+talked about, when he brought
+
+this into the recording
+session, he had chords with it.
+
+He had chord changes
+written for it.
+
+And Miles Davis
+saw this and said
+
+to the guitar player,
+John McLaughlin,
+
+why don't you just
+play the melody?
+
+And it sort of took
+McLaughlin aback.
+
+It was like, well, what am I
+going to do with the chords?
+
+And the piano player
+said, what are we
+
+going to do with the chords?
+
+He said, don't play them.
+
+Just-- Dave Holland was
+the bass player-- just
+
+put a E pedal underneath
+all of this, play the melody
+
+and let that be the whole thing.
+
+And so according to these
+people again at the session,
+
+they did this.
+
+And no one was sure how
+it was going to turn out.
+
+And when they
+heard the playback,
+
+they were just astonished,
+because it made so much sense.
+
+And this is sort of the next
+level after Kind of Blue.
+
+In fact, it was 10 years
+after Kind of Blue.
+
+So it's sort of like
+moving from that,
+
+building on that
+direction, incorporating
+
+some Indian-ish
+type things with it,
+
+and coming out
+with what we have.
+
+So I really do recommend
+you listen to this again.
+
+Try to hear some of these other
+things that are happening.
+
+And when you hear the middle
+section, this other tune,
+
+it's called It's About That
+Time, pay attention to this,
+
+because this now shifts
+the tonal center up
+
+a half step to F. Some
+people say it's mixolydian.
+
+I hear it as a pentatonic sound.
+
+So see if you can maybe
+play along with that.
+
+That would be a good one
+to play around and just see
+
+what you can figure
+out on the bass-line.
+
+And that's all it
+is, is a bass-line,
+
+with a lot of textures.
+
+Remember, we've
+talked about textures
+
+from the other instruments.
+
+And this is particularly so
+with the three keyboards.
+
+So it's a great piece, and
+it bears listening to again.
+
+OK, so the assignment
+for you guys
+
+was to come up with a piece that
+was similarly a long flowing
+
+melody of between
+10 and 15 notes,
+
+and then figure out
+a way to present it.
+
+So who would like to
+present their piece?
+
+AUDIENCE: So the melody sort of
+goes like this. [BANJO PLAYING]
+
+That's just sort of the thing
+that we're going to play around
+
+on, is this.
+[BANJO PLAYING] And there's
+
+a second part that will come in
+occasionally. [BANJO PLAYING]
+
+Just like that, which
+is that second part.
+
+Alright.
+
+So why don't you, ah--
+
+[BANJO PLAYING]
+
+[SAXOPHONE JOINS BANJO]
+
+[APPLAUSE]
+
+PROFESSOR: Very nice.
+
+Play those opening
+notes that you
+
+played when you told us
+what it was made out of.
+
+[BANJO PLAYING]
+
+AUDIENCE: You mean,
+just like the--
+
+PROFESSOR: The
+little melody notes
+
+that you would play it around.
+
+[BANJO PLAYING]
+
+PROFESSOR: Sarah, what
+does that sound like?
+
+What kind of music
+does that sound like?
+
+AUDIENCE: It does kind of
+sound like Indian music.
+
+PROFESSOR: It sounds
+like Indian music.
+
+Have you heard
+much Indian music?
+
+AUDIENCE: Oh, yeah, before.
+
+That's what I thought of.
+
+PROFESSOR: So it must be
+going into your consciousness.
+
+AUDIENCE: Yeah, at
+one point I was like,
+
+oh, it sounds a little Indian.
+
+PROFESSOR: So when you
+hear the concert on Sunday,
+
+what you're going to hear is
+something very similar to that.
+
+That'll be the presentation
+of the raga, that sort of idea
+
+that you just did.
+
+And in fact, when you got
+into that rhythmic thing,
+
+particularly your picking
+style, as well as piano,
+
+that would be very similar to
+what the tabla, the drummer
+
+would be doing, to give
+a percussive thing.
+
+So this is great.
+
+This is like
+unconscious processing
+
+of where we're going.
+
+So brilliant.
+
+And very nice playing
+on the saxophone.
+
+Very nice.
+
+You're bringing out
+what would be called
+
+the characteristic feature of
+the mode or if it was a rag,
+
+there's certain
+particular things.
+
+And Phil Scarf when he
+comes a week from-- well,
+
+it'll be on next
+Monday-- he'll be
+
+talking about that very
+particular, specific thing.
+
+So very well done.
+
+Good job.
+
+Good job.
+
+[APPLAUSE]
+
+PROFESSOR: Who would
+like to go next?
+
+AUDIENCE: It goes from D
+dorian, G mixolydian, C major.
+
+So piano should
+be playing chords.
+
+And then the melody, I was
+thinking flute and oboe
+
+could maybe improvise
+on part of it,
+
+like when you get to the major?
+
+That's C major.
+
+Yeah.
+
+There's not really time to this.
+
+So I sort of suggested
+which notes might be shorter
+
+and which ones might be longer.
+
+But take whatever time you want.
+
+That's why I figured
+maybe it's not best time
+
+for lots of people
+playing at once.
+
+AUDIENCE: [INAUDIBLE] sort of
+loop around a couple times?
+
+AUDIENCE: Yeah, I think
+once would not be enough.
+
+So maybe let's do
+two or three times.
+
+And I'm going to sit this
+out, because transposing
+
+and to keep it quiet.
+
+So I guess flute and piano,
+whenever you're ready.
+
+[PIANO AND FLUTE PLAYING]
+
+[OBOE ENTERS]
+
+[APPLAUSE]
+
+PROFESSOR: So you were
+playing the actual melody.
+
+And you were improvising
+within the mode, or something,
+
+or around it.
+
+Very nice.
+
+AUDIENCE: Liked the
+percussive improvisation
+
+at the very beginning.
+
+AUDIENCE: Oh, yeah, sorry.
+
+I should have tested
+a couple of notes.
+
+PROFESSOR: Very, very nice.
+
+Very nice.
+
+Cool.
+
+AUDIENCE: I've got a
+simple melody which
+
+I'd like again to be
+played by the flute.
+
+Just sort of loop it around.
+
+I didn't explicitly say what
+notes were longer than others.
+
+But in the middle there
+I've got these three notes
+
+which I kind of wanted everyone
+to get in on, specifically.
+
+AUDIENCE: Those
+notes specifically,
+
+like those exact notes?
+
+AUDIENCE: Oh, yeah,
+specifically those notes.
+
+So everyone play like
+in unison, or as you
+
+get further along, yeah.
+
+AUDIENCE: So we should
+all play the whole time,
+
+but those three notes, we
+play the notes in unison?
+
+AUDIENCE: Everyone's
+playing the whole time.
+
+Maybe at the start, actually,
+the first time through,
+
+just the piano.
+
+And then when you loop
+around, then you guys come in.
+
+And for you guys,
+so it's E Phrygian.
+
+Stick with the E
+most of the time,
+
+but also at least at the start
+bring in the A and the B,
+
+specifically.
+
+And it's not [INAUDIBLE].
+
+AUDIENCE: Can we play the
+mode all the time, too?
+
+It's just one at a time?
+
+Do you know?
+
+AUDIENCE: It's just all the
+white notes, from E to E.
+
+[INSTRUMENTS WARMING UP]
+
+[FLUTE AND PIANO PLAYING]
+
+[TRUMPET AND BANJO ENTER]
+
+[APPLAUSE]
+
+PROFESSOR: Very nice.
+
+And so was this one
+mode or two modes?
+
+AUDIENCE: No, that's just
+one mode, just the E Phrygian
+
+throughout.
+
+PROFESSOR: Just one mode.
+
+Very nice.
+
+Very nice.
+
+And was your part prescribed,
+or were you improvising?
+
+AUDIENCE: So there
+were three notes sort
+
+of in the middle of that.
+
+The do do do do do,
+do do do do do do do.
+
+I guess I'm not quite
+singing it in key But, yeah.
+
+So there were three
+notes where every time it
+
+was prescribed, other
+than that, improvising.
+
+PROFESSOR: OK, good.
+
+And the same for
+you other folks?
+
+Very nice.
+
+Very nice.
+
+But you were playing the melody.
+
+AUDIENCE: I had
+the melody, yeah.
+
+PROFESSOR: Very nice.
+
+Good.
+
+Good, good.
+
+[VIOLIN AND GUITAR PLAYING]
+
+[APPLAUSE]
+
+PROFESSOR: Very nice.
+
+So you actually had chords
+written down, chords symboled,
+
+which is an
+interesting way to go.
+
+We haven't had that yet
+today, I don't think.
+
+We might have, did you
+have chords in yours?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: Because I was
+going to write that on top.
+
+I did want to
+mention some on that.
+
+So that's an interesting
+way to think about it.
+
+And we can explore
+this a little more.
+
+I don't want to take time now.
+
+But that's an interesting
+way to think about it.
+
+It's another facet.
+
+Just try this.
+
+Take those first five
+notes, and play them
+
+a little more like a
+rhythmical idea, like this.
+
+Bop, ba bo be bop.
+
+[VIOLIN AND GUITAR PLAYING]
+
+And then the next one.
+
+[VIOLIN AND GUITAR PLAYING] And
+then the next five, same way.
+
+Bop, ba doo be doo.
+
+[VIOLIN AND GUITAR PLAYING] And
+the next, bop, ba da be dop.
+
+[VIOLIN AND GUITAR PLAYING]
+Yeah,
+
+just do that do that
+over and over again.
+
+And Alex, play those same
+chords, but in time now.
+
+So I'm going to count
+this off. [CLAPPING] One,
+
+two, one, two, three, four.
+
+[CLAPPING AND INSTRUMENTS
+ PLAYING]
+
+OK.
+
+I'm just showing that because
+this would be another way
+
+to make a variation
+of what you'd done.
+
+In other words,
+similar to Silent Way,
+
+you've got your
+lyrical thing up front.
+
+And then you could turn it
+into a rhythmical gesture,
+
+let's say.
+
+And if you had yet
+a third instrument,
+
+you guys could be essentially
+the rhythm section,
+
+and somebody else,
+oboe, whatever, flute,
+
+could take a solo
+on top of that.
+
+It's just another thing to think
+about in terms of extension.
+
+Very nice.
+
+Very nice.
+
+[FLUTE PLAYING]
+
+[GUITAR ENTERS]
+
+[APPLAUSE]
+
+PROFESSOR: Now, did you
+have a written part?
+
+AUDIENCE: No.
+
+PROFESSOR: You were just
+making something up.
+
+AUDIENCE: I was making that up.
+
+PROFESSOR: You were improvising.
+
+In other words, you
+were playing this.
+
+So you had a rhythmical
+scheme, but you
+
+didn't put a meter with it.
+
+So it wasn't like 4 4 or 6.
+
+That was very nice.
+
+Very nice.
+
+I was figuring you'd keep
+going until one of you dropped,
+
+mainly you, because you
+have to keep breathing.
+
+But that was really nice.
+
+That was really nice.
+
+We could've gotten
+everybody involved in that.
+
+That would have taken
+up about an hour.
+
+That would have been great.
+
+So just something to remember.
+
+If you get hired
+for a job sometime
+
+and you run out of
+material, you can always
+
+do something like this.
+
+You can fill up easily
+5 minutes, 30 minutes,
+
+and you're golden.
+
+So if you run out of your set
+list, just a practical tip.
+
+Very nice.
+
+So if you want to put your name
+on that and let me have that.
+
+So I guess you guys have to run.
+
+While they're leaving
+and the next person
+
+decides who wants
+to be, I just want
+
+to say a thing about chords.
+
+And I know, Jacob,
+this is your piece.
+
+So I don't want to say anything.
+
+But you had said
+D Dorian, you also
+
+put D minor, D minor
+chord, to indicate
+
+you wanted a D minor chord.
+
+And that's fine.
+
+That's perfectly fine.
+
+Sometimes-- and you see this
+on the lead sheet for So What,
+
+which we looked at,
+and we've studied it--
+
+it'll say D Dorian D minor 7.
+
+It's a shorthand for
+saying that's a chord that
+
+works with the D Dorian scale.
+
+But in fact, it's often
+not so good to use this.
+
+It's much better
+just to put the mode,
+
+because if you do that, then
+the piano player's immediately
+
+going to think, let
+me play that four note
+
+chord, which is triads.
+
+And triads, remember,
+is not the sound
+
+that we typically
+want with modal.
+
+We want a quartal, like
+a fourth base thing.
+
+So when people do this and
+they put that down there,
+
+sometimes you're sort of
+snapped into that other way
+
+of thinking.
+
+It's not that it's wrong.
+
+It's just not quite
+into the idiom
+
+of what we're trying
+to do with modal stuff.
+
+So OK.
+
+Thank you all.
+
+So who would like to go next?
+
+AUDIENCE: I guess we can
+start with a saxophone melody.
+
+There's like a vague rhythm,
+but you can definitely
+
+change that, especially
+after the first run-through.
+
+Electric guitar,
+you'd start out just
+
+like emphasizing the D and
+any other notes basically
+
+you feel like, and
+then you can basically
+
+transition to the
+melody yourself
+
+whenever you feel like it.
+
+And feel free to change
+up the notes [INAUDIBLE].
+
+[SAXOPHONE PLAYING]
+
+[ELECTRIC GUITAR ENTERS]
+
+[APPLAUSE]
+
+PROFESSOR: So that
+again, that was
+
+like, what, a single
+melody and that's all.
+
+Just some verbal
+instructions to-- Very good.
+
+Very nice.
+
+Very nicely played.
+
+OK let's keep moving along.
+
+And I want to urge
+us, if we could
+
+make the presentation
+just a little bit shorter,
+
+just to make sure
+everybody gets a chance
+
+to have their thing heard.
+
+So who would like to go next?
+
+AUDIENCE: Alright.
+
+So this for a flute and a piano.
+
+So it's Dorian.
+
+And it's just a basic melody.
+
+So what I wanted
+was like the flute
+
+to just like start the
+melody and just keep
+
+looping back through it.
+
+And it has a rhythm.
+
+And then I wanted the
+piano to just, I guess,
+
+add their own
+improvisation to it.
+
+[FLUTE PLAYING]
+
+[PIANO ENTERS]
+
+[APPLAUSE]
+
+PROFESSOR: Very nice.
+
+Piano, what were you doing?
+
+Were you leading
+off what that was?
+
+Were you reading
+off that melody?
+
+AUDIENCE: Yeah, so
+I was trying to sort
+
+of align the rhythms,
+playing mostly the fourths.
+
+PROFESSOR: So you
+were making that up,
+
+the fourth idea, but
+you were following that.
+
+AUDIENCE: Yeah, I didn't
+play any of melody.
+
+I was just sort of
+trying to match it.
+
+PROFESSOR: Who did that sound
+like to you, or anybody else?
+
+What did that sound like,
+that piano and flute playing
+
+together?
+
+AUDIENCE: Rite of Spring.
+
+PROFESSOR: Little
+bit, little bit.
+
+Anybody else, classical,
+any other classical?
+
+Sounded very much
+like a Ravel to me.
+
+And in the Kind
+of Blue situation,
+
+I don't know if you've read
+the pages that were up there.
+
+I don't know if this was in
+those pages I put on Stellar.
+
+It talked about how both
+Bill Evans and Miles
+
+Davis adored Ravel.
+
+And that in fact,
+when they would
+
+listen to music in
+their own apartments,
+
+that's who they often
+would listen to.
+
+Interesting for a jazz person.
+
+And that that was very
+definitely in Bill Evans' mind.
+
+So you're channeling this.
+
+So this is great.
+
+It was beautiful.
+
+Beautiful flute playing.
+
+Very, very nice idea.
+
+Really nice idea.
+
+Wonderful.
+
+And I'm getting a kick out of
+the fact that most of you guys
+
+are not playing
+on your own piece.
+
+That's very interesting.
+
+Because you want to
+hear what's going on.
+
+I understand that.
+
+AUDIENCE: So basically
+I would like the guitar
+
+to start off playing the
+melody and kind of set
+
+up a cycle of some sort.
+
+And then I'd like Sarah to
+improvise over his melody,
+
+but starting with notes
+beginning from right to left,
+
+if that's OK.
+
+I hope it works.
+
+I'm not exactly sure yet.
+
+And then I would like
+you to play, I guess,
+
+whatever cycle he sets up if
+you could just play chords
+
+under it, but I guess I'd like
+half to be your own, yeah.
+
+[GUITAR PLAYING]
+
+[FLUTE AND PIANO ENTER]
+
+[APPLAUSE]
+
+PROFESSOR: Very nice.
+
+And again, you
+didn't sing on this.
+
+That's very interesting.
+
+I was sure you were going to.
+
+AUDIENCE: Oh, no.
+
+That's fine.
+
+PROFESSOR: That was very nice.
+
+And actually I think
+it's interesting
+
+how these are just
+emerging, just
+
+by the way people
+are volunteering.
+
+But this sort of could
+be a perfect complement
+
+to what your piece was.
+
+I mean it would
+make sense to me.
+
+And some of the
+rhythmical people, you
+
+were clearly on a similar wave.
+
+AUDIENCE: So sax is
+going to play the melody,
+
+and the rest of
+us will just play
+
+like soft chords in D Dorian.
+
+I wrote out a pretty
+specific rhythm,
+
+but you can take whatever
+liberty you want.
+
+AUDIENCE: What is this?
+
+AUDIENCE: This is just
+the transposition of that.
+
+AUDIENCE: That makes sense, OK.
+
+AUDIENCE: So it
+should be D minor.
+
+[INSTRUMENTS PLAYING]
+
+[APPLAUSE]
+
+PROFESSOR: Very nice, very nice.
+
+I feel we're in the realm of
+French impressionistic music,
+
+here.
+
+This is lovely.
+
+Very peaceful.
+
+Did that work like
+you thought it would,
+
+except for the transposition?
+
+AUDIENCE: Pretty much, yeah.
+
+Just in a different key.
+
+There was one note
+that was, I don't know.
+
+This one.
+
+I don't know what
+happened to that, but.
+
+AUDIENCE: Yeah.
+
+So where I was doing B
+Dorian on the sax, that
+
+should have been a
+G sharp, I think,
+
+so I just made that change.
+
+But yeah, it did
+sound kind of weird.
+
+AUDIENCE: But the general was
+basically what I was going for.
+
+PROFESSOR: Very nice.
+
+Very nice.
+
+OK, who wants to go next?
+
+Of our remaining contestants.
+
+[PIANO PLAYING]
+
+[FLUTE AND OBOE ENTER]
+
+[APPLAUSE]
+
+PROFESSOR: Really nice.
+
+So if I got from
+your instructions,
+
+sort of like intertwining
+or interlocking segments,
+
+is that the idea?
+
+AUDIENCE: Yeah, that was kind
+of again that train wreck.
+
+I think I need to
+fix my reed up.
+
+But that's sounded really nice.
+
+And I expected it,
+and it was cool.
+
+PROFESSOR: Yeah.
+
+Really, really nice.
+
+Very well done.
+
+[PIANO PLAYING]
+
+[TRUMPET ENTERS]
+
+[SAXOPHONE ENTERS]
+
+[APPLAUSE]
+
+AUDIENCE: Very nice, very nice.
+
+Cool.
+
+Cool.
+
+AUDIENCE: So I don't
+have anything written.
+
+I'm just going, I guess, for
+more of an open conception.
+
+But I was thinking just me
+and piano, if that's good.
+
+So I was thinking in D Dorian.
+
+So the only real, like,
+solid concept, I have,
+
+like, something of a melody.
+
+[SAXOPHONE PLAYING]
+
+AUDIENCE: So I
+guess I was thinking
+
+I would just kind
+of riff off of that.
+
+And I wanted it to have kind
+of like a minor sound, I guess.
+
+So I don't know, I
+guess you kind of do
+
+what you want with it.
+
+AUDIENCE: Do you want like a
+beat, or just sort of chords?
+
+AUDIENCE: I mean, I
+guess more of chords.
+
+Yeah.
+
+So I guess you can start it off.
+
+[PIANO PLAYING]
+
+[SAXOPHONE ENTERS]
+
+[APPLAUSE]
+
+PROFESSOR: Very nice, very nice.
+
+And I was waiting for
+someone to do this, not
+
+have anything written down.
+
+AUDIENCE: Yeah.
+
+I can get something
+to you next week.
+
+PROFESSOR: No, no no.
+
+But I was waiting for
+that, because that's often
+
+how our improvisational
+conceptions generate.
+
+I mean, I ask you to
+come up with something.
+
+But I don't think I
+said write it down.
+
+I said come up with something.
+
+And writing it down
+is perfectly fine.
+
+And yours was almost all hand
+written with a couple notes.
+
+Other people had just the notes.
+
+Other people had some
+notes and chords.
+
+Any of these are fine.
+
+But they just give
+us a generative point
+
+from which the work.
+
+So it was very cool.
+
+And obviously, what happened
+in each of these instances
+
+was way more than
+what you had on paper.
+
+That's the idea.
+
+In other words,
+these are wonderful.
+
+And if you didn't
+give me one of these,
+
+and you had it as a written
+out form, I need to see that.
+
+But the point is what happened
+in the room is the music.
+
+That's the music.
+
+These were all starting points.
+
+These were all springboards.
+
+So you're all doing wonderfully.
+
+So give yourselves a
+round of applause, really.
+
+Really nice.
+
+Really nice.
+
+[APPLAUSE]
+
+PROFESSOR: So that's it.
\ No newline at end of file
diff --git a/_kKIQ1h9UuA.txt b/_kKIQ1h9UuA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c63b218e3cd65059be7b02b9bb6a0c3bbd2b3fdc
--- /dev/null
+++ b/_kKIQ1h9UuA.txt
@@ -0,0 +1,11147 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's get started okay so this is
+
+ align:start position:0%
+so let's get started okay so this is
+ 
+
+ align:start position:0%
+so let's get started okay so this is
+actually I will go for a os3 so you can
+
+ align:start position:0%
+actually I will go for a os3 so you can
+ 
+
+ align:start position:0%
+actually I will go for a os3 so you can
+see during the exam number one we have
+
+ align:start position:0%
+see during the exam number one we have
+ 
+
+ align:start position:0%
+see during the exam number one we have
+covered the first half of the goal and
+
+ align:start position:0%
+covered the first half of the goal and
+ 
+
+ align:start position:0%
+covered the first half of the goal and
+we I should be making progress to learn
+
+ align:start position:0%
+we I should be making progress to learn
+ 
+
+ align:start position:0%
+we I should be making progress to learn
+about boundary conditions in one
+
+ align:start position:0%
+about boundary conditions in one
+ 
+
+ align:start position:0%
+about boundary conditions in one
+dimensional system and also in two
+
+ align:start position:0%
+dimensional system and also in two
+ 
+
+ align:start position:0%
+dimensional system and also in two
+dimensional system today and we will
+
+ align:start position:0%
+dimensional system today and we will
+ 
+
+ align:start position:0%
+dimensional system today and we will
+actually talk about phenomena related to
+
+ align:start position:0%
+actually talk about phenomena related to
+ 
+
+ align:start position:0%
+actually talk about phenomena related to
+electromagnetic waves and the optics
+
+ align:start position:0%
+electromagnetic waves and the optics
+ 
+
+ align:start position:0%
+electromagnetic waves and the optics
+today which we will be able to learn a
+
+ align:start position:0%
+today which we will be able to learn a
+ 
+
+ align:start position:0%
+today which we will be able to learn a
+two very important fundamental law
+
+ align:start position:0%
+two very important fundamental law
+ 
+
+ align:start position:0%
+two very important fundamental law
+related to optical optical related to
+
+ align:start position:0%
+related to optical optical related to
+ 
+
+ align:start position:0%
+related to optical optical related to
+geometrical optics okay so that's
+
+ align:start position:0%
+geometrical optics okay so that's
+ 
+
+ align:start position:0%
+geometrical optics okay so that's
+actually the excitement and we started a
+
+ align:start position:0%
+actually the excitement and we started a
+ 
+
+ align:start position:0%
+actually the excitement and we started a
+discussion of two dimensional or three
+
+ align:start position:0%
+discussion of two dimensional or three
+ 
+
+ align:start position:0%
+discussion of two dimensional or three
+dimensional wave last time and actually
+
+ align:start position:0%
+dimensional wave last time and actually
+ 
+
+ align:start position:0%
+dimensional wave last time and actually
+it just in case you haven't realized
+
+ align:start position:0%
+it just in case you haven't realized
+ 
+
+ align:start position:0%
+it just in case you haven't realized
+that there are two ways to go to higher
+
+ align:start position:0%
+that there are two ways to go to higher
+ 
+
+ align:start position:0%
+that there are two ways to go to higher
+dimension okay so the first the first
+
+ align:start position:0%
+dimension okay so the first the first
+ 
+
+ align:start position:0%
+dimension okay so the first the first
+way is to increase the number of objects
+
+ align:start position:0%
+way is to increase the number of objects
+ 
+
+ align:start position:0%
+way is to increase the number of objects
+and the press that in two dimensional
+
+ align:start position:0%
+and the press that in two dimensional
+ 
+
+ align:start position:0%
+and the press that in two dimensional
+three dimensional space and that is
+
+ align:start position:0%
+three dimensional space and that is
+ 
+
+ align:start position:0%
+three dimensional space and that is
+actually the kind of things which we
+
+ align:start position:0%
+actually the kind of things which we
+ 
+
+ align:start position:0%
+actually the kind of things which we
+will discuss today so for example I can
+
+ align:start position:0%
+will discuss today so for example I can
+ 
+
+ align:start position:0%
+will discuss today so for example I can
+have particles arranged in two dimension
+
+ align:start position:0%
+have particles arranged in two dimension
+ 
+
+ align:start position:0%
+have particles arranged in two dimension
+which form membranes and we can also on
+
+ align:start position:0%
+which form membranes and we can also on
+ 
+
+ align:start position:0%
+which form membranes and we can also on
+the other hand change the direction of
+
+ align:start position:0%
+the other hand change the direction of
+ 
+
+ align:start position:0%
+the other hand change the direction of
+the electromagnetic wave for example as
+
+ align:start position:0%
+the electromagnetic wave for example as
+ 
+
+ align:start position:0%
+the electromagnetic wave for example as
+a function of time and that's another
+
+ align:start position:0%
+a function of time and that's another
+ 
+
+ align:start position:0%
+a function of time and that's another
+way to go to a higher dimension and
+
+ align:start position:0%
+way to go to a higher dimension and
+ 
+
+ align:start position:0%
+way to go to a higher dimension and
+today as I mentioned before we are going
+
+ align:start position:0%
+today as I mentioned before we are going
+ 
+
+ align:start position:0%
+today as I mentioned before we are going
+to talk about the first case and on the
+
+ align:start position:0%
+to talk about the first case and on the
+ 
+
+ align:start position:0%
+to talk about the first case and on the
+on Thursday we are going to talk about
+
+ align:start position:0%
+on Thursday we are going to talk about
+ 
+
+ align:start position:0%
+on Thursday we are going to talk about
+the second way to go to higher dimension
+
+ align:start position:0%
+the second way to go to higher dimension
+ 
+
+ align:start position:0%
+the second way to go to higher dimension
+which is related to polarization etc
+
+ align:start position:0%
+which is related to polarization etc
+ 
+
+ align:start position:0%
+which is related to polarization etc
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in general higher order dimensions are
+
+ align:start position:0%
+in general higher order dimensions are
+ 
+
+ align:start position:0%
+in general higher order dimensions are
+hopeless okay they are super complicated
+
+ align:start position:0%
+hopeless okay they are super complicated
+ 
+
+ align:start position:0%
+hopeless okay they are super complicated
+and in general we don't really know how
+
+ align:start position:0%
+and in general we don't really know how
+ 
+
+ align:start position:0%
+and in general we don't really know how
+to solve this kind of system fortunately
+
+ align:start position:0%
+to solve this kind of system fortunately
+ 
+
+ align:start position:0%
+to solve this kind of system fortunately
+okay in ls3 what we have been doing is a
+
+ align:start position:0%
+okay in ls3 what we have been doing is a
+ 
+
+ align:start position:0%
+okay in ls3 what we have been doing is a
+focusing on a small subset of questions
+
+ align:start position:0%
+focusing on a small subset of questions
+ 
+
+ align:start position:0%
+focusing on a small subset of questions
+which are actually highly symmetric
+
+ align:start position:0%
+which are actually highly symmetric
+ 
+
+ align:start position:0%
+which are actually highly symmetric
+therefore we can actually solve it
+
+ align:start position:0%
+therefore we can actually solve it
+ 
+
+ align:start position:0%
+therefore we can actually solve it
+analytically so that would be the focus
+
+ align:start position:0%
+analytically so that would be the focus
+ 
+
+ align:start position:0%
+analytically so that would be the focus
+of all three and so that we can actually
+
+ align:start position:0%
+of all three and so that we can actually
+ 
+
+ align:start position:0%
+of all three and so that we can actually
+learn some physics intuition out of this
+
+ align:start position:0%
+learn some physics intuition out of this
+ 
+
+ align:start position:0%
+learn some physics intuition out of this
+kind of highly idealized system and the
+
+ align:start position:0%
+kind of highly idealized system and the
+ 
+
+ align:start position:0%
+kind of highly idealized system and the
+system which we are going to focus on
+
+ align:start position:0%
+system which we are going to focus on
+ 
+
+ align:start position:0%
+system which we are going to focus on
+today is showing here it's a two
+
+ align:start position:0%
+today is showing here it's a two
+ 
+
+ align:start position:0%
+today is showing here it's a two
+dimensional system which you have array
+
+ align:start position:0%
+dimensional system which you have array
+ 
+
+ align:start position:0%
+dimensional system which you have array
+of masses pressing the X and y XY plane
+
+ align:start position:0%
+of masses pressing the X and y XY plane
+ 
+
+ align:start position:0%
+of masses pressing the X and y XY plane
+and and that is essentially the system
+
+ align:start position:0%
+and and that is essentially the system
+ 
+
+ align:start position:0%
+and and that is essentially the system
+we are going to solve today and we will
+
+ align:start position:0%
+we are going to solve today and we will
+ 
+
+ align:start position:0%
+we are going to solve today and we will
+see that we learned a lot of interesting
+
+ align:start position:0%
+see that we learned a lot of interesting
+ 
+
+ align:start position:0%
+see that we learned a lot of interesting
+phenomena coming from the solution of
+
+ align:start position:0%
+phenomena coming from the solution of
+ 
+
+ align:start position:0%
+phenomena coming from the solution of
+this kind of system before we start a
+
+ align:start position:0%
+this kind of system before we start a
+ 
+
+ align:start position:0%
+this kind of system before we start a
+discussion of two dimensional system I
+
+ align:start position:0%
+discussion of two dimensional system I
+ 
+
+ align:start position:0%
+discussion of two dimensional system I
+would like to remind you what we have
+
+ align:start position:0%
+would like to remind you what we have
+ 
+
+ align:start position:0%
+would like to remind you what we have
+already learned from lecture eight so
+
+ align:start position:0%
+already learned from lecture eight so
+ 
+
+ align:start position:0%
+already learned from lecture eight so
+that was about a system with which
+
+ align:start position:0%
+that was about a system with which
+ 
+
+ align:start position:0%
+that was about a system with which
+consists of infinite number of mass and
+
+ align:start position:0%
+consists of infinite number of mass and
+ 
+
+ align:start position:0%
+consists of infinite number of mass and
+the infinite number of strings and each
+
+ align:start position:0%
+the infinite number of strings and each
+ 
+
+ align:start position:0%
+the infinite number of strings and each
+string have string tension P and the
+
+ align:start position:0%
+string have string tension P and the
+ 
+
+ align:start position:0%
+string have string tension P and the
+other mass when they are in equilibrium
+
+ align:start position:0%
+other mass when they are in equilibrium
+ 
+
+ align:start position:0%
+other mass when they are in equilibrium
+position they the distance between all
+
+ align:start position:0%
+position they the distance between all
+ 
+
+ align:start position:0%
+position they the distance between all
+those mass in the X Direction is a ok so
+
+ align:start position:0%
+those mass in the X Direction is a ok so
+ 
+
+ align:start position:0%
+those mass in the X Direction is a ok so
+we have solved this system before with
+
+ align:start position:0%
+we have solved this system before with
+ 
+
+ align:start position:0%
+we have solved this system before with
+space translation symmetry okay and this
+
+ align:start position:0%
+space translation symmetry okay and this
+ 
+
+ align:start position:0%
+space translation symmetry okay and this
+is just a reminder that the dispersion
+
+ align:start position:0%
+is just a reminder that the dispersion
+ 
+
+ align:start position:0%
+is just a reminder that the dispersion
+relation which we got a lot of time
+
+ align:start position:0%
+relation which we got a lot of time
+ 
+
+ align:start position:0%
+relation which we got a lot of time
+Omega as a function of K is T over N a
+
+ align:start position:0%
+Omega as a function of K is T over N a
+ 
+
+ align:start position:0%
+Omega as a function of K is T over N a
+sign a ka over 2 so that was just a
+
+ align:start position:0%
+sign a ka over 2 so that was just a
+ 
+
+ align:start position:0%
+sign a ka over 2 so that was just a
+reminder of what we have learned from
+
+ align:start position:0%
+reminder of what we have learned from
+ 
+
+ align:start position:0%
+reminder of what we have learned from
+lecture 8 so by now you should realize
+
+ align:start position:0%
+lecture 8 so by now you should realize
+ 
+
+ align:start position:0%
+lecture 8 so by now you should realize
+that okay this dispersion relation is is
+
+ align:start position:0%
+that okay this dispersion relation is is
+ 
+
+ align:start position:0%
+that okay this dispersion relation is is
+young Angelou right this is actually
+
+ align:start position:0%
+young Angelou right this is actually
+ 
+
+ align:start position:0%
+young Angelou right this is actually
+telling you that this is a dispersive
+
+ align:start position:0%
+telling you that this is a dispersive
+ 
+
+ align:start position:0%
+telling you that this is a dispersive
+medium right because if you calculate
+
+ align:start position:0%
+medium right because if you calculate
+ 
+
+ align:start position:0%
+medium right because if you calculate
+the ratio of Omega n K you see that this
+
+ align:start position:0%
+the ratio of Omega n K you see that this
+ 
+
+ align:start position:0%
+the ratio of Omega n K you see that this
+is actually not a constant okay so the
+
+ align:start position:0%
+is actually not a constant okay so the
+ 
+
+ align:start position:0%
+is actually not a constant okay so the
+after all the discussion from previous
+
+ align:start position:0%
+after all the discussion from previous
+ 
+
+ align:start position:0%
+after all the discussion from previous
+lecture you should be able to
+
+ align:start position:0%
+lecture you should be able to
+ 
+
+ align:start position:0%
+lecture you should be able to
+immediately realize that and any waves
+
+ align:start position:0%
+immediately realize that and any waves
+ 
+
+ align:start position:0%
+immediately realize that and any waves
+propagating on this car
+
+ align:start position:0%
+propagating on this car
+ 
+
+ align:start position:0%
+propagating on this car
+the sister will be there will be a
+
+ align:start position:0%
+the sister will be there will be a
+ 
+
+ align:start position:0%
+the sister will be there will be a
+dispersion phenomena happening in this
+
+ align:start position:0%
+dispersion phenomena happening in this
+ 
+
+ align:start position:0%
+dispersion phenomena happening in this
+kind of system okay and also from the
+
+ align:start position:0%
+kind of system okay and also from the
+ 
+
+ align:start position:0%
+kind of system okay and also from the
+previous lecture we'll have learned that
+
+ align:start position:0%
+previous lecture we'll have learned that
+ 
+
+ align:start position:0%
+previous lecture we'll have learned that
+the eigenvectors based on space
+
+ align:start position:0%
+the eigenvectors based on space
+ 
+
+ align:start position:0%
+the eigenvectors based on space
+translation symmetry it's exponential I
+
+ align:start position:0%
+translation symmetry it's exponential I
+ 
+
+ align:start position:0%
+translation symmetry it's exponential I
+K X where X is actually defined as a
+
+ align:start position:0%
+K X where X is actually defined as a
+ 
+
+ align:start position:0%
+K X where X is actually defined as a
+times a we'll say is actually a label to
+
+ align:start position:0%
+times a we'll say is actually a label to
+ 
+
+ align:start position:0%
+times a we'll say is actually a label to
+tell you what which mass I was talking
+
+ align:start position:0%
+tell you what which mass I was talking
+ 
+
+ align:start position:0%
+tell you what which mass I was talking
+about okay now today we are going to
+
+ align:start position:0%
+about okay now today we are going to
+ 
+
+ align:start position:0%
+about okay now today we are going to
+extend this to a two dimensional system
+
+ align:start position:0%
+extend this to a two dimensional system
+ 
+
+ align:start position:0%
+extend this to a two dimensional system
+so so instead of a one dimensional
+
+ align:start position:0%
+so so instead of a one dimensional
+ 
+
+ align:start position:0%
+so so instead of a one dimensional
+system we have a two dimensional array
+
+ align:start position:0%
+system we have a two dimensional array
+ 
+
+ align:start position:0%
+system we have a two dimensional array
+so all the little mass or have mass
+
+ align:start position:0%
+so all the little mass or have mass
+ 
+
+ align:start position:0%
+so all the little mass or have mass
+equal to n and they are placing a XY
+
+ align:start position:0%
+equal to n and they are placing a XY
+ 
+
+ align:start position:0%
+equal to n and they are placing a XY
+plane okay the coordinate system which I
+
+ align:start position:0%
+plane okay the coordinate system which I
+ 
+
+ align:start position:0%
+plane okay the coordinate system which I
+defined is here X is horizontal and Y is
+
+ align:start position:0%
+defined is here X is horizontal and Y is
+ 
+
+ align:start position:0%
+defined is here X is horizontal and Y is
+vertical and the Z's as she pointing to
+
+ align:start position:0%
+vertical and the Z's as she pointing to
+ 
+
+ align:start position:0%
+vertical and the Z's as she pointing to
+you okay and all those little mass can
+
+ align:start position:0%
+you okay and all those little mass can
+ 
+
+ align:start position:0%
+you okay and all those little mass can
+only oscillate toward you or going away
+
+ align:start position:0%
+only oscillate toward you or going away
+ 
+
+ align:start position:0%
+only oscillate toward you or going away
+from you so in the Z direction okay you
+
+ align:start position:0%
+from you so in the Z direction okay you
+ 
+
+ align:start position:0%
+from you so in the Z direction okay you
+can only up also they have been done in
+
+ align:start position:0%
+can only up also they have been done in
+ 
+
+ align:start position:0%
+can only up also they have been done in
+the Z direction okay and in this system
+
+ align:start position:0%
+the Z direction okay and in this system
+ 
+
+ align:start position:0%
+the Z direction okay and in this system
+we have the land scale which is actually
+
+ align:start position:0%
+we have the land scale which is actually
+ 
+
+ align:start position:0%
+we have the land scale which is actually
+the horizontal distance between mass is
+
+ align:start position:0%
+the horizontal distance between mass is
+ 
+
+ align:start position:0%
+the horizontal distance between mass is
+it's called aah
+
+ align:start position:0%
+it's called aah
+ 
+
+ align:start position:0%
+it's called aah
+and in the vertical direction the scale
+
+ align:start position:0%
+and in the vertical direction the scale
+ 
+
+ align:start position:0%
+and in the vertical direction the scale
+at the tip distance between mass is AV
+
+ align:start position:0%
+at the tip distance between mass is AV
+ 
+
+ align:start position:0%
+at the tip distance between mass is AV
+okay also we have string tension a two
+
+ align:start position:0%
+okay also we have string tension a two
+ 
+
+ align:start position:0%
+okay also we have string tension a two
+different kind of string tension for the
+
+ align:start position:0%
+different kind of string tension for the
+ 
+
+ align:start position:0%
+different kind of string tension for the
+vertical and horizontal direction the
+
+ align:start position:0%
+vertical and horizontal direction the
+ 
+
+ align:start position:0%
+vertical and horizontal direction the
+vertical direction you have string
+
+ align:start position:0%
+vertical direction you have string
+ 
+
+ align:start position:0%
+vertical direction you have string
+tension TV and in the horizontal
+
+ align:start position:0%
+tension TV and in the horizontal
+ 
+
+ align:start position:0%
+tension TV and in the horizontal
+direction you have string tension th
+
+ align:start position:0%
+direction you have string tension th
+ 
+
+ align:start position:0%
+direction you have string tension th
+okay so how do we actually describe this
+
+ align:start position:0%
+okay so how do we actually describe this
+ 
+
+ align:start position:0%
+okay so how do we actually describe this
+kind of system right the first thing as
+
+ align:start position:0%
+kind of system right the first thing as
+ 
+
+ align:start position:0%
+kind of system right the first thing as
+we did before is to label all those
+
+ align:start position:0%
+we did before is to label all those
+ 
+
+ align:start position:0%
+we did before is to label all those
+little mass right by my label and my
+
+ align:start position:0%
+little mass right by my label and my
+ 
+
+ align:start position:0%
+little mass right by my label and my
+label is actually called say X and say Y
+
+ align:start position:0%
+label is actually called say X and say Y
+ 
+
+ align:start position:0%
+label is actually called say X and say Y
+which actually tells you
+
+ align:start position:0%
+which actually tells you
+ 
+
+ align:start position:0%
+which actually tells you
+which mass I was talking about in this
+
+ align:start position:0%
+which mass I was talking about in this
+ 
+
+ align:start position:0%
+which mass I was talking about in this
+system okay
+
+ align:start position:0%
+system okay
+ 
+
+ align:start position:0%
+system okay
+once I have defined that the labels I
+
+ align:start position:0%
+once I have defined that the labels I
+ 
+
+ align:start position:0%
+once I have defined that the labels I
+will be able to write the position of
+
+ align:start position:0%
+will be able to write the position of
+ 
+
+ align:start position:0%
+will be able to write the position of
+all those mass the x-direction position
+
+ align:start position:0%
+all those mass the x-direction position
+ 
+
+ align:start position:0%
+all those mass the x-direction position
+and y-direction position in terms of say
+
+ align:start position:0%
+and y-direction position in terms of say
+ 
+
+ align:start position:0%
+and y-direction position in terms of say
+and a right so for example x position of
+
+ align:start position:0%
+and a right so for example x position of
+ 
+
+ align:start position:0%
+and a right so for example x position of
+one of the mass will be written as say x
+
+ align:start position:0%
+one of the mass will be written as say x
+ 
+
+ align:start position:0%
+one of the mass will be written as say x
+times a h and the y position of a
+
+ align:start position:0%
+times a h and the y position of a
+ 
+
+ align:start position:0%
+times a h and the y position of a
+specific mass you can actually write it
+
+ align:start position:0%
+specific mass you can actually write it
+ 
+
+ align:start position:0%
+specific mass you can actually write it
+down in terms of say Y times AP okay so
+
+ align:start position:0%
+down in terms of say Y times AP okay so
+ 
+
+ align:start position:0%
+down in terms of say Y times AP okay so
+all those things are to be pretty
+
+ align:start position:0%
+all those things are to be pretty
+ 
+
+ align:start position:0%
+all those things are to be pretty
+straightforward the interesting part is
+
+ align:start position:0%
+straightforward the interesting part is
+ 
+
+ align:start position:0%
+straightforward the interesting part is
+that as we actually identify in a last
+
+ align:start position:0%
+that as we actually identify in a last
+ 
+
+ align:start position:0%
+that as we actually identify in a last
+lecture this system is highly symmetric
+
+ align:start position:0%
+lecture this system is highly symmetric
+ 
+
+ align:start position:0%
+lecture this system is highly symmetric
+it has space translation symmetry right
+
+ align:start position:0%
+it has space translation symmetry right
+ 
+
+ align:start position:0%
+it has space translation symmetry right
+therefore we can issue the immediately
+
+ align:start position:0%
+therefore we can issue the immediately
+ 
+
+ align:start position:0%
+therefore we can issue the immediately
+figure out won't be the eigenvectors for
+
+ align:start position:0%
+figure out won't be the eigenvectors for
+ 
+
+ align:start position:0%
+figure out won't be the eigenvectors for
+this system
+
+ align:start position:0%
+this system
+ 
+
+ align:start position:0%
+this system
+so the eigenvector very similar to what
+
+ align:start position:0%
+so the eigenvector very similar to what
+ 
+
+ align:start position:0%
+so the eigenvector very similar to what
+have been discussed here where you have
+
+ align:start position:0%
+have been discussed here where you have
+ 
+
+ align:start position:0%
+have been discussed here where you have
+a one dimensional state space
+
+ align:start position:0%
+a one dimensional state space
+ 
+
+ align:start position:0%
+a one dimensional state space
+translation symmetric system exponential
+
+ align:start position:0%
+translation symmetric system exponential
+ 
+
+ align:start position:0%
+translation symmetric system exponential
+I K X was the eigenvector now you have I
+
+ align:start position:0%
+I K X was the eigenvector now you have I
+ 
+
+ align:start position:0%
+I K X was the eigenvector now you have I
+can vector which is actually in two
+
+ align:start position:0%
+can vector which is actually in two
+ 
+
+ align:start position:0%
+can vector which is actually in two
+dimension right because you would like
+
+ align:start position:0%
+dimension right because you would like
+ 
+
+ align:start position:0%
+dimension right because you would like
+to describe not only the X direction but
+
+ align:start position:0%
+to describe not only the X direction but
+ 
+
+ align:start position:0%
+to describe not only the X direction but
+also y direction and the eigen vector
+
+ align:start position:0%
+also y direction and the eigen vector
+ 
+
+ align:start position:0%
+also y direction and the eigen vector
+have exactly the same functional form
+
+ align:start position:0%
+have exactly the same functional form
+ 
+
+ align:start position:0%
+have exactly the same functional form
+because of space translation symmetry
+
+ align:start position:0%
+because of space translation symmetry
+ 
+
+ align:start position:0%
+because of space translation symmetry
+and it's actually like explanation I KX
+
+ align:start position:0%
+and it's actually like explanation I KX
+ 
+
+ align:start position:0%
+and it's actually like explanation I KX
+times X I multiply that by another
+
+ align:start position:0%
+times X I multiply that by another
+ 
+
+ align:start position:0%
+times X I multiply that by another
+explanation function exponential I K Y
+
+ align:start position:0%
+explanation function exponential I K Y
+ 
+
+ align:start position:0%
+explanation function exponential I K Y
+times y okay so I think from until now
+
+ align:start position:0%
+times y okay so I think from until now
+ 
+
+ align:start position:0%
+times y okay so I think from until now
+nothing should surprise surprise you
+
+ align:start position:0%
+nothing should surprise surprise you
+ 
+
+ align:start position:0%
+nothing should surprise surprise you
+because this is actually what we have
+
+ align:start position:0%
+because this is actually what we have
+ 
+
+ align:start position:0%
+because this is actually what we have
+learned from the one-dimensional system
+
+ align:start position:0%
+learned from the one-dimensional system
+ 
+
+ align:start position:0%
+learned from the one-dimensional system
+and asks
+
+ align:start position:0%
+and asks
+ 
+
+ align:start position:0%
+and asks
+based on what we have learned before we
+
+ align:start position:0%
+based on what we have learned before we
+ 
+
+ align:start position:0%
+based on what we have learned before we
+can also immediately write down what
+
+ align:start position:0%
+can also immediately write down what
+ 
+
+ align:start position:0%
+can also immediately write down what
+would be the dispersion relation since
+
+ align:start position:0%
+would be the dispersion relation since
+ 
+
+ align:start position:0%
+would be the dispersion relation since
+we are always considered in very small
+
+ align:start position:0%
+we are always considered in very small
+ 
+
+ align:start position:0%
+we are always considered in very small
+vibration okay
+
+ align:start position:0%
+vibration okay
+ 
+
+ align:start position:0%
+vibration okay
+and this actually these are formulas
+
+ align:start position:0%
+and this actually these are formulas
+ 
+
+ align:start position:0%
+and this actually these are formulas
+still a price therefore you can easily
+
+ align:start position:0%
+still a price therefore you can easily
+ 
+
+ align:start position:0%
+still a price therefore you can easily
+write down the dispersion relation
+
+ align:start position:0%
+write down the dispersion relation
+ 
+
+ align:start position:0%
+write down the dispersion relation
+already Omega square Omega square K
+
+ align:start position:0%
+already Omega square Omega square K
+ 
+
+ align:start position:0%
+already Omega square Omega square K
+would be equal to 4 th over mAh sine
+
+ align:start position:0%
+would be equal to 4 th over mAh sine
+ 
+
+ align:start position:0%
+would be equal to 4 th over mAh sine
+squared K X + H divided by 2 plus 4 T V
+
+ align:start position:0%
+squared K X + H divided by 2 plus 4 T V
+ 
+
+ align:start position:0%
+squared K X + H divided by 2 plus 4 T V
+divided by M a the sign a square k KY a
+
+ align:start position:0%
+divided by M a the sign a square k KY a
+ 
+
+ align:start position:0%
+divided by M a the sign a square k KY a
+v / ok so this is actually pretty
+
+ align:start position:0%
+v / ok so this is actually pretty
+ 
+
+ align:start position:0%
+v / ok so this is actually pretty
+straightforward and and you can see that
+
+ align:start position:0%
+straightforward and and you can see that
+ 
+
+ align:start position:0%
+straightforward and and you can see that
+another Omega is a function of both K X
+
+ align:start position:0%
+another Omega is a function of both K X
+ 
+
+ align:start position:0%
+another Omega is a function of both K X
+and the K Y from the icon from the
+
+ align:start position:0%
+and the K Y from the icon from the
+ 
+
+ align:start position:0%
+and the K Y from the icon from the
+eigenvector we can also write down what
+
+ align:start position:0%
+eigenvector we can also write down what
+ 
+
+ align:start position:0%
+eigenvector we can also write down what
+would be the possible sy X Y now the
+
+ align:start position:0%
+would be the possible sy X Y now the
+ 
+
+ align:start position:0%
+would be the possible sy X Y now the
+size is actually the displacement in the
+
+ align:start position:0%
+size is actually the displacement in the
+ 
+
+ align:start position:0%
+size is actually the displacement in the
+Z direction right we should spare to the
+
+ align:start position:0%
+Z direction right we should spare to the
+ 
+
+ align:start position:0%
+Z direction right we should spare to the
+equilibrium position and that is
+
+ align:start position:0%
+equilibrium position and that is
+ 
+
+ align:start position:0%
+equilibrium position and that is
+actually proportional to the eigenvector
+
+ align:start position:0%
+actually proportional to the eigenvector
+ 
+
+ align:start position:0%
+actually proportional to the eigenvector
+so basically is actually going to be a
+
+ align:start position:0%
+so basically is actually going to be a
+ 
+
+ align:start position:0%
+so basically is actually going to be a
+exponential I exercise X exponential I K
+
+ align:start position:0%
+exponential I exercise X exponential I K
+ 
+
+ align:start position:0%
+exponential I exercise X exponential I K
+Y times y ok and of course I can write
+
+ align:start position:0%
+Y times y ok and of course I can write
+ 
+
+ align:start position:0%
+Y times y ok and of course I can write
+these two turns together right so
+
+ align:start position:0%
+these two turns together right so
+ 
+
+ align:start position:0%
+these two turns together right so
+basically what I will get is a
+
+ align:start position:0%
+basically what I will get is a
+ 
+
+ align:start position:0%
+basically what I will get is a
+exponential I K is a vector times R
+
+ align:start position:0%
+exponential I K is a vector times R
+ 
+
+ align:start position:0%
+exponential I K is a vector times R
+which is a vector so basically K content
+
+ align:start position:0%
+which is a vector so basically K content
+ 
+
+ align:start position:0%
+which is a vector so basically K content
+to component KX and KY + R have also to
+
+ align:start position:0%
+to component KX and KY + R have also to
+ 
+
+ align:start position:0%
+to component KX and KY + R have also to
+company with
+
+ align:start position:0%
+company with
+ 
+
+ align:start position:0%
+company with
+and what okay again we see that this is
+
+ align:start position:0%
+and what okay again we see that this is
+ 
+
+ align:start position:0%
+and what okay again we see that this is
+actually a non-dispersive median okay
+
+ align:start position:0%
+actually a non-dispersive median okay
+ 
+
+ align:start position:0%
+actually a non-dispersive median okay
+and what we are going to do is to make
+
+ align:start position:0%
+and what we are going to do is to make
+ 
+
+ align:start position:0%
+and what we are going to do is to make
+linear combination of all those
+
+ align:start position:0%
+linear combination of all those
+ 
+
+ align:start position:0%
+linear combination of all those
+eigenvectors and the to figure out what
+
+ align:start position:0%
+eigenvectors and the to figure out what
+ 
+
+ align:start position:0%
+eigenvectors and the to figure out what
+would be the behavior of when this
+
+ align:start position:0%
+would be the behavior of when this
+ 
+
+ align:start position:0%
+would be the behavior of when this
+system is oscillating at a specific
+
+ align:start position:0%
+system is oscillating at a specific
+ 
+
+ align:start position:0%
+system is oscillating at a specific
+frequency Omega and that is actually the
+
+ align:start position:0%
+frequency Omega and that is actually the
+ 
+
+ align:start position:0%
+frequency Omega and that is actually the
+corresponding no more more at the
+
+ align:start position:0%
+corresponding no more more at the
+ 
+
+ align:start position:0%
+corresponding no more more at the
+angular frequency Omega okay so that is
+
+ align:start position:0%
+angular frequency Omega okay so that is
+ 
+
+ align:start position:0%
+angular frequency Omega okay so that is
+actually pretty similar to what we have
+
+ align:start position:0%
+actually pretty similar to what we have
+ 
+
+ align:start position:0%
+actually pretty similar to what we have
+done for a white dimensional system okay
+
+ align:start position:0%
+done for a white dimensional system okay
+ 
+
+ align:start position:0%
+done for a white dimensional system okay
+so just a reminder so this is a two
+
+ align:start position:0%
+so just a reminder so this is a two
+ 
+
+ align:start position:0%
+so just a reminder so this is a two
+dimensional system just a reminder about
+
+ align:start position:0%
+dimensional system just a reminder about
+ 
+
+ align:start position:0%
+dimensional system just a reminder about
+one dimensional system or for for a
+
+ align:start position:0%
+one dimensional system or for for a
+ 
+
+ align:start position:0%
+one dimensional system or for for a
+while so so that there are two eigen
+
+ align:start position:0%
+while so so that there are two eigen
+ 
+
+ align:start position:0%
+while so so that there are two eigen
+vectors which actually have identical
+
+ align:start position:0%
+vectors which actually have identical
+ 
+
+ align:start position:0%
+vectors which actually have identical
+Omega right so the first one is
+
+ align:start position:0%
+Omega right so the first one is
+ 
+
+ align:start position:0%
+Omega right so the first one is
+exponential I K X and the second one is
+
+ align:start position:0%
+exponential I K X and the second one is
+ 
+
+ align:start position:0%
+exponential I K X and the second one is
+actually exponential minus ikx what we
+
+ align:start position:0%
+actually exponential minus ikx what we
+ 
+
+ align:start position:0%
+actually exponential minus ikx what we
+have done before is to do a linear
+
+ align:start position:0%
+have done before is to do a linear
+ 
+
+ align:start position:0%
+have done before is to do a linear
+combination of the two explanation
+
+ align:start position:0%
+combination of the two explanation
+ 
+
+ align:start position:0%
+combination of the two explanation
+function right so what we can do is that
+
+ align:start position:0%
+function right so what we can do is that
+ 
+
+ align:start position:0%
+function right so what we can do is that
+okay now I can actually create cosine KX
+
+ align:start position:0%
+okay now I can actually create cosine KX
+ 
+
+ align:start position:0%
+okay now I can actually create cosine KX
+right this is actually 1 over 2
+
+ align:start position:0%
+right this is actually 1 over 2
+ 
+
+ align:start position:0%
+right this is actually 1 over 2
+exponential I K X plus exponential minus
+
+ align:start position:0%
+exponential I K X plus exponential minus
+ 
+
+ align:start position:0%
+exponential I K X plus exponential minus
+ikx and I can also create sine KX and
+
+ align:start position:0%
+ikx and I can also create sine KX and
+ 
+
+ align:start position:0%
+ikx and I can also create sine KX and
+this is as u 1 over 2i exponential ikx
+
+ align:start position:0%
+this is as u 1 over 2i exponential ikx
+ 
+
+ align:start position:0%
+this is as u 1 over 2i exponential ikx
+minus exponential minus I K X right for
+
+ align:start position:0%
+minus exponential minus I K X right for
+ 
+
+ align:start position:0%
+minus exponential minus I K X right for
+this one-dimensional system so that
+
+ align:start position:0%
+this one-dimensional system so that
+ 
+
+ align:start position:0%
+this one-dimensional system so that
+issue how we figure out that this when
+
+ align:start position:0%
+issue how we figure out that this when
+ 
+
+ align:start position:0%
+issue how we figure out that this when
+this system is doing one of the normal
+
+ align:start position:0%
+this system is doing one of the normal
+ 
+
+ align:start position:0%
+this system is doing one of the normal
+mode the shape of the system is like a
+
+ align:start position:0%
+mode the shape of the system is like a
+ 
+
+ align:start position:0%
+mode the shape of the system is like a
+cosine or a sine or in general you can
+
+ align:start position:0%
+cosine or a sine or in general you can
+ 
+
+ align:start position:0%
+cosine or a sine or in general you can
+add these two together and in general it
+
+ align:start position:0%
+add these two together and in general it
+ 
+
+ align:start position:0%
+add these two together and in general it
+can be something like cosine KX plus Phi
+
+ align:start position:0%
+can be something like cosine KX plus Phi
+ 
+
+ align:start position:0%
+can be something like cosine KX plus Phi
+and Phi is actually some phase
+
+ align:start position:0%
+and Phi is actually some phase
+ 
+
+ align:start position:0%
+and Phi is actually some phase
+angle which we you can actually figure
+
+ align:start position:0%
+angle which we you can actually figure
+ 
+
+ align:start position:0%
+angle which we you can actually figure
+out by boundary condition okay but
+
+ align:start position:0%
+out by boundary condition okay but
+ 
+
+ align:start position:0%
+out by boundary condition okay but
+before we introduce any boundary
+
+ align:start position:0%
+before we introduce any boundary
+ 
+
+ align:start position:0%
+before we introduce any boundary
+condition all the K values all the five
+
+ align:start position:0%
+condition all the K values all the five
+ 
+
+ align:start position:0%
+condition all the K values all the five
+values are allowed right just a reminder
+
+ align:start position:0%
+values are allowed right just a reminder
+ 
+
+ align:start position:0%
+values are allowed right just a reminder
+about what we have learned before okay
+
+ align:start position:0%
+about what we have learned before okay
+ 
+
+ align:start position:0%
+about what we have learned before okay
+so the situation is pretty simple you
+
+ align:start position:0%
+so the situation is pretty simple you
+ 
+
+ align:start position:0%
+so the situation is pretty simple you
+have just plus n minus K and then you
+
+ align:start position:0%
+have just plus n minus K and then you
+ 
+
+ align:start position:0%
+have just plus n minus K and then you
+make linear combination of these two
+
+ align:start position:0%
+make linear combination of these two
+ 
+
+ align:start position:0%
+make linear combination of these two
+then you know what would be the shape of
+
+ align:start position:0%
+then you know what would be the shape of
+ 
+
+ align:start position:0%
+then you know what would be the shape of
+the normal mode okay on the other hand
+
+ align:start position:0%
+the normal mode okay on the other hand
+ 
+
+ align:start position:0%
+the normal mode okay on the other hand
+we are now talking about two-dimensional
+
+ align:start position:0%
+we are now talking about two-dimensional
+ 
+
+ align:start position:0%
+we are now talking about two-dimensional
+case okay so let's take a look at this
+
+ align:start position:0%
+case okay so let's take a look at this
+ 
+
+ align:start position:0%
+case okay so let's take a look at this
+dispersion relation okay
+
+ align:start position:0%
+dispersion relation okay
+ 
+
+ align:start position:0%
+dispersion relation okay
+the dispersion relation we have here
+
+ align:start position:0%
+the dispersion relation we have here
+ 
+
+ align:start position:0%
+the dispersion relation we have here
+Omega is a function of K X is a function
+
+ align:start position:0%
+Omega is a function of K X is a function
+ 
+
+ align:start position:0%
+Omega is a function of K X is a function
+of K Y as well okay what does that mean
+
+ align:start position:0%
+of K Y as well okay what does that mean
+ 
+
+ align:start position:0%
+of K Y as well okay what does that mean
+that means I can have multiple choice of
+
+ align:start position:0%
+that means I can have multiple choice of
+ 
+
+ align:start position:0%
+that means I can have multiple choice of
+KX and KY which they all produce the
+
+ align:start position:0%
+KX and KY which they all produce the
+ 
+
+ align:start position:0%
+KX and KY which they all produce the
+same Omega value okay so it's not as
+
+ align:start position:0%
+same Omega value okay so it's not as
+ 
+
+ align:start position:0%
+same Omega value okay so it's not as
+simple as this one anymore as you can
+
+ align:start position:0%
+simple as this one anymore as you can
+ 
+
+ align:start position:0%
+simple as this one anymore as you can
+see right because when I slightly
+
+ align:start position:0%
+see right because when I slightly
+ 
+
+ align:start position:0%
+see right because when I slightly
+increase KX okay what I could do is okay
+
+ align:start position:0%
+increase KX okay what I could do is okay
+ 
+
+ align:start position:0%
+increase KX okay what I could do is okay
+I can slightly reduce KY to compensate
+
+ align:start position:0%
+I can slightly reduce KY to compensate
+ 
+
+ align:start position:0%
+I can slightly reduce KY to compensate
+the difference therefore I can still
+
+ align:start position:0%
+the difference therefore I can still
+ 
+
+ align:start position:0%
+the difference therefore I can still
+keep Omega which is the angular
+
+ align:start position:0%
+keep Omega which is the angular
+ 
+
+ align:start position:0%
+keep Omega which is the angular
+frequency of the oscillation the same
+
+ align:start position:0%
+frequency of the oscillation the same
+ 
+
+ align:start position:0%
+frequency of the oscillation the same
+okay so that can be seen from this
+
+ align:start position:0%
+okay so that can be seen from this
+ 
+
+ align:start position:0%
+okay so that can be seen from this
+demonstration on the slide you can see
+
+ align:start position:0%
+demonstration on the slide you can see
+ 
+
+ align:start position:0%
+demonstration on the slide you can see
+that this is actually one example
+
+ align:start position:0%
+that this is actually one example
+ 
+
+ align:start position:0%
+that this is actually one example
+dispersion relation okay this is
+
+ align:start position:0%
+dispersion relation okay this is
+ 
+
+ align:start position:0%
+dispersion relation okay this is
+actually the formula which we have on
+
+ align:start position:0%
+actually the formula which we have on
+ 
+
+ align:start position:0%
+actually the formula which we have on
+the board and what about if I set all
+
+ align:start position:0%
+the board and what about if I set all
+ 
+
+ align:start position:0%
+the board and what about if I set all
+those parameter and get example Omega
+
+ align:start position:0%
+those parameter and get example Omega
+ 
+
+ align:start position:0%
+those parameter and get example Omega
+square equal to Phi sine square K X and
+
+ align:start position:0%
+square equal to Phi sine square K X and
+ 
+
+ align:start position:0%
+square equal to Phi sine square K X and
+the +5 a sine squared K Y okay so what
+
+ align:start position:0%
+the +5 a sine squared K Y okay so what
+ 
+
+ align:start position:0%
+the +5 a sine squared K Y okay so what
+what will happen okay if I set my aah T
+
+ align:start position:0%
+what will happen okay if I set my aah T
+ 
+
+ align:start position:0%
+what will happen okay if I set my aah T
+and the M value so that I have this
+
+ align:start position:0%
+and the M value so that I have this
+ 
+
+ align:start position:0%
+and the M value so that I have this
+example what will happen if I have that
+
+ align:start position:0%
+example what will happen if I have that
+ 
+
+ align:start position:0%
+example what will happen if I have that
+a dispersion relation
+
+ align:start position:0%
+a dispersion relation
+ 
+
+ align:start position:0%
+a dispersion relation
+so if I go ahead and the proper allowed
+
+ align:start position:0%
+so if I go ahead and the proper allowed
+ 
+
+ align:start position:0%
+so if I go ahead and the proper allowed
+KX and KY value which keep one you see
+
+ align:start position:0%
+KX and KY value which keep one you see
+ 
+
+ align:start position:0%
+KX and KY value which keep one you see
+very definitive of pattern right from
+
+ align:start position:0%
+very definitive of pattern right from
+ 
+
+ align:start position:0%
+very definitive of pattern right from
+this right so you can see that hot
+
+ align:start position:0%
+this right so you can see that hot
+ 
+
+ align:start position:0%
+this right so you can see that hot
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+all those things on the circle can
+
+ align:start position:0%
+all those things on the circle can
+ 
+
+ align:start position:0%
+all those things on the circle can
+produce the angular frequency of Omega
+
+ align:start position:0%
+produce the angular frequency of Omega
+ 
+
+ align:start position:0%
+produce the angular frequency of Omega
+equal to one and what would be there
+
+ align:start position:0%
+equal to one and what would be there
+ 
+
+ align:start position:0%
+equal to one and what would be there
+yeah we all would be that no more more
+
+ align:start position:0%
+yeah we all would be that no more more
+ 
+
+ align:start position:0%
+yeah we all would be that no more more
+will be all possible linear combination
+
+ align:start position:0%
+will be all possible linear combination
+ 
+
+ align:start position:0%
+will be all possible linear combination
+of all those possible K X K Y pair you
+
+ align:start position:0%
+of all those possible K X K Y pair you
+ 
+
+ align:start position:0%
+of all those possible K X K Y pair you
+have a question yeah yes in general I
+
+ align:start position:0%
+have a question yeah yes in general I
+ 
+
+ align:start position:0%
+have a question yeah yes in general I
+think this you mean a circular shape or
+
+ align:start position:0%
+think this you mean a circular shape or
+ 
+
+ align:start position:0%
+think this you mean a circular shape or
+I think in general yes you need to have
+
+ align:start position:0%
+I think in general yes you need to have
+ 
+
+ align:start position:0%
+I think in general yes you need to have
+degeneracy right because you can put a
+
+ align:start position:0%
+degeneracy right because you can put a
+ 
+
+ align:start position:0%
+degeneracy right because you can put a
+shape of nappy circular for example hi
+
+ align:start position:0%
+shape of nappy circular for example hi
+ 
+
+ align:start position:0%
+shape of nappy circular for example hi
+so in general okay so it can be a
+
+ align:start position:0%
+so in general okay so it can be a
+ 
+
+ align:start position:0%
+so in general okay so it can be a
+general function which is up like a lot
+
+ align:start position:0%
+general function which is up like a lot
+ 
+
+ align:start position:0%
+general function which is up like a lot
+like the formula above right but you can
+
+ align:start position:0%
+like the formula above right but you can
+ 
+
+ align:start position:0%
+like the formula above right but you can
+still this argument still a price right
+
+ align:start position:0%
+still this argument still a price right
+ 
+
+ align:start position:0%
+still this argument still a price right
+so if you have some intermediate or make
+
+ align:start position:0%
+so if you have some intermediate or make
+ 
+
+ align:start position:0%
+so if you have some intermediate or make
+up value you can always site the
+
+ align:start position:0%
+up value you can always site the
+ 
+
+ align:start position:0%
+up value you can always site the
+increase or make ax and side it decrease
+
+ align:start position:0%
+increase or make ax and side it decrease
+ 
+
+ align:start position:0%
+increase or make ax and side it decrease
+KY and our still satisfy the same Omega
+
+ align:start position:0%
+KY and our still satisfy the same Omega
+ 
+
+ align:start position:0%
+KY and our still satisfy the same Omega
+value therefore all the normal modes
+
+ align:start position:0%
+value therefore all the normal modes
+ 
+
+ align:start position:0%
+value therefore all the normal modes
+with a specific Omega would be a linear
+
+ align:start position:0%
+with a specific Omega would be a linear
+ 
+
+ align:start position:0%
+with a specific Omega would be a linear
+combination all those possible no more
+
+ align:start position:0%
+combination all those possible no more
+ 
+
+ align:start position:0%
+combination all those possible no more
+more if you all those possible KX and KY
+
+ align:start position:0%
+more if you all those possible KX and KY
+ 
+
+ align:start position:0%
+more if you all those possible KX and KY
+pairs if you have an infinitely long
+
+ align:start position:0%
+pairs if you have an infinitely long
+ 
+
+ align:start position:0%
+pairs if you have an infinitely long
+system okay and that also applies to the
+
+ align:start position:0%
+system okay and that also applies to the
+ 
+
+ align:start position:0%
+system okay and that also applies to the
+other example when I have Omega equal to
+
+ align:start position:0%
+other example when I have Omega equal to
+ 
+
+ align:start position:0%
+other example when I have Omega equal to
+5 then you have slightly different
+
+ align:start position:0%
+5 then you have slightly different
+ 
+
+ align:start position:0%
+5 then you have slightly different
+behavior but the take-home message is
+
+ align:start position:0%
+behavior but the take-home message is
+ 
+
+ align:start position:0%
+behavior but the take-home message is
+that there are many many pairs of KX and
+
+ align:start position:0%
+that there are many many pairs of KX and
+ 
+
+ align:start position:0%
+that there are many many pairs of KX and
+KY which can create the same amount of
+
+ align:start position:0%
+KY which can create the same amount of
+ 
+
+ align:start position:0%
+KY which can create the same amount of
+Omega okay so that makes C's pretty
+
+ align:start position:0%
+Omega okay so that makes C's pretty
+ 
+
+ align:start position:0%
+Omega okay so that makes C's pretty
+complicated but they should be we can
+
+ align:start position:0%
+complicated but they should be we can
+ 
+
+ align:start position:0%
+complicated but they should be we can
+always still try to understand this by
+
+ align:start position:0%
+always still try to understand this by
+ 
+
+ align:start position:0%
+always still try to understand this by
+investigating all the possible care
+
+ align:start position:0%
+investigating all the possible care
+ 
+
+ align:start position:0%
+investigating all the possible care
+pairs of KX and KY and the other hand
+
+ align:start position:0%
+pairs of KX and KY and the other hand
+ 
+
+ align:start position:0%
+pairs of KX and KY and the other hand
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+as what we have discussed before before
+
+ align:start position:0%
+as what we have discussed before before
+ 
+
+ align:start position:0%
+as what we have discussed before before
+you introduced boundary condition for
+
+ align:start position:0%
+you introduced boundary condition for
+ 
+
+ align:start position:0%
+you introduced boundary condition for
+the one-dimensional system okay
+
+ align:start position:0%
+the one-dimensional system okay
+ 
+
+ align:start position:0%
+the one-dimensional system okay
+they are infinite number of possible k
+
+ align:start position:0%
+they are infinite number of possible k
+ 
+
+ align:start position:0%
+they are infinite number of possible k
+value right all the possible K values
+
+ align:start position:0%
+value right all the possible K values
+ 
+
+ align:start position:0%
+value right all the possible K values
+are allowed but after you add boundary
+
+ align:start position:0%
+are allowed but after you add boundary
+ 
+
+ align:start position:0%
+are allowed but after you add boundary
+condition for example I add walls around
+
+ align:start position:0%
+condition for example I add walls around
+ 
+
+ align:start position:0%
+condition for example I add walls around
+this system okay so that I basically
+
+ align:start position:0%
+this system okay so that I basically
+ 
+
+ align:start position:0%
+this system okay so that I basically
+have fixed boundary condition so
+
+ align:start position:0%
+have fixed boundary condition so
+ 
+
+ align:start position:0%
+have fixed boundary condition so
+basically the boundary condition is that
+
+ align:start position:0%
+basically the boundary condition is that
+ 
+
+ align:start position:0%
+basically the boundary condition is that
+the amplitude at X equal to 0 y equal to
+
+ align:start position:0%
+the amplitude at X equal to 0 y equal to
+ 
+
+ align:start position:0%
+the amplitude at X equal to 0 y equal to
+0 or X equal to Phi a times H Phi aah
+
+ align:start position:0%
+0 or X equal to Phi a times H Phi aah
+ 
+
+ align:start position:0%
+0 or X equal to Phi a times H Phi aah
+or y equal to 4ei be okay at the
+
+ align:start position:0%
+or y equal to 4ei be okay at the
+ 
+
+ align:start position:0%
+or y equal to 4ei be okay at the
+boundary the amplitude has to be equal
+
+ align:start position:0%
+boundary the amplitude has to be equal
+ 
+
+ align:start position:0%
+boundary the amplitude has to be equal
+to 0 because it's attached to a wall
+
+ align:start position:0%
+to 0 because it's attached to a wall
+ 
+
+ align:start position:0%
+to 0 because it's attached to a wall
+right okay when this happened
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this means that we will have a 4 & 4 we
+
+ align:start position:0%
+this means that we will have a 4 & 4 we
+ 
+
+ align:start position:0%
+this means that we will have a 4 & 4 we
+have four walls which we have
+
+ align:start position:0%
+have four walls which we have
+ 
+
+ align:start position:0%
+have four walls which we have
+corresponding boundary condition so that
+
+ align:start position:0%
+corresponding boundary condition so that
+ 
+
+ align:start position:0%
+corresponding boundary condition so that
+means I have to satisfy this four
+
+ align:start position:0%
+means I have to satisfy this four
+ 
+
+ align:start position:0%
+means I have to satisfy this four
+boundary condition side zero Y evaluated
+
+ align:start position:0%
+boundary condition side zero Y evaluated
+ 
+
+ align:start position:0%
+boundary condition side zero Y evaluated
+at any time will be equal to sy LH y ki
+
+ align:start position:0%
+at any time will be equal to sy LH y ki
+ 
+
+ align:start position:0%
+at any time will be equal to sy LH y ki
+will be equal to side X 0 T will be
+
+ align:start position:0%
+will be equal to side X 0 T will be
+ 
+
+ align:start position:0%
+will be equal to side X 0 T will be
+equal to Phi X F V T and this all equal
+
+ align:start position:0%
+equal to Phi X F V T and this all equal
+ 
+
+ align:start position:0%
+equal to Phi X F V T and this all equal
+to 0 right so those are not not very
+
+ align:start position:0%
+to 0 right so those are not not very
+ 
+
+ align:start position:0%
+to 0 right so those are not not very
+difficult to understand those are issues
+
+ align:start position:0%
+difficult to understand those are issues
+ 
+
+ align:start position:0%
+difficult to understand those are issues
+just the four walls around this system
+
+ align:start position:0%
+just the four walls around this system
+ 
+
+ align:start position:0%
+just the four walls around this system
+okay once you have all those conditions
+
+ align:start position:0%
+okay once you have all those conditions
+ 
+
+ align:start position:0%
+okay once you have all those conditions
+okay and that I of course I define H
+
+ align:start position:0%
+okay and that I of course I define H
+ 
+
+ align:start position:0%
+okay and that I of course I define H
+will be equal to five times
+
+ align:start position:0%
+will be equal to five times
+ 
+
+ align:start position:0%
+will be equal to five times
+aah right because there are five times
+
+ align:start position:0%
+aah right because there are five times
+ 
+
+ align:start position:0%
+aah right because there are five times
+five strings between the two wars in
+
+ align:start position:0%
+five strings between the two wars in
+ 
+
+ align:start position:0%
+five strings between the two wars in
+the horizontal direction and of course I
+
+ align:start position:0%
+the horizontal direction and of course I
+ 
+
+ align:start position:0%
+the horizontal direction and of course I
+also have defined here air we will be
+
+ align:start position:0%
+also have defined here air we will be
+ 
+
+ align:start position:0%
+also have defined here air we will be
+four times equal to a times a B okay so
+
+ align:start position:0%
+four times equal to a times a B okay so
+ 
+
+ align:start position:0%
+four times equal to a times a B okay so
+once I have all those four boundary
+
+ align:start position:0%
+once I have all those four boundary
+ 
+
+ align:start position:0%
+once I have all those four boundary
+conditions in praise that means I cannot
+
+ align:start position:0%
+conditions in praise that means I cannot
+ 
+
+ align:start position:0%
+conditions in praise that means I cannot
+arbitrarily choose K value and the fact
+
+ align:start position:0%
+arbitrarily choose K value and the fact
+ 
+
+ align:start position:0%
+arbitrarily choose K value and the fact
+right otherwise I will not be able to
+
+ align:start position:0%
+right otherwise I will not be able to
+ 
+
+ align:start position:0%
+right otherwise I will not be able to
+satisfy these four boundary conditions
+
+ align:start position:0%
+satisfy these four boundary conditions
+ 
+
+ align:start position:0%
+satisfy these four boundary conditions
+okay so now we actually will be able to
+
+ align:start position:0%
+okay so now we actually will be able to
+ 
+
+ align:start position:0%
+okay so now we actually will be able to
+figure out that there will be only four
+
+ align:start position:0%
+figure out that there will be only four
+ 
+
+ align:start position:0%
+figure out that there will be only four
+modes okay in this two-dimensional
+
+ align:start position:0%
+modes okay in this two-dimensional
+ 
+
+ align:start position:0%
+modes okay in this two-dimensional
+problem which will give the same Omega
+
+ align:start position:0%
+problem which will give the same Omega
+ 
+
+ align:start position:0%
+problem which will give the same Omega
+what are the four possible note what are
+
+ align:start position:0%
+what are the four possible note what are
+ 
+
+ align:start position:0%
+what are the four possible note what are
+the four four possible eigen vectors
+
+ align:start position:0%
+the four four possible eigen vectors
+ 
+
+ align:start position:0%
+the four four possible eigen vectors
+those are a exponential plus or minus I
+
+ align:start position:0%
+those are a exponential plus or minus I
+ 
+
+ align:start position:0%
+those are a exponential plus or minus I
+K X as X exponential plus minus I K Y as
+
+ align:start position:0%
+K X as X exponential plus minus I K Y as
+ 
+
+ align:start position:0%
+K X as X exponential plus minus I K Y as
+Y okay where the K X because of the
+
+ align:start position:0%
+Y okay where the K X because of the
+ 
+
+ align:start position:0%
+Y okay where the K X because of the
+boundary condition which we have solved
+
+ align:start position:0%
+boundary condition which we have solved
+ 
+
+ align:start position:0%
+boundary condition which we have solved
+that in the one-dimensional system KX
+
+ align:start position:0%
+that in the one-dimensional system KX
+ 
+
+ align:start position:0%
+that in the one-dimensional system KX
+will be equal to NX pi divided by H
+
+ align:start position:0%
+will be equal to NX pi divided by H
+ 
+
+ align:start position:0%
+will be equal to NX pi divided by H
+right in order to make when you know to
+
+ align:start position:0%
+right in order to make when you know to
+ 
+
+ align:start position:0%
+right in order to make when you know to
+to to match the boundary condition at X
+
+ align:start position:0%
+to to match the boundary condition at X
+ 
+
+ align:start position:0%
+to to match the boundary condition at X
+equal to 0 and X equal to L H and K Y
+
+ align:start position:0%
+equal to 0 and X equal to L H and K Y
+ 
+
+ align:start position:0%
+equal to 0 and X equal to L H and K Y
+will be equal to Y times pi divided by L
+
+ align:start position:0%
+will be equal to Y times pi divided by L
+ 
+
+ align:start position:0%
+will be equal to Y times pi divided by L
+V right that is should be a design to
+
+ align:start position:0%
+V right that is should be a design to
+ 
+
+ align:start position:0%
+V right that is should be a design to
+actually match the boundary condition at
+
+ align:start position:0%
+actually match the boundary condition at
+ 
+
+ align:start position:0%
+actually match the boundary condition at
+y equal to 0 and a y equal to LP okay so
+
+ align:start position:0%
+y equal to 0 and a y equal to LP okay so
+ 
+
+ align:start position:0%
+y equal to 0 and a y equal to LP okay so
+you can see that like what we see before
+
+ align:start position:0%
+you can see that like what we see before
+ 
+
+ align:start position:0%
+you can see that like what we see before
+with one-dimensional system after you
+
+ align:start position:0%
+with one-dimensional system after you
+ 
+
+ align:start position:0%
+with one-dimensional system after you
+introduce the boundary condition is not
+
+ align:start position:0%
+introduce the boundary condition is not
+ 
+
+ align:start position:0%
+introduce the boundary condition is not
+an infinite long system anymore
+
+ align:start position:0%
+an infinite long system anymore
+ 
+
+ align:start position:0%
+an infinite long system anymore
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+out K value which is the wave number in
+
+ align:start position:0%
+out K value which is the wave number in
+ 
+
+ align:start position:0%
+out K value which is the wave number in
+X and the y direction was a boy in this
+
+ align:start position:0%
+X and the y direction was a boy in this
+ 
+
+ align:start position:0%
+X and the y direction was a boy in this
+case it says she also become limited and
+
+ align:start position:0%
+case it says she also become limited and
+ 
+
+ align:start position:0%
+case it says she also become limited and
+only limited number of possible values
+
+ align:start position:0%
+only limited number of possible values
+ 
+
+ align:start position:0%
+only limited number of possible values
+are allowed okay
+
+ align:start position:0%
+are allowed okay
+ 
+
+ align:start position:0%
+are allowed okay
+in this case and X is allowed to be
+
+ align:start position:0%
+in this case and X is allowed to be
+ 
+
+ align:start position:0%
+in this case and X is allowed to be
+equal to 1 to until 4:00 and the my is
+
+ align:start position:0%
+equal to 1 to until 4:00 and the my is
+ 
+
+ align:start position:0%
+equal to 1 to until 4:00 and the my is
+equal to 1 to industry in this in this
+
+ align:start position:0%
+equal to 1 to industry in this in this
+ 
+
+ align:start position:0%
+equal to 1 to industry in this in this
+system we are talking about any question
+
+ align:start position:0%
+system we are talking about any question
+ 
+
+ align:start position:0%
+system we are talking about any question
+so what
+
+ align:start position:0%
+so what
+ 
+
+ align:start position:0%
+so what
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so so that so I was talking
+
+ align:start position:0%
+yeah yeah so so that so I was talking
+ 
+
+ align:start position:0%
+yeah yeah so so that so I was talking
+about when I choose KX and KY in the
+
+ align:start position:0%
+about when I choose KX and KY in the
+ 
+
+ align:start position:0%
+about when I choose KX and KY in the
+infinitely long system because K okay
+
+ align:start position:0%
+infinitely long system because K okay
+ 
+
+ align:start position:0%
+infinitely long system because K okay
+all the possible values of KX and KY
+
+ align:start position:0%
+all the possible values of KX and KY
+ 
+
+ align:start position:0%
+all the possible values of KX and KY
+allowed because I have a impeded long
+
+ align:start position:0%
+allowed because I have a impeded long
+ 
+
+ align:start position:0%
+allowed because I have a impeded long
+system with no boundary condition and in
+
+ align:start position:0%
+system with no boundary condition and in
+ 
+
+ align:start position:0%
+system with no boundary condition and in
+that case okay going back to this
+
+ align:start position:0%
+that case okay going back to this
+ 
+
+ align:start position:0%
+that case okay going back to this
+dispersion relation I have the freedom
+
+ align:start position:0%
+dispersion relation I have the freedom
+ 
+
+ align:start position:0%
+dispersion relation I have the freedom
+to okay so when I increase a little bit
+
+ align:start position:0%
+to okay so when I increase a little bit
+ 
+
+ align:start position:0%
+to okay so when I increase a little bit
+KX I can always decrease a little bit
+
+ align:start position:0%
+KX I can always decrease a little bit
+ 
+
+ align:start position:0%
+KX I can always decrease a little bit
+okay why okay so the question is why
+
+ align:start position:0%
+okay why okay so the question is why
+ 
+
+ align:start position:0%
+okay why okay so the question is why
+that's not the case right for the
+
+ align:start position:0%
+that's not the case right for the
+ 
+
+ align:start position:0%
+that's not the case right for the
+discrete case okay as you can see from
+
+ align:start position:0%
+discrete case okay as you can see from
+ 
+
+ align:start position:0%
+discrete case okay as you can see from
+here after we introduce the boundary
+
+ align:start position:0%
+here after we introduce the boundary
+ 
+
+ align:start position:0%
+here after we introduce the boundary
+condition the four boundary conditions
+
+ align:start position:0%
+condition the four boundary conditions
+ 
+
+ align:start position:0%
+condition the four boundary conditions
+here should be described the boundary at
+
+ align:start position:0%
+here should be described the boundary at
+ 
+
+ align:start position:0%
+here should be described the boundary at
+the four walls okay
+
+ align:start position:0%
+the four walls okay
+ 
+
+ align:start position:0%
+the four walls okay
+and what is going to happen is that you
+
+ align:start position:0%
+and what is going to happen is that you
+ 
+
+ align:start position:0%
+and what is going to happen is that you
+will also see that the loud k x value is
+
+ align:start position:0%
+will also see that the loud k x value is
+ 
+
+ align:start position:0%
+will also see that the loud k x value is
+becoming limited right because if you
+
+ align:start position:0%
+becoming limited right because if you
+ 
+
+ align:start position:0%
+becoming limited right because if you
+you cannot choose arbitrarily choose
+
+ align:start position:0%
+you cannot choose arbitrarily choose
+ 
+
+ align:start position:0%
+you cannot choose arbitrarily choose
+wavelength right if you choose society
+
+ align:start position:0%
+wavelength right if you choose society
+ 
+
+ align:start position:0%
+wavelength right if you choose society
+longer wavelengths like what we have
+
+ align:start position:0%
+longer wavelengths like what we have
+ 
+
+ align:start position:0%
+longer wavelengths like what we have
+been trying to do for the infinite
+
+ align:start position:0%
+been trying to do for the infinite
+ 
+
+ align:start position:0%
+been trying to do for the infinite
+Launceston lot doesn't match the
+
+ align:start position:0%
+Launceston lot doesn't match the
+ 
+
+ align:start position:0%
+Launceston lot doesn't match the
+boundary condition okay therefore you
+
+ align:start position:0%
+boundary condition okay therefore you
+ 
+
+ align:start position:0%
+boundary condition okay therefore you
+don't have this degree of freedom to
+
+ align:start position:0%
+don't have this degree of freedom to
+ 
+
+ align:start position:0%
+don't have this degree of freedom to
+choose you know side the higher side is
+
+ align:start position:0%
+choose you know side the higher side is
+ 
+
+ align:start position:0%
+choose you know side the higher side is
+lower KY when I have when I change the
+
+ align:start position:0%
+lower KY when I have when I change the
+ 
+
+ align:start position:0%
+lower KY when I have when I change the
+KX okay so you can see that the the
+
+ align:start position:0%
+KX okay so you can see that the the
+ 
+
+ align:start position:0%
+KX okay so you can see that the the
+allowed value out is quit therefore the
+
+ align:start position:0%
+allowed value out is quit therefore the
+ 
+
+ align:start position:0%
+allowed value out is quit therefore the
+number of possible combination of KX and
+
+ align:start position:0%
+number of possible combination of KX and
+ 
+
+ align:start position:0%
+number of possible combination of KX and
+KY is also limited and in this case it's
+
+ align:start position:0%
+KY is also limited and in this case it's
+ 
+
+ align:start position:0%
+KY is also limited and in this case it's
+actually very likely to be limited to be
+
+ align:start position:0%
+actually very likely to be limited to be
+ 
+
+ align:start position:0%
+actually very likely to be limited to be
+only four pairs which says you pass
+
+ align:start position:0%
+only four pairs which says you pass
+ 
+
+ align:start position:0%
+only four pairs which says you pass
+minus KX and the first minus KY okay all
+
+ align:start position:0%
+minus KX and the first minus KY okay all
+ 
+
+ align:start position:0%
+minus KX and the first minus KY okay all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so thank you for the question okay then
+
+ align:start position:0%
+so thank you for the question okay then
+ 
+
+ align:start position:0%
+so thank you for the question okay then
+once I have those I can do a linear
+
+ align:start position:0%
+once I have those I can do a linear
+ 
+
+ align:start position:0%
+once I have those I can do a linear
+combination of these four possible eigen
+
+ align:start position:0%
+combination of these four possible eigen
+ 
+
+ align:start position:0%
+combination of these four possible eigen
+vectors and also at the same time I will
+
+ align:start position:0%
+vectors and also at the same time I will
+ 
+
+ align:start position:0%
+vectors and also at the same time I will
+try to match the boundary condition
+
+ align:start position:0%
+try to match the boundary condition
+ 
+
+ align:start position:0%
+try to match the boundary condition
+right so if I jump forward basically
+
+ align:start position:0%
+right so if I jump forward basically
+ 
+
+ align:start position:0%
+right so if I jump forward basically
+what you can actually conclude is that
+
+ align:start position:0%
+what you can actually conclude is that
+ 
+
+ align:start position:0%
+what you can actually conclude is that
+sigh and X Y okay so it's with any
+
+ align:start position:0%
+sigh and X Y okay so it's with any
+ 
+
+ align:start position:0%
+sigh and X Y okay so it's with any
+x-value and y-value chosen foot for the
+
+ align:start position:0%
+x-value and y-value chosen foot for the
+ 
+
+ align:start position:0%
+x-value and y-value chosen foot for the
+determination of KX and KY and this is
+
+ align:start position:0%
+determination of KX and KY and this is
+ 
+
+ align:start position:0%
+determination of KX and KY and this is
+actually a function as a function of x
+
+ align:start position:0%
+actually a function as a function of x
+ 
+
+ align:start position:0%
+actually a function as a function of x
+and y know of course also time right
+
+ align:start position:0%
+and y know of course also time right
+ 
+
+ align:start position:0%
+and y know of course also time right
+when I actually also make it oscillate
+
+ align:start position:0%
+when I actually also make it oscillate
+ 
+
+ align:start position:0%
+when I actually also make it oscillate
+as a function of time this will be equal
+
+ align:start position:0%
+as a function of time this will be equal
+ 
+
+ align:start position:0%
+as a function of time this will be equal
+to some arbitrary constant anp2 and X Y
+
+ align:start position:0%
+to some arbitrary constant anp2 and X Y
+ 
+
+ align:start position:0%
+to some arbitrary constant anp2 and X Y
+sine and X PI X T YT pi ll H sine white
+
+ align:start position:0%
+sine and X PI X T YT pi ll H sine white
+ 
+
+ align:start position:0%
+sine and X PI X T YT pi ll H sine white
+I right / LP okay and of course this is
+
+ align:start position:0%
+I right / LP okay and of course this is
+ 
+
+ align:start position:0%
+I right / LP okay and of course this is
+actually you can see that this is a sign
+
+ align:start position:0%
+actually you can see that this is a sign
+ 
+
+ align:start position:0%
+actually you can see that this is a sign
+right it's actually the same as what we
+
+ align:start position:0%
+right it's actually the same as what we
+ 
+
+ align:start position:0%
+right it's actually the same as what we
+have done for the one-dimensional system
+
+ align:start position:0%
+have done for the one-dimensional system
+ 
+
+ align:start position:0%
+have done for the one-dimensional system
+right so if you have two boundary
+
+ align:start position:0%
+right so if you have two boundary
+ 
+
+ align:start position:0%
+right so if you have two boundary
+conditions at the beginning and the end
+
+ align:start position:0%
+conditions at the beginning and the end
+ 
+
+ align:start position:0%
+conditions at the beginning and the end
+therefore the the corresponding no more
+
+ align:start position:0%
+therefore the the corresponding no more
+ 
+
+ align:start position:0%
+therefore the the corresponding no more
+is always a sine function right so
+
+ align:start position:0%
+is always a sine function right so
+ 
+
+ align:start position:0%
+is always a sine function right so
+that's issue what we have learned from
+
+ align:start position:0%
+that's issue what we have learned from
+ 
+
+ align:start position:0%
+that's issue what we have learned from
+from the one-dimensional system and it
+
+ align:start position:0%
+from the one-dimensional system and it
+ 
+
+ align:start position:0%
+from the one-dimensional system and it
+is a so also the case for the
+
+ align:start position:0%
+is a so also the case for the
+ 
+
+ align:start position:0%
+is a so also the case for the
+two-dimensional system and of course we
+
+ align:start position:0%
+two-dimensional system and of course we
+ 
+
+ align:start position:0%
+two-dimensional system and of course we
+don't have don't forget this system this
+
+ align:start position:0%
+don't have don't forget this system this
+ 
+
+ align:start position:0%
+don't have don't forget this system this
+wave function is changing as a function
+
+ align:start position:0%
+wave function is changing as a function
+ 
+
+ align:start position:0%
+wave function is changing as a function
+of time oscillating up and down
+
+ align:start position:0%
+of time oscillating up and down
+ 
+
+ align:start position:0%
+of time oscillating up and down
+harmonically okay therefore we have sine
+
+ align:start position:0%
+harmonically okay therefore we have sine
+ 
+
+ align:start position:0%
+harmonically okay therefore we have sine
+Omega and X Y times T plus beta which is
+
+ align:start position:0%
+Omega and X Y times T plus beta which is
+ 
+
+ align:start position:0%
+Omega and X Y times T plus beta which is
+a face to be determined by initial
+
+ align:start position:0%
+a face to be determined by initial
+ 
+
+ align:start position:0%
+a face to be determined by initial
+conditions okay and you can see that the
+
+ align:start position:0%
+conditions okay and you can see that the
+ 
+
+ align:start position:0%
+conditions okay and you can see that the
+whole
+
+ align:start position:0%
+whole
+ 
+
+ align:start position:0%
+whole
+the whole equation a sign sign is
+
+ align:start position:0%
+the whole equation a sign sign is
+ 
+
+ align:start position:0%
+the whole equation a sign sign is
+multiplied by a sign or megha T plus
+
+ align:start position:0%
+multiplied by a sign or megha T plus
+ 
+
+ align:start position:0%
+multiplied by a sign or megha T plus
+five plus a beta function right so that
+
+ align:start position:0%
+five plus a beta function right so that
+ 
+
+ align:start position:0%
+five plus a beta function right so that
+means the shape is actually going up and
+
+ align:start position:0%
+means the shape is actually going up and
+ 
+
+ align:start position:0%
+means the shape is actually going up and
+down harmonically right so the shape is
+
+ align:start position:0%
+down harmonically right so the shape is
+ 
+
+ align:start position:0%
+down harmonically right so the shape is
+fixed which is sine times sine and the
+
+ align:start position:0%
+fixed which is sine times sine and the
+ 
+
+ align:start position:0%
+fixed which is sine times sine and the
+whole thing is oscillating at the same
+
+ align:start position:0%
+whole thing is oscillating at the same
+ 
+
+ align:start position:0%
+whole thing is oscillating at the same
+frequency at the same phase which is the
+
+ align:start position:0%
+frequency at the same phase which is the
+ 
+
+ align:start position:0%
+frequency at the same phase which is the
+definition of normal more right
+
+ align:start position:0%
+definition of normal more right
+ 
+
+ align:start position:0%
+definition of normal more right
+just a reminder and how do we actually
+
+ align:start position:0%
+just a reminder and how do we actually
+ 
+
+ align:start position:0%
+just a reminder and how do we actually
+imaging what is actually happening that
+
+ align:start position:0%
+imaging what is actually happening that
+ 
+
+ align:start position:0%
+imaging what is actually happening that
+brings me to the demonstration right so
+
+ align:start position:0%
+brings me to the demonstration right so
+ 
+
+ align:start position:0%
+brings me to the demonstration right so
+we can issue the really visualize how
+
+ align:start position:0%
+we can issue the really visualize how
+ 
+
+ align:start position:0%
+we can issue the really visualize how
+this kind of system would look like by a
+
+ align:start position:0%
+this kind of system would look like by a
+ 
+
+ align:start position:0%
+this kind of system would look like by a
+little simulation right so suppose I
+
+ align:start position:0%
+little simulation right so suppose I
+ 
+
+ align:start position:0%
+little simulation right so suppose I
+choose an X and an y equal to one and
+
+ align:start position:0%
+choose an X and an y equal to one and
+ 
+
+ align:start position:0%
+choose an X and an y equal to one and
+see what will happen so this is actually
+
+ align:start position:0%
+see what will happen so this is actually
+ 
+
+ align:start position:0%
+see what will happen so this is actually
+the kind of oscillation you will expect
+
+ align:start position:0%
+the kind of oscillation you will expect
+ 
+
+ align:start position:0%
+the kind of oscillation you will expect
+right so if you choose an exit go to one
+
+ align:start position:0%
+right so if you choose an exit go to one
+ 
+
+ align:start position:0%
+right so if you choose an exit go to one
+and y equal to one then this is a system
+
+ align:start position:0%
+and y equal to one then this is a system
+ 
+
+ align:start position:0%
+and y equal to one then this is a system
+right basically you have sine function
+
+ align:start position:0%
+right basically you have sine function
+ 
+
+ align:start position:0%
+right basically you have sine function
+with no note in x and y direction okay
+
+ align:start position:0%
+with no note in x and y direction okay
+ 
+
+ align:start position:0%
+with no note in x and y direction okay
+therefore if you look at this this this
+
+ align:start position:0%
+therefore if you look at this this this
+ 
+
+ align:start position:0%
+therefore if you look at this this this
+simulation you can see that there will
+
+ align:start position:0%
+simulation you can see that there will
+ 
+
+ align:start position:0%
+simulation you can see that there will
+be no note in the XY plane and and and
+
+ align:start position:0%
+be no note in the XY plane and and and
+ 
+
+ align:start position:0%
+be no note in the XY plane and and and
+all those particles are either going
+
+ align:start position:0%
+all those particles are either going
+ 
+
+ align:start position:0%
+all those particles are either going
+toward you or going away from you right
+
+ align:start position:0%
+toward you or going away from you right
+ 
+
+ align:start position:0%
+toward you or going away from you right
+in the only oscillate in the in the Z
+
+ align:start position:0%
+in the only oscillate in the in the Z
+ 
+
+ align:start position:0%
+in the only oscillate in the in the Z
+Direction okay in this simulation and
+
+ align:start position:0%
+Direction okay in this simulation and
+ 
+
+ align:start position:0%
+Direction okay in this simulation and
+also you can see that now I can increase
+
+ align:start position:0%
+also you can see that now I can increase
+ 
+
+ align:start position:0%
+also you can see that now I can increase
+for example the KX to be so I can
+
+ align:start position:0%
+for example the KX to be so I can
+ 
+
+ align:start position:0%
+for example the KX to be so I can
+increase the KX by setting X to be two
+
+ align:start position:0%
+increase the KX by setting X to be two
+ 
+
+ align:start position:0%
+increase the KX by setting X to be two
+and see what happen so what is going to
+
+ align:start position:0%
+and see what happen so what is going to
+ 
+
+ align:start position:0%
+and see what happen so what is going to
+happen is that if I have higher K X in
+
+ align:start position:0%
+happen is that if I have higher K X in
+ 
+
+ align:start position:0%
+happen is that if I have higher K X in
+the X direction so the next possible
+
+ align:start position:0%
+the X direction so the next possible
+ 
+
+ align:start position:0%
+the X direction so the next possible
+normal mode is that you have
+
+ align:start position:0%
+normal mode is that you have
+ 
+
+ align:start position:0%
+normal mode is that you have
+as for sine wave right in the X
+
+ align:start position:0%
+as for sine wave right in the X
+ 
+
+ align:start position:0%
+as for sine wave right in the X
+direction then what you are going to see
+
+ align:start position:0%
+direction then what you are going to see
+ 
+
+ align:start position:0%
+direction then what you are going to see
+is that you are going to see two
+
+ align:start position:0%
+is that you are going to see two
+ 
+
+ align:start position:0%
+is that you are going to see two
+components in this in this demonstration
+
+ align:start position:0%
+components in this in this demonstration
+ 
+
+ align:start position:0%
+components in this in this demonstration
+and one one is one part of the system
+
+ align:start position:0%
+and one one is one part of the system
+ 
+
+ align:start position:0%
+and one one is one part of the system
+says you moving to where you while the
+
+ align:start position:0%
+says you moving to where you while the
+ 
+
+ align:start position:0%
+says you moving to where you while the
+other part they all have a half part of
+
+ align:start position:0%
+other part they all have a half part of
+ 
+
+ align:start position:0%
+other part they all have a half part of
+the season is actually moving away from
+
+ align:start position:0%
+the season is actually moving away from
+ 
+
+ align:start position:0%
+the season is actually moving away from
+you and you can actually see the note or
+
+ align:start position:0%
+you and you can actually see the note or
+ 
+
+ align:start position:0%
+you and you can actually see the note or
+know the line in this case because we
+
+ align:start position:0%
+know the line in this case because we
+ 
+
+ align:start position:0%
+know the line in this case because we
+are talking about a two dimensional
+
+ align:start position:0%
+are talking about a two dimensional
+ 
+
+ align:start position:0%
+are talking about a two dimensional
+system in the middle of the distribution
+
+ align:start position:0%
+system in the middle of the distribution
+ 
+
+ align:start position:0%
+system in the middle of the distribution
+okay of course we can actually go waste
+
+ align:start position:0%
+okay of course we can actually go waste
+ 
+
+ align:start position:0%
+okay of course we can actually go waste
+go crazy right I can set this to really
+
+ align:start position:0%
+go crazy right I can set this to really
+ 
+
+ align:start position:0%
+go crazy right I can set this to really
+high value so in this case like the
+
+ align:start position:0%
+high value so in this case like the
+ 
+
+ align:start position:0%
+high value so in this case like the
+highest value I can set this three and
+
+ align:start position:0%
+highest value I can set this three and
+ 
+
+ align:start position:0%
+highest value I can set this three and
+the four okay and see what happened and
+
+ align:start position:0%
+the four okay and see what happened and
+ 
+
+ align:start position:0%
+the four okay and see what happened and
+this is actually a beautiful shape which
+
+ align:start position:0%
+this is actually a beautiful shape which
+ 
+
+ align:start position:0%
+this is actually a beautiful shape which
+is actually complicated but
+
+ align:start position:0%
+is actually complicated but
+ 
+
+ align:start position:0%
+is actually complicated but
+understandable which we can as we see
+
+ align:start position:0%
+understandable which we can as we see
+ 
+
+ align:start position:0%
+understandable which we can as we see
+from funding in this demonstration and
+
+ align:start position:0%
+from funding in this demonstration and
+ 
+
+ align:start position:0%
+from funding in this demonstration and
+all those all those little particles
+
+ align:start position:0%
+all those all those little particles
+ 
+
+ align:start position:0%
+all those all those little particles
+indices and other thing up and down at
+
+ align:start position:0%
+indices and other thing up and down at
+ 
+
+ align:start position:0%
+indices and other thing up and down at
+the cent and your frequency and also in
+
+ align:start position:0%
+the cent and your frequency and also in
+ 
+
+ align:start position:0%
+the cent and your frequency and also in
+the same face any questions okay so now
+
+ align:start position:0%
+the same face any questions okay so now
+ 
+
+ align:start position:0%
+the same face any questions okay so now
+we have done the discrete a case right
+
+ align:start position:0%
+we have done the discrete a case right
+ 
+
+ align:start position:0%
+we have done the discrete a case right
+and of course we can also go to the
+
+ align:start position:0%
+and of course we can also go to the
+ 
+
+ align:start position:0%
+and of course we can also go to the
+continuous case right so if we go to a
+
+ align:start position:0%
+continuous case right so if we go to a
+ 
+
+ align:start position:0%
+continuous case right so if we go to a
+continuous limit okay now I can assume
+
+ align:start position:0%
+continuous limit okay now I can assume
+ 
+
+ align:start position:0%
+continuous limit okay now I can assume
+that there is a symmetry between
+
+ align:start position:0%
+that there is a symmetry between
+ 
+
+ align:start position:0%
+that there is a symmetry between
+horizontal direction and the vertical
+
+ align:start position:0%
+horizontal direction and the vertical
+ 
+
+ align:start position:0%
+horizontal direction and the vertical
+direction I assume that th is equal to
+
+ align:start position:0%
+direction I assume that th is equal to
+ 
+
+ align:start position:0%
+direction I assume that th is equal to
+PV is equal to T okay
+
+ align:start position:0%
+PV is equal to T okay
+ 
+
+ align:start position:0%
+PV is equal to T okay
+and also I assume that the time scale in
+
+ align:start position:0%
+and also I assume that the time scale in
+ 
+
+ align:start position:0%
+and also I assume that the time scale in
+the X direction and the y directions are
+
+ align:start position:0%
+the X direction and the y directions are
+ 
+
+ align:start position:0%
+the X direction and the y directions are
+equal and the length scale is a-okay in
+
+ align:start position:0%
+equal and the length scale is a-okay in
+ 
+
+ align:start position:0%
+equal and the length scale is a-okay in
+order to make the whole system
+
+ align:start position:0%
+order to make the whole system
+ 
+
+ align:start position:0%
+order to make the whole system
+continuous okay I need to increase the
+
+ align:start position:0%
+continuous okay I need to increase the
+ 
+
+ align:start position:0%
+continuous okay I need to increase the
+number of objects in this system at the
+
+ align:start position:0%
+number of objects in this system at the
+ 
+
+ align:start position:0%
+number of objects in this system at the
+same time I also need to decrease
+
+ align:start position:0%
+same time I also need to decrease
+ 
+
+ align:start position:0%
+same time I also need to decrease
+the distance between all those objects
+
+ align:start position:0%
+the distance between all those objects
+ 
+
+ align:start position:0%
+the distance between all those objects
+right so therefore I need to have this
+
+ align:start position:0%
+right so therefore I need to have this
+ 
+
+ align:start position:0%
+right so therefore I need to have this
+lens skill goes to zero and what is
+
+ align:start position:0%
+lens skill goes to zero and what is
+ 
+
+ align:start position:0%
+lens skill goes to zero and what is
+going to happen is that if I rewrite my
+
+ align:start position:0%
+going to happen is that if I rewrite my
+ 
+
+ align:start position:0%
+going to happen is that if I rewrite my
+Omega okay which is dispersion which is
+
+ align:start position:0%
+Omega okay which is dispersion which is
+ 
+
+ align:start position:0%
+Omega okay which is dispersion which is
+a dispersion relation what I'm going to
+
+ align:start position:0%
+a dispersion relation what I'm going to
+ 
+
+ align:start position:0%
+a dispersion relation what I'm going to
+get is 40 divided by n times a KX
+
+ align:start position:0%
+get is 40 divided by n times a KX
+ 
+
+ align:start position:0%
+get is 40 divided by n times a KX
+squared a squared divided by 4 plus 40
+
+ align:start position:0%
+squared a squared divided by 4 plus 40
+ 
+
+ align:start position:0%
+squared a squared divided by 4 plus 40
+over MA okay y squared a squared over 4
+
+ align:start position:0%
+over MA okay y squared a squared over 4
+ 
+
+ align:start position:0%
+over MA okay y squared a squared over 4
+all right this is actually because I'm
+
+ align:start position:0%
+all right this is actually because I'm
+ 
+
+ align:start position:0%
+all right this is actually because I'm
+taking a H and V to be equal to a and
+
+ align:start position:0%
+taking a H and V to be equal to a and
+ 
+
+ align:start position:0%
+taking a H and V to be equal to a and
+also having that to be very very small
+
+ align:start position:0%
+also having that to be very very small
+ 
+
+ align:start position:0%
+also having that to be very very small
+value therefore sine theta is roughly 2
+
+ align:start position:0%
+value therefore sine theta is roughly 2
+ 
+
+ align:start position:0%
+value therefore sine theta is roughly 2
+theta right therefore I can immediately
+
+ align:start position:0%
+theta right therefore I can immediately
+ 
+
+ align:start position:0%
+theta right therefore I can immediately
+write down this expression okay and this
+
+ align:start position:0%
+write down this expression okay and this
+ 
+
+ align:start position:0%
+write down this expression okay and this
+will be equal to PA D by D PI + KX
+
+ align:start position:0%
+will be equal to PA D by D PI + KX
+ 
+
+ align:start position:0%
+will be equal to PA D by D PI + KX
+square plus KY school okay so we are
+
+ align:start position:0%
+square plus KY school okay so we are
+ 
+
+ align:start position:0%
+square plus KY school okay so we are
+facing exactly the same situation when I
+
+ align:start position:0%
+facing exactly the same situation when I
+ 
+
+ align:start position:0%
+facing exactly the same situation when I
+decrease a I am going to add more
+
+ align:start position:0%
+decrease a I am going to add more
+ 
+
+ align:start position:0%
+decrease a I am going to add more
+objects into this system right but I
+
+ align:start position:0%
+objects into this system right but I
+ 
+
+ align:start position:0%
+objects into this system right but I
+don't want to have an infinitely large
+
+ align:start position:0%
+don't want to have an infinitely large
+ 
+
+ align:start position:0%
+don't want to have an infinitely large
+mass right therefore I also need to
+
+ align:start position:0%
+mass right therefore I also need to
+ 
+
+ align:start position:0%
+mass right therefore I also need to
+actually fix the ratio of M and a ok so
+
+ align:start position:0%
+actually fix the ratio of M and a ok so
+ 
+
+ align:start position:0%
+actually fix the ratio of M and a ok so
+that actually when I actually increase
+
+ align:start position:0%
+that actually when I actually increase
+ 
+
+ align:start position:0%
+that actually when I actually increase
+number of object I don't actually make
+
+ align:start position:0%
+number of object I don't actually make
+ 
+
+ align:start position:0%
+number of object I don't actually make
+the total mass as it goes to infinity
+
+ align:start position:0%
+the total mass as it goes to infinity
+ 
+
+ align:start position:0%
+the total mass as it goes to infinity
+okay so what I could do is that okay I
+
+ align:start position:0%
+okay so what I could do is that okay I
+ 
+
+ align:start position:0%
+okay so what I could do is that okay I
+can define Rho s put usage with the
+
+ align:start position:0%
+can define Rho s put usage with the
+ 
+
+ align:start position:0%
+can define Rho s put usage with the
+surface mass density okay so the surface
+
+ align:start position:0%
+surface mass density okay so the surface
+ 
+
+ align:start position:0%
+surface mass density okay so the surface
+mass density is defined as n divided by
+
+ align:start position:0%
+mass density is defined as n divided by
+ 
+
+ align:start position:0%
+mass density is defined as n divided by
+a square and I can also define a surface
+
+ align:start position:0%
+a square and I can also define a surface
+ 
+
+ align:start position:0%
+a square and I can also define a surface
+tension
+
+ align:start position:0%
+tension
+ 
+
+ align:start position:0%
+tension
+okay surface tension T s will be equal
+
+ align:start position:0%
+okay surface tension T s will be equal
+ 
+
+ align:start position:0%
+okay surface tension T s will be equal
+to T
+
+ align:start position:0%
+to T
+ 
+
+ align:start position:0%
+to T
+a-okay and in this case okay basically I
+
+ align:start position:0%
+a-okay and in this case okay basically I
+ 
+
+ align:start position:0%
+a-okay and in this case okay basically I
+will be able to control so that when I
+
+ align:start position:0%
+will be able to control so that when I
+ 
+
+ align:start position:0%
+will be able to control so that when I
+increase the number of objects
+
+ align:start position:0%
+increase the number of objects
+ 
+
+ align:start position:0%
+increase the number of objects
+masculine go to infinity and I have a
+
+ align:start position:0%
+masculine go to infinity and I have a
+ 
+
+ align:start position:0%
+masculine go to infinity and I have a
+constant surface tension and constant
+
+ align:start position:0%
+constant surface tension and constant
+ 
+
+ align:start position:0%
+constant surface tension and constant
+surface mass density okay if I have
+
+ align:start position:0%
+surface mass density okay if I have
+ 
+
+ align:start position:0%
+surface mass density okay if I have
+defined these two quantity then this
+
+ align:start position:0%
+defined these two quantity then this
+ 
+
+ align:start position:0%
+defined these two quantity then this
+will become he s divided by Rho s KX
+
+ align:start position:0%
+will become he s divided by Rho s KX
+ 
+
+ align:start position:0%
+will become he s divided by Rho s KX
+square plus KY square and this will be
+
+ align:start position:0%
+square plus KY square and this will be
+ 
+
+ align:start position:0%
+square plus KY square and this will be
+equal to PS divided by Rho s K vector
+
+ align:start position:0%
+equal to PS divided by Rho s K vector
+ 
+
+ align:start position:0%
+equal to PS divided by Rho s K vector
+squared okay and this K vector is a
+
+ align:start position:0%
+squared okay and this K vector is a
+ 
+
+ align:start position:0%
+squared okay and this K vector is a
+two-dimensional vector so we are
+
+ align:start position:0%
+two-dimensional vector so we are
+ 
+
+ align:start position:0%
+two-dimensional vector so we are
+actually almost there to make it
+
+ align:start position:0%
+actually almost there to make it
+ 
+
+ align:start position:0%
+actually almost there to make it
+continuous so now I can make a goes to a
+
+ align:start position:0%
+continuous so now I can make a goes to a
+ 
+
+ align:start position:0%
+continuous so now I can make a goes to a
+very small value with fixed PS and a Rho
+
+ align:start position:0%
+very small value with fixed PS and a Rho
+ 
+
+ align:start position:0%
+very small value with fixed PS and a Rho
+s very similar to what we have learned
+
+ align:start position:0%
+s very similar to what we have learned
+ 
+
+ align:start position:0%
+s very similar to what we have learned
+from the one-dimensional case basically
+
+ align:start position:0%
+from the one-dimensional case basically
+ 
+
+ align:start position:0%
+from the one-dimensional case basically
+what we actually found a lot of time in
+
+ align:start position:0%
+what we actually found a lot of time in
+ 
+
+ align:start position:0%
+what we actually found a lot of time in
+a one-dimensional case is that n minus 1
+
+ align:start position:0%
+a one-dimensional case is that n minus 1
+ 
+
+ align:start position:0%
+a one-dimensional case is that n minus 1
+K matrix become minus T over Rho L by 2
+
+ align:start position:0%
+K matrix become minus T over Rho L by 2
+ 
+
+ align:start position:0%
+K matrix become minus T over Rho L by 2
+square by dou X square in a
+
+ align:start position:0%
+square by dou X square in a
+ 
+
+ align:start position:0%
+square by dou X square in a
+one-dimensional case okay and in the two
+
+ align:start position:0%
+one-dimensional case okay and in the two
+ 
+
+ align:start position:0%
+one-dimensional case okay and in the two
+dimensional case without walking through
+
+ align:start position:0%
+dimensional case without walking through
+ 
+
+ align:start position:0%
+dimensional case without walking through
+all the detail of mass basically what we
+
+ align:start position:0%
+all the detail of mass basically what we
+ 
+
+ align:start position:0%
+all the detail of mass basically what we
+are going to get this partial square
+
+ align:start position:0%
+are going to get this partial square
+ 
+
+ align:start position:0%
+are going to get this partial square
+partial T squared side X Y it's in
+
+ align:start position:0%
+partial T squared side X Y it's in
+ 
+
+ align:start position:0%
+partial T squared side X Y it's in
+tertiary or functional X&Y and the time
+
+ align:start position:0%
+tertiary or functional X&Y and the time
+ 
+
+ align:start position:0%
+tertiary or functional X&Y and the time
+right because this is a 3 a 2
+
+ align:start position:0%
+right because this is a 3 a 2
+ 
+
+ align:start position:0%
+right because this is a 3 a 2
+dimensional system and this will be
+
+ align:start position:0%
+dimensional system and this will be
+ 
+
+ align:start position:0%
+dimensional system and this will be
+equal to v square R square plus X square
+
+ align:start position:0%
+equal to v square R square plus X square
+ 
+
+ align:start position:0%
+equal to v square R square plus X square
+plus R square by 2 y spoon side X Y
+
+ align:start position:0%
+plus R square by 2 y spoon side X Y
+ 
+
+ align:start position:0%
+plus R square by 2 y spoon side X Y
+very similar to what we have done for
+
+ align:start position:0%
+very similar to what we have done for
+ 
+
+ align:start position:0%
+very similar to what we have done for
+the wine dimensional system and of
+
+ align:start position:0%
+the wine dimensional system and of
+ 
+
+ align:start position:0%
+the wine dimensional system and of
+course I can I can actually define this
+
+ align:start position:0%
+course I can I can actually define this
+ 
+
+ align:start position:0%
+course I can I can actually define this
+estelle task where right and basically
+
+ align:start position:0%
+estelle task where right and basically
+ 
+
+ align:start position:0%
+estelle task where right and basically
+what you are going to get is v square L
+
+ align:start position:0%
+what you are going to get is v square L
+ 
+
+ align:start position:0%
+what you are going to get is v square L
+square sy X Y okay so basically we can
+
+ align:start position:0%
+square sy X Y okay so basically we can
+ 
+
+ align:start position:0%
+square sy X Y okay so basically we can
+see this wave equation but this wave
+
+ align:start position:0%
+see this wave equation but this wave
+ 
+
+ align:start position:0%
+see this wave equation but this wave
+equation is now a two dimensional wave
+
+ align:start position:0%
+equation is now a two dimensional wave
+ 
+
+ align:start position:0%
+equation is now a two dimensional wave
+equation okay and we can also figure out
+
+ align:start position:0%
+equation okay and we can also figure out
+ 
+
+ align:start position:0%
+equation okay and we can also figure out
+well be the V value right so what would
+
+ align:start position:0%
+well be the V value right so what would
+ 
+
+ align:start position:0%
+well be the V value right so what would
+be the velocity the velocity which we
+
+ align:start position:0%
+be the velocity the velocity which we
+ 
+
+ align:start position:0%
+be the velocity the velocity which we
+will go to be square root of P s over R
+
+ align:start position:0%
+will go to be square root of P s over R
+ 
+
+ align:start position:0%
+will go to be square root of P s over R
+or s okay this is actually very similar
+
+ align:start position:0%
+or s okay this is actually very similar
+ 
+
+ align:start position:0%
+or s okay this is actually very similar
+to what we have done for the continuous
+
+ align:start position:0%
+to what we have done for the continuous
+ 
+
+ align:start position:0%
+to what we have done for the continuous
+case and in this case what we pressed
+
+ align:start position:0%
+case and in this case what we pressed
+ 
+
+ align:start position:0%
+case and in this case what we pressed
+here over Rho L is TS over Rho s okay
+
+ align:start position:0%
+here over Rho L is TS over Rho s okay
+ 
+
+ align:start position:0%
+here over Rho L is TS over Rho s okay
+therefore what we actually see is that
+
+ align:start position:0%
+therefore what we actually see is that
+ 
+
+ align:start position:0%
+therefore what we actually see is that
+if I increase the surface tension then
+
+ align:start position:0%
+if I increase the surface tension then
+ 
+
+ align:start position:0%
+if I increase the surface tension then
+the velocity will increase if I decrease
+
+ align:start position:0%
+the velocity will increase if I decrease
+ 
+
+ align:start position:0%
+the velocity will increase if I decrease
+the mass per unit area Rho s then I will
+
+ align:start position:0%
+the mass per unit area Rho s then I will
+ 
+
+ align:start position:0%
+the mass per unit area Rho s then I will
+be able to have a much faster troubling
+
+ align:start position:0%
+be able to have a much faster troubling
+ 
+
+ align:start position:0%
+be able to have a much faster troubling
+way from these kind of media okay
+
+ align:start position:0%
+way from these kind of media okay
+ 
+
+ align:start position:0%
+way from these kind of media okay
+and what we can actually immediately
+
+ align:start position:0%
+and what we can actually immediately
+ 
+
+ align:start position:0%
+and what we can actually immediately
+also write down is that the size will be
+
+ align:start position:0%
+also write down is that the size will be
+ 
+
+ align:start position:0%
+also write down is that the size will be
+equal proportional to a sine KX times X
+
+ align:start position:0%
+equal proportional to a sine KX times X
+ 
+
+ align:start position:0%
+equal proportional to a sine KX times X
+sine okay Y times y in sine Omega T plus
+
+ align:start position:0%
+sine okay Y times y in sine Omega T plus
+ 
+
+ align:start position:0%
+sine okay Y times y in sine Omega T plus
+five where Omega is they should be
+
+ align:start position:0%
+five where Omega is they should be
+ 
+
+ align:start position:0%
+five where Omega is they should be
+calculated from the input KX and KY for
+
+ align:start position:0%
+calculated from the input KX and KY for
+ 
+
+ align:start position:0%
+calculated from the input KX and KY for
+this for this standing wave solution
+
+ align:start position:0%
+this for this standing wave solution
+ 
+
+ align:start position:0%
+this for this standing wave solution
+okay and very similarly okay I can also
+
+ align:start position:0%
+okay and very similarly okay I can also
+ 
+
+ align:start position:0%
+okay and very similarly okay I can also
+argue that in the three-dimensional case
+
+ align:start position:0%
+argue that in the three-dimensional case
+ 
+
+ align:start position:0%
+argue that in the three-dimensional case
+I can actually follow exactly the same
+
+ align:start position:0%
+I can actually follow exactly the same
+ 
+
+ align:start position:0%
+I can actually follow exactly the same
+argument basically in the
+
+ align:start position:0%
+argument basically in the
+ 
+
+ align:start position:0%
+argument basically in the
+three-dimensional case as well we
+
+ align:start position:0%
+three-dimensional case as well we
+ 
+
+ align:start position:0%
+three-dimensional case as well we
+already see in the electromagnetic wave
+
+ align:start position:0%
+already see in the electromagnetic wave
+ 
+
+ align:start position:0%
+already see in the electromagnetic wave
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+question the street I mentioned no wave
+
+ align:start position:0%
+question the street I mentioned no wave
+ 
+
+ align:start position:0%
+question the street I mentioned no wave
+equation can be written as partial
+
+ align:start position:0%
+equation can be written as partial
+ 
+
+ align:start position:0%
+equation can be written as partial
+square partial t square side is a
+
+ align:start position:0%
+square partial t square side is a
+ 
+
+ align:start position:0%
+square partial t square side is a
+function of x y and z and t and this
+
+ align:start position:0%
+function of x y and z and t and this
+ 
+
+ align:start position:0%
+function of x y and z and t and this
+will be equal to we square R square
+
+ align:start position:0%
+will be equal to we square R square
+ 
+
+ align:start position:0%
+will be equal to we square R square
+partial x squared plus partial square
+
+ align:start position:0%
+partial x squared plus partial square
+ 
+
+ align:start position:0%
+partial x squared plus partial square
+partial Y square partial square v square
+
+ align:start position:0%
+partial Y square partial square v square
+ 
+
+ align:start position:0%
+partial Y square partial square v square
+sy is a function X Y Z and the questions
+
+ align:start position:0%
+sy is a function X Y Z and the questions
+ 
+
+ align:start position:0%
+sy is a function X Y Z and the questions
+so far
+
+ align:start position:0%
+so far
+ 
+
+ align:start position:0%
+so far
+nope okay so everything is Chris called
+
+ align:start position:0%
+nope okay so everything is Chris called
+ 
+
+ align:start position:0%
+nope okay so everything is Chris called
+the good ear right okay so so this is
+
+ align:start position:0%
+the good ear right okay so so this is
+ 
+
+ align:start position:0%
+the good ear right okay so so this is
+actually the the animation which I show
+
+ align:start position:0%
+actually the the animation which I show
+ 
+
+ align:start position:0%
+actually the the animation which I show
+you before already so this is actually
+
+ align:start position:0%
+you before already so this is actually
+ 
+
+ align:start position:0%
+you before already so this is actually
+the toot I mean to toot I mentioned no
+
+ align:start position:0%
+the toot I mean to toot I mentioned no
+ 
+
+ align:start position:0%
+the toot I mean to toot I mentioned no
+vibration of membranes okay so basically
+
+ align:start position:0%
+vibration of membranes okay so basically
+ 
+
+ align:start position:0%
+vibration of membranes okay so basically
+the first one is actually well I have
+
+ align:start position:0%
+the first one is actually well I have
+ 
+
+ align:start position:0%
+the first one is actually well I have
+shown you when I choose various small K
+
+ align:start position:0%
+shown you when I choose various small K
+ 
+
+ align:start position:0%
+shown you when I choose various small K
+value okay which way should be only make
+
+ align:start position:0%
+value okay which way should be only make
+ 
+
+ align:start position:0%
+value okay which way should be only make
+a stop of the sign and which match the
+
+ align:start position:0%
+a stop of the sign and which match the
+ 
+
+ align:start position:0%
+a stop of the sign and which match the
+boundary country condition then
+
+ align:start position:0%
+boundary country condition then
+ 
+
+ align:start position:0%
+boundary country condition then
+basically you see that their oscillation
+
+ align:start position:0%
+basically you see that their oscillation
+ 
+
+ align:start position:0%
+basically you see that their oscillation
+which you have the middle part which is
+
+ align:start position:0%
+which you have the middle part which is
+ 
+
+ align:start position:0%
+which you have the middle part which is
+either going toward you or going away
+
+ align:start position:0%
+either going toward you or going away
+ 
+
+ align:start position:0%
+either going toward you or going away
+from you in this continuous system so
+
+ align:start position:0%
+from you in this continuous system so
+ 
+
+ align:start position:0%
+from you in this continuous system so
+basically the solution is actually
+
+ align:start position:0%
+basically the solution is actually
+ 
+
+ align:start position:0%
+basically the solution is actually
+romantic about the the same as what we
+
+ align:start position:0%
+romantic about the the same as what we
+ 
+
+ align:start position:0%
+romantic about the the same as what we
+have seen in the discrete sister okay
+
+ align:start position:0%
+have seen in the discrete sister okay
+ 
+
+ align:start position:0%
+have seen in the discrete sister okay
+that's issue what I want to say and also
+
+ align:start position:0%
+that's issue what I want to say and also
+ 
+
+ align:start position:0%
+that's issue what I want to say and also
+of course you can increase the the K
+
+ align:start position:0%
+of course you can increase the the K
+ 
+
+ align:start position:0%
+of course you can increase the the K
+value and so that you go to the higher
+
+ align:start position:0%
+value and so that you go to the higher
+ 
+
+ align:start position:0%
+value and so that you go to the higher
+frequency normal more and you can see
+
+ align:start position:0%
+frequency normal more and you can see
+ 
+
+ align:start position:0%
+frequency normal more and you can see
+that if you have more and more nodal
+
+ align:start position:0%
+that if you have more and more nodal
+ 
+
+ align:start position:0%
+that if you have more and more nodal
+lines okay which is actually the lines
+
+ align:start position:0%
+lines okay which is actually the lines
+ 
+
+ align:start position:0%
+lines okay which is actually the lines
+describing the the the lines which we
+
+ align:start position:0%
+describing the the the lines which we
+ 
+
+ align:start position:0%
+describing the the the lines which we
+actually have no oscillation okay at all
+
+ align:start position:0%
+actually have no oscillation okay at all
+ 
+
+ align:start position:0%
+actually have no oscillation okay at all
+on the surface for example in this case
+
+ align:start position:0%
+on the surface for example in this case
+ 
+
+ align:start position:0%
+on the surface for example in this case
+the nodal line is actually passing
+
+ align:start position:0%
+the nodal line is actually passing
+ 
+
+ align:start position:0%
+the nodal line is actually passing
+through the middle of this figure right
+
+ align:start position:0%
+through the middle of this figure right
+ 
+
+ align:start position:0%
+through the middle of this figure right
+because all those little mass although
+
+ align:start position:0%
+because all those little mass although
+ 
+
+ align:start position:0%
+because all those little mass although
+all the other particles are vibrating
+
+ align:start position:0%
+all the other particles are vibrating
+ 
+
+ align:start position:0%
+all the other particles are vibrating
+like crazy but
+
+ align:start position:0%
+like crazy but
+ 
+
+ align:start position:0%
+like crazy but
+the all the particles on this line the
+
+ align:start position:0%
+the all the particles on this line the
+ 
+
+ align:start position:0%
+the all the particles on this line the
+nodal line as you not at all moving
+
+ align:start position:0%
+nodal line as you not at all moving
+ 
+
+ align:start position:0%
+nodal line as you not at all moving
+because that's actually actually at the
+
+ align:start position:0%
+because that's actually actually at the
+ 
+
+ align:start position:0%
+because that's actually actually at the
+disposition which is actually having one
+
+ align:start position:0%
+disposition which is actually having one
+ 
+
+ align:start position:0%
+disposition which is actually having one
+of the sine function equal to zero
+
+ align:start position:0%
+of the sine function equal to zero
+ 
+
+ align:start position:0%
+of the sine function equal to zero
+therefore no matter what you do as a
+
+ align:start position:0%
+therefore no matter what you do as a
+ 
+
+ align:start position:0%
+therefore no matter what you do as a
+bunch of time how you evolve this system
+
+ align:start position:0%
+bunch of time how you evolve this system
+ 
+
+ align:start position:0%
+bunch of time how you evolve this system
+or those particle at a line who will not
+
+ align:start position:0%
+or those particle at a line who will not
+ 
+
+ align:start position:0%
+or those particle at a line who will not
+move at all okay and this was actually
+
+ align:start position:0%
+move at all okay and this was actually
+ 
+
+ align:start position:0%
+move at all okay and this was actually
+demonstrated from this demo here
+
+ align:start position:0%
+demonstrated from this demo here
+ 
+
+ align:start position:0%
+demonstrated from this demo here
+especially cottony figures right so you
+
+ align:start position:0%
+especially cottony figures right so you
+ 
+
+ align:start position:0%
+especially cottony figures right so you
+can see that in a two dimensional case
+
+ align:start position:0%
+can see that in a two dimensional case
+ 
+
+ align:start position:0%
+can see that in a two dimensional case
+the figures can looks very complicated
+
+ align:start position:0%
+the figures can looks very complicated
+ 
+
+ align:start position:0%
+the figures can looks very complicated
+so basically what is actually showing
+
+ align:start position:0%
+so basically what is actually showing
+ 
+
+ align:start position:0%
+so basically what is actually showing
+here is that you have a square plate and
+
+ align:start position:0%
+here is that you have a square plate and
+ 
+
+ align:start position:0%
+here is that you have a square plate and
+it's attached to vibrator and basically
+
+ align:start position:0%
+it's attached to vibrator and basically
+ 
+
+ align:start position:0%
+it's attached to vibrator and basically
+this vibrator can be control I can
+
+ align:start position:0%
+this vibrator can be control I can
+ 
+
+ align:start position:0%
+this vibrator can be control I can
+change the frequency of the vibration
+
+ align:start position:0%
+change the frequency of the vibration
+ 
+
+ align:start position:0%
+change the frequency of the vibration
+okay when when I reach resonance which
+
+ align:start position:0%
+okay when when I reach resonance which
+ 
+
+ align:start position:0%
+okay when when I reach resonance which
+excite one of the normal okay then this
+
+ align:start position:0%
+excite one of the normal okay then this
+ 
+
+ align:start position:0%
+excite one of the normal okay then this
+this plate will be oscillating in a
+
+ align:start position:0%
+this plate will be oscillating in a
+ 
+
+ align:start position:0%
+this plate will be oscillating in a
+specific pattern and though and those
+
+ align:start position:0%
+specific pattern and though and those
+ 
+
+ align:start position:0%
+specific pattern and though and those
+lines are actually showing you that the
+
+ align:start position:0%
+lines are actually showing you that the
+ 
+
+ align:start position:0%
+lines are actually showing you that the
+press which you have no oscillation at
+
+ align:start position:0%
+press which you have no oscillation at
+ 
+
+ align:start position:0%
+press which you have no oscillation at
+all as a function of time right because
+
+ align:start position:0%
+all as a function of time right because
+ 
+
+ align:start position:0%
+all as a function of time right because
+if I to example now turn on this demo
+
+ align:start position:0%
+if I to example now turn on this demo
+ 
+
+ align:start position:0%
+if I to example now turn on this demo
+again you can see that if I turn on this
+
+ align:start position:0%
+again you can see that if I turn on this
+ 
+
+ align:start position:0%
+again you can see that if I turn on this
+demo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can see that Lois always stand on
+
+ align:start position:0%
+you can see that Lois always stand on
+ 
+
+ align:start position:0%
+you can see that Lois always stand on
+the place of vibrating because now i
+
+ align:start position:0%
+the place of vibrating because now i
+ 
+
+ align:start position:0%
+the place of vibrating because now i
+isolated the disparate when upfront by
+
+ align:start position:0%
+isolated the disparate when upfront by
+ 
+
+ align:start position:0%
+isolated the disparate when upfront by
+the by the vibration generator at the
+
+ align:start position:0%
+the by the vibration generator at the
+ 
+
+ align:start position:0%
+the by the vibration generator at the
+button by the motor at the button and if
+
+ align:start position:0%
+button by the motor at the button and if
+ 
+
+ align:start position:0%
+button by the motor at the button and if
+I change the oscillation frequency so
+
+ align:start position:0%
+I change the oscillation frequency so
+ 
+
+ align:start position:0%
+I change the oscillation frequency so
+you can see that his frequency to the
+
+ align:start position:0%
+you can see that his frequency to the
+ 
+
+ align:start position:0%
+you can see that his frequency to the
+match with one of the normal frequency
+
+ align:start position:0%
+match with one of the normal frequency
+ 
+
+ align:start position:0%
+match with one of the normal frequency
+therefore they were not a lot of
+
+ align:start position:0%
+therefore they were not a lot of
+ 
+
+ align:start position:0%
+therefore they were not a lot of
+activity but if I now change the MP to
+
+ align:start position:0%
+activity but if I now change the MP to
+ 
+
+ align:start position:0%
+activity but if I now change the MP to
+I'm sorry I change the frequency so that
+
+ align:start position:0%
+I'm sorry I change the frequency so that
+ 
+
+ align:start position:0%
+I'm sorry I change the frequency so that
+in match with one of the oscillation
+
+ align:start position:0%
+in match with one of the oscillation
+ 
+
+ align:start position:0%
+in match with one of the oscillation
+frequency for the one of the normal mode
+
+ align:start position:0%
+frequency for the one of the normal mode
+ 
+
+ align:start position:0%
+frequency for the one of the normal mode
+of this system you can see the heart
+
+ align:start position:0%
+of this system you can see the heart
+ 
+
+ align:start position:0%
+of this system you can see the heart
+some really cryptic pattern is formed
+
+ align:start position:0%
+some really cryptic pattern is formed
+ 
+
+ align:start position:0%
+some really cryptic pattern is formed
+right you can see that mood you have
+
+ align:start position:0%
+right you can see that mood you have
+ 
+
+ align:start position:0%
+right you can see that mood you have
+very complicated pattern and if I put my
+
+ align:start position:0%
+very complicated pattern and if I put my
+ 
+
+ align:start position:0%
+very complicated pattern and if I put my
+finger in one of the line here
+
+ align:start position:0%
+finger in one of the line here
+ 
+
+ align:start position:0%
+finger in one of the line here
+I don't feel the vibration but on the
+
+ align:start position:0%
+I don't feel the vibration but on the
+ 
+
+ align:start position:0%
+I don't feel the vibration but on the
+other hand if I put my finger here I can
+
+ align:start position:0%
+other hand if I put my finger here I can
+ 
+
+ align:start position:0%
+other hand if I put my finger here I can
+actually feel that this lot of vibration
+
+ align:start position:0%
+actually feel that this lot of vibration
+ 
+
+ align:start position:0%
+actually feel that this lot of vibration
+at a point I can always change the
+
+ align:start position:0%
+at a point I can always change the
+ 
+
+ align:start position:0%
+at a point I can always change the
+frequency and see what will happen and
+
+ align:start position:0%
+frequency and see what will happen and
+ 
+
+ align:start position:0%
+frequency and see what will happen and
+you can see that now I increase the
+
+ align:start position:0%
+you can see that now I increase the
+ 
+
+ align:start position:0%
+you can see that now I increase the
+frequency and now I actually trying to
+
+ align:start position:0%
+frequency and now I actually trying to
+ 
+
+ align:start position:0%
+frequency and now I actually trying to
+excite another mode
+
+ align:start position:0%
+excite another mode
+ 
+
+ align:start position:0%
+excite another mode
+now I need some more sand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can see that I rent on these Stroh
+
+ align:start position:0%
+you can see that I rent on these Stroh
+ 
+
+ align:start position:0%
+you can see that I rent on these Stroh
+sent on this plate and you can see that
+
+ align:start position:0%
+sent on this plate and you can see that
+ 
+
+ align:start position:0%
+sent on this plate and you can see that
+those Center that she pans around until
+
+ align:start position:0%
+those Center that she pans around until
+ 
+
+ align:start position:0%
+those Center that she pans around until
+is sit until it sees the nodal line
+
+ align:start position:0%
+is sit until it sees the nodal line
+ 
+
+ align:start position:0%
+is sit until it sees the nodal line
+which no vibration actually happened
+
+ align:start position:0%
+which no vibration actually happened
+ 
+
+ align:start position:0%
+which no vibration actually happened
+okay so that's go back to so one of the
+
+ align:start position:0%
+okay so that's go back to so one of the
+ 
+
+ align:start position:0%
+okay so that's go back to so one of the
+lower frequency mode which will show you
+
+ align:start position:0%
+lower frequency mode which will show you
+ 
+
+ align:start position:0%
+lower frequency mode which will show you
+before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the question is okay you can see
+
+ align:start position:0%
+now the question is okay you can see
+ 
+
+ align:start position:0%
+now the question is okay you can see
+this complicated pattern almost look
+
+ align:start position:0%
+this complicated pattern almost look
+ 
+
+ align:start position:0%
+this complicated pattern almost look
+ridiculous okay
+
+ align:start position:0%
+ridiculous okay
+ 
+
+ align:start position:0%
+ridiculous okay
+can we actually reproduce this pattern
+
+ align:start position:0%
+can we actually reproduce this pattern
+ 
+
+ align:start position:0%
+can we actually reproduce this pattern
+by our calculation right okay so we have
+
+ align:start position:0%
+by our calculation right okay so we have
+ 
+
+ align:start position:0%
+by our calculation right okay so we have
+seen that okay I can conclude that the
+
+ align:start position:0%
+seen that okay I can conclude that the
+ 
+
+ align:start position:0%
+seen that okay I can conclude that the
+the normal mode will looks like this
+
+ align:start position:0%
+the normal mode will looks like this
+ 
+
+ align:start position:0%
+the normal mode will looks like this
+right so therefore I must be able to
+
+ align:start position:0%
+right so therefore I must be able to
+ 
+
+ align:start position:0%
+right so therefore I must be able to
+explain all those pattern which is
+
+ align:start position:0%
+explain all those pattern which is
+ 
+
+ align:start position:0%
+explain all those pattern which is
+actually shown and not figure in this
+
+ align:start position:0%
+actually shown and not figure in this
+ 
+
+ align:start position:0%
+actually shown and not figure in this
+experiment right so that's actually what
+
+ align:start position:0%
+experiment right so that's actually what
+ 
+
+ align:start position:0%
+experiment right so that's actually what
+I'm going to do to give you a try
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this is actually a detour and
+
+ align:start position:0%
+so so this is actually a detour and
+ 
+
+ align:start position:0%
+so so this is actually a detour and
+demonstration which I actually wrote so
+
+ align:start position:0%
+demonstration which I actually wrote so
+ 
+
+ align:start position:0%
+demonstration which I actually wrote so
+this demonstration actually have the
+
+ align:start position:0%
+this demonstration actually have the
+ 
+
+ align:start position:0%
+this demonstration actually have the
+solution to this two-dimensional problem
+
+ align:start position:0%
+solution to this two-dimensional problem
+ 
+
+ align:start position:0%
+solution to this two-dimensional problem
+and also the boundary condition is that
+
+ align:start position:0%
+and also the boundary condition is that
+ 
+
+ align:start position:0%
+and also the boundary condition is that
+all say the condition which I actually
+
+ align:start position:0%
+all say the condition which I actually
+ 
+
+ align:start position:0%
+all say the condition which I actually
+comes from my solution is that I'd
+
+ align:start position:0%
+comes from my solution is that I'd
+ 
+
+ align:start position:0%
+comes from my solution is that I'd
+require the center of the plate to be
+
+ align:start position:0%
+require the center of the plate to be
+ 
+
+ align:start position:0%
+require the center of the plate to be
+driven right so because that's actually
+
+ align:start position:0%
+driven right so because that's actually
+ 
+
+ align:start position:0%
+driven right so because that's actually
+where I start to vibrate this plate and
+
+ align:start position:0%
+where I start to vibrate this plate and
+ 
+
+ align:start position:0%
+where I start to vibrate this plate and
+I Drive this plate up and down and see
+
+ align:start position:0%
+I Drive this plate up and down and see
+ 
+
+ align:start position:0%
+I Drive this plate up and down and see
+what is going to happen okay so from
+
+ align:start position:0%
+what is going to happen okay so from
+ 
+
+ align:start position:0%
+what is going to happen okay so from
+this and a digital calculation you can
+
+ align:start position:0%
+this and a digital calculation you can
+ 
+
+ align:start position:0%
+this and a digital calculation you can
+see that you expect a circle okay in the
+
+ align:start position:0%
+see that you expect a circle okay in the
+ 
+
+ align:start position:0%
+see that you expect a circle okay in the
+middle and also four lines in which we
+
+ align:start position:0%
+middle and also four lines in which we
+ 
+
+ align:start position:0%
+middle and also four lines in which we
+should cover this circle and also there
+
+ align:start position:0%
+should cover this circle and also there
+ 
+
+ align:start position:0%
+should cover this circle and also there
+are some strange structure at the edge
+
+ align:start position:0%
+are some strange structure at the edge
+ 
+
+ align:start position:0%
+are some strange structure at the edge
+of the of the plate and you can actually
+
+ align:start position:0%
+of the of the plate and you can actually
+ 
+
+ align:start position:0%
+of the of the plate and you can actually
+compare this calculation to this result
+
+ align:start position:0%
+compare this calculation to this result
+ 
+
+ align:start position:0%
+compare this calculation to this result
+it doesn't really match perfectly right
+
+ align:start position:0%
+it doesn't really match perfectly right
+ 
+
+ align:start position:0%
+it doesn't really match perfectly right
+so you can see that there's an
+
+ align:start position:0%
+so you can see that there's an
+ 
+
+ align:start position:0%
+so you can see that there's an
+imperfection but you choose you get a
+
+ align:start position:0%
+imperfection but you choose you get a
+ 
+
+ align:start position:0%
+imperfection but you choose you get a
+ring in the in the middle and you to see
+
+ align:start position:0%
+ring in the in the middle and you to see
+ 
+
+ align:start position:0%
+ring in the in the middle and you to see
+this 1 2 3 4 5 6 7 8 8 lines produce in
+
+ align:start position:0%
+this 1 2 3 4 5 6 7 8 8 lines produce in
+ 
+
+ align:start position:0%
+this 1 2 3 4 5 6 7 8 8 lines produce in
+this experiment so this is this
+
+ align:start position:0%
+this experiment so this is this
+ 
+
+ align:start position:0%
+this experiment so this is this
+experiment is not perfect because they
+
+ align:start position:0%
+experiment is not perfect because they
+ 
+
+ align:start position:0%
+experiment is not perfect because they
+are like as you know stiffness of this
+
+ align:start position:0%
+are like as you know stiffness of this
+ 
+
+ align:start position:0%
+are like as you know stiffness of this
+thing and also something energy
+
+ align:start position:0%
+thing and also something energy
+ 
+
+ align:start position:0%
+thing and also something energy
+dissipation etcetera but you can see
+
+ align:start position:0%
+dissipation etcetera but you can see
+ 
+
+ align:start position:0%
+dissipation etcetera but you can see
+that sort of we can as we use our
+
+ align:start position:0%
+that sort of we can as we use our
+ 
+
+ align:start position:0%
+that sort of we can as we use our
+calculation to explain this pattern
+
+ align:start position:0%
+calculation to explain this pattern
+ 
+
+ align:start position:0%
+calculation to explain this pattern
+that's really cool
+
+ align:start position:0%
+that's really cool
+ 
+
+ align:start position:0%
+that's really cool
+right and the advantage is that now I
+
+ align:start position:0%
+right and the advantage is that now I
+ 
+
+ align:start position:0%
+right and the advantage is that now I
+have this wonderful simulation I can put
+
+ align:start position:0%
+have this wonderful simulation I can put
+ 
+
+ align:start position:0%
+have this wonderful simulation I can put
+in all the crazy numbers and you will
+
+ align:start position:0%
+in all the crazy numbers and you will
+ 
+
+ align:start position:0%
+in all the crazy numbers and you will
+see that ha if I increase the K value
+
+ align:start position:0%
+see that ha if I increase the K value
+ 
+
+ align:start position:0%
+see that ha if I increase the K value
+and I can actually really make all kinds
+
+ align:start position:0%
+and I can actually really make all kinds
+ 
+
+ align:start position:0%
+and I can actually really make all kinds
+of ridiculous pattern out of this and
+
+ align:start position:0%
+of ridiculous pattern out of this and
+ 
+
+ align:start position:0%
+of ridiculous pattern out of this and
+that all these things Inc actually be
+
+ align:start position:0%
+that all these things Inc actually be
+ 
+
+ align:start position:0%
+that all these things Inc actually be
+kind of realized by this experiment so
+
+ align:start position:0%
+kind of realized by this experiment so
+ 
+
+ align:start position:0%
+kind of realized by this experiment so
+you can see that for example I can now
+
+ align:start position:0%
+you can see that for example I can now
+ 
+
+ align:start position:0%
+you can see that for example I can now
+also turn on this and I can actually
+
+ align:start position:0%
+also turn on this and I can actually
+ 
+
+ align:start position:0%
+also turn on this and I can actually
+increase the temperature so that you
+
+ align:start position:0%
+increase the temperature so that you
+ 
+
+ align:start position:0%
+increase the temperature so that you
+increase the frequency to very high
+
+ align:start position:0%
+increase the frequency to very high
+ 
+
+ align:start position:0%
+increase the frequency to very high
+frequency for example
+
+ align:start position:0%
+frequency for example
+ 
+
+ align:start position:0%
+frequency for example
+then I can see that all the pattern
+
+ align:start position:0%
+then I can see that all the pattern
+ 
+
+ align:start position:0%
+then I can see that all the pattern
+really become much more complicating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now I have a circle and there are
+
+ align:start position:0%
+right now I have a circle and there are
+ 
+
+ align:start position:0%
+right now I have a circle and there are
+many many more structures which is in in
+
+ align:start position:0%
+many many more structures which is in in
+ 
+
+ align:start position:0%
+many many more structures which is in in
+the surrounding area and of course I can
+
+ align:start position:0%
+the surrounding area and of course I can
+ 
+
+ align:start position:0%
+the surrounding area and of course I can
+again increase increase and see what
+
+ align:start position:0%
+again increase increase and see what
+ 
+
+ align:start position:0%
+again increase increase and see what
+happened I don't know what is going to
+
+ align:start position:0%
+happened I don't know what is going to
+ 
+
+ align:start position:0%
+happened I don't know what is going to
+happen because every time I do this
+
+ align:start position:0%
+happen because every time I do this
+ 
+
+ align:start position:0%
+happen because every time I do this
+experiment I get a different pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now this seems to be a very nice
+
+ align:start position:0%
+now this seems to be a very nice
+ 
+
+ align:start position:0%
+now this seems to be a very nice
+frequency it's getting harder and harder
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can see that this is it looks really
+
+ align:start position:0%
+you can see that this is it looks really
+ 
+
+ align:start position:0%
+you can see that this is it looks really
+crazy
+
+ align:start position:0%
+crazy
+ 
+
+ align:start position:0%
+crazy
+holy mackerel right what is what the
+
+ align:start position:0%
+holy mackerel right what is what the
+ 
+
+ align:start position:0%
+holy mackerel right what is what the
+hell is this right so you can see that
+
+ align:start position:0%
+hell is this right so you can see that
+ 
+
+ align:start position:0%
+hell is this right so you can see that
+all this crazy pattern K can be can be
+
+ align:start position:0%
+all this crazy pattern K can be can be
+ 
+
+ align:start position:0%
+all this crazy pattern K can be can be
+created and of course during the break
+
+ align:start position:0%
+created and of course during the break
+ 
+
+ align:start position:0%
+created and of course during the break
+you are welcome to come over and play
+
+ align:start position:0%
+you are welcome to come over and play
+ 
+
+ align:start position:0%
+you are welcome to come over and play
+with this so you can see that we can
+
+ align:start position:0%
+with this so you can see that we can
+ 
+
+ align:start position:0%
+with this so you can see that we can
+actually understand sort of the pattern
+
+ align:start position:0%
+actually understand sort of the pattern
+ 
+
+ align:start position:0%
+actually understand sort of the pattern
+produced from this experiment that's
+
+ align:start position:0%
+produced from this experiment that's
+ 
+
+ align:start position:0%
+produced from this experiment that's
+actually very exciting because that's
+
+ align:start position:0%
+actually very exciting because that's
+ 
+
+ align:start position:0%
+actually very exciting because that's
+actually why we are physicists right we
+
+ align:start position:0%
+actually why we are physicists right we
+ 
+
+ align:start position:0%
+actually why we are physicists right we
+would like to know why those patterns
+
+ align:start position:0%
+would like to know why those patterns
+ 
+
+ align:start position:0%
+would like to know why those patterns
+are formed and now you know why those
+
+ align:start position:0%
+are formed and now you know why those
+ 
+
+ align:start position:0%
+are formed and now you know why those
+patterns are formed because there are no
+
+ align:start position:0%
+patterns are formed because there are no
+ 
+
+ align:start position:0%
+patterns are formed because there are no
+lines in these two dimensional normal
+
+ align:start position:0%
+lines in these two dimensional normal
+ 
+
+ align:start position:0%
+lines in these two dimensional normal
+modes and the lost sense really love to
+
+ align:start position:0%
+modes and the lost sense really love to
+ 
+
+ align:start position:0%
+modes and the lost sense really love to
+sit there because you want to sit in the
+
+ align:start position:0%
+sit there because you want to sit in the
+ 
+
+ align:start position:0%
+sit there because you want to sit in the
+press which we you don't have a lot of
+
+ align:start position:0%
+press which we you don't have a lot of
+ 
+
+ align:start position:0%
+press which we you don't have a lot of
+vibration it's not very comfortable
+
+ align:start position:0%
+vibration it's not very comfortable
+ 
+
+ align:start position:0%
+vibration it's not very comfortable
+right so so you sit in the press which
+
+ align:start position:0%
+right so so you sit in the press which
+ 
+
+ align:start position:0%
+right so so you sit in the press which
+mmm
+
+ align:start position:0%
+mmm
+ 
+
+ align:start position:0%
+mmm
+my brain is your problem where is your
+
+ align:start position:0%
+my brain is your problem where is your
+ 
+
+ align:start position:0%
+my brain is your problem where is your
+problem I sit here where there were no
+
+ align:start position:0%
+problem I sit here where there were no
+ 
+
+ align:start position:0%
+problem I sit here where there were no
+vibration right so that's actually how
+
+ align:start position:0%
+vibration right so that's actually how
+ 
+
+ align:start position:0%
+vibration right so that's actually how
+we actually explain these strange
+
+ align:start position:0%
+we actually explain these strange
+ 
+
+ align:start position:0%
+we actually explain these strange
+figures which we can see and just for
+
+ align:start position:0%
+figures which we can see and just for
+ 
+
+ align:start position:0%
+figures which we can see and just for
+fun you can see that I can also generate
+
+ align:start position:0%
+fun you can see that I can also generate
+ 
+
+ align:start position:0%
+fun you can see that I can also generate
+all kinds of craziness you can input all
+
+ align:start position:0%
+all kinds of craziness you can input all
+ 
+
+ align:start position:0%
+all kinds of craziness you can input all
+kinds of different an x and y value and
+
+ align:start position:0%
+kinds of different an x and y value and
+ 
+
+ align:start position:0%
+kinds of different an x and y value and
+you get all those wonderful figures for
+
+ align:start position:0%
+you get all those wonderful figures for
+ 
+
+ align:start position:0%
+you get all those wonderful figures for
+free maybe we can actually make some
+
+ align:start position:0%
+free maybe we can actually make some
+ 
+
+ align:start position:0%
+free maybe we can actually make some
+t-shirt with all those figures are on
+
+ align:start position:0%
+t-shirt with all those figures are on
+ 
+
+ align:start position:0%
+t-shirt with all those figures are on
+the t-shirt right okay so we had a lot
+
+ align:start position:0%
+the t-shirt right okay so we had a lot
+ 
+
+ align:start position:0%
+the t-shirt right okay so we had a lot
+of fun with this two-dimensional parade
+
+ align:start position:0%
+of fun with this two-dimensional parade
+ 
+
+ align:start position:0%
+of fun with this two-dimensional parade
+how about what would happen if I have a
+
+ align:start position:0%
+how about what would happen if I have a
+ 
+
+ align:start position:0%
+how about what would happen if I have a
+circular parade okay what what does it
+
+ align:start position:0%
+circular parade okay what what does it
+ 
+
+ align:start position:0%
+circular parade okay what what does it
+do okay unfortunately I will not be able
+
+ align:start position:0%
+do okay unfortunately I will not be able
+ 
+
+ align:start position:0%
+do okay unfortunately I will not be able
+to solve the two-dimensional prey
+
+ align:start position:0%
+to solve the two-dimensional prey
+ 
+
+ align:start position:0%
+to solve the two-dimensional prey
+problem in front of you because that
+
+ align:start position:0%
+problem in front of you because that
+ 
+
+ align:start position:0%
+problem in front of you because that
+will give you a passive function right
+
+ align:start position:0%
+will give you a passive function right
+ 
+
+ align:start position:0%
+will give you a passive function right
+which is not the end of the world
+
+ align:start position:0%
+which is not the end of the world
+ 
+
+ align:start position:0%
+which is not the end of the world
+but there is actually kind of
+
+ align:start position:0%
+but there is actually kind of
+ 
+
+ align:start position:0%
+but there is actually kind of
+complicated if I put it in the meter
+
+ align:start position:0%
+complicated if I put it in the meter
+ 
+
+ align:start position:0%
+complicated if I put it in the meter
+exam that says you're not very
+
+ align:start position:0%
+exam that says you're not very
+ 
+
+ align:start position:0%
+exam that says you're not very
+encouraging right so so but I can
+
+ align:start position:0%
+encouraging right so so but I can
+ 
+
+ align:start position:0%
+encouraging right so so but I can
+actually tell you what will be the
+
+ align:start position:0%
+actually tell you what will be the
+ 
+
+ align:start position:0%
+actually tell you what will be the
+solution the solution will be a part of
+
+ align:start position:0%
+solution the solution will be a part of
+ 
+
+ align:start position:0%
+solution the solution will be a part of
+function so basically you will have a
+
+ align:start position:0%
+function so basically you will have a
+ 
+
+ align:start position:0%
+function so basically you will have a
+lot of rings ring like structure if I
+
+ align:start position:0%
+lot of rings ring like structure if I
+ 
+
+ align:start position:0%
+lot of rings ring like structure if I
+have a circuit
+
+ align:start position:0%
+have a circuit
+ 
+
+ align:start position:0%
+have a circuit
+prayed okay and I can actually do an
+
+ align:start position:0%
+prayed okay and I can actually do an
+ 
+
+ align:start position:0%
+prayed okay and I can actually do an
+experiment which racially so shoot the
+
+ align:start position:0%
+experiment which racially so shoot the
+ 
+
+ align:start position:0%
+experiment which racially so shoot the
+behavior of the circular boundary
+
+ align:start position:0%
+behavior of the circular boundary
+ 
+
+ align:start position:0%
+behavior of the circular boundary
+condition and see what kind of pattern
+
+ align:start position:0%
+condition and see what kind of pattern
+ 
+
+ align:start position:0%
+condition and see what kind of pattern
+can we as you see so here I have a
+
+ align:start position:0%
+can we as you see so here I have a
+ 
+
+ align:start position:0%
+can we as you see so here I have a
+Catholic kind of complicated experiment
+
+ align:start position:0%
+Catholic kind of complicated experiment
+ 
+
+ align:start position:0%
+Catholic kind of complicated experiment
+okay so here I have this ring which I
+
+ align:start position:0%
+okay so here I have this ring which I
+ 
+
+ align:start position:0%
+okay so here I have this ring which I
+would like to produce a soap film and on
+
+ align:start position:0%
+would like to produce a soap film and on
+ 
+
+ align:start position:0%
+would like to produce a soap film and on
+this ring okay so see if I and
+
+ align:start position:0%
+this ring okay so see if I and
+ 
+
+ align:start position:0%
+this ring okay so see if I and
+successful kind of okay now I can put
+
+ align:start position:0%
+successful kind of okay now I can put
+ 
+
+ align:start position:0%
+successful kind of okay now I can put
+this soft film in front of in front of
+
+ align:start position:0%
+this soft film in front of in front of
+ 
+
+ align:start position:0%
+this soft film in front of in front of
+in front of the speaker okay I can
+
+ align:start position:0%
+in front of the speaker okay I can
+ 
+
+ align:start position:0%
+in front of the speaker okay I can
+actually isolate the this scene filmed
+
+ align:start position:0%
+actually isolate the this scene filmed
+ 
+
+ align:start position:0%
+actually isolate the this scene filmed
+the membranes by the speaker okay who
+
+ align:start position:0%
+the membranes by the speaker okay who
+ 
+
+ align:start position:0%
+the membranes by the speaker okay who
+don't want to destroy everything here
+
+ align:start position:0%
+don't want to destroy everything here
+ 
+
+ align:start position:0%
+don't want to destroy everything here
+alright so now I can turn down this so
+
+ align:start position:0%
+alright so now I can turn down this so
+ 
+
+ align:start position:0%
+alright so now I can turn down this so
+that we have light and of course I will
+
+ align:start position:0%
+that we have light and of course I will
+ 
+
+ align:start position:0%
+that we have light and of course I will
+turn on the signal generator so that I
+
+ align:start position:0%
+turn on the signal generator so that I
+ 
+
+ align:start position:0%
+turn on the signal generator so that I
+can hear
+
+ align:start position:0%
+can hear
+ 
+
+ align:start position:0%
+can hear
+Hercules she start to vibrate the
+
+ align:start position:0%
+Hercules she start to vibrate the
+ 
+
+ align:start position:0%
+Hercules she start to vibrate the
+membranes and before I do that I have to
+
+ align:start position:0%
+membranes and before I do that I have to
+ 
+
+ align:start position:0%
+membranes and before I do that I have to
+turn everything off right height images
+
+ align:start position:0%
+turn everything off right height images
+ 
+
+ align:start position:0%
+turn everything off right height images
+hide hide
+
+ align:start position:0%
+hide hide
+ 
+
+ align:start position:0%
+hide hide
+alright I hope you can see something can
+
+ align:start position:0%
+alright I hope you can see something can
+ 
+
+ align:start position:0%
+alright I hope you can see something can
+you can you see something
+
+ align:start position:0%
+you can you see something
+ 
+
+ align:start position:0%
+you can you see something
+and okay is kind of difficult to see it
+
+ align:start position:0%
+and okay is kind of difficult to see it
+ 
+
+ align:start position:0%
+and okay is kind of difficult to see it
+okay but that should be there okay now I
+
+ align:start position:0%
+okay but that should be there okay now I
+ 
+
+ align:start position:0%
+okay but that should be there okay now I
+can turn on this speaker and you can see
+
+ align:start position:0%
+can turn on this speaker and you can see
+ 
+
+ align:start position:0%
+can turn on this speaker and you can see
+that there are some pattern which you
+
+ align:start position:0%
+that there are some pattern which you
+ 
+
+ align:start position:0%
+that there are some pattern which you
+still probably difficult to see
+
+ align:start position:0%
+still probably difficult to see
+ 
+
+ align:start position:0%
+still probably difficult to see
+kind of see right there are some rings
+
+ align:start position:0%
+kind of see right there are some rings
+ 
+
+ align:start position:0%
+kind of see right there are some rings
+you can see on the picture so you can
+
+ align:start position:0%
+you can see on the picture so you can
+ 
+
+ align:start position:0%
+you can see on the picture so you can
+see that now I have one - sweet sweet
+
+ align:start position:0%
+see that now I have one - sweet sweet
+ 
+
+ align:start position:0%
+see that now I have one - sweet sweet
+rings right kind of because I couldn't
+
+ align:start position:0%
+rings right kind of because I couldn't
+ 
+
+ align:start position:0%
+rings right kind of because I couldn't
+actually a turn of the okay turn of the
+
+ align:start position:0%
+actually a turn of the okay turn of the
+ 
+
+ align:start position:0%
+actually a turn of the okay turn of the
+light which is as you've emitted from
+
+ align:start position:0%
+light which is as you've emitted from
+ 
+
+ align:start position:0%
+light which is as you've emitted from
+the on the Sun right okay so I cannot
+
+ align:start position:0%
+the on the Sun right okay so I cannot
+ 
+
+ align:start position:0%
+the on the Sun right okay so I cannot
+turn off Sun therefore you can you can
+
+ align:start position:0%
+turn off Sun therefore you can you can
+ 
+
+ align:start position:0%
+turn off Sun therefore you can you can
+barely see this figure also this expose
+
+ align:start position:0%
+barely see this figure also this expose
+ 
+
+ align:start position:0%
+barely see this figure also this expose
+the reliability experiment and you can
+
+ align:start position:0%
+the reliability experiment and you can
+ 
+
+ align:start position:0%
+the reliability experiment and you can
+see that if I increase the frequency
+
+ align:start position:0%
+see that if I increase the frequency
+ 
+
+ align:start position:0%
+see that if I increase the frequency
+okay according to the solution from the
+
+ align:start position:0%
+okay according to the solution from the
+ 
+
+ align:start position:0%
+okay according to the solution from the
+Bessel function you will see more rings
+
+ align:start position:0%
+Bessel function you will see more rings
+ 
+
+ align:start position:0%
+Bessel function you will see more rings
+I got excited
+
+ align:start position:0%
+I got excited
+ 
+
+ align:start position:0%
+I got excited
+right so you can see that now I have one
+
+ align:start position:0%
+right so you can see that now I have one
+ 
+
+ align:start position:0%
+right so you can see that now I have one
+two three four four rings and of course
+
+ align:start position:0%
+two three four four rings and of course
+ 
+
+ align:start position:0%
+two three four four rings and of course
+I can continue to increase increase and
+
+ align:start position:0%
+I can continue to increase increase and
+ 
+
+ align:start position:0%
+I can continue to increase increase and
+increase and you will see that there are
+
+ align:start position:0%
+increase and you will see that there are
+ 
+
+ align:start position:0%
+increase and you will see that there are
+even more rings well produced is
+
+ align:start position:0%
+even more rings well produced is
+ 
+
+ align:start position:0%
+even more rings well produced is
+essentially what I am doing is actually
+
+ align:start position:0%
+essentially what I am doing is actually
+ 
+
+ align:start position:0%
+essentially what I am doing is actually
+really trying to buy beret and excite
+
+ align:start position:0%
+really trying to buy beret and excite
+ 
+
+ align:start position:0%
+really trying to buy beret and excite
+one of the normal mall by this
+
+ align:start position:0%
+one of the normal mall by this
+ 
+
+ align:start position:0%
+one of the normal mall by this
+loudspeaker okay and you can actually
+
+ align:start position:0%
+loudspeaker okay and you can actually
+ 
+
+ align:start position:0%
+loudspeaker okay and you can actually
+kind of see I hope you can kind of see
+
+ align:start position:0%
+kind of see I hope you can kind of see
+ 
+
+ align:start position:0%
+kind of see I hope you can kind of see
+it okay
+
+ align:start position:0%
+it okay
+ 
+
+ align:start position:0%
+it okay
+if you can still see it that means you
+
+ align:start position:0%
+if you can still see it that means you
+ 
+
+ align:start position:0%
+if you can still see it that means you
+you need to check your eye because the
+
+ align:start position:0%
+you need to check your eye because the
+ 
+
+ align:start position:0%
+you need to check your eye because the
+remembrance is broken all right
+
+ align:start position:0%
+remembrance is broken all right
+ 
+
+ align:start position:0%
+remembrance is broken all right
+okay so I think you sort don't get this
+
+ align:start position:0%
+okay so I think you sort don't get this
+ 
+
+ align:start position:0%
+okay so I think you sort don't get this
+idea and I'm going to turn off this
+
+ align:start position:0%
+idea and I'm going to turn off this
+ 
+
+ align:start position:0%
+idea and I'm going to turn off this
+wonderful machine and and go back to the
+
+ align:start position:0%
+wonderful machine and and go back to the
+ 
+
+ align:start position:0%
+wonderful machine and and go back to the
+the lecture so this experiment is kind
+
+ align:start position:0%
+the lecture so this experiment is kind
+ 
+
+ align:start position:0%
+the lecture so this experiment is kind
+of hard to reproduce in your study right
+
+ align:start position:0%
+of hard to reproduce in your study right
+ 
+
+ align:start position:0%
+of hard to reproduce in your study right
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+I think everybody will agree and there
+
+ align:start position:0%
+I think everybody will agree and there
+ 
+
+ align:start position:0%
+I think everybody will agree and there
+is another one which is essentially kind
+
+ align:start position:0%
+is another one which is essentially kind
+ 
+
+ align:start position:0%
+is another one which is essentially kind
+of easy to reproduce which I would
+
+ align:start position:0%
+of easy to reproduce which I would
+ 
+
+ align:start position:0%
+of easy to reproduce which I would
+encourage you to try it okay so if you
+
+ align:start position:0%
+encourage you to try it okay so if you
+ 
+
+ align:start position:0%
+encourage you to try it okay so if you
+have time so this is actually from Jake
+
+ align:start position:0%
+have time so this is actually from Jake
+ 
+
+ align:start position:0%
+have time so this is actually from Jake
+he and she sent me this wonderful video
+
+ align:start position:0%
+he and she sent me this wonderful video
+ 
+
+ align:start position:0%
+he and she sent me this wonderful video
+when I was teaching the arrows because
+
+ align:start position:0%
+when I was teaching the arrows because
+ 
+
+ align:start position:0%
+when I was teaching the arrows because
+they found that they can excite two
+
+ align:start position:0%
+they found that they can excite two
+ 
+
+ align:start position:0%
+they found that they can excite two
+dimensional wave in this way can you see
+
+ align:start position:0%
+dimensional wave in this way can you see
+ 
+
+ align:start position:0%
+dimensional wave in this way can you see
+it it's wonderful you can see they're
+
+ align:start position:0%
+it it's wonderful you can see they're
+ 
+
+ align:start position:0%
+it it's wonderful you can see they're
+very high frequency oscillation which
+
+ align:start position:0%
+very high frequency oscillation which
+ 
+
+ align:start position:0%
+very high frequency oscillation which
+actually excite this two-dimensional
+
+ align:start position:0%
+actually excite this two-dimensional
+ 
+
+ align:start position:0%
+actually excite this two-dimensional
+wave and you can see that lots lots lots
+
+ align:start position:0%
+wave and you can see that lots lots lots
+ 
+
+ align:start position:0%
+wave and you can see that lots lots lots
+of rings are actually excited and you
+
+ align:start position:0%
+of rings are actually excited and you
+ 
+
+ align:start position:0%
+of rings are actually excited and you
+can see very clearly different this this
+
+ align:start position:0%
+can see very clearly different this this
+ 
+
+ align:start position:0%
+can see very clearly different this this
+simple experiment what you really need
+
+ align:start position:0%
+simple experiment what you really need
+ 
+
+ align:start position:0%
+simple experiment what you really need
+is a cup of water and you rub it against
+
+ align:start position:0%
+is a cup of water and you rub it against
+ 
+
+ align:start position:0%
+is a cup of water and you rub it against
+the surface of a table then you will be
+
+ align:start position:0%
+the surface of a table then you will be
+ 
+
+ align:start position:0%
+the surface of a table then you will be
+able to excite all the crazy patterns
+
+ align:start position:0%
+able to excite all the crazy patterns
+ 
+
+ align:start position:0%
+able to excite all the crazy patterns
+which we can actually see from this
+
+ align:start position:0%
+which we can actually see from this
+ 
+
+ align:start position:0%
+which we can actually see from this
+two-dimensional system and with two
+
+ align:start position:0%
+two-dimensional system and with two
+ 
+
+ align:start position:0%
+two-dimensional system and with two
+dimensional boundary conditions okay so
+
+ align:start position:0%
+dimensional boundary conditions okay so
+ 
+
+ align:start position:0%
+dimensional boundary conditions okay so
+we will take a five-minute break before
+
+ align:start position:0%
+we will take a five-minute break before
+ 
+
+ align:start position:0%
+we will take a five-minute break before
+we enter the next part of the discussion
+
+ align:start position:0%
+we enter the next part of the discussion
+ 
+
+ align:start position:0%
+we enter the next part of the discussion
+and we come back at 35
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay welcome back everybody
+
+ align:start position:0%
+okay welcome back everybody
+ 
+
+ align:start position:0%
+okay welcome back everybody
+so what I'm going to do now is to
+
+ align:start position:0%
+so what I'm going to do now is to
+ 
+
+ align:start position:0%
+so what I'm going to do now is to
+continue the discussion what we actually
+
+ align:start position:0%
+continue the discussion what we actually
+ 
+
+ align:start position:0%
+continue the discussion what we actually
+got started of the two dimensional and
+
+ align:start position:0%
+got started of the two dimensional and
+ 
+
+ align:start position:0%
+got started of the two dimensional and
+three dimensional system and we have
+
+ align:start position:0%
+three dimensional system and we have
+ 
+
+ align:start position:0%
+three dimensional system and we have
+underst we have actually studied that
+
+ align:start position:0%
+underst we have actually studied that
+ 
+
+ align:start position:0%
+underst we have actually studied that
+behavior of standing wave ray or normal
+
+ align:start position:0%
+behavior of standing wave ray or normal
+ 
+
+ align:start position:0%
+behavior of standing wave ray or normal
+more for what this two dimensional
+
+ align:start position:0%
+more for what this two dimensional
+ 
+
+ align:start position:0%
+more for what this two dimensional
+system and what I am going to do is to
+
+ align:start position:0%
+system and what I am going to do is to
+ 
+
+ align:start position:0%
+system and what I am going to do is to
+discuss with you a two dimensional
+
+ align:start position:0%
+discuss with you a two dimensional
+ 
+
+ align:start position:0%
+discuss with you a two dimensional
+focusing wave okay so I will stick to a
+
+ align:start position:0%
+focusing wave okay so I will stick to a
+ 
+
+ align:start position:0%
+focusing wave okay so I will stick to a
+really simple example which are plane
+
+ align:start position:0%
+really simple example which are plane
+ 
+
+ align:start position:0%
+really simple example which are plane
+waves okay so in the case of plane wave
+
+ align:start position:0%
+waves okay so in the case of plane wave
+ 
+
+ align:start position:0%
+waves okay so in the case of plane wave
+which we actually discussed when
+
+ align:start position:0%
+which we actually discussed when
+ 
+
+ align:start position:0%
+which we actually discussed when
+actually when we actually discussed the
+
+ align:start position:0%
+actually when we actually discussed the
+ 
+
+ align:start position:0%
+actually when we actually discussed the
+young waves as we have the following
+
+ align:start position:0%
+young waves as we have the following
+ 
+
+ align:start position:0%
+young waves as we have the following
+functional for sigh is a function of R
+
+ align:start position:0%
+functional for sigh is a function of R
+ 
+
+ align:start position:0%
+functional for sigh is a function of R
+and the T and this will be equal to a
+
+ align:start position:0%
+and the T and this will be equal to a
+ 
+
+ align:start position:0%
+and the T and this will be equal to a
+exponential I K is a should lock a is a
+
+ align:start position:0%
+exponential I K is a should lock a is a
+ 
+
+ align:start position:0%
+exponential I K is a should lock a is a
+vector now and is pointing to the
+
+ align:start position:0%
+vector now and is pointing to the
+ 
+
+ align:start position:0%
+vector now and is pointing to the
+direction of the propagation of this
+
+ align:start position:0%
+direction of the propagation of this
+ 
+
+ align:start position:0%
+direction of the propagation of this
+prang wave and the disc a is thought
+
+ align:start position:0%
+prang wave and the disc a is thought
+ 
+
+ align:start position:0%
+prang wave and the disc a is thought
+with our vector minus Omega T which is
+
+ align:start position:0%
+with our vector minus Omega T which is
+ 
+
+ align:start position:0%
+with our vector minus Omega T which is
+the oscillation frequency angular
+
+ align:start position:0%
+the oscillation frequency angular
+ 
+
+ align:start position:0%
+the oscillation frequency angular
+frequency and evaluate E at a specific
+
+ align:start position:0%
+frequency and evaluate E at a specific
+ 
+
+ align:start position:0%
+frequency and evaluate E at a specific
+time and this issue this expression I
+
+ align:start position:0%
+time and this issue this expression I
+ 
+
+ align:start position:0%
+time and this issue this expression I
+should describe a plane wave where the
+
+ align:start position:0%
+should describe a plane wave where the
+ 
+
+ align:start position:0%
+should describe a plane wave where the
+direction of propagation is described by
+
+ align:start position:0%
+direction of propagation is described by
+ 
+
+ align:start position:0%
+direction of propagation is described by
+this K vector and of course you can
+
+ align:start position:0%
+this K vector and of course you can
+ 
+
+ align:start position:0%
+this K vector and of course you can
+actually have the wave front which is
+
+ align:start position:0%
+actually have the wave front which is
+ 
+
+ align:start position:0%
+actually have the wave front which is
+actually the peak position of this pram
+
+ align:start position:0%
+actually the peak position of this pram
+ 
+
+ align:start position:0%
+actually the peak position of this pram
+wave okay and the distance between the
+
+ align:start position:0%
+wave okay and the distance between the
+ 
+
+ align:start position:0%
+wave okay and the distance between the
+peak position okay so you can imagine
+
+ align:start position:0%
+peak position okay so you can imagine
+ 
+
+ align:start position:0%
+peak position okay so you can imagine
+that this is like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second is too wide right so if you if
+
+ align:start position:0%
+second is too wide right so if you if
+ 
+
+ align:start position:0%
+second is too wide right so if you if
+you look at the distance between peak
+
+ align:start position:0%
+you look at the distance between peak
+ 
+
+ align:start position:0%
+you look at the distance between peak
+position that will give you the
+
+ align:start position:0%
+position that will give you the
+ 
+
+ align:start position:0%
+position that will give you the
+wavelength right the wavelength lambda
+
+ align:start position:0%
+wavelength right the wavelength lambda
+ 
+
+ align:start position:0%
+wavelength right the wavelength lambda
+will be equal to 2pi divided by K right
+
+ align:start position:0%
+will be equal to 2pi divided by K right
+ 
+
+ align:start position:0%
+will be equal to 2pi divided by K right
+in this case is the lens of this K
+
+ align:start position:0%
+in this case is the lens of this K
+ 
+
+ align:start position:0%
+in this case is the lens of this K
+vector okay just a reminder about what
+
+ align:start position:0%
+vector okay just a reminder about what
+ 
+
+ align:start position:0%
+vector okay just a reminder about what
+we actually introduced in the previous
+
+ align:start position:0%
+we actually introduced in the previous
+ 
+
+ align:start position:0%
+we actually introduced in the previous
+lecture and we were using this to
+
+ align:start position:0%
+lecture and we were using this to
+ 
+
+ align:start position:0%
+lecture and we were using this to
+describe electromagnetic wave and the
+
+ align:start position:0%
+describe electromagnetic wave and the
+ 
+
+ align:start position:0%
+describe electromagnetic wave and the
+such kind of expression can be also be
+
+ align:start position:0%
+such kind of expression can be also be
+ 
+
+ align:start position:0%
+such kind of expression can be also be
+used to describe some waves and also
+
+ align:start position:0%
+used to describe some waves and also
+ 
+
+ align:start position:0%
+used to describe some waves and also
+vibration on the membranes etc focusing
+
+ align:start position:0%
+vibration on the membranes etc focusing
+ 
+
+ align:start position:0%
+vibration on the membranes etc focusing
+waves okay so if there are no other
+
+ align:start position:0%
+waves okay so if there are no other
+ 
+
+ align:start position:0%
+waves okay so if there are no other
+median okay like what we actually have
+
+ align:start position:0%
+median okay like what we actually have
+ 
+
+ align:start position:0%
+median okay like what we actually have
+in this slide so we have nothing else I
+
+ align:start position:0%
+in this slide so we have nothing else I
+ 
+
+ align:start position:0%
+in this slide so we have nothing else I
+have a membranes with surface tension T
+
+ align:start position:0%
+have a membranes with surface tension T
+ 
+
+ align:start position:0%
+have a membranes with surface tension T
+s and Rho s fish with the mass per unit
+
+ align:start position:0%
+s and Rho s fish with the mass per unit
+ 
+
+ align:start position:0%
+s and Rho s fish with the mass per unit
+area then basically this focusing wave
+
+ align:start position:0%
+area then basically this focusing wave
+ 
+
+ align:start position:0%
+area then basically this focusing wave
+is going to be traveling at the speed of
+
+ align:start position:0%
+is going to be traveling at the speed of
+ 
+
+ align:start position:0%
+is going to be traveling at the speed of
+V which is actually equal to square root
+
+ align:start position:0%
+V which is actually equal to square root
+ 
+
+ align:start position:0%
+V which is actually equal to square root
+of T s over Rho s and I can actually
+
+ align:start position:0%
+of T s over Rho s and I can actually
+ 
+
+ align:start position:0%
+of T s over Rho s and I can actually
+find that to be some constant C / M okay
+
+ align:start position:0%
+find that to be some constant C / M okay
+ 
+
+ align:start position:0%
+find that to be some constant C / M okay
+so C is a some constant and n is
+
+ align:start position:0%
+so C is a some constant and n is
+ 
+
+ align:start position:0%
+so C is a some constant and n is
+actually another constant which actually
+
+ align:start position:0%
+actually another constant which actually
+ 
+
+ align:start position:0%
+actually another constant which actually
+the ratio CN NS s equal to B and I will
+
+ align:start position:0%
+the ratio CN NS s equal to B and I will
+ 
+
+ align:start position:0%
+the ratio CN NS s equal to B and I will
+need that expression later only later
+
+ align:start position:0%
+need that expression later only later
+ 
+
+ align:start position:0%
+need that expression later only later
+not now if I have nothing else okay and
+
+ align:start position:0%
+not now if I have nothing else okay and
+ 
+
+ align:start position:0%
+not now if I have nothing else okay and
+this is this issue's this system
+
+ align:start position:0%
+this is this issue's this system
+ 
+
+ align:start position:0%
+this is this issue's this system
+actually feel the whole universe then
+
+ align:start position:0%
+actually feel the whole universe then
+ 
+
+ align:start position:0%
+actually feel the whole universe then
+what is going to happen is that this pop
+
+ align:start position:0%
+what is going to happen is that this pop
+ 
+
+ align:start position:0%
+what is going to happen is that this pop
+wasting wave is going to be propagating
+
+ align:start position:0%
+wasting wave is going to be propagating
+ 
+
+ align:start position:0%
+wasting wave is going to be propagating
+propagating propagating propagating
+
+ align:start position:0%
+propagating propagating propagating
+ 
+
+ align:start position:0%
+propagating propagating propagating
+nursing will change and until at the
+
+ align:start position:0%
+nursing will change and until at the
+ 
+
+ align:start position:0%
+nursing will change and until at the
+edge of the universe if it doesn't
+
+ align:start position:0%
+edge of the universe if it doesn't
+ 
+
+ align:start position:0%
+edge of the universe if it doesn't
+actually introduce any excitement right
+
+ align:start position:0%
+actually introduce any excitement right
+ 
+
+ align:start position:0%
+actually introduce any excitement right
+okay so that's what we have already
+
+ align:start position:0%
+okay so that's what we have already
+ 
+
+ align:start position:0%
+okay so that's what we have already
+learned from from Yin
+
+ align:start position:0%
+learned from from Yin
+ 
+
+ align:start position:0%
+learned from from Yin
+we have discussed the electromagnetic
+
+ align:start position:0%
+we have discussed the electromagnetic
+ 
+
+ align:start position:0%
+we have discussed the electromagnetic
+interaction and now the same expression
+
+ align:start position:0%
+interaction and now the same expression
+ 
+
+ align:start position:0%
+interaction and now the same expression
+can also be used for the description of
+
+ align:start position:0%
+can also be used for the description of
+ 
+
+ align:start position:0%
+can also be used for the description of
+the membranes and now to make this
+
+ align:start position:0%
+the membranes and now to make this
+ 
+
+ align:start position:0%
+the membranes and now to make this
+problem more exciting what I'm going to
+
+ align:start position:0%
+problem more exciting what I'm going to
+ 
+
+ align:start position:0%
+problem more exciting what I'm going to
+do is to introduce a boundary right so
+
+ align:start position:0%
+do is to introduce a boundary right so
+ 
+
+ align:start position:0%
+do is to introduce a boundary right so
+the boundary is actually in the middle
+
+ align:start position:0%
+the boundary is actually in the middle
+ 
+
+ align:start position:0%
+the boundary is actually in the middle
+of this slide and I assume that
+
+ align:start position:0%
+of this slide and I assume that
+ 
+
+ align:start position:0%
+of this slide and I assume that
+horizontal direction to be X equal to
+
+ align:start position:0%
+horizontal direction to be X equal to
+ 
+
+ align:start position:0%
+horizontal direction to be X equal to
+zero the horizontal direction to be an X
+
+ align:start position:0%
+zero the horizontal direction to be an X
+ 
+
+ align:start position:0%
+zero the horizontal direction to be an X
+direction and the boundary is at X equal
+
+ align:start position:0%
+direction and the boundary is at X equal
+ 
+
+ align:start position:0%
+direction and the boundary is at X equal
+to zero okay and when when this when you
+
+ align:start position:0%
+to zero okay and when when this when you
+ 
+
+ align:start position:0%
+to zero okay and when when this when you
+pass this boundary there's another kind
+
+ align:start position:0%
+pass this boundary there's another kind
+ 
+
+ align:start position:0%
+pass this boundary there's another kind
+of material with surface tension ts
+
+ align:start position:0%
+of material with surface tension ts
+ 
+
+ align:start position:0%
+of material with surface tension ts
+front and slightly different mass per
+
+ align:start position:0%
+front and slightly different mass per
+ 
+
+ align:start position:0%
+front and slightly different mass per
+unit area Rho s Prime okay based on the
+
+ align:start position:0%
+unit area Rho s Prime okay based on the
+ 
+
+ align:start position:0%
+unit area Rho s Prime okay based on the
+expression we got for the velocity we
+
+ align:start position:0%
+expression we got for the velocity we
+ 
+
+ align:start position:0%
+expression we got for the velocity we
+will be able to conclude that V prime
+
+ align:start position:0%
+will be able to conclude that V prime
+ 
+
+ align:start position:0%
+will be able to conclude that V prime
+will be equal to square root of T prime
+
+ align:start position:0%
+will be equal to square root of T prime
+ 
+
+ align:start position:0%
+will be equal to square root of T prime
+s divided by Rho as prom and that will
+
+ align:start position:0%
+s divided by Rho as prom and that will
+ 
+
+ align:start position:0%
+s divided by Rho as prom and that will
+be equal to C over M Prime and C is the
+
+ align:start position:0%
+be equal to C over M Prime and C is the
+ 
+
+ align:start position:0%
+be equal to C over M Prime and C is the
+same constant which we are used for the
+
+ align:start position:0%
+same constant which we are used for the
+ 
+
+ align:start position:0%
+same constant which we are used for the
+laughing side system and it's actually
+
+ align:start position:0%
+laughing side system and it's actually
+ 
+
+ align:start position:0%
+laughing side system and it's actually
+later you will realize that the cell
+
+ align:start position:0%
+later you will realize that the cell
+ 
+
+ align:start position:0%
+later you will realize that the cell
+refraction index in in a discussion okay
+
+ align:start position:0%
+refraction index in in a discussion okay
+ 
+
+ align:start position:0%
+refraction index in in a discussion okay
+so the question which I would like to
+
+ align:start position:0%
+so the question which I would like to
+ 
+
+ align:start position:0%
+so the question which I would like to
+ask is okay now I have a plane wave okay
+
+ align:start position:0%
+ask is okay now I have a plane wave okay
+ 
+
+ align:start position:0%
+ask is okay now I have a plane wave okay
+propagating in the first system and
+
+ align:start position:0%
+propagating in the first system and
+ 
+
+ align:start position:0%
+propagating in the first system and
+Ahmet it meet a boundary and the
+
+ align:start position:0%
+Ahmet it meet a boundary and the
+ 
+
+ align:start position:0%
+Ahmet it meet a boundary and the
+question is what will happen okay when
+
+ align:start position:0%
+question is what will happen okay when
+ 
+
+ align:start position:0%
+question is what will happen okay when
+when I have the incident wave coming
+
+ align:start position:0%
+when I have the incident wave coming
+ 
+
+ align:start position:0%
+when I have the incident wave coming
+into this system okay so before that I
+
+ align:start position:0%
+into this system okay so before that I
+ 
+
+ align:start position:0%
+into this system okay so before that I
+also need to write down the dispersion
+
+ align:start position:0%
+also need to write down the dispersion
+ 
+
+ align:start position:0%
+also need to write down the dispersion
+relation right so this person relation
+
+ align:start position:0%
+relation right so this person relation
+ 
+
+ align:start position:0%
+relation right so this person relation
+can be obtained by plugging in normal
+
+ align:start position:0%
+can be obtained by plugging in normal
+ 
+
+ align:start position:0%
+can be obtained by plugging in normal
+mode sine function size function into
+
+ align:start position:0%
+mode sine function size function into
+ 
+
+ align:start position:0%
+mode sine function size function into
+the wave equation
+
+ align:start position:0%
+the wave equation
+ 
+
+ align:start position:0%
+the wave equation
+right so while I can issue in meeting
+
+ align:start position:0%
+right so while I can issue in meeting
+ 
+
+ align:start position:0%
+right so while I can issue in meeting
+the up 10 is that the dispersion
+
+ align:start position:0%
+the up 10 is that the dispersion
+ 
+
+ align:start position:0%
+the up 10 is that the dispersion
+relation Omega square is actually equal
+
+ align:start position:0%
+relation Omega square is actually equal
+ 
+
+ align:start position:0%
+relation Omega square is actually equal
+to three square KX square plus KY square
+
+ align:start position:0%
+to three square KX square plus KY square
+ 
+
+ align:start position:0%
+to three square KX square plus KY square
+so you can actually check this
+
+ align:start position:0%
+so you can actually check this
+ 
+
+ align:start position:0%
+so you can actually check this
+expression by plugging in this function
+
+ align:start position:0%
+expression by plugging in this function
+ 
+
+ align:start position:0%
+expression by plugging in this function
+into the two dimensional wave equation
+
+ align:start position:0%
+into the two dimensional wave equation
+ 
+
+ align:start position:0%
+into the two dimensional wave equation
+and you will get that expression okay
+
+ align:start position:0%
+and you will get that expression okay
+ 
+
+ align:start position:0%
+and you will get that expression okay
+and that means Omega cannot be arbitrary
+
+ align:start position:0%
+and that means Omega cannot be arbitrary
+ 
+
+ align:start position:0%
+and that means Omega cannot be arbitrary
+number it's as you decided by KX and KY
+
+ align:start position:0%
+number it's as you decided by KX and KY
+ 
+
+ align:start position:0%
+number it's as you decided by KX and KY
+okay or say if Omega S decide and the
+
+ align:start position:0%
+okay or say if Omega S decide and the
+ 
+
+ align:start position:0%
+okay or say if Omega S decide and the
+one of the K is decide then the third
+
+ align:start position:0%
+one of the K is decide then the third
+ 
+
+ align:start position:0%
+one of the K is decide then the third
+number for example in this case KX is as
+
+ align:start position:0%
+number for example in this case KX is as
+ 
+
+ align:start position:0%
+number for example in this case KX is as
+we decided by the dispersion relation
+
+ align:start position:0%
+we decided by the dispersion relation
+ 
+
+ align:start position:0%
+we decided by the dispersion relation
+which we have here okay so coming back
+
+ align:start position:0%
+which we have here okay so coming back
+ 
+
+ align:start position:0%
+which we have here okay so coming back
+to the original problem we are we are
+
+ align:start position:0%
+to the original problem we are we are
+ 
+
+ align:start position:0%
+to the original problem we are we are
+posting so I have now the in certain
+
+ align:start position:0%
+posting so I have now the in certain
+ 
+
+ align:start position:0%
+posting so I have now the in certain
+wave coming into this system okay I
+
+ align:start position:0%
+wave coming into this system okay I
+ 
+
+ align:start position:0%
+wave coming into this system okay I
+would like to know what will happen at
+
+ align:start position:0%
+would like to know what will happen at
+ 
+
+ align:start position:0%
+would like to know what will happen at
+the boundary right when I have two
+
+ align:start position:0%
+the boundary right when I have two
+ 
+
+ align:start position:0%
+the boundary right when I have two
+system with lap inside propagating at
+
+ align:start position:0%
+system with lap inside propagating at
+ 
+
+ align:start position:0%
+system with lap inside propagating at
+the speed of the propagation is V and
+
+ align:start position:0%
+the speed of the propagation is V and
+ 
+
+ align:start position:0%
+the speed of the propagation is V and
+right hand side speed of propagation is
+
+ align:start position:0%
+right hand side speed of propagation is
+ 
+
+ align:start position:0%
+right hand side speed of propagation is
+V Prime
+
+ align:start position:0%
+V Prime
+ 
+
+ align:start position:0%
+V Prime
+what is going to happen as you might
+
+ align:start position:0%
+what is going to happen as you might
+ 
+
+ align:start position:0%
+what is going to happen as you might
+guess that I am going to get refractive
+
+ align:start position:0%
+guess that I am going to get refractive
+ 
+
+ align:start position:0%
+guess that I am going to get refractive
+wave and a transmitted wave right so
+
+ align:start position:0%
+wave and a transmitted wave right so
+ 
+
+ align:start position:0%
+wave and a transmitted wave right so
+that's actually based on what we have
+
+ align:start position:0%
+that's actually based on what we have
+ 
+
+ align:start position:0%
+that's actually based on what we have
+there from the one-dimensional system
+
+ align:start position:0%
+there from the one-dimensional system
+ 
+
+ align:start position:0%
+there from the one-dimensional system
+right if I call this the left hand side
+
+ align:start position:0%
+right if I call this the left hand side
+ 
+
+ align:start position:0%
+right if I call this the left hand side
+and call the right hand side system I
+
+ align:start position:0%
+and call the right hand side system I
+ 
+
+ align:start position:0%
+and call the right hand side system I
+know the right hand side system are okay
+
+ align:start position:0%
+know the right hand side system are okay
+ 
+
+ align:start position:0%
+know the right hand side system are okay
+so I can write down the wave function
+
+ align:start position:0%
+so I can write down the wave function
+ 
+
+ align:start position:0%
+so I can write down the wave function
+side L describing the left hand side
+
+ align:start position:0%
+side L describing the left hand side
+ 
+
+ align:start position:0%
+side L describing the left hand side
+this will be equal to a exponential I K
+
+ align:start position:0%
+this will be equal to a exponential I K
+ 
+
+ align:start position:0%
+this will be equal to a exponential I K
+dot R minus make up this is actually the
+
+ align:start position:0%
+dot R minus make up this is actually the
+ 
+
+ align:start position:0%
+dot R minus make up this is actually the
+incident wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+describing this incident wave and as
+
+ align:start position:0%
+describing this incident wave and as
+ 
+
+ align:start position:0%
+describing this incident wave and as
+will my guess there should be some kind
+
+ align:start position:0%
+will my guess there should be some kind
+ 
+
+ align:start position:0%
+will my guess there should be some kind
+of refraction right so once this wave
+
+ align:start position:0%
+of refraction right so once this wave
+ 
+
+ align:start position:0%
+of refraction right so once this wave
+actually passed through the boundary or
+
+ align:start position:0%
+actually passed through the boundary or
+ 
+
+ align:start position:0%
+actually passed through the boundary or
+touch the boundary there should be some
+
+ align:start position:0%
+touch the boundary there should be some
+ 
+
+ align:start position:0%
+touch the boundary there should be some
+kind of infraction right so the
+
+ align:start position:0%
+kind of infraction right so the
+ 
+
+ align:start position:0%
+kind of infraction right so the
+refraction I can actually write it down
+
+ align:start position:0%
+refraction I can actually write it down
+ 
+
+ align:start position:0%
+refraction I can actually write it down
+in this for a sum over alpha R alpha is
+
+ align:start position:0%
+in this for a sum over alpha R alpha is
+ 
+
+ align:start position:0%
+in this for a sum over alpha R alpha is
+actually the coefficient or mp2 as
+
+ align:start position:0%
+actually the coefficient or mp2 as
+ 
+
+ align:start position:0%
+actually the coefficient or mp2 as
+function of the normal modes with a
+
+ align:start position:0%
+function of the normal modes with a
+ 
+
+ align:start position:0%
+function of the normal modes with a
+function of the focusing wave wave
+
+ align:start position:0%
+function of the focusing wave wave
+ 
+
+ align:start position:0%
+function of the focusing wave wave
+number which I assumed and the I can as
+
+ align:start position:0%
+number which I assumed and the I can as
+ 
+
+ align:start position:0%
+number which I assumed and the I can as
+you sum over all kinds of policy wave
+
+ align:start position:0%
+you sum over all kinds of policy wave
+ 
+
+ align:start position:0%
+you sum over all kinds of policy wave
+number exponential I K alpha times R
+
+ align:start position:0%
+number exponential I K alpha times R
+ 
+
+ align:start position:0%
+number exponential I K alpha times R
+minus Omega right so this is actually a
+
+ align:start position:0%
+minus Omega right so this is actually a
+ 
+
+ align:start position:0%
+minus Omega right so this is actually a
+general form of refractive wave K alpha
+
+ align:start position:0%
+general form of refractive wave K alpha
+ 
+
+ align:start position:0%
+general form of refractive wave K alpha
+is the quite describing the individual
+
+ align:start position:0%
+is the quite describing the individual
+ 
+
+ align:start position:0%
+is the quite describing the individual
+the direction of the individual
+
+ align:start position:0%
+the direction of the individual
+ 
+
+ align:start position:0%
+the direction of the individual
+refracted wave and alpha is actually
+
+ align:start position:0%
+refracted wave and alpha is actually
+ 
+
+ align:start position:0%
+refracted wave and alpha is actually
+labeled in individual refractive wave
+
+ align:start position:0%
+labeled in individual refractive wave
+ 
+
+ align:start position:0%
+labeled in individual refractive wave
+but I don't know what be the functional
+
+ align:start position:0%
+but I don't know what be the functional
+ 
+
+ align:start position:0%
+but I don't know what be the functional
+form for the K alpha for the moment so
+
+ align:start position:0%
+form for the K alpha for the moment so
+ 
+
+ align:start position:0%
+form for the K alpha for the moment so
+therefore I try to sum over all the the
+
+ align:start position:0%
+therefore I try to sum over all the the
+ 
+
+ align:start position:0%
+therefore I try to sum over all the the
+possible alpha and I would would like to
+
+ align:start position:0%
+possible alpha and I would would like to
+ 
+
+ align:start position:0%
+possible alpha and I would would like to
+figure out what would be the allowed
+
+ align:start position:0%
+figure out what would be the allowed
+ 
+
+ align:start position:0%
+figure out what would be the allowed
+alpha by matching the boundary condition
+
+ align:start position:0%
+alpha by matching the boundary condition
+ 
+
+ align:start position:0%
+alpha by matching the boundary condition
+so in short the right hand side turn the
+
+ align:start position:0%
+so in short the right hand side turn the
+ 
+
+ align:start position:0%
+so in short the right hand side turn the
+session it is quite big that refracted
+
+ align:start position:0%
+session it is quite big that refracted
+ 
+
+ align:start position:0%
+session it is quite big that refracted
+wave okay and finally passing through
+
+ align:start position:0%
+wave okay and finally passing through
+ 
+
+ align:start position:0%
+wave okay and finally passing through
+this boundary condition let's look at
+
+ align:start position:0%
+this boundary condition let's look at
+ 
+
+ align:start position:0%
+this boundary condition let's look at
+the right hand side okay right hand side
+
+ align:start position:0%
+the right hand side okay right hand side
+ 
+
+ align:start position:0%
+the right hand side okay right hand side
+side are okay okay it's going to be
+
+ align:start position:0%
+side are okay okay it's going to be
+ 
+
+ align:start position:0%
+side are okay okay it's going to be
+equal to sum over beta all the
+
+ align:start position:0%
+equal to sum over beta all the
+ 
+
+ align:start position:0%
+equal to sum over beta all the
+transmission coefficients top beta has a
+
+ align:start position:0%
+transmission coefficients top beta has a
+ 
+
+ align:start position:0%
+transmission coefficients top beta has a
+which is the original MP to
+
+ align:start position:0%
+which is the original MP to
+ 
+
+ align:start position:0%
+which is the original MP to
+exponential I K beta x times R minus
+
+ align:start position:0%
+exponential I K beta x times R minus
+ 
+
+ align:start position:0%
+exponential I K beta x times R minus
+Omega so again I don't know how what
+
+ align:start position:0%
+Omega so again I don't know how what
+ 
+
+ align:start position:0%
+Omega so again I don't know how what
+would be the behavior of the transmitted
+
+ align:start position:0%
+would be the behavior of the transmitted
+ 
+
+ align:start position:0%
+would be the behavior of the transmitted
+wave therefore I sum over all the
+
+ align:start position:0%
+wave therefore I sum over all the
+ 
+
+ align:start position:0%
+wave therefore I sum over all the
+possible values and this is actually the
+
+ align:start position:0%
+possible values and this is actually the
+ 
+
+ align:start position:0%
+possible values and this is actually the
+functional form for the transmitted wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I also know that K alpha vector
+
+ align:start position:0%
+okay I also know that K alpha vector
+ 
+
+ align:start position:0%
+okay I also know that K alpha vector
+squared will be equal to Omega square
+
+ align:start position:0%
+squared will be equal to Omega square
+ 
+
+ align:start position:0%
+squared will be equal to Omega square
+Rho s over T s and this will be equal to
+
+ align:start position:0%
+Rho s over T s and this will be equal to
+ 
+
+ align:start position:0%
+Rho s over T s and this will be equal to
+Omega square V squared
+
+ align:start position:0%
+Omega square V squared
+ 
+
+ align:start position:0%
+Omega square V squared
+okay because of the dispersion relation
+
+ align:start position:0%
+okay because of the dispersion relation
+ 
+
+ align:start position:0%
+okay because of the dispersion relation
+in the lab hand side right so basically
+
+ align:start position:0%
+in the lab hand side right so basically
+ 
+
+ align:start position:0%
+in the lab hand side right so basically
+if we look at the lab and site
+
+ align:start position:0%
+if we look at the lab and site
+ 
+
+ align:start position:0%
+if we look at the lab and site
+dispersion relation okay the lens square
+
+ align:start position:0%
+dispersion relation okay the lens square
+ 
+
+ align:start position:0%
+dispersion relation okay the lens square
+of this K vector will be equal to Omega
+
+ align:start position:0%
+of this K vector will be equal to Omega
+ 
+
+ align:start position:0%
+of this K vector will be equal to Omega
+square times V squared right this is
+
+ align:start position:0%
+square times V squared right this is
+ 
+
+ align:start position:0%
+square times V squared right this is
+actually just a dispersion relation of a
+
+ align:start position:0%
+actually just a dispersion relation of a
+ 
+
+ align:start position:0%
+actually just a dispersion relation of a
+non dispersive medium right and also I
+
+ align:start position:0%
+non dispersive medium right and also I
+ 
+
+ align:start position:0%
+non dispersive medium right and also I
+can actually figure out what will be the
+
+ align:start position:0%
+can actually figure out what will be the
+ 
+
+ align:start position:0%
+can actually figure out what will be the
+lens for that a lot lens for the cake
+
+ align:start position:0%
+lens for that a lot lens for the cake
+ 
+
+ align:start position:0%
+lens for that a lot lens for the cake
+okay beta right so the K beta square
+
+ align:start position:0%
+okay beta right so the K beta square
+ 
+
+ align:start position:0%
+okay beta right so the K beta square
+will be equal to Omega square V prime
+
+ align:start position:0%
+will be equal to Omega square V prime
+ 
+
+ align:start position:0%
+will be equal to Omega square V prime
+square right because this wave is this
+
+ align:start position:0%
+square right because this wave is this
+ 
+
+ align:start position:0%
+square right because this wave is this
+progressing wave is actually the
+
+ align:start position:0%
+progressing wave is actually the
+ 
+
+ align:start position:0%
+progressing wave is actually the
+transmitted wave is actually traveling
+
+ align:start position:0%
+transmitted wave is actually traveling
+ 
+
+ align:start position:0%
+transmitted wave is actually traveling
+at the second in the second medium okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so look at what we have done here so we
+
+ align:start position:0%
+so look at what we have done here so we
+ 
+
+ align:start position:0%
+so look at what we have done here so we
+have in certain way we were wondering
+
+ align:start position:0%
+have in certain way we were wondering
+ 
+
+ align:start position:0%
+have in certain way we were wondering
+what is going to happen our physics
+
+ align:start position:0%
+what is going to happen our physics
+ 
+
+ align:start position:0%
+what is going to happen our physics
+intuition tells me that you must get a
+
+ align:start position:0%
+intuition tells me that you must get a
+ 
+
+ align:start position:0%
+intuition tells me that you must get a
+refractive wave oscillation frequency
+
+ align:start position:0%
+refractive wave oscillation frequency
+ 
+
+ align:start position:0%
+refractive wave oscillation frequency
+should be the same otherwise as a
+
+ align:start position:0%
+should be the same otherwise as a
+ 
+
+ align:start position:0%
+should be the same otherwise as a
+function of time you cannot match the
+
+ align:start position:0%
+function of time you cannot match the
+ 
+
+ align:start position:0%
+function of time you cannot match the
+level design right hand side and you
+
+ align:start position:0%
+level design right hand side and you
+ 
+
+ align:start position:0%
+level design right hand side and you
+also get a transmitted wave right but I
+
+ align:start position:0%
+also get a transmitted wave right but I
+ 
+
+ align:start position:0%
+also get a transmitted wave right but I
+need it now in trouble because I have so
+
+ align:start position:0%
+need it now in trouble because I have so
+ 
+
+ align:start position:0%
+need it now in trouble because I have so
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+and summing over alpha infinite number
+
+ align:start position:0%
+and summing over alpha infinite number
+ 
+
+ align:start position:0%
+and summing over alpha infinite number
+of turns and I don't know what would be
+
+ align:start position:0%
+of turns and I don't know what would be
+ 
+
+ align:start position:0%
+of turns and I don't know what would be
+the coefficient for the our alpha and
+
+ align:start position:0%
+the coefficient for the our alpha and
+ 
+
+ align:start position:0%
+the coefficient for the our alpha and
+the Tau Beta which are the transmission
+
+ align:start position:0%
+the Tau Beta which are the transmission
+ 
+
+ align:start position:0%
+the Tau Beta which are the transmission
+coefficient and the refraction
+
+ align:start position:0%
+coefficient and the refraction
+ 
+
+ align:start position:0%
+coefficient and the refraction
+coefficients okay
+
+ align:start position:0%
+coefficients okay
+ 
+
+ align:start position:0%
+coefficients okay
+so what I need to do as you might guess
+
+ align:start position:0%
+so what I need to do as you might guess
+ 
+
+ align:start position:0%
+so what I need to do as you might guess
+is to use the boundary condition right
+
+ align:start position:0%
+is to use the boundary condition right
+ 
+
+ align:start position:0%
+is to use the boundary condition right
+so now I am writing down already the
+
+ align:start position:0%
+so now I am writing down already the
+ 
+
+ align:start position:0%
+so now I am writing down already the
+general expression now I'm going to use
+
+ align:start position:0%
+general expression now I'm going to use
+ 
+
+ align:start position:0%
+general expression now I'm going to use
+the boundary condition to actually limit
+
+ align:start position:0%
+the boundary condition to actually limit
+ 
+
+ align:start position:0%
+the boundary condition to actually limit
+the choice of the possible K alpha and
+
+ align:start position:0%
+the choice of the possible K alpha and
+ 
+
+ align:start position:0%
+the choice of the possible K alpha and
+the K beta what is issue the boundary
+
+ align:start position:0%
+the K beta what is issue the boundary
+ 
+
+ align:start position:0%
+the K beta what is issue the boundary
+condition the boundary conditions are
+
+ align:start position:0%
+condition the boundary conditions are
+ 
+
+ align:start position:0%
+condition the boundary conditions are
+that at x equal to zero okay
+
+ align:start position:0%
+that at x equal to zero okay
+ 
+
+ align:start position:0%
+that at x equal to zero okay
+let's actually add the position of this
+
+ align:start position:0%
+let's actually add the position of this
+ 
+
+ align:start position:0%
+let's actually add the position of this
+line the member ins doesn't break right
+
+ align:start position:0%
+line the member ins doesn't break right
+ 
+
+ align:start position:0%
+line the member ins doesn't break right
+otherwise there's a I mean suddenly the
+
+ align:start position:0%
+otherwise there's a I mean suddenly the
+ 
+
+ align:start position:0%
+otherwise there's a I mean suddenly the
+members I should break and this the end
+
+ align:start position:0%
+members I should break and this the end
+ 
+
+ align:start position:0%
+members I should break and this the end
+of the of the discussion right right
+
+ align:start position:0%
+of the of the discussion right right
+ 
+
+ align:start position:0%
+of the of the discussion right right
+there well we have done before right
+
+ align:start position:0%
+there well we have done before right
+ 
+
+ align:start position:0%
+there well we have done before right
+so the member instant break so that the
+
+ align:start position:0%
+so the member instant break so that the
+ 
+
+ align:start position:0%
+so the member instant break so that the
+propagation can continue right okay so
+
+ align:start position:0%
+propagation can continue right okay so
+ 
+
+ align:start position:0%
+propagation can continue right okay so
+what does that mean this means that if I
+
+ align:start position:0%
+what does that mean this means that if I
+ 
+
+ align:start position:0%
+what does that mean this means that if I
+evaluate clsi are at X equal to 0 sy 0 Y
+
+ align:start position:0%
+evaluate clsi are at X equal to 0 sy 0 Y
+ 
+
+ align:start position:0%
+evaluate clsi are at X equal to 0 sy 0 Y
+T okay the left hand side will be equal
+
+ align:start position:0%
+T okay the left hand side will be equal
+ 
+
+ align:start position:0%
+T okay the left hand side will be equal
+to a exponential I K Y times y minus
+
+ align:start position:0%
+to a exponential I K Y times y minus
+ 
+
+ align:start position:0%
+to a exponential I K Y times y minus
+Omega P plus summing over all possible
+
+ align:start position:0%
+Omega P plus summing over all possible
+ 
+
+ align:start position:0%
+Omega P plus summing over all possible
+alpha R alpha a exponential I K Y K
+
+ align:start position:0%
+alpha R alpha a exponential I K Y K
+ 
+
+ align:start position:0%
+alpha R alpha a exponential I K Y K
+alpha Y times y minus Omega okay this is
+
+ align:start position:0%
+alpha Y times y minus Omega okay this is
+ 
+
+ align:start position:0%
+alpha Y times y minus Omega okay this is
+the incident wave transmitted wet
+
+ align:start position:0%
+the incident wave transmitted wet
+ 
+
+ align:start position:0%
+the incident wave transmitted wet
+evaluated at the left hand side which is
+
+ align:start position:0%
+evaluated at the left hand side which is
+ 
+
+ align:start position:0%
+evaluated at the left hand side which is
+the upper popular and that would be
+
+ align:start position:0%
+the upper popular and that would be
+ 
+
+ align:start position:0%
+the upper popular and that would be
+equal to the right hand side which is a
+
+ align:start position:0%
+equal to the right hand side which is a
+ 
+
+ align:start position:0%
+equal to the right hand side which is a
+shaded containing only the transmitted
+
+ align:start position:0%
+shaded containing only the transmitted
+ 
+
+ align:start position:0%
+shaded containing only the transmitted
+wave so
+
+ align:start position:0%
+wave so
+ 
+
+ align:start position:0%
+wave so
+basically you have summing over beta 2
+
+ align:start position:0%
+basically you have summing over beta 2
+ 
+
+ align:start position:0%
+basically you have summing over beta 2
+beta a exponential I K beta Y times R
+
+ align:start position:0%
+beta a exponential I K beta Y times R
+ 
+
+ align:start position:0%
+beta a exponential I K beta Y times R
+minus Omega T and this this is
+
+ align:start position:0%
+minus Omega T and this this is
+ 
+
+ align:start position:0%
+minus Omega T and this this is
+expression this boundary condition
+
+ align:start position:0%
+expression this boundary condition
+ 
+
+ align:start position:0%
+expression this boundary condition
+should hold true for the other possible
+
+ align:start position:0%
+should hold true for the other possible
+ 
+
+ align:start position:0%
+should hold true for the other possible
+Y right because the boundary condition
+
+ align:start position:0%
+Y right because the boundary condition
+ 
+
+ align:start position:0%
+Y right because the boundary condition
+is bad it at X equal to 0 I didn't
+
+ align:start position:0%
+is bad it at X equal to 0 I didn't
+ 
+
+ align:start position:0%
+is bad it at X equal to 0 I didn't
+specify the value of Y right so
+
+ align:start position:0%
+specify the value of Y right so
+ 
+
+ align:start position:0%
+specify the value of Y right so
+therefore I can actually put in all the
+
+ align:start position:0%
+therefore I can actually put in all the
+ 
+
+ align:start position:0%
+therefore I can actually put in all the
+possible oh this should be Y sorry for
+
+ align:start position:0%
+possible oh this should be Y sorry for
+ 
+
+ align:start position:0%
+possible oh this should be Y sorry for
+that I can actually vary the Y okay and
+
+ align:start position:0%
+that I can actually vary the Y okay and
+ 
+
+ align:start position:0%
+that I can actually vary the Y okay and
+I will figure out that huh if I have K Y
+
+ align:start position:0%
+I will figure out that huh if I have K Y
+ 
+
+ align:start position:0%
+I will figure out that huh if I have K Y
+it's not equal to k FR y that means the
+
+ align:start position:0%
+it's not equal to k FR y that means the
+ 
+
+ align:start position:0%
+it's not equal to k FR y that means the
+wavelength of the refractive wave and
+
+ align:start position:0%
+wavelength of the refractive wave and
+ 
+
+ align:start position:0%
+wavelength of the refractive wave and
+the incident wave will be different if I
+
+ align:start position:0%
+the incident wave will be different if I
+ 
+
+ align:start position:0%
+the incident wave will be different if I
+have K Y not equal to beta Y that means
+
+ align:start position:0%
+have K Y not equal to beta Y that means
+ 
+
+ align:start position:0%
+have K Y not equal to beta Y that means
+the transmitted wave wave Lance is going
+
+ align:start position:0%
+the transmitted wave wave Lance is going
+ 
+
+ align:start position:0%
+the transmitted wave wave Lance is going
+to be different from the incident wave
+
+ align:start position:0%
+to be different from the incident wave
+ 
+
+ align:start position:0%
+to be different from the incident wave
+that means no matter what I do as a
+
+ align:start position:0%
+that means no matter what I do as a
+ 
+
+ align:start position:0%
+that means no matter what I do as a
+function of Y the membranes will break
+
+ align:start position:0%
+function of Y the membranes will break
+ 
+
+ align:start position:0%
+function of Y the membranes will break
+right therefore in order to make this
+
+ align:start position:0%
+right therefore in order to make this
+ 
+
+ align:start position:0%
+right therefore in order to make this
+equation that it the only choice is that
+
+ align:start position:0%
+equation that it the only choice is that
+ 
+
+ align:start position:0%
+equation that it the only choice is that
+when K alpha Y would be equal to K beta
+
+ align:start position:0%
+when K alpha Y would be equal to K beta
+ 
+
+ align:start position:0%
+when K alpha Y would be equal to K beta
+Y and equal to K Y so that means the
+
+ align:start position:0%
+Y and equal to K Y so that means the
+ 
+
+ align:start position:0%
+Y and equal to K Y so that means the
+wavelength
+
+ align:start position:0%
+wavelength
+ 
+
+ align:start position:0%
+wavelength
+okay projected in the Y direction should
+
+ align:start position:0%
+okay projected in the Y direction should
+ 
+
+ align:start position:0%
+okay projected in the Y direction should
+be equal for the incident wave
+
+ align:start position:0%
+be equal for the incident wave
+ 
+
+ align:start position:0%
+be equal for the incident wave
+transmitted wave and refractive ways
+
+ align:start position:0%
+transmitted wave and refractive ways
+ 
+
+ align:start position:0%
+transmitted wave and refractive ways
+otherwise you can as you always move a
+
+ align:start position:0%
+otherwise you can as you always move a
+ 
+
+ align:start position:0%
+otherwise you can as you always move a
+little bit in the Y direction and the
+
+ align:start position:0%
+little bit in the Y direction and the
+ 
+
+ align:start position:0%
+little bit in the Y direction and the
+membranes were break okay so that's
+
+ align:start position:0%
+membranes were break okay so that's
+ 
+
+ align:start position:0%
+membranes were break okay so that's
+actually the condition which you can
+
+ align:start position:0%
+actually the condition which you can
+ 
+
+ align:start position:0%
+actually the condition which you can
+actually get and the interesting see is
+
+ align:start position:0%
+actually get and the interesting see is
+ 
+
+ align:start position:0%
+actually get and the interesting see is
+that okay based on this expression K F
+
+ align:start position:0%
+that okay based on this expression K F
+ 
+
+ align:start position:0%
+that okay based on this expression K F
+as the length of the k alpha and the
+
+ align:start position:0%
+as the length of the k alpha and the
+ 
+
+ align:start position:0%
+as the length of the k alpha and the
+length of the K beta is fixed right and
+
+ align:start position:0%
+length of the K beta is fixed right and
+ 
+
+ align:start position:0%
+length of the K beta is fixed right and
+I also know will be the component for
+
+ align:start position:0%
+I also know will be the component for
+ 
+
+ align:start position:0%
+I also know will be the component for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+direction therefore that means the X
+
+ align:start position:0%
+direction therefore that means the X
+ 
+
+ align:start position:0%
+direction therefore that means the X
+direction and the X direction size for
+
+ align:start position:0%
+direction and the X direction size for
+ 
+
+ align:start position:0%
+direction and the X direction size for
+the K Alpha X and the K Y K beta X also
+
+ align:start position:0%
+the K Alpha X and the K Y K beta X also
+ 
+
+ align:start position:0%
+the K Alpha X and the K Y K beta X also
+fixed because of the dispersion relation
+
+ align:start position:0%
+fixed because of the dispersion relation
+ 
+
+ align:start position:0%
+fixed because of the dispersion relation
+okay so so that immediately bring me to
+
+ align:start position:0%
+okay so so that immediately bring me to
+ 
+
+ align:start position:0%
+okay so so that immediately bring me to
+this conclusion that basically K Alpha X
+
+ align:start position:0%
+this conclusion that basically K Alpha X
+ 
+
+ align:start position:0%
+this conclusion that basically K Alpha X
+will be equal to minus Omega square over
+
+ align:start position:0%
+will be equal to minus Omega square over
+ 
+
+ align:start position:0%
+will be equal to minus Omega square over
+V squared minus KY squared and that
+
+ align:start position:0%
+V squared minus KY squared and that
+ 
+
+ align:start position:0%
+V squared minus KY squared and that
+would be equal to minus KX okay so this
+
+ align:start position:0%
+would be equal to minus KX okay so this
+ 
+
+ align:start position:0%
+would be equal to minus KX okay so this
+is with the X component of the
+
+ align:start position:0%
+is with the X component of the
+ 
+
+ align:start position:0%
+is with the X component of the
+refractive wave and the transmitted wave
+
+ align:start position:0%
+refractive wave and the transmitted wave
+ 
+
+ align:start position:0%
+refractive wave and the transmitted wave
+K beta X will be equal to square root of
+
+ align:start position:0%
+K beta X will be equal to square root of
+ 
+
+ align:start position:0%
+K beta X will be equal to square root of
+Omega square over V squared minus KY
+
+ align:start position:0%
+Omega square over V squared minus KY
+ 
+
+ align:start position:0%
+Omega square over V squared minus KY
+square if I draw visualize the relative
+
+ align:start position:0%
+square if I draw visualize the relative
+ 
+
+ align:start position:0%
+square if I draw visualize the relative
+direction of all the three components
+
+ align:start position:0%
+direction of all the three components
+ 
+
+ align:start position:0%
+direction of all the three components
+basically this is actually the direction
+
+ align:start position:0%
+basically this is actually the direction
+ 
+
+ align:start position:0%
+basically this is actually the direction
+of the incident wave okay and the
+
+ align:start position:0%
+of the incident wave okay and the
+ 
+
+ align:start position:0%
+of the incident wave okay and the
+inserting angle is Sita and from this
+
+ align:start position:0%
+inserting angle is Sita and from this
+ 
+
+ align:start position:0%
+inserting angle is Sita and from this
+expression you see that the K Y is equal
+
+ align:start position:0%
+expression you see that the K Y is equal
+ 
+
+ align:start position:0%
+expression you see that the K Y is equal
+to K alpha Y therefore you have a
+
+ align:start position:0%
+to K alpha Y therefore you have a
+ 
+
+ align:start position:0%
+to K alpha Y therefore you have a
+refractive wave but actually only the x
+
+ align:start position:0%
+refractive wave but actually only the x
+ 
+
+ align:start position:0%
+refractive wave but actually only the x
+direction is change sign therefore you
+
+ align:start position:0%
+direction is change sign therefore you
+ 
+
+ align:start position:0%
+direction is change sign therefore you
+have a refractive wave with exactly the
+
+ align:start position:0%
+have a refractive wave with exactly the
+ 
+
+ align:start position:0%
+have a refractive wave with exactly the
+same angle as the in certain angle
+
+ align:start position:0%
+same angle as the in certain angle
+ 
+
+ align:start position:0%
+same angle as the in certain angle
+incident angle theta the reflected the
+
+ align:start position:0%
+incident angle theta the reflected the
+ 
+
+ align:start position:0%
+incident angle theta the reflected the
+refraction angle will be Sita as well
+
+ align:start position:0%
+refraction angle will be Sita as well
+ 
+
+ align:start position:0%
+refraction angle will be Sita as well
+and there will be a transmitted wave
+
+ align:start position:0%
+and there will be a transmitted wave
+ 
+
+ align:start position:0%
+and there will be a transmitted wave
+with Sita prom and this is issued at the
+
+ align:start position:0%
+with Sita prom and this is issued at the
+ 
+
+ align:start position:0%
+with Sita prom and this is issued at the
+ration of the k k prom and the
+
+ align:start position:0%
+ration of the k k prom and the
+ 
+
+ align:start position:0%
+ration of the k k prom and the
+interesting see is that the projection
+
+ align:start position:0%
+interesting see is that the projection
+ 
+
+ align:start position:0%
+interesting see is that the projection
+to the to the y direction the K prime Y
+
+ align:start position:0%
+to the to the y direction the K prime Y
+ 
+
+ align:start position:0%
+to the to the y direction the K prime Y
+has to be equal to the projection of the
+
+ align:start position:0%
+has to be equal to the projection of the
+ 
+
+ align:start position:0%
+has to be equal to the projection of the
+original incident wave in the in the Y
+
+ align:start position:0%
+original incident wave in the in the Y
+ 
+
+ align:start position:0%
+original incident wave in the in the Y
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+okay so that means I will be able to
+
+ align:start position:0%
+okay so that means I will be able to
+ 
+
+ align:start position:0%
+okay so that means I will be able to
+conclude that okay the Y components are
+
+ align:start position:0%
+conclude that okay the Y components are
+ 
+
+ align:start position:0%
+conclude that okay the Y components are
+the same therefore I can conclude
+
+ align:start position:0%
+the same therefore I can conclude
+ 
+
+ align:start position:0%
+the same therefore I can conclude
+that K sine theta will be equal to K
+
+ align:start position:0%
+that K sine theta will be equal to K
+ 
+
+ align:start position:0%
+that K sine theta will be equal to K
+prang sine theta prime okay and kind of
+
+ align:start position:0%
+prang sine theta prime okay and kind of
+ 
+
+ align:start position:0%
+prang sine theta prime okay and kind of
+running out of time and if I define
+
+ align:start position:0%
+running out of time and if I define
+ 
+
+ align:start position:0%
+running out of time and if I define
+already as I define here velocity is
+
+ align:start position:0%
+already as I define here velocity is
+ 
+
+ align:start position:0%
+already as I define here velocity is
+equal to C over N and the V prime is
+
+ align:start position:0%
+equal to C over N and the V prime is
+ 
+
+ align:start position:0%
+equal to C over N and the V prime is
+equal to C over m pant okay what I can
+
+ align:start position:0%
+equal to C over m pant okay what I can
+ 
+
+ align:start position:0%
+equal to C over m pant okay what I can
+actually immediately conclude is that
+
+ align:start position:0%
+actually immediately conclude is that
+ 
+
+ align:start position:0%
+actually immediately conclude is that
+give me one more minute is that if I
+
+ align:start position:0%
+give me one more minute is that if I
+ 
+
+ align:start position:0%
+give me one more minute is that if I
+have an equal to C over V and the Empire
+
+ align:start position:0%
+have an equal to C over V and the Empire
+ 
+
+ align:start position:0%
+have an equal to C over V and the Empire
+is equal to C over B front I can
+
+ align:start position:0%
+is equal to C over B front I can
+ 
+
+ align:start position:0%
+is equal to C over B front I can
+conclude that n sine theta will be equal
+
+ align:start position:0%
+conclude that n sine theta will be equal
+ 
+
+ align:start position:0%
+conclude that n sine theta will be equal
+to L prime sine theta Prime does this
+
+ align:start position:0%
+to L prime sine theta Prime does this
+ 
+
+ align:start position:0%
+to L prime sine theta Prime does this
+look familiar to you
+
+ align:start position:0%
+look familiar to you
+ 
+
+ align:start position:0%
+look familiar to you
+this is actually Snell's law right how
+
+ align:start position:0%
+this is actually Snell's law right how
+ 
+
+ align:start position:0%
+this is actually Snell's law right how
+many of you haven't heard about Snell's
+
+ align:start position:0%
+many of you haven't heard about Snell's
+ 
+
+ align:start position:0%
+many of you haven't heard about Snell's
+law there were a few before yeah okay no
+
+ align:start position:0%
+law there were a few before yeah okay no
+ 
+
+ align:start position:0%
+law there were a few before yeah okay no
+problem at all then you learned it right
+
+ align:start position:0%
+problem at all then you learned it right
+ 
+
+ align:start position:0%
+problem at all then you learned it right
+so that means if I have two kinds of
+
+ align:start position:0%
+so that means if I have two kinds of
+ 
+
+ align:start position:0%
+so that means if I have two kinds of
+systems in my hand and I will be able to
+
+ align:start position:0%
+systems in my hand and I will be able to
+ 
+
+ align:start position:0%
+systems in my hand and I will be able to
+relate the the transmitted wave and
+
+ align:start position:0%
+relate the the transmitted wave and
+ 
+
+ align:start position:0%
+relate the the transmitted wave and
+according to what I have in the incident
+
+ align:start position:0%
+according to what I have in the incident
+ 
+
+ align:start position:0%
+according to what I have in the incident
+wave and you can see that Snell's law
+
+ align:start position:0%
+wave and you can see that Snell's law
+ 
+
+ align:start position:0%
+wave and you can see that Snell's law
+which were famous for optics right the
+
+ align:start position:0%
+which were famous for optics right the
+ 
+
+ align:start position:0%
+which were famous for optics right the
+discussion of optics and here I have no
+
+ align:start position:0%
+discussion of optics and here I have no
+ 
+
+ align:start position:0%
+discussion of optics and here I have no
+knowledge about optics or
+
+ align:start position:0%
+knowledge about optics or
+ 
+
+ align:start position:0%
+knowledge about optics or
+electromagnetic wave so in short what I
+
+ align:start position:0%
+electromagnetic wave so in short what I
+ 
+
+ align:start position:0%
+electromagnetic wave so in short what I
+want to tell you is that we have just
+
+ align:start position:0%
+want to tell you is that we have just
+ 
+
+ align:start position:0%
+want to tell you is that we have just
+proved two of the most important laws of
+
+ align:start position:0%
+proved two of the most important laws of
+ 
+
+ align:start position:0%
+proved two of the most important laws of
+the geometrical optics the refraction
+
+ align:start position:0%
+the geometrical optics the refraction
+ 
+
+ align:start position:0%
+the geometrical optics the refraction
+angle is equal to either the angle and
+
+ align:start position:0%
+angle is equal to either the angle and
+ 
+
+ align:start position:0%
+angle is equal to either the angle and
+the Snell's law without using any
+
+ align:start position:0%
+the Snell's law without using any
+ 
+
+ align:start position:0%
+the Snell's law without using any
+information about the dynamics that
+
+ align:start position:0%
+information about the dynamics that
+ 
+
+ align:start position:0%
+information about the dynamics that
+means all those laws are coming from
+
+ align:start position:0%
+means all those laws are coming from
+ 
+
+ align:start position:0%
+means all those laws are coming from
+pure the boundary condition and the
+
+ align:start position:0%
+pure the boundary condition and the
+ 
+
+ align:start position:0%
+pure the boundary condition and the
+waves therefore you will expect that
+
+ align:start position:0%
+waves therefore you will expect that
+ 
+
+ align:start position:0%
+waves therefore you will expect that
+this will work for water wave some wave
+
+ align:start position:0%
+this will work for water wave some wave
+ 
+
+ align:start position:0%
+this will work for water wave some wave
+electromagnetic wave etc okay so we will
+
+ align:start position:0%
+electromagnetic wave etc okay so we will
+ 
+
+ align:start position:0%
+electromagnetic wave etc okay so we will
+continue the discussion
+
+ align:start position:0%
+continue the discussion
+ 
+
+ align:start position:0%
+continue the discussion
+science thanks for the attention and if
+
+ align:start position:0%
+science thanks for the attention and if
+ 
+
+ align:start position:0%
+science thanks for the attention and if
+I have any questions let me know I will
+
+ align:start position:0%
+I have any questions let me know I will
+ 
+
+ align:start position:0%
+I have any questions let me know I will
+be here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hello everybody we are going to show you
+
+ align:start position:0%
+hello everybody we are going to show you
+ 
+
+ align:start position:0%
+hello everybody we are going to show you
+a demonstration really nice one
+
+ align:start position:0%
+a demonstration really nice one
+ 
+
+ align:start position:0%
+a demonstration really nice one
+though I is a consist of following setup
+
+ align:start position:0%
+though I is a consist of following setup
+ 
+
+ align:start position:0%
+though I is a consist of following setup
+so basically I'm going to press soft
+
+ align:start position:0%
+so basically I'm going to press soft
+ 
+
+ align:start position:0%
+so basically I'm going to press soft
+film here and then behind that is a
+
+ align:start position:0%
+film here and then behind that is a
+ 
+
+ align:start position:0%
+film here and then behind that is a
+loudspeaker which I use a signal
+
+ align:start position:0%
+loudspeaker which I use a signal
+ 
+
+ align:start position:0%
+loudspeaker which I use a signal
+generator and to actually produce some
+
+ align:start position:0%
+generator and to actually produce some
+ 
+
+ align:start position:0%
+generator and to actually produce some
+wave and this song wave is going to
+
+ align:start position:0%
+wave and this song wave is going to
+ 
+
+ align:start position:0%
+wave and this song wave is going to
+oscillate the soft film and then you are
+
+ align:start position:0%
+oscillate the soft film and then you are
+ 
+
+ align:start position:0%
+oscillate the soft film and then you are
+going to see the oscillation were saying
+
+ align:start position:0%
+going to see the oscillation were saying
+ 
+
+ align:start position:0%
+going to see the oscillation were saying
+no more moved pattern on the screen ok
+
+ align:start position:0%
+no more moved pattern on the screen ok
+ 
+
+ align:start position:0%
+no more moved pattern on the screen ok
+so that that is actually the setup which
+
+ align:start position:0%
+so that that is actually the setup which
+ 
+
+ align:start position:0%
+so that that is actually the setup which
+we can actually demonstrate new to time
+
+ align:start position:0%
+we can actually demonstrate new to time
+ 
+
+ align:start position:0%
+we can actually demonstrate new to time
+mentioned no normal modes so the first
+
+ align:start position:0%
+mentioned no normal modes so the first
+ 
+
+ align:start position:0%
+mentioned no normal modes so the first
+thing which I am going to do is to
+
+ align:start position:0%
+thing which I am going to do is to
+ 
+
+ align:start position:0%
+thing which I am going to do is to
+produce a soft film now I'm going to put
+
+ align:start position:0%
+produce a soft film now I'm going to put
+ 
+
+ align:start position:0%
+produce a soft film now I'm going to put
+it back into this setup here you should
+
+ align:start position:0%
+it back into this setup here you should
+ 
+
+ align:start position:0%
+it back into this setup here you should
+be able to see the pattern on the screen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I'm going to turn on the some wave
+
+ align:start position:0%
+then I'm going to turn on the some wave
+ 
+
+ align:start position:0%
+then I'm going to turn on the some wave
+generator you can see immediately that
+
+ align:start position:0%
+generator you can see immediately that
+ 
+
+ align:start position:0%
+generator you can see immediately that
+the pattern is on the screen changed
+
+ align:start position:0%
+the pattern is on the screen changed
+ 
+
+ align:start position:0%
+the pattern is on the screen changed
+because of the song wave trying to
+
+ align:start position:0%
+because of the song wave trying to
+ 
+
+ align:start position:0%
+because of the song wave trying to
+assert a self UHN you can actually see
+
+ align:start position:0%
+assert a self UHN you can actually see
+ 
+
+ align:start position:0%
+assert a self UHN you can actually see
+it directly from here but the
+
+ align:start position:0%
+it directly from here but the
+ 
+
+ align:start position:0%
+it directly from here but the
+essentially looks a much more prominent
+
+ align:start position:0%
+essentially looks a much more prominent
+ 
+
+ align:start position:0%
+essentially looks a much more prominent
+on the screen and now what I'm going to
+
+ align:start position:0%
+on the screen and now what I'm going to
+ 
+
+ align:start position:0%
+on the screen and now what I'm going to
+do is to change the the frequency of the
+
+ align:start position:0%
+do is to change the the frequency of the
+ 
+
+ align:start position:0%
+do is to change the the frequency of the
+sound wave and you can see that now I'm
+
+ align:start position:0%
+sound wave and you can see that now I'm
+ 
+
+ align:start position:0%
+sound wave and you can see that now I'm
+changing it to a higher frequency and
+
+ align:start position:0%
+changing it to a higher frequency and
+ 
+
+ align:start position:0%
+changing it to a higher frequency and
+you can see that there are more
+
+ align:start position:0%
+you can see that there are more
+ 
+
+ align:start position:0%
+you can see that there are more
+complicated pattern form on the screen
+
+ align:start position:0%
+complicated pattern form on the screen
+ 
+
+ align:start position:0%
+complicated pattern form on the screen
+that is because I now exciteing higher
+
+ align:start position:0%
+that is because I now exciteing higher
+ 
+
+ align:start position:0%
+that is because I now exciteing higher
+and higher frequency normal mode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can see that now as you continue
+
+ align:start position:0%
+and you can see that now as you continue
+ 
+
+ align:start position:0%
+and you can see that now as you continue
+in the increased increased the frequency
+
+ align:start position:0%
+in the increased increased the frequency
+ 
+
+ align:start position:0%
+in the increased increased the frequency
+and you can see that now we can see that
+
+ align:start position:0%
+and you can see that now we can see that
+ 
+
+ align:start position:0%
+and you can see that now we can see that
+the pattern become really really
+
+ align:start position:0%
+the pattern become really really
+ 
+
+ align:start position:0%
+the pattern become really really
+infinitely complicated you can see this
+
+ align:start position:0%
+infinitely complicated you can see this
+ 
+
+ align:start position:0%
+infinitely complicated you can see this
+grid developing and you can see that
+
+ align:start position:0%
+grid developing and you can see that
+ 
+
+ align:start position:0%
+grid developing and you can see that
+basically that's two basically two sine
+
+ align:start position:0%
+basically that's two basically two sine
+ 
+
+ align:start position:0%
+basically that's two basically two sine
+function multiplied each other one is
+
+ align:start position:0%
+function multiplied each other one is
+ 
+
+ align:start position:0%
+function multiplied each other one is
+one sine functions in the x-direction
+
+ align:start position:0%
+one sine functions in the x-direction
+ 
+
+ align:start position:0%
+one sine functions in the x-direction
+the other one is in the Y Direction
+
+ align:start position:0%
+the other one is in the Y Direction
+ 
+
+ align:start position:0%
+the other one is in the Y Direction
+horizontal and the vertical direction
+
+ align:start position:0%
+horizontal and the vertical direction
+ 
+
+ align:start position:0%
+horizontal and the vertical direction
+and you can see really beautiful pattern
+
+ align:start position:0%
+and you can see really beautiful pattern
+ 
+
+ align:start position:0%
+and you can see really beautiful pattern
+forming due to the new to this solution
+
+ align:start position:0%
+forming due to the new to this solution
+ 
+
+ align:start position:0%
+forming due to the new to this solution
+wind arrived during the lecture and the
+
+ align:start position:0%
+wind arrived during the lecture and the
+ 
+
+ align:start position:0%
+wind arrived during the lecture and the
+higher frequency I go I can see more
+
+ align:start position:0%
+higher frequency I go I can see more
+ 
+
+ align:start position:0%
+higher frequency I go I can see more
+complicated pattern or many more lines
+
+ align:start position:0%
+complicated pattern or many more lines
+ 
+
+ align:start position:0%
+complicated pattern or many more lines
+developing under screen
+
+ align:start position:0%
+developing under screen
+ 
+
+ align:start position:0%
+developing under screen
+due to the oscillation of the soap film
+
+ align:start position:0%
+due to the oscillation of the soap film
+ 
+
+ align:start position:0%
+due to the oscillation of the soap film
+you can see now we have even more lines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is you getting more more
+
+ align:start position:0%
+and this is you getting more more
+ 
+
+ align:start position:0%
+and this is you getting more more
+difficult to see the pattern because now
+
+ align:start position:0%
+difficult to see the pattern because now
+ 
+
+ align:start position:0%
+difficult to see the pattern because now
+the lines are pretty close to each other
+
+ align:start position:0%
+the lines are pretty close to each other
+ 
+
+ align:start position:0%
+the lines are pretty close to each other
+the Northern Line we can see clear the
+
+ align:start position:0%
+the Northern Line we can see clear the
+ 
+
+ align:start position:0%
+the Northern Line we can see clear the
+other screen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going back down to a lower frequency
+
+ align:start position:0%
+I'm going back down to a lower frequency
+ 
+
+ align:start position:0%
+I'm going back down to a lower frequency
+and you can see that a new frequency
+
+ align:start position:0%
+and you can see that a new frequency
+ 
+
+ align:start position:0%
+and you can see that a new frequency
+oscillation the number of lines is a
+
+ align:start position:0%
+oscillation the number of lines is a
+ 
+
+ align:start position:0%
+oscillation the number of lines is a
+should be smaller and and that is
+
+ align:start position:0%
+should be smaller and and that is
+ 
+
+ align:start position:0%
+should be smaller and and that is
+because of the smoother oscillation
+
+ align:start position:0%
+because of the smoother oscillation
+ 
+
+ align:start position:0%
+because of the smoother oscillation
+frequency and the longer wavelength of
+
+ align:start position:0%
+frequency and the longer wavelength of
+ 
+
+ align:start position:0%
+frequency and the longer wavelength of
+the normal modes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/aPdgRxcP2lA.txt b/aPdgRxcP2lA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..77e1fc1c2433306ee8efac6e1576ad552c338bcc
--- /dev/null
+++ b/aPdgRxcP2lA.txt
@@ -0,0 +1,5115 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm a professor at MIT in the department
+
+ align:start position:0%
+I'm a professor at MIT in the department
+ 
+
+ align:start position:0%
+I'm a professor at MIT in the department
+of urban studies and planning I'd like
+
+ align:start position:0%
+of urban studies and planning I'd like
+ 
+
+ align:start position:0%
+of urban studies and planning I'd like
+to welcome you to another lecture in my
+
+ align:start position:0%
+to welcome you to another lecture in my
+ 
+
+ align:start position:0%
+to welcome you to another lecture in my
+series on Urban Energy Systems and
+
+ align:start position:0%
+series on Urban Energy Systems and
+ 
+
+ align:start position:0%
+series on Urban Energy Systems and
+policy
+
+ align:start position:0%
+policy
+ 
+
+ align:start position:0%
+policy
+today we're going to talk about cities
+
+ align:start position:0%
+today we're going to talk about cities
+ 
+
+ align:start position:0%
+today we're going to talk about cities
+and Industrial admissions
+
+ align:start position:0%
+and Industrial admissions
+ 
+
+ align:start position:0%
+and Industrial admissions
+and what I want to do in this class in
+
+ align:start position:0%
+and what I want to do in this class in
+ 
+
+ align:start position:0%
+and what I want to do in this class in
+this lecture is connect cities to the
+
+ align:start position:0%
+this lecture is connect cities to the
+ 
+
+ align:start position:0%
+this lecture is connect cities to the
+larger issues of Investments
+
+ align:start position:0%
+larger issues of Investments
+ 
+
+ align:start position:0%
+larger issues of Investments
+early because inductible missions don't
+
+ align:start position:0%
+early because inductible missions don't
+ 
+
+ align:start position:0%
+early because inductible missions don't
+always seem to be very present in the
+
+ align:start position:0%
+always seem to be very present in the
+ 
+
+ align:start position:0%
+always seem to be very present in the
+cities so I don't seem to connect to
+
+ align:start position:0%
+cities so I don't seem to connect to
+ 
+
+ align:start position:0%
+cities so I don't seem to connect to
+cities as centers of consumption as I've
+
+ align:start position:0%
+cities as centers of consumption as I've
+ 
+
+ align:start position:0%
+cities as centers of consumption as I've
+been talking to you about in this
+
+ align:start position:0%
+been talking to you about in this
+ 
+
+ align:start position:0%
+been talking to you about in this
+lecture series but also because
+
+ align:start position:0%
+lecture series but also because
+ 
+
+ align:start position:0%
+lecture series but also because
+industrial admissions are a considered
+
+ align:start position:0%
+industrial admissions are a considered
+ 
+
+ align:start position:0%
+industrial admissions are a considered
+an extremely tough to decarbonize sector
+
+ align:start position:0%
+an extremely tough to decarbonize sector
+ 
+
+ align:start position:0%
+an extremely tough to decarbonize sector
+we have to replace the electricity but
+
+ align:start position:0%
+we have to replace the electricity but
+ 
+
+ align:start position:0%
+we have to replace the electricity but
+also quickly the Heat and the materials
+
+ align:start position:0%
+also quickly the Heat and the materials
+ 
+
+ align:start position:0%
+also quickly the Heat and the materials
+we use in ductile systems to reduce our
+
+ align:start position:0%
+we use in ductile systems to reduce our
+ 
+
+ align:start position:0%
+we use in ductile systems to reduce our
+greenhouse gas emissions that doesn't
+
+ align:start position:0%
+greenhouse gas emissions that doesn't
+ 
+
+ align:start position:0%
+greenhouse gas emissions that doesn't
+always seem to be a area or a scale at
+
+ align:start position:0%
+always seem to be a area or a scale at
+ 
+
+ align:start position:0%
+always seem to be a area or a scale at
+which cities can affect this kinds of
+
+ align:start position:0%
+which cities can affect this kinds of
+ 
+
+ align:start position:0%
+which cities can affect this kinds of
+policy but we'll explore that today in
+
+ align:start position:0%
+policy but we'll explore that today in
+ 
+
+ align:start position:0%
+policy but we'll explore that today in
+this lecture how cities can affect or
+
+ align:start position:0%
+this lecture how cities can affect or
+ 
+
+ align:start position:0%
+this lecture how cities can affect or
+reduce their industrial emissions
+
+ align:start position:0%
+reduce their industrial emissions
+ 
+
+ align:start position:0%
+reduce their industrial emissions
+the materials would say are all on the
+
+ align:start position:0%
+the materials would say are all on the
+ 
+
+ align:start position:0%
+the materials would say are all on the
+syllabus if you have the PDFs then
+
+ align:start position:0%
+syllabus if you have the PDFs then
+ 
+
+ align:start position:0%
+syllabus if you have the PDFs then
+please go ahead and you can link to
+
+ align:start position:0%
+please go ahead and you can link to
+ 
+
+ align:start position:0%
+please go ahead and you can link to
+these materials to read them before the
+
+ align:start position:0%
+these materials to read them before the
+ 
+
+ align:start position:0%
+these materials to read them before the
+lecture the lecture will build on these
+
+ align:start position:0%
+lecture the lecture will build on these
+ 
+
+ align:start position:0%
+lecture the lecture will build on these
+materials
+
+ align:start position:0%
+materials
+ 
+
+ align:start position:0%
+materials
+and the themes on it uh focus on today
+
+ align:start position:0%
+and the themes on it uh focus on today
+ 
+
+ align:start position:0%
+and the themes on it uh focus on today
+are consumption as a mechanism of being
+
+ align:start position:0%
+are consumption as a mechanism of being
+ 
+
+ align:start position:0%
+are consumption as a mechanism of being
+asked gas emissions that's something
+
+ align:start position:0%
+asked gas emissions that's something
+ 
+
+ align:start position:0%
+asked gas emissions that's something
+I've said to you before in previous
+
+ align:start position:0%
+I've said to you before in previous
+ 
+
+ align:start position:0%
+I've said to you before in previous
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+I want to emphasized consumption is a
+
+ align:start position:0%
+I want to emphasized consumption is a
+ 
+
+ align:start position:0%
+I want to emphasized consumption is a
+connection to larger Energy Systems I
+
+ align:start position:0%
+connection to larger Energy Systems I
+ 
+
+ align:start position:0%
+connection to larger Energy Systems I
+think I've said to you also in previous
+
+ align:start position:0%
+think I've said to you also in previous
+ 
+
+ align:start position:0%
+think I've said to you also in previous
+lectures how we often focus on changing
+
+ align:start position:0%
+lectures how we often focus on changing
+ 
+
+ align:start position:0%
+lectures how we often focus on changing
+the Energy System how energy is produced
+
+ align:start position:0%
+the Energy System how energy is produced
+ 
+
+ align:start position:0%
+the Energy System how energy is produced
+how it is transmitted but not always
+
+ align:start position:0%
+how it is transmitted but not always
+ 
+
+ align:start position:0%
+how it is transmitted but not always
+thinking about how we can change how
+
+ align:start position:0%
+thinking about how we can change how
+ 
+
+ align:start position:0%
+thinking about how we can change how
+energy is consumed
+
+ align:start position:0%
+energy is consumed
+ 
+
+ align:start position:0%
+energy is consumed
+I'll also argue to you in today's luck
+
+ align:start position:0%
+I'll also argue to you in today's luck
+ 
+
+ align:start position:0%
+I'll also argue to you in today's luck
+through that industrial missions have
+
+ align:start position:0%
+through that industrial missions have
+ 
+
+ align:start position:0%
+through that industrial missions have
+strong very strong environmental justice
+
+ align:start position:0%
+strong very strong environmental justice
+ 
+
+ align:start position:0%
+strong very strong environmental justice
+implications
+
+ align:start position:0%
+implications
+ 
+
+ align:start position:0%
+implications
+it also is perhaps connected to our
+
+ align:start position:0%
+it also is perhaps connected to our
+ 
+
+ align:start position:0%
+it also is perhaps connected to our
+Urban rural Regional and political
+
+ align:start position:0%
+Urban rural Regional and political
+ 
+
+ align:start position:0%
+Urban rural Regional and political
+polarization over climate action
+
+ align:start position:0%
+polarization over climate action
+ 
+
+ align:start position:0%
+polarization over climate action
+and then we'll finish today and in class
+
+ align:start position:0%
+and then we'll finish today and in class
+ 
+
+ align:start position:0%
+and then we'll finish today and in class
+discussion thinking about how we might
+
+ align:start position:0%
+discussion thinking about how we might
+ 
+
+ align:start position:0%
+discussion thinking about how we might
+transform the seductible system both
+
+ align:start position:0%
+transform the seductible system both
+ 
+
+ align:start position:0%
+transform the seductible system both
+within cities and from cities also
+
+ align:start position:0%
+within cities and from cities also
+ 
+
+ align:start position:0%
+within cities and from cities also
+and so if we just start with my eyes
+
+ align:start position:0%
+and so if we just start with my eyes
+ 
+
+ align:start position:0%
+and so if we just start with my eyes
+calculation in chapter 15. he talks
+
+ align:start position:0%
+calculation in chapter 15. he talks
+ 
+
+ align:start position:0%
+calculation in chapter 15. he talks
+about life cycle analysis talks about
+
+ align:start position:0%
+about life cycle analysis talks about
+ 
+
+ align:start position:0%
+about life cycle analysis talks about
+the energy or sustainable energy
+
+ align:start position:0%
+the energy or sustainable energy
+ 
+
+ align:start position:0%
+the energy or sustainable energy
+required to produce raw materials
+
+ align:start position:0%
+required to produce raw materials
+ 
+
+ align:start position:0%
+required to produce raw materials
+uh to sorry obtain raw materials how do
+
+ align:start position:0%
+uh to sorry obtain raw materials how do
+ 
+
+ align:start position:0%
+uh to sorry obtain raw materials how do
+we produce finished goods out of the raw
+
+ align:start position:0%
+we produce finished goods out of the raw
+ 
+
+ align:start position:0%
+we produce finished goods out of the raw
+materials how do we use those materials
+
+ align:start position:0%
+materials how do we use those materials
+ 
+
+ align:start position:0%
+materials how do we use those materials
+acquiring energy and ultimately how do
+
+ align:start position:0%
+acquiring energy and ultimately how do
+ 
+
+ align:start position:0%
+acquiring energy and ultimately how do
+we dispose or uh get rid of materials
+
+ align:start position:0%
+we dispose or uh get rid of materials
+ 
+
+ align:start position:0%
+we dispose or uh get rid of materials
+by calling it waste something we talked
+
+ align:start position:0%
+by calling it waste something we talked
+ 
+
+ align:start position:0%
+by calling it waste something we talked
+about in the last lecture on Energy
+
+ align:start position:0%
+about in the last lecture on Energy
+ 
+
+ align:start position:0%
+about in the last lecture on Energy
+Efficiency
+
+ align:start position:0%
+Efficiency
+ 
+
+ align:start position:0%
+Efficiency
+and the materials he goes to briefly in
+
+ align:start position:0%
+and the materials he goes to briefly in
+ 
+
+ align:start position:0%
+and the materials he goes to briefly in
+chapter 15 are the production of raw
+
+ align:start position:0%
+chapter 15 are the production of raw
+ 
+
+ align:start position:0%
+chapter 15 are the production of raw
+materials like aluminum or steel
+
+ align:start position:0%
+materials like aluminum or steel
+ 
+
+ align:start position:0%
+materials like aluminum or steel
+packaging chips semiconductors paper
+
+ align:start position:0%
+packaging chips semiconductors paper
+ 
+
+ align:start position:0%
+packaging chips semiconductors paper
+building construction and Roads
+
+ align:start position:0%
+building construction and Roads
+ 
+
+ align:start position:0%
+building construction and Roads
+automaking and of course Makai makes the
+
+ align:start position:0%
+automaking and of course Makai makes the
+ 
+
+ align:start position:0%
+automaking and of course Makai makes the
+point that a lot of things aren't
+
+ align:start position:0%
+point that a lot of things aren't
+ 
+
+ align:start position:0%
+point that a lot of things aren't
+necessarily made in the UK anymore
+
+ align:start position:0%
+necessarily made in the UK anymore
+ 
+
+ align:start position:0%
+necessarily made in the UK anymore
+they're quite often imported so that is
+
+ align:start position:0%
+they're quite often imported so that is
+ 
+
+ align:start position:0%
+they're quite often imported so that is
+embodied energy in the form of materials
+
+ align:start position:0%
+embodied energy in the form of materials
+ 
+
+ align:start position:0%
+embodied energy in the form of materials
+and goods being brought into the UK and
+
+ align:start position:0%
+and goods being brought into the UK and
+ 
+
+ align:start position:0%
+and goods being brought into the UK and
+surprisingly if we look at his Stacks we
+
+ align:start position:0%
+surprisingly if we look at his Stacks we
+ 
+
+ align:start position:0%
+surprisingly if we look at his Stacks we
+haven't visited Revisited this concept
+
+ align:start position:0%
+haven't visited Revisited this concept
+ 
+
+ align:start position:0%
+haven't visited Revisited this concept
+for a while if you look at all the
+
+ align:start position:0%
+for a while if you look at all the
+ 
+
+ align:start position:0%
+for a while if you look at all the
+previous chapters we've talked about
+
+ align:start position:0%
+previous chapters we've talked about
+ 
+
+ align:start position:0%
+previous chapters we've talked about
+Heating and Cooling and deaf lights and
+
+ align:start position:0%
+Heating and Cooling and deaf lights and
+ 
+
+ align:start position:0%
+Heating and Cooling and deaf lights and
+cars stuff and the transporting of stuff
+
+ align:start position:0%
+cars stuff and the transporting of stuff
+ 
+
+ align:start position:0%
+cars stuff and the transporting of stuff
+is the largest category so far and so
+
+ align:start position:0%
+is the largest category so far and so
+ 
+
+ align:start position:0%
+is the largest category so far and so
+far by chapter 15 is tipping us over
+
+ align:start position:0%
+far by chapter 15 is tipping us over
+ 
+
+ align:start position:0%
+far by chapter 15 is tipping us over
+into more consumption than we can
+
+ align:start position:0%
+into more consumption than we can
+ 
+
+ align:start position:0%
+into more consumption than we can
+produce from sustainable energy
+
+ align:start position:0%
+produce from sustainable energy
+ 
+
+ align:start position:0%
+produce from sustainable energy
+resources on the right
+
+ align:start position:0%
+resources on the right
+ 
+
+ align:start position:0%
+resources on the right
+if we just think about uh some of these
+
+ align:start position:0%
+if we just think about uh some of these
+ 
+
+ align:start position:0%
+if we just think about uh some of these
+energy uses on the same footing uh the
+
+ align:start position:0%
+energy uses on the same footing uh the
+ 
+
+ align:start position:0%
+energy uses on the same footing uh the
+stuff per person then with eye
+
+ align:start position:0%
+stuff per person then with eye
+ 
+
+ align:start position:0%
+stuff per person then with eye
+calculates in appendix agents around 41
+
+ align:start position:0%
+calculates in appendix agents around 41
+ 
+
+ align:start position:0%
+calculates in appendix agents around 41
+kilowatt hours per day that's 41
+
+ align:start position:0%
+kilowatt hours per day that's 41
+ 
+
+ align:start position:0%
+kilowatt hours per day that's 41
+kilowatt hours per day as kind of a rate
+
+ align:start position:0%
+kilowatt hours per day as kind of a rate
+ 
+
+ align:start position:0%
+kilowatt hours per day as kind of a rate
+of energy use
+
+ align:start position:0%
+of energy use
+ 
+
+ align:start position:0%
+of energy use
+hot water hot air and cooling add up to
+
+ align:start position:0%
+hot water hot air and cooling add up to
+ 
+
+ align:start position:0%
+hot water hot air and cooling add up to
+roughly about 37 kilowatt hours per day
+
+ align:start position:0%
+roughly about 37 kilowatt hours per day
+ 
+
+ align:start position:0%
+roughly about 37 kilowatt hours per day
+and the construction of the house that
+
+ align:start position:0%
+and the construction of the house that
+ 
+
+ align:start position:0%
+and the construction of the house that
+with high estimates uh I think a typical
+
+ align:start position:0%
+with high estimates uh I think a typical
+ 
+
+ align:start position:0%
+with high estimates uh I think a typical
+English house just the shell of the
+
+ align:start position:0%
+English house just the shell of the
+ 
+
+ align:start position:0%
+English house just the shell of the
+house itself is about 42 000 kilowatt
+
+ align:start position:0%
+house itself is about 42 000 kilowatt
+ 
+
+ align:start position:0%
+house itself is about 42 000 kilowatt
+hours over 100 years the house is
+
+ align:start position:0%
+hours over 100 years the house is
+ 
+
+ align:start position:0%
+hours over 100 years the house is
+assumed to last 100 years so if you put
+
+ align:start position:0%
+assumed to last 100 years so if you put
+ 
+
+ align:start position:0%
+assumed to last 100 years so if you put
+that on equal footing it's only 1.2
+
+ align:start position:0%
+that on equal footing it's only 1.2
+ 
+
+ align:start position:0%
+that on equal footing it's only 1.2
+kilowatt hours per day
+
+ align:start position:0%
+kilowatt hours per day
+ 
+
+ align:start position:0%
+kilowatt hours per day
+so we might conclude from these back of
+
+ align:start position:0%
+so we might conclude from these back of
+ 
+
+ align:start position:0%
+so we might conclude from these back of
+the envelope numbers makai's book the
+
+ align:start position:0%
+the envelope numbers makai's book the
+ 
+
+ align:start position:0%
+the envelope numbers makai's book the
+materials and construction aren't really
+
+ align:start position:0%
+materials and construction aren't really
+ 
+
+ align:start position:0%
+materials and construction aren't really
+a problem right
+
+ align:start position:0%
+a problem right
+ 
+
+ align:start position:0%
+a problem right
+well let's just question this for a
+
+ align:start position:0%
+well let's just question this for a
+ 
+
+ align:start position:0%
+well let's just question this for a
+second there's obvious reasons why by
+
+ align:start position:0%
+second there's obvious reasons why by
+ 
+
+ align:start position:0%
+second there's obvious reasons why by
+putting things in the same pudding by
+
+ align:start position:0%
+putting things in the same pudding by
+ 
+
+ align:start position:0%
+putting things in the same pudding by
+kind of amortizing this energy over 100
+
+ align:start position:0%
+kind of amortizing this energy over 100
+ 
+
+ align:start position:0%
+kind of amortizing this energy over 100
+years you might be missing some things
+
+ align:start position:0%
+years you might be missing some things
+ 
+
+ align:start position:0%
+years you might be missing some things
+first the houses that we construct now
+
+ align:start position:0%
+first the houses that we construct now
+ 
+
+ align:start position:0%
+first the houses that we construct now
+in this calculation are assumed to last
+
+ align:start position:0%
+in this calculation are assumed to last
+ 
+
+ align:start position:0%
+in this calculation are assumed to last
+for 100 years not only does that assume
+
+ align:start position:0%
+for 100 years not only does that assume
+ 
+
+ align:start position:0%
+for 100 years not only does that assume
+we don't retrofit or modify them or
+
+ align:start position:0%
+we don't retrofit or modify them or
+ 
+
+ align:start position:0%
+we don't retrofit or modify them or
+redecorate them or demolish them in the
+
+ align:start position:0%
+redecorate them or demolish them in the
+ 
+
+ align:start position:0%
+redecorate them or demolish them in the
+next hundred years which is obviously an
+
+ align:start position:0%
+next hundred years which is obviously an
+ 
+
+ align:start position:0%
+next hundred years which is obviously an
+assumption that probably does not hold
+
+ align:start position:0%
+assumption that probably does not hold
+ 
+
+ align:start position:0%
+assumption that probably does not hold
+in many North American cities let alone
+
+ align:start position:0%
+in many North American cities let alone
+ 
+
+ align:start position:0%
+in many North American cities let alone
+fats developing uh unfreeze
+
+ align:start position:0%
+fats developing uh unfreeze
+ 
+
+ align:start position:0%
+fats developing uh unfreeze
+but also it assumes that the house
+
+ align:start position:0%
+but also it assumes that the house
+ 
+
+ align:start position:0%
+but also it assumes that the house
+construction that we do today is
+
+ align:start position:0%
+construction that we do today is
+ 
+
+ align:start position:0%
+construction that we do today is
+essentially bacon we're locking in that
+
+ align:start position:0%
+essentially bacon we're locking in that
+ 
+
+ align:start position:0%
+essentially bacon we're locking in that
+energy construction now we're locking
+
+ align:start position:0%
+energy construction now we're locking
+ 
+
+ align:start position:0%
+energy construction now we're locking
+the energy implications of that house
+
+ align:start position:0%
+the energy implications of that house
+ 
+
+ align:start position:0%
+the energy implications of that house
+construction now and we're actually
+
+ align:start position:0%
+construction now and we're actually
+ 
+
+ align:start position:0%
+construction now and we're actually
+emitting the carbon emissions of that
+
+ align:start position:0%
+emitting the carbon emissions of that
+ 
+
+ align:start position:0%
+emitting the carbon emissions of that
+now so not only do we calculate this
+
+ align:start position:0%
+now so not only do we calculate this
+ 
+
+ align:start position:0%
+now so not only do we calculate this
+energy basis and kind of average it over
+
+ align:start position:0%
+energy basis and kind of average it over
+ 
+
+ align:start position:0%
+energy basis and kind of average it over
+the next hundred years but it matters
+
+ align:start position:0%
+the next hundred years but it matters
+ 
+
+ align:start position:0%
+the next hundred years but it matters
+much more if we actually do a lot of
+
+ align:start position:0%
+much more if we actually do a lot of
+ 
+
+ align:start position:0%
+much more if we actually do a lot of
+construction and amid a lot of carbon
+
+ align:start position:0%
+construction and amid a lot of carbon
+ 
+
+ align:start position:0%
+construction and amid a lot of carbon
+now much more today than 100 years from
+
+ align:start position:0%
+now much more today than 100 years from
+ 
+
+ align:start position:0%
+now much more today than 100 years from
+now as I've said to you multiple times
+
+ align:start position:0%
+now as I've said to you multiple times
+ 
+
+ align:start position:0%
+now as I've said to you multiple times
+this class we have a mid-century goal of
+
+ align:start position:0%
+this class we have a mid-century goal of
+ 
+
+ align:start position:0%
+this class we have a mid-century goal of
+2015 if we assume that we're going to
+
+ align:start position:0%
+2015 if we assume that we're going to
+ 
+
+ align:start position:0%
+2015 if we assume that we're going to
+stop doing any construction after this
+
+ align:start position:0%
+stop doing any construction after this
+ 
+
+ align:start position:0%
+stop doing any construction after this
+next couple years that might be one
+
+ align:start position:0%
+next couple years that might be one
+ 
+
+ align:start position:0%
+next couple years that might be one
+thing but we still front loaded our uh
+
+ align:start position:0%
+thing but we still front loaded our uh
+ 
+
+ align:start position:0%
+thing but we still front loaded our uh
+energy or our carb emissions today for
+
+ align:start position:0%
+energy or our carb emissions today for
+ 
+
+ align:start position:0%
+energy or our carb emissions today for
+the next 100 years if we make this
+
+ align:start position:0%
+the next 100 years if we make this
+ 
+
+ align:start position:0%
+the next 100 years if we make this
+assumption so perhaps averaging
+
+ align:start position:0%
+assumption so perhaps averaging
+ 
+
+ align:start position:0%
+assumption so perhaps averaging
+everything over the next hundred years
+
+ align:start position:0%
+everything over the next hundred years
+ 
+
+ align:start position:0%
+everything over the next hundred years
+is not the way you should think about it
+
+ align:start position:0%
+is not the way you should think about it
+ 
+
+ align:start position:0%
+is not the way you should think about it
+but another argument I want to make to
+
+ align:start position:0%
+but another argument I want to make to
+ 
+
+ align:start position:0%
+but another argument I want to make to
+you is that there's definitely different
+
+ align:start position:0%
+you is that there's definitely different
+ 
+
+ align:start position:0%
+you is that there's definitely different
+implications of industrial emissions for
+
+ align:start position:0%
+implications of industrial emissions for
+ 
+
+ align:start position:0%
+implications of industrial emissions for
+livelihood and climate action and one of
+
+ align:start position:0%
+livelihood and climate action and one of
+ 
+
+ align:start position:0%
+livelihood and climate action and one of
+the previous lectures I think even the
+
+ align:start position:0%
+the previous lectures I think even the
+ 
+
+ align:start position:0%
+the previous lectures I think even the
+second left period for this class I
+
+ align:start position:0%
+second left period for this class I
+ 
+
+ align:start position:0%
+second left period for this class I
+talked to you about Robert Bullard
+
+ align:start position:0%
+talked to you about Robert Bullard
+ 
+
+ align:start position:0%
+talked to you about Robert Bullard
+Robert Bullard is an article Justin
+
+ align:start position:0%
+Robert Bullard is an article Justin
+ 
+
+ align:start position:0%
+Robert Bullard is an article Justin
+scholar really in some ways the father
+
+ align:start position:0%
+scholar really in some ways the father
+ 
+
+ align:start position:0%
+scholar really in some ways the father
+of a Revival Justice and as I said to
+
+ align:start position:0%
+of a Revival Justice and as I said to
+ 
+
+ align:start position:0%
+of a Revival Justice and as I said to
+you in the second lecture he discovered
+
+ align:start position:0%
+you in the second lecture he discovered
+ 
+
+ align:start position:0%
+you in the second lecture he discovered
+early on in his career as a sociologist
+
+ align:start position:0%
+early on in his career as a sociologist
+ 
+
+ align:start position:0%
+early on in his career as a sociologist
+at 100 of the landfills in Houston were
+
+ align:start position:0%
+at 100 of the landfills in Houston were
+ 
+
+ align:start position:0%
+at 100 of the landfills in Houston were
+located in black neighborhoods though
+
+ align:start position:0%
+located in black neighborhoods though
+ 
+
+ align:start position:0%
+located in black neighborhoods though
+the black population was only 25 percent
+
+ align:start position:0%
+the black population was only 25 percent
+ 
+
+ align:start position:0%
+the black population was only 25 percent
+of Houston's population
+
+ align:start position:0%
+of Houston's population
+ 
+
+ align:start position:0%
+of Houston's population
+at the same time this book uh this paper
+
+ align:start position:0%
+at the same time this book uh this paper
+ 
+
+ align:start position:0%
+at the same time this book uh this paper
+we read by Sandeep I and others this is
+
+ align:start position:0%
+we read by Sandeep I and others this is
+ 
+
+ align:start position:0%
+we read by Sandeep I and others this is
+the same author he was recently wrote a
+
+ align:start position:0%
+the same author he was recently wrote a
+ 
+
+ align:start position:0%
+the same author he was recently wrote a
+book called total transition and it's
+
+ align:start position:0%
+book called total transition and it's
+ 
+
+ align:start position:0%
+book called total transition and it's
+called The Human Side of the renewable
+
+ align:start position:0%
+called The Human Side of the renewable
+ 
+
+ align:start position:0%
+called The Human Side of the renewable
+energy Revolution because he focuses on
+
+ align:start position:0%
+energy Revolution because he focuses on
+ 
+
+ align:start position:0%
+energy Revolution because he focuses on
+workers in the fossil fuel Industries if
+
+ align:start position:0%
+workers in the fossil fuel Industries if
+ 
+
+ align:start position:0%
+workers in the fossil fuel Industries if
+we and argues that if we have a
+
+ align:start position:0%
+we and argues that if we have a
+ 
+
+ align:start position:0%
+we and argues that if we have a
+renewable energy Revolution it is going
+
+ align:start position:0%
+renewable energy Revolution it is going
+ 
+
+ align:start position:0%
+renewable energy Revolution it is going
+to diffrently affect these workers so he
+
+ align:start position:0%
+to diffrently affect these workers so he
+ 
+
+ align:start position:0%
+to diffrently affect these workers so he
+investigates the situations of workers
+
+ align:start position:0%
+investigates the situations of workers
+ 
+
+ align:start position:0%
+investigates the situations of workers
+both in India and in Canada and you know
+
+ align:start position:0%
+both in India and in Canada and you know
+ 
+
+ align:start position:0%
+both in India and in Canada and you know
+this two things are not unconnected
+
+ align:start position:0%
+this two things are not unconnected
+ 
+
+ align:start position:0%
+this two things are not unconnected
+first the invocable adjusted
+
+ align:start position:0%
+first the invocable adjusted
+ 
+
+ align:start position:0%
+first the invocable adjusted
+implications of fossil fuel use and
+
+ align:start position:0%
+implications of fossil fuel use and
+ 
+
+ align:start position:0%
+implications of fossil fuel use and
+consumption and production uh focused on
+
+ align:start position:0%
+consumption and production uh focused on
+ 
+
+ align:start position:0%
+consumption and production uh focused on
+by Robert Bullard and shalanda Baker if
+
+ align:start position:0%
+by Robert Bullard and shalanda Baker if
+ 
+
+ align:start position:0%
+by Robert Bullard and shalanda Baker if
+you remember that article we read maybe
+
+ align:start position:0%
+you remember that article we read maybe
+ 
+
+ align:start position:0%
+you remember that article we read maybe
+a few weeks back
+
+ align:start position:0%
+a few weeks back
+ 
+
+ align:start position:0%
+a few weeks back
+but Sandeep Pai also says that in terms
+
+ align:start position:0%
+but Sandeep Pai also says that in terms
+ 
+
+ align:start position:0%
+but Sandeep Pai also says that in terms
+of Justice implications there's
+
+ align:start position:0%
+of Justice implications there's
+ 
+
+ align:start position:0%
+of Justice implications there's
+obviously a very large literature review
+
+ align:start position:0%
+obviously a very large literature review
+ 
+
+ align:start position:0%
+obviously a very large literature review
+focusing on a large literature looking
+
+ align:start position:0%
+focusing on a large literature looking
+ 
+
+ align:start position:0%
+focusing on a large literature looking
+at why this is going to affect workers
+
+ align:start position:0%
+at why this is going to affect workers
+ 
+
+ align:start position:0%
+at why this is going to affect workers
+and why workers might resist trying to
+
+ align:start position:0%
+and why workers might resist trying to
+ 
+
+ align:start position:0%
+and why workers might resist trying to
+take on an antigen
+
+ align:start position:0%
+take on an antigen
+ 
+
+ align:start position:0%
+take on an antigen
+a similar argument has been made by
+
+ align:start position:0%
+a similar argument has been made by
+ 
+
+ align:start position:0%
+a similar argument has been made by
+motto mildenberger in his book carbon
+
+ align:start position:0%
+motto mildenberger in his book carbon
+ 
+
+ align:start position:0%
+motto mildenberger in his book carbon
+captured he argues that our coalitions
+
+ align:start position:0%
+captured he argues that our coalitions
+ 
+
+ align:start position:0%
+captured he argues that our coalitions
+for climate abton
+
+ align:start position:0%
+for climate abton
+ 
+
+ align:start position:0%
+for climate abton
+are also we have to recognize split that
+
+ align:start position:0%
+are also we have to recognize split that
+ 
+
+ align:start position:0%
+are also we have to recognize split that
+business and labor have influence on the
+
+ align:start position:0%
+business and labor have influence on the
+ 
+
+ align:start position:0%
+business and labor have influence on the
+left and right coalitions for or
+
+ align:start position:0%
+left and right coalitions for or
+ 
+
+ align:start position:0%
+left and right coalitions for or
+opposing climate action so he argues
+
+ align:start position:0%
+opposing climate action so he argues
+ 
+
+ align:start position:0%
+opposing climate action so he argues
+that I'm actually in multiple countries
+
+ align:start position:0%
+that I'm actually in multiple countries
+ 
+
+ align:start position:0%
+that I'm actually in multiple countries
+have been stymied by the fact that even
+
+ align:start position:0%
+have been stymied by the fact that even
+ 
+
+ align:start position:0%
+have been stymied by the fact that even
+businesses or even for coalitions that
+
+ align:start position:0%
+businesses or even for coalitions that
+ 
+
+ align:start position:0%
+businesses or even for coalitions that
+are different planet action business and
+
+ align:start position:0%
+are different planet action business and
+ 
+
+ align:start position:0%
+are different planet action business and
+labor has substantial influence in
+
+ align:start position:0%
+labor has substantial influence in
+ 
+
+ align:start position:0%
+labor has substantial influence in
+stopping or exempting certain industries
+
+ align:start position:0%
+stopping or exempting certain industries
+ 
+
+ align:start position:0%
+stopping or exempting certain industries
+from climate action
+
+ align:start position:0%
+from climate action
+ 
+
+ align:start position:0%
+from climate action
+and so just to give you another sense of
+
+ align:start position:0%
+and so just to give you another sense of
+ 
+
+ align:start position:0%
+and so just to give you another sense of
+how cities are connected to Industrial
+
+ align:start position:0%
+how cities are connected to Industrial
+ 
+
+ align:start position:0%
+how cities are connected to Industrial
+missions quite often in this policy
+
+ align:start position:0%
+missions quite often in this policy
+ 
+
+ align:start position:0%
+missions quite often in this policy
+we've talked about cities that have
+
+ align:start position:0%
+we've talked about cities that have
+ 
+
+ align:start position:0%
+we've talked about cities that have
+relatively High population density and
+
+ align:start position:0%
+relatively High population density and
+ 
+
+ align:start position:0%
+relatively High population density and
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+looking at the population density and
+
+ align:start position:0%
+looking at the population density and
+ 
+
+ align:start position:0%
+looking at the population density and
+population United States this vertical
+
+ align:start position:0%
+population United States this vertical
+ 
+
+ align:start position:0%
+population United States this vertical
+access is the log of population density
+
+ align:start position:0%
+access is the log of population density
+ 
+
+ align:start position:0%
+access is the log of population density
+the horizontal axis is the industrial
+
+ align:start position:0%
+the horizontal axis is the industrial
+ 
+
+ align:start position:0%
+the horizontal axis is the industrial
+greenhouse gas emissions as a percentage
+
+ align:start position:0%
+greenhouse gas emissions as a percentage
+ 
+
+ align:start position:0%
+greenhouse gas emissions as a percentage
+of the total greenhouse gas emissions
+
+ align:start position:0%
+of the total greenhouse gas emissions
+ 
+
+ align:start position:0%
+of the total greenhouse gas emissions
+for the county this is all calculated
+
+ align:start position:0%
+for the county this is all calculated
+ 
+
+ align:start position:0%
+for the county this is all calculated
+from epa's industrial greenhouse gas
+
+ align:start position:0%
+from epa's industrial greenhouse gas
+ 
+
+ align:start position:0%
+from epa's industrial greenhouse gas
+figures you can click on this link and
+
+ align:start position:0%
+figures you can click on this link and
+ 
+
+ align:start position:0%
+figures you can click on this link and
+see the numbers there or calculate them
+
+ align:start position:0%
+see the numbers there or calculate them
+ 
+
+ align:start position:0%
+see the numbers there or calculate them
+for yourself if you want but the point
+
+ align:start position:0%
+for yourself if you want but the point
+ 
+
+ align:start position:0%
+for yourself if you want but the point
+is for cities if you look at the log of
+
+ align:start position:0%
+is for cities if you look at the log of
+ 
+
+ align:start position:0%
+is for cities if you look at the log of
+population density you can see the
+
+ align:start position:0%
+population density you can see the
+ 
+
+ align:start position:0%
+population density you can see the
+United States we have a nice belt curve
+
+ align:start position:0%
+United States we have a nice belt curve
+ 
+
+ align:start position:0%
+United States we have a nice belt curve
+if you put a histogram on the side or a
+
+ align:start position:0%
+if you put a histogram on the side or a
+ 
+
+ align:start position:0%
+if you put a histogram on the side or a
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+the log of population density is
+
+ align:start position:0%
+the log of population density is
+ 
+
+ align:start position:0%
+the log of population density is
+relatively belt or shaped you can see
+
+ align:start position:0%
+relatively belt or shaped you can see
+ 
+
+ align:start position:0%
+relatively belt or shaped you can see
+that means if we take the population
+
+ align:start position:0%
+that means if we take the population
+ 
+
+ align:start position:0%
+that means if we take the population
+density we have a few cities that are
+
+ align:start position:0%
+density we have a few cities that are
+ 
+
+ align:start position:0%
+density we have a few cities that are
+very high population density like New
+
+ align:start position:0%
+very high population density like New
+ 
+
+ align:start position:0%
+very high population density like New
+York and the vast majority of cities are
+
+ align:start position:0%
+York and the vast majority of cities are
+ 
+
+ align:start position:0%
+York and the vast majority of cities are
+lower population density but I take the
+
+ align:start position:0%
+lower population density but I take the
+ 
+
+ align:start position:0%
+lower population density but I take the
+log because it makes the data clear
+
+ align:start position:0%
+log because it makes the data clear
+ 
+
+ align:start position:0%
+log because it makes the data clear
+and so if you consider for example the
+
+ align:start position:0%
+and so if you consider for example the
+ 
+
+ align:start position:0%
+and so if you consider for example the
+highest population density of population
+
+ align:start position:0%
+highest population density of population
+ 
+
+ align:start position:0%
+highest population density of population
+countries in each state Cook County is
+
+ align:start position:0%
+countries in each state Cook County is
+ 
+
+ align:start position:0%
+countries in each state Cook County is
+the seat of Chicago Illinois you can see
+
+ align:start position:0%
+the seat of Chicago Illinois you can see
+ 
+
+ align:start position:0%
+the seat of Chicago Illinois you can see
+it has relatively low industrial gas gas
+
+ align:start position:0%
+it has relatively low industrial gas gas
+ 
+
+ align:start position:0%
+it has relatively low industrial gas gas
+emissions as a percentage of portal for
+
+ align:start position:0%
+emissions as a percentage of portal for
+ 
+
+ align:start position:0%
+emissions as a percentage of portal for
+the other highest population density and
+
+ align:start position:0%
+the other highest population density and
+ 
+
+ align:start position:0%
+the other highest population density and
+population countries in each state
+
+ align:start position:0%
+population countries in each state
+ 
+
+ align:start position:0%
+population countries in each state
+that's true for Maricopa County which is
+
+ align:start position:0%
+that's true for Maricopa County which is
+ 
+
+ align:start position:0%
+that's true for Maricopa County which is
+the home of Phoenix Arizona
+
+ align:start position:0%
+the home of Phoenix Arizona
+ 
+
+ align:start position:0%
+the home of Phoenix Arizona
+Dallas County which is the seat of
+
+ align:start position:0%
+Dallas County which is the seat of
+ 
+
+ align:start position:0%
+Dallas County which is the seat of
+Dallas Texas
+
+ align:start position:0%
+Dallas Texas
+ 
+
+ align:start position:0%
+Dallas Texas
+County Washington Seattle
+
+ align:start position:0%
+County Washington Seattle
+ 
+
+ align:start position:0%
+County Washington Seattle
+has relatively low industrial emissions
+
+ align:start position:0%
+has relatively low industrial emissions
+ 
+
+ align:start position:0%
+has relatively low industrial emissions
+Wayne County is the seat of Detroit
+
+ align:start position:0%
+Wayne County is the seat of Detroit
+ 
+
+ align:start position:0%
+Wayne County is the seat of Detroit
+and New York county is one of the four
+
+ align:start position:0%
+and New York county is one of the four
+ 
+
+ align:start position:0%
+and New York county is one of the four
+very high population counties that
+
+ align:start position:0%
+very high population counties that
+ 
+
+ align:start position:0%
+very high population counties that
+reprise New York and so generally the
+
+ align:start position:0%
+reprise New York and so generally the
+ 
+
+ align:start position:0%
+reprise New York and so generally the
+way we talk about cities as centers of
+
+ align:start position:0%
+way we talk about cities as centers of
+ 
+
+ align:start position:0%
+way we talk about cities as centers of
+consumption if these are the cities that
+
+ align:start position:0%
+consumption if these are the cities that
+ 
+
+ align:start position:0%
+consumption if these are the cities that
+come to mind then yes we have relative
+
+ align:start position:0%
+come to mind then yes we have relative
+ 
+
+ align:start position:0%
+come to mind then yes we have relative
+low industrial emissions associated with
+
+ align:start position:0%
+low industrial emissions associated with
+ 
+
+ align:start position:0%
+low industrial emissions associated with
+cities
+
+ align:start position:0%
+cities
+ 
+
+ align:start position:0%
+cities
+but now let's look at this chart we look
+
+ align:start position:0%
+but now let's look at this chart we look
+ 
+
+ align:start position:0%
+but now let's look at this chart we look
+at this chart we can see that there's
+
+ align:start position:0%
+at this chart we can see that there's
+ 
+
+ align:start position:0%
+at this chart we can see that there's
+all these other cities up here that have
+
+ align:start position:0%
+all these other cities up here that have
+ 
+
+ align:start position:0%
+all these other cities up here that have
+much higher industrial greenhouse gas
+
+ align:start position:0%
+much higher industrial greenhouse gas
+ 
+
+ align:start position:0%
+much higher industrial greenhouse gas
+emissions which cities are those Which
+
+ align:start position:0%
+emissions which cities are those Which
+ 
+
+ align:start position:0%
+emissions which cities are those Which
+counties are those
+
+ align:start position:0%
+counties are those
+ 
+
+ align:start position:0%
+counties are those
+if we looked at the uh Philadelphia also
+
+ align:start position:0%
+if we looked at the uh Philadelphia also
+ 
+
+ align:start position:0%
+if we looked at the uh Philadelphia also
+has relatively low industrial emissions
+
+ align:start position:0%
+has relatively low industrial emissions
+ 
+
+ align:start position:0%
+has relatively low industrial emissions
+as a percentage of this total
+
+ align:start position:0%
+as a percentage of this total
+ 
+
+ align:start position:0%
+as a percentage of this total
+but if we look at the highest population
+
+ align:start position:0%
+but if we look at the highest population
+ 
+
+ align:start position:0%
+but if we look at the highest population
+density and relatively at high
+
+ align:start position:0%
+density and relatively at high
+ 
+
+ align:start position:0%
+density and relatively at high
+industrial admitting counties in each
+
+ align:start position:0%
+industrial admitting counties in each
+ 
+
+ align:start position:0%
+industrial admitting counties in each
+state and we get to a different set of
+
+ align:start position:0%
+state and we get to a different set of
+ 
+
+ align:start position:0%
+state and we get to a different set of
+cities that we don't often talk about in
+
+ align:start position:0%
+cities that we don't often talk about in
+ 
+
+ align:start position:0%
+cities that we don't often talk about in
+urban planning Tulsa Oklahoma Newcastle
+
+ align:start position:0%
+urban planning Tulsa Oklahoma Newcastle
+ 
+
+ align:start position:0%
+urban planning Tulsa Oklahoma Newcastle
+Delaware has you know about a quarter of
+
+ align:start position:0%
+Delaware has you know about a quarter of
+ 
+
+ align:start position:0%
+Delaware has you know about a quarter of
+their emissions are quarter of their
+
+ align:start position:0%
+their emissions are quarter of their
+ 
+
+ align:start position:0%
+their emissions are quarter of their
+greenhouse gas stations are from
+
+ align:start position:0%
+greenhouse gas stations are from
+ 
+
+ align:start position:0%
+greenhouse gas stations are from
+industry
+
+ align:start position:0%
+industry
+ 
+
+ align:start position:0%
+industry
+Denver Colorado has relatively high
+
+ align:start position:0%
+Denver Colorado has relatively high
+ 
+
+ align:start position:0%
+Denver Colorado has relatively high
+balance gas emissions
+
+ align:start position:0%
+balance gas emissions
+ 
+
+ align:start position:0%
+balance gas emissions
+Jefferson County and Alabama has
+
+ align:start position:0%
+Jefferson County and Alabama has
+ 
+
+ align:start position:0%
+Jefferson County and Alabama has
+relatively highly greenhouse gas
+
+ align:start position:0%
+relatively highly greenhouse gas
+ 
+
+ align:start position:0%
+relatively highly greenhouse gas
+stations
+
+ align:start position:0%
+stations
+ 
+
+ align:start position:0%
+stations
+Dallas again shows up in this list and
+
+ align:start position:0%
+Dallas again shows up in this list and
+ 
+
+ align:start position:0%
+Dallas again shows up in this list and
+it's you know about 20 of submissions
+
+ align:start position:0%
+it's you know about 20 of submissions
+ 
+
+ align:start position:0%
+it's you know about 20 of submissions
+are pre-owned gas those 20 it would be
+
+ align:start position:0%
+are pre-owned gas those 20 it would be
+ 
+
+ align:start position:0%
+are pre-owned gas those 20 it would be
+asking applications of its portal so
+
+ align:start position:0%
+asking applications of its portal so
+ 
+
+ align:start position:0%
+asking applications of its portal so
+it's higher than other cities that we
+
+ align:start position:0%
+it's higher than other cities that we
+ 
+
+ align:start position:0%
+it's higher than other cities that we
+looked at
+
+ align:start position:0%
+looked at
+ 
+
+ align:start position:0%
+looked at
+and Cuyahoga County in Ohio the seat of
+
+ align:start position:0%
+and Cuyahoga County in Ohio the seat of
+ 
+
+ align:start position:0%
+and Cuyahoga County in Ohio the seat of
+Cleveland also has surprisingly higher
+
+ align:start position:0%
+Cleveland also has surprisingly higher
+ 
+
+ align:start position:0%
+Cleveland also has surprisingly higher
+but still relatively low green ounce gas
+
+ align:start position:0%
+but still relatively low green ounce gas
+ 
+
+ align:start position:0%
+but still relatively low green ounce gas
+missions
+
+ align:start position:0%
+missions
+ 
+
+ align:start position:0%
+missions
+let's look at some of the cities that
+
+ align:start position:0%
+let's look at some of the cities that
+ 
+
+ align:start position:0%
+let's look at some of the cities that
+had extremely high industrial admissions
+
+ align:start position:0%
+had extremely high industrial admissions
+ 
+
+ align:start position:0%
+had extremely high industrial admissions
+as a percentage of the total what are
+
+ align:start position:0%
+as a percentage of the total what are
+ 
+
+ align:start position:0%
+as a percentage of the total what are
+those cities and counties
+
+ align:start position:0%
+those cities and counties
+ 
+
+ align:start position:0%
+those cities and counties
+if we look at the highest industrial
+
+ align:start position:0%
+if we look at the highest industrial
+ 
+
+ align:start position:0%
+if we look at the highest industrial
+emitting counties with high population
+
+ align:start position:0%
+emitting counties with high population
+ 
+
+ align:start position:0%
+emitting counties with high population
+densities East Baton Rouge Saint John
+
+ align:start position:0%
+densities East Baton Rouge Saint John
+ 
+
+ align:start position:0%
+densities East Baton Rouge Saint John
+the Baptist County uh test you the
+
+ align:start position:0%
+the Baptist County uh test you the
+ 
+
+ align:start position:0%
+the Baptist County uh test you the
+county probably mispronounced that in St
+
+ align:start position:0%
+county probably mispronounced that in St
+ 
+
+ align:start position:0%
+county probably mispronounced that in St
+Charles County and Ascension County are
+
+ align:start position:0%
+Charles County and Ascension County are
+ 
+
+ align:start position:0%
+Charles County and Ascension County are
+all in Louisiana
+
+ align:start position:0%
+all in Louisiana
+ 
+
+ align:start position:0%
+all in Louisiana
+in fact if we go back to Robert
+
+ align:start position:0%
+in fact if we go back to Robert
+ 
+
+ align:start position:0%
+in fact if we go back to Robert
+bullard's the reason why he started
+
+ align:start position:0%
+bullard's the reason why he started
+ 
+
+ align:start position:0%
+bullard's the reason why he started
+studying environmental justice in the
+
+ align:start position:0%
+studying environmental justice in the
+ 
+
+ align:start position:0%
+studying environmental justice in the
+first place you can see that the highest
+
+ align:start position:0%
+first place you can see that the highest
+ 
+
+ align:start position:0%
+first place you can see that the highest
+population density and Industrial
+
+ align:start position:0%
+population density and Industrial
+ 
+
+ align:start position:0%
+population density and Industrial
+admitting counties are all in Louisiana
+
+ align:start position:0%
+admitting counties are all in Louisiana
+ 
+
+ align:start position:0%
+admitting counties are all in Louisiana
+Texas Virginia these are not only places
+
+ align:start position:0%
+Texas Virginia these are not only places
+ 
+
+ align:start position:0%
+Texas Virginia these are not only places
+that are concentrated in a few States
+
+ align:start position:0%
+that are concentrated in a few States
+ 
+
+ align:start position:0%
+that are concentrated in a few States
+remarkably High portions of their
+
+ align:start position:0%
+remarkably High portions of their
+ 
+
+ align:start position:0%
+remarkably High portions of their
+greenhouse gas stations come from
+
+ align:start position:0%
+greenhouse gas stations come from
+ 
+
+ align:start position:0%
+greenhouse gas stations come from
+industry with about 70 percent up to 92
+
+ align:start position:0%
+industry with about 70 percent up to 92
+ 
+
+ align:start position:0%
+industry with about 70 percent up to 92
+percent uh in Covington Virginia they
+
+ align:start position:0%
+percent uh in Covington Virginia they
+ 
+
+ align:start position:0%
+percent uh in Covington Virginia they
+have extremely high populations for
+
+ align:start position:0%
+have extremely high populations for
+ 
+
+ align:start position:0%
+have extremely high populations for
+their area they have very high
+
+ align:start position:0%
+their area they have very high
+ 
+
+ align:start position:0%
+their area they have very high
+population densities but also what I
+
+ align:start position:0%
+population densities but also what I
+ 
+
+ align:start position:0%
+population densities but also what I
+want to emphasize to you is that they
+
+ align:start position:0%
+want to emphasize to you is that they
+ 
+
+ align:start position:0%
+want to emphasize to you is that they
+have extremely high non-white
+
+ align:start position:0%
+have extremely high non-white
+ 
+
+ align:start position:0%
+have extremely high non-white
+populations that in this case not only
+
+ align:start position:0%
+populations that in this case not only
+ 
+
+ align:start position:0%
+populations that in this case not only
+are the people subjects to the
+
+ align:start position:0%
+are the people subjects to the
+ 
+
+ align:start position:0%
+are the people subjects to the
+consequences or the burdens of
+
+ align:start position:0%
+consequences or the burdens of
+ 
+
+ align:start position:0%
+consequences or the burdens of
+industrial missions but these are all
+
+ align:start position:0%
+industrial missions but these are all
+ 
+
+ align:start position:0%
+industrial missions but these are all
+people people who also may work in these
+
+ align:start position:0%
+people people who also may work in these
+ 
+
+ align:start position:0%
+people people who also may work in these
+industries as well so this hopefully
+
+ align:start position:0%
+industries as well so this hopefully
+ 
+
+ align:start position:0%
+industries as well so this hopefully
+brings into
+
+ align:start position:0%
+brings into
+ 
+
+ align:start position:0%
+brings into
+um focused the way that these different
+
+ align:start position:0%
+um focused the way that these different
+ 
+
+ align:start position:0%
+um focused the way that these different
+ideas about livelihood and environmental
+
+ align:start position:0%
+ideas about livelihood and environmental
+ 
+
+ align:start position:0%
+ideas about livelihood and environmental
+burden and climate action can coincide
+
+ align:start position:0%
+burden and climate action can coincide
+ 
+
+ align:start position:0%
+burden and climate action can coincide
+all of these counties are extremely high
+
+ align:start position:0%
+all of these counties are extremely high
+ 
+
+ align:start position:0%
+all of these counties are extremely high
+percentages of non-white population many
+
+ align:start position:0%
+percentages of non-white population many
+ 
+
+ align:start position:0%
+percentages of non-white population many
+cases African-Americans
+
+ align:start position:0%
+cases African-Americans
+ 
+
+ align:start position:0%
+cases African-Americans
+they have high population densities
+
+ align:start position:0%
+they have high population densities
+ 
+
+ align:start position:0%
+they have high population densities
+either essentially highly urbanized
+
+ align:start position:0%
+either essentially highly urbanized
+ 
+
+ align:start position:0%
+either essentially highly urbanized
+areas and they're areas that also have
+
+ align:start position:0%
+areas and they're areas that also have
+ 
+
+ align:start position:0%
+areas and they're areas that also have
+very high industrial missions
+
+ align:start position:0%
+very high industrial missions
+ 
+
+ align:start position:0%
+very high industrial missions
+this is an area in Louisiana known I
+
+ align:start position:0%
+this is an area in Louisiana known I
+ 
+
+ align:start position:0%
+this is an area in Louisiana known I
+guess known uh recently as cancer alley
+
+ align:start position:0%
+guess known uh recently as cancer alley
+ 
+
+ align:start position:0%
+guess known uh recently as cancer alley
+it's a phrase used in this Republica
+
+ align:start position:0%
+it's a phrase used in this Republica
+ 
+
+ align:start position:0%
+it's a phrase used in this Republica
+investigation about welcome to cancer
+
+ align:start position:0%
+investigation about welcome to cancer
+ 
+
+ align:start position:0%
+investigation about welcome to cancer
+alley Where toxic air is about to get
+
+ align:start position:0%
+alley Where toxic air is about to get
+ 
+
+ align:start position:0%
+alley Where toxic air is about to get
+much worse okay the articles about how
+
+ align:start position:0%
+much worse okay the articles about how
+ 
+
+ align:start position:0%
+much worse okay the articles about how
+air quality has improved for decades
+
+ align:start position:0%
+air quality has improved for decades
+ 
+
+ align:start position:0%
+air quality has improved for decades
+across United States but Louisiana's
+
+ align:start position:0%
+across United States but Louisiana's
+ 
+
+ align:start position:0%
+across United States but Louisiana's
+backsliding because their analysis found
+
+ align:start position:0%
+backsliding because their analysis found
+ 
+
+ align:start position:0%
+backsliding because their analysis found
+that many new industrial plants will
+
+ align:start position:0%
+that many new industrial plants will
+ 
+
+ align:start position:0%
+that many new industrial plants will
+increase the concentration of cancer
+
+ align:start position:0%
+increase the concentration of cancer
+ 
+
+ align:start position:0%
+increase the concentration of cancer
+causing chemicals predominantly black
+
+ align:start position:0%
+causing chemicals predominantly black
+ 
+
+ align:start position:0%
+causing chemicals predominantly black
+and poor communities so if we think
+
+ align:start position:0%
+and poor communities so if we think
+ 
+
+ align:start position:0%
+and poor communities so if we think
+about cities industrial missions it's
+
+ align:start position:0%
+about cities industrial missions it's
+ 
+
+ align:start position:0%
+about cities industrial missions it's
+not only cities like New York that are
+
+ align:start position:0%
+not only cities like New York that are
+ 
+
+ align:start position:0%
+not only cities like New York that are
+perhaps centers of consumption but other
+
+ align:start position:0%
+perhaps centers of consumption but other
+ 
+
+ align:start position:0%
+perhaps centers of consumption but other
+cities actually have high percentages of
+
+ align:start position:0%
+cities actually have high percentages of
+ 
+
+ align:start position:0%
+cities actually have high percentages of
+industrial pollution within the city
+
+ align:start position:0%
+industrial pollution within the city
+ 
+
+ align:start position:0%
+industrial pollution within the city
+boundaries or the county boundaries as
+
+ align:start position:0%
+boundaries or the county boundaries as
+ 
+
+ align:start position:0%
+boundaries or the county boundaries as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+if we look at how fossil fuel
+
+ align:start position:0%
+if we look at how fossil fuel
+ 
+
+ align:start position:0%
+if we look at how fossil fuel
+infrastructure is distributed across the
+
+ align:start position:0%
+infrastructure is distributed across the
+ 
+
+ align:start position:0%
+infrastructure is distributed across the
+U.S these are some graphics that my
+
+ align:start position:0%
+U.S these are some graphics that my
+ 
+
+ align:start position:0%
+U.S these are some graphics that my
+student girl alumn and I made a few
+
+ align:start position:0%
+student girl alumn and I made a few
+ 
+
+ align:start position:0%
+student girl alumn and I made a few
+years ago from U.S Energy Information
+
+ align:start position:0%
+years ago from U.S Energy Information
+ 
+
+ align:start position:0%
+years ago from U.S Energy Information
+Administration and homosecurity data you
+
+ align:start position:0%
+Administration and homosecurity data you
+ 
+
+ align:start position:0%
+Administration and homosecurity data you
+can see power plants are relatively
+
+ align:start position:0%
+can see power plants are relatively
+ 
+
+ align:start position:0%
+can see power plants are relatively
+distributed across the U.S this graphic
+
+ align:start position:0%
+distributed across the U.S this graphic
+ 
+
+ align:start position:0%
+distributed across the U.S this graphic
+of coal natural gas and petroleum plants
+
+ align:start position:0%
+of coal natural gas and petroleum plants
+ 
+
+ align:start position:0%
+of coal natural gas and petroleum plants
+effectively follows the population or
+
+ align:start position:0%
+effectively follows the population or
+ 
+
+ align:start position:0%
+effectively follows the population or
+the urban pattern of the United States
+
+ align:start position:0%
+the urban pattern of the United States
+ 
+
+ align:start position:0%
+the urban pattern of the United States
+but you can see that natural gas is
+
+ align:start position:0%
+but you can see that natural gas is
+ 
+
+ align:start position:0%
+but you can see that natural gas is
+probably concentrated in the exact place
+
+ align:start position:0%
+probably concentrated in the exact place
+ 
+
+ align:start position:0%
+probably concentrated in the exact place
+as we've just talked about Texas and
+
+ align:start position:0%
+as we've just talked about Texas and
+ 
+
+ align:start position:0%
+as we've just talked about Texas and
+Louisiana prefer uh Virginia is a
+
+ align:start position:0%
+Louisiana prefer uh Virginia is a
+ 
+
+ align:start position:0%
+Louisiana prefer uh Virginia is a
+different case I think out there look at
+
+ align:start position:0%
+different case I think out there look at
+ 
+
+ align:start position:0%
+different case I think out there look at
+Natural Gas This is highly concentrated
+
+ align:start position:0%
+Natural Gas This is highly concentrated
+ 
+
+ align:start position:0%
+Natural Gas This is highly concentrated
+here partly because of important and
+
+ align:start position:0%
+here partly because of important and
+ 
+
+ align:start position:0%
+here partly because of important and
+Export but also because of petrochemical
+
+ align:start position:0%
+Export but also because of petrochemical
+ 
+
+ align:start position:0%
+Export but also because of petrochemical
+refining and production
+
+ align:start position:0%
+refining and production
+ 
+
+ align:start position:0%
+refining and production
+and if we look at Holy oil and petroleum
+
+ align:start position:0%
+and if we look at Holy oil and petroleum
+ 
+
+ align:start position:0%
+and if we look at Holy oil and petroleum
+we can see our pipelines again run from
+
+ align:start position:0%
+we can see our pipelines again run from
+ 
+
+ align:start position:0%
+we can see our pipelines again run from
+Texas Louisiana pretty much following
+
+ align:start position:0%
+Texas Louisiana pretty much following
+ 
+
+ align:start position:0%
+Texas Louisiana pretty much following
+the urban pattern of the United States
+
+ align:start position:0%
+the urban pattern of the United States
+ 
+
+ align:start position:0%
+the urban pattern of the United States
+we look at cumulative impacts yes we see
+
+ align:start position:0%
+we look at cumulative impacts yes we see
+ 
+
+ align:start position:0%
+we look at cumulative impacts yes we see
+fossil appeal infrastructure
+
+ align:start position:0%
+fossil appeal infrastructure
+ 
+
+ align:start position:0%
+fossil appeal infrastructure
+concentrated across the entire United
+
+ align:start position:0%
+concentrated across the entire United
+ 
+
+ align:start position:0%
+concentrated across the entire United
+States but clearly based on the
+
+ align:start position:0%
+States but clearly based on the
+ 
+
+ align:start position:0%
+States but clearly based on the
+industrial emissions we looked at before
+
+ align:start position:0%
+industrial emissions we looked at before
+ 
+
+ align:start position:0%
+industrial emissions we looked at before
+the industrial emissions are very
+
+ align:start position:0%
+the industrial emissions are very
+ 
+
+ align:start position:0%
+the industrial emissions are very
+differently distributed across urban
+
+ align:start position:0%
+differently distributed across urban
+ 
+
+ align:start position:0%
+differently distributed across urban
+areas and states
+
+ align:start position:0%
+areas and states
+ 
+
+ align:start position:0%
+areas and states
+which brings me to the akman LL 2017
+
+ align:start position:0%
+which brings me to the akman LL 2017
+ 
+
+ align:start position:0%
+which brings me to the akman LL 2017
+paper just to focus on this paper it's
+
+ align:start position:0%
+paper just to focus on this paper it's
+ 
+
+ align:start position:0%
+paper just to focus on this paper it's
+on global climate policies for energy
+
+ align:start position:0%
+on global climate policies for energy
+ 
+
+ align:start position:0%
+on global climate policies for energy
+intensive Industries we're going to go
+
+ align:start position:0%
+intensive Industries we're going to go
+ 
+
+ align:start position:0%
+intensive Industries we're going to go
+through a bunch of acronyms here at the
+
+ align:start position:0%
+through a bunch of acronyms here at the
+ 
+
+ align:start position:0%
+through a bunch of acronyms here at the
+global level we have energy intensive
+
+ align:start position:0%
+global level we have energy intensive
+ 
+
+ align:start position:0%
+global level we have energy intensive
+Industries like steel cement aluminum
+
+ align:start position:0%
+Industries like steel cement aluminum
+ 
+
+ align:start position:0%
+Industries like steel cement aluminum
+fertilizer and Plastics
+
+ align:start position:0%
+fertilizer and Plastics
+ 
+
+ align:start position:0%
+fertilizer and Plastics
+that's e-i-ims ba teams are the best
+
+ align:start position:0%
+that's e-i-ims ba teams are the best
+ 
+
+ align:start position:0%
+that's e-i-ims ba teams are the best
+available Technologies but crucially the
+
+ align:start position:0%
+available Technologies but crucially the
+ 
+
+ align:start position:0%
+available Technologies but crucially the
+paper argues that they only reduce
+
+ align:start position:0%
+paper argues that they only reduce
+ 
+
+ align:start position:0%
+paper argues that they only reduce
+eviction 15 or 30 percent so hopefully
+
+ align:start position:0%
+eviction 15 or 30 percent so hopefully
+ 
+
+ align:start position:0%
+eviction 15 or 30 percent so hopefully
+the five years since this paper is
+
+ align:start position:0%
+the five years since this paper is
+ 
+
+ align:start position:0%
+the five years since this paper is
+written we've come up with more ideas
+
+ align:start position:0%
+written we've come up with more ideas
+ 
+
+ align:start position:0%
+written we've come up with more ideas
+for how to decarbonize industry but at
+
+ align:start position:0%
+for how to decarbonize industry but at
+ 
+
+ align:start position:0%
+for how to decarbonize industry but at
+least the best available Technologies
+
+ align:start position:0%
+least the best available Technologies
+ 
+
+ align:start position:0%
+least the best available Technologies
+five years ago only reduced emissions of
+
+ align:start position:0%
+five years ago only reduced emissions of
+ 
+
+ align:start position:0%
+five years ago only reduced emissions of
+fraction of what we need
+
+ align:start position:0%
+fraction of what we need
+ 
+
+ align:start position:0%
+fraction of what we need
+uh there's a number of other acronyms uh
+
+ align:start position:0%
+uh there's a number of other acronyms uh
+ 
+
+ align:start position:0%
+uh there's a number of other acronyms uh
+quite often about an international
+
+ align:start position:0%
+quite often about an international
+ 
+
+ align:start position:0%
+quite often about an international
+climate negotiations common but
+
+ align:start position:0%
+climate negotiations common but
+ 
+
+ align:start position:0%
+climate negotiations common but
+differentiated responsibilities cbdrs
+
+ align:start position:0%
+differentiated responsibilities cbdrs
+ 
+
+ align:start position:0%
+differentiated responsibilities cbdrs
+Queen development mechanism CBM this is
+
+ align:start position:0%
+Queen development mechanism CBM this is
+ 
+
+ align:start position:0%
+Queen development mechanism CBM this is
+a mechanism intended for rich countries
+
+ align:start position:0%
+a mechanism intended for rich countries
+ 
+
+ align:start position:0%
+a mechanism intended for rich countries
+to help poor countries decarbonize and
+
+ align:start position:0%
+to help poor countries decarbonize and
+ 
+
+ align:start position:0%
+to help poor countries decarbonize and
+meet their indc's their intended
+
+ align:start position:0%
+meet their indc's their intended
+ 
+
+ align:start position:0%
+meet their indc's their intended
+naturally determined contributions this
+
+ align:start position:0%
+naturally determined contributions this
+ 
+
+ align:start position:0%
+naturally determined contributions this
+is what we said in the Paris climate
+
+ align:start position:0%
+is what we said in the Paris climate
+ 
+
+ align:start position:0%
+is what we said in the Paris climate
+agreement every country came said what
+
+ align:start position:0%
+agreement every country came said what
+ 
+
+ align:start position:0%
+agreement every country came said what
+their intended nationally determined
+
+ align:start position:0%
+their intended nationally determined
+ 
+
+ align:start position:0%
+their intended nationally determined
+contribution was or the indc basically
+
+ align:start position:0%
+contribution was or the indc basically
+ 
+
+ align:start position:0%
+contribution was or the indc basically
+every country came and said this is the
+
+ align:start position:0%
+every country came and said this is the
+ 
+
+ align:start position:0%
+every country came and said this is the
+best we can do on climate change
+
+ align:start position:0%
+best we can do on climate change
+ 
+
+ align:start position:0%
+best we can do on climate change
+of course there's a lot of discussion
+
+ align:start position:0%
+of course there's a lot of discussion
+ 
+
+ align:start position:0%
+of course there's a lot of discussion
+now and climate policy about border
+
+ align:start position:0%
+now and climate policy about border
+ 
+
+ align:start position:0%
+now and climate policy about border
+Department adjustments these are the
+
+ align:start position:0%
+Department adjustments these are the
+ 
+
+ align:start position:0%
+Department adjustments these are the
+Border carbon adjustments that rich
+
+ align:start position:0%
+Border carbon adjustments that rich
+ 
+
+ align:start position:0%
+Border carbon adjustments that rich
+countries might use to try to
+
+ align:start position:0%
+countries might use to try to
+ 
+
+ align:start position:0%
+countries might use to try to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to account for the embodied energy that
+
+ align:start position:0%
+to account for the embodied energy that
+ 
+
+ align:start position:0%
+to account for the embodied energy that
+they're importing but also Nest
+
+ align:start position:0%
+they're importing but also Nest
+ 
+
+ align:start position:0%
+they're importing but also Nest
+hopefully not causing additional leakage
+
+ align:start position:0%
+hopefully not causing additional leakage
+ 
+
+ align:start position:0%
+hopefully not causing additional leakage
+of jobs to other countries in other
+
+ align:start position:0%
+of jobs to other countries in other
+ 
+
+ align:start position:0%
+of jobs to other countries in other
+words if other countries seem like they
+
+ align:start position:0%
+words if other countries seem like they
+ 
+
+ align:start position:0%
+words if other countries seem like they
+have low Beyonce gas consumption our
+
+ align:start position:0%
+have low Beyonce gas consumption our
+ 
+
+ align:start position:0%
+have low Beyonce gas consumption our
+emissions Associated consumption and
+
+ align:start position:0%
+emissions Associated consumption and
+ 
+
+ align:start position:0%
+emissions Associated consumption and
+maybe because they're actually exporting
+
+ align:start position:0%
+maybe because they're actually exporting
+ 
+
+ align:start position:0%
+maybe because they're actually exporting
+their goods to rich countries so both
+
+ align:start position:0%
+their goods to rich countries so both
+ 
+
+ align:start position:0%
+their goods to rich countries so both
+rich and poor companies have proposed or
+
+ align:start position:0%
+rich and poor companies have proposed or
+ 
+
+ align:start position:0%
+rich and poor companies have proposed or
+carbon adjustments where we can
+
+ align:start position:0%
+carbon adjustments where we can
+ 
+
+ align:start position:0%
+carbon adjustments where we can
+hopefully account for this at the border
+
+ align:start position:0%
+hopefully account for this at the border
+ 
+
+ align:start position:0%
+hopefully account for this at the border
+when when materials and goods are
+
+ align:start position:0%
+when when materials and goods are
+ 
+
+ align:start position:0%
+when when materials and goods are
+imported
+
+ align:start position:0%
+imported
+ 
+
+ align:start position:0%
+imported
+and finally CCF is something we're going
+
+ align:start position:0%
+and finally CCF is something we're going
+ 
+
+ align:start position:0%
+and finally CCF is something we're going
+to talk about a lot going forward carbon
+
+ align:start position:0%
+to talk about a lot going forward carbon
+ 
+
+ align:start position:0%
+to talk about a lot going forward carbon
+capture and storage often called carbon
+
+ align:start position:0%
+capture and storage often called carbon
+ 
+
+ align:start position:0%
+capture and storage often called carbon
+capture utilization and storage now
+
+ align:start position:0%
+capture utilization and storage now
+ 
+
+ align:start position:0%
+capture utilization and storage now
+just to give you a sense of where
+
+ align:start position:0%
+just to give you a sense of where
+ 
+
+ align:start position:0%
+just to give you a sense of where
+greenhouse gas stations have gone and
+
+ align:start position:0%
+greenhouse gas stations have gone and
+ 
+
+ align:start position:0%
+greenhouse gas stations have gone and
+this is a plot from the Almond paper if
+
+ align:start position:0%
+this is a plot from the Almond paper if
+ 
+
+ align:start position:0%
+this is a plot from the Almond paper if
+the data is normalized in 1990 when the
+
+ align:start position:0%
+the data is normalized in 1990 when the
+ 
+
+ align:start position:0%
+the data is normalized in 1990 when the
+UN started accounting you can see that
+
+ align:start position:0%
+UN started accounting you can see that
+ 
+
+ align:start position:0%
+UN started accounting you can see that
+world emissions have gone up
+
+ align:start position:0%
+world emissions have gone up
+ 
+
+ align:start position:0%
+world emissions have gone up
+admissions in Japan and the EU have gone
+
+ align:start position:0%
+admissions in Japan and the EU have gone
+ 
+
+ align:start position:0%
+admissions in Japan and the EU have gone
+down in the U.S they've stayed
+
+ align:start position:0%
+down in the U.S they've stayed
+ 
+
+ align:start position:0%
+down in the U.S they've stayed
+relatively flat either industrial direct
+
+ align:start position:0%
+relatively flat either industrial direct
+ 
+
+ align:start position:0%
+relatively flat either industrial direct
+greenhouse gas missions but obviously
+
+ align:start position:0%
+greenhouse gas missions but obviously
+ 
+
+ align:start position:0%
+greenhouse gas missions but obviously
+rapidly developing countries like China
+
+ align:start position:0%
+rapidly developing countries like China
+ 
+
+ align:start position:0%
+rapidly developing countries like China
+India and Brazil have rapidly increased
+
+ align:start position:0%
+India and Brazil have rapidly increased
+ 
+
+ align:start position:0%
+India and Brazil have rapidly increased
+their greenhouse gas emissions but we
+
+ align:start position:0%
+their greenhouse gas emissions but we
+ 
+
+ align:start position:0%
+their greenhouse gas emissions but we
+should also recognize that these
+
+ align:start position:0%
+should also recognize that these
+ 
+
+ align:start position:0%
+should also recognize that these
+greenhouse gas stations have increased
+
+ align:start position:0%
+greenhouse gas stations have increased
+ 
+
+ align:start position:0%
+greenhouse gas stations have increased
+in these countries because of their
+
+ align:start position:0%
+in these countries because of their
+ 
+
+ align:start position:0%
+in these countries because of their
+exports to the rich and developed world
+
+ align:start position:0%
+exports to the rich and developed world
+ 
+
+ align:start position:0%
+exports to the rich and developed world
+so this brings up fundamental issues of
+
+ align:start position:0%
+so this brings up fundamental issues of
+ 
+
+ align:start position:0%
+so this brings up fundamental issues of
+efficiency equity and fairness
+
+ align:start position:0%
+efficiency equity and fairness
+ 
+
+ align:start position:0%
+efficiency equity and fairness
+there's a lot of issues that need to be
+
+ align:start position:0%
+there's a lot of issues that need to be
+ 
+
+ align:start position:0%
+there's a lot of issues that need to be
+negotiated within between countries
+
+ align:start position:0%
+negotiated within between countries
+ 
+
+ align:start position:0%
+negotiated within between countries
+around industrial emissions there's the
+
+ align:start position:0%
+around industrial emissions there's the
+ 
+
+ align:start position:0%
+around industrial emissions there's the
+idea of carbon leakage this is where
+
+ align:start position:0%
+idea of carbon leakage this is where
+ 
+
+ align:start position:0%
+idea of carbon leakage this is where
+there will be lots of competitiveness
+
+ align:start position:0%
+there will be lots of competitiveness
+ 
+
+ align:start position:0%
+there will be lots of competitiveness
+and relocation of Industry to other
+
+ align:start position:0%
+and relocation of Industry to other
+ 
+
+ align:start position:0%
+and relocation of Industry to other
+countries
+
+ align:start position:0%
+countries
+ 
+
+ align:start position:0%
+countries
+there's questions about political
+
+ align:start position:0%
+there's questions about political
+ 
+
+ align:start position:0%
+there's questions about political
+stability application infrastructure
+
+ align:start position:0%
+stability application infrastructure
+ 
+
+ align:start position:0%
+stability application infrastructure
+labor legislation and protections access
+
+ align:start position:0%
+labor legislation and protections access
+ 
+
+ align:start position:0%
+labor legislation and protections access
+to markets and feedstock and Industrial
+
+ align:start position:0%
+to markets and feedstock and Industrial
+ 
+
+ align:start position:0%
+to markets and feedstock and Industrial
+policy the reason why we're talking
+
+ align:start position:0%
+policy the reason why we're talking
+ 
+
+ align:start position:0%
+policy the reason why we're talking
+about in this urban planning class is
+
+ align:start position:0%
+about in this urban planning class is
+ 
+
+ align:start position:0%
+about in this urban planning class is
+that we think about all these as issues
+
+ align:start position:0%
+that we think about all these as issues
+ 
+
+ align:start position:0%
+that we think about all these as issues
+to be negotiated within and between
+
+ align:start position:0%
+to be negotiated within and between
+ 
+
+ align:start position:0%
+to be negotiated within and between
+countries be issue for cities how do you
+
+ align:start position:0%
+countries be issue for cities how do you
+ 
+
+ align:start position:0%
+countries be issue for cities how do you
+negotiate these issues the Queens cities
+
+ align:start position:0%
+negotiate these issues the Queens cities
+ 
+
+ align:start position:0%
+negotiate these issues the Queens cities
+and within countries in other words
+
+ align:start position:0%
+and within countries in other words
+ 
+
+ align:start position:0%
+and within countries in other words
+again if we have centers of consumption
+
+ align:start position:0%
+again if we have centers of consumption
+ 
+
+ align:start position:0%
+again if we have centers of consumption
+quite often on the coasts we are drawing
+
+ align:start position:0%
+quite often on the coasts we are drawing
+ 
+
+ align:start position:0%
+quite often on the coasts we are drawing
+on Industrial missions that are in other
+
+ align:start position:0%
+on Industrial missions that are in other
+ 
+
+ align:start position:0%
+on Industrial missions that are in other
+parts of the country or other parts of
+
+ align:start position:0%
+parts of the country or other parts of
+ 
+
+ align:start position:0%
+parts of the country or other parts of
+the world how do we account for this
+
+ align:start position:0%
+the world how do we account for this
+ 
+
+ align:start position:0%
+the world how do we account for this
+consumption what do relatively Rich
+
+ align:start position:0%
+consumption what do relatively Rich
+ 
+
+ align:start position:0%
+consumption what do relatively Rich
+developed areas such as cities in North
+
+ align:start position:0%
+developed areas such as cities in North
+ 
+
+ align:start position:0%
+developed areas such as cities in North
+America have to do to account for their
+
+ align:start position:0%
+America have to do to account for their
+ 
+
+ align:start position:0%
+America have to do to account for their
+missions or how to make up for their
+
+ align:start position:0%
+missions or how to make up for their
+ 
+
+ align:start position:0%
+missions or how to make up for their
+consumption
+
+ align:start position:0%
+consumption
+ 
+
+ align:start position:0%
+consumption
+so this again is a good time to focus on
+
+ align:start position:0%
+so this again is a good time to focus on
+ 
+
+ align:start position:0%
+so this again is a good time to focus on
+how we can scale down to these National
+
+ align:start position:0%
+how we can scale down to these National
+ 
+
+ align:start position:0%
+how we can scale down to these National
+policies and I'll argue to you that a
+
+ align:start position:0%
+policies and I'll argue to you that a
+ 
+
+ align:start position:0%
+policies and I'll argue to you that a
+lot of these policies that exist at the
+
+ align:start position:0%
+lot of these policies that exist at the
+ 
+
+ align:start position:0%
+lot of these policies that exist at the
+national level that are discussed in
+
+ align:start position:0%
+national level that are discussed in
+ 
+
+ align:start position:0%
+national level that are discussed in
+this online paper also have equivalence
+
+ align:start position:0%
+this online paper also have equivalence
+ 
+
+ align:start position:0%
+this online paper also have equivalence
+at the urban scale
+
+ align:start position:0%
+at the urban scale
+ 
+
+ align:start position:0%
+at the urban scale
+for example in the first policy here we
+
+ align:start position:0%
+for example in the first policy here we
+ 
+
+ align:start position:0%
+for example in the first policy here we
+have mitigation policies and measures
+
+ align:start position:0%
+have mitigation policies and measures
+ 
+
+ align:start position:0%
+have mitigation policies and measures
+that have an intended direct effect we
+
+ align:start position:0%
+that have an intended direct effect we
+ 
+
+ align:start position:0%
+that have an intended direct effect we
+have mitigation policies measures with
+
+ align:start position:0%
+have mitigation policies measures with
+ 
+
+ align:start position:0%
+have mitigation policies measures with
+intended long-term effects in the EU we
+
+ align:start position:0%
+intended long-term effects in the EU we
+ 
+
+ align:start position:0%
+intended long-term effects in the EU we
+had a regulated Target for industry
+
+ align:start position:0%
+had a regulated Target for industry
+ 
+
+ align:start position:0%
+had a regulated Target for industry
+together the power sector to reduce gas
+
+ align:start position:0%
+together the power sector to reduce gas
+ 
+
+ align:start position:0%
+together the power sector to reduce gas
+missions provide the emissions creating
+
+ align:start position:0%
+missions provide the emissions creating
+ 
+
+ align:start position:0%
+missions provide the emissions creating
+and scheme we've obviously discussed
+
+ align:start position:0%
+and scheme we've obviously discussed
+ 
+
+ align:start position:0%
+and scheme we've obviously discussed
+possible emissions trading schemes in
+
+ align:start position:0%
+possible emissions trading schemes in
+ 
+
+ align:start position:0%
+possible emissions trading schemes in
+the U.S not only uh does California have
+
+ align:start position:0%
+the U.S not only uh does California have
+ 
+
+ align:start position:0%
+the U.S not only uh does California have
+an emissions trading scheme within
+
+ align:start position:0%
+an emissions trading scheme within
+ 
+
+ align:start position:0%
+an emissions trading scheme within
+California we have the regional
+
+ align:start position:0%
+California we have the regional
+ 
+
+ align:start position:0%
+California we have the regional
+greenhouse gas initiative Reggie on the
+
+ align:start position:0%
+greenhouse gas initiative Reggie on the
+ 
+
+ align:start position:0%
+greenhouse gas initiative Reggie on the
+East Coast trying to create emissions
+
+ align:start position:0%
+East Coast trying to create emissions
+ 
+
+ align:start position:0%
+East Coast trying to create emissions
+within the East Coast or middle States
+
+ align:start position:0%
+within the East Coast or middle States
+ 
+
+ align:start position:0%
+within the East Coast or middle States
+we also had the clean power plan which
+
+ align:start position:0%
+we also had the clean power plan which
+ 
+
+ align:start position:0%
+we also had the clean power plan which
+would allow the power sector in
+
+ align:start position:0%
+would allow the power sector in
+ 
+
+ align:start position:0%
+would allow the power sector in
+different states to meet emissions
+
+ align:start position:0%
+different states to meet emissions
+ 
+
+ align:start position:0%
+different states to meet emissions
+Targets in different ways uh regulations
+
+ align:start position:0%
+Targets in different ways uh regulations
+ 
+
+ align:start position:0%
+Targets in different ways uh regulations
+reducing emissions of industrial gases I
+
+ align:start position:0%
+reducing emissions of industrial gases I
+ 
+
+ align:start position:0%
+reducing emissions of industrial gases I
+think some states have a beasts like
+
+ align:start position:0%
+think some states have a beasts like
+ 
+
+ align:start position:0%
+think some states have a beasts like
+Reggie and California having police
+
+ align:start position:0%
+Reggie and California having police
+ 
+
+ align:start position:0%
+Reggie and California having police
+regulations defined to reduce depictions
+
+ align:start position:0%
+regulations defined to reduce depictions
+ 
+
+ align:start position:0%
+regulations defined to reduce depictions
+of inductible gases and there's Energy
+
+ align:start position:0%
+of inductible gases and there's Energy
+ 
+
+ align:start position:0%
+of inductible gases and there's Energy
+Efficiency directives that can be
+
+ align:start position:0%
+Efficiency directives that can be
+ 
+
+ align:start position:0%
+Efficiency directives that can be
+applied differently at the city and
+
+ align:start position:0%
+applied differently at the city and
+ 
+
+ align:start position:0%
+applied differently at the city and
+state level
+
+ align:start position:0%
+state level
+ 
+
+ align:start position:0%
+state level
+we also have in our most recent
+
+ align:start position:0%
+we also have in our most recent
+ 
+
+ align:start position:0%
+we also have in our most recent
+legislation the inflation reduction act
+
+ align:start position:0%
+legislation the inflation reduction act
+ 
+
+ align:start position:0%
+legislation the inflation reduction act
+we have funding for demonstration of
+
+ align:start position:0%
+we have funding for demonstration of
+ 
+
+ align:start position:0%
+we have funding for demonstration of
+carbon capture and storage and bioenergy
+
+ align:start position:0%
+carbon capture and storage and bioenergy
+ 
+
+ align:start position:0%
+carbon capture and storage and bioenergy
+for occur
+
+ align:start position:0%
+for occur
+ 
+
+ align:start position:0%
+for occur
+Japan has implementation of voluntary
+
+ align:start position:0%
+Japan has implementation of voluntary
+ 
+
+ align:start position:0%
+Japan has implementation of voluntary
+action plans by Industries promoting
+
+ align:start position:0%
+action plans by Industries promoting
+ 
+
+ align:start position:0%
+action plans by Industries promoting
+Energy Efficiency obviously in the last
+
+ align:start position:0%
+Energy Efficiency obviously in the last
+ 
+
+ align:start position:0%
+Energy Efficiency obviously in the last
+few passes we've talked about how cities
+
+ align:start position:0%
+few passes we've talked about how cities
+ 
+
+ align:start position:0%
+few passes we've talked about how cities
+have implemented different Energy
+
+ align:start position:0%
+have implemented different Energy
+ 
+
+ align:start position:0%
+have implemented different Energy
+Efficiency programs we also have
+
+ align:start position:0%
+Efficiency programs we also have
+ 
+
+ align:start position:0%
+Efficiency programs we also have
+subsidies for increasing the adoption of
+
+ align:start position:0%
+subsidies for increasing the adoption of
+ 
+
+ align:start position:0%
+subsidies for increasing the adoption of
+best available Technologies we have a
+
+ align:start position:0%
+best available Technologies we have a
+ 
+
+ align:start position:0%
+best available Technologies we have a
+low carbon technology roadmap relative
+
+ align:start position:0%
+low carbon technology roadmap relative
+ 
+
+ align:start position:0%
+low carbon technology roadmap relative
+to steel
+
+ align:start position:0%
+to steel
+ 
+
+ align:start position:0%
+to steel
+I think we have that in our new
+
+ align:start position:0%
+I think we have that in our new
+ 
+
+ align:start position:0%
+I think we have that in our new
+inflation reduction acts legislation we
+
+ align:start position:0%
+inflation reduction acts legislation we
+ 
+
+ align:start position:0%
+inflation reduction acts legislation we
+definitely have road maps for low carbon
+
+ align:start position:0%
+definitely have road maps for low carbon
+ 
+
+ align:start position:0%
+definitely have road maps for low carbon
+production of industrial production
+
+ align:start position:0%
+production of industrial production
+ 
+
+ align:start position:0%
+production of industrial production
+and finally the energy star program for
+
+ align:start position:0%
+and finally the energy star program for
+ 
+
+ align:start position:0%
+and finally the energy star program for
+industry for adopting energy efficient
+
+ align:start position:0%
+industry for adopting energy efficient
+ 
+
+ align:start position:0%
+industry for adopting energy efficient
+Technologies this is really a U.S level
+
+ align:start position:0%
+Technologies this is really a U.S level
+ 
+
+ align:start position:0%
+Technologies this is really a U.S level
+policy but as I spoke to you about
+
+ align:start position:0%
+policy but as I spoke to you about
+ 
+
+ align:start position:0%
+policy but as I spoke to you about
+benchmarking benchmarking is essentially
+
+ align:start position:0%
+benchmarking benchmarking is essentially
+ 
+
+ align:start position:0%
+benchmarking benchmarking is essentially
+built on energy star we have bench
+
+ align:start position:0%
+built on energy star we have bench
+ 
+
+ align:start position:0%
+built on energy star we have bench
+marketing programs to encourage adopting
+
+ align:start position:0%
+marketing programs to encourage adopting
+ 
+
+ align:start position:0%
+marketing programs to encourage adopting
+Energy Technologies and buildings and so
+
+ align:start position:0%
+Energy Technologies and buildings and so
+ 
+
+ align:start position:0%
+Energy Technologies and buildings and so
+on now what the interesting part for
+
+ align:start position:0%
+on now what the interesting part for
+ 
+
+ align:start position:0%
+on now what the interesting part for
+cities and Industrial missions is the
+
+ align:start position:0%
+cities and Industrial missions is the
+ 
+
+ align:start position:0%
+cities and Industrial missions is the
+policy that exists in developing
+
+ align:start position:0%
+policy that exists in developing
+ 
+
+ align:start position:0%
+policy that exists in developing
+countries and arguably could be applied
+
+ align:start position:0%
+countries and arguably could be applied
+ 
+
+ align:start position:0%
+countries and arguably could be applied
+to cities that are producing a lot of
+
+ align:start position:0%
+to cities that are producing a lot of
+ 
+
+ align:start position:0%
+to cities that are producing a lot of
+inductions like we talked about
+
+ align:start position:0%
+inductions like we talked about
+ 
+
+ align:start position:0%
+inductions like we talked about
+Louisiana Texas and Virginia and other
+
+ align:start position:0%
+Louisiana Texas and Virginia and other
+ 
+
+ align:start position:0%
+Louisiana Texas and Virginia and other
+parts of the country
+
+ align:start position:0%
+parts of the country
+ 
+
+ align:start position:0%
+parts of the country
+we have major programs the Energy
+
+ align:start position:0%
+we have major programs the Energy
+ 
+
+ align:start position:0%
+we have major programs the Energy
+Efficiency in industry in China we have
+
+ align:start position:0%
+Efficiency in industry in China we have
+ 
+
+ align:start position:0%
+Efficiency in industry in China we have
+mandated phase out of outdated backward
+
+ align:start position:0%
+mandated phase out of outdated backward
+ 
+
+ align:start position:0%
+mandated phase out of outdated backward
+Industries we have pricing policies that
+
+ align:start position:0%
+Industries we have pricing policies that
+ 
+
+ align:start position:0%
+Industries we have pricing policies that
+favor Energy Efficiency and we have a
+
+ align:start position:0%
+favor Energy Efficiency and we have a
+ 
+
+ align:start position:0%
+favor Energy Efficiency and we have a
+major clean development mechanisms to
+
+ align:start position:0%
+major clean development mechanisms to
+ 
+
+ align:start position:0%
+major clean development mechanisms to
+help China basically phase out non-co2
+
+ align:start position:0%
+help China basically phase out non-co2
+ 
+
+ align:start position:0%
+help China basically phase out non-co2
+gases
+
+ align:start position:0%
+gases
+ 
+
+ align:start position:0%
+gases
+we have other schemes in India and
+
+ align:start position:0%
+we have other schemes in India and
+ 
+
+ align:start position:0%
+we have other schemes in India and
+Brazil like such as sectoral plans for
+
+ align:start position:0%
+Brazil like such as sectoral plans for
+ 
+
+ align:start position:0%
+Brazil like such as sectoral plans for
+industry including energy conservation
+
+ align:start position:0%
+industry including energy conservation
+ 
+
+ align:start position:0%
+industry including energy conservation
+programs these are all things that can
+
+ align:start position:0%
+programs these are all things that can
+ 
+
+ align:start position:0%
+programs these are all things that can
+and are being applied to Industrial
+
+ align:start position:0%
+and are being applied to Industrial
+ 
+
+ align:start position:0%
+and are being applied to Industrial
+missions in cities that have more higher
+
+ align:start position:0%
+missions in cities that have more higher
+ 
+
+ align:start position:0%
+missions in cities that have more higher
+industrial missions
+
+ align:start position:0%
+industrial missions
+ 
+
+ align:start position:0%
+industrial missions
+this brings me to the wristman paper uh
+
+ align:start position:0%
+this brings me to the wristman paper uh
+ 
+
+ align:start position:0%
+this brings me to the wristman paper uh
+the Smith paper with many co-authors
+
+ align:start position:0%
+the Smith paper with many co-authors
+ 
+
+ align:start position:0%
+the Smith paper with many co-authors
+we're going to use this at the basis
+
+ align:start position:0%
+we're going to use this at the basis
+ 
+
+ align:start position:0%
+we're going to use this at the basis
+part of discussion on class in class and
+
+ align:start position:0%
+part of discussion on class in class and
+ 
+
+ align:start position:0%
+part of discussion on class in class and
+what I want to emphasize to you just
+
+ align:start position:0%
+what I want to emphasize to you just
+ 
+
+ align:start position:0%
+what I want to emphasize to you just
+that maybe a few points in the paper
+
+ align:start position:0%
+that maybe a few points in the paper
+ 
+
+ align:start position:0%
+that maybe a few points in the paper
+before we go into the discussion
+
+ align:start position:0%
+before we go into the discussion
+ 
+
+ align:start position:0%
+before we go into the discussion
+together I visited a figure showing
+
+ align:start position:0%
+together I visited a figure showing
+ 
+
+ align:start position:0%
+together I visited a figure showing
+emissions by sector the left-hand side
+
+ align:start position:0%
+emissions by sector the left-hand side
+ 
+
+ align:start position:0%
+emissions by sector the left-hand side
+has the kind of groupings by sector
+
+ align:start position:0%
+has the kind of groupings by sector
+ 
+
+ align:start position:0%
+has the kind of groupings by sector
+including let's say for buildings
+
+ align:start position:0%
+including let's say for buildings
+ 
+
+ align:start position:0%
+including let's say for buildings
+indirect and direct energy related
+
+ align:start position:0%
+indirect and direct energy related
+ 
+
+ align:start position:0%
+indirect and direct energy related
+emissions is 24 of the heat and
+
+ align:start position:0%
+emissions is 24 of the heat and
+ 
+
+ align:start position:0%
+emissions is 24 of the heat and
+electricity emissions this aggregated if
+
+ align:start position:0%
+electricity emissions this aggregated if
+ 
+
+ align:start position:0%
+electricity emissions this aggregated if
+we group eat electricity and heat
+
+ align:start position:0%
+we group eat electricity and heat
+ 
+
+ align:start position:0%
+we group eat electricity and heat
+emissions together buildings only seem
+
+ align:start position:0%
+emissions together buildings only seem
+ 
+
+ align:start position:0%
+emissions together buildings only seem
+to be about eight percent but this is a
+
+ align:start position:0%
+to be about eight percent but this is a
+ 
+
+ align:start position:0%
+to be about eight percent but this is a
+considerable Divergence from where we
+
+ align:start position:0%
+considerable Divergence from where we
+ 
+
+ align:start position:0%
+considerable Divergence from where we
+started the lecture from in other words
+
+ align:start position:0%
+started the lecture from in other words
+ 
+
+ align:start position:0%
+started the lecture from in other words
+buildings consume a very large portion
+
+ align:start position:0%
+buildings consume a very large portion
+ 
+
+ align:start position:0%
+buildings consume a very large portion
+of energy in this disaggregated view of
+
+ align:start position:0%
+of energy in this disaggregated view of
+ 
+
+ align:start position:0%
+of energy in this disaggregated view of
+both heat and electricity emissions if
+
+ align:start position:0%
+both heat and electricity emissions if
+ 
+
+ align:start position:0%
+both heat and electricity emissions if
+we group it together then we kind of
+
+ align:start position:0%
+we group it together then we kind of
+ 
+
+ align:start position:0%
+we group it together then we kind of
+hide some of the building emissions in
+
+ align:start position:0%
+hide some of the building emissions in
+ 
+
+ align:start position:0%
+hide some of the building emissions in
+the power sector
+
+ align:start position:0%
+the power sector
+ 
+
+ align:start position:0%
+the power sector
+but if we look specifically at how much
+
+ align:start position:0%
+but if we look specifically at how much
+ 
+
+ align:start position:0%
+but if we look specifically at how much
+energy or how much emissions are
+
+ align:start position:0%
+energy or how much emissions are
+ 
+
+ align:start position:0%
+energy or how much emissions are
+associated with different sectors by
+
+ align:start position:0%
+associated with different sectors by
+ 
+
+ align:start position:0%
+associated with different sectors by
+industry you can see the number uh two
+
+ align:start position:0%
+industry you can see the number uh two
+ 
+
+ align:start position:0%
+industry you can see the number uh two
+or three are iron steel chemicals and
+
+ align:start position:0%
+or three are iron steel chemicals and
+ 
+
+ align:start position:0%
+or three are iron steel chemicals and
+Plastics and cement aluminum refining
+
+ align:start position:0%
+Plastics and cement aluminum refining
+ 
+
+ align:start position:0%
+Plastics and cement aluminum refining
+Machinery open paper all of these
+
+ align:start position:0%
+Machinery open paper all of these
+ 
+
+ align:start position:0%
+Machinery open paper all of these
+various manufacturing or production
+
+ align:start position:0%
+various manufacturing or production
+ 
+
+ align:start position:0%
+various manufacturing or production
+activities result in High Ground stats
+
+ align:start position:0%
+activities result in High Ground stats
+ 
+
+ align:start position:0%
+activities result in High Ground stats
+emissions these are a significant
+
+ align:start position:0%
+emissions these are a significant
+ 
+
+ align:start position:0%
+emissions these are a significant
+fraction of the world's freonounced gas
+
+ align:start position:0%
+fraction of the world's freonounced gas
+ 
+
+ align:start position:0%
+fraction of the world's freonounced gas
+emissions we've been talking about
+
+ align:start position:0%
+emissions we've been talking about
+ 
+
+ align:start position:0%
+emissions we've been talking about
+so we'll talk about in our class
+
+ align:start position:0%
+so we'll talk about in our class
+ 
+
+ align:start position:0%
+so we'll talk about in our class
+discussion are various policies
+
+ align:start position:0%
+discussion are various policies
+ 
+
+ align:start position:0%
+discussion are various policies
+interventions on the supply side some of
+
+ align:start position:0%
+interventions on the supply side some of
+ 
+
+ align:start position:0%
+interventions on the supply side some of
+the ones that students were interested
+
+ align:start position:0%
+the ones that students were interested
+ 
+
+ align:start position:0%
+the ones that students were interested
+last year were carbon capture
+
+ align:start position:0%
+last year were carbon capture
+ 
+
+ align:start position:0%
+last year were carbon capture
+utilization storage low carbon
+
+ align:start position:0%
+utilization storage low carbon
+ 
+
+ align:start position:0%
+utilization storage low carbon
+development for developing countries how
+
+ align:start position:0%
+development for developing countries how
+ 
+
+ align:start position:0%
+development for developing countries how
+could we apply that to cities worker
+
+ align:start position:0%
+could we apply that to cities worker
+ 
+
+ align:start position:0%
+could we apply that to cities worker
+retraining programs firms influencing
+
+ align:start position:0%
+retraining programs firms influencing
+ 
+
+ align:start position:0%
+retraining programs firms influencing
+government decisions low carbon steel
+
+ align:start position:0%
+government decisions low carbon steel
+ 
+
+ align:start position:0%
+government decisions low carbon steel
+production electrolysis renewable energy
+
+ align:start position:0%
+production electrolysis renewable energy
+ 
+
+ align:start position:0%
+production electrolysis renewable energy
+production electrication hydrogen
+
+ align:start position:0%
+production electrication hydrogen
+ 
+
+ align:start position:0%
+production electrication hydrogen
+production use on the demand side
+
+ align:start position:0%
+production use on the demand side
+ 
+
+ align:start position:0%
+production use on the demand side
+students discuss last year material
+
+ align:start position:0%
+students discuss last year material
+ 
+
+ align:start position:0%
+students discuss last year material
+substitution material efficiency reduce
+
+ align:start position:0%
+substitution material efficiency reduce
+ 
+
+ align:start position:0%
+substitution material efficiency reduce
+material use pairing of public goods
+
+ align:start position:0%
+material use pairing of public goods
+ 
+
+ align:start position:0%
+material use pairing of public goods
+efficiency standards the circular
+
+ align:start position:0%
+efficiency standards the circular
+ 
+
+ align:start position:0%
+efficiency standards the circular
+economy the data transparency and of
+
+ align:start position:0%
+economy the data transparency and of
+ 
+
+ align:start position:0%
+economy the data transparency and of
+course building codes
+
+ align:start position:0%
+course building codes
+ 
+
+ align:start position:0%
+course building codes
+thank you very much I look forward to
+
+ align:start position:0%
+thank you very much I look forward to
+ 
+
+ align:start position:0%
+thank you very much I look forward to
+our discussion and class in person
\ No newline at end of file
diff --git a/aSk7YbhON_0.txt b/aSk7YbhON_0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a8210dea7bb30bb98d4864fd68ef889607d8c661
--- /dev/null
+++ b/aSk7YbhON_0.txt
@@ -0,0 +1,1251 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about students at MIT so some of you are
+
+ align:start position:0%
+about students at MIT so some of you are
+ 
+
+ align:start position:0%
+about students at MIT so some of you are
+graduating soon and this may be your
+
+ align:start position:0%
+graduating soon and this may be your
+ 
+
+ align:start position:0%
+graduating soon and this may be your
+last chance to ask so well what you do
+
+ align:start position:0%
+last chance to ask so well what you do
+ 
+
+ align:start position:0%
+last chance to ask so well what you do
+that's on you speak up and we have a lot
+
+ align:start position:0%
+that's on you speak up and we have a lot
+ 
+
+ align:start position:0%
+that's on you speak up and we have a lot
+of freedom if we use it in fact a lot
+
+ align:start position:0%
+of freedom if we use it in fact a lot
+ 
+
+ align:start position:0%
+of freedom if we use it in fact a lot
+more than in the past
+
+ align:start position:0%
+more than in the past
+ 
+
+ align:start position:0%
+more than in the past
+so safer take the last thing I mentioned
+
+ align:start position:0%
+so safer take the last thing I mentioned
+ 
+
+ align:start position:0%
+so safer take the last thing I mentioned
+for women of the opportunities to speak
+
+ align:start position:0%
+for women of the opportunities to speak
+ 
+
+ align:start position:0%
+for women of the opportunities to speak
+up and become active and have an impact
+
+ align:start position:0%
+up and become active and have an impact
+ 
+
+ align:start position:0%
+up and become active and have an impact
+is way beyond what it was say fifty
+
+ align:start position:0%
+is way beyond what it was say fifty
+ 
+
+ align:start position:0%
+is way beyond what it was say fifty
+years ago in fact it's talking to me all
+
+ align:start position:0%
+years ago in fact it's talking to me all
+ 
+
+ align:start position:0%
+years ago in fact it's talking to me all
+about this before when every I got a ton
+
+ align:start position:0%
+about this before when every I got a ton
+ 
+
+ align:start position:0%
+about this before when every I got a ton
+of email and a lot of it is from young
+
+ align:start position:0%
+of email and a lot of it is from young
+ 
+
+ align:start position:0%
+of email and a lot of it is from young
+people and one question that keeps
+
+ align:start position:0%
+people and one question that keeps
+ 
+
+ align:start position:0%
+people and one question that keeps
+coming up over and over again is you
+
+ align:start position:0%
+coming up over and over again is you
+ 
+
+ align:start position:0%
+coming up over and over again is you
+know everything's awful what can we do
+
+ align:start position:0%
+know everything's awful what can we do
+ 
+
+ align:start position:0%
+know everything's awful what can we do
+but if you look closely over many years
+
+ align:start position:0%
+but if you look closely over many years
+ 
+
+ align:start position:0%
+but if you look closely over many years
+I've noticed that the kinds of questions
+
+ align:start position:0%
+I've noticed that the kinds of questions
+ 
+
+ align:start position:0%
+I've noticed that the kinds of questions
+you get depend on where the people are
+
+ align:start position:0%
+you get depend on where the people are
+ 
+
+ align:start position:0%
+you get depend on where the people are
+coming from so if people are coming from
+
+ align:start position:0%
+coming from so if people are coming from
+ 
+
+ align:start position:0%
+coming from so if people are coming from
+say when I go down to give talks and the
+
+ align:start position:0%
+say when I go down to give talks and the
+ 
+
+ align:start position:0%
+say when I go down to give talks and the
+immigrants lumps in south los and nobody
+
+ align:start position:0%
+immigrants lumps in south los and nobody
+ 
+
+ align:start position:0%
+immigrants lumps in south los and nobody
+ever asks what they can do they tell me
+
+ align:start position:0%
+ever asks what they can do they tell me
+ 
+
+ align:start position:0%
+ever asks what they can do they tell me
+what they're doing
+
+ align:start position:0%
+what they're doing
+ 
+
+ align:start position:0%
+what they're doing
+I go to remote village in southern
+
+ align:start position:0%
+I go to remote village in southern
+ 
+
+ align:start position:0%
+I go to remote village in southern
+Colombia where people are being murdered
+
+ align:start position:0%
+Colombia where people are being murdered
+ 
+
+ align:start position:0%
+Colombia where people are being murdered
+by paramilitaries and there's a chemical
+
+ align:start position:0%
+by paramilitaries and there's a chemical
+ 
+
+ align:start position:0%
+by paramilitaries and there's a chemical
+company trying to the gold mining
+
+ align:start position:0%
+company trying to the gold mining
+ 
+
+ align:start position:0%
+company trying to the gold mining
+company trying to destroy their water
+
+ align:start position:0%
+company trying to destroy their water
+ 
+
+ align:start position:0%
+company trying to destroy their water
+supply they don't ask me what it what
+
+ align:start position:0%
+supply they don't ask me what it what
+ 
+
+ align:start position:0%
+supply they don't ask me what it what
+should they do they tell me what they're
+
+ align:start position:0%
+should they do they tell me what they're
+ 
+
+ align:start position:0%
+should they do they tell me what they're
+doing when people are privileged and
+
+ align:start position:0%
+doing when people are privileged and
+ 
+
+ align:start position:0%
+doing when people are privileged and
+have every opportunity in front of them
+
+ align:start position:0%
+have every opportunity in front of them
+ 
+
+ align:start position:0%
+have every opportunity in front of them
+they asked what what can we do and the
+
+ align:start position:0%
+they asked what what can we do and the
+ 
+
+ align:start position:0%
+they asked what what can we do and the
+fact is almost anything there's all
+
+ align:start position:0%
+fact is almost anything there's all
+ 
+
+ align:start position:0%
+fact is almost anything there's all
+sorts of opportunities of way more than
+
+ align:start position:0%
+sorts of opportunities of way more than
+ 
+
+ align:start position:0%
+sorts of opportunities of way more than
+there were in the past because we do
+
+ align:start position:0%
+there were in the past because we do
+ 
+
+ align:start position:0%
+there were in the past because we do
+enjoy the legacy of people who have
+
+ align:start position:0%
+enjoy the legacy of people who have
+ 
+
+ align:start position:0%
+enjoy the legacy of people who have
+struggled in the past under much harsher
+
+ align:start position:0%
+struggled in the past under much harsher
+ 
+
+ align:start position:0%
+struggled in the past under much harsher
+conditions and have provided us with the
+
+ align:start position:0%
+conditions and have provided us with the
+ 
+
+ align:start position:0%
+conditions and have provided us with the
+opportunities we now have like say the
+
+ align:start position:0%
+opportunities we now have like say the
+ 
+
+ align:start position:0%
+opportunities we now have like say the
+opportunity is to be a student at MIT
+
+ align:start position:0%
+opportunity is to be a student at MIT
+ 
+
+ align:start position:0%
+opportunity is to be a student at MIT
+that's an opportunity gives you all
+
+ align:start position:0%
+that's an opportunity gives you all
+ 
+
+ align:start position:0%
+that's an opportunity gives you all
+sorts of things it was close to half the
+
+ align:start position:0%
+sorts of things it was close to half the
+ 
+
+ align:start position:0%
+sorts of things it was close to half the
+population fifty years ago it was closed
+
+ align:start position:0%
+population fifty years ago it was closed
+ 
+
+ align:start position:0%
+population fifty years ago it was closed
+of course to minorities almost entirely
+
+ align:start position:0%
+of course to minorities almost entirely
+ 
+
+ align:start position:0%
+of course to minorities almost entirely
+and well that's that's just illustrates
+
+ align:start position:0%
+and well that's that's just illustrates
+ 
+
+ align:start position:0%
+and well that's that's just illustrates
+what's going on all over the society so
+
+ align:start position:0%
+what's going on all over the society so
+ 
+
+ align:start position:0%
+what's going on all over the society so
+this I mean that takes a the thing the
+
+ align:start position:0%
+this I mean that takes a the thing the
+ 
+
+ align:start position:0%
+this I mean that takes a the thing the
+Sanders campaign reason which I think
+
+ align:start position:0%
+Sanders campaign reason which I think
+ 
+
+ align:start position:0%
+Sanders campaign reason which I think
+was the most important aspect of the
+
+ align:start position:0%
+was the most important aspect of the
+ 
+
+ align:start position:0%
+was the most important aspect of the
+2016 election by far out of that there
+
+ align:start position:0%
+2016 election by far out of that there
+ 
+
+ align:start position:0%
+2016 election by far out of that there
+are groups developing that are really
+
+ align:start position:0%
+are groups developing that are really
+ 
+
+ align:start position:0%
+are groups developing that are really
+trying to do things to be part of them
+
+ align:start position:0%
+trying to do things to be part of them
+ 
+
+ align:start position:0%
+trying to do things to be part of them
+make new ones
+
+ align:start position:0%
+make new ones
+ 
+
+ align:start position:0%
+make new ones
+there's any kind of other all sorts of
+
+ align:start position:0%
+there's any kind of other all sorts of
+ 
+
+ align:start position:0%
+there's any kind of other all sorts of
+opportunities and I think the prospects
+
+ align:start position:0%
+opportunities and I think the prospects
+ 
+
+ align:start position:0%
+opportunities and I think the prospects
+for the future are not too bad when you
+
+ align:start position:0%
+for the future are not too bad when you
+ 
+
+ align:start position:0%
+for the future are not too bad when you
+think of people's attitude actual
+
+ align:start position:0%
+think of people's attitude actual
+ 
+
+ align:start position:0%
+think of people's attitude actual
+attitudes and the way those attitudes
+
+ align:start position:0%
+attitudes and the way those attitudes
+ 
+
+ align:start position:0%
+attitudes and the way those attitudes
+can be melded into activists and
+
+ align:start position:0%
+can be melded into activists and
+ 
+
+ align:start position:0%
+can be melded into activists and
+political and other programs to bring
+
+ align:start position:0%
+political and other programs to bring
+ 
+
+ align:start position:0%
+political and other programs to bring
+about changes in the society I don't
+
+ align:start position:0%
+about changes in the society I don't
+ 
+
+ align:start position:0%
+about changes in the society I don't
+think there's a real shortage of
+
+ align:start position:0%
+think there's a real shortage of
+ 
+
+ align:start position:0%
+think there's a real shortage of
+opportunity that there's a you know
+
+ align:start position:0%
+opportunity that there's a you know
+ 
+
+ align:start position:0%
+opportunity that there's a you know
+there's a kind of it there all sorts of
+
+ align:start position:0%
+there's a kind of it there all sorts of
+ 
+
+ align:start position:0%
+there's a kind of it there all sorts of
+efforts to atomize people keep you alone
+
+ align:start position:0%
+efforts to atomize people keep you alone
+ 
+
+ align:start position:0%
+efforts to atomize people keep you alone
+that's one of the functions of social
+
+ align:start position:0%
+that's one of the functions of social
+ 
+
+ align:start position:0%
+that's one of the functions of social
+media incidentally you sit alone with
+
+ align:start position:0%
+media incidentally you sit alone with
+ 
+
+ align:start position:0%
+media incidentally you sit alone with
+your you know your whatever it is device
+
+ align:start position:0%
+your you know your whatever it is device
+ 
+
+ align:start position:0%
+your you know your whatever it is device
+you know and you think you have friends
+
+ align:start position:0%
+you know and you think you have friends
+ 
+
+ align:start position:0%
+you know and you think you have friends
+and Indonesian but you're really
+
+ align:start position:0%
+and Indonesian but you're really
+ 
+
+ align:start position:0%
+and Indonesian but you're really
+separated from the people around you
+
+ align:start position:0%
+separated from the people around you
+ 
+
+ align:start position:0%
+separated from the people around you
+that has a atomization is a very
+
+ align:start position:0%
+that has a atomization is a very
+ 
+
+ align:start position:0%
+that has a atomization is a very
+important way of controlling people but
+
+ align:start position:0%
+important way of controlling people but
+ 
+
+ align:start position:0%
+important way of controlling people but
+you can only do things if you work
+
+ align:start position:0%
+you can only do things if you work
+ 
+
+ align:start position:0%
+you can only do things if you work
+together so when you're all separated
+
+ align:start position:0%
+together so when you're all separated
+ 
+
+ align:start position:0%
+together so when you're all separated
+that's great then those who really run
+
+ align:start position:0%
+that's great then those who really run
+ 
+
+ align:start position:0%
+that's great then those who really run
+things they do get together they don't
+
+ align:start position:0%
+things they do get together they don't
+ 
+
+ align:start position:0%
+things they do get together they don't
+sit around looking at iPads so you can
+
+ align:start position:0%
+sit around looking at iPads so you can
+ 
+
+ align:start position:0%
+sit around looking at iPads so you can
+keep the population in fact that's what
+
+ align:start position:0%
+keep the population in fact that's what
+ 
+
+ align:start position:0%
+keep the population in fact that's what
+one of the main things consumerism is
+
+ align:start position:0%
+one of the main things consumerism is
+ 
+
+ align:start position:0%
+one of the main things consumerism is
+about you take a look at the history the
+
+ align:start position:0%
+about you take a look at the history the
+ 
+
+ align:start position:0%
+about you take a look at the history the
+advertising industry it's quite
+
+ align:start position:0%
+advertising industry it's quite
+ 
+
+ align:start position:0%
+advertising industry it's quite
+interesting the huge advertising public
+
+ align:start position:0%
+interesting the huge advertising public
+ 
+
+ align:start position:0%
+interesting the huge advertising public
+relations industry developed in the
+
+ align:start position:0%
+relations industry developed in the
+ 
+
+ align:start position:0%
+relations industry developed in the
+freest countries in the world in Britain
+
+ align:start position:0%
+freest countries in the world in Britain
+ 
+
+ align:start position:0%
+freest countries in the world in Britain
+in the United States out of century ago
+
+ align:start position:0%
+in the United States out of century ago
+ 
+
+ align:start position:0%
+in the United States out of century ago
+and the reason was pretty clear was
+
+ align:start position:0%
+and the reason was pretty clear was
+ 
+
+ align:start position:0%
+and the reason was pretty clear was
+often stated people had won enough
+
+ align:start position:0%
+often stated people had won enough
+ 
+
+ align:start position:0%
+often stated people had won enough
+freedom so that you couldn't control
+
+ align:start position:0%
+freedom so that you couldn't control
+ 
+
+ align:start position:0%
+freedom so that you couldn't control
+them by force so you had to control them
+
+ align:start position:0%
+them by force so you had to control them
+ 
+
+ align:start position:0%
+them by force so you had to control them
+in other ways and the best way of
+
+ align:start position:0%
+in other ways and the best way of
+ 
+
+ align:start position:0%
+in other ways and the best way of
+controlling them is what was called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convincing them to be concerned with the
+
+ align:start position:0%
+convincing them to be concerned with the
+ 
+
+ align:start position:0%
+convincing them to be concerned with the
+superficial things of life like
+
+ align:start position:0%
+superficial things of life like
+ 
+
+ align:start position:0%
+superficial things of life like
+consumption so if you can get to a stage
+
+ align:start position:0%
+consumption so if you can get to a stage
+ 
+
+ align:start position:0%
+consumption so if you can get to a stage
+where I think it of my granddaughter
+
+ align:start position:0%
+where I think it of my granddaughter
+ 
+
+ align:start position:0%
+where I think it of my granddaughter
+we're teenage girls on a Saturday
+
+ align:start position:0%
+we're teenage girls on a Saturday
+ 
+
+ align:start position:0%
+we're teenage girls on a Saturday
+afternoon the best thing they can think
+
+ align:start position:0%
+afternoon the best thing they can think
+ 
+
+ align:start position:0%
+afternoon the best thing they can think
+of doing is walking through a mall and
+
+ align:start position:0%
+of doing is walking through a mall and
+ 
+
+ align:start position:0%
+of doing is walking through a mall and
+looking at things they can't buy and you
+
+ align:start position:0%
+looking at things they can't buy and you
+ 
+
+ align:start position:0%
+looking at things they can't buy and you
+know that's great too when you've got
+
+ align:start position:0%
+know that's great too when you've got
+ 
+
+ align:start position:0%
+know that's great too when you've got
+get to a society like that and you've
+
+ align:start position:0%
+get to a society like that and you've
+ 
+
+ align:start position:0%
+get to a society like that and you've
+got people under control and there's
+
+ align:start position:0%
+got people under control and there's
+ 
+
+ align:start position:0%
+got people under control and there's
+some pretty obvious things that are
+
+ align:start position:0%
+some pretty obvious things that are
+ 
+
+ align:start position:0%
+some pretty obvious things that are
+never discussed like you've all heard
+
+ align:start position:0%
+never discussed like you've all heard
+ 
+
+ align:start position:0%
+never discussed like you've all heard
+ten million times about the wonders of
+
+ align:start position:0%
+ten million times about the wonders of
+ 
+
+ align:start position:0%
+ten million times about the wonders of
+free market societies but almost no one
+
+ align:start position:0%
+free market societies but almost no one
+ 
+
+ align:start position:0%
+free market societies but almost no one
+tells you that the business world hates
+
+ align:start position:0%
+tells you that the business world hates
+ 
+
+ align:start position:0%
+tells you that the business world hates
+free market societies and in fact they
+
+ align:start position:0%
+free market societies and in fact they
+ 
+
+ align:start position:0%
+free market societies and in fact they
+spend hundreds of billion dollars a year
+
+ align:start position:0%
+spend hundreds of billion dollars a year
+ 
+
+ align:start position:0%
+spend hundreds of billion dollars a year
+to undermine markets it's called
+
+ align:start position:0%
+to undermine markets it's called
+ 
+
+ align:start position:0%
+to undermine markets it's called
+advertising anyone who's studied
+
+ align:start position:0%
+advertising anyone who's studied
+ 
+
+ align:start position:0%
+advertising anyone who's studied
+economics knows that markets the marvels
+
+ align:start position:0%
+economics knows that markets the marvels
+ 
+
+ align:start position:0%
+economics knows that markets the marvels
+of markets are based on informed
+
+ align:start position:0%
+of markets are based on informed
+ 
+
+ align:start position:0%
+of markets are based on informed
+consumers making rational choices that's
+
+ align:start position:0%
+consumers making rational choices that's
+ 
+
+ align:start position:0%
+consumers making rational choices that's
+what you study the mathematics and you
+
+ align:start position:0%
+what you study the mathematics and you
+ 
+
+ align:start position:0%
+what you study the mathematics and you
+make up the models and so on take a look
+
+ align:start position:0%
+make up the models and so on take a look
+ 
+
+ align:start position:0%
+make up the models and so on take a look
+at the real world hundreds of billions
+
+ align:start position:0%
+at the real world hundreds of billions
+ 
+
+ align:start position:0%
+at the real world hundreds of billions
+of dollars are spent every year to
+
+ align:start position:0%
+of dollars are spent every year to
+ 
+
+ align:start position:0%
+of dollars are spent every year to
+ensure that uninformed people make
+
+ align:start position:0%
+ensure that uninformed people make
+ 
+
+ align:start position:0%
+ensure that uninformed people make
+irrational choices
+
+ align:start position:0%
+irrational choices
+ 
+
+ align:start position:0%
+irrational choices
+that's called advertising and if you had
+
+ align:start position:0%
+that's called advertising and if you had
+ 
+
+ align:start position:0%
+that's called advertising and if you had
+a market society if say Ford Motor
+
+ align:start position:0%
+a market society if say Ford Motor
+ 
+
+ align:start position:0%
+a market society if say Ford Motor
+Company has cars to sell what they would
+
+ align:start position:0%
+Company has cars to sell what they would
+ 
+
+ align:start position:0%
+Company has cars to sell what they would
+do is say here are the characteristics
+
+ align:start position:0%
+do is say here are the characteristics
+ 
+
+ align:start position:0%
+do is say here are the characteristics
+of our cars you know small ad on
+
+ align:start position:0%
+of our cars you know small ad on
+ 
+
+ align:start position:0%
+of our cars you know small ad on
+television says here's the
+
+ align:start position:0%
+television says here's the
+ 
+
+ align:start position:0%
+television says here's the
+characteristics here's what consumer
+
+ align:start position:0%
+characteristics here's what consumer
+ 
+
+ align:start position:0%
+characteristics here's what consumer
+report says about it you know that's not
+
+ align:start position:0%
+report says about it you know that's not
+ 
+
+ align:start position:0%
+report says about it you know that's not
+what they do what they do is try to
+
+ align:start position:0%
+what they do what they do is try to
+ 
+
+ align:start position:0%
+what they do what they do is try to
+create illusions so you will be
+
+ align:start position:0%
+create illusions so you will be
+ 
+
+ align:start position:0%
+create illusions so you will be
+uninformed and make an irrational choice
+
+ align:start position:0%
+uninformed and make an irrational choice
+ 
+
+ align:start position:0%
+uninformed and make an irrational choice
+in fact while the Economics Department
+
+ align:start position:0%
+in fact while the Economics Department
+ 
+
+ align:start position:0%
+in fact while the Economics Department
+is talking about rational choice models
+
+ align:start position:0%
+is talking about rational choice models
+ 
+
+ align:start position:0%
+is talking about rational choice models
+and so on with informed consumers the
+
+ align:start position:0%
+and so on with informed consumers the
+ 
+
+ align:start position:0%
+and so on with informed consumers the
+business world is trying to make sure it
+
+ align:start position:0%
+business world is trying to make sure it
+ 
+
+ align:start position:0%
+business world is trying to make sure it
+doesn't happen and of course that's the
+
+ align:start position:0%
+doesn't happen and of course that's the
+ 
+
+ align:start position:0%
+doesn't happen and of course that's the
+thing that has the effect
+
+ align:start position:0%
+thing that has the effect
+ 
+
+ align:start position:0%
+thing that has the effect
+speaking of silencing and how much you
+
+ align:start position:0%
+speaking of silencing and how much you
+ 
+
+ align:start position:0%
+speaking of silencing and how much you
+hear about this in economics person or
+
+ align:start position:0%
+hear about this in economics person or
+ 
+
+ align:start position:0%
+hear about this in economics person or
+in the general discussion I mean it's
+
+ align:start position:0%
+in the general discussion I mean it's
+ 
+
+ align:start position:0%
+in the general discussion I mean it's
+not deep it's not profound it's not
+
+ align:start position:0%
+not deep it's not profound it's not
+ 
+
+ align:start position:0%
+not deep it's not profound it's not
+quantum physics we don't know it's right
+
+ align:start position:0%
+quantum physics we don't know it's right
+ 
+
+ align:start position:0%
+quantum physics we don't know it's right
+in front of your eyes but it's kept
+
+ align:start position:0%
+in front of your eyes but it's kept
+ 
+
+ align:start position:0%
+in front of your eyes but it's kept
+silent those are the kind of things you
+
+ align:start position:0%
+silent those are the kind of things you
+ 
+
+ align:start position:0%
+silent those are the kind of things you
+have to break through thank you so much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
\ No newline at end of file
diff --git a/aewmVftXm1Q.txt b/aewmVftXm1Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8bf6665b4985237618374509167556d46b02ee5e
--- /dev/null
+++ b/aewmVftXm1Q.txt
@@ -0,0 +1,2203 @@
+align:start position:0%
+ 
+the first step of making architecture is
+
+ align:start position:0%
+the first step of making architecture is
+ 
+
+ align:start position:0%
+the first step of making architecture is
+to visit the
+
+ align:start position:0%
+to visit the
+ 
+
+ align:start position:0%
+to visit the
+site it's the site that gives us Clues
+
+ align:start position:0%
+site it's the site that gives us Clues
+ 
+
+ align:start position:0%
+site it's the site that gives us Clues
+as to how to design of course we have a
+
+ align:start position:0%
+as to how to design of course we have a
+ 
+
+ align:start position:0%
+as to how to design of course we have a
+program and we have thoughts about
+
+ align:start position:0%
+program and we have thoughts about
+ 
+
+ align:start position:0%
+program and we have thoughts about
+form but it's really the site that is
+
+ align:start position:0%
+form but it's really the site that is
+ 
+
+ align:start position:0%
+form but it's really the site that is
+the most important at the beginning
+
+ align:start position:0%
+the most important at the beginning
+ 
+
+ align:start position:0%
+the most important at the beginning
+stage in fact we should know the site as
+
+ align:start position:0%
+stage in fact we should know the site as
+ 
+
+ align:start position:0%
+stage in fact we should know the site as
+well as we know our own
+
+ align:start position:0%
+well as we know our own
+ 
+
+ align:start position:0%
+well as we know our own
+backyard the site is our friend for the
+
+ align:start position:0%
+backyard the site is our friend for the
+ 
+
+ align:start position:0%
+backyard the site is our friend for the
+whole process of
+
+ align:start position:0%
+whole process of
+ 
+
+ align:start position:0%
+whole process of
+Designing is what we should keep
+
+ align:start position:0%
+Designing is what we should keep
+ 
+
+ align:start position:0%
+Designing is what we should keep
+returning to keep understanding seeing
+
+ align:start position:0%
+returning to keep understanding seeing
+ 
+
+ align:start position:0%
+returning to keep understanding seeing
+uh during the day at night uh in the
+
+ align:start position:0%
+uh during the day at night uh in the
+ 
+
+ align:start position:0%
+uh during the day at night uh in the
+rain and the Sun It's The Giver of the
+
+ align:start position:0%
+rain and the Sun It's The Giver of the
+ 
+
+ align:start position:0%
+rain and the Sun It's The Giver of the
+original
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideas uh of course uh the program and
+
+ align:start position:0%
+ideas uh of course uh the program and
+ 
+
+ align:start position:0%
+ideas uh of course uh the program and
+the forums and all the rest of important
+
+ align:start position:0%
+the forums and all the rest of important
+ 
+
+ align:start position:0%
+the forums and all the rest of important
+but it's the site that
+
+ align:start position:0%
+but it's the site that
+ 
+
+ align:start position:0%
+but it's the site that
+starts so what you're about to see is a
+
+ align:start position:0%
+starts so what you're about to see is a
+ 
+
+ align:start position:0%
+starts so what you're about to see is a
+site visit to the North
+
+ align:start position:0%
+site visit to the North
+ 
+
+ align:start position:0%
+site visit to the North
+End which is where we're doing a project
+
+ align:start position:0%
+End which is where we're doing a project
+ 
+
+ align:start position:0%
+End which is where we're doing a project
+for design of a
+
+ align:start position:0%
+for design of a
+ 
+
+ align:start position:0%
+for design of a
+house um on the sides of buildings and
+
+ align:start position:0%
+house um on the sides of buildings and
+ 
+
+ align:start position:0%
+house um on the sides of buildings and
+on the roofs of the buildings and then
+
+ align:start position:0%
+on the roofs of the buildings and then
+ 
+
+ align:start position:0%
+on the roofs of the buildings and then
+later in the same area the same site we
+
+ align:start position:0%
+later in the same area the same site we
+ 
+
+ align:start position:0%
+later in the same area the same site we
+will be designing a community
+
+ align:start position:0%
+will be designing a community
+ 
+
+ align:start position:0%
+will be designing a community
+place so the following is that first
+
+ align:start position:0%
+place so the following is that first
+ 
+
+ align:start position:0%
+place so the following is that first
+visit to the site
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think huh challenging you can see the
+
+ align:start position:0%
+think huh challenging you can see the
+ 
+
+ align:start position:0%
+think huh challenging you can see the
+church from here the Nave of it through
+
+ align:start position:0%
+church from here the Nave of it through
+ 
+
+ align:start position:0%
+church from here the Nave of it through
+there yeah I think if you knocked on the
+
+ align:start position:0%
+there yeah I think if you knocked on the
+ 
+
+ align:start position:0%
+there yeah I think if you knocked on the
+door and you know you probably see the
+
+ align:start position:0%
+door and you know you probably see the
+ 
+
+ align:start position:0%
+door and you know you probably see the
+inside of that
+
+ align:start position:0%
+inside of that
+ 
+
+ align:start position:0%
+inside of that
+window uh there's a church and Monastery
+
+ align:start position:0%
+window uh there's a church and Monastery
+ 
+
+ align:start position:0%
+window uh there's a church and Monastery
+or school there I think I think it's
+
+ align:start position:0%
+or school there I think I think it's
+ 
+
+ align:start position:0%
+or school there I think I think it's
+connected and of course you're on the
+
+ align:start position:0%
+connected and of course you're on the
+ 
+
+ align:start position:0%
+connected and of course you're on the
+roof of it you got to attach yourself to
+
+ align:start position:0%
+roof of it you got to attach yourself to
+ 
+
+ align:start position:0%
+roof of it you got to attach yourself to
+the side of that a little bit
+
+ align:start position:0%
+the side of that a little bit
+ 
+
+ align:start position:0%
+the side of that a little bit
+then so it's going to be hanging off and
+
+ align:start position:0%
+then so it's going to be hanging off and
+ 
+
+ align:start position:0%
+then so it's going to be hanging off and
+we do have to think about how structure
+
+ align:start position:0%
+we do have to think about how structure
+ 
+
+ align:start position:0%
+we do have to think about how structure
+is going to work in some general way and
+
+ align:start position:0%
+is going to work in some general way and
+ 
+
+ align:start position:0%
+is going to work in some general way and
+we'll get David Whitney back sometimes
+
+ align:start position:0%
+we'll get David Whitney back sometimes
+ 
+
+ align:start position:0%
+we'll get David Whitney back sometimes
+you're going to Candle leave out
+
+ align:start position:0%
+you're going to Candle leave out
+ 
+
+ align:start position:0%
+you're going to Candle leave out
+sometimes they going to be braces you
+
+ align:start position:0%
+sometimes they going to be braces you
+ 
+
+ align:start position:0%
+sometimes they going to be braces you
+could run things down to the ground you
+
+ align:start position:0%
+could run things down to the ground you
+ 
+
+ align:start position:0%
+could run things down to the ground you
+have no
+
+ align:start position:0%
+have no
+ 
+
+ align:start position:0%
+have no
+um uh limitations of what you can do but
+
+ align:start position:0%
+um uh limitations of what you can do but
+ 
+
+ align:start position:0%
+um uh limitations of what you can do but
+we do want to be structural you could
+
+ align:start position:0%
+we do want to be structural you could
+ 
+
+ align:start position:0%
+we do want to be structural you could
+hang over the side and structurally it
+
+ align:start position:0%
+hang over the side and structurally it
+ 
+
+ align:start position:0%
+hang over the side and structurally it
+would hold on you know uh for instance
+
+ align:start position:0%
+would hold on you know uh for instance
+ 
+
+ align:start position:0%
+would hold on you know uh for instance
+who has the vent site that two vents but
+
+ align:start position:0%
+who has the vent site that two vents but
+ 
+
+ align:start position:0%
+who has the vent site that two vents but
+the one that hangs over okay both of
+
+ align:start position:0%
+the one that hangs over okay both of
+ 
+
+ align:start position:0%
+the one that hangs over okay both of
+them mine's on the the yours is on the
+
+ align:start position:0%
+them mine's on the the yours is on the
+ 
+
+ align:start position:0%
+them mine's on the the yours is on the
+side and one hangs over yeah so that one
+
+ align:start position:0%
+side and one hangs over yeah so that one
+ 
+
+ align:start position:0%
+side and one hangs over yeah so that one
+could hang over uh almost like a shelf
+
+ align:start position:0%
+could hang over uh almost like a shelf
+ 
+
+ align:start position:0%
+could hang over uh almost like a shelf
+coming over the other one is going to
+
+ align:start position:0%
+coming over the other one is going to
+ 
+
+ align:start position:0%
+coming over the other one is going to
+attach itself to the to the
+
+ align:start position:0%
+attach itself to the to the
+ 
+
+ align:start position:0%
+attach itself to the to the
+side um what can anybody see from here
+
+ align:start position:0%
+side um what can anybody see from here
+ 
+
+ align:start position:0%
+side um what can anybody see from here
+that relates to our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again right and we however later right
+
+ align:start position:0%
+again right and we however later right
+ 
+
+ align:start position:0%
+again right and we however later right
+across the street that's our job is
+
+ align:start position:0%
+across the street that's our job is
+ 
+
+ align:start position:0%
+across the street that's our job is
+design a place for us to be which would
+
+ align:start position:0%
+design a place for us to be which would
+ 
+
+ align:start position:0%
+design a place for us to be which would
+include a play could include a
+
+ align:start position:0%
+include a play could include a
+ 
+
+ align:start position:0%
+include a play could include a
+playground that's our site right here
+
+ align:start position:0%
+playground that's our site right here
+ 
+
+ align:start position:0%
+playground that's our site right here
+where that where that playground is is
+
+ align:start position:0%
+where that where that playground is is
+ 
+
+ align:start position:0%
+where that where that playground is is
+part of our site but also all that area
+
+ align:start position:0%
+part of our site but also all that area
+ 
+
+ align:start position:0%
+part of our site but also all that area
+in there and certainly this is a place
+
+ align:start position:0%
+in there and certainly this is a place
+ 
+
+ align:start position:0%
+in there and certainly this is a place
+also that that could be used that way uh
+
+ align:start position:0%
+also that that could be used that way uh
+ 
+
+ align:start position:0%
+also that that could be used that way uh
+this has a special meaning and that's
+
+ align:start position:0%
+this has a special meaning and that's
+ 
+
+ align:start position:0%
+this has a special meaning and that's
+part of your site cluing finding out why
+
+ align:start position:0%
+part of your site cluing finding out why
+ 
+
+ align:start position:0%
+part of your site cluing finding out why
+it's here why all the buildings are here
+
+ align:start position:0%
+it's here why all the buildings are here
+ 
+
+ align:start position:0%
+it's here why all the buildings are here
+for that matter what else do you see
+
+ align:start position:0%
+for that matter what else do you see
+ 
+
+ align:start position:0%
+for that matter what else do you see
+look around quick behind
+
+ align:start position:0%
+look around quick behind
+ 
+
+ align:start position:0%
+look around quick behind
+me huh yeah someone's done what we're
+
+ align:start position:0%
+me huh yeah someone's done what we're
+ 
+
+ align:start position:0%
+me huh yeah someone's done what we're
+doing very
+
+ align:start position:0%
+doing very
+ 
+
+ align:start position:0%
+doing very
+modestly uh they've added already in a
+
+ align:start position:0%
+modestly uh they've added already in a
+ 
+
+ align:start position:0%
+modestly uh they've added already in a
+way on top of the roof and on the side
+
+ align:start position:0%
+way on top of the roof and on the side
+ 
+
+ align:start position:0%
+way on top of the roof and on the side
+and on the side yeah so they've done
+
+ align:start position:0%
+and on the side yeah so they've done
+ 
+
+ align:start position:0%
+and on the side yeah so they've done
+sort of what we're doing but in a very
+
+ align:start position:0%
+sort of what we're doing but in a very
+ 
+
+ align:start position:0%
+sort of what we're doing but in a very
+conservative way I'm not suggesting you
+
+ align:start position:0%
+conservative way I'm not suggesting you
+ 
+
+ align:start position:0%
+conservative way I'm not suggesting you
+be conservative I do think if you went
+
+ align:start position:0%
+be conservative I do think if you went
+ 
+
+ align:start position:0%
+be conservative I do think if you went
+down to uh Paul Rivers's mall and uh go
+
+ align:start position:0%
+down to uh Paul Rivers's mall and uh go
+ 
+
+ align:start position:0%
+down to uh Paul Rivers's mall and uh go
+to the old North Church and look at that
+
+ align:start position:0%
+to the old North Church and look at that
+ 
+
+ align:start position:0%
+to the old North Church and look at that
+one that's hanging on the side it's more
+
+ align:start position:0%
+one that's hanging on the side it's more
+ 
+
+ align:start position:0%
+one that's hanging on the side it's more
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+architecture and it's interesting
+
+ align:start position:0%
+architecture and it's interesting
+ 
+
+ align:start position:0%
+architecture and it's interesting
+because I think it fits into the North
+
+ align:start position:0%
+because I think it fits into the North
+ 
+
+ align:start position:0%
+because I think it fits into the North
+End so part of the issue of this project
+
+ align:start position:0%
+End so part of the issue of this project
+ 
+
+ align:start position:0%
+End so part of the issue of this project
+like the Quarry is how you fit what
+
+ align:start position:0%
+like the Quarry is how you fit what
+ 
+
+ align:start position:0%
+like the Quarry is how you fit what
+you're doing into the context but now
+
+ align:start position:0%
+you're doing into the context but now
+ 
+
+ align:start position:0%
+you're doing into the context but now
+the context is different obviously but
+
+ align:start position:0%
+the context is different obviously but
+ 
+
+ align:start position:0%
+the context is different obviously but
+it doesn't mean it has to be brick and
+
+ align:start position:0%
+it doesn't mean it has to be brick and
+ 
+
+ align:start position:0%
+it doesn't mean it has to be brick and
+Clon or whatever we are sitting on the
+
+ align:start position:0%
+Clon or whatever we are sitting on the
+ 
+
+ align:start position:0%
+Clon or whatever we are sitting on the
+dock of the water of the old water I
+
+ align:start position:0%
+dock of the water of the old water I
+ 
+
+ align:start position:0%
+dock of the water of the old water I
+think somebody might find this out as
+
+ align:start position:0%
+think somebody might find this out as
+ 
+
+ align:start position:0%
+think somebody might find this out as
+far of your clue but this is the
+
+ align:start position:0%
+far of your clue but this is the
+ 
+
+ align:start position:0%
+far of your clue but this is the
+original site but the water was right
+
+ align:start position:0%
+original site but the water was right
+ 
+
+ align:start position:0%
+original site but the water was right
+there as you may know may I have that
+
+ align:start position:0%
+there as you may know may I have that
+ 
+
+ align:start position:0%
+there as you may know may I have that
+growing just for a second that's why
+
+ align:start position:0%
+growing just for a second that's why
+ 
+
+ align:start position:0%
+growing just for a second that's why
+this street is
+
+ align:start position:0%
+this street is
+ 
+
+ align:start position:0%
+this street is
+curved cuz that used to be the in fact I
+
+ align:start position:0%
+curved cuz that used to be the in fact I
+ 
+
+ align:start position:0%
+curved cuz that used to be the in fact I
+think it's still it says North Street
+
+ align:start position:0%
+think it's still it says North Street
+ 
+
+ align:start position:0%
+think it's still it says North Street
+was it was the original Street along the
+
+ align:start position:0%
+was it was the original Street along the
+ 
+
+ align:start position:0%
+was it was the original Street along the
+dock so this is all water this was solid
+
+ align:start position:0%
+dock so this is all water this was solid
+ 
+
+ align:start position:0%
+dock so this is all water this was solid
+as you know Boston over the years is
+
+ align:start position:0%
+as you know Boston over the years is
+ 
+
+ align:start position:0%
+as you know Boston over the years is
+filled in
+
+ align:start position:0%
+filled in
+ 
+
+ align:start position:0%
+filled in
+tremendously All Back Bay is is filled
+
+ align:start position:0%
+tremendously All Back Bay is is filled
+ 
+
+ align:start position:0%
+tremendously All Back Bay is is filled
+all South End is filled
+
+ align:start position:0%
+all South End is filled
+ 
+
+ align:start position:0%
+all South End is filled
+uh all of Cambridge is filled where we
+
+ align:start position:0%
+uh all of Cambridge is filled where we
+ 
+
+ align:start position:0%
+uh all of Cambridge is filled where we
+are is all filled also so it's a it's a
+
+ align:start position:0%
+are is all filled also so it's a it's a
+ 
+
+ align:start position:0%
+are is all filled also so it's a it's a
+habit of cities to do that to fill up
+
+ align:start position:0%
+habit of cities to do that to fill up
+ 
+
+ align:start position:0%
+habit of cities to do that to fill up
+the water what about the person that's
+
+ align:start position:0%
+the water what about the person that's
+ 
+
+ align:start position:0%
+the water what about the person that's
+got this one up
+
+ align:start position:0%
+got this one up
+ 
+
+ align:start position:0%
+got this one up
+here Phil philli he's got an interesting
+
+ align:start position:0%
+here Phil philli he's got an interesting
+ 
+
+ align:start position:0%
+here Phil philli he's got an interesting
+issue how does he do how does he make a
+
+ align:start position:0%
+issue how does he do how does he make a
+ 
+
+ align:start position:0%
+issue how does he do how does he make a
+form up there that relates to that
+
+ align:start position:0%
+form up there that relates to that
+ 
+
+ align:start position:0%
+form up there that relates to that
+little curve or does he that's a context
+
+ align:start position:0%
+little curve or does he that's a context
+ 
+
+ align:start position:0%
+little curve or does he that's a context
+issue just like the
+
+ align:start position:0%
+issue just like the
+ 
+
+ align:start position:0%
+issue just like the
+Quarry how does he what does he do but
+
+ align:start position:0%
+Quarry how does he what does he do but
+ 
+
+ align:start position:0%
+Quarry how does he what does he do but
+he could relate to to that and at the
+
+ align:start position:0%
+he could relate to to that and at the
+ 
+
+ align:start position:0%
+he could relate to to that and at the
+same time the top of it the sky form
+
+ align:start position:0%
+same time the top of it the sky form
+ 
+
+ align:start position:0%
+same time the top of it the sky form
+that we talk about could be something
+
+ align:start position:0%
+that we talk about could be something
+ 
+
+ align:start position:0%
+that we talk about could be something
+entirely
+
+ align:start position:0%
+entirely
+ 
+
+ align:start position:0%
+entirely
+different so it's the same issues as
+
+ align:start position:0%
+different so it's the same issues as
+ 
+
+ align:start position:0%
+different so it's the same issues as
+before land form but the land is up in
+
+ align:start position:0%
+before land form but the land is up in
+ 
+
+ align:start position:0%
+before land form but the land is up in
+the sky and the middle and the sky and
+
+ align:start position:0%
+the sky and the middle and the sky and
+ 
+
+ align:start position:0%
+the sky and the middle and the sky and
+the sky can be something quite different
+
+ align:start position:0%
+the sky can be something quite different
+ 
+
+ align:start position:0%
+the sky can be something quite different
+doesn't have to be the
+
+ align:start position:0%
+doesn't have to be the
+ 
+
+ align:start position:0%
+doesn't have to be the
+same what I don't want you to do is to
+
+ align:start position:0%
+same what I don't want you to do is to
+ 
+
+ align:start position:0%
+same what I don't want you to do is to
+try to as in the Quarry imitate the
+
+ align:start position:0%
+try to as in the Quarry imitate the
+ 
+
+ align:start position:0%
+try to as in the Quarry imitate the
+context we are trying to add something
+
+ align:start position:0%
+context we are trying to add something
+ 
+
+ align:start position:0%
+context we are trying to add something
+that relates but not necessarily the
+
+ align:start position:0%
+that relates but not necessarily the
+ 
+
+ align:start position:0%
+that relates but not necessarily the
+same otherwise you end up with a little
+
+ align:start position:0%
+same otherwise you end up with a little
+ 
+
+ align:start position:0%
+same otherwise you end up with a little
+kind of Walt Disney Colonial whatever
+
+ align:start position:0%
+kind of Walt Disney Colonial whatever
+ 
+
+ align:start position:0%
+kind of Walt Disney Colonial whatever
+stuff which is not the issue but it does
+
+ align:start position:0%
+stuff which is not the issue but it does
+ 
+
+ align:start position:0%
+stuff which is not the issue but it does
+as you can
+
+ align:start position:0%
+as you can
+ 
+
+ align:start position:0%
+as you can
+see our site which is over there for the
+
+ align:start position:0%
+see our site which is over there for the
+ 
+
+ align:start position:0%
+see our site which is over there for the
+community is quite a bit lower than
+
+ align:start position:0%
+community is quite a bit lower than
+ 
+
+ align:start position:0%
+community is quite a bit lower than
+where we are not quite a bit but lower
+
+ align:start position:0%
+where we are not quite a bit but lower
+ 
+
+ align:start position:0%
+where we are not quite a bit but lower
+than this and then lower still than over
+
+ align:start position:0%
+than this and then lower still than over
+ 
+
+ align:start position:0%
+than this and then lower still than over
+here it's going uphill
+
+ align:start position:0%
+here it's going uphill
+ 
+
+ align:start position:0%
+here it's going uphill
+slightly now this area is what we we'
+
+ align:start position:0%
+slightly now this area is what we we'
+ 
+
+ align:start position:0%
+slightly now this area is what we we'
+like to build the E scale out of
+
+ align:start position:0%
+like to build the E scale out of
+ 
+
+ align:start position:0%
+like to build the E scale out of
+cardboard which is the equivalent to our
+
+ align:start position:0%
+cardboard which is the equivalent to our
+ 
+
+ align:start position:0%
+cardboard which is the equivalent to our
+Quarry but instead of a place now we
+
+ align:start position:0%
+Quarry but instead of a place now we
+ 
+
+ align:start position:0%
+Quarry but instead of a place now we
+have sort of a path we're relating to
+
+ align:start position:0%
+have sort of a path we're relating to
+ 
+
+ align:start position:0%
+have sort of a path we're relating to
+each end of the street on the other hand
+
+ align:start position:0%
+each end of the street on the other hand
+ 
+
+ align:start position:0%
+each end of the street on the other hand
+I suggest that you probably when you're
+
+ align:start position:0%
+I suggest that you probably when you're
+ 
+
+ align:start position:0%
+I suggest that you probably when you're
+done building almost everybody can wave
+
+ align:start position:0%
+done building almost everybody can wave
+ 
+
+ align:start position:0%
+done building almost everybody can wave
+to somebody she can wave to
+
+ align:start position:0%
+to somebody she can wave to
+ 
+
+ align:start position:0%
+to somebody she can wave to
+Phillip uh and
+
+ align:start position:0%
+Phillip uh and
+ 
+
+ align:start position:0%
+Phillip uh and
+Stacy so there'll be little
+
+ align:start position:0%
+Stacy so there'll be little
+ 
+
+ align:start position:0%
+Stacy so there'll be little
+subcommunities
+
+ align:start position:0%
+subcommunities
+ 
+
+ align:start position:0%
+subcommunities
+if you're close together in a site
+
+ align:start position:0%
+if you're close together in a site
+ 
+
+ align:start position:0%
+if you're close together in a site
+you're welcome to explore
+
+ align:start position:0%
+you're welcome to explore
+ 
+
+ align:start position:0%
+you're welcome to explore
+connections this is like the Quarry and
+
+ align:start position:0%
+connections this is like the Quarry and
+ 
+
+ align:start position:0%
+connections this is like the Quarry and
+you now are
+
+ align:start position:0%
+you now are
+ 
+
+ align:start position:0%
+you now are
+detectives a good architect in my
+
+ align:start position:0%
+detectives a good architect in my
+ 
+
+ align:start position:0%
+detectives a good architect in my
+opinion starts with the site this is our
+
+ align:start position:0%
+opinion starts with the site this is our
+ 
+
+ align:start position:0%
+opinion starts with the site this is our
+site so you want to learn as much as you
+
+ align:start position:0%
+site so you want to learn as much as you
+ 
+
+ align:start position:0%
+site so you want to learn as much as you
+can about the site and there are
+
+ align:start position:0%
+can about the site and there are
+ 
+
+ align:start position:0%
+can about the site and there are
+different kinds of
+
+ align:start position:0%
+different kinds of
+ 
+
+ align:start position:0%
+different kinds of
+information obviously there's
+
+ align:start position:0%
+information obviously there's
+ 
+
+ align:start position:0%
+information obviously there's
+architectural
+
+ align:start position:0%
+architectural
+ 
+
+ align:start position:0%
+architectural
+form you probably can find any kind of
+
+ align:start position:0%
+form you probably can find any kind of
+ 
+
+ align:start position:0%
+form you probably can find any kind of
+form you want in this site in fact
+
+ align:start position:0%
+form you want in this site in fact
+ 
+
+ align:start position:0%
+form you want in this site in fact
+there's a little surprise around the
+
+ align:start position:0%
+there's a little surprise around the
+ 
+
+ align:start position:0%
+there's a little surprise around the
+corner if you haven't seen it of a
+
+ align:start position:0%
+corner if you haven't seen it of a
+ 
+
+ align:start position:0%
+corner if you haven't seen it of a
+little guy sticking did you see it on
+
+ align:start position:0%
+little guy sticking did you see it on
+ 
+
+ align:start position:0%
+little guy sticking did you see it on
+the corner sticking on the side a little
+
+ align:start position:0%
+the corner sticking on the side a little
+ 
+
+ align:start position:0%
+the corner sticking on the side a little
+bay window there's all kinds of bay
+
+ align:start position:0%
+bay window there's all kinds of bay
+ 
+
+ align:start position:0%
+bay window there's all kinds of bay
+windows up there so form and materials
+
+ align:start position:0%
+windows up there so form and materials
+ 
+
+ align:start position:0%
+windows up there so form and materials
+is one clue that we're looking for but
+
+ align:start position:0%
+is one clue that we're looking for but
+ 
+
+ align:start position:0%
+is one clue that we're looking for but
+equally important is people and what
+
+ align:start position:0%
+equally important is people and what
+ 
+
+ align:start position:0%
+equally important is people and what
+they're doing what's happening here I
+
+ align:start position:0%
+they're doing what's happening here I
+ 
+
+ align:start position:0%
+they're doing what's happening here I
+mean look at what's happening right
+
+ align:start position:0%
+mean look at what's happening right
+ 
+
+ align:start position:0%
+mean look at what's happening right
+around us there are tourists from Iowa
+
+ align:start position:0%
+around us there are tourists from Iowa
+ 
+
+ align:start position:0%
+around us there are tourists from Iowa
+and Ohio and all over the country
+
+ align:start position:0%
+and Ohio and all over the country
+ 
+
+ align:start position:0%
+and Ohio and all over the country
+walking around but there are also
+
+ align:start position:0%
+walking around but there are also
+ 
+
+ align:start position:0%
+walking around but there are also
+residents you can see you can almost
+
+ align:start position:0%
+residents you can see you can almost
+ 
+
+ align:start position:0%
+residents you can see you can almost
+tell the difference Who's Who uh on
+
+ align:start position:0%
+tell the difference Who's Who uh on
+ 
+
+ align:start position:0%
+tell the difference Who's Who uh on
+weekends you'll find uh kids playing in
+
+ align:start position:0%
+weekends you'll find uh kids playing in
+ 
+
+ align:start position:0%
+weekends you'll find uh kids playing in
+the street you go to the Paul rier Mall
+
+ align:start position:0%
+the street you go to the Paul rier Mall
+ 
+
+ align:start position:0%
+the street you go to the Paul rier Mall
+this afternoon and you'll find you may
+
+ align:start position:0%
+this afternoon and you'll find you may
+ 
+
+ align:start position:0%
+this afternoon and you'll find you may
+find kids and tourists going through so
+
+ align:start position:0%
+find kids and tourists going through so
+ 
+
+ align:start position:0%
+find kids and tourists going through so
+it's a mixture you're adding to that
+
+ align:start position:0%
+it's a mixture you're adding to that
+ 
+
+ align:start position:0%
+it's a mixture you're adding to that
+mix be good to know something about who
+
+ align:start position:0%
+mix be good to know something about who
+ 
+
+ align:start position:0%
+mix be good to know something about who
+your neighbors are even though we're
+
+ align:start position:0%
+your neighbors are even though we're
+ 
+
+ align:start position:0%
+your neighbors are even though we're
+building in this Canyon because the next
+
+ align:start position:0%
+building in this Canyon because the next
+ 
+
+ align:start position:0%
+building in this Canyon because the next
+problem of the community place is how to
+
+ align:start position:0%
+problem of the community place is how to
+ 
+
+ align:start position:0%
+problem of the community place is how to
+bring everybody together including
+
+ align:start position:0%
+bring everybody together including
+ 
+
+ align:start position:0%
+bring everybody together including
+yourself there are other Clues there's
+
+ align:start position:0%
+yourself there are other Clues there's
+ 
+
+ align:start position:0%
+yourself there are other Clues there's
+his historic Clues what's the history
+
+ align:start position:0%
+his historic Clues what's the history
+ 
+
+ align:start position:0%
+his historic Clues what's the history
+why is this place why is the Northend
+
+ align:start position:0%
+why is this place why is the Northend
+ 
+
+ align:start position:0%
+why is this place why is the Northend
+like the North End what makes it
+
+ align:start position:0%
+like the North End what makes it
+ 
+
+ align:start position:0%
+like the North End what makes it
+different than the Back Bay
+
+ align:start position:0%
+different than the Back Bay
+ 
+
+ align:start position:0%
+different than the Back Bay
+why uh why are the streets like
+
+ align:start position:0%
+why uh why are the streets like
+ 
+
+ align:start position:0%
+why uh why are the streets like
+this I know why but you that you should
+
+ align:start position:0%
+this I know why but you that you should
+ 
+
+ align:start position:0%
+this I know why but you that you should
+find out so there there's history um of
+
+ align:start position:0%
+find out so there there's history um of
+ 
+
+ align:start position:0%
+find out so there there's history um of
+the place those are
+
+ align:start position:0%
+the place those are
+ 
+
+ align:start position:0%
+the place those are
+Clues um there's real Clues Philip was
+
+ align:start position:0%
+Clues um there's real Clues Philip was
+ 
+
+ align:start position:0%
+Clues um there's real Clues Philip was
+probably going to bring back somebody's
+
+ align:start position:0%
+probably going to bring back somebody's
+ 
+
+ align:start position:0%
+probably going to bring back somebody's
+steps or something you know you don't
+
+ align:start position:0%
+steps or something you know you don't
+ 
+
+ align:start position:0%
+steps or something you know you don't
+have to bring something back why why
+
+ align:start position:0%
+have to bring something back why why
+ 
+
+ align:start position:0%
+have to bring something back why why
+don't you bring back
+
+ align:start position:0%
+don't you bring back
+ 
+
+ align:start position:0%
+don't you bring back
+is uh what I call a clue which is
+
+ align:start position:0%
+is uh what I call a clue which is
+ 
+
+ align:start position:0%
+is uh what I call a clue which is
+something in your head or something
+
+ align:start position:0%
+something in your head or something
+ 
+
+ align:start position:0%
+something in your head or something
+physically so once again when we're back
+
+ align:start position:0%
+physically so once again when we're back
+ 
+
+ align:start position:0%
+physically so once again when we're back
+in the studio we can visualize the site
+
+ align:start position:0%
+in the studio we can visualize the site
+ 
+
+ align:start position:0%
+in the studio we can visualize the site
+as well as your own backyard like the
+
+ align:start position:0%
+as well as your own backyard like the
+ 
+
+ align:start position:0%
+as well as your own backyard like the
+query it's the same thing except it's
+
+ align:start position:0%
+query it's the same thing except it's
+ 
+
+ align:start position:0%
+query it's the same thing except it's
+different so you
+
+ align:start position:0%
+different so you
+ 
+
+ align:start position:0%
+different so you
+start to think
+
+ align:start position:0%
+start to think
+ 
+
+ align:start position:0%
+start to think
+about how you're going to add something
+
+ align:start position:0%
+about how you're going to add something
+ 
+
+ align:start position:0%
+about how you're going to add something
+to the and I'm using this one as an
+
+ align:start position:0%
+to the and I'm using this one as an
+ 
+
+ align:start position:0%
+to the and I'm using this one as an
+example to the side of that building
+
+ align:start position:0%
+example to the side of that building
+ 
+
+ align:start position:0%
+example to the side of that building
+through some
+
+ align:start position:0%
+through some
+ 
+
+ align:start position:0%
+through some
+sketches it seems to me that this person
+
+ align:start position:0%
+sketches it seems to me that this person
+ 
+
+ align:start position:0%
+sketches it seems to me that this person
+has to do something
+
+ align:start position:0%
+has to do something
+ 
+
+ align:start position:0%
+has to do something
+vertically I mean the the the house is
+
+ align:start position:0%
+vertically I mean the the the house is
+ 
+
+ align:start position:0%
+vertically I mean the the the house is
+going to be on several levels I would
+
+ align:start position:0%
+going to be on several levels I would
+ 
+
+ align:start position:0%
+going to be on several levels I would
+think there's a limit to how far you can
+
+ align:start position:0%
+think there's a limit to how far you can
+ 
+
+ align:start position:0%
+think there's a limit to how far you can
+can leave her off whereas on top of this
+
+ align:start position:0%
+can leave her off whereas on top of this
+ 
+
+ align:start position:0%
+can leave her off whereas on top of this
+roof it could be horizontal Philip up
+
+ align:start position:0%
+roof it could be horizontal Philip up
+ 
+
+ align:start position:0%
+roof it could be horizontal Philip up
+there could be horizontal and vertical
+
+ align:start position:0%
+there could be horizontal and vertical
+ 
+
+ align:start position:0%
+there could be horizontal and vertical
+he's not the highest um and who has the
+
+ align:start position:0%
+he's not the highest um and who has the
+ 
+
+ align:start position:0%
+he's not the highest um and who has the
+one right next to our community space
+
+ align:start position:0%
+one right next to our community space
+ 
+
+ align:start position:0%
+one right next to our community space
+not the the later Tower but over there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one Kelly oh that's right Kelly has that
+
+ align:start position:0%
+one Kelly oh that's right Kelly has that
+ 
+
+ align:start position:0%
+one Kelly oh that's right Kelly has that
+that one is important because she kind
+
+ align:start position:0%
+that one is important because she kind
+ 
+
+ align:start position:0%
+that one is important because she kind
+of overlooks the whole
+
+ align:start position:0%
+of overlooks the whole
+ 
+
+ align:start position:0%
+of overlooks the whole
+area she's going to be the person who's
+
+ align:start position:0%
+area she's going to be the person who's
+ 
+
+ align:start position:0%
+area she's going to be the person who's
+going to be kind of the gatekeeper of
+
+ align:start position:0%
+going to be kind of the gatekeeper of
+ 
+
+ align:start position:0%
+going to be kind of the gatekeeper of
+our community area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later who has uh number 12 12 is an
+
+ align:start position:0%
+later who has uh number 12 12 is an
+ 
+
+ align:start position:0%
+later who has uh number 12 12 is an
+interesting one cuz you're on the roof
+
+ align:start position:0%
+interesting one cuz you're on the roof
+ 
+
+ align:start position:0%
+interesting one cuz you're on the roof
+and you're over the side and you're a
+
+ align:start position:0%
+and you're over the side and you're a
+ 
+
+ align:start position:0%
+and you're over the side and you're a
+little bit fit on the outer Li limits of
+
+ align:start position:0%
+little bit fit on the outer Li limits of
+ 
+
+ align:start position:0%
+little bit fit on the outer Li limits of
+the of our
+
+ align:start position:0%
+the of our
+ 
+
+ align:start position:0%
+the of our
+community almost everybody else forms
+
+ align:start position:0%
+community almost everybody else forms
+ 
+
+ align:start position:0%
+community almost everybody else forms
+some communities that one does twoo it
+
+ align:start position:0%
+some communities that one does twoo it
+ 
+
+ align:start position:0%
+some communities that one does twoo it
+connects with three who is three so
+
+ align:start position:0%
+connects with three who is three so
+ 
+
+ align:start position:0%
+connects with three who is three so
+there's there's a little connection
+
+ align:start position:0%
+there's there's a little connection
+ 
+
+ align:start position:0%
+there's there's a little connection
+between the two of you and who's 13
+
+ align:start position:0%
+between the two of you and who's 13
+ 
+
+ align:start position:0%
+between the two of you and who's 13
+you're 13 so there's a community of 12
+
+ align:start position:0%
+you're 13 so there's a community of 12
+ 
+
+ align:start position:0%
+you're 13 so there's a community of 12
+15 and three they're very
+
+ align:start position:0%
+15 and three they're very
+ 
+
+ align:start position:0%
+15 and three they're very
+close Okay what I'd like to have you do
+
+ align:start position:0%
+close Okay what I'd like to have you do
+ 
+
+ align:start position:0%
+close Okay what I'd like to have you do
+is have a good
+
+ align:start position:0%
+is have a good
+ 
+
+ align:start position:0%
+is have a good
+time talk to by the way I I'll show you
+
+ align:start position:0%
+time talk to by the way I I'll show you
+ 
+
+ align:start position:0%
+time talk to by the way I I'll show you
+but I I would like to ask you to just
+
+ align:start position:0%
+but I I would like to ask you to just
+ 
+
+ align:start position:0%
+but I I would like to ask you to just
+kind of nose around talk to
+
+ align:start position:0%
+kind of nose around talk to
+ 
+
+ align:start position:0%
+kind of nose around talk to
+people um look and see and see what you
+
+ align:start position:0%
+people um look and see and see what you
+ 
+
+ align:start position:0%
+people um look and see and see what you
+can bring back see what how many
+
+ align:start position:0%
+can bring back see what how many
+ 
+
+ align:start position:0%
+can bring back see what how many
+different things you can find that might
+
+ align:start position:0%
+different things you can find that might
+ 
+
+ align:start position:0%
+different things you can find that might
+influence what you're designing that's
+
+ align:start position:0%
+influence what you're designing that's
+ 
+
+ align:start position:0%
+influence what you're designing that's
+one the second is to go to Paul re
+
+ align:start position:0%
+one the second is to go to Paul re
+ 
+
+ align:start position:0%
+one the second is to go to Paul re
+River's Mall which is the next street
+
+ align:start position:0%
+River's Mall which is the next street
+ 
+
+ align:start position:0%
+River's Mall which is the next street
+over which is um Handover and go up hand
+
+ align:start position:0%
+over which is um Handover and go up hand
+ 
+
+ align:start position:0%
+over which is um Handover and go up hand
+Handover about two or three blocks and
+
+ align:start position:0%
+Handover about two or three blocks and
+ 
+
+ align:start position:0%
+Handover about two or three blocks and
+it's on your left by the fire
+
+ align:start position:0%
+it's on your left by the fire
+ 
+
+ align:start position:0%
+it's on your left by the fire
+um station go through Paul Rivers's mall
+
+ align:start position:0%
+um station go through Paul Rivers's mall
+ 
+
+ align:start position:0%
+um station go through Paul Rivers's mall
+to the North Church that's where the
+
+ align:start position:0%
+to the North Church that's where the
+ 
+
+ align:start position:0%
+to the North Church that's where the
+lanterns
+
+ align:start position:0%
+lanterns
+ 
+
+ align:start position:0%
+lanterns
+were on the other side to the right you
+
+ align:start position:0%
+were on the other side to the right you
+ 
+
+ align:start position:0%
+were on the other side to the right you
+got to go all the way up to Paul Rivers
+
+ align:start position:0%
+got to go all the way up to Paul Rivers
+ 
+
+ align:start position:0%
+got to go all the way up to Paul Rivers
+uh sorry the north church and then come
+
+ align:start position:0%
+uh sorry the north church and then come
+ 
+
+ align:start position:0%
+uh sorry the north church and then come
+back along the other side you'll find a
+
+ align:start position:0%
+back along the other side you'll find a
+ 
+
+ align:start position:0%
+back along the other side you'll find a
+little quiet Courtyard and find that
+
+ align:start position:0%
+little quiet Courtyard and find that
+ 
+
+ align:start position:0%
+little quiet Courtyard and find that
+building that I spoke about that is
+
+ align:start position:0%
+building that I spoke about that is
+ 
+
+ align:start position:0%
+building that I spoke about that is
+hanging off the side so that's two
+
+ align:start position:0%
+hanging off the side so that's two
+ 
+
+ align:start position:0%
+hanging off the side so that's two
+things but walk around enjoy your
+
+ align:start position:0%
+things but walk around enjoy your
+ 
+
+ align:start position:0%
+things but walk around enjoy your
+and have a canoli or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coffee
\ No newline at end of file
diff --git a/apWRSZbJCyM.txt b/apWRSZbJCyM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f2ec7d12d06533a4941e0cbf53ddf74b2679ce38
--- /dev/null
+++ b/apWRSZbJCyM.txt
@@ -0,0 +1,6243 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think it brings together I think some
+
+ align:start position:0%
+I think it brings together I think some
+ 
+
+ align:start position:0%
+I think it brings together I think some
+of the administrators but also in fact
+
+ align:start position:0%
+of the administrators but also in fact
+ 
+
+ align:start position:0%
+of the administrators but also in fact
+the last word of the text or liberation
+
+ align:start position:0%
+the last word of the text or liberation
+ 
+
+ align:start position:0%
+the last word of the text or liberation
+my point of the week and the future so
+
+ align:start position:0%
+my point of the week and the future so
+ 
+
+ align:start position:0%
+my point of the week and the future so
+this is our presentation on language
+
+ align:start position:0%
+this is our presentation on language
+ 
+
+ align:start position:0%
+this is our presentation on language
+resistance in the liberation welcome to
+
+ align:start position:0%
+resistance in the liberation welcome to
+ 
+
+ align:start position:0%
+resistance in the liberation welcome to
+the last day of class congratulations so
+
+ align:start position:0%
+the last day of class congratulations so
+ 
+
+ align:start position:0%
+the last day of class congratulations so
+as a roadmap we're going to go through
+
+ align:start position:0%
+as a roadmap we're going to go through
+ 
+
+ align:start position:0%
+as a roadmap we're going to go through
+first rethinking literacy the dialogue
+
+ align:start position:0%
+first rethinking literacy the dialogue
+ 
+
+ align:start position:0%
+first rethinking literacy the dialogue
+the piece by ferry and Mikado get up
+
+ align:start position:0%
+the piece by ferry and Mikado get up
+ 
+
+ align:start position:0%
+the piece by ferry and Mikado get up
+Macedo and then we're going to look at
+
+ align:start position:0%
+Macedo and then we're going to look at
+ 
+
+ align:start position:0%
+Macedo and then we're going to look at
+the literacy in critical pedagogy piece
+
+ align:start position:0%
+the literacy in critical pedagogy piece
+ 
+
+ align:start position:0%
+the literacy in critical pedagogy piece
+and then end with the MIT hati hati
+
+ align:start position:0%
+and then end with the MIT hati hati
+ 
+
+ align:start position:0%
+and then end with the MIT hati hati
+initiatives okay so this is just a
+
+ align:start position:0%
+initiatives okay so this is just a
+ 
+
+ align:start position:0%
+initiatives okay so this is just a
+little bit of a background on the
+
+ align:start position:0%
+little bit of a background on the
+ 
+
+ align:start position:0%
+little bit of a background on the
+writers of the first two pieces both of
+
+ align:start position:0%
+writers of the first two pieces both of
+ 
+
+ align:start position:0%
+writers of the first two pieces both of
+them are educators and critical pedagogy
+
+ align:start position:0%
+them are educators and critical pedagogy
+ 
+
+ align:start position:0%
+them are educators and critical pedagogy
+and ones from Brazil and one is caper
+
+ align:start position:0%
+and ones from Brazil and one is caper
+ 
+
+ align:start position:0%
+and ones from Brazil and one is caper
+day an American so in the first piece
+
+ align:start position:0%
+day an American so in the first piece
+ 
+
+ align:start position:0%
+day an American so in the first piece
+fairy mentions the permit the main
+
+ align:start position:0%
+fairy mentions the permit the main
+ 
+
+ align:start position:0%
+fairy mentions the permit the main
+premises of culture and I think that
+
+ align:start position:0%
+premises of culture and I think that
+ 
+
+ align:start position:0%
+premises of culture and I think that
+these are really important to keep in
+
+ align:start position:0%
+these are really important to keep in
+ 
+
+ align:start position:0%
+these are really important to keep in
+mind because this is a really
+
+ align:start position:0%
+mind because this is a really
+ 
+
+ align:start position:0%
+mind because this is a really
+interesting and I think powerful way to
+
+ align:start position:0%
+interesting and I think powerful way to
+ 
+
+ align:start position:0%
+interesting and I think powerful way to
+frame culture the first one is that
+
+ align:start position:0%
+frame culture the first one is that
+ 
+
+ align:start position:0%
+frame culture the first one is that
+cultural cultural processes are
+
+ align:start position:0%
+cultural cultural processes are
+ 
+
+ align:start position:0%
+cultural cultural processes are
+intimately connected with social
+
+ align:start position:0%
+intimately connected with social
+ 
+
+ align:start position:0%
+intimately connected with social
+relations especially with class
+
+ align:start position:0%
+relations especially with class
+ 
+
+ align:start position:0%
+relations especially with class
+relations and class formations with
+
+ align:start position:0%
+relations and class formations with
+ 
+
+ align:start position:0%
+relations and class formations with
+sexual divisions with racial structuring
+
+ align:start position:0%
+sexual divisions with racial structuring
+ 
+
+ align:start position:0%
+sexual divisions with racial structuring
+and social relations and with age
+
+ align:start position:0%
+and social relations and with age
+ 
+
+ align:start position:0%
+and social relations and with age
+oppressions as a form of dependency got
+
+ align:start position:0%
+oppressions as a form of dependency got
+ 
+
+ align:start position:0%
+oppressions as a form of dependency got
+it the second one culture involves power
+
+ align:start position:0%
+it the second one culture involves power
+ 
+
+ align:start position:0%
+it the second one culture involves power
+and helps to produce asymmetries and the
+
+ align:start position:0%
+and helps to produce asymmetries and the
+ 
+
+ align:start position:0%
+and helps to produce asymmetries and the
+abilities of individuals and social
+
+ align:start position:0%
+abilities of individuals and social
+ 
+
+ align:start position:0%
+abilities of individuals and social
+groups to define and realize their needs
+
+ align:start position:0%
+groups to define and realize their needs
+ 
+
+ align:start position:0%
+groups to define and realize their needs
+and third one culture is neither
+
+ align:start position:0%
+and third one culture is neither
+ 
+
+ align:start position:0%
+and third one culture is neither
+autonomous nor an externally determined
+
+ align:start position:0%
+autonomous nor an externally determined
+ 
+
+ align:start position:0%
+autonomous nor an externally determined
+field but obsess but a site of social
+
+ align:start position:0%
+field but obsess but a site of social
+ 
+
+ align:start position:0%
+field but obsess but a site of social
+difficulties and struggles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those ideas are really important to keep
+
+ align:start position:0%
+those ideas are really important to keep
+ 
+
+ align:start position:0%
+those ideas are really important to keep
+in mind because this paper also raises
+
+ align:start position:0%
+in mind because this paper also raises
+ 
+
+ align:start position:0%
+in mind because this paper also raises
+this idea I know it is the social field
+
+ align:start position:0%
+this idea I know it is the social field
+ 
+
+ align:start position:0%
+this idea I know it is the social field
+which is kind of the combination of all
+
+ align:start position:0%
+which is kind of the combination of all
+ 
+
+ align:start position:0%
+which is kind of the combination of all
+of the beliefs myths aspirations hopes
+
+ align:start position:0%
+of the beliefs myths aspirations hopes
+ 
+
+ align:start position:0%
+of the beliefs myths aspirations hopes
+of a book of a society of a culture and
+
+ align:start position:0%
+of a book of a society of a culture and
+ 
+
+ align:start position:0%
+of a book of a society of a culture and
+so it's it includes things such as why
+
+ align:start position:0%
+so it's it includes things such as why
+ 
+
+ align:start position:0%
+so it's it includes things such as why
+racial hierarchies exist
+
+ align:start position:0%
+racial hierarchies exist
+ 
+
+ align:start position:0%
+racial hierarchies exist
+- why sexual divisions exist in like
+
+ align:start position:0%
+- why sexual divisions exist in like
+ 
+
+ align:start position:0%
+- why sexual divisions exist in like
+what roles gender gender people play in
+
+ align:start position:0%
+what roles gender gender people play in
+ 
+
+ align:start position:0%
+what roles gender gender people play in
+a society and it's really important to
+
+ align:start position:0%
+a society and it's really important to
+ 
+
+ align:start position:0%
+a society and it's really important to
+keep that in mind because if you're able
+
+ align:start position:0%
+keep that in mind because if you're able
+ 
+
+ align:start position:0%
+keep that in mind because if you're able
+to keep that in mind then you're able to
+
+ align:start position:0%
+to keep that in mind then you're able to
+ 
+
+ align:start position:0%
+to keep that in mind then you're able to
+think critically about that and through
+
+ align:start position:0%
+think critically about that and through
+ 
+
+ align:start position:0%
+think critically about that and through
+the critical process of engaging whether
+
+ align:start position:0%
+the critical process of engaging whether
+ 
+
+ align:start position:0%
+the critical process of engaging whether
+you're able to change the social field
+
+ align:start position:0%
+you're able to change the social field
+ 
+
+ align:start position:0%
+you're able to change the social field
+and so I think that that's important
+
+ align:start position:0%
+and so I think that that's important
+ 
+
+ align:start position:0%
+and so I think that that's important
+because even though this paper raises a
+
+ align:start position:0%
+because even though this paper raises a
+ 
+
+ align:start position:0%
+because even though this paper raises a
+lot of really powerful ideas it's still
+
+ align:start position:0%
+lot of really powerful ideas it's still
+ 
+
+ align:start position:0%
+lot of really powerful ideas it's still
+not perfect so one of the quotes of this
+
+ align:start position:0%
+not perfect so one of the quotes of this
+ 
+
+ align:start position:0%
+not perfect so one of the quotes of this
+paper is literacies oral dimension is
+
+ align:start position:0%
+paper is literacies oral dimension is
+ 
+
+ align:start position:0%
+paper is literacies oral dimension is
+important even if it takes place in a
+
+ align:start position:0%
+important even if it takes place in a
+ 
+
+ align:start position:0%
+important even if it takes place in a
+culture like that of the United States
+
+ align:start position:0%
+culture like that of the United States
+ 
+
+ align:start position:0%
+culture like that of the United States
+whose memory is predominately written
+
+ align:start position:0%
+whose memory is predominately written
+ 
+
+ align:start position:0%
+whose memory is predominately written
+not oral like that of Africa Africa is
+
+ align:start position:0%
+not oral like that of Africa Africa is
+ 
+
+ align:start position:0%
+not oral like that of Africa Africa is
+notic and so something like that is also
+
+ align:start position:0%
+notic and so something like that is also
+ 
+
+ align:start position:0%
+notic and so something like that is also
+part of the social field and would make
+
+ align:start position:0%
+part of the social field and would make
+ 
+
+ align:start position:0%
+part of the social field and would make
+it into this paper because even though
+
+ align:start position:0%
+it into this paper because even though
+ 
+
+ align:start position:0%
+it into this paper because even though
+ferry and Macedo are thinking critically
+
+ align:start position:0%
+ferry and Macedo are thinking critically
+ 
+
+ align:start position:0%
+ferry and Macedo are thinking critically
+about this they are not engaging with a
+
+ align:start position:0%
+about this they are not engaging with a
+ 
+
+ align:start position:0%
+about this they are not engaging with a
+full reality of cultural objectivity and
+
+ align:start position:0%
+full reality of cultural objectivity and
+ 
+
+ align:start position:0%
+full reality of cultural objectivity and
+being subjects within that yeah the next
+
+ align:start position:0%
+being subjects within that yeah the next
+ 
+
+ align:start position:0%
+being subjects within that yeah the next
+article Oliveri talks about the use of
+
+ align:start position:0%
+article Oliveri talks about the use of
+ 
+
+ align:start position:0%
+article Oliveri talks about the use of
+and he first starts talking about how
+
+ align:start position:0%
+and he first starts talking about how
+ 
+
+ align:start position:0%
+and he first starts talking about how
+the current traditional methods of
+
+ align:start position:0%
+the current traditional methods of
+ 
+
+ align:start position:0%
+the current traditional methods of
+literacy how they tend to ignore the
+
+ align:start position:0%
+literacy how they tend to ignore the
+ 
+
+ align:start position:0%
+literacy how they tend to ignore the
+importance of language in a person's
+
+ align:start position:0%
+importance of language in a person's
+ 
+
+ align:start position:0%
+importance of language in a person's
+education and he bases a lot of his
+
+ align:start position:0%
+education and he bases a lot of his
+ 
+
+ align:start position:0%
+education and he bases a lot of his
+theories on his experiences and from the
+
+ align:start position:0%
+theories on his experiences and from the
+ 
+
+ align:start position:0%
+theories on his experiences and from the
+second quote he says that the sad
+
+ align:start position:0%
+second quote he says that the sad
+ 
+
+ align:start position:0%
+second quote he says that the sad
+reality is that while education import
+
+ align:start position:0%
+reality is that while education import
+ 
+
+ align:start position:0%
+reality is that while education import
+provides access to positions of
+
+ align:start position:0%
+provides access to positions of
+ 
+
+ align:start position:0%
+provides access to positions of
+political and economic power for the
+
+ align:start position:0%
+political and economic power for the
+ 
+
+ align:start position:0%
+political and economic power for the
+high echelon of African society it
+
+ align:start position:0%
+high echelon of African society it
+ 
+
+ align:start position:0%
+high echelon of African society it
+screens out the majority of the masses
+
+ align:start position:0%
+screens out the majority of the masses
+ 
+
+ align:start position:0%
+screens out the majority of the masses
+who failed to learn Portuguese well
+
+ align:start position:0%
+who failed to learn Portuguese well
+ 
+
+ align:start position:0%
+who failed to learn Portuguese well
+enough to acquire the necessary literacy
+
+ align:start position:0%
+enough to acquire the necessary literacy
+ 
+
+ align:start position:0%
+enough to acquire the necessary literacy
+skills for social economic and political
+
+ align:start position:0%
+skills for social economic and political
+ 
+
+ align:start position:0%
+skills for social economic and political
+investment and you could definitely from
+
+ align:start position:0%
+investment and you could definitely from
+ 
+
+ align:start position:0%
+investment and you could definitely from
+the way that he mentions this you could
+
+ align:start position:0%
+the way that he mentions this you could
+ 
+
+ align:start position:0%
+the way that he mentions this you could
+definitely see a lot of like parallelism
+
+ align:start position:0%
+definitely see a lot of like parallelism
+ 
+
+ align:start position:0%
+definitely see a lot of like parallelism
+between what's going on around the world
+
+ align:start position:0%
+between what's going on around the world
+ 
+
+ align:start position:0%
+between what's going on around the world
+and eternity like in the United States
+
+ align:start position:0%
+and eternity like in the United States
+ 
+
+ align:start position:0%
+and eternity like in the United States
+and you could you could definitely see
+
+ align:start position:0%
+and you could you could definitely see
+ 
+
+ align:start position:0%
+and you could you could definitely see
+that the the one percent usually have
+
+ align:start position:0%
+that the the one percent usually have
+ 
+
+ align:start position:0%
+that the the one percent usually have
+the most control over things and that
+
+ align:start position:0%
+the most control over things and that
+ 
+
+ align:start position:0%
+the most control over things and that
+they usually tend to drive policies for
+
+ align:start position:0%
+they usually tend to drive policies for
+ 
+
+ align:start position:0%
+they usually tend to drive policies for
+me but the fact is that when a person is
+
+ align:start position:0%
+me but the fact is that when a person is
+ 
+
+ align:start position:0%
+me but the fact is that when a person is
+taught and during native language
+
+ align:start position:0%
+taught and during native language
+ 
+
+ align:start position:0%
+taught and during native language
+detents you learn things better and
+
+ align:start position:0%
+detents you learn things better and
+ 
+
+ align:start position:0%
+detents you learn things better and
+comprehend things faster and you go to
+
+ align:start position:0%
+comprehend things faster and you go to
+ 
+
+ align:start position:0%
+comprehend things faster and you go to
+the next lake there's usually backlash
+
+ align:start position:0%
+the next lake there's usually backlash
+ 
+
+ align:start position:0%
+the next lake there's usually backlash
+when it comes to different languages
+
+ align:start position:0%
+when it comes to different languages
+ 
+
+ align:start position:0%
+when it comes to different languages
+taught in schools for example in the
+
+ align:start position:0%
+taught in schools for example in the
+ 
+
+ align:start position:0%
+taught in schools for example in the
+u.s. people say that students should
+
+ align:start position:0%
+u.s. people say that students should
+ 
+
+ align:start position:0%
+u.s. people say that students should
+learn how to speak standard American
+
+ align:start position:0%
+learn how to speak standard American
+ 
+
+ align:start position:0%
+learn how to speak standard American
+English but when it comes to providing
+
+ align:start position:0%
+English but when it comes to providing
+ 
+
+ align:start position:0%
+English but when it comes to providing
+these sort of opportunities to minority
+
+ align:start position:0%
+these sort of opportunities to minority
+ 
+
+ align:start position:0%
+these sort of opportunities to minority
+group so I guess for instance like
+
+ align:start position:0%
+group so I guess for instance like
+ 
+
+ align:start position:0%
+group so I guess for instance like
+students of color there's usually some
+
+ align:start position:0%
+students of color there's usually some
+ 
+
+ align:start position:0%
+students of color there's usually some
+regional tensions that develop that that
+
+ align:start position:0%
+regional tensions that develop that that
+ 
+
+ align:start position:0%
+regional tensions that develop that that
+made minority students feel inferior
+
+ align:start position:0%
+made minority students feel inferior
+ 
+
+ align:start position:0%
+made minority students feel inferior
+for example there was an article
+
+ align:start position:0%
+for example there was an article
+ 
+
+ align:start position:0%
+for example there was an article
+mentioned like recently in like March of
+
+ align:start position:0%
+mentioned like recently in like March of
+ 
+
+ align:start position:0%
+mentioned like recently in like March of
+2017 that talked about a robotics team
+
+ align:start position:0%
+2017 that talked about a robotics team
+ 
+
+ align:start position:0%
+2017 that talked about a robotics team
+diversity that recently had won the
+
+ align:start position:0%
+diversity that recently had won the
+ 
+
+ align:start position:0%
+diversity that recently had won the
+challenge and the fact that after they
+
+ align:start position:0%
+challenge and the fact that after they
+ 
+
+ align:start position:0%
+challenge and the fact that after they
+had won students but I guess people in
+
+ align:start position:0%
+had won students but I guess people in
+ 
+
+ align:start position:0%
+had won students but I guess people in
+the crowd started screaming at them and
+
+ align:start position:0%
+the crowd started screaming at them and
+ 
+
+ align:start position:0%
+the crowd started screaming at them and
+telling them to go back to Mexico and so
+
+ align:start position:0%
+telling them to go back to Mexico and so
+ 
+
+ align:start position:0%
+telling them to go back to Mexico and so
+this form of like demeaning commentary
+
+ align:start position:0%
+this form of like demeaning commentary
+ 
+
+ align:start position:0%
+this form of like demeaning commentary
+tends to drive the dropout rate so
+
+ align:start position:0%
+tends to drive the dropout rate so
+ 
+
+ align:start position:0%
+tends to drive the dropout rate so
+minority groups and all this tends to
+
+ align:start position:0%
+minority groups and all this tends to
+ 
+
+ align:start position:0%
+minority groups and all this tends to
+contribute to like the prison sorry the
+
+ align:start position:0%
+contribute to like the prison sorry the
+ 
+
+ align:start position:0%
+contribute to like the prison sorry the
+school to Prison Pipeline has
+
+ align:start position:0%
+school to Prison Pipeline has
+ 
+
+ align:start position:0%
+school to Prison Pipeline has
+seen the infographic it definitely gives
+
+ align:start position:0%
+seen the infographic it definitely gives
+ 
+
+ align:start position:0%
+seen the infographic it definitely gives
+a lot of percentages on that talked
+
+ align:start position:0%
+a lot of percentages on that talked
+ 
+
+ align:start position:0%
+a lot of percentages on that talked
+about this sort of issue in the bottom
+
+ align:start position:0%
+about this sort of issue in the bottom
+ 
+
+ align:start position:0%
+about this sort of issue in the bottom
+when he says that 16% of all males in
+
+ align:start position:0%
+when he says that 16% of all males in
+ 
+
+ align:start position:0%
+when he says that 16% of all males in
+state and federal prison they do not
+
+ align:start position:0%
+state and federal prison they do not
+ 
+
+ align:start position:0%
+state and federal prison they do not
+have a high school diploma and this
+
+ align:start position:0%
+have a high school diploma and this
+ 
+
+ align:start position:0%
+have a high school diploma and this
+sense to me gives the statistics on
+
+ align:start position:0%
+sense to me gives the statistics on
+ 
+
+ align:start position:0%
+sense to me gives the statistics on
+students cooking and all of this 10th
+
+ align:start position:0%
+students cooking and all of this 10th
+ 
+
+ align:start position:0%
+students cooking and all of this 10th
+that tends to stem from the fact that
+
+ align:start position:0%
+that tends to stem from the fact that
+ 
+
+ align:start position:0%
+that tends to stem from the fact that
+minority students do not have the same
+
+ align:start position:0%
+minority students do not have the same
+ 
+
+ align:start position:0%
+minority students do not have the same
+access to education as you think our
+
+ align:start position:0%
+access to education as you think our
+ 
+
+ align:start position:0%
+access to education as you think our
+society and from personal experience I
+
+ align:start position:0%
+society and from personal experience I
+ 
+
+ align:start position:0%
+society and from personal experience I
+can definitely relate to this I went to
+
+ align:start position:0%
+can definitely relate to this I went to
+ 
+
+ align:start position:0%
+can definitely relate to this I went to
+school about like an hour and a half for
+
+ align:start position:0%
+school about like an hour and a half for
+ 
+
+ align:start position:0%
+school about like an hour and a half for
+my house and I definitely did have a lot
+
+ align:start position:0%
+my house and I definitely did have a lot
+ 
+
+ align:start position:0%
+my house and I definitely did have a lot
+of like good role models growing up but
+
+ align:start position:0%
+of like good role models growing up but
+ 
+
+ align:start position:0%
+of like good role models growing up but
+there were definitely and students
+
+ align:start position:0%
+there were definitely and students
+ 
+
+ align:start position:0%
+there were definitely and students
+around my neighborhood that didn't that
+
+ align:start position:0%
+around my neighborhood that didn't that
+ 
+
+ align:start position:0%
+around my neighborhood that didn't that
+definitely didn't have the same access
+
+ align:start position:0%
+definitely didn't have the same access
+ 
+
+ align:start position:0%
+definitely didn't have the same access
+to the same opportunities that I did
+
+ align:start position:0%
+to the same opportunities that I did
+ 
+
+ align:start position:0%
+to the same opportunities that I did
+some of them did drop out to serving
+
+ align:start position:0%
+some of them did drop out to serving
+ 
+
+ align:start position:0%
+some of them did drop out to serving
+others worried big gangs around my
+
+ align:start position:0%
+others worried big gangs around my
+ 
+
+ align:start position:0%
+others worried big gangs around my
+neighborhood and you could definitely
+
+ align:start position:0%
+neighborhood and you could definitely
+ 
+
+ align:start position:0%
+neighborhood and you could definitely
+these are definitely getting better but
+
+ align:start position:0%
+these are definitely getting better but
+ 
+
+ align:start position:0%
+these are definitely getting better but
+things could definitely be improved from
+
+ align:start position:0%
+things could definitely be improved from
+ 
+
+ align:start position:0%
+things could definitely be improved from
+any medicine that emancipatory literacy
+
+ align:start position:0%
+any medicine that emancipatory literacy
+ 
+
+ align:start position:0%
+any medicine that emancipatory literacy
+approach which is what Paula Ferry
+
+ align:start position:0%
+approach which is what Paula Ferry
+ 
+
+ align:start position:0%
+approach which is what Paula Ferry
+mentions yeah so in a monetary literacy
+
+ align:start position:0%
+mentions yeah so in a monetary literacy
+ 
+
+ align:start position:0%
+mentions yeah so in a monetary literacy
+this involves using the language of the
+
+ align:start position:0%
+this involves using the language of the
+ 
+
+ align:start position:0%
+this involves using the language of the
+people rather than the need to teach
+
+ align:start position:0%
+people rather than the need to teach
+ 
+
+ align:start position:0%
+people rather than the need to teach
+students to accept their experiences and
+
+ align:start position:0%
+students to accept their experiences and
+ 
+
+ align:start position:0%
+students to accept their experiences and
+their culture and this moves from the
+
+ align:start position:0%
+their culture and this moves from the
+ 
+
+ align:start position:0%
+their culture and this moves from the
+world of objectivity to the world of
+
+ align:start position:0%
+world of objectivity to the world of
+ 
+
+ align:start position:0%
+world of objectivity to the world of
+subjectivity where individuals learn to
+
+ align:start position:0%
+subjectivity where individuals learn to
+ 
+
+ align:start position:0%
+subjectivity where individuals learn to
+accept themselves for who they are
+
+ align:start position:0%
+accept themselves for who they are
+ 
+
+ align:start position:0%
+accept themselves for who they are
+rather than feel like they're a victim
+
+ align:start position:0%
+rather than feel like they're a victim
+ 
+
+ align:start position:0%
+rather than feel like they're a victim
+of society and pollen fury does mention
+
+ align:start position:0%
+of society and pollen fury does mention
+ 
+
+ align:start position:0%
+of society and pollen fury does mention
+that achieving emancipatory illiteracy
+
+ align:start position:0%
+that achieving emancipatory illiteracy
+ 
+
+ align:start position:0%
+that achieving emancipatory illiteracy
+is hard but it's not impossible and now
+
+ align:start position:0%
+is hard but it's not impossible and now
+ 
+
+ align:start position:0%
+is hard but it's not impossible and now
+and so learning was talked about a few
+
+ align:start position:0%
+and so learning was talked about a few
+ 
+
+ align:start position:0%
+and so learning was talked about a few
+examples of how this is being used today
+
+ align:start position:0%
+examples of how this is being used today
+ 
+
+ align:start position:0%
+examples of how this is being used today
+so considering specifically in the case
+
+ align:start position:0%
+so considering specifically in the case
+ 
+
+ align:start position:0%
+so considering specifically in the case
+of Haiti which Michelle works a lot on
+
+ align:start position:0%
+of Haiti which Michelle works a lot on
+ 
+
+ align:start position:0%
+of Haiti which Michelle works a lot on
+but that mighty Haiti initiative
+
+ align:start position:0%
+but that mighty Haiti initiative
+ 
+
+ align:start position:0%
+but that mighty Haiti initiative
+virtually all of the schooling in both K
+
+ align:start position:0%
+virtually all of the schooling in both K
+ 
+
+ align:start position:0%
+virtually all of the schooling in both K
+through 12 education and then
+
+ align:start position:0%
+through 12 education and then
+ 
+
+ align:start position:0%
+through 12 education and then
+higher education is done in French and
+
+ align:start position:0%
+higher education is done in French and
+ 
+
+ align:start position:0%
+higher education is done in French and
+not in Creole but the problem is that
+
+ align:start position:0%
+not in Creole but the problem is that
+ 
+
+ align:start position:0%
+not in Creole but the problem is that
+most people only speak Creole fluently
+
+ align:start position:0%
+most people only speak Creole fluently
+ 
+
+ align:start position:0%
+most people only speak Creole fluently
+so like 95 percent or so and very few
+
+ align:start position:0%
+so like 95 percent or so and very few
+ 
+
+ align:start position:0%
+so like 95 percent or so and very few
+people speak French fluently at all so
+
+ align:start position:0%
+people speak French fluently at all so
+ 
+
+ align:start position:0%
+people speak French fluently at all so
+when you go through school and
+
+ align:start position:0%
+when you go through school and
+ 
+
+ align:start position:0%
+when you go through school and
+everything is in a language that you
+
+ align:start position:0%
+everything is in a language that you
+ 
+
+ align:start position:0%
+everything is in a language that you
+don't understand how are you supposed to
+
+ align:start position:0%
+don't understand how are you supposed to
+ 
+
+ align:start position:0%
+don't understand how are you supposed to
+be able to actually get any of the
+
+ align:start position:0%
+be able to actually get any of the
+ 
+
+ align:start position:0%
+be able to actually get any of the
+education get any of the social
+
+ align:start position:0%
+education get any of the social
+ 
+
+ align:start position:0%
+education get any of the social
+engagement especially if children are
+
+ align:start position:0%
+engagement especially if children are
+ 
+
+ align:start position:0%
+engagement especially if children are
+punished for speaking Creole in school
+
+ align:start position:0%
+punished for speaking Creole in school
+ 
+
+ align:start position:0%
+punished for speaking Creole in school
+and they like can't interact with each
+
+ align:start position:0%
+and they like can't interact with each
+ 
+
+ align:start position:0%
+and they like can't interact with each
+other it can't ask questions can't
+
+ align:start position:0%
+other it can't ask questions can't
+ 
+
+ align:start position:0%
+other it can't ask questions can't
+gather any of the information that's
+
+ align:start position:0%
+gather any of the information that's
+ 
+
+ align:start position:0%
+gather any of the information that's
+coming at them so it's based on this
+
+ align:start position:0%
+coming at them so it's based on this
+ 
+
+ align:start position:0%
+coming at them so it's based on this
+false belief and really outdated belief
+
+ align:start position:0%
+false belief and really outdated belief
+ 
+
+ align:start position:0%
+false belief and really outdated belief
+about the hierarchy of languages about
+
+ align:start position:0%
+about the hierarchy of languages about
+ 
+
+ align:start position:0%
+about the hierarchy of languages about
+which languages are created or are
+
+ align:start position:0%
+which languages are created or are
+ 
+
+ align:start position:0%
+which languages are created or are
+younger or anything like that and that
+
+ align:start position:0%
+younger or anything like that and that
+ 
+
+ align:start position:0%
+younger or anything like that and that
+Creole isn't developed enough to be able
+
+ align:start position:0%
+Creole isn't developed enough to be able
+ 
+
+ align:start position:0%
+Creole isn't developed enough to be able
+to to be used for technical language for
+
+ align:start position:0%
+to to be used for technical language for
+ 
+
+ align:start position:0%
+to to be used for technical language for
+STEM education to have anything
+
+ align:start position:0%
+STEM education to have anything
+ 
+
+ align:start position:0%
+STEM education to have anything
+translated into Creole and part of that
+
+ align:start position:0%
+translated into Creole and part of that
+ 
+
+ align:start position:0%
+translated into Creole and part of that
+is saying that like Creole isn't
+
+ align:start position:0%
+is saying that like Creole isn't
+ 
+
+ align:start position:0%
+is saying that like Creole isn't
+widespread enough even though Creole has
+
+ align:start position:0%
+widespread enough even though Creole has
+ 
+
+ align:start position:0%
+widespread enough even though Creole has
+almost 10 million speakers finnish has
+
+ align:start position:0%
+almost 10 million speakers finnish has
+ 
+
+ align:start position:0%
+almost 10 million speakers finnish has
+only about 5.5 million speakers and yet
+
+ align:start position:0%
+only about 5.5 million speakers and yet
+ 
+
+ align:start position:0%
+only about 5.5 million speakers and yet
+in finland all of the education is done
+
+ align:start position:0%
+in finland all of the education is done
+ 
+
+ align:start position:0%
+in finland all of the education is done
+in finnish and people have studies have
+
+ align:start position:0%
+in finnish and people have studies have
+ 
+
+ align:start position:0%
+in finnish and people have studies have
+found that in finland kids are much
+
+ align:start position:0%
+found that in finland kids are much
+ 
+
+ align:start position:0%
+found that in finland kids are much
+better much better equipped to be able
+
+ align:start position:0%
+better much better equipped to be able
+ 
+
+ align:start position:0%
+better much better equipped to be able
+to learn a second language and to go
+
+ align:start position:0%
+to learn a second language and to go
+ 
+
+ align:start position:0%
+to learn a second language and to go
+into higher education and gather gather
+
+ align:start position:0%
+into higher education and gather gather
+ 
+
+ align:start position:0%
+into higher education and gather gather
+all of these like technical studies
+
+ align:start position:0%
+all of these like technical studies
+ 
+
+ align:start position:0%
+all of these like technical studies
+because all of their education is done
+
+ align:start position:0%
+because all of their education is done
+ 
+
+ align:start position:0%
+because all of their education is done
+in finnish and over i AP i was doing
+
+ align:start position:0%
+in finnish and over i AP i was doing
+ 
+
+ align:start position:0%
+in finnish and over i AP i was doing
+misty GTL in the Catalunya region in
+
+ align:start position:0%
+misty GTL in the Catalunya region in
+ 
+
+ align:start position:0%
+misty GTL in the Catalunya region in
+Spain and there
+
+ align:start position:0%
+Spain and there
+ 
+
+ align:start position:0%
+Spain and there
+Catalan also has a little under ten
+
+ align:start position:0%
+Catalan also has a little under ten
+ 
+
+ align:start position:0%
+Catalan also has a little under ten
+million speakers but in Catalunya all of
+
+ align:start position:0%
+million speakers but in Catalunya all of
+ 
+
+ align:start position:0%
+million speakers but in Catalunya all of
+the education is in Catalan which made
+
+ align:start position:0%
+the education is in Catalan which made
+ 
+
+ align:start position:0%
+the education is in Catalan which made
+it difficult for me as like a Spanish
+
+ align:start position:0%
+it difficult for me as like a Spanish
+ 
+
+ align:start position:0%
+it difficult for me as like a Spanish
+speaker like not even fluent but trying
+
+ align:start position:0%
+speaker like not even fluent but trying
+ 
+
+ align:start position:0%
+speaker like not even fluent but trying
+to speak Spanish speaker to be able to
+
+ align:start position:0%
+to speak Spanish speaker to be able to
+ 
+
+ align:start position:0%
+to speak Spanish speaker to be able to
+teach the students but they had such a
+
+ align:start position:0%
+teach the students but they had such a
+ 
+
+ align:start position:0%
+teach the students but they had such a
+better experience with all of their
+
+ align:start position:0%
+better experience with all of their
+ 
+
+ align:start position:0%
+better experience with all of their
+textbooks in Catalan all of their
+
+ align:start position:0%
+textbooks in Catalan all of their
+ 
+
+ align:start position:0%
+textbooks in Catalan all of their
+computer software so I was trying to
+
+ align:start position:0%
+computer software so I was trying to
+ 
+
+ align:start position:0%
+computer software so I was trying to
+teach them Inkscape and but
+
+ align:start position:0%
+teach them Inkscape and but
+ 
+
+ align:start position:0%
+teach them Inkscape and but
+everything was in Catalan and I just
+
+ align:start position:0%
+everything was in Catalan and I just
+ 
+
+ align:start position:0%
+everything was in Catalan and I just
+couldn't understand like even how to
+
+ align:start position:0%
+couldn't understand like even how to
+ 
+
+ align:start position:0%
+couldn't understand like even how to
+open a window um so they taught me a lot
+
+ align:start position:0%
+open a window um so they taught me a lot
+ 
+
+ align:start position:0%
+open a window um so they taught me a lot
+about this
+
+ align:start position:0%
+about this
+ 
+
+ align:start position:0%
+about this
+they all of them speak Catalan and
+
+ align:start position:0%
+they all of them speak Catalan and
+ 
+
+ align:start position:0%
+they all of them speak Catalan and
+Spanish and English and then they can
+
+ align:start position:0%
+Spanish and English and then they can
+ 
+
+ align:start position:0%
+Spanish and English and then they can
+like learn German or French on the side
+
+ align:start position:0%
+like learn German or French on the side
+ 
+
+ align:start position:0%
+like learn German or French on the side
+as well so all of them because their
+
+ align:start position:0%
+as well so all of them because their
+ 
+
+ align:start position:0%
+as well so all of them because their
+initial education K through 12 and then
+
+ align:start position:0%
+initial education K through 12 and then
+ 
+
+ align:start position:0%
+initial education K through 12 and then
+higher education if they want it to be
+
+ align:start position:0%
+higher education if they want it to be
+ 
+
+ align:start position:0%
+higher education if they want it to be
+is in Catalan then they can learn all of
+
+ align:start position:0%
+is in Catalan then they can learn all of
+ 
+
+ align:start position:0%
+is in Catalan then they can learn all of
+these other things just as well as we do
+
+ align:start position:0%
+these other things just as well as we do
+ 
+
+ align:start position:0%
+these other things just as well as we do
+like in English with it which is mostly
+
+ align:start position:0%
+like in English with it which is mostly
+ 
+
+ align:start position:0%
+like in English with it which is mostly
+our one and kind of only language in the
+
+ align:start position:0%
+our one and kind of only language in the
+ 
+
+ align:start position:0%
+our one and kind of only language in the
+United States yeah so that was my
+
+ align:start position:0%
+United States yeah so that was my
+ 
+
+ align:start position:0%
+United States yeah so that was my
+experience and what a school that is
+
+ align:start position:0%
+experience and what a school that is
+ 
+
+ align:start position:0%
+experience and what a school that is
+like a really good model in Haiti is the
+
+ align:start position:0%
+like a really good model in Haiti is the
+ 
+
+ align:start position:0%
+like a really good model in Haiti is the
+lkm school I didn't know how to
+
+ align:start position:0%
+lkm school I didn't know how to
+ 
+
+ align:start position:0%
+lkm school I didn't know how to
+pronounce it in Creole so South cam it's
+
+ align:start position:0%
+pronounce it in Creole so South cam it's
+ 
+
+ align:start position:0%
+pronounce it in Creole so South cam it's
+a k310 school in a rural part on an
+
+ align:start position:0%
+a k310 school in a rural part on an
+ 
+
+ align:start position:0%
+a k310 school in a rural part on an
+island of Haiti and their education is
+
+ align:start position:0%
+island of Haiti and their education is
+ 
+
+ align:start position:0%
+island of Haiti and their education is
+starting to be in this model of all
+
+ align:start position:0%
+starting to be in this model of all
+ 
+
+ align:start position:0%
+starting to be in this model of all
+Creole education trying to teach all of
+
+ align:start position:0%
+Creole education trying to teach all of
+ 
+
+ align:start position:0%
+Creole education trying to teach all of
+these subjects all of the technical
+
+ align:start position:0%
+these subjects all of the technical
+ 
+
+ align:start position:0%
+these subjects all of the technical
+terms in Creole and the students are
+
+ align:start position:0%
+terms in Creole and the students are
+ 
+
+ align:start position:0%
+terms in Creole and the students are
+learning much better than the rest of
+
+ align:start position:0%
+learning much better than the rest of
+ 
+
+ align:start position:0%
+learning much better than the rest of
+the students in Haiti who's schooling is
+
+ align:start position:0%
+the students in Haiti who's schooling is
+ 
+
+ align:start position:0%
+the students in Haiti who's schooling is
+at French and who only 10% graduate from
+
+ align:start position:0%
+at French and who only 10% graduate from
+ 
+
+ align:start position:0%
+at French and who only 10% graduate from
+high school
+
+ align:start position:0%
+high school
+ 
+
+ align:start position:0%
+high school
+so the linguistic apartheid part of this
+
+ align:start position:0%
+so the linguistic apartheid part of this
+ 
+
+ align:start position:0%
+so the linguistic apartheid part of this
+is that when you teach somebody in a
+
+ align:start position:0%
+is that when you teach somebody in a
+ 
+
+ align:start position:0%
+is that when you teach somebody in a
+language they don't understand you
+
+ align:start position:0%
+language they don't understand you
+ 
+
+ align:start position:0%
+language they don't understand you
+prevent them from being able to move
+
+ align:start position:0%
+prevent them from being able to move
+ 
+
+ align:start position:0%
+prevent them from being able to move
+into different socio-economic classes to
+
+ align:start position:0%
+into different socio-economic classes to
+ 
+
+ align:start position:0%
+into different socio-economic classes to
+attain the education and the success
+
+ align:start position:0%
+attain the education and the success
+ 
+
+ align:start position:0%
+attain the education and the success
+that they should be able to and this all
+
+ align:start position:0%
+that they should be able to and this all
+ 
+
+ align:start position:0%
+that they should be able to and this all
+leads to a mighty Haiti initiative that
+
+ align:start position:0%
+leads to a mighty Haiti initiative that
+ 
+
+ align:start position:0%
+leads to a mighty Haiti initiative that
+we shall started here between MIT and
+
+ align:start position:0%
+we shall started here between MIT and
+ 
+
+ align:start position:0%
+we shall started here between MIT and
+all the Haitian education systems so a
+
+ align:start position:0%
+all the Haitian education systems so a
+ 
+
+ align:start position:0%
+all the Haitian education systems so a
+couple of their main points are to teach
+
+ align:start position:0%
+couple of their main points are to teach
+ 
+
+ align:start position:0%
+couple of their main points are to teach
+educators in Haiti that teaching and
+
+ align:start position:0%
+educators in Haiti that teaching and
+ 
+
+ align:start position:0%
+educators in Haiti that teaching and
+creole is perfectly fine that it is
+
+ align:start position:0%
+creole is perfectly fine that it is
+ 
+
+ align:start position:0%
+creole is perfectly fine that it is
+actually better for the students that it
+
+ align:start position:0%
+actually better for the students that it
+ 
+
+ align:start position:0%
+actually better for the students that it
+gives them more opportunities and that
+
+ align:start position:0%
+gives them more opportunities and that
+ 
+
+ align:start position:0%
+gives them more opportunities and that
+stem and technical subjects can be
+
+ align:start position:0%
+stem and technical subjects can be
+ 
+
+ align:start position:0%
+stem and technical subjects can be
+taught in Creole so a lot of the worries
+
+ align:start position:0%
+taught in Creole so a lot of the worries
+ 
+
+ align:start position:0%
+taught in Creole so a lot of the worries
+or concerns are that like Creole doesn't
+
+ align:start position:0%
+or concerns are that like Creole doesn't
+ 
+
+ align:start position:0%
+or concerns are that like Creole doesn't
+have words for these languages we didn't
+
+ align:start position:0%
+have words for these languages we didn't
+ 
+
+ align:start position:0%
+have words for these languages we didn't
+have words for a computer either up
+
+ align:start position:0%
+have words for a computer either up
+ 
+
+ align:start position:0%
+have words for a computer either up
+until when they were created a lot of
+
+ align:start position:0%
+until when they were created a lot of
+ 
+
+ align:start position:0%
+until when they were created a lot of
+other languages borrow words from other
+
+ align:start position:0%
+other languages borrow words from other
+ 
+
+ align:start position:0%
+other languages borrow words from other
+languages so I learned Japanese and in
+
+ align:start position:0%
+languages so I learned Japanese and in
+ 
+
+ align:start position:0%
+languages so I learned Japanese and in
+Japanese there's this lovely thing
+
+ align:start position:0%
+Japanese there's this lovely thing
+ 
+
+ align:start position:0%
+Japanese there's this lovely thing
+called katakana where you just grab
+
+ align:start position:0%
+called katakana where you just grab
+ 
+
+ align:start position:0%
+called katakana where you just grab
+where it's your mother language so if
+
+ align:start position:0%
+where it's your mother language so if
+ 
+
+ align:start position:0%
+where it's your mother language so if
+you don't know how to pronounce it you
+
+ align:start position:0%
+you don't know how to pronounce it you
+ 
+
+ align:start position:0%
+you don't know how to pronounce it you
+kind of like make it sound like it and
+
+ align:start position:0%
+kind of like make it sound like it and
+ 
+
+ align:start position:0%
+kind of like make it sound like it and
+oftentimes it
+
+ align:start position:0%
+oftentimes it
+ 
+
+ align:start position:0%
+oftentimes it
+is what has been borrowed so for example
+
+ align:start position:0%
+is what has been borrowed so for example
+ 
+
+ align:start position:0%
+is what has been borrowed so for example
+bread is pun from German and all of
+
+ align:start position:0%
+bread is pun from German and all of
+ 
+
+ align:start position:0%
+bread is pun from German and all of
+these other languages have words
+
+ align:start position:0%
+these other languages have words
+ 
+
+ align:start position:0%
+these other languages have words
+borrowed from other languages and that's
+
+ align:start position:0%
+borrowed from other languages and that's
+ 
+
+ align:start position:0%
+borrowed from other languages and that's
+what globalization does so the same
+
+ align:start position:0%
+what globalization does so the same
+ 
+
+ align:start position:0%
+what globalization does so the same
+thing should be able to happen with
+
+ align:start position:0%
+thing should be able to happen with
+ 
+
+ align:start position:0%
+thing should be able to happen with
+Creole and stem learning and the really
+
+ align:start position:0%
+Creole and stem learning and the really
+ 
+
+ align:start position:0%
+Creole and stem learning and the really
+good results of this or that they
+
+ align:start position:0%
+good results of this or that they
+ 
+
+ align:start position:0%
+good results of this or that they
+affirmed students cultures and
+
+ align:start position:0%
+affirmed students cultures and
+ 
+
+ align:start position:0%
+affirmed students cultures and
+backgrounds and their own upbringing and
+
+ align:start position:0%
+backgrounds and their own upbringing and
+ 
+
+ align:start position:0%
+backgrounds and their own upbringing and
+how the society actually works as
+
+ align:start position:0%
+how the society actually works as
+ 
+
+ align:start position:0%
+how the society actually works as
+opposed to a colonial oppressive society
+
+ align:start position:0%
+opposed to a colonial oppressive society
+ 
+
+ align:start position:0%
+opposed to a colonial oppressive society
+and equalize the students being able to
+
+ align:start position:0%
+and equalize the students being able to
+ 
+
+ align:start position:0%
+and equalize the students being able to
+have more social mobility and to attain
+
+ align:start position:0%
+have more social mobility and to attain
+ 
+
+ align:start position:0%
+have more social mobility and to attain
+what they want and what they should be
+
+ align:start position:0%
+what they want and what they should be
+ 
+
+ align:start position:0%
+what they want and what they should be
+able to so to kind of tie this back to
+
+ align:start position:0%
+able to so to kind of tie this back to
+ 
+
+ align:start position:0%
+able to so to kind of tie this back to
+what we can do to stay woke with regards
+
+ align:start position:0%
+what we can do to stay woke with regards
+ 
+
+ align:start position:0%
+what we can do to stay woke with regards
+to literacy I think it's important to
+
+ align:start position:0%
+to literacy I think it's important to
+ 
+
+ align:start position:0%
+to literacy I think it's important to
+remember that language is a mediating
+
+ align:start position:0%
+remember that language is a mediating
+ 
+
+ align:start position:0%
+remember that language is a mediating
+force of knowledge but it is also
+
+ align:start position:0%
+force of knowledge but it is also
+ 
+
+ align:start position:0%
+force of knowledge but it is also
+knowledge itself and so one approach is
+
+ align:start position:0%
+knowledge itself and so one approach is
+ 
+
+ align:start position:0%
+knowledge itself and so one approach is
+for groups to kind of come together and
+
+ align:start position:0%
+for groups to kind of come together and
+ 
+
+ align:start position:0%
+for groups to kind of come together and
+create a language that describes their
+
+ align:start position:0%
+create a language that describes their
+ 
+
+ align:start position:0%
+create a language that describes their
+experience amongst themselves and then
+
+ align:start position:0%
+experience amongst themselves and then
+ 
+
+ align:start position:0%
+experience amongst themselves and then
+to share that language and to share that
+
+ align:start position:0%
+to share that language and to share that
+ 
+
+ align:start position:0%
+to share that language and to share that
+experience in their own in their own
+
+ align:start position:0%
+experience in their own in their own
+ 
+
+ align:start position:0%
+experience in their own in their own
+language and I think that that is one
+
+ align:start position:0%
+language and I think that that is one
+ 
+
+ align:start position:0%
+language and I think that that is one
+way that we can start breaking away from
+
+ align:start position:0%
+way that we can start breaking away from
+ 
+
+ align:start position:0%
+way that we can start breaking away from
+the kind of putting standard English on
+
+ align:start position:0%
+the kind of putting standard English on
+ 
+
+ align:start position:0%
+the kind of putting standard English on
+a pedestal and can also kind of validate
+
+ align:start position:0%
+a pedestal and can also kind of validate
+ 
+
+ align:start position:0%
+a pedestal and can also kind of validate
+other discourses and other ways of being
+
+ align:start position:0%
+other discourses and other ways of being
+ 
+
+ align:start position:0%
+other discourses and other ways of being
+and other just languages that kind of
+
+ align:start position:0%
+and other just languages that kind of
+ 
+
+ align:start position:0%
+and other just languages that kind of
+already exists in the US and across the
+
+ align:start position:0%
+already exists in the US and across the
+ 
+
+ align:start position:0%
+already exists in the US and across the
+world
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay how have our
+
+ align:start position:0%
+questions okay how have our
+ 
+
+ align:start position:0%
+questions okay how have our
+understandings of literacy evolved in
+
+ align:start position:0%
+understandings of literacy evolved in
+ 
+
+ align:start position:0%
+understandings of literacy evolved in
+response to the internet unprecedented
+
+ align:start position:0%
+response to the internet unprecedented
+ 
+
+ align:start position:0%
+response to the internet unprecedented
+global integration and increased
+
+ align:start position:0%
+global integration and increased
+ 
+
+ align:start position:0%
+global integration and increased
+pressure to preserve human rights for
+
+ align:start position:0%
+pressure to preserve human rights for
+ 
+
+ align:start position:0%
+pressure to preserve human rights for
+example what does it mean that schools
+
+ align:start position:0%
+example what does it mean that schools
+ 
+
+ align:start position:0%
+example what does it mean that schools
+repress the development of subjectivity
+
+ align:start position:0%
+repress the development of subjectivity
+ 
+
+ align:start position:0%
+repress the development of subjectivity
+but due largely ensure literacy
+
+ align:start position:0%
+but due largely ensure literacy
+ 
+
+ align:start position:0%
+but due largely ensure literacy
+how can modern notions of literacy
+
+ align:start position:0%
+how can modern notions of literacy
+ 
+
+ align:start position:0%
+how can modern notions of literacy
+evolved to address phenomena such as the
+
+ align:start position:0%
+evolved to address phenomena such as the
+ 
+
+ align:start position:0%
+evolved to address phenomena such as the
+prolific proliferation of fake news so
+
+ align:start position:0%
+prolific proliferation of fake news so
+ 
+
+ align:start position:0%
+prolific proliferation of fake news so
+if we're moving past literacy as just
+
+ align:start position:0%
+if we're moving past literacy as just
+ 
+
+ align:start position:0%
+if we're moving past literacy as just
+the idea of being able to read and we
+
+ align:start position:0%
+the idea of being able to read and we
+ 
+
+ align:start position:0%
+the idea of being able to read and we
+are entering this new kind of this new
+
+ align:start position:0%
+are entering this new kind of this new
+ 
+
+ align:start position:0%
+are entering this new kind of this new
+waving that's largely pushed by the
+
+ align:start position:0%
+waving that's largely pushed by the
+ 
+
+ align:start position:0%
+waving that's largely pushed by the
+Internet and the influence of Technology
+
+ align:start position:0%
+Internet and the influence of Technology
+ 
+
+ align:start position:0%
+Internet and the influence of Technology
+on the way we live literacy is coming to
+
+ align:start position:0%
+on the way we live literacy is coming to
+ 
+
+ align:start position:0%
+on the way we live literacy is coming to
+being a more critical approach to life
+
+ align:start position:0%
+being a more critical approach to life
+ 
+
+ align:start position:0%
+being a more critical approach to life
+in the sense that fake news is a thing
+
+ align:start position:0%
+in the sense that fake news is a thing
+ 
+
+ align:start position:0%
+in the sense that fake news is a thing
+you know and it's actually quite hard to
+
+ align:start position:0%
+you know and it's actually quite hard to
+ 
+
+ align:start position:0%
+you know and it's actually quite hard to
+distinguish what news is really what
+
+ align:start position:0%
+distinguish what news is really what
+ 
+
+ align:start position:0%
+distinguish what news is really what
+news is fake and the ability to do that
+
+ align:start position:0%
+news is fake and the ability to do that
+ 
+
+ align:start position:0%
+news is fake and the ability to do that
+having that critical lens is maybe the
+
+ align:start position:0%
+having that critical lens is maybe the
+ 
+
+ align:start position:0%
+having that critical lens is maybe the
+next evolution of literacy so any ideas
+
+ align:start position:0%
+next evolution of literacy so any ideas
+ 
+
+ align:start position:0%
+next evolution of literacy so any ideas
+that I guess is the question but
+
+ align:start position:0%
+that I guess is the question but
+ 
+
+ align:start position:0%
+that I guess is the question but
+something that I think is kind of
+
+ align:start position:0%
+something that I think is kind of
+ 
+
+ align:start position:0%
+something that I think is kind of
+hilarious about like integration the
+
+ align:start position:0%
+hilarious about like integration the
+ 
+
+ align:start position:0%
+hilarious about like integration the
+Internet is that I think it
+
+ align:start position:0%
+Internet is that I think it
+ 
+
+ align:start position:0%
+Internet is that I think it
+simultaneously making us more literate
+
+ align:start position:0%
+simultaneously making us more literate
+ 
+
+ align:start position:0%
+simultaneously making us more literate
+and less literate so like or like
+
+ align:start position:0%
+and less literate so like or like
+ 
+
+ align:start position:0%
+and less literate so like or like
+crushing me to be more literate so
+
+ align:start position:0%
+crushing me to be more literate so
+ 
+
+ align:start position:0%
+crushing me to be more literate so
+pressuring you to be more literate now
+
+ align:start position:0%
+pressuring you to be more literate now
+ 
+
+ align:start position:0%
+pressuring you to be more literate now
+there's a bunch of sources that you can
+
+ align:start position:0%
+there's a bunch of sources that you can
+ 
+
+ align:start position:0%
+there's a bunch of sources that you can
+read and like now you can be more
+
+ align:start position:0%
+read and like now you can be more
+ 
+
+ align:start position:0%
+read and like now you can be more
+educated it's all open to the public you
+
+ align:start position:0%
+educated it's all open to the public you
+ 
+
+ align:start position:0%
+educated it's all open to the public you
+have a computer and then there's also
+
+ align:start position:0%
+have a computer and then there's also
+ 
+
+ align:start position:0%
+have a computer and then there's also
+like the pressure to speak English
+
+ align:start position:0%
+like the pressure to speak English
+ 
+
+ align:start position:0%
+like the pressure to speak English
+properly based off either you know like
+
+ align:start position:0%
+properly based off either you know like
+ 
+
+ align:start position:0%
+properly based off either you know like
+this one viral videos old grandma's
+
+ align:start position:0%
+this one viral videos old grandma's
+ 
+
+ align:start position:0%
+this one viral videos old grandma's
+screaming at this
+
+ align:start position:0%
+screaming at this
+ 
+
+ align:start position:0%
+screaming at this
+I hop because she was paying in Spanish
+
+ align:start position:0%
+I hop because she was paying in Spanish
+ 
+
+ align:start position:0%
+I hop because she was paying in Spanish
+or something like that so like it puts
+
+ align:start position:0%
+or something like that so like it puts
+ 
+
+ align:start position:0%
+or something like that so like it puts
+pressure on you to speak English
+
+ align:start position:0%
+pressure on you to speak English
+ 
+
+ align:start position:0%
+pressure on you to speak English
+correctly and then meanwhile because of
+
+ align:start position:0%
+correctly and then meanwhile because of
+ 
+
+ align:start position:0%
+correctly and then meanwhile because of
+like things like Facebook and like any
+
+ align:start position:0%
+like things like Facebook and like any
+ 
+
+ align:start position:0%
+like things like Facebook and like any
+social media people like don't speak
+
+ align:start position:0%
+social media people like don't speak
+ 
+
+ align:start position:0%
+social media people like don't speak
+correctly like typing like you know
+
+ align:start position:0%
+correctly like typing like you know
+ 
+
+ align:start position:0%
+correctly like typing like you know
+abbreviations and stuff that's
+
+ align:start position:0%
+abbreviations and stuff that's
+ 
+
+ align:start position:0%
+abbreviations and stuff that's
+acceptable in tax but like meanwhile
+
+ align:start position:0%
+acceptable in tax but like meanwhile
+ 
+
+ align:start position:0%
+acceptable in tax but like meanwhile
+we're saying like you should speak
+
+ align:start position:0%
+we're saying like you should speak
+ 
+
+ align:start position:0%
+we're saying like you should speak
+English properly so it's kind of a weird
+
+ align:start position:0%
+English properly so it's kind of a weird
+ 
+
+ align:start position:0%
+English properly so it's kind of a weird
+dichotomy I'm interested in the age
+
+ align:start position:0%
+dichotomy I'm interested in the age
+ 
+
+ align:start position:0%
+dichotomy I'm interested in the age
+implications of what you just said kind
+
+ align:start position:0%
+implications of what you just said kind
+ 
+
+ align:start position:0%
+implications of what you just said kind
+of a lining kind of a critique towards
+
+ align:start position:0%
+of a lining kind of a critique towards
+ 
+
+ align:start position:0%
+of a lining kind of a critique towards
+the use of different varieties of
+
+ align:start position:0%
+the use of different varieties of
+ 
+
+ align:start position:0%
+the use of different varieties of
+English with older generations and the
+
+ align:start position:0%
+English with older generations and the
+ 
+
+ align:start position:0%
+English with older generations and the
+use of non-standard varieties of English
+
+ align:start position:0%
+use of non-standard varieties of English
+ 
+
+ align:start position:0%
+use of non-standard varieties of English
+with younger donations I'm interested in
+
+ align:start position:0%
+with younger donations I'm interested in
+ 
+
+ align:start position:0%
+with younger donations I'm interested in
+that yeah I think I mean I guess like so
+
+ align:start position:0%
+that yeah I think I mean I guess like so
+ 
+
+ align:start position:0%
+that yeah I think I mean I guess like so
+like there's a grandma that I know
+
+ align:start position:0%
+like there's a grandma that I know
+ 
+
+ align:start position:0%
+like there's a grandma that I know
+that's on Facebook and like she like
+
+ align:start position:0%
+that's on Facebook and like she like
+ 
+
+ align:start position:0%
+that's on Facebook and like she like
+make sure it's to like type everything
+
+ align:start position:0%
+make sure it's to like type everything
+ 
+
+ align:start position:0%
+make sure it's to like type everything
+out including punctuation like her
+
+ align:start position:0%
+out including punctuation like her
+ 
+
+ align:start position:0%
+out including punctuation like her
+facebook posts are longer and like
+
+ align:start position:0%
+facebook posts are longer and like
+ 
+
+ align:start position:0%
+facebook posts are longer and like
+they're more like here's a card I think
+
+ align:start position:0%
+they're more like here's a card I think
+ 
+
+ align:start position:0%
+they're more like here's a card I think
+today where is like my facebook a I'm
+
+ align:start position:0%
+today where is like my facebook a I'm
+ 
+
+ align:start position:0%
+today where is like my facebook a I'm
+just sharing things but B if I really
+
+ align:start position:0%
+just sharing things but B if I really
+ 
+
+ align:start position:0%
+just sharing things but B if I really
+think it's probably which so I think it
+
+ align:start position:0%
+think it's probably which so I think it
+ 
+
+ align:start position:0%
+think it's probably which so I think it
+does depend on like your age group but
+
+ align:start position:0%
+does depend on like your age group but
+ 
+
+ align:start position:0%
+does depend on like your age group but
+also like going back to the original
+
+ align:start position:0%
+also like going back to the original
+ 
+
+ align:start position:0%
+also like going back to the original
+point of like you know that grandma's
+
+ align:start position:0%
+point of like you know that grandma's
+ 
+
+ align:start position:0%
+point of like you know that grandma's
+screaming at the Hispanic woman and like
+
+ align:start position:0%
+screaming at the Hispanic woman and like
+ 
+
+ align:start position:0%
+screaming at the Hispanic woman and like
+an IHOP like it's not just like an older
+
+ align:start position:0%
+an IHOP like it's not just like an older
+ 
+
+ align:start position:0%
+an IHOP like it's not just like an older
+woman screaming because you know she's
+
+ align:start position:0%
+woman screaming because you know she's
+ 
+
+ align:start position:0%
+woman screaming because you know she's
+more illiterate like there's also like
+
+ align:start position:0%
+more illiterate like there's also like
+ 
+
+ align:start position:0%
+more illiterate like there's also like
+kids who like think like oh you have to
+
+ align:start position:0%
+kids who like think like oh you have to
+ 
+
+ align:start position:0%
+kids who like think like oh you have to
+speak English up here so like they're
+
+ align:start position:0%
+speak English up here so like they're
+ 
+
+ align:start position:0%
+speak English up here so like they're
+you still is that weirdness between like
+
+ align:start position:0%
+you still is that weirdness between like
+ 
+
+ align:start position:0%
+you still is that weirdness between like
+how like older people like act on
+
+ align:start position:0%
+how like older people like act on
+ 
+
+ align:start position:0%
+how like older people like act on
+facebook and stuff like that but I still
+
+ align:start position:0%
+facebook and stuff like that but I still
+ 
+
+ align:start position:0%
+facebook and stuff like that but I still
+think like the point of you know
+
+ align:start position:0%
+think like the point of you know
+ 
+
+ align:start position:0%
+think like the point of you know
+pressuring people is regardless of age
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think because I'm going to be talking
+
+ align:start position:0%
+I think because I'm going to be talking
+ 
+
+ align:start position:0%
+I think because I'm going to be talking
+about language which is dialects in this
+
+ align:start position:0%
+about language which is dialects in this
+ 
+
+ align:start position:0%
+about language which is dialects in this
+class I would kind of risk saying that
+
+ align:start position:0%
+class I would kind of risk saying that
+ 
+
+ align:start position:0%
+class I would kind of risk saying that
+we're kind of creating a new language
+
+ align:start position:0%
+we're kind of creating a new language
+ 
+
+ align:start position:0%
+we're kind of creating a new language
+because of the internet with like all
+
+ align:start position:0%
+because of the internet with like all
+ 
+
+ align:start position:0%
+because of the internet with like all
+the abbreviations and things and the way
+
+ align:start position:0%
+the abbreviations and things and the way
+ 
+
+ align:start position:0%
+the abbreviations and things and the way
+push for speed and everything like that
+
+ align:start position:0%
+push for speed and everything like that
+ 
+
+ align:start position:0%
+push for speed and everything like that
+so I think the reason that old
+
+ align:start position:0%
+so I think the reason that old
+ 
+
+ align:start position:0%
+so I think the reason that old
+generations don't use it as question
+
+ align:start position:0%
+generations don't use it as question
+ 
+
+ align:start position:0%
+generations don't use it as question
+because it I used to it and then like
+
+ align:start position:0%
+because it I used to it and then like
+ 
+
+ align:start position:0%
+because it I used to it and then like
+that differently frame of reference and
+
+ align:start position:0%
+that differently frame of reference and
+ 
+
+ align:start position:0%
+that differently frame of reference and
+they just haven't like learned this new
+
+ align:start position:0%
+they just haven't like learned this new
+ 
+
+ align:start position:0%
+they just haven't like learned this new
+dialect that we're starting to use so I
+
+ align:start position:0%
+dialect that we're starting to use so I
+ 
+
+ align:start position:0%
+dialect that we're starting to use so I
+think that it's a good thing in a sense
+
+ align:start position:0%
+think that it's a good thing in a sense
+ 
+
+ align:start position:0%
+think that it's a good thing in a sense
+but a lot of people who want that
+
+ align:start position:0%
+but a lot of people who want that
+ 
+
+ align:start position:0%
+but a lot of people who want that
+standard American English are going to
+
+ align:start position:0%
+standard American English are going to
+ 
+
+ align:start position:0%
+standard American English are going to
+be pushing us to go back to that as
+
+ align:start position:0%
+be pushing us to go back to that as
+ 
+
+ align:start position:0%
+be pushing us to go back to that as
+opposed to using the Internet in English
+
+ align:start position:0%
+opposed to using the Internet in English
+ 
+
+ align:start position:0%
+opposed to using the Internet in English
+the goys parts like our Cajun taste in
+
+ align:start position:0%
+the goys parts like our Cajun taste in
+ 
+
+ align:start position:0%
+the goys parts like our Cajun taste in
+literacy because of the internet like I
+
+ align:start position:0%
+literacy because of the internet like I
+ 
+
+ align:start position:0%
+literacy because of the internet like I
+didn't know that the onion was satire at
+
+ align:start position:0%
+didn't know that the onion was satire at
+ 
+
+ align:start position:0%
+didn't know that the onion was satire at
+first I said look at the end it existed
+
+ align:start position:0%
+first I said look at the end it existed
+ 
+
+ align:start position:0%
+first I said look at the end it existed
+and then I found I realized that it was
+
+ align:start position:0%
+and then I found I realized that it was
+ 
+
+ align:start position:0%
+and then I found I realized that it was
+satire I think step new ones like that
+
+ align:start position:0%
+satire I think step new ones like that
+ 
+
+ align:start position:0%
+satire I think step new ones like that
+is something that you miss especially
+
+ align:start position:0%
+is something that you miss especially
+ 
+
+ align:start position:0%
+is something that you miss especially
+with the internet because you can't
+
+ align:start position:0%
+with the internet because you can't
+ 
+
+ align:start position:0%
+with the internet because you can't
+really express sarcasm very clearly over
+
+ align:start position:0%
+really express sarcasm very clearly over
+ 
+
+ align:start position:0%
+really express sarcasm very clearly over
+just plain text I think that's something
+
+ align:start position:0%
+just plain text I think that's something
+ 
+
+ align:start position:0%
+just plain text I think that's something
+that we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I think that he said we talked about
+
+ align:start position:0%
+but I think that he said we talked about
+ 
+
+ align:start position:0%
+but I think that he said we talked about
+the onion I think that shows like that
+
+ align:start position:0%
+the onion I think that shows like that
+ 
+
+ align:start position:0%
+the onion I think that shows like that
+show that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I want to bounce up what you rich and he
+
+ align:start position:0%
+I want to bounce up what you rich and he
+ 
+
+ align:start position:0%
+I want to bounce up what you rich and he
+said like with like it's not a bad thing
+
+ align:start position:0%
+said like with like it's not a bad thing
+ 
+
+ align:start position:0%
+said like with like it's not a bad thing
+that we're tending my language I cream
+
+ align:start position:0%
+that we're tending my language I cream
+ 
+
+ align:start position:0%
+that we're tending my language I cream
+it like dimension do you think like
+
+ align:start position:0%
+it like dimension do you think like
+ 
+
+ align:start position:0%
+it like dimension do you think like
+there are certain rules like the way we
+
+ align:start position:0%
+there are certain rules like the way we
+ 
+
+ align:start position:0%
+there are certain rules like the way we
+type and laid there like illiterate like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like for instance punctuating substances
+
+ align:start position:0%
+like for instance punctuating substances
+ 
+
+ align:start position:0%
+like for instance punctuating substances
+with like lol oh haha
+
+ align:start position:0%
+with like lol oh haha
+ 
+
+ align:start position:0%
+with like lol oh haha
+I didn't realize my question is so
+
+ align:start position:0%
+I didn't realize my question is so
+ 
+
+ align:start position:0%
+I didn't realize my question is so
+knowing now that people grow up in a
+
+ align:start position:0%
+knowing now that people grow up in a
+ 
+
+ align:start position:0%
+knowing now that people grow up in a
+type of leaders into whether it's a
+
+ align:start position:0%
+type of leaders into whether it's a
+ 
+
+ align:start position:0%
+type of leaders into whether it's a
+tradition or emancipatory what are the
+
+ align:start position:0%
+tradition or emancipatory what are the
+ 
+
+ align:start position:0%
+tradition or emancipatory what are the
+pros and cons of your type of literacy
+
+ align:start position:0%
+pros and cons of your type of literacy
+ 
+
+ align:start position:0%
+pros and cons of your type of literacy
+and explain the moon why we should move
+
+ align:start position:0%
+and explain the moon why we should move
+ 
+
+ align:start position:0%
+and explain the moon why we should move
+either towards or away from it from an
+
+ align:start position:0%
+either towards or away from it from an
+ 
+
+ align:start position:0%
+either towards or away from it from an
+emancipatory leaders
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean if it's helping people learn I
+
+ align:start position:0%
+I mean if it's helping people learn I
+ 
+
+ align:start position:0%
+I mean if it's helping people learn I
+don't see Adama
+
+ align:start position:0%
+don't see Adama
+ 
+
+ align:start position:0%
+don't see Adama
+especially because it's kind of
+
+ align:start position:0%
+especially because it's kind of
+ 
+
+ align:start position:0%
+especially because it's kind of
+broadening their worldview a a couple of
+
+ align:start position:0%
+broadening their worldview a a couple of
+ 
+
+ align:start position:0%
+broadening their worldview a a couple of
+presentations ago there were the
+
+ align:start position:0%
+presentations ago there were the
+ 
+
+ align:start position:0%
+presentations ago there were the
+students who are playing jeopardy with
+
+ align:start position:0%
+students who are playing jeopardy with
+ 
+
+ align:start position:0%
+students who are playing jeopardy with
+AE and that was kind of like broadening
+
+ align:start position:0%
+AE and that was kind of like broadening
+ 
+
+ align:start position:0%
+AE and that was kind of like broadening
+their worldview like even if you went to
+
+ align:start position:0%
+their worldview like even if you went to
+ 
+
+ align:start position:0%
+their worldview like even if you went to
+the school and didn't speak any you are
+
+ align:start position:0%
+the school and didn't speak any you are
+ 
+
+ align:start position:0%
+the school and didn't speak any you are
+learning about a new language that you
+
+ align:start position:0%
+learning about a new language that you
+ 
+
+ align:start position:0%
+learning about a new language that you
+weren't familiar with and so they were
+
+ align:start position:0%
+weren't familiar with and so they were
+ 
+
+ align:start position:0%
+weren't familiar with and so they were
+able to do this through them inspiratory
+
+ align:start position:0%
+able to do this through them inspiratory
+ 
+
+ align:start position:0%
+able to do this through them inspiratory
+literacy what the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so kind of just play devil's advocate a
+
+ align:start position:0%
+so kind of just play devil's advocate a
+ 
+
+ align:start position:0%
+so kind of just play devil's advocate a
+little bit I think I guess one of the
+
+ align:start position:0%
+little bit I think I guess one of the
+ 
+
+ align:start position:0%
+little bit I think I guess one of the
+dangers of emancipatory
+
+ align:start position:0%
+dangers of emancipatory
+ 
+
+ align:start position:0%
+dangers of emancipatory
+that receipt might be kind of this non
+
+ align:start position:0%
+that receipt might be kind of this non
+ 
+
+ align:start position:0%
+that receipt might be kind of this non
+standardization like with initiatives
+
+ align:start position:0%
+standardization like with initiatives
+ 
+
+ align:start position:0%
+standardization like with initiatives
+like common core things like that we
+
+ align:start position:0%
+like common core things like that we
+ 
+
+ align:start position:0%
+like common core things like that we
+kind of have an educational system that
+
+ align:start position:0%
+kind of have an educational system that
+ 
+
+ align:start position:0%
+kind of have an educational system that
+setup so that everybody's kind of put on
+
+ align:start position:0%
+setup so that everybody's kind of put on
+ 
+
+ align:start position:0%
+setup so that everybody's kind of put on
+the same level to some extent like
+
+ align:start position:0%
+the same level to some extent like
+ 
+
+ align:start position:0%
+the same level to some extent like
+everybody has that same kind of baseline
+
+ align:start position:0%
+everybody has that same kind of baseline
+ 
+
+ align:start position:0%
+everybody has that same kind of baseline
+education but like with emancipatory
+
+ align:start position:0%
+education but like with emancipatory
+ 
+
+ align:start position:0%
+education but like with emancipatory
+literacy i think you're gonna find my
+
+ align:start position:0%
+literacy i think you're gonna find my
+ 
+
+ align:start position:0%
+literacy i think you're gonna find my
+educational programs are geared towards
+
+ align:start position:0%
+educational programs are geared towards
+ 
+
+ align:start position:0%
+educational programs are geared towards
+a specific like cultural norms and
+
+ align:start position:0%
+a specific like cultural norms and
+ 
+
+ align:start position:0%
+a specific like cultural norms and
+things that nature related to whatever
+
+ align:start position:0%
+things that nature related to whatever
+ 
+
+ align:start position:0%
+things that nature related to whatever
+population and targets so I wonder if
+
+ align:start position:0%
+population and targets so I wonder if
+ 
+
+ align:start position:0%
+population and targets so I wonder if
+that could potentially produce a system
+
+ align:start position:0%
+that could potentially produce a system
+ 
+
+ align:start position:0%
+that could potentially produce a system
+in which certain students even though
+
+ align:start position:0%
+in which certain students even though
+ 
+
+ align:start position:0%
+in which certain students even though
+they're receiving an education eyes
+
+ align:start position:0%
+they're receiving an education eyes
+ 
+
+ align:start position:0%
+they're receiving an education eyes
+appeared towards them it's objectively
+
+ align:start position:0%
+appeared towards them it's objectively
+ 
+
+ align:start position:0%
+appeared towards them it's objectively
+not that same quality of students who
+
+ align:start position:0%
+not that same quality of students who
+ 
+
+ align:start position:0%
+not that same quality of students who
+are would seem like more of a
+
+ align:start position:0%
+are would seem like more of a
+ 
+
+ align:start position:0%
+are would seem like more of a
+traditional approach I want to push back
+
+ align:start position:0%
+traditional approach I want to push back
+ 
+
+ align:start position:0%
+traditional approach I want to push back
+on that just a little bit because I
+
+ align:start position:0%
+on that just a little bit because I
+ 
+
+ align:start position:0%
+on that just a little bit because I
+think that the standardized approach to
+
+ align:start position:0%
+think that the standardized approach to
+ 
+
+ align:start position:0%
+think that the standardized approach to
+education is the approach that's been
+
+ align:start position:0%
+education is the approach that's been
+ 
+
+ align:start position:0%
+education is the approach that's been
+taken with the you know teach for test
+
+ align:start position:0%
+taken with the you know teach for test
+ 
+
+ align:start position:0%
+taken with the you know teach for test
+approach and it's failed it's been
+
+ align:start position:0%
+approach and it's failed it's been
+ 
+
+ align:start position:0%
+approach and it's failed it's been
+failing for a while now and I think that
+
+ align:start position:0%
+failing for a while now and I think that
+ 
+
+ align:start position:0%
+failing for a while now and I think that
+a lot of people in education policy and
+
+ align:start position:0%
+a lot of people in education policy and
+ 
+
+ align:start position:0%
+a lot of people in education policy and
+even just teachers are recognizing that
+
+ align:start position:0%
+even just teachers are recognizing that
+ 
+
+ align:start position:0%
+even just teachers are recognizing that
+now and I think that education
+
+ align:start position:0%
+now and I think that education
+ 
+
+ align:start position:0%
+now and I think that education
+emancipatory literacy gives us an
+
+ align:start position:0%
+emancipatory literacy gives us an
+ 
+
+ align:start position:0%
+emancipatory literacy gives us an
+interesting lens to think about how to
+
+ align:start position:0%
+interesting lens to think about how to
+ 
+
+ align:start position:0%
+interesting lens to think about how to
+educate people so that they can learn
+
+ align:start position:0%
+educate people so that they can learn
+ 
+
+ align:start position:0%
+educate people so that they can learn
+and I think maybe another place we can
+
+ align:start position:0%
+and I think maybe another place we can
+ 
+
+ align:start position:0%
+and I think maybe another place we can
+start kind of investing energy is
+
+ align:start position:0%
+start kind of investing energy is
+ 
+
+ align:start position:0%
+start kind of investing energy is
+thinking of ways in society that we can
+
+ align:start position:0%
+thinking of ways in society that we can
+ 
+
+ align:start position:0%
+thinking of ways in society that we can
+value those different ways of knowing
+
+ align:start position:0%
+value those different ways of knowing
+ 
+
+ align:start position:0%
+value those different ways of knowing
+and being and learning so that it's not
+
+ align:start position:0%
+and being and learning so that it's not
+ 
+
+ align:start position:0%
+and being and learning so that it's not
+just uh you went to college so you
+
+ align:start position:0%
+just uh you went to college so you
+ 
+
+ align:start position:0%
+just uh you went to college so you
+deserve to be paid a lot of money kind
+
+ align:start position:0%
+deserve to be paid a lot of money kind
+ 
+
+ align:start position:0%
+deserve to be paid a lot of money kind
+of thing and it's uh oh you can you know
+
+ align:start position:0%
+of thing and it's uh oh you can you know
+ 
+
+ align:start position:0%
+of thing and it's uh oh you can you know
+build the table from scratch how do you
+
+ align:start position:0%
+build the table from scratch how do you
+ 
+
+ align:start position:0%
+build the table from scratch how do you
+get paid to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think MIT is way far the tradition MIT
+
+ align:start position:0%
+I think MIT is way far the tradition MIT
+ 
+
+ align:start position:0%
+I think MIT is way far the tradition MIT
+is the alt-right of traditional
+
+ align:start position:0%
+is the alt-right of traditional
+ 
+
+ align:start position:0%
+is the alt-right of traditional
+literature I just think that there are I
+
+ align:start position:0%
+literature I just think that there are I
+ 
+
+ align:start position:0%
+literature I just think that there are I
+think that the the immense pressure that
+
+ align:start position:0%
+think that the the immense pressure that
+ 
+
+ align:start position:0%
+think that the the immense pressure that
+falls on students just on students
+
+ align:start position:0%
+falls on students just on students
+ 
+
+ align:start position:0%
+falls on students just on students
+physical bodies is definitely a symptom
+
+ align:start position:0%
+physical bodies is definitely a symptom
+ 
+
+ align:start position:0%
+physical bodies is definitely a symptom
+of a larger problem and for me the fact
+
+ align:start position:0%
+of a larger problem and for me the fact
+ 
+
+ align:start position:0%
+of a larger problem and for me the fact
+that that symptom is not enough of an
+
+ align:start position:0%
+that that symptom is not enough of an
+ 
+
+ align:start position:0%
+that that symptom is not enough of an
+impedance to change is heartbreaking
+
+ align:start position:0%
+impedance to change is heartbreaking
+ 
+
+ align:start position:0%
+impedance to change is heartbreaking
+because I think that I did I didn't I
+
+ align:start position:0%
+because I think that I did I didn't I
+ 
+
+ align:start position:0%
+because I think that I did I didn't I
+didn't come to college expecting it to
+
+ align:start position:0%
+didn't come to college expecting it to
+ 
+
+ align:start position:0%
+didn't come to college expecting it to
+be the four best four years of my life
+
+ align:start position:0%
+be the four best four years of my life
+ 
+
+ align:start position:0%
+be the four best four years of my life
+but I didn't come here also expecting to
+
+ align:start position:0%
+but I didn't come here also expecting to
+ 
+
+ align:start position:0%
+but I didn't come here also expecting to
+this suffering I think that there's
+
+ align:start position:0%
+this suffering I think that there's
+ 
+
+ align:start position:0%
+this suffering I think that there's
+definitely got to be a way where I can
+
+ align:start position:0%
+definitely got to be a way where I can
+ 
+
+ align:start position:0%
+definitely got to be a way where I can
+can bloom can reach my best potential
+
+ align:start position:0%
+can bloom can reach my best potential
+ 
+
+ align:start position:0%
+can bloom can reach my best potential
+and I love learning I love like I loved
+
+ align:start position:0%
+and I love learning I love like I loved
+ 
+
+ align:start position:0%
+and I love learning I love like I loved
+school you know and the fact that I yeah
+
+ align:start position:0%
+school you know and the fact that I yeah
+ 
+
+ align:start position:0%
+school you know and the fact that I yeah
+I have just kept running up against the
+
+ align:start position:0%
+I have just kept running up against the
+ 
+
+ align:start position:0%
+I have just kept running up against the
+institution I think as a creative person
+
+ align:start position:0%
+institution I think as a creative person
+ 
+
+ align:start position:0%
+institution I think as a creative person
+has made me kind of step back and think
+
+ align:start position:0%
+has made me kind of step back and think
+ 
+
+ align:start position:0%
+has made me kind of step back and think
+again about events but sorry literacy
+
+ align:start position:0%
+again about events but sorry literacy
+ 
+
+ align:start position:0%
+again about events but sorry literacy
+and how I can do that
+
+ align:start position:0%
+and how I can do that
+ 
+
+ align:start position:0%
+and how I can do that
+after given what you just said I want
+
+ align:start position:0%
+after given what you just said I want
+ 
+
+ align:start position:0%
+after given what you just said I want
+you to issue it to be mit president what
+
+ align:start position:0%
+you to issue it to be mit president what
+ 
+
+ align:start position:0%
+you to issue it to be mit president what
+would you change what how would you make
+
+ align:start position:0%
+would you change what how would you make
+ 
+
+ align:start position:0%
+would you change what how would you make
+it better
+
+ align:start position:0%
+it better
+ 
+
+ align:start position:0%
+it better
+more individually keeping in mind that
+
+ align:start position:0%
+more individually keeping in mind that
+ 
+
+ align:start position:0%
+more individually keeping in mind that
+maybe a certain cause I just reach in
+
+ align:start position:0%
+maybe a certain cause I just reach in
+ 
+
+ align:start position:0%
+maybe a certain cause I just reach in
+terms of a chemist how would you do that
+
+ align:start position:0%
+terms of a chemist how would you do that
+ 
+
+ align:start position:0%
+terms of a chemist how would you do that
+how would you how would you advise the
+
+ align:start position:0%
+how would you how would you advise the
+ 
+
+ align:start position:0%
+how would you how would you advise the
+ministration I think the very first
+
+ align:start position:0%
+ministration I think the very first
+ 
+
+ align:start position:0%
+ministration I think the very first
+thing I would do is have people who are
+
+ align:start position:0%
+thing I would do is have people who are
+ 
+
+ align:start position:0%
+thing I would do is have people who are
+more interested in research and not be
+
+ align:start position:0%
+more interested in research and not be
+ 
+
+ align:start position:0%
+more interested in research and not be
+professors so the ones who are
+
+ align:start position:0%
+professors so the ones who are
+ 
+
+ align:start position:0%
+professors so the ones who are
+interested in research should be doing
+
+ align:start position:0%
+interested in research should be doing
+ 
+
+ align:start position:0%
+interested in research should be doing
+research full-time and the people who
+
+ align:start position:0%
+research full-time and the people who
+ 
+
+ align:start position:0%
+research full-time and the people who
+are interested in teaching should teach
+
+ align:start position:0%
+are interested in teaching should teach
+ 
+
+ align:start position:0%
+are interested in teaching should teach
+because I think that that gives like a
+
+ align:start position:0%
+because I think that that gives like a
+ 
+
+ align:start position:0%
+because I think that that gives like a
+that gives people more impetus to just
+
+ align:start position:0%
+that gives people more impetus to just
+ 
+
+ align:start position:0%
+that gives people more impetus to just
+like connect with their students and
+
+ align:start position:0%
+like connect with their students and
+ 
+
+ align:start position:0%
+like connect with their students and
+actually get to know them and I think in
+
+ align:start position:0%
+actually get to know them and I think in
+ 
+
+ align:start position:0%
+actually get to know them and I think in
+that kind of environment you would
+
+ align:start position:0%
+that kind of environment you would
+ 
+
+ align:start position:0%
+that kind of environment you would
+foster like a safer healthier
+
+ align:start position:0%
+foster like a safer healthier
+ 
+
+ align:start position:0%
+foster like a safer healthier
+environment for learning whereas if you
+
+ align:start position:0%
+environment for learning whereas if you
+ 
+
+ align:start position:0%
+environment for learning whereas if you
+have a professor who is more interested
+
+ align:start position:0%
+have a professor who is more interested
+ 
+
+ align:start position:0%
+have a professor who is more interested
+in like winning the Nobel Prize like
+
+ align:start position:0%
+in like winning the Nobel Prize like
+ 
+
+ align:start position:0%
+in like winning the Nobel Prize like
+what are you like what do you do coming
+
+ align:start position:0%
+what are you like what do you do coming
+ 
+
+ align:start position:0%
+what are you like what do you do coming
+up against that I also would have MIT
+
+ align:start position:0%
+up against that I also would have MIT
+ 
+
+ align:start position:0%
+up against that I also would have MIT
+think very very hard about where the
+
+ align:start position:0%
+think very very hard about where the
+ 
+
+ align:start position:0%
+think very very hard about where the
+funding is coming from what it's going
+
+ align:start position:0%
+funding is coming from what it's going
+ 
+
+ align:start position:0%
+funding is coming from what it's going
+to and how that kind of fits in a global
+
+ align:start position:0%
+to and how that kind of fits in a global
+ 
+
+ align:start position:0%
+to and how that kind of fits in a global
+system where MIT as an institution fits
+
+ align:start position:0%
+system where MIT as an institution fits
+ 
+
+ align:start position:0%
+system where MIT as an institution fits
+in the global system as kind of
+
+ align:start position:0%
+in the global system as kind of
+ 
+
+ align:start position:0%
+in the global system as kind of
+not only an institution that does propel
+
+ align:start position:0%
+not only an institution that does propel
+ 
+
+ align:start position:0%
+not only an institution that does propel
+you to a higher class but kind of does
+
+ align:start position:0%
+you to a higher class but kind of does
+ 
+
+ align:start position:0%
+you to a higher class but kind of does
+that at the expense of a lot of other
+
+ align:start position:0%
+that at the expense of a lot of other
+ 
+
+ align:start position:0%
+that at the expense of a lot of other
+people and systems across the globe even
+
+ align:start position:0%
+people and systems across the globe even
+ 
+
+ align:start position:0%
+people and systems across the globe even
+if it's not directly in the area so I
+
+ align:start position:0%
+if it's not directly in the area so I
+ 
+
+ align:start position:0%
+if it's not directly in the area so I
+think that being more critical and
+
+ align:start position:0%
+think that being more critical and
+ 
+
+ align:start position:0%
+think that being more critical and
+intentional about our values and also
+
+ align:start position:0%
+intentional about our values and also
+ 
+
+ align:start position:0%
+intentional about our values and also
+maybe adding soul to the end of that the
+
+ align:start position:0%
+maybe adding soul to the end of that the
+ 
+
+ align:start position:0%
+maybe adding soul to the end of that the
+end of that of motto the last question
+
+ align:start position:0%
+end of that of motto the last question
+ 
+
+ align:start position:0%
+end of that of motto the last question
+is from your personal experiences or
+
+ align:start position:0%
+is from your personal experiences or
+ 
+
+ align:start position:0%
+is from your personal experiences or
+what you've seen or read about how do
+
+ align:start position:0%
+what you've seen or read about how do
+ 
+
+ align:start position:0%
+what you've seen or read about how do
+you think we can improve students
+
+ align:start position:0%
+you think we can improve students
+ 
+
+ align:start position:0%
+you think we can improve students
+experiences and confidence through
+
+ align:start position:0%
+experiences and confidence through
+ 
+
+ align:start position:0%
+experiences and confidence through
+intentional language use in schools like
+
+ align:start position:0%
+intentional language use in schools like
+ 
+
+ align:start position:0%
+intentional language use in schools like
+what mottos do you think are working or
+
+ align:start position:0%
+what mottos do you think are working or
+ 
+
+ align:start position:0%
+what mottos do you think are working or
+would work but it struggles to secure
+
+ align:start position:0%
+would work but it struggles to secure
+ 
+
+ align:start position:0%
+would work but it struggles to secure
+funding because it also doesn't follow a
+
+ align:start position:0%
+funding because it also doesn't follow a
+ 
+
+ align:start position:0%
+funding because it also doesn't follow a
+standardized Canadian curriculum in fact
+
+ align:start position:0%
+standardized Canadian curriculum in fact
+ 
+
+ align:start position:0%
+standardized Canadian curriculum in fact
+the community has sort of decolonized
+
+ align:start position:0%
+the community has sort of decolonized
+ 
+
+ align:start position:0%
+the community has sort of decolonized
+the curriculum and they teach history
+
+ align:start position:0%
+the curriculum and they teach history
+ 
+
+ align:start position:0%
+the curriculum and they teach history
+for instance not Canadian history they
+
+ align:start position:0%
+for instance not Canadian history they
+ 
+
+ align:start position:0%
+for instance not Canadian history they
+teach Mohawk history and it's been
+
+ align:start position:0%
+teach Mohawk history and it's been
+ 
+
+ align:start position:0%
+teach Mohawk history and it's been
+really affirming for children in the
+
+ align:start position:0%
+really affirming for children in the
+ 
+
+ align:start position:0%
+really affirming for children in the
+community especially a community that
+
+ align:start position:0%
+community especially a community that
+ 
+
+ align:start position:0%
+community especially a community that
+has its own struggles with language
+
+ align:start position:0%
+has its own struggles with language
+ 
+
+ align:start position:0%
+has its own struggles with language
+preservation and revitalization and
+
+ align:start position:0%
+preservation and revitalization and
+ 
+
+ align:start position:0%
+preservation and revitalization and
+passing on the language to continue
+
+ align:start position:0%
+passing on the language to continue
+ 
+
+ align:start position:0%
+passing on the language to continue
+generations especially after a history
+
+ align:start position:0%
+generations especially after a history
+ 
+
+ align:start position:0%
+generations especially after a history
+of residential schooling that you know
+
+ align:start position:0%
+of residential schooling that you know
+ 
+
+ align:start position:0%
+of residential schooling that you know
+main aim was a cultural and linguistic
+
+ align:start position:0%
+main aim was a cultural and linguistic
+ 
+
+ align:start position:0%
+main aim was a cultural and linguistic
+genocide of these people so this is a
+
+ align:start position:0%
+genocide of these people so this is a
+ 
+
+ align:start position:0%
+genocide of these people so this is a
+great model but it's funded entirely by
+
+ align:start position:0%
+great model but it's funded entirely by
+ 
+
+ align:start position:0%
+great model but it's funded entirely by
+a community
+
+ align:start position:0%
+a community
+ 
+
+ align:start position:0%
+a community
+razors and every year struggles with
+
+ align:start position:0%
+razors and every year struggles with
+ 
+
+ align:start position:0%
+razors and every year struggles with
+staying open and it's never certain that
+
+ align:start position:0%
+staying open and it's never certain that
+ 
+
+ align:start position:0%
+staying open and it's never certain that
+it'll be there in the next school year
+
+ align:start position:0%
+it'll be there in the next school year
+ 
+
+ align:start position:0%
+it'll be there in the next school year
+but it seems to have had a really really
+
+ align:start position:0%
+but it seems to have had a really really
+ 
+
+ align:start position:0%
+but it seems to have had a really really
+positive impact on the Mohawk community
+
+ align:start position:0%
+positive impact on the Mohawk community
+ 
+
+ align:start position:0%
+positive impact on the Mohawk community
+in Canada and so programs like that I
+
+ align:start position:0%
+in Canada and so programs like that I
+ 
+
+ align:start position:0%
+in Canada and so programs like that I
+think need to now be funded and that
+
+ align:start position:0%
+think need to now be funded and that
+ 
+
+ align:start position:0%
+think need to now be funded and that
+that involves challenging our our
+
+ align:start position:0%
+that involves challenging our our
+ 
+
+ align:start position:0%
+that involves challenging our our
+federal and local requirements not for
+
+ align:start position:0%
+federal and local requirements not for
+ 
+
+ align:start position:0%
+federal and local requirements not for
+funding and to do that we need to
+
+ align:start position:0%
+funding and to do that we need to
+ 
+
+ align:start position:0%
+funding and to do that we need to
+interrogate what value there is in the
+
+ align:start position:0%
+interrogate what value there is in the
+ 
+
+ align:start position:0%
+interrogate what value there is in the
+curricula we have standardized and why
+
+ align:start position:0%
+curricula we have standardized and why
+ 
+
+ align:start position:0%
+curricula we have standardized and why
+that is considered objectively like the
+
+ align:start position:0%
+that is considered objectively like the
+ 
+
+ align:start position:0%
+that is considered objectively like the
+standard that should impart the best
+
+ align:start position:0%
+standard that should impart the best
+ 
+
+ align:start position:0%
+standard that should impart the best
+learning experience upon students
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go ahead Colleen so bouncing up that and
+
+ align:start position:0%
+go ahead Colleen so bouncing up that and
+ 
+
+ align:start position:0%
+go ahead Colleen so bouncing up that and
+seems like we get to like ensuring the
+
+ align:start position:0%
+seems like we get to like ensuring the
+ 
+
+ align:start position:0%
+seems like we get to like ensuring the
+anything where the next platitudinous is
+
+ align:start position:0%
+anything where the next platitudinous is
+ 
+
+ align:start position:0%
+anything where the next platitudinous is
+inculcated in this like standard
+
+ align:start position:0%
+inculcated in this like standard
+ 
+
+ align:start position:0%
+inculcated in this like standard
+spherical goes into society and then way
+
+ align:start position:0%
+spherical goes into society and then way
+ 
+
+ align:start position:0%
+spherical goes into society and then way
+perpetuates a static critical back on V
+
+ align:start position:0%
+perpetuates a static critical back on V
+ 
+
+ align:start position:0%
+perpetuates a static critical back on V
+M students so I'm curious about if
+
+ align:start position:0%
+M students so I'm curious about if
+ 
+
+ align:start position:0%
+M students so I'm curious about if
+anyone has thoughts about how you could
+
+ align:start position:0%
+anyone has thoughts about how you could
+ 
+
+ align:start position:0%
+anyone has thoughts about how you could
+make knowledge about because one of the
+
+ align:start position:0%
+make knowledge about because one of the
+ 
+
+ align:start position:0%
+make knowledge about because one of the
+main hurdle is see the like instituting
+
+ align:start position:0%
+main hurdle is see the like instituting
+ 
+
+ align:start position:0%
+main hurdle is see the like instituting
+there's like entire continuation
+
+ align:start position:0%
+there's like entire continuation
+ 
+
+ align:start position:0%
+there's like entire continuation
+strictly chief about how the story of
+
+ align:start position:0%
+strictly chief about how the story of
+ 
+
+ align:start position:0%
+strictly chief about how the story of
+America's history has been with Garvey
+
+ align:start position:0%
+America's history has been with Garvey
+ 
+
+ align:start position:0%
+America's history has been with Garvey
+native and genocide slavery and the for
+
+ align:start position:0%
+native and genocide slavery and the for
+ 
+
+ align:start position:0%
+native and genocide slavery and the for
+lack of ever mean that is and best
+
+ align:start position:0%
+lack of ever mean that is and best
+ 
+
+ align:start position:0%
+lack of ever mean that is and best
+estimate how do you make people aware of
+
+ align:start position:0%
+estimate how do you make people aware of
+ 
+
+ align:start position:0%
+estimate how do you make people aware of
+that on a level that they can see those
+
+ align:start position:0%
+that on a level that they can see those
+ 
+
+ align:start position:0%
+that on a level that they can see those
+things playing out to pay and work to
+
+ align:start position:0%
+things playing out to pay and work to
+ 
+
+ align:start position:0%
+things playing out to pay and work to
+interior that curriculum especially
+
+ align:start position:0%
+interior that curriculum especially
+ 
+
+ align:start position:0%
+interior that curriculum especially
+they're coming from a background where
+
+ align:start position:0%
+they're coming from a background where
+ 
+
+ align:start position:0%
+they're coming from a background where
+like racism talk about center because
+
+ align:start position:0%
+like racism talk about center because
+ 
+
+ align:start position:0%
+like racism talk about center because
+it's an uncomfortable topic or if
+
+ align:start position:0%
+it's an uncomfortable topic or if
+ 
+
+ align:start position:0%
+it's an uncomfortable topic or if
+they're just like haven't heard about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+her manipulative clothes on to the where
+
+ align:start position:0%
+her manipulative clothes on to the where
+ 
+
+ align:start position:0%
+her manipulative clothes on to the where
+do you learn to interrogate your own
+
+ align:start position:0%
+do you learn to interrogate your own
+ 
+
+ align:start position:0%
+do you learn to interrogate your own
+beliefs and I feel like that's hard to
+
+ align:start position:0%
+beliefs and I feel like that's hard to
+ 
+
+ align:start position:0%
+beliefs and I feel like that's hard to
+find and I came to this class was like a
+
+ align:start position:0%
+find and I came to this class was like a
+ 
+
+ align:start position:0%
+find and I came to this class was like a
+key part of that for me and I don't know
+
+ align:start position:0%
+key part of that for me and I don't know
+ 
+
+ align:start position:0%
+key part of that for me and I don't know
+if that was because I got started up or
+
+ align:start position:0%
+if that was because I got started up or
+ 
+
+ align:start position:0%
+if that was because I got started up or
+just like I happened to stumble upon a
+
+ align:start position:0%
+just like I happened to stumble upon a
+ 
+
+ align:start position:0%
+just like I happened to stumble upon a
+place where I learned a Tara gave my
+
+ align:start position:0%
+place where I learned a Tara gave my
+ 
+
+ align:start position:0%
+place where I learned a Tara gave my
+beliefs but this isn't that a permit for
+
+ align:start position:0%
+beliefs but this isn't that a permit for
+ 
+
+ align:start position:0%
+beliefs but this isn't that a permit for
+themselves but I don't really have an
+
+ align:start position:0%
+themselves but I don't really have an
+ 
+
+ align:start position:0%
+themselves but I don't really have an
+answer for how we get choked with a
+
+ align:start position:0%
+answer for how we get choked with a
+ 
+
+ align:start position:0%
+answer for how we get choked with a
+value of interrogating kovalyonok how
+
+ align:start position:0%
+value of interrogating kovalyonok how
+ 
+
+ align:start position:0%
+value of interrogating kovalyonok how
+much more enriched your life is gonna be
+
+ align:start position:0%
+much more enriched your life is gonna be
+ 
+
+ align:start position:0%
+much more enriched your life is gonna be
+like you're just knocking off of that
+
+ align:start position:0%
+like you're just knocking off of that
+ 
+
+ align:start position:0%
+like you're just knocking off of that
+economy and possibly how do we have
+
+ align:start position:0%
+economy and possibly how do we have
+ 
+
+ align:start position:0%
+economy and possibly how do we have
+conversations with people who don't want
+
+ align:start position:0%
+conversations with people who don't want
+ 
+
+ align:start position:0%
+conversations with people who don't want
+to have this conversation and I think
+
+ align:start position:0%
+to have this conversation and I think
+ 
+
+ align:start position:0%
+to have this conversation and I think
+like the only way for them to figure out
+
+ align:start position:0%
+like the only way for them to figure out
+ 
+
+ align:start position:0%
+like the only way for them to figure out
+further to target yourselves but like
+
+ align:start position:0%
+further to target yourselves but like
+ 
+
+ align:start position:0%
+further to target yourselves but like
+most those people won't
+
+ align:start position:0%
+most those people won't
+ 
+
+ align:start position:0%
+most those people won't
+so like finding ways to tear it like to
+
+ align:start position:0%
+so like finding ways to tear it like to
+ 
+
+ align:start position:0%
+so like finding ways to tear it like to
+make them a target insult I think is it
+
+ align:start position:0%
+make them a target insult I think is it
+ 
+
+ align:start position:0%
+make them a target insult I think is it
+any like a common problem like
+
+ align:start position:0%
+any like a common problem like
+ 
+
+ align:start position:0%
+any like a common problem like
+throughout history and like
+
+ align:start position:0%
+throughout history and like
+ 
+
+ align:start position:0%
+throughout history and like
+unfortunately I don't know if I
+
+ align:start position:0%
+unfortunately I don't know if I
+ 
+
+ align:start position:0%
+unfortunately I don't know if I
+personally have a group like solution
+
+ align:start position:0%
+personally have a group like solution
+ 
+
+ align:start position:0%
+personally have a group like solution
+for that but I think like more
+
+ align:start position:0%
+for that but I think like more
+ 
+
+ align:start position:0%
+for that but I think like more
+opportunities like this I mean obviously
+
+ align:start position:0%
+opportunities like this I mean obviously
+ 
+
+ align:start position:0%
+opportunities like this I mean obviously
+like you mentioned this before like the
+
+ align:start position:0%
+like you mentioned this before like the
+ 
+
+ align:start position:0%
+like you mentioned this before like the
+people who are taking this class we're
+
+ align:start position:0%
+people who are taking this class we're
+ 
+
+ align:start position:0%
+people who are taking this class we're
+not really diversified in thought right
+
+ align:start position:0%
+not really diversified in thought right
+ 
+
+ align:start position:0%
+not really diversified in thought right
+like we all saw this class out mostly so
+
+ align:start position:0%
+like we all saw this class out mostly so
+ 
+
+ align:start position:0%
+like we all saw this class out mostly so
+I don't know how you can get someone who
+
+ align:start position:0%
+I don't know how you can get someone who
+ 
+
+ align:start position:0%
+I don't know how you can get someone who
+doesn't want to tarry saucily it was
+
+ align:start position:0%
+doesn't want to tarry saucily it was
+ 
+
+ align:start position:0%
+doesn't want to tarry saucily it was
+doing like this so maybe like mandating
+
+ align:start position:0%
+doing like this so maybe like mandating
+ 
+
+ align:start position:0%
+doing like this so maybe like mandating
+something like this where you have to go
+
+ align:start position:0%
+something like this where you have to go
+ 
+
+ align:start position:0%
+something like this where you have to go
+to like a black history class or a
+
+ align:start position:0%
+to like a black history class or a
+ 
+
+ align:start position:0%
+to like a black history class or a
+Native American history class or like
+
+ align:start position:0%
+Native American history class or like
+ 
+
+ align:start position:0%
+Native American history class or like
+whatever might force people to search
+
+ align:start position:0%
+whatever might force people to search
+ 
+
+ align:start position:0%
+whatever might force people to search
+yeah I almost think it might be better
+
+ align:start position:0%
+yeah I almost think it might be better
+ 
+
+ align:start position:0%
+yeah I almost think it might be better
+to not have a separate classroom this is
+
+ align:start position:0%
+to not have a separate classroom this is
+ 
+
+ align:start position:0%
+to not have a separate classroom this is
+your you know well-rounded miss class
+
+ align:start position:0%
+your you know well-rounded miss class
+ 
+
+ align:start position:0%
+your you know well-rounded miss class
+but this is when we're gonna learn about
+
+ align:start position:0%
+but this is when we're gonna learn about
+ 
+
+ align:start position:0%
+but this is when we're gonna learn about
+the others but to integrate what you
+
+ align:start position:0%
+the others but to integrate what you
+ 
+
+ align:start position:0%
+the others but to integrate what you
+would learn in a specific black history
+
+ align:start position:0%
+would learn in a specific black history
+ 
+
+ align:start position:0%
+would learn in a specific black history
+class into the general curriculum which
+
+ align:start position:0%
+class into the general curriculum which
+ 
+
+ align:start position:0%
+class into the general curriculum which
+of course is harder and but I do think
+
+ align:start position:0%
+of course is harder and but I do think
+ 
+
+ align:start position:0%
+of course is harder and but I do think
+would require the same amount of
+
+ align:start position:0%
+would require the same amount of
+ 
+
+ align:start position:0%
+would require the same amount of
+conversations and connections and
+
+ align:start position:0%
+conversations and connections and
+ 
+
+ align:start position:0%
+conversations and connections and
+negotiations as making a requirement you
+
+ align:start position:0%
+negotiations as making a requirement you
+ 
+
+ align:start position:0%
+negotiations as making a requirement you
+know of a separate class but I think
+
+ align:start position:0%
+know of a separate class but I think
+ 
+
+ align:start position:0%
+know of a separate class but I think
+that a better approach that might be
+
+ align:start position:0%
+that a better approach that might be
+ 
+
+ align:start position:0%
+that a better approach that might be
+more palatable and have more positive
+
+ align:start position:0%
+more palatable and have more positive
+ 
+
+ align:start position:0%
+more palatable and have more positive
+effects would be just turned up
+
+ align:start position:0%
+effects would be just turned up
+ 
+
+ align:start position:0%
+effects would be just turned up
+integration decolonizing the courage I
+
+ align:start position:0%
+integration decolonizing the courage I
+ 
+
+ align:start position:0%
+integration decolonizing the courage I
+told you I was gonna say I totally agree
+
+ align:start position:0%
+told you I was gonna say I totally agree
+ 
+
+ align:start position:0%
+told you I was gonna say I totally agree
+with Dana I think that um losing my
+
+ align:start position:0%
+with Dana I think that um losing my
+ 
+
+ align:start position:0%
+with Dana I think that um losing my
+train of thought I totally agree with
+
+ align:start position:0%
+train of thought I totally agree with
+ 
+
+ align:start position:0%
+train of thought I totally agree with
+Dana because I think that the history
+
+ align:start position:0%
+Dana because I think that the history
+ 
+
+ align:start position:0%
+Dana because I think that the history
+will speak for itself I think that
+
+ align:start position:0%
+will speak for itself I think that
+ 
+
+ align:start position:0%
+will speak for itself I think that
+history is like if you know they pulled
+
+ align:start position:0%
+history is like if you know they pulled
+ 
+
+ align:start position:0%
+history is like if you know they pulled
+a full history unlike the United States
+
+ align:start position:0%
+a full history unlike the United States
+ 
+
+ align:start position:0%
+a full history unlike the United States
+for example it's pretty it's pretty
+
+ align:start position:0%
+for example it's pretty it's pretty
+ 
+
+ align:start position:0%
+for example it's pretty it's pretty
+terrible and I think that you do need to
+
+ align:start position:0%
+terrible and I think that you do need to
+ 
+
+ align:start position:0%
+terrible and I think that you do need to
+know the whole history and also need to
+
+ align:start position:0%
+know the whole history and also need to
+ 
+
+ align:start position:0%
+know the whole history and also need to
+get the alternative sides and have those
+
+ align:start position:0%
+get the alternative sides and have those
+ 
+
+ align:start position:0%
+get the alternative sides and have those
+be like integrated into the curriculum I
+
+ align:start position:0%
+be like integrated into the curriculum I
+ 
+
+ align:start position:0%
+be like integrated into the curriculum I
+also was interested in I'm thinking
+
+ align:start position:0%
+also was interested in I'm thinking
+ 
+
+ align:start position:0%
+also was interested in I'm thinking
+about like entry points into these
+
+ align:start position:0%
+about like entry points into these
+ 
+
+ align:start position:0%
+about like entry points into these
+conversations in like ways that like art
+
+ align:start position:0%
+conversations in like ways that like art
+ 
+
+ align:start position:0%
+conversations in like ways that like art
+and humor can function as entry points
+
+ align:start position:0%
+and humor can function as entry points
+ 
+
+ align:start position:0%
+and humor can function as entry points
+in the conversations I've been having
+
+ align:start position:0%
+in the conversations I've been having
+ 
+
+ align:start position:0%
+in the conversations I've been having
+this conversation with a friend of mine
+
+ align:start position:0%
+this conversation with a friend of mine
+ 
+
+ align:start position:0%
+this conversation with a friend of mine
+of how like humor for example gives us a
+
+ align:start position:0%
+of how like humor for example gives us a
+ 
+
+ align:start position:0%
+of how like humor for example gives us a
+way to kind of express some of these
+
+ align:start position:0%
+way to kind of express some of these
+ 
+
+ align:start position:0%
+way to kind of express some of these
+things that are more taboo and kind of
+
+ align:start position:0%
+things that are more taboo and kind of
+ 
+
+ align:start position:0%
+things that are more taboo and kind of
+laughed them off and kind of like
+
+ align:start position:0%
+laughed them off and kind of like
+ 
+
+ align:start position:0%
+laughed them off and kind of like
+integrate them as opposed to everyone
+
+ align:start position:0%
+integrate them as opposed to everyone
+ 
+
+ align:start position:0%
+integrate them as opposed to everyone
+shutting them and people feeling bobbled
+
+ align:start position:0%
+shutting them and people feeling bobbled
+ 
+
+ align:start position:0%
+shutting them and people feeling bobbled
+so I am interested about like humor and
+
+ align:start position:0%
+so I am interested about like humor and
+ 
+
+ align:start position:0%
+so I am interested about like humor and
+art specifically as entry points into
+
+ align:start position:0%
+art specifically as entry points into
+ 
+
+ align:start position:0%
+art specifically as entry points into
+these conversations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Nina I think what she'll say no way
+
+ align:start position:0%
+Nina I think what she'll say no way
+ 
+
+ align:start position:0%
+Nina I think what she'll say no way
+answers the concern that should be
+
+ align:start position:0%
+answers the concern that should be
+ 
+
+ align:start position:0%
+answers the concern that should be
+expressed right so the good should be
+
+ align:start position:0%
+expressed right so the good should be
+ 
+
+ align:start position:0%
+expressed right so the good should be
+put it as is isn't dual Troy that's
+
+ align:start position:0%
+put it as is isn't dual Troy that's
+ 
+
+ align:start position:0%
+put it as is isn't dual Troy that's
+really do people do that right so if
+
+ align:start position:0%
+really do people do that right so if
+ 
+
+ align:start position:0%
+really do people do that right so if
+then ask is right right should be what
+
+ align:start position:0%
+then ask is right right should be what
+ 
+
+ align:start position:0%
+then ask is right right should be what
+could imagine I mean every class like
+
+ align:start position:0%
+could imagine I mean every class like
+ 
+
+ align:start position:0%
+could imagine I mean every class like
+very good twist
+
+ align:start position:0%
+very good twist
+ 
+
+ align:start position:0%
+very good twist
+critical math class chemistry class or
+
+ align:start position:0%
+critical math class chemistry class or
+ 
+
+ align:start position:0%
+critical math class chemistry class or
+being attention to those issues in
+
+ align:start position:0%
+being attention to those issues in
+ 
+
+ align:start position:0%
+being attention to those issues in
+Friday's roaming for that even even if
+
+ align:start position:0%
+Friday's roaming for that even even if
+ 
+
+ align:start position:0%
+Friday's roaming for that even even if
+you take it simple photographic one can
+
+ align:start position:0%
+you take it simple photographic one can
+ 
+
+ align:start position:0%
+you take it simple photographic one can
+even think about what kind of choice is
+
+ align:start position:0%
+even think about what kind of choice is
+ 
+
+ align:start position:0%
+even think about what kind of choice is
+going into making a camera and actually
+
+ align:start position:0%
+going into making a camera and actually
+ 
+
+ align:start position:0%
+going into making a camera and actually
+I have friends were photographers and
+
+ align:start position:0%
+I have friends were photographers and
+ 
+
+ align:start position:0%
+I have friends were photographers and
+they picked me that I feel most cameras
+
+ align:start position:0%
+they picked me that I feel most cameras
+ 
+
+ align:start position:0%
+they picked me that I feel most cameras
+were gonna deal to think because of
+
+ align:start position:0%
+were gonna deal to think because of
+ 
+
+ align:start position:0%
+were gonna deal to think because of
+black people so even there was a white
+
+ align:start position:0%
+black people so even there was a white
+ 
+
+ align:start position:0%
+black people so even there was a white
+of the record you fact that mean takes a
+
+ align:start position:0%
+of the record you fact that mean takes a
+ 
+
+ align:start position:0%
+of the record you fact that mean takes a
+picture with his regular Canon of the
+
+ align:start position:0%
+picture with his regular Canon of the
+ 
+
+ align:start position:0%
+picture with his regular Canon of the
+white person becomes much better in wind
+
+ align:start position:0%
+white person becomes much better in wind
+ 
+
+ align:start position:0%
+white person becomes much better in wind
+exit of the factors of why because the
+
+ align:start position:0%
+exit of the factors of why because the
+ 
+
+ align:start position:0%
+exit of the factors of why because the
+lenses are defined with with the
+
+ align:start position:0%
+lenses are defined with with the
+ 
+
+ align:start position:0%
+lenses are defined with with the
+dominant gaze of the white subject all
+
+ align:start position:0%
+dominant gaze of the white subject all
+ 
+
+ align:start position:0%
+dominant gaze of the white subject all
+right so in had to tweak it camera to
+
+ align:start position:0%
+right so in had to tweak it camera to
+ 
+
+ align:start position:0%
+right so in had to tweak it camera to
+make it take good pictures of black
+
+ align:start position:0%
+make it take good pictures of black
+ 
+
+ align:start position:0%
+make it take good pictures of black
+people so even there even in clean
+
+ align:start position:0%
+people so even there even in clean
+ 
+
+ align:start position:0%
+people so even there even in clean
+physics they should be a way to
+
+ align:start position:0%
+physics they should be a way to
+ 
+
+ align:start position:0%
+physics they should be a way to
+interrogate the the curriculum why
+
+ align:start position:0%
+interrogate the the curriculum why
+ 
+
+ align:start position:0%
+interrogate the the curriculum why
+internet in familial event a couple so
+
+ align:start position:0%
+internet in familial event a couple so
+ 
+
+ align:start position:0%
+internet in familial event a couple so
+in a way it could be both you could both
+
+ align:start position:0%
+in a way it could be both you could both
+ 
+
+ align:start position:0%
+in a way it could be both you could both
+have the military PTSD within the
+
+ align:start position:0%
+have the military PTSD within the
+ 
+
+ align:start position:0%
+have the military PTSD within the
+correct codes more recently and going
+
+ align:start position:0%
+correct codes more recently and going
+ 
+
+ align:start position:0%
+correct codes more recently and going
+back to the last point in American
+
+ align:start position:0%
+back to the last point in American
+ 
+
+ align:start position:0%
+back to the last point in American
+history in biology value to include text
+
+ align:start position:0%
+history in biology value to include text
+ 
+
+ align:start position:0%
+history in biology value to include text
+like I mentioned earlier is to conduct
+
+ align:start position:0%
+like I mentioned earlier is to conduct
+ 
+
+ align:start position:0%
+like I mentioned earlier is to conduct
+and the miss nature of man
+
+ align:start position:0%
+and the miss nature of man
+ 
+
+ align:start position:0%
+and the miss nature of man
+which was it's lots of difficult issues
+
+ align:start position:0%
+which was it's lots of difficult issues
+ 
+
+ align:start position:0%
+which was it's lots of difficult issues
+of ecology how we met hands were
+
+ align:start position:0%
+of ecology how we met hands were
+ 
+
+ align:start position:0%
+of ecology how we met hands were
+measures to show that limited
+
+ align:start position:0%
+measures to show that limited
+ 
+
+ align:start position:0%
+measures to show that limited
+intelligence for example for many years
+
+ align:start position:0%
+intelligence for example for many years
+ 
+
+ align:start position:0%
+intelligence for example for many years
+when you were coming in here to address
+
+ align:start position:0%
+when you were coming in here to address
+ 
+
+ align:start position:0%
+when you were coming in here to address
+and they will take a picture naked and
+
+ align:start position:0%
+and they will take a picture naked and
+ 
+
+ align:start position:0%
+and they will take a picture naked and
+they would look at a picture to decide
+
+ align:start position:0%
+they would look at a picture to decide
+ 
+
+ align:start position:0%
+they would look at a picture to decide
+what kind of student you will become mr.
+
+ align:start position:0%
+what kind of student you will become mr.
+ 
+
+ align:start position:0%
+what kind of student you will become mr.
+physical traits like of the attention of
+
+ align:start position:0%
+physical traits like of the attention of
+ 
+
+ align:start position:0%
+physical traits like of the attention of
+the most out of what was called and
+
+ align:start position:0%
+the most out of what was called and
+ 
+
+ align:start position:0%
+the most out of what was called and
+phenology you know which is the measure
+
+ align:start position:0%
+phenology you know which is the measure
+ 
+
+ align:start position:0%
+phenology you know which is the measure
+so there is plenty plenty of room to
+
+ align:start position:0%
+so there is plenty plenty of room to
+ 
+
+ align:start position:0%
+so there is plenty plenty of room to
+integrate within I I want to express the
+
+ align:start position:0%
+integrate within I I want to express the
+ 
+
+ align:start position:0%
+integrate within I I want to express the
+fact that to do such a thing is not just
+
+ align:start position:0%
+fact that to do such a thing is not just
+ 
+
+ align:start position:0%
+fact that to do such a thing is not just
+to include all of the the hushed
+
+ align:start position:0%
+to include all of the the hushed
+ 
+
+ align:start position:0%
+to include all of the the hushed
+historical abuses that we glossed over
+
+ align:start position:0%
+historical abuses that we glossed over
+ 
+
+ align:start position:0%
+historical abuses that we glossed over
+in our current like curricula but it's
+
+ align:start position:0%
+in our current like curricula but it's
+ 
+
+ align:start position:0%
+in our current like curricula but it's
+also to to acknowledge the good that we
+
+ align:start position:0%
+also to to acknowledge the good that we
+ 
+
+ align:start position:0%
+also to to acknowledge the good that we
+have overlooked so discoveries and
+
+ align:start position:0%
+have overlooked so discoveries and
+ 
+
+ align:start position:0%
+have overlooked so discoveries and
+innovations that other people who are
+
+ align:start position:0%
+innovations that other people who are
+ 
+
+ align:start position:0%
+innovations that other people who are
+not quote-unquote Western and who are
+
+ align:start position:0%
+not quote-unquote Western and who are
+ 
+
+ align:start position:0%
+not quote-unquote Western and who are
+not an Anglo American have made and
+
+ align:start position:0%
+not an Anglo American have made and
+ 
+
+ align:start position:0%
+not an Anglo American have made and
+contributed to the fields of science and
+
+ align:start position:0%
+contributed to the fields of science and
+ 
+
+ align:start position:0%
+contributed to the fields of science and
+history and literature so not only to
+
+ align:start position:0%
+history and literature so not only to
+ 
+
+ align:start position:0%
+history and literature so not only to
+recognize you know visa star goal evils
+
+ align:start position:0%
+recognize you know visa star goal evils
+ 
+
+ align:start position:0%
+recognize you know visa star goal evils
+but also rather grand positive impacts
+
+ align:start position:0%
+but also rather grand positive impacts
+ 
+
+ align:start position:0%
+but also rather grand positive impacts
+that others have had okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/b-PoEwPoRe8.txt b/b-PoEwPoRe8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a020f51f84b8cfa9b7ecddb363a2668ec6f28c07
--- /dev/null
+++ b/b-PoEwPoRe8.txt
@@ -0,0 +1,2888 @@
+align:start position:0%
+ 
+in the face of the challenges of climate
+
+ align:start position:0%
+in the face of the challenges of climate
+ 
+
+ align:start position:0%
+in the face of the challenges of climate
+change and depleting natural
+
+ align:start position:0%
+change and depleting natural
+ 
+
+ align:start position:0%
+change and depleting natural
+resources humans exploring feedable
+
+ align:start position:0%
+resources humans exploring feedable
+ 
+
+ align:start position:0%
+resources humans exploring feedable
+solutions to sustainable
+
+ align:start position:0%
+solutions to sustainable
+ 
+
+ align:start position:0%
+solutions to sustainable
+development Green Technology can can be
+
+ align:start position:0%
+development Green Technology can can be
+ 
+
+ align:start position:0%
+development Green Technology can can be
+one of the good
+
+ align:start position:0%
+one of the good
+ 
+
+ align:start position:0%
+one of the good
+options since 2009 Malaysia has been
+
+ align:start position:0%
+options since 2009 Malaysia has been
+ 
+
+ align:start position:0%
+options since 2009 Malaysia has been
+facilitating the application of Green
+
+ align:start position:0%
+facilitating the application of Green
+ 
+
+ align:start position:0%
+facilitating the application of Green
+Technology through implementing the
+
+ align:start position:0%
+Technology through implementing the
+ 
+
+ align:start position:0%
+Technology through implementing the
+national Green Technology
+
+ align:start position:0%
+national Green Technology
+ 
+
+ align:start position:0%
+national Green Technology
+policy over the centuries humans have
+
+ align:start position:0%
+policy over the centuries humans have
+ 
+
+ align:start position:0%
+policy over the centuries humans have
+tried to change the weather people have
+
+ align:start position:0%
+tried to change the weather people have
+ 
+
+ align:start position:0%
+tried to change the weather people have
+prayed and use strategies to get more
+
+ align:start position:0%
+prayed and use strategies to get more
+ 
+
+ align:start position:0%
+prayed and use strategies to get more
+rain and decrease the
+
+ align:start position:0%
+rain and decrease the
+ 
+
+ align:start position:0%
+rain and decrease the
+heat while we have not intentionally
+
+ align:start position:0%
+heat while we have not intentionally
+ 
+
+ align:start position:0%
+heat while we have not intentionally
+tried to change the climate we have
+
+ align:start position:0%
+tried to change the climate we have
+ 
+
+ align:start position:0%
+tried to change the climate we have
+unintentionally brought about changes
+
+ align:start position:0%
+unintentionally brought about changes
+ 
+
+ align:start position:0%
+unintentionally brought about changes
+that are affecting us
+
+ align:start position:0%
+that are affecting us
+ 
+
+ align:start position:0%
+that are affecting us
+today starting in the middle
+
+ align:start position:0%
+today starting in the middle
+ 
+
+ align:start position:0%
+today starting in the middle
+1700s the Industrial Revolution and
+
+ align:start position:0%
+1700s the Industrial Revolution and
+ 
+
+ align:start position:0%
+1700s the Industrial Revolution and
+modern agricultural practice began to
+
+ align:start position:0%
+modern agricultural practice began to
+ 
+
+ align:start position:0%
+modern agricultural practice began to
+alter the amount of human created carbon
+
+ align:start position:0%
+alter the amount of human created carbon
+ 
+
+ align:start position:0%
+alter the amount of human created carbon
+dioxide emissions in the
+
+ align:start position:0%
+dioxide emissions in the
+ 
+
+ align:start position:0%
+dioxide emissions in the
+atmosphere Global carbon dioxide
+
+ align:start position:0%
+atmosphere Global carbon dioxide
+ 
+
+ align:start position:0%
+atmosphere Global carbon dioxide
+emissions have been rising at an annual
+
+ align:start position:0%
+emissions have been rising at an annual
+ 
+
+ align:start position:0%
+emissions have been rising at an annual
+average of
+
+ align:start position:0%
+average of
+ 
+
+ align:start position:0%
+average of
+2.7% during the past decade countries
+
+ align:start position:0%
+2.7% during the past decade countries
+ 
+
+ align:start position:0%
+2.7% during the past decade countries
+all the world I use different techniques
+
+ align:start position:0%
+all the world I use different techniques
+ 
+
+ align:start position:0%
+all the world I use different techniques
+to reduce carbon
+
+ align:start position:0%
+to reduce carbon
+ 
+
+ align:start position:0%
+to reduce carbon
+emissions these include establishing
+
+ align:start position:0%
+emissions these include establishing
+ 
+
+ align:start position:0%
+emissions these include establishing
+carbon markets creating policy and
+
+ align:start position:0%
+carbon markets creating policy and
+ 
+
+ align:start position:0%
+carbon markets creating policy and
+legislation and Green
+
+ align:start position:0%
+legislation and Green
+ 
+
+ align:start position:0%
+legislation and Green
+Technology my research have focus on
+
+ align:start position:0%
+Technology my research have focus on
+ 
+
+ align:start position:0%
+Technology my research have focus on
+Green Technology in
+
+ align:start position:0%
+Green Technology in
+ 
+
+ align:start position:0%
+Green Technology in
+Malaysia but do you know what Green
+
+ align:start position:0%
+Malaysia but do you know what Green
+ 
+
+ align:start position:0%
+Malaysia but do you know what Green
+Technology is Green Technology is a
+
+ align:start position:0%
+Technology is Green Technology is a
+ 
+
+ align:start position:0%
+Technology is Green Technology is a
+development and application of products
+
+ align:start position:0%
+development and application of products
+ 
+
+ align:start position:0%
+development and application of products
+equipment and system
+
+ align:start position:0%
+equipment and system
+ 
+
+ align:start position:0%
+equipment and system
+that conserve natural
+
+ align:start position:0%
+that conserve natural
+ 
+
+ align:start position:0%
+that conserve natural
+resources which minimizes and reduce
+
+ align:start position:0%
+resources which minimizes and reduce
+ 
+
+ align:start position:0%
+resources which minimizes and reduce
+negative environmental impact of human
+
+ align:start position:0%
+negative environmental impact of human
+ 
+
+ align:start position:0%
+negative environmental impact of human
+activities what makes the technology
+
+ align:start position:0%
+activities what makes the technology
+ 
+
+ align:start position:0%
+activities what makes the technology
+green it minimize environmental
+
+ align:start position:0%
+green it minimize environmental
+ 
+
+ align:start position:0%
+green it minimize environmental
+degradation it has zero or low green gas
+
+ align:start position:0%
+degradation it has zero or low green gas
+ 
+
+ align:start position:0%
+degradation it has zero or low green gas
+emissions it is safe to use and promotes
+
+ align:start position:0%
+emissions it is safe to use and promotes
+ 
+
+ align:start position:0%
+emissions it is safe to use and promotes
+a healthy environmental for all life
+
+ align:start position:0%
+a healthy environmental for all life
+ 
+
+ align:start position:0%
+a healthy environmental for all life
+firms it conserves energy and natural
+
+ align:start position:0%
+firms it conserves energy and natural
+ 
+
+ align:start position:0%
+firms it conserves energy and natural
+resources
+
+ align:start position:0%
+resources
+ 
+
+ align:start position:0%
+resources
+it relies on renewable
+
+ align:start position:0%
+it relies on renewable
+ 
+
+ align:start position:0%
+it relies on renewable
+resources Green Technology is not New
+
+ align:start position:0%
+resources Green Technology is not New
+ 
+
+ align:start position:0%
+resources Green Technology is not New
+Concept people have been trying to go
+
+ align:start position:0%
+Concept people have been trying to go
+ 
+
+ align:start position:0%
+Concept people have been trying to go
+grein for decades including using wind
+
+ align:start position:0%
+grein for decades including using wind
+ 
+
+ align:start position:0%
+grein for decades including using wind
+Motors wind turbines solar power plants
+
+ align:start position:0%
+Motors wind turbines solar power plants
+ 
+
+ align:start position:0%
+Motors wind turbines solar power plants
+and other alternative energy ideas in
+
+ align:start position:0%
+and other alternative energy ideas in
+ 
+
+ align:start position:0%
+and other alternative energy ideas in
+keeping with global Trends Malaysia has
+
+ align:start position:0%
+keeping with global Trends Malaysia has
+ 
+
+ align:start position:0%
+keeping with global Trends Malaysia has
+recently proactively promoted and adopt
+
+ align:start position:0%
+recently proactively promoted and adopt
+ 
+
+ align:start position:0%
+recently proactively promoted and adopt
+Green Technology in 2009
+
+ align:start position:0%
+Green Technology in 2009
+ 
+
+ align:start position:0%
+Green Technology in 2009
+Malaysia established the country's
+
+ align:start position:0%
+Malaysia established the country's
+ 
+
+ align:start position:0%
+Malaysia established the country's
+Ministry of energy Green Technology and
+
+ align:start position:0%
+Ministry of energy Green Technology and
+ 
+
+ align:start position:0%
+Ministry of energy Green Technology and
+water also called Kaa in Malay and
+
+ align:start position:0%
+water also called Kaa in Malay and
+ 
+
+ align:start position:0%
+water also called Kaa in Malay and
+adopted National Green Technology
+
+ align:start position:0%
+adopted National Green Technology
+ 
+
+ align:start position:0%
+adopted National Green Technology
+policy the main goal is to contribute to
+
+ align:start position:0%
+policy the main goal is to contribute to
+ 
+
+ align:start position:0%
+policy the main goal is to contribute to
+economic growth and to reduce Malaysia's
+
+ align:start position:0%
+economic growth and to reduce Malaysia's
+ 
+
+ align:start position:0%
+economic growth and to reduce Malaysia's
+carbon footprint the objective of the
+
+ align:start position:0%
+carbon footprint the objective of the
+ 
+
+ align:start position:0%
+carbon footprint the objective of the
+policy is to connect industrial and
+
+ align:start position:0%
+policy is to connect industrial and
+ 
+
+ align:start position:0%
+policy is to connect industrial and
+government through supporting green
+
+ align:start position:0%
+government through supporting green
+ 
+
+ align:start position:0%
+government through supporting green
+buildings Green Transportation renewable
+
+ align:start position:0%
+buildings Green Transportation renewable
+ 
+
+ align:start position:0%
+buildings Green Transportation renewable
+energy use which and Water Management
+
+ align:start position:0%
+energy use which and Water Management
+ 
+
+ align:start position:0%
+energy use which and Water Management
+the most important components of this
+
+ align:start position:0%
+the most important components of this
+ 
+
+ align:start position:0%
+the most important components of this
+policy include setting up institutions
+
+ align:start position:0%
+policy include setting up institutions
+ 
+
+ align:start position:0%
+policy include setting up institutions
+and launching fiscal instruments setting
+
+ align:start position:0%
+and launching fiscal instruments setting
+ 
+
+ align:start position:0%
+and launching fiscal instruments setting
+up institutions is a key strategy in the
+
+ align:start position:0%
+up institutions is a key strategy in the
+ 
+
+ align:start position:0%
+up institutions is a key strategy in the
+policy since Green Technology involves
+
+ align:start position:0%
+policy since Green Technology involves
+ 
+
+ align:start position:0%
+policy since Green Technology involves
+many different sectors it is important
+
+ align:start position:0%
+many different sectors it is important
+ 
+
+ align:start position:0%
+many different sectors it is important
+to have a structure that involves all
+
+ align:start position:0%
+to have a structure that involves all
+ 
+
+ align:start position:0%
+to have a structure that involves all
+the relevant stakeholders to ensure
+
+ align:start position:0%
+the relevant stakeholders to ensure
+ 
+
+ align:start position:0%
+the relevant stakeholders to ensure
+consensus and support the national green
+
+ align:start position:0%
+consensus and support the national green
+ 
+
+ align:start position:0%
+consensus and support the national green
+technology and climate change Council
+
+ align:start position:0%
+technology and climate change Council
+ 
+
+ align:start position:0%
+technology and climate change Council
+coordinates Green Technology issues
+
+ align:start position:0%
+coordinates Green Technology issues
+ 
+
+ align:start position:0%
+coordinates Green Technology issues
+between the Ministries agencies the
+
+ align:start position:0%
+between the Ministries agencies the
+ 
+
+ align:start position:0%
+between the Ministries agencies the
+private sector and other stakeholders
+
+ align:start position:0%
+private sector and other stakeholders
+ 
+
+ align:start position:0%
+private sector and other stakeholders
+that Implement
+
+ align:start position:0%
+that Implement
+ 
+
+ align:start position:0%
+that Implement
+policies in addition the agencies that
+
+ align:start position:0%
+policies in addition the agencies that
+ 
+
+ align:start position:0%
+policies in addition the agencies that
+assist and contribute to development of
+
+ align:start position:0%
+assist and contribute to development of
+ 
+
+ align:start position:0%
+assist and contribute to development of
+Green Technology like the Green
+
+ align:start position:0%
+Green Technology like the Green
+ 
+
+ align:start position:0%
+Green Technology like the Green
+Technology Corporation as a focal point
+
+ align:start position:0%
+Technology Corporation as a focal point
+ 
+
+ align:start position:0%
+Technology Corporation as a focal point
+for Green Technology development in
+
+ align:start position:0%
+for Green Technology development in
+ 
+
+ align:start position:0%
+for Green Technology development in
+Malaysia Green Technology cooperation
+
+ align:start position:0%
+Malaysia Green Technology cooperation
+ 
+
+ align:start position:0%
+Malaysia Green Technology cooperation
+provide facilities and the services in
+
+ align:start position:0%
+provide facilities and the services in
+ 
+
+ align:start position:0%
+provide facilities and the services in
+advisory and consultancy and energy
+
+ align:start position:0%
+advisory and consultancy and energy
+ 
+
+ align:start position:0%
+advisory and consultancy and energy
+management and training Malaysia Green
+
+ align:start position:0%
+management and training Malaysia Green
+ 
+
+ align:start position:0%
+management and training Malaysia Green
+Technology Finance scheme is the most
+
+ align:start position:0%
+Technology Finance scheme is the most
+ 
+
+ align:start position:0%
+Technology Finance scheme is the most
+important fiscal instruments to attract
+
+ align:start position:0%
+important fiscal instruments to attract
+ 
+
+ align:start position:0%
+important fiscal instruments to attract
+private entities to use green
+
+ align:start position:0%
+private entities to use green
+ 
+
+ align:start position:0%
+private entities to use green
+technology this scheme is for both the
+
+ align:start position:0%
+technology this scheme is for both the
+ 
+
+ align:start position:0%
+technology this scheme is for both the
+users and producers of Green Technology
+
+ align:start position:0%
+users and producers of Green Technology
+ 
+
+ align:start position:0%
+users and producers of Green Technology
+it was initially started with a 1.5
+
+ align:start position:0%
+it was initially started with a 1.5
+ 
+
+ align:start position:0%
+it was initially started with a 1.5
+billion R soft loan and has now
+
+ align:start position:0%
+billion R soft loan and has now
+ 
+
+ align:start position:0%
+billion R soft loan and has now
+increased to 3.5 5 billion rates the
+
+ align:start position:0%
+increased to 3.5 5 billion rates the
+ 
+
+ align:start position:0%
+increased to 3.5 5 billion rates the
+scheme offers a 2% interest subsidy and
+
+ align:start position:0%
+scheme offers a 2% interest subsidy and
+ 
+
+ align:start position:0%
+scheme offers a 2% interest subsidy and
+60% of the loan will be guaranteed by
+
+ align:start position:0%
+60% of the loan will be guaranteed by
+ 
+
+ align:start position:0%
+60% of the loan will be guaranteed by
+the government from 2009 to November
+
+ align:start position:0%
+the government from 2009 to November
+ 
+
+ align:start position:0%
+the government from 2009 to November
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+351 projects were covered by this schem
+
+ align:start position:0%
+351 projects were covered by this schem
+ 
+
+ align:start position:0%
+351 projects were covered by this schem
+including 243 Energy Efficiency projects
+
+ align:start position:0%
+including 243 Energy Efficiency projects
+ 
+
+ align:start position:0%
+including 243 Energy Efficiency projects
+17 green building projects 91 waste and
+
+ align:start position:0%
+17 green building projects 91 waste and
+ 
+
+ align:start position:0%
+17 green building projects 91 waste and
+water projects the majority of projects
+
+ align:start position:0%
+water projects the majority of projects
+ 
+
+ align:start position:0%
+water projects the majority of projects
+are located in in Kumo silano and
+
+ align:start position:0%
+are located in in Kumo silano and
+ 
+
+ align:start position:0%
+are located in in Kumo silano and
+jalo most of project focus on electrical
+
+ align:start position:0%
+jalo most of project focus on electrical
+ 
+
+ align:start position:0%
+jalo most of project focus on electrical
+electronics sub sector and bi technology
+
+ align:start position:0%
+electronics sub sector and bi technology
+ 
+
+ align:start position:0%
+electronics sub sector and bi technology
+sub sector besides action stipulated
+
+ align:start position:0%
+sub sector besides action stipulated
+ 
+
+ align:start position:0%
+sub sector besides action stipulated
+from the ministry level we can also see
+
+ align:start position:0%
+from the ministry level we can also see
+ 
+
+ align:start position:0%
+from the ministry level we can also see
+some progress at a regional level isanda
+
+ align:start position:0%
+some progress at a regional level isanda
+ 
+
+ align:start position:0%
+some progress at a regional level isanda
+Malaysia is an important economic
+
+ align:start position:0%
+Malaysia is an important economic
+ 
+
+ align:start position:0%
+Malaysia is an important economic
+Corridor in the southern part of
+
+ align:start position:0%
+Corridor in the southern part of
+ 
+
+ align:start position:0%
+Corridor in the southern part of
+penisula Malaysia it has recently begun
+
+ align:start position:0%
+penisula Malaysia it has recently begun
+ 
+
+ align:start position:0%
+penisula Malaysia it has recently begun
+low carbon programs the low carbon GR
+
+ align:start position:0%
+low carbon programs the low carbon GR
+ 
+
+ align:start position:0%
+low carbon programs the low carbon GR
+isanda Malaysia
+
+ align:start position:0%
+isanda Malaysia
+ 
+
+ align:start position:0%
+isanda Malaysia
+2025 was endorsed by the prime minister
+
+ align:start position:0%
+2025 was endorsed by the prime minister
+ 
+
+ align:start position:0%
+2025 was endorsed by the prime minister
+of Malaysia in December
+
+ align:start position:0%
+of Malaysia in December
+ 
+
+ align:start position:0%
+of Malaysia in December
+202 this blueprint was prepared by a
+
+ align:start position:0%
+202 this blueprint was prepared by a
+ 
+
+ align:start position:0%
+202 this blueprint was prepared by a
+group of urban planners and
+
+ align:start position:0%
+group of urban planners and
+ 
+
+ align:start position:0%
+group of urban planners and
+researchers Professor hon chinon from
+
+ align:start position:0%
+researchers Professor hon chinon from
+ 
+
+ align:start position:0%
+researchers Professor hon chinon from
+University technology Malaysia is a main
+
+ align:start position:0%
+University technology Malaysia is a main
+ 
+
+ align:start position:0%
+University technology Malaysia is a main
+member of this team I think Green
+
+ align:start position:0%
+member of this team I think Green
+ 
+
+ align:start position:0%
+member of this team I think Green
+Technology policy uh is a very important
+
+ align:start position:0%
+Technology policy uh is a very important
+ 
+
+ align:start position:0%
+Technology policy uh is a very important
+policy because uh it focus on the use of
+
+ align:start position:0%
+policy because uh it focus on the use of
+ 
+
+ align:start position:0%
+policy because uh it focus on the use of
+Green Technology in city building or
+
+ align:start position:0%
+Green Technology in city building or
+ 
+
+ align:start position:0%
+Green Technology in city building or
+City Planning so in our Contex here we
+
+ align:start position:0%
+City Planning so in our Contex here we
+ 
+
+ align:start position:0%
+City Planning so in our Contex here we
+are trying to uh use Energy Efficiency
+
+ align:start position:0%
+are trying to uh use Energy Efficiency
+ 
+
+ align:start position:0%
+are trying to uh use Energy Efficiency
+technology we are trying to use
+
+ align:start position:0%
+technology we are trying to use
+ 
+
+ align:start position:0%
+technology we are trying to use
+renewable energy uh technology and also
+
+ align:start position:0%
+renewable energy uh technology and also
+ 
+
+ align:start position:0%
+renewable energy uh technology and also
+recycling the solid waste management and
+
+ align:start position:0%
+recycling the solid waste management and
+ 
+
+ align:start position:0%
+recycling the solid waste management and
+others urban planning have to reconsider
+
+ align:start position:0%
+others urban planning have to reconsider
+ 
+
+ align:start position:0%
+others urban planning have to reconsider
+how to uh promote green technology or
+
+ align:start position:0%
+how to uh promote green technology or
+ 
+
+ align:start position:0%
+how to uh promote green technology or
+green energy or green transport or green
+
+ align:start position:0%
+green energy or green transport or green
+ 
+
+ align:start position:0%
+green energy or green transport or green
+industry in in in City Planning so I
+
+ align:start position:0%
+industry in in in City Planning so I
+ 
+
+ align:start position:0%
+industry in in in City Planning so I
+think this is a way forward for Malayan
+
+ align:start position:0%
+think this is a way forward for Malayan
+ 
+
+ align:start position:0%
+think this is a way forward for Malayan
+uh development also Malaysia has made
+
+ align:start position:0%
+uh development also Malaysia has made
+ 
+
+ align:start position:0%
+uh development also Malaysia has made
+progress in promoting Green Technology
+
+ align:start position:0%
+progress in promoting Green Technology
+ 
+
+ align:start position:0%
+progress in promoting Green Technology
+interviews with government officials
+
+ align:start position:0%
+interviews with government officials
+ 
+
+ align:start position:0%
+interviews with government officials
+researchers and Industrial firms show
+
+ align:start position:0%
+researchers and Industrial firms show
+ 
+
+ align:start position:0%
+researchers and Industrial firms show
+that many pieces are still missing first
+
+ align:start position:0%
+that many pieces are still missing first
+ 
+
+ align:start position:0%
+that many pieces are still missing first
+information about Green Technology and
+
+ align:start position:0%
+information about Green Technology and
+ 
+
+ align:start position:0%
+information about Green Technology and
+policies are still very limited I
+
+ align:start position:0%
+policies are still very limited I
+ 
+
+ align:start position:0%
+policies are still very limited I
+conducted a questionnaire in 15
+
+ align:start position:0%
+conducted a questionnaire in 15
+ 
+
+ align:start position:0%
+conducted a questionnaire in 15
+factories it shows that one of the main
+
+ align:start position:0%
+factories it shows that one of the main
+ 
+
+ align:start position:0%
+factories it shows that one of the main
+barers for industrial firms to use green
+
+ align:start position:0%
+barers for industrial firms to use green
+ 
+
+ align:start position:0%
+barers for industrial firms to use green
+technology is information the government
+
+ align:start position:0%
+technology is information the government
+ 
+
+ align:start position:0%
+technology is information the government
+inent intention is good but some
+
+ align:start position:0%
+inent intention is good but some
+ 
+
+ align:start position:0%
+inent intention is good but some
+sometimes the are facing another
+
+ align:start position:0%
+sometimes the are facing another
+ 
+
+ align:start position:0%
+sometimes the are facing another
+challenges when it come to the Green
+
+ align:start position:0%
+challenges when it come to the Green
+ 
+
+ align:start position:0%
+challenges when it come to the Green
+Technology or green Industries you know
+
+ align:start position:0%
+Technology or green Industries you know
+ 
+
+ align:start position:0%
+Technology or green Industries you know
+sometime when we when we want to get
+
+ align:start position:0%
+sometime when we when we want to get
+ 
+
+ align:start position:0%
+sometime when we when we want to get
+someone to justify that you are in the
+
+ align:start position:0%
+someone to justify that you are in the
+ 
+
+ align:start position:0%
+someone to justify that you are in the
+green Industries so sometimes we cannot
+
+ align:start position:0%
+green Industries so sometimes we cannot
+ 
+
+ align:start position:0%
+green Industries so sometimes we cannot
+get the right person to confirm to
+
+ align:start position:0%
+get the right person to confirm to
+ 
+
+ align:start position:0%
+get the right person to confirm to
+justify that we are in that field
+
+ align:start position:0%
+justify that we are in that field
+ 
+
+ align:start position:0%
+justify that we are in that field
+sometime we may not be able to get the
+
+ align:start position:0%
+sometime we may not be able to get the
+ 
+
+ align:start position:0%
+sometime we may not be able to get the
+incentive that uh make provision to the
+
+ align:start position:0%
+incentive that uh make provision to the
+ 
+
+ align:start position:0%
+incentive that uh make provision to the
+assembly by the government so this is
+
+ align:start position:0%
+assembly by the government so this is
+ 
+
+ align:start position:0%
+assembly by the government so this is
+another challenge that we are facing uh
+
+ align:start position:0%
+another challenge that we are facing uh
+ 
+
+ align:start position:0%
+another challenge that we are facing uh
+some of this information may not have
+
+ align:start position:0%
+some of this information may not have
+ 
+
+ align:start position:0%
+some of this information may not have
+reached all the industrialist but I
+
+ align:start position:0%
+reached all the industrialist but I
+ 
+
+ align:start position:0%
+reached all the industrialist but I
+think the important part is actually
+
+ align:start position:0%
+think the important part is actually
+ 
+
+ align:start position:0%
+think the important part is actually
+this information have to be disseminated
+
+ align:start position:0%
+this information have to be disseminated
+ 
+
+ align:start position:0%
+this information have to be disseminated
+to a to a bigger group and then I think
+
+ align:start position:0%
+to a to a bigger group and then I think
+ 
+
+ align:start position:0%
+to a to a bigger group and then I think
+um uh we strongly feel that the Chamber
+
+ align:start position:0%
+um uh we strongly feel that the Chamber
+ 
+
+ align:start position:0%
+um uh we strongly feel that the Chamber
+of Commerce or
+
+ align:start position:0%
+of Commerce or
+ 
+
+ align:start position:0%
+of Commerce or
+industrial U association should work
+
+ align:start position:0%
+industrial U association should work
+ 
+
+ align:start position:0%
+industrial U association should work
+closely also trying to get to know more
+
+ align:start position:0%
+closely also trying to get to know more
+ 
+
+ align:start position:0%
+closely also trying to get to know more
+about this uh GRE Tech I think the the
+
+ align:start position:0%
+about this uh GRE Tech I think the the
+ 
+
+ align:start position:0%
+about this uh GRE Tech I think the the
+ministry themselves so know they they
+
+ align:start position:0%
+ministry themselves so know they they
+ 
+
+ align:start position:0%
+ministry themselves so know they they
+trying Ways and Means uh to disseminate
+
+ align:start position:0%
+trying Ways and Means uh to disseminate
+ 
+
+ align:start position:0%
+trying Ways and Means uh to disseminate
+this information so that actually more
+
+ align:start position:0%
+this information so that actually more
+ 
+
+ align:start position:0%
+this information so that actually more
+and more people have opportunity to
+
+ align:start position:0%
+and more people have opportunity to
+ 
+
+ align:start position:0%
+and more people have opportunity to
+access to this uh Green Tech fund did
+
+ align:start position:0%
+access to this uh Green Tech fund did
+ 
+
+ align:start position:0%
+access to this uh Green Tech fund did
+you heard about that Green Technology
+
+ align:start position:0%
+you heard about that Green Technology
+ 
+
+ align:start position:0%
+you heard about that Green Technology
+policy uh what what Green Technology I
+
+ align:start position:0%
+policy uh what what Green Technology I
+ 
+
+ align:start position:0%
+policy uh what what Green Technology I
+myself I I will like all the all these
+
+ align:start position:0%
+myself I I will like all the all these
+ 
+
+ align:start position:0%
+myself I I will like all the all these
+things clean energy now maybe they use
+
+ align:start position:0%
+things clean energy now maybe they use
+ 
+
+ align:start position:0%
+things clean energy now maybe they use
+more on this solar energy wind
+
+ align:start position:0%
+more on this solar energy wind
+ 
+
+ align:start position:0%
+more on this solar energy wind
+energy I think this is the two mean
+
+ align:start position:0%
+energy I think this is the two mean
+ 
+
+ align:start position:0%
+energy I think this is the two mean
+things they using now so solar energy
+
+ align:start position:0%
+things they using now so solar energy
+ 
+
+ align:start position:0%
+things they using now so solar energy
+actually I myself have using it now they
+
+ align:start position:0%
+actually I myself have using it now they
+ 
+
+ align:start position:0%
+actually I myself have using it now they
+use it for as a hobby but later on when
+
+ align:start position:0%
+use it for as a hobby but later on when
+ 
+
+ align:start position:0%
+use it for as a hobby but later on when
+I know more about it maybe I will use it
+
+ align:start position:0%
+I know more about it maybe I will use it
+ 
+
+ align:start position:0%
+I know more about it maybe I will use it
+uh partially to reduce my company's uh
+
+ align:start position:0%
+uh partially to reduce my company's uh
+ 
+
+ align:start position:0%
+uh partially to reduce my company's uh
+electricity to replace the supplies to
+
+ align:start position:0%
+electricity to replace the supplies to
+ 
+
+ align:start position:0%
+electricity to replace the supplies to
+cut down the cost secondly this is a
+
+ align:start position:0%
+cut down the cost secondly this is a
+ 
+
+ align:start position:0%
+cut down the cost secondly this is a
+mismatch between the needs of the firms
+
+ align:start position:0%
+mismatch between the needs of the firms
+ 
+
+ align:start position:0%
+mismatch between the needs of the firms
+and the focus of government programs
+
+ align:start position:0%
+and the focus of government programs
+ 
+
+ align:start position:0%
+and the focus of government programs
+according to the questionnaire
+
+ align:start position:0%
+according to the questionnaire
+ 
+
+ align:start position:0%
+according to the questionnaire
+industrial firms priorities were waste
+
+ align:start position:0%
+industrial firms priorities were waste
+ 
+
+ align:start position:0%
+industrial firms priorities were waste
+water energy utilization solid waste
+
+ align:start position:0%
+water energy utilization solid waste
+ 
+
+ align:start position:0%
+water energy utilization solid waste
+energy Supply and green buildings
+
+ align:start position:0%
+energy Supply and green buildings
+ 
+
+ align:start position:0%
+energy Supply and green buildings
+however most of the G incentives go to
+
+ align:start position:0%
+however most of the G incentives go to
+ 
+
+ align:start position:0%
+however most of the G incentives go to
+energy projects mostly for solar we feel
+
+ align:start position:0%
+energy projects mostly for solar we feel
+ 
+
+ align:start position:0%
+energy projects mostly for solar we feel
+that too much of empasis has been given
+
+ align:start position:0%
+that too much of empasis has been given
+ 
+
+ align:start position:0%
+that too much of empasis has been given
+to solar we are trying to look into
+
+ align:start position:0%
+to solar we are trying to look into
+ 
+
+ align:start position:0%
+to solar we are trying to look into
+other areas like thermal energy and also
+
+ align:start position:0%
+other areas like thermal energy and also
+ 
+
+ align:start position:0%
+other areas like thermal energy and also
+ACH the ocean thermal energy event into
+
+ align:start position:0%
+ACH the ocean thermal energy event into
+ 
+
+ align:start position:0%
+ACH the ocean thermal energy event into
+new new energies as well because
+
+ align:start position:0%
+new new energies as well because
+ 
+
+ align:start position:0%
+new new energies as well because
+initially the Green Technology
+
+ align:start position:0%
+initially the Green Technology
+ 
+
+ align:start position:0%
+initially the Green Technology
+concentration was only by the federal
+
+ align:start position:0%
+concentration was only by the federal
+ 
+
+ align:start position:0%
+concentration was only by the federal
+government uh we didn't incorporate with
+
+ align:start position:0%
+government uh we didn't incorporate with
+ 
+
+ align:start position:0%
+government uh we didn't incorporate with
+the state governments as you can see the
+
+ align:start position:0%
+the state governments as you can see the
+ 
+
+ align:start position:0%
+the state governments as you can see the
+Green Technology Council it's a federal
+
+ align:start position:0%
+Green Technology Council it's a federal
+ 
+
+ align:start position:0%
+Green Technology Council it's a federal
+Council but this year thinking starting
+
+ align:start position:0%
+Council but this year thinking starting
+ 
+
+ align:start position:0%
+Council but this year thinking starting
+from this year we have already
+
+ align:start position:0%
+from this year we have already
+ 
+
+ align:start position:0%
+from this year we have already
+encouraged all the state governments to
+
+ align:start position:0%
+encouraged all the state governments to
+ 
+
+ align:start position:0%
+encouraged all the state governments to
+have their own uh Green Technology
+
+ align:start position:0%
+have their own uh Green Technology
+ 
+
+ align:start position:0%
+have their own uh Green Technology
+Council in state level so once the state
+
+ align:start position:0%
+Council in state level so once the state
+ 
+
+ align:start position:0%
+Council in state level so once the state
+level has their own Green Technology
+
+ align:start position:0%
+level has their own Green Technology
+ 
+
+ align:start position:0%
+level has their own Green Technology
+Council so this kind of information can
+
+ align:start position:0%
+Council so this kind of information can
+ 
+
+ align:start position:0%
+Council so this kind of information can
+be discussed more in in the particular
+
+ align:start position:0%
+be discussed more in in the particular
+ 
+
+ align:start position:0%
+be discussed more in in the particular
+States so then you can see now I I I do
+
+ align:start position:0%
+States so then you can see now I I I do
+ 
+
+ align:start position:0%
+States so then you can see now I I I do
+agree with you the awareness is is
+
+ align:start position:0%
+agree with you the awareness is is
+ 
+
+ align:start position:0%
+agree with you the awareness is is
+pretty much
+
+ align:start position:0%
+pretty much
+ 
+
+ align:start position:0%
+pretty much
+low to improve the we implementation
+
+ align:start position:0%
+low to improve the we implementation
+ 
+
+ align:start position:0%
+low to improve the we implementation
+there's urgent need to have evaluation
+
+ align:start position:0%
+there's urgent need to have evaluation
+ 
+
+ align:start position:0%
+there's urgent need to have evaluation
+of the policy until now there has no
+
+ align:start position:0%
+of the policy until now there has no
+ 
+
+ align:start position:0%
+of the policy until now there has no
+assessment of the Green Technology
+
+ align:start position:0%
+assessment of the Green Technology
+ 
+
+ align:start position:0%
+assessment of the Green Technology
+policy implementation theyve been doing
+
+ align:start position:0%
+policy implementation theyve been doing
+ 
+
+ align:start position:0%
+policy implementation theyve been doing
+so much they've been giving investment I
+
+ align:start position:0%
+so much they've been giving investment I
+ 
+
+ align:start position:0%
+so much they've been giving investment I
+mean uh creating scenario for the
+
+ align:start position:0%
+mean uh creating scenario for the
+ 
+
+ align:start position:0%
+mean uh creating scenario for the
+investment for the Green Technology
+
+ align:start position:0%
+investment for the Green Technology
+ 
+
+ align:start position:0%
+investment for the Green Technology
+players but then as I can tell you that
+
+ align:start position:0%
+players but then as I can tell you that
+ 
+
+ align:start position:0%
+players but then as I can tell you that
+we are not very sure how much benefit
+
+ align:start position:0%
+we are not very sure how much benefit
+ 
+
+ align:start position:0%
+we are not very sure how much benefit
+incur by these people so and how much
+
+ align:start position:0%
+incur by these people so and how much
+ 
+
+ align:start position:0%
+incur by these people so and how much
+green technology has contributed to the
+
+ align:start position:0%
+green technology has contributed to the
+ 
+
+ align:start position:0%
+green technology has contributed to the
+policy itself adopting Green Technology
+
+ align:start position:0%
+policy itself adopting Green Technology
+ 
+
+ align:start position:0%
+policy itself adopting Green Technology
+will not be easy for developing
+
+ align:start position:0%
+will not be easy for developing
+ 
+
+ align:start position:0%
+will not be easy for developing
+countries the most important reason is
+
+ align:start position:0%
+countries the most important reason is
+ 
+
+ align:start position:0%
+countries the most important reason is
+that green technology is a comparatively
+
+ align:start position:0%
+that green technology is a comparatively
+ 
+
+ align:start position:0%
+that green technology is a comparatively
+expensive approach even in developed
+
+ align:start position:0%
+expensive approach even in developed
+ 
+
+ align:start position:0%
+expensive approach even in developed
+countries we still can see that the
+
+ align:start position:0%
+countries we still can see that the
+ 
+
+ align:start position:0%
+countries we still can see that the
+arguments about if Government should
+
+ align:start position:0%
+arguments about if Government should
+ 
+
+ align:start position:0%
+arguments about if Government should
+invest it in Green
+
+ align:start position:0%
+invest it in Green
+ 
+
+ align:start position:0%
+invest it in Green
+Technology but it is clear here from The
+
+ align:start position:0%
+Technology but it is clear here from The
+ 
+
+ align:start position:0%
+Technology but it is clear here from The
+Experience from Malaysia the government
+
+ align:start position:0%
+Experience from Malaysia the government
+ 
+
+ align:start position:0%
+Experience from Malaysia the government
+incentives are still very important to
+
+ align:start position:0%
+incentives are still very important to
+ 
+
+ align:start position:0%
+incentives are still very important to
+encourage Green Technology people say
+
+ align:start position:0%
+encourage Green Technology people say
+ 
+
+ align:start position:0%
+encourage Green Technology people say
+that only developing countries I mean uh
+
+ align:start position:0%
+that only developing countries I mean uh
+ 
+
+ align:start position:0%
+that only developing countries I mean uh
+concentrate too much on subsidies and
+
+ align:start position:0%
+concentrate too much on subsidies and
+ 
+
+ align:start position:0%
+concentrate too much on subsidies and
+incentives but actually it's it's a
+
+ align:start position:0%
+incentives but actually it's it's a
+ 
+
+ align:start position:0%
+incentives but actually it's it's a
+worldwide scenario last mon I went to
+
+ align:start position:0%
+worldwide scenario last mon I went to
+ 
+
+ align:start position:0%
+worldwide scenario last mon I went to
+Holland Netherlands as you can see
+
+ align:start position:0%
+Holland Netherlands as you can see
+ 
+
+ align:start position:0%
+Holland Netherlands as you can see
+Netherland is a very developed country
+
+ align:start position:0%
+Netherland is a very developed country
+ 
+
+ align:start position:0%
+Netherland is a very developed country
+and they really pay much attention to
+
+ align:start position:0%
+and they really pay much attention to
+ 
+
+ align:start position:0%
+and they really pay much attention to
+the environment they very environment
+
+ align:start position:0%
+the environment they very environment
+ 
+
+ align:start position:0%
+the environment they very environment
+friendly people but they have when it
+
+ align:start position:0%
+friendly people but they have when it
+ 
+
+ align:start position:0%
+friendly people but they have when it
+comes to transport industry the
+
+ align:start position:0%
+comes to transport industry the
+ 
+
+ align:start position:0%
+comes to transport industry the
+government in 2013 they came up with
+
+ align:start position:0%
+government in 2013 they came up with
+ 
+
+ align:start position:0%
+government in 2013 they came up with
+this incentive for uh green I mean
+
+ align:start position:0%
+this incentive for uh green I mean
+ 
+
+ align:start position:0%
+this incentive for uh green I mean
+electric vehicles and also plug-in
+
+ align:start position:0%
+electric vehicles and also plug-in
+ 
+
+ align:start position:0%
+electric vehicles and also plug-in
+electric vehicles so when the incentive
+
+ align:start position:0%
+electric vehicles so when the incentive
+ 
+
+ align:start position:0%
+electric vehicles so when the incentive
+was introduced in 2013 the sales of eeve
+
+ align:start position:0%
+was introduced in 2013 the sales of eeve
+ 
+
+ align:start position:0%
+was introduced in 2013 the sales of eeve
+rocketed and the highest sale goes went
+
+ align:start position:0%
+rocketed and the highest sale goes went
+ 
+
+ align:start position:0%
+rocketed and the highest sale goes went
+to uh Mitsubishi Outlander it's known as
+
+ align:start position:0%
+to uh Mitsubishi Outlander it's known as
+ 
+
+ align:start position:0%
+to uh Mitsubishi Outlander it's known as
+PW it's actually a plug-in hybrid
+
+ align:start position:0%
+PW it's actually a plug-in hybrid
+ 
+
+ align:start position:0%
+PW it's actually a plug-in hybrid
+electric vehicle but when the incentive
+
+ align:start position:0%
+electric vehicle but when the incentive
+ 
+
+ align:start position:0%
+electric vehicle but when the incentive
+ended by 31st December 2013 sale of
+
+ align:start position:0%
+ended by 31st December 2013 sale of
+ 
+
+ align:start position:0%
+ended by 31st December 2013 sale of
+electric vehicles in uh Netherlands
+
+ align:start position:0%
+electric vehicles in uh Netherlands
+ 
+
+ align:start position:0%
+electric vehicles in uh Netherlands
+dropped tremendously in
+
+ align:start position:0%
+dropped tremendously in
+ 
+
+ align:start position:0%
+dropped tremendously in
+2014 so as you can see like the
+
+ align:start position:0%
+2014 so as you can see like the
+ 
+
+ align:start position:0%
+2014 so as you can see like the
+lifestyle of people I mean the consumers
+
+ align:start position:0%
+lifestyle of people I mean the consumers
+ 
+
+ align:start position:0%
+lifestyle of people I mean the consumers
+are very much related to incentives and
+
+ align:start position:0%
+are very much related to incentives and
+ 
+
+ align:start position:0%
+are very much related to incentives and
+subsidies secondly for developing
+
+ align:start position:0%
+subsidies secondly for developing
+ 
+
+ align:start position:0%
+subsidies secondly for developing
+countries having consensus will be
+
+ align:start position:0%
+countries having consensus will be
+ 
+
+ align:start position:0%
+countries having consensus will be
+equally critical for launching Green
+
+ align:start position:0%
+equally critical for launching Green
+ 
+
+ align:start position:0%
+equally critical for launching Green
+Technology actions across every area
+
+ align:start position:0%
+Technology actions across every area
+ 
+
+ align:start position:0%
+Technology actions across every area
+from construction to transportation to
+
+ align:start position:0%
+from construction to transportation to
+ 
+
+ align:start position:0%
+from construction to transportation to
+Industry Malaysia has developed
+
+ align:start position:0%
+Industry Malaysia has developed
+ 
+
+ align:start position:0%
+Industry Malaysia has developed
+incentive
+
+ align:start position:0%
+incentive
+ 
+
+ align:start position:0%
+incentive
+policies but local government needs to
+
+ align:start position:0%
+policies but local government needs to
+ 
+
+ align:start position:0%
+policies but local government needs to
+be involved for the knowledge to be
+
+ align:start position:0%
+be involved for the knowledge to be
+ 
+
+ align:start position:0%
+be involved for the knowledge to be
+diffused across the
+
+ align:start position:0%
+diffused across the
+ 
+
+ align:start position:0%
+diffused across the
+country this is also an important law
+
+ align:start position:0%
+country this is also an important law
+ 
+
+ align:start position:0%
+country this is also an important law
+for other non-government institutions
+
+ align:start position:0%
+for other non-government institutions
+ 
+
+ align:start position:0%
+for other non-government institutions
+such as industrial
+
+ align:start position:0%
+such as industrial
+ 
+
+ align:start position:0%
+such as industrial
+associations so where the funding ofme
+
+ align:start position:0%
+associations so where the funding ofme
+ 
+
+ align:start position:0%
+associations so where the funding ofme
+come from the funding of no we have no
+
+ align:start position:0%
+come from the funding of no we have no
+ 
+
+ align:start position:0%
+come from the funding of no we have no
+funding yeah we totally do not have
+
+ align:start position:0%
+funding yeah we totally do not have
+ 
+
+ align:start position:0%
+funding yeah we totally do not have
+funing because we should be self-funded
+
+ align:start position:0%
+funing because we should be self-funded
+ 
+
+ align:start position:0%
+funing because we should be self-funded
+I think self funded so sometime you know
+
+ align:start position:0%
+I think self funded so sometime you know
+ 
+
+ align:start position:0%
+I think self funded so sometime you know
+when the we talk about the funding for
+
+ align:start position:0%
+when the we talk about the funding for
+ 
+
+ align:start position:0%
+when the we talk about the funding for
+the R&D R&D is a long-term investment
+
+ align:start position:0%
+the R&D R&D is a long-term investment
+ 
+
+ align:start position:0%
+the R&D R&D is a long-term investment
+you know at the beginning stage you may
+
+ align:start position:0%
+you know at the beginning stage you may
+ 
+
+ align:start position:0%
+you know at the beginning stage you may
+not see any benefit at all so but you
+
+ align:start position:0%
+not see any benefit at all so but you
+ 
+
+ align:start position:0%
+not see any benefit at all so but you
+have to come up with a lot a lot of
+
+ align:start position:0%
+have to come up with a lot a lot of
+ 
+
+ align:start position:0%
+have to come up with a lot a lot of
+resources for the green product or green
+
+ align:start position:0%
+resources for the green product or green
+ 
+
+ align:start position:0%
+resources for the green product or green
+Industries or even
+
+ align:start position:0%
+Industries or even
+ 
+
+ align:start position:0%
+Industries or even
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effici I think we still have to the
+
+ align:start position:0%
+effici I think we still have to the
+ 
+
+ align:start position:0%
+effici I think we still have to the
+government still have to take the Le you
+
+ align:start position:0%
+government still have to take the Le you
+ 
+
+ align:start position:0%
+government still have to take the Le you
+know uh whether with the University or
+
+ align:start position:0%
+know uh whether with the University or
+ 
+
+ align:start position:0%
+know uh whether with the University or
+whether be the industry I think the
+
+ align:start position:0%
+whether be the industry I think the
+ 
+
+ align:start position:0%
+whether be the industry I think the
+government should take the Le
+
+ align:start position:0%
+government should take the Le
+ 
+
+ align:start position:0%
+government should take the Le
+um I do not have doubt that in terms of
+
+ align:start position:0%
+um I do not have doubt that in terms of
+ 
+
+ align:start position:0%
+um I do not have doubt that in terms of
+the green wi Green Technology green
+
+ align:start position:0%
+the green wi Green Technology green
+ 
+
+ align:start position:0%
+the green wi Green Technology green
+industry we are still so much Divine in
+
+ align:start position:0%
+industry we are still so much Divine in
+ 
+
+ align:start position:0%
+industry we are still so much Divine in
+some of the country in our region know
+
+ align:start position:0%
+some of the country in our region know
+ 
+
+ align:start position:0%
+some of the country in our region know
+Japan Taiwan or even the China I think
+
+ align:start position:0%
+Japan Taiwan or even the China I think
+ 
+
+ align:start position:0%
+Japan Taiwan or even the China I think
+we are still so much so we hope that the
+
+ align:start position:0%
+we are still so much so we hope that the
+ 
+
+ align:start position:0%
+we are still so much so we hope that the
+government will play their role leading
+
+ align:start position:0%
+government will play their role leading
+ 
+
+ align:start position:0%
+government will play their role leading
+the industry especially the and of
+
+ align:start position:0%
+the industry especially the and of
+ 
+
+ align:start position:0%
+the industry especially the and of
+course if possible also we be very much
+
+ align:start position:0%
+course if possible also we be very much
+ 
+
+ align:start position:0%
+course if possible also we be very much
+happy to work together also blaming some
+
+ align:start position:0%
+happy to work together also blaming some
+ 
+
+ align:start position:0%
+happy to work together also blaming some
+of the Ministries you know certain
+
+ align:start position:0%
+of the Ministries you know certain
+ 
+
+ align:start position:0%
+of the Ministries you know certain
+information that never sendross that's
+
+ align:start position:0%
+information that never sendross that's
+ 
+
+ align:start position:0%
+information that never sendross that's
+why the association is playing a very
+
+ align:start position:0%
+why the association is playing a very
+ 
+
+ align:start position:0%
+why the association is playing a very
+important role on this most of time we
+
+ align:start position:0%
+important role on this most of time we
+ 
+
+ align:start position:0%
+important role on this most of time we
+are trying to link up the government and
+
+ align:start position:0%
+are trying to link up the government and
+ 
+
+ align:start position:0%
+are trying to link up the government and
+to the to the to the industry or to the
+
+ align:start position:0%
+to the to the to the industry or to the
+ 
+
+ align:start position:0%
+to the to the to the industry or to the
+players besides the government support
+
+ align:start position:0%
+players besides the government support
+ 
+
+ align:start position:0%
+players besides the government support
+both Federal and local government and
+
+ align:start position:0%
+both Federal and local government and
+ 
+
+ align:start position:0%
+both Federal and local government and
+cooperation from other associations
+
+ align:start position:0%
+cooperation from other associations
+ 
+
+ align:start position:0%
+cooperation from other associations
+public education and capacity building
+
+ align:start position:0%
+public education and capacity building
+ 
+
+ align:start position:0%
+public education and capacity building
+for the labor force are also important
+
+ align:start position:0%
+for the labor force are also important
+ 
+
+ align:start position:0%
+for the labor force are also important
+no matter how difficult it is people in
+
+ align:start position:0%
+no matter how difficult it is people in
+ 
+
+ align:start position:0%
+no matter how difficult it is people in
+Malaysia have become aware that Behavior
+
+ align:start position:0%
+Malaysia have become aware that Behavior
+ 
+
+ align:start position:0%
+Malaysia have become aware that Behavior
+change is much
+
+ align:start position:0%
+change is much
+ 
+
+ align:start position:0%
+change is much
+important without Behavior change
+
+ align:start position:0%
+important without Behavior change
+ 
+
+ align:start position:0%
+important without Behavior change
+nothing will happen we should not only
+
+ align:start position:0%
+nothing will happen we should not only
+ 
+
+ align:start position:0%
+nothing will happen we should not only
+look at mitigation we have to look at
+
+ align:start position:0%
+look at mitigation we have to look at
+ 
+
+ align:start position:0%
+look at mitigation we have to look at
+adaptation adaptation meaning to say
+
+ align:start position:0%
+adaptation adaptation meaning to say
+ 
+
+ align:start position:0%
+adaptation adaptation meaning to say
+that also we have to how to adapt to
+
+ align:start position:0%
+that also we have to how to adapt to
+ 
+
+ align:start position:0%
+that also we have to how to adapt to
+this climate change so mitigation can be
+
+ align:start position:0%
+this climate change so mitigation can be
+ 
+
+ align:start position:0%
+this climate change so mitigation can be
+expensive adaptation should come in
+
+ align:start position:0%
+expensive adaptation should come in
+ 
+
+ align:start position:0%
+expensive adaptation should come in
+together and I think the most
+
+ align:start position:0%
+together and I think the most
+ 
+
+ align:start position:0%
+together and I think the most
+challenging part is the Mind chain the
+
+ align:start position:0%
+challenging part is the Mind chain the
+ 
+
+ align:start position:0%
+challenging part is the Mind chain the
+mindset how do you how do you uh promote
+
+ align:start position:0%
+mindset how do you how do you uh promote
+ 
+
+ align:start position:0%
+mindset how do you how do you uh promote
+uh low carbon Society to the local
+
+ align:start position:0%
+uh low carbon Society to the local
+ 
+
+ align:start position:0%
+uh low carbon Society to the local
+Society so that they have mind the Mind
+
+ align:start position:0%
+Society so that they have mind the Mind
+ 
+
+ align:start position:0%
+Society so that they have mind the Mind
+change their mindset changing from very
+
+ align:start position:0%
+change their mindset changing from very
+ 
+
+ align:start position:0%
+change their mindset changing from very
+high consumption to a low consumption
+
+ align:start position:0%
+high consumption to a low consumption
+ 
+
+ align:start position:0%
+high consumption to a low consumption
+Society so by doing that they could cut
+
+ align:start position:0%
+Society so by doing that they could cut
+ 
+
+ align:start position:0%
+Society so by doing that they could cut
+down their waste they could cut down
+
+ align:start position:0%
+down their waste they could cut down
+ 
+
+ align:start position:0%
+down their waste they could cut down
+their consumption and they could
+
+ align:start position:0%
+their consumption and they could
+ 
+
+ align:start position:0%
+their consumption and they could
+actually improve their qual quality of
+
+ align:start position:0%
+actually improve their qual quality of
+ 
+
+ align:start position:0%
+actually improve their qual quality of
+life even without uh having a very high
+
+ align:start position:0%
+life even without uh having a very high
+ 
+
+ align:start position:0%
+life even without uh having a very high
+consumption so I think uh mindset change
+
+ align:start position:0%
+consumption so I think uh mindset change
+ 
+
+ align:start position:0%
+consumption so I think uh mindset change
+is very important that's why in our
+
+ align:start position:0%
+is very important that's why in our
+ 
+
+ align:start position:0%
+is very important that's why in our
+campaign we we started we call it low
+
+ align:start position:0%
+campaign we we started we call it low
+ 
+
+ align:start position:0%
+campaign we we started we call it low
+carbon Society we don't call low carbon
+
+ align:start position:0%
+carbon Society we don't call low carbon
+ 
+
+ align:start position:0%
+carbon Society we don't call low carbon
+City in developing countries the
+
+ align:start position:0%
+City in developing countries the
+ 
+
+ align:start position:0%
+City in developing countries the
+government and the citizens are eagly
+
+ align:start position:0%
+government and the citizens are eagly
+ 
+
+ align:start position:0%
+government and the citizens are eagly
+looking for ways to grow economically
+
+ align:start position:0%
+looking for ways to grow economically
+ 
+
+ align:start position:0%
+looking for ways to grow economically
+but at the same time protect environment
+
+ align:start position:0%
+but at the same time protect environment
+ 
+
+ align:start position:0%
+but at the same time protect environment
+and mitigate Global Climate
+
+ align:start position:0%
+and mitigate Global Climate
+ 
+
+ align:start position:0%
+and mitigate Global Climate
+challenges critics of Green Technology
+
+ align:start position:0%
+challenges critics of Green Technology
+ 
+
+ align:start position:0%
+challenges critics of Green Technology
+is that it's a very expensive investment
+
+ align:start position:0%
+is that it's a very expensive investment
+ 
+
+ align:start position:0%
+is that it's a very expensive investment
+for developing countries and that is not
+
+ align:start position:0%
+for developing countries and that is not
+ 
+
+ align:start position:0%
+for developing countries and that is not
+easy to get access and adopt because of
+
+ align:start position:0%
+easy to get access and adopt because of
+ 
+
+ align:start position:0%
+easy to get access and adopt because of
+knowledge or barriers from 2009 Malaysia
+
+ align:start position:0%
+knowledge or barriers from 2009 Malaysia
+ 
+
+ align:start position:0%
+knowledge or barriers from 2009 Malaysia
+has taken steps to implement green techn
+
+ align:start position:0%
+has taken steps to implement green techn
+ 
+
+ align:start position:0%
+has taken steps to implement green techn
+know each step has not been easy the
+
+ align:start position:0%
+know each step has not been easy the
+ 
+
+ align:start position:0%
+know each step has not been easy the
+malesia experience with promoting Green
+
+ align:start position:0%
+malesia experience with promoting Green
+ 
+
+ align:start position:0%
+malesia experience with promoting Green
+Technology can provide insights for
+
+ align:start position:0%
+Technology can provide insights for
+ 
+
+ align:start position:0%
+Technology can provide insights for
+other developing and developed countries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
\ No newline at end of file
diff --git a/bnYD88uNtwY.txt b/bnYD88uNtwY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ea16c25034a9e49825937aca2a217e26d0b425d8
--- /dev/null
+++ b/bnYD88uNtwY.txt
@@ -0,0 +1,2667 @@
+align:start position:0%
+ 
+so hi girls my name is zanga and I am
+
+ align:start position:0%
+so hi girls my name is zanga and I am
+ 
+
+ align:start position:0%
+so hi girls my name is zanga and I am
+currently at the MIT coch Institute
+
+ align:start position:0%
+currently at the MIT coch Institute
+ 
+
+ align:start position:0%
+currently at the MIT coch Institute
+which is a building just for cancer
+
+ align:start position:0%
+which is a building just for cancer
+ 
+
+ align:start position:0%
+which is a building just for cancer
+research and today I'm going to talk
+
+ align:start position:0%
+research and today I'm going to talk
+ 
+
+ align:start position:0%
+research and today I'm going to talk
+about the biological engineering that we
+
+ align:start position:0%
+about the biological engineering that we
+ 
+
+ align:start position:0%
+about the biological engineering that we
+do in order to find and image uh deeply
+
+ align:start position:0%
+do in order to find and image uh deeply
+ 
+
+ align:start position:0%
+do in order to find and image uh deeply
+embedded and difficult to reach tumors
+
+ align:start position:0%
+embedded and difficult to reach tumors
+ 
+
+ align:start position:0%
+embedded and difficult to reach tumors
+uh So currently in the clinic the number
+
+ align:start position:0%
+uh So currently in the clinic the number
+ 
+
+ align:start position:0%
+uh So currently in the clinic the number
+one therapy method for cancer is oh
+
+ align:start position:0%
+one therapy method for cancer is oh
+ 
+
+ align:start position:0%
+one therapy method for cancer is oh
+thank
+
+ align:start position:0%
+thank
+ 
+
+ align:start position:0%
+thank
+you um for cancer is a surgical
+
+ align:start position:0%
+you um for cancer is a surgical
+ 
+
+ align:start position:0%
+you um for cancer is a surgical
+debulking which is basically removing of
+
+ align:start position:0%
+debulking which is basically removing of
+ 
+
+ align:start position:0%
+debulking which is basically removing of
+the mass uh tumor masses and then
+
+ align:start position:0%
+the mass uh tumor masses and then
+ 
+
+ align:start position:0%
+the mass uh tumor masses and then
+chemotherapy and so it's very important
+
+ align:start position:0%
+chemotherapy and so it's very important
+ 
+
+ align:start position:0%
+chemotherapy and so it's very important
+uh for surgeons to be able to locate
+
+ align:start position:0%
+uh for surgeons to be able to locate
+ 
+
+ align:start position:0%
+uh for surgeons to be able to locate
+precisely um and early on in the stage
+
+ align:start position:0%
+precisely um and early on in the stage
+ 
+
+ align:start position:0%
+precisely um and early on in the stage
+of the tumor uh the masses that they
+
+ align:start position:0%
+of the tumor uh the masses that they
+ 
+
+ align:start position:0%
+of the tumor uh the masses that they
+want to remove uh to be the most to in
+
+ align:start position:0%
+want to remove uh to be the most to in
+ 
+
+ align:start position:0%
+want to remove uh to be the most to in
+order to do the most effective
+
+ align:start position:0%
+order to do the most effective
+ 
+
+ align:start position:0%
+order to do the most effective
+therapy and so cancer cells are
+
+ align:start position:0%
+therapy and so cancer cells are
+ 
+
+ align:start position:0%
+therapy and so cancer cells are
+basically cells that have unusual
+
+ align:start position:0%
+basically cells that have unusual
+ 
+
+ align:start position:0%
+basically cells that have unusual
+dividing ability so they proliferate
+
+ align:start position:0%
+dividing ability so they proliferate
+ 
+
+ align:start position:0%
+dividing ability so they proliferate
+without stop um and they are
+
+ align:start position:0%
+without stop um and they are
+ 
+
+ align:start position:0%
+without stop um and they are
+differentiated from the regular cells
+
+ align:start position:0%
+differentiated from the regular cells
+ 
+
+ align:start position:0%
+differentiated from the regular cells
+around them by certain markers on the
+
+ align:start position:0%
+around them by certain markers on the
+ 
+
+ align:start position:0%
+around them by certain markers on the
+surface of the
+
+ align:start position:0%
+surface of the
+ 
+
+ align:start position:0%
+surface of the
+cell and so what we want to do is use
+
+ align:start position:0%
+cell and so what we want to do is use
+ 
+
+ align:start position:0%
+cell and so what we want to do is use
+these markers on the surface in the cell
+
+ align:start position:0%
+these markers on the surface in the cell
+ 
+
+ align:start position:0%
+these markers on the surface in the cell
+in order to find and then tell the
+
+ align:start position:0%
+in order to find and then tell the
+ 
+
+ align:start position:0%
+in order to find and then tell the
+locate um where the tumors are and tell
+
+ align:start position:0%
+locate um where the tumors are and tell
+ 
+
+ align:start position:0%
+locate um where the tumors are and tell
+the surgeons okay this is the place
+
+ align:start position:0%
+the surgeons okay this is the place
+ 
+
+ align:start position:0%
+the surgeons okay this is the place
+where I should remove uh the biological
+
+ align:start position:0%
+where I should remove uh the biological
+ 
+
+ align:start position:0%
+where I should remove uh the biological
+tissue and you don't want to damage the
+
+ align:start position:0%
+tissue and you don't want to damage the
+ 
+
+ align:start position:0%
+tissue and you don't want to damage the
+healthy tissue around it so you want to
+
+ align:start position:0%
+healthy tissue around it so you want to
+ 
+
+ align:start position:0%
+healthy tissue around it so you want to
+be very precise um and very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah so there are two tools uh that
+
+ align:start position:0%
+um yeah so there are two tools uh that
+ 
+
+ align:start position:0%
+um yeah so there are two tools uh that
+we use in our lab in order to uh find
+
+ align:start position:0%
+we use in our lab in order to uh find
+ 
+
+ align:start position:0%
+we use in our lab in order to uh find
+the tumors in the body uh the first is
+
+ align:start position:0%
+the tumors in the body uh the first is
+ 
+
+ align:start position:0%
+the tumors in the body uh the first is
+the custombuilt imager uh that we're
+
+ align:start position:0%
+the custombuilt imager uh that we're
+ 
+
+ align:start position:0%
+the custombuilt imager uh that we're
+working on with the with collaboration
+
+ align:start position:0%
+working on with the with collaboration
+ 
+
+ align:start position:0%
+working on with the with collaboration
+um at the Lincoln labs and the second is
+
+ align:start position:0%
+um at the Lincoln labs and the second is
+ 
+
+ align:start position:0%
+um at the Lincoln labs and the second is
+the biological probe it's a little
+
+ align:start position:0%
+the biological probe it's a little
+ 
+
+ align:start position:0%
+the biological probe it's a little
+shuttle that we use in order to go ahead
+
+ align:start position:0%
+shuttle that we use in order to go ahead
+ 
+
+ align:start position:0%
+shuttle that we use in order to go ahead
+and find the cells in the body so we can
+
+ align:start position:0%
+and find the cells in the body so we can
+ 
+
+ align:start position:0%
+and find the cells in the body so we can
+both so we can talk about both of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today so the biological maricle that we
+
+ align:start position:0%
+today so the biological maricle that we
+ 
+
+ align:start position:0%
+today so the biological maricle that we
+use is called the M13 bacteria phage and
+
+ align:start position:0%
+use is called the M13 bacteria phage and
+ 
+
+ align:start position:0%
+use is called the M13 bacteria phage and
+bacteria phage really just means
+
+ align:start position:0%
+bacteria phage really just means
+ 
+
+ align:start position:0%
+bacteria phage really just means
+bacteria eater um so it's a virus so as
+
+ align:start position:0%
+bacteria eater um so it's a virus so as
+ 
+
+ align:start position:0%
+bacteria eater um so it's a virus so as
+with typical viruses it
+
+ align:start position:0%
+with typical viruses it
+ 
+
+ align:start position:0%
+with typical viruses it
+infects bacteria sends its in DNA takes
+
+ align:start position:0%
+infects bacteria sends its in DNA takes
+ 
+
+ align:start position:0%
+infects bacteria sends its in DNA takes
+over the local mechanism of the bacteria
+
+ align:start position:0%
+over the local mechanism of the bacteria
+ 
+
+ align:start position:0%
+over the local mechanism of the bacteria
+and begins to replicate itself um so
+
+ align:start position:0%
+and begins to replicate itself um so
+ 
+
+ align:start position:0%
+and begins to replicate itself um so
+what we can do is hack this system in
+
+ align:start position:0%
+what we can do is hack this system in
+ 
+
+ align:start position:0%
+what we can do is hack this system in
+order to use this molecule for our own
+
+ align:start position:0%
+order to use this molecule for our own
+ 
+
+ align:start position:0%
+order to use this molecule for our own
+benefits it's a very beautiful very
+
+ align:start position:0%
+benefits it's a very beautiful very
+ 
+
+ align:start position:0%
+benefits it's a very beautiful very
+simple sort of molecule um it's just a
+
+ align:start position:0%
+simple sort of molecule um it's just a
+ 
+
+ align:start position:0%
+simple sort of molecule um it's just a
+piece of DNA so a DNA that codes for its
+
+ align:start position:0%
+piece of DNA so a DNA that codes for its
+ 
+
+ align:start position:0%
+piece of DNA so a DNA that codes for its
+D not of information and a bunch of
+
+ align:start position:0%
+D not of information and a bunch of
+ 
+
+ align:start position:0%
+D not of information and a bunch of
+proteins that's wrapped around the
+
+ align:start position:0%
+proteins that's wrapped around the
+ 
+
+ align:start position:0%
+proteins that's wrapped around the
+body and so because we can manipulate
+
+ align:start position:0%
+body and so because we can manipulate
+ 
+
+ align:start position:0%
+body and so because we can manipulate
+the DNA we can change the peptides that
+
+ align:start position:0%
+the DNA we can change the peptides that
+ 
+
+ align:start position:0%
+the DNA we can change the peptides that
+are on the body of the Fage and so we
+
+ align:start position:0%
+are on the body of the Fage and so we
+ 
+
+ align:start position:0%
+are on the body of the Fage and so we
+can change the protein so that they have
+
+ align:start position:0%
+can change the protein so that they have
+ 
+
+ align:start position:0%
+can change the protein so that they have
+specific binding abilities to certain
+
+ align:start position:0%
+specific binding abilities to certain
+ 
+
+ align:start position:0%
+specific binding abilities to certain
+materials or certain lians or certain
+
+ align:start position:0%
+materials or certain lians or certain
+ 
+
+ align:start position:0%
+materials or certain lians or certain
+markers so this is the tumor cell
+
+ align:start position:0%
+markers so this is the tumor cell
+ 
+
+ align:start position:0%
+markers so this is the tumor cell
+markers that I'm talking about um we can
+
+ align:start position:0%
+markers that I'm talking about um we can
+ 
+
+ align:start position:0%
+markers that I'm talking about um we can
+change the protein at the head of the
+
+ align:start position:0%
+change the protein at the head of the
+ 
+
+ align:start position:0%
+change the protein at the head of the
+virus in order to bind specifically to
+
+ align:start position:0%
+virus in order to bind specifically to
+ 
+
+ align:start position:0%
+virus in order to bind specifically to
+the surface of a cancer cell and we can
+
+ align:start position:0%
+the surface of a cancer cell and we can
+ 
+
+ align:start position:0%
+the surface of a cancer cell and we can
+change the proteins on the body of the
+
+ align:start position:0%
+change the proteins on the body of the
+ 
+
+ align:start position:0%
+change the proteins on the body of the
+virus to bind to a specific Imaging
+
+ align:start position:0%
+virus to bind to a specific Imaging
+ 
+
+ align:start position:0%
+virus to bind to a specific Imaging
+agent or therapy agent that we can then
+
+ align:start position:0%
+agent or therapy agent that we can then
+ 
+
+ align:start position:0%
+agent or therapy agent that we can then
+shuttle to the surface of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ourselves so for our system here the
+
+ align:start position:0%
+ourselves so for our system here the
+ 
+
+ align:start position:0%
+ourselves so for our system here the
+Imaging agent that we chose is called a
+
+ align:start position:0%
+Imaging agent that we chose is called a
+ 
+
+ align:start position:0%
+Imaging agent that we chose is called a
+carbon N Tube and so a carbon nanot tube
+
+ align:start position:0%
+carbon N Tube and so a carbon nanot tube
+ 
+
+ align:start position:0%
+carbon N Tube and so a carbon nanot tube
+um is just a piece of graphine that's
+
+ align:start position:0%
+um is just a piece of graphine that's
+ 
+
+ align:start position:0%
+um is just a piece of graphine that's
+been rolled up and what graphine is is
+
+ align:start position:0%
+been rolled up and what graphine is is
+ 
+
+ align:start position:0%
+been rolled up and what graphine is is
+um it's just a single layer of graphite
+
+ align:start position:0%
+um it's just a single layer of graphite
+ 
+
+ align:start position:0%
+um it's just a single layer of graphite
+and graphite is what you find in your
+
+ align:start position:0%
+and graphite is what you find in your
+ 
+
+ align:start position:0%
+and graphite is what you find in your
+pencils in lead and so it has very
+
+ align:start position:0%
+pencils in lead and so it has very
+ 
+
+ align:start position:0%
+pencils in lead and so it has very
+interesting Optical and electrical
+
+ align:start position:0%
+interesting Optical and electrical
+ 
+
+ align:start position:0%
+interesting Optical and electrical
+properties and it's very well studied
+
+ align:start position:0%
+properties and it's very well studied
+ 
+
+ align:start position:0%
+properties and it's very well studied
+but for us what's interesting about it
+
+ align:start position:0%
+but for us what's interesting about it
+ 
+
+ align:start position:0%
+but for us what's interesting about it
+is the wavelength at which it emits
+
+ align:start position:0%
+is the wavelength at which it emits
+ 
+
+ align:start position:0%
+is the wavelength at which it emits
+light um this is in the second window
+
+ align:start position:0%
+light um this is in the second window
+ 
+
+ align:start position:0%
+light um this is in the second window
+near infrared uh wavelength and so it's
+
+ align:start position:0%
+near infrared uh wavelength and so it's
+ 
+
+ align:start position:0%
+near infrared uh wavelength and so it's
+slightly longer than the visible
+
+ align:start position:0%
+slightly longer than the visible
+ 
+
+ align:start position:0%
+slightly longer than the visible
+wavelength
+
+ align:start position:0%
+wavelength
+ 
+
+ align:start position:0%
+wavelength
+and the cool thing about this is it's
+
+ align:start position:0%
+and the cool thing about this is it's
+ 
+
+ align:start position:0%
+and the cool thing about this is it's
+able to penetrate deep uh deeper into
+
+ align:start position:0%
+able to penetrate deep uh deeper into
+ 
+
+ align:start position:0%
+able to penetrate deep uh deeper into
+the biological tissue and you have less
+
+ align:start position:0%
+the biological tissue and you have less
+ 
+
+ align:start position:0%
+the biological tissue and you have less
+scattering and less interference from
+
+ align:start position:0%
+scattering and less interference from
+ 
+
+ align:start position:0%
+scattering and less interference from
+the surrounding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+materials so finally this is the design
+
+ align:start position:0%
+materials so finally this is the design
+ 
+
+ align:start position:0%
+materials so finally this is the design
+of our shuttles that we send in to find
+
+ align:start position:0%
+of our shuttles that we send in to find
+ 
+
+ align:start position:0%
+of our shuttles that we send in to find
+tumor cells um we have the M13 bacteria
+
+ align:start position:0%
+tumor cells um we have the M13 bacteria
+ 
+
+ align:start position:0%
+tumor cells um we have the M13 bacteria
+phage which has a particular protein at
+
+ align:start position:0%
+phage which has a particular protein at
+ 
+
+ align:start position:0%
+phage which has a particular protein at
+the head that detects the tumors
+
+ align:start position:0%
+the head that detects the tumors
+ 
+
+ align:start position:0%
+the head that detects the tumors
+and we have on the body the CNT the
+
+ align:start position:0%
+and we have on the body the CNT the
+ 
+
+ align:start position:0%
+and we have on the body the CNT the
+carbon nanit tube um that is going to
+
+ align:start position:0%
+carbon nanit tube um that is going to
+ 
+
+ align:start position:0%
+carbon nanit tube um that is going to
+light up and tell us oh this is where we
+
+ align:start position:0%
+light up and tell us oh this is where we
+ 
+
+ align:start position:0%
+light up and tell us oh this is where we
+should go ahead and remove the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass so the first model that we have
+
+ align:start position:0%
+mass so the first model that we have
+ 
+
+ align:start position:0%
+mass so the first model that we have
+actually done in our lab is on ovarian
+
+ align:start position:0%
+actually done in our lab is on ovarian
+ 
+
+ align:start position:0%
+actually done in our lab is on ovarian
+tumor and ovarian tumor is one of the
+
+ align:start position:0%
+tumor and ovarian tumor is one of the
+ 
+
+ align:start position:0%
+tumor and ovarian tumor is one of the
+tumor bottles that is very difficult to
+
+ align:start position:0%
+tumor bottles that is very difficult to
+ 
+
+ align:start position:0%
+tumor bottles that is very difficult to
+detect early on um it's unlike you know
+
+ align:start position:0%
+detect early on um it's unlike you know
+ 
+
+ align:start position:0%
+detect early on um it's unlike you know
+things like breast tumor you can't feel
+
+ align:start position:0%
+things like breast tumor you can't feel
+ 
+
+ align:start position:0%
+things like breast tumor you can't feel
+it and when usually when the surgeon or
+
+ align:start position:0%
+it and when usually when the surgeon or
+ 
+
+ align:start position:0%
+it and when usually when the surgeon or
+the doctor diagnoses it's quite late in
+
+ align:start position:0%
+the doctor diagnoses it's quite late in
+ 
+
+ align:start position:0%
+the doctor diagnoses it's quite late in
+the stage of of the tumor so it could
+
+ align:start position:0%
+the stage of of the tumor so it could
+ 
+
+ align:start position:0%
+the stage of of the tumor so it could
+have turned metastatic and metastatic
+
+ align:start position:0%
+have turned metastatic and metastatic
+ 
+
+ align:start position:0%
+have turned metastatic and metastatic
+means that the tumor cells have detached
+
+ align:start position:0%
+means that the tumor cells have detached
+ 
+
+ align:start position:0%
+means that the tumor cells have detached
+from the body and traveled to other
+
+ align:start position:0%
+from the body and traveled to other
+ 
+
+ align:start position:0%
+from the body and traveled to other
+parts of the body and so proliferated
+
+ align:start position:0%
+parts of the body and so proliferated
+ 
+
+ align:start position:0%
+parts of the body and so proliferated
+other tumors throughout the body so this
+
+ align:start position:0%
+other tumors throughout the body so this
+ 
+
+ align:start position:0%
+other tumors throughout the body so this
+is a stage you don't want to
+
+ align:start position:0%
+is a stage you don't want to
+ 
+
+ align:start position:0%
+is a stage you don't want to
+reach so it'll be very cool if you can
+
+ align:start position:0%
+reach so it'll be very cool if you can
+ 
+
+ align:start position:0%
+reach so it'll be very cool if you can
+put our probes into mice with aarian
+
+ align:start position:0%
+put our probes into mice with aarian
+ 
+
+ align:start position:0%
+put our probes into mice with aarian
+tumor light up the tumors give the
+
+ align:start position:0%
+tumor light up the tumors give the
+ 
+
+ align:start position:0%
+tumor light up the tumors give the
+surgeon the image and the surgeon can go
+
+ align:start position:0%
+surgeon the image and the surgeon can go
+ 
+
+ align:start position:0%
+surgeon the image and the surgeon can go
+ahead and move the tumors and the mice
+
+ align:start position:0%
+ahead and move the tumors and the mice
+ 
+
+ align:start position:0%
+ahead and move the tumors and the mice
+will then survive so this is a first
+
+ align:start position:0%
+will then survive so this is a first
+ 
+
+ align:start position:0%
+will then survive so this is a first
+step in putting our system towards
+
+ align:start position:0%
+step in putting our system towards
+ 
+
+ align:start position:0%
+step in putting our system towards
+clinical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+application so this is what happens in
+
+ align:start position:0%
+application so this is what happens in
+ 
+
+ align:start position:0%
+application so this is what happens in
+real life um you see here the stomach
+
+ align:start position:0%
+real life um you see here the stomach
+ 
+
+ align:start position:0%
+real life um you see here the stomach
+cavity of the mice and in the bright
+
+ align:start position:0%
+cavity of the mice and in the bright
+ 
+
+ align:start position:0%
+cavity of the mice and in the bright
+orange you see all the tumor masses that
+
+ align:start position:0%
+orange you see all the tumor masses that
+ 
+
+ align:start position:0%
+orange you see all the tumor masses that
+have lit up so we have injected the mice
+
+ align:start position:0%
+have lit up so we have injected the mice
+ 
+
+ align:start position:0%
+have lit up so we have injected the mice
+with trillions of our tiny little
+
+ align:start position:0%
+with trillions of our tiny little
+ 
+
+ align:start position:0%
+with trillions of our tiny little
+molecular shuttles that carry our CNT to
+
+ align:start position:0%
+molecular shuttles that carry our CNT to
+ 
+
+ align:start position:0%
+molecular shuttles that carry our CNT to
+the location of the
+
+ align:start position:0%
+the location of the
+ 
+
+ align:start position:0%
+the location of the
+tumor and using our imager which we have
+
+ align:start position:0%
+tumor and using our imager which we have
+ 
+
+ align:start position:0%
+tumor and using our imager which we have
+um built
+
+ align:start position:0%
+um built
+ 
+
+ align:start position:0%
+um built
+um with help from the Lincoln Labs um
+
+ align:start position:0%
+um with help from the Lincoln Labs um
+ 
+
+ align:start position:0%
+um with help from the Lincoln Labs um
+the surgeon is able to go in and remove
+
+ align:start position:0%
+the surgeon is able to go in and remove
+ 
+
+ align:start position:0%
+the surgeon is able to go in and remove
+all these nodules and the cool thing
+
+ align:start position:0%
+all these nodules and the cool thing
+ 
+
+ align:start position:0%
+all these nodules and the cool thing
+about the nodules here is we're getting
+
+ align:start position:0%
+about the nodules here is we're getting
+ 
+
+ align:start position:0%
+about the nodules here is we're getting
+the ones that are even below a
+
+ align:start position:0%
+the ones that are even below a
+ 
+
+ align:start position:0%
+the ones that are even below a
+millimeter in diameter so usually when a
+
+ align:start position:0%
+millimeter in diameter so usually when a
+ 
+
+ align:start position:0%
+millimeter in diameter so usually when a
+surgeon goes in without any guidance he
+
+ align:start position:0%
+surgeon goes in without any guidance he
+ 
+
+ align:start position:0%
+surgeon goes in without any guidance he
+might miss these because he's just going
+
+ align:start position:0%
+might miss these because he's just going
+ 
+
+ align:start position:0%
+might miss these because he's just going
+by ey but because he has the imager he
+
+ align:start position:0%
+by ey but because he has the imager he
+ 
+
+ align:start position:0%
+by ey but because he has the imager he
+can go ahead and move most of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tumors so here's an example of what
+
+ align:start position:0%
+tumors so here's an example of what
+ 
+
+ align:start position:0%
+tumors so here's an example of what
+we're doing in real time so during
+
+ align:start position:0%
+we're doing in real time so during
+ 
+
+ align:start position:0%
+we're doing in real time so during
+surgery if the surgeon can directly
+
+ align:start position:0%
+surgery if the surgeon can directly
+ 
+
+ align:start position:0%
+surgery if the surgeon can directly
+refer to the image that he's getting um
+
+ align:start position:0%
+refer to the image that he's getting um
+ 
+
+ align:start position:0%
+refer to the image that he's getting um
+then he can go ahead and Implement our
+
+ align:start position:0%
+then he can go ahead and Implement our
+ 
+
+ align:start position:0%
+then he can go ahead and Implement our
+technology in a very real way so here we
+
+ align:start position:0%
+technology in a very real way so here we
+ 
+
+ align:start position:0%
+technology in a very real way so here we
+see Dr na uh at from MGH he's doing
+
+ align:start position:0%
+see Dr na uh at from MGH he's doing
+ 
+
+ align:start position:0%
+see Dr na uh at from MGH he's doing
+surgery on mice um and you can see on
+
+ align:start position:0%
+surgery on mice um and you can see on
+ 
+
+ align:start position:0%
+surgery on mice um and you can see on
+the screen he can see brightly lit up
+
+ align:start position:0%
+the screen he can see brightly lit up
+ 
+
+ align:start position:0%
+the screen he can see brightly lit up
+this is where the tumors are and this is
+
+ align:start position:0%
+this is where the tumors are and this is
+ 
+
+ align:start position:0%
+this is where the tumors are and this is
+where I should take it them and so
+
+ align:start position:0%
+where I should take it them and so
+ 
+
+ align:start position:0%
+where I should take it them and so
+here's a Serial image of what's
+
+ align:start position:0%
+here's a Serial image of what's
+ 
+
+ align:start position:0%
+here's a Serial image of what's
+happening so here's the probes lighting
+
+ align:start position:0%
+happening so here's the probes lighting
+ 
+
+ align:start position:0%
+happening so here's the probes lighting
+up where the tumors
+
+ align:start position:0%
+up where the tumors
+ 
+
+ align:start position:0%
+up where the tumors
+are this is what happens when the
+
+ align:start position:0%
+are this is what happens when the
+ 
+
+ align:start position:0%
+are this is what happens when the
+surgeon goes in by ey and is like okay
+
+ align:start position:0%
+surgeon goes in by ey and is like okay
+ 
+
+ align:start position:0%
+surgeon goes in by ey and is like okay
+from my experience this is where I
+
+ align:start position:0%
+from my experience this is where I
+ 
+
+ align:start position:0%
+from my experience this is where I
+should take out the tumors and you see
+
+ align:start position:0%
+should take out the tumors and you see
+ 
+
+ align:start position:0%
+should take out the tumors and you see
+that there's quite a bit of mass left um
+
+ align:start position:0%
+that there's quite a bit of mass left um
+ 
+
+ align:start position:0%
+that there's quite a bit of mass left um
+but if we have the
+
+ align:start position:0%
+but if we have the
+ 
+
+ align:start position:0%
+but if we have the
+imager then we have a much cleaner image
+
+ align:start position:0%
+imager then we have a much cleaner image
+ 
+
+ align:start position:0%
+imager then we have a much cleaner image
+at the end of the surgery and so there's
+
+ align:start position:0%
+at the end of the surgery and so there's
+ 
+
+ align:start position:0%
+at the end of the surgery and so there's
+a lot less of a chance that the tumor is
+
+ align:start position:0%
+a lot less of a chance that the tumor is
+ 
+
+ align:start position:0%
+a lot less of a chance that the tumor is
+going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recur so for me personally there are two
+
+ align:start position:0%
+recur so for me personally there are two
+ 
+
+ align:start position:0%
+recur so for me personally there are two
+things I'm doing in order to expand on
+
+ align:start position:0%
+things I'm doing in order to expand on
+ 
+
+ align:start position:0%
+things I'm doing in order to expand on
+our system that we have already built
+
+ align:start position:0%
+our system that we have already built
+ 
+
+ align:start position:0%
+our system that we have already built
+the first is manipulating the M13 phage
+
+ align:start position:0%
+the first is manipulating the M13 phage
+ 
+
+ align:start position:0%
+the first is manipulating the M13 phage
+to different geometries so I call this
+
+ align:start position:0%
+to different geometries so I call this
+ 
+
+ align:start position:0%
+to different geometries so I call this
+en age Ino just means small in
+
+ align:start position:0%
+en age Ino just means small in
+ 
+
+ align:start position:0%
+en age Ino just means small in
+Portuguese
+
+ align:start position:0%
+Portuguese
+ 
+
+ align:start position:0%
+Portuguese
+um and so based on the aspect ratio
+
+ align:start position:0%
+um and so based on the aspect ratio
+ 
+
+ align:start position:0%
+um and so based on the aspect ratio
+which basically is the diameter versus
+
+ align:start position:0%
+which basically is the diameter versus
+ 
+
+ align:start position:0%
+which basically is the diameter versus
+the length um of our phage they might
+
+ align:start position:0%
+the length um of our phage they might
+ 
+
+ align:start position:0%
+the length um of our phage they might
+have very different traveling abilities
+
+ align:start position:0%
+have very different traveling abilities
+ 
+
+ align:start position:0%
+have very different traveling abilities
+in the bloodstream so because of their
+
+ align:start position:0%
+in the bloodstream so because of their
+ 
+
+ align:start position:0%
+in the bloodstream so because of their
+oblong shape they have and a tendency to
+
+ align:start position:0%
+oblong shape they have and a tendency to
+ 
+
+ align:start position:0%
+oblong shape they have and a tendency to
+stick to the walls and Tumble around but
+
+ align:start position:0%
+stick to the walls and Tumble around but
+ 
+
+ align:start position:0%
+stick to the walls and Tumble around but
+if we can change the shape to an optimal
+
+ align:start position:0%
+if we can change the shape to an optimal
+ 
+
+ align:start position:0%
+if we can change the shape to an optimal
+size then there's a chance that they
+
+ align:start position:0%
+size then there's a chance that they
+ 
+
+ align:start position:0%
+size then there's a chance that they
+will travel uh for a longer period of
+
+ align:start position:0%
+will travel uh for a longer period of
+ 
+
+ align:start position:0%
+will travel uh for a longer period of
+time in the bloodstream and so find the
+
+ align:start position:0%
+time in the bloodstream and so find the
+ 
+
+ align:start position:0%
+time in the bloodstream and so find the
+tumors that are farther from the site of
+
+ align:start position:0%
+tumors that are farther from the site of
+ 
+
+ align:start position:0%
+tumors that are farther from the site of
+injection
+
+ align:start position:0%
+injection
+ 
+
+ align:start position:0%
+injection
+the second thing is we are expanding on
+
+ align:start position:0%
+the second thing is we are expanding on
+ 
+
+ align:start position:0%
+the second thing is we are expanding on
+the library of cancers that we can
+
+ align:start position:0%
+the library of cancers that we can
+ 
+
+ align:start position:0%
+the library of cancers that we can
+attack so so far we've looked at ovarian
+
+ align:start position:0%
+attack so so far we've looked at ovarian
+ 
+
+ align:start position:0%
+attack so so far we've looked at ovarian
+tumor um and now I want to look at brain
+
+ align:start position:0%
+tumor um and now I want to look at brain
+ 
+
+ align:start position:0%
+tumor um and now I want to look at brain
+tumor and the most difficult thing about
+
+ align:start position:0%
+tumor and the most difficult thing about
+ 
+
+ align:start position:0%
+tumor and the most difficult thing about
+brain tumor is the bloodb brain barrier
+
+ align:start position:0%
+brain tumor is the bloodb brain barrier
+ 
+
+ align:start position:0%
+brain tumor is the bloodb brain barrier
+so it's just a layer of cells that
+
+ align:start position:0%
+so it's just a layer of cells that
+ 
+
+ align:start position:0%
+so it's just a layer of cells that
+separate your blood from the matter in
+
+ align:start position:0%
+separate your blood from the matter in
+ 
+
+ align:start position:0%
+separate your blood from the matter in
+your brain um and the molecules that
+
+ align:start position:0%
+your brain um and the molecules that
+ 
+
+ align:start position:0%
+your brain um and the molecules that
+pass through are very specific and very
+
+ align:start position:0%
+pass through are very specific and very
+ 
+
+ align:start position:0%
+pass through are very specific and very
+small so it's very hard to deliver from
+
+ align:start position:0%
+small so it's very hard to deliver from
+ 
+
+ align:start position:0%
+small so it's very hard to deliver from
+your bloodstream um various drugs or
+
+ align:start position:0%
+your bloodstream um various drugs or
+ 
+
+ align:start position:0%
+your bloodstream um various drugs or
+Imaging agents to the actual uh brain
+
+ align:start position:0%
+Imaging agents to the actual uh brain
+ 
+
+ align:start position:0%
+Imaging agents to the actual uh brain
+mass so what we have done here is
+
+ align:start position:0%
+mass so what we have done here is
+ 
+
+ align:start position:0%
+mass so what we have done here is
+actually uh engineer the head peptid so
+
+ align:start position:0%
+actually uh engineer the head peptid so
+ 
+
+ align:start position:0%
+actually uh engineer the head peptid so
+the proteins at the head um of our Fage
+
+ align:start position:0%
+the proteins at the head um of our Fage
+ 
+
+ align:start position:0%
+the proteins at the head um of our Fage
+so that it allows for uh travel across
+
+ align:start position:0%
+so that it allows for uh travel across
+ 
+
+ align:start position:0%
+so that it allows for uh travel across
+the blood brain barrier so we can
+
+ align:start position:0%
+the blood brain barrier so we can
+ 
+
+ align:start position:0%
+the blood brain barrier so we can
+deliver these Imaging um molecules to
+
+ align:start position:0%
+deliver these Imaging um molecules to
+ 
+
+ align:start position:0%
+deliver these Imaging um molecules to
+tumors in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain so one thing to remember here is
+
+ align:start position:0%
+brain so one thing to remember here is
+ 
+
+ align:start position:0%
+brain so one thing to remember here is
+that the scale that we're working this
+
+ align:start position:0%
+that the scale that we're working this
+ 
+
+ align:start position:0%
+that the scale that we're working this
+at the scale at which we're working is
+
+ align:start position:0%
+at the scale at which we're working is
+ 
+
+ align:start position:0%
+at the scale at which we're working is
+very very small so if you look at CNT or
+
+ align:start position:0%
+very very small so if you look at CNT or
+ 
+
+ align:start position:0%
+very very small so if you look at CNT or
+the rage really it's about 100 times 100
+
+ align:start position:0%
+the rage really it's about 100 times 100
+ 
+
+ align:start position:0%
+the rage really it's about 100 times 100
+thousand times smaller than a strand of
+
+ align:start position:0%
+thousand times smaller than a strand of
+ 
+
+ align:start position:0%
+thousand times smaller than a strand of
+your hair so there's really really tiny
+
+ align:start position:0%
+your hair so there's really really tiny
+ 
+
+ align:start position:0%
+your hair so there's really really tiny
+things um so when I make these small
+
+ align:start position:0%
+things um so when I make these small
+ 
+
+ align:start position:0%
+things um so when I make these small
+Fage they're even smaller than a regular
+
+ align:start position:0%
+Fage they're even smaller than a regular
+ 
+
+ align:start position:0%
+Fage they're even smaller than a regular
+Fage a regular Fage is about 800
+
+ align:start position:0%
+Fage a regular Fage is about 800
+ 
+
+ align:start position:0%
+Fage a regular Fage is about 800
+nanometers um so here's an example of
+
+ align:start position:0%
+nanometers um so here's an example of
+ 
+
+ align:start position:0%
+nanometers um so here's an example of
+280 nanm Fage 100 nanometer Fage and 50
+
+ align:start position:0%
+280 nanm Fage 100 nanometer Fage and 50
+ 
+
+ align:start position:0%
+280 nanm Fage 100 nanometer Fage and 50
+nimet Fage so when I make them and I
+
+ align:start position:0%
+nimet Fage so when I make them and I
+ 
+
+ align:start position:0%
+nimet Fage so when I make them and I
+want to look at them it's really hard
+
+ align:start position:0%
+want to look at them it's really hard
+ 
+
+ align:start position:0%
+want to look at them it's really hard
+because they're so small and you can't
+
+ align:start position:0%
+because they're so small and you can't
+ 
+
+ align:start position:0%
+because they're so small and you can't
+just use regular light microscopy uh to
+
+ align:start position:0%
+just use regular light microscopy uh to
+ 
+
+ align:start position:0%
+just use regular light microscopy uh to
+detect them um so another interesting
+
+ align:start position:0%
+detect them um so another interesting
+ 
+
+ align:start position:0%
+detect them um so another interesting
+thing that I do is use Atomic Force
+
+ align:start position:0%
+thing that I do is use Atomic Force
+ 
+
+ align:start position:0%
+thing that I do is use Atomic Force
+microscopy I don't know if you've heard
+
+ align:start position:0%
+microscopy I don't know if you've heard
+ 
+
+ align:start position:0%
+microscopy I don't know if you've heard
+of it but what it is is basically you
+
+ align:start position:0%
+of it but what it is is basically you
+ 
+
+ align:start position:0%
+of it but what it is is basically you
+take a sample and you have this very
+
+ align:start position:0%
+take a sample and you have this very
+ 
+
+ align:start position:0%
+take a sample and you have this very
+very tiny needle that scans across the
+
+ align:start position:0%
+very tiny needle that scans across the
+ 
+
+ align:start position:0%
+very tiny needle that scans across the
+surface and so you're getting a topology
+
+ align:start position:0%
+surface and so you're getting a topology
+ 
+
+ align:start position:0%
+surface and so you're getting a topology
+of the surface and from that scanning
+
+ align:start position:0%
+of the surface and from that scanning
+ 
+
+ align:start position:0%
+of the surface and from that scanning
+kind of like reading brail you get a
+
+ align:start position:0%
+kind of like reading brail you get a
+ 
+
+ align:start position:0%
+kind of like reading brail you get a
+good idea of what the profile of your
+
+ align:start position:0%
+good idea of what the profile of your
+ 
+
+ align:start position:0%
+good idea of what the profile of your
+image is so these are the images that I
+
+ align:start position:0%
+image is so these are the images that I
+ 
+
+ align:start position:0%
+image is so these are the images that I
+get from this sort of needle probing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um for the brain tumor another
+
+ align:start position:0%
+um for the brain tumor another
+ 
+
+ align:start position:0%
+um for the brain tumor another
+interesting Factor not only can we you
+
+ align:start position:0%
+interesting Factor not only can we you
+ 
+
+ align:start position:0%
+interesting Factor not only can we you
+know bring the Fage to the surface of
+
+ align:start position:0%
+know bring the Fage to the surface of
+ 
+
+ align:start position:0%
+know bring the Fage to the surface of
+the tumor so this is tumor here shown in
+
+ align:start position:0%
+the tumor so this is tumor here shown in
+ 
+
+ align:start position:0%
+the tumor so this is tumor here shown in
+green um this is tumor that actually has
+
+ align:start position:0%
+green um this is tumor that actually has
+ 
+
+ align:start position:0%
+green um this is tumor that actually has
+green fluorescent protein so that means
+
+ align:start position:0%
+green fluorescent protein so that means
+ 
+
+ align:start position:0%
+green fluorescent protein so that means
+they glow um and if we send in our Fage
+
+ align:start position:0%
+they glow um and if we send in our Fage
+ 
+
+ align:start position:0%
+they glow um and if we send in our Fage
+we see that oh yeah our Fage goes ahead
+
+ align:start position:0%
+we see that oh yeah our Fage goes ahead
+ 
+
+ align:start position:0%
+we see that oh yeah our Fage goes ahead
+and coats in red the tumor but then the
+
+ align:start position:0%
+and coats in red the tumor but then the
+ 
+
+ align:start position:0%
+and coats in red the tumor but then the
+other thing we notice is that the Fage
+
+ align:start position:0%
+other thing we notice is that the Fage
+ 
+
+ align:start position:0%
+other thing we notice is that the Fage
+is actually internalized into the tumor
+
+ align:start position:0%
+is actually internalized into the tumor
+ 
+
+ align:start position:0%
+is actually internalized into the tumor
+cells so the Fage comes and attaches to
+
+ align:start position:0%
+cells so the Fage comes and attaches to
+ 
+
+ align:start position:0%
+cells so the Fage comes and attaches to
+the surface and then the tumor cells
+
+ align:start position:0%
+the surface and then the tumor cells
+ 
+
+ align:start position:0%
+the surface and then the tumor cells
+eats the Fage um so in the blue here is
+
+ align:start position:0%
+eats the Fage um so in the blue here is
+ 
+
+ align:start position:0%
+eats the Fage um so in the blue here is
+the nucleus of a
+
+ align:start position:0%
+the nucleus of a
+ 
+
+ align:start position:0%
+the nucleus of a
+Fage um and in the red spread around the
+
+ align:start position:0%
+Fage um and in the red spread around the
+ 
+
+ align:start position:0%
+Fage um and in the red spread around the
+nucleus in the GOI region is our Fage so
+
+ align:start position:0%
+nucleus in the GOI region is our Fage so
+ 
+
+ align:start position:0%
+nucleus in the GOI region is our Fage so
+just tells us we can possibly deliver
+
+ align:start position:0%
+just tells us we can possibly deliver
+ 
+
+ align:start position:0%
+just tells us we can possibly deliver
+things to inside the cells of the cancer
+
+ align:start position:0%
+things to inside the cells of the cancer
+ 
+
+ align:start position:0%
+things to inside the cells of the cancer
+um so that means we could send in
+
+ align:start position:0%
+um so that means we could send in
+ 
+
+ align:start position:0%
+um so that means we could send in
+therapies that disrupt the function and
+
+ align:start position:0%
+therapies that disrupt the function and
+ 
+
+ align:start position:0%
+therapies that disrupt the function and
+so in this way kill the tumor cell
+
+ align:start position:0%
+so in this way kill the tumor cell
+ 
+
+ align:start position:0%
+so in this way kill the tumor cell
+and so can we not only detect where they
+
+ align:start position:0%
+and so can we not only detect where they
+ 
+
+ align:start position:0%
+and so can we not only detect where they
+are and see if we can remove them
+
+ align:start position:0%
+are and see if we can remove them
+ 
+
+ align:start position:0%
+are and see if we can remove them
+effectively but we can also locally um
+
+ align:start position:0%
+effectively but we can also locally um
+ 
+
+ align:start position:0%
+effectively but we can also locally um
+cure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so overall um today we've looked at
+
+ align:start position:0%
+them so overall um today we've looked at
+ 
+
+ align:start position:0%
+them so overall um today we've looked at
+um the very real medical impact that we
+
+ align:start position:0%
+um the very real medical impact that we
+ 
+
+ align:start position:0%
+um the very real medical impact that we
+can do with imaging and the probe that
+
+ align:start position:0%
+can do with imaging and the probe that
+ 
+
+ align:start position:0%
+can do with imaging and the probe that
+we have biologically engineered in our
+
+ align:start position:0%
+we have biologically engineered in our
+ 
+
+ align:start position:0%
+we have biologically engineered in our
+lab and um the two things that I've done
+
+ align:start position:0%
+lab and um the two things that I've done
+ 
+
+ align:start position:0%
+lab and um the two things that I've done
+is you know look at what we can do to
+
+ align:start position:0%
+is you know look at what we can do to
+ 
+
+ align:start position:0%
+is you know look at what we can do to
+change the geometry and what we can do
+
+ align:start position:0%
+change the geometry and what we can do
+ 
+
+ align:start position:0%
+change the geometry and what we can do
+to change the different cancers that we
+
+ align:start position:0%
+to change the different cancers that we
+ 
+
+ align:start position:0%
+to change the different cancers that we
+can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attack and all of this work of course
+
+ align:start position:0%
+attack and all of this work of course
+ 
+
+ align:start position:0%
+attack and all of this work of course
+isn't possible without the collaboration
+
+ align:start position:0%
+isn't possible without the collaboration
+ 
+
+ align:start position:0%
+isn't possible without the collaboration
+that happens between the colleagues I
+
+ align:start position:0%
+that happens between the colleagues I
+ 
+
+ align:start position:0%
+that happens between the colleagues I
+have at the MIT cook Institute as well
+
+ align:start position:0%
+have at the MIT cook Institute as well
+ 
+
+ align:start position:0%
+have at the MIT cook Institute as well
+as the um scientists we have at the
+
+ align:start position:0%
+as the um scientists we have at the
+ 
+
+ align:start position:0%
+as the um scientists we have at the
+Lincoln labs and so that's another
+
+ align:start position:0%
+Lincoln labs and so that's another
+ 
+
+ align:start position:0%
+Lincoln labs and so that's another
+really cool thing about this project
+
+ align:start position:0%
+really cool thing about this project
+ 
+
+ align:start position:0%
+really cool thing about this project
+it's it's so very Broad and so it brings
+
+ align:start position:0%
+it's it's so very Broad and so it brings
+ 
+
+ align:start position:0%
+it's it's so very Broad and so it brings
+in so many different techniques and
+
+ align:start position:0%
+in so many different techniques and
+ 
+
+ align:start position:0%
+in so many different techniques and
+brings in so many different people and
+
+ align:start position:0%
+brings in so many different people and
+ 
+
+ align:start position:0%
+brings in so many different people and
+so I really want to thank them um and
+
+ align:start position:0%
+so I really want to thank them um and
+ 
+
+ align:start position:0%
+so I really want to thank them um and
+another aspect of this work that I
+
+ align:start position:0%
+another aspect of this work that I
+ 
+
+ align:start position:0%
+another aspect of this work that I
+really find meaningful is that it's F I
+
+ align:start position:0%
+really find meaningful is that it's F I
+ 
+
+ align:start position:0%
+really find meaningful is that it's F I
+am personally funded by families that
+
+ align:start position:0%
+am personally funded by families that
+ 
+
+ align:start position:0%
+am personally funded by families that
+are affected by these types of tumors um
+
+ align:start position:0%
+are affected by these types of tumors um
+ 
+
+ align:start position:0%
+are affected by these types of tumors um
+these types of diseases and so I really
+
+ align:start position:0%
+these types of diseases and so I really
+ 
+
+ align:start position:0%
+these types of diseases and so I really
+want to thank
+
+ align:start position:0%
+want to thank
+ 
+
+ align:start position:0%
+want to thank
+the the goodwi crack hour staller and
+
+ align:start position:0%
+the the goodwi crack hour staller and
+ 
+
+ align:start position:0%
+the the goodwi crack hour staller and
+salmon um families um who have been
+
+ align:start position:0%
+salmon um families um who have been
+ 
+
+ align:start position:0%
+salmon um families um who have been
+really generous with their funding uh
+
+ align:start position:0%
+really generous with their funding uh
+ 
+
+ align:start position:0%
+really generous with their funding uh
+for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+project and yeah finally I want to say
+
+ align:start position:0%
+project and yeah finally I want to say
+ 
+
+ align:start position:0%
+project and yeah finally I want to say
+that for me the M13 is kind of a
+
+ align:start position:0%
+that for me the M13 is kind of a
+ 
+
+ align:start position:0%
+that for me the M13 is kind of a
+building block we're here all as girls
+
+ align:start position:0%
+building block we're here all as girls
+ 
+
+ align:start position:0%
+building block we're here all as girls
+who build and so for me for my building
+
+ align:start position:0%
+who build and so for me for my building
+ 
+
+ align:start position:0%
+who build and so for me for my building
+project is M13 um and I hope that you
+
+ align:start position:0%
+project is M13 um and I hope that you
+ 
+
+ align:start position:0%
+project is M13 um and I hope that you
+guys um are able to understand from this
+
+ align:start position:0%
+guys um are able to understand from this
+ 
+
+ align:start position:0%
+guys um are able to understand from this
+that as an engineer for me it's really
+
+ align:start position:0%
+that as an engineer for me it's really
+ 
+
+ align:start position:0%
+that as an engineer for me it's really
+just about finding creative ways to use
+
+ align:start position:0%
+just about finding creative ways to use
+ 
+
+ align:start position:0%
+just about finding creative ways to use
+my building blocks to make a difference
+
+ align:start position:0%
+my building blocks to make a difference
+ 
+
+ align:start position:0%
+my building blocks to make a difference
+to address the problems that I think are
+
+ align:start position:0%
+to address the problems that I think are
+ 
+
+ align:start position:0%
+to address the problems that I think are
+most important to me um and so yeah
+
+ align:start position:0%
+most important to me um and so yeah
+ 
+
+ align:start position:0%
+most important to me um and so yeah
+thank you very much for listening um
+
+ align:start position:0%
+thank you very much for listening um
+ 
+
+ align:start position:0%
+thank you very much for listening um
+please feel free to ask me any questions
+
+ align:start position:0%
+please feel free to ask me any questions
+ 
+
+ align:start position:0%
+please feel free to ask me any questions
+um I can talk more about myself or I can
+
+ align:start position:0%
+um I can talk more about myself or I can
+ 
+
+ align:start position:0%
+um I can talk more about myself or I can
+talk more about my research
+
+ align:start position:0%
+talk more about my research
+ 
+
+ align:start position:0%
+talk more about my research
+um but yes thank
+
+ align:start position:0%
+um but yes thank
+ 
+
+ align:start position:0%
+um but yes thank
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+you any questions
+
+ align:start position:0%
+you any questions
+ 
+
+ align:start position:0%
+you any questions
+for yes well I you're using specific
+
+ align:start position:0%
+for yes well I you're using specific
+ 
+
+ align:start position:0%
+for yes well I you're using specific
+examples for the cancer but can these
+
+ align:start position:0%
+examples for the cancer but can these
+ 
+
+ align:start position:0%
+examples for the cancer but can these
+detect any type of cancer or is it just
+
+ align:start position:0%
+detect any type of cancer or is it just
+ 
+
+ align:start position:0%
+detect any type of cancer or is it just
+specific to a couple types it can detect
+
+ align:start position:0%
+specific to a couple types it can detect
+ 
+
+ align:start position:0%
+specific to a couple types it can detect
+any type of cancer as long as you have a
+
+ align:start position:0%
+any type of cancer as long as you have a
+ 
+
+ align:start position:0%
+any type of cancer as long as you have a
+specific uh differentiating marker on
+
+ align:start position:0%
+specific uh differentiating marker on
+ 
+
+ align:start position:0%
+specific uh differentiating marker on
+the cancer that you know of yeah so um
+
+ align:start position:0%
+the cancer that you know of yeah so um
+ 
+
+ align:start position:0%
+the cancer that you know of yeah so um
+not only is this useful in cancer it's
+
+ align:start position:0%
+not only is this useful in cancer it's
+ 
+
+ align:start position:0%
+not only is this useful in cancer it's
+also useful in detecting any other
+
+ align:start position:0%
+also useful in detecting any other
+ 
+
+ align:start position:0%
+also useful in detecting any other
+material as long as you're able to
+
+ align:start position:0%
+material as long as you're able to
+ 
+
+ align:start position:0%
+material as long as you're able to
+modify the head so that it is specific
+
+ align:start position:0%
+modify the head so that it is specific
+ 
+
+ align:start position:0%
+modify the head so that it is specific
+to that material or to that um
+
+ align:start position:0%
+to that material or to that um
+ 
+
+ align:start position:0%
+to that material or to that um
+cell then you can do that which makes it
+
+ align:start position:0%
+cell then you can do that which makes it
+ 
+
+ align:start position:0%
+cell then you can do that which makes it
+a very elegant very cool molecule which
+
+ align:start position:0%
+a very elegant very cool molecule which
+ 
+
+ align:start position:0%
+a very elegant very cool molecule which
+is why I think it's you know something I
+
+ align:start position:0%
+is why I think it's you know something I
+ 
+
+ align:start position:0%
+is why I think it's you know something I
+should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using all right thank you thank
+
+ align:start position:0%
+using all right thank you thank
+ 
+
+ align:start position:0%
+using all right thank you thank
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/d5pnfFvggYk.txt b/d5pnfFvggYk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..096904824563871df9a6a5de43b1fce6a03578ac
--- /dev/null
+++ b/d5pnfFvggYk.txt
@@ -0,0 +1,255 @@
+Mathematically speaking, the
+Chebyshev inequality is just a
+
+simple application of the
+Markov inequality.
+
+However, it contains a somewhat
+different message.
+
+Consider a random variable
+that has a
+
+certain mean and variance.
+
+What the Chebyshev inequality
+says is that if the variance
+
+is small, then the random
+variable is unlikely to fall
+
+too far off from the mean.
+
+If the variance is small, we
+have little randomness.
+
+And so X cannot be too
+far from the mean.
+
+In more precise terms, we have
+the following inequality.
+
+The probability that the
+distance from the mean is
+
+larger than or equal to a
+certain number is, at most,
+
+the variance divided by the
+square of that number.
+
+So if the variance is small, the
+probability of falling far
+
+from the mean is also
+going to be small.
+
+And if the number c is large, so
+that we're talking about a
+
+large distance from the mean,
+then the probability of this
+
+event happening falls
+off at a rate at
+
+least 1 over c squared.
+
+By the way, I should add here
+that c is assumed to be a
+
+positive number.
+
+If c was negative, then the
+probability that we're looking
+
+at would be equal to 1 anyway.
+
+And there isn't any point in
+trying obtain a bound for it.
+
+To prove the Chebyshev
+inequality, we will apply the
+
+Markov equality as follows.
+
+The probability of interest is
+the same as the probability
+
+that the square of this quantity
+is larger than or
+
+equal to the square of c.
+
+But now, here we have a
+non-negative random variable.
+
+And we can apply the Markov
+inequality with X replaced by
+
+this random variable and with
+a replaced by c squared.
+
+So this gives us the expected
+value of the random variable
+
+of interest divided
+by c squared.
+
+But we recognize that the
+
+numerator is just the variance.
+
+And this is the Chebyshev
+inequality that we claimed.
+
+As an application of the
+Chebyshev inequality, let us
+
+look at the probability of this
+event that the distance
+
+from the mean is at least k
+standard deviations, where k
+
+is some positive number.
+
+Using the Chebyshev inequality
+with c replaced by k times
+
+sigma, we obtain sigma squared
+over c squared, which in our
+
+case is k squared times
+sigma squared,
+
+which is 1 over k squared.
+
+So what this is saying is that
+if you take, for example, k
+
+equal to 3, the probability that
+you fall three standard
+
+deviations away from the mean
+or more, that probability is
+
+going to be less than or
+equal to 1 over 9.
+
+And this is true no matter
+what kind of
+
+distribution you have.
+
+Let us now revisit our earlier
+example, where X is an
+
+exponential random variable.
+
+And we're interested in the
+probability that the random
+
+variable takes a value larger
+than or equal to a.
+
+The Markov inequality gave
+us a bound of 1 over a.
+
+And as we recall, the exact
+answer to this probability was
+
+e to the minus a.
+
+Let us see what we can get
+using the Chebyshev
+
+inequality.
+
+Now, our random variable
+has a mean of 1.
+
+Let us assume that a is bigger
+than 1, so that we're
+
+considering an event that we
+fall far away from the mean by
+
+a distance of at least
+a minus 1.
+
+That is we write the probability
+that X is larger
+
+than or equal to a as the
+probability that the distance
+
+of X from the mean is larger
+than or equal to a minus 1.
+
+And now, this event is smaller
+than the event that the
+
+absolute value of X minus 1
+is larger than a minus 1.
+
+This is because if this event is
+true, then that event will
+
+also be true.
+
+And now, we can apply the
+Chebyshev inequality.
+
+Here we have the distance
+of X from the mean.
+
+So the Chebyshev inequality
+applied to the random variable
+
+X will have up here
+the variance of X,
+
+which is equal to 1.
+
+And in the denominator, we will
+have a minus 1 squared.
+
+Notice that if a is a large
+number, this quantity here
+
+behaves like 1 over a squared,
+which falls off much faster
+
+than 1 over a.
+
+So at least for large a's, the
+Chebyshev bound is going to
+
+give us a smaller bound and,
+therefore, more informative
+
+than what we obtained from
+the Markov inequality.
+
+In most cases, the Chebyshev
+inequality is, indeed,
+
+stronger and more informative
+than the Markov inequality.
+
+And one of the reasons is that
+it exploits more information
+
+about the distribution of the
+random variable X. That is it
+
+uses knowledge, not just
+about the mean
+
+of the random variable.
+
+But it also uses some
+information about the variance
+
+of the random variable.
\ No newline at end of file
diff --git a/eeauylMvOvA.txt b/eeauylMvOvA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..316a82f8771dbb1c514b45afacaeb9ced51b0bce
--- /dev/null
+++ b/eeauylMvOvA.txt
@@ -0,0 +1,2789 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Our topics part of
+the course by revisiting
+
+another important topic that--
+
+one of the most important topics
+in economics which is
+
+where does capital come from.
+
+This is a topic that is
+essential in economics.
+
+It's also really central, the
+basis, for what is in finance.
+
+So a lot of what we'll
+do today is really--
+
+if you want to learn more about
+it you take more in
+
+economics but also more
+courses in Course 15.
+
+So, basically, we spent a lot of
+time this semester talking
+
+about one input to
+the production
+
+function which is labor.
+
+We talked about labor supply,
+labor demand, monopsony
+
+models, et cetera.
+
+We haven't talked much about
+the other input into the
+
+production function
+which is capital.
+
+Now, partly, that's because
+that's a more awkward concept.
+
+It's clear what labor is.
+
+Labor is the workers working
+in the production process.
+
+Capital's a little bit harder
+because capital's sort of
+
+everything else-- the machine,
+the land, the buildings, other
+
+physical inputs.
+
+And we know where labor
+comes from.
+
+Labor comes from our working.
+
+But it's less clear where
+capital comes from in some
+
+aggregate concept.
+
+So, basically, the key thing is
+that all forms of capital
+
+have a common feature.
+
+All forms of capital have a
+common feature which is what
+
+capital represents is a
+diversion of current
+
+consumption towards future
+production and consumption.
+
+So capital's about diverting
+current consumption towards
+
+future production
+and consumption.
+
+So the original concept of
+capital came from farming
+
+where the notion was that
+farmers every year would take
+
+some of their grain, and, rather
+than eating it, they'd
+
+put it aside to become seed to
+plant for the next year.
+
+That was their capital.
+
+And so they diverted their
+consumption this year which
+
+was eating the grain they grew
+to produce future consumption
+
+through planting those
+seeds and creating
+
+consumption for next year.
+
+So, basically, in a modern
+economy the idea is the same.
+
+And so when we think about
+capital, what I want you to
+
+think about is I want you to
+think about, basically, the
+
+capital as money.
+
+Think of the capital in the
+production function as the
+
+money that we invest in all
+these other things that aren't
+
+labor-- that we invest in
+machines, and we invest in
+
+buildings, and we
+invest in land.
+
+So we want to think about
+capital not as physical
+
+capital but as financial
+capital.
+
+That's the way to be thinking
+about that one aggregate
+
+letter k is this financial
+capital.
+
+It's the money that's invested
+in producing goods, in
+
+building machines, and
+building buildings,
+
+and stuff like that.
+
+OK?
+
+Now, basically, where do
+firms get that money?
+
+So you're a firm.
+
+You want to build a building
+or new machine or
+
+something like that.
+
+Where do firms get that money?
+
+They get that money in
+capital markets.
+
+Capital markets are basically
+pools of money that firms draw
+
+on to invest and
+create capital.
+
+So a capital market--
+
+literally think of it as a pool
+of money that's out there
+
+that firms can tap into if they
+want to build a building
+
+or build a machine
+or buy some land.
+
+They tap into capital markets
+to make those investments.
+
+So while capital physically
+represents lots of different
+
+things, financially it
+represents one thing which is
+
+the pool of money that firms tap
+into to invest, to divert
+
+current consumption to
+future consumption.
+
+OK?
+
+It's the pool of money firms
+tap into to invest. That's
+
+what we mean by capital.
+
+By capital market we represent
+that pool of money.
+
+So think of capital as financial
+capital, and think
+
+of where you get financial
+capital in a capital market as
+
+being that pool of money that
+firms tap into to make
+
+investments to divert
+towards the future.
+
+Now, where does that supply
+of money come from?
+
+Where does that supply
+of money come from?
+
+Well it comes from households'
+decisions on how
+
+much to save. OK?
+
+So the pool of money in capital
+markets, the pool of
+
+money that firms draw on to
+build capital, comes from
+
+households' decisions
+on how much to save.
+
+So now we see the tie to labor,
+the other input in the
+
+production function.
+
+Just as households' decisions on
+how hard to work determines
+
+the labor input into the
+production function,
+
+households' decisions on how
+much to save determines the
+
+capital input into the
+production function.
+
+So just as my decision how much
+to work determines how
+
+much labor is available to
+firms, my decision on how much
+
+to save that's what fills
+up this pool.
+
+OK?
+
+So this pool of financial
+capital is filled up by
+
+household savings and then drawn
+down by firms' demand
+
+for investment.
+
+And that's the way a capital
+market works.
+
+So, basically, if we think
+about capital market
+
+equilibrium--
+
+if you go to Figure 21-1--
+
+we have equilibrium in
+capital markets.
+
+Now this is just like we talked
+about-- this is the
+
+other factor markets.
+
+Just like we talked about labor
+markets and determining
+
+what determines the wage rate
+and the optimum amount of
+
+labor hired, it's same
+with capital markets.
+
+You have some demand
+for capital.
+
+That comes from firms' demand
+for investment.
+
+Firms want new machines.
+
+They want new buildings.
+
+That's downward sloping because,
+initially, there's
+
+very high demand for capital.
+
+But there's a marginal
+diminishing product.
+
+The more capital I have the
+less valuable it is on the
+
+margin, the less you are
+willing to pay for it.
+
+So there's a downward sloping
+demand curve for capital and
+
+an upward sloping
+supply curve.
+
+And the price, in this market,
+is the interest rate.
+
+What is the interest rate?
+
+The interest rate is the rate
+you have to pay households to
+
+get them to lend you money.
+
+So the interest rate, i, is
+the rate you have to pay
+
+households to get them
+to lend you money.
+
+So if that interest rate is
+very high, firms will not
+
+demand much investment because
+they'll have to pay a lot of
+
+money to get the financial
+capital to finance that
+
+investment.
+
+But households will be delighted
+to supply lots of
+
+savings because they're
+getting paid a
+
+high price for it.
+
+So, basically, the interest
+rate serves as the
+
+equilibrating price
+in this market.
+
+Just as the wage serves as the
+equilibrating price in the
+
+labor market, the interest
+rate serves as the
+
+equilibrating price in
+the capital market.
+
+As the interest rate rises,
+folks want to save more,
+
+filling more money into
+that pool of capital.
+
+And firms want to borrow less,
+taking less money out of that
+
+pool of capital.
+
+And when that supply and demand
+is equilibrated, at
+
+point e, is going to be where
+the firm's drawing on the pool
+
+at exactly the rate people are
+putting money into the pool.
+
+And that's going to be
+the equilibrium.
+
+OK, so we want to focus on--
+
+for today's lecture and
+next lecture as well--
+
+is what determines the money
+that goes into that pool.
+
+We know what determines the rate
+at which firms want to
+
+draw out of that pool.
+
+That's basically going to be
+determined by the production
+
+function and all the stuff
+we learned in lectures on
+
+production theory.
+
+You can get your optimal
+demand for capital.
+
+It's going to be determined
+by isocosts and isoquants.
+
+And you get some k star.
+
+But what's going to determine
+what goes into that pool?
+
+That's going to be households'
+decisions to save. And
+
+households' decisions to save,
+we say, are determined by a
+
+process we call intertemporal
+choice.
+
+Added some extra letters there--
+intertemporal choice.
+
+Intertemporal choice--
+
+which is basically, instead
+of thinking about someone
+
+choosing between apples and
+bananas, we think of them
+
+choosing between consumption
+today
+
+and consumption tomorrow.
+
+So think of different periods
+like different goods.
+
+And I'm choosing between
+consumption today and
+
+consumption tomorrow.
+
+That's my intertemporal
+choice--
+
+the rate at which I choose to
+trade off consumption in
+
+different periods.
+
+So for example, I'll illustrate
+how this works.
+
+Let's say that I'm deciding
+whether to just tell MIT,
+
+"Look, I don't want
+to work next year.
+
+I want to stay home and
+take care of my kids.
+
+You're not going to pay me.
+
+I'm taking an unpaid leave for
+a year." Something professors
+
+can do with enough advance
+warning to their
+
+chairman and such.
+
+So I'm going to take an unpaid
+leave next year.
+
+I'm thinking about doing that.
+
+And now I have to
+say, OK, fine.
+
+Next year I'm going to take this
+unpaid leave so I have to
+
+decide how to allocate my--
+and then I'm going to come
+
+back and life will be
+the same thereafter.
+
+So it's just about next year I'm
+going to take this unpaid
+
+leave. I have to decide how to
+allocate my consumption across
+
+this year while I'm working and
+next year while I'm taking
+
+an unpaid leave.
+
+And let's say my salary
+is $80,000 a year.
+
+So one thing I could do is I can
+consume all $80,000 this
+
+year and consume nothing
+next year.
+
+That would not be a very
+satisfactory outcome as I die.
+
+That's obviously not going to
+be a satisfactory outcome.
+
+But what's the alternative?
+
+MIT's paying me this year,
+and they're not
+
+paying me next year.
+
+What's the alternative?
+
+Well, the alternative is I can
+save. And by saving, what we
+
+mean is I can loan some of the
+money that I make out to firms
+
+to invest in their physical
+capital in return for which
+
+they'll give me interest. And
+next year I can live on the
+
+interest I've earned from
+making that loan.
+
+Now, I don't literally go to
+Genzyme and Microsoft and
+
+Apple and say I want to
+loan you money and
+
+negotiate with them.
+
+That obviously would
+be impossible.
+
+What I do is I implicitly loan
+to firms through drawing on
+
+various aspects of the
+capital market.
+
+So does anyone know, how can I
+implicitly loan to a firm?
+
+Let's say I want to--
+
+Yeah?
+
+AUDIENCE: Banks.
+
+PROFESSOR: Banks.
+
+So explain what you mean.
+
+AUDIENCE: You deposit
+money in a savings
+
+account for the bank.
+
+The bank pays you some interest
+rate so that it can
+
+use your money to loan to bigger
+companies that want to
+
+take money out of the bank.
+
+And they, in return, get money
+from the other companies by
+
+the companies paying
+some interest on
+
+what they took out.
+
+PROFESSOR: Exactly.
+
+We call banks financial
+intermediaries.
+
+What that means is they
+basically are the folks who
+
+can get a hold of firms
+and make those loans.
+
+So, in other words, I don't
+loan directly to Genzyme.
+
+I loan to the bank--
+
+Citizens Bank, my bank,
+and Citizens
+
+Bank loans to Genzyme.
+
+Citizens Bank pays me an
+interest rate on my savings--
+
+now close to zero, we'll come
+to that-- but basically pays
+
+me some interest rate.
+
+Genzyme pays them an interest
+rate to borrow money, higher
+
+than what they're paying
+me, and the
+
+difference is bank profit.
+
+So, basically, one way I can
+loan money is I can put in the
+
+bank and get paid interest. we
+don't think about putting in
+
+the bank as a loan, but that's
+basically what you're doing.
+
+You're loaning it to the bank.
+
+And they're paying you interest
+
+rate, i for that loan.
+
+What else can you do?
+
+How else can you--
+
+Yeah?
+
+AUDIENCE: You can
+purchase stocks.
+
+PROFESSOR: You could
+purchase stocks.
+
+So, in other words, what I could
+do is I could directly
+
+go to a public company, and I
+could take some of my $80,000
+
+and buy stock in that company.
+
+There I'm essentially directly
+loaning to them.
+
+I'm directly giving
+them money.
+
+Now, it's not a loan that's paid
+back like a bank loan.
+
+It's loan that's paid back
+hopefully with my stock
+
+becoming more valuable
+or with a dividend.
+
+So how can I loan?
+
+One is I can invest--
+
+I could put it in the bank.
+
+The other is I can buy stock.
+
+I can put it in the bank, and
+the bank pays me interest. I
+
+could buy stock, and that stock
+pays off in two ways.
+
+One is many companies pay what
+we call a dividend, what is
+
+called the dividend, which is
+a quarterly payment that
+
+companies make to their
+shareholders.
+
+So if I invest in a company
+that pays a dividend, then
+
+I'll be getting a quarterly
+check from that company that's
+
+a portion of my investment.
+
+The other is what we call a
+capital gain which is the
+
+stock could go up in value.
+
+So next year, if the stock goes
+up, if the stock market
+
+moves steadily-- it doesn't,
+it jumps up and down, we'll
+
+come to that--
+
+but if it went steadily up I
+could just sell some of that
+
+stock next year and
+have extra money.
+
+So that's the other thing I
+could do with my $80,000.
+
+I could loan to a company
+by buying their stock.
+
+How else can I loan
+to a company?
+
+Yeah?
+
+AUDIENCE: I don't know exactly
+what the difference is, but
+
+couldn't you also invest
+your money in a
+
+mutual fund or something?
+
+PROFESSOR: A mutual fund--
+that's a good point.
+
+That would be loaning--
+
+a mutual fund is essentially
+loaning money to an aggregate
+
+collection of companies.
+
+So there are very different
+ways I can do stock.
+
+I can do a mutual fund, I can
+buy individual stocks.
+
+There's lots of different
+ways, but those are all
+
+different ways to buy stock.
+
+Yeah?
+
+AUDIENCE: You could buy bonds.
+
+PROFESSOR: You could
+buy bonds.
+
+You could buy company bonds
+which is I literally loan
+
+directly to the company.
+
+Stocks aren't really a loan.
+
+I'm literally buying an
+ownership share in the
+
+company, and they're
+paying me back.
+
+I could buy corporate bonds.
+
+I could buy corporate bonds, and
+the way those work is it's
+
+literally cutting out
+the middleman.
+
+I don't loan to Citizens Bank,
+and they loan to the company.
+
+I just loan to the company,
+and they pay me back.
+
+That's a corporate bond.
+
+I can also buy, by the
+way, I can also buy
+
+a government bond.
+
+You may know the government's
+running more than a trillion
+
+dollar deficit right now.
+
+Somebody's got to
+finance that.
+
+So you can loan to the
+government and get paid back
+
+by the government.
+
+OK, let's put the government
+aside for a minute.
+
+Let's focus where we just--
+
+we haven't really
+had a government
+
+sector in our models.
+
+We're where it's just you
+and the companies.
+
+So let's leave the government
+channel aside.
+
+But the other thing I can do
+with my money is I can loan it
+
+through bonds.
+
+The point is that $80,000--
+
+yeah, I'm sorry.
+
+AUDIENCE: With stocks, if I
+were to buy a stock from a
+
+company, wouldn't it be
+primarily and usually through
+
+the secondary market?
+
+I wouldn't be giving any
+money to the company.
+
+I'd just be giving money to
+the previous stockholder.
+
+PROFESSOR: That's true.
+
+It basically depends on whether
+the marginal stock
+
+comes from a new issuance as
+stock by the company or
+
+through stock that's already
+floating around
+
+the secondary market.
+
+That's a good point.
+
+So in some sense the--
+
+likewise with bonds.
+
+A lot of bonds are traded
+in a secondary market.
+
+So I'm thinking about a simple
+model where basically new
+
+stock gets issued by the
+company, I buy it.
+
+More technically you're right.
+
+It's just trading among people,
+but that sort of makes
+
+things complicated.
+
+Let's put that aside for now.
+
+So, basically, the point
+is is my $80,000--
+
+there's lots of things
+I can do with it.
+
+All of them yield
+me some rate--
+
+the key point is all of them
+have the feature that I'm
+
+diverting today's consumption
+for tomorrow's consumption.
+
+I'm taking some of my money
+and, rather than eating it
+
+this year when I'm working,
+I'm loaning it out in some
+
+way, shape, or form and getting
+payback in next year
+
+when I'm not working.
+
+And we can summarize.
+
+Now this is a very complicated
+set of mechanisms, not to
+
+mention the secondary
+market issues.
+
+And this is basically a
+semester of 15.401.
+
+This is basically a semester
+of finance theory.
+
+But basically what we're going
+to do is compress this all
+
+down and say that I get some
+interest rate on my money.
+
+However I do it, let's just say
+that somehow I divert my
+
+money through one of these
+mechanisms, and it yields some
+
+effective interest rate, i.
+
+And you can know behind that
+there's lots of ways I can get
+
+that interest. But for now just
+simplify it down and say
+
+the main thing is I'm diverting
+my consumption now,
+
+and it's yielding some interest
+earnings on that
+
+diverted consumption, i.
+
+So what that means is that for
+every dollar I divert, I get 1
+
+plus i dollars the next year.
+
+So for every dollar of
+consumption I divert, in one
+
+of these forms, I get 1 plus
+i dollars next year.
+
+So, basically, I could
+literally--
+
+if I wanted to-- let's say the
+interest rate was 10%, just
+
+for example.
+
+Now what that means is instead
+of consuming $80,000 this year
+
+and nothing next year, I could
+consume nothing this year and
+
+$88,000 next year.
+
+Obviously, that's not very
+satisfactory either.
+
+So how do we think about that?
+
+We think about that in
+Figure 21-2 shows--
+
+now this is a complicated
+diagram we gotta
+
+use to figure 21-2--
+
+this shows the intertemporal
+choice model, intertemporal
+
+substitution we also call it.
+
+So the deal is that now instead
+of the x-axis being
+
+pizza and the y-axis being
+movies or all the other wacky
+
+things we've done, now the
+x-axis is first period
+
+consumption.
+
+The y-axis is second
+period consumption.
+
+You might say what's a period?
+
+Well a period's whatever I want
+it to be-- a day, a year,
+
+10 years, whatever.
+
+Sometimes I'll say a year.
+
+Sometimes I'll say a period,
+but the point
+
+is it doesn't matter.
+
+It's about the trade-off.
+
+So in my example, c1 is
+consumption this year.
+
+c2's consumption next year.
+
+And my trade-off is I can
+consume $80,000 this year, or,
+
+given the interest rate, I can
+consume $88,000 next year.
+
+Now the trade-off-- that's
+a typo, by the way.
+
+That should be minus 1.1.
+
+OK?
+
+This is a 10% interest rate.
+
+The key point is the trade-off
+is that, basically, I can
+
+trade off for every dollar I
+don't consume this year, I
+
+consume 1 plus i--
+
+1 plus r there, should
+be 1 plus i dollars--
+
+next year.
+
+We use r and i interchangeably
+for the interest rate, so 1
+
+plus i, 1 plus r dollars
+next year.
+
+So, basically, what does the
+interest rate represent?
+
+This is important.
+
+The wage rate I defined as
+the price of leisure.
+
+Remember what the
+wage rate was?
+
+It was the price of leisure,
+that basically by working I
+
+forgoed the ability to--
+
+I'm sorry, by taking leisure
+I forgoed the ability to
+
+earn a wage, w.
+
+So, literally, that was a price
+of sitting around on the
+
+couch was the wage, w,
+I could've earned.
+
+Likewise, the interest rate is
+the price of first period
+
+consumption.
+
+By consuming today, I'm forgoing
+the fact that I
+
+could've earned the interest on
+that money had I consumed
+
+it tomorrow or next year.
+
+So the interest rate is the
+price of first period
+
+consumption, just as the wage
+is the price of leisure.
+
+Yeah?
+
+AUDIENCE: You said before
+that r and i are used
+
+interchangeably for interest.
+Does that play into the cost
+
+function at all?
+
+Is the cost for capital going
+to be the interest rate?
+
+PROFESSOR: I'm going
+to come to that.
+
+That's exactly what I'll talk
+about next lecture.
+
+So, basically, this is the key
+thing, but the key thing to
+
+understand intertemporal
+choice-- and the other
+
+important point to understand on
+why it's a bit harder than
+
+labor is there's an extra--
+
+well it's not harder.
+
+It's the same thing.
+
+Remember, we said we don't model
+bads in this course.
+
+We model goods.
+
+So we're modeling your choice
+of how hard to work.
+
+We model the trade-off between
+consumption and leisure.
+
+And then we said define labor
+as the total amount of hours
+
+available minus leisure.
+
+Same thing here.
+
+We don't model savings.
+
+That's a bad.
+
+Now you might not think
+[? some of these ?]
+
+things are good, but
+savings really by
+
+itself is not a good.
+
+Unless you're Scrooge McDuck--
+
+does anyone know who
+Scrooge McDuck is?
+
+Wow, that hurts.
+
+OK, he was this old cartoon
+character when I was a kid who
+
+used to, like, fill a
+swimming pool with
+
+money and swim in it.
+
+Basically, unless you're like
+that, the savings itself does
+
+not give you utility.
+
+We don't have savings entering
+utility functions.
+
+We have consumption entering
+utility functions.
+
+Savings is a bad.
+
+Savings is the mean by which
+you translate consumption
+
+period one into consumption
+period two.
+
+But from the effect of today
+you wish you didn't have to
+
+save. You just do it because
+you want to make
+
+sure you eat tomorrow.
+
+So we model the good.
+
+The good is consumption in
+period one, and savings is the
+
+difference between income and
+consumption in period one.
+
+So we don't model savings.
+
+We define savings
+as y minus c1.
+
+We model c1, and define
+savings as y minus c1.
+
+You can see that there
+in the diagram.
+
+Now what happens when the
+interest rate changes?
+
+Let's go to Figure 21-3.
+
+What happens when the interest
+rate changes?
+
+Actually, go to 21-4.
+
+OK?
+
+Skip 21-3.
+
+Got to 21-4.
+
+What happens when the interest
+rate changes?
+
+So, initially, we're at a point
+like a and then the
+
+interest rate goes
+up from r to r2.
+
+The interest rate goes up.
+
+Now what does that do?
+
+Well, graphically, it steepens
+the budget constraint.
+
+What that means is it's raised
+the opportunity cost of first
+
+period consumption.
+
+First period consumption is now
+effectively more expensive
+
+because I'm forgoing a better
+savings rate by eating today.
+
+The more of my $80,000 I consume
+today, the less I get
+
+to save for tomorrow.
+
+And that's now a better deal to
+save for tomorrow because
+
+I'm getting a higher interest
+rate on that.
+
+So what does that do?
+
+Well that has two effects.
+
+Just like a change in the wage
+rate has two effects-- a
+
+substitution effect and
+an income effect.
+
+The substitution effect, which
+we can unambiguously sign, is
+
+the fact that now first period
+consumption's gotten more
+
+expensive, so we
+do less of it.
+
+Substitution effects are always
+price goes up, you do
+
+less of the activity.
+
+The substitution effect is first
+period consumption's
+
+gotten more expensive, there'll
+be less of it.
+
+Now here, once again, don't
+slip into thinking about
+
+savings yet.
+
+You'll really get yourself
+in trouble, and
+
+it's a natural tendency.
+
+Model consumption that makes
+savings a residual.
+
+So the activity we're modeling
+here is first period
+
+consumption.
+
+The price of first period
+consumption's gone up, so you
+
+do less of it.
+
+That's the substitution
+effect.
+
+The income effect is
+you're now richer.
+
+And you might say what do
+you mean I'm richer?
+
+I still have the same
+$80,000 in income.
+
+But any given dollar of savings
+yields more income in
+
+the second period.
+
+So, overall, you're richer.
+
+If you take the perspective of
+saying I have two periods in
+
+this model-- first and
+second period.
+
+Any given level of savings
+makes me richer
+
+in the second period.
+
+That means I'm richer.
+
+If I'm richer, I consume more of
+everything including first
+
+period consumption.
+
+So first period consumption
+goes up
+
+from the income effect.
+
+I find this confusing.
+
+I don't know if you guys do, but
+once again-- run through
+
+this again.
+
+I'm richer because for any given
+amount of savings I now
+
+have a total larger sum of
+money over both periods.
+
+When I'm richer I consume
+more of everything.
+
+One of the things that I consume
+more of is first
+
+period consumption.
+
+So, actually, first period
+consumption goes
+
+up, and I save less.
+
+It's sort of bizarre.
+
+Because I'm getting
+more return to my
+
+savings I save less.
+
+Here is the way I like
+to think of the
+
+intuition to make it easier.
+
+The way I like to think of the
+intuition is imagine that you
+
+have a goal for saving--
+something I call a target
+
+savings level.
+
+Imagine you said, look.
+
+Imagine you said that I really
+want to make sure that I have
+
+certain level of savings
+to live on next year.
+
+Well if the interest rate goes
+up, I can save less to get to
+
+that target.
+
+Right?
+
+If I have a target, c2, and the
+interest rate is higher I
+
+can consume more c1 and still
+hit my target of c2.
+
+So that's the income effect.
+
+I can effectively consume more
+c1 because I'm made richer
+
+because any given level of
+savings allows me to consume
+
+more the next period.
+
+Now the target's an extreme
+case, but I find it a useful
+
+intuition for thinking about
+what's going on.
+
+And that's the income effect.
+
+Now, obviously, as with
+anything, this is ambiguous.
+
+If you go to Figure 21-3 now
+here's a case where the income
+
+effect dominates.
+
+Well, actually, go
+back to 21-4.
+
+Let's finish this example.
+
+So here with the substitution
+effect dominating, when the
+
+interest rate goes up I consume
+less in period one
+
+which means I save more.
+
+And that was prior intuition.
+
+A higher interest rate
+means you save more.
+
+But we'll work through the
+mechanics of how we get there.
+
+And the reason the mechanics
+is important is because of
+
+Figure 21-3.
+
+Which as in 21-3, the interest
+rate goes up, but I save less.
+
+The interest rate goes up, but
+I consume more in period one
+
+and therefore save less.
+
+And that's consistent with
+this target notion.
+
+That basically I'm so--
+
+All I care about-- let's say
+in the limit if all I care
+
+about in the limit is exactly
+what I consume the second
+
+period, then, basically, my
+period one's consumption will
+
+definitely go up from a raise in
+the interest rate because,
+
+basically, I'm saying, look, all
+I care about is what I get
+
+in the second period.
+
+Now I can save less and
+get to that target.
+
+So my consumption first
+period goes up.
+
+The income effect dominates.
+
+So the bottom line is, just
+like with labor supply, we
+
+can't tell.
+
+Unlike with goods where it's
+rare to see a Giffen good,
+
+here we honestly don't know
+whether a raise in the
+
+interest rates will raise
+savings or lower savings.
+
+It all depends on the
+strength of the
+
+substitution and income effects.
+
+Let me actually say one of the
+most disturbing things in
+
+empirical economics is we
+actually do have no idea.
+
+Literally, there's no convincing
+study out there
+
+which even tells us which way
+the effect of interest rates
+
+goes on savings.
+
+We think probably the
+substitution effect dominates,
+
+but it's been very
+hard to find a
+
+convincing estimate of that.
+
+So it's a little bit disturbing
+
+for empirical economics.
+
+We'll typically assume it
+dominates, but don't
+
+necessarily assume that
+in the real world.
+
+OK, questions about that--
+
+intertemporal choice
+framework?
+
+OK, now, with that in mind,
+let's now talk about how
+
+capital markets work.
+
+How do capital markets work?
+
+And the key concept for thinking
+about capital markets
+
+is the concept of
+present value.
+
+And the concept of the present
+value is simple.
+
+It's that $1 tomorrow is worth
+less than $1 today.
+
+$1 tomorrow is worth
+less than $1 today.
+
+And why is that?
+
+It's because if I had the
+dollar today, I could've
+
+invested it in something
+productive and had 1 plus i
+
+dollars tomorrow.
+
+So if you give me a dollar today
+I could have 1 plus i
+
+dollars tomorrow.
+
+If you give it to me tomorrow,
+I just have $1.
+
+So by definition, $1 today is
+worth more because I have the
+
+opportunity to save it.
+
+Whereas a $1 tomorrow
+I don't have the
+
+opportunity to save it.
+
+It's too late.
+
+So the key point is you can't
+add up dollars that you
+
+receive in different periods.
+
+So, in other words,
+if I said to you--
+
+if this intertemporal choice
+graph was back pizzas and
+
+movies, and I said you have
+nine pizza plus movies.
+
+You have a total of nine.
+
+You'd be like, what the
+hell does that mean?
+
+It matters if it's nine pizzas
+and zero movies or five movies
+
+and four pizzas?
+
+I don't know what that means.
+
+Those are different things.
+
+You can't add them up.
+
+You can't just say
+I have nine.
+
+Well consumption over time--
+it's the same thing.
+
+You can't just add up your
+consumption tomorrow and
+
+consumption today or a dollar
+tomorrow and a dollar today.
+
+They're different things.
+
+And so you have to account for
+the fact that $1 tomorrow is
+
+worth less than $1 today in
+trying to add them up.
+
+And the way we do that is we
+actually do it through the
+
+concept of present value.
+
+And the idea of present value
+is to translate all future
+
+dollars into today's dollars.
+
+Translate all future dollars
+into today's dollars
+
+recognizing the fact they're
+less valuable in the future.
+
+So the concept of present value
+is the concept of any
+
+future payment's value from
+the perspective of today.
+
+And you should know that any
+future payment will be worth
+
+less than a payment today.
+
+How much less-- that's what
+present value tells you.
+
+How much is a future payment
+worth in today's terms?
+
+So suppose that the interest
+rate is 10%.
+
+Suppose the interest rate
+is 10%, and you want to
+
+have $100 next year.
+
+So you know next year there's
+something you want to buy, and
+
+you have to decide how much do
+I have to save today to have
+
+$100 in period two.
+
+How much do I have to
+save today to have
+
+$100 in period two?
+
+Well if you put in an amount,
+PV, into the bank--
+
+you put PV into the bank, then
+you know next year you're
+
+going to have-- if you put in
+PV in period one, next year
+
+you're going to have
+PV times 1 plus i.
+
+You're going to have your PV
+plus all the interest you
+
+earned on it, or in our
+example, PV times 1.1.
+
+So what that says is that,
+basically, you have to put in
+
+100 over 1.1 into the
+bank today, or
+
+90.9 dollars, $90.90.
+
+If you put $90.90 in the bank
+today, you will have $100
+
+tomorrow or $100 next year--
+whenever the periodicity of
+
+the interest rate.
+
+So, basically, more generally,
+the present value of any
+
+stream of payments is equal to
+that stream's future value--
+
+I'm going to write
+it over here.
+
+It's bigger.
+
+The present value of any stream
+of payments is that
+
+stream's future value over 1
+plus the interest rate to the
+
+t, where t is the year in
+which you get the money.
+
+So any future money you get in
+year t is worth that amount
+
+you get over 1 plus the interest
+rate to the t.
+
+So, basically, the point
+is you have to weigt.
+
+Any money you're going to get,
+you to weight by how far into
+
+the future it is, just like
+if you're adding up these
+
+different goods.
+
+So, essentially, this is kind
+of like saying let's add a
+
+converter machine which can
+convert pizza into movies.
+
+Then I could say well I'll
+just take pizza, put it
+
+through the converter machine,
+and that'll tell me how many
+
+movies I have. That's
+what a utility
+
+function basically does.
+
+This we're saying the
+interest rate is
+
+the converter function.
+
+This present value formula is
+the converter function by
+
+which we convert two goods
+that are different
+
+into the same good.
+
+You convert them through
+this formula.
+
+So, basically, suppose that you
+say to me, "Look, loan me
+
+$30, and I'll pay you back $10
+a year each of the next three
+
+years." Well I should
+say, "Wait a second.
+
+What's the value of that to me?"
+Well the present value of
+
+those repayments is I'm going
+to have $10 in one year, so
+
+that's $10 over 1 plus i.
+
+Let's say the interest
+rate's 10% again.
+
+Next year I got $10.
+
+That's worth 10 over 1 plus 1.
+
+The year after, you're going
+to give me 10 more dollars,
+
+but that's worth 10 over 1 plus
+1 squared because that's
+
+in two years.
+
+If I had that money today, I
+could've invested it, earned
+
+10% and then 10% on that.
+
+And, likewise, the money you
+give me in the third year is
+
+worth 10 over 1.1 cubed.
+
+If you'd given me that money
+today, I could've invested it
+
+and and earned interest
+three times on it.
+
+So the bottom line is
+your repayments
+
+are only worth $24.87.
+
+So I've just given you $30 today
+in return for a stream
+
+of payments that's only
+worth $24.87 today.
+
+I've lost money from that loan
+because I gave you the money
+
+today, and you're paying me back
+in the future when the
+
+money's worth less.
+
+So, basically, the general
+formula we have is that the
+
+present value of any stream of
+future payments is that the
+
+amount of the future payment--
+let's call it f for any fixed
+
+stream of future payments, $10
+forever or $15 forever--
+
+fixed stream of that amount, f,
+times 1 over 1 plus i, plus
+
+1 over 1 plus i squared, plus
+da da da da, plus 1 over 1
+
+plus i to the t.
+
+So if you're going to pay me a
+fixed amount, f, for t years,
+
+here what it's worth
+to me today.
+
+You pay me a fixed amount, f,
+for t years, it's worth this
+
+much to me today.
+
+I'm accounting for how far
+off in the future it is.
+
+Now one important trick we're
+going to do now for the rest
+
+of the semester is we're going
+to take the trick of saying
+
+this is actually--
+
+well this is a messy formula.
+
+It's actually a rather easy
+formula to write down if the
+
+future stream of payments is
+infinite, if we have what we
+
+call a perpetuity.
+
+If we have what we call
+a perpetuity.
+
+A perpetuity is a future stream
+of payments that goes
+
+on forever or long enough that
+we'd consider it forever.
+
+Fifty years is probably
+good enough.
+
+If you have a perpetuity,
+then this formula
+
+can be reduced to--
+
+the present value of any
+perpetuity is the amount of
+
+that perpetuity over
+the interest rate.
+
+It's just taking the infinite
+sum of that product.
+
+They're just taking
+the infinite sum.
+
+Those mathematically inclined
+will know this already.
+
+But it's just taking the
+infinite sum here, you can get
+
+this formula.
+
+So any perpetuity, if you're
+getting a payment forever, the
+
+value of that payment today-- so
+if I said I'll give you $10
+
+forever and the interest rate's
+going to be 10% then
+
+you'd say that's worth
+$100 to me.
+
+If I'm going to give you $10
+forever at a 10% interest
+
+rate, then you'd say well that's
+worth $9.90 the next
+
+year and $8 something the
+next year, et cetera.
+
+And if I add all those up, I get
+approximately the amount
+
+of the payment over
+the interest rate.
+
+So, basically, that is what
+determines present value.
+
+Now we can flip this around and
+we could say, OK, well, if
+
+that's present value what
+determines future value?
+
+Well the future value of getting
+a payment today--
+
+So that's the present value of
+getting payments tomorrow.
+
+The only other thing is what's
+the future value?
+
+What's the future value of
+getting a stream of payments
+
+starting today?
+
+So let's say, starting today,
+I'm going to get $10.
+
+I'm going to get it for a
+certain number of years.
+
+What's that going to be worth
+at the end of the day given
+
+that I can save it
+along the way.
+
+So, in other words, if you
+give me $10 today--
+
+if you give me $10 today, well
+then in one year, next year, I
+
+have $11 because I got to save
+it at the interest rate.
+
+So if you give me $10 today,
+next year I'll have $11.
+
+Now let's say that I
+then keep it in the
+
+bank for another year.
+
+Well the next year, it's worth
+10 times 1 plus i squared, so
+
+10 times 1.1 squared, 10
+times 1.1 squared, or
+
+$12.10 and so on.
+
+So, basically, the point is that
+at the end of each year I
+
+earn the interest on my original
+$10, plus I earn the
+
+interest on the interest I
+earned the previous periods.
+
+So in the long run, at the end
+of t years, which of the
+
+future value, is the amount
+invested, f, times 1
+
+plus i to the t.
+
+That's your future value.
+
+So if you invest a given amount
+of money today for t
+
+years, you end up
+with that much.
+
+If you invest a given amount,
+f, today you end
+
+up with that much--
+
+And the key point, the key
+insight, is the miracle of
+
+compounding.
+
+The miracle of compounding is
+the point that you earn
+
+interest on your interest. And
+what this means is the earlier
+
+you save, the more you'll
+have later on.
+
+So there's an example in the
+book which is very important.
+
+So it's actually thinking
+about--
+
+let's think for a minute
+about retirement.
+
+You might say this
+is sort of crazy.
+
+Maybe not crazy for an old guy
+like me, but you're thinking
+
+I'm just starting
+on my career.
+
+Why would I think about
+retirement?
+
+Here's why you want
+to think about it.
+
+Let's say, for example, that
+you plan to work full time
+
+from age 22 to age 70.
+
+You've got a great idea.
+
+Screw grad school.
+
+You're going right to work.
+
+You've got a great idea,
+and you know you want
+
+to retire at 70.
+
+So you plan to work full time
+from age 22 to age 70.
+
+And let's say that you want to
+save money for your retirement
+
+because you're going
+to retire at 70.
+
+You're going to live forever.
+
+You're a healthy young person.
+
+You think you're going to
+live forever at 70.
+
+So you want to have money
+around when you retire.
+
+And let's say that the
+interest rate you
+
+can save at is 7%.
+
+So you can save money for your
+retirement at 7%, and that's
+
+your choice.
+
+Now let's consider two different
+savings plans.
+
+Savings plan one is that I'm
+going to save $3,000.
+
+You're going to save $3,000
+right off the bat.
+
+And for the first 15 years
+of your working life--
+
+so from 22 to 37--
+
+you're going to save $3,000.
+
+You're going to save $3,000 a
+year savings for 15 years, and
+
+then nothing.
+
+And then once you're 37 and
+you've got to start worrying
+
+about kids' college and
+mortgage, you're not going to
+
+save anything.
+
+So from 22 to 37, when you're
+living high on the hog, you've
+
+got no obligations, you're going
+to save. Once you're 37,
+
+you've got a house, you've got
+kids, you've got things that
+
+are expensive, you're not
+going to save anymore.
+
+So then you go to zero.
+
+Zero savings from age
+37 to age 70.
+
+That's a pretty bold plan.
+
+You're just going to save 15
+years then zero savings.
+
+Well what do you get?
+
+Well after 15 years, if you use
+our future value formula,
+
+if you save $3,000 every year,
+you work out that you will
+
+have $75,387 in the bank.
+
+So it's more than 45-- is not
+just 3,000 times 15 because
+
+you get the compounding.
+
+It's not just 3,000 times 15.
+
+You actually get more than
+that because you got the
+
+compounding along the way.
+
+Then if you just let it sit
+there in the bank-- you don't
+
+do anything.
+
+No more active savings.
+
+You let it sit there.
+
+Then by the time you retire,
+you have that $75,387 times
+
+1.07 to the 33 because you
+let that money sit
+
+there for 33 years.
+
+You let that money sit
+there for 33 years.
+
+That works out to be $703,010.
+
+So by saving for 15 years-- all
+you did was save $3,000
+
+for 15 years, a fraction
+of your career.
+
+And you retire with $703,000.
+
+Now we'll contrast that with
+an alternative plan.
+
+My alternative plan is I'm going
+to save nothing for the
+
+first 15 years because I figure,
+like, I'm young.
+
+I'm gonna party.
+
+I'm going to use
+the money now.
+
+I'll save later.
+
+I'm nowhere near retirement.
+
+Then I get to 37.
+
+I say, wait a second, I'm
+
+starting to see more mortality.
+
+I better worry about
+retirement.
+
+Then I start to save, and I save
+for the next 33 years.
+
+So the new plan is zero per year
+from age 22 to 37, and
+
+then $3,000 a year
+from 37 to 70.
+
+So it's a lot more savings.
+
+You're saving for more than
+twice as long, more
+
+than twice as long.
+
+What do you end up with?
+
+You end up with $356,800--
+
+half, just slightly more than
+half, than what you end up
+
+with the first plan, even though
+you save for twice as
+
+many years.
+
+This is like the parents'
+lecture why you should save.
+
+The point is that saving early
+lets you ride the wave of
+
+compounding for many,
+many years.
+
+Savings late does not
+let you do that.
+
+And as a result, you end
+up with less money.
+
+I take my kids to the science
+museum, and at the science
+
+museum they have these
+little ramps.
+
+And you can drop a ball.
+
+And one is flat then steep, and
+one is steep then flat.
+
+And the one that's steep then
+flat always wins because
+
+there's compounding in
+acceleration the same way.
+
+The point is building up early
+and then riding that velocity
+
+going forward is a lot better
+than starting late.
+
+Questions about that?
+
+So make sure when you get those
+jobs, and they offer
+
+you-- we'll talk next time about
+savings incentives-- and
+
+they offer you those good 401K
+packages, that you take them,
+
+and don't say I'll worry
+about that later.
+
+Now, one last thing.
+
+Last thing I want to cover is
+that we've ignored, so far,
+
+the whole concept
+of inflation.
+
+When I've talked about savings,
+I've presumed that
+
+you've saved the money and
+it's worth something.
+
+But who the hell knows
+what $703,000 will
+
+be worth in 48 years?
+
+What's that even going
+to be worth?
+
+How do we even think
+about that?
+
+Well we have to account for the
+fact that stuff's going to
+
+be more expensive.
+
+So we have to account for
+inflation in doing this.
+
+And the way we do this is by
+recognizing that what we've
+
+done so far is we've
+talked about the
+
+nominal interest rate.
+
+By the nominal interest rate, I
+meant the interest rate that
+
+you actually see posted
+in the bank.
+
+But what matters, ultimately
+for your well-being, is the
+
+real interest rate which is
+what your money can do in
+
+terms of actually
+buying goods.
+
+So I should not care about how
+much money I have next year.
+
+I should care about how many
+goods I can buy next year.
+
+The money's just paper.
+
+What matters is what
+I can get with it.
+
+That's what matters.
+
+So let's say, for example,
+I want to use
+
+all my money on Skittles.
+
+That's just what I want
+to use my money on.
+
+So let's say I have $100,
+and I want to spend
+
+that money on Skittles.
+
+And let's say Skittles
+today are $1 a bag.
+
+And let's say the interest
+rate, once again, is 10%.
+
+And let's say there's
+no inflation.
+
+Inflation equals zero.
+
+So my choice is I can spend
+$100 on Skittles
+
+today and get 100 bags.
+
+So I could have 100
+bags today.
+
+Or I can save it, have
+$110 tomorrow and
+
+get 110 bags of Skittles.
+
+That's my choice.
+
+That's my trade-off.
+
+Now let's say there's
+inflation.
+
+Let's say that prices are rising
+at 10% a year, as well.
+
+So the prices are rising
+10% a year, as well.
+
+What that means is next year
+Skittles cost $1.10 a bag.
+
+So now what's my trade-off?
+
+That means I could
+have 100 bags
+
+today or 100 bags tomorrow.
+
+I don't get any more
+Skittles tomorrow.
+
+I get 10 more dollars,
+but who cares?
+
+Everything costs more.
+
+If everything cost 10% more and
+I get a 10% interest rate,
+
+that interest rate is
+effectively zero in terms of
+
+what I can buy.
+
+The real interest rate
+is the nominal
+
+interest rate minus inflation.
+
+What I care about is
+what I can buy.
+
+So I have to take out
+of the interest rate
+
+what happens to prices.
+
+Because if prices go up,
+it offsets what I'm
+
+earning in the bank.
+
+And so what I care about is I
+care about what the bank posts
+
+minus what inflation will be.
+
+So it's even trickier, right?
+
+Because it's not about what
+inflation was, it's what
+
+inflation will be.
+
+You'll have to guess what
+inflation is going to be.
+
+And so what we care about is
+this real interest rate.
+
+And that's why the interest rate
+that banks pay, a primary
+
+determinant of it
+is inflation.
+
+Right now, we are in the lowest
+inflation period this
+
+nation's seen since
+World War II.
+
+Core inflation--
+
+we don't really get into
+inflation in this course-- but
+
+core inflation, which is
+inflation minus some things
+
+which fluctuate a lot, is
+basically zero in the US.
+
+So, basically, nominal interest
+rates are the same as
+
+real interest rates, and that's
+why the interest rates
+
+you see posted are so incredibly
+low because there's
+
+no inflation.
+
+In the late 1970's, when
+inflation was running at
+
+10-15% a year, interest rates
+were 15 to 20% a year.
+
+Now it wasn't that you could
+get so much more for your
+
+savings in the 1970's.
+
+It was just that stuff was going
+to cost more next year,
+
+so banks, if they wanted to
+induce you to save, had to pay
+
+you a higher interest rate.
+
+So, essentially, banks are going
+to have to pay you to
+
+get you to put your money in.
+
+If in 1978, when the inflation
+rate was 15%--
+
+if banks had offered a 3%
+interest rate no one would've
+
+put money in the banks because
+you would end up losing
+
+effectively.
+
+Effectively, that's a negative
+12% real interest rate.
+
+So what matters is how much
+the bank pays you in cash
+
+minus how much more stuff is
+going to cost. And that's
+
+often what matters.
+
+Now that's a distinction
+we won't spent a lot of
+
+time on later on.
+
+I'll just say interest rate.
+
+I won't say real
+versus nominal.
+
+But you've got to know in your
+head that what matters is the
+
+interest rate is the real
+interest rate, what the bank
+
+pays you, minus how much more
+stuff's going to cost.
+
+Questions about that?
+
+Alright, we'll come
+back next time.
+
+There is class on Wednesday.
+
+It does matter.
+
+And on Wednesday we're going
+to talk about the rest of
+
+capital markets and people's
+savings decisions.
\ No newline at end of file
diff --git a/er_tQOBgo-I.txt b/er_tQOBgo-I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..226e9ff20a2227521fa9b0435288184e96de2e85
--- /dev/null
+++ b/er_tQOBgo-I.txt
@@ -0,0 +1,2299 @@
+align:start position:0%
+ 
+hi welcome back to recitation today I
+
+ align:start position:0%
+hi welcome back to recitation today I
+ 
+
+ align:start position:0%
+hi welcome back to recitation today I
+wanted to talk about something that's
+
+ align:start position:0%
+wanted to talk about something that's
+ 
+
+ align:start position:0%
+wanted to talk about something that's
+mentioned in the notes but wasn't
+
+ align:start position:0%
+mentioned in the notes but wasn't
+ 
+
+ align:start position:0%
+mentioned in the notes but wasn't
+covered in lecture because of the exam
+
+ align:start position:0%
+covered in lecture because of the exam
+ 
+
+ align:start position:0%
+covered in lecture because of the exam
+review so this is uh the the subject is
+
+ align:start position:0%
+review so this is uh the the subject is
+ 
+
+ align:start position:0%
+review so this is uh the the subject is
+hyperbolic trig functions so first I
+
+ align:start position:0%
+hyperbolic trig functions so first I
+ 
+
+ align:start position:0%
+hyperbolic trig functions so first I
+just want to Define them for you and
+
+ align:start position:0%
+just want to Define them for you and
+ 
+
+ align:start position:0%
+just want to Define them for you and
+graph them so we can get a little bit of
+
+ align:start position:0%
+graph them so we can get a little bit of
+ 
+
+ align:start position:0%
+graph them so we can get a little bit of
+a feeling for what these functions are
+
+ align:start position:0%
+a feeling for what these functions are
+ 
+
+ align:start position:0%
+a feeling for what these functions are
+like and then I'm going to explain to
+
+ align:start position:0%
+like and then I'm going to explain to
+ 
+
+ align:start position:0%
+like and then I'm going to explain to
+you why they have the words Hy
+
+ align:start position:0%
+you why they have the words Hy
+ 
+
+ align:start position:0%
+you why they have the words Hy
+hyperbolic and trig in their names um so
+
+ align:start position:0%
+hyperbolic and trig in their names um so
+ 
+
+ align:start position:0%
+hyperbolic and trig in their names um so
+these are these are some interesting
+
+ align:start position:0%
+these are these are some interesting
+ 
+
+ align:start position:0%
+these are these are some interesting
+functions they're not they don't they
+
+ align:start position:0%
+functions they're not they don't they
+ 
+
+ align:start position:0%
+functions they're not they don't they
+don't aren't quite as important as your
+
+ align:start position:0%
+don't aren't quite as important as your
+ 
+
+ align:start position:0%
+don't aren't quite as important as your
+usual sort of circular trig functions
+
+ align:start position:0%
+usual sort of circular trig functions
+ 
+
+ align:start position:0%
+usual sort of circular trig functions
+but but um but but yeah so let me let me
+
+ align:start position:0%
+but but um but but yeah so let me let me
+ 
+
+ align:start position:0%
+but but um but but yeah so let me let me
+introduce them and let me jump in just
+
+ align:start position:0%
+introduce them and let me jump in just
+ 
+
+ align:start position:0%
+introduce them and let me jump in just
+with their definition so so there are
+
+ align:start position:0%
+with their definition so so there are
+ 
+
+ align:start position:0%
+with their definition so so there are
+there are two most important ones just
+
+ align:start position:0%
+there are two most important ones just
+ 
+
+ align:start position:0%
+there are two most important ones just
+like for regular trigonometric functions
+
+ align:start position:0%
+like for regular trigonometric functions
+ 
+
+ align:start position:0%
+like for regular trigonometric functions
+there's the sign and the cosine and then
+
+ align:start position:0%
+there's the sign and the cosine and then
+ 
+
+ align:start position:0%
+there's the sign and the cosine and then
+you can write the other four
+
+ align:start position:0%
+you can write the other four
+ 
+
+ align:start position:0%
+you can write the other four
+trigonometric functions in terms of them
+
+ align:start position:0%
+trigonometric functions in terms of them
+ 
+
+ align:start position:0%
+trigonometric functions in terms of them
+so for hyperbolic Tri functions we have
+
+ align:start position:0%
+so for hyperbolic Tri functions we have
+ 
+
+ align:start position:0%
+so for hyperbolic Tri functions we have
+the hyperbolic cosine and the hyperbolic
+
+ align:start position:0%
+the hyperbolic cosine and the hyperbolic
+ 
+
+ align:start position:0%
+the hyperbolic cosine and the hyperbolic
+sign so the notation here we write C So
+
+ align:start position:0%
+sign so the notation here we write C So
+ 
+
+ align:start position:0%
+sign so the notation here we write C So
+Co the H for hyperbolic so hyperbolic
+
+ align:start position:0%
+Co the H for hyperbolic so hyperbolic
+ 
+
+ align:start position:0%
+Co the H for hyperbolic so hyperbolic
+cosine and usually we pronounce this Kos
+
+ align:start position:0%
+cosine and usually we pronounce this Kos
+ 
+
+ align:start position:0%
+cosine and usually we pronounce this Kos
+um and similarly for the hyperbolic sign
+
+ align:start position:0%
+um and similarly for the hyperbolic sign
+ 
+
+ align:start position:0%
+um and similarly for the hyperbolic sign
+we write SI i n for hyperbolic sign
+
+ align:start position:0%
+we write SI i n for hyperbolic sign
+ 
+
+ align:start position:0%
+we write SI i n for hyperbolic sign
+except in the reverse order and we
+
+ align:start position:0%
+except in the reverse order and we
+ 
+
+ align:start position:0%
+except in the reverse order and we
+usually pronounce this cinch uh so in in
+
+ align:start position:0%
+usually pronounce this cinch uh so in in
+ 
+
+ align:start position:0%
+usually pronounce this cinch uh so in in
+American English as if there were an
+
+ align:start position:0%
+American English as if there were an
+ 
+
+ align:start position:0%
+American English as if there were an
+extra c in there cinch um so okay so
+
+ align:start position:0%
+extra c in there cinch um so okay so
+ 
+
+ align:start position:0%
+extra c in there cinch um so okay so
+these these functions have fairly simp
+
+ align:start position:0%
+these these functions have fairly simp
+ 
+
+ align:start position:0%
+these these functions have fairly simp
+simple definitions in terms of the
+
+ align:start position:0%
+simple definitions in terms of the
+ 
+
+ align:start position:0%
+simple definitions in terms of the
+exponential function e x so C of X is
+
+ align:start position:0%
+exponential function e x so C of X is
+ 
+
+ align:start position:0%
+exponential function e x so C of X is
+defined to be E X Plus e- x / 2 and
+
+ align:start position:0%
+defined to be E X Plus e- x / 2 and
+ 
+
+ align:start position:0%
+defined to be E X Plus e- x / 2 and
+cinch of X is defined to be e x minus e-
+
+ align:start position:0%
+cinch of X is defined to be e x minus e-
+ 
+
+ align:start position:0%
+cinch of X is defined to be e x minus e-
+x divided two so if you remember what
+
+ align:start position:0%
+x divided two so if you remember what
+ 
+
+ align:start position:0%
+x divided two so if you remember what
+your graph of e to the X looks like and
+
+ align:start position:0%
+your graph of e to the X looks like and
+ 
+
+ align:start position:0%
+your graph of e to the X looks like and
+your graph of e to the minus X it's not
+
+ align:start position:0%
+your graph of e to the minus X it's not
+ 
+
+ align:start position:0%
+your graph of e to the minus X it's not
+hard to see that the graphs of Kos X and
+
+ align:start position:0%
+hard to see that the graphs of Kos X and
+ 
+
+ align:start position:0%
+hard to see that the graphs of Kos X and
+cinch X should look sort of like this so
+
+ align:start position:0%
+cinch X should look sort of like this so
+ 
+
+ align:start position:0%
+cinch X should look sort of like this so
+for Kosh X so we see as X gets big so e
+
+ align:start position:0%
+for Kosh X so we see as X gets big so e
+ 
+
+ align:start position:0%
+for Kosh X so we see as X gets big so e
+to Theus X is going to zero it's not
+
+ align:start position:0%
+to Theus X is going to zero it's not
+ 
+
+ align:start position:0%
+to Theus X is going to zero it's not
+very important so it mostly is driven by
+
+ align:start position:0%
+very important so it mostly is driven by
+ 
+
+ align:start position:0%
+very important so it mostly is driven by
+this e to the X part and as e as X gets
+
+ align:start position:0%
+this e to the X part and as e as X gets
+ 
+
+ align:start position:0%
+this e to the X part and as e as X gets
+negative and big uh then this is going
+
+ align:start position:0%
+negative and big uh then this is going
+ 
+
+ align:start position:0%
+negative and big uh then this is going
+to zero and this is getting larger and
+
+ align:start position:0%
+to zero and this is getting larger and
+ 
+
+ align:start position:0%
+to zero and this is getting larger and
+larger so we get something that looks
+
+ align:start position:0%
+larger so we get something that looks
+ 
+
+ align:start position:0%
+larger so we get something that looks
+like this so it it looks a little bit in
+
+ align:start position:0%
+like this so it it looks a little bit in
+ 
+
+ align:start position:0%
+like this so it it looks a little bit in
+this picture it looks a little bit like
+
+ align:start position:0%
+this picture it looks a little bit like
+ 
+
+ align:start position:0%
+this picture it looks a little bit like
+a parabola but the growth here is
+
+ align:start position:0%
+a parabola but the growth here is
+ 
+
+ align:start position:0%
+a parabola but the growth here is
+exponential at both sides so in fact
+
+ align:start position:0%
+exponential at both sides so in fact
+ 
+
+ align:start position:0%
+exponential at both sides so in fact
+this is growing much much much faster
+
+ align:start position:0%
+this is growing much much much faster
+ 
+
+ align:start position:0%
+this is growing much much much faster
+than say 1 plus x^2 um so it's a much a
+
+ align:start position:0%
+than say 1 plus x^2 um so it's a much a
+ 
+
+ align:start position:0%
+than say 1 plus x^2 um so it's a much a
+much steeper
+
+ align:start position:0%
+much steeper
+ 
+
+ align:start position:0%
+much steeper
+curve um okay and it reaches its minimum
+
+ align:start position:0%
+curve um okay and it reaches its minimum
+ 
+
+ align:start position:0%
+curve um okay and it reaches its minimum
+here at xals 0 it has the value 1 + one
+
+ align:start position:0%
+here at xals 0 it has the value 1 + one
+ 
+
+ align:start position:0%
+here at xals 0 it has the value 1 + one
+over two so that's so its minimum there
+
+ align:start position:0%
+over two so that's so its minimum there
+ 
+
+ align:start position:0%
+over two so that's so its minimum there
+is that is x equals z it has its minimum
+
+ align:start position:0%
+is that is x equals z it has its minimum
+ 
+
+ align:start position:0%
+is that is x equals z it has its minimum
+value one for cinch okay so we're taking
+
+ align:start position:0%
+value one for cinch okay so we're taking
+ 
+
+ align:start position:0%
+value one for cinch okay so we're taking
+the difference of them so it's it's
+
+ align:start position:0%
+the difference of them so it's it's
+ 
+
+ align:start position:0%
+the difference of them so it's it's
+similar when X is uh positive and large
+
+ align:start position:0%
+similar when X is uh positive and large
+ 
+
+ align:start position:0%
+similar when X is uh positive and large
+e to the x is big and e to the minus X
+
+ align:start position:0%
+e to the x is big and e to the minus X
+ 
+
+ align:start position:0%
+e to the x is big and e to the minus X
+is is pretty small almost negligible so
+
+ align:start position:0%
+is is pretty small almost negligible so
+ 
+
+ align:start position:0%
+is is pretty small almost negligible so
+we get exponential growth off that side
+
+ align:start position:0%
+we get exponential growth off that side
+ 
+
+ align:start position:0%
+we get exponential growth off that side
+when X becomes negative and large e to
+
+ align:start position:0%
+when X becomes negative and large e to
+ 
+
+ align:start position:0%
+when X becomes negative and large e to
+the x is going to zero e Theus X is
+
+ align:start position:0%
+the x is going to zero e Theus X is
+ 
+
+ align:start position:0%
+the x is going to zero e Theus X is
+becoming large but it's it's we've got a
+
+ align:start position:0%
+becoming large but it's it's we've got a
+ 
+
+ align:start position:0%
+becoming large but it's it's we've got a
+minus sign here so as X goes to minus
+
+ align:start position:0%
+minus sign here so as X goes to minus
+ 
+
+ align:start position:0%
+minus sign here so as X goes to minus
+infinity this curve goes also to minus
+
+ align:start position:0%
+infinity this curve goes also to minus
+ 
+
+ align:start position:0%
+infinity this curve goes also to minus
+infinity and again the growth here is is
+
+ align:start position:0%
+infinity and again the growth here is is
+ 
+
+ align:start position:0%
+infinity and again the growth here is is
+exponential in in both cases um and if
+
+ align:start position:0%
+exponential in in both cases um and if
+ 
+
+ align:start position:0%
+exponential in in both cases um and if
+you you know if you were curious say
+
+ align:start position:0%
+you you know if you were curious say
+ 
+
+ align:start position:0%
+you you know if you were curious say
+about what the slope there at the origin
+
+ align:start position:0%
+about what the slope there at the origin
+ 
+
+ align:start position:0%
+about what the slope there at the origin
+is you could quickly take a derivative
+
+ align:start position:0%
+is you could quickly take a derivative
+ 
+
+ align:start position:0%
+is you could quickly take a derivative
+and check that that that's passing
+
+ align:start position:0%
+and check that that that's passing
+ 
+
+ align:start position:0%
+and check that that that's passing
+through the origin with slope one there
+
+ align:start position:0%
+through the origin with slope one there
+ 
+
+ align:start position:0%
+through the origin with slope one there
+um okay so this is a sort of basic
+
+ align:start position:0%
+um okay so this is a sort of basic
+ 
+
+ align:start position:0%
+um okay so this is a sort of basic
+picture of what these curves look like
+
+ align:start position:0%
+picture of what these curves look like
+ 
+
+ align:start position:0%
+picture of what these curves look like
+um they have some nice properties um and
+
+ align:start position:0%
+um they have some nice properties um and
+ 
+
+ align:start position:0%
+um they have some nice properties um and
+let me talk about them so for example um
+
+ align:start position:0%
+let me talk about them so for example um
+ 
+
+ align:start position:0%
+let me talk about them so for example um
+one nice thing you might notice about
+
+ align:start position:0%
+one nice thing you might notice about
+ 
+
+ align:start position:0%
+one nice thing you might notice about
+these functions is that it's easy to
+
+ align:start position:0%
+these functions is that it's easy to
+ 
+
+ align:start position:0%
+these functions is that it's easy to
+compute their derivatives right so if we
+
+ align:start position:0%
+compute their derivatives right so if we
+ 
+
+ align:start position:0%
+compute their derivatives right so if we
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DDX of Co Kos X X in order to compute
+
+ align:start position:0%
+DDX of Co Kos X X in order to compute
+ 
+
+ align:start position:0%
+DDX of Co Kos X X in order to compute
+that well just look at the definition of
+
+ align:start position:0%
+that well just look at the definition of
+ 
+
+ align:start position:0%
+that well just look at the definition of
+of C right so it's it's really just a
+
+ align:start position:0%
+of C right so it's it's really just a
+ 
+
+ align:start position:0%
+of C right so it's it's really just a
+sum of two exponential functions
+
+ align:start position:0%
+sum of two exponential functions
+ 
+
+ align:start position:0%
+sum of two exponential functions
+exponential functions are easy to take
+
+ align:start position:0%
+exponential functions are easy to take
+ 
+
+ align:start position:0%
+exponential functions are easy to take
+the derivatives take the derivative of e
+
+ align:start position:0%
+the derivatives take the derivative of e
+ 
+
+ align:start position:0%
+the derivatives take the derivative of e
+to the X you get e to the X take the
+
+ align:start position:0%
+to the X you get e to the X take the
+ 
+
+ align:start position:0%
+to the X you get e to the X take the
+derivative of e to the minus X well okay
+
+ align:start position:0%
+derivative of e to the minus X well okay
+ 
+
+ align:start position:0%
+derivative of e to the minus X well okay
+so it's a little chain rule so you get a
+
+ align:start position:0%
+so it's a little chain rule so you get a
+ 
+
+ align:start position:0%
+so it's a little chain rule so you get a
+minus one in front so the derivative of
+
+ align:start position:0%
+minus one in front so the derivative of
+ 
+
+ align:start position:0%
+minus one in front so the derivative of
+Kos X is e x minus e- X over two but we
+
+ align:start position:0%
+Kos X is e x minus e- X over two but we
+ 
+
+ align:start position:0%
+Kos X is e x minus e- X over two but we
+have a name for this this is actually
+
+ align:start position:0%
+have a name for this this is actually
+ 
+
+ align:start position:0%
+have a name for this this is actually
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cinch X so the derivative of Kosh is
+
+ align:start position:0%
+cinch X so the derivative of Kosh is
+ 
+
+ align:start position:0%
+cinch X so the derivative of Kosh is
+cinch and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative of cinch well you okay you
+
+ align:start position:0%
+derivative of cinch well you okay you
+ 
+
+ align:start position:0%
+derivative of cinch well you okay you
+look at the same thing take this this
+
+ align:start position:0%
+look at the same thing take this this
+ 
+
+ align:start position:0%
+look at the same thing take this this
+formula take its derivative well e to
+
+ align:start position:0%
+formula take its derivative well e to
+ 
+
+ align:start position:0%
+formula take its derivative well e to
+the X take its derivative you get e to x
+
+ align:start position:0%
+the X take its derivative you get e to x
+ 
+
+ align:start position:0%
+the X take its derivative you get e to x
+e to Theus X take its derivative you get
+
+ align:start position:0%
+e to Theus X take its derivative you get
+ 
+
+ align:start position:0%
+e to Theus X take its derivative you get
+minus E to Theus X so those two minus
+
+ align:start position:0%
+minus E to Theus X so those two minus
+ 
+
+ align:start position:0%
+minus E to Theus X so those two minus
+signs cancel out and become a plus so
+
+ align:start position:0%
+signs cancel out and become a plus so
+ 
+
+ align:start position:0%
+signs cancel out and become a plus so
+this is E X Plus e- X over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is k x so here you have some
+
+ align:start position:0%
+which is k x so here you have some
+ 
+
+ align:start position:0%
+which is k x so here you have some
+Behavior that's a little bit reminiscent
+
+ align:start position:0%
+Behavior that's a little bit reminiscent
+ 
+
+ align:start position:0%
+Behavior that's a little bit reminiscent
+of the behavior of trig functions right
+
+ align:start position:0%
+of the behavior of trig functions right
+ 
+
+ align:start position:0%
+of the behavior of trig functions right
+for trig functions if you take the
+
+ align:start position:0%
+for trig functions if you take the
+ 
+
+ align:start position:0%
+for trig functions if you take the
+derivative of s you get cosine and if
+
+ align:start position:0%
+derivative of s you get cosine and if
+ 
+
+ align:start position:0%
+derivative of s you get cosine and if
+you take the derivative of cosine you
+
+ align:start position:0%
+you take the derivative of cosine you
+ 
+
+ align:start position:0%
+you take the derivative of cosine you
+almost get back sign but you get minus
+
+ align:start position:0%
+almost get back sign but you get minus
+ 
+
+ align:start position:0%
+almost get back sign but you get minus
+sign so here you don't have that extra
+
+ align:start position:0%
+sign so here you don't have that extra
+ 
+
+ align:start position:0%
+sign so here you don't have that extra
+negative sign floating around right so
+
+ align:start position:0%
+negative sign floating around right so
+ 
+
+ align:start position:0%
+negative sign floating around right so
+you when you take the derivative of C
+
+ align:start position:0%
+you when you take the derivative of C
+ 
+
+ align:start position:0%
+you when you take the derivative of C
+you get cinch on the nose no no minus
+
+ align:start position:0%
+you get cinch on the nose no no minus
+ 
+
+ align:start position:0%
+you get cinch on the nose no no minus
+sign needed um so that's interesting um
+
+ align:start position:0%
+sign needed um so that's interesting um
+ 
+
+ align:start position:0%
+sign needed um so that's interesting um
+but the real reason that these are that
+
+ align:start position:0%
+but the real reason that these are that
+ 
+
+ align:start position:0%
+but the real reason that these are that
+these have the words trig in their name
+
+ align:start position:0%
+these have the words trig in their name
+ 
+
+ align:start position:0%
+these have the words trig in their name
+is um is is actually a little bit deeper
+
+ align:start position:0%
+is um is is actually a little bit deeper
+ 
+
+ align:start position:0%
+is um is is actually a little bit deeper
+so let me come over here and draw a
+
+ align:start position:0%
+so let me come over here and draw a
+ 
+
+ align:start position:0%
+so let me come over here and draw a
+couple pictures so the the the the
+
+ align:start position:0%
+couple pictures so the the the the
+ 
+
+ align:start position:0%
+couple pictures so the the the the
+normal trig functions what sometimes we
+
+ align:start position:0%
+normal trig functions what sometimes we
+ 
+
+ align:start position:0%
+normal trig functions what sometimes we
+call the circular trig functions if we
+
+ align:start position:0%
+call the circular trig functions if we
+ 
+
+ align:start position:0%
+call the circular trig functions if we
+want to distinguish them from the
+
+ align:start position:0%
+want to distinguish them from the
+ 
+
+ align:start position:0%
+want to distinguish them from the
+hyperbolic trig functions um they're
+
+ align:start position:0%
+hyperbolic trig functions um they're
+ 
+
+ align:start position:0%
+hyperbolic trig functions um they're
+they're closely so circular trig
+
+ align:start position:0%
+they're closely so circular trig
+ 
+
+ align:start position:0%
+they're closely so circular trig
+functions they're closely related to the
+
+ align:start position:0%
+functions they're closely related to the
+ 
+
+ align:start position:0%
+functions they're closely related to the
+unit circle so the unit circle
+
+ align:start position:0%
+unit circle so the unit circle
+ 
+
+ align:start position:0%
+unit circle so the unit circle
+has equation x^2 + y^2 =
+
+ align:start position:0%
+has equation x^2 + y^2 =
+ 
+
+ align:start position:0%
+has equation x^2 + y^2 =
+1 it's a circle well it's close enough
+
+ align:start position:0%
+1 it's a circle well it's close enough
+ 
+
+ align:start position:0%
+1 it's a circle well it's close enough
+right um and what what is the the nice
+
+ align:start position:0%
+right um and what what is the the nice
+ 
+
+ align:start position:0%
+right um and what what is the the nice
+relationship between this circle and the
+
+ align:start position:0%
+relationship between this circle and the
+ 
+
+ align:start position:0%
+relationship between this circle and the
+trig functions well if you choose any
+
+ align:start position:0%
+trig functions well if you choose any
+ 
+
+ align:start position:0%
+trig functions well if you choose any
+point on this circle then there exists
+
+ align:start position:0%
+point on this circle then there exists
+ 
+
+ align:start position:0%
+point on this circle then there exists
+some value of t such that this point has
+
+ align:start position:0%
+some value of t such that this point has
+ 
+
+ align:start position:0%
+some value of t such that this point has
+coordinates cosine T
+
+ align:start position:0%
+coordinates cosine T
+ 
+
+ align:start position:0%
+coordinates cosine T
+comma sin T now it happens that the the
+
+ align:start position:0%
+comma sin T now it happens that the the
+ 
+
+ align:start position:0%
+comma sin T now it happens that the the
+that the value of T is actually the the
+
+ align:start position:0%
+that the value of T is actually the the
+ 
+
+ align:start position:0%
+that the value of T is actually the the
+angle that that radius makes with the
+
+ align:start position:0%
+angle that that radius makes with the
+ 
+
+ align:start position:0%
+angle that that radius makes with the
+Positive x-axis but but not going to
+
+ align:start position:0%
+Positive x-axis but but not going to
+ 
+
+ align:start position:0%
+Positive x-axis but but not going to
+worry about that right now it's not the
+
+ align:start position:0%
+worry about that right now it's not the
+ 
+
+ align:start position:0%
+worry about that right now it's not the
+key idea of import so as T varies
+
+ align:start position:0%
+key idea of import so as T varies
+ 
+
+ align:start position:0%
+key idea of import so as T varies
+through the the real numbers the point
+
+ align:start position:0%
+through the the real numbers the point
+ 
+
+ align:start position:0%
+through the the real numbers the point
+cosine T sin T that varies and it just
+
+ align:start position:0%
+cosine T sin T that varies and it just
+ 
+
+ align:start position:0%
+cosine T sin T that varies and it just
+goes around this curve so it traces out
+
+ align:start position:0%
+goes around this curve so it traces out
+ 
+
+ align:start position:0%
+goes around this curve so it traces out
+this circle exactly so the hyperbolic
+
+ align:start position:0%
+this circle exactly so the hyperbolic
+ 
+
+ align:start position:0%
+this circle exactly so the hyperbolic
+trig functions um show up in a in a very
+
+ align:start position:0%
+trig functions um show up in a in a very
+ 
+
+ align:start position:0%
+trig functions um show up in a in a very
+similar situation but instead of looking
+
+ align:start position:0%
+similar situation but instead of looking
+ 
+
+ align:start position:0%
+similar situation but instead of looking
+at the unit circle what we want to look
+
+ align:start position:0%
+at the unit circle what we want to look
+ 
+
+ align:start position:0%
+at the unit circle what we want to look
+at is the unit rectangular hyperbola uh
+
+ align:start position:0%
+at is the unit rectangular hyperbola uh
+ 
+
+ align:start position:0%
+at is the unit rectangular hyperbola uh
+so what do I mean by that well so
+
+ align:start position:0%
+so what do I mean by that well so
+ 
+
+ align:start position:0%
+so what do I mean by that well so
+instead of taking the equation x^2 + y^2
+
+ align:start position:0%
+instead of taking the equation x^2 + y^2
+ 
+
+ align:start position:0%
+instead of taking the equation x^2 + y^2
+= 1 which gives a circle I'm going to
+
+ align:start position:0%
+= 1 which gives a circle I'm going to
+ 
+
+ align:start position:0%
+= 1 which gives a circle I'm going to
+look at a very similar equation that
+
+ align:start position:0%
+look at a very similar equation that
+ 
+
+ align:start position:0%
+look at a very similar equation that
+gives a hyperbola so this is the
+
+ align:start position:0%
+gives a hyperbola so this is the
+ 
+
+ align:start position:0%
+gives a hyperbola so this is the
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+x^2 - y^2 = 1 so if you if you graph the
+
+ align:start position:0%
+x^2 - y^2 = 1 so if you if you graph the
+ 
+
+ align:start position:0%
+x^2 - y^2 = 1 so if you if you graph the
+this this equation what you'll see is
+
+ align:start position:0%
+this this equation what you'll see is
+ 
+
+ align:start position:0%
+this this equation what you'll see is
+that well passes through the point one Z
+
+ align:start position:0%
+that well passes through the point one Z
+ 
+
+ align:start position:0%
+that well passes through the point one Z
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we've got one branch here it's got
+
+ align:start position:0%
+then we've got one branch here it's got
+ 
+
+ align:start position:0%
+then we've got one branch here it's got
+a little ASM toote
+
+ align:start position:0%
+a little ASM toote
+ 
+
+ align:start position:0%
+a little ASM toote
+there and it's got all
+
+ align:start position:0%
+there and it's got all
+ 
+
+ align:start position:0%
+there and it's got all
+right so it's got a right Branch like
+
+ align:start position:0%
+right so it's got a right Branch like
+ 
+
+ align:start position:0%
+right so it's got a right Branch like
+that and also it's symmetric across the
+
+ align:start position:0%
+that and also it's symmetric across the
+ 
+
+ align:start position:0%
+that and also it's symmetric across the
+y AIS so there's
+
+ align:start position:0%
+y AIS so there's
+ 
+
+ align:start position:0%
+y AIS so there's
+a a symmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left Branch here so this is the graph of
+
+ align:start position:0%
+left Branch here so this is the graph of
+ 
+
+ align:start position:0%
+left Branch here so this is the graph of
+the equation x^2 - y^2 = 1 so it's this
+
+ align:start position:0%
+the equation x^2 - y^2 = 1 so it's this
+ 
+
+ align:start position:0%
+the equation x^2 - y^2 = 1 so it's this
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+hyperbola now um what I claim is that
+
+ align:start position:0%
+hyperbola now um what I claim is that
+ 
+
+ align:start position:0%
+hyperbola now um what I claim is that
+Kos and cinch have the same relationship
+
+ align:start position:0%
+Kos and cinch have the same relationship
+ 
+
+ align:start position:0%
+Kos and cinch have the same relationship
+to this hyperbola as cosine and S have
+
+ align:start position:0%
+to this hyperbola as cosine and S have
+ 
+
+ align:start position:0%
+to this hyperbola as cosine and S have
+to the circle well all right so it's I'm
+
+ align:start position:0%
+to the circle well all right so it's I'm
+ 
+
+ align:start position:0%
+to the circle well all right so it's I'm
+fudging a little bit so it turns out
+
+ align:start position:0%
+fudging a little bit so it turns out
+ 
+
+ align:start position:0%
+fudging a little bit so it turns out
+it's only the right half of the
+
+ align:start position:0%
+it's only the right half of the
+ 
+
+ align:start position:0%
+it's only the right half of the
+hyperbola um so what do I mean by that
+
+ align:start position:0%
+hyperbola um so what do I mean by that
+ 
+
+ align:start position:0%
+hyperbola um so what do I mean by that
+well here's what I'd like to do set
+
+ align:start position:0%
+well here's what I'd like to do set
+ 
+
+ align:start position:0%
+well here's what I'd like to do set
+x equals so we're going to introduce a
+
+ align:start position:0%
+x equals so we're going to introduce a
+ 
+
+ align:start position:0%
+x equals so we're going to introduce a
+new variable U and I'm going to set x
+
+ align:start position:0%
+new variable U and I'm going to set x
+ 
+
+ align:start position:0%
+new variable U and I'm going to set x
+equal c u and Y
+
+ align:start position:0%
+equal c u and Y
+ 
+
+ align:start position:0%
+equal c u and Y
+equals cinch U and now I'm going to look
+
+ align:start position:0%
+equals cinch U and now I'm going to look
+ 
+
+ align:start position:0%
+equals cinch U and now I'm going to look
+at the the quantity x^2 minus y^2 so
+
+ align:start position:0%
+at the the quantity x^2 minus y^2 so
+ 
+
+ align:start position:0%
+at the the quantity x^2 minus y^2 so
+x^2 minus y^2 so this
+
+ align:start position:0%
+x^2 minus y^2 so this
+ 
+
+ align:start position:0%
+x^2 minus y^2 so this
+is so we use most of the same notations
+
+ align:start position:0%
+is so we use most of the same notations
+ 
+
+ align:start position:0%
+is so we use most of the same notations
+for hyperbolic trig functions that we do
+
+ align:start position:0%
+for hyperbolic trig functions that we do
+ 
+
+ align:start position:0%
+for hyperbolic trig functions that we do
+for regular trig functions so this is c^
+
+ align:start position:0%
+for regular trig functions so this is c^
+ 
+
+ align:start position:0%
+for regular trig functions so this is c^
+2 U minus
+
+ align:start position:0%
+2 U minus
+ 
+
+ align:start position:0%
+2 U minus
+minus cinch 2
+
+ align:start position:0%
+minus cinch 2
+ 
+
+ align:start position:0%
+minus cinch 2
+U and now we can plug in the formulas
+
+ align:start position:0%
+U and now we can plug in the formulas
+ 
+
+ align:start position:0%
+U and now we can plug in the formulas
+for caution cinch that we have so this
+
+ align:start position:0%
+for caution cinch that we have so this
+ 
+
+ align:start position:0%
+for caution cinch that we have so this
+is equal
+
+ align:start position:0%
+is equal
+ 
+
+ align:start position:0%
+is equal
+to e to the U + e minus U over 2^ 2ar
+
+ align:start position:0%
+to e to the U + e minus U over 2^ 2ar
+ 
+
+ align:start position:0%
+to e to the U + e minus U over 2^ 2ar
+minus E U minus eus U over two quantity
+
+ align:start position:0%
+minus E U minus eus U over two quantity
+ 
+
+ align:start position:0%
+minus E U minus eus U over two quantity
+squared and now we can expand out both
+
+ align:start position:0%
+squared and now we can expand out both
+ 
+
+ align:start position:0%
+squared and now we can expand out both
+of these factors and both of these
+
+ align:start position:0%
+of these factors and both of these
+ 
+
+ align:start position:0%
+of these factors and both of these
+squares rather and and put them together
+
+ align:start position:0%
+squares rather and and put them together
+ 
+
+ align:start position:0%
+squares rather and and put them together
+so all right so over 2^ 2ar is over four
+
+ align:start position:0%
+so all right so over 2^ 2ar is over four
+ 
+
+ align:start position:0%
+so all right so over 2^ 2ar is over four
+and we Square this and we get e to the 2
+
+ align:start position:0%
+and we Square this and we get e to the 2
+ 
+
+ align:start position:0%
+and we Square this and we get e to the 2
+U okay so then we get 2 * e to the U * e
+
+ align:start position:0%
+U okay so then we get 2 * e to the U * e
+ 
+
+ align:start position:0%
+U okay so then we get 2 * e to the U * e
+to the minus U but e to the U * e to the
+
+ align:start position:0%
+to the minus U but e to the U * e to the
+ 
+
+ align:start position:0%
+to the minus U but e to the U * e to the
+minus U is just 1 so +
+
+ align:start position:0%
+minus U is just 1 so +
+ 
+
+ align:start position:0%
+minus U is just 1 so +
+2 plus e to Theus 2 U
+
+ align:start position:0%
+2 plus e to Theus 2 U
+ 
+
+ align:start position:0%
+2 plus e to Theus 2 U
+minus E 2 U - 2 + e- 2 U so same thing
+
+ align:start position:0%
+minus E 2 U - 2 + e- 2 U so same thing
+ 
+
+ align:start position:0%
+minus E 2 U - 2 + e- 2 U so same thing
+over here over
+
+ align:start position:0%
+over here over
+ 
+
+ align:start position:0%
+over here over
+four okay so the the e to the 2 U's
+
+ align:start position:0%
+four okay so the the e to the 2 U's
+ 
+
+ align:start position:0%
+four okay so the the e to the 2 U's
+cancel and the e to the minus 2 U's
+
+ align:start position:0%
+cancel and the e to the minus 2 U's
+ 
+
+ align:start position:0%
+cancel and the e to the minus 2 U's
+cancel and we're left with 2 - - 2
+
+ align:start position:0%
+cancel and we're left with 2 - - 2
+ 
+
+ align:start position:0%
+cancel and we're left with 2 - - 2
+that's four so this is 4 over 4 so this
+
+ align:start position:0%
+that's four so this is 4 over 4 so this
+ 
+
+ align:start position:0%
+that's four so this is 4 over 4 so this
+is equal to 1 okay so if x is equal to
+
+ align:start position:0%
+is equal to 1 okay so if x is equal to
+ 
+
+ align:start position:0%
+is equal to 1 okay so if x is equal to
+kosu and Y is equal to CNU then x^2 -
+
+ align:start position:0%
+kosu and Y is equal to CNU then x^2 -
+ 
+
+ align:start position:0%
+kosu and Y is equal to CNU then x^2 -
+y^2 is equal to 1 so if we choose a
+
+ align:start position:0%
+y^2 is equal to 1 so if we choose a
+ 
+
+ align:start position:0%
+y^2 is equal to 1 so if we choose a
+point kosu C you for some U that point
+
+ align:start position:0%
+point kosu C you for some U that point
+ 
+
+ align:start position:0%
+point kosu C you for some U that point
+lies on this hyperbola that's what this
+
+ align:start position:0%
+lies on this hyperbola that's what this
+ 
+
+ align:start position:0%
+lies on this hyperbola that's what this
+says that this point okay so the point
+
+ align:start position:0%
+says that this point okay so the point
+ 
+
+ align:start position:0%
+says that this point okay so the point
+kosu cinu is somewhere on this
+
+ align:start position:0%
+kosu cinu is somewhere on this
+ 
+
+ align:start position:0%
+kosu cinu is somewhere on this
+hyperbola and what's also true is the is
+
+ align:start position:0%
+hyperbola and what's also true is the is
+ 
+
+ align:start position:0%
+hyperbola and what's also true is the is
+the sort of reverse statement if you
+
+ align:start position:0%
+the sort of reverse statement if you
+ 
+
+ align:start position:0%
+the sort of reverse statement if you
+look at all such points if you let U
+
+ align:start position:0%
+look at all such points if you let U
+ 
+
+ align:start position:0%
+look at all such points if you let U
+vary um and and look at through the real
+
+ align:start position:0%
+vary um and and look at through the real
+ 
+
+ align:start position:0%
+vary um and and look at through the real
+numbers and you ask what happens to this
+
+ align:start position:0%
+numbers and you ask what happens to this
+ 
+
+ align:start position:0%
+numbers and you ask what happens to this
+point kwu C you the answer is that it
+
+ align:start position:0%
+point kwu C you the answer is that it
+ 
+
+ align:start position:0%
+point kwu C you the answer is that it
+that it traces out the right half of
+
+ align:start position:0%
+that it traces out the right half of
+ 
+
+ align:start position:0%
+that it traces out the right half of
+this hyperbola if if you go back to the
+
+ align:start position:0%
+this hyperbola if if you go back to the
+ 
+
+ align:start position:0%
+this hyperbola if if you go back to the
+graph of of yal cos x you'll see the the
+
+ align:start position:0%
+graph of of yal cos x you'll see the the
+ 
+
+ align:start position:0%
+graph of of yal cos x you'll see the the
+the hyperbolic cosine function is always
+
+ align:start position:0%
+the hyperbolic cosine function is always
+ 
+
+ align:start position:0%
+the hyperbolic cosine function is always
+positive so we can't over here we can't
+
+ align:start position:0%
+positive so we can't over here we can't
+ 
+
+ align:start position:0%
+positive so we can't over here we can't
+trace out this left Branch where X is
+
+ align:start position:0%
+trace out this left Branch where X is
+ 
+
+ align:start position:0%
+trace out this left Branch where X is
+negative although it's easy enough to
+
+ align:start position:0%
+negative although it's easy enough to
+ 
+
+ align:start position:0%
+negative although it's easy enough to
+say what does trace out this left Branch
+
+ align:start position:0%
+say what does trace out this left Branch
+ 
+
+ align:start position:0%
+say what does trace out this left Branch
+since it's just the the mirror image
+
+ align:start position:0%
+since it's just the the mirror image
+ 
+
+ align:start position:0%
+since it's just the the mirror image
+this is traced out by minus c
+
+ align:start position:0%
+this is traced out by minus c
+ 
+
+ align:start position:0%
+this is traced out by minus c
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+comma
+
+ align:start position:0%
+comma
+ 
+
+ align:start position:0%
+comma
+cchu so there's a the so the hyperbolic
+
+ align:start position:0%
+cchu so there's a the so the hyperbolic
+ 
+
+ align:start position:0%
+cchu so there's a the so the hyperbolic
+trig functions have the same
+
+ align:start position:0%
+trig functions have the same
+ 
+
+ align:start position:0%
+trig functions have the same
+relationship to this branch of this
+
+ align:start position:0%
+relationship to this branch of this
+ 
+
+ align:start position:0%
+relationship to this branch of this
+hyperbola that the that the regular trig
+
+ align:start position:0%
+hyperbola that the that the regular trig
+ 
+
+ align:start position:0%
+hyperbola that the that the regular trig
+functions have to this circle so there
+
+ align:start position:0%
+functions have to this circle so there
+ 
+
+ align:start position:0%
+functions have to this circle so there
+there's where the words hyperbolic and
+
+ align:start position:0%
+there's where the words hyperbolic and
+ 
+
+ align:start position:0%
+there's where the words hyperbolic and
+and trig functions come from so uh let
+
+ align:start position:0%
+and trig functions come from so uh let
+ 
+
+ align:start position:0%
+and trig functions come from so uh let
+me say one more thing about them which
+
+ align:start position:0%
+me say one more thing about them which
+ 
+
+ align:start position:0%
+me say one more thing about them which
+is we saw that they have this this
+
+ align:start position:0%
+is we saw that they have this this
+ 
+
+ align:start position:0%
+is we saw that they have this this
+analogy with regular trig functions
+
+ align:start position:0%
+analogy with regular trig functions
+ 
+
+ align:start position:0%
+analogy with regular trig functions
+right so instead of satisfying cosine
+
+ align:start position:0%
+right so instead of satisfying cosine
+ 
+
+ align:start position:0%
+right so instead of satisfying cosine
+squ plus sin squ equal 1 they satisfy
+
+ align:start position:0%
+squ plus sin squ equal 1 they satisfy
+ 
+
+ align:start position:0%
+squ plus sin squ equal 1 they satisfy
+cos squ minus sin squal 1 and instead of
+
+ align:start position:0%
+cos squ minus sin squal 1 and instead of
+ 
+
+ align:start position:0%
+cos squ minus sin squal 1 and instead of
+satisfying the derivative of s equals
+
+ align:start position:0%
+satisfying the derivative of s equals
+ 
+
+ align:start position:0%
+satisfying the derivative of s equals
+cosine and the derivative of cosine
+
+ align:start position:0%
+cosine and the derivative of cosine
+ 
+
+ align:start position:0%
+cosine and the derivative of cosine
+equals minus sign they satisfy
+
+ align:start position:0%
+equals minus sign they satisfy
+ 
+
+ align:start position:0%
+equals minus sign they satisfy
+derivative of Kosh equals cinch and
+
+ align:start position:0%
+derivative of Kosh equals cinch and
+ 
+
+ align:start position:0%
+derivative of Kosh equals cinch and
+derivative of cinch equals Kos so
+
+ align:start position:0%
+derivative of cinch equals Kos so
+ 
+
+ align:start position:0%
+derivative of cinch equals Kos so
+similar relationships not exactly the
+
+ align:start position:0%
+similar relationships not exactly the
+ 
+
+ align:start position:0%
+similar relationships not exactly the
+same but similar um so this is true of a
+
+ align:start position:0%
+same but similar um so this is true of a
+ 
+
+ align:start position:0%
+same but similar um so this is true of a
+lot of trig relationships that that
+
+ align:start position:0%
+lot of trig relationships that that
+ 
+
+ align:start position:0%
+lot of trig relationships that that
+there's a corresponding uh formula for
+
+ align:start position:0%
+there's a corresponding uh formula for
+ 
+
+ align:start position:0%
+there's a corresponding uh formula for
+the hyperbolic trig functions so one
+
+ align:start position:0%
+the hyperbolic trig functions so one
+ 
+
+ align:start position:0%
+the hyperbolic trig functions so one
+example of such a formula is is your for
+
+ align:start position:0%
+example of such a formula is is your for
+ 
+
+ align:start position:0%
+example of such a formula is is your for
+example your angle addition formulas so
+
+ align:start position:0%
+example your angle addition formulas so
+ 
+
+ align:start position:0%
+example your angle addition formulas so
+I'm going to just leave this as an
+
+ align:start position:0%
+I'm going to just leave this as an
+ 
+
+ align:start position:0%
+I'm going to just leave this as an
+exercise for you um so let me I guess
+
+ align:start position:0%
+exercise for you um so let me I guess
+ 
+
+ align:start position:0%
+exercise for you um so let me I guess
+I'll just stick it in this funny little
+
+ align:start position:0%
+I'll just stick it in this funny little
+ 
+
+ align:start position:0%
+I'll just stick it in this funny little
+piece of board right here
+
+ align:start position:0%
+piece of board right here
+ 
+
+ align:start position:0%
+piece of board right here
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exercise
+
+ align:start position:0%
+exercise
+ 
+
+ align:start position:0%
+exercise
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+cinch of x +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y and
+
+ align:start position:0%
+y and
+ 
+
+ align:start position:0%
+y and
+Kos of X+
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y in
+
+ align:start position:0%
+Y in
+ 
+
+ align:start position:0%
+Y in
+terms of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cinch
+
+ align:start position:0%
+cinch
+ 
+
+ align:start position:0%
+cinch
+X Kosh
+
+ align:start position:0%
+X Kosh
+ 
+
+ align:start position:0%
+X Kosh
+X cinch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y and Kosh y so in other words find the
+
+ align:start position:0%
+Y and Kosh y so in other words find the
+ 
+
+ align:start position:0%
+Y and Kosh y so in other words find the
+corresponding formula to the angle
+
+ align:start position:0%
+corresponding formula to the angle
+ 
+
+ align:start position:0%
+corresponding formula to the angle
+addition formula in the case of the
+
+ align:start position:0%
+addition formula in the case of the
+ 
+
+ align:start position:0%
+addition formula in the case of the
+hyperbolic trig functions so I'll leave
+
+ align:start position:0%
+hyperbolic trig functions so I'll leave
+ 
+
+ align:start position:0%
+hyperbolic trig functions so I'll leave
+you with that
\ No newline at end of file
diff --git a/fQXFHIsvV-c.txt b/fQXFHIsvV-c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5d9ae12d08382ef6f5e21027c03444f4fde4f374
--- /dev/null
+++ b/fQXFHIsvV-c.txt
@@ -0,0 +1,955 @@
+align:start position:0%
+ 
+after Watson has completed the initial
+
+ align:start position:0%
+after Watson has completed the initial
+ 
+
+ align:start position:0%
+after Watson has completed the initial
+two steps of question analysis and
+
+ align:start position:0%
+two steps of question analysis and
+ 
+
+ align:start position:0%
+two steps of question analysis and
+hypothesis generation it's then time to
+
+ align:start position:0%
+hypothesis generation it's then time to
+ 
+
+ align:start position:0%
+hypothesis generation it's then time to
+move on to step three where each of the
+
+ align:start position:0%
+move on to step three where each of the
+ 
+
+ align:start position:0%
+move on to step three where each of the
+hypotheses are scored in this step
+
+ align:start position:0%
+hypotheses are scored in this step
+ 
+
+ align:start position:0%
+hypotheses are scored in this step
+Watson computes confidence levels for
+
+ align:start position:0%
+Watson computes confidence levels for
+ 
+
+ align:start position:0%
+Watson computes confidence levels for
+each possible answer or hypothesis this
+
+ align:start position:0%
+each possible answer or hypothesis this
+ 
+
+ align:start position:0%
+each possible answer or hypothesis this
+is necessary to accurately estimate the
+
+ align:start position:0%
+is necessary to accurately estimate the
+ 
+
+ align:start position:0%
+is necessary to accurately estimate the
+probability of a proposed answer being
+
+ align:start position:0%
+probability of a proposed answer being
+ 
+
+ align:start position:0%
+probability of a proposed answer being
+correct Watson will only buzz in to
+
+ align:start position:0%
+correct Watson will only buzz in to
+ 
+
+ align:start position:0%
+correct Watson will only buzz in to
+answer a question if a confidence level
+
+ align:start position:0%
+answer a question if a confidence level
+ 
+
+ align:start position:0%
+answer a question if a confidence level
+from one of the hypotheses is above a
+
+ align:start position:0%
+from one of the hypotheses is above a
+ 
+
+ align:start position:0%
+from one of the hypotheses is above a
+threshold to compute these confidence
+
+ align:start position:0%
+threshold to compute these confidence
+ 
+
+ align:start position:0%
+threshold to compute these confidence
+levels Watson combines a large number of
+
+ align:start position:0%
+levels Watson combines a large number of
+ 
+
+ align:start position:0%
+levels Watson combines a large number of
+different methods first Watson starts
+
+ align:start position:0%
+different methods first Watson starts
+ 
+
+ align:start position:0%
+different methods first Watson starts
+with lightweight scoring algorithms to
+
+ align:start position:0%
+with lightweight scoring algorithms to
+ 
+
+ align:start position:0%
+with lightweight scoring algorithms to
+prune down the large set of hypotheses
+
+ align:start position:0%
+prune down the large set of hypotheses
+ 
+
+ align:start position:0%
+prune down the large set of hypotheses
+recall that in step two about 200
+
+ align:start position:0%
+recall that in step two about 200
+ 
+
+ align:start position:0%
+recall that in step two about 200
+different hypotheses were generated an
+
+ align:start position:0%
+different hypotheses were generated an
+ 
+
+ align:start position:0%
+different hypotheses were generated an
+example of a lightweight scoring
+
+ align:start position:0%
+example of a lightweight scoring
+ 
+
+ align:start position:0%
+example of a lightweight scoring
+algorithm is computing the likelihood
+
+ align:start position:0%
+algorithm is computing the likelihood
+ 
+
+ align:start position:0%
+algorithm is computing the likelihood
+that a candidate answer is actually an
+
+ align:start position:0%
+that a candidate answer is actually an
+ 
+
+ align:start position:0%
+that a candidate answer is actually an
+instance of the lap for the Mozart
+
+ align:start position:0%
+instance of the lap for the Mozart
+ 
+
+ align:start position:0%
+instance of the lap for the Mozart
+Symphony question where the lat is this
+
+ align:start position:0%
+Symphony question where the lat is this
+ 
+
+ align:start position:0%
+Symphony question where the lat is this
+planet a candidate answer like Earth
+
+ align:start position:0%
+planet a candidate answer like Earth
+ 
+
+ align:start position:0%
+planet a candidate answer like Earth
+would have a very high score but a
+
+ align:start position:0%
+would have a very high score but a
+ 
+
+ align:start position:0%
+would have a very high score but a
+candidate answer like the moon would
+
+ align:start position:0%
+candidate answer like the moon would
+ 
+
+ align:start position:0%
+candidate answer like the moon would
+have a lower score if the likelihood is
+
+ align:start position:0%
+have a lower score if the likelihood is
+ 
+
+ align:start position:0%
+have a lower score if the likelihood is
+not very high Watson throws away the
+
+ align:start position:0%
+not very high Watson throws away the
+ 
+
+ align:start position:0%
+not very high Watson throws away the
+hypothesis the candidate answers that
+
+ align:start position:0%
+hypothesis the candidate answers that
+ 
+
+ align:start position:0%
+hypothesis the candidate answers that
+pass this death proceed to the next
+
+ align:start position:0%
+pass this death proceed to the next
+ 
+
+ align:start position:0%
+pass this death proceed to the next
+stage of the scoring algorithms Watson
+
+ align:start position:0%
+stage of the scoring algorithms Watson
+ 
+
+ align:start position:0%
+stage of the scoring algorithms Watson
+let's about 100 candidate answers pass
+
+ align:start position:0%
+let's about 100 candidate answers pass
+ 
+
+ align:start position:0%
+let's about 100 candidate answers pass
+on to the next stage then Watson moves
+
+ align:start position:0%
+on to the next stage then Watson moves
+ 
+
+ align:start position:0%
+on to the next stage then Watson moves
+into more advanced scoring analytics
+
+ align:start position:0%
+into more advanced scoring analytics
+ 
+
+ align:start position:0%
+into more advanced scoring analytics
+Watson needs to gather supporting
+
+ align:start position:0%
+Watson needs to gather supporting
+ 
+
+ align:start position:0%
+Watson needs to gather supporting
+evidence for each candidate answer one
+
+ align:start position:0%
+evidence for each candidate answer one
+ 
+
+ align:start position:0%
+evidence for each candidate answer one
+way of doing this is through a method
+
+ align:start position:0%
+way of doing this is through a method
+ 
+
+ align:start position:0%
+way of doing this is through a method
+called passage search where passages are
+
+ align:start position:0%
+called passage search where passages are
+ 
+
+ align:start position:0%
+called passage search where passages are
+retrieved that contain the hypothesis
+
+ align:start position:0%
+retrieved that contain the hypothesis
+ 
+
+ align:start position:0%
+retrieved that contain the hypothesis
+text to simulate this let's see what
+
+ align:start position:0%
+text to simulate this let's see what
+ 
+
+ align:start position:0%
+text to simulate this let's see what
+happens when we search for two of our
+
+ align:start position:0%
+happens when we search for two of our
+ 
+
+ align:start position:0%
+happens when we search for two of our
+hypotheses on Google our first
+
+ align:start position:0%
+hypotheses on Google our first
+ 
+
+ align:start position:0%
+hypotheses on Google our first
+hypothesis is Mozart's last and perhaps
+
+ align:start position:0%
+hypothesis is Mozart's last and perhaps
+ 
+
+ align:start position:0%
+hypothesis is Mozart's last and perhaps
+most powerful Symphony shares its name
+
+ align:start position:0%
+most powerful Symphony shares its name
+ 
+
+ align:start position:0%
+most powerful Symphony shares its name
+with Mercury and our second hypothesis
+
+ align:start position:0%
+with Mercury and our second hypothesis
+ 
+
+ align:start position:0%
+with Mercury and our second hypothesis
+is Mozart's last and perhaps most
+
+ align:start position:0%
+is Mozart's last and perhaps most
+ 
+
+ align:start position:0%
+is Mozart's last and perhaps most
+powerful symphony shares its name with
+
+ align:start position:0%
+powerful symphony shares its name with
+ 
+
+ align:start position:0%
+powerful symphony shares its name with
+Jupiter on Google if we search for mo
+
+ align:start position:0%
+Jupiter on Google if we search for mo
+ 
+
+ align:start position:0%
+Jupiter on Google if we search for mo
+symphonie and mercury we get about
+
+ align:start position:0%
+symphonie and mercury we get about
+ 
+
+ align:start position:0%
+symphonie and mercury we get about
+900,000 results and we get some good
+
+ align:start position:0%
+900,000 results and we get some good
+ 
+
+ align:start position:0%
+900,000 results and we get some good
+results
+
+ align:start position:0%
+results
+ 
+
+ align:start position:0%
+results
+they definitely mention the three words
+
+ align:start position:0%
+they definitely mention the three words
+ 
+
+ align:start position:0%
+they definitely mention the three words
+we searched for but mercury is only next
+
+ align:start position:0%
+we searched for but mercury is only next
+ 
+
+ align:start position:0%
+we searched for but mercury is only next
+to symphony once and there's no mention
+
+ align:start position:0%
+to symphony once and there's no mention
+ 
+
+ align:start position:0%
+to symphony once and there's no mention
+about this being his last symphony now
+
+ align:start position:0%
+about this being his last symphony now
+ 
+
+ align:start position:0%
+about this being his last symphony now
+if we search for Mozart Symphony and
+
+ align:start position:0%
+if we search for Mozart Symphony and
+ 
+
+ align:start position:0%
+if we search for Mozart Symphony and
+Jupiter we get about 1.5 million results
+
+ align:start position:0%
+Jupiter we get about 1.5 million results
+ 
+
+ align:start position:0%
+Jupiter we get about 1.5 million results
+and they look much more promising we see
+
+ align:start position:0%
+and they look much more promising we see
+ 
+
+ align:start position:0%
+and they look much more promising we see
+the phrase last Symphony a couple times
+
+ align:start position:0%
+the phrase last Symphony a couple times
+ 
+
+ align:start position:0%
+the phrase last Symphony a couple times
+and Jupiter symphony more than once
+
+ align:start position:0%
+and Jupiter symphony more than once
+ 
+
+ align:start position:0%
+and Jupiter symphony more than once
+therefore the hypothesis with Jupiter
+
+ align:start position:0%
+therefore the hypothesis with Jupiter
+ 
+
+ align:start position:0%
+therefore the hypothesis with Jupiter
+seems to be more supported than the
+
+ align:start position:0%
+seems to be more supported than the
+ 
+
+ align:start position:0%
+seems to be more supported than the
+hypothesis with Mercury now the scoring
+
+ align:start position:0%
+hypothesis with Mercury now the scoring
+ 
+
+ align:start position:0%
+hypothesis with Mercury now the scoring
+analytics determine the degree of
+
+ align:start position:0%
+analytics determine the degree of
+ 
+
+ align:start position:0%
+analytics determine the degree of
+certainty that the evidence supports the
+
+ align:start position:0%
+certainty that the evidence supports the
+ 
+
+ align:start position:0%
+certainty that the evidence supports the
+candidate answers more than 50 different
+
+ align:start position:0%
+candidate answers more than 50 different
+ 
+
+ align:start position:0%
+candidate answers more than 50 different
+scoring components are used one example
+
+ align:start position:0%
+scoring components are used one example
+ 
+
+ align:start position:0%
+scoring components are used one example
+is analyzing temporal relationships
+
+ align:start position:0%
+is analyzing temporal relationships
+ 
+
+ align:start position:0%
+is analyzing temporal relationships
+consider the Jeopardy question in 1594
+
+ align:start position:0%
+consider the Jeopardy question in 1594
+ 
+
+ align:start position:0%
+consider the Jeopardy question in 1594
+he took a job as a tax collector in
+
+ align:start position:0%
+he took a job as a tax collector in
+ 
+
+ align:start position:0%
+he took a job as a tax collector in
+Andalusia two candidate answers are
+
+ align:start position:0%
+Andalusia two candidate answers are
+ 
+
+ align:start position:0%
+Andalusia two candidate answers are
+thorough and Cervantes
+
+ align:start position:0%
+thorough and Cervantes
+ 
+
+ align:start position:0%
+thorough and Cervantes
+however this algorithm would determine
+
+ align:start position:0%
+however this algorithm would determine
+ 
+
+ align:start position:0%
+however this algorithm would determine
+that Thoreau was not born until 1817 so
+
+ align:start position:0%
+that Thoreau was not born until 1817 so
+ 
+
+ align:start position:0%
+that Thoreau was not born until 1817 so
+it would give a higher score to
+
+ align:start position:0%
+it would give a higher score to
+ 
+
+ align:start position:0%
+it would give a higher score to
+Cervantes once all of the scoring
+
+ align:start position:0%
+Cervantes once all of the scoring
+ 
+
+ align:start position:0%
+Cervantes once all of the scoring
+algorithms are run Watson needs to
+
+ align:start position:0%
+algorithms are run Watson needs to
+ 
+
+ align:start position:0%
+algorithms are run Watson needs to
+select the single best supported
+
+ align:start position:0%
+select the single best supported
+ 
+
+ align:start position:0%
+select the single best supported
+hypothesis before this can be done
+
+ align:start position:0%
+hypothesis before this can be done
+ 
+
+ align:start position:0%
+hypothesis before this can be done
+similar answers need to be merged since
+
+ align:start position:0%
+similar answers need to be merged since
+ 
+
+ align:start position:0%
+similar answers need to be merged since
+multiple candidate answers may be
+
+ align:start position:0%
+multiple candidate answers may be
+ 
+
+ align:start position:0%
+multiple candidate answers may be
+equivalent as an example the candidate
+
+ align:start position:0%
+equivalent as an example the candidate
+ 
+
+ align:start position:0%
+equivalent as an example the candidate
+answers Abraham Lincoln and Honest Abe
+
+ align:start position:0%
+answers Abraham Lincoln and Honest Abe
+ 
+
+ align:start position:0%
+answers Abraham Lincoln and Honest Abe
+refer to the same person so the scores
+
+ align:start position:0%
+refer to the same person so the scores
+ 
+
+ align:start position:0%
+refer to the same person so the scores
+for these two candidate answers need to
+
+ align:start position:0%
+for these two candidate answers need to
+ 
+
+ align:start position:0%
+for these two candidate answers need to
+be combined
+
+ align:start position:0%
+be combined
+ 
+
+ align:start position:0%
+be combined
+Watson should not be viewing similar
+
+ align:start position:0%
+Watson should not be viewing similar
+ 
+
+ align:start position:0%
+Watson should not be viewing similar
+answers as competing choices now Watson
+
+ align:start position:0%
+answers as competing choices now Watson
+ 
+
+ align:start position:0%
+answers as competing choices now Watson
+is ready to rank the hypotheses and
+
+ align:start position:0%
+is ready to rank the hypotheses and
+ 
+
+ align:start position:0%
+is ready to rank the hypotheses and
+estimate an overall confidence for each
+
+ align:start position:0%
+estimate an overall confidence for each
+ 
+
+ align:start position:0%
+estimate an overall confidence for each
+to do this predictive analytics are used
+
+ align:start position:0%
+to do this predictive analytics are used
+ 
+
+ align:start position:0%
+to do this predictive analytics are used
+to compute an overall confidence level
+
+ align:start position:0%
+to compute an overall confidence level
+ 
+
+ align:start position:0%
+to compute an overall confidence level
+for each candidate answer Watson uses
+
+ align:start position:0%
+for each candidate answer Watson uses
+ 
+
+ align:start position:0%
+for each candidate answer Watson uses
+logistic regression the training data is
+
+ align:start position:0%
+logistic regression the training data is
+ 
+
+ align:start position:0%
+logistic regression the training data is
+a set of historical jeopardy questions
+
+ align:start position:0%
+a set of historical jeopardy questions
+ 
+
+ align:start position:0%
+a set of historical jeopardy questions
+and all of the candidate answers each of
+
+ align:start position:0%
+and all of the candidate answers each of
+ 
+
+ align:start position:0%
+and all of the candidate answers each of
+the scoring algorithms is used as an
+
+ align:start position:0%
+the scoring algorithms is used as an
+ 
+
+ align:start position:0%
+the scoring algorithms is used as an
+independent variable then logistic
+
+ align:start position:0%
+independent variable then logistic
+ 
+
+ align:start position:0%
+independent variable then logistic
+regression is used to predict whether or
+
+ align:start position:0%
+regression is used to predict whether or
+ 
+
+ align:start position:0%
+regression is used to predict whether or
+not a candidate answer is correct
+
+ align:start position:0%
+not a candidate answer is correct
+ 
+
+ align:start position:0%
+not a candidate answer is correct
+using the scores this gives each score a
+
+ align:start position:0%
+using the scores this gives each score a
+ 
+
+ align:start position:0%
+using the scores this gives each score a
+weight and computes an overall
+
+ align:start position:0%
+weight and computes an overall
+ 
+
+ align:start position:0%
+weight and computes an overall
+probability or confidence that a
+
+ align:start position:0%
+probability or confidence that a
+ 
+
+ align:start position:0%
+probability or confidence that a
+candidate answer is correct
+
+ align:start position:0%
+candidate answer is correct
+ 
+
+ align:start position:0%
+candidate answer is correct
+it's the highest confidence level for
+
+ align:start position:0%
+it's the highest confidence level for
+ 
+
+ align:start position:0%
+it's the highest confidence level for
+one of the candidate answers for a
+
+ align:start position:0%
+one of the candidate answers for a
+ 
+
+ align:start position:0%
+one of the candidate answers for a
+question is high enough
+
+ align:start position:0%
+question is high enough
+ 
+
+ align:start position:0%
+question is high enough
+Watson buzzes in to answer the question
+
+ align:start position:0%
+Watson buzzes in to answer the question
+ 
+
+ align:start position:0%
+Watson buzzes in to answer the question
+in total the Watson system is composed
+
+ align:start position:0%
+in total the Watson system is composed
+ 
+
+ align:start position:0%
+in total the Watson system is composed
+of eight refrigerator-sized cabinets and
+
+ align:start position:0%
+of eight refrigerator-sized cabinets and
+ 
+
+ align:start position:0%
+of eight refrigerator-sized cabinets and
+has high speed local storage for all
+
+ align:start position:0%
+has high speed local storage for all
+ 
+
+ align:start position:0%
+has high speed local storage for all
+information it originally took over two
+
+ align:start position:0%
+information it originally took over two
+ 
+
+ align:start position:0%
+information it originally took over two
+hours to answer one question and the
+
+ align:start position:0%
+hours to answer one question and the
+ 
+
+ align:start position:0%
+hours to answer one question and the
+team had to reduce us to two to six
+
+ align:start position:0%
+team had to reduce us to two to six
+ 
+
+ align:start position:0%
+team had to reduce us to two to six
+seconds in the next video we'll see how
+
+ align:start position:0%
+seconds in the next video we'll see how
+ 
+
+ align:start position:0%
+seconds in the next video we'll see how
+Watson progressed in the six years
+
+ align:start position:0%
+Watson progressed in the six years
+ 
+
+ align:start position:0%
+Watson progressed in the six years
+between starting and plane on Jeopardy
+
+ align:start position:0%
+between starting and plane on Jeopardy
+ 
+
+ align:start position:0%
+between starting and plane on Jeopardy
+what happened during the game and what
+
+ align:start position:0%
+what happened during the game and what
+ 
+
+ align:start position:0%
+what happened during the game and what
+the Watson team is working on now
\ No newline at end of file
diff --git a/gDpkinitSRM.txt b/gDpkinitSRM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cad6083b4997187f1eed00b26c41f8e3a3db33d8
--- /dev/null
+++ b/gDpkinitSRM.txt
@@ -0,0 +1,1131 @@
+align:start position:0%
+ 
+I'm uh I'm promoter I'm Gillian Gillian
+
+ align:start position:0%
+I'm uh I'm promoter I'm Gillian Gillian
+ 
+
+ align:start position:0%
+I'm uh I'm promoter I'm Gillian Gillian
+and um our game is you know like how on
+
+ align:start position:0%
+and um our game is you know like how on
+ 
+
+ align:start position:0%
+and um our game is you know like how on
+the iPhone you have those games that's
+
+ align:start position:0%
+the iPhone you have those games that's
+ 
+
+ align:start position:0%
+the iPhone you have those games that's
+like jetpack joyride or something it's
+
+ align:start position:0%
+like jetpack joyride or something it's
+ 
+
+ align:start position:0%
+like jetpack joyride or something it's
+like one of those games that has a
+
+ align:start position:0%
+like one of those games that has a
+ 
+
+ align:start position:0%
+like one of those games that has a
+player moving infinitely and you have to
+
+ align:start position:0%
+player moving infinitely and you have to
+ 
+
+ align:start position:0%
+player moving infinitely and you have to
+click to make a jump or go left or right
+
+ align:start position:0%
+click to make a jump or go left or right
+ 
+
+ align:start position:0%
+click to make a jump or go left or right
+so it's kind of based off of that that
+
+ align:start position:0%
+so it's kind of based off of that that
+ 
+
+ align:start position:0%
+so it's kind of based off of that that
+was kind of our inspiration except it's
+
+ align:start position:0%
+was kind of our inspiration except it's
+ 
+
+ align:start position:0%
+was kind of our inspiration except it's
+in 3d and well I guess just play it yeah
+
+ align:start position:0%
+in 3d and well I guess just play it yeah
+ 
+
+ align:start position:0%
+in 3d and well I guess just play it yeah
+he'll just demo it hopefully it'll play
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the cube is moving instantly in the
+
+ align:start position:0%
+so the cube is moving instantly in the
+ 
+
+ align:start position:0%
+so the cube is moving instantly in the
+plane and you can collect coins and
+
+ align:start position:0%
+plane and you can collect coins and
+ 
+
+ align:start position:0%
+plane and you can collect coins and
+that'll make your score go up if you
+
+ align:start position:0%
+that'll make your score go up if you
+ 
+
+ align:start position:0%
+that'll make your score go up if you
+touch a cactus these are like enemies
+
+ align:start position:0%
+touch a cactus these are like enemies
+ 
+
+ align:start position:0%
+touch a cactus these are like enemies
+that'll destroy your lives you have you
+
+ align:start position:0%
+that'll destroy your lives you have you
+ 
+
+ align:start position:0%
+that'll destroy your lives you have you
+start off with five lives right what she
+
+ align:start position:0%
+start off with five lives right what she
+ 
+
+ align:start position:0%
+start off with five lives right what she
+just picked up is a capsule so you see
+
+ align:start position:0%
+just picked up is a capsule so you see
+ 
+
+ align:start position:0%
+just picked up is a capsule so you see
+the little bar at the bottom that's like
+
+ align:start position:0%
+the little bar at the bottom that's like
+ 
+
+ align:start position:0%
+the little bar at the bottom that's like
+how much fuel you have so that you can
+
+ align:start position:0%
+how much fuel you have so that you can
+ 
+
+ align:start position:0%
+how much fuel you have so that you can
+only fly which is hitting spacebar fly
+
+ align:start position:0%
+only fly which is hitting spacebar fly
+ 
+
+ align:start position:0%
+only fly which is hitting spacebar fly
+okay yeah yeah you can also go
+
+ align:start position:0%
+okay yeah yeah you can also go
+ 
+
+ align:start position:0%
+okay yeah yeah you can also go
+underwater so there's like coins under
+
+ align:start position:0%
+underwater so there's like coins under
+ 
+
+ align:start position:0%
+underwater so there's like coins under
+the water and so you like to go under
+
+ align:start position:0%
+the water and so you like to go under
+ 
+
+ align:start position:0%
+the water and so you like to go under
+there you can collect secret coins and
+
+ align:start position:0%
+there you can collect secret coins and
+ 
+
+ align:start position:0%
+there you can collect secret coins and
+then you you fly by pressing spacebar
+
+ align:start position:0%
+then you you fly by pressing spacebar
+ 
+
+ align:start position:0%
+then you you fly by pressing spacebar
+but if you see the bar down there if you
+
+ align:start position:0%
+but if you see the bar down there if you
+ 
+
+ align:start position:0%
+but if you see the bar down there if you
+run out of fuel you can't press you
+
+ align:start position:0%
+run out of fuel you can't press you
+ 
+
+ align:start position:0%
+run out of fuel you can't press you
+can't fly in the the field anymore and
+
+ align:start position:0%
+can't fly in the the field anymore and
+ 
+
+ align:start position:0%
+can't fly in the the field anymore and
+so you just keep going I think we
+
+ align:start position:0%
+so you just keep going I think we
+ 
+
+ align:start position:0%
+so you just keep going I think we
+touched the few cactus along the way
+
+ align:start position:0%
+touched the few cactus along the way
+ 
+
+ align:start position:0%
+touched the few cactus along the way
+yeah our lives are like he was alive by
+
+ align:start position:0%
+yeah our lives are like he was alive by
+ 
+
+ align:start position:0%
+yeah our lives are like he was alive by
+touching the enemies there's okay now
+
+ align:start position:0%
+touching the enemies there's okay now
+ 
+
+ align:start position:0%
+touching the enemies there's okay now
+you know she can fly okay so we have
+
+ align:start position:0%
+you know she can fly okay so we have
+ 
+
+ align:start position:0%
+you know she can fly okay so we have
+like three worlds so this is the desert
+
+ align:start position:0%
+like three worlds so this is the desert
+ 
+
+ align:start position:0%
+like three worlds so this is the desert
+world and then she's going into like the
+
+ align:start position:0%
+world and then she's going into like the
+ 
+
+ align:start position:0%
+world and then she's going into like the
+snow world which also has coins
+
+ align:start position:0%
+snow world which also has coins
+ 
+
+ align:start position:0%
+snow world which also has coins
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah it's it's pretty yeah and then
+
+ align:start position:0%
+yeah it's it's pretty yeah and then
+ 
+
+ align:start position:0%
+yeah it's it's pretty yeah and then
+obviously the coin spin around this
+
+ align:start position:0%
+obviously the coin spin around this
+ 
+
+ align:start position:0%
+obviously the coin spin around this
+world isn't as tall as long as the
+
+ align:start position:0%
+world isn't as tall as long as the
+ 
+
+ align:start position:0%
+world isn't as tall as long as the
+desert world you can see like the forest
+
+ align:start position:0%
+desert world you can see like the forest
+ 
+
+ align:start position:0%
+desert world you can see like the forest
+roll showing up already
+
+ align:start position:0%
+roll showing up already
+ 
+
+ align:start position:0%
+roll showing up already
+there's also coins in the air but you
+
+ align:start position:0%
+there's also coins in the air but you
+ 
+
+ align:start position:0%
+there's also coins in the air but you
+can only get them if you have fuel yeah
+
+ align:start position:0%
+can only get them if you have fuel yeah
+ 
+
+ align:start position:0%
+can only get them if you have fuel yeah
+you have to be like you have to know
+
+ align:start position:0%
+you have to be like you have to know
+ 
+
+ align:start position:0%
+you have to be like you have to know
+exactly where they are oh there you go I
+
+ align:start position:0%
+exactly where they are oh there you go I
+ 
+
+ align:start position:0%
+exactly where they are oh there you go I
+think our high score is 20 so if anyone
+
+ align:start position:0%
+think our high score is 20 so if anyone
+ 
+
+ align:start position:0%
+think our high score is 20 so if anyone
+can beat that yes so you can like run
+
+ align:start position:0%
+can beat that yes so you can like run
+ 
+
+ align:start position:0%
+can beat that yes so you can like run
+into them yeah you can submerge in the
+
+ align:start position:0%
+into them yeah you can submerge in the
+ 
+
+ align:start position:0%
+into them yeah you can submerge in the
+grass so it's like going through a
+
+ align:start position:0%
+grass so it's like going through a
+ 
+
+ align:start position:0%
+grass so it's like going through a
+meadow and it's funny because the grass
+
+ align:start position:0%
+meadow and it's funny because the grass
+ 
+
+ align:start position:0%
+meadow and it's funny because the grass
+is actually a bunch of little trees you
+
+ align:start position:0%
+is actually a bunch of little trees you
+ 
+
+ align:start position:0%
+is actually a bunch of little trees you
+can't see it now but if you like zoom in
+
+ align:start position:0%
+can't see it now but if you like zoom in
+ 
+
+ align:start position:0%
+can't see it now but if you like zoom in
+infinitely you'll see like the tiny
+
+ align:start position:0%
+infinitely you'll see like the tiny
+ 
+
+ align:start position:0%
+infinitely you'll see like the tiny
+little trees swaying it's really funny
+
+ align:start position:0%
+little trees swaying it's really funny
+ 
+
+ align:start position:0%
+little trees swaying it's really funny
+yeah and then yeah that is the end of
+
+ align:start position:0%
+yeah and then yeah that is the end of
+ 
+
+ align:start position:0%
+yeah and then yeah that is the end of
+the game and then I think you'll fall
+
+ align:start position:0%
+the game and then I think you'll fall
+ 
+
+ align:start position:0%
+the game and then I think you'll fall
+infinitely yeah yeah you just fall
+
+ align:start position:0%
+infinitely yeah yeah you just fall
+ 
+
+ align:start position:0%
+infinitely yeah yeah you just fall
+infinitely into space that's our game so
+
+ align:start position:0%
+infinitely into space that's our game so
+ 
+
+ align:start position:0%
+infinitely into space that's our game so
+we can talk about like some challenges
+
+ align:start position:0%
+we can talk about like some challenges
+ 
+
+ align:start position:0%
+we can talk about like some challenges
+that we had um so basically split up the
+
+ align:start position:0%
+that we had um so basically split up the
+ 
+
+ align:start position:0%
+that we had um so basically split up the
+work into two separate groups so um so I
+
+ align:start position:0%
+work into two separate groups so um so I
+ 
+
+ align:start position:0%
+work into two separate groups so um so I
+mostly worked on building the world
+
+ align:start position:0%
+mostly worked on building the world
+ 
+
+ align:start position:0%
+mostly worked on building the world
+because I found like the terraforming
+
+ align:start position:0%
+because I found like the terraforming
+ 
+
+ align:start position:0%
+because I found like the terraforming
+tool of unity like fascinating I spent
+
+ align:start position:0%
+tool of unity like fascinating I spent
+ 
+
+ align:start position:0%
+tool of unity like fascinating I spent
+like hours doing that it's so cool so a
+
+ align:start position:0%
+like hours doing that it's so cool so a
+ 
+
+ align:start position:0%
+like hours doing that it's so cool so a
+lot of the more complicated things like
+
+ align:start position:0%
+lot of the more complicated things like
+ 
+
+ align:start position:0%
+lot of the more complicated things like
+you can see the canyons and the cactus
+
+ align:start position:0%
+you can see the canyons and the cactus
+ 
+
+ align:start position:0%
+you can see the canyons and the cactus
+were and the trees were imported from
+
+ align:start position:0%
+were and the trees were imported from
+ 
+
+ align:start position:0%
+were and the trees were imported from
+Unity assets um all of them were free
+
+ align:start position:0%
+Unity assets um all of them were free
+ 
+
+ align:start position:0%
+Unity assets um all of them were free
+although there are some that are like up
+
+ align:start position:0%
+although there are some that are like up
+ 
+
+ align:start position:0%
+although there are some that are like up
+to like $40 and basically the ground the
+
+ align:start position:0%
+to like $40 and basically the ground the
+ 
+
+ align:start position:0%
+to like $40 and basically the ground the
+terrain I like hand created but the
+
+ align:start position:0%
+terrain I like hand created but the
+ 
+
+ align:start position:0%
+terrain I like hand created but the
+canyons and cacti were created and
+
+ align:start position:0%
+canyons and cacti were created and
+ 
+
+ align:start position:0%
+canyons and cacti were created and
+imported but I did hand place all of
+
+ align:start position:0%
+imported but I did hand place all of
+ 
+
+ align:start position:0%
+imported but I did hand place all of
+them in the hand design
+
+ align:start position:0%
+them in the hand design
+ 
+
+ align:start position:0%
+them in the hand design
+that the river let's see if I can like
+
+ align:start position:0%
+that the river let's see if I can like
+ 
+
+ align:start position:0%
+that the river let's see if I can like
+zoom in um the river it was interesting
+
+ align:start position:0%
+zoom in um the river it was interesting
+ 
+
+ align:start position:0%
+zoom in um the river it was interesting
+to create because um it's not that hard
+
+ align:start position:0%
+to create because um it's not that hard
+ 
+
+ align:start position:0%
+to create because um it's not that hard
+unity makes it relatively easy for you
+
+ align:start position:0%
+unity makes it relatively easy for you
+ 
+
+ align:start position:0%
+unity makes it relatively easy for you
+but to get it to have like the applied
+
+ align:start position:0%
+but to get it to have like the applied
+ 
+
+ align:start position:0%
+but to get it to have like the applied
+the physics to the river properly is
+
+ align:start position:0%
+the physics to the river properly is
+ 
+
+ align:start position:0%
+the physics to the river properly is
+like kind of complicated you can't
+
+ align:start position:0%
+like kind of complicated you can't
+ 
+
+ align:start position:0%
+like kind of complicated you can't
+really tell because of the way we have
+
+ align:start position:0%
+really tell because of the way we have
+ 
+
+ align:start position:0%
+really tell because of the way we have
+it but there's actually water everywhere
+
+ align:start position:0%
+it but there's actually water everywhere
+ 
+
+ align:start position:0%
+it but there's actually water everywhere
+in this world and if you dig deep enough
+
+ align:start position:0%
+in this world and if you dig deep enough
+ 
+
+ align:start position:0%
+in this world and if you dig deep enough
+you will get a pool so I can show you
+
+ align:start position:0%
+you will get a pool so I can show you
+ 
+
+ align:start position:0%
+you will get a pool so I can show you
+that so let's see inspector this is how
+
+ align:start position:0%
+that so let's see inspector this is how
+ 
+
+ align:start position:0%
+that so let's see inspector this is how
+you do the terrain here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concealing water coming up and then she
+
+ align:start position:0%
+concealing water coming up and then she
+ 
+
+ align:start position:0%
+concealing water coming up and then she
+worked on the coding parts as far as the
+
+ align:start position:0%
+worked on the coding parts as far as the
+ 
+
+ align:start position:0%
+worked on the coding parts as far as the
+game address yeah I did mostly the code
+
+ align:start position:0%
+game address yeah I did mostly the code
+ 
+
+ align:start position:0%
+game address yeah I did mostly the code
+and there's not really that many
+
+ align:start position:0%
+and there's not really that many
+ 
+
+ align:start position:0%
+and there's not really that many
+different codes I don't know if you can
+
+ align:start position:0%
+different codes I don't know if you can
+ 
+
+ align:start position:0%
+different codes I don't know if you can
+wear the scripts right so there's
+
+ align:start position:0%
+wear the scripts right so there's
+ 
+
+ align:start position:0%
+wear the scripts right so there's
+there's really only a few simple codes
+
+ align:start position:0%
+there's really only a few simple codes
+ 
+
+ align:start position:0%
+there's really only a few simple codes
+over there but like so the coins they
+
+ align:start position:0%
+over there but like so the coins they
+ 
+
+ align:start position:0%
+over there but like so the coins they
+have their own little code so that they
+
+ align:start position:0%
+have their own little code so that they
+ 
+
+ align:start position:0%
+have their own little code so that they
+spin around which yeah that's that's the
+
+ align:start position:0%
+spin around which yeah that's that's the
+ 
+
+ align:start position:0%
+spin around which yeah that's that's the
+code for the player right and so just a
+
+ align:start position:0%
+code for the player right and so just a
+ 
+
+ align:start position:0%
+code for the player right and so just a
+player so like the the weirdest part was
+
+ align:start position:0%
+player so like the the weirdest part was
+ 
+
+ align:start position:0%
+player so like the the weirdest part was
+to get the cube to always move
+
+ align:start position:0%
+to get the cube to always move
+ 
+
+ align:start position:0%
+to get the cube to always move
+infinitely so like you know originally
+
+ align:start position:0%
+infinitely so like you know originally
+ 
+
+ align:start position:0%
+infinitely so like you know originally
+you could move it forward and backwards
+
+ align:start position:0%
+you could move it forward and backwards
+ 
+
+ align:start position:0%
+you could move it forward and backwards
+but we just have to figure out how to
+
+ align:start position:0%
+but we just have to figure out how to
+ 
+
+ align:start position:0%
+but we just have to figure out how to
+like make it so it never moves backwards
+
+ align:start position:0%
+like make it so it never moves backwards
+ 
+
+ align:start position:0%
+like make it so it never moves backwards
+like that's not an option and so that
+
+ align:start position:0%
+like that's not an option and so that
+ 
+
+ align:start position:0%
+like that's not an option and so that
+was that was just something different
+
+ align:start position:0%
+was that was just something different
+ 
+
+ align:start position:0%
+was that was just something different
+that I had to figure out how to do and
+
+ align:start position:0%
+that I had to figure out how to do and
+ 
+
+ align:start position:0%
+that I had to figure out how to do and
+then this is just like a bunch of
+
+ align:start position:0%
+then this is just like a bunch of
+ 
+
+ align:start position:0%
+then this is just like a bunch of
+different codes actually the hardest
+
+ align:start position:0%
+different codes actually the hardest
+ 
+
+ align:start position:0%
+different codes actually the hardest
+part I think was doing the health bar to
+
+ align:start position:0%
+part I think was doing the health bar to
+ 
+
+ align:start position:0%
+part I think was doing the health bar to
+make it go down so I mean obviously you
+
+ align:start position:0%
+make it go down so I mean obviously you
+ 
+
+ align:start position:0%
+make it go down so I mean obviously you
+can like make integers go down but like
+
+ align:start position:0%
+can like make integers go down but like
+ 
+
+ align:start position:0%
+can like make integers go down but like
+just make that visually happen was
+
+ align:start position:0%
+just make that visually happen was
+ 
+
+ align:start position:0%
+just make that visually happen was
+really weird but that you just have to
+
+ align:start position:0%
+really weird but that you just have to
+ 
+
+ align:start position:0%
+really weird but that you just have to
+like use a local scale or something like
+
+ align:start position:0%
+like use a local scale or something like
+ 
+
+ align:start position:0%
+like use a local scale or something like
+that and so that was that was pretty
+
+ align:start position:0%
+that and so that was that was pretty
+ 
+
+ align:start position:0%
+that and so that was that was pretty
+simple after I figured it out I guess
+
+ align:start position:0%
+simple after I figured it out I guess
+ 
+
+ align:start position:0%
+simple after I figured it out I guess
+but in the process of this heart and
+
+ align:start position:0%
+but in the process of this heart and
+ 
+
+ align:start position:0%
+but in the process of this heart and
+overall the game was really fun to make
+
+ align:start position:0%
+overall the game was really fun to make
+ 
+
+ align:start position:0%
+overall the game was really fun to make
+yeah you actually like worked on it a
+
+ align:start position:0%
+yeah you actually like worked on it a
+ 
+
+ align:start position:0%
+yeah you actually like worked on it a
+lot and like on our own time after class
+
+ align:start position:0%
+lot and like on our own time after class
+ 
+
+ align:start position:0%
+lot and like on our own time after class
+she was here till like 11:00 last night
+
+ align:start position:0%
+she was here till like 11:00 last night
+ 
+
+ align:start position:0%
+she was here till like 11:00 last night
+at my dorm room
+
+ align:start position:0%
+at my dorm room
+ 
+
+ align:start position:0%
+at my dorm room
+because I were just like yeah it was
+
+ align:start position:0%
+because I were just like yeah it was
+ 
+
+ align:start position:0%
+because I were just like yeah it was
+like made me like 30% done until last
+
+ align:start position:0%
+like made me like 30% done until last
+ 
+
+ align:start position:0%
+like made me like 30% done until last
+and it really came together last night
+
+ align:start position:0%
+and it really came together last night
+ 
+
+ align:start position:0%
+and it really came together last night
+and then we were like what could be
+
+ align:start position:0%
+and then we were like what could be
+ 
+
+ align:start position:0%
+and then we were like what could be
+adding more I think we just kept on
+
+ align:start position:0%
+adding more I think we just kept on
+ 
+
+ align:start position:0%
+adding more I think we just kept on
+going in and ass every time we were like
+
+ align:start position:0%
+going in and ass every time we were like
+ 
+
+ align:start position:0%
+going in and ass every time we were like
+we should stop yeah like this is enough
+
+ align:start position:0%
+we should stop yeah like this is enough
+ 
+
+ align:start position:0%
+we should stop yeah like this is enough
+so yeah that's about it yeah that's all
+
+ align:start position:0%
+so yeah that's about it yeah that's all
+ 
+
+ align:start position:0%
+so yeah that's about it yeah that's all
+you have says spacebar to jump but unlit
+
+ align:start position:0%
+you have says spacebar to jump but unlit
+ 
+
+ align:start position:0%
+you have says spacebar to jump but unlit
+until you run out of fuel at which point
+
+ align:start position:0%
+until you run out of fuel at which point
+ 
+
+ align:start position:0%
+until you run out of fuel at which point
+it like locks the spacebar so you can't
+
+ align:start position:0%
+it like locks the spacebar so you can't
+ 
+
+ align:start position:0%
+it like locks the spacebar so you can't
+you can't go up that good yeah yeah you
+
+ align:start position:0%
+you can't go up that good yeah yeah you
+ 
+
+ align:start position:0%
+you can't go up that good yeah yeah you
+like continuous every time you hit the
+
+ align:start position:0%
+like continuous every time you hit the
+ 
+
+ align:start position:0%
+like continuous every time you hit the
+spacebar so you can go every way so you
+
+ align:start position:0%
+spacebar so you can go every way so you
+ 
+
+ align:start position:0%
+spacebar so you can go every way so you
+like continue to fly
\ No newline at end of file
diff --git a/gE1wRDQMR8E.txt b/gE1wRDQMR8E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6e9827e14737c37545b1ed440f62eca1dd3c9df9
--- /dev/null
+++ b/gE1wRDQMR8E.txt
@@ -0,0 +1,1195 @@
+align:start position:0%
+ 
+in the previous video we observed that
+
+ align:start position:0%
+in the previous video we observed that
+ 
+
+ align:start position:0%
+in the previous video we observed that
+age and France population are highly
+
+ align:start position:0%
+age and France population are highly
+ 
+
+ align:start position:0%
+age and France population are highly
+correlated but what is correlation
+
+ align:start position:0%
+correlated but what is correlation
+ 
+
+ align:start position:0%
+correlated but what is correlation
+correlation measures the linear
+
+ align:start position:0%
+correlation measures the linear
+ 
+
+ align:start position:0%
+correlation measures the linear
+relationship between two variables and
+
+ align:start position:0%
+relationship between two variables and
+ 
+
+ align:start position:0%
+relationship between two variables and
+is a number between negative 1 and
+
+ align:start position:0%
+is a number between negative 1 and
+ 
+
+ align:start position:0%
+is a number between negative 1 and
+positive 1 a correlation of positive 1
+
+ align:start position:0%
+positive 1 a correlation of positive 1
+ 
+
+ align:start position:0%
+positive 1 a correlation of positive 1
+means a perfect positive linear
+
+ align:start position:0%
+means a perfect positive linear
+ 
+
+ align:start position:0%
+means a perfect positive linear
+relationship a correlation of negative 1
+
+ align:start position:0%
+relationship a correlation of negative 1
+ 
+
+ align:start position:0%
+relationship a correlation of negative 1
+means a perfect negative linear
+
+ align:start position:0%
+means a perfect negative linear
+ 
+
+ align:start position:0%
+means a perfect negative linear
+relationship in the middle of these two
+
+ align:start position:0%
+relationship in the middle of these two
+ 
+
+ align:start position:0%
+relationship in the middle of these two
+extremes is a correlation of 0 which
+
+ align:start position:0%
+extremes is a correlation of 0 which
+ 
+
+ align:start position:0%
+extremes is a correlation of 0 which
+means that there is no linear
+
+ align:start position:0%
+means that there is no linear
+ 
+
+ align:start position:0%
+means that there is no linear
+relationship between the two variables
+
+ align:start position:0%
+relationship between the two variables
+ 
+
+ align:start position:0%
+relationship between the two variables
+when we say that two variables are
+
+ align:start position:0%
+when we say that two variables are
+ 
+
+ align:start position:0%
+when we say that two variables are
+highly correlated we mean that the
+
+ align:start position:0%
+highly correlated we mean that the
+ 
+
+ align:start position:0%
+highly correlated we mean that the
+absolute value of the correlation is
+
+ align:start position:0%
+absolute value of the correlation is
+ 
+
+ align:start position:0%
+absolute value of the correlation is
+close to 1 let's look at some examples
+
+ align:start position:0%
+close to 1 let's look at some examples
+ 
+
+ align:start position:0%
+close to 1 let's look at some examples
+this plot graphs winter reign on the
+
+ align:start position:0%
+this plot graphs winter reign on the
+ 
+
+ align:start position:0%
+this plot graphs winter reign on the
+x-axis and price on the y-axis by
+
+ align:start position:0%
+x-axis and price on the y-axis by
+ 
+
+ align:start position:0%
+x-axis and price on the y-axis by
+visually inspecting the plot it's hard
+
+ align:start position:0%
+visually inspecting the plot it's hard
+ 
+
+ align:start position:0%
+visually inspecting the plot it's hard
+to detect any linear relationship but it
+
+ align:start position:0%
+to detect any linear relationship but it
+ 
+
+ align:start position:0%
+to detect any linear relationship but it
+turns out that the correlation between
+
+ align:start position:0%
+turns out that the correlation between
+ 
+
+ align:start position:0%
+turns out that the correlation between
+winter rain and price is 0.14 so there's
+
+ align:start position:0%
+winter rain and price is 0.14 so there's
+ 
+
+ align:start position:0%
+winter rain and price is 0.14 so there's
+a slight positive relationship between
+
+ align:start position:0%
+a slight positive relationship between
+ 
+
+ align:start position:0%
+a slight positive relationship between
+these two variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this plot has harvest strain on the
+
+ align:start position:0%
+this plot has harvest strain on the
+ 
+
+ align:start position:0%
+this plot has harvest strain on the
+x-axis and the average growing season
+
+ align:start position:0%
+x-axis and the average growing season
+ 
+
+ align:start position:0%
+x-axis and the average growing season
+temperature on the y-axis it's again
+
+ align:start position:0%
+temperature on the y-axis it's again
+ 
+
+ align:start position:0%
+temperature on the y-axis it's again
+hard to visually see a linear
+
+ align:start position:0%
+hard to visually see a linear
+ 
+
+ align:start position:0%
+hard to visually see a linear
+relationship between the two variables
+
+ align:start position:0%
+relationship between the two variables
+ 
+
+ align:start position:0%
+relationship between the two variables
+and it turns out that the correlation is
+
+ align:start position:0%
+and it turns out that the correlation is
+ 
+
+ align:start position:0%
+and it turns out that the correlation is
+negative 0.06
+
+ align:start position:0%
+negative 0.06
+ 
+
+ align:start position:0%
+negative 0.06
+even closer to 0 than before this plot
+
+ align:start position:0%
+even closer to 0 than before this plot
+ 
+
+ align:start position:0%
+even closer to 0 than before this plot
+shows age of the wine on the x-axis and
+
+ align:start position:0%
+shows age of the wine on the x-axis and
+ 
+
+ align:start position:0%
+shows age of the wine on the x-axis and
+the population of France on the y-axis
+
+ align:start position:0%
+the population of France on the y-axis
+ 
+
+ align:start position:0%
+the population of France on the y-axis
+we can easily see that there's a strong
+
+ align:start position:0%
+we can easily see that there's a strong
+ 
+
+ align:start position:0%
+we can easily see that there's a strong
+negative linear relationship between
+
+ align:start position:0%
+negative linear relationship between
+ 
+
+ align:start position:0%
+negative linear relationship between
+these two variables this makes sense
+
+ align:start position:0%
+these two variables this makes sense
+ 
+
+ align:start position:0%
+these two variables this makes sense
+since the population of France is
+
+ align:start position:0%
+since the population of France is
+ 
+
+ align:start position:0%
+since the population of France is
+increased with time if we compute the
+
+ align:start position:0%
+increased with time if we compute the
+ 
+
+ align:start position:0%
+increased with time if we compute the
+correlation we get negative 0.99 so
+
+ align:start position:0%
+correlation we get negative 0.99 so
+ 
+
+ align:start position:0%
+correlation we get negative 0.99 so
+these two variables are indeed highly
+
+ align:start position:0%
+these two variables are indeed highly
+ 
+
+ align:start position:0%
+these two variables are indeed highly
+correlated let's compute some
+
+ align:start position:0%
+correlated let's compute some
+ 
+
+ align:start position:0%
+correlated let's compute some
+correlations in R we can compute the
+
+ align:start position:0%
+correlations in R we can compute the
+ 
+
+ align:start position:0%
+correlations in R we can compute the
+correlation between a pair of air
+
+ align:start position:0%
+correlation between a pair of air
+ 
+
+ align:start position:0%
+correlation between a pair of air
+balls and our by using the COR function
+
+ align:start position:0%
+balls and our by using the COR function
+ 
+
+ align:start position:0%
+balls and our by using the COR function
+let's compute the correlation between
+
+ align:start position:0%
+let's compute the correlation between
+ 
+
+ align:start position:0%
+let's compute the correlation between
+winter rain and price so we type cor and
+
+ align:start position:0%
+winter rain and price so we type cor and
+ 
+
+ align:start position:0%
+winter rain and price so we type cor and
+then in parentheses we give the names of
+
+ align:start position:0%
+then in parentheses we give the names of
+ 
+
+ align:start position:0%
+then in parentheses we give the names of
+the two variables winter rain and price
+
+ align:start position:0%
+the two variables winter rain and price
+ 
+
+ align:start position:0%
+the two variables winter rain and price
+if we hit enter this function tells us
+
+ align:start position:0%
+if we hit enter this function tells us
+ 
+
+ align:start position:0%
+if we hit enter this function tells us
+that the correlation between the two
+
+ align:start position:0%
+that the correlation between the two
+ 
+
+ align:start position:0%
+that the correlation between the two
+variables is 0.137
+
+ align:start position:0%
+variables is 0.137
+ 
+
+ align:start position:0%
+variables is 0.137
+let's look at another example this time
+
+ align:start position:0%
+let's look at another example this time
+ 
+
+ align:start position:0%
+let's look at another example this time
+we'll compute the correlation between
+
+ align:start position:0%
+we'll compute the correlation between
+ 
+
+ align:start position:0%
+we'll compute the correlation between
+age and France population so again we
+
+ align:start position:0%
+age and France population so again we
+ 
+
+ align:start position:0%
+age and France population so again we
+use the COR function but this time we
+
+ align:start position:0%
+use the COR function but this time we
+ 
+
+ align:start position:0%
+use the COR function but this time we
+give us the two variables age and France
+
+ align:start position:0%
+give us the two variables age and France
+ 
+
+ align:start position:0%
+give us the two variables age and France
+population as we saw earlier age and
+
+ align:start position:0%
+population as we saw earlier age and
+ 
+
+ align:start position:0%
+population as we saw earlier age and
+France population are highly correlated
+
+ align:start position:0%
+France population are highly correlated
+ 
+
+ align:start position:0%
+France population are highly correlated
+with the correlation of negative 0.99 we
+
+ align:start position:0%
+with the correlation of negative 0.99 we
+ 
+
+ align:start position:0%
+with the correlation of negative 0.99 we
+can also compute the correlation between
+
+ align:start position:0%
+can also compute the correlation between
+ 
+
+ align:start position:0%
+can also compute the correlation between
+all pairs of variables in our dataset
+
+ align:start position:0%
+all pairs of variables in our dataset
+ 
+
+ align:start position:0%
+all pairs of variables in our dataset
+using the core function to do so we just
+
+ align:start position:0%
+using the core function to do so we just
+ 
+
+ align:start position:0%
+using the core function to do so we just
+type cor and then our dataset name wine
+
+ align:start position:0%
+type cor and then our dataset name wine
+ 
+
+ align:start position:0%
+type cor and then our dataset name wine
+the output is a grid of numbers with the
+
+ align:start position:0%
+the output is a grid of numbers with the
+ 
+
+ align:start position:0%
+the output is a grid of numbers with the
+rows and columns labeled with the
+
+ align:start position:0%
+rows and columns labeled with the
+ 
+
+ align:start position:0%
+rows and columns labeled with the
+variables in our data set to find the
+
+ align:start position:0%
+variables in our data set to find the
+ 
+
+ align:start position:0%
+variables in our data set to find the
+correlation between two variables you
+
+ align:start position:0%
+correlation between two variables you
+ 
+
+ align:start position:0%
+correlation between two variables you
+just need to find the row for one of
+
+ align:start position:0%
+just need to find the row for one of
+ 
+
+ align:start position:0%
+just need to find the row for one of
+them and the column for the other for
+
+ align:start position:0%
+them and the column for the other for
+ 
+
+ align:start position:0%
+them and the column for the other for
+example we can find the column for age
+
+ align:start position:0%
+example we can find the column for age
+ 
+
+ align:start position:0%
+example we can find the column for age
+and then go down to the row for France
+
+ align:start position:0%
+and then go down to the row for France
+ 
+
+ align:start position:0%
+and then go down to the row for France
+population to see the number that we
+
+ align:start position:0%
+population to see the number that we
+ 
+
+ align:start position:0%
+population to see the number that we
+just computed or we could check if
+
+ align:start position:0%
+just computed or we could check if
+ 
+
+ align:start position:0%
+just computed or we could check if
+winter rain is highly correlated with
+
+ align:start position:0%
+winter rain is highly correlated with
+ 
+
+ align:start position:0%
+winter rain is highly correlated with
+any other independent variables by
+
+ align:start position:0%
+any other independent variables by
+ 
+
+ align:start position:0%
+any other independent variables by
+looking at the winter rain column so how
+
+ align:start position:0%
+looking at the winter rain column so how
+ 
+
+ align:start position:0%
+looking at the winter rain column so how
+does this information help us understand
+
+ align:start position:0%
+does this information help us understand
+ 
+
+ align:start position:0%
+does this information help us understand
+our linear regression model we've
+
+ align:start position:0%
+our linear regression model we've
+ 
+
+ align:start position:0%
+our linear regression model we've
+confirmed that age and France population
+
+ align:start position:0%
+confirmed that age and France population
+ 
+
+ align:start position:0%
+confirmed that age and France population
+are definitely highly correlated so we
+
+ align:start position:0%
+are definitely highly correlated so we
+ 
+
+ align:start position:0%
+are definitely highly correlated so we
+do have multicollinearity problems that
+
+ align:start position:0%
+do have multicollinearity problems that
+ 
+
+ align:start position:0%
+do have multicollinearity problems that
+our model that uses all of the available
+
+ align:start position:0%
+our model that uses all of the available
+ 
+
+ align:start position:0%
+our model that uses all of the available
+independent variables keep in mind that
+
+ align:start position:0%
+independent variables keep in mind that
+ 
+
+ align:start position:0%
+independent variables keep in mind that
+multicollinearity refers to the
+
+ align:start position:0%
+multicollinearity refers to the
+ 
+
+ align:start position:0%
+multicollinearity refers to the
+situation when two independent variables
+
+ align:start position:0%
+situation when two independent variables
+ 
+
+ align:start position:0%
+situation when two independent variables
+are highly correlated a high correlation
+
+ align:start position:0%
+are highly correlated a high correlation
+ 
+
+ align:start position:0%
+are highly correlated a high correlation
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+independent variable and the dependent
+
+ align:start position:0%
+independent variable and the dependent
+ 
+
+ align:start position:0%
+independent variable and the dependent
+variable is a good thing since we're
+
+ align:start position:0%
+variable is a good thing since we're
+ 
+
+ align:start position:0%
+variable is a good thing since we're
+trying to predict the dependent variable
+
+ align:start position:0%
+trying to predict the dependent variable
+ 
+
+ align:start position:0%
+trying to predict the dependent variable
+using the independent variables now due
+
+ align:start position:0%
+using the independent variables now due
+ 
+
+ align:start position:0%
+using the independent variables now due
+to the possibility of multicollinearity
+
+ align:start position:0%
+to the possibility of multicollinearity
+ 
+
+ align:start position:0%
+to the possibility of multicollinearity
+you always want to remove the
+
+ align:start position:0%
+you always want to remove the
+ 
+
+ align:start position:0%
+you always want to remove the
+insignificant variables one at a time
+
+ align:start position:0%
+insignificant variables one at a time
+ 
+
+ align:start position:0%
+insignificant variables one at a time
+let's see what would have happened if we
+
+ align:start position:0%
+let's see what would have happened if we
+ 
+
+ align:start position:0%
+let's see what would have happened if we
+had removed both the age and France
+
+ align:start position:0%
+had removed both the age and France
+ 
+
+ align:start position:0%
+had removed both the age and France
+population since they were both
+
+ align:start position:0%
+population since they were both
+ 
+
+ align:start position:0%
+population since they were both
+insignificant in our model that used all
+
+ align:start position:0%
+insignificant in our model that used all
+ 
+
+ align:start position:0%
+insignificant in our model that used all
+of the independent variables we'll call
+
+ align:start position:0%
+of the independent variables we'll call
+ 
+
+ align:start position:0%
+of the independent variables we'll call
+this new model model five and again
+
+ align:start position:0%
+this new model model five and again
+ 
+
+ align:start position:0%
+this new model model five and again
+we'll use the LM function to predict
+
+ align:start position:0%
+we'll use the LM function to predict
+ 
+
+ align:start position:0%
+we'll use the LM function to predict
+price using as independent variables
+
+ align:start position:0%
+price using as independent variables
+ 
+
+ align:start position:0%
+price using as independent variables
+average growing season temperature
+
+ align:start position:0%
+average growing season temperature
+ 
+
+ align:start position:0%
+average growing season temperature
+harvest rain and winter rain again we'll
+
+ align:start position:0%
+harvest rain and winter rain again we'll
+ 
+
+ align:start position:0%
+harvest rain and winter rain again we'll
+use the data set wine if we take a look
+
+ align:start position:0%
+use the data set wine if we take a look
+ 
+
+ align:start position:0%
+use the data set wine if we take a look
+at the summary of this new model and
+
+ align:start position:0%
+at the summary of this new model and
+ 
+
+ align:start position:0%
+at the summary of this new model and
+look at the coefficients table we can
+
+ align:start position:0%
+look at the coefficients table we can
+ 
+
+ align:start position:0%
+look at the coefficients table we can
+see that average growing season
+
+ align:start position:0%
+see that average growing season
+ 
+
+ align:start position:0%
+see that average growing season
+temperature and harvest rain are very
+
+ align:start position:0%
+temperature and harvest rain are very
+ 
+
+ align:start position:0%
+temperature and harvest rain are very
+significant and winter rain is almost
+
+ align:start position:0%
+significant and winter rain is almost
+ 
+
+ align:start position:0%
+significant and winter rain is almost
+significant so this model looks pretty
+
+ align:start position:0%
+significant so this model looks pretty
+ 
+
+ align:start position:0%
+significant so this model looks pretty
+good but if we look at our r-squared we
+
+ align:start position:0%
+good but if we look at our r-squared we
+ 
+
+ align:start position:0%
+good but if we look at our r-squared we
+can see that it dropped 2.75 the model
+
+ align:start position:0%
+can see that it dropped 2.75 the model
+ 
+
+ align:start position:0%
+can see that it dropped 2.75 the model
+that includes age has an r-squared of
+
+ align:start position:0%
+that includes age has an r-squared of
+ 
+
+ align:start position:0%
+that includes age has an r-squared of
+0.8 III so if we had removed age in
+
+ align:start position:0%
+0.8 III so if we had removed age in
+ 
+
+ align:start position:0%
+0.8 III so if we had removed age in
+France population at the same time we
+
+ align:start position:0%
+France population at the same time we
+ 
+
+ align:start position:0%
+France population at the same time we
+would have missed a significant variable
+
+ align:start position:0%
+would have missed a significant variable
+ 
+
+ align:start position:0%
+would have missed a significant variable
+and the r-squared of our final model
+
+ align:start position:0%
+and the r-squared of our final model
+ 
+
+ align:start position:0%
+and the r-squared of our final model
+would have been lower so why didn't we
+
+ align:start position:0%
+would have been lower so why didn't we
+ 
+
+ align:start position:0%
+would have been lower so why didn't we
+keep France population instead of age
+
+ align:start position:0%
+keep France population instead of age
+ 
+
+ align:start position:0%
+keep France population instead of age
+well we expect age to be significant
+
+ align:start position:0%
+well we expect age to be significant
+ 
+
+ align:start position:0%
+well we expect age to be significant
+older wines are typically more expensive
+
+ align:start position:0%
+older wines are typically more expensive
+ 
+
+ align:start position:0%
+older wines are typically more expensive
+so age makes more intuitive sense in our
+
+ align:start position:0%
+so age makes more intuitive sense in our
+ 
+
+ align:start position:0%
+so age makes more intuitive sense in our
+model multicollinearity reminds us that
+
+ align:start position:0%
+model multicollinearity reminds us that
+ 
+
+ align:start position:0%
+model multicollinearity reminds us that
+coefficients are only interpretable in
+
+ align:start position:0%
+coefficients are only interpretable in
+ 
+
+ align:start position:0%
+coefficients are only interpretable in
+the presence of other variables being
+
+ align:start position:0%
+the presence of other variables being
+ 
+
+ align:start position:0%
+the presence of other variables being
+used high correlations can even cause
+
+ align:start position:0%
+used high correlations can even cause
+ 
+
+ align:start position:0%
+used high correlations can even cause
+coefficients to have an unintuitive sign
+
+ align:start position:0%
+coefficients to have an unintuitive sign
+ 
+
+ align:start position:0%
+coefficients to have an unintuitive sign
+we'll see an example of this in the next
+
+ align:start position:0%
+we'll see an example of this in the next
+ 
+
+ align:start position:0%
+we'll see an example of this in the next
+lecture so we fix the multicollinearity
+
+ align:start position:0%
+lecture so we fix the multicollinearity
+ 
+
+ align:start position:0%
+lecture so we fix the multicollinearity
+issue caused by
+
+ align:start position:0%
+issue caused by
+ 
+
+ align:start position:0%
+issue caused by
+age and France population do we have any
+
+ align:start position:0%
+age and France population do we have any
+ 
+
+ align:start position:0%
+age and France population do we have any
+other highly correlated independent
+
+ align:start position:0%
+other highly correlated independent
+ 
+
+ align:start position:0%
+other highly correlated independent
+variables there is no definitive cutoff
+
+ align:start position:0%
+variables there is no definitive cutoff
+ 
+
+ align:start position:0%
+variables there is no definitive cutoff
+value for what makes a correlation too
+
+ align:start position:0%
+value for what makes a correlation too
+ 
+
+ align:start position:0%
+value for what makes a correlation too
+high but typically a correlation greater
+
+ align:start position:0%
+high but typically a correlation greater
+ 
+
+ align:start position:0%
+high but typically a correlation greater
+than 0.7 or less than negative 0.7 is
+
+ align:start position:0%
+than 0.7 or less than negative 0.7 is
+ 
+
+ align:start position:0%
+than 0.7 or less than negative 0.7 is
+cause for concern if you look back at
+
+ align:start position:0%
+cause for concern if you look back at
+ 
+
+ align:start position:0%
+cause for concern if you look back at
+all of the correlations we computed for
+
+ align:start position:0%
+all of the correlations we computed for
+ 
+
+ align:start position:0%
+all of the correlations we computed for
+our dataset you can see that it doesn't
+
+ align:start position:0%
+our dataset you can see that it doesn't
+ 
+
+ align:start position:0%
+our dataset you can see that it doesn't
+look like we have any other highly
+
+ align:start position:0%
+look like we have any other highly
+ 
+
+ align:start position:0%
+look like we have any other highly
+correlated independent variables so
+
+ align:start position:0%
+correlated independent variables so
+ 
+
+ align:start position:0%
+correlated independent variables so
+we'll stick with model for for the rest
+
+ align:start position:0%
+we'll stick with model for for the rest
+ 
+
+ align:start position:0%
+we'll stick with model for for the rest
+of this lecture the model that uses
+
+ align:start position:0%
+of this lecture the model that uses
+ 
+
+ align:start position:0%
+of this lecture the model that uses
+average growing season temperature
+
+ align:start position:0%
+average growing season temperature
+ 
+
+ align:start position:0%
+average growing season temperature
+harvest rain winter rain and age as the
+
+ align:start position:0%
+harvest rain winter rain and age as the
+ 
+
+ align:start position:0%
+harvest rain winter rain and age as the
+independent variables
\ No newline at end of file
diff --git a/gLnCmUkgUQk.txt b/gLnCmUkgUQk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..efb66e4733fbf4b054748b6ed78ba24677844254
--- /dev/null
+++ b/gLnCmUkgUQk.txt
@@ -0,0 +1,14050 @@
+align:start position:0%
+ 
+all right let's begin today's lecture so
+
+ align:start position:0%
+all right let's begin today's lecture so
+ 
+
+ align:start position:0%
+all right let's begin today's lecture so
+last class we began our adventure with
+
+ align:start position:0%
+last class we began our adventure with
+ 
+
+ align:start position:0%
+last class we began our adventure with
+creating our own data types today we're
+
+ align:start position:0%
+creating our own data types today we're
+ 
+
+ align:start position:0%
+creating our own data types today we're
+going to start off with a little bit of
+
+ align:start position:0%
+going to start off with a little bit of
+ 
+
+ align:start position:0%
+going to start off with a little bit of
+a recap just to remind you um some of
+
+ align:start position:0%
+a recap just to remind you um some of
+ 
+
+ align:start position:0%
+a recap just to remind you um some of
+the details about creating our own data
+
+ align:start position:0%
+the details about creating our own data
+ 
+
+ align:start position:0%
+the details about creating our own data
+types and then going to build upon that
+
+ align:start position:0%
+types and then going to build upon that
+ 
+
+ align:start position:0%
+types and then going to build upon that
+uh coordinate class we started in last
+
+ align:start position:0%
+uh coordinate class we started in last
+ 
+
+ align:start position:0%
+uh coordinate class we started in last
+class we'll build uh we'll build a
+
+ align:start position:0%
+class we'll build uh we'll build a
+ 
+
+ align:start position:0%
+class we'll build uh we'll build a
+circle class and then we'll build some
+
+ align:start position:0%
+circle class and then we'll build some
+ 
+
+ align:start position:0%
+circle class and then we'll build some
+fraction data types all right so the
+
+ align:start position:0%
+fraction data types all right so the
+ 
+
+ align:start position:0%
+fraction data types all right so the
+first thing I'd like to mention is to uh
+
+ align:start position:0%
+first thing I'd like to mention is to uh
+ 
+
+ align:start position:0%
+first thing I'd like to mention is to uh
+remind you guys about sort of um writing
+
+ align:start position:0%
+remind you guys about sort of um writing
+ 
+
+ align:start position:0%
+remind you guys about sort of um writing
+code from these two different
+
+ align:start position:0%
+code from these two different
+ 
+
+ align:start position:0%
+code from these two different
+perspectives right so just like when we
+
+ align:start position:0%
+perspectives right so just like when we
+ 
+
+ align:start position:0%
+perspectives right so just like when we
+wrote uh uh functions we were kind of
+
+ align:start position:0%
+wrote uh uh functions we were kind of
+ 
+
+ align:start position:0%
+wrote uh uh functions we were kind of
+writing the definition of the function
+
+ align:start position:0%
+writing the definition of the function
+ 
+
+ align:start position:0%
+writing the definition of the function
+telling python we have this function
+
+ align:start position:0%
+telling python we have this function
+ 
+
+ align:start position:0%
+telling python we have this function
+that we're defining abstractly and this
+
+ align:start position:0%
+that we're defining abstractly and this
+ 
+
+ align:start position:0%
+that we're defining abstractly and this
+is what it does and then we were calling
+
+ align:start position:0%
+is what it does and then we were calling
+ 
+
+ align:start position:0%
+is what it does and then we were calling
+the function later on in the program
+
+ align:start position:0%
+the function later on in the program
+ 
+
+ align:start position:0%
+the function later on in the program
+many many times well the same thing
+
+ align:start position:0%
+many many times well the same thing
+ 
+
+ align:start position:0%
+many many times well the same thing
+exists uh the same idea exists now that
+
+ align:start position:0%
+exists uh the same idea exists now that
+ 
+
+ align:start position:0%
+exists uh the same idea exists now that
+we're creating creating our own data
+
+ align:start position:0%
+we're creating creating our own data
+ 
+
+ align:start position:0%
+we're creating creating our own data
+types we have to write code from the
+
+ align:start position:0%
+types we have to write code from the
+ 
+
+ align:start position:0%
+types we have to write code from the
+point of view of somebody who's
+
+ align:start position:0%
+point of view of somebody who's
+ 
+
+ align:start position:0%
+point of view of somebody who's
+implementing the class so deciding all
+
+ align:start position:0%
+implementing the class so deciding all
+ 
+
+ align:start position:0%
+implementing the class so deciding all
+of these details that goes into creating
+
+ align:start position:0%
+of these details that goes into creating
+ 
+
+ align:start position:0%
+of these details that goes into creating
+the class itself versus somebody who's
+
+ align:start position:0%
+the class itself versus somebody who's
+ 
+
+ align:start position:0%
+the class itself versus somebody who's
+just using a class that's already been
+
+ align:start position:0%
+just using a class that's already been
+ 
+
+ align:start position:0%
+just using a class that's already been
+written where we create instances a
+
+ align:start position:0%
+written where we create instances a
+ 
+
+ align:start position:0%
+written where we create instances a
+bunch of different objects that just
+
+ align:start position:0%
+bunch of different objects that just
+ 
+
+ align:start position:0%
+bunch of different objects that just
+happen to be this data type
+
+ align:start position:0%
+happen to be this data type
+ 
+
+ align:start position:0%
+happen to be this data type
+so when we implement the class um what
+
+ align:start position:0%
+so when we implement the class um what
+ 
+
+ align:start position:0%
+so when we implement the class um what
+were some of the things we did well um
+
+ align:start position:0%
+were some of the things we did well um
+ 
+
+ align:start position:0%
+were some of the things we did well um
+we're telling python that this object
+
+ align:start position:0%
+we're telling python that this object
+ 
+
+ align:start position:0%
+we're telling python that this object
+now exists we're telling python the name
+
+ align:start position:0%
+now exists we're telling python the name
+ 
+
+ align:start position:0%
+now exists we're telling python the name
+of the data type that we're creating
+
+ align:start position:0%
+of the data type that we're creating
+ 
+
+ align:start position:0%
+of the data type that we're creating
+something we choose we're deciding um
+
+ align:start position:0%
+something we choose we're deciding um
+ 
+
+ align:start position:0%
+something we choose we're deciding um
+we're making these design decisions
+
+ align:start position:0%
+we're making these design decisions
+ 
+
+ align:start position:0%
+we're making these design decisions
+where we decide what attributes make up
+
+ align:start position:0%
+where we decide what attributes make up
+ 
+
+ align:start position:0%
+where we decide what attributes make up
+our class so the attributes are either
+
+ align:start position:0%
+our class so the attributes are either
+ 
+
+ align:start position:0%
+our class so the attributes are either
+data like the properties what are the
+
+ align:start position:0%
+data like the properties what are the
+ 
+
+ align:start position:0%
+data like the properties what are the
+variables that make up your object and
+
+ align:start position:0%
+variables that make up your object and
+ 
+
+ align:start position:0%
+variables that make up your object and
+the behaviors through methods right um
+
+ align:start position:0%
+the behaviors through methods right um
+ 
+
+ align:start position:0%
+the behaviors through methods right um
+so that's implementing the class and
+
+ align:start position:0%
+so that's implementing the class and
+ 
+
+ align:start position:0%
+so that's implementing the class and
+then when we're using the class we're
+
+ align:start position:0%
+then when we're using the class we're
+ 
+
+ align:start position:0%
+then when we're using the class we're
+now saying all right let's assume that
+
+ align:start position:0%
+now saying all right let's assume that
+ 
+
+ align:start position:0%
+now saying all right let's assume that
+this class definition exists there's
+
+ align:start position:0%
+this class definition exists there's
+ 
+
+ align:start position:0%
+this class definition exists there's
+this object that has these behaviors and
+
+ align:start position:0%
+this object that has these behaviors and
+ 
+
+ align:start position:0%
+this object that has these behaviors and
+these data attributes let's now create a
+
+ align:start position:0%
+these data attributes let's now create a
+ 
+
+ align:start position:0%
+these data attributes let's now create a
+whole bunch of objects that are of this
+
+ align:start position:0%
+whole bunch of objects that are of this
+ 
+
+ align:start position:0%
+whole bunch of objects that are of this
+type and this is when we're creating
+
+ align:start position:0%
+type and this is when we're creating
+ 
+
+ align:start position:0%
+type and this is when we're creating
+these instances and then manipulating
+
+ align:start position:0%
+these instances and then manipulating
+ 
+
+ align:start position:0%
+these instances and then manipulating
+all of these instances by running
+
+ align:start position:0%
+all of these instances by running
+ 
+
+ align:start position:0%
+all of these instances by running
+methods on them things like that so when
+
+ align:start position:0%
+methods on them things like that so when
+ 
+
+ align:start position:0%
+methods on them things like that so when
+we're implementing the class right this
+
+ align:start position:0%
+we're implementing the class right this
+ 
+
+ align:start position:0%
+we're implementing the class right this
+thing on the left hand side we're
+
+ align:start position:0%
+thing on the left hand side we're
+ 
+
+ align:start position:0%
+thing on the left hand side we're
+basically um uh telling python in
+
+ align:start position:0%
+basically um uh telling python in
+ 
+
+ align:start position:0%
+basically um uh telling python in
+abstract terms Ms what are the common
+
+ align:start position:0%
+abstract terms Ms what are the common
+ 
+
+ align:start position:0%
+abstract terms Ms what are the common
+properties and behaviors of our data
+
+ align:start position:0%
+properties and behaviors of our data
+ 
+
+ align:start position:0%
+properties and behaviors of our data
+type and then when we're using the class
+
+ align:start position:0%
+type and then when we're using the class
+ 
+
+ align:start position:0%
+type and then when we're using the class
+the thing on the right hand side here
+
+ align:start position:0%
+the thing on the right hand side here
+ 
+
+ align:start position:0%
+the thing on the right hand side here
+we're creating actual objects with very
+
+ align:start position:0%
+we're creating actual objects with very
+ 
+
+ align:start position:0%
+we're creating actual objects with very
+specific values for their data
+
+ align:start position:0%
+specific values for their data
+ 
+
+ align:start position:0%
+specific values for their data
+attributes that we can manipulate in
+
+ align:start position:0%
+attributes that we can manipulate in
+ 
+
+ align:start position:0%
+attributes that we can manipulate in
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+ways so let's remember this coordinate
+
+ align:start position:0%
+ways so let's remember this coordinate
+ 
+
+ align:start position:0%
+ways so let's remember this coordinate
+class that we wrote last lecture okay um
+
+ align:start position:0%
+class that we wrote last lecture okay um
+ 
+
+ align:start position:0%
+class that we wrote last lecture okay um
+this is not new so but I will just go
+
+ align:start position:0%
+this is not new so but I will just go
+ 
+
+ align:start position:0%
+this is not new so but I will just go
+over it real quick so first line here
+
+ align:start position:0%
+over it real quick so first line here
+ 
+
+ align:start position:0%
+over it real quick so first line here
+tells python we're creating a new data
+
+ align:start position:0%
+tells python we're creating a new data
+ 
+
+ align:start position:0%
+tells python we're creating a new data
+type its name is coordinate and this
+
+ align:start position:0%
+type its name is coordinate and this
+ 
+
+ align:start position:0%
+type its name is coordinate and this
+keyword class tells python we're
+
+ align:start position:0%
+keyword class tells python we're
+ 
+
+ align:start position:0%
+keyword class tells python we're
+creating the data type the parenthesis
+
+ align:start position:0%
+creating the data type the parenthesis
+ 
+
+ align:start position:0%
+creating the data type the parenthesis
+here is object which stands for the
+
+ align:start position:0%
+here is object which stands for the
+ 
+
+ align:start position:0%
+here is object which stands for the
+python object data type so it's
+
+ align:start position:0%
+python object data type so it's
+ 
+
+ align:start position:0%
+python object data type so it's
+something really generic um and this in
+
+ align:start position:0%
+something really generic um and this in
+ 
+
+ align:start position:0%
+something really generic um and this in
+the parenthesis here is the parent of
+
+ align:start position:0%
+the parenthesis here is the parent of
+ 
+
+ align:start position:0%
+the parenthesis here is the parent of
+our class right so anything that a
+
+ align:start position:0%
+our class right so anything that a
+ 
+
+ align:start position:0%
+our class right so anything that a
+regular python object can do the very
+
+ align:start position:0%
+regular python object can do the very
+ 
+
+ align:start position:0%
+regular python object can do the very
+basic things our class can do as well
+
+ align:start position:0%
+basic things our class can do as well
+ 
+
+ align:start position:0%
+basic things our class can do as well
+last lecture I mentioned an um an
+
+ align:start position:0%
+last lecture I mentioned an um an
+ 
+
+ align:start position:0%
+last lecture I mentioned an um an
+example of such a basic thing is to take
+
+ align:start position:0%
+example of such a basic thing is to take
+ 
+
+ align:start position:0%
+example of such a basic thing is to take
+a variable name and assign it to an
+
+ align:start position:0%
+a variable name and assign it to an
+ 
+
+ align:start position:0%
+a variable name and assign it to an
+object typee that we
+
+ align:start position:0%
+object typee that we
+ 
+
+ align:start position:0%
+object typee that we
+create the very first method that we
+
+ align:start position:0%
+create the very first method that we
+ 
+
+ align:start position:0%
+create the very first method that we
+should write for a new data type that we
+
+ align:start position:0%
+should write for a new data type that we
+ 
+
+ align:start position:0%
+should write for a new data type that we
+create is the init method and this I uh
+
+ align:start position:0%
+create is the init method and this I uh
+ 
+
+ align:start position:0%
+create is the init method and this I uh
+called a Dunder method because it starts
+
+ align:start position:0%
+called a Dunder method because it starts
+ 
+
+ align:start position:0%
+called a Dunder method because it starts
+with double underscores before the init
+
+ align:start position:0%
+with double underscores before the init
+ 
+
+ align:start position:0%
+with double underscores before the init
+and double UND and ends with double
+
+ align:start position:0%
+and double UND and ends with double
+ 
+
+ align:start position:0%
+and double UND and ends with double
+underscores after the init and that's
+
+ align:start position:0%
+underscores after the init and that's
+ 
+
+ align:start position:0%
+underscores after the init and that's
+the actual name of this method double
+
+ align:start position:0%
+the actual name of this method double
+ 
+
+ align:start position:0%
+the actual name of this method double
+underscore init double underscore okay
+
+ align:start position:0%
+underscore init double underscore okay
+ 
+
+ align:start position:0%
+underscore init double underscore okay
+um so this method is like a Constructor
+
+ align:start position:0%
+um so this method is like a Constructor
+ 
+
+ align:start position:0%
+um so this method is like a Constructor
+for the class it tells python how do you
+
+ align:start position:0%
+for the class it tells python how do you
+ 
+
+ align:start position:0%
+for the class it tells python how do you
+create an actual object of this type so
+
+ align:start position:0%
+create an actual object of this type so
+ 
+
+ align:start position:0%
+create an actual object of this type so
+it's it's a function uh it's just a
+
+ align:start position:0%
+it's it's a function uh it's just a
+ 
+
+ align:start position:0%
+it's it's a function uh it's just a
+function that works only with objects of
+
+ align:start position:0%
+function that works only with objects of
+ 
+
+ align:start position:0%
+function that works only with objects of
+type coordinate so as a function it
+
+ align:start position:0%
+type coordinate so as a function it
+ 
+
+ align:start position:0%
+type coordinate so as a function it
+takes
+
+ align:start position:0%
+takes
+ 
+
+ align:start position:0%
+takes
+parameters um you can see it takes three
+
+ align:start position:0%
+parameters um you can see it takes three
+ 
+
+ align:start position:0%
+parameters um you can see it takes three
+parameters here the self the X and the Y
+
+ align:start position:0%
+parameters here the self the X and the Y
+ 
+
+ align:start position:0%
+parameters here the self the X and the Y
+now when we're actually creating objects
+
+ align:start position:0%
+now when we're actually creating objects
+ 
+
+ align:start position:0%
+now when we're actually creating objects
+of type coordinate we only pass in
+
+ align:start position:0%
+of type coordinate we only pass in
+ 
+
+ align:start position:0%
+of type coordinate we only pass in
+parameters for everything other than
+
+ align:start position:0%
+parameters for everything other than
+ 
+
+ align:start position:0%
+parameters for everything other than
+self because self is a variable name
+
+ align:start position:0%
+self because self is a variable name
+ 
+
+ align:start position:0%
+self because self is a variable name
+that we use to describe cribe having an
+
+ align:start position:0%
+that we use to describe cribe having an
+ 
+
+ align:start position:0%
+that we use to describe cribe having an
+instance of the class without actually
+
+ align:start position:0%
+instance of the class without actually
+ 
+
+ align:start position:0%
+instance of the class without actually
+creating one yet right because remember
+
+ align:start position:0%
+creating one yet right because remember
+ 
+
+ align:start position:0%
+creating one yet right because remember
+what we're doing here in this definition
+
+ align:start position:0%
+what we're doing here in this definition
+ 
+
+ align:start position:0%
+what we're doing here in this definition
+we're telling python that this object
+
+ align:start position:0%
+we're telling python that this object
+ 
+
+ align:start position:0%
+we're telling python that this object
+type now exists we're writing it as we
+
+ align:start position:0%
+type now exists we're writing it as we
+ 
+
+ align:start position:0%
+type now exists we're writing it as we
+speak but we don't have an actual
+
+ align:start position:0%
+speak but we don't have an actual
+ 
+
+ align:start position:0%
+speak but we don't have an actual
+instance to manipulate yet right this is
+
+ align:start position:0%
+instance to manipulate yet right this is
+ 
+
+ align:start position:0%
+instance to manipulate yet right this is
+just the definition and so the self
+
+ align:start position:0%
+just the definition and so the self
+ 
+
+ align:start position:0%
+just the definition and so the self
+tells python that when we're writing
+
+ align:start position:0%
+tells python that when we're writing
+ 
+
+ align:start position:0%
+tells python that when we're writing
+this code we're going to use the self
+
+ align:start position:0%
+this code we're going to use the self
+ 
+
+ align:start position:0%
+this code we're going to use the self
+variable name as sort of a formal name
+
+ align:start position:0%
+variable name as sort of a formal name
+ 
+
+ align:start position:0%
+variable name as sort of a formal name
+to be able to run this method on okay so
+
+ align:start position:0%
+to be able to run this method on okay so
+ 
+
+ align:start position:0%
+to be able to run this method on okay so
+we're going to see in the next slide
+
+ align:start position:0%
+we're going to see in the next slide
+ 
+
+ align:start position:0%
+we're going to see in the next slide
+exactly how what what maps to self when
+
+ align:start position:0%
+exactly how what what maps to self when
+ 
+
+ align:start position:0%
+exactly how what what maps to self when
+we run it but that's what the self means
+
+ align:start position:0%
+we run it but that's what the self means
+ 
+
+ align:start position:0%
+we run it but that's what the self means
+inside the parameter list here and here
+
+ align:start position:0%
+inside the parameter list here and here
+ 
+
+ align:start position:0%
+inside the parameter list here and here
+and then beyond that we use uh self
+
+ align:start position:0%
+and then beyond that we use uh self
+ 
+
+ align:start position:0%
+and then beyond that we use uh self
+within the inip method to tell python
+
+ align:start position:0%
+within the inip method to tell python
+ 
+
+ align:start position:0%
+within the inip method to tell python
+which one of these variables are
+
+ align:start position:0%
+which one of these variables are
+ 
+
+ align:start position:0%
+which one of these variables are
+actually data attributes versus which of
+
+ align:start position:0%
+actually data attributes versus which of
+ 
+
+ align:start position:0%
+actually data attributes versus which of
+these variables are just plain old
+
+ align:start position:0%
+these variables are just plain old
+ 
+
+ align:start position:0%
+these variables are just plain old
+variables as we've been working with so
+
+ align:start position:0%
+variables as we've been working with so
+ 
+
+ align:start position:0%
+variables as we've been working with so
+any variable that's defined using self
+
+ align:start position:0%
+any variable that's defined using self
+ 
+
+ align:start position:0%
+any variable that's defined using self
+dot so here I got self.x and self.y are
+
+ align:start position:0%
+dot so here I got self.x and self.y are
+ 
+
+ align:start position:0%
+dot so here I got self.x and self.y are
+data attributes so that means any object
+
+ align:start position:0%
+data attributes so that means any object
+ 
+
+ align:start position:0%
+data attributes so that means any object
+I create that's of type coordinate I
+
+ align:start position:0%
+I create that's of type coordinate I
+ 
+
+ align:start position:0%
+I create that's of type coordinate I
+know will have a variable X and Y
+
+ align:start position:0%
+know will have a variable X and Y
+ 
+
+ align:start position:0%
+know will have a variable X and Y
+associated with it right because I've
+
+ align:start position:0%
+associated with it right because I've
+ 
+
+ align:start position:0%
+associated with it right because I've
+defined these X and y's using self.x and
+
+ align:start position:0%
+defined these X and y's using self.x and
+ 
+
+ align:start position:0%
+defined these X and y's using self.x and
+self.y now in the last lecture I
+
+ align:start position:0%
+self.y now in the last lecture I
+ 
+
+ align:start position:0%
+self.y now in the last lecture I
+actually had these parameter lists list
+
+ align:start position:0%
+actually had these parameter lists list
+ 
+
+ align:start position:0%
+actually had these parameter lists list
+the parameters in this list here be
+
+ align:start position:0%
+the parameters in this list here be
+ 
+
+ align:start position:0%
+the parameters in this list here be
+different than X and Y I think I had X
+
+ align:start position:0%
+different than X and Y I think I had X
+ 
+
+ align:start position:0%
+different than X and Y I think I had X
+Val y Val um and then I had self.x
+
+ align:start position:0%
+Val y Val um and then I had self.x
+ 
+
+ align:start position:0%
+Val y Val um and then I had self.x
+equals x valal where this x here to the
+
+ align:start position:0%
+equals x valal where this x here to the
+ 
+
+ align:start position:0%
+equals x valal where this x here to the
+right of the equal sign is the X from
+
+ align:start position:0%
+right of the equal sign is the X from
+ 
+
+ align:start position:0%
+right of the equal sign is the X from
+the parameter list right but you know so
+
+ align:start position:0%
+the parameter list right but you know so
+ 
+
+ align:start position:0%
+the parameter list right but you know so
+in that sense it doesn't matter what
+
+ align:start position:0%
+in that sense it doesn't matter what
+ 
+
+ align:start position:0%
+in that sense it doesn't matter what
+these variables are in the parameter
+
+ align:start position:0%
+these variables are in the parameter
+ 
+
+ align:start position:0%
+these variables are in the parameter
+list they're just going to be the same
+
+ align:start position:0%
+list they're just going to be the same
+ 
+
+ align:start position:0%
+list they're just going to be the same
+over here on the right hand side of the
+
+ align:start position:0%
+over here on the right hand side of the
+ 
+
+ align:start position:0%
+over here on the right hand side of the
+equal sign okay but the actual
+
+ align:start position:0%
+equal sign okay but the actual
+ 
+
+ align:start position:0%
+equal sign okay but the actual
+parameters the sorry the actual data
+
+ align:start position:0%
+parameters the sorry the actual data
+ 
+
+ align:start position:0%
+parameters the sorry the actual data
+attributes are self.x and self.y of my
+
+ align:start position:0%
+attributes are self.x and self.y of my
+ 
+
+ align:start position:0%
+attributes are self.x and self.y of my
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+right okay so then we had one method
+
+ align:start position:0%
+right okay so then we had one method
+ 
+
+ align:start position:0%
+right okay so then we had one method
+that we wrote last lecture it was called
+
+ align:start position:0%
+that we wrote last lecture it was called
+ 
+
+ align:start position:0%
+that we wrote last lecture it was called
+distance and it took two parameters so
+
+ align:start position:0%
+distance and it took two parameters so
+ 
+
+ align:start position:0%
+distance and it took two parameters so
+the first one of course is self and this
+
+ align:start position:0%
+the first one of course is self and this
+ 
+
+ align:start position:0%
+the first one of course is self and this
+self represents the thing this object
+
+ align:start position:0%
+self represents the thing this object
+ 
+
+ align:start position:0%
+self represents the thing this object
+that you're going to call the method on
+
+ align:start position:0%
+that you're going to call the method on
+ 
+
+ align:start position:0%
+that you're going to call the method on
+I don't have that object yet so I'm just
+
+ align:start position:0%
+I don't have that object yet so I'm just
+ 
+
+ align:start position:0%
+I don't have that object yet so I'm just
+calling itself for now um because this
+
+ align:start position:0%
+calling itself for now um because this
+ 
+
+ align:start position:0%
+calling itself for now um because this
+is the class definition and then this
+
+ align:start position:0%
+is the class definition and then this
+ 
+
+ align:start position:0%
+is the class definition and then this
+other parameter is no some other
+
+ align:start position:0%
+other parameter is no some other
+ 
+
+ align:start position:0%
+other parameter is no some other
+coordinate object that I'm going to run
+
+ align:start position:0%
+coordinate object that I'm going to run
+ 
+
+ align:start position:0%
+coordinate object that I'm going to run
+this method on so the body of distance
+
+ align:start position:0%
+this method on so the body of distance
+ 
+
+ align:start position:0%
+this method on so the body of distance
+says all right well how do I find the
+
+ align:start position:0%
+says all right well how do I find the
+ 
+
+ align:start position:0%
+says all right well how do I find the
+distance between two uh points in the 2D
+
+ align:start position:0%
+distance between two uh points in the 2D
+ 
+
+ align:start position:0%
+distance between two uh points in the 2D
+plane it's just Pythagoras right so that
+
+ align:start position:0%
+plane it's just Pythagoras right so that
+ 
+
+ align:start position:0%
+plane it's just Pythagoras right so that
+means grab the x value of one of my
+
+ align:start position:0%
+means grab the x value of one of my
+ 
+
+ align:start position:0%
+means grab the x value of one of my
+points subtract the x value of the other
+
+ align:start position:0%
+points subtract the x value of the other
+ 
+
+ align:start position:0%
+points subtract the x value of the other
+point Square them same with the Y's
+
+ align:start position:0%
+point Square them same with the Y's
+ 
+
+ align:start position:0%
+point Square them same with the Y's
+Square them add them take the square
+
+ align:start position:0%
+Square them add them take the square
+ 
+
+ align:start position:0%
+Square them add them take the square
+root so what's the x value of one point
+
+ align:start position:0%
+root so what's the x value of one point
+ 
+
+ align:start position:0%
+root so what's the x value of one point
+well one of the points is going to be
+
+ align:start position:0%
+well one of the points is going to be
+ 
+
+ align:start position:0%
+well one of the points is going to be
+the thing that I'm calling the distance
+
+ align:start position:0%
+the thing that I'm calling the distance
+ 
+
+ align:start position:0%
+the thing that I'm calling the distance
+method on self so I grab the x value of
+
+ align:start position:0%
+method on self so I grab the x value of
+ 
+
+ align:start position:0%
+method on self so I grab the x value of
+self using this do notation
+
+ align:start position:0%
+self using this do notation
+ 
+
+ align:start position:0%
+self using this do notation
+self.x and then what's the x value of
+
+ align:start position:0%
+self.x and then what's the x value of
+ 
+
+ align:start position:0%
+self.x and then what's the x value of
+this other coordinate point well it's
+
+ align:start position:0%
+this other coordinate point well it's
+ 
+
+ align:start position:0%
+this other coordinate point well it's
+called other in my parameter list so I'm
+
+ align:start position:0%
+called other in my parameter list so I'm
+ 
+
+ align:start position:0%
+called other in my parameter list so I'm
+going to grab the x value of other again
+
+ align:start position:0%
+going to grab the x value of other again
+ 
+
+ align:start position:0%
+going to grab the x value of other again
+using do notation okay and then we just
+
+ align:start position:0%
+using do notation okay and then we just
+ 
+
+ align:start position:0%
+using do notation okay and then we just
+do the
+
+ align:start position:0%
+do the
+ 
+
+ align:start position:0%
+do the
+math
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah so you can make methods you can
+
+ align:start position:0%
+yes yeah so you can make methods you can
+ 
+
+ align:start position:0%
+yes yeah so you can make methods you can
+make methods for a particular
+
+ align:start position:0%
+make methods for a particular
+ 
+
+ align:start position:0%
+make methods for a particular
+class right but like you can only call
+
+ align:start position:0%
+class right but like you can only call
+ 
+
+ align:start position:0%
+class right but like you can only call
+those functions that you define call
+
+ align:start position:0%
+those functions that you define call
+ 
+
+ align:start position:0%
+those functions that you define call
+exactly yeah
+
+ align:start position:0%
+exactly yeah
+ 
+
+ align:start position:0%
+exactly yeah
+yeah yeah is there a way we could define
+
+ align:start position:0%
+yeah yeah is there a way we could define
+ 
+
+ align:start position:0%
+yeah yeah is there a way we could define
+a class as something other than an
+
+ align:start position:0%
+a class as something other than an
+ 
+
+ align:start position:0%
+a class as something other than an
+object a class is something other than
+
+ align:start position:0%
+object a class is something other than
+ 
+
+ align:start position:0%
+object a class is something other than
+an object right we put coordinate and
+
+ align:start position:0%
+an object right we put coordinate and
+ 
+
+ align:start position:0%
+an object right we put coordinate and
+object something else in the parenthesis
+
+ align:start position:0%
+object something else in the parenthesis
+ 
+
+ align:start position:0%
+object something else in the parenthesis
+yes we can put other things in the
+
+ align:start position:0%
+yes we can put other things in the
+ 
+
+ align:start position:0%
+yes we can put other things in the
+parentheses so that's actually what
+
+ align:start position:0%
+parentheses so that's actually what
+ 
+
+ align:start position:0%
+parentheses so that's actually what
+Monday's lecture will be about in that
+
+ align:start position:0%
+Monday's lecture will be about in that
+ 
+
+ align:start position:0%
+Monday's lecture will be about in that
+case the thing in the parentheses
+
+ align:start position:0%
+case the thing in the parentheses
+ 
+
+ align:start position:0%
+case the thing in the parentheses
+becomes the parent of the class that
+
+ align:start position:0%
+becomes the parent of the class that
+ 
+
+ align:start position:0%
+becomes the parent of the class that
+you're currently writing so I won't go
+
+ align:start position:0%
+you're currently writing so I won't go
+ 
+
+ align:start position:0%
+you're currently writing so I won't go
+into too much detail but to to have this
+
+ align:start position:0%
+into too much detail but to to have this
+ 
+
+ align:start position:0%
+into too much detail but to to have this
+other object as a parent means that
+
+ align:start position:0%
+other object as a parent means that
+ 
+
+ align:start position:0%
+other object as a parent means that
+everything that that object can do
+
+ align:start position:0%
+everything that that object can do
+ 
+
+ align:start position:0%
+everything that that object can do
+automatically your object can do as well
+
+ align:start position:0%
+automatically your object can do as well
+ 
+
+ align:start position:0%
+automatically your object can do as well
+and then on top of that you can decide a
+
+ align:start position:0%
+and then on top of that you can decide a
+ 
+
+ align:start position:0%
+and then on top of that you can decide a
+bunch of additional stuff your new
+
+ align:start position:0%
+bunch of additional stuff your new
+ 
+
+ align:start position:0%
+bunch of additional stuff your new
+object does but in a sense your
+
+ align:start position:0%
+object does but in a sense your
+ 
+
+ align:start position:0%
+object does but in a sense your
+coordinate object is a whatever this
+
+ align:start position:0%
+coordinate object is a whatever this
+ 
+
+ align:start position:0%
+coordinate object is a whatever this
+thing in the parenthesis is and then it
+
+ align:start position:0%
+thing in the parenthesis is and then it
+ 
+
+ align:start position:0%
+thing in the parenthesis is and then it
+can do a bunch of other stuff as well
+
+ align:start position:0%
+can do a bunch of other stuff as well
+ 
+
+ align:start position:0%
+can do a bunch of other stuff as well
+yeah simar how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we yeah how do that
+
+ align:start position:0%
+we yeah how do that
+ 
+
+ align:start position:0%
+we yeah how do that
+oh to make a copy of the object or a
+
+ align:start position:0%
+oh to make a copy of the object or a
+ 
+
+ align:start position:0%
+oh to make a copy of the object or a
+copy of the class oh so here we're not
+
+ align:start position:0%
+copy of the class oh so here we're not
+ 
+
+ align:start position:0%
+copy of the class oh so here we're not
+you can't make a copy of the class here
+
+ align:start position:0%
+you can't make a copy of the class here
+ 
+
+ align:start position:0%
+you can't make a copy of the class here
+specifically because we're just defining
+
+ align:start position:0%
+specifically because we're just defining
+ 
+
+ align:start position:0%
+specifically because we're just defining
+the class but when you're creating
+
+ align:start position:0%
+the class but when you're creating
+ 
+
+ align:start position:0%
+the class but when you're creating
+coordinate objects then you could Define
+
+ align:start position:0%
+coordinate objects then you could Define
+ 
+
+ align:start position:0%
+coordinate objects then you could Define
+a method that copies your object into
+
+ align:start position:0%
+a method that copies your object into
+ 
+
+ align:start position:0%
+a method that copies your object into
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+object so in essence it would return a
+
+ align:start position:0%
+object so in essence it would return a
+ 
+
+ align:start position:0%
+object so in essence it would return a
+new object of type coordinate with
+
+ align:start position:0%
+new object of type coordinate with
+ 
+
+ align:start position:0%
+new object of type coordinate with
+whatever parameters you'd want to do
+
+ align:start position:0%
+whatever parameters you'd want to do
+ 
+
+ align:start position:0%
+whatever parameters you'd want to do
+yeah so all yeah all these things are
+
+ align:start position:0%
+yeah so all yeah all these things are
+ 
+
+ align:start position:0%
+yeah so all yeah all these things are
+are possible
+
+ align:start position:0%
+are possible
+ 
+
+ align:start position:0%
+are possible
+yeah so let's add one more method to
+
+ align:start position:0%
+yeah so let's add one more method to
+ 
+
+ align:start position:0%
+yeah so let's add one more method to
+this class let's call it 2core origin
+
+ align:start position:0%
+this class let's call it 2core origin
+ 
+
+ align:start position:0%
+this class let's call it 2core origin
+okay so this distance method just to
+
+ align:start position:0%
+okay so this distance method just to
+ 
+
+ align:start position:0%
+okay so this distance method just to
+remind ourselves returned a number right
+
+ align:start position:0%
+remind ourselves returned a number right
+ 
+
+ align:start position:0%
+remind ourselves returned a number right
+so it just took the difference between
+
+ align:start position:0%
+so it just took the difference between
+ 
+
+ align:start position:0%
+so it just took the difference between
+these two points and it returned a
+
+ align:start position:0%
+these two points and it returned a
+ 
+
+ align:start position:0%
+these two points and it returned a
+number just how far away they are but
+
+ align:start position:0%
+number just how far away they are but
+ 
+
+ align:start position:0%
+number just how far away they are but
+this two Origin method is going to do
+
+ align:start position:0%
+this two Origin method is going to do
+ 
+
+ align:start position:0%
+this two Origin method is going to do
+something slightly different essentially
+
+ align:start position:0%
+something slightly different essentially
+ 
+
+ align:start position:0%
+something slightly different essentially
+what I'm going to have this method do is
+
+ align:start position:0%
+what I'm going to have this method do is
+ 
+
+ align:start position:0%
+what I'm going to have this method do is
+to take my point from wherever it is in
+
+ align:start position:0%
+to take my point from wherever it is in
+ 
+
+ align:start position:0%
+to take my point from wherever it is in
+my 2D plane that it has been initialized
+
+ align:start position:0%
+my 2D plane that it has been initialized
+ 
+
+ align:start position:0%
+my 2D plane that it has been initialized
+to and say I'm going to reset it back to
+
+ align:start position:0%
+to and say I'm going to reset it back to
+ 
+
+ align:start position:0%
+to and say I'm going to reset it back to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+origin right so to do that all that
+
+ align:start position:0%
+origin right so to do that all that
+ 
+
+ align:start position:0%
+origin right so to do that all that
+means is I'm going to make its uh x
+
+ align:start position:0%
+means is I'm going to make its uh x
+ 
+
+ align:start position:0%
+means is I'm going to make its uh x
+value and its yvalue be zero so I can
+
+ align:start position:0%
+value and its yvalue be zero so I can
+ 
+
+ align:start position:0%
+value and its yvalue be zero so I can
+manipulate the X and Y data attributes
+
+ align:start position:0%
+manipulate the X and Y data attributes
+ 
+
+ align:start position:0%
+manipulate the X and Y data attributes
+of this particular object to be whatever
+
+ align:start position:0%
+of this particular object to be whatever
+ 
+
+ align:start position:0%
+of this particular object to be whatever
+I want them to be so I can reset them
+
+ align:start position:0%
+I want them to be so I can reset them
+ 
+
+ align:start position:0%
+I want them to be so I can reset them
+both to zero so if I ever call this
+
+ align:start position:0%
+both to zero so if I ever call this
+ 
+
+ align:start position:0%
+both to zero so if I ever call this
+method on an object whose X and Y values
+
+ align:start position:0%
+method on an object whose X and Y values
+ 
+
+ align:start position:0%
+method on an object whose X and Y values
+are something other than zero they'll be
+
+ align:start position:0%
+are something other than zero they'll be
+ 
+
+ align:start position:0%
+are something other than zero they'll be
+reset to zero
+
+ align:start position:0%
+reset to zero
+ 
+
+ align:start position:0%
+reset to zero
+okay so let's actually uh run the code
+
+ align:start position:0%
+okay so let's actually uh run the code
+ 
+
+ align:start position:0%
+okay so let's actually uh run the code
+that that we just wrote so here I've got
+
+ align:start position:0%
+that that we just wrote so here I've got
+ 
+
+ align:start position:0%
+that that we just wrote so here I've got
+two coordinate objects being created so
+
+ align:start position:0%
+two coordinate objects being created so
+ 
+
+ align:start position:0%
+two coordinate objects being created so
+the beauty of writing this class for us
+
+ align:start position:0%
+the beauty of writing this class for us
+ 
+
+ align:start position:0%
+the beauty of writing this class for us
+is that now we can create as many
+
+ align:start position:0%
+is that now we can create as many
+ 
+
+ align:start position:0%
+is that now we can create as many
+coordinate objects as we'd like they all
+
+ align:start position:0%
+coordinate objects as we'd like they all
+ 
+
+ align:start position:0%
+coordinate objects as we'd like they all
+will have an x value and a yvalue
+
+ align:start position:0%
+will have an x value and a yvalue
+ 
+
+ align:start position:0%
+will have an x value and a yvalue
+associated with them it's just that the
+
+ align:start position:0%
+associated with them it's just that the
+ 
+
+ align:start position:0%
+associated with them it's just that the
+specific values for X and Y will be
+
+ align:start position:0%
+specific values for X and Y will be
+ 
+
+ align:start position:0%
+specific values for X and Y will be
+different right so here I've got a
+
+ align:start position:0%
+different right so here I've got a
+ 
+
+ align:start position:0%
+different right so here I've got a
+coordinate object with X3 and y4 being
+
+ align:start position:0%
+coordinate object with X3 and y4 being
+ 
+
+ align:start position:0%
+coordinate object with X3 and y4 being
+created and it's going to be bound by
+
+ align:start position:0%
+created and it's going to be bound by
+ 
+
+ align:start position:0%
+created and it's going to be bound by
+the variable named C and here a
+
+ align:start position:0%
+the variable named C and here a
+ 
+
+ align:start position:0%
+the variable named C and here a
+coordinate object with X and Y values
+
+ align:start position:0%
+coordinate object with X and Y values
+ 
+
+ align:start position:0%
+coordinate object with X and Y values
+both zero bound to a variable named
+
+ align:start position:0%
+both zero bound to a variable named
+ 
+
+ align:start position:0%
+both zero bound to a variable named
+origin okay so then I can use this dot
+
+ align:start position:0%
+origin okay so then I can use this dot
+ 
+
+ align:start position:0%
+origin okay so then I can use this dot
+notation that we talked about last
+
+ align:start position:0%
+notation that we talked about last
+ 
+
+ align:start position:0%
+notation that we talked about last
+lecture to access either data or to run
+
+ align:start position:0%
+lecture to access either data or to run
+ 
+
+ align:start position:0%
+lecture to access either data or to run
+methods on the on on the object so in
+
+ align:start position:0%
+methods on the on on the object so in
+ 
+
+ align:start position:0%
+methods on the on on the object so in
+this print uh print F uh statement here
+
+ align:start position:0%
+this print uh print F uh statement here
+ 
+
+ align:start position:0%
+this print uh print F uh statement here
+I'm using dot notation
+
+ align:start position:0%
+I'm using dot notation
+ 
+
+ align:start position:0%
+I'm using dot notation
+on C and origin to grab the X values of
+
+ align:start position:0%
+on C and origin to grab the X values of
+ 
+
+ align:start position:0%
+on C and origin to grab the X values of
+c over here and origin over here okay
+
+ align:start position:0%
+c over here and origin over here okay
+ 
+
+ align:start position:0%
+c over here and origin over here okay
+and then I'm running the distance method
+
+ align:start position:0%
+and then I'm running the distance method
+ 
+
+ align:start position:0%
+and then I'm running the distance method
+on C so remember dot notation says the
+
+ align:start position:0%
+on C so remember dot notation says the
+ 
+
+ align:start position:0%
+on C so remember dot notation says the
+thing before the dot is going to be an
+
+ align:start position:0%
+thing before the dot is going to be an
+ 
+
+ align:start position:0%
+thing before the dot is going to be an
+object the thing after the dot is going
+
+ align:start position:0%
+object the thing after the dot is going
+ 
+
+ align:start position:0%
+object the thing after the dot is going
+to be the method name that can run on
+
+ align:start position:0%
+to be the method name that can run on
+ 
+
+ align:start position:0%
+to be the method name that can run on
+this object of type whatever this is
+
+ align:start position:0%
+this object of type whatever this is
+ 
+
+ align:start position:0%
+this object of type whatever this is
+coordinate and then in the parentheses
+
+ align:start position:0%
+coordinate and then in the parentheses
+ 
+
+ align:start position:0%
+coordinate and then in the parentheses
+it's just a function we just pass in all
+
+ align:start position:0%
+it's just a function we just pass in all
+ 
+
+ align:start position:0%
+it's just a function we just pass in all
+the variables that that option that that
+
+ align:start position:0%
+the variables that that option that that
+ 
+
+ align:start position:0%
+the variables that that option that that
+method
+
+ align:start position:0%
+method
+ 
+
+ align:start position:0%
+method
+expects right so C do distance will
+
+ align:start position:0%
+expects right so C do distance will
+ 
+
+ align:start position:0%
+expects right so C do distance will
+print whatever you know however far away
+
+ align:start position:0%
+print whatever you know however far away
+ 
+
+ align:start position:0%
+print whatever you know however far away
+it is I no five because those are nice
+
+ align:start position:0%
+it is I no five because those are nice
+ 
+
+ align:start position:0%
+it is I no five because those are nice
+numbers okay so then if we run this
+
+ align:start position:0%
+numbers okay so then if we run this
+ 
+
+ align:start position:0%
+numbers okay so then if we run this
+function that we just wrote to origin
+
+ align:start position:0%
+function that we just wrote to origin
+ 
+
+ align:start position:0%
+function that we just wrote to origin
+this function just to remind you doesn't
+
+ align:start position:0%
+this function just to remind you doesn't
+ 
+
+ align:start position:0%
+this function just to remind you doesn't
+actually return anything right it just
+
+ align:start position:0%
+actually return anything right it just
+ 
+
+ align:start position:0%
+actually return anything right it just
+resets the variables X and Y for that
+
+ align:start position:0%
+resets the variables X and Y for that
+ 
+
+ align:start position:0%
+resets the variables X and Y for that
+particular object back to zero so in
+
+ align:start position:0%
+particular object back to zero so in
+ 
+
+ align:start position:0%
+particular object back to zero so in
+here when I call um this method here
+
+ align:start position:0%
+here when I call um this method here
+ 
+
+ align:start position:0%
+here when I call um this method here
+right again dot notation the thing
+
+ align:start position:0%
+right again dot notation the thing
+ 
+
+ align:start position:0%
+right again dot notation the thing
+before the dot is an object it's C its X
+
+ align:start position:0%
+before the dot is an object it's C its X
+ 
+
+ align:start position:0%
+before the dot is an object it's C its X
+and Y values are currently three and
+
+ align:start position:0%
+and Y values are currently three and
+ 
+
+ align:start position:0%
+and Y values are currently three and
+four but after I run this function it
+
+ align:start position:0%
+four but after I run this function it
+ 
+
+ align:start position:0%
+four but after I run this function it
+returns none by the way its X and Y
+
+ align:start position:0%
+returns none by the way its X and Y
+ 
+
+ align:start position:0%
+returns none by the way its X and Y
+values will be changed to zero and zero
+
+ align:start position:0%
+values will be changed to zero and zero
+ 
+
+ align:start position:0%
+values will be changed to zero and zero
+so if I look at my code here right so
+
+ align:start position:0%
+so if I look at my code here right so
+ 
+
+ align:start position:0%
+so if I look at my code here right so
+here's this print F
+
+ align:start position:0%
+here's this print F
+ 
+
+ align:start position:0%
+here's this print F
+statement right so C's x value is three
+
+ align:start position:0%
+statement right so C's x value is three
+ 
+
+ align:start position:0%
+statement right so C's x value is three
+and C's and origin's X is zero
+
+ align:start position:0%
+and C's and origin's X is zero
+ 
+
+ align:start position:0%
+and C's and origin's X is zero
+fine um and then I've got these two
+
+ align:start position:0%
+fine um and then I've got these two
+ 
+
+ align:start position:0%
+fine um and then I've got these two
+calls here so c.2 origin right I'm
+
+ align:start position:0%
+calls here so c.2 origin right I'm
+ 
+
+ align:start position:0%
+calls here so c.2 origin right I'm
+making this function call before the
+
+ align:start position:0%
+making this function call before the
+ 
+
+ align:start position:0%
+making this function call before the
+function call C's X is three C's Y is
+
+ align:start position:0%
+function call C's X is three C's Y is
+ 
+
+ align:start position:0%
+function call C's X is three C's Y is
+four and after the function call you can
+
+ align:start position:0%
+four and after the function call you can
+ 
+
+ align:start position:0%
+four and after the function call you can
+see C's X is zero and C's Y is zero so
+
+ align:start position:0%
+see C's X is zero and C's Y is zero so
+ 
+
+ align:start position:0%
+see C's X is zero and C's Y is zero so
+I'm literally changing the X and Y
+
+ align:start position:0%
+I'm literally changing the X and Y
+ 
+
+ align:start position:0%
+I'm literally changing the X and Y
+values of this object
+
+ align:start position:0%
+values of this object
+ 
+
+ align:start position:0%
+values of this object
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+okay all right so questions so far so
+
+ align:start position:0%
+okay all right so questions so far so
+ 
+
+ align:start position:0%
+okay all right so questions so far so
+far so good hopefully a recap
+
+ align:start position:0%
+far so good hopefully a recap
+ 
+
+ align:start position:0%
+far so good hopefully a recap
+okay so again sort of similar to the
+
+ align:start position:0%
+okay so again sort of similar to the
+ 
+
+ align:start position:0%
+okay so again sort of similar to the
+first slide we started with right so
+
+ align:start position:0%
+first slide we started with right so
+ 
+
+ align:start position:0%
+first slide we started with right so
+we've got this class coordinate object
+
+ align:start position:0%
+we've got this class coordinate object
+ 
+
+ align:start position:0%
+we've got this class coordinate object
+right the class name is our type so this
+
+ align:start position:0%
+right the class name is our type so this
+ 
+
+ align:start position:0%
+right the class name is our type so this
+object I'm creating is of type
+
+ align:start position:0%
+object I'm creating is of type
+ 
+
+ align:start position:0%
+object I'm creating is of type
+coordinate um we're defining the class
+
+ align:start position:0%
+coordinate um we're defining the class
+ 
+
+ align:start position:0%
+coordinate um we're defining the class
+in a generic way in an abstract way
+
+ align:start position:0%
+in a generic way in an abstract way
+ 
+
+ align:start position:0%
+in a generic way in an abstract way
+right so we have to use the self um uh
+
+ align:start position:0%
+right so we have to use the self um uh
+ 
+
+ align:start position:0%
+right so we have to use the self um uh
+variable either in the parameter list to
+
+ align:start position:0%
+variable either in the parameter list to
+ 
+
+ align:start position:0%
+variable either in the parameter list to
+tell python what's the thing before the
+
+ align:start position:0%
+tell python what's the thing before the
+ 
+
+ align:start position:0%
+tell python what's the thing before the
+dot going to map to well it's going to
+
+ align:start position:0%
+dot going to map to well it's going to
+ 
+
+ align:start position:0%
+dot going to map to well it's going to
+map to self in my parameter list or we
+
+ align:start position:0%
+map to self in my parameter list or we
+ 
+
+ align:start position:0%
+map to self in my parameter list or we
+use the self to tell python what the
+
+ align:start position:0%
+use the self to tell python what the
+ 
+
+ align:start position:0%
+use the self to tell python what the
+data attributes of this object are right
+
+ align:start position:0%
+data attributes of this object are right
+ 
+
+ align:start position:0%
+data attributes of this object are right
+so anything defined with self dot some
+
+ align:start position:0%
+so anything defined with self dot some
+ 
+
+ align:start position:0%
+so anything defined with self dot some
+variable uh name will be a data
+
+ align:start position:0%
+variable uh name will be a data
+ 
+
+ align:start position:0%
+variable uh name will be a data
+attribute that's common across all the
+
+ align:start position:0%
+attribute that's common across all the
+ 
+
+ align:start position:0%
+attribute that's common across all the
+instances I create so from of this type
+
+ align:start position:0%
+instances I create so from of this type
+ 
+
+ align:start position:0%
+instances I create so from of this type
+when we create actual instances that's
+
+ align:start position:0%
+when we create actual instances that's
+ 
+
+ align:start position:0%
+when we create actual instances that's
+when our uh our blueprint our abstract
+
+ align:start position:0%
+when our uh our blueprint our abstract
+ 
+
+ align:start position:0%
+when our uh our blueprint our abstract
+definition now you know gets put into
+
+ align:start position:0%
+definition now you know gets put into
+ 
+
+ align:start position:0%
+definition now you know gets put into
+use and now I'm creating actual uh
+
+ align:start position:0%
+use and now I'm creating actual uh
+ 
+
+ align:start position:0%
+use and now I'm creating actual uh
+objects that I can uh grab X values from
+
+ align:start position:0%
+objects that I can uh grab X values from
+ 
+
+ align:start position:0%
+objects that I can uh grab X values from
+change X values from you know get
+
+ align:start position:0%
+change X values from you know get
+ 
+
+ align:start position:0%
+change X values from you know get
+distances between other objects and so
+
+ align:start position:0%
+distances between other objects and so
+ 
+
+ align:start position:0%
+distances between other objects and so
+on and so on okay so what I'd like to do
+
+ align:start position:0%
+on and so on okay so what I'd like to do
+ 
+
+ align:start position:0%
+on and so on okay so what I'd like to do
+next is to um take this coordinate class
+
+ align:start position:0%
+next is to um take this coordinate class
+ 
+
+ align:start position:0%
+next is to um take this coordinate class
+and build uh a circle class with it so
+
+ align:start position:0%
+and build uh a circle class with it so
+ 
+
+ align:start position:0%
+and build uh a circle class with it so
+this comes uh sort of hand inand with
+
+ align:start position:0%
+this comes uh sort of hand inand with
+ 
+
+ align:start position:0%
+this comes uh sort of hand inand with
+the idea of when you're deciding how to
+
+ align:start position:0%
+the idea of when you're deciding how to
+ 
+
+ align:start position:0%
+the idea of when you're deciding how to
+create a class you get to make the
+
+ align:start position:0%
+create a class you get to make the
+ 
+
+ align:start position:0%
+create a class you get to make the
+design decision right so when the finger
+
+ align:start position:0%
+design decision right so when the finger
+ 
+
+ align:start position:0%
+design decision right so when the finger
+exercise for Monday's lecture today's
+
+ align:start position:0%
+exercise for Monday's lecture today's
+ 
+
+ align:start position:0%
+exercise for Monday's lecture today's
+Wednesday yes Monday's lecture um you
+
+ align:start position:0%
+Wednesday yes Monday's lecture um you
+ 
+
+ align:start position:0%
+Wednesday yes Monday's lecture um you
+guys had to create a a center uh sorry a
+
+ align:start position:0%
+guys had to create a a center uh sorry a
+ 
+
+ align:start position:0%
+guys had to create a a center uh sorry a
+circle class right but the way we
+
+ align:start position:0%
+circle class right but the way we
+ 
+
+ align:start position:0%
+circle class right but the way we
+defined the circle class in that finger
+
+ align:start position:0%
+defined the circle class in that finger
+ 
+
+ align:start position:0%
+defined the circle class in that finger
+exercise was basically by that circle's
+
+ align:start position:0%
+exercise was basically by that circle's
+ 
+
+ align:start position:0%
+exercise was basically by that circle's
+radius that's the only sort of way we
+
+ align:start position:0%
+radius that's the only sort of way we
+ 
+
+ align:start position:0%
+radius that's the only sort of way we
+abstracted that Circle right but now in
+
+ align:start position:0%
+abstracted that Circle right but now in
+ 
+
+ align:start position:0%
+abstracted that Circle right but now in
+in this lecture we're going to make a
+
+ align:start position:0%
+in this lecture we're going to make a
+ 
+
+ align:start position:0%
+in this lecture we're going to make a
+different design decision and say that
+
+ align:start position:0%
+different design decision and say that
+ 
+
+ align:start position:0%
+different design decision and say that
+let's say and say that a circle will now
+
+ align:start position:0%
+let's say and say that a circle will now
+ 
+
+ align:start position:0%
+let's say and say that a circle will now
+be defined using two things the first is
+
+ align:start position:0%
+be defined using two things the first is
+ 
+
+ align:start position:0%
+be defined using two things the first is
+the radius right so I'm going to say
+
+ align:start position:0%
+the radius right so I'm going to say
+ 
+
+ align:start position:0%
+the radius right so I'm going to say
+that that's an integer and the second is
+
+ align:start position:0%
+that that's an integer and the second is
+ 
+
+ align:start position:0%
+that that's an integer and the second is
+going to be the center of the circle
+
+ align:start position:0%
+going to be the center of the circle
+ 
+
+ align:start position:0%
+going to be the center of the circle
+right so as in the picture there I'm
+
+ align:start position:0%
+right so as in the picture there I'm
+ 
+
+ align:start position:0%
+right so as in the picture there I'm
+going to say that a circle is you know
+
+ align:start position:0%
+going to say that a circle is you know
+ 
+
+ align:start position:0%
+going to say that a circle is you know
+based on this Center and this radius and
+
+ align:start position:0%
+based on this Center and this radius and
+ 
+
+ align:start position:0%
+based on this Center and this radius and
+the center is not going to be a float
+
+ align:start position:0%
+the center is not going to be a float
+ 
+
+ align:start position:0%
+the center is not going to be a float
+it's not going to be a tuple it's not
+
+ align:start position:0%
+it's not going to be a tuple it's not
+ 
+
+ align:start position:0%
+it's not going to be a tuple it's not
+going to be an INT it's going to be a a
+
+ align:start position:0%
+going to be an INT it's going to be a a
+ 
+
+ align:start position:0%
+going to be an INT it's going to be a a
+coordinate
+
+ align:start position:0%
+coordinate
+ 
+
+ align:start position:0%
+coordinate
+object right the data type that we were
+
+ align:start position:0%
+object right the data type that we were
+ 
+
+ align:start position:0%
+object right the data type that we were
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+writing
+
+ align:start position:0%
+writing
+ 
+
+ align:start position:0%
+writing
+okay all right good it's not a secret
+
+ align:start position:0%
+okay all right good it's not a secret
+ 
+
+ align:start position:0%
+okay all right good it's not a secret
+but that didn't lower my voice on
+
+ align:start position:0%
+but that didn't lower my voice on
+ 
+
+ align:start position:0%
+but that didn't lower my voice on
+purpose just just wanted to let that
+
+ align:start position:0%
+purpose just just wanted to let that
+ 
+
+ align:start position:0%
+purpose just just wanted to let that
+sink in right so the one of our data
+
+ align:start position:0%
+sink in right so the one of our data
+ 
+
+ align:start position:0%
+sink in right so the one of our data
+attributes for the circle class is a
+
+ align:start position:0%
+attributes for the circle class is a
+ 
+
+ align:start position:0%
+attributes for the circle class is a
+coordinate object so we're using an
+
+ align:start position:0%
+coordinate object so we're using an
+ 
+
+ align:start position:0%
+coordinate object so we're using an
+object that we just wrote to create a
+
+ align:start position:0%
+object that we just wrote to create a
+ 
+
+ align:start position:0%
+object that we just wrote to create a
+more complex object a circle okay so
+
+ align:start position:0%
+more complex object a circle okay so
+ 
+
+ align:start position:0%
+more complex object a circle okay so
+here's my class definition uh the data
+
+ align:start position:0%
+here's my class definition uh the data
+ 
+
+ align:start position:0%
+here's my class definition uh the data
+type is called Circle again it inherits
+
+ align:start position:0%
+type is called Circle again it inherits
+ 
+
+ align:start position:0%
+type is called Circle again it inherits
+all uh the parent of circle is just a
+
+ align:start position:0%
+all uh the parent of circle is just a
+ 
+
+ align:start position:0%
+all uh the parent of circle is just a
+generic python object first method we
+
+ align:start position:0%
+generic python object first method we
+ 
+
+ align:start position:0%
+generic python object first method we
+have to write is the init
+
+ align:start position:0%
+have to write is the init
+ 
+
+ align:start position:0%
+have to write is the init
+method uh first parameter is self so
+
+ align:start position:0%
+method uh first parameter is self so
+ 
+
+ align:start position:0%
+method uh first parameter is self so
+this thing that I'm creating right now
+
+ align:start position:0%
+this thing that I'm creating right now
+ 
+
+ align:start position:0%
+this thing that I'm creating right now
+and I say that to create a circle I have
+
+ align:start position:0%
+and I say that to create a circle I have
+ 
+
+ align:start position:0%
+and I say that to create a circle I have
+to give it a center and I have to give
+
+ align:start position:0%
+to give it a center and I have to give
+ 
+
+ align:start position:0%
+to give it a center and I have to give
+it a
+
+ align:start position:0%
+it a
+ 
+
+ align:start position:0%
+it a
+radius the data attributes of the circle
+
+ align:start position:0%
+radius the data attributes of the circle
+ 
+
+ align:start position:0%
+radius the data attributes of the circle
+class right so the the two attributes
+
+ align:start position:0%
+class right so the the two attributes
+ 
+
+ align:start position:0%
+class right so the the two attributes
+that make up my circle are this self.
+
+ align:start position:0%
+that make up my circle are this self.
+ 
+
+ align:start position:0%
+that make up my circle are this self.
+Center so the center variable here and
+
+ align:start position:0%
+Center so the center variable here and
+ 
+
+ align:start position:0%
+Center so the center variable here and
+self. radius right so these two things
+
+ align:start position:0%
+self. radius right so these two things
+ 
+
+ align:start position:0%
+self. radius right so these two things
+together make up our Circle
+
+ align:start position:0%
+together make up our Circle
+ 
+
+ align:start position:0%
+together make up our Circle
+object and initially in the init method
+
+ align:start position:0%
+object and initially in the init method
+ 
+
+ align:start position:0%
+object and initially in the init method
+right and when we conru Constructor
+
+ align:start position:0%
+right and when we conru Constructor
+ 
+
+ align:start position:0%
+right and when we conru Constructor
+object we're just going to set these two
+
+ align:start position:0%
+object we're just going to set these two
+ 
+
+ align:start position:0%
+object we're just going to set these two
+things to be whatever is passed in as
+
+ align:start position:0%
+things to be whatever is passed in as
+ 
+
+ align:start position:0%
+things to be whatever is passed in as
+parameters in that uh in the
+
+ align:start position:0%
+parameters in that uh in the
+ 
+
+ align:start position:0%
+parameters in that uh in the
+Constructor okay all
+
+ align:start position:0%
+Constructor okay all
+ 
+
+ align:start position:0%
+Constructor okay all
+right so what I'd like to say is that
+
+ align:start position:0%
+right so what I'd like to say is that
+ 
+
+ align:start position:0%
+right so what I'd like to say is that
+this um Center thing uh Center parameter
+
+ align:start position:0%
+this um Center thing uh Center parameter
+ 
+
+ align:start position:0%
+this um Center thing uh Center parameter
+will be a coordinate object and radius
+
+ align:start position:0%
+will be a coordinate object and radius
+ 
+
+ align:start position:0%
+will be a coordinate object and radius
+will be an INT now notice in this code
+
+ align:start position:0%
+will be an INT now notice in this code
+ 
+
+ align:start position:0%
+will be an INT now notice in this code
+I'm not actually enforcing this right I
+
+ align:start position:0%
+I'm not actually enforcing this right I
+ 
+
+ align:start position:0%
+I'm not actually enforcing this right I
+could create a set a circle object by
+
+ align:start position:0%
+could create a set a circle object by
+ 
+
+ align:start position:0%
+could create a set a circle object by
+just passing in two
+
+ align:start position:0%
+just passing in two
+ 
+
+ align:start position:0%
+just passing in two
+strings right at this point this code
+
+ align:start position:0%
+strings right at this point this code
+ 
+
+ align:start position:0%
+strings right at this point this code
+doesn't care right nowhere am I
+
+ align:start position:0%
+doesn't care right nowhere am I
+ 
+
+ align:start position:0%
+doesn't care right nowhere am I
+enforcing the fact that Center is a
+
+ align:start position:0%
+enforcing the fact that Center is a
+ 
+
+ align:start position:0%
+enforcing the fact that Center is a
+coordinate and radius will be in it but
+
+ align:start position:0%
+coordinate and radius will be in it but
+ 
+
+ align:start position:0%
+coordinate and radius will be in it but
+you know that's just something that we
+
+ align:start position:0%
+you know that's just something that we
+ 
+
+ align:start position:0%
+you know that's just something that we
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+know so then when we create the actual
+
+ align:start position:0%
+know so then when we create the actual
+ 
+
+ align:start position:0%
+know so then when we create the actual
+um object down here right my underscore
+
+ align:start position:0%
+um object down here right my underscore
+ 
+
+ align:start position:0%
+um object down here right my underscore
+circle is going to be a variable that's
+
+ align:start position:0%
+circle is going to be a variable that's
+ 
+
+ align:start position:0%
+circle is going to be a variable that's
+bound to my circle object so here I'm
+
+ align:start position:0%
+bound to my circle object so here I'm
+ 
+
+ align:start position:0%
+bound to my circle object so here I'm
+invoking the name of my class Circle and
+
+ align:start position:0%
+invoking the name of my class Circle and
+ 
+
+ align:start position:0%
+invoking the name of my class Circle and
+then what are the two parameters I'm
+
+ align:start position:0%
+then what are the two parameters I'm
+ 
+
+ align:start position:0%
+then what are the two parameters I'm
+passing in well the first one I said
+
+ align:start position:0%
+passing in well the first one I said
+ 
+
+ align:start position:0%
+passing in well the first one I said
+right up here that it should be a center
+
+ align:start position:0%
+right up here that it should be a center
+ 
+
+ align:start position:0%
+right up here that it should be a center
+a a coordinate object so Center is a
+
+ align:start position:0%
+a a coordinate object so Center is a
+ 
+
+ align:start position:0%
+a a coordinate object so Center is a
+variable name and what is it well I had
+
+ align:start position:0%
+variable name and what is it well I had
+ 
+
+ align:start position:0%
+variable name and what is it well I had
+to create this coordinate object right
+
+ align:start position:0%
+to create this coordinate object right
+ 
+
+ align:start position:0%
+to create this coordinate object right
+so I'm just invoking the name of
+
+ align:start position:0%
+so I'm just invoking the name of
+ 
+
+ align:start position:0%
+so I'm just invoking the name of
+coordinate this class that creates for
+
+ align:start position:0%
+coordinate this class that creates for
+ 
+
+ align:start position:0%
+coordinate this class that creates for
+me a coordinate object and I happen to
+
+ align:start position:0%
+me a coordinate object and I happen to
+ 
+
+ align:start position:0%
+me a coordinate object and I happen to
+put the center of the circle at two
+
+ align:start position:0%
+put the center of the circle at two
+ 
+
+ align:start position:0%
+put the center of the circle at two
+comma 2 uh yeah
+
+ align:start position:0%
+comma 2 uh yeah
+ 
+
+ align:start position:0%
+comma 2 uh yeah
+okay so this Center thing is a
+
+ align:start position:0%
+okay so this Center thing is a
+ 
+
+ align:start position:0%
+okay so this Center thing is a
+coordinate object right it's not a tuple
+
+ align:start position:0%
+coordinate object right it's not a tuple
+ 
+
+ align:start position:0%
+coordinate object right it's not a tuple
+or float or whatever it's a coordinate
+
+ align:start position:0%
+or float or whatever it's a coordinate
+ 
+
+ align:start position:0%
+or float or whatever it's a coordinate
+object and then the radius of this uh
+
+ align:start position:0%
+object and then the radius of this uh
+ 
+
+ align:start position:0%
+object and then the radius of this uh
+circle is two an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+INT everyone okay with that okay so what
+
+ align:start position:0%
+INT everyone okay with that okay so what
+ 
+
+ align:start position:0%
+INT everyone okay with that okay so what
+I'd like you to do next is to modify
+
+ align:start position:0%
+I'd like you to do next is to modify
+ 
+
+ align:start position:0%
+I'd like you to do next is to modify
+this init method just slightly just to
+
+ align:start position:0%
+this init method just slightly just to
+ 
+
+ align:start position:0%
+this init method just slightly just to
+show you that the init method doesn't
+
+ align:start position:0%
+show you that the init method doesn't
+ 
+
+ align:start position:0%
+show you that the init method doesn't
+just always set the data attributes and
+
+ align:start position:0%
+just always set the data attributes and
+ 
+
+ align:start position:0%
+just always set the data attributes and
+it's done it can do a lot of
+
+ align:start position:0%
+it's done it can do a lot of
+ 
+
+ align:start position:0%
+it's done it can do a lot of
+initialization code one of the more
+
+ align:start position:0%
+initialization code one of the more
+ 
+
+ align:start position:0%
+initialization code one of the more
+important things it can do is to try to
+
+ align:start position:0%
+important things it can do is to try to
+ 
+
+ align:start position:0%
+important things it can do is to try to
+enforce the types on the uh on the
+
+ align:start position:0%
+enforce the types on the uh on the
+ 
+
+ align:start position:0%
+enforce the types on the uh on the
+parameters here right so what I'd like
+
+ align:start position:0%
+parameters here right so what I'd like
+ 
+
+ align:start position:0%
+parameters here right so what I'd like
+you to do is add to this code to uh to
+
+ align:start position:0%
+you to do is add to this code to uh to
+ 
+
+ align:start position:0%
+you to do is add to this code to uh to
+to check that the type of Center is a
+
+ align:start position:0%
+to check that the type of Center is a
+ 
+
+ align:start position:0%
+to check that the type of Center is a
+coordinate and the type of radius is an
+
+ align:start position:0%
+coordinate and the type of radius is an
+ 
+
+ align:start position:0%
+coordinate and the type of radius is an
+integer and only if those two things are
+
+ align:start position:0%
+integer and only if those two things are
+ 
+
+ align:start position:0%
+integer and only if those two things are
+true then do you set uh the the two data
+
+ align:start position:0%
+true then do you set uh the the two data
+ 
+
+ align:start position:0%
+true then do you set uh the the two data
+attributes and otherwise raise for me a
+
+ align:start position:0%
+attributes and otherwise raise for me a
+ 
+
+ align:start position:0%
+attributes and otherwise raise for me a
+value error
+
+ align:start position:0%
+value error
+ 
+
+ align:start position:0%
+value error
+okay so that should be around
+
+ align:start position:0%
+okay so that should be around
+ 
+
+ align:start position:0%
+okay so that should be around
+uh line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+48 okay does anyone have some code for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah not equal coordinate yep so that's
+
+ align:start position:0%
+yeah not equal coordinate yep so that's
+ 
+
+ align:start position:0%
+yeah not equal coordinate yep so that's
+raise value a
+
+ align:start position:0%
+raise value a
+ 
+
+ align:start position:0%
+raise value a
+yep cool so that takes care of one
+
+ align:start position:0%
+yep cool so that takes care of one
+ 
+
+ align:start position:0%
+yep cool so that takes care of one
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep so if the type of radius because
+
+ align:start position:0%
+yep so if the type of radius because
+ 
+
+ align:start position:0%
+yep so if the type of radius because
+that's the parameter passed in not equal
+
+ align:start position:0%
+that's the parameter passed in not equal
+ 
+
+ align:start position:0%
+that's the parameter passed in not equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+int raise value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there so if if we drop into each of any
+
+ align:start position:0%
+there so if if we drop into each of any
+ 
+
+ align:start position:0%
+there so if if we drop into each of any
+of these ifs then we immediately raise
+
+ align:start position:0%
+of these ifs then we immediately raise
+ 
+
+ align:start position:0%
+of these ifs then we immediately raise
+the value error right the code doesn't
+
+ align:start position:0%
+the value error right the code doesn't
+ 
+
+ align:start position:0%
+the value error right the code doesn't
+complete and then only if we didn't drop
+
+ align:start position:0%
+complete and then only if we didn't drop
+ 
+
+ align:start position:0%
+complete and then only if we didn't drop
+into this one or this one do we then go
+
+ align:start position:0%
+into this one or this one do we then go
+ 
+
+ align:start position:0%
+into this one or this one do we then go
+on to create my object so then here we
+
+ align:start position:0%
+on to create my object so then here we
+ 
+
+ align:start position:0%
+on to create my object so then here we
+are these two lines here will uh succeed
+
+ align:start position:0%
+are these two lines here will uh succeed
+ 
+
+ align:start position:0%
+are these two lines here will uh succeed
+right so there's no error raised or
+
+ align:start position:0%
+right so there's no error raised or
+ 
+
+ align:start position:0%
+right so there's no error raised or
+anything like that but then this line
+
+ align:start position:0%
+anything like that but then this line
+ 
+
+ align:start position:0%
+anything like that but then this line
+here raised our value error because we
+
+ align:start position:0%
+here raised our value error because we
+ 
+
+ align:start position:0%
+here raised our value error because we
+tried to create a circle where the
+
+ align:start position:0%
+tried to create a circle where the
+ 
+
+ align:start position:0%
+tried to create a circle where the
+center is an integer right obviously not
+
+ align:start position:0%
+center is an integer right obviously not
+ 
+
+ align:start position:0%
+center is an integer right obviously not
+a coordinate object and then here again
+
+ align:start position:0%
+a coordinate object and then here again
+ 
+
+ align:start position:0%
+a coordinate object and then here again
+we raised our value error because we
+
+ align:start position:0%
+we raised our value error because we
+ 
+
+ align:start position:0%
+we raised our value error because we
+tried to pass in a string as the radius
+
+ align:start position:0%
+tried to pass in a string as the radius
+ 
+
+ align:start position:0%
+tried to pass in a string as the radius
+any questions about this
+
+ align:start position:0%
+any questions about this
+ 
+
+ align:start position:0%
+any questions about this
+code
+
+ align:start position:0%
+code
+ 
+
+ align:start position:0%
+code
+oh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry yeah so it's it's important to
+
+ align:start position:0%
+sorry yeah so it's it's important to
+ 
+
+ align:start position:0%
+sorry yeah so it's it's important to
+place them before you actually create
+
+ align:start position:0%
+place them before you actually create
+ 
+
+ align:start position:0%
+place them before you actually create
+the object right because you don't want
+
+ align:start position:0%
+the object right because you don't want
+ 
+
+ align:start position:0%
+the object right because you don't want
+to create it unless unless uh yeah
+
+ align:start position:0%
+to create it unless unless uh yeah
+ 
+
+ align:start position:0%
+to create it unless unless uh yeah
+unless
+
+ align:start position:0%
+unless
+ 
+
+ align:start position:0%
+unless
+everything's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+appropriate
+
+ align:start position:0%
+appropriate
+ 
+
+ align:start position:0%
+appropriate
+okay so now let's add one more useful
+
+ align:start position:0%
+okay so now let's add one more useful
+ 
+
+ align:start position:0%
+okay so now let's add one more useful
+method to our class
+
+ align:start position:0%
+method to our class
+ 
+
+ align:start position:0%
+method to our class
+Circle now that we've defined a a circle
+
+ align:start position:0%
+Circle now that we've defined a a circle
+ 
+
+ align:start position:0%
+Circle now that we've defined a a circle
+using a center point and a radius we can
+
+ align:start position:0%
+using a center point and a radius we can
+ 
+
+ align:start position:0%
+using a center point and a radius we can
+add this little function that checks if
+
+ align:start position:0%
+add this little function that checks if
+ 
+
+ align:start position:0%
+add this little function that checks if
+another coordinate
+
+ align:start position:0%
+another coordinate
+ 
+
+ align:start position:0%
+another coordinate
+object is inside our
+
+ align:start position:0%
+object is inside our
+ 
+
+ align:start position:0%
+object is inside our
+Circle okay so again I'm not going to be
+
+ align:start position:0%
+Circle okay so again I'm not going to be
+ 
+
+ align:start position:0%
+Circle okay so again I'm not going to be
+able to
+
+ align:start position:0%
+able to
+ 
+
+ align:start position:0%
+able to
+enforce um that this point is a
+
+ align:start position:0%
+enforce um that this point is a
+ 
+
+ align:start position:0%
+enforce um that this point is a
+coordinate object but you know you could
+
+ align:start position:0%
+coordinate object but you know you could
+ 
+
+ align:start position:0%
+coordinate object but you know you could
+do it in the dock string or you could do
+
+ align:start position:0%
+do it in the dock string or you could do
+ 
+
+ align:start position:0%
+do it in the dock string or you could do
+a check or something like that but you
+
+ align:start position:0%
+a check or something like that but you
+ 
+
+ align:start position:0%
+a check or something like that but you
+know again we're just going to assume
+
+ align:start position:0%
+know again we're just going to assume
+ 
+
+ align:start position:0%
+know again we're just going to assume
+the user using this method is going to
+
+ align:start position:0%
+the user using this method is going to
+ 
+
+ align:start position:0%
+the user using this method is going to
+follow the rules so how is this method
+
+ align:start position:0%
+follow the rules so how is this method
+ 
+
+ align:start position:0%
+follow the rules so how is this method
+going to work the idea here is that
+
+ align:start position:0%
+going to work the idea here is that
+ 
+
+ align:start position:0%
+going to work the idea here is that
+we're going to use the center which is a
+
+ align:start position:0%
+we're going to use the center which is a
+ 
+
+ align:start position:0%
+we're going to use the center which is a
+coordinate object and some other point
+
+ align:start position:0%
+coordinate object and some other point
+ 
+
+ align:start position:0%
+coordinate object and some other point
+you know P wherever it may be what we're
+
+ align:start position:0%
+you know P wherever it may be what we're
+ 
+
+ align:start position:0%
+you know P wherever it may be what we're
+going to do is we're going to say what's
+
+ align:start position:0%
+going to do is we're going to say what's
+ 
+
+ align:start position:0%
+going to do is we're going to say what's
+the distance between this point and the
+
+ align:start position:0%
+the distance between this point and the
+ 
+
+ align:start position:0%
+the distance between this point and the
+center of the circle if it's greater
+
+ align:start position:0%
+center of the circle if it's greater
+ 
+
+ align:start position:0%
+center of the circle if it's greater
+than the radius we know the point is
+
+ align:start position:0%
+than the radius we know the point is
+ 
+
+ align:start position:0%
+than the radius we know the point is
+outside the circle if it's smaller than
+
+ align:start position:0%
+outside the circle if it's smaller than
+ 
+
+ align:start position:0%
+outside the circle if it's smaller than
+the radius we know the point is in the
+
+ align:start position:0%
+the radius we know the point is in the
+ 
+
+ align:start position:0%
+the radius we know the point is in the
+circle right so this code is just
+
+ align:start position:0%
+circle right so this code is just
+ 
+
+ align:start position:0%
+circle right so this code is just
+enforcing that so we have uh just a
+
+ align:start position:0%
+enforcing that so we have uh just a
+ 
+
+ align:start position:0%
+enforcing that so we have uh just a
+simple return
+
+ align:start position:0%
+simple return
+ 
+
+ align:start position:0%
+simple return
+statement that's going to run the
+
+ align:start position:0%
+statement that's going to run the
+ 
+
+ align:start position:0%
+statement that's going to run the
+distance method right this is a method
+
+ align:start position:0%
+distance method right this is a method
+ 
+
+ align:start position:0%
+distance method right this is a method
+that we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrote back in the coordinate class right
+
+ align:start position:0%
+wrote back in the coordinate class right
+ 
+
+ align:start position:0%
+wrote back in the coordinate class right
+that's fine because you know what point
+
+ align:start position:0%
+that's fine because you know what point
+ 
+
+ align:start position:0%
+that's fine because you know what point
+is an object of type coordinate and
+
+ align:start position:0%
+is an object of type coordinate and
+ 
+
+ align:start position:0%
+is an object of type coordinate and
+self. Center so the center of this
+
+ align:start position:0%
+self. Center so the center of this
+ 
+
+ align:start position:0%
+self. Center so the center of this
+circle object I'm trying to manipulate
+
+ align:start position:0%
+circle object I'm trying to manipulate
+ 
+
+ align:start position:0%
+circle object I'm trying to manipulate
+right to tell if another point is inside
+
+ align:start position:0%
+right to tell if another point is inside
+ 
+
+ align:start position:0%
+right to tell if another point is inside
+me or not is also a coordinate object
+
+ align:start position:0%
+me or not is also a coordinate object
+ 
+
+ align:start position:0%
+me or not is also a coordinate object
+object so why not we already wrote the
+
+ align:start position:0%
+object so why not we already wrote the
+ 
+
+ align:start position:0%
+object so why not we already wrote the
+code that calculates the distance
+
+ align:start position:0%
+code that calculates the distance
+ 
+
+ align:start position:0%
+code that calculates the distance
+between these two points so let's call
+
+ align:start position:0%
+between these two points so let's call
+ 
+
+ align:start position:0%
+between these two points so let's call
+it so here I've got the thing before the
+
+ align:start position:0%
+it so here I've got the thing before the
+ 
+
+ align:start position:0%
+it so here I've got the thing before the
+dot a coordinate object dot notation the
+
+ align:start position:0%
+dot a coordinate object dot notation the
+ 
+
+ align:start position:0%
+dot a coordinate object dot notation the
+method I want to run on this coordinate
+
+ align:start position:0%
+method I want to run on this coordinate
+ 
+
+ align:start position:0%
+method I want to run on this coordinate
+object and then in parentheses this is
+
+ align:start position:0%
+object and then in parentheses this is
+ 
+
+ align:start position:0%
+object and then in parentheses this is
+another coordinate object so this will
+
+ align:start position:0%
+another coordinate object so this will
+ 
+
+ align:start position:0%
+another coordinate object so this will
+just tell me some number for how far
+
+ align:start position:0%
+just tell me some number for how far
+ 
+
+ align:start position:0%
+just tell me some number for how far
+away these two points are and all we do
+
+ align:start position:0%
+away these two points are and all we do
+ 
+
+ align:start position:0%
+away these two points are and all we do
+is return whether that number is less
+
+ align:start position:0%
+is return whether that number is less
+ 
+
+ align:start position:0%
+is return whether that number is less
+than the
+
+ align:start position:0%
+than the
+ 
+
+ align:start position:0%
+than the
+radius okay does that make
+
+ align:start position:0%
+radius okay does that make
+ 
+
+ align:start position:0%
+radius okay does that make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+and again this only works if point the
+
+ align:start position:0%
+and again this only works if point the
+ 
+
+ align:start position:0%
+and again this only works if point the
+thing that's passed in here is a
+
+ align:start position:0%
+thing that's passed in here is a
+ 
+
+ align:start position:0%
+thing that's passed in here is a
+coordinate object right otherwise this
+
+ align:start position:0%
+coordinate object right otherwise this
+ 
+
+ align:start position:0%
+coordinate object right otherwise this
+code will fail because it's going to try
+
+ align:start position:0%
+code will fail because it's going to try
+ 
+
+ align:start position:0%
+code will fail because it's going to try
+to pass in uh it's going to try to run
+
+ align:start position:0%
+to pass in uh it's going to try to run
+ 
+
+ align:start position:0%
+to pass in uh it's going to try to run
+the distance method on a string for
+
+ align:start position:0%
+the distance method on a string for
+ 
+
+ align:start position:0%
+the distance method on a string for
+example and of course the string doesn't
+
+ align:start position:0%
+example and of course the string doesn't
+ 
+
+ align:start position:0%
+example and of course the string doesn't
+have a distance method right so down
+
+ align:start position:0%
+have a distance method right so down
+ 
+
+ align:start position:0%
+have a distance method right so down
+here uh these two lines are exactly as
+
+ align:start position:0%
+here uh these two lines are exactly as
+ 
+
+ align:start position:0%
+here uh these two lines are exactly as
+we had before we create a circle object
+
+ align:start position:0%
+we had before we create a circle object
+ 
+
+ align:start position:0%
+we had before we create a circle object
+whose Center is at 2 comma 2 and radius
+
+ align:start position:0%
+whose Center is at 2 comma 2 and radius
+ 
+
+ align:start position:0%
+whose Center is at 2 comma 2 and radius
+is two and then I've got another
+
+ align:start position:0%
+is two and then I've got another
+ 
+
+ align:start position:0%
+is two and then I've got another
+coordinate object down down here uh it's
+
+ align:start position:0%
+coordinate object down down here uh it's
+ 
+
+ align:start position:0%
+coordinate object down down here uh it's
+uh at 1 comma 1 right so clearly within
+
+ align:start position:0%
+uh at 1 comma 1 right so clearly within
+ 
+
+ align:start position:0%
+uh at 1 comma 1 right so clearly within
+the circle so that print statement will
+
+ align:start position:0%
+the circle so that print statement will
+ 
+
+ align:start position:0%
+the circle so that print statement will
+then print true right so that's just
+
+ align:start position:0%
+then print true right so that's just
+ 
+
+ align:start position:0%
+then print true right so that's just
+basically what I wrote this is a
+
+ align:start position:0%
+basically what I wrote this is a
+ 
+
+ align:start position:0%
+basically what I wrote this is a
+coordinate object this is the method
+
+ align:start position:0%
+coordinate object this is the method
+ 
+
+ align:start position:0%
+coordinate object this is the method
+this is another coordinate
+
+ align:start position:0%
+this is another coordinate
+ 
+
+ align:start position:0%
+this is another coordinate
+object right so let's run
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so this is exactly the code from the
+
+ align:start position:0%
+it so this is exactly the code from the
+ 
+
+ align:start position:0%
+it so this is exactly the code from the
+slide so if I run this method on a
+
+ align:start position:0%
+slide so if I run this method on a
+ 
+
+ align:start position:0%
+slide so if I run this method on a
+coordinate object that's one comma one
+
+ align:start position:0%
+coordinate object that's one comma one
+ 
+
+ align:start position:0%
+coordinate object that's one comma one
+somewhere in here so true and otherwise
+
+ align:start position:0%
+somewhere in here so true and otherwise
+ 
+
+ align:start position:0%
+somewhere in here so true and otherwise
+if I run it on coordinate object right
+
+ align:start position:0%
+if I run it on coordinate object right
+ 
+
+ align:start position:0%
+if I run it on coordinate object right
+here P 10 comma 10 clearly outside the
+
+ align:start position:0%
+here P 10 comma 10 clearly outside the
+ 
+
+ align:start position:0%
+here P 10 comma 10 clearly outside the
+circle it prints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+false
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay um uh yes that's exactly what I
+
+ align:start position:0%
+okay um uh yes that's exactly what I
+ 
+
+ align:start position:0%
+okay um uh yes that's exactly what I
+said already okay
+
+ align:start position:0%
+said already okay
+ 
+
+ align:start position:0%
+said already okay
+good so now I want you to answer this
+
+ align:start position:0%
+good so now I want you to answer this
+ 
+
+ align:start position:0%
+good so now I want you to answer this
+question nothing to code here but I've
+
+ align:start position:0%
+question nothing to code here but I've
+ 
+
+ align:start position:0%
+question nothing to code here but I've
+got these two is inside method so the
+
+ align:start position:0%
+got these two is inside method so the
+ 
+
+ align:start position:0%
+got these two is inside method so the
+first one here is inside one is exactly
+
+ align:start position:0%
+first one here is inside one is exactly
+ 
+
+ align:start position:0%
+first one here is inside one is exactly
+the one that we just saw right it runs
+
+ align:start position:0%
+the one that we just saw right it runs
+ 
+
+ align:start position:0%
+the one that we just saw right it runs
+dist distance method with point and
+
+ align:start position:0%
+dist distance method with point and
+ 
+
+ align:start position:0%
+dist distance method with point and
+self. Center is inside two looks
+
+ align:start position:0%
+self. Center is inside two looks
+ 
+
+ align:start position:0%
+self. Center is inside two looks
+slightly different the differences I've
+
+ align:start position:0%
+slightly different the differences I've
+ 
+
+ align:start position:0%
+slightly different the differences I've
+highlighted in this box what I'd like
+
+ align:start position:0%
+highlighted in this box what I'd like
+ 
+
+ align:start position:0%
+highlighted in this box what I'd like
+you to tell me we can do a show of hands
+
+ align:start position:0%
+you to tell me we can do a show of hands
+ 
+
+ align:start position:0%
+you to tell me we can do a show of hands
+is are these two function these two
+
+ align:start position:0%
+is are these two function these two
+ 
+
+ align:start position:0%
+is are these two function these two
+methods functionally equivalent that is
+
+ align:start position:0%
+methods functionally equivalent that is
+ 
+
+ align:start position:0%
+methods functionally equivalent that is
+will they return the same thing given
+
+ align:start position:0%
+will they return the same thing given
+ 
+
+ align:start position:0%
+will they return the same thing given
+the same input right so think about it
+
+ align:start position:0%
+the same input right so think about it
+ 
+
+ align:start position:0%
+the same input right so think about it
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+will do a show of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hands so who thinks yes they are
+
+ align:start position:0%
+hands so who thinks yes they are
+ 
+
+ align:start position:0%
+hands so who thinks yes they are
+functionally
+
+ align:start position:0%
+functionally
+ 
+
+ align:start position:0%
+functionally
+equivalent like given the same input
+
+ align:start position:0%
+equivalent like given the same input
+ 
+
+ align:start position:0%
+equivalent like given the same input
+they will both return true right in part
+
+ align:start position:0%
+they will both return true right in part
+ 
+
+ align:start position:0%
+they will both return true right in part
+false okay who thinks no they are not
+
+ align:start position:0%
+false okay who thinks no they are not
+ 
+
+ align:start position:0%
+false okay who thinks no they are not
+functionally
+
+ align:start position:0%
+functionally
+ 
+
+ align:start position:0%
+functionally
+equivalent some half and
+
+ align:start position:0%
+equivalent some half and
+ 
+
+ align:start position:0%
+equivalent some half and
+half okay well let's think about what
+
+ align:start position:0%
+half okay well let's think about what
+ 
+
+ align:start position:0%
+half okay well let's think about what
+the distance method is
+
+ align:start position:0%
+the distance method is
+ 
+
+ align:start position:0%
+the distance method is
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+it's being run on an object of
+
+ align:start position:0%
+it's being run on an object of
+ 
+
+ align:start position:0%
+it's being run on an object of
+type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what coordinate exactly so in here is
+
+ align:start position:0%
+what coordinate exactly so in here is
+ 
+
+ align:start position:0%
+what coordinate exactly so in here is
+point an object of type coordinate yes
+
+ align:start position:0%
+point an object of type coordinate yes
+ 
+
+ align:start position:0%
+point an object of type coordinate yes
+okay and then here what is the a
+
+ align:start position:0%
+okay and then here what is the a
+ 
+
+ align:start position:0%
+okay and then here what is the a
+parameter to the distance method is it
+
+ align:start position:0%
+parameter to the distance method is it
+ 
+
+ align:start position:0%
+parameter to the distance method is it
+object of type coordinate self. Center
+
+ align:start position:0%
+object of type coordinate self. Center
+ 
+
+ align:start position:0%
+object of type coordinate self. Center
+is it an object of type coordinate yes
+
+ align:start position:0%
+is it an object of type coordinate yes
+ 
+
+ align:start position:0%
+is it an object of type coordinate yes
+so now let's look that is inside two
+
+ align:start position:0%
+so now let's look that is inside two
+ 
+
+ align:start position:0%
+so now let's look that is inside two
+what is the type of self.
+
+ align:start position:0%
+what is the type of self.
+ 
+
+ align:start position:0%
+what is the type of self.
+Center coordinate and we're running the
+
+ align:start position:0%
+Center coordinate and we're running the
+ 
+
+ align:start position:0%
+Center coordinate and we're running the
+distance method on this object of type
+
+ align:start position:0%
+distance method on this object of type
+ 
+
+ align:start position:0%
+distance method on this object of type
+coordinate and what is the object in the
+
+ align:start position:0%
+coordinate and what is the object in the
+ 
+
+ align:start position:0%
+coordinate and what is the object in the
+parameter list here what's its
+
+ align:start position:0%
+parameter list here what's its
+ 
+
+ align:start position:0%
+parameter list here what's its
+type
+
+ align:start position:0%
+type
+ 
+
+ align:start position:0%
+type
+coordinate so when we wrote the distance
+
+ align:start position:0%
+coordinate so when we wrote the distance
+ 
+
+ align:start position:0%
+coordinate so when we wrote the distance
+method does it
+
+ align:start position:0%
+method does it
+ 
+
+ align:start position:0%
+method does it
+matter which object we call the method
+
+ align:start position:0%
+matter which object we call the method
+ 
+
+ align:start position:0%
+matter which object we call the method
+on to get the distance between these two
+
+ align:start position:0%
+on to get the distance between these two
+ 
+
+ align:start position:0%
+on to get the distance between these two
+points no right because the distance
+
+ align:start position:0%
+points no right because the distance
+ 
+
+ align:start position:0%
+points no right because the distance
+between say saying I want the distance
+
+ align:start position:0%
+between say saying I want the distance
+ 
+
+ align:start position:0%
+between say saying I want the distance
+between this point and this point is the
+
+ align:start position:0%
+between this point and this point is the
+ 
+
+ align:start position:0%
+between this point and this point is the
+same as saying I want the distance
+
+ align:start position:0%
+same as saying I want the distance
+ 
+
+ align:start position:0%
+same as saying I want the distance
+between this point and this point right
+
+ align:start position:0%
+between this point and this point right
+ 
+
+ align:start position:0%
+between this point and this point right
+it's just the order is
+
+ align:start position:0%
+it's just the order is
+ 
+
+ align:start position:0%
+it's just the order is
+different right so just the way that
+
+ align:start position:0%
+different right so just the way that
+ 
+
+ align:start position:0%
+different right so just the way that
+this distance method works right it
+
+ align:start position:0%
+this distance method works right it
+ 
+
+ align:start position:0%
+this distance method works right it
+doesn't actually matter which object I
+
+ align:start position:0%
+doesn't actually matter which object I
+ 
+
+ align:start position:0%
+doesn't actually matter which object I
+call the method on
+
+ align:start position:0%
+call the method on
+ 
+
+ align:start position:0%
+call the method on
+right as long as they're both coordinate
+
+ align:start position:0%
+right as long as they're both coordinate
+ 
+
+ align:start position:0%
+right as long as they're both coordinate
+objects which they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are does that make sense is that all
+
+ align:start position:0%
+are does that make sense is that all
+ 
+
+ align:start position:0%
+are does that make sense is that all
+right any questions about this for those
+
+ align:start position:0%
+right any questions about this for those
+ 
+
+ align:start position:0%
+right any questions about this for those
+in the not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah self do Center self. Center is an
+
+ align:start position:0%
+yeah self do Center self. Center is an
+ 
+
+ align:start position:0%
+yeah self do Center self. Center is an
+object of type coordinate not
+
+ align:start position:0%
+object of type coordinate not
+ 
+
+ align:start position:0%
+object of type coordinate not
+Circle because so self is a
+
+ align:start position:0%
+Circle because so self is a
+ 
+
+ align:start position:0%
+Circle because so self is a
+circle right because self is is talking
+
+ align:start position:0%
+circle right because self is is talking
+ 
+
+ align:start position:0%
+circle right because self is is talking
+about me the class that I'm currently
+
+ align:start position:0%
+about me the class that I'm currently
+ 
+
+ align:start position:0%
+about me the class that I'm currently
+defining and the class I'm currently
+
+ align:start position:0%
+defining and the class I'm currently
+ 
+
+ align:start position:0%
+defining and the class I'm currently
+defining is a
+
+ align:start position:0%
+defining is a
+ 
+
+ align:start position:0%
+defining is a
+circle but self. center right we even
+
+ align:start position:0%
+circle but self. center right we even
+ 
+
+ align:start position:0%
+circle but self. center right we even
+wrote code we would like to enforce that
+
+ align:start position:0%
+wrote code we would like to enforce that
+ 
+
+ align:start position:0%
+wrote code we would like to enforce that
+it is a cord an object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so we could have put parentheses
+
+ align:start position:0%
+right so we could have put parentheses
+ 
+
+ align:start position:0%
+right so we could have put parentheses
+around this self. Center if we wanted to
+
+ align:start position:0%
+around this self. Center if we wanted to
+ 
+
+ align:start position:0%
+around this self. Center if we wanted to
+and then called the distance on that
+
+ align:start position:0%
+and then called the distance on that
+ 
+
+ align:start position:0%
+and then called the distance on that
+does that make
+
+ align:start position:0%
+does that make
+ 
+
+ align:start position:0%
+does that make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+okay all right so that's all I had
+
+ align:start position:0%
+okay all right so that's all I had
+ 
+
+ align:start position:0%
+okay all right so that's all I had
+regarding the circle class now we're
+
+ align:start position:0%
+regarding the circle class now we're
+ 
+
+ align:start position:0%
+regarding the circle class now we're
+going to switch gears and we're going to
+
+ align:start position:0%
+going to switch gears and we're going to
+ 
+
+ align:start position:0%
+going to switch gears and we're going to
+look at fractions right so numerator
+
+ align:start position:0%
+look at fractions right so numerator
+ 
+
+ align:start position:0%
+look at fractions right so numerator
+slash denominator situation here so
+
+ align:start position:0%
+slash denominator situation here so
+ 
+
+ align:start position:0%
+slash denominator situation here so
+we're gonna create a new data type to
+
+ align:start position:0%
+we're gonna create a new data type to
+ 
+
+ align:start position:0%
+we're gonna create a new data type to
+represent a number as a fraction so
+
+ align:start position:0%
+represent a number as a fraction so
+ 
+
+ align:start position:0%
+represent a number as a fraction so
+first thing we need to do is make the
+
+ align:start position:0%
+first thing we need to do is make the
+ 
+
+ align:start position:0%
+first thing we need to do is make the
+design decision what data will represent
+
+ align:start position:0%
+design decision what data will represent
+ 
+
+ align:start position:0%
+design decision what data will represent
+our fraction so think about it you guys
+
+ align:start position:0%
+our fraction so think about it you guys
+ 
+
+ align:start position:0%
+our fraction so think about it you guys
+tell me what do you think what's a
+
+ align:start position:0%
+tell me what do you think what's a
+ 
+
+ align:start position:0%
+tell me what do you think what's a
+reasonable set of data that could
+
+ align:start position:0%
+reasonable set of data that could
+ 
+
+ align:start position:0%
+reasonable set of data that could
+represent our number as a
+
+ align:start position:0%
+represent our number as a
+ 
+
+ align:start position:0%
+represent our number as a
+fraction when you think of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah a set of two two things maybe
+
+ align:start position:0%
+yeah a set of two two things maybe
+ 
+
+ align:start position:0%
+yeah a set of two two things maybe
+integers right one representing the
+
+ align:start position:0%
+integers right one representing the
+ 
+
+ align:start position:0%
+integers right one representing the
+numerator the thing above the the line
+
+ align:start position:0%
+numerator the thing above the the line
+ 
+
+ align:start position:0%
+numerator the thing above the the line
+and one the denominator the thing below
+
+ align:start position:0%
+and one the denominator the thing below
+ 
+
+ align:start position:0%
+and one the denominator the thing below
+the line good that's exactly what I had
+
+ align:start position:0%
+the line good that's exactly what I had
+ 
+
+ align:start position:0%
+the line good that's exactly what I had
+in mind what are some behaviors of
+
+ align:start position:0%
+in mind what are some behaviors of
+ 
+
+ align:start position:0%
+in mind what are some behaviors of
+fractions you guys tell
+
+ align:start position:0%
+fractions you guys tell
+ 
+
+ align:start position:0%
+fractions you guys tell
+me what should what things should
+
+ align:start position:0%
+me what should what things should
+ 
+
+ align:start position:0%
+me what should what things should
+fractions do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah yes adding them multiplying
+
+ align:start position:0%
+yeah yes adding them multiplying
+ 
+
+ align:start position:0%
+yeah yes adding them multiplying
+fraction
+
+ align:start position:0%
+fraction
+ 
+
+ align:start position:0%
+fraction
+together dividing them uh inverting a
+
+ align:start position:0%
+together dividing them uh inverting a
+ 
+
+ align:start position:0%
+together dividing them uh inverting a
+fraction also something we could do
+
+ align:start position:0%
+fraction also something we could do
+ 
+
+ align:start position:0%
+fraction also something we could do
+right so one over what it currently is
+
+ align:start position:0%
+right so one over what it currently is
+ 
+
+ align:start position:0%
+right so one over what it currently is
+things like that all right so we're
+
+ align:start position:0%
+things like that all right so we're
+ 
+
+ align:start position:0%
+things like that all right so we're
+going to write it together um the full
+
+ align:start position:0%
+going to write it together um the full
+ 
+
+ align:start position:0%
+going to write it together um the full
+code is actually in the python file so
+
+ align:start position:0%
+code is actually in the python file so
+ 
+
+ align:start position:0%
+code is actually in the python file so
+mostly I'm going to go through the
+
+ align:start position:0%
+mostly I'm going to go through the
+ 
+
+ align:start position:0%
+mostly I'm going to go through the
+slides just because it's incremental so
+
+ align:start position:0%
+slides just because it's incremental so
+ 
+
+ align:start position:0%
+slides just because it's incremental so
+it's easier for me to talk about it um
+
+ align:start position:0%
+it's easier for me to talk about it um
+ 
+
+ align:start position:0%
+it's easier for me to talk about it um
+but you know the exact full code is is
+
+ align:start position:0%
+but you know the exact full code is is
+ 
+
+ align:start position:0%
+but you know the exact full code is is
+already in the in the python file if
+
+ align:start position:0%
+already in the in the python file if
+ 
+
+ align:start position:0%
+already in the in the python file if
+you're running it
+
+ align:start position:0%
+you're running it
+ 
+
+ align:start position:0%
+you're running it
+later so the first thing we're going to
+
+ align:start position:0%
+later so the first thing we're going to
+ 
+
+ align:start position:0%
+later so the first thing we're going to
+do is is create this uh fraction class
+
+ align:start position:0%
+do is is create this uh fraction class
+ 
+
+ align:start position:0%
+do is is create this uh fraction class
+and I'm actually going to name it simple
+
+ align:start position:0%
+and I'm actually going to name it simple
+ 
+
+ align:start position:0%
+and I'm actually going to name it simple
+fraction instead of fraction because
+
+ align:start position:0%
+fraction instead of fraction because
+ 
+
+ align:start position:0%
+fraction instead of fraction because
+we're going to improve upon this simple
+
+ align:start position:0%
+we're going to improve upon this simple
+ 
+
+ align:start position:0%
+we're going to improve upon this simple
+fraction object uh in a little bit so
+
+ align:start position:0%
+fraction object uh in a little bit so
+ 
+
+ align:start position:0%
+fraction object uh in a little bit so
+this one I'm just going to call Simple
+
+ align:start position:0%
+this one I'm just going to call Simple
+ 
+
+ align:start position:0%
+this one I'm just going to call Simple
+fraction uh like before it's parent it
+
+ align:start position:0%
+fraction uh like before it's parent it
+ 
+
+ align:start position:0%
+fraction uh like before it's parent it
+is is the generic python object right so
+
+ align:start position:0%
+is is the generic python object right so
+ 
+
+ align:start position:0%
+is is the generic python object right so
+again very very simple it it um you know
+
+ align:start position:0%
+again very very simple it it um you know
+ 
+
+ align:start position:0%
+again very very simple it it um you know
+it doesn't do anything special yet the
+
+ align:start position:0%
+it doesn't do anything special yet the
+ 
+
+ align:start position:0%
+it doesn't do anything special yet the
+first method we need to write is the
+
+ align:start position:0%
+first method we need to write is the
+ 
+
+ align:start position:0%
+first method we need to write is the
+init method so how do we initialize a
+
+ align:start position:0%
+init method so how do we initialize a
+ 
+
+ align:start position:0%
+init method so how do we initialize a
+fraction object obviously we don't want
+
+ align:start position:0%
+fraction object obviously we don't want
+ 
+
+ align:start position:0%
+fraction object obviously we don't want
+the numerator or the denominator to be
+
+ align:start position:0%
+the numerator or the denominator to be
+ 
+
+ align:start position:0%
+the numerator or the denominator to be
+empty right so when we create a simple
+
+ align:start position:0%
+empty right so when we create a simple
+ 
+
+ align:start position:0%
+empty right so when we create a simple
+fraction object we want the user to tell
+
+ align:start position:0%
+fraction object we want the user to tell
+ 
+
+ align:start position:0%
+fraction object we want the user to tell
+us the values for the numerator and the
+
+ align:start position:0%
+us the values for the numerator and the
+ 
+
+ align:start position:0%
+us the values for the numerator and the
+denominator so those are the two
+
+ align:start position:0%
+denominator so those are the two
+ 
+
+ align:start position:0%
+denominator so those are the two
+parameters that I would love the user to
+
+ align:start position:0%
+parameters that I would love the user to
+ 
+
+ align:start position:0%
+parameters that I would love the user to
+uh to uh initiate this fraction
+
+ align:start position:0%
+uh to uh initiate this fraction
+ 
+
+ align:start position:0%
+uh to uh initiate this fraction
+with and then what are going to uh what
+
+ align:start position:0%
+with and then what are going to uh what
+ 
+
+ align:start position:0%
+with and then what are going to uh what
+will be the two uh data attributes that
+
+ align:start position:0%
+will be the two uh data attributes that
+ 
+
+ align:start position:0%
+will be the two uh data attributes that
+we had decided on well numerator so
+
+ align:start position:0%
+we had decided on well numerator so
+ 
+
+ align:start position:0%
+we had decided on well numerator so
+self. num and self. denom will be the
+
+ align:start position:0%
+self. num and self. denom will be the
+ 
+
+ align:start position:0%
+self. num and self. denom will be the
+two data attributes
+
+ align:start position:0%
+two data attributes
+ 
+
+ align:start position:0%
+two data attributes
+right so self. Nom and self. denom are
+
+ align:start position:0%
+right so self. Nom and self. denom are
+ 
+
+ align:start position:0%
+right so self. Nom and self. denom are
+our data attributes and they're going to
+
+ align:start position:0%
+our data attributes and they're going to
+ 
+
+ align:start position:0%
+our data attributes and they're going to
+be set initially to whatever is passed
+
+ align:start position:0%
+be set initially to whatever is passed
+ 
+
+ align:start position:0%
+be set initially to whatever is passed
+in uh that Constructor uh
+
+ align:start position:0%
+in uh that Constructor uh
+ 
+
+ align:start position:0%
+in uh that Constructor uh
+call okay so far so good let's write a
+
+ align:start position:0%
+call okay so far so good let's write a
+ 
+
+ align:start position:0%
+call okay so far so good let's write a
+method that helps us multiply two
+
+ align:start position:0%
+method that helps us multiply two
+ 
+
+ align:start position:0%
+method that helps us multiply two
+fraction objects together so we'll call
+
+ align:start position:0%
+fraction objects together so we'll call
+ 
+
+ align:start position:0%
+fraction objects together so we'll call
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+times so this times method will be
+
+ align:start position:0%
+times so this times method will be
+ 
+
+ align:start position:0%
+times so this times method will be
+called on an object the thing before the
+
+ align:start position:0%
+called on an object the thing before the
+ 
+
+ align:start position:0%
+called on an object the thing before the
+dot that object that thing before the
+
+ align:start position:0%
+dot that object that thing before the
+ 
+
+ align:start position:0%
+dot that object that thing before the
+dot will get mapped to self and then the
+
+ align:start position:0%
+dot will get mapped to self and then the
+ 
+
+ align:start position:0%
+dot will get mapped to self and then the
+thing in the parentheses the one other
+
+ align:start position:0%
+thing in the parentheses the one other
+ 
+
+ align:start position:0%
+thing in the parentheses the one other
+parameter will be mapped to
+
+ align:start position:0%
+parameter will be mapped to
+ 
+
+ align:start position:0%
+parameter will be mapped to
+OT okay so how do we multiply two
+
+ align:start position:0%
+OT okay so how do we multiply two
+ 
+
+ align:start position:0%
+OT okay so how do we multiply two
+fraction objects together take the
+
+ align:start position:0%
+fraction objects together take the
+ 
+
+ align:start position:0%
+fraction objects together take the
+numerators multiply them take the
+
+ align:start position:0%
+numerators multiply them take the
+ 
+
+ align:start position:0%
+numerators multiply them take the
+denominators multiply them you got your
+
+ align:start position:0%
+denominators multiply them you got your
+ 
+
+ align:start position:0%
+denominators multiply them you got your
+new numerator and you got your new
+
+ align:start position:0%
+new numerator and you got your new
+ 
+
+ align:start position:0%
+new numerator and you got your new
+denominator right so how do we grab the
+
+ align:start position:0%
+denominator right so how do we grab the
+ 
+
+ align:start position:0%
+denominator right so how do we grab the
+numerators of both of these objects so
+
+ align:start position:0%
+numerators of both of these objects so
+ 
+
+ align:start position:0%
+numerators of both of these objects so
+the numerator of the thing before the
+
+ align:start position:0%
+the numerator of the thing before the
+ 
+
+ align:start position:0%
+the numerator of the thing before the
+dot right that maps to self is self. n
+
+ align:start position:0%
+dot right that maps to self is self. n
+ 
+
+ align:start position:0%
+dot right that maps to self is self. n
+and the the numerator of the other
+
+ align:start position:0%
+and the the numerator of the other
+ 
+
+ align:start position:0%
+and the the numerator of the other
+object that's going to be in the par
+
+ align:start position:0%
+object that's going to be in the par
+ 
+
+ align:start position:0%
+object that's going to be in the par
+parameter list is the name of my
+
+ align:start position:0%
+parameter list is the name of my
+ 
+
+ align:start position:0%
+parameter list is the name of my
+parameter otth do their numerator
+
+ align:start position:0%
+parameter otth do their numerator
+ 
+
+ align:start position:0%
+parameter otth do their numerator
+no everyone okay so
+
+ align:start position:0%
+no everyone okay so
+ 
+
+ align:start position:0%
+no everyone okay so
+far yes okay I saw some head knots
+
+ align:start position:0%
+far yes okay I saw some head knots
+ 
+
+ align:start position:0%
+far yes okay I saw some head knots
+that's good the denominator will be the
+
+ align:start position:0%
+that's good the denominator will be the
+ 
+
+ align:start position:0%
+that's good the denominator will be the
+same so my new denominator is just
+
+ align:start position:0%
+same so my new denominator is just
+ 
+
+ align:start position:0%
+same so my new denominator is just
+multiplying my denominator the thing
+
+ align:start position:0%
+multiplying my denominator the thing
+ 
+
+ align:start position:0%
+multiplying my denominator the thing
+before the dot with the thing in the
+
+ align:start position:0%
+before the dot with the thing in the
+ 
+
+ align:start position:0%
+before the dot with the thing in the
+parameter denominator okay so I've got
+
+ align:start position:0%
+parameter denominator okay so I've got
+ 
+
+ align:start position:0%
+parameter denominator okay so I've got
+my new numerator my new denominator and
+
+ align:start position:0%
+my new numerator my new denominator and
+ 
+
+ align:start position:0%
+my new numerator my new denominator and
+all I'm going to do is do the division
+
+ align:start position:0%
+all I'm going to do is do the division
+ 
+
+ align:start position:0%
+all I'm going to do is do the division
+and return this value what's the type of
+
+ align:start position:0%
+and return this value what's the type of
+ 
+
+ align:start position:0%
+and return this value what's the type of
+the return here what's this method going
+
+ align:start position:0%
+the return here what's this method going
+ 
+
+ align:start position:0%
+the return here what's this method going
+to return what
+
+ align:start position:0%
+to return what
+ 
+
+ align:start position:0%
+to return what
+type a float exactly yeah good yep
+
+ align:start position:0%
+type a float exactly yeah good yep
+ 
+
+ align:start position:0%
+type a float exactly yeah good yep
+because all I'm doing is dividing one
+
+ align:start position:0%
+because all I'm doing is dividing one
+ 
+
+ align:start position:0%
+because all I'm doing is dividing one
+number by another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+okay perfect so that's uh what I've
+
+ align:start position:0%
+okay perfect so that's uh what I've
+ 
+
+ align:start position:0%
+okay perfect so that's uh what I've
+already said now we can Define another
+
+ align:start position:0%
+already said now we can Define another
+ 
+
+ align:start position:0%
+already said now we can Define another
+method plus to add two uh two fraction
+
+ align:start position:0%
+method plus to add two uh two fraction
+ 
+
+ align:start position:0%
+method plus to add two uh two fraction
+objects together very similar thing
+
+ align:start position:0%
+objects together very similar thing
+ 
+
+ align:start position:0%
+objects together very similar thing
+except the top is going to be slightly
+
+ align:start position:0%
+except the top is going to be slightly
+ 
+
+ align:start position:0%
+except the top is going to be slightly
+different right you take the numerator
+
+ align:start position:0%
+different right you take the numerator
+ 
+
+ align:start position:0%
+different right you take the numerator
+of one times the denominator of the
+
+ align:start position:0%
+of one times the denominator of the
+ 
+
+ align:start position:0%
+of one times the denominator of the
+other plus the numerator of other times
+
+ align:start position:0%
+other plus the numerator of other times
+ 
+
+ align:start position:0%
+other plus the numerator of other times
+the denominator of the first one the
+
+ align:start position:0%
+the denominator of the first one the
+ 
+
+ align:start position:0%
+the denominator of the first one the
+Cris cross thing the denominator is the
+
+ align:start position:0%
+Cris cross thing the denominator is the
+ 
+
+ align:start position:0%
+Cris cross thing the denominator is the
+same right just multiply the denoms
+
+ align:start position:0%
+same right just multiply the denoms
+ 
+
+ align:start position:0%
+same right just multiply the denoms
+together and again we return the
+
+ align:start position:0%
+together and again we return the
+ 
+
+ align:start position:0%
+together and again we return the
+division Top divid by bottom again the
+
+ align:start position:0%
+division Top divid by bottom again the
+ 
+
+ align:start position:0%
+division Top divid by bottom again the
+uh the return of this method will be a
+
+ align:start position:0%
+uh the return of this method will be a
+ 
+
+ align:start position:0%
+uh the return of this method will be a
+float so even though I'm multiplying or
+
+ align:start position:0%
+float so even though I'm multiplying or
+ 
+
+ align:start position:0%
+float so even though I'm multiplying or
+adding these two fraction objects
+
+ align:start position:0%
+adding these two fraction objects
+ 
+
+ align:start position:0%
+adding these two fraction objects
+together my return will be a float fine
+
+ align:start position:0%
+together my return will be a float fine
+ 
+
+ align:start position:0%
+together my return will be a float fine
+so let's run the code I'm creating two
+
+ align:start position:0%
+so let's run the code I'm creating two
+ 
+
+ align:start position:0%
+so let's run the code I'm creating two
+simple fraction objects first one is
+
+ align:start position:0%
+simple fraction objects first one is
+ 
+
+ align:start position:0%
+simple fraction objects first one is
+going to be accessed using variable
+
+ align:start position:0%
+going to be accessed using variable
+ 
+
+ align:start position:0%
+going to be accessed using variable
+named F1 so this one represents the
+
+ align:start position:0%
+named F1 so this one represents the
+ 
+
+ align:start position:0%
+named F1 so this one represents the
+number 3
+
+ align:start position:0%
+number 3
+ 
+
+ align:start position:0%
+number 3
+over4 second one is accessed by variable
+
+ align:start position:0%
+over4 second one is accessed by variable
+ 
+
+ align:start position:0%
+over4 second one is accessed by variable
+named F2 and this one represents the
+
+ align:start position:0%
+named F2 and this one represents the
+ 
+
+ align:start position:0%
+named F2 and this one represents the
+fraction one over4
+
+ align:start position:0%
+fraction one over4
+ 
+
+ align:start position:0%
+fraction one over4
+okay so now if I access the numer
+
+ align:start position:0%
+okay so now if I access the numer
+ 
+
+ align:start position:0%
+okay so now if I access the numer
+numerator of
+
+ align:start position:0%
+numerator of
+ 
+
+ align:start position:0%
+numerator of
+F1 python says well what's the object
+
+ align:start position:0%
+F1 python says well what's the object
+ 
+
+ align:start position:0%
+F1 python says well what's the object
+before the dot it's F1 so what is your
+
+ align:start position:0%
+before the dot it's F1 so what is your
+ 
+
+ align:start position:0%
+before the dot it's F1 so what is your
+numerator well I set it to three so this
+
+ align:start position:0%
+numerator well I set it to three so this
+ 
+
+ align:start position:0%
+numerator well I set it to three so this
+one tells me it's three right pretty
+
+ align:start position:0%
+one tells me it's three right pretty
+ 
+
+ align:start position:0%
+one tells me it's three right pretty
+simple same thing with the denominator
+
+ align:start position:0%
+simple same thing with the denominator
+ 
+
+ align:start position:0%
+simple same thing with the denominator
+of F1 again it looks at the thing before
+
+ align:start position:0%
+of F1 again it looks at the thing before
+ 
+
+ align:start position:0%
+of F1 again it looks at the thing before
+the dot it's a fraction object it says
+
+ align:start position:0%
+the dot it's a fraction object it says
+ 
+
+ align:start position:0%
+the dot it's a fraction object it says
+do you have a dnom a data attribute you
+
+ align:start position:0%
+do you have a dnom a data attribute you
+ 
+
+ align:start position:0%
+do you have a dnom a data attribute you
+do and its value is four so that's
+
+ align:start position:0%
+do and its value is four so that's
+ 
+
+ align:start position:0%
+do and its value is four so that's
+four now what's the result of fub1 do
+
+ align:start position:0%
+four now what's the result of fub1 do
+ 
+
+ align:start position:0%
+four now what's the result of fub1 do
+plus F2 super weird way to write WR it
+
+ align:start position:0%
+plus F2 super weird way to write WR it
+ 
+
+ align:start position:0%
+plus F2 super weird way to write WR it
+but um it's what we've got so far right
+
+ align:start position:0%
+but um it's what we've got so far right
+ 
+
+ align:start position:0%
+but um it's what we've got so far right
+so the thing before the dot is an
+
+ align:start position:0%
+so the thing before the dot is an
+ 
+
+ align:start position:0%
+so the thing before the dot is an
+object it's a simple fraction
+
+ align:start position:0%
+object it's a simple fraction
+ 
+
+ align:start position:0%
+object it's a simple fraction
+object and the thing before the dot
+
+ align:start position:0%
+object and the thing before the dot
+ 
+
+ align:start position:0%
+object and the thing before the dot
+remember maps to self in my parameter
+
+ align:start position:0%
+remember maps to self in my parameter
+ 
+
+ align:start position:0%
+remember maps to self in my parameter
+list right because this it's just a
+
+ align:start position:0%
+list right because this it's just a
+ 
+
+ align:start position:0%
+list right because this it's just a
+function so like usual functions you
+
+ align:start position:0%
+function so like usual functions you
+ 
+
+ align:start position:0%
+function so like usual functions you
+know a a bunch of lectures ago we
+
+ align:start position:0%
+know a a bunch of lectures ago we
+ 
+
+ align:start position:0%
+know a a bunch of lectures ago we
+basically map the actual parameters when
+
+ align:start position:0%
+basically map the actual parameters when
+ 
+
+ align:start position:0%
+basically map the actual parameters when
+we run the function to the formal
+
+ align:start position:0%
+we run the function to the formal
+ 
+
+ align:start position:0%
+we run the function to the formal
+parameters the things for my function
+
+ align:start position:0%
+parameters the things for my function
+ 
+
+ align:start position:0%
+parameters the things for my function
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+so the actual parameter here for self is
+
+ align:start position:0%
+so the actual parameter here for self is
+ 
+
+ align:start position:0%
+so the actual parameter here for self is
+the thing before the dot F1 and the and
+
+ align:start position:0%
+the thing before the dot F1 and the and
+ 
+
+ align:start position:0%
+the thing before the dot F1 and the and
+the uh and the parameter F2 gets mapped
+
+ align:start position:0%
+the uh and the parameter F2 gets mapped
+ 
+
+ align:start position:0%
+the uh and the parameter F2 gets mapped
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+OT that's how we read that so this is
+
+ align:start position:0%
+OT that's how we read that so this is
+ 
+
+ align:start position:0%
+OT that's how we read that so this is
+just doing the the addition right so
+
+ align:start position:0%
+just doing the the addition right so
+ 
+
+ align:start position:0%
+just doing the the addition right so
+this will give me 1.0 because it's a
+
+ align:start position:0%
+this will give me 1.0 because it's a
+ 
+
+ align:start position:0%
+this will give me 1.0 because it's a
+float same with the times the thing
+
+ align:start position:0%
+float same with the times the thing
+ 
+
+ align:start position:0%
+float same with the times the thing
+before the dot maps to self and every
+
+ align:start position:0%
+before the dot maps to self and every
+ 
+
+ align:start position:0%
+before the dot maps to self and every
+other parameter in the parameter list
+
+ align:start position:0%
+other parameter in the parameter list
+ 
+
+ align:start position:0%
+other parameter in the parameter list
+maps to all everything else except for
+
+ align:start position:0%
+maps to all everything else except for
+ 
+
+ align:start position:0%
+maps to all everything else except for
+self so this one will do 3 over 16 to
+
+ align:start position:0%
+self so this one will do 3 over 16 to
+ 
+
+ align:start position:0%
+self so this one will do 3 over 16 to
+give me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+875 okay everyone okay so far the trick
+
+ align:start position:0%
+875 okay everyone okay so far the trick
+ 
+
+ align:start position:0%
+875 okay everyone okay so far the trick
+here is to remember that the thing
+
+ align:start position:0%
+here is to remember that the thing
+ 
+
+ align:start position:0%
+here is to remember that the thing
+before the dot maps to self in the fun
+
+ align:start position:0%
+before the dot maps to self in the fun
+ 
+
+ align:start position:0%
+before the dot maps to self in the fun
+in the method definition and then
+
+ align:start position:0%
+in the method definition and then
+ 
+
+ align:start position:0%
+in the method definition and then
+everything else maps to everything other
+
+ align:start position:0%
+everything else maps to everything other
+ 
+
+ align:start position:0%
+everything else maps to everything other
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+self
+
+ align:start position:0%
+self
+ 
+
+ align:start position:0%
+self
+okay I'm glad everything's okay so far
+
+ align:start position:0%
+okay I'm glad everything's okay so far
+ 
+
+ align:start position:0%
+okay I'm glad everything's okay so far
+because I'm going to get you to write
+
+ align:start position:0%
+because I'm going to get you to write
+ 
+
+ align:start position:0%
+because I'm going to get you to write
+this uh this code here it looks like a
+
+ align:start position:0%
+this uh this code here it looks like a
+ 
+
+ align:start position:0%
+this uh this code here it looks like a
+lot but um the first half of it it is
+
+ align:start position:0%
+lot but um the first half of it it is
+ 
+
+ align:start position:0%
+lot but um the first half of it it is
+just re uh defining the init method for
+
+ align:start position:0%
+just re uh defining the init method for
+ 
+
+ align:start position:0%
+just re uh defining the init method for
+simple fraction I want you to write
+
+ align:start position:0%
+simple fraction I want you to write
+ 
+
+ align:start position:0%
+simple fraction I want you to write
+these two methods and they're going to
+
+ align:start position:0%
+these two methods and they're going to
+ 
+
+ align:start position:0%
+these two methods and they're going to
+be on liners basically so get
+
+ align:start position:0%
+be on liners basically so get
+ 
+
+ align:start position:0%
+be on liners basically so get
+inverse will return something and it
+
+ align:start position:0%
+inverse will return something and it
+ 
+
+ align:start position:0%
+inverse will return something and it
+returns a float representing one over
+
+ align:start position:0%
+returns a float representing one over
+ 
+
+ align:start position:0%
+returns a float representing one over
+myself right so if the input as is in
+
+ align:start position:0%
+myself right so if the input as is in
+ 
+
+ align:start position:0%
+myself right so if the input as is in
+this example here if I have a simple
+
+ align:start position:0%
+this example here if I have a simple
+ 
+
+ align:start position:0%
+this example here if I have a simple
+fraction object representing 3 over
+
+ align:start position:0%
+fraction object representing 3 over
+ 
+
+ align:start position:0%
+fraction object representing 3 over
+4 if I call get inverse on it right here
+
+ align:start position:0%
+4 if I call get inverse on it right here
+ 
+
+ align:start position:0%
+4 if I call get inverse on it right here
+f1. get inverse self becomes F1 and I
+
+ align:start position:0%
+f1. get inverse self becomes F1 and I
+ 
+
+ align:start position:0%
+f1. get inverse self becomes F1 and I
+would like it to return and therefore
+
+ align:start position:0%
+would like it to return and therefore
+ 
+
+ align:start position:0%
+would like it to return and therefore
+print 4 over3 so 1.3 3 3 3 3 3 3 okay
+
+ align:start position:0%
+print 4 over3 so 1.3 3 3 3 3 3 3 okay
+ 
+
+ align:start position:0%
+print 4 over3 so 1.3 3 3 3 3 3 3 okay
+that's get inverse and then invert is a
+
+ align:start position:0%
+that's get inverse and then invert is a
+ 
+
+ align:start position:0%
+that's get inverse and then invert is a
+method that doesn't return anything so
+
+ align:start position:0%
+method that doesn't return anything so
+ 
+
+ align:start position:0%
+method that doesn't return anything so
+it returns none and instead it just
+
+ align:start position:0%
+it returns none and instead it just
+ 
+
+ align:start position:0%
+it returns none and instead it just
+internally switches the numerator and
+
+ align:start position:0%
+internally switches the numerator and
+ 
+
+ align:start position:0%
+internally switches the numerator and
+the denominator of self right so self's
+
+ align:start position:0%
+the denominator of self right so self's
+ 
+
+ align:start position:0%
+the denominator of self right so self's
+numerator becomes whatever its
+
+ align:start position:0%
+numerator becomes whatever its
+ 
+
+ align:start position:0%
+numerator becomes whatever its
+denominator is and the other way around
+
+ align:start position:0%
+denominator is and the other way around
+ 
+
+ align:start position:0%
+denominator is and the other way around
+right so when you call it this one
+
+ align:start position:0%
+right so when you call it this one
+ 
+
+ align:start position:0%
+right so when you call it this one
+doesn't print anything but instead if we
+
+ align:start position:0%
+doesn't print anything but instead if we
+ 
+
+ align:start position:0%
+doesn't print anything but instead if we
+access f1's numerator and denominator
+
+ align:start position:0%
+access f1's numerator and denominator
+ 
+
+ align:start position:0%
+access f1's numerator and denominator
+they will have been
+
+ align:start position:0%
+they will have been
+ 
+
+ align:start position:0%
+they will have been
+switched okay so this is down on
+
+ align:start position:0%
+switched okay so this is down on
+ 
+
+ align:start position:0%
+switched okay so this is down on
+line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+133 give you a couple moments and then
+
+ align:start position:0%
+133 give you a couple moments and then
+ 
+
+ align:start position:0%
+133 give you a couple moments and then
+we can write it together should not be a
+
+ align:start position:0%
+we can write it together should not be a
+ 
+
+ align:start position:0%
+we can write it together should not be a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+code okay how do we write the get
+
+ align:start position:0%
+code okay how do we write the get
+ 
+
+ align:start position:0%
+code okay how do we write the get
+inverse so remember you have to return
+
+ align:start position:0%
+inverse so remember you have to return
+ 
+
+ align:start position:0%
+inverse so remember you have to return
+something how do we return yeah one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over one over
+
+ align:start position:0%
+over one over
+ 
+
+ align:start position:0%
+over one over
+self so remember self is an object of
+
+ align:start position:0%
+self so remember self is an object of
+ 
+
+ align:start position:0%
+self so remember self is an object of
+type simple fraction right so we need to
+
+ align:start position:0%
+type simple fraction right so we need to
+ 
+
+ align:start position:0%
+type simple fraction right so we need to
+manipulate its numerator and the
+
+ align:start position:0%
+manipulate its numerator and the
+ 
+
+ align:start position:0%
+manipulate its numerator and the
+denominator if we want to do the return
+
+ align:start position:0%
+denominator if we want to do the return
+ 
+
+ align:start position:0%
+denominator if we want to do the return
+because if we just do
+
+ align:start position:0%
+because if we just do
+ 
+
+ align:start position:0%
+because if we just do
+this um is it this one yeah this one
+
+ align:start position:0%
+this um is it this one yeah this one
+ 
+
+ align:start position:0%
+this um is it this one yeah this one
+here then python says oh sorry it's
+
+ align:start position:0%
+here then python says oh sorry it's
+ 
+
+ align:start position:0%
+here then python says oh sorry it's
+trying to divide one an integer by an
+
+ align:start position:0%
+trying to divide one an integer by an
+ 
+
+ align:start position:0%
+trying to divide one an integer by an
+object of types simple fraction right
+
+ align:start position:0%
+object of types simple fraction right
+ 
+
+ align:start position:0%
+object of types simple fraction right
+and that's the error that we get here
+
+ align:start position:0%
+and that's the error that we get here
+ 
+
+ align:start position:0%
+and that's the error that we get here
+and it doesn't know how to do a division
+
+ align:start position:0%
+and it doesn't know how to do a division
+ 
+
+ align:start position:0%
+and it doesn't know how to do a division
+between an integer and a simple fraction
+
+ align:start position:0%
+between an integer and a simple fraction
+ 
+
+ align:start position:0%
+between an integer and a simple fraction
+so how can we do that by working with
+
+ align:start position:0%
+so how can we do that by working with
+ 
+
+ align:start position:0%
+so how can we do that by working with
+actual numbers that are part of my
+
+ align:start position:0%
+actual numbers that are part of my
+ 
+
+ align:start position:0%
+actual numbers that are part of my
+simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fraction anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah self. denom divided by self. num
+
+ align:start position:0%
+yeah self. denom divided by self. num
+ 
+
+ align:start position:0%
+yeah self. denom divided by self. num
+yep we can do that yep or one over self.
+
+ align:start position:0%
+yep we can do that yep or one over self.
+ 
+
+ align:start position:0%
+yep we can do that yep or one over self.
+num divid by self. D num that's also
+
+ align:start position:0%
+num divid by self. D num that's also
+ 
+
+ align:start position:0%
+num divid by self. D num that's also
+fine yeah but this is a little bit
+
+ align:start position:0%
+fine yeah but this is a little bit
+ 
+
+ align:start position:0%
+fine yeah but this is a little bit
+cleaner so now dnom is an integer right
+
+ align:start position:0%
+cleaner so now dnom is an integer right
+ 
+
+ align:start position:0%
+cleaner so now dnom is an integer right
+because when we create it we pass in int
+
+ align:start position:0%
+because when we create it we pass in int
+ 
+
+ align:start position:0%
+because when we create it we pass in int
+int so Dam and num are integers which
+
+ align:start position:0%
+int so Dam and num are integers which
+ 
+
+ align:start position:0%
+int so Dam and num are integers which
+means that python knows how to do a
+
+ align:start position:0%
+means that python knows how to do a
+ 
+
+ align:start position:0%
+means that python knows how to do a
+division between a number and another
+
+ align:start position:0%
+division between a number and another
+ 
+
+ align:start position:0%
+division between a number and another
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+yeah so if we run that now it prints
+
+ align:start position:0%
+yeah so if we run that now it prints
+ 
+
+ align:start position:0%
+yeah so if we run that now it prints
+1.33333 exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay how do we do the invert function
+
+ align:start position:0%
+okay how do we do the invert function
+ 
+
+ align:start position:0%
+okay how do we do the invert function
+method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry sorry go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that yeah yep that's one way to do
+
+ align:start position:0%
+like that yeah yep that's one way to do
+ 
+
+ align:start position:0%
+like that yeah yep that's one way to do
+it yep so you can see now accessing the
+
+ align:start position:0%
+it yep so you can see now accessing the
+ 
+
+ align:start position:0%
+it yep so you can see now accessing the
+new numerator and denominator gives me
+
+ align:start position:0%
+new numerator and denominator gives me
+ 
+
+ align:start position:0%
+new numerator and denominator gives me
+four over three any other ways that
+
+ align:start position:0%
+four over three any other ways that
+ 
+
+ align:start position:0%
+four over three any other ways that
+you've done it yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep the tupo trick I like
+
+ align:start position:0%
+yep the tupo trick I like
+ 
+
+ align:start position:0%
+yep the tupo trick I like
+it self done
+
+ align:start position:0%
+it self done
+ 
+
+ align:start position:0%
+it self done
+yep perfect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes oh okay yeah that also works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah perfect all all very valid ways of
+
+ align:start position:0%
+yeah perfect all all very valid ways of
+ 
+
+ align:start position:0%
+yeah perfect all all very valid ways of
+of doing it nice yep so notice this
+
+ align:start position:0%
+of doing it nice yep so notice this
+ 
+
+ align:start position:0%
+of doing it nice yep so notice this
+there's no return for this one right I
+
+ align:start position:0%
+there's no return for this one right I
+ 
+
+ align:start position:0%
+there's no return for this one right I
+didn't want to return anything python
+
+ align:start position:0%
+didn't want to return anything python
+ 
+
+ align:start position:0%
+didn't want to return anything python
+will automatically return none and these
+
+ align:start position:0%
+will automatically return none and these
+ 
+
+ align:start position:0%
+will automatically return none and these
+internal uh numerator and denominators
+
+ align:start position:0%
+internal uh numerator and denominators
+ 
+
+ align:start position:0%
+internal uh numerator and denominators
+will have been flipped
+
+ align:start position:0%
+will have been flipped
+ 
+
+ align:start position:0%
+will have been flipped
+perfect questions about this
+
+ align:start position:0%
+perfect questions about this
+ 
+
+ align:start position:0%
+perfect questions about this
+code
+
+ align:start position:0%
+code
+ 
+
+ align:start position:0%
+code
+okay so let's try it out a little bit
+
+ align:start position:0%
+okay so let's try it out a little bit
+ 
+
+ align:start position:0%
+okay so let's try it out a little bit
+more so here I've got these two uh
+
+ align:start position:0%
+more so here I've got these two uh
+ 
+
+ align:start position:0%
+more so here I've got these two uh
+additions right so um this is exactly
+
+ align:start position:0%
+additions right so um this is exactly
+ 
+
+ align:start position:0%
+additions right so um this is exactly
+what we had previously the exact same
+
+ align:start position:0%
+what we had previously the exact same
+ 
+
+ align:start position:0%
+what we had previously the exact same
+code code what's weird though and you
+
+ align:start position:0%
+code code what's weird though and you
+ 
+
+ align:start position:0%
+code code what's weird though and you
+might have been um uh weirded out by
+
+ align:start position:0%
+might have been um uh weirded out by
+ 
+
+ align:start position:0%
+might have been um uh weirded out by
+this too when we first ran it is I am
+
+ align:start position:0%
+this too when we first ran it is I am
+ 
+
+ align:start position:0%
+this too when we first ran it is I am
+doing operations with two fraction
+
+ align:start position:0%
+doing operations with two fraction
+ 
+
+ align:start position:0%
+doing operations with two fraction
+objects and yet the plus and the m and
+
+ align:start position:0%
+objects and yet the plus and the m and
+ 
+
+ align:start position:0%
+objects and yet the plus and the m and
+the times methods give me floats which
+
+ align:start position:0%
+the times methods give me floats which
+ 
+
+ align:start position:0%
+the times methods give me floats which
+is a little weird right ideally if we're
+
+ align:start position:0%
+is a little weird right ideally if we're
+ 
+
+ align:start position:0%
+is a little weird right ideally if we're
+working with fraction objects I would
+
+ align:start position:0%
+working with fraction objects I would
+ 
+
+ align:start position:0%
+working with fraction objects I would
+like the return to also be a fraction
+
+ align:start position:0%
+like the return to also be a fraction
+ 
+
+ align:start position:0%
+like the return to also be a fraction
+object so I can then work with more
+
+ align:start position:0%
+object so I can then work with more
+ 
+
+ align:start position:0%
+object so I can then work with more
+fraction objects later on that's one
+
+ align:start position:0%
+fraction objects later on that's one
+ 
+
+ align:start position:0%
+fraction objects later on that's one
+weird thing another weird thing is if if
+
+ align:start position:0%
+weird thing another weird thing is if if
+ 
+
+ align:start position:0%
+weird thing another weird thing is if if
+we then print one of our objects that
+
+ align:start position:0%
+we then print one of our objects that
+ 
+
+ align:start position:0%
+we then print one of our objects that
+we've created F1 in this case we use
+
+ align:start position:0%
+we've created F1 in this case we use
+ 
+
+ align:start position:0%
+we've created F1 in this case we use
+print statements often right to debug
+
+ align:start position:0%
+print statements often right to debug
+ 
+
+ align:start position:0%
+print statements often right to debug
+and things like that if I use the print
+
+ align:start position:0%
+and things like that if I use the print
+ 
+
+ align:start position:0%
+and things like that if I use the print
+statement on an object of type that I've
+
+ align:start position:0%
+statement on an object of type that I've
+ 
+
+ align:start position:0%
+statement on an object of type that I've
+created in this case a simple fraction
+
+ align:start position:0%
+created in this case a simple fraction
+ 
+
+ align:start position:0%
+created in this case a simple fraction
+python spits this
+
+ align:start position:0%
+python spits this
+ 
+
+ align:start position:0%
+python spits this
+out it says hey your object is an object
+
+ align:start position:0%
+out it says hey your object is an object
+ 
+
+ align:start position:0%
+out it says hey your object is an object
+of type simple fraction at this memory
+
+ align:start position:0%
+of type simple fraction at this memory
+ 
+
+ align:start position:0%
+of type simple fraction at this memory
+location no thank you that's not very
+
+ align:start position:0%
+location no thank you that's not very
+ 
+
+ align:start position:0%
+location no thank you that's not very
+useful to me right what I'd like to know
+
+ align:start position:0%
+useful to me right what I'd like to know
+ 
+
+ align:start position:0%
+useful to me right what I'd like to know
+is maybe a nice represent of my fraction
+
+ align:start position:0%
+is maybe a nice represent of my fraction
+ 
+
+ align:start position:0%
+is maybe a nice represent of my fraction
+object like
+
+ align:start position:0%
+object like
+ 
+
+ align:start position:0%
+object like
+34 right I don't care about what memory
+
+ align:start position:0%
+34 right I don't care about what memory
+ 
+
+ align:start position:0%
+34 right I don't care about what memory
+location it's at and one more thing we'd
+
+ align:start position:0%
+location it's at and one more thing we'd
+ 
+
+ align:start position:0%
+location it's at and one more thing we'd
+like to try to do this is a class that
+
+ align:start position:0%
+like to try to do this is a class that
+ 
+
+ align:start position:0%
+like to try to do this is a class that
+that represents something numerical so
+
+ align:start position:0%
+that represents something numerical so
+ 
+
+ align:start position:0%
+that represents something numerical so
+something that people might
+
+ align:start position:0%
+something that people might
+ 
+
+ align:start position:0%
+something that people might
+instinctually want to do is to use
+
+ align:start position:0%
+instinctually want to do is to use
+ 
+
+ align:start position:0%
+instinctually want to do is to use
+operators like the star or the Plus or
+
+ align:start position:0%
+operators like the star or the Plus or
+ 
+
+ align:start position:0%
+operators like the star or the Plus or
+the slash right to divide add multiply
+
+ align:start position:0%
+the slash right to divide add multiply
+ 
+
+ align:start position:0%
+the slash right to divide add multiply
+these fraction things but if we run the
+
+ align:start position:0%
+these fraction things but if we run the
+ 
+
+ align:start position:0%
+these fraction things but if we run the
+star operator between object of type
+
+ align:start position:0%
+star operator between object of type
+ 
+
+ align:start position:0%
+star operator between object of type
+simple fraction right times another
+
+ align:start position:0%
+simple fraction right times another
+ 
+
+ align:start position:0%
+simple fraction right times another
+object times of type simple fraction
+
+ align:start position:0%
+object times of type simple fraction
+ 
+
+ align:start position:0%
+object times of type simple fraction
+python gives us an error um and I'll
+
+ align:start position:0%
+python gives us an error um and I'll
+ 
+
+ align:start position:0%
+python gives us an error um and I'll
+even show you the
+
+ align:start position:0%
+even show you the
+ 
+
+ align:start position:0%
+even show you the
+error
+
+ align:start position:0%
+error
+ 
+
+ align:start position:0%
+error
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here right so here I am printing my
+
+ align:start position:0%
+here right so here I am printing my
+ 
+
+ align:start position:0%
+here right so here I am printing my
+object right so it spits this out which
+
+ align:start position:0%
+object right so it spits this out which
+ 
+
+ align:start position:0%
+object right so it spits this out which
+is fine but not what I want this one you
+
+ align:start position:0%
+is fine but not what I want this one you
+ 
+
+ align:start position:0%
+is fine but not what I want this one you
+know obviously we've seen this it
+
+ align:start position:0%
+know obviously we've seen this it
+ 
+
+ align:start position:0%
+know obviously we've seen this it
+already prints this out and then if I
+
+ align:start position:0%
+already prints this out and then if I
+ 
+
+ align:start position:0%
+already prints this out and then if I
+try to multiply my two simple fraction
+
+ align:start position:0%
+try to multiply my two simple fraction
+ 
+
+ align:start position:0%
+try to multiply my two simple fraction
+object objects together it says I don't
+
+ align:start position:0%
+object objects together it says I don't
+ 
+
+ align:start position:0%
+object objects together it says I don't
+know how to do that right so it's
+
+ align:start position:0%
+know how to do that right so it's
+ 
+
+ align:start position:0%
+know how to do that right so it's
+unsupported operan types so the operant
+
+ align:start position:0%
+unsupported operan types so the operant
+ 
+
+ align:start position:0%
+unsupported operan types so the operant
+simple fraction and simple fraction are
+
+ align:start position:0%
+simple fraction and simple fraction are
+ 
+
+ align:start position:0%
+simple fraction and simple fraction are
+not supported with the star operator
+
+ align:start position:0%
+not supported with the star operator
+ 
+
+ align:start position:0%
+not supported with the star operator
+well no surprise there how is python
+
+ align:start position:0%
+well no surprise there how is python
+ 
+
+ align:start position:0%
+well no surprise there how is python
+supposed to know how to multiply two
+
+ align:start position:0%
+supposed to know how to multiply two
+ 
+
+ align:start position:0%
+supposed to know how to multiply two
+simple fraction objects together right
+
+ align:start position:0%
+simple fraction objects together right
+ 
+
+ align:start position:0%
+simple fraction objects together right
+right before I even ran this program I
+
+ align:start position:0%
+right before I even ran this program I
+ 
+
+ align:start position:0%
+right before I even ran this program I
+didn't even know what a simple fraction
+
+ align:start position:0%
+didn't even know what a simple fraction
+ 
+
+ align:start position:0%
+didn't even know what a simple fraction
+object was right so we need to tell it
+
+ align:start position:0%
+object was right so we need to tell it
+ 
+
+ align:start position:0%
+object was right so we need to tell it
+all of these
+
+ align:start position:0%
+all of these
+ 
+
+ align:start position:0%
+all of these
+details and we will do just that
+
+ align:start position:0%
+details and we will do just that
+ 
+
+ align:start position:0%
+details and we will do just that
+so all of these um uh operators print
+
+ align:start position:0%
+so all of these um uh operators print
+ 
+
+ align:start position:0%
+so all of these um uh operators print
+Len that we've been using Star ad right
+
+ align:start position:0%
+Len that we've been using Star ad right
+ 
+
+ align:start position:0%
+Len that we've been using Star ad right
+less than greater than even the square
+
+ align:start position:0%
+less than greater than even the square
+ 
+
+ align:start position:0%
+less than greater than even the square
+brackets to index into something these
+
+ align:start position:0%
+brackets to index into something these
+ 
+
+ align:start position:0%
+brackets to index into something these
+are actually shorthand notations right
+
+ align:start position:0%
+are actually shorthand notations right
+ 
+
+ align:start position:0%
+are actually shorthand notations right
+they're really common operations that
+
+ align:start position:0%
+they're really common operations that
+ 
+
+ align:start position:0%
+they're really common operations that
+you want to do and python lets you use
+
+ align:start position:0%
+you want to do and python lets you use
+ 
+
+ align:start position:0%
+you want to do and python lets you use
+these common operations in instead of
+
+ align:start position:0%
+these common operations in instead of
+ 
+
+ align:start position:0%
+these common operations in instead of
+writing these really verbose function
+
+ align:start position:0%
+writing these really verbose function
+ 
+
+ align:start position:0%
+writing these really verbose function
+names but really behind the
+
+ align:start position:0%
+names but really behind the
+ 
+
+ align:start position:0%
+names but really behind the
+scenes all of these shorthand operations
+
+ align:start position:0%
+scenes all of these shorthand operations
+ 
+
+ align:start position:0%
+scenes all of these shorthand operations
+actually run a
+
+ align:start position:0%
+actually run a
+ 
+
+ align:start position:0%
+actually run a
+method okay again not a secret I'm not
+
+ align:start position:0%
+method okay again not a secret I'm not
+ 
+
+ align:start position:0%
+method okay again not a secret I'm not
+lowering my voice because it's a secret
+
+ align:start position:0%
+lowering my voice because it's a secret
+ 
+
+ align:start position:0%
+lowering my voice because it's a secret
+but it's just it's really cool so all of
+
+ align:start position:0%
+but it's just it's really cool so all of
+ 
+
+ align:start position:0%
+but it's just it's really cool so all of
+these operations like the multiplication
+
+ align:start position:0%
+these operations like the multiplication
+ 
+
+ align:start position:0%
+these operations like the multiplication
+or the print statement just gets
+
+ align:start position:0%
+or the print statement just gets
+ 
+
+ align:start position:0%
+or the print statement just gets
+replaced with a method okay and the
+
+ align:start position:0%
+replaced with a method okay and the
+ 
+
+ align:start position:0%
+replaced with a method okay and the
+method names look like this they are
+
+ align:start position:0%
+method names look like this they are
+ 
+
+ align:start position:0%
+method names look like this they are
+Dunder methods just like the init method
+
+ align:start position:0%
+Dunder methods just like the init method
+ 
+
+ align:start position:0%
+Dunder methods just like the init method
+was a special method that python ran
+
+ align:start position:0%
+was a special method that python ran
+ 
+
+ align:start position:0%
+was a special method that python ran
+when something special happened like
+
+ align:start position:0%
+when something special happened like
+ 
+
+ align:start position:0%
+when something special happened like
+you're creating an object
+
+ align:start position:0%
+you're creating an object
+ 
+
+ align:start position:0%
+you're creating an object
+well when something special happens like
+
+ align:start position:0%
+well when something special happens like
+ 
+
+ align:start position:0%
+well when something special happens like
+you're using the plus operator between
+
+ align:start position:0%
+you're using the plus operator between
+ 
+
+ align:start position:0%
+you're using the plus operator between
+an object of your type and something
+
+ align:start position:0%
+an object of your type and something
+ 
+
+ align:start position:0%
+an object of your type and something
+else python will also run this special
+
+ align:start position:0%
+else python will also run this special
+ 
+
+ align:start position:0%
+else python will also run this special
+Dunder method behind the scenes right
+
+ align:start position:0%
+Dunder method behind the scenes right
+ 
+
+ align:start position:0%
+Dunder method behind the scenes right
+and same here if I want to multiply my
+
+ align:start position:0%
+and same here if I want to multiply my
+ 
+
+ align:start position:0%
+and same here if I want to multiply my
+object with something else python will
+
+ align:start position:0%
+object with something else python will
+ 
+
+ align:start position:0%
+object with something else python will
+run this special Dunder method behind
+
+ align:start position:0%
+run this special Dunder method behind
+ 
+
+ align:start position:0%
+run this special Dunder method behind
+the scenes if I want to print an object
+
+ align:start position:0%
+the scenes if I want to print an object
+ 
+
+ align:start position:0%
+the scenes if I want to print an object
+of my type python will run this special
+
+ align:start position:0%
+of my type python will run this special
+ 
+
+ align:start position:0%
+of my type python will run this special
+Dunder method behind the scenes right um
+
+ align:start position:0%
+Dunder method behind the scenes right um
+ 
+
+ align:start position:0%
+Dunder method behind the scenes right um
+even something like casting if I want to
+
+ align:start position:0%
+even something like casting if I want to
+ 
+
+ align:start position:0%
+even something like casting if I want to
+cast my object to to a float or to a
+
+ align:start position:0%
+cast my object to to a float or to a
+ 
+
+ align:start position:0%
+cast my object to to a float or to a
+string or something python will run this
+
+ align:start position:0%
+string or something python will run this
+ 
+
+ align:start position:0%
+string or something python will run this
+special Dunder method behind the scenes
+
+ align:start position:0%
+special Dunder method behind the scenes
+ 
+
+ align:start position:0%
+special Dunder method behind the scenes
+um and then you know there's a whole
+
+ align:start position:0%
+um and then you know there's a whole
+ 
+
+ align:start position:0%
+um and then you know there's a whole
+bunch of other ones even indexing into a
+
+ align:start position:0%
+bunch of other ones even indexing into a
+ 
+
+ align:start position:0%
+bunch of other ones even indexing into a
+list or sorry not a list indexing into
+
+ align:start position:0%
+list or sorry not a list indexing into
+ 
+
+ align:start position:0%
+list or sorry not a list indexing into
+an object of your type so if you make an
+
+ align:start position:0%
+an object of your type so if you make an
+ 
+
+ align:start position:0%
+an object of your type so if you make an
+object like a q or a stack where you
+
+ align:start position:0%
+object like a q or a stack where you
+ 
+
+ align:start position:0%
+object like a q or a stack where you
+know you have a bunch of sequences of
+
+ align:start position:0%
+know you have a bunch of sequences of
+ 
+
+ align:start position:0%
+know you have a bunch of sequences of
+objects you can tell python how to index
+
+ align:start position:0%
+objects you can tell python how to index
+ 
+
+ align:start position:0%
+objects you can tell python how to index
+into an object of your type into an
+
+ align:start position:0%
+into an object of your type into an
+ 
+
+ align:start position:0%
+into an object of your type into an
+object that's a q right so all of these
+
+ align:start position:0%
+object that's a q right so all of these
+ 
+
+ align:start position:0%
+object that's a q right so all of these
+things uh um all of these methods need
+
+ align:start position:0%
+things uh um all of these methods need
+ 
+
+ align:start position:0%
+things uh um all of these methods need
+to be implemented somewhere now most of
+
+ align:start position:0%
+to be implemented somewhere now most of
+ 
+
+ align:start position:0%
+to be implemented somewhere now most of
+them are not implemented in the basic uh
+
+ align:start position:0%
+them are not implemented in the basic uh
+ 
+
+ align:start position:0%
+them are not implemented in the basic uh
+python object except for the Str Str so
+
+ align:start position:0%
+python object except for the Str Str so
+ 
+
+ align:start position:0%
+python object except for the Str Str so
+the Str Str method actually just prints
+
+ align:start position:0%
+the Str Str method actually just prints
+ 
+
+ align:start position:0%
+the Str Str method actually just prints
+the memory location of this object
+
+ align:start position:0%
+the memory location of this object
+ 
+
+ align:start position:0%
+the memory location of this object
+that's exactly what we had seen right by
+
+ align:start position:0%
+that's exactly what we had seen right by
+ 
+
+ align:start position:0%
+that's exactly what we had seen right by
+the default Behavior but none of these
+
+ align:start position:0%
+the default Behavior but none of these
+ 
+
+ align:start position:0%
+the default Behavior but none of these
+other ones are really implemented and so
+
+ align:start position:0%
+other ones are really implemented and so
+ 
+
+ align:start position:0%
+other ones are really implemented and so
+if you want the object that you're
+
+ align:start position:0%
+if you want the object that you're
+ 
+
+ align:start position:0%
+if you want the object that you're
+currently writing to work with the star
+
+ align:start position:0%
+currently writing to work with the star
+ 
+
+ align:start position:0%
+currently writing to work with the star
+or the Plus or the double equal sign to
+
+ align:start position:0%
+or the Plus or the double equal sign to
+ 
+
+ align:start position:0%
+or the Plus or the double equal sign to
+test for test for equality between this
+
+ align:start position:0%
+test for test for equality between this
+ 
+
+ align:start position:0%
+test for test for equality between this
+object and and something else you have
+
+ align:start position:0%
+object and and something else you have
+ 
+
+ align:start position:0%
+object and and something else you have
+to write the method in your class
+
+ align:start position:0%
+to write the method in your class
+ 
+
+ align:start position:0%
+to write the method in your class
+definition okay so you have to implement
+
+ align:start position:0%
+definition okay so you have to implement
+ 
+
+ align:start position:0%
+definition okay so you have to implement
+it to tell python that this is what you
+
+ align:start position:0%
+it to tell python that this is what you
+ 
+
+ align:start position:0%
+it to tell python that this is what you
+want to do when somebody uses this
+
+ align:start position:0%
+want to do when somebody uses this
+ 
+
+ align:start position:0%
+want to do when somebody uses this
+special shorthand notation so let's
+
+ align:start position:0%
+special shorthand notation so let's
+ 
+
+ align:start position:0%
+special shorthand notation so let's
+start with the print because it's the
+
+ align:start position:0%
+start with the print because it's the
+ 
+
+ align:start position:0%
+start with the print because it's the
+most basic thing you will probably want
+
+ align:start position:0%
+most basic thing you will probably want
+ 
+
+ align:start position:0%
+most basic thing you will probably want
+to implement when you create a new data
+
+ align:start position:0%
+to implement when you create a new data
+ 
+
+ align:start position:0%
+to implement when you create a new data
+type right for debugging purposes you'll
+
+ align:start position:0%
+type right for debugging purposes you'll
+ 
+
+ align:start position:0%
+type right for debugging purposes you'll
+find yourself Instinct saying hey print
+
+ align:start position:0%
+find yourself Instinct saying hey print
+ 
+
+ align:start position:0%
+find yourself Instinct saying hey print
+you know F1 to print this fraction
+
+ align:start position:0%
+you know F1 to print this fraction
+ 
+
+ align:start position:0%
+you know F1 to print this fraction
+object to see what it looks like and so
+
+ align:start position:0%
+object to see what it looks like and so
+ 
+
+ align:start position:0%
+object to see what it looks like and so
+the Str Str method is one of the really
+
+ align:start position:0%
+the Str Str method is one of the really
+ 
+
+ align:start position:0%
+the Str Str method is one of the really
+basic things you should Implement right
+
+ align:start position:0%
+basic things you should Implement right
+ 
+
+ align:start position:0%
+basic things you should Implement right
+after the inip
+
+ align:start position:0%
+after the inip
+ 
+
+ align:start position:0%
+after the inip
+method okay so let's look at it in the
+
+ align:start position:0%
+method okay so let's look at it in the
+ 
+
+ align:start position:0%
+method okay so let's look at it in the
+context of the coordinate object so here
+
+ align:start position:0%
+context of the coordinate object so here
+ 
+
+ align:start position:0%
+context of the coordinate object so here
+I've got my coordinate object 3 comma 4
+
+ align:start position:0%
+I've got my coordinate object 3 comma 4
+ 
+
+ align:start position:0%
+I've got my coordinate object 3 comma 4
+and even when I print this coordinate
+
+ align:start position:0%
+and even when I print this coordinate
+ 
+
+ align:start position:0%
+and even when I print this coordinate
+object python tells me this uh still un
+
+ align:start position:0%
+object python tells me this uh still un
+ 
+
+ align:start position:0%
+object python tells me this uh still un
+informative message that this object is
+
+ align:start position:0%
+informative message that this object is
+ 
+
+ align:start position:0%
+informative message that this object is
+of type coordinate at this memory
+
+ align:start position:0%
+of type coordinate at this memory
+ 
+
+ align:start position:0%
+of type coordinate at this memory
+location okay I don't care well instead
+
+ align:start position:0%
+location okay I don't care well instead
+ 
+
+ align:start position:0%
+location okay I don't care well instead
+what I would really like to do is say
+
+ align:start position:0%
+what I would really like to do is say
+ 
+
+ align:start position:0%
+what I would really like to do is say
+hey I want to represent a coordinate
+
+ align:start position:0%
+hey I want to represent a coordinate
+ 
+
+ align:start position:0%
+hey I want to represent a coordinate
+object by something like this angle
+
+ align:start position:0%
+object by something like this angle
+ 
+
+ align:start position:0%
+object by something like this angle
+bracket the value of the x coordinate
+
+ align:start position:0%
+bracket the value of the x coordinate
+ 
+
+ align:start position:0%
+bracket the value of the x coordinate
+comma the value of the y-coordinate
+
+ align:start position:0%
+comma the value of the y-coordinate
+ 
+
+ align:start position:0%
+comma the value of the y-coordinate
+close angle
+
+ align:start position:0%
+close angle
+ 
+
+ align:start position:0%
+close angle
+bracket right so that would be a far
+
+ align:start position:0%
+bracket right so that would be a far
+ 
+
+ align:start position:0%
+bracket right so that would be a far
+more informative print statement than
+
+ align:start position:0%
+more informative print statement than
+ 
+
+ align:start position:0%
+more informative print statement than
+what memory location this thing is at
+
+ align:start position:0%
+what memory location this thing is at
+ 
+
+ align:start position:0%
+what memory location this thing is at
+right so let's do that well here we are
+
+ align:start position:0%
+right so let's do that well here we are
+ 
+
+ align:start position:0%
+right so let's do that well here we are
+uh our our our um our coordinate object
+
+ align:start position:0%
+uh our our our um our coordinate object
+ 
+
+ align:start position:0%
+uh our our our um our coordinate object
+the distance the init like we had before
+
+ align:start position:0%
+the distance the init like we had before
+ 
+
+ align:start position:0%
+the distance the init like we had before
+and here I'm defining my Str Str method
+
+ align:start position:0%
+and here I'm defining my Str Str method
+ 
+
+ align:start position:0%
+and here I'm defining my Str Str method
+right so double Str
+
+ align:start position:0%
+right so double Str
+ 
+
+ align:start position:0%
+right so double Str
+strore no other parameters except for
+
+ align:start position:0%
+strore no other parameters except for
+ 
+
+ align:start position:0%
+strore no other parameters except for
+self so me calling this method on an
+
+ align:start position:0%
+self so me calling this method on an
+ 
+
+ align:start position:0%
+self so me calling this method on an
+object and what is this uh going to do
+
+ align:start position:0%
+object and what is this uh going to do
+ 
+
+ align:start position:0%
+object and what is this uh going to do
+it will return not
+
+ align:start position:0%
+it will return not
+ 
+
+ align:start position:0%
+it will return not
+print return a
+
+ align:start position:0%
+print return a
+ 
+
+ align:start position:0%
+print return a
+string and the string is going to
+
+ align:start position:0%
+string and the string is going to
+ 
+
+ align:start position:0%
+string and the string is going to
+represent the thing you want to be
+
+ align:start position:0%
+represent the thing you want to be
+ 
+
+ align:start position:0%
+represent the thing you want to be
+printed out right so it returns a string
+
+ align:start position:0%
+printed out right so it returns a string
+ 
+
+ align:start position:0%
+printed out right so it returns a string
+doesn't print it however you want to
+
+ align:start position:0%
+doesn't print it however you want to
+ 
+
+ align:start position:0%
+doesn't print it however you want to
+make up the string is up to you so here
+
+ align:start position:0%
+make up the string is up to you so here
+ 
+
+ align:start position:0%
+make up the string is up to you so here
+I've just used concatenation of a bunch
+
+ align:start position:0%
+I've just used concatenation of a bunch
+ 
+
+ align:start position:0%
+I've just used concatenation of a bunch
+of stuff so I'm concatenating the angle
+
+ align:start position:0%
+of stuff so I'm concatenating the angle
+ 
+
+ align:start position:0%
+of stuff so I'm concatenating the angle
+bracket with uh the x value of my
+
+ align:start position:0%
+bracket with uh the x value of my
+ 
+
+ align:start position:0%
+bracket with uh the x value of my
+current object cast to a string
+
+ align:start position:0%
+current object cast to a string
+ 
+
+ align:start position:0%
+current object cast to a string
+concatenated with the comma concatenated
+
+ align:start position:0%
+concatenated with the comma concatenated
+ 
+
+ align:start position:0%
+concatenated with the comma concatenated
+with the Y value of my current object
+
+ align:start position:0%
+with the Y value of my current object
+ 
+
+ align:start position:0%
+with the Y value of my current object
+cast to a string concatenated with the
+
+ align:start position:0%
+cast to a string concatenated with the
+ 
+
+ align:start position:0%
+cast to a string concatenated with the
+closed angle bracket right that's the
+
+ align:start position:0%
+closed angle bracket right that's the
+ 
+
+ align:start position:0%
+closed angle bracket right that's the
+design decision we made to um for how a
+
+ align:start position:0%
+design decision we made to um for how a
+ 
+
+ align:start position:0%
+design decision we made to um for how a
+coordinate object should be
+
+ align:start position:0%
+coordinate object should be
+ 
+
+ align:start position:0%
+coordinate object should be
+printed everyone okay so
+
+ align:start position:0%
+printed everyone okay so
+ 
+
+ align:start position:0%
+printed everyone okay so
+far
+
+ align:start position:0%
+far
+ 
+
+ align:start position:0%
+far
+okay so if you want to use an F string
+
+ align:start position:0%
+okay so if you want to use an F string
+ 
+
+ align:start position:0%
+okay so if you want to use an F string
+to make up this thing to return totally
+
+ align:start position:0%
+to make up this thing to return totally
+ 
+
+ align:start position:0%
+to make up this thing to return totally
+fine if you want to make a variable
+
+ align:start position:0%
+fine if you want to make a variable
+ 
+
+ align:start position:0%
+fine if you want to make a variable
+right in between the return and the
+
+ align:start position:0%
+right in between the return and the
+ 
+
+ align:start position:0%
+right in between the return and the
+definition here that you just keep
+
+ align:start position:0%
+definition here that you just keep
+ 
+
+ align:start position:0%
+definition here that you just keep
+concatenating with so you can
+
+ align:start position:0%
+concatenating with so you can
+ 
+
+ align:start position:0%
+concatenating with so you can
+concatenate it with new lines and things
+
+ align:start position:0%
+concatenate it with new lines and things
+ 
+
+ align:start position:0%
+concatenate it with new lines and things
+like that also totally fine at the end
+
+ align:start position:0%
+like that also totally fine at the end
+ 
+
+ align:start position:0%
+like that also totally fine at the end
+you just have to return that string that
+
+ align:start position:0%
+you just have to return that string that
+ 
+
+ align:start position:0%
+you just have to return that string that
+represents the thing you want to pre
+
+ align:start position:0%
+represents the thing you want to pre
+ 
+
+ align:start position:0%
+represents the thing you want to pre
+print it
+
+ align:start position:0%
+print it
+ 
+
+ align:start position:0%
+print it
+out so now let's see what happens when
+
+ align:start position:0%
+out so now let's see what happens when
+ 
+
+ align:start position:0%
+out so now let's see what happens when
+we actually run the the code right so
+
+ align:start position:0%
+we actually run the the code right so
+ 
+
+ align:start position:0%
+we actually run the the code right so
+here I'm creating a coordinate object
+
+ align:start position:0%
+here I'm creating a coordinate object
+ 
+
+ align:start position:0%
+here I'm creating a coordinate object
+and then I'm printing that coordinate
+
+ align:start position:0%
+and then I'm printing that coordinate
+ 
+
+ align:start position:0%
+and then I'm printing that coordinate
+object well python says hey you just
+
+ align:start position:0%
+object well python says hey you just
+ 
+
+ align:start position:0%
+object well python says hey you just
+called a special shorthand notation on
+
+ align:start position:0%
+called a special shorthand notation on
+ 
+
+ align:start position:0%
+called a special shorthand notation on
+an object of type coordinate let me see
+
+ align:start position:0%
+an object of type coordinate let me see
+ 
+
+ align:start position:0%
+an object of type coordinate let me see
+if you implemented the St Str method it
+
+ align:start position:0%
+if you implemented the St Str method it
+ 
+
+ align:start position:0%
+if you implemented the St Str method it
+looks in the class definition it sees
+
+ align:start position:0%
+looks in the class definition it sees
+ 
+
+ align:start position:0%
+looks in the class definition it sees
+the Str Str method implemented here and
+
+ align:start position:0%
+the Str Str method implemented here and
+ 
+
+ align:start position:0%
+the Str Str method implemented here and
+then it runs the code inside and says Ah
+
+ align:start position:0%
+then it runs the code inside and says Ah
+ 
+
+ align:start position:0%
+then it runs the code inside and says Ah
+you want to grab C's x value and C's yv
+
+ align:start position:0%
+you want to grab C's x value and C's yv
+ 
+
+ align:start position:0%
+you want to grab C's x value and C's yv
+value and concatenated with these things
+
+ align:start position:0%
+value and concatenated with these things
+ 
+
+ align:start position:0%
+value and concatenated with these things
+here sure I can do that for you and then
+
+ align:start position:0%
+here sure I can do that for you and then
+ 
+
+ align:start position:0%
+here sure I can do that for you and then
+it goes and prints this out to the
+
+ align:start position:0%
+it goes and prints this out to the
+ 
+
+ align:start position:0%
+it goes and prints this out to the
+screen okay very cool right now we can
+
+ align:start position:0%
+screen okay very cool right now we can
+ 
+
+ align:start position:0%
+screen okay very cool right now we can
+decide how to print objects that we
+
+ align:start position:0%
+decide how to print objects that we
+ 
+
+ align:start position:0%
+decide how to print objects that we
+create all right so let's try to wrap
+
+ align:start position:0%
+create all right so let's try to wrap
+ 
+
+ align:start position:0%
+create all right so let's try to wrap
+our minds around types here okay so if
+
+ align:start position:0%
+our minds around types here okay so if
+ 
+
+ align:start position:0%
+our minds around types here okay so if
+we print this
+
+ align:start position:0%
+we print this
+ 
+
+ align:start position:0%
+we print this
+c c is an instance of a coordinate
+
+ align:start position:0%
+c c is an instance of a coordinate
+ 
+
+ align:start position:0%
+c c is an instance of a coordinate
+object right it's it's it's it's a it's
+
+ align:start position:0%
+object right it's it's it's it's a it's
+ 
+
+ align:start position:0%
+object right it's it's it's it's a it's
+it's an actual object that we're
+
+ align:start position:0%
+it's an actual object that we're
+ 
+
+ align:start position:0%
+it's an actual object that we're
+manipulating it's not the class
+
+ align:start position:0%
+manipulating it's not the class
+ 
+
+ align:start position:0%
+manipulating it's not the class
+definition it's not anything abstract
+
+ align:start position:0%
+definition it's not anything abstract
+ 
+
+ align:start position:0%
+definition it's not anything abstract
+like that it's an actual object like the
+
+ align:start position:0%
+like that it's an actual object like the
+ 
+
+ align:start position:0%
+like that it's an actual object like the
+integer three right is an actual
+
+ align:start position:0%
+integer three right is an actual
+ 
+
+ align:start position:0%
+integer three right is an actual
+object so if we print that C python uses
+
+ align:start position:0%
+object so if we print that C python uses
+ 
+
+ align:start position:0%
+object so if we print that C python uses
+the Str strr method well what if we
+
+ align:start position:0%
+the Str strr method well what if we
+ 
+
+ align:start position:0%
+the Str strr method well what if we
+print the type of C somebody tell me
+
+ align:start position:0%
+print the type of C somebody tell me
+ 
+
+ align:start position:0%
+print the type of C somebody tell me
+what's the type of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C coordinate yeah it's the class name
+
+ align:start position:0%
+C coordinate yeah it's the class name
+ 
+
+ align:start position:0%
+C coordinate yeah it's the class name
+that we defined so when we print the
+
+ align:start position:0%
+that we defined so when we print the
+ 
+
+ align:start position:0%
+that we defined so when we print the
+type of C python says this is a class
+
+ align:start position:0%
+type of C python says this is a class
+ 
+
+ align:start position:0%
+type of C python says this is a class
+coordinate which makes sense because if
+
+ align:start position:0%
+coordinate which makes sense because if
+ 
+
+ align:start position:0%
+coordinate which makes sense because if
+we just replace type of C here with what
+
+ align:start position:0%
+we just replace type of C here with what
+ 
+
+ align:start position:0%
+we just replace type of C here with what
+it is coordinate we'll get the same
+
+ align:start position:0%
+it is coordinate we'll get the same
+ 
+
+ align:start position:0%
+it is coordinate we'll get the same
+print statement if we just print
+
+ align:start position:0%
+print statement if we just print
+ 
+
+ align:start position:0%
+print statement if we just print
+coordinate python says this is a class
+
+ align:start position:0%
+coordinate python says this is a class
+ 
+
+ align:start position:0%
+coordinate python says this is a class
+of type coordinate right so those two
+
+ align:start position:0%
+of type coordinate right so those two
+ 
+
+ align:start position:0%
+of type coordinate right so those two
+lines are equivalent and then let me
+
+ align:start position:0%
+lines are equivalent and then let me
+ 
+
+ align:start position:0%
+lines are equivalent and then let me
+blow your minds a little bit more what
+
+ align:start position:0%
+blow your minds a little bit more what
+ 
+
+ align:start position:0%
+blow your minds a little bit more what
+if we print the type of coordinate well
+
+ align:start position:0%
+if we print the type of coordinate well
+ 
+
+ align:start position:0%
+if we print the type of coordinate well
+what is
+
+ align:start position:0%
+what is
+ 
+
+ align:start position:0%
+what is
+coordinate it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+type right we're defining a new type in
+
+ align:start position:0%
+type right we're defining a new type in
+ 
+
+ align:start position:0%
+type right we're defining a new type in
+Python called a coordinate so coordinate
+
+ align:start position:0%
+Python called a coordinate so coordinate
+ 
+
+ align:start position:0%
+Python called a coordinate so coordinate
+is a new data type in Python so it's
+
+ align:start position:0%
+is a new data type in Python so it's
+ 
+
+ align:start position:0%
+is a new data type in Python so it's
+type
+
+ align:start position:0%
+type
+ 
+
+ align:start position:0%
+type
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+type okay so every everything in Python
+
+ align:start position:0%
+type okay so every everything in Python
+ 
+
+ align:start position:0%
+type okay so every everything in Python
+is an object even
+
+ align:start position:0%
+is an object even
+ 
+
+ align:start position:0%
+is an object even
+types okay one more thing so we've used
+
+ align:start position:0%
+types okay one more thing so we've used
+ 
+
+ align:start position:0%
+types okay one more thing so we've used
+um the type of something equals
+
+ align:start position:0%
+um the type of something equals
+ 
+
+ align:start position:0%
+um the type of something equals
+something else right when we check that
+
+ align:start position:0%
+something else right when we check that
+ 
+
+ align:start position:0%
+something else right when we check that
+the type of uh the the circle's Center
+
+ align:start position:0%
+the type of uh the the circle's Center
+ 
+
+ align:start position:0%
+the type of uh the the circle's Center
+was a coordinate that's one way to check
+
+ align:start position:0%
+was a coordinate that's one way to check
+ 
+
+ align:start position:0%
+was a coordinate that's one way to check
+for types another way is to use this is
+
+ align:start position:0%
+for types another way is to use this is
+ 
+
+ align:start position:0%
+for types another way is to use this is
+instance function just as an aside so
+
+ align:start position:0%
+instance function just as an aside so
+ 
+
+ align:start position:0%
+instance function just as an aside so
+you can um check that uh C is an
+
+ align:start position:0%
+you can um check that uh C is an
+ 
+
+ align:start position:0%
+you can um check that uh C is an
+instance of type coordinate uh by using
+
+ align:start position:0%
+instance of type coordinate uh by using
+ 
+
+ align:start position:0%
+instance of type coordinate uh by using
+this is instance method and you know
+
+ align:start position:0%
+this is instance method and you know
+ 
+
+ align:start position:0%
+this is instance method and you know
+this will tell you true and you know
+
+ align:start position:0%
+this will tell you true and you know
+ 
+
+ align:start position:0%
+this will tell you true and you know
+just to draw a parallel you can say you
+
+ align:start position:0%
+just to draw a parallel you can say you
+ 
+
+ align:start position:0%
+just to draw a parallel you can say you
+know is instance three comma int that
+
+ align:start position:0%
+know is instance three comma int that
+ 
+
+ align:start position:0%
+know is instance three comma int that
+would also say true right because three
+
+ align:start position:0%
+would also say true right because three
+ 
+
+ align:start position:0%
+would also say true right because three
+is an object of type integer it's just
+
+ align:start position:0%
+is an object of type integer it's just
+ 
+
+ align:start position:0%
+is an object of type integer it's just
+another way to check for
+
+ align:start position:0%
+another way to check for
+ 
+
+ align:start position:0%
+another way to check for
+types okay so the remainder of this
+
+ align:start position:0%
+types okay so the remainder of this
+ 
+
+ align:start position:0%
+types okay so the remainder of this
+class I would like to go back to our
+
+ align:start position:0%
+class I would like to go back to our
+ 
+
+ align:start position:0%
+class I would like to go back to our
+fraction
+
+ align:start position:0%
+fraction
+ 
+
+ align:start position:0%
+fraction
+class and make it
+
+ align:start position:0%
+class and make it
+ 
+
+ align:start position:0%
+class and make it
+better now that we know uh Dunder
+
+ align:start position:0%
+better now that we know uh Dunder
+ 
+
+ align:start position:0%
+better now that we know uh Dunder
+methods right let's Implement a whole
+
+ align:start position:0%
+methods right let's Implement a whole
+ 
+
+ align:start position:0%
+methods right let's Implement a whole
+bunch of Dunder methods methods to help
+
+ align:start position:0%
+bunch of Dunder methods methods to help
+ 
+
+ align:start position:0%
+bunch of Dunder methods methods to help
+us um to help us and and people who want
+
+ align:start position:0%
+us um to help us and and people who want
+ 
+
+ align:start position:0%
+us um to help us and and people who want
+to use our class use it in a more
+
+ align:start position:0%
+to use our class use it in a more
+ 
+
+ align:start position:0%
+to use our class use it in a more
+efficient way right so we're going to
+
+ align:start position:0%
+efficient way right so we're going to
+ 
+
+ align:start position:0%
+efficient way right so we're going to
+implement the star operator the plus
+
+ align:start position:0%
+implement the star operator the plus
+ 
+
+ align:start position:0%
+implement the star operator the plus
+operator we're going to implement the
+
+ align:start position:0%
+operator we're going to implement the
+ 
+
+ align:start position:0%
+operator we're going to implement the
+print and then we're going to implement
+
+ align:start position:0%
+print and then we're going to implement
+ 
+
+ align:start position:0%
+print and then we're going to implement
+uh Implement uh converting to a
+
+ align:start position:0%
+uh Implement uh converting to a
+ 
+
+ align:start position:0%
+uh Implement uh converting to a
+float all right so the first thing that
+
+ align:start position:0%
+float all right so the first thing that
+ 
+
+ align:start position:0%
+float all right so the first thing that
+we should probably add is the strr
+
+ align:start position:0%
+we should probably add is the strr
+ 
+
+ align:start position:0%
+we should probably add is the strr
+method right because then it will help
+
+ align:start position:0%
+method right because then it will help
+ 
+
+ align:start position:0%
+method right because then it will help
+us in debugging when we print an object
+
+ align:start position:0%
+us in debugging when we print an object
+ 
+
+ align:start position:0%
+us in debugging when we print an object
+of type
+
+ align:start position:0%
+of type
+ 
+
+ align:start position:0%
+of type
+fraction so let's define double uncore
+
+ align:start position:0%
+fraction so let's define double uncore
+ 
+
+ align:start position:0%
+fraction so let's define double uncore
+store right again no parameters except
+
+ align:start position:0%
+store right again no parameters except
+ 
+
+ align:start position:0%
+store right again no parameters except
+for self because that's the the uh the
+
+ align:start position:0%
+for self because that's the the uh the
+ 
+
+ align:start position:0%
+for self because that's the the uh the
+method we're the object we're calling
+
+ align:start position:0%
+method we're the object we're calling
+ 
+
+ align:start position:0%
+method we're the object we're calling
+this method
+
+ align:start position:0%
+this method
+ 
+
+ align:start position:0%
+this method
+on and again however you want to uh form
+
+ align:start position:0%
+on and again however you want to uh form
+ 
+
+ align:start position:0%
+on and again however you want to uh form
+this string is up to you you can use f
+
+ align:start position:0%
+this string is up to you you can use f
+ 
+
+ align:start position:0%
+this string is up to you you can use f
+strings or a variable that you keep uh
+
+ align:start position:0%
+strings or a variable that you keep uh
+ 
+
+ align:start position:0%
+strings or a variable that you keep uh
+adding on to um I just did it straight
+
+ align:start position:0%
+adding on to um I just did it straight
+ 
+
+ align:start position:0%
+adding on to um I just did it straight
+in here with concatenation so I've got
+
+ align:start position:0%
+in here with concatenation so I've got
+ 
+
+ align:start position:0%
+in here with concatenation so I've got
+the numerator slash the denominator as a
+
+ align:start position:0%
+the numerator slash the denominator as a
+ 
+
+ align:start position:0%
+the numerator slash the denominator as a
+very reasonable way to represent a
+
+ align:start position:0%
+very reasonable way to represent a
+ 
+
+ align:start position:0%
+very reasonable way to represent a
+string right so three slash four as 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over4 okay so one thing I guess to keep
+
+ align:start position:0%
+over4 okay so one thing I guess to keep
+ 
+
+ align:start position:0%
+over4 okay so one thing I guess to keep
+keep keep track of is if you're
+
+ align:start position:0%
+keep keep track of is if you're
+ 
+
+ align:start position:0%
+keep keep track of is if you're
+concatenating you just have to remember
+
+ align:start position:0%
+concatenating you just have to remember
+ 
+
+ align:start position:0%
+concatenating you just have to remember
+to cast the strings right if it's a
+
+ align:start position:0%
+to cast the strings right if it's a
+ 
+
+ align:start position:0%
+to cast the strings right if it's a
+number that or something that's not a
+
+ align:start position:0%
+number that or something that's not a
+ 
+
+ align:start position:0%
+number that or something that's not a
+string so let's try it out I've got
+
+ align:start position:0%
+string so let's try it out I've got
+ 
+
+ align:start position:0%
+string so let's try it out I've got
+three fraction objects here okay so the
+
+ align:start position:0%
+three fraction objects here okay so the
+ 
+
+ align:start position:0%
+three fraction objects here okay so the
+first two we've already seen so I've got
+
+ align:start position:0%
+first two we've already seen so I've got
+ 
+
+ align:start position:0%
+first two we've already seen so I've got
+a fraction representing 3 over4 a
+
+ align:start position:0%
+a fraction representing 3 over4 a
+ 
+
+ align:start position:0%
+a fraction representing 3 over4 a
+fraction representing 1 over4 and F3 is
+
+ align:start position:0%
+fraction representing 1 over4 and F3 is
+ 
+
+ align:start position:0%
+fraction representing 1 over4 and F3 is
+now going to be a fraction representing
+
+ align:start position:0%
+now going to be a fraction representing
+ 
+
+ align:start position:0%
+now going to be a fraction representing
+5 over
+
+ align:start position:0%
+5 over
+ 
+
+ align:start position:0%
+5 over
+one okay if we print F1 again python
+
+ align:start position:0%
+one okay if we print F1 again python
+ 
+
+ align:start position:0%
+one okay if we print F1 again python
+asks hey did you implement an Str Str
+
+ align:start position:0%
+asks hey did you implement an Str Str
+ 
+
+ align:start position:0%
+asks hey did you implement an Str Str
+method in your class
+
+ align:start position:0%
+method in your class
+ 
+
+ align:start position:0%
+method in your class
+definition yes you did good job let me
+
+ align:start position:0%
+definition yes you did good job let me
+ 
+
+ align:start position:0%
+definition yes you did good job let me
+use it so then it uses this right so it
+
+ align:start position:0%
+use it so then it uses this right so it
+ 
+
+ align:start position:0%
+use it so then it uses this right so it
+grabs the numerator of F1 slash the
+
+ align:start position:0%
+grabs the numerator of F1 slash the
+ 
+
+ align:start position:0%
+grabs the numerator of F1 slash the
+numerator of sorry the denominator of F1
+
+ align:start position:0%
+numerator of sorry the denominator of F1
+ 
+
+ align:start position:0%
+numerator of sorry the denominator of F1
+so this will print three the numerator
+
+ align:start position:0%
+so this will print three the numerator
+ 
+
+ align:start position:0%
+so this will print three the numerator
+of F1 slash the denominator of
+
+ align:start position:0%
+of F1 slash the denominator of
+ 
+
+ align:start position:0%
+of F1 slash the denominator of
+fub1 okay same with F2 except that now
+
+ align:start position:0%
+fub1 okay same with F2 except that now
+ 
+
+ align:start position:0%
+fub1 okay same with F2 except that now
+it's going to grab f 2's numerator and
+
+ align:start position:0%
+it's going to grab f 2's numerator and
+ 
+
+ align:start position:0%
+it's going to grab f 2's numerator and
+denominator
+
+ align:start position:0%
+denominator
+ 
+
+ align:start position:0%
+denominator
+one4 so notice now it's not doing the
+
+ align:start position:0%
+one4 so notice now it's not doing the
+ 
+
+ align:start position:0%
+one4 so notice now it's not doing the
+divisions like it did before or sorry
+
+ align:start position:0%
+divisions like it did before or sorry
+ 
+
+ align:start position:0%
+divisions like it did before or sorry
+never mind we're not there yet there's
+
+ align:start position:0%
+never mind we're not there yet there's
+ 
+
+ align:start position:0%
+never mind we're not there yet there's
+nothing to divide it's just grabbing the
+
+ align:start position:0%
+nothing to divide it's just grabbing the
+ 
+
+ align:start position:0%
+nothing to divide it's just grabbing the
+numerators and denominators and just
+
+ align:start position:0%
+numerators and denominators and just
+ 
+
+ align:start position:0%
+numerators and denominators and just
+printing them out right it's not doing
+
+ align:start position:0%
+printing them out right it's not doing
+ 
+
+ align:start position:0%
+printing them out right it's not doing
+any divisions now when we print five uh
+
+ align:start position:0%
+any divisions now when we print five uh
+ 
+
+ align:start position:0%
+any divisions now when we print five uh
+the the the uh the fraction object
+
+ align:start position:0%
+the the the uh the fraction object
+ 
+
+ align:start position:0%
+the the the uh the fraction object
+representing five over one it prints
+
+ align:start position:0%
+representing five over one it prints
+ 
+
+ align:start position:0%
+representing five over one it prints
+fiveash one
+
+ align:start position:0%
+fiveash one
+ 
+
+ align:start position:0%
+fiveash one
+I don't like that because it looks weird
+
+ align:start position:0%
+I don't like that because it looks weird
+ 
+
+ align:start position:0%
+I don't like that because it looks weird
+right do you like that no so then I'm
+
+ align:start position:0%
+right do you like that no so then I'm
+ 
+
+ align:start position:0%
+right do you like that no so then I'm
+gonna have you fix
+
+ align:start position:0%
+gonna have you fix
+ 
+
+ align:start position:0%
+gonna have you fix
+it um change the Str Str method just a
+
+ align:start position:0%
+it um change the Str Str method just a
+ 
+
+ align:start position:0%
+it um change the Str Str method just a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+bit such that if the denominator is
+
+ align:start position:0%
+bit such that if the denominator is
+ 
+
+ align:start position:0%
+bit such that if the denominator is
+one just have it print the numerator
+
+ align:start position:0%
+one just have it print the numerator
+ 
+
+ align:start position:0%
+one just have it print the numerator
+right and otherwise the representation
+
+ align:start position:0%
+right and otherwise the representation
+ 
+
+ align:start position:0%
+right and otherwise the representation
+should be as before numerator SL
+
+ align:start position:0%
+should be as before numerator SL
+ 
+
+ align:start position:0%
+should be as before numerator SL
+denominator okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this should be down
+
+ align:start position:0%
+so this should be down
+ 
+
+ align:start position:0%
+so this should be down
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+14 where is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it very far down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+265 okay anyone have some code for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep yep we can do an else that else is
+
+ align:start position:0%
+yep yep we can do an else that else is
+ 
+
+ align:start position:0%
+yep yep we can do an else that else is
+not needed I don't think because if we
+
+ align:start position:0%
+not needed I don't think because if we
+ 
+
+ align:start position:0%
+not needed I don't think because if we
+dropped into the if we just immediately
+
+ align:start position:0%
+dropped into the if we just immediately
+ 
+
+ align:start position:0%
+dropped into the if we just immediately
+return otherwise we would just do the
+
+ align:start position:0%
+return otherwise we would just do the
+ 
+
+ align:start position:0%
+return otherwise we would just do the
+the remaining thing but perfectly fine
+
+ align:start position:0%
+the remaining thing but perfectly fine
+ 
+
+ align:start position:0%
+the remaining thing but perfectly fine
+yep and let's run
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it right so the a is a fraction
+
+ align:start position:0%
+it right so the a is a fraction
+ 
+
+ align:start position:0%
+it right so the a is a fraction
+representing one over four so it nicely
+
+ align:start position:0%
+representing one over four so it nicely
+ 
+
+ align:start position:0%
+representing one over four so it nicely
+printed one over four and B the fraction
+
+ align:start position:0%
+printed one over four and B the fraction
+ 
+
+ align:start position:0%
+printed one over four and B the fraction
+3 over one is just printing three
+
+ align:start position:0%
+3 over one is just printing three
+ 
+
+ align:start position:0%
+3 over one is just printing three
+good questions about this
+
+ align:start position:0%
+good questions about this
+ 
+
+ align:start position:0%
+good questions about this
+code okay for the remaining lecture
+
+ align:start position:0%
+code okay for the remaining lecture
+ 
+
+ align:start position:0%
+code okay for the remaining lecture
+though we're not going to use this
+
+ align:start position:0%
+though we're not going to use this
+ 
+
+ align:start position:0%
+though we're not going to use this
+modified this nicer better Str Str
+
+ align:start position:0%
+modified this nicer better Str Str
+ 
+
+ align:start position:0%
+modified this nicer better Str Str
+method so let's just forget what we just
+
+ align:start position:0%
+method so let's just forget what we just
+ 
+
+ align:start position:0%
+method so let's just forget what we just
+did and just remember that it looks like
+
+ align:start position:0%
+did and just remember that it looks like
+ 
+
+ align:start position:0%
+did and just remember that it looks like
+this okay just yeah okay so now let's
+
+ align:start position:0%
+this okay just yeah okay so now let's
+ 
+
+ align:start position:0%
+this okay just yeah okay so now let's
+implement the dunder methods for
+
+ align:start position:0%
+implement the dunder methods for
+ 
+
+ align:start position:0%
+implement the dunder methods for
+addition multiplication division things
+
+ align:start position:0%
+addition multiplication division things
+ 
+
+ align:start position:0%
+addition multiplication division things
+like that so I'm going to do the
+
+ align:start position:0%
+like that so I'm going to do the
+ 
+
+ align:start position:0%
+like that so I'm going to do the
+multiplication just because it's not as
+
+ align:start position:0%
+multiplication just because it's not as
+ 
+
+ align:start position:0%
+multiplication just because it's not as
+long for the numerator so just
+
+ align:start position:0%
+long for the numerator so just
+ 
+
+ align:start position:0%
+long for the numerator so just
+convenience factor here the left hand
+
+ align:start position:0%
+convenience factor here the left hand
+ 
+
+ align:start position:0%
+convenience factor here the left hand
+side I've got our old simple fraction
+
+ align:start position:0%
+side I've got our old simple fraction
+ 
+
+ align:start position:0%
+side I've got our old simple fraction
+code and the right hand side has my new
+
+ align:start position:0%
+code and the right hand side has my new
+ 
+
+ align:start position:0%
+code and the right hand side has my new
+fraction code okay so the old simple
+
+ align:start position:0%
+fraction code okay so the old simple
+ 
+
+ align:start position:0%
+fraction code okay so the old simple
+fraction code remember had this times
+
+ align:start position:0%
+fraction code remember had this times
+ 
+
+ align:start position:0%
+fraction code remember had this times
+method that uh took in an OT it
+
+ align:start position:0%
+method that uh took in an OT it
+ 
+
+ align:start position:0%
+method that uh took in an OT it
+calculated a new numerator and a new
+
+ align:start position:0%
+calculated a new numerator and a new
+ 
+
+ align:start position:0%
+calculated a new numerator and a new
+denominator and returned this okay now
+
+ align:start position:0%
+denominator and returned this okay now
+ 
+
+ align:start position:0%
+denominator and returned this okay now
+my new fraction code will no longer need
+
+ align:start position:0%
+my new fraction code will no longer need
+ 
+
+ align:start position:0%
+my new fraction code will no longer need
+to call times right so we're not even
+
+ align:start position:0%
+to call times right so we're not even
+ 
+
+ align:start position:0%
+to call times right so we're not even
+going to implement a method called times
+
+ align:start position:0%
+going to implement a method called times
+ 
+
+ align:start position:0%
+going to implement a method called times
+instead we're going to uh implement the
+
+ align:start position:0%
+instead we're going to uh implement the
+ 
+
+ align:start position:0%
+instead we're going to uh implement the
+method behind the scenes for the
+
+ align:start position:0%
+method behind the scenes for the
+ 
+
+ align:start position:0%
+method behind the scenes for the
+shorthand notation star to multiply two
+
+ align:start position:0%
+shorthand notation star to multiply two
+ 
+
+ align:start position:0%
+shorthand notation star to multiply two
+fraction fraction objects so we need to
+
+ align:start position:0%
+fraction fraction objects so we need to
+ 
+
+ align:start position:0%
+fraction fraction objects so we need to
+implement DF dcore M dou underscore
+
+ align:start position:0%
+implement DF dcore M dou underscore
+ 
+
+ align:start position:0%
+implement DF dcore M dou underscore
+parameter list is the same because we
+
+ align:start position:0%
+parameter list is the same because we
+ 
+
+ align:start position:0%
+parameter list is the same because we
+still have a thing before the star and a
+
+ align:start position:0%
+still have a thing before the star and a
+ 
+
+ align:start position:0%
+still have a thing before the star and a
+thing after the star as the two fraction
+
+ align:start position:0%
+thing after the star as the two fraction
+ 
+
+ align:start position:0%
+thing after the star as the two fraction
+object we'd like to
+
+ align:start position:0%
+object we'd like to
+ 
+
+ align:start position:0%
+object we'd like to
+multiply within the code itself the new
+
+ align:start position:0%
+multiply within the code itself the new
+ 
+
+ align:start position:0%
+multiply within the code itself the new
+calculations of the new numerator and
+
+ align:start position:0%
+calculations of the new numerator and
+ 
+
+ align:start position:0%
+calculations of the new numerator and
+the new denominator are the same as well
+
+ align:start position:0%
+the new denominator are the same as well
+ 
+
+ align:start position:0%
+the new denominator are the same as well
+right we're still grabbing the
+
+ align:start position:0%
+right we're still grabbing the
+ 
+
+ align:start position:0%
+right we're still grabbing the
+numerators of self and other the
+
+ align:start position:0%
+numerators of self and other the
+ 
+
+ align:start position:0%
+numerators of self and other the
+denominators of self and other
+
+ align:start position:0%
+denominators of self and other
+ 
+
+ align:start position:0%
+denominators of self and other
+multiplying those together right
+
+ align:start position:0%
+multiplying those together right
+ 
+
+ align:start position:0%
+multiplying those together right
+what's different is in the returns right
+
+ align:start position:0%
+what's different is in the returns right
+ 
+
+ align:start position:0%
+what's different is in the returns right
+what was the return type for the uh the
+
+ align:start position:0%
+what was the return type for the uh the
+ 
+
+ align:start position:0%
+what was the return type for the uh the
+times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method a decimal yeah a float exactly
+
+ align:start position:0%
+method a decimal yeah a float exactly
+ 
+
+ align:start position:0%
+method a decimal yeah a float exactly
+what's the return type of my
+
+ align:start position:0%
+what's the return type of my
+ 
+
+ align:start position:0%
+what's the return type of my
+new method the
+
+ align:start position:0%
+new method the
+ 
+
+ align:start position:0%
+new method the
+mole a fraction exactly so yes I'm
+
+ align:start position:0%
+mole a fraction exactly so yes I'm
+ 
+
+ align:start position:0%
+mole a fraction exactly so yes I'm
+operating with fraction objects so I'm
+
+ align:start position:0%
+operating with fraction objects so I'm
+ 
+
+ align:start position:0%
+operating with fraction objects so I'm
+expecting that the return type of this
+
+ align:start position:0%
+expecting that the return type of this
+ 
+
+ align:start position:0%
+expecting that the return type of this
+method the star double mole is also a
+
+ align:start position:0%
+method the star double mole is also a
+ 
+
+ align:start position:0%
+method the star double mole is also a
+fraction object so then I can just keep
+
+ align:start position:0%
+fraction object so then I can just keep
+ 
+
+ align:start position:0%
+fraction object so then I can just keep
+working with fraction objects throughout
+
+ align:start position:0%
+working with fraction objects throughout
+ 
+
+ align:start position:0%
+working with fraction objects throughout
+my code not having to worry about
+
+ align:start position:0%
+my code not having to worry about
+ 
+
+ align:start position:0%
+my code not having to worry about
+whether this thing is now a float or not
+
+ align:start position:0%
+whether this thing is now a float or not
+ 
+
+ align:start position:0%
+whether this thing is now a float or not
+right so how are we creating this
+
+ align:start position:0%
+right so how are we creating this
+ 
+
+ align:start position:0%
+right so how are we creating this
+fraction object well just like we would
+
+ align:start position:0%
+fraction object well just like we would
+ 
+
+ align:start position:0%
+fraction object well just like we would
+create a regular fraction object up in
+
+ align:start position:0%
+create a regular fraction object up in
+ 
+
+ align:start position:0%
+create a regular fraction object up in
+you know the previous slides right so
+
+ align:start position:0%
+you know the previous slides right so
+ 
+
+ align:start position:0%
+you know the previous slides right so
+here right here's an example of us
+
+ align:start position:0%
+here right here's an example of us
+ 
+
+ align:start position:0%
+here right here's an example of us
+creating a new fraction object right
+
+ align:start position:0%
+creating a new fraction object right
+ 
+
+ align:start position:0%
+creating a new fraction object right
+numerator one denominator uh four well
+
+ align:start position:0%
+numerator one denominator uh four well
+ 
+
+ align:start position:0%
+numerator one denominator uh four well
+same here this method me will return a
+
+ align:start position:0%
+same here this method me will return a
+ 
+
+ align:start position:0%
+same here this method me will return a
+new fraction object whose numerator is
+
+ align:start position:0%
+new fraction object whose numerator is
+ 
+
+ align:start position:0%
+new fraction object whose numerator is
+the thing that I just calculated the top
+
+ align:start position:0%
+the thing that I just calculated the top
+ 
+
+ align:start position:0%
+the thing that I just calculated the top
+and the denominator is the thing that I
+
+ align:start position:0%
+and the denominator is the thing that I
+ 
+
+ align:start position:0%
+and the denominator is the thing that I
+just calculated
+
+ align:start position:0%
+just calculated
+ 
+
+ align:start position:0%
+just calculated
+bottom does that make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+okay so this one returns a float this
+
+ align:start position:0%
+okay so this one returns a float this
+ 
+
+ align:start position:0%
+okay so this one returns a float this
+one returns a fraction okay let's run it
+
+ align:start position:0%
+one returns a fraction okay let's run it
+ 
+
+ align:start position:0%
+one returns a fraction okay let's run it
+so a is fraction one over4 B is a
+
+ align:start position:0%
+so a is fraction one over4 B is a
+ 
+
+ align:start position:0%
+so a is fraction one over4 B is a
+fraction representing 3 over four good
+
+ align:start position:0%
+fraction representing 3 over four good
+ 
+
+ align:start position:0%
+fraction representing 3 over four good
+those are the numbers we've been working
+
+ align:start position:0%
+those are the numbers we've been working
+ 
+
+ align:start position:0%
+those are the numbers we've been working
+with if we print a the print statement
+
+ align:start position:0%
+with if we print a the print statement
+ 
+
+ align:start position:0%
+with if we print a the print statement
+says this is the fraction object 1 sl4
+
+ align:start position:0%
+says this is the fraction object 1 sl4
+ 
+
+ align:start position:0%
+says this is the fraction object 1 sl4
+right whose representation is one sl4
+
+ align:start position:0%
+right whose representation is one sl4
+ 
+
+ align:start position:0%
+right whose representation is one sl4
+now if I use the star operator between A
+
+ align:start position:0%
+now if I use the star operator between A
+ 
+
+ align:start position:0%
+now if I use the star operator between A
+and B the thing before the star is kind
+
+ align:start position:0%
+and B the thing before the star is kind
+ 
+
+ align:start position:0%
+and B the thing before the star is kind
+of like the thing before the dot it's
+
+ align:start position:0%
+of like the thing before the dot it's
+ 
+
+ align:start position:0%
+of like the thing before the dot it's
+the self it gets mapped to self in my
+
+ align:start position:0%
+the self it gets mapped to self in my
+ 
+
+ align:start position:0%
+the self it gets mapped to self in my
+double uncore Mo and the thing after the
+
+ align:start position:0%
+double uncore Mo and the thing after the
+ 
+
+ align:start position:0%
+double uncore Mo and the thing after the
+star right the second parameter so to
+
+ align:start position:0%
+star right the second parameter so to
+ 
+
+ align:start position:0%
+star right the second parameter so to
+speak is the uh is the is is the one
+
+ align:start position:0%
+speak is the uh is the is is the one
+ 
+
+ align:start position:0%
+speak is the uh is the is is the one
+parameter that my method takes right
+
+ align:start position:0%
+parameter that my method takes right
+ 
+
+ align:start position:0%
+parameter that my method takes right
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+so this will create will run the mole
+
+ align:start position:0%
+so this will create will run the mole
+ 
+
+ align:start position:0%
+so this will create will run the mole
+method behind the scenes right so python
+
+ align:start position:0%
+method behind the scenes right so python
+ 
+
+ align:start position:0%
+method behind the scenes right so python
+when it sees that star asks do you have
+
+ align:start position:0%
+when it sees that star asks do you have
+ 
+
+ align:start position:0%
+when it sees that star asks do you have
+a mole method implemented in your class
+
+ align:start position:0%
+a mole method implemented in your class
+ 
+
+ align:start position:0%
+a mole method implemented in your class
+fraction because the thing before the
+
+ align:start position:0%
+fraction because the thing before the
+ 
+
+ align:start position:0%
+fraction because the thing before the
+star is a fraction object yes we do what
+
+ align:start position:0%
+star is a fraction object yes we do what
+ 
+
+ align:start position:0%
+star is a fraction object yes we do what
+does it return well it does the
+
+ align:start position:0%
+does it return well it does the
+ 
+
+ align:start position:0%
+does it return well it does the
+multiplication and in the end the return
+
+ align:start position:0%
+multiplication and in the end the return
+ 
+
+ align:start position:0%
+multiplication and in the end the return
+of this method is this thing here right
+
+ align:start position:0%
+of this method is this thing here right
+ 
+
+ align:start position:0%
+of this method is this thing here right
+so I literally just you know made this
+
+ align:start position:0%
+so I literally just you know made this
+ 
+
+ align:start position:0%
+so I literally just you know made this
+uh I guess copied this from the return
+
+ align:start position:0%
+uh I guess copied this from the return
+ 
+
+ align:start position:0%
+uh I guess copied this from the return
+using the numbers of A and B so it
+
+ align:start position:0%
+using the numbers of A and B so it
+ 
+
+ align:start position:0%
+using the numbers of A and B so it
+creates a new fraction object whose
+
+ align:start position:0%
+creates a new fraction object whose
+ 
+
+ align:start position:0%
+creates a new fraction object whose
+numerator is three and denominator is
+
+ align:start position:0%
+numerator is three and denominator is
+ 
+
+ align:start position:0%
+numerator is three and denominator is
+16 so C equals fraction parentheses 3
+
+ align:start position:0%
+16 so C equals fraction parentheses 3
+ 
+
+ align:start position:0%
+16 so C equals fraction parentheses 3
+comma 16 basically just another fraction
+
+ align:start position:0%
+comma 16 basically just another fraction
+ 
+
+ align:start position:0%
+comma 16 basically just another fraction
+object so now when I print
+
+ align:start position:0%
+object so now when I print
+ 
+
+ align:start position:0%
+object so now when I print
+C it's going to use the Str Str method
+
+ align:start position:0%
+C it's going to use the Str Str method
+ 
+
+ align:start position:0%
+C it's going to use the Str Str method
+for a fraction object right because C is
+
+ align:start position:0%
+for a fraction object right because C is
+ 
+
+ align:start position:0%
+for a fraction object right because C is
+a fraction object right there right
+
+ align:start position:0%
+a fraction object right there right
+ 
+
+ align:start position:0%
+a fraction object right there right
+that's exactly what C was so this will
+
+ align:start position:0%
+that's exactly what C was so this will
+ 
+
+ align:start position:0%
+that's exactly what C was so this will
+also print the way we asked to print
+
+ align:start position:0%
+also print the way we asked to print
+ 
+
+ align:start position:0%
+also print the way we asked to print
+fraction objects numerator SL
+
+ align:start position:0%
+fraction objects numerator SL
+ 
+
+ align:start position:0%
+fraction objects numerator SL
+denominator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3/16 everyone okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far okay so the following lines are all
+
+ align:start position:0%
+far okay so the following lines are all
+ 
+
+ align:start position:0%
+far okay so the following lines are all
+equivalent okay um using the shorthand
+
+ align:start position:0%
+equivalent okay um using the shorthand
+ 
+
+ align:start position:0%
+equivalent okay um using the shorthand
+notation very nice very pythonic way to
+
+ align:start position:0%
+notation very nice very pythonic way to
+ 
+
+ align:start position:0%
+notation very nice very pythonic way to
+multiply two fractions together but
+
+ align:start position:0%
+multiply two fractions together but
+ 
+
+ align:start position:0%
+multiply two fractions together but
+behind the scenes this is just running a
+
+ align:start position:0%
+behind the scenes this is just running a
+ 
+
+ align:start position:0%
+behind the scenes this is just running a
+method
+
+ align:start position:0%
+method
+ 
+
+ align:start position:0%
+method
+so of course if you really want to you
+
+ align:start position:0%
+so of course if you really want to you
+ 
+
+ align:start position:0%
+so of course if you really want to you
+can just use the same old way of calling
+
+ align:start position:0%
+can just use the same old way of calling
+ 
+
+ align:start position:0%
+can just use the same old way of calling
+a method right thing before the dot dot
+
+ align:start position:0%
+a method right thing before the dot dot
+ 
+
+ align:start position:0%
+a method right thing before the dot dot
+method name parentheses parameter
+
+ align:start position:0%
+method name parentheses parameter
+ 
+
+ align:start position:0%
+method name parentheses parameter
+list so here thing before the dot is a
+
+ align:start position:0%
+list so here thing before the dot is a
+ 
+
+ align:start position:0%
+list so here thing before the dot is a
+DOT the name of my method Dore Moore
+
+ align:start position:0%
+DOT the name of my method Dore Moore
+ 
+
+ align:start position:0%
+DOT the name of my method Dore Moore
+parentheses all of the parameter list
+
+ align:start position:0%
+parentheses all of the parameter list
+ 
+
+ align:start position:0%
+parentheses all of the parameter list
+except for the thing I'm calling it on
+
+ align:start position:0%
+except for the thing I'm calling it on
+ 
+
+ align:start position:0%
+except for the thing I'm calling it on
+right so those two are equivalent and of
+
+ align:start position:0%
+right so those two are equivalent and of
+ 
+
+ align:start position:0%
+right so those two are equivalent and of
+course last time I mentioned uh s sort
+
+ align:start position:0%
+course last time I mentioned uh s sort
+ 
+
+ align:start position:0%
+course last time I mentioned uh s sort
+of a way to hopefully
+
+ align:start position:0%
+of a way to hopefully
+ 
+
+ align:start position:0%
+of a way to hopefully
+demystify um running these methods where
+
+ align:start position:0%
+demystify um running these methods where
+ 
+
+ align:start position:0%
+demystify um running these methods where
+you know the self becomes this thing
+
+ align:start position:0%
+you know the self becomes this thing
+ 
+
+ align:start position:0%
+you know the self becomes this thing
+before the dot you could call the method
+
+ align:start position:0%
+before the dot you could call the method
+ 
+
+ align:start position:0%
+before the dot you could call the method
+on the name of your data type right the
+
+ align:start position:0%
+on the name of your data type right the
+ 
+
+ align:start position:0%
+on the name of your data type right the
+the type that you're currently creating
+
+ align:start position:0%
+the type that you're currently creating
+ 
+
+ align:start position:0%
+the type that you're currently creating
+fraction so fraction is not an instance
+
+ align:start position:0%
+fraction so fraction is not an instance
+ 
+
+ align:start position:0%
+fraction so fraction is not an instance
+right a was an instance it was an actual
+
+ align:start position:0%
+right a was an instance it was an actual
+ 
+
+ align:start position:0%
+right a was an instance it was an actual
+object that we created but fraction is
+
+ align:start position:0%
+object that we created but fraction is
+ 
+
+ align:start position:0%
+object that we created but fraction is
+just the name of my class so if you call
+
+ align:start position:0%
+just the name of my class so if you call
+ 
+
+ align:start position:0%
+just the name of my class so if you call
+the method on the name of your class
+
+ align:start position:0%
+the method on the name of your class
+ 
+
+ align:start position:0%
+the method on the name of your class
+then python expects the full parameter
+
+ align:start position:0%
+then python expects the full parameter
+ 
+
+ align:start position:0%
+then python expects the full parameter
+list right so something for self
+
+ align:start position:0%
+list right so something for self
+ 
+
+ align:start position:0%
+list right so something for self
+something for others something for
+
+ align:start position:0%
+something for others something for
+ 
+
+ align:start position:0%
+something for others something for
+whatever parameters you have and so
+
+ align:start position:0%
+whatever parameters you have and so
+ 
+
+ align:start position:0%
+whatever parameters you have and so
+there we would explicitly pass in both A
+
+ align:start position:0%
+there we would explicitly pass in both A
+ 
+
+ align:start position:0%
+there we would explicitly pass in both A
+and B as part of my parameter list
+
+ align:start position:0%
+and B as part of my parameter list
+ 
+
+ align:start position:0%
+and B as part of my parameter list
+because the thing before the dot is not
+
+ align:start position:0%
+because the thing before the dot is not
+ 
+
+ align:start position:0%
+because the thing before the dot is not
+an object so there's no there it doesn't
+
+ align:start position:0%
+an object so there's no there it doesn't
+ 
+
+ align:start position:0%
+an object so there's no there it doesn't
+map it to self okay but I would never
+
+ align:start position:0%
+map it to self okay but I would never
+ 
+
+ align:start position:0%
+map it to self okay but I would never
+ever
+
+ align:start position:0%
+ever
+ 
+
+ align:start position:0%
+ever
+ever uh run a line of code like this
+
+ align:start position:0%
+ever uh run a line of code like this
+ 
+
+ align:start position:0%
+ever uh run a line of code like this
+this last one here right this is just
+
+ align:start position:0%
+this last one here right this is just
+ 
+
+ align:start position:0%
+this last one here right this is just
+for your information it's non pythonic
+
+ align:start position:0%
+for your information it's non pythonic
+ 
+
+ align:start position:0%
+for your information it's non pythonic
+it's just very verbose right and so this
+
+ align:start position:0%
+it's just very verbose right and so this
+ 
+
+ align:start position:0%
+it's just very verbose right and so this
+uh these uh these Dunder methods help us
+
+ align:start position:0%
+uh these uh these Dunder methods help us
+ 
+
+ align:start position:0%
+uh these uh these Dunder methods help us
+abstract away a bunch of these details
+
+ align:start position:0%
+abstract away a bunch of these details
+ 
+
+ align:start position:0%
+abstract away a bunch of these details
+right so how annoying would it be to
+
+ align:start position:0%
+right so how annoying would it be to
+ 
+
+ align:start position:0%
+right so how annoying would it be to
+always use dot notation when we want to
+
+ align:start position:0%
+always use dot notation when we want to
+ 
+
+ align:start position:0%
+always use dot notation when we want to
+multiply an integer with another integer
+
+ align:start position:0%
+multiply an integer with another integer
+ 
+
+ align:start position:0%
+multiply an integer with another integer
+can you imagine constantly writing three
+
+ align:start position:0%
+can you imagine constantly writing three
+ 
+
+ align:start position:0%
+can you imagine constantly writing three
+do square m Square
+
+ align:start position:0%
+do square m Square
+ 
+
+ align:start position:0%
+do square m Square
+4 that would be very bad code it would
+
+ align:start position:0%
+4 that would be very bad code it would
+ 
+
+ align:start position:0%
+4 that would be very bad code it would
+take forever to read right and so we're
+
+ align:start position:0%
+take forever to read right and so we're
+ 
+
+ align:start position:0%
+take forever to read right and so we're
+abstracting away all the details for
+
+ align:start position:0%
+abstracting away all the details for
+ 
+
+ align:start position:0%
+abstracting away all the details for
+calling these methods into these nice
+
+ align:start position:0%
+calling these methods into these nice
+ 
+
+ align:start position:0%
+calling these methods into these nice
+low shorthand notations and as I said
+
+ align:start position:0%
+low shorthand notations and as I said
+ 
+
+ align:start position:0%
+low shorthand notations and as I said
+the shorthand notations exist for a lot
+
+ align:start position:0%
+the shorthand notations exist for a lot
+ 
+
+ align:start position:0%
+the shorthand notations exist for a lot
+of different operations we saw print you
+
+ align:start position:0%
+of different operations we saw print you
+ 
+
+ align:start position:0%
+of different operations we saw print you
+can do length comparisons like equality
+
+ align:start position:0%
+can do length comparisons like equality
+ 
+
+ align:start position:0%
+can do length comparisons like equality
+even you know indexing into things you
+
+ align:start position:0%
+even you know indexing into things you
+ 
+
+ align:start position:0%
+even you know indexing into things you
+can always you can abstract all of those
+
+ align:start position:0%
+can always you can abstract all of those
+ 
+
+ align:start position:0%
+can always you can abstract all of those
+away um with into shorthand notations
+
+ align:start position:0%
+away um with into shorthand notations
+ 
+
+ align:start position:0%
+away um with into shorthand notations
+and behind the scenes these methods will
+
+ align:start position:0%
+and behind the scenes these methods will
+ 
+
+ align:start position:0%
+and behind the scenes these methods will
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+run okay so big idea right exactly what
+
+ align:start position:0%
+run okay so big idea right exactly what
+ 
+
+ align:start position:0%
+run okay so big idea right exactly what
+I said all these Special Operations that
+
+ align:start position:0%
+I said all these Special Operations that
+ 
+
+ align:start position:0%
+I said all these Special Operations that
+we've been using
+
+ align:start position:0%
+we've been using
+ 
+
+ align:start position:0%
+we've been using
+already behind the scenes these methods
+
+ align:start position:0%
+already behind the scenes these methods
+ 
+
+ align:start position:0%
+already behind the scenes these methods
+get run and these methods were written
+
+ align:start position:0%
+get run and these methods were written
+ 
+
+ align:start position:0%
+get run and these methods were written
+inside the class definition for the
+
+ align:start position:0%
+inside the class definition for the
+ 
+
+ align:start position:0%
+inside the class definition for the
+types that we've been using right so
+
+ align:start position:0%
+types that we've been using right so
+ 
+
+ align:start position:0%
+types that we've been using right so
+when we index into a list L square
+
+ align:start position:0%
+when we index into a list L square
+ 
+
+ align:start position:0%
+when we index into a list L square
+brackets three or whatever there's a
+
+ align:start position:0%
+brackets three or whatever there's a
+ 
+
+ align:start position:0%
+brackets three or whatever there's a
+method being called behind the scenes in
+
+ align:start position:0%
+method being called behind the scenes in
+ 
+
+ align:start position:0%
+method being called behind the scenes in
+the list class to grab the element at
+
+ align:start position:0%
+the list class to grab the element at
+ 
+
+ align:start position:0%
+the list class to grab the element at
+index three I don't remember the dunder
+
+ align:start position:0%
+index three I don't remember the dunder
+ 
+
+ align:start position:0%
+index three I don't remember the dunder
+method name for that but probably like
+
+ align:start position:0%
+method name for that but probably like
+ 
+
+ align:start position:0%
+method name for that but probably like
+double uncore index double uncore I
+
+ align:start position:0%
+double uncore index double uncore I
+ 
+
+ align:start position:0%
+double uncore index double uncore I
+don't know but there is some method
+
+ align:start position:0%
+don't know but there is some method
+ 
+
+ align:start position:0%
+don't know but there is some method
+behind the
+
+ align:start position:0%
+behind the
+ 
+
+ align:start position:0%
+behind the
+scenes all right let's do a couple more
+
+ align:start position:0%
+scenes all right let's do a couple more
+ 
+
+ align:start position:0%
+scenes all right let's do a couple more
+things sorry
+
+ align:start position:0%
+things sorry
+ 
+
+ align:start position:0%
+things sorry
+forget the D name for something is way
+
+ align:start position:0%
+forget the D name for something is way
+ 
+
+ align:start position:0%
+forget the D name for something is way
+to ask python uh you can't ask python
+
+ align:start position:0%
+to ask python uh you can't ask python
+ 
+
+ align:start position:0%
+to ask python uh you can't ask python
+but you can look at the documentation I
+
+ align:start position:0%
+but you can look at the documentation I
+ 
+
+ align:start position:0%
+but you can look at the documentation I
+think it's uh like in python.org there's
+
+ align:start position:0%
+think it's uh like in python.org there's
+ 
+
+ align:start position:0%
+think it's uh like in python.org there's
+a website that lists basically
+
+ align:start position:0%
+a website that lists basically
+ 
+
+ align:start position:0%
+a website that lists basically
+everything that you can that's a Dunder
+
+ align:start position:0%
+everything that you can that's a Dunder
+ 
+
+ align:start position:0%
+everything that you can that's a Dunder
+method yeah under categories like in all
+
+ align:start position:0%
+method yeah under categories like in all
+ 
+
+ align:start position:0%
+method yeah under categories like in all
+the indexing type stuff all the
+
+ align:start position:0%
+the indexing type stuff all the
+ 
+
+ align:start position:0%
+the indexing type stuff all the
+numerical type stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah um okay so let's do one more thing
+
+ align:start position:0%
+yeah um okay so let's do one more thing
+ 
+
+ align:start position:0%
+yeah um okay so let's do one more thing
+let's uh uh say that well we're working
+
+ align:start position:0%
+let's uh uh say that well we're working
+ 
+
+ align:start position:0%
+let's uh uh say that well we're working
+with fraction objects and so
+
+ align:start position:0%
+with fraction objects and so
+ 
+
+ align:start position:0%
+with fraction objects and so
+uh the dunder methods that we're writing
+
+ align:start position:0%
+uh the dunder methods that we're writing
+ 
+
+ align:start position:0%
+uh the dunder methods that we're writing
+are now returning other fraction
+
+ align:start position:0%
+are now returning other fraction
+ 
+
+ align:start position:0%
+are now returning other fraction
+objects so let's allow the user the
+
+ align:start position:0%
+objects so let's allow the user the
+ 
+
+ align:start position:0%
+objects so let's allow the user the
+opportunity to cast one of these
+
+ align:start position:0%
+opportunity to cast one of these
+ 
+
+ align:start position:0%
+opportunity to cast one of these
+fraction objects to a float just in case
+
+ align:start position:0%
+fraction objects to a float just in case
+ 
+
+ align:start position:0%
+fraction objects to a float just in case
+they would like to grab the you know the
+
+ align:start position:0%
+they would like to grab the you know the
+ 
+
+ align:start position:0%
+they would like to grab the you know the
+the the float value of
+
+ align:start position:0%
+the the float value of
+ 
+
+ align:start position:0%
+the the float value of
+316 right that's a very reasonable thing
+
+ align:start position:0%
+316 right that's a very reasonable thing
+ 
+
+ align:start position:0%
+316 right that's a very reasonable thing
+they might want to do so let's you know
+
+ align:start position:0%
+they might want to do so let's you know
+ 
+
+ align:start position:0%
+they might want to do so let's you know
+get ahead of them and add that as part
+
+ align:start position:0%
+get ahead of them and add that as part
+ 
+
+ align:start position:0%
+get ahead of them and add that as part
+of our class definition so to uh cast
+
+ align:start position:0%
+of our class definition so to uh cast
+ 
+
+ align:start position:0%
+of our class definition so to uh cast
+things to a FL in this particular case
+
+ align:start position:0%
+things to a FL in this particular case
+ 
+
+ align:start position:0%
+things to a FL in this particular case
+the dunder method for that iscore float
+
+ align:start position:0%
+the dunder method for that iscore float
+ 
+
+ align:start position:0%
+the dunder method for that iscore float
+double
+
+ align:start position:0%
+double
+ 
+
+ align:start position:0%
+double
+underscore and all it's going to do is
+
+ align:start position:0%
+underscore and all it's going to do is
+ 
+
+ align:start position:0%
+underscore and all it's going to do is
+grab the numerator of self and divide it
+
+ align:start position:0%
+grab the numerator of self and divide it
+ 
+
+ align:start position:0%
+grab the numerator of self and divide it
+by the denominator of self right so this
+
+ align:start position:0%
+by the denominator of self right so this
+ 
+
+ align:start position:0%
+by the denominator of self right so this
+will just do a division self. num is a
+
+ align:start position:0%
+will just do a division self. num is a
+ 
+
+ align:start position:0%
+will just do a division self. num is a
+number self. denom is another number it
+
+ align:start position:0%
+number self. denom is another number it
+ 
+
+ align:start position:0%
+number self. denom is another number it
+does the division and this returns a
+
+ align:start position:0%
+does the division and this returns a
+ 
+
+ align:start position:0%
+does the division and this returns a
+float right so here when we multiply C
+
+ align:start position:0%
+float right so here when we multiply C
+ 
+
+ align:start position:0%
+float right so here when we multiply C
+is equal to a * B remember that c became
+
+ align:start position:0%
+is equal to a * B remember that c became
+ 
+
+ align:start position:0%
+is equal to a * B remember that c became
+a fraction object with numerator 3 and
+
+ align:start position:0%
+a fraction object with numerator 3 and
+ 
+
+ align:start position:0%
+a fraction object with numerator 3 and
+denom minator 16 right you remember that
+
+ align:start position:0%
+denom minator 16 right you remember that
+ 
+
+ align:start position:0%
+denom minator 16 right you remember that
+so then when we cast it to a float down
+
+ align:start position:0%
+so then when we cast it to a float down
+ 
+
+ align:start position:0%
+so then when we cast it to a float down
+here python says hey did you implement
+
+ align:start position:0%
+here python says hey did you implement
+ 
+
+ align:start position:0%
+here python says hey did you implement
+the dunder method double uncore float
+
+ align:start position:0%
+the dunder method double uncore float
+ 
+
+ align:start position:0%
+the dunder method double uncore float
+double underscore oh yeah you did let me
+
+ align:start position:0%
+double underscore oh yeah you did let me
+ 
+
+ align:start position:0%
+double underscore oh yeah you did let me
+just go ahead and do the thing that you
+
+ align:start position:0%
+just go ahead and do the thing that you
+ 
+
+ align:start position:0%
+just go ahead and do the thing that you
+want me to do inside it so it takes the
+
+ align:start position:0%
+want me to do inside it so it takes the
+ 
+
+ align:start position:0%
+want me to do inside it so it takes the
+three divides it by the 16 and it prints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay let's try it out a little bit
+
+ align:start position:0%
+right okay let's try it out a little bit
+ 
+
+ align:start position:0%
+right okay let's try it out a little bit
+more so here I've got two action objects
+
+ align:start position:0%
+more so here I've got two action objects
+ 
+
+ align:start position:0%
+more so here I've got two action objects
+um one representing 1 over 4 the other
+
+ align:start position:0%
+um one representing 1 over 4 the other
+ 
+
+ align:start position:0%
+um one representing 1 over 4 the other
+one representing 2 over 3 I multiply
+
+ align:start position:0%
+one representing 2 over 3 I multiply
+ 
+
+ align:start position:0%
+one representing 2 over 3 I multiply
+those two together again this gives me a
+
+ align:start position:0%
+those two together again this gives me a
+ 
+
+ align:start position:0%
+those two together again this gives me a
+fraction object right because it's
+
+ align:start position:0%
+fraction object right because it's
+ 
+
+ align:start position:0%
+fraction object right because it's
+running the the mold Dunder method and
+
+ align:start position:0%
+running the the mold Dunder method and
+ 
+
+ align:start position:0%
+running the the mold Dunder method and
+the mold Dunder method gives me uh a
+
+ align:start position:0%
+the mold Dunder method gives me uh a
+ 
+
+ align:start position:0%
+the mold Dunder method gives me uh a
+fraction object with a new numerator and
+
+ align:start position:0%
+fraction object with a new numerator and
+ 
+
+ align:start position:0%
+fraction object with a new numerator and
+denominator so when I print the return
+
+ align:start position:0%
+denominator so when I print the return
+ 
+
+ align:start position:0%
+denominator so when I print the return
+of that when I print C this prints the
+
+ align:start position:0%
+of that when I print C this prints the
+ 
+
+ align:start position:0%
+of that when I print C this prints the
+new numerator which is 2 * 1 divided by
+
+ align:start position:0%
+new numerator which is 2 * 1 divided by
+ 
+
+ align:start position:0%
+new numerator which is 2 * 1 divided by
+the new denominator which is 4 * 3 so it
+
+ align:start position:0%
+the new denominator which is 4 * 3 so it
+ 
+
+ align:start position:0%
+the new denominator which is 4 * 3 so it
+prints 2 over 12
+
+ align:start position:0%
+prints 2 over 12
+ 
+
+ align:start position:0%
+prints 2 over 12
+does that look okay to
+
+ align:start position:0%
+does that look okay to
+ 
+
+ align:start position:0%
+does that look okay to
+you I mean it looks okay but suppose
+
+ align:start position:0%
+you I mean it looks okay but suppose
+ 
+
+ align:start position:0%
+you I mean it looks okay but suppose
+you're doing you know calculations with
+
+ align:start position:0%
+you're doing you know calculations with
+ 
+
+ align:start position:0%
+you're doing you know calculations with
+a whole bunch of numbers and at some
+
+ align:start position:0%
+a whole bunch of numbers and at some
+ 
+
+ align:start position:0%
+a whole bunch of numbers and at some
+point you get to really big numerators
+
+ align:start position:0%
+point you get to really big numerators
+ 
+
+ align:start position:0%
+point you get to really big numerators
+and really big
+
+ align:start position:0%
+and really big
+ 
+
+ align:start position:0%
+and really big
+denominators but
+
+ align:start position:0%
+denominators but
+ 
+
+ align:start position:0%
+denominators but
+then you stared it long enough and
+
+ align:start position:0%
+then you stared it long enough and
+ 
+
+ align:start position:0%
+then you stared it long enough and
+realize that that big numerator divided
+
+ align:start position:0%
+realize that that big numerator divided
+ 
+
+ align:start position:0%
+realize that that big numerator divided
+by that big denominator is actually
+
+ align:start position:0%
+by that big denominator is actually
+ 
+
+ align:start position:0%
+by that big denominator is actually
+something like one
+
+ align:start position:0%
+something like one
+ 
+
+ align:start position:0%
+something like one
+over4 right so this is not
+
+ align:start position:0%
+over4 right so this is not
+ 
+
+ align:start position:0%
+over4 right so this is not
+reduced right which is fine our code is
+
+ align:start position:0%
+reduced right which is fine our code is
+ 
+
+ align:start position:0%
+reduced right which is fine our code is
+not doing the reduction but it would be
+
+ align:start position:0%
+not doing the reduction but it would be
+ 
+
+ align:start position:0%
+not doing the reduction but it would be
+nice to write a method that allows the
+
+ align:start position:0%
+nice to write a method that allows the
+ 
+
+ align:start position:0%
+nice to write a method that allows the
+user to reduce a fraction right that
+
+ align:start position:0%
+user to reduce a fraction right that
+ 
+
+ align:start position:0%
+user to reduce a fraction right that
+would be really nice so can we fix this
+
+ align:start position:0%
+would be really nice so can we fix this
+ 
+
+ align:start position:0%
+would be really nice so can we fix this
+yes we can otherwise we wouldn't be here
+
+ align:start position:0%
+yes we can otherwise we wouldn't be here
+ 
+
+ align:start position:0%
+yes we can otherwise we wouldn't be here
+so let's write this method to reduce a
+
+ align:start position:0%
+so let's write this method to reduce a
+ 
+
+ align:start position:0%
+so let's write this method to reduce a
+fraction object it looks like a
+
+ align:start position:0%
+fraction object it looks like a
+ 
+
+ align:start position:0%
+fraction object it looks like a
+lot but it's not trust me okay it's just
+
+ align:start position:0%
+lot but it's not trust me okay it's just
+ 
+
+ align:start position:0%
+lot but it's not trust me okay it's just
+a bunch of if eles so the first part
+
+ align:start position:0%
+a bunch of if eles so the first part
+ 
+
+ align:start position:0%
+a bunch of if eles so the first part
+part of it is a little helper function
+
+ align:start position:0%
+part of it is a little helper function
+ 
+
+ align:start position:0%
+part of it is a little helper function
+not a method right notice there's no
+
+ align:start position:0%
+not a method right notice there's no
+ 
+
+ align:start position:0%
+not a method right notice there's no
+self going on in this gcd function right
+
+ align:start position:0%
+self going on in this gcd function right
+ 
+
+ align:start position:0%
+self going on in this gcd function right
+this is just a regular function that I
+
+ align:start position:0%
+this is just a regular function that I
+ 
+
+ align:start position:0%
+this is just a regular function that I
+will use to help me get the greatest
+
+ align:start position:0%
+will use to help me get the greatest
+ 
+
+ align:start position:0%
+will use to help me get the greatest
+common divisor for the two parameters n
+
+ align:start position:0%
+common divisor for the two parameters n
+ 
+
+ align:start position:0%
+common divisor for the two parameters n
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+D okay because when I have two numbers
+
+ align:start position:0%
+D okay because when I have two numbers
+ 
+
+ align:start position:0%
+D okay because when I have two numbers
+right if I want to reduce them I find
+
+ align:start position:0%
+right if I want to reduce them I find
+ 
+
+ align:start position:0%
+right if I want to reduce them I find
+the greatest common divisors and I'm
+
+ align:start position:0%
+the greatest common divisors and I'm
+ 
+
+ align:start position:0%
+the greatest common divisors and I'm
+going to divide the top and the Bottom
+
+ align:start position:0%
+going to divide the top and the Bottom
+ 
+
+ align:start position:0%
+going to divide the top and the Bottom
+by that divisor right and that will help
+
+ align:start position:0%
+by that divisor right and that will help
+ 
+
+ align:start position:0%
+by that divisor right and that will help
+me reduce it so this gcd function helps
+
+ align:start position:0%
+me reduce it so this gcd function helps
+ 
+
+ align:start position:0%
+me reduce it so this gcd function helps
+me find this greatest common
+
+ align:start position:0%
+me find this greatest common
+ 
+
+ align:start position:0%
+me find this greatest common
+divisor all right so here I'm just
+
+ align:start position:0%
+divisor all right so here I'm just
+ 
+
+ align:start position:0%
+divisor all right so here I'm just
+defining the function I'm not actually
+
+ align:start position:0%
+defining the function I'm not actually
+ 
+
+ align:start position:0%
+defining the function I'm not actually
+using it and then I've got uh two uh an
+
+ align:start position:0%
+using it and then I've got uh two uh an
+ 
+
+ align:start position:0%
+using it and then I've got uh two uh an
+if and an L if so if the denominator is
+
+ align:start position:0%
+if and an L if so if the denominator is
+ 
+
+ align:start position:0%
+if and an L if so if the denominator is
+zero something's super weird so I'm just
+
+ align:start position:0%
+zero something's super weird so I'm just
+ 
+
+ align:start position:0%
+zero something's super weird so I'm just
+going to return none right because
+
+ align:start position:0%
+going to return none right because
+ 
+
+ align:start position:0%
+going to return none right because
+having a fraction where the denominator
+
+ align:start position:0%
+having a fraction where the denominator
+ 
+
+ align:start position:0%
+having a fraction where the denominator
+zero maybe something went wrong else if
+
+ align:start position:0%
+zero maybe something went wrong else if
+ 
+
+ align:start position:0%
+zero maybe something went wrong else if
+the denominator is one we don't need to
+
+ align:start position:0%
+the denominator is one we don't need to
+ 
+
+ align:start position:0%
+the denominator is one we don't need to
+do any red reduction right right no
+
+ align:start position:0%
+do any red reduction right right no
+ 
+
+ align:start position:0%
+do any red reduction right right no
+reducing is needed so we just return the
+
+ align:start position:0%
+reducing is needed so we just return the
+ 
+
+ align:start position:0%
+reducing is needed so we just return the
+numerator and else I do have two actual
+
+ align:start position:0%
+numerator and else I do have two actual
+ 
+
+ align:start position:0%
+numerator and else I do have two actual
+numbers that I could maybe could
+
+ align:start position:0%
+numbers that I could maybe could
+ 
+
+ align:start position:0%
+numbers that I could maybe could
+potentially reduce so let's just uh
+
+ align:start position:0%
+potentially reduce so let's just uh
+ 
+
+ align:start position:0%
+potentially reduce so let's just uh
+reduce them the first line here runs
+
+ align:start position:0%
+reduce them the first line here runs
+ 
+
+ align:start position:0%
+reduce them the first line here runs
+this function this helper function that
+
+ align:start position:0%
+this function this helper function that
+ 
+
+ align:start position:0%
+this function this helper function that
+I wrote on the numerator and denominator
+
+ align:start position:0%
+I wrote on the numerator and denominator
+ 
+
+ align:start position:0%
+I wrote on the numerator and denominator
+to grab the greatest common divisor so
+
+ align:start position:0%
+to grab the greatest common divisor so
+ 
+
+ align:start position:0%
+to grab the greatest common divisor so
+you know if it's 2 over 12 it'll find
+
+ align:start position:0%
+you know if it's 2 over 12 it'll find
+ 
+
+ align:start position:0%
+you know if it's 2 over 12 it'll find
+two then the next line here take the
+
+ align:start position:0%
+two then the next line here take the
+ 
+
+ align:start position:0%
+two then the next line here take the
+numer the numerator and divides by that
+
+ align:start position:0%
+numer the numerator and divides by that
+ 
+
+ align:start position:0%
+numer the numerator and divides by that
+greatest common divisor and casts it to
+
+ align:start position:0%
+greatest common divisor and casts it to
+ 
+
+ align:start position:0%
+greatest common divisor and casts it to
+an INT right because I want my numerator
+
+ align:start position:0%
+an INT right because I want my numerator
+ 
+
+ align:start position:0%
+an INT right because I want my numerator
+to be an INT and my denominator to be an
+
+ align:start position:0%
+to be an INT and my denominator to be an
+ 
+
+ align:start position:0%
+to be an INT and my denominator to be an
+INT right so it'll take the numerator
+
+ align:start position:0%
+INT right so it'll take the numerator
+ 
+
+ align:start position:0%
+INT right so it'll take the numerator
+and divide by for example two same with
+
+ align:start position:0%
+and divide by for example two same with
+ 
+
+ align:start position:0%
+and divide by for example two same with
+denominator I'm going to take my
+
+ align:start position:0%
+denominator I'm going to take my
+ 
+
+ align:start position:0%
+denominator I'm going to take my
+denominator and divide by that same gcd
+
+ align:start position:0%
+denominator and divide by that same gcd
+ 
+
+ align:start position:0%
+denominator and divide by that same gcd
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+found casting to an in so my new top and
+
+ align:start position:0%
+found casting to an in so my new top and
+ 
+
+ align:start position:0%
+found casting to an in so my new top and
+my new bottom will now be used to create
+
+ align:start position:0%
+my new bottom will now be used to create
+ 
+
+ align:start position:0%
+my new bottom will now be used to create
+a new fraction object
+
+ align:start position:0%
+a new fraction object
+ 
+
+ align:start position:0%
+a new fraction object
+that is in reduced form so one6 for the
+
+ align:start position:0%
+that is in reduced form so one6 for the
+ 
+
+ align:start position:0%
+that is in reduced form so one6 for the
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+212 right so here it is this is my
+
+ align:start position:0%
+212 right so here it is this is my
+ 
+
+ align:start position:0%
+212 right so here it is this is my
+previous example where I multiplied that
+
+ align:start position:0%
+previous example where I multiplied that
+ 
+
+ align:start position:0%
+previous example where I multiplied that
+thing that gave
+
+ align:start position:0%
+thing that gave
+ 
+
+ align:start position:0%
+thing that gave
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+212 and then if I do c. reduce python
+
+ align:start position:0%
+212 and then if I do c. reduce python
+ 
+
+ align:start position:0%
+212 and then if I do c. reduce python
+will call the reduce method on C so the
+
+ align:start position:0%
+will call the reduce method on C so the
+ 
+
+ align:start position:0%
+will call the reduce method on C so the
+object that's uh whose numerator is two
+
+ align:start position:0%
+object that's uh whose numerator is two
+ 
+
+ align:start position:0%
+object that's uh whose numerator is two
+and denominator is 12 and then this will
+
+ align:start position:0%
+and denominator is 12 and then this will
+ 
+
+ align:start position:0%
+and denominator is 12 and then this will
+reduce it to 1 over six and we will
+
+ align:start position:0%
+reduce it to 1 over six and we will
+ 
+
+ align:start position:0%
+reduce it to 1 over six and we will
+print call the Str Str method on an OB
+
+ align:start position:0%
+print call the Str Str method on an OB
+ 
+
+ align:start position:0%
+print call the Str Str method on an OB
+of type um fraction to give me one over
+
+ align:start position:0%
+of type um fraction to give me one over
+ 
+
+ align:start position:0%
+of type um fraction to give me one over
+six everyone okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes um you could put it outside the
+
+ align:start position:0%
+yes um you could put it outside the
+ 
+
+ align:start position:0%
+yes um you could put it outside the
+reduce but since it's being used
+
+ align:start position:0%
+reduce but since it's being used
+ 
+
+ align:start position:0%
+reduce but since it's being used
+specifically in the reduce we'd like to
+
+ align:start position:0%
+specifically in the reduce we'd like to
+ 
+
+ align:start position:0%
+specifically in the reduce we'd like to
+just keep it within right so it's not if
+
+ align:start position:0%
+just keep it within right so it's not if
+ 
+
+ align:start position:0%
+just keep it within right so it's not if
+it doesn't need to be used by other
+
+ align:start position:0%
+it doesn't need to be used by other
+ 
+
+ align:start position:0%
+it doesn't need to be used by other
+things we'll just keep it only to the
+
+ align:start position:0%
+things we'll just keep it only to the
+ 
+
+ align:start position:0%
+things we'll just keep it only to the
+sort of scope where it needs to exist
+
+ align:start position:0%
+sort of scope where it needs to exist
+ 
+
+ align:start position:0%
+sort of scope where it needs to exist
+but it it can be outside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so one thing is weird here
+
+ align:start position:0%
+yeah okay so one thing is weird here
+ 
+
+ align:start position:0%
+yeah okay so one thing is weird here
+though right this L if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here um what is the type uh that is gets
+
+ align:start position:0%
+here um what is the type uh that is gets
+ 
+
+ align:start position:0%
+here um what is the type uh that is gets
+returned from the elves you guys tell me
+
+ align:start position:0%
+returned from the elves you guys tell me
+ 
+
+ align:start position:0%
+returned from the elves you guys tell me
+what's this type here that gets returned
+
+ align:start position:0%
+what's this type here that gets returned
+ 
+
+ align:start position:0%
+what's this type here that gets returned
+down in the else fraction what is the
+
+ align:start position:0%
+down in the else fraction what is the
+ 
+
+ align:start position:0%
+down in the else fraction what is the
+type being returned in the L if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes an
+
+ align:start position:0%
+yes an
+ 
+
+ align:start position:0%
+yes an
+INT so if the denominator happens to be
+
+ align:start position:0%
+INT so if the denominator happens to be
+ 
+
+ align:start position:0%
+INT so if the denominator happens to be
+a one this function uh this method
+
+ align:start position:0%
+a one this function uh this method
+ 
+
+ align:start position:0%
+a one this function uh this method
+reduce returns an
+
+ align:start position:0%
+reduce returns an
+ 
+
+ align:start position:0%
+reduce returns an
+integer if it's not it returns a
+
+ align:start position:0%
+integer if it's not it returns a
+ 
+
+ align:start position:0%
+integer if it's not it returns a
+fraction so if at some point in the
+
+ align:start position:0%
+fraction so if at some point in the
+ 
+
+ align:start position:0%
+fraction so if at some point in the
+future you're mixing you know you you
+
+ align:start position:0%
+future you're mixing you know you you
+ 
+
+ align:start position:0%
+future you're mixing you know you you
+happen to reduce something that has a
+
+ align:start position:0%
+happen to reduce something that has a
+ 
+
+ align:start position:0%
+happen to reduce something that has a
+denominator of one you're now working
+
+ align:start position:0%
+denominator of one you're now working
+ 
+
+ align:start position:0%
+denominator of one you're now working
+with integers and then potentially you'd
+
+ align:start position:0%
+with integers and then potentially you'd
+ 
+
+ align:start position:0%
+with integers and then potentially you'd
+be doing further operations by mixing
+
+ align:start position:0%
+be doing further operations by mixing
+ 
+
+ align:start position:0%
+be doing further operations by mixing
+that with fraction object so as an
+
+ align:start position:0%
+that with fraction object so as an
+ 
+
+ align:start position:0%
+that with fraction object so as an
+example here I've got a fraction object
+
+ align:start position:0%
+example here I've got a fraction object
+ 
+
+ align:start position:0%
+example here I've got a fraction object
+a 4 over one B 3 over9 reducing a gives
+
+ align:start position:0%
+a 4 over one B 3 over9 reducing a gives
+ 
+
+ align:start position:0%
+a 4 over one B 3 over9 reducing a gives
+me a four fine it's the integer four and
+
+ align:start position:0%
+me a four fine it's the integer four and
+ 
+
+ align:start position:0%
+me a four fine it's the integer four and
+reducing B gives me one over three it's
+
+ align:start position:0%
+reducing B gives me one over three it's
+ 
+
+ align:start position:0%
+reducing B gives me one over three it's
+fraction one over three right so the
+
+ align:start position:0%
+fraction one over three right so the
+ 
+
+ align:start position:0%
+fraction one over three right so the
+type just to show you exactly you know
+
+ align:start position:0%
+type just to show you exactly you know
+ 
+
+ align:start position:0%
+type just to show you exactly you know
+that I'm not lying uh the type of the A
+
+ align:start position:0%
+that I'm not lying uh the type of the A
+ 
+
+ align:start position:0%
+that I'm not lying uh the type of the A
+reduced is an INT right that's what the
+
+ align:start position:0%
+reduced is an INT right that's what the
+ 
+
+ align:start position:0%
+reduced is an INT right that's what the
+code is doing and the type of b reduced
+
+ align:start position:0%
+code is doing and the type of b reduced
+ 
+
+ align:start position:0%
+code is doing and the type of b reduced
+is a fraction
+
+ align:start position:0%
+is a fraction
+ 
+
+ align:start position:0%
+is a fraction
+so then when we do the star operator
+
+ align:start position:0%
+so then when we do the star operator
+ 
+
+ align:start position:0%
+so then when we do the star operator
+between AR and BR Python's going to say
+
+ align:start position:0%
+between AR and BR Python's going to say
+ 
+
+ align:start position:0%
+between AR and BR Python's going to say
+you're trying to multiply an in with a
+
+ align:start position:0%
+you're trying to multiply an in with a
+ 
+
+ align:start position:0%
+you're trying to multiply an in with a
+fraction did you ever tell me how to do
+
+ align:start position:0%
+fraction did you ever tell me how to do
+ 
+
+ align:start position:0%
+fraction did you ever tell me how to do
+that no right we told it how to multiply
+
+ align:start position:0%
+that no right we told it how to multiply
+ 
+
+ align:start position:0%
+that no right we told it how to multiply
+a fraction in another fraction but not
+
+ align:start position:0%
+a fraction in another fraction but not
+ 
+
+ align:start position:0%
+a fraction in another fraction but not
+an INT with a fraction and so python
+
+ align:start position:0%
+an INT with a fraction and so python
+ 
+
+ align:start position:0%
+an INT with a fraction and so python
+will fail here right so one thing that
+
+ align:start position:0%
+will fail here right so one thing that
+ 
+
+ align:start position:0%
+will fail here right so one thing that
+you can do to fix it is to change uh
+
+ align:start position:0%
+you can do to fix it is to change uh
+ 
+
+ align:start position:0%
+you can do to fix it is to change uh
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+L if here so let's have everything
+
+ align:start position:0%
+L if here so let's have everything
+ 
+
+ align:start position:0%
+L if here so let's have everything
+consistent so I want you to do this
+
+ align:start position:0%
+consistent so I want you to do this
+ 
+
+ align:start position:0%
+consistent so I want you to do this
+change instead of returning self. num
+
+ align:start position:0%
+change instead of returning self. num
+ 
+
+ align:start position:0%
+change instead of returning self. num
+return for me a fraction object
+
+ align:start position:0%
+return for me a fraction object
+ 
+
+ align:start position:0%
+return for me a fraction object
+representing the numerator
+
+ align:start position:0%
+representing the numerator
+ 
+
+ align:start position:0%
+representing the numerator
+right all right does anyone know just a
+
+ align:start position:0%
+right all right does anyone know just a
+ 
+
+ align:start position:0%
+right all right does anyone know just a
+small change to instead of returning
+
+ align:start position:0%
+small change to instead of returning
+ 
+
+ align:start position:0%
+small change to instead of returning
+self. num what should I
+
+ align:start position:0%
+self. num what should I
+ 
+
+ align:start position:0%
+self. num what should I
+return how do I make a fraction object
+
+ align:start position:0%
+return how do I make a fraction object
+ 
+
+ align:start position:0%
+return how do I make a fraction object
+just invoke the name of fraction right
+
+ align:start position:0%
+just invoke the name of fraction right
+ 
+
+ align:start position:0%
+just invoke the name of fraction right
+what's the numerator of this fraction
+
+ align:start position:0%
+what's the numerator of this fraction
+ 
+
+ align:start position:0%
+what's the numerator of this fraction
+object supposed to be
+
+ align:start position:0%
+object supposed to be
+ 
+
+ align:start position:0%
+object supposed to be
+it's already there self. num what's the
+
+ align:start position:0%
+it's already there self. num what's the
+ 
+
+ align:start position:0%
+it's already there self. num what's the
+denominator of this fraction
+
+ align:start position:0%
+denominator of this fraction
+ 
+
+ align:start position:0%
+denominator of this fraction
+object yeah exactly so it just returns a
+
+ align:start position:0%
+object yeah exactly so it just returns a
+ 
+
+ align:start position:0%
+object yeah exactly so it just returns a
+fraction object whose numerator is
+
+ align:start position:0%
+fraction object whose numerator is
+ 
+
+ align:start position:0%
+fraction object whose numerator is
+selfon num and denominator is one
+
+ align:start position:0%
+selfon num and denominator is one
+ 
+
+ align:start position:0%
+selfon num and denominator is one
+exactly right so now all the different
+
+ align:start position:0%
+exactly right so now all the different
+ 
+
+ align:start position:0%
+exactly right so now all the different
+cases except for this randomly weird
+
+ align:start position:0%
+cases except for this randomly weird
+ 
+
+ align:start position:0%
+cases except for this randomly weird
+denominator being zero right in case
+
+ align:start position:0%
+denominator being zero right in case
+ 
+
+ align:start position:0%
+denominator being zero right in case
+that happens some something's gone wrong
+
+ align:start position:0%
+that happens some something's gone wrong
+ 
+
+ align:start position:0%
+that happens some something's gone wrong
+maybe all the other cases are returning
+
+ align:start position:0%
+maybe all the other cases are returning
+ 
+
+ align:start position:0%
+maybe all the other cases are returning
+a fraction object which is good because
+
+ align:start position:0%
+a fraction object which is good because
+ 
+
+ align:start position:0%
+a fraction object which is good because
+now it's consistent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right oh yeah exactly so we did say we
+
+ align:start position:0%
+right oh yeah exactly so we did say we
+ 
+
+ align:start position:0%
+right oh yeah exactly so we did say we
+didn't want it to be five over one but
+
+ align:start position:0%
+didn't want it to be five over one but
+ 
+
+ align:start position:0%
+didn't want it to be five over one but
+this is actually using the old Str Str
+
+ align:start position:0%
+this is actually using the old Str Str
+ 
+
+ align:start position:0%
+this is actually using the old Str Str
+method where we didn't do that check so
+
+ align:start position:0%
+method where we didn't do that check so
+ 
+
+ align:start position:0%
+method where we didn't do that check so
+it will print five over one but if we
+
+ align:start position:0%
+it will print five over one but if we
+ 
+
+ align:start position:0%
+it will print five over one but if we
+you know if we do the check if self. D
+
+ align:start position:0%
+you know if we do the check if self. D
+ 
+
+ align:start position:0%
+you know if we do the check if self. D
+Nom equal one then return stir self. n
+
+ align:start position:0%
+Nom equal one then return stir self. n
+ 
+
+ align:start position:0%
+Nom equal one then return stir self. n
+like if we add that then it won't do
+
+ align:start position:0%
+like if we add that then it won't do
+ 
+
+ align:start position:0%
+like if we add that then it won't do
+that yeah but this is just using the old
+
+ align:start position:0%
+that yeah but this is just using the old
+ 
+
+ align:start position:0%
+that yeah but this is just using the old
+uh strr method that doesn't do that nice
+
+ align:start position:0%
+uh strr method that doesn't do that nice
+ 
+
+ align:start position:0%
+uh strr method that doesn't do that nice
+formatting for
+
+ align:start position:0%
+formatting for
+ 
+
+ align:start position:0%
+formatting for
+us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions right we've been working a lot
+
+ align:start position:0%
+questions right we've been working a lot
+ 
+
+ align:start position:0%
+questions right we've been working a lot
+with returning new objects of the same
+
+ align:start position:0%
+with returning new objects of the same
+ 
+
+ align:start position:0%
+with returning new objects of the same
+type that we're writing right that's
+
+ align:start position:0%
+type that we're writing right that's
+ 
+
+ align:start position:0%
+type that we're writing right that's
+sort of a new thing
+
+ align:start position:0%
+sort of a new thing
+ 
+
+ align:start position:0%
+sort of a new thing
+today okay
+
+ align:start position:0%
+today okay
+ 
+
+ align:start position:0%
+today okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so what's the purpose of these two
+
+ align:start position:0%
+so what's the purpose of these two
+ 
+
+ align:start position:0%
+so what's the purpose of these two
+lectures right so hopefully it shows
+
+ align:start position:0%
+lectures right so hopefully it shows
+ 
+
+ align:start position:0%
+lectures right so hopefully it shows
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um it's very useful to uh to bundle data
+
+ align:start position:0%
+um it's very useful to uh to bundle data
+ 
+
+ align:start position:0%
+um it's very useful to uh to bundle data
+and behaviors together right so the
+
+ align:start position:0%
+and behaviors together right so the
+ 
+
+ align:start position:0%
+and behaviors together right so the
+ultimate goal when we're writing
+
+ align:start position:0%
+ultimate goal when we're writing
+ 
+
+ align:start position:0%
+ultimate goal when we're writing
+programs is to write code that's modular
+
+ align:start position:0%
+programs is to write code that's modular
+ 
+
+ align:start position:0%
+programs is to write code that's modular
+organized right because in the future
+
+ align:start position:0%
+organized right because in the future
+ 
+
+ align:start position:0%
+organized right because in the future
+you might want to build upon this code
+
+ align:start position:0%
+you might want to build upon this code
+ 
+
+ align:start position:0%
+you might want to build upon this code
+in the future you might want to read
+
+ align:start position:0%
+in the future you might want to read
+ 
+
+ align:start position:0%
+in the future you might want to read
+this code to use it for something else
+
+ align:start position:0%
+this code to use it for something else
+ 
+
+ align:start position:0%
+this code to use it for something else
+in the future other people might want to
+
+ align:start position:0%
+in the future other people might want to
+ 
+
+ align:start position:0%
+in the future other people might want to
+read this code or use this code this
+
+ align:start position:0%
+read this code or use this code this
+ 
+
+ align:start position:0%
+read this code or use this code this
+class that you wrote to build more
+
+ align:start position:0%
+class that you wrote to build more
+ 
+
+ align:start position:0%
+class that you wrote to build more
+complex classes right like we use the
+
+ align:start position:0%
+complex classes right like we use the
+ 
+
+ align:start position:0%
+complex classes right like we use the
+coordinate class to build a circle class
+
+ align:start position:0%
+coordinate class to build a circle class
+ 
+
+ align:start position:0%
+coordinate class to build a circle class
+right other people might use your circle
+
+ align:start position:0%
+right other people might use your circle
+ 
+
+ align:start position:0%
+right other people might use your circle
+class to build I don't know a sphere
+
+ align:start position:0%
+class to build I don't know a sphere
+ 
+
+ align:start position:0%
+class to build I don't know a sphere
+class or something like that something
+
+ align:start position:0%
+class or something like that something
+ 
+
+ align:start position:0%
+class or something like that something
+more complicated and so it's really nice
+
+ align:start position:0%
+more complicated and so it's really nice
+ 
+
+ align:start position:0%
+more complicated and so it's really nice
+to create these little data types that
+
+ align:start position:0%
+to create these little data types that
+ 
+
+ align:start position:0%
+to create these little data types that
+are't organized right modular and so
+
+ align:start position:0%
+are't organized right modular and so
+ 
+
+ align:start position:0%
+are't organized right modular and so
+we're basically bundling together these
+
+ align:start position:0%
+we're basically bundling together these
+ 
+
+ align:start position:0%
+we're basically bundling together these
+data right so what makes up your object
+
+ align:start position:0%
+data right so what makes up your object
+ 
+
+ align:start position:0%
+data right so what makes up your object
+and behaviors together so we can use
+
+ align:start position:0%
+and behaviors together so we can use
+ 
+
+ align:start position:0%
+and behaviors together so we can use
+these objects in a nicely consistent way
+
+ align:start position:0%
+these objects in a nicely consistent way
+ 
+
+ align:start position:0%
+these objects in a nicely consistent way
+so remember back when we were learning
+
+ align:start position:0%
+so remember back when we were learning
+ 
+
+ align:start position:0%
+so remember back when we were learning
+about functions right the ideas of
+
+ align:start position:0%
+about functions right the ideas of
+ 
+
+ align:start position:0%
+about functions right the ideas of
+decomposition and abstraction were very
+
+ align:start position:0%
+decomposition and abstraction were very
+ 
+
+ align:start position:0%
+decomposition and abstraction were very
+important functions basically took a
+
+ align:start position:0%
+important functions basically took a
+ 
+
+ align:start position:0%
+important functions basically took a
+chunk of code and decompose them into
+
+ align:start position:0%
+chunk of code and decompose them into
+ 
+
+ align:start position:0%
+chunk of code and decompose them into
+one module that we could reuse many many
+
+ align:start position:0%
+one module that we could reuse many many
+ 
+
+ align:start position:0%
+one module that we could reuse many many
+different places right and we abstracted
+
+ align:start position:0%
+different places right and we abstracted
+ 
+
+ align:start position:0%
+different places right and we abstracted
+away the details of the function through
+
+ align:start position:0%
+away the details of the function through
+ 
+
+ align:start position:0%
+away the details of the function through
+doc string so people didn't have to slog
+
+ align:start position:0%
+doc string so people didn't have to slog
+ 
+
+ align:start position:0%
+doc string so people didn't have to slog
+through a whole bunch of code to figure
+
+ align:start position:0%
+through a whole bunch of code to figure
+ 
+
+ align:start position:0%
+through a whole bunch of code to figure
+out what the function did all they did
+
+ align:start position:0%
+out what the function did all they did
+ 
+
+ align:start position:0%
+out what the function did all they did
+was read the doc string and they knew
+
+ align:start position:0%
+was read the doc string and they knew
+ 
+
+ align:start position:0%
+was read the doc string and they knew
+exactly what we
+
+ align:start position:0%
+exactly what we
+ 
+
+ align:start position:0%
+exactly what we
+wanted now object oriented programming
+
+ align:start position:0%
+wanted now object oriented programming
+ 
+
+ align:start position:0%
+wanted now object oriented programming
+and python classes have that same big
+
+ align:start position:0%
+and python classes have that same big
+ 
+
+ align:start position:0%
+and python classes have that same big
+composition and abstraction energy right
+
+ align:start position:0%
+composition and abstraction energy right
+ 
+
+ align:start position:0%
+composition and abstraction energy right
+they've got a bunch of modules that
+
+ align:start position:0%
+they've got a bunch of modules that
+ 
+
+ align:start position:0%
+they've got a bunch of modules that
+we're creating here where we're bundling
+
+ align:start position:0%
+we're creating here where we're bundling
+ 
+
+ align:start position:0%
+we're creating here where we're bundling
+together data and behaviors right so we
+
+ align:start position:0%
+together data and behaviors right so we
+ 
+
+ align:start position:0%
+together data and behaviors right so we
+can create a whole bunch of objects that
+
+ align:start position:0%
+can create a whole bunch of objects that
+ 
+
+ align:start position:0%
+can create a whole bunch of objects that
+behave in the exact same way nicely
+
+ align:start position:0%
+behave in the exact same way nicely
+ 
+
+ align:start position:0%
+behave in the exact same way nicely
+consistent so that we know that if I
+
+ align:start position:0%
+consistent so that we know that if I
+ 
+
+ align:start position:0%
+consistent so that we know that if I
+create a coordinate object here it's
+
+ align:start position:0%
+create a coordinate object here it's
+ 
+
+ align:start position:0%
+create a coordinate object here it's
+going to have an X and A yvalue and if I
+
+ align:start position:0%
+going to have an X and A yvalue and if I
+ 
+
+ align:start position:0%
+going to have an X and A yvalue and if I
+create another coordinate object it's
+
+ align:start position:0%
+create another coordinate object it's
+ 
+
+ align:start position:0%
+create another coordinate object it's
+also going to have an X and A yvalue
+
+ align:start position:0%
+also going to have an X and A yvalue
+ 
+
+ align:start position:0%
+also going to have an X and A yvalue
+it's not suddenly going to have an X Y
+
+ align:start position:0%
+it's not suddenly going to have an X Y
+ 
+
+ align:start position:0%
+it's not suddenly going to have an X Y
+and Z value right so creating these
+
+ align:start position:0%
+and Z value right so creating these
+ 
+
+ align:start position:0%
+and Z value right so creating these
+objects that work in a consistent way is
+
+ align:start position:0%
+objects that work in a consistent way is
+ 
+
+ align:start position:0%
+objects that work in a consistent way is
+is very very is a very um you know
+
+ align:start position:0%
+is very very is a very um you know
+ 
+
+ align:start position:0%
+is very very is a very um you know
+decomposition uh and abstraction uh uh
+
+ align:start position:0%
+decomposition uh and abstraction uh uh
+ 
+
+ align:start position:0%
+decomposition uh and abstraction uh uh
+you are working with the ideas of
+
+ align:start position:0%
+you are working with the ideas of
+ 
+
+ align:start position:0%
+you are working with the ideas of
+decomposition abstraction just like
+
+ align:start position:0%
+decomposition abstraction just like
+ 
+
+ align:start position:0%
+decomposition abstraction just like
+functions did okay so next lecture we
+
+ align:start position:0%
+functions did okay so next lecture we
+ 
+
+ align:start position:0%
+functions did okay so next lecture we
+will be starting on we'll do a little
+
+ align:start position:0%
+will be starting on we'll do a little
+ 
+
+ align:start position:0%
+will be starting on we'll do a little
+bit more of these classes and then we'll
+
+ align:start position:0%
+bit more of these classes and then we'll
+ 
+
+ align:start position:0%
+bit more of these classes and then we'll
+start on inheritance so having parents
+
+ align:start position:0%
+start on inheritance so having parents
+ 
+
+ align:start position:0%
+start on inheritance so having parents
+the objects that we created all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
\ No newline at end of file
diff --git a/gWLC3r6EHl0.txt b/gWLC3r6EHl0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c27054db1e0d7c380cc5f93dd29556ac82e43e04
--- /dev/null
+++ b/gWLC3r6EHl0.txt
@@ -0,0 +1,1067 @@
+align:start position:0%
+ 
+so when we analyzed Newton's Second Law
+
+ align:start position:0%
+so when we analyzed Newton's Second Law
+ 
+
+ align:start position:0%
+so when we analyzed Newton's Second Law
+applied to this compound system we had
+
+ align:start position:0%
+applied to this compound system we had
+ 
+
+ align:start position:0%
+applied to this compound system we had
+two equations for M1 um object one and
+
+ align:start position:0%
+two equations for M1 um object one and
+ 
+
+ align:start position:0%
+two equations for M1 um object one and
+object two and what we found is that we
+
+ align:start position:0%
+object two and what we found is that we
+ 
+
+ align:start position:0%
+object two and what we found is that we
+had three unknowns the tension in the
+
+ align:start position:0%
+had three unknowns the tension in the
+ 
+
+ align:start position:0%
+had three unknowns the tension in the
+string and the accelerations of the two
+
+ align:start position:0%
+string and the accelerations of the two
+ 
+
+ align:start position:0%
+string and the accelerations of the two
+objects now how do we F how do we solve
+
+ align:start position:0%
+objects now how do we F how do we solve
+ 
+
+ align:start position:0%
+objects now how do we F how do we solve
+this system well we're missing one
+
+ align:start position:0%
+this system well we're missing one
+ 
+
+ align:start position:0%
+this system well we're missing one
+condition which is a constraint
+
+ align:start position:0%
+condition which is a constraint
+ 
+
+ align:start position:0%
+condition which is a constraint
+condition which is as object two moves
+
+ align:start position:0%
+condition which is as object two moves
+ 
+
+ align:start position:0%
+condition which is as object two moves
+and object one moves they have to move
+
+ align:start position:0%
+and object one moves they have to move
+ 
+
+ align:start position:0%
+and object one moves they have to move
+in some relation ship together and now
+
+ align:start position:0%
+in some relation ship together and now
+ 
+
+ align:start position:0%
+in some relation ship together and now
+what we'd like to do is show an analytic
+
+ align:start position:0%
+what we'd like to do is show an analytic
+ 
+
+ align:start position:0%
+what we'd like to do is show an analytic
+approach for finding that constraint
+
+ align:start position:0%
+approach for finding that constraint
+ 
+
+ align:start position:0%
+approach for finding that constraint
+condition and what the way we think
+
+ align:start position:0%
+condition and what the way we think
+ 
+
+ align:start position:0%
+condition and what the way we think
+about it is that we'll call L equal to
+
+ align:start position:0%
+about it is that we'll call L equal to
+ 
+
+ align:start position:0%
+about it is that we'll call L equal to
+the length of the
+
+ align:start position:0%
+the length of the
+ 
+
+ align:start position:0%
+the length of the
+string and this quantity is a
+
+ align:start position:0%
+string and this quantity is a
+ 
+
+ align:start position:0%
+string and this quantity is a
+constant and what we'd like to do is
+
+ align:start position:0%
+constant and what we'd like to do is
+ 
+
+ align:start position:0%
+constant and what we'd like to do is
+introduce coordinate functions for our
+
+ align:start position:0%
+introduce coordinate functions for our
+ 
+
+ align:start position:0%
+introduce coordinate functions for our
+object one and our object two and
+
+ align:start position:0%
+object one and our object two and
+ 
+
+ align:start position:0%
+object one and our object two and
+express l in terms of those coordinate
+
+ align:start position:0%
+express l in terms of those coordinate
+ 
+
+ align:start position:0%
+express l in terms of those coordinate
+functions and then take two derivatives
+
+ align:start position:0%
+functions and then take two derivatives
+ 
+
+ align:start position:0%
+functions and then take two derivatives
+of L set that equal to zero because it's
+
+ align:start position:0%
+of L set that equal to zero because it's
+ 
+
+ align:start position:0%
+of L set that equal to zero because it's
+a constant and that will give us a
+
+ align:start position:0%
+a constant and that will give us a
+ 
+
+ align:start position:0%
+a constant and that will give us a
+relationship between the accelerations
+
+ align:start position:0%
+relationship between the accelerations
+ 
+
+ align:start position:0%
+relationship between the accelerations
+of objects one and two now this is a
+
+ align:start position:0%
+of objects one and two now this is a
+ 
+
+ align:start position:0%
+of objects one and two now this is a
+little bit tricky and so what we want to
+
+ align:start position:0%
+little bit tricky and so what we want to
+ 
+
+ align:start position:0%
+little bit tricky and so what we want to
+do is very carefully show how we
+
+ align:start position:0%
+do is very carefully show how we
+ 
+
+ align:start position:0%
+do is very carefully show how we
+introduce coordinate functions recall
+
+ align:start position:0%
+introduce coordinate functions recall
+ 
+
+ align:start position:0%
+introduce coordinate functions recall
+that we had J hat one down and J hat two
+
+ align:start position:0%
+that we had J hat one down and J hat two
+ 
+
+ align:start position:0%
+that we had J hat one down and J hat two
+downwards what that implies is that
+
+ align:start position:0%
+downwards what that implies is that
+ 
+
+ align:start position:0%
+downwards what that implies is that
+we're choosing some origin and we're
+
+ align:start position:0%
+we're choosing some origin and we're
+ 
+
+ align:start position:0%
+we're choosing some origin and we're
+let's choose an origin up here and for a
+
+ align:start position:0%
+let's choose an origin up here and for a
+ 
+
+ align:start position:0%
+let's choose an origin up here and for a
+coordinate function for object one it
+
+ align:start position:0%
+coordinate function for object one it
+ 
+
+ align:start position:0%
+coordinate function for object one it
+has to be consistent with our choice of
+
+ align:start position:0%
+has to be consistent with our choice of
+ 
+
+ align:start position:0%
+has to be consistent with our choice of
+what we mean by jat1 so in this sense y1
+
+ align:start position:0%
+what we mean by jat1 so in this sense y1
+ 
+
+ align:start position:0%
+what we mean by jat1 so in this sense y1
+is a positive quantity when we're going
+
+ align:start position:0%
+is a positive quantity when we're going
+ 
+
+ align:start position:0%
+is a positive quantity when we're going
+downward um now what about coordinate
+
+ align:start position:0%
+downward um now what about coordinate
+ 
+
+ align:start position:0%
+downward um now what about coordinate
+functions for the other objects in the
+
+ align:start position:0%
+functions for the other objects in the
+ 
+
+ align:start position:0%
+functions for the other objects in the
+system well let's look at a few things
+
+ align:start position:0%
+system well let's look at a few things
+ 
+
+ align:start position:0%
+system well let's look at a few things
+first um this is a fixed distance we'll
+
+ align:start position:0%
+first um this is a fixed distance we'll
+ 
+
+ align:start position:0%
+first um this is a fixed distance we'll
+call it S1 between the center of the
+
+ align:start position:0%
+call it S1 between the center of the
+ 
+
+ align:start position:0%
+call it S1 between the center of the
+pulley
+
+ align:start position:0%
+pulley
+ 
+
+ align:start position:0%
+pulley
+and between the ceiling and the center
+
+ align:start position:0%
+and between the ceiling and the center
+ 
+
+ align:start position:0%
+and between the ceiling and the center
+of the pulley and let's make each of the
+
+ align:start position:0%
+of the pulley and let's make each of the
+ 
+
+ align:start position:0%
+of the pulley and let's make each of the
+pulleys a radius
+
+ align:start position:0%
+pulleys a radius
+ 
+
+ align:start position:0%
+pulleys a radius
+R and let's call this a
+
+ align:start position:0%
+R and let's call this a
+ 
+
+ align:start position:0%
+R and let's call this a
+function y
+
+ align:start position:0%
+function y
+ 
+
+ align:start position:0%
+function y
+b and let's make this Y 2 of T so now we
+
+ align:start position:0%
+b and let's make this Y 2 of T so now we
+ 
+
+ align:start position:0%
+b and let's make this Y 2 of T so now we
+have coordinate functions for two and
+
+ align:start position:0%
+have coordinate functions for two and
+ 
+
+ align:start position:0%
+have coordinate functions for two and
+coordinate functions for one and again
+
+ align:start position:0%
+coordinate functions for one and again
+ 
+
+ align:start position:0%
+coordinate functions for one and again
+recall that this distance here S2 is a
+
+ align:start position:0%
+recall that this distance here S2 is a
+ 
+
+ align:start position:0%
+recall that this distance here S2 is a
+fixed
+
+ align:start position:0%
+fixed
+ 
+
+ align:start position:0%
+fixed
+distance and when Define these
+
+ align:start position:0%
+distance and when Define these
+ 
+
+ align:start position:0%
+distance and when Define these
+coordinate functions in this fashion we
+
+ align:start position:0%
+coordinate functions in this fashion we
+ 
+
+ align:start position:0%
+coordinate functions in this fashion we
+know that the second derivative d^2
+
+ align:start position:0%
+know that the second derivative d^2
+ 
+
+ align:start position:0%
+know that the second derivative d^2
+y1 DT ^2 this is precisely what we mean
+
+ align:start position:0%
+y1 DT ^2 this is precisely what we mean
+ 
+
+ align:start position:0%
+y1 DT ^2 this is precisely what we mean
+by the acceleration of object one and in
+
+ align:start position:0%
+by the acceleration of object one and in
+ 
+
+ align:start position:0%
+by the acceleration of object one and in
+the similar fashion d^2 Y 2 DT ^2 is
+
+ align:start position:0%
+the similar fashion d^2 Y 2 DT ^2 is
+ 
+
+ align:start position:0%
+the similar fashion d^2 Y 2 DT ^2 is
+what we mean by the acceleration of
+
+ align:start position:0%
+what we mean by the acceleration of
+ 
+
+ align:start position:0%
+what we mean by the acceleration of
+object 2 so we've introduced a
+
+ align:start position:0%
+object 2 so we've introduced a
+ 
+
+ align:start position:0%
+object 2 so we've introduced a
+coordinate system we've made it very
+
+ align:start position:0%
+coordinate system we've made it very
+ 
+
+ align:start position:0%
+coordinate system we've made it very
+clear what we mean by the accelerations
+
+ align:start position:0%
+clear what we mean by the accelerations
+ 
+
+ align:start position:0%
+clear what we mean by the accelerations
+of A1 and A2 and now let's look at our
+
+ align:start position:0%
+of A1 and A2 and now let's look at our
+ 
+
+ align:start position:0%
+of A1 and A2 and now let's look at our
+constraint condition that the length of
+
+ align:start position:0%
+constraint condition that the length of
+ 
+
+ align:start position:0%
+constraint condition that the length of
+the string is constant so what we're
+
+ align:start position:0%
+the string is constant so what we're
+ 
+
+ align:start position:0%
+the string is constant so what we're
+going to do is try to see if we can
+
+ align:start position:0%
+going to do is try to see if we can
+ 
+
+ align:start position:0%
+going to do is try to see if we can
+express the length of this string in
+
+ align:start position:0%
+express the length of this string in
+ 
+
+ align:start position:0%
+express the length of this string in
+terms of all the coordinate functions
+
+ align:start position:0%
+terms of all the coordinate functions
+ 
+
+ align:start position:0%
+terms of all the coordinate functions
+and some of these ancillary quantities
+
+ align:start position:0%
+and some of these ancillary quantities
+ 
+
+ align:start position:0%
+and some of these ancillary quantities
+so what we have here is that the length
+
+ align:start position:0%
+so what we have here is that the length
+ 
+
+ align:start position:0%
+so what we have here is that the length
+of the string is
+
+ align:start position:0%
+of the string is
+ 
+
+ align:start position:0%
+of the string is
+YB going down here so the length of the
+
+ align:start position:0%
+YB going down here so the length of the
+ 
+
+ align:start position:0%
+YB going down here so the length of the
+string has a factor YB it wraps around
+
+ align:start position:0%
+string has a factor YB it wraps around
+ 
+
+ align:start position:0%
+string has a factor YB it wraps around
+pulley B so that's pi
+
+ align:start position:0%
+pulley B so that's pi
+ 
+
+ align:start position:0%
+pulley B so that's pi
+r and it goes up to this length
+
+ align:start position:0%
+r and it goes up to this length
+ 
+
+ align:start position:0%
+r and it goes up to this length
+here now this length is YB minus
+
+ align:start position:0%
+here now this length is YB minus
+ 
+
+ align:start position:0%
+here now this length is YB minus
+S1 so that's YB minus
+
+ align:start position:0%
+S1 so that's YB minus
+ 
+
+ align:start position:0%
+S1 so that's YB minus
+S1 we wrap around the pulley
+
+ align:start position:0%
+S1 we wrap around the pulley
+ 
+
+ align:start position:0%
+S1 we wrap around the pulley
+again that's pi r and now we have this
+
+ align:start position:0%
+again that's pi r and now we have this
+ 
+
+ align:start position:0%
+again that's pi r and now we have this
+length here which is y1
+
+ align:start position:0%
+length here which is y1
+ 
+
+ align:start position:0%
+length here which is y1
+minus S1 now
+
+ align:start position:0%
+minus S1 now
+ 
+
+ align:start position:0%
+minus S1 now
+S1 yeah and let's just make sure we have
+
+ align:start position:0%
+S1 yeah and let's just make sure we have
+ 
+
+ align:start position:0%
+S1 yeah and let's just make sure we have
+all of our quantities here now we also
+
+ align:start position:0%
+all of our quantities here now we also
+ 
+
+ align:start position:0%
+all of our quantities here now we also
+have another constraint condition that
+
+ align:start position:0%
+have another constraint condition that
+ 
+
+ align:start position:0%
+have another constraint condition that
+this length of the string call this
+
+ align:start position:0%
+this length of the string call this
+ 
+
+ align:start position:0%
+this length of the string call this
+we're going to call this
+
+ align:start position:0%
+we're going to call this
+ 
+
+ align:start position:0%
+we're going to call this
+L1 we have a second string here
+
+ align:start position:0%
+L1 we have a second string here
+ 
+
+ align:start position:0%
+L1 we have a second string here
+L2 and L2 is given by
+
+ align:start position:0%
+L2 and L2 is given by
+ 
+
+ align:start position:0%
+L2 and L2 is given by
+Y2 this length is Y2
+
+ align:start position:0%
+Y2 this length is Y2
+ 
+
+ align:start position:0%
+Y2 this length is Y2
+minus YB and that was what we called
+
+ align:start position:0%
+minus YB and that was what we called
+ 
+
+ align:start position:0%
+minus YB and that was what we called
+this constant
+
+ align:start position:0%
+this constant
+ 
+
+ align:start position:0%
+this constant
+S2 so we now have two string lengths L2
+
+ align:start position:0%
+S2 so we now have two string lengths L2
+ 
+
+ align:start position:0%
+S2 so we now have two string lengths L2
+= Y2 minus YB and both of these string
+
+ align:start position:0%
+= Y2 minus YB and both of these string
+ 
+
+ align:start position:0%
+= Y2 minus YB and both of these string
+lengths are constant and we have the
+
+ align:start position:0%
+lengths are constant and we have the
+ 
+
+ align:start position:0%
+lengths are constant and we have the
+following facts let's start with this
+
+ align:start position:0%
+following facts let's start with this
+ 
+
+ align:start position:0%
+following facts let's start with this
+one first that the second derivative of
+
+ align:start position:0%
+one first that the second derivative of
+ 
+
+ align:start position:0%
+one first that the second derivative of
+L2 DT ^2 because the length of the
+
+ align:start position:0%
+L2 DT ^2 because the length of the
+ 
+
+ align:start position:0%
+L2 DT ^2 because the length of the
+string is a constant that's zero and
+
+ align:start position:0%
+string is a constant that's zero and
+ 
+
+ align:start position:0%
+string is a constant that's zero and
+that tells us two derivatives of this is
+
+ align:start position:0%
+that tells us two derivatives of this is
+ 
+
+ align:start position:0%
+that tells us two derivatives of this is
+A2 and two derivatives of that is AB and
+
+ align:start position:0%
+A2 and two derivatives of that is AB and
+ 
+
+ align:start position:0%
+A2 and two derivatives of that is AB and
+this is something that we saw before
+
+ align:start position:0%
+this is something that we saw before
+ 
+
+ align:start position:0%
+this is something that we saw before
+that Block B and two are moving together
+
+ align:start position:0%
+that Block B and two are moving together
+ 
+
+ align:start position:0%
+that Block B and two are moving together
+so when we treated the system as just B
+
+ align:start position:0%
+so when we treated the system as just B
+ 
+
+ align:start position:0%
+so when we treated the system as just B
+and two together we see that the
+
+ align:start position:0%
+and two together we see that the
+ 
+
+ align:start position:0%
+and two together we see that the
+acceleration of two and the acceleration
+
+ align:start position:0%
+acceleration of two and the acceleration
+ 
+
+ align:start position:0%
+acceleration of two and the acceleration
+of pulley B are the same so we could
+
+ align:start position:0%
+of pulley B are the same so we could
+ 
+
+ align:start position:0%
+of pulley B are the same so we could
+have just said that before we began now
+
+ align:start position:0%
+have just said that before we began now
+ 
+
+ align:start position:0%
+have just said that before we began now
+let's put these equations aside for the
+
+ align:start position:0%
+let's put these equations aside for the
+ 
+
+ align:start position:0%
+let's put these equations aside for the
+moment and now let's consider taking two
+
+ align:start position:0%
+moment and now let's consider taking two
+ 
+
+ align:start position:0%
+moment and now let's consider taking two
+derivatives of
+
+ align:start position:0%
+derivatives of
+ 
+
+ align:start position:0%
+derivatives of
+length of string one we call string one
+
+ align:start position:0%
+length of string one we call string one
+ 
+
+ align:start position:0%
+length of string one we call string one
+is this object here we'll call this
+
+ align:start position:0%
+is this object here we'll call this
+ 
+
+ align:start position:0%
+is this object here we'll call this
+string
+
+ align:start position:0%
+string
+ 
+
+ align:start position:0%
+string
+one and this string two now again then
+
+ align:start position:0%
+one and this string two now again then
+ 
+
+ align:start position:0%
+one and this string two now again then
+if we take two derivatives let's look at
+
+ align:start position:0%
+if we take two derivatives let's look at
+ 
+
+ align:start position:0%
+if we take two derivatives let's look at
+our expression first um we see that we
+
+ align:start position:0%
+our expression first um we see that we
+ 
+
+ align:start position:0%
+our expression first um we see that we
+have two factors of YB and we have a
+
+ align:start position:0%
+have two factors of YB and we have a
+ 
+
+ align:start position:0%
+have two factors of YB and we have a
+bunch of constants whose derivative is
+
+ align:start position:0%
+bunch of constants whose derivative is
+ 
+
+ align:start position:0%
+bunch of constants whose derivative is
+zero so we don't have to worry about the
+
+ align:start position:0%
+zero so we don't have to worry about the
+ 
+
+ align:start position:0%
+zero so we don't have to worry about the
+wraparound distances the pi RS we don't
+
+ align:start position:0%
+wraparound distances the pi RS we don't
+ 
+
+ align:start position:0%
+wraparound distances the pi RS we don't
+have to worry about the constants S1 all
+
+ align:start position:0%
+have to worry about the constants S1 all
+ 
+
+ align:start position:0%
+have to worry about the constants S1 all
+we have to think about is which
+
+ align:start position:0%
+we have to think about is which
+ 
+
+ align:start position:0%
+we have to think about is which
+quantities are changing in time so we
+
+ align:start position:0%
+quantities are changing in time so we
+ 
+
+ align:start position:0%
+quantities are changing in time so we
+have 2 a when we take two derivatives
+
+ align:start position:0%
+have 2 a when we take two derivatives
+ 
+
+ align:start position:0%
+have 2 a when we take two derivatives
+and we have one factor of A1 and that's
+
+ align:start position:0%
+and we have one factor of A1 and that's
+ 
+
+ align:start position:0%
+and we have one factor of A1 and that's
+zero and now because the block and two
+
+ align:start position:0%
+zero and now because the block and two
+ 
+
+ align:start position:0%
+zero and now because the block and two
+and pulley B are accelerating together
+
+ align:start position:0%
+and pulley B are accelerating together
+ 
+
+ align:start position:0%
+and pulley B are accelerating together
+we have our condition which is 2 A2 + A1
+
+ align:start position:0%
+we have our condition which is 2 A2 + A1
+ 
+
+ align:start position:0%
+we have our condition which is 2 A2 + A1
+is z or that A1 is equal to minus 2
+
+ align:start position:0%
+is z or that A1 is equal to minus 2
+ 
+
+ align:start position:0%
+is z or that A1 is equal to minus 2
+A2 and that is the extra constraint
+
+ align:start position:0%
+A2 and that is the extra constraint
+ 
+
+ align:start position:0%
+A2 and that is the extra constraint
+condition that will enabled us to solve
+
+ align:start position:0%
+condition that will enabled us to solve
+ 
+
+ align:start position:0%
+condition that will enabled us to solve
+the system of equations
\ No newline at end of file
diff --git a/gWdAc-rPHW8.txt b/gWdAc-rPHW8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..84ebbb559def56e7748d3d281df98f9a33476296
--- /dev/null
+++ b/gWdAc-rPHW8.txt
@@ -0,0 +1,17600 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if there are no immediate questions
+
+ align:start position:0%
+if there are no immediate questions
+ 
+
+ align:start position:0%
+if there are no immediate questions
+um that's good and uh if so then I'll go
+
+ align:start position:0%
+um that's good and uh if so then I'll go
+ 
+
+ align:start position:0%
+um that's good and uh if so then I'll go
+ahead and share screen and I will launch
+
+ align:start position:0%
+ahead and share screen and I will launch
+ 
+
+ align:start position:0%
+ahead and share screen and I will launch
+into our continuing adventure with
+
+ align:start position:0%
+into our continuing adventure with
+ 
+
+ align:start position:0%
+into our continuing adventure with
+quantum theory which is frankly one of
+
+ align:start position:0%
+quantum theory which is frankly one of
+ 
+
+ align:start position:0%
+quantum theory which is frankly one of
+my favorite Adventures ever
+
+ align:start position:0%
+my favorite Adventures ever
+ 
+
+ align:start position:0%
+my favorite Adventures ever
+uh speaking just for myself okay
+
+ align:start position:0%
+uh speaking just for myself okay
+ 
+
+ align:start position:0%
+uh speaking just for myself okay
+so you will hopefully remember uh on our
+
+ align:start position:0%
+so you will hopefully remember uh on our
+ 
+
+ align:start position:0%
+so you will hopefully remember uh on our
+previous class session we looked at
+
+ align:start position:0%
+previous class session we looked at
+ 
+
+ align:start position:0%
+previous class session we looked at
+um Vera Heisenberg's introduction of
+
+ align:start position:0%
+um Vera Heisenberg's introduction of
+ 
+
+ align:start position:0%
+um Vera Heisenberg's introduction of
+what came to be called Matrix mechanics
+
+ align:start position:0%
+what came to be called Matrix mechanics
+ 
+
+ align:start position:0%
+what came to be called Matrix mechanics
+uh in um sort of spring summer 1925 and
+
+ align:start position:0%
+uh in um sort of spring summer 1925 and
+ 
+
+ align:start position:0%
+uh in um sort of spring summer 1925 and
+what brought him to it what was he
+
+ align:start position:0%
+what brought him to it what was he
+ 
+
+ align:start position:0%
+what brought him to it what was he
+reacting against and a little taste of
+
+ align:start position:0%
+reacting against and a little taste of
+ 
+
+ align:start position:0%
+reacting against and a little taste of
+what people thought it might all add up
+
+ align:start position:0%
+what people thought it might all add up
+ 
+
+ align:start position:0%
+what people thought it might all add up
+to and today we're going to look
+
+ align:start position:0%
+to and today we're going to look
+ 
+
+ align:start position:0%
+to and today we're going to look
+actually at a kind of um complementary
+
+ align:start position:0%
+actually at a kind of um complementary
+ 
+
+ align:start position:0%
+actually at a kind of um complementary
+set of developments that were unfolding
+
+ align:start position:0%
+set of developments that were unfolding
+ 
+
+ align:start position:0%
+set of developments that were unfolding
+very close in time very rapid series of
+
+ align:start position:0%
+very close in time very rapid series of
+ 
+
+ align:start position:0%
+very close in time very rapid series of
+period of development but now looking at
+
+ align:start position:0%
+period of development but now looking at
+ 
+
+ align:start position:0%
+period of development but now looking at
+what became known as wave mechanics and
+
+ align:start position:0%
+what became known as wave mechanics and
+ 
+
+ align:start position:0%
+what became known as wave mechanics and
+some of its uh features that people
+
+ align:start position:0%
+some of its uh features that people
+ 
+
+ align:start position:0%
+some of its uh features that people
+began to really puzzle about
+
+ align:start position:0%
+began to really puzzle about
+ 
+
+ align:start position:0%
+began to really puzzle about
+so for today we'll we'll look at some of
+
+ align:start position:0%
+so for today we'll we'll look at some of
+ 
+
+ align:start position:0%
+so for today we'll we'll look at some of
+Erwin Schrodinger's most famous work
+
+ align:start position:0%
+Erwin Schrodinger's most famous work
+ 
+
+ align:start position:0%
+Erwin Schrodinger's most famous work
+again some of this might already be
+
+ align:start position:0%
+again some of this might already be
+ 
+
+ align:start position:0%
+again some of this might already be
+familiar to some of you but probably not
+
+ align:start position:0%
+familiar to some of you but probably not
+ 
+
+ align:start position:0%
+familiar to some of you but probably not
+to all and I think it's fun to just sort
+
+ align:start position:0%
+to all and I think it's fun to just sort
+ 
+
+ align:start position:0%
+to all and I think it's fun to just sort
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+go back through and and zoom out of it
+
+ align:start position:0%
+go back through and and zoom out of it
+ 
+
+ align:start position:0%
+go back through and and zoom out of it
+and say what what did Schrodinger think
+
+ align:start position:0%
+and say what what did Schrodinger think
+ 
+
+ align:start position:0%
+and say what what did Schrodinger think
+he was doing and why uh let alone what's
+
+ align:start position:0%
+he was doing and why uh let alone what's
+ 
+
+ align:start position:0%
+he was doing and why uh let alone what's
+the form of the equation
+
+ align:start position:0%
+the form of the equation
+ 
+
+ align:start position:0%
+the form of the equation
+um that he uh that he put together so
+
+ align:start position:0%
+um that he uh that he put together so
+ 
+
+ align:start position:0%
+um that he uh that he put together so
+that's the part one
+
+ align:start position:0%
+that's the part one
+ 
+
+ align:start position:0%
+that's the part one
+then we're going to look in Parts two
+
+ align:start position:0%
+then we're going to look in Parts two
+ 
+
+ align:start position:0%
+then we're going to look in Parts two
+and very briefly of a shorter part three
+
+ align:start position:0%
+and very briefly of a shorter part three
+ 
+
+ align:start position:0%
+and very briefly of a shorter part three
+at some of the implications that
+
+ align:start position:0%
+at some of the implications that
+ 
+
+ align:start position:0%
+at some of the implications that
+physicists began all ready to Grapple
+
+ align:start position:0%
+physicists began all ready to Grapple
+ 
+
+ align:start position:0%
+physicists began all ready to Grapple
+with implications of Schrodinger's wave
+
+ align:start position:0%
+with implications of Schrodinger's wave
+ 
+
+ align:start position:0%
+with implications of Schrodinger's wave
+mechanics really pretty quickly and for
+
+ align:start position:0%
+mechanics really pretty quickly and for
+ 
+
+ align:start position:0%
+mechanics really pretty quickly and for
+for both part two and part three
+
+ align:start position:0%
+for both part two and part three
+ 
+
+ align:start position:0%
+for both part two and part three
+um you know again as often happens for
+
+ align:start position:0%
+um you know again as often happens for
+ 
+
+ align:start position:0%
+um you know again as often happens for
+class session I'll try to cover some of
+
+ align:start position:0%
+class session I'll try to cover some of
+ 
+
+ align:start position:0%
+class session I'll try to cover some of
+the main highlights some of the most
+
+ align:start position:0%
+the main highlights some of the most
+ 
+
+ align:start position:0%
+the main highlights some of the most
+what I think most interesting or Salient
+
+ align:start position:0%
+what I think most interesting or Salient
+ 
+
+ align:start position:0%
+what I think most interesting or Salient
+points and then some of the details some
+
+ align:start position:0%
+points and then some of the details some
+ 
+
+ align:start position:0%
+points and then some of the details some
+of the extra derivations and so on are
+
+ align:start position:0%
+of the extra derivations and so on are
+ 
+
+ align:start position:0%
+of the extra derivations and so on are
+in those optional lecture notes strictly
+
+ align:start position:0%
+in those optional lecture notes strictly
+ 
+
+ align:start position:0%
+in those optional lecture notes strictly
+optional they are available on canvas
+
+ align:start position:0%
+optional they are available on canvas
+ 
+
+ align:start position:0%
+optional they are available on canvas
+but if something goes by too quickly or
+
+ align:start position:0%
+but if something goes by too quickly or
+ 
+
+ align:start position:0%
+but if something goes by too quickly or
+I just had to sort of skim over some of
+
+ align:start position:0%
+I just had to sort of skim over some of
+ 
+
+ align:start position:0%
+I just had to sort of skim over some of
+the intervening steps that sometimes
+
+ align:start position:0%
+the intervening steps that sometimes
+ 
+
+ align:start position:0%
+the intervening steps that sometimes
+happens and hopefully those lecture
+
+ align:start position:0%
+happens and hopefully those lecture
+ 
+
+ align:start position:0%
+happens and hopefully those lecture
+notes will help fill that in
+
+ align:start position:0%
+notes will help fill that in
+ 
+
+ align:start position:0%
+notes will help fill that in
+for those of you who want to dig in a
+
+ align:start position:0%
+for those of you who want to dig in a
+ 
+
+ align:start position:0%
+for those of you who want to dig in a
+bit more so that's our plan for today
+
+ align:start position:0%
+bit more so that's our plan for today
+ 
+
+ align:start position:0%
+bit more so that's our plan for today
+so just to remind ourselves again coming
+
+ align:start position:0%
+so just to remind ourselves again coming
+ 
+
+ align:start position:0%
+so just to remind ourselves again coming
+looking back to the previous class
+
+ align:start position:0%
+looking back to the previous class
+ 
+
+ align:start position:0%
+looking back to the previous class
+session
+
+ align:start position:0%
+session
+ 
+
+ align:start position:0%
+session
+starting in the spring of 1925 after
+
+ align:start position:0%
+starting in the spring of 1925 after
+ 
+
+ align:start position:0%
+starting in the spring of 1925 after
+that kind of uh bout of severe hay fever
+
+ align:start position:0%
+that kind of uh bout of severe hay fever
+ 
+
+ align:start position:0%
+that kind of uh bout of severe hay fever
+that chased Vander Heisenberg
+
+ align:start position:0%
+that chased Vander Heisenberg
+ 
+
+ align:start position:0%
+that chased Vander Heisenberg
+temporarily out of Copenhagen and to
+
+ align:start position:0%
+temporarily out of Copenhagen and to
+ 
+
+ align:start position:0%
+temporarily out of Copenhagen and to
+this uh really quite lovely looking
+
+ align:start position:0%
+this uh really quite lovely looking
+ 
+
+ align:start position:0%
+this uh really quite lovely looking
+island of Helga land uh in the North Sea
+
+ align:start position:0%
+island of Helga land uh in the North Sea
+ 
+
+ align:start position:0%
+island of Helga land uh in the North Sea
+uh during that span of spring and summer
+
+ align:start position:0%
+uh during that span of spring and summer
+ 
+
+ align:start position:0%
+uh during that span of spring and summer
+25 Heisenberg introduced a new a whole
+
+ align:start position:0%
+25 Heisenberg introduced a new a whole
+ 
+
+ align:start position:0%
+25 Heisenberg introduced a new a whole
+new way of trying to think about Quantum
+
+ align:start position:0%
+new way of trying to think about Quantum
+ 
+
+ align:start position:0%
+new way of trying to think about Quantum
+Theory this was now
+
+ align:start position:0%
+Theory this was now
+ 
+
+ align:start position:0%
+Theory this was now
+something like 25 years into various
+
+ align:start position:0%
+something like 25 years into various
+ 
+
+ align:start position:0%
+something like 25 years into various
+physicists grappling with something
+
+ align:start position:0%
+physicists grappling with something
+ 
+
+ align:start position:0%
+physicists grappling with something
+having to do with quantum theory going
+
+ align:start position:0%
+having to do with quantum theory going
+ 
+
+ align:start position:0%
+having to do with quantum theory going
+back to Max Planck's work that was first
+
+ align:start position:0%
+back to Max Planck's work that was first
+ 
+
+ align:start position:0%
+back to Max Planck's work that was first
+published in 1900 we saw through our
+
+ align:start position:0%
+published in 1900 we saw through our
+ 
+
+ align:start position:0%
+published in 1900 we saw through our
+several kind of moments of sitting with
+
+ align:start position:0%
+several kind of moments of sitting with
+ 
+
+ align:start position:0%
+several kind of moments of sitting with
+with what was called the old quantum
+
+ align:start position:0%
+with what was called the old quantum
+ 
+
+ align:start position:0%
+with what was called the old quantum
+theory that it wasn't quite so obvious
+
+ align:start position:0%
+theory that it wasn't quite so obvious
+ 
+
+ align:start position:0%
+theory that it wasn't quite so obvious
+that that
+
+ align:start position:0%
+that that
+ 
+
+ align:start position:0%
+that that
+collection of ideas was adding up to any
+
+ align:start position:0%
+collection of ideas was adding up to any
+ 
+
+ align:start position:0%
+collection of ideas was adding up to any
+one new thing or that they'd even fit
+
+ align:start position:0%
+one new thing or that they'd even fit
+ 
+
+ align:start position:0%
+one new thing or that they'd even fit
+together and that was a concern that
+
+ align:start position:0%
+together and that was a concern that
+ 
+
+ align:start position:0%
+together and that was a concern that
+people like Heisenberg and some of his
+
+ align:start position:0%
+people like Heisenberg and some of his
+ 
+
+ align:start position:0%
+people like Heisenberg and some of his
+young colleagues really sought to tackle
+
+ align:start position:0%
+young colleagues really sought to tackle
+ 
+
+ align:start position:0%
+young colleagues really sought to tackle
+they wanted to have a first principles
+
+ align:start position:0%
+they wanted to have a first principles
+ 
+
+ align:start position:0%
+they wanted to have a first principles
+approach to Quantum Theory a quantum
+
+ align:start position:0%
+approach to Quantum Theory a quantum
+ 
+
+ align:start position:0%
+approach to Quantum Theory a quantum
+mechanics rather than what looked
+
+ align:start position:0%
+mechanics rather than what looked
+ 
+
+ align:start position:0%
+mechanics rather than what looked
+already to them as well as to many of us
+
+ align:start position:0%
+already to them as well as to many of us
+ 
+
+ align:start position:0%
+already to them as well as to many of us
+today this kind of grab bag uh which
+
+ align:start position:0%
+today this kind of grab bag uh which
+ 
+
+ align:start position:0%
+today this kind of grab bag uh which
+which had characterized the so-called
+
+ align:start position:0%
+which had characterized the so-called
+ 
+
+ align:start position:0%
+which had characterized the so-called
+old quantum theory where people would
+
+ align:start position:0%
+old quantum theory where people would
+ 
+
+ align:start position:0%
+old quantum theory where people would
+begin with uh quite traditional
+
+ align:start position:0%
+begin with uh quite traditional
+ 
+
+ align:start position:0%
+begin with uh quite traditional
+expressions for the energy of this or
+
+ align:start position:0%
+expressions for the energy of this or
+ 
+
+ align:start position:0%
+expressions for the energy of this or
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+you know a momentum of that take either
+
+ align:start position:0%
+you know a momentum of that take either
+ 
+
+ align:start position:0%
+you know a momentum of that take either
+uh Newtonian or maxwellian expressions
+
+ align:start position:0%
+uh Newtonian or maxwellian expressions
+ 
+
+ align:start position:0%
+uh Newtonian or maxwellian expressions
+and then just kind of staple on at the
+
+ align:start position:0%
+and then just kind of staple on at the
+ 
+
+ align:start position:0%
+and then just kind of staple on at the
+end some new usually not very well
+
+ align:start position:0%
+end some new usually not very well
+ 
+
+ align:start position:0%
+end some new usually not very well
+explained Quantum conditions and kind of
+
+ align:start position:0%
+explained Quantum conditions and kind of
+ 
+
+ align:start position:0%
+explained Quantum conditions and kind of
+ad hoc new rule
+
+ align:start position:0%
+ad hoc new rule
+ 
+
+ align:start position:0%
+ad hoc new rule
+and Heisenberg again his very good
+
+ align:start position:0%
+and Heisenberg again his very good
+ 
+
+ align:start position:0%
+and Heisenberg again his very good
+friend from grad school days both
+
+ align:start position:0%
+friend from grad school days both
+ 
+
+ align:start position:0%
+friend from grad school days both
+getting powerly and a lot of these
+
+ align:start position:0%
+getting powerly and a lot of these
+ 
+
+ align:start position:0%
+getting powerly and a lot of these
+younger folks were by the Year mid-1920s
+
+ align:start position:0%
+younger folks were by the Year mid-1920s
+ 
+
+ align:start position:0%
+younger folks were by the Year mid-1920s
+we're looking to do something different
+
+ align:start position:0%
+we're looking to do something different
+ 
+
+ align:start position:0%
+we're looking to do something different
+they wanted to have a first principles
+
+ align:start position:0%
+they wanted to have a first principles
+ 
+
+ align:start position:0%
+they wanted to have a first principles
+theories uh all its own that might
+
+ align:start position:0%
+theories uh all its own that might
+ 
+
+ align:start position:0%
+theories uh all its own that might
+account for phenomena at the atomic
+
+ align:start position:0%
+account for phenomena at the atomic
+ 
+
+ align:start position:0%
+account for phenomena at the atomic
+scale or smaller
+
+ align:start position:0%
+scale or smaller
+ 
+
+ align:start position:0%
+scale or smaller
+uh and and we saw last time heisberg in
+
+ align:start position:0%
+uh and and we saw last time heisberg in
+ 
+
+ align:start position:0%
+uh and and we saw last time heisberg in
+particular was Guided by by by a kind of
+
+ align:start position:0%
+particular was Guided by by by a kind of
+ 
+
+ align:start position:0%
+particular was Guided by by by a kind of
+approach that sounded very much to it
+
+ align:start position:0%
+approach that sounded very much to it
+ 
+
+ align:start position:0%
+approach that sounded very much to it
+sounded very much like
+
+ align:start position:0%
+sounded very much like
+ 
+
+ align:start position:0%
+sounded very much like
+what Albert Einstein had announced back
+
+ align:start position:0%
+what Albert Einstein had announced back
+ 
+
+ align:start position:0%
+what Albert Einstein had announced back
+in 1905 and thinking about uh the
+
+ align:start position:0%
+in 1905 and thinking about uh the
+ 
+
+ align:start position:0%
+in 1905 and thinking about uh the
+electrodynamics of moving bodies
+
+ align:start position:0%
+electrodynamics of moving bodies
+ 
+
+ align:start position:0%
+electrodynamics of moving bodies
+Heisenberg starts sounding a lot like a
+
+ align:start position:0%
+Heisenberg starts sounding a lot like a
+ 
+
+ align:start position:0%
+Heisenberg starts sounding a lot like a
+kind of um acolyte of the physicist and
+
+ align:start position:0%
+kind of um acolyte of the physicist and
+ 
+
+ align:start position:0%
+kind of um acolyte of the physicist and
+philosopher Ernst Mach so you saw in the
+
+ align:start position:0%
+philosopher Ernst Mach so you saw in the
+ 
+
+ align:start position:0%
+philosopher Ernst Mach so you saw in the
+opening pages of of Heisenberg's article
+
+ align:start position:0%
+opening pages of of Heisenberg's article
+ 
+
+ align:start position:0%
+opening pages of of Heisenberg's article
+that we had in the English translation
+
+ align:start position:0%
+that we had in the English translation
+ 
+
+ align:start position:0%
+that we had in the English translation
+in our reader then even in the opening
+
+ align:start position:0%
+in our reader then even in the opening
+ 
+
+ align:start position:0%
+in our reader then even in the opening
+paragraph he says we're we're going to
+
+ align:start position:0%
+paragraph he says we're we're going to
+ 
+
+ align:start position:0%
+paragraph he says we're we're going to
+keep fooling ourselves or or get or
+
+ align:start position:0%
+keep fooling ourselves or or get or
+ 
+
+ align:start position:0%
+keep fooling ourselves or or get or
+chasing our own Tails basically if we
+
+ align:start position:0%
+chasing our own Tails basically if we
+ 
+
+ align:start position:0%
+chasing our own Tails basically if we
+keep trying to talk about things that
+
+ align:start position:0%
+keep trying to talk about things that
+ 
+
+ align:start position:0%
+keep trying to talk about things that
+are not even in principle observable for
+
+ align:start position:0%
+are not even in principle observable for
+ 
+
+ align:start position:0%
+are not even in principle observable for
+which examples of which he mentioned
+
+ align:start position:0%
+which examples of which he mentioned
+ 
+
+ align:start position:0%
+which examples of which he mentioned
+would be things like the orbit of an
+
+ align:start position:0%
+would be things like the orbit of an
+ 
+
+ align:start position:0%
+would be things like the orbit of an
+electron in an atom we don't watch the
+
+ align:start position:0%
+electron in an atom we don't watch the
+ 
+
+ align:start position:0%
+electron in an atom we don't watch the
+electrons zooming around like a planet
+
+ align:start position:0%
+electrons zooming around like a planet
+ 
+
+ align:start position:0%
+electrons zooming around like a planet
+in the solar system let's stop trying to
+
+ align:start position:0%
+in the solar system let's stop trying to
+ 
+
+ align:start position:0%
+in the solar system let's stop trying to
+calculate those features and focus
+
+ align:start position:0%
+calculate those features and focus
+ 
+
+ align:start position:0%
+calculate those features and focus
+instead on things that really are
+
+ align:start position:0%
+instead on things that really are
+ 
+
+ align:start position:0%
+instead on things that really are
+objects of positive experience like the
+
+ align:start position:0%
+objects of positive experience like the
+ 
+
+ align:start position:0%
+objects of positive experience like the
+emission lines these spectral lines that
+
+ align:start position:0%
+emission lines these spectral lines that
+ 
+
+ align:start position:0%
+emission lines these spectral lines that
+come out when certain gases of atoms are
+
+ align:start position:0%
+come out when certain gases of atoms are
+ 
+
+ align:start position:0%
+come out when certain gases of atoms are
+excited so Eisenberg began looking at
+
+ align:start position:0%
+excited so Eisenberg began looking at
+ 
+
+ align:start position:0%
+excited so Eisenberg began looking at
+things like the observable features of
+
+ align:start position:0%
+things like the observable features of
+ 
+
+ align:start position:0%
+things like the observable features of
+these spectral lines okay so he reasoned
+
+ align:start position:0%
+these spectral lines okay so he reasoned
+ 
+
+ align:start position:0%
+these spectral lines okay so he reasoned
+then we saw in particular that since the
+
+ align:start position:0%
+then we saw in particular that since the
+ 
+
+ align:start position:0%
+then we saw in particular that since the
+frequencies of these emission lines
+
+ align:start position:0%
+frequencies of these emission lines
+ 
+
+ align:start position:0%
+frequencies of these emission lines
+especially for very simple spectral like
+
+ align:start position:0%
+especially for very simple spectral like
+ 
+
+ align:start position:0%
+especially for very simple spectral like
+for a hydrogen atom the frequencies obey
+
+ align:start position:0%
+for a hydrogen atom the frequencies obey
+ 
+
+ align:start position:0%
+for a hydrogen atom the frequencies obey
+this law of addition that one line in
+
+ align:start position:0%
+this law of addition that one line in
+ 
+
+ align:start position:0%
+this law of addition that one line in
+the Spectrum could be written the actual
+
+ align:start position:0%
+the Spectrum could be written the actual
+ 
+
+ align:start position:0%
+the Spectrum could be written the actual
+numerical frequency the number of cycles
+
+ align:start position:0%
+numerical frequency the number of cycles
+ 
+
+ align:start position:0%
+numerical frequency the number of cycles
+per second uh obeyed these kinds of
+
+ align:start position:0%
+per second uh obeyed these kinds of
+ 
+
+ align:start position:0%
+per second uh obeyed these kinds of
+relationships with their two other
+
+ align:start position:0%
+relationships with their two other
+ 
+
+ align:start position:0%
+relationships with their two other
+distinct emission lines the sum of whose
+
+ align:start position:0%
+distinct emission lines the sum of whose
+ 
+
+ align:start position:0%
+distinct emission lines the sum of whose
+frequencies would add up to this third
+
+ align:start position:0%
+frequencies would add up to this third
+ 
+
+ align:start position:0%
+frequencies would add up to this third
+one and it could be it could be extended
+
+ align:start position:0%
+one and it could be it could be extended
+ 
+
+ align:start position:0%
+one and it could be it could be extended
+Beyond just pairs threes Force fives
+
+ align:start position:0%
+Beyond just pairs threes Force fives
+ 
+
+ align:start position:0%
+Beyond just pairs threes Force fives
+that there were these
+
+ align:start position:0%
+that there were these
+ 
+
+ align:start position:0%
+that there were these
+addition relationships between the
+
+ align:start position:0%
+addition relationships between the
+ 
+
+ align:start position:0%
+addition relationships between the
+frequencies of light that really
+
+ align:start position:0%
+frequencies of light that really
+ 
+
+ align:start position:0%
+frequencies of light that really
+genuinely was emitted by these excited
+
+ align:start position:0%
+genuinely was emitted by these excited
+ 
+
+ align:start position:0%
+genuinely was emitted by these excited
+hydrogen atoms and then and then Heisman
+
+ align:start position:0%
+hydrogen atoms and then and then Heisman
+ 
+
+ align:start position:0%
+hydrogen atoms and then and then Heisman
+or reasoned that when we characterize
+
+ align:start position:0%
+or reasoned that when we characterize
+ 
+
+ align:start position:0%
+or reasoned that when we characterize
+the light uh maxwellian or otherwise the
+
+ align:start position:0%
+the light uh maxwellian or otherwise the
+ 
+
+ align:start position:0%
+the light uh maxwellian or otherwise the
+frequency appears in the exponent which
+
+ align:start position:0%
+frequency appears in the exponent which
+ 
+
+ align:start position:0%
+frequency appears in the exponent which
+suggested to Heisenberg that the
+
+ align:start position:0%
+suggested to Heisenberg that the
+ 
+
+ align:start position:0%
+suggested to Heisenberg that the
+amplitude should multiply if the if the
+
+ align:start position:0%
+amplitude should multiply if the if the
+ 
+
+ align:start position:0%
+amplitude should multiply if the if the
+frequencies are adding according to this
+
+ align:start position:0%
+frequencies are adding according to this
+ 
+
+ align:start position:0%
+frequencies are adding according to this
+law of addition and the frequencies are
+
+ align:start position:0%
+law of addition and the frequencies are
+ 
+
+ align:start position:0%
+law of addition and the frequencies are
+one way of characterizing the light that
+
+ align:start position:0%
+one way of characterizing the light that
+ 
+
+ align:start position:0%
+one way of characterizing the light that
+comes out then shouldn't the amplitudes
+
+ align:start position:0%
+comes out then shouldn't the amplitudes
+ 
+
+ align:start position:0%
+comes out then shouldn't the amplitudes
+of those Associated light waves multiply
+
+ align:start position:0%
+of those Associated light waves multiply
+ 
+
+ align:start position:0%
+of those Associated light waves multiply
+and that's what he found two of his
+
+ align:start position:0%
+and that's what he found two of his
+ 
+
+ align:start position:0%
+and that's what he found two of his
+great surprise alone on the island of
+
+ align:start position:0%
+great surprise alone on the island of
+ 
+
+ align:start position:0%
+great surprise alone on the island of
+Helga land that these amplitudes didn't
+
+ align:start position:0%
+Helga land that these amplitudes didn't
+ 
+
+ align:start position:0%
+Helga land that these amplitudes didn't
+behave the way he expected them to in
+
+ align:start position:0%
+behave the way he expected them to in
+ 
+
+ align:start position:0%
+behave the way he expected them to in
+fact the the outcome of multiplying two
+
+ align:start position:0%
+fact the the outcome of multiplying two
+ 
+
+ align:start position:0%
+fact the the outcome of multiplying two
+of those things together depending on
+
+ align:start position:0%
+of those things together depending on
+ 
+
+ align:start position:0%
+of those things together depending on
+the order in which they were multiplied
+
+ align:start position:0%
+the order in which they were multiplied
+ 
+
+ align:start position:0%
+the order in which they were multiplied
+uh and so he returned or started very
+
+ align:start position:0%
+uh and so he returned or started very
+ 
+
+ align:start position:0%
+uh and so he returned or started very
+soon afterwards a position in gertington
+
+ align:start position:0%
+soon afterwards a position in gertington
+ 
+
+ align:start position:0%
+soon afterwards a position in gertington
+and his senior advisor there Max Bourne
+
+ align:start position:0%
+and his senior advisor there Max Bourne
+ 
+
+ align:start position:0%
+and his senior advisor there Max Bourne
+clarified these are matrices the fact
+
+ align:start position:0%
+clarified these are matrices the fact
+ 
+
+ align:start position:0%
+clarified these are matrices the fact
+that the uh outcome of the
+
+ align:start position:0%
+that the uh outcome of the
+ 
+
+ align:start position:0%
+that the uh outcome of the
+multiplication depends on the order is a
+
+ align:start position:0%
+multiplication depends on the order is a
+ 
+
+ align:start position:0%
+multiplication depends on the order is a
+generic feature of matrices whereas
+
+ align:start position:0%
+generic feature of matrices whereas
+ 
+
+ align:start position:0%
+generic feature of matrices whereas
+mathematicians would say matrices do not
+
+ align:start position:0%
+mathematicians would say matrices do not
+ 
+
+ align:start position:0%
+mathematicians would say matrices do not
+commute and so soon after that this work
+
+ align:start position:0%
+commute and so soon after that this work
+ 
+
+ align:start position:0%
+commute and so soon after that this work
+became known as Matrix mechanics
+
+ align:start position:0%
+became known as Matrix mechanics
+ 
+
+ align:start position:0%
+became known as Matrix mechanics
+and then Heisenberg continued working on
+
+ align:start position:0%
+and then Heisenberg continued working on
+ 
+
+ align:start position:0%
+and then Heisenberg continued working on
+that uh sharpening the formalism working
+
+ align:start position:0%
+that uh sharpening the formalism working
+ 
+
+ align:start position:0%
+that uh sharpening the formalism working
+directly with maxborn and some other
+
+ align:start position:0%
+directly with maxborn and some other
+ 
+
+ align:start position:0%
+directly with maxborn and some other
+colleagues but also trying to figure out
+
+ align:start position:0%
+colleagues but also trying to figure out
+ 
+
+ align:start position:0%
+colleagues but also trying to figure out
+conceptually what might it mean if the
+
+ align:start position:0%
+conceptually what might it mean if the
+ 
+
+ align:start position:0%
+conceptually what might it mean if the
+world is characterized the atomic world
+
+ align:start position:0%
+world is characterized the atomic world
+ 
+
+ align:start position:0%
+world is characterized the atomic world
+is characterized by these strange arrays
+
+ align:start position:0%
+is characterized by these strange arrays
+ 
+
+ align:start position:0%
+is characterized by these strange arrays
+of numbers whose mathematics was at
+
+ align:start position:0%
+of numbers whose mathematics was at
+ 
+
+ align:start position:0%
+of numbers whose mathematics was at
+least to him rather unexpected and
+
+ align:start position:0%
+least to him rather unexpected and
+ 
+
+ align:start position:0%
+least to him rather unexpected and
+foreign and where it seemed to be like
+
+ align:start position:0%
+foreign and where it seemed to be like
+ 
+
+ align:start position:0%
+foreign and where it seemed to be like
+the outcome would depend on the order in
+
+ align:start position:0%
+the outcome would depend on the order in
+ 
+
+ align:start position:0%
+the outcome would depend on the order in
+which you did stuff it could be that our
+
+ align:start position:0%
+which you did stuff it could be that our
+ 
+
+ align:start position:0%
+which you did stuff it could be that our
+operations on the quantum realm could
+
+ align:start position:0%
+operations on the quantum realm could
+ 
+
+ align:start position:0%
+operations on the quantum realm could
+have an impact on what we could ever see
+
+ align:start position:0%
+have an impact on what we could ever see
+ 
+
+ align:start position:0%
+have an impact on what we could ever see
+or measure and the thinking along those
+
+ align:start position:0%
+or measure and the thinking along those
+ 
+
+ align:start position:0%
+or measure and the thinking along those
+lines about what would it take to
+
+ align:start position:0%
+lines about what would it take to
+ 
+
+ align:start position:0%
+lines about what would it take to
+perform certain kinds of measurements of
+
+ align:start position:0%
+perform certain kinds of measurements of
+ 
+
+ align:start position:0%
+perform certain kinds of measurements of
+things like an electron
+
+ align:start position:0%
+things like an electron
+ 
+
+ align:start position:0%
+things like an electron
+uh scattering heinergy light off of it
+
+ align:start position:0%
+uh scattering heinergy light off of it
+ 
+
+ align:start position:0%
+uh scattering heinergy light off of it
+and so on uh that he that Heisenberg
+
+ align:start position:0%
+and so on uh that he that Heisenberg
+ 
+
+ align:start position:0%
+and so on uh that he that Heisenberg
+began to articulate his uncertainty
+
+ align:start position:0%
+began to articulate his uncertainty
+ 
+
+ align:start position:0%
+began to articulate his uncertainty
+principle uh that there's there seemed
+
+ align:start position:0%
+principle uh that there's there seemed
+ 
+
+ align:start position:0%
+principle uh that there's there seemed
+to be a consequence of the fact that
+
+ align:start position:0%
+to be a consequence of the fact that
+ 
+
+ align:start position:0%
+to be a consequence of the fact that
+these matrices uh don't commute with
+
+ align:start position:0%
+these matrices uh don't commute with
+ 
+
+ align:start position:0%
+these matrices uh don't commute with
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+there was an irreducible uncertainty in
+
+ align:start position:0%
+there was an irreducible uncertainty in
+ 
+
+ align:start position:0%
+there was an irreducible uncertainty in
+the sharpness uh the accuracy or
+
+ align:start position:0%
+the sharpness uh the accuracy or
+ 
+
+ align:start position:0%
+the sharpness uh the accuracy or
+Precision with which we could ever
+
+ align:start position:0%
+Precision with which we could ever
+ 
+
+ align:start position:0%
+Precision with which we could ever
+specify at the same moment the position
+
+ align:start position:0%
+specify at the same moment the position
+ 
+
+ align:start position:0%
+specify at the same moment the position
+of say an electron uh and its
+
+ align:start position:0%
+of say an electron uh and its
+ 
+
+ align:start position:0%
+of say an electron uh and its
+simultaneous momentum along the X
+
+ align:start position:0%
+simultaneous momentum along the X
+ 
+
+ align:start position:0%
+simultaneous momentum along the X
+direction that there was a trade-off
+
+ align:start position:0%
+direction that there was a trade-off
+ 
+
+ align:start position:0%
+direction that there was a trade-off
+whose scale like so many of these things
+
+ align:start position:0%
+whose scale like so many of these things
+ 
+
+ align:start position:0%
+whose scale like so many of these things
+was set by planks Cuts so that was what
+
+ align:start position:0%
+was set by planks Cuts so that was what
+ 
+
+ align:start position:0%
+was set by planks Cuts so that was what
+we mostly looked at last time and as I
+
+ align:start position:0%
+we mostly looked at last time and as I
+ 
+
+ align:start position:0%
+we mostly looked at last time and as I
+as I gave a kind of foreshadowing for
+
+ align:start position:0%
+as I gave a kind of foreshadowing for
+ 
+
+ align:start position:0%
+as I gave a kind of foreshadowing for
+today right around that same time in
+
+ align:start position:0%
+today right around that same time in
+ 
+
+ align:start position:0%
+today right around that same time in
+just a remarkably close
+
+ align:start position:0%
+just a remarkably close
+ 
+
+ align:start position:0%
+just a remarkably close
+um span of of weeks and months
+
+ align:start position:0%
+um span of of weeks and months
+ 
+
+ align:start position:0%
+um span of of weeks and months
+there was a really quite different
+
+ align:start position:0%
+there was a really quite different
+ 
+
+ align:start position:0%
+there was a really quite different
+approach to some of those very same
+
+ align:start position:0%
+approach to some of those very same
+ 
+
+ align:start position:0%
+approach to some of those very same
+questions being worked out by Verna
+
+ align:start position:0%
+questions being worked out by Verna
+ 
+
+ align:start position:0%
+questions being worked out by Verna
+Heisenberg and we had an excerpt from
+
+ align:start position:0%
+Heisenberg and we had an excerpt from
+ 
+
+ align:start position:0%
+Heisenberg and we had an excerpt from
+this really quite a wonderful biography
+
+ align:start position:0%
+this really quite a wonderful biography
+ 
+
+ align:start position:0%
+this really quite a wonderful biography
+by uh Walter Moore part of today's
+
+ align:start position:0%
+by uh Walter Moore part of today's
+ 
+
+ align:start position:0%
+by uh Walter Moore part of today's
+readings was a little section of Moore's
+
+ align:start position:0%
+readings was a little section of Moore's
+ 
+
+ align:start position:0%
+readings was a little section of Moore's
+book talking through how did trojaner
+
+ align:start position:0%
+book talking through how did trojaner
+ 
+
+ align:start position:0%
+book talking through how did trojaner
+think about what became known as wave
+
+ align:start position:0%
+think about what became known as wave
+ 
+
+ align:start position:0%
+think about what became known as wave
+mechanics so I want to talk a little bit
+
+ align:start position:0%
+mechanics so I want to talk a little bit
+ 
+
+ align:start position:0%
+mechanics so I want to talk a little bit
+about that
+
+ align:start position:0%
+about that
+ 
+
+ align:start position:0%
+about that
+so this was happening not in the spring
+
+ align:start position:0%
+so this was happening not in the spring
+ 
+
+ align:start position:0%
+so this was happening not in the spring
+summer of 25 but in sort of winter
+
+ align:start position:0%
+summer of 25 but in sort of winter
+ 
+
+ align:start position:0%
+summer of 25 but in sort of winter
+spring 26 but really just a few months
+
+ align:start position:0%
+spring 26 but really just a few months
+ 
+
+ align:start position:0%
+spring 26 but really just a few months
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+um Aaron Schrodinger began introducing a
+
+ align:start position:0%
+um Aaron Schrodinger began introducing a
+ 
+
+ align:start position:0%
+um Aaron Schrodinger began introducing a
+different first principles approach to
+
+ align:start position:0%
+different first principles approach to
+ 
+
+ align:start position:0%
+different first principles approach to
+Quantum Theory much like Heisenberg and
+
+ align:start position:0%
+Quantum Theory much like Heisenberg and
+ 
+
+ align:start position:0%
+Quantum Theory much like Heisenberg and
+Paulie and these other kind of young
+
+ align:start position:0%
+Paulie and these other kind of young
+ 
+
+ align:start position:0%
+Paulie and these other kind of young
+young uh researchers Schrodinger also
+
+ align:start position:0%
+young uh researchers Schrodinger also
+ 
+
+ align:start position:0%
+young uh researchers Schrodinger also
+thought there should be a kind of way of
+
+ align:start position:0%
+thought there should be a kind of way of
+ 
+
+ align:start position:0%
+thought there should be a kind of way of
+building a a new Theory from the ground
+
+ align:start position:0%
+building a a new Theory from the ground
+ 
+
+ align:start position:0%
+building a a new Theory from the ground
+up to treat the behavior of atoms in
+
+ align:start position:0%
+up to treat the behavior of atoms in
+ 
+
+ align:start position:0%
+up to treat the behavior of atoms in
+parts of atoms but he followed a
+
+ align:start position:0%
+parts of atoms but he followed a
+ 
+
+ align:start position:0%
+parts of atoms but he followed a
+different conceptual path he was working
+
+ align:start position:0%
+different conceptual path he was working
+ 
+
+ align:start position:0%
+different conceptual path he was working
+quite independently of Heisenberg in
+
+ align:start position:0%
+quite independently of Heisenberg in
+ 
+
+ align:start position:0%
+quite independently of Heisenberg in
+these early steps
+
+ align:start position:0%
+these early steps
+ 
+
+ align:start position:0%
+these early steps
+so Heisenberg had built upon these ideas
+
+ align:start position:0%
+so Heisenberg had built upon these ideas
+ 
+
+ align:start position:0%
+so Heisenberg had built upon these ideas
+about discreetness uh he was influenced
+
+ align:start position:0%
+about discreetness uh he was influenced
+ 
+
+ align:start position:0%
+about discreetness uh he was influenced
+by Bohr's work and ultimately tried to
+
+ align:start position:0%
+by Bohr's work and ultimately tried to
+ 
+
+ align:start position:0%
+by Bohr's work and ultimately tried to
+kind of extract away from Bohr's work uh
+
+ align:start position:0%
+kind of extract away from Bohr's work uh
+ 
+
+ align:start position:0%
+kind of extract away from Bohr's work uh
+but Schrodinger actually went a
+
+ align:start position:0%
+but Schrodinger actually went a
+ 
+
+ align:start position:0%
+but Schrodinger actually went a
+different way he was mostly inspired
+
+ align:start position:0%
+different way he was mostly inspired
+ 
+
+ align:start position:0%
+different way he was mostly inspired
+most directly inspired his work not by
+
+ align:start position:0%
+most directly inspired his work not by
+ 
+
+ align:start position:0%
+most directly inspired his work not by
+the kind of boar Adam or this notion of
+
+ align:start position:0%
+the kind of boar Adam or this notion of
+ 
+
+ align:start position:0%
+the kind of boar Adam or this notion of
+kind of very rigid discrete
+
+ align:start position:0%
+kind of very rigid discrete
+ 
+
+ align:start position:0%
+kind of very rigid discrete
+Quantum jobs but rather by Louis de
+
+ align:start position:0%
+Quantum jobs but rather by Louis de
+ 
+
+ align:start position:0%
+Quantum jobs but rather by Louis de
+brois a very suggestive idea from 1924
+
+ align:start position:0%
+brois a very suggestive idea from 1924
+ 
+
+ align:start position:0%
+brois a very suggestive idea from 1924
+about matter waves and here's this again
+
+ align:start position:0%
+about matter waves and here's this again
+ 
+
+ align:start position:0%
+about matter waves and here's this again
+kind of cartoon version of the bottom
+
+ align:start position:0%
+kind of cartoon version of the bottom
+ 
+
+ align:start position:0%
+kind of cartoon version of the bottom
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+trying to show Dubois suggestion for why
+
+ align:start position:0%
+trying to show Dubois suggestion for why
+ 
+
+ align:start position:0%
+trying to show Dubois suggestion for why
+these very discreet orbits that Niels
+
+ align:start position:0%
+these very discreet orbits that Niels
+ 
+
+ align:start position:0%
+these very discreet orbits that Niels
+Bohr had identified of say the uh the
+
+ align:start position:0%
+Bohr had identified of say the uh the
+ 
+
+ align:start position:0%
+Bohr had identified of say the uh the
+behavior of an electron in the hydrogen
+
+ align:start position:0%
+behavior of an electron in the hydrogen
+ 
+
+ align:start position:0%
+behavior of an electron in the hydrogen
+atom why might those special orbits be
+
+ align:start position:0%
+atom why might those special orbits be
+ 
+
+ align:start position:0%
+atom why might those special orbits be
+picked out as stable maybe there was an
+
+ align:start position:0%
+picked out as stable maybe there was an
+ 
+
+ align:start position:0%
+picked out as stable maybe there was an
+inherent waviness of the electron and
+
+ align:start position:0%
+inherent waviness of the electron and
+ 
+
+ align:start position:0%
+inherent waviness of the electron and
+you had to have a constructive
+
+ align:start position:0%
+you had to have a constructive
+ 
+
+ align:start position:0%
+you had to have a constructive
+interference for a stable orbit anything
+
+ align:start position:0%
+interference for a stable orbit anything
+ 
+
+ align:start position:0%
+interference for a stable orbit anything
+else would suffer destructiveness those
+
+ align:start position:0%
+else would suffer destructiveness those
+ 
+
+ align:start position:0%
+else would suffer destructiveness those
+are the kinds of things that really
+
+ align:start position:0%
+are the kinds of things that really
+ 
+
+ align:start position:0%
+are the kinds of things that really
+caught Schrodinger's imagination very
+
+ align:start position:0%
+caught Schrodinger's imagination very
+ 
+
+ align:start position:0%
+caught Schrodinger's imagination very
+soon after devroy himself had introduced
+
+ align:start position:0%
+soon after devroy himself had introduced
+ 
+
+ align:start position:0%
+soon after devroy himself had introduced
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+so Schrodinger was coming from a bit of
+
+ align:start position:0%
+so Schrodinger was coming from a bit of
+ 
+
+ align:start position:0%
+so Schrodinger was coming from a bit of
+a different Community he was originally
+
+ align:start position:0%
+a different Community he was originally
+ 
+
+ align:start position:0%
+a different Community he was originally
+from Vienna he was at the time teaching
+
+ align:start position:0%
+from Vienna he was at the time teaching
+ 
+
+ align:start position:0%
+from Vienna he was at the time teaching
+in Zurich he wasn't from Copenhagen he
+
+ align:start position:0%
+in Zurich he wasn't from Copenhagen he
+ 
+
+ align:start position:0%
+in Zurich he wasn't from Copenhagen he
+wasn't working in gerting and he was a
+
+ align:start position:0%
+wasn't working in gerting and he was a
+ 
+
+ align:start position:0%
+wasn't working in gerting and he was a
+little bit uh kind of different network
+
+ align:start position:0%
+little bit uh kind of different network
+ 
+
+ align:start position:0%
+little bit uh kind of different network
+perhaps more important he was also a
+
+ align:start position:0%
+perhaps more important he was also a
+ 
+
+ align:start position:0%
+perhaps more important he was also a
+generation older than Heisenberg and
+
+ align:start position:0%
+generation older than Heisenberg and
+ 
+
+ align:start position:0%
+generation older than Heisenberg and
+Paul he was basically very nearly the
+
+ align:start position:0%
+Paul he was basically very nearly the
+ 
+
+ align:start position:0%
+Paul he was basically very nearly the
+same age as Albert Einstein they became
+
+ align:start position:0%
+same age as Albert Einstein they became
+ 
+
+ align:start position:0%
+same age as Albert Einstein they became
+very close friends closer in age to
+
+ align:start position:0%
+very close friends closer in age to
+ 
+
+ align:start position:0%
+very close friends closer in age to
+Niels Bohr he'd been working as a
+
+ align:start position:0%
+Niels Bohr he'd been working as a
+ 
+
+ align:start position:0%
+Niels Bohr he'd been working as a
+professional theoretical physicist for
+
+ align:start position:0%
+professional theoretical physicist for
+ 
+
+ align:start position:0%
+professional theoretical physicist for
+decades by the time this stuff came up
+
+ align:start position:0%
+decades by the time this stuff came up
+ 
+
+ align:start position:0%
+decades by the time this stuff came up
+unlike Heisenberg and Paulie who were
+
+ align:start position:0%
+unlike Heisenberg and Paulie who were
+ 
+
+ align:start position:0%
+unlike Heisenberg and Paulie who were
+very very close uh who were working very
+
+ align:start position:0%
+very very close uh who were working very
+ 
+
+ align:start position:0%
+very very close uh who were working very
+soon after their own phds Schrodinger
+
+ align:start position:0%
+soon after their own phds Schrodinger
+ 
+
+ align:start position:0%
+soon after their own phds Schrodinger
+was was a kind of established researcher
+
+ align:start position:0%
+was was a kind of established researcher
+ 
+
+ align:start position:0%
+was was a kind of established researcher
+and and his approach to this question I
+
+ align:start position:0%
+and and his approach to this question I
+ 
+
+ align:start position:0%
+and and his approach to this question I
+think sort of shows that you we could
+
+ align:start position:0%
+think sort of shows that you we could
+ 
+
+ align:start position:0%
+think sort of shows that you we could
+characterize his approach to the new
+
+ align:start position:0%
+characterize his approach to the new
+ 
+
+ align:start position:0%
+characterize his approach to the new
+quantum mechanics the new Quantum realm
+
+ align:start position:0%
+quantum mechanics the new Quantum realm
+ 
+
+ align:start position:0%
+quantum mechanics the new Quantum realm
+as an effort to sort of retain as much
+
+ align:start position:0%
+as an effort to sort of retain as much
+ 
+
+ align:start position:0%
+as an effort to sort of retain as much
+of of the kind of look and feel of the
+
+ align:start position:0%
+of of the kind of look and feel of the
+ 
+
+ align:start position:0%
+of of the kind of look and feel of the
+toolkit of time-tested physics as he
+
+ align:start position:0%
+toolkit of time-tested physics as he
+ 
+
+ align:start position:0%
+toolkit of time-tested physics as he
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+and I'm just going to pause briefly and
+
+ align:start position:0%
+and I'm just going to pause briefly and
+ 
+
+ align:start position:0%
+and I'm just going to pause briefly and
+mention some of you might know uh so for
+
+ align:start position:0%
+mention some of you might know uh so for
+ 
+
+ align:start position:0%
+mention some of you might know uh so for
+the tool kits Heisenberg introding will
+
+ align:start position:0%
+the tool kits Heisenberg introding will
+ 
+
+ align:start position:0%
+the tool kits Heisenberg introding will
+look very distinct with schroingers
+
+ align:start position:0%
+look very distinct with schroingers
+ 
+
+ align:start position:0%
+look very distinct with schroingers
+seeming to be a little bit more almost
+
+ align:start position:0%
+seeming to be a little bit more almost
+ 
+
+ align:start position:0%
+seeming to be a little bit more almost
+conservative in the sense of let's
+
+ align:start position:0%
+conservative in the sense of let's
+ 
+
+ align:start position:0%
+conservative in the sense of let's
+retain as much as possible and
+
+ align:start position:0%
+retain as much as possible and
+ 
+
+ align:start position:0%
+retain as much as possible and
+Heisenberg saying you know it's a new
+
+ align:start position:0%
+Heisenberg saying you know it's a new
+ 
+
+ align:start position:0%
+Heisenberg saying you know it's a new
+it's a new world we need a conceptual
+
+ align:start position:0%
+it's a new world we need a conceptual
+ 
+
+ align:start position:0%
+it's a new world we need a conceptual
+Revolution we'll use new new techniques
+
+ align:start position:0%
+Revolution we'll use new new techniques
+ 
+
+ align:start position:0%
+Revolution we'll use new new techniques
+and yet socially and personally they
+
+ align:start position:0%
+and yet socially and personally they
+ 
+
+ align:start position:0%
+and yet socially and personally they
+were almost inverted so Schrodinger even
+
+ align:start position:0%
+were almost inverted so Schrodinger even
+ 
+
+ align:start position:0%
+were almost inverted so Schrodinger even
+in his day was known as as a remarkably
+
+ align:start position:0%
+in his day was known as as a remarkably
+ 
+
+ align:start position:0%
+in his day was known as as a remarkably
+um uh
+
+ align:start position:0%
+um uh
+ 
+
+ align:start position:0%
+um uh
+sort of uh Bohemian leading a Bohemian
+
+ align:start position:0%
+sort of uh Bohemian leading a Bohemian
+ 
+
+ align:start position:0%
+sort of uh Bohemian leading a Bohemian
+lifestyle not the kind of traditional
+
+ align:start position:0%
+lifestyle not the kind of traditional
+ 
+
+ align:start position:0%
+lifestyle not the kind of traditional
+Family Values he had open relationships
+
+ align:start position:0%
+Family Values he had open relationships
+ 
+
+ align:start position:0%
+Family Values he had open relationships
+with multiple within a Time
+
+ align:start position:0%
+with multiple within a Time
+ 
+
+ align:start position:0%
+with multiple within a Time
+he raised children from that he had with
+
+ align:start position:0%
+he raised children from that he had with
+ 
+
+ align:start position:0%
+he raised children from that he had with
+one person raised them with his with his
+
+ align:start position:0%
+one person raised them with his with his
+ 
+
+ align:start position:0%
+one person raised them with his with his
+wife and I mean it was a really unusual
+
+ align:start position:0%
+wife and I mean it was a really unusual
+ 
+
+ align:start position:0%
+wife and I mean it was a really unusual
+Arrangement that actually his own
+
+ align:start position:0%
+Arrangement that actually his own
+ 
+
+ align:start position:0%
+Arrangement that actually his own
+contemporaries thought would talk about
+
+ align:start position:0%
+contemporaries thought would talk about
+ 
+
+ align:start position:0%
+contemporaries thought would talk about
+and stood out and Heisenberg as we know
+
+ align:start position:0%
+and stood out and Heisenberg as we know
+ 
+
+ align:start position:0%
+and stood out and Heisenberg as we know
+was pursuing actually very fairly to
+
+ align:start position:0%
+was pursuing actually very fairly to
+ 
+
+ align:start position:0%
+was pursuing actually very fairly to
+traditional stereotypical kind of
+
+ align:start position:0%
+traditional stereotypical kind of
+ 
+
+ align:start position:0%
+traditional stereotypical kind of
+personal family life so so who's
+
+ align:start position:0%
+personal family life so so who's
+ 
+
+ align:start position:0%
+personal family life so so who's
+conservative whose radical actually sort
+
+ align:start position:0%
+conservative whose radical actually sort
+ 
+
+ align:start position:0%
+conservative whose radical actually sort
+of uh different about what kinds of
+
+ align:start position:0%
+of uh different about what kinds of
+ 
+
+ align:start position:0%
+of uh different about what kinds of
+aspects of their life and work we're
+
+ align:start position:0%
+aspects of their life and work we're
+ 
+
+ align:start position:0%
+aspects of their life and work we're
+trying to characterize and again Moore's
+
+ align:start position:0%
+trying to characterize and again Moore's
+ 
+
+ align:start position:0%
+trying to characterize and again Moore's
+biography I think is really quite quite
+
+ align:start position:0%
+biography I think is really quite quite
+ 
+
+ align:start position:0%
+biography I think is really quite quite
+astonishing for this rounded view of
+
+ align:start position:0%
+astonishing for this rounded view of
+ 
+
+ align:start position:0%
+astonishing for this rounded view of
+schroederer not only how he got to a few
+
+ align:start position:0%
+schroederer not only how he got to a few
+ 
+
+ align:start position:0%
+schroederer not only how he got to a few
+equations so I recommend that uh more of
+
+ align:start position:0%
+equations so I recommend that uh more of
+ 
+
+ align:start position:0%
+equations so I recommend that uh more of
+the book you might enjoy Beyond just the
+
+ align:start position:0%
+the book you might enjoy Beyond just the
+ 
+
+ align:start position:0%
+the book you might enjoy Beyond just the
+excerpt that I gave okay what you're
+
+ align:start position:0%
+excerpt that I gave okay what you're
+ 
+
+ align:start position:0%
+excerpt that I gave okay what you're
+going to do so we know from his own
+
+ align:start position:0%
+going to do so we know from his own
+ 
+
+ align:start position:0%
+going to do so we know from his own
+private notebooks that have survived
+
+ align:start position:0%
+private notebooks that have survived
+ 
+
+ align:start position:0%
+private notebooks that have survived
+this work was happening in sort of
+
+ align:start position:0%
+this work was happening in sort of
+ 
+
+ align:start position:0%
+this work was happening in sort of
+December 1925 uh January 1926 really
+
+ align:start position:0%
+December 1925 uh January 1926 really
+ 
+
+ align:start position:0%
+December 1925 uh January 1926 really
+just roughly half a year after shorting
+
+ align:start position:0%
+just roughly half a year after shorting
+ 
+
+ align:start position:0%
+just roughly half a year after shorting
+his first Publications Schrodinger began
+
+ align:start position:0%
+his first Publications Schrodinger began
+ 
+
+ align:start position:0%
+his first Publications Schrodinger began
+with the usual expression for energy
+
+ align:start position:0%
+with the usual expression for energy
+ 
+
+ align:start position:0%
+with the usual expression for energy
+just the sort of Newtonian expression
+
+ align:start position:0%
+just the sort of Newtonian expression
+ 
+
+ align:start position:0%
+just the sort of Newtonian expression
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+the kinetic energy and the potential
+
+ align:start position:0%
+the kinetic energy and the potential
+ 
+
+ align:start position:0%
+the kinetic energy and the potential
+energy but then he immediately
+
+ align:start position:0%
+energy but then he immediately
+ 
+
+ align:start position:0%
+energy but then he immediately
+immediately tried to pick up on what de
+
+ align:start position:0%
+immediately tried to pick up on what de
+ 
+
+ align:start position:0%
+immediately tried to pick up on what de
+bruy had suggested uh about these matter
+
+ align:start position:0%
+bruy had suggested uh about these matter
+ 
+
+ align:start position:0%
+bruy had suggested uh about these matter
+waves and so short here it was again
+
+ align:start position:0%
+waves and so short here it was again
+ 
+
+ align:start position:0%
+waves and so short here it was again
+very uh senior very Seasons mathematical
+
+ align:start position:0%
+very uh senior very Seasons mathematical
+ 
+
+ align:start position:0%
+very uh senior very Seasons mathematical
+physicist by this point reason that if
+
+ align:start position:0%
+physicist by this point reason that if
+ 
+
+ align:start position:0%
+physicist by this point reason that if
+if something about waves something about
+
+ align:start position:0%
+if something about waves something about
+ 
+
+ align:start position:0%
+if something about waves something about
+matter waves is going to be so important
+
+ align:start position:0%
+matter waves is going to be so important
+ 
+
+ align:start position:0%
+matter waves is going to be so important
+moving forward well let's use what we
+
+ align:start position:0%
+moving forward well let's use what we
+ 
+
+ align:start position:0%
+moving forward well let's use what we
+know about how to quantitatively
+
+ align:start position:0%
+know about how to quantitatively
+ 
+
+ align:start position:0%
+know about how to quantitatively
+characterize the behavior of waves so we
+
+ align:start position:0%
+characterize the behavior of waves so we
+ 
+
+ align:start position:0%
+characterize the behavior of waves so we
+did he went in a kind of wranglerish way
+
+ align:start position:0%
+did he went in a kind of wranglerish way
+ 
+
+ align:start position:0%
+did he went in a kind of wranglerish way
+and said well let's consider a wave
+
+ align:start position:0%
+and said well let's consider a wave
+ 
+
+ align:start position:0%
+and said well let's consider a wave
+equation how would we characterize for
+
+ align:start position:0%
+equation how would we characterize for
+ 
+
+ align:start position:0%
+equation how would we characterize for
+example the behavior of a standing wave
+
+ align:start position:0%
+example the behavior of a standing wave
+ 
+
+ align:start position:0%
+example the behavior of a standing wave
+and we would write down this very simple
+
+ align:start position:0%
+and we would write down this very simple
+ 
+
+ align:start position:0%
+and we would write down this very simple
+looking expression simple certainly to
+
+ align:start position:0%
+looking expression simple certainly to
+ 
+
+ align:start position:0%
+looking expression simple certainly to
+someone like schroding are very familiar
+
+ align:start position:0%
+someone like schroding are very familiar
+ 
+
+ align:start position:0%
+someone like schroding are very familiar
+and as many of you probably know we saw
+
+ align:start position:0%
+and as many of you probably know we saw
+ 
+
+ align:start position:0%
+and as many of you probably know we saw
+briefly in some earlier lectures this uh
+
+ align:start position:0%
+briefly in some earlier lectures this uh
+ 
+
+ align:start position:0%
+briefly in some earlier lectures this uh
+parameter K here is called The Wave
+
+ align:start position:0%
+parameter K here is called The Wave
+ 
+
+ align:start position:0%
+parameter K here is called The Wave
+number it's inversely proportional to
+
+ align:start position:0%
+number it's inversely proportional to
+ 
+
+ align:start position:0%
+number it's inversely proportional to
+the wavelength so we can characterize
+
+ align:start position:0%
+the wavelength so we can characterize
+ 
+
+ align:start position:0%
+the wavelength so we can characterize
+the behavior of any kind of wave in
+
+ align:start position:0%
+the behavior of any kind of wave in
+ 
+
+ align:start position:0%
+the behavior of any kind of wave in
+terms of a wavelength and ask how is the
+
+ align:start position:0%
+terms of a wavelength and ask how is the
+ 
+
+ align:start position:0%
+terms of a wavelength and ask how is the
+amplitude of that wave kind of changing
+
+ align:start position:0%
+amplitude of that wave kind of changing
+ 
+
+ align:start position:0%
+amplitude of that wave kind of changing
+over time oh excuse me across space how
+
+ align:start position:0%
+over time oh excuse me across space how
+ 
+
+ align:start position:0%
+over time oh excuse me across space how
+is the wave
+
+ align:start position:0%
+is the wave
+ 
+
+ align:start position:0%
+is the wave
+behaving as we move from one position to
+
+ align:start position:0%
+behaving as we move from one position to
+ 
+
+ align:start position:0%
+behaving as we move from one position to
+the other and that's what this
+
+ align:start position:0%
+the other and that's what this
+ 
+
+ align:start position:0%
+the other and that's what this
+expression is is quantifying
+
+ align:start position:0%
+expression is is quantifying
+ 
+
+ align:start position:0%
+expression is is quantifying
+but now de broy had said there was
+
+ align:start position:0%
+but now de broy had said there was
+ 
+
+ align:start position:0%
+but now de broy had said there was
+something very specific about a
+
+ align:start position:0%
+something very specific about a
+ 
+
+ align:start position:0%
+something very specific about a
+wavelength for matter the debris
+
+ align:start position:0%
+wavelength for matter the debris
+ 
+
+ align:start position:0%
+wavelength for matter the debris
+wavelength it should be proportional to
+
+ align:start position:0%
+wavelength it should be proportional to
+ 
+
+ align:start position:0%
+wavelength it should be proportional to
+Roy suggested to Planck's Constant and
+
+ align:start position:0%
+Roy suggested to Planck's Constant and
+ 
+
+ align:start position:0%
+Roy suggested to Planck's Constant and
+inversely proportional to the momentum
+
+ align:start position:0%
+inversely proportional to the momentum
+ 
+
+ align:start position:0%
+inversely proportional to the momentum
+of that particle of that Quantum object
+
+ align:start position:0%
+of that particle of that Quantum object
+ 
+
+ align:start position:0%
+of that particle of that Quantum object
+so now if the wave number is related to
+
+ align:start position:0%
+so now if the wave number is related to
+ 
+
+ align:start position:0%
+so now if the wave number is related to
+a wavelength and Deborah's wavelength is
+
+ align:start position:0%
+a wavelength and Deborah's wavelength is
+ 
+
+ align:start position:0%
+a wavelength and Deborah's wavelength is
+related to a momentum it was actually
+
+ align:start position:0%
+related to a momentum it was actually
+ 
+
+ align:start position:0%
+related to a momentum it was actually
+not a very uh difficult
+
+ align:start position:0%
+not a very uh difficult
+ 
+
+ align:start position:0%
+not a very uh difficult
+so here's the steps for children to say
+
+ align:start position:0%
+so here's the steps for children to say
+ 
+
+ align:start position:0%
+so here's the steps for children to say
+maybe this K this wave number that
+
+ align:start position:0%
+maybe this K this wave number that
+ 
+
+ align:start position:0%
+maybe this K this wave number that
+appears in any old wave equation for
+
+ align:start position:0%
+appears in any old wave equation for
+ 
+
+ align:start position:0%
+appears in any old wave equation for
+classical waves of a guitar or ocean
+
+ align:start position:0%
+classical waves of a guitar or ocean
+ 
+
+ align:start position:0%
+classical waves of a guitar or ocean
+waves in the water maybe that K is
+
+ align:start position:0%
+waves in the water maybe that K is
+ 
+
+ align:start position:0%
+waves in the water maybe that K is
+actually deeply related to the momentum
+
+ align:start position:0%
+actually deeply related to the momentum
+ 
+
+ align:start position:0%
+actually deeply related to the momentum
+in a way that actually is new that comes
+
+ align:start position:0%
+in a way that actually is new that comes
+ 
+
+ align:start position:0%
+in a way that actually is new that comes
+straightly straight from De brois
+
+ align:start position:0%
+straightly straight from De brois
+ 
+
+ align:start position:0%
+straightly straight from De brois
+suggestion and if so if we can relate K
+
+ align:start position:0%
+suggestion and if so if we can relate K
+ 
+
+ align:start position:0%
+suggestion and if so if we can relate K
+to the momentum as usual scaled by
+
+ align:start position:0%
+to the momentum as usual scaled by
+ 
+
+ align:start position:0%
+to the momentum as usual scaled by
+Planck's constant here then we go back
+
+ align:start position:0%
+Planck's constant here then we go back
+ 
+
+ align:start position:0%
+Planck's constant here then we go back
+to this quite standard equation for a
+
+ align:start position:0%
+to this quite standard equation for a
+ 
+
+ align:start position:0%
+to this quite standard equation for a
+standing wave of any kind and now we
+
+ align:start position:0%
+standing wave of any kind and now we
+ 
+
+ align:start position:0%
+standing wave of any kind and now we
+want to characterize something
+
+ align:start position:0%
+want to characterize something
+ 
+
+ align:start position:0%
+want to characterize something
+specifically Quantum theoretic then we
+
+ align:start position:0%
+specifically Quantum theoretic then we
+ 
+
+ align:start position:0%
+specifically Quantum theoretic then we
+can substitute the k for the momentum
+
+ align:start position:0%
+can substitute the k for the momentum
+ 
+
+ align:start position:0%
+can substitute the k for the momentum
+with keeping track of our H bar
+
+ align:start position:0%
+with keeping track of our H bar
+ 
+
+ align:start position:0%
+with keeping track of our H bar
+and now it looks like we actually have a
+
+ align:start position:0%
+and now it looks like we actually have a
+ 
+
+ align:start position:0%
+and now it looks like we actually have a
+whole new way of thinking about the
+
+ align:start position:0%
+whole new way of thinking about the
+ 
+
+ align:start position:0%
+whole new way of thinking about the
+momentum of any Quantum object maybe the
+
+ align:start position:0%
+momentum of any Quantum object maybe the
+ 
+
+ align:start position:0%
+momentum of any Quantum object maybe the
+momentum is just a measure of the kind
+
+ align:start position:0%
+momentum is just a measure of the kind
+ 
+
+ align:start position:0%
+momentum is just a measure of the kind
+of spatial gradients of some Associated
+
+ align:start position:0%
+of spatial gradients of some Associated
+ 
+
+ align:start position:0%
+of spatial gradients of some Associated
+matter wave
+
+ align:start position:0%
+matter wave
+ 
+
+ align:start position:0%
+matter wave
+so maybe there's a whole new operator
+
+ align:start position:0%
+so maybe there's a whole new operator
+ 
+
+ align:start position:0%
+so maybe there's a whole new operator
+maybe there's a new object that tells us
+
+ align:start position:0%
+maybe there's a new object that tells us
+ 
+
+ align:start position:0%
+maybe there's a new object that tells us
+that relates the momentum of some object
+
+ align:start position:0%
+that relates the momentum of some object
+ 
+
+ align:start position:0%
+that relates the momentum of some object
+to the kind of to the gradient of its
+
+ align:start position:0%
+to the kind of to the gradient of its
+ 
+
+ align:start position:0%
+to the kind of to the gradient of its
+Associated matter wave with the with as
+
+ align:start position:0%
+Associated matter wave with the with as
+ 
+
+ align:start position:0%
+Associated matter wave with the with as
+usual the scaling the kind of sense of
+
+ align:start position:0%
+usual the scaling the kind of sense of
+ 
+
+ align:start position:0%
+usual the scaling the kind of sense of
+scale or sense of proportion provided by
+
+ align:start position:0%
+scale or sense of proportion provided by
+ 
+
+ align:start position:0%
+scale or sense of proportion provided by
+Planck's constant so what what
+
+ align:start position:0%
+Planck's constant so what what
+ 
+
+ align:start position:0%
+Planck's constant so what what
+Schrodinger was doing here was trying to
+
+ align:start position:0%
+Schrodinger was doing here was trying to
+ 
+
+ align:start position:0%
+Schrodinger was doing here was trying to
+build in an equation where where uh try
+
+ align:start position:0%
+build in an equation where where uh try
+ 
+
+ align:start position:0%
+build in an equation where where uh try
+to build up an equation where Planck's
+
+ align:start position:0%
+to build up an equation where Planck's
+ 
+
+ align:start position:0%
+to build up an equation where Planck's
+constant was kind of built in from the
+
+ align:start position:0%
+constant was kind of built in from the
+ 
+
+ align:start position:0%
+constant was kind of built in from the
+start not appended at the end not let's
+
+ align:start position:0%
+start not appended at the end not let's
+ 
+
+ align:start position:0%
+start not appended at the end not let's
+solve for some solutions then sort of
+
+ align:start position:0%
+solve for some solutions then sort of
+ 
+
+ align:start position:0%
+solve for some solutions then sort of
+smack on some new constraint but trying
+
+ align:start position:0%
+smack on some new constraint but trying
+ 
+
+ align:start position:0%
+smack on some new constraint but trying
+to build a first principles equation
+
+ align:start position:0%
+to build a first principles equation
+ 
+
+ align:start position:0%
+to build a first principles equation
+that would describe how matter behaves
+
+ align:start position:0%
+that would describe how matter behaves
+ 
+
+ align:start position:0%
+that would describe how matter behaves
+where Planck's constant is immediately
+
+ align:start position:0%
+where Planck's constant is immediately
+ 
+
+ align:start position:0%
+where Planck's constant is immediately
+kind of setting the scale from the start
+
+ align:start position:0%
+kind of setting the scale from the start
+ 
+
+ align:start position:0%
+kind of setting the scale from the start
+and so with that
+
+ align:start position:0%
+and so with that
+ 
+
+ align:start position:0%
+and so with that
+series of kind of uh of of reasonings he
+
+ align:start position:0%
+series of kind of uh of of reasonings he
+ 
+
+ align:start position:0%
+series of kind of uh of of reasonings he
+referring arrived we would Now call the
+
+ align:start position:0%
+referring arrived we would Now call the
+ 
+
+ align:start position:0%
+referring arrived we would Now call the
+time independent schroedering equation
+
+ align:start position:0%
+time independent schroedering equation
+ 
+
+ align:start position:0%
+time independent schroedering equation
+and it really was you can see where it
+
+ align:start position:0%
+and it really was you can see where it
+ 
+
+ align:start position:0%
+and it really was you can see where it
+comes from it's starting from the from
+
+ align:start position:0%
+comes from it's starting from the from
+ 
+
+ align:start position:0%
+comes from it's starting from the from
+the typical relation between kinetic and
+
+ align:start position:0%
+the typical relation between kinetic and
+ 
+
+ align:start position:0%
+the typical relation between kinetic and
+potential energy but trying to kind of
+
+ align:start position:0%
+potential energy but trying to kind of
+ 
+
+ align:start position:0%
+potential energy but trying to kind of
+plug in these insights and kind of
+
+ align:start position:0%
+plug in these insights and kind of
+ 
+
+ align:start position:0%
+plug in these insights and kind of
+quantify these insights from DuBois from
+
+ align:start position:0%
+quantify these insights from DuBois from
+ 
+
+ align:start position:0%
+quantify these insights from DuBois from
+De bruy right from the start okay so uh
+
+ align:start position:0%
+De bruy right from the start okay so uh
+ 
+
+ align:start position:0%
+De bruy right from the start okay so uh
+you many of you probably seen this
+
+ align:start position:0%
+you many of you probably seen this
+ 
+
+ align:start position:0%
+you many of you probably seen this
+before that we still call it the
+
+ align:start position:0%
+before that we still call it the
+ 
+
+ align:start position:0%
+before that we still call it the
+charging the wave equation and let's
+
+ align:start position:0%
+charging the wave equation and let's
+ 
+
+ align:start position:0%
+charging the wave equation and let's
+just talk for a few minutes about the
+
+ align:start position:0%
+just talk for a few minutes about the
+ 
+
+ align:start position:0%
+just talk for a few minutes about the
+nature of that expression first of all
+
+ align:start position:0%
+nature of that expression first of all
+ 
+
+ align:start position:0%
+nature of that expression first of all
+it's all Continuum this wave function
+
+ align:start position:0%
+it's all Continuum this wave function
+ 
+
+ align:start position:0%
+it's all Continuum this wave function
+PSI seems to behave just like any other
+
+ align:start position:0%
+PSI seems to behave just like any other
+ 
+
+ align:start position:0%
+PSI seems to behave just like any other
+wave quantity at least there's no reason
+
+ align:start position:0%
+wave quantity at least there's no reason
+ 
+
+ align:start position:0%
+wave quantity at least there's no reason
+to think it wouldn't from this
+
+ align:start position:0%
+to think it wouldn't from this
+ 
+
+ align:start position:0%
+to think it wouldn't from this
+expression it should be sort of varying
+
+ align:start position:0%
+expression it should be sort of varying
+ 
+
+ align:start position:0%
+expression it should be sort of varying
+continuously across space gently sort of
+
+ align:start position:0%
+continuously across space gently sort of
+ 
+
+ align:start position:0%
+continuously across space gently sort of
+you know having a slightly different
+
+ align:start position:0%
+you know having a slightly different
+ 
+
+ align:start position:0%
+you know having a slightly different
+value here than there there's nothing of
+
+ align:start position:0%
+value here than there there's nothing of
+ 
+
+ align:start position:0%
+value here than there there's nothing of
+a kind of inherent radical discreteness
+
+ align:start position:0%
+a kind of inherent radical discreteness
+ 
+
+ align:start position:0%
+a kind of inherent radical discreteness
+uh that we that's that sort of faces us
+
+ align:start position:0%
+uh that we that's that sort of faces us
+ 
+
+ align:start position:0%
+uh that we that's that sort of faces us
+when we look at
+
+ align:start position:0%
+when we look at
+ 
+
+ align:start position:0%
+when we look at
+Schrodinger's equation it looks like it
+
+ align:start position:0%
+Schrodinger's equation it looks like it
+ 
+
+ align:start position:0%
+Schrodinger's equation it looks like it
+other than the presence of of Planck's
+
+ align:start position:0%
+other than the presence of of Planck's
+ 
+
+ align:start position:0%
+other than the presence of of Planck's
+constant the form of the equation the
+
+ align:start position:0%
+constant the form of the equation the
+ 
+
+ align:start position:0%
+constant the form of the equation the
+mathematical form looks quite familiar
+
+ align:start position:0%
+mathematical form looks quite familiar
+ 
+
+ align:start position:0%
+mathematical form looks quite familiar
+it's a differential equation for how
+
+ align:start position:0%
+it's a differential equation for how
+ 
+
+ align:start position:0%
+it's a differential equation for how
+some quantity is going to change over
+
+ align:start position:0%
+some quantity is going to change over
+ 
+
+ align:start position:0%
+some quantity is going to change over
+space any later as you know as many of
+
+ align:start position:0%
+space any later as you know as many of
+ 
+
+ align:start position:0%
+space any later as you know as many of
+you know he introduced a Time varying
+
+ align:start position:0%
+you know he introduced a Time varying
+ 
+
+ align:start position:0%
+you know he introduced a Time varying
+version where the same quantity PSI
+
+ align:start position:0%
+version where the same quantity PSI
+ 
+
+ align:start position:0%
+version where the same quantity PSI
+could be continuously smoothly varying
+
+ align:start position:0%
+could be continuously smoothly varying
+ 
+
+ align:start position:0%
+could be continuously smoothly varying
+over time as well as across space so
+
+ align:start position:0%
+over time as well as across space so
+ 
+
+ align:start position:0%
+over time as well as across space so
+it's it's again retaining the kind of
+
+ align:start position:0%
+it's it's again retaining the kind of
+ 
+
+ align:start position:0%
+it's it's again retaining the kind of
+look and feel of Continuum based
+
+ align:start position:0%
+look and feel of Continuum based
+ 
+
+ align:start position:0%
+look and feel of Continuum based
+differential equations it doesn't have
+
+ align:start position:0%
+differential equations it doesn't have
+ 
+
+ align:start position:0%
+differential equations it doesn't have
+these kind of ad hoc discreteness
+
+ align:start position:0%
+these kind of ad hoc discreteness
+ 
+
+ align:start position:0%
+these kind of ad hoc discreteness
+um uh kind of um features that seem to
+
+ align:start position:0%
+um uh kind of um features that seem to
+ 
+
+ align:start position:0%
+um uh kind of um features that seem to
+be kind of put in By Hand by someone
+
+ align:start position:0%
+be kind of put in By Hand by someone
+ 
+
+ align:start position:0%
+be kind of put in By Hand by someone
+like Bohr in the Bohr model
+
+ align:start position:0%
+like Bohr in the Bohr model
+ 
+
+ align:start position:0%
+like Bohr in the Bohr model
+so one of his first tests and again we
+
+ align:start position:0%
+so one of his first tests and again we
+ 
+
+ align:start position:0%
+so one of his first tests and again we
+know this from his own private notebook
+
+ align:start position:0%
+know this from his own private notebook
+ 
+
+ align:start position:0%
+know this from his own private notebook
+right he was having a ski skiing
+
+ align:start position:0%
+right he was having a ski skiing
+ 
+
+ align:start position:0%
+right he was having a ski skiing
+vacation with not his wife but with two
+
+ align:start position:0%
+vacation with not his wife but with two
+ 
+
+ align:start position:0%
+vacation with not his wife but with two
+very much younger twin women in the
+
+ align:start position:0%
+very much younger twin women in the
+ 
+
+ align:start position:0%
+very much younger twin women in the
+midst of which he would take these
+
+ align:start position:0%
+midst of which he would take these
+ 
+
+ align:start position:0%
+midst of which he would take these
+breaks and try to calculate it's quite
+
+ align:start position:0%
+breaks and try to calculate it's quite
+ 
+
+ align:start position:0%
+breaks and try to calculate it's quite
+astonishing and so one of the first
+
+ align:start position:0%
+astonishing and so one of the first
+ 
+
+ align:start position:0%
+astonishing and so one of the first
+tests you knew he had to apply this
+
+ align:start position:0%
+tests you knew he had to apply this
+ 
+
+ align:start position:0%
+tests you knew he had to apply this
+formulas or two was the now time-honored
+
+ align:start position:0%
+formulas or two was the now time-honored
+ 
+
+ align:start position:0%
+formulas or two was the now time-honored
+hydrogen atom so he said what if the
+
+ align:start position:0%
+hydrogen atom so he said what if the
+ 
+
+ align:start position:0%
+hydrogen atom so he said what if the
+potential energy is not any old form but
+
+ align:start position:0%
+potential energy is not any old form but
+ 
+
+ align:start position:0%
+potential energy is not any old form but
+it's the specific form he'd need to
+
+ align:start position:0%
+it's the specific form he'd need to
+ 
+
+ align:start position:0%
+it's the specific form he'd need to
+characterize the mutual attraction
+
+ align:start position:0%
+characterize the mutual attraction
+ 
+
+ align:start position:0%
+characterize the mutual attraction
+between an electron and a proton and a
+
+ align:start position:0%
+between an electron and a proton and a
+ 
+
+ align:start position:0%
+between an electron and a proton and a
+hydrogen atom put in the coulomb
+
+ align:start position:0%
+hydrogen atom put in the coulomb
+ 
+
+ align:start position:0%
+hydrogen atom put in the coulomb
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+and then he found again just on his own
+
+ align:start position:0%
+and then he found again just on his own
+ 
+
+ align:start position:0%
+and then he found again just on his own
+in this kind of ski chalet uh right
+
+ align:start position:0%
+in this kind of ski chalet uh right
+ 
+
+ align:start position:0%
+in this kind of ski chalet uh right
+around the holiday right around New
+
+ align:start position:0%
+around the holiday right around New
+ 
+
+ align:start position:0%
+around the holiday right around New
+Year's get solutions to this equation
+
+ align:start position:0%
+Year's get solutions to this equation
+ 
+
+ align:start position:0%
+Year's get solutions to this equation
+will correspond to very specific values
+
+ align:start position:0%
+will correspond to very specific values
+ 
+
+ align:start position:0%
+will correspond to very specific values
+for the energy if you notice here the
+
+ align:start position:0%
+for the energy if you notice here the
+ 
+
+ align:start position:0%
+for the energy if you notice here the
+first in this whole series of articles
+
+ align:start position:0%
+first in this whole series of articles
+ 
+
+ align:start position:0%
+first in this whole series of articles
+that he wrote were called quantization
+
+ align:start position:0%
+that he wrote were called quantization
+ 
+
+ align:start position:0%
+that he wrote were called quantization
+as an eigenvalue problem again that's a
+
+ align:start position:0%
+as an eigenvalue problem again that's a
+ 
+
+ align:start position:0%
+as an eigenvalue problem again that's a
+hint he wants to work with familiar
+
+ align:start position:0%
+hint he wants to work with familiar
+ 
+
+ align:start position:0%
+hint he wants to work with familiar
+differential equations what he's done
+
+ align:start position:0%
+differential equations what he's done
+ 
+
+ align:start position:0%
+differential equations what he's done
+here is he has some differential
+
+ align:start position:0%
+here is he has some differential
+ 
+
+ align:start position:0%
+here is he has some differential
+operators some some some uh combination
+
+ align:start position:0%
+operators some some some uh combination
+ 
+
+ align:start position:0%
+operators some some some uh combination
+of terms that that quantify the kind of
+
+ align:start position:0%
+of terms that that quantify the kind of
+ 
+
+ align:start position:0%
+of terms that that quantify the kind of
+rates of change of some continuous
+
+ align:start position:0%
+rates of change of some continuous
+ 
+
+ align:start position:0%
+rates of change of some continuous
+property that's this side and there
+
+ align:start position:0%
+property that's this side and there
+ 
+
+ align:start position:0%
+property that's this side and there
+should be some eigenvalues of that
+
+ align:start position:0%
+should be some eigenvalues of that
+ 
+
+ align:start position:0%
+should be some eigenvalues of that
+differential operator some allowable
+
+ align:start position:0%
+differential operator some allowable
+ 
+
+ align:start position:0%
+differential operator some allowable
+um uh numerical kind of coefficients
+
+ align:start position:0%
+um uh numerical kind of coefficients
+ 
+
+ align:start position:0%
+um uh numerical kind of coefficients
+that will characterize the the the
+
+ align:start position:0%
+that will characterize the the the
+ 
+
+ align:start position:0%
+that will characterize the the the
+changing across space of that quantity
+
+ align:start position:0%
+changing across space of that quantity
+ 
+
+ align:start position:0%
+changing across space of that quantity
+and so he finds just by putting in the
+
+ align:start position:0%
+and so he finds just by putting in the
+ 
+
+ align:start position:0%
+and so he finds just by putting in the
+the coulomb potential for the hydrogen
+
+ align:start position:0%
+the coulomb potential for the hydrogen
+ 
+
+ align:start position:0%
+the coulomb potential for the hydrogen
+atom that this very kind of
+
+ align:start position:0%
+atom that this very kind of
+ 
+
+ align:start position:0%
+atom that this very kind of
+generic looking or familiar kind of
+
+ align:start position:0%
+generic looking or familiar kind of
+ 
+
+ align:start position:0%
+generic looking or familiar kind of
+format of a differential equation will
+
+ align:start position:0%
+format of a differential equation will
+ 
+
+ align:start position:0%
+format of a differential equation will
+yield exactly exactly the same energy
+
+ align:start position:0%
+yield exactly exactly the same energy
+ 
+
+ align:start position:0%
+yield exactly exactly the same energy
+Spectrum exactly the same allowable
+
+ align:start position:0%
+Spectrum exactly the same allowable
+ 
+
+ align:start position:0%
+Spectrum exactly the same allowable
+values for the eigenvalues of the energy
+
+ align:start position:0%
+values for the eigenvalues of the energy
+ 
+
+ align:start position:0%
+values for the eigenvalues of the energy
+the same coefficients here that will
+
+ align:start position:0%
+the same coefficients here that will
+ 
+
+ align:start position:0%
+the same coefficients here that will
+satisfy the equation exactly the same
+
+ align:start position:0%
+satisfy the equation exactly the same
+ 
+
+ align:start position:0%
+satisfy the equation exactly the same
+series as what Bohr had found from very
+
+ align:start position:0%
+series as what Bohr had found from very
+ 
+
+ align:start position:0%
+series as what Bohr had found from very
+different starting points so therefore
+
+ align:start position:0%
+different starting points so therefore
+ 
+
+ align:start position:0%
+different starting points so therefore
+schroding's equation as well would
+
+ align:start position:0%
+schroding's equation as well would
+ 
+
+ align:start position:0%
+schroding's equation as well would
+reproduce the successes like the Balmer
+
+ align:start position:0%
+reproduce the successes like the Balmer
+ 
+
+ align:start position:0%
+reproduce the successes like the Balmer
+Spectrum it should predict precisely the
+
+ align:start position:0%
+Spectrum it should predict precisely the
+ 
+
+ align:start position:0%
+Spectrum it should predict precisely the
+same frequencies of those emission lines
+
+ align:start position:0%
+same frequencies of those emission lines
+ 
+
+ align:start position:0%
+same frequencies of those emission lines
+from excited hydrogen atoms so schroding
+
+ align:start position:0%
+from excited hydrogen atoms so schroding
+ 
+
+ align:start position:0%
+from excited hydrogen atoms so schroding
+again had a sense that he was maybe onto
+
+ align:start position:0%
+again had a sense that he was maybe onto
+ 
+
+ align:start position:0%
+again had a sense that he was maybe onto
+something uh important here why how does
+
+ align:start position:0%
+something uh important here why how does
+ 
+
+ align:start position:0%
+something uh important here why how does
+that work and again many of you probably
+
+ align:start position:0%
+that work and again many of you probably
+ 
+
+ align:start position:0%
+that work and again many of you probably
+done these done this calculation in
+
+ align:start position:0%
+done these done this calculation in
+ 
+
+ align:start position:0%
+done these done this calculation in
+problem sets or seen it done in lecture
+
+ align:start position:0%
+problem sets or seen it done in lecture
+ 
+
+ align:start position:0%
+problem sets or seen it done in lecture
+class for others of you it's an exciting
+
+ align:start position:0%
+class for others of you it's an exciting
+ 
+
+ align:start position:0%
+class for others of you it's an exciting
+thing to look forward to
+
+ align:start position:0%
+thing to look forward to
+ 
+
+ align:start position:0%
+thing to look forward to
+so I'm not going to go through the whole
+
+ align:start position:0%
+so I'm not going to go through the whole
+ 
+
+ align:start position:0%
+so I'm not going to go through the whole
+calculation but I just want to make sure
+
+ align:start position:0%
+calculation but I just want to make sure
+ 
+
+ align:start position:0%
+calculation but I just want to make sure
+we understand the kinds of steps that
+
+ align:start position:0%
+we understand the kinds of steps that
+ 
+
+ align:start position:0%
+we understand the kinds of steps that
+Jordan was following how does this
+
+ align:start position:0%
+Jordan was following how does this
+ 
+
+ align:start position:0%
+Jordan was following how does this
+Continuum based equation this
+
+ align:start position:0%
+Continuum based equation this
+ 
+
+ align:start position:0%
+Continuum based equation this
+differential equation for some some
+
+ align:start position:0%
+differential equation for some some
+ 
+
+ align:start position:0%
+differential equation for some some
+smoothly varying quantity PSI how would
+
+ align:start position:0%
+smoothly varying quantity PSI how would
+ 
+
+ align:start position:0%
+smoothly varying quantity PSI how would
+that ever give us a discrete uh energy
+
+ align:start position:0%
+that ever give us a discrete uh energy
+ 
+
+ align:start position:0%
+that ever give us a discrete uh energy
+Spectrum how what would this with this
+
+ align:start position:0%
+Spectrum how what would this with this
+ 
+
+ align:start position:0%
+Spectrum how what would this with this
+integer n that bore had a good came from
+
+ align:start position:0%
+integer n that bore had a good came from
+ 
+
+ align:start position:0%
+integer n that bore had a good came from
+some fundamental discreetness in the
+
+ align:start position:0%
+some fundamental discreetness in the
+ 
+
+ align:start position:0%
+some fundamental discreetness in the
+behavior of electrons how does that come
+
+ align:start position:0%
+behavior of electrons how does that come
+ 
+
+ align:start position:0%
+behavior of electrons how does that come
+from Schrodinger's equation
+
+ align:start position:0%
+from Schrodinger's equation
+ 
+
+ align:start position:0%
+from Schrodinger's equation
+so let's step back and think about a
+
+ align:start position:0%
+so let's step back and think about a
+ 
+
+ align:start position:0%
+so let's step back and think about a
+simpler case involving standing waves
+
+ align:start position:0%
+simpler case involving standing waves
+ 
+
+ align:start position:0%
+simpler case involving standing waves
+let's just consider Motion One Direction
+
+ align:start position:0%
+let's just consider Motion One Direction
+ 
+
+ align:start position:0%
+let's just consider Motion One Direction
+sort of the x-axis and let's imagine we
+
+ align:start position:0%
+sort of the x-axis and let's imagine we
+ 
+
+ align:start position:0%
+sort of the x-axis and let's imagine we
+have a guitar string or a violin string
+
+ align:start position:0%
+have a guitar string or a violin string
+ 
+
+ align:start position:0%
+have a guitar string or a violin string
+where the end points are anchored so
+
+ align:start position:0%
+where the end points are anchored so
+ 
+
+ align:start position:0%
+where the end points are anchored so
+whatever the legitimate Solutions are
+
+ align:start position:0%
+whatever the legitimate Solutions are
+ 
+
+ align:start position:0%
+whatever the legitimate Solutions are
+for this wave equation PSI being say the
+
+ align:start position:0%
+for this wave equation PSI being say the
+ 
+
+ align:start position:0%
+for this wave equation PSI being say the
+amplitude of the wave in this case
+
+ align:start position:0%
+amplitude of the wave in this case
+ 
+
+ align:start position:0%
+amplitude of the wave in this case
+and the wave has to vanish at the origin
+
+ align:start position:0%
+and the wave has to vanish at the origin
+ 
+
+ align:start position:0%
+and the wave has to vanish at the origin
+and at the length L where the other end
+
+ align:start position:0%
+and at the length L where the other end
+ 
+
+ align:start position:0%
+and at the length L where the other end
+of the of the Rope or the string is
+
+ align:start position:0%
+of the of the Rope or the string is
+ 
+
+ align:start position:0%
+of the of the Rope or the string is
+anchored
+
+ align:start position:0%
+anchored
+ 
+
+ align:start position:0%
+anchored
+so how do we combine that with the
+
+ align:start position:0%
+so how do we combine that with the
+ 
+
+ align:start position:0%
+so how do we combine that with the
+general solutions for this difference
+
+ align:start position:0%
+general solutions for this difference
+ 
+
+ align:start position:0%
+general solutions for this difference
+equation here's again here's our
+
+ align:start position:0%
+equation here's again here's our
+ 
+
+ align:start position:0%
+equation here's again here's our
+differential operator so to speak
+
+ align:start position:0%
+differential operator so to speak
+ 
+
+ align:start position:0%
+differential operator so to speak
+well if we ignore the the boundary
+
+ align:start position:0%
+well if we ignore the the boundary
+ 
+
+ align:start position:0%
+well if we ignore the the boundary
+conditions if we ignore the fact that
+
+ align:start position:0%
+conditions if we ignore the fact that
+ 
+
+ align:start position:0%
+conditions if we ignore the fact that
+this string is anchored at both ends
+
+ align:start position:0%
+this string is anchored at both ends
+ 
+
+ align:start position:0%
+this string is anchored at both ends
+then we can very quickly write down the
+
+ align:start position:0%
+then we can very quickly write down the
+ 
+
+ align:start position:0%
+then we can very quickly write down the
+most General series of solutions of this
+
+ align:start position:0%
+most General series of solutions of this
+ 
+
+ align:start position:0%
+most General series of solutions of this
+wave equation it will it will oscillate
+
+ align:start position:0%
+wave equation it will it will oscillate
+ 
+
+ align:start position:0%
+wave equation it will it will oscillate
+across space like us like Sines and
+
+ align:start position:0%
+across space like us like Sines and
+ 
+
+ align:start position:0%
+across space like us like Sines and
+cosines with some characteristic wave
+
+ align:start position:0%
+cosines with some characteristic wave
+ 
+
+ align:start position:0%
+cosines with some characteristic wave
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+uh and different coefficients but now if
+
+ align:start position:0%
+uh and different coefficients but now if
+ 
+
+ align:start position:0%
+uh and different coefficients but now if
+we apply the boundary conditions then
+
+ align:start position:0%
+we apply the boundary conditions then
+ 
+
+ align:start position:0%
+we apply the boundary conditions then
+not all these Solutions are viable
+
+ align:start position:0%
+not all these Solutions are viable
+ 
+
+ align:start position:0%
+not all these Solutions are viable
+anymore some of them no longer solve the
+
+ align:start position:0%
+anymore some of them no longer solve the
+ 
+
+ align:start position:0%
+anymore some of them no longer solve the
+relevance uh irrelevant equation and in
+
+ align:start position:0%
+relevance uh irrelevant equation and in
+ 
+
+ align:start position:0%
+relevance uh irrelevant equation and in
+fact if we apply these these particular
+
+ align:start position:0%
+fact if we apply these these particular
+ 
+
+ align:start position:0%
+fact if we apply these these particular
+boundary conditions to this very general
+
+ align:start position:0%
+boundary conditions to this very general
+ 
+
+ align:start position:0%
+boundary conditions to this very general
+equation differential equation then the
+
+ align:start position:0%
+equation differential equation then the
+ 
+
+ align:start position:0%
+equation differential equation then the
+allowable Solutions have a discrete set
+
+ align:start position:0%
+allowable Solutions have a discrete set
+ 
+
+ align:start position:0%
+allowable Solutions have a discrete set
+of eigenvalues the way the the wave
+
+ align:start position:0%
+of eigenvalues the way the the wave
+ 
+
+ align:start position:0%
+of eigenvalues the way the the wave
+number K in this case becomes not annual
+
+ align:start position:0%
+number K in this case becomes not annual
+ 
+
+ align:start position:0%
+number K in this case becomes not annual
+continuous value but in fact kind of
+
+ align:start position:0%
+continuous value but in fact kind of
+ 
+
+ align:start position:0%
+continuous value but in fact kind of
+snaps into place with only integer
+
+ align:start position:0%
+snaps into place with only integer
+ 
+
+ align:start position:0%
+snaps into place with only integer
+allowed a series of of allowable wave
+
+ align:start position:0%
+allowed a series of of allowable wave
+ 
+
+ align:start position:0%
+allowed a series of of allowable wave
+numbers so the wave number could be one
+
+ align:start position:0%
+numbers so the wave number could be one
+ 
+
+ align:start position:0%
+numbers so the wave number could be one
+time some basic um reference wave number
+
+ align:start position:0%
+time some basic um reference wave number
+ 
+
+ align:start position:0%
+time some basic um reference wave number
+or two times that but not 1.8 times that
+
+ align:start position:0%
+or two times that but not 1.8 times that
+ 
+
+ align:start position:0%
+or two times that but not 1.8 times that
+we get a quantum a discrete Spectrum uh
+
+ align:start position:0%
+we get a quantum a discrete Spectrum uh
+ 
+
+ align:start position:0%
+we get a quantum a discrete Spectrum uh
+by solving a a Continuum based
+
+ align:start position:0%
+by solving a a Continuum based
+ 
+
+ align:start position:0%
+by solving a a Continuum based
+differential equation and applying the
+
+ align:start position:0%
+differential equation and applying the
+ 
+
+ align:start position:0%
+differential equation and applying the
+appropriate boundary conditions and so
+
+ align:start position:0%
+appropriate boundary conditions and so
+ 
+
+ align:start position:0%
+appropriate boundary conditions and so
+for the hydrogen atom
+
+ align:start position:0%
+for the hydrogen atom
+ 
+
+ align:start position:0%
+for the hydrogen atom
+shorting a reason similarly it wasn't
+
+ align:start position:0%
+shorting a reason similarly it wasn't
+ 
+
+ align:start position:0%
+shorting a reason similarly it wasn't
+that the electron was somehow glued in
+
+ align:start position:0%
+that the electron was somehow glued in
+ 
+
+ align:start position:0%
+that the electron was somehow glued in
+space and could only be here versus
+
+ align:start position:0%
+space and could only be here versus
+ 
+
+ align:start position:0%
+space and could only be here versus
+there like the war had suggested in this
+
+ align:start position:0%
+there like the war had suggested in this
+ 
+
+ align:start position:0%
+there like the war had suggested in this
+kind of uh ad hoc way but rather
+
+ align:start position:0%
+kind of uh ad hoc way but rather
+ 
+
+ align:start position:0%
+kind of uh ad hoc way but rather
+Schrodinger said well we're going to
+
+ align:start position:0%
+Schrodinger said well we're going to
+ 
+
+ align:start position:0%
+Schrodinger said well we're going to
+solve this differential equation for
+
+ align:start position:0%
+solve this differential equation for
+ 
+
+ align:start position:0%
+solve this differential equation for
+some general smoothly varying quantity
+
+ align:start position:0%
+some general smoothly varying quantity
+ 
+
+ align:start position:0%
+some general smoothly varying quantity
+PSI and let's apply some reasonable
+
+ align:start position:0%
+PSI and let's apply some reasonable
+ 
+
+ align:start position:0%
+PSI and let's apply some reasonable
+battery conditions that the amplitude
+
+ align:start position:0%
+battery conditions that the amplitude
+ 
+
+ align:start position:0%
+battery conditions that the amplitude
+should vanish at the origin the the
+
+ align:start position:0%
+should vanish at the origin the the
+ 
+
+ align:start position:0%
+should vanish at the origin the the
+electron should not be found in the
+
+ align:start position:0%
+electron should not be found in the
+ 
+
+ align:start position:0%
+electron should not be found in the
+nucleus uh so the so the wave function
+
+ align:start position:0%
+nucleus uh so the so the wave function
+ 
+
+ align:start position:0%
+nucleus uh so the so the wave function
+just somehow described in the electron's
+
+ align:start position:0%
+just somehow described in the electron's
+ 
+
+ align:start position:0%
+just somehow described in the electron's
+motion will vary will vanish at the
+
+ align:start position:0%
+motion will vary will vanish at the
+ 
+
+ align:start position:0%
+motion will vary will vanish at the
+origin and the electron shouldn't be
+
+ align:start position:0%
+origin and the electron shouldn't be
+ 
+
+ align:start position:0%
+origin and the electron shouldn't be
+found infinitely far away from its
+
+ align:start position:0%
+found infinitely far away from its
+ 
+
+ align:start position:0%
+found infinitely far away from its
+host's nucleus so the way the amplitude
+
+ align:start position:0%
+host's nucleus so the way the amplitude
+ 
+
+ align:start position:0%
+host's nucleus so the way the amplitude
+for whatever's waving whatever kind of
+
+ align:start position:0%
+for whatever's waving whatever kind of
+ 
+
+ align:start position:0%
+for whatever's waving whatever kind of
+debris-like matter wave is associated
+
+ align:start position:0%
+debris-like matter wave is associated
+ 
+
+ align:start position:0%
+debris-like matter wave is associated
+with electron that should have Vanishing
+
+ align:start position:0%
+with electron that should have Vanishing
+ 
+
+ align:start position:0%
+with electron that should have Vanishing
+amplitude when you're arbitrarily far
+
+ align:start position:0%
+amplitude when you're arbitrarily far
+ 
+
+ align:start position:0%
+amplitude when you're arbitrarily far
+away from the rest of the atom
+
+ align:start position:0%
+away from the rest of the atom
+ 
+
+ align:start position:0%
+away from the rest of the atom
+if you impose those boundary conditions
+
+ align:start position:0%
+if you impose those boundary conditions
+ 
+
+ align:start position:0%
+if you impose those boundary conditions
+it's a little more complicated but
+
+ align:start position:0%
+it's a little more complicated but
+ 
+
+ align:start position:0%
+it's a little more complicated but
+conceptually it's like this kind of uh
+
+ align:start position:0%
+conceptually it's like this kind of uh
+ 
+
+ align:start position:0%
+conceptually it's like this kind of uh
+standing wave on the string of fixed
+
+ align:start position:0%
+standing wave on the string of fixed
+ 
+
+ align:start position:0%
+standing wave on the string of fixed
+endpoints that's what forces a discrete
+
+ align:start position:0%
+endpoints that's what forces a discrete
+ 
+
+ align:start position:0%
+endpoints that's what forces a discrete
+Spectrum for the allowable energies not
+
+ align:start position:0%
+Spectrum for the allowable energies not
+ 
+
+ align:start position:0%
+Spectrum for the allowable energies not
+not restricting the kind of motion of
+
+ align:start position:0%
+not restricting the kind of motion of
+ 
+
+ align:start position:0%
+not restricting the kind of motion of
+the electron per se
+
+ align:start position:0%
+the electron per se
+ 
+
+ align:start position:0%
+the electron per se
+so Schrodinger now has retained the kind
+
+ align:start position:0%
+so Schrodinger now has retained the kind
+ 
+
+ align:start position:0%
+so Schrodinger now has retained the kind
+of look and feel of manipulating
+
+ align:start position:0%
+of look and feel of manipulating
+ 
+
+ align:start position:0%
+of look and feel of manipulating
+differential equations familiar for for
+
+ align:start position:0%
+differential equations familiar for for
+ 
+
+ align:start position:0%
+differential equations familiar for for
+a long time by that by that point he has
+
+ align:start position:0%
+a long time by that by that point he has
+ 
+
+ align:start position:0%
+a long time by that by that point he has
+a way of of reproducing this kind of
+
+ align:start position:0%
+a way of of reproducing this kind of
+ 
+
+ align:start position:0%
+a way of of reproducing this kind of
+inherent discreetness for things like
+
+ align:start position:0%
+inherent discreetness for things like
+ 
+
+ align:start position:0%
+inherent discreetness for things like
+the emission of these spectral lines uh
+
+ align:start position:0%
+the emission of these spectral lines uh
+ 
+
+ align:start position:0%
+the emission of these spectral lines uh
+but not by but by doing by building up
+
+ align:start position:0%
+but not by but by doing by building up
+ 
+
+ align:start position:0%
+but not by but by doing by building up
+this kind of um waviness of of nature
+
+ align:start position:0%
+this kind of um waviness of of nature
+ 
+
+ align:start position:0%
+this kind of um waviness of of nature
+from the start rather than imposing a
+
+ align:start position:0%
+from the start rather than imposing a
+ 
+
+ align:start position:0%
+from the start rather than imposing a
+kind of ad hoc Quantum condition that's
+
+ align:start position:0%
+kind of ad hoc Quantum condition that's
+ 
+
+ align:start position:0%
+kind of ad hoc Quantum condition that's
+what voting was kind of working toward
+
+ align:start position:0%
+what voting was kind of working toward
+ 
+
+ align:start position:0%
+what voting was kind of working toward
+uh in that winter of 25 26. he also then
+
+ align:start position:0%
+uh in that winter of 25 26. he also then
+ 
+
+ align:start position:0%
+uh in that winter of 25 26. he also then
+quickly realizes that solutions to his
+
+ align:start position:0%
+quickly realizes that solutions to his
+ 
+
+ align:start position:0%
+quickly realizes that solutions to his
+equation are are wave functions I should
+
+ align:start position:0%
+equation are are wave functions I should
+ 
+
+ align:start position:0%
+equation are are wave functions I should
+obey something called superposition
+
+ align:start position:0%
+obey something called superposition
+ 
+
+ align:start position:0%
+obey something called superposition
+which we've seen briefly in previous uh
+
+ align:start position:0%
+which we've seen briefly in previous uh
+ 
+
+ align:start position:0%
+which we've seen briefly in previous uh
+classes class sessions even this term if
+
+ align:start position:0%
+classes class sessions even this term if
+ 
+
+ align:start position:0%
+classes class sessions even this term if
+there was one solution to that equation
+
+ align:start position:0%
+there was one solution to that equation
+ 
+
+ align:start position:0%
+there was one solution to that equation
+and a separate solution then the sum of
+
+ align:start position:0%
+and a separate solution then the sum of
+ 
+
+ align:start position:0%
+and a separate solution then the sum of
+them will also be a solution for that
+
+ align:start position:0%
+them will also be a solution for that
+ 
+
+ align:start position:0%
+them will also be a solution for that
+matter the difference that you can take
+
+ align:start position:0%
+matter the difference that you can take
+ 
+
+ align:start position:0%
+matter the difference that you can take
+uh legitimate solutions to the wave
+
+ align:start position:0%
+uh legitimate solutions to the wave
+ 
+
+ align:start position:0%
+uh legitimate solutions to the wave
+equation and add them and the the
+
+ align:start position:0%
+equation and add them and the the
+ 
+
+ align:start position:0%
+equation and add them and the the
+resulting sum will also be a solution
+
+ align:start position:0%
+resulting sum will also be a solution
+ 
+
+ align:start position:0%
+resulting sum will also be a solution
+and that means that these wave functions
+
+ align:start position:0%
+and that means that these wave functions
+ 
+
+ align:start position:0%
+and that means that these wave functions
+could do all the things that waves do
+
+ align:start position:0%
+could do all the things that waves do
+ 
+
+ align:start position:0%
+could do all the things that waves do
+they could undergo interference for
+
+ align:start position:0%
+they could undergo interference for
+ 
+
+ align:start position:0%
+they could undergo interference for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+and again here's just a quick example if
+
+ align:start position:0%
+and again here's just a quick example if
+ 
+
+ align:start position:0%
+and again here's just a quick example if
+you have two waves of the same amplitude
+
+ align:start position:0%
+you have two waves of the same amplitude
+ 
+
+ align:start position:0%
+you have two waves of the same amplitude
+but different uh wavelength then in
+
+ align:start position:0%
+but different uh wavelength then in
+ 
+
+ align:start position:0%
+but different uh wavelength then in
+places where the amplitudes happen to
+
+ align:start position:0%
+places where the amplitudes happen to
+ 
+
+ align:start position:0%
+places where the amplitudes happen to
+line up where Crest is near Crest and
+
+ align:start position:0%
+line up where Crest is near Crest and
+ 
+
+ align:start position:0%
+line up where Crest is near Crest and
+you add those waves together
+
+ align:start position:0%
+you add those waves together
+ 
+
+ align:start position:0%
+you add those waves together
+we'll get constructive interference the
+
+ align:start position:0%
+we'll get constructive interference the
+ 
+
+ align:start position:0%
+we'll get constructive interference the
+resulting wave will have a height nearly
+
+ align:start position:0%
+resulting wave will have a height nearly
+ 
+
+ align:start position:0%
+resulting wave will have a height nearly
+twice as tall as either wave alone on
+
+ align:start position:0%
+twice as tall as either wave alone on
+ 
+
+ align:start position:0%
+twice as tall as either wave alone on
+the other hand in other locations where
+
+ align:start position:0%
+the other hand in other locations where
+ 
+
+ align:start position:0%
+the other hand in other locations where
+a Crest is nearly lined up with a trough
+
+ align:start position:0%
+a Crest is nearly lined up with a trough
+ 
+
+ align:start position:0%
+a Crest is nearly lined up with a trough
+they'll just about cancel each other out
+
+ align:start position:0%
+they'll just about cancel each other out
+ 
+
+ align:start position:0%
+they'll just about cancel each other out
+and the resulting amps which will be
+
+ align:start position:0%
+and the resulting amps which will be
+ 
+
+ align:start position:0%
+and the resulting amps which will be
+much smaller you can have destructive
+
+ align:start position:0%
+much smaller you can have destructive
+ 
+
+ align:start position:0%
+much smaller you can have destructive
+interference all those things that are
+
+ align:start position:0%
+interference all those things that are
+ 
+
+ align:start position:0%
+interference all those things that are
+familiar from water waves from sound
+
+ align:start position:0%
+familiar from water waves from sound
+ 
+
+ align:start position:0%
+familiar from water waves from sound
+waves from light waves into maxwellian
+
+ align:start position:0%
+waves from light waves into maxwellian
+ 
+
+ align:start position:0%
+waves from light waves into maxwellian
+context all those things seem to carry
+
+ align:start position:0%
+context all those things seem to carry
+ 
+
+ align:start position:0%
+context all those things seem to carry
+over to Solutions of Schrodinger's wave
+
+ align:start position:0%
+over to Solutions of Schrodinger's wave
+ 
+
+ align:start position:0%
+over to Solutions of Schrodinger's wave
+equation as well even though it's
+
+ align:start position:0%
+equation as well even though it's
+ 
+
+ align:start position:0%
+equation as well even though it's
+seemingly describing something like an
+
+ align:start position:0%
+seemingly describing something like an
+ 
+
+ align:start position:0%
+seemingly describing something like an
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+so that really uh kind of forced the
+
+ align:start position:0%
+so that really uh kind of forced the
+ 
+
+ align:start position:0%
+so that really uh kind of forced the
+question if this wave function PSI has
+
+ align:start position:0%
+question if this wave function PSI has
+ 
+
+ align:start position:0%
+question if this wave function PSI has
+definite wave-like properties what was
+
+ align:start position:0%
+definite wave-like properties what was
+ 
+
+ align:start position:0%
+definite wave-like properties what was
+it what was it a wave of or in it starts
+
+ align:start position:0%
+it what was it a wave of or in it starts
+ 
+
+ align:start position:0%
+it what was it a wave of or in it starts
+to sound like the questions about light
+
+ align:start position:0%
+to sound like the questions about light
+ 
+
+ align:start position:0%
+to sound like the questions about light
+that we began this class with
+
+ align:start position:0%
+that we began this class with
+ 
+
+ align:start position:0%
+that we began this class with
+so what what is doing the waving if PSI
+
+ align:start position:0%
+so what what is doing the waving if PSI
+ 
+
+ align:start position:0%
+so what what is doing the waving if PSI
+is uh behaves like a wave and that'll be
+
+ align:start position:0%
+is uh behaves like a wave and that'll be
+ 
+
+ align:start position:0%
+is uh behaves like a wave and that'll be
+getting even more bizarre here's we
+
+ align:start position:0%
+getting even more bizarre here's we
+ 
+
+ align:start position:0%
+getting even more bizarre here's we
+begin to break from just the familiar uh
+
+ align:start position:0%
+begin to break from just the familiar uh
+ 
+
+ align:start position:0%
+begin to break from just the familiar uh
+physics of sort of classical waves and
+
+ align:start position:0%
+physics of sort of classical waves and
+ 
+
+ align:start position:0%
+physics of sort of classical waves and
+again Schrodinger to his credit was very
+
+ align:start position:0%
+again Schrodinger to his credit was very
+ 
+
+ align:start position:0%
+again Schrodinger to his credit was very
+quick to notice this himself and really
+
+ align:start position:0%
+quick to notice this himself and really
+ 
+
+ align:start position:0%
+quick to notice this himself and really
+point it out and begin to try to try to
+
+ align:start position:0%
+point it out and begin to try to try to
+ 
+
+ align:start position:0%
+point it out and begin to try to try to
+puzzle it through
+
+ align:start position:0%
+puzzle it through
+ 
+
+ align:start position:0%
+puzzle it through
+if you consider a system with more than
+
+ align:start position:0%
+if you consider a system with more than
+ 
+
+ align:start position:0%
+if you consider a system with more than
+one electron let's say as simple as just
+
+ align:start position:0%
+one electron let's say as simple as just
+ 
+
+ align:start position:0%
+one electron let's say as simple as just
+two electrons not just one
+
+ align:start position:0%
+two electrons not just one
+ 
+
+ align:start position:0%
+two electrons not just one
+then the equation suddenly depends on
+
+ align:start position:0%
+then the equation suddenly depends on
+ 
+
+ align:start position:0%
+then the equation suddenly depends on
+many many coordinates the interaction
+
+ align:start position:0%
+many many coordinates the interaction
+ 
+
+ align:start position:0%
+many many coordinates the interaction
+potential that key portion within the
+
+ align:start position:0%
+potential that key portion within the
+ 
+
+ align:start position:0%
+potential that key portion within the
+schroding equation well now in general
+
+ align:start position:0%
+schroding equation well now in general
+ 
+
+ align:start position:0%
+schroding equation well now in general
+depend on the location of both electron
+
+ align:start position:0%
+depend on the location of both electron
+ 
+
+ align:start position:0%
+depend on the location of both electron
+one and electron two now each they're
+
+ align:start position:0%
+one and electron two now each they're
+ 
+
+ align:start position:0%
+one and electron two now each they're
+each existing in three-dimensional Space
+
+ align:start position:0%
+each existing in three-dimensional Space
+ 
+
+ align:start position:0%
+each existing in three-dimensional Space
+X Y and Z they could be at different
+
+ align:start position:0%
+X Y and Z they could be at different
+ 
+
+ align:start position:0%
+X Y and Z they could be at different
+locations so the the the potential
+
+ align:start position:0%
+locations so the the the potential
+ 
+
+ align:start position:0%
+locations so the the the potential
+energy of that two body system will now
+
+ align:start position:0%
+energy of that two body system will now
+ 
+
+ align:start position:0%
+energy of that two body system will now
+in general depend on six direct six
+
+ align:start position:0%
+in general depend on six direct six
+ 
+
+ align:start position:0%
+in general depend on six direct six
+spatial coordinates not just three
+
+ align:start position:0%
+spatial coordinates not just three
+ 
+
+ align:start position:0%
+spatial coordinates not just three
+so now Solutions PSI solutions to
+
+ align:start position:0%
+so now Solutions PSI solutions to
+ 
+
+ align:start position:0%
+so now Solutions PSI solutions to
+Schrodinger's wave equation will
+
+ align:start position:0%
+Schrodinger's wave equation will
+ 
+
+ align:start position:0%
+Schrodinger's wave equation will
+themselves depend on Six Dimensions six
+
+ align:start position:0%
+themselves depend on Six Dimensions six
+ 
+
+ align:start position:0%
+themselves depend on Six Dimensions six
+coordinates of space Not Just Three
+
+ align:start position:0%
+coordinates of space Not Just Three
+ 
+
+ align:start position:0%
+coordinates of space Not Just Three
+that's not like a water wave or a sound
+
+ align:start position:0%
+that's not like a water wave or a sound
+ 
+
+ align:start position:0%
+that's not like a water wave or a sound
+wave or a light wave
+
+ align:start position:0%
+wave or a light wave
+ 
+
+ align:start position:0%
+wave or a light wave
+so even though the mathematics was in
+
+ align:start position:0%
+so even though the mathematics was in
+ 
+
+ align:start position:0%
+so even though the mathematics was in
+many ways very familiar and Schrodinger
+
+ align:start position:0%
+many ways very familiar and Schrodinger
+ 
+
+ align:start position:0%
+many ways very familiar and Schrodinger
+used that's a great effect to find
+
+ align:start position:0%
+used that's a great effect to find
+ 
+
+ align:start position:0%
+used that's a great effect to find
+solutions to figure out why there's a
+
+ align:start position:0%
+solutions to figure out why there's a
+ 
+
+ align:start position:0%
+solutions to figure out why there's a
+seemingly quantized or discrete spectrum
+
+ align:start position:0%
+seemingly quantized or discrete spectrum
+ 
+
+ align:start position:0%
+seemingly quantized or discrete spectrum
+of eigenvalues and all that it wasn't
+
+ align:start position:0%
+of eigenvalues and all that it wasn't
+ 
+
+ align:start position:0%
+of eigenvalues and all that it wasn't
+actually just just classical waves and
+
+ align:start position:0%
+actually just just classical waves and
+ 
+
+ align:start position:0%
+actually just just classical waves and
+there were even mathematically some some
+
+ align:start position:0%
+there were even mathematically some some
+ 
+
+ align:start position:0%
+there were even mathematically some some
+unexpected features that they're
+
+ align:start position:0%
+unexpected features that they're
+ 
+
+ align:start position:0%
+unexpected features that they're
+shorting himself again to elucidate get
+
+ align:start position:0%
+shorting himself again to elucidate get
+ 
+
+ align:start position:0%
+shorting himself again to elucidate get
+PSI whatever it was was not just like a
+
+ align:start position:0%
+PSI whatever it was was not just like a
+ 
+
+ align:start position:0%
+PSI whatever it was was not just like a
+water wave in fact it seemed to live in
+
+ align:start position:0%
+water wave in fact it seemed to live in
+ 
+
+ align:start position:0%
+water wave in fact it seemed to live in
+some higher dimensional abstract
+
+ align:start position:0%
+some higher dimensional abstract
+ 
+
+ align:start position:0%
+some higher dimensional abstract
+mathematical space that would quickly
+
+ align:start position:0%
+mathematical space that would quickly
+ 
+
+ align:start position:0%
+mathematical space that would quickly
+become known as configuration space
+
+ align:start position:0%
+become known as configuration space
+ 
+
+ align:start position:0%
+become known as configuration space
+rather than the space in which we seem
+
+ align:start position:0%
+rather than the space in which we seem
+ 
+
+ align:start position:0%
+rather than the space in which we seem
+to move around every day
+
+ align:start position:0%
+to move around every day
+ 
+
+ align:start position:0%
+to move around every day
+so that was what Schrodinger began
+
+ align:start position:0%
+so that was what Schrodinger began
+ 
+
+ align:start position:0%
+so that was what Schrodinger began
+publishing as early as January 1926 he
+
+ align:start position:0%
+publishing as early as January 1926 he
+ 
+
+ align:start position:0%
+publishing as early as January 1926 he
+wrote a series of papers very very uh
+
+ align:start position:0%
+wrote a series of papers very very uh
+ 
+
+ align:start position:0%
+wrote a series of papers very very uh
+quickly one after the other in a kind of
+
+ align:start position:0%
+quickly one after the other in a kind of
+ 
+
+ align:start position:0%
+quickly one after the other in a kind of
+four-part series throughout that winter
+
+ align:start position:0%
+four-part series throughout that winter
+ 
+
+ align:start position:0%
+four-part series throughout that winter
+and spring of 1926 and so before long uh
+
+ align:start position:0%
+and spring of 1926 and so before long uh
+ 
+
+ align:start position:0%
+and spring of 1926 and so before long uh
+both Schrodinger and Heisenberg
+
+ align:start position:0%
+both Schrodinger and Heisenberg
+ 
+
+ align:start position:0%
+both Schrodinger and Heisenberg
+themselves and soon many members of this
+
+ align:start position:0%
+themselves and soon many members of this
+ 
+
+ align:start position:0%
+themselves and soon many members of this
+kind of tight-knit community uh were
+
+ align:start position:0%
+kind of tight-knit community uh were
+ 
+
+ align:start position:0%
+kind of tight-knit community uh were
+beginning to to do a kind of compare and
+
+ align:start position:0%
+beginning to to do a kind of compare and
+ 
+
+ align:start position:0%
+beginning to to do a kind of compare and
+contrast exercise there were now two
+
+ align:start position:0%
+contrast exercise there were now two
+ 
+
+ align:start position:0%
+contrast exercise there were now two
+quite different looking first principles
+
+ align:start position:0%
+quite different looking first principles
+ 
+
+ align:start position:0%
+quite different looking first principles
+um uh approaches to a new quantum theory
+
+ align:start position:0%
+um uh approaches to a new quantum theory
+ 
+
+ align:start position:0%
+um uh approaches to a new quantum theory
+on offer Heisenberg's Matrix mechanics
+
+ align:start position:0%
+on offer Heisenberg's Matrix mechanics
+ 
+
+ align:start position:0%
+on offer Heisenberg's Matrix mechanics
+uh Schrodinger's wave mechanics they
+
+ align:start position:0%
+uh Schrodinger's wave mechanics they
+ 
+
+ align:start position:0%
+uh Schrodinger's wave mechanics they
+looked nothing alike they seemed to make
+
+ align:start position:0%
+looked nothing alike they seemed to make
+ 
+
+ align:start position:0%
+looked nothing alike they seemed to make
+very different starting assumptions and
+
+ align:start position:0%
+very different starting assumptions and
+ 
+
+ align:start position:0%
+very different starting assumptions and
+they they had different kinds of strange
+
+ align:start position:0%
+they they had different kinds of strange
+ 
+
+ align:start position:0%
+they they had different kinds of strange
+features they were strange in different
+
+ align:start position:0%
+features they were strange in different
+ 
+
+ align:start position:0%
+features they were strange in different
+ways
+
+ align:start position:0%
+ways
+ 
+
+ align:start position:0%
+ways
+so Schrodinger eventually caught up with
+
+ align:start position:0%
+so Schrodinger eventually caught up with
+ 
+
+ align:start position:0%
+so Schrodinger eventually caught up with
+some of Heisenberg's papers and he added
+
+ align:start position:0%
+some of Heisenberg's papers and he added
+ 
+
+ align:start position:0%
+some of Heisenberg's papers and he added
+a footnote into one of Schrodinger's own
+
+ align:start position:0%
+a footnote into one of Schrodinger's own
+ 
+
+ align:start position:0%
+a footnote into one of Schrodinger's own
+uh follow-up articles in that first
+
+ align:start position:0%
+uh follow-up articles in that first
+ 
+
+ align:start position:0%
+uh follow-up articles in that first
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+I think this is not in his very first
+
+ align:start position:0%
+I think this is not in his very first
+ 
+
+ align:start position:0%
+I think this is not in his very first
+article but sometime later that spring
+
+ align:start position:0%
+article but sometime later that spring
+ 
+
+ align:start position:0%
+article but sometime later that spring
+in a footnote
+
+ align:start position:0%
+in a footnote
+ 
+
+ align:start position:0%
+in a footnote
+he writes as you see here my theory was
+
+ align:start position:0%
+he writes as you see here my theory was
+ 
+
+ align:start position:0%
+he writes as you see here my theory was
+inspired by Louis de broy and by short
+
+ align:start position:0%
+inspired by Louis de broy and by short
+ 
+
+ align:start position:0%
+inspired by Louis de broy and by short
+but but incomplete remarks by Albert
+
+ align:start position:0%
+but but incomplete remarks by Albert
+ 
+
+ align:start position:0%
+but but incomplete remarks by Albert
+Einstein no genetic relation whatever
+
+ align:start position:0%
+Einstein no genetic relation whatever
+ 
+
+ align:start position:0%
+Einstein no genetic relation whatever
+with Heisenberg is known to me I knew of
+
+ align:start position:0%
+with Heisenberg is known to me I knew of
+ 
+
+ align:start position:0%
+with Heisenberg is known to me I knew of
+his theory of course but felt
+
+ align:start position:0%
+his theory of course but felt
+ 
+
+ align:start position:0%
+his theory of course but felt
+discouraged not to say repelled by the
+
+ align:start position:0%
+discouraged not to say repelled by the
+ 
+
+ align:start position:0%
+discouraged not to say repelled by the
+methods of transcendental algebra what
+
+ align:start position:0%
+methods of transcendental algebra what
+ 
+
+ align:start position:0%
+methods of transcendental algebra what
+we now call matrices which appeared very
+
+ align:start position:0%
+we now call matrices which appeared very
+ 
+
+ align:start position:0%
+we now call matrices which appeared very
+difficult to me and by the lack of
+
+ align:start position:0%
+difficult to me and by the lack of
+ 
+
+ align:start position:0%
+difficult to me and by the lack of
+visualizability so that's about as rude
+
+ align:start position:0%
+visualizability so that's about as rude
+ 
+
+ align:start position:0%
+visualizability so that's about as rude
+as you can get in a footnote in a
+
+ align:start position:0%
+as you can get in a footnote in a
+ 
+
+ align:start position:0%
+as you can get in a footnote in a
+physics journal at least at that time I
+
+ align:start position:0%
+physics journal at least at that time I
+ 
+
+ align:start position:0%
+physics journal at least at that time I
+was discouraged and repelled by my
+
+ align:start position:0%
+was discouraged and repelled by my
+ 
+
+ align:start position:0%
+was discouraged and repelled by my
+colleague's work
+
+ align:start position:0%
+colleague's work
+ 
+
+ align:start position:0%
+colleague's work
+Heisenberg was a little less uh
+
+ align:start position:0%
+Heisenberg was a little less uh
+ 
+
+ align:start position:0%
+Heisenberg was a little less uh
+restrained he wrote just in a private
+
+ align:start position:0%
+restrained he wrote just in a private
+ 
+
+ align:start position:0%
+restrained he wrote just in a private
+letter to his friend Wolfgang Paoli
+
+ align:start position:0%
+letter to his friend Wolfgang Paoli
+ 
+
+ align:start position:0%
+letter to his friend Wolfgang Paoli
+around that same time just uh a little
+
+ align:start position:0%
+around that same time just uh a little
+ 
+
+ align:start position:0%
+around that same time just uh a little
+uh correspondence exchange Heisman said
+
+ align:start position:0%
+uh correspondence exchange Heisman said
+ 
+
+ align:start position:0%
+uh correspondence exchange Heisman said
+The more I reflect on the physical
+
+ align:start position:0%
+The more I reflect on the physical
+ 
+
+ align:start position:0%
+The more I reflect on the physical
+portion of Schrodinger's Theory the more
+
+ align:start position:0%
+portion of Schrodinger's Theory the more
+ 
+
+ align:start position:0%
+portion of Schrodinger's Theory the more
+disgusting I find it Russ Schrodinger
+
+ align:start position:0%
+disgusting I find it Russ Schrodinger
+ 
+
+ align:start position:0%
+disgusting I find it Russ Schrodinger
+writes on the visualizability of his
+
+ align:start position:0%
+writes on the visualizability of his
+ 
+
+ align:start position:0%
+writes on the visualizability of his
+theory I considered trash after all
+
+ align:start position:0%
+theory I considered trash after all
+ 
+
+ align:start position:0%
+theory I considered trash after all
+these waves live in sort of six or more
+
+ align:start position:0%
+these waves live in sort of six or more
+ 
+
+ align:start position:0%
+these waves live in sort of six or more
+dimensional space that seems no more
+
+ align:start position:0%
+dimensional space that seems no more
+ 
+
+ align:start position:0%
+dimensional space that seems no more
+visualizable than these abstract
+
+ align:start position:0%
+visualizable than these abstract
+ 
+
+ align:start position:0%
+visualizable than these abstract
+matrices so this is really a remarkable
+
+ align:start position:0%
+matrices so this is really a remarkable
+ 
+
+ align:start position:0%
+matrices so this is really a remarkable
+clash between two people working on very
+
+ align:start position:0%
+clash between two people working on very
+ 
+
+ align:start position:0%
+clash between two people working on very
+similar topics at the same time and
+
+ align:start position:0%
+similar topics at the same time and
+ 
+
+ align:start position:0%
+similar topics at the same time and
+finding each other's work clearly
+
+ align:start position:0%
+finding each other's work clearly
+ 
+
+ align:start position:0%
+finding each other's work clearly
+lacking not just a repulsive disgusting
+
+ align:start position:0%
+lacking not just a repulsive disgusting
+ 
+
+ align:start position:0%
+lacking not just a repulsive disgusting
+and so it was all the more surprising
+
+ align:start position:0%
+and so it was all the more surprising
+ 
+
+ align:start position:0%
+and so it was all the more surprising
+and really unexpected when several other
+
+ align:start position:0%
+and really unexpected when several other
+ 
+
+ align:start position:0%
+and really unexpected when several other
+physicists actually schroding himself
+
+ align:start position:0%
+physicists actually schroding himself
+ 
+
+ align:start position:0%
+physicists actually schroding himself
+and then two others uh Pascal yordon who
+
+ align:start position:0%
+and then two others uh Pascal yordon who
+ 
+
+ align:start position:0%
+and then two others uh Pascal yordon who
+was another young physicist about the
+
+ align:start position:0%
+was another young physicist about the
+ 
+
+ align:start position:0%
+was another young physicist about the
+same age as Heisenberg and Paulie Jordan
+
+ align:start position:0%
+same age as Heisenberg and Paulie Jordan
+ 
+
+ align:start position:0%
+same age as Heisenberg and Paulie Jordan
+was uh also a young physicist in
+
+ align:start position:0%
+was uh also a young physicist in
+ 
+
+ align:start position:0%
+was uh also a young physicist in
+gertingen so he began working directly
+
+ align:start position:0%
+gertingen so he began working directly
+ 
+
+ align:start position:0%
+gertingen so he began working directly
+with Heisenberg to elaborate Matrix
+
+ align:start position:0%
+with Heisenberg to elaborate Matrix
+ 
+
+ align:start position:0%
+with Heisenberg to elaborate Matrix
+mechanics and then separately still Paul
+
+ align:start position:0%
+mechanics and then separately still Paul
+ 
+
+ align:start position:0%
+mechanics and then separately still Paul
+durac a young uh British physicist who
+
+ align:start position:0%
+durac a young uh British physicist who
+ 
+
+ align:start position:0%
+durac a young uh British physicist who
+at this point was on a fellowship in
+
+ align:start position:0%
+at this point was on a fellowship in
+ 
+
+ align:start position:0%
+at this point was on a fellowship in
+Cambridge England all independently
+
+ align:start position:0%
+Cambridge England all independently
+ 
+
+ align:start position:0%
+Cambridge England all independently
+within a very short span of time all
+
+ align:start position:0%
+within a very short span of time all
+ 
+
+ align:start position:0%
+within a very short span of time all
+three of those physicists demonstrated
+
+ align:start position:0%
+three of those physicists demonstrated
+ 
+
+ align:start position:0%
+three of those physicists demonstrated
+by the summer of 1926 that these two
+
+ align:start position:0%
+by the summer of 1926 that these two
+ 
+
+ align:start position:0%
+by the summer of 1926 that these two
+quite different looking approaches
+
+ align:start position:0%
+quite different looking approaches
+ 
+
+ align:start position:0%
+quite different looking approaches
+Heisenberg's Matrix mechanics schroding
+
+ align:start position:0%
+Heisenberg's Matrix mechanics schroding
+ 
+
+ align:start position:0%
+Heisenberg's Matrix mechanics schroding
+his wave mechanics were actually
+
+ align:start position:0%
+his wave mechanics were actually
+ 
+
+ align:start position:0%
+his wave mechanics were actually
+mathematically equivalent you could
+
+ align:start position:0%
+mathematically equivalent you could
+ 
+
+ align:start position:0%
+mathematically equivalent you could
+actually build a mathematical kind of
+
+ align:start position:0%
+actually build a mathematical kind of
+ 
+
+ align:start position:0%
+actually build a mathematical kind of
+one-to-one mapping to any expression you
+
+ align:start position:0%
+one-to-one mapping to any expression you
+ 
+
+ align:start position:0%
+one-to-one mapping to any expression you
+might try to formulate in Matrix
+
+ align:start position:0%
+might try to formulate in Matrix
+ 
+
+ align:start position:0%
+might try to formulate in Matrix
+mechanics and put that in wave mechanics
+
+ align:start position:0%
+mechanics and put that in wave mechanics
+ 
+
+ align:start position:0%
+mechanics and put that in wave mechanics
+or vice versa so it looks disgusting and
+
+ align:start position:0%
+or vice versa so it looks disgusting and
+ 
+
+ align:start position:0%
+or vice versa so it looks disgusting and
+repulsive and uh unvisualizable one to
+
+ align:start position:0%
+repulsive and uh unvisualizable one to
+ 
+
+ align:start position:0%
+repulsive and uh unvisualizable one to
+the other between Schrodinger and
+
+ align:start position:0%
+the other between Schrodinger and
+ 
+
+ align:start position:0%
+the other between Schrodinger and
+Heisenberg I looked like these were
+
+ align:start position:0%
+Heisenberg I looked like these were
+ 
+
+ align:start position:0%
+Heisenberg I looked like these were
+really just remarkably different ways of
+
+ align:start position:0%
+really just remarkably different ways of
+ 
+
+ align:start position:0%
+really just remarkably different ways of
+trying to carve up the world and yet
+
+ align:start position:0%
+trying to carve up the world and yet
+ 
+
+ align:start position:0%
+trying to carve up the world and yet
+again within just a matter of of a few
+
+ align:start position:0%
+again within just a matter of of a few
+ 
+
+ align:start position:0%
+again within just a matter of of a few
+months uh people have found at least a
+
+ align:start position:0%
+months uh people have found at least a
+ 
+
+ align:start position:0%
+months uh people have found at least a
+mathematical bridge between them and it
+
+ align:start position:0%
+mathematical bridge between them and it
+ 
+
+ align:start position:0%
+mathematical bridge between them and it
+was that last work
+
+ align:start position:0%
+was that last work
+ 
+
+ align:start position:0%
+was that last work
+uh that really made a kind of uh again a
+
+ align:start position:0%
+uh that really made a kind of uh again a
+ 
+
+ align:start position:0%
+uh that really made a kind of uh again a
+map between Matrix and wave mechanics
+
+ align:start position:0%
+map between Matrix and wave mechanics
+ 
+
+ align:start position:0%
+map between Matrix and wave mechanics
+that really convinced people already by
+
+ align:start position:0%
+that really convinced people already by
+ 
+
+ align:start position:0%
+that really convinced people already by
+1926 to begin referring to a new single
+
+ align:start position:0%
+1926 to begin referring to a new single
+ 
+
+ align:start position:0%
+1926 to begin referring to a new single
+thing a new thing called quantum
+
+ align:start position:0%
+thing a new thing called quantum
+ 
+
+ align:start position:0%
+thing a new thing called quantum
+mechanics not just Matrix mechanics not
+
+ align:start position:0%
+mechanics not just Matrix mechanics not
+ 
+
+ align:start position:0%
+mechanics not just Matrix mechanics not
+just wave mechanics but now one thing
+
+ align:start position:0%
+just wave mechanics but now one thing
+ 
+
+ align:start position:0%
+just wave mechanics but now one thing
+called quantum mechanics and to then
+
+ align:start position:0%
+called quantum mechanics and to then
+ 
+
+ align:start position:0%
+called quantum mechanics and to then
+start using the phrase old quantum
+
+ align:start position:0%
+start using the phrase old quantum
+ 
+
+ align:start position:0%
+start using the phrase old quantum
+theory to refer to that kind of grab bag
+
+ align:start position:0%
+theory to refer to that kind of grab bag
+ 
+
+ align:start position:0%
+theory to refer to that kind of grab bag
+of techniques that we looked at uh that
+
+ align:start position:0%
+of techniques that we looked at uh that
+ 
+
+ align:start position:0%
+of techniques that we looked at uh that
+had come sort of before
+
+ align:start position:0%
+had come sort of before
+ 
+
+ align:start position:0%
+had come sort of before
+1925-26 so the new quantum mechanics was
+
+ align:start position:0%
+1925-26 so the new quantum mechanics was
+ 
+
+ align:start position:0%
+1925-26 so the new quantum mechanics was
+heralded really by that name almost in
+
+ align:start position:0%
+heralded really by that name almost in
+ 
+
+ align:start position:0%
+heralded really by that name almost in
+real time just remarkable kind of
+
+ align:start position:0%
+real time just remarkable kind of
+ 
+
+ align:start position:0%
+real time just remarkable kind of
+convergence by summer and fall of 1926.
+
+ align:start position:0%
+convergence by summer and fall of 1926.
+ 
+
+ align:start position:0%
+convergence by summer and fall of 1926.
+so I'm going to pause there I see a
+
+ align:start position:0%
+so I'm going to pause there I see a
+ 
+
+ align:start position:0%
+so I'm going to pause there I see a
+couple questions come up in the chat
+
+ align:start position:0%
+couple questions come up in the chat
+ 
+
+ align:start position:0%
+couple questions come up in the chat
+time for some other discussion any
+
+ align:start position:0%
+time for some other discussion any
+ 
+
+ align:start position:0%
+time for some other discussion any
+questions on that stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Alex asked is this is Helga land the
+
+ align:start position:0%
+so Alex asked is this is Helga land the
+ 
+
+ align:start position:0%
+so Alex asked is this is Helga land the
+same island the British tried to blow up
+
+ align:start position:0%
+same island the British tried to blow up
+ 
+
+ align:start position:0%
+same island the British tried to blow up
+after World War II I have no idea what
+
+ align:start position:0%
+after World War II I have no idea what
+ 
+
+ align:start position:0%
+after World War II I have no idea what
+happened that that's news to me it might
+
+ align:start position:0%
+happened that that's news to me it might
+ 
+
+ align:start position:0%
+happened that that's news to me it might
+be I mean Wikipedia at least could
+
+ align:start position:0%
+be I mean Wikipedia at least could
+ 
+
+ align:start position:0%
+be I mean Wikipedia at least could
+inform us I don't know
+
+ align:start position:0%
+inform us I don't know
+ 
+
+ align:start position:0%
+inform us I don't know
+um did configuration space ever become
+
+ align:start position:0%
+um did configuration space ever become
+ 
+
+ align:start position:0%
+um did configuration space ever become
+generalized to Hilbert space Fisher asks
+
+ align:start position:0%
+generalized to Hilbert space Fisher asks
+ 
+
+ align:start position:0%
+generalized to Hilbert space Fisher asks
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yes I I'm not sure I'd say generalized
+
+ align:start position:0%
+yes I I'm not sure I'd say generalized
+ 
+
+ align:start position:0%
+yes I I'm not sure I'd say generalized
+too they're separately and also actually
+
+ align:start position:0%
+too they're separately and also actually
+ 
+
+ align:start position:0%
+too they're separately and also actually
+pretty soon afterwards by people like
+
+ align:start position:0%
+pretty soon afterwards by people like
+ 
+
+ align:start position:0%
+pretty soon afterwards by people like
+like Paul durac uh began trying to
+
+ align:start position:0%
+like Paul durac uh began trying to
+ 
+
+ align:start position:0%
+like Paul durac uh began trying to
+formulate this new quantum mechanics uh
+
+ align:start position:0%
+formulate this new quantum mechanics uh
+ 
+
+ align:start position:0%
+formulate this new quantum mechanics uh
+in in a in a more mathematically kind of
+
+ align:start position:0%
+in in a in a more mathematically kind of
+ 
+
+ align:start position:0%
+in in a in a more mathematically kind of
+first principles way thinking about
+
+ align:start position:0%
+first principles way thinking about
+ 
+
+ align:start position:0%
+first principles way thinking about
+vectors and Vector spaces and so on and
+
+ align:start position:0%
+vectors and Vector spaces and so on and
+ 
+
+ align:start position:0%
+vectors and Vector spaces and so on and
+that comes not only from Dirac but
+
+ align:start position:0%
+that comes not only from Dirac but
+ 
+
+ align:start position:0%
+that comes not only from Dirac but
+people like Dirac and John fonome and
+
+ align:start position:0%
+people like Dirac and John fonome and
+ 
+
+ align:start position:0%
+people like Dirac and John fonome and
+others so they were replacing
+
+ align:start position:0%
+others so they were replacing
+ 
+
+ align:start position:0%
+others so they were replacing
+configuration space per se but they were
+
+ align:start position:0%
+configuration space per se but they were
+ 
+
+ align:start position:0%
+configuration space per se but they were
+certainly trying to think more carefully
+
+ align:start position:0%
+certainly trying to think more carefully
+ 
+
+ align:start position:0%
+certainly trying to think more carefully
+about the kinds of spaces the kinds of
+
+ align:start position:0%
+about the kinds of spaces the kinds of
+ 
+
+ align:start position:0%
+about the kinds of spaces the kinds of
+mathematical spaces in which something
+
+ align:start position:0%
+mathematical spaces in which something
+ 
+
+ align:start position:0%
+mathematical spaces in which something
+like a Quantum State might reside so if
+
+ align:start position:0%
+like a Quantum State might reside so if
+ 
+
+ align:start position:0%
+like a Quantum State might reside so if
+you're thinking about a Quantum wave
+
+ align:start position:0%
+you're thinking about a Quantum wave
+ 
+
+ align:start position:0%
+you're thinking about a Quantum wave
+function that's in configuration space
+
+ align:start position:0%
+function that's in configuration space
+ 
+
+ align:start position:0%
+function that's in configuration space
+if you think about
+
+ align:start position:0%
+if you think about
+ 
+
+ align:start position:0%
+if you think about
+um a Quantum State as a kind of
+
+ align:start position:0%
+um a Quantum State as a kind of
+ 
+
+ align:start position:0%
+um a Quantum State as a kind of
+eigenvector in some abstract Hilbert
+
+ align:start position:0%
+eigenvector in some abstract Hilbert
+ 
+
+ align:start position:0%
+eigenvector in some abstract Hilbert
+space right then then that's the
+
+ align:start position:0%
+space right then then that's the
+ 
+
+ align:start position:0%
+space right then then that's the
+direction that the Iraq especially
+
+ align:start position:0%
+direction that the Iraq especially
+ 
+
+ align:start position:0%
+direction that the Iraq especially
+starts to formalize he writes an
+
+ align:start position:0%
+starts to formalize he writes an
+ 
+
+ align:start position:0%
+starts to formalize he writes an
+extraordinarily influential textbook in
+
+ align:start position:0%
+extraordinarily influential textbook in
+ 
+
+ align:start position:0%
+extraordinarily influential textbook in
+fact I showed its cover on the previous
+
+ align:start position:0%
+fact I showed its cover on the previous
+ 
+
+ align:start position:0%
+fact I showed its cover on the previous
+slide first edition 1930 that's pretty
+
+ align:start position:0%
+slide first edition 1930 that's pretty
+ 
+
+ align:start position:0%
+slide first edition 1930 that's pretty
+quick to have a textbook on stuff that
+
+ align:start position:0%
+quick to have a textbook on stuff that
+ 
+
+ align:start position:0%
+quick to have a textbook on stuff that
+was really just a few years old and then
+
+ align:start position:0%
+was really just a few years old and then
+ 
+
+ align:start position:0%
+was really just a few years old and then
+with the Hilbert spaces people began to
+
+ align:start position:0%
+with the Hilbert spaces people began to
+ 
+
+ align:start position:0%
+with the Hilbert spaces people began to
+realize these could be of of almost
+
+ align:start position:0%
+realize these could be of of almost
+ 
+
+ align:start position:0%
+realize these could be of of almost
+arbitrary Dimension so Hilbert spaces
+
+ align:start position:0%
+arbitrary Dimension so Hilbert spaces
+ 
+
+ align:start position:0%
+arbitrary Dimension so Hilbert spaces
+could be two Dimensions they could be
+
+ align:start position:0%
+could be two Dimensions they could be
+ 
+
+ align:start position:0%
+could be two Dimensions they could be
+ten thousand Dimensions they could be
+
+ align:start position:0%
+ten thousand Dimensions they could be
+ 
+
+ align:start position:0%
+ten thousand Dimensions they could be
+infinite dimensional and so in that
+
+ align:start position:0%
+infinite dimensional and so in that
+ 
+
+ align:start position:0%
+infinite dimensional and so in that
+sense they're similar to configuration
+
+ align:start position:0%
+sense they're similar to configuration
+ 
+
+ align:start position:0%
+sense they're similar to configuration
+space and not being limited to only X Y
+
+ align:start position:0%
+space and not being limited to only X Y
+ 
+
+ align:start position:0%
+space and not being limited to only X Y
+and Z but they're not quite this they're
+
+ align:start position:0%
+and Z but they're not quite this they're
+ 
+
+ align:start position:0%
+and Z but they're not quite this they're
+not exactly the same kind of thing it's
+
+ align:start position:0%
+not exactly the same kind of thing it's
+ 
+
+ align:start position:0%
+not exactly the same kind of thing it's
+really people like Paul Dirac Who start
+
+ align:start position:0%
+really people like Paul Dirac Who start
+ 
+
+ align:start position:0%
+really people like Paul Dirac Who start
+pushing very heavily in that direction
+
+ align:start position:0%
+pushing very heavily in that direction
+ 
+
+ align:start position:0%
+pushing very heavily in that direction
+uh silos with their opinions on each
+
+ align:start position:0%
+uh silos with their opinions on each
+ 
+
+ align:start position:0%
+uh silos with their opinions on each
+other's work ever change
+
+ align:start position:0%
+other's work ever change
+ 
+
+ align:start position:0%
+other's work ever change
+um that's a good question I think they
+
+ align:start position:0%
+um that's a good question I think they
+ 
+
+ align:start position:0%
+um that's a good question I think they
+stopped calling each other's work
+
+ align:start position:0%
+stopped calling each other's work
+ 
+
+ align:start position:0%
+stopped calling each other's work
+disgusting in print so that's like a
+
+ align:start position:0%
+disgusting in print so that's like a
+ 
+
+ align:start position:0%
+disgusting in print so that's like a
+plus uh and I think Schrodinger himself
+
+ align:start position:0%
+plus uh and I think Schrodinger himself
+ 
+
+ align:start position:0%
+plus uh and I think Schrodinger himself
+since he was one of the people who did
+
+ align:start position:0%
+since he was one of the people who did
+ 
+
+ align:start position:0%
+since he was one of the people who did
+find this mathematical Bridge a kind of
+
+ align:start position:0%
+find this mathematical Bridge a kind of
+ 
+
+ align:start position:0%
+find this mathematical Bridge a kind of
+equivalence between the two approaches
+
+ align:start position:0%
+equivalence between the two approaches
+ 
+
+ align:start position:0%
+equivalence between the two approaches
+Schrodinger I think after that began to
+
+ align:start position:0%
+Schrodinger I think after that began to
+ 
+
+ align:start position:0%
+Schrodinger I think after that began to
+realize there are
+
+ align:start position:0%
+realize there are
+ 
+
+ align:start position:0%
+realize there are
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+conveniences of either approach so it's
+
+ align:start position:0%
+conveniences of either approach so it's
+ 
+
+ align:start position:0%
+conveniences of either approach so it's
+not one versus the other since they
+
+ align:start position:0%
+not one versus the other since they
+ 
+
+ align:start position:0%
+not one versus the other since they
+could be mathematically mapped but as
+
+ align:start position:0%
+could be mathematically mapped but as
+ 
+
+ align:start position:0%
+could be mathematically mapped but as
+each of you probably learned just from
+
+ align:start position:0%
+each of you probably learned just from
+ 
+
+ align:start position:0%
+each of you probably learned just from
+you know problem sets for certain kinds
+
+ align:start position:0%
+you know problem sets for certain kinds
+ 
+
+ align:start position:0%
+you know problem sets for certain kinds
+of questions we might choose to ask for
+
+ align:start position:0%
+of questions we might choose to ask for
+ 
+
+ align:start position:0%
+of questions we might choose to ask for
+certain kinds of calculations one
+
+ align:start position:0%
+certain kinds of calculations one
+ 
+
+ align:start position:0%
+certain kinds of calculations one
+starting approach one coordinate system
+
+ align:start position:0%
+starting approach one coordinate system
+ 
+
+ align:start position:0%
+starting approach one coordinate system
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+um a way of characterizing the balance
+
+ align:start position:0%
+um a way of characterizing the balance
+ 
+
+ align:start position:0%
+um a way of characterizing the balance
+of forces and all that that's often more
+
+ align:start position:0%
+of forces and all that that's often more
+ 
+
+ align:start position:0%
+of forces and all that that's often more
+convenient than others even if in
+
+ align:start position:0%
+convenient than others even if in
+ 
+
+ align:start position:0%
+convenient than others even if in
+principle we could have mapped it into a
+
+ align:start position:0%
+principle we could have mapped it into a
+ 
+
+ align:start position:0%
+principle we could have mapped it into a
+different format that's how people begin
+
+ align:start position:0%
+different format that's how people begin
+ 
+
+ align:start position:0%
+different format that's how people begin
+to talk more and more about the the kind
+
+ align:start position:0%
+to talk more and more about the the kind
+ 
+
+ align:start position:0%
+to talk more and more about the the kind
+of comparing contrast exercise between
+
+ align:start position:0%
+of comparing contrast exercise between
+ 
+
+ align:start position:0%
+of comparing contrast exercise between
+wave mechanics and major mechanics if
+
+ align:start position:0%
+wave mechanics and major mechanics if
+ 
+
+ align:start position:0%
+wave mechanics and major mechanics if
+they are fundamentally mappable then
+
+ align:start position:0%
+they are fundamentally mappable then
+ 
+
+ align:start position:0%
+they are fundamentally mappable then
+sort of use whichever makes most sense
+
+ align:start position:0%
+sort of use whichever makes most sense
+ 
+
+ align:start position:0%
+sort of use whichever makes most sense
+for a given problem I suppose to say
+
+ align:start position:0%
+for a given problem I suppose to say
+ 
+
+ align:start position:0%
+for a given problem I suppose to say
+choose one versus the other so Lucas
+
+ align:start position:0%
+choose one versus the other so Lucas
+ 
+
+ align:start position:0%
+choose one versus the other so Lucas
+hopefully uh tells us that Helga land
+
+ align:start position:0%
+hopefully uh tells us that Helga land
+ 
+
+ align:start position:0%
+hopefully uh tells us that Helga land
+was a site of one of the largest
+
+ align:start position:0%
+was a site of one of the largest
+ 
+
+ align:start position:0%
+was a site of one of the largest
+non-nuclear explosions ever I had no
+
+ align:start position:0%
+non-nuclear explosions ever I had no
+ 
+
+ align:start position:0%
+non-nuclear explosions ever I had no
+idea my goodness thank you I didn't know
+
+ align:start position:0%
+idea my goodness thank you I didn't know
+ 
+
+ align:start position:0%
+idea my goodness thank you I didn't know
+that thank you both to to Alex and Lucas
+
+ align:start position:0%
+that thank you both to to Alex and Lucas
+ 
+
+ align:start position:0%
+that thank you both to to Alex and Lucas
+I've never been to Helga land um I was
+
+ align:start position:0%
+I've never been to Helga land um I was
+ 
+
+ align:start position:0%
+I've never been to Helga land um I was
+hard to travel now to put it mildly that
+
+ align:start position:0%
+hard to travel now to put it mildly that
+ 
+
+ align:start position:0%
+hard to travel now to put it mildly that
+would be an awesome field trip though we
+
+ align:start position:0%
+would be an awesome field trip though we
+ 
+
+ align:start position:0%
+would be an awesome field trip though we
+should we should at least take a a
+
+ align:start position:0%
+should we should at least take a a
+ 
+
+ align:start position:0%
+should we should at least take a a
+virtual field trip we can look into that
+
+ align:start position:0%
+virtual field trip we can look into that
+ 
+
+ align:start position:0%
+virtual field trip we can look into that
+um good so my understanding is Helga
+
+ align:start position:0%
+um good so my understanding is Helga
+ 
+
+ align:start position:0%
+um good so my understanding is Helga
+land it has been contested territory
+
+ align:start position:0%
+land it has been contested territory
+ 
+
+ align:start position:0%
+land it has been contested territory
+again Wikipedia can tell us who it's a
+
+ align:start position:0%
+again Wikipedia can tell us who it's a
+ 
+
+ align:start position:0%
+again Wikipedia can tell us who it's a
+territory of what nation has been an
+
+ align:start position:0%
+territory of what nation has been an
+ 
+
+ align:start position:0%
+territory of what nation has been an
+unstable question Germany Denmark
+
+ align:start position:0%
+unstable question Germany Denmark
+ 
+
+ align:start position:0%
+unstable question Germany Denmark
+probably others it seems to sit in North
+
+ align:start position:0%
+probably others it seems to sit in North
+ 
+
+ align:start position:0%
+probably others it seems to sit in North
+Sea North Sea pretty close to to the
+
+ align:start position:0%
+Sea North Sea pretty close to to the
+ 
+
+ align:start position:0%
+Sea North Sea pretty close to to the
+coasts of both Germany and Denmark so I
+
+ align:start position:0%
+coasts of both Germany and Denmark so I
+ 
+
+ align:start position:0%
+coasts of both Germany and Denmark so I
+knew it's been kind of contestants and I
+
+ align:start position:0%
+knew it's been kind of contestants and I
+ 
+
+ align:start position:0%
+knew it's been kind of contestants and I
+thought it was also a lovely kind of
+
+ align:start position:0%
+thought it was also a lovely kind of
+ 
+
+ align:start position:0%
+thought it was also a lovely kind of
+vacation spot for much of the 19th
+
+ align:start position:0%
+vacation spot for much of the 19th
+ 
+
+ align:start position:0%
+vacation spot for much of the 19th
+century I didn't realize it was um uh
+
+ align:start position:0%
+century I didn't realize it was um uh
+ 
+
+ align:start position:0%
+century I didn't realize it was um uh
+subject to such a bombardment
+
+ align:start position:0%
+subject to such a bombardment
+ 
+
+ align:start position:0%
+subject to such a bombardment
+so that's a preview as you you may have
+
+ align:start position:0%
+so that's a preview as you you may have
+ 
+
+ align:start position:0%
+so that's a preview as you you may have
+guessed we're going to be coming to the
+
+ align:start position:0%
+guessed we're going to be coming to the
+ 
+
+ align:start position:0%
+guessed we're going to be coming to the
+second world war in this class pretty
+
+ align:start position:0%
+second world war in this class pretty
+ 
+
+ align:start position:0%
+second world war in this class pretty
+soon actually so we'll be getting to uh
+
+ align:start position:0%
+soon actually so we'll be getting to uh
+ 
+
+ align:start position:0%
+soon actually so we'll be getting to uh
+to similar kinds of themes actually
+
+ align:start position:0%
+to similar kinds of themes actually
+ 
+
+ align:start position:0%
+to similar kinds of themes actually
+within about two classes so so keep that
+
+ align:start position:0%
+within about two classes so so keep that
+ 
+
+ align:start position:0%
+within about two classes so so keep that
+theme in mind I guess
+
+ align:start position:0%
+theme in mind I guess
+ 
+
+ align:start position:0%
+theme in mind I guess
+any of the questions about Schrodinger
+
+ align:start position:0%
+any of the questions about Schrodinger
+ 
+
+ align:start position:0%
+any of the questions about Schrodinger
+the wave equation superposition
+
+ align:start position:0%
+the wave equation superposition
+ 
+
+ align:start position:0%
+the wave equation superposition
+discrete eigenvalue Spectra
+
+ align:start position:0%
+discrete eigenvalue Spectra
+ 
+
+ align:start position:0%
+discrete eigenvalue Spectra
+they're fun
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh if not then I think I'll I'll press
+
+ align:start position:0%
+uh if not then I think I'll I'll press
+ 
+
+ align:start position:0%
+uh if not then I think I'll I'll press
+on we can we can look at um the next
+
+ align:start position:0%
+on we can we can look at um the next
+ 
+
+ align:start position:0%
+on we can we can look at um the next
+part of class of course obviously please
+
+ align:start position:0%
+part of class of course obviously please
+ 
+
+ align:start position:0%
+part of class of course obviously please
+keep your questions coming if if more
+
+ align:start position:0%
+keep your questions coming if if more
+ 
+
+ align:start position:0%
+keep your questions coming if if more
+questions come up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's look now at the second part for
+
+ align:start position:0%
+so let's look now at the second part for
+ 
+
+ align:start position:0%
+so let's look now at the second part for
+today and again here I just reminder
+
+ align:start position:0%
+today and again here I just reminder
+ 
+
+ align:start position:0%
+today and again here I just reminder
+there is the the uh optional lecture
+
+ align:start position:0%
+there is the the uh optional lecture
+ 
+
+ align:start position:0%
+there is the the uh optional lecture
+notes that go into this a little bit
+
+ align:start position:0%
+notes that go into this a little bit
+ 
+
+ align:start position:0%
+notes that go into this a little bit
+more explicitly as well
+
+ align:start position:0%
+more explicitly as well
+ 
+
+ align:start position:0%
+more explicitly as well
+so let's talk about something called the
+
+ align:start position:0%
+so let's talk about something called the
+ 
+
+ align:start position:0%
+so let's talk about something called the
+double slit experiment which again might
+
+ align:start position:0%
+double slit experiment which again might
+ 
+
+ align:start position:0%
+double slit experiment which again might
+be something uh that at least some of
+
+ align:start position:0%
+be something uh that at least some of
+ 
+
+ align:start position:0%
+be something uh that at least some of
+you have heard about before some of you
+
+ align:start position:0%
+you have heard about before some of you
+ 
+
+ align:start position:0%
+you have heard about before some of you
+might have even been able to do a
+
+ align:start position:0%
+might have even been able to do a
+ 
+
+ align:start position:0%
+might have even been able to do a
+version in junior lab for that matter
+
+ align:start position:0%
+version in junior lab for that matter
+ 
+
+ align:start position:0%
+version in junior lab for that matter
+I'm not sure
+
+ align:start position:0%
+I'm not sure
+ 
+
+ align:start position:0%
+I'm not sure
+this is a just a remarkably fruitful
+
+ align:start position:0%
+this is a just a remarkably fruitful
+ 
+
+ align:start position:0%
+this is a just a remarkably fruitful
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+experiment it's sort of the pedagogical
+
+ align:start position:0%
+experiment it's sort of the pedagogical
+ 
+
+ align:start position:0%
+experiment it's sort of the pedagogical
+gift that keeps on giving and I don't
+
+ align:start position:0%
+gift that keeps on giving and I don't
+ 
+
+ align:start position:0%
+gift that keeps on giving and I don't
+it's not just me who think so look at
+
+ align:start position:0%
+it's not just me who think so look at
+ 
+
+ align:start position:0%
+it's not just me who think so look at
+this remarkable series of uh of people
+
+ align:start position:0%
+this remarkable series of uh of people
+ 
+
+ align:start position:0%
+this remarkable series of uh of people
+who have come back time and time again
+
+ align:start position:0%
+who have come back time and time again
+ 
+
+ align:start position:0%
+who have come back time and time again
+to the double slit so Heisenberg's
+
+ align:start position:0%
+to the double slit so Heisenberg's
+ 
+
+ align:start position:0%
+to the double slit so Heisenberg's
+lectured on it as early as 1929 perhaps
+
+ align:start position:0%
+lectured on it as early as 1929 perhaps
+ 
+
+ align:start position:0%
+lectured on it as early as 1929 perhaps
+earlier but that's the first case we
+
+ align:start position:0%
+earlier but that's the first case we
+ 
+
+ align:start position:0%
+earlier but that's the first case we
+know about schroding was lecturing on
+
+ align:start position:0%
+know about schroding was lecturing on
+ 
+
+ align:start position:0%
+know about schroding was lecturing on
+this as early as 1936 and maybe earlier
+
+ align:start position:0%
+this as early as 1936 and maybe earlier
+ 
+
+ align:start position:0%
+this as early as 1936 and maybe earlier
+but we have summer school lecture notes
+
+ align:start position:0%
+but we have summer school lecture notes
+ 
+
+ align:start position:0%
+but we have summer school lecture notes
+from as early as 1936 where Schrodinger
+
+ align:start position:0%
+from as early as 1936 where Schrodinger
+ 
+
+ align:start position:0%
+from as early as 1936 where Schrodinger
+featured it as well
+
+ align:start position:0%
+featured it as well
+ 
+
+ align:start position:0%
+featured it as well
+Niels Bohr featured this very famously
+
+ align:start position:0%
+Niels Bohr featured this very famously
+ 
+
+ align:start position:0%
+Niels Bohr featured this very famously
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+very well-known uh discussion of his
+
+ align:start position:0%
+very well-known uh discussion of his
+ 
+
+ align:start position:0%
+very well-known uh discussion of his
+long debate with Albert Einstein over a
+
+ align:start position:0%
+long debate with Albert Einstein over a
+ 
+
+ align:start position:0%
+long debate with Albert Einstein over a
+quantum theory that was another one of
+
+ align:start position:0%
+quantum theory that was another one of
+ 
+
+ align:start position:0%
+quantum theory that was another one of
+the readings for today was an excerpt a
+
+ align:start position:0%
+the readings for today was an excerpt a
+ 
+
+ align:start position:0%
+the readings for today was an excerpt a
+kind of shortened version of boys very
+
+ align:start position:0%
+kind of shortened version of boys very
+ 
+
+ align:start position:0%
+kind of shortened version of boys very
+famous characterization of his long
+
+ align:start position:0%
+famous characterization of his long
+ 
+
+ align:start position:0%
+famous characterization of his long
+debate with Einstein coming closer to
+
+ align:start position:0%
+debate with Einstein coming closer to
+ 
+
+ align:start position:0%
+debate with Einstein coming closer to
+our own time uh uh in the 1960s Richard
+
+ align:start position:0%
+our own time uh uh in the 1960s Richard
+ 
+
+ align:start position:0%
+our own time uh uh in the 1960s Richard
+Feynman declared that this the double
+
+ align:start position:0%
+Feynman declared that this the double
+ 
+
+ align:start position:0%
+Feynman declared that this the double
+slit has in it the very heart of quantum
+
+ align:start position:0%
+slit has in it the very heart of quantum
+ 
+
+ align:start position:0%
+slit has in it the very heart of quantum
+mechanics he said this is basically all
+
+ align:start position:0%
+mechanics he said this is basically all
+ 
+
+ align:start position:0%
+mechanics he said this is basically all
+you need to know practically about
+
+ align:start position:0%
+you need to know practically about
+ 
+
+ align:start position:0%
+you need to know practically about
+Quantum Theory and even really much more
+
+ align:start position:0%
+Quantum Theory and even really much more
+ 
+
+ align:start position:0%
+Quantum Theory and even really much more
+recently readers of physics World
+
+ align:start position:0%
+recently readers of physics World
+ 
+
+ align:start position:0%
+recently readers of physics World
+magazine which as you may know is the
+
+ align:start position:0%
+magazine which as you may know is the
+ 
+
+ align:start position:0%
+magazine which as you may know is the
+kind of physics today of the of the UK
+
+ align:start position:0%
+kind of physics today of the of the UK
+ 
+
+ align:start position:0%
+kind of physics today of the of the UK
+physics Society they voted this double
+
+ align:start position:0%
+physics Society they voted this double
+ 
+
+ align:start position:0%
+physics Society they voted this double
+slit experiment the single most
+
+ align:start position:0%
+slit experiment the single most
+ 
+
+ align:start position:0%
+slit experiment the single most
+beautiful experiment in the history of
+
+ align:start position:0%
+beautiful experiment in the history of
+ 
+
+ align:start position:0%
+beautiful experiment in the history of
+all of physics not the history of 20th
+
+ align:start position:0%
+all of physics not the history of 20th
+ 
+
+ align:start position:0%
+all of physics not the history of 20th
+century physics since the Earth cooled
+
+ align:start position:0%
+century physics since the Earth cooled
+ 
+
+ align:start position:0%
+century physics since the Earth cooled
+and humans have done experiments to
+
+ align:start position:0%
+and humans have done experiments to
+ 
+
+ align:start position:0%
+and humans have done experiments to
+learn about nature
+
+ align:start position:0%
+learn about nature
+ 
+
+ align:start position:0%
+learn about nature
+readers of physics World magazine
+
+ align:start position:0%
+readers of physics World magazine
+ 
+
+ align:start position:0%
+readers of physics World magazine
+concluded the single most beautiful
+
+ align:start position:0%
+concluded the single most beautiful
+ 
+
+ align:start position:0%
+concluded the single most beautiful
+effort of any kind ever was a double
+
+ align:start position:0%
+effort of any kind ever was a double
+ 
+
+ align:start position:0%
+effort of any kind ever was a double
+slit experiment so let's spend at least
+
+ align:start position:0%
+slit experiment so let's spend at least
+ 
+
+ align:start position:0%
+slit experiment so let's spend at least
+a few minutes giving giving proper uh
+
+ align:start position:0%
+a few minutes giving giving proper uh
+ 
+
+ align:start position:0%
+a few minutes giving giving proper uh
+well-deserved attention to a doubles
+
+ align:start position:0%
+well-deserved attention to a doubles
+ 
+
+ align:start position:0%
+well-deserved attention to a doubles
+thing so here's my very bad cartoon
+
+ align:start position:0%
+thing so here's my very bad cartoon
+ 
+
+ align:start position:0%
+thing so here's my very bad cartoon
+version of a double slit I'm going to
+
+ align:start position:0%
+version of a double slit I'm going to
+ 
+
+ align:start position:0%
+version of a double slit I'm going to
+really follow what Richard feynman's
+
+ align:start position:0%
+really follow what Richard feynman's
+ 
+
+ align:start position:0%
+really follow what Richard feynman's
+approach in what became in the kind of
+
+ align:start position:0%
+approach in what became in the kind of
+ 
+
+ align:start position:0%
+approach in what became in the kind of
+canonical way of of introducing the
+
+ align:start position:0%
+canonical way of of introducing the
+ 
+
+ align:start position:0%
+canonical way of of introducing the
+devil so that I've really lifted much of
+
+ align:start position:0%
+devil so that I've really lifted much of
+ 
+
+ align:start position:0%
+devil so that I've really lifted much of
+this from from finding this very famous
+
+ align:start position:0%
+this from from finding this very famous
+ 
+
+ align:start position:0%
+this from from finding this very famous
+version of this in the final lectures
+
+ align:start position:0%
+version of this in the final lectures
+ 
+
+ align:start position:0%
+version of this in the final lectures
+from the early 60s
+
+ align:start position:0%
+from the early 60s
+ 
+
+ align:start position:0%
+from the early 60s
+uh he would have had better pictures but
+
+ align:start position:0%
+uh he would have had better pictures but
+ 
+
+ align:start position:0%
+uh he would have had better pictures but
+the idea is a piece of it so let's
+
+ align:start position:0%
+the idea is a piece of it so let's
+ 
+
+ align:start position:0%
+the idea is a piece of it so let's
+imagine first the behavior of classical
+
+ align:start position:0%
+imagine first the behavior of classical
+ 
+
+ align:start position:0%
+imagine first the behavior of classical
+particles these could be baseballs or
+
+ align:start position:0%
+particles these could be baseballs or
+ 
+
+ align:start position:0%
+particles these could be baseballs or
+basketballs or or bullets fired from a
+
+ align:start position:0%
+basketballs or or bullets fired from a
+ 
+
+ align:start position:0%
+basketballs or or bullets fired from a
+gun or any kind of traject uh
+
+ align:start position:0%
+gun or any kind of traject uh
+ 
+
+ align:start position:0%
+gun or any kind of traject uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+projectile
+
+ align:start position:0%
+projectile
+ 
+
+ align:start position:0%
+projectile
+so let's imagine we're firing bullets
+
+ align:start position:0%
+so let's imagine we're firing bullets
+ 
+
+ align:start position:0%
+so let's imagine we're firing bullets
+one at a time toward a bulletproof wall
+
+ align:start position:0%
+one at a time toward a bulletproof wall
+ 
+
+ align:start position:0%
+one at a time toward a bulletproof wall
+so this wall here this thick wall is
+
+ align:start position:0%
+so this wall here this thick wall is
+ 
+
+ align:start position:0%
+so this wall here this thick wall is
+meant to be bulletproof sorry and yet
+
+ align:start position:0%
+meant to be bulletproof sorry and yet
+ 
+
+ align:start position:0%
+meant to be bulletproof sorry and yet
+there are two narrow slits in the wall
+
+ align:start position:0%
+there are two narrow slits in the wall
+ 
+
+ align:start position:0%
+there are two narrow slits in the wall
+we'll just label those slits this space
+
+ align:start position:0%
+we'll just label those slits this space
+ 
+
+ align:start position:0%
+we'll just label those slits this space
+here so that a the slit B the slits are
+
+ align:start position:0%
+here so that a the slit B the slits are
+ 
+
+ align:start position:0%
+here so that a the slit B the slits are
+a distance D apart
+
+ align:start position:0%
+a distance D apart
+ 
+
+ align:start position:0%
+a distance D apart
+and then we have some backstop here
+
+ align:start position:0%
+and then we have some backstop here
+ 
+
+ align:start position:0%
+and then we have some backstop here
+where the bullets will kind of Lodge and
+
+ align:start position:0%
+where the bullets will kind of Lodge and
+ 
+
+ align:start position:0%
+where the bullets will kind of Lodge and
+then when it's safe to uh and the guns
+
+ align:start position:0%
+then when it's safe to uh and the guns
+ 
+
+ align:start position:0%
+then when it's safe to uh and the guns
+put away we can go out and count up the
+
+ align:start position:0%
+put away we can go out and count up the
+ 
+
+ align:start position:0%
+put away we can go out and count up the
+number of bullets that landed here
+
+ align:start position:0%
+number of bullets that landed here
+ 
+
+ align:start position:0%
+number of bullets that landed here
+versus here versus here so we're going
+
+ align:start position:0%
+versus here versus here so we're going
+ 
+
+ align:start position:0%
+versus here versus here so we're going
+to ultimately try to add up we're going
+
+ align:start position:0%
+to ultimately try to add up we're going
+ 
+
+ align:start position:0%
+to ultimately try to add up we're going
+to make a kind of histogram and plot the
+
+ align:start position:0%
+to make a kind of histogram and plot the
+ 
+
+ align:start position:0%
+to make a kind of histogram and plot the
+number of bullets per location as we
+
+ align:start position:0%
+number of bullets per location as we
+ 
+
+ align:start position:0%
+number of bullets per location as we
+March up in this direction of the
+
+ align:start position:0%
+March up in this direction of the
+ 
+
+ align:start position:0%
+March up in this direction of the
+backstop so we want to then figure out
+
+ align:start position:0%
+backstop so we want to then figure out
+ 
+
+ align:start position:0%
+backstop so we want to then figure out
+in a sense the probability distribution
+
+ align:start position:0%
+in a sense the probability distribution
+ 
+
+ align:start position:0%
+in a sense the probability distribution
+where our bullets most likely to wind up
+
+ align:start position:0%
+where our bullets most likely to wind up
+ 
+
+ align:start position:0%
+where our bullets most likely to wind up
+on this backdrop when either uh one slot
+
+ align:start position:0%
+on this backdrop when either uh one slot
+ 
+
+ align:start position:0%
+on this backdrop when either uh one slot
+is open the other slot is open or both
+
+ align:start position:0%
+is open the other slot is open or both
+ 
+
+ align:start position:0%
+is open the other slot is open or both
+are open that's our exercise here with
+
+ align:start position:0%
+are open that's our exercise here with
+ 
+
+ align:start position:0%
+are open that's our exercise here with
+classical objects like um baseballs or
+
+ align:start position:0%
+classical objects like um baseballs or
+ 
+
+ align:start position:0%
+classical objects like um baseballs or
+in this case bullets fire from a gun
+
+ align:start position:0%
+in this case bullets fire from a gun
+ 
+
+ align:start position:0%
+in this case bullets fire from a gun
+so let's first imagine that slit a is
+
+ align:start position:0%
+so let's first imagine that slit a is
+ 
+
+ align:start position:0%
+so let's first imagine that slit a is
+open but slit B is closed with some firm
+
+ align:start position:0%
+open but slit B is closed with some firm
+ 
+
+ align:start position:0%
+open but slit B is closed with some firm
+bulletproof you know kind of shielding
+
+ align:start position:0%
+bulletproof you know kind of shielding
+ 
+
+ align:start position:0%
+bulletproof you know kind of shielding
+so then our number of bullets will look
+
+ align:start position:0%
+so then our number of bullets will look
+ 
+
+ align:start position:0%
+so then our number of bullets will look
+like this it's been smoothed out uh
+
+ align:start position:0%
+like this it's been smoothed out uh
+ 
+
+ align:start position:0%
+like this it's been smoothed out uh
+let's say if we shot 10 000 bullets then
+
+ align:start position:0%
+let's say if we shot 10 000 bullets then
+ 
+
+ align:start position:0%
+let's say if we shot 10 000 bullets then
+it would actually be a pretty smooth
+
+ align:start position:0%
+it would actually be a pretty smooth
+ 
+
+ align:start position:0%
+it would actually be a pretty smooth
+curve it would be basically a gaussian
+
+ align:start position:0%
+curve it would be basically a gaussian
+ 
+
+ align:start position:0%
+curve it would be basically a gaussian
+it would look like a kind of um
+
+ align:start position:0%
+it would look like a kind of um
+ 
+
+ align:start position:0%
+it would look like a kind of um
+bell-shaped curve centered around the
+
+ align:start position:0%
+bell-shaped curve centered around the
+ 
+
+ align:start position:0%
+bell-shaped curve centered around the
+open slit most bullets would be found
+
+ align:start position:0%
+open slit most bullets would be found
+ 
+
+ align:start position:0%
+open slit most bullets would be found
+directly behind the open slit but
+
+ align:start position:0%
+directly behind the open slit but
+ 
+
+ align:start position:0%
+directly behind the open slit but
+there'll be some some modest scatter
+
+ align:start position:0%
+there'll be some some modest scatter
+ 
+
+ align:start position:0%
+there'll be some some modest scatter
+some width to the distribution so to
+
+ align:start position:0%
+some width to the distribution so to
+ 
+
+ align:start position:0%
+some width to the distribution so to
+speak
+
+ align:start position:0%
+speak
+ 
+
+ align:start position:0%
+speak
+likewise if we then sealed up slit a
+
+ align:start position:0%
+likewise if we then sealed up slit a
+ 
+
+ align:start position:0%
+likewise if we then sealed up slit a
+with some bulletproof shielding and open
+
+ align:start position:0%
+with some bulletproof shielding and open
+ 
+
+ align:start position:0%
+with some bulletproof shielding and open
+to only slip B and performed and shot
+
+ align:start position:0%
+to only slip B and performed and shot
+ 
+
+ align:start position:0%
+to only slip B and performed and shot
+another 10 000 bullets at it one at a
+
+ align:start position:0%
+another 10 000 bullets at it one at a
+ 
+
+ align:start position:0%
+another 10 000 bullets at it one at a
+time and then did the same counting
+
+ align:start position:0%
+time and then did the same counting
+ 
+
+ align:start position:0%
+time and then did the same counting
+exercise we could make a separate
+
+ align:start position:0%
+exercise we could make a separate
+ 
+
+ align:start position:0%
+exercise we could make a separate
+histogram it looks remarkably similar
+
+ align:start position:0%
+histogram it looks remarkably similar
+ 
+
+ align:start position:0%
+histogram it looks remarkably similar
+not surprising it's such a symmetrical
+
+ align:start position:0%
+not surprising it's such a symmetrical
+ 
+
+ align:start position:0%
+not surprising it's such a symmetrical
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+so if only slit B is open then the vast
+
+ align:start position:0%
+so if only slit B is open then the vast
+ 
+
+ align:start position:0%
+so if only slit B is open then the vast
+majority of bullets are found directly
+
+ align:start position:0%
+majority of bullets are found directly
+ 
+
+ align:start position:0%
+majority of bullets are found directly
+behind that open slit and there'll be
+
+ align:start position:0%
+behind that open slit and there'll be
+ 
+
+ align:start position:0%
+behind that open slit and there'll be
+some kind of bell-shaped curve it
+
+ align:start position:0%
+some kind of bell-shaped curve it
+ 
+
+ align:start position:0%
+some kind of bell-shaped curve it
+basically kind of gaussian distribution
+
+ align:start position:0%
+basically kind of gaussian distribution
+ 
+
+ align:start position:0%
+basically kind of gaussian distribution
+on either side there'll be some modest
+
+ align:start position:0%
+on either side there'll be some modest
+ 
+
+ align:start position:0%
+on either side there'll be some modest
+scatter and then if we then open both
+
+ align:start position:0%
+scatter and then if we then open both
+ 
+
+ align:start position:0%
+scatter and then if we then open both
+slits fire another ten thousand bullets
+
+ align:start position:0%
+slits fire another ten thousand bullets
+ 
+
+ align:start position:0%
+slits fire another ten thousand bullets
+at the at the bulletproof wall with both
+
+ align:start position:0%
+at the at the bulletproof wall with both
+ 
+
+ align:start position:0%
+at the at the bulletproof wall with both
+slits A and B open do the same exercise
+
+ align:start position:0%
+slits A and B open do the same exercise
+ 
+
+ align:start position:0%
+slits A and B open do the same exercise
+and make our histogram the resulting
+
+ align:start position:0%
+and make our histogram the resulting
+ 
+
+ align:start position:0%
+and make our histogram the resulting
+distribution is just the sum of the
+
+ align:start position:0%
+distribution is just the sum of the
+ 
+
+ align:start position:0%
+distribution is just the sum of the
+previous two so now there are a fair
+
+ align:start position:0%
+previous two so now there are a fair
+ 
+
+ align:start position:0%
+previous two so now there are a fair
+number of bullets that wind up in the
+
+ align:start position:0%
+number of bullets that wind up in the
+ 
+
+ align:start position:0%
+number of bullets that wind up in the
+middle because some are coming from the
+
+ align:start position:0%
+middle because some are coming from the
+ 
+
+ align:start position:0%
+middle because some are coming from the
+tail of this distribution some are
+
+ align:start position:0%
+tail of this distribution some are
+ 
+
+ align:start position:0%
+tail of this distribution some are
+coming from the tail of this
+
+ align:start position:0%
+coming from the tail of this
+ 
+
+ align:start position:0%
+coming from the tail of this
+distribution and so some of them wind up
+
+ align:start position:0%
+distribution and so some of them wind up
+ 
+
+ align:start position:0%
+distribution and so some of them wind up
+in the middle
+
+ align:start position:0%
+in the middle
+ 
+
+ align:start position:0%
+in the middle
+it's the sum of those two but
+
+ align:start position:0%
+it's the sum of those two but
+ 
+
+ align:start position:0%
+it's the sum of those two but
+nonetheless the distribution is clearly
+
+ align:start position:0%
+nonetheless the distribution is clearly
+ 
+
+ align:start position:0%
+nonetheless the distribution is clearly
+still peaked in the positions directly
+
+ align:start position:0%
+still peaked in the positions directly
+ 
+
+ align:start position:0%
+still peaked in the positions directly
+behind the two open slits so we have the
+
+ align:start position:0%
+behind the two open slits so we have the
+ 
+
+ align:start position:0%
+behind the two open slits so we have the
+resulting probability distribution the
+
+ align:start position:0%
+resulting probability distribution the
+ 
+
+ align:start position:0%
+resulting probability distribution the
+histogram when we add up when both sits
+
+ align:start position:0%
+histogram when we add up when both sits
+ 
+
+ align:start position:0%
+histogram when we add up when both sits
+are open really is just the sum of those
+
+ align:start position:0%
+are open really is just the sum of those
+ 
+
+ align:start position:0%
+are open really is just the sum of those
+two separate ones and so for classical
+
+ align:start position:0%
+two separate ones and so for classical
+ 
+
+ align:start position:0%
+two separate ones and so for classical
+particles these probability
+
+ align:start position:0%
+particles these probability
+ 
+
+ align:start position:0%
+particles these probability
+distributions are of independent events
+
+ align:start position:0%
+distributions are of independent events
+ 
+
+ align:start position:0%
+distributions are of independent events
+and therefore the probabilities in this
+
+ align:start position:0%
+and therefore the probabilities in this
+ 
+
+ align:start position:0%
+and therefore the probabilities in this
+case simply add we can get the
+
+ align:start position:0%
+case simply add we can get the
+ 
+
+ align:start position:0%
+case simply add we can get the
+probability distribution for the for the
+
+ align:start position:0%
+probability distribution for the for the
+ 
+
+ align:start position:0%
+probability distribution for the for the
+combined Series so let's A and B open
+
+ align:start position:0%
+combined Series so let's A and B open
+ 
+
+ align:start position:0%
+combined Series so let's A and B open
+simply by adding two independent
+
+ align:start position:0%
+simply by adding two independent
+ 
+
+ align:start position:0%
+simply by adding two independent
+possibilities each bullet either went
+
+ align:start position:0%
+possibilities each bullet either went
+ 
+
+ align:start position:0%
+possibilities each bullet either went
+through slit a in which case it followed
+
+ align:start position:0%
+through slit a in which case it followed
+ 
+
+ align:start position:0%
+through slit a in which case it followed
+this distribution or each bullet or an
+
+ align:start position:0%
+this distribution or each bullet or an
+ 
+
+ align:start position:0%
+this distribution or each bullet or an
+individual bullets went through slit B
+
+ align:start position:0%
+individual bullets went through slit B
+ 
+
+ align:start position:0%
+individual bullets went through slit B
+add up those two options here's our
+
+ align:start position:0%
+add up those two options here's our
+ 
+
+ align:start position:0%
+add up those two options here's our
+resulting distribution not too
+
+ align:start position:0%
+resulting distribution not too
+ 
+
+ align:start position:0%
+resulting distribution not too
+surprising
+
+ align:start position:0%
+surprising
+ 
+
+ align:start position:0%
+surprising
+now let's try a second version with
+
+ align:start position:0%
+now let's try a second version with
+ 
+
+ align:start position:0%
+now let's try a second version with
+waves and this could be macroscopic
+
+ align:start position:0%
+waves and this could be macroscopic
+ 
+
+ align:start position:0%
+waves and this could be macroscopic
+waves for example ocean waves I in my
+
+ align:start position:0%
+waves for example ocean waves I in my
+ 
+
+ align:start position:0%
+waves for example ocean waves I in my
+little write-up I talk about you know
+
+ align:start position:0%
+little write-up I talk about you know
+ 
+
+ align:start position:0%
+little write-up I talk about you know
+doing this near the coast of Australia
+
+ align:start position:0%
+doing this near the coast of Australia
+ 
+
+ align:start position:0%
+doing this near the coast of Australia
+with waves approaching the Great Barrier
+
+ align:start position:0%
+with waves approaching the Great Barrier
+ 
+
+ align:start position:0%
+with waves approaching the Great Barrier
+Reef but it could be even in an
+
+ align:start position:0%
+Reef but it could be even in an
+ 
+
+ align:start position:0%
+Reef but it could be even in an
+artificial wave pool with with some
+
+ align:start position:0%
+artificial wave pool with with some
+ 
+
+ align:start position:0%
+artificial wave pool with with some
+barrier
+
+ align:start position:0%
+barrier
+ 
+
+ align:start position:0%
+barrier
+so now we have some some Reef or some
+
+ align:start position:0%
+so now we have some some Reef or some
+ 
+
+ align:start position:0%
+so now we have some some Reef or some
+some uh structure that can block waves
+
+ align:start position:0%
+some uh structure that can block waves
+ 
+
+ align:start position:0%
+some uh structure that can block waves
+that are coming from further away
+
+ align:start position:0%
+that are coming from further away
+ 
+
+ align:start position:0%
+that are coming from further away
+they're approaching here's the shore and
+
+ align:start position:0%
+they're approaching here's the shore and
+ 
+
+ align:start position:0%
+they're approaching here's the shore and
+we have some barrier that will block
+
+ align:start position:0%
+we have some barrier that will block
+ 
+
+ align:start position:0%
+we have some barrier that will block
+waves from passing through here but the
+
+ align:start position:0%
+waves from passing through here but the
+ 
+
+ align:start position:0%
+waves from passing through here but the
+barrier has these two narrow slits which
+
+ align:start position:0%
+barrier has these two narrow slits which
+ 
+
+ align:start position:0%
+barrier has these two narrow slits which
+again we can label A and B and there is
+
+ align:start position:0%
+again we can label A and B and there is
+ 
+
+ align:start position:0%
+again we can label A and B and there is
+distance D apart so now what we want to
+
+ align:start position:0%
+distance D apart so now what we want to
+ 
+
+ align:start position:0%
+distance D apart so now what we want to
+do is measure the the the intensity of
+
+ align:start position:0%
+do is measure the the the intensity of
+ 
+
+ align:start position:0%
+do is measure the the the intensity of
+the Waves uh that lap up on shore
+
+ align:start position:0%
+the Waves uh that lap up on shore
+ 
+
+ align:start position:0%
+the Waves uh that lap up on shore
+clearly some water gets through slits A
+
+ align:start position:0%
+clearly some water gets through slits A
+ 
+
+ align:start position:0%
+clearly some water gets through slits A
+and B so what's the pattern of waves
+
+ align:start position:0%
+and B so what's the pattern of waves
+ 
+
+ align:start position:0%
+and B so what's the pattern of waves
+that we find on the shoreline and how
+
+ align:start position:0%
+that we find on the shoreline and how
+ 
+
+ align:start position:0%
+that we find on the shoreline and how
+does the intensity of that wave vary as
+
+ align:start position:0%
+does the intensity of that wave vary as
+ 
+
+ align:start position:0%
+does the intensity of that wave vary as
+we measure uh as we March along in
+
+ align:start position:0%
+we measure uh as we March along in
+ 
+
+ align:start position:0%
+we measure uh as we March along in
+location and again we'll project the the
+
+ align:start position:0%
+location and again we'll project the the
+ 
+
+ align:start position:0%
+location and again we'll project the the
+positions of slits uh A and B on the
+
+ align:start position:0%
+positions of slits uh A and B on the
+ 
+
+ align:start position:0%
+positions of slits uh A and B on the
+shore and that's about the varying
+
+ align:start position:0%
+shore and that's about the varying
+ 
+
+ align:start position:0%
+shore and that's about the varying
+intensity of the resulting wave as a
+
+ align:start position:0%
+intensity of the resulting wave as a
+ 
+
+ align:start position:0%
+intensity of the resulting wave as a
+function of distance or location
+
+ align:start position:0%
+function of distance or location
+ 
+
+ align:start position:0%
+function of distance or location
+so once again let's start with only one
+
+ align:start position:0%
+so once again let's start with only one
+ 
+
+ align:start position:0%
+so once again let's start with only one
+of those slits open so we're going to
+
+ align:start position:0%
+of those slits open so we're going to
+ 
+
+ align:start position:0%
+of those slits open so we're going to
+close slit B with some kind of dam we're
+
+ align:start position:0%
+close slit B with some kind of dam we're
+ 
+
+ align:start position:0%
+close slit B with some kind of dam we're
+going to block one of those slits so
+
+ align:start position:0%
+going to block one of those slits so
+ 
+
+ align:start position:0%
+going to block one of those slits so
+water can only get through that one uh
+
+ align:start position:0%
+water can only get through that one uh
+ 
+
+ align:start position:0%
+water can only get through that one uh
+narrow slit a and therefore we'll have a
+
+ align:start position:0%
+narrow slit a and therefore we'll have a
+ 
+
+ align:start position:0%
+narrow slit a and therefore we'll have a
+clearly peaked distribution the wave
+
+ align:start position:0%
+clearly peaked distribution the wave
+ 
+
+ align:start position:0%
+clearly peaked distribution the wave
+that results that we find unsure is
+
+ align:start position:0%
+that results that we find unsure is
+ 
+
+ align:start position:0%
+that results that we find unsure is
+virtually uh zero far away from that
+
+ align:start position:0%
+virtually uh zero far away from that
+ 
+
+ align:start position:0%
+virtually uh zero far away from that
+sort of location of slit a the
+
+ align:start position:0%
+sort of location of slit a the
+ 
+
+ align:start position:0%
+sort of location of slit a the
+projection onto the shore of the open
+
+ align:start position:0%
+projection onto the shore of the open
+ 
+
+ align:start position:0%
+projection onto the shore of the open
+slit It's very clearly peaked right
+
+ align:start position:0%
+slit It's very clearly peaked right
+ 
+
+ align:start position:0%
+slit It's very clearly peaked right
+directly behind the open slit we in fact
+
+ align:start position:0%
+directly behind the open slit we in fact
+ 
+
+ align:start position:0%
+directly behind the open slit we in fact
+we can characterize the intensity of the
+
+ align:start position:0%
+we can characterize the intensity of the
+ 
+
+ align:start position:0%
+we can characterize the intensity of the
+wave as the square of some amplitude
+
+ align:start position:0%
+wave as the square of some amplitude
+ 
+
+ align:start position:0%
+wave as the square of some amplitude
+it's a wave it has some amplitude and
+
+ align:start position:0%
+it's a wave it has some amplitude and
+ 
+
+ align:start position:0%
+it's a wave it has some amplitude and
+some phase and the amp and the intensity
+
+ align:start position:0%
+some phase and the amp and the intensity
+ 
+
+ align:start position:0%
+some phase and the amp and the intensity
+goes clearly as the square of this of
+
+ align:start position:0%
+goes clearly as the square of this of
+ 
+
+ align:start position:0%
+goes clearly as the square of this of
+this height or this of this amplitude
+
+ align:start position:0%
+this height or this of this amplitude
+ 
+
+ align:start position:0%
+this height or this of this amplitude
+and it's basically is very clearly
+
+ align:start position:0%
+and it's basically is very clearly
+ 
+
+ align:start position:0%
+and it's basically is very clearly
+dramatically peaked behind the open slit
+
+ align:start position:0%
+dramatically peaked behind the open slit
+ 
+
+ align:start position:0%
+dramatically peaked behind the open slit
+now we sort of place the dam in front of
+
+ align:start position:0%
+now we sort of place the dam in front of
+ 
+
+ align:start position:0%
+now we sort of place the dam in front of
+slit a open slit B same kind of story
+
+ align:start position:0%
+slit a open slit B same kind of story
+ 
+
+ align:start position:0%
+slit a open slit B same kind of story
+but as many of you probably know once we
+
+ align:start position:0%
+but as many of you probably know once we
+ 
+
+ align:start position:0%
+but as many of you probably know once we
+open both slits A and B we get a totally
+
+ align:start position:0%
+open both slits A and B we get a totally
+ 
+
+ align:start position:0%
+open both slits A and B we get a totally
+different story now we get one of these
+
+ align:start position:0%
+different story now we get one of these
+ 
+
+ align:start position:0%
+different story now we get one of these
+kind of characteristic interference
+
+ align:start position:0%
+kind of characteristic interference
+ 
+
+ align:start position:0%
+kind of characteristic interference
+patterns on the shore not merely the sum
+
+ align:start position:0%
+patterns on the shore not merely the sum
+ 
+
+ align:start position:0%
+patterns on the shore not merely the sum
+of these two distributions together and
+
+ align:start position:0%
+of these two distributions together and
+ 
+
+ align:start position:0%
+of these two distributions together and
+if we do a little more work we can
+
+ align:start position:0%
+if we do a little more work we can
+ 
+
+ align:start position:0%
+if we do a little more work we can
+realize we can still characterize the
+
+ align:start position:0%
+realize we can still characterize the
+ 
+
+ align:start position:0%
+realize we can still characterize the
+resulting intensity by summing something
+
+ align:start position:0%
+resulting intensity by summing something
+ 
+
+ align:start position:0%
+resulting intensity by summing something
+together not by summing the two
+
+ align:start position:0%
+together not by summing the two
+ 
+
+ align:start position:0%
+together not by summing the two
+intensities actually by summing the two
+
+ align:start position:0%
+intensities actually by summing the two
+ 
+
+ align:start position:0%
+intensities actually by summing the two
+amplitudes first and then squaring that
+
+ align:start position:0%
+amplitudes first and then squaring that
+ 
+
+ align:start position:0%
+amplitudes first and then squaring that
+and that's what allows for these
+
+ align:start position:0%
+and that's what allows for these
+ 
+
+ align:start position:0%
+and that's what allows for these
+interference patterns much like we saw
+
+ align:start position:0%
+interference patterns much like we saw
+ 
+
+ align:start position:0%
+interference patterns much like we saw
+with the standing waves earlier in
+
+ align:start position:0%
+with the standing waves earlier in
+ 
+
+ align:start position:0%
+with the standing waves earlier in
+regions where uh two crests happen to
+
+ align:start position:0%
+regions where uh two crests happen to
+ 
+
+ align:start position:0%
+regions where uh two crests happen to
+align we'll get a sharp constructive
+
+ align:start position:0%
+align we'll get a sharp constructive
+ 
+
+ align:start position:0%
+align we'll get a sharp constructive
+interference a heightened peak in
+
+ align:start position:0%
+interference a heightened peak in
+ 
+
+ align:start position:0%
+interference a heightened peak in
+regions where there might have been one
+
+ align:start position:0%
+regions where there might have been one
+ 
+
+ align:start position:0%
+regions where there might have been one
+large Peak but a very small uh um trough
+
+ align:start position:0%
+large Peak but a very small uh um trough
+ 
+
+ align:start position:0%
+large Peak but a very small uh um trough
+on the other side will get a destructive
+
+ align:start position:0%
+on the other side will get a destructive
+ 
+
+ align:start position:0%
+on the other side will get a destructive
+interference so in fact when we when we
+
+ align:start position:0%
+interference so in fact when we when we
+ 
+
+ align:start position:0%
+interference so in fact when we when we
+add the amplitudes and then Square the
+
+ align:start position:0%
+add the amplitudes and then Square the
+ 
+
+ align:start position:0%
+add the amplitudes and then Square the
+resulting intensity looks nothing like
+
+ align:start position:0%
+resulting intensity looks nothing like
+ 
+
+ align:start position:0%
+resulting intensity looks nothing like
+the sum of the two intensities because
+
+ align:start position:0%
+the sum of the two intensities because
+ 
+
+ align:start position:0%
+the sum of the two intensities because
+that would Overlook that would discount
+
+ align:start position:0%
+that would Overlook that would discount
+ 
+
+ align:start position:0%
+that would Overlook that would discount
+all these uh ways that the waves can
+
+ align:start position:0%
+all these uh ways that the waves can
+ 
+
+ align:start position:0%
+all these uh ways that the waves can
+actually interfere with each other and
+
+ align:start position:0%
+actually interfere with each other and
+ 
+
+ align:start position:0%
+actually interfere with each other and
+one indication of that
+
+ align:start position:0%
+one indication of that
+ 
+
+ align:start position:0%
+one indication of that
+is this characteristic feature of the
+
+ align:start position:0%
+is this characteristic feature of the
+ 
+
+ align:start position:0%
+is this characteristic feature of the
+interference pattern the point on the
+
+ align:start position:0%
+interference pattern the point on the
+ 
+
+ align:start position:0%
+interference pattern the point on the
+shore with the largest intensity is a
+
+ align:start position:0%
+shore with the largest intensity is a
+ 
+
+ align:start position:0%
+shore with the largest intensity is a
+point between either two slits whereas
+
+ align:start position:0%
+point between either two slits whereas
+ 
+
+ align:start position:0%
+point between either two slits whereas
+when either is open alone that's the
+
+ align:start position:0%
+when either is open alone that's the
+ 
+
+ align:start position:0%
+when either is open alone that's the
+point of actually virtually Vanishing
+
+ align:start position:0%
+point of actually virtually Vanishing
+ 
+
+ align:start position:0%
+point of actually virtually Vanishing
+intensity so the greatest intensity is
+
+ align:start position:0%
+intensity so the greatest intensity is
+ 
+
+ align:start position:0%
+intensity so the greatest intensity is
+at a spot where neither a scenario on
+
+ align:start position:0%
+at a spot where neither a scenario on
+ 
+
+ align:start position:0%
+at a spot where neither a scenario on
+its own had much power at all and so
+
+ align:start position:0%
+its own had much power at all and so
+ 
+
+ align:start position:0%
+its own had much power at all and so
+again this is a characteristic of
+
+ align:start position:0%
+again this is a characteristic of
+ 
+
+ align:start position:0%
+again this is a characteristic of
+classical wave behavior that the
+
+ align:start position:0%
+classical wave behavior that the
+ 
+
+ align:start position:0%
+classical wave behavior that the
+intensity goes as the square of the sum
+
+ align:start position:0%
+intensity goes as the square of the sum
+ 
+
+ align:start position:0%
+intensity goes as the square of the sum
+not the sum and the squares and since
+
+ align:start position:0%
+not the sum and the squares and since
+ 
+
+ align:start position:0%
+not the sum and the squares and since
+the amplitudes can be both positive and
+
+ align:start position:0%
+the amplitudes can be both positive and
+ 
+
+ align:start position:0%
+the amplitudes can be both positive and
+negative it can even they can even be
+
+ align:start position:0%
+negative it can even they can even be
+ 
+
+ align:start position:0%
+negative it can even they can even be
+complex numbers there could be all kinds
+
+ align:start position:0%
+complex numbers there could be all kinds
+ 
+
+ align:start position:0%
+complex numbers there could be all kinds
+of situations in which the sum
+
+ align:start position:0%
+of situations in which the sum
+ 
+
+ align:start position:0%
+of situations in which the sum
+uh is uh this is in which the square of
+
+ align:start position:0%
+uh is uh this is in which the square of
+ 
+
+ align:start position:0%
+uh is uh this is in which the square of
+the sum is quite different than the sum
+
+ align:start position:0%
+the sum is quite different than the sum
+ 
+
+ align:start position:0%
+the sum is quite different than the sum
+of the squares
+
+ align:start position:0%
+of the squares
+ 
+
+ align:start position:0%
+of the squares
+characteristic wave-like uh interference
+
+ align:start position:0%
+characteristic wave-like uh interference
+ 
+
+ align:start position:0%
+characteristic wave-like uh interference
+pattern again probably pretty familiar
+
+ align:start position:0%
+pattern again probably pretty familiar
+ 
+
+ align:start position:0%
+pattern again probably pretty familiar
+so now what happens when we now move to
+
+ align:start position:0%
+so now what happens when we now move to
+ 
+
+ align:start position:0%
+so now what happens when we now move to
+the quantum Realm
+
+ align:start position:0%
+the quantum Realm
+ 
+
+ align:start position:0%
+the quantum Realm
+now let's imagine some cathode ray like
+
+ align:start position:0%
+now let's imagine some cathode ray like
+ 
+
+ align:start position:0%
+now let's imagine some cathode ray like
+JJ Thompson had or of the sort that um
+
+ align:start position:0%
+JJ Thompson had or of the sort that um
+ 
+
+ align:start position:0%
+JJ Thompson had or of the sort that um
+that was by this point quite familiar
+
+ align:start position:0%
+that was by this point quite familiar
+ 
+
+ align:start position:0%
+that was by this point quite familiar
+even by the 1920s things like what um uh
+
+ align:start position:0%
+even by the 1920s things like what um uh
+ 
+
+ align:start position:0%
+even by the 1920s things like what um uh
+girmer and Davison used in 1927 to think
+
+ align:start position:0%
+girmer and Davison used in 1927 to think
+ 
+
+ align:start position:0%
+girmer and Davison used in 1927 to think
+about uh Del boring waves this was
+
+ align:start position:0%
+about uh Del boring waves this was
+ 
+
+ align:start position:0%
+about uh Del boring waves this was
+already literally a feasible experiment
+
+ align:start position:0%
+already literally a feasible experiment
+ 
+
+ align:start position:0%
+already literally a feasible experiment
+as early as the mid-1920s people tried
+
+ align:start position:0%
+as early as the mid-1920s people tried
+ 
+
+ align:start position:0%
+as early as the mid-1920s people tried
+to do it
+
+ align:start position:0%
+to do it
+ 
+
+ align:start position:0%
+to do it
+so let's imagine shooting out single
+
+ align:start position:0%
+so let's imagine shooting out single
+ 
+
+ align:start position:0%
+so let's imagine shooting out single
+electrons one at a time from some Source
+
+ align:start position:0%
+electrons one at a time from some Source
+ 
+
+ align:start position:0%
+electrons one at a time from some Source
+some cathode ray let's say some electron
+
+ align:start position:0%
+some cathode ray let's say some electron
+ 
+
+ align:start position:0%
+some cathode ray let's say some electron
+gun we're going to send one electron at
+
+ align:start position:0%
+gun we're going to send one electron at
+ 
+
+ align:start position:0%
+gun we're going to send one electron at
+a time we're not going to have a
+
+ align:start position:0%
+a time we're not going to have a
+ 
+
+ align:start position:0%
+a time we're not going to have a
+continuous sprayer then we'll spend send
+
+ align:start position:0%
+continuous sprayer then we'll spend send
+ 
+
+ align:start position:0%
+continuous sprayer then we'll spend send
+one shut down the device let it cool go
+
+ align:start position:0%
+one shut down the device let it cool go
+ 
+
+ align:start position:0%
+one shut down the device let it cool go
+out for a coffee come back an hour later
+
+ align:start position:0%
+out for a coffee come back an hour later
+ 
+
+ align:start position:0%
+out for a coffee come back an hour later
+send out one more electron we can really
+
+ align:start position:0%
+send out one more electron we can really
+ 
+
+ align:start position:0%
+send out one more electron we can really
+take our time
+
+ align:start position:0%
+take our time
+ 
+
+ align:start position:0%
+take our time
+so at any given moment there's only one
+
+ align:start position:0%
+so at any given moment there's only one
+ 
+
+ align:start position:0%
+so at any given moment there's only one
+electron in in play in the device
+
+ align:start position:0%
+electron in in play in the device
+ 
+
+ align:start position:0%
+electron in in play in the device
+we're going to aim those 100 time
+
+ align:start position:0%
+we're going to aim those 100 time
+ 
+
+ align:start position:0%
+we're going to aim those 100 time
+electrons at a device this is by the way
+
+ align:start position:0%
+electrons at a device this is by the way
+ 
+
+ align:start position:0%
+electrons at a device this is by the way
+taken this illustration is taken from
+
+ align:start position:0%
+taken this illustration is taken from
+ 
+
+ align:start position:0%
+taken this illustration is taken from
+Bohr's essay about his debates with
+
+ align:start position:0%
+Bohr's essay about his debates with
+ 
+
+ align:start position:0%
+Bohr's essay about his debates with
+Einstein you hopefully recognize it from
+
+ align:start position:0%
+Einstein you hopefully recognize it from
+ 
+
+ align:start position:0%
+Einstein you hopefully recognize it from
+your reader so we're going to send these
+
+ align:start position:0%
+your reader so we're going to send these
+ 
+
+ align:start position:0%
+your reader so we're going to send these
+electrons one at a time toward a device
+
+ align:start position:0%
+electrons one at a time toward a device
+ 
+
+ align:start position:0%
+electrons one at a time toward a device
+that has two slits the electrons will be
+
+ align:start position:0%
+that has two slits the electrons will be
+ 
+
+ align:start position:0%
+that has two slits the electrons will be
+blocked if they hit anywhere here but
+
+ align:start position:0%
+blocked if they hit anywhere here but
+ 
+
+ align:start position:0%
+blocked if they hit anywhere here but
+they can get through either this slit or
+
+ align:start position:0%
+they can get through either this slit or
+ 
+
+ align:start position:0%
+they can get through either this slit or
+that slit and we have the opportunity to
+
+ align:start position:0%
+that slit and we have the opportunity to
+ 
+
+ align:start position:0%
+that slit and we have the opportunity to
+open or close each lit independently
+
+ align:start position:0%
+open or close each lit independently
+ 
+
+ align:start position:0%
+open or close each lit independently
+and then behind the the wall with two
+
+ align:start position:0%
+and then behind the the wall with two
+ 
+
+ align:start position:0%
+and then behind the the wall with two
+slits we have an array of very closely
+
+ align:start position:0%
+slits we have an array of very closely
+ 
+
+ align:start position:0%
+slits we have an array of very closely
+spaced detectors electron detectors uh
+
+ align:start position:0%
+spaced detectors electron detectors uh
+ 
+
+ align:start position:0%
+spaced detectors electron detectors uh
+and so we can measure with very good
+
+ align:start position:0%
+and so we can measure with very good
+ 
+
+ align:start position:0%
+and so we can measure with very good
+resolution the where electrons are
+
+ align:start position:0%
+resolution the where electrons are
+ 
+
+ align:start position:0%
+resolution the where electrons are
+detected as a function of position along
+
+ align:start position:0%
+detected as a function of position along
+ 
+
+ align:start position:0%
+detected as a function of position along
+this kind of backstop this array of
+
+ align:start position:0%
+this kind of backstop this array of
+ 
+
+ align:start position:0%
+this kind of backstop this array of
+detectors
+
+ align:start position:0%
+detectors
+ 
+
+ align:start position:0%
+detectors
+we also can arrange things so the
+
+ align:start position:0%
+we also can arrange things so the
+ 
+
+ align:start position:0%
+we also can arrange things so the
+distance between the two slits the
+
+ align:start position:0%
+distance between the two slits the
+ 
+
+ align:start position:0%
+distance between the two slits the
+distance Little D uh is say 10 000 times
+
+ align:start position:0%
+distance Little D uh is say 10 000 times
+ 
+
+ align:start position:0%
+distance Little D uh is say 10 000 times
+larger than the uh characteristic wave
+
+ align:start position:0%
+larger than the uh characteristic wave
+ 
+
+ align:start position:0%
+larger than the uh characteristic wave
+in a scale the devoid wavelength of
+
+ align:start position:0%
+in a scale the devoid wavelength of
+ 
+
+ align:start position:0%
+in a scale the devoid wavelength of
+those electrons so the electron if it's
+
+ align:start position:0%
+those electrons so the electron if it's
+ 
+
+ align:start position:0%
+those electrons so the electron if it's
+approaching uh if it's anywhere near
+
+ align:start position:0%
+approaching uh if it's anywhere near
+ 
+
+ align:start position:0%
+approaching uh if it's anywhere near
+this lit it should be ten thousand sort
+
+ align:start position:0%
+this lit it should be ten thousand sort
+ 
+
+ align:start position:0%
+this lit it should be ten thousand sort
+of electron distances away from that
+
+ align:start position:0%
+of electron distances away from that
+ 
+
+ align:start position:0%
+of electron distances away from that
+slit and vice versa it somehow it should
+
+ align:start position:0%
+slit and vice versa it somehow it should
+ 
+
+ align:start position:0%
+slit and vice versa it somehow it should
+have a kind of localized Behavior as it
+
+ align:start position:0%
+have a kind of localized Behavior as it
+ 
+
+ align:start position:0%
+have a kind of localized Behavior as it
+encounters the slits moreover each of
+
+ align:start position:0%
+encounters the slits moreover each of
+ 
+
+ align:start position:0%
+encounters the slits moreover each of
+the detectors is going to detect the
+
+ align:start position:0%
+the detectors is going to detect the
+ 
+
+ align:start position:0%
+the detectors is going to detect the
+location of electron when they're very
+
+ align:start position:0%
+location of electron when they're very
+ 
+
+ align:start position:0%
+location of electron when they're very
+very small uh region of space so we're
+
+ align:start position:0%
+very small uh region of space so we're
+ 
+
+ align:start position:0%
+very small uh region of space so we're
+not going to expect to find a kind of
+
+ align:start position:0%
+not going to expect to find a kind of
+ 
+
+ align:start position:0%
+not going to expect to find a kind of
+splayed out wave of electrons each one
+
+ align:start position:0%
+splayed out wave of electrons each one
+ 
+
+ align:start position:0%
+splayed out wave of electrons each one
+is detected as a point-like discrete uh
+
+ align:start position:0%
+is detected as a point-like discrete uh
+ 
+
+ align:start position:0%
+is detected as a point-like discrete uh
+particulate detection because we've
+
+ align:start position:0%
+particulate detection because we've
+ 
+
+ align:start position:0%
+particulate detection because we've
+these very high resolution detectors in
+
+ align:start position:0%
+these very high resolution detectors in
+ 
+
+ align:start position:0%
+these very high resolution detectors in
+the back
+
+ align:start position:0%
+the back
+ 
+
+ align:start position:0%
+the back
+so we're going to release one electron
+
+ align:start position:0%
+so we're going to release one electron
+ 
+
+ align:start position:0%
+so we're going to release one electron
+at a time wait one hour between and do
+
+ align:start position:0%
+at a time wait one hour between and do
+ 
+
+ align:start position:0%
+at a time wait one hour between and do
+that ten thousand times which as I like
+
+ align:start position:0%
+that ten thousand times which as I like
+ 
+
+ align:start position:0%
+that ten thousand times which as I like
+to say is why we actually have graduate
+
+ align:start position:0%
+to say is why we actually have graduate
+ 
+
+ align:start position:0%
+to say is why we actually have graduate
+students I mean who's going to patients
+
+ align:start position:0%
+students I mean who's going to patients
+ 
+
+ align:start position:0%
+students I mean who's going to patients
+for that with many thanks to our
+
+ align:start position:0%
+for that with many thanks to our
+ 
+
+ align:start position:0%
+for that with many thanks to our
+teaching assistants so this is you know
+
+ align:start position:0%
+teaching assistants so this is you know
+ 
+
+ align:start position:0%
+teaching assistants so this is you know
+going to take months
+
+ align:start position:0%
+going to take months
+ 
+
+ align:start position:0%
+going to take months
+but we care about the nature of the
+
+ align:start position:0%
+but we care about the nature of the
+ 
+
+ align:start position:0%
+but we care about the nature of the
+universe uh and so we're going to just
+
+ align:start position:0%
+universe uh and so we're going to just
+ 
+
+ align:start position:0%
+universe uh and so we're going to just
+go plow through and do this now we're
+
+ align:start position:0%
+go plow through and do this now we're
+ 
+
+ align:start position:0%
+go plow through and do this now we're
+going to do the same kind of accounting
+
+ align:start position:0%
+going to do the same kind of accounting
+ 
+
+ align:start position:0%
+going to do the same kind of accounting
+exercise as we've done with both the um
+
+ align:start position:0%
+exercise as we've done with both the um
+ 
+
+ align:start position:0%
+exercise as we've done with both the um
+classical particles of the classical
+
+ align:start position:0%
+classical particles of the classical
+ 
+
+ align:start position:0%
+classical particles of the classical
+waves we're going to make a kind of
+
+ align:start position:0%
+waves we're going to make a kind of
+ 
+
+ align:start position:0%
+waves we're going to make a kind of
+histogram of the number of electrons
+
+ align:start position:0%
+histogram of the number of electrons
+ 
+
+ align:start position:0%
+histogram of the number of electrons
+that are found in each of these uh sort
+
+ align:start position:0%
+that are found in each of these uh sort
+ 
+
+ align:start position:0%
+that are found in each of these uh sort
+of bins each of these detector bins as a
+
+ align:start position:0%
+of bins each of these detector bins as a
+ 
+
+ align:start position:0%
+of bins each of these detector bins as a
+function of location
+
+ align:start position:0%
+function of location
+ 
+
+ align:start position:0%
+function of location
+so once again we'll start by keeping one
+
+ align:start position:0%
+so once again we'll start by keeping one
+ 
+
+ align:start position:0%
+so once again we'll start by keeping one
+slit closed so the electrons can only
+
+ align:start position:0%
+slit closed so the electrons can only
+ 
+
+ align:start position:0%
+slit closed so the electrons can only
+pass through the other slit so if only
+
+ align:start position:0%
+pass through the other slit so if only
+ 
+
+ align:start position:0%
+pass through the other slit so if only
+slit a is open we get this very strongly
+
+ align:start position:0%
+slit a is open we get this very strongly
+ 
+
+ align:start position:0%
+slit a is open we get this very strongly
+peaked distribution directly behind the
+
+ align:start position:0%
+peaked distribution directly behind the
+ 
+
+ align:start position:0%
+peaked distribution directly behind the
+Oakley slit just like with the bullets
+
+ align:start position:0%
+Oakley slit just like with the bullets
+ 
+
+ align:start position:0%
+Oakley slit just like with the bullets
+if slit a is closed but only slit B is
+
+ align:start position:0%
+if slit a is closed but only slit B is
+ 
+
+ align:start position:0%
+if slit a is closed but only slit B is
+open again it very strongly Peaks
+
+ align:start position:0%
+open again it very strongly Peaks
+ 
+
+ align:start position:0%
+open again it very strongly Peaks
+distribution and so it looks a lot like
+
+ align:start position:0%
+distribution and so it looks a lot like
+ 
+
+ align:start position:0%
+distribution and so it looks a lot like
+the classical particles in fact if
+
+ align:start position:0%
+the classical particles in fact if
+ 
+
+ align:start position:0%
+the classical particles in fact if
+you've taken Junior lab you probably
+
+ align:start position:0%
+you've taken Junior lab you probably
+ 
+
+ align:start position:0%
+you've taken Junior lab you probably
+would learn to say those little Wiggles
+
+ align:start position:0%
+would learn to say those little Wiggles
+ 
+
+ align:start position:0%
+would learn to say those little Wiggles
+are clearly instrumental error that
+
+ align:start position:0%
+are clearly instrumental error that
+ 
+
+ align:start position:0%
+are clearly instrumental error that
+statistical uh uh insignificance they
+
+ align:start position:0%
+statistical uh uh insignificance they
+ 
+
+ align:start position:0%
+statistical uh uh insignificance they
+never rise above about one percent of
+
+ align:start position:0%
+never rise above about one percent of
+ 
+
+ align:start position:0%
+never rise above about one percent of
+the central Peak it really looks like
+
+ align:start position:0%
+the central Peak it really looks like
+ 
+
+ align:start position:0%
+the central Peak it really looks like
+electrons behaving like bullets they're
+
+ align:start position:0%
+electrons behaving like bullets they're
+ 
+
+ align:start position:0%
+electrons behaving like bullets they're
+each emitted like a tiny little discrete
+
+ align:start position:0%
+each emitted like a tiny little discrete
+ 
+
+ align:start position:0%
+each emitted like a tiny little discrete
+particle they're encountering one slit
+
+ align:start position:0%
+particle they're encountering one slit
+ 
+
+ align:start position:0%
+particle they're encountering one slit
+or the other because we've arranged the
+
+ align:start position:0%
+or the other because we've arranged the
+ 
+
+ align:start position:0%
+or the other because we've arranged the
+distance to be so extreme they're all
+
+ align:start position:0%
+distance to be so extreme they're all
+ 
+
+ align:start position:0%
+distance to be so extreme they're all
+being detected as one little blip on
+
+ align:start position:0%
+being detected as one little blip on
+ 
+
+ align:start position:0%
+being detected as one little blip on
+that detector screen they look like
+
+ align:start position:0%
+that detector screen they look like
+ 
+
+ align:start position:0%
+that detector screen they look like
+little baseballs or bullets
+
+ align:start position:0%
+little baseballs or bullets
+ 
+
+ align:start position:0%
+little baseballs or bullets
+and yet
+
+ align:start position:0%
+and yet
+ 
+
+ align:start position:0%
+and yet
+when we then look at the pattern when
+
+ align:start position:0%
+when we then look at the pattern when
+ 
+
+ align:start position:0%
+when we then look at the pattern when
+both slits are open but only one
+
+ align:start position:0%
+both slits are open but only one
+ 
+
+ align:start position:0%
+both slits are open but only one
+electron went through at a time
+
+ align:start position:0%
+electron went through at a time
+ 
+
+ align:start position:0%
+electron went through at a time
+we get right back to this very familiar
+
+ align:start position:0%
+we get right back to this very familiar
+ 
+
+ align:start position:0%
+we get right back to this very familiar
+wave pattern this chest
+
+ align:start position:0%
+wave pattern this chest
+ 
+
+ align:start position:0%
+wave pattern this chest
+how this can happen has kept people up
+
+ align:start position:0%
+how this can happen has kept people up
+ 
+
+ align:start position:0%
+how this can happen has kept people up
+at night for now very nearly 100 years
+
+ align:start position:0%
+at night for now very nearly 100 years
+ 
+
+ align:start position:0%
+at night for now very nearly 100 years
+and I hope we're not too blase about it
+
+ align:start position:0%
+and I hope we're not too blase about it
+ 
+
+ align:start position:0%
+and I hope we're not too blase about it
+even today
+
+ align:start position:0%
+even today
+ 
+
+ align:start position:0%
+even today
+that looks like particles when only one
+
+ align:start position:0%
+that looks like particles when only one
+ 
+
+ align:start position:0%
+that looks like particles when only one
+slits open it looks like waves when both
+
+ align:start position:0%
+slits open it looks like waves when both
+ 
+
+ align:start position:0%
+slits open it looks like waves when both
+sets are open and yet and yet we've been
+
+ align:start position:0%
+sets are open and yet and yet we've been
+ 
+
+ align:start position:0%
+sets are open and yet and yet we've been
+super careful to only send one electron
+
+ align:start position:0%
+super careful to only send one electron
+ 
+
+ align:start position:0%
+super careful to only send one electron
+through at a time unlike a water wave is
+
+ align:start position:0%
+through at a time unlike a water wave is
+ 
+
+ align:start position:0%
+through at a time unlike a water wave is
+clearly an extended continuous object
+
+ align:start position:0%
+clearly an extended continuous object
+ 
+
+ align:start position:0%
+clearly an extended continuous object
+clearly the wave can interfere with
+
+ align:start position:0%
+clearly the wave can interfere with
+ 
+
+ align:start position:0%
+clearly the wave can interfere with
+itself it is literally an extended
+
+ align:start position:0%
+itself it is literally an extended
+ 
+
+ align:start position:0%
+itself it is literally an extended
+object which has many moving Parts these
+
+ align:start position:0%
+object which has many moving Parts these
+ 
+
+ align:start position:0%
+object which has many moving Parts these
+electrons are tiny little pellets we we
+
+ align:start position:0%
+electrons are tiny little pellets we we
+ 
+
+ align:start position:0%
+electrons are tiny little pellets we we
+can we we emit them as little discrete
+
+ align:start position:0%
+can we we emit them as little discrete
+ 
+
+ align:start position:0%
+can we we emit them as little discrete
+bundles
+
+ align:start position:0%
+bundles
+ 
+
+ align:start position:0%
+bundles
+uh we only have one in play at a times
+
+ align:start position:0%
+uh we only have one in play at a times
+ 
+
+ align:start position:0%
+uh we only have one in play at a times
+there's not like two electrons could
+
+ align:start position:0%
+there's not like two electrons could
+ 
+
+ align:start position:0%
+there's not like two electrons could
+have influenced each other by repelling
+
+ align:start position:0%
+have influenced each other by repelling
+ 
+
+ align:start position:0%
+have influenced each other by repelling
+each other and made some kind of
+
+ align:start position:0%
+each other and made some kind of
+ 
+
+ align:start position:0%
+each other and made some kind of
+characteristic uh pattern because they
+
+ align:start position:0%
+characteristic uh pattern because they
+ 
+
+ align:start position:0%
+characteristic uh pattern because they
+were interacting with each other we've
+
+ align:start position:0%
+were interacting with each other we've
+ 
+
+ align:start position:0%
+were interacting with each other we've
+sent only one through the time and
+
+ align:start position:0%
+sent only one through the time and
+ 
+
+ align:start position:0%
+sent only one through the time and
+waited a whole hour in between
+
+ align:start position:0%
+waited a whole hour in between
+ 
+
+ align:start position:0%
+waited a whole hour in between
+we've done that ten thousand individual
+
+ align:start position:0%
+we've done that ten thousand individual
+ 
+
+ align:start position:0%
+we've done that ten thousand individual
+times and yet the pattern that builds up
+
+ align:start position:0%
+times and yet the pattern that builds up
+ 
+
+ align:start position:0%
+times and yet the pattern that builds up
+one individual point-like detection at a
+
+ align:start position:0%
+one individual point-like detection at a
+ 
+
+ align:start position:0%
+one individual point-like detection at a
+time is this undeniable very familiar
+
+ align:start position:0%
+time is this undeniable very familiar
+ 
+
+ align:start position:0%
+time is this undeniable very familiar
+wave pattern where much as we would
+
+ align:start position:0%
+wave pattern where much as we would
+ 
+
+ align:start position:0%
+wave pattern where much as we would
+expect now from the ocean waves the
+
+ align:start position:0%
+expect now from the ocean waves the
+ 
+
+ align:start position:0%
+expect now from the ocean waves the
+resulting probability distribution goes
+
+ align:start position:0%
+resulting probability distribution goes
+ 
+
+ align:start position:0%
+resulting probability distribution goes
+like the square of the sum and
+
+ align:start position:0%
+like the square of the sum and
+ 
+
+ align:start position:0%
+like the square of the sum and
+definitely not like the sum of the
+
+ align:start position:0%
+definitely not like the sum of the
+ 
+
+ align:start position:0%
+definitely not like the sum of the
+squares it is not the sum of this
+
+ align:start position:0%
+squares it is not the sum of this
+ 
+
+ align:start position:0%
+squares it is not the sum of this
+distribution plus that one it is
+
+ align:start position:0%
+distribution plus that one it is
+ 
+
+ align:start position:0%
+distribution plus that one it is
+absolutely emphatically not like 10 000
+
+ align:start position:0%
+absolutely emphatically not like 10 000
+ 
+
+ align:start position:0%
+absolutely emphatically not like 10 000
+baseballs thrown at a wall with two
+
+ align:start position:0%
+baseballs thrown at a wall with two
+ 
+
+ align:start position:0%
+baseballs thrown at a wall with two
+holes or bullets shot at some barrier it
+
+ align:start position:0%
+holes or bullets shot at some barrier it
+ 
+
+ align:start position:0%
+holes or bullets shot at some barrier it
+looks just like the water wave even
+
+ align:start position:0%
+looks just like the water wave even
+ 
+
+ align:start position:0%
+looks just like the water wave even
+though this built up over time from 10
+
+ align:start position:0%
+though this built up over time from 10
+ 
+
+ align:start position:0%
+though this built up over time from 10
+000 independent events
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if I were to unmute you all I should
+
+ align:start position:0%
+now if I were to unmute you all I should
+ 
+
+ align:start position:0%
+now if I were to unmute you all I should
+hear you screaming with either joy and
+
+ align:start position:0%
+hear you screaming with either joy and
+ 
+
+ align:start position:0%
+hear you screaming with either joy and
+ecstasy or real deep despair either way
+
+ align:start position:0%
+ecstasy or real deep despair either way
+ 
+
+ align:start position:0%
+ecstasy or real deep despair either way
+this should not be an emotionally
+
+ align:start position:0%
+this should not be an emotionally
+ 
+
+ align:start position:0%
+this should not be an emotionally
+neutral statement so what comes from all
+
+ align:start position:0%
+neutral statement so what comes from all
+ 
+
+ align:start position:0%
+neutral statement so what comes from all
+this is uh Max born the Gooding and
+
+ align:start position:0%
+this is uh Max born the Gooding and
+ 
+
+ align:start position:0%
+this is uh Max born the Gooding and
+theoristic contemporary of Einstein and
+
+ align:start position:0%
+theoristic contemporary of Einstein and
+ 
+
+ align:start position:0%
+theoristic contemporary of Einstein and
+Destroyer Heisenberg's Mentor who taught
+
+ align:start position:0%
+Destroyer Heisenberg's Mentor who taught
+ 
+
+ align:start position:0%
+Destroyer Heisenberg's Mentor who taught
+Mentor that these were matrices
+
+ align:start position:0%
+Mentor that these were matrices
+ 
+
+ align:start position:0%
+Mentor that these were matrices
+Max Bourne then suggests from exactly
+
+ align:start position:0%
+Max Bourne then suggests from exactly
+ 
+
+ align:start position:0%
+Max Bourne then suggests from exactly
+these kinds of of uh of kind of
+
+ align:start position:0%
+these kinds of of uh of kind of
+ 
+
+ align:start position:0%
+these kinds of of uh of kind of
+reasoning as early as the summer of 1926
+
+ align:start position:0%
+reasoning as early as the summer of 1926
+ 
+
+ align:start position:0%
+reasoning as early as the summer of 1926
+that what is this wave side the thing
+
+ align:start position:0%
+that what is this wave side the thing
+ 
+
+ align:start position:0%
+that what is this wave side the thing
+that is a solution to Schrodinger's wave
+
+ align:start position:0%
+that is a solution to Schrodinger's wave
+ 
+
+ align:start position:0%
+that is a solution to Schrodinger's wave
+equation it seems to be not a physical
+
+ align:start position:0%
+equation it seems to be not a physical
+ 
+
+ align:start position:0%
+equation it seems to be not a physical
+bit of the electron it's not some sort
+
+ align:start position:0%
+bit of the electron it's not some sort
+ 
+
+ align:start position:0%
+bit of the electron it's not some sort
+of electron density that's spread out in
+
+ align:start position:0%
+of electron density that's spread out in
+ 
+
+ align:start position:0%
+of electron density that's spread out in
+space it seems to be related to the
+
+ align:start position:0%
+space it seems to be related to the
+ 
+
+ align:start position:0%
+space it seems to be related to the
+likely behavior of the of the associated
+
+ align:start position:0%
+likely behavior of the of the associated
+ 
+
+ align:start position:0%
+likely behavior of the of the associated
+particle it's not a physical bit of the
+
+ align:start position:0%
+particle it's not a physical bit of the
+ 
+
+ align:start position:0%
+particle it's not a physical bit of the
+particle it's a description of the way
+
+ align:start position:0%
+particle it's a description of the way
+ 
+
+ align:start position:0%
+particle it's a description of the way
+that particle is likely to behave in
+
+ align:start position:0%
+that particle is likely to behave in
+ 
+
+ align:start position:0%
+that particle is likely to behave in
+particular it's what comes to be called
+
+ align:start position:0%
+particular it's what comes to be called
+ 
+
+ align:start position:0%
+particular it's what comes to be called
+a probability amplitude not the
+
+ align:start position:0%
+a probability amplitude not the
+ 
+
+ align:start position:0%
+a probability amplitude not the
+probability not the peak uh that has
+
+ align:start position:0%
+probability not the peak uh that has
+ 
+
+ align:start position:0%
+probability not the peak uh that has
+this value on our histogram but actually
+
+ align:start position:0%
+this value on our histogram but actually
+ 
+
+ align:start position:0%
+this value on our histogram but actually
+this the object whose absolute Square
+
+ align:start position:0%
+this the object whose absolute Square
+ 
+
+ align:start position:0%
+this the object whose absolute Square
+gives rise to this to this thick black
+
+ align:start position:0%
+gives rise to this to this thick black
+ 
+
+ align:start position:0%
+gives rise to this to this thick black
+line pattern so the probability Bourne
+
+ align:start position:0%
+line pattern so the probability Bourne
+ 
+
+ align:start position:0%
+line pattern so the probability Bourne
+says we now call this born's
+
+ align:start position:0%
+says we now call this born's
+ 
+
+ align:start position:0%
+says we now call this born's
+interpretation the probability to find
+
+ align:start position:0%
+interpretation the probability to find
+ 
+
+ align:start position:0%
+interpretation the probability to find
+electron um to find an electron here
+
+ align:start position:0%
+electron um to find an electron here
+ 
+
+ align:start position:0%
+electron um to find an electron here
+versus here versus here goes like the
+
+ align:start position:0%
+versus here versus here goes like the
+ 
+
+ align:start position:0%
+versus here versus here goes like the
+absolute square of this wave like
+
+ align:start position:0%
+absolute square of this wave like
+ 
+
+ align:start position:0%
+absolute square of this wave like
+quantity Schrodinger's wave function
+
+ align:start position:0%
+quantity Schrodinger's wave function
+ 
+
+ align:start position:0%
+quantity Schrodinger's wave function
+that's what gets worked out within six
+
+ align:start position:0%
+that's what gets worked out within six
+ 
+
+ align:start position:0%
+that's what gets worked out within six
+months of Schrodinger's first
+
+ align:start position:0%
+months of Schrodinger's first
+ 
+
+ align:start position:0%
+months of Schrodinger's first
+publication on this uh in by thinking
+
+ align:start position:0%
+publication on this uh in by thinking
+ 
+
+ align:start position:0%
+publication on this uh in by thinking
+about what is actually uh observable in
+
+ align:start position:0%
+about what is actually uh observable in
+ 
+
+ align:start position:0%
+about what is actually uh observable in
+experiments involving these wave-like
+
+ align:start position:0%
+experiments involving these wave-like
+ 
+
+ align:start position:0%
+experiments involving these wave-like
+features
+
+ align:start position:0%
+features
+ 
+
+ align:start position:0%
+features
+so again that was a thought experiment
+
+ align:start position:0%
+so again that was a thought experiment
+ 
+
+ align:start position:0%
+so again that was a thought experiment
+uh in 1926 by 1920s literally by 1927
+
+ align:start position:0%
+uh in 1926 by 1920s literally by 1927
+ 
+
+ align:start position:0%
+uh in 1926 by 1920s literally by 1927
+there were efforts to try to do this
+
+ align:start position:0%
+there were efforts to try to do this
+ 
+
+ align:start position:0%
+there were efforts to try to do this
+experimentally nowadays we have very
+
+ align:start position:0%
+experimentally nowadays we have very
+ 
+
+ align:start position:0%
+experimentally nowadays we have very
+fancy equipment with high Precision
+
+ align:start position:0%
+fancy equipment with high Precision
+ 
+
+ align:start position:0%
+fancy equipment with high Precision
+sources and detectors so here's a series
+
+ align:start position:0%
+sources and detectors so here's a series
+ 
+
+ align:start position:0%
+sources and detectors so here's a series
+of images courtesy from my colleagues um
+
+ align:start position:0%
+of images courtesy from my colleagues um
+ 
+
+ align:start position:0%
+of images courtesy from my colleagues um
+uh Robert Austin and Lyman page at
+
+ align:start position:0%
+uh Robert Austin and Lyman page at
+ 
+
+ align:start position:0%
+uh Robert Austin and Lyman page at
+Princeton this is not something we can
+
+ align:start position:0%
+Princeton this is not something we can
+ 
+
+ align:start position:0%
+Princeton this is not something we can
+do as an in-class demo or as an
+
+ align:start position:0%
+do as an in-class demo or as an
+ 
+
+ align:start position:0%
+do as an in-class demo or as an
+undergraduate Laboratory so these are
+
+ align:start position:0%
+undergraduate Laboratory so these are
+ 
+
+ align:start position:0%
+undergraduate Laboratory so these are
+this is real data this isn't simulated
+
+ align:start position:0%
+this is real data this isn't simulated
+ 
+
+ align:start position:0%
+this is real data this isn't simulated
+these are
+
+ align:start position:0%
+these are
+ 
+
+ align:start position:0%
+these are
+snapshots of the kind of fluorescent
+
+ align:start position:0%
+snapshots of the kind of fluorescent
+ 
+
+ align:start position:0%
+snapshots of the kind of fluorescent
+screen uh of an actual double slit
+
+ align:start position:0%
+screen uh of an actual double slit
+ 
+
+ align:start position:0%
+screen uh of an actual double slit
+experiment done at different moments in
+
+ align:start position:0%
+experiment done at different moments in
+ 
+
+ align:start position:0%
+experiment done at different moments in
+time as the pattern builds up so
+
+ align:start position:0%
+time as the pattern builds up so
+ 
+
+ align:start position:0%
+time as the pattern builds up so
+individual photons were fired out of the
+
+ align:start position:0%
+individual photons were fired out of the
+ 
+
+ align:start position:0%
+individual photons were fired out of the
+screen with two slits literally one at a
+
+ align:start position:0%
+screen with two slits literally one at a
+ 
+
+ align:start position:0%
+screen with two slits literally one at a
+time and now we can do single Photon
+
+ align:start position:0%
+time and now we can do single Photon
+ 
+
+ align:start position:0%
+time and now we can do single Photon
+experiments which is quite extraordinary
+
+ align:start position:0%
+experiments which is quite extraordinary
+ 
+
+ align:start position:0%
+experiments which is quite extraordinary
+and then you can detect where each
+
+ align:start position:0%
+and then you can detect where each
+ 
+
+ align:start position:0%
+and then you can detect where each
+individual Photon was uh was detected so
+
+ align:start position:0%
+individual Photon was uh was detected so
+ 
+
+ align:start position:0%
+individual Photon was uh was detected so
+these are little little
+
+ align:start position:0%
+these are little little
+ 
+
+ align:start position:0%
+these are little little
+pinpricks of light or an individual
+
+ align:start position:0%
+pinpricks of light or an individual
+ 
+
+ align:start position:0%
+pinpricks of light or an individual
+Photon interacted with the with the
+
+ align:start position:0%
+Photon interacted with the with the
+ 
+
+ align:start position:0%
+Photon interacted with the with the
+fluorescent photo detector so you have
+
+ align:start position:0%
+fluorescent photo detector so you have
+ 
+
+ align:start position:0%
+fluorescent photo detector so you have
+mostly black and screen because we've
+
+ align:start position:0%
+mostly black and screen because we've
+ 
+
+ align:start position:0%
+mostly black and screen because we've
+only sent a couple photons through one
+
+ align:start position:0%
+only sent a couple photons through one
+ 
+
+ align:start position:0%
+only sent a couple photons through one
+at a time so far very localized
+
+ align:start position:0%
+at a time so far very localized
+ 
+
+ align:start position:0%
+at a time so far very localized
+individual detections here and here but
+
+ align:start position:0%
+individual detections here and here but
+ 
+
+ align:start position:0%
+individual detections here and here but
+not here that's after the first one
+
+ align:start position:0%
+not here that's after the first one
+ 
+
+ align:start position:0%
+not here that's after the first one
+thirtieth of a second they're shooting
+
+ align:start position:0%
+thirtieth of a second they're shooting
+ 
+
+ align:start position:0%
+thirtieth of a second they're shooting
+rapidly one Photon at a time and only
+
+ align:start position:0%
+rapidly one Photon at a time and only
+ 
+
+ align:start position:0%
+rapidly one Photon at a time and only
+one at a time
+
+ align:start position:0%
+one at a time
+ 
+
+ align:start position:0%
+one at a time
+after a whole second has gone by you
+
+ align:start position:0%
+after a whole second has gone by you
+ 
+
+ align:start position:0%
+after a whole second has gone by you
+have accumulating pattern now you have
+
+ align:start position:0%
+have accumulating pattern now you have
+ 
+
+ align:start position:0%
+have accumulating pattern now you have
+several hundred photons individually
+
+ align:start position:0%
+several hundred photons individually
+ 
+
+ align:start position:0%
+several hundred photons individually
+detected
+
+ align:start position:0%
+detected
+ 
+
+ align:start position:0%
+detected
+wait a hundred seconds and you see very
+
+ align:start position:0%
+wait a hundred seconds and you see very
+ 
+
+ align:start position:0%
+wait a hundred seconds and you see very
+clearly this wave like interference
+
+ align:start position:0%
+clearly this wave like interference
+ 
+
+ align:start position:0%
+clearly this wave like interference
+pattern exactly the pattern described by
+
+ align:start position:0%
+pattern exactly the pattern described by
+ 
+
+ align:start position:0%
+pattern exactly the pattern described by
+that by that born interpretation even
+
+ align:start position:0%
+that by that born interpretation even
+ 
+
+ align:start position:0%
+that by that born interpretation even
+though this is built from thousands of
+
+ align:start position:0%
+though this is built from thousands of
+ 
+
+ align:start position:0%
+though this is built from thousands of
+otherwise Independents located in time
+
+ align:start position:0%
+otherwise Independents located in time
+ 
+
+ align:start position:0%
+otherwise Independents located in time
+and space detections of individual
+
+ align:start position:0%
+and space detections of individual
+ 
+
+ align:start position:0%
+and space detections of individual
+Quantum so we have we we shoot out
+
+ align:start position:0%
+Quantum so we have we we shoot out
+ 
+
+ align:start position:0%
+Quantum so we have we we shoot out
+individual quanta particulate like we
+
+ align:start position:0%
+individual quanta particulate like we
+ 
+
+ align:start position:0%
+individual quanta particulate like we
+detect individual quanta particularly
+
+ align:start position:0%
+detect individual quanta particularly
+ 
+
+ align:start position:0%
+detect individual quanta particularly
+like and they can interfere with each
+
+ align:start position:0%
+like and they can interfere with each
+ 
+
+ align:start position:0%
+like and they can interfere with each
+other because we make sure only one's
+
+ align:start position:0%
+other because we make sure only one's
+ 
+
+ align:start position:0%
+other because we make sure only one's
+sort of in the device at a time and yet
+
+ align:start position:0%
+sort of in the device at a time and yet
+ 
+
+ align:start position:0%
+sort of in the device at a time and yet
+over time they somehow build up this
+
+ align:start position:0%
+over time they somehow build up this
+ 
+
+ align:start position:0%
+over time they somehow build up this
+very characteristic wave-like
+
+ align:start position:0%
+very characteristic wave-like
+ 
+
+ align:start position:0%
+very characteristic wave-like
+interference pattern that is what's
+
+ align:start position:0%
+interference pattern that is what's
+ 
+
+ align:start position:0%
+interference pattern that is what's
+called the double slit experiment so let
+
+ align:start position:0%
+called the double slit experiment so let
+ 
+
+ align:start position:0%
+called the double slit experiment so let
+me pause there
+
+ align:start position:0%
+me pause there
+ 
+
+ align:start position:0%
+me pause there
+how do we go from one electron every
+
+ align:start position:0%
+how do we go from one electron every
+ 
+
+ align:start position:0%
+how do we go from one electron every
+hour to 100 uh every second oh good so
+
+ align:start position:0%
+hour to 100 uh every second oh good so
+ 
+
+ align:start position:0%
+hour to 100 uh every second oh good so
+Alex good question so uh the the data I
+
+ align:start position:0%
+Alex good question so uh the the data I
+ 
+
+ align:start position:0%
+Alex good question so uh the the data I
+just showed was actually with photons uh
+
+ align:start position:0%
+just showed was actually with photons uh
+ 
+
+ align:start position:0%
+just showed was actually with photons uh
+the Princeton group you one can do with
+
+ align:start position:0%
+the Princeton group you one can do with
+ 
+
+ align:start position:0%
+the Princeton group you one can do with
+electrons as well uh they were using uh
+
+ align:start position:0%
+electrons as well uh they were using uh
+ 
+
+ align:start position:0%
+electrons as well uh they were using uh
+uh let's say a
+
+ align:start position:0%
+uh let's say a
+ 
+
+ align:start position:0%
+uh let's say a
+a photon source that emits single
+
+ align:start position:0%
+a photon source that emits single
+ 
+
+ align:start position:0%
+a photon source that emits single
+photons rapidly so they really were
+
+ align:start position:0%
+photons rapidly so they really were
+ 
+
+ align:start position:0%
+photons rapidly so they really were
+shooting out only one Photon at a time
+
+ align:start position:0%
+shooting out only one Photon at a time
+ 
+
+ align:start position:0%
+shooting out only one Photon at a time
+but they can produce many photons per
+
+ align:start position:0%
+but they can produce many photons per
+ 
+
+ align:start position:0%
+but they can produce many photons per
+second so the timing when we're dealing
+
+ align:start position:0%
+second so the timing when we're dealing
+ 
+
+ align:start position:0%
+second so the timing when we're dealing
+that with that particular source of
+
+ align:start position:0%
+that with that particular source of
+ 
+
+ align:start position:0%
+that with that particular source of
+individual quantity this the time that
+
+ align:start position:0%
+individual quantity this the time that
+ 
+
+ align:start position:0%
+individual quantity this the time that
+What's called the duty cycle shorter we
+
+ align:start position:0%
+What's called the duty cycle shorter we
+ 
+
+ align:start position:0%
+What's called the duty cycle shorter we
+also have very rapid Electronics now in
+
+ align:start position:0%
+also have very rapid Electronics now in
+ 
+
+ align:start position:0%
+also have very rapid Electronics now in
+like 1927. so the electronics can
+
+ align:start position:0%
+like 1927. so the electronics can
+ 
+
+ align:start position:0%
+like 1927. so the electronics can
+actually actually resolve individual
+
+ align:start position:0%
+actually actually resolve individual
+ 
+
+ align:start position:0%
+actually actually resolve individual
+detections in a tiny fraction a second
+
+ align:start position:0%
+detections in a tiny fraction a second
+ 
+
+ align:start position:0%
+detections in a tiny fraction a second
+so conceptually it's as if we had gone
+
+ align:start position:0%
+so conceptually it's as if we had gone
+ 
+
+ align:start position:0%
+so conceptually it's as if we had gone
+back to my cartoon turned on our machine
+
+ align:start position:0%
+back to my cartoon turned on our machine
+ 
+
+ align:start position:0%
+back to my cartoon turned on our machine
+shot out one particle turn it off went
+
+ align:start position:0%
+shot out one particle turn it off went
+ 
+
+ align:start position:0%
+shot out one particle turn it off went
+away it's just now we can do that with
+
+ align:start position:0%
+away it's just now we can do that with
+ 
+
+ align:start position:0%
+away it's just now we can do that with
+with um with a kind of high duty cycle
+
+ align:start position:0%
+with um with a kind of high duty cycle
+ 
+
+ align:start position:0%
+with um with a kind of high duty cycle
+rapid Electronics but but conceptually
+
+ align:start position:0%
+rapid Electronics but but conceptually
+ 
+
+ align:start position:0%
+rapid Electronics but but conceptually
+it to my mind it's quite similar
+
+ align:start position:0%
+it to my mind it's quite similar
+ 
+
+ align:start position:0%
+it to my mind it's quite similar
+uh Vittorio asks how as you do the
+
+ align:start position:0%
+uh Vittorio asks how as you do the
+ 
+
+ align:start position:0%
+uh Vittorio asks how as you do the
+experiment with progressively heavier
+
+ align:start position:0%
+experiment with progressively heavier
+ 
+
+ align:start position:0%
+experiment with progressively heavier
+particles oh good question is there a
+
+ align:start position:0%
+particles oh good question is there a
+ 
+
+ align:start position:0%
+particles oh good question is there a
+certain point when the resulting pattern
+
+ align:start position:0%
+certain point when the resulting pattern
+ 
+
+ align:start position:0%
+certain point when the resulting pattern
+begins to look like what you'd expect
+
+ align:start position:0%
+begins to look like what you'd expect
+ 
+
+ align:start position:0%
+begins to look like what you'd expect
+from two bullets oh thank you Victoria
+
+ align:start position:0%
+from two bullets oh thank you Victoria
+ 
+
+ align:start position:0%
+from two bullets oh thank you Victoria
+what a wonderful question
+
+ align:start position:0%
+what a wonderful question
+ 
+
+ align:start position:0%
+what a wonderful question
+that is a question uh that is still
+
+ align:start position:0%
+that is a question uh that is still
+ 
+
+ align:start position:0%
+that is a question uh that is still
+occupying literally many of my friends
+
+ align:start position:0%
+occupying literally many of my friends
+ 
+
+ align:start position:0%
+occupying literally many of my friends
+let alone colleagues around the world
+
+ align:start position:0%
+let alone colleagues around the world
+ 
+
+ align:start position:0%
+let alone colleagues around the world
+the short answer is yes the longer
+
+ align:start position:0%
+the short answer is yes the longer
+ 
+
+ align:start position:0%
+the short answer is yes the longer
+answer is
+
+ align:start position:0%
+answer is
+ 
+
+ align:start position:0%
+answer is
+um is why and how and Jade's quite right
+
+ align:start position:0%
+um is why and how and Jade's quite right
+ 
+
+ align:start position:0%
+um is why and how and Jade's quite right
+uh Jade it puts in the chat this
+
+ align:start position:0%
+uh Jade it puts in the chat this
+ 
+
+ align:start position:0%
+uh Jade it puts in the chat this
+experiment has been done a comparable
+
+ align:start position:0%
+experiment has been done a comparable
+ 
+
+ align:start position:0%
+experiment has been done a comparable
+experiment with objects as large as
+
+ align:start position:0%
+experiment with objects as large as
+ 
+
+ align:start position:0%
+experiment with objects as large as
+Buckyballs C60 molecules of 60 carbon
+
+ align:start position:0%
+Buckyballs C60 molecules of 60 carbon
+ 
+
+ align:start position:0%
+Buckyballs C60 molecules of 60 carbon
+atoms in one bound State not just
+
+ align:start position:0%
+atoms in one bound State not just
+ 
+
+ align:start position:0%
+atoms in one bound State not just
+individual electrons so an object as
+
+ align:start position:0%
+individual electrons so an object as
+ 
+
+ align:start position:0%
+individual electrons so an object as
+long as large as a buckyball which is I
+
+ align:start position:0%
+long as large as a buckyball which is I
+ 
+
+ align:start position:0%
+long as large as a buckyball which is I
+think not a billion but several tens of
+
+ align:start position:0%
+think not a billion but several tens of
+ 
+
+ align:start position:0%
+think not a billion but several tens of
+millions of times larger than an
+
+ align:start position:0%
+millions of times larger than an
+ 
+
+ align:start position:0%
+millions of times larger than an
+individual electron
+
+ align:start position:0%
+individual electron
+ 
+
+ align:start position:0%
+individual electron
+we still find this characteristic
+
+ align:start position:0%
+we still find this characteristic
+ 
+
+ align:start position:0%
+we still find this characteristic
+Quantum interference very clearly again
+
+ align:start position:0%
+Quantum interference very clearly again
+ 
+
+ align:start position:0%
+Quantum interference very clearly again
+it's sort of uh well within statistical
+
+ align:start position:0%
+it's sort of uh well within statistical
+ 
+
+ align:start position:0%
+it's sort of uh well within statistical
+uh you know significance and in fact
+
+ align:start position:0%
+uh you know significance and in fact
+ 
+
+ align:start position:0%
+uh you know significance and in fact
+that's an experiment that one of my
+
+ align:start position:0%
+that's an experiment that one of my
+ 
+
+ align:start position:0%
+that's an experiment that one of my
+colleagues Anton zyler and his group had
+
+ align:start position:0%
+colleagues Anton zyler and his group had
+ 
+
+ align:start position:0%
+colleagues Anton zyler and his group had
+done quite some time ago
+
+ align:start position:0%
+done quite some time ago
+ 
+
+ align:start position:0%
+done quite some time ago
+so the question is where does that stop
+
+ align:start position:0%
+so the question is where does that stop
+ 
+
+ align:start position:0%
+so the question is where does that stop
+I had I had a very beloved physics
+
+ align:start position:0%
+I had I had a very beloved physics
+ 
+
+ align:start position:0%
+I had I had a very beloved physics
+professor of my own uh when I was an
+
+ align:start position:0%
+professor of my own uh when I was an
+ 
+
+ align:start position:0%
+professor of my own uh when I was an
+undergraduate it was very senior he'd
+
+ align:start position:0%
+undergraduate it was very senior he'd
+ 
+
+ align:start position:0%
+undergraduate it was very senior he'd
+actually just retired we're still
+
+ align:start position:0%
+actually just retired we're still
+ 
+
+ align:start position:0%
+actually just retired we're still
+teaching uh just for fun and he used to
+
+ align:start position:0%
+teaching uh just for fun and he used to
+ 
+
+ align:start position:0%
+teaching uh just for fun and he used to
+joke that when he was in graduate school
+
+ align:start position:0%
+joke that when he was in graduate school
+ 
+
+ align:start position:0%
+joke that when he was in graduate school
+he and his buddies would wonder could
+
+ align:start position:0%
+he and his buddies would wonder could
+ 
+
+ align:start position:0%
+he and his buddies would wonder could
+they get themselves to interfere if they
+
+ align:start position:0%
+they get themselves to interfere if they
+ 
+
+ align:start position:0%
+they get themselves to interfere if they
+rode their bicycle through two standing
+
+ align:start position:0%
+rode their bicycle through two standing
+ 
+
+ align:start position:0%
+rode their bicycle through two standing
+posts efficiently quickly like what
+
+ align:start position:0%
+posts efficiently quickly like what
+ 
+
+ align:start position:0%
+posts efficiently quickly like what
+something when when they don't interfere
+
+ align:start position:0%
+something when when they don't interfere
+ 
+
+ align:start position:0%
+something when when they don't interfere
+with themselves right an individual
+
+ align:start position:0%
+with themselves right an individual
+ 
+
+ align:start position:0%
+with themselves right an individual
+human on a bicycle doesn't undergo uh at
+
+ align:start position:0%
+human on a bicycle doesn't undergo uh at
+ 
+
+ align:start position:0%
+human on a bicycle doesn't undergo uh at
+least not in any obvious way this kind
+
+ align:start position:0%
+least not in any obvious way this kind
+ 
+
+ align:start position:0%
+least not in any obvious way this kind
+of interference it doesn't seem to
+
+ align:start position:0%
+of interference it doesn't seem to
+ 
+
+ align:start position:0%
+of interference it doesn't seem to
+happen with
+
+ align:start position:0%
+happen with
+ 
+
+ align:start position:0%
+happen with
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+with with things we could shrink down to
+
+ align:start position:0%
+with with things we could shrink down to
+ 
+
+ align:start position:0%
+with with things we could shrink down to
+look at microscopically uh at the scale
+
+ align:start position:0%
+look at microscopically uh at the scale
+ 
+
+ align:start position:0%
+look at microscopically uh at the scale
+of say amoebas which people have tried
+
+ align:start position:0%
+of say amoebas which people have tried
+ 
+
+ align:start position:0%
+of say amoebas which people have tried
+but it does happen with you know
+
+ align:start position:0%
+but it does happen with you know
+ 
+
+ align:start position:0%
+but it does happen with you know
+enormous molecules enormous on the size
+
+ align:start position:0%
+enormous molecules enormous on the size
+ 
+
+ align:start position:0%
+enormous molecules enormous on the size
+of parts of atoms so where is that line
+
+ align:start position:0%
+of parts of atoms so where is that line
+ 
+
+ align:start position:0%
+of parts of atoms so where is that line
+and and what causes the transition and
+
+ align:start position:0%
+and and what causes the transition and
+ 
+
+ align:start position:0%
+and and what causes the transition and
+behavior if we're all made up of atoms
+
+ align:start position:0%
+behavior if we're all made up of atoms
+ 
+
+ align:start position:0%
+behavior if we're all made up of atoms
+and electrons and electrons and atoms
+
+ align:start position:0%
+and electrons and electrons and atoms
+ 
+
+ align:start position:0%
+and electrons and electrons and atoms
+behave in this fundamentally quantum
+
+ align:start position:0%
+behave in this fundamentally quantum
+ 
+
+ align:start position:0%
+behave in this fundamentally quantum
+mechanical way why don't we why don't
+
+ align:start position:0%
+mechanical way why don't we why don't
+ 
+
+ align:start position:0%
+mechanical way why don't we why don't
+why why didn't my professor on his
+
+ align:start position:0%
+why why didn't my professor on his
+ 
+
+ align:start position:0%
+why why didn't my professor on his
+bicycle uh get diffracted when he when
+
+ align:start position:0%
+bicycle uh get diffracted when he when
+ 
+
+ align:start position:0%
+bicycle uh get diffracted when he when
+he biked through between two uh standing
+
+ align:start position:0%
+he biked through between two uh standing
+ 
+
+ align:start position:0%
+he biked through between two uh standing
+posts so that's what's often now called
+
+ align:start position:0%
+posts so that's what's often now called
+ 
+
+ align:start position:0%
+posts so that's what's often now called
+the the quantum to classical transition
+
+ align:start position:0%
+the the quantum to classical transition
+ 
+
+ align:start position:0%
+the the quantum to classical transition
+if you have nothing better to do with
+
+ align:start position:0%
+if you have nothing better to do with
+ 
+
+ align:start position:0%
+if you have nothing better to do with
+yourself in the next 17 years I suggest
+
+ align:start position:0%
+yourself in the next 17 years I suggest
+ 
+
+ align:start position:0%
+yourself in the next 17 years I suggest
+you start googling that and read every
+
+ align:start position:0%
+you start googling that and read every
+ 
+
+ align:start position:0%
+you start googling that and read every
+paper on it it's enormously complicated
+
+ align:start position:0%
+paper on it it's enormously complicated
+ 
+
+ align:start position:0%
+paper on it it's enormously complicated
+and still very much on the Forefront of
+
+ align:start position:0%
+and still very much on the Forefront of
+ 
+
+ align:start position:0%
+and still very much on the Forefront of
+the research Frontier for many people
+
+ align:start position:0%
+the research Frontier for many people
+ 
+
+ align:start position:0%
+the research Frontier for many people
+and we and we just January collectively
+
+ align:start position:0%
+and we and we just January collectively
+ 
+
+ align:start position:0%
+and we and we just January collectively
+the community genuinely doesn't know
+
+ align:start position:0%
+the community genuinely doesn't know
+ 
+
+ align:start position:0%
+the community genuinely doesn't know
+we're getting better at characterizing
+
+ align:start position:0%
+we're getting better at characterizing
+ 
+
+ align:start position:0%
+we're getting better at characterizing
+where the break is where the line is but
+
+ align:start position:0%
+where the break is where the line is but
+ 
+
+ align:start position:0%
+where the break is where the line is but
+not why and not what would cause the
+
+ align:start position:0%
+not why and not what would cause the
+ 
+
+ align:start position:0%
+not why and not what would cause the
+behavior to transition from one very
+
+ align:start position:0%
+behavior to transition from one very
+ 
+
+ align:start position:0%
+behavior to transition from one very
+specific kind of behavior to the other
+
+ align:start position:0%
+specific kind of behavior to the other
+ 
+
+ align:start position:0%
+specific kind of behavior to the other
+what about so other colleagues are
+
+ align:start position:0%
+what about so other colleagues are
+ 
+
+ align:start position:0%
+what about so other colleagues are
+trying to do this with living objects so
+
+ align:start position:0%
+trying to do this with living objects so
+ 
+
+ align:start position:0%
+trying to do this with living objects so
+it turns out viruses some kinds of
+
+ align:start position:0%
+it turns out viruses some kinds of
+ 
+
+ align:start position:0%
+it turns out viruses some kinds of
+viruses might be just small enough for
+
+ align:start position:0%
+viruses might be just small enough for
+ 
+
+ align:start position:0%
+viruses might be just small enough for
+this to work and yet much much bigger
+
+ align:start position:0%
+this to work and yet much much bigger
+ 
+
+ align:start position:0%
+this to work and yet much much bigger
+than Buckyballs so people are trying to
+
+ align:start position:0%
+than Buckyballs so people are trying to
+ 
+
+ align:start position:0%
+than Buckyballs so people are trying to
+get living things seemingly living
+
+ align:start position:0%
+get living things seemingly living
+ 
+
+ align:start position:0%
+get living things seemingly living
+things like viruses to Quantum age of
+
+ align:start position:0%
+things like viruses to Quantum age of
+ 
+
+ align:start position:0%
+things like viruses to Quantum age of
+fear that's not been done yet but that's
+
+ align:start position:0%
+fear that's not been done yet but that's
+ 
+
+ align:start position:0%
+fear that's not been done yet but that's
+one thing people are trying so this this
+
+ align:start position:0%
+one thing people are trying so this this
+ 
+
+ align:start position:0%
+one thing people are trying so this this
+question of how big could it get and
+
+ align:start position:0%
+question of how big could it get and
+ 
+
+ align:start position:0%
+question of how big could it get and
+still show this inherent quantumness
+
+ align:start position:0%
+still show this inherent quantumness
+ 
+
+ align:start position:0%
+still show this inherent quantumness
+that is uh still very much a live issue
+
+ align:start position:0%
+that is uh still very much a live issue
+ 
+
+ align:start position:0%
+that is uh still very much a live issue
+and and there's as it is too fast as to
+
+ align:start position:0%
+and and there's as it is too fast as to
+ 
+
+ align:start position:0%
+and and there's as it is too fast as to
+it what's the scale but even more subtly
+
+ align:start position:0%
+it what's the scale but even more subtly
+ 
+
+ align:start position:0%
+it what's the scale but even more subtly
+what's the reason why that stops working
+
+ align:start position:0%
+what's the reason why that stops working
+ 
+
+ align:start position:0%
+what's the reason why that stops working
+as we continue making it considering
+
+ align:start position:0%
+as we continue making it considering
+ 
+
+ align:start position:0%
+as we continue making it considering
+larger objects so so thank you for that
+
+ align:start position:0%
+larger objects so so thank you for that
+ 
+
+ align:start position:0%
+larger objects so so thank you for that
+question great question
+
+ align:start position:0%
+question great question
+ 
+
+ align:start position:0%
+question great question
+any other questions about the double
+
+ align:start position:0%
+any other questions about the double
+ 
+
+ align:start position:0%
+any other questions about the double
+slit about this um what should have been
+
+ align:start position:0%
+slit about this um what should have been
+ 
+
+ align:start position:0%
+slit about this um what should have been
+the the sort of you know the scream I
+
+ align:start position:0%
+the the sort of you know the scream I
+ 
+
+ align:start position:0%
+the the sort of you know the scream I
+mean all of these should have just been
+
+ align:start position:0%
+mean all of these should have just been
+ 
+
+ align:start position:0%
+mean all of these should have just been
+unmuted just
+
+ align:start position:0%
+unmuted just
+ 
+
+ align:start position:0%
+unmuted just
+just howling at the moon at least that's
+
+ align:start position:0%
+just howling at the moon at least that's
+ 
+
+ align:start position:0%
+just howling at the moon at least that's
+how I feel and I still think about this
+
+ align:start position:0%
+how I feel and I still think about this
+ 
+
+ align:start position:0%
+how I feel and I still think about this
+maybe that's maybe that's my problem I
+
+ align:start position:0%
+maybe that's maybe that's my problem I
+ 
+
+ align:start position:0%
+maybe that's maybe that's my problem I
+just find that just astonishing people
+
+ align:start position:0%
+just find that just astonishing people
+ 
+
+ align:start position:0%
+just find that just astonishing people
+that it's not just a thought experiment
+
+ align:start position:0%
+that it's not just a thought experiment
+ 
+
+ align:start position:0%
+that it's not just a thought experiment
+we can do that now with individual
+
+ align:start position:0%
+we can do that now with individual
+ 
+
+ align:start position:0%
+we can do that now with individual
+Quantum with super careful control on
+
+ align:start position:0%
+Quantum with super careful control on
+ 
+
+ align:start position:0%
+Quantum with super careful control on
+our source on our detectors have really
+
+ align:start position:0%
+our source on our detectors have really
+ 
+
+ align:start position:0%
+our source on our detectors have really
+extraordinarily High statistical
+
+ align:start position:0%
+extraordinarily High statistical
+ 
+
+ align:start position:0%
+extraordinarily High statistical
+significance on all the measurements
+
+ align:start position:0%
+significance on all the measurements
+ 
+
+ align:start position:0%
+significance on all the measurements
+and and fire what looked for all intents
+
+ align:start position:0%
+and and fire what looked for all intents
+ 
+
+ align:start position:0%
+and and fire what looked for all intents
+and purpose to be like little tiny
+
+ align:start position:0%
+and purpose to be like little tiny
+ 
+
+ align:start position:0%
+and purpose to be like little tiny
+baseballs
+
+ align:start position:0%
+baseballs
+ 
+
+ align:start position:0%
+baseballs
+and somehow they know somehow their
+
+ align:start position:0%
+and somehow they know somehow their
+ 
+
+ align:start position:0%
+and somehow they know somehow their
+behavior is guided in a way that that
+
+ align:start position:0%
+behavior is guided in a way that that
+ 
+
+ align:start position:0%
+behavior is guided in a way that that
+baseballs and bullets just just aren't
+
+ align:start position:0%
+baseballs and bullets just just aren't
+ 
+
+ align:start position:0%
+baseballs and bullets just just aren't
+your basketballs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if that's just okay for all of you then
+
+ align:start position:0%
+if that's just okay for all of you then
+ 
+
+ align:start position:0%
+if that's just okay for all of you then
+I mean come on that's just like that's
+
+ align:start position:0%
+I mean come on that's just like that's
+ 
+
+ align:start position:0%
+I mean come on that's just like that's
+covet speaking that should just
+
+ align:start position:0%
+covet speaking that should just
+ 
+
+ align:start position:0%
+covet speaking that should just
+okay you get the point any other
+
+ align:start position:0%
+okay you get the point any other
+ 
+
+ align:start position:0%
+okay you get the point any other
+questions on either my mental state or
+
+ align:start position:0%
+questions on either my mental state or
+ 
+
+ align:start position:0%
+questions on either my mental state or
+emotional state or on uh the double slit
+
+ align:start position:0%
+emotional state or on uh the double slit
+ 
+
+ align:start position:0%
+emotional state or on uh the double slit
+experiment if not we'll go into one last
+
+ align:start position:0%
+experiment if not we'll go into one last
+ 
+
+ align:start position:0%
+experiment if not we'll go into one last
+little part one kind of Coda for double
+
+ align:start position:0%
+little part one kind of Coda for double
+ 
+
+ align:start position:0%
+little part one kind of Coda for double
+sit and then we'll have time for
+
+ align:start position:0%
+sit and then we'll have time for
+ 
+
+ align:start position:0%
+sit and then we'll have time for
+questions as well
+
+ align:start position:0%
+questions as well
+ 
+
+ align:start position:0%
+questions as well
+okay so I'll get it together I'll put
+
+ align:start position:0%
+okay so I'll get it together I'll put
+ 
+
+ align:start position:0%
+okay so I'll get it together I'll put
+myself together I'll talk now about this
+
+ align:start position:0%
+myself together I'll talk now about this
+ 
+
+ align:start position:0%
+myself together I'll talk now about this
+last part uh which also started being
+
+ align:start position:0%
+last part uh which also started being
+ 
+
+ align:start position:0%
+last part uh which also started being
+thought thought about very early uh even
+
+ align:start position:0%
+thought thought about very early uh even
+ 
+
+ align:start position:0%
+thought thought about very early uh even
+in the in the late 1920s as further ways
+
+ align:start position:0%
+in the in the late 1920s as further ways
+ 
+
+ align:start position:0%
+in the in the late 1920s as further ways
+to try to probe what's going on when we
+
+ align:start position:0%
+to try to probe what's going on when we
+ 
+
+ align:start position:0%
+to try to probe what's going on when we
+think about this Quantum level so again
+
+ align:start position:0%
+think about this Quantum level so again
+ 
+
+ align:start position:0%
+think about this Quantum level so again
+this I'm going to do especially
+
+ align:start position:0%
+this I'm going to do especially
+ 
+
+ align:start position:0%
+this I'm going to do especially
+schematically in in the class session
+
+ align:start position:0%
+schematically in in the class session
+ 
+
+ align:start position:0%
+schematically in in the class session
+there is a bit more uh explicit
+
+ align:start position:0%
+there is a bit more uh explicit
+ 
+
+ align:start position:0%
+there is a bit more uh explicit
+discussion in the in the optional
+
+ align:start position:0%
+discussion in the in the optional
+ 
+
+ align:start position:0%
+discussion in the in the optional
+lecture notes on the course site
+
+ align:start position:0%
+lecture notes on the course site
+ 
+
+ align:start position:0%
+lecture notes on the course site
+let's go back to that same setup the one
+
+ align:start position:0%
+let's go back to that same setup the one
+ 
+
+ align:start position:0%
+let's go back to that same setup the one
+we just ended on let's say we're sending
+
+ align:start position:0%
+we just ended on let's say we're sending
+ 
+
+ align:start position:0%
+we just ended on let's say we're sending
+one electron at a time uh waiting in you
+
+ align:start position:0%
+one electron at a time uh waiting in you
+ 
+
+ align:start position:0%
+one electron at a time uh waiting in you
+know uh ample time in between
+
+ align:start position:0%
+know uh ample time in between
+ 
+
+ align:start position:0%
+know uh ample time in between
+firing them toward this this uh system
+
+ align:start position:0%
+firing them toward this this uh system
+ 
+
+ align:start position:0%
+firing them toward this this uh system
+with a where the distance between this A
+
+ align:start position:0%
+with a where the distance between this A
+ 
+
+ align:start position:0%
+with a where the distance between this A
+and B is much much larger than uh the
+
+ align:start position:0%
+and B is much much larger than uh the
+ 
+
+ align:start position:0%
+and B is much much larger than uh the
+kind of characteristic size of of the
+
+ align:start position:0%
+kind of characteristic size of of the
+ 
+
+ align:start position:0%
+kind of characteristic size of of the
+particles themselves but now we want to
+
+ align:start position:0%
+particles themselves but now we want to
+ 
+
+ align:start position:0%
+particles themselves but now we want to
+say these particles clearly must have
+
+ align:start position:0%
+say these particles clearly must have
+ 
+
+ align:start position:0%
+say these particles clearly must have
+gone through either slit a or split B
+
+ align:start position:0%
+gone through either slit a or split B
+ 
+
+ align:start position:0%
+gone through either slit a or split B
+that seems like a reasonable
+
+ align:start position:0%
+that seems like a reasonable
+ 
+
+ align:start position:0%
+that seems like a reasonable
+question to ponder which slit do they
+
+ align:start position:0%
+question to ponder which slit do they
+ 
+
+ align:start position:0%
+question to ponder which slit do they
+pass through on any individual
+
+ align:start position:0%
+pass through on any individual
+ 
+
+ align:start position:0%
+pass through on any individual
+experimental rut the distance between
+
+ align:start position:0%
+experimental rut the distance between
+ 
+
+ align:start position:0%
+experimental rut the distance between
+this the slits is so much larger than
+
+ align:start position:0%
+this the slits is so much larger than
+ 
+
+ align:start position:0%
+this the slits is so much larger than
+the character size the the each particle
+
+ align:start position:0%
+the character size the the each particle
+ 
+
+ align:start position:0%
+the character size the the each particle
+must have had to have selected must have
+
+ align:start position:0%
+must have had to have selected must have
+ 
+
+ align:start position:0%
+must have had to have selected must have
+had to have chosen to go through either
+
+ align:start position:0%
+had to have chosen to go through either
+ 
+
+ align:start position:0%
+had to have chosen to go through either
+slit a or slit B
+
+ align:start position:0%
+slit a or slit B
+ 
+
+ align:start position:0%
+slit a or slit B
+so why don't we try to find out and this
+
+ align:start position:0%
+so why don't we try to find out and this
+ 
+
+ align:start position:0%
+so why don't we try to find out and this
+was a very clever idea Heisenberg
+
+ align:start position:0%
+was a very clever idea Heisenberg
+ 
+
+ align:start position:0%
+was a very clever idea Heisenberg
+lectures on this even in those 1929
+
+ align:start position:0%
+lectures on this even in those 1929
+ 
+
+ align:start position:0%
+lectures on this even in those 1929
+lectures and others have developed it
+
+ align:start position:0%
+lectures and others have developed it
+ 
+
+ align:start position:0%
+lectures and others have developed it
+since then let's put a bunch of test
+
+ align:start position:0%
+since then let's put a bunch of test
+ 
+
+ align:start position:0%
+since then let's put a bunch of test
+particles behind only one of the slits
+
+ align:start position:0%
+particles behind only one of the slits
+ 
+
+ align:start position:0%
+particles behind only one of the slits
+so that way it'll be like an alarm
+
+ align:start position:0%
+so that way it'll be like an alarm
+ 
+
+ align:start position:0%
+so that way it'll be like an alarm
+system if an electron happens to go
+
+ align:start position:0%
+system if an electron happens to go
+ 
+
+ align:start position:0%
+system if an electron happens to go
+through slit a it'll it'll smack into
+
+ align:start position:0%
+through slit a it'll it'll smack into
+ 
+
+ align:start position:0%
+through slit a it'll it'll smack into
+these test particles we'll have
+
+ align:start position:0%
+these test particles we'll have
+ 
+
+ align:start position:0%
+these test particles we'll have
+collisions we'll have scattered
+
+ align:start position:0%
+collisions we'll have scattered
+ 
+
+ align:start position:0%
+collisions we'll have scattered
+particles zooming out of this region of
+
+ align:start position:0%
+particles zooming out of this region of
+ 
+
+ align:start position:0%
+particles zooming out of this region of
+the experiment that we could then detect
+
+ align:start position:0%
+the experiment that we could then detect
+ 
+
+ align:start position:0%
+the experiment that we could then detect
+and measure and if no test particles are
+
+ align:start position:0%
+and measure and if no test particles are
+ 
+
+ align:start position:0%
+and measure and if no test particles are
+scattered then we know the electron must
+
+ align:start position:0%
+scattered then we know the electron must
+ 
+
+ align:start position:0%
+scattered then we know the electron must
+have gone through the other slip so
+
+ align:start position:0%
+have gone through the other slip so
+ 
+
+ align:start position:0%
+have gone through the other slip so
+we're going to Bunch together get in a
+
+ align:start position:0%
+we're going to Bunch together get in a
+ 
+
+ align:start position:0%
+we're going to Bunch together get in a
+kind of close in space some targets
+
+ align:start position:0%
+kind of close in space some targets
+ 
+
+ align:start position:0%
+kind of close in space some targets
+behind only one of the two open slits
+
+ align:start position:0%
+behind only one of the two open slits
+ 
+
+ align:start position:0%
+behind only one of the two open slits
+and that way we have what's called a
+
+ align:start position:0%
+and that way we have what's called a
+ 
+
+ align:start position:0%
+and that way we have what's called a
+slit detector we have some mechanism of
+
+ align:start position:0%
+slit detector we have some mechanism of
+ 
+
+ align:start position:0%
+slit detector we have some mechanism of
+determining event by event through which
+
+ align:start position:0%
+determining event by event through which
+ 
+
+ align:start position:0%
+determining event by event through which
+slit the particle actually passed
+
+ align:start position:0%
+slit the particle actually passed
+ 
+
+ align:start position:0%
+slit the particle actually passed
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and so now what happens when both slits
+
+ align:start position:0%
+and so now what happens when both slits
+ 
+
+ align:start position:0%
+and so now what happens when both slits
+are open but we measure through these
+
+ align:start position:0%
+are open but we measure through these
+ 
+
+ align:start position:0%
+are open but we measure through these
+slip detectors through which slit each
+
+ align:start position:0%
+slip detectors through which slit each
+ 
+
+ align:start position:0%
+slip detectors through which slit each
+electron passed then the distribution
+
+ align:start position:0%
+electron passed then the distribution
+ 
+
+ align:start position:0%
+electron passed then the distribution
+even for these quantum mechanical
+
+ align:start position:0%
+even for these quantum mechanical
+ 
+
+ align:start position:0%
+even for these quantum mechanical
+electrons the distribution reverts back
+
+ align:start position:0%
+electrons the distribution reverts back
+ 
+
+ align:start position:0%
+electrons the distribution reverts back
+to this thoroughly
+
+ align:start position:0%
+to this thoroughly
+ 
+
+ align:start position:0%
+to this thoroughly
+classical sum of two independent
+
+ align:start position:0%
+classical sum of two independent
+ 
+
+ align:start position:0%
+classical sum of two independent
+probabilities
+
+ align:start position:0%
+probabilities
+ 
+
+ align:start position:0%
+probabilities
+so we do our usual experiment we do this
+
+ align:start position:0%
+so we do our usual experiment we do this
+ 
+
+ align:start position:0%
+so we do our usual experiment we do this
+10 000 times sometimes we see the
+
+ align:start position:0%
+10 000 times sometimes we see the
+ 
+
+ align:start position:0%
+10 000 times sometimes we see the
+scattered particles from behind slit a
+
+ align:start position:0%
+scattered particles from behind slit a
+ 
+
+ align:start position:0%
+scattered particles from behind slit a
+sometimes we see no scattered particles
+
+ align:start position:0%
+sometimes we see no scattered particles
+ 
+
+ align:start position:0%
+sometimes we see no scattered particles
+it must have gone through slip B and
+
+ align:start position:0%
+it must have gone through slip B and
+ 
+
+ align:start position:0%
+it must have gone through slip B and
+then separately from that we count up
+
+ align:start position:0%
+then separately from that we count up
+ 
+
+ align:start position:0%
+then separately from that we count up
+where do all the electrons actually wind
+
+ align:start position:0%
+where do all the electrons actually wind
+ 
+
+ align:start position:0%
+where do all the electrons actually wind
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+at that backstop with our closely spaced
+
+ align:start position:0%
+at that backstop with our closely spaced
+ 
+
+ align:start position:0%
+at that backstop with our closely spaced
+detectors and we get basically the
+
+ align:start position:0%
+detectors and we get basically the
+ 
+
+ align:start position:0%
+detectors and we get basically the
+classical distribution it looks like the
+
+ align:start position:0%
+classical distribution it looks like the
+ 
+
+ align:start position:0%
+classical distribution it looks like the
+sum of two independent classical
+
+ align:start position:0%
+sum of two independent classical
+ 
+
+ align:start position:0%
+sum of two independent classical
+particle-like distributions when we ask
+
+ align:start position:0%
+particle-like distributions when we ask
+ 
+
+ align:start position:0%
+particle-like distributions when we ask
+through which slit each individual each
+
+ align:start position:0%
+through which slit each individual each
+ 
+
+ align:start position:0%
+through which slit each individual each
+individual particle passed the particles
+
+ align:start position:0%
+individual particle passed the particles
+ 
+
+ align:start position:0%
+individual particle passed the particles
+give us a particle-like answer they pass
+
+ align:start position:0%
+give us a particle-like answer they pass
+ 
+
+ align:start position:0%
+give us a particle-like answer they pass
+through I just let a or slit B and had
+
+ align:start position:0%
+through I just let a or slit B and had
+ 
+
+ align:start position:0%
+through I just let a or slit B and had
+correspondingly no interference pattern
+
+ align:start position:0%
+correspondingly no interference pattern
+ 
+
+ align:start position:0%
+correspondingly no interference pattern
+between those two options
+
+ align:start position:0%
+between those two options
+ 
+
+ align:start position:0%
+between those two options
+on the other hand I mean don't even try
+
+ align:start position:0%
+on the other hand I mean don't even try
+ 
+
+ align:start position:0%
+on the other hand I mean don't even try
+to ask through which slit do those
+
+ align:start position:0%
+to ask through which slit do those
+ 
+
+ align:start position:0%
+to ask through which slit do those
+individual particles pass we remove that
+
+ align:start position:0%
+individual particles pass we remove that
+ 
+
+ align:start position:0%
+individual particles pass we remove that
+slit detector altogether then we get
+
+ align:start position:0%
+slit detector altogether then we get
+ 
+
+ align:start position:0%
+slit detector altogether then we get
+back to the results that we'd already
+
+ align:start position:0%
+back to the results that we'd already
+ 
+
+ align:start position:0%
+back to the results that we'd already
+found that when both slits are open we
+
+ align:start position:0%
+found that when both slits are open we
+ 
+
+ align:start position:0%
+found that when both slits are open we
+get this characteristic wave like
+
+ align:start position:0%
+get this characteristic wave like
+ 
+
+ align:start position:0%
+get this characteristic wave like
+interference pattern for and we only get
+
+ align:start position:0%
+interference pattern for and we only get
+ 
+
+ align:start position:0%
+interference pattern for and we only get
+that when we've given up even the
+
+ align:start position:0%
+that when we've given up even the
+ 
+
+ align:start position:0%
+that when we've given up even the
+opportunity to ask this particle-like
+
+ align:start position:0%
+opportunity to ask this particle-like
+ 
+
+ align:start position:0%
+opportunity to ask this particle-like
+question about which slit uh had
+
+ align:start position:0%
+question about which slit uh had
+ 
+
+ align:start position:0%
+question about which slit uh had
+actually uh through which that had
+
+ align:start position:0%
+actually uh through which that had
+ 
+
+ align:start position:0%
+actually uh through which that had
+individual particles passed so we are
+
+ align:start position:0%
+individual particles passed so we are
+ 
+
+ align:start position:0%
+individual particles passed so we are
+allowed to ask a question we actually
+
+ align:start position:0%
+allowed to ask a question we actually
+ 
+
+ align:start position:0%
+allowed to ask a question we actually
+can ask the question that people have
+
+ align:start position:0%
+can ask the question that people have
+ 
+
+ align:start position:0%
+can ask the question that people have
+done it with a slightly more
+
+ align:start position:0%
+done it with a slightly more
+ 
+
+ align:start position:0%
+done it with a slightly more
+sophisticated version than just that
+
+ align:start position:0%
+sophisticated version than just that
+ 
+
+ align:start position:0%
+sophisticated version than just that
+cartoon and yet somehow the nature of
+
+ align:start position:0%
+cartoon and yet somehow the nature of
+ 
+
+ align:start position:0%
+cartoon and yet somehow the nature of
+the results changes very deeply and
+
+ align:start position:0%
+the results changes very deeply and
+ 
+
+ align:start position:0%
+the results changes very deeply and
+fundamentally based on the nature of the
+
+ align:start position:0%
+fundamentally based on the nature of the
+ 
+
+ align:start position:0%
+fundamentally based on the nature of the
+question we asked
+
+ align:start position:0%
+question we asked
+ 
+
+ align:start position:0%
+question we asked
+so again you can see why that happens
+
+ align:start position:0%
+so again you can see why that happens
+ 
+
+ align:start position:0%
+so again you can see why that happens
+that's really I'm being pretty schematic
+
+ align:start position:0%
+that's really I'm being pretty schematic
+ 
+
+ align:start position:0%
+that's really I'm being pretty schematic
+and kind of waving my hands it's only a
+
+ align:start position:0%
+and kind of waving my hands it's only a
+ 
+
+ align:start position:0%
+and kind of waving my hands it's only a
+couple lines of algebra and you might
+
+ align:start position:0%
+couple lines of algebra and you might
+ 
+
+ align:start position:0%
+couple lines of algebra and you might
+have already guessed it if I go back to
+
+ align:start position:0%
+have already guessed it if I go back to
+ 
+
+ align:start position:0%
+have already guessed it if I go back to
+cartoon
+
+ align:start position:0%
+cartoon
+ 
+
+ align:start position:0%
+cartoon
+just to say quickly what's going to
+
+ align:start position:0%
+just to say quickly what's going to
+ 
+
+ align:start position:0%
+just to say quickly what's going to
+happen here in order for this to be a
+
+ align:start position:0%
+happen here in order for this to be a
+ 
+
+ align:start position:0%
+happen here in order for this to be a
+reliable slip detector this bundle of
+
+ align:start position:0%
+reliable slip detector this bundle of
+ 
+
+ align:start position:0%
+reliable slip detector this bundle of
+particles has to really be behind a and
+
+ align:start position:0%
+particles has to really be behind a and
+ 
+
+ align:start position:0%
+particles has to really be behind a and
+not behind B that means that the spread
+
+ align:start position:0%
+not behind B that means that the spread
+ 
+
+ align:start position:0%
+not behind B that means that the spread
+in space can't be arbitrarily large if
+
+ align:start position:0%
+in space can't be arbitrarily large if
+ 
+
+ align:start position:0%
+in space can't be arbitrarily large if
+we call this vertical Direction the Y
+
+ align:start position:0%
+we call this vertical Direction the Y
+ 
+
+ align:start position:0%
+we call this vertical Direction the Y
+Direction like my arrow here shows then
+
+ align:start position:0%
+Direction like my arrow here shows then
+ 
+
+ align:start position:0%
+Direction like my arrow here shows then
+the Delta y of this distribution can't
+
+ align:start position:0%
+the Delta y of this distribution can't
+ 
+
+ align:start position:0%
+the Delta y of this distribution can't
+be too big in fact it has to be much
+
+ align:start position:0%
+be too big in fact it has to be much
+ 
+
+ align:start position:0%
+be too big in fact it has to be much
+smaller than the distance d
+
+ align:start position:0%
+smaller than the distance d
+ 
+
+ align:start position:0%
+smaller than the distance d
+if the distribution were too big then we
+
+ align:start position:0%
+if the distribution were too big then we
+ 
+
+ align:start position:0%
+if the distribution were too big then we
+could see that test particles were
+
+ align:start position:0%
+could see that test particles were
+ 
+
+ align:start position:0%
+could see that test particles were
+scattered into but they would no longer
+
+ align:start position:0%
+scattered into but they would no longer
+ 
+
+ align:start position:0%
+scattered into but they would no longer
+tell us whether the particle had gone
+
+ align:start position:0%
+tell us whether the particle had gone
+ 
+
+ align:start position:0%
+tell us whether the particle had gone
+through a or slip B we would lose the
+
+ align:start position:0%
+through a or slip B we would lose the
+ 
+
+ align:start position:0%
+through a or slip B we would lose the
+resolution in space if the if the bundle
+
+ align:start position:0%
+resolution in space if the if the bundle
+ 
+
+ align:start position:0%
+resolution in space if the if the bundle
+of particles was too far spread out in
+
+ align:start position:0%
+of particles was too far spread out in
+ 
+
+ align:start position:0%
+of particles was too far spread out in
+the y direction so we have to contain or
+
+ align:start position:0%
+the y direction so we have to contain or
+ 
+
+ align:start position:0%
+the y direction so we have to contain or
+compress the distribution of test
+
+ align:start position:0%
+compress the distribution of test
+ 
+
+ align:start position:0%
+compress the distribution of test
+particles within a small region Delta y
+
+ align:start position:0%
+particles within a small region Delta y
+ 
+
+ align:start position:0%
+particles within a small region Delta y
+but that means they must have a
+
+ align:start position:0%
+but that means they must have a
+ 
+
+ align:start position:0%
+but that means they must have a
+correspondingly large uncertainty in the
+
+ align:start position:0%
+correspondingly large uncertainty in the
+ 
+
+ align:start position:0%
+correspondingly large uncertainty in the
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+because of the uncertainty principle and
+
+ align:start position:0%
+because of the uncertainty principle and
+ 
+
+ align:start position:0%
+because of the uncertainty principle and
+therefore there'll be a correspondingly
+
+ align:start position:0%
+therefore there'll be a correspondingly
+ 
+
+ align:start position:0%
+therefore there'll be a correspondingly
+large uncertainty in The Recoil momentum
+
+ align:start position:0%
+large uncertainty in The Recoil momentum
+ 
+
+ align:start position:0%
+large uncertainty in The Recoil momentum
+of the electron after scattering of
+
+ align:start position:0%
+of the electron after scattering of
+ 
+
+ align:start position:0%
+of the electron after scattering of
+exactly the right amount this part's
+
+ align:start position:0%
+exactly the right amount this part's
+ 
+
+ align:start position:0%
+exactly the right amount this part's
+kind of amazing of exactly the right
+
+ align:start position:0%
+kind of amazing of exactly the right
+ 
+
+ align:start position:0%
+kind of amazing of exactly the right
+amount needed to perfectly wash out
+
+ align:start position:0%
+amount needed to perfectly wash out
+ 
+
+ align:start position:0%
+amount needed to perfectly wash out
+those very clear interference fringes to
+
+ align:start position:0%
+those very clear interference fringes to
+ 
+
+ align:start position:0%
+those very clear interference fringes to
+get back to two bell-shaped curves and
+
+ align:start position:0%
+get back to two bell-shaped curves and
+ 
+
+ align:start position:0%
+get back to two bell-shaped curves and
+so that very uh regular very narrow
+
+ align:start position:0%
+so that very uh regular very narrow
+ 
+
+ align:start position:0%
+so that very uh regular very narrow
+peaks of the interference changes so
+
+ align:start position:0%
+peaks of the interference changes so
+ 
+
+ align:start position:0%
+peaks of the interference changes so
+it's literally the uncertainty principle
+
+ align:start position:0%
+it's literally the uncertainty principle
+ 
+
+ align:start position:0%
+it's literally the uncertainty principle
+that precludes
+
+ align:start position:0%
+that precludes
+ 
+
+ align:start position:0%
+that precludes
+being able to both measure through which
+
+ align:start position:0%
+being able to both measure through which
+ 
+
+ align:start position:0%
+being able to both measure through which
+slits an individual particle past and
+
+ align:start position:0%
+slits an individual particle past and
+ 
+
+ align:start position:0%
+slits an individual particle past and
+also retain these very clear uh features
+
+ align:start position:0%
+also retain these very clear uh features
+ 
+
+ align:start position:0%
+also retain these very clear uh features
+of the interference pattern that's
+
+ align:start position:0%
+of the interference pattern that's
+ 
+
+ align:start position:0%
+of the interference pattern that's
+pretty I think it's pretty amazing and
+
+ align:start position:0%
+pretty I think it's pretty amazing and
+ 
+
+ align:start position:0%
+pretty I think it's pretty amazing and
+very beautiful and it's only a couple
+
+ align:start position:0%
+very beautiful and it's only a couple
+ 
+
+ align:start position:0%
+very beautiful and it's only a couple
+lines of algebra to show so if that if
+
+ align:start position:0%
+lines of algebra to show so if that if
+ 
+
+ align:start position:0%
+lines of algebra to show so if that if
+even this most recent hand waving uh
+
+ align:start position:0%
+even this most recent hand waving uh
+ 
+
+ align:start position:0%
+even this most recent hand waving uh
+effort of mine is was too quick I
+
+ align:start position:0%
+effort of mine is was too quick I
+ 
+
+ align:start position:0%
+effort of mine is was too quick I
+encourage you to look at the lecture
+
+ align:start position:0%
+encourage you to look at the lecture
+ 
+
+ align:start position:0%
+encourage you to look at the lecture
+notes but that's the upshot
+
+ align:start position:0%
+notes but that's the upshot
+ 
+
+ align:start position:0%
+notes but that's the upshot
+so so what we really finding
+
+ align:start position:0%
+so so what we really finding
+ 
+
+ align:start position:0%
+so so what we really finding
+conceptually and this is what people
+
+ align:start position:0%
+conceptually and this is what people
+ 
+
+ align:start position:0%
+conceptually and this is what people
+began to kind of uh converge around by
+
+ align:start position:0%
+began to kind of uh converge around by
+ 
+
+ align:start position:0%
+began to kind of uh converge around by
+even by the late 1920s
+
+ align:start position:0%
+even by the late 1920s
+ 
+
+ align:start position:0%
+even by the late 1920s
+was if we ask a kind of particle-like
+
+ align:start position:0%
+was if we ask a kind of particle-like
+ 
+
+ align:start position:0%
+was if we ask a kind of particle-like
+question such as what was your path
+
+ align:start position:0%
+question such as what was your path
+ 
+
+ align:start position:0%
+question such as what was your path
+through which slit did an individual
+
+ align:start position:0%
+through which slit did an individual
+ 
+
+ align:start position:0%
+through which slit did an individual
+particle pass we will get a definite
+
+ align:start position:0%
+particle pass we will get a definite
+ 
+
+ align:start position:0%
+particle pass we will get a definite
+answer we'll get a particle-like answer
+
+ align:start position:0%
+answer we'll get a particle-like answer
+ 
+
+ align:start position:0%
+answer we'll get a particle-like answer
+each particle either went through a or
+
+ align:start position:0%
+each particle either went through a or
+ 
+
+ align:start position:0%
+each particle either went through a or
+wet through slip B with corresponding
+
+ align:start position:0%
+wet through slip B with corresponding
+ 
+
+ align:start position:0%
+wet through slip B with corresponding
+kind of particle-like Statistics it's
+
+ align:start position:0%
+kind of particle-like Statistics it's
+ 
+
+ align:start position:0%
+kind of particle-like Statistics it's
+all consistent we'll get a clear answer
+
+ align:start position:0%
+all consistent we'll get a clear answer
+ 
+
+ align:start position:0%
+all consistent we'll get a clear answer
+and the whole rest of the problem will
+
+ align:start position:0%
+and the whole rest of the problem will
+ 
+
+ align:start position:0%
+and the whole rest of the problem will
+be consistent with particle-like
+
+ align:start position:0%
+be consistent with particle-like
+ 
+
+ align:start position:0%
+be consistent with particle-like
+questions and answers
+
+ align:start position:0%
+questions and answers
+ 
+
+ align:start position:0%
+questions and answers
+on the other hand if we ask a wave-like
+
+ align:start position:0%
+on the other hand if we ask a wave-like
+ 
+
+ align:start position:0%
+on the other hand if we ask a wave-like
+question how does this wave function
+
+ align:start position:0%
+question how does this wave function
+ 
+
+ align:start position:0%
+question how does this wave function
+evolve in the in the region between the
+
+ align:start position:0%
+evolve in the in the region between the
+ 
+
+ align:start position:0%
+evolve in the in the region between the
+slits and the detector for example then
+
+ align:start position:0%
+slits and the detector for example then
+ 
+
+ align:start position:0%
+slits and the detector for example then
+we'll get a wave-like answer the way the
+
+ align:start position:0%
+we'll get a wave-like answer the way the
+ 
+
+ align:start position:0%
+we'll get a wave-like answer the way the
+probability amplitude is schroding a
+
+ align:start position:0%
+probability amplitude is schroding a
+ 
+
+ align:start position:0%
+probability amplitude is schroding a
+wave function will spread out in space
+
+ align:start position:0%
+wave function will spread out in space
+ 
+
+ align:start position:0%
+wave function will spread out in space
+and some regions they'll be constructive
+
+ align:start position:0%
+and some regions they'll be constructive
+ 
+
+ align:start position:0%
+and some regions they'll be constructive
+interference and the likelihood defined
+
+ align:start position:0%
+interference and the likelihood defined
+ 
+
+ align:start position:0%
+interference and the likelihood defined
+electron will be higher in other regions
+
+ align:start position:0%
+electron will be higher in other regions
+ 
+
+ align:start position:0%
+electron will be higher in other regions
+of space you'll get destructed
+
+ align:start position:0%
+of space you'll get destructed
+ 
+
+ align:start position:0%
+of space you'll get destructed
+interference because corresponding is
+
+ align:start position:0%
+interference because corresponding is
+ 
+
+ align:start position:0%
+interference because corresponding is
+lower likelihood for an electron to be
+
+ align:start position:0%
+lower likelihood for an electron to be
+ 
+
+ align:start position:0%
+lower likelihood for an electron to be
+found but we we only get wave-like
+
+ align:start position:0%
+found but we we only get wave-like
+ 
+
+ align:start position:0%
+found but we we only get wave-like
+answers when we ask wave-like questions
+
+ align:start position:0%
+answers when we ask wave-like questions
+ 
+
+ align:start position:0%
+answers when we ask wave-like questions
+so let me summarize and we'll have a few
+
+ align:start position:0%
+so let me summarize and we'll have a few
+ 
+
+ align:start position:0%
+so let me summarize and we'll have a few
+moments for some discussion and
+
+ align:start position:0%
+moments for some discussion and
+ 
+
+ align:start position:0%
+moments for some discussion and
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+so in a really quite limited span of
+
+ align:start position:0%
+so in a really quite limited span of
+ 
+
+ align:start position:0%
+so in a really quite limited span of
+time really in less than a whole
+
+ align:start position:0%
+time really in less than a whole
+ 
+
+ align:start position:0%
+time really in less than a whole
+calendar year between spring of 1925 and
+
+ align:start position:0%
+calendar year between spring of 1925 and
+ 
+
+ align:start position:0%
+calendar year between spring of 1925 and
+spring of 1926 both Nano Heisenberg and
+
+ align:start position:0%
+spring of 1926 both Nano Heisenberg and
+ 
+
+ align:start position:0%
+spring of 1926 both Nano Heisenberg and
+separately Eric schreiker introduced
+
+ align:start position:0%
+separately Eric schreiker introduced
+ 
+
+ align:start position:0%
+separately Eric schreiker introduced
+whole new approaches to what they were
+
+ align:start position:0%
+whole new approaches to what they were
+ 
+
+ align:start position:0%
+whole new approaches to what they were
+seeking a kind of first principles
+
+ align:start position:0%
+seeking a kind of first principles
+ 
+
+ align:start position:0%
+seeking a kind of first principles
+theory of the quantum realm a quantum
+
+ align:start position:0%
+theory of the quantum realm a quantum
+ 
+
+ align:start position:0%
+theory of the quantum realm a quantum
+mechanics rather than this kind of grab
+
+ align:start position:0%
+mechanics rather than this kind of grab
+ 
+
+ align:start position:0%
+mechanics rather than this kind of grab
+bag of ad hoc Quantum conditions
+
+ align:start position:0%
+bag of ad hoc Quantum conditions
+ 
+
+ align:start position:0%
+bag of ad hoc Quantum conditions
+so you're looking for this quantitative
+
+ align:start position:0%
+so you're looking for this quantitative
+ 
+
+ align:start position:0%
+so you're looking for this quantitative
+description of the atomic realm that had
+
+ align:start position:0%
+description of the atomic realm that had
+ 
+
+ align:start position:0%
+description of the atomic realm that had
+certain Quantum ideas built in from the
+
+ align:start position:0%
+certain Quantum ideas built in from the
+ 
+
+ align:start position:0%
+certain Quantum ideas built in from the
+start discrete spectral lines from
+
+ align:start position:0%
+start discrete spectral lines from
+ 
+
+ align:start position:0%
+start discrete spectral lines from
+excited atoms debris wave matter waves
+
+ align:start position:0%
+excited atoms debris wave matter waves
+ 
+
+ align:start position:0%
+excited atoms debris wave matter waves
+and so on rather than kind of stapling
+
+ align:start position:0%
+and so on rather than kind of stapling
+ 
+
+ align:start position:0%
+and so on rather than kind of stapling
+these on at the end
+
+ align:start position:0%
+these on at the end
+ 
+
+ align:start position:0%
+these on at the end
+now these approaches looked quite
+
+ align:start position:0%
+now these approaches looked quite
+ 
+
+ align:start position:0%
+now these approaches looked quite
+different at first and even kind of not
+
+ align:start position:0%
+different at first and even kind of not
+ 
+
+ align:start position:0%
+different at first and even kind of not
+very encouraging to be polite about it
+
+ align:start position:0%
+very encouraging to be polite about it
+ 
+
+ align:start position:0%
+very encouraging to be polite about it
+to each other's inventors Heisenberg's
+
+ align:start position:0%
+to each other's inventors Heisenberg's
+ 
+
+ align:start position:0%
+to each other's inventors Heisenberg's
+approach really emphasized and built
+
+ align:start position:0%
+approach really emphasized and built
+ 
+
+ align:start position:0%
+approach really emphasized and built
+upon this what he considered a kind of
+
+ align:start position:0%
+upon this what he considered a kind of
+ 
+
+ align:start position:0%
+upon this what he considered a kind of
+inherent discreetness that was the main
+
+ align:start position:0%
+inherent discreetness that was the main
+ 
+
+ align:start position:0%
+inherent discreetness that was the main
+lesson of the quantum as far as
+
+ align:start position:0%
+lesson of the quantum as far as
+ 
+
+ align:start position:0%
+lesson of the quantum as far as
+Heisenberg was concerned Schrodinger in
+
+ align:start position:0%
+Heisenberg was concerned Schrodinger in
+ 
+
+ align:start position:0%
+Heisenberg was concerned Schrodinger in
+the meantime built separately on
+
+ align:start position:0%
+the meantime built separately on
+ 
+
+ align:start position:0%
+the meantime built separately on
+Deborah's suggestion the real lesson is
+
+ align:start position:0%
+Deborah's suggestion the real lesson is
+ 
+
+ align:start position:0%
+Deborah's suggestion the real lesson is
+is a surprise and continua that even
+
+ align:start position:0%
+is a surprise and continua that even
+ 
+
+ align:start position:0%
+is a surprise and continua that even
+solid matter like electrons have
+
+ align:start position:0%
+solid matter like electrons have
+ 
+
+ align:start position:0%
+solid matter like electrons have
+Associated wave-like Behavior they're
+
+ align:start position:0%
+Associated wave-like Behavior they're
+ 
+
+ align:start position:0%
+Associated wave-like Behavior they're
+building on different kind of conceptual
+
+ align:start position:0%
+building on different kind of conceptual
+ 
+
+ align:start position:0%
+building on different kind of conceptual
+building blocks and yet by the summer of
+
+ align:start position:0%
+building blocks and yet by the summer of
+ 
+
+ align:start position:0%
+building blocks and yet by the summer of
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+several physicists had had built this
+
+ align:start position:0%
+several physicists had had built this
+ 
+
+ align:start position:0%
+several physicists had had built this
+kind of mathematical map between these
+
+ align:start position:0%
+kind of mathematical map between these
+ 
+
+ align:start position:0%
+kind of mathematical map between these
+very very different looking approaches
+
+ align:start position:0%
+very very different looking approaches
+ 
+
+ align:start position:0%
+very very different looking approaches
+and even though there was now in
+
+ align:start position:0%
+and even though there was now in
+ 
+
+ align:start position:0%
+and even though there was now in
+arguably one internally consistent
+
+ align:start position:0%
+arguably one internally consistent
+ 
+
+ align:start position:0%
+arguably one internally consistent
+mathematical approach what it all meant
+
+ align:start position:0%
+mathematical approach what it all meant
+ 
+
+ align:start position:0%
+mathematical approach what it all meant
+about the world was as unclear then
+
+ align:start position:0%
+about the world was as unclear then
+ 
+
+ align:start position:0%
+about the world was as unclear then
+often as it remains even to this day
+
+ align:start position:0%
+often as it remains even to this day
+ 
+
+ align:start position:0%
+often as it remains even to this day
+uh so one question was what's this wave
+
+ align:start position:0%
+uh so one question was what's this wave
+ 
+
+ align:start position:0%
+uh so one question was what's this wave
+the wave function is now uh an object
+
+ align:start position:0%
+the wave function is now uh an object
+ 
+
+ align:start position:0%
+the wave function is now uh an object
+that can be manipulated using familiar
+
+ align:start position:0%
+that can be manipulated using familiar
+ 
+
+ align:start position:0%
+that can be manipulated using familiar
+techniques it's a differential equation
+
+ align:start position:0%
+techniques it's a differential equation
+ 
+
+ align:start position:0%
+techniques it's a differential equation
+we can understand the spectrum of
+
+ align:start position:0%
+we can understand the spectrum of
+ 
+
+ align:start position:0%
+we can understand the spectrum of
+allowable eigenvalues but what is it
+
+ align:start position:0%
+allowable eigenvalues but what is it
+ 
+
+ align:start position:0%
+allowable eigenvalues but what is it
+actually telling us about the world and
+
+ align:start position:0%
+actually telling us about the world and
+ 
+
+ align:start position:0%
+actually telling us about the world and
+with Max Bourne's suggestion in the
+
+ align:start position:0%
+with Max Bourne's suggestion in the
+ 
+
+ align:start position:0%
+with Max Bourne's suggestion in the
+summer of 1926 physicists pretty quickly
+
+ align:start position:0%
+summer of 1926 physicists pretty quickly
+ 
+
+ align:start position:0%
+summer of 1926 physicists pretty quickly
+came to the idea that the wave function
+
+ align:start position:0%
+came to the idea that the wave function
+ 
+
+ align:start position:0%
+came to the idea that the wave function
+is not telling us about the physical
+
+ align:start position:0%
+is not telling us about the physical
+ 
+
+ align:start position:0%
+is not telling us about the physical
+extent of an object in space but
+
+ align:start position:0%
+extent of an object in space but
+ 
+
+ align:start position:0%
+extent of an object in space but
+actually about the likelihood for events
+
+ align:start position:0%
+actually about the likelihood for events
+ 
+
+ align:start position:0%
+actually about the likelihood for events
+to happen and in particular this
+
+ align:start position:0%
+to happen and in particular this
+ 
+
+ align:start position:0%
+to happen and in particular this
+absolute square of this wave-like
+
+ align:start position:0%
+absolute square of this wave-like
+ 
+
+ align:start position:0%
+absolute square of this wave-like
+quantity should give us the probability
+
+ align:start position:0%
+quantity should give us the probability
+ 
+
+ align:start position:0%
+quantity should give us the probability
+quickly on the heels of that less than a
+
+ align:start position:0%
+quickly on the heels of that less than a
+ 
+
+ align:start position:0%
+quickly on the heels of that less than a
+whole year later by Spring of 27
+
+ align:start position:0%
+whole year later by Spring of 27
+ 
+
+ align:start position:0%
+whole year later by Spring of 27
+Heisenberg had derived is now famous
+
+ align:start position:0%
+Heisenberg had derived is now famous
+ 
+
+ align:start position:0%
+Heisenberg had derived is now famous
+because certainly principle that there
+
+ align:start position:0%
+because certainly principle that there
+ 
+
+ align:start position:0%
+because certainly principle that there
+are these unavoidable trade-offs within
+
+ align:start position:0%
+are these unavoidable trade-offs within
+ 
+
+ align:start position:0%
+are these unavoidable trade-offs within
+in the Precision with which we could
+
+ align:start position:0%
+in the Precision with which we could
+ 
+
+ align:start position:0%
+in the Precision with which we could
+ever hope to specify characteristics of
+
+ align:start position:0%
+ever hope to specify characteristics of
+ 
+
+ align:start position:0%
+ever hope to specify characteristics of
+the kind of quantum realm a kind of
+
+ align:start position:0%
+the kind of quantum realm a kind of
+ 
+
+ align:start position:0%
+the kind of quantum realm a kind of
+pairwise trade-off where we could make
+
+ align:start position:0%
+pairwise trade-off where we could make
+ 
+
+ align:start position:0%
+pairwise trade-off where we could make
+one quantity really sharp but only at
+
+ align:start position:0%
+one quantity really sharp but only at
+ 
+
+ align:start position:0%
+one quantity really sharp but only at
+the expense of making some corresponding
+
+ align:start position:0%
+the expense of making some corresponding
+ 
+
+ align:start position:0%
+the expense of making some corresponding
+or complementary quantity uh very
+
+ align:start position:0%
+or complementary quantity uh very
+ 
+
+ align:start position:0%
+or complementary quantity uh very
+imprecise and the trade-off the Seesaw
+
+ align:start position:0%
+imprecise and the trade-off the Seesaw
+ 
+
+ align:start position:0%
+imprecise and the trade-off the Seesaw
+again uh being uh controlled by flank's
+
+ align:start position:0%
+again uh being uh controlled by flank's
+ 
+
+ align:start position:0%
+again uh being uh controlled by flank's
+constant and then these kinds of broader
+
+ align:start position:0%
+constant and then these kinds of broader
+ 
+
+ align:start position:0%
+constant and then these kinds of broader
+conceptual dualities like this wave
+
+ align:start position:0%
+conceptual dualities like this wave
+ 
+
+ align:start position:0%
+conceptual dualities like this wave
+particle duality we've seen now a few
+
+ align:start position:0%
+particle duality we've seen now a few
+ 
+
+ align:start position:0%
+particle duality we've seen now a few
+times the type of answer we could ever
+
+ align:start position:0%
+times the type of answer we could ever
+ 
+
+ align:start position:0%
+times the type of answer we could ever
+hope to find depends on the type of
+
+ align:start position:0%
+hope to find depends on the type of
+ 
+
+ align:start position:0%
+hope to find depends on the type of
+question we ask so it's not though that
+
+ align:start position:0%
+question we ask so it's not though that
+ 
+
+ align:start position:0%
+question we ask so it's not though that
+the electron really is a particle or a
+
+ align:start position:0%
+the electron really is a particle or a
+ 
+
+ align:start position:0%
+the electron really is a particle or a
+wave that it's a kind of contextual
+
+ align:start position:0%
+wave that it's a kind of contextual
+ 
+
+ align:start position:0%
+wave that it's a kind of contextual
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+though what kind of properties do we
+
+ align:start position:0%
+though what kind of properties do we
+ 
+
+ align:start position:0%
+though what kind of properties do we
+hope to investigate then we're going to
+
+ align:start position:0%
+hope to investigate then we're going to
+ 
+
+ align:start position:0%
+hope to investigate then we're going to
+foreclose some answers from ever even
+
+ align:start position:0%
+foreclose some answers from ever even
+ 
+
+ align:start position:0%
+foreclose some answers from ever even
+being possible even as we get other
+
+ align:start position:0%
+being possible even as we get other
+ 
+
+ align:start position:0%
+being possible even as we get other
+quite definite answers so Niels Bohr
+
+ align:start position:0%
+quite definite answers so Niels Bohr
+ 
+
+ align:start position:0%
+quite definite answers so Niels Bohr
+partly from his uh intense discussions
+
+ align:start position:0%
+partly from his uh intense discussions
+ 
+
+ align:start position:0%
+partly from his uh intense discussions
+with with Heisenberg with other
+
+ align:start position:0%
+with with Heisenberg with other
+ 
+
+ align:start position:0%
+with with Heisenberg with other
+colleagues he used that to enunciate a
+
+ align:start position:0%
+colleagues he used that to enunciate a
+ 
+
+ align:start position:0%
+colleagues he used that to enunciate a
+very general philosophy of the quantum
+
+ align:start position:0%
+very general philosophy of the quantum
+ 
+
+ align:start position:0%
+very general philosophy of the quantum
+Realm by uh September of 1927 right on
+
+ align:start position:0%
+Realm by uh September of 1927 right on
+ 
+
+ align:start position:0%
+Realm by uh September of 1927 right on
+the heels of this which he came to call
+
+ align:start position:0%
+the heels of this which he came to call
+ 
+
+ align:start position:0%
+the heels of this which he came to call
+complementary so it's not an either or
+
+ align:start position:0%
+complementary so it's not an either or
+ 
+
+ align:start position:0%
+complementary so it's not an either or
+world it's a both and that we are we are
+
+ align:start position:0%
+world it's a both and that we are we are
+ 
+
+ align:start position:0%
+world it's a both and that we are we are
+required in this case to draw on both
+
+ align:start position:0%
+required in this case to draw on both
+ 
+
+ align:start position:0%
+required in this case to draw on both
+ideas and actual mathematical techniques
+
+ align:start position:0%
+ideas and actual mathematical techniques
+ 
+
+ align:start position:0%
+ideas and actual mathematical techniques
+with which we characterize wave behavior
+
+ align:start position:0%
+with which we characterize wave behavior
+ 
+
+ align:start position:0%
+with which we characterize wave behavior
+and ideas and techniques with which we
+
+ align:start position:0%
+and ideas and techniques with which we
+ 
+
+ align:start position:0%
+and ideas and techniques with which we
+characterize particle Behavior they are
+
+ align:start position:0%
+characterize particle Behavior they are
+ 
+
+ align:start position:0%
+characterize particle Behavior they are
+mutually exclusive we literally can't
+
+ align:start position:0%
+mutually exclusive we literally can't
+ 
+
+ align:start position:0%
+mutually exclusive we literally can't
+use them at the same time and yet we
+
+ align:start position:0%
+use them at the same time and yet we
+ 
+
+ align:start position:0%
+use them at the same time and yet we
+need both a complete description
+
+ align:start position:0%
+need both a complete description
+ 
+
+ align:start position:0%
+need both a complete description
+requires both even though they don't fit
+
+ align:start position:0%
+requires both even though they don't fit
+ 
+
+ align:start position:0%
+requires both even though they don't fit
+together at once and that Tabor was the
+
+ align:start position:0%
+together at once and that Tabor was the
+ 
+
+ align:start position:0%
+together at once and that Tabor was the
+deepest meaning the deepest lesson of
+
+ align:start position:0%
+deepest meaning the deepest lesson of
+ 
+
+ align:start position:0%
+deepest meaning the deepest lesson of
+quantum theory not everyone agreed but
+
+ align:start position:0%
+quantum theory not everyone agreed but
+ 
+
+ align:start position:0%
+quantum theory not everyone agreed but
+that's where Bohr arrived by 1927. okay
+
+ align:start position:0%
+that's where Bohr arrived by 1927. okay
+ 
+
+ align:start position:0%
+that's where Bohr arrived by 1927. okay
+any questions on any of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is so straightforward so boringly
+
+ align:start position:0%
+that is so straightforward so boringly
+ 
+
+ align:start position:0%
+that is so straightforward so boringly
+familiar
+
+ align:start position:0%
+familiar
+ 
+
+ align:start position:0%
+familiar
+but there's not even a single question
+
+ align:start position:0%
+but there's not even a single question
+ 
+
+ align:start position:0%
+but there's not even a single question
+to ask about the fundamental nature of
+
+ align:start position:0%
+to ask about the fundamental nature of
+ 
+
+ align:start position:0%
+to ask about the fundamental nature of
+reality
+
+ align:start position:0%
+reality
+ 
+
+ align:start position:0%
+reality
+boy holiday weekends
+
+ align:start position:0%
+boy holiday weekends
+ 
+
+ align:start position:0%
+boy holiday weekends
+no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+if you'll if you'll permit me on
+
+ align:start position:0%
+if you'll if you'll permit me on
+ 
+
+ align:start position:0%
+if you'll if you'll permit me on
+tomorrow's class I'm going to try to
+
+ align:start position:0%
+tomorrow's class I'm going to try to
+ 
+
+ align:start position:0%
+tomorrow's class I'm going to try to
+shake your Quantum complacency even
+
+ align:start position:0%
+shake your Quantum complacency even
+ 
+
+ align:start position:0%
+shake your Quantum complacency even
+further so tomorrow we'll explore
+
+ align:start position:0%
+further so tomorrow we'll explore
+ 
+
+ align:start position:0%
+further so tomorrow we'll explore
+Quantum weirdness uh in in even more
+
+ align:start position:0%
+Quantum weirdness uh in in even more
+ 
+
+ align:start position:0%
+Quantum weirdness uh in in even more
+Direction so if this stuff is humdrum
+
+ align:start position:0%
+Direction so if this stuff is humdrum
+ 
+
+ align:start position:0%
+Direction so if this stuff is humdrum
+and familiar give me give me one more
+
+ align:start position:0%
+and familiar give me give me one more
+ 
+
+ align:start position:0%
+and familiar give me give me one more
+shot for tomorrow so Fisher asks for
+
+ align:start position:0%
+shot for tomorrow so Fisher asks for
+ 
+
+ align:start position:0%
+shot for tomorrow so Fisher asks for
+shorting his work more quickly except it
+
+ align:start position:0%
+shorting his work more quickly except it
+ 
+
+ align:start position:0%
+shorting his work more quickly except it
+because it was more basic in mechanics I
+
+ align:start position:0%
+because it was more basic in mechanics I
+ 
+
+ align:start position:0%
+because it was more basic in mechanics I
+think that's absolutely right Fisher uh
+
+ align:start position:0%
+think that's absolutely right Fisher uh
+ 
+
+ align:start position:0%
+think that's absolutely right Fisher uh
+and I think
+
+ align:start position:0%
+and I think
+ 
+
+ align:start position:0%
+and I think
+there was a kind of
+
+ align:start position:0%
+there was a kind of
+ 
+
+ align:start position:0%
+there was a kind of
+um people could could do stuff with it
+
+ align:start position:0%
+um people could could do stuff with it
+ 
+
+ align:start position:0%
+um people could could do stuff with it
+right so so even while the concepts were
+
+ align:start position:0%
+right so so even while the concepts were
+ 
+
+ align:start position:0%
+right so so even while the concepts were
+still very far from Clear what what is
+
+ align:start position:0%
+still very far from Clear what what is
+ 
+
+ align:start position:0%
+still very far from Clear what what is
+we for what's the wave function what is
+
+ align:start position:0%
+we for what's the wave function what is
+ 
+
+ align:start position:0%
+we for what's the wave function what is
+a wave of what is it telling us that was
+
+ align:start position:0%
+a wave of what is it telling us that was
+ 
+
+ align:start position:0%
+a wave of what is it telling us that was
+by no means clear and even after the
+
+ align:start position:0%
+by no means clear and even after the
+ 
+
+ align:start position:0%
+by no means clear and even after the
+answers that we would now recognize were
+
+ align:start position:0%
+answers that we would now recognize were
+ 
+
+ align:start position:0%
+answers that we would now recognize were
+put forward those weren't you know those
+
+ align:start position:0%
+put forward those weren't you know those
+ 
+
+ align:start position:0%
+put forward those weren't you know those
+didn't claim consensus right away and
+
+ align:start position:0%
+didn't claim consensus right away and
+ 
+
+ align:start position:0%
+didn't claim consensus right away and
+yet in between people can still do stuff
+
+ align:start position:0%
+yet in between people can still do stuff
+ 
+
+ align:start position:0%
+yet in between people can still do stuff
+right you could train PhD students to
+
+ align:start position:0%
+right you could train PhD students to
+ 
+
+ align:start position:0%
+right you could train PhD students to
+look at this or that specific question
+
+ align:start position:0%
+look at this or that specific question
+ 
+
+ align:start position:0%
+look at this or that specific question
+because the firm the apparatus the
+
+ align:start position:0%
+because the firm the apparatus the
+ 
+
+ align:start position:0%
+because the firm the apparatus the
+mathematical apparatus was already
+
+ align:start position:0%
+mathematical apparatus was already
+ 
+
+ align:start position:0%
+mathematical apparatus was already
+something that practiced you know since
+
+ align:start position:0%
+something that practiced you know since
+ 
+
+ align:start position:0%
+something that practiced you know since
+their youngest earliest studies so I
+
+ align:start position:0%
+their youngest earliest studies so I
+ 
+
+ align:start position:0%
+their youngest earliest studies so I
+think that really had a lot to do with
+
+ align:start position:0%
+think that really had a lot to do with
+ 
+
+ align:start position:0%
+think that really had a lot to do with
+with how rapidly Schrodinger's work was
+
+ align:start position:0%
+with how rapidly Schrodinger's work was
+ 
+
+ align:start position:0%
+with how rapidly Schrodinger's work was
+really welcomed
+
+ align:start position:0%
+really welcomed
+ 
+
+ align:start position:0%
+really welcomed
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and that it helped obviously it helped a
+
+ align:start position:0%
+and that it helped obviously it helped a
+ 
+
+ align:start position:0%
+and that it helped obviously it helped a
+lot when Schrodinger and and uh Jordan
+
+ align:start position:0%
+lot when Schrodinger and and uh Jordan
+ 
+
+ align:start position:0%
+lot when Schrodinger and and uh Jordan
+and Dirac uh elucidated the kind of
+
+ align:start position:0%
+and Dirac uh elucidated the kind of
+ 
+
+ align:start position:0%
+and Dirac uh elucidated the kind of
+mathematical mapping so then it really
+
+ align:start position:0%
+mathematical mapping so then it really
+ 
+
+ align:start position:0%
+mathematical mapping so then it really
+became a question of convenience and not
+
+ align:start position:0%
+became a question of convenience and not
+ 
+
+ align:start position:0%
+became a question of convenience and not
+either or it's not like I had to vote
+
+ align:start position:0%
+either or it's not like I had to vote
+ 
+
+ align:start position:0%
+either or it's not like I had to vote
+for team Schrodinger versus Team
+
+ align:start position:0%
+for team Schrodinger versus Team
+ 
+
+ align:start position:0%
+for team Schrodinger versus Team
+Heisenberg now I could say oh this set
+
+ align:start position:0%
+Heisenberg now I could say oh this set
+ 
+
+ align:start position:0%
+Heisenberg now I could say oh this set
+of techniques is familiar to me I have
+
+ align:start position:0%
+of techniques is familiar to me I have
+ 
+
+ align:start position:0%
+of techniques is familiar to me I have
+lots of experience from classical
+
+ align:start position:0%
+lots of experience from classical
+ 
+
+ align:start position:0%
+lots of experience from classical
+mechanics or or Maxwell or whatever and
+
+ align:start position:0%
+mechanics or or Maxwell or whatever and
+ 
+
+ align:start position:0%
+mechanics or or Maxwell or whatever and
+so then it became a kind of um tool of
+
+ align:start position:0%
+so then it became a kind of um tool of
+ 
+
+ align:start position:0%
+so then it became a kind of um tool of
+choice and these tools were much more
+
+ align:start position:0%
+choice and these tools were much more
+ 
+
+ align:start position:0%
+choice and these tools were much more
+familiar to many more people at the time
+
+ align:start position:0%
+familiar to many more people at the time
+ 
+
+ align:start position:0%
+familiar to many more people at the time
+that's absolutely that absolutely played
+
+ align:start position:0%
+that's absolutely that absolutely played
+ 
+
+ align:start position:0%
+that's absolutely that absolutely played
+a role in in hastening um many people's
+
+ align:start position:0%
+a role in in hastening um many people's
+ 
+
+ align:start position:0%
+a role in in hastening um many people's
+attention to this stuff good good point
+
+ align:start position:0%
+attention to this stuff good good point
+ 
+
+ align:start position:0%
+attention to this stuff good good point
+uh Aiden asked is Heisman position
+
+ align:start position:0%
+uh Aiden asked is Heisman position
+ 
+
+ align:start position:0%
+uh Aiden asked is Heisman position
+principal kind of spiritual
+
+ align:start position:0%
+principal kind of spiritual
+ 
+
+ align:start position:0%
+principal kind of spiritual
+uh for some people yes although that
+
+ align:start position:0%
+uh for some people yes although that
+ 
+
+ align:start position:0%
+uh for some people yes although that
+gets uh there's a lot to say about that
+
+ align:start position:0%
+gets uh there's a lot to say about that
+ 
+
+ align:start position:0%
+gets uh there's a lot to say about that
+uh are there those who think a more
+
+ align:start position:0%
+uh are there those who think a more
+ 
+
+ align:start position:0%
+uh are there those who think a more
+literal analysis would be that we simply
+
+ align:start position:0%
+literal analysis would be that we simply
+ 
+
+ align:start position:0%
+literal analysis would be that we simply
+need to discover reform observation not
+
+ align:start position:0%
+need to discover reform observation not
+ 
+
+ align:start position:0%
+need to discover reform observation not
+involve test particles so so Aiden I
+
+ align:start position:0%
+involve test particles so so Aiden I
+ 
+
+ align:start position:0%
+involve test particles so so Aiden I
+thought you're going a different way
+
+ align:start position:0%
+thought you're going a different way
+ 
+
+ align:start position:0%
+thought you're going a different way
+first so one one topic which is
+
+ align:start position:0%
+first so one one topic which is
+ 
+
+ align:start position:0%
+first so one one topic which is
+I'll say controversial some people
+
+ align:start position:0%
+I'll say controversial some people
+ 
+
+ align:start position:0%
+I'll say controversial some people
+pursue what other people think it is
+
+ align:start position:0%
+pursue what other people think it is
+ 
+
+ align:start position:0%
+pursue what other people think it is
+full of holes
+
+ align:start position:0%
+full of holes
+ 
+
+ align:start position:0%
+full of holes
+one idea would be to say does the
+
+ align:start position:0%
+one idea would be to say does the
+ 
+
+ align:start position:0%
+one idea would be to say does the
+uncertainty principle give us a physical
+
+ align:start position:0%
+uncertainty principle give us a physical
+ 
+
+ align:start position:0%
+uncertainty principle give us a physical
+reason why there might be something like
+
+ align:start position:0%
+reason why there might be something like
+ 
+
+ align:start position:0%
+reason why there might be something like
+free will
+
+ align:start position:0%
+free will
+ 
+
+ align:start position:0%
+free will
+Consciousness and the experience of free
+
+ align:start position:0%
+Consciousness and the experience of free
+ 
+
+ align:start position:0%
+Consciousness and the experience of free
+will if
+
+ align:start position:0%
+will if
+ 
+
+ align:start position:0%
+will if
+you consume part of the concern going
+
+ align:start position:0%
+you consume part of the concern going
+ 
+
+ align:start position:0%
+you consume part of the concern going
+back to the A's the days of both uh
+
+ align:start position:0%
+back to the A's the days of both uh
+ 
+
+ align:start position:0%
+back to the A's the days of both uh
+Newton and and for that matter of
+
+ align:start position:0%
+Newton and and for that matter of
+ 
+
+ align:start position:0%
+Newton and and for that matter of
+Maxwell if if we live in a universe in
+
+ align:start position:0%
+Maxwell if if we live in a universe in
+ 
+
+ align:start position:0%
+Maxwell if if we live in a universe in
+which determinism holds
+
+ align:start position:0%
+which determinism holds
+ 
+
+ align:start position:0%
+which determinism holds
+perfectly if
+
+ align:start position:0%
+perfectly if
+ 
+
+ align:start position:0%
+perfectly if
+events in the future are uniquely
+
+ align:start position:0%
+events in the future are uniquely
+ 
+
+ align:start position:0%
+events in the future are uniquely
+determined by events in the past and and
+
+ align:start position:0%
+determined by events in the past and and
+ 
+
+ align:start position:0%
+determined by events in the past and and
+then we you know turn on our kind of
+
+ align:start position:0%
+then we you know turn on our kind of
+ 
+
+ align:start position:0%
+then we you know turn on our kind of
+sci-fi imaginations and imagine we're
+
+ align:start position:0%
+sci-fi imaginations and imagine we're
+ 
+
+ align:start position:0%
+sci-fi imaginations and imagine we're
+made of of matter
+
+ align:start position:0%
+made of of matter
+ 
+
+ align:start position:0%
+made of of matter
+atoms and and molecules if atoms and
+
+ align:start position:0%
+atoms and and molecules if atoms and
+ 
+
+ align:start position:0%
+atoms and and molecules if atoms and
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+um you know
+
+ align:start position:0%
+um you know
+ 
+
+ align:start position:0%
+um you know
+have to obey the laws of nature then in
+
+ align:start position:0%
+have to obey the laws of nature then in
+ 
+
+ align:start position:0%
+have to obey the laws of nature then in
+principle they're subject to determinism
+
+ align:start position:0%
+principle they're subject to determinism
+ 
+
+ align:start position:0%
+principle they're subject to determinism
+at least in a pre-quantum mechanical way
+
+ align:start position:0%
+at least in a pre-quantum mechanical way
+ 
+
+ align:start position:0%
+at least in a pre-quantum mechanical way
+then you know then aren't we all just
+
+ align:start position:0%
+then you know then aren't we all just
+ 
+
+ align:start position:0%
+then you know then aren't we all just
+pre-programmed or we merely machines uh
+
+ align:start position:0%
+pre-programmed or we merely machines uh
+ 
+
+ align:start position:0%
+pre-programmed or we merely machines uh
+with no more free will than comets who
+
+ align:start position:0%
+with no more free will than comets who
+ 
+
+ align:start position:0%
+with no more free will than comets who
+can't help but follow a keplerian orbit
+
+ align:start position:0%
+can't help but follow a keplerian orbit
+ 
+
+ align:start position:0%
+can't help but follow a keplerian orbit
+as they orbit the Sun and believe it or
+
+ align:start position:0%
+as they orbit the Sun and believe it or
+ 
+
+ align:start position:0%
+as they orbit the Sun and believe it or
+not that was a debate that got people
+
+ align:start position:0%
+not that was a debate that got people
+ 
+
+ align:start position:0%
+not that was a debate that got people
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+excited and exercised and mad at each
+
+ align:start position:0%
+excited and exercised and mad at each
+ 
+
+ align:start position:0%
+excited and exercised and mad at each
+other for a long long time and so there
+
+ align:start position:0%
+other for a long long time and so there
+ 
+
+ align:start position:0%
+other for a long long time and so there
+was some thought by some people early on
+
+ align:start position:0%
+was some thought by some people early on
+ 
+
+ align:start position:0%
+was some thought by some people early on
+starting really in the 1920s and 30s
+
+ align:start position:0%
+starting really in the 1920s and 30s
+ 
+
+ align:start position:0%
+starting really in the 1920s and 30s
+that maybe the uncertainty principle by
+
+ align:start position:0%
+that maybe the uncertainty principle by
+ 
+
+ align:start position:0%
+that maybe the uncertainty principle by
+breaking the kind of iron hold of
+
+ align:start position:0%
+breaking the kind of iron hold of
+ 
+
+ align:start position:0%
+breaking the kind of iron hold of
+determinism leaves a kind of space
+
+ align:start position:0%
+determinism leaves a kind of space
+ 
+
+ align:start position:0%
+determinism leaves a kind of space
+within our scientific theorizing for
+
+ align:start position:0%
+within our scientific theorizing for
+ 
+
+ align:start position:0%
+within our scientific theorizing for
+things that seemed or one or at least
+
+ align:start position:0%
+things that seemed or one or at least
+ 
+
+ align:start position:0%
+things that seemed or one or at least
+some might have hoped were not you know
+
+ align:start position:0%
+some might have hoped were not you know
+ 
+
+ align:start position:0%
+some might have hoped were not you know
+fully uniquely determined whether that's
+
+ align:start position:0%
+fully uniquely determined whether that's
+ 
+
+ align:start position:0%
+fully uniquely determined whether that's
+our own sense of individuality where the
+
+ align:start position:0%
+our own sense of individuality where the
+ 
+
+ align:start position:0%
+our own sense of individuality where the
+course of human events and liberality
+
+ align:start position:0%
+course of human events and liberality
+ 
+
+ align:start position:0%
+course of human events and liberality
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+now that gets a little a little tricky
+
+ align:start position:0%
+now that gets a little a little tricky
+ 
+
+ align:start position:0%
+now that gets a little a little tricky
+because unfortunately the uncertain
+
+ align:start position:0%
+because unfortunately the uncertain
+ 
+
+ align:start position:0%
+because unfortunately the uncertain
+critical argues at least most physicists
+
+ align:start position:0%
+critical argues at least most physicists
+ 
+
+ align:start position:0%
+critical argues at least most physicists
+would say the upside of the uncertainty
+
+ align:start position:0%
+would say the upside of the uncertainty
+ 
+
+ align:start position:0%
+would say the upside of the uncertainty
+principle is that everything's random
+
+ align:start position:0%
+principle is that everything's random
+ 
+
+ align:start position:0%
+principle is that everything's random
+that's and that's not quite how my
+
+ align:start position:0%
+that's and that's not quite how my
+ 
+
+ align:start position:0%
+that's and that's not quite how my
+thoughts feel well actually before the
+
+ align:start position:0%
+thoughts feel well actually before the
+ 
+
+ align:start position:0%
+thoughts feel well actually before the
+covid-19 my thoughts didn't always feel
+
+ align:start position:0%
+covid-19 my thoughts didn't always feel
+ 
+
+ align:start position:0%
+covid-19 my thoughts didn't always feel
+only random now they did but I mean so
+
+ align:start position:0%
+only random now they did but I mean so
+ 
+
+ align:start position:0%
+only random now they did but I mean so
+appealing to the certain principle
+
+ align:start position:0%
+appealing to the certain principle
+ 
+
+ align:start position:0%
+appealing to the certain principle
+breaks the hold of determinism but what
+
+ align:start position:0%
+breaks the hold of determinism but what
+ 
+
+ align:start position:0%
+breaks the hold of determinism but what
+it seems good in its place is random
+
+ align:start position:0%
+it seems good in its place is random
+ 
+
+ align:start position:0%
+it seems good in its place is random
+mush as opposed to something that
+
+ align:start position:0%
+mush as opposed to something that
+ 
+
+ align:start position:0%
+mush as opposed to something that
+otherwise might answer to the kind of
+
+ align:start position:0%
+otherwise might answer to the kind of
+ 
+
+ align:start position:0%
+otherwise might answer to the kind of
+lived experience or phenomena of
+
+ align:start position:0%
+lived experience or phenomena of
+ 
+
+ align:start position:0%
+lived experience or phenomena of
+something like Free Will so it's not
+
+ align:start position:0%
+something like Free Will so it's not
+ 
+
+ align:start position:0%
+something like Free Will so it's not
+like that's a single answer that that's
+
+ align:start position:0%
+like that's a single answer that that's
+ 
+
+ align:start position:0%
+like that's a single answer that that's
+done but that opens a space for kind of
+
+ align:start position:0%
+done but that opens a space for kind of
+ 
+
+ align:start position:0%
+done but that opens a space for kind of
+theorizing uh that goes on to this day
+
+ align:start position:0%
+theorizing uh that goes on to this day
+ 
+
+ align:start position:0%
+theorizing uh that goes on to this day
+um sometimes on the margins of both kind
+
+ align:start position:0%
+um sometimes on the margins of both kind
+ 
+
+ align:start position:0%
+um sometimes on the margins of both kind
+of physics and also of areas like
+
+ align:start position:0%
+of physics and also of areas like
+ 
+
+ align:start position:0%
+of physics and also of areas like
+neuroscience and philosophy but at least
+
+ align:start position:0%
+neuroscience and philosophy but at least
+ 
+
+ align:start position:0%
+neuroscience and philosophy but at least
+it opens up a different way of asking
+
+ align:start position:0%
+it opens up a different way of asking
+ 
+
+ align:start position:0%
+it opens up a different way of asking
+legitimate hard questions with some new
+
+ align:start position:0%
+legitimate hard questions with some new
+ 
+
+ align:start position:0%
+legitimate hard questions with some new
+conceptual inputs let me put it that way
+
+ align:start position:0%
+conceptual inputs let me put it that way
+ 
+
+ align:start position:0%
+conceptual inputs let me put it that way
+so even though I don't think people have
+
+ align:start position:0%
+so even though I don't think people have
+ 
+
+ align:start position:0%
+so even though I don't think people have
+found that answer yet it's interesting
+
+ align:start position:0%
+found that answer yet it's interesting
+ 
+
+ align:start position:0%
+found that answer yet it's interesting
+that that opens a space to ask old
+
+ align:start position:0%
+that that opens a space to ask old
+ 
+
+ align:start position:0%
+that that opens a space to ask old
+questions maybe in some new ways
+
+ align:start position:0%
+questions maybe in some new ways
+ 
+
+ align:start position:0%
+questions maybe in some new ways
+um I wrote a book a couple years ago
+
+ align:start position:0%
+um I wrote a book a couple years ago
+ 
+
+ align:start position:0%
+um I wrote a book a couple years ago
+called how the hippies saved physics
+
+ align:start position:0%
+called how the hippies saved physics
+ 
+
+ align:start position:0%
+called how the hippies saved physics
+it's very obnoxious title where people
+
+ align:start position:0%
+it's very obnoxious title where people
+ 
+
+ align:start position:0%
+it's very obnoxious title where people
+thought maybe there were other kind of
+
+ align:start position:0%
+thought maybe there were other kind of
+ 
+
+ align:start position:0%
+thought maybe there were other kind of
+unexplained or unaccounted for phenomena
+
+ align:start position:0%
+unexplained or unaccounted for phenomena
+ 
+
+ align:start position:0%
+unexplained or unaccounted for phenomena
+that quantum theory might be able to
+
+ align:start position:0%
+that quantum theory might be able to
+ 
+
+ align:start position:0%
+that quantum theory might be able to
+account for like um claims of ESP or
+
+ align:start position:0%
+account for like um claims of ESP or
+ 
+
+ align:start position:0%
+account for like um claims of ESP or
+other so-called occult phenomena mind
+
+ align:start position:0%
+other so-called occult phenomena mind
+ 
+
+ align:start position:0%
+other so-called occult phenomena mind
+reading for example and again I don't
+
+ align:start position:0%
+reading for example and again I don't
+ 
+
+ align:start position:0%
+reading for example and again I don't
+think they explained that at all but it
+
+ align:start position:0%
+think they explained that at all but it
+ 
+
+ align:start position:0%
+think they explained that at all but it
+was a way of trying to reason about
+
+ align:start position:0%
+was a way of trying to reason about
+ 
+
+ align:start position:0%
+was a way of trying to reason about
+strange or unexpected human scaled
+
+ align:start position:0%
+strange or unexpected human scaled
+ 
+
+ align:start position:0%
+strange or unexpected human scaled
+phenomena using a new set of tools that
+
+ align:start position:0%
+phenomena using a new set of tools that
+ 
+
+ align:start position:0%
+phenomena using a new set of tools that
+really weren't going to go away like the
+
+ align:start position:0%
+really weren't going to go away like the
+ 
+
+ align:start position:0%
+really weren't going to go away like the
+uncertain principle or like things we'll
+
+ align:start position:0%
+uncertain principle or like things we'll
+ 
+
+ align:start position:0%
+uncertain principle or like things we'll
+talk about in tomorrow's class things
+
+ align:start position:0%
+talk about in tomorrow's class things
+ 
+
+ align:start position:0%
+talk about in tomorrow's class things
+like quantum entanglement so I'm not
+
+ align:start position:0%
+like quantum entanglement so I'm not
+ 
+
+ align:start position:0%
+like quantum entanglement so I'm not
+telling you that's the answer I'm
+
+ align:start position:0%
+telling you that's the answer I'm
+ 
+
+ align:start position:0%
+telling you that's the answer I'm
+telling you that opened up a space for
+
+ align:start position:0%
+telling you that opened up a space for
+ 
+
+ align:start position:0%
+telling you that opened up a space for
+people to ask
+
+ align:start position:0%
+people to ask
+ 
+
+ align:start position:0%
+people to ask
+either familiar questions from
+
+ align:start position:0%
+either familiar questions from
+ 
+
+ align:start position:0%
+either familiar questions from
+unfamiliar perspectives or sometimes ask
+
+ align:start position:0%
+unfamiliar perspectives or sometimes ask
+ 
+
+ align:start position:0%
+unfamiliar perspectives or sometimes ask
+new kinds of questions so in that sense
+
+ align:start position:0%
+new kinds of questions so in that sense
+ 
+
+ align:start position:0%
+new kinds of questions so in that sense
+what's the ultimate meaning of the
+
+ align:start position:0%
+what's the ultimate meaning of the
+ 
+
+ align:start position:0%
+what's the ultimate meaning of the
+uncertainties well I don't know when
+
+ align:start position:0%
+uncertainties well I don't know when
+ 
+
+ align:start position:0%
+uncertainties well I don't know when
+frankly I don't think anyone knows or at
+
+ align:start position:0%
+frankly I don't think anyone knows or at
+ 
+
+ align:start position:0%
+frankly I don't think anyone knows or at
+least it's still a subject of really
+
+ align:start position:0%
+least it's still a subject of really
+ 
+
+ align:start position:0%
+least it's still a subject of really
+robust debate like that Quantum to
+
+ align:start position:0%
+robust debate like that Quantum to
+ 
+
+ align:start position:0%
+robust debate like that Quantum to
+classical transition
+
+ align:start position:0%
+classical transition
+ 
+
+ align:start position:0%
+classical transition
+and I think it's fantastic that we have
+
+ align:start position:0%
+and I think it's fantastic that we have
+ 
+
+ align:start position:0%
+and I think it's fantastic that we have
+tools to even pose as questions now so I
+
+ align:start position:0%
+tools to even pose as questions now so I
+ 
+
+ align:start position:0%
+tools to even pose as questions now so I
+get excited by the nature of the
+
+ align:start position:0%
+get excited by the nature of the
+ 
+
+ align:start position:0%
+get excited by the nature of the
+question rather than having a favorite
+
+ align:start position:0%
+question rather than having a favorite
+ 
+
+ align:start position:0%
+question rather than having a favorite
+answer that's my own that's just me kind
+
+ align:start position:0%
+answer that's my own that's just me kind
+ 
+
+ align:start position:0%
+answer that's my own that's just me kind
+of proselytizing so Richard asks once
+
+ align:start position:0%
+of proselytizing so Richard asks once
+ 
+
+ align:start position:0%
+of proselytizing so Richard asks once
+General activity was wide they accepted
+
+ align:start position:0%
+General activity was wide they accepted
+ 
+
+ align:start position:0%
+General activity was wide they accepted
+where people already ringing alarm Bells
+
+ align:start position:0%
+where people already ringing alarm Bells
+ 
+
+ align:start position:0%
+where people already ringing alarm Bells
+about the conflicts being generated yes
+
+ align:start position:0%
+about the conflicts being generated yes
+ 
+
+ align:start position:0%
+about the conflicts being generated yes
+yes they were including uh Albert
+
+ align:start position:0%
+yes they were including uh Albert
+ 
+
+ align:start position:0%
+yes they were including uh Albert
+Einstein himself who had a few opinions
+
+ align:start position:0%
+Einstein himself who had a few opinions
+ 
+
+ align:start position:0%
+Einstein himself who had a few opinions
+on the matter uh and so
+
+ align:start position:0%
+on the matter uh and so
+ 
+
+ align:start position:0%
+on the matter uh and so
+it just goes back in large project
+
+ align:start position:0%
+it just goes back in large project
+ 
+
+ align:start position:0%
+it just goes back in large project
+things like um the the fall of the
+
+ align:start position:0%
+things like um the the fall of the
+ 
+
+ align:start position:0%
+things like um the the fall of the
+determinism and we'll come to actually
+
+ align:start position:0%
+determinism and we'll come to actually
+ 
+
+ align:start position:0%
+determinism and we'll come to actually
+some of these examples even in
+
+ align:start position:0%
+some of these examples even in
+ 
+
+ align:start position:0%
+some of these examples even in
+tomorrow's class so we'll come to some
+
+ align:start position:0%
+tomorrow's class so we'll come to some
+ 
+
+ align:start position:0%
+tomorrow's class so we'll come to some
+of Einstein's most enduring critiques of
+
+ align:start position:0%
+of Einstein's most enduring critiques of
+ 
+
+ align:start position:0%
+of Einstein's most enduring critiques of
+quantum theory in the light of us
+
+ align:start position:0%
+quantum theory in the light of us
+ 
+
+ align:start position:0%
+quantum theory in the light of us
+thinking about things like relativity uh
+
+ align:start position:0%
+thinking about things like relativity uh
+ 
+
+ align:start position:0%
+thinking about things like relativity uh
+tomorrow so partly I'll just bracket
+
+ align:start position:0%
+tomorrow so partly I'll just bracket
+ 
+
+ align:start position:0%
+tomorrow so partly I'll just bracket
+that and I'll just simply say yes it's a
+
+ align:start position:0%
+that and I'll just simply say yes it's a
+ 
+
+ align:start position:0%
+that and I'll just simply say yes it's a
+great question we'll see some examples
+
+ align:start position:0%
+great question we'll see some examples
+ 
+
+ align:start position:0%
+great question we'll see some examples
+tomorrow we can talk more
+
+ align:start position:0%
+tomorrow we can talk more
+ 
+
+ align:start position:0%
+tomorrow we can talk more
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh Lulu asked how's my mental emotional
+
+ align:start position:0%
+uh Lulu asked how's my mental emotional
+ 
+
+ align:start position:0%
+uh Lulu asked how's my mental emotional
+state I think you can see I'm still
+
+ align:start position:0%
+state I think you can see I'm still
+ 
+
+ align:start position:0%
+state I think you can see I'm still
+agitated I love this stuff uh and and
+
+ align:start position:0%
+agitated I love this stuff uh and and
+ 
+
+ align:start position:0%
+agitated I love this stuff uh and and
+tomorrow I won't be able to contain
+
+ align:start position:0%
+tomorrow I won't be able to contain
+ 
+
+ align:start position:0%
+tomorrow I won't be able to contain
+myself I'll talk about some of my own
+
+ align:start position:0%
+myself I'll talk about some of my own
+ 
+
+ align:start position:0%
+myself I'll talk about some of my own
+groups research and the foundations of
+
+ align:start position:0%
+groups research and the foundations of
+ 
+
+ align:start position:0%
+groups research and the foundations of
+quantum mechanics
+
+ align:start position:0%
+quantum mechanics
+ 
+
+ align:start position:0%
+quantum mechanics
+so good I mean not the research is so
+
+ align:start position:0%
+so good I mean not the research is so
+ 
+
+ align:start position:0%
+so good I mean not the research is so
+good the question's so good okay Aiden
+
+ align:start position:0%
+good the question's so good okay Aiden
+ 
+
+ align:start position:0%
+good the question's so good okay Aiden
+says uh does Heisman mean there's
+
+ align:start position:0%
+says uh does Heisman mean there's
+ 
+
+ align:start position:0%
+says uh does Heisman mean there's
+neither people Norwich right so so what
+
+ align:start position:0%
+neither people Norwich right so so what
+ 
+
+ align:start position:0%
+neither people Norwich right so so what
+we can do is recognize that now as a
+
+ align:start position:0%
+we can do is recognize that now as a
+ 
+
+ align:start position:0%
+we can do is recognize that now as a
+question with which we need as a
+
+ align:start position:0%
+question with which we need as a
+ 
+
+ align:start position:0%
+question with which we need as a
+community now have new tools to try to
+
+ align:start position:0%
+community now have new tools to try to
+ 
+
+ align:start position:0%
+community now have new tools to try to
+puzzle through our answers I'll put it
+
+ align:start position:0%
+puzzle through our answers I'll put it
+ 
+
+ align:start position:0%
+puzzle through our answers I'll put it
+that way
+
+ align:start position:0%
+that way
+ 
+
+ align:start position:0%
+that way
+um I mean one of the things that happens
+
+ align:start position:0%
+um I mean one of the things that happens
+ 
+
+ align:start position:0%
+um I mean one of the things that happens
+is uh people try to explain certain uh
+
+ align:start position:0%
+is uh people try to explain certain uh
+ 
+
+ align:start position:0%
+is uh people try to explain certain uh
+esoteric features of Consciousness using
+
+ align:start position:0%
+esoteric features of Consciousness using
+ 
+
+ align:start position:0%
+esoteric features of Consciousness using
+quantum theory but then it turns out
+
+ align:start position:0%
+quantum theory but then it turns out
+ 
+
+ align:start position:0%
+quantum theory but then it turns out
+that human brains are uh dense hot and
+
+ align:start position:0%
+that human brains are uh dense hot and
+ 
+
+ align:start position:0%
+that human brains are uh dense hot and
+wet and a lot of these Quantum effects
+
+ align:start position:0%
+wet and a lot of these Quantum effects
+ 
+
+ align:start position:0%
+wet and a lot of these Quantum effects
+work really well when we're near vacuum
+
+ align:start position:0%
+work really well when we're near vacuum
+ 
+
+ align:start position:0%
+work really well when we're near vacuum
+at low temperatures and you know like
+
+ align:start position:0%
+at low temperatures and you know like
+ 
+
+ align:start position:0%
+at low temperatures and you know like
+super dry so even though some things
+
+ align:start position:0%
+super dry so even though some things
+ 
+
+ align:start position:0%
+super dry so even though some things
+could happen in principle among Quantum
+
+ align:start position:0%
+could happen in principle among Quantum
+ 
+
+ align:start position:0%
+could happen in principle among Quantum
+objects having to maintain a kind of
+
+ align:start position:0%
+objects having to maintain a kind of
+ 
+
+ align:start position:0%
+objects having to maintain a kind of
+inherent quantumness is really hard in
+
+ align:start position:0%
+inherent quantumness is really hard in
+ 
+
+ align:start position:0%
+inherent quantumness is really hard in
+an environment like the human brain so
+
+ align:start position:0%
+an environment like the human brain so
+ 
+
+ align:start position:0%
+an environment like the human brain so
+again that launches new kinds of
+
+ align:start position:0%
+again that launches new kinds of
+ 
+
+ align:start position:0%
+again that launches new kinds of
+questions and investigations rather than
+
+ align:start position:0%
+questions and investigations rather than
+ 
+
+ align:start position:0%
+questions and investigations rather than
+again than saying oh we've solved so
+
+ align:start position:0%
+again than saying oh we've solved so
+ 
+
+ align:start position:0%
+again than saying oh we've solved so
+those things become really interesting
+
+ align:start position:0%
+those things become really interesting
+ 
+
+ align:start position:0%
+those things become really interesting
+and lots of smart people ask a hard
+
+ align:start position:0%
+and lots of smart people ask a hard
+ 
+
+ align:start position:0%
+and lots of smart people ask a hard
+question about them around the world
+
+ align:start position:0%
+question about them around the world
+ 
+
+ align:start position:0%
+question about them around the world
+because we have this new injection of
+
+ align:start position:0%
+because we have this new injection of
+ 
+
+ align:start position:0%
+because we have this new injection of
+kind of new conceptual things uh to
+
+ align:start position:0%
+kind of new conceptual things uh to
+ 
+
+ align:start position:0%
+kind of new conceptual things uh to
+really wonder about let me pause there I
+
+ align:start position:0%
+really wonder about let me pause there I
+ 
+
+ align:start position:0%
+really wonder about let me pause there I
+don't want to run too long uh remember
+
+ align:start position:0%
+don't want to run too long uh remember
+ 
+
+ align:start position:0%
+don't want to run too long uh remember
+we have class tomorrow twice in uh in a
+
+ align:start position:0%
+we have class tomorrow twice in uh in a
+ 
+
+ align:start position:0%
+we have class tomorrow twice in uh in a
+row this week uh we're back at our
+
+ align:start position:0%
+row this week uh we're back at our
+ 
+
+ align:start position:0%
+row this week uh we're back at our
+ordinary Zoom link you can find it
+
+ align:start position:0%
+ordinary Zoom link you can find it
+ 
+
+ align:start position:0%
+ordinary Zoom link you can find it
+through canvas and so tomorrow we'll sit
+
+ align:start position:0%
+through canvas and so tomorrow we'll sit
+ 
+
+ align:start position:0%
+through canvas and so tomorrow we'll sit
+a little bit longer with some of these
+
+ align:start position:0%
+a little bit longer with some of these
+ 
+
+ align:start position:0%
+a little bit longer with some of these
+uh weird and wacky Quantum phenomena
+
+ align:start position:0%
+uh weird and wacky Quantum phenomena
+ 
+
+ align:start position:0%
+uh weird and wacky Quantum phenomena
+so stay well see you tomorrow talk to
+
+ align:start position:0%
+so stay well see you tomorrow talk to
+ 
+
+ align:start position:0%
+so stay well see you tomorrow talk to
+you soon
\ No newline at end of file
diff --git a/gZ9DWdzGNqQ.txt b/gZ9DWdzGNqQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..64aaaeb18e17172b165dec2e966b160b36846ec7
--- /dev/null
+++ b/gZ9DWdzGNqQ.txt
@@ -0,0 +1,1219 @@
+align:start position:0%
+ 
+in this case study we're going to see
+
+ align:start position:0%
+in this case study we're going to see
+ 
+
+ align:start position:0%
+in this case study we're going to see
+how we can create a photo illustration
+
+ align:start position:0%
+how we can create a photo illustration
+ 
+
+ align:start position:0%
+how we can create a photo illustration
+of your work the idea here is to show
+
+ align:start position:0%
+of your work the idea here is to show
+ 
+
+ align:start position:0%
+of your work the idea here is to show
+how a liquid battery works for a final
+
+ align:start position:0%
+how a liquid battery works for a final
+ 
+
+ align:start position:0%
+how a liquid battery works for a final
+illustration so first create
+
+ align:start position:0%
+illustration so first create
+ 
+
+ align:start position:0%
+illustration so first create
+photographic bits and pieces and put
+
+ align:start position:0%
+photographic bits and pieces and put
+ 
+
+ align:start position:0%
+photographic bits and pieces and put
+them all together think of it just as if
+
+ align:start position:0%
+them all together think of it just as if
+ 
+
+ align:start position:0%
+them all together think of it just as if
+you were drawing the pieces and putting
+
+ align:start position:0%
+you were drawing the pieces and putting
+ 
+
+ align:start position:0%
+you were drawing the pieces and putting
+those sketches together after I met with
+
+ align:start position:0%
+those sketches together after I met with
+ 
+
+ align:start position:0%
+those sketches together after I met with
+the researchers for a brainstorming
+
+ align:start position:0%
+the researchers for a brainstorming
+ 
+
+ align:start position:0%
+the researchers for a brainstorming
+meeting I got all of this material from
+
+ align:start position:0%
+meeting I got all of this material from
+ 
+
+ align:start position:0%
+meeting I got all of this material from
+them including a diagram that described
+
+ align:start position:0%
+them including a diagram that described
+ 
+
+ align:start position:0%
+them including a diagram that described
+my idea to create a model of how a
+
+ align:start position:0%
+my idea to create a model of how a
+ 
+
+ align:start position:0%
+my idea to create a model of how a
+liquid battery works this is the way I
+
+ align:start position:0%
+liquid battery works this is the way I
+ 
+
+ align:start position:0%
+liquid battery works this is the way I
+imagined the shoot to go okay first I
+
+ align:start position:0%
+imagined the shoot to go okay first I
+ 
+
+ align:start position:0%
+imagined the shoot to go okay first I
+would take an optical quality cuvette
+
+ align:start position:0%
+would take an optical quality cuvette
+ 
+
+ align:start position:0%
+would take an optical quality cuvette
+and would then pour the mercury and the
+
+ align:start position:0%
+and would then pour the mercury and the
+ 
+
+ align:start position:0%
+and would then pour the mercury and the
+water into the cuvette and somehow
+
+ align:start position:0%
+water into the cuvette and somehow
+ 
+
+ align:start position:0%
+water into the cuvette and somehow
+suspending with a clamp a strip of metal
+
+ align:start position:0%
+suspending with a clamp a strip of metal
+ 
+
+ align:start position:0%
+suspending with a clamp a strip of metal
+foam which is an important part of the
+
+ align:start position:0%
+foam which is an important part of the
+ 
+
+ align:start position:0%
+foam which is an important part of the
+science and because I was imagining a
+
+ align:start position:0%
+science and because I was imagining a
+ 
+
+ align:start position:0%
+science and because I was imagining a
+full container of this material after
+
+ align:start position:0%
+full container of this material after
+ 
+
+ align:start position:0%
+full container of this material after
+making the image I would then crop out
+
+ align:start position:0%
+making the image I would then crop out
+ 
+
+ align:start position:0%
+making the image I would then crop out
+the right side we don't need to see the
+
+ align:start position:0%
+the right side we don't need to see the
+ 
+
+ align:start position:0%
+the right side we don't need to see the
+clamping device and then flip the left
+
+ align:start position:0%
+clamping device and then flip the left
+ 
+
+ align:start position:0%
+clamping device and then flip the left
+side or a small portion of the left side
+
+ align:start position:0%
+side or a small portion of the left side
+ 
+
+ align:start position:0%
+side or a small portion of the left side
+over to the right to then make the full
+
+ align:start position:0%
+over to the right to then make the full
+ 
+
+ align:start position:0%
+over to the right to then make the full
+container and the final model now
+
+ align:start position:0%
+container and the final model now
+ 
+
+ align:start position:0%
+container and the final model now
+remember this is not a documentary image
+
+ align:start position:0%
+remember this is not a documentary image
+ 
+
+ align:start position:0%
+remember this is not a documentary image
+this is a photo illustration for
+
+ align:start position:0%
+this is a photo illustration for
+ 
+
+ align:start position:0%
+this is a photo illustration for
+hopefully a cover submission that's the
+
+ align:start position:0%
+hopefully a cover submission that's the
+ 
+
+ align:start position:0%
+hopefully a cover submission that's the
+idea okay so first I start looking at
+
+ align:start position:0%
+idea okay so first I start looking at
+ 
+
+ align:start position:0%
+idea okay so first I start looking at
+the cuvette the vessel into which I was
+
+ align:start position:0%
+the cuvette the vessel into which I was
+ 
+
+ align:start position:0%
+the cuvette the vessel into which I was
+going to be inserting and pouring all
+
+ align:start position:0%
+going to be inserting and pouring all
+ 
+
+ align:start position:0%
+going to be inserting and pouring all
+the components I put it on a lightbox
+
+ align:start position:0%
+the components I put it on a lightbox
+ 
+
+ align:start position:0%
+the components I put it on a lightbox
+and liked what I saw the picture was
+
+ align:start position:0%
+and liked what I saw the picture was
+ 
+
+ align:start position:0%
+and liked what I saw the picture was
+going to be simple and licked fairly
+
+ align:start position:0%
+going to be simple and licked fairly
+ 
+
+ align:start position:0%
+going to be simple and licked fairly
+well then I practiced inserting the
+
+ align:start position:0%
+well then I practiced inserting the
+ 
+
+ align:start position:0%
+well then I practiced inserting the
+metal foam with a clamping apparatus to
+
+ align:start position:0%
+metal foam with a clamping apparatus to
+ 
+
+ align:start position:0%
+metal foam with a clamping apparatus to
+see if it was doable and it was at least
+
+ align:start position:0%
+see if it was doable and it was at least
+ 
+
+ align:start position:0%
+see if it was doable and it was at least
+with an empty container sort of dry run
+
+ align:start position:0%
+with an empty container sort of dry run
+ 
+
+ align:start position:0%
+with an empty container sort of dry run
+so to speak so the next photograph I
+
+ align:start position:0%
+so to speak so the next photograph I
+ 
+
+ align:start position:0%
+so to speak so the next photograph I
+took was with the Mercury and water in
+
+ align:start position:0%
+took was with the Mercury and water in
+ 
+
+ align:start position:0%
+took was with the Mercury and water in
+the container which looked fine too
+
+ align:start position:0%
+the container which looked fine too
+ 
+
+ align:start position:0%
+the container which looked fine too
+I then discarded that by the way into
+
+ align:start position:0%
+I then discarded that by the way into
+ 
+
+ align:start position:0%
+I then discarded that by the way into
+special container the researchers
+
+ align:start position:0%
+special container the researchers
+ 
+
+ align:start position:0%
+special container the researchers
+provided and sort of started all over
+
+ align:start position:0%
+provided and sort of started all over
+ 
+
+ align:start position:0%
+provided and sort of started all over
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+and tried for the next steps which was
+
+ align:start position:0%
+and tried for the next steps which was
+ 
+
+ align:start position:0%
+and tried for the next steps which was
+going to be inserting the foam at a
+
+ align:start position:0%
+going to be inserting the foam at a
+ 
+
+ align:start position:0%
+going to be inserting the foam at a
+certain level with the water I played a
+
+ align:start position:0%
+certain level with the water I played a
+ 
+
+ align:start position:0%
+certain level with the water I played a
+little with lighting by shining a
+
+ align:start position:0%
+little with lighting by shining a
+ 
+
+ align:start position:0%
+little with lighting by shining a
+tungsten lamp on to it it gave a warmer
+
+ align:start position:0%
+tungsten lamp on to it it gave a warmer
+ 
+
+ align:start position:0%
+tungsten lamp on to it it gave a warmer
+feel which I liked then I plopped it
+
+ align:start position:0%
+feel which I liked then I plopped it
+ 
+
+ align:start position:0%
+feel which I liked then I plopped it
+further into the water to see how that
+
+ align:start position:0%
+further into the water to see how that
+ 
+
+ align:start position:0%
+further into the water to see how that
+was going to look and again I changed
+
+ align:start position:0%
+was going to look and again I changed
+ 
+
+ align:start position:0%
+was going to look and again I changed
+the lighting by adding a little lamp
+
+ align:start position:0%
+the lighting by adding a little lamp
+ 
+
+ align:start position:0%
+the lighting by adding a little lamp
+light onto this material so I was
+
+ align:start position:0%
+light onto this material so I was
+ 
+
+ align:start position:0%
+light onto this material so I was
+getting there
+
+ align:start position:0%
+getting there
+ 
+
+ align:start position:0%
+getting there
+eventually this is the image that I
+
+ align:start position:0%
+eventually this is the image that I
+ 
+
+ align:start position:0%
+eventually this is the image that I
+wound up with well sort of wound up with
+
+ align:start position:0%
+wound up with well sort of wound up with
+ 
+
+ align:start position:0%
+wound up with well sort of wound up with
+and I'll tell you frankly I was a bit
+
+ align:start position:0%
+and I'll tell you frankly I was a bit
+ 
+
+ align:start position:0%
+and I'll tell you frankly I was a bit
+nervous dealing with the mercury and
+
+ align:start position:0%
+nervous dealing with the mercury and
+ 
+
+ align:start position:0%
+nervous dealing with the mercury and
+pouring it out and dealing with that and
+
+ align:start position:0%
+pouring it out and dealing with that and
+ 
+
+ align:start position:0%
+pouring it out and dealing with that and
+the water especially while having the
+
+ align:start position:0%
+the water especially while having the
+ 
+
+ align:start position:0%
+the water especially while having the
+important cautionary instructions always
+
+ align:start position:0%
+important cautionary instructions always
+ 
+
+ align:start position:0%
+important cautionary instructions always
+sitting in front of me so again making
+
+ align:start position:0%
+sitting in front of me so again making
+ 
+
+ align:start position:0%
+sitting in front of me so again making
+the pieces photographically and then
+
+ align:start position:0%
+the pieces photographically and then
+ 
+
+ align:start position:0%
+the pieces photographically and then
+putting them together was the way to go
+
+ align:start position:0%
+putting them together was the way to go
+ 
+
+ align:start position:0%
+putting them together was the way to go
+remember this is an illustration using
+
+ align:start position:0%
+remember this is an illustration using
+ 
+
+ align:start position:0%
+remember this is an illustration using
+photographs for the purpose of creating
+
+ align:start position:0%
+photographs for the purpose of creating
+ 
+
+ align:start position:0%
+photographs for the purpose of creating
+a model of the technique of how a liquid
+
+ align:start position:0%
+a model of the technique of how a liquid
+ 
+
+ align:start position:0%
+a model of the technique of how a liquid
+battery works and this is how I did it
+
+ align:start position:0%
+battery works and this is how I did it
+ 
+
+ align:start position:0%
+battery works and this is how I did it
+I'm using Photoshop here but you can use
+
+ align:start position:0%
+I'm using Photoshop here but you can use
+ 
+
+ align:start position:0%
+I'm using Photoshop here but you can use
+other software of course and take a look
+
+ align:start position:0%
+other software of course and take a look
+ 
+
+ align:start position:0%
+other software of course and take a look
+at the real-life part of this where
+
+ align:start position:0%
+at the real-life part of this where
+ 
+
+ align:start position:0%
+at the real-life part of this where
+we're using one images for the receiver
+
+ align:start position:0%
+we're using one images for the receiver
+ 
+
+ align:start position:0%
+we're using one images for the receiver
+of the piece on the right side which is
+
+ align:start position:0%
+of the piece on the right side which is
+ 
+
+ align:start position:0%
+of the piece on the right side which is
+what we had been talking about so I'm
+
+ align:start position:0%
+what we had been talking about so I'm
+ 
+
+ align:start position:0%
+what we had been talking about so I'm
+first going to select the right side
+
+ align:start position:0%
+first going to select the right side
+ 
+
+ align:start position:0%
+first going to select the right side
+copy and paste into the image on the
+
+ align:start position:0%
+copy and paste into the image on the
+ 
+
+ align:start position:0%
+copy and paste into the image on the
+left side the container with all the
+
+ align:start position:0%
+left side the container with all the
+ 
+
+ align:start position:0%
+left side the container with all the
+material move it around a little bit see
+
+ align:start position:0%
+material move it around a little bit see
+ 
+
+ align:start position:0%
+material move it around a little bit see
+if it has the potential of being doable
+
+ align:start position:0%
+if it has the potential of being doable
+ 
+
+ align:start position:0%
+if it has the potential of being doable
+it's not bad I think when it's flattened
+
+ align:start position:0%
+it's not bad I think when it's flattened
+ 
+
+ align:start position:0%
+it's not bad I think when it's flattened
+it'll look better I think it can work so
+
+ align:start position:0%
+it'll look better I think it can work so
+ 
+
+ align:start position:0%
+it'll look better I think it can work so
+I will in fact flatten the image and if
+
+ align:start position:0%
+I will in fact flatten the image and if
+ 
+
+ align:start position:0%
+I will in fact flatten the image and if
+you remember we were going to crop out
+
+ align:start position:0%
+you remember we were going to crop out
+ 
+
+ align:start position:0%
+you remember we were going to crop out
+the right side which is what we're going
+
+ align:start position:0%
+the right side which is what we're going
+ 
+
+ align:start position:0%
+the right side which is what we're going
+to do here crop make the image as full
+
+ align:start position:0%
+to do here crop make the image as full
+ 
+
+ align:start position:0%
+to do here crop make the image as full
+as we can with
+
+ align:start position:0%
+as we can with
+ 
+
+ align:start position:0%
+as we can with
+out the right-side cropping it out okay
+
+ align:start position:0%
+out the right-side cropping it out okay
+ 
+
+ align:start position:0%
+out the right-side cropping it out okay
+that looks pretty okay and now as we had
+
+ align:start position:0%
+that looks pretty okay and now as we had
+ 
+
+ align:start position:0%
+that looks pretty okay and now as we had
+previously talked about in the animation
+
+ align:start position:0%
+previously talked about in the animation
+ 
+
+ align:start position:0%
+previously talked about in the animation
+we're going to flip one side to another
+
+ align:start position:0%
+we're going to flip one side to another
+ 
+
+ align:start position:0%
+we're going to flip one side to another
+but first in order to do that I'm going
+
+ align:start position:0%
+but first in order to do that I'm going
+ 
+
+ align:start position:0%
+but first in order to do that I'm going
+to expand the canvas to make room for
+
+ align:start position:0%
+to expand the canvas to make room for
+ 
+
+ align:start position:0%
+to expand the canvas to make room for
+the new piece that we're going to start
+
+ align:start position:0%
+the new piece that we're going to start
+ 
+
+ align:start position:0%
+the new piece that we're going to start
+working with so I am in fact taking a
+
+ align:start position:0%
+working with so I am in fact taking a
+ 
+
+ align:start position:0%
+working with so I am in fact taking a
+piece at the left side which is what we
+
+ align:start position:0%
+piece at the left side which is what we
+ 
+
+ align:start position:0%
+piece at the left side which is what we
+talked about
+
+ align:start position:0%
+talked about
+ 
+
+ align:start position:0%
+talked about
+I'm copy and pasting there it is again
+
+ align:start position:0%
+I'm copy and pasting there it is again
+ 
+
+ align:start position:0%
+I'm copy and pasting there it is again
+and we're going to flip it to make up
+
+ align:start position:0%
+and we're going to flip it to make up
+ 
+
+ align:start position:0%
+and we're going to flip it to make up
+for the empty side we'll just flip it
+
+ align:start position:0%
+for the empty side we'll just flip it
+ 
+
+ align:start position:0%
+for the empty side we'll just flip it
+horizontally move it around a bit and
+
+ align:start position:0%
+horizontally move it around a bit and
+ 
+
+ align:start position:0%
+horizontally move it around a bit and
+with a little fudging we get a pretty
+
+ align:start position:0%
+with a little fudging we get a pretty
+ 
+
+ align:start position:0%
+with a little fudging we get a pretty
+nice start for an image that we're
+
+ align:start position:0%
+nice start for an image that we're
+ 
+
+ align:start position:0%
+nice start for an image that we're
+getting to I decided to play more about
+
+ align:start position:0%
+getting to I decided to play more about
+ 
+
+ align:start position:0%
+getting to I decided to play more about
+raising it one more level and so I went
+
+ align:start position:0%
+raising it one more level and so I went
+ 
+
+ align:start position:0%
+raising it one more level and so I went
+back to what we have seen before and in
+
+ align:start position:0%
+back to what we have seen before and in
+ 
+
+ align:start position:0%
+back to what we have seen before and in
+another image where I basically take
+
+ align:start position:0%
+another image where I basically take
+ 
+
+ align:start position:0%
+another image where I basically take
+this pretty good image select the
+
+ align:start position:0%
+this pretty good image select the
+ 
+
+ align:start position:0%
+this pretty good image select the
+background invert the selection so that
+
+ align:start position:0%
+background invert the selection so that
+ 
+
+ align:start position:0%
+background invert the selection so that
+we have in fact selected the liquid
+
+ align:start position:0%
+we have in fact selected the liquid
+ 
+
+ align:start position:0%
+we have in fact selected the liquid
+battery copy and paste and you see here
+
+ align:start position:0%
+battery copy and paste and you see here
+ 
+
+ align:start position:0%
+battery copy and paste and you see here
+we have another layer of just the liquid
+
+ align:start position:0%
+we have another layer of just the liquid
+ 
+
+ align:start position:0%
+we have another layer of just the liquid
+battery and went to layer style and went
+
+ align:start position:0%
+battery and went to layer style and went
+ 
+
+ align:start position:0%
+battery and went to layer style and went
+back to our old drop shadow friend and I
+
+ align:start position:0%
+back to our old drop shadow friend and I
+ 
+
+ align:start position:0%
+back to our old drop shadow friend and I
+played with making a drop shadow which I
+
+ align:start position:0%
+played with making a drop shadow which I
+ 
+
+ align:start position:0%
+played with making a drop shadow which I
+did like I tend to think that it just
+
+ align:start position:0%
+did like I tend to think that it just
+ 
+
+ align:start position:0%
+did like I tend to think that it just
+pushes it away and I think it worked
+
+ align:start position:0%
+pushes it away and I think it worked
+ 
+
+ align:start position:0%
+pushes it away and I think it worked
+quite well eventually what I did wind up
+
+ align:start position:0%
+quite well eventually what I did wind up
+ 
+
+ align:start position:0%
+quite well eventually what I did wind up
+doing is playing a little bit with
+
+ align:start position:0%
+doing is playing a little bit with
+ 
+
+ align:start position:0%
+doing is playing a little bit with
+putting a different background for
+
+ align:start position:0%
+putting a different background for
+ 
+
+ align:start position:0%
+putting a different background for
+example making a gradient that wasn't
+
+ align:start position:0%
+example making a gradient that wasn't
+ 
+
+ align:start position:0%
+example making a gradient that wasn't
+going to work I didn't even know what I
+
+ align:start position:0%
+going to work I didn't even know what I
+ 
+
+ align:start position:0%
+going to work I didn't even know what I
+had in mind but I really wanted
+
+ align:start position:0%
+had in mind but I really wanted
+ 
+
+ align:start position:0%
+had in mind but I really wanted
+something a little more dramatic so
+
+ align:start position:0%
+something a little more dramatic so
+ 
+
+ align:start position:0%
+something a little more dramatic so
+going back to the picture without the
+
+ align:start position:0%
+going back to the picture without the
+ 
+
+ align:start position:0%
+going back to the picture without the
+color in the background on keeping the
+
+ align:start position:0%
+color in the background on keeping the
+ 
+
+ align:start position:0%
+color in the background on keeping the
+drop shadow I went to adjustments
+
+ align:start position:0%
+drop shadow I went to adjustments
+ 
+
+ align:start position:0%
+drop shadow I went to adjustments
+decided to invert the whole picture and
+
+ align:start position:0%
+decided to invert the whole picture and
+ 
+
+ align:start position:0%
+decided to invert the whole picture and
+yes that's quite a unusual image and but
+
+ align:start position:0%
+yes that's quite a unusual image and but
+ 
+
+ align:start position:0%
+yes that's quite a unusual image and but
+decided to do it and play a little bit
+
+ align:start position:0%
+decided to do it and play a little bit
+ 
+
+ align:start position:0%
+decided to do it and play a little bit
+with the hue to get that blue back to
+
+ align:start position:0%
+with the hue to get that blue back to
+ 
+
+ align:start position:0%
+with the hue to get that blue back to
+the orange that I sort of liked wasn't
+
+ align:start position:0%
+the orange that I sort of liked wasn't
+ 
+
+ align:start position:0%
+the orange that I sort of liked wasn't
+quite enough I increase the saturation a
+
+ align:start position:0%
+quite enough I increase the saturation a
+ 
+
+ align:start position:0%
+quite enough I increase the saturation a
+little bit and there it is this was the
+
+ align:start position:0%
+little bit and there it is this was the
+ 
+
+ align:start position:0%
+little bit and there it is this was the
+final image that I showed to the
+
+ align:start position:0%
+final image that I showed to the
+ 
+
+ align:start position:0%
+final image that I showed to the
+researcher and frankly I think we got
+
+ align:start position:0%
+researcher and frankly I think we got
+ 
+
+ align:start position:0%
+researcher and frankly I think we got
+ourselves a winner unfortunately not the
+
+ align:start position:0%
+ourselves a winner unfortunately not the
+ 
+
+ align:start position:0%
+ourselves a winner unfortunately not the
+cover of the journal which I really we
+
+ align:start position:0%
+cover of the journal which I really we
+ 
+
+ align:start position:0%
+cover of the journal which I really we
+were hoping that would happen but it did
+
+ align:start position:0%
+were hoping that would happen but it did
+ 
+
+ align:start position:0%
+were hoping that would happen but it did
+get the home page of the journal and a
+
+ align:start position:0%
+get the home page of the journal and a
+ 
+
+ align:start position:0%
+get the home page of the journal and a
+couple of other home pages of various
+
+ align:start position:0%
+couple of other home pages of various
+ 
+
+ align:start position:0%
+couple of other home pages of various
+journals and it got a lot of attention
+
+ align:start position:0%
+journals and it got a lot of attention
+ 
+
+ align:start position:0%
+journals and it got a lot of attention
+first of all of course the science was
+
+ align:start position:0%
+first of all of course the science was
+ 
+
+ align:start position:0%
+first of all of course the science was
+important but we pretty much agree that
+
+ align:start position:0%
+important but we pretty much agree that
+ 
+
+ align:start position:0%
+important but we pretty much agree that
+making an image to draw attention to the
+
+ align:start position:0%
+making an image to draw attention to the
+ 
+
+ align:start position:0%
+making an image to draw attention to the
+science really is what this image making
+
+ align:start position:0%
+science really is what this image making
+ 
+
+ align:start position:0%
+science really is what this image making
+is about I hope you enjoy this and see
+
+ align:start position:0%
+is about I hope you enjoy this and see
+ 
+
+ align:start position:0%
+is about I hope you enjoy this and see
+the thinking that is extensive when you
+
+ align:start position:0%
+the thinking that is extensive when you
+ 
+
+ align:start position:0%
+the thinking that is extensive when you
+get into something that's complicated
\ No newline at end of file
diff --git a/gyaqXwi4BDk.txt b/gyaqXwi4BDk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ddb68b1f2e0d880a4a522696fc12587254d843c8
--- /dev/null
+++ b/gyaqXwi4BDk.txt
@@ -0,0 +1,13931 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's get started on Thursday we
+
+ align:start position:0%
+okay let's get started on Thursday we
+ 
+
+ align:start position:0%
+okay let's get started on Thursday we
+are really privileged to have John
+
+ align:start position:0%
+are really privileged to have John
+ 
+
+ align:start position:0%
+are really privileged to have John
+Bentley who is one of the Masters of
+
+ align:start position:0%
+Bentley who is one of the Masters of
+ 
+
+ align:start position:0%
+Bentley who is one of the Masters of
+performance engineering come and give us
+
+ align:start position:0%
+performance engineering come and give us
+ 
+
+ align:start position:0%
+performance engineering come and give us
+a guest lecture in 1982 he wrote this
+
+ align:start position:0%
+a guest lecture in 1982 he wrote this
+ 
+
+ align:start position:0%
+a guest lecture in 1982 he wrote this
+wonderful little book from which we
+
+ align:start position:0%
+wonderful little book from which we
+ 
+
+ align:start position:0%
+wonderful little book from which we
+adapted the Bentley rules that you folks
+
+ align:start position:0%
+adapted the Bentley rules that you folks
+ 
+
+ align:start position:0%
+adapted the Bentley rules that you folks
+have seen and he's also famous for
+
+ align:start position:0%
+have seen and he's also famous for
+ 
+
+ align:start position:0%
+have seen and he's also famous for
+things like KD trees who's seen KD trees
+
+ align:start position:0%
+things like KD trees who's seen KD trees
+ 
+
+ align:start position:0%
+things like KD trees who's seen KD trees
+yeah so he invented KD trees and who's
+
+ align:start position:0%
+yeah so he invented KD trees and who's
+ 
+
+ align:start position:0%
+yeah so he invented KD trees and who's
+ever used the master method of the
+
+ align:start position:0%
+ever used the master method of the
+ 
+
+ align:start position:0%
+ever used the master method of the
+current saw he invented the master
+
+ align:start position:0%
+current saw he invented the master
+ 
+
+ align:start position:0%
+current saw he invented the master
+method of recurrence solving and so I
+
+ align:start position:0%
+method of recurrence solving and so I
+ 
+
+ align:start position:0%
+method of recurrence solving and so I
+mean he's just a wonderful wonderful
+
+ align:start position:0%
+mean he's just a wonderful wonderful
+ 
+
+ align:start position:0%
+mean he's just a wonderful wonderful
+fellow with lots and lots of insights
+
+ align:start position:0%
+fellow with lots and lots of insights
+ 
+
+ align:start position:0%
+fellow with lots and lots of insights
+and just like a superior performance
+
+ align:start position:0%
+and just like a superior performance
+ 
+
+ align:start position:0%
+and just like a superior performance
+engineer and he's going to talk give a
+
+ align:start position:0%
+engineer and he's going to talk give a
+ 
+
+ align:start position:0%
+engineer and he's going to talk give a
+guest lecture on Thursday and so I would
+
+ align:start position:0%
+guest lecture on Thursday and so I would
+ 
+
+ align:start position:0%
+guest lecture on Thursday and so I would
+encourage you to bring your friends
+
+ align:start position:0%
+encourage you to bring your friends
+ 
+
+ align:start position:0%
+encourage you to bring your friends
+bring friends maybe who dropped the
+
+ align:start position:0%
+bring friends maybe who dropped the
+ 
+
+ align:start position:0%
+bring friends maybe who dropped the
+class okay because this is like this is
+
+ align:start position:0%
+class okay because this is like this is
+ 
+
+ align:start position:0%
+class okay because this is like this is
+the and and others who you may who you
+
+ align:start position:0%
+the and and others who you may who you
+ 
+
+ align:start position:0%
+the and and others who you may who you
+know if any of you have urops other
+
+ align:start position:0%
+know if any of you have urops other
+ 
+
+ align:start position:0%
+know if any of you have urops other
+people in your research group whether
+
+ align:start position:0%
+people in your research group whether
+ 
+
+ align:start position:0%
+people in your research group whether
+there are graduate students or whatever
+
+ align:start position:0%
+there are graduate students or whatever
+ 
+
+ align:start position:0%
+there are graduate students or whatever
+they're all welcome to come because this
+
+ align:start position:0%
+they're all welcome to come because this
+ 
+
+ align:start position:0%
+they're all welcome to come because this
+is really you know one of the
+
+ align:start position:0%
+is really you know one of the
+ 
+
+ align:start position:0%
+is really you know one of the
+opportunities you get to to actually
+
+ align:start position:0%
+opportunities you get to to actually
+ 
+
+ align:start position:0%
+opportunities you get to to actually
+meet one of the you know legends of the
+
+ align:start position:0%
+meet one of the you know legends of the
+ 
+
+ align:start position:0%
+meet one of the you know legends of the
+field if you will and you know have a
+
+ align:start position:0%
+field if you will and you know have a
+ 
+
+ align:start position:0%
+field if you will and you know have a
+and you'll see he's very approachable
+
+ align:start position:0%
+and you'll see he's very approachable
+ 
+
+ align:start position:0%
+and you'll see he's very approachable
+he's very approachable so um so anyway
+
+ align:start position:0%
+he's very approachable so um so anyway
+ 
+
+ align:start position:0%
+he's very approachable so um so anyway
+my advertisement for John Bentley good
+
+ align:start position:0%
+my advertisement for John Bentley good
+ 
+
+ align:start position:0%
+my advertisement for John Bentley good
+so let's start I want to talk about
+
+ align:start position:0%
+so let's start I want to talk about
+ 
+
+ align:start position:0%
+so let's start I want to talk about
+speculative parallelism for a little bit
+
+ align:start position:0%
+speculative parallelism for a little bit
+ 
+
+ align:start position:0%
+speculative parallelism for a little bit
+because that's kind of what you need to
+
+ align:start position:0%
+because that's kind of what you need to
+ 
+
+ align:start position:0%
+because that's kind of what you need to
+make the code go fast so if you look at
+
+ align:start position:0%
+make the code go fast so if you look at
+ 
+
+ align:start position:0%
+make the code go fast so if you look at
+code like alpha beta it turns out that
+
+ align:start position:0%
+code like alpha beta it turns out that
+ 
+
+ align:start position:0%
+code like alpha beta it turns out that
+it's inherently serial okay that is if
+
+ align:start position:0%
+it's inherently serial okay that is if
+ 
+
+ align:start position:0%
+it's inherently serial okay that is if
+you don't you know if you try to do
+
+ align:start position:0%
+you don't you know if you try to do
+ 
+
+ align:start position:0%
+you don't you know if you try to do
+things in parallel then you miss the
+
+ align:start position:0%
+things in parallel then you miss the
+ 
+
+ align:start position:0%
+things in parallel then you miss the
+cut-offs and if you miss the cut-offs
+
+ align:start position:0%
+cut-offs and if you miss the cut-offs
+ 
+
+ align:start position:0%
+cut-offs and if you miss the cut-offs
+you know the beta cut-offs then
+
+ align:start position:0%
+you know the beta cut-offs then
+ 
+
+ align:start position:0%
+you know the beta cut-offs then
+you start doing work that you wouldn't
+
+ align:start position:0%
+you start doing work that you wouldn't
+ 
+
+ align:start position:0%
+you start doing work that you wouldn't
+necessarily need to do and so the only
+
+ align:start position:0%
+necessarily need to do and so the only
+ 
+
+ align:start position:0%
+necessarily need to do and so the only
+way to sort of make this type of code
+
+ align:start position:0%
+way to sort of make this type of code
+ 
+
+ align:start position:0%
+way to sort of make this type of code
+run fast is to use speculation which is
+
+ align:start position:0%
+run fast is to use speculation which is
+ 
+
+ align:start position:0%
+run fast is to use speculation which is
+to say that you're gonna guess that you
+
+ align:start position:0%
+to say that you're gonna guess that you
+ 
+
+ align:start position:0%
+to say that you're gonna guess that you
+can do stuff in parallel and it'll be
+
+ align:start position:0%
+can do stuff in parallel and it'll be
+ 
+
+ align:start position:0%
+can do stuff in parallel and it'll be
+worthwhile and then occasionally you're
+
+ align:start position:0%
+worthwhile and then occasionally you're
+ 
+
+ align:start position:0%
+worthwhile and then occasionally you're
+going to be wrong but the trick is well
+
+ align:start position:0%
+going to be wrong but the trick is well
+ 
+
+ align:start position:0%
+going to be wrong but the trick is well
+how do you minimize the wasted effort
+
+ align:start position:0%
+how do you minimize the wasted effort
+ 
+
+ align:start position:0%
+how do you minimize the wasted effort
+when things go wrong so let's just take
+
+ align:start position:0%
+when things go wrong so let's just take
+ 
+
+ align:start position:0%
+when things go wrong so let's just take
+a look at a very simple example of of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speculative parallelism which is Thresh
+
+ align:start position:0%
+speculative parallelism which is Thresh
+ 
+
+ align:start position:0%
+speculative parallelism which is Thresh
+holding a sum so here we have a little
+
+ align:start position:0%
+holding a sum so here we have a little
+ 
+
+ align:start position:0%
+holding a sum so here we have a little
+program that is returning a boolean it
+
+ align:start position:0%
+program that is returning a boolean it
+ 
+
+ align:start position:0%
+program that is returning a boolean it
+takes as input an array of size n so
+
+ align:start position:0%
+takes as input an array of size n so
+ 
+
+ align:start position:0%
+takes as input an array of size n so
+threshold in sums you have an array a of
+
+ align:start position:0%
+threshold in sums you have an array a of
+ 
+
+ align:start position:0%
+threshold in sums you have an array a of
+length n and a limit and these are all
+
+ align:start position:0%
+length n and a limit and these are all
+ 
+
+ align:start position:0%
+length n and a limit and these are all
+unsigned integers say and I start out
+
+ align:start position:0%
+unsigned integers say and I start out
+ 
+
+ align:start position:0%
+unsigned integers say and I start out
+the summit zero and what I'm gonna do is
+
+ align:start position:0%
+the summit zero and what I'm gonna do is
+ 
+
+ align:start position:0%
+the summit zero and what I'm gonna do is
+add up all the elements of the array and
+
+ align:start position:0%
+add up all the elements of the array and
+ 
+
+ align:start position:0%
+add up all the elements of the array and
+if it exceeds the limit then I'm gonna
+
+ align:start position:0%
+if it exceeds the limit then I'm gonna
+ 
+
+ align:start position:0%
+if it exceeds the limit then I'm gonna
+return okay and so um how might I
+
+ align:start position:0%
+return okay and so um how might I
+ 
+
+ align:start position:0%
+return okay and so um how might I
+optimize this code a little bit yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no let's say on one one processor on one
+
+ align:start position:0%
+no let's say on one one processor on one
+ 
+
+ align:start position:0%
+no let's say on one one processor on one
+processor what might you do yeah once
+
+ align:start position:0%
+processor what might you do yeah once
+ 
+
+ align:start position:0%
+processor what might you do yeah once
+you check so that once you would exceed
+
+ align:start position:0%
+you check so that once you would exceed
+ 
+
+ align:start position:0%
+you check so that once you would exceed
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+why keep adding the other numbers okay
+
+ align:start position:0%
+why keep adding the other numbers okay
+ 
+
+ align:start position:0%
+why keep adding the other numbers okay
+so here's a code that does that quit
+
+ align:start position:0%
+so here's a code that does that quit
+ 
+
+ align:start position:0%
+so here's a code that does that quit
+early if the partial product ever sees
+
+ align:start position:0%
+early if the partial product ever sees
+ 
+
+ align:start position:0%
+early if the partial product ever sees
+the threshold this isn't necessarily an
+
+ align:start position:0%
+the threshold this isn't necessarily an
+ 
+
+ align:start position:0%
+the threshold this isn't necessarily an
+optimization it was noticed that now in
+
+ align:start position:0%
+optimization it was noticed that now in
+ 
+
+ align:start position:0%
+optimization it was noticed that now in
+the optimization not only do I have you
+
+ align:start position:0%
+the optimization not only do I have you
+ 
+
+ align:start position:0%
+the optimization not only do I have you
+know a memory reference and in addition
+
+ align:start position:0%
+know a memory reference and in addition
+ 
+
+ align:start position:0%
+know a memory reference and in addition
+I also now have a you know I also have a
+
+ align:start position:0%
+I also now have a you know I also have a
+ 
+
+ align:start position:0%
+I also now have a you know I also have a
+unpredictable branch actually it's
+
+ align:start position:0%
+unpredictable branch actually it's
+ 
+
+ align:start position:0%
+unpredictable branch actually it's
+predictable branch sorry predictable
+
+ align:start position:0%
+predictable branch sorry predictable
+ 
+
+ align:start position:0%
+predictable branch sorry predictable
+branch but it's still one more one more
+
+ align:start position:0%
+branch but it's still one more one more
+ 
+
+ align:start position:0%
+branch but it's still one more one more
+step because it's always going to
+
+ align:start position:0%
+step because it's always going to
+ 
+
+ align:start position:0%
+step because it's always going to
+predict that it's not exceeding until it
+
+ align:start position:0%
+predict that it's not exceeding until it
+ 
+
+ align:start position:0%
+predict that it's not exceeding until it
+actually does exceed so that'll be
+
+ align:start position:0%
+actually does exceed so that'll be
+ 
+
+ align:start position:0%
+actually does exceed so that'll be
+pretty predictable and but still I've
+
+ align:start position:0%
+pretty predictable and but still I've
+ 
+
+ align:start position:0%
+pretty predictable and but still I've
+added something into the loop so that
+
+ align:start position:0%
+added something into the loop so that
+ 
+
+ align:start position:0%
+added something into the loop so that
+maybe so how might I mitigate that
+
+ align:start position:0%
+maybe so how might I mitigate that
+ 
+
+ align:start position:0%
+maybe so how might I mitigate that
+problem so I don't want to add too much
+
+ align:start position:0%
+problem so I don't want to add too much
+ 
+
+ align:start position:0%
+problem so I don't want to add too much
+into the inner loop yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so basically I can do what's called
+
+ align:start position:0%
+yeah so basically I can do what's called
+ 
+
+ align:start position:0%
+yeah so basically I can do what's called
+strip mining I replace the loop of n
+
+ align:start position:0%
+strip mining I replace the loop of n
+ 
+
+ align:start position:0%
+strip mining I replace the loop of n
+iterations with a loop of let's say n
+
+ align:start position:0%
+iterations with a loop of let's say n
+ 
+
+ align:start position:0%
+iterations with a loop of let's say n
+over four iterations with an inner loop
+
+ align:start position:0%
+over four iterations with an inner loop
+ 
+
+ align:start position:0%
+over four iterations with an inner loop
+of four iterations and every fourth
+
+ align:start position:0%
+of four iterations and every fourth
+ 
+
+ align:start position:0%
+of four iterations and every fourth
+iteration I check to see whether or not
+
+ align:start position:0%
+iteration I check to see whether or not
+ 
+
+ align:start position:0%
+iteration I check to see whether or not
+I've exceeded okay so that the cost of
+
+ align:start position:0%
+I've exceeded okay so that the cost of
+ 
+
+ align:start position:0%
+I've exceeded okay so that the cost of
+the the check is going to be you know
+
+ align:start position:0%
+the the check is going to be you know
+ 
+
+ align:start position:0%
+the the check is going to be you know
+relatively small at that point okay so
+
+ align:start position:0%
+relatively small at that point okay so
+ 
+
+ align:start position:0%
+relatively small at that point okay so
+there are ways of of making this sort of
+
+ align:start position:0%
+there are ways of of making this sort of
+ 
+
+ align:start position:0%
+there are ways of of making this sort of
+go fast okay so now we want to make this
+
+ align:start position:0%
+go fast okay so now we want to make this
+ 
+
+ align:start position:0%
+go fast okay so now we want to make this
+operate in parallel okay and the problem
+
+ align:start position:0%
+operate in parallel okay and the problem
+ 
+
+ align:start position:0%
+operate in parallel okay and the problem
+in when I operate in parallel is that is
+
+ align:start position:0%
+in when I operate in parallel is that is
+ 
+
+ align:start position:0%
+in when I operate in parallel is that is
+that as I'm adding stuff up I want to do
+
+ align:start position:0%
+that as I'm adding stuff up I want to do
+ 
+
+ align:start position:0%
+that as I'm adding stuff up I want to do
+it so I'm going to do this here with a
+
+ align:start position:0%
+it so I'm going to do this here with a
+ 
+
+ align:start position:0%
+it so I'm going to do this here with a
+reducer and so basically I'm going to
+
+ align:start position:0%
+reducer and so basically I'm going to
+ 
+
+ align:start position:0%
+reducer and so basically I'm going to
+add up the values in the reducer but now
+
+ align:start position:0%
+add up the values in the reducer but now
+ 
+
+ align:start position:0%
+add up the values in the reducer but now
+I'd like to do the same thing of being
+
+ align:start position:0%
+I'd like to do the same thing of being
+ 
+
+ align:start position:0%
+I'd like to do the same thing of being
+able to quit early and so the question
+
+ align:start position:0%
+able to quit early and so the question
+ 
+
+ align:start position:0%
+able to quit early and so the question
+is well how can we paralyze a short
+
+ align:start position:0%
+is well how can we paralyze a short
+ 
+
+ align:start position:0%
+is well how can we paralyze a short
+circuited loop okay how can we and so
+
+ align:start position:0%
+circuited loop okay how can we and so
+ 
+
+ align:start position:0%
+circuited loop okay how can we and so
+the way I'm going to do this and this is
+
+ align:start position:0%
+the way I'm going to do this and this is
+ 
+
+ align:start position:0%
+the way I'm going to do this and this is
+sort of by hand here but it's going to
+
+ align:start position:0%
+sort of by hand here but it's going to
+ 
+
+ align:start position:0%
+sort of by hand here but it's going to
+give you so actually as you know
+
+ align:start position:0%
+give you so actually as you know
+ 
+
+ align:start position:0%
+give you so actually as you know
+underneath the loop is really a divide
+
+ align:start position:0%
+underneath the loop is really a divide
+ 
+
+ align:start position:0%
+underneath the loop is really a divide
+and conquer loop and so you know I could
+
+ align:start position:0%
+and conquer loop and so you know I could
+ 
+
+ align:start position:0%
+and conquer loop and so you know I could
+I could write it as a as a parallel loop
+
+ align:start position:0%
+I could write it as a as a parallel loop
+ 
+
+ align:start position:0%
+I could write it as a as a parallel loop
+and now it becomes I think a little bit
+
+ align:start position:0%
+and now it becomes I think a little bit
+ 
+
+ align:start position:0%
+and now it becomes I think a little bit
+clearer how I could in this case what
+
+ align:start position:0%
+clearer how I could in this case what
+ 
+
+ align:start position:0%
+clearer how I could in this case what
+I'm going to do is is return the value
+
+ align:start position:0%
+I'm going to do is is return the value
+ 
+
+ align:start position:0%
+I'm going to do is is return the value
+of the sum and now the question is well
+
+ align:start position:0%
+of the sum and now the question is well
+ 
+
+ align:start position:0%
+of the sum and now the question is well
+how can I quit early and save the work
+
+ align:start position:0%
+how can I quit early and save the work
+ 
+
+ align:start position:0%
+how can I quit early and save the work
+if I exceed the threshold okay
+
+ align:start position:0%
+if I exceed the threshold okay
+ 
+
+ align:start position:0%
+if I exceed the threshold okay
+understanding that you know when I'm
+
+ align:start position:0%
+understanding that you know when I'm
+ 
+
+ align:start position:0%
+understanding that you know when I'm
+executing this in something like silk
+
+ align:start position:0%
+executing this in something like silk
+ 
+
+ align:start position:0%
+executing this in something like silk
+you know it's going to tend to you know
+
+ align:start position:0%
+you know it's going to tend to you know
+ 
+
+ align:start position:0%
+you know it's going to tend to you know
+go down one path and often it's going to
+
+ align:start position:0%
+go down one path and often it's going to
+ 
+
+ align:start position:0%
+go down one path and often it's going to
+be a serial execution so I'd like if
+
+ align:start position:0%
+be a serial execution so I'd like if
+ 
+
+ align:start position:0%
+be a serial execution so I'd like if
+it's if it's possible so here's here's
+
+ align:start position:0%
+it's if it's possible so here's here's
+ 
+
+ align:start position:0%
+it's if it's possible so here's here's
+one way of doing it which is then I
+
+ align:start position:0%
+one way of doing it which is then I
+ 
+
+ align:start position:0%
+one way of doing it which is then I
+add a and abort flag to the code and
+
+ align:start position:0%
+add a and abort flag to the code and
+ 
+
+ align:start position:0%
+add a and abort flag to the code and
+which is going to say whether I should
+
+ align:start position:0%
+which is going to say whether I should
+ 
+
+ align:start position:0%
+which is going to say whether I should
+keep going or whether I have actually
+
+ align:start position:0%
+keep going or whether I have actually
+ 
+
+ align:start position:0%
+keep going or whether I have actually
+exceeded at that point and so I'm going
+
+ align:start position:0%
+exceeded at that point and so I'm going
+ 
+
+ align:start position:0%
+exceeded at that point and so I'm going
+to use that recursively and now I take a
+
+ align:start position:0%
+to use that recursively and now I take a
+ 
+
+ align:start position:0%
+to use that recursively and now I take a
+look at for each time through the loop
+
+ align:start position:0%
+look at for each time through the loop
+ 
+
+ align:start position:0%
+look at for each time through the loop
+or through the divide and conquer I look
+
+ align:start position:0%
+or through the divide and conquer I look
+ 
+
+ align:start position:0%
+or through the divide and conquer I look
+to see whether the sum is greater than a
+
+ align:start position:0%
+to see whether the sum is greater than a
+ 
+
+ align:start position:0%
+to see whether the sum is greater than a
+limit and I haven't you know already
+
+ align:start position:0%
+limit and I haven't you know already
+ 
+
+ align:start position:0%
+limit and I haven't you know already
+aborted the flag then I set the abort
+
+ align:start position:0%
+aborted the flag then I set the abort
+ 
+
+ align:start position:0%
+aborted the flag then I set the abort
+flag to be true okay
+
+ align:start position:0%
+flag to be true okay
+ 
+
+ align:start position:0%
+flag to be true okay
+why do I bother testing the abort flag
+
+ align:start position:0%
+why do I bother testing the abort flag
+ 
+
+ align:start position:0%
+why do I bother testing the abort flag
+before I set it to true so notice that
+
+ align:start position:0%
+before I set it to true so notice that
+ 
+
+ align:start position:0%
+before I set it to true so notice that
+that setting the abort flag is a race
+
+ align:start position:0%
+that setting the abort flag is a race
+ 
+
+ align:start position:0%
+that setting the abort flag is a race
+isn't it a determinacy race okay because
+
+ align:start position:0%
+isn't it a determinacy race okay because
+ 
+
+ align:start position:0%
+isn't it a determinacy race okay because
+I have great thank you it's because I
+
+ align:start position:0%
+I have great thank you it's because I
+ 
+
+ align:start position:0%
+I have great thank you it's because I
+have the the stuff operating in parallel
+
+ align:start position:0%
+have the the stuff operating in parallel
+ 
+
+ align:start position:0%
+have the the stuff operating in parallel
+is all trying to set the abort flag
+
+ align:start position:0%
+is all trying to set the abort flag
+ 
+
+ align:start position:0%
+is all trying to set the abort flag
+whenever something abort so I can have
+
+ align:start position:0%
+whenever something abort so I can have
+ 
+
+ align:start position:0%
+whenever something abort so I can have
+two guys who are in parallel setting the
+
+ align:start position:0%
+two guys who are in parallel setting the
+ 
+
+ align:start position:0%
+two guys who are in parallel setting the
+abort flag but if they're setting it
+
+ align:start position:0%
+abort flag but if they're setting it
+ 
+
+ align:start position:0%
+abort flag but if they're setting it
+they're setting it to the same value so
+
+ align:start position:0%
+they're setting it to the same value so
+ 
+
+ align:start position:0%
+they're setting it to the same value so
+it's a benign race okay assuming your
+
+ align:start position:0%
+it's a benign race okay assuming your
+ 
+
+ align:start position:0%
+it's a benign race okay assuming your
+memory model is such that you can
+
+ align:start position:0%
+memory model is such that you can
+ 
+
+ align:start position:0%
+memory model is such that you can
+actually set the values so so what
+
+ align:start position:0%
+actually set the values so so what
+ 
+
+ align:start position:0%
+actually set the values so so what
+happens here when why do i why do you
+
+ align:start position:0%
+happens here when why do i why do you
+ 
+
+ align:start position:0%
+happens here when why do i why do you
+bother checking this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what happens when several guys in
+
+ align:start position:0%
+so what happens when several guys in
+ 
+
+ align:start position:0%
+so what happens when several guys in
+parallel want to write to the same
+
+ align:start position:0%
+parallel want to write to the same
+ 
+
+ align:start position:0%
+parallel want to write to the same
+variable this is quiz one stuff yeah
+
+ align:start position:0%
+variable this is quiz one stuff yeah
+ 
+
+ align:start position:0%
+variable this is quiz one stuff yeah
+yeah you can have it bouncing along the
+
+ align:start position:0%
+yeah you can have it bouncing along the
+ 
+
+ align:start position:0%
+yeah you can have it bouncing along the
+cache it will serialize it right because
+
+ align:start position:0%
+cache it will serialize it right because
+ 
+
+ align:start position:0%
+cache it will serialize it right because
+because if they're all trying to to
+
+ align:start position:0%
+because if they're all trying to to
+ 
+
+ align:start position:0%
+because if they're all trying to to
+write then they have to get exclusive
+
+ align:start position:0%
+write then they have to get exclusive
+ 
+
+ align:start position:0%
+write then they have to get exclusive
+access for it to write and modify it and
+
+ align:start position:0%
+access for it to write and modify it and
+ 
+
+ align:start position:0%
+access for it to write and modify it and
+so that happens boom boom boom one at a
+
+ align:start position:0%
+so that happens boom boom boom one at a
+ 
+
+ align:start position:0%
+so that happens boom boom boom one at a
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and so by checking it first it can be in
+
+ align:start position:0%
+and so by checking it first it can be in
+ 
+
+ align:start position:0%
+and so by checking it first it can be in
+a shared state and then only one guy has
+
+ align:start position:0%
+a shared state and then only one guy has
+ 
+
+ align:start position:0%
+a shared state and then only one guy has
+to one guy clobbers it and then it'll
+
+ align:start position:0%
+to one guy clobbers it and then it'll
+ 
+
+ align:start position:0%
+to one guy clobbers it and then it'll
+update all the other ones so it makes it
+
+ align:start position:0%
+update all the other ones so it makes it
+ 
+
+ align:start position:0%
+update all the other ones so it makes it
+so we don't continually have a true
+
+ align:start position:0%
+so we don't continually have a true
+ 
+
+ align:start position:0%
+so we don't continually have a true
+sharing race and then in the checking to
+
+ align:start position:0%
+sharing race and then in the checking to
+ 
+
+ align:start position:0%
+sharing race and then in the checking to
+see if it exceeds we basically just
+
+ align:start position:0%
+see if it exceeds we basically just
+ 
+
+ align:start position:0%
+see if it exceeds we basically just
+check to see if you know we basically
+
+ align:start position:0%
+check to see if you know we basically
+ 
+
+ align:start position:0%
+check to see if you know we basically
+call this function we set the abort flag
+
+ align:start position:0%
+call this function we set the abort flag
+ 
+
+ align:start position:0%
+call this function we set the abort flag
+to false and then we return the sum of
+
+ align:start position:0%
+to false and then we return the sum of
+ 
+
+ align:start position:0%
+to false and then we return the sum of
+all the values and if it aborts then it
+
+ align:start position:0%
+all the values and if it aborts then it
+ 
+
+ align:start position:0%
+all the values and if it aborts then it
+just returns early okay so it doesn't
+
+ align:start position:0%
+just returns early okay so it doesn't
+ 
+
+ align:start position:0%
+just returns early okay so it doesn't
+have to keep going through the
+
+ align:start position:0%
+have to keep going through the
+ 
+
+ align:start position:0%
+have to keep going through the
+computation and of course once again you
+
+ align:start position:0%
+computation and of course once again you
+ 
+
+ align:start position:0%
+computation and of course once again you
+can coerce in the leaves and so forth so
+
+ align:start position:0%
+can coerce in the leaves and so forth so
+ 
+
+ align:start position:0%
+can coerce in the leaves and so forth so
+so this is non-deterministic code right
+
+ align:start position:0%
+so this is non-deterministic code right
+ 
+
+ align:start position:0%
+so this is non-deterministic code right
+which we should never write unless we
+
+ align:start position:0%
+which we should never write unless we
+ 
+
+ align:start position:0%
+which we should never write unless we
+have to okay because that's the only way
+
+ align:start position:0%
+have to okay because that's the only way
+ 
+
+ align:start position:0%
+have to okay because that's the only way
+of getting performance and you have to
+
+ align:start position:0%
+of getting performance and you have to
+ 
+
+ align:start position:0%
+of getting performance and you have to
+make sure you of course you reset the
+
+ align:start position:0%
+make sure you of course you reset the
+ 
+
+ align:start position:0%
+make sure you of course you reset the
+abort flag after the use and then
+
+ align:start position:0%
+abort flag after the use and then
+ 
+
+ align:start position:0%
+abort flag after the use and then
+actually do you need a memory fence here
+
+ align:start position:0%
+actually do you need a memory fence here
+ 
+
+ align:start position:0%
+actually do you need a memory fence here
+on the abort flag do you need to set you
+
+ align:start position:0%
+on the abort flag do you need to set you
+ 
+
+ align:start position:0%
+on the abort flag do you need to set you
+know where where would you put a an
+
+ align:start position:0%
+know where where would you put a an
+ 
+
+ align:start position:0%
+know where where would you put a an
+abort flag to make sure that the value
+
+ align:start position:0%
+abort flag to make sure that the value
+ 
+
+ align:start position:0%
+abort flag to make sure that the value
+was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes or what what would you have to
+
+ align:start position:0%
+yeah yes or what what would you have to
+ 
+
+ align:start position:0%
+yeah yes or what what would you have to
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+okay so so indeed it turns out you don't
+
+ align:start position:0%
+okay so so indeed it turns out you don't
+ 
+
+ align:start position:0%
+okay so so indeed it turns out you don't
+need a memory fence here and the reason
+
+ align:start position:0%
+need a memory fence here and the reason
+ 
+
+ align:start position:0%
+need a memory fence here and the reason
+is because the code is correct whether
+
+ align:start position:0%
+is because the code is correct whether
+ 
+
+ align:start position:0%
+is because the code is correct whether
+it's the initial value force or whether
+
+ align:start position:0%
+it's the initial value force or whether
+ 
+
+ align:start position:0%
+it's the initial value force or whether
+it's become true so it doesn't matter
+
+ align:start position:0%
+it's become true so it doesn't matter
+ 
+
+ align:start position:0%
+it's become true so it doesn't matter
+when it becomes true and so there's an
+
+ align:start position:0%
+when it becomes true and so there's an
+ 
+
+ align:start position:0%
+when it becomes true and so there's an
+issue of if you put in the fence then
+
+ align:start position:0%
+issue of if you put in the fence then
+ 
+
+ align:start position:0%
+issue of if you put in the fence then
+you know that it becomes true earlier
+
+ align:start position:0%
+you know that it becomes true earlier
+ 
+
+ align:start position:0%
+you know that it becomes true earlier
+okay rather than waiting for the
+
+ align:start position:0%
+okay rather than waiting for the
+ 
+
+ align:start position:0%
+okay rather than waiting for the
+convocation but that may actually slow
+
+ align:start position:0%
+convocation but that may actually slow
+ 
+
+ align:start position:0%
+convocation but that may actually slow
+things down because memory fences are
+
+ align:start position:0%
+things down because memory fences are
+ 
+
+ align:start position:0%
+things down because memory fences are
+expensive but because the transition is
+
+ align:start position:0%
+expensive but because the transition is
+ 
+
+ align:start position:0%
+expensive but because the transition is
+always from false to true during the
+
+ align:start position:0%
+always from false to true during the
+ 
+
+ align:start position:0%
+always from false to true during the
+execution you don't actually need a
+
+ align:start position:0%
+execution you don't actually need a
+ 
+
+ align:start position:0%
+execution you don't actually need a
+memory fence there okay in order to make
+
+ align:start position:0%
+memory fence there okay in order to make
+ 
+
+ align:start position:0%
+memory fence there okay in order to make
+sure that you've got the correct value
+
+ align:start position:0%
+sure that you've got the correct value
+ 
+
+ align:start position:0%
+sure that you've got the correct value
+does that make sense so you don't need a
+
+ align:start position:0%
+does that make sense so you don't need a
+ 
+
+ align:start position:0%
+does that make sense so you don't need a
+memory fence so so that's a classic
+
+ align:start position:0%
+memory fence so so that's a classic
+ 
+
+ align:start position:0%
+memory fence so so that's a classic
+instance of speculative parallelism it
+
+ align:start position:0%
+instance of speculative parallelism it
+ 
+
+ align:start position:0%
+instance of speculative parallelism it
+occurs when a program spawns some
+
+ align:start position:0%
+occurs when a program spawns some
+ 
+
+ align:start position:0%
+occurs when a program spawns some
+parallel work that might not be
+
+ align:start position:0%
+parallel work that might not be
+ 
+
+ align:start position:0%
+parallel work that might not be
+performed in a serial execution so
+
+ align:start position:0%
+performed in a serial execution so
+ 
+
+ align:start position:0%
+performed in a serial execution so
+you're performing it anticipating that
+
+ align:start position:0%
+you're performing it anticipating that
+ 
+
+ align:start position:0%
+you're performing it anticipating that
+you're probably going to need to do it
+
+ align:start position:0%
+you're probably going to need to do it
+ 
+
+ align:start position:0%
+you're probably going to need to do it
+okay and then typically what you want to
+
+ align:start position:0%
+okay and then typically what you want to
+ 
+
+ align:start position:0%
+okay and then typically what you want to
+do is have some way of backing out if
+
+ align:start position:0%
+do is have some way of backing out if
+ 
+
+ align:start position:0%
+do is have some way of backing out if
+you discover that that you've made made
+
+ align:start position:0%
+you discover that that you've made made
+ 
+
+ align:start position:0%
+you discover that that you've made made
+it you know that you didn't need to do
+
+ align:start position:0%
+it you know that you didn't need to do
+ 
+
+ align:start position:0%
+it you know that you didn't need to do
+that way have some way of making sure
+
+ align:start position:0%
+that way have some way of making sure
+ 
+
+ align:start position:0%
+that way have some way of making sure
+that you don't do any more okay so basic
+
+ align:start position:0%
+that you don't do any more okay so basic
+ 
+
+ align:start position:0%
+that you don't do any more okay so basic
+rule of thumb of speculation is don't
+
+ align:start position:0%
+rule of thumb of speculation is don't
+ 
+
+ align:start position:0%
+rule of thumb of speculation is don't
+spawn speculative work unless there's
+
+ align:start position:0%
+spawn speculative work unless there's
+ 
+
+ align:start position:0%
+spawn speculative work unless there's
+little other opportunity for parallelism
+
+ align:start position:0%
+little other opportunity for parallelism
+ 
+
+ align:start position:0%
+little other opportunity for parallelism
+and there's a good chance that will be
+
+ align:start position:0%
+and there's a good chance that will be
+ 
+
+ align:start position:0%
+and there's a good chance that will be
+needed so one of the things I've seen in
+
+ align:start position:0%
+needed so one of the things I've seen in
+ 
+
+ align:start position:0%
+needed so one of the things I've seen in
+research papers no less is people who
+
+ align:start position:0%
+research papers no less is people who
+ 
+
+ align:start position:0%
+research papers no less is people who
+say oh I'm going to you know I have a
+
+ align:start position:0%
+say oh I'm going to you know I have a
+ 
+
+ align:start position:0%
+say oh I'm going to you know I have a
+calculation where I'm trying to find say
+
+ align:start position:0%
+calculation where I'm trying to find say
+ 
+
+ align:start position:0%
+calculation where I'm trying to find say
+the minimum of a bunch of values and so
+
+ align:start position:0%
+the minimum of a bunch of values and so
+ 
+
+ align:start position:0%
+the minimum of a bunch of values and so
+I'm gonna you know spawn off you know
+
+ align:start position:0%
+I'm gonna you know spawn off you know
+ 
+
+ align:start position:0%
+I'm gonna you know spawn off you know
+end things each of which is looking for
+
+ align:start position:0%
+end things each of which is looking for
+ 
+
+ align:start position:0%
+end things each of which is looking for
+the minimum as soon as the minimum one
+
+ align:start position:0%
+the minimum as soon as the minimum one
+ 
+
+ align:start position:0%
+the minimum as soon as the minimum one
+comes back I'm going to retract all the
+
+ align:start position:0%
+comes back I'm going to retract all the
+ 
+
+ align:start position:0%
+comes back I'm going to retract all the
+other computations and I'm gonna get
+
+ align:start position:0%
+other computations and I'm gonna get
+ 
+
+ align:start position:0%
+other computations and I'm gonna get
+super linear speed-up that way because
+
+ align:start position:0%
+super linear speed-up that way because
+ 
+
+ align:start position:0%
+super linear speed-up that way because
+because in the serial execution I might
+
+ align:start position:0%
+because in the serial execution I might
+ 
+
+ align:start position:0%
+because in the serial execution I might
+have done the longer one first and maybe
+
+ align:start position:0%
+have done the longer one first and maybe
+ 
+
+ align:start position:0%
+have done the longer one first and maybe
+the minimum is not the not the first one
+
+ align:start position:0%
+the minimum is not the not the first one
+ 
+
+ align:start position:0%
+the minimum is not the not the first one
+or whatever and so they they claim super
+
+ align:start position:0%
+or whatever and so they they claim super
+ 
+
+ align:start position:0%
+or whatever and so they they claim super
+linear speed-up by doing speculative
+
+ align:start position:0%
+linear speed-up by doing speculative
+ 
+
+ align:start position:0%
+linear speed-up by doing speculative
+parallelism but that's not really that's
+
+ align:start position:0%
+parallelism but that's not really that's
+ 
+
+ align:start position:0%
+parallelism but that's not really that's
+not really a good example because there
+
+ align:start position:0%
+not really a good example because there
+ 
+
+ align:start position:0%
+not really a good example because there
+was a better serial code if that was
+
+ align:start position:0%
+was a better serial code if that was
+ 
+
+ align:start position:0%
+was a better serial code if that was
+really a good way of doing it they
+
+ align:start position:0%
+really a good way of doing it they
+ 
+
+ align:start position:0%
+really a good way of doing it they
+should have been doing what's called
+
+ align:start position:0%
+should have been doing what's called
+ 
+
+ align:start position:0%
+should have been doing what's called
+dovetailing which is they doing a little
+
+ align:start position:0%
+dovetailing which is they doing a little
+ 
+
+ align:start position:0%
+dovetailing which is they doing a little
+bit of this computation a little bit of
+
+ align:start position:0%
+bit of this computation a little bit of
+ 
+
+ align:start position:0%
+bit of this computation a little bit of
+this a little bit of this a little bit
+
+ align:start position:0%
+this a little bit of this a little bit
+ 
+
+ align:start position:0%
+this a little bit of this a little bit
+of this etc and then going back that
+
+ align:start position:0%
+of this etc and then going back that
+ 
+
+ align:start position:0%
+of this etc and then going back that
+would have been a better algorithm for
+
+ align:start position:0%
+would have been a better algorithm for
+ 
+
+ align:start position:0%
+would have been a better algorithm for
+which you would then use it and the risk
+
+ align:start position:0%
+which you would then use it and the risk
+ 
+
+ align:start position:0%
+which you would then use it and the risk
+they have is that they're spawning off
+
+ align:start position:0%
+they have is that they're spawning off
+ 
+
+ align:start position:0%
+they have is that they're spawning off
+and things of which most of them may not
+
+ align:start position:0%
+and things of which most of them may not
+ 
+
+ align:start position:0%
+and things of which most of them may not
+be needed and now they don't get any
+
+ align:start position:0%
+be needed and now they don't get any
+ 
+
+ align:start position:0%
+be needed and now they don't get any
+speed up even though they've just used a
+
+ align:start position:0%
+speed up even though they've just used a
+ 
+
+ align:start position:0%
+speed up even though they've just used a
+lot more work and that's often is is a
+
+ align:start position:0%
+lot more work and that's often is is a
+ 
+
+ align:start position:0%
+lot more work and that's often is is a
+bad bad choice so usually you don't want
+
+ align:start position:0%
+bad bad choice so usually you don't want
+ 
+
+ align:start position:0%
+bad bad choice so usually you don't want
+to spawn speculative work unless there's
+
+ align:start position:0%
+to spawn speculative work unless there's
+ 
+
+ align:start position:0%
+to spawn speculative work unless there's
+little other opportunity and there's a
+
+ align:start position:0%
+little other opportunity and there's a
+ 
+
+ align:start position:0%
+little other opportunity and there's a
+good chance it'll be needed okay
+
+ align:start position:0%
+good chance it'll be needed okay
+ 
+
+ align:start position:0%
+good chance it'll be needed okay
+my experience is you know how much what
+
+ align:start position:0%
+my experience is you know how much what
+ 
+
+ align:start position:0%
+my experience is you know how much what
+kind of chance do you need you need to
+
+ align:start position:0%
+kind of chance do you need you need to
+ 
+
+ align:start position:0%
+kind of chance do you need you need to
+you know have certainly less than you
+
+ align:start position:0%
+you know have certainly less than you
+ 
+
+ align:start position:0%
+you know have certainly less than you
+know for parallelism you've got to have
+
+ align:start position:0%
+know for parallelism you've got to have
+ 
+
+ align:start position:0%
+know for parallelism you've got to have
+if if the chance that you're going to
+
+ align:start position:0%
+if if the chance that you're going to
+ 
+
+ align:start position:0%
+if if the chance that you're going to
+need the work if you have P processors
+
+ align:start position:0%
+need the work if you have P processors
+ 
+
+ align:start position:0%
+need the work if you have P processors
+if the chance that it could be not
+
+ align:start position:0%
+if the chance that it could be not
+ 
+
+ align:start position:0%
+if the chance that it could be not
+needed is is less than actually have a
+
+ align:start position:0%
+needed is is less than actually have a
+ 
+
+ align:start position:0%
+needed is is less than actually have a
+theorem at the end which I'll which I'll
+
+ align:start position:0%
+theorem at the end which I'll which I'll
+ 
+
+ align:start position:0%
+theorem at the end which I'll which I'll
+I'll refer you to ok because a little
+
+ align:start position:0%
+I'll refer you to ok because a little
+ 
+
+ align:start position:0%
+I'll refer you to ok because a little
+bit hard to say because I didn't put on
+
+ align:start position:0%
+bit hard to say because I didn't put on
+ 
+
+ align:start position:0%
+bit hard to say because I didn't put on
+the slide but there's there's a final
+
+ align:start position:0%
+the slide but there's there's a final
+ 
+
+ align:start position:0%
+the slide but there's there's a final
+slide for this which gives a nice little
+
+ align:start position:0%
+slide for this which gives a nice little
+ 
+
+ align:start position:0%
+slide for this which gives a nice little
+theorem about when you should do this so
+
+ align:start position:0%
+theorem about when you should do this so
+ 
+
+ align:start position:0%
+theorem about when you should do this so
+now let's talk about parallel alpha beta
+
+ align:start position:0%
+now let's talk about parallel alpha beta
+ 
+
+ align:start position:0%
+now let's talk about parallel alpha beta
+search because that's kind of what
+
+ align:start position:0%
+search because that's kind of what
+ 
+
+ align:start position:0%
+search because that's kind of what
+you're doing with your principle
+
+ align:start position:0%
+you're doing with your principle
+ 
+
+ align:start position:0%
+you're doing with your principle
+variation search and so if you remember
+
+ align:start position:0%
+variation search and so if you remember
+ 
+
+ align:start position:0%
+variation search and so if you remember
+the analysis done by Knuth and Morris
+
+ align:start position:0%
+the analysis done by Knuth and Morris
+ 
+
+ align:start position:0%
+the analysis done by Knuth and Morris
+they basically showed that for gram tree
+
+ align:start position:0%
+they basically showed that for gram tree
+ 
+
+ align:start position:0%
+they basically showed that for gram tree
+with branching factor B and depth D and
+
+ align:start position:0%
+with branching factor B and depth D and
+ 
+
+ align:start position:0%
+with branching factor B and depth D and
+alpha beta search with move searched in
+
+ align:start position:0%
+alpha beta search with move searched in
+ 
+
+ align:start position:0%
+alpha beta search with move searched in
+best first order examines that exactly B
+
+ align:start position:0%
+best first order examines that exactly B
+ 
+
+ align:start position:0%
+best first order examines that exactly B
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+d over 2 plus B to the floor of D over 2
+
+ align:start position:0%
+d over 2 plus B to the floor of D over 2
+ 
+
+ align:start position:0%
+d over 2 plus B to the floor of D over 2
+minus 1 nodes at ply D so that's
+
+ align:start position:0%
+minus 1 nodes at ply D so that's
+ 
+
+ align:start position:0%
+minus 1 nodes at ply D so that's
+basically square routing the amount of
+
+ align:start position:0%
+basically square routing the amount of
+ 
+
+ align:start position:0%
+basically square routing the amount of
+work that you would need if you did a
+
+ align:start position:0%
+work that you would need if you did a
+ 
+
+ align:start position:0%
+work that you would need if you did a
+full depth fly that's with alpha beta ok
+
+ align:start position:0%
+full depth fly that's with alpha beta ok
+ 
+
+ align:start position:0%
+full depth fly that's with alpha beta ok
+so naive algorithm looks at B to the D
+
+ align:start position:0%
+so naive algorithm looks at B to the D
+ 
+
+ align:start position:0%
+so naive algorithm looks at B to the D
+nodes at depth D and so for the same
+
+ align:start position:0%
+nodes at depth D and so for the same
+ 
+
+ align:start position:0%
+nodes at depth D and so for the same
+work the search depth is effectively
+
+ align:start position:0%
+work the search depth is effectively
+ 
+
+ align:start position:0%
+work the search depth is effectively
+doubled or the work is Square rooted ok
+
+ align:start position:0%
+doubled or the work is Square rooted ok
+ 
+
+ align:start position:0%
+doubled or the work is Square rooted ok
+so that we saw last time in Helens
+
+ align:start position:0%
+so that we saw last time in Helens
+ 
+
+ align:start position:0%
+so that we saw last time in Helens
+lecture ok so the key optimization here
+
+ align:start position:0%
+lecture ok so the key optimization here
+ 
+
+ align:start position:0%
+lecture ok so the key optimization here
+is pruning the game tree and as I
+
+ align:start position:0%
+is pruning the game tree and as I
+ 
+
+ align:start position:0%
+is pruning the game tree and as I
+mentioned the beginning of this when you
+
+ align:start position:0%
+mentioned the beginning of this when you
+ 
+
+ align:start position:0%
+mentioned the beginning of this when you
+prune the game tree you've got what's
+
+ align:start position:0%
+prune the game tree you've got what's
+ 
+
+ align:start position:0%
+prune the game tree you've got what's
+effectively a serial thing and if you if
+
+ align:start position:0%
+effectively a serial thing and if you if
+ 
+
+ align:start position:0%
+effectively a serial thing and if you if
+you let something go ahead you may be
+
+ align:start position:0%
+you let something go ahead you may be
+ 
+
+ align:start position:0%
+you let something go ahead you may be
+working on something that would be
+
+ align:start position:0%
+working on something that would be
+ 
+
+ align:start position:0%
+working on something that would be
+pruned so then how does the parallelism
+
+ align:start position:0%
+pruned so then how does the parallelism
+ 
+
+ align:start position:0%
+pruned so then how does the parallelism
+really help you there you're just
+
+ align:start position:0%
+really help you there you're just
+ 
+
+ align:start position:0%
+really help you there you're just
+wasting processors it could be better
+
+ align:start position:0%
+wasting processors it could be better
+ 
+
+ align:start position:0%
+wasting processors it could be better
+spent perhaps elsewhere except where
+
+ align:start position:0%
+spent perhaps elsewhere except where
+ 
+
+ align:start position:0%
+spent perhaps elsewhere except where
+else can you spend it because there's no
+
+ align:start position:0%
+else can you spend it because there's no
+ 
+
+ align:start position:0%
+else can you spend it because there's no
+other parallelism in the in the code so
+
+ align:start position:0%
+other parallelism in the in the code so
+ 
+
+ align:start position:0%
+other parallelism in the in the code so
+we want to find some solution so the
+
+ align:start position:0%
+we want to find some solution so the
+ 
+
+ align:start position:0%
+we want to find some solution so the
+solution comes for a from an idea from a
+
+ align:start position:0%
+solution comes for a from an idea from a
+ 
+
+ align:start position:0%
+solution comes for a from an idea from a
+very nice paper by Burkhardt manin and
+
+ align:start position:0%
+very nice paper by Burkhardt manin and
+ 
+
+ align:start position:0%
+very nice paper by Burkhardt manin and
+some of his students in Germany and they
+
+ align:start position:0%
+some of his students in Germany and they
+ 
+
+ align:start position:0%
+some of his students in Germany and they
+made the observation that in a best
+
+ align:start position:0%
+made the observation that in a best
+ 
+
+ align:start position:0%
+made the observation that in a best
+ordered tree the degree of every node is
+
+ align:start position:0%
+ordered tree the degree of every node is
+ 
+
+ align:start position:0%
+ordered tree the degree of every node is
+either either 1 or maximal this is this
+
+ align:start position:0%
+either either 1 or maximal this is this
+ 
+
+ align:start position:0%
+either either 1 or maximal this is this
+is not their observation this is
+
+ align:start position:0%
+is not their observation this is
+ 
+
+ align:start position:0%
+is not their observation this is
+actually the observation in the knuth
+
+ align:start position:0%
+actually the observation in the knuth
+ 
+
+ align:start position:0%
+actually the observation in the knuth
+paper ok so when you have a best ordered
+
+ align:start position:0%
+paper ok so when you have a best ordered
+ 
+
+ align:start position:0%
+paper ok so when you have a best ordered
+tree if you can get all the moves
+
+ align:start position:0%
+tree if you can get all the moves
+ 
+
+ align:start position:0%
+tree if you can get all the moves
+ordered in their true order ok then it
+
+ align:start position:0%
+ordered in their true order ok then it
+ 
+
+ align:start position:0%
+ordered in their true order ok then it
+turns out that either you're you're
+
+ align:start position:0%
+turns out that either you're you're
+ 
+
+ align:start position:0%
+turns out that either you're you're
+exploring all the children or you are
+
+ align:start position:0%
+exploring all the children or you are
+ 
+
+ align:start position:0%
+exploring all the children or you are
+refuting something and you get a cut off
+
+ align:start position:0%
+refuting something and you get a cut off
+ 
+
+ align:start position:0%
+refuting something and you get a cut off
+from the very first one that you look at
+
+ align:start position:0%
+from the very first one that you look at
+ 
+
+ align:start position:0%
+from the very first one that you look at
+ok and so in this case for example it
+
+ align:start position:0%
+ok and so in this case for example it
+ 
+
+ align:start position:0%
+ok and so in this case for example it
+turns out on the principle variation
+
+ align:start position:0%
+turns out on the principle variation
+ 
+
+ align:start position:0%
+turns out on the principle variation
+those are all full
+
+ align:start position:0%
+those are all full
+ 
+
+ align:start position:0%
+those are all full
+with sorry they have you have to explore
+
+ align:start position:0%
+with sorry they have you have to explore
+ 
+
+ align:start position:0%
+with sorry they have you have to explore
+all the children and then from there on
+
+ align:start position:0%
+all the children and then from there on
+ 
+
+ align:start position:0%
+all the children and then from there on
+it alternates one level it's it you know
+
+ align:start position:0%
+it alternates one level it's it you know
+ 
+
+ align:start position:0%
+it alternates one level it's it you know
+it you have just a single child that
+
+ align:start position:0%
+it you have just a single child that
+ 
+
+ align:start position:0%
+it you have just a single child that
+needs to be explored and when you
+
+ align:start position:0%
+needs to be explored and when you
+ 
+
+ align:start position:0%
+needs to be explored and when you
+explore it if it's best ordered you will
+
+ align:start position:0%
+explore it if it's best ordered you will
+ 
+
+ align:start position:0%
+explore it if it's best ordered you will
+get a beta cutoff for the for the others
+
+ align:start position:0%
+get a beta cutoff for the for the others
+ 
+
+ align:start position:0%
+get a beta cutoff for the for the others
+and then it alternates and then it's
+
+ align:start position:0%
+and then it alternates and then it's
+ 
+
+ align:start position:0%
+and then it alternates and then it's
+full width' and so their idea was to say
+
+ align:start position:0%
+full width' and so their idea was to say
+ 
+
+ align:start position:0%
+full width' and so their idea was to say
+well if the first child fails to
+
+ align:start position:0%
+well if the first child fails to
+ 
+
+ align:start position:0%
+well if the first child fails to
+generate a beta cutoff speculate that in
+
+ align:start position:0%
+generate a beta cutoff speculate that in
+ 
+
+ align:start position:0%
+generate a beta cutoff speculate that in
+fact you have the best one and the
+
+ align:start position:0%
+fact you have the best one and the
+ 
+
+ align:start position:0%
+fact you have the best one and the
+remaining children can be searched in
+
+ align:start position:0%
+remaining children can be searched in
+ 
+
+ align:start position:0%
+remaining children can be searched in
+parallel without wasting any work okay
+
+ align:start position:0%
+parallel without wasting any work okay
+ 
+
+ align:start position:0%
+parallel without wasting any work okay
+so if it fails you're gonna say oh I'm
+
+ align:start position:0%
+so if it fails you're gonna say oh I'm
+ 
+
+ align:start position:0%
+so if it fails you're gonna say oh I'm
+gonna speculate that this is in fact a
+
+ align:start position:0%
+gonna speculate that this is in fact a
+ 
+
+ align:start position:0%
+gonna speculate that this is in fact a
+full-width thing now in practice you
+
+ align:start position:0%
+full-width thing now in practice you
+ 
+
+ align:start position:0%
+full-width thing now in practice you
+don't necessarily get things best
+
+ align:start position:0%
+don't necessarily get things best
+ 
+
+ align:start position:0%
+don't necessarily get things best
+ordered but they're a bunch of
+
+ align:start position:0%
+ordered but they're a bunch of
+ 
+
+ align:start position:0%
+ordered but they're a bunch of
+heuristics in the code we've given you
+
+ align:start position:0%
+heuristics in the code we've given you
+ 
+
+ align:start position:0%
+heuristics in the code we've given you
+and in in chess code to make it so that
+
+ align:start position:0%
+and in in chess code to make it so that
+ 
+
+ align:start position:0%
+and in in chess code to make it so that
+you tend to do things in the in the
+
+ align:start position:0%
+you tend to do things in the in the
+ 
+
+ align:start position:0%
+you tend to do things in the in the
+proper order the most important of those
+
+ align:start position:0%
+proper order the most important of those
+ 
+
+ align:start position:0%
+proper order the most important of those
+is have you if you've seen the move
+
+ align:start position:0%
+is have you if you've seen the move
+ 
+
+ align:start position:0%
+is have you if you've seen the move
+before okay and it's in the
+
+ align:start position:0%
+before okay and it's in the
+ 
+
+ align:start position:0%
+before okay and it's in the
+transposition table you use the move
+
+ align:start position:0%
+transposition table you use the move
+ 
+
+ align:start position:0%
+transposition table you use the move
+that you've seen before even if it's to
+
+ align:start position:0%
+that you've seen before even if it's to
+ 
+
+ align:start position:0%
+that you've seen before even if it's to
+a shallower depth okay you guess that
+
+ align:start position:0%
+a shallower depth okay you guess that
+ 
+
+ align:start position:0%
+a shallower depth okay you guess that
+that's going to be their best move still
+
+ align:start position:0%
+that's going to be their best move still
+ 
+
+ align:start position:0%
+that's going to be their best move still
+even if you search deeper and that's
+
+ align:start position:0%
+even if you search deeper and that's
+ 
+
+ align:start position:0%
+even if you search deeper and that's
+pretty good and then you so they call
+
+ align:start position:0%
+pretty good and then you so they call
+ 
+
+ align:start position:0%
+pretty good and then you so they call
+that the young siblings weight algorithm
+
+ align:start position:0%
+that the young siblings weight algorithm
+ 
+
+ align:start position:0%
+that the young siblings weight algorithm
+they actually call it the young brothers
+
+ align:start position:0%
+they actually call it the young brothers
+ 
+
+ align:start position:0%
+they actually call it the young brothers
+weight but in the modern era we call it
+
+ align:start position:0%
+weight but in the modern era we call it
+ 
+
+ align:start position:0%
+weight but in the modern era we call it
+young siblings weight okay
+
+ align:start position:0%
+young siblings weight okay
+ 
+
+ align:start position:0%
+young siblings weight okay
+and we abort sub computations that prove
+
+ align:start position:0%
+and we abort sub computations that prove
+ 
+
+ align:start position:0%
+and we abort sub computations that prove
+to be unnecessary so you're gonna start
+
+ align:start position:0%
+to be unnecessary so you're gonna start
+ 
+
+ align:start position:0%
+to be unnecessary so you're gonna start
+out searching but then you want to you
+
+ align:start position:0%
+out searching but then you want to you
+ 
+
+ align:start position:0%
+out searching but then you want to you
+know get rid of things that you discover
+
+ align:start position:0%
+know get rid of things that you discover
+ 
+
+ align:start position:0%
+know get rid of things that you discover
+oops you know I did get a cutoff from
+
+ align:start position:0%
+oops you know I did get a cutoff from
+ 
+
+ align:start position:0%
+oops you know I did get a cutoff from
+searching from one of these things I
+
+ align:start position:0%
+searching from one of these things I
+ 
+
+ align:start position:0%
+searching from one of these things I
+don't need to do this let's not have it
+
+ align:start position:0%
+don't need to do this let's not have it
+ 
+
+ align:start position:0%
+don't need to do this let's not have it
+keep spawning and generating you know
+
+ align:start position:0%
+keep spawning and generating you know
+ 
+
+ align:start position:0%
+keep spawning and generating you know
+working some other thing let's let's
+
+ align:start position:0%
+working some other thing let's let's
+ 
+
+ align:start position:0%
+working some other thing let's let's
+let's abort it and here's the idea for
+
+ align:start position:0%
+let's abort it and here's the idea for
+ 
+
+ align:start position:0%
+let's abort it and here's the idea for
+the abort mechanism so what you do is
+
+ align:start position:0%
+the abort mechanism so what you do is
+ 
+
+ align:start position:0%
+the abort mechanism so what you do is
+you you know the abort can occur at any
+
+ align:start position:0%
+you you know the abort can occur at any
+ 
+
+ align:start position:0%
+you you know the abort can occur at any
+given node saying I don't need to you
+
+ align:start position:0%
+given node saying I don't need to you
+ 
+
+ align:start position:0%
+given node saying I don't need to you
+get a beta cutoff you want to abort all
+
+ align:start position:0%
+get a beta cutoff you want to abort all
+ 
+
+ align:start position:0%
+get a beta cutoff you want to abort all
+the children that wouldn't have been
+
+ align:start position:0%
+the children that wouldn't have been
+ 
+
+ align:start position:0%
+the children that wouldn't have been
+searched anyway but they may have
+
+ align:start position:0%
+searched anyway but they may have
+ 
+
+ align:start position:0%
+searched anyway but they may have
+already been spawned off so you have a
+
+ align:start position:0%
+already been spawned off so you have a
+ 
+
+ align:start position:0%
+already been spawned off so you have a
+record in each node that tells you
+
+ align:start position:0%
+record in each node that tells you
+ 
+
+ align:start position:0%
+record in each node that tells you
+whether or not you've aborted
+
+ align:start position:0%
+whether or not you've aborted
+ 
+
+ align:start position:0%
+whether or not you've aborted
+and what you do is you just simply climb
+
+ align:start position:0%
+and what you do is you just simply climb
+ 
+
+ align:start position:0%
+and what you do is you just simply climb
+up the tree okay to see whether or not
+
+ align:start position:0%
+up the tree okay to see whether or not
+ 
+
+ align:start position:0%
+up the tree okay to see whether or not
+you know periodically whether or not you
+
+ align:start position:0%
+you know periodically whether or not you
+ 
+
+ align:start position:0%
+you know periodically whether or not you
+have an ancestor who is aborted if you
+
+ align:start position:0%
+have an ancestor who is aborted if you
+ 
+
+ align:start position:0%
+have an ancestor who is aborted if you
+have an ancestor that's aborted says I'm
+
+ align:start position:0%
+have an ancestor that's aborted says I'm
+ 
+
+ align:start position:0%
+have an ancestor that's aborted says I'm
+aborting my sub you know the the side
+
+ align:start position:0%
+aborting my sub you know the the side
+ 
+
+ align:start position:0%
+aborting my sub you know the the side
+computations then you say oh I'm done
+
+ align:start position:0%
+computations then you say oh I'm done
+ 
+
+ align:start position:0%
+computations then you say oh I'm done
+and I just have to return okay and so
+
+ align:start position:0%
+and I just have to return okay and so
+ 
+
+ align:start position:0%
+and I just have to return okay and so
+you check that on a regular basis okay
+
+ align:start position:0%
+you check that on a regular basis okay
+ 
+
+ align:start position:0%
+you check that on a regular basis okay
+so does that do people follow what that
+
+ align:start position:0%
+so does that do people follow what that
+ 
+
+ align:start position:0%
+so does that do people follow what that
+mechanism is and so that's basically
+
+ align:start position:0%
+mechanism is and so that's basically
+ 
+
+ align:start position:0%
+mechanism is and so that's basically
+what you're going to be implementing for
+
+ align:start position:0%
+what you're going to be implementing for
+ 
+
+ align:start position:0%
+what you're going to be implementing for
+you know for the parallelization okay is
+
+ align:start position:0%
+you know for the parallelization okay is
+ 
+
+ align:start position:0%
+you know for the parallelization okay is
+this thing of climbing up you're gonna
+
+ align:start position:0%
+this thing of climbing up you're gonna
+ 
+
+ align:start position:0%
+this thing of climbing up you're gonna
+spawn you know you're gonna guess after
+
+ align:start position:0%
+spawn you know you're gonna guess after
+ 
+
+ align:start position:0%
+spawn you know you're gonna guess after
+you've searched one child that it's good
+
+ align:start position:0%
+you've searched one child that it's good
+ 
+
+ align:start position:0%
+you've searched one child that it's good
+hey actually some people say why don't
+
+ align:start position:0%
+hey actually some people say why don't
+ 
+
+ align:start position:0%
+hey actually some people say why don't
+you check two before you you know search
+
+ align:start position:0%
+you check two before you you know search
+ 
+
+ align:start position:0%
+you check two before you you know search
+the others okay and so that you're even
+
+ align:start position:0%
+the others okay and so that you're even
+ 
+
+ align:start position:0%
+the others okay and so that you're even
+more sure that you don't have a cut off
+
+ align:start position:0%
+more sure that you don't have a cut off
+ 
+
+ align:start position:0%
+more sure that you don't have a cut off
+because neither the first two aborted
+
+ align:start position:0%
+because neither the first two aborted
+ 
+
+ align:start position:0%
+because neither the first two aborted
+because in practice of course the game
+
+ align:start position:0%
+because in practice of course the game
+ 
+
+ align:start position:0%
+because in practice of course the game
+tree is not best ordered and so you're
+
+ align:start position:0%
+tree is not best ordered and so you're
+ 
+
+ align:start position:0%
+tree is not best ordered and so you're
+gonna waste some work okay so but the
+
+ align:start position:0%
+gonna waste some work okay so but the
+ 
+
+ align:start position:0%
+gonna waste some work okay so but the
+idea is you're going to pull up the tree
+
+ align:start position:0%
+idea is you're going to pull up the tree
+ 
+
+ align:start position:0%
+idea is you're going to pull up the tree
+to see whether or not and of course you
+
+ align:start position:0%
+to see whether or not and of course you
+ 
+
+ align:start position:0%
+to see whether or not and of course you
+don't want to pull on every evaluation
+
+ align:start position:0%
+don't want to pull on every evaluation
+ 
+
+ align:start position:0%
+don't want to pull on every evaluation
+that you do you want to just pull
+
+ align:start position:0%
+that you do you want to just pull
+ 
+
+ align:start position:0%
+that you do you want to just pull
+frequently so if you may have a counter
+
+ align:start position:0%
+frequently so if you may have a counter
+ 
+
+ align:start position:0%
+frequently so if you may have a counter
+in there that says okay every tenth time
+
+ align:start position:0%
+in there that says okay every tenth time
+ 
+
+ align:start position:0%
+in there that says okay every tenth time
+I'm going to pull up the tree or every
+
+ align:start position:0%
+I'm going to pull up the tree or every
+ 
+
+ align:start position:0%
+I'm going to pull up the tree or every
+you know you put a voodoo parameter
+
+ align:start position:0%
+you know you put a voodoo parameter
+ 
+
+ align:start position:0%
+you know you put a voodoo parameter
+there that says how often it makes sense
+
+ align:start position:0%
+there that says how often it makes sense
+ 
+
+ align:start position:0%
+there that says how often it makes sense
+to actually check because there's cost
+
+ align:start position:0%
+to actually check because there's cost
+ 
+
+ align:start position:0%
+to actually check because there's cost
+you going up and checking ok versus
+
+ align:start position:0%
+you going up and checking ok versus
+ 
+
+ align:start position:0%
+you going up and checking ok versus
+versus exploring more of the tree okay
+
+ align:start position:0%
+versus exploring more of the tree okay
+ 
+
+ align:start position:0%
+versus exploring more of the tree okay
+and so I have an example here and I
+
+ align:start position:0%
+and so I have an example here and I
+ 
+
+ align:start position:0%
+and so I have an example here and I
+think this is where I'm gonna cut this
+
+ align:start position:0%
+think this is where I'm gonna cut this
+ 
+
+ align:start position:0%
+think this is where I'm gonna cut this
+short so let me there's an example which
+
+ align:start position:0%
+short so let me there's an example which
+ 
+
+ align:start position:0%
+short so let me there's an example which
+I suggest you take a look at I want to
+
+ align:start position:0%
+I suggest you take a look at I want to
+ 
+
+ align:start position:0%
+I suggest you take a look at I want to
+as I say spend time doing QA and talking
+
+ align:start position:0%
+as I say spend time doing QA and talking
+ 
+
+ align:start position:0%
+as I say spend time doing QA and talking
+about the other parts of the program and
+
+ align:start position:0%
+about the other parts of the program and
+ 
+
+ align:start position:0%
+about the other parts of the program and
+give you folks some good ideas for for
+
+ align:start position:0%
+give you folks some good ideas for for
+ 
+
+ align:start position:0%
+give you folks some good ideas for for
+things so this is sort of the theory
+
+ align:start position:0%
+things so this is sort of the theory
+ 
+
+ align:start position:0%
+things so this is sort of the theory
+thing and then I have some slides that
+
+ align:start position:0%
+thing and then I have some slides that
+ 
+
+ align:start position:0%
+thing and then I have some slides that
+will explain this with examples and more
+
+ align:start position:0%
+will explain this with examples and more
+ 
+
+ align:start position:0%
+will explain this with examples and more
+depth because I don't expect that
+
+ align:start position:0%
+depth because I don't expect that
+ 
+
+ align:start position:0%
+depth because I don't expect that
+everybody got every detail of this okay
+
+ align:start position:0%
+everybody got every detail of this okay
+ 
+
+ align:start position:0%
+everybody got every detail of this okay
+so this is the so I have some
+
+ align:start position:0%
+so this is the so I have some
+ 
+
+ align:start position:0%
+so this is the so I have some
+examples and so forth in here that I'm
+
+ align:start position:0%
+examples and so forth in here that I'm
+ 
+
+ align:start position:0%
+examples and so forth in here that I'm
+gonna let you guys look at on your own
+
+ align:start position:0%
+gonna let you guys look at on your own
+ 
+
+ align:start position:0%
+gonna let you guys look at on your own
+okay now if you paralyze the spawning
+
+ align:start position:0%
+okay now if you paralyze the spawning
+ 
+
+ align:start position:0%
+okay now if you paralyze the spawning
+off loop okay of of the the younger
+
+ align:start position:0%
+off loop okay of of the the younger
+ 
+
+ align:start position:0%
+off loop okay of of the the younger
+siblings you will get a code with races
+
+ align:start position:0%
+siblings you will get a code with races
+ 
+
+ align:start position:0%
+siblings you will get a code with races
+okay and the reason you get races is
+
+ align:start position:0%
+okay and the reason you get races is
+ 
+
+ align:start position:0%
+okay and the reason you get races is
+because there are several there are
+
+ align:start position:0%
+because there are several there are
+ 
+
+ align:start position:0%
+because there are several there are
+three data structures okay that the
+
+ align:start position:0%
+three data structures okay that the
+ 
+
+ align:start position:0%
+three data structures okay that the
+search is employing that are that are
+
+ align:start position:0%
+search is employing that are that are
+ 
+
+ align:start position:0%
+search is employing that are that are
+kind of global the first is the
+
+ align:start position:0%
+kind of global the first is the
+ 
+
+ align:start position:0%
+kind of global the first is the
+transposition table looking things up to
+
+ align:start position:0%
+transposition table looking things up to
+ 
+
+ align:start position:0%
+transposition table looking things up to
+see whether or not you've seen them
+
+ align:start position:0%
+see whether or not you've seen them
+ 
+
+ align:start position:0%
+see whether or not you've seen them
+before that's a major optimization you
+
+ align:start position:0%
+before that's a major optimization you
+ 
+
+ align:start position:0%
+before that's a major optimization you
+don't want to get rid of the
+
+ align:start position:0%
+don't want to get rid of the
+ 
+
+ align:start position:0%
+don't want to get rid of the
+transposition table and so you have a
+
+ align:start position:0%
+transposition table and so you have a
+ 
+
+ align:start position:0%
+transposition table and so you have a
+choice for the transposition table what
+
+ align:start position:0%
+choice for the transposition table what
+ 
+
+ align:start position:0%
+choice for the transposition table what
+are you going to do with it are you
+
+ align:start position:0%
+are you going to do with it are you
+ 
+
+ align:start position:0%
+are you going to do with it are you
+going to lock it so that the races
+
+ align:start position:0%
+going to lock it so that the races
+ 
+
+ align:start position:0%
+going to lock it so that the races
+become at least your data race free and
+
+ align:start position:0%
+become at least your data race free and
+ 
+
+ align:start position:0%
+become at least your data race free and
+updated atomically or you could
+
+ align:start position:0%
+updated atomically or you could
+ 
+
+ align:start position:0%
+updated atomically or you could
+replicate it for example you could have
+
+ align:start position:0%
+replicate it for example you could have
+ 
+
+ align:start position:0%
+replicate it for example you could have
+a worker local copy of the data
+
+ align:start position:0%
+a worker local copy of the data
+ 
+
+ align:start position:0%
+a worker local copy of the data
+structure and each each worker that is
+
+ align:start position:0%
+structure and each each worker that is
+ 
+
+ align:start position:0%
+structure and each each worker that is
+working on it only accesses their own
+
+ align:start position:0%
+working on it only accesses their own
+ 
+
+ align:start position:0%
+working on it only accesses their own
+local copies okay you know or you know
+
+ align:start position:0%
+local copies okay you know or you know
+ 
+
+ align:start position:0%
+local copies okay you know or you know
+you can use a you can make a copy when
+
+ align:start position:0%
+you can use a you can make a copy when
+ 
+
+ align:start position:0%
+you can use a you can make a copy when
+things are stolen or you can make just
+
+ align:start position:0%
+things are stolen or you can make just
+ 
+
+ align:start position:0%
+things are stolen or you can make just
+one where you just maintain it locally
+
+ align:start position:0%
+one where you just maintain it locally
+ 
+
+ align:start position:0%
+one where you just maintain it locally
+or you can decide that well you know
+
+ align:start position:0%
+or you can decide that well you know
+ 
+
+ align:start position:0%
+or you can decide that well you know
+even if there's a race there the odds
+
+ align:start position:0%
+even if there's a race there the odds
+ 
+
+ align:start position:0%
+even if there's a race there the odds
+that it's going to affect how I play in
+
+ align:start position:0%
+that it's going to affect how I play in
+ 
+
+ align:start position:0%
+that it's going to affect how I play in
+the game are not that high so I'll run
+
+ align:start position:0%
+the game are not that high so I'll run
+ 
+
+ align:start position:0%
+the game are not that high so I'll run
+with race okay because any other
+
+ align:start position:0%
+with race okay because any other
+ 
+
+ align:start position:0%
+with race okay because any other
+solution is going to be is going to be
+
+ align:start position:0%
+solution is going to be is going to be
+ 
+
+ align:start position:0%
+solution is going to be is going to be
+more expensive okay and and then maybe
+
+ align:start position:0%
+more expensive okay and and then maybe
+ 
+
+ align:start position:0%
+more expensive okay and and then maybe
+you get funny answers so one thing is
+
+ align:start position:0%
+you get funny answers so one thing is
+ 
+
+ align:start position:0%
+you get funny answers so one thing is
+for for that kind of data structure let
+
+ align:start position:0%
+for for that kind of data structure let
+ 
+
+ align:start position:0%
+for for that kind of data structure let
+me just recommend is that you have some
+
+ align:start position:0%
+me just recommend is that you have some
+ 
+
+ align:start position:0%
+me just recommend is that you have some
+way of turning off the data structure so
+
+ align:start position:0%
+way of turning off the data structure so
+ 
+
+ align:start position:0%
+way of turning off the data structure so
+that you can actually do the parallel
+
+ align:start position:0%
+that you can actually do the parallel
+ 
+
+ align:start position:0%
+that you can actually do the parallel
+search and get deterministic repeatable
+
+ align:start position:0%
+search and get deterministic repeatable
+ 
+
+ align:start position:0%
+search and get deterministic repeatable
+results
+
+ align:start position:0%
+results
+ 
+
+ align:start position:0%
+results
+okay so even though it may be aborting
+
+ align:start position:0%
+okay so even though it may be aborting
+ 
+
+ align:start position:0%
+okay so even though it may be aborting
+some things may not be aborting you want
+
+ align:start position:0%
+some things may not be aborting you want
+ 
+
+ align:start position:0%
+some things may not be aborting you want
+to have some way of executing and so for
+
+ align:start position:0%
+to have some way of executing and so for
+ 
+
+ align:start position:0%
+to have some way of executing and so for
+example you want to be able to turn off
+
+ align:start position:0%
+example you want to be able to turn off
+ 
+
+ align:start position:0%
+example you want to be able to turn off
+even the speculation in your code so you
+
+ align:start position:0%
+even the speculation in your code so you
+ 
+
+ align:start position:0%
+even the speculation in your code so you
+can test all the other things in your
+
+ align:start position:0%
+can test all the other things in your
+ 
+
+ align:start position:0%
+can test all the other things in your
+code that don't depend on the
+
+ align:start position:0%
+code that don't depend on the
+ 
+
+ align:start position:0%
+code that don't depend on the
+speculation okay because if you have
+
+ align:start position:0%
+speculation okay because if you have
+ 
+
+ align:start position:0%
+speculation okay because if you have
+something that's not deterministic as I
+
+ align:start position:0%
+something that's not deterministic as I
+ 
+
+ align:start position:0%
+something that's not deterministic as I
+say it's a nightmare to debug okay so we
+
+ align:start position:0%
+say it's a nightmare to debug okay so we
+ 
+
+ align:start position:0%
+say it's a nightmare to debug okay so we
+valued you know your value you're gonna
+
+ align:start position:0%
+valued you know your value you're gonna
+ 
+
+ align:start position:0%
+valued you know your value you're gonna
+do the evaluation function hey turn off
+
+ align:start position:0%
+do the evaluation function hey turn off
+ 
+
+ align:start position:0%
+do the evaluation function hey turn off
+if you're testing it turn off the
+
+ align:start position:0%
+if you're testing it turn off the
+ 
+
+ align:start position:0%
+if you're testing it turn off the
+speculation that you should be able to
+
+ align:start position:0%
+speculation that you should be able to
+ 
+
+ align:start position:0%
+speculation that you should be able to
+find out whether you've got bugs in your
+
+ align:start position:0%
+find out whether you've got bugs in your
+ 
+
+ align:start position:0%
+find out whether you've got bugs in your
+evaluation function there's no point in
+
+ align:start position:0%
+evaluation function there's no point in
+ 
+
+ align:start position:0%
+evaluation function there's no point in
+discovering you of a bug and it's like
+
+ align:start position:0%
+discovering you of a bug and it's like
+ 
+
+ align:start position:0%
+discovering you of a bug and it's like
+well where did it come from or whatever
+
+ align:start position:0%
+well where did it come from or whatever
+ 
+
+ align:start position:0%
+well where did it come from or whatever
+okay so you want to have things
+
+ align:start position:0%
+okay so you want to have things
+ 
+
+ align:start position:0%
+okay so you want to have things
+returning out and also you want to have
+
+ align:start position:0%
+returning out and also you want to have
+ 
+
+ align:start position:0%
+returning out and also you want to have
+ways of turning off for example access
+
+ align:start position:0%
+ways of turning off for example access
+ 
+
+ align:start position:0%
+ways of turning off for example access
+to the transposition table yes I'm going
+
+ align:start position:0%
+to the transposition table yes I'm going
+ 
+
+ align:start position:0%
+to the transposition table yes I'm going
+to speculate but no I'm not going to
+
+ align:start position:0%
+to speculate but no I'm not going to
+ 
+
+ align:start position:0%
+to speculate but no I'm not going to
+access the transposition table in
+
+ align:start position:0%
+access the transposition table in
+ 
+
+ align:start position:0%
+access the transposition table in
+parallel because because I may get a
+
+ align:start position:0%
+parallel because because I may get a
+ 
+
+ align:start position:0%
+parallel because because I may get a
+race on the entry in the transposition
+
+ align:start position:0%
+race on the entry in the transposition
+ 
+
+ align:start position:0%
+race on the entry in the transposition
+table okay
+
+ align:start position:0%
+table okay
+ 
+
+ align:start position:0%
+table okay
+I will the the hint that I will give you
+
+ align:start position:0%
+I will the the hint that I will give you
+ 
+
+ align:start position:0%
+I will the the hint that I will give you
+for that is that in the in the code that
+
+ align:start position:0%
+for that is that in the in the code that
+ 
+
+ align:start position:0%
+for that is that in the in the code that
+for our program that took second prize
+
+ align:start position:0%
+for our program that took second prize
+ 
+
+ align:start position:0%
+for our program that took second prize
+in the world computer Chess Championship
+
+ align:start position:0%
+in the world computer Chess Championship
+ 
+
+ align:start position:0%
+in the world computer Chess Championship
+many years ago I think it was in 1999
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where we we actually almost won the
+
+ align:start position:0%
+where we we actually almost won the
+ 
+
+ align:start position:0%
+where we we actually almost won the
+tournament and it's a and we got we lost
+
+ align:start position:0%
+tournament and it's a and we got we lost
+ 
+
+ align:start position:0%
+tournament and it's a and we got we lost
+in the playoff we we would have won the
+
+ align:start position:0%
+in the playoff we we would have won the
+ 
+
+ align:start position:0%
+in the playoff we we would have won the
+tournament except that we suggested our
+
+ align:start position:0%
+tournament except that we suggested our
+ 
+
+ align:start position:0%
+tournament except that we suggested our
+programmers suggested a rule change at
+
+ align:start position:0%
+programmers suggested a rule change at
+ 
+
+ align:start position:0%
+programmers suggested a rule change at
+the beginning of the tournament that
+
+ align:start position:0%
+the beginning of the tournament that
+ 
+
+ align:start position:0%
+the beginning of the tournament that
+everybody agreed to and then we were on
+
+ align:start position:0%
+everybody agreed to and then we were on
+ 
+
+ align:start position:0%
+everybody agreed to and then we were on
+the short end of that otherwise we would
+
+ align:start position:0%
+the short end of that otherwise we would
+ 
+
+ align:start position:0%
+the short end of that otherwise we would
+have been world champions and that was
+
+ align:start position:0%
+have been world champions and that was
+ 
+
+ align:start position:0%
+have been world champions and that was
+the last competition against computers
+
+ align:start position:0%
+the last competition against computers
+ 
+
+ align:start position:0%
+the last competition against computers
+that deep-blue the IBM computer that
+
+ align:start position:0%
+that deep-blue the IBM computer that
+ 
+
+ align:start position:0%
+that deep-blue the IBM computer that
+beat Kasparov the the human channa it's
+
+ align:start position:0%
+beat Kasparov the the human channa it's
+ 
+
+ align:start position:0%
+beat Kasparov the the human channa it's
+just a few months later they performed
+
+ align:start position:0%
+just a few months later they performed
+ 
+
+ align:start position:0%
+just a few months later they performed
+it and we actually they placed third in
+
+ align:start position:0%
+it and we actually they placed third in
+ 
+
+ align:start position:0%
+it and we actually they placed third in
+the tournament we tied for first
+
+ align:start position:0%
+the tournament we tied for first
+ 
+
+ align:start position:0%
+the tournament we tied for first
+our only loss was to deep blue okay and
+
+ align:start position:0%
+our only loss was to deep blue okay and
+ 
+
+ align:start position:0%
+our only loss was to deep blue okay and
+we were running on an 1824 node soup
+
+ align:start position:0%
+we were running on an 1824 node soup
+ 
+
+ align:start position:0%
+we were running on an 1824 node soup
+computer at Sandia National Labs a
+
+ align:start position:0%
+computer at Sandia National Labs a
+ 
+
+ align:start position:0%
+computer at Sandia National Labs a
+computer that probably is today less
+
+ align:start position:0%
+computer that probably is today less
+ 
+
+ align:start position:0%
+computer that probably is today less
+powerful than this okay so but it was
+
+ align:start position:0%
+powerful than this okay so but it was
+ 
+
+ align:start position:0%
+powerful than this okay so but it was
+you know it was very big type of
+
+ align:start position:0%
+you know it was very big type of
+ 
+
+ align:start position:0%
+you know it was very big type of
+computation so we you know and we were
+
+ align:start position:0%
+computation so we you know and we were
+ 
+
+ align:start position:0%
+computation so we you know and we were
+you know it they basically said if
+
+ align:start position:0%
+you know it they basically said if
+ 
+
+ align:start position:0%
+you know it they basically said if
+there's a tie they're gonna base base
+
+ align:start position:0%
+there's a tie they're gonna base base
+ 
+
+ align:start position:0%
+there's a tie they're gonna base base
+who wins on strength of opponents so you
+
+ align:start position:0%
+who wins on strength of opponents so you
+ 
+
+ align:start position:0%
+who wins on strength of opponents so you
+take a look at your opponent's records
+
+ align:start position:0%
+take a look at your opponent's records
+ 
+
+ align:start position:0%
+take a look at your opponent's records
+and if you had stronger opponents you'll
+
+ align:start position:0%
+and if you had stronger opponents you'll
+ 
+
+ align:start position:0%
+and if you had stronger opponents you'll
+win against somebody and we said you
+
+ align:start position:0%
+win against somebody and we said you
+ 
+
+ align:start position:0%
+win against somebody and we said you
+know if there's a tie just between two
+
+ align:start position:0%
+know if there's a tie just between two
+ 
+
+ align:start position:0%
+know if there's a tie just between two
+programs we should really have them you
+
+ align:start position:0%
+programs we should really have them you
+ 
+
+ align:start position:0%
+programs we should really have them you
+know face off against each other as an
+
+ align:start position:0%
+know face off against each other as an
+ 
+
+ align:start position:0%
+know face off against each other as an
+extra round and everything yeah that's a
+
+ align:start position:0%
+extra round and everything yeah that's a
+ 
+
+ align:start position:0%
+extra round and everything yeah that's a
+good idea and then wouldn't you know at
+
+ align:start position:0%
+good idea and then wouldn't you know at
+ 
+
+ align:start position:0%
+good idea and then wouldn't you know at
+the end we had the strongest you know
+
+ align:start position:0%
+the end we had the strongest you know
+ 
+
+ align:start position:0%
+the end we had the strongest you know
+opponents and and we were tied with
+
+ align:start position:0%
+opponents and and we were tied with
+ 
+
+ align:start position:0%
+opponents and and we were tied with
+another program called fritz an
+
+ align:start position:0%
+another program called fritz an
+ 
+
+ align:start position:0%
+another program called fritz an
+excellent program and we were out
+
+ align:start position:0%
+excellent program and we were out
+ 
+
+ align:start position:0%
+excellent program and we were out
+searching fritz in the in the playoff
+
+ align:start position:0%
+searching fritz in the in the playoff
+ 
+
+ align:start position:0%
+searching fritz in the in the playoff
+game and then we saw a move that in
+
+ align:start position:0%
+game and then we saw a move that in
+ 
+
+ align:start position:0%
+game and then we saw a move that in
+afterwards we when we were able to do
+
+ align:start position:0%
+afterwards we when we were able to do
+ 
+
+ align:start position:0%
+afterwards we when we were able to do
+offline searches deeper we were out
+
+ align:start position:0%
+offline searches deeper we were out
+ 
+
+ align:start position:0%
+offline searches deeper we were out
+searching them by like two ply okay and
+
+ align:start position:0%
+searching them by like two ply okay and
+ 
+
+ align:start position:0%
+searching them by like two ply okay and
+then but then we there's a move that
+
+ align:start position:0%
+then but then we there's a move that
+ 
+
+ align:start position:0%
+then but then we there's a move that
+looks like it's a good move for the
+
+ align:start position:0%
+looks like it's a good move for the
+ 
+
+ align:start position:0%
+looks like it's a good move for the
+depth we were looking at it doesn't look
+
+ align:start position:0%
+depth we were looking at it doesn't look
+ 
+
+ align:start position:0%
+depth we were looking at it doesn't look
+like a good move if you search much
+
+ align:start position:0%
+like a good move if you search much
+ 
+
+ align:start position:0%
+like a good move if you search much
+deeper or frankly if you search much
+
+ align:start position:0%
+deeper or frankly if you search much
+ 
+
+ align:start position:0%
+deeper or frankly if you search much
+shallower is one of these things where
+
+ align:start position:0%
+shallower is one of these things where
+ 
+
+ align:start position:0%
+shallower is one of these things where
+just look like a good move for the ply
+
+ align:start position:0%
+just look like a good move for the ply
+ 
+
+ align:start position:0%
+just look like a good move for the ply
+we happen to be searching because
+
+ align:start position:0%
+we happen to be searching because
+ 
+
+ align:start position:0%
+we happen to be searching because
+there's no guarantee because you can't
+
+ align:start position:0%
+there's no guarantee because you can't
+ 
+
+ align:start position:0%
+there's no guarantee because you can't
+see the end of the game there's no
+
+ align:start position:0%
+see the end of the game there's no
+ 
+
+ align:start position:0%
+see the end of the game there's no
+guarantee that if you search deeper
+
+ align:start position:0%
+guarantee that if you search deeper
+ 
+
+ align:start position:0%
+guarantee that if you search deeper
+you're actually going to beat somebody
+
+ align:start position:0%
+you're actually going to beat somebody
+ 
+
+ align:start position:0%
+you're actually going to beat somebody
+else okay sometime because there's the
+
+ align:start position:0%
+else okay sometime because there's the
+ 
+
+ align:start position:0%
+else okay sometime because there's the
+horizon effect of you can't just simply
+
+ align:start position:0%
+horizon effect of you can't just simply
+ 
+
+ align:start position:0%
+horizon effect of you can't just simply
+can't see what's coming up in the future
+
+ align:start position:0%
+can't see what's coming up in the future
+ 
+
+ align:start position:0%
+can't see what's coming up in the future
+you can only see sort of on average so
+
+ align:start position:0%
+you can only see sort of on average so
+ 
+
+ align:start position:0%
+you can only see sort of on average so
+we made this bad move we almost
+
+ align:start position:0%
+we made this bad move we almost
+ 
+
+ align:start position:0%
+we made this bad move we almost
+recovered we almost tied had we tied we
+
+ align:start position:0%
+recovered we almost tied had we tied we
+ 
+
+ align:start position:0%
+recovered we almost tied had we tied we
+would have been world champions because
+
+ align:start position:0%
+would have been world champions because
+ 
+
+ align:start position:0%
+would have been world champions because
+we had the stronger we won the
+
+ align:start position:0%
+we had the stronger we won the
+ 
+
+ align:start position:0%
+we had the stronger we won the
+tiebreaker and we weren't able to
+
+ align:start position:0%
+tiebreaker and we weren't able to
+ 
+
+ align:start position:0%
+tiebreaker and we weren't able to
+recover from the from the error and so
+
+ align:start position:0%
+recover from the from the error and so
+ 
+
+ align:start position:0%
+recover from the from the error and so
+we took second prize as like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway in that program we decided that
+
+ align:start position:0%
+anyway in that program we decided that
+ 
+
+ align:start position:0%
+anyway in that program we decided that
+we were just gonna let there be a race
+
+ align:start position:0%
+we were just gonna let there be a race
+ 
+
+ align:start position:0%
+we were just gonna let there be a race
+and the Rhian the transposition table
+
+ align:start position:0%
+and the Rhian the transposition table
+ 
+
+ align:start position:0%
+and the Rhian the transposition table
+and the reason was we calculated what
+
+ align:start position:0%
+and the reason was we calculated what
+ 
+
+ align:start position:0%
+and the reason was we calculated what
+are the odds that the race actually
+
+ align:start position:0%
+are the odds that the race actually
+ 
+
+ align:start position:0%
+are the odds that the race actually
+affects the value that you would
+
+ align:start position:0%
+affects the value that you would
+ 
+
+ align:start position:0%
+affects the value that you would
+actually pick that value and if it
+
+ align:start position:0%
+actually pick that value and if it
+ 
+
+ align:start position:0%
+actually pick that value and if it
+affected the value what are the odds
+
+ align:start position:0%
+affected the value what are the odds
+ 
+
+ align:start position:0%
+affected the value what are the odds
+that affects the move that you're gonna
+
+ align:start position:0%
+that affects the move that you're gonna
+ 
+
+ align:start position:0%
+that affects the move that you're gonna
+make and it affects the move you're
+
+ align:start position:0%
+make and it affects the move you're
+ 
+
+ align:start position:0%
+make and it affects the move you're
+gonna make what are the odds that
+
+ align:start position:0%
+gonna make what are the odds that
+ 
+
+ align:start position:0%
+gonna make what are the odds that
+affects the the game and if he affects
+
+ align:start position:0%
+affects the the game and if he affects
+ 
+
+ align:start position:0%
+affects the the game and if he affects
+the game what are the odds that affects
+
+ align:start position:0%
+the game what are the odds that affects
+ 
+
+ align:start position:0%
+the game what are the odds that affects
+your result in the tournament and when
+
+ align:start position:0%
+your result in the tournament and when
+ 
+
+ align:start position:0%
+your result in the tournament and when
+you figured all these things out it was
+
+ align:start position:0%
+you figured all these things out it was
+ 
+
+ align:start position:0%
+you figured all these things out it was
+like and we would slow the program down
+
+ align:start position:0%
+like and we would slow the program down
+ 
+
+ align:start position:0%
+like and we would slow the program down
+more by putting in for example locking
+
+ align:start position:0%
+more by putting in for example locking
+ 
+
+ align:start position:0%
+more by putting in for example locking
+okay because that would slow down every
+
+ align:start position:0%
+okay because that would slow down every
+ 
+
+ align:start position:0%
+okay because that would slow down every
+access then we would if we just if we
+
+ align:start position:0%
+access then we would if we just if we
+ 
+
+ align:start position:0%
+access then we would if we just if we
+just ran things because one of the
+
+ align:start position:0%
+just ran things because one of the
+ 
+
+ align:start position:0%
+just ran things because one of the
+things that happens in alpha beta that
+
+ align:start position:0%
+things that happens in alpha beta that
+ 
+
+ align:start position:0%
+things that happens in alpha beta that
+that thing is if you get an extreme
+
+ align:start position:0%
+that thing is if you get an extreme
+ 
+
+ align:start position:0%
+that thing is if you get an extreme
+value usually those are locked off
+
+ align:start position:0%
+value usually those are locked off
+ 
+
+ align:start position:0%
+value usually those are locked off
+because if it's such a good move for you
+
+ align:start position:0%
+because if it's such a good move for you
+ 
+
+ align:start position:0%
+because if it's such a good move for you
+your opponent's not going to let you
+
+ align:start position:0%
+your opponent's not going to let you
+ 
+
+ align:start position:0%
+your opponent's not going to let you
+play it so if you ended up with a score
+
+ align:start position:0%
+play it so if you ended up with a score
+ 
+
+ align:start position:0%
+play it so if you ended up with a score
+that was extreme because it was based on
+
+ align:start position:0%
+that was extreme because it was based on
+ 
+
+ align:start position:0%
+that was extreme because it was based on
+a value that you were racing on usually
+
+ align:start position:0%
+a value that you were racing on usually
+ 
+
+ align:start position:0%
+a value that you were racing on usually
+it's gonna not even propagate up to the
+
+ align:start position:0%
+it's gonna not even propagate up to the
+ 
+
+ align:start position:0%
+it's gonna not even propagate up to the
+root of the tree so anyway so we just
+
+ align:start position:0%
+root of the tree so anyway so we just
+ 
+
+ align:start position:0%
+root of the tree so anyway so we just
+ran you know naked so to speak so there
+
+ align:start position:0%
+ran you know naked so to speak so there
+ 
+
+ align:start position:0%
+ran you know naked so to speak so there
+are two other data structures you're
+
+ align:start position:0%
+are two other data structures you're
+ 
+
+ align:start position:0%
+are two other data structures you're
+gonna have to worry about to make
+
+ align:start position:0%
+gonna have to worry about to make
+ 
+
+ align:start position:0%
+gonna have to worry about to make
+decision about another one is the killer
+
+ align:start position:0%
+decision about another one is the killer
+ 
+
+ align:start position:0%
+decision about another one is the killer
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+data structure so the killer data
+
+ align:start position:0%
+data structure so the killer data
+ 
+
+ align:start position:0%
+data structure so the killer data
+structure is a heuristic that says you
+
+ align:start position:0%
+structure is a heuristic that says you
+ 
+
+ align:start position:0%
+structure is a heuristic that says you
+know at a given depth of code you tend
+
+ align:start position:0%
+know at a given depth of code you tend
+ 
+
+ align:start position:0%
+know at a given depth of code you tend
+to see the same moves that are good and
+
+ align:start position:0%
+to see the same moves that are good and
+ 
+
+ align:start position:0%
+to see the same moves that are good and
+a move that is good for one for one
+
+ align:start position:0%
+a move that is good for one for one
+ 
+
+ align:start position:0%
+a move that is good for one for one
+thing at a given depth tends to be good
+
+ align:start position:0%
+thing at a given depth tends to be good
+ 
+
+ align:start position:0%
+thing at a given depth tends to be good
+for something else so for example it may
+
+ align:start position:0%
+for something else so for example it may
+ 
+
+ align:start position:0%
+for something else so for example it may
+be that you know you play Bishop takes
+
+ align:start position:0%
+be that you know you play Bishop takes
+ 
+
+ align:start position:0%
+be that you know you play Bishop takes
+Queen
+
+ align:start position:0%
+Queen
+ 
+
+ align:start position:0%
+Queen
+okay so you've won the other players
+
+ align:start position:0%
+okay so you've won the other players
+ 
+
+ align:start position:0%
+okay so you've won the other players
+Queen and then their response is thier
+
+ align:start position:0%
+Queen and then their response is thier
+ 
+
+ align:start position:0%
+Queen and then their response is thier
+response is to do something irrelevant
+
+ align:start position:0%
+response is to do something irrelevant
+ 
+
+ align:start position:0%
+response is to do something irrelevant
+okay well now you've you know you made
+
+ align:start position:0%
+okay well now you've you know you made
+ 
+
+ align:start position:0%
+okay well now you've you know you made
+them okay well there's a lot of other
+
+ align:start position:0%
+them okay well there's a lot of other
+ 
+
+ align:start position:0%
+them okay well there's a lot of other
+moves where you know you could make them
+
+ align:start position:0%
+moves where you know you could make them
+ 
+
+ align:start position:0%
+moves where you know you could make them
+on that move okay for which they're
+
+ align:start position:0%
+on that move okay for which they're
+ 
+
+ align:start position:0%
+on that move okay for which they're
+playing things on the board that are
+
+ align:start position:0%
+playing things on the board that are
+ 
+
+ align:start position:0%
+playing things on the board that are
+irrelevant okay and so the same type of
+
+ align:start position:0%
+irrelevant okay and so the same type of
+ 
+
+ align:start position:0%
+irrelevant okay and so the same type of
+move tends to be a killer always you're
+
+ align:start position:0%
+move tends to be a killer always you're
+ 
+
+ align:start position:0%
+move tends to be a killer always you're
+you're able to you know at that depth in
+
+ align:start position:0%
+you're able to you know at that depth in
+ 
+
+ align:start position:0%
+you're able to you know at that depth in
+that position you're you're able to make
+
+ align:start position:0%
+that position you're you're able to make
+ 
+
+ align:start position:0%
+that position you're you're able to make
+the same move in it you know if they
+
+ align:start position:0%
+the same move in it you know if they
+ 
+
+ align:start position:0%
+the same move in it you know if they
+don't address the issue that's always a
+
+ align:start position:0%
+don't address the issue that's always a
+ 
+
+ align:start position:0%
+don't address the issue that's always a
+good move to check and so that ends up
+
+ align:start position:0%
+good move to check and so that ends up
+ 
+
+ align:start position:0%
+good move to check and so that ends up
+being ordered near the front so the
+
+ align:start position:0%
+being ordered near the front so the
+ 
+
+ align:start position:0%
+being ordered near the front so the
+killer table keeps track of that and I
+
+ align:start position:0%
+killer table keeps track of that and I
+ 
+
+ align:start position:0%
+killer table keeps track of that and I
+think in our code we have two killers is
+
+ align:start position:0%
+think in our code we have two killers is
+ 
+
+ align:start position:0%
+think in our code we have two killers is
+that right Helen I think we it's I think
+
+ align:start position:0%
+that right Helen I think we it's I think
+ 
+
+ align:start position:0%
+that right Helen I think we it's I think
+it's set up to allow you to do for up to
+
+ align:start position:0%
+it's set up to allow you to do for up to
+ 
+
+ align:start position:0%
+it's set up to allow you to do for up to
+four killers but we only do two in the
+
+ align:start position:0%
+four killers but we only do two in the
+ 
+
+ align:start position:0%
+four killers but we only do two in the
+code that we gave you I mean you can
+
+ align:start position:0%
+code that we gave you I mean you can
+ 
+
+ align:start position:0%
+code that we gave you I mean you can
+enable it and see whether four killers
+
+ align:start position:0%
+enable it and see whether four killers
+ 
+
+ align:start position:0%
+enable it and see whether four killers
+me but that's a shared data structure
+
+ align:start position:0%
+me but that's a shared data structure
+ 
+
+ align:start position:0%
+me but that's a shared data structure
+and so one of the questions is should
+
+ align:start position:0%
+and so one of the questions is should
+ 
+
+ align:start position:0%
+and so one of the questions is should
+you be keeping a local copy of that or
+
+ align:start position:0%
+you be keeping a local copy of that or
+ 
+
+ align:start position:0%
+you be keeping a local copy of that or
+should you be you know using a global
+
+ align:start position:0%
+should you be you know using a global
+ 
+
+ align:start position:0%
+should you be you know using a global
+one that they all share okay and
+
+ align:start position:0%
+one that they all share okay and
+ 
+
+ align:start position:0%
+one that they all share okay and
+updating it the third one is the best
+
+ align:start position:0%
+updating it the third one is the best
+ 
+
+ align:start position:0%
+updating it the third one is the best
+move table which is used to order all
+
+ align:start position:0%
+move table which is used to order all
+ 
+
+ align:start position:0%
+move table which is used to order all
+the low order things so the first thing
+
+ align:start position:0%
+the low order things so the first thing
+ 
+
+ align:start position:0%
+the low order things so the first thing
+we most important is did you get a move
+
+ align:start position:0%
+we most important is did you get a move
+ 
+
+ align:start position:0%
+we most important is did you get a move
+out of the transposition table that
+
+ align:start position:0%
+out of the transposition table that
+ 
+
+ align:start position:0%
+out of the transposition table that
+tends to be quite accurate then second
+
+ align:start position:0%
+tends to be quite accurate then second
+ 
+
+ align:start position:0%
+tends to be quite accurate then second
+is did you get a move out of did you get
+
+ align:start position:0%
+is did you get a move out of did you get
+ 
+
+ align:start position:0%
+is did you get a move out of did you get
+a move out of the killer table and
+
+ align:start position:0%
+a move out of the killer table and
+ 
+
+ align:start position:0%
+a move out of the killer table and
+finally it's sort of like statistically
+
+ align:start position:0%
+finally it's sort of like statistically
+ 
+
+ align:start position:0%
+finally it's sort of like statistically
+how good are these moves have you seen
+
+ align:start position:0%
+how good are these moves have you seen
+ 
+
+ align:start position:0%
+how good are these moves have you seen
+these a lot before and if you've seen
+
+ align:start position:0%
+these a lot before and if you've seen
+ 
+
+ align:start position:0%
+these a lot before and if you've seen
+them a lot before that's how the other
+
+ align:start position:0%
+them a lot before that's how the other
+ 
+
+ align:start position:0%
+them a lot before that's how the other
+moves get ordered and that's kept in the
+
+ align:start position:0%
+moves get ordered and that's kept in the
+ 
+
+ align:start position:0%
+moves get ordered and that's kept in the
+best move table and once again that's a
+
+ align:start position:0%
+best move table and once again that's a
+ 
+
+ align:start position:0%
+best move table and once again that's a
+shared table in the search you're gonna
+
+ align:start position:0%
+shared table in the search you're gonna
+ 
+
+ align:start position:0%
+shared table in the search you're gonna
+have to figure out do you want to do a
+
+ align:start position:0%
+have to figure out do you want to do a
+ 
+
+ align:start position:0%
+have to figure out do you want to do a
+thread-local you know worker local copy
+
+ align:start position:0%
+thread-local you know worker local copy
+ 
+
+ align:start position:0%
+thread-local you know worker local copy
+or do you want to do you want to you
+
+ align:start position:0%
+or do you want to do you want to you
+ 
+
+ align:start position:0%
+or do you want to do you want to you
+know synchronize it or how are you going
+
+ align:start position:0%
+know synchronize it or how are you going
+ 
+
+ align:start position:0%
+know synchronize it or how are you going
+to manage that data structure okay and
+
+ align:start position:0%
+to manage that data structure okay and
+ 
+
+ align:start position:0%
+to manage that data structure okay and
+the answer I would say is different for
+
+ align:start position:0%
+the answer I would say is different for
+ 
+
+ align:start position:0%
+the answer I would say is different for
+the compared to what you do with a
+
+ align:start position:0%
+the compared to what you do with a
+ 
+
+ align:start position:0%
+the compared to what you do with a
+transposition table okay transposition
+
+ align:start position:0%
+transposition table okay transposition
+ 
+
+ align:start position:0%
+transposition table okay transposition
+table generally it's not worth locking
+
+ align:start position:0%
+table generally it's not worth locking
+ 
+
+ align:start position:0%
+table generally it's not worth locking
+or or whatever and it is good to share
+
+ align:start position:0%
+or or whatever and it is good to share
+ 
+
+ align:start position:0%
+or or whatever and it is good to share
+because if you have seen that move
+
+ align:start position:0%
+because if you have seen that move
+ 
+
+ align:start position:0%
+because if you have seen that move
+before that saved you a huge amount of
+
+ align:start position:0%
+before that saved you a huge amount of
+ 
+
+ align:start position:0%
+before that saved you a huge amount of
+computation
+
+ align:start position:0%
+computation
+ 
+
+ align:start position:0%
+computation
+to be able to look it up and not not do
+
+ align:start position:0%
+to be able to look it up and not not do
+ 
+
+ align:start position:0%
+to be able to look it up and not not do
+it okay so those are some of the tips
+
+ align:start position:0%
+it okay so those are some of the tips
+ 
+
+ align:start position:0%
+it okay so those are some of the tips
+for parallelization which we'll get to
+
+ align:start position:0%
+for parallelization which we'll get to
+ 
+
+ align:start position:0%
+for parallelization which we'll get to
+in the beta too but now I want to talk
+
+ align:start position:0%
+in the beta too but now I want to talk
+ 
+
+ align:start position:0%
+in the beta too but now I want to talk
+about for most of the rest of time talk
+
+ align:start position:0%
+about for most of the rest of time talk
+ 
+
+ align:start position:0%
+about for most of the rest of time talk
+about some of the other things that you
+
+ align:start position:0%
+about some of the other things that you
+ 
+
+ align:start position:0%
+about some of the other things that you
+can do with the code you've currently
+
+ align:start position:0%
+can do with the code you've currently
+ 
+
+ align:start position:0%
+can do with the code you've currently
+got and let me take these in some some
+
+ align:start position:0%
+got and let me take these in some some
+ 
+
+ align:start position:0%
+got and let me take these in some some
+order and then we can ask questions so
+
+ align:start position:0%
+order and then we can ask questions so
+ 
+
+ align:start position:0%
+order and then we can ask questions so
+open you who's contemplating doing an
+
+ align:start position:0%
+open you who's contemplating doing an
+ 
+
+ align:start position:0%
+open you who's contemplating doing an
+opening book anybody for for beta one
+
+ align:start position:0%
+opening book anybody for for beta one
+ 
+
+ align:start position:0%
+opening book anybody for for beta one
+they're gonna do an opening book for
+
+ align:start position:0%
+they're gonna do an opening book for
+ 
+
+ align:start position:0%
+they're gonna do an opening book for
+beta 1 or beta 2 hoo-hoo for beta 1 let
+
+ align:start position:0%
+beta 1 or beta 2 hoo-hoo for beta 1 let
+ 
+
+ align:start position:0%
+beta 1 or beta 2 hoo-hoo for beta 1 let
+me see okay beta 2 who wants to do an
+
+ align:start position:0%
+me see okay beta 2 who wants to do an
+ 
+
+ align:start position:0%
+me see okay beta 2 who wants to do an
+opening book beta for the final okay
+
+ align:start position:0%
+opening book beta for the final okay
+ 
+
+ align:start position:0%
+opening book beta for the final okay
+yeah okay so you know the idea here is
+
+ align:start position:0%
+yeah okay so you know the idea here is
+ 
+
+ align:start position:0%
+yeah okay so you know the idea here is
+to pre-compute best moves at the
+
+ align:start position:0%
+to pre-compute best moves at the
+ 
+
+ align:start position:0%
+to pre-compute best moves at the
+beginning of the game you know so that
+
+ align:start position:0%
+beginning of the game you know so that
+ 
+
+ align:start position:0%
+beginning of the game you know so that
+you know it's like well we know what the
+
+ align:start position:0%
+you know it's like well we know what the
+ 
+
+ align:start position:0%
+you know it's like well we know what the
+starting position is so what on I you
+
+ align:start position:0%
+starting position is so what on I you
+ 
+
+ align:start position:0%
+starting position is so what on I you
+know spend $1,000 or whatever on Amazon
+
+ align:start position:0%
+know spend $1,000 or whatever on Amazon
+ 
+
+ align:start position:0%
+know spend $1,000 or whatever on Amazon
+and and you know compute things to some
+
+ align:start position:0%
+and and you know compute things to some
+ 
+
+ align:start position:0%
+and and you know compute things to some
+ungodly ply right and see what the best
+
+ align:start position:0%
+ungodly ply right and see what the best
+ 
+
+ align:start position:0%
+ungodly ply right and see what the best
+moves are at the beginning of the game
+
+ align:start position:0%
+moves are at the beginning of the game
+ 
+
+ align:start position:0%
+moves are at the beginning of the game
+and put that into a book so I don't have
+
+ align:start position:0%
+and put that into a book so I don't have
+ 
+
+ align:start position:0%
+and put that into a book so I don't have
+to search those so that's the idea I
+
+ align:start position:0%
+to search those so that's the idea I
+ 
+
+ align:start position:0%
+to search those so that's the idea I
+think to begin with there are lower
+
+ align:start position:0%
+think to begin with there are lower
+ 
+
+ align:start position:0%
+think to begin with there are lower
+hanging fruit than then the opening book
+
+ align:start position:0%
+hanging fruit than then the opening book
+ 
+
+ align:start position:0%
+hanging fruit than then the opening book
+you know if you look at it you're going
+
+ align:start position:0%
+you know if you look at it you're going
+ 
+
+ align:start position:0%
+you know if you look at it you're going
+to be in opening book you know if you're
+
+ align:start position:0%
+to be in opening book you know if you're
+ 
+
+ align:start position:0%
+to be in opening book you know if you're
+lucky for you know six or eight moves
+
+ align:start position:0%
+lucky for you know six or eight moves
+ 
+
+ align:start position:0%
+lucky for you know six or eight moves
+and the games tend to last have you
+
+ align:start position:0%
+and the games tend to last have you
+ 
+
+ align:start position:0%
+and the games tend to last have you
+looked to see how long games last ten to
+
+ align:start position:0%
+looked to see how long games last ten to
+ 
+
+ align:start position:0%
+looked to see how long games last ten to
+last yeah what is it
+
+ align:start position:0%
+last yeah what is it
+ 
+
+ align:start position:0%
+last yeah what is it
+no most games don't go 4096 we don't let
+
+ align:start position:0%
+no most games don't go 4096 we don't let
+ 
+
+ align:start position:0%
+no most games don't go 4096 we don't let
+them go that long anyway so anybody's
+
+ align:start position:0%
+them go that long anyway so anybody's
+ 
+
+ align:start position:0%
+them go that long anyway so anybody's
+take a look statistically to see how
+
+ align:start position:0%
+take a look statistically to see how
+ 
+
+ align:start position:0%
+take a look statistically to see how
+long games are I think they tend to be
+
+ align:start position:0%
+long games are I think they tend to be
+ 
+
+ align:start position:0%
+long games are I think they tend to be
+like 40 or 50 moves okay I mean this
+
+ align:start position:0%
+like 40 or 50 moves okay I mean this
+ 
+
+ align:start position:0%
+like 40 or 50 moves okay I mean this
+year is different from other years
+
+ align:start position:0%
+year is different from other years
+ 
+
+ align:start position:0%
+year is different from other years
+because we have different rules but I
+
+ align:start position:0%
+because we have different rules but I
+ 
+
+ align:start position:0%
+because we have different rules but I
+think it's like 40 or 50 moves so you're
+
+ align:start position:0%
+think it's like 40 or 50 moves so you're
+ 
+
+ align:start position:0%
+think it's like 40 or 50 moves so you're
+not spending you know so you're doing
+
+ align:start position:0%
+not spending you know so you're doing
+ 
+
+ align:start position:0%
+not spending you know so you're doing
+something that will help you in 10% of
+
+ align:start position:0%
+something that will help you in 10% of
+ 
+
+ align:start position:0%
+something that will help you in 10% of
+the game where's there other places you
+
+ align:start position:0%
+the game where's there other places you
+ 
+
+ align:start position:0%
+the game where's there other places you
+could do it we're going to help you in
+
+ align:start position:0%
+could do it we're going to help you in
+ 
+
+ align:start position:0%
+could do it we're going to help you in
+the whole game nevertheless we've had
+
+ align:start position:0%
+the whole game nevertheless we've had
+ 
+
+ align:start position:0%
+the whole game nevertheless we've had
+teams that did a great job on opening
+
+ align:start position:0%
+teams that did a great job on opening
+ 
+
+ align:start position:0%
+teams that did a great job on opening
+books and clobbered people by you know
+
+ align:start position:0%
+books and clobbered people by you know
+ 
+
+ align:start position:0%
+books and clobbered people by you know
+by having a fantastic opening book okay
+
+ align:start position:0%
+by having a fantastic opening book okay
+ 
+
+ align:start position:0%
+by having a fantastic opening book okay
+it's actually cheaper to keep separate
+
+ align:start position:0%
+it's actually cheaper to keep separate
+ 
+
+ align:start position:0%
+it's actually cheaper to keep separate
+opening books for each side than to keep
+
+ align:start position:0%
+opening books for each side than to keep
+ 
+
+ align:start position:0%
+opening books for each side than to keep
+one opening book for both sides okay and
+
+ align:start position:0%
+one opening book for both sides okay and
+ 
+
+ align:start position:0%
+one opening book for both sides okay and
+in this game it's actually fairly easy
+
+ align:start position:0%
+in this game it's actually fairly easy
+ 
+
+ align:start position:0%
+in this game it's actually fairly easy
+to keep a symmetry thing and and
+
+ align:start position:0%
+to keep a symmetry thing and and
+ 
+
+ align:start position:0%
+to keep a symmetry thing and and
+basically have an one opening book that
+
+ align:start position:0%
+basically have an one opening book that
+ 
+
+ align:start position:0%
+basically have an one opening book that
+works for the side on move okay and that
+
+ align:start position:0%
+works for the side on move okay and that
+ 
+
+ align:start position:0%
+works for the side on move okay and that
+store that allows you to store you don't
+
+ align:start position:0%
+store that allows you to store you don't
+ 
+
+ align:start position:0%
+store that allows you to store you don't
+have to store you know if if I make a
+
+ align:start position:0%
+have to store you know if if I make a
+ 
+
+ align:start position:0%
+have to store you know if if I make a
+given move if I have a given position I
+
+ align:start position:0%
+given move if I have a given position I
+ 
+
+ align:start position:0%
+given move if I have a given position I
+only need in principle to store one
+
+ align:start position:0%
+only need in principle to store one
+ 
+
+ align:start position:0%
+only need in principle to store one
+answer for that position okay whereas
+
+ align:start position:0%
+answer for that position okay whereas
+ 
+
+ align:start position:0%
+answer for that position okay whereas
+then my opponent may make any number of
+
+ align:start position:0%
+then my opponent may make any number of
+ 
+
+ align:start position:0%
+then my opponent may make any number of
+moves for which then I only need to know
+
+ align:start position:0%
+moves for which then I only need to know
+ 
+
+ align:start position:0%
+moves for which then I only need to know
+one move what's my best move in that
+
+ align:start position:0%
+one move what's my best move in that
+ 
+
+ align:start position:0%
+one move what's my best move in that
+position so you can see that you're only
+
+ align:start position:0%
+position so you can see that you're only
+ 
+
+ align:start position:0%
+position so you can see that you're only
+having two you know you have once again
+
+ align:start position:0%
+having two you know you have once again
+ 
+
+ align:start position:0%
+having two you know you have once again
+this property that on my move I only
+
+ align:start position:0%
+this property that on my move I only
+ 
+
+ align:start position:0%
+this property that on my move I only
+need to have one move stored my
+
+ align:start position:0%
+need to have one move stored my
+ 
+
+ align:start position:0%
+need to have one move stored my
+opponent's moves I need to have all the
+
+ align:start position:0%
+opponent's moves I need to have all the
+ 
+
+ align:start position:0%
+opponent's moves I need to have all the
+moves stored okay and then my move I
+
+ align:start position:0%
+moves stored okay and then my move I
+ 
+
+ align:start position:0%
+moves stored okay and then my move I
+have one move story and that basically
+
+ align:start position:0%
+have one move story and that basically
+ 
+
+ align:start position:0%
+have one move story and that basically
+means you're effectively going twice the
+
+ align:start position:0%
+means you're effectively going twice the
+ 
+
+ align:start position:0%
+means you're effectively going twice the
+depth as if you kept all my moves and
+
+ align:start position:0%
+depth as if you kept all my moves and
+ 
+
+ align:start position:0%
+depth as if you kept all my moves and
+then all of the other opponent's moves
+
+ align:start position:0%
+then all of the other opponent's moves
+ 
+
+ align:start position:0%
+then all of the other opponent's moves
+and then all of those because when I do
+
+ align:start position:0%
+and then all of those because when I do
+ 
+
+ align:start position:0%
+and then all of those because when I do
+that it's like well why am i you know
+
+ align:start position:0%
+that it's like well why am i you know
+ 
+
+ align:start position:0%
+that it's like well why am i you know
+why do I need to know what the what the
+
+ align:start position:0%
+why do I need to know what the what the
+ 
+
+ align:start position:0%
+why do I need to know what the what the
+the best move so it's better to keep
+
+ align:start position:0%
+the best move so it's better to keep
+ 
+
+ align:start position:0%
+the best move so it's better to keep
+them separate when you build the opening
+
+ align:start position:0%
+them separate when you build the opening
+ 
+
+ align:start position:0%
+them separate when you build the opening
+book you'll store a lot less you have a
+
+ align:start position:0%
+book you'll store a lot less you have a
+ 
+
+ align:start position:0%
+book you'll store a lot less you have a
+lot smaller storage you'll be able to
+
+ align:start position:0%
+lot smaller storage you'll be able to
+ 
+
+ align:start position:0%
+lot smaller storage you'll be able to
+store
+
+ align:start position:0%
+store
+ 
+
+ align:start position:0%
+store
+more moves if you do that okay but I
+
+ align:start position:0%
+more moves if you do that okay but I
+ 
+
+ align:start position:0%
+more moves if you do that okay but I
+would say not necessarily the best the
+
+ align:start position:0%
+would say not necessarily the best the
+ 
+
+ align:start position:0%
+would say not necessarily the best the
+first thing I would go to optimize and
+
+ align:start position:0%
+first thing I would go to optimize and
+ 
+
+ align:start position:0%
+first thing I would go to optimize and
+but it's also the case that this is a
+
+ align:start position:0%
+but it's also the case that this is a
+ 
+
+ align:start position:0%
+but it's also the case that this is a
+place where you know one of the teams
+
+ align:start position:0%
+place where you know one of the teams
+ 
+
+ align:start position:0%
+place where you know one of the teams
+you know built a fabulous opening book
+
+ align:start position:0%
+you know built a fabulous opening book
+ 
+
+ align:start position:0%
+you know built a fabulous opening book
+one year and and one of the things about
+
+ align:start position:0%
+one year and and one of the things about
+ 
+
+ align:start position:0%
+one year and and one of the things about
+the opening book is it allows you also
+
+ align:start position:0%
+the opening book is it allows you also
+ 
+
+ align:start position:0%
+the opening book is it allows you also
+to sort of threshold and say you know in
+
+ align:start position:0%
+to sort of threshold and say you know in
+ 
+
+ align:start position:0%
+to sort of threshold and say you know in
+a given move I don't just have to have
+
+ align:start position:0%
+a given move I don't just have to have
+ 
+
+ align:start position:0%
+a given move I don't just have to have
+one move let me have three moves you
+
+ align:start position:0%
+one move let me have three moves you
+ 
+
+ align:start position:0%
+one move let me have three moves you
+know and pick randomly among them so
+
+ align:start position:0%
+know and pick randomly among them so
+ 
+
+ align:start position:0%
+know and pick randomly among them so
+that I'm not predictable what the team
+
+ align:start position:0%
+that I'm not predictable what the team
+ 
+
+ align:start position:0%
+that I'm not predictable what the team
+did that used the opening book is they
+
+ align:start position:0%
+did that used the opening book is they
+ 
+
+ align:start position:0%
+did that used the opening book is they
+observed that everybody was using words
+
+ align:start position:0%
+observed that everybody was using words
+ 
+
+ align:start position:0%
+observed that everybody was using words
+just searching from the beginning so
+
+ align:start position:0%
+just searching from the beginning so
+ 
+
+ align:start position:0%
+just searching from the beginning so
+they were all finding exactly the same
+
+ align:start position:0%
+they were all finding exactly the same
+ 
+
+ align:start position:0%
+they were all finding exactly the same
+moves at the beginning of the game and
+
+ align:start position:0%
+moves at the beginning of the game and
+ 
+
+ align:start position:0%
+moves at the beginning of the game and
+so they knew exactly what the path was
+
+ align:start position:0%
+so they knew exactly what the path was
+ 
+
+ align:start position:0%
+so they knew exactly what the path was
+that all the other programs were gonna
+
+ align:start position:0%
+that all the other programs were gonna
+ 
+
+ align:start position:0%
+that all the other programs were gonna
+follow and so they could make the best
+
+ align:start position:0%
+follow and so they could make the best
+ 
+
+ align:start position:0%
+follow and so they could make the best
+move on their move but if you have
+
+ align:start position:0%
+move on their move but if you have
+ 
+
+ align:start position:0%
+move on their move but if you have
+something that's got some randomness to
+
+ align:start position:0%
+something that's got some randomness to
+ 
+
+ align:start position:0%
+something that's got some randomness to
+it and there is a jitter in there who
+
+ align:start position:0%
+it and there is a jitter in there who
+ 
+
+ align:start position:0%
+it and there is a jitter in there who
+found the randomness the place we insert
+
+ align:start position:0%
+found the randomness the place we insert
+ 
+
+ align:start position:0%
+found the randomness the place we insert
+randomness and the code right so there
+
+ align:start position:0%
+randomness and the code right so there
+ 
+
+ align:start position:0%
+randomness and the code right so there
+was I think Zach had a had a comment on
+
+ align:start position:0%
+was I think Zach had a had a comment on
+ 
+
+ align:start position:0%
+was I think Zach had a had a comment on
+Piazza about that so there's a place in
+
+ align:start position:0%
+Piazza about that so there's a place in
+ 
+
+ align:start position:0%
+Piazza about that so there's a place in
+the code where we did there the amount
+
+ align:start position:0%
+the code where we did there the amount
+ 
+
+ align:start position:0%
+the code where we did there the amount
+so that you will get unpredictable
+
+ align:start position:0%
+so that you will get unpredictable
+ 
+
+ align:start position:0%
+so that you will get unpredictable
+results and that way you won't always
+
+ align:start position:0%
+results and that way you won't always
+ 
+
+ align:start position:0%
+results and that way you won't always
+play the same move okay just by changing
+
+ align:start position:0%
+play the same move okay just by changing
+ 
+
+ align:start position:0%
+play the same move okay just by changing
+things this is like you know a tent you
+
+ align:start position:0%
+things this is like you know a tent you
+ 
+
+ align:start position:0%
+things this is like you know a tent you
+know hundredths of a pawn value is like
+
+ align:start position:0%
+know hundredths of a pawn value is like
+ 
+
+ align:start position:0%
+know hundredths of a pawn value is like
+not very big and like who cares whether
+
+ align:start position:0%
+not very big and like who cares whether
+ 
+
+ align:start position:0%
+not very big and like who cares whether
+or not you know we have you know it's
+
+ align:start position:0%
+or not you know we have you know it's
+ 
+
+ align:start position:0%
+or not you know we have you know it's
+you know we're not actually these
+
+ align:start position:0%
+you know we're not actually these
+ 
+
+ align:start position:0%
+you know we're not actually these
+heuristics aren't measuring things so
+
+ align:start position:0%
+heuristics aren't measuring things so
+ 
+
+ align:start position:0%
+heuristics aren't measuring things so
+closely that we care about a tenth of
+
+ align:start position:0%
+closely that we care about a tenth of
+ 
+
+ align:start position:0%
+closely that we care about a tenth of
+book a hundredth of a pawn so you can
+
+ align:start position:0%
+book a hundredth of a pawn so you can
+ 
+
+ align:start position:0%
+book a hundredth of a pawn so you can
+dither things and have one move be
+
+ align:start position:0%
+dither things and have one move be
+ 
+
+ align:start position:0%
+dither things and have one move be
+better than another and not really
+
+ align:start position:0%
+better than another and not really
+ 
+
+ align:start position:0%
+better than another and not really
+affect the quality of the playing okay
+
+ align:start position:0%
+affect the quality of the playing okay
+ 
+
+ align:start position:0%
+affect the quality of the playing okay
+so it is a good idea to do something to
+
+ align:start position:0%
+so it is a good idea to do something to
+ 
+
+ align:start position:0%
+so it is a good idea to do something to
+not be so predictable okay but to build
+
+ align:start position:0%
+not be so predictable okay but to build
+ 
+
+ align:start position:0%
+not be so predictable okay but to build
+a full opening book it that's a lot of
+
+ align:start position:0%
+a full opening book it that's a lot of
+ 
+
+ align:start position:0%
+a full opening book it that's a lot of
+work for beta one okay for beta two in
+
+ align:start position:0%
+work for beta one okay for beta two in
+ 
+
+ align:start position:0%
+work for beta one okay for beta two in
+the final yeah you know you'll get to
+
+ align:start position:0%
+the final yeah you know you'll get to
+ 
+
+ align:start position:0%
+the final yeah you know you'll get to
+that point the next thing is iterative
+
+ align:start position:0%
+that point the next thing is iterative
+ 
+
+ align:start position:0%
+that point the next thing is iterative
+deepening to people understand how
+
+ align:start position:0%
+deepening to people understand how
+ 
+
+ align:start position:0%
+deepening to people understand how
+part of the search code works yeah no
+
+ align:start position:0%
+part of the search code works yeah no
+ 
+
+ align:start position:0%
+part of the search code works yeah no
+let me go over it okay so you can
+
+ align:start position:0%
+let me go over it okay so you can
+ 
+
+ align:start position:0%
+let me go over it okay so you can
+imagine saying I'm gonna search to depth
+
+ align:start position:0%
+imagine saying I'm gonna search to depth
+ 
+
+ align:start position:0%
+imagine saying I'm gonna search to depth
+D and in fact instead of just searching
+
+ align:start position:0%
+D and in fact instead of just searching
+ 
+
+ align:start position:0%
+D and in fact instead of just searching
+the epithelia depth one search if you
+
+ align:start position:0%
+the epithelia depth one search if you
+ 
+
+ align:start position:0%
+the epithelia depth one search if you
+look at the code there if there's a
+
+ align:start position:0%
+look at the code there if there's a
+ 
+
+ align:start position:0%
+look at the code there if there's a
+depth one search and we do a depth to
+
+ align:start position:0%
+depth one search and we do a depth to
+ 
+
+ align:start position:0%
+depth one search and we do a depth to
+search then we do a depth research then
+
+ align:start position:0%
+search then we do a depth research then
+ 
+
+ align:start position:0%
+search then we do a depth research then
+we do a depth for search and we keep
+
+ align:start position:0%
+we do a depth for search and we keep
+ 
+
+ align:start position:0%
+we do a depth for search and we keep
+doing that until our time control
+
+ align:start position:0%
+doing that until our time control
+ 
+
+ align:start position:0%
+doing that until our time control
+expires why is that a good strategy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generally well first of all the amount
+
+ align:start position:0%
+generally well first of all the amount
+ 
+
+ align:start position:0%
+generally well first of all the amount
+of work with each depth is growing
+
+ align:start position:0%
+of work with each depth is growing
+ 
+
+ align:start position:0%
+of work with each depth is growing
+exponentially so you're only spending in
+
+ align:start position:0%
+exponentially so you're only spending in
+ 
+
+ align:start position:0%
+exponentially so you're only spending in
+principle a constant factor more work
+
+ align:start position:0%
+principle a constant factor more work
+ 
+
+ align:start position:0%
+principle a constant factor more work
+than you would if you search to depth D
+
+ align:start position:0%
+than you would if you search to depth D
+ 
+
+ align:start position:0%
+than you would if you search to depth D
+right off the bat okay but the important
+
+ align:start position:0%
+right off the bat okay but the important
+ 
+
+ align:start position:0%
+right off the bat okay but the important
+thing is that you can keep move or
+
+ align:start position:0%
+thing is that you can keep move or
+ 
+
+ align:start position:0%
+thing is that you can keep move or
+during information as you search deeper
+
+ align:start position:0%
+during information as you search deeper
+ 
+
+ align:start position:0%
+during information as you search deeper
+and the move ordering information
+
+ align:start position:0%
+and the move ordering information
+ 
+
+ align:start position:0%
+and the move ordering information
+remember we want this we want our
+
+ align:start position:0%
+remember we want this we want our
+ 
+
+ align:start position:0%
+remember we want this we want our
+searches to use best first move ordering
+
+ align:start position:0%
+searches to use best first move ordering
+ 
+
+ align:start position:0%
+searches to use best first move ordering
+so that we get all the cut-offs we can
+
+ align:start position:0%
+so that we get all the cut-offs we can
+ 
+
+ align:start position:0%
+so that we get all the cut-offs we can
+possibly get okay for pruning and so by
+
+ align:start position:0%
+possibly get okay for pruning and so by
+ 
+
+ align:start position:0%
+possibly get okay for pruning and so by
+searching it easier actually you end up
+
+ align:start position:0%
+searching it easier actually you end up
+ 
+
+ align:start position:0%
+searching it easier actually you end up
+with better move ordering okay because
+
+ align:start position:0%
+with better move ordering okay because
+ 
+
+ align:start position:0%
+with better move ordering okay because
+when you find the same position the in
+
+ align:start position:0%
+when you find the same position the in
+ 
+
+ align:start position:0%
+when you find the same position the in
+the transposition table you say oh well
+
+ align:start position:0%
+the transposition table you say oh well
+ 
+
+ align:start position:0%
+the transposition table you say oh well
+I didn't search it as deep as I need to
+
+ align:start position:0%
+I didn't search it as deep as I need to
+ 
+
+ align:start position:0%
+I didn't search it as deep as I need to
+search it now so I can't use the value
+
+ align:start position:0%
+search it now so I can't use the value
+ 
+
+ align:start position:0%
+search it now so I can't use the value
+that's in the transposition table for
+
+ align:start position:0%
+that's in the transposition table for
+ 
+
+ align:start position:0%
+that's in the transposition table for
+the position because it may be say you
+
+ align:start position:0%
+the position because it may be say you
+ 
+
+ align:start position:0%
+the position because it may be say you
+know I've searched something that's you
+
+ align:start position:0%
+know I've searched something that's you
+ 
+
+ align:start position:0%
+know I've searched something that's you
+know apply 8 in the transmission table
+
+ align:start position:0%
+know apply 8 in the transmission table
+ 
+
+ align:start position:0%
+know apply 8 in the transmission table
+but I've got a search to apply 9 not
+
+ align:start position:0%
+but I've got a search to apply 9 not
+ 
+
+ align:start position:0%
+but I've got a search to apply 9 not
+good enough a search but the value the
+
+ align:start position:0%
+good enough a search but the value the
+ 
+
+ align:start position:0%
+good enough a search but the value the
+the move that you've found at ply 8
+
+ align:start position:0%
+the move that you've found at ply 8
+ 
+
+ align:start position:0%
+the move that you've found at ply 8
+that's probably a pretty good first move
+
+ align:start position:0%
+that's probably a pretty good first move
+ 
+
+ align:start position:0%
+that's probably a pretty good first move
+you know pretty good best move guess it
+
+ align:start position:0%
+you know pretty good best move guess it
+ 
+
+ align:start position:0%
+you know pretty good best move guess it
+best move okay so by doing iterative
+
+ align:start position:0%
+best move okay so by doing iterative
+ 
+
+ align:start position:0%
+best move okay so by doing iterative
+deepening you actually get the move
+
+ align:start position:0%
+deepening you actually get the move
+ 
+
+ align:start position:0%
+deepening you actually get the move
+ordering for all those intermediate
+
+ align:start position:0%
+ordering for all those intermediate
+ 
+
+ align:start position:0%
+ordering for all those intermediate
+positions you know really really really
+
+ align:start position:0%
+positions you know really really really
+ 
+
+ align:start position:0%
+positions you know really really really
+strongly because that transposition
+
+ align:start position:0%
+strongly because that transposition
+ 
+
+ align:start position:0%
+strongly because that transposition
+table is the very best information
+
+ align:start position:0%
+table is the very best information
+ 
+
+ align:start position:0%
+table is the very best information
+you've got for what the first move is
+
+ align:start position:0%
+you've got for what the first move is
+ 
+
+ align:start position:0%
+you've got for what the first move is
+what your best move is sorry ok and also
+
+ align:start position:0%
+what your best move is sorry ok and also
+ 
+
+ align:start position:0%
+what your best move is sorry ok and also
+as I mentioned it's a good mechanism for
+
+ align:start position:0%
+as I mentioned it's a good mechanism for
+ 
+
+ align:start position:0%
+as I mentioned it's a good mechanism for
+time control is that clear
+
+ align:start position:0%
+time control is that clear
+ 
+
+ align:start position:0%
+time control is that clear
+so that's why you bother is one of these
+
+ align:start position:0%
+so that's why you bother is one of these
+ 
+
+ align:start position:0%
+so that's why you bother is one of these
+things that looks like it's redundant
+
+ align:start position:0%
+things that looks like it's redundant
+ 
+
+ align:start position:0%
+things that looks like it's redundant
+why are you searching if you're gonna
+
+ align:start position:0%
+why are you searching if you're gonna
+ 
+
+ align:start position:0%
+why are you searching if you're gonna
+search the depth dy search the depth D
+
+ align:start position:0%
+search the depth dy search the depth D
+ 
+
+ align:start position:0%
+search the depth dy search the depth D
+minus one you need to do that as part of
+
+ align:start position:0%
+minus one you need to do that as part of
+ 
+
+ align:start position:0%
+minus one you need to do that as part of
+depth e well no because you're gonna get
+
+ align:start position:0%
+depth e well no because you're gonna get
+ 
+
+ align:start position:0%
+depth e well no because you're gonna get
+move ordering information this can be
+
+ align:start position:0%
+move ordering information this can be
+ 
+
+ align:start position:0%
+move ordering information this can be
+really valuable when you search the
+
+ align:start position:0%
+really valuable when you search the
+ 
+
+ align:start position:0%
+really valuable when you search the
+depth key minus one so when you search
+
+ align:start position:0%
+depth key minus one so when you search
+ 
+
+ align:start position:0%
+depth key minus one so when you search
+the depth D you've got much better
+
+ align:start position:0%
+the depth D you've got much better
+ 
+
+ align:start position:0%
+the depth D you've got much better
+pruning than if you just went straight
+
+ align:start position:0%
+pruning than if you just went straight
+ 
+
+ align:start position:0%
+pruning than if you just went straight
+to depth D and had no information about
+
+ align:start position:0%
+to depth D and had no information about
+ 
+
+ align:start position:0%
+to depth D and had no information about
+the move ordering does that make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in game database so here's the idea if
+
+ align:start position:0%
+in game database so here's the idea if
+ 
+
+ align:start position:0%
+in game database so here's the idea if
+there's a few enough pieces on the board
+
+ align:start position:0%
+there's a few enough pieces on the board
+ 
+
+ align:start position:0%
+there's a few enough pieces on the board
+you can pre-compute the outcomes and
+
+ align:start position:0%
+you can pre-compute the outcomes and
+ 
+
+ align:start position:0%
+you can pre-compute the outcomes and
+store them in a database okay so so for
+
+ align:start position:0%
+store them in a database okay so so for
+ 
+
+ align:start position:0%
+store them in a database okay so so for
+example the most common database to come
+
+ align:start position:0%
+example the most common database to come
+ 
+
+ align:start position:0%
+example the most common database to come
+up with is the King versus King database
+
+ align:start position:0%
+up with is the King versus King database
+ 
+
+ align:start position:0%
+up with is the King versus King database
+okay so if you do King versus King that
+
+ align:start position:0%
+okay so if you do King versus King that
+ 
+
+ align:start position:0%
+okay so if you do King versus King that
+means that it's not that you expect the
+
+ align:start position:0%
+means that it's not that you expect the
+ 
+
+ align:start position:0%
+means that it's not that you expect the
+game will end up as King versus King
+
+ align:start position:0%
+game will end up as King versus King
+ 
+
+ align:start position:0%
+game will end up as King versus King
+it's that you're gonna encounter that in
+
+ align:start position:0%
+it's that you're gonna encounter that in
+ 
+
+ align:start position:0%
+it's that you're gonna encounter that in
+the search it'd be nice to know who has
+
+ align:start position:0%
+the search it'd be nice to know who has
+ 
+
+ align:start position:0%
+the search it'd be nice to know who has
+the win if your King versus King now the
+
+ align:start position:0%
+the win if your King versus King now the
+ 
+
+ align:start position:0%
+the win if your King versus King now the
+code actually plays optimally for King
+
+ align:start position:0%
+code actually plays optimally for King
+ 
+
+ align:start position:0%
+code actually plays optimally for King
+versus King okay the code we gave you
+
+ align:start position:0%
+versus King okay the code we gave you
+ 
+
+ align:start position:0%
+versus King okay the code we gave you
+will we'll do we'll play the King versus
+
+ align:start position:0%
+will we'll do we'll play the King versus
+ 
+
+ align:start position:0%
+will we'll do we'll play the King versus
+King you know perfectly well and in fact
+
+ align:start position:0%
+King you know perfectly well and in fact
+ 
+
+ align:start position:0%
+King you know perfectly well and in fact
+there's just two heuristics that are
+
+ align:start position:0%
+there's just two heuristics that are
+ 
+
+ align:start position:0%
+there's just two heuristics that are
+responsible for that one is the the
+
+ align:start position:0%
+responsible for that one is the the
+ 
+
+ align:start position:0%
+responsible for that one is the the
+lives called K aggressive heuristic and
+
+ align:start position:0%
+lives called K aggressive heuristic and
+ 
+
+ align:start position:0%
+lives called K aggressive heuristic and
+the other one is which basically makes
+
+ align:start position:0%
+the other one is which basically makes
+ 
+
+ align:start position:0%
+the other one is which basically makes
+you move towards your opponent and the
+
+ align:start position:0%
+you move towards your opponent and the
+ 
+
+ align:start position:0%
+you move towards your opponent and the
+other one is the the K face heuristic
+
+ align:start position:0%
+other one is the the K face heuristic
+ 
+
+ align:start position:0%
+other one is the the K face heuristic
+which makes you point towards your
+
+ align:start position:0%
+which makes you point towards your
+ 
+
+ align:start position:0%
+which makes you point towards your
+opponent and those two things turn out
+
+ align:start position:0%
+opponent and those two things turn out
+ 
+
+ align:start position:0%
+opponent and those two things turn out
+to do a pretty good job of when there's
+
+ align:start position:0%
+to do a pretty good job of when there's
+ 
+
+ align:start position:0%
+to do a pretty good job of when there's
+when there's two kings and playing they
+
+ align:start position:0%
+when there's two kings and playing they
+ 
+
+ align:start position:0%
+when there's two kings and playing they
+go through this little any immed it'd
+
+ align:start position:0%
+go through this little any immed it'd
+ 
+
+ align:start position:0%
+go through this little any immed it'd
+everybody do that by hand by the way do
+
+ align:start position:0%
+everybody do that by hand by the way do
+ 
+
+ align:start position:0%
+everybody do that by hand by the way do
+you play King versus King so a really
+
+ align:start position:0%
+you play King versus King so a really
+ 
+
+ align:start position:0%
+you play King versus King so a really
+good idea if you want to understand the
+
+ align:start position:0%
+good idea if you want to understand the
+ 
+
+ align:start position:0%
+good idea if you want to understand the
+game is just is just go and do a king
+
+ align:start position:0%
+game is just is just go and do a king
+ 
+
+ align:start position:0%
+game is just is just go and do a king
+versus King version of the of the game
+
+ align:start position:0%
+versus King version of the of the game
+ 
+
+ align:start position:0%
+versus King version of the of the game
+get an eight by eight chessboard and
+
+ align:start position:0%
+get an eight by eight chessboard and
+ 
+
+ align:start position:0%
+get an eight by eight chessboard and
+just put down two tokens that you call
+
+ align:start position:0%
+just put down two tokens that you call
+ 
+
+ align:start position:0%
+just put down two tokens that you call
+our Kings that have orientations and
+
+ align:start position:0%
+our Kings that have orientations and
+ 
+
+ align:start position:0%
+our Kings that have orientations and
+then just just the two of you and a
+
+ align:start position:0%
+then just just the two of you and a
+ 
+
+ align:start position:0%
+then just just the two of you and a
+friend just try to
+
+ align:start position:0%
+friend just try to
+ 
+
+ align:start position:0%
+friend just try to
+see if you you know one can make the
+
+ align:start position:0%
+see if you you know one can make the
+ 
+
+ align:start position:0%
+see if you you know one can make the
+other and you'll see that it goes
+
+ align:start position:0%
+other and you'll see that it goes
+ 
+
+ align:start position:0%
+other and you'll see that it goes
+through a very ritualistic type of
+
+ align:start position:0%
+through a very ritualistic type of
+ 
+
+ align:start position:0%
+through a very ritualistic type of
+behavior which ends up with one of the
+
+ align:start position:0%
+behavior which ends up with one of the
+ 
+
+ align:start position:0%
+behavior which ends up with one of the
+Kings being mated so it's nice to know
+
+ align:start position:0%
+Kings being mated so it's nice to know
+ 
+
+ align:start position:0%
+Kings being mated so it's nice to know
+which one it's going to be so if you
+
+ align:start position:0%
+which one it's going to be so if you
+ 
+
+ align:start position:0%
+which one it's going to be so if you
+encounter that but here's the question
+
+ align:start position:0%
+encounter that but here's the question
+ 
+
+ align:start position:0%
+encounter that but here's the question
+is how many games actually make it to an
+
+ align:start position:0%
+is how many games actually make it to an
+ 
+
+ align:start position:0%
+is how many games actually make it to an
+end game once again you have to look at
+
+ align:start position:0%
+end game once again you have to look at
+ 
+
+ align:start position:0%
+end game once again you have to look at
+what the odds are there because if games
+
+ align:start position:0%
+what the odds are there because if games
+ 
+
+ align:start position:0%
+what the odds are there because if games
+are ending in the middle game there may
+
+ align:start position:0%
+are ending in the middle game there may
+ 
+
+ align:start position:0%
+are ending in the middle game there may
+not be any need to search all the way to
+
+ align:start position:0%
+not be any need to search all the way to
+ 
+
+ align:start position:0%
+not be any need to search all the way to
+the end game okay so so that's something
+
+ align:start position:0%
+the end game okay so so that's something
+ 
+
+ align:start position:0%
+the end game okay so so that's something
+that you need to weigh okay now if you
+
+ align:start position:0%
+that you need to weigh okay now if you
+ 
+
+ align:start position:0%
+that you need to weigh okay now if you
+do an endgame database it doesn't
+
+ align:start position:0%
+do an endgame database it doesn't
+ 
+
+ align:start position:0%
+do an endgame database it doesn't
+suffice to just or win loss or draw for
+
+ align:start position:0%
+suffice to just or win loss or draw for
+ 
+
+ align:start position:0%
+suffice to just or win loss or draw for
+a position and the reason is because you
+
+ align:start position:0%
+a position and the reason is because you
+ 
+
+ align:start position:0%
+a position and the reason is because you
+can get into a situation where you've
+
+ align:start position:0%
+can get into a situation where you've
+ 
+
+ align:start position:0%
+can get into a situation where you've
+got a winning position and then you say
+
+ align:start position:0%
+got a winning position and then you say
+ 
+
+ align:start position:0%
+got a winning position and then you say
+okay well let me move to another winning
+
+ align:start position:0%
+okay well let me move to another winning
+ 
+
+ align:start position:0%
+okay well let me move to another winning
+position and another winning position
+
+ align:start position:0%
+position and another winning position
+ 
+
+ align:start position:0%
+position and another winning position
+and another winning position oh and I'm
+
+ align:start position:0%
+and another winning position oh and I'm
+ 
+
+ align:start position:0%
+and another winning position oh and I'm
+back it to my original winning position
+
+ align:start position:0%
+back it to my original winning position
+ 
+
+ align:start position:0%
+back it to my original winning position
+and I just keep going around in a circle
+
+ align:start position:0%
+and I just keep going around in a circle
+ 
+
+ align:start position:0%
+and I just keep going around in a circle
+always in a winning position never
+
+ align:start position:0%
+always in a winning position never
+ 
+
+ align:start position:0%
+always in a winning position never
+moving towards the win okay and that of
+
+ align:start position:0%
+moving towards the win okay and that of
+ 
+
+ align:start position:0%
+moving towards the win okay and that of
+course will end up in a draw so you need
+
+ align:start position:0%
+course will end up in a draw so you need
+ 
+
+ align:start position:0%
+course will end up in a draw so you need
+to know which direction do you go for
+
+ align:start position:0%
+to know which direction do you go for
+ 
+
+ align:start position:0%
+to know which direction do you go for
+the winning position so the typical
+
+ align:start position:0%
+the winning position so the typical
+ 
+
+ align:start position:0%
+the winning position so the typical
+thing you do there is you keep the
+
+ align:start position:0%
+thing you do there is you keep the
+ 
+
+ align:start position:0%
+thing you do there is you keep the
+distance to mate to avoid cycling so you
+
+ align:start position:0%
+distance to mate to avoid cycling so you
+ 
+
+ align:start position:0%
+distance to mate to avoid cycling so you
+go from instead of keeping just a
+
+ align:start position:0%
+go from instead of keeping just a
+ 
+
+ align:start position:0%
+go from instead of keeping just a
+boolean value you say here's my distance
+
+ align:start position:0%
+boolean value you say here's my distance
+ 
+
+ align:start position:0%
+boolean value you say here's my distance
+to winning okay my distance to winning
+
+ align:start position:0%
+to winning okay my distance to winning
+ 
+
+ align:start position:0%
+to winning okay my distance to winning
+is six now when I'm searching I don't
+
+ align:start position:0%
+is six now when I'm searching I don't
+ 
+
+ align:start position:0%
+is six now when I'm searching I don't
+want to go a distance to winning that
+
+ align:start position:0%
+want to go a distance to winning that
+ 
+
+ align:start position:0%
+want to go a distance to winning that
+seven or six I want to go to a distance
+
+ align:start position:0%
+seven or six I want to go to a distance
+ 
+
+ align:start position:0%
+seven or six I want to go to a distance
+of winning that's five when I make my
+
+ align:start position:0%
+of winning that's five when I make my
+ 
+
+ align:start position:0%
+of winning that's five when I make my
+move okay
+
+ align:start position:0%
+move okay
+ 
+
+ align:start position:0%
+move okay
+so it's very important to make sure that
+
+ align:start position:0%
+so it's very important to make sure that
+ 
+
+ align:start position:0%
+so it's very important to make sure that
+you maintain the distance in order to
+
+ align:start position:0%
+you maintain the distance in order to
+ 
+
+ align:start position:0%
+you maintain the distance in order to
+avoid cycling you know quiescence search
+
+ align:start position:0%
+avoid cycling you know quiescence search
+ 
+
+ align:start position:0%
+avoid cycling you know quiescence search
+we talked about quiescence which is you
+
+ align:start position:0%
+we talked about quiescence which is you
+ 
+
+ align:start position:0%
+we talked about quiescence which is you
+know to make sure that when you're doing
+
+ align:start position:0%
+know to make sure that when you're doing
+ 
+
+ align:start position:0%
+know to make sure that when you're doing
+the evaluation you're not in the middle
+
+ align:start position:0%
+the evaluation you're not in the middle
+ 
+
+ align:start position:0%
+the evaluation you're not in the middle
+of an exchange you know so you zap their
+
+ align:start position:0%
+of an exchange you know so you zap their
+ 
+
+ align:start position:0%
+of an exchange you know so you zap their
+pawn they're gonna zap your pawn or
+
+ align:start position:0%
+pawn they're gonna zap your pawn or
+ 
+
+ align:start position:0%
+pawn they're gonna zap your pawn or
+maybe even zap your king okay and you
+
+ align:start position:0%
+maybe even zap your king okay and you
+ 
+
+ align:start position:0%
+maybe even zap your king okay and you
+don't want to evaluate in the middle
+
+ align:start position:0%
+don't want to evaluate in the middle
+ 
+
+ align:start position:0%
+don't want to evaluate in the middle
+there and so the idea of quiescence is
+
+ align:start position:0%
+there and so the idea of quiescence is
+ 
+
+ align:start position:0%
+there and so the idea of quiescence is
+that when you're done with the regular
+
+ align:start position:0%
+that when you're done with the regular
+ 
+
+ align:start position:0%
+that when you're done with the regular
+search you just play off moves that
+
+ align:start position:0%
+search you just play off moves that
+ 
+
+ align:start position:0%
+search you just play off moves that
+involve captures and
+
+ align:start position:0%
+involve captures and
+ 
+
+ align:start position:0%
+involve captures and
+you evaluate the position okay so that's
+
+ align:start position:0%
+you evaluate the position okay so that's
+ 
+
+ align:start position:0%
+you evaluate the position okay so that's
+quieting the position okay makes sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another heuristic there is no move
+
+ align:start position:0%
+another heuristic there is no move
+ 
+
+ align:start position:0%
+another heuristic there is no move
+pruning in most positions there's always
+
+ align:start position:0%
+pruning in most positions there's always
+ 
+
+ align:start position:0%
+pruning in most positions there's always
+something better to do than nothing so
+
+ align:start position:0%
+something better to do than nothing so
+ 
+
+ align:start position:0%
+something better to do than nothing so
+sitting still is usually not as good as
+
+ align:start position:0%
+sitting still is usually not as good as
+ 
+
+ align:start position:0%
+sitting still is usually not as good as
+actually making a move okay
+
+ align:start position:0%
+actually making a move okay
+ 
+
+ align:start position:0%
+actually making a move okay
+and so the idea is suppose that I can
+
+ align:start position:0%
+and so the idea is suppose that I can
+ 
+
+ align:start position:0%
+and so the idea is suppose that I can
+forfeit my move and search a shallower
+
+ align:start position:0%
+forfeit my move and search a shallower
+ 
+
+ align:start position:0%
+forfeit my move and search a shallower
+depth and I still have the best position
+
+ align:start position:0%
+depth and I still have the best position
+ 
+
+ align:start position:0%
+depth and I still have the best position
+okay then I still am winning well then
+
+ align:start position:0%
+okay then I still am winning well then
+ 
+
+ align:start position:0%
+okay then I still am winning well then
+and it generates a cutoff then why
+
+ align:start position:0%
+and it generates a cutoff then why
+ 
+
+ align:start position:0%
+and it generates a cutoff then why
+bother exploring any other moves I
+
+ align:start position:0%
+bother exploring any other moves I
+ 
+
+ align:start position:0%
+bother exploring any other moves I
+probably am in a really good position
+
+ align:start position:0%
+probably am in a really good position
+ 
+
+ align:start position:0%
+probably am in a really good position
+here okay and if if I don't manage to
+
+ align:start position:0%
+here okay and if if I don't manage to
+ 
+
+ align:start position:0%
+here okay and if if I don't manage to
+get a cut off from the no move then I
+
+ align:start position:0%
+get a cut off from the no move then I
+ 
+
+ align:start position:0%
+get a cut off from the no move then I
+you know then I do the full the full
+
+ align:start position:0%
+you know then I do the full the full
+ 
+
+ align:start position:0%
+you know then I do the full the full
+depth search okay so so the place this
+
+ align:start position:0%
+depth search okay so so the place this
+ 
+
+ align:start position:0%
+depth search okay so so the place this
+is dangerous is in zoogs wang in chess
+
+ align:start position:0%
+is dangerous is in zoogs wang in chess
+ 
+
+ align:start position:0%
+is dangerous is in zoogs wang in chess
+it's called zoogs along situations so
+
+ align:start position:0%
+it's called zoogs along situations so
+ 
+
+ align:start position:0%
+it's called zoogs along situations so
+slugs along a situation where everything
+
+ align:start position:0%
+slugs along a situation where everything
+ 
+
+ align:start position:0%
+slugs along a situation where everything
+is fine but if you have to make a move
+
+ align:start position:0%
+is fine but if you have to make a move
+ 
+
+ align:start position:0%
+is fine but if you have to make a move
+you lose so usually making and having
+
+ align:start position:0%
+you lose so usually making and having
+ 
+
+ align:start position:0%
+you lose so usually making and having
+the advantage of a move that's called
+
+ align:start position:0%
+the advantage of a move that's called
+ 
+
+ align:start position:0%
+the advantage of a move that's called
+the initiative in chess and that's a
+
+ align:start position:0%
+the initiative in chess and that's a
+ 
+
+ align:start position:0%
+the initiative in chess and that's a
+good thing you want the initiative you
+
+ align:start position:0%
+good thing you want the initiative you
+ 
+
+ align:start position:0%
+good thing you want the initiative you
+want to have the extra move over your
+
+ align:start position:0%
+want to have the extra move over your
+ 
+
+ align:start position:0%
+want to have the extra move over your
+opponent but there are some situations
+
+ align:start position:0%
+opponent but there are some situations
+ 
+
+ align:start position:0%
+opponent but there are some situations
+where if you move you lose okay and so
+
+ align:start position:0%
+where if you move you lose okay and so
+ 
+
+ align:start position:0%
+where if you move you lose okay and so
+you want to make sure you don't have a
+
+ align:start position:0%
+you want to make sure you don't have a
+ 
+
+ align:start position:0%
+you want to make sure you don't have a
+Zhuge Liang situation I don't actually
+
+ align:start position:0%
+Zhuge Liang situation I don't actually
+ 
+
+ align:start position:0%
+Zhuge Liang situation I don't actually
+know if there's a Zhuge Liang situation
+
+ align:start position:0%
+know if there's a Zhuge Liang situation
+ 
+
+ align:start position:0%
+know if there's a Zhuge Liang situation
+in lesser chess okay so it's if somebody
+
+ align:start position:0%
+in lesser chess okay so it's if somebody
+ 
+
+ align:start position:0%
+in lesser chess okay so it's if somebody
+comes up with one I'd be interested to
+
+ align:start position:0%
+comes up with one I'd be interested to
+ 
+
+ align:start position:0%
+comes up with one I'd be interested to
+see that you know where if you had to
+
+ align:start position:0%
+see that you know where if you had to
+ 
+
+ align:start position:0%
+see that you know where if you had to
+move I lose but if I sits there so what
+
+ align:start position:0%
+move I lose but if I sits there so what
+ 
+
+ align:start position:0%
+move I lose but if I sits there so what
+in chess what they do is in the end game
+
+ align:start position:0%
+in chess what they do is in the end game
+ 
+
+ align:start position:0%
+in chess what they do is in the end game
+that's when zoogs lines come up they
+
+ align:start position:0%
+that's when zoogs lines come up they
+ 
+
+ align:start position:0%
+that's when zoogs lines come up they
+turn off the null move pruning so is
+
+ align:start position:0%
+turn off the null move pruning so is
+ 
+
+ align:start position:0%
+turn off the null move pruning so is
+this clear what null move does for you
+
+ align:start position:0%
+this clear what null move does for you
+ 
+
+ align:start position:0%
+this clear what null move does for you
+what what's going on there so I see some
+
+ align:start position:0%
+what what's going on there so I see some
+ 
+
+ align:start position:0%
+what what's going on there so I see some
+people who are quizzical anybody want to
+
+ align:start position:0%
+people who are quizzical anybody want to
+ 
+
+ align:start position:0%
+people who are quizzical anybody want to
+ask a question I see some people hide
+
+ align:start position:0%
+ask a question I see some people hide
+ 
+
+ align:start position:0%
+ask a question I see some people hide
+with sort of quizzical looks on their
+
+ align:start position:0%
+with sort of quizzical looks on their
+ 
+
+ align:start position:0%
+with sort of quizzical looks on their
+faces
+
+ align:start position:0%
+faces
+ 
+
+ align:start position:0%
+faces
+okay the idea is for no movies my
+
+ align:start position:0%
+okay the idea is for no movies my
+ 
+
+ align:start position:0%
+okay the idea is for no movies my
+position is so good okay that even if I
+
+ align:start position:0%
+position is so good okay that even if I
+ 
+
+ align:start position:0%
+position is so good okay that even if I
+do nothing I still win okay so I don't
+
+ align:start position:0%
+do nothing I still win okay so I don't
+ 
+
+ align:start position:0%
+do nothing I still win okay so I don't
+want to search anymore in this part of
+
+ align:start position:0%
+want to search anymore in this part of
+ 
+
+ align:start position:0%
+want to search anymore in this part of
+it because you're you know I get a beta
+
+ align:start position:0%
+it because you're you know I get a beta
+ 
+
+ align:start position:0%
+it because you're you know I get a beta
+cutoff you're not gonna let me make this
+
+ align:start position:0%
+cutoff you're not gonna let me make this
+ 
+
+ align:start position:0%
+cutoff you're not gonna let me make this
+move that the move that got me here yeah
+
+ align:start position:0%
+move that the move that got me here yeah
+ 
+
+ align:start position:0%
+move that the move that got me here yeah
+question oh did you really
+
+ align:start position:0%
+question oh did you really
+ 
+
+ align:start position:0%
+question oh did you really
+yeah okay that was it okay good yeah my
+
+ align:start position:0%
+yeah okay that was it okay good yeah my
+ 
+
+ align:start position:0%
+yeah okay that was it okay good yeah my
+move is so good I could I can do nothing
+
+ align:start position:0%
+move is so good I could I can do nothing
+ 
+
+ align:start position:0%
+move is so good I could I can do nothing
+and I still win okay and so why bother
+
+ align:start position:0%
+and I still win okay and so why bother
+ 
+
+ align:start position:0%
+and I still win okay and so why bother
+you know let me verify that without
+
+ align:start position:0%
+you know let me verify that without
+ 
+
+ align:start position:0%
+you know let me verify that without
+necessary doing as deep a search so no
+
+ align:start position:0%
+necessary doing as deep a search so no
+ 
+
+ align:start position:0%
+necessary doing as deep a search so no
+move is fairly cheap to do and it you
+
+ align:start position:0%
+move is fairly cheap to do and it you
+ 
+
+ align:start position:0%
+move is fairly cheap to do and it you
+know often results in you know for in a
+
+ align:start position:0%
+know often results in you know for in a
+ 
+
+ align:start position:0%
+know often results in you know for in a
+lot of positions for cutoff and if I
+
+ align:start position:0%
+lot of positions for cutoff and if I
+ 
+
+ align:start position:0%
+lot of positions for cutoff and if I
+don't get a cutoff then I just do the
+
+ align:start position:0%
+don't get a cutoff then I just do the
+ 
+
+ align:start position:0%
+don't get a cutoff then I just do the
+normal search okay this is a pretty
+
+ align:start position:0%
+normal search okay this is a pretty
+ 
+
+ align:start position:0%
+normal search okay this is a pretty
+complicated piece of code isn't it okay
+
+ align:start position:0%
+complicated piece of code isn't it okay
+ 
+
+ align:start position:0%
+complicated piece of code isn't it okay
+you know pretty complicated okay
+
+ align:start position:0%
+you know pretty complicated okay
+ 
+
+ align:start position:0%
+you know pretty complicated okay
+there are other situations we mentioned
+
+ align:start position:0%
+there are other situations we mentioned
+ 
+
+ align:start position:0%
+there are other situations we mentioned
+killers okay
+
+ align:start position:0%
+killers okay
+ 
+
+ align:start position:0%
+killers okay
+there's also move extensions so typical
+
+ align:start position:0%
+there's also move extensions so typical
+ 
+
+ align:start position:0%
+there's also move extensions so typical
+move extensions that people look at is
+
+ align:start position:0%
+move extensions that people look at is
+ 
+
+ align:start position:0%
+move extensions that people look at is
+you grant an extra ply in chess if the
+
+ align:start position:0%
+you grant an extra ply in chess if the
+ 
+
+ align:start position:0%
+you grant an extra ply in chess if the
+king is in check or for certain captures
+
+ align:start position:0%
+king is in check or for certain captures
+ 
+
+ align:start position:0%
+king is in check or for certain captures
+or if you have a forced move so suppose
+
+ align:start position:0%
+or if you have a forced move so suppose
+ 
+
+ align:start position:0%
+or if you have a forced move so suppose
+you have a move and it's the only move
+
+ align:start position:0%
+you have a move and it's the only move
+ 
+
+ align:start position:0%
+you have a move and it's the only move
+you can make then don't count that as
+
+ align:start position:0%
+you can make then don't count that as
+ 
+
+ align:start position:0%
+you can make then don't count that as
+apply so you can search deeper along
+
+ align:start position:0%
+apply so you can search deeper along
+ 
+
+ align:start position:0%
+apply so you can search deeper along
+lines where they're forced moves that's
+
+ align:start position:0%
+lines where they're forced moves that's
+ 
+
+ align:start position:0%
+lines where they're forced moves that's
+what they do in chess lie search s not
+
+ align:start position:0%
+what they do in chess lie search s not
+ 
+
+ align:start position:0%
+what they do in chess lie search s not
+quite so clear what you do okay which
+
+ align:start position:0%
+quite so clear what you do okay which
+ 
+
+ align:start position:0%
+quite so clear what you do okay which
+ones you would do extensions for okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it it's rare that you have just
+
+ align:start position:0%
+because it it's rare that you have just
+ 
+
+ align:start position:0%
+because it it's rare that you have just
+one move in in lesser chess compared to
+
+ align:start position:0%
+one move in in lesser chess compared to
+ 
+
+ align:start position:0%
+one move in in lesser chess compared to
+in in Chester where you ever by force
+
+ align:start position:0%
+in in Chester where you ever by force
+ 
+
+ align:start position:0%
+in in Chester where you ever by force
+move it's like if you don't do this
+
+ align:start position:0%
+move it's like if you don't do this
+ 
+
+ align:start position:0%
+move it's like if you don't do this
+you're going to get captured or you know
+
+ align:start position:0%
+you're going to get captured or you know
+ 
+
+ align:start position:0%
+you're going to get captured or you know
+made it or what have you
+
+ align:start position:0%
+made it or what have you
+ 
+
+ align:start position:0%
+made it or what have you
+okay so that may come up in less your
+
+ align:start position:0%
+okay so that may come up in less your
+ 
+
+ align:start position:0%
+okay so that may come up in less your
+chest but anyway it's it's something to
+
+ align:start position:0%
+chest but anyway it's it's something to
+ 
+
+ align:start position:0%
+chest but anyway it's it's something to
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+so the transposition table so we talk
+
+ align:start position:0%
+so the transposition table so we talk
+ 
+
+ align:start position:0%
+so the transposition table so we talk
+about this as a search tree but it's
+
+ align:start position:0%
+about this as a search tree but it's
+ 
+
+ align:start position:0%
+about this as a search tree but it's
+really a dag because I can get to the
+
+ align:start position:0%
+really a dag because I can get to the
+ 
+
+ align:start position:0%
+really a dag because I can get to the
+same position by transposing moves you
+
+ align:start position:0%
+same position by transposing moves you
+ 
+
+ align:start position:0%
+same position by transposing moves you
+know this guy does a this guy does B
+
+ align:start position:0%
+know this guy does a this guy does B
+ 
+
+ align:start position:0%
+know this guy does a this guy does B
+this guy does C this guy does D I may
+
+ align:start position:0%
+this guy does C this guy does D I may
+ 
+
+ align:start position:0%
+this guy does C this guy does D I may
+get it's the same thing by doing you
+
+ align:start position:0%
+get it's the same thing by doing you
+ 
+
+ align:start position:0%
+get it's the same thing by doing you
+know a d c b I transpose those two moves
+
+ align:start position:0%
+know a d c b I transpose those two moves
+ 
+
+ align:start position:0%
+know a d c b I transpose those two moves
+and I get to exactly the same position
+
+ align:start position:0%
+and I get to exactly the same position
+ 
+
+ align:start position:0%
+and I get to exactly the same position
+okay and so I'd like not to search that
+
+ align:start position:0%
+okay and so I'd like not to search that
+ 
+
+ align:start position:0%
+okay and so I'd like not to search that
+position again if I've seen it and
+
+ align:start position:0%
+position again if I've seen it and
+ 
+
+ align:start position:0%
+position again if I've seen it and
+that's what the transposition does
+
+ align:start position:0%
+that's what the transposition does
+ 
+
+ align:start position:0%
+that's what the transposition does
+there's a quality score that is in the
+
+ align:start position:0%
+there's a quality score that is in the
+ 
+
+ align:start position:0%
+there's a quality score that is in the
+transposition table that tells you how
+
+ align:start position:0%
+transposition table that tells you how
+ 
+
+ align:start position:0%
+transposition table that tells you how
+good a move you've made and the quality
+
+ align:start position:0%
+good a move you've made and the quality
+ 
+
+ align:start position:0%
+good a move you've made and the quality
+is essentially the depth that you had to
+
+ align:start position:0%
+is essentially the depth that you had to
+ 
+
+ align:start position:0%
+is essentially the depth that you had to
+search in order to establish the value
+
+ align:start position:0%
+search in order to establish the value
+ 
+
+ align:start position:0%
+search in order to establish the value
+that's stored in the transposition table
+
+ align:start position:0%
+that's stored in the transposition table
+ 
+
+ align:start position:0%
+that's stored in the transposition table
+and so you don't want to use something
+
+ align:start position:0%
+and so you don't want to use something
+ 
+
+ align:start position:0%
+and so you don't want to use something
+of too low quality when you're searching
+
+ align:start position:0%
+of too low quality when you're searching
+ 
+
+ align:start position:0%
+of too low quality when you're searching
+if you have to search the depth D
+
+ align:start position:0%
+if you have to search the depth D
+ 
+
+ align:start position:0%
+if you have to search the depth D
+something of quality D minus 1 is not
+
+ align:start position:0%
+something of quality D minus 1 is not
+ 
+
+ align:start position:0%
+something of quality D minus 1 is not
+good enough ok because otherwise you'll
+
+ align:start position:0%
+good enough ok because otherwise you'll
+ 
+
+ align:start position:0%
+good enough ok because otherwise you'll
+not be searching you know the full tree
+
+ align:start position:0%
+not be searching you know the full tree
+ 
+
+ align:start position:0%
+not be searching you know the full tree
+but something typically that is deeper
+
+ align:start position:0%
+but something typically that is deeper
+ 
+
+ align:start position:0%
+but something typically that is deeper
+you know certainly you know if you if if
+
+ align:start position:0%
+you know certainly you know if you if if
+ 
+
+ align:start position:0%
+you know certainly you know if you if if
+I'm looking at depth D and I find
+
+ align:start position:0%
+I'm looking at depth D and I find
+ 
+
+ align:start position:0%
+I'm looking at depth D and I find
+something in transposition table that's
+
+ align:start position:0%
+something in transposition table that's
+ 
+
+ align:start position:0%
+something in transposition table that's
+d plus 1 or D plus 2 that's great to use
+
+ align:start position:0%
+d plus 1 or D plus 2 that's great to use
+ 
+
+ align:start position:0%
+d plus 1 or D plus 2 that's great to use
+that just gave me an even deeper view of
+
+ align:start position:0%
+that just gave me an even deeper view of
+ 
+
+ align:start position:0%
+that just gave me an even deeper view of
+what's behind that move okay and so if
+
+ align:start position:0%
+what's behind that move okay and so if
+ 
+
+ align:start position:0%
+what's behind that move okay and so if
+you look at the logic there you'll see
+
+ align:start position:0%
+you look at the logic there you'll see
+ 
+
+ align:start position:0%
+you look at the logic there you'll see
+that that's how they do it it's very
+
+ align:start position:0%
+that that's how they do it it's very
+ 
+
+ align:start position:0%
+that that's how they do it it's very
+tricky one of the things that's tricky
+
+ align:start position:0%
+tricky one of the things that's tricky
+ 
+
+ align:start position:0%
+tricky one of the things that's tricky
+is when you find a mate how you store
+
+ align:start position:0%
+is when you find a mate how you store
+ 
+
+ align:start position:0%
+is when you find a mate how you store
+that in the transposition table and
+
+ align:start position:0%
+that in the transposition table and
+ 
+
+ align:start position:0%
+that in the transposition table and
+you'll see there's special code for
+
+ align:start position:0%
+you'll see there's special code for
+ 
+
+ align:start position:0%
+you'll see there's special code for
+handling mate positions and the reason
+
+ align:start position:0%
+handling mate positions and the reason
+ 
+
+ align:start position:0%
+handling mate positions and the reason
+is because what you're interested in
+
+ align:start position:0%
+is because what you're interested in
+ 
+
+ align:start position:0%
+is because what you're interested in
+doing when you find a mate is knowing
+
+ align:start position:0%
+doing when you find a mate is knowing
+ 
+
+ align:start position:0%
+doing when you find a mate is knowing
+your distance to mate but not from that
+
+ align:start position:0%
+your distance to mate but not from that
+ 
+
+ align:start position:0%
+your distance to mate but not from that
+position the distance our mate from the
+
+ align:start position:0%
+position the distance our mate from the
+ 
+
+ align:start position:0%
+position the distance our mate from the
+root of your search okay so for example
+
+ align:start position:0%
+root of your search okay so for example
+ 
+
+ align:start position:0%
+root of your search okay so for example
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you know let's say this is the root of
+
+ align:start position:0%
+you know let's say this is the root of
+ 
+
+ align:start position:0%
+you know let's say this is the root of
+my searched and I searched down to a
+
+ align:start position:0%
+my searched and I searched down to a
+ 
+
+ align:start position:0%
+my searched and I searched down to a
+given point and now I do a lookup in the
+
+ align:start position:0%
+given point and now I do a lookup in the
+ 
+
+ align:start position:0%
+given point and now I do a lookup in the
+transposition table and I discovered
+
+ align:start position:0%
+transposition table and I discovered
+ 
+
+ align:start position:0%
+transposition table and I discovered
+that there's a mate in five here okay
+
+ align:start position:0%
+that there's a mate in five here okay
+ 
+
+ align:start position:0%
+that there's a mate in five here okay
+and this is let's say let's I have
+
+ align:start position:0%
+and this is let's say let's I have
+ 
+
+ align:start position:0%
+and this is let's say let's I have
+searched nine-ply or something okay well
+
+ align:start position:0%
+searched nine-ply or something okay well
+ 
+
+ align:start position:0%
+searched nine-ply or something okay well
+if I store that this is a mate in five
+
+ align:start position:0%
+if I store that this is a mate in five
+ 
+
+ align:start position:0%
+if I store that this is a mate in five
+and I store the value for mate and five
+
+ align:start position:0%
+and I store the value for mate and five
+ 
+
+ align:start position:0%
+and I store the value for mate and five
+then if it makes it up to the top here
+
+ align:start position:0%
+then if it makes it up to the top here
+ 
+
+ align:start position:0%
+then if it makes it up to the top here
+it thinks there's a mate and five but
+
+ align:start position:0%
+it thinks there's a mate and five but
+ 
+
+ align:start position:0%
+it thinks there's a mate and five but
+there isn't a mate in five there's a
+
+ align:start position:0%
+there isn't a mate in five there's a
+ 
+
+ align:start position:0%
+there isn't a mate in five there's a
+mate in 14 okay so when you look it up
+
+ align:start position:0%
+mate in 14 okay so when you look it up
+ 
+
+ align:start position:0%
+mate in 14 okay so when you look it up
+and you discover there's a mate and five
+
+ align:start position:0%
+and you discover there's a mate and five
+ 
+
+ align:start position:0%
+and you discover there's a mate and five
+in the table you have to do a little bit
+
+ align:start position:0%
+in the table you have to do a little bit
+ 
+
+ align:start position:0%
+in the table you have to do a little bit
+of a calculation to translate that into
+
+ align:start position:0%
+of a calculation to translate that into
+ 
+
+ align:start position:0%
+of a calculation to translate that into
+being a mate in in 14 as the value
+
+ align:start position:0%
+being a mate in in 14 as the value
+ 
+
+ align:start position:0%
+being a mate in in 14 as the value
+that's going to be used here rather than
+
+ align:start position:0%
+that's going to be used here rather than
+ 
+
+ align:start position:0%
+that's going to be used here rather than
+a mate in five does that make sense so
+
+ align:start position:0%
+a mate in five does that make sense so
+ 
+
+ align:start position:0%
+a mate in five does that make sense so
+you'll see that's the logic that's in
+
+ align:start position:0%
+you'll see that's the logic that's in
+ 
+
+ align:start position:0%
+you'll see that's the logic that's in
+there for dealing with mates so mate
+
+ align:start position:0%
+there for dealing with mates so mate
+ 
+
+ align:start position:0%
+there for dealing with mates so mate
+basically takes a very large number way
+
+ align:start position:0%
+basically takes a very large number way
+ 
+
+ align:start position:0%
+basically takes a very large number way
+larger than all the material on the
+
+ align:start position:0%
+larger than all the material on the
+ 
+
+ align:start position:0%
+larger than all the material on the
+board and then it subtracts what your
+
+ align:start position:0%
+board and then it subtracts what your
+ 
+
+ align:start position:0%
+board and then it subtracts what your
+number of ply is to get to get to me so
+
+ align:start position:0%
+number of ply is to get to get to me so
+ 
+
+ align:start position:0%
+number of ply is to get to get to me so
+some big number
+
+ align:start position:0%
+some big number
+ 
+
+ align:start position:0%
+some big number
+you know I don't know 32,000 or
+
+ align:start position:0%
+you know I don't know 32,000 or
+ 
+
+ align:start position:0%
+you know I don't know 32,000 or
+something minus the depth to me is what
+
+ align:start position:0%
+something minus the depth to me is what
+ 
+
+ align:start position:0%
+something minus the depth to me is what
+you is what is how you represent a mate
+
+ align:start position:0%
+you is what is how you represent a mate
+ 
+
+ align:start position:0%
+you is what is how you represent a mate
+you know so some very very big number
+
+ align:start position:0%
+you know so some very very big number
+ 
+
+ align:start position:0%
+you know so some very very big number
+and and then minus the minus the depth
+
+ align:start position:0%
+and and then minus the minus the depth
+ 
+
+ align:start position:0%
+and and then minus the minus the depth
+and that way you can make sure that
+
+ align:start position:0%
+and that way you can make sure that
+ 
+
+ align:start position:0%
+and that way you can make sure that
+you're going for a mate in 13 instead of
+
+ align:start position:0%
+you're going for a mate in 13 instead of
+ 
+
+ align:start position:0%
+you're going for a mate in 13 instead of
+a mate and 14 for example you know
+
+ align:start position:0%
+a mate and 14 for example you know
+ 
+
+ align:start position:0%
+a mate and 14 for example you know
+preferring that you take the shorter
+
+ align:start position:0%
+preferring that you take the shorter
+ 
+
+ align:start position:0%
+preferring that you take the shorter
+path make sense
+
+ align:start position:0%
+path make sense
+ 
+
+ align:start position:0%
+path make sense
+so that's one of the things to look out
+
+ align:start position:0%
+so that's one of the things to look out
+ 
+
+ align:start position:0%
+so that's one of the things to look out
+in there and there's also a lot of stuff
+
+ align:start position:0%
+in there and there's also a lot of stuff
+ 
+
+ align:start position:0%
+in there and there's also a lot of stuff
+in there the transposition table has we
+
+ align:start position:0%
+in there the transposition table has we
+ 
+
+ align:start position:0%
+in there the transposition table has we
+talked about caching it's actually a K
+
+ align:start position:0%
+talked about caching it's actually a K
+ 
+
+ align:start position:0%
+talked about caching it's actually a K
+associative cache K way associative
+
+ align:start position:0%
+associative cache K way associative
+ 
+
+ align:start position:0%
+associative cache K way associative
+cache and so you can a very K to see
+
+ align:start position:0%
+cache and so you can a very K to see
+ 
+
+ align:start position:0%
+cache and so you can a very K to see
+what's the best choice of you know how
+
+ align:start position:0%
+what's the best choice of you know how
+ 
+
+ align:start position:0%
+what's the best choice of you know how
+many how many entries you should have
+
+ align:start position:0%
+many how many entries you should have
+ 
+
+ align:start position:0%
+many how many entries you should have
+the more entries you have the longer it
+
+ align:start position:0%
+the more entries you have the longer it
+ 
+
+ align:start position:0%
+the more entries you have the longer it
+will take you to search them
+
+ align:start position:0%
+will take you to search them
+ 
+
+ align:start position:0%
+will take you to search them
+on the other hand the more likely it is
+
+ align:start position:0%
+on the other hand the more likely it is
+ 
+
+ align:start position:0%
+on the other hand the more likely it is
+that good moves stay in the cache okay
+
+ align:start position:0%
+that good moves stay in the cache okay
+ 
+
+ align:start position:0%
+that good moves stay in the cache okay
+so you can decide what's what's the
+
+ align:start position:0%
+so you can decide what's what's the
+ 
+
+ align:start position:0%
+so you can decide what's what's the
+right trade-off there okay so there's a
+
+ align:start position:0%
+right trade-off there okay so there's a
+ 
+
+ align:start position:0%
+right trade-off there okay so there's a
+good tuning optimization there okay
+
+ align:start position:0%
+good tuning optimization there okay
+ 
+
+ align:start position:0%
+good tuning optimization there okay
+questions any questions about
+
+ align:start position:0%
+questions any questions about
+ 
+
+ align:start position:0%
+questions any questions about
+transposition table transmission today
+
+ align:start position:0%
+transposition table transmission today
+ 
+
+ align:start position:0%
+transposition table transmission today
+is a major optimization so Zobrist
+
+ align:start position:0%
+is a major optimization so Zobrist
+ 
+
+ align:start position:0%
+is a major optimization so Zobrist
+hashing so most of these we taught Helen
+
+ align:start position:0%
+hashing so most of these we taught Helen
+ 
+
+ align:start position:0%
+hashing so most of these we taught Helen
+talked about at some level but I wanted
+
+ align:start position:0%
+talked about at some level but I wanted
+ 
+
+ align:start position:0%
+talked about at some level but I wanted
+to sort of give a chance to have people
+
+ align:start position:0%
+to sort of give a chance to have people
+ 
+
+ align:start position:0%
+to sort of give a chance to have people
+ask questions nobody's asking questions
+
+ align:start position:0%
+ask questions nobody's asking questions
+ 
+
+ align:start position:0%
+ask questions nobody's asking questions
+came here for Q&A all you're getting is
+
+ align:start position:0%
+came here for Q&A all you're getting is
+ 
+
+ align:start position:0%
+came here for Q&A all you're getting is
+a okay so let me explain Zobrist hashing
+
+ align:start position:0%
+a okay so let me explain Zobrist hashing
+ 
+
+ align:start position:0%
+a okay so let me explain Zobrist hashing
+again a little bit okay so so Zobrist
+
+ align:start position:0%
+again a little bit okay so so Zobrist
+ 
+
+ align:start position:0%
+again a little bit okay so so Zobrist
+hashing very clever idea so we have our
+
+ align:start position:0%
+hashing very clever idea so we have our
+ 
+
+ align:start position:0%
+hashing very clever idea so we have our
+board right with with a bunch of pieces
+
+ align:start position:0%
+board right with with a bunch of pieces
+ 
+
+ align:start position:0%
+board right with with a bunch of pieces
+on it that's probably the wrong number
+
+ align:start position:0%
+on it that's probably the wrong number
+ 
+
+ align:start position:0%
+on it that's probably the wrong number
+of squares right that's seven by six
+
+ align:start position:0%
+of squares right that's seven by six
+ 
+
+ align:start position:0%
+of squares right that's seven by six
+okay who cares okay so so the idea is
+
+ align:start position:0%
+okay who cares okay so so the idea is
+ 
+
+ align:start position:0%
+okay who cares okay so so the idea is
+that what I'm going to do is have a
+
+ align:start position:0%
+that what I'm going to do is have a
+ 
+
+ align:start position:0%
+that what I'm going to do is have a
+table of random numbers that I'm going
+
+ align:start position:0%
+table of random numbers that I'm going
+ 
+
+ align:start position:0%
+table of random numbers that I'm going
+to compute in advance and this is gonna
+
+ align:start position:0%
+to compute in advance and this is gonna
+ 
+
+ align:start position:0%
+to compute in advance and this is gonna
+be indexed by you know my row my column
+
+ align:start position:0%
+be indexed by you know my row my column
+ 
+
+ align:start position:0%
+be indexed by you know my row my column
+my piece type and my orientation okay
+
+ align:start position:0%
+my piece type and my orientation okay
+ 
+
+ align:start position:0%
+my piece type and my orientation okay
+and every different combination of row
+
+ align:start position:0%
+and every different combination of row
+ 
+
+ align:start position:0%
+and every different combination of row
+column type and orientation corresponds
+
+ align:start position:0%
+column type and orientation corresponds
+ 
+
+ align:start position:0%
+column type and orientation corresponds
+to a different random number in the
+
+ align:start position:0%
+to a different random number in the
+ 
+
+ align:start position:0%
+to a different random number in the
+table okay okay if some sort of random
+
+ align:start position:0%
+table okay okay if some sort of random
+ 
+
+ align:start position:0%
+table okay okay if some sort of random
+number there okay so you know so and
+
+ align:start position:0%
+number there okay so you know so and
+ 
+
+ align:start position:0%
+number there okay so you know so and
+what my hash function is is it's the XOR
+
+ align:start position:0%
+what my hash function is is it's the XOR
+ 
+
+ align:start position:0%
+what my hash function is is it's the XOR
+of all of the values of all the pieces
+
+ align:start position:0%
+of all of the values of all the pieces
+ 
+
+ align:start position:0%
+of all of the values of all the pieces
+that are on this table with their
+
+ align:start position:0%
+that are on this table with their
+ 
+
+ align:start position:0%
+that are on this table with their
+orientations okay so if I have a king
+
+ align:start position:0%
+orientations okay so if I have a king
+ 
+
+ align:start position:0%
+orientations okay so if I have a king
+here you know that's a White King
+
+ align:start position:0%
+here you know that's a White King
+ 
+
+ align:start position:0%
+here you know that's a White King
+I guess I need to know who's who's not
+
+ align:start position:0%
+I guess I need to know who's who's not
+ 
+
+ align:start position:0%
+I guess I need to know who's who's not
+just what the type is I also need to
+
+ align:start position:0%
+just what the type is I also need to
+ 
+
+ align:start position:0%
+just what the type is I also need to
+know whether it's white or black right
+
+ align:start position:0%
+know whether it's white or black right
+ 
+
+ align:start position:0%
+know whether it's white or black right
+so the the side okay I think actually
+
+ align:start position:0%
+so the the side okay I think actually
+ 
+
+ align:start position:0%
+so the the side okay I think actually
+that gets encoded somehow but in any
+
+ align:start position:0%
+that gets encoded somehow but in any
+ 
+
+ align:start position:0%
+that gets encoded somehow but in any
+case yeah I think maybe in the type we
+
+ align:start position:0%
+case yeah I think maybe in the type we
+ 
+
+ align:start position:0%
+case yeah I think maybe in the type we
+actually keep whether it's a whiter pawn
+
+ align:start position:0%
+actually keep whether it's a whiter pawn
+ 
+
+ align:start position:0%
+actually keep whether it's a whiter pawn
+black pawn yeah it's in the type I think
+
+ align:start position:0%
+black pawn yeah it's in the type I think
+ 
+
+ align:start position:0%
+black pawn yeah it's in the type I think
+is the way we actually implement it that
+
+ align:start position:0%
+is the way we actually implement it that
+ 
+
+ align:start position:0%
+is the way we actually implement it that
+okay so there's white king black king
+
+ align:start position:0%
+okay so there's white king black king
+ 
+
+ align:start position:0%
+okay so there's white king black king
+white pawn black pawn or space so if I
+
+ align:start position:0%
+white pawn black pawn or space so if I
+ 
+
+ align:start position:0%
+white pawn black pawn or space so if I
+have a king there that corresponds to a
+
+ align:start position:0%
+have a king there that corresponds to a
+ 
+
+ align:start position:0%
+have a king there that corresponds to a
+certain value if I end up with a pawn
+
+ align:start position:0%
+certain value if I end up with a pawn
+ 
+
+ align:start position:0%
+certain value if I end up with a pawn
+here I'll say a white pawn then that
+
+ align:start position:0%
+here I'll say a white pawn then that
+ 
+
+ align:start position:0%
+here I'll say a white pawn then that
+will be another one and I XOR those
+
+ align:start position:0%
+will be another one and I XOR those
+ 
+
+ align:start position:0%
+will be another one and I XOR those
+together and I take the black King okay
+
+ align:start position:0%
+together and I take the black King okay
+ 
+
+ align:start position:0%
+together and I take the black King okay
+and I XOR his position is and the you
+
+ align:start position:0%
+and I XOR his position is and the you
+ 
+
+ align:start position:0%
+and I XOR his position is and the you
+know black pawn XOR that in and so I XOR
+
+ align:start position:0%
+know black pawn XOR that in and so I XOR
+ 
+
+ align:start position:0%
+know black pawn XOR that in and so I XOR
+all these four values
+
+ align:start position:0%
+all these four values
+ 
+
+ align:start position:0%
+all these four values
+that's the hash function that I use to
+
+ align:start position:0%
+that's the hash function that I use to
+ 
+
+ align:start position:0%
+that's the hash function that I use to
+do things like look up things in the
+
+ align:start position:0%
+do things like look up things in the
+ 
+
+ align:start position:0%
+do things like look up things in the
+transposition table now if I had to
+
+ align:start position:0%
+transposition table now if I had to
+ 
+
+ align:start position:0%
+transposition table now if I had to
+compute this every time I change the
+
+ align:start position:0%
+compute this every time I change the
+ 
+
+ align:start position:0%
+compute this every time I change the
+position you know that's if I have a lot
+
+ align:start position:0%
+position you know that's if I have a lot
+ 
+
+ align:start position:0%
+position you know that's if I have a lot
+of pieces how many pieces I've got I've
+
+ align:start position:0%
+of pieces how many pieces I've got I've
+ 
+
+ align:start position:0%
+of pieces how many pieces I've got I've
+got seven eight sixteen pieces right
+
+ align:start position:0%
+got seven eight sixteen pieces right
+ 
+
+ align:start position:0%
+got seven eight sixteen pieces right
+there's each side has seven pawns in a
+
+ align:start position:0%
+there's each side has seven pawns in a
+ 
+
+ align:start position:0%
+there's each side has seven pawns in a
+king so sixteen pieces I have to do 16 X
+
+ align:start position:0%
+king so sixteen pieces I have to do 16 X
+ 
+
+ align:start position:0%
+king so sixteen pieces I have to do 16 X
+Wars in order to compute my hash
+
+ align:start position:0%
+Wars in order to compute my hash
+ 
+
+ align:start position:0%
+Wars in order to compute my hash
+function so Zobrist rationing is really
+
+ align:start position:0%
+function so Zobrist rationing is really
+ 
+
+ align:start position:0%
+function so Zobrist rationing is really
+a lot clever it takes advantage of that
+
+ align:start position:0%
+a lot clever it takes advantage of that
+ 
+
+ align:start position:0%
+a lot clever it takes advantage of that
+XOR trick that I taught you in the first
+
+ align:start position:0%
+XOR trick that I taught you in the first
+ 
+
+ align:start position:0%
+XOR trick that I taught you in the first
+now it wasn't the first it was in the
+
+ align:start position:0%
+now it wasn't the first it was in the
+ 
+
+ align:start position:0%
+now it wasn't the first it was in the
+the was the second lecture yeah you know
+
+ align:start position:0%
+the was the second lecture yeah you know
+ 
+
+ align:start position:0%
+the was the second lecture yeah you know
+the bit tricks lecture okay and that is
+
+ align:start position:0%
+the bit tricks lecture okay and that is
+ 
+
+ align:start position:0%
+the bit tricks lecture okay and that is
+that XOR is its own inverse so if I want
+
+ align:start position:0%
+that XOR is its own inverse so if I want
+ 
+
+ align:start position:0%
+that XOR is its own inverse so if I want
+to remove a piece let's say I'm going to
+
+ align:start position:0%
+to remove a piece let's say I'm going to
+ 
+
+ align:start position:0%
+to remove a piece let's say I'm going to
+move this pawn okay from here to here so
+
+ align:start position:0%
+move this pawn okay from here to here so
+ 
+
+ align:start position:0%
+move this pawn okay from here to here so
+I remove this piece what do I do to my
+
+ align:start position:0%
+I remove this piece what do I do to my
+ 
+
+ align:start position:0%
+I remove this piece what do I do to my
+hash function to remove a piece I look
+
+ align:start position:0%
+hash function to remove a piece I look
+ 
+
+ align:start position:0%
+hash function to remove a piece I look
+up the value for that pawn in the hash
+
+ align:start position:0%
+up the value for that pawn in the hash
+ 
+
+ align:start position:0%
+up the value for that pawn in the hash
+table and I XOR that into my hash for
+
+ align:start position:0%
+table and I XOR that into my hash for
+ 
+
+ align:start position:0%
+table and I XOR that into my hash for
+the table and I now have
+
+ align:start position:0%
+the table and I now have
+ 
+
+ align:start position:0%
+the table and I now have
+hache for those three pieces left that
+
+ align:start position:0%
+hache for those three pieces left that
+ 
+
+ align:start position:0%
+hache for those three pieces left that
+make sense so I have my hash function
+
+ align:start position:0%
+make sense so I have my hash function
+ 
+
+ align:start position:0%
+make sense so I have my hash function
+which is a hash of the four things I'm
+
+ align:start position:0%
+which is a hash of the four things I'm
+ 
+
+ align:start position:0%
+which is a hash of the four things I'm
+not sure you guys can see very well over
+
+ align:start position:0%
+not sure you guys can see very well over
+ 
+
+ align:start position:0%
+not sure you guys can see very well over
+there but and I basically simply XOR it
+
+ align:start position:0%
+there but and I basically simply XOR it
+ 
+
+ align:start position:0%
+there but and I basically simply XOR it
+with the hash of you know the pawn that
+
+ align:start position:0%
+with the hash of you know the pawn that
+ 
+
+ align:start position:0%
+with the hash of you know the pawn that
+I removed you know from the you know of
+
+ align:start position:0%
+I removed you know from the you know of
+ 
+
+ align:start position:0%
+I removed you know from the you know of
+the pawn that I removed in this case and
+
+ align:start position:0%
+the pawn that I removed in this case and
+ 
+
+ align:start position:0%
+the pawn that I removed in this case and
+now I moved it to here so what do I do I
+
+ align:start position:0%
+now I moved it to here so what do I do I
+ 
+
+ align:start position:0%
+now I moved it to here so what do I do I
+look up that one and I XOR it that value
+
+ align:start position:0%
+look up that one and I XOR it that value
+ 
+
+ align:start position:0%
+look up that one and I XOR it that value
+in here for the new position near the
+
+ align:start position:0%
+in here for the new position near the
+ 
+
+ align:start position:0%
+in here for the new position near the
+new pawn position and that gives me now
+
+ align:start position:0%
+new pawn position and that gives me now
+ 
+
+ align:start position:0%
+new pawn position and that gives me now
+the the the hash for the new table with
+
+ align:start position:0%
+the the the hash for the new table with
+ 
+
+ align:start position:0%
+the the the hash for the new table with
+a pawn in that position so any move that
+
+ align:start position:0%
+a pawn in that position so any move that
+ 
+
+ align:start position:0%
+a pawn in that position so any move that
+I make I can basically update my hash
+
+ align:start position:0%
+I make I can basically update my hash
+ 
+
+ align:start position:0%
+I make I can basically update my hash
+function with only two X source and XOR
+
+ align:start position:0%
+function with only two X source and XOR
+ 
+
+ align:start position:0%
+function with only two X source and XOR
+czar very fast there one instruction you
+
+ align:start position:0%
+czar very fast there one instruction you
+ 
+
+ align:start position:0%
+czar very fast there one instruction you
+know there one and they can do lots of X
+
+ align:start position:0%
+know there one and they can do lots of X
+ 
+
+ align:start position:0%
+know there one and they can do lots of X
+ORS and stuff so this is actually very
+
+ align:start position:0%
+ORS and stuff so this is actually very
+ 
+
+ align:start position:0%
+ORS and stuff so this is actually very
+very cheap thing to do
+
+ align:start position:0%
+very cheap thing to do
+ 
+
+ align:start position:0%
+very cheap thing to do
+okay very cheap thing to do so that's
+
+ align:start position:0%
+okay very cheap thing to do so that's
+ 
+
+ align:start position:0%
+okay very cheap thing to do so that's
+Zobrist hashing that you can keep these
+
+ align:start position:0%
+Zobrist hashing that you can keep these
+ 
+
+ align:start position:0%
+Zobrist hashing that you can keep these
+these things up to date and that's
+
+ align:start position:0%
+these things up to date and that's
+ 
+
+ align:start position:0%
+these things up to date and that's
+something we implemented for you that's
+
+ align:start position:0%
+something we implemented for you that's
+ 
+
+ align:start position:0%
+something we implemented for you that's
+an optimization that was a freebie we
+
+ align:start position:0%
+an optimization that was a freebie we
+ 
+
+ align:start position:0%
+an optimization that was a freebie we
+could have given you the hash function
+
+ align:start position:0%
+could have given you the hash function
+ 
+
+ align:start position:0%
+could have given you the hash function
+you know like this and had you implement
+
+ align:start position:0%
+you know like this and had you implement
+ 
+
+ align:start position:0%
+you know like this and had you implement
+that but this is one of the ones we gave
+
+ align:start position:0%
+that but this is one of the ones we gave
+ 
+
+ align:start position:0%
+that but this is one of the ones we gave
+you as a freebie for optimization you're
+
+ align:start position:0%
+you as a freebie for optimization you're
+ 
+
+ align:start position:0%
+you as a freebie for optimization you're
+not all saying thank you very much
+
+ align:start position:0%
+not all saying thank you very much
+ 
+
+ align:start position:0%
+not all saying thank you very much
+professor leiserson
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now in some sense I took away an
+
+ align:start position:0%
+okay now in some sense I took away an
+ 
+
+ align:start position:0%
+okay now in some sense I took away an
+opportunity for optimisation didn't I
+
+ align:start position:0%
+opportunity for optimisation didn't I
+ 
+
+ align:start position:0%
+opportunity for optimisation didn't I
+there okay and so in the transposition
+
+ align:start position:0%
+there okay and so in the transposition
+ 
+
+ align:start position:0%
+there okay and so in the transposition
+table there are records for the Zobrist
+
+ align:start position:0%
+table there are records for the Zobrist
+ 
+
+ align:start position:0%
+table there are records for the Zobrist
+key the score the move the quality also
+
+ align:start position:0%
+key the score the move the quality also
+ 
+
+ align:start position:0%
+key the score the move the quality also
+a bound type whether it's upper lower or
+
+ align:start position:0%
+a bound type whether it's upper lower or
+ 
+
+ align:start position:0%
+a bound type whether it's upper lower or
+exact because when I return something
+
+ align:start position:0%
+exact because when I return something
+ 
+
+ align:start position:0%
+exact because when I return something
+from alpha-beta I only know a bound on
+
+ align:start position:0%
+from alpha-beta I only know a bound on
+ 
+
+ align:start position:0%
+from alpha-beta I only know a bound on
+it if it's if it's greater than alpha or
+
+ align:start position:0%
+it if it's if it's greater than alpha or
+ 
+
+ align:start position:0%
+it if it's if it's greater than alpha or
+less than beta and in some sense the age
+
+ align:start position:0%
+less than beta and in some sense the age
+ 
+
+ align:start position:0%
+less than beta and in some sense the age
+of how how old is this move because as
+
+ align:start position:0%
+of how how old is this move because as
+ 
+
+ align:start position:0%
+of how how old is this move because as
+things get older I also want to age them
+
+ align:start position:0%
+things get older I also want to age them
+ 
+
+ align:start position:0%
+things get older I also want to age them
+out of the table
+
+ align:start position:0%
+out of the table
+ 
+
+ align:start position:0%
+out of the table
+there's several aging things therein
+
+ align:start position:0%
+there's several aging things therein
+ 
+
+ align:start position:0%
+there's several aging things therein
+you'll see the best move table also has
+
+ align:start position:0%
+you'll see the best move table also has
+ 
+
+ align:start position:0%
+you'll see the best move table also has
+an aging process whereas every time it
+
+ align:start position:0%
+an aging process whereas every time it
+ 
+
+ align:start position:0%
+an aging process whereas every time it
+updates the values gives a new value it
+
+ align:start position:0%
+updates the values gives a new value it
+ 
+
+ align:start position:0%
+updates the values gives a new value it
+ages all the other values so that they
+
+ align:start position:0%
+ages all the other values so that they
+ 
+
+ align:start position:0%
+ages all the other values so that they
+gradually disappear and aren't relevant
+
+ align:start position:0%
+gradually disappear and aren't relevant
+ 
+
+ align:start position:0%
+gradually disappear and aren't relevant
+one of the ones that people have get
+
+ align:start position:0%
+one of the ones that people have get
+ 
+
+ align:start position:0%
+one of the ones that people have get
+confused about is the late move
+
+ align:start position:0%
+confused about is the late move
+ 
+
+ align:start position:0%
+confused about is the late move
+reductions
+
+ align:start position:0%
+reductions
+ 
+
+ align:start position:0%
+reductions
+okay so called LMR okay this is the
+
+ align:start position:0%
+okay so called LMR okay this is the
+ 
+
+ align:start position:0%
+okay so called LMR okay this is the
+situation where I have I'm going to do
+
+ align:start position:0%
+situation where I have I'm going to do
+ 
+
+ align:start position:0%
+situation where I have I'm going to do
+let's say my parallel search to you know
+
+ align:start position:0%
+let's say my parallel search to you know
+ 
+
+ align:start position:0%
+let's say my parallel search to you know
+of all my moves and the question is you
+
+ align:start position:0%
+of all my moves and the question is you
+ 
+
+ align:start position:0%
+of all my moves and the question is you
+know it's again you're trying to prune
+
+ align:start position:0%
+know it's again you're trying to prune
+ 
+
+ align:start position:0%
+know it's again you're trying to prune
+everything you can okay and so this is
+
+ align:start position:0%
+everything you can okay and so this is
+ 
+
+ align:start position:0%
+everything you can okay and so this is
+the idea is which are the moves that are
+
+ align:start position:0%
+the idea is which are the moves that are
+ 
+
+ align:start position:0%
+the idea is which are the moves that are
+more important to search deeper the ones
+
+ align:start position:0%
+more important to search deeper the ones
+ 
+
+ align:start position:0%
+more important to search deeper the ones
+near the beginning of your move list if
+
+ align:start position:0%
+near the beginning of your move list if
+ 
+
+ align:start position:0%
+near the beginning of your move list if
+it's sorted in best first order or the
+
+ align:start position:0%
+it's sorted in best first order or the
+ 
+
+ align:start position:0%
+it's sorted in best first order or the
+ones towards the end of your move list
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so where where is it most important to
+
+ align:start position:0%
+so where where is it most important to
+ 
+
+ align:start position:0%
+so where where is it most important to
+search deeply for things that you think
+
+ align:start position:0%
+search deeply for things that you think
+ 
+
+ align:start position:0%
+search deeply for things that you think
+are possibly the best move or the ones
+
+ align:start position:0%
+are possibly the best move or the ones
+ 
+
+ align:start position:0%
+are possibly the best move or the ones
+that you think are the worst moves yeah
+
+ align:start position:0%
+that you think are the worst moves yeah
+ 
+
+ align:start position:0%
+that you think are the worst moves yeah
+yeah it makes sense to search the best
+
+ align:start position:0%
+yeah it makes sense to search the best
+ 
+
+ align:start position:0%
+yeah it makes sense to search the best
+moves right so the idea is well if
+
+ align:start position:0%
+moves right so the idea is well if
+ 
+
+ align:start position:0%
+moves right so the idea is well if
+something is way down on the move
+
+ align:start position:0%
+something is way down on the move
+ 
+
+ align:start position:0%
+something is way down on the move
+ordering list why search it as deeply
+
+ align:start position:0%
+ordering list why search it as deeply
+ 
+
+ align:start position:0%
+ordering list why search it as deeply
+it's probably not as good a move and so
+
+ align:start position:0%
+it's probably not as good a move and so
+ 
+
+ align:start position:0%
+it's probably not as good a move and so
+let me search it more shallow I probably
+
+ align:start position:0%
+let me search it more shallow I probably
+ 
+
+ align:start position:0%
+let me search it more shallow I probably
+don't lose much of an opportunity to
+
+ align:start position:0%
+don't lose much of an opportunity to
+ 
+
+ align:start position:0%
+don't lose much of an opportunity to
+discover that that's actually a you know
+
+ align:start position:0%
+discover that that's actually a you know
+ 
+
+ align:start position:0%
+discover that that's actually a you know
+is indeed a bad move okay there's a
+
+ align:start position:0%
+is indeed a bad move okay there's a
+ 
+
+ align:start position:0%
+is indeed a bad move okay there's a
+reason that got ordered down there and
+
+ align:start position:0%
+reason that got ordered down there and
+ 
+
+ align:start position:0%
+reason that got ordered down there and
+so that's late move reduction so with a
+
+ align:start position:0%
+so that's late move reduction so with a
+ 
+
+ align:start position:0%
+so that's late move reduction so with a
+good move ordering a beta it kind of
+
+ align:start position:0%
+good move ordering a beta it kind of
+ 
+
+ align:start position:0%
+good move ordering a beta it kind of
+will either occur right away or not also
+
+ align:start position:0%
+will either occur right away or not also
+ 
+
+ align:start position:0%
+will either occur right away or not also
+you search the first few moves normally
+
+ align:start position:0%
+you search the first few moves normally
+ 
+
+ align:start position:0%
+you search the first few moves normally
+and then you start reducing the depth
+
+ align:start position:0%
+and then you start reducing the depth
+ 
+
+ align:start position:0%
+and then you start reducing the depth
+for four moves I believe in our code we
+
+ align:start position:0%
+for four moves I believe in our code we
+ 
+
+ align:start position:0%
+for four moves I believe in our code we
+have two numbers where we reduce by
+
+ align:start position:0%
+have two numbers where we reduce by
+ 
+
+ align:start position:0%
+have two numbers where we reduce by
+depth one after a certain number of
+
+ align:start position:0%
+depth one after a certain number of
+ 
+
+ align:start position:0%
+depth one after a certain number of
+moves and reduced by depth two after a
+
+ align:start position:0%
+moves and reduced by depth two after a
+ 
+
+ align:start position:0%
+moves and reduced by depth two after a
+certain number of other moves those are
+
+ align:start position:0%
+certain number of other moves those are
+ 
+
+ align:start position:0%
+certain number of other moves those are
+things that you can tune I wouldn't tune
+
+ align:start position:0%
+things that you can tune I wouldn't tune
+ 
+
+ align:start position:0%
+things that you can tune I wouldn't tune
+them very much I don't think just
+
+ align:start position:0%
+them very much I don't think just
+ 
+
+ align:start position:0%
+them very much I don't think just
+because and once again I could probably
+
+ align:start position:0%
+because and once again I could probably
+ 
+
+ align:start position:0%
+because and once again I could probably
+be wrong here and some of those discover
+
+ align:start position:0%
+be wrong here and some of those discover
+ 
+
+ align:start position:0%
+be wrong here and some of those discover
+oh you know if you tune it like this
+
+ align:start position:0%
+oh you know if you tune it like this
+ 
+
+ align:start position:0%
+oh you know if you tune it like this
+it's way better okay but those are those
+
+ align:start position:0%
+it's way better okay but those are those
+ 
+
+ align:start position:0%
+it's way better okay but those are those
+are that's the idea of the late move
+
+ align:start position:0%
+are that's the idea of the late move
+ 
+
+ align:start position:0%
+are that's the idea of the late move
+reductions probably one of the most
+
+ align:start position:0%
+reductions probably one of the most
+ 
+
+ align:start position:0%
+reductions probably one of the most
+important things to think about is the
+
+ align:start position:0%
+important things to think about is the
+ 
+
+ align:start position:0%
+important things to think about is the
+move is the representation of the board
+
+ align:start position:0%
+move is the representation of the board
+ 
+
+ align:start position:0%
+move is the representation of the board
+right now we represent the board as it
+
+ align:start position:0%
+right now we represent the board as it
+ 
+
+ align:start position:0%
+right now we represent the board as it
+is okay that's a terrible representation
+
+ align:start position:0%
+is okay that's a terrible representation
+ 
+
+ align:start position:0%
+is okay that's a terrible representation
+it's very you know time-consuming
+
+ align:start position:0%
+it's very you know time-consuming
+ 
+
+ align:start position:0%
+it's very you know time-consuming
+there's sort of two major ways you can
+
+ align:start position:0%
+there's sort of two major ways you can
+ 
+
+ align:start position:0%
+there's sort of two major ways you can
+do it oh I didn't put the other one here
+
+ align:start position:0%
+do it oh I didn't put the other one here
+ 
+
+ align:start position:0%
+do it oh I didn't put the other one here
+okay well anyway so one of them is bit
+
+ align:start position:0%
+okay well anyway so one of them is bit
+ 
+
+ align:start position:0%
+okay well anyway so one of them is bit
+boards here you use a 64 bit to
+
+ align:start position:0%
+boards here you use a 64 bit to
+ 
+
+ align:start position:0%
+boards here you use a 64 bit to
+represent for example where all the
+
+ align:start position:0%
+represent for example where all the
+ 
+
+ align:start position:0%
+represent for example where all the
+pawns are on the 64 squares of the board
+
+ align:start position:0%
+pawns are on the 64 squares of the board
+ 
+
+ align:start position:0%
+pawns are on the 64 squares of the board
+okay and then you can use pop count and
+
+ align:start position:0%
+okay and then you can use pop count and
+ 
+
+ align:start position:0%
+okay and then you can use pop count and
+other bit tricks to do move generation
+
+ align:start position:0%
+other bit tricks to do move generation
+ 
+
+ align:start position:0%
+other bit tricks to do move generation
+and to implement other chess concepts
+
+ align:start position:0%
+and to implement other chess concepts
+ 
+
+ align:start position:0%
+and to implement other chess concepts
+okay so if you're looking to see what
+
+ align:start position:0%
+okay so if you're looking to see what
+ 
+
+ align:start position:0%
+okay so if you're looking to see what
+are the possible places upon can move
+
+ align:start position:0%
+are the possible places upon can move
+ 
+
+ align:start position:0%
+are the possible places upon can move
+and you want to say can they move right
+
+ align:start position:0%
+and you want to say can they move right
+ 
+
+ align:start position:0%
+and you want to say can they move right
+and let's say it's stored in row major
+
+ align:start position:0%
+and let's say it's stored in row major
+ 
+
+ align:start position:0%
+and let's say it's stored in row major
+order you can just do a right shift by
+
+ align:start position:0%
+order you can just do a right shift by
+ 
+
+ align:start position:0%
+order you can just do a right shift by
+one and that tells you where are all the
+
+ align:start position:0%
+one and that tells you where are all the
+ 
+
+ align:start position:0%
+one and that tells you where are all the
+places that pawns those pawns could move
+
+ align:start position:0%
+places that pawns those pawns could move
+ 
+
+ align:start position:0%
+places that pawns those pawns could move
+and now you can just pick them off one
+
+ align:start position:0%
+and now you can just pick them off one
+ 
+
+ align:start position:0%
+and now you can just pick them off one
+bit at a time to generate your move list
+
+ align:start position:0%
+bit at a time to generate your move list
+ 
+
+ align:start position:0%
+bit at a time to generate your move list
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and and then you can do it that way if
+
+ align:start position:0%
+and and then you can do it that way if
+ 
+
+ align:start position:0%
+and and then you can do it that way if
+you're gonna move up a thing well then
+
+ align:start position:0%
+you're gonna move up a thing well then
+ 
+
+ align:start position:0%
+you're gonna move up a thing well then
+you're actually doing a shift by or down
+
+ align:start position:0%
+you're actually doing a shift by or down
+ 
+
+ align:start position:0%
+you're actually doing a shift by or down
+you're doing a shift by how much by 8
+
+ align:start position:0%
+you're doing a shift by how much by 8
+ 
+
+ align:start position:0%
+you're doing a shift by how much by 8
+right to move up or down okay if you're
+
+ align:start position:0%
+right to move up or down okay if you're
+ 
+
+ align:start position:0%
+right to move up or down okay if you're
+storing things in row major all right
+
+ align:start position:0%
+storing things in row major all right
+ 
+
+ align:start position:0%
+storing things in row major all right
+that makes sense right
+
+ align:start position:0%
+that makes sense right
+ 
+
+ align:start position:0%
+that makes sense right
+so if it's it's 8 by 8 and you're
+
+ align:start position:0%
+so if it's it's 8 by 8 and you're
+ 
+
+ align:start position:0%
+so if it's it's 8 by 8 and you're
+keeping a bit for each thing then if I
+
+ align:start position:0%
+keeping a bit for each thing then if I
+ 
+
+ align:start position:0%
+keeping a bit for each thing then if I
+want to generate you know where is this
+
+ align:start position:0%
+want to generate you know where is this
+ 
+
+ align:start position:0%
+want to generate you know where is this
+one if I shift this whole thing stored
+
+ align:start position:0%
+one if I shift this whole thing stored
+ 
+
+ align:start position:0%
+one if I shift this whole thing stored
+in row major order by 8 if I shift it
+
+ align:start position:0%
+in row major order by 8 if I shift it
+ 
+
+ align:start position:0%
+in row major order by 8 if I shift it
+right it basically puts it there okay so
+
+ align:start position:0%
+right it basically puts it there okay so
+ 
+
+ align:start position:0%
+right it basically puts it there okay so
+moving it by you know 7 8 9 that gives
+
+ align:start position:0%
+moving it by you know 7 8 9 that gives
+ 
+
+ align:start position:0%
+moving it by you know 7 8 9 that gives
+you and then shifting it by 1 gives you
+
+ align:start position:0%
+you and then shifting it by 1 gives you
+ 
+
+ align:start position:0%
+you and then shifting it by 1 gives you
+the you know or minus 1 gives you this
+
+ align:start position:0%
+the you know or minus 1 gives you this
+ 
+
+ align:start position:0%
+the you know or minus 1 gives you this
+or left by 1 and then similarly you can
+
+ align:start position:0%
+or left by 1 and then similarly you can
+ 
+
+ align:start position:0%
+or left by 1 and then similarly you can
+do by you know shifting by 7 8 or 9 that
+
+ align:start position:0%
+do by you know shifting by 7 8 or 9 that
+ 
+
+ align:start position:0%
+do by you know shifting by 7 8 or 9 that
+way and I can generate all the possible
+
+ align:start position:0%
+way and I can generate all the possible
+ 
+
+ align:start position:0%
+way and I can generate all the possible
+moves so that's one way of doing move
+
+ align:start position:0%
+moves so that's one way of doing move
+ 
+
+ align:start position:0%
+moves so that's one way of doing move
+generation he's using bit for it and
+
+ align:start position:0%
+generation he's using bit for it and
+ 
+
+ align:start position:0%
+generation he's using bit for it and
+there are a lot of things for example
+
+ align:start position:0%
+there are a lot of things for example
+ 
+
+ align:start position:0%
+there are a lot of things for example
+that you can do with bit boards in
+
+ align:start position:0%
+that you can do with bit boards in
+ 
+
+ align:start position:0%
+that you can do with bit boards in
+parallel because you can say did I make
+
+ align:start position:0%
+parallel because you can say did I make
+ 
+
+ align:start position:0%
+parallel because you can say did I make
+a capture here okay or let me use a bit
+
+ align:start position:0%
+a capture here okay or let me use a bit
+ 
+
+ align:start position:0%
+a capture here okay or let me use a bit
+board to represent where the laser goes
+
+ align:start position:0%
+board to represent where the laser goes
+ 
+
+ align:start position:0%
+board to represent where the laser goes
+did I make a move that is that is going
+
+ align:start position:0%
+did I make a move that is that is going
+ 
+
+ align:start position:0%
+did I make a move that is that is going
+to affect the path of laser okay because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because you know one of the major
+
+ align:start position:0%
+because you know one of the major
+ 
+
+ align:start position:0%
+because you know one of the major
+optimizations you can do is in the in
+
+ align:start position:0%
+optimizations you can do is in the in
+ 
+
+ align:start position:0%
+optimizations you can do is in the in
+the evaluations in dealing with a laser
+
+ align:start position:0%
+the evaluations in dealing with a laser
+ 
+
+ align:start position:0%
+the evaluations in dealing with a laser
+okay because you're spending a lot of
+
+ align:start position:0%
+okay because you're spending a lot of
+ 
+
+ align:start position:0%
+okay because you're spending a lot of
+time stroking out Laser positions what's
+
+ align:start position:0%
+time stroking out Laser positions what's
+ 
+
+ align:start position:0%
+time stroking out Laser positions what's
+the point of doing that if you made a
+
+ align:start position:0%
+the point of doing that if you made a
+ 
+
+ align:start position:0%
+the point of doing that if you made a
+move of something and it didn't affect
+
+ align:start position:0%
+move of something and it didn't affect
+ 
+
+ align:start position:0%
+move of something and it didn't affect
+where the laser goes why bother
+
+ align:start position:0%
+where the laser goes why bother
+ 
+
+ align:start position:0%
+where the laser goes why bother
+you know doing it out you can just cash
+
+ align:start position:0%
+you know doing it out you can just cash
+ 
+
+ align:start position:0%
+you know doing it out you can just cash
+what the what the value of the laser is
+
+ align:start position:0%
+what the what the value of the laser is
+ 
+
+ align:start position:0%
+what the what the value of the laser is
+and there are a lot of lot more good
+
+ align:start position:0%
+and there are a lot of lot more good
+ 
+
+ align:start position:0%
+and there are a lot of lot more good
+stuff on the chest programming wiki okay
+
+ align:start position:0%
+stuff on the chest programming wiki okay
+ 
+
+ align:start position:0%
+stuff on the chest programming wiki okay
+so yeah question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah you got to be careful there right
+
+ align:start position:0%
+yeah you got to be careful there right
+ 
+
+ align:start position:0%
+yeah you got to be careful there right
+because if I do a shift to the right for
+
+ align:start position:0%
+because if I do a shift to the right for
+ 
+
+ align:start position:0%
+because if I do a shift to the right for
+example so what will I do
+
+ align:start position:0%
+example so what will I do
+ 
+
+ align:start position:0%
+example so what will I do
+I'll just do a mask to eliminate all the
+
+ align:start position:0%
+I'll just do a mask to eliminate all the
+ 
+
+ align:start position:0%
+I'll just do a mask to eliminate all the
+things that got wrapped around okay
+
+ align:start position:0%
+things that got wrapped around okay
+ 
+
+ align:start position:0%
+things that got wrapped around okay
+right so two instructions or whatever
+
+ align:start position:0%
+right so two instructions or whatever
+ 
+
+ align:start position:0%
+right so two instructions or whatever
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+details yes details are good though good
+
+ align:start position:0%
+details yes details are good though good
+ 
+
+ align:start position:0%
+details yes details are good though good
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+good question who's timed their program
+
+ align:start position:0%
+good question who's timed their program
+ 
+
+ align:start position:0%
+good question who's timed their program
+where are the where are the
+
+ align:start position:0%
+where are the where are the
+ 
+
+ align:start position:0%
+where are the where are the
+opportunities that you see for
+
+ align:start position:0%
+opportunities that you see for
+ 
+
+ align:start position:0%
+opportunities that you see for
+performance engineering for a first pass
+
+ align:start position:0%
+performance engineering for a first pass
+ 
+
+ align:start position:0%
+performance engineering for a first pass
+what are those expensive things what do
+
+ align:start position:0%
+what are those expensive things what do
+ 
+
+ align:start position:0%
+what are those expensive things what do
+you have as expensive thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry the marking laser path yep good
+
+ align:start position:0%
+sorry the marking laser path yep good
+ 
+
+ align:start position:0%
+sorry the marking laser path yep good
+what else is is time expensive
+
+ align:start position:0%
+what else is is time expensive
+ 
+
+ align:start position:0%
+what else is is time expensive
+yeah laser coverage boy that is really
+
+ align:start position:0%
+yeah laser coverage boy that is really
+ 
+
+ align:start position:0%
+yeah laser coverage boy that is really
+expensive okay that is really expensive
+
+ align:start position:0%
+expensive okay that is really expensive
+ 
+
+ align:start position:0%
+expensive okay that is really expensive
+so where else is expensive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else is expensive so I would
+
+ align:start position:0%
+what else is expensive so I would
+ 
+
+ align:start position:0%
+what else is expensive so I would
+definitely go after you know L cover
+
+ align:start position:0%
+definitely go after you know L cover
+ 
+
+ align:start position:0%
+definitely go after you know L cover
+that's a that's a huge one to go after
+
+ align:start position:0%
+that's a that's a huge one to go after
+ 
+
+ align:start position:0%
+that's a that's a huge one to go after
+one of the things by the way if you are
+
+ align:start position:0%
+one of the things by the way if you are
+ 
+
+ align:start position:0%
+one of the things by the way if you are
+making your your changes to the code and
+
+ align:start position:0%
+making your your changes to the code and
+ 
+
+ align:start position:0%
+making your your changes to the code and
+you're gonna change the representation
+
+ align:start position:0%
+you're gonna change the representation
+ 
+
+ align:start position:0%
+you're gonna change the representation
+leave the old representation there take
+
+ align:start position:0%
+leave the old representation there take
+ 
+
+ align:start position:0%
+leave the old representation there take
+it out at the end add the new
+
+ align:start position:0%
+it out at the end add the new
+ 
+
+ align:start position:0%
+it out at the end add the new
+representation and put in assertions
+
+ align:start position:0%
+representation and put in assertions
+ 
+
+ align:start position:0%
+representation and put in assertions
+that say that things are equivalent or
+
+ align:start position:0%
+that say that things are equivalent or
+ 
+
+ align:start position:0%
+that say that things are equivalent or
+whatever but don't get rid of the old
+
+ align:start position:0%
+whatever but don't get rid of the old
+ 
+
+ align:start position:0%
+whatever but don't get rid of the old
+stuff because you'll end up with broken
+
+ align:start position:0%
+stuff because you'll end up with broken
+ 
+
+ align:start position:0%
+stuff because you'll end up with broken
+code and definitely using use things
+
+ align:start position:0%
+code and definitely using use things
+ 
+
+ align:start position:0%
+code and definitely using use things
+like perfectiy to tell you whether or
+
+ align:start position:0%
+like perfectiy to tell you whether or
+ 
+
+ align:start position:0%
+like perfectiy to tell you whether or
+not you you know made any change you
+
+ align:start position:0%
+not you you know made any change you
+ 
+
+ align:start position:0%
+not you you know made any change you
+know made any changes if you touch
+
+ align:start position:0%
+know made any changes if you touch
+ 
+
+ align:start position:0%
+know made any changes if you touch
+anything with move ordering sorry not a
+
+ align:start position:0%
+anything with move ordering sorry not a
+ 
+
+ align:start position:0%
+anything with move ordering sorry not a
+move generation not move ordered move
+
+ align:start position:0%
+move generation not move ordered move
+ 
+
+ align:start position:0%
+move generation not move ordered move
+generation so where else is expensive
+
+ align:start position:0%
+generation so where else is expensive
+ 
+
+ align:start position:0%
+generation so where else is expensive
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure you want to get your how much
+
+ align:start position:0%
+sure you want to get your how much
+ 
+
+ align:start position:0%
+sure you want to get your how much
+detail do you want how it actually works
+
+ align:start position:0%
+detail do you want how it actually works
+ 
+
+ align:start position:0%
+detail do you want how it actually works
+okay so what it's supposed to do is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's supposed to do is figure out how
+
+ align:start position:0%
+what's supposed to do is figure out how
+ 
+
+ align:start position:0%
+what's supposed to do is figure out how
+safe what you're the idea is I want my
+
+ align:start position:0%
+safe what you're the idea is I want my
+ 
+
+ align:start position:0%
+safe what you're the idea is I want my
+laser to get closer to your King and I
+
+ align:start position:0%
+laser to get closer to your King and I
+ 
+
+ align:start position:0%
+laser to get closer to your King and I
+want your laser not to be close to my
+
+ align:start position:0%
+want your laser not to be close to my
+ 
+
+ align:start position:0%
+want your laser not to be close to my
+king
+
+ align:start position:0%
+king
+ 
+
+ align:start position:0%
+king
+right and if I can move into positions
+
+ align:start position:0%
+right and if I can move into positions
+ 
+
+ align:start position:0%
+right and if I can move into positions
+where my laser is closer to your King
+
+ align:start position:0%
+where my laser is closer to your King
+ 
+
+ align:start position:0%
+where my laser is closer to your King
+but your laser doesn't get closer to my
+
+ align:start position:0%
+but your laser doesn't get closer to my
+ 
+
+ align:start position:0%
+but your laser doesn't get closer to my
+King that's a good sort of thing but
+
+ align:start position:0%
+King that's a good sort of thing but
+ 
+
+ align:start position:0%
+King that's a good sort of thing but
+when we say get the laser close you know
+
+ align:start position:0%
+when we say get the laser close you know
+ 
+
+ align:start position:0%
+when we say get the laser close you know
+what happens when I've got say let me do
+
+ align:start position:0%
+what happens when I've got say let me do
+ 
+
+ align:start position:0%
+what happens when I've got say let me do
+it this way a position like this so
+
+ align:start position:0%
+it this way a position like this so
+ 
+
+ align:start position:0%
+it this way a position like this so
+here's the okay suppose I look at this
+
+ align:start position:0%
+here's the okay suppose I look at this
+ 
+
+ align:start position:0%
+here's the okay suppose I look at this
+position how close does the laser get
+
+ align:start position:0%
+position how close does the laser get
+ 
+
+ align:start position:0%
+position how close does the laser get
+Mike let's say I'm black here and I look
+
+ align:start position:0%
+Mike let's say I'm black here and I look
+ 
+
+ align:start position:0%
+Mike let's say I'm black here and I look
+at the laser well the path of the laser
+
+ align:start position:0%
+at the laser well the path of the laser
+ 
+
+ align:start position:0%
+at the laser well the path of the laser
+is it bounces there and goes across
+
+ align:start position:0%
+is it bounces there and goes across
+ 
+
+ align:start position:0%
+is it bounces there and goes across
+right okay so I didn't get very close to
+
+ align:start position:0%
+right okay so I didn't get very close to
+ 
+
+ align:start position:0%
+right okay so I didn't get very close to
+the King there but I'm one move away
+
+ align:start position:0%
+the King there but I'm one move away
+ 
+
+ align:start position:0%
+the King there but I'm one move away
+from getting it pretty close because if
+
+ align:start position:0%
+from getting it pretty close because if
+ 
+
+ align:start position:0%
+from getting it pretty close because if
+I just move this guy out of the way now
+
+ align:start position:0%
+I just move this guy out of the way now
+ 
+
+ align:start position:0%
+I just move this guy out of the way now
+I've got it really quite close okay so
+
+ align:start position:0%
+I've got it really quite close okay so
+ 
+
+ align:start position:0%
+I've got it really quite close okay so
+if I compare that to let's say a
+
+ align:start position:0%
+if I compare that to let's say a
+ 
+
+ align:start position:0%
+if I compare that to let's say a
+situation where instead of the the
+
+ align:start position:0%
+situation where instead of the the
+ 
+
+ align:start position:0%
+situation where instead of the the
+plants are there let's say a pawn is
+
+ align:start position:0%
+plants are there let's say a pawn is
+ 
+
+ align:start position:0%
+plants are there let's say a pawn is
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+now the laser is actually closer to the
+
+ align:start position:0%
+now the laser is actually closer to the
+ 
+
+ align:start position:0%
+now the laser is actually closer to the
+King that it was in the first position
+
+ align:start position:0%
+King that it was in the first position
+ 
+
+ align:start position:0%
+King that it was in the first position
+but it's a much worse position right the
+
+ align:start position:0%
+but it's a much worse position right the
+ 
+
+ align:start position:0%
+but it's a much worse position right the
+first one was much better when I had the
+
+ align:start position:0%
+first one was much better when I had the
+ 
+
+ align:start position:0%
+first one was much better when I had the
+pawns here and here because I was simply
+
+ align:start position:0%
+pawns here and here because I was simply
+ 
+
+ align:start position:0%
+pawns here and here because I was simply
+one move away from getting it really
+
+ align:start position:0%
+one move away from getting it really
+ 
+
+ align:start position:0%
+one move away from getting it really
+close and so if you use just the direct
+
+ align:start position:0%
+close and so if you use just the direct
+ 
+
+ align:start position:0%
+close and so if you use just the direct
+laser thing and we did some tests on
+
+ align:start position:0%
+laser thing and we did some tests on
+ 
+
+ align:start position:0%
+laser thing and we did some tests on
+this this turns out to be not very it
+
+ align:start position:0%
+this this turns out to be not very it
+ 
+
+ align:start position:0%
+this this turns out to be not very it
+doesn't guide the program very well on
+
+ align:start position:0%
+doesn't guide the program very well on
+ 
+
+ align:start position:0%
+doesn't guide the program very well on
+getting into situations where my laser
+
+ align:start position:0%
+getting into situations where my laser
+ 
+
+ align:start position:0%
+getting into situations where my laser
+is getting close to your king
+
+ align:start position:0%
+is getting close to your king
+ 
+
+ align:start position:0%
+is getting close to your king
+that makes sense so then we said well
+
+ align:start position:0%
+that makes sense so then we said well
+ 
+
+ align:start position:0%
+that makes sense so then we said well
+how can we you know how should we
+
+ align:start position:0%
+how can we you know how should we
+ 
+
+ align:start position:0%
+how can we you know how should we
+measure on how close the laser get so
+
+ align:start position:0%
+measure on how close the laser get so
+ 
+
+ align:start position:0%
+measure on how close the laser get so
+what we said is well let's take a look
+
+ align:start position:0%
+what we said is well let's take a look
+ 
+
+ align:start position:0%
+what we said is well let's take a look
+at all the possible moves from here of
+
+ align:start position:0%
+at all the possible moves from here of
+ 
+
+ align:start position:0%
+at all the possible moves from here of
+one move you know and then look to see
+
+ align:start position:0%
+one move you know and then look to see
+ 
+
+ align:start position:0%
+one move you know and then look to see
+how close we get things and the way we
+
+ align:start position:0%
+how close we get things and the way we
+ 
+
+ align:start position:0%
+how close we get things and the way we
+did that is we said let's you know this
+
+ align:start position:0%
+did that is we said let's you know this
+ 
+
+ align:start position:0%
+did that is we said let's you know this
+took actually Helen and I worked on this
+
+ align:start position:0%
+took actually Helen and I worked on this
+ 
+
+ align:start position:0%
+took actually Helen and I worked on this
+really hard okay because this is a new
+
+ align:start position:0%
+really hard okay because this is a new
+ 
+
+ align:start position:0%
+really hard okay because this is a new
+heuristic that we have not used in
+
+ align:start position:0%
+heuristic that we have not used in
+ 
+
+ align:start position:0%
+heuristic that we have not used in
+previous years and it works great it's
+
+ align:start position:0%
+previous years and it works great it's
+ 
+
+ align:start position:0%
+previous years and it works great it's
+just slow as anything okay but it works
+
+ align:start position:0%
+just slow as anything okay but it works
+ 
+
+ align:start position:0%
+just slow as anything okay but it works
+well so you have to evaluate is it worth
+
+ align:start position:0%
+well so you have to evaluate is it worth
+ 
+
+ align:start position:0%
+well so you have to evaluate is it worth
+doing something if it's really slow it
+
+ align:start position:0%
+doing something if it's really slow it
+ 
+
+ align:start position:0%
+doing something if it's really slow it
+may be that you do better to use a
+
+ align:start position:0%
+may be that you do better to use a
+ 
+
+ align:start position:0%
+may be that you do better to use a
+simpler heuristic and get deeper search
+
+ align:start position:0%
+simpler heuristic and get deeper search
+ 
+
+ align:start position:0%
+simpler heuristic and get deeper search
+than it is spending a lot of time
+
+ align:start position:0%
+than it is spending a lot of time
+ 
+
+ align:start position:0%
+than it is spending a lot of time
+evaluating but anyway we gave you one
+
+ align:start position:0%
+evaluating but anyway we gave you one
+ 
+
+ align:start position:0%
+evaluating but anyway we gave you one
+that if you can make it go fast should
+
+ align:start position:0%
+that if you can make it go fast should
+ 
+
+ align:start position:0%
+that if you can make it go fast should
+be really good so what the idea is that
+
+ align:start position:0%
+be really good so what the idea is that
+ 
+
+ align:start position:0%
+be really good so what the idea is that
+what we do is we look at all the
+
+ align:start position:0%
+what we do is we look at all the
+ 
+
+ align:start position:0%
+what we do is we look at all the
+different paths from moving any piece
+
+ align:start position:0%
+different paths from moving any piece
+ 
+
+ align:start position:0%
+different paths from moving any piece
+want you know one piece and look at the
+
+ align:start position:0%
+want you know one piece and look at the
+ 
+
+ align:start position:0%
+want you know one piece and look at the
+paths of the laser and what we do is we
+
+ align:start position:0%
+paths of the laser and what we do is we
+ 
+
+ align:start position:0%
+paths of the laser and what we do is we
+go we count one for every position that
+
+ align:start position:0%
+go we count one for every position that
+ 
+
+ align:start position:0%
+go we count one for every position that
+we go away 2 3 4 5 6 7 etc we actually
+
+ align:start position:0%
+we go away 2 3 4 5 6 7 etc we actually
+ 
+
+ align:start position:0%
+we go away 2 3 4 5 6 7 etc we actually
+add an extra value if we bounce off in
+
+ align:start position:0%
+add an extra value if we bounce off in
+ 
+
+ align:start position:0%
+add an extra value if we bounce off in
+an opponent's how much do we add Helen
+
+ align:start position:0%
+an opponent's how much do we add Helen
+ 
+
+ align:start position:0%
+an opponent's how much do we add Helen
+do we add one or two if we bounce off an
+
+ align:start position:0%
+do we add one or two if we bounce off an
+ 
+
+ align:start position:0%
+do we add one or two if we bounce off an
+opponent I think - yeah so if this is an
+
+ align:start position:0%
+opponent I think - yeah so if this is an
+ 
+
+ align:start position:0%
+opponent I think - yeah so if this is an
+opponent's pawn we would basically go
+
+ align:start position:0%
+opponent's pawn we would basically go
+ 
+
+ align:start position:0%
+opponent's pawn we would basically go
+from 3 to 5 6 7 you know 8 9 and we
+
+ align:start position:0%
+from 3 to 5 6 7 you know 8 9 and we
+ 
+
+ align:start position:0%
+from 3 to 5 6 7 you know 8 9 and we
+basically do that for all the moves and
+
+ align:start position:0%
+basically do that for all the moves and
+ 
+
+ align:start position:0%
+basically do that for all the moves and
+the way we combine them is we take the
+
+ align:start position:0%
+the way we combine them is we take the
+ 
+
+ align:start position:0%
+the way we combine them is we take the
+minimum number that I can get there ok
+
+ align:start position:0%
+minimum number that I can get there ok
+ 
+
+ align:start position:0%
+minimum number that I can get there ok
+what's the what's the cheapest way I can
+
+ align:start position:0%
+what's the what's the cheapest way I can
+ 
+
+ align:start position:0%
+what's the what's the cheapest way I can
+get to every every square that the laser
+
+ align:start position:0%
+get to every every square that the laser
+ 
+
+ align:start position:0%
+get to every every square that the laser
+goes so we take all the different moves
+
+ align:start position:0%
+goes so we take all the different moves
+ 
+
+ align:start position:0%
+goes so we take all the different moves
+we stroke them out and we take the
+
+ align:start position:0%
+we stroke them out and we take the
+ 
+
+ align:start position:0%
+we stroke them out and we take the
+minimum so if I have another path let's
+
+ align:start position:0%
+minimum so if I have another path let's
+ 
+
+ align:start position:0%
+minimum so if I have another path let's
+say by turning the king it will go this
+
+ align:start position:0%
+say by turning the king it will go this
+ 
+
+ align:start position:0%
+say by turning the king it will go this
+way and there's a you know there's
+
+ align:start position:0%
+way and there's a you know there's
+ 
+
+ align:start position:0%
+way and there's a you know there's
+another one here that's my pawn ok then
+
+ align:start position:0%
+another one here that's my pawn ok then
+ 
+
+ align:start position:0%
+another one here that's my pawn ok then
+I may get there in 1 2 3 4 5 6 7 and so
+
+ align:start position:0%
+I may get there in 1 2 3 4 5 6 7 and so
+ 
+
+ align:start position:0%
+I may get there in 1 2 3 4 5 6 7 and so
+then this would become a value of 7 here
+
+ align:start position:0%
+then this would become a value of 7 here
+ 
+
+ align:start position:0%
+then this would become a value of 7 here
+okay so that's the first thing is we
+
+ align:start position:0%
+okay so that's the first thing is we
+ 
+
+ align:start position:0%
+okay so that's the first thing is we
+basically get a map of you know how
+
+ align:start position:0%
+basically get a map of you know how
+ 
+
+ align:start position:0%
+basically get a map of you know how
+close are things and the second thing we
+
+ align:start position:0%
+close are things and the second thing we
+ 
+
+ align:start position:0%
+close are things and the second thing we
+do is say well how valuable is it to
+
+ align:start position:0%
+do is say well how valuable is it to
+ 
+
+ align:start position:0%
+do is say well how valuable is it to
+have these these you know to be near the
+
+ align:start position:0%
+have these these you know to be near the
+ 
+
+ align:start position:0%
+have these these you know to be near the
+particular King and then what we ended
+
+ align:start position:0%
+particular King and then what we ended
+ 
+
+ align:start position:0%
+particular King and then what we ended
+up with is something where if I look at
+
+ align:start position:0%
+up with is something where if I look at
+ 
+
+ align:start position:0%
+up with is something where if I look at
+the if I look at the distance that I am
+
+ align:start position:0%
+the if I look at the distance that I am
+ 
+
+ align:start position:0%
+the if I look at the distance that I am
+away let's say this one for example is
+
+ align:start position:0%
+away let's say this one for example is
+ 
+
+ align:start position:0%
+away let's say this one for example is
+one row in one column away this is zero
+
+ align:start position:0%
+one row in one column away this is zero
+ 
+
+ align:start position:0%
+one row in one column away this is zero
+row zero columns we use I think it's one
+
+ align:start position:0%
+row zero columns we use I think it's one
+ 
+
+ align:start position:0%
+row zero columns we use I think it's one
+over the row plus one times one over the
+
+ align:start position:0%
+over the row plus one times one over the
+ 
+
+ align:start position:0%
+over the row plus one times one over the
+column plus one okay as a multiplier to
+
+ align:start position:0%
+column plus one okay as a multiplier to
+ 
+
+ align:start position:0%
+column plus one okay as a multiplier to
+wait how good it is that we've been
+
+ align:start position:0%
+wait how good it is that we've been
+ 
+
+ align:start position:0%
+wait how good it is that we've been
+close to the king and we invert these
+
+ align:start position:0%
+close to the king and we invert these
+ 
+
+ align:start position:0%
+close to the king and we invert these
+values so that they're you know so the
+
+ align:start position:0%
+values so that they're you know so the
+ 
+
+ align:start position:0%
+values so that they're you know so the
+closer you you know so that it's better
+
+ align:start position:0%
+closer you you know so that it's better
+ 
+
+ align:start position:0%
+closer you you know so that it's better
+to have a smaller number there and we
+
+ align:start position:0%
+to have a smaller number there and we
+ 
+
+ align:start position:0%
+to have a smaller number there and we
+add them up okay and that basically
+
+ align:start position:0%
+add them up okay and that basically
+ 
+
+ align:start position:0%
+add them up okay and that basically
+gives we I don't quite add them up we
+
+ align:start position:0%
+gives we I don't quite add them up we
+ 
+
+ align:start position:0%
+gives we I don't quite add them up we
+actually no I'm sorry what we do is we
+
+ align:start position:0%
+actually no I'm sorry what we do is we
+ 
+
+ align:start position:0%
+actually no I'm sorry what we do is we
+look at these things as a fraction of my
+
+ align:start position:0%
+look at these things as a fraction of my
+ 
+
+ align:start position:0%
+look at these things as a fraction of my
+shortest path distance sorry that's what
+
+ align:start position:0%
+shortest path distance sorry that's what
+ 
+
+ align:start position:0%
+shortest path distance sorry that's what
+we did yes I'm sorry that is a previous
+
+ align:start position:0%
+we did yes I'm sorry that is a previous
+ 
+
+ align:start position:0%
+we did yes I'm sorry that is a previous
+sourcing so so here for example let's
+
+ align:start position:0%
+sourcing so so here for example let's
+ 
+
+ align:start position:0%
+sourcing so so here for example let's
+say this is the nine the shortest way of
+
+ align:start position:0%
+say this is the nine the shortest way of
+ 
+
+ align:start position:0%
+say this is the nine the shortest way of
+getting there is one two three four five
+
+ align:start position:0%
+getting there is one two three four five
+ 
+
+ align:start position:0%
+getting there is one two three four five
+six seven eight
+
+ align:start position:0%
+six seven eight
+ 
+
+ align:start position:0%
+six seven eight
+so this would actually when we do the
+
+ align:start position:0%
+so this would actually when we do the
+ 
+
+ align:start position:0%
+so this would actually when we do the
+conversion this would we give a value of
+
+ align:start position:0%
+conversion this would we give a value of
+ 
+
+ align:start position:0%
+conversion this would we give a value of
+eight ninths for being in that square
+
+ align:start position:0%
+eight ninths for being in that square
+ 
+
+ align:start position:0%
+eight ninths for being in that square
+okay so we didn't get it where's this
+
+ align:start position:0%
+okay so we didn't get it where's this
+ 
+
+ align:start position:0%
+okay so we didn't get it where's this
+one the shortest path distance is 7
+
+ align:start position:0%
+one the shortest path distance is 7
+ 
+
+ align:start position:0%
+one the shortest path distance is 7
+because of this path and you can get
+
+ align:start position:0%
+because of this path and you can get
+ 
+
+ align:start position:0%
+because of this path and you can get
+there and seven this would have a value
+
+ align:start position:0%
+there and seven this would have a value
+ 
+
+ align:start position:0%
+there and seven this would have a value
+of one so this is better you know and so
+
+ align:start position:0%
+of one so this is better you know and so
+ 
+
+ align:start position:0%
+of one so this is better you know and so
+we do that for all the squares we get a
+
+ align:start position:0%
+we do that for all the squares we get a
+ 
+
+ align:start position:0%
+we do that for all the squares we get a
+fraction of how much do we do and then
+
+ align:start position:0%
+fraction of how much do we do and then
+ 
+
+ align:start position:0%
+fraction of how much do we do and then
+we wait it by something like this which
+
+ align:start position:0%
+we wait it by something like this which
+ 
+
+ align:start position:0%
+we wait it by something like this which
+falls away quickly but it's important in
+
+ align:start position:0%
+falls away quickly but it's important in
+ 
+
+ align:start position:0%
+falls away quickly but it's important in
+heuristics like this to have a smooth
+
+ align:start position:0%
+heuristics like this to have a smooth
+ 
+
+ align:start position:0%
+heuristics like this to have a smooth
+path so that you can get things closer
+
+ align:start position:0%
+path so that you can get things closer
+ 
+
+ align:start position:0%
+path so that you can get things closer
+if I made all these things be 0 it
+
+ align:start position:0%
+if I made all these things be 0 it
+ 
+
+ align:start position:0%
+if I made all these things be 0 it
+wouldn't know that it could you know
+
+ align:start position:0%
+wouldn't know that it could you know
+ 
+
+ align:start position:0%
+wouldn't know that it could you know
+move up and get a little bit better you
+
+ align:start position:0%
+move up and get a little bit better you
+ 
+
+ align:start position:0%
+move up and get a little bit better you
+know in the second or third order
+
+ align:start position:0%
+know in the second or third order
+ 
+
+ align:start position:0%
+know in the second or third order
+you know digit to get closer and so then
+
+ align:start position:0%
+you know digit to get closer and so then
+ 
+
+ align:start position:0%
+you know digit to get closer and so then
+we add it all up and that ends up being
+
+ align:start position:0%
+we add it all up and that ends up being
+ 
+
+ align:start position:0%
+we add it all up and that ends up being
+a number we discovered that sort of in
+
+ align:start position:0%
+a number we discovered that sort of in
+ 
+
+ align:start position:0%
+a number we discovered that sort of in
+the range of
+
+ align:start position:0%
+the range of
+ 
+
+ align:start position:0%
+the range of
+you know you know like what did we
+
+ align:start position:0%
+you know you know like what did we
+ 
+
+ align:start position:0%
+you know you know like what did we
+figure the range was there there's like
+
+ align:start position:0%
+figure the range was there there's like
+ 
+
+ align:start position:0%
+figure the range was there there's like
+you know up to like four or so right
+
+ align:start position:0%
+you know up to like four or so right
+ 
+
+ align:start position:0%
+you know up to like four or so right
+something something like four on average
+
+ align:start position:0%
+something something like four on average
+ 
+
+ align:start position:0%
+something something like four on average
+you know would be the maximum value
+
+ align:start position:0%
+you know would be the maximum value
+ 
+
+ align:start position:0%
+you know would be the maximum value
+would be and then we said okay then we
+
+ align:start position:0%
+would be and then we said okay then we
+ 
+
+ align:start position:0%
+would be and then we said okay then we
+have this magic constant multiplier that
+
+ align:start position:0%
+have this magic constant multiplier that
+ 
+
+ align:start position:0%
+have this magic constant multiplier that
+you can play with that says okay let's
+
+ align:start position:0%
+you can play with that says okay let's
+ 
+
+ align:start position:0%
+you can play with that says okay let's
+represent that as a fraction of a pawn
+
+ align:start position:0%
+represent that as a fraction of a pawn
+ 
+
+ align:start position:0%
+represent that as a fraction of a pawn
+how much is that worth and we multiply
+
+ align:start position:0%
+how much is that worth and we multiply
+ 
+
+ align:start position:0%
+how much is that worth and we multiply
+by that value okay so that's what we're
+
+ align:start position:0%
+by that value okay so that's what we're
+ 
+
+ align:start position:0%
+by that value okay so that's what we're
+doing okay so that it makes it so that
+
+ align:start position:0%
+doing okay so that it makes it so that
+ 
+
+ align:start position:0%
+doing okay so that it makes it so that
+we do tend to move the laser our laser
+
+ align:start position:0%
+we do tend to move the laser our laser
+ 
+
+ align:start position:0%
+we do tend to move the laser our laser
+closer we subtract how close the
+
+ align:start position:0%
+closer we subtract how close the
+ 
+
+ align:start position:0%
+closer we subtract how close the
+opponent can get from us and then we say
+
+ align:start position:0%
+opponent can get from us and then we say
+ 
+
+ align:start position:0%
+opponent can get from us and then we say
+that's the evaluation now if you have a
+
+ align:start position:0%
+that's the evaluation now if you have a
+ 
+
+ align:start position:0%
+that's the evaluation now if you have a
+better way of determining whether a
+
+ align:start position:0%
+better way of determining whether a
+ 
+
+ align:start position:0%
+better way of determining whether a
+laser is getting close than this one
+
+ align:start position:0%
+laser is getting close than this one
+ 
+
+ align:start position:0%
+laser is getting close than this one
+that's cheaper to compute that's good
+
+ align:start position:0%
+that's cheaper to compute that's good
+ 
+
+ align:start position:0%
+that's cheaper to compute that's good
+okay for first pass I would just simply
+
+ align:start position:0%
+okay for first pass I would just simply
+ 
+
+ align:start position:0%
+okay for first pass I would just simply
+try to make this go fast because for
+
+ align:start position:0%
+try to make this go fast because for
+ 
+
+ align:start position:0%
+try to make this go fast because for
+many of the moves that you're going to
+
+ align:start position:0%
+many of the moves that you're going to
+ 
+
+ align:start position:0%
+many of the moves that you're going to
+look at is going to be moving this pawn
+
+ align:start position:0%
+look at is going to be moving this pawn
+ 
+
+ align:start position:0%
+look at is going to be moving this pawn
+you know to there nothing changed
+
+ align:start position:0%
+you know to there nothing changed
+ 
+
+ align:start position:0%
+you know to there nothing changed
+there's no point in there stroking this
+
+ align:start position:0%
+there's no point in there stroking this
+ 
+
+ align:start position:0%
+there's no point in there stroking this
+out and cakung are the minimum etc
+
+ align:start position:0%
+out and cakung are the minimum etc
+ 
+
+ align:start position:0%
+out and cakung are the minimum etc
+because i didn't touch the laser path
+
+ align:start position:0%
+because i didn't touch the laser path
+ 
+
+ align:start position:0%
+because i didn't touch the laser path
+things are gonna touch a laser path are
+
+ align:start position:0%
+things are gonna touch a laser path are
+ 
+
+ align:start position:0%
+things are gonna touch a laser path are
+things that you move on or off the path
+
+ align:start position:0%
+things that you move on or off the path
+ 
+
+ align:start position:0%
+things that you move on or off the path
+so why bother okay and so if there's a
+
+ align:start position:0%
+so why bother okay and so if there's a
+ 
+
+ align:start position:0%
+so why bother okay and so if there's a
+clever way of hashing this you know so
+
+ align:start position:0%
+clever way of hashing this you know so
+ 
+
+ align:start position:0%
+clever way of hashing this you know so
+that you're caching it so that you can
+
+ align:start position:0%
+that you're caching it so that you can
+ 
+
+ align:start position:0%
+that you're caching it so that you can
+you know do things that's good too
+
+ align:start position:0%
+you know do things that's good too
+ 
+
+ align:start position:0%
+you know do things that's good too
+okay any questions about other things
+
+ align:start position:0%
+okay any questions about other things
+ 
+
+ align:start position:0%
+okay any questions about other things
+that could be done so another place I'll
+
+ align:start position:0%
+that could be done so another place I'll
+ 
+
+ align:start position:0%
+that could be done so another place I'll
+tell you that's a good idea to look at
+
+ align:start position:0%
+tell you that's a good idea to look at
+ 
+
+ align:start position:0%
+tell you that's a good idea to look at
+is especially once you get this
+
+ align:start position:0%
+is especially once you get this
+ 
+
+ align:start position:0%
+is especially once you get this
+heuristic operate a little bit faster is
+
+ align:start position:0%
+heuristic operate a little bit faster is
+ 
+
+ align:start position:0%
+heuristic operate a little bit faster is
+the sorting of moves okay is is actually
+
+ align:start position:0%
+the sorting of moves okay is is actually
+ 
+
+ align:start position:0%
+the sorting of moves okay is is actually
+pretty expensive
+
+ align:start position:0%
+pretty expensive
+ 
+
+ align:start position:0%
+pretty expensive
+okay what's the you know once you figure
+
+ align:start position:0%
+okay what's the you know once you figure
+ 
+
+ align:start position:0%
+okay what's the you know once you figure
+out here all the moves there are a lot
+
+ align:start position:0%
+out here all the moves there are a lot
+ 
+
+ align:start position:0%
+out here all the moves there are a lot
+of moves now you go through and you do a
+
+ align:start position:0%
+of moves now you go through and you do a
+ 
+
+ align:start position:0%
+of moves now you go through and you do a
+sort and if you think about it you know
+
+ align:start position:0%
+sort and if you think about it you know
+ 
+
+ align:start position:0%
+sort and if you think about it you know
+in a best move order tree sometimes you
+
+ align:start position:0%
+in a best move order tree sometimes you
+ 
+
+ align:start position:0%
+in a best move order tree sometimes you
+only explore one of those so why'd you
+
+ align:start position:0%
+only explore one of those so why'd you
+ 
+
+ align:start position:0%
+only explore one of those so why'd you
+bother sorting all of them okay on the
+
+ align:start position:0%
+bother sorting all of them okay on the
+ 
+
+ align:start position:0%
+bother sorting all of them okay on the
+other hand sometimes you do need to sort
+
+ align:start position:0%
+other hand sometimes you do need to sort
+ 
+
+ align:start position:0%
+other hand sometimes you do need to sort
+all of them so how you optimize that
+
+ align:start position:0%
+all of them so how you optimize that
+ 
+
+ align:start position:0%
+all of them so how you optimize that
+sort so that you don't waste time
+
+ align:start position:0%
+sort so that you don't waste time
+ 
+
+ align:start position:0%
+sort so that you don't waste time
+sorting stuff that you're not going to
+
+ align:start position:0%
+sorting stuff that you're not going to
+ 
+
+ align:start position:0%
+sorting stuff that you're not going to
+actually ever explore
+
+ align:start position:0%
+actually ever explore
+ 
+
+ align:start position:0%
+actually ever explore
+another opportunity for optimization
+
+ align:start position:0%
+another opportunity for optimization
+ 
+
+ align:start position:0%
+another opportunity for optimization
+okay yeah question the moves are sorted
+
+ align:start position:0%
+okay yeah question the moves are sorted
+ 
+
+ align:start position:0%
+okay yeah question the moves are sorted
+by these things like that there there's
+
+ align:start position:0%
+by these things like that there there's
+ 
+
+ align:start position:0%
+by these things like that there there's
+a sort key in there that represents a
+
+ align:start position:0%
+a sort key in there that represents a
+ 
+
+ align:start position:0%
+a sort key in there that represents a
+whole bunch of things like whether it
+
+ align:start position:0%
+whole bunch of things like whether it
+ 
+
+ align:start position:0%
+whole bunch of things like whether it
+was a killer if it's a killer or it's a
+
+ align:start position:0%
+was a killer if it's a killer or it's a
+ 
+
+ align:start position:0%
+was a killer if it's a killer or it's a
+transposition table value gets a very
+
+ align:start position:0%
+transposition table value gets a very
+ 
+
+ align:start position:0%
+transposition table value gets a very
+big value if it's a statistical thing
+
+ align:start position:0%
+big value if it's a statistical thing
+ 
+
+ align:start position:0%
+big value if it's a statistical thing
+that the history table says in
+
+ align:start position:0%
+that the history table says in
+ 
+
+ align:start position:0%
+that the history table says in
+historically this has been a pretty good
+
+ align:start position:0%
+historically this has been a pretty good
+ 
+
+ align:start position:0%
+historically this has been a pretty good
+move then you get another value and then
+
+ align:start position:0%
+move then you get another value and then
+ 
+
+ align:start position:0%
+move then you get another value and then
+exchanges get ordered and so forth so
+
+ align:start position:0%
+exchanges get ordered and so forth so
+ 
+
+ align:start position:0%
+exchanges get ordered and so forth so
+there's a bunch of things that are you
+
+ align:start position:0%
+there's a bunch of things that are you
+ 
+
+ align:start position:0%
+there's a bunch of things that are you
+know where where you end up with
+
+ align:start position:0%
+know where where you end up with
+ 
+
+ align:start position:0%
+know where where you end up with
+information and then it sorts those
+
+ align:start position:0%
+information and then it sorts those
+ 
+
+ align:start position:0%
+information and then it sorts those
+things okay so that's actually kind of
+
+ align:start position:0%
+things okay so that's actually kind of
+ 
+
+ align:start position:0%
+things okay so that's actually kind of
+complicated logic in terms of what the
+
+ align:start position:0%
+complicated logic in terms of what the
+ 
+
+ align:start position:0%
+complicated logic in terms of what the
+actual values are that are used there
+
+ align:start position:0%
+actual values are that are used there
+ 
+
+ align:start position:0%
+actual values are that are used there
+but the idea is you know here all the
+
+ align:start position:0%
+but the idea is you know here all the
+ 
+
+ align:start position:0%
+but the idea is you know here all the
+moves now let's figure out what's the
+
+ align:start position:0%
+moves now let's figure out what's the
+ 
+
+ align:start position:0%
+moves now let's figure out what's the
+best our best guess as to what they are
+
+ align:start position:0%
+best our best guess as to what they are
+ 
+
+ align:start position:0%
+best our best guess as to what they are
+most of the good moves are coming out of
+
+ align:start position:0%
+most of the good moves are coming out of
+ 
+
+ align:start position:0%
+most of the good moves are coming out of
+the transposition table right
+
+ align:start position:0%
+the transposition table right
+ 
+
+ align:start position:0%
+the transposition table right
+but sometimes the transposition table
+
+ align:start position:0%
+but sometimes the transposition table
+ 
+
+ align:start position:0%
+but sometimes the transposition table
+you know it's not it says it's not a
+
+ align:start position:0%
+you know it's not it says it's not a
+ 
+
+ align:start position:0%
+you know it's not it says it's not a
+very good move and there may be a better
+
+ align:start position:0%
+very good move and there may be a better
+ 
+
+ align:start position:0%
+very good move and there may be a better
+move okay so the quality of what you get
+
+ align:start position:0%
+move okay so the quality of what you get
+ 
+
+ align:start position:0%
+move okay so the quality of what you get
+out of transposition table is good but
+
+ align:start position:0%
+out of transposition table is good but
+ 
+
+ align:start position:0%
+out of transposition table is good but
+doesn't mean you know that that's always
+
+ align:start position:0%
+doesn't mean you know that that's always
+ 
+
+ align:start position:0%
+doesn't mean you know that that's always
+the best move okay yeah any other
+
+ align:start position:0%
+the best move okay yeah any other
+ 
+
+ align:start position:0%
+the best move okay yeah any other
+questions about what should be worked on
+
+ align:start position:0%
+questions about what should be worked on
+ 
+
+ align:start position:0%
+questions about what should be worked on
+let me just make sure I okay go ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where does the sorting happen that
+
+ align:start position:0%
+where does the sorting happen that
+ 
+
+ align:start position:0%
+where does the sorting happen that
+happens at the I think at the move
+
+ align:start position:0%
+happens at the I think at the move
+ 
+
+ align:start position:0%
+happens at the I think at the move
+generation is that where it is is the
+
+ align:start position:0%
+generation is that where it is is the
+ 
+
+ align:start position:0%
+generation is that where it is is the
+sort in the move generation or is it in
+
+ align:start position:0%
+sort in the move generation or is it in
+ 
+
+ align:start position:0%
+sort in the move generation or is it in
+search I think it's in search I think
+
+ align:start position:0%
+search I think it's in search I think
+ 
+
+ align:start position:0%
+search I think it's in search I think
+you're right
+
+ align:start position:0%
+you're right
+ 
+
+ align:start position:0%
+you're right
+search calls move generation and then
+
+ align:start position:0%
+search calls move generation and then
+ 
+
+ align:start position:0%
+search calls move generation and then
+sorts it okay I think that's right
+
+ align:start position:0%
+sorts it okay I think that's right
+ 
+
+ align:start position:0%
+sorts it okay I think that's right
+yeah question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+very tiny board implementation yes well
+
+ align:start position:0%
+very tiny board implementation yes well
+ 
+
+ align:start position:0%
+very tiny board implementation yes well
+as I say keep the old one around well I
+
+ align:start position:0%
+as I say keep the old one around well I
+ 
+
+ align:start position:0%
+as I say keep the old one around well I
+you use the old one while you're still
+
+ align:start position:0%
+you use the old one while you're still
+ 
+
+ align:start position:0%
+you use the old one while you're still
+getting the new one right okay it's also
+
+ align:start position:0%
+getting the new one right okay it's also
+ 
+
+ align:start position:0%
+getting the new one right okay it's also
+good to be able to go from old
+
+ align:start position:0%
+good to be able to go from old
+ 
+
+ align:start position:0%
+good to be able to go from old
+representation to new representation and
+
+ align:start position:0%
+representation to new representation and
+ 
+
+ align:start position:0%
+representation to new representation and
+having conversion functions okay but
+
+ align:start position:0%
+having conversion functions okay but
+ 
+
+ align:start position:0%
+having conversion functions okay but
+yeah making representation changes you
+
+ align:start position:0%
+yeah making representation changes you
+ 
+
+ align:start position:0%
+yeah making representation changes you
+know painful painful and is it's
+
+ align:start position:0%
+know painful painful and is it's
+ 
+
+ align:start position:0%
+know painful painful and is it's
+probably boy if there was one tool I
+
+ align:start position:0%
+probably boy if there was one tool I
+ 
+
+ align:start position:0%
+probably boy if there was one tool I
+would love that would automate stuff
+
+ align:start position:0%
+would love that would automate stuff
+ 
+
+ align:start position:0%
+would love that would automate stuff
+like that that would be it you know to
+
+ align:start position:0%
+like that that would be it you know to
+ 
+
+ align:start position:0%
+like that that would be it you know to
+be able to change representations of
+
+ align:start position:0%
+be able to change representations of
+ 
+
+ align:start position:0%
+be able to change representations of
+things and still have things go well I
+
+ align:start position:0%
+things and still have things go well I
+ 
+
+ align:start position:0%
+things and still have things go well I
+should have mentioned by the way the
+
+ align:start position:0%
+should have mentioned by the way the
+ 
+
+ align:start position:0%
+should have mentioned by the way the
+other representation besides bit board
+
+ align:start position:0%
+other representation besides bit board
+ 
+
+ align:start position:0%
+other representation besides bit board
+another one is just to keep a list of
+
+ align:start position:0%
+another one is just to keep a list of
+ 
+
+ align:start position:0%
+another one is just to keep a list of
+the pieces and their positions okay
+
+ align:start position:0%
+the pieces and their positions okay
+ 
+
+ align:start position:0%
+the pieces and their positions okay
+because that's going to be smaller than
+
+ align:start position:0%
+because that's going to be smaller than
+ 
+
+ align:start position:0%
+because that's going to be smaller than
+keeping this great big board okay then
+
+ align:start position:0%
+keeping this great big board okay then
+ 
+
+ align:start position:0%
+keeping this great big board okay then
+you keep this list sorted or do you not
+
+ align:start position:0%
+you keep this list sorted or do you not
+ 
+
+ align:start position:0%
+you keep this list sorted or do you not
+keep it sorted and do you but the
+
+ align:start position:0%
+keep it sorted and do you but the
+ 
+
+ align:start position:0%
+keep it sorted and do you but the
+advantage of that is particularly as the
+
+ align:start position:0%
+advantage of that is particularly as the
+ 
+
+ align:start position:0%
+advantage of that is particularly as the
+game goes on that list gets shorter and
+
+ align:start position:0%
+game goes on that list gets shorter and
+ 
+
+ align:start position:0%
+game goes on that list gets shorter and
+shorter okay and so so you're you know
+
+ align:start position:0%
+shorter okay and so so you're you know
+ 
+
+ align:start position:0%
+shorter okay and so so you're you know
+if you're doing less and manipulating
+
+ align:start position:0%
+if you're doing less and manipulating
+ 
+
+ align:start position:0%
+if you're doing less and manipulating
+the the board position that's a that's
+
+ align:start position:0%
+the the board position that's a that's
+ 
+
+ align:start position:0%
+the the board position that's a that's
+generally a good thing so for the board
+
+ align:start position:0%
+generally a good thing so for the board
+ 
+
+ align:start position:0%
+generally a good thing so for the board
+reputation my recommendation is to
+
+ align:start position:0%
+reputation my recommendation is to
+ 
+
+ align:start position:0%
+reputation my recommendation is to
+refactor all the board axes into a
+
+ align:start position:0%
+refactor all the board axes into a
+ 
+
+ align:start position:0%
+refactor all the board axes into a
+function and then you would still use
+
+ align:start position:0%
+function and then you would still use
+ 
+
+ align:start position:0%
+function and then you would still use
+the old representation in the function
+
+ align:start position:0%
+the old representation in the function
+ 
+
+ align:start position:0%
+the old representation in the function
+then you can validate that you refactor
+
+ align:start position:0%
+then you can validate that you refactor
+ 
+
+ align:start position:0%
+then you can validate that you refactor
+everything correctly and then you can
+
+ align:start position:0%
+everything correctly and then you can
+ 
+
+ align:start position:0%
+everything correctly and then you can
+easily change the board reputation to
+
+ align:start position:0%
+easily change the board reputation to
+ 
+
+ align:start position:0%
+easily change the board reputation to
+whatever you want and keep changing it
+
+ align:start position:0%
+whatever you want and keep changing it
+ 
+
+ align:start position:0%
+whatever you want and keep changing it
+without having to do a lot of refactor
+
+ align:start position:0%
+without having to do a lot of refactor
+ 
+
+ align:start position:0%
+without having to do a lot of refactor
+off that for that so find all the board
+
+ align:start position:0%
+off that for that so find all the board
+ 
+
+ align:start position:0%
+off that for that so find all the board
+accesses and refactor that to a function
+
+ align:start position:0%
+accesses and refactor that to a function
+ 
+
+ align:start position:0%
+accesses and refactor that to a function
+call before you modify it because the
+
+ align:start position:0%
+call before you modify it because the
+ 
+
+ align:start position:0%
+call before you modify it because the
+you know the compiler will inline that
+
+ align:start position:0%
+you know the compiler will inline that
+ 
+
+ align:start position:0%
+you know the compiler will inline that
+stuff so you know putting in a function
+
+ align:start position:0%
+stuff so you know putting in a function
+ 
+
+ align:start position:0%
+stuff so you know putting in a function
+call is not necessarily a bad idea and
+
+ align:start position:0%
+call is not necessarily a bad idea and
+ 
+
+ align:start position:0%
+call is not necessarily a bad idea and
+if it doesn't you can put it in a macro
+
+ align:start position:0%
+if it doesn't you can put it in a macro
+ 
+
+ align:start position:0%
+if it doesn't you can put it in a macro
+and it'll be effectively the same thing
+
+ align:start position:0%
+and it'll be effectively the same thing
+ 
+
+ align:start position:0%
+and it'll be effectively the same thing
+so great idea great idea okay yeah
+
+ align:start position:0%
+so great idea great idea okay yeah
+ 
+
+ align:start position:0%
+so great idea great idea okay yeah
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+testing testing testing you know if you
+
+ align:start position:0%
+testing testing testing you know if you
+ 
+
+ align:start position:0%
+testing testing testing you know if you
+can test and know that when you make a
+
+ align:start position:0%
+can test and know that when you make a
+ 
+
+ align:start position:0%
+can test and know that when you make a
+change it's correct you know and that
+
+ align:start position:0%
+change it's correct you know and that
+ 
+
+ align:start position:0%
+change it's correct you know and that
+you're not that's probably the number
+
+ align:start position:0%
+you're not that's probably the number
+ 
+
+ align:start position:0%
+you're not that's probably the number
+one hole that people go into is they
+
+ align:start position:0%
+one hole that people go into is they
+ 
+
+ align:start position:0%
+one hole that people go into is they
+don't test adequately so having good
+
+ align:start position:0%
+don't test adequately so having good
+ 
+
+ align:start position:0%
+don't test adequately so having good
+test infrastructure you know it's good
+
+ align:start position:0%
+test infrastructure you know it's good
+ 
+
+ align:start position:0%
+test infrastructure you know it's good
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as long as you're doing it
+
+ align:start position:0%
+as long as you're doing it
+ 
+
+ align:start position:0%
+as long as you're doing it
+deterministically yes that's because
+
+ align:start position:0%
+deterministically yes that's because
+ 
+
+ align:start position:0%
+deterministically yes that's because
+there's a randomness thing you turn off
+
+ align:start position:0%
+there's a randomness thing you turn off
+ 
+
+ align:start position:0%
+there's a randomness thing you turn off
+the ran there's a little variable you
+
+ align:start position:0%
+the ran there's a little variable you
+ 
+
+ align:start position:0%
+the ran there's a little variable you
+can set the variable to be not random
+
+ align:start position:0%
+can set the variable to be not random
+ 
+
+ align:start position:0%
+can set the variable to be not random
+and then it will be yes it's run
+
+ align:start position:0%
+and then it will be yes it's run
+ 
+
+ align:start position:0%
+and then it will be yes it's run
+serially and risk can give her the mic
+
+ align:start position:0%
+serially and risk can give her the mic
+ 
+
+ align:start position:0%
+serially and risk can give her the mic
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah juice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I got out of the opening phone I
+
+ align:start position:0%
+yeah I got out of the opening phone I
+ 
+
+ align:start position:0%
+yeah I got out of the opening phone I
+said the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah it shouldn't be if you run serially
+
+ align:start position:0%
+yeah it shouldn't be if you run serially
+ 
+
+ align:start position:0%
+yeah it shouldn't be if you run serially
+the only things that you know should be
+
+ align:start position:0%
+the only things that you know should be
+ 
+
+ align:start position:0%
+the only things that you know should be
+doing things as if you're doing I mean
+
+ align:start position:0%
+doing things as if you're doing I mean
+ 
+
+ align:start position:0%
+doing things as if you're doing I mean
+it should be deterministic if you turn
+
+ align:start position:0%
+it should be deterministic if you turn
+ 
+
+ align:start position:0%
+it should be deterministic if you turn
+off the the random number generator so
+
+ align:start position:0%
+off the the random number generator so
+ 
+
+ align:start position:0%
+off the the random number generator so
+as I say that's put in so that it will
+
+ align:start position:0%
+as I say that's put in so that it will
+ 
+
+ align:start position:0%
+as I say that's put in so that it will
+behave you know not predictably but
+
+ align:start position:0%
+behave you know not predictably but
+ 
+
+ align:start position:0%
+behave you know not predictably but
+that's exactly the kind of thing you
+
+ align:start position:0%
+that's exactly the kind of thing you
+ 
+
+ align:start position:0%
+that's exactly the kind of thing you
+want to find right at the beginning so
+
+ align:start position:0%
+want to find right at the beginning so
+ 
+
+ align:start position:0%
+want to find right at the beginning so
+as exactly things find out all the ways
+
+ align:start position:0%
+as exactly things find out all the ways
+ 
+
+ align:start position:0%
+as exactly things find out all the ways
+of making it deterministic and that
+
+ align:start position:0%
+of making it deterministic and that
+ 
+
+ align:start position:0%
+of making it deterministic and that
+would be really important for beta-2
+
+ align:start position:0%
+would be really important for beta-2
+ 
+
+ align:start position:0%
+would be really important for beta-2
+okay so Thursday okay we have you know
+
+ align:start position:0%
+okay so Thursday okay we have you know
+ 
+
+ align:start position:0%
+okay so Thursday okay we have you know
+John Bentley legend of the field
+
+ align:start position:0%
+John Bentley legend of the field
+ 
+
+ align:start position:0%
+John Bentley legend of the field
+okay opportunity to meet a celebrity
+
+ align:start position:0%
+okay opportunity to meet a celebrity
+ 
+
+ align:start position:0%
+okay opportunity to meet a celebrity
+okay bring friends okay he's going to
+
+ align:start position:0%
+okay bring friends okay he's going to
+ 
+
+ align:start position:0%
+okay bring friends okay he's going to
+give a great lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/iMz0LiqjFmE.txt b/iMz0LiqjFmE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8adbff083fa7d2e0bcfc62ca146ebf3dd970f758
--- /dev/null
+++ b/iMz0LiqjFmE.txt
@@ -0,0 +1,7371 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we were doing velocities and
+
+ align:start position:0%
+so we were doing velocities and
+ 
+
+ align:start position:0%
+so we were doing velocities and
+accelerations we came up with si
+
+ align:start position:0%
+accelerations we came up with si
+ 
+
+ align:start position:0%
+accelerations we came up with si
+continue to remind us talking about
+
+ align:start position:0%
+continue to remind us talking about
+ 
+
+ align:start position:0%
+continue to remind us talking about
+velocities and accelerations of a point
+
+ align:start position:0%
+velocities and accelerations of a point
+ 
+
+ align:start position:0%
+velocities and accelerations of a point
+with respect to another point to which
+
+ align:start position:0%
+with respect to another point to which
+ 
+
+ align:start position:0%
+with respect to another point to which
+we've attached make this point here to
+
+ align:start position:0%
+we've attached make this point here to
+ 
+
+ align:start position:0%
+we've attached make this point here to
+which we've attached a reference frame X
+
+ align:start position:0%
+which we've attached a reference frame X
+ 
+
+ align:start position:0%
+which we've attached a reference frame X
+prime Y prime Z prime and there's a
+
+ align:start position:0%
+prime Y prime Z prime and there's a
+ 
+
+ align:start position:0%
+prime Y prime Z prime and there's a
+vector that goes between these two and a
+
+ align:start position:0%
+vector that goes between these two and a
+ 
+
+ align:start position:0%
+vector that goes between these two and a
+vector that goes there so that we can
+
+ align:start position:0%
+vector that goes there so that we can
+ 
+
+ align:start position:0%
+vector that goes there so that we can
+say R of B with respect to O my inertial
+
+ align:start position:0%
+say R of B with respect to O my inertial
+ 
+
+ align:start position:0%
+say R of B with respect to O my inertial
+frame is R of a with respect to O plus R
+
+ align:start position:0%
+frame is R of a with respect to O plus R
+ 
+
+ align:start position:0%
+frame is R of a with respect to O plus R
+of B with respect to a these are all
+
+ align:start position:0%
+of B with respect to a these are all
+ 
+
+ align:start position:0%
+of B with respect to a these are all
+vectors and then from these we derive
+
+ align:start position:0%
+vectors and then from these we derive
+ 
+
+ align:start position:0%
+vectors and then from these we derive
+velocities and acceleration formulas and
+
+ align:start position:0%
+velocities and acceleration formulas and
+ 
+
+ align:start position:0%
+velocities and acceleration formulas and
+so we've come up with a couple of very
+
+ align:start position:0%
+so we've come up with a couple of very
+ 
+
+ align:start position:0%
+so we've come up with a couple of very
+handy formulas the velocity formula
+
+ align:start position:0%
+handy formulas the velocity formula
+ 
+
+ align:start position:0%
+handy formulas the velocity formula
+velocity of B with respect to O is the
+
+ align:start position:0%
+velocity of B with respect to O is the
+ 
+
+ align:start position:0%
+velocity of B with respect to O is the
+velocity of a with respect to O plus you
+
+ align:start position:0%
+velocity of a with respect to O plus you
+ 
+
+ align:start position:0%
+velocity of a with respect to O plus you
+have to take time derivative of this and
+
+ align:start position:0%
+have to take time derivative of this and
+ 
+
+ align:start position:0%
+have to take time derivative of this and
+so I'm going to give you just the
+
+ align:start position:0%
+so I'm going to give you just the
+ 
+
+ align:start position:0%
+so I'm going to give you just the
+general expression here just as a brief
+
+ align:start position:0%
+general expression here just as a brief
+ 
+
+ align:start position:0%
+general expression here just as a brief
+reminder it's the derivative of B with
+
+ align:start position:0%
+reminder it's the derivative of B with
+ 
+
+ align:start position:0%
+reminder it's the derivative of B with
+respect to a has seen in the a XYZ frame
+
+ align:start position:0%
+respect to a has seen in the a XYZ frame
+ 
+
+ align:start position:0%
+respect to a has seen in the a XYZ frame
+plus Omega with respect to O cross RBA
+
+ align:start position:0%
+plus Omega with respect to O cross RBA
+ 
+
+ align:start position:0%
+plus Omega with respect to O cross RBA
+these are all vectors so that's the ball
+
+ align:start position:0%
+these are all vectors so that's the ball
+ 
+
+ align:start position:0%
+these are all vectors so that's the ball
+that's the velocity formula remember
+
+ align:start position:0%
+that's the velocity formula remember
+ 
+
+ align:start position:0%
+that's the velocity formula remember
+this is the if you're in the frame
+
+ align:start position:0%
+this is the if you're in the frame
+ 
+
+ align:start position:0%
+this is the if you're in the frame
+rotating and translating with it this is
+
+ align:start position:0%
+rotating and translating with it this is
+ 
+
+ align:start position:0%
+rotating and translating with it this is
+the change of length of the vector and
+
+ align:start position:0%
+the change of length of the vector and
+ 
+
+ align:start position:0%
+the change of length of the vector and
+this then is the contribution to the
+
+ align:start position:0%
+this then is the contribution to the
+ 
+
+ align:start position:0%
+this then is the contribution to the
+velocity that you see in the fixed frame
+
+ align:start position:0%
+velocity that you see in the fixed frame
+ 
+
+ align:start position:0%
+velocity that you see in the fixed frame
+that comes from the rotation and we then
+
+ align:start position:0%
+that comes from the rotation and we then
+ 
+
+ align:start position:0%
+that comes from the rotation and we then
+got into polar coordinates and we found
+
+ align:start position:0%
+got into polar coordinates and we found
+ 
+
+ align:start position:0%
+got into polar coordinates and we found
+out that if you use polar coordinates
+
+ align:start position:0%
+out that if you use polar coordinates
+ 
+
+ align:start position:0%
+out that if you use polar coordinates
+then you can express this as the
+
+ align:start position:0%
+then you can express this as the
+ 
+
+ align:start position:0%
+then you can express this as the
+velocity of a with respect to O plus r
+
+ align:start position:0%
+velocity of a with respect to O plus r
+ 
+
+ align:start position:0%
+velocity of a with respect to O plus r
+dot R hat and I should really say
+
+ align:start position:0%
+dot R hat and I should really say
+ 
+
+ align:start position:0%
+dot R hat and I should really say
+cylindrical coordinates z dot
+
+ align:start position:0%
+cylindrical coordinates z dot
+ 
+
+ align:start position:0%
+cylindrical coordinates z dot
+k hat plus r theta dot theta hat so
+
+ align:start position:0%
+k hat plus r theta dot theta hat so
+ 
+
+ align:start position:0%
+k hat plus r theta dot theta hat so
+that's exactly the same thing this is
+
+ align:start position:0%
+that's exactly the same thing this is
+ 
+
+ align:start position:0%
+that's exactly the same thing this is
+full 3d vector notation this is a
+
+ align:start position:0%
+full 3d vector notation this is a
+ 
+
+ align:start position:0%
+full 3d vector notation this is a
+special case of a coordinate system
+
+ align:start position:0%
+special case of a coordinate system
+ 
+
+ align:start position:0%
+special case of a coordinate system
+which we call Koller coordinates and we
+
+ align:start position:0%
+which we call Koller coordinates and we
+ 
+
+ align:start position:0%
+which we call Koller coordinates and we
+have came up with another formula for
+
+ align:start position:0%
+have came up with another formula for
+ 
+
+ align:start position:0%
+have came up with another formula for
+accelerations the full 3d vector version
+
+ align:start position:0%
+accelerations the full 3d vector version
+ 
+
+ align:start position:0%
+accelerations the full 3d vector version
+of that a with respect to O plus this is
+
+ align:start position:0%
+of that a with respect to O plus this is
+ 
+
+ align:start position:0%
+of that a with respect to O plus this is
+the acceleration of B with respect to a
+
+ align:start position:0%
+the acceleration of B with respect to a
+ 
+
+ align:start position:0%
+the acceleration of B with respect to a
+but as seen in the a XYZ frame to Omega
+
+ align:start position:0%
+but as seen in the a XYZ frame to Omega
+ 
+
+ align:start position:0%
+but as seen in the a XYZ frame to Omega
+cross and this is the velocity as seen
+
+ align:start position:0%
+cross and this is the velocity as seen
+ 
+
+ align:start position:0%
+cross and this is the velocity as seen
+in the XYZ frame so these things this is
+
+ align:start position:0%
+in the XYZ frame so these things this is
+ 
+
+ align:start position:0%
+in the XYZ frame so these things this is
+no contribution from acceleration this
+
+ align:start position:0%
+no contribution from acceleration this
+ 
+
+ align:start position:0%
+no contribution from acceleration this
+is no contribution from acceleration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus Omega dot cross R b/a plus Omega
+
+ align:start position:0%
+plus Omega dot cross R b/a plus Omega
+ 
+
+ align:start position:0%
+plus Omega dot cross R b/a plus Omega
+cross Omega cross R b/a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all vectors this is a movement of the
+
+ align:start position:0%
+all vectors this is a movement of the
+ 
+
+ align:start position:0%
+all vectors this is a movement of the
+frame the acceleration of it with
+
+ align:start position:0%
+frame the acceleration of it with
+ 
+
+ align:start position:0%
+frame the acceleration of it with
+respect to this is pure translation this
+
+ align:start position:0%
+respect to this is pure translation this
+ 
+
+ align:start position:0%
+respect to this is pure translation this
+is the acceleration of the dog on the
+
+ align:start position:0%
+is the acceleration of the dog on the
+ 
+
+ align:start position:0%
+is the acceleration of the dog on the
+merry-go-round with respect to the
+
+ align:start position:0%
+merry-go-round with respect to the
+ 
+
+ align:start position:0%
+merry-go-round with respect to the
+center of the coordinate system there
+
+ align:start position:0%
+center of the coordinate system there
+ 
+
+ align:start position:0%
+center of the coordinate system there
+does not involve rotation this is this
+
+ align:start position:0%
+does not involve rotation this is this
+ 
+
+ align:start position:0%
+does not involve rotation this is this
+term that we call Coriolis this is a
+
+ align:start position:0%
+term that we call Coriolis this is a
+ 
+
+ align:start position:0%
+term that we call Coriolis this is a
+term we call Euler this is the angular
+
+ align:start position:0%
+term we call Euler this is the angular
+ 
+
+ align:start position:0%
+term we call Euler this is the angular
+speed up of the system angular
+
+ align:start position:0%
+speed up of the system angular
+ 
+
+ align:start position:0%
+speed up of the system angular
+acceleration and this is centripetal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you do these if you want to go to
+
+ align:start position:0%
+and if you do these if you want to go to
+ 
+
+ align:start position:0%
+and if you do these if you want to go to
+cylindrical coordinates and what we're
+
+ align:start position:0%
+cylindrical coordinates and what we're
+ 
+
+ align:start position:0%
+cylindrical coordinates and what we're
+going to do next is just do some
+
+ align:start position:0%
+going to do next is just do some
+ 
+
+ align:start position:0%
+going to do next is just do some
+applications here the acceleration of B
+
+ align:start position:0%
+applications here the acceleration of B
+ 
+
+ align:start position:0%
+applications here the acceleration of B
+with respect to O and cylindrical
+
+ align:start position:0%
+with respect to O and cylindrical
+ 
+
+ align:start position:0%
+with respect to O and cylindrical
+coordinates translation piece plus a now
+
+ align:start position:0%
+coordinates translation piece plus a now
+ 
+
+ align:start position:0%
+coordinates translation piece plus a now
+in cylindrical it's useful to group
+
+ align:start position:0%
+in cylindrical it's useful to group
+ 
+
+ align:start position:0%
+in cylindrical it's useful to group
+these so I'm going to put together this
+
+ align:start position:0%
+these so I'm going to put together this
+ 
+
+ align:start position:0%
+these so I'm going to put together this
+term and this term because they're both
+
+ align:start position:0%
+term and this term because they're both
+ 
+
+ align:start position:0%
+term and this term because they're both
+in the R hat direction and I'm going to
+
+ align:start position:0%
+in the R hat direction and I'm going to
+ 
+
+ align:start position:0%
+in the R hat direction and I'm going to
+put together these two terms because
+
+ align:start position:0%
+put together these two terms because
+ 
+
+ align:start position:0%
+put together these two terms because
+they're both in the theta hat direction
+
+ align:start position:0%
+they're both in the theta hat direction
+ 
+
+ align:start position:0%
+they're both in the theta hat direction
+and I need is e zwk because it's
+
+ align:start position:0%
+and I need is e zwk because it's
+ 
+
+ align:start position:0%
+and I need is e zwk because it's
+cylindrical and then I have the theta
+
+ align:start position:0%
+cylindrical and then I have the theta
+ 
+
+ align:start position:0%
+cylindrical and then I have the theta
+hat piece R theta double dot plus 2 r
+
+ align:start position:0%
+hat piece R theta double dot plus 2 r
+ 
+
+ align:start position:0%
+hat piece R theta double dot plus 2 r
+dot theta dot theta hat that's this is
+
+ align:start position:0%
+dot theta dot theta hat that's this is
+ 
+
+ align:start position:0%
+dot theta dot theta hat that's this is
+the same thing as this except this is
+
+ align:start position:0%
+the same thing as this except this is
+ 
+
+ align:start position:0%
+the same thing as this except this is
+expressed in cylindrical coordinates in
+
+ align:start position:0%
+expressed in cylindrical coordinates in
+ 
+
+ align:start position:0%
+expressed in cylindrical coordinates in
+cylindrical coordinates are particularly
+
+ align:start position:0%
+cylindrical coordinates are particularly
+ 
+
+ align:start position:0%
+cylindrical coordinates are particularly
+good for doing the kind of problems that
+
+ align:start position:0%
+good for doing the kind of problems that
+ 
+
+ align:start position:0%
+good for doing the kind of problems that
+are mostly done at the level of this
+
+ align:start position:0%
+are mostly done at the level of this
+ 
+
+ align:start position:0%
+are mostly done at the level of this
+course which we call planar motion
+
+ align:start position:0%
+course which we call planar motion
+ 
+
+ align:start position:0%
+course which we call planar motion
+problems confined to an XY plane and
+
+ align:start position:0%
+problems confined to an XY plane and
+ 
+
+ align:start position:0%
+problems confined to an XY plane and
+confined to single axis rotation in the
+
+ align:start position:0%
+confined to single axis rotation in the
+ 
+
+ align:start position:0%
+confined to single axis rotation in the
+Z which is this is a high coordinate
+
+ align:start position:0%
+Z which is this is a high coordinate
+ 
+
+ align:start position:0%
+Z which is this is a high coordinate
+system it's ideally suited to do
+
+ align:start position:0%
+system it's ideally suited to do
+ 
+
+ align:start position:0%
+system it's ideally suited to do
+problems like that and that's why we use
+
+ align:start position:0%
+problems like that and that's why we use
+ 
+
+ align:start position:0%
+problems like that and that's why we use
+it so now let's do let's do some
+
+ align:start position:0%
+it so now let's do let's do some
+ 
+
+ align:start position:0%
+it so now let's do let's do some
+examples and this gets into this is
+
+ align:start position:0%
+examples and this gets into this is
+ 
+
+ align:start position:0%
+examples and this gets into this is
+really quite a powerful now that you
+
+ align:start position:0%
+really quite a powerful now that you
+ 
+
+ align:start position:0%
+really quite a powerful now that you
+have these two equations you can do a
+
+ align:start position:0%
+have these two equations you can do a
+ 
+
+ align:start position:0%
+have these two equations you can do a
+lot of kinematics and dynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we started last time right at the
+
+ align:start position:0%
+so we started last time right at the
+ 
+
+ align:start position:0%
+so we started last time right at the
+very end I said okay let's do this
+
+ align:start position:0%
+very end I said okay let's do this
+ 
+
+ align:start position:0%
+very end I said okay let's do this
+problem really quickly right constant
+
+ align:start position:0%
+problem really quickly right constant
+ 
+
+ align:start position:0%
+problem really quickly right constant
+rotation rate constant radius no angular
+
+ align:start position:0%
+rotation rate constant radius no angular
+ 
+
+ align:start position:0%
+rotation rate constant radius no angular
+acceleration no change in length of the
+
+ align:start position:0%
+acceleration no change in length of the
+ 
+
+ align:start position:0%
+acceleration no change in length of the
+thing pretty simple problem and we
+
+ align:start position:0%
+thing pretty simple problem and we
+ 
+
+ align:start position:0%
+thing pretty simple problem and we
+exhibit it off really fast and I wanted
+
+ align:start position:0%
+exhibit it off really fast and I wanted
+ 
+
+ align:start position:0%
+exhibit it off really fast and I wanted
+to start there do that really quickly so
+
+ align:start position:0%
+to start there do that really quickly so
+ 
+
+ align:start position:0%
+to start there do that really quickly so
+this is my case one it's my ball on the
+
+ align:start position:0%
+this is my case one it's my ball on the
+ 
+
+ align:start position:0%
+this is my case one it's my ball on the
+string here's point a here's point B
+
+ align:start position:0%
+string here's point a here's point B
+ 
+
+ align:start position:0%
+string here's point a here's point B
+here's the theta hat direction R hat
+
+ align:start position:0%
+here's the theta hat direction R hat
+ 
+
+ align:start position:0%
+here's the theta hat direction R hat
+direction okay and it has some constant
+
+ align:start position:0%
+direction okay and it has some constant
+ 
+
+ align:start position:0%
+direction okay and it has some constant
+length R here so r dot R double dot R
+
+ align:start position:0%
+length R here so r dot R double dot R
+ 
+
+ align:start position:0%
+length R here so r dot R double dot R
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+there's no also Z C dot Z double dot
+
+ align:start position:0%
+there's no also Z C dot Z double dot
+ 
+
+ align:start position:0%
+there's no also Z C dot Z double dot
+we're just no Z motion at all those are
+
+ align:start position:0%
+we're just no Z motion at all those are
+ 
+
+ align:start position:0%
+we're just no Z motion at all those are
+all 0 theta dot is a constant I'll call
+
+ align:start position:0%
+all 0 theta dot is a constant I'll call
+ 
+
+ align:start position:0%
+all 0 theta dot is a constant I'll call
+it cap Omega in the K hat direction
+
+ align:start position:0%
+it cap Omega in the K hat direction
+ 
+
+ align:start position:0%
+it cap Omega in the K hat direction
+right hand rule theta double dot zero so
+
+ align:start position:0%
+right hand rule theta double dot zero so
+ 
+
+ align:start position:0%
+right hand rule theta double dot zero so
+with the way the easy way to use these
+
+ align:start position:0%
+with the way the easy way to use these
+ 
+
+ align:start position:0%
+with the way the easy way to use these
+formulas is you just started knocking
+
+ align:start position:0%
+formulas is you just started knocking
+ 
+
+ align:start position:0%
+formulas is you just started knocking
+out all the terms that you don't need so
+
+ align:start position:0%
+out all the terms that you don't need so
+ 
+
+ align:start position:0%
+out all the terms that you don't need so
+but let's just to give you a little
+
+ align:start position:0%
+but let's just to give you a little
+ 
+
+ align:start position:0%
+but let's just to give you a little
+quick review of how to use these things
+
+ align:start position:0%
+quick review of how to use these things
+ 
+
+ align:start position:0%
+quick review of how to use these things
+let's use the vector full 3d version of
+
+ align:start position:0%
+let's use the vector full 3d version of
+ 
+
+ align:start position:0%
+let's use the vector full 3d version of
+velocity equation for a second the full
+
+ align:start position:0%
+velocity equation for a second the full
+ 
+
+ align:start position:0%
+velocity equation for a second the full
+3d version says the velocity of air is
+
+ align:start position:0%
+3d version says the velocity of air is
+ 
+
+ align:start position:0%
+3d version says the velocity of air is
+respect to O what's that in this problem
+
+ align:start position:0%
+respect to O what's that in this problem
+ 
+
+ align:start position:0%
+respect to O what's that in this problem
+that's not the translating term so I was
+
+ align:start position:0%
+that's not the translating term so I was
+ 
+
+ align:start position:0%
+that's not the translating term so I was
+standing still not going anywhere but if
+
+ align:start position:0%
+standing still not going anywhere but if
+ 
+
+ align:start position:0%
+standing still not going anywhere but if
+we're walking along I'd still spend that
+
+ align:start position:0%
+we're walking along I'd still spend that
+ 
+
+ align:start position:0%
+we're walking along I'd still spend that
+thing ok so this problem this term is
+
+ align:start position:0%
+thing ok so this problem this term is
+ 
+
+ align:start position:0%
+thing ok so this problem this term is
+zero this problem r dot
+
+ align:start position:0%
+zero this problem r dot
+ 
+
+ align:start position:0%
+zero this problem r dot
+let's go here what's this is the rate of
+
+ align:start position:0%
+let's go here what's this is the rate of
+ 
+
+ align:start position:0%
+let's go here what's this is the rate of
+change of the length of the string in
+
+ align:start position:0%
+change of the length of the string in
+ 
+
+ align:start position:0%
+change of the length of the string in
+the coordinate system of the string
+
+ align:start position:0%
+the coordinate system of the string
+ 
+
+ align:start position:0%
+the coordinate system of the string
+walking along so what's our dot okay so
+
+ align:start position:0%
+walking along so what's our dot okay so
+ 
+
+ align:start position:0%
+walking along so what's our dot okay so
+that terms 0 and Omega cross R b/a
+
+ align:start position:0%
+that terms 0 and Omega cross R b/a
+ 
+
+ align:start position:0%
+that terms 0 and Omega cross R b/a
+well R is in the our hat capital r r hat
+
+ align:start position:0%
+well R is in the our hat capital r r hat
+ 
+
+ align:start position:0%
+well R is in the our hat capital r r hat
+cross with omega a k right k cross r is
+
+ align:start position:0%
+cross with omega a k right k cross r is
+ 
+
+ align:start position:0%
+cross with omega a k right k cross r is
+k cross our hat theta hat so we get our
+
+ align:start position:0%
+k cross our hat theta hat so we get our
+ 
+
+ align:start position:0%
+k cross our hat theta hat so we get our
+familiar this first term is 0 the second
+
+ align:start position:0%
+familiar this first term is 0 the second
+ 
+
+ align:start position:0%
+familiar this first term is 0 the second
+term is 0 the third term we just get our
+
+ align:start position:0%
+term is 0 the third term we just get our
+ 
+
+ align:start position:0%
+term is 0 the third term we just get our
+R Omega in the theta hat direction we
+
+ align:start position:0%
+R Omega in the theta hat direction we
+ 
+
+ align:start position:0%
+R Omega in the theta hat direction we
+know that to be true the point I'm just
+
+ align:start position:0%
+know that to be true the point I'm just
+ 
+
+ align:start position:0%
+know that to be true the point I'm just
+trying to make here is you can always
+
+ align:start position:0%
+trying to make here is you can always
+ 
+
+ align:start position:0%
+trying to make here is you can always
+just fall back and use the vector
+
+ align:start position:0%
+just fall back and use the vector
+ 
+
+ align:start position:0%
+just fall back and use the vector
+formula full 3d vector formulas of both
+
+ align:start position:0%
+formula full 3d vector formulas of both
+ 
+
+ align:start position:0%
+formula full 3d vector formulas of both
+just plug it in and everything will just
+
+ align:start position:0%
+just plug it in and everything will just
+ 
+
+ align:start position:0%
+just plug it in and everything will just
+drop out you can also then go to these
+
+ align:start position:0%
+drop out you can also then go to these
+ 
+
+ align:start position:0%
+drop out you can also then go to these
+simply to the cylindrical coordinate
+
+ align:start position:0%
+simply to the cylindrical coordinate
+ 
+
+ align:start position:0%
+simply to the cylindrical coordinate
+terms when you happen to have it all
+
+ align:start position:0%
+terms when you happen to have it all
+ 
+
+ align:start position:0%
+terms when you happen to have it all
+expressed in those in coordinates of
+
+ align:start position:0%
+expressed in those in coordinates of
+ 
+
+ align:start position:0%
+expressed in those in coordinates of
+that kind of make it simpler for you
+
+ align:start position:0%
+that kind of make it simpler for you
+ 
+
+ align:start position:0%
+that kind of make it simpler for you
+okay so now let's quickly then do the
+
+ align:start position:0%
+okay so now let's quickly then do the
+ 
+
+ align:start position:0%
+okay so now let's quickly then do the
+acceleration of B with respect to O and
+
+ align:start position:0%
+acceleration of B with respect to O and
+ 
+
+ align:start position:0%
+acceleration of B with respect to O and
+let's use the formulation already in
+
+ align:start position:0%
+let's use the formulation already in
+ 
+
+ align:start position:0%
+let's use the formulation already in
+cylindrical coordinates what's a with
+
+ align:start position:0%
+cylindrical coordinates what's a with
+ 
+
+ align:start position:0%
+cylindrical coordinates what's a with
+respect to 0
+
+ align:start position:0%
+respect to 0
+ 
+
+ align:start position:0%
+respect to 0
+what's our double dot how about the r
+
+ align:start position:0%
+what's our double dot how about the r
+ 
+
+ align:start position:0%
+what's our double dot how about the r
+theta dot squared term 0 or not nope
+
+ align:start position:0%
+theta dot squared term 0 or not nope
+ 
+
+ align:start position:0%
+theta dot squared term 0 or not nope
+let's go on z double dot r theta double
+
+ align:start position:0%
+let's go on z double dot r theta double
+ 
+
+ align:start position:0%
+let's go on z double dot r theta double
+dot r dot theta dot okay we only end up
+
+ align:start position:0%
+dot r dot theta dot okay we only end up
+ 
+
+ align:start position:0%
+dot r dot theta dot okay we only end up
+with one term actually i'm going to keep
+
+ align:start position:0%
+with one term actually i'm going to keep
+ 
+
+ align:start position:0%
+with one term actually i'm going to keep
+this one for a second able to respect oh
+
+ align:start position:0%
+this one for a second able to respect oh
+ 
+
+ align:start position:0%
+this one for a second able to respect oh
+- and we came up with our r theta dot
+
+ align:start position:0%
+- and we came up with our r theta dot
+ 
+
+ align:start position:0%
+- and we came up with our r theta dot
+squared R hat term I leave this in here
+
+ align:start position:0%
+squared R hat term I leave this in here
+ 
+
+ align:start position:0%
+squared R hat term I leave this in here
+because I actually don't don't have to
+
+ align:start position:0%
+because I actually don't don't have to
+ 
+
+ align:start position:0%
+because I actually don't don't have to
+say if I were if I want it now to do
+
+ align:start position:0%
+say if I were if I want it now to do
+ 
+
+ align:start position:0%
+say if I were if I want it now to do
+this problem if I ask you to do a
+
+ align:start position:0%
+this problem if I ask you to do a
+ 
+
+ align:start position:0%
+this problem if I ask you to do a
+problem where I'm doing this and I start
+
+ align:start position:0%
+problem where I'm doing this and I start
+ 
+
+ align:start position:0%
+problem where I'm doing this and I start
+accelerating do you know how to do it
+
+ align:start position:0%
+accelerating do you know how to do it
+ 
+
+ align:start position:0%
+accelerating do you know how to do it
+there's answers still there right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's let's do a quick free body
+
+ align:start position:0%
+what's let's do a quick free body
+ 
+
+ align:start position:0%
+what's let's do a quick free body
+diagram here's our mass my master
+
+ align:start position:0%
+diagram here's our mass my master
+ 
+
+ align:start position:0%
+diagram here's our mass my master
+coordinate system out here let's draw
+
+ align:start position:0%
+coordinate system out here let's draw
+ 
+
+ align:start position:0%
+coordinate system out here let's draw
+let's say it's you know right here at 90
+
+ align:start position:0%
+let's say it's you know right here at 90
+ 
+
+ align:start position:0%
+let's say it's you know right here at 90
+degrees what are the external forces on
+
+ align:start position:0%
+degrees what are the external forces on
+ 
+
+ align:start position:0%
+degrees what are the external forces on
+the mass in this problem so there's
+
+ align:start position:0%
+the mass in this problem so there's
+ 
+
+ align:start position:0%
+the mass in this problem so there's
+tension in the string right okay so now
+
+ align:start position:0%
+tension in the string right okay so now
+ 
+
+ align:start position:0%
+tension in the string right okay so now
+this is a really trivially simple
+
+ align:start position:0%
+this is a really trivially simple
+ 
+
+ align:start position:0%
+this is a really trivially simple
+problem so the point of the emphasis I'm
+
+ align:start position:0%
+problem so the point of the emphasis I'm
+ 
+
+ align:start position:0%
+problem so the point of the emphasis I'm
+here is on the concept so now when
+
+ align:start position:0%
+here is on the concept so now when
+ 
+
+ align:start position:0%
+here is on the concept so now when
+you're asked to come up with an equation
+
+ align:start position:0%
+you're asked to come up with an equation
+ 
+
+ align:start position:0%
+you're asked to come up with an equation
+of motion or compute the forces on a
+
+ align:start position:0%
+of motion or compute the forces on a
+ 
+
+ align:start position:0%
+of motion or compute the forces on a
+mass Newton use Newton's second law F
+
+ align:start position:0%
+mass Newton use Newton's second law F
+ 
+
+ align:start position:0%
+mass Newton use Newton's second law F
+equals mass times acceleration you now
+
+ align:start position:0%
+equals mass times acceleration you now
+ 
+
+ align:start position:0%
+equals mass times acceleration you now
+have the complete 3d vector formulation
+
+ align:start position:0%
+have the complete 3d vector formulation
+ 
+
+ align:start position:0%
+have the complete 3d vector formulation
+for acceleration of a syst particle you
+
+ align:start position:0%
+for acceleration of a syst particle you
+ 
+
+ align:start position:0%
+for acceleration of a syst particle you
+know translating rotating coordinate
+
+ align:start position:0%
+know translating rotating coordinate
+ 
+
+ align:start position:0%
+know translating rotating coordinate
+system that's all you need to compute
+
+ align:start position:0%
+system that's all you need to compute
+ 
+
+ align:start position:0%
+system that's all you need to compute
+accelerations for lots and lots of
+
+ align:start position:0%
+accelerations for lots and lots of
+ 
+
+ align:start position:0%
+accelerations for lots and lots of
+difficult problems and so if you can
+
+ align:start position:0%
+difficult problems and so if you can
+ 
+
+ align:start position:0%
+difficult problems and so if you can
+write down the acceleration you say it's
+
+ align:start position:0%
+write down the acceleration you say it's
+ 
+
+ align:start position:0%
+write down the acceleration you say it's
+equal to what mask'd if you've
+
+ align:start position:0%
+equal to what mask'd if you've
+ 
+
+ align:start position:0%
+equal to what mask'd if you've
+multiplied mass times that acceleration
+
+ align:start position:0%
+multiplied mass times that acceleration
+ 
+
+ align:start position:0%
+multiplied mass times that acceleration
+what's that equal to the forces that
+
+ align:start position:0%
+what's that equal to the forces that
+ 
+
+ align:start position:0%
+what's that equal to the forces that
+must be acting on the system and that's
+
+ align:start position:0%
+must be acting on the system and that's
+ 
+
+ align:start position:0%
+must be acting on the system and that's
+the point here so now I want to know the
+
+ align:start position:0%
+the point here so now I want to know the
+ 
+
+ align:start position:0%
+the point here so now I want to know the
+forces on the system the summation of
+
+ align:start position:0%
+forces on the system the summation of
+ 
+
+ align:start position:0%
+forces on the system the summation of
+the external forces and then these are
+
+ align:start position:0%
+the external forces and then these are
+ 
+
+ align:start position:0%
+the external forces and then these are
+vectors and you can do them component by
+
+ align:start position:0%
+vectors and you can do them component by
+ 
+
+ align:start position:0%
+vectors and you can do them component by
+component the sum of the external forces
+
+ align:start position:0%
+component the sum of the external forces
+ 
+
+ align:start position:0%
+component the sum of the external forces
+in the R hat direction must be equal to
+
+ align:start position:0%
+in the R hat direction must be equal to
+ 
+
+ align:start position:0%
+in the R hat direction must be equal to
+the mass in this case just a particle
+
+ align:start position:0%
+the mass in this case just a particle
+ 
+
+ align:start position:0%
+the mass in this case just a particle
+times the acceleration of that particle
+
+ align:start position:0%
+times the acceleration of that particle
+ 
+
+ align:start position:0%
+times the acceleration of that particle
+and in this problem then that would be
+
+ align:start position:0%
+and in this problem then that would be
+ 
+
+ align:start position:0%
+and in this problem then that would be
+the mass times acceleration of a with
+
+ align:start position:0%
+the mass times acceleration of a with
+ 
+
+ align:start position:0%
+the mass times acceleration of a with
+respect to O minus R theta dot squared R
+
+ align:start position:0%
+respect to O minus R theta dot squared R
+ 
+
+ align:start position:0%
+respect to O minus R theta dot squared R
+hat
+
+ align:start position:0%
+hat
+ 
+
+ align:start position:0%
+hat
+and this would have to be the are comp
+
+ align:start position:0%
+and this would have to be the are comp
+ 
+
+ align:start position:0%
+and this would have to be the are comp
+they are hat component of this thing
+
+ align:start position:0%
+they are hat component of this thing
+ 
+
+ align:start position:0%
+they are hat component of this thing
+right I've said I just want the are
+
+ align:start position:0%
+right I've said I just want the are
+ 
+
+ align:start position:0%
+right I've said I just want the are
+component I'd have to figure out if I
+
+ align:start position:0%
+component I'd have to figure out if I
+ 
+
+ align:start position:0%
+component I'd have to figure out if I
+was running along if I had a in the same
+
+ align:start position:0%
+was running along if I had a in the same
+ 
+
+ align:start position:0%
+was running along if I had a in the same
+direction as our hat what part of that
+
+ align:start position:0%
+direction as our hat what part of that
+ 
+
+ align:start position:0%
+direction as our hat what part of that
+accelerations in that direction that
+
+ align:start position:0%
+accelerations in that direction that
+ 
+
+ align:start position:0%
+accelerations in that direction that
+would come here if there's zero is make
+
+ align:start position:0%
+would come here if there's zero is make
+ 
+
+ align:start position:0%
+would come here if there's zero is make
+it zero so let's just say no let's just
+
+ align:start position:0%
+it zero so let's just say no let's just
+ 
+
+ align:start position:0%
+it zero so let's just say no let's just
+let the acceleration of a with respect
+
+ align:start position:0%
+let the acceleration of a with respect
+ 
+
+ align:start position:0%
+let the acceleration of a with respect
+to O be zero then that says the sum of
+
+ align:start position:0%
+to O be zero then that says the sum of
+ 
+
+ align:start position:0%
+to O be zero then that says the sum of
+the forces in the r direction is equal
+
+ align:start position:0%
+the forces in the r direction is equal
+ 
+
+ align:start position:0%
+the forces in the r direction is equal
+to the mass minus m r theta dot squared
+
+ align:start position:0%
+to the mass minus m r theta dot squared
+ 
+
+ align:start position:0%
+to the mass minus m r theta dot squared
+and if we were to draw a Freebody
+
+ align:start position:0%
+and if we were to draw a Freebody
+ 
+
+ align:start position:0%
+and if we were to draw a Freebody
+diagram we would find out that ah there
+
+ align:start position:0%
+diagram we would find out that ah there
+ 
+
+ align:start position:0%
+diagram we would find out that ah there
+must be a tension on the string pulling
+
+ align:start position:0%
+must be a tension on the string pulling
+ 
+
+ align:start position:0%
+must be a tension on the string pulling
+it on the mass sufficient to give it the
+
+ align:start position:0%
+it on the mass sufficient to give it the
+ 
+
+ align:start position:0%
+it on the mass sufficient to give it the
+acceleration that you've computed so
+
+ align:start position:0%
+acceleration that you've computed so
+ 
+
+ align:start position:0%
+acceleration that you've computed so
+every problem when you're asked to
+
+ align:start position:0%
+every problem when you're asked to
+ 
+
+ align:start position:0%
+every problem when you're asked to
+compute the force or the next step up
+
+ align:start position:0%
+compute the force or the next step up
+ 
+
+ align:start position:0%
+compute the force or the next step up
+find the equation of motion the equation
+
+ align:start position:0%
+find the equation of motion the equation
+ 
+
+ align:start position:0%
+find the equation of motion the equation
+of motion is just spin it it's just you
+
+ align:start position:0%
+of motion is just spin it it's just you
+ 
+
+ align:start position:0%
+of motion is just spin it it's just you
+know writing this thing out okay the now
+
+ align:start position:0%
+know writing this thing out okay the now
+ 
+
+ align:start position:0%
+know writing this thing out okay the now
+okay I want to move on to a more
+
+ align:start position:0%
+okay I want to move on to a more
+ 
+
+ align:start position:0%
+okay I want to move on to a more
+interesting problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right I'm going to do I want to do
+
+ align:start position:0%
+all right I'm going to do I want to do
+ 
+
+ align:start position:0%
+all right I'm going to do I want to do
+this problem so it's a hollow tube and
+
+ align:start position:0%
+this problem so it's a hollow tube and
+ 
+
+ align:start position:0%
+this problem so it's a hollow tube and
+we're going to look at things like what
+
+ align:start position:0%
+we're going to look at things like what
+ 
+
+ align:start position:0%
+we're going to look at things like what
+happened put a ping-pong ball in it okay
+
+ align:start position:0%
+happened put a ping-pong ball in it okay
+ 
+
+ align:start position:0%
+happened put a ping-pong ball in it okay
+and if I swing this tube around ping
+
+ align:start position:0%
+and if I swing this tube around ping
+ 
+
+ align:start position:0%
+and if I swing this tube around ping
+pong ball is going to come out right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there must be some forces on that
+
+ align:start position:0%
+okay there must be some forces on that
+ 
+
+ align:start position:0%
+okay there must be some forces on that
+thing to cause it to come out there must
+
+ align:start position:0%
+thing to cause it to come out there must
+ 
+
+ align:start position:0%
+thing to cause it to come out there must
+be some accelerations on that thing so
+
+ align:start position:0%
+be some accelerations on that thing so
+ 
+
+ align:start position:0%
+be some accelerations on that thing so
+if I could conceivably have an R a theta
+
+ align:start position:0%
+if I could conceivably have an R a theta
+ 
+
+ align:start position:0%
+if I could conceivably have an R a theta
+double dot acceleration it certainly is
+
+ align:start position:0%
+double dot acceleration it certainly is
+ 
+
+ align:start position:0%
+double dot acceleration it certainly is
+going to have theta dot rotation rates
+
+ align:start position:0%
+going to have theta dot rotation rates
+ 
+
+ align:start position:0%
+going to have theta dot rotation rates
+the balls allowed to move there can be
+
+ align:start position:0%
+the balls allowed to move there can be
+ 
+
+ align:start position:0%
+the balls allowed to move there can be
+non zero R dots are double dots a lot
+
+ align:start position:0%
+non zero R dots are double dots a lot
+ 
+
+ align:start position:0%
+non zero R dots are double dots a lot
+going on inside of this simple little -
+
+ align:start position:0%
+going on inside of this simple little -
+ 
+
+ align:start position:0%
+going on inside of this simple little -
+all right so let's that's what I want to
+
+ align:start position:0%
+all right so let's that's what I want to
+ 
+
+ align:start position:0%
+all right so let's that's what I want to
+figure out let's see if we can come up
+
+ align:start position:0%
+figure out let's see if we can come up
+ 
+
+ align:start position:0%
+figure out let's see if we can come up
+with a model for this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's my z-axis I have a rotation
+
+ align:start position:0%
+so here's my z-axis I have a rotation
+ 
+
+ align:start position:0%
+so here's my z-axis I have a rotation
+around it some theta dot k hat direction
+
+ align:start position:0%
+around it some theta dot k hat direction
+ 
+
+ align:start position:0%
+around it some theta dot k hat direction
+here's my tube it's rotating around so
+
+ align:start position:0%
+here's my tube it's rotating around so
+ 
+
+ align:start position:0%
+here's my tube it's rotating around so
+this is sort of a side view your view of
+
+ align:start position:0%
+this is sort of a side view your view of
+ 
+
+ align:start position:0%
+this is sort of a side view your view of
+the tube here's a ping-pong ball in
+
+ align:start position:0%
+the tube here's a ping-pong ball in
+ 
+
+ align:start position:0%
+the tube here's a ping-pong ball in
+there and I'm going to I'm going to
+
+ align:start position:0%
+there and I'm going to I'm going to
+ 
+
+ align:start position:0%
+there and I'm going to I'm going to
+idealize that ping-pong ball as a for a
+
+ align:start position:0%
+idealize that ping-pong ball as a for a
+ 
+
+ align:start position:0%
+idealize that ping-pong ball as a for a
+minute a little more general problem I
+
+ align:start position:0%
+minute a little more general problem I
+ 
+
+ align:start position:0%
+minute a little more general problem I
+have got let's say I have kind of a nut
+
+ align:start position:0%
+have got let's say I have kind of a nut
+ 
+
+ align:start position:0%
+have got let's say I have kind of a nut
+on this thing a disc something on the
+
+ align:start position:0%
+on this thing a disc something on the
+ 
+
+ align:start position:0%
+on this thing a disc something on the
+outs hanging on to the outside and I can
+
+ align:start position:0%
+outs hanging on to the outside and I can
+ 
+
+ align:start position:0%
+outs hanging on to the outside and I can
+control the rate at which the speed at
+
+ align:start position:0%
+control the rate at which the speed at
+ 
+
+ align:start position:0%
+control the rate at which the speed at
+which this thing goes out ping-pong ball
+
+ align:start position:0%
+which this thing goes out ping-pong ball
+ 
+
+ align:start position:0%
+which this thing goes out ping-pong ball
+that's just that's a this is going to be
+
+ align:start position:0%
+that's just that's a this is going to be
+ 
+
+ align:start position:0%
+that's just that's a this is going to be
+an application of this but I want to be
+
+ align:start position:0%
+an application of this but I want to be
+ 
+
+ align:start position:0%
+an application of this but I want to be
+able to do several other versions like
+
+ align:start position:0%
+able to do several other versions like
+ 
+
+ align:start position:0%
+able to do several other versions like
+can like make the speed constant for a
+
+ align:start position:0%
+can like make the speed constant for a
+ 
+
+ align:start position:0%
+can like make the speed constant for a
+second okay and looking down on this
+
+ align:start position:0%
+second okay and looking down on this
+ 
+
+ align:start position:0%
+second okay and looking down on this
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+top view here's our initial frame maybe
+
+ align:start position:0%
+top view here's our initial frame maybe
+ 
+
+ align:start position:0%
+top view here's our initial frame maybe
+out here like this here's my mass so in
+
+ align:start position:0%
+out here like this here's my mass so in
+ 
+
+ align:start position:0%
+out here like this here's my mass so in
+polar coordinates here is your theta the
+
+ align:start position:0%
+polar coordinates here is your theta the
+ 
+
+ align:start position:0%
+polar coordinates here is your theta the
+R is this this is your R hat this is
+
+ align:start position:0%
+R is this this is your R hat this is
+ 
+
+ align:start position:0%
+R is this this is your R hat this is
+your theta hat directions okay I'm going
+
+ align:start position:0%
+your theta hat directions okay I'm going
+ 
+
+ align:start position:0%
+your theta hat directions okay I'm going
+to let the velocity of a with respect to
+
+ align:start position:0%
+to let the velocity of a with respect to
+ 
+
+ align:start position:0%
+to let the velocity of a with respect to
+O be zero so there's no translation of
+
+ align:start position:0%
+O be zero so there's no translation of
+ 
+
+ align:start position:0%
+O be zero so there's no translation of
+this system and z z dot z double dot
+
+ align:start position:0%
+this system and z z dot z double dot
+ 
+
+ align:start position:0%
+this system and z z dot z double dot
+those are all zero nothing's happening
+
+ align:start position:0%
+those are all zero nothing's happening
+ 
+
+ align:start position:0%
+those are all zero nothing's happening
+in the z direction so I want to first
+
+ align:start position:0%
+in the z direction so I want to first
+ 
+
+ align:start position:0%
+in the z direction so I want to first
+compute the velocity of B with respect
+
+ align:start position:0%
+compute the velocity of B with respect
+ 
+
+ align:start position:0%
+compute the velocity of B with respect
+to O and you got to be able to do that
+
+ align:start position:0%
+to O and you got to be able to do that
+ 
+
+ align:start position:0%
+to O and you got to be able to do that
+sort of by inspection right it comes
+
+ align:start position:0%
+sort of by inspection right it comes
+ 
+
+ align:start position:0%
+sort of by inspection right it comes
+only from oh I haven't told you now what
+
+ align:start position:0%
+only from oh I haven't told you now what
+ 
+
+ align:start position:0%
+only from oh I haven't told you now what
+do I want to hope make happen in this
+
+ align:start position:0%
+do I want to hope make happen in this
+ 
+
+ align:start position:0%
+do I want to hope make happen in this
+problem I want to let
+
+ align:start position:0%
+problem I want to let
+ 
+
+ align:start position:0%
+problem I want to let
+our dot it's going to be some VR and
+
+ align:start position:0%
+our dot it's going to be some VR and
+ 
+
+ align:start position:0%
+our dot it's going to be some VR and
+it's constant I'm not going to go quite
+
+ align:start position:0%
+it's constant I'm not going to go quite
+ 
+
+ align:start position:0%
+it's constant I'm not going to go quite
+to my ping pong shooter here yet I'm
+
+ align:start position:0%
+to my ping pong shooter here yet I'm
+ 
+
+ align:start position:0%
+to my ping pong shooter here yet I'm
+going to do a slightly simpler problem
+
+ align:start position:0%
+going to do a slightly simpler problem
+ 
+
+ align:start position:0%
+going to do a slightly simpler problem
+first so this is a constant that means
+
+ align:start position:0%
+first so this is a constant that means
+ 
+
+ align:start position:0%
+first so this is a constant that means
+our double dot is zero so this thing is
+
+ align:start position:0%
+our double dot is zero so this thing is
+ 
+
+ align:start position:0%
+our double dot is zero so this thing is
+just like let's say you had threads on
+
+ align:start position:0%
+just like let's say you had threads on
+ 
+
+ align:start position:0%
+just like let's say you had threads on
+this thing and it's a screw and it's
+
+ align:start position:0%
+this thing and it's a screw and it's
+ 
+
+ align:start position:0%
+this thing and it's a screw and it's
+just moving its way out at a constant
+
+ align:start position:0%
+just moving its way out at a constant
+ 
+
+ align:start position:0%
+just moving its way out at a constant
+rate and I'm going to have constant
+
+ align:start position:0%
+rate and I'm going to have constant
+ 
+
+ align:start position:0%
+rate and I'm going to have constant
+angular so theta dot and I'll call that
+
+ align:start position:0%
+angular so theta dot and I'll call that
+ 
+
+ align:start position:0%
+angular so theta dot and I'll call that
+cap Omega K so the angular rate is also
+
+ align:start position:0%
+cap Omega K so the angular rate is also
+ 
+
+ align:start position:0%
+cap Omega K so the angular rate is also
+constant all right if that's the case
+
+ align:start position:0%
+constant all right if that's the case
+ 
+
+ align:start position:0%
+constant all right if that's the case
+can you tell me so what to be with V of
+
+ align:start position:0%
+can you tell me so what to be with V of
+ 
+
+ align:start position:0%
+can you tell me so what to be with V of
+B with respect to my fixed frame oh well
+
+ align:start position:0%
+B with respect to my fixed frame oh well
+ 
+
+ align:start position:0%
+B with respect to my fixed frame oh well
+any time you're not sure you go back to
+
+ align:start position:0%
+any time you're not sure you go back to
+ 
+
+ align:start position:0%
+any time you're not sure you go back to
+this formula throw out terms and no Z
+
+ align:start position:0%
+this formula throw out terms and no Z
+ 
+
+ align:start position:0%
+this formula throw out terms and no Z
+dot term this is constant this is zero
+
+ align:start position:0%
+dot term this is constant this is zero
+ 
+
+ align:start position:0%
+dot term this is constant this is zero
+zero zero you have this term some VR and
+
+ align:start position:0%
+zero zero you have this term some VR and
+ 
+
+ align:start position:0%
+zero zero you have this term some VR and
+the R hat direction you have this term
+
+ align:start position:0%
+the R hat direction you have this term
+ 
+
+ align:start position:0%
+the R hat direction you have this term
+right wherever it happens to be in the
+
+ align:start position:0%
+right wherever it happens to be in the
+ 
+
+ align:start position:0%
+right wherever it happens to be in the
+theta hat direction okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our dot R hat Direction plus R theta dot
+
+ align:start position:0%
+our dot R hat Direction plus R theta dot
+ 
+
+ align:start position:0%
+our dot R hat Direction plus R theta dot
+in the theta hat direction
+
+ align:start position:0%
+in the theta hat direction
+ 
+
+ align:start position:0%
+in the theta hat direction
+okay we need acceleration next V with
+
+ align:start position:0%
+okay we need acceleration next V with
+ 
+
+ align:start position:0%
+okay we need acceleration next V with
+respect to O and now you crank through
+
+ align:start position:0%
+respect to O and now you crank through
+ 
+
+ align:start position:0%
+respect to O and now you crank through
+the terms again this time first term is
+
+ align:start position:0%
+the terms again this time first term is
+ 
+
+ align:start position:0%
+the terms again this time first term is
+zero second term is zero because it's
+
+ align:start position:0%
+zero second term is zero because it's
+ 
+
+ align:start position:0%
+zero second term is zero because it's
+constant third term is definitely not
+
+ align:start position:0%
+constant third term is definitely not
+ 
+
+ align:start position:0%
+constant third term is definitely not
+zero four three zero fifth term zero
+
+ align:start position:0%
+zero four three zero fifth term zero
+ 
+
+ align:start position:0%
+zero four three zero fifth term zero
+this term not zero so let me just write
+
+ align:start position:0%
+this term not zero so let me just write
+ 
+
+ align:start position:0%
+this term not zero so let me just write
+them so you get a minus R theta dot
+
+ align:start position:0%
+them so you get a minus R theta dot
+ 
+
+ align:start position:0%
+them so you get a minus R theta dot
+squared R hat and that's the radial
+
+ align:start position:0%
+squared R hat and that's the radial
+ 
+
+ align:start position:0%
+squared R hat and that's the radial
+Direction term plus 2 r dot theta dot
+
+ align:start position:0%
+Direction term plus 2 r dot theta dot
+ 
+
+ align:start position:0%
+Direction term plus 2 r dot theta dot
+theta ad that's the accelerations so you
+
+ align:start position:0%
+theta ad that's the accelerations so you
+ 
+
+ align:start position:0%
+theta ad that's the accelerations so you
+have an acceleration now in the R hat
+
+ align:start position:0%
+have an acceleration now in the R hat
+ 
+
+ align:start position:0%
+have an acceleration now in the R hat
+direction and in the theta hat direction
+
+ align:start position:0%
+direction and in the theta hat direction
+ 
+
+ align:start position:0%
+direction and in the theta hat direction
+if there's acceleration to those
+
+ align:start position:0%
+if there's acceleration to those
+ 
+
+ align:start position:0%
+if there's acceleration to those
+directions there must be forces F equals
+
+ align:start position:0%
+directions there must be forces F equals
+ 
+
+ align:start position:0%
+directions there must be forces F equals
+Newton's second law now says you know
+
+ align:start position:0%
+Newton's second law now says you know
+ 
+
+ align:start position:0%
+Newton's second law now says you know
+again the force is the mass times the
+
+ align:start position:0%
+again the force is the mass times the
+ 
+
+ align:start position:0%
+again the force is the mass times the
+acceleration and this is a vector this
+
+ align:start position:0%
+acceleration and this is a vector this
+ 
+
+ align:start position:0%
+acceleration and this is a vector this
+is a vector it has two components and
+
+ align:start position:0%
+is a vector it has two components and
+ 
+
+ align:start position:0%
+is a vector it has two components and
+the nice thing about these Newton's laws
+
+ align:start position:0%
+the nice thing about these Newton's laws
+ 
+
+ align:start position:0%
+the nice thing about these Newton's laws
+and vectors you can break the problems
+
+ align:start position:0%
+and vectors you can break the problems
+ 
+
+ align:start position:0%
+and vectors you can break the problems
+down into their vector components and
+
+ align:start position:0%
+down into their vector components and
+ 
+
+ align:start position:0%
+down into their vector components and
+treat the our direction as one equation
+
+ align:start position:0%
+treat the our direction as one equation
+ 
+
+ align:start position:0%
+treat the our direction as one equation
+of motion in the theta direction as a
+
+ align:start position:0%
+of motion in the theta direction as a
+ 
+
+ align:start position:0%
+of motion in the theta direction as a
+separate one
+
+ align:start position:0%
+separate one
+ 
+
+ align:start position:0%
+separate one
+so we might want to draw a Freebody
+
+ align:start position:0%
+so we might want to draw a Freebody
+ 
+
+ align:start position:0%
+so we might want to draw a Freebody
+diagram here's this block working its
+
+ align:start position:0%
+diagram here's this block working its
+ 
+
+ align:start position:0%
+diagram here's this block working its
+way out we know that there's probably
+
+ align:start position:0%
+way out we know that there's probably
+ 
+
+ align:start position:0%
+way out we know that there's probably
+some axial force I'm just going to call
+
+ align:start position:0%
+some axial force I'm just going to call
+ 
+
+ align:start position:0%
+some axial force I'm just going to call
+it t and there's some other unknown
+
+ align:start position:0%
+it t and there's some other unknown
+ 
+
+ align:start position:0%
+it t and there's some other unknown
+force here in the theta hat direction so
+
+ align:start position:0%
+force here in the theta hat direction so
+ 
+
+ align:start position:0%
+force here in the theta hat direction so
+this is my theta hat I've drawn this
+
+ align:start position:0%
+this is my theta hat I've drawn this
+ 
+
+ align:start position:0%
+this is my theta hat I've drawn this
+just intentionally in the positive R hat
+
+ align:start position:0%
+just intentionally in the positive R hat
+ 
+
+ align:start position:0%
+just intentionally in the positive R hat
+direction the sign that it comes out
+
+ align:start position:0%
+direction the sign that it comes out
+ 
+
+ align:start position:0%
+direction the sign that it comes out
+will tell us which direction it really
+
+ align:start position:0%
+will tell us which direction it really
+ 
+
+ align:start position:0%
+will tell us which direction it really
+is if you if you're not certain just
+
+ align:start position:0%
+is if you if you're not certain just
+ 
+
+ align:start position:0%
+is if you if you're not certain just
+draw it positive in the positive R hat
+
+ align:start position:0%
+draw it positive in the positive R hat
+ 
+
+ align:start position:0%
+draw it positive in the positive R hat
+direction and this is the that's your
+
+ align:start position:0%
+direction and this is the that's your
+ 
+
+ align:start position:0%
+direction and this is the that's your
+free body diagram if I wanted to put
+
+ align:start position:0%
+free body diagram if I wanted to put
+ 
+
+ align:start position:0%
+free body diagram if I wanted to put
+gravity in there
+
+ align:start position:0%
+gravity in there
+ 
+
+ align:start position:0%
+gravity in there
+I might have but
+
+ align:start position:0%
+I might have but
+ 
+
+ align:start position:0%
+I might have but
+we're doing this in the horizontal plane
+
+ align:start position:0%
+we're doing this in the horizontal plane
+ 
+
+ align:start position:0%
+we're doing this in the horizontal plane
+we'll call gravity is in and out this
+
+ align:start position:0%
+we'll call gravity is in and out this
+ 
+
+ align:start position:0%
+we'll call gravity is in and out this
+way it's in the Z direction and we know
+
+ align:start position:0%
+way it's in the Z direction and we know
+ 
+
+ align:start position:0%
+way it's in the Z direction and we know
+it's constrained can't move Z double dot
+
+ align:start position:0%
+it's constrained can't move Z double dot
+ 
+
+ align:start position:0%
+it's constrained can't move Z double dot
+zero so there's probably some there's
+
+ align:start position:0%
+zero so there's probably some there's
+ 
+
+ align:start position:0%
+zero so there's probably some there's
+certainly a support force that picks up
+
+ align:start position:0%
+certainly a support force that picks up
+ 
+
+ align:start position:0%
+certainly a support force that picks up
+the weight but this is in our horizontal
+
+ align:start position:0%
+the weight but this is in our horizontal
+ 
+
+ align:start position:0%
+the weight but this is in our horizontal
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+there's your Freebody diagram and we can
+
+ align:start position:0%
+there's your Freebody diagram and we can
+ 
+
+ align:start position:0%
+there's your Freebody diagram and we can
+write two equations to solve for these
+
+ align:start position:0%
+write two equations to solve for these
+ 
+
+ align:start position:0%
+write two equations to solve for these
+things so some some of the forces in the
+
+ align:start position:0%
+things so some some of the forces in the
+ 
+
+ align:start position:0%
+things so some some of the forces in the
+R hat direction is T and that must be
+
+ align:start position:0%
+R hat direction is T and that must be
+ 
+
+ align:start position:0%
+R hat direction is T and that must be
+equal to the mass times the acceleration
+
+ align:start position:0%
+equal to the mass times the acceleration
+ 
+
+ align:start position:0%
+equal to the mass times the acceleration
+in the R - M R theta dot squared in the
+
+ align:start position:0%
+in the R - M R theta dot squared in the
+ 
+
+ align:start position:0%
+in the R - M R theta dot squared in the
+R hat direction
+
+ align:start position:0%
+R hat direction
+ 
+
+ align:start position:0%
+R hat direction
+sure enough the tension has to go has to
+
+ align:start position:0%
+sure enough the tension has to go has to
+ 
+
+ align:start position:0%
+sure enough the tension has to go has to
+pull inwards in the minus our hat
+
+ align:start position:0%
+pull inwards in the minus our hat
+ 
+
+ align:start position:0%
+pull inwards in the minus our hat
+direction and that's the fold result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where are they okay so if this and bring
+
+ align:start position:0%
+where are they okay so if this and bring
+ 
+
+ align:start position:0%
+where are they okay so if this and bring
+the ball to the outside where you can
+
+ align:start position:0%
+the ball to the outside where you can
+ 
+
+ align:start position:0%
+the ball to the outside where you can
+see it this thing is going in this
+
+ align:start position:0%
+see it this thing is going in this
+ 
+
+ align:start position:0%
+see it this thing is going in this
+direction right horizontal plane XY
+
+ align:start position:0%
+direction right horizontal plane XY
+ 
+
+ align:start position:0%
+direction right horizontal plane XY
+plane it's moving it's fixed rate out
+
+ align:start position:0%
+plane it's moving it's fixed rate out
+ 
+
+ align:start position:0%
+plane it's moving it's fixed rate out
+all right so it's speed when it's in
+
+ align:start position:0%
+all right so it's speed when it's in
+ 
+
+ align:start position:0%
+all right so it's speed when it's in
+here is our over to Omega in that
+
+ align:start position:0%
+here is our over to Omega in that
+ 
+
+ align:start position:0%
+here is our over to Omega in that
+direction when a speed wind is out here
+
+ align:start position:0%
+direction when a speed wind is out here
+ 
+
+ align:start position:0%
+direction when a speed wind is out here
+it's our Omega in that direction so
+
+ align:start position:0%
+it's our Omega in that direction so
+ 
+
+ align:start position:0%
+it's our Omega in that direction so
+clearly it's it's picking up speed right
+
+ align:start position:0%
+clearly it's it's picking up speed right
+ 
+
+ align:start position:0%
+clearly it's it's picking up speed right
+if it's picking up speed is the picking
+
+ align:start position:0%
+if it's picking up speed is the picking
+ 
+
+ align:start position:0%
+if it's picking up speed is the picking
+up kinetic energy is their work being
+
+ align:start position:0%
+up kinetic energy is their work being
+ 
+
+ align:start position:0%
+up kinetic energy is their work being
+done on it somehow to build up that
+
+ align:start position:0%
+done on it somehow to build up that
+ 
+
+ align:start position:0%
+done on it somehow to build up that
+energy so there must be some forces at
+
+ align:start position:0%
+energy so there must be some forces at
+ 
+
+ align:start position:0%
+energy so there must be some forces at
+play okay so there's a there's a normal
+
+ align:start position:0%
+play okay so there's a there's a normal
+ 
+
+ align:start position:0%
+play okay so there's a there's a normal
+force from the wall of this thing
+
+ align:start position:0%
+force from the wall of this thing
+ 
+
+ align:start position:0%
+force from the wall of this thing
+pushing this ball sideways to speed it
+
+ align:start position:0%
+pushing this ball sideways to speed it
+ 
+
+ align:start position:0%
+pushing this ball sideways to speed it
+up for sure that's one force and the
+
+ align:start position:0%
+up for sure that's one force and the
+ 
+
+ align:start position:0%
+up for sure that's one force and the
+other force is because I'm cannot
+
+ align:start position:0%
+other force is because I'm cannot
+ 
+
+ align:start position:0%
+other force is because I'm cannot
+allowing this thing just to go freely
+
+ align:start position:0%
+allowing this thing just to go freely
+ 
+
+ align:start position:0%
+allowing this thing just to go freely
+out I'm constraining it to constant
+
+ align:start position:0%
+out I'm constraining it to constant
+ 
+
+ align:start position:0%
+out I'm constraining it to constant
+speed out it would really like to go a
+
+ align:start position:0%
+speed out it would really like to go a
+ 
+
+ align:start position:0%
+speed out it would really like to go a
+lot faster than that so what's holding
+
+ align:start position:0%
+lot faster than that so what's holding
+ 
+
+ align:start position:0%
+lot faster than that so what's holding
+it back it's at any instant of time it
+
+ align:start position:0%
+it back it's at any instant of time it
+ 
+
+ align:start position:0%
+it back it's at any instant of time it
+has centripetal acceleration and what's
+
+ align:start position:0%
+has centripetal acceleration and what's
+ 
+
+ align:start position:0%
+has centripetal acceleration and what's
+whole what's keep making it go in the
+
+ align:start position:0%
+whole what's keep making it go in the
+ 
+
+ align:start position:0%
+whole what's keep making it go in the
+circle is a force that is in this case
+
+ align:start position:0%
+circle is a force that is in this case
+ 
+
+ align:start position:0%
+circle is a force that is in this case
+if that were a nut with threads it
+
+ align:start position:0%
+if that were a nut with threads it
+ 
+
+ align:start position:0%
+if that were a nut with threads it
+forces and the threads are applying to
+
+ align:start position:0%
+forces and the threads are applying to
+ 
+
+ align:start position:0%
+forces and the threads are applying to
+the knot to keep it from getting from
+
+ align:start position:0%
+the knot to keep it from getting from
+ 
+
+ align:start position:0%
+the knot to keep it from getting from
+running away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I've broken down I've chosen I the
+
+ align:start position:0%
+well I've broken down I've chosen I the
+ 
+
+ align:start position:0%
+well I've broken down I've chosen I the
+total force acting on this thing is some
+
+ align:start position:0%
+total force acting on this thing is some
+ 
+
+ align:start position:0%
+total force acting on this thing is some
+combination of a force in that direction
+
+ align:start position:0%
+combination of a force in that direction
+ 
+
+ align:start position:0%
+combination of a force in that direction
+and a combination in the axial direction
+
+ align:start position:0%
+and a combination in the axial direction
+ 
+
+ align:start position:0%
+and a combination in the axial direction
+so it has some net net vector direction
+
+ align:start position:0%
+so it has some net net vector direction
+ 
+
+ align:start position:0%
+so it has some net net vector direction
+that's neither this nor that right but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this this thing is rotating about
+
+ align:start position:0%
+so this this thing is rotating about
+ 
+
+ align:start position:0%
+so this this thing is rotating about
+some center over here right so this is
+
+ align:start position:0%
+some center over here right so this is
+ 
+
+ align:start position:0%
+some center over here right so this is
+theta dot theta is going in this
+
+ align:start position:0%
+theta dot theta is going in this
+ 
+
+ align:start position:0%
+theta dot theta is going in this
+direction theta dot and it's just we've
+
+ align:start position:0%
+direction theta dot and it's just we've
+ 
+
+ align:start position:0%
+direction theta dot and it's just we've
+chosen a coordinate system that has unit
+
+ align:start position:0%
+chosen a coordinate system that has unit
+ 
+
+ align:start position:0%
+chosen a coordinate system that has unit
+vectors R hat and theta hat and so it
+
+ align:start position:0%
+vectors R hat and theta hat and so it
+ 
+
+ align:start position:0%
+vectors R hat and theta hat and so it
+makes sense we can express the
+
+ align:start position:0%
+makes sense we can express the
+ 
+
+ align:start position:0%
+makes sense we can express the
+acceleration in terms of those two
+
+ align:start position:0%
+acceleration in terms of those two
+ 
+
+ align:start position:0%
+acceleration in terms of those two
+components it makes sense to express the
+
+ align:start position:0%
+components it makes sense to express the
+ 
+
+ align:start position:0%
+components it makes sense to express the
+forces in the same direction so I've
+
+ align:start position:0%
+forces in the same direction so I've
+ 
+
+ align:start position:0%
+forces in the same direction so I've
+just arbitrarily said I have some
+
+ align:start position:0%
+just arbitrarily said I have some
+ 
+
+ align:start position:0%
+just arbitrarily said I have some
+unknown force that's in this direction
+
+ align:start position:0%
+unknown force that's in this direction
+ 
+
+ align:start position:0%
+unknown force that's in this direction
+and I have another unknown force in that
+
+ align:start position:0%
+and I have another unknown force in that
+ 
+
+ align:start position:0%
+and I have another unknown force in that
+direction and but I know that that I'm
+
+ align:start position:0%
+direction and but I know that that I'm
+ 
+
+ align:start position:0%
+direction and but I know that that I'm
+saying there account for all forces in
+
+ align:start position:0%
+saying there account for all forces in
+ 
+
+ align:start position:0%
+saying there account for all forces in
+this direction whatever their source
+
+ align:start position:0%
+this direction whatever their source
+ 
+
+ align:start position:0%
+this direction whatever their source
+that tells me that some of the external
+
+ align:start position:0%
+that tells me that some of the external
+ 
+
+ align:start position:0%
+that tells me that some of the external
+forces in the theta hat direction in
+
+ align:start position:0%
+forces in the theta hat direction in
+ 
+
+ align:start position:0%
+forces in the theta hat direction in
+this case is this unknown F but I know
+
+ align:start position:0%
+this case is this unknown F but I know
+ 
+
+ align:start position:0%
+this case is this unknown F but I know
+from Newton that that's got to be equal
+
+ align:start position:0%
+from Newton that that's got to be equal
+ 
+
+ align:start position:0%
+from Newton that that's got to be equal
+to the mass times acceleration in that
+
+ align:start position:0%
+to the mass times acceleration in that
+ 
+
+ align:start position:0%
+to the mass times acceleration in that
+direction but in this case then that is
+
+ align:start position:0%
+direction but in this case then that is
+ 
+
+ align:start position:0%
+direction but in this case then that is
+2m r dot theta dot theta hat okay so
+
+ align:start position:0%
+2m r dot theta dot theta hat okay so
+ 
+
+ align:start position:0%
+2m r dot theta dot theta hat okay so
+there must that got this right district
+
+ align:start position:0%
+there must that got this right district
+ 
+
+ align:start position:0%
+there must that got this right district
+way ssin and applying Newton's second
+
+ align:start position:0%
+way ssin and applying Newton's second
+ 
+
+ align:start position:0%
+way ssin and applying Newton's second
+law I can find out what that force must
+
+ align:start position:0%
+law I can find out what that force must
+ 
+
+ align:start position:0%
+law I can find out what that force must
+be then it would have been a lot more
+
+ align:start position:0%
+be then it would have been a lot more
+ 
+
+ align:start position:0%
+be then it would have been a lot more
+work if I had drawn it in some arbitrary
+
+ align:start position:0%
+work if I had drawn it in some arbitrary
+ 
+
+ align:start position:0%
+work if I had drawn it in some arbitrary
+in-between direction because then I'd
+
+ align:start position:0%
+in-between direction because then I'd
+ 
+
+ align:start position:0%
+in-between direction because then I'd
+have to break it down into its
+
+ align:start position:0%
+have to break it down into its
+ 
+
+ align:start position:0%
+have to break it down into its
+components to write this so I've done it
+
+ align:start position:0%
+components to write this so I've done it
+ 
+
+ align:start position:0%
+components to write this so I've done it
+made it as easy as possible for myself
+
+ align:start position:0%
+made it as easy as possible for myself
+ 
+
+ align:start position:0%
+made it as easy as possible for myself
+so there's a force like this and there
+
+ align:start position:0%
+so there's a force like this and there
+ 
+
+ align:start position:0%
+so there's a force like this and there
+is another force like that this one week
+
+ align:start position:0%
+is another force like that this one week
+ 
+
+ align:start position:0%
+is another force like that this one week
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+was caused by the centripetal
+
+ align:start position:0%
+was caused by the centripetal
+ 
+
+ align:start position:0%
+was caused by the centripetal
+acceleration or this force causes the
+
+ align:start position:0%
+acceleration or this force causes the
+ 
+
+ align:start position:0%
+acceleration or this force causes the
+centripetal acceleration in order to
+
+ align:start position:0%
+centripetal acceleration in order to
+ 
+
+ align:start position:0%
+centripetal acceleration in order to
+make something go in a circular path you
+
+ align:start position:0%
+make something go in a circular path you
+ 
+
+ align:start position:0%
+make something go in a circular path you
+have to exert a force on it that's the
+
+ align:start position:0%
+have to exert a force on it that's the
+ 
+
+ align:start position:0%
+have to exert a force on it that's the
+force and in order to accelerate
+
+ align:start position:0%
+force and in order to accelerate
+ 
+
+ align:start position:0%
+force and in order to accelerate
+something angular ly you have to apply a
+
+ align:start position:0%
+something angular ly you have to apply a
+ 
+
+ align:start position:0%
+something angular ly you have to apply a
+force that comes from the euler term and
+
+ align:start position:0%
+force that comes from the euler term and
+ 
+
+ align:start position:0%
+force that comes from the euler term and
+this is the curious term this is the
+
+ align:start position:0%
+this is the curious term this is the
+ 
+
+ align:start position:0%
+this is the curious term this is the
+Coriolis term and that's so where does
+
+ align:start position:0%
+Coriolis term and that's so where does
+ 
+
+ align:start position:0%
+Coriolis term and that's so where does
+it come from you know that's the it's a
+
+ align:start position:0%
+it come from you know that's the it's a
+ 
+
+ align:start position:0%
+it come from you know that's the it's a
+that's that's the crux of the matter
+
+ align:start position:0%
+that's that's the crux of the matter
+ 
+
+ align:start position:0%
+that's that's the crux of the matter
+here where does it come from so part of
+
+ align:start position:0%
+here where does it come from so part of
+ 
+
+ align:start position:0%
+here where does it come from so part of
+the reading that you need to do now is
+
+ align:start position:0%
+the reading that you need to do now is
+ 
+
+ align:start position:0%
+the reading that you need to do now is
+chapter 15 chapter 15 most of it is
+
+ align:start position:0%
+chapter 15 chapter 15 most of it is
+ 
+
+ align:start position:0%
+chapter 15 chapter 15 most of it is
+going to be to complete review it just
+
+ align:start position:0%
+going to be to complete review it just
+ 
+
+ align:start position:0%
+going to be to complete review it just
+says the conservation of a linear
+
+ align:start position:0%
+says the conservation of a linear
+ 
+
+ align:start position:0%
+says the conservation of a linear
+momentum impulse and momentum but it
+
+ align:start position:0%
+momentum impulse and momentum but it
+ 
+
+ align:start position:0%
+momentum impulse and momentum but it
+also gets into angular momentum so we're
+
+ align:start position:0%
+also gets into angular momentum so we're
+ 
+
+ align:start position:0%
+also gets into angular momentum so we're
+going to talk quite a lot about angular
+
+ align:start position:0%
+going to talk quite a lot about angular
+ 
+
+ align:start position:0%
+going to talk quite a lot about angular
+momentum but and I want to do very brief
+
+ align:start position:0%
+momentum but and I want to do very brief
+ 
+
+ align:start position:0%
+momentum but and I want to do very brief
+little review right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that it so that it applies to this
+
+ align:start position:0%
+that it so that it applies to this
+ 
+
+ align:start position:0%
+that it so that it applies to this
+problem so we've come up with an
+
+ align:start position:0%
+problem so we've come up with an
+ 
+
+ align:start position:0%
+problem so we've come up with an
+expression that the force in the theta
+
+ align:start position:0%
+expression that the force in the theta
+ 
+
+ align:start position:0%
+expression that the force in the theta
+Direction here comes there's got to be
+
+ align:start position:0%
+Direction here comes there's got to be
+ 
+
+ align:start position:0%
+Direction here comes there's got to be
+that 2m r dot theta dot so here's my
+
+ align:start position:0%
+that 2m r dot theta dot so here's my
+ 
+
+ align:start position:0%
+that 2m r dot theta dot so here's my
+point O and a for that matter but
+
+ align:start position:0%
+point O and a for that matter but
+ 
+
+ align:start position:0%
+point O and a for that matter but
+looking down on our problem here's my
+
+ align:start position:0%
+looking down on our problem here's my
+ 
+
+ align:start position:0%
+looking down on our problem here's my
+mass some instant in time my rotation
+
+ align:start position:0%
+mass some instant in time my rotation
+ 
+
+ align:start position:0%
+mass some instant in time my rotation
+rate is theta dot work actually colic
+
+ align:start position:0%
+rate is theta dot work actually colic
+ 
+
+ align:start position:0%
+rate is theta dot work actually colic
+it's constant so it's K hat like that
+
+ align:start position:0%
+it's constant so it's K hat like that
+ 
+
+ align:start position:0%
+it's constant so it's K hat like that
+Kappa Omega K hat this is my R hat
+
+ align:start position:0%
+Kappa Omega K hat this is my R hat
+ 
+
+ align:start position:0%
+Kappa Omega K hat this is my R hat
+direction theta hat now this is I'm
+
+ align:start position:0%
+direction theta hat now this is I'm
+ 
+
+ align:start position:0%
+direction theta hat now this is I'm
+going to treat this as a particle not
+
+ align:start position:0%
+going to treat this as a particle not
+ 
+
+ align:start position:0%
+going to treat this as a particle not
+long we're going to be talking about the
+
+ align:start position:0%
+long we're going to be talking about the
+ 
+
+ align:start position:0%
+long we're going to be talking about the
+dynamics of rigid bodies we're just
+
+ align:start position:0%
+dynamics of rigid bodies we're just
+ 
+
+ align:start position:0%
+dynamics of rigid bodies we're just
+doing particles for the moment we think
+
+ align:start position:0%
+doing particles for the moment we think
+ 
+
+ align:start position:0%
+doing particles for the moment we think
+of them just as point masses and don't
+
+ align:start position:0%
+of them just as point masses and don't
+ 
+
+ align:start position:0%
+of them just as point masses and don't
+deal with their with their finite extent
+
+ align:start position:0%
+deal with their with their finite extent
+ 
+
+ align:start position:0%
+deal with their with their finite extent
+so we're still thinking of this as a
+
+ align:start position:0%
+so we're still thinking of this as a
+ 
+
+ align:start position:0%
+so we're still thinking of this as a
+particle and I'm going to write down the
+
+ align:start position:0%
+particle and I'm going to write down the
+ 
+
+ align:start position:0%
+particle and I'm going to write down the
+definition of the angular momentum of a
+
+ align:start position:0%
+definition of the angular momentum of a
+ 
+
+ align:start position:0%
+definition of the angular momentum of a
+particle this is be out here with
+
+ align:start position:0%
+particle this is be out here with
+ 
+
+ align:start position:0%
+particle this is be out here with
+respect to my fixed frame here at O and
+
+ align:start position:0%
+respect to my fixed frame here at O and
+ 
+
+ align:start position:0%
+respect to my fixed frame here at O and
+I'm going to use a lowercase H to
+
+ align:start position:0%
+I'm going to use a lowercase H to
+ 
+
+ align:start position:0%
+I'm going to use a lowercase H to
+describe angular momentum of particles
+
+ align:start position:0%
+describe angular momentum of particles
+ 
+
+ align:start position:0%
+describe angular momentum of particles
+that I'll be using to use capital H to
+
+ align:start position:0%
+that I'll be using to use capital H to
+ 
+
+ align:start position:0%
+that I'll be using to use capital H to
+describe the angular momentum of rigid
+
+ align:start position:0%
+describe the angular momentum of rigid
+ 
+
+ align:start position:0%
+describe the angular momentum of rigid
+bodies so this is a particle definition
+
+ align:start position:0%
+bodies so this is a particle definition
+ 
+
+ align:start position:0%
+bodies so this is a particle definition
+of the angular momentum of a particle
+
+ align:start position:0%
+of the angular momentum of a particle
+ 
+
+ align:start position:0%
+of the angular momentum of a particle
+with respect to a fixed point what we're
+
+ align:start position:0%
+with respect to a fixed point what we're
+ 
+
+ align:start position:0%
+with respect to a fixed point what we're
+going to come back to that that'll turn
+
+ align:start position:0%
+going to come back to that that'll turn
+ 
+
+ align:start position:0%
+going to come back to that that'll turn
+out to have some significance the
+
+ align:start position:0%
+out to have some significance the
+ 
+
+ align:start position:0%
+out to have some significance the
+definition of this is it's our B oh the
+
+ align:start position:0%
+definition of this is it's our B oh the
+ 
+
+ align:start position:0%
+definition of this is it's our B oh the
+position vector cross with the linear
+
+ align:start position:0%
+position vector cross with the linear
+ 
+
+ align:start position:0%
+position vector cross with the linear
+momentum evaluated in the fixed frame so
+
+ align:start position:0%
+momentum evaluated in the fixed frame so
+ 
+
+ align:start position:0%
+momentum evaluated in the fixed frame so
+that's the definition of angular
+
+ align:start position:0%
+that's the definition of angular
+ 
+
+ align:start position:0%
+that's the definition of angular
+momentum which is you have linear
+
+ align:start position:0%
+momentum which is you have linear
+ 
+
+ align:start position:0%
+momentum which is you have linear
+momentum and it's the cross product with
+
+ align:start position:0%
+momentum and it's the cross product with
+ 
+
+ align:start position:0%
+momentum and it's the cross product with
+the position vector out to it so in this
+
+ align:start position:0%
+the position vector out to it so in this
+ 
+
+ align:start position:0%
+the position vector out to it so in this
+case the rbo is
+
+ align:start position:0%
+case the rbo is
+ 
+
+ align:start position:0%
+case the rbo is
+Capital are our hat this is well it's
+
+ align:start position:0%
+Capital are our hat this is well it's
+ 
+
+ align:start position:0%
+Capital are our hat this is well it's
+not it's not this various excuses I'm
+
+ align:start position:0%
+not it's not this various excuses I'm
+ 
+
+ align:start position:0%
+not it's not this various excuses I'm
+not going to use it better or not I
+
+ align:start position:0%
+not going to use it better or not I
+ 
+
+ align:start position:0%
+not going to use it better or not I
+don't want to this I use as a constant I
+
+ align:start position:0%
+don't want to this I use as a constant I
+ 
+
+ align:start position:0%
+don't want to this I use as a constant I
+better keep it as the variable pardon
+
+ align:start position:0%
+better keep it as the variable pardon
+ 
+
+ align:start position:0%
+better keep it as the variable pardon
+that so it's our whatever the local
+
+ align:start position:0%
+that so it's our whatever the local
+ 
+
+ align:start position:0%
+that so it's our whatever the local
+position is in the R hat direction
+
+ align:start position:0%
+position is in the R hat direction
+ 
+
+ align:start position:0%
+position is in the R hat direction
+crossed with the linear momentum
+
+ align:start position:0%
+crossed with the linear momentum
+ 
+
+ align:start position:0%
+crossed with the linear momentum
+what's the linear momentum of that
+
+ align:start position:0%
+what's the linear momentum of that
+ 
+
+ align:start position:0%
+what's the linear momentum of that
+particle mass times velocity what's the
+
+ align:start position:0%
+particle mass times velocity what's the
+ 
+
+ align:start position:0%
+particle mass times velocity what's the
+velocity theta dot where do we write it
+
+ align:start position:0%
+velocity theta dot where do we write it
+ 
+
+ align:start position:0%
+velocity theta dot where do we write it
+up here someplace
+
+ align:start position:0%
+up here someplace
+ 
+
+ align:start position:0%
+up here someplace
+are the total velocity is r dot R hat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus R theta dot theta hat right and we
+
+ align:start position:0%
+plus R theta dot theta hat right and we
+ 
+
+ align:start position:0%
+plus R theta dot theta hat right and we
+need a mass in here so mass times
+
+ align:start position:0%
+need a mass in here so mass times
+ 
+
+ align:start position:0%
+need a mass in here so mass times
+velocity would be the momentum and we
+
+ align:start position:0%
+velocity would be the momentum and we
+ 
+
+ align:start position:0%
+velocity would be the momentum and we
+need the cross products without our hat
+
+ align:start position:0%
+need the cross products without our hat
+ 
+
+ align:start position:0%
+need the cross products without our hat
+cross our hat you get nothing from that
+
+ align:start position:0%
+cross our hat you get nothing from that
+ 
+
+ align:start position:0%
+cross our hat you get nothing from that
+and our hat cross theta hat positive or
+
+ align:start position:0%
+and our hat cross theta hat positive or
+ 
+
+ align:start position:0%
+and our hat cross theta hat positive or
+negative positive K right so this
+
+ align:start position:0%
+negative positive K right so this
+ 
+
+ align:start position:0%
+negative positive K right so this
+becomes M R squared theta dot in the K
+
+ align:start position:0%
+becomes M R squared theta dot in the K
+ 
+
+ align:start position:0%
+becomes M R squared theta dot in the K
+hat direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is this one is a constant
+
+ align:start position:0%
+and this is this one is a constant
+ 
+
+ align:start position:0%
+and this is this one is a constant
+alright this is cap Omega okay so this
+
+ align:start position:0%
+alright this is cap Omega okay so this
+ 
+
+ align:start position:0%
+alright this is cap Omega okay so this
+is my angular momentum of my particle
+
+ align:start position:0%
+is my angular momentum of my particle
+ 
+
+ align:start position:0%
+is my angular momentum of my particle
+with respect to this fixed reference
+
+ align:start position:0%
+with respect to this fixed reference
+ 
+
+ align:start position:0%
+with respect to this fixed reference
+frame and so last one final step that
+
+ align:start position:0%
+frame and so last one final step that
+ 
+
+ align:start position:0%
+frame and so last one final step that
+you know from your previous physics is
+
+ align:start position:0%
+you know from your previous physics is
+ 
+
+ align:start position:0%
+you know from your previous physics is
+well house torque related to angular
+
+ align:start position:0%
+well house torque related to angular
+ 
+
+ align:start position:0%
+well house torque related to angular
+momentum take again what do you remember
+
+ align:start position:0%
+momentum take again what do you remember
+ 
+
+ align:start position:0%
+momentum take again what do you remember
+time derivative so D by DT of HBO here
+
+ align:start position:0%
+time derivative so D by DT of HBO here
+ 
+
+ align:start position:0%
+time derivative so D by DT of HBO here
+the time rate of change of this vector
+
+ align:start position:0%
+the time rate of change of this vector
+ 
+
+ align:start position:0%
+the time rate of change of this vector
+is the torque with respect to this point
+
+ align:start position:0%
+is the torque with respect to this point
+ 
+
+ align:start position:0%
+is the torque with respect to this point
+with respect to O so what are constants
+
+ align:start position:0%
+with respect to O so what are constants
+ 
+
+ align:start position:0%
+with respect to O so what are constants
+in this thing we don't have to deal with
+
+ align:start position:0%
+in this thing we don't have to deal with
+ 
+
+ align:start position:0%
+in this thing we don't have to deal with
+their derivatives K hat is it does the
+
+ align:start position:0%
+their derivatives K hat is it does the
+ 
+
+ align:start position:0%
+their derivatives K hat is it does the
+direction of the angular momentum change
+
+ align:start position:0%
+direction of the angular momentum change
+ 
+
+ align:start position:0%
+direction of the angular momentum change
+it's upwards the derivative of K the
+
+ align:start position:0%
+it's upwards the derivative of K the
+ 
+
+ align:start position:0%
+it's upwards the derivative of K the
+unit vector K does it change in this
+
+ align:start position:0%
+unit vector K does it change in this
+ 
+
+ align:start position:0%
+unit vector K does it change in this
+problem no so there's no time for it to
+
+ align:start position:0%
+problem no so there's no time for it to
+ 
+
+ align:start position:0%
+problem no so there's no time for it to
+zero it's times derivative is zero the M
+
+ align:start position:0%
+zero it's times derivative is zero the M
+ 
+
+ align:start position:0%
+zero it's times derivative is zero the M
+time derivative is zero the only thing
+
+ align:start position:0%
+time derivative is zero the only thing
+ 
+
+ align:start position:0%
+time derivative is zero the only thing
+you have to take derivative is r so to
+
+ align:start position:0%
+you have to take derivative is r so to
+ 
+
+ align:start position:0%
+you have to take derivative is r so to
+our r dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the torque is 2m r r dot Kappa Omega
+
+ align:start position:0%
+so the torque is 2m r r dot Kappa Omega
+ 
+
+ align:start position:0%
+so the torque is 2m r r dot Kappa Omega
+and it's all in the K direction and that
+
+ align:start position:0%
+and it's all in the K direction and that
+ 
+
+ align:start position:0%
+and it's all in the K direction and that
+had better be our vo cross F torque
+
+ align:start position:0%
+had better be our vo cross F torque
+ 
+
+ align:start position:0%
+had better be our vo cross F torque
+comes as a force times the moment arm
+
+ align:start position:0%
+comes as a force times the moment arm
+ 
+
+ align:start position:0%
+comes as a force times the moment arm
+right and we computed here a force in
+
+ align:start position:0%
+right and we computed here a force in
+ 
+
+ align:start position:0%
+right and we computed here a force in
+the theta direction so what would give
+
+ align:start position:0%
+the theta direction so what would give
+ 
+
+ align:start position:0%
+the theta direction so what would give
+us a torque in the K direction at R
+
+ align:start position:0%
+us a torque in the K direction at R
+ 
+
+ align:start position:0%
+us a torque in the K direction at R
+cross theta R hat cross theta hat gives
+
+ align:start position:0%
+cross theta R hat cross theta hat gives
+ 
+
+ align:start position:0%
+cross theta R hat cross theta hat gives
+you a K right R cross and this force the
+
+ align:start position:0%
+you a K right R cross and this force the
+ 
+
+ align:start position:0%
+you a K right R cross and this force the
+part of the force we have two forces one
+
+ align:start position:0%
+part of the force we have two forces one
+ 
+
+ align:start position:0%
+part of the force we have two forces one
+in the r direction and one in the theta
+
+ align:start position:0%
+in the r direction and one in the theta
+ 
+
+ align:start position:0%
+in the r direction and one in the theta
+direction the cross product this term up
+
+ align:start position:0%
+direction the cross product this term up
+ 
+
+ align:start position:0%
+direction the cross product this term up
+here the t gives you nothing right
+
+ align:start position:0%
+here the t gives you nothing right
+ 
+
+ align:start position:0%
+here the t gives you nothing right
+across our hat across our hat so the
+
+ align:start position:0%
+across our hat across our hat so the
+ 
+
+ align:start position:0%
+across our hat across our hat so the
+only force that matters here is this
+
+ align:start position:0%
+only force that matters here is this
+ 
+
+ align:start position:0%
+only force that matters here is this
+Coriolis one okay and so that force is
+
+ align:start position:0%
+Coriolis one okay and so that force is
+ 
+
+ align:start position:0%
+Coriolis one okay and so that force is
+2m r dot theta dot and we have the R
+
+ align:start position:0%
+2m r dot theta dot and we have the R
+ 
+
+ align:start position:0%
+2m r dot theta dot and we have the R
+cross we know this comes out in the K
+
+ align:start position:0%
+cross we know this comes out in the K
+ 
+
+ align:start position:0%
+cross we know this comes out in the K
+direction and we get an R in here when
+
+ align:start position:0%
+direction and we get an R in here when
+ 
+
+ align:start position:0%
+direction and we get an R in here when
+we compute this product and this to me
+
+ align:start position:0%
+we compute this product and this to me
+ 
+
+ align:start position:0%
+we compute this product and this to me
+looks an awful lot like this except I
+
+ align:start position:0%
+looks an awful lot like this except I
+ 
+
+ align:start position:0%
+looks an awful lot like this except I
+missed an R squared how do I do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh no it's not our squared it started
+
+ align:start position:0%
+oh no it's not our squared it started
+ 
+
+ align:start position:0%
+oh no it's not our squared it started
+off over here as the angular momentum
+
+ align:start position:0%
+off over here as the angular momentum
+ 
+
+ align:start position:0%
+off over here as the angular momentum
+has in our square it took the derivative
+
+ align:start position:0%
+has in our square it took the derivative
+ 
+
+ align:start position:0%
+has in our square it took the derivative
+it dropped down to two our our dot
+
+ align:start position:0%
+it dropped down to two our our dot
+ 
+
+ align:start position:0%
+it dropped down to two our our dot
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+so the Coriolis force what's it got to
+
+ align:start position:0%
+so the Coriolis force what's it got to
+ 
+
+ align:start position:0%
+so the Coriolis force what's it got to
+do with the angular momentum that's kind
+
+ align:start position:0%
+do with the angular momentum that's kind
+ 
+
+ align:start position:0%
+do with the angular momentum that's kind
+of the point of the exercise here in
+
+ align:start position:0%
+of the point of the exercise here in
+ 
+
+ align:start position:0%
+of the point of the exercise here in
+order for this ping-pong ball to excel
+
+ align:start position:0%
+order for this ping-pong ball to excel
+ 
+
+ align:start position:0%
+order for this ping-pong ball to excel
+to be accelerated it's as it goes slowly
+
+ align:start position:0%
+to be accelerated it's as it goes slowly
+ 
+
+ align:start position:0%
+to be accelerated it's as it goes slowly
+out this tube the angular momentum is
+
+ align:start position:0%
+out this tube the angular momentum is
+ 
+
+ align:start position:0%
+out this tube the angular momentum is
+increasing in order to change angular
+
+ align:start position:0%
+increasing in order to change angular
+ 
+
+ align:start position:0%
+increasing in order to change angular
+momentum with time you have to apply a
+
+ align:start position:0%
+momentum with time you have to apply a
+ 
+
+ align:start position:0%
+momentum with time you have to apply a
+torque the torque that you have to apply
+
+ align:start position:0%
+torque the torque that you have to apply
+ 
+
+ align:start position:0%
+torque the torque that you have to apply
+is 2m RR dot in the K direction and that
+
+ align:start position:0%
+is 2m RR dot in the K direction and that
+ 
+
+ align:start position:0%
+is 2m RR dot in the K direction and that
+is our cross the Coriolis force so the
+
+ align:start position:0%
+is our cross the Coriolis force so the
+ 
+
+ align:start position:0%
+is our cross the Coriolis force so the
+Coriolis force in this case is the force
+
+ align:start position:0%
+Coriolis force in this case is the force
+ 
+
+ align:start position:0%
+Coriolis force in this case is the force
+that's necessary to increase the angular
+
+ align:start position:0%
+that's necessary to increase the angular
+ 
+
+ align:start position:0%
+that's necessary to increase the angular
+one of the angular momentum system
+
+ align:start position:0%
+one of the angular momentum system
+ 
+
+ align:start position:0%
+one of the angular momentum system
+that's very often the reason that's
+
+ align:start position:0%
+that's very often the reason that's
+ 
+
+ align:start position:0%
+that's very often the reason that's
+where it what Coriolis force is about so
+
+ align:start position:0%
+where it what Coriolis force is about so
+ 
+
+ align:start position:0%
+where it what Coriolis force is about so
+when you shoot an artillery piece in on
+
+ align:start position:0%
+when you shoot an artillery piece in on
+ 
+
+ align:start position:0%
+when you shoot an artillery piece in on
+the earth
+
+ align:start position:0%
+the earth
+ 
+
+ align:start position:0%
+the earth
+you got the projectile going out there
+
+ align:start position:0%
+you got the projectile going out there
+ 
+
+ align:start position:0%
+you got the projectile going out there
+it has angular momentum with respect to
+
+ align:start position:0%
+it has angular momentum with respect to
+ 
+
+ align:start position:0%
+it has angular momentum with respect to
+the earth and you'll find out that this
+
+ align:start position:0%
+the earth and you'll find out that this
+ 
+
+ align:start position:0%
+the earth and you'll find out that this
+little term pops up and in fact the
+
+ align:start position:0%
+little term pops up and in fact the
+ 
+
+ align:start position:0%
+little term pops up and in fact the
+projectile doesn't go straight it curves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's lots of things that because of
+
+ align:start position:0%
+there's lots of things that because of
+ 
+
+ align:start position:0%
+there's lots of things that because of
+conservation of angular momentum you end
+
+ align:start position:0%
+conservation of angular momentum you end
+ 
+
+ align:start position:0%
+conservation of angular momentum you end
+up with this term popping up in this
+
+ align:start position:0%
+up with this term popping up in this
+ 
+
+ align:start position:0%
+up with this term popping up in this
+case angular momentum is not conserved
+
+ align:start position:0%
+case angular momentum is not conserved
+ 
+
+ align:start position:0%
+case angular momentum is not conserved
+it's increasing so you have this force
+
+ align:start position:0%
+it's increasing so you have this force
+ 
+
+ align:start position:0%
+it's increasing so you have this force
+to make it happen any questions about
+
+ align:start position:0%
+to make it happen any questions about
+ 
+
+ align:start position:0%
+to make it happen any questions about
+this we're going to see a lot you're
+
+ align:start position:0%
+this we're going to see a lot you're
+ 
+
+ align:start position:0%
+this we're going to see a lot you're
+going to use this one a lot you going to
+
+ align:start position:0%
+going to use this one a lot you going to
+ 
+
+ align:start position:0%
+going to use this one a lot you going to
+work with it a lot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so anytime you see changes in angular
+
+ align:start position:0%
+so anytime you see changes in angular
+ 
+
+ align:start position:0%
+so anytime you see changes in angular
+momentum happening in a problem in these
+
+ align:start position:0%
+momentum happening in a problem in these
+ 
+
+ align:start position:0%
+momentum happening in a problem in these
+moat in these problems with circular
+
+ align:start position:0%
+moat in these problems with circular
+ 
+
+ align:start position:0%
+moat in these problems with circular
+motion velocities of parts increasing
+
+ align:start position:0%
+motion velocities of parts increasing
+ 
+
+ align:start position:0%
+motion velocities of parts increasing
+and radius you'll almost always see this
+
+ align:start position:0%
+and radius you'll almost always see this
+ 
+
+ align:start position:0%
+and radius you'll almost always see this
+term pop up anytime you see these
+
+ align:start position:0%
+term pop up anytime you see these
+ 
+
+ align:start position:0%
+term pop up anytime you see these
+changes in angular momentum you'll often
+
+ align:start position:0%
+changes in angular momentum you'll often
+ 
+
+ align:start position:0%
+changes in angular momentum you'll often
+see the Coriolis term
+
+ align:start position:0%
+see the Coriolis term
+ 
+
+ align:start position:0%
+see the Coriolis term
+all right now we're going to do a let's
+
+ align:start position:0%
+all right now we're going to do a let's
+ 
+
+ align:start position:0%
+all right now we're going to do a let's
+do a really another interesting problem
+
+ align:start position:0%
+do a really another interesting problem
+ 
+
+ align:start position:0%
+do a really another interesting problem
+simple but interesting and that is
+
+ align:start position:0%
+simple but interesting and that is
+ 
+
+ align:start position:0%
+simple but interesting and that is
+really to go let's go do this problem
+
+ align:start position:0%
+really to go let's go do this problem
+ 
+
+ align:start position:0%
+really to go let's go do this problem
+where the things really allowed to come
+
+ align:start position:0%
+where the things really allowed to come
+ 
+
+ align:start position:0%
+where the things really allowed to come
+freely out okay all right
+
+ align:start position:0%
+freely out okay all right
+ 
+
+ align:start position:0%
+freely out okay all right
+you're ready to fend yourselves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right a little short stick is pretty
+
+ align:start position:0%
+all right a little short stick is pretty
+ 
+
+ align:start position:0%
+all right a little short stick is pretty
+effective at throwing candy all right
+
+ align:start position:0%
+effective at throwing candy all right
+ 
+
+ align:start position:0%
+effective at throwing candy all right
+you got your safety glasses on you want
+
+ align:start position:0%
+you got your safety glasses on you want
+ 
+
+ align:start position:0%
+you got your safety glasses on you want
+me to see if I can get one up there also
+
+ align:start position:0%
+me to see if I can get one up there also
+ 
+
+ align:start position:0%
+me to see if I can get one up there also
+I obviously haven't practiced this right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+last one actually this just two more all
+
+ align:start position:0%
+last one actually this just two more all
+ 
+
+ align:start position:0%
+last one actually this just two more all
+right what makes this work all right
+
+ align:start position:0%
+right what makes this work all right
+ 
+
+ align:start position:0%
+right what makes this work all right
+let's do that let's do this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry let's look at our candy shooter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm whipping this thing around
+
+ align:start position:0%
+so I'm whipping this thing around
+ 
+
+ align:start position:0%
+so I'm whipping this thing around
+candies coming out of here is it B again
+
+ align:start position:0%
+candies coming out of here is it B again
+ 
+
+ align:start position:0%
+candies coming out of here is it B again
+I got a nosy not mess with the Z part z
+
+ align:start position:0%
+I got a nosy not mess with the Z part z
+ 
+
+ align:start position:0%
+I got a nosy not mess with the Z part z
+part is trivial to usually deal with
+
+ align:start position:0%
+part is trivial to usually deal with
+ 
+
+ align:start position:0%
+part is trivial to usually deal with
+because it's totally independent just
+
+ align:start position:0%
+because it's totally independent just
+ 
+
+ align:start position:0%
+because it's totally independent just
+separate equations doesn't complicate
+
+ align:start position:0%
+separate equations doesn't complicate
+ 
+
+ align:start position:0%
+separate equations doesn't complicate
+things much at all even when you have Z
+
+ align:start position:0%
+things much at all even when you have Z
+ 
+
+ align:start position:0%
+things much at all even when you have Z
+now in this case the velocity and here's
+
+ align:start position:0%
+now in this case the velocity and here's
+ 
+
+ align:start position:0%
+now in this case the velocity and here's
+my old frame here the velocity of B with
+
+ align:start position:0%
+my old frame here the velocity of B with
+ 
+
+ align:start position:0%
+my old frame here the velocity of B with
+respect to O well now it's got boss I'm
+
+ align:start position:0%
+respect to O well now it's got boss I'm
+ 
+
+ align:start position:0%
+respect to O well now it's got boss I'm
+not going to move I'm standing still
+
+ align:start position:0%
+not going to move I'm standing still
+ 
+
+ align:start position:0%
+not going to move I'm standing still
+when I do it so the first term is zero
+
+ align:start position:0%
+when I do it so the first term is zero
+ 
+
+ align:start position:0%
+when I do it so the first term is zero
+it's got an R term r dot in the R hat
+
+ align:start position:0%
+it's got an R term r dot in the R hat
+ 
+
+ align:start position:0%
+it's got an R term r dot in the R hat
+direction and it has an R theta dot
+
+ align:start position:0%
+direction and it has an R theta dot
+ 
+
+ align:start position:0%
+direction and it has an R theta dot
+theta hat term okay and these can now
+
+ align:start position:0%
+theta hat term okay and these can now
+ 
+
+ align:start position:0%
+theta hat term okay and these can now
+this might be changing this might have a
+
+ align:start position:0%
+this might be changing this might have a
+ 
+
+ align:start position:0%
+this might be changing this might have a
+time derivative our double dot certainly
+
+ align:start position:0%
+time derivative our double dot certainly
+ 
+
+ align:start position:0%
+time derivative our double dot certainly
+does it's accelerating coming out of
+
+ align:start position:0%
+does it's accelerating coming out of
+ 
+
+ align:start position:0%
+does it's accelerating coming out of
+that tube and my theta angular motion it
+
+ align:start position:0%
+that tube and my theta angular motion it
+ 
+
+ align:start position:0%
+that tube and my theta angular motion it
+can be accelerating too so we're gonna
+
+ align:start position:0%
+can be accelerating too so we're gonna
+ 
+
+ align:start position:0%
+can be accelerating too so we're gonna
+have to deal with those I need to know
+
+ align:start position:0%
+have to deal with those I need to know
+ 
+
+ align:start position:0%
+have to deal with those I need to know
+the accelerations now having to
+
+ align:start position:0%
+the accelerations now having to
+ 
+
+ align:start position:0%
+the accelerations now having to
+emphasize it but it till now but it I
+
+ align:start position:0%
+emphasize it but it till now but it I
+ 
+
+ align:start position:0%
+emphasize it but it till now but it I
+find it conceptually useful too and when
+
+ align:start position:0%
+find it conceptually useful too and when
+ 
+
+ align:start position:0%
+find it conceptually useful too and when
+you work with polar coordinates you have
+
+ align:start position:0%
+you work with polar coordinates you have
+ 
+
+ align:start position:0%
+you work with polar coordinates you have
+this you can it you can have this
+
+ align:start position:0%
+this you can it you can have this
+ 
+
+ align:start position:0%
+this you can it you can have this
+ability to aggregate the terms in these
+
+ align:start position:0%
+ability to aggregate the terms in these
+ 
+
+ align:start position:0%
+ability to aggregate the terms in these
+two component directions so this you
+
+ align:start position:0%
+two component directions so this you
+ 
+
+ align:start position:0%
+two component directions so this you
+have this ball that our terms go
+
+ align:start position:0%
+have this ball that our terms go
+ 
+
+ align:start position:0%
+have this ball that our terms go
+together and we've left the Z double dot
+
+ align:start position:0%
+together and we've left the Z double dot
+ 
+
+ align:start position:0%
+together and we've left the Z double dot
+term it's just separate by itself drops
+
+ align:start position:0%
+term it's just separate by itself drops
+ 
+
+ align:start position:0%
+term it's just separate by itself drops
+out easily and you have the theta hat
+
+ align:start position:0%
+out easily and you have the theta hat
+ 
+
+ align:start position:0%
+out easily and you have the theta hat
+term and that's the R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theta double dot plus 2 r dot theta dot
+
+ align:start position:0%
+theta double dot plus 2 r dot theta dot
+ 
+
+ align:start position:0%
+theta double dot plus 2 r dot theta dot
+and these are in the theta hat direction
+
+ align:start position:0%
+and these are in the theta hat direction
+ 
+
+ align:start position:0%
+and these are in the theta hat direction
+there's your Coriolis term your Euler
+
+ align:start position:0%
+there's your Coriolis term your Euler
+ 
+
+ align:start position:0%
+there's your Coriolis term your Euler
+acceleration term centripetal term yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I don't know if I ought to tell you
+
+ align:start position:0%
+well I don't know if I ought to tell you
+ 
+
+ align:start position:0%
+well I don't know if I ought to tell you
+secrets about me because it's going to
+
+ align:start position:0%
+secrets about me because it's going to
+ 
+
+ align:start position:0%
+secrets about me because it's going to
+give you an advantage on the quiz but I
+
+ align:start position:0%
+give you an advantage on the quiz but I
+ 
+
+ align:start position:0%
+give you an advantage on the quiz but I
+have almost never ever been known to ask
+
+ align:start position:0%
+have almost never ever been known to ask
+ 
+
+ align:start position:0%
+have almost never ever been known to ask
+a question that says derive ok but I'll
+
+ align:start position:0%
+a question that says derive ok but I'll
+ 
+
+ align:start position:0%
+a question that says derive ok but I'll
+sure ask you concept questions I really
+
+ align:start position:0%
+sure ask you concept questions I really
+ 
+
+ align:start position:0%
+sure ask you concept questions I really
+want you understand the principles I
+
+ align:start position:0%
+want you understand the principles I
+ 
+
+ align:start position:0%
+want you understand the principles I
+really need I'm not I don't get real
+
+ align:start position:0%
+really need I'm not I don't get real
+ 
+
+ align:start position:0%
+really need I'm not I don't get real
+hung up on a have you need a grungy
+
+ align:start position:0%
+hung up on a have you need a grungy
+ 
+
+ align:start position:0%
+hung up on a have you need a grungy
+grind-it-out
+
+ align:start position:0%
+grind-it-out
+ 
+
+ align:start position:0%
+grind-it-out
+things do I want you to remember the
+
+ align:start position:0%
+things do I want you to remember the
+ 
+
+ align:start position:0%
+things do I want you to remember the
+formula for how to take the derivative
+
+ align:start position:0%
+formula for how to take the derivative
+ 
+
+ align:start position:0%
+formula for how to take the derivative
+of a vector in rotating frame yeah
+
+ align:start position:0%
+of a vector in rotating frame yeah
+ 
+
+ align:start position:0%
+of a vector in rotating frame yeah
+that's what that that's where these have
+
+ align:start position:0%
+that's what that that's where these have
+ 
+
+ align:start position:0%
+that's what that that's where these have
+come from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you had better remember this these two
+
+ align:start position:0%
+you had better remember this these two
+ 
+
+ align:start position:0%
+you had better remember this these two
+formulas the velocity formula and this
+
+ align:start position:0%
+formulas the velocity formula and this
+ 
+
+ align:start position:0%
+formulas the velocity formula and this
+and the acceleration format are just
+
+ align:start position:0%
+and the acceleration format are just
+ 
+
+ align:start position:0%
+and the acceleration format are just
+core to this course now the way quizzes
+
+ align:start position:0%
+core to this course now the way quizzes
+ 
+
+ align:start position:0%
+core to this course now the way quizzes
+are done first quiz you come in with one
+
+ align:start position:0%
+are done first quiz you come in with one
+ 
+
+ align:start position:0%
+are done first quiz you come in with one
+sheet of paper what would it better be
+
+ align:start position:0%
+sheet of paper what would it better be
+ 
+
+ align:start position:0%
+sheet of paper what would it better be
+on your paper ok and second quiz two
+
+ align:start position:0%
+on your paper ok and second quiz two
+ 
+
+ align:start position:0%
+on your paper ok and second quiz two
+sheets final three sheets that kind of
+
+ align:start position:0%
+sheets final three sheets that kind of
+ 
+
+ align:start position:0%
+sheets final three sheets that kind of
+thing ok conceptually you got forces in
+
+ align:start position:0%
+thing ok conceptually you got forces in
+ 
+
+ align:start position:0%
+thing ok conceptually you got forces in
+the armed forces in the Z forces in
+
+ align:start position:0%
+the armed forces in the Z forces in
+ 
+
+ align:start position:0%
+the armed forces in the Z forces in
+accelerations in R theta R theta and Z
+
+ align:start position:0%
+accelerations in R theta R theta and Z
+ 
+
+ align:start position:0%
+accelerations in R theta R theta and Z
+forces R theta and Z so here's here's
+
+ align:start position:0%
+forces R theta and Z so here's here's
+ 
+
+ align:start position:0%
+forces R theta and Z so here's here's
+here's the and for these planar motion
+
+ align:start position:0%
+here's the and for these planar motion
+ 
+
+ align:start position:0%
+here's the and for these planar motion
+problems this one's sure easy to use so
+
+ align:start position:0%
+problems this one's sure easy to use so
+ 
+
+ align:start position:0%
+problems this one's sure easy to use so
+let's think about this problem I'm going
+
+ align:start position:0%
+let's think about this problem I'm going
+ 
+
+ align:start position:0%
+let's think about this problem I'm going
+to let this be frictionless just to make
+
+ align:start position:0%
+to let this be frictionless just to make
+ 
+
+ align:start position:0%
+to let this be frictionless just to make
+it easy all right
+
+ align:start position:0%
+it easy all right
+ 
+
+ align:start position:0%
+it easy all right
+so what possible forces act on the
+
+ align:start position:0%
+so what possible forces act on the
+ 
+
+ align:start position:0%
+so what possible forces act on the
+punkah candy let's do a free body
+
+ align:start position:0%
+punkah candy let's do a free body
+ 
+
+ align:start position:0%
+punkah candy let's do a free body
+diagram of the chunk of candy coming out
+
+ align:start position:0%
+diagram of the chunk of candy coming out
+ 
+
+ align:start position:0%
+diagram of the chunk of candy coming out
+of here what are the forces in the let's
+
+ align:start position:0%
+of here what are the forces in the let's
+ 
+
+ align:start position:0%
+of here what are the forces in the let's
+keep it planar you know we can get
+
+ align:start position:0%
+keep it planar you know we can get
+ 
+
+ align:start position:0%
+keep it planar you know we can get
+gravity into this but I'm just let's
+
+ align:start position:0%
+gravity into this but I'm just let's
+ 
+
+ align:start position:0%
+gravity into this but I'm just let's
+just do it in a plane so I'm just going
+
+ align:start position:0%
+just do it in a plane so I'm just going
+ 
+
+ align:start position:0%
+just do it in a plane so I'm just going
+horizontal and slinging this thing
+
+ align:start position:0%
+horizontal and slinging this thing
+ 
+
+ align:start position:0%
+horizontal and slinging this thing
+gravity is in the Z 2
+
+ align:start position:0%
+gravity is in the Z 2
+ 
+
+ align:start position:0%
+gravity is in the Z 2
+direction and I'm constrained it in the
+
+ align:start position:0%
+direction and I'm constrained it in the
+ 
+
+ align:start position:0%
+direction and I'm constrained it in the
+Z so not there must it's somebody
+
+ align:start position:0%
+Z so not there must it's somebody
+ 
+
+ align:start position:0%
+Z so not there must it's somebody
+something supporting the gravity and the
+
+ align:start position:0%
+something supporting the gravity and the
+ 
+
+ align:start position:0%
+something supporting the gravity and the
+tube so definitely there's an mg on this
+
+ align:start position:0%
+tube so definitely there's an mg on this
+ 
+
+ align:start position:0%
+tube so definitely there's an mg on this
+thing downwards but it's in the Z
+
+ align:start position:0%
+thing downwards but it's in the Z
+ 
+
+ align:start position:0%
+thing downwards but it's in the Z
+direction and we're just not we're not
+
+ align:start position:0%
+direction and we're just not we're not
+ 
+
+ align:start position:0%
+direction and we're just not we're not
+letting it move in the Z what about the
+
+ align:start position:0%
+letting it move in the Z what about the
+ 
+
+ align:start position:0%
+letting it move in the Z what about the
+horizontal distance R this is my R hat
+
+ align:start position:0%
+horizontal distance R this is my R hat
+ 
+
+ align:start position:0%
+horizontal distance R this is my R hat
+direction this is my theta hat direction
+
+ align:start position:0%
+direction this is my theta hat direction
+ 
+
+ align:start position:0%
+direction this is my theta hat direction
+whoops not either theta is going this
+
+ align:start position:0%
+whoops not either theta is going this
+ 
+
+ align:start position:0%
+whoops not either theta is going this
+way so I've drawn this as a side view
+
+ align:start position:0%
+way so I've drawn this as a side view
+ 
+
+ align:start position:0%
+way so I've drawn this as a side view
+what's the force in the R hat direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in order to do this problem you got
+
+ align:start position:0%
+okay in order to do this problem you got
+ 
+
+ align:start position:0%
+okay in order to do this problem you got
+to figure that out what are the forces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are the source of forces in the r
+
+ align:start position:0%
+what are the source of forces in the r
+ 
+
+ align:start position:0%
+what are the source of forces in the r
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+here's your R direction say what mind
+
+ align:start position:0%
+here's your R direction say what mind
+ 
+
+ align:start position:0%
+here's your R direction say what mind
+you guys let me be yeah there are not
+
+ align:start position:0%
+you guys let me be yeah there are not
+ 
+
+ align:start position:0%
+you guys let me be yeah there are not
+any is that what you said aren't any and
+
+ align:start position:0%
+any is that what you said aren't any and
+ 
+
+ align:start position:0%
+any is that what you said aren't any and
+why is that right so there's no forces
+
+ align:start position:0%
+why is that right so there's no forces
+ 
+
+ align:start position:0%
+why is that right so there's no forces
+in the r direction so there's no forces
+
+ align:start position:0%
+in the r direction so there's no forces
+ 
+
+ align:start position:0%
+in the r direction so there's no forces
+on this thing in the r and if we this is
+
+ align:start position:0%
+on this thing in the r and if we this is
+ 
+
+ align:start position:0%
+on this thing in the r and if we this is
+so then this is a side view we could do
+
+ align:start position:0%
+so then this is a side view we could do
+ 
+
+ align:start position:0%
+so then this is a side view we could do
+the top view looking down top view you
+
+ align:start position:0%
+the top view looking down top view you
+ 
+
+ align:start position:0%
+the top view looking down top view you
+got your XY you also have your here's
+
+ align:start position:0%
+got your XY you also have your here's
+ 
+
+ align:start position:0%
+got your XY you also have your here's
+the thing here's the ball here's the r
+
+ align:start position:0%
+the thing here's the ball here's the r
+ 
+
+ align:start position:0%
+the thing here's the ball here's the r
+hat here's the theta hat now Freebody
+
+ align:start position:0%
+hat here's the theta hat now Freebody
+ 
+
+ align:start position:0%
+hat here's the theta hat now Freebody
+diagram in the top view well there's
+
+ align:start position:0%
+diagram in the top view well there's
+ 
+
+ align:start position:0%
+diagram in the top view well there's
+some force here probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah absolutely she's commenting that we
+
+ align:start position:0%
+ah absolutely she's commenting that we
+ 
+
+ align:start position:0%
+ah absolutely she's commenting that we
+do have accelerations in the R hat
+
+ align:start position:0%
+do have accelerations in the R hat
+ 
+
+ align:start position:0%
+do have accelerations in the R hat
+direction right and no force so you're
+
+ align:start position:0%
+direction right and no force so you're
+ 
+
+ align:start position:0%
+direction right and no force so you're
+getting that's the conundrum of this
+
+ align:start position:0%
+getting that's the conundrum of this
+ 
+
+ align:start position:0%
+getting that's the conundrum of this
+problem that's the point of this problem
+
+ align:start position:0%
+problem that's the point of this problem
+ 
+
+ align:start position:0%
+problem that's the point of this problem
+so let me continue ok Freebody diagram
+
+ align:start position:0%
+so let me continue ok Freebody diagram
+ 
+
+ align:start position:0%
+so let me continue ok Freebody diagram
+so I'm allowing and looking down on it
+
+ align:start position:0%
+so I'm allowing and looking down on it
+ 
+
+ align:start position:0%
+so I'm allowing and looking down on it
+I'm lying for some force it's a normal
+
+ align:start position:0%
+I'm lying for some force it's a normal
+ 
+
+ align:start position:0%
+I'm lying for some force it's a normal
+force that comes from the pipe exerting
+
+ align:start position:0%
+force that comes from the pipe exerting
+ 
+
+ align:start position:0%
+force that comes from the pipe exerting
+the force on the candy and it since it's
+
+ align:start position:0%
+the force on the candy and it since it's
+ 
+
+ align:start position:0%
+the force on the candy and it since it's
+frictionless it can only be normal to
+
+ align:start position:0%
+frictionless it can only be normal to
+ 
+
+ align:start position:0%
+frictionless it can only be normal to
+the pipe ok so there's there's the free
+
+ align:start position:0%
+the pipe ok so there's there's the free
+ 
+
+ align:start position:0%
+the pipe ok so there's there's the free
+body diagram in the top view so we can
+
+ align:start position:0%
+body diagram in the top view so we can
+ 
+
+ align:start position:0%
+body diagram in the top view so we can
+write two equations we can write three
+
+ align:start position:0%
+write two equations we can write three
+ 
+
+ align:start position:0%
+write two equations we can write three
+equations this one equal to zero this
+
+ align:start position:0%
+equations this one equal to zero this
+ 
+
+ align:start position:0%
+equations this one equal to zero this
+one in the R hat direction this one in
+
+ align:start position:0%
+one in the R hat direction this one in
+ 
+
+ align:start position:0%
+one in the R hat direction this one in
+the theta hat direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some of the forces our hat direction
+
+ align:start position:0%
+some of the forces our hat direction
+ 
+
+ align:start position:0%
+some of the forces our hat direction
+must be zero and we have a mass we have
+
+ align:start position:0%
+must be zero and we have a mass we have
+ 
+
+ align:start position:0%
+must be zero and we have a mass we have
+an acceleration solve for R double dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remarkable there's no force in the R hat
+
+ align:start position:0%
+remarkable there's no force in the R hat
+ 
+
+ align:start position:0%
+remarkable there's no force in the R hat
+direction the the position of the object
+
+ align:start position:0%
+direction the the position of the object
+ 
+
+ align:start position:0%
+direction the the position of the object
+the R coordinate it has a velocity it
+
+ align:start position:0%
+the R coordinate it has a velocity it
+ 
+
+ align:start position:0%
+the R coordinate it has a velocity it
+has an acceleration but the total
+
+ align:start position:0%
+has an acceleration but the total
+ 
+
+ align:start position:0%
+has an acceleration but the total
+acceleration in the R hat Direction is
+
+ align:start position:0%
+acceleration in the R hat Direction is
+ 
+
+ align:start position:0%
+acceleration in the R hat Direction is
+actually zero the rate of change of the
+
+ align:start position:0%
+actually zero the rate of change of the
+ 
+
+ align:start position:0%
+actually zero the rate of change of the
+of the velocity of this thing in the
+
+ align:start position:0%
+of the velocity of this thing in the
+ 
+
+ align:start position:0%
+of the velocity of this thing in the
+radial direction R double dot is non
+
+ align:start position:0%
+radial direction R double dot is non
+ 
+
+ align:start position:0%
+radial direction R double dot is non
+zero but there are no forces on it I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have pondered another way to explain
+
+ align:start position:0%
+have pondered another way to explain
+ 
+
+ align:start position:0%
+have pondered another way to explain
+this I'm still thinking about it
+
+ align:start position:0%
+this I'm still thinking about it
+ 
+
+ align:start position:0%
+this I'm still thinking about it
+and you think about this too how do you
+
+ align:start position:0%
+and you think about this too how do you
+ 
+
+ align:start position:0%
+and you think about this too how do you
+know how do you explain this in the
+
+ align:start position:0%
+know how do you explain this in the
+ 
+
+ align:start position:0%
+know how do you explain this in the
+absence of forces and it's kind of is
+
+ align:start position:0%
+absence of forces and it's kind of is
+ 
+
+ align:start position:0%
+absence of forces and it's kind of is
+partly where the concept comes from of
+
+ align:start position:0%
+partly where the concept comes from of
+ 
+
+ align:start position:0%
+partly where the concept comes from of
+fictitious forces that centrifugal force
+
+ align:start position:0%
+fictitious forces that centrifugal force
+ 
+
+ align:start position:0%
+fictitious forces that centrifugal force
+is a force it's not it's an acceleration
+
+ align:start position:0%
+is a force it's not it's an acceleration
+ 
+
+ align:start position:0%
+is a force it's not it's an acceleration
+this is just saying that let's go back
+
+ align:start position:0%
+this is just saying that let's go back
+ 
+
+ align:start position:0%
+this is just saying that let's go back
+to this problem in order to make
+
+ align:start position:0%
+to this problem in order to make
+ 
+
+ align:start position:0%
+to this problem in order to make
+something go in a circle you have you
+
+ align:start position:0%
+something go in a circle you have you
+ 
+
+ align:start position:0%
+something go in a circle you have you
+have to put a force on it to caused the
+
+ align:start position:0%
+have to put a force on it to caused the
+ 
+
+ align:start position:0%
+have to put a force on it to caused the
+centripetal acceleration you have to
+
+ align:start position:0%
+centripetal acceleration you have to
+ 
+
+ align:start position:0%
+centripetal acceleration you have to
+allow the thing to go out if you're not
+
+ align:start position:0%
+allow the thing to go out if you're not
+ 
+
+ align:start position:0%
+allow the thing to go out if you're not
+forcing it to go in a circle you have to
+
+ align:start position:0%
+forcing it to go in a circle you have to
+ 
+
+ align:start position:0%
+forcing it to go in a circle you have to
+allow it to go out at that rate in order
+
+ align:start position:0%
+allow it to go out at that rate in order
+ 
+
+ align:start position:0%
+allow it to go out at that rate in order
+for there to be no sand trip Atal
+
+ align:start position:0%
+for there to be no sand trip Atal
+ 
+
+ align:start position:0%
+for there to be no sand trip Atal
+accelerations on the object yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the y-direction to get it started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does it experience and trip it'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration so there's no rotation does
+
+ align:start position:0%
+acceleration so there's no rotation does
+ 
+
+ align:start position:0%
+acceleration so there's no rotation does
+it an experienced centripetal
+
+ align:start position:0%
+it an experienced centripetal
+ 
+
+ align:start position:0%
+it an experienced centripetal
+acceleration what do you think yeah okay
+
+ align:start position:0%
+acceleration what do you think yeah okay
+ 
+
+ align:start position:0%
+acceleration what do you think yeah okay
+it's because it goes through curved
+
+ align:start position:0%
+it's because it goes through curved
+ 
+
+ align:start position:0%
+it's because it goes through curved
+motion at any instant time when it's
+
+ align:start position:0%
+motion at any instant time when it's
+ 
+
+ align:start position:0%
+motion at any instant time when it's
+doing that there's a radius of curvature
+
+ align:start position:0%
+doing that there's a radius of curvature
+ 
+
+ align:start position:0%
+doing that there's a radius of curvature
+you can at that instant time think of it
+
+ align:start position:0%
+you can at that instant time think of it
+ 
+
+ align:start position:0%
+you can at that instant time think of it
+as being in a circular path okay and
+
+ align:start position:0%
+as being in a circular path okay and
+ 
+
+ align:start position:0%
+as being in a circular path okay and
+sometimes it's just really easy to do
+
+ align:start position:0%
+sometimes it's just really easy to do
+ 
+
+ align:start position:0%
+sometimes it's just really easy to do
+these kind of problems with normal and
+
+ align:start position:0%
+these kind of problems with normal and
+ 
+
+ align:start position:0%
+these kind of problems with normal and
+tangential coordinates so if I wanted
+
+ align:start position:0%
+tangential coordinates so if I wanted
+ 
+
+ align:start position:0%
+tangential coordinates so if I wanted
+I've got a I'm looking down on the XY
+
+ align:start position:0%
+I've got a I'm looking down on the XY
+ 
+
+ align:start position:0%
+I've got a I'm looking down on the XY
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+gravity's into the earth so I'm looking
+
+ align:start position:0%
+gravity's into the earth so I'm looking
+ 
+
+ align:start position:0%
+gravity's into the earth so I'm looking
+down on a vehicle a car and that car
+
+ align:start position:0%
+down on a vehicle a car and that car
+ 
+
+ align:start position:0%
+down on a vehicle a car and that car
+guys kind of drunk he's going down the
+
+ align:start position:0%
+guys kind of drunk he's going down the
+ 
+
+ align:start position:0%
+guys kind of drunk he's going down the
+road like this okay so here's my Y
+
+ align:start position:0%
+road like this okay so here's my Y
+ 
+
+ align:start position:0%
+road like this okay so here's my Y
+here's my x and y equals some well a
+
+ align:start position:0%
+here's my x and y equals some well a
+ 
+
+ align:start position:0%
+here's my x and y equals some well a
+sine 2pi over the wavelength two PI over
+
+ align:start position:0%
+sine 2pi over the wavelength two PI over
+ 
+
+ align:start position:0%
+sine 2pi over the wavelength two PI over
+lambda times X and some a sine K X and
+
+ align:start position:0%
+lambda times X and some a sine K X and
+ 
+
+ align:start position:0%
+lambda times X and some a sine K X and
+as you drive down that I'm interview if
+
+ align:start position:0%
+as you drive down that I'm interview if
+ 
+
+ align:start position:0%
+as you drive down that I'm interview if
+you're in a car and you're doing that
+
+ align:start position:0%
+you're in a car and you're doing that
+ 
+
+ align:start position:0%
+you're in a car and you're doing that
+you get thrown side-to-side in the car
+
+ align:start position:0%
+you get thrown side-to-side in the car
+ 
+
+ align:start position:0%
+you get thrown side-to-side in the car
+right so you are being accelerated and
+
+ align:start position:0%
+right so you are being accelerated and
+ 
+
+ align:start position:0%
+right so you are being accelerated and
+so we want to be able to calculate the
+
+ align:start position:0%
+so we want to be able to calculate the
+ 
+
+ align:start position:0%
+so we want to be able to calculate the
+acceleration due to the fact that you're
+
+ align:start position:0%
+acceleration due to the fact that you're
+ 
+
+ align:start position:0%
+acceleration due to the fact that you're
+going down and doing a curved path and
+
+ align:start position:0%
+going down and doing a curved path and
+ 
+
+ align:start position:0%
+going down and doing a curved path and
+as we deal with these things with a
+
+ align:start position:0%
+as we deal with these things with a
+ 
+
+ align:start position:0%
+as we deal with these things with a
+sometimes with a convenient little set
+
+ align:start position:0%
+sometimes with a convenient little set
+ 
+
+ align:start position:0%
+sometimes with a convenient little set
+of coordinates that are our normal and
+
+ align:start position:0%
+of coordinates that are our normal and
+ 
+
+ align:start position:0%
+of coordinates that are our normal and
+tangential unit vectors you normal and
+
+ align:start position:0%
+tangential unit vectors you normal and
+ 
+
+ align:start position:0%
+tangential unit vectors you normal and
+you tangential at any instant in time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we know that in the so this is if
+
+ align:start position:0%
+and we know that in the so this is if
+ 
+
+ align:start position:0%
+and we know that in the so this is if
+this is along the path at any instant in
+
+ align:start position:0%
+this is along the path at any instant in
+ 
+
+ align:start position:0%
+this is along the path at any instant in
+time you're right here what direction is
+
+ align:start position:0%
+time you're right here what direction is
+ 
+
+ align:start position:0%
+time you're right here what direction is
+your velocity just definition of
+
+ align:start position:0%
+your velocity just definition of
+ 
+
+ align:start position:0%
+your velocity just definition of
+velocity tangent to the path right okay
+
+ align:start position:0%
+velocity tangent to the path right okay
+ 
+
+ align:start position:0%
+velocity tangent to the path right okay
+so a it's a time the velocity has got to
+
+ align:start position:0%
+so a it's a time the velocity has got to
+ 
+
+ align:start position:0%
+so a it's a time the velocity has got to
+be tangent to the path at that moment
+
+ align:start position:0%
+be tangent to the path at that moment
+ 
+
+ align:start position:0%
+be tangent to the path at that moment
+okay so velocity has some the vector has
+
+ align:start position:0%
+okay so velocity has some the vector has
+ 
+
+ align:start position:0%
+okay so velocity has some the vector has
+a magnitude and a unit vector u T here
+
+ align:start position:0%
+a magnitude and a unit vector u T here
+ 
+
+ align:start position:0%
+a magnitude and a unit vector u T here
+alcoholic tangent dollar to it and the
+
+ align:start position:0%
+alcoholic tangent dollar to it and the
+ 
+
+ align:start position:0%
+alcoholic tangent dollar to it and the
+acceleration of this thing is your time
+
+ align:start position:0%
+acceleration of this thing is your time
+ 
+
+ align:start position:0%
+acceleration of this thing is your time
+derivative of this and that's going to
+
+ align:start position:0%
+derivative of this and that's going to
+ 
+
+ align:start position:0%
+derivative of this and that's going to
+give you a V dot u t hat plus AV and now
+
+ align:start position:0%
+give you a V dot u t hat plus AV and now
+ 
+
+ align:start position:0%
+give you a V dot u t hat plus AV and now
+you need a time derivative of this guy
+
+ align:start position:0%
+you need a time derivative of this guy
+ 
+
+ align:start position:0%
+you need a time derivative of this guy
+but this is a unit length vector you can
+
+ align:start position:0%
+but this is a unit length vector you can
+ 
+
+ align:start position:0%
+but this is a unit length vector you can
+plug it into that equation for the
+
+ align:start position:0%
+plug it into that equation for the
+ 
+
+ align:start position:0%
+plug it into that equation for the
+derivative of a rotating vector and
+
+ align:start position:0%
+derivative of a rotating vector and
+ 
+
+ align:start position:0%
+derivative of a rotating vector and
+calculate what this should be you could
+
+ align:start position:0%
+calculate what this should be you could
+ 
+
+ align:start position:0%
+calculate what this should be you could
+also just draw it out now so I'll draw
+
+ align:start position:0%
+also just draw it out now so I'll draw
+ 
+
+ align:start position:0%
+also just draw it out now so I'll draw
+this for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many do at a time I'll just be able
+
+ align:start position:0%
+how many do at a time I'll just be able
+ 
+
+ align:start position:0%
+how many do at a time I'll just be able
+to finish this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's my unit vector in the tangential
+
+ align:start position:0%
+here's my unit vector in the tangential
+ 
+
+ align:start position:0%
+here's my unit vector in the tangential
+direction as I'm going around this curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is my tangential direction there at
+
+ align:start position:0%
+this is my tangential direction there at
+ 
+
+ align:start position:0%
+this is my tangential direction there at
+that it there's some incident I have a
+
+ align:start position:0%
+that it there's some incident I have a
+ 
+
+ align:start position:0%
+that it there's some incident I have a
+radius we call that row and in the
+
+ align:start position:0%
+radius we call that row and in the
+ 
+
+ align:start position:0%
+radius we call that row and in the
+little time delta T I go through an
+
+ align:start position:0%
+little time delta T I go through an
+ 
+
+ align:start position:0%
+little time delta T I go through an
+angle Delta Theta in delta T and this is
+
+ align:start position:0%
+angle Delta Theta in delta T and this is
+ 
+
+ align:start position:0%
+angle Delta Theta in delta T and this is
+my UT vector here it changes by a little
+
+ align:start position:0%
+my UT vector here it changes by a little
+ 
+
+ align:start position:0%
+my UT vector here it changes by a little
+bit that's the change in the UT unit
+
+ align:start position:0%
+bit that's the change in the UT unit
+ 
+
+ align:start position:0%
+bit that's the change in the UT unit
+vector in this time delta T and it goes
+
+ align:start position:0%
+vector in this time delta T and it goes
+ 
+
+ align:start position:0%
+vector in this time delta T and it goes
+perpendicular and it goes in the
+
+ align:start position:0%
+perpendicular and it goes in the
+ 
+
+ align:start position:0%
+perpendicular and it goes in the
+positive u in direction so Delta the
+
+ align:start position:0%
+positive u in direction so Delta the
+ 
+
+ align:start position:0%
+positive u in direction so Delta the
+easiest way to write this one Delta u T
+
+ align:start position:0%
+easiest way to write this one Delta u T
+ 
+
+ align:start position:0%
+easiest way to write this one Delta u T
+equals some theta dot delta T that's the
+
+ align:start position:0%
+equals some theta dot delta T that's the
+ 
+
+ align:start position:0%
+equals some theta dot delta T that's the
+angle times the times the length of the
+
+ align:start position:0%
+angle times the times the length of the
+ 
+
+ align:start position:0%
+angle times the times the length of the
+unit vector 1 that's the distance it
+
+ align:start position:0%
+unit vector 1 that's the distance it
+ 
+
+ align:start position:0%
+unit vector 1 that's the distance it
+goes so one so R Omega 1 theta dot is
+
+ align:start position:0%
+goes so one so R Omega 1 theta dot is
+ 
+
+ align:start position:0%
+goes so one so R Omega 1 theta dot is
+the distance that this unit vector goes
+
+ align:start position:0%
+the distance that this unit vector goes
+ 
+
+ align:start position:0%
+the distance that this unit vector goes
+through in delta T and the direction it
+
+ align:start position:0%
+through in delta T and the direction it
+ 
+
+ align:start position:0%
+through in delta T and the direction it
+goes in is u normal hat so Delta u T
+
+ align:start position:0%
+goes in is u normal hat so Delta u T
+ 
+
+ align:start position:0%
+goes in is u normal hat so Delta u T
+over delta T limit as T goes to zero you
+
+ align:start position:0%
+over delta T limit as T goes to zero you
+ 
+
+ align:start position:0%
+over delta T limit as T goes to zero you
+get theta dot u and just like before so
+
+ align:start position:0%
+get theta dot u and just like before so
+ 
+
+ align:start position:0%
+get theta dot u and just like before so
+the time derivative of this unit vector
+
+ align:start position:0%
+the time derivative of this unit vector
+ 
+
+ align:start position:0%
+the time derivative of this unit vector
+in the tangential direction is just
+
+ align:start position:0%
+in the tangential direction is just
+ 
+
+ align:start position:0%
+in the tangential direction is just
+stated dot time in the normal direction
+
+ align:start position:0%
+stated dot time in the normal direction
+ 
+
+ align:start position:0%
+stated dot time in the normal direction
+and then from that we can
+
+ align:start position:0%
+and then from that we can
+ 
+
+ align:start position:0%
+and then from that we can
+very quickly derive the rest of this
+
+ align:start position:0%
+very quickly derive the rest of this
+ 
+
+ align:start position:0%
+very quickly derive the rest of this
+acceleration the acceleration that is
+
+ align:start position:0%
+acceleration the acceleration that is
+ 
+
+ align:start position:0%
+acceleration the acceleration that is
+that Plus this we now know an expression
+
+ align:start position:0%
+that Plus this we now know an expression
+ 
+
+ align:start position:0%
+that Plus this we now know an expression
+for this is my U T dot term and plug
+
+ align:start position:0%
+for this is my U T dot term and plug
+ 
+
+ align:start position:0%
+for this is my U T dot term and plug
+that in here this then we need an
+
+ align:start position:0%
+that in here this then we need an
+ 
+
+ align:start position:0%
+that in here this then we need an
+expression for V what's the V well if
+
+ align:start position:0%
+expression for V what's the V well if
+ 
+
+ align:start position:0%
+expression for V what's the V well if
+that instant time it has some radius Rho
+
+ align:start position:0%
+that instant time it has some radius Rho
+ 
+
+ align:start position:0%
+that instant time it has some radius Rho
+it has an angular velocity theta dot so
+
+ align:start position:0%
+it has an angular velocity theta dot so
+ 
+
+ align:start position:0%
+it has an angular velocity theta dot so
+Rho theta dot would be the B here so I'm
+
+ align:start position:0%
+Rho theta dot would be the B here so I'm
+ 
+
+ align:start position:0%
+Rho theta dot would be the B here so I'm
+looking for an expression for V u T dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's V theta dot e UN but theta dot
+
+ align:start position:0%
+so that's V theta dot e UN but theta dot
+ 
+
+ align:start position:0%
+so that's V theta dot e UN but theta dot
+is V over Rho V squared sorry about this
+
+ align:start position:0%
+is V over Rho V squared sorry about this
+ 
+
+ align:start position:0%
+is V over Rho V squared sorry about this
+over Rho u n so this guy up here this is
+
+ align:start position:0%
+over Rho u n so this guy up here this is
+ 
+
+ align:start position:0%
+over Rho u n so this guy up here this is
+V dot u T plus V squared I'll rewrite it
+
+ align:start position:0%
+V dot u T plus V squared I'll rewrite it
+ 
+
+ align:start position:0%
+V dot u T plus V squared I'll rewrite it
+over Rho u n so if you're speeding up if
+
+ align:start position:0%
+over Rho u n so if you're speeding up if
+ 
+
+ align:start position:0%
+over Rho u n so if you're speeding up if
+you're going from 30 miles an hour to 40
+
+ align:start position:0%
+you're going from 30 miles an hour to 40
+ 
+
+ align:start position:0%
+you're going from 30 miles an hour to 40
+miles an hour
+
+ align:start position:0%
+miles an hour
+ 
+
+ align:start position:0%
+miles an hour
+that's your tangential that's your P
+
+ align:start position:0%
+that's your tangential that's your P
+ 
+
+ align:start position:0%
+that's your tangential that's your P
+speed along the path that's this term
+
+ align:start position:0%
+speed along the path that's this term
+ 
+
+ align:start position:0%
+speed along the path that's this term
+but because you're going around the
+
+ align:start position:0%
+but because you're going around the
+ 
+
+ align:start position:0%
+but because you're going around the
+curve you have an acceleration B squared
+
+ align:start position:0%
+curve you have an acceleration B squared
+ 
+
+ align:start position:0%
+curve you have an acceleration B squared
+over Rho when you've run this into this
+
+ align:start position:0%
+over Rho when you've run this into this
+ 
+
+ align:start position:0%
+over Rho when you've run this into this
+before in physics this is where it comes
+
+ align:start position:0%
+before in physics this is where it comes
+ 
+
+ align:start position:0%
+before in physics this is where it comes
+from okay this is a centripetal
+
+ align:start position:0%
+from okay this is a centripetal
+ 
+
+ align:start position:0%
+from okay this is a centripetal
+acceleration like term if you replace V
+
+ align:start position:0%
+acceleration like term if you replace V
+ 
+
+ align:start position:0%
+acceleration like term if you replace V
+with Rho theta dot you'd get R theta dot
+
+ align:start position:0%
+with Rho theta dot you'd get R theta dot
+ 
+
+ align:start position:0%
+with Rho theta dot you'd get R theta dot
+squared so you can either put it in
+
+ align:start position:0%
+squared so you can either put it in
+ 
+
+ align:start position:0%
+squared so you can either put it in
+terms of V squared of a row or you can
+
+ align:start position:0%
+terms of V squared of a row or you can
+ 
+
+ align:start position:0%
+terms of V squared of a row or you can
+put it into in terms of Rho theta dot
+
+ align:start position:0%
+put it into in terms of Rho theta dot
+ 
+
+ align:start position:0%
+put it into in terms of Rho theta dot
+squared and Rho theta dot squared sounds
+
+ align:start position:0%
+squared and Rho theta dot squared sounds
+ 
+
+ align:start position:0%
+squared and Rho theta dot squared sounds
+a lot like my acceleration term right
+
+ align:start position:0%
+a lot like my acceleration term right
+ 
+
+ align:start position:0%
+a lot like my acceleration term right
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+so with that simple little formula you
+
+ align:start position:0%
+so with that simple little formula you
+ 
+
+ align:start position:0%
+so with that simple little formula you
+can do you need one other thing and you
+
+ align:start position:0%
+can do you need one other thing and you
+ 
+
+ align:start position:0%
+can do you need one other thing and you
+need to and you just go look it up in
+
+ align:start position:0%
+need to and you just go look it up in
+ 
+
+ align:start position:0%
+need to and you just go look it up in
+the book there is an expression from
+
+ align:start position:0%
+the book there is an expression from
+ 
+
+ align:start position:0%
+the book there is an expression from
+calculus for the radius of curvature of
+
+ align:start position:0%
+calculus for the radius of curvature of
+ 
+
+ align:start position:0%
+calculus for the radius of curvature of
+a path right and it has things it has
+
+ align:start position:0%
+a path right and it has things it has
+ 
+
+ align:start position:0%
+a path right and it has things it has
+first and second derivatives of Y with
+
+ align:start position:0%
+first and second derivatives of Y with
+ 
+
+ align:start position:0%
+first and second derivatives of Y with
+respect to X so you need a dy/dx and a
+
+ align:start position:0%
+respect to X so you need a dy/dx and a
+ 
+
+ align:start position:0%
+respect to X so you need a dy/dx and a
+d2y DX squared from a sine function you
+
+ align:start position:0%
+d2y DX squared from a sine function you
+ 
+
+ align:start position:0%
+d2y DX squared from a sine function you
+can calculate that so you calculate Rho
+
+ align:start position:0%
+can calculate that so you calculate Rho
+ 
+
+ align:start position:0%
+can calculate that so you calculate Rho
+from this from the formula that's in the
+
+ align:start position:0%
+from this from the formula that's in the
+ 
+
+ align:start position:0%
+from this from the formula that's in the
+book for calculating radius of curvature
+
+ align:start position:0%
+book for calculating radius of curvature
+ 
+
+ align:start position:0%
+book for calculating radius of curvature
+and you're done all right so see you on
+
+ align:start position:0%
+and you're done all right so see you on
+ 
+
+ align:start position:0%
+and you're done all right so see you on
+Thursday
\ No newline at end of file
diff --git a/itWklzE8MP0.txt b/itWklzE8MP0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f1c87eeb026b02a50e76858807a8d8fda0186016
--- /dev/null
+++ b/itWklzE8MP0.txt
@@ -0,0 +1,2947 @@
+align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+graphical view here is
+
+ align:start position:0%
+graphical view here is
+ 
+
+ align:start position:0%
+graphical view here is
+addresses the question of what is the
+
+ align:start position:0%
+addresses the question of what is the
+ 
+
+ align:start position:0%
+addresses the question of what is the
+right size of your initial project
+
+ align:start position:0%
+right size of your initial project
+ 
+
+ align:start position:0%
+right size of your initial project
+and so i have
+
+ align:start position:0%
+and so i have
+ 
+
+ align:start position:0%
+and so i have
+four curves here depending upon the
+
+ align:start position:0%
+four curves here depending upon the
+ 
+
+ align:start position:0%
+four curves here depending upon the
+alpha the alpha equals ones indicate
+
+ align:start position:0%
+alpha the alpha equals ones indicate
+ 
+
+ align:start position:0%
+alpha the alpha equals ones indicate
+that there's no economies of scale
+
+ align:start position:0%
+that there's no economies of scale
+ 
+
+ align:start position:0%
+that there's no economies of scale
+and as we go
+
+ align:start position:0%
+and as we go
+ 
+
+ align:start position:0%
+and as we go
+lower alpha means that there's lower
+
+ align:start position:0%
+lower alpha means that there's lower
+ 
+
+ align:start position:0%
+lower alpha means that there's lower
+exponent on the economy of the scale
+
+ align:start position:0%
+exponent on the economy of the scale
+ 
+
+ align:start position:0%
+exponent on the economy of the scale
+which means they're greater you get to a
+
+ align:start position:0%
+which means they're greater you get to a
+ 
+
+ align:start position:0%
+which means they're greater you get to a
+different design and as an extension of
+
+ align:start position:0%
+different design and as an extension of
+ 
+
+ align:start position:0%
+different design and as an extension of
+the garage case you see that the optimal
+
+ align:start position:0%
+the garage case you see that the optimal
+ 
+
+ align:start position:0%
+the garage case you see that the optimal
+design here is
+
+ align:start position:0%
+design here is
+ 
+
+ align:start position:0%
+design here is
+increases along with economies of scale
+
+ align:start position:0%
+increases along with economies of scale
+ 
+
+ align:start position:0%
+increases along with economies of scale
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there are certain fixed costs so that
+
+ align:start position:0%
+there are certain fixed costs so that
+ 
+
+ align:start position:0%
+there are certain fixed costs so that
+the 25 units a day
+
+ align:start position:0%
+the 25 units a day
+ 
+
+ align:start position:0%
+the 25 units a day
+tons per day didn't seem like the best
+
+ align:start position:0%
+tons per day didn't seem like the best
+ 
+
+ align:start position:0%
+tons per day didn't seem like the best
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh so 50 seemed to be the right one
+
+ align:start position:0%
+uh so 50 seemed to be the right one
+ 
+
+ align:start position:0%
+uh so 50 seemed to be the right one
+given the fixed costs and everything
+
+ align:start position:0%
+given the fixed costs and everything
+ 
+
+ align:start position:0%
+given the fixed costs and everything
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+so all this is fairly straightforward uh
+
+ align:start position:0%
+so all this is fairly straightforward uh
+ 
+
+ align:start position:0%
+so all this is fairly straightforward uh
+from the garage case
+
+ align:start position:0%
+from the garage case
+ 
+
+ align:start position:0%
+from the garage case
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there is a
+
+ align:start position:0%
+there is a
+ 
+
+ align:start position:0%
+there is a
+general lesson here that is we might
+
+ align:start position:0%
+general lesson here that is we might
+ 
+
+ align:start position:0%
+general lesson here that is we might
+digest them is there's a trade-off
+
+ align:start position:0%
+digest them is there's a trade-off
+ 
+
+ align:start position:0%
+digest them is there's a trade-off
+between the economy the scale and the
+
+ align:start position:0%
+between the economy the scale and the
+ 
+
+ align:start position:0%
+between the economy the scale and the
+plant size when anticipating future
+
+ align:start position:0%
+plant size when anticipating future
+ 
+
+ align:start position:0%
+plant size when anticipating future
+growth
+
+ align:start position:0%
+growth
+ 
+
+ align:start position:0%
+growth
+this was not part of the mytex uh
+
+ align:start position:0%
+this was not part of the mytex uh
+ 
+
+ align:start position:0%
+this was not part of the mytex uh
+simple-minded
+
+ align:start position:0%
+simple-minded
+ 
+
+ align:start position:0%
+simple-minded
+homework assignment but
+
+ align:start position:0%
+homework assignment but
+ 
+
+ align:start position:0%
+homework assignment but
+it is the kind of thing that you think
+
+ align:start position:0%
+it is the kind of thing that you think
+ 
+
+ align:start position:0%
+it is the kind of thing that you think
+about and in this particular case the
+
+ align:start position:0%
+about and in this particular case the
+ 
+
+ align:start position:0%
+about and in this particular case the
+economy the scale and the example
+
+ align:start position:0%
+economy the scale and the example
+ 
+
+ align:start position:0%
+economy the scale and the example
+problem weren't very large so that
+
+ align:start position:0%
+problem weren't very large so that
+ 
+
+ align:start position:0%
+problem weren't very large so that
+building over
+
+ align:start position:0%
+building over
+ 
+
+ align:start position:0%
+building over
+uh as large as you could over that time
+
+ align:start position:0%
+uh as large as you could over that time
+ 
+
+ align:start position:0%
+uh as large as you could over that time
+was not very good um
+
+ align:start position:0%
+was not very good um
+ 
+
+ align:start position:0%
+was not very good um
+not obviously to be a good example
+
+ align:start position:0%
+not obviously to be a good example
+ 
+
+ align:start position:0%
+not obviously to be a good example
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+here is i think a really interesting
+
+ align:start position:0%
+here is i think a really interesting
+ 
+
+ align:start position:0%
+here is i think a really interesting
+table that is uh we're now looking at
+
+ align:start position:0%
+table that is uh we're now looking at
+ 
+
+ align:start position:0%
+table that is uh we're now looking at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uncertainty
+
+ align:start position:0%
+uncertainty
+ 
+
+ align:start position:0%
+uncertainty
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+as shown in this graph here there is uh
+
+ align:start position:0%
+as shown in this graph here there is uh
+ 
+
+ align:start position:0%
+as shown in this graph here there is uh
+the projection that is that the
+
+ align:start position:0%
+the projection that is that the
+ 
+
+ align:start position:0%
+the projection that is that the
+kepler offshore marine was going for
+
+ align:start position:0%
+kepler offshore marine was going for
+ 
+
+ align:start position:0%
+kepler offshore marine was going for
+which had been used which was it was
+
+ align:start position:0%
+which had been used which was it was
+ 
+
+ align:start position:0%
+which had been used which was it was
+growing
+
+ align:start position:0%
+growing
+ 
+
+ align:start position:0%
+growing
+the red line has sort of disappeared
+
+ align:start position:0%
+the red line has sort of disappeared
+ 
+
+ align:start position:0%
+the red line has sort of disappeared
+here but it's here and then leveling off
+
+ align:start position:0%
+here but it's here and then leveling off
+ 
+
+ align:start position:0%
+here but it's here and then leveling off
+over time over this 20 years and we
+
+ align:start position:0%
+over time over this 20 years and we
+ 
+
+ align:start position:0%
+over time over this 20 years and we
+had applied a deterministic
+
+ align:start position:0%
+had applied a deterministic
+ 
+
+ align:start position:0%
+had applied a deterministic
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a uncertainty parameters to have it vary
+
+ align:start position:0%
+a uncertainty parameters to have it vary
+ 
+
+ align:start position:0%
+a uncertainty parameters to have it vary
+around here and of course we don't we
+
+ align:start position:0%
+around here and of course we don't we
+ 
+
+ align:start position:0%
+around here and of course we don't we
+had no
+
+ align:start position:0%
+had no
+ 
+
+ align:start position:0%
+had no
+special bases on it but recognize those
+
+ align:start position:0%
+special bases on it but recognize those
+ 
+
+ align:start position:0%
+special bases on it but recognize those
+uncertainty and it wasn't trivial so
+
+ align:start position:0%
+uncertainty and it wasn't trivial so
+ 
+
+ align:start position:0%
+uncertainty and it wasn't trivial so
+here's the ones we're working with now
+
+ align:start position:0%
+here's the ones we're working with now
+ 
+
+ align:start position:0%
+here's the ones we're working with now
+uh here's where we have the parametric
+
+ align:start position:0%
+uh here's where we have the parametric
+ 
+
+ align:start position:0%
+uh here's where we have the parametric
+analysis so
+
+ align:start position:0%
+analysis so
+ 
+
+ align:start position:0%
+analysis so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+clearly
+
+ align:start position:0%
+clearly
+ 
+
+ align:start position:0%
+clearly
+uh the design depends upon the economy
+
+ align:start position:0%
+uh the design depends upon the economy
+ 
+
+ align:start position:0%
+uh the design depends upon the economy
+of the scale so
+
+ align:start position:0%
+of the scale so
+ 
+
+ align:start position:0%
+of the scale so
+uh here is the four that we were looking
+
+ align:start position:0%
+uh here is the four that we were looking
+ 
+
+ align:start position:0%
+uh here is the four that we were looking
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+from none to about the most except that
+
+ align:start position:0%
+from none to about the most except that
+ 
+
+ align:start position:0%
+from none to about the most except that
+i've seen in practice but
+
+ align:start position:0%
+i've seen in practice but
+ 
+
+ align:start position:0%
+i've seen in practice but
+seem to be appropriate as the range
+
+ align:start position:0%
+seem to be appropriate as the range
+ 
+
+ align:start position:0%
+seem to be appropriate as the range
+and if we look at the optimal capacity
+
+ align:start position:0%
+and if we look at the optimal capacity
+ 
+
+ align:start position:0%
+and if we look at the optimal capacity
+in terms of tons per day
+
+ align:start position:0%
+in terms of tons per day
+ 
+
+ align:start position:0%
+in terms of tons per day
+as i just showed you with the graph
+
+ align:start position:0%
+as i just showed you with the graph
+ 
+
+ align:start position:0%
+as i just showed you with the graph
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the more on economies of scale the
+
+ align:start position:0%
+the more on economies of scale the
+ 
+
+ align:start position:0%
+the more on economies of scale the
+larger is the the better design from the
+
+ align:start position:0%
+larger is the the better design from the
+ 
+
+ align:start position:0%
+larger is the the better design from the
+economic point of view
+
+ align:start position:0%
+economic point of view
+ 
+
+ align:start position:0%
+economic point of view
+the moment you impose uncertainty
+
+ align:start position:0%
+the moment you impose uncertainty
+ 
+
+ align:start position:0%
+the moment you impose uncertainty
+very similar to the garage case the
+
+ align:start position:0%
+very similar to the garage case the
+ 
+
+ align:start position:0%
+very similar to the garage case the
+optimal design shifts
+
+ align:start position:0%
+optimal design shifts
+ 
+
+ align:start position:0%
+optimal design shifts
+because you find out that well you build
+
+ align:start position:0%
+because you find out that well you build
+ 
+
+ align:start position:0%
+because you find out that well you build
+something too large for the demand and
+
+ align:start position:0%
+something too large for the demand and
+ 
+
+ align:start position:0%
+something too large for the demand and
+you lost and on the other hand if the
+
+ align:start position:0%
+you lost and on the other hand if the
+ 
+
+ align:start position:0%
+you lost and on the other hand if the
+demand was higher you didn't
+
+ align:start position:0%
+demand was higher you didn't
+ 
+
+ align:start position:0%
+demand was higher you didn't
+particularly have any gain because you
+
+ align:start position:0%
+particularly have any gain because you
+ 
+
+ align:start position:0%
+particularly have any gain because you
+only produce so much
+
+ align:start position:0%
+only produce so much
+ 
+
+ align:start position:0%
+only produce so much
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+what you see here systematically when we
+
+ align:start position:0%
+what you see here systematically when we
+ 
+
+ align:start position:0%
+what you see here systematically when we
+think about the design itself
+
+ align:start position:0%
+think about the design itself
+ 
+
+ align:start position:0%
+think about the design itself
+the optimal design from a deterministic
+
+ align:start position:0%
+the optimal design from a deterministic
+ 
+
+ align:start position:0%
+the optimal design from a deterministic
+point of view and with an uncertain
+
+ align:start position:0%
+point of view and with an uncertain
+ 
+
+ align:start position:0%
+point of view and with an uncertain
+perspective can be lower now the amount
+
+ align:start position:0%
+perspective can be lower now the amount
+ 
+
+ align:start position:0%
+perspective can be lower now the amount
+it's lower here depends upon the
+
+ align:start position:0%
+it's lower here depends upon the
+ 
+
+ align:start position:0%
+it's lower here depends upon the
+uncertainty that we impose
+
+ align:start position:0%
+uncertainty that we impose
+ 
+
+ align:start position:0%
+uncertainty that we impose
+granted but the effect is
+
+ align:start position:0%
+granted but the effect is
+ 
+
+ align:start position:0%
+granted but the effect is
+it drives it slower that is the kind of
+
+ align:start position:0%
+it drives it slower that is the kind of
+ 
+
+ align:start position:0%
+it drives it slower that is the kind of
+effect you can imagine happening that
+
+ align:start position:0%
+effect you can imagine happening that
+ 
+
+ align:start position:0%
+effect you can imagine happening that
+you can sort of anticipate and it may
+
+ align:start position:0%
+you can sort of anticipate and it may
+ 
+
+ align:start position:0%
+you can sort of anticipate and it may
+not happen if the uncertainty was less
+
+ align:start position:0%
+not happen if the uncertainty was less
+ 
+
+ align:start position:0%
+not happen if the uncertainty was less
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+uh the uncertain design for the higher
+
+ align:start position:0%
+uh the uncertain design for the higher
+ 
+
+ align:start position:0%
+uh the uncertain design for the higher
+economies of scale might be the same
+
+ align:start position:0%
+economies of scale might be the same
+ 
+
+ align:start position:0%
+economies of scale might be the same
+here but and that's why it's a it's the
+
+ align:start position:0%
+here but and that's why it's a it's the
+ 
+
+ align:start position:0%
+here but and that's why it's a it's the
+uh lower or equal uh
+
+ align:start position:0%
+uh lower or equal uh
+ 
+
+ align:start position:0%
+uh lower or equal uh
+so this is not necessarily it but it is
+
+ align:start position:0%
+so this is not necessarily it but it is
+ 
+
+ align:start position:0%
+so this is not necessarily it but it is
+in this case
+
+ align:start position:0%
+in this case
+ 
+
+ align:start position:0%
+in this case
+by the same token
+
+ align:start position:0%
+by the same token
+ 
+
+ align:start position:0%
+by the same token
+we can think about the net present value
+
+ align:start position:0%
+we can think about the net present value
+ 
+
+ align:start position:0%
+we can think about the net present value
+of the project so here is the npv if
+
+ align:start position:0%
+of the project so here is the npv if
+ 
+
+ align:start position:0%
+of the project so here is the npv if
+uncertainty is ignored and it goes from
+
+ align:start position:0%
+uncertainty is ignored and it goes from
+ 
+
+ align:start position:0%
+uncertainty is ignored and it goes from
+uh it goes through these values and the
+
+ align:start position:0%
+uh it goes through these values and the
+ 
+
+ align:start position:0%
+uh it goes through these values and the
+moment we now recognize the uncertainty
+
+ align:start position:0%
+moment we now recognize the uncertainty
+ 
+
+ align:start position:0%
+moment we now recognize the uncertainty
+it says as we're given here we see that
+
+ align:start position:0%
+it says as we're given here we see that
+ 
+
+ align:start position:0%
+it says as we're given here we see that
+again it is they are lesser um than the
+
+ align:start position:0%
+again it is they are lesser um than the
+ 
+
+ align:start position:0%
+again it is they are lesser um than the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+than the ones with the deterministic
+
+ align:start position:0%
+than the ones with the deterministic
+ 
+
+ align:start position:0%
+than the ones with the deterministic
+analysis so these are sort of
+
+ align:start position:0%
+analysis so these are sort of
+ 
+
+ align:start position:0%
+analysis so these are sort of
+absolutely standard effects and the
+
+ align:start position:0%
+absolutely standard effects and the
+ 
+
+ align:start position:0%
+absolutely standard effects and the
+results from the
+
+ align:start position:0%
+results from the
+ 
+
+ align:start position:0%
+results from the
+flow of averages as they apply here to
+
+ align:start position:0%
+flow of averages as they apply here to
+ 
+
+ align:start position:0%
+flow of averages as they apply here to
+cap capacity constrained systems
+
+ align:start position:0%
+cap capacity constrained systems
+ 
+
+ align:start position:0%
+cap capacity constrained systems
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this being lesser all the time when you
+
+ align:start position:0%
+this being lesser all the time when you
+ 
+
+ align:start position:0%
+this being lesser all the time when you
+recognize uncertainty applies to this
+
+ align:start position:0%
+recognize uncertainty applies to this
+ 
+
+ align:start position:0%
+recognize uncertainty applies to this
+kind of situation it does not apply
+
+ align:start position:0%
+kind of situation it does not apply
+ 
+
+ align:start position:0%
+kind of situation it does not apply
+necessarily we have network effects such
+
+ align:start position:0%
+necessarily we have network effects such
+ 
+
+ align:start position:0%
+necessarily we have network effects such
+as amazon or internet or google uh where
+
+ align:start position:0%
+as amazon or internet or google uh where
+ 
+
+ align:start position:0%
+as amazon or internet or google uh where
+it may pl the non-linearities play in
+
+ align:start position:0%
+it may pl the non-linearities play in
+ 
+
+ align:start position:0%
+it may pl the non-linearities play in
+the other way
+
+ align:start position:0%
+the other way
+ 
+
+ align:start position:0%
+the other way
+but the point being is that it's a clear
+
+ align:start position:0%
+but the point being is that it's a clear
+ 
+
+ align:start position:0%
+but the point being is that it's a clear
+evidence of the flaw of averages and the
+
+ align:start position:0%
+evidence of the flaw of averages and the
+ 
+
+ align:start position:0%
+evidence of the flaw of averages and the
+reason i bother spending time on the
+
+ align:start position:0%
+reason i bother spending time on the
+ 
+
+ align:start position:0%
+reason i bother spending time on the
+floor of averages is precisely because
+
+ align:start position:0%
+floor of averages is precisely because
+ 
+
+ align:start position:0%
+floor of averages is precisely because
+it drives these kinds of
+
+ align:start position:0%
+it drives these kinds of
+ 
+
+ align:start position:0%
+it drives these kinds of
+of differences in case of capacity
+
+ align:start position:0%
+of differences in case of capacity
+ 
+
+ align:start position:0%
+of differences in case of capacity
+constrained installations whether
+
+ align:start position:0%
+constrained installations whether
+ 
+
+ align:start position:0%
+constrained installations whether
+they're warehouses or electric power
+
+ align:start position:0%
+they're warehouses or electric power
+ 
+
+ align:start position:0%
+they're warehouses or electric power
+plants or whatever
+
+ align:start position:0%
+plants or whatever
+ 
+
+ align:start position:0%
+plants or whatever
+this is the kind of effect you would
+
+ align:start position:0%
+this is the kind of effect you would
+ 
+
+ align:start position:0%
+this is the kind of effect you would
+expect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a general lesson two
+
+ align:start position:0%
+so a general lesson two
+ 
+
+ align:start position:0%
+so a general lesson two
+i'm suggesting to you
+
+ align:start position:0%
+i'm suggesting to you
+ 
+
+ align:start position:0%
+i'm suggesting to you
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+when invested in capacity limited
+
+ align:start position:0%
+when invested in capacity limited
+ 
+
+ align:start position:0%
+when invested in capacity limited
+facilities
+
+ align:start position:0%
+facilities
+ 
+
+ align:start position:0%
+facilities
+the realistic analysis of recognized
+
+ align:start position:0%
+the realistic analysis of recognized
+ 
+
+ align:start position:0%
+the realistic analysis of recognized
+uncertainty
+
+ align:start position:0%
+uncertainty
+ 
+
+ align:start position:0%
+uncertainty
+contrasts with the deterministic
+
+ align:start position:0%
+contrasts with the deterministic
+ 
+
+ align:start position:0%
+contrasts with the deterministic
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+you are if you deal with a deterministic
+
+ align:start position:0%
+you are if you deal with a deterministic
+ 
+
+ align:start position:0%
+you are if you deal with a deterministic
+analysis you're dealing with
+
+ align:start position:0%
+analysis you're dealing with
+ 
+
+ align:start position:0%
+analysis you're dealing with
+uh with basically a fairy tale that's a
+
+ align:start position:0%
+uh with basically a fairy tale that's a
+ 
+
+ align:start position:0%
+uh with basically a fairy tale that's a
+rather rude way of talking about it
+
+ align:start position:0%
+rather rude way of talking about it
+ 
+
+ align:start position:0%
+rather rude way of talking about it
+maybe because people are doing this all
+
+ align:start position:0%
+maybe because people are doing this all
+ 
+
+ align:start position:0%
+maybe because people are doing this all
+the time but the fact is you're dealing
+
+ align:start position:0%
+the time but the fact is you're dealing
+ 
+
+ align:start position:0%
+the time but the fact is you're dealing
+with an unrealistic situation and you
+
+ align:start position:0%
+with an unrealistic situation and you
+ 
+
+ align:start position:0%
+with an unrealistic situation and you
+are consequently going to get the wrong
+
+ align:start position:0%
+are consequently going to get the wrong
+ 
+
+ align:start position:0%
+are consequently going to get the wrong
+answer and in particular for the
+
+ align:start position:0%
+answer and in particular for the
+ 
+
+ align:start position:0%
+answer and in particular for the
+capacity constraint situation
+
+ align:start position:0%
+capacity constraint situation
+ 
+
+ align:start position:0%
+capacity constraint situation
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+realistic answer is that you have lower
+
+ align:start position:0%
+realistic answer is that you have lower
+ 
+
+ align:start position:0%
+realistic answer is that you have lower
+expected value and probably smaller
+
+ align:start position:0%
+expected value and probably smaller
+ 
+
+ align:start position:0%
+expected value and probably smaller
+modules are economically optimal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+all right so i will uh any i want to
+
+ align:start position:0%
+all right so i will uh any i want to
+ 
+
+ align:start position:0%
+all right so i will uh any i want to
+stop here again indra uh
+
+ align:start position:0%
+stop here again indra uh
+ 
+
+ align:start position:0%
+stop here again indra uh
+is there
+
+ align:start position:0%
+is there
+ 
+
+ align:start position:0%
+is there
+oop
+
+ align:start position:0%
+oop
+ 
+
+ align:start position:0%
+oop
+uh is there any uh question here uh that
+
+ align:start position:0%
+uh is there any uh question here uh that
+ 
+
+ align:start position:0%
+uh is there any uh question here uh that
+people would like to ask i want to be
+
+ align:start position:0%
+people would like to ask i want to be
+ 
+
+ align:start position:0%
+people would like to ask i want to be
+sure that this point is understood or
+
+ align:start position:0%
+sure that this point is understood or
+ 
+
+ align:start position:0%
+sure that this point is understood or
+if you debate it that we can have the
+
+ align:start position:0%
+if you debate it that we can have the
+ 
+
+ align:start position:0%
+if you debate it that we can have the
+debate about it and i can resolve any
+
+ align:start position:0%
+debate about it and i can resolve any
+ 
+
+ align:start position:0%
+debate about it and i can resolve any
+questions that might occur
+
+ align:start position:0%
+questions that might occur
+ 
+
+ align:start position:0%
+questions that might occur
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if anyone has a question yeah we have
+
+ align:start position:0%
+if anyone has a question yeah we have
+ 
+
+ align:start position:0%
+if anyone has a question yeah we have
+joshua joshua go ahead
+
+ align:start position:0%
+joshua joshua go ahead
+ 
+
+ align:start position:0%
+joshua joshua go ahead
+professor just looking for clarification
+
+ align:start position:0%
+professor just looking for clarification
+ 
+
+ align:start position:0%
+professor just looking for clarification
+when you say that for capacity limited
+
+ align:start position:0%
+when you say that for capacity limited
+ 
+
+ align:start position:0%
+when you say that for capacity limited
+facilities or whatnot um
+
+ align:start position:0%
+facilities or whatnot um
+ 
+
+ align:start position:0%
+facilities or whatnot um
+you're taking away the upside because
+
+ align:start position:0%
+you're taking away the upside because
+ 
+
+ align:start position:0%
+you're taking away the upside because
+you can only go up to that capacity and
+
+ align:start position:0%
+you can only go up to that capacity and
+ 
+
+ align:start position:0%
+you can only go up to that capacity and
+so the uncertainty that's presented only
+
+ align:start position:0%
+so the uncertainty that's presented only
+ 
+
+ align:start position:0%
+so the uncertainty that's presented only
+provides you the downside up to the to
+
+ align:start position:0%
+provides you the downside up to the to
+ 
+
+ align:start position:0%
+provides you the downside up to the to
+up to that mean or the average
+
+ align:start position:0%
+up to that mean or the average
+ 
+
+ align:start position:0%
+up to that mean or the average
+and that's the major effect yes i mean
+
+ align:start position:0%
+and that's the major effect yes i mean
+ 
+
+ align:start position:0%
+and that's the major effect yes i mean
+you could think well
+
+ align:start position:0%
+you could think well
+ 
+
+ align:start position:0%
+you could think well
+maybe we could raise our prices for it
+
+ align:start position:0%
+maybe we could raise our prices for it
+ 
+
+ align:start position:0%
+maybe we could raise our prices for it
+so maybe we can compensate for you know
+
+ align:start position:0%
+so maybe we can compensate for you know
+ 
+
+ align:start position:0%
+so maybe we can compensate for you know
+if this is tight demand
+
+ align:start position:0%
+if this is tight demand
+ 
+
+ align:start position:0%
+if this is tight demand
+that implies there's no competition of
+
+ align:start position:0%
+that implies there's no competition of
+ 
+
+ align:start position:0%
+that implies there's no competition of
+course but uh
+
+ align:start position:0%
+course but uh
+ 
+
+ align:start position:0%
+course but uh
+so the major effect is in that direction
+
+ align:start position:0%
+so the major effect is in that direction
+ 
+
+ align:start position:0%
+so the major effect is in that direction
+and of course there are uh exceptions
+
+ align:start position:0%
+and of course there are uh exceptions
+ 
+
+ align:start position:0%
+and of course there are uh exceptions
+and modulate but that is the main effect
+
+ align:start position:0%
+and modulate but that is the main effect
+ 
+
+ align:start position:0%
+and modulate but that is the main effect
+that we're looking that one can account
+
+ align:start position:0%
+that we're looking that one can account
+ 
+
+ align:start position:0%
+that we're looking that one can account
+for yes that's what i meant to say are
+
+ align:start position:0%
+for yes that's what i meant to say are
+ 
+
+ align:start position:0%
+for yes that's what i meant to say are
+you concerned about that or
+
+ align:start position:0%
+you concerned about that or
+ 
+
+ align:start position:0%
+you concerned about that or
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+are you just validating it or what how
+
+ align:start position:0%
+are you just validating it or what how
+ 
+
+ align:start position:0%
+are you just validating it or what how
+are we listening how are you thinking
+
+ align:start position:0%
+are we listening how are you thinking
+ 
+
+ align:start position:0%
+are we listening how are you thinking
+about it i think that that makes a lot
+
+ align:start position:0%
+about it i think that that makes a lot
+ 
+
+ align:start position:0%
+about it i think that that makes a lot
+of sense and appreciate the
+
+ align:start position:0%
+of sense and appreciate the
+ 
+
+ align:start position:0%
+of sense and appreciate the
+clarification i think it's just um
+
+ align:start position:0%
+clarification i think it's just um
+ 
+
+ align:start position:0%
+clarification i think it's just um
+uh how do you
+
+ align:start position:0%
+uh how do you
+ 
+
+ align:start position:0%
+uh how do you
+how do you then um
+
+ align:start position:0%
+how do you then um
+ 
+
+ align:start position:0%
+how do you then um
+absorb the risk associated with allowing
+
+ align:start position:0%
+absorb the risk associated with allowing
+ 
+
+ align:start position:0%
+absorb the risk associated with allowing
+yourself
+
+ align:start position:0%
+yourself
+ 
+
+ align:start position:0%
+yourself
+to get the upside you know to get
+
+ align:start position:0%
+to get the upside you know to get
+ 
+
+ align:start position:0%
+to get the upside you know to get
+above the mean with capacity you you uh
+
+ align:start position:0%
+above the mean with capacity you you uh
+ 
+
+ align:start position:0%
+above the mean with capacity you you uh
+any business would would have
+
+ align:start position:0%
+any business would would have
+ 
+
+ align:start position:0%
+any business would would have
+significant risk in that case well
+
+ align:start position:0%
+significant risk in that case well
+ 
+
+ align:start position:0%
+significant risk in that case well
+that's where the modularity comes in
+
+ align:start position:0%
+that's where the modularity comes in
+ 
+
+ align:start position:0%
+that's where the modularity comes in
+because um
+
+ align:start position:0%
+because um
+ 
+
+ align:start position:0%
+because um
+this is recognizing uncertainty but it
+
+ align:start position:0%
+this is recognizing uncertainty but it
+ 
+
+ align:start position:0%
+this is recognizing uncertainty but it
+also means that okay well we're going to
+
+ align:start position:0%
+also means that okay well we're going to
+ 
+
+ align:start position:0%
+also means that okay well we're going to
+impose flex we're going to allow for
+
+ align:start position:0%
+impose flex we're going to allow for
+ 
+
+ align:start position:0%
+impose flex we're going to allow for
+flexibility we say right
+
+ align:start position:0%
+flexibility we say right
+ 
+
+ align:start position:0%
+flexibility we say right
+um if demand is picking up we're going
+
+ align:start position:0%
+um if demand is picking up we're going
+ 
+
+ align:start position:0%
+um if demand is picking up we're going
+to put in some more modules now
+
+ align:start position:0%
+to put in some more modules now
+ 
+
+ align:start position:0%
+to put in some more modules now
+uh in the garage case
+
+ align:start position:0%
+uh in the garage case
+ 
+
+ align:start position:0%
+uh in the garage case
+the starter set was you waited two years
+
+ align:start position:0%
+the starter set was you waited two years
+ 
+
+ align:start position:0%
+the starter set was you waited two years
+to see if the gross was there well
+
+ align:start position:0%
+to see if the gross was there well
+ 
+
+ align:start position:0%
+to see if the gross was there well
+depending upon the business and
+
+ align:start position:0%
+depending upon the business and
+ 
+
+ align:start position:0%
+depending upon the business and
+depending how long it takes to add the
+
+ align:start position:0%
+depending how long it takes to add the
+ 
+
+ align:start position:0%
+depending how long it takes to add the
+capacity you might decide to do it
+
+ align:start position:0%
+capacity you might decide to do it
+ 
+
+ align:start position:0%
+capacity you might decide to do it
+earlier or later or whatever but the
+
+ align:start position:0%
+earlier or later or whatever but the
+ 
+
+ align:start position:0%
+earlier or later or whatever but the
+idea is okay
+
+ align:start position:0%
+idea is okay
+ 
+
+ align:start position:0%
+idea is okay
+we have if we've planned this correctly
+
+ align:start position:0%
+we have if we've planned this correctly
+ 
+
+ align:start position:0%
+we have if we've planned this correctly
+we haven't forgotten the upside
+
+ align:start position:0%
+we haven't forgotten the upside
+ 
+
+ align:start position:0%
+we haven't forgotten the upside
+opportunity we just are going to make
+
+ align:start position:0%
+opportunity we just are going to make
+ 
+
+ align:start position:0%
+opportunity we just are going to make
+sure that it's around so if we're
+
+ align:start position:0%
+sure that it's around so if we're
+ 
+
+ align:start position:0%
+sure that it's around so if we're
+starting here in year zero
+
+ align:start position:0%
+starting here in year zero
+ 
+
+ align:start position:0%
+starting here in year zero
+uh year one we're not going to build all
+
+ align:start position:0%
+uh year one we're not going to build all
+ 
+
+ align:start position:0%
+uh year one we're not going to build all
+the way up for here we're going to say
+
+ align:start position:0%
+the way up for here we're going to say
+ 
+
+ align:start position:0%
+the way up for here we're going to say
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+when year three comes around and it
+
+ align:start position:0%
+when year three comes around and it
+ 
+
+ align:start position:0%
+when year three comes around and it
+looks like the capacity of the demand is
+
+ align:start position:0%
+looks like the capacity of the demand is
+ 
+
+ align:start position:0%
+looks like the capacity of the demand is
+really growing we're going to add
+
+ align:start position:0%
+really growing we're going to add
+ 
+
+ align:start position:0%
+really growing we're going to add
+capacity we haven't closed we haven't
+
+ align:start position:0%
+capacity we haven't closed we haven't
+ 
+
+ align:start position:0%
+capacity we haven't closed we haven't
+closed it off
+
+ align:start position:0%
+closed it off
+ 
+
+ align:start position:0%
+closed it off
+but in that particular year when there
+
+ align:start position:0%
+but in that particular year when there
+ 
+
+ align:start position:0%
+but in that particular year when there
+was demand was higher than we were at
+
+ align:start position:0%
+was demand was higher than we were at
+ 
+
+ align:start position:0%
+was demand was higher than we were at
+capacity for well we didn't gain as much
+
+ align:start position:0%
+capacity for well we didn't gain as much
+ 
+
+ align:start position:0%
+capacity for well we didn't gain as much
+but we'll catch it up uh somewhat later
+
+ align:start position:0%
+but we'll catch it up uh somewhat later
+ 
+
+ align:start position:0%
+but we'll catch it up uh somewhat later
+on so but if yeah that's what i'm saying
+
+ align:start position:0%
+on so but if yeah that's what i'm saying
+ 
+
+ align:start position:0%
+on so but if yeah that's what i'm saying
+for those of you who operated things i
+
+ align:start position:0%
+for those of you who operated things i
+ 
+
+ align:start position:0%
+for those of you who operated things i
+mean you have to realize that the
+
+ align:start position:0%
+mean you have to realize that the
+ 
+
+ align:start position:0%
+mean you have to realize that the
+capacity
+
+ align:start position:0%
+capacity
+ 
+
+ align:start position:0%
+capacity
+there's the plate capacity on the
+
+ align:start position:0%
+there's the plate capacity on the
+ 
+
+ align:start position:0%
+there's the plate capacity on the
+production facility and then there is
+
+ align:start position:0%
+production facility and then there is
+ 
+
+ align:start position:0%
+production facility and then there is
+the actual capacity because
+
+ align:start position:0%
+the actual capacity because
+ 
+
+ align:start position:0%
+the actual capacity because
+there's a glitch or you have to close it
+
+ align:start position:0%
+there's a glitch or you have to close it
+ 
+
+ align:start position:0%
+there's a glitch or you have to close it
+for maintenance or so forth and on the
+
+ align:start position:0%
+for maintenance or so forth and on the
+ 
+
+ align:start position:0%
+for maintenance or so forth and on the
+other hand you could have produced more
+
+ align:start position:0%
+other hand you could have produced more
+ 
+
+ align:start position:0%
+other hand you could have produced more
+than the plate capacity because you
+
+ align:start position:0%
+than the plate capacity because you
+ 
+
+ align:start position:0%
+than the plate capacity because you
+decided to work overtime and not and
+
+ align:start position:0%
+decided to work overtime and not and
+ 
+
+ align:start position:0%
+decided to work overtime and not and
+forgo maintenance for a while that you
+
+ align:start position:0%
+forgo maintenance for a while that you
+ 
+
+ align:start position:0%
+forgo maintenance for a while that you
+had assumed and so forth there are a lot
+
+ align:start position:0%
+had assumed and so forth there are a lot
+ 
+
+ align:start position:0%
+had assumed and so forth there are a lot
+of ways in which capacity is not like
+
+ align:start position:0%
+of ways in which capacity is not like
+ 
+
+ align:start position:0%
+of ways in which capacity is not like
+this cup of coffee which will only take
+
+ align:start position:0%
+this cup of coffee which will only take
+ 
+
+ align:start position:0%
+this cup of coffee which will only take
+so much and if it
+
+ align:start position:0%
+so much and if it
+ 
+
+ align:start position:0%
+so much and if it
+and you can't get any more into it but
+
+ align:start position:0%
+and you can't get any more into it but
+ 
+
+ align:start position:0%
+and you can't get any more into it but
+it's more like a capacity of people on a
+
+ align:start position:0%
+it's more like a capacity of people on a
+ 
+
+ align:start position:0%
+it's more like a capacity of people on a
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+on a bus or on a subway car well it may
+
+ align:start position:0%
+on a bus or on a subway car well it may
+ 
+
+ align:start position:0%
+on a bus or on a subway car well it may
+say capacity for 20 standing and 30
+
+ align:start position:0%
+say capacity for 20 standing and 30
+ 
+
+ align:start position:0%
+say capacity for 20 standing and 30
+seating but you all know situations
+
+ align:start position:0%
+seating but you all know situations
+ 
+
+ align:start position:0%
+seating but you all know situations
+where you've had greater capacity and
+
+ align:start position:0%
+where you've had greater capacity and
+ 
+
+ align:start position:0%
+where you've had greater capacity and
+others where right now you're not
+
+ align:start position:0%
+others where right now you're not
+ 
+
+ align:start position:0%
+others where right now you're not
+allowed to sit close together so the
+
+ align:start position:0%
+allowed to sit close together so the
+ 
+
+ align:start position:0%
+allowed to sit close together so the
+capacity is actually smaller so capacity
+
+ align:start position:0%
+capacity is actually smaller so capacity
+ 
+
+ align:start position:0%
+capacity is actually smaller so capacity
+is a rather
+
+ align:start position:0%
+is a rather
+ 
+
+ align:start position:0%
+is a rather
+uh in practice is somewhat of a fluid
+
+ align:start position:0%
+uh in practice is somewhat of a fluid
+ 
+
+ align:start position:0%
+uh in practice is somewhat of a fluid
+quite a bit of a fluid thing yes
+
+ align:start position:0%
+quite a bit of a fluid thing yes
+ 
+
+ align:start position:0%
+quite a bit of a fluid thing yes
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i'm trying to point to the general
+
+ align:start position:0%
+i'm trying to point to the general
+ 
+
+ align:start position:0%
+i'm trying to point to the general
+phenomenon here um but the ways in which
+
+ align:start position:0%
+phenomenon here um but the ways in which
+ 
+
+ align:start position:0%
+phenomenon here um but the ways in which
+in the real world it gets to be
+
+ align:start position:0%
+in the real world it gets to be
+ 
+
+ align:start position:0%
+in the real world it gets to be
+complicated yes absolutely
+
+ align:start position:0%
+complicated yes absolutely
+ 
+
+ align:start position:0%
+complicated yes absolutely
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right my work now with this moroccan
+
+ align:start position:0%
+right my work now with this moroccan
+ 
+
+ align:start position:0%
+right my work now with this moroccan
+company is exploring exactly those kinds
+
+ align:start position:0%
+company is exploring exactly those kinds
+ 
+
+ align:start position:0%
+company is exploring exactly those kinds
+of issues so
+
+ align:start position:0%
+of issues so
+ 
+
+ align:start position:0%
+of issues so
+just to say that uh i'll pass over this
+
+ align:start position:0%
+just to say that uh i'll pass over this
+ 
+
+ align:start position:0%
+just to say that uh i'll pass over this
+slide which is simply to say that once
+
+ align:start position:0%
+slide which is simply to say that once
+ 
+
+ align:start position:0%
+slide which is simply to say that once
+you move
+
+ align:start position:0%
+you move
+ 
+
+ align:start position:0%
+you move
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+thinking about not just a combination of
+
+ align:start position:0%
+thinking about not just a combination of
+ 
+
+ align:start position:0%
+thinking about not just a combination of
+size and timing but also add that other
+
+ align:start position:0%
+size and timing but also add that other
+ 
+
+ align:start position:0%
+size and timing but also add that other
+dimension of location in this case of
+
+ align:start position:0%
+dimension of location in this case of
+ 
+
+ align:start position:0%
+dimension of location in this case of
+five possible locations um that the
+
+ align:start position:0%
+five possible locations um that the
+ 
+
+ align:start position:0%
+five possible locations um that the
+complexity of uh
+
+ align:start position:0%
+complexity of uh
+ 
+
+ align:start position:0%
+complexity of uh
+of the analysis increases greatly and um
+
+ align:start position:0%
+of the analysis increases greatly and um
+ 
+
+ align:start position:0%
+of the analysis increases greatly and um
+so the analysis is more complicated
+
+ align:start position:0%
+so the analysis is more complicated
+ 
+
+ align:start position:0%
+so the analysis is more complicated
+but that's just as a footnote
+
+ align:start position:0%
+but that's just as a footnote
+ 
+
+ align:start position:0%
+but that's just as a footnote
+so now let's look at the optimal design
+
+ align:start position:0%
+so now let's look at the optimal design
+ 
+
+ align:start position:0%
+so now let's look at the optimal design
+here and this is again very similar to
+
+ align:start position:0%
+here and this is again very similar to
+ 
+
+ align:start position:0%
+here and this is again very similar to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+garage case where
+
+ align:start position:0%
+garage case where
+ 
+
+ align:start position:0%
+garage case where
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+building it large
+
+ align:start position:0%
+building it large
+ 
+
+ align:start position:0%
+building it large
+and fixed
+
+ align:start position:0%
+and fixed
+ 
+
+ align:start position:0%
+and fixed
+uh has the
+
+ align:start position:0%
+uh has the
+ 
+
+ align:start position:0%
+uh has the
+this performance here for these numbers
+
+ align:start position:0%
+this performance here for these numbers
+ 
+
+ align:start position:0%
+this performance here for these numbers
+an expected value uh quite reasonable
+
+ align:start position:0%
+an expected value uh quite reasonable
+ 
+
+ align:start position:0%
+an expected value uh quite reasonable
+but uh it could be if you build it
+
+ align:start position:0%
+but uh it could be if you build it
+ 
+
+ align:start position:0%
+but uh it could be if you build it
+nobody comes sort of the way it was the
+
+ align:start position:0%
+nobody comes sort of the way it was the
+ 
+
+ align:start position:0%
+nobody comes sort of the way it was the
+first years of the salting plant you
+
+ align:start position:0%
+first years of the salting plant you
+ 
+
+ align:start position:0%
+first years of the salting plant you
+could have a big loss
+
+ align:start position:0%
+could have a big loss
+ 
+
+ align:start position:0%
+could have a big loss
+and your capacity limited to a certain
+
+ align:start position:0%
+and your capacity limited to a certain
+ 
+
+ align:start position:0%
+and your capacity limited to a certain
+amount
+
+ align:start position:0%
+amount
+ 
+
+ align:start position:0%
+amount
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if you had a flexible modular uh
+
+ align:start position:0%
+if you had a flexible modular uh
+ 
+
+ align:start position:0%
+if you had a flexible modular uh
+solution where you allowed yourself to
+
+ align:start position:0%
+solution where you allowed yourself to
+ 
+
+ align:start position:0%
+solution where you allowed yourself to
+time the
+
+ align:start position:0%
+time the
+ 
+
+ align:start position:0%
+time the
+increases of capacity according to the
+
+ align:start position:0%
+increases of capacity according to the
+ 
+
+ align:start position:0%
+increases of capacity according to the
+demand you weren't going to lose very
+
+ align:start position:0%
+demand you weren't going to lose very
+ 
+
+ align:start position:0%
+demand you weren't going to lose very
+much because you started small and
+
+ align:start position:0%
+much because you started small and
+ 
+
+ align:start position:0%
+much because you started small and
+um there was a lot not so much to lose
+
+ align:start position:0%
+um there was a lot not so much to lose
+ 
+
+ align:start position:0%
+um there was a lot not so much to lose
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+the losses uh were
+
+ align:start position:0%
+the losses uh were
+ 
+
+ align:start position:0%
+the losses uh were
+several a couple million dollars by this
+
+ align:start position:0%
+several a couple million dollars by this
+ 
+
+ align:start position:0%
+several a couple million dollars by this
+comparison
+
+ align:start position:0%
+comparison
+ 
+
+ align:start position:0%
+comparison
+uh but if the demand really picked up
+
+ align:start position:0%
+uh but if the demand really picked up
+ 
+
+ align:start position:0%
+uh but if the demand really picked up
+you could expand expand expand so that
+
+ align:start position:0%
+you could expand expand expand so that
+ 
+
+ align:start position:0%
+you could expand expand expand so that
+you had a much better performance
+
+ align:start position:0%
+you had a much better performance
+ 
+
+ align:start position:0%
+you had a much better performance
+overall and in this case as often
+
+ align:start position:0%
+overall and in this case as often
+ 
+
+ align:start position:0%
+overall and in this case as often
+happens but not necessarily the flexible
+
+ align:start position:0%
+happens but not necessarily the flexible
+ 
+
+ align:start position:0%
+happens but not necessarily the flexible
+demand compared with the inflexible
+
+ align:start position:0%
+demand compared with the inflexible
+ 
+
+ align:start position:0%
+demand compared with the inflexible
+demand perform
+
+ align:start position:0%
+demand perform
+ 
+
+ align:start position:0%
+demand perform
+was better overall
+
+ align:start position:0%
+was better overall
+ 
+
+ align:start position:0%
+was better overall
+so that was uh
+
+ align:start position:0%
+so that was uh
+ 
+
+ align:start position:0%
+so that was uh
+that was that those target curves for
+
+ align:start position:0%
+that was that those target curves for
+ 
+
+ align:start position:0%
+that was that those target curves for
+that comparison
+
+ align:start position:0%
+that comparison
+ 
+
+ align:start position:0%
+that comparison
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+note by the way that the increase in
+
+ align:start position:0%
+note by the way that the increase in
+ 
+
+ align:start position:0%
+note by the way that the increase in
+value so of course this is not
+
+ align:start position:0%
+value so of course this is not
+ 
+
+ align:start position:0%
+value so of course this is not
+guaranteed but in this particular case
+
+ align:start position:0%
+guaranteed but in this particular case
+ 
+
+ align:start position:0%
+guaranteed but in this particular case
+was from about 14 and changed to about
+
+ align:start position:0%
+was from about 14 and changed to about
+ 
+
+ align:start position:0%
+was from about 14 and changed to about
+21 which is about 50 increase in value
+
+ align:start position:0%
+21 which is about 50 increase in value
+ 
+
+ align:start position:0%
+21 which is about 50 increase in value
+so that with no new technology nothing
+
+ align:start position:0%
+so that with no new technology nothing
+ 
+
+ align:start position:0%
+so that with no new technology nothing
+no sort of miraculum involved you can
+
+ align:start position:0%
+no sort of miraculum involved you can
+ 
+
+ align:start position:0%
+no sort of miraculum involved you can
+increase
+
+ align:start position:0%
+increase
+ 
+
+ align:start position:0%
+increase
+simply by recognizing uncertainty you
+
+ align:start position:0%
+simply by recognizing uncertainty you
+ 
+
+ align:start position:0%
+simply by recognizing uncertainty you
+could increase the perspective expect
+
+ align:start position:0%
+could increase the perspective expect
+ 
+
+ align:start position:0%
+could increase the perspective expect
+perspective expected value by 50 it's
+
+ align:start position:0%
+perspective expected value by 50 it's
+ 
+
+ align:start position:0%
+perspective expected value by 50 it's
+really quite remarkable and
+
+ align:start position:0%
+really quite remarkable and
+ 
+
+ align:start position:0%
+really quite remarkable and
+of course there are details about how it
+
+ align:start position:0%
+of course there are details about how it
+ 
+
+ align:start position:0%
+of course there are details about how it
+actually gonna work out and so forth
+
+ align:start position:0%
+actually gonna work out and so forth
+ 
+
+ align:start position:0%
+actually gonna work out and so forth
+but it
+
+ align:start position:0%
+but it
+ 
+
+ align:start position:0%
+but it
+emphasizes the great prospects for
+
+ align:start position:0%
+emphasizes the great prospects for
+ 
+
+ align:start position:0%
+emphasizes the great prospects for
+flexible design under some circumstances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/izl46nTo1ng.txt b/izl46nTo1ng.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c0230cee7fb8cc80769667c5824ff356e569aaef
--- /dev/null
+++ b/izl46nTo1ng.txt
@@ -0,0 +1,17149 @@
+align:start position:0%
+ 
+so this is an outline of what i'm going
+
+ align:start position:0%
+so this is an outline of what i'm going
+ 
+
+ align:start position:0%
+so this is an outline of what i'm going
+to talk about and we're going to begin
+
+ align:start position:0%
+to talk about and we're going to begin
+ 
+
+ align:start position:0%
+to talk about and we're going to begin
+by sort of
+
+ align:start position:0%
+by sort of
+ 
+
+ align:start position:0%
+by sort of
+getting at this question of why complex
+
+ align:start position:0%
+getting at this question of why complex
+ 
+
+ align:start position:0%
+getting at this question of why complex
+trait human genetics is so difficult
+
+ align:start position:0%
+trait human genetics is so difficult
+ 
+
+ align:start position:0%
+trait human genetics is so difficult
+um and then go through each of the steps
+
+ align:start position:0%
+um and then go through each of the steps
+ 
+
+ align:start position:0%
+um and then go through each of the steps
+that you would do if you were actually
+
+ align:start position:0%
+that you would do if you were actually
+ 
+
+ align:start position:0%
+that you would do if you were actually
+doing this work the first question you
+
+ align:start position:0%
+doing this work the first question you
+ 
+
+ align:start position:0%
+doing this work the first question you
+would get asked on an nih grant
+
+ align:start position:0%
+would get asked on an nih grant
+ 
+
+ align:start position:0%
+would get asked on an nih grant
+application is is your phenotype
+
+ align:start position:0%
+application is is your phenotype
+ 
+
+ align:start position:0%
+application is is your phenotype
+heritable
+
+ align:start position:0%
+heritable
+ 
+
+ align:start position:0%
+heritable
+and so some evidence of heritability or
+
+ align:start position:0%
+and so some evidence of heritability or
+ 
+
+ align:start position:0%
+and so some evidence of heritability or
+doing a study to determine heritability
+
+ align:start position:0%
+doing a study to determine heritability
+ 
+
+ align:start position:0%
+doing a study to determine heritability
+is often the first step in in a genetic
+
+ align:start position:0%
+is often the first step in in a genetic
+ 
+
+ align:start position:0%
+is often the first step in in a genetic
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+so we're going to talk a little bit
+
+ align:start position:0%
+so we're going to talk a little bit
+ 
+
+ align:start position:0%
+so we're going to talk a little bit
+about heritability and how you define
+
+ align:start position:0%
+about heritability and how you define
+ 
+
+ align:start position:0%
+about heritability and how you define
+that and then identifying disease
+
+ align:start position:0%
+that and then identifying disease
+ 
+
+ align:start position:0%
+that and then identifying disease
+phenotypes so that's a critical issue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the difference between a sub-phenotype
+
+ align:start position:0%
+the difference between a sub-phenotype
+ 
+
+ align:start position:0%
+the difference between a sub-phenotype
+and an intermediate phenotype
+
+ align:start position:0%
+and an intermediate phenotype
+ 
+
+ align:start position:0%
+and an intermediate phenotype
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how you want to look at those things
+
+ align:start position:0%
+how you want to look at those things
+ 
+
+ align:start position:0%
+how you want to look at those things
+then developing your study design
+
+ align:start position:0%
+then developing your study design
+ 
+
+ align:start position:0%
+then developing your study design
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the paper that i just was telling you
+
+ align:start position:0%
+the paper that i just was telling you
+ 
+
+ align:start position:0%
+the paper that i just was telling you
+about this paper that's coming out in
+
+ align:start position:0%
+about this paper that's coming out in
+ 
+
+ align:start position:0%
+about this paper that's coming out in
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+these people looked at two relative
+
+ align:start position:0%
+these people looked at two relative
+ 
+
+ align:start position:0%
+these people looked at two relative
+genetic isolates the population of
+
+ align:start position:0%
+genetic isolates the population of
+ 
+
+ align:start position:0%
+genetic isolates the population of
+finland and the uh uh saginay loch
+
+ align:start position:0%
+finland and the uh uh saginay loch
+ 
+
+ align:start position:0%
+finland and the uh uh saginay loch
+sanchez population in northeast quebec
+
+ align:start position:0%
+sanchez population in northeast quebec
+ 
+
+ align:start position:0%
+sanchez population in northeast quebec
+french canadians
+
+ align:start position:0%
+french canadians
+ 
+
+ align:start position:0%
+french canadians
+so these are populations where they had
+
+ align:start position:0%
+so these are populations where they had
+ 
+
+ align:start position:0%
+so these are populations where they had
+a limited number of founders
+
+ align:start position:0%
+a limited number of founders
+ 
+
+ align:start position:0%
+a limited number of founders
+and so uh the thought is is that they're
+
+ align:start position:0%
+and so uh the thought is is that they're
+ 
+
+ align:start position:0%
+and so uh the thought is is that they're
+more genetically homogeneous and it
+
+ align:start position:0%
+more genetically homogeneous and it
+ 
+
+ align:start position:0%
+more genetically homogeneous and it
+might be easier to find genes in these
+
+ align:start position:0%
+might be easier to find genes in these
+ 
+
+ align:start position:0%
+might be easier to find genes in these
+populations but what's the big concern
+
+ align:start position:0%
+populations but what's the big concern
+ 
+
+ align:start position:0%
+populations but what's the big concern
+if you found a gene in the fins
+
+ align:start position:0%
+if you found a gene in the fins
+ 
+
+ align:start position:0%
+if you found a gene in the fins
+what would be your biggest concern about
+
+ align:start position:0%
+what would be your biggest concern about
+ 
+
+ align:start position:0%
+what would be your biggest concern about
+about that
+
+ align:start position:0%
+about that
+ 
+
+ align:start position:0%
+about that
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+exactly that you know maybe that gene
+
+ align:start position:0%
+exactly that you know maybe that gene
+ 
+
+ align:start position:0%
+exactly that you know maybe that gene
+might not replicate or be a significant
+
+ align:start position:0%
+might not replicate or be a significant
+ 
+
+ align:start position:0%
+might not replicate or be a significant
+gene in an outbred population you know
+
+ align:start position:0%
+gene in an outbred population you know
+ 
+
+ align:start position:0%
+gene in an outbred population you know
+in a country such as the united states
+
+ align:start position:0%
+in a country such as the united states
+ 
+
+ align:start position:0%
+in a country such as the united states
+where there's a lot of
+
+ align:start position:0%
+where there's a lot of
+ 
+
+ align:start position:0%
+where there's a lot of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+ethnic variation and diversity so
+
+ align:start position:0%
+ethnic variation and diversity so
+ 
+
+ align:start position:0%
+ethnic variation and diversity so
+it may be easier to find genes in
+
+ align:start position:0%
+it may be easier to find genes in
+ 
+
+ align:start position:0%
+it may be easier to find genes in
+genetic isolates but it may be more
+
+ align:start position:0%
+genetic isolates but it may be more
+ 
+
+ align:start position:0%
+genetic isolates but it may be more
+difficult
+
+ align:start position:0%
+difficult
+ 
+
+ align:start position:0%
+difficult
+in terms of their generalizability so
+
+ align:start position:0%
+in terms of their generalizability so
+ 
+
+ align:start position:0%
+in terms of their generalizability so
+give me some other examples of
+
+ align:start position:0%
+give me some other examples of
+ 
+
+ align:start position:0%
+give me some other examples of
+relative genetic isolates around the
+
+ align:start position:0%
+relative genetic isolates around the
+ 
+
+ align:start position:0%
+relative genetic isolates around the
+world populations that would be
+
+ align:start position:0%
+world populations that would be
+ 
+
+ align:start position:0%
+world populations that would be
+considered relative genetic isolates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+iceland yes absolutely iceland so that's
+
+ align:start position:0%
+iceland yes absolutely iceland so that's
+ 
+
+ align:start position:0%
+iceland yes absolutely iceland so that's
+where decode is
+
+ align:start position:0%
+where decode is
+ 
+
+ align:start position:0%
+where decode is
+is working decode is our number one
+
+ align:start position:0%
+is working decode is our number one
+ 
+
+ align:start position:0%
+is working decode is our number one
+competitor in copd research they're the
+
+ align:start position:0%
+competitor in copd research they're the
+ 
+
+ align:start position:0%
+competitor in copd research they're the
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+company that that's actually doing uh um
+
+ align:start position:0%
+company that that's actually doing uh um
+ 
+
+ align:start position:0%
+company that that's actually doing uh um
+copd stuff
+
+ align:start position:0%
+copd stuff
+ 
+
+ align:start position:0%
+copd stuff
+what else where else could you go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what might be the disadvantage of a
+
+ align:start position:0%
+what might be the disadvantage of a
+ 
+
+ align:start position:0%
+what might be the disadvantage of a
+tribal population or a disadvantage of a
+
+ align:start position:0%
+tribal population or a disadvantage of a
+ 
+
+ align:start position:0%
+tribal population or a disadvantage of a
+of a small
+
+ align:start position:0%
+of a small
+ 
+
+ align:start position:0%
+of a small
+island population like tristan de cunha
+
+ align:start position:0%
+island population like tristan de cunha
+ 
+
+ align:start position:0%
+island population like tristan de cunha
+which is where they first went to do
+
+ align:start position:0%
+which is where they first went to do
+ 
+
+ align:start position:0%
+which is where they first went to do
+genetic isolate work in in asthma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah small number of people so
+
+ align:start position:0%
+yeah small number of people so
+ 
+
+ align:start position:0%
+yeah small number of people so
+you know you got a limited number of uh
+
+ align:start position:0%
+you know you got a limited number of uh
+ 
+
+ align:start position:0%
+you know you got a limited number of uh
+meiosis in a population like that you're
+
+ align:start position:0%
+meiosis in a population like that you're
+ 
+
+ align:start position:0%
+meiosis in a population like that you're
+not going to get too many recombinations
+
+ align:start position:0%
+not going to get too many recombinations
+ 
+
+ align:start position:0%
+not going to get too many recombinations
+so you just sort of run out of gas
+
+ align:start position:0%
+so you just sort of run out of gas
+ 
+
+ align:start position:0%
+so you just sort of run out of gas
+because you don't have a big enough
+
+ align:start position:0%
+because you don't have a big enough
+ 
+
+ align:start position:0%
+because you don't have a big enough
+sample size let's
+
+ align:start position:0%
+sample size let's
+ 
+
+ align:start position:0%
+sample size let's
+switch boundaries
+
+ align:start position:0%
+switch boundaries
+ 
+
+ align:start position:0%
+switch boundaries
+possibly um the fins the swiss
+
+ align:start position:0%
+possibly um the fins the swiss
+ 
+
+ align:start position:0%
+possibly um the fins the swiss
+uh the northern uh um
+
+ align:start position:0%
+uh the northern uh um
+ 
+
+ align:start position:0%
+uh the northern uh um
+um the um
+
+ align:start position:0%
+um the um
+ 
+
+ align:start position:0%
+um the um
+ashkenazi jews um
+
+ align:start position:0%
+ashkenazi jews um
+ 
+
+ align:start position:0%
+ashkenazi jews um
+costa rica
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why costa rica
+
+ align:start position:0%
+why costa rica
+ 
+
+ align:start position:0%
+why costa rica
+why costa rica because
+
+ align:start position:0%
+why costa rica because
+ 
+
+ align:start position:0%
+why costa rica because
+costa rica is surrounded by volcanoes it
+
+ align:start position:0%
+costa rica is surrounded by volcanoes it
+ 
+
+ align:start position:0%
+costa rica is surrounded by volcanoes it
+was the one place in central america
+
+ align:start position:0%
+was the one place in central america
+ 
+
+ align:start position:0%
+was the one place in central america
+that uh the span you know there's not a
+
+ align:start position:0%
+that uh the span you know there's not a
+ 
+
+ align:start position:0%
+that uh the span you know there's not a
+huge
+
+ align:start position:0%
+huge
+ 
+
+ align:start position:0%
+huge
+spanish influx because there was no gold
+
+ align:start position:0%
+spanish influx because there was no gold
+ 
+
+ align:start position:0%
+spanish influx because there was no gold
+there so there's a limited number of
+
+ align:start position:0%
+there so there's a limited number of
+ 
+
+ align:start position:0%
+there so there's a limited number of
+spanish founders in the 15th century
+
+ align:start position:0%
+spanish founders in the 15th century
+ 
+
+ align:start position:0%
+spanish founders in the 15th century
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+pushed the indians to the
+
+ align:start position:0%
+pushed the indians to the
+ 
+
+ align:start position:0%
+pushed the indians to the
+periphery and they settled the
+
+ align:start position:0%
+periphery and they settled the
+ 
+
+ align:start position:0%
+periphery and they settled the
+central valley of costa rica so you've
+
+ align:start position:0%
+central valley of costa rica so you've
+ 
+
+ align:start position:0%
+central valley of costa rica so you've
+got this
+
+ align:start position:0%
+got this
+ 
+
+ align:start position:0%
+got this
+200 founders
+
+ align:start position:0%
+200 founders
+ 
+
+ align:start position:0%
+200 founders
+in the 14th century very little
+
+ align:start position:0%
+in the 14th century very little
+ 
+
+ align:start position:0%
+in the 14th century very little
+intermarriage and perfect church records
+
+ align:start position:0%
+intermarriage and perfect church records
+ 
+
+ align:start position:0%
+intermarriage and perfect church records
+very large pedigrees it's one of the
+
+ align:start position:0%
+very large pedigrees it's one of the
+ 
+
+ align:start position:0%
+very large pedigrees it's one of the
+it's probably the closest next to the
+
+ align:start position:0%
+it's probably the closest next to the
+ 
+
+ align:start position:0%
+it's probably the closest next to the
+saginay lock science gen population in
+
+ align:start position:0%
+saginay lock science gen population in
+ 
+
+ align:start position:0%
+saginay lock science gen population in
+quebec
+
+ align:start position:0%
+quebec
+ 
+
+ align:start position:0%
+quebec
+genetic isolates uh in the western
+
+ align:start position:0%
+genetic isolates uh in the western
+ 
+
+ align:start position:0%
+genetic isolates uh in the western
+hemisphere and we're actually doing a
+
+ align:start position:0%
+hemisphere and we're actually doing a
+ 
+
+ align:start position:0%
+hemisphere and we're actually doing a
+big study there we actually have six big
+
+ align:start position:0%
+big study there we actually have six big
+ 
+
+ align:start position:0%
+big study there we actually have six big
+pedigrees with over 120 people in each
+
+ align:start position:0%
+pedigrees with over 120 people in each
+ 
+
+ align:start position:0%
+pedigrees with over 120 people in each
+pedigree
+
+ align:start position:0%
+pedigree
+ 
+
+ align:start position:0%
+pedigree
+we've just finished the collection of
+
+ align:start position:0%
+we've just finished the collection of
+ 
+
+ align:start position:0%
+we've just finished the collection of
+these pedigrees we're about to do a
+
+ align:start position:0%
+these pedigrees we're about to do a
+ 
+
+ align:start position:0%
+these pedigrees we're about to do a
+genome scan
+
+ align:start position:0%
+genome scan
+ 
+
+ align:start position:0%
+genome scan
+that tom is actually doing for us
+
+ align:start position:0%
+that tom is actually doing for us
+ 
+
+ align:start position:0%
+that tom is actually doing for us
+most of the
+
+ align:start position:0%
+most of the
+ 
+
+ align:start position:0%
+most of the
+people are isolated by geography that
+
+ align:start position:0%
+people are isolated by geography that
+ 
+
+ align:start position:0%
+people are isolated by geography that
+you've mentioned with the exception of
+
+ align:start position:0%
+you've mentioned with the exception of
+ 
+
+ align:start position:0%
+you've mentioned with the exception of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+nazis right so
+
+ align:start position:0%
+nazis right so
+ 
+
+ align:start position:0%
+nazis right so
+we can broaden
+
+ align:start position:0%
+we can broaden
+ 
+
+ align:start position:0%
+we can broaden
+uh your i guess the definition of
+
+ align:start position:0%
+uh your i guess the definition of
+ 
+
+ align:start position:0%
+uh your i guess the definition of
+genetic isolate to include things like
+
+ align:start position:0%
+genetic isolate to include things like
+ 
+
+ align:start position:0%
+genetic isolate to include things like
+economic like things that utilize it
+
+ align:start position:0%
+economic like things that utilize it
+ 
+
+ align:start position:0%
+economic like things that utilize it
+people like you know royal families back
+
+ align:start position:0%
+people like you know royal families back
+ 
+
+ align:start position:0%
+people like you know royal families back
+in the old days you know i only were
+
+ align:start position:0%
+in the old days you know i only were
+ 
+
+ align:start position:0%
+in the old days you know i only were
+married because of social status and yes
+
+ align:start position:0%
+married because of social status and yes
+ 
+
+ align:start position:0%
+married because of social status and yes
+but now there's things where you know
+
+ align:start position:0%
+but now there's things where you know
+ 
+
+ align:start position:0%
+but now there's things where you know
+people with certain economic status mail
+
+ align:start position:0%
+people with certain economic status mail
+ 
+
+ align:start position:0%
+people with certain economic status mail
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+and then they come in here can we
+
+ align:start position:0%
+and then they come in here can we
+ 
+
+ align:start position:0%
+and then they come in here can we
+see a certain set of people where
+
+ align:start position:0%
+see a certain set of people where
+ 
+
+ align:start position:0%
+see a certain set of people where
+they're married
+
+ align:start position:0%
+they're married
+ 
+
+ align:start position:0%
+they're married
+yeah it turns out i think that geography
+
+ align:start position:0%
+yeah it turns out i think that geography
+ 
+
+ align:start position:0%
+yeah it turns out i think that geography
+is actually a much better
+
+ align:start position:0%
+is actually a much better
+ 
+
+ align:start position:0%
+is actually a much better
+uh uh um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think i think that yeah i think if it
+
+ align:start position:0%
+i think i think that yeah i think if it
+ 
+
+ align:start position:0%
+i think i think that yeah i think if it
+was happening families or people have a
+
+ align:start position:0%
+was happening families or people have a
+ 
+
+ align:start position:0%
+was happening families or people have a
+chance to procreate by physical
+
+ align:start position:0%
+chance to procreate by physical
+ 
+
+ align:start position:0%
+chance to procreate by physical
+proximity they will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think the geography is a lot better
+
+ align:start position:0%
+i think the geography is a lot better
+ 
+
+ align:start position:0%
+i think the geography is a lot better
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+historically it's
+
+ align:start position:0%
+historically it's
+ 
+
+ align:start position:0%
+historically it's
+a much more reliable
+
+ align:start position:0%
+a much more reliable
+ 
+
+ align:start position:0%
+a much more reliable
+guide to a genetic isolate than any sort
+
+ align:start position:0%
+guide to a genetic isolate than any sort
+ 
+
+ align:start position:0%
+guide to a genetic isolate than any sort
+of social convention i think
+
+ align:start position:0%
+of social convention i think
+ 
+
+ align:start position:0%
+of social convention i think
+er er er exactly for the reasons that
+
+ align:start position:0%
+er er er exactly for the reasons that
+ 
+
+ align:start position:0%
+er er er exactly for the reasons that
+zach
+
+ align:start position:0%
+zach
+ 
+
+ align:start position:0%
+zach
+groups like
+
+ align:start position:0%
+groups like
+ 
+
+ align:start position:0%
+groups like
+jerusalem they're so strong social
+
+ align:start position:0%
+jerusalem they're so strong social
+ 
+
+ align:start position:0%
+jerusalem they're so strong social
+pressure yeah like then you know what
+
+ align:start position:0%
+pressure yeah like then you know what
+ 
+
+ align:start position:0%
+pressure yeah like then you know what
+that would they may be they may be the
+
+ align:start position:0%
+that would they may be they may be the
+ 
+
+ align:start position:0%
+that would they may be they may be the
+exception to the rule but i think you
+
+ align:start position:0%
+exception to the rule but i think you
+ 
+
+ align:start position:0%
+exception to the rule but i think you
+know populations like iceland costa rica
+
+ align:start position:0%
+know populations like iceland costa rica
+ 
+
+ align:start position:0%
+know populations like iceland costa rica
+um tristan de cunha finland
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amish would would
+
+ align:start position:0%
+amish would would
+ 
+
+ align:start position:0%
+amish would would
+fall into fall into that group the
+
+ align:start position:0%
+fall into fall into that group the
+ 
+
+ align:start position:0%
+fall into fall into that group the
+mormons
+
+ align:start position:0%
+mormons
+ 
+
+ align:start position:0%
+mormons
+maybe a little bit less so
+
+ align:start position:0%
+maybe a little bit less so
+ 
+
+ align:start position:0%
+maybe a little bit less so
+um the big advantage of the mormons is
+
+ align:start position:0%
+um the big advantage of the mormons is
+ 
+
+ align:start position:0%
+um the big advantage of the mormons is
+not so much that they're a relative
+
+ align:start position:0%
+not so much that they're a relative
+ 
+
+ align:start position:0%
+not so much that they're a relative
+genetic isolate but that they have very
+
+ align:start position:0%
+genetic isolate but that they have very
+ 
+
+ align:start position:0%
+genetic isolate but that they have very
+large families and they have very good
+
+ align:start position:0%
+large families and they have very good
+ 
+
+ align:start position:0%
+large families and they have very good
+church records so you know those are
+
+ align:start position:0%
+church records so you know those are
+ 
+
+ align:start position:0%
+church records so you know those are
+sort of other
+
+ align:start position:0%
+sort of other
+ 
+
+ align:start position:0%
+sort of other
+characteristics that sort of are helpful
+
+ align:start position:0%
+characteristics that sort of are helpful
+ 
+
+ align:start position:0%
+characteristics that sort of are helpful
+but the
+
+ align:start position:0%
+but the
+ 
+
+ align:start position:0%
+but the
+idea behind the genetic isolate is is
+
+ align:start position:0%
+idea behind the genetic isolate is is
+ 
+
+ align:start position:0%
+idea behind the genetic isolate is is
+that you've got a relatively
+
+ align:start position:0%
+that you've got a relatively
+ 
+
+ align:start position:0%
+that you've got a relatively
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+homogeneous
+
+ align:start position:0%
+homogeneous
+ 
+
+ align:start position:0%
+homogeneous
+set of alleles that circulating in the
+
+ align:start position:0%
+set of alleles that circulating in the
+ 
+
+ align:start position:0%
+set of alleles that circulating in the
+population mormons do
+
+ align:start position:0%
+population mormons do
+ 
+
+ align:start position:0%
+population mormons do
+intermarry and and so they're maybe
+
+ align:start position:0%
+intermarry and and so they're maybe
+ 
+
+ align:start position:0%
+intermarry and and so they're maybe
+i don't i don't know that you'd consider
+
+ align:start position:0%
+i don't i don't know that you'd consider
+ 
+
+ align:start position:0%
+i don't i don't know that you'd consider
+them really a genetic isolate whereas uh
+
+ align:start position:0%
+them really a genetic isolate whereas uh
+ 
+
+ align:start position:0%
+them really a genetic isolate whereas uh
+uh i think that uh the amish and the
+
+ align:start position:0%
+uh i think that uh the amish and the
+ 
+
+ align:start position:0%
+uh i think that uh the amish and the
+hutterites and the uh um ashkenazis are
+
+ align:start position:0%
+hutterites and the uh um ashkenazis are
+ 
+
+ align:start position:0%
+hutterites and the uh um ashkenazis are
+people where there is some set of
+
+ align:start position:0%
+people where there is some set of
+ 
+
+ align:start position:0%
+people where there is some set of
+co-social conventions that those people
+
+ align:start position:0%
+co-social conventions that those people
+ 
+
+ align:start position:0%
+co-social conventions that those people
+are much more likely to uh intermarry
+
+ align:start position:0%
+are much more likely to uh intermarry
+ 
+
+ align:start position:0%
+are much more likely to uh intermarry
+the reason i ask is because it seems
+
+ align:start position:0%
+the reason i ask is because it seems
+ 
+
+ align:start position:0%
+the reason i ask is because it seems
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that the trend might be uh
+
+ align:start position:0%
+that the trend might be uh
+ 
+
+ align:start position:0%
+that the trend might be uh
+you know especially nowadays with
+
+ align:start position:0%
+you know especially nowadays with
+ 
+
+ align:start position:0%
+you know especially nowadays with
+transportation leaders that finding
+
+ align:start position:0%
+transportation leaders that finding
+ 
+
+ align:start position:0%
+transportation leaders that finding
+geographic isolated population is going
+
+ align:start position:0%
+geographic isolated population is going
+ 
+
+ align:start position:0%
+geographic isolated population is going
+to decline
+
+ align:start position:0%
+to decline
+ 
+
+ align:start position:0%
+to decline
+right this isn't this isn't the only way
+
+ align:start position:0%
+right this isn't this isn't the only way
+ 
+
+ align:start position:0%
+right this isn't this isn't the only way
+to do this i mean uh um
+
+ align:start position:0%
+to do this i mean uh um
+ 
+
+ align:start position:0%
+to do this i mean uh um
+and i think it is important to sort of
+
+ align:start position:0%
+and i think it is important to sort of
+ 
+
+ align:start position:0%
+and i think it is important to sort of
+make the distinction between
+
+ align:start position:0%
+make the distinction between
+ 
+
+ align:start position:0%
+make the distinction between
+uh uh um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know linkage and fine mapping
+
+ align:start position:0%
+you know linkage and fine mapping
+ 
+
+ align:start position:0%
+you know linkage and fine mapping
+and uh um those two things may be
+
+ align:start position:0%
+and uh um those two things may be
+ 
+
+ align:start position:0%
+and uh um those two things may be
+somewhat different the the the
+
+ align:start position:0%
+somewhat different the the the
+ 
+
+ align:start position:0%
+somewhat different the the the
+advantages of an outbred population is
+
+ align:start position:0%
+advantages of an outbred population is
+ 
+
+ align:start position:0%
+advantages of an outbred population is
+is that the
+
+ align:start position:0%
+is that the
+ 
+
+ align:start position:0%
+is that the
+degree of linkage this equilibrium will
+
+ align:start position:0%
+degree of linkage this equilibrium will
+ 
+
+ align:start position:0%
+degree of linkage this equilibrium will
+be relatively narrow and some of these
+
+ align:start position:0%
+be relatively narrow and some of these
+ 
+
+ align:start position:0%
+be relatively narrow and some of these
+genetic isolated populations the degree
+
+ align:start position:0%
+genetic isolated populations the degree
+ 
+
+ align:start position:0%
+genetic isolated populations the degree
+of linkage to secretion can be very
+
+ align:start position:0%
+of linkage to secretion can be very
+ 
+
+ align:start position:0%
+of linkage to secretion can be very
+large that means you can get
+
+ align:start position:0%
+large that means you can get
+ 
+
+ align:start position:0%
+large that means you can get
+do the do the linkage part pretty
+
+ align:start position:0%
+do the do the linkage part pretty
+ 
+
+ align:start position:0%
+do the do the linkage part pretty
+effectively but the association part is
+
+ align:start position:0%
+effectively but the association part is
+ 
+
+ align:start position:0%
+effectively but the association part is
+more difficult because you've got these
+
+ align:start position:0%
+more difficult because you've got these
+ 
+
+ align:start position:0%
+more difficult because you've got these
+big ld blocks that you've got to uh
+
+ align:start position:0%
+big ld blocks that you've got to uh
+ 
+
+ align:start position:0%
+big ld blocks that you've got to uh
+work with and you may not be able to get
+
+ align:start position:0%
+work with and you may not be able to get
+ 
+
+ align:start position:0%
+work with and you may not be able to get
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+to the gene
+
+ align:start position:0%
+to the gene
+ 
+
+ align:start position:0%
+to the gene
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so anyway we'll go through the stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are sort of all of the steps that
+
+ align:start position:0%
+these are sort of all of the steps that
+ 
+
+ align:start position:0%
+these are sort of all of the steps that
+you would do in a typical study and
+
+ align:start position:0%
+you would do in a typical study and
+ 
+
+ align:start position:0%
+you would do in a typical study and
+we'll just go through each of these so
+
+ align:start position:0%
+we'll just go through each of these so
+ 
+
+ align:start position:0%
+we'll just go through each of these so
+i'm going to use asthma as my example
+
+ align:start position:0%
+i'm going to use asthma as my example
+ 
+
+ align:start position:0%
+i'm going to use asthma as my example
+because this is the disease i know the
+
+ align:start position:0%
+because this is the disease i know the
+ 
+
+ align:start position:0%
+because this is the disease i know the
+best and the point here is is that
+
+ align:start position:0%
+best and the point here is is that
+ 
+
+ align:start position:0%
+best and the point here is is that
+asthma prevalence in western developed
+
+ align:start position:0%
+asthma prevalence in western developed
+ 
+
+ align:start position:0%
+asthma prevalence in western developed
+countries has gone up a lot so do you
+
+ align:start position:0%
+countries has gone up a lot so do you
+ 
+
+ align:start position:0%
+countries has gone up a lot so do you
+think that this is a genetic thing or do
+
+ align:start position:0%
+think that this is a genetic thing or do
+ 
+
+ align:start position:0%
+think that this is a genetic thing or do
+you think it's
+
+ align:start position:0%
+you think it's
+ 
+
+ align:start position:0%
+you think it's
+something else
+
+ align:start position:0%
+something else
+ 
+
+ align:start position:0%
+something else
+so over the 20-year period sort of 82
+
+ align:start position:0%
+so over the 20-year period sort of 82
+ 
+
+ align:start position:0%
+so over the 20-year period sort of 82
+000 you've had more than a doubling in
+
+ align:start position:0%
+000 you've had more than a doubling in
+ 
+
+ align:start position:0%
+000 you've had more than a doubling in
+the number of cases so over a 20-year
+
+ align:start position:0%
+the number of cases so over a 20-year
+ 
+
+ align:start position:0%
+the number of cases so over a 20-year
+period doubling in the number of cases
+
+ align:start position:0%
+period doubling in the number of cases
+ 
+
+ align:start position:0%
+period doubling in the number of cases
+genetic or environment
+
+ align:start position:0%
+genetic or environment
+ 
+
+ align:start position:0%
+genetic or environment
+why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there are three potential what
+
+ align:start position:0%
+okay so there are three potential what
+ 
+
+ align:start position:0%
+okay so there are three potential what
+are the three population genetic
+
+ align:start position:0%
+are the three population genetic
+ 
+
+ align:start position:0%
+are the three population genetic
+mechanisms that
+
+ align:start position:0%
+mechanisms that
+ 
+
+ align:start position:0%
+mechanisms that
+uh something like this could could
+
+ align:start position:0%
+uh something like this could could
+ 
+
+ align:start position:0%
+uh something like this could could
+uh could occur uh a genetic explanation
+
+ align:start position:0%
+uh could occur uh a genetic explanation
+ 
+
+ align:start position:0%
+uh could occur uh a genetic explanation
+genetic explanation
+
+ align:start position:0%
+genetic explanation
+ 
+
+ align:start position:0%
+genetic explanation
+so you you you you you're i'll give you
+
+ align:start position:0%
+so you you you you you're i'll give you
+ 
+
+ align:start position:0%
+so you you you you you're i'll give you
+at least half credit
+
+ align:start position:0%
+at least half credit
+ 
+
+ align:start position:0%
+at least half credit
+but but you're definitely not 100 right
+
+ align:start position:0%
+but but you're definitely not 100 right
+ 
+
+ align:start position:0%
+but but you're definitely not 100 right
+um the first genetic mechanism would be
+
+ align:start position:0%
+um the first genetic mechanism would be
+ 
+
+ align:start position:0%
+um the first genetic mechanism would be
+spontaneous mutation right you had some
+
+ align:start position:0%
+spontaneous mutation right you had some
+ 
+
+ align:start position:0%
+spontaneous mutation right you had some
+spontaneous mutation and
+
+ align:start position:0%
+spontaneous mutation and
+ 
+
+ align:start position:0%
+spontaneous mutation and
+it caused this epidemic of diseases is
+
+ align:start position:0%
+it caused this epidemic of diseases is
+ 
+
+ align:start position:0%
+it caused this epidemic of diseases is
+that possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you already said no it's not possible
+
+ align:start position:0%
+you already said no it's not possible
+ 
+
+ align:start position:0%
+you already said no it's not possible
+and you're and you're right it's not but
+
+ align:start position:0%
+and you're and you're right it's not but
+ 
+
+ align:start position:0%
+and you're and you're right it's not but
+you have to know what the spontaneous
+
+ align:start position:0%
+you have to know what the spontaneous
+ 
+
+ align:start position:0%
+you have to know what the spontaneous
+mutation rate is which is about
+
+ align:start position:0%
+mutation rate is which is about
+ 
+
+ align:start position:0%
+mutation rate is which is about
+1 times 10 to the minus 8 base pairs per
+
+ align:start position:0%
+1 times 10 to the minus 8 base pairs per
+ 
+
+ align:start position:0%
+1 times 10 to the minus 8 base pairs per
+generation so it's pretty low
+
+ align:start position:0%
+generation so it's pretty low
+ 
+
+ align:start position:0%
+generation so it's pretty low
+you know we're spontaneously mutating
+
+ align:start position:0%
+you know we're spontaneously mutating
+ 
+
+ align:start position:0%
+you know we're spontaneously mutating
+all of the time but we're not
+
+ align:start position:0%
+all of the time but we're not
+ 
+
+ align:start position:0%
+all of the time but we're not
+spontaneously mutating fast enough
+
+ align:start position:0%
+spontaneously mutating fast enough
+ 
+
+ align:start position:0%
+spontaneously mutating fast enough
+to double the number of cases in a
+
+ align:start position:0%
+to double the number of cases in a
+ 
+
+ align:start position:0%
+to double the number of cases in a
+20-year period of time
+
+ align:start position:0%
+20-year period of time
+ 
+
+ align:start position:0%
+20-year period of time
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what's the second possible genetic
+
+ align:start position:0%
+what's the second possible genetic
+ 
+
+ align:start position:0%
+what's the second possible genetic
+mechanism
+
+ align:start position:0%
+mechanism
+ 
+
+ align:start position:0%
+mechanism
+natural selection right
+
+ align:start position:0%
+natural selection right
+ 
+
+ align:start position:0%
+natural selection right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+natural selection gonna do that
+
+ align:start position:0%
+natural selection gonna do that
+ 
+
+ align:start position:0%
+natural selection gonna do that
+well particularly with the disease like
+
+ align:start position:0%
+well particularly with the disease like
+ 
+
+ align:start position:0%
+well particularly with the disease like
+asthma where there's no selection
+
+ align:start position:0%
+asthma where there's no selection
+ 
+
+ align:start position:0%
+asthma where there's no selection
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+in no reproductive advantages or
+
+ align:start position:0%
+in no reproductive advantages or
+ 
+
+ align:start position:0%
+in no reproductive advantages or
+disadvantages right you all know plenty
+
+ align:start position:0%
+disadvantages right you all know plenty
+ 
+
+ align:start position:0%
+disadvantages right you all know plenty
+of people with asthma and they're able
+
+ align:start position:0%
+of people with asthma and they're able
+ 
+
+ align:start position:0%
+of people with asthma and they're able
+to reproduce just like everybody else so
+
+ align:start position:0%
+to reproduce just like everybody else so
+ 
+
+ align:start position:0%
+to reproduce just like everybody else so
+it couldn't be natural selection and
+
+ align:start position:0%
+it couldn't be natural selection and
+ 
+
+ align:start position:0%
+it couldn't be natural selection and
+what's the third population genetic
+
+ align:start position:0%
+what's the third population genetic
+ 
+
+ align:start position:0%
+what's the third population genetic
+mechanism that could uh
+
+ align:start position:0%
+mechanism that could uh
+ 
+
+ align:start position:0%
+mechanism that could uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the third one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genetic drift
+
+ align:start position:0%
+genetic drift
+ 
+
+ align:start position:0%
+genetic drift
+so you know you had some
+
+ align:start position:0%
+so you know you had some
+ 
+
+ align:start position:0%
+so you know you had some
+mutant asthmatic that came into the
+
+ align:start position:0%
+mutant asthmatic that came into the
+ 
+
+ align:start position:0%
+mutant asthmatic that came into the
+american population and over 20 years of
+
+ align:start position:0%
+american population and over 20 years of
+ 
+
+ align:start position:0%
+american population and over 20 years of
+time they
+
+ align:start position:0%
+time they
+ 
+
+ align:start position:0%
+time they
+intermarried with all these other people
+
+ align:start position:0%
+intermarried with all these other people
+ 
+
+ align:start position:0%
+intermarried with all these other people
+and doubled the asthma ring plausible or
+
+ align:start position:0%
+and doubled the asthma ring plausible or
+ 
+
+ align:start position:0%
+and doubled the asthma ring plausible or
+implausible
+
+ align:start position:0%
+implausible
+ 
+
+ align:start position:0%
+implausible
+no can't happen okay so you're right it
+
+ align:start position:0%
+no can't happen okay so you're right it
+ 
+
+ align:start position:0%
+no can't happen okay so you're right it
+can't be genetic
+
+ align:start position:0%
+can't be genetic
+ 
+
+ align:start position:0%
+can't be genetic
+so i i could give you i'd give you half
+
+ align:start position:0%
+so i i could give you i'd give you half
+ 
+
+ align:start position:0%
+so i i could give you i'd give you half
+credit but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+i mean this is most geneticists don't
+
+ align:start position:0%
+i mean this is most geneticists don't
+ 
+
+ align:start position:0%
+i mean this is most geneticists don't
+think like this but they should think
+
+ align:start position:0%
+think like this but they should think
+ 
+
+ align:start position:0%
+think like this but they should think
+like this the reality is is that all of
+
+ align:start position:0%
+like this the reality is is that all of
+ 
+
+ align:start position:0%
+like this the reality is is that all of
+these genes
+
+ align:start position:0%
+these genes
+ 
+
+ align:start position:0%
+these genes
+operate in a developmental and an
+
+ align:start position:0%
+operate in a developmental and an
+ 
+
+ align:start position:0%
+operate in a developmental and an
+environmental context all of your genes
+
+ align:start position:0%
+environmental context all of your genes
+ 
+
+ align:start position:0%
+environmental context all of your genes
+do so the true underlying model for
+
+ align:start position:0%
+do so the true underlying model for
+ 
+
+ align:start position:0%
+do so the true underlying model for
+disease causation is gene by environment
+
+ align:start position:0%
+disease causation is gene by environment
+ 
+
+ align:start position:0%
+disease causation is gene by environment
+interaction so it could very well be
+
+ align:start position:0%
+interaction so it could very well be
+ 
+
+ align:start position:0%
+interaction so it could very well be
+that there was some
+
+ align:start position:0%
+that there was some
+ 
+
+ align:start position:0%
+that there was some
+dramatic change in the environment and
+
+ align:start position:0%
+dramatic change in the environment and
+ 
+
+ align:start position:0%
+dramatic change in the environment and
+now that's interacting with some other
+
+ align:start position:0%
+now that's interacting with some other
+ 
+
+ align:start position:0%
+now that's interacting with some other
+genes that it wasn't they weren't
+
+ align:start position:0%
+genes that it wasn't they weren't
+ 
+
+ align:start position:0%
+genes that it wasn't they weren't
+interacting before with and now you've
+
+ align:start position:0%
+interacting before with and now you've
+ 
+
+ align:start position:0%
+interacting before with and now you've
+got this marked explosion in a number of
+
+ align:start position:0%
+got this marked explosion in a number of
+ 
+
+ align:start position:0%
+got this marked explosion in a number of
+cases and that's almost
+
+ align:start position:0%
+cases and that's almost
+ 
+
+ align:start position:0%
+cases and that's almost
+certainly is the most
+
+ align:start position:0%
+certainly is the most
+ 
+
+ align:start position:0%
+certainly is the most
+comprehensive
+
+ align:start position:0%
+comprehensive
+ 
+
+ align:start position:0%
+comprehensive
+explanation but it would have to devolve
+
+ align:start position:0%
+explanation but it would have to devolve
+ 
+
+ align:start position:0%
+explanation but it would have to devolve
+from some sort of environmental change
+
+ align:start position:0%
+from some sort of environmental change
+ 
+
+ align:start position:0%
+from some sort of environmental change
+rather than some sort of primary change
+
+ align:start position:0%
+rather than some sort of primary change
+ 
+
+ align:start position:0%
+rather than some sort of primary change
+in in the genes but it could easily be
+
+ align:start position:0%
+in in the genes but it could easily be
+ 
+
+ align:start position:0%
+in in the genes but it could easily be
+that there is interaction between
+
+ align:start position:0%
+that there is interaction between
+ 
+
+ align:start position:0%
+that there is interaction between
+whatever the environmental exposure is
+
+ align:start position:0%
+whatever the environmental exposure is
+ 
+
+ align:start position:0%
+whatever the environmental exposure is
+and uh some of the underlying
+
+ align:start position:0%
+and uh some of the underlying
+ 
+
+ align:start position:0%
+and uh some of the underlying
+polymorphisms that may be disease
+
+ align:start position:0%
+polymorphisms that may be disease
+ 
+
+ align:start position:0%
+polymorphisms that may be disease
+related that are different now than they
+
+ align:start position:0%
+related that are different now than they
+ 
+
+ align:start position:0%
+related that are different now than they
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+back here when the
+
+ align:start position:0%
+back here when the
+ 
+
+ align:start position:0%
+back here when the
+disease rate was a lot lower
+
+ align:start position:0%
+disease rate was a lot lower
+ 
+
+ align:start position:0%
+disease rate was a lot lower
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so big health problem i don't want to
+
+ align:start position:0%
+so big health problem i don't want to
+ 
+
+ align:start position:0%
+so big health problem i don't want to
+dwell on this but the uh uh because
+
+ align:start position:0%
+dwell on this but the uh uh because
+ 
+
+ align:start position:0%
+dwell on this but the uh uh because
+that's not the purpose of this course
+
+ align:start position:0%
+that's not the purpose of this course
+ 
+
+ align:start position:0%
+that's not the purpose of this course
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+uh um
+
+ align:start position:0%
+uh um
+ 
+
+ align:start position:0%
+uh um
+all this means is that people will give
+
+ align:start position:0%
+all this means is that people will give
+ 
+
+ align:start position:0%
+all this means is that people will give
+you money to study this and they you
+
+ align:start position:0%
+you money to study this and they you
+ 
+
+ align:start position:0%
+you money to study this and they you
+know they weren't so keen on doing that
+
+ align:start position:0%
+know they weren't so keen on doing that
+ 
+
+ align:start position:0%
+know they weren't so keen on doing that
+um 20 or 30 years ago
+
+ align:start position:0%
+um 20 or 30 years ago
+ 
+
+ align:start position:0%
+um 20 or 30 years ago
+the other important point is this
+
+ align:start position:0%
+the other important point is this
+ 
+
+ align:start position:0%
+the other important point is this
+disease is a disease of children
+
+ align:start position:0%
+disease is a disease of children
+ 
+
+ align:start position:0%
+disease is a disease of children
+so you're going to think about it i
+
+ align:start position:0%
+so you're going to think about it i
+ 
+
+ align:start position:0%
+so you're going to think about it i
+usually tell people 90 this is data
+
+ align:start position:0%
+usually tell people 90 this is data
+ 
+
+ align:start position:0%
+usually tell people 90 this is data
+looking at the age of onset in a closed
+
+ align:start position:0%
+looking at the age of onset in a closed
+ 
+
+ align:start position:0%
+looking at the age of onset in a closed
+population in olmsted county what's the
+
+ align:start position:0%
+population in olmsted county what's the
+ 
+
+ align:start position:0%
+population in olmsted county what's the
+famous
+
+ align:start position:0%
+famous
+ 
+
+ align:start position:0%
+famous
+medical center in olmsted county
+
+ align:start position:0%
+medical center in olmsted county
+ 
+
+ align:start position:0%
+medical center in olmsted county
+minnesota
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you weren't supposed to answer that
+
+ align:start position:0%
+you weren't supposed to answer that
+ 
+
+ align:start position:0%
+you weren't supposed to answer that
+there was the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mayo clinic mayo clinic so mayo clinic
+
+ align:start position:0%
+mayo clinic mayo clinic so mayo clinic
+ 
+
+ align:start position:0%
+mayo clinic mayo clinic so mayo clinic
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+everybody in olmsted county
+
+ align:start position:0%
+everybody in olmsted county
+ 
+
+ align:start position:0%
+everybody in olmsted county
+goes to the mayo clinic now
+
+ align:start position:0%
+goes to the mayo clinic now
+ 
+
+ align:start position:0%
+goes to the mayo clinic now
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+saudi princes and cheeks and
+
+ align:start position:0%
+saudi princes and cheeks and
+ 
+
+ align:start position:0%
+saudi princes and cheeks and
+famous people from all over the world
+
+ align:start position:0%
+famous people from all over the world
+ 
+
+ align:start position:0%
+famous people from all over the world
+and the uh um
+
+ align:start position:0%
+and the uh um
+ 
+
+ align:start position:0%
+and the uh um
+uh um
+
+ align:start position:0%
+uh um
+ 
+
+ align:start position:0%
+uh um
+who was the king of jordan king
+
+ align:start position:0%
+who was the king of jordan king
+ 
+
+ align:start position:0%
+who was the king of jordan king
+saying he you know he went there first
+
+ align:start position:0%
+saying he you know he went there first
+ 
+
+ align:start position:0%
+saying he you know he went there first
+he went there for his uh
+
+ align:start position:0%
+he went there for his uh
+ 
+
+ align:start position:0%
+he went there for his uh
+yeah so zach's mother another famous
+
+ align:start position:0%
+yeah so zach's mother another famous
+ 
+
+ align:start position:0%
+yeah so zach's mother another famous
+person went to the mayo clinic so they
+
+ align:start position:0%
+person went to the mayo clinic so they
+ 
+
+ align:start position:0%
+person went to the mayo clinic so they
+get a lot of people from outside but
+
+ align:start position:0%
+get a lot of people from outside but
+ 
+
+ align:start position:0%
+get a lot of people from outside but
+this data is based on the people who
+
+ align:start position:0%
+this data is based on the people who
+ 
+
+ align:start position:0%
+this data is based on the people who
+live in olmsted county now if you live
+
+ align:start position:0%
+live in olmsted county now if you live
+ 
+
+ align:start position:0%
+live in olmsted county now if you live
+in olmsted county you don't go anywhere
+
+ align:start position:0%
+in olmsted county you don't go anywhere
+ 
+
+ align:start position:0%
+in olmsted county you don't go anywhere
+okay you just sit right there and you
+
+ align:start position:0%
+okay you just sit right there and you
+ 
+
+ align:start position:0%
+okay you just sit right there and you
+stay there so
+
+ align:start position:0%
+stay there so
+ 
+
+ align:start position:0%
+stay there so
+this was a fairly stable population and
+
+ align:start position:0%
+this was a fairly stable population and
+ 
+
+ align:start position:0%
+this was a fairly stable population and
+they were able to capture all of the
+
+ align:start position:0%
+they were able to capture all of the
+ 
+
+ align:start position:0%
+they were able to capture all of the
+incident asthma cases and document them
+
+ align:start position:0%
+incident asthma cases and document them
+ 
+
+ align:start position:0%
+incident asthma cases and document them
+because they were all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going to the mayo medical center and
+
+ align:start position:0%
+going to the mayo medical center and
+ 
+
+ align:start position:0%
+going to the mayo medical center and
+they had their chart records so 90 of
+
+ align:start position:0%
+they had their chart records so 90 of
+ 
+
+ align:start position:0%
+they had their chart records so 90 of
+all of the people who were diagnosed in
+
+ align:start position:0%
+all of the people who were diagnosed in
+ 
+
+ align:start position:0%
+all of the people who were diagnosed in
+as asthmatic in olmsted county were
+
+ align:start position:0%
+as asthmatic in olmsted county were
+ 
+
+ align:start position:0%
+as asthmatic in olmsted county were
+diagnosed before the age of six
+
+ align:start position:0%
+diagnosed before the age of six
+ 
+
+ align:start position:0%
+diagnosed before the age of six
+so this is a very very important point
+
+ align:start position:0%
+so this is a very very important point
+ 
+
+ align:start position:0%
+so this is a very very important point
+so this is the
+
+ align:start position:0%
+so this is the
+ 
+
+ align:start position:0%
+so this is the
+opposite of alzheimer's disease right
+
+ align:start position:0%
+opposite of alzheimer's disease right
+ 
+
+ align:start position:0%
+opposite of alzheimer's disease right
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+if you think about genetics this is
+
+ align:start position:0%
+if you think about genetics this is
+ 
+
+ align:start position:0%
+if you think about genetics this is
+great for geneticists because i only
+
+ align:start position:0%
+great for geneticists because i only
+ 
+
+ align:start position:0%
+great for geneticists because i only
+have to wait
+
+ align:start position:0%
+have to wait
+ 
+
+ align:start position:0%
+have to wait
+six years from the time that the kid is
+
+ align:start position:0%
+six years from the time that the kid is
+ 
+
+ align:start position:0%
+six years from the time that the kid is
+born and i'm going to know whether
+
+ align:start position:0%
+born and i'm going to know whether
+ 
+
+ align:start position:0%
+born and i'm going to know whether
+they've got the disease phenotype or not
+
+ align:start position:0%
+they've got the disease phenotype or not
+ 
+
+ align:start position:0%
+they've got the disease phenotype or not
+if i was waiting for alzheimer's cases
+
+ align:start position:0%
+if i was waiting for alzheimer's cases
+ 
+
+ align:start position:0%
+if i was waiting for alzheimer's cases
+it would be
+
+ align:start position:0%
+it would be
+ 
+
+ align:start position:0%
+it would be
+waiting for godot i'd be waiting a long
+
+ align:start position:0%
+waiting for godot i'd be waiting a long
+ 
+
+ align:start position:0%
+waiting for godot i'd be waiting a long
+time before
+
+ align:start position:0%
+time before
+ 
+
+ align:start position:0%
+time before
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i'd get my cases now there's ways around
+
+ align:start position:0%
+i'd get my cases now there's ways around
+ 
+
+ align:start position:0%
+i'd get my cases now there's ways around
+that for the old people right and what
+
+ align:start position:0%
+that for the old people right and what
+ 
+
+ align:start position:0%
+that for the old people right and what
+did geneticists do how did they find the
+
+ align:start position:0%
+did geneticists do how did they find the
+ 
+
+ align:start position:0%
+did geneticists do how did they find the
+bronco one gene what did what did they
+
+ align:start position:0%
+bronco one gene what did what did they
+ 
+
+ align:start position:0%
+bronco one gene what did what did they
+do to to enhance the the probability
+
+ align:start position:0%
+do to to enhance the the probability
+ 
+
+ align:start position:0%
+do to to enhance the the probability
+that you would find if you're looking at
+
+ align:start position:0%
+that you would find if you're looking at
+ 
+
+ align:start position:0%
+that you would find if you're looking at
+people older older people
+
+ align:start position:0%
+people older older people
+ 
+
+ align:start position:0%
+people older older people
+how do you
+
+ align:start position:0%
+how do you
+ 
+
+ align:start position:0%
+how do you
+enrich for a genetic cause of a disease
+
+ align:start position:0%
+enrich for a genetic cause of a disease
+ 
+
+ align:start position:0%
+enrich for a genetic cause of a disease
+what do you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+education doesn't have anything to do
+
+ align:start position:0%
+education doesn't have anything to do
+ 
+
+ align:start position:0%
+education doesn't have anything to do
+with i'm afraid
+
+ align:start position:0%
+with i'm afraid
+ 
+
+ align:start position:0%
+with i'm afraid
+no you just what characteristic of the
+
+ align:start position:0%
+no you just what characteristic of the
+ 
+
+ align:start position:0%
+no you just what characteristic of the
+cases would make you think it's more
+
+ align:start position:0%
+cases would make you think it's more
+ 
+
+ align:start position:0%
+cases would make you think it's more
+likely to be genetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what family history
+
+ align:start position:0%
+what family history
+ 
+
+ align:start position:0%
+what family history
+family family history but what
+
+ align:start position:0%
+family family history but what
+ 
+
+ align:start position:0%
+family family history but what
+specifically a
+
+ align:start position:0%
+specifically a
+ 
+
+ align:start position:0%
+specifically a
+family history age of onset right you're
+
+ align:start position:0%
+family history age of onset right you're
+ 
+
+ align:start position:0%
+family history age of onset right you're
+looking for genetic causes of heart
+
+ align:start position:0%
+looking for genetic causes of heart
+ 
+
+ align:start position:0%
+looking for genetic causes of heart
+attacks you're going to take the people
+
+ align:start position:0%
+attacks you're going to take the people
+ 
+
+ align:start position:0%
+attacks you're going to take the people
+that have heart attacks when they're
+
+ align:start position:0%
+that have heart attacks when they're
+ 
+
+ align:start position:0%
+that have heart attacks when they're
+aged 50. so ed silverman who's the world
+
+ align:start position:0%
+aged 50. so ed silverman who's the world
+ 
+
+ align:start position:0%
+aged 50. so ed silverman who's the world
+leader in copd genetics in my laboratory
+
+ align:start position:0%
+leader in copd genetics in my laboratory
+ 
+
+ align:start position:0%
+leader in copd genetics in my laboratory
+is looking for early onset copd cases so
+
+ align:start position:0%
+is looking for early onset copd cases so
+ 
+
+ align:start position:0%
+is looking for early onset copd cases so
+he gets cases where the age of onset is
+
+ align:start position:0%
+he gets cases where the age of onset is
+ 
+
+ align:start position:0%
+he gets cases where the age of onset is
+younger than the age of 52.
+
+ align:start position:0%
+younger than the age of 52.
+ 
+
+ align:start position:0%
+younger than the age of 52.
+so that's young
+
+ align:start position:0%
+so that's young
+ 
+
+ align:start position:0%
+so that's young
+so if you're looking at alzheimer's
+
+ align:start position:0%
+so if you're looking at alzheimer's
+ 
+
+ align:start position:0%
+so if you're looking at alzheimer's
+cases you'd say well we want all of the
+
+ align:start position:0%
+cases you'd say well we want all of the
+ 
+
+ align:start position:0%
+cases you'd say well we want all of the
+cases of alzheimer's people before the
+
+ align:start position:0%
+cases of alzheimer's people before the
+ 
+
+ align:start position:0%
+cases of alzheimer's people before the
+age of 60. this is how mary claire king
+
+ align:start position:0%
+age of 60. this is how mary claire king
+ 
+
+ align:start position:0%
+age of 60. this is how mary claire king
+found barack one she looked at all of
+
+ align:start position:0%
+found barack one she looked at all of
+ 
+
+ align:start position:0%
+found barack one she looked at all of
+the early onset breast cancer cases
+
+ align:start position:0%
+the early onset breast cancer cases
+ 
+
+ align:start position:0%
+the early onset breast cancer cases
+people who got breast cancer in their
+
+ align:start position:0%
+people who got breast cancer in their
+ 
+
+ align:start position:0%
+people who got breast cancer in their
+20s their 30s their 40s
+
+ align:start position:0%
+20s their 30s their 40s
+ 
+
+ align:start position:0%
+20s their 30s their 40s
+instead of looking at older
+
+ align:start position:0%
+instead of looking at older
+ 
+
+ align:start position:0%
+instead of looking at older
+postmenopausal women which is almost
+
+ align:start position:0%
+postmenopausal women which is almost
+ 
+
+ align:start position:0%
+postmenopausal women which is almost
+certainly another disease okay so if
+
+ align:start position:0%
+certainly another disease okay so if
+ 
+
+ align:start position:0%
+certainly another disease okay so if
+you're looking at old people one of the
+
+ align:start position:0%
+you're looking at old people one of the
+ 
+
+ align:start position:0%
+you're looking at old people one of the
+clever ways that geneticists enrich for
+
+ align:start position:0%
+clever ways that geneticists enrich for
+ 
+
+ align:start position:0%
+clever ways that geneticists enrich for
+uh uh um genetic susceptibility is by
+
+ align:start position:0%
+uh uh um genetic susceptibility is by
+ 
+
+ align:start position:0%
+uh uh um genetic susceptibility is by
+looking at early age of onset
+
+ align:start position:0%
+looking at early age of onset
+ 
+
+ align:start position:0%
+looking at early age of onset
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+of selecting potentially
+
+ align:start position:0%
+of selecting potentially
+ 
+
+ align:start position:0%
+of selecting potentially
+a special case of a particular disease
+
+ align:start position:0%
+a special case of a particular disease
+ 
+
+ align:start position:0%
+a special case of a particular disease
+absolutely right it's it's it's a little
+
+ align:start position:0%
+absolutely right it's it's it's a little
+ 
+
+ align:start position:0%
+absolutely right it's it's it's a little
+bit like in some perverse kind of way
+
+ align:start position:0%
+bit like in some perverse kind of way
+ 
+
+ align:start position:0%
+bit like in some perverse kind of way
+it's a little bit like the genetic
+
+ align:start position:0%
+it's a little bit like the genetic
+ 
+
+ align:start position:0%
+it's a little bit like the genetic
+isolate you might find a gene that is
+
+ align:start position:0%
+isolate you might find a gene that is
+ 
+
+ align:start position:0%
+isolate you might find a gene that is
+specific for
+
+ align:start position:0%
+specific for
+ 
+
+ align:start position:0%
+specific for
+that particular type
+
+ align:start position:0%
+that particular type
+ 
+
+ align:start position:0%
+that particular type
+of early onset disease so you find a
+
+ align:start position:0%
+of early onset disease so you find a
+ 
+
+ align:start position:0%
+of early onset disease so you find a
+gene for early onset alzheimer's but not
+
+ align:start position:0%
+gene for early onset alzheimer's but not
+ 
+
+ align:start position:0%
+gene for early onset alzheimer's but not
+for garden variety
+
+ align:start position:0%
+for garden variety
+ 
+
+ align:start position:0%
+for garden variety
+old age alzheimer's that occurs in
+
+ align:start position:0%
+old age alzheimer's that occurs in
+ 
+
+ align:start position:0%
+old age alzheimer's that occurs in
+uh um
+
+ align:start position:0%
+uh um
+ 
+
+ align:start position:0%
+uh um
+virtually everybody by the time they're
+
+ align:start position:0%
+virtually everybody by the time they're
+ 
+
+ align:start position:0%
+virtually everybody by the time they're
+90.
+
+ align:start position:0%
+90.
+ 
+
+ align:start position:0%
+90.
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+you you're you're right but it's a it's
+
+ align:start position:0%
+you you're you're right but it's a it's
+ 
+
+ align:start position:0%
+you you're you're right but it's a it's
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+uh you know we're still
+
+ align:start position:0%
+uh you know we're still
+ 
+
+ align:start position:0%
+uh you know we're still
+and i think what geneticists would say
+
+ align:start position:0%
+and i think what geneticists would say
+ 
+
+ align:start position:0%
+and i think what geneticists would say
+the early stages of this and because
+
+ align:start position:0%
+the early stages of this and because
+ 
+
+ align:start position:0%
+the early stages of this and because
+we're still in the early stages most of
+
+ align:start position:0%
+we're still in the early stages most of
+ 
+
+ align:start position:0%
+we're still in the early stages most of
+us would be happy if we found any gene
+
+ align:start position:0%
+us would be happy if we found any gene
+ 
+
+ align:start position:0%
+us would be happy if we found any gene
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you know you're going to be in science
+
+ align:start position:0%
+you know you're going to be in science
+ 
+
+ align:start position:0%
+you know you're going to be in science
+if you find that early onset gene and
+
+ align:start position:0%
+if you find that early onset gene and
+ 
+
+ align:start position:0%
+if you find that early onset gene and
+nobody's going to be criticizing you
+
+ align:start position:0%
+nobody's going to be criticizing you
+ 
+
+ align:start position:0%
+nobody's going to be criticizing you
+because it's not the gene for all
+
+ align:start position:0%
+because it's not the gene for all
+ 
+
+ align:start position:0%
+because it's not the gene for all
+uh breast cancer or all alzheimer's
+
+ align:start position:0%
+uh breast cancer or all alzheimer's
+ 
+
+ align:start position:0%
+uh breast cancer or all alzheimer's
+we'll get another example hanging fruit
+
+ align:start position:0%
+we'll get another example hanging fruit
+ 
+
+ align:start position:0%
+we'll get another example hanging fruit
+exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a little bit more about the disease
+
+ align:start position:0%
+so a little bit more about the disease
+ 
+
+ align:start position:0%
+so a little bit more about the disease
+most of the kids are allergic
+
+ align:start position:0%
+most of the kids are allergic
+ 
+
+ align:start position:0%
+most of the kids are allergic
+allergy is probably the big reason why
+
+ align:start position:0%
+allergy is probably the big reason why
+ 
+
+ align:start position:0%
+allergy is probably the big reason why
+the asthma epidemic occurred
+
+ align:start position:0%
+the asthma epidemic occurred
+ 
+
+ align:start position:0%
+the asthma epidemic occurred
+and that means that um
+
+ align:start position:0%
+and that means that um
+ 
+
+ align:start position:0%
+and that means that um
+you know there's
+
+ align:start position:0%
+you know there's
+ 
+
+ align:start position:0%
+you know there's
+they have this particular type of an
+
+ align:start position:0%
+they have this particular type of an
+ 
+
+ align:start position:0%
+they have this particular type of an
+inflammatory process where antigen
+
+ align:start position:0%
+inflammatory process where antigen
+ 
+
+ align:start position:0%
+inflammatory process where antigen
+presented to dendritic cells in the
+
+ align:start position:0%
+presented to dendritic cells in the
+ 
+
+ align:start position:0%
+presented to dendritic cells in the
+airways activate these uh cd4 positive t
+
+ align:start position:0%
+airways activate these uh cd4 positive t
+ 
+
+ align:start position:0%
+airways activate these uh cd4 positive t
+lymphocytes which then elaborate this
+
+ align:start position:0%
+lymphocytes which then elaborate this
+ 
+
+ align:start position:0%
+lymphocytes which then elaborate this
+series of inflammatory cytokines which
+
+ align:start position:0%
+series of inflammatory cytokines which
+ 
+
+ align:start position:0%
+series of inflammatory cytokines which
+go to these inflammatory cells which
+
+ align:start position:0%
+go to these inflammatory cells which
+ 
+
+ align:start position:0%
+go to these inflammatory cells which
+then infiltrate the airways and set up
+
+ align:start position:0%
+then infiltrate the airways and set up
+ 
+
+ align:start position:0%
+then infiltrate the airways and set up
+an inflammatory reaction with
+
+ align:start position:0%
+an inflammatory reaction with
+ 
+
+ align:start position:0%
+an inflammatory reaction with
+coughing wheezing airways responsiveness
+
+ align:start position:0%
+coughing wheezing airways responsiveness
+ 
+
+ align:start position:0%
+coughing wheezing airways responsiveness
+etc etc etc
+
+ align:start position:0%
+etc etc etc
+ 
+
+ align:start position:0%
+etc etc etc
+this is all well known but it does sort
+
+ align:start position:0%
+this is all well known but it does sort
+ 
+
+ align:start position:0%
+this is all well known but it does sort
+of suggest a whole host of other
+
+ align:start position:0%
+of suggest a whole host of other
+ 
+
+ align:start position:0%
+of suggest a whole host of other
+potential phenotypes that you could
+
+ align:start position:0%
+potential phenotypes that you could
+ 
+
+ align:start position:0%
+potential phenotypes that you could
+potentially look at
+
+ align:start position:0%
+potentially look at
+ 
+
+ align:start position:0%
+potentially look at
+and it also gets at this concept of
+
+ align:start position:0%
+and it also gets at this concept of
+ 
+
+ align:start position:0%
+and it also gets at this concept of
+ontogeny of the immune system where
+
+ align:start position:0%
+ontogeny of the immune system where
+ 
+
+ align:start position:0%
+ontogeny of the immune system where
+you know uh t null cells
+
+ align:start position:0%
+you know uh t null cells
+ 
+
+ align:start position:0%
+you know uh t null cells
+at some point differentiate into these
+
+ align:start position:0%
+at some point differentiate into these
+ 
+
+ align:start position:0%
+at some point differentiate into these
+th1 and th2 cells which are determined
+
+ align:start position:0%
+th1 and th2 cells which are determined
+ 
+
+ align:start position:0%
+th1 and th2 cells which are determined
+their phenotype is determined by which
+
+ align:start position:0%
+their phenotype is determined by which
+ 
+
+ align:start position:0%
+their phenotype is determined by which
+cytokines they actually elaborate and
+
+ align:start position:0%
+cytokines they actually elaborate and
+ 
+
+ align:start position:0%
+cytokines they actually elaborate and
+i've got a question mark here but
+
+ align:start position:0%
+i've got a question mark here but
+ 
+
+ align:start position:0%
+i've got a question mark here but
+actually this particular step which is
+
+ align:start position:0%
+actually this particular step which is
+ 
+
+ align:start position:0%
+actually this particular step which is
+sort of the
+
+ align:start position:0%
+sort of the
+ 
+
+ align:start position:0%
+sort of the
+crosstalk and interaction between these
+
+ align:start position:0%
+crosstalk and interaction between these
+ 
+
+ align:start position:0%
+crosstalk and interaction between these
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+types of cells are controlled by two
+
+ align:start position:0%
+types of cells are controlled by two
+ 
+
+ align:start position:0%
+types of cells are controlled by two
+specific uh uh
+
+ align:start position:0%
+specific uh uh
+ 
+
+ align:start position:0%
+specific uh uh
+genes that elaborate cytokines il-10 and
+
+ align:start position:0%
+genes that elaborate cytokines il-10 and
+ 
+
+ align:start position:0%
+genes that elaborate cytokines il-10 and
+tgf beta and
+
+ align:start position:0%
+tgf beta and
+ 
+
+ align:start position:0%
+tgf beta and
+we've genotyped both of those genes
+
+ align:start position:0%
+we've genotyped both of those genes
+ 
+
+ align:start position:0%
+we've genotyped both of those genes
+in in asthma and copd and
+
+ align:start position:0%
+in in asthma and copd and
+ 
+
+ align:start position:0%
+in in asthma and copd and
+they're they're important in both
+
+ align:start position:0%
+they're they're important in both
+ 
+
+ align:start position:0%
+they're they're important in both
+diseases um now it's important for you
+
+ align:start position:0%
+diseases um now it's important for you
+ 
+
+ align:start position:0%
+diseases um now it's important for you
+to understand that i sort of skewed
+
+ align:start position:0%
+to understand that i sort of skewed
+ 
+
+ align:start position:0%
+to understand that i sort of skewed
+things a little bit because i told you
+
+ align:start position:0%
+things a little bit because i told you
+ 
+
+ align:start position:0%
+things a little bit because i told you
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+asthma is a th2 disease and teach two
+
+ align:start position:0%
+asthma is a th2 disease and teach two
+ 
+
+ align:start position:0%
+asthma is a th2 disease and teach two
+diseases have
+
+ align:start position:0%
+diseases have
+ 
+
+ align:start position:0%
+diseases have
+increased you know there's this increase
+
+ align:start position:0%
+increased you know there's this increase
+ 
+
+ align:start position:0%
+increased you know there's this increase
+in allergic rhinitis food allergy asthma
+
+ align:start position:0%
+in allergic rhinitis food allergy asthma
+ 
+
+ align:start position:0%
+in allergic rhinitis food allergy asthma
+etc etc this novel gene that i was
+
+ align:start position:0%
+etc etc this novel gene that i was
+ 
+
+ align:start position:0%
+etc etc this novel gene that i was
+telling you about just a few minutes ago
+
+ align:start position:0%
+telling you about just a few minutes ago
+ 
+
+ align:start position:0%
+telling you about just a few minutes ago
+it's going to come out in science on
+
+ align:start position:0%
+it's going to come out in science on
+ 
+
+ align:start position:0%
+it's going to come out in science on
+friday that gene is expressed in the
+
+ align:start position:0%
+friday that gene is expressed in the
+ 
+
+ align:start position:0%
+friday that gene is expressed in the
+skin and in
+
+ align:start position:0%
+skin and in
+ 
+
+ align:start position:0%
+skin and in
+gut epithelium and in airway epithelium
+
+ align:start position:0%
+gut epithelium and in airway epithelium
+ 
+
+ align:start position:0%
+gut epithelium and in airway epithelium
+suggesting that
+
+ align:start position:0%
+suggesting that
+ 
+
+ align:start position:0%
+suggesting that
+may be important in all these different
+
+ align:start position:0%
+may be important in all these different
+ 
+
+ align:start position:0%
+may be important in all these different
+types of allergic diseases which again
+
+ align:start position:0%
+types of allergic diseases which again
+ 
+
+ align:start position:0%
+types of allergic diseases which again
+has heightened people's interest in the
+
+ align:start position:0%
+has heightened people's interest in the
+ 
+
+ align:start position:0%
+has heightened people's interest in the
+gene
+
+ align:start position:0%
+gene
+ 
+
+ align:start position:0%
+gene
+and its potential uh um
+
+ align:start position:0%
+and its potential uh um
+ 
+
+ align:start position:0%
+and its potential uh um
+importance
+
+ align:start position:0%
+importance
+ 
+
+ align:start position:0%
+importance
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+it's also important to recognize that
+
+ align:start position:0%
+it's also important to recognize that
+ 
+
+ align:start position:0%
+it's also important to recognize that
+th1 diseases have also increased so give
+
+ align:start position:0%
+th1 diseases have also increased so give
+ 
+
+ align:start position:0%
+th1 diseases have also increased so give
+me some example of some th1 diseases
+
+ align:start position:0%
+me some example of some th1 diseases
+ 
+
+ align:start position:0%
+me some example of some th1 diseases
+so the epidemiology and the reason i'm
+
+ align:start position:0%
+so the epidemiology and the reason i'm
+ 
+
+ align:start position:0%
+so the epidemiology and the reason i'm
+bringing this up is is that people most
+
+ align:start position:0%
+bringing this up is is that people most
+ 
+
+ align:start position:0%
+bringing this up is is that people most
+of the immunology community is focused
+
+ align:start position:0%
+of the immunology community is focused
+ 
+
+ align:start position:0%
+of the immunology community is focused
+on this is why it's important if you're
+
+ align:start position:0%
+on this is why it's important if you're
+ 
+
+ align:start position:0%
+on this is why it's important if you're
+going to be a good geneticist you got to
+
+ align:start position:0%
+going to be a good geneticist you got to
+ 
+
+ align:start position:0%
+going to be a good geneticist you got to
+really know your disease you can't just
+
+ align:start position:0%
+really know your disease you can't just
+ 
+
+ align:start position:0%
+really know your disease you can't just
+sort of wave your hand at it and say oh
+
+ align:start position:0%
+sort of wave your hand at it and say oh
+ 
+
+ align:start position:0%
+sort of wave your hand at it and say oh
+and i think that the age of the
+
+ align:start position:0%
+and i think that the age of the
+ 
+
+ align:start position:0%
+and i think that the age of the
+generalist geneticist the geneticist
+
+ align:start position:0%
+generalist geneticist the geneticist
+ 
+
+ align:start position:0%
+generalist geneticist the geneticist
+that sort of oh you know i'm going to
+
+ align:start position:0%
+that sort of oh you know i'm going to
+ 
+
+ align:start position:0%
+that sort of oh you know i'm going to
+study this disease and i'm going to
+
+ align:start position:0%
+study this disease and i'm going to
+ 
+
+ align:start position:0%
+study this disease and i'm going to
+study that disease
+
+ align:start position:0%
+study that disease
+ 
+
+ align:start position:0%
+study that disease
+not with complex traits that's not going
+
+ align:start position:0%
+not with complex traits that's not going
+ 
+
+ align:start position:0%
+not with complex traits that's not going
+to work you're going to have to really
+
+ align:start position:0%
+to work you're going to have to really
+ 
+
+ align:start position:0%
+to work you're going to have to really
+know your disease because you have to
+
+ align:start position:0%
+know your disease because you have to
+ 
+
+ align:start position:0%
+know your disease because you have to
+know the environment you're gonna have
+
+ align:start position:0%
+know the environment you're gonna have
+ 
+
+ align:start position:0%
+know the environment you're gonna have
+to know the
+
+ align:start position:0%
+to know the
+ 
+
+ align:start position:0%
+to know the
+natural history you're gonna have to
+
+ align:start position:0%
+natural history you're gonna have to
+ 
+
+ align:start position:0%
+natural history you're gonna have to
+know the intermediate phenotypes and you
+
+ align:start position:0%
+know the intermediate phenotypes and you
+ 
+
+ align:start position:0%
+know the intermediate phenotypes and you
+have to really understand
+
+ align:start position:0%
+have to really understand
+ 
+
+ align:start position:0%
+have to really understand
+the biology
+
+ align:start position:0%
+the biology
+ 
+
+ align:start position:0%
+the biology
+uh uh as well the point here is is these
+
+ align:start position:0%
+uh uh as well the point here is is these
+ 
+
+ align:start position:0%
+uh uh as well the point here is is these
+th1 disease give me an example of a th1
+
+ align:start position:0%
+th1 disease give me an example of a th1
+ 
+
+ align:start position:0%
+th1 disease give me an example of a th1
+disease
+
+ align:start position:0%
+disease
+ 
+
+ align:start position:0%
+disease
+well i'm thinking about that um
+
+ align:start position:0%
+well i'm thinking about that um
+ 
+
+ align:start position:0%
+well i'm thinking about that um
+can you um tell me
+
+ align:start position:0%
+can you um tell me
+ 
+
+ align:start position:0%
+can you um tell me
+the autoimmune diseases like
+
+ align:start position:0%
+the autoimmune diseases like
+ 
+
+ align:start position:0%
+the autoimmune diseases like
+inflammatory bowel disease what are they
+
+ align:start position:0%
+inflammatory bowel disease what are they
+ 
+
+ align:start position:0%
+inflammatory bowel disease what are they
+they are th1 so crohn's disease
+
+ align:start position:0%
+they are th1 so crohn's disease
+ 
+
+ align:start position:0%
+they are th1 so crohn's disease
+th1 disease
+
+ align:start position:0%
+th1 disease
+ 
+
+ align:start position:0%
+th1 disease
+juvenile rheumatoid arthritis th1
+
+ align:start position:0%
+juvenile rheumatoid arthritis th1
+ 
+
+ align:start position:0%
+juvenile rheumatoid arthritis th1
+disease
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+psoriasis th1 disease
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+juvenile diabetes t1 disease
+
+ align:start position:0%
+juvenile diabetes t1 disease
+ 
+
+ align:start position:0%
+juvenile diabetes t1 disease
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the reason so if the prevalence of these
+
+ align:start position:0%
+the reason so if the prevalence of these
+ 
+
+ align:start position:0%
+the reason so if the prevalence of these
+has gone up and the prevalence of the
+
+ align:start position:0%
+has gone up and the prevalence of the
+ 
+
+ align:start position:0%
+has gone up and the prevalence of the
+these has gone up people are thinking
+
+ align:start position:0%
+these has gone up people are thinking
+ 
+
+ align:start position:0%
+these has gone up people are thinking
+that there's something going on
+
+ align:start position:0%
+that there's something going on
+ 
+
+ align:start position:0%
+that there's something going on
+further up
+
+ align:start position:0%
+further up
+ 
+
+ align:start position:0%
+further up
+here that
+
+ align:start position:0%
+here that
+ 
+
+ align:start position:0%
+here that
+has to do with t reg cells
+
+ align:start position:0%
+has to do with t reg cells
+ 
+
+ align:start position:0%
+has to do with t reg cells
+cells that regulate t null cells in
+
+ align:start position:0%
+cells that regulate t null cells in
+ 
+
+ align:start position:0%
+cells that regulate t null cells in
+terms of their differentiation because
+
+ align:start position:0%
+terms of their differentiation because
+ 
+
+ align:start position:0%
+terms of their differentiation because
+it can't be just at this level that the
+
+ align:start position:0%
+it can't be just at this level that the
+ 
+
+ align:start position:0%
+it can't be just at this level that the
+immunologic defect is so
+
+ align:start position:0%
+immunologic defect is so
+ 
+
+ align:start position:0%
+immunologic defect is so
+it raises the possibility that there are
+
+ align:start position:0%
+it raises the possibility that there are
+ 
+
+ align:start position:0%
+it raises the possibility that there are
+genes uh a fox p3
+
+ align:start position:0%
+genes uh a fox p3
+ 
+
+ align:start position:0%
+genes uh a fox p3
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+getter
+
+ align:start position:0%
+getter
+ 
+
+ align:start position:0%
+getter
+t-bat a whole bunch of other genes that
+
+ align:start position:0%
+t-bat a whole bunch of other genes that
+ 
+
+ align:start position:0%
+t-bat a whole bunch of other genes that
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+proximal to the th1 th2 cd4 lymphocyte
+
+ align:start position:0%
+proximal to the th1 th2 cd4 lymphocyte
+ 
+
+ align:start position:0%
+proximal to the th1 th2 cd4 lymphocyte
+that may be important in all of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+immune diseases and people are just now
+
+ align:start position:0%
+immune diseases and people are just now
+ 
+
+ align:start position:0%
+immune diseases and people are just now
+starting to look at
+
+ align:start position:0%
+starting to look at
+ 
+
+ align:start position:0%
+starting to look at
+at that and obviously the environmental
+
+ align:start position:0%
+at that and obviously the environmental
+ 
+
+ align:start position:0%
+at that and obviously the environmental
+and genetic factors that influence
+
+ align:start position:0%
+and genetic factors that influence
+ 
+
+ align:start position:0%
+and genetic factors that influence
+the differentiation of the immune system
+
+ align:start position:0%
+the differentiation of the immune system
+ 
+
+ align:start position:0%
+the differentiation of the immune system
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+you know how do people actually tolerize
+
+ align:start position:0%
+you know how do people actually tolerize
+ 
+
+ align:start position:0%
+you know how do people actually tolerize
+the foreign antigen
+
+ align:start position:0%
+the foreign antigen
+ 
+
+ align:start position:0%
+the foreign antigen
+that's the kind of really simple
+
+ align:start position:0%
+that's the kind of really simple
+ 
+
+ align:start position:0%
+that's the kind of really simple
+complicated question that if you could
+
+ align:start position:0%
+complicated question that if you could
+ 
+
+ align:start position:0%
+complicated question that if you could
+figure out an answer that you win a
+
+ align:start position:0%
+figure out an answer that you win a
+ 
+
+ align:start position:0%
+figure out an answer that you win a
+nobel prize
+
+ align:start position:0%
+nobel prize
+ 
+
+ align:start position:0%
+nobel prize
+so that's what my laboratory is starting
+
+ align:start position:0%
+so that's what my laboratory is starting
+ 
+
+ align:start position:0%
+so that's what my laboratory is starting
+to work on
+
+ align:start position:0%
+to work on
+ 
+
+ align:start position:0%
+to work on
+um so this is just to show you
+
+ align:start position:0%
+um so this is just to show you
+ 
+
+ align:start position:0%
+um so this is just to show you
+again what i've already told you that
+
+ align:start position:0%
+again what i've already told you that
+ 
+
+ align:start position:0%
+again what i've already told you that
+there are a bunch of
+
+ align:start position:0%
+there are a bunch of
+ 
+
+ align:start position:0%
+there are a bunch of
+factors mostly bacteria and viruses and
+
+ align:start position:0%
+factors mostly bacteria and viruses and
+ 
+
+ align:start position:0%
+factors mostly bacteria and viruses and
+parasites
+
+ align:start position:0%
+parasites
+ 
+
+ align:start position:0%
+parasites
+that influence this teach one teach to
+
+ align:start position:0%
+that influence this teach one teach to
+ 
+
+ align:start position:0%
+that influence this teach one teach to
+differentiation
+
+ align:start position:0%
+differentiation
+ 
+
+ align:start position:0%
+differentiation
+and uh um environmental factors that
+
+ align:start position:0%
+and uh um environmental factors that
+ 
+
+ align:start position:0%
+and uh um environmental factors that
+influence those things are presumed to
+
+ align:start position:0%
+influence those things are presumed to
+ 
+
+ align:start position:0%
+influence those things are presumed to
+be important and one would want to know
+
+ align:start position:0%
+be important and one would want to know
+ 
+
+ align:start position:0%
+be important and one would want to know
+both the genes and the environmental
+
+ align:start position:0%
+both the genes and the environmental
+ 
+
+ align:start position:0%
+both the genes and the environmental
+factors that are involved in in this
+
+ align:start position:0%
+factors that are involved in in this
+ 
+
+ align:start position:0%
+factors that are involved in in this
+particular disease there happen to be a
+
+ align:start position:0%
+particular disease there happen to be a
+ 
+
+ align:start position:0%
+particular disease there happen to be a
+whole host of
+
+ align:start position:0%
+whole host of
+ 
+
+ align:start position:0%
+whole host of
+environmental factors that are
+
+ align:start position:0%
+environmental factors that are
+ 
+
+ align:start position:0%
+environmental factors that are
+correlates
+
+ align:start position:0%
+correlates
+ 
+
+ align:start position:0%
+correlates
+of those sorts of changes and i've
+
+ align:start position:0%
+of those sorts of changes and i've
+ 
+
+ align:start position:0%
+of those sorts of changes and i've
+listed a bunch of them
+
+ align:start position:0%
+listed a bunch of them
+ 
+
+ align:start position:0%
+listed a bunch of them
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+we got very interested in this when we
+
+ align:start position:0%
+we got very interested in this when we
+ 
+
+ align:start position:0%
+we got very interested in this when we
+went to china in 1996 to do an asthma
+
+ align:start position:0%
+went to china in 1996 to do an asthma
+ 
+
+ align:start position:0%
+went to china in 1996 to do an asthma
+genetic study and i noticed how
+
+ align:start position:0%
+genetic study and i noticed how
+ 
+
+ align:start position:0%
+genetic study and i noticed how
+different the environment was uh there
+
+ align:start position:0%
+different the environment was uh there
+ 
+
+ align:start position:0%
+different the environment was uh there
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know this
+
+ align:start position:0%
+you know this
+ 
+
+ align:start position:0%
+you know this
+left-hand
+
+ align:start position:0%
+left-hand
+ 
+
+ align:start position:0%
+left-hand
+category would sort of summarize what
+
+ align:start position:0%
+category would sort of summarize what
+ 
+
+ align:start position:0%
+category would sort of summarize what
+you would see if you were standing in
+
+ align:start position:0%
+you would see if you were standing in
+ 
+
+ align:start position:0%
+you would see if you were standing in
+rural china which you would see in terms
+
+ align:start position:0%
+rural china which you would see in terms
+ 
+
+ align:start position:0%
+rural china which you would see in terms
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+environmental exposures
+
+ align:start position:0%
+environmental exposures
+ 
+
+ align:start position:0%
+environmental exposures
+very very low asthma rates in the rural
+
+ align:start position:0%
+very very low asthma rates in the rural
+ 
+
+ align:start position:0%
+very very low asthma rates in the rural
+china it's about one percent
+
+ align:start position:0%
+china it's about one percent
+ 
+
+ align:start position:0%
+china it's about one percent
+energy is a progressive increase in
+
+ align:start position:0%
+energy is a progressive increase in
+ 
+
+ align:start position:0%
+energy is a progressive increase in
+gradient in terms of disease prevalence
+
+ align:start position:0%
+gradient in terms of disease prevalence
+ 
+
+ align:start position:0%
+gradient in terms of disease prevalence
+as you march towards beijing or shanghai
+
+ align:start position:0%
+as you march towards beijing or shanghai
+ 
+
+ align:start position:0%
+as you march towards beijing or shanghai
+you know much much higher
+
+ align:start position:0%
+you know much much higher
+ 
+
+ align:start position:0%
+you know much much higher
+higher rates let me ask
+
+ align:start position:0%
+higher rates let me ask
+ 
+
+ align:start position:0%
+higher rates let me ask
+some questions
+
+ align:start position:0%
+some questions
+ 
+
+ align:start position:0%
+some questions
+is it not actually
+
+ align:start position:0%
+is it not actually
+ 
+
+ align:start position:0%
+is it not actually
+wrong that
+
+ align:start position:0%
+wrong that
+ 
+
+ align:start position:0%
+wrong that
+chinese populations i thought the
+
+ align:start position:0%
+chinese populations i thought the
+ 
+
+ align:start position:0%
+chinese populations i thought the
+families were limited no
+
+ align:start position:0%
+families were limited no
+ 
+
+ align:start position:0%
+families were limited no
+see that's again
+
+ align:start position:0%
+see that's again
+ 
+
+ align:start position:0%
+see that's again
+a little bit of knowledge is a bad thing
+
+ align:start position:0%
+a little bit of knowledge is a bad thing
+ 
+
+ align:start position:0%
+a little bit of knowledge is a bad thing
+if you get into rural china
+
+ align:start position:0%
+if you get into rural china
+ 
+
+ align:start position:0%
+if you get into rural china
+actually where where
+
+ align:start position:0%
+actually where where
+ 
+
+ align:start position:0%
+actually where where
+uh farming is what everybody does
+
+ align:start position:0%
+uh farming is what everybody does
+ 
+
+ align:start position:0%
+uh farming is what everybody does
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+although the central government would
+
+ align:start position:0%
+although the central government would
+ 
+
+ align:start position:0%
+although the central government would
+say you could there's a there's a
+
+ align:start position:0%
+say you could there's a there's a
+ 
+
+ align:start position:0%
+say you could there's a there's a
+a a two-child policy or a one-child
+
+ align:start position:0%
+a a two-child policy or a one-child
+ 
+
+ align:start position:0%
+a a two-child policy or a one-child
+policy uh you know in rural china they
+
+ align:start position:0%
+policy uh you know in rural china they
+ 
+
+ align:start position:0%
+policy uh you know in rural china they
+just they have as many children as they
+
+ align:start position:0%
+just they have as many children as they
+ 
+
+ align:start position:0%
+just they have as many children as they
+may not register them with social
+
+ align:start position:0%
+may not register them with social
+ 
+
+ align:start position:0%
+may not register them with social
+security but if they need three kids to
+
+ align:start position:0%
+security but if they need three kids to
+ 
+
+ align:start position:0%
+security but if they need three kids to
+run the farm or four kids they have as
+
+ align:start position:0%
+run the farm or four kids they have as
+ 
+
+ align:start position:0%
+run the farm or four kids they have as
+many kids as they want so
+
+ align:start position:0%
+many kids as they want so
+ 
+
+ align:start position:0%
+many kids as they want so
+we found a lot of families with four
+
+ align:start position:0%
+we found a lot of families with four
+ 
+
+ align:start position:0%
+we found a lot of families with four
+five six eight kids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so why has it been presumed to be
+
+ align:start position:0%
+so why has it been presumed to be
+ 
+
+ align:start position:0%
+so why has it been presumed to be
+difficult to do this kind of work what
+
+ align:start position:0%
+difficult to do this kind of work what
+ 
+
+ align:start position:0%
+difficult to do this kind of work what
+what's the reason that it's difficult i
+
+ align:start position:0%
+what's the reason that it's difficult i
+ 
+
+ align:start position:0%
+what's the reason that it's difficult i
+think these are some of the reason
+
+ align:start position:0%
+think these are some of the reason
+ 
+
+ align:start position:0%
+think these are some of the reason
+reasons and and some of them relate to
+
+ align:start position:0%
+reasons and and some of them relate to
+ 
+
+ align:start position:0%
+reasons and and some of them relate to
+the issues of study design the things
+
+ align:start position:0%
+the issues of study design the things
+ 
+
+ align:start position:0%
+the issues of study design the things
+that we were talking about you know one
+
+ align:start position:0%
+that we were talking about you know one
+ 
+
+ align:start position:0%
+that we were talking about you know one
+is this whole idea of genetic
+
+ align:start position:0%
+is this whole idea of genetic
+ 
+
+ align:start position:0%
+is this whole idea of genetic
+heterogeneity particularly if the
+
+ align:start position:0%
+heterogeneity particularly if the
+ 
+
+ align:start position:0%
+heterogeneity particularly if the
+underlying model here is gene by
+
+ align:start position:0%
+underlying model here is gene by
+ 
+
+ align:start position:0%
+underlying model here is gene by
+environment interaction presumably you
+
+ align:start position:0%
+environment interaction presumably you
+ 
+
+ align:start position:0%
+environment interaction presumably you
+could get the same phenotype
+
+ align:start position:0%
+could get the same phenotype
+ 
+
+ align:start position:0%
+could get the same phenotype
+and these phenotypes are determined by
+
+ align:start position:0%
+and these phenotypes are determined by
+ 
+
+ align:start position:0%
+and these phenotypes are determined by
+multiple genes
+
+ align:start position:0%
+multiple genes
+ 
+
+ align:start position:0%
+multiple genes
+and you know you can get the same
+
+ align:start position:0%
+and you know you can get the same
+ 
+
+ align:start position:0%
+and you know you can get the same
+phenotype either high ige or airways
+
+ align:start position:0%
+phenotype either high ige or airways
+ 
+
+ align:start position:0%
+phenotype either high ige or airways
+responsiveness in population a with a
+
+ align:start position:0%
+responsiveness in population a with a
+ 
+
+ align:start position:0%
+responsiveness in population a with a
+very different constellation of genes
+
+ align:start position:0%
+very different constellation of genes
+ 
+
+ align:start position:0%
+very different constellation of genes
+and environmental exposures and you can
+
+ align:start position:0%
+and environmental exposures and you can
+ 
+
+ align:start position:0%
+and environmental exposures and you can
+get the same thing
+
+ align:start position:0%
+get the same thing
+ 
+
+ align:start position:0%
+get the same thing
+in population b with with different
+
+ align:start position:0%
+in population b with with different
+ 
+
+ align:start position:0%
+in population b with with different
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the this is the genetic heterogeneity
+
+ align:start position:0%
+the this is the genetic heterogeneity
+ 
+
+ align:start position:0%
+the this is the genetic heterogeneity
+thing is a reason for focusing on a
+
+ align:start position:0%
+thing is a reason for focusing on a
+ 
+
+ align:start position:0%
+thing is a reason for focusing on a
+genetic isolate
+
+ align:start position:0%
+genetic isolate
+ 
+
+ align:start position:0%
+genetic isolate
+but then you have to worry about the
+
+ align:start position:0%
+but then you have to worry about the
+ 
+
+ align:start position:0%
+but then you have to worry about the
+generalizability question so in fact in
+
+ align:start position:0%
+generalizability question so in fact in
+ 
+
+ align:start position:0%
+generalizability question so in fact in
+asthma there are four positionally
+
+ align:start position:0%
+asthma there are four positionally
+ 
+
+ align:start position:0%
+asthma there are four positionally
+cloned genes counting the paper that's
+
+ align:start position:0%
+cloned genes counting the paper that's
+ 
+
+ align:start position:0%
+cloned genes counting the paper that's
+going to come out on friday in science
+
+ align:start position:0%
+going to come out on friday in science
+ 
+
+ align:start position:0%
+going to come out on friday in science
+and and of those four the first is the
+
+ align:start position:0%
+and and of those four the first is the
+ 
+
+ align:start position:0%
+and and of those four the first is the
+only one that's people have really
+
+ align:start position:0%
+only one that's people have really
+ 
+
+ align:start position:0%
+only one that's people have really
+attempted to replicate
+
+ align:start position:0%
+attempted to replicate
+ 
+
+ align:start position:0%
+attempted to replicate
+um and it's sort of gotten mixed results
+
+ align:start position:0%
+um and it's sort of gotten mixed results
+ 
+
+ align:start position:0%
+um and it's sort of gotten mixed results
+you know there are some people that are
+
+ align:start position:0%
+you know there are some people that are
+ 
+
+ align:start position:0%
+you know there are some people that are
+replicated and some people that haven't
+
+ align:start position:0%
+replicated and some people that haven't
+ 
+
+ align:start position:0%
+replicated and some people that haven't
+so it's one of those genes that probably
+
+ align:start position:0%
+so it's one of those genes that probably
+ 
+
+ align:start position:0%
+so it's one of those genes that probably
+falls into this category of it well it's
+
+ align:start position:0%
+falls into this category of it well it's
+ 
+
+ align:start position:0%
+falls into this category of it well it's
+not a major gene it's a minor gene
+
+ align:start position:0%
+not a major gene it's a minor gene
+ 
+
+ align:start position:0%
+not a major gene it's a minor gene
+it's one of the 200 genes that determine
+
+ align:start position:0%
+it's one of the 200 genes that determine
+ 
+
+ align:start position:0%
+it's one of the 200 genes that determine
+asthma but it's not one of the top 10 in
+
+ align:start position:0%
+asthma but it's not one of the top 10 in
+ 
+
+ align:start position:0%
+asthma but it's not one of the top 10 in
+every population what's your guess about
+
+ align:start position:0%
+every population what's your guess about
+ 
+
+ align:start position:0%
+every population what's your guess about
+eugene
+
+ align:start position:0%
+eugene
+ 
+
+ align:start position:0%
+eugene
+my guess my guess about this new genius
+
+ align:start position:0%
+my guess my guess about this new genius
+ 
+
+ align:start position:0%
+my guess my guess about this new genius
+is that it's a major player yeah
+
+ align:start position:0%
+is that it's a major player yeah
+ 
+
+ align:start position:0%
+is that it's a major player yeah
+i think that
+
+ align:start position:0%
+i think that
+ 
+
+ align:start position:0%
+i think that
+you know uh um
+
+ align:start position:0%
+you know uh um
+ 
+
+ align:start position:0%
+you know uh um
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+having said that
+
+ align:start position:0%
+having said that
+ 
+
+ align:start position:0%
+having said that
+the point that i made to this science
+
+ align:start position:0%
+the point that i made to this science
+ 
+
+ align:start position:0%
+the point that i made to this science
+writer who was doing this is it you know
+
+ align:start position:0%
+writer who was doing this is it you know
+ 
+
+ align:start position:0%
+writer who was doing this is it you know
+as it's
+
+ align:start position:0%
+as it's
+ 
+
+ align:start position:0%
+as it's
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+you know it's
+
+ align:start position:0%
+you know it's
+ 
+
+ align:start position:0%
+you know it's
+that's what science is all about is you
+
+ align:start position:0%
+that's what science is all about is you
+ 
+
+ align:start position:0%
+that's what science is all about is you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+replicating this seeing how
+
+ align:start position:0%
+replicating this seeing how
+ 
+
+ align:start position:0%
+replicating this seeing how
+important it really is and seeing what
+
+ align:start position:0%
+important it really is and seeing what
+ 
+
+ align:start position:0%
+important it really is and seeing what
+actually happens you know i mean i i
+
+ align:start position:0%
+actually happens you know i mean i i
+ 
+
+ align:start position:0%
+actually happens you know i mean i i
+think you can get a clue as to
+
+ align:start position:0%
+think you can get a clue as to
+ 
+
+ align:start position:0%
+think you can get a clue as to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+whether you've got hold of an area where
+
+ align:start position:0%
+whether you've got hold of an area where
+ 
+
+ align:start position:0%
+whether you've got hold of an area where
+there's a potential major locus or not
+
+ align:start position:0%
+there's a potential major locus or not
+ 
+
+ align:start position:0%
+there's a potential major locus or not
+by looking at the replicability of the
+
+ align:start position:0%
+by looking at the replicability of the
+ 
+
+ align:start position:0%
+by looking at the replicability of the
+linkage peaks in a particular reason
+
+ align:start position:0%
+linkage peaks in a particular reason
+ 
+
+ align:start position:0%
+linkage peaks in a particular reason
+region for a complex trade in other
+
+ align:start position:0%
+region for a complex trade in other
+ 
+
+ align:start position:0%
+region for a complex trade in other
+words if you've got a region where
+
+ align:start position:0%
+words if you've got a region where
+ 
+
+ align:start position:0%
+words if you've got a region where
+there's a linkage peak and and there are
+
+ align:start position:0%
+there's a linkage peak and and there are
+ 
+
+ align:start position:0%
+there's a linkage peak and and there are
+10 different studies in 10 different
+
+ align:start position:0%
+10 different studies in 10 different
+ 
+
+ align:start position:0%
+10 different studies in 10 different
+populations and that there's always a
+
+ align:start position:0%
+populations and that there's always a
+ 
+
+ align:start position:0%
+populations and that there's always a
+peak in the same region
+
+ align:start position:0%
+peak in the same region
+ 
+
+ align:start position:0%
+peak in the same region
+then the chances are that there's a
+
+ align:start position:0%
+then the chances are that there's a
+ 
+
+ align:start position:0%
+then the chances are that there's a
+major gene in there that's probably
+
+ align:start position:0%
+major gene in there that's probably
+ 
+
+ align:start position:0%
+major gene in there that's probably
+going to apply to a bunch of different
+
+ align:start position:0%
+going to apply to a bunch of different
+ 
+
+ align:start position:0%
+going to apply to a bunch of different
+populations well this is the going back
+
+ align:start position:0%
+populations well this is the going back
+ 
+
+ align:start position:0%
+populations well this is the going back
+to the science article that this is a
+
+ align:start position:0%
+to the science article that this is a
+ 
+
+ align:start position:0%
+to the science article that this is a
+region where there have been a number of
+
+ align:start position:0%
+region where there have been a number of
+ 
+
+ align:start position:0%
+region where there have been a number of
+people have found
+
+ align:start position:0%
+people have found
+ 
+
+ align:start position:0%
+people have found
+a peak there
+
+ align:start position:0%
+a peak there
+ 
+
+ align:start position:0%
+a peak there
+you know the other problem here is is
+
+ align:start position:0%
+you know the other problem here is is
+ 
+
+ align:start position:0%
+you know the other problem here is is
+that unlike
+
+ align:start position:0%
+that unlike
+ 
+
+ align:start position:0%
+that unlike
+single gene disorders where there's a
+
+ align:start position:0%
+single gene disorders where there's a
+ 
+
+ align:start position:0%
+single gene disorders where there's a
+known mode of inheritance you get
+
+ align:start position:0%
+known mode of inheritance you get
+ 
+
+ align:start position:0%
+known mode of inheritance you get
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+under the kitchen sink here right so you
+
+ align:start position:0%
+under the kitchen sink here right so you
+ 
+
+ align:start position:0%
+under the kitchen sink here right so you
+get some of these genes or autosomal
+
+ align:start position:0%
+get some of these genes or autosomal
+ 
+
+ align:start position:0%
+get some of these genes or autosomal
+recessives and some are autosomal
+
+ align:start position:0%
+recessives and some are autosomal
+ 
+
+ align:start position:0%
+recessives and some are autosomal
+dominance and some are uh
+
+ align:start position:0%
+dominance and some are uh
+ 
+
+ align:start position:0%
+dominance and some are uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you're getting a whole bunch of things
+
+ align:start position:0%
+you're getting a whole bunch of things
+ 
+
+ align:start position:0%
+you're getting a whole bunch of things
+jumbled up in one phenotype which makes
+
+ align:start position:0%
+jumbled up in one phenotype which makes
+ 
+
+ align:start position:0%
+jumbled up in one phenotype which makes
+it very difficult
+
+ align:start position:0%
+it very difficult
+ 
+
+ align:start position:0%
+it very difficult
+and then there's this problem of
+
+ align:start position:0%
+and then there's this problem of
+ 
+
+ align:start position:0%
+and then there's this problem of
+phenocopies
+
+ align:start position:0%
+phenocopies
+ 
+
+ align:start position:0%
+phenocopies
+so what's what's a phenocopy
+
+ align:start position:0%
+so what's what's a phenocopy
+ 
+
+ align:start position:0%
+so what's what's a phenocopy
+give me a give me a give me an example
+
+ align:start position:0%
+give me a give me a give me an example
+ 
+
+ align:start position:0%
+give me a give me a give me an example
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+your own
+
+ align:start position:0%
+your own
+ 
+
+ align:start position:0%
+your own
+clinical experience of somebody who's
+
+ align:start position:0%
+clinical experience of somebody who's
+ 
+
+ align:start position:0%
+clinical experience of somebody who's
+a phenocopy who's not not due to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well just like you can get these
+
+ align:start position:0%
+well just like you can get these
+ 
+
+ align:start position:0%
+well just like you can get these
+diseases from jeans you can get them
+
+ align:start position:0%
+diseases from jeans you can get them
+ 
+
+ align:start position:0%
+diseases from jeans you can get them
+from exposures in the environment so
+
+ align:start position:0%
+from exposures in the environment so
+ 
+
+ align:start position:0%
+from exposures in the environment so
+what what if you've got some guy who
+
+ align:start position:0%
+what what if you've got some guy who
+ 
+
+ align:start position:0%
+what what if you've got some guy who
+smokes four packs a day and he's 50
+
+ align:start position:0%
+smokes four packs a day and he's 50
+ 
+
+ align:start position:0%
+smokes four packs a day and he's 50
+years old and he has a whopping big
+
+ align:start position:0%
+years old and he has a whopping big
+ 
+
+ align:start position:0%
+years old and he has a whopping big
+heart attack
+
+ align:start position:0%
+heart attack
+ 
+
+ align:start position:0%
+heart attack
+well maybe he you know when you
+
+ align:start position:0%
+well maybe he you know when you
+ 
+
+ align:start position:0%
+well maybe he you know when you
+inclusivity has no family history but
+
+ align:start position:0%
+inclusivity has no family history but
+ 
+
+ align:start position:0%
+inclusivity has no family history but
+you smoke four packs a day well
+
+ align:start position:0%
+you smoke four packs a day well
+ 
+
+ align:start position:0%
+you smoke four packs a day well
+you can get a heart attack from smoking
+
+ align:start position:0%
+you can get a heart attack from smoking
+ 
+
+ align:start position:0%
+you can get a heart attack from smoking
+for four packs a day and you don't need
+
+ align:start position:0%
+for four packs a day and you don't need
+ 
+
+ align:start position:0%
+for four packs a day and you don't need
+to have any genes at all for heart
+
+ align:start position:0%
+to have any genes at all for heart
+ 
+
+ align:start position:0%
+to have any genes at all for heart
+attack you can just so that's a
+
+ align:start position:0%
+attack you can just so that's a
+ 
+
+ align:start position:0%
+attack you can just so that's a
+phenocopy he's going to look like
+
+ align:start position:0%
+phenocopy he's going to look like
+ 
+
+ align:start position:0%
+phenocopy he's going to look like
+somebody who's a genetic susceptible
+
+ align:start position:0%
+somebody who's a genetic susceptible
+ 
+
+ align:start position:0%
+somebody who's a genetic susceptible
+because he
+
+ align:start position:0%
+because he
+ 
+
+ align:start position:0%
+because he
+you know had a heart attack at 50 years
+
+ align:start position:0%
+you know had a heart attack at 50 years
+ 
+
+ align:start position:0%
+you know had a heart attack at 50 years
+old but it's all due to environmental
+
+ align:start position:0%
+old but it's all due to environmental
+ 
+
+ align:start position:0%
+old but it's all due to environmental
+exposure
+
+ align:start position:0%
+exposure
+ 
+
+ align:start position:0%
+exposure
+incomplete penetrance
+
+ align:start position:0%
+incomplete penetrance
+ 
+
+ align:start position:0%
+incomplete penetrance
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+this is a pop problem even in single
+
+ align:start position:0%
+this is a pop problem even in single
+ 
+
+ align:start position:0%
+this is a pop problem even in single
+gene disorders right because they're
+
+ align:start position:0%
+gene disorders right because they're
+ 
+
+ align:start position:0%
+gene disorders right because they're
+clearly examples um hemochromatosis
+
+ align:start position:0%
+clearly examples um hemochromatosis
+ 
+
+ align:start position:0%
+clearly examples um hemochromatosis
+cystic fibrosis very different spectrum
+
+ align:start position:0%
+cystic fibrosis very different spectrum
+ 
+
+ align:start position:0%
+cystic fibrosis very different spectrum
+of diseases and these what we know
+
+ align:start position:0%
+of diseases and these what we know
+ 
+
+ align:start position:0%
+of diseases and these what we know
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+the cftr gene causes cystic fibrosis you
+
+ align:start position:0%
+the cftr gene causes cystic fibrosis you
+ 
+
+ align:start position:0%
+the cftr gene causes cystic fibrosis you
+get some people who have completely
+
+ align:start position:0%
+get some people who have completely
+ 
+
+ align:start position:0%
+get some people who have completely
+normal lung function
+
+ align:start position:0%
+normal lung function
+ 
+
+ align:start position:0%
+normal lung function
+no lung disease at all
+
+ align:start position:0%
+no lung disease at all
+ 
+
+ align:start position:0%
+no lung disease at all
+and all they've got is mild pancreatic
+
+ align:start position:0%
+and all they've got is mild pancreatic
+ 
+
+ align:start position:0%
+and all they've got is mild pancreatic
+insufficiency and you've got other
+
+ align:start position:0%
+insufficiency and you've got other
+ 
+
+ align:start position:0%
+insufficiency and you've got other
+people who were totally debilitated from
+
+ align:start position:0%
+people who were totally debilitated from
+ 
+
+ align:start position:0%
+people who were totally debilitated from
+it so
+
+ align:start position:0%
+it so
+ 
+
+ align:start position:0%
+it so
+part of that can be penetrants part of
+
+ align:start position:0%
+part of that can be penetrants part of
+ 
+
+ align:start position:0%
+part of that can be penetrants part of
+it can be environmental exposure but
+
+ align:start position:0%
+it can be environmental exposure but
+ 
+
+ align:start position:0%
+it can be environmental exposure but
+incomplete penetrance is important then
+
+ align:start position:0%
+incomplete penetrance is important then
+ 
+
+ align:start position:0%
+incomplete penetrance is important then
+you've got this problem with multiple
+
+ align:start position:0%
+you've got this problem with multiple
+ 
+
+ align:start position:0%
+you've got this problem with multiple
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+people have very
+
+ align:start position:0%
+people have very
+ 
+
+ align:start position:0%
+people have very
+the lay public has a very sort of
+
+ align:start position:0%
+the lay public has a very sort of
+ 
+
+ align:start position:0%
+the lay public has a very sort of
+delusional kind you know they think the
+
+ align:start position:0%
+delusional kind you know they think the
+ 
+
+ align:start position:0%
+delusional kind you know they think the
+genes are immutable you know if you've
+
+ align:start position:0%
+genes are immutable you know if you've
+ 
+
+ align:start position:0%
+genes are immutable you know if you've
+got those genes that's it you know it
+
+ align:start position:0%
+got those genes that's it you know it
+ 
+
+ align:start position:0%
+got those genes that's it you know it
+can't be changed and they also they're
+
+ align:start position:0%
+can't be changed and they also they're
+ 
+
+ align:start position:0%
+can't be changed and they also they're
+monolithic they're really big whereas
+
+ align:start position:0%
+monolithic they're really big whereas
+ 
+
+ align:start position:0%
+monolithic they're really big whereas
+the reality is is that anyone you know
+
+ align:start position:0%
+the reality is is that anyone you know
+ 
+
+ align:start position:0%
+the reality is is that anyone you know
+you got 33 000 genes in the genome take
+
+ align:start position:0%
+you got 33 000 genes in the genome take
+ 
+
+ align:start position:0%
+you got 33 000 genes in the genome take
+a disease like asthma which isn't very
+
+ align:start position:0%
+a disease like asthma which isn't very
+ 
+
+ align:start position:0%
+a disease like asthma which isn't very
+complicated maybe they're 200
+
+ align:start position:0%
+complicated maybe they're 200
+ 
+
+ align:start position:0%
+complicated maybe they're 200
+250 i don't know
+
+ align:start position:0%
+250 i don't know
+ 
+
+ align:start position:0%
+250 i don't know
+a lot
+
+ align:start position:0%
+a lot
+ 
+
+ align:start position:0%
+a lot
+that are probably important maybe 10
+
+ align:start position:0%
+that are probably important maybe 10
+ 
+
+ align:start position:0%
+that are probably important maybe 10
+that play
+
+ align:start position:0%
+that play
+ 
+
+ align:start position:0%
+that play
+a a a a role in most every population um
+
+ align:start position:0%
+a a a a role in most every population um
+ 
+
+ align:start position:0%
+a a a a role in most every population um
+and a lot of environmental things going
+
+ align:start position:0%
+and a lot of environmental things going
+ 
+
+ align:start position:0%
+and a lot of environmental things going
+on and it makes it very complicated and
+
+ align:start position:0%
+on and it makes it very complicated and
+ 
+
+ align:start position:0%
+on and it makes it very complicated and
+that's why guys like
+
+ align:start position:0%
+that's why guys like
+ 
+
+ align:start position:0%
+that's why guys like
+this guy are going to make big bucks
+
+ align:start position:0%
+this guy are going to make big bucks
+ 
+
+ align:start position:0%
+this guy are going to make big bucks
+because they're going to be able to
+
+ align:start position:0%
+because they're going to be able to
+ 
+
+ align:start position:0%
+because they're going to be able to
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+all of the different pathways and
+
+ align:start position:0%
+all of the different pathways and
+ 
+
+ align:start position:0%
+all of the different pathways and
+you know the different genes together in
+
+ align:start position:0%
+you know the different genes together in
+ 
+
+ align:start position:0%
+you know the different genes together in
+some more realistic model of
+
+ align:start position:0%
+some more realistic model of
+ 
+
+ align:start position:0%
+some more realistic model of
+you know systems biology or some actual
+
+ align:start position:0%
+you know systems biology or some actual
+ 
+
+ align:start position:0%
+you know systems biology or some actual
+way of looking at this but the point
+
+ align:start position:0%
+way of looking at this but the point
+ 
+
+ align:start position:0%
+way of looking at this but the point
+here basically is look
+
+ align:start position:0%
+here basically is look
+ 
+
+ align:start position:0%
+here basically is look
+it's complicated to do this stuff
+
+ align:start position:0%
+it's complicated to do this stuff
+ 
+
+ align:start position:0%
+it's complicated to do this stuff
+again going back to what i said earlier
+
+ align:start position:0%
+again going back to what i said earlier
+ 
+
+ align:start position:0%
+again going back to what i said earlier
+it's getting a lot easier so
+
+ align:start position:0%
+it's getting a lot easier so
+ 
+
+ align:start position:0%
+it's getting a lot easier so
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+one position like clone gene for asthma
+
+ align:start position:0%
+one position like clone gene for asthma
+ 
+
+ align:start position:0%
+one position like clone gene for asthma
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+two positionally cloned gene from
+
+ align:start position:0%
+two positionally cloned gene from
+ 
+
+ align:start position:0%
+two positionally cloned gene from
+from asthma 2004 first paper is already
+
+ align:start position:0%
+from asthma 2004 first paper is already
+ 
+
+ align:start position:0%
+from asthma 2004 first paper is already
+out and there's probably going to be
+
+ align:start position:0%
+out and there's probably going to be
+ 
+
+ align:start position:0%
+out and there's probably going to be
+four or five more
+
+ align:start position:0%
+four or five more
+ 
+
+ align:start position:0%
+four or five more
+so it can be four or five this year year
+
+ align:start position:0%
+so it can be four or five this year year
+ 
+
+ align:start position:0%
+so it can be four or five this year year
+after that they're going to be probably
+
+ align:start position:0%
+after that they're going to be probably
+ 
+
+ align:start position:0%
+after that they're going to be probably
+10 and all of a sudden now you got 20
+
+ align:start position:0%
+10 and all of a sudden now you got 20
+ 
+
+ align:start position:0%
+10 and all of a sudden now you got 20
+genes identified for the disease by
+
+ align:start position:0%
+genes identified for the disease by
+ 
+
+ align:start position:0%
+genes identified for the disease by
+positional cloning and that is the
+
+ align:start position:0%
+positional cloning and that is the
+ 
+
+ align:start position:0%
+positional cloning and that is the
+history of complex trait genetics and
+
+ align:start position:0%
+history of complex trait genetics and
+ 
+
+ align:start position:0%
+history of complex trait genetics and
+it's going to be it's it's happening
+
+ align:start position:0%
+it's going to be it's it's happening
+ 
+
+ align:start position:0%
+it's going to be it's it's happening
+right now right this very moment
+
+ align:start position:0%
+right now right this very moment
+ 
+
+ align:start position:0%
+right now right this very moment
+all across the world labs like mine are
+
+ align:start position:0%
+all across the world labs like mine are
+ 
+
+ align:start position:0%
+all across the world labs like mine are
+right in the middle of the fray doing
+
+ align:start position:0%
+right in the middle of the fray doing
+ 
+
+ align:start position:0%
+right in the middle of the fray doing
+this stuff
+
+ align:start position:0%
+this stuff
+ 
+
+ align:start position:0%
+this stuff
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+simply put the single most exciting time
+
+ align:start position:0%
+simply put the single most exciting time
+ 
+
+ align:start position:0%
+simply put the single most exciting time
+to be doing human genetics and
+
+ align:start position:0%
+to be doing human genetics and
+ 
+
+ align:start position:0%
+to be doing human genetics and
+uh uh it's
+
+ align:start position:0%
+uh uh it's
+ 
+
+ align:start position:0%
+uh uh it's
+going to go on for a while but who knows
+
+ align:start position:0%
+going to go on for a while but who knows
+ 
+
+ align:start position:0%
+going to go on for a while but who knows
+for how long
+
+ align:start position:0%
+for how long
+ 
+
+ align:start position:0%
+for how long
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so then there's this other problem of
+
+ align:start position:0%
+so then there's this other problem of
+ 
+
+ align:start position:0%
+so then there's this other problem of
+pleiotropy which is
+
+ align:start position:0%
+pleiotropy which is
+ 
+
+ align:start position:0%
+pleiotropy which is
+you know you could have one gene and it
+
+ align:start position:0%
+you know you could have one gene and it
+ 
+
+ align:start position:0%
+you know you could have one gene and it
+can do a lot of different things you get
+
+ align:start position:0%
+can do a lot of different things you get
+ 
+
+ align:start position:0%
+can do a lot of different things you get
+the cftr gene that gives you lung
+
+ align:start position:0%
+the cftr gene that gives you lung
+ 
+
+ align:start position:0%
+the cftr gene that gives you lung
+disease pancreatic insufficiency
+
+ align:start position:0%
+disease pancreatic insufficiency
+ 
+
+ align:start position:0%
+disease pancreatic insufficiency
+infertility you know it's all has to do
+
+ align:start position:0%
+infertility you know it's all has to do
+ 
+
+ align:start position:0%
+infertility you know it's all has to do
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+mucosa and epithelia and different organ
+
+ align:start position:0%
+mucosa and epithelia and different organ
+ 
+
+ align:start position:0%
+mucosa and epithelia and different organ
+systems where this particular gene is
+
+ align:start position:0%
+systems where this particular gene is
+ 
+
+ align:start position:0%
+systems where this particular gene is
+expressed so one of the genes we're
+
+ align:start position:0%
+expressed so one of the genes we're
+ 
+
+ align:start position:0%
+expressed so one of the genes we're
+looking at and so jeff did jeff talk to
+
+ align:start position:0%
+looking at and so jeff did jeff talk to
+ 
+
+ align:start position:0%
+looking at and so jeff did jeff talk to
+you about uh crh1
+
+ align:start position:0%
+you about uh crh1
+ 
+
+ align:start position:0%
+you about uh crh1
+did we show you the data about crh1 last
+
+ align:start position:0%
+did we show you the data about crh1 last
+ 
+
+ align:start position:0%
+did we show you the data about crh1 last
+week
+
+ align:start position:0%
+week
+ 
+
+ align:start position:0%
+week
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that gene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gene is expressed is that gene expressed
+
+ align:start position:0%
+gene is expressed is that gene expressed
+ 
+
+ align:start position:0%
+gene is expressed is that gene expressed
+in the lung
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes or no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+not expressed in the lung
+
+ align:start position:0%
+not expressed in the lung
+ 
+
+ align:start position:0%
+not expressed in the lung
+so it's the
+
+ align:start position:0%
+so it's the
+ 
+
+ align:start position:0%
+so it's the
+receptor for crf or crh and it's
+
+ align:start position:0%
+receptor for crf or crh and it's
+ 
+
+ align:start position:0%
+receptor for crf or crh and it's
+expressed in the brain
+
+ align:start position:0%
+expressed in the brain
+ 
+
+ align:start position:0%
+expressed in the brain
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what other disease might that gene
+
+ align:start position:0%
+what other disease might that gene
+ 
+
+ align:start position:0%
+what other disease might that gene
+potentially be important in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he's an endocrinologist he's forbidden
+
+ align:start position:0%
+he's an endocrinologist he's forbidden
+ 
+
+ align:start position:0%
+he's an endocrinologist he's forbidden
+from answering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a comes from the hypothalamus
+
+ align:start position:0%
+it's a comes from the hypothalamus
+ 
+
+ align:start position:0%
+it's a comes from the hypothalamus
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah clinical or pimple disease
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hypertension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are endocrine causes of
+
+ align:start position:0%
+there are endocrine causes of
+ 
+
+ align:start position:0%
+there are endocrine causes of
+hypertension your physiology course yet
+
+ align:start position:0%
+hypertension your physiology course yet
+ 
+
+ align:start position:0%
+hypertension your physiology course yet
+oh no all right
+
+ align:start position:0%
+oh no all right
+ 
+
+ align:start position:0%
+oh no all right
+anybody had physiology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hpa
+
+ align:start position:0%
+hpa
+ 
+
+ align:start position:0%
+hpa
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+no come on i think calm diseases man
+
+ align:start position:0%
+no come on i think calm diseases man
+ 
+
+ align:start position:0%
+no come on i think calm diseases man
+common common common disease
+
+ align:start position:0%
+common common common disease
+ 
+
+ align:start position:0%
+common common common disease
+i'll tell you it's depression okay
+
+ align:start position:0%
+i'll tell you it's depression okay
+ 
+
+ align:start position:0%
+i'll tell you it's depression okay
+it's it's actually it's an it's it's
+
+ align:start position:0%
+it's it's actually it's an it's it's
+ 
+
+ align:start position:0%
+it's it's actually it's an it's it's
+been studied a huge amount and you know
+
+ align:start position:0%
+been studied a huge amount and you know
+ 
+
+ align:start position:0%
+been studied a huge amount and you know
+they've sectioned brains of people who
+
+ align:start position:0%
+they've sectioned brains of people who
+ 
+
+ align:start position:0%
+they've sectioned brains of people who
+committed suicide and this
+
+ align:start position:0%
+committed suicide and this
+ 
+
+ align:start position:0%
+committed suicide and this
+i mean all kinds of things show that cr
+
+ align:start position:0%
+i mean all kinds of things show that cr
+ 
+
+ align:start position:0%
+i mean all kinds of things show that cr
+crf and cr1 which is the ligand and the
+
+ align:start position:0%
+crf and cr1 which is the ligand and the
+ 
+
+ align:start position:0%
+crf and cr1 which is the ligand and the
+receptor are important in
+
+ align:start position:0%
+receptor are important in
+ 
+
+ align:start position:0%
+receptor are important in
+affective disorders is there any linkage
+
+ align:start position:0%
+affective disorders is there any linkage
+ 
+
+ align:start position:0%
+affective disorders is there any linkage
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+there's an association between our
+
+ align:start position:0%
+there's an association between our
+ 
+
+ align:start position:0%
+there's an association between our
+capital type and depression and
+
+ align:start position:0%
+capital type and depression and
+ 
+
+ align:start position:0%
+capital type and depression and
+julia lucinia's mexican-american
+
+ align:start position:0%
+julia lucinia's mexican-american
+ 
+
+ align:start position:0%
+julia lucinia's mexican-american
+yeah oh yeah really cool yeah
+
+ align:start position:0%
+yeah oh yeah really cool yeah
+ 
+
+ align:start position:0%
+yeah oh yeah really cool yeah
+so that's pleiotropy uh and then
+
+ align:start position:0%
+so that's pleiotropy uh and then
+ 
+
+ align:start position:0%
+so that's pleiotropy uh and then
+obviously you've got this problem with
+
+ align:start position:0%
+obviously you've got this problem with
+ 
+
+ align:start position:0%
+obviously you've got this problem with
+penetrance that
+
+ align:start position:0%
+penetrance that
+ 
+
+ align:start position:0%
+penetrance that
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+individuals with a genotype will
+
+ align:start position:0%
+individuals with a genotype will
+ 
+
+ align:start position:0%
+individuals with a genotype will
+actually express the trait
+
+ align:start position:0%
+actually express the trait
+ 
+
+ align:start position:0%
+actually express the trait
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know ige genes can be important in
+
+ align:start position:0%
+you know ige genes can be important in
+ 
+
+ align:start position:0%
+you know ige genes can be important in
+hay fever they can be important in
+
+ align:start position:0%
+hay fever they can be important in
+ 
+
+ align:start position:0%
+hay fever they can be important in
+asthma uh and and there are some people
+
+ align:start position:0%
+asthma uh and and there are some people
+ 
+
+ align:start position:0%
+asthma uh and and there are some people
+who don't have
+
+ align:start position:0%
+who don't have
+ 
+
+ align:start position:0%
+who don't have
+high ig at all even though they've got
+
+ align:start position:0%
+high ig at all even though they've got
+ 
+
+ align:start position:0%
+high ig at all even though they've got
+the gene so uh um
+
+ align:start position:0%
+the gene so uh um
+ 
+
+ align:start position:0%
+the gene so uh um
+and and these are some other examples of
+
+ align:start position:0%
+and and these are some other examples of
+ 
+
+ align:start position:0%
+and and these are some other examples of
+things like the the basic point i'm
+
+ align:start position:0%
+things like the the basic point i'm
+ 
+
+ align:start position:0%
+things like the the basic point i'm
+trying to make here is is that these are
+
+ align:start position:0%
+trying to make here is is that these are
+ 
+
+ align:start position:0%
+trying to make here is is that these are
+reasons that have been given for why
+
+ align:start position:0%
+reasons that have been given for why
+ 
+
+ align:start position:0%
+reasons that have been given for why
+doing this stuff this are
+
+ align:start position:0%
+doing this stuff this are
+ 
+
+ align:start position:0%
+doing this stuff this are
+hard but i'll tell you something the
+
+ align:start position:0%
+hard but i'll tell you something the
+ 
+
+ align:start position:0%
+hard but i'll tell you something the
+really the hard part has been developing
+
+ align:start position:0%
+really the hard part has been developing
+ 
+
+ align:start position:0%
+really the hard part has been developing
+the bioinformatics infrastructure the
+
+ align:start position:0%
+the bioinformatics infrastructure the
+ 
+
+ align:start position:0%
+the bioinformatics infrastructure the
+tools the bioinformatics tools and cheap
+
+ align:start position:0%
+tools the bioinformatics tools and cheap
+ 
+
+ align:start position:0%
+tools the bioinformatics tools and cheap
+reliable
+
+ align:start position:0%
+reliable
+ 
+
+ align:start position:0%
+reliable
+genotyping that those have really been
+
+ align:start position:0%
+genotyping that those have really been
+ 
+
+ align:start position:0%
+genotyping that those have really been
+the things that have been important
+
+ align:start position:0%
+the things that have been important
+ 
+
+ align:start position:0%
+the things that have been important
+and just in the little bit of time that
+
+ align:start position:0%
+and just in the little bit of time that
+ 
+
+ align:start position:0%
+and just in the little bit of time that
+i've been doing this
+
+ align:start position:0%
+i've been doing this
+ 
+
+ align:start position:0%
+i've been doing this
+my genotyping costs are have gone from
+
+ align:start position:0%
+my genotyping costs are have gone from
+ 
+
+ align:start position:0%
+my genotyping costs are have gone from
+a dollar 20 a sniff genotype
+
+ align:start position:0%
+a dollar 20 a sniff genotype
+ 
+
+ align:start position:0%
+a dollar 20 a sniff genotype
+down to next year
+
+ align:start position:0%
+down to next year
+ 
+
+ align:start position:0%
+down to next year
+uh i'll be down at about 15 20 cents of
+
+ align:start position:0%
+uh i'll be down at about 15 20 cents of
+ 
+
+ align:start position:0%
+uh i'll be down at about 15 20 cents of
+sniff genotype
+
+ align:start position:0%
+sniff genotype
+ 
+
+ align:start position:0%
+sniff genotype
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+there are
+
+ align:start position:0%
+there are
+ 
+
+ align:start position:0%
+there are
+three million snips
+
+ align:start position:0%
+three million snips
+ 
+
+ align:start position:0%
+three million snips
+minimum three to five million in the
+
+ align:start position:0%
+minimum three to five million in the
+ 
+
+ align:start position:0%
+minimum three to five million in the
+human genome now i'm not going to type
+
+ align:start position:0%
+human genome now i'm not going to type
+ 
+
+ align:start position:0%
+human genome now i'm not going to type
+it three to five million but i gotta
+
+ align:start position:0%
+it three to five million but i gotta
+ 
+
+ align:start position:0%
+it three to five million but i gotta
+type
+
+ align:start position:0%
+type
+ 
+
+ align:start position:0%
+type
+in any one experiment i got to be able
+
+ align:start position:0%
+in any one experiment i got to be able
+ 
+
+ align:start position:0%
+in any one experiment i got to be able
+to type
+
+ align:start position:0%
+to type
+ 
+
+ align:start position:0%
+to type
+a thousand over a a 10 20
+
+ align:start position:0%
+a thousand over a a 10 20
+ 
+
+ align:start position:0%
+a thousand over a a 10 20
+uh uh um megabase region so
+
+ align:start position:0%
+uh uh um megabase region so
+ 
+
+ align:start position:0%
+uh uh um megabase region so
+you know one of these linkage peaks so i
+
+ align:start position:0%
+you know one of these linkage peaks so i
+ 
+
+ align:start position:0%
+you know one of these linkage peaks so i
+got to do a lot of genotyping in a lot
+
+ align:start position:0%
+got to do a lot of genotyping in a lot
+ 
+
+ align:start position:0%
+got to do a lot of genotyping in a lot
+of people and it's expensive the very
+
+ align:start position:0%
+of people and it's expensive the very
+ 
+
+ align:start position:0%
+of people and it's expensive the very
+first positionally cloned gene for
+
+ align:start position:0%
+first positionally cloned gene for
+ 
+
+ align:start position:0%
+first positionally cloned gene for
+asthma took six years and fifteen point
+
+ align:start position:0%
+asthma took six years and fifteen point
+ 
+
+ align:start position:0%
+asthma took six years and fifteen point
+six million dollars we could do that
+
+ align:start position:0%
+six million dollars we could do that
+ 
+
+ align:start position:0%
+six million dollars we could do that
+experiment today for two million dollars
+
+ align:start position:0%
+experiment today for two million dollars
+ 
+
+ align:start position:0%
+experiment today for two million dollars
+and a regular nih grant and that has
+
+ align:start position:0%
+and a regular nih grant and that has
+ 
+
+ align:start position:0%
+and a regular nih grant and that has
+totally changed the field that's the
+
+ align:start position:0%
+totally changed the field that's the
+ 
+
+ align:start position:0%
+totally changed the field that's the
+kind of thing that's really making
+
+ align:start position:0%
+kind of thing that's really making
+ 
+
+ align:start position:0%
+kind of thing that's really making
+this possible
+
+ align:start position:0%
+this possible
+ 
+
+ align:start position:0%
+this possible
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so i already said that
+
+ align:start position:0%
+okay so i already said that
+ 
+
+ align:start position:0%
+okay so i already said that
+if you're if you're going to think like
+
+ align:start position:0%
+if you're if you're going to think like
+ 
+
+ align:start position:0%
+if you're if you're going to think like
+a geneticist everybody has to know a
+
+ align:start position:0%
+a geneticist everybody has to know a
+ 
+
+ align:start position:0%
+a geneticist everybody has to know a
+little bit of population genetics so you
+
+ align:start position:0%
+little bit of population genetics so you
+ 
+
+ align:start position:0%
+little bit of population genetics so you
+have to understand the concepts of
+
+ align:start position:0%
+have to understand the concepts of
+ 
+
+ align:start position:0%
+have to understand the concepts of
+linkage disequilibrium drifts
+
+ align:start position:0%
+linkage disequilibrium drifts
+ 
+
+ align:start position:0%
+linkage disequilibrium drifts
+natural selection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+et cetera et cetera i'm reminded of the
+
+ align:start position:0%
+et cetera et cetera i'm reminded of the
+ 
+
+ align:start position:0%
+et cetera et cetera i'm reminded of the
+fact that uh somebody asked the
+
+ align:start position:0%
+fact that uh somebody asked the
+ 
+
+ align:start position:0%
+fact that uh somebody asked the
+president united states whether he
+
+ align:start position:0%
+president united states whether he
+ 
+
+ align:start position:0%
+president united states whether he
+believed in evolution and his answer was
+
+ align:start position:0%
+believed in evolution and his answer was
+ 
+
+ align:start position:0%
+believed in evolution and his answer was
+the jury's still out
+
+ align:start position:0%
+the jury's still out
+ 
+
+ align:start position:0%
+the jury's still out
+really yeah
+
+ align:start position:0%
+really yeah
+ 
+
+ align:start position:0%
+really yeah
+that's what he said
+
+ align:start position:0%
+that's what he said
+ 
+
+ align:start position:0%
+that's what he said
+um so this is your former classmate
+
+ align:start position:0%
+um so this is your former classmate
+ 
+
+ align:start position:0%
+um so this is your former classmate
+right right
+
+ align:start position:0%
+right right
+ 
+
+ align:start position:0%
+right right
+um i went to high school with the
+
+ align:start position:0%
+um i went to high school with the
+ 
+
+ align:start position:0%
+um i went to high school with the
+president um
+
+ align:start position:0%
+president um
+ 
+
+ align:start position:0%
+president um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is the first question that you're
+
+ align:start position:0%
+this is the first question that you're
+ 
+
+ align:start position:0%
+this is the first question that you're
+going to get asked
+
+ align:start position:0%
+going to get asked
+ 
+
+ align:start position:0%
+going to get asked
+if you're writing a grant you know the
+
+ align:start position:0%
+if you're writing a grant you know the
+ 
+
+ align:start position:0%
+if you're writing a grant you know the
+first thing that you have to address
+
+ align:start position:0%
+first thing that you have to address
+ 
+
+ align:start position:0%
+first thing that you have to address
+is is the disease or the phenotype that
+
+ align:start position:0%
+is is the disease or the phenotype that
+ 
+
+ align:start position:0%
+is is the disease or the phenotype that
+you're interested in is it heritable so
+
+ align:start position:0%
+you're interested in is it heritable so
+ 
+
+ align:start position:0%
+you're interested in is it heritable so
+there's lots of different ways to
+
+ align:start position:0%
+there's lots of different ways to
+ 
+
+ align:start position:0%
+there's lots of different ways to
+measure this you can
+
+ align:start position:0%
+measure this you can
+ 
+
+ align:start position:0%
+measure this you can
+calculate a heritability estimates you
+
+ align:start position:0%
+calculate a heritability estimates you
+ 
+
+ align:start position:0%
+calculate a heritability estimates you
+can do twin studies you can develop this
+
+ align:start position:0%
+can do twin studies you can develop this
+ 
+
+ align:start position:0%
+can do twin studies you can develop this
+concept of risk to relatives which is
+
+ align:start position:0%
+concept of risk to relatives which is
+ 
+
+ align:start position:0%
+concept of risk to relatives which is
+you know you look at the risk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in in the uh pro bands divided by or
+
+ align:start position:0%
+uh in in the uh pro bands divided by or
+ 
+
+ align:start position:0%
+uh in in the uh pro bands divided by or
+the relatives divided by the risk in the
+
+ align:start position:0%
+the relatives divided by the risk in the
+ 
+
+ align:start position:0%
+the relatives divided by the risk in the
+population at large or you can look at
+
+ align:start position:0%
+population at large or you can look at
+ 
+
+ align:start position:0%
+population at large or you can look at
+familial aggregation but the point is
+
+ align:start position:0%
+familial aggregation but the point is
+ 
+
+ align:start position:0%
+familial aggregation but the point is
+you got to gather the evidence and if
+
+ align:start position:0%
+you got to gather the evidence and if
+ 
+
+ align:start position:0%
+you got to gather the evidence and if
+you don't know that your phenotype is
+
+ align:start position:0%
+you don't know that your phenotype is
+ 
+
+ align:start position:0%
+you don't know that your phenotype is
+heritable you're going to have to
+
+ align:start position:0%
+heritable you're going to have to
+ 
+
+ align:start position:0%
+heritable you're going to have to
+demonstrate that it's heritable before
+
+ align:start position:0%
+demonstrate that it's heritable before
+ 
+
+ align:start position:0%
+demonstrate that it's heritable before
+anybody's going to give you a grant to
+
+ align:start position:0%
+anybody's going to give you a grant to
+ 
+
+ align:start position:0%
+anybody's going to give you a grant to
+study it because that's what geneticists
+
+ align:start position:0%
+study it because that's what geneticists
+ 
+
+ align:start position:0%
+study it because that's what geneticists
+say they say they want to know that
+
+ align:start position:0%
+say they say they want to know that
+ 
+
+ align:start position:0%
+say they say they want to know that
+they want to know the answer to that
+
+ align:start position:0%
+they want to know the answer to that
+ 
+
+ align:start position:0%
+they want to know the answer to that
+question so i i think it's asthma
+
+ align:start position:0%
+question so i i think it's asthma
+ 
+
+ align:start position:0%
+question so i i think it's asthma
+doesn't necessarily have a high
+
+ align:start position:0%
+doesn't necessarily have a high
+ 
+
+ align:start position:0%
+doesn't necessarily have a high
+heritability but it clearly is a
+
+ align:start position:0%
+heritability but it clearly is a
+ 
+
+ align:start position:0%
+heritability but it clearly is a
+heritable disease this is data from one
+
+ align:start position:0%
+heritable disease this is data from one
+ 
+
+ align:start position:0%
+heritable disease this is data from one
+uh a twin study from danish twin
+
+ align:start position:0%
+uh a twin study from danish twin
+ 
+
+ align:start position:0%
+uh a twin study from danish twin
+registry that looked at the concordance
+
+ align:start position:0%
+registry that looked at the concordance
+ 
+
+ align:start position:0%
+registry that looked at the concordance
+of uh um
+
+ align:start position:0%
+of uh um
+ 
+
+ align:start position:0%
+of uh um
+asthma in identical and fraternal twins
+
+ align:start position:0%
+asthma in identical and fraternal twins
+ 
+
+ align:start position:0%
+asthma in identical and fraternal twins
+identical twins share 100 percent of
+
+ align:start position:0%
+identical twins share 100 percent of
+ 
+
+ align:start position:0%
+identical twins share 100 percent of
+their genotype fraternal twins uh uh um
+
+ align:start position:0%
+their genotype fraternal twins uh uh um
+ 
+
+ align:start position:0%
+their genotype fraternal twins uh uh um
+share fifty percent
+
+ align:start position:0%
+share fifty percent
+ 
+
+ align:start position:0%
+share fifty percent
+uh um uh uh of their alleles
+
+ align:start position:0%
+uh um uh uh of their alleles
+ 
+
+ align:start position:0%
+uh um uh uh of their alleles
+you know everybody knows that twins also
+
+ align:start position:0%
+you know everybody knows that twins also
+ 
+
+ align:start position:0%
+you know everybody knows that twins also
+share the environment so that's another
+
+ align:start position:0%
+share the environment so that's another
+ 
+
+ align:start position:0%
+share the environment so that's another
+factor that's uh
+
+ align:start position:0%
+factor that's uh
+ 
+
+ align:start position:0%
+factor that's uh
+at issue here but the reality is is that
+
+ align:start position:0%
+at issue here but the reality is is that
+ 
+
+ align:start position:0%
+at issue here but the reality is is that
+there clearly is evidence of
+
+ align:start position:0%
+there clearly is evidence of
+ 
+
+ align:start position:0%
+there clearly is evidence of
+heritability of the disease you get very
+
+ align:start position:0%
+heritability of the disease you get very
+ 
+
+ align:start position:0%
+heritability of the disease you get very
+different you know that the problem here
+
+ align:start position:0%
+different you know that the problem here
+ 
+
+ align:start position:0%
+different you know that the problem here
+is that heritability estimates are
+
+ align:start position:0%
+is that heritability estimates are
+ 
+
+ align:start position:0%
+is that heritability estimates are
+always dependent on
+
+ align:start position:0%
+always dependent on
+ 
+
+ align:start position:0%
+always dependent on
+environmental exposures as well because
+
+ align:start position:0%
+environmental exposures as well because
+ 
+
+ align:start position:0%
+environmental exposures as well because
+the true underlying model and disease
+
+ align:start position:0%
+the true underlying model and disease
+ 
+
+ align:start position:0%
+the true underlying model and disease
+prevalence so the true underlying model
+
+ align:start position:0%
+prevalence so the true underlying model
+ 
+
+ align:start position:0%
+prevalence so the true underlying model
+for all of these diseases is clearly
+
+ align:start position:0%
+for all of these diseases is clearly
+ 
+
+ align:start position:0%
+for all of these diseases is clearly
+still going to be a gene by environment
+
+ align:start position:0%
+still going to be a gene by environment
+ 
+
+ align:start position:0%
+still going to be a gene by environment
+interaction
+
+ align:start position:0%
+interaction
+ 
+
+ align:start position:0%
+interaction
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+after you've decided that the phenotypes
+
+ align:start position:0%
+after you've decided that the phenotypes
+ 
+
+ align:start position:0%
+after you've decided that the phenotypes
+that you're interested in are heritable
+
+ align:start position:0%
+that you're interested in are heritable
+ 
+
+ align:start position:0%
+that you're interested in are heritable
+then you've got to go out and you've got
+
+ align:start position:0%
+then you've got to go out and you've got
+ 
+
+ align:start position:0%
+then you've got to go out and you've got
+to say okay i've got these phenotypes
+
+ align:start position:0%
+to say okay i've got these phenotypes
+ 
+
+ align:start position:0%
+to say okay i've got these phenotypes
+and i'm going to genotype them
+
+ align:start position:0%
+and i'm going to genotype them
+ 
+
+ align:start position:0%
+and i'm going to genotype them
+in a population you can either look at
+
+ align:start position:0%
+in a population you can either look at
+ 
+
+ align:start position:0%
+in a population you can either look at
+disease phenotypes the advantages of
+
+ align:start position:0%
+disease phenotypes the advantages of
+ 
+
+ align:start position:0%
+disease phenotypes the advantages of
+this is that people want to look at
+
+ align:start position:0%
+this is that people want to look at
+ 
+
+ align:start position:0%
+this is that people want to look at
+asthma they want asthma genes they they
+
+ align:start position:0%
+asthma they want asthma genes they they
+ 
+
+ align:start position:0%
+asthma they want asthma genes they they
+want to find
+
+ align:start position:0%
+want to find
+ 
+
+ align:start position:0%
+want to find
+quote the gene for asthma unquote which
+
+ align:start position:0%
+quote the gene for asthma unquote which
+ 
+
+ align:start position:0%
+quote the gene for asthma unquote which
+we already know is probably a false
+
+ align:start position:0%
+we already know is probably a false
+ 
+
+ align:start position:0%
+we already know is probably a false
+concept
+
+ align:start position:0%
+concept
+ 
+
+ align:start position:0%
+concept
+but the problem with a lot of disease
+
+ align:start position:0%
+but the problem with a lot of disease
+ 
+
+ align:start position:0%
+but the problem with a lot of disease
+phenotypes is that they even though
+
+ align:start position:0%
+phenotypes is that they even though
+ 
+
+ align:start position:0%
+phenotypes is that they even though
+they're maybe binary clinically
+
+ align:start position:0%
+they're maybe binary clinically
+ 
+
+ align:start position:0%
+they're maybe binary clinically
+they may be
+
+ align:start position:0%
+they may be
+ 
+
+ align:start position:0%
+they may be
+real problems in terms of making that
+
+ align:start position:0%
+real problems in terms of making that
+ 
+
+ align:start position:0%
+real problems in terms of making that
+diagnosis
+
+ align:start position:0%
+diagnosis
+ 
+
+ align:start position:0%
+diagnosis
+in a way that would be useful for a a
+
+ align:start position:0%
+in a way that would be useful for a a
+ 
+
+ align:start position:0%
+in a way that would be useful for a a
+research study
+
+ align:start position:0%
+research study
+ 
+
+ align:start position:0%
+research study
+the problem with asthma is it's a
+
+ align:start position:0%
+the problem with asthma is it's a
+ 
+
+ align:start position:0%
+the problem with asthma is it's a
+syndrome right i mean there is no
+
+ align:start position:0%
+syndrome right i mean there is no
+ 
+
+ align:start position:0%
+syndrome right i mean there is no
+one way of diagnosing asthma so that you
+
+ align:start position:0%
+one way of diagnosing asthma so that you
+ 
+
+ align:start position:0%
+one way of diagnosing asthma so that you
+can say you take this test and i can
+
+ align:start position:0%
+can say you take this test and i can
+ 
+
+ align:start position:0%
+can say you take this test and i can
+guarantee you that everybody that takes
+
+ align:start position:0%
+guarantee you that everybody that takes
+ 
+
+ align:start position:0%
+guarantee you that everybody that takes
+this test is going to have the disease
+
+ align:start position:0%
+this test is going to have the disease
+ 
+
+ align:start position:0%
+this test is going to have the disease
+and everybody who has a negative test
+
+ align:start position:0%
+and everybody who has a negative test
+ 
+
+ align:start position:0%
+and everybody who has a negative test
+doesn't have the disease
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah but the fev1 doesn't tell you
+
+ align:start position:0%
+yeah but the fev1 doesn't tell you
+ 
+
+ align:start position:0%
+yeah but the fev1 doesn't tell you
+whether somebody's got asthma or not
+
+ align:start position:0%
+whether somebody's got asthma or not
+ 
+
+ align:start position:0%
+whether somebody's got asthma or not
+i can show you people who have reduced
+
+ align:start position:0%
+i can show you people who have reduced
+ 
+
+ align:start position:0%
+i can show you people who have reduced
+fev1 and have cystic fibrosis or have
+
+ align:start position:0%
+fev1 and have cystic fibrosis or have
+ 
+
+ align:start position:0%
+fev1 and have cystic fibrosis or have
+interstitial lung disease or have uh
+
+ align:start position:0%
+interstitial lung disease or have uh
+ 
+
+ align:start position:0%
+interstitial lung disease or have uh
+copd i mean they can have a lot of
+
+ align:start position:0%
+copd i mean they can have a lot of
+ 
+
+ align:start position:0%
+copd i mean they can have a lot of
+different things right uh so it lacks
+
+ align:start position:0%
+different things right uh so it lacks
+ 
+
+ align:start position:0%
+different things right uh so it lacks
+sensitivity and specificity the fev one
+
+ align:start position:0%
+sensitivity and specificity the fev one
+ 
+
+ align:start position:0%
+sensitivity and specificity the fev one
+and that's true for every single test
+
+ align:start position:0%
+and that's true for every single test
+ 
+
+ align:start position:0%
+and that's true for every single test
+you know i mean
+
+ align:start position:0%
+you know i mean
+ 
+
+ align:start position:0%
+you know i mean
+elevated ige well you could have
+
+ align:start position:0%
+elevated ige well you could have
+ 
+
+ align:start position:0%
+elevated ige well you could have
+elevated ig from parasitic disease or
+
+ align:start position:0%
+elevated ig from parasitic disease or
+ 
+
+ align:start position:0%
+elevated ig from parasitic disease or
+from uh uh uh eosinophilic pneumonia or
+
+ align:start position:0%
+from uh uh uh eosinophilic pneumonia or
+ 
+
+ align:start position:0%
+from uh uh uh eosinophilic pneumonia or
+from 20 other different things so
+
+ align:start position:0%
+from 20 other different things so
+ 
+
+ align:start position:0%
+from 20 other different things so
+there is no single test
+
+ align:start position:0%
+there is no single test
+ 
+
+ align:start position:0%
+there is no single test
+and and and the same may be true for
+
+ align:start position:0%
+and and and the same may be true for
+ 
+
+ align:start position:0%
+and and and the same may be true for
+most complex traits
+
+ align:start position:0%
+most complex traits
+ 
+
+ align:start position:0%
+most complex traits
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there may be some phenotypes that are a
+
+ align:start position:0%
+there may be some phenotypes that are a
+ 
+
+ align:start position:0%
+there may be some phenotypes that are a
+little easier to measure like you know
+
+ align:start position:0%
+little easier to measure like you know
+ 
+
+ align:start position:0%
+little easier to measure like you know
+say well
+
+ align:start position:0%
+say well
+ 
+
+ align:start position:0%
+say well
+i want to study obesity
+
+ align:start position:0%
+i want to study obesity
+ 
+
+ align:start position:0%
+i want to study obesity
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+how fat is fat or
+
+ align:start position:0%
+how fat is fat or
+ 
+
+ align:start position:0%
+how fat is fat or
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+people who are fat like this
+
+ align:start position:0%
+people who are fat like this
+ 
+
+ align:start position:0%
+people who are fat like this
+different from people who are fat like
+
+ align:start position:0%
+different from people who are fat like
+ 
+
+ align:start position:0%
+different from people who are fat like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+you know i mean there's all sorts of
+
+ align:start position:0%
+you know i mean there's all sorts of
+ 
+
+ align:start position:0%
+you know i mean there's all sorts of
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+ways of looking fat so
+
+ align:start position:0%
+ways of looking fat so
+ 
+
+ align:start position:0%
+ways of looking fat so
+or being fat so
+
+ align:start position:0%
+or being fat so
+ 
+
+ align:start position:0%
+or being fat so
+you know any one of these phenotypes has
+
+ align:start position:0%
+you know any one of these phenotypes has
+ 
+
+ align:start position:0%
+you know any one of these phenotypes has
+complications and and and
+
+ align:start position:0%
+complications and and and
+ 
+
+ align:start position:0%
+complications and and and
+i can tell you this from from when i
+
+ align:start position:0%
+i can tell you this from from when i
+ 
+
+ align:start position:0%
+i can tell you this from from when i
+first got into this
+
+ align:start position:0%
+first got into this
+ 
+
+ align:start position:0%
+first got into this
+all i knew was phenotype i was a
+
+ align:start position:0%
+all i knew was phenotype i was a
+ 
+
+ align:start position:0%
+all i knew was phenotype i was a
+world-class phenotyper i knew all of the
+
+ align:start position:0%
+world-class phenotyper i knew all of the
+ 
+
+ align:start position:0%
+world-class phenotyper i knew all of the
+nuances of phenotype and everything
+
+ align:start position:0%
+nuances of phenotype and everything
+ 
+
+ align:start position:0%
+nuances of phenotype and everything
+there is to know about phenotype and
+
+ align:start position:0%
+there is to know about phenotype and
+ 
+
+ align:start position:0%
+there is to know about phenotype and
+that's tends to be what happens when you
+
+ align:start position:0%
+that's tends to be what happens when you
+ 
+
+ align:start position:0%
+that's tends to be what happens when you
+when you talk to clinicians because they
+
+ align:start position:0%
+when you talk to clinicians because they
+ 
+
+ align:start position:0%
+when you talk to clinicians because they
+understand that more so
+
+ align:start position:0%
+understand that more so
+ 
+
+ align:start position:0%
+understand that more so
+this stuff is really really important
+
+ align:start position:0%
+this stuff is really really important
+ 
+
+ align:start position:0%
+this stuff is really really important
+but it's not going to get you very far
+
+ align:start position:0%
+but it's not going to get you very far
+ 
+
+ align:start position:0%
+but it's not going to get you very far
+if you don't know all the other stuff
+
+ align:start position:0%
+if you don't know all the other stuff
+ 
+
+ align:start position:0%
+if you don't know all the other stuff
+you got to know all the other things but
+
+ align:start position:0%
+you got to know all the other things but
+ 
+
+ align:start position:0%
+you got to know all the other things but
+but i'm not i think the point is
+
+ align:start position:0%
+but i'm not i think the point is
+ 
+
+ align:start position:0%
+but i'm not i think the point is
+you do have to know this and again it's
+
+ align:start position:0%
+you do have to know this and again it's
+ 
+
+ align:start position:0%
+you do have to know this and again it's
+the current problem there's a lot of
+
+ align:start position:0%
+the current problem there's a lot of
+ 
+
+ align:start position:0%
+the current problem there's a lot of
+numbers actually
+
+ align:start position:0%
+numbers actually
+ 
+
+ align:start position:0%
+numbers actually
+exactly well it goes back to the point
+
+ align:start position:0%
+exactly well it goes back to the point
+ 
+
+ align:start position:0%
+exactly well it goes back to the point
+that i was making earlier which i think
+
+ align:start position:0%
+that i was making earlier which i think
+ 
+
+ align:start position:0%
+that i was making earlier which i think
+is is that
+
+ align:start position:0%
+is is that
+ 
+
+ align:start position:0%
+is is that
+genetics is moving from a field
+
+ align:start position:0%
+genetics is moving from a field
+ 
+
+ align:start position:0%
+genetics is moving from a field
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+genetics were generalists to a field
+
+ align:start position:0%
+genetics were generalists to a field
+ 
+
+ align:start position:0%
+genetics were generalists to a field
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+geneticists are specialists you get
+
+ align:start position:0%
+geneticists are specialists you get
+ 
+
+ align:start position:0%
+geneticists are specialists you get
+people who specialize in respiratory
+
+ align:start position:0%
+people who specialize in respiratory
+ 
+
+ align:start position:0%
+people who specialize in respiratory
+genetics cardiovascular genetics obesity
+
+ align:start position:0%
+genetics cardiovascular genetics obesity
+ 
+
+ align:start position:0%
+genetics cardiovascular genetics obesity
+genetics diabetes genetics the days of
+
+ align:start position:0%
+genetics diabetes genetics the days of
+ 
+
+ align:start position:0%
+genetics diabetes genetics the days of
+sort of the person that can roam around
+
+ align:start position:0%
+sort of the person that can roam around
+ 
+
+ align:start position:0%
+sort of the person that can roam around
+and do all of these things no no no i
+
+ align:start position:0%
+and do all of these things no no no i
+ 
+
+ align:start position:0%
+and do all of these things no no no i
+don't think that's going to happen
+
+ align:start position:0%
+don't think that's going to happen
+ 
+
+ align:start position:0%
+don't think that's going to happen
+uh in five years six years you're gonna
+
+ align:start position:0%
+uh in five years six years you're gonna
+ 
+
+ align:start position:0%
+uh in five years six years you're gonna
+have to be able to go in there and focus
+
+ align:start position:0%
+have to be able to go in there and focus
+ 
+
+ align:start position:0%
+have to be able to go in there and focus
+on a specific disease because it's going
+
+ align:start position:0%
+on a specific disease because it's going
+ 
+
+ align:start position:0%
+on a specific disease because it's going
+to be too complicated for you to be able
+
+ align:start position:0%
+to be too complicated for you to be able
+ 
+
+ align:start position:0%
+to be too complicated for you to be able
+to do otherwise
+
+ align:start position:0%
+to do otherwise
+ 
+
+ align:start position:0%
+to do otherwise
+then you've got this other type of
+
+ align:start position:0%
+then you've got this other type of
+ 
+
+ align:start position:0%
+then you've got this other type of
+phenotypes where you can say well
+
+ align:start position:0%
+phenotypes where you can say well
+ 
+
+ align:start position:0%
+phenotypes where you can say well
+okay we want to look at asthma
+
+ align:start position:0%
+okay we want to look at asthma
+ 
+
+ align:start position:0%
+okay we want to look at asthma
+but what about looking at intermediate
+
+ align:start position:0%
+but what about looking at intermediate
+ 
+
+ align:start position:0%
+but what about looking at intermediate
+phenotypes
+
+ align:start position:0%
+phenotypes
+ 
+
+ align:start position:0%
+phenotypes
+so give me some examples of an
+
+ align:start position:0%
+so give me some examples of an
+ 
+
+ align:start position:0%
+so give me some examples of an
+intermediate phenotype related to my
+
+ align:start position:0%
+intermediate phenotype related to my
+ 
+
+ align:start position:0%
+intermediate phenotype related to my
+disease of interest what would be an
+
+ align:start position:0%
+disease of interest what would be an
+ 
+
+ align:start position:0%
+disease of interest what would be an
+intermediate phenotype
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolutely fev1 what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i had it up on a number of slides so ige
+
+ align:start position:0%
+i had it up on a number of slides so ige
+ 
+
+ align:start position:0%
+i had it up on a number of slides so ige
+level right the measure of allergy skin
+
+ align:start position:0%
+level right the measure of allergy skin
+ 
+
+ align:start position:0%
+level right the measure of allergy skin
+test reactivity airways responsiveness
+
+ align:start position:0%
+test reactivity airways responsiveness
+ 
+
+ align:start position:0%
+test reactivity airways responsiveness
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symptom score sputum production
+
+ align:start position:0%
+symptom score sputum production
+ 
+
+ align:start position:0%
+symptom score sputum production
+i mean the uh uh exhale then oh i mean
+
+ align:start position:0%
+i mean the uh uh exhale then oh i mean
+ 
+
+ align:start position:0%
+i mean the uh uh exhale then oh i mean
+the list goes on and on and on you can
+
+ align:start position:0%
+the list goes on and on and on you can
+ 
+
+ align:start position:0%
+the list goes on and on and on you can
+create hundreds
+
+ align:start position:0%
+create hundreds
+ 
+
+ align:start position:0%
+create hundreds
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+for obesity you could be looking at
+
+ align:start position:0%
+for obesity you could be looking at
+ 
+
+ align:start position:0%
+for obesity you could be looking at
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+body mass index as the primary phenotype
+
+ align:start position:0%
+body mass index as the primary phenotype
+ 
+
+ align:start position:0%
+body mass index as the primary phenotype
+to define
+
+ align:start position:0%
+to define
+ 
+
+ align:start position:0%
+to define
+obesity but then you could look at
+
+ align:start position:0%
+obesity but then you could look at
+ 
+
+ align:start position:0%
+obesity but then you could look at
+absolute fat mass or percent body fat or
+
+ align:start position:0%
+absolute fat mass or percent body fat or
+ 
+
+ align:start position:0%
+absolute fat mass or percent body fat or
+waist hip ratio or
+
+ align:start position:0%
+waist hip ratio or
+ 
+
+ align:start position:0%
+waist hip ratio or
+insulin resistance or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do ct scans of somebody's abdominal fat
+
+ align:start position:0%
+do ct scans of somebody's abdominal fat
+ 
+
+ align:start position:0%
+do ct scans of somebody's abdominal fat
+deposition i mean there's a million
+
+ align:start position:0%
+deposition i mean there's a million
+ 
+
+ align:start position:0%
+deposition i mean there's a million
+different ways of potentially going at
+
+ align:start position:0%
+different ways of potentially going at
+ 
+
+ align:start position:0%
+different ways of potentially going at
+this the advantage here is is that
+
+ align:start position:0%
+this the advantage here is is that
+ 
+
+ align:start position:0%
+this the advantage here is is that
+sometimes these are more objective than
+
+ align:start position:0%
+sometimes these are more objective than
+ 
+
+ align:start position:0%
+sometimes these are more objective than
+sort of a subjective oh it's asthma it's
+
+ align:start position:0%
+sort of a subjective oh it's asthma it's
+ 
+
+ align:start position:0%
+sort of a subjective oh it's asthma it's
+not asthma um and it may be quote closer
+
+ align:start position:0%
+not asthma um and it may be quote closer
+ 
+
+ align:start position:0%
+not asthma um and it may be quote closer
+to the gene in the sense that you know
+
+ align:start position:0%
+to the gene in the sense that you know
+ 
+
+ align:start position:0%
+to the gene in the sense that you know
+you've got somebody's ige level you know
+
+ align:start position:0%
+you've got somebody's ige level you know
+ 
+
+ align:start position:0%
+you've got somebody's ige level you know
+you have some idea of sort of
+
+ align:start position:0%
+you have some idea of sort of
+ 
+
+ align:start position:0%
+you have some idea of sort of
+genes that determine that and it can be
+
+ align:start position:0%
+genes that determine that and it can be
+ 
+
+ align:start position:0%
+genes that determine that and it can be
+quantitative you can do a
+
+ align:start position:0%
+quantitative you can do a
+ 
+
+ align:start position:0%
+quantitative you can do a
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+approach
+
+ align:start position:0%
+approach
+ 
+
+ align:start position:0%
+approach
+statistically
+
+ align:start position:0%
+statistically
+ 
+
+ align:start position:0%
+statistically
+to quantitative traits then you can use
+
+ align:start position:0%
+to quantitative traits then you can use
+ 
+
+ align:start position:0%
+to quantitative traits then you can use
+if you're looking at binary traits
+
+ align:start position:0%
+if you're looking at binary traits
+ 
+
+ align:start position:0%
+if you're looking at binary traits
+like if someone comes in and
+
+ align:start position:0%
+like if someone comes in and
+ 
+
+ align:start position:0%
+like if someone comes in and
+you look at them and say okay this
+
+ align:start position:0%
+you look at them and say okay this
+ 
+
+ align:start position:0%
+you look at them and say okay this
+person has
+
+ align:start position:0%
+person has
+ 
+
+ align:start position:0%
+person has
+some form of ask
+
+ align:start position:0%
+some form of ask
+ 
+
+ align:start position:0%
+some form of ask
+difficulty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intermediate phenotypes and that
+
+ align:start position:0%
+intermediate phenotypes and that
+ 
+
+ align:start position:0%
+intermediate phenotypes and that
+that correlates them with like narrowing
+
+ align:start position:0%
+that correlates them with like narrowing
+ 
+
+ align:start position:0%
+that correlates them with like narrowing
+the diagnosis from okay you don't really
+
+ align:start position:0%
+the diagnosis from okay you don't really
+ 
+
+ align:start position:0%
+the diagnosis from okay you don't really
+have or you have this so you have this
+
+ align:start position:0%
+have or you have this so you have this
+ 
+
+ align:start position:0%
+have or you have this so you have this
+type of basketball is that
+
+ align:start position:0%
+type of basketball is that
+ 
+
+ align:start position:0%
+type of basketball is that
+well it's it's it's it's it's it it
+
+ align:start position:0%
+well it's it's it's it's it's it it
+ 
+
+ align:start position:0%
+well it's it's it's it's it's it it
+the way i prefer to think about it and i
+
+ align:start position:0%
+the way i prefer to think about it and i
+ 
+
+ align:start position:0%
+the way i prefer to think about it and i
+think it's probably a better way for you
+
+ align:start position:0%
+think it's probably a better way for you
+ 
+
+ align:start position:0%
+think it's probably a better way for you
+to think about it is is it
+
+ align:start position:0%
+to think about it is is it
+ 
+
+ align:start position:0%
+to think about it is is it
+you got to get away from this is where
+
+ align:start position:0%
+you got to get away from this is where
+ 
+
+ align:start position:0%
+you got to get away from this is where
+thinking like a doctor and a clinician
+
+ align:start position:0%
+thinking like a doctor and a clinician
+ 
+
+ align:start position:0%
+thinking like a doctor and a clinician
+is bad in the world of clinical medicine
+
+ align:start position:0%
+is bad in the world of clinical medicine
+ 
+
+ align:start position:0%
+is bad in the world of clinical medicine
+it's just like religion
+
+ align:start position:0%
+it's just like religion
+ 
+
+ align:start position:0%
+it's just like religion
+you either have the disease or you don't
+
+ align:start position:0%
+you either have the disease or you don't
+ 
+
+ align:start position:0%
+you either have the disease or you don't
+there's no such thing as being a little
+
+ align:start position:0%
+there's no such thing as being a little
+ 
+
+ align:start position:0%
+there's no such thing as being a little
+bit pregnant you're pregnant or you're
+
+ align:start position:0%
+bit pregnant you're pregnant or you're
+ 
+
+ align:start position:0%
+bit pregnant you're pregnant or you're
+not pregnant okay
+
+ align:start position:0%
+not pregnant okay
+ 
+
+ align:start position:0%
+not pregnant okay
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+you have to have bypass surgery or you
+
+ align:start position:0%
+you have to have bypass surgery or you
+ 
+
+ align:start position:0%
+you have to have bypass surgery or you
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+clinicians live in a binary world
+
+ align:start position:0%
+clinicians live in a binary world
+ 
+
+ align:start position:0%
+clinicians live in a binary world
+real scientists live in the world of
+
+ align:start position:0%
+real scientists live in the world of
+ 
+
+ align:start position:0%
+real scientists live in the world of
+continuous distributions okay
+
+ align:start position:0%
+continuous distributions okay
+ 
+
+ align:start position:0%
+continuous distributions okay
+so so you you know you can have
+
+ align:start position:0%
+so so you you know you can have
+ 
+
+ align:start position:0%
+so so you you know you can have
+uh uh uh
+
+ align:start position:0%
+uh uh uh
+ 
+
+ align:start position:0%
+uh uh uh
+when when are you fat are you fat with a
+
+ align:start position:0%
+when when are you fat are you fat with a
+ 
+
+ align:start position:0%
+when when are you fat are you fat with a
+body mass index of 23 24 25
+
+ align:start position:0%
+body mass index of 23 24 25
+ 
+
+ align:start position:0%
+body mass index of 23 24 25
+26 when you hi when do you have high
+
+ align:start position:0%
+26 when you hi when do you have high
+ 
+
+ align:start position:0%
+26 when you hi when do you have high
+blood pressure when it's 130 over 80 or
+
+ align:start position:0%
+blood pressure when it's 130 over 80 or
+ 
+
+ align:start position:0%
+blood pressure when it's 130 over 80 or
+140 over 90 or
+
+ align:start position:0%
+140 over 90 or
+ 
+
+ align:start position:0%
+140 over 90 or
+you know you know when when is that so i
+
+ align:start position:0%
+you know you know when when is that so i
+ 
+
+ align:start position:0%
+you know you know when when is that so i
+think that and the other thing is is
+
+ align:start position:0%
+think that and the other thing is is
+ 
+
+ align:start position:0%
+think that and the other thing is is
+that the way to think about these is
+
+ align:start position:0%
+that the way to think about these is
+ 
+
+ align:start position:0%
+that the way to think about these is
+kind of like overlapping venn diagrams
+
+ align:start position:0%
+kind of like overlapping venn diagrams
+ 
+
+ align:start position:0%
+kind of like overlapping venn diagrams
+the clinical phenotype is actually
+
+ align:start position:0%
+the clinical phenotype is actually
+ 
+
+ align:start position:0%
+the clinical phenotype is actually
+a composite of these overlapping venn
+
+ align:start position:0%
+a composite of these overlapping venn
+ 
+
+ align:start position:0%
+a composite of these overlapping venn
+diagrams that are all have separate
+
+ align:start position:0%
+diagrams that are all have separate
+ 
+
+ align:start position:0%
+diagrams that are all have separate
+genetic determinants
+
+ align:start position:0%
+genetic determinants
+ 
+
+ align:start position:0%
+genetic determinants
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+things that
+
+ align:start position:0%
+things that
+ 
+
+ align:start position:0%
+things that
+contribute to them separate genetic and
+
+ align:start position:0%
+contribute to them separate genetic and
+ 
+
+ align:start position:0%
+contribute to them separate genetic and
+environ sort of like dissecting a layer
+
+ align:start position:0%
+environ sort of like dissecting a layer
+ 
+
+ align:start position:0%
+environ sort of like dissecting a layer
+and peeling an onion where you've got
+
+ align:start position:0%
+and peeling an onion where you've got
+ 
+
+ align:start position:0%
+and peeling an onion where you've got
+all these different uh um
+
+ align:start position:0%
+all these different uh um
+ 
+
+ align:start position:0%
+all these different uh um
+different things but i think in in many
+
+ align:start position:0%
+different things but i think in in many
+ 
+
+ align:start position:0%
+different things but i think in in many
+ways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+being a clinician can help
+
+ align:start position:0%
+being a clinician can help
+ 
+
+ align:start position:0%
+being a clinician can help
+you as a research scientist but in some
+
+ align:start position:0%
+you as a research scientist but in some
+ 
+
+ align:start position:0%
+you as a research scientist but in some
+ways it can also hurt because
+
+ align:start position:0%
+ways it can also hurt because
+ 
+
+ align:start position:0%
+ways it can also hurt because
+you start to think in these absolute
+
+ align:start position:0%
+you start to think in these absolute
+ 
+
+ align:start position:0%
+you start to think in these absolute
+terms so i think the better way to think
+
+ align:start position:0%
+terms so i think the better way to think
+ 
+
+ align:start position:0%
+terms so i think the better way to think
+about it is is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these intermediate phenotypes overlapped
+
+ align:start position:0%
+these intermediate phenotypes overlapped
+ 
+
+ align:start position:0%
+these intermediate phenotypes overlapped
+create clinical phenotypes and
+
+ align:start position:0%
+create clinical phenotypes and
+ 
+
+ align:start position:0%
+create clinical phenotypes and
+yes you're what you're trying to do is
+
+ align:start position:0%
+yes you're what you're trying to do is
+ 
+
+ align:start position:0%
+yes you're what you're trying to do is
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+stratify in some way or
+
+ align:start position:0%
+stratify in some way or
+ 
+
+ align:start position:0%
+stratify in some way or
+classify people in some way so you're
+
+ align:start position:0%
+classify people in some way so you're
+ 
+
+ align:start position:0%
+classify people in some way so you're
+you're you're creating homogeneity so
+
+ align:start position:0%
+you're you're creating homogeneity so
+ 
+
+ align:start position:0%
+you're you're creating homogeneity so
+that you can actually identify the
+
+ align:start position:0%
+that you can actually identify the
+ 
+
+ align:start position:0%
+that you can actually identify the
+genetic determinants of
+
+ align:start position:0%
+genetic determinants of
+ 
+
+ align:start position:0%
+genetic determinants of
+of a disease or an intermediate
+
+ align:start position:0%
+of a disease or an intermediate
+ 
+
+ align:start position:0%
+of a disease or an intermediate
+phenotype so you want to go in that
+
+ align:start position:0%
+phenotype so you want to go in that
+ 
+
+ align:start position:0%
+phenotype so you want to go in that
+direction but but most of these things
+
+ align:start position:0%
+direction but but most of these things
+ 
+
+ align:start position:0%
+direction but but most of these things
+lack
+
+ align:start position:0%
+lack
+ 
+
+ align:start position:0%
+lack
+sufficient sensitivity and specificity
+
+ align:start position:0%
+sufficient sensitivity and specificity
+ 
+
+ align:start position:0%
+sufficient sensitivity and specificity
+to really be a uh
+
+ align:start position:0%
+to really be a uh
+ 
+
+ align:start position:0%
+to really be a uh
+terribly helpful this is just a list of
+
+ align:start position:0%
+terribly helpful this is just a list of
+ 
+
+ align:start position:0%
+terribly helpful this is just a list of
+some of the phenotypes that people have
+
+ align:start position:0%
+some of the phenotypes that people have
+ 
+
+ align:start position:0%
+some of the phenotypes that people have
+looked at in asthma i've starred some of
+
+ align:start position:0%
+looked at in asthma i've starred some of
+ 
+
+ align:start position:0%
+looked at in asthma i've starred some of
+the ones that
+
+ align:start position:0%
+the ones that
+ 
+
+ align:start position:0%
+the ones that
+people have focused on in terms of
+
+ align:start position:0%
+people have focused on in terms of
+ 
+
+ align:start position:0%
+people have focused on in terms of
+linkage peaks that have actually been
+
+ align:start position:0%
+linkage peaks that have actually been
+ 
+
+ align:start position:0%
+linkage peaks that have actually been
+identified
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this is interesting because there's
+
+ align:start position:0%
+but this is interesting because there's
+ 
+
+ align:start position:0%
+but this is interesting because there's
+clearly a bias in the literature because
+
+ align:start position:0%
+clearly a bias in the literature because
+ 
+
+ align:start position:0%
+clearly a bias in the literature because
+there's a whole bunch of these other
+
+ align:start position:0%
+there's a whole bunch of these other
+ 
+
+ align:start position:0%
+there's a whole bunch of these other
+phenotypes where
+
+ align:start position:0%
+phenotypes where
+ 
+
+ align:start position:0%
+phenotypes where
+you could just disease and i could
+
+ align:start position:0%
+you could just disease and i could
+ 
+
+ align:start position:0%
+you could just disease and i could
+create a list 30 more of these where
+
+ align:start position:0%
+create a list 30 more of these where
+ 
+
+ align:start position:0%
+create a list 30 more of these where
+people haven't looked it so so this just
+
+ align:start position:0%
+people haven't looked it so so this just
+ 
+
+ align:start position:0%
+people haven't looked it so so this just
+gets to the point that there's plenty of
+
+ align:start position:0%
+gets to the point that there's plenty of
+ 
+
+ align:start position:0%
+gets to the point that there's plenty of
+work here for anybody who wants to do
+
+ align:start position:0%
+work here for anybody who wants to do
+ 
+
+ align:start position:0%
+work here for anybody who wants to do
+this stuff because
+
+ align:start position:0%
+this stuff because
+ 
+
+ align:start position:0%
+this stuff because
+you can go out and i got a junior person
+
+ align:start position:0%
+you can go out and i got a junior person
+ 
+
+ align:start position:0%
+you can go out and i got a junior person
+in my lab he's got a bunch of phenotypes
+
+ align:start position:0%
+in my lab he's got a bunch of phenotypes
+ 
+
+ align:start position:0%
+in my lab he's got a bunch of phenotypes
+that he's really interested in and he's
+
+ align:start position:0%
+that he's really interested in and he's
+ 
+
+ align:start position:0%
+that he's really interested in and he's
+going to go out and he's going to
+
+ align:start position:0%
+going to go out and he's going to
+ 
+
+ align:start position:0%
+going to go out and he's going to
+determine their heritability and then
+
+ align:start position:0%
+determine their heritability and then
+ 
+
+ align:start position:0%
+determine their heritability and then
+he's going to write another grant and
+
+ align:start position:0%
+he's going to write another grant and
+ 
+
+ align:start position:0%
+he's going to write another grant and
+he's going to map the genes for him and
+
+ align:start position:0%
+he's going to map the genes for him and
+ 
+
+ align:start position:0%
+he's going to map the genes for him and
+so on and so forth because he he wants
+
+ align:start position:0%
+so on and so forth because he he wants
+ 
+
+ align:start position:0%
+so on and so forth because he he wants
+to have his own little
+
+ align:start position:0%
+to have his own little
+ 
+
+ align:start position:0%
+to have his own little
+area to sort of work
+
+ align:start position:0%
+area to sort of work
+ 
+
+ align:start position:0%
+area to sort of work
+on so then the next thing so now
+
+ align:start position:0%
+on so then the next thing so now
+ 
+
+ align:start position:0%
+on so then the next thing so now
+we're kind of at the point where you you
+
+ align:start position:0%
+we're kind of at the point where you you
+ 
+
+ align:start position:0%
+we're kind of at the point where you you
+know you gotta i gotta move a little
+
+ align:start position:0%
+know you gotta i gotta move a little
+ 
+
+ align:start position:0%
+know you gotta i gotta move a little
+faster we're not gonna make our way
+
+ align:start position:0%
+faster we're not gonna make our way
+ 
+
+ align:start position:0%
+faster we're not gonna make our way
+through this but you gotta have a study
+
+ align:start position:0%
+through this but you gotta have a study
+ 
+
+ align:start position:0%
+through this but you gotta have a study
+design and there's a bunch of different
+
+ align:start position:0%
+design and there's a bunch of different
+ 
+
+ align:start position:0%
+design and there's a bunch of different
+ways of doing this okay
+
+ align:start position:0%
+ways of doing this okay
+ 
+
+ align:start position:0%
+ways of doing this okay
+you can do linkage you can do
+
+ align:start position:0%
+you can do linkage you can do
+ 
+
+ align:start position:0%
+you can do linkage you can do
+association yeah and and
+
+ align:start position:0%
+association yeah and and
+ 
+
+ align:start position:0%
+association yeah and and
+amongst the linkage studies you can do
+
+ align:start position:0%
+amongst the linkage studies you can do
+ 
+
+ align:start position:0%
+amongst the linkage studies you can do
+allele sharing uh uh um
+
+ align:start position:0%
+allele sharing uh uh um
+ 
+
+ align:start position:0%
+allele sharing uh uh um
+methods which are distribution free or
+
+ align:start position:0%
+methods which are distribution free or
+ 
+
+ align:start position:0%
+methods which are distribution free or
+you can uh um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do sort of um
+
+ align:start position:0%
+do sort of um
+ 
+
+ align:start position:0%
+do sort of um
+continuous distributions and and focus
+
+ align:start position:0%
+continuous distributions and and focus
+ 
+
+ align:start position:0%
+continuous distributions and and focus
+on that
+
+ align:start position:0%
+on that
+ 
+
+ align:start position:0%
+on that
+there are two types of genetic
+
+ align:start position:0%
+there are two types of genetic
+ 
+
+ align:start position:0%
+there are two types of genetic
+association studies the family based and
+
+ align:start position:0%
+association studies the family based and
+ 
+
+ align:start position:0%
+association studies the family based and
+the case control important point here is
+
+ align:start position:0%
+the case control important point here is
+ 
+
+ align:start position:0%
+the case control important point here is
+is that they're very different
+
+ align:start position:0%
+is that they're very different
+ 
+
+ align:start position:0%
+is that they're very different
+you know here you have the genotype
+
+ align:start position:0%
+you know here you have the genotype
+ 
+
+ align:start position:0%
+you know here you have the genotype
+uh three people
+
+ align:start position:0%
+uh three people
+ 
+
+ align:start position:0%
+uh three people
+here you have to genotype only two
+
+ align:start position:0%
+here you have to genotype only two
+ 
+
+ align:start position:0%
+here you have to genotype only two
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+different hypotheses
+
+ align:start position:0%
+different hypotheses
+ 
+
+ align:start position:0%
+different hypotheses
+here you're looking at the
+
+ align:start position:0%
+here you're looking at the
+ 
+
+ align:start position:0%
+here you're looking at the
+alleles or the
+
+ align:start position:0%
+alleles or the
+ 
+
+ align:start position:0%
+alleles or the
+genotypes
+
+ align:start position:0%
+genotypes
+ 
+
+ align:start position:0%
+genotypes
+in the cases relative to the controls
+
+ align:start position:0%
+in the cases relative to the controls
+ 
+
+ align:start position:0%
+in the cases relative to the controls
+it's the little frequency of the
+
+ align:start position:0%
+it's the little frequency of the
+ 
+
+ align:start position:0%
+it's the little frequency of the
+genotype frequency in the cases versus
+
+ align:start position:0%
+genotype frequency in the cases versus
+ 
+
+ align:start position:0%
+genotype frequency in the cases versus
+the controls here you're looking at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transmitted alleles from a heterozygous
+
+ align:start position:0%
+transmitted alleles from a heterozygous
+ 
+
+ align:start position:0%
+transmitted alleles from a heterozygous
+parent to an affected offspring
+
+ align:start position:0%
+parent to an affected offspring
+ 
+
+ align:start position:0%
+parent to an affected offspring
+so very different hypotheses different
+
+ align:start position:0%
+so very different hypotheses different
+ 
+
+ align:start position:0%
+so very different hypotheses different
+study designs
+
+ align:start position:0%
+study designs
+ 
+
+ align:start position:0%
+study designs
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+important thing to recognize is that in
+
+ align:start position:0%
+important thing to recognize is that in
+ 
+
+ align:start position:0%
+important thing to recognize is that in
+any association study
+
+ align:start position:0%
+any association study
+ 
+
+ align:start position:0%
+any association study
+um the association between a variant and
+
+ align:start position:0%
+um the association between a variant and
+ 
+
+ align:start position:0%
+um the association between a variant and
+a phenotype can be due to a causal
+
+ align:start position:0%
+a phenotype can be due to a causal
+ 
+
+ align:start position:0%
+a phenotype can be due to a causal
+relationship it can be the linkage
+
+ align:start position:0%
+relationship it can be the linkage
+ 
+
+ align:start position:0%
+relationship it can be the linkage
+of disequilibrium or it can be due to
+
+ align:start position:0%
+of disequilibrium or it can be due to
+ 
+
+ align:start position:0%
+of disequilibrium or it can be due to
+population admixture which means that
+
+ align:start position:0%
+population admixture which means that
+ 
+
+ align:start position:0%
+population admixture which means that
+usually in the context of a case control
+
+ align:start position:0%
+usually in the context of a case control
+ 
+
+ align:start position:0%
+usually in the context of a case control
+study not a family-based study you've
+
+ align:start position:0%
+study not a family-based study you've
+ 
+
+ align:start position:0%
+study not a family-based study you've
+got different allele frequencies
+
+ align:start position:0%
+got different allele frequencies
+ 
+
+ align:start position:0%
+got different allele frequencies
+segregating in the cases and the
+
+ align:start position:0%
+segregating in the cases and the
+ 
+
+ align:start position:0%
+segregating in the cases and the
+controls because you've got different
+
+ align:start position:0%
+controls because you've got different
+ 
+
+ align:start position:0%
+controls because you've got different
+population histories
+
+ align:start position:0%
+population histories
+ 
+
+ align:start position:0%
+population histories
+evolutionary histories
+
+ align:start position:0%
+evolutionary histories
+ 
+
+ align:start position:0%
+evolutionary histories
+uh uh that have determined those allele
+
+ align:start position:0%
+uh uh that have determined those allele
+ 
+
+ align:start position:0%
+uh uh that have determined those allele
+frequencies so the most extreme example
+
+ align:start position:0%
+frequencies so the most extreme example
+ 
+
+ align:start position:0%
+frequencies so the most extreme example
+would be i had a thousand italian cases
+
+ align:start position:0%
+would be i had a thousand italian cases
+ 
+
+ align:start position:0%
+would be i had a thousand italian cases
+of asthma and i'm comparing it to a
+
+ align:start position:0%
+of asthma and i'm comparing it to a
+ 
+
+ align:start position:0%
+of asthma and i'm comparing it to a
+thousand swiss controls
+
+ align:start position:0%
+thousand swiss controls
+ 
+
+ align:start position:0%
+thousand swiss controls
+uh uh who don't have asthma and even
+
+ align:start position:0%
+uh uh who don't have asthma and even
+ 
+
+ align:start position:0%
+uh uh who don't have asthma and even
+though these two groups are predominant
+
+ align:start position:0%
+though these two groups are predominant
+ 
+
+ align:start position:0%
+though these two groups are predominant
+or caucasian
+
+ align:start position:0%
+or caucasian
+ 
+
+ align:start position:0%
+or caucasian
+their evolutionary history may be
+
+ align:start position:0%
+their evolutionary history may be
+ 
+
+ align:start position:0%
+their evolutionary history may be
+different and the allele frequencies may
+
+ align:start position:0%
+different and the allele frequencies may
+ 
+
+ align:start position:0%
+different and the allele frequencies may
+be different as a result of that so this
+
+ align:start position:0%
+be different as a result of that so this
+ 
+
+ align:start position:0%
+be different as a result of that so this
+is even within an ethnic group
+
+ align:start position:0%
+is even within an ethnic group
+ 
+
+ align:start position:0%
+is even within an ethnic group
+you can get these different allele
+
+ align:start position:0%
+you can get these different allele
+ 
+
+ align:start position:0%
+you can get these different allele
+frequencies and this is because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ethnicity or self-designated ethnicity
+
+ align:start position:0%
+ethnicity or self-designated ethnicity
+ 
+
+ align:start position:0%
+ethnicity or self-designated ethnicity
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+only a weak
+
+ align:start position:0%
+only a weak
+ 
+
+ align:start position:0%
+only a weak
+predictor of evolutionary history
+
+ align:start position:0%
+predictor of evolutionary history
+ 
+
+ align:start position:0%
+predictor of evolutionary history
+i know what's your example or remarkable
+
+ align:start position:0%
+i know what's your example or remarkable
+ 
+
+ align:start position:0%
+i know what's your example or remarkable
+example so you've compared a link
+
+ align:start position:0%
+example so you've compared a link
+ 
+
+ align:start position:0%
+example so you've compared a link
+an association study for costa rica
+
+ align:start position:0%
+an association study for costa rica
+ 
+
+ align:start position:0%
+an association study for costa rica
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+germans and italians with two
+
+ align:start position:0%
+germans and italians with two
+ 
+
+ align:start position:0%
+germans and italians with two
+populations sure enough we find a
+
+ align:start position:0%
+populations sure enough we find a
+ 
+
+ align:start position:0%
+populations sure enough we find a
+linkage association between pasta eating
+
+ align:start position:0%
+linkage association between pasta eating
+ 
+
+ align:start position:0%
+linkage association between pasta eating
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+some peaks
+
+ align:start position:0%
+some peaks
+ 
+
+ align:start position:0%
+some peaks
+um a genome because in fact we'd be
+
+ align:start position:0%
+um a genome because in fact we'd be
+ 
+
+ align:start position:0%
+um a genome because in fact we'd be
+looking for is linkage to the fact that
+
+ align:start position:0%
+looking for is linkage to the fact that
+ 
+
+ align:start position:0%
+looking for is linkage to the fact that
+you're in italian
+
+ align:start position:0%
+you're in italian
+ 
+
+ align:start position:0%
+you're in italian
+and just by the fact that the italians
+
+ align:start position:0%
+and just by the fact that the italians
+ 
+
+ align:start position:0%
+and just by the fact that the italians
+have a distinct distribution of
+
+ align:start position:0%
+have a distinct distribution of
+ 
+
+ align:start position:0%
+have a distinct distribution of
+polymorphisms then the germans gonna
+
+ align:start position:0%
+polymorphisms then the germans gonna
+ 
+
+ align:start position:0%
+polymorphisms then the germans gonna
+create this pasta association when in
+
+ align:start position:0%
+create this pasta association when in
+ 
+
+ align:start position:0%
+create this pasta association when in
+fact when you're looking at different
+
+ align:start position:0%
+fact when you're looking at different
+ 
+
+ align:start position:0%
+fact when you're looking at different
+populations
+
+ align:start position:0%
+populations
+ 
+
+ align:start position:0%
+populations
+so these
+
+ align:start position:0%
+so these
+ 
+
+ align:start position:0%
+so these
+uh some of the guys in my lab wrote an
+
+ align:start position:0%
+uh some of the guys in my lab wrote an
+ 
+
+ align:start position:0%
+uh some of the guys in my lab wrote an
+article
+
+ align:start position:0%
+article
+ 
+
+ align:start position:0%
+article
+demonstrating all of the potential
+
+ align:start position:0%
+demonstrating all of the potential
+ 
+
+ align:start position:0%
+demonstrating all of the potential
+problems in the case control type of
+
+ align:start position:0%
+problems in the case control type of
+ 
+
+ align:start position:0%
+problems in the case control type of
+uh a genetic association study and one
+
+ align:start position:0%
+uh a genetic association study and one
+ 
+
+ align:start position:0%
+uh a genetic association study and one
+of the things that's really impressive
+
+ align:start position:0%
+of the things that's really impressive
+ 
+
+ align:start position:0%
+of the things that's really impressive
+about this paper in science is is it we
+
+ align:start position:0%
+about this paper in science is is it we
+ 
+
+ align:start position:0%
+about this paper in science is is it we
+all use genetic association
+
+ align:start position:0%
+all use genetic association
+ 
+
+ align:start position:0%
+all use genetic association
+as part of the fine mapping process to
+
+ align:start position:0%
+as part of the fine mapping process to
+ 
+
+ align:start position:0%
+as part of the fine mapping process to
+map a linkage peak
+
+ align:start position:0%
+map a linkage peak
+ 
+
+ align:start position:0%
+map a linkage peak
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+this is very important but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because even if you can get rid of the
+
+ align:start position:0%
+because even if you can get rid of the
+ 
+
+ align:start position:0%
+because even if you can get rid of the
+population admixture problem
+
+ align:start position:0%
+population admixture problem
+ 
+
+ align:start position:0%
+population admixture problem
+linkage this equilibrium is always an
+
+ align:start position:0%
+linkage this equilibrium is always an
+ 
+
+ align:start position:0%
+linkage this equilibrium is always an
+issue and so you're never going to know
+
+ align:start position:0%
+issue and so you're never going to know
+ 
+
+ align:start position:0%
+issue and so you're never going to know
+for sure if you're
+
+ align:start position:0%
+for sure if you're
+ 
+
+ align:start position:0%
+for sure if you're
+at the gene
+
+ align:start position:0%
+at the gene
+ 
+
+ align:start position:0%
+at the gene
+or you're just close by to it
+
+ align:start position:0%
+or you're just close by to it
+ 
+
+ align:start position:0%
+or you're just close by to it
+and so you're gonna have to have
+
+ align:start position:0%
+and so you're gonna have to have
+ 
+
+ align:start position:0%
+and so you're gonna have to have
+something else
+
+ align:start position:0%
+something else
+ 
+
+ align:start position:0%
+something else
+to show that you've actually found the
+
+ align:start position:0%
+to show that you've actually found the
+ 
+
+ align:start position:0%
+to show that you've actually found the
+gene you're not getting into science
+
+ align:start position:0%
+gene you're not getting into science
+ 
+
+ align:start position:0%
+gene you're not getting into science
+just with genetic association
+
+ align:start position:0%
+just with genetic association
+ 
+
+ align:start position:0%
+just with genetic association
+okay and so the people in the paper
+
+ align:start position:0%
+okay and so the people in the paper
+ 
+
+ align:start position:0%
+okay and so the people in the paper
+that's coming out this week
+
+ align:start position:0%
+that's coming out this week
+ 
+
+ align:start position:0%
+that's coming out this week
+they have
+
+ align:start position:0%
+they have
+ 
+
+ align:start position:0%
+they have
+expressed the gene
+
+ align:start position:0%
+expressed the gene
+ 
+
+ align:start position:0%
+expressed the gene
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+bronchial tissue they've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done immunohistochemistry to show that
+
+ align:start position:0%
+done immunohistochemistry to show that
+ 
+
+ align:start position:0%
+done immunohistochemistry to show that
+the gene is expressed in epithelium uh
+
+ align:start position:0%
+the gene is expressed in epithelium uh
+ 
+
+ align:start position:0%
+the gene is expressed in epithelium uh
+they replicated their results in a
+
+ align:start position:0%
+they replicated their results in a
+ 
+
+ align:start position:0%
+they replicated their results in a
+different population et cetera et cetera
+
+ align:start position:0%
+different population et cetera et cetera
+ 
+
+ align:start position:0%
+different population et cetera et cetera
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the the thing about the candidate
+
+ align:start position:0%
+the the thing about the candidate
+ 
+
+ align:start position:0%
+the the thing about the candidate
+about about the case control studies and
+
+ align:start position:0%
+about about the case control studies and
+ 
+
+ align:start position:0%
+about about the case control studies and
+about even family based association is
+
+ align:start position:0%
+about even family based association is
+ 
+
+ align:start position:0%
+about even family based association is
+that these studies are really easy to do
+
+ align:start position:0%
+that these studies are really easy to do
+ 
+
+ align:start position:0%
+that these studies are really easy to do
+and so there's lots of them in the
+
+ align:start position:0%
+and so there's lots of them in the
+ 
+
+ align:start position:0%
+and so there's lots of them in the
+literature so it's really important for
+
+ align:start position:0%
+literature so it's really important for
+ 
+
+ align:start position:0%
+literature so it's really important for
+you to know you know going back to this
+
+ align:start position:0%
+you to know you know going back to this
+ 
+
+ align:start position:0%
+you to know you know going back to this
+slide it's really important for you to
+
+ align:start position:0%
+slide it's really important for you to
+ 
+
+ align:start position:0%
+slide it's really important for you to
+sort of know
+
+ align:start position:0%
+sort of know
+ 
+
+ align:start position:0%
+sort of know
+these potential problems
+
+ align:start position:0%
+these potential problems
+ 
+
+ align:start position:0%
+these potential problems
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+you want to be able to read this
+
+ align:start position:0%
+you want to be able to read this
+ 
+
+ align:start position:0%
+you want to be able to read this
+literature and say yeah these guys
+
+ align:start position:0%
+literature and say yeah these guys
+ 
+
+ align:start position:0%
+literature and say yeah these guys
+really found something or maybe they
+
+ align:start position:0%
+really found something or maybe they
+ 
+
+ align:start position:0%
+really found something or maybe they
+didn't
+
+ align:start position:0%
+didn't
+ 
+
+ align:start position:0%
+didn't
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the advantages of this candidate
+
+ align:start position:0%
+the advantages of this candidate
+ 
+
+ align:start position:0%
+the advantages of this candidate
+gene thing is is that it's
+
+ align:start position:0%
+gene thing is is that it's
+ 
+
+ align:start position:0%
+gene thing is is that it's
+cheap and easy the the the the
+
+ align:start position:0%
+cheap and easy the the the the
+ 
+
+ align:start position:0%
+cheap and easy the the the the
+you compare remember i said that now
+
+ align:start position:0%
+you compare remember i said that now
+ 
+
+ align:start position:0%
+you compare remember i said that now
+four positionally cloned genes that have
+
+ align:start position:0%
+four positionally cloned genes that have
+ 
+
+ align:start position:0%
+four positionally cloned genes that have
+used
+
+ align:start position:0%
+used
+ 
+
+ align:start position:0%
+used
+this type of genome screen
+
+ align:start position:0%
+this type of genome screen
+ 
+
+ align:start position:0%
+this type of genome screen
+approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+that have been identified since the
+
+ align:start position:0%
+that have been identified since the
+ 
+
+ align:start position:0%
+that have been identified since the
+human genome was mapped in 1996 well you
+
+ align:start position:0%
+human genome was mapped in 1996 well you
+ 
+
+ align:start position:0%
+human genome was mapped in 1996 well you
+know that's
+
+ align:start position:0%
+know that's
+ 
+
+ align:start position:0%
+know that's
+seven years that's not even one gene a
+
+ align:start position:0%
+seven years that's not even one gene a
+ 
+
+ align:start position:0%
+seven years that's not even one gene a
+year that's pretty meek
+
+ align:start position:0%
+year that's pretty meek
+ 
+
+ align:start position:0%
+year that's pretty meek
+or weak
+
+ align:start position:0%
+or weak
+ 
+
+ align:start position:0%
+or weak
+that's because this is very
+
+ align:start position:0%
+that's because this is very
+ 
+
+ align:start position:0%
+that's because this is very
+expensive technologically intensive but
+
+ align:start position:0%
+expensive technologically intensive but
+ 
+
+ align:start position:0%
+expensive technologically intensive but
+the thing that's great about this is you
+
+ align:start position:0%
+the thing that's great about this is you
+ 
+
+ align:start position:0%
+the thing that's great about this is you
+come up with a novel gene at the end of
+
+ align:start position:0%
+come up with a novel gene at the end of
+ 
+
+ align:start position:0%
+come up with a novel gene at the end of
+the time so you know it's not dependent
+
+ align:start position:0%
+the time so you know it's not dependent
+ 
+
+ align:start position:0%
+the time so you know it's not dependent
+on what anybody knows about pathobiology
+
+ align:start position:0%
+on what anybody knows about pathobiology
+ 
+
+ align:start position:0%
+on what anybody knows about pathobiology
+so you could go this way you could say
+
+ align:start position:0%
+so you could go this way you could say
+ 
+
+ align:start position:0%
+so you could go this way you could say
+look i know
+
+ align:start position:0%
+look i know
+ 
+
+ align:start position:0%
+look i know
+that ige is important in asthma so i
+
+ align:start position:0%
+that ige is important in asthma so i
+ 
+
+ align:start position:0%
+that ige is important in asthma so i
+know that we ought to be screening
+
+ align:start position:0%
+know that we ought to be screening
+ 
+
+ align:start position:0%
+know that we ought to be screening
+il13 il4 l4 receptor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ctla4 all of those genes in the pathway
+
+ align:start position:0%
+ctla4 all of those genes in the pathway
+ 
+
+ align:start position:0%
+ctla4 all of those genes in the pathway
+that determines ig makes sense right
+
+ align:start position:0%
+that determines ig makes sense right
+ 
+
+ align:start position:0%
+that determines ig makes sense right
+screen those genes because
+
+ align:start position:0%
+screen those genes because
+ 
+
+ align:start position:0%
+screen those genes because
+we've already said that people with
+
+ align:start position:0%
+we've already said that people with
+ 
+
+ align:start position:0%
+we've already said that people with
+asthma have high ig well
+
+ align:start position:0%
+asthma have high ig well
+ 
+
+ align:start position:0%
+asthma have high ig well
+you know you you check those genes and
+
+ align:start position:0%
+you know you you check those genes and
+ 
+
+ align:start position:0%
+you know you you check those genes and
+yeah in fact they are
+
+ align:start position:0%
+yeah in fact they are
+ 
+
+ align:start position:0%
+yeah in fact they are
+most of those genes are
+
+ align:start position:0%
+most of those genes are
+ 
+
+ align:start position:0%
+most of those genes are
+asthma
+
+ align:start position:0%
+asthma
+ 
+
+ align:start position:0%
+asthma
+allergy genes it's not kind of not real
+
+ align:start position:0%
+allergy genes it's not kind of not real
+ 
+
+ align:start position:0%
+allergy genes it's not kind of not real
+exciting though you know it's not like
+
+ align:start position:0%
+exciting though you know it's not like
+ 
+
+ align:start position:0%
+exciting though you know it's not like
+everybody's gonna jump up and say oh my
+
+ align:start position:0%
+everybody's gonna jump up and say oh my
+ 
+
+ align:start position:0%
+everybody's gonna jump up and say oh my
+god you know io13 is an asthma gene well
+
+ align:start position:0%
+god you know io13 is an asthma gene well
+ 
+
+ align:start position:0%
+god you know io13 is an asthma gene well
+you know molecular biologist says yeah
+
+ align:start position:0%
+you know molecular biologist says yeah
+ 
+
+ align:start position:0%
+you know molecular biologist says yeah
+well we knew that 10 years ago what's
+
+ align:start position:0%
+well we knew that 10 years ago what's
+ 
+
+ align:start position:0%
+well we knew that 10 years ago what's
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+what's great about that well
+
+ align:start position:0%
+what's great about that well
+ 
+
+ align:start position:0%
+what's great about that well
+i mean
+
+ align:start position:0%
+i mean
+ 
+
+ align:start position:0%
+i mean
+there are interesting things about it
+
+ align:start position:0%
+there are interesting things about it
+ 
+
+ align:start position:0%
+there are interesting things about it
+because you actually can get to the
+
+ align:start position:0%
+because you actually can get to the
+ 
+
+ align:start position:0%
+because you actually can get to the
+level it's going to change molecular
+
+ align:start position:0%
+level it's going to change molecular
+ 
+
+ align:start position:0%
+level it's going to change molecular
+biology too because you're actually
+
+ align:start position:0%
+biology too because you're actually
+ 
+
+ align:start position:0%
+biology too because you're actually
+going to get the level where you say
+
+ align:start position:0%
+going to get the level where you say
+ 
+
+ align:start position:0%
+going to get the level where you say
+well it's these three variants in the
+
+ align:start position:0%
+well it's these three variants in the
+ 
+
+ align:start position:0%
+well it's these three variants in the
+promoter it's this variant in exon one
+
+ align:start position:0%
+promoter it's this variant in exon one
+ 
+
+ align:start position:0%
+promoter it's this variant in exon one
+and it's this particular haplotype
+
+ align:start position:0%
+and it's this particular haplotype
+ 
+
+ align:start position:0%
+and it's this particular haplotype
+that's determining the effect on ige
+
+ align:start position:0%
+that's determining the effect on ige
+ 
+
+ align:start position:0%
+that's determining the effect on ige
+level so
+
+ align:start position:0%
+level so
+ 
+
+ align:start position:0%
+level so
+molecular biology is going to change
+
+ align:start position:0%
+molecular biology is going to change
+ 
+
+ align:start position:0%
+molecular biology is going to change
+because people aren't going to just be
+
+ align:start position:0%
+because people aren't going to just be
+ 
+
+ align:start position:0%
+because people aren't going to just be
+aren't going to get away with knocking
+
+ align:start position:0%
+aren't going to get away with knocking
+ 
+
+ align:start position:0%
+aren't going to get away with knocking
+out a gene or or looking at a whole
+
+ align:start position:0%
+out a gene or or looking at a whole
+ 
+
+ align:start position:0%
+out a gene or or looking at a whole
+gene effect they're going to actually
+
+ align:start position:0%
+gene effect they're going to actually
+ 
+
+ align:start position:0%
+gene effect they're going to actually
+have to go in there and determine
+
+ align:start position:0%
+have to go in there and determine
+ 
+
+ align:start position:0%
+have to go in there and determine
+the particular variants that are
+
+ align:start position:0%
+the particular variants that are
+ 
+
+ align:start position:0%
+the particular variants that are
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+in terms of the molecular mechanisms
+
+ align:start position:0%
+in terms of the molecular mechanisms
+ 
+
+ align:start position:0%
+in terms of the molecular mechanisms
+so i don't want to sort of then
+
+ align:start position:0%
+so i don't want to sort of then
+ 
+
+ align:start position:0%
+so i don't want to sort of then
+denigrate this because i this is we do
+
+ align:start position:0%
+denigrate this because i this is we do
+ 
+
+ align:start position:0%
+denigrate this because i this is we do
+all of us do a lot of this stuff
+
+ align:start position:0%
+all of us do a lot of this stuff
+ 
+
+ align:start position:0%
+all of us do a lot of this stuff
+to keep ourselves busy while we're
+
+ align:start position:0%
+to keep ourselves busy while we're
+ 
+
+ align:start position:0%
+to keep ourselves busy while we're
+trying to do these really big
+
+ align:start position:0%
+trying to do these really big
+ 
+
+ align:start position:0%
+trying to do these really big
+experiments that are very expensive and
+
+ align:start position:0%
+experiments that are very expensive and
+ 
+
+ align:start position:0%
+experiments that are very expensive and
+take a long time
+
+ align:start position:0%
+take a long time
+ 
+
+ align:start position:0%
+take a long time
+um skip that so let's talk a little bit
+
+ align:start position:0%
+um skip that so let's talk a little bit
+ 
+
+ align:start position:0%
+um skip that so let's talk a little bit
+about linkage linkage is this idea of
+
+ align:start position:0%
+about linkage linkage is this idea of
+ 
+
+ align:start position:0%
+about linkage linkage is this idea of
+you take these microsatellite markers
+
+ align:start position:0%
+you take these microsatellite markers
+ 
+
+ align:start position:0%
+you take these microsatellite markers
+all the way across the genome
+
+ align:start position:0%
+all the way across the genome
+ 
+
+ align:start position:0%
+all the way across the genome
+it's a property of families it's not a
+
+ align:start position:0%
+it's a property of families it's not a
+ 
+
+ align:start position:0%
+it's a property of families it's not a
+property of individuals and you're
+
+ align:start position:0%
+property of individuals and you're
+ 
+
+ align:start position:0%
+property of individuals and you're
+looking to see if there's a particular
+
+ align:start position:0%
+looking to see if there's a particular
+ 
+
+ align:start position:0%
+looking to see if there's a particular
+region of the genome contains a gene
+
+ align:start position:0%
+region of the genome contains a gene
+ 
+
+ align:start position:0%
+region of the genome contains a gene
+that's related to the phenotype of
+
+ align:start position:0%
+that's related to the phenotype of
+ 
+
+ align:start position:0%
+that's related to the phenotype of
+interest that's segregating uh in these
+
+ align:start position:0%
+interest that's segregating uh in these
+ 
+
+ align:start position:0%
+interest that's segregating uh in these
+families uh um
+
+ align:start position:0%
+families uh um
+ 
+
+ align:start position:0%
+families uh um
+uh uh uh
+
+ align:start position:0%
+uh uh uh
+ 
+
+ align:start position:0%
+uh uh uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+using identity by dissent so
+
+ align:start position:0%
+using identity by dissent so
+ 
+
+ align:start position:0%
+using identity by dissent so
+what you do is you know you have some
+
+ align:start position:0%
+what you do is you know you have some
+ 
+
+ align:start position:0%
+what you do is you know you have some
+extended pedigree like this
+
+ align:start position:0%
+extended pedigree like this
+ 
+
+ align:start position:0%
+extended pedigree like this
+what you could do
+
+ align:start position:0%
+what you could do
+ 
+
+ align:start position:0%
+what you could do
+is you could
+
+ align:start position:0%
+is you could
+ 
+
+ align:start position:0%
+is you could
+do segregation analysis to develop a
+
+ align:start position:0%
+do segregation analysis to develop a
+ 
+
+ align:start position:0%
+do segregation analysis to develop a
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+to see how the disease is actually
+
+ align:start position:0%
+to see how the disease is actually
+ 
+
+ align:start position:0%
+to see how the disease is actually
+segregating in this population but
+
+ align:start position:0%
+segregating in this population but
+ 
+
+ align:start position:0%
+segregating in this population but
+that's pretty difficult for complex
+
+ align:start position:0%
+that's pretty difficult for complex
+ 
+
+ align:start position:0%
+that's pretty difficult for complex
+traits it's not easy to do
+
+ align:start position:0%
+traits it's not easy to do
+ 
+
+ align:start position:0%
+traits it's not easy to do
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you could also
+
+ align:start position:0%
+you could also
+ 
+
+ align:start position:0%
+you could also
+use this approach the allele sharing
+
+ align:start position:0%
+use this approach the allele sharing
+ 
+
+ align:start position:0%
+use this approach the allele sharing
+approach which assumes no mode of
+
+ align:start position:0%
+approach which assumes no mode of
+ 
+
+ align:start position:0%
+approach which assumes no mode of
+inheritance just says we collected a
+
+ align:start position:0%
+inheritance just says we collected a
+ 
+
+ align:start position:0%
+inheritance just says we collected a
+whole bunch of sib pairs who are
+
+ align:start position:0%
+whole bunch of sib pairs who are
+ 
+
+ align:start position:0%
+whole bunch of sib pairs who are
+affected and we're going to test whether
+
+ align:start position:0%
+affected and we're going to test whether
+ 
+
+ align:start position:0%
+affected and we're going to test whether
+these affected
+
+ align:start position:0%
+these affected
+ 
+
+ align:start position:0%
+these affected
+relatives have inherited a region
+
+ align:start position:0%
+relatives have inherited a region
+ 
+
+ align:start position:0%
+relatives have inherited a region
+of the genome identity by descent more
+
+ align:start position:0%
+of the genome identity by descent more
+ 
+
+ align:start position:0%
+of the genome identity by descent more
+often than expected under random
+
+ align:start position:0%
+often than expected under random
+ 
+
+ align:start position:0%
+often than expected under random
+mendelian segregation and the nice thing
+
+ align:start position:0%
+mendelian segregation and the nice thing
+ 
+
+ align:start position:0%
+mendelian segregation and the nice thing
+about this is that it's easy but it's
+
+ align:start position:0%
+about this is that it's easy but it's
+ 
+
+ align:start position:0%
+about this is that it's easy but it's
+not very powerful i mean the problem is
+
+ align:start position:0%
+not very powerful i mean the problem is
+ 
+
+ align:start position:0%
+not very powerful i mean the problem is
+you need a lot of sid pairs
+
+ align:start position:0%
+you need a lot of sid pairs
+ 
+
+ align:start position:0%
+you need a lot of sid pairs
+uh and even then even with over 300 sid
+
+ align:start position:0%
+uh and even then even with over 300 sid
+ 
+
+ align:start position:0%
+uh and even then even with over 300 sid
+pairs you don't get such great power um
+
+ align:start position:0%
+pairs you don't get such great power um
+ 
+
+ align:start position:0%
+pairs you don't get such great power um
+using this approach so uh um
+
+ align:start position:0%
+using this approach so uh um
+ 
+
+ align:start position:0%
+using this approach so uh um
+power goes up
+
+ align:start position:0%
+power goes up
+ 
+
+ align:start position:0%
+power goes up
+if the disease is more heritable
+
+ align:start position:0%
+if the disease is more heritable
+ 
+
+ align:start position:0%
+if the disease is more heritable
+um and you can do with less sid pairs
+
+ align:start position:0%
+um and you can do with less sid pairs
+ 
+
+ align:start position:0%
+um and you can do with less sid pairs
+but the reality is is that even with a
+
+ align:start position:0%
+but the reality is is that even with a
+ 
+
+ align:start position:0%
+but the reality is is that even with a
+huge number of sid pairs you you may not
+
+ align:start position:0%
+huge number of sid pairs you you may not
+ 
+
+ align:start position:0%
+huge number of sid pairs you you may not
+have a lot of power if the lambda
+
+ align:start position:0%
+have a lot of power if the lambda
+ 
+
+ align:start position:0%
+have a lot of power if the lambda
+is down here
+
+ align:start position:0%
+is down here
+ 
+
+ align:start position:0%
+is down here
+which it is for asthma probably so
+
+ align:start position:0%
+which it is for asthma probably so
+ 
+
+ align:start position:0%
+which it is for asthma probably so
+i think that this is why
+
+ align:start position:0%
+i think that this is why
+ 
+
+ align:start position:0%
+i think that this is why
+people have focused on
+
+ align:start position:0%
+people have focused on
+ 
+
+ align:start position:0%
+people have focused on
+extended pedigrees in these relative
+
+ align:start position:0%
+extended pedigrees in these relative
+ 
+
+ align:start position:0%
+extended pedigrees in these relative
+genetic isolates and that's why we're so
+
+ align:start position:0%
+genetic isolates and that's why we're so
+ 
+
+ align:start position:0%
+genetic isolates and that's why we're so
+excited about costa rica uh the finns
+
+ align:start position:0%
+excited about costa rica uh the finns
+ 
+
+ align:start position:0%
+excited about costa rica uh the finns
+are clearly excited about finland and
+
+ align:start position:0%
+are clearly excited about finland and
+ 
+
+ align:start position:0%
+are clearly excited about finland and
+decode is
+
+ align:start position:0%
+decode is
+ 
+
+ align:start position:0%
+decode is
+doing what it's doing in iceland
+
+ align:start position:0%
+doing what it's doing in iceland
+ 
+
+ align:start position:0%
+doing what it's doing in iceland
+um whether we're going to be successful
+
+ align:start position:0%
+um whether we're going to be successful
+ 
+
+ align:start position:0%
+um whether we're going to be successful
+or not i don't know but
+
+ align:start position:0%
+or not i don't know but
+ 
+
+ align:start position:0%
+or not i don't know but
+the basic approach is is that whether
+
+ align:start position:0%
+the basic approach is is that whether
+ 
+
+ align:start position:0%
+the basic approach is is that whether
+you're using an outbred population or a
+
+ align:start position:0%
+you're using an outbred population or a
+ 
+
+ align:start position:0%
+you're using an outbred population or a
+genetic isolate and whether you're using
+
+ align:start position:0%
+genetic isolate and whether you're using
+ 
+
+ align:start position:0%
+genetic isolate and whether you're using
+sib pairs or pedigrees is you've got
+
+ align:start position:0%
+sib pairs or pedigrees is you've got
+ 
+
+ align:start position:0%
+sib pairs or pedigrees is you've got
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+usually die and try nucleotide repeat uh
+
+ align:start position:0%
+usually die and try nucleotide repeat uh
+ 
+
+ align:start position:0%
+usually die and try nucleotide repeat uh
+str microsatellite markers
+
+ align:start position:0%
+str microsatellite markers
+ 
+
+ align:start position:0%
+str microsatellite markers
+um most of the genome services use about
+
+ align:start position:0%
+um most of the genome services use about
+ 
+
+ align:start position:0%
+um most of the genome services use about
+400 of these markers
+
+ align:start position:0%
+400 of these markers
+ 
+
+ align:start position:0%
+400 of these markers
+equally randomly spaced across the
+
+ align:start position:0%
+equally randomly spaced across the
+ 
+
+ align:start position:0%
+equally randomly spaced across the
+genome and what you do is you do just
+
+ align:start position:0%
+genome and what you do is you do just
+ 
+
+ align:start position:0%
+genome and what you do is you do just
+do a form of logistic regression
+
+ align:start position:0%
+do a form of logistic regression
+ 
+
+ align:start position:0%
+do a form of logistic regression
+basically where you would do a lot score
+
+ align:start position:0%
+basically where you would do a lot score
+ 
+
+ align:start position:0%
+basically where you would do a lot score
+log of the odds ratio calculation
+
+ align:start position:0%
+log of the odds ratio calculation
+ 
+
+ align:start position:0%
+log of the odds ratio calculation
+between relating phenotype in the family
+
+ align:start position:0%
+between relating phenotype in the family
+ 
+
+ align:start position:0%
+between relating phenotype in the family
+to these markers and what you do is you
+
+ align:start position:0%
+to these markers and what you do is you
+ 
+
+ align:start position:0%
+to these markers and what you do is you
+get a peak a linkage peak that is the
+
+ align:start position:0%
+get a peak a linkage peak that is the
+ 
+
+ align:start position:0%
+get a peak a linkage peak that is the
+lod score
+
+ align:start position:0%
+lod score
+ 
+
+ align:start position:0%
+lod score
+for that relationship between the
+
+ align:start position:0%
+for that relationship between the
+ 
+
+ align:start position:0%
+for that relationship between the
+markers and
+
+ align:start position:0%
+markers and
+ 
+
+ align:start position:0%
+markers and
+the uh um the phenotype and what that
+
+ align:start position:0%
+the uh um the phenotype and what that
+ 
+
+ align:start position:0%
+the uh um the phenotype and what that
+says is
+
+ align:start position:0%
+says is
+ 
+
+ align:start position:0%
+says is
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+there's a gene or multiple genes in this
+
+ align:start position:0%
+there's a gene or multiple genes in this
+ 
+
+ align:start position:0%
+there's a gene or multiple genes in this
+particular region on a chromosome that's
+
+ align:start position:0%
+particular region on a chromosome that's
+ 
+
+ align:start position:0%
+particular region on a chromosome that's
+associated with a particular phenotype
+
+ align:start position:0%
+associated with a particular phenotype
+ 
+
+ align:start position:0%
+associated with a particular phenotype
+and then you have to then going down and
+
+ align:start position:0%
+and then you have to then going down and
+ 
+
+ align:start position:0%
+and then you have to then going down and
+put more markers first more str markers
+
+ align:start position:0%
+put more markers first more str markers
+ 
+
+ align:start position:0%
+put more markers first more str markers
+and then micro uh snips and and
+
+ align:start position:0%
+and then micro uh snips and and
+ 
+
+ align:start position:0%
+and then micro uh snips and and
+gradually map that region until you've
+
+ align:start position:0%
+gradually map that region until you've
+ 
+
+ align:start position:0%
+gradually map that region until you've
+actually got it down to a very very
+
+ align:start position:0%
+actually got it down to a very very
+ 
+
+ align:start position:0%
+actually got it down to a very very
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+region of a particular
+
+ align:start position:0%
+region of a particular
+ 
+
+ align:start position:0%
+region of a particular
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+thousand base pairs or whatever we can
+
+ align:start position:0%
+thousand base pairs or whatever we can
+ 
+
+ align:start position:0%
+thousand base pairs or whatever we can
+say it's a gene or
+
+ align:start position:0%
+say it's a gene or
+ 
+
+ align:start position:0%
+say it's a gene or
+one or two genes in this uh a relatively
+
+ align:start position:0%
+one or two genes in this uh a relatively
+ 
+
+ align:start position:0%
+one or two genes in this uh a relatively
+large region so that's that takes a lot
+
+ align:start position:0%
+large region so that's that takes a lot
+ 
+
+ align:start position:0%
+large region so that's that takes a lot
+of genotyping and a lot of work so our
+
+ align:start position:0%
+of genotyping and a lot of work so our
+ 
+
+ align:start position:0%
+of genotyping and a lot of work so our
+experiments now over the next year we
+
+ align:start position:0%
+experiments now over the next year we
+ 
+
+ align:start position:0%
+experiments now over the next year we
+have all these linkage peaks and asthma
+
+ align:start position:0%
+have all these linkage peaks and asthma
+ 
+
+ align:start position:0%
+have all these linkage peaks and asthma
+and copd each experiment is going to be
+
+ align:start position:0%
+and copd each experiment is going to be
+ 
+
+ align:start position:0%
+and copd each experiment is going to be
+about 200 000 is going to be 1500 1600
+
+ align:start position:0%
+about 200 000 is going to be 1500 1600
+ 
+
+ align:start position:0%
+about 200 000 is going to be 1500 1600
+snips in each of these regions
+
+ align:start position:0%
+snips in each of these regions
+ 
+
+ align:start position:0%
+snips in each of these regions
+and and we're going to uh fine map three
+
+ align:start position:0%
+and and we're going to uh fine map three
+ 
+
+ align:start position:0%
+and and we're going to uh fine map three
+or four regions over the course of the
+
+ align:start position:0%
+or four regions over the course of the
+ 
+
+ align:start position:0%
+or four regions over the course of the
+next year and hopefully we will be in
+
+ align:start position:0%
+next year and hopefully we will be in
+ 
+
+ align:start position:0%
+next year and hopefully we will be in
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+what's the best
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+snips for 100 base pairs kind of thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the order of one per uh you know one
+
+ align:start position:0%
+on the order of one per uh you know one
+ 
+
+ align:start position:0%
+on the order of one per uh you know one
+per thousand about one per thousand
+
+ align:start position:0%
+per thousand about one per thousand
+ 
+
+ align:start position:0%
+per thousand about one per thousand
+basis that's about what we're shooting
+
+ align:start position:0%
+basis that's about what we're shooting
+ 
+
+ align:start position:0%
+basis that's about what we're shooting
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+so this is just a summary of all of the
+
+ align:start position:0%
+so this is just a summary of all of the
+ 
+
+ align:start position:0%
+so this is just a summary of all of the
+genome screens that have been done in
+
+ align:start position:0%
+genome screens that have been done in
+ 
+
+ align:start position:0%
+genome screens that have been done in
+asthma just to show you that
+
+ align:start position:0%
+asthma just to show you that
+ 
+
+ align:start position:0%
+asthma just to show you that
+uh most of them have used but sid pair
+
+ align:start position:0%
+uh most of them have used but sid pair
+ 
+
+ align:start position:0%
+uh most of them have used but sid pair
+studies most of them have been
+
+ align:start position:0%
+studies most of them have been
+ 
+
+ align:start position:0%
+studies most of them have been
+relatively small but we do get a
+
+ align:start position:0%
+relatively small but we do get a
+ 
+
+ align:start position:0%
+relatively small but we do get a
+substantial amount of replication these
+
+ align:start position:0%
+substantial amount of replication these
+ 
+
+ align:start position:0%
+substantial amount of replication these
+are regions across the genome this one
+
+ align:start position:0%
+are regions across the genome this one
+ 
+
+ align:start position:0%
+are regions across the genome this one
+right here that's the gene that was just
+
+ align:start position:0%
+right here that's the gene that was just
+ 
+
+ align:start position:0%
+right here that's the gene that was just
+mapped
+
+ align:start position:0%
+mapped
+ 
+
+ align:start position:0%
+mapped
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+several populations including the finns
+
+ align:start position:0%
+several populations including the finns
+ 
+
+ align:start position:0%
+several populations including the finns
+showed a peak in this region
+
+ align:start position:0%
+showed a peak in this region
+ 
+
+ align:start position:0%
+showed a peak in this region
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+they got this gene and then they went to
+
+ align:start position:0%
+they got this gene and then they went to
+ 
+
+ align:start position:0%
+they got this gene and then they went to
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+canadians and they said can we replicate
+
+ align:start position:0%
+canadians and they said can we replicate
+ 
+
+ align:start position:0%
+canadians and they said can we replicate
+it in your population the interesting
+
+ align:start position:0%
+it in your population the interesting
+ 
+
+ align:start position:0%
+it in your population the interesting
+thing is it was asthma in the fins but
+
+ align:start position:0%
+thing is it was asthma in the fins but
+ 
+
+ align:start position:0%
+thing is it was asthma in the fins but
+it's high ige in the canadians so
+
+ align:start position:0%
+it's high ige in the canadians so
+ 
+
+ align:start position:0%
+it's high ige in the canadians so
+it shows you that this
+
+ align:start position:0%
+it shows you that this
+ 
+
+ align:start position:0%
+it shows you that this
+problem of
+
+ align:start position:0%
+problem of
+ 
+
+ align:start position:0%
+problem of
+phenotypic heterogeneity and genetic
+
+ align:start position:0%
+phenotypic heterogeneity and genetic
+ 
+
+ align:start position:0%
+phenotypic heterogeneity and genetic
+heterogeneity is a big issue
+
+ align:start position:0%
+heterogeneity is a big issue
+ 
+
+ align:start position:0%
+heterogeneity is a big issue
+here so it isn't a perfect
+
+ align:start position:0%
+here so it isn't a perfect
+ 
+
+ align:start position:0%
+here so it isn't a perfect
+replication
+
+ align:start position:0%
+replication
+ 
+
+ align:start position:0%
+replication
+at the phenotype level between these two
+
+ align:start position:0%
+at the phenotype level between these two
+ 
+
+ align:start position:0%
+at the phenotype level between these two
+populations but they've got all this
+
+ align:start position:0%
+populations but they've got all this
+ 
+
+ align:start position:0%
+populations but they've got all this
+other stuff the expression and
+
+ align:start position:0%
+other stuff the expression and
+ 
+
+ align:start position:0%
+other stuff the expression and
+everything else that proves that they've
+
+ align:start position:0%
+everything else that proves that they've
+ 
+
+ align:start position:0%
+everything else that proves that they've
+really got the gene
+
+ align:start position:0%
+really got the gene
+ 
+
+ align:start position:0%
+really got the gene
+but the one the one we're working on
+
+ align:start position:0%
+but the one the one we're working on
+ 
+
+ align:start position:0%
+but the one the one we're working on
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+uh um actually not on here it's i didn't
+
+ align:start position:0%
+uh um actually not on here it's i didn't
+ 
+
+ align:start position:0%
+uh um actually not on here it's i didn't
+leave it off intentionally but it's it's
+
+ align:start position:0%
+leave it off intentionally but it's it's
+ 
+
+ align:start position:0%
+leave it off intentionally but it's it's
+12q
+
+ align:start position:0%
+12q
+ 
+
+ align:start position:0%
+12q
+uh and it's one of the ones that's the
+
+ align:start position:0%
+uh and it's one of the ones that's the
+ 
+
+ align:start position:0%
+uh and it's one of the ones that's the
+most replicable
+
+ align:start position:0%
+most replicable
+ 
+
+ align:start position:0%
+most replicable
+uh here it is here it's in this slide
+
+ align:start position:0%
+uh here it is here it's in this slide
+ 
+
+ align:start position:0%
+uh here it is here it's in this slide
+right here
+
+ align:start position:0%
+right here
+ 
+
+ align:start position:0%
+right here
+so this is uh this is a very good region
+
+ align:start position:0%
+so this is uh this is a very good region
+ 
+
+ align:start position:0%
+so this is uh this is a very good region
+and there's now sydney here um but it's
+
+ align:start position:0%
+and there's now sydney here um but it's
+ 
+
+ align:start position:0%
+and there's now sydney here um but it's
+also got a very low p value so that's
+
+ align:start position:0%
+also got a very low p value so that's
+ 
+
+ align:start position:0%
+also got a very low p value so that's
+one of the better ones now you know you
+
+ align:start position:0%
+one of the better ones now you know you
+ 
+
+ align:start position:0%
+one of the better ones now you know you
+can already see from this
+
+ align:start position:0%
+can already see from this
+ 
+
+ align:start position:0%
+can already see from this
+each one of these this region has five
+
+ align:start position:0%
+each one of these this region has five
+ 
+
+ align:start position:0%
+each one of these this region has five
+or six different genes in this region
+
+ align:start position:0%
+or six different genes in this region
+ 
+
+ align:start position:0%
+or six different genes in this region
+there's the cytokine cluster is here
+
+ align:start position:0%
+there's the cytokine cluster is here
+ 
+
+ align:start position:0%
+there's the cytokine cluster is here
+beta-2 adrenergic receptors here il13 is
+
+ align:start position:0%
+beta-2 adrenergic receptors here il13 is
+ 
+
+ align:start position:0%
+beta-2 adrenergic receptors here il13 is
+here cd14 is here so there's a whole
+
+ align:start position:0%
+here cd14 is here so there's a whole
+ 
+
+ align:start position:0%
+here cd14 is here so there's a whole
+bunch of small genes and here nobody
+
+ align:start position:0%
+bunch of small genes and here nobody
+ 
+
+ align:start position:0%
+bunch of small genes and here nobody
+knows whether there's a big big gene or
+
+ align:start position:0%
+knows whether there's a big big gene or
+ 
+
+ align:start position:0%
+knows whether there's a big big gene or
+not you know maybe that that linkage
+
+ align:start position:0%
+not you know maybe that that linkage
+ 
+
+ align:start position:0%
+not you know maybe that that linkage
+peak is just being
+
+ align:start position:0%
+peak is just being
+ 
+
+ align:start position:0%
+peak is just being
+given by the fact that there's a whole
+
+ align:start position:0%
+given by the fact that there's a whole
+ 
+
+ align:start position:0%
+given by the fact that there's a whole
+bunch of small genes in in in that
+
+ align:start position:0%
+bunch of small genes in in in that
+ 
+
+ align:start position:0%
+bunch of small genes in in in that
+region um
+
+ align:start position:0%
+region um
+ 
+
+ align:start position:0%
+region um
+this this one the one we're working in
+
+ align:start position:0%
+this this one the one we're working in
+ 
+
+ align:start position:0%
+this this one the one we're working in
+this is uh 30 megabases it's huge
+
+ align:start position:0%
+this is uh 30 megabases it's huge
+ 
+
+ align:start position:0%
+this is uh 30 megabases it's huge
+huge region so
+
+ align:start position:0%
+huge region so
+ 
+
+ align:start position:0%
+huge region so
+but you can see from just looking at
+
+ align:start position:0%
+but you can see from just looking at
+ 
+
+ align:start position:0%
+but you can see from just looking at
+this that one two three four five six
+
+ align:start position:0%
+this that one two three four five six
+ 
+
+ align:start position:0%
+this that one two three four five six
+seven eight nine
+
+ align:start position:0%
+seven eight nine
+ 
+
+ align:start position:0%
+seven eight nine
+and there's another i mean these are 20
+
+ align:start position:0%
+and there's another i mean these are 20
+ 
+
+ align:start position:0%
+and there's another i mean these are 20
+regions each of them about 20 to 30
+
+ align:start position:0%
+regions each of them about 20 to 30
+ 
+
+ align:start position:0%
+regions each of them about 20 to 30
+20 to 40 megabases
+
+ align:start position:0%
+20 to 40 megabases
+ 
+
+ align:start position:0%
+20 to 40 megabases
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+there could be five or six genes in each
+
+ align:start position:0%
+there could be five or six genes in each
+ 
+
+ align:start position:0%
+there could be five or six genes in each
+one of these regions and at least two of
+
+ align:start position:0%
+one of these regions and at least two of
+ 
+
+ align:start position:0%
+one of these regions and at least two of
+the positionally cloned genes there were
+
+ align:start position:0%
+the positionally cloned genes there were
+ 
+
+ align:start position:0%
+the positionally cloned genes there were
+two genes in the region
+
+ align:start position:0%
+two genes in the region
+ 
+
+ align:start position:0%
+two genes in the region
+and and you couldn't tell from the
+
+ align:start position:0%
+and and you couldn't tell from the
+ 
+
+ align:start position:0%
+and and you couldn't tell from the
+articles in fact this finnish article
+
+ align:start position:0%
+articles in fact this finnish article
+ 
+
+ align:start position:0%
+articles in fact this finnish article
+that's about to come out you can there's
+
+ align:start position:0%
+that's about to come out you can there's
+ 
+
+ align:start position:0%
+that's about to come out you can there's
+a second gene they identified and they
+
+ align:start position:0%
+a second gene they identified and they
+ 
+
+ align:start position:0%
+a second gene they identified and they
+don't have the molecular biology on that
+
+ align:start position:0%
+don't have the molecular biology on that
+ 
+
+ align:start position:0%
+don't have the molecular biology on that
+in the paper
+
+ align:start position:0%
+in the paper
+ 
+
+ align:start position:0%
+in the paper
+and they don't they're not sure what
+
+ align:start position:0%
+and they don't they're not sure what
+ 
+
+ align:start position:0%
+and they don't they're not sure what
+that gene is doing
+
+ align:start position:0%
+that gene is doing
+ 
+
+ align:start position:0%
+that gene is doing
+so you're actually gonna do a pineapple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+probably
+
+ align:start position:0%
+probably
+ 
+
+ align:start position:0%
+probably
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so these are some of the issues in doing
+
+ align:start position:0%
+so these are some of the issues in doing
+ 
+
+ align:start position:0%
+so these are some of the issues in doing
+the type of linkage studies that i
+
+ align:start position:0%
+the type of linkage studies that i
+ 
+
+ align:start position:0%
+the type of linkage studies that i
+talked about multiple markers multiple
+
+ align:start position:0%
+talked about multiple markers multiple
+ 
+
+ align:start position:0%
+talked about multiple markers multiple
+phenotypes multiple comparisons
+
+ align:start position:0%
+phenotypes multiple comparisons
+ 
+
+ align:start position:0%
+phenotypes multiple comparisons
+phenotypes are correlated markers not
+
+ align:start position:0%
+phenotypes are correlated markers not
+ 
+
+ align:start position:0%
+phenotypes are correlated markers not
+independent you know you got to do so
+
+ align:start position:0%
+independent you know you got to do so
+ 
+
+ align:start position:0%
+independent you know you got to do so
+there's a lot of statistical issues you
+
+ align:start position:0%
+there's a lot of statistical issues you
+ 
+
+ align:start position:0%
+there's a lot of statistical issues you
+know this this work is really exciting i
+
+ align:start position:0%
+know this this work is really exciting i
+ 
+
+ align:start position:0%
+know this this work is really exciting i
+think because it combines
+
+ align:start position:0%
+think because it combines
+ 
+
+ align:start position:0%
+think because it combines
+genetics clinical medicine molecular
+
+ align:start position:0%
+genetics clinical medicine molecular
+ 
+
+ align:start position:0%
+genetics clinical medicine molecular
+genetics statistics
+
+ align:start position:0%
+genetics statistics
+ 
+
+ align:start position:0%
+genetics statistics
+evolutionary it's all this stuff is all
+
+ align:start position:0%
+evolutionary it's all this stuff is all
+ 
+
+ align:start position:0%
+evolutionary it's all this stuff is all
+mixed together so a lot of important
+
+ align:start position:0%
+mixed together so a lot of important
+ 
+
+ align:start position:0%
+mixed together so a lot of important
+statistical issues in doing these genome
+
+ align:start position:0%
+statistical issues in doing these genome
+ 
+
+ align:start position:0%
+statistical issues in doing these genome
+screens
+
+ align:start position:0%
+screens
+ 
+
+ align:start position:0%
+screens
+so then you got a genotype to people
+
+ align:start position:0%
+so then you got a genotype to people
+ 
+
+ align:start position:0%
+so then you got a genotype to people
+you've already said that you know snips
+
+ align:start position:0%
+you've already said that you know snips
+ 
+
+ align:start position:0%
+you've already said that you know snips
+are the primary
+
+ align:start position:0%
+are the primary
+ 
+
+ align:start position:0%
+are the primary
+genetic variation in the human genome
+
+ align:start position:0%
+genetic variation in the human genome
+ 
+
+ align:start position:0%
+genetic variation in the human genome
+but we found
+
+ align:start position:0%
+but we found
+ 
+
+ align:start position:0%
+but we found
+indels we found
+
+ align:start position:0%
+indels we found
+ 
+
+ align:start position:0%
+indels we found
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+repeats we found
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+snips and indels together i mean there's
+
+ align:start position:0%
+snips and indels together i mean there's
+ 
+
+ align:start position:0%
+snips and indels together i mean there's
+all kinds of stuff uh in general snips
+
+ align:start position:0%
+all kinds of stuff uh in general snips
+ 
+
+ align:start position:0%
+all kinds of stuff uh in general snips
+occur about
+
+ align:start position:0%
+occur about
+ 
+
+ align:start position:0%
+occur about
+you know between one and a thousand and
+
+ align:start position:0%
+you know between one and a thousand and
+ 
+
+ align:start position:0%
+you know between one and a thousand and
+one and two thousand base pairs they're
+
+ align:start position:0%
+one and two thousand base pairs they're
+ 
+
+ align:start position:0%
+one and two thousand base pairs they're
+approximately three
+
+ align:start position:0%
+approximately three
+ 
+
+ align:start position:0%
+approximately three
+um maybe three to five million in the
+
+ align:start position:0%
+um maybe three to five million in the
+ 
+
+ align:start position:0%
+um maybe three to five million in the
+human genome and you know it's using
+
+ align:start position:0%
+human genome and you know it's using
+ 
+
+ align:start position:0%
+human genome and you know it's using
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+as the primary source of genetic
+
+ align:start position:0%
+as the primary source of genetic
+ 
+
+ align:start position:0%
+as the primary source of genetic
+variation that we're actually sort of
+
+ align:start position:0%
+variation that we're actually sort of
+ 
+
+ align:start position:0%
+variation that we're actually sort of
+going at trying to map these genes
+
+ align:start position:0%
+going at trying to map these genes
+ 
+
+ align:start position:0%
+going at trying to map these genes
+there's a whole host of questions about
+
+ align:start position:0%
+there's a whole host of questions about
+ 
+
+ align:start position:0%
+there's a whole host of questions about
+how do you pick snips you know we wrote
+
+ align:start position:0%
+how do you pick snips you know we wrote
+ 
+
+ align:start position:0%
+how do you pick snips you know we wrote
+a paper together zach and i with some of
+
+ align:start position:0%
+a paper together zach and i with some of
+ 
+
+ align:start position:0%
+a paper together zach and i with some of
+our colleagues about
+
+ align:start position:0%
+our colleagues about
+ 
+
+ align:start position:0%
+our colleagues about
+haplotype tagging snips
+
+ align:start position:0%
+haplotype tagging snips
+ 
+
+ align:start position:0%
+haplotype tagging snips
+there's other approaches to using
+
+ align:start position:0%
+there's other approaches to using
+ 
+
+ align:start position:0%
+there's other approaches to using
+linkage disequilibrium to define the
+
+ align:start position:0%
+linkage disequilibrium to define the
+ 
+
+ align:start position:0%
+linkage disequilibrium to define the
+snips that you want to genotype so lots
+
+ align:start position:0%
+snips that you want to genotype so lots
+ 
+
+ align:start position:0%
+snips that you want to genotype so lots
+of issues there
+
+ align:start position:0%
+of issues there
+ 
+
+ align:start position:0%
+of issues there
+where sort of bioinformatics is
+
+ align:start position:0%
+where sort of bioinformatics is
+ 
+
+ align:start position:0%
+where sort of bioinformatics is
+interfacing with human genetics
+
+ align:start position:0%
+interfacing with human genetics
+ 
+
+ align:start position:0%
+interfacing with human genetics
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+no one really knows
+
+ align:start position:0%
+no one really knows
+ 
+
+ align:start position:0%
+no one really knows
+you know this is probably not 30 million
+
+ align:start position:0%
+you know this is probably not 30 million
+ 
+
+ align:start position:0%
+you know this is probably not 30 million
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is probably three
+
+ align:start position:0%
+is probably three
+ 
+
+ align:start position:0%
+is probably three
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+you know no one really knows how many of
+
+ align:start position:0%
+you know no one really knows how many of
+ 
+
+ align:start position:0%
+you know no one really knows how many of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+snips are actually coding
+
+ align:start position:0%
+snips are actually coding
+ 
+
+ align:start position:0%
+snips are actually coding
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i think everybody does know
+
+ align:start position:0%
+i think everybody does know
+ 
+
+ align:start position:0%
+i think everybody does know
+that there are more than coding snips
+
+ align:start position:0%
+that there are more than coding snips
+ 
+
+ align:start position:0%
+that there are more than coding snips
+that are important
+
+ align:start position:0%
+that are important
+ 
+
+ align:start position:0%
+that are important
+promoter snips are important coding
+
+ align:start position:0%
+promoter snips are important coding
+ 
+
+ align:start position:0%
+promoter snips are important coding
+snips are important snips in the three
+
+ align:start position:0%
+snips are important snips in the three
+ 
+
+ align:start position:0%
+snips are important snips in the three
+prime ut are important because they're
+
+ align:start position:0%
+prime ut are important because they're
+ 
+
+ align:start position:0%
+prime ut are important because they're
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+transcription factor binding and
+
+ align:start position:0%
+transcription factor binding and
+ 
+
+ align:start position:0%
+transcription factor binding and
+potentially change message level whole
+
+ align:start position:0%
+potentially change message level whole
+ 
+
+ align:start position:0%
+potentially change message level whole
+host of different and and any one snip
+
+ align:start position:0%
+host of different and and any one snip
+ 
+
+ align:start position:0%
+host of different and and any one snip
+is probably in and of itself isn't going
+
+ align:start position:0%
+is probably in and of itself isn't going
+ 
+
+ align:start position:0%
+is probably in and of itself isn't going
+to change function
+
+ align:start position:0%
+to change function
+ 
+
+ align:start position:0%
+to change function
+in a gene
+
+ align:start position:0%
+in a gene
+ 
+
+ align:start position:0%
+in a gene
+all that dramatically so people are
+
+ align:start position:0%
+all that dramatically so people are
+ 
+
+ align:start position:0%
+all that dramatically so people are
+going towards this idea of you know
+
+ align:start position:0%
+going towards this idea of you know
+ 
+
+ align:start position:0%
+going towards this idea of you know
+analyzing data at the molecular level by
+
+ align:start position:0%
+analyzing data at the molecular level by
+ 
+
+ align:start position:0%
+analyzing data at the molecular level by
+looking at
+
+ align:start position:0%
+looking at
+ 
+
+ align:start position:0%
+looking at
+relevant functional haplotypes you know
+
+ align:start position:0%
+relevant functional haplotypes you know
+ 
+
+ align:start position:0%
+relevant functional haplotypes you know
+if you've got a couple snips in the
+
+ align:start position:0%
+if you've got a couple snips in the
+ 
+
+ align:start position:0%
+if you've got a couple snips in the
+promoter
+
+ align:start position:0%
+promoter
+ 
+
+ align:start position:0%
+promoter
+uh um
+
+ align:start position:0%
+uh um
+ 
+
+ align:start position:0%
+uh um
+you know another that's a non-synonymous
+
+ align:start position:0%
+you know another that's a non-synonymous
+ 
+
+ align:start position:0%
+you know another that's a non-synonymous
+c-snip and an exon another that's uh um
+
+ align:start position:0%
+c-snip and an exon another that's uh um
+ 
+
+ align:start position:0%
+c-snip and an exon another that's uh um
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+a splice site another that's in the
+
+ align:start position:0%
+a splice site another that's in the
+ 
+
+ align:start position:0%
+a splice site another that's in the
+three prime utr that's determining
+
+ align:start position:0%
+three prime utr that's determining
+ 
+
+ align:start position:0%
+three prime utr that's determining
+message level of stability we combine
+
+ align:start position:0%
+message level of stability we combine
+ 
+
+ align:start position:0%
+message level of stability we combine
+all of those snips to try to get an
+
+ align:start position:0%
+all of those snips to try to get an
+ 
+
+ align:start position:0%
+all of those snips to try to get an
+effect across that whole gene
+
+ align:start position:0%
+effect across that whole gene
+ 
+
+ align:start position:0%
+effect across that whole gene
+uh in terms of looking at that gene and
+
+ align:start position:0%
+uh in terms of looking at that gene and
+ 
+
+ align:start position:0%
+uh in terms of looking at that gene and
+its impact on on phenotype
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is just a little bit about data
+
+ align:start position:0%
+so this is just a little bit about data
+ 
+
+ align:start position:0%
+so this is just a little bit about data
+analysis you know you can either look at
+
+ align:start position:0%
+analysis you know you can either look at
+ 
+
+ align:start position:0%
+analysis you know you can either look at
+continuous quantitative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantitative traits or qualitative
+
+ align:start position:0%
+quantitative traits or qualitative
+ 
+
+ align:start position:0%
+quantitative traits or qualitative
+traits they're parametric and
+
+ align:start position:0%
+traits they're parametric and
+ 
+
+ align:start position:0%
+traits they're parametric and
+non-parametric approaches to this
+
+ align:start position:0%
+non-parametric approaches to this
+ 
+
+ align:start position:0%
+non-parametric approaches to this
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then you you know you use all the stuff
+
+ align:start position:0%
+then you you know you use all the stuff
+ 
+
+ align:start position:0%
+then you you know you use all the stuff
+you actually find the gene
+
+ align:start position:0%
+you actually find the gene
+ 
+
+ align:start position:0%
+you actually find the gene
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i think that people are not doing the
+
+ align:start position:0%
+i think that people are not doing the
+ 
+
+ align:start position:0%
+i think that people are not doing the
+initial work was done with yak and back
+
+ align:start position:0%
+initial work was done with yak and back
+ 
+
+ align:start position:0%
+initial work was done with yak and back
+clones but now we're past
+
+ align:start position:0%
+clones but now we're past
+ 
+
+ align:start position:0%
+clones but now we're past
+the idea of doing that because there's
+
+ align:start position:0%
+the idea of doing that because there's
+ 
+
+ align:start position:0%
+the idea of doing that because there's
+enough markers with a hat map project
+
+ align:start position:0%
+enough markers with a hat map project
+ 
+
+ align:start position:0%
+enough markers with a hat map project
+across the genome that we can go into
+
+ align:start position:0%
+across the genome that we can go into
+ 
+
+ align:start position:0%
+across the genome that we can go into
+almost any region now in the genome and
+
+ align:start position:0%
+almost any region now in the genome and
+ 
+
+ align:start position:0%
+almost any region now in the genome and
+we can come up with
+
+ align:start position:0%
+we can come up with
+ 
+
+ align:start position:0%
+we can come up with
+validated snips across that region so
+
+ align:start position:0%
+validated snips across that region so
+ 
+
+ align:start position:0%
+validated snips across that region so
+that we can actually pick snips and
+
+ align:start position:0%
+that we can actually pick snips and
+ 
+
+ align:start position:0%
+that we can actually pick snips and
+genotype them and go directly and this
+
+ align:start position:0%
+genotype them and go directly and this
+ 
+
+ align:start position:0%
+genotype them and go directly and this
+is what's accelerating the pace of uh
+
+ align:start position:0%
+is what's accelerating the pace of uh
+ 
+
+ align:start position:0%
+is what's accelerating the pace of uh
+positional cloning
+
+ align:start position:0%
+positional cloning
+ 
+
+ align:start position:0%
+positional cloning
+at the moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are some of the things that i
+
+ align:start position:0%
+so these are some of the things that i
+ 
+
+ align:start position:0%
+so these are some of the things that i
+haven't really talked about this this is
+
+ align:start position:0%
+haven't really talked about this this is
+ 
+
+ align:start position:0%
+haven't really talked about this this is
+introductory this lecture but you know
+
+ align:start position:0%
+introductory this lecture but you know
+ 
+
+ align:start position:0%
+introductory this lecture but you know
+you really get into this you know how do
+
+ align:start position:0%
+you really get into this you know how do
+ 
+
+ align:start position:0%
+you really get into this you know how do
+you do haplotype analysis
+
+ align:start position:0%
+you do haplotype analysis
+ 
+
+ align:start position:0%
+you do haplotype analysis
+uh ancestral haplotype analysis or
+
+ align:start position:0%
+uh ancestral haplotype analysis or
+ 
+
+ align:start position:0%
+uh ancestral haplotype analysis or
+linkage disequilibrium mapping
+
+ align:start position:0%
+linkage disequilibrium mapping
+ 
+
+ align:start position:0%
+linkage disequilibrium mapping
+molecular methods or tissue expression
+
+ align:start position:0%
+molecular methods or tissue expression
+ 
+
+ align:start position:0%
+molecular methods or tissue expression
+all of these things can potentially be
+
+ align:start position:0%
+all of these things can potentially be
+ 
+
+ align:start position:0%
+all of these things can potentially be
+helpful in the fine mapping process we
+
+ align:start position:0%
+helpful in the fine mapping process we
+ 
+
+ align:start position:0%
+helpful in the fine mapping process we
+you know we've been very interested
+
+ align:start position:0%
+you know we've been very interested
+ 
+
+ align:start position:0%
+you know we've been very interested
+and have a project with zac where we
+
+ align:start position:0%
+and have a project with zac where we
+ 
+
+ align:start position:0%
+and have a project with zac where we
+wanted to use
+
+ align:start position:0%
+wanted to use
+ 
+
+ align:start position:0%
+wanted to use
+mouse expression and
+
+ align:start position:0%
+mouse expression and
+ 
+
+ align:start position:0%
+mouse expression and
+mouse qtl analysis to help us with human
+
+ align:start position:0%
+mouse qtl analysis to help us with human
+ 
+
+ align:start position:0%
+mouse qtl analysis to help us with human
+uh oppositional cloning we're not sure
+
+ align:start position:0%
+uh oppositional cloning we're not sure
+ 
+
+ align:start position:0%
+uh oppositional cloning we're not sure
+if our project's going to be funded so
+
+ align:start position:0%
+if our project's going to be funded so
+ 
+
+ align:start position:0%
+if our project's going to be funded so
+we don't know if we're actually going to
+
+ align:start position:0%
+we don't know if we're actually going to
+ 
+
+ align:start position:0%
+we don't know if we're actually going to
+get a chance to do that
+
+ align:start position:0%
+get a chance to do that
+ 
+
+ align:start position:0%
+get a chance to do that
+at the end of the day you want to be
+
+ align:start position:0%
+at the end of the day you want to be
+ 
+
+ align:start position:0%
+at the end of the day you want to be
+able to look at the impact of
+
+ align:start position:0%
+able to look at the impact of
+ 
+
+ align:start position:0%
+able to look at the impact of
+polymorphic variation in the gene that
+
+ align:start position:0%
+polymorphic variation in the gene that
+ 
+
+ align:start position:0%
+polymorphic variation in the gene that
+you found and see whether that
+
+ align:start position:0%
+you found and see whether that
+ 
+
+ align:start position:0%
+you found and see whether that
+polymorphic how much of
+
+ align:start position:0%
+polymorphic how much of
+ 
+
+ align:start position:0%
+polymorphic how much of
+the phenotypic variance is explained by
+
+ align:start position:0%
+the phenotypic variance is explained by
+ 
+
+ align:start position:0%
+the phenotypic variance is explained by
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh of polymorphism and that gets back to
+
+ align:start position:0%
+uh of polymorphism and that gets back to
+ 
+
+ align:start position:0%
+uh of polymorphism and that gets back to
+this question of
+
+ align:start position:0%
+this question of
+ 
+
+ align:start position:0%
+this question of
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+you found a gene by positional cloning
+
+ align:start position:0%
+you found a gene by positional cloning
+ 
+
+ align:start position:0%
+you found a gene by positional cloning
+how do you know it's really a
+
+ align:start position:0%
+how do you know it's really a
+ 
+
+ align:start position:0%
+how do you know it's really a
+significant gene well does it replicate
+
+ align:start position:0%
+significant gene well does it replicate
+ 
+
+ align:start position:0%
+significant gene well does it replicate
+across different populations in
+
+ align:start position:0%
+across different populations in
+ 
+
+ align:start position:0%
+across different populations in
+different conditions is it important in
+
+ align:start position:0%
+different conditions is it important in
+ 
+
+ align:start position:0%
+different conditions is it important in
+different kinds of asthma uh does it
+
+ align:start position:0%
+different kinds of asthma uh does it
+ 
+
+ align:start position:0%
+different kinds of asthma uh does it
+seem to be explaining a significant
+
+ align:start position:0%
+seem to be explaining a significant
+ 
+
+ align:start position:0%
+seem to be explaining a significant
+amount of the variation so this is one
+
+ align:start position:0%
+amount of the variation so this is one
+ 
+
+ align:start position:0%
+amount of the variation so this is one
+example it's a poor example because it's
+
+ align:start position:0%
+example it's a poor example because it's
+ 
+
+ align:start position:0%
+example it's a poor example because it's
+not a it's not a really good one this is
+
+ align:start position:0%
+not a it's not a really good one this is
+ 
+
+ align:start position:0%
+not a it's not a really good one this is
+a gene
+
+ align:start position:0%
+a gene
+ 
+
+ align:start position:0%
+a gene
+cd14 that we genotyped in the
+
+ align:start position:0%
+cd14 that we genotyped in the
+ 
+
+ align:start position:0%
+cd14 that we genotyped in the
+programming genomic applications this
+
+ align:start position:0%
+programming genomic applications this
+ 
+
+ align:start position:0%
+programming genomic applications this
+gene is the
+
+ align:start position:0%
+gene is the
+ 
+
+ align:start position:0%
+gene is the
+gene that
+
+ align:start position:0%
+gene that
+ 
+
+ align:start position:0%
+gene that
+binds
+
+ align:start position:0%
+binds
+ 
+
+ align:start position:0%
+binds
+lps or lipopolysaccharide
+
+ align:start position:0%
+lps or lipopolysaccharide
+ 
+
+ align:start position:0%
+lps or lipopolysaccharide
+to the membrane of the monocyte and then
+
+ align:start position:0%
+to the membrane of the monocyte and then
+ 
+
+ align:start position:0%
+to the membrane of the monocyte and then
+transduces that signal
+
+ align:start position:0%
+transduces that signal
+ 
+
+ align:start position:0%
+transduces that signal
+to the t cell to produce a th1 cytokine
+
+ align:start position:0%
+to the t cell to produce a th1 cytokine
+ 
+
+ align:start position:0%
+to the t cell to produce a th1 cytokine
+so we found a polymorphism in this gene
+
+ align:start position:0%
+so we found a polymorphism in this gene
+ 
+
+ align:start position:0%
+so we found a polymorphism in this gene
+as part of the program in genomic
+
+ align:start position:0%
+as part of the program in genomic
+ 
+
+ align:start position:0%
+as part of the program in genomic
+applications
+
+ align:start position:0%
+applications
+ 
+
+ align:start position:0%
+applications
+it's a c to t polymorphism so here's the
+
+ align:start position:0%
+it's a c to t polymorphism so here's the
+ 
+
+ align:start position:0%
+it's a c to t polymorphism so here's the
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t variant here's the uh heterozygote and
+
+ align:start position:0%
+t variant here's the uh heterozygote and
+ 
+
+ align:start position:0%
+t variant here's the uh heterozygote and
+here's the c
+
+ align:start position:0%
+here's the c
+ 
+
+ align:start position:0%
+here's the c
+and you can see that
+
+ align:start position:0%
+and you can see that
+ 
+
+ align:start position:0%
+and you can see that
+if you look at a dominant model where
+
+ align:start position:0%
+if you look at a dominant model where
+ 
+
+ align:start position:0%
+if you look at a dominant model where
+the c's are together that
+
+ align:start position:0%
+the c's are together that
+ 
+
+ align:start position:0%
+the c's are together that
+anybody that has a c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genotype
+
+ align:start position:0%
+genotype
+ 
+
+ align:start position:0%
+genotype
+actually is likely to have more positive
+
+ align:start position:0%
+actually is likely to have more positive
+ 
+
+ align:start position:0%
+actually is likely to have more positive
+skin tests than those who are tt and
+
+ align:start position:0%
+skin tests than those who are tt and
+ 
+
+ align:start position:0%
+skin tests than those who are tt and
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+genetic variation is associated with
+
+ align:start position:0%
+genetic variation is associated with
+ 
+
+ align:start position:0%
+genetic variation is associated with
+variation in soluble
+
+ align:start position:0%
+variation in soluble
+ 
+
+ align:start position:0%
+variation in soluble
+uh uh cd14 levels in peripheral blood so
+
+ align:start position:0%
+uh uh cd14 levels in peripheral blood so
+ 
+
+ align:start position:0%
+uh uh cd14 levels in peripheral blood so
+there's a relationship between genotype
+
+ align:start position:0%
+there's a relationship between genotype
+ 
+
+ align:start position:0%
+there's a relationship between genotype
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intermediate phenotype and a
+
+ align:start position:0%
+intermediate phenotype and a
+ 
+
+ align:start position:0%
+intermediate phenotype and a
+relationship to the the the uh to
+
+ align:start position:0%
+relationship to the the the uh to
+ 
+
+ align:start position:0%
+relationship to the the the uh to
+allergy ultimately
+
+ align:start position:0%
+allergy ultimately
+ 
+
+ align:start position:0%
+allergy ultimately
+uh i'm sorry is that supposed to show
+
+ align:start position:0%
+uh i'm sorry is that supposed to show
+ 
+
+ align:start position:0%
+uh i'm sorry is that supposed to show
+the difference between the two
+
+ align:start position:0%
+the difference between the two
+ 
+
+ align:start position:0%
+the difference between the two
+it's small but it was significant okay
+
+ align:start position:0%
+it's small but it was significant okay
+ 
+
+ align:start position:0%
+it's small but it was significant okay
+well i think the point here is that this
+
+ align:start position:0%
+well i think the point here is that this
+ 
+
+ align:start position:0%
+well i think the point here is that this
+is one snip
+
+ align:start position:0%
+is one snip
+ 
+
+ align:start position:0%
+is one snip
+you know this gets back to the point
+
+ align:start position:0%
+you know this gets back to the point
+ 
+
+ align:start position:0%
+you know this gets back to the point
+that you know it's not even a haplotype
+
+ align:start position:0%
+that you know it's not even a haplotype
+ 
+
+ align:start position:0%
+that you know it's not even a haplotype
+in this gene uh and and still there is
+
+ align:start position:0%
+in this gene uh and and still there is
+ 
+
+ align:start position:0%
+in this gene uh and and still there is
+uh and you know these are modest numbers
+
+ align:start position:0%
+uh and you know these are modest numbers
+ 
+
+ align:start position:0%
+uh and you know these are modest numbers
+they're not huge but they're but there
+
+ align:start position:0%
+they're not huge but they're but there
+ 
+
+ align:start position:0%
+they're not huge but they're but there
+was clearly a difference um
+
+ align:start position:0%
+was clearly a difference um
+ 
+
+ align:start position:0%
+was clearly a difference um
+probably the sort of level of difference
+
+ align:start position:0%
+probably the sort of level of difference
+ 
+
+ align:start position:0%
+probably the sort of level of difference
+you'd expect if it was just a single
+
+ align:start position:0%
+you'd expect if it was just a single
+ 
+
+ align:start position:0%
+you'd expect if it was just a single
+sniff i mean
+
+ align:start position:0%
+sniff i mean
+ 
+
+ align:start position:0%
+sniff i mean
+it's none of these effects are going to
+
+ align:start position:0%
+it's none of these effects are going to
+ 
+
+ align:start position:0%
+it's none of these effects are going to
+be very large at the level of an
+
+ align:start position:0%
+be very large at the level of an
+ 
+
+ align:start position:0%
+be very large at the level of an
+individual variant at the level of a
+
+ align:start position:0%
+individual variant at the level of a
+ 
+
+ align:start position:0%
+individual variant at the level of a
+gene with a haplotype
+
+ align:start position:0%
+gene with a haplotype
+ 
+
+ align:start position:0%
+gene with a haplotype
+with a really significant gene maybe so
+
+ align:start position:0%
+with a really significant gene maybe so
+ 
+
+ align:start position:0%
+with a really significant gene maybe so
+but but not certainly not one snip
+
+ align:start position:0%
+but but not certainly not one snip
+ 
+
+ align:start position:0%
+but but not certainly not one snip
+so these are some of the skills that if
+
+ align:start position:0%
+so these are some of the skills that if
+ 
+
+ align:start position:0%
+so these are some of the skills that if
+you guys want to do this work if you
+
+ align:start position:0%
+you guys want to do this work if you
+ 
+
+ align:start position:0%
+you guys want to do this work if you
+were going to come to my laboratory
+
+ align:start position:0%
+were going to come to my laboratory
+ 
+
+ align:start position:0%
+were going to come to my laboratory
+i would want you to
+
+ align:start position:0%
+i would want you to
+ 
+
+ align:start position:0%
+i would want you to
+know something about you know you you'd
+
+ align:start position:0%
+know something about you know you you'd
+ 
+
+ align:start position:0%
+know something about you know you you'd
+want to be you want to know something
+
+ align:start position:0%
+want to be you want to know something
+ 
+
+ align:start position:0%
+want to be you want to know something
+about this and how to genotype then
+
+ align:start position:0%
+about this and how to genotype then
+ 
+
+ align:start position:0%
+about this and how to genotype then
+afterwards through the disease
+
+ align:start position:0%
+afterwards through the disease
+ 
+
+ align:start position:0%
+afterwards through the disease
+study design statistical methodology
+
+ align:start position:0%
+study design statistical methodology
+ 
+
+ align:start position:0%
+study design statistical methodology
+phenotyping environmental exposures and
+
+ align:start position:0%
+phenotyping environmental exposures and
+ 
+
+ align:start position:0%
+phenotyping environmental exposures and
+i probably ought to add to this list
+
+ align:start position:0%
+i probably ought to add to this list
+ 
+
+ align:start position:0%
+i probably ought to add to this list
+bioinformatics
+
+ align:start position:0%
+bioinformatics
+ 
+
+ align:start position:0%
+bioinformatics
+because without good bioinformatics
+
+ align:start position:0%
+because without good bioinformatics
+ 
+
+ align:start position:0%
+because without good bioinformatics
+skills you're going to be lost
+
+ align:start position:0%
+skills you're going to be lost
+ 
+
+ align:start position:0%
+skills you're going to be lost
+uh and you know it's hard to know
+
+ align:start position:0%
+uh and you know it's hard to know
+ 
+
+ align:start position:0%
+uh and you know it's hard to know
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+where on the spectrum you know people
+
+ align:start position:0%
+where on the spectrum you know people
+ 
+
+ align:start position:0%
+where on the spectrum you know people
+wanna
+
+ align:start position:0%
+wanna
+ 
+
+ align:start position:0%
+wanna
+sort of you could
+
+ align:start position:0%
+sort of you could
+ 
+
+ align:start position:0%
+sort of you could
+do this and never have anything to do
+
+ align:start position:0%
+do this and never have anything to do
+ 
+
+ align:start position:0%
+do this and never have anything to do
+with the phenotyping and just focus on
+
+ align:start position:0%
+with the phenotyping and just focus on
+ 
+
+ align:start position:0%
+with the phenotyping and just focus on
+the functional variation
+
+ align:start position:0%
+the functional variation
+ 
+
+ align:start position:0%
+the functional variation
+uh from genes that these guys are
+
+ align:start position:0%
+uh from genes that these guys are
+ 
+
+ align:start position:0%
+uh from genes that these guys are
+are actually finding or you might sort
+
+ align:start position:0%
+are actually finding or you might sort
+ 
+
+ align:start position:0%
+are actually finding or you might sort
+of situate yourself somewhere in the
+
+ align:start position:0%
+of situate yourself somewhere in the
+ 
+
+ align:start position:0%
+of situate yourself somewhere in the
+middle
+
+ align:start position:0%
+middle
+ 
+
+ align:start position:0%
+middle
+um you know i've got people in my lab
+
+ align:start position:0%
+um you know i've got people in my lab
+ 
+
+ align:start position:0%
+um you know i've got people in my lab
+that are doing just this
+
+ align:start position:0%
+that are doing just this
+ 
+
+ align:start position:0%
+that are doing just this
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+very few people that are doing just this
+
+ align:start position:0%
+very few people that are doing just this
+ 
+
+ align:start position:0%
+very few people that are doing just this
+but i have some that are sitting in the
+
+ align:start position:0%
+but i have some that are sitting in the
+ 
+
+ align:start position:0%
+but i have some that are sitting in the
+middle
+
+ align:start position:0%
+middle
+ 
+
+ align:start position:0%
+middle
+so where are this going in the future i
+
+ align:start position:0%
+so where are this going in the future i
+ 
+
+ align:start position:0%
+so where are this going in the future i
+mean i think that
+
+ align:start position:0%
+mean i think that
+ 
+
+ align:start position:0%
+mean i think that
+uh um what's driving the field is
+
+ align:start position:0%
+uh um what's driving the field is
+ 
+
+ align:start position:0%
+uh um what's driving the field is
+high throughput sequencing and high
+
+ align:start position:0%
+high throughput sequencing and high
+ 
+
+ align:start position:0%
+high throughput sequencing and high
+throughput genotyping combined with
+
+ align:start position:0%
+throughput genotyping combined with
+ 
+
+ align:start position:0%
+throughput genotyping combined with
+bioinformatics in the presence of having
+
+ align:start position:0%
+bioinformatics in the presence of having
+ 
+
+ align:start position:0%
+bioinformatics in the presence of having
+lots of populations to do this kind of
+
+ align:start position:0%
+lots of populations to do this kind of
+ 
+
+ align:start position:0%
+lots of populations to do this kind of
+work you know that's what's really
+
+ align:start position:0%
+work you know that's what's really
+ 
+
+ align:start position:0%
+work you know that's what's really
+necessary is you got to have well
+
+ align:start position:0%
+necessary is you got to have well
+ 
+
+ align:start position:0%
+necessary is you got to have well
+phenotype populations in my lab these
+
+ align:start position:0%
+phenotype populations in my lab these
+ 
+
+ align:start position:0%
+phenotype populations in my lab these
+are all the different populations that
+
+ align:start position:0%
+are all the different populations that
+ 
+
+ align:start position:0%
+are all the different populations that
+we have for asthma we've got these
+
+ align:start position:0%
+we have for asthma we've got these
+ 
+
+ align:start position:0%
+we have for asthma we've got these
+extended pedigrees we've got affected
+
+ align:start position:0%
+extended pedigrees we've got affected
+ 
+
+ align:start position:0%
+extended pedigrees we've got affected
+sid pairs we've got trios and we've got
+
+ align:start position:0%
+sid pairs we've got trios and we've got
+ 
+
+ align:start position:0%
+sid pairs we've got trios and we've got
+individual cases and controls
+
+ align:start position:0%
+individual cases and controls
+ 
+
+ align:start position:0%
+individual cases and controls
+so that we can test the genes in
+
+ align:start position:0%
+so that we can test the genes in
+ 
+
+ align:start position:0%
+so that we can test the genes in
+multiple different populations and and
+
+ align:start position:0%
+multiple different populations and and
+ 
+
+ align:start position:0%
+multiple different populations and and
+under different
+
+ align:start position:0%
+under different
+ 
+
+ align:start position:0%
+under different
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+so why don't i stop there and i'd be
+
+ align:start position:0%
+so why don't i stop there and i'd be
+ 
+
+ align:start position:0%
+so why don't i stop there and i'd be
+glad to answer any questions that people
+
+ align:start position:0%
+glad to answer any questions that people
+ 
+
+ align:start position:0%
+glad to answer any questions that people
+have about any of the things that i said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure of proteins
+
+ align:start position:0%
+structure of proteins
+ 
+
+ align:start position:0%
+structure of proteins
+yeah well i mean i think that that means
+
+ align:start position:0%
+yeah well i mean i think that that means
+ 
+
+ align:start position:0%
+yeah well i mean i think that that means
+this is that
+
+ align:start position:0%
+this is that
+ 
+
+ align:start position:0%
+this is that
+you know actually getting into
+
+ align:start position:0%
+you know actually getting into
+ 
+
+ align:start position:0%
+you know actually getting into
+you know once you
+
+ align:start position:0%
+you know once you
+ 
+
+ align:start position:0%
+you know once you
+once you've got a relationship with a
+
+ align:start position:0%
+once you've got a relationship with a
+ 
+
+ align:start position:0%
+once you've got a relationship with a
+gene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what you have to do is
+
+ align:start position:0%
+what you have to do is
+ 
+
+ align:start position:0%
+what you have to do is
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+get down and figure out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are the variants in that gene and
+
+ align:start position:0%
+what are the variants in that gene and
+ 
+
+ align:start position:0%
+what are the variants in that gene and
+what are they doing and and that that
+
+ align:start position:0%
+what are they doing and and that that
+ 
+
+ align:start position:0%
+what are they doing and and that that
+can proceed human genetics can
+
+ align:start position:0%
+can proceed human genetics can
+ 
+
+ align:start position:0%
+can proceed human genetics can
+contribute to that at the level of
+
+ align:start position:0%
+contribute to that at the level of
+ 
+
+ align:start position:0%
+contribute to that at the level of
+genetic association so for example we um
+
+ align:start position:0%
+genetic association so for example we um
+ 
+
+ align:start position:0%
+genetic association so for example we um
+laurie glimscher who's an immunologist
+
+ align:start position:0%
+laurie glimscher who's an immunologist
+ 
+
+ align:start position:0%
+laurie glimscher who's an immunologist
+at the school of public health
+
+ align:start position:0%
+at the school of public health
+ 
+
+ align:start position:0%
+at the school of public health
+identified a gene
+
+ align:start position:0%
+identified a gene
+ 
+
+ align:start position:0%
+identified a gene
+that controls
+
+ align:start position:0%
+that controls
+ 
+
+ align:start position:0%
+that controls
+uh t-cell differentiation
+
+ align:start position:0%
+uh t-cell differentiation
+ 
+
+ align:start position:0%
+uh t-cell differentiation
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it's tbx-21 or t-bet is the name of the
+
+ align:start position:0%
+it's tbx-21 or t-bet is the name of the
+ 
+
+ align:start position:0%
+it's tbx-21 or t-bet is the name of the
+gene and she created a knockout mouse
+
+ align:start position:0%
+gene and she created a knockout mouse
+ 
+
+ align:start position:0%
+gene and she created a knockout mouse
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh when you knock this gene out in the
+
+ align:start position:0%
+uh when you knock this gene out in the
+ 
+
+ align:start position:0%
+uh when you knock this gene out in the
+mouse you get tremendous airways
+
+ align:start position:0%
+mouse you get tremendous airways
+ 
+
+ align:start position:0%
+mouse you get tremendous airways
+responsiveness and allergic
+
+ align:start position:0%
+responsiveness and allergic
+ 
+
+ align:start position:0%
+responsiveness and allergic
+inflammation it looks like an asthma
+
+ align:start position:0%
+inflammation it looks like an asthma
+ 
+
+ align:start position:0%
+inflammation it looks like an asthma
+gene in the mouse
+
+ align:start position:0%
+gene in the mouse
+ 
+
+ align:start position:0%
+gene in the mouse
+and and
+
+ align:start position:0%
+and and
+ 
+
+ align:start position:0%
+and and
+so we sequenced that gene
+
+ align:start position:0%
+so we sequenced that gene
+ 
+
+ align:start position:0%
+so we sequenced that gene
+and then we started to
+
+ align:start position:0%
+and then we started to
+ 
+
+ align:start position:0%
+and then we started to
+look at we found a variant in the gene
+
+ align:start position:0%
+look at we found a variant in the gene
+ 
+
+ align:start position:0%
+look at we found a variant in the gene
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+in the coding region it's it's a
+
+ align:start position:0%
+in the coding region it's it's a
+ 
+
+ align:start position:0%
+in the coding region it's it's a
+non-synonymous c-snip in the coding
+
+ align:start position:0%
+non-synonymous c-snip in the coding
+ 
+
+ align:start position:0%
+non-synonymous c-snip in the coding
+region it's very rare it's only occurs
+
+ align:start position:0%
+region it's very rare it's only occurs
+ 
+
+ align:start position:0%
+region it's very rare it's only occurs
+in about three percent of people but it
+
+ align:start position:0%
+in about three percent of people but it
+ 
+
+ align:start position:0%
+in about three percent of people but it
+turns out that that coding region
+
+ align:start position:0%
+turns out that that coding region
+ 
+
+ align:start position:0%
+turns out that that coding region
+variant
+
+ align:start position:0%
+variant
+ 
+
+ align:start position:0%
+variant
+is uh um
+
+ align:start position:0%
+is uh um
+ 
+
+ align:start position:0%
+is uh um
+determines
+
+ align:start position:0%
+determines
+ 
+
+ align:start position:0%
+determines
+which patients who get inhaled steroids
+
+ align:start position:0%
+which patients who get inhaled steroids
+ 
+
+ align:start position:0%
+which patients who get inhaled steroids
+get better
+
+ align:start position:0%
+get better
+ 
+
+ align:start position:0%
+get better
+the people that have that variant
+
+ align:start position:0%
+the people that have that variant
+ 
+
+ align:start position:0%
+the people that have that variant
+and get inhaled steroids have their
+
+ align:start position:0%
+and get inhaled steroids have their
+ 
+
+ align:start position:0%
+and get inhaled steroids have their
+airways responsiveness completely
+
+ align:start position:0%
+airways responsiveness completely
+ 
+
+ align:start position:0%
+airways responsiveness completely
+returned to normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're about to submit it to the lancet
+
+ align:start position:0%
+we're about to submit it to the lancet
+ 
+
+ align:start position:0%
+we're about to submit it to the lancet
+we're actually working with laurie to
+
+ align:start position:0%
+we're actually working with laurie to
+ 
+
+ align:start position:0%
+we're actually working with laurie to
+it's pretty exciting
+
+ align:start position:0%
+it's pretty exciting
+ 
+
+ align:start position:0%
+it's pretty exciting
+it's it's it's exciting because it's
+
+ align:start position:0%
+it's it's it's exciting because it's
+ 
+
+ align:start position:0%
+it's it's it's exciting because it's
+example of how you can actually you
+
+ align:start position:0%
+example of how you can actually you
+ 
+
+ align:start position:0%
+example of how you can actually you
+don't have to even go to the animal
+
+ align:start position:0%
+don't have to even go to the animal
+ 
+
+ align:start position:0%
+don't have to even go to the animal
+model and so she then
+
+ align:start position:0%
+model and so she then
+ 
+
+ align:start position:0%
+model and so she then
+crea
+
+ align:start position:0%
+crea
+ 
+
+ align:start position:0%
+crea
+has created you know her mouse model she
+
+ align:start position:0%
+has created you know her mouse model she
+ 
+
+ align:start position:0%
+has created you know her mouse model she
+started to do some experiments with
+
+ align:start position:0%
+started to do some experiments with
+ 
+
+ align:start position:0%
+started to do some experiments with
+steroids and steroids are probably
+
+ align:start position:0%
+steroids and steroids are probably
+ 
+
+ align:start position:0%
+steroids and steroids are probably
+important in controlling t-bed
+
+ align:start position:0%
+important in controlling t-bed
+ 
+
+ align:start position:0%
+important in controlling t-bed
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+and she didn't know that
+
+ align:start position:0%
+and she didn't know that
+ 
+
+ align:start position:0%
+and she didn't know that
+so that's an example of
+
+ align:start position:0%
+so that's an example of
+ 
+
+ align:start position:0%
+so that's an example of
+structure function relationships where
+
+ align:start position:0%
+structure function relationships where
+ 
+
+ align:start position:0%
+structure function relationships where
+you're trying to figure out
+
+ align:start position:0%
+you're trying to figure out
+ 
+
+ align:start position:0%
+you're trying to figure out
+what a gene actually does and it is
+
+ align:start position:0%
+what a gene actually does and it is
+ 
+
+ align:start position:0%
+what a gene actually does and it is
+important to recognize
+
+ align:start position:0%
+important to recognize
+ 
+
+ align:start position:0%
+important to recognize
+there are some genes
+
+ align:start position:0%
+there are some genes
+ 
+
+ align:start position:0%
+there are some genes
+that have been around for a while
+
+ align:start position:0%
+that have been around for a while
+ 
+
+ align:start position:0%
+that have been around for a while
+and and
+
+ align:start position:0%
+and and
+ 
+
+ align:start position:0%
+and and
+people still don't know we know there's
+
+ align:start position:0%
+people still don't know we know there's
+ 
+
+ align:start position:0%
+people still don't know we know there's
+a relationship to a disease phenotype
+
+ align:start position:0%
+a relationship to a disease phenotype
+ 
+
+ align:start position:0%
+a relationship to a disease phenotype
+but we don't know how the hell they work
+
+ align:start position:0%
+but we don't know how the hell they work
+ 
+
+ align:start position:0%
+but we don't know how the hell they work
+so figuring out that structure function
+
+ align:start position:0%
+so figuring out that structure function
+ 
+
+ align:start position:0%
+so figuring out that structure function
+stuff can take a long time potentially
+
+ align:start position:0%
+stuff can take a long time potentially
+ 
+
+ align:start position:0%
+stuff can take a long time potentially
+and doing the genetic association and
+
+ align:start position:0%
+and doing the genetic association and
+ 
+
+ align:start position:0%
+and doing the genetic association and
+the fine mapping may actually now
+
+ align:start position:0%
+the fine mapping may actually now
+ 
+
+ align:start position:0%
+the fine mapping may actually now
+proceed at a faster pace and and not
+
+ align:start position:0%
+proceed at a faster pace and and not
+ 
+
+ align:start position:0%
+proceed at a faster pace and and not
+take as much time
+
+ align:start position:0%
+take as much time
+ 
+
+ align:start position:0%
+take as much time
+but i think it's um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can actually do
+
+ align:start position:0%
+you can actually do
+ 
+
+ align:start position:0%
+you can actually do
+a lot of structure function stuff
+
+ align:start position:0%
+a lot of structure function stuff
+ 
+
+ align:start position:0%
+a lot of structure function stuff
+usually what we do is when we get an
+
+ align:start position:0%
+usually what we do is when we get an
+ 
+
+ align:start position:0%
+usually what we do is when we get an
+association we will type every damn
+
+ align:start position:0%
+association we will type every damn
+ 
+
+ align:start position:0%
+association we will type every damn
+we'll sequence that gene we'll type
+
+ align:start position:0%
+we'll sequence that gene we'll type
+ 
+
+ align:start position:0%
+we'll sequence that gene we'll type
+every damn variant we can find in that
+
+ align:start position:0%
+every damn variant we can find in that
+ 
+
+ align:start position:0%
+every damn variant we can find in that
+gene in in the population and look at
+
+ align:start position:0%
+gene in in the population and look at
+ 
+
+ align:start position:0%
+gene in in the population and look at
+every thing that could be related to a
+
+ align:start position:0%
+every thing that could be related to a
+ 
+
+ align:start position:0%
+every thing that could be related to a
+an interesting phenotype because we're
+
+ align:start position:0%
+an interesting phenotype because we're
+ 
+
+ align:start position:0%
+an interesting phenotype because we're
+searching for clues to how to help our
+
+ align:start position:0%
+searching for clues to how to help our
+ 
+
+ align:start position:0%
+searching for clues to how to help our
+molecular biology colleagues in uh
+
+ align:start position:0%
+molecular biology colleagues in uh
+ 
+
+ align:start position:0%
+molecular biology colleagues in uh
+trying to help them
+
+ align:start position:0%
+trying to help them
+ 
+
+ align:start position:0%
+trying to help them
+figure out what the gene is actually
+
+ align:start position:0%
+figure out what the gene is actually
+ 
+
+ align:start position:0%
+figure out what the gene is actually
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh well you could do that i mean we're
+
+ align:start position:0%
+uh well you could do that i mean we're
+ 
+
+ align:start position:0%
+uh well you could do that i mean we're
+trying to work with this guy
+
+ align:start position:0%
+trying to work with this guy
+ 
+
+ align:start position:0%
+trying to work with this guy
+he's got people in his lab who
+
+ align:start position:0%
+he's got people in his lab who
+ 
+
+ align:start position:0%
+he's got people in his lab who
+have ideas about how to
+
+ align:start position:0%
+have ideas about how to
+ 
+
+ align:start position:0%
+have ideas about how to
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+get clues
+
+ align:start position:0%
+get clues
+ 
+
+ align:start position:0%
+get clues
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+like the stuff that drazen showed you
+
+ align:start position:0%
+like the stuff that drazen showed you
+ 
+
+ align:start position:0%
+like the stuff that drazen showed you
+last week
+
+ align:start position:0%
+last week
+ 
+
+ align:start position:0%
+last week
+that gene crh1
+
+ align:start position:0%
+that gene crh1
+ 
+
+ align:start position:0%
+that gene crh1
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+know there's a relationship to steroid
+
+ align:start position:0%
+know there's a relationship to steroid
+ 
+
+ align:start position:0%
+know there's a relationship to steroid
+treatment response
+
+ align:start position:0%
+treatment response
+ 
+
+ align:start position:0%
+treatment response
+but we don't know
+
+ align:start position:0%
+but we don't know
+ 
+
+ align:start position:0%
+but we don't know
+what the variant is in the gene so we
+
+ align:start position:0%
+what the variant is in the gene so we
+ 
+
+ align:start position:0%
+what the variant is in the gene so we
+sequence the gene completely
+
+ align:start position:0%
+sequence the gene completely
+ 
+
+ align:start position:0%
+sequence the gene completely
+and now we've got two indels
+
+ align:start position:0%
+and now we've got two indels
+ 
+
+ align:start position:0%
+and now we've got two indels
+in that gene that sit right at intron
+
+ align:start position:0%
+in that gene that sit right at intron
+ 
+
+ align:start position:0%
+in that gene that sit right at intron
+exon junctions so
+
+ align:start position:0%
+exon junctions so
+ 
+
+ align:start position:0%
+exon junctions so
+the presumed what we're thinking is that
+
+ align:start position:0%
+the presumed what we're thinking is that
+ 
+
+ align:start position:0%
+the presumed what we're thinking is that
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+insertion deletion polymorphisms may be
+
+ align:start position:0%
+insertion deletion polymorphisms may be
+ 
+
+ align:start position:0%
+insertion deletion polymorphisms may be
+changing alternative splice sites so
+
+ align:start position:0%
+changing alternative splice sites so
+ 
+
+ align:start position:0%
+changing alternative splice sites so
+we're going to have to try to prove that
+
+ align:start position:0%
+we're going to have to try to prove that
+ 
+
+ align:start position:0%
+we're going to have to try to prove that
+that's one of the hypotheses that we're
+
+ align:start position:0%
+that's one of the hypotheses that we're
+ 
+
+ align:start position:0%
+that's one of the hypotheses that we're
+going to investigate in the renewal of
+
+ align:start position:0%
+going to investigate in the renewal of
+ 
+
+ align:start position:0%
+going to investigate in the renewal of
+the grant is trying to look at that
+
+ align:start position:0%
+the grant is trying to look at that
+ 
+
+ align:start position:0%
+the grant is trying to look at that
+um we also
+
+ align:start position:0%
+um we also
+ 
+
+ align:start position:0%
+um we also
+uh um so
+
+ align:start position:0%
+uh um so
+ 
+
+ align:start position:0%
+uh um so
+you know you have to let the gene tell
+
+ align:start position:0%
+you know you have to let the gene tell
+ 
+
+ align:start position:0%
+you know you have to let the gene tell
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where its variation is and and how it
+
+ align:start position:0%
+where its variation is and and how it
+ 
+
+ align:start position:0%
+where its variation is and and how it
+might be
+
+ align:start position:0%
+might be
+ 
+
+ align:start position:0%
+might be
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+contributing to phenotype
+
+ align:start position:0%
+contributing to phenotype
+ 
+
+ align:start position:0%
+contributing to phenotype
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+uh the first thing usually is to
+
+ align:start position:0%
+uh the first thing usually is to
+ 
+
+ align:start position:0%
+uh the first thing usually is to
+sequence the gene completely second
+
+ align:start position:0%
+sequence the gene completely second
+ 
+
+ align:start position:0%
+sequence the gene completely second
+thing would be to then do a very careful
+
+ align:start position:0%
+thing would be to then do a very careful
+ 
+
+ align:start position:0%
+thing would be to then do a very careful
+analysis of the
+
+ align:start position:0%
+analysis of the
+ 
+
+ align:start position:0%
+analysis of the
+new variants and the re-sequenced
+
+ align:start position:0%
+new variants and the re-sequenced
+ 
+
+ align:start position:0%
+new variants and the re-sequenced
+variants that you found in relationship
+
+ align:start position:0%
+variants that you found in relationship
+ 
+
+ align:start position:0%
+variants that you found in relationship
+to the phenotype of interest
+
+ align:start position:0%
+to the phenotype of interest
+ 
+
+ align:start position:0%
+to the phenotype of interest
+for phenotypes of interest and see if
+
+ align:start position:0%
+for phenotypes of interest and see if
+ 
+
+ align:start position:0%
+for phenotypes of interest and see if
+you can find
+
+ align:start position:0%
+you can find
+ 
+
+ align:start position:0%
+you can find
+either haplotypes or
+
+ align:start position:0%
+either haplotypes or
+ 
+
+ align:start position:0%
+either haplotypes or
+individual snips or insertion deletion
+
+ align:start position:0%
+individual snips or insertion deletion
+ 
+
+ align:start position:0%
+individual snips or insertion deletion
+polymorphisms or transcription factor
+
+ align:start position:0%
+polymorphisms or transcription factor
+ 
+
+ align:start position:0%
+polymorphisms or transcription factor
+binding sites are things that could
+
+ align:start position:0%
+binding sites are things that could
+ 
+
+ align:start position:0%
+binding sites are things that could
+potentially explain
+
+ align:start position:0%
+potentially explain
+ 
+
+ align:start position:0%
+potentially explain
+the genetic association so then you can
+
+ align:start position:0%
+the genetic association so then you can
+ 
+
+ align:start position:0%
+the genetic association so then you can
+do that and then you have to go into an
+
+ align:start position:0%
+do that and then you have to go into an
+ 
+
+ align:start position:0%
+do that and then you have to go into an
+animal model
+
+ align:start position:0%
+animal model
+ 
+
+ align:start position:0%
+animal model
+and test those
+
+ align:start position:0%
+and test those
+ 
+
+ align:start position:0%
+and test those
+in a more rigorous way usually so scott
+
+ align:start position:0%
+in a more rigorous way usually so scott
+ 
+
+ align:start position:0%
+in a more rigorous way usually so scott
+how far off do you think is the day when
+
+ align:start position:0%
+how far off do you think is the day when
+ 
+
+ align:start position:0%
+how far off do you think is the day when
+a commission of the brigham
+
+ align:start position:0%
+a commission of the brigham
+ 
+
+ align:start position:0%
+a commission of the brigham
+will be able to come with you and say i
+
+ align:start position:0%
+will be able to come with you and say i
+ 
+
+ align:start position:0%
+will be able to come with you and say i
+have a disease
+
+ align:start position:0%
+have a disease
+ 
+
+ align:start position:0%
+have a disease
+i have 500 patients cases and 500
+
+ align:start position:0%
+i have 500 patients cases and 500
+ 
+
+ align:start position:0%
+i have 500 patients cases and 500
+controls
+
+ align:start position:0%
+controls
+ 
+
+ align:start position:0%
+controls
+i think
+
+ align:start position:0%
+i think
+ 
+
+ align:start position:0%
+i think
+i want to verify that with a climate
+
+ align:start position:0%
+i want to verify that with a climate
+ 
+
+ align:start position:0%
+i want to verify that with a climate
+that this is
+
+ align:start position:0%
+that this is
+ 
+
+ align:start position:0%
+that this is
+on the long arm of the chromosome
+
+ align:start position:0%
+on the long arm of the chromosome
+ 
+
+ align:start position:0%
+on the long arm of the chromosome
+and i want to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you're really asking the question is
+
+ align:start position:0%
+so you're really asking the question is
+ 
+
+ align:start position:0%
+so you're really asking the question is
+i think the question you're asking is
+
+ align:start position:0%
+i think the question you're asking is
+ 
+
+ align:start position:0%
+i think the question you're asking is
+how far away is whole genome association
+
+ align:start position:0%
+how far away is whole genome association
+ 
+
+ align:start position:0%
+how far away is whole genome association
+how far away is whole genomic
+
+ align:start position:0%
+how far away is whole genomic
+ 
+
+ align:start position:0%
+how far away is whole genomic
+association where it's within the reach
+
+ align:start position:0%
+association where it's within the reach
+ 
+
+ align:start position:0%
+association where it's within the reach
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+significant but not impossible clinical
+
+ align:start position:0%
+significant but not impossible clinical
+ 
+
+ align:start position:0%
+significant but not impossible clinical
+studies
+
+ align:start position:0%
+studies
+ 
+
+ align:start position:0%
+studies
+uh max three years
+
+ align:start position:0%
+uh max three years
+ 
+
+ align:start position:0%
+uh max three years
+max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+i mean george church
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's all about the genotyping costs zach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean he
+
+ align:start position:0%
+i mean he
+ 
+
+ align:start position:0%
+i mean he
+he listen he thinks he's
+
+ align:start position:0%
+he listen he thinks he's
+ 
+
+ align:start position:0%
+he listen he thinks he's
+close to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know the
+
+ align:start position:0%
+you know the
+ 
+
+ align:start position:0%
+you know the
+thousand dollar genome so if he's really
+
+ align:start position:0%
+thousand dollar genome so if he's really
+ 
+
+ align:start position:0%
+thousand dollar genome so if he's really
+close to the thousand dollar genome and
+
+ align:start position:0%
+close to the thousand dollar genome and
+ 
+
+ align:start position:0%
+close to the thousand dollar genome and
+genotyping snip genotyping costs really
+
+ align:start position:0%
+genotyping snip genotyping costs really
+ 
+
+ align:start position:0%
+genotyping snip genotyping costs really
+drop continue to drop as dramatically as
+
+ align:start position:0%
+drop continue to drop as dramatically as
+ 
+
+ align:start position:0%
+drop continue to drop as dramatically as
+they've dropped over the last three
+
+ align:start position:0%
+they've dropped over the last three
+ 
+
+ align:start position:0%
+they've dropped over the last three
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+i would see whole genome association
+
+ align:start position:0%
+i would see whole genome association
+ 
+
+ align:start position:0%
+i would see whole genome association
+being within the range
+
+ align:start position:0%
+being within the range
+ 
+
+ align:start position:0%
+being within the range
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+a a
+
+ align:start position:0%
+a a
+ 
+
+ align:start position:0%
+a a
+reasonable budget
+
+ align:start position:0%
+reasonable budget
+ 
+
+ align:start position:0%
+reasonable budget
+you know in a two or three year period
+
+ align:start position:0%
+you know in a two or three year period
+ 
+
+ align:start position:0%
+you know in a two or three year period
+of time
+
+ align:start position:0%
+of time
+ 
+
+ align:start position:0%
+of time
+all right on that note thanks very much
\ No newline at end of file
diff --git a/j0Bhj4eCCws.txt b/j0Bhj4eCCws.txt
new file mode 100644
index 0000000000000000000000000000000000000000..434d2b5993d32333b6e311797264ad6fa935e3a6
--- /dev/null
+++ b/j0Bhj4eCCws.txt
@@ -0,0 +1,4331 @@
+align:start position:0%
+ 
+All right. It is the last session. You
+
+ align:start position:0%
+All right. It is the last session. You
+ 
+
+ align:start position:0%
+All right. It is the last session. You
+have survived the first day almost.
+
+ align:start position:0%
+have survived the first day almost.
+ 
+
+ align:start position:0%
+have survived the first day almost.
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+I'm really excited about this session uh
+
+ align:start position:0%
+I'm really excited about this session uh
+ 
+
+ align:start position:0%
+I'm really excited about this session uh
+because we started the day we started
+
+ align:start position:0%
+because we started the day we started
+ 
+
+ align:start position:0%
+because we started the day we started
+the day looking at the planetary scale
+
+ align:start position:0%
+the day looking at the planetary scale
+ 
+
+ align:start position:0%
+the day looking at the planetary scale
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+honestly from a little bit of a a
+
+ align:start position:0%
+honestly from a little bit of a a
+ 
+
+ align:start position:0%
+honestly from a little bit of a a
+slightly grim perspective. I don't think
+
+ align:start position:0%
+slightly grim perspective. I don't think
+ 
+
+ align:start position:0%
+slightly grim perspective. I don't think
+anyone left that session feeling really
+
+ align:start position:0%
+anyone left that session feeling really
+ 
+
+ align:start position:0%
+anyone left that session feeling really
+light and excited about the state of the
+
+ align:start position:0%
+light and excited about the state of the
+ 
+
+ align:start position:0%
+light and excited about the state of the
+world.
+
+ align:start position:0%
+world.
+ 
+
+ align:start position:0%
+world.
+Um so now we proceeded to talk about
+
+ align:start position:0%
+Um so now we proceeded to talk about
+ 
+
+ align:start position:0%
+Um so now we proceeded to talk about
+people because no change happens without
+
+ align:start position:0%
+people because no change happens without
+ 
+
+ align:start position:0%
+people because no change happens without
+people and then about what people can do
+
+ align:start position:0%
+people and then about what people can do
+ 
+
+ align:start position:0%
+people and then about what people can do
+in set rules policy and now we are going
+
+ align:start position:0%
+in set rules policy and now we are going
+ 
+
+ align:start position:0%
+in set rules policy and now we are going
+to go ahead and go back to the scale
+
+ align:start position:0%
+to go ahead and go back to the scale
+ 
+
+ align:start position:0%
+to go ahead and go back to the scale
+question but from the perspective
+
+ align:start position:0%
+question but from the perspective
+ 
+
+ align:start position:0%
+question but from the perspective
+of with people with technology with
+
+ align:start position:0%
+of with people with technology with
+ 
+
+ align:start position:0%
+of with people with technology with
+ideas with rules
+
+ align:start position:0%
+ideas with rules
+ 
+
+ align:start position:0%
+ideas with rules
+what can we accomplish?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, so I hope we're going to end the day
+
+ align:start position:0%
+Um, so I hope we're going to end the day
+ 
+
+ align:start position:0%
+Um, so I hope we're going to end the day
+with a lot of excitement. Um, and we
+
+ align:start position:0%
+with a lot of excitement. Um, and we
+ 
+
+ align:start position:0%
+with a lot of excitement. Um, and we
+also have two um relatively new friends
+
+ align:start position:0%
+also have two um relatively new friends
+ 
+
+ align:start position:0%
+also have two um relatively new friends
+of mine who I deeply admire and I'm
+
+ align:start position:0%
+of mine who I deeply admire and I'm
+ 
+
+ align:start position:0%
+of mine who I deeply admire and I'm
+excited to have joining us. Both not
+
+ align:start position:0%
+excited to have joining us. Both not
+ 
+
+ align:start position:0%
+excited to have joining us. Both not
+present. So we have two videos
+
+ align:start position:0%
+present. So we have two videos
+ 
+
+ align:start position:0%
+present. So we have two videos
+sandwiching our our session today. Um,
+
+ align:start position:0%
+sandwiching our our session today. Um,
+ 
+
+ align:start position:0%
+sandwiching our our session today. Um,
+and I am going to start with one uh the
+
+ align:start position:0%
+and I am going to start with one uh the
+ 
+
+ align:start position:0%
+and I am going to start with one uh the
+growth of gens in Europe. Sanjie Kumar
+
+ align:start position:0%
+growth of gens in Europe. Sanjie Kumar
+ 
+
+ align:start position:0%
+growth of gens in Europe. Sanjie Kumar
+is joining us I believe. Are you in
+
+ align:start position:0%
+is joining us I believe. Are you in
+ 
+
+ align:start position:0%
+is joining us I believe. Are you in
+Brussels Sanjie? Yes, I am. Lovely.
+
+ align:start position:0%
+Brussels Sanjie? Yes, I am. Lovely.
+ 
+
+ align:start position:0%
+Brussels Sanjie? Yes, I am. Lovely.
+Lovely evening in Brussels. You're
+
+ align:start position:0%
+Lovely evening in Brussels. You're
+ 
+
+ align:start position:0%
+Lovely evening in Brussels. You're
+>> you lovely to see you up there.
+
+ align:start position:0%
+>> you lovely to see you up there.
+ 
+
+ align:start position:0%
+>> you lovely to see you up there.
+>> Uh and I am going to ask you to
+
+ align:start position:0%
+>> Uh and I am going to ask you to
+ 
+
+ align:start position:0%
+>> Uh and I am going to ask you to
+introduce yourself to everyone and then
+
+ align:start position:0%
+introduce yourself to everyone and then
+ 
+
+ align:start position:0%
+introduce yourself to everyone and then
+go ahead and proceed with your
+
+ align:start position:0%
+go ahead and proceed with your
+ 
+
+ align:start position:0%
+go ahead and proceed with your
+presentation.
+
+ align:start position:0%
+presentation.
+ 
+
+ align:start position:0%
+presentation.
+>> Brilliant. Thank you. Thank you so much
+
+ align:start position:0%
+>> Brilliant. Thank you. Thank you so much
+ 
+
+ align:start position:0%
+>> Brilliant. Thank you. Thank you so much
+Z. Firstly for the kind introduction and
+
+ align:start position:0%
+Z. Firstly for the kind introduction and
+ 
+
+ align:start position:0%
+Z. Firstly for the kind introduction and
+for the the opportunity to come and uh
+
+ align:start position:0%
+for the the opportunity to come and uh
+ 
+
+ align:start position:0%
+for the the opportunity to come and uh
+talk to everybody in the room. Um my
+
+ align:start position:0%
+talk to everybody in the room. Um my
+ 
+
+ align:start position:0%
+talk to everybody in the room. Um my
+name is Sanjikuma.
+
+ align:start position:0%
+name is Sanjikuma.
+ 
+
+ align:start position:0%
+name is Sanjikuma.
+I'm the head of policy at the European
+
+ align:start position:0%
+I'm the head of policy at the European
+ 
+
+ align:start position:0%
+I'm the head of policy at the European
+Geothermal Energy Council, which means
+
+ align:start position:0%
+Geothermal Energy Council, which means
+ 
+
+ align:start position:0%
+Geothermal Energy Council, which means
+that my role is to really grow markets
+
+ align:start position:0%
+that my role is to really grow markets
+ 
+
+ align:start position:0%
+that my role is to really grow markets
+for geothermal across Europe. Um, that's
+
+ align:start position:0%
+for geothermal across Europe. Um, that's
+ 
+
+ align:start position:0%
+for geothermal across Europe. Um, that's
+the European Union, but also countries
+
+ align:start position:0%
+the European Union, but also countries
+ 
+
+ align:start position:0%
+the European Union, but also countries
+outside such as, um, uh, Iceland,
+
+ align:start position:0%
+outside such as, um, uh, Iceland,
+ 
+
+ align:start position:0%
+outside such as, um, uh, Iceland,
+Norway, uh, down to Turkey, the Western
+
+ align:start position:0%
+Norway, uh, down to Turkey, the Western
+ 
+
+ align:start position:0%
+Norway, uh, down to Turkey, the Western
+Balkans, and Ukraine. So, I look at what
+
+ align:start position:0%
+Balkans, and Ukraine. So, I look at what
+ 
+
+ align:start position:0%
+Balkans, and Ukraine. So, I look at what
+are the regulatory frameworks, what are
+
+ align:start position:0%
+are the regulatory frameworks, what are
+ 
+
+ align:start position:0%
+are the regulatory frameworks, what are
+the financial structures that we need to
+
+ align:start position:0%
+the financial structures that we need to
+ 
+
+ align:start position:0%
+the financial structures that we need to
+grow geothermal. And what I'm going to
+
+ align:start position:0%
+grow geothermal. And what I'm going to
+ 
+
+ align:start position:0%
+grow geothermal. And what I'm going to
+do is kind of share some of the
+
+ align:start position:0%
+do is kind of share some of the
+ 
+
+ align:start position:0%
+do is kind of share some of the
+experiences that we've had in Europe.
+
+ align:start position:0%
+experiences that we've had in Europe.
+ 
+
+ align:start position:0%
+experiences that we've had in Europe.
+Um, let me start off with some pretty uh
+
+ align:start position:0%
+Um, let me start off with some pretty uh
+ 
+
+ align:start position:0%
+Um, let me start off with some pretty uh
+basic uh things about uh the kind of the
+
+ align:start position:0%
+basic uh things about uh the kind of the
+ 
+
+ align:start position:0%
+basic uh things about uh the kind of the
+content of Europe. Um, and then I'm
+
+ align:start position:0%
+content of Europe. Um, and then I'm
+ 
+
+ align:start position:0%
+content of Europe. Um, and then I'm
+going to kind of give you some ideas
+
+ align:start position:0%
+going to kind of give you some ideas
+ 
+
+ align:start position:0%
+going to kind of give you some ideas
+about how you can perhaps build upon the
+
+ align:start position:0%
+about how you can perhaps build upon the
+ 
+
+ align:start position:0%
+about how you can perhaps build upon the
+session that you've had before the
+
+ align:start position:0%
+session that you've had before the
+ 
+
+ align:start position:0%
+session that you've had before the
+discussions you've had uh this morning
+
+ align:start position:0%
+discussions you've had uh this morning
+ 
+
+ align:start position:0%
+discussions you've had uh this morning
+and then the discussions you're going to
+
+ align:start position:0%
+and then the discussions you're going to
+ 
+
+ align:start position:0%
+and then the discussions you're going to
+have um uh tomorrow. So let's start off
+
+ align:start position:0%
+have um uh tomorrow. So let's start off
+ 
+
+ align:start position:0%
+have um uh tomorrow. So let's start off
+with some basics. uh there about Europe
+
+ align:start position:0%
+with some basics. uh there about Europe
+ 
+
+ align:start position:0%
+with some basics. uh there about Europe
+is uh generally um our um heat gradient
+
+ align:start position:0%
+is uh generally um our um heat gradient
+ 
+
+ align:start position:0%
+is uh generally um our um heat gradient
+is quite low. We have lower temperatures
+
+ align:start position:0%
+is quite low. We have lower temperatures
+ 
+
+ align:start position:0%
+is quite low. We have lower temperatures
+so we don't have a lot of power
+
+ align:start position:0%
+so we don't have a lot of power
+ 
+
+ align:start position:0%
+so we don't have a lot of power
+generation. Uh what we do have is a lot
+
+ align:start position:0%
+generation. Uh what we do have is a lot
+ 
+
+ align:start position:0%
+generation. Uh what we do have is a lot
+of heating. Um our market is geared
+
+ align:start position:0%
+of heating. Um our market is geared
+ 
+
+ align:start position:0%
+of heating. Um our market is geared
+towards heating and that heat market is
+
+ align:start position:0%
+towards heating and that heat market is
+ 
+
+ align:start position:0%
+towards heating and that heat market is
+transitioning. As it stands at the
+
+ align:start position:0%
+transitioning. As it stands at the
+ 
+
+ align:start position:0%
+transitioning. As it stands at the
+moment there are about 10 million people
+
+ align:start position:0%
+moment there are about 10 million people
+ 
+
+ align:start position:0%
+moment there are about 10 million people
+across Europe who benefit from different
+
+ align:start position:0%
+across Europe who benefit from different
+ 
+
+ align:start position:0%
+across Europe who benefit from different
+types of geothermal heat pumps. These
+
+ align:start position:0%
+types of geothermal heat pumps. These
+ 
+
+ align:start position:0%
+types of geothermal heat pumps. These
+are small uh closed loop systems to uh
+
+ align:start position:0%
+are small uh closed loop systems to uh
+ 
+
+ align:start position:0%
+are small uh closed loop systems to uh
+large openloop systems. uh we have
+
+ align:start position:0%
+large openloop systems. uh we have
+ 
+
+ align:start position:0%
+large openloop systems. uh we have
+district heating uh direct use um and
+
+ align:start position:0%
+district heating uh direct use um and
+ 
+
+ align:start position:0%
+district heating uh direct use um and
+that's really for uh cities. We also in
+
+ align:start position:0%
+that's really for uh cities. We also in
+ 
+
+ align:start position:0%
+that's really for uh cities. We also in
+a few countries have a lot of district
+
+ align:start position:0%
+a few countries have a lot of district
+ 
+
+ align:start position:0%
+a few countries have a lot of district
+heating systems just for the agriculture
+
+ align:start position:0%
+heating systems just for the agriculture
+ 
+
+ align:start position:0%
+heating systems just for the agriculture
+community. So when it comes to thinking
+
+ align:start position:0%
+community. So when it comes to thinking
+ 
+
+ align:start position:0%
+community. So when it comes to thinking
+about your your doing new kind of
+
+ align:start position:0%
+about your your doing new kind of
+ 
+
+ align:start position:0%
+about your your doing new kind of
+customer base I know a lot of the
+
+ align:start position:0%
+customer base I know a lot of the
+ 
+
+ align:start position:0%
+customer base I know a lot of the
+conversation is going to be around
+
+ align:start position:0%
+conversation is going to be around
+ 
+
+ align:start position:0%
+conversation is going to be around
+residential consumers. There is a whole
+
+ align:start position:0%
+residential consumers. There is a whole
+ 
+
+ align:start position:0%
+residential consumers. There is a whole
+world outside the residential space. Um
+
+ align:start position:0%
+world outside the residential space. Um
+ 
+
+ align:start position:0%
+world outside the residential space. Um
+and people like farmers we found in
+
+ align:start position:0%
+and people like farmers we found in
+ 
+
+ align:start position:0%
+and people like farmers we found in
+Europe are very very vocal and generally
+
+ align:start position:0%
+Europe are very very vocal and generally
+ 
+
+ align:start position:0%
+Europe are very very vocal and generally
+tend to get their own way. So and they
+
+ align:start position:0%
+tend to get their own way. So and they
+ 
+
+ align:start position:0%
+tend to get their own way. So and they
+have a desire to have a permanent supply
+
+ align:start position:0%
+have a desire to have a permanent supply
+ 
+
+ align:start position:0%
+have a desire to have a permanent supply
+of heating and cooling. So it's a
+
+ align:start position:0%
+of heating and cooling. So it's a
+ 
+
+ align:start position:0%
+of heating and cooling. So it's a
+fantastic customer base. Factories.
+
+ align:start position:0%
+fantastic customer base. Factories.
+ 
+
+ align:start position:0%
+fantastic customer base. Factories.
+There's some of the big car makers in
+
+ align:start position:0%
+There's some of the big car makers in
+ 
+
+ align:start position:0%
+There's some of the big car makers in
+Europe have just uh uh installed
+
+ align:start position:0%
+Europe have just uh uh installed
+ 
+
+ align:start position:0%
+Europe have just uh uh installed
+geothermal heating and cooling systems
+
+ align:start position:0%
+geothermal heating and cooling systems
+ 
+
+ align:start position:0%
+geothermal heating and cooling systems
+um uh for their uh for their factories,
+
+ align:start position:0%
+um uh for their uh for their factories,
+ 
+
+ align:start position:0%
+um uh for their uh for their factories,
+for their head offices. It's it's really
+
+ align:start position:0%
+for their head offices. It's it's really
+ 
+
+ align:start position:0%
+for their head offices. It's it's really
+big. And of course, we've got 11 million
+
+ align:start position:0%
+big. And of course, we've got 11 million
+ 
+
+ align:start position:0%
+big. And of course, we've got 11 million
+consumers tapped into geothermal power.
+
+ align:start position:0%
+consumers tapped into geothermal power.
+ 
+
+ align:start position:0%
+consumers tapped into geothermal power.
+Um, but what I want to do is just to
+
+ align:start position:0%
+Um, but what I want to do is just to
+ 
+
+ align:start position:0%
+Um, but what I want to do is just to
+deep dive a little bit into what the
+
+ align:start position:0%
+deep dive a little bit into what the
+ 
+
+ align:start position:0%
+deep dive a little bit into what the
+situation in Europe is, why it's perhaps
+
+ align:start position:0%
+situation in Europe is, why it's perhaps
+ 
+
+ align:start position:0%
+situation in Europe is, why it's perhaps
+different to the US, but the challenges
+
+ align:start position:0%
+different to the US, but the challenges
+ 
+
+ align:start position:0%
+different to the US, but the challenges
+that we face are the same challenges
+
+ align:start position:0%
+that we face are the same challenges
+ 
+
+ align:start position:0%
+that we face are the same challenges
+that you're going to face as you start
+
+ align:start position:0%
+that you're going to face as you start
+ 
+
+ align:start position:0%
+that you're going to face as you start
+to scale up uh geothermal in particular,
+
+ align:start position:0%
+to scale up uh geothermal in particular,
+ 
+
+ align:start position:0%
+to scale up uh geothermal in particular,
+especially network geothermal. So, let's
+
+ align:start position:0%
+especially network geothermal. So, let's
+ 
+
+ align:start position:0%
+especially network geothermal. So, let's
+start off with some basics. Um like
+
+ align:start position:0%
+start off with some basics. Um like
+ 
+
+ align:start position:0%
+start off with some basics. Um like
+everywhere else in the world, the bulk
+
+ align:start position:0%
+everywhere else in the world, the bulk
+ 
+
+ align:start position:0%
+everywhere else in the world, the bulk
+of our heating and cooling supply is
+
+ align:start position:0%
+of our heating and cooling supply is
+ 
+
+ align:start position:0%
+of our heating and cooling supply is
+fossilbased. Um where we have
+
+ align:start position:0%
+fossilbased. Um where we have
+ 
+
+ align:start position:0%
+fossilbased. Um where we have
+non-fossilbased heating cooling, it's
+
+ align:start position:0%
+non-fossilbased heating cooling, it's
+ 
+
+ align:start position:0%
+non-fossilbased heating cooling, it's
+largely coming from combustible biomass.
+
+ align:start position:0%
+largely coming from combustible biomass.
+ 
+
+ align:start position:0%
+largely coming from combustible biomass.
+Um and over the last five or six years,
+
+ align:start position:0%
+Um and over the last five or six years,
+ 
+
+ align:start position:0%
+Um and over the last five or six years,
+there's been a quite a ugly discussion
+
+ align:start position:0%
+there's been a quite a ugly discussion
+ 
+
+ align:start position:0%
+there's been a quite a ugly discussion
+around toning down the amount of biomass
+
+ align:start position:0%
+around toning down the amount of biomass
+ 
+
+ align:start position:0%
+around toning down the amount of biomass
+uh to just focusing on that can be that
+
+ align:start position:0%
+uh to just focusing on that can be that
+ 
+
+ align:start position:0%
+uh to just focusing on that can be that
+which can be sustainably sourced. And
+
+ align:start position:0%
+which can be sustainably sourced. And
+ 
+
+ align:start position:0%
+which can be sustainably sourced. And
+what that's effectively done is put a
+
+ align:start position:0%
+what that's effectively done is put a
+ 
+
+ align:start position:0%
+what that's effectively done is put a
+ceiling on the amount of biomass we're
+
+ align:start position:0%
+ceiling on the amount of biomass we're
+ 
+
+ align:start position:0%
+ceiling on the amount of biomass we're
+going to use uh in heating. So the
+
+ align:start position:0%
+going to use uh in heating. So the
+ 
+
+ align:start position:0%
+going to use uh in heating. So the
+growth market that they've had in the
+
+ align:start position:0%
+growth market that they've had in the
+ 
+
+ align:start position:0%
+growth market that they've had in the
+past is going to start to diminish. And
+
+ align:start position:0%
+past is going to start to diminish. And
+ 
+
+ align:start position:0%
+past is going to start to diminish. And
+what that's really doing is it's kind of
+
+ align:start position:0%
+what that's really doing is it's kind of
+ 
+
+ align:start position:0%
+what that's really doing is it's kind of
+paving the way for um heat pumps um and
+
+ align:start position:0%
+paving the way for um heat pumps um and
+ 
+
+ align:start position:0%
+paving the way for um heat pumps um and
+for kind of direct use geothermal. And
+
+ align:start position:0%
+for kind of direct use geothermal. And
+ 
+
+ align:start position:0%
+for kind of direct use geothermal. And
+when we talk about heat pumps in a
+
+ align:start position:0%
+when we talk about heat pumps in a
+ 
+
+ align:start position:0%
+when we talk about heat pumps in a
+European context, almost everybody
+
+ align:start position:0%
+European context, almost everybody
+ 
+
+ align:start position:0%
+European context, almost everybody
+thinks of airsource heat pumps. So the
+
+ align:start position:0%
+thinks of airsource heat pumps. So the
+ 
+
+ align:start position:0%
+thinks of airsource heat pumps. So the
+language that we use to describe uh
+
+ align:start position:0%
+language that we use to describe uh
+ 
+
+ align:start position:0%
+language that we use to describe uh
+electric heating with uh ground source
+
+ align:start position:0%
+electric heating with uh ground source
+ 
+
+ align:start position:0%
+electric heating with uh ground source
+heat pumps, geothermal heat pumps is
+
+ align:start position:0%
+heat pumps, geothermal heat pumps is
+ 
+
+ align:start position:0%
+heat pumps, geothermal heat pumps is
+something we're going to come back to
+
+ align:start position:0%
+something we're going to come back to
+ 
+
+ align:start position:0%
+something we're going to come back to
+later on. We also have a legacy system
+
+ align:start position:0%
+later on. We also have a legacy system
+ 
+
+ align:start position:0%
+later on. We also have a legacy system
+of district heating. So, a lot of these
+
+ align:start position:0%
+of district heating. So, a lot of these
+ 
+
+ align:start position:0%
+of district heating. So, a lot of these
+are in former Soviet countries, but you
+
+ align:start position:0%
+are in former Soviet countries, but you
+ 
+
+ align:start position:0%
+are in former Soviet countries, but you
+also have them in Baltic places, sorry,
+
+ align:start position:0%
+also have them in Baltic places, sorry,
+ 
+
+ align:start position:0%
+also have them in Baltic places, sorry,
+in the Scandinavian countries such as
+
+ align:start position:0%
+in the Scandinavian countries such as
+ 
+
+ align:start position:0%
+in the Scandinavian countries such as
+Denmark um and Finland um uh where you
+
+ align:start position:0%
+Denmark um and Finland um uh where you
+ 
+
+ align:start position:0%
+Denmark um and Finland um uh where you
+have effectively heat networks that were
+
+ align:start position:0%
+have effectively heat networks that were
+ 
+
+ align:start position:0%
+have effectively heat networks that were
+built on the back of a a coal plant, a
+
+ align:start position:0%
+built on the back of a a coal plant, a
+ 
+
+ align:start position:0%
+built on the back of a a coal plant, a
+gas plant or a waste incineration plant,
+
+ align:start position:0%
+gas plant or a waste incineration plant,
+ 
+
+ align:start position:0%
+gas plant or a waste incineration plant,
+and you take the excess heat and you
+
+ align:start position:0%
+and you take the excess heat and you
+ 
+
+ align:start position:0%
+and you take the excess heat and you
+pump it at high temperatures at vast
+
+ align:start position:0%
+pump it at high temperatures at vast
+ 
+
+ align:start position:0%
+pump it at high temperatures at vast
+quantities through um a network. Um
+
+ align:start position:0%
+quantities through um a network. Um
+ 
+
+ align:start position:0%
+quantities through um a network. Um
+these are extremely inefficient. They're
+
+ align:start position:0%
+these are extremely inefficient. They're
+ 
+
+ align:start position:0%
+these are extremely inefficient. They're
+very very polluting. And what's been
+
+ align:start position:0%
+very very polluting. And what's been
+ 
+
+ align:start position:0%
+very very polluting. And what's been
+happening over the last 20 years is that
+
+ align:start position:0%
+happening over the last 20 years is that
+ 
+
+ align:start position:0%
+happening over the last 20 years is that
+people have just been jumping using uh
+
+ align:start position:0%
+people have just been jumping using uh
+ 
+
+ align:start position:0%
+people have just been jumping using uh
+things like airsource heat pumps,
+
+ align:start position:0%
+things like airsource heat pumps,
+ 
+
+ align:start position:0%
+things like airsource heat pumps,
+geothermal heat pumps to get themselves
+
+ align:start position:0%
+geothermal heat pumps to get themselves
+ 
+
+ align:start position:0%
+geothermal heat pumps to get themselves
+off of these district heating systems.
+
+ align:start position:0%
+off of these district heating systems.
+ 
+
+ align:start position:0%
+off of these district heating systems.
+So this industry has a tarnished
+
+ align:start position:0%
+So this industry has a tarnished
+ 
+
+ align:start position:0%
+So this industry has a tarnished
+reputation. But if we're serious about
+
+ align:start position:0%
+reputation. But if we're serious about
+ 
+
+ align:start position:0%
+reputation. But if we're serious about
+decarbonization, we're going to have to
+
+ align:start position:0%
+decarbonization, we're going to have to
+ 
+
+ align:start position:0%
+decarbonization, we're going to have to
+rethink uh district heating and cooling
+
+ align:start position:0%
+rethink uh district heating and cooling
+ 
+
+ align:start position:0%
+rethink uh district heating and cooling
+systems. And this becomes really
+
+ align:start position:0%
+systems. And this becomes really
+ 
+
+ align:start position:0%
+systems. And this becomes really
+important to you. So it's within that
+
+ align:start position:0%
+important to you. So it's within that
+ 
+
+ align:start position:0%
+important to you. So it's within that
+context of a multitude of supplies. um
+
+ align:start position:0%
+context of a multitude of supplies. um
+ 
+
+ align:start position:0%
+context of a multitude of supplies. um
+renewable energies incumbent fossils
+
+ align:start position:0%
+renewable energies incumbent fossils
+ 
+
+ align:start position:0%
+renewable energies incumbent fossils
+that network geothermal has to operate
+
+ align:start position:0%
+that network geothermal has to operate
+ 
+
+ align:start position:0%
+that network geothermal has to operate
+in. So that's our competition base. Um
+
+ align:start position:0%
+in. So that's our competition base. Um
+ 
+
+ align:start position:0%
+in. So that's our competition base. Um
+the other thing which is quite important
+
+ align:start position:0%
+the other thing which is quite important
+ 
+
+ align:start position:0%
+the other thing which is quite important
+to us and will become an issue for you
+
+ align:start position:0%
+to us and will become an issue for you
+ 
+
+ align:start position:0%
+to us and will become an issue for you
+later on um is the fact that we have a
+
+ align:start position:0%
+later on um is the fact that we have a
+ 
+
+ align:start position:0%
+later on um is the fact that we have a
+largely densely populated uh
+
+ align:start position:0%
+largely densely populated uh
+ 
+
+ align:start position:0%
+largely densely populated uh
+geographical spaces. So we don't have
+
+ align:start position:0%
+geographical spaces. So we don't have
+ 
+
+ align:start position:0%
+geographical spaces. So we don't have
+vast lands in which we can do drilling
+
+ align:start position:0%
+vast lands in which we can do drilling
+ 
+
+ align:start position:0%
+vast lands in which we can do drilling
+and great uh um uh big uh uh uh
+
+ align:start position:0%
+and great uh um uh big uh uh uh
+ 
+
+ align:start position:0%
+and great uh um uh big uh uh uh
+networks. we have to operate in tightly
+
+ align:start position:0%
+networks. we have to operate in tightly
+ 
+
+ align:start position:0%
+networks. we have to operate in tightly
+confined spaces. Um, and environmental
+
+ align:start position:0%
+confined spaces. Um, and environmental
+ 
+
+ align:start position:0%
+confined spaces. Um, and environmental
+protection is absolutely key. And what
+
+ align:start position:0%
+protection is absolutely key. And what
+ 
+
+ align:start position:0%
+protection is absolutely key. And what
+we found is is that as the geothermal
+
+ align:start position:0%
+we found is is that as the geothermal
+ 
+
+ align:start position:0%
+we found is is that as the geothermal
+sector grows, the regulators,
+
+ align:start position:0%
+sector grows, the regulators,
+ 
+
+ align:start position:0%
+sector grows, the regulators,
+particularly those that are looking at
+
+ align:start position:0%
+particularly those that are looking at
+ 
+
+ align:start position:0%
+particularly those that are looking at
+protecting water,
+
+ align:start position:0%
+protecting water,
+ 
+
+ align:start position:0%
+protecting water,
+drinking water, surface water, those
+
+ align:start position:0%
+drinking water, surface water, those
+ 
+
+ align:start position:0%
+drinking water, surface water, those
+that are very very nervous about uh kind
+
+ align:start position:0%
+that are very very nervous about uh kind
+ 
+
+ align:start position:0%
+that are very very nervous about uh kind
+of geothermal activities around them,
+
+ align:start position:0%
+of geothermal activities around them,
+ 
+
+ align:start position:0%
+of geothermal activities around them,
+but also are very concerned and are
+
+ align:start position:0%
+but also are very concerned and are
+ 
+
+ align:start position:0%
+but also are very concerned and are
+driven by the perception of negative
+
+ align:start position:0%
+driven by the perception of negative
+ 
+
+ align:start position:0%
+driven by the perception of negative
+impacts. This has in some cases slowed
+
+ align:start position:0%
+impacts. This has in some cases slowed
+ 
+
+ align:start position:0%
+impacts. This has in some cases slowed
+down a lot of growth that we've seen in
+
+ align:start position:0%
+down a lot of growth that we've seen in
+ 
+
+ align:start position:0%
+down a lot of growth that we've seen in
+in some of the the really advancing
+
+ align:start position:0%
+in some of the the really advancing
+ 
+
+ align:start position:0%
+in some of the the really advancing
+countries such as the Netherlands where
+
+ align:start position:0%
+countries such as the Netherlands where
+ 
+
+ align:start position:0%
+countries such as the Netherlands where
+now it's much harder to for us to get a
+
+ align:start position:0%
+now it's much harder to for us to get a
+ 
+
+ align:start position:0%
+now it's much harder to for us to get a
+permit. So permitting becomes an issue
+
+ align:start position:0%
+permit. So permitting becomes an issue
+ 
+
+ align:start position:0%
+permit. So permitting becomes an issue
+once you start to see a a reasonable
+
+ align:start position:0%
+once you start to see a a reasonable
+ 
+
+ align:start position:0%
+once you start to see a a reasonable
+size of growth um within uh your
+
+ align:start position:0%
+size of growth um within uh your
+ 
+
+ align:start position:0%
+size of growth um within uh your
+geothermal systems. The other two things
+
+ align:start position:0%
+geothermal systems. The other two things
+ 
+
+ align:start position:0%
+geothermal systems. The other two things
+from this one um is that when we often
+
+ align:start position:0%
+from this one um is that when we often
+ 
+
+ align:start position:0%
+from this one um is that when we often
+talk about geothermal in a European
+
+ align:start position:0%
+talk about geothermal in a European
+ 
+
+ align:start position:0%
+talk about geothermal in a European
+context, you can see from the three uh
+
+ align:start position:0%
+context, you can see from the three uh
+ 
+
+ align:start position:0%
+context, you can see from the three uh
+different types of uh geothermal heat
+
+ align:start position:0%
+different types of uh geothermal heat
+ 
+
+ align:start position:0%
+different types of uh geothermal heat
+pumps that we tend to focus on the first
+
+ align:start position:0%
+pumps that we tend to focus on the first
+ 
+
+ align:start position:0%
+pumps that we tend to focus on the first
+two. Um so vertical ball holds or uh two
+
+ align:start position:0%
+two. Um so vertical ball holds or uh two
+ 
+
+ align:start position:0%
+two. Um so vertical ball holds or uh two
+vertical ball holds linked to a
+
+ align:start position:0%
+vertical ball holds linked to a
+ 
+
+ align:start position:0%
+vertical ball holds linked to a
+hydrothermal source. The the the example
+
+ align:start position:0%
+hydrothermal source. The the the example
+ 
+
+ align:start position:0%
+hydrothermal source. The the the example
+that you have at the end with a loop
+
+ align:start position:0%
+that you have at the end with a loop
+ 
+
+ align:start position:0%
+that you have at the end with a loop
+that's quite shallow, there's just not
+
+ align:start position:0%
+that's quite shallow, there's just not
+ 
+
+ align:start position:0%
+that's quite shallow, there's just not
+enough space for that to really operate
+
+ align:start position:0%
+enough space for that to really operate
+ 
+
+ align:start position:0%
+enough space for that to really operate
+in a European context. So that means
+
+ align:start position:0%
+in a European context. So that means
+ 
+
+ align:start position:0%
+in a European context. So that means
+that we are looking at deeper pipes of
+
+ align:start position:0%
+that we are looking at deeper pipes of
+ 
+
+ align:start position:0%
+that we are looking at deeper pipes of
+drilling much more sophisticated
+
+ align:start position:0%
+drilling much more sophisticated
+ 
+
+ align:start position:0%
+drilling much more sophisticated
+uh and access to land that becomes more
+
+ align:start position:0%
+uh and access to land that becomes more
+ 
+
+ align:start position:0%
+uh and access to land that becomes more
+important as well as being able to get
+
+ align:start position:0%
+important as well as being able to get
+ 
+
+ align:start position:0%
+important as well as being able to get
+drilling rigs into uh people's gardens
+
+ align:start position:0%
+drilling rigs into uh people's gardens
+ 
+
+ align:start position:0%
+drilling rigs into uh people's gardens
+or whole uh down streets. One of the
+
+ align:start position:0%
+or whole uh down streets. One of the
+ 
+
+ align:start position:0%
+or whole uh down streets. One of the
+other things that's happened is in a few
+
+ align:start position:0%
+other things that's happened is in a few
+ 
+
+ align:start position:0%
+other things that's happened is in a few
+countries where the market has started
+
+ align:start position:0%
+countries where the market has started
+ 
+
+ align:start position:0%
+countries where the market has started
+to grow and it hasn't been regulated. Um
+
+ align:start position:0%
+to grow and it hasn't been regulated. Um
+ 
+
+ align:start position:0%
+to grow and it hasn't been regulated. Um
+we've had the issue of thermal
+
+ align:start position:0%
+we've had the issue of thermal
+ 
+
+ align:start position:0%
+we've had the issue of thermal
+interference where people have been kind
+
+ align:start position:0%
+interference where people have been kind
+ 
+
+ align:start position:0%
+interference where people have been kind
+of installing geothermal heat pumps in
+
+ align:start position:0%
+of installing geothermal heat pumps in
+ 
+
+ align:start position:0%
+of installing geothermal heat pumps in
+their back gardens but they're too close
+
+ align:start position:0%
+their back gardens but they're too close
+ 
+
+ align:start position:0%
+their back gardens but they're too close
+to somebody else's back garden and what
+
+ align:start position:0%
+to somebody else's back garden and what
+ 
+
+ align:start position:0%
+to somebody else's back garden and what
+you do then is they install a heat pump
+
+ align:start position:0%
+you do then is they install a heat pump
+ 
+
+ align:start position:0%
+you do then is they install a heat pump
+a geothermal heat pump and you're
+
+ align:start position:0%
+a geothermal heat pump and you're
+ 
+
+ align:start position:0%
+a geothermal heat pump and you're
+effectively diminishing the the overall
+
+ align:start position:0%
+effectively diminishing the the overall
+ 
+
+ align:start position:0%
+effectively diminishing the the overall
+thermal efficiency of that one. there's
+
+ align:start position:0%
+thermal efficiency of that one. there's
+ 
+
+ align:start position:0%
+thermal efficiency of that one. there's
+le lawsuits in Ireland uh for example it
+
+ align:start position:0%
+le lawsuits in Ireland uh for example it
+ 
+
+ align:start position:0%
+le lawsuits in Ireland uh for example it
+kind of again dampened down uh the
+
+ align:start position:0%
+kind of again dampened down uh the
+ 
+
+ align:start position:0%
+kind of again dampened down uh the
+growth in that market. So these are the
+
+ align:start position:0%
+growth in that market. So these are the
+ 
+
+ align:start position:0%
+growth in that market. So these are the
+kind of things that you're going to have
+
+ align:start position:0%
+kind of things that you're going to have
+ 
+
+ align:start position:0%
+kind of things that you're going to have
+to start to think through and for us the
+
+ align:start position:0%
+to start to think through and for us the
+ 
+
+ align:start position:0%
+to start to think through and for us the
+the the most important issue becomes
+
+ align:start position:0%
+the the most important issue becomes
+ 
+
+ align:start position:0%
+the the most important issue becomes
+permitting. Um you can see from the the
+
+ align:start position:0%
+permitting. Um you can see from the the
+ 
+
+ align:start position:0%
+permitting. Um you can see from the the
+map at the bottom that's a map of France
+
+ align:start position:0%
+map at the bottom that's a map of France
+ 
+
+ align:start position:0%
+map at the bottom that's a map of France
+at a 100 meter depth. um all the areas
+
+ align:start position:0%
+at a 100 meter depth. um all the areas
+ 
+
+ align:start position:0%
+at a 100 meter depth. um all the areas
+where if you're going to install a
+
+ align:start position:0%
+where if you're going to install a
+ 
+
+ align:start position:0%
+where if you're going to install a
+geothermal heat pump, the zones in
+
+ align:start position:0%
+geothermal heat pump, the zones in
+ 
+
+ align:start position:0%
+geothermal heat pump, the zones in
+green, you just have to do a simple
+
+ align:start position:0%
+green, you just have to do a simple
+ 
+
+ align:start position:0%
+green, you just have to do a simple
+email to your local government just to
+
+ align:start position:0%
+email to your local government just to
+ 
+
+ align:start position:0%
+email to your local government just to
+say, "Hey, this is where I'm installing
+
+ align:start position:0%
+say, "Hey, this is where I'm installing
+ 
+
+ align:start position:0%
+say, "Hey, this is where I'm installing
+my uh ball hole. Uh this is how this is
+
+ align:start position:0%
+my uh ball hole. Uh this is how this is
+ 
+
+ align:start position:0%
+my uh ball hole. Uh this is how this is
+the kind of depth it's going to be. Um
+
+ align:start position:0%
+the kind of depth it's going to be. Um
+ 
+
+ align:start position:0%
+the kind of depth it's going to be. Um
+and this is the kind of the geoloccation
+
+ align:start position:0%
+and this is the kind of the geoloccation
+ 
+
+ align:start position:0%
+and this is the kind of the geoloccation
+as possibly
+
+ align:start position:0%
+as possibly
+ 
+
+ align:start position:0%
+as possibly
+get it. Um and then that can be noted
+
+ align:start position:0%
+get it. Um and then that can be noted
+ 
+
+ align:start position:0%
+get it. Um and then that can be noted
+somewhere in a registry so that later on
+
+ align:start position:0%
+somewhere in a registry so that later on
+ 
+
+ align:start position:0%
+somewhere in a registry so that later on
+in maybe 1015 years time if somebody
+
+ align:start position:0%
+in maybe 1015 years time if somebody
+ 
+
+ align:start position:0%
+in maybe 1015 years time if somebody
+else wants to plot something they can
+
+ align:start position:0%
+else wants to plot something they can
+ 
+
+ align:start position:0%
+else wants to plot something they can
+very quickly check and see if there's
+
+ align:start position:0%
+very quickly check and see if there's
+ 
+
+ align:start position:0%
+very quickly check and see if there's
+going to be any kind of uh negative
+
+ align:start position:0%
+going to be any kind of uh negative
+ 
+
+ align:start position:0%
+going to be any kind of uh negative
+impact on any additional systems coming
+
+ align:start position:0%
+impact on any additional systems coming
+ 
+
+ align:start position:0%
+impact on any additional systems coming
+on. Then you have orange areas. Orange
+
+ align:start position:0%
+on. Then you have orange areas. Orange
+ 
+
+ align:start position:0%
+on. Then you have orange areas. Orange
+areas are sensitive subsurface activity
+
+ align:start position:0%
+areas are sensitive subsurface activity
+ 
+
+ align:start position:0%
+areas are sensitive subsurface activity
+and you need to get some form of an
+
+ align:start position:0%
+and you need to get some form of an
+ 
+
+ align:start position:0%
+and you need to get some form of an
+external recognition. Again this is for
+
+ align:start position:0%
+external recognition. Again this is for
+ 
+
+ align:start position:0%
+external recognition. Again this is for
+like a 100 m 200 m depth. there needs to
+
+ align:start position:0%
+like a 100 m 200 m depth. there needs to
+ 
+
+ align:start position:0%
+like a 100 m 200 m depth. there needs to
+be some form of third party assessment.
+
+ align:start position:0%
+be some form of third party assessment.
+ 
+
+ align:start position:0%
+be some form of third party assessment.
+And then the red areas are really where
+
+ align:start position:0%
+And then the red areas are really where
+ 
+
+ align:start position:0%
+And then the red areas are really where
+you need to have a full environmental
+
+ align:start position:0%
+you need to have a full environmental
+ 
+
+ align:start position:0%
+you need to have a full environmental
+impact assessment. They're very
+
+ align:start position:0%
+impact assessment. They're very
+ 
+
+ align:start position:0%
+impact assessment. They're very
+sensitive areas. Um and you can see that
+
+ align:start position:0%
+sensitive areas. Um and you can see that
+ 
+
+ align:start position:0%
+sensitive areas. Um and you can see that
+the what the kind of the the
+
+ align:start position:0%
+the what the kind of the the
+ 
+
+ align:start position:0%
+the what the kind of the the
+congregation of red dots um uh on the um
+
+ align:start position:0%
+congregation of red dots um uh on the um
+ 
+
+ align:start position:0%
+congregation of red dots um uh on the um
+on the eastern part of France is the
+
+ align:start position:0%
+on the eastern part of France is the
+ 
+
+ align:start position:0%
+on the eastern part of France is the
+Alsas region and the Alsas region is a
+
+ align:start position:0%
+Alsas region and the Alsas region is a
+ 
+
+ align:start position:0%
+Alsas region and the Alsas region is a
+volcanic uh region. There have been
+
+ align:start position:0%
+volcanic uh region. There have been
+ 
+
+ align:start position:0%
+volcanic uh region. There have been
+examples where people have drilled uh uh
+
+ align:start position:0%
+examples where people have drilled uh uh
+ 
+
+ align:start position:0%
+examples where people have drilled uh uh
+geothermal heat pumps and in one case
+
+ align:start position:0%
+geothermal heat pumps and in one case
+ 
+
+ align:start position:0%
+geothermal heat pumps and in one case
+actually uh damaged eight or nine
+
+ align:start position:0%
+actually uh damaged eight or nine
+ 
+
+ align:start position:0%
+actually uh damaged eight or nine
+properties within a village and that led
+
+ align:start position:0%
+properties within a village and that led
+ 
+
+ align:start position:0%
+properties within a village and that led
+to a variety of lawsuits um and really
+
+ align:start position:0%
+to a variety of lawsuits um and really
+ 
+
+ align:start position:0%
+to a variety of lawsuits um and really
+did give a negative impression to
+
+ align:start position:0%
+did give a negative impression to
+ 
+
+ align:start position:0%
+did give a negative impression to
+geothermal even though France is one of
+
+ align:start position:0%
+geothermal even though France is one of
+ 
+
+ align:start position:0%
+geothermal even though France is one of
+those countries that's really gung-ho um
+
+ align:start position:0%
+those countries that's really gung-ho um
+ 
+
+ align:start position:0%
+those countries that's really gung-ho um
+in our SAS the mayor of ours all of them
+
+ align:start position:0%
+in our SAS the mayor of ours all of them
+ 
+
+ align:start position:0%
+in our SAS the mayor of ours all of them
+don't like geothermal and they lump all
+
+ align:start position:0%
+don't like geothermal and they lump all
+ 
+
+ align:start position:0%
+don't like geothermal and they lump all
+geothermal into this uh basket so we
+
+ align:start position:0%
+geothermal into this uh basket so we
+ 
+
+ align:start position:0%
+geothermal into this uh basket so we
+need to be very very sensitive around
+
+ align:start position:0%
+need to be very very sensitive around
+ 
+
+ align:start position:0%
+need to be very very sensitive around
+the environmental impacts as your market
+
+ align:start position:0%
+the environmental impacts as your market
+ 
+
+ align:start position:0%
+the environmental impacts as your market
+starts to grow. Um, just a kind of quick
+
+ align:start position:0%
+starts to grow. Um, just a kind of quick
+ 
+
+ align:start position:0%
+starts to grow. Um, just a kind of quick
+thing, I I noticed you might not be able
+
+ align:start position:0%
+thing, I I noticed you might not be able
+ 
+
+ align:start position:0%
+thing, I I noticed you might not be able
+to see this graphic clearly, but you can
+
+ align:start position:0%
+to see this graphic clearly, but you can
+ 
+
+ align:start position:0%
+to see this graphic clearly, but you can
+blow up the screen when you get the the
+
+ align:start position:0%
+blow up the screen when you get the the
+ 
+
+ align:start position:0%
+blow up the screen when you get the the
+slides. Uh, Sweden is the largest
+
+ align:start position:0%
+slides. Uh, Sweden is the largest
+ 
+
+ align:start position:0%
+slides. Uh, Sweden is the largest
+country in terms of installed capacity.
+
+ align:start position:0%
+country in terms of installed capacity.
+ 
+
+ align:start position:0%
+country in terms of installed capacity.
+Germany second, uh, France is third. But
+
+ align:start position:0%
+Germany second, uh, France is third. But
+ 
+
+ align:start position:0%
+Germany second, uh, France is third. But
+really, the countries to look at if
+
+ align:start position:0%
+really, the countries to look at if
+ 
+
+ align:start position:0%
+really, the countries to look at if
+you're going to look at them are
+
+ align:start position:0%
+you're going to look at them are
+ 
+
+ align:start position:0%
+you're going to look at them are
+Belgium, the Netherlands, and Poland.
+
+ align:start position:0%
+Belgium, the Netherlands, and Poland.
+ 
+
+ align:start position:0%
+Belgium, the Netherlands, and Poland.
+These these really have grown uh roughly
+
+ align:start position:0%
+These these really have grown uh roughly
+ 
+
+ align:start position:0%
+These these really have grown uh roughly
+over the last decade. is a new entrance
+
+ align:start position:0%
+over the last decade. is a new entrance
+ 
+
+ align:start position:0%
+over the last decade. is a new entrance
+and that that's where all the innovation
+
+ align:start position:0%
+and that that's where all the innovation
+ 
+
+ align:start position:0%
+and that that's where all the innovation
+is happening and part of the innovation
+
+ align:start position:0%
+is happening and part of the innovation
+ 
+
+ align:start position:0%
+is happening and part of the innovation
+story in a country like Belgium is
+
+ align:start position:0%
+story in a country like Belgium is
+ 
+
+ align:start position:0%
+story in a country like Belgium is
+around network geos. I'm going to come
+
+ align:start position:0%
+around network geos. I'm going to come
+ 
+
+ align:start position:0%
+around network geos. I'm going to come
+on to that later on as to why that's the
+
+ align:start position:0%
+on to that later on as to why that's the
+ 
+
+ align:start position:0%
+on to that later on as to why that's the
+case. Um and then what you can see here
+
+ align:start position:0%
+case. Um and then what you can see here
+ 
+
+ align:start position:0%
+case. Um and then what you can see here
+is is on the figure 14 is the kind of
+
+ align:start position:0%
+is is on the figure 14 is the kind of
+ 
+
+ align:start position:0%
+is is on the figure 14 is the kind of
+the density of heat pumps uh per
+
+ align:start position:0%
+the density of heat pumps uh per
+ 
+
+ align:start position:0%
+the density of heat pumps uh per
+thousand households. So again Sweden is
+
+ align:start position:0%
+thousand households. So again Sweden is
+ 
+
+ align:start position:0%
+thousand households. So again Sweden is
+the most populous country. In Sweden,
+
+ align:start position:0%
+the most populous country. In Sweden,
+ 
+
+ align:start position:0%
+the most populous country. In Sweden,
+home buyers generally tend to look at
+
+ align:start position:0%
+home buyers generally tend to look at
+ 
+
+ align:start position:0%
+home buyers generally tend to look at
+five criteria uh when they're purchasing
+
+ align:start position:0%
+five criteria uh when they're purchasing
+ 
+
+ align:start position:0%
+five criteria uh when they're purchasing
+a new property, and a geothermal heat
+
+ align:start position:0%
+a new property, and a geothermal heat
+ 
+
+ align:start position:0%
+a new property, and a geothermal heat
+pump is normally the fourth orif fifth
+
+ align:start position:0%
+pump is normally the fourth orif fifth
+ 
+
+ align:start position:0%
+pump is normally the fourth orif fifth
+thing that they look at. Um before the
+
+ align:start position:0%
+thing that they look at. Um before the
+ 
+
+ align:start position:0%
+thing that they look at. Um before the
+construction industry collapsed in
+
+ align:start position:0%
+construction industry collapsed in
+ 
+
+ align:start position:0%
+construction industry collapsed in
+around 2000 2020, um geothermal houses
+
+ align:start position:0%
+around 2000 2020, um geothermal houses
+ 
+
+ align:start position:0%
+around 2000 2020, um geothermal houses
+with geothermal heat pumps sold for 12
+
+ align:start position:0%
+with geothermal heat pumps sold for 12
+ 
+
+ align:start position:0%
+with geothermal heat pumps sold for 12
+to 15,000 euros more than houses that
+
+ align:start position:0%
+to 15,000 euros more than houses that
+ 
+
+ align:start position:0%
+to 15,000 euros more than houses that
+didn't. Um, so there was a clear
+
+ align:start position:0%
+didn't. Um, so there was a clear
+ 
+
+ align:start position:0%
+didn't. Um, so there was a clear
+recognition in a mature market that this
+
+ align:start position:0%
+recognition in a mature market that this
+ 
+
+ align:start position:0%
+recognition in a mature market that this
+really does add value to your property.
+
+ align:start position:0%
+really does add value to your property.
+ 
+
+ align:start position:0%
+really does add value to your property.
+Um, we haven't quite seen that in other
+
+ align:start position:0%
+Um, we haven't quite seen that in other
+ 
+
+ align:start position:0%
+Um, we haven't quite seen that in other
+countries, but as they start to grow and
+
+ align:start position:0%
+countries, but as they start to grow and
+ 
+
+ align:start position:0%
+countries, but as they start to grow and
+they become much more populous, we
+
+ align:start position:0%
+they become much more populous, we
+ 
+
+ align:start position:0%
+they become much more populous, we
+expect this to be the Estonia to be the
+
+ align:start position:0%
+expect this to be the Estonia to be the
+ 
+
+ align:start position:0%
+expect this to be the Estonia to be the
+next big country. Um, where you've got a
+
+ align:start position:0%
+next big country. Um, where you've got a
+ 
+
+ align:start position:0%
+next big country. Um, where you've got a
+lot of geothermal heat pumps in there.
+
+ align:start position:0%
+lot of geothermal heat pumps in there.
+ 
+
+ align:start position:0%
+lot of geothermal heat pumps in there.
+Um now what's happened is is that you've
+
+ align:start position:0%
+Um now what's happened is is that you've
+ 
+
+ align:start position:0%
+Um now what's happened is is that you've
+had kind of conventional story around
+
+ align:start position:0%
+had kind of conventional story around
+ 
+
+ align:start position:0%
+had kind of conventional story around
+district heating and uh um uh geothermal
+
+ align:start position:0%
+district heating and uh um uh geothermal
+ 
+
+ align:start position:0%
+district heating and uh um uh geothermal
+heat pumps and then out of nowhere
+
+ align:start position:0%
+heat pumps and then out of nowhere
+ 
+
+ align:start position:0%
+heat pumps and then out of nowhere
+network GFL came onto the scene and they
+
+ align:start position:0%
+network GFL came onto the scene and they
+ 
+
+ align:start position:0%
+network GFL came onto the scene and they
+were young and sexy and fresh and
+
+ align:start position:0%
+were young and sexy and fresh and
+ 
+
+ align:start position:0%
+were young and sexy and fresh and
+everyone's like oh my god I need to have
+
+ align:start position:0%
+everyone's like oh my god I need to have
+ 
+
+ align:start position:0%
+everyone's like oh my god I need to have
+this. Um but this has come uh really
+
+ align:start position:0%
+this. Um but this has come uh really
+ 
+
+ align:start position:0%
+this. Um but this has come uh really
+from three uh angles. So the first angle
+
+ align:start position:0%
+from three uh angles. So the first angle
+ 
+
+ align:start position:0%
+from three uh angles. So the first angle
+is is that district heating, you had a
+
+ align:start position:0%
+is is that district heating, you had a
+ 
+
+ align:start position:0%
+is is that district heating, you had a
+lot of people leaving district heating
+
+ align:start position:0%
+lot of people leaving district heating
+ 
+
+ align:start position:0%
+lot of people leaving district heating
+systems and what you started to find is
+
+ align:start position:0%
+systems and what you started to find is
+ 
+
+ align:start position:0%
+systems and what you started to find is
+that they were in communities and once
+
+ align:start position:0%
+that they were in communities and once
+ 
+
+ align:start position:0%
+that they were in communities and once
+you start to take a community off a
+
+ align:start position:0%
+you start to take a community off a
+ 
+
+ align:start position:0%
+you start to take a community off a
+district heating system, the overall
+
+ align:start position:0%
+district heating system, the overall
+ 
+
+ align:start position:0%
+district heating system, the overall
+cost profile and the efficiency of that
+
+ align:start position:0%
+cost profile and the efficiency of that
+ 
+
+ align:start position:0%
+cost profile and the efficiency of that
+district heating system become a
+
+ align:start position:0%
+district heating system become a
+ 
+
+ align:start position:0%
+district heating system become a
+problem. Um so it's it's caused negative
+
+ align:start position:0%
+problem. Um so it's it's caused negative
+ 
+
+ align:start position:0%
+problem. Um so it's it's caused negative
+tension with the district heating
+
+ align:start position:0%
+tension with the district heating
+ 
+
+ align:start position:0%
+tension with the district heating
+community. On the other hand, you've had
+
+ align:start position:0%
+community. On the other hand, you've had
+ 
+
+ align:start position:0%
+community. On the other hand, you've had
+lots of uh people who were looking at
+
+ align:start position:0%
+lots of uh people who were looking at
+ 
+
+ align:start position:0%
+lots of uh people who were looking at
+doing their own individual installation
+
+ align:start position:0%
+doing their own individual installation
+ 
+
+ align:start position:0%
+doing their own individual installation
+and then they suddenly realized well
+
+ align:start position:0%
+and then they suddenly realized well
+ 
+
+ align:start position:0%
+and then they suddenly realized well
+actually we can band together and create
+
+ align:start position:0%
+actually we can band together and create
+ 
+
+ align:start position:0%
+actually we can band together and create
+a community energy scheme. And in a
+
+ align:start position:0%
+a community energy scheme. And in a
+ 
+
+ align:start position:0%
+a community energy scheme. And in a
+country like Belgium, community energy
+
+ align:start position:0%
+country like Belgium, community energy
+ 
+
+ align:start position:0%
+country like Belgium, community energy
+is really the thing that's driving uh
+
+ align:start position:0%
+is really the thing that's driving uh
+ 
+
+ align:start position:0%
+is really the thing that's driving uh
+this push towards network geothermal.
+
+ align:start position:0%
+this push towards network geothermal.
+ 
+
+ align:start position:0%
+this push towards network geothermal.
+It's not just communities. It's, you
+
+ align:start position:0%
+It's not just communities. It's, you
+ 
+
+ align:start position:0%
+It's not just communities. It's, you
+know, property developers. It's rural
+
+ align:start position:0%
+know, property developers. It's rural
+ 
+
+ align:start position:0%
+know, property developers. It's rural
+communities. It's a variety of people
+
+ align:start position:0%
+communities. It's a variety of people
+ 
+
+ align:start position:0%
+communities. It's a variety of people
+just saying, "Look, it makes sense for
+
+ align:start position:0%
+just saying, "Look, it makes sense for
+ 
+
+ align:start position:0%
+just saying, "Look, it makes sense for
+us to work together to build a common
+
+ align:start position:0%
+us to work together to build a common
+ 
+
+ align:start position:0%
+us to work together to build a common
+infrastructure because then it's so much
+
+ align:start position:0%
+infrastructure because then it's so much
+ 
+
+ align:start position:0%
+infrastructure because then it's so much
+cheaper." And just for full disclosure,
+
+ align:start position:0%
+cheaper." And just for full disclosure,
+ 
+
+ align:start position:0%
+cheaper." And just for full disclosure,
+I'm trying to set one up in my street. I
+
+ align:start position:0%
+I'm trying to set one up in my street. I
+ 
+
+ align:start position:0%
+I'm trying to set one up in my street. I
+live opposite the school. I want the
+
+ align:start position:0%
+live opposite the school. I want the
+ 
+
+ align:start position:0%
+live opposite the school. I want the
+school to to have all the bore holes and
+
+ align:start position:0%
+school to to have all the bore holes and
+ 
+
+ align:start position:0%
+school to to have all the bore holes and
+for us to pay a small fee to connect to
+
+ align:start position:0%
+for us to pay a small fee to connect to
+ 
+
+ align:start position:0%
+for us to pay a small fee to connect to
+their system. I've got um of uh of the
+
+ align:start position:0%
+their system. I've got um of uh of the
+ 
+
+ align:start position:0%
+their system. I've got um of uh of the
+72 uh houses in my uh uh in my my two
+
+ align:start position:0%
+72 uh houses in my uh uh in my my two
+ 
+
+ align:start position:0%
+72 uh houses in my uh uh in my my two
+blocks, we've got 30. so far who were
+
+ align:start position:0%
+blocks, we've got 30. so far who were
+ 
+
+ align:start position:0%
+blocks, we've got 30. so far who were
+keen. We need to get everyone else on
+
+ align:start position:0%
+keen. We need to get everyone else on
+ 
+
+ align:start position:0%
+keen. We need to get everyone else on
+board and then we need to lobby the
+
+ align:start position:0%
+board and then we need to lobby the
+ 
+
+ align:start position:0%
+board and then we need to lobby the
+school to agree to do this one and get
+
+ align:start position:0%
+school to agree to do this one and get
+ 
+
+ align:start position:0%
+school to agree to do this one and get
+some way in which we can finance it. But
+
+ align:start position:0%
+some way in which we can finance it. But
+ 
+
+ align:start position:0%
+some way in which we can finance it. But
+you know individual installations are
+
+ align:start position:0%
+you know individual installations are
+ 
+
+ align:start position:0%
+you know individual installations are
+not the default option anymore. People
+
+ align:start position:0%
+not the default option anymore. People
+ 
+
+ align:start position:0%
+not the default option anymore. People
+want to be part of a um a collective
+
+ align:start position:0%
+want to be part of a um a collective
+ 
+
+ align:start position:0%
+want to be part of a um a collective
+system. It's part of the normalization
+
+ align:start position:0%
+system. It's part of the normalization
+ 
+
+ align:start position:0%
+system. It's part of the normalization
+of the technology as well. And then the
+
+ align:start position:0%
+of the technology as well. And then the
+ 
+
+ align:start position:0%
+of the technology as well. And then the
+third element and I'm going to spend a
+
+ align:start position:0%
+third element and I'm going to spend a
+ 
+
+ align:start position:0%
+third element and I'm going to spend a
+bit of time on this later on is the
+
+ align:start position:0%
+bit of time on this later on is the
+ 
+
+ align:start position:0%
+bit of time on this later on is the
+planning aspect because Europe has been
+
+ align:start position:0%
+planning aspect because Europe has been
+ 
+
+ align:start position:0%
+planning aspect because Europe has been
+heavily dependent upon imported gas and
+
+ align:start position:0%
+heavily dependent upon imported gas and
+ 
+
+ align:start position:0%
+heavily dependent upon imported gas and
+the crisis that happened after Ukraine
+
+ align:start position:0%
+the crisis that happened after Ukraine
+ 
+
+ align:start position:0%
+the crisis that happened after Ukraine
+was invaded. Uh the kind of response was
+
+ align:start position:0%
+was invaded. Uh the kind of response was
+ 
+
+ align:start position:0%
+was invaded. Uh the kind of response was
+saying okay well we need to make someone
+
+ align:start position:0%
+saying okay well we need to make someone
+ 
+
+ align:start position:0%
+saying okay well we need to make someone
+responsible for planning a transition.
+
+ align:start position:0%
+responsible for planning a transition.
+ 
+
+ align:start position:0%
+responsible for planning a transition.
+Um and you know whilst you'll have all
+
+ align:start position:0%
+Um and you know whilst you'll have all
+ 
+
+ align:start position:0%
+Um and you know whilst you'll have all
+the kind of campaigners saying look the
+
+ align:start position:0%
+the kind of campaigners saying look the
+ 
+
+ align:start position:0%
+the kind of campaigners saying look the
+revolution is going to be exciting.
+
+ align:start position:0%
+revolution is going to be exciting.
+ 
+
+ align:start position:0%
+revolution is going to be exciting.
+We're going to be manning the
+
+ align:start position:0%
+We're going to be manning the
+ 
+
+ align:start position:0%
+We're going to be manning the
+barricades. It's not true. The energy
+
+ align:start position:0%
+barricades. It's not true. The energy
+ 
+
+ align:start position:0%
+barricades. It's not true. The energy
+revolution is all about logistics and
+
+ align:start position:0%
+revolution is all about logistics and
+ 
+
+ align:start position:0%
+revolution is all about logistics and
+planning and finance. That's all it is.
+
+ align:start position:0%
+planning and finance. That's all it is.
+ 
+
+ align:start position:0%
+planning and finance. That's all it is.
+Um I can see Hela smiling K
+
+ align:start position:0%
+Um I can see Hela smiling K
+ 
+
+ align:start position:0%
+Um I can see Hela smiling K
+on this point, but it really is that
+
+ align:start position:0%
+on this point, but it really is that
+ 
+
+ align:start position:0%
+on this point, but it really is that
+pedantic. You need to know, you need to
+
+ align:start position:0%
+pedantic. You need to know, you need to
+ 
+
+ align:start position:0%
+pedantic. You need to know, you need to
+get out maps of streets and start
+
+ align:start position:0%
+get out maps of streets and start
+ 
+
+ align:start position:0%
+get out maps of streets and start
+working out well actually what parts can
+
+ align:start position:0%
+working out well actually what parts can
+ 
+
+ align:start position:0%
+working out well actually what parts can
+we convert quickly who goes first, who
+
+ align:start position:0%
+we convert quickly who goes first, who
+ 
+
+ align:start position:0%
+we convert quickly who goes first, who
+goes second, who goes third. But more
+
+ align:start position:0%
+goes second, who goes third. But more
+ 
+
+ align:start position:0%
+goes second, who goes third. But more
+importantly, who makes those decisions?
+
+ align:start position:0%
+importantly, who makes those decisions?
+ 
+
+ align:start position:0%
+importantly, who makes those decisions?
+So let me give you some examples to kind
+
+ align:start position:0%
+So let me give you some examples to kind
+ 
+
+ align:start position:0%
+So let me give you some examples to kind
+of illustrate this transition. and and
+
+ align:start position:0%
+of illustrate this transition. and and
+ 
+
+ align:start position:0%
+of illustrate this transition. and and
+Sanjie, I'm gonna I'm gonna briefly say
+
+ align:start position:0%
+Sanjie, I'm gonna I'm gonna briefly say
+ 
+
+ align:start position:0%
+Sanjie, I'm gonna I'm gonna briefly say
+because you're on the screen that um a
+
+ align:start position:0%
+because you're on the screen that um a
+ 
+
+ align:start position:0%
+because you're on the screen that um a
+couple minutes for the examples would be
+
+ align:start position:0%
+couple minutes for the examples would be
+ 
+
+ align:start position:0%
+couple minutes for the examples would be
+wonderful. Thank you.
+
+ align:start position:0%
+wonderful. Thank you.
+ 
+
+ align:start position:0%
+wonderful. Thank you.
+>> Yeah. Yeah. No, no, I I'm gonna race
+
+ align:start position:0%
+>> Yeah. Yeah. No, no, I I'm gonna race
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. No, no, I I'm gonna race
+through these ones. In fact, I'll just
+
+ align:start position:0%
+through these ones. In fact, I'll just
+ 
+
+ align:start position:0%
+through these ones. In fact, I'll just
+give you one example here. Enfield
+
+ align:start position:0%
+give you one example here. Enfield
+ 
+
+ align:start position:0%
+give you one example here. Enfield
+Council, this is a local authority. They
+
+ align:start position:0%
+Council, this is a local authority. They
+ 
+
+ align:start position:0%
+Council, this is a local authority. They
+converted to geothermal not because they
+
+ align:start position:0%
+converted to geothermal not because they
+ 
+
+ align:start position:0%
+converted to geothermal not because they
+loved their network geothermal, but
+
+ align:start position:0%
+loved their network geothermal, but
+ 
+
+ align:start position:0%
+loved their network geothermal, but
+because their uh the people who were
+
+ align:start position:0%
+because their uh the people who were
+ 
+
+ align:start position:0%
+because their uh the people who were
+living in the four tower blocks, you can
+
+ align:start position:0%
+living in the four tower blocks, you can
+ 
+
+ align:start position:0%
+living in the four tower blocks, you can
+see two of them behind you. they were
+
+ align:start position:0%
+see two of them behind you. they were
+ 
+
+ align:start position:0%
+see two of them behind you. they were
+massively massively indebted in terms of
+
+ align:start position:0%
+massively massively indebted in terms of
+ 
+
+ align:start position:0%
+massively massively indebted in terms of
+their energy costs. So they had a social
+
+ align:start position:0%
+their energy costs. So they had a social
+ 
+
+ align:start position:0%
+their energy costs. So they had a social
+political crisis. Um they looked at all
+
+ align:start position:0%
+political crisis. Um they looked at all
+ 
+
+ align:start position:0%
+political crisis. Um they looked at all
+sorts of options and opted for network
+
+ align:start position:0%
+sorts of options and opted for network
+ 
+
+ align:start position:0%
+sorts of options and opted for network
+geothermal. Instead of refurbishing one
+
+ align:start position:0%
+geothermal. Instead of refurbishing one
+ 
+
+ align:start position:0%
+geothermal. Instead of refurbishing one
+building and one building block by by
+
+ align:start position:0%
+building and one building block by by
+ 
+
+ align:start position:0%
+building and one building block by by
+block, what they decided to do was all
+
+ align:start position:0%
+block, what they decided to do was all
+ 
+
+ align:start position:0%
+block, what they decided to do was all
+four of them in one go. And then you got
+
+ align:start position:0%
+four of them in one go. And then you got
+ 
+
+ align:start position:0%
+four of them in one go. And then you got
+the real system efficiencies kicking
+
+ align:start position:0%
+the real system efficiencies kicking
+ 
+
+ align:start position:0%
+the real system efficiencies kicking
+through. And you can see the savings,
+
+ align:start position:0%
+through. And you can see the savings,
+ 
+
+ align:start position:0%
+through. And you can see the savings,
+you know, between 450 to 700 pounds per
+
+ align:start position:0%
+you know, between 450 to 700 pounds per
+ 
+
+ align:start position:0%
+you know, between 450 to 700 pounds per
+year uh depending on the residents. to
+
+ align:start position:0%
+year uh depending on the residents. to
+ 
+
+ align:start position:0%
+year uh depending on the residents. to
+the energy consumption within those
+
+ align:start position:0%
+the energy consumption within those
+ 
+
+ align:start position:0%
+the energy consumption within those
+buildings. This is my favorite project
+
+ align:start position:0%
+buildings. This is my favorite project
+ 
+
+ align:start position:0%
+buildings. This is my favorite project
+simply because this is in the heart of
+
+ align:start position:0%
+simply because this is in the heart of
+ 
+
+ align:start position:0%
+simply because this is in the heart of
+Brussels and it proves that where you
+
+ align:start position:0%
+Brussels and it proves that where you
+ 
+
+ align:start position:0%
+Brussels and it proves that where you
+have listed buildings, you can actually
+
+ align:start position:0%
+have listed buildings, you can actually
+ 
+
+ align:start position:0%
+have listed buildings, you can actually
+do geothermal projects and that's part
+
+ align:start position:0%
+do geothermal projects and that's part
+ 
+
+ align:start position:0%
+do geothermal projects and that's part
+of the sexy thing about it and that's
+
+ align:start position:0%
+of the sexy thing about it and that's
+ 
+
+ align:start position:0%
+of the sexy thing about it and that's
+really where network geothermal has
+
+ align:start position:0%
+really where network geothermal has
+ 
+
+ align:start position:0%
+really where network geothermal has
+kicked off in Brussels. Our SPA hospital
+
+ align:start position:0%
+kicked off in Brussels. Our SPA hospital
+ 
+
+ align:start position:0%
+kicked off in Brussels. Our SPA hospital
+is a 16th century uh site. You cannot
+
+ align:start position:0%
+is a 16th century uh site. You cannot
+ 
+
+ align:start position:0%
+is a 16th century uh site. You cannot
+touch this building place at all.
+
+ align:start position:0%
+touch this building place at all.
+ 
+
+ align:start position:0%
+touch this building place at all.
+There's a huge complex of uh uh schools.
+
+ align:start position:0%
+There's a huge complex of uh uh schools.
+ 
+
+ align:start position:0%
+There's a huge complex of uh uh schools.
+It's a UNUSCO heritage site. geothermal
+
+ align:start position:0%
+It's a UNUSCO heritage site. geothermal
+ 
+
+ align:start position:0%
+It's a UNUSCO heritage site. geothermal
+was the only option and rather than
+
+ align:start position:0%
+was the only option and rather than
+ 
+
+ align:start position:0%
+was the only option and rather than
+doing individual ground source heat
+
+ align:start position:0%
+doing individual ground source heat
+ 
+
+ align:start position:0%
+doing individual ground source heat
+pumps creating the heat network was
+
+ align:start position:0%
+pumps creating the heat network was
+ 
+
+ align:start position:0%
+pumps creating the heat network was
+really where you got the system
+
+ align:start position:0%
+really where you got the system
+ 
+
+ align:start position:0%
+really where you got the system
+efficiencies coming through the biggest
+
+ align:start position:0%
+efficiencies coming through the biggest
+ 
+
+ align:start position:0%
+efficiencies coming through the biggest
+project in Spain this is really what I
+
+ align:start position:0%
+project in Spain this is really what I
+ 
+
+ align:start position:0%
+project in Spain this is really what I
+want to talk to you about couple of
+
+ align:start position:0%
+want to talk to you about couple of
+ 
+
+ align:start position:0%
+want to talk to you about couple of
+things policy matters now um what's
+
+ align:start position:0%
+things policy matters now um what's
+ 
+
+ align:start position:0%
+things policy matters now um what's
+absolutely essential is that even if
+
+ align:start position:0%
+absolutely essential is that even if
+ 
+
+ align:start position:0%
+absolutely essential is that even if
+geothermal isn't mentioned in the first
+
+ align:start position:0%
+geothermal isn't mentioned in the first
+ 
+
+ align:start position:0%
+geothermal isn't mentioned in the first
+round of policy once you start to get
+
+ align:start position:0%
+round of policy once you start to get
+ 
+
+ align:start position:0%
+round of policy once you start to get
+people thinking about what zero looks
+
+ align:start position:0%
+people thinking about what zero looks
+ 
+
+ align:start position:0%
+people thinking about what zero looks
+like what a fully renewable system uh uh
+
+ align:start position:0%
+like what a fully renewable system uh uh
+ 
+
+ align:start position:0%
+like what a fully renewable system uh uh
+uh uh could be they'll almost always
+
+ align:start position:0%
+uh uh could be they'll almost always
+ 
+
+ align:start position:0%
+uh uh could be they'll almost always
+come and discover geothermal and then
+
+ align:start position:0%
+come and discover geothermal and then
+ 
+
+ align:start position:0%
+come and discover geothermal and then
+they'll start complaining by saying why
+
+ align:start position:0%
+they'll start complaining by saying why
+ 
+
+ align:start position:0%
+they'll start complaining by saying why
+didn't you tell us this existed before
+
+ align:start position:0%
+didn't you tell us this existed before
+ 
+
+ align:start position:0%
+didn't you tell us this existed before
+and what happened in Wunia which is a
+
+ align:start position:0%
+and what happened in Wunia which is a
+ 
+
+ align:start position:0%
+and what happened in Wunia which is a
+small part of Belgium um is they
+
+ align:start position:0%
+small part of Belgium um is they
+ 
+
+ align:start position:0%
+small part of Belgium um is they
+invested just put 35 million euros up
+
+ align:start position:0%
+invested just put 35 million euros up
+ 
+
+ align:start position:0%
+invested just put 35 million euros up
+front for some very basic grants they
+
+ align:start position:0%
+front for some very basic grants they
+ 
+
+ align:start position:0%
+front for some very basic grants they
+did a lot of iconic projects but more
+
+ align:start position:0%
+did a lot of iconic projects but more
+ 
+
+ align:start position:0%
+did a lot of iconic projects but more
+importantly you had Carlo the energy
+
+ align:start position:0%
+importantly you had Carlo the energy
+ 
+
+ align:start position:0%
+importantly you had Carlo the energy
+company all of a sudden become a
+
+ align:start position:0%
+company all of a sudden become a
+ 
+
+ align:start position:0%
+company all of a sudden become a
+national champion in network geothermal
+
+ align:start position:0%
+national champion in network geothermal
+ 
+
+ align:start position:0%
+national champion in network geothermal
+and Resiolia who were the engineering
+
+ align:start position:0%
+and Resiolia who were the engineering
+ 
+
+ align:start position:0%
+and Resiolia who were the engineering
+design company are now winning contracts
+
+ align:start position:0%
+design company are now winning contracts
+ 
+
+ align:start position:0%
+design company are now winning contracts
+all across Europe so there's an
+
+ align:start position:0%
+all across Europe so there's an
+ 
+
+ align:start position:0%
+all across Europe so there's an
+industrial policy story more than just
+
+ align:start position:0%
+industrial policy story more than just
+ 
+
+ align:start position:0%
+industrial policy story more than just
+the energy savings but what I said
+
+ align:start position:0%
+the energy savings but what I said
+ 
+
+ align:start position:0%
+the energy savings but what I said
+earlier the planning bit is absolutely
+
+ align:start position:0%
+earlier the planning bit is absolutely
+ 
+
+ align:start position:0%
+earlier the planning bit is absolutely
+essential and the two key things in the
+
+ align:start position:0%
+essential and the two key things in the
+ 
+
+ align:start position:0%
+essential and the two key things in the
+planning bit is to make sure that
+
+ align:start position:0%
+planning bit is to make sure that
+ 
+
+ align:start position:0%
+planning bit is to make sure that
+whenever you're conducting a plan it has
+
+ align:start position:0%
+whenever you're conducting a plan it has
+ 
+
+ align:start position:0%
+whenever you're conducting a plan it has
+to be based on local renewable energy
+
+ align:start position:0%
+to be based on local renewable energy
+ 
+
+ align:start position:0%
+to be based on local renewable energy
+supplies if you take those two words out
+
+ align:start position:0%
+supplies if you take those two words out
+ 
+
+ align:start position:0%
+supplies if you take those two words out
+of it you will end up with you know
+
+ align:start position:0%
+of it you will end up with you know
+ 
+
+ align:start position:0%
+of it you will end up with you know
+biomass you'll end up with a variety of
+
+ align:start position:0%
+biomass you'll end up with a variety of
+ 
+
+ align:start position:0%
+biomass you'll end up with a variety of
+you know Frankenstein solutions if you
+
+ align:start position:0%
+you know Frankenstein solutions if you
+ 
+
+ align:start position:0%
+you know Frankenstein solutions if you
+want to keep it towards geothermal
+
+ align:start position:0%
+want to keep it towards geothermal
+ 
+
+ align:start position:0%
+want to keep it towards geothermal
+you've got to focus on the locality and
+
+ align:start position:0%
+you've got to focus on the locality and
+ 
+
+ align:start position:0%
+you've got to focus on the locality and
+the renewable aspect around it But
+
+ align:start position:0%
+the renewable aspect around it But
+ 
+
+ align:start position:0%
+the renewable aspect around it But
+really what's super pertinent around
+
+ align:start position:0%
+really what's super pertinent around
+ 
+
+ align:start position:0%
+really what's super pertinent around
+this is the the fact that words matter.
+
+ align:start position:0%
+this is the the fact that words matter.
+ 
+
+ align:start position:0%
+this is the the fact that words matter.
+So when we describe uh network
+
+ align:start position:0%
+So when we describe uh network
+ 
+
+ align:start position:0%
+So when we describe uh network
+geothermal, the reason why we'd say
+
+ align:start position:0%
+geothermal, the reason why we'd say
+ 
+
+ align:start position:0%
+geothermal, the reason why we'd say
+network geothermal and not fifth
+
+ align:start position:0%
+network geothermal and not fifth
+ 
+
+ align:start position:0%
+network geothermal and not fifth
+generation district heating or network
+
+ align:start position:0%
+generation district heating or network
+ 
+
+ align:start position:0%
+generation district heating or network
+uh uh uh sorry heat pump networks is
+
+ align:start position:0%
+uh uh uh sorry heat pump networks is
+ 
+
+ align:start position:0%
+uh uh uh sorry heat pump networks is
+that they don't have the word geothermal
+
+ align:start position:0%
+that they don't have the word geothermal
+ 
+
+ align:start position:0%
+that they don't have the word geothermal
+in. And if you don't have the word
+
+ align:start position:0%
+in. And if you don't have the word
+ 
+
+ align:start position:0%
+in. And if you don't have the word
+geothermal, you're going to miss all of
+
+ align:start position:0%
+geothermal, you're going to miss all of
+ 
+
+ align:start position:0%
+geothermal, you're going to miss all of
+the things that you need to go through
+
+ align:start position:0%
+the things that you need to go through
+ 
+
+ align:start position:0%
+the things that you need to go through
+to get to the network geothermal system.
+
+ align:start position:0%
+to get to the network geothermal system.
+ 
+
+ align:start position:0%
+to get to the network geothermal system.
+Always focus on who makes the
+
+ align:start position:0%
+Always focus on who makes the
+ 
+
+ align:start position:0%
+Always focus on who makes the
+investment. So in the some of the
+
+ align:start position:0%
+investment. So in the some of the
+ 
+
+ align:start position:0%
+investment. So in the some of the
+examples I've showed you, it's the local
+
+ align:start position:0%
+examples I've showed you, it's the local
+ 
+
+ align:start position:0%
+examples I've showed you, it's the local
+government, it's a community, it's a
+
+ align:start position:0%
+government, it's a community, it's a
+ 
+
+ align:start position:0%
+government, it's a community, it's a
+property developer, their needs are
+
+ align:start position:0%
+property developer, their needs are
+ 
+
+ align:start position:0%
+property developer, their needs are
+completely different, but the way in
+
+ align:start position:0%
+completely different, but the way in
+ 
+
+ align:start position:0%
+completely different, but the way in
+which they access finance is also
+
+ align:start position:0%
+which they access finance is also
+ 
+
+ align:start position:0%
+which they access finance is also
+completely different. So it changes the
+
+ align:start position:0%
+completely different. So it changes the
+ 
+
+ align:start position:0%
+completely different. So it changes the
+gambit. Um business models are the most
+
+ align:start position:0%
+gambit. Um business models are the most
+ 
+
+ align:start position:0%
+gambit. Um business models are the most
+important thing. It's not about can you
+
+ align:start position:0%
+important thing. It's not about can you
+ 
+
+ align:start position:0%
+important thing. It's not about can you
+do the project, it's about how do you
+
+ align:start position:0%
+do the project, it's about how do you
+ 
+
+ align:start position:0%
+do the project, it's about how do you
+make it profitable for everybody and
+
+ align:start position:0%
+make it profitable for everybody and
+ 
+
+ align:start position:0%
+make it profitable for everybody and
+that's where the innovation around you
+
+ align:start position:0%
+that's where the innovation around you
+ 
+
+ align:start position:0%
+that's where the innovation around you
+know whether you have an onbalance or
+
+ align:start position:0%
+know whether you have an onbalance or
+ 
+
+ align:start position:0%
+know whether you have an onbalance or
+offbalance sheet. um what's the size and
+
+ align:start position:0%
+offbalance sheet. um what's the size and
+ 
+
+ align:start position:0%
+offbalance sheet. um what's the size and
+the length of the project? How do you
+
+ align:start position:0%
+the length of the project? How do you
+ 
+
+ align:start position:0%
+the length of the project? How do you
+build in the modules? How do you kind of
+
+ align:start position:0%
+build in the modules? How do you kind of
+ 
+
+ align:start position:0%
+build in the modules? How do you kind of
+seg uh disagregate the different prices
+
+ align:start position:0%
+seg uh disagregate the different prices
+ 
+
+ align:start position:0%
+seg uh disagregate the different prices
+that people pay? This is the most
+
+ align:start position:0%
+that people pay? This is the most
+ 
+
+ align:start position:0%
+that people pay? This is the most
+important thing when it comes to
+
+ align:start position:0%
+important thing when it comes to
+ 
+
+ align:start position:0%
+important thing when it comes to
+designing a system at scale.
+
+ align:start position:0%
+designing a system at scale.
+ 
+
+ align:start position:0%
+designing a system at scale.
+Uh super important drilling is sexy. So
+
+ align:start position:0%
+Uh super important drilling is sexy. So
+ 
+
+ align:start position:0%
+Uh super important drilling is sexy. So
+whilst everyone talks about the energy
+
+ align:start position:0%
+whilst everyone talks about the energy
+ 
+
+ align:start position:0%
+whilst everyone talks about the energy
+savings, the greenhouse gas emission
+
+ align:start position:0%
+savings, the greenhouse gas emission
+ 
+
+ align:start position:0%
+savings, the greenhouse gas emission
+reductions, that's great, but in the
+
+ align:start position:0%
+reductions, that's great, but in the
+ 
+
+ align:start position:0%
+reductions, that's great, but in the
+geothermal world, once you've done an
+
+ align:start position:0%
+geothermal world, once you've done an
+ 
+
+ align:start position:0%
+geothermal world, once you've done an
+installation, you will not see
+
+ align:start position:0%
+installation, you will not see
+ 
+
+ align:start position:0%
+installation, you will not see
+geothermal ever again. apart from two
+
+ align:start position:0%
+geothermal ever again. apart from two
+ 
+
+ align:start position:0%
+geothermal ever again. apart from two
+black pipes coming out into a into your
+
+ align:start position:0%
+black pipes coming out into a into your
+ 
+
+ align:start position:0%
+black pipes coming out into a into your
+heat pump.
+
+ align:start position:0%
+heat pump.
+ 
+
+ align:start position:0%
+heat pump.
+>> So, the drilling bit is where you get
+
+ align:start position:0%
+>> So, the drilling bit is where you get
+ 
+
+ align:start position:0%
+>> So, the drilling bit is where you get
+people attracted.
+
+ align:start position:0%
+people attracted.
+ 
+
+ align:start position:0%
+people attracted.
+>> Two more things, super important. You've
+
+ align:start position:0%
+>> Two more things, super important. You've
+ 
+
+ align:start position:0%
+>> Two more things, super important. You've
+got to have more and more people
+
+ align:start position:0%
+got to have more and more people
+ 
+
+ align:start position:0%
+got to have more and more people
+providing the service of uh designing
+
+ align:start position:0%
+providing the service of uh designing
+ 
+
+ align:start position:0%
+providing the service of uh designing
+and install installation. The more you
+
+ align:start position:0%
+and install installation. The more you
+ 
+
+ align:start position:0%
+and install installation. The more you
+do that, the more competitive the price
+
+ align:start position:0%
+do that, the more competitive the price
+ 
+
+ align:start position:0%
+do that, the more competitive the price
+becomes, the more you start to get
+
+ align:start position:0%
+becomes, the more you start to get
+ 
+
+ align:start position:0%
+becomes, the more you start to get
+suppliers chasing markets. And this is
+
+ align:start position:0%
+suppliers chasing markets. And this is
+ 
+
+ align:start position:0%
+suppliers chasing markets. And this is
+really the space we want to get to. And
+
+ align:start position:0%
+really the space we want to get to. And
+ 
+
+ align:start position:0%
+really the space we want to get to. And
+then the final thing is is that whilst
+
+ align:start position:0%
+then the final thing is is that whilst
+ 
+
+ align:start position:0%
+then the final thing is is that whilst
+we talk about the energy service
+
+ align:start position:0%
+we talk about the energy service
+ 
+
+ align:start position:0%
+we talk about the energy service
+delivery, the real political win is an
+
+ align:start position:0%
+delivery, the real political win is an
+ 
+
+ align:start position:0%
+delivery, the real political win is an
+industrial policy. Can you set up
+
+ align:start position:0%
+industrial policy. Can you set up
+ 
+
+ align:start position:0%
+industrial policy. Can you set up
+manufacturing uh uh any part of the
+
+ align:start position:0%
+manufacturing uh uh any part of the
+ 
+
+ align:start position:0%
+manufacturing uh uh any part of the
+component features? Can you create
+
+ align:start position:0%
+component features? Can you create
+ 
+
+ align:start position:0%
+component features? Can you create
+companies with design experts or
+
+ align:start position:0%
+companies with design experts or
+ 
+
+ align:start position:0%
+companies with design experts or
+training experts or drilling experts?
+
+ align:start position:0%
+training experts or drilling experts?
+ 
+
+ align:start position:0%
+training experts or drilling experts?
+That's where you get the real value for
+
+ align:start position:0%
+That's where you get the real value for
+ 
+
+ align:start position:0%
+That's where you get the real value for
+money. That's where the competitions
+
+ align:start position:0%
+money. That's where the competitions
+ 
+
+ align:start position:0%
+money. That's where the competitions
+really start to wake up. So on that
+
+ align:start position:0%
+really start to wake up. So on that
+ 
+
+ align:start position:0%
+really start to wake up. So on that
+note, think global,
+
+ align:start position:0%
+note, think global,
+ 
+
+ align:start position:0%
+note, think global,
+think global, go.
+
+ align:start position:0%
+think global, go.
+ 
+
+ align:start position:0%
+think global, go.
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+>> Thank you. Thank you, Sanjief. And I I I
+
+ align:start position:0%
+>> Thank you. Thank you, Sanjief. And I I I
+ 
+
+ align:start position:0%
+>> Thank you. Thank you, Sanjief. And I I I
+see that you uh your previous slide you
+
+ align:start position:0%
+see that you uh your previous slide you
+ 
+
+ align:start position:0%
+see that you uh your previous slide you
+apparently agree with our
+
+ align:start position:0%
+apparently agree with our
+ 
+
+ align:start position:0%
+apparently agree with our
+administration's drill baby drill. Um
+
+ align:start position:0%
+administration's drill baby drill. Um
+ 
+
+ align:start position:0%
+administration's drill baby drill. Um
+so thank you for covering so much.
\ No newline at end of file
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index 0000000000000000000000000000000000000000..f306fb56aa86957d7334b2f203a06ddda2a898db
--- /dev/null
+++ b/j1H3jAAGlEA.txt
@@ -0,0 +1,2282 @@
+PATRICK WINSTON: Today
+we're going to be
+
+talking about Search.
+
+I know you're going to
+turn blue with yet
+
+another lecture on Search.
+
+Those of you who are taking
+computer science subjects,
+
+you've probably seen in 601.
+
+You'll see it again
+as theory course.
+
+But we're going to do it for
+a little different purpose.
+
+I want you to develop some
+intuition about various kinds
+
+of Search work.
+
+And I want to talk a little bit
+about Search as a model of
+
+what goes on in our heads.
+
+And toward the end, if there's
+time, I'd like to do a
+
+demonstration for you of
+something never before
+
+demonstrated to a 603.4 class,
+because it was only completed
+
+last spring.
+
+And some finishing touches were
+added by me this morning.
+
+Always dangerous, but we'll
+see what happens.
+
+There's Cambridge.
+
+You all recognize
+it, of course.
+
+You might want to get from some
+starting position s to
+
+some goal position g.
+
+So, you'll hire a cab and
+hope for the best.
+
+So, here's what might
+happen, not too hot.
+
+Let's move the starting
+position over here.
+
+I've had cab drivers
+like this New York.
+
+But it's not a very good path.
+
+It's the path of a thief.
+
+Let's change the way that the
+search is done to that of a
+
+beginner, an honest beginner.
+
+Not too bad.
+
+Now, let's have a look at how
+the Search would happen if the
+
+cab driver was a Ph.D.
+in physics
+
+after his third post-doc.
+
+These are not actually
+traverse.
+
+These are just things that the
+driver is thinking about, and
+
+that is the very best of
+all possible paths.
+
+So, the thief does
+a horrible job.
+
+The beginner does a pretty
+good job, but
+
+not an optimal job.
+
+This is the optimal job as
+produced by the Ph.D. in
+
+physics after his
+third post-doc.
+
+So, would you like to understand
+how those all work?
+
+The answer, of course, is yes.
+
+I'm going to talk to you about
+procedures that are different
+
+from the way that you just
+solved this problem.
+
+I imagine that if I said to you,
+please find a path for s
+
+to g, you would, within
+a few seconds, find
+
+a pretty good path--
+
+not the optimal one, but
+a pretty good one--
+
+using your eyes.
+
+And we're not going to tell
+you about how that works,
+
+because we don't know
+how that works.
+
+But we do know that problem
+solving with the eyes is an
+
+important part of our
+total intelligence.
+
+And we'll never have a complete
+theory of human
+
+intelligence until we can
+understand the contributions
+
+of the human visual system to
+solving everyday problems like
+
+finding a pretty good
+path in that map.
+
+But, alas, we can't talk about
+that, because we don't know
+
+how to do it.
+
+We're working on it.
+
+But we don't know
+how to do it.
+
+So, I'm not going to use
+Cambridge in my illustrations.
+
+There's too much there to
+work through in an hour.
+
+So, we're going to use this map
+over here which has been
+
+designed to illustrate a
+few important points.
+
+You, too, can find a path
+through that graph pretty
+
+easily with your eyes.
+
+Our programs don't have eyes,
+and they don't have visually
+
+grounded algorithms, so they're
+going to have to do
+
+something else.
+
+And the very first kind of
+search we want to talk about
+
+is called the British
+Museum approach.
+
+This is a slur against at least
+the British Museum, if
+
+not the entire nation, because
+the way you do a British
+
+Museum search is you find
+every possible path.
+
+So, it'll be helpful to have a
+diagram of all possible paths
+
+on the board.
+
+We're going to start with
+a British Museum search.
+
+From the starting position, it's
+clear, you can go from my
+
+s to either a or b.
+
+And already there's an
+important quiz point.
+
+Whenever we have these kinds of
+problems on a quiz, we ask
+
+you to develop the tree
+associated with a search in
+
+lexical order.
+
+So, the nodes there under s
+are listed alphabetically,
+
+just to have an orderly
+way of doing it.
+
+So, from a we can go
+either b or d.
+
+And another convention of the
+subject, another thing you
+
+have to keep in mind in quizzes,
+is it we don't have
+
+these searches bite
+their own tail.
+
+So, I could have said that
+if I'm at a, I can
+
+also go back to s.
+
+But no path is ever allowed
+them to bite itself, to go
+
+around and enter and get
+back to a place that's
+
+already on the path.
+
+Now if I go on to b first, that
+means that from b I can
+
+go to either a or c.
+
+This is getting fat
+pretty fast.
+
+But let's see, s, a, b.
+
+The only place I can go
+is c and then to e.
+
+s, a, d, without biting my own
+tail and going back to a, the
+
+only place I can go is g.
+
+s b, a, I can only go
+to d and then to g.
+
+And finally, s, b, c,
+I can only go to e.
+
+So, that is a complete set of
+paths as produced by any
+
+program that you will feel you'd
+like to write that finds
+
+all possible paths.
+
+I haven't been very precise
+about how to do that, because
+
+you don't have to be.
+
+You can't save much work by
+being clever, because you have
+
+to find everything.
+
+So, that's the British Museum
+expansion of the tree.
+
+So, what have I done?
+
+I've been playing around
+with a map.
+
+I showed you an example
+of a map.
+
+And pretty soon you're
+going to think that
+
+Search is about maps.
+
+So, before going even another
+tiny step, I want to emphasize
+
+that Search is not
+equal to maps.
+
+Search is about choice.
+
+And I happen to illustrate
+these searches with maps,
+
+because they are particularly
+cogent.
+
+But Search is not about maps.
+
+It's about the choices you make
+when you're trying to
+
+make decisions.
+
+These things I'm going to be
+talking to you about today are
+
+choices you make when
+you explore the map.
+
+You can make other kinds of
+choices when you're exploring
+
+other kinds of things.
+
+And, in fact, at the end, if
+there's time, I'll show you
+
+how you do searches when you're
+solving problems in a
+
+humanities class.
+
+That's the British
+Museum algorithm.
+
+Search is not about maps.
+
+Our first gold star idea,
+Search is about choice.
+
+But for our illustration,
+Search is about maps.
+
+So, the first kind of Search we
+want to talk about that's
+
+real is Depth-first Search.
+
+And the idea of Depth-first
+Search is that you barrel
+
+ahead in a single-minded way.
+
+So, from s, your choices
+are a or b.
+
+And you always go down the left
+branch by convention.
+
+So, from s, we go to a.
+
+From a we have two choices.
+
+We can go to either b or
+d following our lexical
+
+convention.
+
+After that, we can go to c.
+
+And after that we can go to e.
+
+And too bad for us,
+we're stuck.
+
+What are we going to do.
+
+We've got into a dead
+end, all is lost.
+
+But of course, all isn't lost.
+
+Because we have the choice of
+backing up to the place where
+
+we last made a decision and
+choosing another branch.
+
+So, that process is called
+variously back-up or
+
+backtracking.
+
+At this point, we would
+say, ah, dead end.
+
+The first place we find when we
+back up the tree where we
+
+made a choice is when we
+chose b instead of d.
+
+So, we go back up there and
+take the other route.
+
+s, a, d now goes to g.
+
+And we're done.
+
+We're going to make up a little
+table here of things
+
+that we can embellish our
+basic searches with.
+
+And one of the things we can
+embellish our basic searches
+
+with is this backtracking
+idea.
+
+Now, backtrack is not relevant
+to the British Museum
+
+algorithm, because you've
+got to find everything.
+
+You can't quit when you've
+found one path.
+
+But you'd always want to use
+backtracking with Depth-first
+
+Search, because you may plunge
+on down and miss the path that
+
+gets to the goal.
+
+Now, you might ask me, is
+backtracking, therefore,
+
+always part of Depth-first
+Search?
+
+And you can read textbooks
+that do it either way.
+
+Count on it.
+
+If we give you a Search problem
+on a quiz, we'll tell
+
+you whether or not your Search
+is supposed to use
+
+backtracking.
+
+We consider it to be
+an optional thing.
+
+You'd be pretty stupid not to
+use this optional thing when
+
+you're doing Depth-first
+Search.
+
+But we'll separate these
+ideas out and call
+
+it an optional add-on.
+
+so, that's Depth-first
+Search, very simple.
+
+Now, the natural companion to
+Depth-first Search will be
+
+Breadth-first Search,
+Breadth-first.
+
+And the way it works is you
+build up this tree level by
+
+level, and at some point, when
+you scan across a level,
+
+you'll find that you've
+completed a path
+
+that goes to the goal.
+
+So, level by level, s can
+go to either a or b.
+
+a can go either to b or d.
+
+And b can go to either a or c.
+
+So, you see what we're doing.
+
+We're going level by level.
+
+And we haven't hit a level
+with a goal in it yet, so
+
+we've got to keep going.
+
+Note that we're building up
+quite a bit of stuff here,
+
+quite a lot of growth in the
+size of the path set that
+
+we're keeping in mind.
+
+At the next level, we have b
+going to c, d going to g, a
+
+going to d, and c going to e.
+
+And now, when we scan
+across, we do hit g.
+
+So, we found a path with
+Breadth-first Search, just as
+
+we found a path with
+Depth-first Search.
+
+Now, you might say, well,
+why didn't you just quit
+
+when you hit g?
+
+Implementation detail.
+
+We'll talk about a sample
+implementation.
+
+You can write it in
+any way you want.
+
+But now that we know what these
+searches are, let's
+
+speed things up a little bit
+here and do a couple searches
+
+that now have names.
+
+The first type will be
+Depth-first, boom.
+
+That's the one that produces
+the thief path.
+
+And then we can also do a
+Breadth-first Search, which we
+
+haven't tried yet.
+
+What do you suppose is
+going to happen?
+
+Is it going to be fast, slow,
+produce a good path,
+
+produce a bad path?
+
+I don't know, let's try it.
+
+I had to speed it up, you see,
+because it's doing an awful
+
+lot of Search.
+
+It's generating an awful
+lot of paths.
+
+Finally, you got a path.
+
+Is it the best path?
+
+I don't think so.
+
+But we're not going to talk
+about optimal paths today.
+
+We're just going to talk
+about pretty good
+
+paths, heuristic paths.
+
+Let's move the starting position
+here in the middle.
+
+Do you think Breadth-first
+Search is going to be stupid?
+
+I think it's going to
+be pretty stupid.
+
+Let's see what happens.
+
+This Search is a lot to the
+left, which you would never do
+
+with you eye.
+
+Let me slow that down just
+to demonstrate it.
+
+It finds a shorter path, because
+it's right there in
+
+the middle.
+
+But it spends a lot of its time
+looking off to the left.
+
+It's pretty stupid.
+
+But that's how it works.
+
+So, now that we've got two
+examples of searches on the
+
+table, I'd like to just write
+a little flow chart for how
+
+the search might work.
+
+Because if I do that, then it'll
+be easier for us to see
+
+what kind of small differences
+there are between the
+
+implementations of these
+various searches.
+
+So, what we're going to do is
+we're going to develop a
+
+waiting list, a queue, a
+line, whatever you'd
+
+like to call it.
+
+Let's call if a queue.
+
+We're going to develop a queue
+of paths that are under
+
+consideration.
+
+So, the first step in our
+algorithm will be to
+
+initialize our queue.
+
+And I think what I'll do is
+I'll simulate Depth-first
+
+Search on this problem
+up there on the
+
+left using this algorithm.
+
+I need to have some way of
+representing my paths.
+
+And what I want to do is I'm
+going to betray my heritage as
+
+a list programmer, because I'm
+just going to put these up as
+
+if there were lisp
+s-expressions.
+
+To begin with, I just
+have one path.
+
+And it has only one
+node in it, s.
+
+That's the whole path.
+
+The next thing I do after I
+initialize the queue is I
+
+extend first path
+on the queue.
+
+OK, when I extend s,
+I get two paths.
+
+I get s goes to a, and
+I get s goes to b.
+
+I take the first one off
+the front of the queue.
+
+And I put back the two
+that are produced by
+
+extending that path.
+
+Now, after I've extended the
+first path on the queue, I
+
+have to but those extended
+paths on to the queue.
+
+In here there's an explicit step
+where I've checked to see
+
+if that first path
+is a winner.
+
+If it's not, I extend it.
+
+And I have to put those
+paths onto the queue.
+
+So, I'll say that what
+I do is I end queue.
+
+Now, I've done one step.
+
+And let's let me do
+another step.
+
+I'm going to take this
+first path off.
+
+I'm going to extend that path.
+
+And where do I put these new
+paths on the queue if I'm
+
+doing Depth-first Search?
+
+Well, I want to work with the
+path that I've just generated.
+
+I'm taking this plunge down
+deep into the search tree.
+
+So, since I want to keep going
+down into the stuff that I
+
+just generated, where then do I
+want to put these two paths?
+
+At the end of the queue?
+
+I don't think so, because
+it'll be a long
+
+time getting there.
+
+I want to put them on the
+front of the queue.
+
+For Depth-first Search, I
+want to put them on the
+
+front of the queue.
+
+And that's why s, a, b goes
+here, and s, a, d, and then
+
+that's s, b.
+
+So, s, b is still there.
+
+That's still a valid
+possibility.
+
+But now I've stuck two paths
+in front of it, both of the
+
+ones I generated by taking a
+path off the front of the
+
+queue, discovering that it
+doesn't go to the goal,
+
+extending it and putting those
+back on the queue.
+
+I might as well complete
+this illustration here.
+
+While I'm at it, I take the s,
+a, b off, s, a, b, and I can
+
+go only there to c.
+
+But, of course, I keep s, a,
+d and s, b on the queue.
+
+Now, I take the front off the
+queue again, and I get s, a,
+
+b, c, e, and not to forget
+s, a, d and s, b.
+
+I take the first one
+off the queue.
+
+It doesn't go to the goal.
+
+I try to extend it, but
+there's nothing there.
+
+I've reached a dead end.
+
+So, in this operation, all I'm
+doing is taking the front one
+
+off the queue and shortening
+the queue.
+
+We're almost home.
+
+I take s, a,d off of queue.
+
+And I get s, a, d, c.
+
+And, of course, I
+still have s, b.
+
+Now, the next time I visit the
+situation, buried in that
+
+first step, I discover a path
+that actually does get to
+
+goal, and I'm done.
+
+So, each time around I
+visualize the queue.
+
+I check to see if I'm done.
+
+If not, I take the extensions
+and put them
+
+somewhere on the queue.
+
+And then I go back in.
+
+And then here there's a varied
+test which checks to see if
+
+we're done.
+
+That's how the Depth-first
+Search algorithm works.
+
+And now, would we have to start
+all over again if we did
+
+Breadth-first Search?
+
+Nope.
+
+Same algorithm.
+
+All the code we've got
+needs one line
+
+replaced, one line changed.
+
+What do I have to do different
+in order to get a
+
+Breadth-first Search out
+of this instead of
+
+a Depth-first Search?
+
+Tanya?
+
+TANYA: Change [INAUDIBLE]
+on the queue.
+
+PATRICK WINSTON: And where
+do I put it on the queue?
+
+She says to change it.
+
+TANYA: On the back?
+
+PATRICK WINSTON: Put
+it on the back.
+
+So, with Breadth-first Search
+all I have to do
+
+is put on the back.
+
+Now, if we were content with a
+inefficient search, and didn't
+
+care much about how good our
+path was, we'd be done.
+
+And we could go home.
+
+But we are a little concerned
+about the
+
+efficiency of our search.
+
+And we would like a
+pretty good path.
+
+So, we're going to have
+to stick around
+
+for a little while.
+
+Now, you may have noticed, up
+there in that the development
+
+of the Breadth-first Search,
+that the algorithm is
+
+incredibly stupid.
+
+Why is the algorithm
+incredibly stupid?
+
+Ty, what do you think?
+
+TY: It can't tell whether it's
+getting closer or further away
+
+from the goal.
+
+PATRICK WINSTON: It certainly
+can't tell whether it's
+
+getting closer or further
+away from the goal.
+
+And we're going to deal
+with that in a minute.
+
+But it's even stupider
+than that.
+
+Why is it stupid?
+
+What's your name?
+
+DYLAN: Dylan.
+
+It [? hits ?] the same
+nodes twice.
+
+PATRICK WINSTON: Dylan said it's
+extending paths that go
+
+to the same node
+more than once.
+
+Let's see what Dylan's
+talking about.
+
+Down here, it extends a.
+
+But it's already extended
+a up there.
+
+Down here, it extends a
+path that goes to b.
+
+And it's already extended
+a path that goes to d.
+
+Over here, it could extend a
+path that went through c, but
+
+it's already got a path
+that goes through c.
+
+So, all of these paths
+are duplicated.
+
+And we're still going
+through them.
+
+That's incredibly stupid.
+
+What we're going to do is
+we're going to amend our
+
+algorithm just a little bit.
+
+And we're not going to extend
+the first path on the queue
+
+unless final node never
+before extended.
+
+What we're going to do is we're
+going to look to see if
+
+there-- we've got this path.
+
+And we're going to extend it.
+
+And it's got a final note.
+
+If we've ever extended a path
+that goes to that final node,
+
+and it was a final node on
+that path, then we're not
+
+going to do it again.
+
+We got to keep a list of places
+that have already been
+
+the last piece of a path
+that was extended.
+
+Everybody got that?
+
+It's a little awkward to say it,
+because it's the last node
+
+we care about.
+
+If a path terminates in a node,
+and if some other path
+
+previously terminated in that
+node and got extended--
+
+we're not going to
+do it again.
+
+Because it's a waste of time.
+
+Now, let's see if this
+actually helps.
+
+Now, use the extended list.
+
+Let's see, well, gee,
+we got that place
+
+in the center there.
+
+Let's just repeat the
+previous search.
+
+Wow, it's taking a long time.
+
+But notice it put 103 paths
+back on the queue.
+
+Now, let's add a filter
+and try again.
+
+A lot less.
+
+So, let's speed this up, and
+we'll start way over here.
+
+You remember how tedious
+that search was.
+
+And now we'll repeat it with
+this list, boom, there it is.
+
+That's all because we didn't do
+that silly thing of going
+
+back through the final
+node that's
+
+already been gone through.
+
+So, you would never not
+want to do this.
+
+We better list this
+as another option.
+
+It doesn't help with a British
+Museum algorithm, because
+
+nothing helps with the British
+Museum algorithm.
+
+Does it help with Depth-first?
+
+Yes.
+
+Does it help with
+Breadth-first?
+
+Yes.
+
+Do we do backtracking
+with Breadth-first?
+
+No, because backtracking
+can't do us any good.
+
+OK, we're almost, except that
+search that's starting in the
+
+middle is still pretty stupid.
+
+Both the Breadth-first version
+and the Depth-first version
+
+are going off to the left.
+
+And we would never do that with
+our eyes in any case.
+
+The next thing we want to do is
+we want to have ourselves a
+
+slightly more informed search
+by taking into consideration
+
+whether we seem to be
+getting anywhere.
+
+So, in general, it's a good
+thing to get closer to where
+
+we want to go.
+
+In general, if we've got a
+choice of going to a node
+
+that's close to the goal or a
+node that's not so close to
+
+the goal, we'll always want
+to go to the one that's
+
+close to the goal.
+
+And as soon as we add that to
+what we're doing, we have
+
+another kind of Search,
+which goes by the
+
+name of Hill Climbing.
+
+And it's just like Depth-first
+Search, except instead of
+
+using lexical order to break
+ties, we're going to break
+
+ties according to which node
+is closer to the goal.
+
+I went to some trouble
+to talk to you about
+
+this enqueued list.
+
+And having gone to that
+trouble, I'm now
+
+going to ignore it.
+
+Not because it isn't a good
+idea, but because trying to
+
+keep track of everything
+in the example is
+
+confusing the example.
+
+It won't work out right in the
+small example and all that.
+
+Put the queueing thing aside,
+queued list aside, and think
+
+instead just about the value
+of going in the direction
+
+that's getting us closer
+to the goal.
+
+In Hill Climbing Search, just
+like a Depth-first Search, we
+
+have a and b.
+
+And we're still going to list
+them lexically on underneath
+
+the parent node.
+
+But now which one is so
+closer to the goal?
+
+Now, this time b is closer
+to the goal than a.
+
+So, instead of following the
+Depth-first course, which
+
+would take us down through a,
+we're going to go to the one
+
+that's closest which
+goes through b.
+
+And b can either go to a or c.
+
+b is six units away from the
+goal. a is about seven plus,
+
+not drawn exactly to scale.
+
+Use the numbers not your eyes.
+
+Now where are we?
+
+It's symmetric, so a and
+c are both equally
+
+far from the goal.
+
+Now we're going to use
+the lexical order
+
+to break the tie.
+
+Now from s, b, a,
+we'll go to d.
+
+And now, which is closest
+to the goal?
+
+That's the only choice
+we have.
+
+So, now we have no choice but
+to go down to the goal.
+
+That's the Hill Climbing way
+of doing the search.
+
+And notice that this time
+there's no backtracking.
+
+It's not the optimal path.
+
+It's not the best path.
+
+But at least there's
+no backtracking.
+
+That's not always true.
+
+That's just an artifact of
+this particular example.
+
+Do you think Hill Climbing would
+produce a faster search?
+
+I think so.
+
+Let's see what happens
+when we add these
+
+things at one at a time.
+
+First, let's turn off
+our extended list.
+
+We turned off our
+extended list.
+
+And we're going to do
+Depth-first again just for the
+
+sake of comparison.
+
+It produces a very roundabout
+path with 48 enqueueings.
+
+Now, let's switch over
+to Hill Climbing.
+
+And what do think?
+
+Do you think it will produce
+a straighter path, fewer
+
+enqueueings?
+
+Boom.
+
+You wouldn't not want to
+do that, would you?
+
+If you've got some kind of
+heuristic that tells you that
+
+you're getting close to the
+goal, you should use it.
+
+Now, it's easy to modify my
+example over there so that
+
+getting close to the goal
+gets you trapped in a
+
+blind alley on e.
+
+That's easy to do.
+
+But that's just an artifact
+of the example.
+
+In general, you want to go along
+a path that gets you
+
+closer to the goal.
+
+So, that's 23.
+
+I don't know, let's see if using
+the extended list filter
+
+does any good.
+
+Yeah, still 23.
+
+So, in that particular case
+the extension list didn't
+
+actually do us any good, because
+we're driving so
+
+directly toward the goal.
+
+OK, that's that.
+
+Now, let's see, is there
+any analog to--
+
+well, we might say that this
+is yet another way of
+
+distinguishing the searches.
+
+And that is, is it an
+informed search?
+
+Is it making use of any kind
+of heuristic information?
+
+Certainly, a British Museum
+is not, Depth is
+
+not, Breadth is not.
+
+And now let's consider what
+we got for Hill Climbing.
+
+Do we want to use
+backtracking?
+
+Sure.
+
+Do we want to use an
+enqueued list?
+
+Sure.
+
+And it is informed, because it's
+taking advantage of this
+
+extra information.
+
+It may not be in your problem.
+
+It's not often the case you've
+got this information in a map.
+
+Your problem may not have any
+heuristic measurement of
+
+distance to the goal.
+
+In which case, you
+can't do it.
+
+But if you've got it,
+you should use it.
+
+Oh, yeah, there's one more.
+
+And I've already given it away
+by having it on my chart.
+
+It's called Beam Search.
+
+And just as Hill Climbing is
+an analog of Depth-first
+
+Search, Beam Search is a
+complement or addition of an
+
+informing heuristic to
+Breadth-first Search.
+
+What you do is you start
+off just like
+
+Breadth-first Search.
+
+But you say I'm going to limit
+the number of paths I'm going
+
+to consider at any level to
+some small, fixed number,
+
+like, in this case,
+how about two.
+
+So, I'm going to say that
+I have a Beam of
+
+two for my Beam Search.
+
+Otherwise, I proceed just
+like Breadth-first
+
+Search, b, d, a, g.
+
+And now I've got that stupid
+thing where I'm duplicating my
+
+nodes, because I'm forgetting
+about the enqueued list.
+
+But to illustrate Beam Search,
+what about I'm going to do now
+
+is I'm going to take all these
+paths I've got at the second
+
+level, and I'm only going
+to keep the best two.
+
+That's my beam width.
+
+And the best two are the two
+that get closest to the goal.
+
+So, those four, b, c, a,
+and d, which two get
+
+closest to the goal?
+
+Now, b and d.
+
+These guys are trimmed off.
+
+I'm only keeping two
+at every level.
+
+Now, going down from b and
+d, I have, at the next
+
+level, c and g.
+
+And now I've found the goal.
+
+So, I'm done.
+
+We could do that here, too.
+
+We could choose a Beam
+Search, not bad.
+
+Let's see, let's try this
+thing from the middle.
+
+Let's slow my speed
+down a little bit.
+
+Now, are we going to see
+anything going off to the left
+
+like we did with ordinary
+Breadth-first Search?
+
+No, because it's smart.
+
+It doesn't say, I want to go to
+a place that's further away
+
+from my goal.
+
+Now, let's see, maybe we can go
+back to our algorithm now
+
+and talk about that enqueueing
+mechanism and
+
+talk about Hill Climbing.
+
+Can I use the same basic search
+mechanism, just change
+
+that one line again?
+
+Yes.
+
+How do I add new paths to
+the queue this time?
+
+Well, it's very much like
+Hill Climbing, right?
+
+I want to add them
+to the front but
+
+with one little flourish.
+
+What's the flourish?
+
+[? Krishna, ?] what
+do you think?
+
+Remember, I want to use my
+heuristic information.
+
+So, I not only add them to the
+front, but amongst the ones
+
+I'm adding to the front,
+what do I do?
+
+AUDIENCE:Check the distance?
+
+PATRICK WINSTON: Check
+the distance.
+
+And how do you arrange them?
+
+AUDIENCE:[? You ?]
+
+[? keep the ?] minimum
+[? first. ?]
+
+PATRICK WINSTON: Yeah, you
+can put the minimum
+
+first if you like.
+
+But let's sort them.
+
+We'll sort them, that will
+keep everything straight.
+
+So Hill Climbing is
+front-sorted.
+
+And, finally, how about Beam?
+
+What do we do with Beam Search
+to add them to the queue?
+
+Well, it doesn't matter where we
+add them, because all we're
+
+going to do is we're going
+to keep the w best.
+
+So, with Beam, we'll just
+abbreviate that by
+
+saying keep w best.
+
+Now, you have some of the basic
+
+searches in you're toolkit.
+
+There's one more that's
+sometimes talked about.
+
+We've got Depth, Breadth, Best,
+and Beam, one more is
+
+Best, Best-first Search.
+
+It's a variant where you say,
+I've got this tree.
+
+It's got a bunch of paths that
+terminate in leaves.
+
+Let me just always work on
+the leaf node that's
+
+closest to the goal.
+
+It can skip around a little bit
+from one place to another.
+
+Because as it pursues one path,
+it may not do very well
+
+in some other path
+quite distant.
+
+And the tree will become
+the best one.
+
+We've actually seen an instance
+of that in then
+
+integration program.
+
+It's capable of skipping all
+over the place, because it's
+
+always taking the easiest
+problem in the search tree, in
+
+the and/or tree, working
+on that.
+
+That's Best-first Search.
+
+You can do these sorts
+of things in
+
+continuous spaces, too.
+
+And you've done the
+mathematics of
+
+that in 1802 or something.
+
+But in continuous spaces, the
+Hill Climbing sometimes leads
+
+to problems or doesn't
+do very well.
+
+What kind of a problem can you
+encounter in a continuous
+
+space with Hill Climbing?
+
+Well, how would you do
+Hill Climbing in
+
+a continuous space?
+
+Let's say we're in the
+mountains, and a big
+
+fog has come up.
+
+We're trying to get to the
+top of the hill before
+
+we freeze to death.
+
+And we take a few steps north,
+a few steps east, west, and
+
+south using our compass.
+
+And we check to see which
+direction seems to be doing
+
+the best job of getting
+us moving upward.
+
+And that's our Hill Climbing
+approach, right?
+
+We have explored four directions
+we can go and pick
+
+the best one.
+
+And from there, we pick four,
+try all those, pick the best
+
+one, and away we go.
+
+We've got ourselves a Hill
+Climbing algorithm.
+
+What's wrong with it?
+
+Or what can be wrong with it?
+
+Sometimes it works just fine.
+
+Yes.
+
+SPEAKER 1: You might get stuck
+in a local maximum.
+
+PATRICK WINSTON: We might get
+stuck in a local maximum.
+
+So, problem letter a is that if
+this is your space, it may
+
+look like that.
+
+And you may get stuck
+on a local maximum.
+
+Is there any other kind of
+problem that can come up?
+
+Well, it all depends on what
+the space is like.
+
+Here's a problem where the
+space has local maxima.
+
+Now, a lot of people have
+been killed on Mt.
+
+Washington when the
+fog comes up.
+
+And they do freeze
+to death, why?
+
+The reason they freeze to death
+is the Hill Climbing
+
+fails them, and they can't
+get to the top
+
+to the ranger station.
+
+And the reason is that there
+are large lawns on the
+
+shoulders of Mt.
+
+Washington.
+
+It's quite flat.
+
+So, it's the telephone
+pole problem.
+
+That space looks like this.
+
+Well, this isn't what Mt.
+
+Washington looks like.
+
+But it's the telephone
+pole problem.
+
+So, when you're wandering
+around here, the idea of
+
+trying a few directions and
+picking the one that's best
+
+doesn't help any, because
+it's flat.
+
+That can be a problem
+with Hill Climbing.
+
+Now, there's one more problem
+with Hill Climbing that most
+
+people don't know about.
+
+But it works like this.
+
+This is a particularly
+acute problem in
+
+high dimensional spaces.
+
+I'll illustrate it
+here just in two.
+
+And I'm going to switch from
+a regular kind of view to a
+
+contour map.
+
+So, my contour map is going to
+betray the presence of a sharp
+
+bridge along the
+45 degree line.
+
+Now you see how you can
+get in trouble there.
+
+You get in trouble, because
+if you take a step in each
+
+direction, every direction
+takes you downhill.
+
+And you think you're
+at the top.
+
+So, suppose you're right
+here and you go north.
+
+That takes you down over
+a contour line.
+
+If you go south, that
+also takes you down
+
+over contour lines.
+
+Likewise, going west and east
+all appear to be taking you
+
+down, whereas, in fact, you're
+climbing a ridge.
+
+And that contour line is the
+highest that I've shown.
+
+So, sometimes you
+can get fooled--
+
+not stuck, but fooled-- into
+thinking you're at the top
+
+when you're actually not.
+
+Now, this is a model
+something.
+
+This subject is about modeling
+intelligence.
+
+And this is a kind of algorithm
+you frequently need
+
+in order to build an
+intelligent system.
+
+But do we have any kind of
+Search happening in our heads?
+
+If we're going to model what
+goes on inside our heads, do
+
+we have to model any kind of
+searching in order to do the
+
+kinds of things that
+we humans do?
+
+I suppose so.
+
+Anytime we make a plan, we're
+actually evaluating a bunch of
+
+choices and seeing
+how they work.
+
+Let me see if I can illustrate
+it another way.
+
+This is a system that I showed
+you a little bit of last time.
+
+And, shoot, I might as well
+review one or two things here.
+
+I showed you a Macbeth story.
+
+This is the story
+I showed you.
+
+And if you had this in a
+humanities class, the simplest
+
+questions that might be asked
+is why did Macduff kill
+
+Macbeth down there
+at the bottom?
+
+Did I demonstrate the answering
+of questions last
+
+time, or just the development
+of the graph?
+
+I can't remember.
+
+But we'll do it again, anyway.
+
+This is somewhat stylized
+English.
+
+Just so you'll know,
+it doesn't have
+
+to be stylized English.
+
+This is English that's made
+available to the Genesis
+
+system by way of something
+called Story Workbench.
+
+There's no free lunch.
+
+Either you can use your human
+resources to rewrite the plot
+
+in third grade English.
+
+Or you can use your human
+resources to take a more
+
+natural, adult-type version of
+the story and decorate it with
+
+annotations that make it
+possible to absorb it.
+
+Just this summer, in a miracle
+of summer [? Europe, ?]
+
+[? Brit ?]
+
+[? van ?]
+
+[? Zijp-- ?]
+
+one of you--
+
+connected these two
+systems together.
+
+So, we can now work with stories
+that are expressed in
+
+pretty natural English.
+
+Everything in our system is
+expressed in English,
+
+including common sense
+knowledge--
+
+like if somebody kills
+you, you're dead--
+
+but more importantly, for
+today's illustration, that
+
+reflective level knowledge,
+that knowledge about what
+
+revenge is.
+
+Here you are.
+
+You're in the humanities class,
+and someone says,
+
+what's really going
+on in the story?
+
+Not the details of who
+kills whom, but is
+
+there a Pyrrhic victory?
+
+Does somebody have a success?
+
+Is there an act of revenge?
+
+These are all kinds of things
+you might be asked about in
+
+some kind of humanities class.
+
+So, let me fire up the
+genesis system.
+
+Pray for internet
+connectivity.
+
+Launch the system on a read of
+that Macbeth story that I
+
+showed you just a moment ago.
+
+At the moment, it's absorbing
+information about background
+
+knowledge, and about reflective
+level knowledge,
+
+and all that sort of thing.
+
+It's building itself
+this thing we call
+
+an elaboration graph.
+
+It's not quite there yet.
+
+It's still reading background
+knowledge.
+
+Now it's reading Macbeth.
+
+It's building it's elaboration
+graph, the same thing you saw
+
+last time, except not quite.
+
+Do you see that stuff
+down at the bottom?
+
+Those are higher level concepts
+that it's managed to
+
+find in the Macbeth story.
+
+So, its found a revenge.
+
+How did it do that?
+
+It searched.
+
+It had a description of what a
+revenge is, and it looked to
+
+see if that pattern
+was exhibited in
+
+the elaboration graph.
+
+So, in a combination of things
+that were said explicitly and
+
+things that were produced by
+knee-jerk if/then rules, the
+
+elaboration graph was
+sufficiently instantiated that
+
+the revenge pattern
+could be found.
+
+That's interesting, Pyrrhic
+victory is a little harder.
+
+You'd probably get an a if you
+said, oh, there's a Pyrrhic
+
+victory in here.
+
+There it is.
+
+So, I'll blow that up a
+little bit so you can
+
+see what that is.
+
+You know what a Pyrrhic
+victory is.
+
+It's a situation where
+everything seems to be going
+
+good at first, and
+then not so hot.
+
+So, Macbeth wants to
+be King down here.
+
+And eventually that leads
+to becoming King.
+
+But too bad for Macbeth, because
+eventually he gets
+
+killed in consequence.
+
+So, it's a Pyrrhic victory.
+
+All that produced by Search
+programs who are looking
+
+through this graph.
+
+Now once you've got the
+capability of doing that, of
+
+course, then you can find
+all sorts of things.
+
+And you can report
+them in English.
+
+But, more interestingly, you
+can answer questions.
+
+Why did Macbeth--
+
+it cares not a hoot about
+capitalization.
+
+ARTIFICIAL INTELLIGENCE: On a
+common sense level, it looks
+
+like Dr. Jekyll thinks Macduff
+killed Macbeth because Macbeth
+
+angered Macduff on a
+reflective level.
+
+It looks like Dr. Jekyll thinks
+Macduff killed Macbeth
+
+as part of acts of mistake,
+Pyrrhic victory, and revenge.
+
+PATRICK WINSTON: Pretty
+corny speech output.
+
+But you see the point.
+
+How did it get the stuff on
+the common sense level?
+
+The same way all those programs
+that build goal trees
+
+report, answers the questions.
+
+It's just looking locally around
+in the connections in
+
+the goal tree.
+
+How did it get the stuff on
+the reflective level?
+
+By reporting on the searches
+that produced information--
+
+it does that by looking for
+higher level thoughts about
+
+its own thoughts and reporting
+in which of those higher level
+
+thoughts the incident we asked
+about actually occurs.
+
+So, let's see, just for fun, we
+might be interested in why
+
+Macbeth murdered Duncan.
+
+Wouldn't this be handy if you
+hadn't actually read the play,
+
+and here it is, you've got
+to write that paper?
+
+ARTIFICIAL INTELLIGENCE:
+On a common sense
+
+level, it looks like--
+
+PATRICK WINSTON: I'll pull the
+plug on that, because that's
+
+just annoying.
+
+Yeah, pretty good, Macbeth wants
+to be King, and Duncan
+
+is the King.
+
+Let's see, why did Macbeth
+become King?
+
+Oh, it won't answer
+the question
+
+unless I spell it right.
+
+I wouldn't be able to show that
+to you until last spring.
+
+In fact, I wouldn't have been
+able to show you this today
+
+until last week with a
+tweak this morning.
+
+Because we've just now connected
+the language output
+
+to, of course, [? Cass's ?]
+
+parser system, which is running
+in reverse, in order
+
+to generate that English.
+
+So, that's something that has
+never before been seen by any
+
+eyes but me.
+
+So, that will conclude what
+we have to do today.
\ No newline at end of file
diff --git a/jLvgNmGuxGk.txt b/jLvgNmGuxGk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..987f1b68de77315c2a23e5ef3964809eda6987a2
--- /dev/null
+++ b/jLvgNmGuxGk.txt
@@ -0,0 +1,16834 @@
+align:start position:0%
+ 
+there's quiz one
+
+ align:start position:0%
+there's quiz one
+ 
+
+ align:start position:0%
+there's quiz one
+which will be out today and
+
+ align:start position:0%
+which will be out today and
+ 
+
+ align:start position:0%
+which will be out today and
+the rules for that are slightly
+
+ align:start position:0%
+the rules for that are slightly
+ 
+
+ align:start position:0%
+the rules for that are slightly
+different from the homework problems
+
+ align:start position:0%
+different from the homework problems
+ 
+
+ align:start position:0%
+different from the homework problems
+it counts twice as much as a homework
+
+ align:start position:0%
+it counts twice as much as a homework
+ 
+
+ align:start position:0%
+it counts twice as much as a homework
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+and it's longer
+
+ align:start position:0%
+and it's longer
+ 
+
+ align:start position:0%
+and it's longer
+not twice as long but something like
+
+ align:start position:0%
+not twice as long but something like
+ 
+
+ align:start position:0%
+not twice as long but something like
+that and so you have also a little bit
+
+ align:start position:0%
+that and so you have also a little bit
+ 
+
+ align:start position:0%
+that and so you have also a little bit
+more time to do it it's not just one
+
+ align:start position:0%
+more time to do it it's not just one
+ 
+
+ align:start position:0%
+more time to do it it's not just one
+week
+
+ align:start position:0%
+week
+ 
+
+ align:start position:0%
+week
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+it's a bit of work so don't leave it too
+
+ align:start position:0%
+it's a bit of work so don't leave it too
+ 
+
+ align:start position:0%
+it's a bit of work so don't leave it too
+late please start on it fairly soon
+
+ align:start position:0%
+late please start on it fairly soon
+ 
+
+ align:start position:0%
+late please start on it fairly soon
+and this is where you're supposed to
+
+ align:start position:0%
+and this is where you're supposed to
+ 
+
+ align:start position:0%
+and this is where you're supposed to
+work on your own
+
+ align:start position:0%
+work on your own
+ 
+
+ align:start position:0%
+work on your own
+uh not not collaborate so
+
+ align:start position:0%
+uh not not collaborate so
+ 
+
+ align:start position:0%
+uh not not collaborate so
+okay and it covers uh you know whatever
+
+ align:start position:0%
+okay and it covers uh you know whatever
+ 
+
+ align:start position:0%
+okay and it covers uh you know whatever
+we did up to this point
+
+ align:start position:0%
+we did up to this point
+ 
+
+ align:start position:0%
+we did up to this point
+uh with a bit more emphasis on recent
+
+ align:start position:0%
+uh with a bit more emphasis on recent
+ 
+
+ align:start position:0%
+uh with a bit more emphasis on recent
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+and i guess only the last question has
+
+ align:start position:0%
+and i guess only the last question has
+ 
+
+ align:start position:0%
+and i guess only the last question has
+to do with the patent we're discussing
+
+ align:start position:0%
+to do with the patent we're discussing
+ 
+
+ align:start position:0%
+to do with the patent we're discussing
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i should be able to deal with the other
+
+ align:start position:0%
+i should be able to deal with the other
+ 
+
+ align:start position:0%
+i should be able to deal with the other
+four right away
+
+ align:start position:0%
+four right away
+ 
+
+ align:start position:0%
+four right away
+okay a little uh sidebar here about um
+
+ align:start position:0%
+okay a little uh sidebar here about um
+ 
+
+ align:start position:0%
+okay a little uh sidebar here about um
+intellectual property
+
+ align:start position:0%
+intellectual property
+ 
+
+ align:start position:0%
+intellectual property
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+starting off with the fact that some
+
+ align:start position:0%
+starting off with the fact that some
+ 
+
+ align:start position:0%
+starting off with the fact that some
+people don't like that terminology
+
+ align:start position:0%
+people don't like that terminology
+ 
+
+ align:start position:0%
+people don't like that terminology
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+you know uh how can an idea be property
+
+ align:start position:0%
+you know uh how can an idea be property
+ 
+
+ align:start position:0%
+you know uh how can an idea be property
+a little bit like
+
+ align:start position:0%
+a little bit like
+ 
+
+ align:start position:0%
+a little bit like
+uh how can a company be a person
+
+ align:start position:0%
+uh how can a company be a person
+ 
+
+ align:start position:0%
+uh how can a company be a person
+well it's you know an awkward thing in
+
+ align:start position:0%
+well it's you know an awkward thing in
+ 
+
+ align:start position:0%
+well it's you know an awkward thing in
+law that
+
+ align:start position:0%
+law that
+ 
+
+ align:start position:0%
+law that
+you have to come up with some way of
+
+ align:start position:0%
+you have to come up with some way of
+ 
+
+ align:start position:0%
+you have to come up with some way of
+formalizing these things and so in this
+
+ align:start position:0%
+formalizing these things and so in this
+ 
+
+ align:start position:0%
+formalizing these things and so in this
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+ideas are treated as property to some
+
+ align:start position:0%
+ideas are treated as property to some
+ 
+
+ align:start position:0%
+ideas are treated as property to some
+extent there are several different types
+
+ align:start position:0%
+extent there are several different types
+ 
+
+ align:start position:0%
+extent there are several different types
+of intellectual property first of all we
+
+ align:start position:0%
+of intellectual property first of all we
+ 
+
+ align:start position:0%
+of intellectual property first of all we
+have patents which is what we'll be
+
+ align:start position:0%
+have patents which is what we'll be
+ 
+
+ align:start position:0%
+have patents which is what we'll be
+talking about and they're different
+
+ align:start position:0%
+talking about and they're different
+ 
+
+ align:start position:0%
+talking about and they're different
+types of patents
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the so-called utility patents
+
+ align:start position:0%
+the so-called utility patents
+ 
+
+ align:start position:0%
+the so-called utility patents
+i.e useful
+
+ align:start position:0%
+i.e useful
+ 
+
+ align:start position:0%
+i.e useful
+and not to say the others aren't useful
+
+ align:start position:0%
+and not to say the others aren't useful
+ 
+
+ align:start position:0%
+and not to say the others aren't useful
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+their design patterns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example jerome little lamelton's
+
+ align:start position:0%
+so for example jerome little lamelton's
+ 
+
+ align:start position:0%
+so for example jerome little lamelton's
+first patent
+
+ align:start position:0%
+first patent
+ 
+
+ align:start position:0%
+first patent
+was a
+
+ align:start position:0%
+was a
+ 
+
+ align:start position:0%
+was a
+basically a design patent
+
+ align:start position:0%
+basically a design patent
+ 
+
+ align:start position:0%
+basically a design patent
+for a baseball cap with a hole in it and
+
+ align:start position:0%
+for a baseball cap with a hole in it and
+ 
+
+ align:start position:0%
+for a baseball cap with a hole in it and
+a tube
+
+ align:start position:0%
+a tube
+ 
+
+ align:start position:0%
+a tube
+that you could blow through so this is
+
+ align:start position:0%
+that you could blow through so this is
+ 
+
+ align:start position:0%
+that you could blow through so this is
+the inverse of the beer baseball cap and
+
+ align:start position:0%
+the inverse of the beer baseball cap and
+ 
+
+ align:start position:0%
+the inverse of the beer baseball cap and
+there'd be a propeller and as you blow
+
+ align:start position:0%
+there'd be a propeller and as you blow
+ 
+
+ align:start position:0%
+there'd be a propeller and as you blow
+through it the propeller would turn
+
+ align:start position:0%
+through it the propeller would turn
+ 
+
+ align:start position:0%
+through it the propeller would turn
+another famous design patent
+
+ align:start position:0%
+another famous design patent
+ 
+
+ align:start position:0%
+another famous design patent
+is apples designed for a cell phone
+
+ align:start position:0%
+is apples designed for a cell phone
+ 
+
+ align:start position:0%
+is apples designed for a cell phone
+and their design pattern says that it
+
+ align:start position:0%
+and their design pattern says that it
+ 
+
+ align:start position:0%
+and their design pattern says that it
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+a rectangle with rounded corners
+
+ align:start position:0%
+a rectangle with rounded corners
+ 
+
+ align:start position:0%
+a rectangle with rounded corners
+and there was a lawsuit with where they
+
+ align:start position:0%
+and there was a lawsuit with where they
+ 
+
+ align:start position:0%
+and there was a lawsuit with where they
+sued samsung
+
+ align:start position:0%
+sued samsung
+ 
+
+ align:start position:0%
+sued samsung
+because their phone
+
+ align:start position:0%
+because their phone
+ 
+
+ align:start position:0%
+because their phone
+you know with a rectangle with rounded
+
+ align:start position:0%
+you know with a rectangle with rounded
+ 
+
+ align:start position:0%
+you know with a rectangle with rounded
+corners
+
+ align:start position:0%
+corners
+ 
+
+ align:start position:0%
+corners
+and the jury awarded uh apple a billion
+
+ align:start position:0%
+and the jury awarded uh apple a billion
+ 
+
+ align:start position:0%
+and the jury awarded uh apple a billion
+dollars so
+
+ align:start position:0%
+dollars so
+ 
+
+ align:start position:0%
+dollars so
+big money involves here and you know you
+
+ align:start position:0%
+big money involves here and you know you
+ 
+
+ align:start position:0%
+big money involves here and you know you
+might say well
+
+ align:start position:0%
+might say well
+ 
+
+ align:start position:0%
+might say well
+what should a cell phone look like other
+
+ align:start position:0%
+what should a cell phone look like other
+ 
+
+ align:start position:0%
+what should a cell phone look like other
+than this you know this is it but it's
+
+ align:start position:0%
+than this you know this is it but it's
+ 
+
+ align:start position:0%
+than this you know this is it but it's
+not completely crazy because at the time
+
+ align:start position:0%
+not completely crazy because at the time
+ 
+
+ align:start position:0%
+not completely crazy because at the time
+they invented it you know phones were
+
+ align:start position:0%
+they invented it you know phones were
+ 
+
+ align:start position:0%
+they invented it you know phones were
+these big concrete things you held in
+
+ align:start position:0%
+these big concrete things you held in
+ 
+
+ align:start position:0%
+these big concrete things you held in
+your hand and so
+
+ align:start position:0%
+your hand and so
+ 
+
+ align:start position:0%
+your hand and so
+anyway uh not
+
+ align:start position:0%
+anyway uh not
+ 
+
+ align:start position:0%
+anyway uh not
+not to argue about the merits of this
+
+ align:start position:0%
+not to argue about the merits of this
+ 
+
+ align:start position:0%
+not to argue about the merits of this
+and and of course it's been appealed and
+
+ align:start position:0%
+and and of course it's been appealed and
+ 
+
+ align:start position:0%
+and and of course it's been appealed and
+so in the end i don't know what will
+
+ align:start position:0%
+so in the end i don't know what will
+ 
+
+ align:start position:0%
+so in the end i don't know what will
+happen i guess some some large amount of
+
+ align:start position:0%
+happen i guess some some large amount of
+ 
+
+ align:start position:0%
+happen i guess some some large amount of
+money will transfer
+
+ align:start position:0%
+money will transfer
+ 
+
+ align:start position:0%
+money will transfer
+uh change hands an amount of money which
+
+ align:start position:0%
+uh change hands an amount of money which
+ 
+
+ align:start position:0%
+uh change hands an amount of money which
+is astronomical to us mere mortals but
+
+ align:start position:0%
+is astronomical to us mere mortals but
+ 
+
+ align:start position:0%
+is astronomical to us mere mortals but
+probably for these companies you know
+
+ align:start position:0%
+probably for these companies you know
+ 
+
+ align:start position:0%
+probably for these companies you know
+it's a small change so
+
+ align:start position:0%
+it's a small change so
+ 
+
+ align:start position:0%
+it's a small change so
+we shouldn't feel too sorry for them
+
+ align:start position:0%
+we shouldn't feel too sorry for them
+ 
+
+ align:start position:0%
+we shouldn't feel too sorry for them
+so patents
+
+ align:start position:0%
+so patents
+ 
+
+ align:start position:0%
+so patents
+we mentioned last time this was the kind
+
+ align:start position:0%
+we mentioned last time this was the kind
+ 
+
+ align:start position:0%
+we mentioned last time this was the kind
+of social contract where
+
+ align:start position:0%
+of social contract where
+ 
+
+ align:start position:0%
+of social contract where
+you explain exactly how to do something
+
+ align:start position:0%
+you explain exactly how to do something
+ 
+
+ align:start position:0%
+you explain exactly how to do something
+in return for having a limited monopoly
+
+ align:start position:0%
+in return for having a limited monopoly
+ 
+
+ align:start position:0%
+in return for having a limited monopoly
+that lasts a certain number of years and
+
+ align:start position:0%
+that lasts a certain number of years and
+ 
+
+ align:start position:0%
+that lasts a certain number of years and
+the you know the rules change slightly
+
+ align:start position:0%
+the you know the rules change slightly
+ 
+
+ align:start position:0%
+the you know the rules change slightly
+as as time goes on
+
+ align:start position:0%
+as as time goes on
+ 
+
+ align:start position:0%
+as as time goes on
+uh by the way um
+
+ align:start position:0%
+uh by the way um
+ 
+
+ align:start position:0%
+uh by the way um
+you are supposed to explain
+
+ align:start position:0%
+you are supposed to explain
+ 
+
+ align:start position:0%
+you are supposed to explain
+uh how to do it and in particular
+
+ align:start position:0%
+uh how to do it and in particular
+ 
+
+ align:start position:0%
+uh how to do it and in particular
+if you know a good way of doing it and
+
+ align:start position:0%
+if you know a good way of doing it and
+ 
+
+ align:start position:0%
+if you know a good way of doing it and
+in your patent you only describe a lousy
+
+ align:start position:0%
+in your patent you only describe a lousy
+ 
+
+ align:start position:0%
+in your patent you only describe a lousy
+way of doing it that could be grounds
+
+ align:start position:0%
+way of doing it that could be grounds
+ 
+
+ align:start position:0%
+way of doing it that could be grounds
+later on for invalidating a patent
+
+ align:start position:0%
+later on for invalidating a patent
+ 
+
+ align:start position:0%
+later on for invalidating a patent
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that's called best mode so there's lots
+
+ align:start position:0%
+that's called best mode so there's lots
+ 
+
+ align:start position:0%
+that's called best mode so there's lots
+and lots of
+
+ align:start position:0%
+and lots of
+ 
+
+ align:start position:0%
+and lots of
+terminology
+
+ align:start position:0%
+terminology
+ 
+
+ align:start position:0%
+terminology
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in the litigation there's sort of
+
+ align:start position:0%
+in the litigation there's sort of
+ 
+
+ align:start position:0%
+in the litigation there's sort of
+standard things that that come up one of
+
+ align:start position:0%
+standard things that that come up one of
+ 
+
+ align:start position:0%
+standard things that that come up one of
+them is best mode so in in one machine
+
+ align:start position:0%
+them is best mode so in in one machine
+ 
+
+ align:start position:0%
+them is best mode so in in one machine
+vision patent
+
+ align:start position:0%
+vision patent
+ 
+
+ align:start position:0%
+vision patent
+for a wheel alignment
+
+ align:start position:0%
+for a wheel alignment
+ 
+
+ align:start position:0%
+for a wheel alignment
+so that one has cameras and leds and
+
+ align:start position:0%
+so that one has cameras and leds and
+ 
+
+ align:start position:0%
+so that one has cameras and leds and
+it determines the axis of rotation of
+
+ align:start position:0%
+it determines the axis of rotation of
+ 
+
+ align:start position:0%
+it determines the axis of rotation of
+the wheel
+
+ align:start position:0%
+the wheel
+ 
+
+ align:start position:0%
+the wheel
+and the axis of the steering that you it
+
+ align:start position:0%
+and the axis of the steering that you it
+ 
+
+ align:start position:0%
+and the axis of the steering that you it
+turns around when you
+
+ align:start position:0%
+turns around when you
+ 
+
+ align:start position:0%
+turns around when you
+turn your steering wheel
+
+ align:start position:0%
+turn your steering wheel
+ 
+
+ align:start position:0%
+turn your steering wheel
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+the pattern that was
+
+ align:start position:0%
+the pattern that was
+ 
+
+ align:start position:0%
+the pattern that was
+claimed to have been infringed
+
+ align:start position:0%
+claimed to have been infringed
+ 
+
+ align:start position:0%
+claimed to have been infringed
+uh did not uh disclose the best mode it
+
+ align:start position:0%
+uh did not uh disclose the best mode it
+ 
+
+ align:start position:0%
+uh did not uh disclose the best mode it
+disclosed the method that if you
+
+ align:start position:0%
+disclosed the method that if you
+ 
+
+ align:start position:0%
+disclosed the method that if you
+actually implement it
+
+ align:start position:0%
+actually implement it
+ 
+
+ align:start position:0%
+actually implement it
+uh it gives gives you the correct answer
+
+ align:start position:0%
+uh it gives gives you the correct answer
+ 
+
+ align:start position:0%
+uh it gives gives you the correct answer
+if you have perfect measurements
+
+ align:start position:0%
+if you have perfect measurements
+ 
+
+ align:start position:0%
+if you have perfect measurements
+but with uh realistic measurements it
+
+ align:start position:0%
+but with uh realistic measurements it
+ 
+
+ align:start position:0%
+but with uh realistic measurements it
+would have an error of you know a degree
+
+ align:start position:0%
+would have an error of you know a degree
+ 
+
+ align:start position:0%
+would have an error of you know a degree
+or two
+
+ align:start position:0%
+or two
+ 
+
+ align:start position:0%
+or two
+and that's not good enough you know if
+
+ align:start position:0%
+and that's not good enough you know if
+ 
+
+ align:start position:0%
+and that's not good enough you know if
+you have a car like a bmw they measure
+
+ align:start position:0%
+you have a car like a bmw they measure
+ 
+
+ align:start position:0%
+you have a car like a bmw they measure
+they specify those angles to 0.01
+
+ align:start position:0%
+they specify those angles to 0.01
+ 
+
+ align:start position:0%
+they specify those angles to 0.01
+degrees so anyway so they had a problem
+
+ align:start position:0%
+degrees so anyway so they had a problem
+ 
+
+ align:start position:0%
+degrees so anyway so they had a problem
+there because they did not disclose the
+
+ align:start position:0%
+there because they did not disclose the
+ 
+
+ align:start position:0%
+there because they did not disclose the
+best mode
+
+ align:start position:0%
+best mode
+ 
+
+ align:start position:0%
+best mode
+okay utility patterns and we talked
+
+ align:start position:0%
+okay utility patterns and we talked
+ 
+
+ align:start position:0%
+okay utility patterns and we talked
+about the structure of those i'll just
+
+ align:start position:0%
+about the structure of those i'll just
+ 
+
+ align:start position:0%
+about the structure of those i'll just
+briefly talk about some of the others so
+
+ align:start position:0%
+briefly talk about some of the others so
+ 
+
+ align:start position:0%
+briefly talk about some of the others so
+copyright um you know you can protect
+
+ align:start position:0%
+copyright um you know you can protect
+ 
+
+ align:start position:0%
+copyright um you know you can protect
+artistic expression
+
+ align:start position:0%
+artistic expression
+ 
+
+ align:start position:0%
+artistic expression
+using copyright so if you write a book
+
+ align:start position:0%
+using copyright so if you write a book
+ 
+
+ align:start position:0%
+using copyright so if you write a book
+there's a copyright on that if you
+
+ align:start position:0%
+there's a copyright on that if you
+ 
+
+ align:start position:0%
+there's a copyright on that if you
+record a song there's a copyright on
+
+ align:start position:0%
+record a song there's a copyright on
+ 
+
+ align:start position:0%
+record a song there's a copyright on
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if you choreograph some ballet as a
+
+ align:start position:0%
+if you choreograph some ballet as a
+ 
+
+ align:start position:0%
+if you choreograph some ballet as a
+copyright on that
+
+ align:start position:0%
+copyright on that
+ 
+
+ align:start position:0%
+copyright on that
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+exceptions so for example
+
+ align:start position:0%
+exceptions so for example
+ 
+
+ align:start position:0%
+exceptions so for example
+if i want to talk about some topic
+
+ align:start position:0%
+if i want to talk about some topic
+ 
+
+ align:start position:0%
+if i want to talk about some topic
+i am allowed in class to present a
+
+ align:start position:0%
+i am allowed in class to present a
+ 
+
+ align:start position:0%
+i am allowed in class to present a
+portion of that material without
+
+ align:start position:0%
+portion of that material without
+ 
+
+ align:start position:0%
+portion of that material without
+violating the copyright without having
+
+ align:start position:0%
+violating the copyright without having
+ 
+
+ align:start position:0%
+violating the copyright without having
+to ask the author you know how much do
+
+ align:start position:0%
+to ask the author you know how much do
+ 
+
+ align:start position:0%
+to ask the author you know how much do
+you want for me to use your
+
+ align:start position:0%
+you want for me to use your
+ 
+
+ align:start position:0%
+you want for me to use your
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+there are also exceptions
+
+ align:start position:0%
+there are also exceptions
+ 
+
+ align:start position:0%
+there are also exceptions
+where you use
+
+ align:start position:0%
+where you use
+ 
+
+ align:start position:0%
+where you use
+extracts so for example if you're
+
+ align:start position:0%
+extracts so for example if you're
+ 
+
+ align:start position:0%
+extracts so for example if you're
+writing a news article
+
+ align:start position:0%
+writing a news article
+ 
+
+ align:start position:0%
+writing a news article
+or say you've got a blog about a movie
+
+ align:start position:0%
+or say you've got a blog about a movie
+ 
+
+ align:start position:0%
+or say you've got a blog about a movie
+and there's a particular part of the
+
+ align:start position:0%
+and there's a particular part of the
+ 
+
+ align:start position:0%
+and there's a particular part of the
+movie that you'd like to talk about
+
+ align:start position:0%
+movie that you'd like to talk about
+ 
+
+ align:start position:0%
+movie that you'd like to talk about
+under certain circumstances you can clip
+
+ align:start position:0%
+under certain circumstances you can clip
+ 
+
+ align:start position:0%
+under certain circumstances you can clip
+that out and use it
+
+ align:start position:0%
+that out and use it
+ 
+
+ align:start position:0%
+that out and use it
+and of course you can imagine there's a
+
+ align:start position:0%
+and of course you can imagine there's a
+ 
+
+ align:start position:0%
+and of course you can imagine there's a
+lot of fun that lawyers have with this
+
+ align:start position:0%
+lot of fun that lawyers have with this
+ 
+
+ align:start position:0%
+lot of fun that lawyers have with this
+because a lot of music is extracted from
+
+ align:start position:0%
+because a lot of music is extracted from
+ 
+
+ align:start position:0%
+because a lot of music is extracted from
+other music and put together and is that
+
+ align:start position:0%
+other music and put together and is that
+ 
+
+ align:start position:0%
+other music and put together and is that
+legal or is that copyright infringement
+
+ align:start position:0%
+legal or is that copyright infringement
+ 
+
+ align:start position:0%
+legal or is that copyright infringement
+copyright used to be basically
+
+ align:start position:0%
+copyright used to be basically
+ 
+
+ align:start position:0%
+copyright used to be basically
+for the lifetime of the author you know
+
+ align:start position:0%
+for the lifetime of the author you know
+ 
+
+ align:start position:0%
+for the lifetime of the author you know
+if you write a book you should benefit
+
+ align:start position:0%
+if you write a book you should benefit
+ 
+
+ align:start position:0%
+if you write a book you should benefit
+up to a certain
+
+ align:start position:0%
+up to a certain
+ 
+
+ align:start position:0%
+up to a certain
+point when you're not around and you
+
+ align:start position:0%
+point when you're not around and you
+ 
+
+ align:start position:0%
+point when you're not around and you
+don't benefit well of course the heirs
+
+ align:start position:0%
+don't benefit well of course the heirs
+ 
+
+ align:start position:0%
+don't benefit well of course the heirs
+of famous authors didn't like that so
+
+ align:start position:0%
+of famous authors didn't like that so
+ 
+
+ align:start position:0%
+of famous authors didn't like that so
+that was changed
+
+ align:start position:0%
+that was changed
+ 
+
+ align:start position:0%
+that was changed
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+now we have the the sony bono uh
+
+ align:start position:0%
+now we have the the sony bono uh
+ 
+
+ align:start position:0%
+now we have the the sony bono uh
+system of copyright basically
+
+ align:start position:0%
+system of copyright basically
+ 
+
+ align:start position:0%
+system of copyright basically
+he was the person who convinced congress
+
+ align:start position:0%
+he was the person who convinced congress
+ 
+
+ align:start position:0%
+he was the person who convinced congress
+to change the laws and now it's uh
+
+ align:start position:0%
+to change the laws and now it's uh
+ 
+
+ align:start position:0%
+to change the laws and now it's uh
+author's life plus 75 years and they've
+
+ align:start position:0%
+author's life plus 75 years and they've
+ 
+
+ align:start position:0%
+author's life plus 75 years and they've
+been periodically updating it so it's
+
+ align:start position:0%
+been periodically updating it so it's
+ 
+
+ align:start position:0%
+been periodically updating it so it's
+basically author's life plus infinity
+
+ align:start position:0%
+basically author's life plus infinity
+ 
+
+ align:start position:0%
+basically author's life plus infinity
+because every time we get close to the
+
+ align:start position:0%
+because every time we get close to the
+ 
+
+ align:start position:0%
+because every time we get close to the
+limit they say oh well let's upgrade
+
+ align:start position:0%
+limit they say oh well let's upgrade
+ 
+
+ align:start position:0%
+limit they say oh well let's upgrade
+these poor heirs they can't live without
+
+ align:start position:0%
+these poor heirs they can't live without
+ 
+
+ align:start position:0%
+these poor heirs they can't live without
+the royalties from from this so
+
+ align:start position:0%
+the royalties from from this so
+ 
+
+ align:start position:0%
+the royalties from from this so
+excuse me if i'm being sarcastic so
+
+ align:start position:0%
+excuse me if i'm being sarcastic so
+ 
+
+ align:start position:0%
+excuse me if i'm being sarcastic so
+okay so that's copyright and by the way
+
+ align:start position:0%
+okay so that's copyright and by the way
+ 
+
+ align:start position:0%
+okay so that's copyright and by the way
+that was very important for a while uh
+
+ align:start position:0%
+that was very important for a while uh
+ 
+
+ align:start position:0%
+that was very important for a while uh
+and still is uh in software because
+
+ align:start position:0%
+and still is uh in software because
+ 
+
+ align:start position:0%
+and still is uh in software because
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+the rule was you couldn't copy you
+
+ align:start position:0%
+the rule was you couldn't copy you
+ 
+
+ align:start position:0%
+the rule was you couldn't copy you
+couldn't patent uh mathematics or or an
+
+ align:start position:0%
+couldn't patent uh mathematics or or an
+ 
+
+ align:start position:0%
+couldn't patent uh mathematics or or an
+idea abstract idea uh and so a lot of uh
+
+ align:start position:0%
+idea abstract idea uh and so a lot of uh
+ 
+
+ align:start position:0%
+idea abstract idea uh and so a lot of uh
+the courts typically held that you know
+
+ align:start position:0%
+the courts typically held that you know
+ 
+
+ align:start position:0%
+the courts typically held that you know
+that's what programs are their ideas
+
+ align:start position:0%
+that's what programs are their ideas
+ 
+
+ align:start position:0%
+that's what programs are their ideas
+they're abstract stuff they're not you
+
+ align:start position:0%
+they're abstract stuff they're not you
+ 
+
+ align:start position:0%
+they're abstract stuff they're not you
+can't hold them and weigh them
+
+ align:start position:0%
+can't hold them and weigh them
+ 
+
+ align:start position:0%
+can't hold them and weigh them
+and so uh the way people protected
+
+ align:start position:0%
+and so uh the way people protected
+ 
+
+ align:start position:0%
+and so uh the way people protected
+themselves was to send their programs
+
+ align:start position:0%
+themselves was to send their programs
+ 
+
+ align:start position:0%
+themselves was to send their programs
+into the copyright office
+
+ align:start position:0%
+into the copyright office
+ 
+
+ align:start position:0%
+into the copyright office
+and register them there and
+
+ align:start position:0%
+and register them there and
+ 
+
+ align:start position:0%
+and register them there and
+you can imagine that you know say you
+
+ align:start position:0%
+you can imagine that you know say you
+ 
+
+ align:start position:0%
+you can imagine that you know say you
+have some operating system like ibm 360
+
+ align:start position:0%
+have some operating system like ibm 360
+ 
+
+ align:start position:0%
+have some operating system like ibm 360
+operating system and you send in your
+
+ align:start position:0%
+operating system and you send in your
+ 
+
+ align:start position:0%
+operating system and you send in your
+750 million lines of code to the
+
+ align:start position:0%
+750 million lines of code to the
+ 
+
+ align:start position:0%
+750 million lines of code to the
+copyright office
+
+ align:start position:0%
+copyright office
+ 
+
+ align:start position:0%
+copyright office
+that was quite quite an exciting event
+
+ align:start position:0%
+that was quite quite an exciting event
+ 
+
+ align:start position:0%
+that was quite quite an exciting event
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+certainly if someone
+
+ align:start position:0%
+certainly if someone
+ 
+
+ align:start position:0%
+certainly if someone
+makes an exact copy of your program then
+
+ align:start position:0%
+makes an exact copy of your program then
+ 
+
+ align:start position:0%
+makes an exact copy of your program then
+you can sue them under under this law of
+
+ align:start position:0%
+you can sue them under under this law of
+ 
+
+ align:start position:0%
+you can sue them under under this law of
+course uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know with all of these they're
+
+ align:start position:0%
+you know with all of these they're
+ 
+
+ align:start position:0%
+you know with all of these they're
+people who are working to get around
+
+ align:start position:0%
+people who are working to get around
+ 
+
+ align:start position:0%
+people who are working to get around
+these laws and so in the case of
+
+ align:start position:0%
+these laws and so in the case of
+ 
+
+ align:start position:0%
+these laws and so in the case of
+copyright there was this notion of a
+
+ align:start position:0%
+copyright there was this notion of a
+ 
+
+ align:start position:0%
+copyright there was this notion of a
+clean room
+
+ align:start position:0%
+clean room
+ 
+
+ align:start position:0%
+clean room
+so what you would do is
+
+ align:start position:0%
+so what you would do is
+ 
+
+ align:start position:0%
+so what you would do is
+you'd have a bunch of people that
+
+ align:start position:0%
+you'd have a bunch of people that
+ 
+
+ align:start position:0%
+you'd have a bunch of people that
+understood programs well analyze what
+
+ align:start position:0%
+understood programs well analyze what
+ 
+
+ align:start position:0%
+understood programs well analyze what
+someone else's program is doing
+
+ align:start position:0%
+someone else's program is doing
+ 
+
+ align:start position:0%
+someone else's program is doing
+kind of reverse engineering it
+
+ align:start position:0%
+kind of reverse engineering it
+ 
+
+ align:start position:0%
+kind of reverse engineering it
+but they weren't allowed to show it to
+
+ align:start position:0%
+but they weren't allowed to show it to
+ 
+
+ align:start position:0%
+but they weren't allowed to show it to
+another group of people
+
+ align:start position:0%
+another group of people
+ 
+
+ align:start position:0%
+another group of people
+they were able to they were only able to
+
+ align:start position:0%
+they were able to they were only able to
+ 
+
+ align:start position:0%
+they were able to they were only able to
+tell them what what it does and then
+
+ align:start position:0%
+tell them what what it does and then
+ 
+
+ align:start position:0%
+tell them what what it does and then
+this other group of people would write
+
+ align:start position:0%
+this other group of people would write
+ 
+
+ align:start position:0%
+this other group of people would write
+the code and supposedly because they
+
+ align:start position:0%
+the code and supposedly because they
+ 
+
+ align:start position:0%
+the code and supposedly because they
+didn't see the original code there was
+
+ align:start position:0%
+didn't see the original code there was
+ 
+
+ align:start position:0%
+didn't see the original code there was
+not a copyright violation so
+
+ align:start position:0%
+not a copyright violation so
+ 
+
+ align:start position:0%
+not a copyright violation so
+okay um not sure that's
+
+ align:start position:0%
+okay um not sure that's
+ 
+
+ align:start position:0%
+okay um not sure that's
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+and it's not totally unreasonable
+
+ align:start position:0%
+and it's not totally unreasonable
+ 
+
+ align:start position:0%
+and it's not totally unreasonable
+in that if you look at the code line by
+
+ align:start position:0%
+in that if you look at the code line by
+ 
+
+ align:start position:0%
+in that if you look at the code line by
+line it's likely to be totally different
+
+ align:start position:0%
+line it's likely to be totally different
+ 
+
+ align:start position:0%
+line it's likely to be totally different
+you know they'll use different variable
+
+ align:start position:0%
+you know they'll use different variable
+ 
+
+ align:start position:0%
+you know they'll use different variable
+names and stuff so
+
+ align:start position:0%
+names and stuff so
+ 
+
+ align:start position:0%
+names and stuff so
+okay then there's a trademark so
+
+ align:start position:0%
+okay then there's a trademark so
+ 
+
+ align:start position:0%
+okay then there's a trademark so
+trademark
+
+ align:start position:0%
+trademark
+ 
+
+ align:start position:0%
+trademark
+is um
+
+ align:start position:0%
+is um
+ 
+
+ align:start position:0%
+is um
+much more restricted it's just you know
+
+ align:start position:0%
+much more restricted it's just you know
+ 
+
+ align:start position:0%
+much more restricted it's just you know
+if you want to
+
+ align:start position:0%
+if you want to
+ 
+
+ align:start position:0%
+if you want to
+call your company dunker donuts you can
+
+ align:start position:0%
+call your company dunker donuts you can
+ 
+
+ align:start position:0%
+call your company dunker donuts you can
+uh trademark that
+
+ align:start position:0%
+uh trademark that
+ 
+
+ align:start position:0%
+uh trademark that
+and but it has to be
+
+ align:start position:0%
+and but it has to be
+ 
+
+ align:start position:0%
+and but it has to be
+uh unique in the field and it has to not
+
+ align:start position:0%
+uh unique in the field and it has to not
+ 
+
+ align:start position:0%
+uh unique in the field and it has to not
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+you know there's a whole bunch of rules
+
+ align:start position:0%
+you know there's a whole bunch of rules
+ 
+
+ align:start position:0%
+you know there's a whole bunch of rules
+but basically you can't use a common
+
+ align:start position:0%
+but basically you can't use a common
+ 
+
+ align:start position:0%
+but basically you can't use a common
+word like you can't call your company
+
+ align:start position:0%
+word like you can't call your company
+ 
+
+ align:start position:0%
+word like you can't call your company
+time space because that's those are
+
+ align:start position:0%
+time space because that's those are
+ 
+
+ align:start position:0%
+time space because that's those are
+common words and so a lot of company
+
+ align:start position:0%
+common words and so a lot of company
+ 
+
+ align:start position:0%
+common words and so a lot of company
+names are slightly misspelled versions
+
+ align:start position:0%
+names are slightly misspelled versions
+ 
+
+ align:start position:0%
+names are slightly misspelled versions
+of common words
+
+ align:start position:0%
+of common words
+ 
+
+ align:start position:0%
+of common words
+the other thing is that
+
+ align:start position:0%
+the other thing is that
+ 
+
+ align:start position:0%
+the other thing is that
+the trademark may include
+
+ align:start position:0%
+the trademark may include
+ 
+
+ align:start position:0%
+the trademark may include
+particular shapes particular markings so
+
+ align:start position:0%
+particular shapes particular markings so
+ 
+
+ align:start position:0%
+particular shapes particular markings so
+you can distort some later
+
+ align:start position:0%
+you can distort some later
+ 
+
+ align:start position:0%
+you can distort some later
+and color
+
+ align:start position:0%
+and color
+ 
+
+ align:start position:0%
+and color
+so you know dunker donuts
+
+ align:start position:0%
+so you know dunker donuts
+ 
+
+ align:start position:0%
+so you know dunker donuts
+has two colors that they've copyrighted
+
+ align:start position:0%
+has two colors that they've copyrighted
+ 
+
+ align:start position:0%
+has two colors that they've copyrighted
+and i'm proud to say i have hats that
+
+ align:start position:0%
+and i'm proud to say i have hats that
+ 
+
+ align:start position:0%
+and i'm proud to say i have hats that
+have both of those colors they're very
+
+ align:start position:0%
+have both of those colors they're very
+ 
+
+ align:start position:0%
+have both of those colors they're very
+useful in hunting season which is
+
+ align:start position:0%
+useful in hunting season which is
+ 
+
+ align:start position:0%
+useful in hunting season which is
+approximately what's happening right now
+
+ align:start position:0%
+approximately what's happening right now
+ 
+
+ align:start position:0%
+approximately what's happening right now
+where i live so
+
+ align:start position:0%
+where i live so
+ 
+
+ align:start position:0%
+where i live so
+you can use color to protect yourself
+
+ align:start position:0%
+you can use color to protect yourself
+ 
+
+ align:start position:0%
+you can use color to protect yourself
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+they have to be unique to the field so
+
+ align:start position:0%
+they have to be unique to the field so
+ 
+
+ align:start position:0%
+they have to be unique to the field so
+you may have a trademark on the name
+
+ align:start position:0%
+you may have a trademark on the name
+ 
+
+ align:start position:0%
+you may have a trademark on the name
+in the rubber industry
+
+ align:start position:0%
+in the rubber industry
+ 
+
+ align:start position:0%
+in the rubber industry
+uh and someone else has it in the
+
+ align:start position:0%
+uh and someone else has it in the
+ 
+
+ align:start position:0%
+uh and someone else has it in the
+semiconductor industry they don't
+
+ align:start position:0%
+semiconductor industry they don't
+ 
+
+ align:start position:0%
+semiconductor industry they don't
+conflict and
+
+ align:start position:0%
+conflict and
+ 
+
+ align:start position:0%
+conflict and
+there's a famous case about that where
+
+ align:start position:0%
+there's a famous case about that where
+ 
+
+ align:start position:0%
+there's a famous case about that where
+again apple apple sued the beatles
+
+ align:start position:0%
+again apple apple sued the beatles
+ 
+
+ align:start position:0%
+again apple apple sued the beatles
+why well because when the beatles
+
+ align:start position:0%
+why well because when the beatles
+ 
+
+ align:start position:0%
+why well because when the beatles
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+they formed their own company called
+
+ align:start position:0%
+they formed their own company called
+ 
+
+ align:start position:0%
+they formed their own company called
+apple
+
+ align:start position:0%
+apple
+ 
+
+ align:start position:0%
+apple
+may not know that but in any case so
+
+ align:start position:0%
+may not know that but in any case so
+ 
+
+ align:start position:0%
+may not know that but in any case so
+apple sued them and they lost because
+
+ align:start position:0%
+apple sued them and they lost because
+ 
+
+ align:start position:0%
+apple sued them and they lost because
+it's they're not there's no confusion of
+
+ align:start position:0%
+it's they're not there's no confusion of
+ 
+
+ align:start position:0%
+it's they're not there's no confusion of
+the client the customer right they're in
+
+ align:start position:0%
+the client the customer right they're in
+ 
+
+ align:start position:0%
+the client the customer right they're in
+two totally different fields one is
+
+ align:start position:0%
+two totally different fields one is
+ 
+
+ align:start position:0%
+two totally different fields one is
+music
+
+ align:start position:0%
+music
+ 
+
+ align:start position:0%
+music
+and the other one is computers and of
+
+ align:start position:0%
+and the other one is computers and of
+ 
+
+ align:start position:0%
+and the other one is computers and of
+course apple claimed oh well but we
+
+ align:start position:0%
+course apple claimed oh well but we
+ 
+
+ align:start position:0%
+course apple claimed oh well but we
+distribute music so it's it is the same
+
+ align:start position:0%
+distribute music so it's it is the same
+ 
+
+ align:start position:0%
+distribute music so it's it is the same
+thing well whatever anyway
+
+ align:start position:0%
+thing well whatever anyway
+ 
+
+ align:start position:0%
+thing well whatever anyway
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the last thing is trade secret which is
+
+ align:start position:0%
+the last thing is trade secret which is
+ 
+
+ align:start position:0%
+the last thing is trade secret which is
+you know no protection at all you just
+
+ align:start position:0%
+you know no protection at all you just
+ 
+
+ align:start position:0%
+you know no protection at all you just
+hide what you're doing you don't tell
+
+ align:start position:0%
+hide what you're doing you don't tell
+ 
+
+ align:start position:0%
+hide what you're doing you don't tell
+anyone exactly how you're doing it and
+
+ align:start position:0%
+anyone exactly how you're doing it and
+ 
+
+ align:start position:0%
+anyone exactly how you're doing it and
+you know classic example of that is
+
+ align:start position:0%
+you know classic example of that is
+ 
+
+ align:start position:0%
+you know classic example of that is
+coca-cola
+
+ align:start position:0%
+coca-cola
+ 
+
+ align:start position:0%
+coca-cola
+there's a safe down in atlanta georgia
+
+ align:start position:0%
+there's a safe down in atlanta georgia
+ 
+
+ align:start position:0%
+there's a safe down in atlanta georgia
+which has the formula for the
+
+ align:start position:0%
+which has the formula for the
+ 
+
+ align:start position:0%
+which has the formula for the
+ingredients in coca-cola
+
+ align:start position:0%
+ingredients in coca-cola
+ 
+
+ align:start position:0%
+ingredients in coca-cola
+and supposedly you know
+
+ align:start position:0%
+and supposedly you know
+ 
+
+ align:start position:0%
+and supposedly you know
+very few people know what's what's in
+
+ align:start position:0%
+very few people know what's what's in
+ 
+
+ align:start position:0%
+very few people know what's what's in
+there and
+
+ align:start position:0%
+there and
+ 
+
+ align:start position:0%
+there and
+uh the danger of course of i mean the
+
+ align:start position:0%
+uh the danger of course of i mean the
+ 
+
+ align:start position:0%
+uh the danger of course of i mean the
+good part is that it's unlimited i mean
+
+ align:start position:0%
+good part is that it's unlimited i mean
+ 
+
+ align:start position:0%
+good part is that it's unlimited i mean
+there's no like expiration date like on
+
+ align:start position:0%
+there's no like expiration date like on
+ 
+
+ align:start position:0%
+there's no like expiration date like on
+patents and the bad part is you know if
+
+ align:start position:0%
+patents and the bad part is you know if
+ 
+
+ align:start position:0%
+patents and the bad part is you know if
+it ever comes out there's no recourse
+
+ align:start position:0%
+it ever comes out there's no recourse
+ 
+
+ align:start position:0%
+it ever comes out there's no recourse
+there it is everyone now knows what to
+
+ align:start position:0%
+there it is everyone now knows what to
+ 
+
+ align:start position:0%
+there it is everyone now knows what to
+mix up to make coca-cola so
+
+ align:start position:0%
+mix up to make coca-cola so
+ 
+
+ align:start position:0%
+mix up to make coca-cola so
+um it's a risky uh thing but it's
+
+ align:start position:0%
+um it's a risky uh thing but it's
+ 
+
+ align:start position:0%
+um it's a risky uh thing but it's
+certainly much cheaper than pursuing
+
+ align:start position:0%
+certainly much cheaper than pursuing
+ 
+
+ align:start position:0%
+certainly much cheaper than pursuing
+some of the other avenues you don't have
+
+ align:start position:0%
+some of the other avenues you don't have
+ 
+
+ align:start position:0%
+some of the other avenues you don't have
+to pay lawyers for it
+
+ align:start position:0%
+to pay lawyers for it
+ 
+
+ align:start position:0%
+to pay lawyers for it
+and there is a certain
+
+ align:start position:0%
+and there is a certain
+ 
+
+ align:start position:0%
+and there is a certain
+legal recourse you know if somebody
+
+ align:start position:0%
+legal recourse you know if somebody
+ 
+
+ align:start position:0%
+legal recourse you know if somebody
+signs a non-disclosure agreement when
+
+ align:start position:0%
+signs a non-disclosure agreement when
+ 
+
+ align:start position:0%
+signs a non-disclosure agreement when
+joining your company and then they walk
+
+ align:start position:0%
+joining your company and then they walk
+ 
+
+ align:start position:0%
+joining your company and then they walk
+off with a formula for coca-cola and
+
+ align:start position:0%
+off with a formula for coca-cola and
+ 
+
+ align:start position:0%
+off with a formula for coca-cola and
+tell pepsi caller how to do it then you
+
+ align:start position:0%
+tell pepsi caller how to do it then you
+ 
+
+ align:start position:0%
+tell pepsi caller how to do it then you
+can sue them but you know the cat's out
+
+ align:start position:0%
+can sue them but you know the cat's out
+ 
+
+ align:start position:0%
+can sue them but you know the cat's out
+of the bag it's not
+
+ align:start position:0%
+of the bag it's not
+ 
+
+ align:start position:0%
+of the bag it's not
+so easy to recover from that kind of
+
+ align:start position:0%
+so easy to recover from that kind of
+ 
+
+ align:start position:0%
+so easy to recover from that kind of
+loss
+
+ align:start position:0%
+loss
+ 
+
+ align:start position:0%
+loss
+okay just a quick um overview of
+
+ align:start position:0%
+okay just a quick um overview of
+ 
+
+ align:start position:0%
+okay just a quick um overview of
+what's called the intellectual property
+
+ align:start position:0%
+what's called the intellectual property
+ 
+
+ align:start position:0%
+what's called the intellectual property
+and you know richard stallman would
+
+ align:start position:0%
+and you know richard stallman would
+ 
+
+ align:start position:0%
+and you know richard stallman would
+definitely complain that i use that
+
+ align:start position:0%
+definitely complain that i use that
+ 
+
+ align:start position:0%
+definitely complain that i use that
+terminology because he doesn't think
+
+ align:start position:0%
+terminology because he doesn't think
+ 
+
+ align:start position:0%
+terminology because he doesn't think
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+ideas should be treated as property just
+
+ align:start position:0%
+ideas should be treated as property just
+ 
+
+ align:start position:0%
+ideas should be treated as property just
+as some people don't think that
+
+ align:start position:0%
+as some people don't think that
+ 
+
+ align:start position:0%
+as some people don't think that
+companies should be treated as persons
+
+ align:start position:0%
+companies should be treated as persons
+ 
+
+ align:start position:0%
+companies should be treated as persons
+in under the law but there you are
+
+ align:start position:0%
+in under the law but there you are
+ 
+
+ align:start position:0%
+in under the law but there you are
+okay back to the particular patent so
+
+ align:start position:0%
+okay back to the particular patent so
+ 
+
+ align:start position:0%
+okay back to the particular patent so
+this particular patent is kind of real
+
+ align:start position:0%
+this particular patent is kind of real
+ 
+
+ align:start position:0%
+this particular patent is kind of real
+low level
+
+ align:start position:0%
+low level
+ 
+
+ align:start position:0%
+low level
+i wanted to start with something very
+
+ align:start position:0%
+i wanted to start with something very
+ 
+
+ align:start position:0%
+i wanted to start with something very
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+you know finding edges
+
+ align:start position:0%
+you know finding edges
+ 
+
+ align:start position:0%
+you know finding edges
+very accurately finding edges very
+
+ align:start position:0%
+very accurately finding edges very
+ 
+
+ align:start position:0%
+very accurately finding edges very
+accurately so where are we going with
+
+ align:start position:0%
+accurately so where are we going with
+ 
+
+ align:start position:0%
+accurately so where are we going with
+that well the idea is that once we found
+
+ align:start position:0%
+that well the idea is that once we found
+ 
+
+ align:start position:0%
+that well the idea is that once we found
+edges and we're describing uh
+
+ align:start position:0%
+edges and we're describing uh
+ 
+
+ align:start position:0%
+edges and we're describing uh
+images using edges
+
+ align:start position:0%
+images using edges
+ 
+
+ align:start position:0%
+images using edges
+we can
+
+ align:start position:0%
+we can
+ 
+
+ align:start position:0%
+we can
+do more elaborate things like
+
+ align:start position:0%
+do more elaborate things like
+ 
+
+ align:start position:0%
+do more elaborate things like
+recognition and
+
+ align:start position:0%
+recognition and
+ 
+
+ align:start position:0%
+recognition and
+determining the position and determining
+
+ align:start position:0%
+determining the position and determining
+ 
+
+ align:start position:0%
+determining the position and determining
+the attitude of an object and most of uh
+
+ align:start position:0%
+the attitude of an object and most of uh
+ 
+
+ align:start position:0%
+the attitude of an object and most of uh
+what we'll be doing
+
+ align:start position:0%
+what we'll be doing
+ 
+
+ align:start position:0%
+what we'll be doing
+after finishing with this pattern is in
+
+ align:start position:0%
+after finishing with this pattern is in
+ 
+
+ align:start position:0%
+after finishing with this pattern is in
+in 2d where you know the world of course
+
+ align:start position:0%
+in 2d where you know the world of course
+ 
+
+ align:start position:0%
+in 2d where you know the world of course
+the 3d but there are lots of cases where
+
+ align:start position:0%
+the 3d but there are lots of cases where
+ 
+
+ align:start position:0%
+the 3d but there are lots of cases where
+2d machine vision is incredibly
+
+ align:start position:0%
+2d machine vision is incredibly
+ 
+
+ align:start position:0%
+2d machine vision is incredibly
+successful
+
+ align:start position:0%
+successful
+ 
+
+ align:start position:0%
+successful
+and um you know
+
+ align:start position:0%
+and um you know
+ 
+
+ align:start position:0%
+and um you know
+one thing that's important to point out
+
+ align:start position:0%
+one thing that's important to point out
+ 
+
+ align:start position:0%
+one thing that's important to point out
+is that it has to be incredibly accurate
+
+ align:start position:0%
+is that it has to be incredibly accurate
+ 
+
+ align:start position:0%
+is that it has to be incredibly accurate
+you know like if if your thing works 70
+
+ align:start position:0%
+you know like if if your thing works 70
+ 
+
+ align:start position:0%
+you know like if if your thing works 70
+of the time
+
+ align:start position:0%
+of the time
+ 
+
+ align:start position:0%
+of the time
+forget it
+
+ align:start position:0%
+forget it
+ 
+
+ align:start position:0%
+forget it
+it's got to be
+
+ align:start position:0%
+it's got to be
+ 
+
+ align:start position:0%
+it's got to be
+working
+
+ align:start position:0%
+working
+ 
+
+ align:start position:0%
+working
+99.999 of the time so these methods are
+
+ align:start position:0%
+99.999 of the time so these methods are
+ 
+
+ align:start position:0%
+99.999 of the time so these methods are
+you know very carefully thought out and
+
+ align:start position:0%
+you know very carefully thought out and
+ 
+
+ align:start position:0%
+you know very carefully thought out and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+tuned to have extremely good performance
+
+ align:start position:0%
+tuned to have extremely good performance
+ 
+
+ align:start position:0%
+tuned to have extremely good performance
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what we'll find is that
+
+ align:start position:0%
+what we'll find is that
+ 
+
+ align:start position:0%
+what we'll find is that
+in the 2d world this is possible it's a
+
+ align:start position:0%
+in the 2d world this is possible it's a
+ 
+
+ align:start position:0%
+in the 2d world this is possible it's a
+little harder once you get to 3d so once
+
+ align:start position:0%
+little harder once you get to 3d so once
+ 
+
+ align:start position:0%
+little harder once you get to 3d so once
+we've done
+
+ align:start position:0%
+we've done
+ 
+
+ align:start position:0%
+we've done
+position and attitude in 2d
+
+ align:start position:0%
+position and attitude in 2d
+ 
+
+ align:start position:0%
+position and attitude in 2d
+we'll
+
+ align:start position:0%
+we'll
+ 
+
+ align:start position:0%
+we'll
+progress to 3d which is a more
+
+ align:start position:0%
+progress to 3d which is a more
+ 
+
+ align:start position:0%
+progress to 3d which is a more
+interesting problem but you know let's
+
+ align:start position:0%
+interesting problem but you know let's
+ 
+
+ align:start position:0%
+interesting problem but you know let's
+get some of the basics sorted out
+
+ align:start position:0%
+get some of the basics sorted out
+ 
+
+ align:start position:0%
+get some of the basics sorted out
+so i'll just sort of
+
+ align:start position:0%
+so i'll just sort of
+ 
+
+ align:start position:0%
+so i'll just sort of
+quickly
+
+ align:start position:0%
+quickly
+ 
+
+ align:start position:0%
+quickly
+review
+
+ align:start position:0%
+review
+ 
+
+ align:start position:0%
+review
+what this patent did
+
+ align:start position:0%
+what this patent did
+ 
+
+ align:start position:0%
+what this patent did
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+we'll start so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+first idea was to look at the brightness
+
+ align:start position:0%
+first idea was to look at the brightness
+ 
+
+ align:start position:0%
+first idea was to look at the brightness
+gradient and so just a
+
+ align:start position:0%
+gradient and so just a
+ 
+
+ align:start position:0%
+gradient and so just a
+quick story on that so here we've got
+
+ align:start position:0%
+quick story on that so here we've got
+ 
+
+ align:start position:0%
+quick story on that so here we've got
+you know brightness as a function of x
+
+ align:start position:0%
+you know brightness as a function of x
+ 
+
+ align:start position:0%
+you know brightness as a function of x
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's a point where the curvature
+
+ align:start position:0%
+there's a point where the curvature
+ 
+
+ align:start position:0%
+there's a point where the curvature
+becomes zero and changes sign
+
+ align:start position:0%
+becomes zero and changes sign
+ 
+
+ align:start position:0%
+becomes zero and changes sign
+and that's called an inflection point
+
+ align:start position:0%
+and that's called an inflection point
+ 
+
+ align:start position:0%
+and that's called an inflection point
+and that's what we're looking for
+
+ align:start position:0%
+and that's what we're looking for
+ 
+
+ align:start position:0%
+and that's what we're looking for
+so the edge is actually spread out over
+
+ align:start position:0%
+so the edge is actually spread out over
+ 
+
+ align:start position:0%
+so the edge is actually spread out over
+several pixel but we're trying to
+
+ align:start position:0%
+several pixel but we're trying to
+ 
+
+ align:start position:0%
+several pixel but we're trying to
+identify very accurately a particular
+
+ align:start position:0%
+identify very accurately a particular
+ 
+
+ align:start position:0%
+identify very accurately a particular
+point on the edge
+
+ align:start position:0%
+point on the edge
+ 
+
+ align:start position:0%
+point on the edge
+then we looked at the derivative
+
+ align:start position:0%
+then we looked at the derivative
+ 
+
+ align:start position:0%
+then we looked at the derivative
+and there we're looking at a peak we're
+
+ align:start position:0%
+and there we're looking at a peak we're
+ 
+
+ align:start position:0%
+and there we're looking at a peak we're
+searching for a peak
+
+ align:start position:0%
+searching for a peak
+ 
+
+ align:start position:0%
+searching for a peak
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+some methods use second derivative
+
+ align:start position:0%
+some methods use second derivative
+ 
+
+ align:start position:0%
+some methods use second derivative
+and look for zero crossing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but importantly this is
+
+ align:start position:0%
+but importantly this is
+ 
+
+ align:start position:0%
+but importantly this is
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the gradient direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is of course a 1d cross section
+
+ align:start position:0%
+so this is of course a 1d cross section
+ 
+
+ align:start position:0%
+so this is of course a 1d cross section
+and we're dealing with images so
+
+ align:start position:0%
+and we're dealing with images so
+ 
+
+ align:start position:0%
+and we're dealing with images so
+how do we take the cross section well
+
+ align:start position:0%
+how do we take the cross section well
+ 
+
+ align:start position:0%
+how do we take the cross section well
+we're only interested in
+
+ align:start position:0%
+we're only interested in
+ 
+
+ align:start position:0%
+we're only interested in
+the direction that is perpendicular to
+
+ align:start position:0%
+the direction that is perpendicular to
+ 
+
+ align:start position:0%
+the direction that is perpendicular to
+the edge and so these graphs and these
+
+ align:start position:0%
+the edge and so these graphs and these
+ 
+
+ align:start position:0%
+the edge and so these graphs and these
+ideas correspond to that
+
+ align:start position:0%
+ideas correspond to that
+ 
+
+ align:start position:0%
+ideas correspond to that
+okay then
+
+ align:start position:0%
+okay then
+ 
+
+ align:start position:0%
+okay then
+we talked a little bit about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things that are sometimes called
+
+ align:start position:0%
+things that are sometimes called
+ 
+
+ align:start position:0%
+things that are sometimes called
+stencils
+
+ align:start position:0%
+stencils
+ 
+
+ align:start position:0%
+stencils
+and sometimes called computational
+
+ align:start position:0%
+and sometimes called computational
+ 
+
+ align:start position:0%
+and sometimes called computational
+molecules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what we're trying to do is in the
+
+ align:start position:0%
+what we're trying to do is in the
+ 
+
+ align:start position:0%
+what we're trying to do is in the
+discrete world we're trying to estimate
+
+ align:start position:0%
+discrete world we're trying to estimate
+ 
+
+ align:start position:0%
+discrete world we're trying to estimate
+derivatives and so of course
+
+ align:start position:0%
+derivatives and so of course
+ 
+
+ align:start position:0%
+derivatives and so of course
+um you know there's some obvious ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's there's a way of getting an
+
+ align:start position:0%
+so there's there's a way of getting an
+ 
+
+ align:start position:0%
+so there's there's a way of getting an
+approximation for e sub x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here's another one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are all some of the ones that
+
+ align:start position:0%
+these are all some of the ones that
+ 
+
+ align:start position:0%
+these are all some of the ones that
+we already looked at
+
+ align:start position:0%
+we already looked at
+ 
+
+ align:start position:0%
+we already looked at
+so there are lots of ways of estimating
+
+ align:start position:0%
+so there are lots of ways of estimating
+ 
+
+ align:start position:0%
+so there are lots of ways of estimating
+the derivatives and how do we know which
+
+ align:start position:0%
+the derivatives and how do we know which
+ 
+
+ align:start position:0%
+the derivatives and how do we know which
+one to choose well uh their trade-offs
+
+ align:start position:0%
+one to choose well uh their trade-offs
+ 
+
+ align:start position:0%
+one to choose well uh their trade-offs
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+saw that
+
+ align:start position:0%
+saw that
+ 
+
+ align:start position:0%
+saw that
+one way to
+
+ align:start position:0%
+one way to
+ 
+
+ align:start position:0%
+one way to
+progress is to
+
+ align:start position:0%
+progress is to
+ 
+
+ align:start position:0%
+progress is to
+use taylor series expansion to see what
+
+ align:start position:0%
+use taylor series expansion to see what
+ 
+
+ align:start position:0%
+use taylor series expansion to see what
+the lowest order error term is because
+
+ align:start position:0%
+the lowest order error term is because
+ 
+
+ align:start position:0%
+the lowest order error term is because
+we the higher we can push that if it's a
+
+ align:start position:0%
+we the higher we can push that if it's a
+ 
+
+ align:start position:0%
+we the higher we can push that if it's a
+third order error term uh it's better
+
+ align:start position:0%
+third order error term uh it's better
+ 
+
+ align:start position:0%
+third order error term uh it's better
+than if it was a second order error term
+
+ align:start position:0%
+than if it was a second order error term
+ 
+
+ align:start position:0%
+than if it was a second order error term
+and if two methods have the same order
+
+ align:start position:0%
+and if two methods have the same order
+ 
+
+ align:start position:0%
+and if two methods have the same order
+of error term then we look at the
+
+ align:start position:0%
+of error term then we look at the
+ 
+
+ align:start position:0%
+of error term then we look at the
+coefficient and if it's lower
+
+ align:start position:0%
+coefficient and if it's lower
+ 
+
+ align:start position:0%
+coefficient and if it's lower
+you know like like these two have the
+
+ align:start position:0%
+you know like like these two have the
+ 
+
+ align:start position:0%
+you know like like these two have the
+same uh
+
+ align:start position:0%
+same uh
+ 
+
+ align:start position:0%
+same uh
+lowest order error term and also what
+
+ align:start position:0%
+lowest order error term and also what
+ 
+
+ align:start position:0%
+lowest order error term and also what
+was very important was you know where
+
+ align:start position:0%
+was very important was you know where
+ 
+
+ align:start position:0%
+was very important was you know where
+are we trying to estimate the derivative
+
+ align:start position:0%
+are we trying to estimate the derivative
+ 
+
+ align:start position:0%
+are we trying to estimate the derivative
+and we decided that
+
+ align:start position:0%
+and we decided that
+ 
+
+ align:start position:0%
+and we decided that
+we get the best results
+
+ align:start position:0%
+we get the best results
+ 
+
+ align:start position:0%
+we get the best results
+at those particular points
+
+ align:start position:0%
+at those particular points
+ 
+
+ align:start position:0%
+at those particular points
+now some of those points are offset by
+
+ align:start position:0%
+now some of those points are offset by
+ 
+
+ align:start position:0%
+now some of those points are offset by
+half a pixel from the pixel grid and
+
+ align:start position:0%
+half a pixel from the pixel grid and
+ 
+
+ align:start position:0%
+half a pixel from the pixel grid and
+that's why people don't use them but
+
+ align:start position:0%
+that's why people don't use them but
+ 
+
+ align:start position:0%
+that's why people don't use them but
+that's silly because
+
+ align:start position:0%
+that's silly because
+ 
+
+ align:start position:0%
+that's silly because
+what's wrong with having some quantities
+
+ align:start position:0%
+what's wrong with having some quantities
+ 
+
+ align:start position:0%
+what's wrong with having some quantities
+on the pixel grid the image
+
+ align:start position:0%
+on the pixel grid the image
+ 
+
+ align:start position:0%
+on the pixel grid the image
+and some quantities on a grid that's
+
+ align:start position:0%
+and some quantities on a grid that's
+ 
+
+ align:start position:0%
+and some quantities on a grid that's
+offset by half as long as you know that
+
+ align:start position:0%
+offset by half as long as you know that
+ 
+
+ align:start position:0%
+offset by half as long as you know that
+it's offset by half you can
+
+ align:start position:0%
+it's offset by half you can
+ 
+
+ align:start position:0%
+it's offset by half you can
+translate any result on that grid into a
+
+ align:start position:0%
+translate any result on that grid into a
+ 
+
+ align:start position:0%
+translate any result on that grid into a
+result on the other group
+
+ align:start position:0%
+result on the other group
+ 
+
+ align:start position:0%
+result on the other group
+we can also analyze these in the fourier
+
+ align:start position:0%
+we can also analyze these in the fourier
+ 
+
+ align:start position:0%
+we can also analyze these in the fourier
+transform domain in terms of how they
+
+ align:start position:0%
+transform domain in terms of how they
+ 
+
+ align:start position:0%
+transform domain in terms of how they
+affect higher frequency content and
+
+ align:start position:0%
+affect higher frequency content and
+ 
+
+ align:start position:0%
+affect higher frequency content and
+we won't do that right now but
+
+ align:start position:0%
+we won't do that right now but
+ 
+
+ align:start position:0%
+we won't do that right now but
+that that's second
+
+ align:start position:0%
+that that's second
+ 
+
+ align:start position:0%
+that that's second
+set of methods we can use to
+
+ align:start position:0%
+set of methods we can use to
+ 
+
+ align:start position:0%
+set of methods we can use to
+decide which which of these is better
+
+ align:start position:0%
+decide which which of these is better
+ 
+
+ align:start position:0%
+decide which which of these is better
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+these derivative estimators can become
+
+ align:start position:0%
+these derivative estimators can become
+ 
+
+ align:start position:0%
+these derivative estimators can become
+quite complicated if you're looking for
+
+ align:start position:0%
+quite complicated if you're looking for
+ 
+
+ align:start position:0%
+quite complicated if you're looking for
+high precision so for example in in
+
+ align:start position:0%
+high precision so for example in in
+ 
+
+ align:start position:0%
+high precision so for example in in
+analyzing uh
+
+ align:start position:0%
+analyzing uh
+ 
+
+ align:start position:0%
+analyzing uh
+muscle electrical signals
+
+ align:start position:0%
+muscle electrical signals
+ 
+
+ align:start position:0%
+muscle electrical signals
+there's quite a bit of noise and there's
+
+ align:start position:0%
+there's quite a bit of noise and there's
+ 
+
+ align:start position:0%
+there's quite a bit of noise and there's
+quite a lot of
+
+ align:start position:0%
+quite a lot of
+ 
+
+ align:start position:0%
+quite a lot of
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+distortion of the signal as it
+
+ align:start position:0%
+distortion of the signal as it
+ 
+
+ align:start position:0%
+distortion of the signal as it
+progresses through uh tissue
+
+ align:start position:0%
+progresses through uh tissue
+ 
+
+ align:start position:0%
+progresses through uh tissue
+and so you know when people are trying
+
+ align:start position:0%
+and so you know when people are trying
+ 
+
+ align:start position:0%
+and so you know when people are trying
+to estimate the first derivative they in
+
+ align:start position:0%
+to estimate the first derivative they in
+ 
+
+ align:start position:0%
+to estimate the first derivative they in
+one case one paper i saw use a 39 degree
+
+ align:start position:0%
+one case one paper i saw use a 39 degree
+ 
+
+ align:start position:0%
+one case one paper i saw use a 39 degree
+approximation so they use a pattern like
+
+ align:start position:0%
+approximation so they use a pattern like
+ 
+
+ align:start position:0%
+approximation so they use a pattern like
+this that's you know 39
+
+ align:start position:0%
+this that's you know 39
+ 
+
+ align:start position:0%
+this that's you know 39
+elements long and
+
+ align:start position:0%
+elements long and
+ 
+
+ align:start position:0%
+elements long and
+they feel that that way they can control
+
+ align:start position:0%
+they feel that that way they can control
+ 
+
+ align:start position:0%
+they feel that that way they can control
+the trade-off between suppressing the
+
+ align:start position:0%
+the trade-off between suppressing the
+ 
+
+ align:start position:0%
+the trade-off between suppressing the
+noise and getting very accurate results
+
+ align:start position:0%
+noise and getting very accurate results
+ 
+
+ align:start position:0%
+noise and getting very accurate results
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we're using very low order
+
+ align:start position:0%
+we're using very low order
+ 
+
+ align:start position:0%
+we're using very low order
+partly because
+
+ align:start position:0%
+partly because
+ 
+
+ align:start position:0%
+partly because
+you know it's easier and partly because
+
+ align:start position:0%
+you know it's easier and partly because
+ 
+
+ align:start position:0%
+you know it's easier and partly because
+one other trade-off is if you make them
+
+ align:start position:0%
+one other trade-off is if you make them
+ 
+
+ align:start position:0%
+one other trade-off is if you make them
+too long then they start to
+
+ align:start position:0%
+too long then they start to
+ 
+
+ align:start position:0%
+too long then they start to
+have different
+
+ align:start position:0%
+have different
+ 
+
+ align:start position:0%
+have different
+features interacting with each other so
+
+ align:start position:0%
+features interacting with each other so
+ 
+
+ align:start position:0%
+features interacting with each other so
+here we're trying to detect an edge now
+
+ align:start position:0%
+here we're trying to detect an edge now
+ 
+
+ align:start position:0%
+here we're trying to detect an edge now
+if you use an edge operator that's 100
+
+ align:start position:0%
+if you use an edge operator that's 100
+ 
+
+ align:start position:0%
+if you use an edge operator that's 100
+pixels long and there's another edge
+
+ align:start position:0%
+pixels long and there's another edge
+ 
+
+ align:start position:0%
+pixels long and there's another edge
+within that 100 pixels it's going to
+
+ align:start position:0%
+within that 100 pixels it's going to
+ 
+
+ align:start position:0%
+within that 100 pixels it's going to
+interfere with the results so we we try
+
+ align:start position:0%
+interfere with the results so we we try
+ 
+
+ align:start position:0%
+interfere with the results so we we try
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+compromise on the one hand we get better
+
+ align:start position:0%
+compromise on the one hand we get better
+ 
+
+ align:start position:0%
+compromise on the one hand we get better
+results with bigger support
+
+ align:start position:0%
+results with bigger support
+ 
+
+ align:start position:0%
+results with bigger support
+better noise suppression but at the same
+
+ align:start position:0%
+better noise suppression but at the same
+ 
+
+ align:start position:0%
+better noise suppression but at the same
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+we run more into the problem of what
+
+ align:start position:0%
+we run more into the problem of what
+ 
+
+ align:start position:0%
+we run more into the problem of what
+happens when two edges get close to each
+
+ align:start position:0%
+happens when two edges get close to each
+ 
+
+ align:start position:0%
+happens when two edges get close to each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+and in particular
+
+ align:start position:0%
+and in particular
+ 
+
+ align:start position:0%
+and in particular
+you know here's an image of the corner
+
+ align:start position:0%
+you know here's an image of the corner
+ 
+
+ align:start position:0%
+you know here's an image of the corner
+of a cube
+
+ align:start position:0%
+of a cube
+ 
+
+ align:start position:0%
+of a cube
+and yeah over here
+
+ align:start position:0%
+and yeah over here
+ 
+
+ align:start position:0%
+and yeah over here
+you know we can we could have
+
+ align:start position:0%
+you know we can we could have
+ 
+
+ align:start position:0%
+you know we can we could have
+potentially quite a large support but
+
+ align:start position:0%
+potentially quite a large support but
+ 
+
+ align:start position:0%
+potentially quite a large support but
+when we're back here
+
+ align:start position:0%
+when we're back here
+ 
+
+ align:start position:0%
+when we're back here
+edges get pretty close together and then
+
+ align:start position:0%
+edges get pretty close together and then
+ 
+
+ align:start position:0%
+edges get pretty close together and then
+a large support means that you're
+
+ align:start position:0%
+a large support means that you're
+ 
+
+ align:start position:0%
+a large support means that you're
+combining information about different
+
+ align:start position:0%
+combining information about different
+ 
+
+ align:start position:0%
+combining information about different
+edges and you won't get the results you
+
+ align:start position:0%
+edges and you won't get the results you
+ 
+
+ align:start position:0%
+edges and you won't get the results you
+you would like
+
+ align:start position:0%
+you would like
+ 
+
+ align:start position:0%
+you would like
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's first derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if our model is we find the peak
+
+ align:start position:0%
+and if our model is we find the peak
+ 
+
+ align:start position:0%
+and if our model is we find the peak
+in the gradient direction of the first
+
+ align:start position:0%
+in the gradient direction of the first
+ 
+
+ align:start position:0%
+in the gradient direction of the first
+derivative then that's all we need but
+
+ align:start position:0%
+derivative then that's all we need but
+ 
+
+ align:start position:0%
+derivative then that's all we need but
+for some purposes we might want higher
+
+ align:start position:0%
+for some purposes we might want higher
+ 
+
+ align:start position:0%
+for some purposes we might want higher
+order derivatives
+
+ align:start position:0%
+order derivatives
+ 
+
+ align:start position:0%
+order derivatives
+and we'll see some examples of that
+
+ align:start position:0%
+and we'll see some examples of that
+ 
+
+ align:start position:0%
+and we'll see some examples of that
+later so
+
+ align:start position:0%
+later so
+ 
+
+ align:start position:0%
+later so
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one way to think about this is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second derivative is just the first
+
+ align:start position:0%
+second derivative is just the first
+ 
+
+ align:start position:0%
+second derivative is just the first
+derivative applied twice
+
+ align:start position:0%
+derivative applied twice
+ 
+
+ align:start position:0%
+derivative applied twice
+and so we can run our numerical
+
+ align:start position:0%
+and so we can run our numerical
+ 
+
+ align:start position:0%
+and so we can run our numerical
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+a second time and that corresponds to
+
+ align:start position:0%
+a second time and that corresponds to
+ 
+
+ align:start position:0%
+a second time and that corresponds to
+convolution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the result is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that we can easily compute second
+
+ align:start position:0%
+so that we can easily compute second
+ 
+
+ align:start position:0%
+so that we can easily compute second
+order derivatives this way and let me
+
+ align:start position:0%
+order derivatives this way and let me
+ 
+
+ align:start position:0%
+order derivatives this way and let me
+just make sure we understand what this
+
+ align:start position:0%
+just make sure we understand what this
+ 
+
+ align:start position:0%
+just make sure we understand what this
+is so these computational molecules the
+
+ align:start position:0%
+is so these computational molecules the
+ 
+
+ align:start position:0%
+is so these computational molecules the
+way they work is that
+
+ align:start position:0%
+way they work is that
+ 
+
+ align:start position:0%
+way they work is that
+you put them down on the image grid and
+
+ align:start position:0%
+you put them down on the image grid and
+ 
+
+ align:start position:0%
+you put them down on the image grid and
+then you multiply the gray levels by
+
+ align:start position:0%
+then you multiply the gray levels by
+ 
+
+ align:start position:0%
+then you multiply the gray levels by
+whatever the weight is at this point so
+
+ align:start position:0%
+whatever the weight is at this point so
+ 
+
+ align:start position:0%
+whatever the weight is at this point so
+multiply that by one put it in
+
+ align:start position:0%
+multiply that by one put it in
+ 
+
+ align:start position:0%
+multiply that by one put it in
+accumulator take that one multiply it by
+
+ align:start position:0%
+accumulator take that one multiply it by
+ 
+
+ align:start position:0%
+accumulator take that one multiply it by
+-2 add that to the accumulator take that
+
+ align:start position:0%
+-2 add that to the accumulator take that
+ 
+
+ align:start position:0%
+-2 add that to the accumulator take that
+one multiply it by one add that to the
+
+ align:start position:0%
+one multiply it by one add that to the
+ 
+
+ align:start position:0%
+one multiply it by one add that to the
+accumulator and then finally take the
+
+ align:start position:0%
+accumulator and then finally take the
+ 
+
+ align:start position:0%
+accumulator and then finally take the
+result and divide by epsilon squared
+
+ align:start position:0%
+result and divide by epsilon squared
+ 
+
+ align:start position:0%
+result and divide by epsilon squared
+well often we don't care about constant
+
+ align:start position:0%
+well often we don't care about constant
+ 
+
+ align:start position:0%
+well often we don't care about constant
+factors so we might drop that but
+
+ align:start position:0%
+factors so we might drop that but
+ 
+
+ align:start position:0%
+factors so we might drop that but
+if we're actually thinking about
+
+ align:start position:0%
+if we're actually thinking about
+ 
+
+ align:start position:0%
+if we're actually thinking about
+derivatives we should we should do that
+
+ align:start position:0%
+derivatives we should we should do that
+ 
+
+ align:start position:0%
+derivatives we should we should do that
+so that's one thing
+
+ align:start position:0%
+so that's one thing
+ 
+
+ align:start position:0%
+so that's one thing
+and we're really talking about
+
+ align:start position:0%
+and we're really talking about
+ 
+
+ align:start position:0%
+and we're really talking about
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+right so we apply this to every place in
+
+ align:start position:0%
+right so we apply this to every place in
+ 
+
+ align:start position:0%
+right so we apply this to every place in
+the image
+
+ align:start position:0%
+the image
+ 
+
+ align:start position:0%
+the image
+slide it along if you like to produce a
+
+ align:start position:0%
+slide it along if you like to produce a
+ 
+
+ align:start position:0%
+slide it along if you like to produce a
+new image
+
+ align:start position:0%
+new image
+ 
+
+ align:start position:0%
+new image
+results at a bunch of points
+
+ align:start position:0%
+results at a bunch of points
+ 
+
+ align:start position:0%
+results at a bunch of points
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+how do we know that
+
+ align:start position:0%
+how do we know that
+ 
+
+ align:start position:0%
+how do we know that
+you know if we want a sanity check well
+
+ align:start position:0%
+you know if we want a sanity check well
+ 
+
+ align:start position:0%
+you know if we want a sanity check well
+a way of making
+
+ align:start position:0%
+a way of making
+ 
+
+ align:start position:0%
+a way of making
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+making a check on this is to
+
+ align:start position:0%
+making a check on this is to
+ 
+
+ align:start position:0%
+making a check on this is to
+try it on some function where you know
+
+ align:start position:0%
+try it on some function where you know
+ 
+
+ align:start position:0%
+try it on some function where you know
+what the answer is
+
+ align:start position:0%
+what the answer is
+ 
+
+ align:start position:0%
+what the answer is
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so we know that in this case uh
+
+ align:start position:0%
+right so we know that in this case uh
+ 
+
+ align:start position:0%
+right so we know that in this case uh
+the answer should be 2. so so let's
+
+ align:start position:0%
+the answer should be 2. so so let's
+ 
+
+ align:start position:0%
+the answer should be 2. so so let's
+apply this
+
+ align:start position:0%
+apply this
+ 
+
+ align:start position:0%
+apply this
+and well we have to decide where we're
+
+ align:start position:0%
+and well we have to decide where we're
+ 
+
+ align:start position:0%
+and well we have to decide where we're
+applying it so let's suppose that this
+
+ align:start position:0%
+applying it so let's suppose that this
+ 
+
+ align:start position:0%
+applying it so let's suppose that this
+is uh
+
+ align:start position:0%
+is uh
+ 
+
+ align:start position:0%
+is uh
+zero this is one this is minus one
+
+ align:start position:0%
+zero this is one this is minus one
+ 
+
+ align:start position:0%
+zero this is one this is minus one
+so we're plunking this down
+
+ align:start position:0%
+so we're plunking this down
+ 
+
+ align:start position:0%
+so we're plunking this down
+and so what do we get well uh in this
+
+ align:start position:0%
+and so what do we get well uh in this
+ 
+
+ align:start position:0%
+and so what do we get well uh in this
+case epsilon is obviously one so that's
+
+ align:start position:0%
+case epsilon is obviously one so that's
+ 
+
+ align:start position:0%
+case epsilon is obviously one so that's
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+times and then 1 times
+
+ align:start position:0%
+times and then 1 times
+ 
+
+ align:start position:0%
+times and then 1 times
+-1 well that's 2
+
+ align:start position:0%
+-1 well that's 2
+ 
+
+ align:start position:0%
+-1 well that's 2
+no sorry 1 times
+
+ align:start position:0%
+no sorry 1 times
+ 
+
+ align:start position:0%
+no sorry 1 times
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 times -1 squared is 1. then we have
+
+ align:start position:0%
+1 times -1 squared is 1. then we have
+ 
+
+ align:start position:0%
+1 times -1 squared is 1. then we have
+minus 2 times x squared with 0
+
+ align:start position:0%
+minus 2 times x squared with 0
+ 
+
+ align:start position:0%
+minus 2 times x squared with 0
+and plus 1
+
+ align:start position:0%
+and plus 1
+ 
+
+ align:start position:0%
+and plus 1
+times 1 squared and so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2.
+
+ align:start position:0%
+2.
+ 
+
+ align:start position:0%
+2.
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so apparently it works
+
+ align:start position:0%
+so apparently it works
+ 
+
+ align:start position:0%
+so apparently it works
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you know the different ways of designing
+
+ align:start position:0%
+you know the different ways of designing
+ 
+
+ align:start position:0%
+you know the different ways of designing
+these computational molecules
+
+ align:start position:0%
+these computational molecules
+ 
+
+ align:start position:0%
+these computational molecules
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+certainly convolution is one and then
+
+ align:start position:0%
+certainly convolution is one and then
+ 
+
+ align:start position:0%
+certainly convolution is one and then
+you'd want to check them so the another
+
+ align:start position:0%
+you'd want to check them so the another
+ 
+
+ align:start position:0%
+you'd want to check them so the another
+thing you might want to check is well
+
+ align:start position:0%
+thing you might want to check is well
+ 
+
+ align:start position:0%
+thing you might want to check is well
+what if f of x is x
+
+ align:start position:0%
+what if f of x is x
+ 
+
+ align:start position:0%
+what if f of x is x
+uh okay well then we're going to get
+
+ align:start position:0%
+uh okay well then we're going to get
+ 
+
+ align:start position:0%
+uh okay well then we're going to get
+1 times -1
+
+ align:start position:0%
+1 times -1
+ 
+
+ align:start position:0%
+1 times -1
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+1 times 1 the answer is 0 which is what
+
+ align:start position:0%
+1 times 1 the answer is 0 which is what
+ 
+
+ align:start position:0%
+1 times 1 the answer is 0 which is what
+it should be right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what if f of x is one
+
+ align:start position:0%
+what if f of x is one
+ 
+
+ align:start position:0%
+what if f of x is one
+so you want to check it for
+
+ align:start position:0%
+so you want to check it for
+ 
+
+ align:start position:0%
+so you want to check it for
+polynomials of low order up to the order
+
+ align:start position:0%
+polynomials of low order up to the order
+ 
+
+ align:start position:0%
+polynomials of low order up to the order
+of the derivative you're trying to get
+
+ align:start position:0%
+of the derivative you're trying to get
+ 
+
+ align:start position:0%
+of the derivative you're trying to get
+so if f of x is one then of course we
+
+ align:start position:0%
+so if f of x is one then of course we
+ 
+
+ align:start position:0%
+so if f of x is one then of course we
+get one minus two plus one is zero which
+
+ align:start position:0%
+get one minus two plus one is zero which
+ 
+
+ align:start position:0%
+get one minus two plus one is zero which
+is again what what you what it should be
+
+ align:start position:0%
+is again what what you what it should be
+ 
+
+ align:start position:0%
+is again what what you what it should be
+because the second derivative is zero
+
+ align:start position:0%
+because the second derivative is zero
+ 
+
+ align:start position:0%
+because the second derivative is zero
+so one of the constraints on these
+
+ align:start position:0%
+so one of the constraints on these
+ 
+
+ align:start position:0%
+so one of the constraints on these
+operators if they're supposed to be
+
+ align:start position:0%
+operators if they're supposed to be
+ 
+
+ align:start position:0%
+operators if they're supposed to be
+derivative operators is that the weights
+
+ align:start position:0%
+derivative operators is that the weights
+ 
+
+ align:start position:0%
+derivative operators is that the weights
+add up to zero
+
+ align:start position:0%
+add up to zero
+ 
+
+ align:start position:0%
+add up to zero
+that makes sense
+
+ align:start position:0%
+that makes sense
+ 
+
+ align:start position:0%
+that makes sense
+okay uh well so that's just one uh
+
+ align:start position:0%
+okay uh well so that's just one uh
+ 
+
+ align:start position:0%
+okay uh well so that's just one uh
+one dimension so to speak what about
+
+ align:start position:0%
+one dimension so to speak what about
+ 
+
+ align:start position:0%
+one dimension so to speak what about
+d2 dxdy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can just do that and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so because
+
+ align:start position:0%
+right so because
+ 
+
+ align:start position:0%
+right so because
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+the x derivative and that's the y
+
+ align:start position:0%
+the x derivative and that's the y
+ 
+
+ align:start position:0%
+the x derivative and that's the y
+derivative and uh composition of
+
+ align:start position:0%
+derivative and uh composition of
+ 
+
+ align:start position:0%
+derivative and uh composition of
+differentiation
+
+ align:start position:0%
+differentiation
+ 
+
+ align:start position:0%
+differentiation
+corresponds to convolution so that's a
+
+ align:start position:0%
+corresponds to convolution so that's a
+ 
+
+ align:start position:0%
+corresponds to convolution so that's a
+we're kind of sneaking in some stuff
+
+ align:start position:0%
+we're kind of sneaking in some stuff
+ 
+
+ align:start position:0%
+we're kind of sneaking in some stuff
+here one of them is that you know uh
+
+ align:start position:0%
+here one of them is that you know uh
+ 
+
+ align:start position:0%
+here one of them is that you know uh
+we're used to dealing with linear shift
+
+ align:start position:0%
+we're used to dealing with linear shift
+ 
+
+ align:start position:0%
+we're used to dealing with linear shift
+invariant systems but it turns out that
+
+ align:start position:0%
+invariant systems but it turns out that
+ 
+
+ align:start position:0%
+invariant systems but it turns out that
+of course derivative operations are
+
+ align:start position:0%
+of course derivative operations are
+ 
+
+ align:start position:0%
+of course derivative operations are
+linear shift invariant in that if i take
+
+ align:start position:0%
+linear shift invariant in that if i take
+ 
+
+ align:start position:0%
+linear shift invariant in that if i take
+the derivative of a function
+
+ align:start position:0%
+the derivative of a function
+ 
+
+ align:start position:0%
+the derivative of a function
+and then take the derivative of the same
+
+ align:start position:0%
+and then take the derivative of the same
+ 
+
+ align:start position:0%
+and then take the derivative of the same
+function shifted what i'm going to get
+
+ align:start position:0%
+function shifted what i'm going to get
+ 
+
+ align:start position:0%
+function shifted what i'm going to get
+is the derivative shifted right
+
+ align:start position:0%
+is the derivative shifted right
+ 
+
+ align:start position:0%
+is the derivative shifted right
+if i take the derivative of the sum of
+
+ align:start position:0%
+if i take the derivative of the sum of
+ 
+
+ align:start position:0%
+if i take the derivative of the sum of
+two functions i'm going to get the sum
+
+ align:start position:0%
+two functions i'm going to get the sum
+ 
+
+ align:start position:0%
+two functions i'm going to get the sum
+of the derivatives so
+
+ align:start position:0%
+of the derivatives so
+ 
+
+ align:start position:0%
+of the derivatives so
+that's a very important thing to
+
+ align:start position:0%
+that's a very important thing to
+ 
+
+ align:start position:0%
+that's a very important thing to
+exploit
+
+ align:start position:0%
+exploit
+ 
+
+ align:start position:0%
+exploit
+is that um you know derivatives taking
+
+ align:start position:0%
+is that um you know derivatives taking
+ 
+
+ align:start position:0%
+is that um you know derivatives taking
+derivatives can be considered
+
+ align:start position:0%
+derivatives can be considered
+ 
+
+ align:start position:0%
+derivatives can be considered
+convolution and so all of the good stuff
+
+ align:start position:0%
+convolution and so all of the good stuff
+ 
+
+ align:start position:0%
+convolution and so all of the good stuff
+we know about that applies
+
+ align:start position:0%
+we know about that applies
+ 
+
+ align:start position:0%
+we know about that applies
+so let's see what this gives us
+
+ align:start position:0%
+so let's see what this gives us
+ 
+
+ align:start position:0%
+so let's see what this gives us
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um uh what we're going to do basically
+
+ align:start position:0%
+um uh what we're going to do basically
+ 
+
+ align:start position:0%
+um uh what we're going to do basically
+is take one of these
+
+ align:start position:0%
+is take one of these
+ 
+
+ align:start position:0%
+is take one of these
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+flip it and superimpose it on the other
+
+ align:start position:0%
+flip it and superimpose it on the other
+ 
+
+ align:start position:0%
+flip it and superimpose it on the other
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if i superimpose it over here of course
+
+ align:start position:0%
+if i superimpose it over here of course
+ 
+
+ align:start position:0%
+if i superimpose it over here of course
+i get zero because
+
+ align:start position:0%
+i get zero because
+ 
+
+ align:start position:0%
+i get zero because
+i'm multiplying
+
+ align:start position:0%
+i'm multiplying
+ 
+
+ align:start position:0%
+i'm multiplying
+you know we assume the background is
+
+ align:start position:0%
+you know we assume the background is
+ 
+
+ align:start position:0%
+you know we assume the background is
+zero we assume that the only values
+
+ align:start position:0%
+zero we assume that the only values
+ 
+
+ align:start position:0%
+zero we assume that the only values
+we're showing are the non-zero values
+
+ align:start position:0%
+we're showing are the non-zero values
+ 
+
+ align:start position:0%
+we're showing are the non-zero values
+okay but then what if i move it here
+
+ align:start position:0%
+okay but then what if i move it here
+ 
+
+ align:start position:0%
+okay but then what if i move it here
+well then there's an overlap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then i move it over there there's an
+
+ align:start position:0%
+and then i move it over there there's an
+ 
+
+ align:start position:0%
+and then i move it over there there's an
+overlap and i can move it down here
+
+ align:start position:0%
+overlap and i can move it down here
+ 
+
+ align:start position:0%
+overlap and i can move it down here
+there's an overlap and i move it down
+
+ align:start position:0%
+there's an overlap and i move it down
+ 
+
+ align:start position:0%
+there's an overlap and i move it down
+here and again so i expect to get
+
+ align:start position:0%
+here and again so i expect to get
+ 
+
+ align:start position:0%
+here and again so i expect to get
+four values
+
+ align:start position:0%
+four values
+ 
+
+ align:start position:0%
+four values
+out of this convolution and so
+
+ align:start position:0%
+out of this convolution and so
+ 
+
+ align:start position:0%
+out of this convolution and so
+i'm going to get something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so my 2 by 2 stencil for estimating
+
+ align:start position:0%
+and so my 2 by 2 stencil for estimating
+ 
+
+ align:start position:0%
+and so my 2 by 2 stencil for estimating
+the mixed derivative is is just that and
+
+ align:start position:0%
+the mixed derivative is is just that and
+ 
+
+ align:start position:0%
+the mixed derivative is is just that and
+it makes perfect sense one thing to
+
+ align:start position:0%
+it makes perfect sense one thing to
+ 
+
+ align:start position:0%
+it makes perfect sense one thing to
+watch out for is that
+
+ align:start position:0%
+watch out for is that
+ 
+
+ align:start position:0%
+watch out for is that
+in convolution
+
+ align:start position:0%
+in convolution
+ 
+
+ align:start position:0%
+in convolution
+you know we flip one of the two
+
+ align:start position:0%
+you know we flip one of the two
+ 
+
+ align:start position:0%
+you know we flip one of the two
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+and uh then then slide it across and try
+
+ align:start position:0%
+and uh then then slide it across and try
+ 
+
+ align:start position:0%
+and uh then then slide it across and try
+it in all possible places uh over here
+
+ align:start position:0%
+it in all possible places uh over here
+ 
+
+ align:start position:0%
+it in all possible places uh over here
+sometimes we're
+
+ align:start position:0%
+sometimes we're
+ 
+
+ align:start position:0%
+sometimes we're
+using computational stencils that are
+
+ align:start position:0%
+using computational stencils that are
+ 
+
+ align:start position:0%
+using computational stencils that are
+not flipped
+
+ align:start position:0%
+not flipped
+ 
+
+ align:start position:0%
+not flipped
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we may end up with some sign reversal
+
+ align:start position:0%
+we may end up with some sign reversal
+ 
+
+ align:start position:0%
+we may end up with some sign reversal
+but you want to
+
+ align:start position:0%
+but you want to
+ 
+
+ align:start position:0%
+but you want to
+you can always check
+
+ align:start position:0%
+you can always check
+ 
+
+ align:start position:0%
+you can always check
+on a simple polynomial to see whether
+
+ align:start position:0%
+on a simple polynomial to see whether
+ 
+
+ align:start position:0%
+on a simple polynomial to see whether
+it's working the right way around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the way this one here
+
+ align:start position:0%
+by the way this one here
+ 
+
+ align:start position:0%
+by the way this one here
+we can sort of take a diagonal view of
+
+ align:start position:0%
+we can sort of take a diagonal view of
+ 
+
+ align:start position:0%
+we can sort of take a diagonal view of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+it's a little bit like
+
+ align:start position:0%
+it's a little bit like
+ 
+
+ align:start position:0%
+it's a little bit like
+right if i project this down
+
+ align:start position:0%
+right if i project this down
+ 
+
+ align:start position:0%
+right if i project this down
+so there's a plus one far out on this
+
+ align:start position:0%
+so there's a plus one far out on this
+ 
+
+ align:start position:0%
+so there's a plus one far out on this
+side there's a plus one far out on that
+
+ align:start position:0%
+side there's a plus one far out on that
+ 
+
+ align:start position:0%
+side there's a plus one far out on that
+side and then there's a minus
+
+ align:start position:0%
+side and then there's a minus
+ 
+
+ align:start position:0%
+side and then there's a minus
+two there two minus ones in the middle
+
+ align:start position:0%
+two there two minus ones in the middle
+ 
+
+ align:start position:0%
+two there two minus ones in the middle
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this looks awfully like a second
+
+ align:start position:0%
+this looks awfully like a second
+ 
+
+ align:start position:0%
+this looks awfully like a second
+derivative uh you know like the one
+
+ align:start position:0%
+derivative uh you know like the one
+ 
+
+ align:start position:0%
+derivative uh you know like the one
+we had over here just rotated 45 degrees
+
+ align:start position:0%
+we had over here just rotated 45 degrees
+ 
+
+ align:start position:0%
+we had over here just rotated 45 degrees
+and of course
+
+ align:start position:0%
+and of course
+ 
+
+ align:start position:0%
+and of course
+this mixed partial derivative
+
+ align:start position:0%
+this mixed partial derivative
+ 
+
+ align:start position:0%
+this mixed partial derivative
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+uh in a rotated coordinate system just
+
+ align:start position:0%
+uh in a rotated coordinate system just
+ 
+
+ align:start position:0%
+uh in a rotated coordinate system just
+d2 dx squared
+
+ align:start position:0%
+d2 dx squared
+ 
+
+ align:start position:0%
+d2 dx squared
+right so if i take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is my original
+
+ align:start position:0%
+so this is my original
+ 
+
+ align:start position:0%
+so this is my original
+coordinate system and then i look at the
+
+ align:start position:0%
+coordinate system and then i look at the
+ 
+
+ align:start position:0%
+coordinate system and then i look at the
+world in this coordinate system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the second derivative
+
+ align:start position:0%
+then the second derivative
+ 
+
+ align:start position:0%
+then the second derivative
+e x prime x prime
+
+ align:start position:0%
+e x prime x prime
+ 
+
+ align:start position:0%
+e x prime x prime
+is the same as
+
+ align:start position:0%
+is the same as
+ 
+
+ align:start position:0%
+is the same as
+that mixed derivative
+
+ align:start position:0%
+that mixed derivative
+ 
+
+ align:start position:0%
+that mixed derivative
+so you know we kind of think of e x y as
+
+ align:start position:0%
+so you know we kind of think of e x y as
+ 
+
+ align:start position:0%
+so you know we kind of think of e x y as
+a very different animal from e x
+
+ align:start position:0%
+a very different animal from e x
+ 
+
+ align:start position:0%
+a very different animal from e x
+x and e y y but but it isn't
+
+ align:start position:0%
+x and e y y but but it isn't
+ 
+
+ align:start position:0%
+x and e y y but but it isn't
+oh yeah just a little bit more of this
+
+ align:start position:0%
+oh yeah just a little bit more of this
+ 
+
+ align:start position:0%
+oh yeah just a little bit more of this
+before we go on um
+
+ align:start position:0%
+before we go on um
+ 
+
+ align:start position:0%
+before we go on um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+and we already mentioned the laplacian
+
+ align:start position:0%
+and we already mentioned the laplacian
+ 
+
+ align:start position:0%
+and we already mentioned the laplacian
+let's just bring that in here again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we had a second derivative operator
+
+ align:start position:0%
+so we had a second derivative operator
+ 
+
+ align:start position:0%
+so we had a second derivative operator
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and so in the case of the laplacian
+
+ align:start position:0%
+and so in the case of the laplacian
+ 
+
+ align:start position:0%
+and so in the case of the laplacian
+we're adding two of them in different in
+
+ align:start position:0%
+we're adding two of them in different in
+ 
+
+ align:start position:0%
+we're adding two of them in different in
+orthogonal directions
+
+ align:start position:0%
+orthogonal directions
+ 
+
+ align:start position:0%
+orthogonal directions
+so we could just do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so that's just this thing
+
+ align:start position:0%
+right so that's just this thing
+ 
+
+ align:start position:0%
+right so that's just this thing
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+it the same thing rotated 90 degrees and
+
+ align:start position:0%
+it the same thing rotated 90 degrees and
+ 
+
+ align:start position:0%
+it the same thing rotated 90 degrees and
+so so that's one way of writing the
+
+ align:start position:0%
+so so that's one way of writing the
+ 
+
+ align:start position:0%
+so so that's one way of writing the
+laplacian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that turns out to um also be a good
+
+ align:start position:0%
+that turns out to um also be a good
+ 
+
+ align:start position:0%
+that turns out to um also be a good
+approximation uh to the laplacian how do
+
+ align:start position:0%
+approximation uh to the laplacian how do
+ 
+
+ align:start position:0%
+approximation uh to the laplacian how do
+i know well there are lots of ways of
+
+ align:start position:0%
+i know well there are lots of ways of
+ 
+
+ align:start position:0%
+i know well there are lots of ways of
+checking one is
+
+ align:start position:0%
+checking one is
+ 
+
+ align:start position:0%
+checking one is
+taylor series
+
+ align:start position:0%
+taylor series
+ 
+
+ align:start position:0%
+taylor series
+another way is apply it to test
+
+ align:start position:0%
+another way is apply it to test
+ 
+
+ align:start position:0%
+another way is apply it to test
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+see if it gets the right result and
+
+ align:start position:0%
+see if it gets the right result and
+ 
+
+ align:start position:0%
+see if it gets the right result and
+another way is fourier transform but
+
+ align:start position:0%
+another way is fourier transform but
+ 
+
+ align:start position:0%
+another way is fourier transform but
+you know those and and you'll see that
+
+ align:start position:0%
+you know those and and you'll see that
+ 
+
+ align:start position:0%
+you know those and and you'll see that
+this is really the same pattern rotated
+
+ align:start position:0%
+this is really the same pattern rotated
+ 
+
+ align:start position:0%
+this is really the same pattern rotated
+45 degrees
+
+ align:start position:0%
+45 degrees
+ 
+
+ align:start position:0%
+45 degrees
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+now the separation is square root of two
+
+ align:start position:0%
+now the separation is square root of two
+ 
+
+ align:start position:0%
+now the separation is square root of two
+times as large
+
+ align:start position:0%
+times as large
+ 
+
+ align:start position:0%
+times as large
+so i end up having to change the the
+
+ align:start position:0%
+so i end up having to change the the
+ 
+
+ align:start position:0%
+so i end up having to change the the
+weight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+now i mentioned that the laplacian is
+
+ align:start position:0%
+now i mentioned that the laplacian is
+ 
+
+ align:start position:0%
+now i mentioned that the laplacian is
+the lowest order linear differential
+
+ align:start position:0%
+the lowest order linear differential
+ 
+
+ align:start position:0%
+the lowest order linear differential
+operator that's rotationally symmetric
+
+ align:start position:0%
+operator that's rotationally symmetric
+ 
+
+ align:start position:0%
+operator that's rotationally symmetric
+well neither of these looks particularly
+
+ align:start position:0%
+well neither of these looks particularly
+ 
+
+ align:start position:0%
+well neither of these looks particularly
+rotationally symmetric so
+
+ align:start position:0%
+rotationally symmetric so
+ 
+
+ align:start position:0%
+rotationally symmetric so
+can we make one that's a bit more i mean
+
+ align:start position:0%
+can we make one that's a bit more i mean
+ 
+
+ align:start position:0%
+can we make one that's a bit more i mean
+on a square grid
+
+ align:start position:0%
+on a square grid
+ 
+
+ align:start position:0%
+on a square grid
+you can't but we can do better than
+
+ align:start position:0%
+you can't but we can do better than
+ 
+
+ align:start position:0%
+you can't but we can do better than
+these and one way is to combine them to
+
+ align:start position:0%
+these and one way is to combine them to
+ 
+
+ align:start position:0%
+these and one way is to combine them to
+take a weighted sum of these two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i've taken uh
+
+ align:start position:0%
+okay so i've taken uh
+ 
+
+ align:start position:0%
+okay so i've taken uh
+i don't know four times this one
+
+ align:start position:0%
+i don't know four times this one
+ 
+
+ align:start position:0%
+i don't know four times this one
+plus one times uh this one
+
+ align:start position:0%
+plus one times uh this one
+ 
+
+ align:start position:0%
+plus one times uh this one
+and and i get this operator and it's a
+
+ align:start position:0%
+and and i get this operator and it's a
+ 
+
+ align:start position:0%
+and and i get this operator and it's a
+little bit smoother in terms of
+
+ align:start position:0%
+little bit smoother in terms of
+ 
+
+ align:start position:0%
+little bit smoother in terms of
+rotational symmetry uh the the corner
+
+ align:start position:0%
+rotational symmetry uh the the corner
+ 
+
+ align:start position:0%
+rotational symmetry uh the the corner
+ones aren't zero
+
+ align:start position:0%
+ones aren't zero
+ 
+
+ align:start position:0%
+ones aren't zero
+uh but they also don't have the same
+
+ align:start position:0%
+uh but they also don't have the same
+ 
+
+ align:start position:0%
+uh but they also don't have the same
+weight as the diagonal one the the up
+
+ align:start position:0%
+weight as the diagonal one the the up
+ 
+
+ align:start position:0%
+weight as the diagonal one the the up
+and down ones um
+
+ align:start position:0%
+and down ones um
+ 
+
+ align:start position:0%
+and down ones um
+because they're further from the center
+
+ align:start position:0%
+because they're further from the center
+ 
+
+ align:start position:0%
+because they're further from the center
+so how do i know that's a good
+
+ align:start position:0%
+so how do i know that's a good
+ 
+
+ align:start position:0%
+so how do i know that's a good
+combination
+
+ align:start position:0%
+combination
+ 
+
+ align:start position:0%
+combination
+how did people get to that one well
+
+ align:start position:0%
+how did people get to that one well
+ 
+
+ align:start position:0%
+how did people get to that one well
+again you look at the taylor series and
+
+ align:start position:0%
+again you look at the taylor series and
+ 
+
+ align:start position:0%
+again you look at the taylor series and
+it turns out that the lowest order error
+
+ align:start position:0%
+it turns out that the lowest order error
+ 
+
+ align:start position:0%
+it turns out that the lowest order error
+term for this one is one larger than the
+
+ align:start position:0%
+term for this one is one larger than the
+ 
+
+ align:start position:0%
+term for this one is one larger than the
+lowest order error term for either of
+
+ align:start position:0%
+lowest order error term for either of
+ 
+
+ align:start position:0%
+lowest order error term for either of
+these two
+
+ align:start position:0%
+these two
+ 
+
+ align:start position:0%
+these two
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it's better uh
+
+ align:start position:0%
+it's better uh
+ 
+
+ align:start position:0%
+it's better uh
+more work right if you do if you apply
+
+ align:start position:0%
+more work right if you do if you apply
+ 
+
+ align:start position:0%
+more work right if you do if you apply
+this to your image
+
+ align:start position:0%
+this to your image
+ 
+
+ align:start position:0%
+this to your image
+uh you're doing
+
+ align:start position:0%
+uh you're doing
+ 
+
+ align:start position:0%
+uh you're doing
+not quite twice as much work but you're
+
+ align:start position:0%
+not quite twice as much work but you're
+ 
+
+ align:start position:0%
+not quite twice as much work but you're
+doing more work because you have to take
+
+ align:start position:0%
+doing more work because you have to take
+ 
+
+ align:start position:0%
+doing more work because you have to take
+into account all of the corner ones
+
+ align:start position:0%
+into account all of the corner ones
+ 
+
+ align:start position:0%
+into account all of the corner ones
+which this this operator doesn't or
+
+ align:start position:0%
+which this this operator doesn't or
+ 
+
+ align:start position:0%
+which this this operator doesn't or
+conversely the up and down and west and
+
+ align:start position:0%
+conversely the up and down and west and
+ 
+
+ align:start position:0%
+conversely the up and down and west and
+east ones uh there so
+
+ align:start position:0%
+east ones uh there so
+ 
+
+ align:start position:0%
+east ones uh there so
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know if we wanted to we could do a
+
+ align:start position:0%
+you know if we wanted to we could do a
+ 
+
+ align:start position:0%
+you know if we wanted to we could do a
+more detailed analysis of the error
+
+ align:start position:0%
+more detailed analysis of the error
+ 
+
+ align:start position:0%
+more detailed analysis of the error
+terms but
+
+ align:start position:0%
+terms but
+ 
+
+ align:start position:0%
+terms but
+that's that's pretty boring so we won't
+
+ align:start position:0%
+that's that's pretty boring so we won't
+ 
+
+ align:start position:0%
+that's that's pretty boring so we won't
+do that anyway so those are
+
+ align:start position:0%
+do that anyway so those are
+ 
+
+ align:start position:0%
+do that anyway so those are
+kind of all of the computational
+
+ align:start position:0%
+kind of all of the computational
+ 
+
+ align:start position:0%
+kind of all of the computational
+molecules we're going to need and as you
+
+ align:start position:0%
+molecules we're going to need and as you
+ 
+
+ align:start position:0%
+molecules we're going to need and as you
+can see the the options the the
+
+ align:start position:0%
+can see the the options the the
+ 
+
+ align:start position:0%
+can see the the options the the
+different versions
+
+ align:start position:0%
+different versions
+ 
+
+ align:start position:0%
+different versions
+uh that are trying to compute the same
+
+ align:start position:0%
+uh that are trying to compute the same
+ 
+
+ align:start position:0%
+uh that are trying to compute the same
+sort of thing of course on a hexagonal
+
+ align:start position:0%
+sort of thing of course on a hexagonal
+ 
+
+ align:start position:0%
+sort of thing of course on a hexagonal
+grid
+
+ align:start position:0%
+grid
+ 
+
+ align:start position:0%
+grid
+this looks much better
+
+ align:start position:0%
+this looks much better
+ 
+
+ align:start position:0%
+this looks much better
+because we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can do something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which uh you know looks nice and
+
+ align:start position:0%
+which uh you know looks nice and
+ 
+
+ align:start position:0%
+which uh you know looks nice and
+rotationally symmetric yeah what's the
+
+ align:start position:0%
+rotationally symmetric yeah what's the
+ 
+
+ align:start position:0%
+rotationally symmetric yeah what's the
+one in the middle
+
+ align:start position:0%
+one in the middle
+ 
+
+ align:start position:0%
+one in the middle
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+-20 so so can anyone think of how you
+
+ align:start position:0%
+-20 so so can anyone think of how you
+ 
+
+ align:start position:0%
+-20 so so can anyone think of how you
+could determine that it should be minus
+
+ align:start position:0%
+could determine that it should be minus
+ 
+
+ align:start position:0%
+could determine that it should be minus
+20 without actually doing a lot of area
+
+ align:start position:0%
+20 without actually doing a lot of area
+ 
+
+ align:start position:0%
+20 without actually doing a lot of area
+algebra
+
+ align:start position:0%
+algebra
+ 
+
+ align:start position:0%
+algebra
+they have to sum to zero right why is
+
+ align:start position:0%
+they have to sum to zero right why is
+ 
+
+ align:start position:0%
+they have to sum to zero right why is
+that well because when you apply this
+
+ align:start position:0%
+that well because when you apply this
+ 
+
+ align:start position:0%
+that well because when you apply this
+operator to f of x equals one
+
+ align:start position:0%
+operator to f of x equals one
+ 
+
+ align:start position:0%
+operator to f of x equals one
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+laplacian is zero and so if you apply
+
+ align:start position:0%
+laplacian is zero and so if you apply
+ 
+
+ align:start position:0%
+laplacian is zero and so if you apply
+this to the function that's one
+
+ align:start position:0%
+this to the function that's one
+ 
+
+ align:start position:0%
+this to the function that's one
+everywhere obviously you'll just be
+
+ align:start position:0%
+everywhere obviously you'll just be
+ 
+
+ align:start position:0%
+everywhere obviously you'll just be
+adding all the weights and so they they
+
+ align:start position:0%
+adding all the weights and so they they
+ 
+
+ align:start position:0%
+adding all the weights and so they they
+need to add how do i know it's one over
+
+ align:start position:0%
+need to add how do i know it's one over
+ 
+
+ align:start position:0%
+need to add how do i know it's one over
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+well one way to get it is is to apply
+
+ align:start position:0%
+well one way to get it is is to apply
+ 
+
+ align:start position:0%
+well one way to get it is is to apply
+this to a test function like you know if
+
+ align:start position:0%
+this to a test function like you know if
+ 
+
+ align:start position:0%
+this to a test function like you know if
+f of x is x squared plus y squared where
+
+ align:start position:0%
+f of x is x squared plus y squared where
+ 
+
+ align:start position:0%
+f of x is x squared plus y squared where
+i know that the answer is
+
+ align:start position:0%
+i know that the answer is
+ 
+
+ align:start position:0%
+i know that the answer is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and then you know
+
+ align:start position:0%
+and then you know
+ 
+
+ align:start position:0%
+and then you know
+go from there
+
+ align:start position:0%
+go from there
+ 
+
+ align:start position:0%
+go from there
+or i can get it from this argument which
+
+ align:start position:0%
+or i can get it from this argument which
+ 
+
+ align:start position:0%
+or i can get it from this argument which
+is the weighted argument that i'm taking
+
+ align:start position:0%
+is the weighted argument that i'm taking
+ 
+
+ align:start position:0%
+is the weighted argument that i'm taking
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+four times one of those and one of those
+
+ align:start position:0%
+four times one of those and one of those
+ 
+
+ align:start position:0%
+four times one of those and one of those
+and this one has a factor of 2 in there
+
+ align:start position:0%
+and this one has a factor of 2 in there
+ 
+
+ align:start position:0%
+and this one has a factor of 2 in there
+so you end up with
+
+ align:start position:0%
+so you end up with
+ 
+
+ align:start position:0%
+so you end up with
+i don't know
+
+ align:start position:0%
+i don't know
+ 
+
+ align:start position:0%
+i don't know
+a half plus a
+
+ align:start position:0%
+a half plus a
+ 
+
+ align:start position:0%
+a half plus a
+quarter no
+
+ align:start position:0%
+quarter no
+ 
+
+ align:start position:0%
+quarter no
+anyway it comes out to 6 epsilon squared
+
+ align:start position:0%
+anyway it comes out to 6 epsilon squared
+ 
+
+ align:start position:0%
+anyway it comes out to 6 epsilon squared
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's sort of annoying that
+
+ align:start position:0%
+so it's sort of annoying that
+ 
+
+ align:start position:0%
+so it's sort of annoying that
+we don't have hexagonal pixels
+
+ align:start position:0%
+we don't have hexagonal pixels
+ 
+
+ align:start position:0%
+we don't have hexagonal pixels
+by the way there are some situations
+
+ align:start position:0%
+by the way there are some situations
+ 
+
+ align:start position:0%
+by the way there are some situations
+where people are
+
+ align:start position:0%
+where people are
+ 
+
+ align:start position:0%
+where people are
+very concerned about
+
+ align:start position:0%
+very concerned about
+ 
+
+ align:start position:0%
+very concerned about
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you know efficiency
+
+ align:start position:0%
+you know efficiency
+ 
+
+ align:start position:0%
+you know efficiency
+you know like trying to image the black
+
+ align:start position:0%
+you know like trying to image the black
+ 
+
+ align:start position:0%
+you know like trying to image the black
+hole at the center of our galaxy using
+
+ align:start position:0%
+hole at the center of our galaxy using
+ 
+
+ align:start position:0%
+hole at the center of our galaxy using
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+radio frequencies
+
+ align:start position:0%
+radio frequencies
+ 
+
+ align:start position:0%
+radio frequencies
+by you and you know each antenna you put
+
+ align:start position:0%
+by you and you know each antenna you put
+ 
+
+ align:start position:0%
+by you and you know each antenna you put
+up costs a pile of money so you want to
+
+ align:start position:0%
+up costs a pile of money so you want to
+ 
+
+ align:start position:0%
+up costs a pile of money so you want to
+make sure that this grid of antennas is
+
+ align:start position:0%
+make sure that this grid of antennas is
+ 
+
+ align:start position:0%
+make sure that this grid of antennas is
+the most efficient way of sampling the
+
+ align:start position:0%
+the most efficient way of sampling the
+ 
+
+ align:start position:0%
+the most efficient way of sampling the
+fourier transform space in that case and
+
+ align:start position:0%
+fourier transform space in that case and
+ 
+
+ align:start position:0%
+fourier transform space in that case and
+so it turns out that this way of
+
+ align:start position:0%
+so it turns out that this way of
+ 
+
+ align:start position:0%
+so it turns out that this way of
+sampling
+
+ align:start position:0%
+sampling
+ 
+
+ align:start position:0%
+sampling
+is four over pi as efficient as that way
+
+ align:start position:0%
+is four over pi as efficient as that way
+ 
+
+ align:start position:0%
+is four over pi as efficient as that way
+of sampling so there are places where
+
+ align:start position:0%
+of sampling so there are places where
+ 
+
+ align:start position:0%
+of sampling so there are places where
+people do this and and for example
+
+ align:start position:0%
+people do this and and for example
+ 
+
+ align:start position:0%
+people do this and and for example
+briefly in
+
+ align:start position:0%
+briefly in
+ 
+
+ align:start position:0%
+briefly in
+you know almost all chips are laid out
+
+ align:start position:0%
+you know almost all chips are laid out
+ 
+
+ align:start position:0%
+you know almost all chips are laid out
+on a rectangular pattern
+
+ align:start position:0%
+on a rectangular pattern
+ 
+
+ align:start position:0%
+on a rectangular pattern
+because that's very easy to do and check
+
+ align:start position:0%
+because that's very easy to do and check
+ 
+
+ align:start position:0%
+because that's very easy to do and check
+but if it comes down to packing density
+
+ align:start position:0%
+but if it comes down to packing density
+ 
+
+ align:start position:0%
+but if it comes down to packing density
+and you know particularly if you have
+
+ align:start position:0%
+and you know particularly if you have
+ 
+
+ align:start position:0%
+and you know particularly if you have
+something that has a very simple
+
+ align:start position:0%
+something that has a very simple
+ 
+
+ align:start position:0%
+something that has a very simple
+repeating pattern then sometimes there's
+
+ align:start position:0%
+repeating pattern then sometimes there's
+ 
+
+ align:start position:0%
+repeating pattern then sometimes there's
+an advantage so there were memory chips
+
+ align:start position:0%
+an advantage so there were memory chips
+ 
+
+ align:start position:0%
+an advantage so there were memory chips
+for a while that used the hexagonal
+
+ align:start position:0%
+for a while that used the hexagonal
+ 
+
+ align:start position:0%
+for a while that used the hexagonal
+layout but they've since disappeared
+
+ align:start position:0%
+layout but they've since disappeared
+ 
+
+ align:start position:0%
+layout but they've since disappeared
+because now we're stacking things
+
+ align:start position:0%
+because now we're stacking things
+ 
+
+ align:start position:0%
+because now we're stacking things
+vertically and right now it doesn't seem
+
+ align:start position:0%
+vertically and right now it doesn't seem
+ 
+
+ align:start position:0%
+vertically and right now it doesn't seem
+to be an efficient way to go
+
+ align:start position:0%
+to be an efficient way to go
+ 
+
+ align:start position:0%
+to be an efficient way to go
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+oh so
+
+ align:start position:0%
+oh so
+ 
+
+ align:start position:0%
+oh so
+while we're here
+
+ align:start position:0%
+while we're here
+ 
+
+ align:start position:0%
+while we're here
+i should mention i mentioned already
+
+ align:start position:0%
+i should mention i mentioned already
+ 
+
+ align:start position:0%
+i should mention i mentioned already
+that the laplacian is the lowest order
+
+ align:start position:0%
+that the laplacian is the lowest order
+ 
+
+ align:start position:0%
+that the laplacian is the lowest order
+linear operator differential operator
+
+ align:start position:0%
+linear operator differential operator
+ 
+
+ align:start position:0%
+linear operator differential operator
+that's rotationally symmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's a non-linear one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this operator is rotationally
+
+ align:start position:0%
+so this operator is rotationally
+ 
+
+ align:start position:0%
+so this operator is rotationally
+symmetric what do i mean by that i mean
+
+ align:start position:0%
+symmetric what do i mean by that i mean
+ 
+
+ align:start position:0%
+symmetric what do i mean by that i mean
+that if you rotate the coordinate system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know for example over here
+
+ align:start position:0%
+you know for example over here
+ 
+
+ align:start position:0%
+you know for example over here
+and you compute
+
+ align:start position:0%
+and you compute
+ 
+
+ align:start position:0%
+and you compute
+e sub x
+
+ align:start position:0%
+e sub x
+ 
+
+ align:start position:0%
+e sub x
+dash and square it and add e sub y dash
+
+ align:start position:0%
+dash and square it and add e sub y dash
+ 
+
+ align:start position:0%
+dash and square it and add e sub y dash
+and square it you'll get the same answer
+
+ align:start position:0%
+and square it you'll get the same answer
+ 
+
+ align:start position:0%
+and square it you'll get the same answer
+as if you take
+
+ align:start position:0%
+as if you take
+ 
+
+ align:start position:0%
+as if you take
+so so it doesn't depend on the
+
+ align:start position:0%
+so so it doesn't depend on the
+ 
+
+ align:start position:0%
+so so it doesn't depend on the
+orientation of the
+
+ align:start position:0%
+orientation of the
+ 
+
+ align:start position:0%
+orientation of the
+x axis
+
+ align:start position:0%
+x axis
+ 
+
+ align:start position:0%
+x axis
+and so this is lower order of course in
+
+ align:start position:0%
+and so this is lower order of course in
+ 
+
+ align:start position:0%
+and so this is lower order of course in
+laplacian because it's first order but
+
+ align:start position:0%
+laplacian because it's first order but
+ 
+
+ align:start position:0%
+laplacian because it's first order but
+it's non-linear so
+
+ align:start position:0%
+it's non-linear so
+ 
+
+ align:start position:0%
+it's non-linear so
+nevertheless we run into this quite a
+
+ align:start position:0%
+nevertheless we run into this quite a
+ 
+
+ align:start position:0%
+nevertheless we run into this quite a
+bit because remember uh roberts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use these stencils
+
+ align:start position:0%
+use these stencils
+ 
+
+ align:start position:0%
+use these stencils
+which you can just think of as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ways of computing the derivatives in the
+
+ align:start position:0%
+ways of computing the derivatives in the
+ 
+
+ align:start position:0%
+ways of computing the derivatives in the
+rotated coordinate system and then he
+
+ align:start position:0%
+rotated coordinate system and then he
+ 
+
+ align:start position:0%
+rotated coordinate system and then he
+took the square root of the sum of
+
+ align:start position:0%
+took the square root of the sum of
+ 
+
+ align:start position:0%
+took the square root of the sum of
+squares
+
+ align:start position:0%
+squares
+ 
+
+ align:start position:0%
+squares
+and that was his edge detector
+
+ align:start position:0%
+and that was his edge detector
+ 
+
+ align:start position:0%
+and that was his edge detector
+and so it's equivalent to doing this and
+
+ align:start position:0%
+and so it's equivalent to doing this and
+ 
+
+ align:start position:0%
+and so it's equivalent to doing this and
+for his purposes that
+
+ align:start position:0%
+for his purposes that
+ 
+
+ align:start position:0%
+for his purposes that
+took less computation and he already
+
+ align:start position:0%
+took less computation and he already
+ 
+
+ align:start position:0%
+took less computation and he already
+knew in 1965
+
+ align:start position:0%
+knew in 1965
+ 
+
+ align:start position:0%
+knew in 1965
+that what you want to do is
+
+ align:start position:0%
+that what you want to do is
+ 
+
+ align:start position:0%
+that what you want to do is
+make sure that your ex and ey refer to
+
+ align:start position:0%
+make sure that your ex and ey refer to
+ 
+
+ align:start position:0%
+make sure that your ex and ey refer to
+the same point in pixel space
+
+ align:start position:0%
+the same point in pixel space
+ 
+
+ align:start position:0%
+the same point in pixel space
+a lesson which has since been forgotten
+
+ align:start position:0%
+a lesson which has since been forgotten
+ 
+
+ align:start position:0%
+a lesson which has since been forgotten
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+except here um okay
+
+ align:start position:0%
+except here um okay
+ 
+
+ align:start position:0%
+except here um okay
+so that was the front end and this has
+
+ align:start position:0%
+so that was the front end and this has
+ 
+
+ align:start position:0%
+so that was the front end and this has
+to be very efficient because it's run on
+
+ align:start position:0%
+to be very efficient because it's run on
+ 
+
+ align:start position:0%
+to be very efficient because it's run on
+every pixel
+
+ align:start position:0%
+every pixel
+ 
+
+ align:start position:0%
+every pixel
+and it also lends itself to special
+
+ align:start position:0%
+and it also lends itself to special
+ 
+
+ align:start position:0%
+and it also lends itself to special
+purpose hardware of course
+
+ align:start position:0%
+purpose hardware of course
+ 
+
+ align:start position:0%
+purpose hardware of course
+so the next step was
+
+ align:start position:0%
+so the next step was
+ 
+
+ align:start position:0%
+so the next step was
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+subpixel
+
+ align:start position:0%
+subpixel
+ 
+
+ align:start position:0%
+subpixel
+edge detection method so we used what
+
+ align:start position:0%
+edge detection method so we used what
+ 
+
+ align:start position:0%
+edge detection method so we used what
+is called non-maximum suppression
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+this weird terminology i mean why not
+
+ align:start position:0%
+this weird terminology i mean why not
+ 
+
+ align:start position:0%
+this weird terminology i mean why not
+just say finding the maximum
+
+ align:start position:0%
+just say finding the maximum
+ 
+
+ align:start position:0%
+just say finding the maximum
+but there it is so what where did that
+
+ align:start position:0%
+but there it is so what where did that
+ 
+
+ align:start position:0%
+but there it is so what where did that
+terminology come from well the idea is
+
+ align:start position:0%
+terminology come from well the idea is
+ 
+
+ align:start position:0%
+terminology come from well the idea is
+that we apply this edge operator
+
+ align:start position:0%
+that we apply this edge operator
+ 
+
+ align:start position:0%
+that we apply this edge operator
+everywhere and in most places it has a
+
+ align:start position:0%
+everywhere and in most places it has a
+ 
+
+ align:start position:0%
+everywhere and in most places it has a
+kind of feeble response but on the edges
+
+ align:start position:0%
+kind of feeble response but on the edges
+ 
+
+ align:start position:0%
+kind of feeble response but on the edges
+it really kicks up and so one approach
+
+ align:start position:0%
+it really kicks up and so one approach
+ 
+
+ align:start position:0%
+it really kicks up and so one approach
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+you know let's just threshold so if if
+
+ align:start position:0%
+you know let's just threshold so if if
+ 
+
+ align:start position:0%
+you know let's just threshold so if if
+we get a strong response from one of
+
+ align:start position:0%
+we get a strong response from one of
+ 
+
+ align:start position:0%
+we get a strong response from one of
+these molecules here then
+
+ align:start position:0%
+these molecules here then
+ 
+
+ align:start position:0%
+these molecules here then
+that's then we're on the edge and if not
+
+ align:start position:0%
+that's then we're on the edge and if not
+ 
+
+ align:start position:0%
+that's then we're on the edge and if not
+then then we're not well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+involves um early decision making
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because once you've made that decision
+
+ align:start position:0%
+because once you've made that decision
+ 
+
+ align:start position:0%
+because once you've made that decision
+uh that's it you'll you you know you
+
+ align:start position:0%
+uh that's it you'll you you know you
+ 
+
+ align:start position:0%
+uh that's it you'll you you know you
+you'll throw away
+
+ align:start position:0%
+you'll throw away
+ 
+
+ align:start position:0%
+you'll throw away
+you'll throw away that edge point and
+
+ align:start position:0%
+you'll throw away that edge point and
+ 
+
+ align:start position:0%
+you'll throw away that edge point and
+never
+
+ align:start position:0%
+never
+ 
+
+ align:start position:0%
+never
+never
+
+ align:start position:0%
+never
+ 
+
+ align:start position:0%
+never
+do any computation with it again because
+
+ align:start position:0%
+do any computation with it again because
+ 
+
+ align:start position:0%
+do any computation with it again because
+you've decided it's below threshold or
+
+ align:start position:0%
+you've decided it's below threshold or
+ 
+
+ align:start position:0%
+you've decided it's below threshold or
+vice versa you picked it as being a
+
+ align:start position:0%
+vice versa you picked it as being a
+ 
+
+ align:start position:0%
+vice versa you picked it as being a
+threshold so
+
+ align:start position:0%
+threshold so
+ 
+
+ align:start position:0%
+threshold so
+a big
+
+ align:start position:0%
+a big
+ 
+
+ align:start position:0%
+a big
+in the patent bill silver makes a big
+
+ align:start position:0%
+in the patent bill silver makes a big
+ 
+
+ align:start position:0%
+in the patent bill silver makes a big
+fuss about
+
+ align:start position:0%
+fuss about
+ 
+
+ align:start position:0%
+fuss about
+avoiding thresholds
+
+ align:start position:0%
+avoiding thresholds
+ 
+
+ align:start position:0%
+avoiding thresholds
+if possible and
+
+ align:start position:0%
+if possible and
+ 
+
+ align:start position:0%
+if possible and
+not making decisions too early that's
+
+ align:start position:0%
+not making decisions too early that's
+ 
+
+ align:start position:0%
+not making decisions too early that's
+his sort of main motivation for not
+
+ align:start position:0%
+his sort of main motivation for not
+ 
+
+ align:start position:0%
+his sort of main motivation for not
+using thresholds
+
+ align:start position:0%
+using thresholds
+ 
+
+ align:start position:0%
+using thresholds
+so some previous
+
+ align:start position:0%
+so some previous
+ 
+
+ align:start position:0%
+so some previous
+edge detection work
+
+ align:start position:0%
+edge detection work
+ 
+
+ align:start position:0%
+edge detection work
+did work that way you apply some
+
+ align:start position:0%
+did work that way you apply some
+ 
+
+ align:start position:0%
+did work that way you apply some
+operator which has a strong response on
+
+ align:start position:0%
+operator which has a strong response on
+ 
+
+ align:start position:0%
+operator which has a strong response on
+the edge and then you threshold and
+
+ align:start position:0%
+the edge and then you threshold and
+ 
+
+ align:start position:0%
+the edge and then you threshold and
+now you get
+
+ align:start position:0%
+now you get
+ 
+
+ align:start position:0%
+now you get
+responses but they're not just right on
+
+ align:start position:0%
+responses but they're not just right on
+ 
+
+ align:start position:0%
+responses but they're not just right on
+the edge because we saw that the edge is
+
+ align:start position:0%
+the edge because we saw that the edge is
+ 
+
+ align:start position:0%
+the edge because we saw that the edge is
+a slow smooth transition so there'll be
+
+ align:start position:0%
+a slow smooth transition so there'll be
+ 
+
+ align:start position:0%
+a slow smooth transition so there'll be
+neighboring points that also have a
+
+ align:start position:0%
+neighboring points that also have a
+ 
+
+ align:start position:0%
+neighboring points that also have a
+strong response
+
+ align:start position:0%
+strong response
+ 
+
+ align:start position:0%
+strong response
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+with noise
+
+ align:start position:0%
+with noise
+ 
+
+ align:start position:0%
+with noise
+there will be points in the background
+
+ align:start position:0%
+there will be points in the background
+ 
+
+ align:start position:0%
+there will be points in the background
+where noise just happens to add up and
+
+ align:start position:0%
+where noise just happens to add up and
+ 
+
+ align:start position:0%
+where noise just happens to add up and
+now there seems to be an edge there so
+
+ align:start position:0%
+now there seems to be an edge there so
+ 
+
+ align:start position:0%
+now there seems to be an edge there so
+that's undesirable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the previous methods worked by
+
+ align:start position:0%
+so the previous methods worked by
+ 
+
+ align:start position:0%
+so the previous methods worked by
+thresholding and
+
+ align:start position:0%
+thresholding and
+ 
+
+ align:start position:0%
+thresholding and
+looking
+
+ align:start position:0%
+looking
+ 
+
+ align:start position:0%
+looking
+for things that had a strong edge
+
+ align:start position:0%
+for things that had a strong edge
+ 
+
+ align:start position:0%
+for things that had a strong edge
+response and here instead what we're
+
+ align:start position:0%
+response and here instead what we're
+ 
+
+ align:start position:0%
+response and here instead what we're
+doing is we're going to remove
+
+ align:start position:0%
+doing is we're going to remove
+ 
+
+ align:start position:0%
+doing is we're going to remove
+everything except the maximum but
+
+ align:start position:0%
+everything except the maximum but
+ 
+
+ align:start position:0%
+everything except the maximum but
+maximum in what sense well again just in
+
+ align:start position:0%
+maximum in what sense well again just in
+ 
+
+ align:start position:0%
+maximum in what sense well again just in
+the gradient direction
+
+ align:start position:0%
+the gradient direction
+ 
+
+ align:start position:0%
+the gradient direction
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here here we deal with the unfortunate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fact that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to quantize the gradient
+
+ align:start position:0%
+we're going to quantize the gradient
+ 
+
+ align:start position:0%
+we're going to quantize the gradient
+directions so we're only going to have
+
+ align:start position:0%
+directions so we're only going to have
+ 
+
+ align:start position:0%
+directions so we're only going to have
+you know compass directions
+
+ align:start position:0%
+you know compass directions
+ 
+
+ align:start position:0%
+you know compass directions
+east northeast north northwest west
+
+ align:start position:0%
+east northeast north northwest west
+ 
+
+ align:start position:0%
+east northeast north northwest west
+etcetera eight of them
+
+ align:start position:0%
+etcetera eight of them
+ 
+
+ align:start position:0%
+etcetera eight of them
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+let's suppose that this is our quantized
+
+ align:start position:0%
+let's suppose that this is our quantized
+ 
+
+ align:start position:0%
+let's suppose that this is our quantized
+gradient direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+step through the image
+
+ align:start position:0%
+step through the image
+ 
+
+ align:start position:0%
+step through the image
+and we consider
+
+ align:start position:0%
+and we consider
+ 
+
+ align:start position:0%
+and we consider
+those three values
+
+ align:start position:0%
+those three values
+ 
+
+ align:start position:0%
+those three values
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the non-maximum suppression says that we
+
+ align:start position:0%
+the non-maximum suppression says that we
+ 
+
+ align:start position:0%
+the non-maximum suppression says that we
+will accept this as a potential edge
+
+ align:start position:0%
+will accept this as a potential edge
+ 
+
+ align:start position:0%
+will accept this as a potential edge
+point only if
+
+ align:start position:0%
+point only if
+ 
+
+ align:start position:0%
+point only if
+this is true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because if
+
+ align:start position:0%
+right because if
+ 
+
+ align:start position:0%
+right because if
+g minus was bigger than g zero well then
+
+ align:start position:0%
+g minus was bigger than g zero well then
+ 
+
+ align:start position:0%
+g minus was bigger than g zero well then
+that's going to be the edge point
+
+ align:start position:0%
+that's going to be the edge point
+ 
+
+ align:start position:0%
+that's going to be the edge point
+and remember that the edge is running at
+
+ align:start position:0%
+and remember that the edge is running at
+ 
+
+ align:start position:0%
+and remember that the edge is running at
+right angles to this lot
+
+ align:start position:0%
+right angles to this lot
+ 
+
+ align:start position:0%
+right angles to this lot
+so the the actual underlying edge is is
+
+ align:start position:0%
+so the the actual underlying edge is is
+ 
+
+ align:start position:0%
+so the the actual underlying edge is is
+is like this
+
+ align:start position:0%
+is like this
+ 
+
+ align:start position:0%
+is like this
+and we're looking in the gradient
+
+ align:start position:0%
+and we're looking in the gradient
+ 
+
+ align:start position:0%
+and we're looking in the gradient
+direction and the gradient direction is
+
+ align:start position:0%
+direction and the gradient direction is
+ 
+
+ align:start position:0%
+direction and the gradient direction is
+of course perpendicular to the edge
+
+ align:start position:0%
+of course perpendicular to the edge
+ 
+
+ align:start position:0%
+of course perpendicular to the edge
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then we talked about how
+
+ align:start position:0%
+and then we talked about how
+ 
+
+ align:start position:0%
+and then we talked about how
+there's this asymmetry
+
+ align:start position:0%
+there's this asymmetry
+ 
+
+ align:start position:0%
+there's this asymmetry
+because occasionally we're going to find
+
+ align:start position:0%
+because occasionally we're going to find
+ 
+
+ align:start position:0%
+because occasionally we're going to find
+that g 0 is equal to g minus or g 0 is
+
+ align:start position:0%
+that g 0 is equal to g minus or g 0 is
+ 
+
+ align:start position:0%
+that g 0 is equal to g minus or g 0 is
+equal to g plus and we don't want to
+
+ align:start position:0%
+equal to g plus and we don't want to
+ 
+
+ align:start position:0%
+equal to g plus and we don't want to
+declare both of them to be edge points
+
+ align:start position:0%
+declare both of them to be edge points
+ 
+
+ align:start position:0%
+declare both of them to be edge points
+we want to have a tie breaker
+
+ align:start position:0%
+we want to have a tie breaker
+ 
+
+ align:start position:0%
+we want to have a tie breaker
+so that only one of them gets elected
+
+ align:start position:0%
+so that only one of them gets elected
+ 
+
+ align:start position:0%
+so that only one of them gets elected
+and which one is well it's arbitrary you
+
+ align:start position:0%
+and which one is well it's arbitrary you
+ 
+
+ align:start position:0%
+and which one is well it's arbitrary you
+can you know you could easily well have
+
+ align:start position:0%
+can you know you could easily well have
+ 
+
+ align:start position:0%
+can you know you could easily well have
+done that
+
+ align:start position:0%
+done that
+ 
+
+ align:start position:0%
+done that
+as long as there's a way of
+
+ align:start position:0%
+as long as there's a way of
+ 
+
+ align:start position:0%
+as long as there's a way of
+breaking that
+
+ align:start position:0%
+breaking that
+ 
+
+ align:start position:0%
+breaking that
+tie
+
+ align:start position:0%
+tie
+ 
+
+ align:start position:0%
+tie
+okay and then
+
+ align:start position:0%
+okay and then
+ 
+
+ align:start position:0%
+okay and then
+we said okay now we can plot
+
+ align:start position:0%
+we said okay now we can plot
+ 
+
+ align:start position:0%
+we said okay now we can plot
+the profile of this edge response along
+
+ align:start position:0%
+the profile of this edge response along
+ 
+
+ align:start position:0%
+the profile of this edge response along
+the gradient direction
+
+ align:start position:0%
+the gradient direction
+ 
+
+ align:start position:0%
+the gradient direction
+and we get
+
+ align:start position:0%
+and we get
+ 
+
+ align:start position:0%
+and we get
+a picture like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we can fit some curve to it for
+
+ align:start position:0%
+and then we can fit some curve to it for
+ 
+
+ align:start position:0%
+and then we can fit some curve to it for
+example we can fit a parabola to it
+
+ align:start position:0%
+example we can fit a parabola to it
+ 
+
+ align:start position:0%
+example we can fit a parabola to it
+and we find the peak of the parabola
+
+ align:start position:0%
+and we find the peak of the parabola
+ 
+
+ align:start position:0%
+and we find the peak of the parabola
+and that's our sub pixel edge position
+
+ align:start position:0%
+and that's our sub pixel edge position
+ 
+
+ align:start position:0%
+and that's our sub pixel edge position
+so so several points there one of them
+
+ align:start position:0%
+so so several points there one of them
+ 
+
+ align:start position:0%
+so so several points there one of them
+is you know why fit a parabola well
+
+ align:start position:0%
+is you know why fit a parabola well
+ 
+
+ align:start position:0%
+is you know why fit a parabola well
+that's arbitrary uh you know the the
+
+ align:start position:0%
+that's arbitrary uh you know the the
+ 
+
+ align:start position:0%
+that's arbitrary uh you know the the
+shape of that curve
+
+ align:start position:0%
+shape of that curve
+ 
+
+ align:start position:0%
+shape of that curve
+depends on the optics the image sensor
+
+ align:start position:0%
+depends on the optics the image sensor
+ 
+
+ align:start position:0%
+depends on the optics the image sensor
+the thing you're looking at
+
+ align:start position:0%
+the thing you're looking at
+ 
+
+ align:start position:0%
+the thing you're looking at
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+but we only get three samples of it so
+
+ align:start position:0%
+but we only get three samples of it so
+ 
+
+ align:start position:0%
+but we only get three samples of it so
+treating it as a smooth curve the lowest
+
+ align:start position:0%
+treating it as a smooth curve the lowest
+ 
+
+ align:start position:0%
+treating it as a smooth curve the lowest
+order polynomial that will work is
+
+ align:start position:0%
+order polynomial that will work is
+ 
+
+ align:start position:0%
+order polynomial that will work is
+second order so uh one option we have is
+
+ align:start position:0%
+second order so uh one option we have is
+ 
+
+ align:start position:0%
+second order so uh one option we have is
+to use that and not to say that that's
+
+ align:start position:0%
+to use that and not to say that that's
+ 
+
+ align:start position:0%
+to use that and not to say that that's
+the only option or the best one but it's
+
+ align:start position:0%
+the only option or the best one but it's
+ 
+
+ align:start position:0%
+the only option or the best one but it's
+you know pretty good guess
+
+ align:start position:0%
+you know pretty good guess
+ 
+
+ align:start position:0%
+you know pretty good guess
+uh next thing is that what what's s well
+
+ align:start position:0%
+uh next thing is that what what's s well
+ 
+
+ align:start position:0%
+uh next thing is that what what's s well
+s is the displacement from g0
+
+ align:start position:0%
+s is the displacement from g0
+ 
+
+ align:start position:0%
+s is the displacement from g0
+so in here
+
+ align:start position:0%
+so in here
+ 
+
+ align:start position:0%
+so in here
+s0 would be that point
+
+ align:start position:0%
+s0 would be that point
+ 
+
+ align:start position:0%
+s0 would be that point
+and then if s is say
+
+ align:start position:0%
+and then if s is say
+ 
+
+ align:start position:0%
+and then if s is say
+well if we get over here then s is a
+
+ align:start position:0%
+well if we get over here then s is a
+ 
+
+ align:start position:0%
+well if we get over here then s is a
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+no so if we get over here then s is a
+
+ align:start position:0%
+no so if we get over here then s is a
+ 
+
+ align:start position:0%
+no so if we get over here then s is a
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+right we're halfway to that point and
+
+ align:start position:0%
+right we're halfway to that point and
+ 
+
+ align:start position:0%
+right we're halfway to that point and
+obviously it doesn't make sense for s to
+
+ align:start position:0%
+obviously it doesn't make sense for s to
+ 
+
+ align:start position:0%
+obviously it doesn't make sense for s to
+be bigger than a half because then this
+
+ align:start position:0%
+be bigger than a half because then this
+ 
+
+ align:start position:0%
+be bigger than a half because then this
+would have been the maximum
+
+ align:start position:0%
+would have been the maximum
+ 
+
+ align:start position:0%
+would have been the maximum
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+and same in the other direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notice that s is not in units of pixels
+
+ align:start position:0%
+notice that s is not in units of pixels
+ 
+
+ align:start position:0%
+notice that s is not in units of pixels
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+in this diagonal case
+
+ align:start position:0%
+in this diagonal case
+ 
+
+ align:start position:0%
+in this diagonal case
+s equals 1 is that distance which is the
+
+ align:start position:0%
+s equals 1 is that distance which is the
+ 
+
+ align:start position:0%
+s equals 1 is that distance which is the
+square root of 2
+
+ align:start position:0%
+square root of 2
+ 
+
+ align:start position:0%
+square root of 2
+times the pixel spacing
+
+ align:start position:0%
+times the pixel spacing
+ 
+
+ align:start position:0%
+times the pixel spacing
+right whereas if we happen to get the
+
+ align:start position:0%
+right whereas if we happen to get the
+ 
+
+ align:start position:0%
+right whereas if we happen to get the
+quantized direction over here
+
+ align:start position:0%
+quantized direction over here
+ 
+
+ align:start position:0%
+quantized direction over here
+then s would be the pixel spacing
+
+ align:start position:0%
+then s would be the pixel spacing
+ 
+
+ align:start position:0%
+then s would be the pixel spacing
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that's something to keep in mind that it
+
+ align:start position:0%
+that's something to keep in mind that it
+ 
+
+ align:start position:0%
+that's something to keep in mind that it
+all depends on the actual gradient
+
+ align:start position:0%
+all depends on the actual gradient
+ 
+
+ align:start position:0%
+all depends on the actual gradient
+direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+avoid thresholds yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so now um
+
+ align:start position:0%
+and so now um
+ 
+
+ align:start position:0%
+and so now um
+we have uh a potential edge point
+
+ align:start position:0%
+we have uh a potential edge point
+ 
+
+ align:start position:0%
+we have uh a potential edge point
+uh and notice we're not doing any
+
+ align:start position:0%
+uh and notice we're not doing any
+ 
+
+ align:start position:0%
+uh and notice we're not doing any
+thresholding so
+
+ align:start position:0%
+thresholding so
+ 
+
+ align:start position:0%
+thresholding so
+we get we're gonna get these points all
+
+ align:start position:0%
+we get we're gonna get these points all
+ 
+
+ align:start position:0%
+we get we're gonna get these points all
+over the show not just on on the edge we
+
+ align:start position:0%
+over the show not just on on the edge we
+ 
+
+ align:start position:0%
+over the show not just on on the edge we
+haven't done any thresholding so here
+
+ align:start position:0%
+haven't done any thresholding so here
+ 
+
+ align:start position:0%
+haven't done any thresholding so here
+you know we we mark uh this place
+
+ align:start position:0%
+you know we we mark uh this place
+ 
+
+ align:start position:0%
+you know we we mark uh this place
+based on
+
+ align:start position:0%
+based on
+ 
+
+ align:start position:0%
+based on
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+square root of 2 s delta where delta is
+
+ align:start position:0%
+square root of 2 s delta where delta is
+ 
+
+ align:start position:0%
+square root of 2 s delta where delta is
+the pixel spacing so just to be precise
+
+ align:start position:0%
+the pixel spacing so just to be precise
+ 
+
+ align:start position:0%
+the pixel spacing so just to be precise
+so that's that's where we think the edge
+
+ align:start position:0%
+so that's that's where we think the edge
+ 
+
+ align:start position:0%
+so that's that's where we think the edge
+is so i've drawn the edge here but
+
+ align:start position:0%
+is so i've drawn the edge here but
+ 
+
+ align:start position:0%
+is so i've drawn the edge here but
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+now with sub pixel interpolation
+
+ align:start position:0%
+now with sub pixel interpolation
+ 
+
+ align:start position:0%
+now with sub pixel interpolation
+we find it's it's there
+
+ align:start position:0%
+we find it's it's there
+ 
+
+ align:start position:0%
+we find it's it's there
+so if we just were to go with the peak
+
+ align:start position:0%
+so if we just were to go with the peak
+ 
+
+ align:start position:0%
+so if we just were to go with the peak
+in that curve uh on a discrete grid then
+
+ align:start position:0%
+in that curve uh on a discrete grid then
+ 
+
+ align:start position:0%
+in that curve uh on a discrete grid then
+we'd find that the edge runs through
+
+ align:start position:0%
+we'd find that the edge runs through
+ 
+
+ align:start position:0%
+we'd find that the edge runs through
+that point but now we know it's it's
+
+ align:start position:0%
+that point but now we know it's it's
+ 
+
+ align:start position:0%
+that point but now we know it's it's
+over there
+
+ align:start position:0%
+over there
+ 
+
+ align:start position:0%
+over there
+okay but in order to get there we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will quantize the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we quantize the edge direction
+
+ align:start position:0%
+we quantize the edge direction
+ 
+
+ align:start position:0%
+we quantize the edge direction
+and so we can
+
+ align:start position:0%
+and so we can
+ 
+
+ align:start position:0%
+and so we can
+improve things slightly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so i suppose i should draw that
+
+ align:start position:0%
+right so i suppose i should draw that
+ 
+
+ align:start position:0%
+right so i suppose i should draw that
+again and make it less messy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's our quantized direction
+
+ align:start position:0%
+so here's our quantized direction
+ 
+
+ align:start position:0%
+so here's our quantized direction
+and here's some point we found that's uh
+
+ align:start position:0%
+and here's some point we found that's uh
+ 
+
+ align:start position:0%
+and here's some point we found that's uh
+an edge point
+
+ align:start position:0%
+an edge point
+ 
+
+ align:start position:0%
+an edge point
+and then suppose that the actual
+
+ align:start position:0%
+and then suppose that the actual
+ 
+
+ align:start position:0%
+and then suppose that the actual
+gradient direction
+
+ align:start position:0%
+gradient direction
+ 
+
+ align:start position:0%
+gradient direction
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+slightly different
+
+ align:start position:0%
+slightly different
+ 
+
+ align:start position:0%
+slightly different
+it can't be hugely different
+
+ align:start position:0%
+it can't be hugely different
+ 
+
+ align:start position:0%
+it can't be hugely different
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+then we would have picked a different
+
+ align:start position:0%
+then we would have picked a different
+ 
+
+ align:start position:0%
+then we would have picked a different
+compass direction
+
+ align:start position:0%
+compass direction
+ 
+
+ align:start position:0%
+compass direction
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that's the gradient direction so the h
+
+ align:start position:0%
+that's the gradient direction so the h
+ 
+
+ align:start position:0%
+that's the gradient direction so the h
+has to be perpendicular to it so i can
+
+ align:start position:0%
+has to be perpendicular to it so i can
+ 
+
+ align:start position:0%
+has to be perpendicular to it so i can
+draw a perpendicular to the green line
+
+ align:start position:0%
+draw a perpendicular to the green line
+ 
+
+ align:start position:0%
+draw a perpendicular to the green line
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+that passes through this point
+
+ align:start position:0%
+that passes through this point
+ 
+
+ align:start position:0%
+that passes through this point
+so the edge actually
+
+ align:start position:0%
+so the edge actually
+ 
+
+ align:start position:0%
+so the edge actually
+is like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+when i report a potential
+
+ align:start position:0%
+when i report a potential
+ 
+
+ align:start position:0%
+when i report a potential
+edge point i can report any point on on
+
+ align:start position:0%
+edge point i can report any point on on
+ 
+
+ align:start position:0%
+edge point i can report any point on on
+that line
+
+ align:start position:0%
+that line
+ 
+
+ align:start position:0%
+that line
+and which one do i pick well the
+
+ align:start position:0%
+and which one do i pick well the
+ 
+
+ align:start position:0%
+and which one do i pick well the
+simplest one is just to pick the one i
+
+ align:start position:0%
+simplest one is just to pick the one i
+ 
+
+ align:start position:0%
+simplest one is just to pick the one i
+calculated
+
+ align:start position:0%
+calculated
+ 
+
+ align:start position:0%
+calculated
+i can however slightly improve the
+
+ align:start position:0%
+i can however slightly improve the
+ 
+
+ align:start position:0%
+i can however slightly improve the
+result by uh instead picking this one
+
+ align:start position:0%
+result by uh instead picking this one
+ 
+
+ align:start position:0%
+result by uh instead picking this one
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+well it's closer to the origin it's
+
+ align:start position:0%
+well it's closer to the origin it's
+ 
+
+ align:start position:0%
+well it's closer to the origin it's
+closer to the actual peak
+
+ align:start position:0%
+closer to the actual peak
+ 
+
+ align:start position:0%
+closer to the actual peak
+and so it's
+
+ align:start position:0%
+and so it's
+ 
+
+ align:start position:0%
+and so it's
+less likely to be
+
+ align:start position:0%
+less likely to be
+ 
+
+ align:start position:0%
+less likely to be
+subject to noise
+
+ align:start position:0%
+subject to noise
+ 
+
+ align:start position:0%
+subject to noise
+it's not a huge improvement but you know
+
+ align:start position:0%
+it's not a huge improvement but you know
+ 
+
+ align:start position:0%
+it's not a huge improvement but you know
+they decided this was a worthwhile
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+additional step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it also actually aids in
+
+ align:start position:0%
+it also actually aids in
+ 
+
+ align:start position:0%
+it also actually aids in
+a step that we will be getting to in a
+
+ align:start position:0%
+a step that we will be getting to in a
+ 
+
+ align:start position:0%
+a step that we will be getting to in a
+second where we chain together the edges
+
+ align:start position:0%
+second where we chain together the edges
+ 
+
+ align:start position:0%
+second where we chain together the edges
+okay so that's the idea so we project
+
+ align:start position:0%
+okay so that's the idea so we project
+ 
+
+ align:start position:0%
+okay so that's the idea so we project
+we project from the quantized uh
+
+ align:start position:0%
+we project from the quantized uh
+ 
+
+ align:start position:0%
+we project from the quantized uh
+gradient direction down onto the actual
+
+ align:start position:0%
+gradient direction down onto the actual
+ 
+
+ align:start position:0%
+gradient direction down onto the actual
+gradient direction and
+
+ align:start position:0%
+gradient direction and
+ 
+
+ align:start position:0%
+gradient direction and
+that's the plane position step
+
+ align:start position:0%
+that's the plane position step
+ 
+
+ align:start position:0%
+that's the plane position step
+what next o so then
+
+ align:start position:0%
+what next o so then
+ 
+
+ align:start position:0%
+what next o so then
+we get to the bias compensation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we we said that we somewhat
+
+ align:start position:0%
+okay so we we said that we somewhat
+ 
+
+ align:start position:0%
+okay so we we said that we somewhat
+arbitrarily picked the parabola
+
+ align:start position:0%
+arbitrarily picked the parabola
+ 
+
+ align:start position:0%
+arbitrarily picked the parabola
+and then as you know in the patent
+
+ align:start position:0%
+and then as you know in the patent
+ 
+
+ align:start position:0%
+and then as you know in the patent
+there's a second method which uses
+
+ align:start position:0%
+there's a second method which uses
+ 
+
+ align:start position:0%
+there's a second method which uses
+a rooftop a triangular shape
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he uses that
+
+ align:start position:0%
+he uses that
+ 
+
+ align:start position:0%
+he uses that
+it fits that and finds the peak of that
+
+ align:start position:0%
+it fits that and finds the peak of that
+ 
+
+ align:start position:0%
+it fits that and finds the peak of that
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and that gives you another possible
+
+ align:start position:0%
+and that gives you another possible
+ 
+
+ align:start position:0%
+and that gives you another possible
+position for where the edge really is
+
+ align:start position:0%
+position for where the edge really is
+ 
+
+ align:start position:0%
+position for where the edge really is
+and we said that in certain
+
+ align:start position:0%
+and we said that in certain
+ 
+
+ align:start position:0%
+and we said that in certain
+circumstances one may be more accurate
+
+ align:start position:0%
+circumstances one may be more accurate
+ 
+
+ align:start position:0%
+circumstances one may be more accurate
+give you a more accurate answer than the
+
+ align:start position:0%
+give you a more accurate answer than the
+ 
+
+ align:start position:0%
+give you a more accurate answer than the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+but what you can imagine doing is
+
+ align:start position:0%
+but what you can imagine doing is
+ 
+
+ align:start position:0%
+but what you can imagine doing is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+you know experimentally
+
+ align:start position:0%
+you know experimentally
+ 
+
+ align:start position:0%
+you know experimentally
+moving the edge
+
+ align:start position:0%
+moving the edge
+ 
+
+ align:start position:0%
+moving the edge
+by very small increments
+
+ align:start position:0%
+by very small increments
+ 
+
+ align:start position:0%
+by very small increments
+tiny sub pixel increments and seeing
+
+ align:start position:0%
+tiny sub pixel increments and seeing
+ 
+
+ align:start position:0%
+tiny sub pixel increments and seeing
+what your method gives you and then
+
+ align:start position:0%
+what your method gives you and then
+ 
+
+ align:start position:0%
+what your method gives you and then
+plotting that
+
+ align:start position:0%
+plotting that
+ 
+
+ align:start position:0%
+plotting that
+against what it should have been right
+
+ align:start position:0%
+against what it should have been right
+ 
+
+ align:start position:0%
+against what it should have been right
+so this is an experiment where
+
+ align:start position:0%
+so this is an experiment where
+ 
+
+ align:start position:0%
+so this is an experiment where
+you have the camera looking at an edge
+
+ align:start position:0%
+you have the camera looking at an edge
+ 
+
+ align:start position:0%
+you have the camera looking at an edge
+and then you
+
+ align:start position:0%
+and then you
+ 
+
+ align:start position:0%
+and then you
+move the edge or the camera by some tiny
+
+ align:start position:0%
+move the edge or the camera by some tiny
+ 
+
+ align:start position:0%
+move the edge or the camera by some tiny
+amount
+
+ align:start position:0%
+amount
+ 
+
+ align:start position:0%
+amount
+in increments and and you measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now ideally
+
+ align:start position:0%
+now ideally
+ 
+
+ align:start position:0%
+now ideally
+you know your magic method for peak
+
+ align:start position:0%
+you know your magic method for peak
+ 
+
+ align:start position:0%
+you know your magic method for peak
+finding
+
+ align:start position:0%
+finding
+ 
+
+ align:start position:0%
+finding
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+always give you
+
+ align:start position:0%
+always give you
+ 
+
+ align:start position:0%
+always give you
+the correct peak value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it may not
+
+ align:start position:0%
+it may not
+ 
+
+ align:start position:0%
+it may not
+so ideally you get a 45 degree
+
+ align:start position:0%
+so ideally you get a 45 degree
+ 
+
+ align:start position:0%
+so ideally you get a 45 degree
+line and again we're only interested in
+
+ align:start position:0%
+line and again we're only interested in
+ 
+
+ align:start position:0%
+line and again we're only interested in
+the range from minus a half to plus a
+
+ align:start position:0%
+the range from minus a half to plus a
+ 
+
+ align:start position:0%
+the range from minus a half to plus a
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+and now all of these methods should give
+
+ align:start position:0%
+and now all of these methods should give
+ 
+
+ align:start position:0%
+and now all of these methods should give
+you the correct answer in three cases
+
+ align:start position:0%
+you the correct answer in three cases
+ 
+
+ align:start position:0%
+you the correct answer in three cases
+no matter what you do
+
+ align:start position:0%
+no matter what you do
+ 
+
+ align:start position:0%
+no matter what you do
+if you act if your peak is actually a g
+
+ align:start position:0%
+if you act if your peak is actually a g
+ 
+
+ align:start position:0%
+if you act if your peak is actually a g
+zero then it should return g zero that
+
+ align:start position:0%
+zero then it should return g zero that
+ 
+
+ align:start position:0%
+zero then it should return g zero that
+position s equals zero and similarly if
+
+ align:start position:0%
+position s equals zero and similarly if
+ 
+
+ align:start position:0%
+position s equals zero and similarly if
+you were halfway between pixels it
+
+ align:start position:0%
+you were halfway between pixels it
+ 
+
+ align:start position:0%
+you were halfway between pixels it
+should give you the and both of these
+
+ align:start position:0%
+should give you the and both of these
+ 
+
+ align:start position:0%
+should give you the and both of these
+methods do
+
+ align:start position:0%
+methods do
+ 
+
+ align:start position:0%
+methods do
+they satisfy that requirement but what
+
+ align:start position:0%
+they satisfy that requirement but what
+ 
+
+ align:start position:0%
+they satisfy that requirement but what
+happens in between well uh as i
+
+ align:start position:0%
+happens in between well uh as i
+ 
+
+ align:start position:0%
+happens in between well uh as i
+mentioned that depends on
+
+ align:start position:0%
+mentioned that depends on
+ 
+
+ align:start position:0%
+mentioned that depends on
+you know exactly what shape the edge has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and you might end up with you know
+
+ align:start position:0%
+so and you might end up with you know
+ 
+
+ align:start position:0%
+so and you might end up with you know
+something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or maybe something like that
+
+ align:start position:0%
+or maybe something like that
+ 
+
+ align:start position:0%
+or maybe something like that
+so typically the departures from the
+
+ align:start position:0%
+so typically the departures from the
+ 
+
+ align:start position:0%
+so typically the departures from the
+diagonal will be quite small and
+
+ align:start position:0%
+diagonal will be quite small and
+ 
+
+ align:start position:0%
+diagonal will be quite small and
+typically they'll be quite smooth
+
+ align:start position:0%
+typically they'll be quite smooth
+ 
+
+ align:start position:0%
+typically they'll be quite smooth
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+you know you could keep a lookup table
+
+ align:start position:0%
+you know you could keep a lookup table
+ 
+
+ align:start position:0%
+you know you could keep a lookup table
+of this or something to compensate for
+
+ align:start position:0%
+of this or something to compensate for
+ 
+
+ align:start position:0%
+of this or something to compensate for
+it but it's it's not really worthwhile
+
+ align:start position:0%
+it but it's it's not really worthwhile
+ 
+
+ align:start position:0%
+it but it's it's not really worthwhile
+it's it's a relatively small correction
+
+ align:start position:0%
+it's it's a relatively small correction
+ 
+
+ align:start position:0%
+it's it's a relatively small correction
+again but in going down to the the aim
+
+ align:start position:0%
+again but in going down to the the aim
+ 
+
+ align:start position:0%
+again but in going down to the the aim
+is uh 1 40th of a pixel
+
+ align:start position:0%
+is uh 1 40th of a pixel
+ 
+
+ align:start position:0%
+is uh 1 40th of a pixel
+accuracy
+
+ align:start position:0%
+accuracy
+ 
+
+ align:start position:0%
+accuracy
+so you know if you think about it that's
+
+ align:start position:0%
+so you know if you think about it that's
+ 
+
+ align:start position:0%
+so you know if you think about it that's
+that's quite amazing that you can do
+
+ align:start position:0%
+that's quite amazing that you can do
+ 
+
+ align:start position:0%
+that's quite amazing that you can do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one part of it
+
+ align:start position:0%
+and one part of it
+ 
+
+ align:start position:0%
+and one part of it
+one part of it is this plane position
+
+ align:start position:0%
+one part of it is this plane position
+ 
+
+ align:start position:0%
+one part of it is this plane position
+correction and one part of it is this
+
+ align:start position:0%
+correction and one part of it is this
+ 
+
+ align:start position:0%
+correction and one part of it is this
+and so what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is done
+
+ align:start position:0%
+what is done
+ 
+
+ align:start position:0%
+what is done
+is to
+
+ align:start position:0%
+is to
+ 
+
+ align:start position:0%
+is to
+approximate whatever that shape is
+
+ align:start position:0%
+approximate whatever that shape is
+ 
+
+ align:start position:0%
+approximate whatever that shape is
+with this function
+
+ align:start position:0%
+with this function
+ 
+
+ align:start position:0%
+with this function
+and so for example
+
+ align:start position:0%
+and so for example
+ 
+
+ align:start position:0%
+and so for example
+for b equals 0
+
+ align:start position:0%
+for b equals 0
+ 
+
+ align:start position:0%
+for b equals 0
+we get s prime equals s so that's just
+
+ align:start position:0%
+we get s prime equals s so that's just
+ 
+
+ align:start position:0%
+we get s prime equals s so that's just
+the diagonal line that's the ideal case
+
+ align:start position:0%
+the diagonal line that's the ideal case
+ 
+
+ align:start position:0%
+the diagonal line that's the ideal case
+for b greater than 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then that means that s prime
+
+ align:start position:0%
+then that means that s prime
+ 
+
+ align:start position:0%
+then that means that s prime
+is uh s raised to a power greater than
+
+ align:start position:0%
+is uh s raised to a power greater than
+ 
+
+ align:start position:0%
+is uh s raised to a power greater than
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and so that means it's going to bow uh
+
+ align:start position:0%
+and so that means it's going to bow uh
+ 
+
+ align:start position:0%
+and so that means it's going to bow uh
+this way
+
+ align:start position:0%
+this way
+ 
+
+ align:start position:0%
+this way
+as as the red curve does
+
+ align:start position:0%
+as as the red curve does
+ 
+
+ align:start position:0%
+as as the red curve does
+and if b is less than zero that means
+
+ align:start position:0%
+and if b is less than zero that means
+ 
+
+ align:start position:0%
+and if b is less than zero that means
+that s prime is s raised to a power
+
+ align:start position:0%
+that s prime is s raised to a power
+ 
+
+ align:start position:0%
+that s prime is s raised to a power
+that's slightly less than one so that's
+
+ align:start position:0%
+that's slightly less than one so that's
+ 
+
+ align:start position:0%
+that's slightly less than one so that's
+like approximating square root so that's
+
+ align:start position:0%
+like approximating square root so that's
+ 
+
+ align:start position:0%
+like approximating square root so that's
+this uh bowed upper upper curve
+
+ align:start position:0%
+this uh bowed upper upper curve
+ 
+
+ align:start position:0%
+this uh bowed upper upper curve
+which i'll show in green
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+green
+
+ align:start position:0%
+green
+ 
+
+ align:start position:0%
+green
+and the other one is red
+
+ align:start position:0%
+and the other one is red
+ 
+
+ align:start position:0%
+and the other one is red
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the point the point is that
+
+ align:start position:0%
+what's the point the point is that
+ 
+
+ align:start position:0%
+what's the point the point is that
+this is a small correction
+
+ align:start position:0%
+this is a small correction
+ 
+
+ align:start position:0%
+this is a small correction
+so it doesn't really pay to try and be
+
+ align:start position:0%
+so it doesn't really pay to try and be
+ 
+
+ align:start position:0%
+so it doesn't really pay to try and be
+too fussy but you want to do it and this
+
+ align:start position:0%
+too fussy but you want to do it and this
+ 
+
+ align:start position:0%
+too fussy but you want to do it and this
+is a one parameter fit
+
+ align:start position:0%
+is a one parameter fit
+ 
+
+ align:start position:0%
+is a one parameter fit
+to the type of curve that what's the b
+
+ align:start position:0%
+to the type of curve that what's the b
+ 
+
+ align:start position:0%
+to the type of curve that what's the b
+is the one parameter
+
+ align:start position:0%
+is the one parameter
+ 
+
+ align:start position:0%
+is the one parameter
+and so uh
+
+ align:start position:0%
+and so uh
+ 
+
+ align:start position:0%
+and so uh
+you could calibrate it
+
+ align:start position:0%
+you could calibrate it
+ 
+
+ align:start position:0%
+you could calibrate it
+based on
+
+ align:start position:0%
+based on
+ 
+
+ align:start position:0%
+based on
+this method
+
+ align:start position:0%
+this method
+ 
+
+ align:start position:0%
+this method
+you know get one value of b you could
+
+ align:start position:0%
+you know get one value of b you could
+ 
+
+ align:start position:0%
+you know get one value of b you could
+calibrate it based on this method get a
+
+ align:start position:0%
+calibrate it based on this method get a
+ 
+
+ align:start position:0%
+calibrate it based on this method get a
+different value of b then
+
+ align:start position:0%
+different value of b then
+ 
+
+ align:start position:0%
+different value of b then
+you notice that if we are happen to be
+
+ align:start position:0%
+you notice that if we are happen to be
+ 
+
+ align:start position:0%
+you notice that if we are happen to be
+working east-west
+
+ align:start position:0%
+working east-west
+ 
+
+ align:start position:0%
+working east-west
+the spacing between pixels is much less
+
+ align:start position:0%
+the spacing between pixels is much less
+ 
+
+ align:start position:0%
+the spacing between pixels is much less
+than if we're working
+
+ align:start position:0%
+than if we're working
+ 
+
+ align:start position:0%
+than if we're working
+northeast
+
+ align:start position:0%
+northeast
+ 
+
+ align:start position:0%
+northeast
+and so it turns out you want a different
+
+ align:start position:0%
+and so it turns out you want a different
+ 
+
+ align:start position:0%
+and so it turns out you want a different
+value of b
+
+ align:start position:0%
+value of b
+ 
+
+ align:start position:0%
+value of b
+for for this case than you do for that
+
+ align:start position:0%
+for for this case than you do for that
+ 
+
+ align:start position:0%
+for for this case than you do for that
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+fortunately the only two cases you know
+
+ align:start position:0%
+fortunately the only two cases you know
+ 
+
+ align:start position:0%
+fortunately the only two cases you know
+they're the ones that are east west
+
+ align:start position:0%
+they're the ones that are east west
+ 
+
+ align:start position:0%
+they're the ones that are east west
+north south and then the ones in between
+
+ align:start position:0%
+north south and then the ones in between
+ 
+
+ align:start position:0%
+north south and then the ones in between
+but you you can use a different value of
+
+ align:start position:0%
+but you you can use a different value of
+ 
+
+ align:start position:0%
+but you you can use a different value of
+b for those two
+
+ align:start position:0%
+b for those two
+ 
+
+ align:start position:0%
+b for those two
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and you know again you could do
+
+ align:start position:0%
+and you know again you could do
+ 
+
+ align:start position:0%
+and you know again you could do
+something more elaborate but
+
+ align:start position:0%
+something more elaborate but
+ 
+
+ align:start position:0%
+something more elaborate but
+since it's a small correction it's only
+
+ align:start position:0%
+since it's a small correction it's only
+ 
+
+ align:start position:0%
+since it's a small correction it's only
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+affect
+
+ align:start position:0%
+affect
+ 
+
+ align:start position:0%
+affect
+a small fraction of a pixel also
+
+ align:start position:0%
+a small fraction of a pixel also
+ 
+
+ align:start position:0%
+a small fraction of a pixel also
+um you don't want to be too clever here
+
+ align:start position:0%
+um you don't want to be too clever here
+ 
+
+ align:start position:0%
+um you don't want to be too clever here
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+this curve is going to change a little
+
+ align:start position:0%
+this curve is going to change a little
+ 
+
+ align:start position:0%
+this curve is going to change a little
+bit with circumstances you know if if
+
+ align:start position:0%
+bit with circumstances you know if if
+ 
+
+ align:start position:0%
+bit with circumstances you know if if
+your camera is slightly out of focus
+
+ align:start position:0%
+your camera is slightly out of focus
+ 
+
+ align:start position:0%
+your camera is slightly out of focus
+you'll get a slightly different result
+
+ align:start position:0%
+you'll get a slightly different result
+ 
+
+ align:start position:0%
+you'll get a slightly different result
+if the corners of the cardboard box
+
+ align:start position:0%
+if the corners of the cardboard box
+ 
+
+ align:start position:0%
+if the corners of the cardboard box
+you're looking at are somewhat
+
+ align:start position:0%
+you're looking at are somewhat
+ 
+
+ align:start position:0%
+you're looking at are somewhat
+damaged then you'll get a different edge
+
+ align:start position:0%
+damaged then you'll get a different edge
+ 
+
+ align:start position:0%
+damaged then you'll get a different edge
+response and so on so you don't want to
+
+ align:start position:0%
+response and so on so you don't want to
+ 
+
+ align:start position:0%
+response and so on so you don't want to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+too overly clever
+
+ align:start position:0%
+too overly clever
+ 
+
+ align:start position:0%
+too overly clever
+okay now a lot of this depends on the
+
+ align:start position:0%
+okay now a lot of this depends on the
+ 
+
+ align:start position:0%
+okay now a lot of this depends on the
+actual edge transition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know we we drew one just
+
+ align:start position:0%
+and you know we we drew one just
+ 
+
+ align:start position:0%
+and you know we we drew one just
+by hand and uh
+
+ align:start position:0%
+by hand and uh
+ 
+
+ align:start position:0%
+by hand and uh
+then uh
+
+ align:start position:0%
+then uh
+ 
+
+ align:start position:0%
+then uh
+came up with these methods for finding
+
+ align:start position:0%
+came up with these methods for finding
+ 
+
+ align:start position:0%
+came up with these methods for finding
+out where the edge actually is but uh
+
+ align:start position:0%
+out where the edge actually is but uh
+ 
+
+ align:start position:0%
+out where the edge actually is but uh
+realistically what you know what's
+
+ align:start position:0%
+realistically what you know what's
+ 
+
+ align:start position:0%
+realistically what you know what's
+causing these edges to be fuzzy
+
+ align:start position:0%
+causing these edges to be fuzzy
+ 
+
+ align:start position:0%
+causing these edges to be fuzzy
+and we already said that it's a good
+
+ align:start position:0%
+and we already said that it's a good
+ 
+
+ align:start position:0%
+and we already said that it's a good
+thing they are fuzzy otherwise we
+
+ align:start position:0%
+thing they are fuzzy otherwise we
+ 
+
+ align:start position:0%
+thing they are fuzzy otherwise we
+wouldn't be able to um do the sub-pixel
+
+ align:start position:0%
+wouldn't be able to um do the sub-pixel
+ 
+
+ align:start position:0%
+wouldn't be able to um do the sub-pixel
+recovery
+
+ align:start position:0%
+recovery
+ 
+
+ align:start position:0%
+recovery
+we'd be suffering from uh huge aliasing
+
+ align:start position:0%
+we'd be suffering from uh huge aliasing
+ 
+
+ align:start position:0%
+we'd be suffering from uh huge aliasing
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+so it's it's a good thing they're fussy
+
+ align:start position:0%
+so it's it's a good thing they're fussy
+ 
+
+ align:start position:0%
+so it's it's a good thing they're fussy
+but you know why are they fuzzy well one
+
+ align:start position:0%
+but you know why are they fuzzy well one
+ 
+
+ align:start position:0%
+but you know why are they fuzzy well one
+reason is the defocus
+
+ align:start position:0%
+reason is the defocus
+ 
+
+ align:start position:0%
+reason is the defocus
+so let's just look at that uh as a
+
+ align:start position:0%
+so let's just look at that uh as a
+ 
+
+ align:start position:0%
+so let's just look at that uh as a
+special case that's of interest for
+
+ align:start position:0%
+special case that's of interest for
+ 
+
+ align:start position:0%
+special case that's of interest for
+other reasons so here's our lens
+
+ align:start position:0%
+other reasons so here's our lens
+ 
+
+ align:start position:0%
+other reasons so here's our lens
+and you know the objects up there
+
+ align:start position:0%
+and you know the objects up there
+ 
+
+ align:start position:0%
+and you know the objects up there
+and it's suppose that
+
+ align:start position:0%
+and it's suppose that
+ 
+
+ align:start position:0%
+and it's suppose that
+it's it's a point
+
+ align:start position:0%
+it's it's a point
+ 
+
+ align:start position:0%
+it's it's a point
+light source
+
+ align:start position:0%
+light source
+ 
+
+ align:start position:0%
+light source
+and this is the in focus plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+that distant light source
+
+ align:start position:0%
+that distant light source
+ 
+
+ align:start position:0%
+that distant light source
+star maybe is image as a point
+
+ align:start position:0%
+star maybe is image as a point
+ 
+
+ align:start position:0%
+star maybe is image as a point
+but our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+camera
+
+ align:start position:0%
+camera
+ 
+
+ align:start position:0%
+camera
+has the
+
+ align:start position:0%
+has the
+ 
+
+ align:start position:0%
+has the
+image plane slightly
+
+ align:start position:0%
+image plane slightly
+ 
+
+ align:start position:0%
+image plane slightly
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+and so the picture will be slightly out
+
+ align:start position:0%
+and so the picture will be slightly out
+ 
+
+ align:start position:0%
+and so the picture will be slightly out
+of focus
+
+ align:start position:0%
+of focus
+ 
+
+ align:start position:0%
+of focus
+so what did i call this
+
+ align:start position:0%
+so what did i call this
+ 
+
+ align:start position:0%
+so what did i call this
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+and i guess i call this delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+when i look at the image of that star
+
+ align:start position:0%
+when i look at the image of that star
+ 
+
+ align:start position:0%
+when i look at the image of that star
+it's no longer a impulse a point
+
+ align:start position:0%
+it's no longer a impulse a point
+ 
+
+ align:start position:0%
+it's no longer a impulse a point
+it's a circle
+
+ align:start position:0%
+it's a circle
+ 
+
+ align:start position:0%
+it's a circle
+so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniform uniform brightness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if i want to plot it as a function
+
+ align:start position:0%
+and if i want to plot it as a function
+ 
+
+ align:start position:0%
+and if i want to plot it as a function
+of x and y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it would look like this and
+
+ align:start position:0%
+it would look like this and
+ 
+
+ align:start position:0%
+it would look like this and
+i don't know i call this a pill box
+
+ align:start position:0%
+i don't know i call this a pill box
+ 
+
+ align:start position:0%
+i don't know i call this a pill box
+i guess people don't have pill boxes
+
+ align:start position:0%
+i guess people don't have pill boxes
+ 
+
+ align:start position:0%
+i guess people don't have pill boxes
+anymore but it's a cylinder of constant
+
+ align:start position:0%
+anymore but it's a cylinder of constant
+ 
+
+ align:start position:0%
+anymore but it's a cylinder of constant
+height
+
+ align:start position:0%
+height
+ 
+
+ align:start position:0%
+height
+and if i want to describe it
+
+ align:start position:0%
+and if i want to describe it
+ 
+
+ align:start position:0%
+and if i want to describe it
+mathematically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's that
+
+ align:start position:0%
+so what's that
+ 
+
+ align:start position:0%
+so what's that
+big r is the radius of of the little
+
+ align:start position:0%
+big r is the radius of of the little
+ 
+
+ align:start position:0%
+big r is the radius of of the little
+pill box
+
+ align:start position:0%
+pill box
+ 
+
+ align:start position:0%
+pill box
+and i divide by 1 over pi r squared
+
+ align:start position:0%
+and i divide by 1 over pi r squared
+ 
+
+ align:start position:0%
+and i divide by 1 over pi r squared
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+the same energy is being deposited into
+
+ align:start position:0%
+the same energy is being deposited into
+ 
+
+ align:start position:0%
+the same energy is being deposited into
+that area no matter how out of focus i
+
+ align:start position:0%
+that area no matter how out of focus i
+ 
+
+ align:start position:0%
+that area no matter how out of focus i
+am
+
+ align:start position:0%
+am
+ 
+
+ align:start position:0%
+am
+so if i'm in focus it's all that
+
+ align:start position:0%
+so if i'm in focus it's all that
+ 
+
+ align:start position:0%
+so if i'm in focus it's all that
+concentrated at one point if i'm out of
+
+ align:start position:0%
+concentrated at one point if i'm out of
+ 
+
+ align:start position:0%
+concentrated at one point if i'm out of
+focus that same amount of light is
+
+ align:start position:0%
+focus that same amount of light is
+ 
+
+ align:start position:0%
+focus that same amount of light is
+spread into a larger and larger
+
+ align:start position:0%
+spread into a larger and larger
+ 
+
+ align:start position:0%
+spread into a larger and larger
+circle
+
+ align:start position:0%
+circle
+ 
+
+ align:start position:0%
+circle
+and so i compensate for that by dividing
+
+ align:start position:0%
+and so i compensate for that by dividing
+ 
+
+ align:start position:0%
+and so i compensate for that by dividing
+by the pi the area of the circle
+
+ align:start position:0%
+by the pi the area of the circle
+ 
+
+ align:start position:0%
+by the pi the area of the circle
+and then what's this so this is the unit
+
+ align:start position:0%
+and then what's this so this is the unit
+ 
+
+ align:start position:0%
+and then what's this so this is the unit
+step function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so for r
+
+ align:start position:0%
+so for r
+ 
+
+ align:start position:0%
+so for r
+equal to zero
+
+ align:start position:0%
+equal to zero
+ 
+
+ align:start position:0%
+equal to zero
+this will be u of sum minus quantity so
+
+ align:start position:0%
+this will be u of sum minus quantity so
+ 
+
+ align:start position:0%
+this will be u of sum minus quantity so
+that will be zero so i get one minus
+
+ align:start position:0%
+that will be zero so i get one minus
+ 
+
+ align:start position:0%
+that will be zero so i get one minus
+zero and so
+
+ align:start position:0%
+zero and so
+ 
+
+ align:start position:0%
+zero and so
+this will just be one and then when i
+
+ align:start position:0%
+this will just be one and then when i
+ 
+
+ align:start position:0%
+this will just be one and then when i
+get out to the radius if i go past the
+
+ align:start position:0%
+get out to the radius if i go past the
+ 
+
+ align:start position:0%
+get out to the radius if i go past the
+radius if little r is bigger than big r
+
+ align:start position:0%
+radius if little r is bigger than big r
+ 
+
+ align:start position:0%
+radius if little r is bigger than big r
+this will be equal the step function is
+
+ align:start position:0%
+this will be equal the step function is
+ 
+
+ align:start position:0%
+this will be equal the step function is
+one right because this will be greater
+
+ align:start position:0%
+one right because this will be greater
+ 
+
+ align:start position:0%
+one right because this will be greater
+than zero
+
+ align:start position:0%
+than zero
+ 
+
+ align:start position:0%
+than zero
+and so i get one minus one is zero so
+
+ align:start position:0%
+and so i get one minus one is zero so
+ 
+
+ align:start position:0%
+and so i get one minus one is zero so
+it's it's just a fancy way of
+
+ align:start position:0%
+it's it's just a fancy way of
+ 
+
+ align:start position:0%
+it's it's just a fancy way of
+saying the same thing as that diagram
+
+ align:start position:0%
+saying the same thing as that diagram
+ 
+
+ align:start position:0%
+saying the same thing as that diagram
+uh the other thing i need is you know
+
+ align:start position:0%
+uh the other thing i need is you know
+ 
+
+ align:start position:0%
+uh the other thing i need is you know
+what is r what is big r how big is it
+
+ align:start position:0%
+what is r what is big r how big is it
+ 
+
+ align:start position:0%
+what is r what is big r how big is it
+well it's obviously going to depend on
+
+ align:start position:0%
+well it's obviously going to depend on
+ 
+
+ align:start position:0%
+well it's obviously going to depend on
+how far out of focus i am so it's going
+
+ align:start position:0%
+how far out of focus i am so it's going
+ 
+
+ align:start position:0%
+how far out of focus i am so it's going
+to depend on delta
+
+ align:start position:0%
+to depend on delta
+ 
+
+ align:start position:0%
+to depend on delta
+and it's going to depend on the size of
+
+ align:start position:0%
+and it's going to depend on the size of
+ 
+
+ align:start position:0%
+and it's going to depend on the size of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lens
+
+ align:start position:0%
+lens
+ 
+
+ align:start position:0%
+lens
+something like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this is just similar triangles
+
+ align:start position:0%
+right this is just similar triangles
+ 
+
+ align:start position:0%
+right this is just similar triangles
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+oh a f uh which is this distance here
+
+ align:start position:0%
+oh a f uh which is this distance here
+ 
+
+ align:start position:0%
+oh a f uh which is this distance here
+from the lens to the uh image in focus
+
+ align:start position:0%
+from the lens to the uh image in focus
+ 
+
+ align:start position:0%
+from the lens to the uh image in focus
+image plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so obviously as i go more out of
+
+ align:start position:0%
+okay so obviously as i go more out of
+ 
+
+ align:start position:0%
+okay so obviously as i go more out of
+focus as i move the image plane
+
+ align:start position:0%
+focus as i move the image plane
+ 
+
+ align:start position:0%
+focus as i move the image plane
+further up this radius gets bigger
+
+ align:start position:0%
+further up this radius gets bigger
+ 
+
+ align:start position:0%
+further up this radius gets bigger
+and the brightness gets less because i'm
+
+ align:start position:0%
+and the brightness gets less because i'm
+ 
+
+ align:start position:0%
+and the brightness gets less because i'm
+now putting the same energy into into a
+
+ align:start position:0%
+now putting the same energy into into a
+ 
+
+ align:start position:0%
+now putting the same energy into into a
+larger area
+
+ align:start position:0%
+larger area
+ 
+
+ align:start position:0%
+larger area
+and so this is uh called the point
+
+ align:start position:0%
+and so this is uh called the point
+ 
+
+ align:start position:0%
+and so this is uh called the point
+spread function
+
+ align:start position:0%
+spread function
+ 
+
+ align:start position:0%
+spread function
+psf point spread function for this
+
+ align:start position:0%
+psf point spread function for this
+ 
+
+ align:start position:0%
+psf point spread function for this
+system when it's out of focus
+
+ align:start position:0%
+system when it's out of focus
+ 
+
+ align:start position:0%
+system when it's out of focus
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+this is used a lot
+
+ align:start position:0%
+this is used a lot
+ 
+
+ align:start position:0%
+this is used a lot
+in understanding
+
+ align:start position:0%
+in understanding
+ 
+
+ align:start position:0%
+in understanding
+the effect of being out of focus you
+
+ align:start position:0%
+the effect of being out of focus you
+ 
+
+ align:start position:0%
+the effect of being out of focus you
+know we think of it as blurring and of
+
+ align:start position:0%
+know we think of it as blurring and of
+ 
+
+ align:start position:0%
+know we think of it as blurring and of
+course we can think of it in terms of
+
+ align:start position:0%
+course we can think of it in terms of
+ 
+
+ align:start position:0%
+course we can think of it in terms of
+the fourier transform in terms of
+
+ align:start position:0%
+the fourier transform in terms of
+ 
+
+ align:start position:0%
+the fourier transform in terms of
+removing some or suppressing higher
+
+ align:start position:0%
+removing some or suppressing higher
+ 
+
+ align:start position:0%
+removing some or suppressing higher
+frequency content
+
+ align:start position:0%
+frequency content
+ 
+
+ align:start position:0%
+frequency content
+and it's the higher frequency content
+
+ align:start position:0%
+and it's the higher frequency content
+ 
+
+ align:start position:0%
+and it's the higher frequency content
+that makes things look
+
+ align:start position:0%
+that makes things look
+ 
+
+ align:start position:0%
+that makes things look
+sharp
+
+ align:start position:0%
+sharp
+ 
+
+ align:start position:0%
+sharp
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in our case blurs the edge so let's see
+
+ align:start position:0%
+in our case blurs the edge so let's see
+ 
+
+ align:start position:0%
+in our case blurs the edge so let's see
+what the effect is on on the edge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well basically
+
+ align:start position:0%
+well basically
+ 
+
+ align:start position:0%
+well basically
+we're going to
+
+ align:start position:0%
+we're going to
+ 
+
+ align:start position:0%
+we're going to
+have a response which we can calculate
+
+ align:start position:0%
+have a response which we can calculate
+ 
+
+ align:start position:0%
+have a response which we can calculate
+geometrically by superimposing the edge
+
+ align:start position:0%
+geometrically by superimposing the edge
+ 
+
+ align:start position:0%
+geometrically by superimposing the edge
+and the circle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's take a simplest case where
+
+ align:start position:0%
+so let's take a simplest case where
+ 
+
+ align:start position:0%
+so let's take a simplest case where
+you know there's black on one side of
+
+ align:start position:0%
+you know there's black on one side of
+ 
+
+ align:start position:0%
+you know there's black on one side of
+the edge and white on the other
+
+ align:start position:0%
+the edge and white on the other
+ 
+
+ align:start position:0%
+the edge and white on the other
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+we have a radio a circle of a certain
+
+ align:start position:0%
+we have a radio a circle of a certain
+ 
+
+ align:start position:0%
+we have a radio a circle of a certain
+radius
+
+ align:start position:0%
+radius
+ 
+
+ align:start position:0%
+radius
+and what are we looking at well we're
+
+ align:start position:0%
+and what are we looking at well we're
+ 
+
+ align:start position:0%
+and what are we looking at well we're
+looking at this overlap you know that's
+
+ align:start position:0%
+looking at this overlap you know that's
+ 
+
+ align:start position:0%
+looking at this overlap you know that's
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+be what controls how bright
+
+ align:start position:0%
+be what controls how bright
+ 
+
+ align:start position:0%
+be what controls how bright
+things appear
+
+ align:start position:0%
+things appear
+ 
+
+ align:start position:0%
+things appear
+and then we're going to move this thing
+
+ align:start position:0%
+and then we're going to move this thing
+ 
+
+ align:start position:0%
+and then we're going to move this thing
+across the edge to see how the response
+
+ align:start position:0%
+across the edge to see how the response
+ 
+
+ align:start position:0%
+across the edge to see how the response
+varies so we take this disc and we slide
+
+ align:start position:0%
+varies so we take this disc and we slide
+ 
+
+ align:start position:0%
+varies so we take this disc and we slide
+it across and obviously until it touches
+
+ align:start position:0%
+it across and obviously until it touches
+ 
+
+ align:start position:0%
+it across and obviously until it touches
+nothing happens there's no output
+
+ align:start position:0%
+nothing happens there's no output
+ 
+
+ align:start position:0%
+nothing happens there's no output
+and also obviously once we get over here
+
+ align:start position:0%
+and also obviously once we get over here
+ 
+
+ align:start position:0%
+and also obviously once we get over here
+the output is constant it's one
+
+ align:start position:0%
+the output is constant it's one
+ 
+
+ align:start position:0%
+the output is constant it's one
+nothing more changes so there's a
+
+ align:start position:0%
+nothing more changes so there's a
+ 
+
+ align:start position:0%
+nothing more changes so there's a
+transition
+
+ align:start position:0%
+transition
+ 
+
+ align:start position:0%
+transition
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+x being
+
+ align:start position:0%
+x being
+ 
+
+ align:start position:0%
+x being
+minus r and x being plus r where there's
+
+ align:start position:0%
+minus r and x being plus r where there's
+ 
+
+ align:start position:0%
+minus r and x being plus r where there's
+some sort of change between zero and one
+
+ align:start position:0%
+some sort of change between zero and one
+ 
+
+ align:start position:0%
+some sort of change between zero and one
+and and that's what we're trying to
+
+ align:start position:0%
+and and that's what we're trying to
+ 
+
+ align:start position:0%
+and and that's what we're trying to
+calculate
+
+ align:start position:0%
+calculate
+ 
+
+ align:start position:0%
+calculate
+well unfortunately uh it's not
+
+ align:start position:0%
+well unfortunately uh it's not
+ 
+
+ align:start position:0%
+well unfortunately uh it's not
+quite that
+
+ align:start position:0%
+quite that
+ 
+
+ align:start position:0%
+quite that
+simple so
+
+ align:start position:0%
+simple so
+ 
+
+ align:start position:0%
+simple so
+we could just write the answer out by
+
+ align:start position:0%
+we could just write the answer out by
+ 
+
+ align:start position:0%
+we could just write the answer out by
+inspection but we can't get it this way
+
+ align:start position:0%
+inspection but we can't get it this way
+ 
+
+ align:start position:0%
+inspection but we can't get it this way
+okay you know
+
+ align:start position:0%
+okay you know
+ 
+
+ align:start position:0%
+okay you know
+there's probably a formula for a sector
+
+ align:start position:0%
+there's probably a formula for a sector
+ 
+
+ align:start position:0%
+there's probably a formula for a sector
+of a circle like that but i don't know
+
+ align:start position:0%
+of a circle like that but i don't know
+ 
+
+ align:start position:0%
+of a circle like that but i don't know
+what it is so
+
+ align:start position:0%
+what it is so
+ 
+
+ align:start position:0%
+what it is so
+let's do it uh using things we do know
+
+ align:start position:0%
+let's do it uh using things we do know
+ 
+
+ align:start position:0%
+let's do it uh using things we do know
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+a couple of things we know we know how
+
+ align:start position:0%
+a couple of things we know we know how
+ 
+
+ align:start position:0%
+a couple of things we know we know how
+to compute the area of a triangle well
+
+ align:start position:0%
+to compute the area of a triangle well
+ 
+
+ align:start position:0%
+to compute the area of a triangle well
+probably know several ways of computing
+
+ align:start position:0%
+probably know several ways of computing
+ 
+
+ align:start position:0%
+probably know several ways of computing
+the area of a triangle
+
+ align:start position:0%
+the area of a triangle
+ 
+
+ align:start position:0%
+the area of a triangle
+and we also know how to compute the area
+
+ align:start position:0%
+and we also know how to compute the area
+ 
+
+ align:start position:0%
+and we also know how to compute the area
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+sector of a circle so
+
+ align:start position:0%
+sector of a circle so
+ 
+
+ align:start position:0%
+sector of a circle so
+let me draw
+
+ align:start position:0%
+let me draw
+ 
+
+ align:start position:0%
+let me draw
+that here
+
+ align:start position:0%
+that here
+ 
+
+ align:start position:0%
+that here
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+that's the sector of the circle that's
+
+ align:start position:0%
+that's the sector of the circle that's
+ 
+
+ align:start position:0%
+that's the sector of the circle that's
+the triangle i'm looking at
+
+ align:start position:0%
+the triangle i'm looking at
+ 
+
+ align:start position:0%
+the triangle i'm looking at
+and it's obvious that the quantity i
+
+ align:start position:0%
+and it's obvious that the quantity i
+ 
+
+ align:start position:0%
+and it's obvious that the quantity i
+want is the difference
+
+ align:start position:0%
+want is the difference
+ 
+
+ align:start position:0%
+want is the difference
+right it's what's left over when i
+
+ align:start position:0%
+right it's what's left over when i
+ 
+
+ align:start position:0%
+right it's what's left over when i
+subtract that triangle from
+
+ align:start position:0%
+subtract that triangle from
+ 
+
+ align:start position:0%
+subtract that triangle from
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+area
+
+ align:start position:0%
+area
+ 
+
+ align:start position:0%
+area
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm going to call this angle theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+this bran this thing here is obviously r
+
+ align:start position:0%
+this bran this thing here is obviously r
+ 
+
+ align:start position:0%
+this bran this thing here is obviously r
+squared minus x squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so x is the position
+
+ align:start position:0%
+so x is the position
+ 
+
+ align:start position:0%
+so x is the position
+x0 means that you're right on top of the
+
+ align:start position:0%
+x0 means that you're right on top of the
+ 
+
+ align:start position:0%
+x0 means that you're right on top of the
+edge that the circle is bisected by the
+
+ align:start position:0%
+edge that the circle is bisected by the
+ 
+
+ align:start position:0%
+edge that the circle is bisected by the
+edge and then x can get as large as plus
+
+ align:start position:0%
+edge and then x can get as large as plus
+ 
+
+ align:start position:0%
+edge and then x can get as large as plus
+r before it saturates or minus r before
+
+ align:start position:0%
+r before it saturates or minus r before
+ 
+
+ align:start position:0%
+r before it saturates or minus r before
+it saturates
+
+ align:start position:0%
+it saturates
+ 
+
+ align:start position:0%
+it saturates
+okay so the area of the
+
+ align:start position:0%
+okay so the area of the
+ 
+
+ align:start position:0%
+okay so the area of the
+sector is 2 r squared theta
+
+ align:start position:0%
+sector is 2 r squared theta
+ 
+
+ align:start position:0%
+sector is 2 r squared theta
+write this this sector here
+
+ align:start position:0%
+write this this sector here
+ 
+
+ align:start position:0%
+write this this sector here
+and we can check you know when theta is
+
+ align:start position:0%
+and we can check you know when theta is
+ 
+
+ align:start position:0%
+and we can check you know when theta is
+2 pi
+
+ align:start position:0%
+2 pi
+ 
+
+ align:start position:0%
+2 pi
+um hmm okay i guess oh this is theta can
+
+ align:start position:0%
+um hmm okay i guess oh this is theta can
+ 
+
+ align:start position:0%
+um hmm okay i guess oh this is theta can
+only get up to pi
+
+ align:start position:0%
+only get up to pi
+ 
+
+ align:start position:0%
+only get up to pi
+so uh we would get uh
+
+ align:start position:0%
+so uh we would get uh
+ 
+
+ align:start position:0%
+so uh we would get uh
+oh pi r squared how about
+
+ align:start position:0%
+oh pi r squared how about
+ 
+
+ align:start position:0%
+oh pi r squared how about
+let's check that again so theta is the
+
+ align:start position:0%
+let's check that again so theta is the
+ 
+
+ align:start position:0%
+let's check that again so theta is the
+half angle of the sector
+
+ align:start position:0%
+half angle of the sector
+ 
+
+ align:start position:0%
+half angle of the sector
+and so it can only get as large as pi
+
+ align:start position:0%
+and so it can only get as large as pi
+ 
+
+ align:start position:0%
+and so it can only get as large as pi
+and if it's equal to pi that means we've
+
+ align:start position:0%
+and if it's equal to pi that means we've
+ 
+
+ align:start position:0%
+and if it's equal to pi that means we've
+covered the whole circle and we should
+
+ align:start position:0%
+covered the whole circle and we should
+ 
+
+ align:start position:0%
+covered the whole circle and we should
+get the area of the circle which is pi r
+
+ align:start position:0%
+get the area of the circle which is pi r
+ 
+
+ align:start position:0%
+get the area of the circle which is pi r
+squared right so okay so we get r
+
+ align:start position:0%
+squared right so okay so we get r
+ 
+
+ align:start position:0%
+squared right so okay so we get r
+squared theta
+
+ align:start position:0%
+squared theta
+ 
+
+ align:start position:0%
+squared theta
+and then we have to subtract from that
+
+ align:start position:0%
+and then we have to subtract from that
+ 
+
+ align:start position:0%
+and then we have to subtract from that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+triangle area
+
+ align:start position:0%
+triangle area
+ 
+
+ align:start position:0%
+triangle area
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right it's the
+
+ align:start position:0%
+right it's the
+ 
+
+ align:start position:0%
+right it's the
+half the base times the height
+
+ align:start position:0%
+half the base times the height
+ 
+
+ align:start position:0%
+half the base times the height
+so the base is uh
+
+ align:start position:0%
+so the base is uh
+ 
+
+ align:start position:0%
+so the base is uh
+two times this quantity
+
+ align:start position:0%
+two times this quantity
+ 
+
+ align:start position:0%
+two times this quantity
+right because this quantity is just that
+
+ align:start position:0%
+right because this quantity is just that
+ 
+
+ align:start position:0%
+right because this quantity is just that
+section so that's the base and then the
+
+ align:start position:0%
+section so that's the base and then the
+ 
+
+ align:start position:0%
+section so that's the base and then the
+height is x
+
+ align:start position:0%
+height is x
+ 
+
+ align:start position:0%
+height is x
+and so half base times height gives me
+
+ align:start position:0%
+and so half base times height gives me
+ 
+
+ align:start position:0%
+and so half base times height gives me
+that and
+
+ align:start position:0%
+that and
+ 
+
+ align:start position:0%
+that and
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theta is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given by this quantity
+
+ align:start position:0%
+given by this quantity
+ 
+
+ align:start position:0%
+given by this quantity
+and so i end up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean the
+
+ align:start position:0%
+i mean the
+ 
+
+ align:start position:0%
+i mean the
+the details aren't too exciting here
+
+ align:start position:0%
+the details aren't too exciting here
+ 
+
+ align:start position:0%
+the details aren't too exciting here
+i'm not going to expect you to remember
+
+ align:start position:0%
+i'm not going to expect you to remember
+ 
+
+ align:start position:0%
+i'm not going to expect you to remember
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+but we can plot that
+
+ align:start position:0%
+but we can plot that
+ 
+
+ align:start position:0%
+but we can plot that
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+see what sort of transition it gives us
+
+ align:start position:0%
+see what sort of transition it gives us
+ 
+
+ align:start position:0%
+see what sort of transition it gives us
+and what's more we can then feed it into
+
+ align:start position:0%
+and what's more we can then feed it into
+ 
+
+ align:start position:0%
+and what's more we can then feed it into
+this algorithm of this pattern to see
+
+ align:start position:0%
+this algorithm of this pattern to see
+ 
+
+ align:start position:0%
+this algorithm of this pattern to see
+how accurately it will determine the
+
+ align:start position:0%
+how accurately it will determine the
+ 
+
+ align:start position:0%
+how accurately it will determine the
+edge position and in particular we can
+
+ align:start position:0%
+edge position and in particular we can
+ 
+
+ align:start position:0%
+edge position and in particular we can
+plot the diagram that i just erased here
+
+ align:start position:0%
+plot the diagram that i just erased here
+ 
+
+ align:start position:0%
+plot the diagram that i just erased here
+which had s versus s bar
+
+ align:start position:0%
+which had s versus s bar
+ 
+
+ align:start position:0%
+which had s versus s bar
+right we in other words if this is how
+
+ align:start position:0%
+right we in other words if this is how
+ 
+
+ align:start position:0%
+right we in other words if this is how
+the edge is formed if this is why the
+
+ align:start position:0%
+the edge is formed if this is why the
+ 
+
+ align:start position:0%
+the edge is formed if this is why the
+edge has that smooth transition then
+
+ align:start position:0%
+edge has that smooth transition then
+ 
+
+ align:start position:0%
+edge has that smooth transition then
+this will allow me to calculate
+
+ align:start position:0%
+this will allow me to calculate
+ 
+
+ align:start position:0%
+this will allow me to calculate
+the error
+
+ align:start position:0%
+the error
+ 
+
+ align:start position:0%
+the error
+and the error ought to be pretty small
+
+ align:start position:0%
+and the error ought to be pretty small
+ 
+
+ align:start position:0%
+and the error ought to be pretty small
+but it's non-zero and if you want high
+
+ align:start position:0%
+but it's non-zero and if you want high
+ 
+
+ align:start position:0%
+but it's non-zero and if you want high
+accuracy you have to take it into
+
+ align:start position:0%
+accuracy you have to take it into
+ 
+
+ align:start position:0%
+accuracy you have to take it into
+account
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+another way of looking at this is to
+
+ align:start position:0%
+another way of looking at this is to
+ 
+
+ align:start position:0%
+another way of looking at this is to
+plot this diagram so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so where does that come from that
+
+ align:start position:0%
+so so where does that come from that
+ 
+
+ align:start position:0%
+so so where does that come from that
+that looks like a circle except it's um
+
+ align:start position:0%
+that looks like a circle except it's um
+ 
+
+ align:start position:0%
+that looks like a circle except it's um
+elliptical because it's been
+
+ align:start position:0%
+elliptical because it's been
+ 
+
+ align:start position:0%
+elliptical because it's been
+increased in height by two
+
+ align:start position:0%
+increased in height by two
+ 
+
+ align:start position:0%
+increased in height by two
+well if you think about it
+
+ align:start position:0%
+well if you think about it
+ 
+
+ align:start position:0%
+well if you think about it
+when i move this
+
+ align:start position:0%
+when i move this
+ 
+
+ align:start position:0%
+when i move this
+uh edge or the circle
+
+ align:start position:0%
+uh edge or the circle
+ 
+
+ align:start position:0%
+uh edge or the circle
+then i am
+
+ align:start position:0%
+then i am
+ 
+
+ align:start position:0%
+then i am
+adding or subtracting
+
+ align:start position:0%
+adding or subtracting
+ 
+
+ align:start position:0%
+adding or subtracting
+an area you know infinitesimal area
+
+ align:start position:0%
+an area you know infinitesimal area
+ 
+
+ align:start position:0%
+an area you know infinitesimal area
+that has a height equal to this quantity
+
+ align:start position:0%
+that has a height equal to this quantity
+ 
+
+ align:start position:0%
+that has a height equal to this quantity
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+in other words just you know twice the
+
+ align:start position:0%
+in other words just you know twice the
+ 
+
+ align:start position:0%
+in other words just you know twice the
+height of the circle there
+
+ align:start position:0%
+height of the circle there
+ 
+
+ align:start position:0%
+height of the circle there
+so actually
+
+ align:start position:0%
+so actually
+ 
+
+ align:start position:0%
+so actually
+i don't need for some purpose i don't
+
+ align:start position:0%
+i don't need for some purpose i don't
+ 
+
+ align:start position:0%
+i don't need for some purpose i don't
+need to do all that hairy math i can
+
+ align:start position:0%
+need to do all that hairy math i can
+ 
+
+ align:start position:0%
+need to do all that hairy math i can
+just look at that diagram and
+
+ align:start position:0%
+just look at that diagram and
+ 
+
+ align:start position:0%
+just look at that diagram and
+immediately write down uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brightness derivative is that and and oh
+
+ align:start position:0%
+brightness derivative is that and and oh
+ 
+
+ align:start position:0%
+brightness derivative is that and and oh
+it has a peak at zero well
+
+ align:start position:0%
+it has a peak at zero well
+ 
+
+ align:start position:0%
+it has a peak at zero well
+we expect that
+
+ align:start position:0%
+we expect that
+ 
+
+ align:start position:0%
+we expect that
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+while i'm here i can look at the second
+
+ align:start position:0%
+while i'm here i can look at the second
+ 
+
+ align:start position:0%
+while i'm here i can look at the second
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+and it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looks like that and it's x over
+
+ align:start position:0%
+looks like that and it's x over
+ 
+
+ align:start position:0%
+looks like that and it's x over
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's just the derivative of that which
+
+ align:start position:0%
+it's just the derivative of that which
+ 
+
+ align:start position:0%
+it's just the derivative of that which
+is pretty easy but
+
+ align:start position:0%
+is pretty easy but
+ 
+
+ align:start position:0%
+is pretty easy but
+what's e
+
+ align:start position:0%
+what's e
+ 
+
+ align:start position:0%
+what's e
+well it's the integral of this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we we just
+
+ align:start position:0%
+and we we just
+ 
+
+ align:start position:0%
+and we we just
+we just did that integral
+
+ align:start position:0%
+we just did that integral
+ 
+
+ align:start position:0%
+we just did that integral
+in a somewhat painful way but but it's
+
+ align:start position:0%
+in a somewhat painful way but but it's
+ 
+
+ align:start position:0%
+in a somewhat painful way but but it's
+probably just as well because i don't
+
+ align:start position:0%
+probably just as well because i don't
+ 
+
+ align:start position:0%
+probably just as well because i don't
+remember what the integral of that is
+
+ align:start position:0%
+remember what the integral of that is
+ 
+
+ align:start position:0%
+remember what the integral of that is
+and you know
+
+ align:start position:0%
+and you know
+ 
+
+ align:start position:0%
+and you know
+there it is
+
+ align:start position:0%
+there it is
+ 
+
+ align:start position:0%
+there it is
+i think okay
+
+ align:start position:0%
+i think okay
+ 
+
+ align:start position:0%
+i think okay
+okay so uh what can we do with this we
+
+ align:start position:0%
+okay so uh what can we do with this we
+ 
+
+ align:start position:0%
+okay so uh what can we do with this we
+can now feed this into the algorithm and
+
+ align:start position:0%
+can now feed this into the algorithm and
+ 
+
+ align:start position:0%
+can now feed this into the algorithm and
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+if this is how
+
+ align:start position:0%
+if this is how
+ 
+
+ align:start position:0%
+if this is how
+why the edges smoothly varying because
+
+ align:start position:0%
+why the edges smoothly varying because
+ 
+
+ align:start position:0%
+why the edges smoothly varying because
+it's out of focus then
+
+ align:start position:0%
+it's out of focus then
+ 
+
+ align:start position:0%
+it's out of focus then
+this is the relationship between the
+
+ align:start position:0%
+this is the relationship between the
+ 
+
+ align:start position:0%
+this is the relationship between the
+true position of the edge and the one i
+
+ align:start position:0%
+true position of the edge and the one i
+ 
+
+ align:start position:0%
+true position of the edge and the one i
+compute by say using the
+
+ align:start position:0%
+compute by say using the
+ 
+
+ align:start position:0%
+compute by say using the
+the parabola argument and therefore i
+
+ align:start position:0%
+the parabola argument and therefore i
+ 
+
+ align:start position:0%
+the parabola argument and therefore i
+can compensate for it
+
+ align:start position:0%
+can compensate for it
+ 
+
+ align:start position:0%
+can compensate for it
+now of course in a real imaging
+
+ align:start position:0%
+now of course in a real imaging
+ 
+
+ align:start position:0%
+now of course in a real imaging
+situation there'll be more than just the
+
+ align:start position:0%
+situation there'll be more than just the
+ 
+
+ align:start position:0%
+situation there'll be more than just the
+defocus of the lens so uh it probably uh
+
+ align:start position:0%
+defocus of the lens so uh it probably uh
+ 
+
+ align:start position:0%
+defocus of the lens so uh it probably uh
+doesn't pay to be too
+
+ align:start position:0%
+doesn't pay to be too
+ 
+
+ align:start position:0%
+doesn't pay to be too
+too careful about this
+
+ align:start position:0%
+too careful about this
+ 
+
+ align:start position:0%
+too careful about this
+okay now um
+
+ align:start position:0%
+okay now um
+ 
+
+ align:start position:0%
+okay now um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+suppose that you're a patent infringer
+
+ align:start position:0%
+suppose that you're a patent infringer
+ 
+
+ align:start position:0%
+suppose that you're a patent infringer
+or you're trying to infringe this
+
+ align:start position:0%
+or you're trying to infringe this
+ 
+
+ align:start position:0%
+or you're trying to infringe this
+pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+there are a number of ways to go
+
+ align:start position:0%
+there are a number of ways to go
+ 
+
+ align:start position:0%
+there are a number of ways to go
+basically you look at the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components of each claim and you see if
+
+ align:start position:0%
+components of each claim and you see if
+ 
+
+ align:start position:0%
+components of each claim and you see if
+there's one of the components that maybe
+
+ align:start position:0%
+there's one of the components that maybe
+ 
+
+ align:start position:0%
+there's one of the components that maybe
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+avoid maybe you can do it in a different
+
+ align:start position:0%
+avoid maybe you can do it in a different
+ 
+
+ align:start position:0%
+avoid maybe you can do it in a different
+way or maybe you can do it in a better
+
+ align:start position:0%
+way or maybe you can do it in a better
+ 
+
+ align:start position:0%
+way or maybe you can do it in a better
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+just arguing whether something's better
+
+ align:start position:0%
+just arguing whether something's better
+ 
+
+ align:start position:0%
+just arguing whether something's better
+or not uh doesn't
+
+ align:start position:0%
+or not uh doesn't
+ 
+
+ align:start position:0%
+or not uh doesn't
+help it's it has to be different
+
+ align:start position:0%
+help it's it has to be different
+ 
+
+ align:start position:0%
+help it's it has to be different
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now there's some some things here
+
+ align:start position:0%
+and now there's some some things here
+ 
+
+ align:start position:0%
+and now there's some some things here
+that aren't that uh pleasant one of them
+
+ align:start position:0%
+that aren't that uh pleasant one of them
+ 
+
+ align:start position:0%
+that aren't that uh pleasant one of them
+is this quantization of gradient
+
+ align:start position:0%
+is this quantization of gradient
+ 
+
+ align:start position:0%
+is this quantization of gradient
+directions and the reason it's not that
+
+ align:start position:0%
+directions and the reason it's not that
+ 
+
+ align:start position:0%
+directions and the reason it's not that
+great is because it introduces
+
+ align:start position:0%
+great is because it introduces
+ 
+
+ align:start position:0%
+great is because it introduces
+the awkwardness that the spacing is
+
+ align:start position:0%
+the awkwardness that the spacing is
+ 
+
+ align:start position:0%
+the awkwardness that the spacing is
+comes in two sizes you know pixel
+
+ align:start position:0%
+comes in two sizes you know pixel
+ 
+
+ align:start position:0%
+comes in two sizes you know pixel
+spacing and square root of two times
+
+ align:start position:0%
+spacing and square root of two times
+ 
+
+ align:start position:0%
+spacing and square root of two times
+pixel spacing and these these effects of
+
+ align:start position:0%
+pixel spacing and these these effects of
+ 
+
+ align:start position:0%
+pixel spacing and these these effects of
+defocus etc
+
+ align:start position:0%
+defocus etc
+ 
+
+ align:start position:0%
+defocus etc
+are they are on pixel grid they're in
+
+ align:start position:0%
+are they are on pixel grid they're in
+ 
+
+ align:start position:0%
+are they are on pixel grid they're in
+units of pixel spacing and so now we're
+
+ align:start position:0%
+units of pixel spacing and so now we're
+ 
+
+ align:start position:0%
+units of pixel spacing and so now we're
+sampling it in two different ways so we
+
+ align:start position:0%
+sampling it in two different ways so we
+ 
+
+ align:start position:0%
+sampling it in two different ways so we
+expect to get a slightly different error
+
+ align:start position:0%
+expect to get a slightly different error
+ 
+
+ align:start position:0%
+expect to get a slightly different error
+contribution so how can we avoid that
+
+ align:start position:0%
+contribution so how can we avoid that
+ 
+
+ align:start position:0%
+contribution so how can we avoid that
+so here are a couple of ways of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea is we don't want
+
+ align:start position:0%
+so the idea is we don't want
+ 
+
+ align:start position:0%
+so the idea is we don't want
+quantized
+
+ align:start position:0%
+quantized
+ 
+
+ align:start position:0%
+quantized
+gradient directions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so suppose our gradient is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+if we follow the
+
+ align:start position:0%
+if we follow the
+ 
+
+ align:start position:0%
+if we follow the
+the preferred method in the patent
+
+ align:start position:0%
+the preferred method in the patent
+ 
+
+ align:start position:0%
+the preferred method in the patent
+again notice that that method doesn't
+
+ align:start position:0%
+again notice that that method doesn't
+ 
+
+ align:start position:0%
+again notice that that method doesn't
+show up in any of the claims it's so
+
+ align:start position:0%
+show up in any of the claims it's so
+ 
+
+ align:start position:0%
+show up in any of the claims it's so
+which is good because that means that
+
+ align:start position:0%
+which is good because that means that
+ 
+
+ align:start position:0%
+which is good because that means that
+you could easily
+
+ align:start position:0%
+you could easily
+ 
+
+ align:start position:0%
+you could easily
+circumvent the patent but
+
+ align:start position:0%
+circumvent the patent but
+ 
+
+ align:start position:0%
+circumvent the patent but
+it is the preferred method that's shown
+
+ align:start position:0%
+it is the preferred method that's shown
+ 
+
+ align:start position:0%
+it is the preferred method that's shown
+in in the specification
+
+ align:start position:0%
+in in the specification
+ 
+
+ align:start position:0%
+in in the specification
+then we would quantize this and we would
+
+ align:start position:0%
+then we would quantize this and we would
+ 
+
+ align:start position:0%
+then we would quantize this and we would
+work with
+
+ align:start position:0%
+work with
+ 
+
+ align:start position:0%
+work with
+the diagonal
+
+ align:start position:0%
+the diagonal
+ 
+
+ align:start position:0%
+the diagonal
+but let's instead say well how about
+
+ align:start position:0%
+but let's instead say well how about
+ 
+
+ align:start position:0%
+but let's instead say well how about
+this how about
+
+ align:start position:0%
+this how about
+ 
+
+ align:start position:0%
+this how about
+if i figured out what the if i knew what
+
+ align:start position:0%
+if i figured out what the if i knew what
+ 
+
+ align:start position:0%
+if i figured out what the if i knew what
+the value was there
+
+ align:start position:0%
+the value was there
+ 
+
+ align:start position:0%
+the value was there
+i know what the value is here
+
+ align:start position:0%
+i know what the value is here
+ 
+
+ align:start position:0%
+i know what the value is here
+you know how about this arrangement so
+
+ align:start position:0%
+you know how about this arrangement so
+ 
+
+ align:start position:0%
+you know how about this arrangement so
+this could be g0 and that's g plus and
+
+ align:start position:0%
+this could be g0 and that's g plus and
+ 
+
+ align:start position:0%
+this could be g0 and that's g plus and
+that's g minus
+
+ align:start position:0%
+that's g minus
+ 
+
+ align:start position:0%
+that's g minus
+then i would avoid the quantization of
+
+ align:start position:0%
+then i would avoid the quantization of
+ 
+
+ align:start position:0%
+then i would avoid the quantization of
+gradient direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how do i do that well i only know
+
+ align:start position:0%
+and how do i do that well i only know
+ 
+
+ align:start position:0%
+and how do i do that well i only know
+the values on the actual pixel grid
+
+ align:start position:0%
+the values on the actual pixel grid
+ 
+
+ align:start position:0%
+the values on the actual pixel grid
+and so tada i interpolate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i use interpolation to go from the
+
+ align:start position:0%
+so i use interpolation to go from the
+ 
+
+ align:start position:0%
+so i use interpolation to go from the
+values on the grid to the value over
+
+ align:start position:0%
+values on the grid to the value over
+ 
+
+ align:start position:0%
+values on the grid to the value over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and because i'm interpolating along this
+
+ align:start position:0%
+and because i'm interpolating along this
+ 
+
+ align:start position:0%
+and because i'm interpolating along this
+line i can actually easily just use uh
+
+ align:start position:0%
+line i can actually easily just use uh
+ 
+
+ align:start position:0%
+line i can actually easily just use uh
+one 1d linear interpolation
+
+ align:start position:0%
+one 1d linear interpolation
+ 
+
+ align:start position:0%
+one 1d linear interpolation
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+how does that work well if i have a
+
+ align:start position:0%
+how does that work well if i have a
+ 
+
+ align:start position:0%
+how does that work well if i have a
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then i can say well
+
+ align:start position:0%
+then i can say well
+ 
+
+ align:start position:0%
+then i can say well
+i know the value here another value
+
+ align:start position:0%
+i know the value here another value
+ 
+
+ align:start position:0%
+i know the value here another value
+there and let's say it's a straight line
+
+ align:start position:0%
+there and let's say it's a straight line
+ 
+
+ align:start position:0%
+there and let's say it's a straight line
+in between and then the formula for this
+
+ align:start position:0%
+in between and then the formula for this
+ 
+
+ align:start position:0%
+in between and then the formula for this
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean you can
+
+ align:start position:0%
+i mean you can
+ 
+
+ align:start position:0%
+i mean you can
+come up with that yourself but you can
+
+ align:start position:0%
+come up with that yourself but you can
+ 
+
+ align:start position:0%
+come up with that yourself but you can
+easily check it first of all it's linear
+
+ align:start position:0%
+easily check it first of all it's linear
+ 
+
+ align:start position:0%
+easily check it first of all it's linear
+in x
+
+ align:start position:0%
+in x
+ 
+
+ align:start position:0%
+in x
+and then at x equals a
+
+ align:start position:0%
+and then at x equals a
+ 
+
+ align:start position:0%
+and then at x equals a
+we get only this
+
+ align:start position:0%
+we get only this
+ 
+
+ align:start position:0%
+we get only this
+term and the b minus a
+
+ align:start position:0%
+term and the b minus a
+ 
+
+ align:start position:0%
+term and the b minus a
+cancels the b minus a and at x equals b
+
+ align:start position:0%
+cancels the b minus a and at x equals b
+ 
+
+ align:start position:0%
+cancels the b minus a and at x equals b
+uh this term drops out so we only have
+
+ align:start position:0%
+uh this term drops out so we only have
+ 
+
+ align:start position:0%
+uh this term drops out so we only have
+that and again the b minus a can okay so
+
+ align:start position:0%
+that and again the b minus a can okay so
+ 
+
+ align:start position:0%
+that and again the b minus a can okay so
+it's easy to do that in in 1d and of
+
+ align:start position:0%
+it's easy to do that in in 1d and of
+ 
+
+ align:start position:0%
+it's easy to do that in in 1d and of
+course you can extend that to so-called
+
+ align:start position:0%
+course you can extend that to so-called
+ 
+
+ align:start position:0%
+course you can extend that to so-called
+bilinear interpolation in in 2d
+
+ align:start position:0%
+bilinear interpolation in in 2d
+ 
+
+ align:start position:0%
+bilinear interpolation in in 2d
+but we don't actually even need that
+
+ align:start position:0%
+but we don't actually even need that
+ 
+
+ align:start position:0%
+but we don't actually even need that
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+approximate the value here by
+
+ align:start position:0%
+approximate the value here by
+ 
+
+ align:start position:0%
+approximate the value here by
+interpolation and we can use more
+
+ align:start position:0%
+interpolation and we can use more
+ 
+
+ align:start position:0%
+interpolation and we can use more
+sophisticated methods
+
+ align:start position:0%
+sophisticated methods
+ 
+
+ align:start position:0%
+sophisticated methods
+of interpolation for example we can use
+
+ align:start position:0%
+of interpolation for example we can use
+ 
+
+ align:start position:0%
+of interpolation for example we can use
+cubic spline interpolation
+
+ align:start position:0%
+cubic spline interpolation
+ 
+
+ align:start position:0%
+cubic spline interpolation
+which we won't talk about here but
+
+ align:start position:0%
+which we won't talk about here but
+ 
+
+ align:start position:0%
+which we won't talk about here but
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+you know involves more points but gives
+
+ align:start position:0%
+you know involves more points but gives
+ 
+
+ align:start position:0%
+you know involves more points but gives
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+an interpolation that's a smooth cubic
+
+ align:start position:0%
+an interpolation that's a smooth cubic
+ 
+
+ align:start position:0%
+an interpolation that's a smooth cubic
+curve which in some cases is more
+
+ align:start position:0%
+curve which in some cases is more
+ 
+
+ align:start position:0%
+curve which in some cases is more
+accurate
+
+ align:start position:0%
+accurate
+ 
+
+ align:start position:0%
+accurate
+okay and then we perform whatever we did
+
+ align:start position:0%
+okay and then we perform whatever we did
+ 
+
+ align:start position:0%
+okay and then we perform whatever we did
+and we end up you know somewhere there
+
+ align:start position:0%
+and we end up you know somewhere there
+ 
+
+ align:start position:0%
+and we end up you know somewhere there
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we we don't need the uh plane position
+
+ align:start position:0%
+we we don't need the uh plane position
+ 
+
+ align:start position:0%
+we we don't need the uh plane position
+step because we're actually on the
+
+ align:start position:0%
+step because we're actually on the
+ 
+
+ align:start position:0%
+step because we're actually on the
+gradient direction we're exactly where
+
+ align:start position:0%
+gradient direction we're exactly where
+ 
+
+ align:start position:0%
+gradient direction we're exactly where
+you want to be
+
+ align:start position:0%
+you want to be
+ 
+
+ align:start position:0%
+you want to be
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um that
+
+ align:start position:0%
+um that
+ 
+
+ align:start position:0%
+um that
+you know you wonder why why didn't they
+
+ align:start position:0%
+you know you wonder why why didn't they
+ 
+
+ align:start position:0%
+you know you wonder why why didn't they
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+well uh
+
+ align:start position:0%
+well uh
+ 
+
+ align:start position:0%
+well uh
+they don't say it but
+
+ align:start position:0%
+they don't say it but
+ 
+
+ align:start position:0%
+they don't say it but
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+two two reasons one that i can think of
+
+ align:start position:0%
+two two reasons one that i can think of
+ 
+
+ align:start position:0%
+two two reasons one that i can think of
+one is that before we complained because
+
+ align:start position:0%
+one is that before we complained because
+ 
+
+ align:start position:0%
+one is that before we complained because
+sometimes we were using pixel spacing
+
+ align:start position:0%
+sometimes we were using pixel spacing
+ 
+
+ align:start position:0%
+sometimes we were using pixel spacing
+and sometimes square root of two times
+
+ align:start position:0%
+and sometimes square root of two times
+ 
+
+ align:start position:0%
+and sometimes square root of two times
+pixel spacing well now we can have
+
+ align:start position:0%
+pixel spacing well now we can have
+ 
+
+ align:start position:0%
+pixel spacing well now we can have
+anything in between
+
+ align:start position:0%
+anything in between
+ 
+
+ align:start position:0%
+anything in between
+not not just those two values and that
+
+ align:start position:0%
+not not just those two values and that
+ 
+
+ align:start position:0%
+not not just those two values and that
+correction graph the bias graph
+
+ align:start position:0%
+correction graph the bias graph
+ 
+
+ align:start position:0%
+correction graph the bias graph
+you know will be different for all of
+
+ align:start position:0%
+you know will be different for all of
+ 
+
+ align:start position:0%
+you know will be different for all of
+those values so you've got to i don't
+
+ align:start position:0%
+those values so you've got to i don't
+ 
+
+ align:start position:0%
+those values so you've got to i don't
+know quantize it
+
+ align:start position:0%
+know quantize it
+ 
+
+ align:start position:0%
+know quantize it
+build a lookup table
+
+ align:start position:0%
+build a lookup table
+ 
+
+ align:start position:0%
+build a lookup table
+no no not insurmountable problems but an
+
+ align:start position:0%
+no no not insurmountable problems but an
+ 
+
+ align:start position:0%
+no no not insurmountable problems but an
+extra hassle and you wonder you know is
+
+ align:start position:0%
+extra hassle and you wonder you know is
+ 
+
+ align:start position:0%
+extra hassle and you wonder you know is
+it worth it
+
+ align:start position:0%
+it worth it
+ 
+
+ align:start position:0%
+it worth it
+so that's one reason
+
+ align:start position:0%
+so that's one reason
+ 
+
+ align:start position:0%
+so that's one reason
+you might not choose this the other
+
+ align:start position:0%
+you might not choose this the other
+ 
+
+ align:start position:0%
+you might not choose this the other
+reason is that
+
+ align:start position:0%
+reason is that
+ 
+
+ align:start position:0%
+reason is that
+you did an interpolation
+
+ align:start position:0%
+you did an interpolation
+ 
+
+ align:start position:0%
+you did an interpolation
+and how accurate is that
+
+ align:start position:0%
+and how accurate is that
+ 
+
+ align:start position:0%
+and how accurate is that
+you know you've gone away from the
+
+ align:start position:0%
+you know you've gone away from the
+ 
+
+ align:start position:0%
+you know you've gone away from the
+values that you actually know for sure
+
+ align:start position:0%
+values that you actually know for sure
+ 
+
+ align:start position:0%
+values that you actually know for sure
+to something that you interpolated using
+
+ align:start position:0%
+to something that you interpolated using
+ 
+
+ align:start position:0%
+to something that you interpolated using
+a method that you chose in some
+
+ align:start position:0%
+a method that you chose in some
+ 
+
+ align:start position:0%
+a method that you chose in some
+arbitrary fashion you know how good is
+
+ align:start position:0%
+arbitrary fashion you know how good is
+ 
+
+ align:start position:0%
+arbitrary fashion you know how good is
+it so that that'll introduce some error
+
+ align:start position:0%
+it so that that'll introduce some error
+ 
+
+ align:start position:0%
+it so that that'll introduce some error
+as well now in many cases that error
+
+ align:start position:0%
+as well now in many cases that error
+ 
+
+ align:start position:0%
+as well now in many cases that error
+wouldn't matter it'd be so small
+
+ align:start position:0%
+wouldn't matter it'd be so small
+ 
+
+ align:start position:0%
+wouldn't matter it'd be so small
+but you know if you're going for a 40th
+
+ align:start position:0%
+but you know if you're going for a 40th
+ 
+
+ align:start position:0%
+but you know if you're going for a 40th
+of a pixel accuracy
+
+ align:start position:0%
+of a pixel accuracy
+ 
+
+ align:start position:0%
+of a pixel accuracy
+that even that small error can be
+
+ align:start position:0%
+that even that small error can be
+ 
+
+ align:start position:0%
+that even that small error can be
+significant
+
+ align:start position:0%
+significant
+ 
+
+ align:start position:0%
+significant
+okay so that's one
+
+ align:start position:0%
+okay so that's one
+ 
+
+ align:start position:0%
+okay so that's one
+one method uh one alternative and um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of its problems is
+
+ align:start position:0%
+one of its problems is
+ 
+
+ align:start position:0%
+one of its problems is
+uh changing size of this step
+
+ align:start position:0%
+uh changing size of this step
+ 
+
+ align:start position:0%
+uh changing size of this step
+uh from a pixel to square root of two
+
+ align:start position:0%
+uh from a pixel to square root of two
+ 
+
+ align:start position:0%
+uh from a pixel to square root of two
+well what if we
+
+ align:start position:0%
+well what if we
+ 
+
+ align:start position:0%
+well what if we
+get rid of that and we just have a fixed
+
+ align:start position:0%
+get rid of that and we just have a fixed
+ 
+
+ align:start position:0%
+get rid of that and we just have a fixed
+size so
+
+ align:start position:0%
+size so
+ 
+
+ align:start position:0%
+size so
+here's again our
+
+ align:start position:0%
+here's again our
+ 
+
+ align:start position:0%
+here's again our
+pixel grid we know the values at all of
+
+ align:start position:0%
+pixel grid we know the values at all of
+ 
+
+ align:start position:0%
+pixel grid we know the values at all of
+the intersections of these lines
+
+ align:start position:0%
+the intersections of these lines
+ 
+
+ align:start position:0%
+the intersections of these lines
+and this is g0
+
+ align:start position:0%
+and this is g0
+ 
+
+ align:start position:0%
+and this is g0
+and now we say well let's just draw a
+
+ align:start position:0%
+and now we say well let's just draw a
+ 
+
+ align:start position:0%
+and now we say well let's just draw a
+circle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again we'll pick the
+
+ align:start position:0%
+and again we'll pick the
+ 
+
+ align:start position:0%
+and again we'll pick the
+we'll pick some gradient direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use that value
+
+ align:start position:0%
+use that value
+ 
+
+ align:start position:0%
+use that value
+and that value and that value and those
+
+ align:start position:0%
+and that value and that value and those
+ 
+
+ align:start position:0%
+and that value and that value and those
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+equally spaced they're always the same
+
+ align:start position:0%
+equally spaced they're always the same
+ 
+
+ align:start position:0%
+equally spaced they're always the same
+distance from each other
+
+ align:start position:0%
+distance from each other
+ 
+
+ align:start position:0%
+distance from each other
+no matter what the gradient direction so
+
+ align:start position:0%
+no matter what the gradient direction so
+ 
+
+ align:start position:0%
+no matter what the gradient direction so
+i've kind of now dealt with two issues
+
+ align:start position:0%
+i've kind of now dealt with two issues
+ 
+
+ align:start position:0%
+i've kind of now dealt with two issues
+the one is there's no quantization of
+
+ align:start position:0%
+the one is there's no quantization of
+ 
+
+ align:start position:0%
+the one is there's no quantization of
+the gradient direction
+
+ align:start position:0%
+the gradient direction
+ 
+
+ align:start position:0%
+the gradient direction
+and there's none of this change of the
+
+ align:start position:0%
+and there's none of this change of the
+ 
+
+ align:start position:0%
+and there's none of this change of the
+you know what does s equals one mean
+
+ align:start position:0%
+you know what does s equals one mean
+ 
+
+ align:start position:0%
+you know what does s equals one mean
+uh before that could take on two values
+
+ align:start position:0%
+uh before that could take on two values
+ 
+
+ align:start position:0%
+uh before that could take on two values
+and over here it could take on a range
+
+ align:start position:0%
+and over here it could take on a range
+ 
+
+ align:start position:0%
+and over here it could take on a range
+of values well here it's always the same
+
+ align:start position:0%
+of values well here it's always the same
+ 
+
+ align:start position:0%
+of values well here it's always the same
+it's it's the the pixel spacing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+of course i don't know the value here so
+
+ align:start position:0%
+of course i don't know the value here so
+ 
+
+ align:start position:0%
+of course i don't know the value here so
+i have to use interpolation which is now
+
+ align:start position:0%
+i have to use interpolation which is now
+ 
+
+ align:start position:0%
+i have to use interpolation which is now
+a 2d interpolation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so i can use bilinear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or i could for example use bicubic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+again you know why didn't they do this
+
+ align:start position:0%
+again you know why didn't they do this
+ 
+
+ align:start position:0%
+again you know why didn't they do this
+well it's extra work
+
+ align:start position:0%
+well it's extra work
+ 
+
+ align:start position:0%
+well it's extra work
+particularly with a bicubic we need to
+
+ align:start position:0%
+particularly with a bicubic we need to
+ 
+
+ align:start position:0%
+particularly with a bicubic we need to
+take into account more pixels than we
+
+ align:start position:0%
+take into account more pixels than we
+ 
+
+ align:start position:0%
+take into account more pixels than we
+have here
+
+ align:start position:0%
+have here
+ 
+
+ align:start position:0%
+have here
+you know go out
+
+ align:start position:0%
+you know go out
+ 
+
+ align:start position:0%
+you know go out
+to a five by five grid not just a three
+
+ align:start position:0%
+to a five by five grid not just a three
+ 
+
+ align:start position:0%
+to a five by five grid not just a three
+by three grid
+
+ align:start position:0%
+by three grid
+ 
+
+ align:start position:0%
+by three grid
+bilinear is not terribly accurate so we
+
+ align:start position:0%
+bilinear is not terribly accurate so we
+ 
+
+ align:start position:0%
+bilinear is not terribly accurate so we
+may not want to use that so
+
+ align:start position:0%
+may not want to use that so
+ 
+
+ align:start position:0%
+may not want to use that so
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+so you can see that
+
+ align:start position:0%
+so you can see that
+ 
+
+ align:start position:0%
+so you can see that
+even though
+
+ align:start position:0%
+even though
+ 
+
+ align:start position:0%
+even though
+a lot of things are described in the
+
+ align:start position:0%
+a lot of things are described in the
+ 
+
+ align:start position:0%
+a lot of things are described in the
+pattern there is also some hidden stuff
+
+ align:start position:0%
+pattern there is also some hidden stuff
+ 
+
+ align:start position:0%
+pattern there is also some hidden stuff
+going on they probably experimented with
+
+ align:start position:0%
+going on they probably experimented with
+ 
+
+ align:start position:0%
+going on they probably experimented with
+all of this and picked something that
+
+ align:start position:0%
+all of this and picked something that
+ 
+
+ align:start position:0%
+all of this and picked something that
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+very accurate and yet simple and that's
+
+ align:start position:0%
+very accurate and yet simple and that's
+ 
+
+ align:start position:0%
+very accurate and yet simple and that's
+how we got to that method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the last thing i want to talk about
+
+ align:start position:0%
+now the last thing i want to talk about
+ 
+
+ align:start position:0%
+now the last thing i want to talk about
+today is uh
+
+ align:start position:0%
+today is uh
+ 
+
+ align:start position:0%
+today is uh
+multiscale they do
+
+ align:start position:0%
+multiscale they do
+ 
+
+ align:start position:0%
+multiscale they do
+uh point out in this patent
+
+ align:start position:0%
+uh point out in this patent
+ 
+
+ align:start position:0%
+uh point out in this patent
+that you might want to do this at
+
+ align:start position:0%
+that you might want to do this at
+ 
+
+ align:start position:0%
+that you might want to do this at
+multiple scales
+
+ align:start position:0%
+multiple scales
+ 
+
+ align:start position:0%
+multiple scales
+they don't make a big fuss of it here
+
+ align:start position:0%
+they don't make a big fuss of it here
+ 
+
+ align:start position:0%
+they don't make a big fuss of it here
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+we already mentioned that that's
+
+ align:start position:0%
+we already mentioned that that's
+ 
+
+ align:start position:0%
+we already mentioned that that's
+something you want to do
+
+ align:start position:0%
+something you want to do
+ 
+
+ align:start position:0%
+something you want to do
+there are some edges which are very
+
+ align:start position:0%
+there are some edges which are very
+ 
+
+ align:start position:0%
+there are some edges which are very
+sharp and they will be best found at the
+
+ align:start position:0%
+sharp and they will be best found at the
+ 
+
+ align:start position:0%
+sharp and they will be best found at the
+highest resolution and then there's some
+
+ align:start position:0%
+highest resolution and then there's some
+ 
+
+ align:start position:0%
+highest resolution and then there's some
+other edges that are kind of blurry
+
+ align:start position:0%
+other edges that are kind of blurry
+ 
+
+ align:start position:0%
+other edges that are kind of blurry
+either because they're out of focus or
+
+ align:start position:0%
+either because they're out of focus or
+ 
+
+ align:start position:0%
+either because they're out of focus or
+because the object doesn't have a sharp
+
+ align:start position:0%
+because the object doesn't have a sharp
+ 
+
+ align:start position:0%
+because the object doesn't have a sharp
+transition you know if the object has a
+
+ align:start position:0%
+transition you know if the object has a
+ 
+
+ align:start position:0%
+transition you know if the object has a
+smoothly turning
+
+ align:start position:0%
+smoothly turning
+ 
+
+ align:start position:0%
+smoothly turning
+curvature then there'll be a transition
+
+ align:start position:0%
+curvature then there'll be a transition
+ 
+
+ align:start position:0%
+curvature then there'll be a transition
+in brightness from whatever the
+
+ align:start position:0%
+in brightness from whatever the
+ 
+
+ align:start position:0%
+in brightness from whatever the
+brightness is for one planar surface to
+
+ align:start position:0%
+brightness is for one planar surface to
+ 
+
+ align:start position:0%
+brightness is for one planar surface to
+the brightness for a different planar
+
+ align:start position:0%
+the brightness for a different planar
+ 
+
+ align:start position:0%
+the brightness for a different planar
+surface but they're all these in between
+
+ align:start position:0%
+surface but they're all these in between
+ 
+
+ align:start position:0%
+surface but they're all these in between
+values so the transition won't be on one
+
+ align:start position:0%
+values so the transition won't be on one
+ 
+
+ align:start position:0%
+values so the transition won't be on one
+pixel it'll be spread out
+
+ align:start position:0%
+pixel it'll be spread out
+ 
+
+ align:start position:0%
+pixel it'll be spread out
+over many pixels
+
+ align:start position:0%
+over many pixels
+ 
+
+ align:start position:0%
+over many pixels
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+see do i want to do this now or
+
+ align:start position:0%
+see do i want to do this now or
+ 
+
+ align:start position:0%
+see do i want to do this now or
+we haven't talked about chordic so um
+
+ align:start position:0%
+we haven't talked about chordic so um
+ 
+
+ align:start position:0%
+we haven't talked about chordic so um
+i'm just looking at time we don't have
+
+ align:start position:0%
+i'm just looking at time we don't have
+ 
+
+ align:start position:0%
+i'm just looking at time we don't have
+much time so when i why don't i do a
+
+ align:start position:0%
+much time so when i why don't i do a
+ 
+
+ align:start position:0%
+much time so when i why don't i do a
+codec
+
+ align:start position:0%
+codec
+ 
+
+ align:start position:0%
+codec
+so this was the method
+
+ align:start position:0%
+so this was the method
+ 
+
+ align:start position:0%
+so this was the method
+to go from e x e y to
+
+ align:start position:0%
+to go from e x e y to
+ 
+
+ align:start position:0%
+to go from e x e y to
+e zero
+
+ align:start position:0%
+e zero
+ 
+
+ align:start position:0%
+e zero
+e theta
+
+ align:start position:0%
+e theta
+ 
+
+ align:start position:0%
+e theta
+right where
+
+ align:start position:0%
+right where
+ 
+
+ align:start position:0%
+right where
+e zero e0 so it's just a cartesian to
+
+ align:start position:0%
+e zero e0 so it's just a cartesian to
+ 
+
+ align:start position:0%
+e zero e0 so it's just a cartesian to
+polar coordinate transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know square roots and 810
+
+ align:start position:0%
+you know square roots and 810
+ 
+
+ align:start position:0%
+you know square roots and 810
+take some computing you'd have to
+
+ align:start position:0%
+take some computing you'd have to
+ 
+
+ align:start position:0%
+take some computing you'd have to
+probably use a lookup table to speed
+
+ align:start position:0%
+probably use a lookup table to speed
+ 
+
+ align:start position:0%
+probably use a lookup table to speed
+that up so
+
+ align:start position:0%
+that up so
+ 
+
+ align:start position:0%
+that up so
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+what is their preferred uh
+
+ align:start position:0%
+what is their preferred uh
+ 
+
+ align:start position:0%
+what is their preferred uh
+implementation of this so the idea is
+
+ align:start position:0%
+implementation of this so the idea is
+ 
+
+ align:start position:0%
+implementation of this so the idea is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+we rotate the coordinate system
+
+ align:start position:0%
+we rotate the coordinate system
+ 
+
+ align:start position:0%
+we rotate the coordinate system
+so we have
+
+ align:start position:0%
+so we have
+ 
+
+ align:start position:0%
+so we have
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+we have some gradient
+
+ align:start position:0%
+we have some gradient
+ 
+
+ align:start position:0%
+we have some gradient
+e x e y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if we knew
+
+ align:start position:0%
+if we knew
+ 
+
+ align:start position:0%
+if we knew
+that angle then we could just rotate it
+
+ align:start position:0%
+that angle then we could just rotate it
+ 
+
+ align:start position:0%
+that angle then we could just rotate it
+down and then the length of it
+
+ align:start position:0%
+down and then the length of it
+ 
+
+ align:start position:0%
+down and then the length of it
+e x
+
+ align:start position:0%
+e x
+ 
+
+ align:start position:0%
+e x
+would be e0
+
+ align:start position:0%
+would be e0
+ 
+
+ align:start position:0%
+would be e0
+and e y would be zero right so so we're
+
+ align:start position:0%
+and e y would be zero right so so we're
+ 
+
+ align:start position:0%
+and e y would be zero right so so we're
+aiming for where
+
+ align:start position:0%
+aiming for where
+ 
+
+ align:start position:0%
+aiming for where
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+zero is just e x prime
+
+ align:start position:0%
+zero is just e x prime
+ 
+
+ align:start position:0%
+zero is just e x prime
+and e theta e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and e y
+
+ align:start position:0%
+and e y
+ 
+
+ align:start position:0%
+and e y
+prime is zero
+
+ align:start position:0%
+prime is zero
+ 
+
+ align:start position:0%
+prime is zero
+when you write it this way around that
+
+ align:start position:0%
+when you write it this way around that
+ 
+
+ align:start position:0%
+when you write it this way around that
+makes more sense
+
+ align:start position:0%
+makes more sense
+ 
+
+ align:start position:0%
+makes more sense
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we don't know theta
+
+ align:start position:0%
+now we don't know theta
+ 
+
+ align:start position:0%
+now we don't know theta
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+we can
+
+ align:start position:0%
+we can
+ 
+
+ align:start position:0%
+we can
+rotate
+
+ align:start position:0%
+rotate
+ 
+
+ align:start position:0%
+rotate
+using some test angles and by an
+
+ align:start position:0%
+using some test angles and by an
+ 
+
+ align:start position:0%
+using some test angles and by an
+iterative method
+
+ align:start position:0%
+iterative method
+ 
+
+ align:start position:0%
+iterative method
+uh you know keep on improving keep on
+
+ align:start position:0%
+uh you know keep on improving keep on
+ 
+
+ align:start position:0%
+uh you know keep on improving keep on
+coming closer to to this situation where
+
+ align:start position:0%
+coming closer to to this situation where
+ 
+
+ align:start position:0%
+coming closer to to this situation where
+the y component of the gradient is
+
+ align:start position:0%
+the y component of the gradient is
+ 
+
+ align:start position:0%
+the y component of the gradient is
+reduced to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+superscripts in parenthesis again refer
+
+ align:start position:0%
+superscripts in parenthesis again refer
+ 
+
+ align:start position:0%
+superscripts in parenthesis again refer
+to the iteration number
+
+ align:start position:0%
+to the iteration number
+ 
+
+ align:start position:0%
+to the iteration number
+rather than being powers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course we know in 2d a rotation
+
+ align:start position:0%
+and of course we know in 2d a rotation
+ 
+
+ align:start position:0%
+and of course we know in 2d a rotation
+matrix is just very simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+one thing we can do is have a sequence
+
+ align:start position:0%
+one thing we can do is have a sequence
+ 
+
+ align:start position:0%
+one thing we can do is have a sequence
+of thetas that we try
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+when when we're finished with this
+
+ align:start position:0%
+when when we're finished with this
+ 
+
+ align:start position:0%
+when when we're finished with this
+iteration when we decide to stop
+
+ align:start position:0%
+iteration when we decide to stop
+ 
+
+ align:start position:0%
+iteration when we decide to stop
+the answer for the angle is just the sum
+
+ align:start position:0%
+the answer for the angle is just the sum
+ 
+
+ align:start position:0%
+the answer for the angle is just the sum
+of all of those
+
+ align:start position:0%
+of all of those
+ 
+
+ align:start position:0%
+of all of those
+increments we make so
+
+ align:start position:0%
+increments we make so
+ 
+
+ align:start position:0%
+increments we make so
+you can imagine various strategies like
+
+ align:start position:0%
+you can imagine various strategies like
+ 
+
+ align:start position:0%
+you can imagine various strategies like
+you can try an angle and suppose that
+
+ align:start position:0%
+you can try an angle and suppose that
+ 
+
+ align:start position:0%
+you can try an angle and suppose that
+this goes the wrong way well then maybe
+
+ align:start position:0%
+this goes the wrong way well then maybe
+ 
+
+ align:start position:0%
+this goes the wrong way well then maybe
+take half that angle
+
+ align:start position:0%
+take half that angle
+ 
+
+ align:start position:0%
+take half that angle
+and try that or
+
+ align:start position:0%
+and try that or
+ 
+
+ align:start position:0%
+and try that or
+you could try turning through that angle
+
+ align:start position:0%
+you could try turning through that angle
+ 
+
+ align:start position:0%
+you could try turning through that angle
+positive and through the angle negative
+
+ align:start position:0%
+positive and through the angle negative
+ 
+
+ align:start position:0%
+positive and through the angle negative
+and compare the two results see which
+
+ align:start position:0%
+and compare the two results see which
+ 
+
+ align:start position:0%
+and compare the two results see which
+one works better and then keep on
+
+ align:start position:0%
+one works better and then keep on
+ 
+
+ align:start position:0%
+one works better and then keep on
+reducing the size of the angle
+
+ align:start position:0%
+reducing the size of the angle
+ 
+
+ align:start position:0%
+reducing the size of the angle
+until you converge until or at least
+
+ align:start position:0%
+until you converge until or at least
+ 
+
+ align:start position:0%
+until you converge until or at least
+until you're you know happy enough with
+
+ align:start position:0%
+until you're you know happy enough with
+ 
+
+ align:start position:0%
+until you're you know happy enough with
+the results so
+
+ align:start position:0%
+the results so
+ 
+
+ align:start position:0%
+the results so
+so each time reduce
+
+ align:start position:0%
+so each time reduce
+ 
+
+ align:start position:0%
+so each time reduce
+each step
+
+ align:start position:0%
+each step
+ 
+
+ align:start position:0%
+each step
+reduce
+
+ align:start position:0%
+reduce
+ 
+
+ align:start position:0%
+reduce
+the magnitude of ey
+
+ align:start position:0%
+the magnitude of ey
+ 
+
+ align:start position:0%
+the magnitude of ey
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it will increase the other one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because as we rotate closer to
+
+ align:start position:0%
+right because as we rotate closer to
+ 
+
+ align:start position:0%
+right because as we rotate closer to
+the x-axis
+
+ align:start position:0%
+the x-axis
+ 
+
+ align:start position:0%
+the x-axis
+the projection of this onto the x-axis
+
+ align:start position:0%
+the projection of this onto the x-axis
+ 
+
+ align:start position:0%
+the projection of this onto the x-axis
+will will increase
+
+ align:start position:0%
+will will increase
+ 
+
+ align:start position:0%
+will will increase
+okay so that's the the iteration
+
+ align:start position:0%
+okay so that's the the iteration
+ 
+
+ align:start position:0%
+okay so that's the the iteration
+and how do we pick the thetas well we
+
+ align:start position:0%
+and how do we pick the thetas well we
+ 
+
+ align:start position:0%
+and how do we pick the thetas well we
+could do this theta zero is pi over two
+
+ align:start position:0%
+could do this theta zero is pi over two
+ 
+
+ align:start position:0%
+could do this theta zero is pi over two
+theta one is pi over four
+
+ align:start position:0%
+theta one is pi over four
+ 
+
+ align:start position:0%
+theta one is pi over four
+theta two is pi over eight
+
+ align:start position:0%
+theta two is pi over eight
+ 
+
+ align:start position:0%
+theta two is pi over eight
+you know and so on
+
+ align:start position:0%
+you know and so on
+ 
+
+ align:start position:0%
+you know and so on
+that'd be one sort of obvious approach
+
+ align:start position:0%
+that'd be one sort of obvious approach
+ 
+
+ align:start position:0%
+that'd be one sort of obvious approach
+so we try and turn through these
+
+ align:start position:0%
+so we try and turn through these
+ 
+
+ align:start position:0%
+so we try and turn through these
+different angles and see if it
+
+ align:start position:0%
+different angles and see if it
+ 
+
+ align:start position:0%
+different angles and see if it
+and we accept we accept the change if it
+
+ align:start position:0%
+and we accept we accept the change if it
+ 
+
+ align:start position:0%
+and we accept we accept the change if it
+satisfies this condition
+
+ align:start position:0%
+satisfies this condition
+ 
+
+ align:start position:0%
+satisfies this condition
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+magnitude that e y is reduced it doesn't
+
+ align:start position:0%
+magnitude that e y is reduced it doesn't
+ 
+
+ align:start position:0%
+magnitude that e y is reduced it doesn't
+have to be positive so it could
+
+ align:start position:0%
+have to be positive so it could
+ 
+
+ align:start position:0%
+have to be positive so it could
+overcompensate as long as the magnitude
+
+ align:start position:0%
+overcompensate as long as the magnitude
+ 
+
+ align:start position:0%
+overcompensate as long as the magnitude
+is reduced and you can always flip it to
+
+ align:start position:0%
+is reduced and you can always flip it to
+ 
+
+ align:start position:0%
+is reduced and you can always flip it to
+make it positive again if you want to
+
+ align:start position:0%
+make it positive again if you want to
+ 
+
+ align:start position:0%
+make it positive again if you want to
+um so you can do that um but it's
+
+ align:start position:0%
+um so you can do that um but it's
+ 
+
+ align:start position:0%
+um so you can do that um but it's
+expensive for two reasons one is you got
+
+ align:start position:0%
+expensive for two reasons one is you got
+ 
+
+ align:start position:0%
+expensive for two reasons one is you got
+the cosines and the sines
+
+ align:start position:0%
+the cosines and the sines
+ 
+
+ align:start position:0%
+the cosines and the sines
+but you could build a table obviously
+
+ align:start position:0%
+but you could build a table obviously
+ 
+
+ align:start position:0%
+but you could build a table obviously
+you could just store the cosines and
+
+ align:start position:0%
+you could just store the cosines and
+ 
+
+ align:start position:0%
+you could just store the cosines and
+sines of these angles the other one is
+
+ align:start position:0%
+sines of these angles the other one is
+ 
+
+ align:start position:0%
+sines of these angles the other one is
+you need each time you need four
+
+ align:start position:0%
+you need each time you need four
+ 
+
+ align:start position:0%
+you need each time you need four
+multiplications and two additions
+
+ align:start position:0%
+multiplications and two additions
+ 
+
+ align:start position:0%
+multiplications and two additions
+it doesn't sound like much but remember
+
+ align:start position:0%
+it doesn't sound like much but remember
+ 
+
+ align:start position:0%
+it doesn't sound like much but remember
+this happens several times because of
+
+ align:start position:0%
+this happens several times because of
+ 
+
+ align:start position:0%
+this happens several times because of
+the iterations and it happens at every
+
+ align:start position:0%
+the iterations and it happens at every
+ 
+
+ align:start position:0%
+the iterations and it happens at every
+pixel so it's expensive
+
+ align:start position:0%
+pixel so it's expensive
+ 
+
+ align:start position:0%
+pixel so it's expensive
+so how to avoid multiplication
+
+ align:start position:0%
+so how to avoid multiplication
+ 
+
+ align:start position:0%
+so how to avoid multiplication
+well what we can do is
+
+ align:start position:0%
+well what we can do is
+ 
+
+ align:start position:0%
+well what we can do is
+pick the angles very carefully
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose that we pick the angles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that there are inverse powers of 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then that matrix there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the rotation matrix
+
+ align:start position:0%
+the rotation matrix
+ 
+
+ align:start position:0%
+the rotation matrix
+just becomes this
+
+ align:start position:0%
+just becomes this
+ 
+
+ align:start position:0%
+just becomes this
+and the matrix part of this
+
+ align:start position:0%
+and the matrix part of this
+ 
+
+ align:start position:0%
+and the matrix part of this
+is very easy to compute you know
+
+ align:start position:0%
+is very easy to compute you know
+ 
+
+ align:start position:0%
+is very easy to compute you know
+multiplication by one doesn't cost us
+
+ align:start position:0%
+multiplication by one doesn't cost us
+ 
+
+ align:start position:0%
+multiplication by one doesn't cost us
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+and this is just a shift and shifts are
+
+ align:start position:0%
+and this is just a shift and shifts are
+ 
+
+ align:start position:0%
+and this is just a shift and shifts are
+extremely cheap
+
+ align:start position:0%
+extremely cheap
+ 
+
+ align:start position:0%
+extremely cheap
+and then we have an addition so it
+
+ align:start position:0%
+and then we have an addition so it
+ 
+
+ align:start position:0%
+and then we have an addition so it
+reduces the whole thing down to two
+
+ align:start position:0%
+reduces the whole thing down to two
+ 
+
+ align:start position:0%
+reduces the whole thing down to two
+additions
+
+ align:start position:0%
+additions
+ 
+
+ align:start position:0%
+additions
+from uh four multiplications and two
+
+ align:start position:0%
+from uh four multiplications and two
+ 
+
+ align:start position:0%
+from uh four multiplications and two
+additions
+
+ align:start position:0%
+additions
+ 
+
+ align:start position:0%
+additions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh well then we have and we do this
+
+ align:start position:0%
+uh well then we have and we do this
+ 
+
+ align:start position:0%
+uh well then we have and we do this
+repeatedly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+and you can see that the angle we're
+
+ align:start position:0%
+and you can see that the angle we're
+ 
+
+ align:start position:0%
+and you can see that the angle we're
+turning through gets smaller and smaller
+
+ align:start position:0%
+turning through gets smaller and smaller
+ 
+
+ align:start position:0%
+turning through gets smaller and smaller
+what what is that angle
+
+ align:start position:0%
+what what is that angle
+ 
+
+ align:start position:0%
+what what is that angle
+let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can compute it from that formula
+
+ align:start position:0%
+we can compute it from that formula
+ 
+
+ align:start position:0%
+we can compute it from that formula
+after a while it basically uh
+
+ align:start position:0%
+after a while it basically uh
+ 
+
+ align:start position:0%
+after a while it basically uh
+gets
+
+ align:start position:0%
+gets
+ 
+
+ align:start position:0%
+gets
+halved
+
+ align:start position:0%
+halved
+ 
+
+ align:start position:0%
+halved
+initially because of the non-linear
+
+ align:start position:0%
+initially because of the non-linear
+ 
+
+ align:start position:0%
+initially because of the non-linear
+nature of trigonometric functions it's
+
+ align:start position:0%
+nature of trigonometric functions it's
+ 
+
+ align:start position:0%
+nature of trigonometric functions it's
+not half but eventually it becomes r and
+
+ align:start position:0%
+not half but eventually it becomes r and
+ 
+
+ align:start position:0%
+not half but eventually it becomes r and
+then uh when you're done you you end up
+
+ align:start position:0%
+then uh when you're done you you end up
+ 
+
+ align:start position:0%
+then uh when you're done you you end up
+over here you end up with a product of
+
+ align:start position:0%
+over here you end up with a product of
+ 
+
+ align:start position:0%
+over here you end up with a product of
+all of these cosine theta i's
+
+ align:start position:0%
+all of these cosine theta i's
+ 
+
+ align:start position:0%
+all of these cosine theta i's
+and so what do you do with that well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe you don't care because it's just a
+
+ align:start position:0%
+maybe you don't care because it's just a
+ 
+
+ align:start position:0%
+maybe you don't care because it's just a
+constant multiplier
+
+ align:start position:0%
+constant multiplier
+ 
+
+ align:start position:0%
+constant multiplier
+but suppose you do care
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can pre-compute it
+
+ align:start position:0%
+you can pre-compute it
+ 
+
+ align:start position:0%
+you can pre-compute it
+and actually
+
+ align:start position:0%
+and actually
+ 
+
+ align:start position:0%
+and actually
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+1.16 very quickly it converges very fast
+
+ align:start position:0%
+1.16 very quickly it converges very fast
+ 
+
+ align:start position:0%
+1.16 very quickly it converges very fast
+so you can just use 1.16
+
+ align:start position:0%
+so you can just use 1.16
+ 
+
+ align:start position:0%
+so you can just use 1.16
+okay so that's the basic idea of chordic
+
+ align:start position:0%
+okay so that's the basic idea of chordic
+ 
+
+ align:start position:0%
+okay so that's the basic idea of chordic
+that we rotate but through special
+
+ align:start position:0%
+that we rotate but through special
+ 
+
+ align:start position:0%
+that we rotate but through special
+angles
+
+ align:start position:0%
+angles
+ 
+
+ align:start position:0%
+angles
+that have this property that were the
+
+ align:start position:0%
+that have this property that were the
+ 
+
+ align:start position:0%
+that have this property that were the
+you know the tangent of theta i is one
+
+ align:start position:0%
+you know the tangent of theta i is one
+ 
+
+ align:start position:0%
+you know the tangent of theta i is one
+over uh two to the i
+
+ align:start position:0%
+over uh two to the i
+ 
+
+ align:start position:0%
+over uh two to the i
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+it takes a bit longer to explain it in
+
+ align:start position:0%
+it takes a bit longer to explain it in
+ 
+
+ align:start position:0%
+it takes a bit longer to explain it in
+the paper but that's the basic idea and
+
+ align:start position:0%
+the paper but that's the basic idea and
+ 
+
+ align:start position:0%
+the paper but that's the basic idea and
+so uh the iterative process is
+
+ align:start position:0%
+so uh the iterative process is
+ 
+
+ align:start position:0%
+so uh the iterative process is
+you um you change through that angle and
+
+ align:start position:0%
+you um you change through that angle and
+ 
+
+ align:start position:0%
+you um you change through that angle and
+if it improves the answer you keep it
+
+ align:start position:0%
+if it improves the answer you keep it
+ 
+
+ align:start position:0%
+if it improves the answer you keep it
+and then you keep track of whether it
+
+ align:start position:0%
+and then you keep track of whether it
+ 
+
+ align:start position:0%
+and then you keep track of whether it
+got negative or not and the first thing
+
+ align:start position:0%
+got negative or not and the first thing
+ 
+
+ align:start position:0%
+got negative or not and the first thing
+you have to do is get it to the
+
+ align:start position:0%
+you have to do is get it to the
+ 
+
+ align:start position:0%
+you have to do is get it to the
+first octant you know the whole idea
+
+ align:start position:0%
+first octant you know the whole idea
+ 
+
+ align:start position:0%
+first octant you know the whole idea
+here is that you're working in this
+
+ align:start position:0%
+here is that you're working in this
+ 
+
+ align:start position:0%
+here is that you're working in this
+regime
+
+ align:start position:0%
+regime
+ 
+
+ align:start position:0%
+regime
+but that's obviously trivial you just
+
+ align:start position:0%
+but that's obviously trivial you just
+ 
+
+ align:start position:0%
+but that's obviously trivial you just
+look at the signs of x and y
+
+ align:start position:0%
+look at the signs of x and y
+ 
+
+ align:start position:0%
+look at the signs of x and y
+and whether
+
+ align:start position:0%
+and whether
+ 
+
+ align:start position:0%
+and whether
+y is greater than x and you can reduce
+
+ align:start position:0%
+y is greater than x and you can reduce
+ 
+
+ align:start position:0%
+y is greater than x and you can reduce
+it to the first auction
+
+ align:start position:0%
+it to the first auction
+ 
+
+ align:start position:0%
+it to the first auction
+okay so next time we'll talk about
+
+ align:start position:0%
+okay so next time we'll talk about
+ 
+
+ align:start position:0%
+okay so next time we'll talk about
+multi-scale
+
+ align:start position:0%
+multi-scale
+ 
+
+ align:start position:0%
+multi-scale
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we'll talk a little bit about
+
+ align:start position:0%
+we'll talk a little bit about
+ 
+
+ align:start position:0%
+we'll talk a little bit about
+sampling and aliasing because
+
+ align:start position:0%
+sampling and aliasing because
+ 
+
+ align:start position:0%
+sampling and aliasing because
+because that's part of the multi-scale
+
+ align:start position:0%
+because that's part of the multi-scale
+ 
+
+ align:start position:0%
+because that's part of the multi-scale
+story so again please start early on the
+
+ align:start position:0%
+story so again please start early on the
+ 
+
+ align:start position:0%
+story so again please start early on the
+quiz it's more work than the typical
+
+ align:start position:0%
+quiz it's more work than the typical
+ 
+
+ align:start position:0%
+quiz it's more work than the typical
+homework problem
\ No newline at end of file
diff --git a/jg7XtfWa_Yg.txt b/jg7XtfWa_Yg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1a8ecd11864903ee1de1639fa0a67443a953dbae
--- /dev/null
+++ b/jg7XtfWa_Yg.txt
@@ -0,0 +1,9323 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a second recitation on
+
+ align:start position:0%
+this is a second recitation on
+ 
+
+ align:start position:0%
+this is a second recitation on
+cholesterol and it's really sort of
+
+ align:start position:0%
+cholesterol and it's really sort of
+ 
+
+ align:start position:0%
+cholesterol and it's really sort of
+focused on this question of how do you
+
+ align:start position:0%
+focused on this question of how do you
+ 
+
+ align:start position:0%
+focused on this question of how do you
+sense cholesterol in a membrane okay so
+
+ align:start position:0%
+sense cholesterol in a membrane okay so
+ 
+
+ align:start position:0%
+sense cholesterol in a membrane okay so
+that's really sort of a tough problem
+
+ align:start position:0%
+that's really sort of a tough problem
+ 
+
+ align:start position:0%
+that's really sort of a tough problem
+and they've developed new tools and
+
+ align:start position:0%
+and they've developed new tools and
+ 
+
+ align:start position:0%
+and they've developed new tools and
+that's what we're gonna be talking about
+
+ align:start position:0%
+that's what we're gonna be talking about
+ 
+
+ align:start position:0%
+that's what we're gonna be talking about
+what the tools are and whether you would
+
+ align:start position:0%
+what the tools are and whether you would
+ 
+
+ align:start position:0%
+what the tools are and whether you would
+think they were adequate to be able to
+
+ align:start position:0%
+think they were adequate to be able to
+ 
+
+ align:start position:0%
+think they were adequate to be able to
+address this question about what kinds
+
+ align:start position:0%
+address this question about what kinds
+ 
+
+ align:start position:0%
+address this question about what kinds
+of changes in concentration of
+
+ align:start position:0%
+of changes in concentration of
+ 
+
+ align:start position:0%
+of changes in concentration of
+cholesterol number one can you measure
+
+ align:start position:0%
+cholesterol number one can you measure
+ 
+
+ align:start position:0%
+cholesterol number one can you measure
+them and number two what effects do they
+
+ align:start position:0%
+them and number two what effects do they
+ 
+
+ align:start position:0%
+them and number two what effects do they
+have in terms of whether you're gonna
+
+ align:start position:0%
+have in terms of whether you're gonna
+ 
+
+ align:start position:0%
+have in terms of whether you're gonna
+turn on cholesterol biosynthesis and
+
+ align:start position:0%
+turn on cholesterol biosynthesis and
+ 
+
+ align:start position:0%
+turn on cholesterol biosynthesis and
+uptake because you need more cholesterol
+
+ align:start position:0%
+uptake because you need more cholesterol
+ 
+
+ align:start position:0%
+uptake because you need more cholesterol
+or you're gonna turn the whole thing
+
+ align:start position:0%
+or you're gonna turn the whole thing
+ 
+
+ align:start position:0%
+or you're gonna turn the whole thing
+okay so we've been focusing as we
+
+ align:start position:0%
+okay so we've been focusing as we
+ 
+
+ align:start position:0%
+okay so we've been focusing as we
+described in the last few lectures in
+
+ align:start position:0%
+described in the last few lectures in
+ 
+
+ align:start position:0%
+described in the last few lectures in
+the endoplasmic reticulum and what would
+
+ align:start position:0%
+the endoplasmic reticulum and what would
+ 
+
+ align:start position:0%
+the endoplasmic reticulum and what would
+the cholesterol chain tweeted the
+
+ align:start position:0%
+the cholesterol chain tweeted the
+ 
+
+ align:start position:0%
+the cholesterol chain tweeted the
+Colossus what kinds of changes in
+
+ align:start position:0%
+Colossus what kinds of changes in
+ 
+
+ align:start position:0%
+Colossus what kinds of changes in
+cholesterol
+
+ align:start position:0%
+cholesterol
+ 
+
+ align:start position:0%
+cholesterol
+did they see in the experiments they
+
+ align:start position:0%
+did they see in the experiments they
+ 
+
+ align:start position:0%
+did they see in the experiments they
+were doing in this paper what would the
+
+ align:start position:0%
+were doing in this paper what would the
+ 
+
+ align:start position:0%
+were doing in this paper what would the
+range of changes that they saw yeah so I
+
+ align:start position:0%
+range of changes that they saw yeah so I
+ 
+
+ align:start position:0%
+range of changes that they saw yeah so I
+don't see so so something low say they
+
+ align:start position:0%
+don't see so so something low say they
+ 
+
+ align:start position:0%
+don't see so so something low say they
+were trying to do this same experiment
+
+ align:start position:0%
+were trying to do this same experiment
+ 
+
+ align:start position:0%
+were trying to do this same experiment
+in the plasma membrane how do we know
+
+ align:start position:0%
+in the plasma membrane how do we know
+ 
+
+ align:start position:0%
+in the plasma membrane how do we know
+it's the ER membrane that does this
+
+ align:start position:0%
+it's the ER membrane that does this
+ 
+
+ align:start position:0%
+it's the ER membrane that does this
+sensing that's what the whole paper is
+
+ align:start position:0%
+sensing that's what the whole paper is
+ 
+
+ align:start position:0%
+sensing that's what the whole paper is
+focused on that's what everything we
+
+ align:start position:0%
+focused on that's what everything we
+ 
+
+ align:start position:0%
+focused on that's what everything we
+focused on in class say you wanted to do
+
+ align:start position:0%
+focused on in class say you wanted to do
+ 
+
+ align:start position:0%
+focused on in class say you wanted to do
+a similar kind of experiment in the
+
+ align:start position:0%
+a similar kind of experiment in the
+ 
+
+ align:start position:0%
+a similar kind of experiment in the
+plasma membrane do you remember what I
+
+ align:start position:0%
+plasma membrane do you remember what I
+ 
+
+ align:start position:0%
+plasma membrane do you remember what I
+said about the levels of cholesterol so
+
+ align:start position:0%
+said about the levels of cholesterol so
+ 
+
+ align:start position:0%
+said about the levels of cholesterol so
+they distributed throughout the cell
+
+ align:start position:0%
+they distributed throughout the cell
+ 
+
+ align:start position:0%
+they distributed throughout the cell
+right in all membranes where is the most
+
+ align:start position:0%
+right in all membranes where is the most
+ 
+
+ align:start position:0%
+right in all membranes where is the most
+cholesterol okay so if you don't
+
+ align:start position:0%
+cholesterol okay so if you don't
+ 
+
+ align:start position:0%
+cholesterol okay so if you don't
+remember it's the plasma membrane okay
+
+ align:start position:0%
+remember it's the plasma membrane okay
+ 
+
+ align:start position:0%
+remember it's the plasma membrane okay
+so say instead of having seven or eight
+
+ align:start position:0%
+so say instead of having seven or eight
+ 
+
+ align:start position:0%
+so say instead of having seven or eight
+percent of the lipids cholesterol say
+
+ align:start position:0%
+percent of the lipids cholesterol say
+ 
+
+ align:start position:0%
+percent of the lipids cholesterol say
+you had forty percent that's an
+
+ align:start position:0%
+you had forty percent that's an
+ 
+
+ align:start position:0%
+you had forty percent that's an
+over-exaggeration do you think this kind
+
+ align:start position:0%
+over-exaggeration do you think this kind
+ 
+
+ align:start position:0%
+over-exaggeration do you think this kind
+of an experiment would be hard to do
+
+ align:start position:0%
+of an experiment would be hard to do
+ 
+
+ align:start position:0%
+of an experiment would be hard to do
+that they've talked about in this paper
+
+ align:start position:0%
+that they've talked about in this paper
+ 
+
+ align:start position:0%
+that they've talked about in this paper
+so you would want to do this if you
+
+ align:start position:0%
+so you would want to do this if you
+ 
+
+ align:start position:0%
+so you would want to do this if you
+tried to do the same experiment with the
+
+ align:start position:0%
+tried to do the same experiment with the
+ 
+
+ align:start position:0%
+tried to do the same experiment with the
+plasma membrane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the key issue that you need to think
+
+ align:start position:0%
+so the key issue that you need to think
+ 
+
+ align:start position:0%
+so the key issue that you need to think
+about is go back and look at the changes
+
+ align:start position:0%
+about is go back and look at the changes
+ 
+
+ align:start position:0%
+about is go back and look at the changes
+you know they they did a whole bunch of
+
+ align:start position:0%
+you know they they did a whole bunch of
+ 
+
+ align:start position:0%
+you know they they did a whole bunch of
+different experiments say sort of I mean
+
+ align:start position:0%
+different experiments say sort of I mean
+ 
+
+ align:start position:0%
+different experiments say sort of I mean
+the numbers of score she but they came
+
+ align:start position:0%
+the numbers of score she but they came
+ 
+
+ align:start position:0%
+the numbers of score she but they came
+up with numbers that sort of reproduce
+
+ align:start position:0%
+up with numbers that sort of reproduce
+ 
+
+ align:start position:0%
+up with numbers that sort of reproduce
+themselves I thought in a sort of an
+
+ align:start position:0%
+themselves I thought in a sort of an
+ 
+
+ align:start position:0%
+themselves I thought in a sort of an
+amazing way but now say you wanted to do
+
+ align:start position:0%
+amazing way but now say you wanted to do
+ 
+
+ align:start position:0%
+amazing way but now say you wanted to do
+this in in the plasma membrane where the
+
+ align:start position:0%
+this in in the plasma membrane where the
+ 
+
+ align:start position:0%
+this in in the plasma membrane where the
+levels of cholesterol are much higher do
+
+ align:start position:0%
+levels of cholesterol are much higher do
+ 
+
+ align:start position:0%
+levels of cholesterol are much higher do
+you think it would be easy to do using
+
+ align:start position:0%
+you think it would be easy to do using
+ 
+
+ align:start position:0%
+you think it would be easy to do using
+the same techniques that are described
+
+ align:start position:0%
+the same techniques that are described
+ 
+
+ align:start position:0%
+the same techniques that are described
+that we're gonna discuss or not and what
+
+ align:start position:0%
+that we're gonna discuss or not and what
+ 
+
+ align:start position:0%
+that we're gonna discuss or not and what
+would the issues be yeah so I don't know
+
+ align:start position:0%
+would the issues be yeah so I don't know
+ 
+
+ align:start position:0%
+would the issues be yeah so I don't know
+so that's an interesting question so
+
+ align:start position:0%
+so that's an interesting question so
+ 
+
+ align:start position:0%
+so that's an interesting question so
+you'd have to deplete so that's gonna be
+
+ align:start position:0%
+you'd have to deplete so that's gonna be
+ 
+
+ align:start position:0%
+you'd have to deplete so that's gonna be
+it we're gonna have to control the less
+
+ align:start position:0%
+it we're gonna have to control the less
+ 
+
+ align:start position:0%
+it we're gonna have to control the less
+cholesterol levels but what change in if
+
+ align:start position:0%
+cholesterol levels but what change in if
+ 
+
+ align:start position:0%
+cholesterol levels but what change in if
+you looked at the changes in levels of
+
+ align:start position:0%
+you looked at the changes in levels of
+ 
+
+ align:start position:0%
+you looked at the changes in levels of
+cholesterol in the ER how much did they
+
+ align:start position:0%
+cholesterol in the ER how much did they
+ 
+
+ align:start position:0%
+cholesterol in the ER how much did they
+change they changed from what to what
+
+ align:start position:0%
+change they changed from what to what
+ 
+
+ align:start position:0%
+change they changed from what to what
+from 2% to 7% okay say that you were
+
+ align:start position:0%
+from 2% to 7% okay say that you were
+ 
+
+ align:start position:0%
+from 2% to 7% okay say that you were
+sort of in that same range of change
+
+ align:start position:0%
+sort of in that same range of change
+ 
+
+ align:start position:0%
+sort of in that same range of change
+that was going to turn on a switch in in
+
+ align:start position:0%
+that was going to turn on a switch in in
+ 
+
+ align:start position:0%
+that was going to turn on a switch in in
+the plasma membrane and say you could
+
+ align:start position:0%
+the plasma membrane and say you could
+ 
+
+ align:start position:0%
+the plasma membrane and say you could
+control the levels do you think it would
+
+ align:start position:0%
+control the levels do you think it would
+ 
+
+ align:start position:0%
+control the levels do you think it would
+be easy to see that so you start with
+
+ align:start position:0%
+be easy to see that so you start with
+ 
+
+ align:start position:0%
+be easy to see that so you start with
+40% say that's sort of the norm say the
+
+ align:start position:0%
+40% say that's sort of the norm say the
+ 
+
+ align:start position:0%
+40% say that's sort of the norm say the
+change was very similar to what you see
+
+ align:start position:0%
+change was very similar to what you see
+ 
+
+ align:start position:0%
+change was very similar to what you see
+in the change in the ER do you think
+
+ align:start position:0%
+in the change in the ER do you think
+ 
+
+ align:start position:0%
+in the change in the ER do you think
+that would be easy to detect no because
+
+ align:start position:0%
+that would be easy to detect no because
+ 
+
+ align:start position:0%
+that would be easy to detect no because
+now you have two big numbers and there's
+
+ align:start position:0%
+now you have two big numbers and there's
+ 
+
+ align:start position:0%
+now you have two big numbers and there's
+a huge amount of error in this method of
+
+ align:start position:0%
+a huge amount of error in this method of
+ 
+
+ align:start position:0%
+a huge amount of error in this method of
+analysis so those are the kinds of
+
+ align:start position:0%
+analysis so those are the kinds of
+ 
+
+ align:start position:0%
+analysis so those are the kinds of
+things I'm trying to get you to think
+
+ align:start position:0%
+things I'm trying to get you to think
+ 
+
+ align:start position:0%
+things I'm trying to get you to think
+about I don't know why it's the ER I
+
+ align:start position:0%
+about I don't know why it's the ER I
+ 
+
+ align:start position:0%
+about I don't know why it's the ER I
+mean everybody's focused on the ER okay
+
+ align:start position:0%
+mean everybody's focused on the ER okay
+ 
+
+ align:start position:0%
+mean everybody's focused on the ER okay
+good cholesterol and other organelles I
+
+ align:start position:0%
+good cholesterol and other organelles I
+ 
+
+ align:start position:0%
+good cholesterol and other organelles I
+have a different regulatory mechanism or
+
+ align:start position:0%
+have a different regulatory mechanism or
+ 
+
+ align:start position:0%
+have a different regulatory mechanism or
+somehow be connected still to what's
+
+ align:start position:0%
+somehow be connected still to what's
+ 
+
+ align:start position:0%
+somehow be connected still to what's
+going on in the air it could be
+
+ align:start position:0%
+going on in the air it could be
+ 
+
+ align:start position:0%
+going on in the air it could be
+I mean we have the simplest you started
+
+ align:start position:0%
+I mean we have the simplest you started
+ 
+
+ align:start position:0%
+I mean we have the simplest you started
+out with the simplest model you can get
+
+ align:start position:0%
+out with the simplest model you can get
+ 
+
+ align:start position:0%
+out with the simplest model you can get
+and you test it but then as you learn
+
+ align:start position:0%
+and you test it but then as you learn
+ 
+
+ align:start position:0%
+and you test it but then as you learn
+more people you know we have more and
+
+ align:start position:0%
+more people you know we have more and
+ 
+
+ align:start position:0%
+more people you know we have more and
+more technology we learn new things you
+
+ align:start position:0%
+more technology we learn new things you
+ 
+
+ align:start position:0%
+more technology we learn new things you
+go back and you revisit and rethink
+
+ align:start position:0%
+go back and you revisit and rethink
+ 
+
+ align:start position:0%
+go back and you revisit and rethink
+about what's going on so the key
+
+ align:start position:0%
+about what's going on so the key
+ 
+
+ align:start position:0%
+about what's going on so the key
+question is it's really sort of this
+
+ align:start position:0%
+question is it's really sort of this
+ 
+
+ align:start position:0%
+question is it's really sort of this
+switch having cholesterol that keeps it
+
+ align:start position:0%
+switch having cholesterol that keeps it
+ 
+
+ align:start position:0%
+switch having cholesterol that keeps it
+in the membrane or not having
+
+ align:start position:0%
+in the membrane or not having
+ 
+
+ align:start position:0%
+in the membrane or not having
+cholesterol and the question is what are
+
+ align:start position:0%
+cholesterol and the question is what are
+ 
+
+ align:start position:0%
+cholesterol and the question is what are
+the differences in the levels that allow
+
+ align:start position:0%
+the differences in the levels that allow
+ 
+
+ align:start position:0%
+the differences in the levels that allow
+turn on of cholesterol biosynthesis and
+
+ align:start position:0%
+turn on of cholesterol biosynthesis and
+ 
+
+ align:start position:0%
+turn on of cholesterol biosynthesis and
+LDL
+
+ align:start position:0%
+LDL
+ 
+
+ align:start position:0%
+LDL
+biosynthesis which then allows uptake of
+
+ align:start position:0%
+biosynthesis which then allows uptake of
+ 
+
+ align:start position:0%
+biosynthesis which then allows uptake of
+cholesterol from the diet okay so that's
+
+ align:start position:0%
+cholesterol from the diet okay so that's
+ 
+
+ align:start position:0%
+cholesterol from the diet okay so that's
+the question and what does this look
+
+ align:start position:0%
+the question and what does this look
+ 
+
+ align:start position:0%
+the question and what does this look
+like if people hadn't measured this by
+
+ align:start position:0%
+like if people hadn't measured this by
+ 
+
+ align:start position:0%
+like if people hadn't measured this by
+any method and I'm this model I've gone
+
+ align:start position:0%
+any method and I'm this model I've gone
+ 
+
+ align:start position:0%
+any method and I'm this model I've gone
+through a number of times in class today
+
+ align:start position:0%
+through a number of times in class today
+ 
+
+ align:start position:0%
+through a number of times in class today
+so I'm not gonna go through it again
+
+ align:start position:0%
+so I'm not gonna go through it again
+ 
+
+ align:start position:0%
+so I'm not gonna go through it again
+hopefully you all know that and some
+
+ align:start position:0%
+hopefully you all know that and some
+ 
+
+ align:start position:0%
+hopefully you all know that and some
+forming a head or you have the picture
+
+ align:start position:0%
+forming a head or you have the picture
+ 
+
+ align:start position:0%
+forming a head or you have the picture
+in front of you so you can remember it
+
+ align:start position:0%
+in front of you so you can remember it
+ 
+
+ align:start position:0%
+in front of you so you can remember it
+so these are the questions I want to
+
+ align:start position:0%
+so these are the questions I want to
+ 
+
+ align:start position:0%
+so these are the questions I want to
+pose and I want you guys to do the
+
+ align:start position:0%
+pose and I want you guys to do the
+ 
+
+ align:start position:0%
+pose and I want you guys to do the
+talking today okay and what I'm gonna do
+
+ align:start position:0%
+talking today okay and what I'm gonna do
+ 
+
+ align:start position:0%
+talking today okay and what I'm gonna do
+is I have most of the figures on on my
+
+ align:start position:0%
+is I have most of the figures on on my
+ 
+
+ align:start position:0%
+is I have most of the figures on on my
+PowerPoint so we can bring them up and
+
+ align:start position:0%
+PowerPoint so we can bring them up and
+ 
+
+ align:start position:0%
+PowerPoint so we can bring them up and
+look at them and you can tell me what
+
+ align:start position:0%
+look at them and you can tell me what
+ 
+
+ align:start position:0%
+look at them and you can tell me what
+you see
+
+ align:start position:0%
+you see
+ 
+
+ align:start position:0%
+you see
+and then other every everybody might be
+
+ align:start position:0%
+and then other every everybody might be
+ 
+
+ align:start position:0%
+and then other every everybody might be
+seeing something different
+
+ align:start position:0%
+seeing something different
+ 
+
+ align:start position:0%
+seeing something different
+and so we're thinking about this
+
+ align:start position:0%
+and so we're thinking about this
+ 
+
+ align:start position:0%
+and so we're thinking about this
+differently and maybe we come to some
+
+ align:start position:0%
+differently and maybe we come to some
+ 
+
+ align:start position:0%
+differently and maybe we come to some
+kind of consensus about whether these
+
+ align:start position:0%
+kind of consensus about whether these
+ 
+
+ align:start position:0%
+kind of consensus about whether these
+experiments were carried out well or not
+
+ align:start position:0%
+experiments were carried out well or not
+ 
+
+ align:start position:0%
+experiments were carried out well or not
+so so one of the first things so these
+
+ align:start position:0%
+so so one of the first things so these
+ 
+
+ align:start position:0%
+so so one of the first things so these
+are the sort of be the general things
+
+ align:start position:0%
+are the sort of be the general things
+ 
+
+ align:start position:0%
+are the sort of be the general things
+and then we'll step through them but
+
+ align:start position:0%
+and then we'll step through them but
+ 
+
+ align:start position:0%
+and then we'll step through them but
+they wanted to perturb the cellular
+
+ align:start position:0%
+they wanted to perturb the cellular
+ 
+
+ align:start position:0%
+they wanted to perturb the cellular
+cholesterol levels and how did they end
+
+ align:start position:0%
+cholesterol levels and how did they end
+ 
+
+ align:start position:0%
+cholesterol levels and how did they end
+up doing that did that did that make
+
+ align:start position:0%
+up doing that did that did that make
+ 
+
+ align:start position:0%
+up doing that did that did that make
+sense we talked a little bit about this
+
+ align:start position:0%
+sense we talked a little bit about this
+ 
+
+ align:start position:0%
+sense we talked a little bit about this
+already I mean what did they use as
+
+ align:start position:0%
+already I mean what did they use as
+ 
+
+ align:start position:0%
+already I mean what did they use as
+tools to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you need to speak louder because I
+
+ align:start position:0%
+so you need to speak louder because I
+ 
+
+ align:start position:0%
+so you need to speak louder because I
+really am deaf sorry so that's one place
+
+ align:start position:0%
+really am deaf sorry so that's one place
+ 
+
+ align:start position:0%
+really am deaf sorry so that's one place
+so they can deplete cholesterol for the
+
+ align:start position:0%
+so they can deplete cholesterol for the
+ 
+
+ align:start position:0%
+so they can deplete cholesterol for the
+media but then where do they do so the
+
+ align:start position:0%
+media but then where do they do so the
+ 
+
+ align:start position:0%
+media but then where do they do so the
+whole paper is sort of about this how
+
+ align:start position:0%
+whole paper is sort of about this how
+ 
+
+ align:start position:0%
+whole paper is sort of about this how
+did they control the so weights let's
+
+ align:start position:0%
+did they control the so weights let's
+ 
+
+ align:start position:0%
+did they control the so weights let's
+assume that they can do that and that's
+
+ align:start position:0%
+assume that they can do that and that's
+ 
+
+ align:start position:0%
+assume that they can do that and that's
+you know they got good at that I think a
+
+ align:start position:0%
+you know they got good at that I think a
+ 
+
+ align:start position:0%
+you know they got good at that I think a
+lot of people have used that method and
+
+ align:start position:0%
+lot of people have used that method and
+ 
+
+ align:start position:0%
+lot of people have used that method and
+so they can deplete media so why do they
+
+ align:start position:0%
+so they can deplete media so why do they
+ 
+
+ align:start position:0%
+so they can deplete media so why do they
+hide it how did they deplete cholesterol
+
+ align:start position:0%
+hide it how did they deplete cholesterol
+ 
+
+ align:start position:0%
+hide it how did they deplete cholesterol
+there were some unusual ways to deplete
+
+ align:start position:0%
+there were some unusual ways to deplete
+ 
+
+ align:start position:0%
+there were some unusual ways to deplete
+cholesterol in this paper did any of you
+
+ align:start position:0%
+cholesterol in this paper did any of you
+ 
+
+ align:start position:0%
+cholesterol in this paper did any of you
+pick up on that great
+
+ align:start position:0%
+pick up on that great
+ 
+
+ align:start position:0%
+pick up on that great
+so just what did you think that was
+
+ align:start position:0%
+so just what did you think that was
+ 
+
+ align:start position:0%
+so just what did you think that was
+unusual did any of you look up what that
+
+ align:start position:0%
+unusual did any of you look up what that
+ 
+
+ align:start position:0%
+unusual did any of you look up what that
+was yeah so but but what was interesting
+
+ align:start position:0%
+was yeah so but but what was interesting
+ 
+
+ align:start position:0%
+was yeah so but but what was interesting
+about it it was you know hydroxypropyl
+
+ align:start position:0%
+about it it was you know hydroxypropyl
+ 
+
+ align:start position:0%
+about it it was you know hydroxypropyl
+remember HP cyclodextrin okay we're
+
+ align:start position:0%
+remember HP cyclodextrin okay we're
+ 
+
+ align:start position:0%
+remember HP cyclodextrin okay we're
+gonna we're gonna look at this a minute
+
+ align:start position:0%
+gonna we're gonna look at this a minute
+ 
+
+ align:start position:0%
+gonna we're gonna look at this a minute
+but what do we know what was the other
+
+ align:start position:0%
+but what do we know what was the other
+ 
+
+ align:start position:0%
+but what do we know what was the other
+molecule they used to add cholesterol
+
+ align:start position:0%
+molecule they used to add cholesterol
+ 
+
+ align:start position:0%
+molecule they used to add cholesterol
+back right so methyl it's like low
+
+ align:start position:0%
+back right so methyl it's like low
+ 
+
+ align:start position:0%
+back right so methyl it's like low
+dexter i'm going to show you the
+
+ align:start position:0%
+dexter i'm going to show you the
+ 
+
+ align:start position:0%
+dexter i'm going to show you the
+structure but they aren't very different
+
+ align:start position:0%
+structure but they aren't very different
+ 
+
+ align:start position:0%
+structure but they aren't very different
+so I mean did any of any of you ever
+
+ align:start position:0%
+so I mean did any of any of you ever
+ 
+
+ align:start position:0%
+so I mean did any of any of you ever
+heard of cyclodextrins Igor
+
+ align:start position:0%
+heard of cyclodextrins Igor
+ 
+
+ align:start position:0%
+heard of cyclodextrins Igor
+I mean people won the Nobel Prize for
+
+ align:start position:0%
+I mean people won the Nobel Prize for
+ 
+
+ align:start position:0%
+I mean people won the Nobel Prize for
+that don't want it Breslow spent his
+
+ align:start position:0%
+that don't want it Breslow spent his
+ 
+
+ align:start position:0%
+that don't want it Breslow spent his
+whole life studying host-guest
+
+ align:start position:0%
+whole life studying host-guest
+ 
+
+ align:start position:0%
+whole life studying host-guest
+interactions so I mean you guys I don't
+
+ align:start position:0%
+interactions so I mean you guys I don't
+ 
+
+ align:start position:0%
+interactions so I mean you guys I don't
+know what you they teach you it now
+
+ align:start position:0%
+know what you they teach you it now
+ 
+
+ align:start position:0%
+know what you they teach you it now
+anymore but I mean they that used to be
+
+ align:start position:0%
+anymore but I mean they that used to be
+ 
+
+ align:start position:0%
+anymore but I mean they that used to be
+something that was taught a lot
+
+ align:start position:0%
+something that was taught a lot
+ 
+
+ align:start position:0%
+something that was taught a lot
+host-guest interactions trying to
+
+ align:start position:0%
+host-guest interactions trying to
+ 
+
+ align:start position:0%
+host-guest interactions trying to
+understand weak non covalent
+
+ align:start position:0%
+understand weak non covalent
+ 
+
+ align:start position:0%
+understand weak non covalent
+interactions is the basis for
+
+ align:start position:0%
+interactions is the basis for
+ 
+
+ align:start position:0%
+interactions is the basis for
+understanding catalysis but to me that
+
+ align:start position:0%
+understanding catalysis but to me that
+ 
+
+ align:start position:0%
+understanding catalysis but to me that
+was one immediately when I saw this and
+
+ align:start position:0%
+was one immediately when I saw this and
+ 
+
+ align:start position:0%
+was one immediately when I saw this and
+what the heck's going on so then I
+
+ align:start position:0%
+what the heck's going on so then I
+ 
+
+ align:start position:0%
+what the heck's going on so then I
+googled it and you know immediately you
+
+ align:start position:0%
+googled it and you know immediately you
+ 
+
+ align:start position:0%
+googled it and you know immediately you
+know I don't know anything about
+
+ align:start position:0%
+know I don't know anything about
+ 
+
+ align:start position:0%
+know I don't know anything about
+hydroxypropyl you'll google it you look
+
+ align:start position:0%
+hydroxypropyl you'll google it you look
+ 
+
+ align:start position:0%
+hydroxypropyl you'll google it you look
+it up and then you look at it and you
+
+ align:start position:0%
+it up and then you look at it and you
+ 
+
+ align:start position:0%
+it up and then you look at it and you
+know if you were a chemist and you were
+
+ align:start position:0%
+know if you were a chemist and you were
+ 
+
+ align:start position:0%
+know if you were a chemist and you were
+really really interested in the molecule
+
+ align:start position:0%
+really really interested in the molecule
+ 
+
+ align:start position:0%
+really really interested in the molecule
+interactions you might make a model of
+
+ align:start position:0%
+interactions you might make a model of
+ 
+
+ align:start position:0%
+interactions you might make a model of
+it and then see if you could you know
+
+ align:start position:0%
+it and then see if you could you know
+ 
+
+ align:start position:0%
+it and then see if you could you know
+what is the difference between that one
+
+ align:start position:0%
+what is the difference between that one
+ 
+
+ align:start position:0%
+what is the difference between that one
+little group when you look at the
+
+ align:start position:0%
+little group when you look at the
+ 
+
+ align:start position:0%
+little group when you look at the
+structure it's sort of amazing and
+
+ align:start position:0%
+structure it's sort of amazing and
+ 
+
+ align:start position:0%
+structure it's sort of amazing and
+that's like the basis
+
+ align:start position:0%
+that's like the basis
+ 
+
+ align:start position:0%
+that's like the basis
+of most of the experiments so you need
+
+ align:start position:0%
+of most of the experiments so you need
+ 
+
+ align:start position:0%
+of most of the experiments so you need
+to believe that they figured that out
+
+ align:start position:0%
+to believe that they figured that out
+ 
+
+ align:start position:0%
+to believe that they figured that out
+okay and that's not in this paper so if
+
+ align:start position:0%
+okay and that's not in this paper so if
+ 
+
+ align:start position:0%
+okay and that's not in this paper so if
+you really cared about it you would have
+
+ align:start position:0%
+you really cared about it you would have
+ 
+
+ align:start position:0%
+you really cared about it you would have
+to go back and read orally or papers and
+
+ align:start position:0%
+to go back and read orally or papers and
+ 
+
+ align:start position:0%
+to go back and read orally or papers and
+see what are the experiments that led
+
+ align:start position:0%
+see what are the experiments that led
+ 
+
+ align:start position:0%
+see what are the experiments that led
+them to focus on these molecules how
+
+ align:start position:0%
+them to focus on these molecules how
+ 
+
+ align:start position:0%
+them to focus on these molecules how
+else did they end up getting cholesterol
+
+ align:start position:0%
+else did they end up getting cholesterol
+ 
+
+ align:start position:0%
+else did they end up getting cholesterol
+levels back into the cell do you
+
+ align:start position:0%
+levels back into the cell do you
+ 
+
+ align:start position:0%
+levels back into the cell do you
+remember what the other method was so
+
+ align:start position:0%
+remember what the other method was so
+ 
+
+ align:start position:0%
+remember what the other method was so
+we'll come back and we'll talk about
+
+ align:start position:0%
+we'll come back and we'll talk about
+ 
+
+ align:start position:0%
+we'll come back and we'll talk about
+this in a minute so that was one of the
+
+ align:start position:0%
+this in a minute so that was one of the
+ 
+
+ align:start position:0%
+this in a minute so that was one of the
+methods okay so they did add two kind of
+
+ align:start position:0%
+methods okay so they did add two kind of
+ 
+
+ align:start position:0%
+methods okay so they did add two kind of
+sterols and they trying to figure out
+
+ align:start position:0%
+sterols and they trying to figure out
+ 
+
+ align:start position:0%
+sterols and they trying to figure out
+this is sort of another unknown what was
+
+ align:start position:0%
+this is sort of another unknown what was
+ 
+
+ align:start position:0%
+this is sort of another unknown what was
+the difference between the sterols
+
+ align:start position:0%
+the difference between the sterols
+ 
+
+ align:start position:0%
+the difference between the sterols
+simply a hydroxyl group okay say you had
+
+ align:start position:0%
+simply a hydroxyl group okay say you had
+ 
+
+ align:start position:0%
+simply a hydroxyl group okay say you had
+if you looked at this cholesterol was
+
+ align:start position:0%
+if you looked at this cholesterol was
+ 
+
+ align:start position:0%
+if you looked at this cholesterol was
+this guy okay and then they had
+
+ align:start position:0%
+this guy okay and then they had
+ 
+
+ align:start position:0%
+this guy okay and then they had
+something like this guy twenty five I
+
+ align:start position:0%
+something like this guy twenty five I
+ 
+
+ align:start position:0%
+something like this guy twenty five I
+don't remember where is this on the side
+
+ align:start position:0%
+don't remember where is this on the side
+ 
+
+ align:start position:0%
+don't remember where is this on the side
+chains hanging out of the little cheer
+
+ align:start position:0%
+chains hanging out of the little cheer
+ 
+
+ align:start position:0%
+chains hanging out of the little cheer
+this system you have I don't think they
+
+ align:start position:0%
+this system you have I don't think they
+ 
+
+ align:start position:0%
+this system you have I don't think they
+learned very much from that and in fact
+
+ align:start position:0%
+learned very much from that and in fact
+ 
+
+ align:start position:0%
+learned very much from that and in fact
+on your problem set you had all of these
+
+ align:start position:0%
+on your problem set you had all of these
+ 
+
+ align:start position:0%
+on your problem set you had all of these
+different cholesterol analogues I mean I
+
+ align:start position:0%
+different cholesterol analogues I mean I
+ 
+
+ align:start position:0%
+different cholesterol analogues I mean I
+think we still really don't get it I
+
+ align:start position:0%
+think we still really don't get it I
+ 
+
+ align:start position:0%
+think we still really don't get it I
+mean that's complicated we talked about
+
+ align:start position:0%
+mean that's complicated we talked about
+ 
+
+ align:start position:0%
+mean that's complicated we talked about
+this in class you have these
+
+ align:start position:0%
+this in class you have these
+ 
+
+ align:start position:0%
+this in class you have these
+transmembrane helix ease what is it
+
+ align:start position:0%
+transmembrane helix ease what is it
+ 
+
+ align:start position:0%
+transmembrane helix ease what is it
+that's actually the signaling agent so
+
+ align:start position:0%
+that's actually the signaling agent so
+ 
+
+ align:start position:0%
+that's actually the signaling agent so
+people are still asking that questions
+
+ align:start position:0%
+people are still asking that questions
+ 
+
+ align:start position:0%
+people are still asking that questions
+and and we haven't quite gotten that far
+
+ align:start position:0%
+and and we haven't quite gotten that far
+ 
+
+ align:start position:0%
+and and we haven't quite gotten that far
+but if you you've read the reading for
+
+ align:start position:0%
+but if you you've read the reading for
+ 
+
+ align:start position:0%
+but if you you've read the reading for
+HMG co-reductase degradation which is
+
+ align:start position:0%
+HMG co-reductase degradation which is
+ 
+
+ align:start position:0%
+HMG co-reductase degradation which is
+what we're going to be talking about in
+
+ align:start position:0%
+what we're going to be talking about in
+ 
+
+ align:start position:0%
+what we're going to be talking about in
+class the signal or is not the steroid
+
+ align:start position:0%
+class the signal or is not the steroid
+ 
+
+ align:start position:0%
+class the signal or is not the steroid
+the sterile it's someone Ostroff okay
+
+ align:start position:0%
+the sterile it's someone Ostroff okay
+ 
+
+ align:start position:0%
+the sterile it's someone Ostroff okay
+now we have you seen one nostril the
+
+ align:start position:0%
+now we have you seen one nostril the
+ 
+
+ align:start position:0%
+now we have you seen one nostril the
+biosynthetic pathway sort of has one
+
+ align:start position:0%
+biosynthetic pathway sort of has one
+ 
+
+ align:start position:0%
+biosynthetic pathway sort of has one
+Oster all sitting in the middle it's not
+
+ align:start position:0%
+Oster all sitting in the middle it's not
+ 
+
+ align:start position:0%
+Oster all sitting in the middle it's not
+all that different structurally from
+
+ align:start position:0%
+all that different structurally from
+ 
+
+ align:start position:0%
+all that different structurally from
+cholesterol you need to go back in it's
+
+ align:start position:0%
+cholesterol you need to go back in it's
+ 
+
+ align:start position:0%
+cholesterol you need to go back in it's
+got fork they all have they both have
+
+ align:start position:0%
+got fork they all have they both have
+ 
+
+ align:start position:0%
+got fork they all have they both have
+four membered rings they have different
+
+ align:start position:0%
+four membered rings they have different
+ 
+
+ align:start position:0%
+four membered rings they have different
+extra methyl groups so people are trying
+
+ align:start position:0%
+extra methyl groups so people are trying
+ 
+
+ align:start position:0%
+extra methyl groups so people are trying
+to sort of sort that out I don't think
+
+ align:start position:0%
+to sort of sort that out I don't think
+ 
+
+ align:start position:0%
+to sort of sort that out I don't think
+we really know but how well so they had
+
+ align:start position:0%
+we really know but how well so they had
+ 
+
+ align:start position:0%
+we really know but how well so they had
+so you're right they use sterols
+
+ align:start position:0%
+so you're right they use sterols
+ 
+
+ align:start position:0%
+so you're right they use sterols
+they didn't use that they didn't see
+
+ align:start position:0%
+they didn't use that they didn't see
+ 
+
+ align:start position:0%
+they didn't use that they didn't see
+very much difference with the Searles
+
+ align:start position:0%
+very much difference with the Searles
+ 
+
+ align:start position:0%
+very much difference with the Searles
+what was the other way which is sort of
+
+ align:start position:0%
+what was the other way which is sort of
+ 
+
+ align:start position:0%
+what was the other way which is sort of
+unusual that they added cholesterol back
+
+ align:start position:0%
+unusual that they added cholesterol back
+ 
+
+ align:start position:0%
+unusual that they added cholesterol back
+into this system so they could add it
+
+ align:start position:0%
+into this system so they could add it
+ 
+
+ align:start position:0%
+into this system so they could add it
+back with the methyl cyclodextrin they
+
+ align:start position:0%
+back with the methyl cyclodextrin they
+ 
+
+ align:start position:0%
+back with the methyl cyclodextrin they
+told you that that worked and if you
+
+ align:start position:0%
+told you that that worked and if you
+ 
+
+ align:start position:0%
+told you that that worked and if you
+believe that then and you look at the
+
+ align:start position:0%
+believe that then and you look at the
+ 
+
+ align:start position:0%
+believe that then and you look at the
+data it looked like that was happening
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nobody remembers okay well we'll get to
+
+ align:start position:0%
+nobody remembers okay well we'll get to
+ 
+
+ align:start position:0%
+nobody remembers okay well we'll get to
+that in a little bit okay so the
+
+ align:start position:0%
+that in a little bit okay so the
+ 
+
+ align:start position:0%
+that in a little bit okay so the
+question we're focusing on is what are
+
+ align:start position:0%
+question we're focusing on is what are
+ 
+
+ align:start position:0%
+question we're focusing on is what are
+the changes in concentrations of
+
+ align:start position:0%
+the changes in concentrations of
+ 
+
+ align:start position:0%
+the changes in concentrations of
+cholesterol in the ER okay so what
+
+ align:start position:0%
+cholesterol in the ER okay so what
+ 
+
+ align:start position:0%
+cholesterol in the ER okay so what
+method did they use to try to separate
+
+ align:start position:0%
+method did they use to try to separate
+ 
+
+ align:start position:0%
+method did they use to try to separate
+the ER membranes from all the other
+
+ align:start position:0%
+the ER membranes from all the other
+ 
+
+ align:start position:0%
+the ER membranes from all the other
+membranes they didn't separated the what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so that's good you can separate out
+
+ align:start position:0%
+a so that's good you can separate out
+ 
+
+ align:start position:0%
+a so that's good you can separate out
+the nucleus and you could do that by
+
+ align:start position:0%
+the nucleus and you could do that by
+ 
+
+ align:start position:0%
+the nucleus and you could do that by
+ultracentrifugation we've seen that used
+
+ align:start position:0%
+ultracentrifugation we've seen that used
+ 
+
+ align:start position:0%
+ultracentrifugation we've seen that used
+a number different kinds of
+
+ align:start position:0%
+a number different kinds of
+ 
+
+ align:start position:0%
+a number different kinds of
+ultracentrifugation we've seen the
+
+ align:start position:0%
+ultracentrifugation we've seen the
+ 
+
+ align:start position:0%
+ultracentrifugation we've seen the
+different particles that so lipoproteins
+
+ align:start position:0%
+different particles that so lipoproteins
+ 
+
+ align:start position:0%
+different particles that so lipoproteins
+in the diet how did how do we separate
+
+ align:start position:0%
+in the diet how did how do we separate
+ 
+
+ align:start position:0%
+in the diet how did how do we separate
+those we talked about that class briefly
+
+ align:start position:0%
+those we talked about that class briefly
+ 
+
+ align:start position:0%
+those we talked about that class briefly
+we did we have you haven't had any
+
+ align:start position:0%
+we did we have you haven't had any
+ 
+
+ align:start position:0%
+we did we have you haven't had any
+papers to read but what was some method
+
+ align:start position:0%
+papers to read but what was some method
+ 
+
+ align:start position:0%
+papers to read but what was some method
+of separation if you look at all those
+
+ align:start position:0%
+of separation if you look at all those
+ 
+
+ align:start position:0%
+of separation if you look at all those
+particles remember we had a little
+
+ align:start position:0%
+particles remember we had a little
+ 
+
+ align:start position:0%
+particles remember we had a little
+cartoon of all the particles and we
+
+ align:start position:0%
+cartoon of all the particles and we
+ 
+
+ align:start position:0%
+cartoon of all the particles and we
+focused on LDL which is the particle
+
+ align:start position:0%
+focused on LDL which is the particle
+ 
+
+ align:start position:0%
+focused on LDL which is the particle
+that has the most cholesterol so that's
+
+ align:start position:0%
+that has the most cholesterol so that's
+ 
+
+ align:start position:0%
+that has the most cholesterol so that's
+where everybody's focusing on that what
+
+ align:start position:0%
+where everybody's focusing on that what
+ 
+
+ align:start position:0%
+where everybody's focusing on that what
+was the basis of the separation whistle
+
+ align:start position:0%
+was the basis of the separation whistle
+ 
+
+ align:start position:0%
+was the basis of the separation whistle
+what you need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah ultracentrifugation but what was it
+
+ align:start position:0%
+yeah ultracentrifugation but what was it
+ 
+
+ align:start position:0%
+yeah ultracentrifugation but what was it
+how did okay yeah okay so they have
+
+ align:start position:0%
+how did okay yeah okay so they have
+ 
+
+ align:start position:0%
+how did okay yeah okay so they have
+different density gradients okay and so
+
+ align:start position:0%
+different density gradients okay and so
+ 
+
+ align:start position:0%
+different density gradients okay and so
+that's going to be a key thing and
+
+ align:start position:0%
+that's going to be a key thing and
+ 
+
+ align:start position:0%
+that's going to be a key thing and
+that's because if you look at the
+
+ align:start position:0%
+that's because if you look at the
+ 
+
+ align:start position:0%
+that's because if you look at the
+composition and they have different
+
+ align:start position:0%
+composition and they have different
+ 
+
+ align:start position:0%
+composition and they have different
+amounts of proteins different amounts of
+
+ align:start position:0%
+amounts of proteins different amounts of
+ 
+
+ align:start position:0%
+amounts of proteins different amounts of
+fats and they have different they float
+
+ align:start position:0%
+fats and they have different they float
+ 
+
+ align:start position:0%
+fats and they have different they float
+differently so that's the method that
+
+ align:start position:0%
+differently so that's the method that
+ 
+
+ align:start position:0%
+differently so that's the method that
+they're gonna use here is that a good
+
+ align:start position:0%
+they're gonna use here is that a good
+ 
+
+ align:start position:0%
+they're gonna use here is that a good
+method can you think of a better method
+
+ align:start position:0%
+method can you think of a better method
+ 
+
+ align:start position:0%
+method can you think of a better method
+so in order to sort of understand the
+
+ align:start position:0%
+so in order to sort of understand the
+ 
+
+ align:start position:0%
+so in order to sort of understand the
+switch for cholesterol you got to be
+
+ align:start position:0%
+switch for cholesterol you got to be
+ 
+
+ align:start position:0%
+switch for cholesterol you got to be
+able to measure the changes in
+
+ align:start position:0%
+able to measure the changes in
+ 
+
+ align:start position:0%
+able to measure the changes in
+cholesterol right not an easy problem
+
+ align:start position:0%
+cholesterol right not an easy problem
+ 
+
+ align:start position:0%
+cholesterol right not an easy problem
+because cholesterol is really insoluble
+
+ align:start position:0%
+because cholesterol is really insoluble
+ 
+
+ align:start position:0%
+because cholesterol is really insoluble
+in everything okay and so how much is
+
+ align:start position:0%
+in everything okay and so how much is
+ 
+
+ align:start position:0%
+in everything okay and so how much is
+really in there and how does it change
+
+ align:start position:0%
+really in there and how does it change
+ 
+
+ align:start position:0%
+really in there and how does it change
+under different sets of conditions so is
+
+ align:start position:0%
+under different sets of conditions so is
+ 
+
+ align:start position:0%
+under different sets of conditions so is
+this a good method what do you think
+
+ align:start position:0%
+this a good method what do you think
+ 
+
+ align:start position:0%
+this a good method what do you think
+we'll look at the the method and a
+
+ align:start position:0%
+we'll look at the the method and a
+ 
+
+ align:start position:0%
+we'll look at the the method and a
+little more detail woman when I pull up
+
+ align:start position:0%
+little more detail woman when I pull up
+ 
+
+ align:start position:0%
+little more detail woman when I pull up
+the figures but what did you think when
+
+ align:start position:0%
+the figures but what did you think when
+ 
+
+ align:start position:0%
+the figures but what did you think when
+you read the when you read the paper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so so the question is you know you
+
+ align:start position:0%
+yeah so so the question is you know you
+ 
+
+ align:start position:0%
+yeah so so the question is you know you
+could you separate I mean even
+
+ align:start position:0%
+could you separate I mean even
+ 
+
+ align:start position:0%
+could you separate I mean even
+separating the nucleus from the cytosol
+
+ align:start position:0%
+separating the nucleus from the cytosol
+ 
+
+ align:start position:0%
+separating the nucleus from the cytosol
+it's not so trivial okay by these
+
+ align:start position:0%
+it's not so trivial okay by these
+ 
+
+ align:start position:0%
+it's not so trivial okay by these
+methods and really gross methods and
+
+ align:start position:0%
+methods and really gross methods and
+ 
+
+ align:start position:0%
+methods and really gross methods and
+during the centrifugation things diffuse
+
+ align:start position:0%
+during the centrifugation things diffuse
+ 
+
+ align:start position:0%
+during the centrifugation things diffuse
+you know so if you ever enclosed
+
+ align:start position:0%
+you know so if you ever enclosed
+ 
+
+ align:start position:0%
+you know so if you ever enclosed
+separations its equilibrate again so
+
+ align:start position:0%
+separations its equilibrate again so
+ 
+
+ align:start position:0%
+separations its equilibrate again so
+you're getting your proteins or your
+
+ align:start position:0%
+you're getting your proteins or your
+ 
+
+ align:start position:0%
+you're getting your proteins or your
+lipids are spreading out is there
+
+ align:start position:0%
+lipids are spreading out is there
+ 
+
+ align:start position:0%
+lipids are spreading out is there
+anything else any of you experience with
+
+ align:start position:0%
+anything else any of you experience with
+ 
+
+ align:start position:0%
+anything else any of you experience with
+insoluble I mean this is where you we're
+
+ align:start position:0%
+insoluble I mean this is where you we're
+ 
+
+ align:start position:0%
+insoluble I mean this is where you we're
+dealing with it's an insoluble mess and
+
+ align:start position:0%
+dealing with it's an insoluble mess and
+ 
+
+ align:start position:0%
+dealing with it's an insoluble mess and
+how do you how do you separate things in
+
+ align:start position:0%
+how do you how do you separate things in
+ 
+
+ align:start position:0%
+how do you how do you separate things in
+a way that you have control over it so
+
+ align:start position:0%
+a way that you have control over it so
+ 
+
+ align:start position:0%
+a way that you have control over it so
+that you can address the key questions
+
+ align:start position:0%
+that you can address the key questions
+ 
+
+ align:start position:0%
+that you can address the key questions
+in this paper nobody nobody thought
+
+ align:start position:0%
+in this paper nobody nobody thought
+ 
+
+ align:start position:0%
+in this paper nobody nobody thought
+about anything else you did you like
+
+ align:start position:0%
+about anything else you did you like
+ 
+
+ align:start position:0%
+about anything else you did you like
+this method we convinced by the data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so so so that's an incredibly
+
+ align:start position:0%
+yeah so so so that's an incredibly
+ 
+
+ align:start position:0%
+yeah so so so that's an incredibly
+important question because lipids
+
+ align:start position:0%
+important question because lipids
+ 
+
+ align:start position:0%
+important question because lipids
+confused
+
+ align:start position:0%
+confused
+ 
+
+ align:start position:0%
+confused
+you know they could mix the question is
+
+ align:start position:0%
+you know they could mix the question is
+ 
+
+ align:start position:0%
+you know they could mix the question is
+one of the rate constants for all of
+
+ align:start position:0%
+one of the rate constants for all of
+ 
+
+ align:start position:0%
+one of the rate constants for all of
+that and we don't really teach very much
+
+ align:start position:0%
+that and we don't really teach very much
+ 
+
+ align:start position:0%
+that and we don't really teach very much
+in the introductory courses about lipids
+
+ align:start position:0%
+in the introductory courses about lipids
+ 
+
+ align:start position:0%
+in the introductory courses about lipids
+and their partitioning between other
+
+ align:start position:0%
+and their partitioning between other
+ 
+
+ align:start position:0%
+and their partitioning between other
+membranes and fusion and all that stuff
+
+ align:start position:0%
+membranes and fusion and all that stuff
+ 
+
+ align:start position:0%
+membranes and fusion and all that stuff
+but if you think about it that's what
+
+ align:start position:0%
+but if you think about it that's what
+ 
+
+ align:start position:0%
+but if you think about it that's what
+the cell is right you get a plasma
+
+ align:start position:0%
+the cell is right you get a plasma
+ 
+
+ align:start position:0%
+the cell is right you get a plasma
+membrane and all these membranes around
+
+ align:start position:0%
+membrane and all these membranes around
+ 
+
+ align:start position:0%
+membrane and all these membranes around
+all these little organelles that's sort
+
+ align:start position:0%
+all these little organelles that's sort
+ 
+
+ align:start position:0%
+all these little organelles that's sort
+of an amazing observation and we've seen
+
+ align:start position:0%
+of an amazing observation and we've seen
+ 
+
+ align:start position:0%
+of an amazing observation and we've seen
+in class already what have we seen to
+
+ align:start position:0%
+in class already what have we seen to
+ 
+
+ align:start position:0%
+in class already what have we seen to
+get an LDL receptor from here to the
+
+ align:start position:0%
+get an LDL receptor from here to the
+ 
+
+ align:start position:0%
+get an LDL receptor from here to the
+plasma membrane how do we have to do
+
+ align:start position:0%
+plasma membrane how do we have to do
+ 
+
+ align:start position:0%
+plasma membrane how do we have to do
+that we had to use these little vesicles
+
+ align:start position:0%
+that we had to use these little vesicles
+ 
+
+ align:start position:0%
+that we had to use these little vesicles
+right so you're you're generating
+
+ align:start position:0%
+right so you're you're generating
+ 
+
+ align:start position:0%
+right so you're you're generating
+something over here it goes through the
+
+ align:start position:0%
+something over here it goes through the
+ 
+
+ align:start position:0%
+something over here it goes through the
+golgi stack again another set of
+
+ align:start position:0%
+golgi stack again another set of
+ 
+
+ align:start position:0%
+golgi stack again another set of
+membranes it's got to come out the
+
+ align:start position:0%
+membranes it's got to come out the
+ 
+
+ align:start position:0%
+membranes it's got to come out the
+different levels of the golgi stack and
+
+ align:start position:0%
+different levels of the golgi stack and
+ 
+
+ align:start position:0%
+different levels of the golgi stack and
+then it's still gotta get into the
+
+ align:start position:0%
+then it's still gotta get into the
+ 
+
+ align:start position:0%
+then it's still gotta get into the
+plasma membrane infused and dump its
+
+ align:start position:0%
+plasma membrane infused and dump its
+ 
+
+ align:start position:0%
+plasma membrane infused and dump its
+cargo so I think it's sort of an amazing
+
+ align:start position:0%
+cargo so I think it's sort of an amazing
+ 
+
+ align:start position:0%
+cargo so I think it's sort of an amazing
+process and people interested in
+
+ align:start position:0%
+process and people interested in
+ 
+
+ align:start position:0%
+process and people interested in
+evolution this is one of the major
+
+ align:start position:0%
+evolution this is one of the major
+ 
+
+ align:start position:0%
+evolution this is one of the major
+things people are focused on is how do
+
+ align:start position:0%
+things people are focused on is how do
+ 
+
+ align:start position:0%
+things people are focused on is how do
+you how can you make cells a little fake
+
+ align:start position:0%
+you how can you make cells a little fake
+ 
+
+ align:start position:0%
+you how can you make cells a little fake
+cells artificial cells that can
+
+ align:start position:0%
+cells artificial cells that can
+ 
+
+ align:start position:0%
+cells artificial cells that can
+replicate themselves you can make it and
+
+ align:start position:0%
+replicate themselves you can make it and
+ 
+
+ align:start position:0%
+replicate themselves you can make it and
+they can they're gonna have to divide
+
+ align:start position:0%
+they can they're gonna have to divide
+ 
+
+ align:start position:0%
+they can they're gonna have to divide
+and infuse and it's exactly the same
+
+ align:start position:0%
+and infuse and it's exactly the same
+ 
+
+ align:start position:0%
+and infuse and it's exactly the same
+problem here and so this question of
+
+ align:start position:0%
+problem here and so this question of
+ 
+
+ align:start position:0%
+problem here and so this question of
+fluidity is an extremely important
+
+ align:start position:0%
+fluidity is an extremely important
+ 
+
+ align:start position:0%
+fluidity is an extremely important
+question and a lot of people that focus
+
+ align:start position:0%
+question and a lot of people that focus
+ 
+
+ align:start position:0%
+question and a lot of people that focus
+on lipids which is not a popular target
+
+ align:start position:0%
+on lipids which is not a popular target
+ 
+
+ align:start position:0%
+on lipids which is not a popular target
+a popular thing to study because it's so
+
+ align:start position:0%
+a popular thing to study because it's so
+ 
+
+ align:start position:0%
+a popular thing to study because it's so
+hard it's incredibly important and
+
+ align:start position:0%
+hard it's incredibly important and
+ 
+
+ align:start position:0%
+hard it's incredibly important and
+people that look at membrane proteins
+
+ align:start position:0%
+people that look at membrane proteins
+ 
+
+ align:start position:0%
+people that look at membrane proteins
+you know they almost always have lipids
+
+ align:start position:0%
+you know they almost always have lipids
+ 
+
+ align:start position:0%
+you know they almost always have lipids
+on them but and then when you do them
+
+ align:start position:0%
+on them but and then when you do them
+ 
+
+ align:start position:0%
+on them but and then when you do them
+yourself you have a detergent which is
+
+ align:start position:0%
+yourself you have a detergent which is
+ 
+
+ align:start position:0%
+yourself you have a detergent which is
+not a real lipid and does that change
+
+ align:start position:0%
+not a real lipid and does that change
+ 
+
+ align:start position:0%
+not a real lipid and does that change
+the property so all of these questions I
+
+ align:start position:0%
+the property so all of these questions I
+ 
+
+ align:start position:0%
+the property so all of these questions I
+think are really sort of central to what
+
+ align:start position:0%
+think are really sort of central to what
+ 
+
+ align:start position:0%
+think are really sort of central to what
+happens in the membranes which is a
+
+ align:start position:0%
+happens in the membranes which is a
+ 
+
+ align:start position:0%
+happens in the membranes which is a
+a lot of stuff inside the cell so I
+
+ align:start position:0%
+a lot of stuff inside the cell so I
+ 
+
+ align:start position:0%
+a lot of stuff inside the cell so I
+think it's good to question what they
+
+ align:start position:0%
+think it's good to question what they
+ 
+
+ align:start position:0%
+think it's good to question what they
+did I think their results turned out to
+
+ align:start position:0%
+did I think their results turned out to
+ 
+
+ align:start position:0%
+did I think their results turned out to
+be quite interesting okay but we'll come
+
+ align:start position:0%
+be quite interesting okay but we'll come
+ 
+
+ align:start position:0%
+be quite interesting okay but we'll come
+back I think it that was a hard problem
+
+ align:start position:0%
+back I think it that was a hard problem
+ 
+
+ align:start position:0%
+back I think it that was a hard problem
+and so we'll come back and we'll look at
+
+ align:start position:0%
+and so we'll come back and we'll look at
+ 
+
+ align:start position:0%
+and so we'll come back and we'll look at
+this and so then let's give let's say
+
+ align:start position:0%
+this and so then let's give let's say
+ 
+
+ align:start position:0%
+this and so then let's give let's say
+that we could end up separating things
+
+ align:start position:0%
+that we could end up separating things
+ 
+
+ align:start position:0%
+that we could end up separating things
+then the question is what was the key
+
+ align:start position:0%
+then the question is what was the key
+ 
+
+ align:start position:0%
+then the question is what was the key
+type of measurement they made where they
+
+ align:start position:0%
+type of measurement they made where they
+ 
+
+ align:start position:0%
+type of measurement they made where they
+could correlate the changes that it
+
+ align:start position:0%
+could correlate the changes that it
+ 
+
+ align:start position:0%
+could correlate the changes that it
+should correlate the changes in
+
+ align:start position:0%
+should correlate the changes in
+ 
+
+ align:start position:0%
+should correlate the changes in
+cholesterol levels we talked about you
+
+ align:start position:0%
+cholesterol levels we talked about you
+ 
+
+ align:start position:0%
+cholesterol levels we talked about you
+couldn't control perhaps the cholesterol
+
+ align:start position:0%
+couldn't control perhaps the cholesterol
+ 
+
+ align:start position:0%
+couldn't control perhaps the cholesterol
+levels with the cyclodextrin but then
+
+ align:start position:0%
+levels with the cyclodextrin but then
+ 
+
+ align:start position:0%
+levels with the cyclodextrin but then
+how did they correlate the changes in
+
+ align:start position:0%
+how did they correlate the changes in
+ 
+
+ align:start position:0%
+how did they correlate the changes in
+the cholesterol levels in the membrane
+
+ align:start position:0%
+the cholesterol levels in the membrane
+ 
+
+ align:start position:0%
+the cholesterol levels in the membrane
+with this transcriptional regulation
+
+ align:start position:0%
+with this transcriptional regulation
+ 
+
+ align:start position:0%
+with this transcriptional regulation
+okay and so which that is what happens
+
+ align:start position:0%
+okay and so which that is what happens
+ 
+
+ align:start position:0%
+okay and so which that is what happens
+with the steroid responsive element
+
+ align:start position:0%
+with the steroid responsive element
+ 
+
+ align:start position:0%
+with the steroid responsive element
+binding protein the transcription factor
+
+ align:start position:0%
+binding protein the transcription factor
+ 
+
+ align:start position:0%
+binding protein the transcription factor
+so what happens in that process what
+
+ align:start position:0%
+so what happens in that process what
+ 
+
+ align:start position:0%
+so what happens in that process what
+what are the changes in the srebp
+
+ align:start position:0%
+what are the changes in the srebp
+ 
+
+ align:start position:0%
+what are the changes in the srebp
+dependent on the concentrations of the
+
+ align:start position:0%
+dependent on the concentrations of the
+ 
+
+ align:start position:0%
+dependent on the concentrations of the
+cholesterol and how did they take
+
+ align:start position:0%
+cholesterol and how did they take
+ 
+
+ align:start position:0%
+cholesterol and how did they take
+advantage of that in answering this
+
+ align:start position:0%
+advantage of that in answering this
+ 
+
+ align:start position:0%
+advantage of that in answering this
+question about whether what the
+
+ align:start position:0%
+question about whether what the
+ 
+
+ align:start position:0%
+question about whether what the
+cholesterol levels were that allows you
+
+ align:start position:0%
+cholesterol levels were that allows you
+ 
+
+ align:start position:0%
+cholesterol levels were that allows you
+to turn on transcription of LDL receptor
+
+ align:start position:0%
+to turn on transcription of LDL receptor
+ 
+
+ align:start position:0%
+to turn on transcription of LDL receptor
+and hmg-coa reductase so what's the
+
+ align:start position:0%
+and hmg-coa reductase so what's the
+ 
+
+ align:start position:0%
+and hmg-coa reductase so what's the
+major a say we'll look at that as well
+
+ align:start position:0%
+major a say we'll look at that as well
+ 
+
+ align:start position:0%
+major a say we'll look at that as well
+so if you go back and you look at the
+
+ align:start position:0%
+so if you go back and you look at the
+ 
+
+ align:start position:0%
+so if you go back and you look at the
+model what happens in this model all
+
+ align:start position:0%
+model what happens in this model all
+ 
+
+ align:start position:0%
+model what happens in this model all
+right here we go
+
+ align:start position:0%
+right here we go
+ 
+
+ align:start position:0%
+right here we go
+what happens in this model what's
+
+ align:start position:0%
+what happens in this model what's
+ 
+
+ align:start position:0%
+what happens in this model what's
+happening to srebp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this scalp scalp that's this guy
+
+ align:start position:0%
+now this scalp scalp that's this guy
+ 
+
+ align:start position:0%
+now this scalp scalp that's this guy
+okay so scalp that's a key player that's
+
+ align:start position:0%
+okay so scalp that's a key player that's
+ 
+
+ align:start position:0%
+okay so scalp that's a key player that's
+what we talked about I know the names
+
+ align:start position:0%
+what we talked about I know the names
+ 
+
+ align:start position:0%
+what we talked about I know the names
+are all confusing so you're going to
+
+ align:start position:0%
+are all confusing so you're going to
+ 
+
+ align:start position:0%
+are all confusing so you're going to
+need to write these down good
+
+ align:start position:0%
+need to write these down good
+ 
+
+ align:start position:0%
+need to write these down good
+remember the names are very confusing
+
+ align:start position:0%
+remember the names are very confusing
+ 
+
+ align:start position:0%
+remember the names are very confusing
+yeah great all right
+
+ align:start position:0%
+yeah great all right
+ 
+
+ align:start position:0%
+yeah great all right
+so how could you take advantage of that
+
+ align:start position:0%
+so how could you take advantage of that
+ 
+
+ align:start position:0%
+so how could you take advantage of that
+that that's this is the key observation
+
+ align:start position:0%
+that that's this is the key observation
+ 
+
+ align:start position:0%
+that that's this is the key observation
+that they're taking advantage of to ask
+
+ align:start position:0%
+that they're taking advantage of to ask
+ 
+
+ align:start position:0%
+that they're taking advantage of to ask
+the question since this whole process is
+
+ align:start position:0%
+the question since this whole process is
+ 
+
+ align:start position:0%
+the question since this whole process is
+dependent on the concentration of
+
+ align:start position:0%
+dependent on the concentration of
+ 
+
+ align:start position:0%
+dependent on the concentration of
+cholesterol you if you have high
+
+ align:start position:0%
+cholesterol you if you have high
+ 
+
+ align:start position:0%
+cholesterol you if you have high
+cholesterol there's no way you want this
+
+ align:start position:0%
+cholesterol there's no way you want this
+ 
+
+ align:start position:0%
+cholesterol there's no way you want this
+to happen
+
+ align:start position:0%
+to happen
+ 
+
+ align:start position:0%
+to happen
+you want to shut it off if you have low
+
+ align:start position:0%
+you want to shut it off if you have low
+ 
+
+ align:start position:0%
+you want to shut it off if you have low
+cholesterol you want to turn these guys
+
+ align:start position:0%
+cholesterol you want to turn these guys
+ 
+
+ align:start position:0%
+cholesterol you want to turn these guys
+on okay so this movement is the key and
+
+ align:start position:0%
+on okay so this movement is the key and
+ 
+
+ align:start position:0%
+on okay so this movement is the key and
+what do we see if if we look at what
+
+ align:start position:0%
+what do we see if if we look at what
+ 
+
+ align:start position:0%
+what do we see if if we look at what
+happens to this protein srebp what
+
+ align:start position:0%
+happens to this protein srebp what
+ 
+
+ align:start position:0%
+happens to this protein srebp what
+happens to it during this process it
+
+ align:start position:0%
+happens to it during this process it
+ 
+
+ align:start position:0%
+happens to it during this process it
+gets cleaved and what happens - how
+
+ align:start position:0%
+gets cleaved and what happens - how
+ 
+
+ align:start position:0%
+gets cleaved and what happens - how
+could you monitor - that cleavage how do
+
+ align:start position:0%
+could you monitor - that cleavage how do
+ 
+
+ align:start position:0%
+could you monitor - that cleavage how do
+they do it in the paper they couldn't
+
+ align:start position:0%
+they do it in the paper they couldn't
+ 
+
+ align:start position:0%
+they do it in the paper they couldn't
+use a floor where they didn't do that
+
+ align:start position:0%
+use a floor where they didn't do that
+ 
+
+ align:start position:0%
+use a floor where they didn't do that
+they did a what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so they can just separate by a gel
+
+ align:start position:0%
+yeah so they can just separate by a gel
+ 
+
+ align:start position:0%
+yeah so they can just separate by a gel
+so to me this is an actually quite an
+
+ align:start position:0%
+so to me this is an actually quite an
+ 
+
+ align:start position:0%
+so to me this is an actually quite an
+easy a se because if you look at this I
+
+ align:start position:0%
+easy a se because if you look at this I
+ 
+
+ align:start position:0%
+easy a se because if you look at this I
+don't remember what the molecular weight
+
+ align:start position:0%
+don't remember what the molecular weight
+ 
+
+ align:start position:0%
+don't remember what the molecular weight
+is but it's a lot smaller over here and
+
+ align:start position:0%
+is but it's a lot smaller over here and
+ 
+
+ align:start position:0%
+is but it's a lot smaller over here and
+so that turns out to be a great I'll say
+
+ align:start position:0%
+so that turns out to be a great I'll say
+ 
+
+ align:start position:0%
+so that turns out to be a great I'll say
+so that part of that that part of their
+
+ align:start position:0%
+so that part of that that part of their
+ 
+
+ align:start position:0%
+so that part of that that part of their
+analysis I think was a really smart part
+
+ align:start position:0%
+analysis I think was a really smart part
+ 
+
+ align:start position:0%
+analysis I think was a really smart part
+of the analysis and so then the question
+
+ align:start position:0%
+of the analysis and so then the question
+ 
+
+ align:start position:0%
+of the analysis and so then the question
+becomes can you quantitate all of this
+
+ align:start position:0%
+becomes can you quantitate all of this
+ 
+
+ align:start position:0%
+becomes can you quantitate all of this
+so if you have a lot of cholesterol this
+
+ align:start position:0%
+so if you have a lot of cholesterol this
+ 
+
+ align:start position:0%
+so if you have a lot of cholesterol this
+doesn't happen and so everything is
+
+ align:start position:0%
+doesn't happen and so everything is
+ 
+
+ align:start position:0%
+doesn't happen and so everything is
+bigger and resides in the membrane you
+
+ align:start position:0%
+bigger and resides in the membrane you
+ 
+
+ align:start position:0%
+bigger and resides in the membrane you
+could even probably look at that whereas
+
+ align:start position:0%
+could even probably look at that whereas
+ 
+
+ align:start position:0%
+could even probably look at that whereas
+when the cholesterol is really lower
+
+ align:start position:0%
+when the cholesterol is really lower
+ 
+
+ align:start position:0%
+when the cholesterol is really lower
+things things go there and it's
+
+ align:start position:0%
+things things go there and it's
+ 
+
+ align:start position:0%
+things things go there and it's
+everything in between the question is
+
+ align:start position:0%
+everything in between the question is
+ 
+
+ align:start position:0%
+everything in between the question is
+what is the concept can you measure if
+
+ align:start position:0%
+what is the concept can you measure if
+ 
+
+ align:start position:0%
+what is the concept can you measure if
+you have X percent cholesterol in the ER
+
+ align:start position:0%
+you have X percent cholesterol in the ER
+ 
+
+ align:start position:0%
+you have X percent cholesterol in the ER
+how much do you have to decrease it to
+
+ align:start position:0%
+how much do you have to decrease it to
+ 
+
+ align:start position:0%
+how much do you have to decrease it to
+see a change or switch and where this
+
+ align:start position:0%
+see a change or switch and where this
+ 
+
+ align:start position:0%
+see a change or switch and where this
+protein goes so I think the experiment
+
+ align:start position:0%
+protein goes so I think the experiment
+ 
+
+ align:start position:0%
+protein goes so I think the experiment
+the experimental design is actually
+
+ align:start position:0%
+the experimental design is actually
+ 
+
+ align:start position:0%
+the experimental design is actually
+amazingly creative okay but then you
+
+ align:start position:0%
+amazingly creative okay but then you
+ 
+
+ align:start position:0%
+amazingly creative okay but then you
+sell you see the data off the other side
+
+ align:start position:0%
+sell you see the data off the other side
+ 
+
+ align:start position:0%
+sell you see the data off the other side
+and what I want to do now is is sort of
+
+ align:start position:0%
+and what I want to do now is is sort of
+ 
+
+ align:start position:0%
+and what I want to do now is is sort of
+focus on what what the issues are okay
+
+ align:start position:0%
+focus on what what the issues are okay
+ 
+
+ align:start position:0%
+focus on what what the issues are okay
+so we're going to come back and look at
+
+ align:start position:0%
+so we're going to come back and look at
+ 
+
+ align:start position:0%
+so we're going to come back and look at
+how did they look at srebp so you could
+
+ align:start position:0%
+how did they look at srebp so you could
+ 
+
+ align:start position:0%
+how did they look at srebp so you could
+look at this a number of ways you could
+
+ align:start position:0%
+look at this a number of ways you could
+ 
+
+ align:start position:0%
+look at this a number of ways you could
+look at this by protein gel directly how
+
+ align:start position:0%
+look at this by protein gel directly how
+ 
+
+ align:start position:0%
+look at this by protein gel directly how
+else do people look at proteins using
+
+ align:start position:0%
+else do people look at proteins using
+ 
+
+ align:start position:0%
+else do people look at proteins using
+westerns what's the Western anybody know
+
+ align:start position:0%
+westerns what's the Western anybody know
+ 
+
+ align:start position:0%
+westerns what's the Western anybody know
+what a Western analysis is I didn't I
+
+ align:start position:0%
+what a Western analysis is I didn't I
+ 
+
+ align:start position:0%
+what a Western analysis is I didn't I
+asked you that a beginning of class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how else do you detect proteins you've
+
+ align:start position:0%
+how else do you detect proteins you've
+ 
+
+ align:start position:0%
+how else do you detect proteins you've
+seen this on the first half of the
+
+ align:start position:0%
+seen this on the first half of the
+ 
+
+ align:start position:0%
+seen this on the first half of the
+semester a lot yeah antibodies so if you
+
+ align:start position:0%
+semester a lot yeah antibodies so if you
+ 
+
+ align:start position:0%
+semester a lot yeah antibodies so if you
+have any antibodies to this and we'll
+
+ align:start position:0%
+have any antibodies to this and we'll
+ 
+
+ align:start position:0%
+have any antibodies to this and we'll
+talk about that because the Western
+
+ align:start position:0%
+talk about that because the Western
+ 
+
+ align:start position:0%
+talk about that because the Western
+analysis which people use all the time
+
+ align:start position:0%
+analysis which people use all the time
+ 
+
+ align:start position:0%
+analysis which people use all the time
+and you can't pit there's so many issues
+
+ align:start position:0%
+and you can't pit there's so many issues
+ 
+
+ align:start position:0%
+and you can't pit there's so many issues
+with it that I think I want you to think
+
+ align:start position:0%
+with it that I think I want you to think
+ 
+
+ align:start position:0%
+with it that I think I want you to think
+about what the issues are okay and then
+
+ align:start position:0%
+about what the issues are okay and then
+ 
+
+ align:start position:0%
+about what the issues are okay and then
+you correlate the two changing the
+
+ align:start position:0%
+you correlate the two changing the
+ 
+
+ align:start position:0%
+you correlate the two changing the
+levels of cholesterol which they measure
+
+ align:start position:0%
+levels of cholesterol which they measure
+ 
+
+ align:start position:0%
+levels of cholesterol which they measure
+by mass spec after separation and
+
+ align:start position:0%
+by mass spec after separation and
+ 
+
+ align:start position:0%
+by mass spec after separation and
+purification of lipids and the cleavage
+
+ align:start position:0%
+purification of lipids and the cleavage
+ 
+
+ align:start position:0%
+purification of lipids and the cleavage
+and then they plot the data and and
+
+ align:start position:0%
+and then they plot the data and and
+ 
+
+ align:start position:0%
+and then they plot the data and and
+that's where they got the analysis from
+
+ align:start position:0%
+that's where they got the analysis from
+ 
+
+ align:start position:0%
+that's where they got the analysis from
+okay so the first thing that you want to
+
+ align:start position:0%
+okay so the first thing that you want to
+ 
+
+ align:start position:0%
+okay so the first thing that you want to
+do the first thing and the key to
+
+ align:start position:0%
+do the first thing and the key to
+ 
+
+ align:start position:0%
+do the first thing and the key to
+everything is separation of the
+
+ align:start position:0%
+everything is separation of the
+ 
+
+ align:start position:0%
+everything is separation of the
+membranes okay and so this is a cartoon
+
+ align:start position:0%
+membranes okay and so this is a cartoon
+ 
+
+ align:start position:0%
+membranes okay and so this is a cartoon
+of when you put something you load
+
+ align:start position:0%
+of when you put something you load
+ 
+
+ align:start position:0%
+of when you put something you load
+something on the top and you have a
+
+ align:start position:0%
+something on the top and you have a
+ 
+
+ align:start position:0%
+something on the top and you have a
+gradient and the gradient could be made
+
+ align:start position:0%
+gradient and the gradient could be made
+ 
+
+ align:start position:0%
+gradient and the gradient could be made
+of a number of things have any of you
+
+ align:start position:0%
+of a number of things have any of you
+ 
+
+ align:start position:0%
+of a number of things have any of you
+ever run these kinds of gradients okay
+
+ align:start position:0%
+ever run these kinds of gradients okay
+ 
+
+ align:start position:0%
+ever run these kinds of gradients okay
+so you can make them out of glycerol you
+
+ align:start position:0%
+so you can make them out of glycerol you
+ 
+
+ align:start position:0%
+so you can make them out of glycerol you
+can make them less gross did anybody
+
+ align:start position:0%
+can make them less gross did anybody
+ 
+
+ align:start position:0%
+can make them less gross did anybody
+look at how these gradients for me did
+
+ align:start position:0%
+look at how these gradients for me did
+ 
+
+ align:start position:0%
+look at how these gradients for me did
+you read the experimental carefully
+
+ align:start position:0%
+you read the experimental carefully
+ 
+
+ align:start position:0%
+you read the experimental carefully
+enough to look at that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah how do you make a sucrose gradient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have no idea but I said huh yeah so
+
+ align:start position:0%
+you have no idea but I said huh yeah so
+ 
+
+ align:start position:0%
+you have no idea but I said huh yeah so
+layering so what you'd really like to do
+
+ align:start position:0%
+layering so what you'd really like to do
+ 
+
+ align:start position:0%
+layering so what you'd really like to do
+is have a continuous gradient or
+
+ align:start position:0%
+is have a continuous gradient or
+ 
+
+ align:start position:0%
+is have a continuous gradient or
+something but that sucrose is incredibly
+
+ align:start position:0%
+something but that sucrose is incredibly
+ 
+
+ align:start position:0%
+something but that sucrose is incredibly
+viscous so if you were trying to make a
+
+ align:start position:0%
+viscous so if you were trying to make a
+ 
+
+ align:start position:0%
+viscous so if you were trying to make a
+linear gradient which you could do by
+
+ align:start position:0%
+linear gradient which you could do by
+ 
+
+ align:start position:0%
+linear gradient which you could do by
+mixing two things of different
+
+ align:start position:0%
+mixing two things of different
+ 
+
+ align:start position:0%
+mixing two things of different
+concentrations if you could get them to
+
+ align:start position:0%
+concentrations if you could get them to
+ 
+
+ align:start position:0%
+concentrations if you could get them to
+stir really well and then add it in and
+
+ align:start position:0%
+stir really well and then add it in and
+ 
+
+ align:start position:0%
+stir really well and then add it in and
+you could generate a gradient but it's
+
+ align:start position:0%
+you could generate a gradient but it's
+ 
+
+ align:start position:0%
+you could generate a gradient but it's
+so hard to do that what happens is they
+
+ align:start position:0%
+so hard to do that what happens is they
+ 
+
+ align:start position:0%
+so hard to do that what happens is they
+end up layering it so they make x % y %
+
+ align:start position:0%
+end up layering it so they make x % y %
+ 
+
+ align:start position:0%
+end up layering it so they make x % y %
+z percent they put it down okay and then
+
+ align:start position:0%
+z percent they put it down okay and then
+ 
+
+ align:start position:0%
+z percent they put it down okay and then
+they try to layer something on top of it
+
+ align:start position:0%
+they try to layer something on top of it
+ 
+
+ align:start position:0%
+they try to layer something on top of it
+and then and so and then they put
+
+ align:start position:0%
+and then and so and then they put
+ 
+
+ align:start position:0%
+and then and so and then they put
+whatever they interested in at the top
+
+ align:start position:0%
+whatever they interested in at the top
+ 
+
+ align:start position:0%
+whatever they interested in at the top
+and then they they centrifuge it okay so
+
+ align:start position:0%
+and then they they centrifuge it okay so
+ 
+
+ align:start position:0%
+and then they they centrifuge it okay so
+what are the issues is this do you think
+
+ align:start position:0%
+what are the issues is this do you think
+ 
+
+ align:start position:0%
+what are the issues is this do you think
+this is what the gradient would look
+
+ align:start position:0%
+this is what the gradient would look
+ 
+
+ align:start position:0%
+this is what the gradient would look
+like well so what are the issues when
+
+ align:start position:0%
+like well so what are the issues when
+ 
+
+ align:start position:0%
+like well so what are the issues when
+you're doing this when you when you
+
+ align:start position:0%
+you're doing this when you when you
+ 
+
+ align:start position:0%
+you're doing this when you when you
+layer it so and this is why the data
+
+ align:start position:0%
+layer it so and this is why the data
+ 
+
+ align:start position:0%
+layer it so and this is why the data
+which we'll talk about in a minute is
+
+ align:start position:0%
+which we'll talk about in a minute is
+ 
+
+ align:start position:0%
+which we'll talk about in a minute is
+that is the data part of the issue is
+
+ align:start position:0%
+that is the data part of the issue is
+ 
+
+ align:start position:0%
+that is the data part of the issue is
+this method that's why you need to think
+
+ align:start position:0%
+this method that's why you need to think
+ 
+
+ align:start position:0%
+this method that's why you need to think
+about the method and there are better
+
+ align:start position:0%
+about the method and there are better
+ 
+
+ align:start position:0%
+about the method and there are better
+ways to do this and it really depends on
+
+ align:start position:0%
+ways to do this and it really depends on
+ 
+
+ align:start position:0%
+ways to do this and it really depends on
+what you're trying to separate you know
+
+ align:start position:0%
+what you're trying to separate you know
+ 
+
+ align:start position:0%
+what you're trying to separate you know
+so if this ban there was a little say
+
+ align:start position:0%
+so if this ban there was a little say
+ 
+
+ align:start position:0%
+so if this ban there was a little say
+these were two bands you wouldn't really
+
+ align:start position:0%
+these were two bands you wouldn't really
+ 
+
+ align:start position:0%
+these were two bands you wouldn't really
+get very much separation at all if there
+
+ align:start position:0%
+get very much separation at all if there
+ 
+
+ align:start position:0%
+get very much separation at all if there
+were two separate things that sedimented
+
+ align:start position:0%
+were two separate things that sedimented
+ 
+
+ align:start position:0%
+were two separate things that sedimented
+under these conditions very close
+
+ align:start position:0%
+under these conditions very close
+ 
+
+ align:start position:0%
+under these conditions very close
+together okay so what would happen when
+
+ align:start position:0%
+together okay so what would happen when
+ 
+
+ align:start position:0%
+together okay so what would happen when
+you're sedimenting this I mean does
+
+ align:start position:0%
+you're sedimenting this I mean does
+ 
+
+ align:start position:0%
+you're sedimenting this I mean does
+anybody have any idea how long it takes
+
+ align:start position:0%
+anybody have any idea how long it takes
+ 
+
+ align:start position:0%
+anybody have any idea how long it takes
+do you think you'd do this in like a
+
+ align:start position:0%
+do you think you'd do this in like a
+ 
+
+ align:start position:0%
+do you think you'd do this in like a
+centrifuge just spin it for three
+
+ align:start position:0%
+centrifuge just spin it for three
+ 
+
+ align:start position:0%
+centrifuge just spin it for three
+minutes and then you know so it you
+
+ align:start position:0%
+minutes and then you know so it you
+ 
+
+ align:start position:0%
+minutes and then you know so it you
+sometimes you sediment these things for
+
+ align:start position:0%
+sometimes you sediment these things for
+ 
+
+ align:start position:0%
+sometimes you sediment these things for
+16 20 hours okay so what happens during
+
+ align:start position:0%
+16 20 hours okay so what happens during
+ 
+
+ align:start position:0%
+16 20 hours okay so what happens during
+the sedimentation that might make this
+
+ align:start position:0%
+the sedimentation that might make this
+ 
+
+ align:start position:0%
+the sedimentation that might make this
+more challenging in terms of separating
+
+ align:start position:0%
+more challenging in terms of separating
+ 
+
+ align:start position:0%
+more challenging in terms of separating
+what you want to separate yeah so
+
+ align:start position:0%
+what you want to separate yeah so
+ 
+
+ align:start position:0%
+what you want to separate yeah so
+exactly you have diffusion and even when
+
+ align:start position:0%
+exactly you have diffusion and even when
+ 
+
+ align:start position:0%
+exactly you have diffusion and even when
+you've layered things on top of each
+
+ align:start position:0%
+you've layered things on top of each
+ 
+
+ align:start position:0%
+you've layered things on top of each
+other like that you start to have
+
+ align:start position:0%
+other like that you start to have
+ 
+
+ align:start position:0%
+other like that you start to have
+diffusion and if you shake up the tube a
+
+ align:start position:0%
+diffusion and if you shake up the tube a
+ 
+
+ align:start position:0%
+diffusion and if you shake up the tube a
+little bit it's all over so how you
+
+ align:start position:0%
+little bit it's all over so how you
+ 
+
+ align:start position:0%
+little bit it's all over so how you
+prepare these things is not so true
+
+ align:start position:0%
+prepare these things is not so true
+ 
+
+ align:start position:0%
+prepare these things is not so true
+these people still use these methods but
+
+ align:start position:0%
+these people still use these methods but
+ 
+
+ align:start position:0%
+these people still use these methods but
+I would like to see better man
+
+ align:start position:0%
+I would like to see better man
+ 
+
+ align:start position:0%
+I would like to see better man
+and so they tried you know one method
+
+ align:start position:0%
+and so they tried you know one method
+ 
+
+ align:start position:0%
+and so they tried you know one method
+with sucrose and then they that wasn't
+
+ align:start position:0%
+with sucrose and then they that wasn't
+ 
+
+ align:start position:0%
+with sucrose and then they that wasn't
+good enough we'll look at the data so
+
+ align:start position:0%
+good enough we'll look at the data so
+ 
+
+ align:start position:0%
+good enough we'll look at the data so
+they went to a second method and you
+
+ align:start position:0%
+they went to a second method and you
+ 
+
+ align:start position:0%
+they went to a second method and you
+know where did they come up with this I
+
+ align:start position:0%
+know where did they come up with this I
+ 
+
+ align:start position:0%
+know where did they come up with this I
+have no idea where they came up with
+
+ align:start position:0%
+have no idea where they came up with
+ 
+
+ align:start position:0%
+have no idea where they came up with
+this but it was an MD PhD student in her
+
+ align:start position:0%
+this but it was an MD PhD student in her
+ 
+
+ align:start position:0%
+this but it was an MD PhD student in her
+class who has seen this in one of its
+
+ align:start position:0%
+class who has seen this in one of its
+ 
+
+ align:start position:0%
+class who has seen this in one of its
+classes and they use it in some blood
+
+ align:start position:0%
+classes and they use it in some blood
+ 
+
+ align:start position:0%
+classes and they use it in some blood
+tests so I think that's probably where
+
+ align:start position:0%
+tests so I think that's probably where
+ 
+
+ align:start position:0%
+tests so I think that's probably where
+these guys got it from because they're
+
+ align:start position:0%
+these guys got it from because they're
+ 
+
+ align:start position:0%
+these guys got it from because they're
+both MD and Brown and goes you know both
+
+ align:start position:0%
+both MD and Brown and goes you know both
+ 
+
+ align:start position:0%
+both MD and Brown and goes you know both
+MDS but again it's just another make way
+
+ align:start position:0%
+MDS but again it's just another make way
+ 
+
+ align:start position:0%
+MDS but again it's just another make way
+to make a gradient and I'm not sure why
+
+ align:start position:0%
+to make a gradient and I'm not sure why
+ 
+
+ align:start position:0%
+to make a gradient and I'm not sure why
+this gradient works as effectively as it
+
+ align:start position:0%
+this gradient works as effectively as it
+ 
+
+ align:start position:0%
+this gradient works as effectively as it
+does so but the first gradient didn't
+
+ align:start position:0%
+does so but the first gradient didn't
+ 
+
+ align:start position:0%
+does so but the first gradient didn't
+work so great and we'll look at that
+
+ align:start position:0%
+work so great and we'll look at that
+ 
+
+ align:start position:0%
+work so great and we'll look at that
+data so then they added on a few more
+
+ align:start position:0%
+data so then they added on a few more
+ 
+
+ align:start position:0%
+data so then they added on a few more
+steps because they weren't happy with
+
+ align:start position:0%
+steps because they weren't happy with
+ 
+
+ align:start position:0%
+steps because they weren't happy with
+the level of separation so looking at
+
+ align:start position:0%
+the level of separation so looking at
+ 
+
+ align:start position:0%
+the level of separation so looking at
+membranes I mean I think this is gonna
+
+ align:start position:0%
+membranes I mean I think this is gonna
+ 
+
+ align:start position:0%
+membranes I mean I think this is gonna
+be more and more looking at membranes
+
+ align:start position:0%
+be more and more looking at membranes
+ 
+
+ align:start position:0%
+be more and more looking at membranes
+because membranes you have two leaflets
+
+ align:start position:0%
+because membranes you have two leaflets
+ 
+
+ align:start position:0%
+because membranes you have two leaflets
+the lipids in the leaflets are different
+
+ align:start position:0%
+the lipids in the leaflets are different
+ 
+
+ align:start position:0%
+the lipids in the leaflets are different
+do you think that affects the biology I
+
+ align:start position:0%
+do you think that affects the biology I
+ 
+
+ align:start position:0%
+do you think that affects the biology I
+guarantee you it affects the biology and
+
+ align:start position:0%
+guarantee you it affects the biology and
+ 
+
+ align:start position:0%
+guarantee you it affects the biology and
+ways that we would really like to
+
+ align:start position:0%
+ways that we would really like to
+ 
+
+ align:start position:0%
+ways that we would really like to
+understand that I don't think we
+
+ align:start position:0%
+understand that I don't think we
+ 
+
+ align:start position:0%
+understand that I don't think we
+understand very well when you isolate a
+
+ align:start position:0%
+understand very well when you isolate a
+ 
+
+ align:start position:0%
+understand very well when you isolate a
+membrane protein have any of you ever
+
+ align:start position:0%
+membrane protein have any of you ever
+ 
+
+ align:start position:0%
+membrane protein have any of you ever
+isolated a membrane protein no so you
+
+ align:start position:0%
+isolated a membrane protein no so you
+ 
+
+ align:start position:0%
+isolated a membrane protein no so you
+have an insoluble much you know it's
+
+ align:start position:0%
+have an insoluble much you know it's
+ 
+
+ align:start position:0%
+have an insoluble much you know it's
+it's in this lipid system how do you
+
+ align:start position:0%
+it's in this lipid system how do you
+ 
+
+ align:start position:0%
+it's in this lipid system how do you
+think you get it out so you can go
+
+ align:start position:0%
+think you get it out so you can go
+ 
+
+ align:start position:0%
+think you get it out so you can go
+through the steps it a protein
+
+ align:start position:0%
+through the steps it a protein
+ 
+
+ align:start position:0%
+through the steps it a protein
+purification that you've talked about or
+
+ align:start position:0%
+purification that you've talked about or
+ 
+
+ align:start position:0%
+purification that you've talked about or
+you have probably done at an
+
+ align:start position:0%
+you have probably done at an
+ 
+
+ align:start position:0%
+you have probably done at an
+introductory lab course what is the
+
+ align:start position:0%
+introductory lab course what is the
+ 
+
+ align:start position:0%
+introductory lab course what is the
+first thing you need to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah soluble eyes and how do you soluble
+
+ align:start position:0%
+yeah soluble eyes and how do you soluble
+ 
+
+ align:start position:0%
+yeah soluble eyes and how do you soluble
+eyes it yeah with some kind of detergent
+
+ align:start position:0%
+eyes it yeah with some kind of detergent
+ 
+
+ align:start position:0%
+eyes it yeah with some kind of detergent
+it's sort of like what you saw with the
+
+ align:start position:0%
+it's sort of like what you saw with the
+ 
+
+ align:start position:0%
+it's sort of like what you saw with the
+chylomicrons right or the bile acids
+
+ align:start position:0%
+chylomicrons right or the bile acids
+ 
+
+ align:start position:0%
+chylomicrons right or the bile acids
+that we talked about so you can use
+
+ align:start position:0%
+that we talked about so you can use
+ 
+
+ align:start position:0%
+that we talked about so you can use
+different and people have their own
+
+ align:start position:0%
+different and people have their own
+ 
+
+ align:start position:0%
+different and people have their own
+favorite detergents but again that
+
+ align:start position:0%
+favorite detergents but again that
+ 
+
+ align:start position:0%
+favorite detergents but again that
+changes things but otherwise you can't
+
+ align:start position:0%
+changes things but otherwise you can't
+ 
+
+ align:start position:0%
+changes things but otherwise you can't
+purify purify anything unless you happen
+
+ align:start position:0%
+purify purify anything unless you happen
+ 
+
+ align:start position:0%
+purify purify anything unless you happen
+to have a membrane where you know it's
+
+ align:start position:0%
+to have a membrane where you know it's
+ 
+
+ align:start position:0%
+to have a membrane where you know it's
+the only protein in the membrane is so
+
+ align:start position:0%
+the only protein in the membrane is so
+ 
+
+ align:start position:0%
+the only protein in the membrane is so
+when you're interested in which of
+
+ align:start position:0%
+when you're interested in which of
+ 
+
+ align:start position:0%
+when you're interested in which of
+course doesn't exist
+
+ align:start position:0%
+course doesn't exist
+ 
+
+ align:start position:0%
+course doesn't exist
+okay so anyhow they went through that
+
+ align:start position:0%
+okay so anyhow they went through that
+ 
+
+ align:start position:0%
+okay so anyhow they went through that
+and then what do they end up seeing so
+
+ align:start position:0%
+and then what do they end up seeing so
+ 
+
+ align:start position:0%
+and then what do they end up seeing so
+they went through different steps and
+
+ align:start position:0%
+they went through different steps and
+ 
+
+ align:start position:0%
+they went through different steps and
+they separate they separate them into
+
+ align:start position:0%
+they separate they separate them into
+ 
+
+ align:start position:0%
+they separate they separate them into
+different the supernatant and/or the
+
+ align:start position:0%
+different the supernatant and/or the
+ 
+
+ align:start position:0%
+different the supernatant and/or the
+light and the heavy fraction membrane
+
+ align:start position:0%
+light and the heavy fraction membrane
+ 
+
+ align:start position:0%
+light and the heavy fraction membrane
+fractions and then they have to analyze
+
+ align:start position:0%
+fractions and then they have to analyze
+ 
+
+ align:start position:0%
+fractions and then they have to analyze
+it and so the question is how do they
+
+ align:start position:0%
+it and so the question is how do they
+ 
+
+ align:start position:0%
+it and so the question is how do they
+analyze to tell how well these
+
+ align:start position:0%
+analyze to tell how well these
+ 
+
+ align:start position:0%
+analyze to tell how well these
+separations actually worked what was the
+
+ align:start position:0%
+separations actually worked what was the
+ 
+
+ align:start position:0%
+separations actually worked what was the
+method that they did to determine
+
+ align:start position:0%
+method that they did to determine
+ 
+
+ align:start position:0%
+method that they did to determine
+whether they separated the ER from the
+
+ align:start position:0%
+whether they separated the ER from the
+ 
+
+ align:start position:0%
+whether they separated the ER from the
+plasma membrane from the golgi stacks
+
+ align:start position:0%
+plasma membrane from the golgi stacks
+ 
+
+ align:start position:0%
+plasma membrane from the golgi stacks
+from the lysosomes from the peri auxes
+
+ align:start position:0%
+from the lysosomes from the peri auxes
+ 
+
+ align:start position:0%
+from the lysosomes from the peri auxes
+ohms okay so they have all we have all
+
+ align:start position:0%
+ohms okay so they have all we have all
+ 
+
+ align:start position:0%
+ohms okay so they have all we have all
+these little organelles in there what
+
+ align:start position:0%
+these little organelles in there what
+ 
+
+ align:start position:0%
+these little organelles in there what
+did they do to to test each one of these
+
+ align:start position:0%
+did they do to to test each one of these
+ 
+
+ align:start position:0%
+did they do to to test each one of these
+fractions okay let me ask you this
+
+ align:start position:0%
+fractions okay let me ask you this
+ 
+
+ align:start position:0%
+fractions okay let me ask you this
+question how did they get how do you
+
+ align:start position:0%
+question how did they get how do you
+ 
+
+ align:start position:0%
+question how did they get how do you
+think they got the infirmity réalité of
+
+ align:start position:0%
+think they got the infirmity réalité of
+ 
+
+ align:start position:0%
+think they got the infirmity réalité of
+these gradients to do the experiments
+
+ align:start position:0%
+these gradients to do the experiments
+ 
+
+ align:start position:0%
+these gradients to do the experiments
+that I was just talking about so they
+
+ align:start position:0%
+that I was just talking about so they
+ 
+
+ align:start position:0%
+that I was just talking about so they
+want to analyze what's in each of these
+
+ align:start position:0%
+want to analyze what's in each of these
+ 
+
+ align:start position:0%
+want to analyze what's in each of these
+bands okay how do they get it out of
+
+ align:start position:0%
+bands okay how do they get it out of
+ 
+
+ align:start position:0%
+bands okay how do they get it out of
+this tube
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what do you think you just stick it
+
+ align:start position:0%
+so what do you think you just stick it
+ 
+
+ align:start position:0%
+so what do you think you just stick it
+down in and suck it out well I mean you
+
+ align:start position:0%
+down in and suck it out well I mean you
+ 
+
+ align:start position:0%
+down in and suck it out well I mean you
+know so what do you think say you could
+
+ align:start position:0%
+know so what do you think say you could
+ 
+
+ align:start position:0%
+know so what do you think say you could
+you could do that right you open the top
+
+ align:start position:0%
+you could do that right you open the top
+ 
+
+ align:start position:0%
+you could do that right you open the top
+you stick it in you carefully stick it
+
+ align:start position:0%
+you stick it in you carefully stick it
+ 
+
+ align:start position:0%
+you stick it in you carefully stick it
+in if you could see it lots of times you
+
+ align:start position:0%
+in if you could see it lots of times you
+ 
+
+ align:start position:0%
+in if you could see it lots of times you
+can see these lipids because they're
+
+ align:start position:0%
+can see these lipids because they're
+ 
+
+ align:start position:0%
+can see these lipids because they're
+they're like opaque or something so you
+
+ align:start position:0%
+they're like opaque or something so you
+ 
+
+ align:start position:0%
+they're like opaque or something so you
+can see or if you have if you have still
+
+ align:start position:0%
+can see or if you have if you have still
+ 
+
+ align:start position:0%
+can see or if you have if you have still
+have your sucrose layers lots of times
+
+ align:start position:0%
+have your sucrose layers lots of times
+ 
+
+ align:start position:0%
+have your sucrose layers lots of times
+they layer in between the different
+
+ align:start position:0%
+they layer in between the different
+ 
+
+ align:start position:0%
+they layer in between the different
+concentrations of the sucrose and you
+
+ align:start position:0%
+concentrations of the sucrose and you
+ 
+
+ align:start position:0%
+concentrations of the sucrose and you
+see white stuff precipitating so you
+
+ align:start position:0%
+see white stuff precipitating so you
+ 
+
+ align:start position:0%
+see white stuff precipitating so you
+could conceivably stick a pipette from
+
+ align:start position:0%
+could conceivably stick a pipette from
+ 
+
+ align:start position:0%
+could conceivably stick a pipette from
+the top and suck it out okay absolutely
+
+ align:start position:0%
+the top and suck it out okay absolutely
+ 
+
+ align:start position:0%
+the top and suck it out okay absolutely
+with your term all together layers so
+
+ align:start position:0%
+with your term all together layers so
+ 
+
+ align:start position:0%
+with your term all together layers so
+here you doing doing something it's
+
+ align:start position:0%
+here you doing doing something it's
+ 
+
+ align:start position:0%
+here you doing doing something it's
+already a very hard experiment because
+
+ align:start position:0%
+already a very hard experiment because
+ 
+
+ align:start position:0%
+already a very hard experiment because
+they're all being perturbed anyhow
+
+ align:start position:0%
+they're all being perturbed anyhow
+ 
+
+ align:start position:0%
+they're all being perturbed anyhow
+because of diffusion so is there any
+
+ align:start position:0%
+because of diffusion so is there any
+ 
+
+ align:start position:0%
+because of diffusion so is there any
+other way you could think about
+
+ align:start position:0%
+other way you could think about
+ 
+
+ align:start position:0%
+other way you could think about
+separating these things and so the hint
+
+ align:start position:0%
+separating these things and so the hint
+ 
+
+ align:start position:0%
+separating these things and so the hint
+is that they use plastic tubes so these
+
+ align:start position:0%
+is that they use plastic tubes so these
+ 
+
+ align:start position:0%
+is that they use plastic tubes so these
+things are not glass you know no
+
+ align:start position:0%
+things are not glass you know no
+ 
+
+ align:start position:0%
+things are not glass you know no
+centrifuges well I mean oh so you don't
+
+ align:start position:0%
+centrifuges well I mean oh so you don't
+ 
+
+ align:start position:0%
+centrifuges well I mean oh so you don't
+do that that could be yeah okay so you
+
+ align:start position:0%
+do that that could be yeah okay so you
+ 
+
+ align:start position:0%
+do that that could be yeah okay so you
+could but then in that but you then have
+
+ align:start position:0%
+could but then in that but you then have
+ 
+
+ align:start position:0%
+could but then in that but you then have
+to if you were cutting it you felt to
+
+ align:start position:0%
+to if you were cutting it you felt to
+ 
+
+ align:start position:0%
+to if you were cutting it you felt to
+get it out of the tube right okay unless
+
+ align:start position:0%
+get it out of the tube right okay unless
+ 
+
+ align:start position:0%
+get it out of the tube right okay unless
+you had a saw that didn't have any
+
+ align:start position:0%
+you had a saw that didn't have any
+ 
+
+ align:start position:0%
+you had a saw that didn't have any
+vibrations when you were cutting it of
+
+ align:start position:0%
+vibrations when you were cutting it of
+ 
+
+ align:start position:0%
+vibrations when you were cutting it of
+course which would not happen
+
+ align:start position:0%
+course which would not happen
+ 
+
+ align:start position:0%
+course which would not happen
+okay but if you look here in this cut in
+
+ align:start position:0%
+okay but if you look here in this cut in
+ 
+
+ align:start position:0%
+okay but if you look here in this cut in
+this cartoon so I gave you this what are
+
+ align:start position:0%
+this cartoon so I gave you this what are
+ 
+
+ align:start position:0%
+this cartoon so I gave you this what are
+they doing here this sticking a syringe
+
+ align:start position:0%
+they doing here this sticking a syringe
+ 
+
+ align:start position:0%
+they doing here this sticking a syringe
+in through the side of the tube and
+
+ align:start position:0%
+in through the side of the tube and
+ 
+
+ align:start position:0%
+in through the side of the tube and
+that's still what people use so you can
+
+ align:start position:0%
+that's still what people use so you can
+ 
+
+ align:start position:0%
+that's still what people use so you can
+suck out if you can see something you
+
+ align:start position:0%
+suck out if you can see something you
+ 
+
+ align:start position:0%
+suck out if you can see something you
+know so you have to be able to see in
+
+ align:start position:0%
+know so you have to be able to see in
+ 
+
+ align:start position:0%
+know so you have to be able to see in
+some way to know where to suck it out so
+
+ align:start position:0%
+some way to know where to suck it out so
+ 
+
+ align:start position:0%
+some way to know where to suck it out so
+you might have a way actually in doing
+
+ align:start position:0%
+you might have a way actually in doing
+ 
+
+ align:start position:0%
+you might have a way actually in doing
+ultracentrifugation I think with the
+
+ align:start position:0%
+ultracentrifugation I think with the
+ 
+
+ align:start position:0%
+ultracentrifugation I think with the
+lipids you can see them by eyeball but
+
+ align:start position:0%
+lipids you can see them by eyeball but
+ 
+
+ align:start position:0%
+lipids you can see them by eyeball but
+you might look at absorption if you if
+
+ align:start position:0%
+you might look at absorption if you if
+ 
+
+ align:start position:0%
+you might look at absorption if you if
+they have proteins you could monitor
+
+ align:start position:0%
+they have proteins you could monitor
+ 
+
+ align:start position:0%
+they have proteins you could monitor
+absorption through the gradient and that
+
+ align:start position:0%
+absorption through the gradient and that
+ 
+
+ align:start position:0%
+absorption through the gradient and that
+might tell you how to fractionate things
+
+ align:start position:0%
+might tell you how to fractionate things
+ 
+
+ align:start position:0%
+might tell you how to fractionate things
+but anyhow that's also an issue because
+
+ align:start position:0%
+but anyhow that's also an issue because
+ 
+
+ align:start position:0%
+but anyhow that's also an issue because
+before they can do the next step in the
+
+ align:start position:0%
+before they can do the next step in the
+ 
+
+ align:start position:0%
+before they can do the next step in the
+analysis they've got to get the material
+
+ align:start position:0%
+analysis they've got to get the material
+ 
+
+ align:start position:0%
+analysis they've got to get the material
+out okay so they've got the material out
+
+ align:start position:0%
+out okay so they've got the material out
+ 
+
+ align:start position:0%
+out okay so they've got the material out
+in each of these steps and then how do
+
+ align:start position:0%
+in each of these steps and then how do
+ 
+
+ align:start position:0%
+in each of these steps and then how do
+they look at this they get thick and
+
+ align:start position:0%
+they look at this they get thick and
+ 
+
+ align:start position:0%
+they look at this they get thick and
+pull it out
+
+ align:start position:0%
+pull it out
+ 
+
+ align:start position:0%
+pull it out
+so what are they looking for to tell
+
+ align:start position:0%
+so what are they looking for to tell
+ 
+
+ align:start position:0%
+so what are they looking for to tell
+them how effective this method is right
+
+ align:start position:0%
+them how effective this method is right
+ 
+
+ align:start position:0%
+them how effective this method is right
+it's at exactly so what are they so to
+
+ align:start position:0%
+it's at exactly so what are they so to
+ 
+
+ align:start position:0%
+it's at exactly so what are they so to
+do that what they're gonna have to do is
+
+ align:start position:0%
+do that what they're gonna have to do is
+ 
+
+ align:start position:0%
+do that what they're gonna have to do is
+we're going to before we look at the
+
+ align:start position:0%
+we're going to before we look at the
+ 
+
+ align:start position:0%
+we're going to before we look at the
+details of the method I want to go
+
+ align:start position:0%
+details of the method I want to go
+ 
+
+ align:start position:0%
+details of the method I want to go
+through a Western blot okay yeah so what
+
+ align:start position:0%
+through a Western blot okay yeah so what
+ 
+
+ align:start position:0%
+through a Western blot okay yeah so what
+do we know about a Western blot yeah yep
+
+ align:start position:0%
+do we know about a Western blot yeah yep
+ 
+
+ align:start position:0%
+do we know about a Western blot yeah yep
+about the which method yeah yeah yeah
+
+ align:start position:0%
+about the which method yeah yeah yeah
+ 
+
+ align:start position:0%
+about the which method yeah yeah yeah
+you could do that yeah I mean there's a
+
+ align:start position:0%
+you could do that yeah I mean there's a
+ 
+
+ align:start position:0%
+you could do that yeah I mean there's a
+lot of ways to crack up themselves I
+
+ align:start position:0%
+lot of ways to crack up themselves I
+ 
+
+ align:start position:0%
+lot of ways to crack up themselves I
+don't know which one's the best
+
+ align:start position:0%
+don't know which one's the best
+ 
+
+ align:start position:0%
+don't know which one's the best
+mammalian cells are really easy to open
+
+ align:start position:0%
+mammalian cells are really easy to open
+ 
+
+ align:start position:0%
+mammalian cells are really easy to open
+sometimes I like to do is freeze and
+
+ align:start position:0%
+sometimes I like to do is freeze and
+ 
+
+ align:start position:0%
+sometimes I like to do is freeze and
+thaw them sometimes you have like a
+
+ align:start position:0%
+thaw them sometimes you have like a
+ 
+
+ align:start position:0%
+thaw them sometimes you have like a
+little just a mortar and pestle or
+
+ align:start position:0%
+little just a mortar and pestle or
+ 
+
+ align:start position:0%
+little just a mortar and pestle or
+something like that but that's that it
+
+ align:start position:0%
+something like that but that's that it
+ 
+
+ align:start position:0%
+something like that but that's that it
+mean yeast cells you you roll them
+
+ align:start position:0%
+mean yeast cells you you roll them
+ 
+
+ align:start position:0%
+mean yeast cells you you roll them
+yep them enough cells so you can do
+
+ align:start position:0%
+yep them enough cells so you can do
+ 
+
+ align:start position:0%
+yep them enough cells so you can do
+something if you only have a tiny amount
+
+ align:start position:0%
+something if you only have a tiny amount
+ 
+
+ align:start position:0%
+something if you only have a tiny amount
+of cells it makes it really challenging
+
+ align:start position:0%
+of cells it makes it really challenging
+ 
+
+ align:start position:0%
+of cells it makes it really challenging
+with beads because it covers the beads
+
+ align:start position:0%
+with beads because it covers the beads
+ 
+
+ align:start position:0%
+with beads because it covers the beads
+see sticking to that absolutely I'm sure
+
+ align:start position:0%
+see sticking to that absolutely I'm sure
+ 
+
+ align:start position:0%
+see sticking to that absolutely I'm sure
+you have to look at all of that kind of
+
+ align:start position:0%
+you have to look at all of that kind of
+ 
+
+ align:start position:0%
+you have to look at all of that kind of
+stuff so how you choose that's an
+
+ align:start position:0%
+stuff so how you choose that's an
+ 
+
+ align:start position:0%
+stuff so how you choose that's an
+important thing to look at how you
+
+ align:start position:0%
+important thing to look at how you
+ 
+
+ align:start position:0%
+important thing to look at how you
+choose to crack open the cells and I
+
+ align:start position:0%
+choose to crack open the cells and I
+ 
+
+ align:start position:0%
+choose to crack open the cells and I
+mean it's the same with bacterial cells
+
+ align:start position:0%
+mean it's the same with bacterial cells
+ 
+
+ align:start position:0%
+mean it's the same with bacterial cells
+there there are three four ways to crack
+
+ align:start position:0%
+there there are three four ways to crack
+ 
+
+ align:start position:0%
+there there are three four ways to crack
+open the cells and I can tell you only
+
+ align:start position:0%
+open the cells and I can tell you only
+ 
+
+ align:start position:0%
+open the cells and I can tell you only
+one of them really works efficiently and
+
+ align:start position:0%
+one of them really works efficiently and
+ 
+
+ align:start position:0%
+one of them really works efficiently and
+a lot of people when they use some of
+
+ align:start position:0%
+a lot of people when they use some of
+ 
+
+ align:start position:0%
+a lot of people when they use some of
+the others you know they do something
+
+ align:start position:0%
+the others you know they do something
+ 
+
+ align:start position:0%
+the others you know they do something
+and they assume it works but they never
+
+ align:start position:0%
+and they assume it works but they never
+ 
+
+ align:start position:0%
+and they assume it works but they never
+check to see whether the cell walls have
+
+ align:start position:0%
+check to see whether the cell walls have
+ 
+
+ align:start position:0%
+check to see whether the cell walls have
+been cracked open a lot of times they
+
+ align:start position:0%
+been cracked open a lot of times they
+ 
+
+ align:start position:0%
+been cracked open a lot of times they
+haven't and so what you get out is very
+
+ align:start position:0%
+haven't and so what you get out is very
+ 
+
+ align:start position:0%
+haven't and so what you get out is very
+very low levels of protein because you
+
+ align:start position:0%
+very low levels of protein because you
+ 
+
+ align:start position:0%
+very low levels of protein because you
+haven't cracked open the cells so
+
+ align:start position:0%
+haven't cracked open the cells so
+ 
+
+ align:start position:0%
+haven't cracked open the cells so
+figuring out I mean mammalian cells are
+
+ align:start position:0%
+figuring out I mean mammalian cells are
+ 
+
+ align:start position:0%
+figuring out I mean mammalian cells are
+apparently I don't work with those
+
+ align:start position:0%
+apparently I don't work with those
+ 
+
+ align:start position:0%
+apparently I don't work with those
+myself but they're apparently much
+
+ align:start position:0%
+myself but they're apparently much
+ 
+
+ align:start position:0%
+myself but they're apparently much
+easier to disrupt than bacteria or you
+
+ align:start position:0%
+easier to disrupt than bacteria or you
+ 
+
+ align:start position:0%
+easier to disrupt than bacteria or you
+know if you look at fungi a fungi are
+
+ align:start position:0%
+know if you look at fungi a fungi are
+ 
+
+ align:start position:0%
+know if you look at fungi a fungi are
+really hard to crack crack open Easter
+
+ align:start position:0%
+really hard to crack crack open Easter
+ 
+
+ align:start position:0%
+really hard to crack crack open Easter
+so anyhow that's that's an important
+
+ align:start position:0%
+so anyhow that's that's an important
+ 
+
+ align:start position:0%
+so anyhow that's that's an important
+thing to look at so every one of these
+
+ align:start position:0%
+thing to look at so every one of these
+ 
+
+ align:start position:0%
+thing to look at so every one of these
+things I mean it again may be the devil
+
+ align:start position:0%
+things I mean it again may be the devil
+ 
+
+ align:start position:0%
+things I mean it again may be the devil
+the devil is in the detail
+
+ align:start position:0%
+the devil is in the detail
+ 
+
+ align:start position:0%
+the devil is in the detail
+but when you're doing your own research
+
+ align:start position:0%
+but when you're doing your own research
+ 
+
+ align:start position:0%
+but when you're doing your own research
+it doesn't matter what method you you're
+
+ align:start position:0%
+it doesn't matter what method you you're
+ 
+
+ align:start position:0%
+it doesn't matter what method you you're
+looking at the first time around you
+
+ align:start position:0%
+looking at the first time around you
+ 
+
+ align:start position:0%
+looking at the first time around you
+need to look at it in detail and
+
+ align:start position:0%
+need to look at it in detail and
+ 
+
+ align:start position:0%
+need to look at it in detail and
+convince yourself that this is a good
+
+ align:start position:0%
+convince yourself that this is a good
+ 
+
+ align:start position:0%
+convince yourself that this is a good
+way to chase this down and you look at
+
+ align:start position:0%
+way to chase this down and you look at
+ 
+
+ align:start position:0%
+way to chase this down and you look at
+it in detail the first time around and
+
+ align:start position:0%
+it in detail the first time around and
+ 
+
+ align:start position:0%
+it in detail the first time around and
+when you convince yourself it's working
+
+ align:start position:0%
+when you convince yourself it's working
+ 
+
+ align:start position:0%
+when you convince yourself it's working
+really well in doing what you want to do
+
+ align:start position:0%
+really well in doing what you want to do
+ 
+
+ align:start position:0%
+really well in doing what you want to do
+then you you just use it now that's the
+
+ align:start position:0%
+then you you just use it now that's the
+ 
+
+ align:start position:0%
+then you you just use it now that's the
+end of it you don't have to go back and
+
+ align:start position:0%
+end of it you don't have to go back and
+ 
+
+ align:start position:0%
+end of it you don't have to go back and
+keep thinking about this over and over
+
+ align:start position:0%
+keep thinking about this over and over
+ 
+
+ align:start position:0%
+keep thinking about this over and over
+again but so the method we're going to
+
+ align:start position:0%
+again but so the method we're going to
+ 
+
+ align:start position:0%
+again but so the method we're going to
+use is a Western blot okay so we got
+
+ align:start position:0%
+use is a Western blot okay so we got
+ 
+
+ align:start position:0%
+use is a Western blot okay so we got
+this stuff out and have you all have you
+
+ align:start position:0%
+this stuff out and have you all have you
+ 
+
+ align:start position:0%
+this stuff out and have you all have you
+all run sds-page shells
+
+ align:start position:0%
+all run sds-page shells
+ 
+
+ align:start position:0%
+all run sds-page shells
+okay so sds-page gels separate proteins
+
+ align:start position:0%
+okay so sds-page gels separate proteins
+ 
+
+ align:start position:0%
+okay so sds-page gels separate proteins
+how by the what not charge right but
+
+ align:start position:0%
+how by the what not charge right but
+ 
+
+ align:start position:0%
+how by the what not charge right but
+they but yeah it's based on size because
+
+ align:start position:0%
+they but yeah it's based on size because
+ 
+
+ align:start position:0%
+they but yeah it's based on size because
+it's coated with every protein ratio is
+
+ align:start position:0%
+it's coated with every protein ratio is
+ 
+
+ align:start position:0%
+it's coated with every protein ratio is
+coated with this detergent sodium
+
+ align:start position:0%
+coated with this detergent sodium
+ 
+
+ align:start position:0%
+coated with this detergent sodium
+dodecyl sulfate which makes them migrate
+
+ align:start position:0%
+dodecyl sulfate which makes them migrate
+ 
+
+ align:start position:0%
+dodecyl sulfate which makes them migrate
+pretty much like the molecular weight
+
+ align:start position:0%
+pretty much like the molecular weight
+ 
+
+ align:start position:0%
+pretty much like the molecular weight
+but if you've done these it's not
+
+ align:start position:0%
+but if you've done these it's not
+ 
+
+ align:start position:0%
+but if you've done these it's not
+exactly like the molecular weight you
+
+ align:start position:0%
+exactly like the molecular weight you
+ 
+
+ align:start position:0%
+exactly like the molecular weight you
+can do standards where you know the
+
+ align:start position:0%
+can do standards where you know the
+ 
+
+ align:start position:0%
+can do standards where you know the
+molecular weight you can do a standard
+
+ align:start position:0%
+molecular weight you can do a standard
+ 
+
+ align:start position:0%
+molecular weight you can do a standard
+curve and then you see where your
+
+ align:start position:0%
+curve and then you see where your
+ 
+
+ align:start position:0%
+curve and then you see where your
+protein migrates and sometimes say
+
+ align:start position:0%
+protein migrates and sometimes say
+ 
+
+ align:start position:0%
+protein migrates and sometimes say
+migrate a little faster sometimes a
+
+ align:start position:0%
+migrate a little faster sometimes a
+ 
+
+ align:start position:0%
+migrate a little faster sometimes a
+little slower but it's it's okay so you
+
+ align:start position:0%
+little slower but it's it's okay so you
+ 
+
+ align:start position:0%
+little slower but it's it's okay so you
+you run this and then what do you do
+
+ align:start position:0%
+you run this and then what do you do
+ 
+
+ align:start position:0%
+you run this and then what do you do
+does anybody know what you do next to do
+
+ align:start position:0%
+does anybody know what you do next to do
+ 
+
+ align:start position:0%
+does anybody know what you do next to do
+a Western
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the next thing they did was
+
+ align:start position:0%
+right so the next thing they did was
+ 
+
+ align:start position:0%
+right so the next thing they did was
+they used whoops I'm going to put all of
+
+ align:start position:0%
+they used whoops I'm going to put all of
+ 
+
+ align:start position:0%
+they used whoops I'm going to put all of
+these up so they transferred it to a
+
+ align:start position:0%
+these up so they transferred it to a
+ 
+
+ align:start position:0%
+these up so they transferred it to a
+membrane okay and why did they have to
+
+ align:start position:0%
+membrane okay and why did they have to
+ 
+
+ align:start position:0%
+membrane okay and why did they have to
+transfer it into a membrane to do this
+
+ align:start position:0%
+transfer it into a membrane to do this
+ 
+
+ align:start position:0%
+transfer it into a membrane to do this
+analysis and this is an extra step and
+
+ align:start position:0%
+analysis and this is an extra step and
+ 
+
+ align:start position:0%
+analysis and this is an extra step and
+it turns out so you know we're gonna
+
+ align:start position:0%
+it turns out so you know we're gonna
+ 
+
+ align:start position:0%
+it turns out so you know we're gonna
+look at an antibody interacting with a
+
+ align:start position:0%
+look at an antibody interacting with a
+ 
+
+ align:start position:0%
+look at an antibody interacting with a
+protein why don't we just look at the
+
+ align:start position:0%
+protein why don't we just look at the
+ 
+
+ align:start position:0%
+protein why don't we just look at the
+antibody interacting where the protein
+
+ align:start position:0%
+antibody interacting where the protein
+ 
+
+ align:start position:0%
+antibody interacting where the protein
+to start with right it doesn't have very
+
+ align:start position:0%
+to start with right it doesn't have very
+ 
+
+ align:start position:0%
+to start with right it doesn't have very
+good access it's really not very
+
+ align:start position:0%
+good access it's really not very
+ 
+
+ align:start position:0%
+good access it's really not very
+efficient so people found pretty much by
+
+ align:start position:0%
+efficient so people found pretty much by
+ 
+
+ align:start position:0%
+efficient so people found pretty much by
+trial and error that you needed to
+
+ align:start position:0%
+trial and error that you needed to
+ 
+
+ align:start position:0%
+trial and error that you needed to
+transfer this to a membrane I mean we
+
+ align:start position:0%
+transfer this to a membrane I mean we
+ 
+
+ align:start position:0%
+transfer this to a membrane I mean we
+have hundreds of kinds of membranes how
+
+ align:start position:0%
+have hundreds of kinds of membranes how
+ 
+
+ align:start position:0%
+have hundreds of kinds of membranes how
+do they choose nitrocellulose okay is if
+
+ align:start position:0%
+do they choose nitrocellulose okay is if
+ 
+
+ align:start position:0%
+do they choose nitrocellulose okay is if
+any of you have want run westerns you
+
+ align:start position:0%
+any of you have want run westerns you
+ 
+
+ align:start position:0%
+any of you have want run westerns you
+know remember what kind of a membrane
+
+ align:start position:0%
+know remember what kind of a membrane
+ 
+
+ align:start position:0%
+know remember what kind of a membrane
+you used did you use nitrocellulose they
+
+ align:start position:0%
+you used did you use nitrocellulose they
+ 
+
+ align:start position:0%
+you used did you use nitrocellulose they
+you do this an undergraduate class don't
+
+ align:start position:0%
+you do this an undergraduate class don't
+ 
+
+ align:start position:0%
+you do this an undergraduate class don't
+you don't you you don't do a Western
+
+ align:start position:0%
+you don't you you don't do a Western
+ 
+
+ align:start position:0%
+you don't you you don't do a Western
+okay we used to do yeah in what kind of
+
+ align:start position:0%
+okay we used to do yeah in what kind of
+ 
+
+ align:start position:0%
+okay we used to do yeah in what kind of
+a membrane was it in biology okay so
+
+ align:start position:0%
+a membrane was it in biology okay so
+ 
+
+ align:start position:0%
+a membrane was it in biology okay so
+what remember you remember what the
+
+ align:start position:0%
+what remember you remember what the
+ 
+
+ align:start position:0%
+what remember you remember what the
+membrane was yeah it's not nature
+
+ align:start position:0%
+membrane was yeah it's not nature
+ 
+
+ align:start position:0%
+membrane was yeah it's not nature
+cellulose oh this PVDF polyvinyl
+
+ align:start position:0%
+cellulose oh this PVDF polyvinyl
+ 
+
+ align:start position:0%
+cellulose oh this PVDF polyvinyl
+difluoride is the standard one that
+
+ align:start position:0%
+difluoride is the standard one that
+ 
+
+ align:start position:0%
+difluoride is the standard one that
+people use now it works much better than
+
+ align:start position:0%
+people use now it works much better than
+ 
+
+ align:start position:0%
+people use now it works much better than
+nitro cellulous this paper is really old
+
+ align:start position:0%
+nitro cellulous this paper is really old
+ 
+
+ align:start position:0%
+nitro cellulous this paper is really old
+and so they're looking at nitro
+
+ align:start position:0%
+and so they're looking at nitro
+ 
+
+ align:start position:0%
+and so they're looking at nitro
+cellulous okay so then they they do this
+
+ align:start position:0%
+cellulous okay so then they they do this
+ 
+
+ align:start position:0%
+cellulous okay so then they they do this
+okay and then what do they do next they
+
+ align:start position:0%
+okay and then what do they do next they
+ 
+
+ align:start position:0%
+okay and then what do they do next they
+have an antibody we'll look at the
+
+ align:start position:0%
+have an antibody we'll look at the
+ 
+
+ align:start position:0%
+have an antibody we'll look at the
+details of this in a minute that can
+
+ align:start position:0%
+details of this in a minute that can
+ 
+
+ align:start position:0%
+details of this in a minute that can
+recognize the protein that can find it
+
+ align:start position:0%
+recognize the protein that can find it
+ 
+
+ align:start position:0%
+recognize the protein that can find it
+on the membrane okay and then what we're
+
+ align:start position:0%
+on the membrane okay and then what we're
+ 
+
+ align:start position:0%
+on the membrane okay and then what we're
+gonna see is you still can't see
+
+ align:start position:0%
+gonna see is you still can't see
+ 
+
+ align:start position:0%
+gonna see is you still can't see
+anything really because you don't have
+
+ align:start position:0%
+anything really because you don't have
+ 
+
+ align:start position:0%
+anything really because you don't have
+very much material there and you can't
+
+ align:start position:0%
+very much material there and you can't
+ 
+
+ align:start position:0%
+very much material there and you can't
+observer you don't have enough to stain
+
+ align:start position:0%
+observer you don't have enough to stain
+ 
+
+ align:start position:0%
+observer you don't have enough to stain
+off and house by Kumasi so you're gonna
+
+ align:start position:0%
+off and house by Kumasi so you're gonna
+ 
+
+ align:start position:0%
+off and house by Kumasi so you're gonna
+have to implement so then you're gonna
+
+ align:start position:0%
+have to implement so then you're gonna
+ 
+
+ align:start position:0%
+have to implement so then you're gonna
+make an antibody to an antibody and then
+
+ align:start position:0%
+make an antibody to an antibody and then
+ 
+
+ align:start position:0%
+make an antibody to an antibody and then
+you have to figure out how to then
+
+ align:start position:0%
+you have to figure out how to then
+ 
+
+ align:start position:0%
+you have to figure out how to then
+amplify the signal and we'll look at
+
+ align:start position:0%
+amplify the signal and we'll look at
+ 
+
+ align:start position:0%
+amplify the signal and we'll look at
+that in a second is this what you ran a
+
+ align:start position:0%
+that in a second is this what you ran a
+ 
+
+ align:start position:0%
+that in a second is this what you ran a
+Western is this what westerns look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so that's good you have to block
+
+ align:start position:0%
+yeah so that's good you have to block
+ 
+
+ align:start position:0%
+yeah so that's good you have to block
+everything if you're using crude extract
+
+ align:start position:0%
+everything if you're using crude extract
+ 
+
+ align:start position:0%
+everything if you're using crude extract
+okay so in this case we would be using
+
+ align:start position:0%
+okay so in this case we would be using
+ 
+
+ align:start position:0%
+okay so in this case we would be using
+the crude mixture well not a crude
+
+ align:start position:0%
+the crude mixture well not a crude
+ 
+
+ align:start position:0%
+the crude mixture well not a crude
+mixture it's been fractionated by the
+
+ align:start position:0%
+mixture it's been fractionated by the
+ 
+
+ align:start position:0%
+mixture it's been fractionated by the
+ultracentrifugation it's been
+
+ align:start position:0%
+ultracentrifugation it's been
+ 
+
+ align:start position:0%
+ultracentrifugation it's been
+fractionated but you still have mixtures
+
+ align:start position:0%
+fractionated but you still have mixtures
+ 
+
+ align:start position:0%
+fractionated but you still have mixtures
+of proteins in there have any of you
+
+ align:start position:0%
+of proteins in there have any of you
+ 
+
+ align:start position:0%
+of proteins in there have any of you
+ever looked at westerns in a paper
+
+ align:start position:0%
+ever looked at westerns in a paper
+ 
+
+ align:start position:0%
+ever looked at westerns in a paper
+well even the papers you had to read the
+
+ align:start position:0%
+well even the papers you had to read the
+ 
+
+ align:start position:0%
+well even the papers you had to read the
+paper on the PC go back and look at the
+
+ align:start position:0%
+paper on the PC go back and look at the
+ 
+
+ align:start position:0%
+paper on the PC go back and look at the
+P CK pcsk9 paper that had westerns in it
+
+ align:start position:0%
+P CK pcsk9 paper that had westerns in it
+ 
+
+ align:start position:0%
+P CK pcsk9 paper that had westerns in it
+what do you see do people show you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something that looks like this and if
+
+ align:start position:0%
+something that looks like this and if
+ 
+
+ align:start position:0%
+something that looks like this and if
+they did show you that what would it
+
+ align:start position:0%
+they did show you that what would it
+ 
+
+ align:start position:0%
+they did show you that what would it
+look like so you have an antibody that's
+
+ align:start position:0%
+look like so you have an antibody that's
+ 
+
+ align:start position:0%
+look like so you have an antibody that's
+specific for the protein of interest
+
+ align:start position:0%
+specific for the protein of interest
+ 
+
+ align:start position:0%
+specific for the protein of interest
+whatever that is supposedly specific
+
+ align:start position:0%
+whatever that is supposedly specific
+ 
+
+ align:start position:0%
+whatever that is supposedly specific
+what do you see what do you think you
+
+ align:start position:0%
+what do you see what do you think you
+ 
+
+ align:start position:0%
+what do you see what do you think you
+see do you think antibodies are specific
+
+ align:start position:0%
+see do you think antibodies are specific
+ 
+
+ align:start position:0%
+see do you think antibodies are specific
+I think I have an example of a typical
+
+ align:start position:0%
+I think I have an example of a typical
+ 
+
+ align:start position:0%
+I think I have an example of a typical
+Western yeah yeah so when you look at
+
+ align:start position:0%
+Western yeah yeah so when you look at
+ 
+
+ align:start position:0%
+Western yeah yeah so when you look at
+when you look at a paper you should go
+
+ align:start position:0%
+when you look at a paper you should go
+ 
+
+ align:start position:0%
+when you look at a paper you should go
+back you should pay attention to this
+
+ align:start position:0%
+back you should pay attention to this
+ 
+
+ align:start position:0%
+back you should pay attention to this
+when you read a paper if you're doing
+
+ align:start position:0%
+when you read a paper if you're doing
+ 
+
+ align:start position:0%
+when you read a paper if you're doing
+anything in biology what do you see you
+
+ align:start position:0%
+anything in biology what do you see you
+ 
+
+ align:start position:0%
+anything in biology what do you see you
+never see a gel ever what you see is a
+
+ align:start position:0%
+never see a gel ever what you see is a
+ 
+
+ align:start position:0%
+never see a gel ever what you see is a
+slice of a gel where they cut off this
+
+ align:start position:0%
+slice of a gel where they cut off this
+ 
+
+ align:start position:0%
+slice of a gel where they cut off this
+whole way to they cut up all this stuff
+
+ align:start position:0%
+whole way to they cut up all this stuff
+ 
+
+ align:start position:0%
+whole way to they cut up all this stuff
+and all this stuff the reason they do
+
+ align:start position:0%
+and all this stuff the reason they do
+ 
+
+ align:start position:0%
+and all this stuff the reason they do
+that is because it's a hell of a mess
+
+ align:start position:0%
+that is because it's a hell of a mess
+ 
+
+ align:start position:0%
+that is because it's a hell of a mess
+okay so let me just show you we're
+
+ align:start position:0%
+okay so let me just show you we're
+ 
+
+ align:start position:0%
+okay so let me just show you we're
+typical I mean I don't care what kind of
+
+ align:start position:0%
+typical I mean I don't care what kind of
+ 
+
+ align:start position:0%
+typical I mean I don't care what kind of
+a antibody you're using in crude
+
+ align:start position:0%
+a antibody you're using in crude
+ 
+
+ align:start position:0%
+a antibody you're using in crude
+extracts it's a mess because you have
+
+ align:start position:0%
+extracts it's a mess because you have
+ 
+
+ align:start position:0%
+extracts it's a mess because you have
+nonspecific interactions well just look
+
+ align:start position:0%
+nonspecific interactions well just look
+ 
+
+ align:start position:0%
+nonspecific interactions well just look
+at that so that would be something like
+
+ align:start position:0%
+at that so that would be something like
+ 
+
+ align:start position:0%
+at that so that would be something like
+you might see depending on how much
+
+ align:start position:0%
+you might see depending on how much
+ 
+
+ align:start position:0%
+you might see depending on how much
+antibody you have so when you see this
+
+ align:start position:0%
+antibody you have so when you see this
+ 
+
+ align:start position:0%
+antibody you have so when you see this
+the reason everybody reports data like
+
+ align:start position:0%
+the reason everybody reports data like
+ 
+
+ align:start position:0%
+the reason everybody reports data like
+that now so it looks like it's really
+
+ align:start position:0%
+that now so it looks like it's really
+ 
+
+ align:start position:0%
+that now so it looks like it's really
+clean but in reality I think if it's
+
+ align:start position:0%
+clean but in reality I think if it's
+ 
+
+ align:start position:0%
+clean but in reality I think if it's
+dirty of that then in my opinion I would
+
+ align:start position:0%
+dirty of that then in my opinion I would
+ 
+
+ align:start position:0%
+dirty of that then in my opinion I would
+make you publish the whole gel but
+
+ align:start position:0%
+make you publish the whole gel but
+ 
+
+ align:start position:0%
+make you publish the whole gel but
+people want to do that they just
+
+ align:start position:0%
+people want to do that they just
+ 
+
+ align:start position:0%
+people want to do that they just
+cut off the little band they're
+
+ align:start position:0%
+cut off the little band they're
+ 
+
+ align:start position:0%
+cut off the little band they're
+interested in they can see it changed in
+
+ align:start position:0%
+interested in they can see it changed in
+ 
+
+ align:start position:0%
+interested in they can see it changed in
+concentration using this method but you
+
+ align:start position:0%
+concentration using this method but you
+ 
+
+ align:start position:0%
+concentration using this method but you
+should be aware of the fact that
+
+ align:start position:0%
+should be aware of the fact that
+ 
+
+ align:start position:0%
+should be aware of the fact that
+antibodies in general or specific as you
+
+ align:start position:0%
+antibodies in general or specific as you
+ 
+
+ align:start position:0%
+antibodies in general or specific as you
+think they're gonna be yeah well I mean
+
+ align:start position:0%
+think they're gonna be yeah well I mean
+ 
+
+ align:start position:0%
+think they're gonna be yeah well I mean
+I think you know probably depends on the
+
+ align:start position:0%
+I think you know probably depends on the
+ 
+
+ align:start position:0%
+I think you know probably depends on the
+journal and it probably depends on the
+
+ align:start position:0%
+journal and it probably depends on the
+ 
+
+ align:start position:0%
+journal and it probably depends on the
+reviewer but I would say we're going
+
+ align:start position:0%
+reviewer but I would say we're going
+ 
+
+ align:start position:0%
+reviewer but I would say we're going
+away from data this is something that is
+
+ align:start position:0%
+away from data this is something that is
+ 
+
+ align:start position:0%
+away from data this is something that is
+a pet peeve for me we don't and all the
+
+ align:start position:0%
+a pet peeve for me we don't and all the
+ 
+
+ align:start position:0%
+a pet peeve for me we don't and all the
+data which i think is alright is
+
+ align:start position:0%
+data which i think is alright is
+ 
+
+ align:start position:0%
+data which i think is alright is
+published and supplementary information
+
+ align:start position:0%
+published and supplementary information
+ 
+
+ align:start position:0%
+published and supplementary information
+as opposed to a paper I think if you
+
+ align:start position:0%
+as opposed to a paper I think if you
+ 
+
+ align:start position:0%
+as opposed to a paper I think if you
+have something really dirty you should
+
+ align:start position:0%
+have something really dirty you should
+ 
+
+ align:start position:0%
+have something really dirty you should
+publish in the paper in the main body of
+
+ align:start position:0%
+publish in the paper in the main body of
+ 
+
+ align:start position:0%
+publish in the paper in the main body of
+the paper do something that's really
+
+ align:start position:0%
+the paper do something that's really
+ 
+
+ align:start position:0%
+the paper do something that's really
+clean and it looks like that it's fine
+
+ align:start position:0%
+clean and it looks like that it's fine
+ 
+
+ align:start position:0%
+clean and it looks like that it's fine
+with me you don't even have to publish
+
+ align:start position:0%
+with me you don't even have to publish
+ 
+
+ align:start position:0%
+with me you don't even have to publish
+it if you could believe what people were
+
+ align:start position:0%
+it if you could believe what people were
+ 
+
+ align:start position:0%
+it if you could believe what people were
+saying okay because people know what
+
+ align:start position:0%
+saying okay because people know what
+ 
+
+ align:start position:0%
+saying okay because people know what
+this looks like a lot of people
+
+ align:start position:0%
+this looks like a lot of people
+ 
+
+ align:start position:0%
+this looks like a lot of people
+everybody uses westerns but if it's a
+
+ align:start position:0%
+everybody uses westerns but if it's a
+ 
+
+ align:start position:0%
+everybody uses westerns but if it's a
+real mess then you need to let your
+
+ align:start position:0%
+real mess then you need to let your
+ 
+
+ align:start position:0%
+real mess then you need to let your
+reader know that this is not such an
+
+ align:start position:0%
+reader know that this is not such an
+ 
+
+ align:start position:0%
+reader know that this is not such an
+easy experiment and it's not so
+
+ align:start position:0%
+easy experiment and it's not so
+ 
+
+ align:start position:0%
+easy experiment and it's not so
+clear-cut that's what your objective is
+
+ align:start position:0%
+clear-cut that's what your objective is
+ 
+
+ align:start position:0%
+clear-cut that's what your objective is
+is to show people the data from which
+
+ align:start position:0%
+is to show people the data from which
+ 
+
+ align:start position:0%
+is to show people the data from which
+you drew your conclusions and then they
+
+ align:start position:0%
+you drew your conclusions and then they
+ 
+
+ align:start position:0%
+you drew your conclusions and then they
+can draw their own conclusions which may
+
+ align:start position:0%
+can draw their own conclusions which may
+ 
+
+ align:start position:0%
+can draw their own conclusions which may
+be different okay
+
+ align:start position:0%
+be different okay
+ 
+
+ align:start position:0%
+be different okay
+so let's look at the apparatus to do
+
+ align:start position:0%
+so let's look at the apparatus to do
+ 
+
+ align:start position:0%
+so let's look at the apparatus to do
+this okay so you know how do you get
+
+ align:start position:0%
+this okay so you know how do you get
+ 
+
+ align:start position:0%
+this okay so you know how do you get
+from here to here so you have a gel you
+
+ align:start position:0%
+from here to here so you have a gel you
+ 
+
+ align:start position:0%
+from here to here so you have a gel you
+run the gel a poly acrylamide gel what
+
+ align:start position:0%
+run the gel a poly acrylamide gel what
+ 
+
+ align:start position:0%
+run the gel a poly acrylamide gel what
+do you do so you put the membrane on the
+
+ align:start position:0%
+do you do so you put the membrane on the
+ 
+
+ align:start position:0%
+do you do so you put the membrane on the
+gel and what do you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah so you have to you're
+
+ align:start position:0%
+okay yeah so you have to you're
+ 
+
+ align:start position:0%
+okay yeah so you have to you're
+transferring it based on applying a
+
+ align:start position:0%
+transferring it based on applying a
+ 
+
+ align:start position:0%
+transferring it based on applying a
+voltage across this system so here's
+
+ align:start position:0%
+voltage across this system so here's
+ 
+
+ align:start position:0%
+voltage across this system so here's
+your gel okay and here's your membrane
+
+ align:start position:0%
+your gel okay and here's your membrane
+ 
+
+ align:start position:0%
+your gel okay and here's your membrane
+nitrocellulose membrane okay and then
+
+ align:start position:0%
+nitrocellulose membrane okay and then
+ 
+
+ align:start position:0%
+nitrocellulose membrane okay and then
+they have filter paper above and above
+
+ align:start position:0%
+they have filter paper above and above
+ 
+
+ align:start position:0%
+they have filter paper above and above
+the gel and below the membrane and why
+
+ align:start position:0%
+the gel and below the membrane and why
+ 
+
+ align:start position:0%
+the gel and below the membrane and why
+do you think they have the filter paper
+
+ align:start position:0%
+do you think they have the filter paper
+ 
+
+ align:start position:0%
+do you think they have the filter paper
+paper there did you when you were in the
+
+ align:start position:0%
+paper there did you when you were in the
+ 
+
+ align:start position:0%
+paper there did you when you were in the
+gel did you have filter paper yeah how
+
+ align:start position:0%
+gel did you have filter paper yeah how
+ 
+
+ align:start position:0%
+gel did you have filter paper yeah how
+do you think they decide how to do this
+
+ align:start position:0%
+do you think they decide how to do this
+ 
+
+ align:start position:0%
+do you think they decide how to do this
+transfer do you think this is
+
+ align:start position:0%
+transfer do you think this is
+ 
+
+ align:start position:0%
+transfer do you think this is
+straightforward you know do you run it
+
+ align:start position:0%
+straightforward you know do you run it
+ 
+
+ align:start position:0%
+straightforward you know do you run it
+for an hour do you run it for five hours
+
+ align:start position:0%
+for an hour do you run it for five hours
+ 
+
+ align:start position:0%
+for an hour do you run it for five hours
+do you run it for 15 minutes what is the
+
+ align:start position:0%
+do you run it for 15 minutes what is the
+ 
+
+ align:start position:0%
+do you run it for 15 minutes what is the
+voltage you use to do the transfer do
+
+ align:start position:0%
+voltage you use to do the transfer do
+ 
+
+ align:start position:0%
+voltage you use to do the transfer do
+you think any of that it's hard to
+
+ align:start position:0%
+you think any of that it's hard to
+ 
+
+ align:start position:0%
+you think any of that it's hard to
+figure out okay so how do you figure
+
+ align:start position:0%
+figure out okay so how do you figure
+ 
+
+ align:start position:0%
+figure out okay so how do you figure
+that out do you just somebody told you
+
+ align:start position:0%
+that out do you just somebody told you
+ 
+
+ align:start position:0%
+that out do you just somebody told you
+that this is a good way to do it
+
+ align:start position:0%
+that this is a good way to do it
+ 
+
+ align:start position:0%
+that this is a good way to do it
+yeah so that might be a place you start
+
+ align:start position:0%
+yeah so that might be a place you start
+ 
+
+ align:start position:0%
+yeah so that might be a place you start
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you do it because somebody gave you a
+
+ align:start position:0%
+so you do it because somebody gave you a
+ 
+
+ align:start position:0%
+so you do it because somebody gave you a
+recipe okay but then what do you need to
+
+ align:start position:0%
+recipe okay but then what do you need to
+ 
+
+ align:start position:0%
+recipe okay but then what do you need to
+do to make sure this recipe is correct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so and then how do you do that so
+
+ align:start position:0%
+right so and then how do you do that so
+ 
+
+ align:start position:0%
+right so and then how do you do that so
+that that's true every protein is gonna
+
+ align:start position:0%
+that that's true every protein is gonna
+ 
+
+ align:start position:0%
+that that's true every protein is gonna
+be different and if you have a protein
+
+ align:start position:0%
+be different and if you have a protein
+ 
+
+ align:start position:0%
+be different and if you have a protein
+if you have a clean protein versus a
+
+ align:start position:0%
+if you have a clean protein versus a
+ 
+
+ align:start position:0%
+if you have a clean protein versus a
+mess of proteins and you try to do this
+
+ align:start position:0%
+mess of proteins and you try to do this
+ 
+
+ align:start position:0%
+mess of proteins and you try to do this
+transfer the transfer conditions will be
+
+ align:start position:0%
+transfer the transfer conditions will be
+ 
+
+ align:start position:0%
+transfer the transfer conditions will be
+different so for example if you really
+
+ align:start position:0%
+different so for example if you really
+ 
+
+ align:start position:0%
+different so for example if you really
+want to look at the concentration of
+
+ align:start position:0%
+want to look at the concentration of
+ 
+
+ align:start position:0%
+want to look at the concentration of
+something inside the cell and the crude
+
+ align:start position:0%
+something inside the cell and the crude
+ 
+
+ align:start position:0%
+something inside the cell and the crude
+extracts you never compare it to a
+
+ align:start position:0%
+extracts you never compare it to a
+ 
+
+ align:start position:0%
+extracts you never compare it to a
+standard with clean protein because this
+
+ align:start position:0%
+standard with clean protein because this
+ 
+
+ align:start position:0%
+standard with clean protein because this
+transfer is different so you need in the
+
+ align:start position:0%
+transfer is different so you need in the
+ 
+
+ align:start position:0%
+transfer is different so you need in the
+back of your mind if you care about
+
+ align:start position:0%
+back of your mind if you care about
+ 
+
+ align:start position:0%
+back of your mind if you care about
+quantitating this you need to understand
+
+ align:start position:0%
+quantitating this you need to understand
+ 
+
+ align:start position:0%
+quantitating this you need to understand
+the basis of the transfer okay so why do
+
+ align:start position:0%
+the basis of the transfer okay so why do
+ 
+
+ align:start position:0%
+the basis of the transfer okay so why do
+you think they have these filter papers
+
+ align:start position:0%
+you think they have these filter papers
+ 
+
+ align:start position:0%
+you think they have these filter papers
+here so this goes back to what controls
+
+ align:start position:0%
+here so this goes back to what controls
+ 
+
+ align:start position:0%
+here so this goes back to what controls
+you you would do to see whether your
+
+ align:start position:0%
+you you would do to see whether your
+ 
+
+ align:start position:0%
+you you would do to see whether your
+transfer was working so what would you
+
+ align:start position:0%
+transfer was working so what would you
+ 
+
+ align:start position:0%
+transfer was working so what would you
+look for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did you do this what did you do why do
+
+ align:start position:0%
+did you do this what did you do why do
+ 
+
+ align:start position:0%
+did you do this what did you do why do
+you have that what did you do with the
+
+ align:start position:0%
+you have that what did you do with the
+ 
+
+ align:start position:0%
+you have that what did you do with the
+filter papers in your you did what no no
+
+ align:start position:0%
+filter papers in your you did what no no
+ 
+
+ align:start position:0%
+filter papers in your you did what no no
+that's not what you do yeah I mean you
+
+ align:start position:0%
+that's not what you do yeah I mean you
+ 
+
+ align:start position:0%
+that's not what you do yeah I mean you
+might want to do some of that too but
+
+ align:start position:0%
+might want to do some of that too but
+ 
+
+ align:start position:0%
+might want to do some of that too but
+what is the bit in terms of thinking
+
+ align:start position:0%
+what is the bit in terms of thinking
+ 
+
+ align:start position:0%
+what is the bit in terms of thinking
+about whether your transfer is
+
+ align:start position:0%
+about whether your transfer is
+ 
+
+ align:start position:0%
+about whether your transfer is
+successful you know figuring out the
+
+ align:start position:0%
+successful you know figuring out the
+ 
+
+ align:start position:0%
+successful you know figuring out the
+conditions to blot from the gel to a
+
+ align:start position:0%
+conditions to blot from the gel to a
+ 
+
+ align:start position:0%
+conditions to blot from the gel to a
+piece of paper it's not trivial okay
+
+ align:start position:0%
+piece of paper it's not trivial okay
+ 
+
+ align:start position:0%
+piece of paper it's not trivial okay
+and so this there is a standard way that
+
+ align:start position:0%
+and so this there is a standard way that
+ 
+
+ align:start position:0%
+and so this there is a standard way that
+you do this initially to try but then
+
+ align:start position:0%
+you do this initially to try but then
+ 
+
+ align:start position:0%
+you do this initially to try but then
+you have to make sure that that method
+
+ align:start position:0%
+you have to make sure that that method
+ 
+
+ align:start position:0%
+you have to make sure that that method
+is working and lots of times it doesn't
+
+ align:start position:0%
+is working and lots of times it doesn't
+ 
+
+ align:start position:0%
+is working and lots of times it doesn't
+work so it's something that's going to
+
+ align:start position:0%
+work so it's something that's going to
+ 
+
+ align:start position:0%
+work so it's something that's going to
+be experimentally determined so the
+
+ align:start position:0%
+be experimentally determined so the
+ 
+
+ align:start position:0%
+be experimentally determined so the
+question is what happens if you did what
+
+ align:start position:0%
+question is what happens if you did what
+ 
+
+ align:start position:0%
+question is what happens if you did what
+would you think would happen if you do
+
+ align:start position:0%
+would you think would happen if you do
+ 
+
+ align:start position:0%
+would you think would happen if you do
+this for six or seven hours whereas a
+
+ align:start position:0%
+this for six or seven hours whereas a
+ 
+
+ align:start position:0%
+this for six or seven hours whereas a
+normal blot would take two hours right
+
+ align:start position:0%
+normal blot would take two hours right
+ 
+
+ align:start position:0%
+normal blot would take two hours right
+it would go right into the filter paper
+
+ align:start position:0%
+it would go right into the filter paper
+ 
+
+ align:start position:0%
+it would go right into the filter paper
+or even off the filter paper so what you
+
+ align:start position:0%
+or even off the filter paper so what you
+ 
+
+ align:start position:0%
+or even off the filter paper so what you
+do is you take the filter paper out you
+
+ align:start position:0%
+do is you take the filter paper out you
+ 
+
+ align:start position:0%
+do is you take the filter paper out you
+look for protein being found okay what
+
+ align:start position:0%
+look for protein being found okay what
+ 
+
+ align:start position:0%
+look for protein being found okay what
+about the gel what do you do with the
+
+ align:start position:0%
+about the gel what do you do with the
+ 
+
+ align:start position:0%
+about the gel what do you do with the
+gel after your experiments over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right make sure that the proteins not on
+
+ align:start position:0%
+right make sure that the proteins not on
+ 
+
+ align:start position:0%
+right make sure that the proteins not on
+it so these are simple controls but
+
+ align:start position:0%
+it so these are simple controls but
+ 
+
+ align:start position:0%
+it so these are simple controls but
+these are the controls you always do
+
+ align:start position:0%
+these are the controls you always do
+ 
+
+ align:start position:0%
+these are the controls you always do
+until you work out the conditions to
+
+ align:start position:0%
+until you work out the conditions to
+ 
+
+ align:start position:0%
+until you work out the conditions to
+make sure this works and it's pretty
+
+ align:start position:0%
+make sure this works and it's pretty
+ 
+
+ align:start position:0%
+make sure this works and it's pretty
+critical to make sure you have good
+
+ align:start position:0%
+critical to make sure you have good
+ 
+
+ align:start position:0%
+critical to make sure you have good
+transfer so then if you look at the area
+
+ align:start position:0%
+transfer so then if you look at the area
+ 
+
+ align:start position:0%
+transfer so then if you look at the area
+so this is the antibody thing that they
+
+ align:start position:0%
+so this is the antibody thing that they
+ 
+
+ align:start position:0%
+so this is the antibody thing that they
+do is anybody thought about these kinds
+
+ align:start position:0%
+do is anybody thought about these kinds
+ 
+
+ align:start position:0%
+do is anybody thought about these kinds
+of assays you've seen them I think
+
+ align:start position:0%
+of assays you've seen them I think
+ 
+
+ align:start position:0%
+of assays you've seen them I think
+already in class but you have what's
+
+ align:start position:0%
+already in class but you have what's
+ 
+
+ align:start position:0%
+already in class but you have what's
+wrong with this picture the target
+
+ align:start position:0%
+wrong with this picture the target
+ 
+
+ align:start position:0%
+wrong with this picture the target
+protein what's wrong with this picture
+
+ align:start position:0%
+protein what's wrong with this picture
+ 
+
+ align:start position:0%
+protein what's wrong with this picture
+and the target so here's your
+
+ align:start position:0%
+and the target so here's your
+ 
+
+ align:start position:0%
+and the target so here's your
+nitrocellulose filter paper what's wrong
+
+ align:start position:0%
+nitrocellulose filter paper what's wrong
+ 
+
+ align:start position:0%
+nitrocellulose filter paper what's wrong
+with this / - should be unfolded yeah so
+
+ align:start position:0%
+with this / - should be unfolded yeah so
+ 
+
+ align:start position:0%
+with this / - should be unfolded yeah so
+you're doing SDS page it's unfolded so
+
+ align:start position:0%
+you're doing SDS page it's unfolded so
+ 
+
+ align:start position:0%
+you're doing SDS page it's unfolded so
+then we react it with an antibody
+
+ align:start position:0%
+then we react it with an antibody
+ 
+
+ align:start position:0%
+then we react it with an antibody
+presumably we have a good antibody but
+
+ align:start position:0%
+presumably we have a good antibody but
+ 
+
+ align:start position:0%
+presumably we have a good antibody but
+you've already learned in the first half
+
+ align:start position:0%
+you've already learned in the first half
+ 
+
+ align:start position:0%
+you've already learned in the first half
+of this course it having really good
+
+ align:start position:0%
+of this course it having really good
+ 
+
+ align:start position:0%
+of this course it having really good
+antibodies is not so trivial you can get
+
+ align:start position:0%
+antibodies is not so trivial you can get
+ 
+
+ align:start position:0%
+antibodies is not so trivial you can get
+them but most of the time they are not
+
+ align:start position:0%
+them but most of the time they are not
+ 
+
+ align:start position:0%
+them but most of the time they are not
+specific if you're looking at crude
+
+ align:start position:0%
+specific if you're looking at crude
+ 
+
+ align:start position:0%
+specific if you're looking at crude
+extracts they have little epitopes they
+
+ align:start position:0%
+extracts they have little epitopes they
+ 
+
+ align:start position:0%
+extracts they have little epitopes they
+recognize if you're using monoclonal
+
+ align:start position:0%
+recognize if you're using monoclonal
+ 
+
+ align:start position:0%
+recognize if you're using monoclonal
+that could be present and other proteins
+
+ align:start position:0%
+that could be present and other proteins
+ 
+
+ align:start position:0%
+that could be present and other proteins
+and so and furthermore that how do you
+
+ align:start position:0%
+and so and furthermore that how do you
+ 
+
+ align:start position:0%
+and so and furthermore that how do you
+how are you detecting something approach
+
+ align:start position:0%
+how are you detecting something approach
+ 
+
+ align:start position:0%
+how are you detecting something approach
+an antibody is a protein it has
+
+ align:start position:0%
+an antibody is a protein it has
+ 
+
+ align:start position:0%
+an antibody is a protein it has
+absorption at 280 again this is too low
+
+ align:start position:0%
+absorption at 280 again this is too low
+ 
+
+ align:start position:0%
+absorption at 280 again this is too low
+to see so putting an antibody on it is
+
+ align:start position:0%
+to see so putting an antibody on it is
+ 
+
+ align:start position:0%
+to see so putting an antibody on it is
+still going to be too low to detect so
+
+ align:start position:0%
+still going to be too low to detect so
+ 
+
+ align:start position:0%
+still going to be too low to detect so
+how do you detect your signal so have
+
+ align:start position:0%
+how do you detect your signal so have
+ 
+
+ align:start position:0%
+how do you detect your signal so have
+you done this so I'm surprised they
+
+ align:start position:0%
+you done this so I'm surprised they
+ 
+
+ align:start position:0%
+you done this so I'm surprised they
+don't do this in your introductory class
+
+ align:start position:0%
+don't do this in your introductory class
+ 
+
+ align:start position:0%
+don't do this in your introductory class
+they don't do westerns at all okay so
+
+ align:start position:0%
+they don't do westerns at all okay so
+ 
+
+ align:start position:0%
+they don't do westerns at all okay so
+what you're looking at is an antibody -
+
+ align:start position:0%
+what you're looking at is an antibody -
+ 
+
+ align:start position:0%
+what you're looking at is an antibody -
+an antibody okay so you put your
+
+ align:start position:0%
+an antibody okay so you put your
+ 
+
+ align:start position:0%
+an antibody okay so you put your
+antibody on that's specific for your
+
+ align:start position:0%
+antibody on that's specific for your
+ 
+
+ align:start position:0%
+antibody on that's specific for your
+protein and then you make an antibody
+
+ align:start position:0%
+protein and then you make an antibody
+ 
+
+ align:start position:0%
+protein and then you make an antibody
+and another organism that can
+
+ align:start position:0%
+and another organism that can
+ 
+
+ align:start position:0%
+and another organism that can
+specifically recognize antibodies in
+
+ align:start position:0%
+specifically recognize antibodies in
+ 
+
+ align:start position:0%
+specifically recognize antibodies in
+general okay so if this is to a mouse
+
+ align:start position:0%
+general okay so if this is to a mouse
+ 
+
+ align:start position:0%
+general okay so if this is to a mouse
+you make it in a go and and isolate that
+
+ align:start position:0%
+you make it in a go and and isolate that
+ 
+
+ align:start position:0%
+you make it in a go and and isolate that
+and then what you do is derivatives the
+
+ align:start position:0%
+and then what you do is derivatives the
+ 
+
+ align:start position:0%
+and then what you do is derivatives the
+second antibody with what a protein okay
+
+ align:start position:0%
+second antibody with what a protein okay
+ 
+
+ align:start position:0%
+second antibody with what a protein okay
+that can can function as a catalyst
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well did what what did you say well no I
+
+ align:start position:0%
+well did what what did you say well no I
+ 
+
+ align:start position:0%
+well did what what did you say well no I
+mean I don't know whether it's more
+
+ align:start position:0%
+mean I don't know whether it's more
+ 
+
+ align:start position:0%
+mean I don't know whether it's more
+expensive or not but yeah so you'd have
+
+ align:start position:0%
+expensive or not but yeah so you'd have
+ 
+
+ align:start position:0%
+expensive or not but yeah so you'd have
+to derivative guys every primary
+
+ align:start position:0%
+to derivative guys every primary
+ 
+
+ align:start position:0%
+to derivative guys every primary
+antibody and so this is sort of a
+
+ align:start position:0%
+antibody and so this is sort of a
+ 
+
+ align:start position:0%
+antibody and so this is sort of a
+standard procedure you couldn't
+
+ align:start position:0%
+standard procedure you couldn't
+ 
+
+ align:start position:0%
+standard procedure you couldn't
+derivatives the primary antibody so
+
+ align:start position:0%
+derivatives the primary antibody so
+ 
+
+ align:start position:0%
+derivatives the primary antibody so
+that's not a bad question
+
+ align:start position:0%
+that's not a bad question
+ 
+
+ align:start position:0%
+that's not a bad question
+and so what you're doing now you can buy
+
+ align:start position:0%
+and so what you're doing now you can buy
+ 
+
+ align:start position:0%
+and so what you're doing now you can buy
+these commercially you know so they have
+
+ align:start position:0%
+these commercially you know so they have
+ 
+
+ align:start position:0%
+these commercially you know so they have
+go rabbit rabbit
+
+ align:start position:0%
+go rabbit rabbit
+ 
+
+ align:start position:0%
+go rabbit rabbit
+mouse whatever antibodies and the key is
+
+ align:start position:0%
+mouse whatever antibodies and the key is
+ 
+
+ align:start position:0%
+mouse whatever antibodies and the key is
+the amplification of the signal and use
+
+ align:start position:0%
+the amplification of the signal and use
+ 
+
+ align:start position:0%
+the amplification of the signal and use
+enzymes to amplify the signal does
+
+ align:start position:0%
+enzymes to amplify the signal does
+ 
+
+ align:start position:0%
+enzymes to amplify the signal does
+anybody know what the enzymes are with
+
+ align:start position:0%
+anybody know what the enzymes are with
+ 
+
+ align:start position:0%
+anybody know what the enzymes are with
+the enzymes do to amplify the signal to
+
+ align:start position:0%
+the enzymes do to amplify the signal to
+ 
+
+ align:start position:0%
+the enzymes do to amplify the signal to
+something that's colored okay so does
+
+ align:start position:0%
+something that's colored okay so does
+ 
+
+ align:start position:0%
+something that's colored okay so does
+anybody know what that horseradish
+
+ align:start position:0%
+anybody know what that horseradish
+ 
+
+ align:start position:0%
+anybody know what that horseradish
+peroxidase have you ever heard of
+
+ align:start position:0%
+peroxidase have you ever heard of
+ 
+
+ align:start position:0%
+peroxidase have you ever heard of
+horseradish peroxidase so that's a heme
+
+ align:start position:0%
+horseradish peroxidase so that's a heme
+ 
+
+ align:start position:0%
+horseradish peroxidase so that's a heme
+iron we're gonna be talking about heme
+
+ align:start position:0%
+iron we're gonna be talking about heme
+ 
+
+ align:start position:0%
+iron we're gonna be talking about heme
+iron is pretty soon and hydrogen
+
+ align:start position:0%
+iron is pretty soon and hydrogen
+ 
+
+ align:start position:0%
+iron is pretty soon and hydrogen
+peroxide and makes our chemically very
+
+ align:start position:0%
+peroxide and makes our chemically very
+ 
+
+ align:start position:0%
+peroxide and makes our chemically very
+reactive iron oxide species that can
+
+ align:start position:0%
+reactive iron oxide species that can
+ 
+
+ align:start position:0%
+reactive iron oxide species that can
+oxidize a dye that changes color and it
+
+ align:start position:0%
+oxidize a dye that changes color and it
+ 
+
+ align:start position:0%
+oxidize a dye that changes color and it
+has an extremely high extinction
+
+ align:start position:0%
+has an extremely high extinction
+ 
+
+ align:start position:0%
+has an extremely high extinction
+coefficient so you can see it and it
+
+ align:start position:0%
+coefficient so you can see it and it
+ 
+
+ align:start position:0%
+coefficient so you can see it and it
+does the catalytically and the lifetime
+
+ align:start position:0%
+does the catalytically and the lifetime
+ 
+
+ align:start position:0%
+does the catalytically and the lifetime
+of the dye is long enough so it
+
+ align:start position:0%
+of the dye is long enough so it
+ 
+
+ align:start position:0%
+of the dye is long enough so it
+accumulates and you can get really
+
+ align:start position:0%
+accumulates and you can get really
+ 
+
+ align:start position:0%
+accumulates and you can get really
+amplification over your signal or you
+
+ align:start position:0%
+amplification over your signal or you
+ 
+
+ align:start position:0%
+amplification over your signal or you
+can use a phosphatase that liberate
+
+ align:start position:0%
+can use a phosphatase that liberate
+ 
+
+ align:start position:0%
+can use a phosphatase that liberate
+something that's highly colored again
+
+ align:start position:0%
+something that's highly colored again
+ 
+
+ align:start position:0%
+something that's highly colored again
+and you can see it so this is a standard
+
+ align:start position:0%
+and you can see it so this is a standard
+ 
+
+ align:start position:0%
+and you can see it so this is a standard
+method that everybody uses and so that's
+
+ align:start position:0%
+method that everybody uses and so that's
+ 
+
+ align:start position:0%
+method that everybody uses and so that's
+our gel so now we're looking at sort of
+
+ align:start position:0%
+our gel so now we're looking at sort of
+ 
+
+ align:start position:0%
+our gel so now we're looking at sort of
+we're at the end already but we're
+
+ align:start position:0%
+we're at the end already but we're
+ 
+
+ align:start position:0%
+we're at the end already but we're
+looking at these gels and what do you
+
+ align:start position:0%
+looking at these gels and what do you
+ 
+
+ align:start position:0%
+looking at these gels and what do you
+see through the different steps so if we
+
+ align:start position:0%
+see through the different steps so if we
+ 
+
+ align:start position:0%
+see through the different steps so if we
+look through the first gradient through
+
+ align:start position:0%
+look through the first gradient through
+ 
+
+ align:start position:0%
+look through the first gradient through
+the sucrose gradient that gets us
+
+ align:start position:0%
+the sucrose gradient that gets us
+ 
+
+ align:start position:0%
+the sucrose gradient that gets us
+through DNA okay and if you look say at
+
+ align:start position:0%
+through DNA okay and if you look say at
+ 
+
+ align:start position:0%
+through DNA okay and if you look say at
+Lane E and our goal is to separate
+
+ align:start position:0%
+Lane E and our goal is to separate
+ 
+
+ align:start position:0%
+Lane E and our goal is to separate
+proteins that are specifically localized
+
+ align:start position:0%
+proteins that are specifically localized
+ 
+
+ align:start position:0%
+proteins that are specifically localized
+in each one of these membranes so you
+
+ align:start position:0%
+in each one of these membranes so you
+ 
+
+ align:start position:0%
+in each one of these membranes so you
+need to believe that's true
+
+ align:start position:0%
+need to believe that's true
+ 
+
+ align:start position:0%
+need to believe that's true
+okay that people have selected the right
+
+ align:start position:0%
+okay that people have selected the right
+ 
+
+ align:start position:0%
+okay that people have selected the right
+group of proteins to look for and you
+
+ align:start position:0%
+group of proteins to look for and you
+ 
+
+ align:start position:0%
+group of proteins to look for and you
+notice they do more than one okay so
+
+ align:start position:0%
+notice they do more than one okay so
+ 
+
+ align:start position:0%
+notice they do more than one okay so
+they look at multiple proteins why do
+
+ align:start position:0%
+they look at multiple proteins why do
+ 
+
+ align:start position:0%
+they look at multiple proteins why do
+you think you need how do you think it's
+
+ align:start position:0%
+you think you need how do you think it's
+ 
+
+ align:start position:0%
+you think you need how do you think it's
+easy to select the proteins to look for
+
+ align:start position:0%
+easy to select the proteins to look for
+ 
+
+ align:start position:0%
+easy to select the proteins to look for
+and why or why not so I mean they
+
+ align:start position:0%
+and why or why not so I mean they
+ 
+
+ align:start position:0%
+and why or why not so I mean they
+obviously have selected a group of
+
+ align:start position:0%
+obviously have selected a group of
+ 
+
+ align:start position:0%
+obviously have selected a group of
+proteins and I think you know people
+
+ align:start position:0%
+proteins and I think you know people
+ 
+
+ align:start position:0%
+proteins and I think you know people
+most people would agree that they've
+
+ align:start position:0%
+most people would agree that they've
+ 
+
+ align:start position:0%
+most people would agree that they've
+selected a good group of proteins but
+
+ align:start position:0%
+selected a good group of proteins but
+ 
+
+ align:start position:0%
+selected a good group of proteins but
+what do we know now about proteins -
+
+ align:start position:0%
+what do we know now about proteins -
+ 
+
+ align:start position:0%
+what do we know now about proteins -
+they stay in one place you know they
+
+ align:start position:0%
+they stay in one place you know they
+ 
+
+ align:start position:0%
+they stay in one place you know they
+move around and so so but someone might
+
+ align:start position:0%
+move around and so so but someone might
+ 
+
+ align:start position:0%
+move around and so so but someone might
+be present and very low amount sometimes
+
+ align:start position:0%
+be present and very low amount sometimes
+ 
+
+ align:start position:0%
+be present and very low amount sometimes
+in much higher amounts and so you need
+
+ align:start position:0%
+in much higher amounts and so you need
+ 
+
+ align:start position:0%
+in much higher amounts and so you need
+to have more than one protein as a
+
+ align:start position:0%
+to have more than one protein as a
+ 
+
+ align:start position:0%
+to have more than one protein as a
+control to make sure you're looking at
+
+ align:start position:0%
+control to make sure you're looking at
+ 
+
+ align:start position:0%
+control to make sure you're looking at
+in the right region and what do you see
+
+ align:start position:0%
+in the right region and what do you see
+ 
+
+ align:start position:0%
+in the right region and what do you see
+in E if you look over here it tells you
+
+ align:start position:0%
+in E if you look over here it tells you
+ 
+
+ align:start position:0%
+in E if you look over here it tells you
+what the organelle is and if you look at
+
+ align:start position:0%
+what the organelle is and if you look at
+ 
+
+ align:start position:0%
+what the organelle is and if you look at
+this protein this is localized to the
+
+ align:start position:0%
+this protein this is localized to the
+ 
+
+ align:start position:0%
+this protein this is localized to the
+lysosomes we talked about that in class
+
+ align:start position:0%
+lysosomes we talked about that in class
+ 
+
+ align:start position:0%
+lysosomes we talked about that in class
+if you looked at this protein it's
+
+ align:start position:0%
+if you looked at this protein it's
+ 
+
+ align:start position:0%
+if you looked at this protein it's
+localized to the peroxisomes so in
+
+ align:start position:0%
+localized to the peroxisomes so in
+ 
+
+ align:start position:0%
+localized to the peroxisomes so in
+addition to the ones we care about the
+
+ align:start position:0%
+addition to the ones we care about the
+ 
+
+ align:start position:0%
+addition to the ones we care about the
+ER proteins we're also getting proteins
+
+ align:start position:0%
+ER proteins we're also getting proteins
+ 
+
+ align:start position:0%
+ER proteins we're also getting proteins
+that are localized in other membranes so
+
+ align:start position:0%
+that are localized in other membranes so
+ 
+
+ align:start position:0%
+that are localized in other membranes so
+that's when they went to the next to the
+
+ align:start position:0%
+that's when they went to the next to the
+ 
+
+ align:start position:0%
+that's when they went to the next to the
+next method and they added on another
+
+ align:start position:0%
+next method and they added on another
+ 
+
+ align:start position:0%
+next method and they added on another
+gradient to try to separate out again
+
+ align:start position:0%
+gradient to try to separate out again
+ 
+
+ align:start position:0%
+gradient to try to separate out again
+the lysosomal and the peroxisome old
+
+ align:start position:0%
+the lysosomal and the peroxisome old
+ 
+
+ align:start position:0%
+the lysosomal and the peroxisome old
+proteins and you can see they were
+
+ align:start position:0%
+proteins and you can see they were
+ 
+
+ align:start position:0%
+proteins and you can see they were
+pretty successful at this there's none
+
+ align:start position:0%
+pretty successful at this there's none
+ 
+
+ align:start position:0%
+pretty successful at this there's none
+of these proteins left in this gradient
+
+ align:start position:0%
+of these proteins left in this gradient
+ 
+
+ align:start position:0%
+of these proteins left in this gradient
+okay so that's that's good and they took
+
+ align:start position:0%
+okay so that's that's good and they took
+ 
+
+ align:start position:0%
+okay so that's that's good and they took
+it a step further do you remember what
+
+ align:start position:0%
+it a step further do you remember what
+ 
+
+ align:start position:0%
+it a step further do you remember what
+this is what are they looking for down
+
+ align:start position:0%
+this is what are they looking for down
+ 
+
+ align:start position:0%
+this is what are they looking for down
+here in this yeah so enzymatic
+
+ align:start position:0%
+here in this yeah so enzymatic
+ 
+
+ align:start position:0%
+here in this yeah so enzymatic
+activities are localized in certain
+
+ align:start position:0%
+activities are localized in certain
+ 
+
+ align:start position:0%
+activities are localized in certain
+organelle so they again did a second
+
+ align:start position:0%
+organelle so they again did a second
+ 
+
+ align:start position:0%
+organelle so they again did a second
+experiment to look at all of that so I
+
+ align:start position:0%
+experiment to look at all of that so I
+ 
+
+ align:start position:0%
+experiment to look at all of that so I
+mean they were very careful in this they
+
+ align:start position:0%
+mean they were very careful in this they
+ 
+
+ align:start position:0%
+mean they were very careful in this they
+figured out how to separate and that's
+
+ align:start position:0%
+figured out how to separate and that's
+ 
+
+ align:start position:0%
+figured out how to separate and that's
+the key thing for them to analyzing the
+
+ align:start position:0%
+the key thing for them to analyzing the
+ 
+
+ align:start position:0%
+the key thing for them to analyzing the
+concentration of cholesterol in these
+
+ align:start position:0%
+concentration of cholesterol in these
+ 
+
+ align:start position:0%
+concentration of cholesterol in these
+membranes and what they looked at we're
+
+ align:start position:0%
+membranes and what they looked at we're
+ 
+
+ align:start position:0%
+membranes and what they looked at we're
+over time but is the concentration of
+
+ align:start position:0%
+over time but is the concentration of
+ 
+
+ align:start position:0%
+over time but is the concentration of
+cholesterol compared to the total amount
+
+ align:start position:0%
+cholesterol compared to the total amount
+ 
+
+ align:start position:0%
+cholesterol compared to the total amount
+of lipids okay and
+
+ align:start position:0%
+of lipids okay and
+ 
+
+ align:start position:0%
+of lipids okay and
+how do they do that analysis you know
+
+ align:start position:0%
+how do they do that analysis you know
+ 
+
+ align:start position:0%
+how do they do that analysis you know
+there's Jean Kennedy who's at Harvard
+
+ align:start position:0%
+there's Jean Kennedy who's at Harvard
+ 
+
+ align:start position:0%
+there's Jean Kennedy who's at Harvard
+Medical School he's in his 90s now
+
+ align:start position:0%
+Medical School he's in his 90s now
+ 
+
+ align:start position:0%
+Medical School he's in his 90s now
+really trained all the lipid chemists in
+
+ align:start position:0%
+really trained all the lipid chemists in
+ 
+
+ align:start position:0%
+really trained all the lipid chemists in
+the whole country and they figured out
+
+ align:start position:0%
+the whole country and they figured out
+ 
+
+ align:start position:0%
+the whole country and they figured out
+many years ago how to separate lipid
+
+ align:start position:0%
+many years ago how to separate lipid
+ 
+
+ align:start position:0%
+many years ago how to separate lipid
+fractions with methanol chloroform
+
+ align:start position:0%
+fractions with methanol chloroform
+ 
+
+ align:start position:0%
+fractions with methanol chloroform
+extract something that you guys probably
+
+ align:start position:0%
+extract something that you guys probably
+ 
+
+ align:start position:0%
+extract something that you guys probably
+haven't thought about at all but we're
+
+ align:start position:0%
+haven't thought about at all but we're
+ 
+
+ align:start position:0%
+haven't thought about at all but we're
+really pretty good at separating things
+
+ align:start position:0%
+really pretty good at separating things
+ 
+
+ align:start position:0%
+really pretty good at separating things
+and it's nothing more than an extraction
+
+ align:start position:0%
+and it's nothing more than an extraction
+ 
+
+ align:start position:0%
+and it's nothing more than an extraction
+like you do as organic chemists to
+
+ align:start position:0%
+like you do as organic chemists to
+ 
+
+ align:start position:0%
+like you do as organic chemists to
+purify and separate things we figured
+
+ align:start position:0%
+purify and separate things we figured
+ 
+
+ align:start position:0%
+purify and separate things we figured
+that out and so then they use mass spec
+
+ align:start position:0%
+that out and so then they use mass spec
+ 
+
+ align:start position:0%
+that out and so then they use mass spec
+to allow them to quantitate the amount
+
+ align:start position:0%
+to allow them to quantitate the amount
+ 
+
+ align:start position:0%
+to allow them to quantitate the amount
+of glycerol and then in the end what
+
+ align:start position:0%
+of glycerol and then in the end what
+ 
+
+ align:start position:0%
+of glycerol and then in the end what
+they go so they use now spec they use
+
+ align:start position:0%
+they go so they use now spec they use
+ 
+
+ align:start position:0%
+they go so they use now spec they use
+western blots and they can change the
+
+ align:start position:0%
+western blots and they can change the
+ 
+
+ align:start position:0%
+western blots and they can change the
+concentration of the cholesterol and do
+
+ align:start position:0%
+concentration of the cholesterol and do
+ 
+
+ align:start position:0%
+concentration of the cholesterol and do
+the experiments over and over again to
+
+ align:start position:0%
+the experiments over and over again to
+ 
+
+ align:start position:0%
+the experiments over and over again to
+see what happens and when they do that
+
+ align:start position:0%
+see what happens and when they do that
+ 
+
+ align:start position:0%
+see what happens and when they do that
+this is the picture of cyclodextrin so
+
+ align:start position:0%
+this is the picture of cyclodextrin so
+ 
+
+ align:start position:0%
+this is the picture of cyclodextrin so
+you can see the only difference is this
+
+ align:start position:0%
+you can see the only difference is this
+ 
+
+ align:start position:0%
+you can see the only difference is this
+group here versus that with a methyl and
+
+ align:start position:0%
+group here versus that with a methyl and
+ 
+
+ align:start position:0%
+group here versus that with a methyl and
+one so this is hydroxy propyl hydroxy
+
+ align:start position:0%
+one so this is hydroxy propyl hydroxy
+ 
+
+ align:start position:0%
+one so this is hydroxy propyl hydroxy
+broeckel propanol cyclodextrin okay so
+
+ align:start position:0%
+broeckel propanol cyclodextrin okay so
+ 
+
+ align:start position:0%
+broeckel propanol cyclodextrin okay so
+it's like a cavity like this and all the
+
+ align:start position:0%
+it's like a cavity like this and all the
+ 
+
+ align:start position:0%
+it's like a cavity like this and all the
+other only other change here is a methyl
+
+ align:start position:0%
+other only other change here is a methyl
+ 
+
+ align:start position:0%
+other only other change here is a methyl
+group removing that and they have very
+
+ align:start position:0%
+group removing that and they have very
+ 
+
+ align:start position:0%
+group removing that and they have very
+very different properties about binding
+
+ align:start position:0%
+very different properties about binding
+ 
+
+ align:start position:0%
+very different properties about binding
+and releasing cholesterol which somebody
+
+ align:start position:0%
+and releasing cholesterol which somebody
+ 
+
+ align:start position:0%
+and releasing cholesterol which somebody
+had to do a lot of studying on to be
+
+ align:start position:0%
+had to do a lot of studying on to be
+ 
+
+ align:start position:0%
+had to do a lot of studying on to be
+able to ensure that they can use it to
+
+ align:start position:0%
+able to ensure that they can use it to
+ 
+
+ align:start position:0%
+able to ensure that they can use it to
+to remove cholesterol and then to add it
+
+ align:start position:0%
+to remove cholesterol and then to add it
+ 
+
+ align:start position:0%
+to remove cholesterol and then to add it
+back to the media and so you have to
+
+ align:start position:0%
+back to the media and so you have to
+ 
+
+ align:start position:0%
+back to the media and so you have to
+think about the exchange kinetics you
+
+ align:start position:0%
+think about the exchange kinetics you
+ 
+
+ align:start position:0%
+think about the exchange kinetics you
+have to think about a lot of things this
+
+ align:start position:0%
+have to think about a lot of things this
+ 
+
+ align:start position:0%
+have to think about a lot of things this
+is not trivial to set this up to figure
+
+ align:start position:0%
+is not trivial to set this up to figure
+ 
+
+ align:start position:0%
+is not trivial to set this up to figure
+out how to control the levels of
+
+ align:start position:0%
+out how to control the levels of
+ 
+
+ align:start position:0%
+out how to control the levels of
+cholesterol and then what they do is
+
+ align:start position:0%
+cholesterol and then what they do is
+ 
+
+ align:start position:0%
+cholesterol and then what they do is
+this is like a typical assay and this is
+
+ align:start position:0%
+this is like a typical assay and this is
+ 
+
+ align:start position:0%
+this is like a typical assay and this is
+the the end what you can do is this
+
+ align:start position:0%
+the the end what you can do is this
+ 
+
+ align:start position:0%
+the the end what you can do is this
+removes cholesterol and you can see it
+
+ align:start position:0%
+removes cholesterol and you can see it
+ 
+
+ align:start position:0%
+removes cholesterol and you can see it
+change this reports on low levels of
+
+ align:start position:0%
+change this reports on low levels of
+ 
+
+ align:start position:0%
+change this reports on low levels of
+cholesterol a lot which is happening
+
+ align:start position:0%
+cholesterol a lot which is happening
+ 
+
+ align:start position:0%
+cholesterol a lot which is happening
+over here allows the protein to move to
+
+ align:start position:0%
+over here allows the protein to move to
+ 
+
+ align:start position:0%
+over here allows the protein to move to
+the nucleus where it's smaller
+
+ align:start position:0%
+the nucleus where it's smaller
+ 
+
+ align:start position:0%
+the nucleus where it's smaller
+and that's how they knew the correlation
+
+ align:start position:0%
+and that's how they knew the correlation
+ 
+
+ align:start position:0%
+and that's how they knew the correlation
+the correlation between the levels in
+
+ align:start position:0%
+the correlation between the levels in
+ 
+
+ align:start position:0%
+the correlation between the levels in
+the nucleus and the levels of
+
+ align:start position:0%
+the nucleus and the levels of
+ 
+
+ align:start position:0%
+the nucleus and the levels of
+cholesterol so I thought this was a
+
+ align:start position:0%
+cholesterol so I thought this was a
+ 
+
+ align:start position:0%
+cholesterol so I thought this was a
+pretty cool paper and in these kinds of
+
+ align:start position:0%
+pretty cool paper and in these kinds of
+ 
+
+ align:start position:0%
+pretty cool paper and in these kinds of
+methods I think will be applicable to a
+
+ align:start position:0%
+methods I think will be applicable to a
+ 
+
+ align:start position:0%
+methods I think will be applicable to a
+wide range of things when if people are
+
+ align:start position:0%
+wide range of things when if people are
+ 
+
+ align:start position:0%
+wide range of things when if people are
+ever do biochemistry looking at the
+
+ align:start position:0%
+ever do biochemistry looking at the
+ 
+
+ align:start position:0%
+ever do biochemistry looking at the
+function of membranes so okay guys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/kKyrR0cFrEg.txt b/kKyrR0cFrEg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6a619193276cd6925fcfcb79fcbef93d7598efd9
--- /dev/null
+++ b/kKyrR0cFrEg.txt
@@ -0,0 +1,4289 @@
+ANNOUNCER: The
+following content is
+
+provided under a
+Creative Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK.
+
+Welcome back to
+computational systems biology
+
+We have the honor
+today of having
+
+Professor Ron Weiss visit us.
+
+As I told you on
+Tuesday, he's going
+
+to talk about synthetic biology.
+
+And Ron is probably
+from both the department
+
+of biological engineering and
+the Computer Science department
+
+and also a founding member
+of the Synthetic Biology
+
+Center at MIT.
+
+And now, thank you, Ron.
+
+PROF.
+
+RON WEISS: Thank you, Dave.
+
+Thanks for inviting me here.
+
+Did you mention our background?
+
+Dave was actually--
+advised me when I first
+
+came to our graduate
+school at MIT.
+
+And at the time, I was
+working on digital video
+
+and information retrieval.
+
+And Dave started getting
+into the business of biology.
+
+This is back in the early '90s.
+
+And I was like, this is cool
+stuff but it's really messy.
+
+How can you engineer
+with these molecules?
+
+PROFESSOR: And we've
+got the answer to that.
+
+PROF.
+
+RON WEISS: Yeah.
+
+So we'll see.
+
+So let's see if the answer
+is-- it does actually work.
+
+So yeah, so I-- after being
+a non-believer-- I don't know
+
+if non-believer, but just--
+I didn't feel I quite
+
+had the engineering
+capabilities.
+
+Towards around '96
+or so is when I
+
+decided to actually
+make the switch.
+
+At the time, I was
+working-- around '96,
+
+I was working at this
+notion of how can we
+
+use what we know in biology
+to understand how we program
+
+computers and especially
+situations where you have
+
+lots and lots of computing
+elements like-- things
+
+like smartDOS.
+
+I don't know if people have
+heard, but amorphous computing.
+
+So back in the mid
+'90s or so, this notion
+
+that we would be able to
+embed computation everywhere
+
+was kind of an exciting notion.
+
+And I thought to myself, where--
+how could I get inspired?
+
+And I thought, well,
+biology obviously
+
+could serve as
+great inspiration.
+
+Because that's a situation where
+you have millions or billions
+
+of little computing
+elements that
+
+don't have too much power,
+kind of interact locally.
+
+But they still perform
+very robust operations.
+
+And so I performed a
+variety of simulations,
+
+for example, of embryogenesis
+and other processes
+
+to try to understand what
+happens in biology and can
+
+I again use that to
+program computers
+
+or little tiny computers.
+
+And I remember one
+day, I just decided
+
+to flip the arrow and
+basically rather than trying
+
+to use biology to understand or
+program computers, I decided,
+
+let me use what I know
+in computing to actually
+
+try to program biology, OK?
+
+And so now that
+field is basically
+
+called synthetic biology.
+
+So I've been in that field--
+it's hard to count now,
+
+but I guess maybe
+18 years or so.
+
+And it's been fun and
+has not been easy.
+
+But I think at
+least we're starting
+
+to make some-- we're
+making some progress.
+
+So I'll try to tell you about
+some of our efforts there.
+
+And I certainly encourage
+you to ask me questions.
+
+So please interrupt me
+at any point in time.
+
+Any kind of question
+is fair game.
+
+Dave promised me that you
+guys are a tough crowd.
+
+So let's see.
+
+And you can always stump.
+
+Let's try to have that happen.
+
+So when I look at this, I get
+excited as an engineer, OK?
+
+And I think to myself, wow.
+
+This could be really cool to
+be able to program something
+
+like this, again,
+in the same way
+
+that we may program computers.
+
+And so this notion of genetic
+engineering in a direct way,
+
+in a way where we
+can create new DNA,
+
+certainly has been around
+since the '70s or so.
+
+And so this notion
+has allowed us
+
+as a community to create
+various mechanisms that
+
+control what the cells do.
+
+So for example, transcriptional
+regulation, translational-- so
+
+being able to regulate
+things in a cell,
+
+be able to create
+genetically encoded sensors,
+
+cell-cell communication
+mechanisms, synthesis
+
+of various interesting
+molecules--
+
+biofuels, pharmaceuticals,
+and control physical aspects.
+
+And so those capabilities
+have been around
+
+before synthetic biology.
+
+But if you were
+to ask me what is
+
+different about
+synthetic biology,
+
+I would say it's really the
+emphasis on systems level
+
+engineering.
+
+OK, so this notion
+that we are not just
+
+trying to engineer
+over expression
+
+of this gene or that gene
+or a couple of genes,
+
+but really trying
+to understand how
+
+to create systems
+of interactions.
+
+So in the same way that
+systems biology has
+
+come to the forefront
+with this notion
+
+that you can't understand a
+cell by understanding what
+
+is the exact purpose of this
+particular gene-- we always
+
+have to think about it within
+the context of a pathway
+
+within the context of the entire
+organism-- in the same way,
+
+when we want to be able to get
+cells to do interesting things,
+
+we have to think about
+the system as a whole.
+
+And to get the
+sophistication that we need,
+
+we need to understand how to
+connect these various elements,
+
+regulatory elements, all
+these kinds of elements,
+
+in reliable, predictable
+ways, efficient ways
+
+and so on to be able
+to get the cells to be
+
+as programmable as computers.
+
+So that if you were to ask
+me what synthetic biology is,
+
+that would be my answer.
+
+And so now you know it and
+you can tell all your friends
+
+that it's a completely
+defined notion and so on.
+
+Maybe if yo ask
+other people, they'll
+
+give you slightly
+different answers.
+
+But there you go.
+
+So how do we develop an
+engineering discipline out
+
+of that?
+
+OK, so that's really how
+can we get undergrads
+
+to come in and take Synbio
+101 where it's really
+
+a well defined mechanism and set
+of methodologies and practices
+
+that allow us to
+do this reliably.
+
+OK, and so we often
+try to get inspired
+
+by how other
+disciplines approach
+
+the engineering of
+complex systems.
+
+And so kind of an
+obvious one would
+
+be of computing
+or robotics where
+
+there's this notion of, for
+example, bottom up assembly.
+
+And so you start
+with basic devices
+
+and think about how
+to create modules
+
+that have specific behaviors in
+them and then put those modules
+
+and integrate those modules
+to create these autonomous
+
+entities such as robots.
+
+And we often think about
+how to create communities
+
+of interactions, communities of
+robots in this case, and so on.
+
+And so that's worked
+quite well in a variety
+
+of different other
+engineering disciplines.
+
+And so we often
+ask the question,
+
+can we import these mechanisms
+into the world of biology?
+
+So can we take basic
+mechanisms of regulation--
+
+it could be
+transcriptional, it could
+
+be other modes of regulation--
+and then wind these things up
+
+to create customizable pathways
+that we then embed into cells?
+
+And then we can create
+programmable communities
+
+of bacteria.
+
+We can create programmable
+tissues of mammalian cells
+
+and so on.
+
+And so the question is, is
+this a useful and efficient way
+
+to approach things?
+
+So for example, how are these
+different approaches similar?
+
+What can we borrow
+from here that
+
+make sense to push
+on over there?
+
+And I will say when
+I started working
+
+in synthetic biology,
+most of my efforts
+
+were really focused on
+adapting and implementing
+
+these things-- so adapting
+them from other disciplines
+
+and trying to understand how to
+implement them into the world
+
+the biology.
+
+But as time has
+gone by and as we've
+
+started to understand and
+appreciate the cell more
+
+and more, we are also
+quite interested in how
+
+these things are
+different as well.
+
+So what makes engineering
+biological systems
+
+a truly unique, new
+engineering discipline?
+
+What would you do in
+the world of biology
+
+that might be different
+than what you would
+
+do with computers or robots
+or building bridges and cars
+
+and planes and so on?
+
+And so that that's become more
+and more of an important focus
+
+in my lab and I think in
+the community as a whole
+
+although not yet everywhere.
+
+And you often see
+situations where
+
+people come in from other
+disciplines and just think,
+
+oh, we'll just program
+it, engineer it,
+
+just like we do in
+computing and so on.
+
+And it doesn't just
+work like that.
+
+So when we approach these
+tasks of programming the cells,
+
+we usually divide things up into
+modules of sensors, processing,
+
+and actuation.
+
+So for example, we would
+want to develop sensors
+
+that can detect in live cells
+levels of microRNA messenger
+
+and then proteins
+and then connect them
+
+to synthetic regulatory circuits
+that we embed in the cells, OK?
+
+So it's important that these
+sensors not just, for example,
+
+give us fluorescent
+readouts, but it's important
+
+that these sensors then connect
+to the regulatory networks
+
+that we have in mind and so that
+these regulatory networks can
+
+then integrate multiple
+pieces of information
+
+and make decisions
+about actuation.
+
+So how do we turn on specific
+proteins that will then
+
+influence that
+particular cell or even
+
+the environment in a
+programmable fashion
+
+as dictated by the levels
+of particular sensors
+
+as well as by other
+mechanisms or, for example,
+
+from looking at
+historical information
+
+that the cell itself
+has processed as well?
+
+And so this is, I
+would say, represents
+
+the paradigm for most
+of the things that
+
+do take place in
+synthetic biology.
+
+And so why do we
+want to do this?
+
+It's not the program the next
+version of the iOS or iPhone
+
+or something like that.
+
+even though that
+initially that was
+
+one of the things
+that was discussed,
+
+it's not just for the
+sake of computation,
+
+but really for the sake
+of specific applications.
+
+So for example, if we have
+really slow logic gates that
+
+work on the order of
+hours or even days,
+
+that might be fine if the
+application, for example,
+
+is a tissue engineering
+application, OK?
+
+And so in synthetic
+biology, initial emphasis
+
+is really been on what
+can we do with microbial,
+
+let's say, communities or
+individuals, for example,
+
+for synthesis of
+high value compounds?
+
+I mentioned bioenergy,
+environmental applications
+
+as well.
+
+So that, I would say, was
+most of the emphasis there.
+
+But over the last
+few years, there's
+
+been a growing interest in
+health-related applications.
+
+And so my lab in particular
+looks at mostly health related
+
+applications.
+
+And so I'll give you
+examples of those today, OK?
+
+And those include things
+involved with cancer, diabetes,
+
+in tissues by design.
+
+And in order to
+do this, in order
+
+to have this programmability,
+you want to think about scales.
+
+So you want to think about how
+much DNA does it take to do X?
+
+And to a large extent, that
+controls the sophistication.
+
+It really is an important
+defining element
+
+what we do is the
+scale of the DNA
+
+that we can actually
+engineer reliably quickly,
+
+efficiently, predictably,
+in high throughput fashion,
+
+and in inexpensive ways.
+
+So we would start with
+things on the order of genes
+
+where I would say that that's
+really the basic elements.
+
+I would say that a single
+gene that you overexposes
+
+or a few genes than
+you inducibly express,
+
+I wouldn't count that
+as synthetic biology.
+
+But when it gets
+kind of interesting
+
+for synthetic biology is
+when we have this circuitry,
+
+where we now embed interactions
+that didn't previously
+
+exist in that
+particular cell context.
+
+And so most of synthetic biology
+has been really at this level
+
+right here-- actually,
+mostly from here
+
+to here in terms of
+the scale of the DNA
+
+and now trying to go beyond
+that-- more along the lines
+
+can we create something
+that's 20,000 bases, 50,000
+
+bases of DNA?
+
+OK, is this something that
+a graduate student can
+
+come into the lab
+and say, I want
+
+to design something that will
+take 20,000 to 50,000 bases?
+
+Is this a reasonable
+thing to consider?
+
+OK, and then the question
+would be, what kind of power
+
+does that provide to you?
+
+What things can
+you do with that?
+
+Beyond that, people have
+explored this notion
+
+of minimal life and even
+full genome rewrites.
+
+I would say at this
+point, this is--
+
+what some people clump that in
+with synthetic biology, which
+
+is fine.
+
+We don't have, at the
+moment, really good ways
+
+of being able to engineer
+minimal life from scratch
+
+or even in a really
+fundamentally different way.
+
+So most of the efforts
+on minimal life
+
+would be take an
+organism and try
+
+to figure out what to knock out,
+right, as opposed to saying,
+
+I'm going to engineer
+this new minimal organism.
+
+And I'm going to
+define what reactions
+
+to put in there from scratch.
+
+And I'm going to create
+a whole bunch of new ones
+
+that didn't exist before.
+
+OK, in the future, will
+we be able to do this?
+
+Hopefully, OK?
+
+Not quite yet-- this is really
+where the action of right now.
+
+And again, driving
+force for this
+
+is how inexpensive
+is DNA synthesis.
+
+And so we're following
+some kind of Moore's law
+
+with respect to dropping costs
+in terms of DNA synthesis.
+
+And this is one
+of the enabling--
+
+I don't know if it's-- it's not
+the only enabling technology.
+
+But is one of the most
+important enabling technologies
+
+is the fact that
+it is less and less
+
+expensive to be
+able to order longer
+
+and longer sequences of DNA.
+
+And so this notion
+that, for example,
+
+you'll be able to design
+something that's, again,
+
+that's 20,000 to
+50,000 bases of DNA
+
+and just go online
+and order to that
+
+and have your advisor
+willingly pay for that-- not
+
+at the level of 20,000
+to 50,000 bases yet.
+
+But that's going to change.
+
+And that's going
+to get to the point
+
+where those really become
+available to everyone.
+
+And I think that's going
+to fundamentally change
+
+how we do business in
+biological engineering
+
+and how we do, I would
+say, almost everything
+
+in biology as a whole.
+
+So if you have-- even if you
+don't care about engineering
+
+new biological
+functions but you want
+
+to understand biological systems
+and your adviser told you,
+
+well, just design a whole bunch
+of circuits that will allow you
+
+to regulate things
+in arbitrary ways
+
+to learn something about
+the underlying networks that
+
+control a natural
+systems, again, I
+
+think that that fundamentally
+changes what kinds of questions
+
+you will ask.
+
+OK, so I'll talk
+about basic design.
+
+I'll talk about scalability.
+
+So how do we go from
+these basic elements
+
+to bigger and bigger things?
+
+And then I'll talk
+about some recent things
+
+that we're doing where we're
+building this foundation.
+
+But we think that this
+foundation then can matter.
+
+I think this foundation can
+change how you approach things
+
+that really don't have
+the greatest of solutions.
+
+Now, they really change
+the paradigm, for example,
+
+for cancer, for this
+notion of building tissues
+
+by design on chips and
+for diabetes and so on.
+
+OK, so we start with parts.
+
+So just about
+everything that we do,
+
+we define what are
+the basic parts that
+
+are available in our toolbox.
+
+And so these will be
+transcriptional regulatory
+
+parts.
+
+We do things at the
+translational level.
+
+We do things also at the
+protein-protein level.
+
+One of the things we
+often do, not always,
+
+is engineer cell-cell
+interactions.
+
+Could be by means of
+cell-cell communication.
+
+We often want to find out
+what's going on in the cell.
+
+So just like when
+we program-- where
+
+we create a new software,
+new computer program,
+
+we have debugging
+outputs that tell us
+
+what the program is doing.
+
+Usually, the way we do this
+is with fluorescent protein.
+
+It could be with dyes too.
+
+So they tell us,
+you know, here's
+
+how your circuit is behaving.
+
+Here's how the cell
+might be behaving.
+
+And another set
+of parts would be
+
+ones where we want to be
+able to create sensors
+
+and actuators inside the cell.
+
+What are specific
+biomarker levels?
+
+How can we affect what
+the cell is doing?
+
+For example, one
+that gets used a lot
+
+is kill the cell is one
+of the favorite actuators
+
+that people are using.
+
+Another one would be, let's
+say, tell this stem cell
+
+to differentiate into
+a different cell type.
+
+That would be another
+kind of actuator.
+
+A different one might make the
+cell-- make this high value
+
+compound that would be
+relevant for some application.
+
+And so right now, if
+you're looking for parts,
+
+they actually used to be
+stored in Stata up until--
+
+or big libraries of
+synthetic biology parts
+
+were stored in Stata that up
+until about two years or so.
+
+So I don't know how many
+people know about iGEM.
+
+Any folks know about iGEM?
+
+So iGEM was started at
+MIT, was headquartered,
+
+as I mentioned again
+here, in Stata.
+
+There are these couple of
+big freezer that were on the,
+
+I think, the fourth floor here.
+
+And they stored
+5,000 to 10,000 parts
+
+that word commonly used by
+synthetic biology folks.
+
+OK, so now they
+moved over closer
+
+to Cambridge brewing company.
+
+And they're not affiliated
+directly with MIT anymore
+
+and they have 15,000
+parts or so available.
+
+So if you want to get
+started in synthetic biology,
+
+this is one quick
+way to do that.
+
+You can contact iGEM
+headquarters and say, please
+
+send me 1,000 parts, OK?
+
+And as long as you're
+credible and not
+
+from one of those
+blacklisted countries,
+
+then they typically
+will send it to you.
+
+So that's a good way
+to get started, OK?
+
+So what are these parts?
+
+So this is actually going
+back to my Ph.D. here.
+
+This is one of the parts
+that I characterized.
+
+So this notion of an inverter--
+so digital logic convert.
+
+So I assume people
+here-- everybody
+
+is familiar with logic gates.
+
+Is that true?
+
+OK, raise your hand if
+you are familiar with it.
+
+I just want to see- oh.
+
+Just trying to calibrate--
+and again, ask me questions.
+
+So this notion that you have
+a single input, single output
+
+device that works on binary
+values that has-- basically
+
+inverts the signal.
+
+So you have zero on the input.
+
+You have one on the output.
+
+One in the input, you
+have zero in the output.
+
+And so one of the
+ways in which you
+
+can implement this in
+a biological system
+
+is just use
+transcriptional repression.
+
+OK, so if you have
+no repressor present,
+
+then you have a high
+level of output protein.
+
+If you have a
+repressor present, it
+
+represses the production
+of the alpha protein.
+
+And so in theory, you
+should be able to use
+
+this as a digital logic gate.
+
+OK, and so that-- sounds--
+looks pretty simple here.
+
+But for my Ph.D., it
+took me about three years
+
+to do something like this just
+to give you an indication.
+
+Now it's a lot faster.
+
+Now you can do this in-- you
+can do many of those in a day.
+
+So there has been progress.
+
+Here's another one of those
+gates that I used for my Ph.D.
+
+And so this is now not just a
+repressor, but a repressor that
+
+can be inactivated by
+a small molecule, OK?
+
+And so the way it
+works is you have
+
+this repressor that
+works as before.
+
+And then when a small
+molecule comes in,
+
+it prevents a repressor
+from binding the promoter.
+
+And as a result of that, even
+if the repressor is present,
+
+you can have activation
+of the output protein, OK?
+
+So this is what's called a
+not x or y or it implements
+
+the implies logic function.
+
+How many people use the implies
+logic function to do anything?
+
+OK.
+
+So it's not a commonly
+used logic function.
+
+And you won't find it--
+there's no logic gate that
+
+does the implies logic
+function in a typical computer.
+
+But this is a useful
+logic function
+
+that we can implement in cells.
+
+And it allows external control
+of gene expression, OK?
+
+And so this is a
+simple way-- and so
+
+once you can do that as
+a user, essentially you
+
+can interact with
+the cells and modify
+
+what's going on inside the
+cell, OK, using a pretty simple
+
+looking mechanism that predates
+synthetic biology, if you will.
+
+But I don't know if it was
+called the implies logic
+
+function before.
+
+So anyway, so then logic gates--
+can we build logic circuits?
+
+This is where I would
+say synthetic biology
+
+starts kicking in.
+
+And so this is one of the first
+logic circuits that we built.
+
+And the question was, OK-- looks
+nice to have this logic gate
+
+representation.
+
+In biology, does this
+make any sense at all?
+
+Can you really do digital
+logic inside cells?
+
+Can you take noisy
+biological components
+
+and actually implement reliable
+digital computation in cells?
+
+And it wasn't an obvious
+thing, I would say.
+
+Is it 100% obvious now?
+
+In some situations,
+I think we can
+
+claim that we can build
+digital logic that's
+
+reasonably reliable.
+
+So in this particular case, I'm
+showing you this implies logic
+
+function that allows us
+to have small molecule
+
+induction of a
+cascade of not logic
+
+gates or transcriptional
+repressors.
+
+And so the nice thing
+about this in particular
+
+is the fact that this is the
+input output steady state is
+
+that as the circuit so
+goes from blue to black
+
+to this yellow color here is
+as the circuit gets longer,
+
+as a cascade gets longer, it
+actually becomes more digital.
+
+It actually becomes
+more step-like, OK?
+
+More on off.
+
+So we're going from this
+blue input output function
+
+to this yellow.
+
+So now we have over
+1,000 fold change
+
+in the output in
+response to two to four
+
+fold change in the input.
+
+OK, and then we have
+good noise margins,
+
+good signal restorations,
+all these good things
+
+that we need to have for
+the creation of larger
+
+and larger reliable
+digital circuits.
+
+So the basis of digital
+computation is that you have--
+
+and the reason why you can
+actually create computers
+
+is that you can have logic gates
+that do signal restoration--
+
+that the output is a
+better representation
+
+of the digital meaning
+then the input.
+
+So as the signal , propagates
+this analog signal could be
+
+voltage.
+
+But it could be
+protein concentrations.
+
+As it traverses through
+the logic gates,
+
+it needs to actually become
+cleaner in order for us
+
+to be able to have reliable
+digital computation.
+
+So people have figured
+out how to do this
+
+with electronics
+a long time ago.
+
+We figured out how to do it
+with synthetic biology, let's
+
+say, 10 to 15 years ago.
+
+And nature has figured out how
+to do this billions of years
+
+ago, OK?
+
+So things like
+cooperativity-- so I
+
+assume you've looked a
+little bit on cooperatively
+
+in, let's say, gene regulation.
+
+OK, so that is a situation
+where you get a nonlinear
+
+response in a system that
+biology has figured out
+
+is a useful mechanism so that
+signals that come in actually
+
+result in some kind of
+actual digital behavior.
+
+So you get non-linear
+signal processing
+
+in these regulatory elements.
+
+And at the end of, let's say,
+a signal transduction cascade,
+
+the output is
+either high or low.
+
+There's no-- for the most
+part, there's no in between.
+
+The transition between
+high and low is super fast.
+
+OK, so in a sense,
+that's creating
+
+digital or discrete outputs.
+
+And that's really critical
+for many situations--
+
+certainly in synthetic biology,
+but many situations in biology
+
+as well.
+
+So one example would be, let's
+say, stem cell differentiation.
+
+You want the cells to be able
+to make a discrete decision.
+
+Should I make-- should I
+become a kidney cell or a liver
+
+cell or a muscle cell and so on.
+
+So those are discrete
+decisions that
+
+have to be made by the cells.
+
+And so the cells have
+come up-- or nature's
+
+come up with mechanisms
+to guarantee that.
+
+And so we've now figured
+out how to do that ourselves
+
+in a synthetic fashion as well.
+
+It's important to note that
+when we engineer these systems,
+
+we don't just think
+about digital behavior.
+
+So we spent an equal amount
+of time perhaps thinking
+
+about how to implement things
+that have transient properties
+
+or things that have more kind
+of analog behavior to them.
+
+And that's absolutely critical
+to be able to program cells
+
+to do whatever we want.
+
+So this is an example
+where we have engineered
+
+cell-cell communication
+where sender cells make
+
+a small diffusible
+molecule which
+
+then goes to receiver cells.
+
+OK, so now the receiver cells
+don't just have an on response,
+
+but rather they
+have a pulse, OK?
+
+So a signal travels from the
+sender to the receiver cells.
+
+And the cells, what
+we engineer them to do
+
+is have a pulse response.
+
+And the idea is to have GFP
+go up-- a Green Fluorescent
+
+Protein go up--
+and then go down.
+
+And so to be able to
+do that, we engineered
+
+a feed forward
+motif where we have
+
+binding of the small
+molecule to this activator
+
+which activates two
+things simultaneously--
+
+a green fluorescent
+protein and a repressor
+
+which then represses the
+green fluorescent protein.
+
+And then-- so the idea is that
+the green fluorescent protein
+
+goes up.
+
+And then eventually,
+the repressor
+
+builds up to sufficient
+levels to repress
+
+the green fluorescent protein.
+
+So again, one of those
+simple looking motifs.
+
+This is about three
+years to actually make
+
+that happen around
+the 2004 frame.
+
+Looks simple.
+
+If you study a naturally
+occurring system that
+
+has this motif, you say,
+oh yeah-- no problem.
+
+Yeah, we have this
+feed forward motif.
+
+And obviously, you can do this
+kind of information processing
+
+function.
+
+Let's move on to another motif.
+
+You actually try to build this
+in a lab in a new organism,
+
+I'm not sure if it
+can drive you insane.
+
+But it is not trivial to
+actually make it work.
+
+It's much easier now
+than it was 10 years ago.
+
+But you still have
+to pay attention
+
+to a lot of things-- rate
+constants, threshold matching,
+
+and so on to actually
+make it happen.
+
+But eventually, after
+looking-- creating--
+
+so this is our first
+attempt at this
+
+was this blue line right here.
+
+So a completely flat line, OK?
+
+Input comes in, nothing happens.
+
+So I would say that pretty
+much typifies synthetic biology
+
+maybe up until today.
+
+You build something.
+
+You think it's going to work.
+
+It doesn't work.
+
+And then you stop crying
+after a little while.
+
+But then you have to think
+about how do I fix this.
+
+And so this iterative
+design debug cycle
+
+is absolutely critical.
+
+So what you normally do is you
+create computational models
+
+that tell you how different
+rate constants in the system
+
+affect the behavior
+of your circuit, OK?
+
+For example, you could
+do sensitivity analysis.
+
+Which rate constants
+have the most influence
+
+on the performance
+of your system?
+
+And so we did some sensitivity
+analysis here and learned
+
+that, for example, the
+degradation of this repressor
+
+makes-- one of the
+things rate constants
+
+makes the biggest difference
+is on the performance
+
+of the system or its
+affinity to the binding
+
+site on its respective promoter.
+
+Yes.
+
+AUDIENCE: Just knowing the sheer
+[INAUDIBLE] entire circuit,
+
+it started off with the
+[INAUDIBLE] constant?
+
+PROF.
+
+RON WEISS: No.
+
+I wish it was.
+
+Because that would
+make life a lot easier.
+
+And we are trying to
+get better at that.
+
+So we're trying
+to-- so here's maybe
+
+two ways of thinking about that.
+
+One challenge would
+be somebody comes in,
+
+gives you DNA
+sequence, and you have
+
+to predict the rate constants.
+
+OK, so I would term that person
+an adversary, not your friend.
+
+It's just too hard to do that.
+
+Now, an easier task would be
+give your adversary or friend
+
+limited choices and
+say in the freezer,
+
+I have these DNA
+sequences that consist,
+
+let's say, of
+specific promoters,
+
+specific ribosome binding
+sites, specific proteins
+
+with specific degradation
+tags on the proteins, OK?
+
+And that's-- you're allowing
+that adversary or friend
+
+to only use those elements
+in the design of a circuit.
+
+And then they come back
+to you and they say,
+
+now predict what
+the circuit will do.
+
+You still-- it still
+doesn't work yet.
+
+But I think-- but I
+would say that's how
+
+we would phrase
+the challenge, OK?
+
+Stick to things that we know and
+allow us to even characterize
+
+those things ahead of time.
+
+What we have that--
+unfortunately,
+
+I don't have that here.
+
+But what we have
+done-- so people
+
+can get a kind of a
+general characterization.
+
+So they can say it'll be roughly
+this input output behavior.
+
+And when I say
+roughly, the errors
+
+could be on the order
+of five to 10-fold.
+
+That's approximately what's
+been published so far.
+
+Now, five to tenfold
+depending on your perspective
+
+could be great because
+it's biology or could
+
+suck if you're an engineer.
+
+It just depends on if you're
+trying to do something
+
+like get green
+fluorescent protein
+
+to turn on and off,
+tenfold is probably great
+
+if you're doing this
+in a Petri dish.
+
+If you're trying to
+create a cancer classifier
+
+circuit you put into
+humans to kill cancer cells
+
+but not harm healthy cells,
+tenfold is probably not
+
+great I wouldn't take
+a circuit like that
+
+into me, especially if that
+circuit controls, for example,
+
+the production of a
+killer protein, which I'll
+
+try to show you a
+circuit that does that.
+
+We recently have
+been able-- we're
+
+in the process of submitting
+a paper about this-- been
+
+able to show that if you have
+really good characterization
+
+of regulatory elements such
+as these repressor devices--
+
+and you have to do a lot
+more characterization
+
+and you do the-- we can
+get within 20% on average
+
+on predicting the behavior
+in mammalian cells, actually.
+
+And so as an
+engineer, I would be
+
+happy with 10%, 20% percent
+for many, many applications.
+
+So I think we've
+gotten better at it.
+
+But it's not quite perfect yet.
+
+One of the things
+about that approach
+
+is that we don't
+necessarily know
+
+the rate constant
+for everything.
+
+What we do know, however,
+is a very detailed behavior,
+
+both steady state
+and dynamic behavior,
+
+of a repressor promoter pair.
+
+So we don't know, for example,
+what's the binding affinity
+
+or what's the rate
+constant for the repressor
+
+binding the promoter,
+what's the rate
+
+constant for RNA polymerase
+binding that promoter, what's
+
+the exact translation rate
+or transcription right too.
+
+But we do know what's the
+input output behavior.
+
+And that's actually been enough
+to get really good predictions.
+
+But I would say these
+kinds of predictions
+
+are one of the most important
+aspects and challenges
+
+and bottlenecks of
+synthetic biology.
+
+So those include--
+again, the challenges
+
+include how fast
+can you build DNA.
+
+But wouldn't it be nice
+if you can actually
+
+predict what the DNA does?
+
+So it's just as
+important, if not more.
+
+And also having--
+so those are two
+
+of the important challenges.
+
+I'd say another
+one would be-- OK,
+
+so if you can predict
+things how many parts
+
+do you have in your freezer that
+you can actually put together
+
+and they're
+well-characterized actually
+
+now build the circuits?
+
+Probably three of the
+most important challenges.
+
+And so if you go back to what
+we'll call the post generator,
+
+this is a loop tape of bacteria
+that now respond to the pulse.
+
+So sender cells that then
+secreted the small molecule
+
+then went into receiver cells.
+
+And they light up.
+
+So one of the things to
+note here is that it works.
+
+The other thing to note here is
+that it's not perfect, right?
+
+And so the amount of
+heterogeneity here I think
+
+is quite astounding.
+
+So if you take the
+average behavior,
+
+it's actually quite predictable.
+
+But if you now start
+looking at the distribution
+
+in the response,
+it's staggering.
+
+And we quantified that.
+
+And so we quantified what's
+the distribution in terms
+
+of the fluorescence levels
+that-- the peak and also
+
+the buildup and so on.
+
+And we then correlated
+that also-- we
+
+created the stochastic
+simulations that then correlate
+
+reasonably well with the system.
+
+So we can get simulations
+to generally correspond
+
+with what we're seeing
+at the population level.
+
+But I do want to
+bring up this point
+
+that when you think about
+engineering biological systems,
+
+don't try to figure out how to
+engineer a single cell to do
+
+something reliably, OK?
+
+So you always want
+to think about kind
+
+of statistical engineering.
+
+You want to think about, I'm
+going to create a circuit.
+
+And when I put this circuit
+into a population of cells,
+
+this is the distribution
+of behaviors
+
+that I'm going to get.
+
+Because if you're
+trying to depend
+
+on any individual cell giving
+you exactly the behavior
+
+that you're looking for, it
+is just-- it's going to fail.
+
+So you have to really
+think about distributions.
+
+And that I think changes
+things a little bit.
+
+So that's not
+normally the way you
+
+think about-- maybe
+that's the way Microsoft
+
+thinks about programming.
+
+So if 90% of the time, the
+computer doesn't crash,
+
+that's pretty good.
+
+Probably Bill Gates
+agrees with that, right?
+
+But that's not what we want.
+
+That's not what we
+typically do with software.
+
+So to kind of further
+think about this
+
+in terms of populations,
+we program something else
+
+which was a pattern formation.
+
+So now we have the desire to
+create senders and receivers
+
+where the senders send the
+same message to the receivers.
+
+Now we have a longer
+feed forward motif.
+
+OK, so this feed forward
+motif has two branches.
+
+And so these two
+branches actually
+
+have a different impact
+on the final output.
+
+One has-- there's two repressors
+meaning that input comes in.
+
+It activates a fluorescent
+protein and another one
+
+represses the
+fluorescent protein.
+
+OK, so it's an incoherent
+feed forward motif.
+
+And so what we use that here
+is not for post generation,
+
+but rather to define a
+range of concentrations
+
+that would turn on
+the final output, OK?
+
+So it would be activated--
+the range of concentration
+
+would be activated starting
+with this branch right here
+
+and then ultimately
+repressed by this.
+
+So this defines the
+low threshold and this
+
+defines the high threshold.
+
+So under the low threshold,
+nothing gets activated.
+
+Whenever you have
+just the right amount,
+
+it activates this
+which represses
+
+this which allows this
+fluorescent protein
+
+to get turned on.
+
+OK, so this branch right
+here is more sensitive.
+
+So it defines when
+this thing goes up,
+
+when the response goes up.
+
+And then this is less sensitive.
+
+So this defines under
+high concentrations
+
+when the output goes down.
+
+So we basically have a
+non monotonic response
+
+to the input, which is
+low then high then low.
+
+So that's the design
+that we had in mind.
+
+And the idea is that
+whenever you put,
+
+let's say, receiver cells
+everywhere in a Petri dish
+
+and you put senders
+in the middle,
+
+then the communication
+signal basically builds up.
+
+There's a chemical gradient.
+
+Each cell interprets
+the chemical gradient
+
+and then decides whether to
+make a fluorescent protein.
+
+And then only-- because there's
+this steady chemical gradient
+
+due to diffusion and
+decay of the signal,
+
+then you would get some
+kind of a bullseye pattern.
+
+So that was the hope at least.
+
+And so to give you again
+a timescale, so it took me
+
+about I think three hours on
+a plane to make the slide.
+
+It took us about three weeks to
+create the computational model.
+
+And again, for whatever
+reason, three years
+
+was the magic number to create
+the actual functional circuit.
+
+So that was an older
+version of PowerPoint.
+
+But I haven't tried
+it on the new.
+
+But anyways, so we created this.
+
+This is a computational model.
+
+We actually used a
+computational model
+
+to predict how changes
+in rate constants
+
+would affect this band detect,
+the region where we're actually
+
+responding to the signal.
+
+And we used that to engineer
+different responses.
+
+And so we created eventually
+three different responses input
+
+versus output.
+
+And we put different
+fluorescent proteins on them--
+
+a red fluorescent protein and
+a green fluorescent protein.
+
+This is the experimental
+set up over here.
+
+And after 16 hours of waiting,
+this is basically what we got.
+
+So we got a lot of bacteria
+to make all kinds of patterns.
+
+And we were very
+happy about this.
+
+We danced around in the lab
+a little bit-- you know, yay!
+
+So this was fun on those rare
+occasions where things actually
+
+work.
+
+So we said, let's
+have some more fun.
+
+And so we put senders
+in other configurations.
+
+And so we have
+programmable patterns
+
+of bacterial communities.
+
+So I'm not sure
+of is this useful.
+
+I'm not sure by itself besides
+having some fun with it.
+
+But one of the things we're
+using this for right now--
+
+and depending on time,
+I may get to that
+
+later-- is this notion of
+embedding these circuits
+
+in mammalian stem cells or
+actually also in human IPS
+
+cells so that we engineer these
+human IPS cells to communicate
+
+with one another
+to make decisions.
+
+And then those
+decisions actually
+
+lead to differentiation
+patterns, right?
+
+So you can imagine
+in principle, if you
+
+can create three dimensional
+versions of these
+
+and use those to cause the
+cells to make differentiation
+
+decisions so that red
+would mean make neurons,
+
+green would mean make muscle,
+different colors-- yellow
+
+would mean make bone and so on.
+
+So in principle, you might
+be able to create tissues
+
+by design.
+
+OK, so that's something that
+we are working on actively
+
+in the lab right now.
+
+So we don't quite have a working
+heart in a Petri dish yet.
+
+We won't for a little while.
+
+But we taking some baby
+steps along the way.
+
+And so we have been able to
+get cell-cell communication
+
+to work.
+
+We've been able to get
+programmed stem cell
+
+differentiation to work.
+
+And hopefully, I'll
+be able to show you
+
+some images that we have of
+some recent examples where
+
+we take human IPS and actually
+created these embryonic liver
+
+buds that have lots and
+lots of interesting--
+
+and actually all
+the cell types that
+
+are known to exist in
+the embryonic liver.
+
+So there are some
+progress along the way.
+
+Now, we don't anticipate
+to replace your liver,
+
+you know, any time soon.
+
+So don't destroy it.
+
+So actually one near
+term application
+
+that we're
+specifically looking at
+
+is if we can take-- imagine
+taking your own fiberglass,
+
+de-differentiating them
+into human IPS cells--
+
+those are your human IPS cells--
+and then differentiate them
+
+into, like, this
+liver-like environment
+
+and put that in a
+Petri dish and then
+
+test out the effect of
+drugs on your mini liver.
+
+OK, so maybe it's a
+good idea to test drugs
+
+on things that resemble
+human tissue as
+
+opposed to some random
+mouse that may or may not
+
+be as correlated with what
+the drug would actually
+
+do to actual human cells.
+
+And if we actually even do it
+in the patient specific manner,
+
+I think that really
+changes the way drug
+
+development would actually work.
+
+And that's something that I
+think within the next few years
+
+could become a reality.
+
+They're talking about
+the next-- beginning
+
+to do that within the next one
+to three years in a laboratory
+
+setting.
+
+So I think that is near
+term and realistic.
+
+So one of the things
+that we did notice
+
+is that when we engineer
+the small systems,
+
+its intuition works quite well.
+
+So I can look at
+this circuit design
+
+and say, if I modify this,
+this is what's going to happen.
+
+If I modify this, that's
+what's going to happen.
+
+So you can use intuition and
+it works reasonably well.
+
+And what happened in I would
+say the first 8 to 10 years
+
+of synthetic
+biology, every paper
+
+would have a
+computational design.
+
+But most of those
+would build something.
+
+And in order to publish, we also
+tacked on a computational model
+
+that correlates really well
+with the experimental results.
+
+And we are just as guilty of
+doing that as anyone else, OK?
+
+So it wasn't critical to
+have a computational model
+
+to create something
+successfully in the lab.
+
+And I think that
+that is changing.
+
+So we have examples right now
+of designs where-- I'm not sure
+
+if I'll get to that today,
+but we have published
+
+on that-- designs
+where it involves
+
+about 20 to 25 components.
+
+And it's related to
+a diabetes system
+
+the retired engineer where we
+can have intuition about it.
+
+But our intuition doesn't
+work great anymore, guys.
+
+So we might have some
+intuition about the system.
+
+But the computational
+analysis would all of a sudden
+
+shed light and
+provide insight that
+
+is very difficult to
+get this by drawing
+
+this thing on a blackboard.
+
+OK, and so I think that
+computational design tools are
+
+becoming absolutely essential.
+
+They can provide insight
+into system behavior
+
+that you can't get just
+using intuition alone.
+
+But in another aspect
+of computational design
+
+is one where imagine being able
+to specify want this behavior.
+
+And then the
+computational design tool
+
+says, here's 1,000 different
+versions of circuits
+
+that you should build and test.
+
+OK, and so it's still
+difficult for a human
+
+to generate easily 1,000
+different versions of a circuit
+
+to build and test.
+
+It is becoming easy
+to actually build--
+
+I wouldn't say-- maybe
+easy is a strong word--
+
+feasible to generate
+1,000 versions
+
+of a particular circuit.
+
+I'll give you an example.
+
+Very recently in my lab,
+one of the graduate students
+
+has come up with a
+framework that-- he
+
+is generating 200 versions of
+a circuit in three hours, OK?
+
+And they're pretty much
+gotten to the point
+
+where they're all correct.
+
+In three hours--
+so that really, I
+
+think, changes what you
+do in synthetic biology.
+
+And so again, having
+that be connected
+
+to a computational design
+tool that tells you
+
+which ones to build
+would be rather useful.
+
+And so specifically
+recognizing that-- this
+
+is a collaboration
+with some folks at BBN.
+
+And actually Jake Beal was one
+of my former graduate student
+
+colleagues.
+
+So he was in the same lab as me.
+
+And then Doug Densmore is
+from Boston University.
+
+And so the notion
+here is that this
+
+is what we want synthetic
+biology to look like.
+
+OK, so if you're
+trying-- or maybe
+
+all of biological engineering.
+
+But we'll start with
+synthetic biology.
+
+So if you want to
+program biology,
+
+should you really care
+what the ribosome binding
+
+site is for the
+lambda repressor?
+
+You know, hopefully not, right?
+
+What you should
+do, just like when
+
+you program your simulations in
+MATLAB, you don't think about,
+
+well, here's the shift register
+in this Intel Pentium chip.
+
+And this is how it's working
+to simulate this ODE over here.
+
+That's just not the level
+at which your program.
+
+So you think really
+at a high level.
+
+And then you have compilers
+and lots of infrastructure
+
+that takes care of
+everything in between.
+
+And so maybe someday in the
+future, the graduate students
+
+maybe five to 10 years will
+look back at synthetic biology
+
+graduate students
+now and would just
+
+have a lot of pity for
+them and, oh my god.
+
+You actually had to
+know what elements
+
+you were using in circuit and
+actually build them by hand?
+
+You know, wow.
+
+And so here's a notion that
+we start with a high level
+
+description.
+
+And by the way, this
+is now-- there's
+
+a website that you can go
+through right now and get
+
+a free account and then type
+in a high level program.
+
+And it will actually create
+a low level genetic circuit
+
+representation.
+
+It will also give you MATLAB
+simulation files of this.
+
+And so, in this course
+I'm teaching to undergrads
+
+right now that many of them
+didn't even hold pipettes
+
+before they started the
+course, one of the first things
+
+that we taught
+them was this tool.
+
+So before telling
+them, for example, this
+
+is the way the lac repressor
+works by DNA looping, we said,
+
+there are these things
+called repressors.
+
+And when there's more of
+them, there's less output.
+
+Now let's design with that.
+
+This is, I think, heresy to
+biology as a whole probably.
+
+I don't know that-- this is the
+first time that we've actually
+
+tried to do that.
+
+And I think it's
+actually worked out OK.
+
+But teach them enough so
+that they can move forward.
+
+And then, yes,
+let's simultaneously
+
+be teaching them about
+the underlying biology
+
+and mechanisms as much
+as they need to know.
+
+But what can they
+do if they just
+
+know that there's
+this thing called
+
+a transcriptional repressor?
+
+And then the bio
+compiler will figure out
+
+everything that needs to happen.
+
+And so we're actually-- so they
+did a whole bunch of designs.
+
+And starting next week, we're
+going to be testing them out.
+
+So we will find out whether
+that was a useful way
+
+to teach biological engineering.
+
+But I think so.
+
+I think it is.
+
+Because they seem to understand
+what design means, OK?
+
+Because that's a thing
+that we focus on-- design
+
+as kind of a first class object.
+
+OK, so what you do is you write
+code that looks like this.
+
+Has anybody programmed in
+code that looks like this?
+
+It should be-- so Lisp.
+
+OK, one person only?
+
+Any computational?
+
+OK, we usually get
+one or two people.
+
+But I was hoping for more here.
+
+So anyways, for the people that
+should be ashamed of themselves
+
+and haven't programmed in
+lisp, this is a simple program.
+
+This is, if the
+input is high, it
+
+produces cyan
+fluorescent protein.
+
+Or else, it will produce a
+yellow fluorescent protein.
+
+And so the bio compiler then
+automatically takes that
+
+and first translates
+that into a data flow.
+
+So you have a data
+flow-- and I'll
+
+actually go through
+an example of that--
+
+and then creates an
+abstract gene circuit
+
+and then looks at essentially
+what you have in the freezer
+
+and says, well, this
+is the actual DNA
+
+sequence that would
+implement this.
+
+And it creates robot
+instructions to assemble this
+
+so that God forbid you
+would have to actually touch
+
+a pipette to build this.
+
+And then we have a robot,
+liquid handling robot,
+
+that does most of the assembly.
+
+Now, this pipeline is
+not fully end to end yet.
+
+So it's not-- if you came to
+my lab right now, the still-- I
+
+could tell you that
+this works but then I
+
+would be slightly lying.
+
+Is-- mostly works.
+
+But it's actually-- there
+are companies right now that
+
+will go from this level--
+about this level--
+
+not this level, but this level.
+
+And actually, this
+is mostly automated.
+
+So-- to the point where the
+only thing that's not automated
+
+is somebody, not necessary
+your op, but maybe a technician
+
+goes from a robot
+and takes a plate
+
+and puts it in another robot.
+
+And, like, everything
+else is essentially
+
+automated in DNA assembly
+
+So those companies have, I
+guess, more money than us.
+
+But eventually, this is the
+way DNA assembly will happen.
+
+So we're collaborating
+with some people.
+
+I'm doing this
+with microfluidics.
+
+The problem with this
+robot-- it's $150,000.
+
+So we can't put it on
+everyone's bench yet.
+
+But we are collaborating
+with Lincoln Labs
+
+to have microfluidic devices
+that would cost around
+
+$3,000 that would do this.
+
+And we've already demonstrated
+with the microfluidic devices
+
+we can do DNA assembly
+of large circuits.
+
+So this is not that
+far away that everyone
+
+will have microfluidics.
+
+They program here.
+
+And they get the DNA assembled.
+
+And then they realize
+it doesn't work.
+
+But at least there'd
+be a lot faster
+
+to realize that things
+don't work, which is good.
+
+So let's look at how this
+compiler, bio compiler,
+
+works to see that
+it's not magic.
+
+So this is saying
+green if not IPTG.
+
+So IPTG is a small molecule
+that we have a sensor for.
+
+And then the
+information gets routed
+
+to an inverter which
+then gets routed
+
+to activate a green
+fluorescent protein.
+
+So you can take a program
+specified like this
+
+and automatically convert
+it into a data flow graph.
+
+And then the data flow
+can be translated-- again,
+
+this is automated
+and this is also
+
+automated in a
+rather simple way--
+
+to an actual portions
+of the gene circuit.
+
+So IPTG sensor is
+simply this motif.
+
+So you have a repressor
+that responds to IPTG.
+
+And then it basically
+inactivates the repressor.
+
+So more IPTG, more output.
+
+And so this is the
+IPTG sensor box.
+
+And this is how
+you implement this.
+
+Not gate-- so I showed you
+how a not gate already works.
+
+So a repressor
+represses the output.
+
+Green fluorescent
+protein, you just
+
+have to have an
+activator that activates
+
+a green fluorescent protein.
+
+So every data flow
+box can automatically
+
+be converted into a small motif.
+
+And then what we're
+missing is the glue.
+
+And so the glue is just these
+transcriptional activators
+
+and repressors.
+
+And so once you put them in
+there, then this is a circuit.
+
+And so this is an automatic
+way to go from here to here.
+
+And it can do rather
+complex circuits and logic.
+
+It can't do everything yet.
+
+But it can do an
+interesting set of things.
+
+OK, so this is-- again,
+it's not completely finished
+
+in the sense that I
+haven't told you what A is.
+
+I haven't told you what B is.
+
+So there's a whole
+bunch of things
+
+that still are-- we
+have-- either published on
+
+or still need to be designed.
+
+But there is, for example,
+tool called matchmaker
+
+which will decide what's
+a good protein A, what's
+
+a good protein B. So things like
+that-- so those things already
+
+exist.
+
+Anybody look at this and figure
+out why this is not perfect?
+
+So we have an input that
+represses a repressor, which
+
+means that more input,
+more activator-- sorry.
+
+More input, more
+protein here, which
+
+represses B, which
+activates GFP.
+
+So the compiler spits
+that out automatically.
+
+But you may not want to
+build this right away.
+
+Any ideas why?
+
+I'm sure John would.
+
+AUDIENCE: So basically, you
+have this A can directly repress
+
+object, so you activate B?
+
+PROF.
+
+RON WEISS: So this is what
+it-- the first version of B.
+
+But A represses B.
+B activates GFP.
+
+So why not just hook A up
+to regulate GFP directly?
+
+So this seems like a
+non-optimal solution.
+
+And so you can get the compiler
+to figure that out too.
+
+And so what you do is
+you say copy propagation.
+
+So these are actually just
+tools that are available.
+
+These are mechanisms
+that are part
+
+of normal compilers--
+normal software compilers.
+
+So they do something called
+copy propogation-- means
+
+that A, if it sees that A--
+the compiler sees A regulates
+
+B, A represses B,
+and B activates A.
+
+So you can just say, well, let
+A just directly regulate this.
+
+And then the compiler realizes,
+well, B doesn't do anything.
+
+Let's get rid of it.
+
+And then the promoter
+doesn't do anything.
+
+Let's get rid of it.
+
+And now the compiler
+figured this out.
+
+And that's using just
+basic compiler technology.
+
+OK, so it's able to do that.
+
+So the difference in your
+life between four and three
+
+may not be huge.
+
+But the difference in your
+life between 15 and five
+
+could be the difference
+between getting your Ph.D
+
+or going insane, dropping out,
+and then starting a company
+
+and becoming a billionaire.
+
+OK, so-- but this is
+what the compiler can do.
+
+And that does make a difference.
+
+And it may be able to come up
+with optimizations that you
+
+wouldn't be able to really
+easily come up with or even
+
+at all under a reasonable
+amount of time.
+
+So the compiler can do
+combinatorial logic.
+
+It can do state.
+
+There's also some aspects that
+can do spatial things as well.
+
+And again, this is
+available online right now.
+
+I'm going to-- maybe I
+should skip a few things.
+
+So very quickly, I'll tell you.
+
+So in the lab-- so
+it's nice [INAUDIBLE]
+
+But if you can't do
+anything in the lab,
+
+then nobody believes
+you in the world
+
+of biology or synthetic biology.
+
+So we can build big things.
+
+So here, you can-- there's a
+library of promoters and genes
+
+that we have available.
+
+And you can decide,
+I want to build
+
+a new circuit has these
+promoter gene pairs.
+
+And within five days, you can
+create in the lab that circuit.
+
+And we've been able
+to demonstrate things
+
+that are 61, 64 Kb that
+you build in five days.
+
+And you build them efficiently.
+
+And then the undergrads
+that we're teaching also
+
+have been able to--
+again, these are
+
+people to barely
+knew what pipette
+
+are in the beginning a semester
+can now efficiently build
+
+large circuits.
+
+So that's become an
+easy to use technology.
+
+And then I mention
+this notion that you
+
+can build this one at a time.
+
+But this very recent
+development where
+
+you could build 200
+versions of these at a time.
+
+OK, so you can build them.
+
+We can then-- again,
+I'll skip this part.
+
+You could build them.
+
+You can put them
+into mammalian cells.
+
+These things work.
+
+And we have lots and lots
+of parts-- regulatory parts.
+
+And so let me skip this
+particular example.
+
+So this is-- the two
+sentence explanation
+
+is, OK, you build lots of parts.
+
+You can build modules.
+
+And then you put
+modules together.
+
+And guess what?
+
+This is biology.
+
+So these modules actually
+affect each other,
+
+potentially in undesirable ways.
+
+So they can place
+things like load.
+
+So whenever you have a module
+that works really well-- maybe
+
+I will show you one slide.
+
+But I won't show you
+how we solved it.
+
+But one slide-- so
+this is a circuit.
+
+Any idea what this
+circuit might do?
+
+So this is a regulatory circuit.
+
+They have an activator
+activating itself
+
+and a repressor that
+represses the activator.
+
+Have you seen this motif?
+
+So it's a-- some people are
+whispering to themselves,
+
+doing this.
+
+So this is a
+relaxation oscillator.
+
+When you do it by
+yourself, it works great.
+
+So these are simulations.
+
+But then if you
+connect it-- so it's
+
+nice to have an
+oscillator in a cell,
+
+again, if you want to
+have blinking bacteria
+
+or mammalian cells
+which is, again, fun.
+
+But then you typically want
+to connect it to something.
+
+So you spent three years
+building an oscillator,
+
+got it to work.
+
+And now your adviser says, OK,
+let's just get a paper on this.
+
+But before we get
+the paper, I want
+
+you to connect it to
+something meaningful.
+
+Because we want to go for
+a high impact journal.
+
+And then you connect
+it to something.
+
+And you realize that it
+doesn't work anymore.
+
+I think you're really
+pissed off at-- you
+
+will be pissed off
+at your adviser.
+
+I don't know if your adviser
+would want to be mean to you.
+
+But anyways, so that's a
+real problem in biology
+
+or synthetic biology
+is that these things
+
+have impacts on each
+other that, first of all,
+
+are going to be
+undesirable but because
+
+of unique aspects, for
+example, of the substrate.
+
+Now, they're not
+as unique as you
+
+might think because
+these load issues also
+
+come to play in
+electronic circuits.
+
+And so in electronics
+circuits, these things
+
+have been solved decades
+ago with these notions
+
+of load drivers.
+
+So if you have a module that
+has, for example, high fanout
+
+and it controls many
+things, then guess what?
+
+Those things that it's
+trying to control,
+
+even though the arrows are
+pointing one direction,
+
+they actually have an
+upstream effect too.
+
+So those modules that you think
+you're-- the downstream modules
+
+that you're just controlling,
+they actually have an impact
+
+on the upstream.
+
+So what you do-- in electronics,
+you just build a load driver.
+
+And it basically
+takes care of things.
+
+So now there's no kind
+of parasitic effect.
+
+And so we've demonstrated
+that we can also
+
+build-- so this is a
+notion of retroactivity.
+
+And this is work with
+Domitilla Del Vecchio here.
+
+And we've demonstrated
+that we can-- so I wont'
+
+go into the details here-- so
+we can actually solve this.
+
+So this is a real problem
+even in simple circuits
+
+experimentally.
+
+And then it uses this cool
+notion of timescale separation
+
+to solve it.
+
+But we can take these things
+that are highly affected
+
+to go from black to red
+and put a load driver in
+
+and then it fixes it.
+
+So this should hopefully lead
+to the generation of much more
+
+predictable circuit
+construction targeting
+
+one of the real challenges in
+scaling going from simple toy
+
+modules to large scale systems.
+
+So I'll skip that and then move
+on to another example-- oh,
+
+sorry, an example
+of an application.
+
+So in this particular
+case-- again, besides
+
+turning GFP on and off, what
+can we do with synthetic biology
+
+that we can't necessarily do
+without synthetic biology?
+
+And so one of the most
+important challenges
+
+in cancer therapeutics
+is specificity--
+
+perhaps the most important.
+
+There are other things
+that are important
+
+such as delivery of
+a therapeutic agent.
+
+But as you improve specificity
+that it can actually
+
+change how you do delivery
+of a therapeutic agent.
+
+So if you have a therapeutic
+agent that's much more specific
+
+and has no side effects, you
+can deliver lots and lots more.
+
+So these things
+are highly related.
+
+So imagine a therapeutic agent
+that recognizes something
+
+on a cell surface and then
+says, this is a tumor cell.
+
+Kill it.
+
+So there are actually a
+lot of efforts ongoing that
+
+have this particular approach.
+
+So whether it's small molecules,
+whether these vesicles that
+
+contain various cell surface--
+various molecules that bind
+
+to cell surface receptors,
+a really hot area right
+
+now is these engineered
+killer T cells.
+
+So this notion that
+you can actually
+
+engineer your immune system
+by placing various receptors
+
+on these killer T
+cells which then
+
+go and then bind tumor cells
+by recognizing something
+
+on the cell surface
+and then kill those.
+
+Sounds great, maybe, depending
+on your perspective, or not
+
+so great, depending
+on your perspective.
+
+So what's happened with
+those is they're really
+
+sometimes great at
+eliminating your tumors.
+
+But then the side effects
+can be horrendous.
+
+And so what happens is that
+those cell surface markers
+
+that exist on the tumor
+cells-- guess what?
+
+They're also present on
+healthy cells as well.
+
+And so the side effects for
+those killer T cells approaches
+
+have been, I mean, just
+terrible in various patients.
+
+So one-- this should
+not be a shock.
+
+One marker is typically not
+enough to distinguish a cancer
+
+cell versus a healthy cell.
+
+Seems pretty obvious.
+
+So actually, what they've been
+doing with these engineered
+
+killer T cells is
+now just saying, OK,
+
+has to be this cell
+surface receptors,
+
+but also cannot be this.
+
+So it's like, and biomarker
+one and not-- you know,
+
+biomarker one, and
+not biomarker two.
+
+OK, so they're starting to
+engineer more logic into these,
+
+more multi-input logic
+into these things.
+
+And so they haven't done
+any clinical trials.
+
+But I saw a couple weeks
+ago where they've actually
+
+made progress in Petri dishes.
+
+So we recognized this as
+an issue several years ago.
+
+And this is work
+with Coby Benson.
+
+And so really, all the
+information that you want
+
+is actually inside the cell to
+make a highly precise decision
+
+about whether this particular
+cell is cancerous or not.
+
+OK, so the idea is when
+the therapeutic agent,
+
+does the computation
+by integrating
+
+multiple pieces of the
+sensory information
+
+and then decides whether
+to express a killer protein
+
+or not.
+
+Now, even if this is not
+the cure for cancer--
+
+can't really
+guarantee that, right?
+
+But even if this is
+not, just this notion
+
+of being able to create multi
+input circuits to go into cells
+
+and analyze in live
+cells real time what's
+
+going on in the cell
+with various molecules
+
+that might be interesting-- that
+has applications I would again
+
+say just about anywhere you
+could imagine in biology.
+
+So one of the
+things, for example,
+
+we're looking at-- I mentioned
+this notion of organs
+
+on a chip or programmed
+organs on a chip.
+
+So one of the things
+we're looking at now
+
+is placing these types
+of sensory circuits
+
+into cells within
+this organ on a chip.
+
+And so the idea would be expose
+cells to these drug candidates.
+
+And then the cells
+light up in different
+
+colors to tell you how
+they're responding to it.
+
+So for example, certain color
+green would mean just fine.
+
+Green with red and
+yellow would indicate
+
+that some apoptotic
+pathway is being expressed
+
+or this drug is affecting
+this proliferation
+
+path or this pathway
+or that pathway.
+
+And so these
+mechanisms can tell you
+
+in real time in
+single cells-- also
+
+specially-- what kind
+of impact there is to,
+
+let's say, the drug
+candidate you're looking at.
+
+So again, this is
+something that I
+
+think would have an impact
+today if it was available,
+
+but realistically
+making prototypes
+
+within the next
+year to three years.
+
+OK, so we started with
+looking at HeLa cancer cells
+
+as an example.
+
+And so we did some
+bioinformatics.
+
+And we saw that based on
+microRNA profiles that
+
+were available to us, this
+would be a bio program that
+
+would distinguish HeLa cells
+from all other cell types.
+
+And so some of you are
+familiar with this way
+
+of annotating logic.
+
+Pretty ugly if you're not
+used it, but it's simple.
+
+This just says, these
+microRNAs have to be low
+
+and these microRNAs
+have to be high.
+
+And that's a HeLa cancer cell.
+
+Because that's the
+basic logic in this.
+
+So it's a rather
+simple logic statement.
+
+What we would argue is
+that every cell type
+
+would have a logic
+statement that
+
+would be true of that cell type
+and not true of other cells.
+
+It's almost by definition.
+
+There's something different
+about that cell than other cell
+
+types.
+
+Now, it gets
+interesting when you
+
+start talking about
+heterogeneous population.
+
+So for example, and that's--
+I won't get into details about
+
+that.
+
+But there is heterogeneity.
+
+There's heterogeneity in tumors.
+
+So the cool thing you can do--
+this is a six input and gate.
+
+So if you have heterogeneity,
+where you can do
+
+is you can have a six input
+and gate with an or operation.
+
+So you can identify this
+sub population of the tumor
+
+has this microRNA profile.
+
+And this cell population has
+a different microRNA profile.
+
+And all you have to do is
+create a new logic circuit
+
+and just combine them as like
+a cocktail drug as an or gate.
+
+So this is a really
+general approach
+
+that I think should
+be relevant, again,
+
+for any kind of population.
+
+And you can also
+set the thresholds
+
+and have all these fun things
+that you can do with it.
+
+So I think the question really
+is, is that microRNA expression
+
+profile sufficiently
+small so that it
+
+can be encoded on a circuit
+that you can deliver into cells?
+
+And can you do it reliably?
+
+That really is the challenge.
+
+OK, so the idea is that you
+have a therapeutic agent,
+
+goes into a cell
+does the computation,
+
+and then decides whether to
+make a killer protein or not.
+
+OK, so how does
+this actually work?
+
+So how do we implement an and
+gate with inverted inputs?
+
+OK, so that's one
+portion of the circuit.
+
+So it's actually-- for microRNA,
+it's actually pretty easy.
+
+So what you do is you
+put microRNA target sites
+
+on the gene of interest
+or the output gene.
+
+And so the idea is that the
+only way that this gene is being
+
+expressed, this output
+protein is expressed,
+
+is when this is low and
+this is low and this is low.
+
+So in principle, this
+is pretty easy to do.
+
+OK, so that's how we have
+a three input and gate
+
+with inverted inputs.
+
+And now we can
+add logic to that.
+
+So now if we want to make sure
+that the output is high also
+
+when this input as high as well.
+
+And so what we do-- so
+remember the first circuit
+
+that I showed you
+was this cascade.
+
+And the cascade was a bunch
+of repressors that would then
+
+cascade that did the
+not not operation.
+
+So when you think about
+the not not operation,
+
+it doesn't seem like a
+very useful operation.
+
+But this here, the not not
+operation, is actually useful.
+
+So it can convert
+a microRNA sensor
+
+into something that can be
+integrated with other sensors
+
+to create the four
+input logic function.
+
+So this microRNA has
+to be high in order
+
+to repress this
+repressor which then
+
+represses the final output.
+
+So the only time that the
+final output can be high
+
+is when this is high and
+these three are low, OK?
+
+And then you can continue.
+
+And you can add another one.
+
+This is slightly more
+complex in the sense
+
+that now, essentially the
+sum of these microRNAs
+
+has to be high in
+order for this branch
+
+to allow expression here.
+
+So it's slightly more
+complex in the sense
+
+that it's not just--
+it's like a plus-- again,
+
+like a plus operation,
+which we found
+
+to be actually the
+relevant operation here.
+
+And so the only
+time the output high
+
+is when this microRNA is
+high, combination of these two
+
+is high, and these are low.
+
+Anybody see a
+potential problem here?
+
+A potential crosstalk?
+
+So everybody here
+understand the circuit?
+
+Raise your hand if you actually
+understand the circuit.
+
+OK, that's not a lot of people.
+
+OK, maybe I should
+go back for a second.
+
+Everybody-- raise your hand
+if you understand this.
+
+OK, so if microRNA is
+high, they repress--
+
+they result in
+degradation of the RNA.
+
+So all of these have to be low
+in order for this to be high.
+
+OK, now if we had
+this, this RNA--
+
+let's focus just on
+this maybe to simplify.
+
+So this microRNA
+represses-- this
+
+is a repressor which
+represses this, OK?
+
+So if this microRNA is low,
+then this repressor as high.
+
+And as a result of
+that, this repressor
+
+represses this
+promoter regardless.
+
+So it doesn't matter
+what these are.
+
+If this is low, this
+repressor is high.
+
+And then there's no way that
+this output can be high.
+
+Now, if this is
+microRNA is high,
+
+then this becomes low, allowing
+this to potentially be high.
+
+Doesn't guarantee it, but
+it has a potential of doing.
+
+OK, now raise your hand
+if you understand that.
+
+OK, more.
+
+OK, cool.
+
+That's progress.
+
+By the way, this was
+not a trivial circuit.
+
+There's a lot of
+connections here.
+
+And then we connect the same--
+now we have the same repressor.
+
+So this microRNA--
+these set of microRNAs
+
+repress the same repressor
+which is now repressing this.
+
+So why is it the
+case that you need--
+
+let's just assume
+this is one microRNA,
+
+this is another micro.
+
+Why do you need both microRNAs
+to allow high output?
+
+And then I will not
+let anyone leave
+
+until you answer the question.
+
+And I can sit down.
+
+So why-- and then
+we'll stop there.
+
+And everybody will believe
+me that the cure for cancer,
+
+you got it figure it out.
+
+Otherwise-- so
+there's-- oh, thank you.
+
+Letting-- you will be the hero.
+
+AUDIENCE: So if the
+microRNAs are not present,
+
+then you're going to get an
+expression of Lacks E. So--
+
+PROF.
+
+RON WEISS: Lack I.
+
+AUDIENCE: Yeah, like eyes.
+
+So only if both the microRNAs
+are high and present
+
+do you repress both
+of the lack I's
+
+which then allow for
+the expression of the--
+
+PROF.
+
+RON WEISS: Exactly.
+
+And what happens if
+one of them is present
+
+and the other one is not?
+
+So if this microRNA is
+present and this one is not?
+
+AUDIENCE: Then the lack
+I still gets expressed
+
+because the other one
+is still not repressed.
+
+PROF.
+
+RON WEISS: Exactly.
+
+So the only way that
+you can actually
+
+have no expression of lack
+I is when this is high
+
+and this is high.
+
+So this is essentially
+like a two input and gate.
+
+These two have to be high
+to allow this promoter
+
+to potentially be high.
+
+And in the other three logic
+cases where one of those
+
+is low, lack I is
+expressed and hence
+
+does not allow the output
+protein to be expressed, OK?
+
+Yeah.
+
+AUDIENCE: So why do
+you have the partition?
+
+All three are
+acting the same way.
+
+PROF.
+
+RON WEISS: Ah, great question.
+
+So what happens if microRNA
+21, 17, and 38 were all here?
+
+So that's a great question.
+
+So that's a question, right?
+
+So if you put microRNA
+21 here, 17, and 38?
+
+What is the logic function here?
+
+Yeah.
+
+AUDIENCE: Then you
+only need one of them
+
+in order to degrade the RNA.
+
+And then you won't
+get the same logic.
+
+PROF.
+
+RON WEISS: Great.
+
+So then it becomes
+essentially an or.
+
+This will be an or
+operation of the microRNAs
+
+where what we want is an and
+operation on the microRNA.
+
+So that by having
+two separate paths
+
+that have the same repressor
+where they converge
+
+on the same repressor, we
+achieve the and operation.
+
+Where we have them on
+the same repressor,
+
+they do the or operation.
+
+That's a great question.
+
+OK, so this works.
+
+And maybe I'll say thank you.
+
+I'll stop there.
\ No newline at end of file
diff --git a/kNmiTTKiYd4.txt b/kNmiTTKiYd4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f47c8391dcb030d1929f0fbde398916343f0c7aa
--- /dev/null
+++ b/kNmiTTKiYd4.txt
@@ -0,0 +1,2140 @@
+[MUSIC PLAYING]
+
+PROFESSOR: Last time, we took a
+look at an explicit control
+
+evaluator for Lisp, and that
+bridged the gap between all
+
+these high-level languages
+like Lisp and the query
+
+language and all of that stuff,
+bridged the gap between
+
+that and a conventional
+register machine.
+
+And in fact, you can think of
+the explicit control evaluator
+
+either as, say, the code for a
+Lisp interpreter if you wanted
+
+to implement it in the assembly
+language of some
+
+conventional register transfer
+machine, or, if you like, you
+
+can think of it as the microcode
+of some machine
+
+that's going to be specially
+designed to run Lisp.
+
+In either case, what we're
+doing is we're taking a
+
+machine that speaks some
+low-level language, and we're
+
+raising the machine to a
+high-level language like Lisp
+
+by writing an interpreter.
+
+So for instance, here,
+conceptually, is a special
+
+purpose machine for computing
+factorials.
+
+It takes in five and
+puts out 120.
+
+And what this special purpose
+machine is is actually a Lisp
+
+interpreter that's configured
+itself to run factorials,
+
+because you fit into
+it a description of
+
+the factorial machine.
+
+So that's what an
+interpreter is.
+
+It configures itself to emulate
+a machine whose
+
+description you read in.
+
+Now, inside the Lisp
+interpreter, what's that?
+
+Well, that might be your general
+register language
+
+interpreter that configures
+itself to behave like a Lisp
+
+interpreter, because you
+put in a whole bunch of
+
+instructions in register
+language.
+
+This is the explicit
+control evaluator.
+
+And then it also has some sort
+of library, a library of
+
+primitive operators and Lisp
+operations and all sorts of
+
+things like that.
+
+That's the general strategy
+of interpretation.
+
+And the point is, what we're
+doing is we're writing an
+
+interpreter to raise the machine
+to the level of the
+
+programs that we
+want to write.
+
+Well, there's another strategy,
+a different one,
+
+which is compilation.
+
+Compilation's a little
+bit different.
+
+Here--here we might have
+produced a special purpose
+
+machine for, for computing
+factorials, starting with some
+
+sort of machine that speaks
+register language, except
+
+we're going to do a different
+strategy.
+
+We take our factorial program.
+
+We use that as the source
+code into a compiler.
+
+What the compiler will do is
+translate that factorial
+
+program into some register
+machine language.
+
+And this will now be not the
+explicit control evaluator for
+
+Lisp, this will be some
+register language for
+
+computing factorials.
+
+So this is the translation
+of that.
+
+That will go into some sort of
+loader which will combine this
+
+code with code selected from the
+library to do things like
+
+primitive multiplication.
+
+And then we'll produce a load
+module which configures the
+
+register language machine
+to be a special
+
+purpose factorial machine.
+
+So that's a, that's a
+different strategy.
+
+In interpretation, we're raising
+the machine to the
+
+level of our language,
+like Lisp.
+
+In compilation, we're taking our
+program and lowering it to
+
+the language that's spoken
+by the machine.
+
+Well, how do these two
+strategies compare?
+
+The compiler can produce code
+that will execute more
+
+efficiently.
+
+The essential reason for that is
+that if you think about the
+
+register operations that are
+running, the interpreter has
+
+to produce register operations
+which, in principle, are going
+
+to be general enough to execute
+any Lisp procedure.
+
+Whereas the compiler only has
+to worry about producing a
+
+special bunch of register
+operations for, for doing the
+
+particular Lisp procedure
+that you've compiled.
+
+Or another way to say that is
+that the interpreter is a
+
+general purpose simulator, that
+when you read in a Lisp
+
+procedure, then those can
+simulate the program described
+
+by that, by that procedure.
+
+So the interpreter is worrying
+about making a general purpose
+
+simulator, whereas the compiler,
+in effect, is
+
+configuring the thing to
+be the machine that the
+
+interpreter would have
+been simulating.
+
+So the compiler can be faster.
+
+On the other hand, the
+interpreter is a nicer
+
+environment for debugging.
+
+And the reason for that is that
+we've got the source code
+
+actually there.
+
+We're interpreting it.
+
+That's what we're
+working with.
+
+And we also have the
+library around.
+
+See, the interpreter--the
+library sitting there is part
+
+of the interpreter.
+
+The compiler only pulls out from
+the library what it needs
+
+to run the program.
+
+So if you're in the middle of
+debugging, and you might like
+
+to write a little extra program
+to examine some run
+
+time data structure or to
+produce some computation that
+
+you didn't think of when you
+wrote the program, the
+
+interpreter can do that
+perfectly well, whereas the
+
+compiler can't.
+
+So there are sort of dual,
+dual advantages.
+
+The compiler will produce code
+that executes faster.
+
+The interpreter is a better
+environment for debugging.
+
+And most Lisp systems end up
+having both, end up being
+
+configured so you have an
+interpreter that you use when
+
+you're developing your code.
+
+Then you can speed it
+up by compiling.
+
+And very often, you can arrange
+that compiled code and
+
+interpreted code can
+call each other.
+
+We'll see how to do that.
+
+That's not hard.
+
+In fact, the way we'll--
+
+in the compiler we're going to
+make, the way we'll arrange
+
+for compiled coding and
+interpreted code to call, to
+
+call each other, is that we'll
+have the compiler use exactly
+
+the same register conventions
+as the interpreter.
+
+Well, the idea of a compiler is
+very much like the idea of
+
+an interpreter or evaluator.
+
+It's the same thing.
+
+See, the evaluator walks over
+the code and performs some
+
+register operations.
+
+That's what we did yesterday.
+
+Well, the compiler essentially
+would like to walk over the
+
+code and produce the register
+operations that the evaluator
+
+would have done were it
+evaluating the thing.
+
+And that gives us a model
+for how to implement a
+
+zeroth-order compiler, a
+very bad compiler but
+
+essentially a compiler.
+
+A model for doing that is you
+just take the evaluator, you
+
+run it over the code, but
+instead of executing the
+
+actual operations, you
+just save them away.
+
+And that's your compiled code.
+
+So let me give you an
+example of that.
+
+Suppose we're going to
+compile--suppose we want to
+
+compile the expression f of x.
+
+So let's assume that we've got
+f of x in the x register and
+
+something in the environment
+register.
+
+And now imagine starting
+up the evaluator.
+
+Well, it looks at the expression
+and it sees that
+
+it's an application.
+
+And it branches to a place in
+the evaluator code we saw
+
+called ev-application.
+
+And then it begins.
+
+It stores away the operands and
+unev, and then it's going
+
+to put the operator in exp,
+and it's going to go
+
+recursively evaluate it.
+
+That's the process that
+we walk through.
+
+And if you start looking at
+the code, you start seeing
+
+some register operations.
+
+You see assign to unev the
+operands, assign to exp the
+
+operator, save the environment,
+generate
+
+that, and so on.
+
+Well, if we look on the overhead
+here, we can see, we
+
+can see those operations
+starting to be produced.
+
+Here's sort of the first real
+operation that the evaluator
+
+would have done.
+
+It pulls the operands out of the
+exp register and assigns
+
+it to unev. And then it assigns
+something to the
+
+expression register, and it
+saves continue, and it saves
+
+env.
+
+And all I'm doing here is
+writing down the register
+
+assignments that the evaluator
+would have done in
+
+executing that code.
+
+And can zoom out a little bit.
+
+Altogether, there are about
+19 operations there.
+
+And this is the--this will be
+the piece of code up until the
+
+point where the evaluator
+branches off to
+
+apply-dispatch.
+
+And in fact, in this compiler,
+we're not going to worry about
+
+apply-dispatch at all.
+
+We're going to have
+everything--we're going to
+
+have both interpreted code
+and compiled code.
+
+Always evaluate procedures,
+always apply procedures by
+
+going to apply-dispatch.
+
+That will easily allow
+interpreted code and compiled
+
+code to call each other.
+
+Well, in principle, that's
+all we need to do.
+
+You just run the evaluator.
+
+So the compiler's a lot
+like the evaluator.
+
+You run it, except it stashes
+away these operations instead
+
+of actually executing them.
+
+Well, that's not, that's
+not quite true.
+
+There's only one little
+lie in that.
+
+What you have to worry about is
+if you have a, a predicate.
+
+If you have some kind of test
+you want to do, obviously, at
+
+the point when you're compiling
+it, you don't know
+
+which branch of these--of a
+conditional like this you're
+
+going to do.
+
+So you can't say which one the
+evaluator would have done.
+
+So all you do there
+is very simple.
+
+You compile both branches.
+
+So you compile a structure
+that looks like this.
+
+That'll compile into something
+that says, the code, the code
+
+for P. And it puts its results
+in, say, the val register.
+
+So you walk the interpreter over
+the predicate and make
+
+sure that the result would
+go into the val register.
+
+And then you compile an
+instruction that says, branch
+
+if, if val is true, to a place
+we'll call label one.
+
+Then we, we will put the
+code for B to walk the
+
+interpreter--walk the
+interpreter over B. And then
+
+go to put in an instruction
+that says, go to the next
+
+thing, whatever, whatever was
+supposed to happen after this
+
+thing was done.
+
+You put in that instruction.
+
+And here you put label one.
+
+And here you put the
+code for A. And you
+
+put go to next thing.
+
+So that's how you treat
+a conditional.
+
+You generate a little
+block like that.
+
+And other than that, this
+zeroth-order compiler is the
+
+same as the evaluator.
+
+It's just stashing away the
+instructions instead of
+
+executing them.
+
+That seems pretty simple,
+but we've gained
+
+something by that.
+
+See, already that's
+going to be more
+
+efficient than the evaluator.
+
+Because, if you watch the
+evaluator run, it's not only
+
+generating the register
+operations we wrote down, it's
+
+also doing things to decide
+which ones to generate.
+
+So the very first thing it does,
+say, here for instance,
+
+is go do some tests and decide
+that this is an application,
+
+and then branch off to the
+place that, that handles
+
+applications.
+
+In other words, what the
+evaluator's doing is
+
+simultaneously analyzing the
+code to see what to do, and
+
+running these operations.
+
+And when you--
+
+if you run the evaluator a
+million times, that analysis
+
+phase happens a million times,
+whereas in the compiler, it's
+
+happened once, and then you
+just have the register
+
+operations themselves.
+
+Ok, that's a, a zeroth-order
+compiler, but it is a
+
+wretched, wretched compiler.
+
+It's really dumb.
+
+Let's--let's go back and, and
+look at this overhead.
+
+So look at look at some
+of the operations
+
+this thing is doing.
+
+We're supposedly looking
+at the operations and
+
+interpreting f of x.
+
+Now, look here what
+it's doing.
+
+For example, here it
+assigns to exp the
+
+operator in fetch of exp.
+
+But see, there's no reason to
+do that, because this is--
+
+the compiler knows that the
+operator, fetch of exp, is f
+
+right here.
+
+So there's no reason why this
+instruction should say that.
+
+It should say, we'll
+assign to exp, f.
+
+Or in fact, you don't
+need exp at all.
+
+There's no reason it should
+have exp at all.
+
+What, what did exp
+get used for?
+
+Well, if we come down here,
+we're going to assign to val,
+
+look up the stuff in exp
+in the environment.
+
+So what we really should do is
+get rid of the exp register
+
+altogether, and just change
+this instruction to say,
+
+assign to val, look up the
+variable value of the symbol f
+
+in the environment.
+
+Similarly, back up here, we
+don't need unev at all,
+
+because we know what the
+operands of fetch of exp are
+
+for this piece of code.
+
+It's the, it's the list x.
+
+So in some sense, you don't
+want unev and exp at all.
+
+See, what they really are in
+some sense, those aren't
+
+registers of the actual machine
+
+that's supposed to run.
+
+Those are registers that have to
+do with arranging the thing
+
+that can simulate
+that machine.
+
+So they're always going to hold
+expressions which, from
+
+the compiler's point of view,
+are just constants, so can be
+
+put right into the code.
+
+So you can forget about all the
+operations worrying about
+
+exp and unev and just
+use those constants.
+
+Similarly, again, if we go, go
+back and look here, there are
+
+things like assign to
+continue eval-args.
+
+Now, that has nothing
+to do with anything.
+
+That was just the evaluator
+keeping track of where it
+
+should go next, to evaluate the
+arguments in some, in some
+
+application.
+
+But of course, that's irrelevant
+to the compiler,
+
+because you--
+
+the analysis phase will have
+already done that.
+
+So this is completely
+irrelevant.
+
+So a lot of these, these
+assignments to continue have
+
+not to do where the running
+machine is supposed to
+
+continue in keeping track
+of its state.
+
+It has to, to do with where the
+evaluator analysis should
+
+continue, and those are
+completely irrelevant.
+
+So we can get rid of them.
+
+Ok, well, if we, if we simply
+do that, make those kinds of
+
+optimizations, get rid, get rid
+of worrying about exp and
+
+unev, and get rid of these
+irrelevant register
+
+assignments to continue, then we
+can take this literal code,
+
+these sort of 19 instructions
+that the, that the evaluator
+
+would have done, and
+then replace them.
+
+Let's look at the,
+at the slide.
+
+Replace them by--we get rid
+of about half of them.
+
+And again, this is just sort
+of filtering what the
+
+evaluator would have done
+by getting rid of
+
+the irrelevant stuff.
+
+And you see, for instance, here
+the--where the evaluator
+
+said, assign val, look up
+variable value, fetch of exp,
+
+here we have put in
+the constant f.
+
+Here we've put in
+the constant x.
+
+So there's a, there's a little
+better compiler.
+
+It's still pretty dumb.
+
+It's still doing a lot
+of dumb things.
+
+Again, if we go look at the
+slide again, look at the very
+
+beginning here, we see a save
+the environment, assign
+
+something to the val register,
+and restore the environment.
+
+Where'd that come from?
+
+That came from the evaluator
+back here saying, oh, I'm in
+
+the middle of evaluating
+an application.
+
+So I'm going to recursively
+call eval dispatch.
+
+So I'd better save the thing I'm
+going to need later, which
+
+is the environment.
+
+This was the result
+of recursively
+
+calling eval dispatch.
+
+It was evaluating the symbol
+f in that case.
+
+Then it came back from eval
+dispatch, restored the
+
+environment.
+
+But in fact, the actual thing
+it ended up doing in the
+
+evaluation is not going to hurt
+the environment at all.
+
+So there's no reason to be
+saving the environment and
+
+restoring the environment
+here.
+
+Similarly, here I'm saving the
+argument list. That's a piece
+
+of the argument evaluation
+loop, saving the argument
+
+list, and here you restore it.
+
+But the actual thing that you
+ended up doing didn't trash
+
+the argument list. So there
+was no reason to save it.
+
+So another way to say, another
+way to say that is that the,
+
+the evaluator has to be
+maximally pessimistic, because
+
+as far from its point of view
+it's just going off to
+
+evaluate something.
+
+So it better save what it's
+going to need later.
+
+But once you've done the
+analysis, the compiler is in a
+
+position to say, well, what
+actually did I need to save?
+
+And doesn't need to do any--
+it doesn't need to be as
+
+careful as the evaluator,
+because it knows what it
+
+actually needs.
+
+Well, in any case, if we do that
+and eliminate all those
+
+redundant saves and restores,
+then we can
+
+get it down to this.
+
+And you see there are actually
+only three instructions that
+
+we actually need, down from the
+initial 11 or so, or the
+
+initial 20 or so in
+the original one.
+
+And that's just saying, of those
+register operations,
+
+which ones did we
+actually need?
+
+Let me just sort of summarize
+that in another way, just to
+
+show you in a little
+better picture.
+
+Here's a picture of starting--
+
+This is looking at all the
+saves and restores.
+
+So here's the expression, f
+of x, and then this traces
+
+through, on the bottom here,
+the various places in the
+
+evaluator that were passed when
+the evaluation happened.
+
+And then here, here
+you see arrows.
+
+Arrow down means
+register saved.
+
+So the first thing that
+happened is the
+
+environment got saved.
+
+And over here, the environment
+got restored.
+
+And these-- so there are all the
+pairs of stack operations.
+
+Now, if you go ahead and say,
+well, let's remember that we
+
+don't--that unev, for instance,
+is a completely
+
+useless register.
+
+And if we use the constant
+structure of the code, well,
+
+we don't need, we don't need
+to save unev. We don't need
+
+unev at all.
+
+And then, depending on how we
+set up the discipline of
+
+the--of calling other things
+that apply, we may or may not
+
+need to save continue.
+
+That's the first step I did.
+
+And then we can look and see
+what's actually, what's
+
+actually needed.
+
+See, we don't-- didn't really
+need to save env or
+
+cross-evaluating f, because
+it wouldn't, it
+
+wouldn't trash it.
+
+So if we take advantage of that,
+and see the evaluation
+
+of f here, doesn't really need
+to worry about, about hurting
+
+env. And similarly, the
+evaluation of x here, when the
+
+evaluator did that it said, oh,
+I'd better preserve the
+
+function register around that,
+because I might need it later.
+
+And I better preserve
+the argument list.
+
+Whereas the compiler is now in
+a position to know, well, we
+
+didn't really need
+to save-- to do
+
+those saves and restores.
+
+So in fact, all of the stack
+operations done by the
+
+evaluator turned out to be
+unnecessary or overly
+
+pessimistic.
+
+And the compiler is in a
+position to know that.
+
+Well that's the basic idea.
+
+We take the evaluator, we
+eliminate the things that you
+
+don't need, that in some sense
+have nothing to do with the
+
+compiler at all, just the
+evaluator, and then you see
+
+which stack operations
+are unnecessary.
+
+That's the basic structure of
+the compiler that's described
+
+in the book.
+
+Let me just show you
+how that examples a
+
+little bit too simple.
+
+To see how you, how you actually
+save a lot, let's
+
+look at a little bit more
+complicated expression.
+
+F of G of X and 1.
+
+And I'm not going to go
+through all the code.
+
+There's a, there's a
+fair pile of it.
+
+I think there are, there are
+something like 16 pairs of
+
+register saves and restores
+as the evaluator
+
+walks through that.
+
+Here's a diagram of them.
+
+Let's see.
+
+You see what's going on.
+
+You start out by--the evaluator
+says, oh, I'm about
+
+to do an application.
+
+I'll preserve the environment.
+
+I'll restore it here.
+
+Then I'm about to do
+the first operand.
+
+Here it recursively goes
+to the evaluator.
+
+The evaluator says, oh, this is
+an application, I'll save
+
+the environment, do the operator
+of that combination,
+
+restore it here.
+
+This save--this restore matches
+that save. And so on.
+
+There's unev here, which turns
+out to be completely
+
+unnecessary, continues getting
+bumped around here.
+
+The function register is
+getting, getting saved across
+
+the first operands, across
+the operands.
+
+All sorts of things
+are going on.
+
+But if you say, well, what of
+those really were the business
+
+of the compiler as opposed to
+the evaluator, you get rid of
+
+a whole bunch.
+
+And then on top of that, if
+you say things like, the
+
+evaluation of F doesn't hurt the
+environment register, or
+
+simply looking up the symbol X,
+you don't have to protect
+
+the function register
+against that.
+
+So you come down to just
+a couple of, a
+
+couple of pairs here.
+
+And still, you can do
+a little better.
+
+Look what's going on here with
+the environment register.
+
+The environment register comes
+along and says, oh, here's a
+
+combination.
+
+This evaluator, by the way,
+doesn't know anything about G.
+
+So here it says, so it says,
+I'd better save the
+
+environment register, because
+evaluating G might be some
+
+arbitrary piece of code that
+would trash it, and I'm going
+
+to need it later, after
+this argument, for
+
+doing the second argument.
+
+So that's why this one didn't go
+away, because the compiler
+
+made no assumptions about
+what G would do.
+
+On the other hand, if you look
+at what the second argument
+
+is, that's just looking
+up one.
+
+That doesn't need this
+environment register.
+
+So there's no reason
+to save it.
+
+So in fact, you can get
+rid of that one, too.
+
+And from this whole pile of, of
+register operations, if you
+
+simply do a little bit of
+reasoning like that, you get
+
+down to, I think, just two pairs
+of saves and restores.
+
+And those, in fact, could go
+away further if you, if you
+
+knew something about G.
+
+So again, the general idea is
+that the reason the compiler
+
+can be better is that the
+interpreter doesn't know what
+
+it's about to encounter.
+
+It has to be maximally
+pessimistic in saving things
+
+to protect itself.
+
+The compiler only has
+to deal with what
+
+actually had to be saved.
+
+And there are two reasons
+that something might
+
+not have to be saved.
+
+One is that what you're
+protecting it against, in
+
+fact, didn't trash the register,
+like it was just a
+
+variable look-up.
+
+And the other one is, that the
+thing that you were saving it
+
+for might turn out not
+to actually need it.
+
+So those are the two basic
+pieces of knowledge that the
+
+compiler can take advantage
+of in making
+
+the code more efficient.
+
+Let's break for questions.
+
+AUDIENCE: You kept saying that
+the uneval register, unev
+
+register didn't need
+to be used at all.
+
+Does that mean that you
+could just map a
+
+six-register machine?
+
+Or is that, in this particular
+example, it
+
+didn't need to be used?
+
+PROFESSOR: For the compiler,
+you could generate code for
+
+the six-register, five, right?
+
+Because that exp
+goes away also.
+
+Assuming--yeah, you can get
+rid of both exp and unev,
+
+because, see, those are data
+structures of the evaluator.
+
+Those are all things that would
+be constants from the
+
+point of view of the compiler.
+
+The only thing is this
+particular compiler is set up
+
+so that interpreted code and
+compiled code can coexist.
+
+So the way to think about it is,
+is maybe you build a chip
+
+which is the evaluator, and what
+the compiler might do is
+
+generate code for that chip.
+
+It just wouldn't use two
+of the registers.
+
+All right, let's take a break.
+
+[MUSIC PLAYING]
+
+We just looked at what the
+compiler is supposed to do.
+
+Now let's very briefly look
+at how, how this gets
+
+accomplished.
+
+And I'm going to give
+no details.
+
+There's, there's a giant pile of
+code in the book that gives
+
+all the details.
+
+But what I want to do is
+just show you the, the
+
+essential idea here.
+
+Worry about the details
+some other time.
+
+Let's imagine that we're
+compiling an expression that
+
+looks like there's some
+operator, and
+
+there are two arguments.
+
+Now, the--
+
+what's the code that the
+compiler should generate?
+
+Well, first of all, it should
+recursively go off and compile
+
+the operator.
+
+So it says, I'll compile
+the operator.
+
+And where I'm going to need that
+is to be in the function
+
+register, eventually.
+
+So I'll compile some
+instructions that will compile
+
+the operator and end up
+with the result in
+
+the function register.
+
+The next thing it's going to do,
+another piece is to say,
+
+well, I have to compile
+the first argument.
+
+So it calls itself
+recursively.
+
+And let's say the result
+will go into val.
+
+And then what it's going to need
+to do is start setting up
+
+the argument list. So it'll say,
+assign to argl cons of
+
+fetch-- so it generates this
+literal instruction--
+
+fetch of val onto empty list.
+
+However, it might
+have to work--
+
+when it gets here, it's going
+to need the environment.
+
+It's going to need whatever
+environment was here in order
+
+to do this evaluation of
+the first argument.
+
+So it has to ensure that the
+compilation of this operand,
+
+or it has to protect the
+function register against
+
+whatever might happen in the
+compilation of this operand.
+
+So it puts a note here and says,
+oh, this piece should be
+
+done preserving the environment
+register.
+
+Similarly, here, after it gets
+done compiling the first
+
+operand, it's going to say,
+I better compile--
+
+I'm going to need to know
+the environment
+
+for the second operand.
+
+So it puts a little note here,
+saying, yeah, this is also
+
+done preserving env. Now it goes
+on and says, well, the
+
+next chunk of code is the one
+that's going to compile the
+
+second argument.
+
+And let's say it'll compile
+it with a targeted to
+
+val, as they say.
+
+And then it'll generate the
+literal instruction, building
+
+up the argument list. So it'll
+say, assign to argl cons of
+
+the new value it just got onto
+the old argument list.
+
+However, in order to have the
+old argument list, it better
+
+have arranged that the argument
+list didn't get
+
+trashed by whatever
+happened in here.
+
+So it puts a little note here
+and says, oh, this has to be
+
+done preserving argl.
+
+Now it's got the argument
+list set up.
+
+And it's all ready to go
+to apply dispatch.
+
+It generates this literal
+instruction.
+
+Because now it's got the
+arguments in argl and the
+
+operator in fun, but wait, it's
+only got the operator in
+
+fun if it had ensured that
+this block of code didn't
+
+trash what was in the
+function register.
+
+So it puts a little note here
+and says, oh, yes, all this
+
+stuff here had better
+be done preserving
+
+the function register.
+
+So that's the little--so when
+it starts ticking--so
+
+basically, what the compiler
+does is append a whole bunch
+
+of code sequences.
+
+See, what it's got in it is
+little primitive pieces of
+
+things, like how to look up
+a symbol, how to do a
+
+conditional.
+
+Those are all little
+pieces of things.
+
+And then it appends them
+together in this sort of
+
+discipline.
+
+So the basic means of combining
+things is to append
+
+two code sequences.
+
+That's what's going on here.
+
+And it's a little bit tricky.
+
+The idea is that it appends
+two code sequences, taking
+
+care to preserve a register.
+
+So the actual append operation
+looks like this.
+
+What it wants to
+do is say, if--
+
+here's what it means to append
+two code sequences.
+
+So if sequence one
+needs register--
+
+I should change this.
+
+Append sequence one
+to sequence two,
+
+preserving some register.
+
+Let me say, and.
+
+So it's clear that sequence
+one comes first.
+
+So if sequence two needs the
+register and sequence one
+
+modifies the register, then
+the instructions that the
+
+compiler spits out are,
+save the register.
+
+Here's the code.
+
+You generate this code.
+
+Save the register, and then you
+put out the recursively
+
+compiled stuff for
+sequence one.
+
+And then you restore
+the register.
+
+And then you put out the
+recursively compiled stuff for
+
+sequence two.
+
+That's in the case where
+you need to do it.
+
+Sequence two actually needs the
+register, and sequence one
+
+actually clobbers it.
+
+So that's sort of if.
+
+Otherwise, all you spit out is
+sequence one followed by
+
+sequence two.
+
+So that's the basic operation
+for sticking together these
+
+bits of code fragments,
+these bits of
+
+instructions into a sequence.
+
+And you see, from this point
+of view, the difference
+
+between the interpreter and the
+compiler, in some sense,
+
+is that where the compiler has
+these preserving notes, and
+
+says, maybe I'll actually
+generate the saves and
+
+restores and maybe I won't,
+the interpreter being
+
+maximally pessimistic always has
+a save and restore here.
+
+That's the essential
+difference.
+
+Well, in order to do this, of
+course, the compiler needs
+
+some theory of what code
+sequences need
+
+and modifier registers.
+
+So the tiny little fragments
+that you put in, like the
+
+basic primitive code fragments,
+say, what are the
+
+operations that you do when
+you look up a variable?
+
+What are the sequence of things
+that you do when you
+
+compile a constant or
+apply a function?
+
+Those have little notations in
+there about what they need and
+
+what they modify.
+
+So the bottom-level
+data structures--
+
+Well, I'll say this.
+
+A code sequence to the compiler
+looks like this.
+
+It has the actual sequence
+of instructions.
+
+And then, along with
+it, there's the set
+
+of registers modified.
+
+And then there's the set
+of registers needed.
+
+So that's the information the
+compiler has that it draws on
+
+in order to be able to
+do this operation.
+
+And where do those come from?
+
+Well, those come from, you might
+expect, for the very
+
+primitive ones, we're going
+to put them in by hand.
+
+And then, when we combine two
+sequences, we'll figure out
+
+what these things should be.
+
+So for example, a very primitive
+one, let's see.
+
+How about doing a register
+assignment.
+
+So a primitive sequence might
+say, oh, it's code fragment.
+
+Its code instruction is assigned
+to R1, fetch of R2.
+
+So this is an example.
+
+That might be an example of a
+sequence of instructions.
+
+And along with that, it'll
+say, oh, what I need to
+
+remember is that that modifies
+R1, and then it needs R2.
+
+So when you're first building
+this compiler, you put in
+
+little fragments of
+stuff like that.
+
+And now, when it combines two
+sequences, if I'm going to
+
+combine, let's say, sequence
+one, that modifies a bunch of
+
+registers M1, and needs a
+bunch of registers N1.
+
+And I'm going to combine
+that with sequence two.
+
+That modifies a bunch of
+registers M2, and needs a
+
+bunch of registers N2.
+
+Then, well, we can
+reason it out.
+
+The new code fragment,
+sequence one, and--
+
+followed by sequence two, well,
+
+what's it going to modify?
+
+The things that it will modify
+are the things that are
+
+modified either by sequence
+one or sequence two.
+
+So the union of these
+two sets are what
+
+the new thing modifies.
+
+And then you say, well, what is
+this--what registers is it
+
+going to need?
+
+It's going to need the things
+that are, first of all, needed
+
+by sequence one.
+
+So what it needs is
+sequence one.
+
+And then, well, not quite all of
+the ones that are needed by
+
+sequence one.
+
+What it needs are the ones that
+are needed by sequence
+
+two that have not been set
+up by sequence one.
+
+So it's sort of the union of the
+things that sequence two
+
+needs minus the ones that
+sequence one modifies.
+
+Because it worries about
+setting them up.
+
+So there's the basic structure
+of the compiler.
+
+The way you do register
+optimizations is you have some
+
+strategies for what needs
+to be preserved.
+
+That depends on a
+data structure.
+
+Well, it depends on the
+operation of what it means to
+
+put things together.
+
+Preserving something, that
+depends on knowing what
+
+registers are needed
+and modified
+
+by these code fragments.
+
+That depends on having little
+data structures, which say, a
+
+code sequence is the actual
+instructions, what they modify
+
+and what they need.
+
+That comes from, at
+the primitive
+
+level, building it in.
+
+At the primitive level, it's
+going to be completely obvious
+
+what something needs
+and modifies.
+
+Plus, this particular way that
+says, when I build up bigger
+
+ones, here's how I generate
+the new set of registers
+
+modified and the new set
+of registers needed.
+
+And that's the whole--
+
+well, I shouldn't say that's
+the whole thing.
+
+That's the whole thing except
+for about 30 pages of details
+
+in the book.
+
+But it is a perfectly usable
+rudimentary compiler.
+
+Let me kind of show
+you what it does.
+
+Suppose we start out with
+recursive factorial.
+
+And these slides are going to
+be much too small to read.
+
+I just want to flash through
+the code and show you about
+
+how much it is.
+
+That starts out with--here's a
+first block of it, where it
+
+compiles a procedure entry and
+does a bunch of assignments.
+
+And this thing is basically up
+through the part where it sets
+
+up to do the predicate
+and test whether
+
+the predicate's true.
+
+The second part is what
+results from--
+
+in the recursive call to
+fact of n minus one.
+
+And this last part is coming
+back from that and then taking
+
+care of the constant case.
+
+So that's about how
+much code it
+
+would produce for factorial.
+
+We could make this compiler
+much, much better, of course.
+
+The main way we could make
+it better is to allow the
+
+compiler to make any assumptions
+at all about what
+
+happens when you call
+a procedure.
+
+So this compiler, for instance,
+doesn't even know,
+
+say, that multiplication
+is something that
+
+could be coded in line.
+
+Instead, it sets up this
+whole mechanism.
+
+It goes to apply-dispatch.
+
+That's a tremendous waste,
+because what you do every time
+
+you go to apply-dispatch is
+you have to concept this
+
+argument list, because it's
+a very general thing
+
+you're going to.
+
+In any real compiler, of course,
+you're going to have
+
+registers for holding
+arguments.
+
+And you're going to start
+preserving and saving the way
+
+you use those registers
+similar to the
+
+same strategy here.
+
+So that's probably the very main
+way that this particular
+
+compiler in the book
+could be fixed.
+
+There are other things like
+looking up variable values and
+
+making more efficient primitive
+operations and all
+
+sorts of things.
+
+Essentially, a good Lisp
+compiler can absorb an
+
+arbitrary amount of effort.
+
+And probably one of the reasons
+that Lisp is slow with
+
+compared to languages like
+FORTRAN is that, if you look
+
+over history at the amount of
+effort that's gone into
+
+building Lisp compilers, it's
+nowhere near the amount of
+
+effort that's gone into
+FORTRAN compilers.
+
+And maybe that's something that
+will change over the next
+
+couple of years.
+
+OK, let's break.
+
+Questions?
+
+AUDIENCE: One of the very
+first classes--
+
+I don't know if it was during
+class or after class- you
+
+showed me the, say, addition has
+a primitive that we don't
+
+see, and-percent add or
+something like that.
+
+Is that because, if you're doing
+inline code you'd want
+
+to just do it for two
+operators, operands?
+
+But if you had more operands,
+you'd want to
+
+do something special?
+
+PROFESSOR: Yeah, you're looking
+in the actual scheme
+
+implementation.
+
+There's a plus, and a plus
+is some operator.
+
+And then if you go look inside
+the code for plus, you see
+
+something called--
+
+I forget-- and-percent plus
+or something like that.
+
+And what's going on there is
+that particular kind of
+
+optimization.
+
+Because, see, general
+plus takes an
+
+arbitrary number of arguments.
+
+So the most general plus says,
+oh, if I have an argument
+
+list, I'd better cons it up in
+some list and then figure out
+
+how many there were or
+something like that.
+
+That's terribly inefficient,
+especially since most of the
+
+time you're probably
+adding two numbers.
+
+You don't want to really have to
+cons this argument list. So
+
+what you'd like to do is build
+the code for plus with a bunch
+
+of entries.
+
+So most of what it's
+doing is the same.
+
+However, there might be a
+special entry that you'd go to
+
+if you knew there were
+only two arguments.
+
+And those you'll put
+in registers.
+
+They won't be in an argument
+list and you won't have to
+
+[UNINTELLIGIBLE].
+
+That's how a lot of
+these things work.
+
+OK, let's take a break.
+
+[MUSIC PLAYING]
\ No newline at end of file
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--- /dev/null
+++ b/kYgBLGwuBpw.txt
@@ -0,0 +1,1915 @@
+PROFESSOR: All right.
+
+The end of this lecture
+generated so much excitement
+
+that we've continued on into the
+start of the next segment.
+
+So I think we'd better begin.
+
+What I told you, as several
+people were clever enough to
+
+observe, that the number of
+planes between the origin and
+
+intercept plane is equal to A
+times B times C, where the
+
+intercept is A T1 out plus
+B T2 out equals C T3 out.
+
+That is true only if the
+numbers A, B, and C are
+
+mutually prime.
+
+If it's something like 4,
+2, 1, you won't get
+
+that number of planes.
+
+You'll get a submultiple.
+
+And the reason for that is that
+some of the planes, when
+
+you generate them by these three
+different translations
+
+in different directions, some
+of them are mapped on top of
+
+existing planes.
+
+And I'm not going to attempt to
+prove this, but let me just
+
+tell you the result, that if
+A and B contain some common
+
+factor, p, and B and C contain
+some common factor, q, and in
+
+the worst possible case, A and C
+contains some common factor,
+
+r, then the number of intervals
+is equal to A times
+
+B times C divided by
+p times q times r.
+
+And probably the best way to
+show that is let you show, on
+
+a problem set in the very near
+future, to actually map out
+
+the planes in the
+two-dimensional situation, for
+
+a and b that are mutually prime,
+and then do the same
+
+thing for a and b that contain
+some common factor.
+
+So this is the so-called
+Miller indices, the
+
+Miller-Bravais indices, and
+everybody hears about them,
+
+but it is not at all clear why
+one takes this very indirect
+
+and non-intuitive way
+of defining the
+
+orientation of a plane.
+
+And the reason for this,
+ultimately, is that in x-ray
+
+diffraction, you want to
+integrate up the scattering of
+
+all atoms in a crystal.
+
+So you want to integrate over
+a plane that contains the
+
+atoms, and this locus has a
+convenient form only if you
+
+choose these indices to find the
+orientation of the plane.
+
+And what comes out of this, as
+I said to a couple of people
+
+during intermission, is that the
+amplitude of the scattered
+
+wave has some summation
+over all of the atoms.
+
+And in that phase of that ray,
+that is e to the plus 2 pi i,
+
+hx plus ky plus lz.
+
+Very, very simple form.
+
+And it has that form only
+because the locus, the way
+
+this plane is defined was done
+very, very carefully.
+
+So it's something beyond just
+simple geometry that forms a
+
+reason for it.
+
+Let me say a couple more things
+in general about the
+
+Miller-Bravais indices.
+
+They are very, very intuitive,
+counter-intuitive.
+
+Let's suppose that this is a,
+and this is b, and this is c.
+
+And I put down here, again, the
+equations of the entire
+
+set of planes in the stack.
+
+And let's look at the first
+planes and ask what the
+
+intercepts are.
+
+The intercepts on x, y, and z
+are going to be 1 over h on x,
+
+1 over k on y, and
+1 over l times z.
+
+So the first plane from the
+origin is going to be 1 over h
+
+of the a translation, 1 over k
+of the b translation, and 1
+
+over l of the c translation.
+
+So this gives us one way
+of determining, given a
+
+particular rational plane, show
+it relative to the three
+
+translations.
+
+From the first plane from the
+origin, h is going to be 1
+
+over the intercept on T1.
+
+I'll call it a, which is
+what we usually do.
+
+k is going to be 1 over the
+intercept on b, and l is going
+
+to be 1 over the intercept
+on c for the first
+
+plane from the origin.
+
+So if you have a drawing of the
+set of planes relative to
+
+the translation, such as the
+one that I obliterated from
+
+just a moment ago, reciprocals
+of the intercepts of the first
+
+plane from the origin give you
+h, k, and l very easily.
+
+The thing that is
+counter-intuitive is that, if
+
+you look out of context at the
+three indices, h, k, and l,
+
+you have the feeling that as l
+gets larger, the intercept of
+
+the plane on c should gradually
+creep up from here,
+
+to here, to here, and so
+on, as l gets larger.
+
+Actually, the reverse is true.
+
+As l increases, the intercept on
+c gets smaller and smaller
+
+and smaller and smaller, until
+finally, when l is infinity,
+
+the intercept is 0.
+
+So it's counter-intuitive.
+
+The intercept on the axis gets
+larger as the Miller index
+
+gets larger.
+
+Let me give you a proprietary
+Uncle Bernie's secret method
+
+for determining Miller indices
+without stress and strain.
+
+This works every time.
+
+Find the intercepts
+of any plane.
+
+And we know from these
+equations what those
+
+are going to be.
+
+For the nth plane, the
+intercepts are going to be n
+
+over h, n over k on b,
+and n over l on c.
+
+Take the reciprocals.
+
+And the reciprocals are going
+to be h over n, k over
+
+n, and l over n.
+
+And then find whatever integer,
+n, you must multiply
+
+those reciprocals by in order
+to convert them to mutually
+
+prime intercepts, and you've
+got the Miller indices in a
+
+no-brainer, automatic fashion.
+
+Another bit of jargon.
+
+We will also use the basis
+vectors to define locations
+
+and to define directions
+in a lattice.
+
+To distinguish three integers
+that indicate a plane, and you
+
+all know this from previous
+experience, the parentheses
+
+says plane, an individual
+plane.
+
+There are other times when you
+would like to use the indices
+
+of one representative plane to
+indicate the entire set of
+
+planes that are related by the
+symmetry of the crystal.
+
+So let me give one
+specific example.
+
+Suppose we had a cubic crystal,
+where these are the
+
+three translations that form
+the edge of the unit cell.
+
+And let's say that this is a1,
+this is a2, and this is a3.
+
+I'm using a1, a2, and
+a3, not a, b, and c.
+
+But let's not go there.
+
+OK, these are lattice points.
+
+And if I look at this plane
+that's perpendicular to a1 and
+
+cuts it at one lattice
+point, l, this would
+
+be the 1, 0, 0 plane.
+
+And I would indicate that that
+is an individual plane that
+
+we're talking about.
+
+But if this crystal is cubic,
+all six faces of the set, 1,
+
+0, 0; 0, 1, 0; 0, 0, 1; and then
+the plane that's in the
+
+opposite direction, minus
+1, 0, 0; 0, minus 1, 0;
+
+and 0, 0, minus 1.
+
+These six planes define the
+surfaces of the cube.
+
+So there are times, since these
+are equivalent to planes
+
+and will have the same
+properties, the same hardness,
+
+the same [? edge ?] bits and
+everything else, there are
+
+times when we may want to
+refer to the entire
+
+symmetrical set.
+
+And we do that.
+
+We call that set a form.
+
+It is a symmetry-related set.
+
+And you can pick any
+one you like.
+
+Generally, you pick one with
+simple indices, like the one
+
+that is perpendicular to
+the translation a.
+
+And then you indicate
+by braces, which is
+
+the symbol for set.
+
+This means the set 1, 0, 0, and
+that would correspond to
+
+all six of these faces.
+
+The number, if you do this in
+reverse, and I'm going to give
+
+you the indices, what are
+the separate faces?
+
+That depends on the symmetry.
+
+So to give you an example, if
+I have a unit cell that has
+
+three orthogonal translations,
+and this is a, and this is b,
+
+and this is c, so that there
+is no cubic symmetry to it.
+
+This face, which would be 1,
+0, 0, and the one that cuts
+
+the axes at minus a, minus 1, 0
+0, those are going to be the
+
+only faces with a single 1 and
+a pair of 0's which are
+
+equivalent by symmetry.
+
+So in this case, for this brick
+shaped unit cell, 1, 0,
+
+0 would mean this pair of two
+faces, rather than six.
+
+So to go from a representative
+face to the set of planes, you
+
+have to know the symmetry.
+
+If you can write the planes on
+the basis of symmetry, take
+
+one representative and
+let that be the form.
+
+So it leads one to observe
+that crystals undergoing
+
+plastic deformation
+have bad form.
+
+Yeah?
+
+AUDIENCE: Is that different
+from when you
+
+talk about a direction?
+
+PROFESSOR: Yes, yes.
+
+You will see in just a moment
+that we use the same system of
+
+three integers, but in order to
+distinguish which one he's
+
+talking about when one's
+thinking about integers with a
+
+different set of numbers.
+
+Again, if we use the lattice as
+the basis of a coordinate
+
+system, another thing we might
+want to specify is the
+
+orientation of a rational
+direction.
+
+And let me go to a
+two-dimensional case.
+
+Assume that c goes
+straight up.
+
+Directions of easy plastic
+deformation will very often
+
+involve integral number
+of translations.
+
+For example, this direction here
+is obtained by going one
+
+translation in the a
+direction plus one
+
+translation in the b direction.
+
+So we could use the pair of
+integers 1, 1, and if we are
+
+normal to see we'd use a 0
+for the third integer.
+
+But how are we going to tell
+whether we're talking about a
+
+direction or a plane?
+
+And the way one does that is
+to use square braces to
+
+indicate one particular
+direction.
+
+You may want to also indicate
+the location of a particular
+
+atom within the unit cell.
+
+In order to do that, one could
+really use the location of a
+
+vector, the components of a
+vector, xa plus yb plus zc,
+
+the vector from the origin to
+that atom as coefficients
+
+which correspond to
+the atom location.
+
+So if that is the case,
+the numbers
+
+are usually not integers.
+
+And one simply uses the
+three integers in
+
+an unadorned fashion.
+
+So the lattice translations
+give you the basis of a
+
+coordinate system, and we use
+those to specify features,
+
+rational or not, of planes and
+directions and coordinates.
+
+OK, any questions here?
+
+OK, we are next going to take
+the first small step in a
+
+process of synthesis.
+
+We have found that there are,
+in two dimensions, five
+
+distinct kinds of lattices.
+
+The oblique, the rectangular,
+the centric rectangular, the
+
+square, and the hexagonal.
+
+Five kinds of lattices.
+
+We've shown, to this point, that
+each of these lattices
+
+can accommodate a certain
+rotational symmetry.
+
+1 or 2 here.
+
+m and m for the rectangular
+and centric rectangular.
+
+4, the fourfold axis
+for a square.
+
+3 or 6 for the hexagonal
+lattice.
+
+So what I would like to do next,
+after we make a brief
+
+direct diversion, is to combine
+with each of these
+
+nets one of the two symmetries
+which can be
+
+accommodated in that net.
+
+And what we will have determined
+then are the
+
+patterns' lattice and symmetry,
+which can exist in
+
+two dimensions.
+
+The sort of things we look at
+actually, like the pattern of
+
+square tiles on the floor, or
+the two-dimensional pattern
+
+that is on a fabric design.
+
+So we'll derive those
+exhaustively.
+
+The thing that results is
+something that is called a
+
+plane group.
+
+And I'm going to take this
+through in detail because
+
+there are not that many
+combinations that can be made.
+
+And the number is enough
+to count on
+
+your fingers and toes.
+
+You've got to use both, so
+they're a fair number, but not
+
+a staggering number.
+
+If we were to do this exercise
+in three dimensions, there
+
+would be 230 distinct
+combinations.
+
+And that's too much for
+anybody to go through.
+
+I know of very few people who
+work professionally in this
+
+area who've actually sat down
+and derived every single one.
+
+If you know the principles of
+the derivation and know how
+
+you could go about doing it if
+you were forced to, that's
+
+sufficient.
+
+The results are tabulated in
+an admirable compilation.
+
+We mentioned that at
+the beginning.
+
+This is the International
+Tables for X-ray
+
+Crystallography, Volume 1.
+
+So what we should end up with is
+a way for you to go to this
+
+reference data and know
+how to interpret it
+
+and make use of it.
+
+But this is a nice microcosm.
+
+There are not many plane
+groups, and to do this
+
+exhaustively, will let us see
+the sort of reasoning that
+
+goes into it.
+
+I have to tell you that this
+is not in Buerger's book.
+
+We're going to do
+two-dimensional
+
+crystallography first,
+and then extend
+
+it in a third direction.
+
+In fact, I know of no
+book that does this.
+
+And so you're going to get a
+unique, handwritten document
+
+by none other than yours truly
+that will do this in detail
+
+every step of the way.
+
+And I don't know of any other
+place where this is done.
+
+Now, what is the origin
+of this name?
+
+Plane, well, these
+are symmetries
+
+confined to a plane.
+
+And then there's this mysterious
+term, group.
+
+And the corresponding thing
+in 3D is something
+
+called a space group.
+
+This is a language derived from
+a branch of mathematics
+
+that is called group theory, and
+it is exactly the language
+
+that describes things
+that we've mentioned
+
+conversationally, such as if you
+take two transformations
+
+and perform them in succession,
+they're going to
+
+give you a third that
+has to be present.
+
+If you've got two present,
+there must be a third.
+
+We talk about symmetries
+being self consistent.
+
+If you have a rotation operation
+that is not an
+
+integral submultiple of 2 pi,
+it's not going to be self
+
+consistent because you go
+around, and around, and
+
+around, and you will never
+come exactly full circle.
+
+So group theory is a branch of
+mathematics that deals with
+
+concepts of this sort.
+
+So it's not very hard to
+develop, and it gives its
+
+ideas to the notation that is
+used in crystallography.
+
+So let me say a few words
+about group theory.
+
+What is a group?
+
+A group is a set of elements--
+
+And what are elements?
+
+Elements are things--
+
+For which a law of combination
+is defined.
+
+And the nature of the elements
+can be very,
+
+very different things.
+
+They could be numbers.
+
+They could be complex numbers,
+and the law of combination
+
+here might be multiplication.
+
+They could be matrices, for
+which the law of combination
+
+is defined as matrix
+multiplication.
+
+Or they could be pots of
+different color paint, for
+
+which the law of combination is
+defined as mixing the two
+
+colors 50-50.
+
+I don't know any practical
+application of that sort of
+
+group, but nevertheless, it
+follows the definition, a set
+
+of things for which a law of
+combination is defined.
+
+And in addition, which satisfies
+three so-called
+
+group postulates.
+
+And the group postulates are
+the combination of any two
+
+elements is also a member
+of the group.
+
+The second group postulate
+is that the identity--
+
+I'm going to call it
+just identity--
+
+and let me define, identity
+is doing nothing--
+
+Is also a member of the group.
+
+And if we define the identity
+operation as I, this means
+
+that for every element, I
+followed by a or a followed by
+
+I, is the same as a by itself.
+
+If the law of multiplication
+were just arithmetic
+
+multiplication, then number
+1 would be the identity
+
+operation because 1 times any
+number gives you the number.
+
+Any number times 1 gives you
+the same number back again.
+
+And the third postulate is that,
+for every element, an
+
+inverse exists--
+
+let's call the elements
+a and a minus 1--
+
+such that a followed by a
+minus 1 is equal to the
+
+identity operation, and the
+inverse element followed by
+
+the original element, a, is also
+the identity operation.
+
+So if the law of combination
+were defined as
+
+multiplication, you would have
+to find, for every number,
+
+another number, which multiplied
+by it, gives you
+
+the number 1.
+
+OK, let me now illustrate with
+a couple of simple examples.
+
+Let's consider the set of
+numbers 1, n minus 1.
+
+The number of elements in the
+group is said to be the rank
+
+of the group, or some people
+like to use the term order.
+
+And I don't like that term
+because second order or fourth
+
+order is a term applied to
+quantities which are not
+
+terribly important.
+
+So we expand this except for
+higher order terms, which are
+
+negligible.
+
+And I don't like that
+connotation.
+
+So I will not use order,
+although it's sometimes used
+
+to talk about the
+rank of a group.
+
+The rank or order of the group
+is simply the number of
+
+elements contained in a set.
+
+So let's show that the numbers
+1 and minus 1 constitute a
+
+group of rank two.
+
+Is the combination of any
+pair of elements also a
+
+member of the group?
+
+Well, to do this, it's
+convenient to set up an array
+
+called the group multiplication
+table.
+
+And what you do is you simply
+put the elements of the group
+
+along a row.
+
+And in this case, it's
+1 and minus 1.
+
+And then you put the same
+elements along a column, and
+
+then you combine them.
+
+1 times 1 is 1.
+
+Minus 1 times 1 is minus 1.
+
+1 times minus 1 is minus 1.
+
+Minus 1 times minus
+1 is plus 1.
+
+Sometimes, as I'm giving this
+part of the lecture, somebody
+
+passes down the hallway, and
+they hear 1 times 1 is 1.
+
+1 times minus 1--
+
+and they go in reverse to see
+what in the world could be
+
+going on in this high-powered
+mathematical lecture.
+
+That's why I close the door.
+
+OK, so any combination
+of elements is also a
+
+member of the group.
+
+Is the identity operation
+present?
+
+Yes because minus 1 times plus
+1 or plus 1 times minus 1
+
+gives you the same element
+back again.
+
+So for every element in the
+group, the combination of any
+
+two elements is present.
+
+For each operation, we've shown
+that an inverse exists
+
+and for every element there's an
+identity operation, and the
+
+inverse exists.
+
+So the pair of numbers, not
+terribly exciting, 1 and minus
+
+1 where the law of combination
+is defined is a
+
+group of rank 2.
+
+I'll give you another example.
+
+I won't bother to carry out all
+the terms, but the numbers
+
+1, minus 1, i, and minus i,
+where i is equal to the square
+
+root of minus 1, and where the
+law of combination is defined
+
+as multiplication, constitute
+a group of rank 4.
+
+With this simple introduction,
+I think one can see that
+
+symmetry transformations can be
+regarded as operations that
+
+are elements in a group.
+
+And let me give you
+a simple example.
+
+Let's look at a combination.
+
+We still haven't considered the
+mind-boggling possibility
+
+of having more than one symmetry
+element present in a
+
+space at the same time.
+
+But let's suppose we have two
+mirror planes that are
+
+completely orthogonal, and see
+what sort of pattern they
+
+would generate.
+
+Here's a first motif.
+
+If I call this mirror plane m1,
+and this mirror plane m2.
+
+m1 is going to take this
+object and reflect
+
+it across to here.
+
+m2 will take this object and
+reflect it down to here.
+
+Take this one, and reflect
+it down to here.
+
+And now I know how this is
+related to this, how this is
+
+related to this, how this
+is related to this.
+
+But this one and this one are
+exactly the same thing.
+
+And those two objects are not
+related by reflection.
+
+If this is a right-handed one,
+this is a left-handed one,
+
+this is a left-handed one, and
+this is a right-handed one.
+
+So if something relates these
+two, it has to be something
+
+that does not produce
+an enantiomorph.
+
+The only thing that's possible
+then would be translation.
+
+And these two guys are not
+parallel to one another.
+
+You can't get this one
+by just sliding
+
+this parallel to itself.
+
+The only thing that's
+left is rotation.
+
+And, lo and behold, we can get
+from this one to this one by a
+
+180-degree rotation.
+
+And we can get from this
+one to this one by
+
+a 180-degree rotation.
+
+So here's an example of a way
+in which we've combined
+
+without showing why this is
+possible, or how I got there.
+
+Here's a combination of symmetry
+elements that gives
+
+us a possible arrangement
+of objects in space.
+
+It's going to be convenient to
+have a notation to indicate
+
+such combinations.
+
+And we call them Harry, George,
+and Sam, or some
+
+popular, affectionate name.
+
+Or call them number 1,
+number 2, number 3.
+
+But a nice notation is going to
+be a descriptive one which
+
+tells you what you have.
+
+And what is done in
+crystallography is to indicate
+
+these possible combinations
+by a running list of the
+
+different kinds of symmetry
+elements that are present.
+
+And here, we've got a twofold
+axis, for which the symbol is
+
+2, and two mirror planes that
+are different and function in
+
+different ways in the pattern.
+
+So this combination
+is called 2mm.
+
+OK, that's getting ahead
+of our story.
+
+But what I wanted to do now is
+to show you that this set of
+
+symmetry elements contains
+four operations that
+
+constitute a group.
+
+There's the operation
+of a one-fold axis.
+
+That's the identity operation.
+
+There is a reflection
+across the first
+
+type of mirror plane.
+
+And notice, now, the utility
+of having a symbol that
+
+indicates a specific
+operation rather
+
+than a symmetry element.
+
+There's a second reflection
+operation, sigma 2, and there
+
+is a rotation operation through
+a 180 degrees, A pi.
+
+So I'd like to show that these
+four operations constitute a
+
+group of rank 4.
+
+So how do we show this?
+
+We first set up the group
+multiplication table.
+
+And then we simply
+combine these
+
+four operations pairwise.
+
+Put the same 1, sigma 1,
+sigma 2, and A pi down
+
+this side of the array.
+
+Doing nothing, doing nothing, is
+the same as a one-fold axis
+
+doing nothing.
+
+Doing a reflection sigma 1
+followed by doing nothing
+
+gives you sigma 1 back again.
+
+Doing a reflection sigma 2
+followed by doing nothing
+
+gives you sigma 2 back again.
+
+And similarly, rotating
+A pi followed by doing
+
+nothing is the same.
+
+If I go along the columns,
+doing nothing followed by
+
+sigma 1 is sigma 1.
+
+Sigma 1 and 1 combined
+is sigma 2.
+
+A pi combined with
+sigma 1 is A pi.
+
+So far so good, but
+not surprising.
+
+Doing sigma 1 and following it
+by sigma 1 is reflecting left
+
+to right across mirror plane 1,
+and then reflecting right
+
+back again.
+
+So that is going to be a
+one-fold axis doing nothing.
+
+Doing sigma 1 following up by
+sigma 2 would reflect across,
+
+and then follow up by reflection
+in the second
+
+mirror plane.
+
+I get from the first one
+to the final one by
+
+the rotation A pi.
+
+So this is A pi.
+
+And if I do the first
+reflection, sigma 1, and
+
+follow that by A pi, that gets
+me from number 1 to number 2
+
+to number 3.
+
+And I get from number 1 to
+number 3 directly by the
+
+reflection operation, sigma 2.
+
+OK, you notice what's
+happening?
+
+I get the same four elements
+back again in
+
+every column or row.
+
+Sigma 1, 1, A pi, sigma 2.
+
+And if I rattle these off
+quickly, this as A pi.
+
+This is identity, and
+this is sigma 1.
+
+And this will be sigma 2.
+
+This will be sigma 1.
+
+And this will be the
+identity operation.
+
+So the first group postulate
+is satisfied.
+
+These four elements combined
+pairwise always give you
+
+nothing but one of these
+elements back.
+
+An identity operation is present
+because the one-fold
+
+rotation axis is the same as
+leaving the thing alone.
+
+And we've seen that for every
+operation, an inverse exists
+
+because 1 occurs once in
+each row and column.
+
+So sigma 2 is its own inverse,
+and for sigma 1, sigma 1 is
+
+its own inverse.
+
+For A pi, A pi is
+its own inverse.
+
+So an inverse exists.
+
+So we've got a group.
+
+And this is another way of
+saying, in general terms, if
+
+we put two mirror planes and a
+twofold axis together in this
+
+specific fashion, these
+operations, when they go to
+
+work on an initial motif,
+reproduce a finite set of
+
+objects and not a clutter that
+just fills space and never
+
+closes upon itself.
+
+Yes, sir?
+
+AUDIENCE: I see why you have
+sigma 1, sigma 2, A pi in that
+
+group, but why do you have the
+1, which is a conversion?
+
+PROFESSOR: OK.
+
+If I didn't put it in-- no,
+that's the identity operation.
+
+This is a one-fold axis.
+
+Just this 2 was a
+twofold axis.
+
+So one-fold axis is a nice
+symbol for identity because it
+
+doesn't do anything.
+
+It picks something up and
+puts it right back down
+
+where it came from.
+
+OK.
+
+Yeah.
+
+That's deceptive because 1,
+when we're talking about
+
+multiplication of numbers,
+also functions as
+
+the identity operation.
+
+Yeah?
+
+AUDIENCE: If all these
+symmetries are commutative,
+
+[? that is, ?]
+
+if they all commute, do you
+really [INAUDIBLE] bottom
+
+diagonal [INAUDIBLE]?
+
+PROFESSOR: In general, yes.
+
+AUDIENCE: Generally?
+
+PROFESSOR: Yeah.
+
+Actually, this is a special
+group because if I have two
+
+elements, a, and take b and
+follow it by a, that is the
+
+same result as a
+followed by b.
+
+And a group that has
+this character
+
+is said to be abelian.
+
+There's a standing rotten joke
+in mathematics that asks
+
+rhetorically, what is
+purple and commutes?
+
+The answer is an
+abelian grape.
+
+I don't think it's terribly
+funny either, but if you had a
+
+gaggle of mathematicians here,
+they would chortle and double
+
+over in laughter.
+
+Ha, ha, ha, abelian grape.
+
+Well, I don't feel badly.
+
+You react about the same
+way to some of my
+
+funny things, too.
+
+But you get used to that
+sort of thing.
+
+All right.
+
+The feeling I want to leave you
+with at this point is the
+
+idea that group theory and
+some of its concepts are
+
+exactly what we're meaning when
+we grope for a definition
+
+of the fact that a certain
+collection of symmetry
+
+operation should be finite.
+
+That is to say, it's finite.
+
+The operations combined on
+each other have to give a
+
+finite number, must constitute
+a group.
+
+And the main reason for being
+familiar with this is that
+
+group theory forms the basis of
+a lot of the words that are
+
+used to describe the
+
+combinations of symmetry elements.
+
+For example, what we have
+derived here, the symmetry
+
+that's called 2mm, is something
+that's called a
+
+point group.
+
+Point because there is at
+least one point in space
+
+that's left unchanged, and
+that's this point of
+
+intersection of all three
+symmetry elements.
+
+And it's called a group
+because the individual
+
+operations of these symmetry
+elements, when combined
+
+according to group theory,
+can be shown to
+
+constitute a group.
+
+The patterns that we get when we
+add symmetry elements to a
+
+lattice are groups in the
+sense, if you regard the
+
+pattern as extending infinitely
+in all directions,
+
+that the combination of any
+two elements gives you
+
+something that's also
+in the group.
+
+But the number of elements
+is infinite.
+
+For example, in the lattice,
+here's T1.
+
+Here's T2.
+
+Every other lattice point
+can be described as some
+
+combination of T1
+followed by T2.
+
+But the numbers in
+front of those
+
+translations can be infinite.
+
+If we put a symmetry element
+in this lattice, like a
+
+twofold axis, for example, the
+translations reproduce this
+
+twofold axis to an infinite
+number of locations.
+
+But yet, all of the group
+postulates are satisfied.
+
+The number of elements in the
+group does, however, not have
+
+to be finite.
+
+So that is another distinction
+that's worth making, that
+
+there are infinite groups and
+there are finite groups.
+
+And the number of elements
+can be infinite.
+
+Collection of symmetry elements
+that leave one point
+
+in space unmoved is called
+a point group.
+
+If we do something like this,
+put a twofold axis in
+
+combination with a pair of
+translations, that is an
+
+infinite set of operations that
+acts on all of space.
+
+This is something that's
+called a space group.
+
+Another designation,
+distinction, that's sometimes
+
+useful to make are
+crystallographic point groups,
+
+such as this one, 2mm, as
+opposed to combinations of
+
+symmetry elements, which are
+perfectly lovely and which are
+
+valid groups, such as a
+combination of rotations of 2
+
+pi over 5, or a combination
+of a fivefold axis
+
+with a mirror plane.
+
+Perfectly lovely symbols,
+constitute groups, but these
+
+are non-crystallographic
+
+These would be
+
+non-crystallographic point groups.
+
+Satisfy all the requirements of
+the group, but if it's to
+
+be in a crystal, the fivefold
+axis must be combined with
+
+translation, and that's
+impossible.
+
+So you can have
+
+non-crystallographic point groups.
+
+There are no
+non-crystallographic space
+
+groups because they are, by
+definition, something that
+
+involve translation yet
+constitute groups.
+
+All right.
+
+Set the stage for next time, so
+you all come back excited.
+
+We have shown that there are a
+limited number of symmetry
+
+elements that are possible in
+a lattice, rotation 1, 2, 3,
+
+4, and 6 in a mirror plane.
+
+And these are now examples
+of what we would call
+
+crystallographic point groups.
+
+These would be the sort of
+symmetry elements that are
+
+candidates for two-dimensional
+patterns.
+
+But are these the only
+symmetries that can be added
+
+to lattices?
+
+Could we not combine a mirror
+plane with a twofold axis?
+
+The answer I say to
+that is, sure.
+
+You bet you can.
+
+You just did it for us.
+
+But could you combine a mirror
+plane with a threefold axis, a
+
+mirror plane with a fourfold
+axis, a mirror plane with a
+
+sixfold axis?
+
+The answer to all of those
+questions are yes.
+
+So there are going to be spaces
+here, where there will
+
+be additional groups.
+
+And when we're done, we will
+have the two-dimensional
+
+crystallographic point groups.
+
+But now I have to be able
+to complete something.
+
+If I take A pi and combine it
+with a mirror operation sigma
+
+1, what do I get?
+
+If I take A 2 pi over 3, a
+threefold rotation, combine
+
+that with a mirror plane
+that passes through
+
+it, what do I get?
+
+Again, a characteristic of
+symmetry theory is that
+
+whenever I take a motif and
+repeat it by operation number
+
+1 to get a second motif, and
+then I repeat that by
+
+operation number
+2, I have three
+
+things that are identical.
+
+And there must be some way,
+some operation, that
+
+automatically arises that
+tells me how number 1 is
+
+related to number 2.
+
+Number 1 is related
+to number 3.
+
+Tied in with group theory, this
+says that if you combine
+
+operation 1 in a space, if
+it's to be a group, if
+
+operation number 2 is present,
+you must combine those two
+
+steps, and whatever pops up must
+be a member of the set of
+
+operations that are present.
+
+So we're going to have to come
+up with something that I call
+
+combination theorems.
+
+And this is simply expressing
+the result of a combination of
+
+two elements in a group
+multiplication table.
+
+It goes with a caveat.
+
+If you're so excited about this
+stuff, you're going to
+
+run home and start reading
+Buerger's book as
+
+soon as you get there.
+
+You can regard these symmetry
+transformations as operators.
+
+And you're familiar with other
+sorts of operators like d by
+
+dx, d by dy.
+
+And when you apply them in
+succession, you actually write
+
+it as a product.
+
+d by dy followed by d by dx you
+write as d squared dxdy.
+
+Or you write it as d squared
+dx squared when you
+
+differentiate twice.
+
+You don't mean you take the
+differential of the function
+
+with respect to x and
+then square it.
+
+You mean you do this
+operation twice.
+
+So these are all operators.
+
+And what we usually understand
+is that if you do d by dy
+
+first and then follow that with
+d by dx, the sequence of
+
+operation goes from
+right to left.
+
+And I think that will come right
+quite naturally to you.
+
+You do that with differentials
+and other sort of operators.
+
+That is what we'll do.
+
+Not Martin Buerger.
+
+A very strong-minded person,
+and he did what
+
+he thought was sensible.
+
+And he said we read things
+from left to right.
+
+We read everything from
+left to right.
+
+So I will be damned if I'm going
+to write d by dx, d by
+
+dy to be a sequence of
+operations that goes from
+
+right to left.
+
+So all throughout Buerger's
+book-- and it's easy to get
+
+adjusted to, if he writes A dot
+B, he means B followed by
+
+A. Whereas normally, in the
+calculus of operations, we
+
+will use, as the rest of the
+world does, this is A followed
+
+by B. Trivial point, but one
+that can throw you for a loop
+
+the first time you see
+it in Buerger's book
+
+if you follow it.
+
+Distinction does not matter
+if the group is abelian.
+
+So that the order of operations
+doesn't make any
+
+difference.
+
+OK, that's enough for one day.
+
+Beginning next time, know we
+will start to begin this
+
+process of synthesis.
+
+And the first thing we'll ask
+is, how do you combine a
+
+rotation operation with a
+reflection operation?
+
+See you next week.
\ No newline at end of file
diff --git a/kefsxztSX74.txt b/kefsxztSX74.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6e428b88847cb71a4c50d9e6b9eb4191693e7094
--- /dev/null
+++ b/kefsxztSX74.txt
@@ -0,0 +1,1947 @@
+align:start position:0%
+ 
+last time we discussed the differential
+
+ align:start position:0%
+last time we discussed the differential
+ 
+
+ align:start position:0%
+last time we discussed the differential
+equation I'll be posting notes very soon
+
+ align:start position:0%
+equation I'll be posting notes very soon
+ 
+
+ align:start position:0%
+equation I'll be posting notes very soon
+I'll probably this afternoon at some
+
+ align:start position:0%
+I'll probably this afternoon at some
+ 
+
+ align:start position:0%
+I'll probably this afternoon at some
+time and last time we solve the
+
+ align:start position:0%
+time and last time we solve the
+ 
+
+ align:start position:0%
+time and last time we solve the
+differential equation we found the
+
+ align:start position:0%
+differential equation we found the
+ 
+
+ align:start position:0%
+differential equation we found the
+energy eigenstates and then turned into
+
+ align:start position:0%
+energy eigenstates and then turned into
+ 
+
+ align:start position:0%
+energy eigenstates and then turned into
+an algebraic analysis in which we
+
+ align:start position:0%
+an algebraic analysis in which we
+ 
+
+ align:start position:0%
+an algebraic analysis in which we
+factorize the Hamiltonian which meant
+
+ align:start position:0%
+factorize the Hamiltonian which meant
+ 
+
+ align:start position:0%
+factorize the Hamiltonian which meant
+essentially you could write the
+
+ align:start position:0%
+essentially you could write the
+ 
+
+ align:start position:0%
+essentially you could write the
+Hamiltonian up to an overall constant
+
+ align:start position:0%
+Hamiltonian up to an overall constant
+ 
+
+ align:start position:0%
+Hamiltonian up to an overall constant
+that it doesn't complicate matters as
+
+ align:start position:0%
+that it doesn't complicate matters as
+ 
+
+ align:start position:0%
+that it doesn't complicate matters as
+the product of an a dagger a and that
+
+ align:start position:0%
+the product of an a dagger a and that
+ 
+
+ align:start position:0%
+the product of an a dagger a and that
+was very useful to show for example at
+
+ align:start position:0%
+was very useful to show for example at
+ 
+
+ align:start position:0%
+was very useful to show for example at
+any energy eigenstate would have to have
+
+ align:start position:0%
+any energy eigenstate would have to have
+ 
+
+ align:start position:0%
+any energy eigenstate would have to have
+energy greater than H Omega over 2 we
+
+ align:start position:0%
+energy greater than H Omega over 2 we
+ 
+
+ align:start position:0%
+energy greater than H Omega over 2 we
+call this a dagger a the number operator
+
+ align:start position:0%
+call this a dagger a the number operator
+ 
+
+ align:start position:0%
+call this a dagger a the number operator
+n which is a hermitian operator recall
+
+ align:start position:0%
+n which is a hermitian operator recall
+ 
+
+ align:start position:0%
+n which is a hermitian operator recall
+that the dagger of a product of
+
+ align:start position:0%
+that the dagger of a product of
+ 
+
+ align:start position:0%
+that the dagger of a product of
+operators is the reverse order product
+
+ align:start position:0%
+operators is the reverse order product
+ 
+
+ align:start position:0%
+operators is the reverse order product
+of the dagger so the dagger of a dagger
+
+ align:start position:0%
+of the dagger so the dagger of a dagger
+ 
+
+ align:start position:0%
+of the dagger so the dagger of a dagger
+a is itself and then a was related to X
+
+ align:start position:0%
+a is itself and then a was related to X
+ 
+
+ align:start position:0%
+a is itself and then a was related to X
+and P and so was a dagger recall that X
+
+ align:start position:0%
+and P and so was a dagger recall that X
+ 
+
+ align:start position:0%
+and P and so was a dagger recall that X
+and P are hermitian and their overall
+
+ align:start position:0%
+and P are hermitian and their overall
+ 
+
+ align:start position:0%
+and P are hermitian and their overall
+constants here that we wrote last time
+
+ align:start position:0%
+constants here that we wrote last time
+ 
+
+ align:start position:0%
+constants here that we wrote last time
+but now they're not that urgent and a
+
+ align:start position:0%
+but now they're not that urgent and a
+ 
+
+ align:start position:0%
+but now they're not that urgent and a
+and a dagger the commutator is equal to
+
+ align:start position:0%
+and a dagger the commutator is equal to
+ 
+
+ align:start position:0%
+and a dagger the commutator is equal to
+1 that was very useful finally we also
+
+ align:start position:0%
+1 that was very useful finally we also
+ 
+
+ align:start position:0%
+1 that was very useful finally we also
+show that while the energy of any state
+
+ align:start position:0%
+show that while the energy of any state
+ 
+
+ align:start position:0%
+show that while the energy of any state
+would have to be greater than H Omega
+
+ align:start position:0%
+would have to be greater than H Omega
+ 
+
+ align:start position:0%
+would have to be greater than H Omega
+over 2 if you had a stay that is killed
+
+ align:start position:0%
+over 2 if you had a stay that is killed
+ 
+
+ align:start position:0%
+over 2 if you had a stay that is killed
+by a heart it will have the lowest
+
+ align:start position:0%
+by a heart it will have the lowest
+ 
+
+ align:start position:0%
+by a heart it will have the lowest
+allowed energy which is H Omega over 2
+
+ align:start position:0%
+allowed energy which is H Omega over 2
+ 
+
+ align:start position:0%
+allowed energy which is H Omega over 2
+and therefore that is the ground state
+
+ align:start position:0%
+and therefore that is the ground state
+ 
+
+ align:start position:0%
+and therefore that is the ground state
+and we looked at this differential
+
+ align:start position:0%
+and we looked at this differential
+ 
+
+ align:start position:0%
+and we looked at this differential
+equation and we found this Gaussian wave
+
+ align:start position:0%
+equation and we found this Gaussian wave
+ 
+
+ align:start position:0%
+equation and we found this Gaussian wave
+function and it's a first order
+
+ align:start position:0%
+function and it's a first order
+ 
+
+ align:start position:0%
+function and it's a first order
+differential equation and
+
+ align:start position:0%
+differential equation and
+ 
+
+ align:start position:0%
+differential equation and
+referre has just one solution and
+
+ align:start position:0%
+referre has just one solution and
+ 
+
+ align:start position:0%
+referre has just one solution and
+therefore there is just one ground state
+
+ align:start position:0%
+therefore there is just one ground state
+ 
+
+ align:start position:0%
+therefore there is just one ground state
+and it's a bound state and of course you
+
+ align:start position:0%
+and it's a bound state and of course you
+ 
+
+ align:start position:0%
+and it's a bound state and of course you
+wouldn't expect more than one ground
+
+ align:start position:0%
+wouldn't expect more than one ground
+ 
+
+ align:start position:0%
+wouldn't expect more than one ground
+state because there's no degeneracies in
+
+ align:start position:0%
+state because there's no degeneracies in
+ 
+
+ align:start position:0%
+state because there's no degeneracies in
+the bound state spectrum of a
+
+ align:start position:0%
+the bound state spectrum of a
+ 
+
+ align:start position:0%
+the bound state spectrum of a
+one-dimensional potential so we found
+
+ align:start position:0%
+one-dimensional potential so we found
+ 
+
+ align:start position:0%
+one-dimensional potential so we found
+one ground state was Phi 0 and it's
+
+ align:start position:0%
+one ground state was Phi 0 and it's
+ 
+
+ align:start position:0%
+one ground state was Phi 0 and it's
+killed by a which it means that it's
+
+ align:start position:0%
+killed by a which it means that it's
+ 
+
+ align:start position:0%
+killed by a which it means that it's
+killed by n hat because a is to the
+
+ align:start position:0%
+killed by n hat because a is to the
+ 
+
+ align:start position:0%
+killed by n hat because a is to the
+right in an hat
+
+ align:start position:0%
+right in an hat
+ 
+
+ align:start position:0%
+right in an hat
+so the a finds Phi 0 and just kills it
+
+ align:start position:0%
+so the a finds Phi 0 and just kills it
+ 
+
+ align:start position:0%
+so the a finds Phi 0 and just kills it
+now the other thing to know this is that
+
+ align:start position:0%
+now the other thing to know this is that
+ 
+
+ align:start position:0%
+now the other thing to know this is that
+the Hamiltonian is really pretty much
+
+ align:start position:0%
+the Hamiltonian is really pretty much
+ 
+
+ align:start position:0%
+the Hamiltonian is really pretty much
+the same thing as the number operator
+
+ align:start position:0%
+the same thing as the number operator
+ 
+
+ align:start position:0%
+the same thing as the number operator
+multiplied by something with units of
+
+ align:start position:0%
+multiplied by something with units of
+ 
+
+ align:start position:0%
+multiplied by something with units of
+energy the number operator has no units
+
+ align:start position:0%
+energy the number operator has no units
+ 
+
+ align:start position:0%
+energy the number operator has no units
+because a and a dagger have no units and
+
+ align:start position:0%
+because a and a dagger have no units and
+ 
+
+ align:start position:0%
+because a and a dagger have no units and
+that's very useful so it's like a
+
+ align:start position:0%
+that's very useful so it's like a
+ 
+
+ align:start position:0%
+that's very useful so it's like a
+dimensionless version of the energy and
+
+ align:start position:0%
+dimensionless version of the energy and
+ 
+
+ align:start position:0%
+dimensionless version of the energy and
+certainly if you have an eigenstate of H
+
+ align:start position:0%
+certainly if you have an eigenstate of H
+ 
+
+ align:start position:0%
+certainly if you have an eigenstate of H
+it must be an eigenstate of n and the
+
+ align:start position:0%
+it must be an eigenstate of n and the
+ 
+
+ align:start position:0%
+it must be an eigenstate of n and the
+eigen the eigenvalue of n if we call it
+
+ align:start position:0%
+eigen the eigenvalue of n if we call it
+ 
+
+ align:start position:0%
+eigen the eigenvalue of n if we call it
+capital n therefore you can imagine this
+
+ align:start position:0%
+capital n therefore you can imagine this
+ 
+
+ align:start position:0%
+capital n therefore you can imagine this
+equation acting on an eigenstate which
+
+ align:start position:0%
+equation acting on an eigenstate which
+ 
+
+ align:start position:0%
+equation acting on an eigenstate which
+happens to be an eigenstate of N or of H
+
+ align:start position:0%
+happens to be an eigenstate of N or of H
+ 
+
+ align:start position:0%
+happens to be an eigenstate of N or of H
+on the left hand side you would read the
+
+ align:start position:0%
+on the left hand side you would read the
+ 
+
+ align:start position:0%
+on the left hand side you would read the
+energy and on the right hand side you
+
+ align:start position:0%
+energy and on the right hand side you
+ 
+
+ align:start position:0%
+energy and on the right hand side you
+would read the eigenvalue of the N
+
+ align:start position:0%
+would read the eigenvalue of the N
+ 
+
+ align:start position:0%
+would read the eigenvalue of the N
+operator so that gives you a very nice
+
+ align:start position:0%
+operator so that gives you a very nice
+ 
+
+ align:start position:0%
+operator so that gives you a very nice
+simple expression that you see that the
+
+ align:start position:0%
+simple expression that you see that the
+ 
+
+ align:start position:0%
+simple expression that you see that the
+energy is the number plus 1/2 multiplied
+
+ align:start position:0%
+energy is the number plus 1/2 multiplied
+ 
+
+ align:start position:0%
+energy is the number plus 1/2 multiplied
+by H bar armino so that's pretty much
+
+ align:start position:0%
+by H bar armino so that's pretty much
+ 
+
+ align:start position:0%
+by H bar armino so that's pretty much
+the content of what we reach last
+
+ align:start position:0%
+the content of what we reach last
+ 
+
+ align:start position:0%
+the content of what we reach last
+element now we have to complete this
+
+ align:start position:0%
+element now we have to complete this
+ 
+
+ align:start position:0%
+element now we have to complete this
+solution and the plan for today is to
+
+ align:start position:0%
+solution and the plan for today is to
+ 
+
+ align:start position:0%
+solution and the plan for today is to
+complete the solution familiarize
+
+ align:start position:0%
+complete the solution familiarize
+ 
+
+ align:start position:0%
+complete the solution familiarize
+ourselves with these operators learn how
+
+ align:start position:0%
+ourselves with these operators learn how
+ 
+
+ align:start position:0%
+ourselves with these operators learn how
+to work with the harmonic oscillator
+
+ align:start position:0%
+to work with the harmonic oscillator
+ 
+
+ align:start position:0%
+to work with the harmonic oscillator
+with them and then we'll leave the
+
+ align:start position:0%
+with them and then we'll leave the
+ 
+
+ align:start position:0%
+with them and then we'll leave the
+harmonic oscillator for 4
+
+ align:start position:0%
+harmonic oscillator for 4
+ 
+
+ align:start position:0%
+harmonic oscillator for 4
+the time being let you do some exercises
+
+ align:start position:0%
+the time being let you do some exercises
+ 
+
+ align:start position:0%
+the time being let you do some exercises
+with it but turn to scattering state so
+
+ align:start position:0%
+with it but turn to scattering state so
+ 
+
+ align:start position:0%
+with it but turn to scattering state so
+the second part of today's lecture we
+
+ align:start position:0%
+the second part of today's lecture we
+ 
+
+ align:start position:0%
+the second part of today's lecture we
+will be talking about scattering States
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so of when we looked at this thing
+
+ align:start position:0%
+okay so of when we looked at this thing
+ 
+
+ align:start position:0%
+okay so of when we looked at this thing
+and you have a number operator which
+
+ align:start position:0%
+and you have a number operator which
+ 
+
+ align:start position:0%
+and you have a number operator which
+includes the Hamiltonian it's a good
+
+ align:start position:0%
+includes the Hamiltonian it's a good
+ 
+
+ align:start position:0%
+includes the Hamiltonian it's a good
+idea to try to understand how it
+
+ align:start position:0%
+idea to try to understand how it
+ 
+
+ align:start position:0%
+idea to try to understand how it
+interacts with the other operators that
+
+ align:start position:0%
+interacts with the other operators that
+ 
+
+ align:start position:0%
+interacts with the other operators that
+you have here and a good question
+
+ align:start position:0%
+you have here and a good question
+ 
+
+ align:start position:0%
+you have here and a good question
+whenever you have operators is the
+
+ align:start position:0%
+whenever you have operators is the
+ 
+
+ align:start position:0%
+whenever you have operators is the
+commutator so you can ask what is the
+
+ align:start position:0%
+commutator so you can ask what is the
+ 
+
+ align:start position:0%
+commutator so you can ask what is the
+commutator of n with a and this
+
+ align:start position:0%
+commutator of n with a and this
+ 
+
+ align:start position:0%
+commutator of n with a and this
+commutator is going to show up but you
+
+ align:start position:0%
+commutator is going to show up but you
+ 
+
+ align:start position:0%
+commutator is going to show up but you
+know it's basically the kind of thing
+
+ align:start position:0%
+know it's basically the kind of thing
+ 
+
+ align:start position:0%
+know it's basically the kind of thing
+you have a and a dagger you ask what is
+
+ align:start position:0%
+you have a and a dagger you ask what is
+ 
+
+ align:start position:0%
+you have a and a dagger you ask what is
+the commutator if you have n now you ask
+
+ align:start position:0%
+the commutator if you have n now you ask
+ 
+
+ align:start position:0%
+the commutator if you have n now you ask
+what is the commutator with the other
+
+ align:start position:0%
+what is the commutator with the other
+ 
+
+ align:start position:0%
+what is the commutator with the other
+thing so n with a would be the
+
+ align:start position:0%
+thing so n with a would be the
+ 
+
+ align:start position:0%
+thing so n with a would be the
+commutator of a dagger with a with a
+
+ align:start position:0%
+commutator of a dagger with a with a
+ 
+
+ align:start position:0%
+commutator of a dagger with a with a
+like that and sometimes I will not write
+
+ align:start position:0%
+like that and sometimes I will not write
+ 
+
+ align:start position:0%
+like that and sometimes I will not write
+the hats to write things more quickly
+
+ align:start position:0%
+the hats to write things more quickly
+ 
+
+ align:start position:0%
+the hats to write things more quickly
+now in this commutator you can move the
+
+ align:start position:0%
+now in this commutator you can move the
+ 
+
+ align:start position:0%
+now in this commutator you can move the
+a out and you have a dagger a a and a
+
+ align:start position:0%
+a out and you have a dagger a a and a
+ 
+
+ align:start position:0%
+a out and you have a dagger a a and a
+dagger a is minus 1 because a dagger is
+
+ align:start position:0%
+dagger a is minus 1 because a dagger is
+ 
+
+ align:start position:0%
+dagger a is minus 1 because a dagger is
+1 so this is minus a so that's pretty
+
+ align:start position:0%
+1 so this is minus a so that's pretty
+ 
+
+ align:start position:0%
+1 so this is minus a so that's pretty
+nice it's simple
+
+ align:start position:0%
+nice it's simple
+ 
+
+ align:start position:0%
+nice it's simple
+how about n with a dagger well this
+
+ align:start position:0%
+how about n with a dagger well this
+ 
+
+ align:start position:0%
+how about n with a dagger well this
+would be a dagger a with a dagger a
+
+ align:start position:0%
+would be a dagger a with a dagger a
+ 
+
+ align:start position:0%
+would be a dagger a with a dagger a
+dagger with a dagger commute so this a
+
+ align:start position:0%
+dagger with a dagger commute so this a
+ 
+
+ align:start position:0%
+dagger with a dagger commute so this a
+dagger can go out and you get a a dagger
+
+ align:start position:0%
+dagger can go out and you get a a dagger
+ 
+
+ align:start position:0%
+dagger can go out and you get a a dagger
+and that's 1 so you get a dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's it's a nice kind of commutation
+
+ align:start position:0%
+so it's it's a nice kind of commutation
+ 
+
+ align:start position:0%
+so it's it's a nice kind of commutation
+relation you have commutation reserved X
+
+ align:start position:0%
+relation you have commutation reserved X
+ 
+
+ align:start position:0%
+relation you have commutation reserved X
+with P given a constant now n with a
+
+ align:start position:0%
+with P given a constant now n with a
+ 
+
+ align:start position:0%
+with P given a constant now n with a
+gives a number times a and commutator
+
+ align:start position:0%
+gives a number times a and commutator
+ 
+
+ align:start position:0%
+gives a number times a and commutator
+with a dagger gives a number times a
+
+ align:start position:0%
+with a dagger gives a number times a
+ 
+
+ align:start position:0%
+with a dagger gives a number times a
+dagger and those numbers are pretty
+
+ align:start position:0%
+dagger and those numbers are pretty
+ 
+
+ align:start position:0%
+dagger and those numbers are pretty
+significant so I'll write this again and
+
+ align:start position:0%
+significant so I'll write this again and
+ 
+
+ align:start position:0%
+significant so I'll write this again and
+with a is minus a m n with a dagger is
+
+ align:start position:0%
+with a is minus a m n with a dagger is
+ 
+
+ align:start position:0%
+with a is minus a m n with a dagger is
+plus a dagger this is part of the reason
+
+ align:start position:0%
+plus a dagger this is part of the reason
+ 
+
+ align:start position:0%
+plus a dagger this is part of the reason
+as we will see soon that the name of a
+
+ align:start position:0%
+as we will see soon that the name of a
+ 
+
+ align:start position:0%
+as we will see soon that the name of a
+which we call destruction operator
+
+ align:start position:0%
+which we call destruction operator
+ 
+
+ align:start position:0%
+which we call destruction operator
+because it destroys the vacuum it's
+
+ align:start position:0%
+because it destroys the vacuum it's
+ 
+
+ align:start position:0%
+because it destroys the vacuum it's
+sometimes called lowering operator
+
+ align:start position:0%
+sometimes called lowering operator
+ 
+
+ align:start position:0%
+sometimes called lowering operator
+because it comes with a negative sign
+
+ align:start position:0%
+because it comes with a negative sign
+ 
+
+ align:start position:0%
+because it comes with a negative sign
+here and we'll see a better reason for
+
+ align:start position:0%
+here and we'll see a better reason for
+ 
+
+ align:start position:0%
+here and we'll see a better reason for
+that name this is a dagger is something
+
+ align:start position:0%
+that name this is a dagger is something
+ 
+
+ align:start position:0%
+that name this is a dagger is something
+for the creation operator or the racing
+
+ align:start position:0%
+for the creation operator or the racing
+ 
+
+ align:start position:0%
+for the creation operator or the racing
+operator because it increases some
+
+ align:start position:0%
+operator because it increases some
+ 
+
+ align:start position:0%
+operator because it increases some
+number as you will see and here it's
+
+ align:start position:0%
+number as you will see and here it's
+ 
+
+ align:start position:0%
+number as you will see and here it's
+reflected by this plus but we need a
+
+ align:start position:0%
+reflected by this plus but we need a
+ 
+
+ align:start position:0%
+reflected by this plus but we need a
+little more than that
+
+ align:start position:0%
+little more than that
+ 
+
+ align:start position:0%
+little more than that
+we need a little more commutator than
+
+ align:start position:0%
+we need a little more commutator than
+ 
+
+ align:start position:0%
+we need a little more commutator than
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example if I would have the
+
+ align:start position:0%
+so for example if I would have the
+ 
+
+ align:start position:0%
+so for example if I would have the
+commutator of a with a dagger to the K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can imagine this and I wanted to you
+
+ align:start position:0%
+you can imagine this and I wanted to you
+ 
+
+ align:start position:0%
+you can imagine this and I wanted to you
+see you have to become very used and
+
+ align:start position:0%
+see you have to become very used and
+ 
+
+ align:start position:0%
+see you have to become very used and
+very comfortable with this commutation
+
+ align:start position:0%
+very comfortable with this commutation
+ 
+
+ align:start position:0%
+very comfortable with this commutation
+relations and and sometimes the only way
+
+ align:start position:0%
+relations and and sometimes the only way
+ 
+
+ align:start position:0%
+relations and and sometimes the only way
+to do that is to just do example so I'm
+
+ align:start position:0%
+to do that is to just do example so I'm
+ 
+
+ align:start position:0%
+to do that is to just do example so I'm
+doing this with a k here maybe when you
+
+ align:start position:0%
+doing this with a k here maybe when you
+ 
+
+ align:start position:0%
+doing this with a k here maybe when you
+review this lecture you should do it
+
+ align:start position:0%
+review this lecture you should do it
+ 
+
+ align:start position:0%
+review this lecture you should do it
+with k equal 2 or K equal 3 and do it a
+
+ align:start position:0%
+with k equal 2 or K equal 3 and do it a
+ 
+
+ align:start position:0%
+with k equal 2 or K equal 3 and do it a
+few times until you're comfortable with
+
+ align:start position:0%
+few times until you're comfortable with
+ 
+
+ align:start position:0%
+few times until you're comfortable with
+these things and you know what
+
+ align:start position:0%
+these things and you know what
+ 
+
+ align:start position:0%
+these things and you know what
+identities you've been using if if this
+
+ align:start position:0%
+identities you've been using if if this
+ 
+
+ align:start position:0%
+identities you've been using if if this
+was a little quick then go more slowly
+
+ align:start position:0%
+was a little quick then go more slowly
+ 
+
+ align:start position:0%
+was a little quick then go more slowly
+and make absolutely sure you don't how
+
+ align:start position:0%
+and make absolutely sure you don't how
+ 
+
+ align:start position:0%
+and make absolutely sure you don't how
+to do those commentators in here I'm
+
+ align:start position:0%
+to do those commentators in here I'm
+ 
+
+ align:start position:0%
+to do those commentators in here I'm
+going to say what happens you have an a
+
+ align:start position:0%
+going to say what happens you have an a
+ 
+
+ align:start position:0%
+going to say what happens you have an a
+and you have to move it across a string
+
+ align:start position:0%
+and you have to move it across a string
+ 
+
+ align:start position:0%
+and you have to move it across a string
+of a K a hat now moving an A across and
+
+ align:start position:0%
+of a K a hat now moving an A across and
+ 
+
+ align:start position:0%
+of a K a hat now moving an A across and
+a hat because of the commutator gives
+
+ align:start position:0%
+a hat because of the commutator gives
+ 
+
+ align:start position:0%
+a hat because of the commutator gives
+you a factor of 1 but it destroys the a
+
+ align:start position:0%
+you a factor of 1 but it destroys the a
+ 
+
+ align:start position:0%
+you a factor of 1 but it destroys the a
+and the a hat so this as you move the a
+
+ align:start position:0%
+and the a hat so this as you move the a
+ 
+
+ align:start position:0%
+and the a hat so this as you move the a
+across the egg hats because this is a
+
+ align:start position:0%
+across the egg hats because this is a
+ 
+
+ align:start position:0%
+across the egg hats because this is a
+with all the a hats here - the a hat and
+
+ align:start position:0%
+with all the a hats here - the a hat and
+ 
+
+ align:start position:0%
+with all the a hats here - the a hat and
+the a there so if you could just move
+
+ align:start position:0%
+the a there so if you could just move
+ 
+
+ align:start position:0%
+the a there so if you could just move
+the a all the way across then you cancel
+
+ align:start position:0%
+the a all the way across then you cancel
+ 
+
+ align:start position:0%
+the a all the way across then you cancel
+with this what you get is what happens
+
+ align:start position:0%
+with this what you get is what happens
+ 
+
+ align:start position:0%
+with this what you get is what happens
+when you're moving it across and you're
+
+ align:start position:0%
+when you're moving it across and you're
+ 
+
+ align:start position:0%
+when you're moving it across and you're
+moving across a string of those so each
+
+ align:start position:0%
+moving across a string of those so each
+ 
+
+ align:start position:0%
+moving across a string of those so each
+time you try to move on a across a new
+
+ align:start position:0%
+time you try to move on a across a new
+ 
+
+ align:start position:0%
+time you try to move on a across a new
+hat you get this factor of 1 and you
+
+ align:start position:0%
+hat you get this factor of 1 and you
+ 
+
+ align:start position:0%
+hat you get this factor of 1 and you
+kill the a and you kill 1 a dagger so
+
+ align:start position:0%
+kill the a and you kill 1 a dagger so
+ 
+
+ align:start position:0%
+kill the a and you kill 1 a dagger so
+this answer will not have an A and it
+
+ align:start position:0%
+this answer will not have an A and it
+ 
+
+ align:start position:0%
+this answer will not have an A and it
+will have one less
+
+ align:start position:0%
+will have one less
+ 
+
+ align:start position:0%
+will have one less
+a dagger so a dagger to the K minus one
+
+ align:start position:0%
+a dagger so a dagger to the K minus one
+ 
+
+ align:start position:0%
+a dagger so a dagger to the K minus one
+and then I would argue and you should do
+
+ align:start position:0%
+and then I would argue and you should do
+ 
+
+ align:start position:0%
+and then I would argue and you should do
+it in more slowly that you have to go
+
+ align:start position:0%
+it in more slowly that you have to go
+ 
+
+ align:start position:0%
+it in more slowly that you have to go
+across K of those and each time you get
+
+ align:start position:0%
+across K of those and each time you get
+ 
+
+ align:start position:0%
+across K of those and each time you get
+a factor of one and you lose the a and
+
+ align:start position:0%
+a factor of one and you lose the a and
+ 
+
+ align:start position:0%
+a factor of one and you lose the a and
+the a dagger so at the end you get a K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you know you should realize that
+
+ align:start position:0%
+and if you know you should realize that
+ 
+
+ align:start position:0%
+and if you know you should realize that
+this is not all that different from the
+
+ align:start position:0%
+this is not all that different from the
+ 
+
+ align:start position:0%
+this is not all that different from the
+kind of commutator you had like P with X
+
+ align:start position:0%
+kind of commutator you had like P with X
+ 
+
+ align:start position:0%
+kind of commutator you had like P with X
+to the N this was very similar it might
+
+ align:start position:0%
+to the N this was very similar it might
+ 
+
+ align:start position:0%
+to the N this was very similar it might
+be a good time to review how that was
+
+ align:start position:0%
+be a good time to review how that was
+ 
+
+ align:start position:0%
+be a good time to review how that was
+done in which that pretty much gives you
+
+ align:start position:0%
+done in which that pretty much gives you
+ 
+
+ align:start position:0%
+done in which that pretty much gives you
+an X to the N minus 1 times a factor of
+
+ align:start position:0%
+an X to the N minus 1 times a factor of
+ 
+
+ align:start position:0%
+an X to the N minus 1 times a factor of
+n because piece had derivative you could
+
+ align:start position:0%
+n because piece had derivative you could
+ 
+
+ align:start position:0%
+n because piece had derivative you could
+almost think of a as the derivative with
+
+ align:start position:0%
+almost think of a as the derivative with
+ 
+
+ align:start position:0%
+almost think of a as the derivative with
+respect to a dagger and then this
+
+ align:start position:0%
+respect to a dagger and then this
+ 
+
+ align:start position:0%
+respect to a dagger and then this
+commutator would be 1 so so this is true
+
+ align:start position:0%
+commutator would be 1 so so this is true
+ 
+
+ align:start position:0%
+commutator would be 1 so so this is true
+and there's also if you want a dagger
+
+ align:start position:0%
+and there's also if you want a dagger
+ 
+
+ align:start position:0%
+and there's also if you want a dagger
+with a to the N right the K this would
+
+ align:start position:0%
+with a to the N right the K this would
+ 
+
+ align:start position:0%
+with a to the N right the K this would
+give you if you had just one of them you
+
+ align:start position:0%
+give you if you had just one of them you
+ 
+
+ align:start position:0%
+give you if you had just one of them you
+will get a minus sign because a dagger
+
+ align:start position:0%
+will get a minus sign because a dagger
+ 
+
+ align:start position:0%
+will get a minus sign because a dagger
+with a is that but the same thing holds
+
+ align:start position:0%
+with a is that but the same thing holds
+ 
+
+ align:start position:0%
+with a is that but the same thing holds
+you're going to get one less a hat so a
+
+ align:start position:0%
+you're going to get one less a hat so a
+ 
+
+ align:start position:0%
+you're going to get one less a hat so a
+hat to the K minus 1 a factor of K
+
+ align:start position:0%
+hat to the K minus 1 a factor of K
+ 
+
+ align:start position:0%
+hat to the K minus 1 a factor of K
+because K times you're going to move an
+
+ align:start position:0%
+because K times you're going to move an
+ 
+
+ align:start position:0%
+because K times you're going to move an
+a dagger across an A and a minus because
+
+ align:start position:0%
+a dagger across an A and a minus because
+ 
+
+ align:start position:0%
+a dagger across an A and a minus because
+you're getting a dagger commutator with
+
+ align:start position:0%
+you're getting a dagger commutator with
+ 
+
+ align:start position:0%
+you're getting a dagger commutator with
+a as opposed to a commutator with a
+
+ align:start position:0%
+a as opposed to a commutator with a
+ 
+
+ align:start position:0%
+a as opposed to a commutator with a
+dagger who just want so these are two
+
+ align:start position:0%
+dagger who just want so these are two
+ 
+
+ align:start position:0%
+dagger who just want so these are two
+very nice and useful equations that you
+
+ align:start position:0%
+very nice and useful equations that you
+ 
+
+ align:start position:0%
+very nice and useful equations that you
+should be comfortable with now this
+
+ align:start position:0%
+should be comfortable with now this
+ 
+
+ align:start position:0%
+should be comfortable with now this
+implies that you can do more with the N
+
+ align:start position:0%
+implies that you can do more with the N
+ 
+
+ align:start position:0%
+implies that you can do more with the N
+operator so
+
+ align:start position:0%
+operator so
+ 
+
+ align:start position:0%
+operator so
+n with a hat to the K this time will be
+
+ align:start position:0%
+n with a hat to the K this time will be
+ 
+
+ align:start position:0%
+n with a hat to the K this time will be
+minus K a hat to the K it doesn't change
+
+ align:start position:0%
+minus K a hat to the K it doesn't change
+ 
+
+ align:start position:0%
+minus K a hat to the K it doesn't change
+the number of a hat because you're now
+
+ align:start position:0%
+the number of a hat because you're now
+ 
+
+ align:start position:0%
+the number of a hat because you're now
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+baking commentators with a dagger a so
+
+ align:start position:0%
+baking commentators with a dagger a so
+ 
+
+ align:start position:0%
+baking commentators with a dagger a so
+each time you have this commuted with
+
+ align:start position:0%
+each time you have this commuted with
+ 
+
+ align:start position:0%
+each time you have this commuted with
+one a hat the a dagger and the a if you
+
+ align:start position:0%
+one a hat the a dagger and the a if you
+ 
+
+ align:start position:0%
+one a hat the a dagger and the a if you
+want but you have another a back so the
+
+ align:start position:0%
+want but you have another a back so the
+ 
+
+ align:start position:0%
+want but you have another a back so the
+power is the same the sign comes from
+
+ align:start position:0%
+power is the same the sign comes from
+ 
+
+ align:start position:0%
+power is the same the sign comes from
+this sign so yes it should have a heart
+
+ align:start position:0%
+this sign so yes it should have a heart
+ 
+
+ align:start position:0%
+this sign so yes it should have a heart
+and sorry yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and similarly n a hat dagger to the K
+
+ align:start position:0%
+and similarly n a hat dagger to the K
+ 
+
+ align:start position:0%
+and similarly n a hat dagger to the K
+this is K a hat dagger to the K so what
+
+ align:start position:0%
+this is K a hat dagger to the K so what
+ 
+
+ align:start position:0%
+this is K a hat dagger to the K so what
+happened before that the end operator
+
+ align:start position:0%
+happened before that the end operator
+ 
+
+ align:start position:0%
+happened before that the end operator
+and hot operator leaves the a the same
+
+ align:start position:0%
+and hot operator leaves the a the same
+ 
+
+ align:start position:0%
+and hot operator leaves the a the same
+at puts a number leaves the a dagger the
+
+ align:start position:0%
+at puts a number leaves the a dagger the
+ 
+
+ align:start position:0%
+at puts a number leaves the a dagger the
+same and puts a number here you see it
+
+ align:start position:0%
+same and puts a number here you see it
+ 
+
+ align:start position:0%
+same and puts a number here you see it
+happening again and with a collection
+
+ align:start position:0%
+happening again and with a collection
+ 
+
+ align:start position:0%
+happening again and with a collection
+with a string of a hat gives you the
+
+ align:start position:0%
+with a string of a hat gives you the
+ 
+
+ align:start position:0%
+with a string of a hat gives you the
+same string but the number and with a
+
+ align:start position:0%
+same string but the number and with a
+ 
+
+ align:start position:0%
+same string but the number and with a
+collection of a daggers gives you the
+
+ align:start position:0%
+collection of a daggers gives you the
+ 
+
+ align:start position:0%
+collection of a daggers gives you the
+same collection of a daggers with a
+
+ align:start position:0%
+same collection of a daggers with a
+ 
+
+ align:start position:0%
+same collection of a daggers with a
+number and the number happens to be the
+
+ align:start position:0%
+number and the number happens to be the
+ 
+
+ align:start position:0%
+number and the number happens to be the
+number of A's or the number of a dieters
+
+ align:start position:0%
+number of A's or the number of a dieters
+ 
+
+ align:start position:0%
+number of A's or the number of a dieters
+so that's the reason it's called a
+
+ align:start position:0%
+so that's the reason it's called a
+ 
+
+ align:start position:0%
+so that's the reason it's called a
+number operator because the eigenvalues
+
+ align:start position:0%
+number operator because the eigenvalues
+ 
+
+ align:start position:0%
+number operator because the eigenvalues
+are the number of creation operators or
+
+ align:start position:0%
+are the number of creation operators or
+ 
+
+ align:start position:0%
+are the number of creation operators or
+the number of destruction operators I
+
+ align:start position:0%
+the number of destruction operators I
+ 
+
+ align:start position:0%
+the number of destruction operators I
+was a little
+
+ align:start position:0%
+was a little
+ 
+
+ align:start position:0%
+was a little
+glib by calling it the eigenvalue but it
+
+ align:start position:0%
+glib by calling it the eigenvalue but it
+ 
+
+ align:start position:0%
+glib by calling it the eigenvalue but it
+almost looks like an eigenvalue equation
+
+ align:start position:0%
+almost looks like an eigenvalue equation
+ 
+
+ align:start position:0%
+almost looks like an eigenvalue equation
+which have an operator another operator
+
+ align:start position:0%
+which have an operator another operator
+ 
+
+ align:start position:0%
+which have an operator another operator
+and your number times the second
+
+ align:start position:0%
+and your number times the second
+ 
+
+ align:start position:0%
+and your number times the second
+operator it's not exactly an eigenvalue
+
+ align:start position:0%
+operator it's not exactly an eigenvalue
+ 
+
+ align:start position:0%
+operator it's not exactly an eigenvalue
+equation though because eigenvalues you
+
+ align:start position:0%
+equation though because eigenvalues you
+ 
+
+ align:start position:0%
+equation though because eigenvalues you
+would just have this acting on the
+
+ align:start position:0%
+would just have this acting on the
+ 
+
+ align:start position:0%
+would just have this acting on the
+second one but the fact that this case
+
+ align:start position:0%
+second one but the fact that this case
+ 
+
+ align:start position:0%
+second one but the fact that this case
+appear here are the reason these are
+
+ align:start position:0%
+appear here are the reason these are
+ 
+
+ align:start position:0%
+appear here are the reason these are
+called number operators so what's a
+
+ align:start position:0%
+called number operators so what's a
+ 
+
+ align:start position:0%
+called number operators so what's a
+little quick for many of you some you
+
+ align:start position:0%
+little quick for many of you some you
+ 
+
+ align:start position:0%
+little quick for many of you some you
+may have seen this before with a little
+
+ align:start position:0%
+may have seen this before with a little
+ 
+
+ align:start position:0%
+may have seen this before with a little
+slow but the important thing is after a
+
+ align:start position:0%
+slow but the important thing is after a
+ 
+
+ align:start position:0%
+slow but the important thing is after a
+couple of days from now or by Friday you
+
+ align:start position:0%
+couple of days from now or by Friday you
+ 
+
+ align:start position:0%
+couple of days from now or by Friday you
+find all this very straightforward
\ No newline at end of file
diff --git a/l-BNoAPe6qo.txt b/l-BNoAPe6qo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..795ec4a561d159b8a533afdd7575ed0009eb7696
--- /dev/null
+++ b/l-BNoAPe6qo.txt
@@ -0,0 +1,2426 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So, our first
+question here is about
+
+limiting reactants.
+
+So, that's something you will
+encounter in your review
+
+reading for the sections, that
+kind of review -- what we hope
+
+you have picked up from high
+school or will pick up quickly
+
+by doing some review.
+
+So, how about we have everyone
+take ten more seconds on the
+
+clicker question, get your
+final answer in here.
+
+All right.
+
+So, let's see what we have.
+
+All right, so it looks like
+we weren't showing the
+
+percentages here, but it looks
+like hopefully most of you
+
+were able to get the correct
+answer of H2 being the
+
+limiting reactant.
+
+It looks like we're still
+figuring out -- this room was
+
+just renovated, we're still
+working out exactly how the
+
+electronics work.
+
+So, normally we'll see a
+percentage of how many of you
+
+got it, but I'm going to say it
+was probably about 95% got
+
+the answer right.
+
+So, good job there.
+
+If you didn't get the answer
+right -- we'll send these
+
+questions to your TA, so any
+time you get a clicker
+
+question wrong and you're
+confused, bring it up in the
+
+next recitation section
+and you'll be able
+
+to discuss it there.
+
+So, starting in, we can switch
+over to the to the notes now.
+
+When we left off on Wednesday,
+what we had really been doing
+
+is trying to give you an
+overview of all of the
+
+different topics that
+we're going to be
+
+going over this semester.
+
+And also, to make a couple of
+those connections between the
+
+principles we're learning, and
+some of the exciting research
+
+that's going on at MIT in the
+Chemistry Department, and
+
+also, to give you the idea that
+we are going to be trying
+
+to make these connections
+between the chemistry and
+
+things like human health
+or medicine.
+
+So, now we get to actually take
+a step back and start at
+
+the beginning, because before we
+can talk about some of the
+
+more complex issues, which
+involve interactions between
+
+molecules reacting or even
+when we're talking about
+
+individual molecules -- the
+bonds that form between
+
+individual atoms -- before any
+of that we actually need to
+
+establish a way that we're going
+to describe and think
+
+about how an individual
+atom behaves.
+
+And the way that we'll do this
+is starting with talking about
+
+the discovery of the electron
+and the nucleus here.
+
+Once we go through that, we
+will be able to talk about
+
+describing an atom using
+classical physics.
+
+So, once we have an atom and a
+nucleus, what we'll try to do
+
+is apply the classical
+mechanics to
+
+explain how that behaves.
+
+What we'll find is that this
+fails, and once this fails
+
+we're going to need
+another option.
+
+Luckily for us, we have quantum
+mechanics, which we'll
+
+be talking about for the
+next few lectures, and
+
+we'll dive into that.
+
+We might get a chance to
+introduce it today, but
+
+certainly in next class we'll
+be introducing this new kind
+
+of mechanics that's going
+to allow to describe
+
+the behavior of atoms.
+
+So, I want to point out that it
+makes a lot of sense for us
+
+to start with the discovery of
+the electron and the nucleus,
+
+because it really highlights
+one of the big issues that
+
+comes up in all chemistry
+research that you do, and that
+
+is how do we actually study,
+or in this case, how do we
+
+discover atoms or sub-particles
+that we actually
+
+can't see at all.
+
+And there are lots of solutions
+that chemists come
+
+up with -- there's always new
+techniques that allow us to do
+
+this, and these are just some
+of the first, and we'll go
+
+through them in a little
+bit of detail here.
+
+So, this all starts, in terms
+of putting it in its
+
+historical context at the turn
+of the Century, we said we'd
+
+start right in on the
+20th Century of
+
+where chemistry was.
+
+And where we where at the start
+of the 20th Century in
+
+the late 1890's is that we were
+at a place where there
+
+was great confidence in our
+understanding of the universe,
+
+and our understanding of
+how all matter worked.
+
+So, people in the chemistry
+community and in the physics
+
+community had this general
+feeling that the theoretical
+
+structure of the entire universe
+was pretty well
+
+understood.
+
+And they had this feeling
+because there had just been
+
+this huge boon of discovery,
+of scientific advances that
+
+included Newtonian mechanics,
+it included Dalton's atomic
+
+theory of matter, also
+thermodynamics and classical
+
+electromagnetism.
+
+So, you can understand they
+really felt quite confident at
+
+this time that we could explain
+everything that was
+
+going on, and in fact, a really
+telling quote from the
+
+time was said by a professor at
+the University of Chicago,
+
+and what he said is, "Our future
+discoveries must be
+
+looked for in the sixth
+decimal place."
+
+So, basically what he's saying
+here is we pretty much
+
+understand what's going on,
+there's nothing new to really
+
+discover, all we need to do is
+measure things more precisely.
+
+So, that's not exactly the case,
+and we're going to start
+
+in at the point where right
+around this time of great
+
+confidence of feeling all has
+been conquered, there are some
+
+observations and discoveries
+that are made that completely
+
+break down these theories.
+
+For example, in terms of the
+atomic theory of matter, at
+
+the time at the turn of the
+Century, the understanding was
+
+that atoms were the most basic
+constituent of matter, meaning
+
+you couldn't break atoms up into
+anything smaller -- that
+
+was it, you're done.
+
+And with using Newtonian
+mechanics, it was assumed
+
+since this type of mechanics
+worked so well to describe
+
+everything we could see, it
+could even describe the
+
+universe and planets, that, of
+course, we could use Newtonian
+
+mechanics to describe how an
+electron -- actually, we
+
+didn't even know about an
+electron here, but how atoms
+
+behaved, and it turns out this
+is not the case, and the first
+
+step in discovering this is not
+the case, was accomplished
+
+by J.J. Thomson, and J.J.
+Thomson is credited for
+
+discovering the electron.
+
+He was a physicist in England,
+and what his laboratory was
+
+studying is something called
+cathode rays, and cathode rays
+
+are simply rays that are emitted
+when you have a high
+
+voltage difference between
+two electrodes.
+
+So, if you look at this set up,
+what he did when he was
+
+studying these rays is he had
+an evacuated tube, which is
+
+schematically shown here, where
+it's evacuated of all
+
+it's air and filled instead just
+with hydrogen gas, and he
+
+had this high voltage difference
+between an anode
+
+and a cathode, and he actually
+put a little hole in the anode
+
+here, so these cathode rays that
+were produced could shoot
+
+out of the cathode and actually
+could be detected as
+
+this luminescent spot on
+a detector screen.
+
+So, lots of people were studying
+cathode rays at the
+
+time -- one reason is they
+actually gave off this bright
+
+glow -- if you put them in an
+evacuated glass tube, you got
+
+these crazy patterns
+and glowing colors.
+
+So, for that reason
+it was a very hot
+
+issue in terms of research.
+
+But also, no one really knew
+what these were and Thomson
+
+was seeking to figure out some
+more properties of them, and
+
+he had the theory that maybe
+they were actually charged
+
+particles of some sort, and
+others had proposed this in
+
+the past, but they didn't really
+have an experimental
+
+set up to test it.
+
+And that's what Thomson did.
+
+And what we did was he put two
+detection plates on either
+
+side of these cathode rays,
+and when he put a voltage
+
+difference between these two
+plates, he wanted to see if he
+
+could actually bend the rays and
+test if they're actually
+
+charged or not.
+
+So, when the voltage difference
+between the plates
+
+is zero, or when we just don't
+have the plates there at all,
+
+the cathode rays are not bent,
+they just go right in a
+
+straight line, and they can be
+detected on this screen.
+
+When he actually cranked up the
+voltage between these two
+
+plates, what he saw was really
+amazing to him, which is that
+
+he actually was able to bend
+these rays -- this had never
+
+been observed before in any
+capacity, and he was able to
+
+detect on his screen that there
+was this deflection, and
+
+he could even measure
+the degree of the
+
+deflection that he had.
+
+So, we know now that we have
+charged particles.
+
+Are these negatively or
+positively charged, based on
+
+this evidence?
+
+STUDENT: Negatively.
+
+PROFESSOR: Yeah, that's right.
+
+So, what we have here, cathode
+rays we now know are
+
+negatively charged particles.
+
+And, in fact, he named these
+negatively charged particles.
+
+Does anyone know what
+he named them?
+
+No, not electrons --
+very good guess.
+
+He named them corpuscles.
+
+Has anyone heard
+of corpuscles?
+
+A little bit.
+
+Yeah, so it was later named that
+these particles were, in
+
+fact, electrons, and that's
+what they are.
+
+J.J. Thomson continued to call
+them corpuscles for many,
+
+many, many years after everyone
+else called them
+
+electrons, but I'm sure no one
+minded because he did, in
+
+fact, discover them.
+
+And he was actually able to find
+out more than just that
+
+these were charged.
+
+From classical electromagnetism,
+he could
+
+actually relate the degree of
+deflection that he saw to the
+
+charge and the mass
+of the particles.
+
+So, using that he could say that
+delta x, and we'll put
+
+sub-negative, because we know
+now that these are negative
+
+particles, is proportional to
+the charge on that particle
+
+over m, which is the mass.
+
+So, we have e being equal to
+the charge of the negative
+
+particles, and m, of course,
+is equal to the
+
+mass of those particles.
+
+So, Thomson didn't stop here,
+he actually continued
+
+experimenting with different
+voltages.
+
+And what he found was if he
+really, really ramped the
+
+voltage up between those two
+plates, he could actually
+
+detect something else.
+
+And what he could detect here is
+that there was this little
+
+spot of luminescence that he
+could see on the screen that
+
+was barely deflected at all --
+certainly in comparison to how
+
+strongly this first particle
+was deflected.
+
+The second particle was
+deflected almost not at all.
+
+But what he could tell from
+the fact that there was a
+
+second particle at all, and the
+fact that it was in this
+
+direction, is that in addition
+to his negative particle, he
+
+also, of course, had a positive
+particle that was
+
+within this stream of rays
+that were coming out.
+
+So, of course, he can use the
+same relationship for the
+
+positive particle, so delta
+x now of the positive is
+
+proportional to the charge on
+the positive particle all over
+
+the mass of the positive
+particle.
+
+So, this is interesting
+for several reasons.
+
+What did he manage to pull out
+information-wise from using
+
+these two relationships?
+
+And actually to do this, he made
+a few more observations.
+
+The first, which I just stated,
+is that the deflection
+
+of that negative particle was
+just far and away more
+
+extreme, much, much larger
+than that of
+
+the positive particle.
+
+The other assumption that he
+made here is that the charge
+
+on the two particles
+was equal.
+
+So, how could he know that
+the charge on the two
+
+particles was equal?
+
+And actually he couldn't exactly
+know it -- it was a
+
+very good assumption that he
+made, and he could make the
+
+assumption because he, in fact,
+did know that what he
+
+started with was this
+hydrogen gas.
+
+So, he was starting
+with hydrogen.
+
+If some negative particle was
+popping out from the hydrogen,
+
+then what he must be left with
+is h-plus, and since hydrogen
+
+itself is neutral, the h-plus
+and the electron had to add up
+
+to be a neutral charge.
+
+So, that means the charges of
+the two pieces, the positive
+
+and negative particle,
+must be equal in
+
+terms of absolute charge.
+
+So, using this relationship, he
+could then actually figure
+
+out by knowing, which he knows
+how much each of them were
+
+deflected, he could now try to
+think about whether or not he
+
+could make some relationship
+between the masses -- between
+
+the mass of the positive and
+the negative particle.
+
+So, this relationship he was
+looking at was starting with
+
+the deflection, and the absolute
+distance that the
+
+particles were deflected.
+
+So, what he could set that equal
+to is he knows what x is
+
+proportional to in terms of
+the negative particle, so
+
+that's just the absolute value
+of the charge over the mass of
+
+the negative particle.
+
+He could divide all of that by
+the absolute value of the
+
+charge of the positive particle,
+all over the mass of
+
+the positive particle.
+
+And as we said, he made the
+assumption that those two
+
+charges were equal, so
+we can go ahead and
+
+cross those right out.
+
+So, what that told him was if
+he knew the relationship
+
+between how far they were each
+displaced, he could also know
+
+something about the
+
+relationship of the two masses.
+
+So essentially, there was an
+inversely proportional
+
+relationship between how far the
+particles were displaced,
+
+and what the mass of the two
+particles turned out to be.
+
+So, because he, of course,
+observed that the negative
+
+particle travelled -- it was
+deflected much, much further
+
+by those plates, what he could
+also assume and make the
+
+conclusion of is that the mass
+of that negative particle is
+
+actually larger or smaller?
+
+STUDENT: Smaller.
+
+PROFESSOR: Much, much smaller,
+exactly, then the mass of the
+
+positive particle.
+
+So essentially, what he found
+here is the relationship
+
+between the mass of an electron
+and the mass of the
+
+rest of the atom, the rest of
+the hydrogen atom there, which
+
+is an ion in this case.
+
+And, in fact, it's so much
+smaller, it's close to 2,000
+
+times smaller, that we can
+make the assumption that
+
+essentially the electrons
+take up no mass.
+
+I mean they take up a teeny
+bit, but essentially, when
+
+we're thinking about the set up
+of the atom, we don't have
+
+to account for them as using
+up a lot of the mass we're
+
+discussing.
+
+So, Thomson came up with a
+model for the atom due to
+
+this, and this is called the
+Plum Pudding model of the
+
+atom, and he was, as we said,
+English, so plum pudding is
+
+kind of a British food.
+
+Has anyone here ever
+had plum pudding?
+
+A couple of people.
+
+Okay.
+
+I've never even seen it, so
+that's good -- you must be
+
+better travelled than I.
+
+So, the idea that he had here
+was he treated the whole of
+
+the atom as sort of this
+positive pudding, so the
+
+majority of the atom was just
+kind of this goopy, positive
+
+stuff that you could think
+about, and within the pudding,
+
+he had all these negative
+charges, which were the
+
+electrons, and they were the
+raisins or the plums that were
+
+in the pudding.
+
+So this was a revolutionary
+model of an atom when we
+
+thought of the fact that before
+this experiment, the
+
+understanding was an atom could
+not be divisible into
+
+smaller parts, and now here we
+are with subatomic particles
+
+with electrons, and this
+wonderful Plum Pudding model.
+
+So, for those of you that
+haven't actually had plum
+
+pudding, which myself
+is included, I threw
+
+a picture up here.
+
+This was my first glance at plum
+pudding, and I guess you
+
+can see that this must be that
+positive part -- most of the
+
+plums are within that, and you
+can see all these little
+
+raisins or plums in here, that
+would be that negative charge.
+
+So, that already was a big
+advancement from where the
+
+understanding was at the time.
+
+We already moved way forward and
+completely revolutionizing
+
+the understanding of an atom in
+that there's something in
+
+an atom -- it's not the smallest
+thing there is.
+
+However, as you know, we
+didn't stop at the plum
+
+pudding model, which is good,
+because it's a little goofy,
+
+so it's nice to move on from
+that and move on we did.
+
+About 10 to 15 years later,
+another physicist, Ernest
+
+Rutherford, actually put this
+plum pudding model to test,
+
+and he did it through studies
+that he'd been doing on
+
+radiation that was emitting
+something
+
+called alpha particles.
+
+So, Rutherford, some of you may
+recognize that name, is a
+
+very famous physicist who made
+a lot of contributions in
+
+terms of radioactivity.
+
+When he was studying these
+alpha particles, he was
+
+actually the first person to
+identify the difference
+
+between different types of
+particles that radioactive
+
+materials emit.
+
+And he got this particular
+material that he was studying,
+
+radium bromide from his good
+friend, Marie Curie, who,
+
+obviously, also was a leader,
+really the leader in figuring
+
+out much of how radioactive
+materials work.
+
+She has two Nobel Prizes
+for her work
+
+in radioactive materials.
+
+And something that maybe many
+of you think, which I know I
+
+always think when I hear about
+radioactivity studies in the
+
+early 1900's, is oh, my gosh,
+this sounds really dangerous,
+
+right, they're using radium
+bromide, and this is pretty
+
+dangerous radioactive
+material.
+
+So, for those of you that don't
+know radium is extremely
+
+radioactive, even in the range
+of radioactivity, and one of
+
+the major problems with it is
+that if it does get in your
+
+body, the radium is treated
+as calcium in your body.
+
+So, you can imagine what happens
+as it gets deposited
+
+into your bones, which is not
+the ideal situation after a
+
+long day in the lab.
+
+So, this is really a pretty
+dangerous situation that's
+
+always interesting
+to point out.
+
+He got this from Marie Curie --
+you can imagine they used
+
+the postal service, I'm not sure
+how else they would have
+
+transferred it to each other.
+
+So, it really brings
+up some issues.
+
+The first thing I did when I
+heard that is actually look up
+
+to see how, in fact, Ernest
+Rutherford did die in 1937,
+
+and you'll be happy to know,
+it actually wasn't from
+
+radiation poisoning or from bone
+cancer, so that's really
+
+good that that worked out okay
+for him, and that he did get
+
+to, sort of safely, at least
+end his life before the
+
+radiation ended it.
+
+But it's really interesting
+the studies that he did do
+
+with radium bromide, and he was
+
+studying the alpha particles.
+
+And what was known about alpha
+particles at the time is that
+
+they were these charged
+particles and that they were
+
+very heavy.
+
+Does anyone know more than what
+Rutherford knew at the
+
+time, what alpha particles
+actually are?
+
+Yeah, good.
+
+So, they're actually helium
+atoms, helium ions.
+
+And this wasn't really important
+for the studies, it
+
+didn't matter that didn't know
+what they are, but it's nice
+
+to kind of know now -- that we
+do know what they were using.
+
+And he was doing quite a
+few studies with them.
+
+One experiment that he was doing
+is detecting the number
+
+of particles that were being
+emitted by this radium bromide
+
+as a rate, so he would measure
+the number of particles per
+
+minute that the radium
+bromide was emitting.
+
+And what he used was a detector
+here, so he here
+
+could detect how many
+particles were
+
+hitting this detector.
+
+He had actually developed this
+detector with a postdoc by the
+
+name of Hans Geiger.
+
+Does that name ring a bell?
+
+STUDENT: Geiger counter.
+
+PROFESSOR: Um-hmm,
+a Geiger counter.
+
+So, this, in fact, is my very
+schematic representation of a
+
+Geiger counter.
+
+For those of you don't know what
+that is, it's simply an
+
+instrument that counts
+radioactive particles in the
+
+air, and now that you're at MIT,
+you'll all have a chance
+
+to see one first hand, if you're
+ever in any of the
+
+labs, especially in the
+chemistry or bio labs.
+
+As carefully as people work with
+radioactivity here, and
+
+using often much, much safer
+radioactive materials than
+
+radium bromide, and using them,
+and special hoods, and
+
+having special procedures,
+they still do a lot of
+
+checking with these Geiger
+counters to make sure
+
+everything's safe.
+
+You'll actually see a man
+walking around with one,
+
+sometimes in the halls, just
+kind of like this -- you hear
+
+that click, click, click.
+
+That's a good sound, it means
+low levels of radiation.
+
+He'll walk by your hood, so
+click by your hood --
+
+I always get a little nervous
+when he walked by my hood, I
+
+don't know why, I never worked
+with radioactive material.
+
+But I was convinced
+I'd hear the
+
+click-click-click-click-click,
+which is what tells you you're
+
+in trouble.
+
+So, I've never heard the
+click-click-click-click-click,
+
+and we might bring a Geiger
+counter in here some time
+
+later in the semester so we can
+check all of you out, and
+
+hopefully we won't hear any
+when we do that either.
+
+So, one thing that he discovered
+with this detector
+
+initially, and he was the first
+to discover this, is
+
+that radioactive material,
+including radium bromide, have
+
+a characteristic rate that they
+emit, radioactive decay.
+
+So basically they're decaying
+at a constant rate, which
+
+means, of course, that you can
+figure out how old things are
+
+by seeing how much
+they've decayed.
+
+So, he was really the first
+person to discover you could
+
+do this, which was used to make
+the first somewhat close
+
+approximation of the
+age of the earth.
+
+So that's a pretty exciting
+set of experiments he did.
+
+But one thing that he wanted
+to do specific to
+
+understanding the atom, and
+using these alpha particles,
+
+these heavy-charged particles,
+was to test if this Plum
+
+Pudding model actually fit
+what he could observe.
+
+So, what he did was he first
+recorded the count rate of
+
+radium bromide before it's going
+through any kind of a
+
+plum pudding atom, and he found
+that it had a count rate
+
+of 132,000 alpha particles per
+minute were being detected by
+
+this Geiger counter.
+
+He then set up a situation where
+he put a very, very thin
+
+piece of gold foil right in what
+would be in the stream of
+
+the alpha particles.
+
+So, it was only 10 to the
+negative, 9 meters thick, so
+
+about one nanometer, so that's
+really thin, it's thinner than
+
+a strand of hair.
+
+So you can imagine, we actually
+don't need to think
+
+of it as a piece of gold foil,
+it might be easier to think of
+
+it as a couple of
+layers of atoms.
+
+So basically he's trying to put
+some atoms in the way of
+
+the alpha particle.
+
+And what he would expect is if
+this Plum Pudding model is
+
+true, nothing's really going
+to happen to the particles,
+
+right, they should go straight
+through, because if they hit
+
+an electron, those
+are so small.
+
+We figured out the mass is so
+tiny that it shouldn't really
+
+deflect them very much.
+
+And, of course, all that's left
+is this positive pudding.
+
+So that's not going to
+do anything either.
+
+And what he found when he did
+this experiment, was that the
+
+count rate with still 132,000
+counts per minute.
+
+So, what he could conclude thus
+far was that this was
+
+really consistent with the
+Plum Pudding model.
+
+All of his heavily-charged alpha
+particles were going
+
+right through this thin
+layer of gold atoms.
+
+So, you might think that he
+would stop his experiments
+
+here, and maybe he would have,
+but as I mentioned, he did
+
+have a postdoc working with
+him by the name of Geiger.
+
+He also had an undergraduate, we
+could say maybe even a UROP
+
+working with him, and this was
+by the name of Marsden was the
+
+name of this UROP.
+
+And Rutherford realized, you
+know I have these two people
+
+that are very excited to work on
+this project, I don't need
+
+to spend time doing it.
+
+Maybe it's not the best way for
+me to spend time looking
+
+to see if I can find any
+bounced-back particles since
+
+all the particles are
+accounted for.
+
+But, you know, this
+undergraduate's very eager to
+
+do it, let's let
+him have a try.
+
+And something you might find in
+your UROP experience is you
+
+have a unique advantage as an
+undergraduate, which is that
+
+there's not a lot of pressure
+to actually make a huge
+
+discovery or necessarily
+accomplish a great amount.
+
+You have a little more pressure
+in grad school, but
+
+sometimes that means when
+you're an undergrad your
+
+advisor will decide to put you
+on projects that maybe when
+
+you look at them seem
+a little bit silly.
+
+So this project was, let's see
+if we can detect any alpha
+
+particles by making a detector
+that swings around.
+
+So, some people might say,
+why are we doing this?
+
+We know we started with a
+132,000 alpha particles.
+
+We detected a 132,000
+alpha particles.
+
+What are we even looking for?
+
+We have to build this whole new
+detector, is this really
+
+the best use of my time?
+
+As an undergrad, you don't have
+to worry about it, you're
+
+just worried about learning.
+
+You can take these big risks of
+time, and if at the end of
+
+the day there's nothing to
+detect, you still know how to
+
+build a detector.
+
+So, keep that in mind if
+you're not over-the-top
+
+excited about the prospects
+of some of your research.
+
+You might be surprised
+at what you find out.
+
+And this is exactly what
+happened with Marsden who
+
+discovered that when he shot
+the alpha particles at the
+
+gold foil, he detected something
+on his detector that
+
+click, click, click went
+a little bit faster.
+
+So, what he detected was that
+there were 20 alpha particles
+
+per minute.
+
+Does that sound significant?
+
+It depends, right?
+
+So hopefully, the first
+experiment he did, which I
+
+know that they certainly did
+do was maybe it's just
+
+background noise, right?
+
+So, they took away that gold
+foil and said is just the
+
+alpha particles hitting
+it some other way?
+
+And no, it wasn't.
+
+When he took away the gold
+foil, the count rate
+
+went down to zero.
+
+If he switched from gold to
+let's say iron, he also tried
+
+platinum, a number of different
+foils, he found that
+
+they count rate, it still was 20
+alpha particles per minute.
+
+So, this is an absolutely
+outstanding discovery, even
+
+though, if we think about it,
+what is the probability that
+
+this happened, how often
+did this happen?
+
+It actually almost happened
+not at all.
+
+We can figure out exactly what
+the probability of this
+
+backscattering was just by
+dividing the count rate of the
+
+number particle that were
+backscattered divided by the
+
+count rate of the incident
+particles.
+
+So essentially, we just
+have 20, and our 20
+
+is divided by 132,000.
+
+So, we end up with a not so
+large probability of 2 times
+
+10 to the negative 4.
+
+But still, we can't even
+overstate how exciting this
+
+discovery was.
+
+Rutherford, the advisor here,
+he had a lot of good things
+
+happen in his life,
+as I mentioned.
+
+He was the person responsible
+for being able to first date
+
+the age of our earth.
+
+That's a pretty nice thing.
+
+He was also married, he had a
+child, which I hear is very
+
+nice, very exciting, also.
+
+But yet, when he saw this one
+single experiment from this
+
+undergraduate, he described this
+as the most incredible
+
+event that had ever happened
+to him in his life.
+
+So, this was a pretty
+big deal.
+
+We won't tell his daughter.
+
+And he gave a very good analogy
+in saying, "It was
+
+almost as incredible as if you'd
+fired a 15 inch shell at
+
+a piece of tissue paper, and
+it came back and hit you."
+
+And that really illustrates
+what's happening here, because
+
+if we think of the Plum
+Pudding model, it's
+
+essentially this very thin film,
+right, there's nothing
+
+that should hit if we send alpha
+particles through it.
+
+But what we actually
+have is that
+
+something's bouncing back.
+
+So, what happened is Rutherford
+needed to come up
+
+with a new model for the atom
+with several interpretations
+
+that came out of these
+experiments, and some of these
+
+interpretations were that, of
+course, we now know that these
+
+gold atoms, they must be mostly
+empty, and the reason
+
+that we know that they must be
+mostly empty is because all
+
+but 20 of these 132,000
+particles
+
+went all the way through.
+
+So they weren't hitting
+anything, we're dealing with
+
+mostly empty space.
+
+But he also realized that when
+they did hit something, what
+
+they hit what unbelievably
+massive, but also that that
+
+mass was concentrated into this
+very, very small space.
+
+So eventually, this is what we
+have come to call the nucleus
+
+of an atom.
+
+And the nucleus name was used
+as an analogy to the nucleus
+
+of a cell, so in some ways that
+makes it easier to see
+
+the connection, but I think it
+can also be a little bit
+
+confusing for maybe 7th graders
+that are learning both
+
+at the same time, that this
+nucleus acts very different
+
+from a nucleus in a cell,
+although, of course, there
+
+many of them in the
+nucleus of a cell.
+
+There are some other things that
+Rutherford was able to
+
+figure out.
+
+One is the diameter of the
+nucleus, and that turns out to
+
+be 10 to the negative
+14 meters.
+
+If we think about the size of
+a typical cell -- excuse me,
+
+now I'm getting confused
+about nuclei.
+
+If we think of the size of a
+typical atom, we would say
+
+that would be about 10 to
+the negative 10 meters.
+
+So, we can see the diameter
+of a nucleus is absolutely
+
+smaller, really concentrating
+that mass into
+
+a very small space.
+
+So, you might be asking
+how did he
+
+actually figure that out?
+
+We'll do the calculation
+ourselves.
+
+In fact, we'll do the whole
+experiment ourselves, minus
+
+the radioactivity in just a
+minute, so we'll be able to
+
+answer that question for you.
+
+He also figured out that
+the charge of the
+
+nucleus was a plus ze.
+
+This makes sense intuitively as
+well, because z is just the
+
+atomic number.
+
+So, let's say we have an atomic
+number of 3, that means
+
+we have 3 electrons, so we
+better hope to get our neutral
+
+atom that we have a charge
+of plus 3 in the nucleus.
+
+So, I mentioned at the
+beginning, while he was
+
+working with this radium
+bromide, that I was very
+
+relieved to see that it did
+not kill him to do these
+
+experiments.
+
+However, I think I will share
+with you that the cause of his
+
+death was, in fact, related to
+his research here, even though
+
+it was a little more
+tangled up.
+
+So, what happened, of course,
+after he discovered the
+
+nucleus, not surprising, he won
+a Nobel Prize for this --
+
+I would hope that he would.
+
+And in addition to winning a
+Nobel Prize, he was also
+
+knighted, which was a nice
+bonus for someone born in
+
+England, that's a great thing
+to happen to them.
+
+The problem that he ran into is
+at some point a little bit
+
+later in his life, he had a
+hernia which was a pretty
+
+standard case, but what he
+was going to need was an
+
+operation on it.
+
+And the glitch came that at
+least at the time, if you were
+
+a knight, you could only be
+operated on by a doctor that
+
+was also titled.
+
+So, Rutherford had a little bit
+of waiting to do for that
+
+doctor to show up, and it turns
+out the wait was too
+
+long, and he actually passed
+away because he discovered the
+
+nucleus and got a Noble Prize
+and became knighted.
+
+So, it's still dangerous.
+
+If that opportunity comes up
+for you, maybe you want to
+
+check into the policies of how
+that works with the doctor
+
+situation now.
+
+Hopefully they've cleared
+it up a little bit.
+
+So, what we want to do now is
+see if we can understand how
+
+this backscattering
+experiment worked.
+
+So, we will do our own
+backscattering experiment.
+
+And we'll ask you to imagine
+a few things.
+
+First is that we have this mono
+layer of gold particles.
+
+So let's see if Professor
+Drennan is able
+
+to help us out here.
+
+Oh, great.
+
+So, that is her daughter, Sam
+that you see strapped to the
+
+chest, and Dr. Patti Christie
+helping us out here.
+
+All right.
+
+So, we'll move this up to the
+front in just a minute, but
+
+I'm going to explain how this
+experiment works, and we'll do
+
+the calculation first before
+the excitement breaks out.
+
+But I'm sure you can easily see
+how these styrofoam balls
+
+could, in fact, be a mono
+layer of gold nuclei.
+
+We have 266, as some of you
+might know who saw me counting
+
+ping-pong balls the other
+day in office hours.
+
+We have 266 ping-pong balls, and
+we need someone, hopefully
+
+you, to be some radioactive
+material that are going to be
+
+emitting these ping-pong
+balls.
+
+And when the time comes, in just
+a minute, I'll ask the
+
+TAs to come down and hand these
+out very quickly to you,
+
+so we can do this experiment.
+
+But first, let's go through how
+we're going to determine
+
+what Rutherford determined,
+which was he was interested in
+
+knowing, which we said
+what the diameter
+
+of the nuclei were.
+
+So, we're going to do the same
+thing and figure out the
+
+diameter of these styrofoam
+balls here, and we can do it
+
+by using the relationship
+of how many backscatter.
+
+So, if we think about the
+probability of backscattering,
+
+which is the exact same thing
+that we saw Rutherford
+
+calculate, using the 20
+divided by 132,000.
+
+But in our case, the probability
+of backscattering
+
+is going to be the number of
+balls that backscatter, and
+
+that's going to be divided
+by the total number
+
+of ping-pong balls.
+
+So, do you remember
+what that was?
+
+STUDENT: 266.
+
+PROFESSOR: 266.
+
+Good information retention.
+
+All right.
+
+So, we have the probability
+here.
+
+So, in terms of the number of
+balls scattered over the
+
+total, we can also relate the
+probability to the area of all
+
+of those nuclei divided
+by the total area that
+
+the atoms take up.
+
+Right, this makes a lot of
+sense, because if the entire
+
+atom was made up of nuclei,
+then we would have 100%
+
+probability of hitting one of
+these nuclei and having things
+
+bounce back.
+
+So, here we have the area of
+the nuclei we'll figure out
+
+adding those all together versus
+the space of all of the
+
+atoms put together.
+
+So, not only did Professor
+Sayer, who's in the Chemistry
+
+Department who put together this
+contraption for all of
+
+you, not only did she magnify
+the size of these gold nuclei,
+
+but she actually had to smoosh
+all of these atoms closer
+
+together then they normally
+would be.
+
+If, in fact, a gold nucleus was
+this size here, we would
+
+need to use another lecture hall
+in order to find a place
+
+to put this nucleus
+right here.
+
+This is a little bit of a
+tricky experiment, so we
+
+decided we'll just smoosh it all
+in, and we'll actually be
+
+able to account for it, because
+we'll take into
+
+account the area of all
+of those atoms.
+
+I think this board does not
+like to go by itself.
+
+All right.
+
+So we can figure out what that
+is, the area of all of the
+
+nuclei is going to be the number
+of nuclei times the
+
+area per nucleus, and we're
+going to talk about the
+
+cross-section here to
+keep it simple.
+
+And all of that is divided
+by the area of the
+
+atoms, which is 1 .
+
+39 meters squared, measuring
+that space there.
+
+So, the number of nuclei, if we
+were to sit and count these
+
+as well, is 119.
+
+So, we'll multiply that by just
+pi, r squared, to get
+
+that cross-section, and divide
+all of that by 1 .
+
+39 meters squared.
+
+So, what we have here is a
+relationship that can tell us
+
+what the probability of
+backscattering is, but what we
+
+want to pull out, since we can
+experimentally measure what
+
+the probability is, what we need
+to pull out is the radius
+
+or the diameter of these
+nuclei, so we can just,
+
+instead of solving for p, we can
+switch it around and solve
+
+for the radius.
+
+So, that's going to be equal to
+the probability raised to
+
+the 1/2 times 6 .
+
+098 times 10 to the
+negative 2 meters.
+
+So, actually, just for
+discussion sake, it makes a
+
+little more sense for us to talk
+about the diameter, so
+
+that's just twice the radius.
+
+So, once we figure out what
+our probability of
+
+backscattering is, we'll just
+raise that to the 1/2, and
+
+we'll multiply that by 12 .
+
+20 centimeters.
+
+All right.
+
+So now all we have to do is
+figure out this probability of
+
+backscattering.
+
+We know we need to divide by
+266, but what we need you to
+
+help us with is to figure out
+this top number here and see
+
+how many particles are
+going to backscatter.
+
+So, if the TAs can come up
+and quickly hand out
+
+1 particle to everyone.
+
+And a few people will need to
+throw 2, if you feel like you
+
+have particularly good aim.
+
+PROFESSOR: So, as you're getting
+your ping-pong balls
+
+-- do not throw them yet.
+
+Let me explain to you
+what constitutes
+
+a backscatter event.
+
+So, it'll be considered a
+backscatter event if your
+
+ping-pong ball hits
+one of the nuclei.
+
+It's not going to be a
+backscatter event if your
+
+ping-pong ball hits
+the frame or these
+
+strings, or the top part.
+
+So, in a few minutes, not now,
+we're going to ask you to
+
+stand up, and you can kind of
+come over more toward the
+
+center of the room if you want,
+and aim your ping-pong
+
+ball at the lattice here, follow
+the ping-pong ball with
+
+your eye, and discover, watching
+it, whether it's a
+
+backscatter -- it hits one of
+the nuclei and bounces back
+
+towards you, or if it goes
+through, and also if your
+
+ping-pong ball doesn't land
+anywhere in the vicinity of
+
+this at all, then keep
+that in mind.
+
+And then at the end of the
+experiment we'll ask you what
+
+happened to your ping-pong ball,
+and you'll let us know,
+
+and we can calculate the number
+of backscatter events.
+
+Are there any questions
+before we get started?
+
+Raise your hand if you don't
+if you don't have a
+
+ping-pong ball yet.
+
+Any questions before
+we get started?
+
+All right.
+
+So, we'll come around and
+get ping-pong balls
+
+to the rest of you.
+
+Those of you who have your
+ping-pong balls can now begin
+
+the experiment.
+
+[EXPERIMENTING]
+
+PROFESSOR: All right.
+
+Any last shots?
+
+There we go.
+
+All right.
+
+So, it looks like we were a
+little bit successful, I saw
+
+some backbouncing.
+
+We were going to have a clicker
+slide on how many
+
+bounced back, but it looks like
+we're having a little
+
+technical difficulty
+with that.
+
+So, what I'll ask is can you
+stand up if you had your
+
+particle bounce back?
+
+All right, so let's count
+how many we have here.
+
+So, 13 backscattered.
+
+TAs, if you can maybe pick up
+these ping-pong balls for me.
+
+I'm sure it would be very
+amusing if I fell, but I'd
+
+rather not.
+
+All right, so, we have
+13 divided by 266.
+
+All right, MIT students, who
+has a calculator on them?
+
+Actually, I should probably do
+it as well, so I know I'm
+
+hearing correctly.
+
+So, are you getting 0 .
+
+0489 or so?
+
+All right.
+
+So, we've got our probability.
+
+We can go ahead and plug that
+in, take the square root of
+
+it, multiply it by 12 .
+
+2.
+
+What are you getting
+for your diameters?
+
+Yup, that's what I got, too.
+
+All right.
+
+So, we have 2 .
+
+70 for our diameter, and
+that's in centimeters.
+
+So, we actually did a pretty
+good job here.
+
+It turns out that the diameter
+is actually 2 .
+
+5 centimeters.
+
+So, good job, experiment well
+done, plus we were not exposed
+
+to radioactivity, which
+is a bonus.
+
+So, this is exactly how
+Rutherford did discover that
+
+these particles were present
+and made this new model for
+
+the atom that we now know has
+both a nucleus, and we know
+
+the size, and also
+has electrons.
+
+So, to finish up today, we won't
+get through all of it.
+
+But the next thing we can
+actually talk about is now
+
+that we know we have an atom
+that has a nucleus, let's say
+
+somewhere in the center, and
+it has electrons around it,
+
+thinking on our most simple
+example, which is hydrogen, we
+
+have a nucleus and an electron
+that have to hang together in
+
+the atom in some way, and we
+need to think about well how
+
+can we describe how atoms
+behave, and specifically, how
+
+do we describe how any single
+atom stays together where the
+
+two are associated, but at
+the same time they don't
+
+immediately collapse
+into themselves.
+
+So, what we can do is try
+using the classical
+
+description of the atom and
+see where this takes us.
+
+So, if we think about the force
+that occurs between a
+
+positively and a negatively
+charged particle, what we have
+
+is essentially a Coulomb force,
+so we can describe this
+
+as a force of attraction.
+
+We can use the Coulomb force law
+to explain this where we
+
+can describe the force
+as a function of r.
+
+So, let's think about what
+we're saying here.
+
+We're describing the force
+that's holding these two
+
+particles together, and it's
+related to the charge of each
+
+of the particles, where e is
+the absolute value of an
+
+electron's charge.
+
+So, an electron has a charge of
+negative e, we've written
+
+here, and the nucleus has
+a charge of positive e.
+
+And then we have r, which is
+simply the distance between
+
+the two charges.
+
+And what we see is that the
+force is inversely related to
+
+the distance between
+the two charges.
+
+And we can simplify this
+expression as saying negative
+
+e squared over 4 pi, epsilon
+nought r squared.
+
+Epsilon nought is a constant,
+it's something you might see
+
+in physics as well.
+
+Essentially for our purposes
+here, you can just think of it
+
+as a conversion factor.
+
+What we need to do is get rid
+of the Coulomb tag that we
+
+have -- that's how we measure
+our electron charges --
+
+charge, and so we use this
+epsilon nought quite often,
+
+this permativity constant
+of a vacuum to make that
+
+conversion.
+
+And I'll just point out here
+also, this is a conversion
+
+factor you'll use quite
+frequently -- many of you,
+
+quite on accident, will memorize
+it as you use it over
+
+and over again.
+
+But I do want to point out
+that you don't have to
+
+memorize it for any exams in
+this class, we will give you a
+
+sheet that has all the needed
+constants that you're going to
+
+use on there, so save up that
+brain space for other
+
+information. ah
+
+So, we can use Coulomb's force
+law, and we can think about
+
+these different scenarios.
+
+So, when you come in on Monday,
+we're going to start
+
+off, you can think for the
+weekend -- you probably only
+
+need to think for a second about
+what happens when r goes
+
+to infinity, but that's where
+we'll start on Monday.
+
+And let me just suggest to all
+of you also, that you get
+
+those problem sets started
+this weekend.
+
+You should absolutely finish,
+at least through part a this
+
+weekend, and save part
+b for next week.
+
+So, have a great weekend.
\ No newline at end of file
diff --git a/l-tzjenXrvI.txt b/l-tzjenXrvI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c86966ffd829c4c84d955f286bf61d377dea141f
--- /dev/null
+++ b/l-tzjenXrvI.txt
@@ -0,0 +1,2399 @@
+PATRICK WINSTON: Many of you,
+maybe most of you, will never
+
+have to work another search
+problem by hand in your
+
+natural life.
+
+Others will want to
+take another run
+
+at it on the final.
+
+I've been much criticized
+for this way of doing
+
+grading in the class.
+
+But the way I look at it is that
+the relationship between
+
+students and instructors ought
+to be less adversarial than it
+
+used to be in the good old days
+when I was a student.
+
+I especially remember an
+examination we took--
+
+all of us took-- on Rayleigh
+scattering.
+
+That was 803, I think.
+
+And back in the old days, we
+had to take four physics
+
+courses, not just two.
+
+And we had to take four math
+courses, not just two.
+
+Back in the days when--
+
+well, I was going to
+say men were men.
+
+But most of us were
+men in those days.
+
+I think we only had 20
+women in our class.
+
+Anyway, we had a quiz on
+Rayleigh scattering.
+
+And I thought, well, this
+is pretty hard.
+
+And then I got my quiz back.
+
+26.
+
+I thought, well, I've
+been found out.
+
+I'm going to flunk out.
+
+My father will make me
+go to law school.
+
+I'll never attract
+anyone to marry.
+
+Horrible things will happen.
+
+Then the instructor announced
+the class average was 18.
+
+I was two standard deviations
+above that.
+
+They gave us the same exam
+two weeks later,
+
+and accounts vary.
+
+Some people say that the class
+average went down.
+
+Anyway, today we're going
+to study some stuff.
+
+We're going to study some
+stuff that will make it
+
+possible for you to understand
+how you can do that
+
+computation in just a couple
+of seconds, even with the
+
+delays introduced by
+the redrawing.
+
+Now this particular program--
+
+I'm not real sure and I don't
+have a proof, but I think it
+
+will take more than the lifetime
+of the universe to
+
+find a legitimate coloring of
+the continental United States.
+
+But by the end of the next
+class, you'll see how to do
+
+that lickety-split in just
+couple of seconds, even with
+
+the re-display delays.
+
+Now we could, of course,
+do this in two ways.
+
+One way is I could start off
+by saying, let C be a
+
+constraint satisfaction
+problem and just
+
+give you the result.
+
+And anybody can do that.
+
+That's great.
+
+And you needed to learn
+some stuff that way.
+
+But there are some things that
+you needed to learn, I think,
+
+a different way.
+
+And that different way involves
+my telling you the
+
+story of how it all
+came to be.
+
+This is a new field, pretty
+much, and therefore I know
+
+most of the people in it.
+
+And I know all of the people
+who did the work that I'm
+
+going to tell you about today.
+
+I'm going to tell you a little
+bit about the struggle for
+
+coming up with the ideas that
+led to one of the most
+
+powerful methods you'll learn
+about in the subject.
+
+It all has to do, originally,
+with an attempt to make a
+
+computer capable of seeing.
+
+And everybody said to
+themselves, well, let's start
+
+with seeing simple things,
+like children's blocks.
+
+And so Adolfo Guzman, a graduate
+student of Marvin
+
+Minsky's, was charged with the
+summer project, which led to
+
+his Ph.D. thesis, of writing a
+program that could look at a
+
+line drawing and determine
+how many objects
+
+are in the line drawing.
+
+So for example, there behind my
+outline is a line drawing.
+
+And you believe instantly that
+there are two objects there,
+
+even though in some deep
+sense, it's ambiguous.
+
+There are all sorts of ways
+that you could, through
+
+trickery, arrange something with
+even seven objects that
+
+look that way.
+
+But most people would say
+there are two objects.
+
+So Guzman set about the
+problem of figuring
+
+out how to do that.
+
+And then his work was followed
+by Dave Huffman.
+
+And his work was followed
+up by Dave Waltz.
+
+And his work was followed up by
+Jane [? Froyter ?], who's
+
+not listed there quite yet.
+
+And I want to tell you a little
+bit of story how that
+
+all happened.
+
+So Guzman took a lot
+of pictures.
+
+He went to Boston Baby, the
+precursor to Toys R Us,
+
+purchased a large block set on
+a government contract, and
+
+went about the business of
+taking a lot of pictures of
+
+them so he'd get a feel
+for the domain.
+
+And eventually he decided that
+he could build a program that
+
+could determine that there are
+two objects here by using the
+
+lines as a quanta of evidence
+about which faces belong
+
+together in an object.
+
+So he said, after studying these
+for a long time, that
+
+these drawings tend to have a
+lot of arrow-type junctions
+
+and a lot of fork-type
+junctions.
+
+And when you see an arrow, it's
+a little bit of evidence
+
+that the objects on either
+side of the shaft are the
+
+same-- the face on either side
+of the shaft belong to the
+
+same object.
+
+And over here, the fork-type
+junction suggests that
+
+pairwise, three pairs
+of faces seem to
+
+belong to the same object.
+
+So with that idea, he could come
+back to a drawing like
+
+this and start decorating it
+with these so-called links,
+
+these quanta of evidence
+that faces
+
+belong to the same object.
+
+And if I've done it right,
+you get something
+
+that looks like so.
+
+It's a little hard to
+see what's going on
+
+on the drawing itself.
+
+So let me number these.
+
+Now I have an
+easier-to-deal-with picture.
+
+There are two links between
+1 and 2 and 1 and 3.
+
+One link between 2 and 3.
+
+One between 2 and 4.
+
+Two here.
+
+Two here.
+
+And one each from
+all of these.
+
+So Guzman produces this evidence
+for how the problem
+
+ought to be solved and then he
+begins to think about various
+
+ways of using the evidence.
+
+So he could, and did, decide
+that one link is enough to
+
+presume that the faces belong
+to the same object.
+
+And you can see that that's
+a little bit too liberal.
+
+Because that says
+that the whole
+
+thing is just one object.
+
+So Guzman rejected the one-link
+theory and went to
+
+the two-link theory.
+
+And the two-link theory says,
+oh, well, let's see.
+
+If we insist that two links
+should be there before we are
+
+willing to decide that it's the
+same object, then these
+
+three faces are pulled together
+into one object.
+
+These three are pulled together
+into one object.
+
+But alas, 7 doesn't share two
+links with anything, so it's
+
+left dangling out there.
+
+So plainly, the two-link theory
+is too conservative.
+
+So that as you would soon
+discover in any [INAUDIBLE]
+
+project, would lead you to a
+third theory, which is two
+
+lengths repeated.
+
+So now that we've formed these
+super regions, we can come
+
+back and say we'll merge super
+regions if they're connected
+
+together by two or more links.
+
+So nothing new happens
+up here.
+
+But this super region
+is joined at 7
+
+by two or more links.
+
+So it pulls everything
+together like so.
+
+So that worked fine.
+
+Well, it didn't work fine.
+
+There were lots of examples
+of situations
+
+where it didn't work--
+
+in situations that were
+considered nonsensical by us
+
+humans because it seemed silly,
+the kind of conclusions
+
+that it reached.
+
+So when Guzman presented this
+work in his Ph.D. thesis
+
+defense, it's said--
+
+and who knows if it's true--
+but it's said that Marvin
+
+Minsky thought it was
+great work and we
+
+should make him a professor.
+
+It happens that Dave Huffman was
+also on the committee and
+
+said that it was ad hoc and the
+thesis should be rejected.
+
+So we had two polar opposites
+of impressions there.
+
+Dave Huffman, by the way--
+
+you've heard that name
+before, I imagine.
+
+It's the guy who invented
+Huffman coating as a term
+
+paper in a information theory
+course taught by Bob Fano.
+
+He got an A, they say.
+
+So Huffman didn't like it.
+
+He thought it was a little
+bit too ad hoc.
+
+It was too heuristic.
+
+It didn't take advantage
+of anything we
+
+might know about physics.
+
+And so people began to say,
+well, why does it work?
+
+And when does it not work?
+
+And that's just about the best
+question you can answer in a
+
+situation like this.
+
+And by playing with some more
+of Guzman's pictures and
+
+reflecting on them, it turned
+out that it worked because the
+
+world is full of three-face
+junctions.
+
+Or let me say three-face
+vertexes because they're out
+
+there in the world.
+
+We'll reserve the word junction
+for something else.
+
+And three-face vertexes
+generally project into either
+
+an arrow or a fork.
+
+So Guzman's whole program worked
+on the weak backward
+
+conclusion that if you see one
+of those, it probably came
+
+from one of these.
+
+So this is in the drawing.
+
+That's in the world.
+
+So by a process that's neither
+deduction or induction, but
+
+rather abduction, you see
+one of those guys.
+
+And you say, well, they often
+come from three-face vertexes
+
+in the world, so if you see one,
+it probably came from a
+
+three-face vertex
+in the world.
+
+That's abduction.
+
+So once Huffman saw all that,
+being a mathematician, he
+
+began to think about how one
+might develop a different and
+
+better theory.
+
+But we have to recognize that
+all this work started off with
+
+the efforts of Guzman, who
+was an experimentalist.
+
+And Huffman was a
+mathematician.
+
+So naturally, they approached
+the problem differently.
+
+So Huffman says, I'm not going
+to concern myself too much
+
+with the actual problem that
+Guzman was trying to solve.
+
+Rather, I'm going to work in a
+very simple world, which I can
+
+deal with mathematically.
+
+So he decided that he was going
+to work in a world which
+
+had several characteristics.
+
+Characteristic number one was
+that the world would be
+
+presented in general position.
+
+That is to say, no
+screw cases.
+
+So if you see a cube, it's
+going to look like this.
+
+And it's not going to
+look like this.
+
+So that's out.
+
+And this is in.
+
+And the idea here is that that's
+not general position,
+
+because if you perturb your
+point of view a little bit,
+
+you'll change those T junctions
+
+into forks and arrows.
+
+So we know it had to deal
+with those kinds of
+
+weird kinds of cases.
+
+So that's presumption
+number one.
+
+Presumption number two is that
+we're going to be dealing with
+
+a world that's trihedral.
+
+That means all vertexes out
+there are going to be formed
+
+from three planes.
+
+So you're going to have the
+intersection of three planes.
+
+So how many kinds of junctions
+can you see if the world is
+
+composed that way is the
+question that Huffman sent
+
+himself upon.
+
+The next assumption was that
+there are going to be four
+
+kinds of lines.
+
+See, Guzman only recognized
+two kinds of lines-- lines
+
+that have a length and lines
+that don't have a link.
+
+And they don't have very much to
+do with the physical world.
+
+So Huffman says, I want to get
+the constraint out of the
+
+physical world.
+
+So I'm going to deal with
+four kinds of lines--
+
+concave, convex, and boundary.
+
+So each of those kinds
+of lines is going to
+
+have its own notation.
+
+We'll call the convex lines
+plus, the concave lines minus,
+
+and a boundary lines are going
+to get an arrow on them,
+
+depending on which side
+of the object--
+
+which side you would see the
+object if you walk along the
+
+direction of this
+little arrow.
+
+STUDENT: Question.
+
+Which is concave and
+which is convex?
+
+You said something and you
+wrote the opposite.
+
+PATRICK WINSTON: Yeah, sorry.
+
+Thank you.
+
+So concave, convex,
+and boundary.
+
+Thank you.
+
+So this down here, that's
+a concave line.
+
+And that would get
+a minus label.
+
+Oh, I don't know.
+
+These lines you're seeing here,
+if there were stuff
+
+behind them instead of
+me, then all those
+
+would be convex lines.
+
+Many times you see
+a boundary line.
+
+For example, now you don't see
+both sides of that line down
+
+here at the bottom.
+
+So that's a boundary line.
+
+And the arrow would point in
+that direction, so as to keep
+
+the stuff of the object on the
+right as you walk along a kind
+
+of mathematical convention.
+
+So three kinds of lines,
+four kinds of labels.
+
+And there's some things
+left out.
+
+That's because Huffman wanted
+to keep his problem simple,
+
+something he could
+manage by hand.
+
+What's left out?
+
+Cracks are left out.
+
+Shadows are left out.
+
+There's a presumption that
+there's nothing of interest
+
+here with respect to that.
+
+So let's have a little
+vocabulary before I go on.
+
+And I'll try to stick to it.
+
+But there's the stuff out there,
+and that consists of
+
+vertexes and edges.
+
+And over here, on the
+blackboard, we'll have
+
+junctions and lines.
+
+And I'll try to stick
+to that vocabulary.
+
+All right?
+
+Yes, Christopher?
+
+STUDENT: Didn't you say there
+were four types of lines?
+
+PATRICK WINSTON: Yeah, there
+are four kinds of--
+
+the question is, didn't
+I say there were
+
+four kinds of lines?
+
+There are three kinds of lines,
+but since we can label
+
+a boundary line in
+either direction,
+
+we have four labels.
+
+OK?
+
+It depends on which side of the
+object the stuff is on.
+
+And that will be clear,
+I think, as
+
+soon as I do an example.
+
+So one, two, three
+assumptions.
+
+A little bit of vocabulary.
+
+So we have the possibility of
+making a complete catalog.
+
+This is so simple.
+
+We have the possibility of
+making a complete catalog of
+
+all the ways that lines can
+come together to form a
+
+junction with respect to
+these four labels.
+
+Now at first you might say, oh
+my god, that will take a
+
+couple of years.
+
+But maybe it won't take
+a couple of years.
+
+And in the end, to perhaps your
+surprise, you discover
+
+that there are only 18 ways to
+arrange the labels around a
+
+junction in this world.
+
+Everything else is excluded.
+
+If you have something that's not
+in the set we're going to
+
+produce now, it can't be built
+with trihedral vertexes.
+
+So I've listed up there six L's,
+five forks, four T's, and
+
+three arrows.
+
+Let's see if I can figure out
+why there are those 18 and
+
+nothing else.
+
+Well, if we have three vertexes
+coming together, that
+
+means there are eight
+octants, right?
+
+And the stuff of the object may
+fill 1, 2, 3, 4, 5, 6, 7
+
+or all eight octants.
+
+Now of course, if you
+fill all eight
+
+octants, there's no junction.
+
+So we don't consider
+that case.
+
+If we don't fill any the
+octants, there's no junction.
+
+There's no vertex.
+
+So we don't consider
+that case.
+
+But if just one of the eight
+octants is filled with stuff,
+
+then we can look at
+it from any of the
+
+seven remaining octants.
+
+So right now, you're looking
+at it from one of the seven
+
+remaining octants.
+
+And if I'm not mistaken,
+you're going to see a
+
+fork-style junction
+there, right?
+
+And you're going to see a
+fork-style junction in which
+
+all of the edges are convex.
+
+An unfortunate selection of
+names, because the linguists
+
+tell me that we index
+all of our words
+
+by the first forename.
+
+And those have the same
+first forename, so
+
+they're easily confused.
+
+So here's a fork-style
+junction.
+
+And we know that one way that's
+legitimate for the
+
+lines to come in is
+with four pluses.
+
+Now that's not the only
+way you can see that.
+
+And here's another way.
+
+There's an L-style
+junction, right?
+
+And both of those are
+boundary lines.
+
+And we want to draw the boundary
+line indicators on
+
+there so that if we walk along
+the arrows, the stuff of the
+
+object would be on the right.
+
+So I suppose, to make it easier
+to me do my drawing, I
+
+should look at it this way.
+
+And then I would say, well, that
+has to be a legitimate
+
+way of labeling a junction.
+
+Are there any more?
+
+Well, there's seven altogether,
+but many of them
+
+are the same.
+
+There is one more that's a
+little different, though.
+
+I can hold this guy
+up like so.
+
+And if I'm holding at the right
+angle for you, you see
+
+an arrow-style junction,
+right?
+
+Two boundaries, and the
+barb is convex.
+
+So in this particular
+case, I've got that.
+
+I've got that.
+
+And I've got a plus there.
+
+And that's there happen to be
+for the one octant filled with
+
+stuff case.
+
+I happen to be able to
+reverse this, though.
+
+And here's the seven octants
+filled case.
+
+So that tells us that it's
+possible to have a vertex out
+
+there in a space that when
+reduced to a junction on the
+
+board deserves three minus
+labels, because all of these
+
+that you're seeing
+now are concave.
+
+So another fork-style junction
+looks like so.
+
+And since there's only one
+octant to look at from, that
+
+completes our analysis of the
+seven octants filled case.
+
+Now we have a couple of other
+possibilities here.
+
+We might have five octants
+filled with stuff.
+
+So that means there are three
+octants that we can look from.
+
+So let's suppose that
+these little chalk
+
+pieces are little people.
+
+And they're looking at this
+junction down there, where
+
+this white object is fused
+with the table.
+
+I'm fusing it with the table
+because I want to consider it
+
+to be one object.
+
+We can view it from the three
+objects indicated by those
+
+three little chalk pieces.
+
+And ask ourselves, well, in the
+event that we look at it
+
+from those three places,
+what do we see?
+
+And if we look at it from the
+perspective of the piece of
+
+purple chalk--
+
+I'll have to walk around
+and be sure--
+
+looks like an arrow
+junction with two
+
+concaves and a convex.
+
+Did I get that right?
+
+So I'm looking at it from
+this perspective.
+
+It's an arrow.
+
+This is convex and these two
+are concave because I fused
+
+the paper box with the table.
+
+Looking at it from the
+perspective of this blue guy--
+
+let me rotate it so you can have
+a better understanding of
+
+the blue guy--
+
+it looks like a concave
+line and a boundary.
+
+So it's an L. And this
+one is a boundary.
+
+And that's concave.
+
+And by a kind of symmetry, we're
+also going to get that
+
+one from the other side, the
+third of the three octants.
+
+Well, we're off and running.
+
+But we still have an
+awful lot to go.
+
+And we could manage to deal with
+it by thinking about this
+
+object once again.
+
+But instead of this situation
+out here, to turn it around
+
+and look at this vertex.
+
+Think about the junctions
+that it can produce.
+
+I think I'll do that for you.
+
+Because you really have to play
+with this and move it
+
+around a little bit to see how
+things are going to look.
+
+So let me think about how that's
+going to work out.
+
+I know that one of the
+possibilities is going
+
+to look like so.
+
+I might as well not hide
+that from you.
+
+It's going to be what happens
+when there's a little man
+
+looking up at the junction.
+
+And this one's going
+to be minus.
+
+And now we've got two more
+that are just like that.
+
+Look like so.
+
+And you say, oops.
+
+You say, aren't those
+just a rotational
+
+variance of each other?
+
+And the answer is sure.
+
+I write them all down, because
+if you get a fork-style
+
+junction in space, there are
+three different ways it could
+
+be labeled.
+
+Depending on which of
+the lines you put
+
+the minus label on.
+
+So that takes care of that.
+
+And then there's one more of
+these fork-style junctions.
+
+And that's plus, plus, minus
+that derives from this case.
+
+And there appear to
+be three more of
+
+these L-style junctions.
+
+And they look like, let's
+see, plus, then plus.
+
+I'm having to think this
+through as I go.
+
+And then--
+
+and that's it.
+
+Well, what about the T's?
+
+Well, in this world, the only
+way you can get a T is if some
+
+object is obscuring
+another object.
+
+And if an object is obscuring
+a line, it can
+
+be any line at all.
+
+So that's why the four remaining
+ones are easy beyond
+
+description to label.
+
+And of course, the cross
+pieces of the T are all
+
+boundary lines, with the
+obscuring object on the right.
+
+Now let's see.
+
+We've taken care now of the one,
+three, five, and seven
+
+octants filled cases.
+
+What about two, four, and six?
+
+Well, it turns out you can have
+vertexes that are made
+
+that way too.
+
+But they will have more
+than three faces.
+
+They'll have six faces.
+
+They'll be like what happens
+when an object comes together
+
+at a point, like so.
+
+Like that.
+
+You can play with it a little
+bit and see that if you have
+
+two, four, or six objects filled
+with stuff, there are
+
+more than three faces.
+
+So we're going to
+ignore those.
+
+So our constraint is going to
+be a little more severe than
+
+would be suggested by the
+terminology Huffman uses.
+
+They're going to be trihedral
+all right, but they're also
+
+going to be three faces.
+
+So we went to a lot
+of work there.
+
+But what have we discovered?
+
+We've discovered that in this
+world, this is a complete,
+
+100% percent, nothing excluded,
+nothing else can be
+
+there, catalog of all possible
+ways the junctions can have
+
+line labels arranged
+around them.
+
+There's nothing else
+in this world.
+
+So that's a very powerful
+constraint.
+
+So now let's see what
+we can do with it.
+
+This example is usually more fun
+when the Red Sox are doing
+
+better, but they're not.
+
+Yet we'll use it any way.
+
+We're going to start
+with an object that
+
+looks like home plate.
+
+And I'll ask you the question.
+
+Can you build one of those?
+
+I don't know.
+
+Let's give it a shot.
+
+We're going to assume that
+this object is hanging,
+
+floating in space.
+
+So therefore, all of these lines
+around the boundary are
+
+boundary lines, like so.
+
+Now that gets us off to a good--
+it's just hanging in
+
+space, Christopher, all right?
+
+You look confused.
+
+It's just hanging in space so
+that all the lines around the
+
+edges are places where you see
+only one side has stuff on it.
+
+So that enables us to just
+quickly run around the
+
+periphery and put arrow labels
+on all those outside lines.
+
+Now we have a lot
+of arrow-style
+
+junctions on the boundary.
+
+That's commonly the case.
+
+So we can run over to our
+catalog of all possible
+
+labels, and we see that if we
+have an arrow with boundaries
+
+on its barbs, there's
+only one of those.
+
+So I know instantly that there
+must be a plus on the shaft.
+
+So we can come back here and
+take all these arrows here.
+
+And label them with plus
+lines on their shafts.
+
+Now a line can't change its
+nature along its length.
+
+So if it's a plus line on one
+end, it's going to be a plus
+
+line on the other end.
+
+All right?
+
+So what else can we do?
+
+Here deep inside is a
+fork-style junction.
+
+It's got convex markers on
+both of those two lines.
+
+So we go over to our catalog and
+say, what can we say about
+
+it, given that there are pluses
+on two of its lines?
+
+Whoop, that means that
+the third one has to
+
+be a plus as well.
+
+And now we're done.
+
+We've labeled everything.
+
+Except--
+
+look at this.
+
+What about that guy?
+
+There's an L-style junction
+with pluses on
+
+both of its two lines.
+
+Is there one of those
+in my catalog?
+
+No.
+
+Therefore, I haven't passed
+a necessary condition for
+
+constructability in the
+world that I've made.
+
+You can't make it.
+
+You can't construct it.
+
+So Huffman's ideas give us a
+way of testing something to
+
+see if it's not possible for
+it to be in this world.
+
+If it passes the test, does
+that mean it's possible?
+
+No.
+
+It's a necessary but not
+sufficient condition.
+
+On this one--
+
+blue-collar occupation--
+
+on this one, maybe it
+will help if we
+
+put in another line.
+
+For example, we could
+put a line like so.
+
+You feel better about it now?
+
+I don't know.
+
+Let's see.
+
+This has to be a plus for the
+same argument we used on
+
+several other arrows before.
+
+That gives us an arrow-style
+junction here with a plus on
+
+everything.
+
+Is there such a junction
+label?
+
+No.
+
+We lose.
+
+It doesn't help.
+
+You think you can make
+it, but you can't.
+
+STUDENT: You could actually
+construct it as
+
+a 3-D object, though.
+
+PATRICK WINSTON: He
+thinks you can
+
+construct it as a 3-D object.
+
+Let me show you the next
+example, Christopher.
+
+Consider this example.
+
+Can you make that?
+
+Your intuition is yes.
+
+So let's label it.
+
+Oh, I've already lost.
+
+We just boost that up a
+little bit to make the
+
+situation more clear.
+
+So already, I've got myself in
+a situation where I can't
+
+label that.
+
+But you feel like
+you can make it.
+
+So what's wrong?
+
+What's wrong is--
+
+what, Elliott?
+
+STUDENT: You have
+an obscured--
+
+or, we're presuming that we have
+an obscured [INAUDIBLE]
+
+alley from the upper-left corner
+to the [INAUDIBLE].
+
+PATRICK WINSTON: Putting a
+little interpretation on what
+
+Elliott has said.
+
+If you look at this situation
+back here, you get a
+
+four-faced junction there.
+
+So you can make it.
+
+But not with three faces.
+
+So some of these look like
+you could make it.
+
+But they can't be labeled
+because you need more than
+
+four faces at a junction.
+
+And we can carry that
+idea back here.
+
+You can make this OK.
+
+But this junction, you've got
+two in the back and two here.
+
+So it has four faces.
+
+Same idea.
+
+So that's Guzman's
+contribution.
+
+That's Huffman's contribution.
+
+Huffman was a mathematician.
+
+But we wanted to build robots
+back in those days.
+
+And neither one of these guys
+solved the problem of dealing
+
+with natural objects with
+shadows, with cracks, with
+
+more than trihedral vertexes
+in space, and
+
+what to do about that?
+
+Well, that was a problem that
+another graduate student,
+
+David Waltz, set
+about to solve.
+
+So Waltz decided that he would
+not be content unless he added
+
+cracks, shadows, non-trihedral
+vertexes.
+
+Uh--
+
+yeah, non-trihedral vertexes.
+
+And light.
+
+These considerations led
+Waltz to go from
+
+four labels to 50-plus.
+
+Because he had to pack a lot
+of information into each of
+
+the labels he put on a line.
+
+What kind of light
+was on the right?
+
+What kind of light
+was on the left?
+
+Maybe it's a crack.
+
+Maybe it's a crack that--
+
+all sorts of considerations.
+
+Here we had 18 ways that
+lines can come
+
+together around junctions.
+
+That went to thousands of
+junctions in Waltz's world.
+
+So here's Guzman.
+
+He writes a program that
+sort of works.
+
+Down below, we have Huffman.
+
+Huffman, who has a theory but
+solves the wrong problem.
+
+So here comes Waltz, and he's
+trying to solve the right
+
+problem with a satisfying
+theory that has a
+
+generalizable principle.
+
+So when we get all through
+this, we'll talk about
+
+criteria for success.
+
+And we'll conclude that to
+have a really successful
+
+thing, you need a problem,
+to start with.
+
+You need a method that works.
+
+And you have to show
+that it works
+
+because of some principal.
+
+So Guzman had the problem and
+something that worked.
+
+Huffman had a method which
+worked on the wrong problem.
+
+And it's left to Waltz to
+bring it all together.
+
+So Waltz does all this work.
+
+And now he has, instead at 18
+labels, he has thousands.
+
+Instead of four-line labels,
+he has more than 50.
+
+So naturally, it becomes
+difficult to
+
+work these by hand.
+
+We were able to work those
+Huffman examples by hand.
+
+We started with labeling
+everything on the boundary and
+
+worked our way in.
+
+There's no particular
+method there.
+
+It was just easy to work
+out the puzzle.
+
+But poor Waltz, he didn't
+have that luxury.
+
+So he might have, in a typical
+scene, he might have tens or
+
+even hundreds of junctions to
+label and no easy way of
+
+dealing with it.
+
+So naturally writes himself a
+depth-first search program.
+
+So here is vertex, or rather
+junction number 1.
+
+There are many choices for which
+label can be used on it.
+
+And for each of those choices,
+whatever he's decided junction
+
+number 2 is has its own suite
+of possibilities.
+
+And so it becomes a
+simple depth-first
+
+search problem, right?
+
+So in actuality, as
+soon as Waltz--
+
+he was my office mate
+at the time.
+
+I can tell you this
+for a fact.
+
+As soon as he wrote this
+program, he kept looking over
+
+at the computer--
+
+they were big in those days.
+
+They all had lights.
+
+So you looked over at the
+computer to see if the lights
+
+were still blinking.
+
+Because he'd start this
+depth-first search program up
+
+and nothing would happen.
+
+He thought the computer
+had crashed.
+
+Nothing happened.
+
+Why did nothing happen?
+
+Because the search base is
+exponential and much too big
+
+for an ordinary computer,
+or maybe
+
+even an ordinary universe.
+
+So Waltz has to do
+something else.
+
+He has to come up with a new
+method for using all these
+
+labels that he's--
+
+after about a year and a half's
+worth of hard work,
+
+with lots of paper on his
+desk in little blocks.
+
+After year and a half of hard
+work getting all these
+
+junction labels figured out, he
+then has to come up with a
+
+method for figuring out
+how to use them.
+
+And so we don't know whether
+to think his biggest
+
+contribution was that label
+set or his method.
+
+And probably both deserve
+about equal billing.
+
+Oh, I don't know how to explain
+what Waltz did.
+
+Well, one way is to
+do an example.
+
+And I think I will hazard
+an example.
+
+Let's see.
+
+Let me find some space.
+
+I think I'm reduced to
+going over here.
+
+But that will be convenient,
+since the
+
+line labels are here.
+
+Here's my example.
+
+And you say, how can I give you
+just part of a picture?
+
+Well, you can assume
+I'm looking at
+
+this through a window.
+
+So the edge of the window form
+boundary lines, and they exert
+
+no constraint whatsoever
+on what's behind them.
+
+So this is a legitimate
+drawing to
+
+have to think about.
+
+By the way, is this ambiguous?
+
+Or do you get a firm sense
+that there's a unique
+
+interpretation of
+all those lines?
+
+I think there's a unique
+interpretation
+
+of all those lines.
+
+What I'm going to do is I'm
+actually going to solve this
+
+problem using Huffman's labels
+but Waltz's method.
+
+Because I can't simulate on the
+blackboard something with
+
+50 line types and thousands
+of line junctions.
+
+So I'm going to use
+Huffman's set to
+
+demonstrate Waltz's algorithm.
+
+So Waltz's algorithm involves
+starting out by plopping on
+
+some junction all of the
+possible labels that the
+
+answer has to be drawn from.
+
+So let me number these in the
+order that we're going to
+
+visit them.
+
+Like so.
+
+And so far, I've just put down
+the three fork options that
+
+are resident on that
+first junction.
+
+And I have to take note of
+exactly what they do with the
+
+lines that come out
+of the junction.
+
+So let's see.
+
+I'll just copy them down.
+
+One possibility is this one.
+
+Another possibility
+is this one.
+
+And another possibility
+is plus, plus, minus.
+
+Oops, I've got plus, plus.
+
+No, that's right.
+
+So that right so far?
+
+All I've done is copy
+the junction
+
+labelings from my library.
+
+And at this point, Waltz's
+algorithm says there's nothing
+
+else to do but go on to
+junction number two.
+
+And unfortunately, sadly, there
+are lots of labelings
+
+that have to be considered
+on junction number 2.
+
+Six of them.
+
+1, 2, 3, 4, 5, 6.
+
+So one of them looks
+like that.
+
+Another one looks like that.
+
+One of them is plus
+here, arrow in.
+
+Another one is plus
+here, arrow out.
+
+Another one is minus
+here, arrow down.
+
+And minus here, arrow up.
+
+I think I've copied
+those all right.
+
+But now, having copied those
+down, Waltz's algorithm looks
+
+around at the neighboring
+junctions and says, are any of
+
+the things that I just placed on
+junction two disallowed by
+
+what I've already placed on
+a neighboring junction?
+
+So it looks over here
+in step number two.
+
+And it sees that these three
+arrows require the line that
+
+joins junctions 1 and 2 to
+be either minus or plus.
+
+So of the six possibilities, I
+can only keep the ones that
+
+are likewise content to put
+a plus on that line
+
+that joins the two.
+
+So that means that the influence
+flowing from
+
+junction 1 eliminates that
+one, eliminates that one,
+
+eliminates that one, and
+eliminates that one.
+
+So half of them are gone.
+
+All the ones that try to put a
+boundary line on that line
+
+between 1 and 2 are
+disallowed.
+
+All right?
+
+Now likewise, we could say,
+well, of the remaining ones,
+
+do they restrict what I
+can do at junction 1?
+
+So let's see.
+
+Here's a minus.
+
+And here's a plus.
+
+So all these possibilities over
+here are still alive.
+
+So now, continuing on, we have
+to see what we can do at
+
+junction 3.
+
+These are arrow labels again.
+
+So we have to copy exactly
+the same labels
+
+set as we had before.
+
+And now we look down at junction
+2 and say, well, what
+
+does that tell me about the
+three that I've just placed?
+
+If we look up from junction
+2 to see what kind of
+
+constraints it puts on here,
+we have this one alive and
+
+this one alive.
+
+I guess we've eliminated
+four of the six.
+
+So we have these two alive.
+
+And they both but
+boundary lines--
+
+I think I must have had this
+boundary line wrong, right?
+
+No, that's right.
+
+Oh yes, I see.
+
+Plus.
+
+This one goes--
+
+hang on a second.
+
+You let me do something wrong.
+
+So plus is out.
+
+And that must be
+one that goes--
+
+this minus goes up.
+
+Oh, yes.
+
+I'm too hasty and uncertain
+about what I was doing.
+
+So let's see.
+
+This guy has a boundary
+going down.
+
+And this guy has a boundary
+going up.
+
+All of the others have
+been eliminated.
+
+So that means that something
+that tries to put a concave
+
+line there is gone.
+
+And something that tries to put
+a plus line there is gone.
+
+So the influence flowing up in
+this direction in the third
+
+step eliminates that guy and
+eliminates that guy, leaving
+
+only this guy.
+
+But now, the thing I was worried
+about is you have to
+
+also at this point go down to
+2 and see if there's any
+
+further constraint on what can
+survive down there, based on
+
+what has happened over
+here at junction 3.
+
+Now let's see.
+
+This one goes up, which is
+compatible with a survivor.
+
+But this one goes down,
+which is not
+
+compatible with a survivor.
+
+So when I bring this down in
+step three, this guy is
+
+eliminated.
+
+So now I'm down to just one
+interpretation for what can be
+
+going on at vertex number 2.
+
+And one interpretation
+for vertex number 3.
+
+Now let's see.
+
+This can propagate.
+
+So now that I've made a change
+on vertex number 2, I have to
+
+also see if that causes a change
+at vertex number 1.
+
+So it's propagating through.
+
+And now I can see that the only
+possibility here is a
+
+minus, the label that's coming
+down from our survivor.
+
+So that eliminates these two.
+
+Whew!
+
+It's hard to do this by hand,
+but I've got three of the four
+
+things labeled.
+
+And even with just three of the
+four labeled, I'm down to
+
+a single interpretation for all
+of the junctions and the
+
+lines between them.
+
+So there's one left.
+
+We have to deal with
+that fork vertex.
+
+We better deal with it, because
+for all we know, this
+
+is not a legal drawing
+in this world.
+
+We have five fork vertexes
+to place.
+
+But you know what?
+
+I don't have to draw much here,
+because I know this is
+
+forced to be a plus now.
+
+And this is forced
+to be a plus now.
+
+And there's only one fork
+vertex with any
+
+pluses on it at all.
+
+So now I can come through and
+say, well, the only possible
+
+survivor is this one.
+
+These are gone.
+
+And now I have an
+interpretation
+
+for all of the junctions.
+
+And I see that the winners
+are this one.
+
+And this one.
+
+And this one.
+
+And this one.
+
+So I've got a unique
+interpretation.
+
+This line is convex.
+
+This one is concave.
+
+This is a boundary.
+
+That's a boundary.
+
+And this line is convex,
+and that's convex.
+
+Now that's a lot of work.
+
+So I better check and make
+sure I got it right.
+
+You'd like to see this
+demonstrated to make sure I
+
+haven't made a mistake.
+
+I'm sure of that.
+
+Let's see.
+
+That it?
+
+So each of the places where a
+line is obscured has four
+
+possibilities, labeled E. The
+arrow junctions are labeled A.
+
+The forks-- there are five of
+them-- at the fork junction 5.
+
+So let's just step through here
+and see what happens.
+
+Boom.
+
+I've got it.
+
+I did do it right.
+
+So let's try some more.
+
+What do you think will
+happen with this one?
+
+Unique solution?
+
+It stopped.
+
+Bug in my program?
+
+Unthinkable.
+
+What's happened?
+
+It is genuinely ambiguous.
+
+It can be something hanging
+down from the ceiling.
+
+Or it could be something that
+we can think of as a step
+
+going up from left to right.
+
+Let's look at something
+more complicated.
+
+You think it'll work?
+
+Not enough constraint for us
+to figure that one out.
+
+It's equally ambiguous, but a
+little bit larger example.
+
+What about this one?
+
+Yeah, but the stuff is creeping
+up from the lower
+
+left up to the upper right.
+
+Yeah, bingo.
+
+It worked.
+
+It's unambiguous.
+
+It's variation on the same
+theme we had before.
+
+But let me, just for fun, take
+these two lines out.
+
+What do you think
+will happen now?
+
+Seems to be doing just fine
+until it hits the upper
+
+right-hand corner and discovers
+
+it can't label stuff.
+
+So it propagates back down.
+
+And what looked OK in
+the lower left is
+
+no good after all.
+
+So these results are kind of
+consistent with what we humans
+
+do when we look at these
+kinds of things.
+
+So it's very likely that we,
+in our heads, do have some
+
+constraint propagation
+apparatus
+
+that we use in vision.
+
+But putting that aside, we can
+think about other kinds of
+
+intelligence different from
+human, that might use this
+
+kind of mechanism to solve
+problems that involve a lot of
+
+constraint in finding
+a solution.
+
+So here, we saw the constraint
+propagation activity at work
+
+on line drawing analysis.
+
+But next time, what we're going
+do is we're going to see
+
+at work in map coloring.
+
+And who cares about
+map coloring?
+
+People who do scheduling,
+because that turns out to be
+
+the same problem.
\ No newline at end of file
diff --git a/lo-5afXPHx0.txt b/lo-5afXPHx0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5534c7dff75b6ea3f48f1cdd8614ad1d01dad9df
--- /dev/null
+++ b/lo-5afXPHx0.txt
@@ -0,0 +1,3723 @@
+align:start position:0%
+ 
+so now that we've
+
+ align:start position:0%
+so now that we've
+ 
+
+ align:start position:0%
+so now that we've
+discussed prevalence and risk scenarios
+
+ align:start position:0%
+discussed prevalence and risk scenarios
+ 
+
+ align:start position:0%
+discussed prevalence and risk scenarios
+we come to a very important topic which
+
+ align:start position:0%
+we come to a very important topic which
+ 
+
+ align:start position:0%
+we come to a very important topic which
+is when should you impose the guideline
+
+ align:start position:0%
+is when should you impose the guideline
+ 
+
+ align:start position:0%
+is when should you impose the guideline
+obviously when the the epidemic
+
+ align:start position:0%
+obviously when the the epidemic
+ 
+
+ align:start position:0%
+obviously when the the epidemic
+is raging at a very high rate is feels
+
+ align:start position:0%
+is raging at a very high rate is feels
+ 
+
+ align:start position:0%
+is raging at a very high rate is feels
+out of control
+
+ align:start position:0%
+out of control
+ 
+
+ align:start position:0%
+out of control
+it's spreading we want to impose the
+
+ align:start position:0%
+it's spreading we want to impose the
+ 
+
+ align:start position:0%
+it's spreading we want to impose the
+guideline that we've discussed which
+
+ align:start position:0%
+guideline that we've discussed which
+ 
+
+ align:start position:0%
+guideline that we've discussed which
+limits the indoor reproductive number
+
+ align:start position:0%
+limits the indoor reproductive number
+ 
+
+ align:start position:0%
+limits the indoor reproductive number
+for each space within some tolerance and
+
+ align:start position:0%
+for each space within some tolerance and
+ 
+
+ align:start position:0%
+for each space within some tolerance and
+that would for example give us some
+
+ align:start position:0%
+that would for example give us some
+ 
+
+ align:start position:0%
+that would for example give us some
+number n1
+
+ align:start position:0%
+number n1
+ 
+
+ align:start position:0%
+number n1
+from the safety guideline r in less than
+
+ align:start position:0%
+from the safety guideline r in less than
+ 
+
+ align:start position:0%
+from the safety guideline r in less than
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+which is going to be smaller than the
+
+ align:start position:0%
+which is going to be smaller than the
+ 
+
+ align:start position:0%
+which is going to be smaller than the
+normal occupancy of that room for a
+
+ align:start position:0%
+normal occupancy of that room for a
+ 
+
+ align:start position:0%
+normal occupancy of that room for a
+given time and all the other factors
+
+ align:start position:0%
+given time and all the other factors
+ 
+
+ align:start position:0%
+given time and all the other factors
+that we've been discussing
+
+ align:start position:0%
+that we've been discussing
+ 
+
+ align:start position:0%
+that we've been discussing
+but what happens as the prevalence of
+
+ align:start position:0%
+but what happens as the prevalence of
+ 
+
+ align:start position:0%
+but what happens as the prevalence of
+infection goes down generically there
+
+ align:start position:0%
+infection goes down generically there
+ 
+
+ align:start position:0%
+infection goes down generically there
+must be some sort of curve like this
+
+ align:start position:0%
+must be some sort of curve like this
+ 
+
+ align:start position:0%
+must be some sort of curve like this
+and we'd like to understand what is the
+
+ align:start position:0%
+and we'd like to understand what is the
+ 
+
+ align:start position:0%
+and we'd like to understand what is the
+simplest reasonable model we can come up
+
+ align:start position:0%
+simplest reasonable model we can come up
+ 
+
+ align:start position:0%
+simplest reasonable model we can come up
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+that can tell us how to relax the
+
+ align:start position:0%
+that can tell us how to relax the
+ 
+
+ align:start position:0%
+that can tell us how to relax the
+approximation so for example let's think
+
+ align:start position:0%
+approximation so for example let's think
+ 
+
+ align:start position:0%
+approximation so for example let's think
+of a school or a business
+
+ align:start position:0%
+of a school or a business
+ 
+
+ align:start position:0%
+of a school or a business
+where we typically have this a lot of
+
+ align:start position:0%
+where we typically have this a lot of
+ 
+
+ align:start position:0%
+where we typically have this a lot of
+the same people there every day
+
+ align:start position:0%
+the same people there every day
+ 
+
+ align:start position:0%
+the same people there every day
+but some others are coming and going or
+
+ align:start position:0%
+but some others are coming and going or
+ 
+
+ align:start position:0%
+but some others are coming and going or
+maybe going home and getting infected
+
+ align:start position:0%
+maybe going home and getting infected
+ 
+
+ align:start position:0%
+maybe going home and getting infected
+and coming in so the rate of infection
+
+ align:start position:0%
+and coming in so the rate of infection
+ 
+
+ align:start position:0%
+and coming in so the rate of infection
+is is low so we expect typically the
+
+ align:start position:0%
+is is low so we expect typically the
+ 
+
+ align:start position:0%
+is is low so we expect typically the
+number of infected people is zero or
+
+ align:start position:0%
+number of infected people is zero or
+ 
+
+ align:start position:0%
+number of infected people is zero or
+occasionally one
+
+ align:start position:0%
+occasionally one
+ 
+
+ align:start position:0%
+occasionally one
+and as the prevalence goes down then you
+
+ align:start position:0%
+and as the prevalence goes down then you
+ 
+
+ align:start position:0%
+and as the prevalence goes down then you
+know we
+
+ align:start position:0%
+know we
+ 
+
+ align:start position:0%
+know we
+start to see uh you know that the
+
+ align:start position:0%
+start to see uh you know that the
+ 
+
+ align:start position:0%
+start to see uh you know that the
+situation is getting safer and safer
+
+ align:start position:0%
+situation is getting safer and safer
+ 
+
+ align:start position:0%
+situation is getting safer and safer
+so the certain point p1 where we start
+
+ align:start position:0%
+so the certain point p1 where we start
+ 
+
+ align:start position:0%
+so the certain point p1 where we start
+to say you know what we can actually
+
+ align:start position:0%
+to say you know what we can actually
+ 
+
+ align:start position:0%
+to say you know what we can actually
+increase the occupancy of the space with
+
+ align:start position:0%
+increase the occupancy of the space with
+ 
+
+ align:start position:0%
+increase the occupancy of the space with
+everything else held fixed
+
+ align:start position:0%
+everything else held fixed
+ 
+
+ align:start position:0%
+everything else held fixed
+while still wearing masks and then we
+
+ align:start position:0%
+while still wearing masks and then we
+ 
+
+ align:start position:0%
+while still wearing masks and then we
+hit the normal occupancy and you might
+
+ align:start position:0%
+hit the normal occupancy and you might
+ 
+
+ align:start position:0%
+hit the normal occupancy and you might
+call that kind of the new normal where
+
+ align:start position:0%
+call that kind of the new normal where
+ 
+
+ align:start position:0%
+call that kind of the new normal where
+we're going about our business the room
+
+ align:start position:0%
+we're going about our business the room
+ 
+
+ align:start position:0%
+we're going about our business the room
+is filled with the typical number of
+
+ align:start position:0%
+is filled with the typical number of
+ 
+
+ align:start position:0%
+is filled with the typical number of
+people let's say the classroom is back
+
+ align:start position:0%
+people let's say the classroom is back
+ 
+
+ align:start position:0%
+people let's say the classroom is back
+to its normal size we don't have any
+
+ align:start position:0%
+to its normal size we don't have any
+ 
+
+ align:start position:0%
+to its normal size we don't have any
+remote teaching going on
+
+ align:start position:0%
+remote teaching going on
+ 
+
+ align:start position:0%
+remote teaching going on
+but we're wearing masks or taking other
+
+ align:start position:0%
+but we're wearing masks or taking other
+ 
+
+ align:start position:0%
+but we're wearing masks or taking other
+factor factors into accounts such as
+
+ align:start position:0%
+factor factors into accounts such as
+ 
+
+ align:start position:0%
+factor factors into accounts such as
+higher ventilation rates let's say
+
+ align:start position:0%
+higher ventilation rates let's say
+ 
+
+ align:start position:0%
+higher ventilation rates let's say
+open windows but then we continue
+
+ align:start position:0%
+open windows but then we continue
+ 
+
+ align:start position:0%
+open windows but then we continue
+lowering the prevalence there's a
+
+ align:start position:0%
+lowering the prevalence there's a
+ 
+
+ align:start position:0%
+lowering the prevalence there's a
+certain point where we get rid of those
+
+ align:start position:0%
+certain point where we get rid of those
+ 
+
+ align:start position:0%
+certain point where we get rid of those
+other precautions
+
+ align:start position:0%
+other precautions
+ 
+
+ align:start position:0%
+other precautions
+so extra opening of windows or more
+
+ align:start position:0%
+so extra opening of windows or more
+ 
+
+ align:start position:0%
+so extra opening of windows or more
+importantly the dominant effect is the
+
+ align:start position:0%
+importantly the dominant effect is the
+ 
+
+ align:start position:0%
+importantly the dominant effect is the
+removal of the mass because we know
+
+ align:start position:0%
+removal of the mass because we know
+ 
+
+ align:start position:0%
+removal of the mass because we know
+that's a significant factor
+
+ align:start position:0%
+that's a significant factor
+ 
+
+ align:start position:0%
+that's a significant factor
+and then you might call that back to the
+
+ align:start position:0%
+and then you might call that back to the
+ 
+
+ align:start position:0%
+and then you might call that back to the
+real normal actually not the new normal
+
+ align:start position:0%
+real normal actually not the new normal
+ 
+
+ align:start position:0%
+real normal actually not the new normal
+where we are back to full occupancy and
+
+ align:start position:0%
+where we are back to full occupancy and
+ 
+
+ align:start position:0%
+where we are back to full occupancy and
+really not taking any extra precautions
+
+ align:start position:0%
+really not taking any extra precautions
+ 
+
+ align:start position:0%
+really not taking any extra precautions
+that's going to happen at a rather low
+
+ align:start position:0%
+that's going to happen at a rather low
+ 
+
+ align:start position:0%
+that's going to happen at a rather low
+prevalence but we hope that that time
+
+ align:start position:0%
+prevalence but we hope that that time
+ 
+
+ align:start position:0%
+prevalence but we hope that that time
+will eventually come
+
+ align:start position:0%
+will eventually come
+ 
+
+ align:start position:0%
+will eventually come
+and hopefully not so far in the future
+
+ align:start position:0%
+and hopefully not so far in the future
+ 
+
+ align:start position:0%
+and hopefully not so far in the future
+and i mentioned here a very important
+
+ align:start position:0%
+and i mentioned here a very important
+ 
+
+ align:start position:0%
+and i mentioned here a very important
+point we've not talked about yet in this
+
+ align:start position:0%
+point we've not talked about yet in this
+ 
+
+ align:start position:0%
+point we've not talked about yet in this
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+but we should keep in the back of our
+
+ align:start position:0%
+but we should keep in the back of our
+ 
+
+ align:start position:0%
+but we should keep in the back of our
+minds is when i talk about
+
+ align:start position:0%
+minds is when i talk about
+ 
+
+ align:start position:0%
+minds is when i talk about
+occupancy i'm really talking about the
+
+ align:start position:0%
+occupancy i'm really talking about the
+ 
+
+ align:start position:0%
+occupancy i'm really talking about the
+number of successful people we just saw
+
+ align:start position:0%
+number of successful people we just saw
+ 
+
+ align:start position:0%
+number of successful people we just saw
+that on the last couple boards
+
+ align:start position:0%
+that on the last couple boards
+ 
+
+ align:start position:0%
+that on the last couple boards
+but the number of susceptible people are
+
+ align:start position:0%
+but the number of susceptible people are
+ 
+
+ align:start position:0%
+but the number of susceptible people are
+really only those
+
+ align:start position:0%
+really only those
+ 
+
+ align:start position:0%
+really only those
+that are not immune to the disease
+
+ align:start position:0%
+that are not immune to the disease
+ 
+
+ align:start position:0%
+that are not immune to the disease
+for example by vaccination so
+
+ align:start position:0%
+for example by vaccination so
+ 
+
+ align:start position:0%
+for example by vaccination so
+as the vac as more and more people
+
+ align:start position:0%
+as the vac as more and more people
+ 
+
+ align:start position:0%
+as the vac as more and more people
+become vaccinated
+
+ align:start position:0%
+become vaccinated
+ 
+
+ align:start position:0%
+become vaccinated
+then this occupancy number might for
+
+ align:start position:0%
+then this occupancy number might for
+ 
+
+ align:start position:0%
+then this occupancy number might for
+example let's say as a typical
+
+ align:start position:0%
+example let's say as a typical
+ 
+
+ align:start position:0%
+example let's say as a typical
+opportunity of 25 people in a class
+
+ align:start position:0%
+opportunity of 25 people in a class
+ 
+
+ align:start position:0%
+opportunity of 25 people in a class
+as more and more people are vaccinated
+
+ align:start position:0%
+as more and more people are vaccinated
+ 
+
+ align:start position:0%
+as more and more people are vaccinated
+the number that we plug in this formula
+
+ align:start position:0%
+the number that we plug in this formula
+ 
+
+ align:start position:0%
+the number that we plug in this formula
+here might actually be lower
+
+ align:start position:0%
+here might actually be lower
+ 
+
+ align:start position:0%
+here might actually be lower
+when we adapt just make decisions
+
+ align:start position:0%
+when we adapt just make decisions
+ 
+
+ align:start position:0%
+when we adapt just make decisions
+because there are fewer and fewer
+
+ align:start position:0%
+because there are fewer and fewer
+ 
+
+ align:start position:0%
+because there are fewer and fewer
+susceptible people that are left so
+
+ align:start position:0%
+susceptible people that are left so
+ 
+
+ align:start position:0%
+susceptible people that are left so
+that's another very important factor to
+
+ align:start position:0%
+that's another very important factor to
+ 
+
+ align:start position:0%
+that's another very important factor to
+keep in mind
+
+ align:start position:0%
+keep in mind
+ 
+
+ align:start position:0%
+keep in mind
+of course also vaccination has the
+
+ align:start position:0%
+of course also vaccination has the
+ 
+
+ align:start position:0%
+of course also vaccination has the
+indirect effect of lowering the
+
+ align:start position:0%
+indirect effect of lowering the
+ 
+
+ align:start position:0%
+indirect effect of lowering the
+prevalence that is seen in the
+
+ align:start position:0%
+prevalence that is seen in the
+ 
+
+ align:start position:0%
+prevalence that is seen in the
+population as we start to stamp out the
+
+ align:start position:0%
+population as we start to stamp out the
+ 
+
+ align:start position:0%
+population as we start to stamp out the
+epidemic so we also have that effect
+
+ align:start position:0%
+epidemic so we also have that effect
+ 
+
+ align:start position:0%
+epidemic so we also have that effect
+so i won't talk about that any further
+
+ align:start position:0%
+so i won't talk about that any further
+ 
+
+ align:start position:0%
+so i won't talk about that any further
+now but come back to this calculation
+
+ align:start position:0%
+now but come back to this calculation
+ 
+
+ align:start position:0%
+now but come back to this calculation
+based on the risk scenario the second
+
+ align:start position:0%
+based on the risk scenario the second
+ 
+
+ align:start position:0%
+based on the risk scenario the second
+one that i talked about last time where
+
+ align:start position:0%
+one that i talked about last time where
+ 
+
+ align:start position:0%
+one that i talked about last time where
+we take into account
+
+ align:start position:0%
+we take into account
+ 
+
+ align:start position:0%
+we take into account
+prevalence so let's look at the three
+
+ align:start position:0%
+prevalence so let's look at the three
+ 
+
+ align:start position:0%
+prevalence so let's look at the three
+different cases here so the first one
+
+ align:start position:0%
+different cases here so the first one
+ 
+
+ align:start position:0%
+different cases here so the first one
+is where we have restricted occupancy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is where we've decided there's an
+
+ align:start position:0%
+this is where we've decided there's an
+ 
+
+ align:start position:0%
+this is where we've decided there's an
+n1
+
+ align:start position:0%
+n1
+ 
+
+ align:start position:0%
+n1
+which is epsilon over average beta
+
+ align:start position:0%
+which is epsilon over average beta
+ 
+
+ align:start position:0%
+which is epsilon over average beta
+tau so all the physical parameters are
+
+ align:start position:0%
+tau so all the physical parameters are
+ 
+
+ align:start position:0%
+tau so all the physical parameters are
+buried in there
+
+ align:start position:0%
+buried in there
+ 
+
+ align:start position:0%
+buried in there
+and this is going to be something less
+
+ align:start position:0%
+and this is going to be something less
+ 
+
+ align:start position:0%
+and this is going to be something less
+than the normal occupancy and 0.
+
+ align:start position:0%
+than the normal occupancy and 0.
+ 
+
+ align:start position:0%
+than the normal occupancy and 0.
+now what is the tau we want to think
+
+ align:start position:0%
+now what is the tau we want to think
+ 
+
+ align:start position:0%
+now what is the tau we want to think
+about well if we have a school or
+
+ align:start position:0%
+about well if we have a school or
+ 
+
+ align:start position:0%
+about well if we have a school or
+business
+
+ align:start position:0%
+business
+ 
+
+ align:start position:0%
+business
+this would be the cumulative time that
+
+ align:start position:0%
+this would be the cumulative time that
+ 
+
+ align:start position:0%
+this would be the cumulative time that
+people spend together
+
+ align:start position:0%
+people spend together
+ 
+
+ align:start position:0%
+people spend together
+to the point where the number of days
+
+ align:start position:0%
+to the point where the number of days
+ 
+
+ align:start position:0%
+to the point where the number of days
+they spend together is let's say on the
+
+ align:start position:0%
+they spend together is let's say on the
+ 
+
+ align:start position:0%
+they spend together is let's say on the
+order of a week
+
+ align:start position:0%
+order of a week
+ 
+
+ align:start position:0%
+order of a week
+would be a reasonable number to think
+
+ align:start position:0%
+would be a reasonable number to think
+ 
+
+ align:start position:0%
+would be a reasonable number to think
+about because
+
+ align:start position:0%
+about because
+ 
+
+ align:start position:0%
+about because
+if we write tau as sort of the hours
+
+ align:start position:0%
+if we write tau as sort of the hours
+ 
+
+ align:start position:0%
+if we write tau as sort of the hours
+typical hours per day
+
+ align:start position:0%
+typical hours per day
+ 
+
+ align:start position:0%
+typical hours per day
+times some kind of maximum number of
+
+ align:start position:0%
+times some kind of maximum number of
+ 
+
+ align:start position:0%
+times some kind of maximum number of
+days
+
+ align:start position:0%
+days
+ 
+
+ align:start position:0%
+days
+this maximum number of days could be set
+
+ align:start position:0%
+this maximum number of days could be set
+ 
+
+ align:start position:0%
+this maximum number of days could be set
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+for example the testing frequency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example here at mit we are testing
+
+ align:start position:0%
+for example here at mit we are testing
+ 
+
+ align:start position:0%
+for example here at mit we are testing
+our entire population
+
+ align:start position:0%
+our entire population
+ 
+
+ align:start position:0%
+our entire population
+at least once a week in order for anyone
+
+ align:start position:0%
+at least once a week in order for anyone
+ 
+
+ align:start position:0%
+at least once a week in order for anyone
+including myself to be admitting to the
+
+ align:start position:0%
+including myself to be admitting to the
+ 
+
+ align:start position:0%
+including myself to be admitting to the
+to the campus
+
+ align:start position:0%
+to the campus
+ 
+
+ align:start position:0%
+to the campus
+and so we are definitely testing within
+
+ align:start position:0%
+and so we are definitely testing within
+ 
+
+ align:start position:0%
+and so we are definitely testing within
+a week and catching new infections at
+
+ align:start position:0%
+a week and catching new infections at
+ 
+
+ align:start position:0%
+a week and catching new infections at
+that rate
+
+ align:start position:0%
+that rate
+ 
+
+ align:start position:0%
+that rate
+it could also be motivated by the
+
+ align:start position:0%
+it could also be motivated by the
+ 
+
+ align:start position:0%
+it could also be motivated by the
+incubation time
+
+ align:start position:0%
+incubation time
+ 
+
+ align:start position:0%
+incubation time
+which is the time to show symptoms and
+
+ align:start position:0%
+which is the time to show symptoms and
+ 
+
+ align:start position:0%
+which is the time to show symptoms and
+most people will remove themselves and
+
+ align:start position:0%
+most people will remove themselves and
+ 
+
+ align:start position:0%
+most people will remove themselves and
+we know that's around
+
+ align:start position:0%
+we know that's around
+ 
+
+ align:start position:0%
+we know that's around
+5.5 days as a typically reported values
+
+ align:start position:0%
+5.5 days as a typically reported values
+ 
+
+ align:start position:0%
+5.5 days as a typically reported values
+again on the order of a week
+
+ align:start position:0%
+again on the order of a week
+ 
+
+ align:start position:0%
+again on the order of a week
+and there's also of course other ways
+
+ align:start position:0%
+and there's also of course other ways
+ 
+
+ align:start position:0%
+and there's also of course other ways
+that people are removed or recut or they
+
+ align:start position:0%
+that people are removed or recut or they
+ 
+
+ align:start position:0%
+that people are removed or recut or they
+recover
+
+ align:start position:0%
+recover
+ 
+
+ align:start position:0%
+recover
+so as removal and recovery which is
+
+ align:start position:0%
+so as removal and recovery which is
+ 
+
+ align:start position:0%
+so as removal and recovery which is
+another way
+
+ align:start position:0%
+another way
+ 
+
+ align:start position:0%
+another way
+that if you start to go more than let's
+
+ align:start position:0%
+that if you start to go more than let's
+ 
+
+ align:start position:0%
+that if you start to go more than let's
+say two weeks we start to think
+
+ align:start position:0%
+say two weeks we start to think
+ 
+
+ align:start position:0%
+say two weeks we start to think
+an effective person that didn't get
+
+ align:start position:0%
+an effective person that didn't get
+ 
+
+ align:start position:0%
+an effective person that didn't get
+removed enough in the hospital has
+
+ align:start position:0%
+removed enough in the hospital has
+ 
+
+ align:start position:0%
+removed enough in the hospital has
+probably recovered
+
+ align:start position:0%
+probably recovered
+ 
+
+ align:start position:0%
+probably recovered
+so if we think of a certain number of
+
+ align:start position:0%
+so if we think of a certain number of
+ 
+
+ align:start position:0%
+so if we think of a certain number of
+days and hours per day that gives us a
+
+ align:start position:0%
+days and hours per day that gives us a
+ 
+
+ align:start position:0%
+days and hours per day that gives us a
+tau
+
+ align:start position:0%
+tau
+ 
+
+ align:start position:0%
+tau
+that is going to go into this formula
+
+ align:start position:0%
+that is going to go into this formula
+ 
+
+ align:start position:0%
+that is going to go into this formula
+and actually i should also mention that
+
+ align:start position:0%
+and actually i should also mention that
+ 
+
+ align:start position:0%
+and actually i should also mention that
+for simplicity here
+
+ align:start position:0%
+for simplicity here
+ 
+
+ align:start position:0%
+for simplicity here
+you know technically this should be n
+
+ align:start position:0%
+you know technically this should be n
+ 
+
+ align:start position:0%
+you know technically this should be n
+1 minus 1 and i can either include that
+
+ align:start position:0%
+1 minus 1 and i can either include that
+ 
+
+ align:start position:0%
+1 minus 1 and i can either include that
+or not when i do this calculation but
+
+ align:start position:0%
+or not when i do this calculation but
+ 
+
+ align:start position:0%
+or not when i do this calculation but
+i'm generally thinking
+
+ align:start position:0%
+i'm generally thinking
+ 
+
+ align:start position:0%
+i'm generally thinking
+of n one which is going to be you know
+
+ align:start position:0%
+of n one which is going to be you know
+ 
+
+ align:start position:0%
+of n one which is going to be you know
+bigger than one so think of like
+
+ align:start position:0%
+bigger than one so think of like
+ 
+
+ align:start position:0%
+bigger than one so think of like
+an occupancy of ten people in a
+
+ align:start position:0%
+an occupancy of ten people in a
+ 
+
+ align:start position:0%
+an occupancy of ten people in a
+classroom or something might be a limit
+
+ align:start position:0%
+classroom or something might be a limit
+ 
+
+ align:start position:0%
+classroom or something might be a limit
+uh that we would be interested in
+
+ align:start position:0%
+uh that we would be interested in
+ 
+
+ align:start position:0%
+uh that we would be interested in
+considering but certainly we can put the
+
+ align:start position:0%
+considering but certainly we can put the
+ 
+
+ align:start position:0%
+considering but certainly we can put the
+the one in there if we want to so now
+
+ align:start position:0%
+the one in there if we want to so now
+ 
+
+ align:start position:0%
+the one in there if we want to so now
+let's ask ourselves how would we
+
+ align:start position:0%
+let's ask ourselves how would we
+ 
+
+ align:start position:0%
+let's ask ourselves how would we
+start to reopen the space once we've
+
+ align:start position:0%
+start to reopen the space once we've
+ 
+
+ align:start position:0%
+start to reopen the space once we've
+decided
+
+ align:start position:0%
+decided
+ 
+
+ align:start position:0%
+decided
+on a sort of safe occupancy uh during
+
+ align:start position:0%
+on a sort of safe occupancy uh during
+ 
+
+ align:start position:0%
+on a sort of safe occupancy uh during
+the greatest level of restrictions
+
+ align:start position:0%
+the greatest level of restrictions
+ 
+
+ align:start position:0%
+the greatest level of restrictions
+so that would then lead us into a phase
+
+ align:start position:0%
+so that would then lead us into a phase
+ 
+
+ align:start position:0%
+so that would then lead us into a phase
+of relaxing restrictions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this would still be with masks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so keeping in mind that mass are an
+
+ align:start position:0%
+so keeping in mind that mass are an
+ 
+
+ align:start position:0%
+so keeping in mind that mass are an
+essential part of
+
+ align:start position:0%
+essential part of
+ 
+
+ align:start position:0%
+essential part of
+achieving a reasonable occupancy when
+
+ align:start position:0%
+achieving a reasonable occupancy when
+ 
+
+ align:start position:0%
+achieving a reasonable occupancy when
+the pandemic is high
+
+ align:start position:0%
+the pandemic is high
+ 
+
+ align:start position:0%
+the pandemic is high
+and there's a lot of prevalence and that
+
+ align:start position:0%
+and there's a lot of prevalence and that
+ 
+
+ align:start position:0%
+and there's a lot of prevalence and that
+we would only sort of start to
+
+ align:start position:0%
+we would only sort of start to
+ 
+
+ align:start position:0%
+we would only sort of start to
+relax occupancy first before we take
+
+ align:start position:0%
+relax occupancy first before we take
+ 
+
+ align:start position:0%
+relax occupancy first before we take
+away the suggestion to to wear mass
+
+ align:start position:0%
+away the suggestion to to wear mass
+ 
+
+ align:start position:0%
+away the suggestion to to wear mass
+and that would be then the last step so
+
+ align:start position:0%
+and that would be then the last step so
+ 
+
+ align:start position:0%
+and that would be then the last step so
+for relaxing restrictions
+
+ align:start position:0%
+for relaxing restrictions
+ 
+
+ align:start position:0%
+for relaxing restrictions
+we're then going to be interested in the
+
+ align:start position:0%
+we're then going to be interested in the
+ 
+
+ align:start position:0%
+we're then going to be interested in the
+indoor reproductive number
+
+ align:start position:0%
+indoor reproductive number
+ 
+
+ align:start position:0%
+indoor reproductive number
+being less than now a rescaled value
+
+ align:start position:0%
+being less than now a rescaled value
+ 
+
+ align:start position:0%
+being less than now a rescaled value
+which would be
+
+ align:start position:0%
+which would be
+ 
+
+ align:start position:0%
+which would be
+epsilon over p i q i
+
+ align:start position:0%
+epsilon over p i q i
+ 
+
+ align:start position:0%
+epsilon over p i q i
+n and the inter-reproductive number
+
+ align:start position:0%
+n and the inter-reproductive number
+ 
+
+ align:start position:0%
+n and the inter-reproductive number
+remember is n minus 1 but it's
+
+ align:start position:0%
+remember is n minus 1 but it's
+ 
+
+ align:start position:0%
+remember is n minus 1 but it's
+approximately n times
+
+ align:start position:0%
+approximately n times
+ 
+
+ align:start position:0%
+approximately n times
+beta tau so i've replaced again n
+
+ align:start position:0%
+beta tau so i've replaced again n
+ 
+
+ align:start position:0%
+beta tau so i've replaced again n
+minus 1 with n just to kind of get a
+
+ align:start position:0%
+minus 1 with n just to kind of get a
+ 
+
+ align:start position:0%
+minus 1 with n just to kind of get a
+simpler formula
+
+ align:start position:0%
+simpler formula
+ 
+
+ align:start position:0%
+simpler formula
+and so notice now here n is in both
+
+ align:start position:0%
+and so notice now here n is in both
+ 
+
+ align:start position:0%
+and so notice now here n is in both
+sides of the equations if i want to
+
+ align:start position:0%
+sides of the equations if i want to
+ 
+
+ align:start position:0%
+sides of the equations if i want to
+solve for the value
+
+ align:start position:0%
+solve for the value
+ 
+
+ align:start position:0%
+solve for the value
+n2 which is this yellow curve here i'm
+
+ align:start position:0%
+n2 which is this yellow curve here i'm
+ 
+
+ align:start position:0%
+n2 which is this yellow curve here i'm
+actually going to have to
+
+ align:start position:0%
+actually going to have to
+ 
+
+ align:start position:0%
+actually going to have to
+put the ends on one side and take a
+
+ align:start position:0%
+put the ends on one side and take a
+ 
+
+ align:start position:0%
+put the ends on one side and take a
+square root
+
+ align:start position:0%
+square root
+ 
+
+ align:start position:0%
+square root
+so i'll get my n2 then would be
+
+ align:start position:0%
+so i'll get my n2 then would be
+ 
+
+ align:start position:0%
+so i'll get my n2 then would be
+the square root of epsilon
+
+ align:start position:0%
+the square root of epsilon
+ 
+
+ align:start position:0%
+the square root of epsilon
+over beta tau times
+
+ align:start position:0%
+over beta tau times
+ 
+
+ align:start position:0%
+over beta tau times
+p p i times q i
+
+ align:start position:0%
+p p i times q i
+ 
+
+ align:start position:0%
+p p i times q i
+and i remember also another
+
+ align:start position:0%
+and i remember also another
+ 
+
+ align:start position:0%
+and i remember also another
+approximation here is that p i is
+
+ align:start position:0%
+approximation here is that p i is
+ 
+
+ align:start position:0%
+approximation here is that p i is
+definitely much less than one we're
+
+ align:start position:0%
+definitely much less than one we're
+ 
+
+ align:start position:0%
+definitely much less than one we're
+looking limit of very low prevalence
+
+ align:start position:0%
+looking limit of very low prevalence
+ 
+
+ align:start position:0%
+looking limit of very low prevalence
+and so also therefore qi is basically
+
+ align:start position:0%
+and so also therefore qi is basically
+ 
+
+ align:start position:0%
+and so also therefore qi is basically
+tending to 1 because it's 1 minus pi
+
+ align:start position:0%
+tending to 1 because it's 1 minus pi
+ 
+
+ align:start position:0%
+tending to 1 because it's 1 minus pi
+and so that factor is really not that
+
+ align:start position:0%
+and so that factor is really not that
+ 
+
+ align:start position:0%
+and so that factor is really not that
+important and notice
+
+ align:start position:0%
+important and notice
+ 
+
+ align:start position:0%
+important and notice
+also epsilon over beta tau that's n1
+
+ align:start position:0%
+also epsilon over beta tau that's n1
+ 
+
+ align:start position:0%
+also epsilon over beta tau that's n1
+so n2 is approximately related to n1
+
+ align:start position:0%
+so n2 is approximately related to n1
+ 
+
+ align:start position:0%
+so n2 is approximately related to n1
+by the square root of n1 divided by
+
+ align:start position:0%
+by the square root of n1 divided by
+ 
+
+ align:start position:0%
+by the square root of n1 divided by
+pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so that's this that's this number
+
+ align:start position:0%
+so so that's this that's this number
+ 
+
+ align:start position:0%
+so so that's this that's this number
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so as a function of prevalence this
+
+ align:start position:0%
+so as a function of prevalence this
+ 
+
+ align:start position:0%
+so as a function of prevalence this
+yellow curve is one over square root
+
+ align:start position:0%
+yellow curve is one over square root
+ 
+
+ align:start position:0%
+yellow curve is one over square root
+of prevalence and
+
+ align:start position:0%
+of prevalence and
+ 
+
+ align:start position:0%
+of prevalence and
+one nice thing about writing it this way
+
+ align:start position:0%
+one nice thing about writing it this way
+ 
+
+ align:start position:0%
+one nice thing about writing it this way
+is that i can decide on a reopening
+
+ align:start position:0%
+is that i can decide on a reopening
+ 
+
+ align:start position:0%
+is that i can decide on a reopening
+protocol
+
+ align:start position:0%
+protocol
+ 
+
+ align:start position:0%
+protocol
+without actually redoing my calculation
+
+ align:start position:0%
+without actually redoing my calculation
+ 
+
+ align:start position:0%
+without actually redoing my calculation
+with all those complicated variables
+
+ align:start position:0%
+with all those complicated variables
+ 
+
+ align:start position:0%
+with all those complicated variables
+including the restons epsilon and all
+
+ align:start position:0%
+including the restons epsilon and all
+ 
+
+ align:start position:0%
+including the restons epsilon and all
+the factors that go into beta because
+
+ align:start position:0%
+the factors that go into beta because
+ 
+
+ align:start position:0%
+the factors that go into beta because
+i've lumped them into n1 what i'm saying
+
+ align:start position:0%
+i've lumped them into n1 what i'm saying
+ 
+
+ align:start position:0%
+i've lumped them into n1 what i'm saying
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is that we've already done a calculation
+
+ align:start position:0%
+is that we've already done a calculation
+ 
+
+ align:start position:0%
+is that we've already done a calculation
+and decided to impose a certain
+
+ align:start position:0%
+and decided to impose a certain
+ 
+
+ align:start position:0%
+and decided to impose a certain
+occupancy restriction on a certain space
+
+ align:start position:0%
+occupancy restriction on a certain space
+ 
+
+ align:start position:0%
+occupancy restriction on a certain space
+based on principles that we've been
+
+ align:start position:0%
+based on principles that we've been
+ 
+
+ align:start position:0%
+based on principles that we've been
+discussing
+
+ align:start position:0%
+discussing
+ 
+
+ align:start position:0%
+discussing
+in this course but now as prevalence
+
+ align:start position:0%
+in this course but now as prevalence
+ 
+
+ align:start position:0%
+in this course but now as prevalence
+goes down according to the simple
+
+ align:start position:0%
+goes down according to the simple
+ 
+
+ align:start position:0%
+goes down according to the simple
+formula whenever n2
+
+ align:start position:0%
+formula whenever n2
+ 
+
+ align:start position:0%
+formula whenever n2
+is bigger than one you know we would use
+
+ align:start position:0%
+is bigger than one you know we would use
+ 
+
+ align:start position:0%
+is bigger than one you know we would use
+this if n2
+
+ align:start position:0%
+this if n2
+ 
+
+ align:start position:0%
+this if n2
+is is bigger than n1 so basically when
+
+ align:start position:0%
+is is bigger than n1 so basically when
+ 
+
+ align:start position:0%
+is is bigger than n1 so basically when
+these two curves cross
+
+ align:start position:0%
+these two curves cross
+ 
+
+ align:start position:0%
+these two curves cross
+as you get to lower prevalence you'll
+
+ align:start position:0%
+as you get to lower prevalence you'll
+ 
+
+ align:start position:0%
+as you get to lower prevalence you'll
+now switch to two and you'll start
+
+ align:start position:0%
+now switch to two and you'll start
+ 
+
+ align:start position:0%
+now switch to two and you'll start
+increasing
+
+ align:start position:0%
+increasing
+ 
+
+ align:start position:0%
+increasing
+and you will do that until you get to n0
+
+ align:start position:0%
+and you will do that until you get to n0
+ 
+
+ align:start position:0%
+and you will do that until you get to n0
+so we'll do this this is the relaxing
+
+ align:start position:0%
+so we'll do this this is the relaxing
+ 
+
+ align:start position:0%
+so we'll do this this is the relaxing
+restrictions and then we'll stop
+
+ align:start position:0%
+restrictions and then we'll stop
+ 
+
+ align:start position:0%
+restrictions and then we'll stop
+and then we'll we'll uh yeah so
+
+ align:start position:0%
+and then we'll we'll uh yeah so
+ 
+
+ align:start position:0%
+and then we'll we'll uh yeah so
+basically we'll go well
+
+ align:start position:0%
+basically we'll go well
+ 
+
+ align:start position:0%
+basically we'll go well
+n2 can when n2 is bigger than we allow
+
+ align:start position:0%
+n2 can when n2 is bigger than we allow
+ 
+
+ align:start position:0%
+n2 can when n2 is bigger than we allow
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um until uh n2
+
+ align:start position:0%
+um until uh n2
+ 
+
+ align:start position:0%
+um until uh n2
+equals n1 and that's this this this time
+
+ align:start position:0%
+equals n1 and that's this this this time
+ 
+
+ align:start position:0%
+equals n1 and that's this this this time
+here p
+
+ align:start position:0%
+here p
+ 
+
+ align:start position:0%
+here p
+p2 so basically uh we start imposing
+
+ align:start position:0%
+p2 so basically uh we start imposing
+ 
+
+ align:start position:0%
+p2 so basically uh we start imposing
+restrictions at p1
+
+ align:start position:0%
+restrictions at p1
+ 
+
+ align:start position:0%
+restrictions at p1
+so p1 so so basically we start
+
+ align:start position:0%
+so p1 so so basically we start
+ 
+
+ align:start position:0%
+so p1 so so basically we start
+relaxing restrictions when p1 so the
+
+ align:start position:0%
+relaxing restrictions when p1 so the
+ 
+
+ align:start position:0%
+relaxing restrictions when p1 so the
+when the prevalence equals p1
+
+ align:start position:0%
+when the prevalence equals p1
+ 
+
+ align:start position:0%
+when the prevalence equals p1
+that would be uh when
+
+ align:start position:0%
+that would be uh when
+ 
+
+ align:start position:0%
+that would be uh when
+when n2 is equal to n1 and so that would
+
+ align:start position:0%
+when n2 is equal to n1 and so that would
+ 
+
+ align:start position:0%
+when n2 is equal to n1 and so that would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+when pi p1
+
+ align:start position:0%
+when pi p1
+ 
+
+ align:start position:0%
+when pi p1
+is 1 over n1
+
+ align:start position:0%
+is 1 over n1
+ 
+
+ align:start position:0%
+is 1 over n1
+so essentially that's when you expect to
+
+ align:start position:0%
+so essentially that's when you expect to
+ 
+
+ align:start position:0%
+so essentially that's when you expect to
+find one
+
+ align:start position:0%
+find one
+ 
+
+ align:start position:0%
+find one
+infected person so this is approximately
+
+ align:start position:0%
+infected person so this is approximately
+ 
+
+ align:start position:0%
+infected person so this is approximately
+one over and one so up here
+
+ align:start position:0%
+one over and one so up here
+ 
+
+ align:start position:0%
+one over and one so up here
+you uh when you go below this you're
+
+ align:start position:0%
+you uh when you go below this you're
+ 
+
+ align:start position:0%
+you uh when you go below this you're
+saying well it's actually unlikely that
+
+ align:start position:0%
+saying well it's actually unlikely that
+ 
+
+ align:start position:0%
+saying well it's actually unlikely that
+during the time tau we even get one
+
+ align:start position:0%
+during the time tau we even get one
+ 
+
+ align:start position:0%
+during the time tau we even get one
+infected person
+
+ align:start position:0%
+infected person
+ 
+
+ align:start position:0%
+infected person
+and that's when we start to relax okay
+
+ align:start position:0%
+and that's when we start to relax okay
+ 
+
+ align:start position:0%
+and that's when we start to relax okay
+so that's the first kind of crossover
+
+ align:start position:0%
+so that's the first kind of crossover
+ 
+
+ align:start position:0%
+so that's the first kind of crossover
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+and there's a second crossover point
+
+ align:start position:0%
+and there's a second crossover point
+ 
+
+ align:start position:0%
+and there's a second crossover point
+when this is equal to p2
+
+ align:start position:0%
+when this is equal to p2
+ 
+
+ align:start position:0%
+when this is equal to p2
+sorry is equal to n0 that's what's what
+
+ align:start position:0%
+sorry is equal to n0 that's what's what
+ 
+
+ align:start position:0%
+sorry is equal to n0 that's what's what
+p2 is
+
+ align:start position:0%
+p2 is
+ 
+
+ align:start position:0%
+p2 is
+and so basically uh p2 which is when we
+
+ align:start position:0%
+and so basically uh p2 which is when we
+ 
+
+ align:start position:0%
+and so basically uh p2 which is when we
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+you know hit the saturation point and
+
+ align:start position:0%
+you know hit the saturation point and
+ 
+
+ align:start position:0%
+you know hit the saturation point and
+that's kind of when we've like reopened
+
+ align:start position:0%
+that's kind of when we've like reopened
+ 
+
+ align:start position:0%
+that's kind of when we've like reopened
+in some sense to the full
+
+ align:start position:0%
+in some sense to the full
+ 
+
+ align:start position:0%
+in some sense to the full
+normal situation that would be
+
+ align:start position:0%
+normal situation that would be
+ 
+
+ align:start position:0%
+normal situation that would be
+uh when n2 is equal to n0
+
+ align:start position:0%
+uh when n2 is equal to n0
+ 
+
+ align:start position:0%
+uh when n2 is equal to n0
+wait sorry i wrote here n2 equals n1
+
+ align:start position:0%
+wait sorry i wrote here n2 equals n1
+ 
+
+ align:start position:0%
+wait sorry i wrote here n2 equals n1
+sorry i meant when n2 equals n0
+
+ align:start position:0%
+sorry i meant when n2 equals n0
+ 
+
+ align:start position:0%
+sorry i meant when n2 equals n0
+sorry that's when that's the time p2
+
+ align:start position:0%
+sorry that's when that's the time p2
+ 
+
+ align:start position:0%
+sorry that's when that's the time p2
+here when n2 is equal to n0 that's when
+
+ align:start position:0%
+here when n2 is equal to n0 that's when
+ 
+
+ align:start position:0%
+here when n2 is equal to n0 that's when
+we cut off
+
+ align:start position:0%
+we cut off
+ 
+
+ align:start position:0%
+we cut off
+so this is n0 and we solve for pi
+
+ align:start position:0%
+so this is n0 and we solve for pi
+ 
+
+ align:start position:0%
+so this is n0 and we solve for pi
+you can see that we get n1
+
+ align:start position:0%
+you can see that we get n1
+ 
+
+ align:start position:0%
+you can see that we get n1
+over n0 squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that is the place where i then switch
+
+ align:start position:0%
+so that is the place where i then switch
+ 
+
+ align:start position:0%
+so that is the place where i then switch
+and now i'm going to cap the occupancy
+
+ align:start position:0%
+and now i'm going to cap the occupancy
+ 
+
+ align:start position:0%
+and now i'm going to cap the occupancy
+at n0 so maybe to summarize here
+
+ align:start position:0%
+at n0 so maybe to summarize here
+ 
+
+ align:start position:0%
+at n0 so maybe to summarize here
+what i would say is that the occupancy
+
+ align:start position:0%
+what i would say is that the occupancy
+ 
+
+ align:start position:0%
+what i would say is that the occupancy
+should be less than or equal to
+
+ align:start position:0%
+should be less than or equal to
+ 
+
+ align:start position:0%
+should be less than or equal to
+uh n1 for uh
+
+ align:start position:0%
+uh n1 for uh
+ 
+
+ align:start position:0%
+uh n1 for uh
+pi greater than p1 it'll be n2
+
+ align:start position:0%
+pi greater than p1 it'll be n2
+ 
+
+ align:start position:0%
+pi greater than p1 it'll be n2
+which depends on pi for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi between p1
+
+ align:start position:0%
+pi between p1
+ 
+
+ align:start position:0%
+pi between p1
+or p2 and p1
+
+ align:start position:0%
+or p2 and p1
+ 
+
+ align:start position:0%
+or p2 and p1
+and then as the prevalence gets lower we
+
+ align:start position:0%
+and then as the prevalence gets lower we
+ 
+
+ align:start position:0%
+and then as the prevalence gets lower we
+go to full occupancy n0
+
+ align:start position:0%
+go to full occupancy n0
+ 
+
+ align:start position:0%
+go to full occupancy n0
+when pi is less than p2
+
+ align:start position:0%
+when pi is less than p2
+ 
+
+ align:start position:0%
+when pi is less than p2
+so this is basically this full curve of
+
+ align:start position:0%
+so this is basically this full curve of
+ 
+
+ align:start position:0%
+so this is basically this full curve of
+reopening
+
+ align:start position:0%
+reopening
+ 
+
+ align:start position:0%
+reopening
+and then the final decision to make is
+
+ align:start position:0%
+and then the final decision to make is
+ 
+
+ align:start position:0%
+and then the final decision to make is
+when do we return completely normal and
+
+ align:start position:0%
+when do we return completely normal and
+ 
+
+ align:start position:0%
+when do we return completely normal and
+take away
+
+ align:start position:0%
+take away
+ 
+
+ align:start position:0%
+take away
+certain restrictions we've done so here
+
+ align:start position:0%
+certain restrictions we've done so here
+ 
+
+ align:start position:0%
+certain restrictions we've done so here
+i mentioned mass we could also include
+
+ align:start position:0%
+i mentioned mass we could also include
+ 
+
+ align:start position:0%
+i mentioned mass we could also include
+in this calculation
+
+ align:start position:0%
+in this calculation
+ 
+
+ align:start position:0%
+in this calculation
+you know relaxing other restrictions
+
+ align:start position:0%
+you know relaxing other restrictions
+ 
+
+ align:start position:0%
+you know relaxing other restrictions
+such as maybe not having the ventilation
+
+ align:start position:0%
+such as maybe not having the ventilation
+ 
+
+ align:start position:0%
+such as maybe not having the ventilation
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+quite so high so that would be when we
+
+ align:start position:0%
+quite so high so that would be when we
+ 
+
+ align:start position:0%
+quite so high so that would be when we
+finally go back
+
+ align:start position:0%
+finally go back
+ 
+
+ align:start position:0%
+finally go back
+to no restrictions of any kind we're
+
+ align:start position:0%
+to no restrictions of any kind we're
+ 
+
+ align:start position:0%
+to no restrictions of any kind we're
+sort of back to normal
+
+ align:start position:0%
+sort of back to normal
+ 
+
+ align:start position:0%
+sort of back to normal
+so this means no masks
+
+ align:start position:0%
+so this means no masks
+ 
+
+ align:start position:0%
+so this means no masks
+no other precautions full occupancy
+
+ align:start position:0%
+no other precautions full occupancy
+ 
+
+ align:start position:0%
+no other precautions full occupancy
+so in this case we need r in
+
+ align:start position:0%
+so in this case we need r in
+ 
+
+ align:start position:0%
+so in this case we need r in
+is going to be less than epsilon over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well let's see here it's the same as
+
+ align:start position:0%
+well let's see here it's the same as
+ 
+
+ align:start position:0%
+well let's see here it's the same as
+before we have this p i
+
+ align:start position:0%
+before we have this p i
+ 
+
+ align:start position:0%
+before we have this p i
+n that we just looked at technically
+
+ align:start position:0%
+n that we just looked at technically
+ 
+
+ align:start position:0%
+n that we just looked at technically
+times q i
+
+ align:start position:0%
+times q i
+ 
+
+ align:start position:0%
+times q i
+but now we have another factor pm
+
+ align:start position:0%
+but now we have another factor pm
+ 
+
+ align:start position:0%
+but now we have another factor pm
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+because compared to the case with no
+
+ align:start position:0%
+because compared to the case with no
+ 
+
+ align:start position:0%
+because compared to the case with no
+mass we know the bound in the guidelines
+
+ align:start position:0%
+mass we know the bound in the guidelines
+ 
+
+ align:start position:0%
+mass we know the bound in the guidelines
+so the effect of beta
+
+ align:start position:0%
+so the effect of beta
+ 
+
+ align:start position:0%
+so the effect of beta
+just gets rescaled by pm squared so
+
+ align:start position:0%
+just gets rescaled by pm squared so
+ 
+
+ align:start position:0%
+just gets rescaled by pm squared so
+technically that's
+
+ align:start position:0%
+technically that's
+ 
+
+ align:start position:0%
+technically that's
+that's in uh are in here but now you
+
+ align:start position:0%
+that's in uh are in here but now you
+ 
+
+ align:start position:0%
+that's in uh are in here but now you
+know we have this sort of extra factor
+
+ align:start position:0%
+know we have this sort of extra factor
+ 
+
+ align:start position:0%
+know we have this sort of extra factor
+you kind of think of it like a rescaling
+
+ align:start position:0%
+you kind of think of it like a rescaling
+ 
+
+ align:start position:0%
+you kind of think of it like a rescaling
+of epsilon
+
+ align:start position:0%
+of epsilon
+ 
+
+ align:start position:0%
+of epsilon
+and so what that's going to do for us
+
+ align:start position:0%
+and so what that's going to do for us
+ 
+
+ align:start position:0%
+and so what that's going to do for us
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+is that there's a the uh
+
+ align:start position:0%
+is that there's a the uh
+ 
+
+ align:start position:0%
+is that there's a the uh
+there's another curve that goes
+
+ align:start position:0%
+there's another curve that goes
+ 
+
+ align:start position:0%
+there's another curve that goes
+kind of like this which is just like
+
+ align:start position:0%
+kind of like this which is just like
+ 
+
+ align:start position:0%
+kind of like this which is just like
+this one but it's shifted by a factor
+
+ align:start position:0%
+this one but it's shifted by a factor
+ 
+
+ align:start position:0%
+this one but it's shifted by a factor
+pm cubed rpm squared sorry which is kind
+
+ align:start position:0%
+pm cubed rpm squared sorry which is kind
+ 
+
+ align:start position:0%
+pm cubed rpm squared sorry which is kind
+of like the case where you had so this
+
+ align:start position:0%
+of like the case where you had so this
+ 
+
+ align:start position:0%
+of like the case where you had so this
+is like this is like
+
+ align:start position:0%
+is like this is like
+ 
+
+ align:start position:0%
+is like this is like
+no masks it's like the n2 with no masks
+
+ align:start position:0%
+no masks it's like the n2 with no masks
+ 
+
+ align:start position:0%
+no masks it's like the n2 with no masks
+and the other curve is with
+
+ align:start position:0%
+and the other curve is with
+ 
+
+ align:start position:0%
+and the other curve is with
+masks and there's a rescaling factor
+
+ align:start position:0%
+masks and there's a rescaling factor
+ 
+
+ align:start position:0%
+masks and there's a rescaling factor
+which really has to do with
+
+ align:start position:0%
+which really has to do with
+ 
+
+ align:start position:0%
+which really has to do with
+the sort of remediation that you've done
+
+ align:start position:0%
+the sort of remediation that you've done
+ 
+
+ align:start position:0%
+the sort of remediation that you've done
+and in this case
+
+ align:start position:0%
+and in this case
+ 
+
+ align:start position:0%
+and in this case
+p3 would then just be pm squared
+
+ align:start position:0%
+p3 would then just be pm squared
+ 
+
+ align:start position:0%
+p3 would then just be pm squared
+times p2 so if our pm is a factor of 10
+
+ align:start position:0%
+times p2 so if our pm is a factor of 10
+ 
+
+ align:start position:0%
+times p2 so if our pm is a factor of 10
+percent let's say mass are capturing 10
+
+ align:start position:0%
+percent let's say mass are capturing 10
+ 
+
+ align:start position:0%
+percent let's say mass are capturing 10
+or letting 10 percent of infectious
+
+ align:start position:0%
+or letting 10 percent of infectious
+ 
+
+ align:start position:0%
+or letting 10 percent of infectious
+droplets get through the pm squared
+
+ align:start position:0%
+droplets get through the pm squared
+ 
+
+ align:start position:0%
+droplets get through the pm squared
+might be a factor of 100
+
+ align:start position:0%
+might be a factor of 100
+ 
+
+ align:start position:0%
+might be a factor of 100
+so then we would wait till the
+
+ align:start position:0%
+so then we would wait till the
+ 
+
+ align:start position:0%
+so then we would wait till the
+prevalence is 100 times smaller
+
+ align:start position:0%
+prevalence is 100 times smaller
+ 
+
+ align:start position:0%
+prevalence is 100 times smaller
+before we finally allow people to remove
+
+ align:start position:0%
+before we finally allow people to remove
+ 
+
+ align:start position:0%
+before we finally allow people to remove
+mass and be at full occupancy
+
+ align:start position:0%
+mass and be at full occupancy
+ 
+
+ align:start position:0%
+mass and be at full occupancy
+and you could make a similar calculation
+
+ align:start position:0%
+and you could make a similar calculation
+ 
+
+ align:start position:0%
+and you could make a similar calculation
+for other types of restrictions
+
+ align:start position:0%
+for other types of restrictions
+ 
+
+ align:start position:0%
+for other types of restrictions
+and in fact you can calculate such a
+
+ align:start position:0%
+and in fact you can calculate such a
+ 
+
+ align:start position:0%
+and in fact you can calculate such a
+curve for a given room
+
+ align:start position:0%
+curve for a given room
+ 
+
+ align:start position:0%
+curve for a given room
+given scenario of human behavior
+
+ align:start position:0%
+given scenario of human behavior
+ 
+
+ align:start position:0%
+given scenario of human behavior
+and interventions such as filtration or
+
+ align:start position:0%
+and interventions such as filtration or
+ 
+
+ align:start position:0%
+and interventions such as filtration or
+ventilation
+
+ align:start position:0%
+ventilation
+ 
+
+ align:start position:0%
+ventilation
+and what the theory allows you to do is
+
+ align:start position:0%
+and what the theory allows you to do is
+ 
+
+ align:start position:0%
+and what the theory allows you to do is
+to of course recalculate n1
+
+ align:start position:0%
+to of course recalculate n1
+ 
+
+ align:start position:0%
+to of course recalculate n1
+and then you can recalculate n2 as well
+
+ align:start position:0%
+and then you can recalculate n2 as well
+ 
+
+ align:start position:0%
+and then you can recalculate n2 as well
+and so you can say well what if actually
+
+ align:start position:0%
+and so you can say well what if actually
+ 
+
+ align:start position:0%
+and so you can say well what if actually
+i don't like this curve i would like to
+
+ align:start position:0%
+i don't like this curve i would like to
+ 
+
+ align:start position:0%
+i don't like this curve i would like to
+try to reopen my school
+
+ align:start position:0%
+try to reopen my school
+ 
+
+ align:start position:0%
+try to reopen my school
+sooner okay how would i do that well i
+
+ align:start position:0%
+sooner okay how would i do that well i
+ 
+
+ align:start position:0%
+sooner okay how would i do that well i
+know that if i
+
+ align:start position:0%
+know that if i
+ 
+
+ align:start position:0%
+know that if i
+make various interventions i can raise
+
+ align:start position:0%
+make various interventions i can raise
+ 
+
+ align:start position:0%
+make various interventions i can raise
+the pink curve so i can end up somewhere
+
+ align:start position:0%
+the pink curve so i can end up somewhere
+ 
+
+ align:start position:0%
+the pink curve so i can end up somewhere
+here let's just say
+
+ align:start position:0%
+here let's just say
+ 
+
+ align:start position:0%
+here let's just say
+this might be with uh
+
+ align:start position:0%
+this might be with uh
+ 
+
+ align:start position:0%
+this might be with uh
+safety interventions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually one such innervation
+
+ align:start position:0%
+actually one such innervation
+ 
+
+ align:start position:0%
+actually one such innervation
+intervention by the way is masks
+
+ align:start position:0%
+intervention by the way is masks
+ 
+
+ align:start position:0%
+intervention by the way is masks
+themselves because if i follow this
+
+ align:start position:0%
+themselves because if i follow this
+ 
+
+ align:start position:0%
+themselves because if i follow this
+curve all the way down here there's some
+
+ align:start position:0%
+curve all the way down here there's some
+ 
+
+ align:start position:0%
+curve all the way down here there's some
+curve down here which is no masks
+
+ align:start position:0%
+curve down here which is no masks
+ 
+
+ align:start position:0%
+curve down here which is no masks
+which is the safety guideline with no
+
+ align:start position:0%
+which is the safety guideline with no
+ 
+
+ align:start position:0%
+which is the safety guideline with no
+mass and if i turn on mass
+
+ align:start position:0%
+mass and if i turn on mass
+ 
+
+ align:start position:0%
+mass and if i turn on mass
+i go up okay but when i make that
+
+ align:start position:0%
+i go up okay but when i make that
+ 
+
+ align:start position:0%
+i go up okay but when i make that
+intervention
+
+ align:start position:0%
+intervention
+ 
+
+ align:start position:0%
+intervention
+also p2 notice scales like like uh
+
+ align:start position:0%
+also p2 notice scales like like uh
+ 
+
+ align:start position:0%
+also p2 notice scales like like uh
+also like n1 and so that's actually
+
+ align:start position:0%
+also like n1 and so that's actually
+ 
+
+ align:start position:0%
+also like n1 and so that's actually
+moving in this direction
+
+ align:start position:0%
+moving in this direction
+ 
+
+ align:start position:0%
+moving in this direction
+and so i've essentially moved this
+
+ align:start position:0%
+and so i've essentially moved this
+ 
+
+ align:start position:0%
+and so i've essentially moved this
+yellow curve and so
+
+ align:start position:0%
+yellow curve and so
+ 
+
+ align:start position:0%
+yellow curve and so
+i'm i'm now going to say well you know
+
+ align:start position:0%
+i'm i'm now going to say well you know
+ 
+
+ align:start position:0%
+i'm i'm now going to say well you know
+with a different set
+
+ align:start position:0%
+with a different set
+ 
+
+ align:start position:0%
+with a different set
+of of interventions i can make the room
+
+ align:start position:0%
+of of interventions i can make the room
+ 
+
+ align:start position:0%
+of of interventions i can make the room
+safer
+
+ align:start position:0%
+safer
+ 
+
+ align:start position:0%
+safer
+and what that does it gives me more
+
+ align:start position:0%
+and what that does it gives me more
+ 
+
+ align:start position:0%
+and what that does it gives me more
+people in the room but it also
+
+ align:start position:0%
+people in the room but it also
+ 
+
+ align:start position:0%
+people in the room but it also
+means that i can that i change sort of
+
+ align:start position:0%
+means that i can that i change sort of
+ 
+
+ align:start position:0%
+means that i can that i change sort of
+when i make the decision reopen in
+
+ align:start position:0%
+when i make the decision reopen in
+ 
+
+ align:start position:0%
+when i make the decision reopen in
+particular i can kind of get myself to
+
+ align:start position:0%
+particular i can kind of get myself to
+ 
+
+ align:start position:0%
+particular i can kind of get myself to
+full occupancy at a higher prevalence
+
+ align:start position:0%
+full occupancy at a higher prevalence
+ 
+
+ align:start position:0%
+full occupancy at a higher prevalence
+because the room is actually now made
+
+ align:start position:0%
+because the room is actually now made
+ 
+
+ align:start position:0%
+because the room is actually now made
+safer
+
+ align:start position:0%
+safer
+ 
+
+ align:start position:0%
+safer
+so uh i noted but on the other hand this
+
+ align:start position:0%
+so uh i noted but on the other hand this
+ 
+
+ align:start position:0%
+so uh i noted but on the other hand this
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+this switch here was at one over n1 so
+
+ align:start position:0%
+this switch here was at one over n1 so
+ 
+
+ align:start position:0%
+this switch here was at one over n1 so
+kind of this this part kind of shrinks a
+
+ align:start position:0%
+kind of this this part kind of shrinks a
+ 
+
+ align:start position:0%
+kind of this this part kind of shrinks a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+as this ultimately kind of goes up to
+
+ align:start position:0%
+as this ultimately kind of goes up to
+ 
+
+ align:start position:0%
+as this ultimately kind of goes up to
+full occupancy
+
+ align:start position:0%
+full occupancy
+ 
+
+ align:start position:0%
+full occupancy
+so so basically um i think compared to
+
+ align:start position:0%
+so so basically um i think compared to
+ 
+
+ align:start position:0%
+so so basically um i think compared to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+current situation or the typical
+
+ align:start position:0%
+current situation or the typical
+ 
+
+ align:start position:0%
+current situation or the typical
+situation where policy makers are making
+
+ align:start position:0%
+situation where policy makers are making
+ 
+
+ align:start position:0%
+situation where policy makers are making
+decisions
+
+ align:start position:0%
+decisions
+ 
+
+ align:start position:0%
+decisions
+based on something like the six-foot
+
+ align:start position:0%
+based on something like the six-foot
+ 
+
+ align:start position:0%
+based on something like the six-foot
+rule and you know a somewhat
+
+ align:start position:0%
+rule and you know a somewhat
+ 
+
+ align:start position:0%
+rule and you know a somewhat
+arbitrary feeling about what is a high
+
+ align:start position:0%
+arbitrary feeling about what is a high
+ 
+
+ align:start position:0%
+arbitrary feeling about what is a high
+prevalence is it one percent is it point
+
+ align:start position:0%
+prevalence is it one percent is it point
+ 
+
+ align:start position:0%
+prevalence is it one percent is it point
+one percent and we decide okay now we
+
+ align:start position:0%
+one percent and we decide okay now we
+ 
+
+ align:start position:0%
+one percent and we decide okay now we
+can close our schools or reopen our
+
+ align:start position:0%
+can close our schools or reopen our
+ 
+
+ align:start position:0%
+can close our schools or reopen our
+schools or set the occupancy at half
+
+ align:start position:0%
+schools or set the occupancy at half
+ 
+
+ align:start position:0%
+schools or set the occupancy at half
+the guideline tells you how to set
+
+ align:start position:0%
+the guideline tells you how to set
+ 
+
+ align:start position:0%
+the guideline tells you how to set
+occupancy for sort of the worst case
+
+ align:start position:0%
+occupancy for sort of the worst case
+ 
+
+ align:start position:0%
+occupancy for sort of the worst case
+scenario when the pandemic is is is is
+
+ align:start position:0%
+scenario when the pandemic is is is is
+ 
+
+ align:start position:0%
+scenario when the pandemic is is is is
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+very wide you know prevalent in society
+
+ align:start position:0%
+very wide you know prevalent in society
+ 
+
+ align:start position:0%
+very wide you know prevalent in society
+but now also through these kinds of
+
+ align:start position:0%
+but now also through these kinds of
+ 
+
+ align:start position:0%
+but now also through these kinds of
+calculations we can make rational
+
+ align:start position:0%
+calculations we can make rational
+ 
+
+ align:start position:0%
+calculations we can make rational
+decisions about how to reopen
+
+ align:start position:0%
+decisions about how to reopen
+ 
+
+ align:start position:0%
+decisions about how to reopen
+i'm not advocating necessarily for the
+
+ align:start position:0%
+i'm not advocating necessarily for the
+ 
+
+ align:start position:0%
+i'm not advocating necessarily for the
+exact formulas that you find on the
+
+ align:start position:0%
+exact formulas that you find on the
+ 
+
+ align:start position:0%
+exact formulas that you find on the
+board here
+
+ align:start position:0%
+board here
+ 
+
+ align:start position:0%
+board here
+but the principles i'm showing you could
+
+ align:start position:0%
+but the principles i'm showing you could
+ 
+
+ align:start position:0%
+but the principles i'm showing you could
+lead to quantitative and scientifically
+
+ align:start position:0%
+lead to quantitative and scientifically
+ 
+
+ align:start position:0%
+lead to quantitative and scientifically
+justifiable ways
+
+ align:start position:0%
+justifiable ways
+ 
+
+ align:start position:0%
+justifiable ways
+of taking a specific space and a
+
+ align:start position:0%
+of taking a specific space and a
+ 
+
+ align:start position:0%
+of taking a specific space and a
+specific usage of that space and
+
+ align:start position:0%
+specific usage of that space and
+ 
+
+ align:start position:0%
+specific usage of that space and
+deciding how to close as prevalence goes
+
+ align:start position:0%
+deciding how to close as prevalence goes
+ 
+
+ align:start position:0%
+deciding how to close as prevalence goes
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+and reopen as prevalence goes down
+
+ align:start position:0%
+and reopen as prevalence goes down
+ 
+
+ align:start position:0%
+and reopen as prevalence goes down
+including ultimately returning to normal
+
+ align:start position:0%
+including ultimately returning to normal
+ 
+
+ align:start position:0%
+including ultimately returning to normal
+and removing mass
+
+ align:start position:0%
+and removing mass
+ 
+
+ align:start position:0%
+and removing mass
+and all other forms of precaution as the
+
+ align:start position:0%
+and all other forms of precaution as the
+ 
+
+ align:start position:0%
+and all other forms of precaution as the
+epidemic disappears
\ No newline at end of file
diff --git a/m00PjHTq6jU.txt b/m00PjHTq6jU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a97e35334bb9c59f76327ff77d88904f8ab9a605
--- /dev/null
+++ b/m00PjHTq6jU.txt
@@ -0,0 +1,3649 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high-quality
+educational resources for free.
+
+To make a donation, or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: I think
+it's a good idea
+
+to review where we
+were because we're
+
+kind of in the middle
+of a discussion.
+
+We're actually on part three.
+
+And probably, there will
+be four parts all together
+
+of our discussion of
+homogeneous expansion.
+
+So I have a few slides to just
+review where we were last time.
+
+We were building a mathematical
+model of our homogeneously
+
+expanding universe.
+
+And we modeled it as
+a finite-sized sphere
+
+where we promised
+that in the end
+
+we will take the limit as
+the size of that sphere
+
+goes to infinity and
+fills all the space.
+
+But it started with some
+initial maximum, R max i, i
+
+for initial.
+
+We arranged for it to have
+a uniform density, rho.
+
+We started at a
+time called t sub i.
+
+There were some initial
+maximum radius, R max i.
+
+And we also set this up to
+exhibit Hubble expansion.
+
+And we're going to
+try to calculate
+
+how it evolves from there.
+
+But we're going to start
+it Hubble expanding.
+
+And Hubble expanding
+means that we're
+
+starting with every particle
+having an initial velocity
+
+which is a constant, H sub i,
+the initial value of the Hubble
+
+expansion rate,
+times the vector r.
+
+That is, the vector that goes
+from the origin to the point
+
+where the particle is located.
+
+And that corresponds
+to Hubble expansion
+
+centered on the
+center of our sphere.
+
+So these are our
+initial conditions.
+
+We just put them in
+by hand because we
+
+think they form a good model for
+what our universe looks like.
+
+And then, the laws of
+evolution should take over
+
+to govern what's
+going to happen later.
+
+And since we haven't
+studied general relativity,
+
+we'll be using
+Newton's law of gravity
+
+to discover how it behaves.
+
+But I promised you
+at the beginning
+
+that we will, in fact, get
+exactly the same equation
+
+that we would have gotten had
+we used general relativity.
+
+And we'll talk later
+today, probably,
+
+about why that's the case.
+
+So this is the initial setup.
+
+Any questions about
+the initial setup?
+
+OK, then we derived
+a lot of equations.
+
+And everything really
+follows from the statement
+
+at the top here, which is
+understanding what Newton tells
+
+us about the gravitational
+field of a spherical shell.
+
+We could always think
+of our solid sphere
+
+as being made up of shells.
+
+So if we know how
+a shell behaves,
+
+we know all we need to know.
+
+And Newton told us.
+
+He told us that inside a
+spherical shell, the effect
+
+of gravity, which I'm
+describing in terms
+
+of the gravitational
+acceleration vector, little g,
+
+inside a shell, the
+gravitational field is exactly
+
+0.
+
+The force is coming from all
+different parts of the shell,
+
+pulling outward,
+cancel each other.
+
+And the net force on any object
+anywhere inside the shell
+
+is exactly 0.
+
+Outside, the entire
+shell acts exactly
+
+as if it were a single
+point mass located
+
+at the origin with the
+same total mass, m.
+
+So incredibly simple.
+
+It's hard to believe it's
+so simple, but it is.
+
+By the way, if you use
+Gauss's law of gravity,
+
+it becomes very obvious
+that those statements
+
+are the right statements.
+
+Newton know about
+Gauss's law of gravity,
+
+so Newton derived
+those statements
+
+by brute force
+integration, which
+
+is more of a tour de force.
+
+But something Newton was
+capable of doing it, and he did.
+
+To describe how the
+system is going to evolve,
+
+moving onward, we introduce
+something that's a little bit
+
+complicated, a function r, which
+is a function of two variables,
+
+r sub i and t.
+
+And r represents
+the radius at time t
+
+of the shell that was
+initially at radius r sub i.
+
+And our goal here is not just
+to keep track of the particle
+
+on the outside,
+which is for example,
+
+what Ryden does in her textbook.
+
+Ryden assumes that
+everything stays homogeneous.
+
+And then if you follow what
+happens to the outer edge,
+
+you know everything.
+
+But we're not going to
+make that assumption.
+
+We're going to conclude
+that it remains homogeneous,
+
+but we're going to derive it.
+
+Which means that we need to know
+the motion of every particle
+
+inside the sphere
+to be able to tell
+
+if it's going to
+stay homogeneous.
+
+And that's why we're introducing
+this more general description
+
+where r is a
+function of r sub i.
+
+So that function of
+the extra variable
+
+will tell us how every particle
+moves as the system evolves.
+
+We know that we're going to
+maintain spherical symmetry
+
+because we start with
+spherical symmetry
+
+and the force law respects
+spherical symmetry.
+
+So we're building that
+in from the beginning.
+
+We're not allowing things to
+depend on angular variables
+
+theta or phi.
+
+But assuming spherical
+symmetry, motion just
+
+is described entirely by
+giving the r-coordinate
+
+of each particle.
+
+And this function r of r i
+t does that-- exactly that.
+
+Then, we said that
+at a given radius,
+
+this description
+about shells tells us
+
+that the shells that
+are outside that radius
+
+don't do anything
+at a given radius.
+
+But the shells that are
+inside act like a point mass,
+
+as if it was all at the origin.
+
+So to understand how a given
+shell is going to evolve,
+
+all we really need to
+know is the total mass
+
+inside that shell.
+
+And that's given
+by M of r sub i,
+
+the mass inside the
+shell at radius r sub i.
+
+And that's just the
+volume of the shell
+
+initially times the
+initial mass density.
+
+As these shells move, the
+total mass inside a shell
+
+will remain exactly
+the same as it
+
+was as long as there's
+no crossings of shells.
+
+Now, the shell crossing
+issue is hard to talk about.
+
+But in the end, it
+just doesn't happen
+
+so you don't need
+to worry about it.
+
+But the argument was
+that initially we
+
+know the shells are moving
+apart from each other
+
+because we built in
+this Hubble expansion
+
+where everything is moving
+away from everything else.
+
+So if shells are
+ever going to cross,
+
+they're not going to
+cross immediately.
+
+It will take some time for
+these velocities to reverse,
+
+and the shells that were moving
+apart to move together and hit.
+
+So there's unambiguously
+at least a period of time
+
+where there are no
+shell crossings.
+
+And we could write
+down the equations
+
+that describe the motion
+during this period
+
+where there are no
+shell crossings.
+
+Now, if there was going
+to be a shell crossing,
+
+the equations that
+we're writing down
+
+would have to hold
+right up until the time
+
+of that first crossing.
+
+Because as long as
+there's no crossings,
+
+our equations are valid.
+
+Which means that if there was
+going to be a shell crossing,
+
+the equations we're writing
+down had better show it.
+
+Because the equations
+that we're writing down
+
+have to be valid right
+up until the instant
+
+of any possible shell crossing.
+
+And what we're going to
+find is that the equations
+
+are going to lead to just
+homogeneous evolution
+
+where there are no
+shell crossings.
+
+And therefore, that's
+the conclusion.
+
+If there were going to
+be any shell crossings,
+
+these equations would
+have to show it.
+
+They don't show it, so there
+are no shell crossings.
+
+So it's a complicated
+paragraph, but the bottom line
+
+is simple- we can
+ignore shell crossings.
+
+And that means that the total
+mass inside of any shell
+
+will remain exactly
+constant with time
+
+given by its initial value.
+
+And this formula is
+the initial value.
+
+And therefore, it
+holds at all time.
+
+Any questions about that?
+
+Any questions about the
+shell crossing issue?
+
+OK, good.
+
+So whoops, sorry about that.
+
+So M of r sub i is the mass
+inside the shell at radius r
+
+sub i.
+
+And then we can write down-- now
+we use Newton's law of gravity
+
+directly.
+
+We can write down
+the acceleration
+
+of a given particle in
+terms of its radius r
+
+and its initial radius r sub i.
+
+Its initial radius determines
+how much mass is inside.
+
+M of r sub i is
+independent of time.
+
+But the actual radius it's
+at determines how far away
+
+it is, or describes how far
+away it is from the origin.
+
+And that's the 1 over r squared
+that appears in the force law.
+
+So we have the time dependent r
+in the denominator and the time
+
+independent initial r sub i
+that appears in the numerator.
+
+And it's all proportional
+to a unit vector r
+
+hat pulling everything
+radially inward
+
+because of the
+minus sign in front.
+
+So gravity is pulling
+everything inward,
+
+which is what we'd expect.
+
+So this formula is
+the key formula.
+
+It's a vector
+formula, but we know
+
+that all the motion is radial.
+
+So all we really
+have to keep track
+
+of is the radius as
+a function of time.
+
+So we can turn
+this vector formula
+
+into a formula for
+little r itself.
+
+Just the radius number,
+the radial coordinate.
+
+And we get r double dot is minus
+4 pi over 3 G r sub i cubed rho
+
+sub i, taking the
+formula for M of ri
+
+from the line above
+divided by r squared.
+
+And the r in this formula--
+I didn't write the arguments,
+
+but it means this
+function r, which
+
+is a function of two
+arguments, r sub i and t.
+
+So this differential equation
+now governs our entire system
+
+and tells us everything
+we need to know
+
+or everything we can know
+about the actual dynamics.
+
+But to solve a
+differential equation
+
+of that sort, a second
+order differential equation,
+
+we need initial conditions.
+
+And we already described the
+initial conditions in words.
+
+Now we have to just figure out
+what those initial conditions
+
+are saying about r and r dot.
+
+And the answer is
+straightforward.
+
+We argued it last time.
+
+The initial conditions
+are that r at time t
+
+sub i is just r sub i.
+
+That was really the definition
+of r sub i in the first place.
+
+And r dot is just H
+sub i times v coming
+
+from the formula we had
+for the initial velocities.
+
+So these three equations,
+the two initial conditions
+
+and the differential
+equation, lead in principle
+
+to a mathematical solution
+that's completely unique
+
+and determined by
+those equations.
+
+And our goal now is
+just to figure out
+
+what that solution looks like.
+
+And we discovered a
+marvelous scaling property.
+
+That is, instead
+of talking about r,
+
+we divided r by r sub i and
+defined a new function, which
+
+we initially called u.
+
+Initially, thinking
+of it as a function
+
+of these two variables.
+
+We can write down
+new equations for u.
+
+And those equations
+end up not having
+
+any r sub i's in them at all.
+
+And once we realized
+that, we realized
+
+we don't need to call
+it u of r sub i and t.
+
+It's really just
+a function of t.
+
+And at that point, we
+renamed it because we also
+
+realized that it actually
+is our old friend the scale
+
+factor, a of t.
+
+So a of t is just r of r sub
+i and t divided by r sub i.
+
+And then the reason
+this is a scale
+
+factor is seen most clearly from
+that equation, which is really
+
+this equation just rearranged.
+
+The physical distance of
+a particle from the origin
+
+is equal to the scale
+factor times r sub i
+
+where r sub i plays the role
+of the coordinate distance.
+
+r sub i is a time-independent
+measure indicating
+
+which shell you're
+talking about.
+
+So the equations for a then
+are the equations for u,
+
+which are the equations for
+r just divided by r sub i.
+
+And we can write down
+what those equations are.
+
+We have a differential
+equation for a
+
+and two initial
+conditions where r
+
+sub i has dropped
+out all together.
+
+The differential equation
+is given immediately
+
+from the one we had up
+here, but we could also we
+
+write it in terms
+of what rho of t is.
+
+I didn't write the
+equation here because I
+
+guess I was running out of room.
+
+But we also figured out
+how rho of t behaves.
+
+And it behaves in
+the obvious way.
+
+As the space
+expands, the density
+
+just goes down as the volume.
+
+And the volume grows like a
+cubed, the cube of the scale
+
+factor, because volume's
+proportional to radius cubed.
+
+So rho of t is just rho sub
+i divided by a of t cubed.
+
+And putting that in, we
+can go from that equation
+
+to this equation.
+
+And this equation makes
+no reference anymore
+
+to the initial time.
+
+It's just an equation for what
+deceleration you see, what
+
+value of a double dot
+you see, as a function
+
+of the mass density
+and a itself.
+
+OK, any questions about any
+of those differential equation
+
+manipulations?
+
+Yes.
+
+AUDIENCE: In the homework, it
+says that this equation is not
+
+entirely general.
+
+We can't use it in all cases.
+
+Whereas, the other version
+that we get from the energy
+
+conservation is completely OK?
+
+PROFESSOR: That is correct, yes.
+
+AUDIENCE: It says it in
+there, but why is that?
+
+PROFESSOR: Why is it true?
+
+Well, as long as you have only
+non-relativistic matter, which
+
+is what we're
+talking about here,
+
+both of these-- this
+equation is golden
+
+and so is the equation
+we're about to talk
+
+about the derivation of,
+the conservation of energy
+
+equation.
+
+So as long as we have the
+context in which we derived it,
+
+it's completely valid.
+
+But on the homework
+set, we're talking
+
+about more general cases.
+
+We gave a different formula
+for the scale factor,
+
+which corresponds to a
+different situation in terms
+
+of the underlying materials
+that are building that universe.
+
+And where the change
+occurs is when
+
+one introduces a
+nonzero pressure.
+
+This gas of particles
+that we're talking about
+
+is just non-relativistic
+particles
+
+moving with the
+Hubble expansion.
+
+There's no internal velocity
+which generates a pressure.
+
+And it's pressure that
+makes a difference.
+
+This formula assume
+zero pressure.
+
+We will learn later
+how to correct it
+
+when there's a nonzero pressure.
+
+And the other formula
+doesn't depend on pressure,
+
+so it's valid whether
+there's pressure or not.
+
+But at the moment, we have
+no real way of knowing that.
+
+We'll talk later
+about why that's true.
+
+Other questions?
+
+No.
+
+OK, great.
+
+OK, one more slide here,
+not too much on it.
+
+At the end of the last
+class, we took the equation
+
+that I just wrote on
+the previous slide.
+
+I just copied it to this slide,
+the equation for a double dot,
+
+written in terms of the
+initial mass density.
+
+And discovered that it
+can be integrated once
+
+to produce a kind of a
+conservation of energy
+
+equation.
+
+And all you do is
+you start with this,
+
+write it by putting everything
+on one side of the equation,
+
+a double dot plus 4 pi over 3 G
+rho i over a squared equals 0.
+
+And then, multiply the
+whole equation by a dot.
+
+And a dot is called
+an integrating factor.
+
+It turns the expression
+into a total derivative.
+
+So once you write
+it this way, it
+
+is equivalent to dE dt
+equals 0, where e is just
+
+defined to be this
+quantity that would
+
+have better as a
+triple equal sign.
+
+e is just defined
+to be that quantity.
+
+And if you then write
+down what dE dt means,
+
+it means exactly that.
+
+So it's the same equation.
+
+So given our second
+order equation,
+
+we can write down a
+first order equation,
+
+which is that E is
+equal to a constant.
+
+And we commented last time that
+the physical interpretation
+
+of E is-- I'm not
+sure what to say.
+
+There are multiple physical
+interpretations of E
+
+is probably what I want to say.
+
+And one physical
+interpretation is
+
+if you multiply by
+the right factors,
+
+it does describe the actual
+energy of a test particle
+
+just on the boundary of our
+sphere, on the outer boundary.
+
+It doesn't really describe
+directly the total energy
+
+of a particle inside that
+sphere because calculating
+
+the potential energy of a
+particle inside the sphere
+
+is more complicated.
+
+And it doesn't give
+you the simple answer.
+
+So it doesn't really describe
+particles on the inside,
+
+except you could argue
+that if you-- talking
+
+about a particle on the inside,
+the particles outside of it
+
+don't matter.
+
+And you pretend
+they're not there.
+
+And then it does
+describe the energy.
+
+That is, you could
+think of any particle
+
+as being on the
+outside of the sphere
+
+and ignore what's outside it.
+
+But that's extra sentences
+that you have to put in.
+
+On the homework, you
+will also discover
+
+that for this finite-sized
+Newtonian sphere,
+
+there's certainly a
+well-defined Newtonian
+
+expression for the total
+energy of the sphere.
+
+And that's also
+proportional to this E.
+
+So by multiplying it
+by different constant,
+
+you can turn it into the
+total energy of the sphere.
+
+So it's actually
+related to energy
+
+and it's definitely conserved.
+
+Those are the important
+statements to takeaway.
+
+And that's where we
+left off last time.
+
+And we'll pick up from
+there now pretty much
+
+on the blackboard for
+the rest of lecture.
+
+Are there any further
+questions about these slides?
+
+OK.
+
+In that case, we will go on.
+
+The first thing I want to do is
+to take the same conservation
+
+law that we have up
+there and rewrite it
+
+in a way that's
+more conventional.
+
+And perhaps, more useful.
+
+But certainly,
+more conventional.
+
+We started with knowing that a
+quantity called E is conserved.
+
+And it's equal to 1/2 a dot
+squared minus 4 pi over 3
+
+G rho i over a.
+
+OK, then we also
+know that rho of t
+
+is equal to rho sub i divided
+by a cubed of t, which just says
+
+that matter thins out with
+the volume which grows
+
+as the cube of the scale factor.
+
+And that can be used to
+manipulate this equation.
+
+For reasons that will
+become clearer in a minute,
+
+I'm just going to manipulate
+this equation by multiplying it
+
+by 2 over a squared.
+
+Just because this will
+get me the equation
+
+I'm trying to get to.
+
+So if I multiply the left-hand
+side by 2 over a squared,
+
+I have to multiply the
+right-hand side by 2
+
+over a squared.
+
+The 2 cancels the half.
+
+The first term becomes
+a dot over a squared.
+
+And you might remember the a dot
+over a is the Hubble expansion
+
+rate, so it has some
+physical significance.
+
+And then, minus the 2 turns the
+4 pi over 3 into 8 pi over 3.
+
+And the a squared multiplies
+the a to make an a cubed.
+
+And then here, we have
+rho i over a cubed, which
+
+in fact is just the
+current value of rho.
+
+So we can rewrite this as a
+dot over a squared minus 8 pi
+
+over 3 G rho.
+
+No a's anymore on
+the right-hand side.
+
+Well, on a's anymore
+in this term.
+
+OK, now the convention
+that brings our notation
+
+into contact with the
+rest of the world.
+
+Nobody talks about
+E, by the way.
+
+That's just my convention.
+
+But to make contact
+with the rest
+
+of the world, the rest
+of the world talks
+
+about a number called
+little k, lowercase k.
+
+And it connects to our notation
+by being equal to minus 2E
+
+divided by c squared.
+
+And with that connection, we
+can write our conservation law
+
+in what is the standard
+way of writing it,
+
+at least in many textbooks.
+
+And that's it.
+
+So I put a box around it.
+
+And this equation was first
+derived by Alexander Friedmann
+
+using general
+relativity in 1922.
+
+And it is, therefore, usually
+called the Friedmann equation.
+
+Alexander Friedmann, by the
+way, was a Russian meteorologist
+
+by profession.
+
+But as a meteorologist,
+he knew a lot
+
+about differential equations.
+
+And when general relativity came
+out, he got interested in it
+
+and was the first person to
+derive using general relativity
+
+the equations that described
+an expanding universe.
+
+And he wrote two famous
+papers-- now famous papers--
+
+in 1922 and 1923.
+
+One of them talking about
+the system of equations
+
+where k is positive
+and another talking
+
+about where it's negative.
+
+I forget which
+order they were in.
+
+But they correspond to
+open and closed universes,
+
+which we'll talk about
+more in a few minutes.
+
+Now, I just should remind you
+to have our equations together.
+
+We also had the all-important
+equation for a double dot.
+
+And as I was just describing
+an answer to a question,
+
+we don't know yet how
+to generalize this
+
+to other kinds of matter besides
+the non non-relativistic dust
+
+that we just derived them for.
+
+They're certainly both correct
+for our non-relativistic dust.
+
+But when we try to generalize
+them, what we'll find
+
+is that the top equation
+will remain true exactly
+
+for any kind of matter, while
+the bottom equation assumes
+
+that pressure equals 0.
+
+Now, the standard terminology
+is to call the top equation
+
+the Friedmann equation.
+
+In fact, both of
+these equations,
+
+with this one including the
+pressure term that we don't
+
+have yet, appeared in
+Friedmann's original papers.
+
+So I usually refer to
+these two equations
+
+as the Friedmann
+equations-- plural.
+
+But many textbooks refer to just
+the top one as the Friedmann
+
+equation and don't give a
+name to that equation, which
+
+is also OK if you want.
+
+Yes.
+
+AUDIENCE: Didn't we
+get the top equation
+
+from the bottom equation?
+
+PROFESSOR: We did.
+
+That's right.
+
+So how does that jive?
+
+The answer is-- and we'll
+be coming to this later.
+
+But the answer is that when
+we got the top equation
+
+from the bottom equation,
+we used that equation.
+
+And this equation
+will no longer hold
+
+when there's a
+significant pressure.
+
+And in fact, when we derive
+it later-- I forget what order
+
+we'll do things in.
+
+But we'll make sure that
+all three of these equations
+
+are consistent when
+we include pressure.
+
+The reason the top
+equation changes
+
+if you include pressure--
+may not be obvious.
+
+But if I tell you
+why it happens,
+
+it will become obvious.
+
+The top equation looks like
+it's just how things thin out.
+
+Like a cubed.
+
+But rho is the
+total mass density.
+
+And relativistically, it's
+equivalent to the energy
+
+density.
+
+If you just multiply
+by c squared,
+
+that becomes the energy
+density by the E equals
+
+mc squared equality.
+
+So it's a question of
+how much energy there
+
+is inside this sphere or box.
+
+And if you imagine
+a box changing size,
+
+if it's filled with a gas
+with a positive pressure,
+
+as that box changes
+size, the pressure
+
+does work on the boundary.
+
+If you think of it as a piston.
+
+And if we have a positive
+pressure and a gas expands,
+
+it loses energy.
+
+And relativistically, that
+means it has to also lose mass.
+
+The total mass inside the
+box does not remain constant
+
+as it expands, which
+is the idea that we
+
+use when we derive that
+rho i over a cubed.
+
+So rho i over a cubed
+is the right behavior
+
+for the total mass
+density or energy
+
+density for a zero pressure gas.
+
+But when you include
+pressure and take
+
+into account relativity, that's
+not the right formula anymore.
+
+AUDIENCE: The top one, it
+just cancels out somehow?
+
+PROFESSOR: Well, the pressure
+ends up canceling out,
+
+so that this ends
+up still being true
+
+and this ends up
+being different.
+
+And we'll see later
+how it happens.
+
+I just want to indicate where
+the changes are going to be.
+
+We'll see what the changes
+are when we get there.
+
+AUDIENCE: What happened
+to the third factor
+
+of a in the second equation?
+
+PROFESSOR: There's a
+factor of a missing, sorry.
+
+Yes, thank you very much.
+
+It's important to get
+the equations right.
+
+That wasn't
+Friedmann's equation.
+
+That was Alan's equation.
+
+Now it's Friedmann's equation.
+
+He got it right.
+
+OK, any other errors or
+questions to bring up?
+
+OK.
+
+Now is probably a good time to
+talk about the question of why
+
+we were so fortunate to discover
+that the Friedmann equation
+
+that we derived agrees exactly
+with general relativity.
+
+There is a simple reason for it.
+
+I don't think it's
+an accident at all.
+
+The reason for it,
+as I understand it,
+
+is that we assume
+from the beginning--
+
+and we would be assuming
+this whether we're
+
+talking about the
+Newtonian calculation
+
+or the corresponding general
+relativity calculation.
+
+We assume from the
+beginning that we
+
+are modeling a completely
+homogeneous system, where
+
+every part of it is identical
+to every other part.
+
+And once you assume
+that homogeneity,
+
+it means that if you know
+what happens in a little box,
+
+a meter by a meter
+by a meter say.
+
+If you know what
+happens in a little box,
+
+you know what happens
+everywhere because you assume
+
+that what happens everywhere
+is exactly the same as what's
+
+happening in that box.
+
+So that implies
+that if Newton is
+
+right for what
+happens in the box,
+
+Newton has to be
+right for what's
+
+happening in the universe.
+
+And we do expect
+Newtonian physics
+
+to work on small scales,
+scales of a meter,
+
+and small velocities.
+
+The Hubble expansion of
+a meter is negligible.
+
+So we expect Newton to give
+us a proper description of how
+
+the system is behaving
+on small scales.
+
+And the assumption
+of homogeneity
+
+guarantees that if you
+understand the small scales,
+
+you also understand
+the large scales.
+
+So I think we are guaranteed
+that this had better give us
+
+the same results as
+general relativity or else
+
+Newtonian physics is
+not the proper limit
+
+of general relativity.
+
+But it is.
+
+We would not accept
+general relativity
+
+if it did not give
+Newtonian physics
+
+for small scales
+and low velocities.
+
+So we expect to get the
+same answer as Gr and we do.
+
+This is exactly
+what Gr would give.
+
+And this is exactly what Gr
+would give also for the case
+
+where there's no pressure--
+the case we're doing.
+
+OK, any questions about that?
+
+OK, next item.
+
+I would like to
+say a couple words
+
+about the units in
+which we're going
+
+to define these quantities.
+
+So far, in our
+mathematical model,
+
+r and r sub i are distances.
+
+And therefore, they're
+measured in whatever units
+
+you're using to
+measure distances.
+
+And I'll pretend
+we're using SI units.
+
+So I'll say meters.
+
+We could use light
+years, or whatever.
+
+It doesn't really matter.
+
+But they're both measured
+in ordinary distance units.
+
+And earlier when we talked
+about scale factors and things,
+
+I told you that many
+books do it this way.
+
+Think of both the
+co-moving coordinates
+
+and the physical distances
+as being measured
+
+in meters and the scale
+factor being dimensionless.
+
+But I told you I don't
+like to do it that way
+
+because I think it's
+clearer to recognize
+
+that these co-moving
+coordinates don't have
+
+any real relationship
+to actual distances.
+
+At least not as time changes.
+
+So for me, it's better
+to have a different unit
+
+to describe the co-moving
+coordinate systems.
+
+So I would like to
+introduce that here.
+
+And all I need to do really is
+say that let the unit of r sub
+
+i be called a notch.
+
+Now, we already
+called it a meter,
+
+but that doesn't really
+mean that a meter is
+
+the same as a notch.
+
+Because when we
+called it a meter,
+
+we were not really
+taking into account
+
+the fact that it's only
+a meter at time t sub i.
+
+So another way of
+describing this definition,
+
+which might not sound like we're
+trying to redefine the meter,
+
+is to say that the statement r
+sub i equals 5 notches, which
+
+is the kind of statement I'm
+going to make now because I'm
+
+only going to talk about r
+sub i measured in notches.
+
+When I say r sub i
+is 5 notches, that's
+
+equivalent to saying that the
+particle labeled by r sub i
+
+equals 5-- 5 notches-- was
+at 5 meters from the origin
+
+at time t sub i.
+
+So giving the value of a
+co-moving coordinate in notches
+
+tells you exactly
+what distance it
+
+was from the origin
+at time t sub i.
+
+Now, the reason why I don't
+use this to just say, well,
+
+why don't we call it
+meters, is that we're now
+
+going to forget about t sub i.
+
+If you look at
+equations we have,
+
+t sub i no longer
+appears in any of them.
+
+t sub i was just our
+way of getting started.
+
+And we could have started
+at any time we wanted.
+
+And once we have
+these equations,
+
+we can talk about times
+earlier than t sub
+
+i, times later than t sub i.
+
+And there's nothing special
+about t sub i anymore.
+
+But r sub i we're going to
+keep as our permanent label
+
+for every shell, which means
+for every particle there will be
+
+a value of r sub i attached
+to that particle which will be
+
+maintained as the
+system evolves.
+
+And it will be clearly
+playing the role
+
+of what we've called the
+co-moving coordinate.
+
+And therefore, we will
+want to keep r sub i
+
+and we'll want to call
+its unit something.
+
+And I'm just saying I'm
+going to call them notches.
+
+You can call them
+meters if you want,
+
+but I'm going to
+call them notches.
+
+So using this language, I'm not
+changing any of the equations
+
+that we wrote.
+
+So we will still have r being
+equal to a of t times r sub i.
+
+But now, r will be
+measured in meters.
+
+a of t I will think of
+as meters per notch.
+
+And r sub i will me
+measured in notches.
+
+And the scale factor a of t
+will be playing the same role
+
+it played ever since we
+introduced the word scale
+
+factor.
+
+It just means that when
+the scale factor doubles,
+
+all distances in our
+model double exactly.
+
+Now that we have the sort
+of new system of units,
+
+I just want to work out
+the units of an object
+
+where the units are
+not all obvious.
+
+What are the units of
+this thing that we've
+
+defined that we called k,
+which is related to this thing
+
+that we defined that was called
+E, where E was not really
+
+an energy?
+
+But we can work out what k is.
+
+I'm using square brackets
+to mean units of.
+
+k can be thought of as being
+defined by this equation.
+
+Or in any case, this
+equation certainly
+
+must be dimensionally
+consistent because we derived
+
+it and you didn't point out
+that I made any mistakes,
+
+so I must not have.
+
+So the units of kc
+squared over a squared
+
+should be the same as the
+units of a dot squared
+
+over a squared.
+
+And if I multiply through
+to write units of k--
+
+to relate them to a dot,
+we get the units of k
+
+have to be the same
+as the units of 1/c
+
+squared times a dot squared.
+
+The a squareds in
+the denominator
+
+here just cancel each other.
+
+So the units of k has to be
+the same as the units of 1/c
+
+squared a dot squared.
+
+And we know what they are.
+
+The units of 1/c squared
+is second squared
+
+per meter squared.
+
+Meter per second
+squared, but upside down.
+
+That's the 1/c squared factor.
+
+And a dot is meters per notch
+per second because of the dot.
+
+So meters per notch would be a.
+
+a dot would have
+an extra second.
+
+And the whole thing gets
+squared because it's
+
+a dot squared here.
+
+And you see then that
+the meter squares cancel.
+
+The second squareds cancel.
+
+And we just get the peculiar
+answer 1 over a notch squared.
+
+Now, there's probably not a
+lot of intuition behind that.
+
+But what it clearly
+does say is that we
+
+can make k change its
+numerical value by changing
+
+our value for the notch.
+
+And that's important to know.
+
+And it's a clear consequence
+of what we just did.
+
+So now we can talk about
+different conventions
+
+that people use for
+defining the notch.
+
+And hence, k, which are
+clearly related to each other
+
+we've now learned.
+
+So first of all, in the
+construction that we just
+
+did-- starting out with our
+sphere, and letting it grow,
+
+and defining the maximum sphere
+as r max comma i and so on.
+
+In that construction, our
+initial value of t-- excuse
+
+me, our initial value
+of a, a of ti, was one.
+
+And the way we
+first did it where
+
+all lengths were
+measured in meters.
+
+And with our new definition that
+r sub i is measured in notches
+
+so that a is meters
+per notch, it
+
+means that in the system
+we just had, a of t sub
+
+i was 1 meter per notch.
+
+And since we
+already did this, we
+
+don't really want to change it.
+
+But I point out that t sub i,
+if you look at our equations,
+
+survives in only one place,
+which is in this equation.
+
+It has disappeared from
+every other equation
+
+we're going to be keeping.
+
+So we are perfectly safe in just
+forgetting about this equation.
+
+Or if we want to
+remember about it,
+
+we could just say, well, yeah,
+t sub i had some significance.
+
+It was the time at which
+the scale factor happened
+
+to have been equal to
+1 meters per notch.
+
+But otherwise, it
+has no importance.
+
+There's a different time
+when the scale factor was
+
+10 meters per notch, or
+1 light year per notch.
+
+So since t sub i is of
+no relevance whatever,
+
+we can safely forget
+the above equation.
+
+Or we could think of it as
+the definition of t sub i,
+
+where we don't care
+anything else about t sub i.
+
+So it was just some
+symbol that was
+
+used in some
+earlier calculation.
+
+So we now just have a
+scale factor a of t.
+
+And we can talk about how
+we might normalize it.
+
+And there are basically
+two important conventions
+
+that are in use in textbooks.
+
+Some textbooks, which include
+Barbara Ryden's textbook
+
+that we're using,
+define a of t to be
+
+equal to 1, which I will call
+1 meter per not much today.
+
+So a of t is just defined to be
+1 today as a common notation.
+
+It's notation that
+Barbara Ryden uses.
+
+And that makes a notch
+equal to a meter today.
+
+There's another
+common convention,
+
+which is to recognize that since
+k has units 1 over notches,
+
+we can make k any value we
+want without changing any
+
+of the physics, just changing
+our definition of the notch,
+
+which is up for grabs.
+
+Nobody has yet
+defined the notch.
+
+We're defining it now.
+
+So we can choose the
+definition of a notch
+
+to make the value of
+k something simple.
+
+And the obvious choice for
+the simplest real number
+
+that you could imagine
+that's not 0 is 1.
+
+So we could choose
+the definition
+
+of the notch to
+make k equal to 1.
+
+Except that we can't
+change the sign of k.
+
+The sign of k makes important
+differences in this equation.
+
+And we don't want to make the
+definition of a notch negative
+
+or imaginary, I
+guess, is what you
+
+need to change the sign of k.
+
+So as long as
+notches are real, we
+
+can only change positive k's
+to different positive k's
+
+and negative k's to different
+values of negative k.
+
+So the convention would be
+that when k is not equal to 0--
+
+it can be 0 as a special case.
+
+But when k is not equal
+to 0, define the notch
+
+so that k is equal
+to plus or minus 1.
+
+I would say that
+this convention is
+
+more common than that
+convention of the books
+
+that I've read in my
+lifetime, but both conventions
+
+are in use.
+
+And one sees from this
+dimensional relationship
+
+that one can certainly
+choose a notch
+
+to make k if it's nonzero
+have any value you
+
+want of the same sign.
+
+And that means you can
+always make k plus or minus
+
+1 if it's not 0.
+
+The books that use this as their
+convention, generally speaking,
+
+leave the notch undefined
+when k equals 0.
+
+Undefined means arbitrary.
+
+And there's no problem with
+that because k and the notch
+
+never really appear in
+final physical quantities.
+
+The notch always
+was just your choice
+
+of how to write down your
+co-moving map of what
+
+the universe looks like.
+
+OK, any questions about these
+funny issues involving units?
+
+OK, good.
+
+The next thing I
+want to do now is
+
+to start talking about
+solutions to this equation.
+
+And I guess I'll leave the
+equation there and start
+
+on the new blackboard.
+
+OK, I'm going to rewrite
+the equation almost the way
+
+it was written on the top there.
+
+In fact, exactly as it
+was written on top there.
+
+I'm going to
+rewrite the equation
+
+as E equals 1/2 a dot squared
+minus 4 pi over 3 G rho sub i
+
+over a.
+
+And the reason I'm writing it
+in this way rather than any
+
+of the other six or seven
+ways that we've written it,
+
+is that this way the only
+time-varying thing is a itself.
+
+And if we want to talk
+about what the differential
+
+equation tells us about
+the time variation of a,
+
+it helps a lot if we're writing
+an equation where a of t
+
+is the only thing
+that varies with time.
+
+And this is at least
+one way of doing that.
+
+So in particular, I used
+rho sub i rather than rho.
+
+So the behavior of this
+equation might very well
+
+depend on the sign of E.
+And we'll see that it does.
+
+And if we think it might
+depend on the sign of E,
+
+we realize from the
+beginning that E
+
+could be positive,
+negative, or 0.
+
+There are those three cases.
+
+So those are the cases
+we want to look at.
+
+E can be positive,
+negative, or 0.
+
+So we'll take them
+one at a time.
+
+It will help to make things
+completely obvious to rewrite
+
+this as an equation
+for a dot squared.
+
+I'll multiply by 2.
+
+And write this as
+equation a dot squared
+
+is equal to 2E plus 8 pi
+over 3 G rho sub i over a.
+
+8 pi instead of 4 pi
+because we multiplied by 2.
+
+And we notice that this term,
+proportional to rho sub i
+
+over a, is
+unambiguously positive.
+
+We're not going to have
+any negative mass densities
+
+in our problem.
+
+There's no way that can happen.
+
+And a is always positive.
+
+So the right term is positive.
+
+a dot squared had
+better be positive
+
+because it's the
+square of something.
+
+E could, in principle,
+have either sign.
+
+And we'll talk about both
+cases, or the 0 case.
+
+But if we start with the
+case where E is positive,
+
+just to consider these
+three cases one at a time.
+
+So suppose E is greater than 0.
+
+And remind you that E
+and k had opposite signs.
+
+So that would imply
+that k was negative.
+
+So if we start by considering
+the k negative case or the E
+
+positive case, then we see that
+we have a positive number here
+
+and a positive number there.
+
+So they will add up to always
+give us a positive number.
+
+a dot squared will
+always be positive.
+
+And it will just mean that
+a dot will be positive.
+
+Square root of a positive
+number is a positive number.
+
+At least it's only the positive
+square root that matters here.
+
+So a will just keep growing
+forever in this case.
+
+a dot squared will
+never fall below 2E.
+
+So it will be a lower
+bound to a dot squared.
+
+And that means there will
+always be a minimum expansion
+
+rate that the
+universe will have.
+
+So in this case, a
+increases forever.
+
+And that's called
+an open universe.
+
+And it's one of the
+three possibilities
+
+that we're going to
+be investigating here.
+
+Next case is E
+less than 0, which
+
+is the more common notation of
+k means k is greater than 0.
+
+In this case, if you think of
+E as an energy, which it really
+
+is, it means we have
+less than 0 energy.
+
+Which means that we basically
+have a bound system.
+
+And the equation tells us that
+it acts like a bound system.
+
+We don't have to rely
+on that intuition,
+
+but that is the right intuition.
+
+The equation up there tells
+us that if E is negative,
+
+the total right-hand side
+had better be positive
+
+because the left-hand side is
+positive and the left-hand side
+
+cannot go negative.
+
+But this term is going to
+get smaller and smaller
+
+as a increases.
+
+And as this term gets
+smaller and smaller,
+
+it runs the risk of no
+longer outweighing this term
+
+and giving possibly
+a negative answer.
+
+And what has to happen is a
+cannot get any bigger than
+
+the value it would have where
+the right-hand side would
+
+vanish.
+
+So a continues to grow
+because a dot is positive.
+
+This gets smaller and
+smaller until this term
+
+equals that term in magnitude.
+
+And then, a dot goes to 0.
+
+What happens next
+is not completely
+
+obvious from this
+equation, but it
+
+means that we have an
+expanding universe that's
+
+reached a maximum
+size and then stopped.
+
+Then, what is actually
+obvious is from this equation
+
+is that it will
+start to collapse.
+
+So this case corresponds
+to a universe that
+
+reaches a maximum size and then
+turns around and collapses.
+
+So a has a maximum value.
+
+And we can read off
+from that equation what
+
+it is, a max is
+just the value that
+
+makes the right-hand
+side of that equation 0,
+
+which is minus 4 pi G
+rho sub i divided by 3E.
+
+And remember, E is
+negative for this case,
+
+so this is a positive number.
+
+So a has some positive
+maximum value.
+
+Reaches that value, and then
+turns around and collapses.
+
+Yes?
+
+AUDIENCE: Sorry, I don't know
+if you said this already,
+
+but since a dot squared is
+equal to some quantity, when you
+
+solve for a dot, you can have
+positive and negative solution.
+
+Why do we discount
+the negative solution?
+
+PROFESSOR: OK,
+very good question.
+
+The question if
+you didn't hear it
+
+is, why do we discount
+the negative solution
+
+when we have an equation
+for a dot squared?
+
+Couldn't a dot be
+positive or negative?
+
+And the answer is it
+certainly could be either.
+
+And both solutions
+exist as valid solutions
+
+to these equations.
+
+But we started out with
+an initial condition
+
+that a dot was positive.
+
+Our initial value
+of a dot was H i.
+
+And once it's positive,
+it can't change sign
+
+according to that equation.
+
+Except by going
+through 0, which is
+
+what we're talking about now.
+
+But it will only change
+sign when it goes through 0.
+
+So it reaches a maximum
+value, then it does collapse.
+
+And in the collapsing
+phase, that same equation,
+
+a dot squared equals
+the right-hand side,
+
+holds where it would be
+the negative solution that
+
+describes the collapsing phase.
+
+So the verbal description
+of what's happening here
+
+is that the universe
+reaches a maximum size
+
+and then collapses.
+
+And it collapses all the way
+to a equals 0 in this model.
+
+And that's often
+called the Big Crunch
+
+for lack of a better word.
+
+The Big Crunch being
+the collapsing form that
+
+corresponds to the
+Big Bang, which
+
+is the instant which
+all this starts.
+
+And this was called
+an open universe.
+
+As you could
+probably guess, this
+
+is called a closed universe.
+
+OK.
+
+And now finally, we want
+to consider a case where
+
+E is not positive
+and not negative.
+
+The case that we're
+left with is E equals 0.
+
+And that's called
+the critical case.
+
+So the critical value
+for E is E is equal to 0.
+
+And that means that k
+is equal to 0 as well.
+
+It implies k equals 0.
+
+And notice that this
+is a special case.
+
+E is a real number.
+
+It can be positive,
+negative, and 0 is just
+
+a particular value on the
+borderline between those two.
+
+For the people who are in the
+habit of rescaling notches
+
+so that k is always
+plus 1, minus 1, or 0,
+
+it makes it sound like there are
+three totally distinct cases.
+
+But that's only because
+of the rescaling
+
+that those people are doing.
+
+If you keep track of E as your
+variable, which you certainly
+
+can, you do see that
+the flat case, E equals
+
+0-- the critical
+case-- is really
+
+just the borderline
+of the other two.
+
+And it's therefore, arbitrarily
+close to both of the other two.
+
+It really is where they meet.
+
+But working out the equations,
+we have in this case
+
+a dot over a squared is
+equal to 8 pi over 3 G rho.
+
+And in general, it's minus
+kc squared over a squared.
+
+But we're now considering
+the case where that vanishes.
+
+And that means we
+have a unique value
+
+for rho in terms
+of a dot over a.
+
+And at this point, it's
+worth reminding ourselves
+
+that a dot over a is just
+H. So this is H squared.
+
+So for this critical
+case, the case
+
+that's just on the borderline
+between being open and closed--
+
+and we'll be calling it flat.
+
+For this critical case, we
+have a definite relationship
+
+between rho and H.
+So rho has to equal
+
+what we call the
+critical density, which
+
+you get by just
+solving that equation.
+
+And it's 3H squared over 8 pi G.
+
+And we see, therefore, that
+rho being equal to rho c
+
+is this dividing line
+between open and closed.
+
+And if you think back about
+the signs of what we had,
+
+what you'll see is
+that rho bigger rho
+
+c is what corresponds
+to a closed universe.
+
+Rho less than rho c
+is what corresponds
+
+to an open universe.
+
+And rho equals rho
+c can be called
+
+either a critical
+universe or we'll
+
+be calling it a flat universe.
+
+And the meaning of the word
+"flat" will be motivated later.
+
+For now, these words--
+open, closed, and flat--
+
+refer to the time
+evolution of the universe.
+
+We'll see later that
+it's also connected
+
+to the geometry of the universe,
+but we're not there yet.
+
+Then the word "flat"
+will make some sense.
+
+Yes.
+
+AUDIENCE: How do we know there's
+not some very large entity,
+
+like some cluster of
+black holes or something
+
+that renders all of this not
+applicable to our universe?
+
+PROFESSOR: OK.
+
+The question is, how
+do we know there's not
+
+some humongous perturbation,
+some huge collection
+
+of black holes that
+renders this all
+
+inapplicable to our universe?
+
+The answer is that it
+works for our universe.
+
+That is, observationally
+we can test these things
+
+in a number of ways.
+
+Tests include calculations
+of the production
+
+of the light chemical
+elements in the Big Bang.
+
+Tests include making predictions
+for what the cosmic background
+
+radiation should
+look like in detail.
+
+And those tests work
+extraordinarily well.
+
+So that's why we
+believe the picture.
+
+But you're right,
+we don't have really
+
+direct confirmation
+of most of this.
+
+And if there was some
+giant conglomeration
+
+of mass out there someplace, it
+might not have been found yet.
+
+But so far, this
+picture works very well.
+
+That's all I can say.
+
+And there really is
+quite a bit of evidence.
+
+We'll maybe talk
+more about it later.
+
+Any other questions?
+
+OK.
+
+So having understood
+the importance
+
+of this critical
+density, it might
+
+be nice to know what the
+value for the critical density
+
+for our universe is.
+
+And we can calculate it because
+it just depends on the Hubble
+
+expansion rate, an the
+Hubble expansion rate
+
+has been measured.
+
+So if we try to put
+in numbers, it's
+
+useful to write the present
+value of the Hubble expansion
+
+rate, as it's often
+written, as 100 times h sub
+
+0 kilometers per
+second per megaparsec.
+
+So this defines h sub
+0, little h sub 0.
+
+And I think the main advantage
+of using this notation
+
+is that you don't have to keep
+writing kilometers per second
+
+per megaparsec which gets to
+be a real pain to keep writing.
+
+So little h sub 0 is just
+a dimensionless number
+
+that defines the
+Hubble expansion rate.
+
+And it does then allow you
+to write other formulas
+
+in simple ways.
+
+Numerically, Newton's
+constant you can look up.
+
+It's 6.672 times
+10 to the minus 8
+
+centimeter cubed per
+gram per second squared.
+
+And when you put these equations
+together, all you need to know
+
+is G and H squared to
+know what rho critical is.
+
+You find that rho critical can
+be written initially for any H0
+
+as 1.88 h0 squared
+coming from the h squared
+
+in the original formula times
+10 to the minus 29 grams
+
+per centimeter cubed.
+
+And note the whopping smallness
+of that 10 to the minus 29.
+
+The mass density of
+our universe is, as far
+
+as we know, equal to
+this critical density.
+
+We know it's equal to
+within about a half
+
+of a percent or so.
+
+And h0 is near 1.
+
+h0, according to
+Planck, is 0.67--
+
+according to the
+Planck satellite
+
+measurement of the
+Hubble parameter
+
+And if you put
+that into here, you
+
+get the critical density
+is about 8.4 times 10
+
+to the minus 30 grams
+per centimeter cubed.
+
+And that is equivalent to about
+5 protons per cubic meter.
+
+So I've written
+the answer in terms
+
+of grams per cubic
+centimeter because
+
+to me that's a very
+natural unit for density
+
+because it's the
+density of water.
+
+We're saying that the average
+density of the universe is only
+
+about 10 to the minus
+29 quantity 8.410.
+
+The average density of the
+universe is only about 10
+
+to the minus 29 times
+the density of water.
+
+So it's an unbelievably empty
+universe that we're living in.
+
+It's hard to believe the
+universe is that empty,
+
+but there are large spaces
+between the galaxies
+
+that we look at.
+
+So the universe is
+incredibly empty.
+
+And in fact, this is a
+vastly better vacuum.
+
+An average part of the universe
+is a vastly better vacuum
+
+than can be made on
+Earth by any machinery
+
+that we have access to.
+
+So the best vacuum is empty
+space, just middle of nowhere.
+
+And it's vastly better
+than what we can actually
+
+produce on Earth.
+
+Yes.
+
+AUDIENCE: I see you
+used protons here,
+
+5 protons per cubic medium.
+
+So is this density corresponding
+to density of baryonic matter,
+
+or all types of matter?
+
+PROFESSOR: This is actually
+all types of matters,
+
+even though I'm using my
+proton as a meter stick.
+
+But it is the total mass
+density of the universe that's
+
+very close to the
+critical value.
+
+And I was just about
+to say something
+
+about what the total
+mass is made up of.
+
+Cosmologists define-- this
+was certainly mentioned
+
+in my first lecture-- a
+Greek letter capital Omega
+
+to mean the actual mass
+density of the universe divided
+
+by this critical density.
+
+So omega equals 1 in
+this language corresponds
+
+to a flat universe at
+this critical point.
+
+Omega bigger than 1 corresponds
+to a closed universe.
+
+And omega less
+than 1 corresponds
+
+to an open universe.
+
+And today, we know that
+omega is equal to 1
+
+to an accuracy of about
+a half of a percent.
+
+To a very good accuracy we
+know omega is very close to 1.
+
+It's made up of
+different contributions.
+
+And these tend to vary with
+time-- as the best measurements
+
+tend to vary with
+time by a few percent.
+
+But omega matter-- and
+here I mean visible
+
+plus dark matter--
+is roughly about 0.3.
+
+And most of the universe
+today, as we mentioned earlier,
+
+the universe today is pretty
+much dark energy-dominated.
+
+So omega dark energy
+is about equal to 0.70.
+
+And omega total is
+pretty close to 1.
+
+Plus or minus about
+a half of a percent.
+
+So one of the
+implications here is
+
+that we've been assuming
+in our calculation so far
+
+that we're talking about nothing
+but non-relativistic matter.
+
+That's actually only about
+30% of the actual matter
+
+in the current universe.
+
+So I did say this
+is the beginning.
+
+The current universe today
+does not obey the equations
+
+that we've written
+down very accurately.
+
+It's pretty far off.
+
+But the equations
+that we wrote down
+
+are pretty accurate
+for the history
+
+of our universe from a
+period of about 50,000 years
+
+after the Big Bang up
+to about 9 billion years
+
+after the Big Bang.
+
+Yes.
+
+AUDIENCE: Before dark
+energy was discovered,
+
+did they think omega
+was [INAUDIBLE]?
+
+PROFESSOR: Yes.
+
+At least many people did.
+
+Before dark energy
+was discovered,
+
+there was a controversy
+in the community
+
+over what we thought omega was.
+
+Those of us who had
+faith in inflation
+
+believed that omega
+would be 1 because that's
+
+what inflation predicts.
+
+Astronomers who just had
+faith in observations
+
+believed that omega
+was 0.2 or 0.3
+
+because that's what they saw.
+
+And the truth ended
+up being somewhat
+
+in between in the
+sense that omega
+
+total we now all agree
+is very close to 1
+
+as inflation predicts.
+
+But it's still true that the
+stuff that the astronomers saw
+
+at this earlier time did
+only add up to 0.2 or 0.3.
+
+So they correctly estimated
+what they were looking at
+
+and they had no way of
+knowing that there was also
+
+this dark energy component
+until it was finally
+
+discovered in 1998.
+
+Yes.
+
+AUDIENCE: If we don't know what
+dark energy is, observationally
+
+how have we been
+able to measure that?
+
+PROFESSOR: How do we
+measure it so accurately
+
+if we don't know
+what it is, right?
+
+Right.
+
+Well, the answer
+is while we're not
+
+sure what it is, we
+actually do think
+
+we know a lot of its properties.
+
+And essentially, almost
+all properties that
+
+are relevant to cosmology.
+
+We just don't know what's
+sort of like inside.
+
+So we know it creates
+repulsive gravity.
+
+We know how much repulsive
+gravity it creates.
+
+And we also know to
+reasonable accuracy
+
+how the dark energy
+has been evolving
+
+with time, which is
+really that it's not
+
+been evolving with time.
+
+And that determines
+what its pressure is.
+
+It determines, in
+fact-- to not evolve
+
+with time we'll see later
+requires the pressure
+
+to be equal to the negative
+of the energy density.
+
+Pressure is related to how
+energies change with time, as I
+
+mentioned a few minutes
+ago in a different context.
+
+If you have a box that expands
+and there's a pressure,
+
+the pressure does dp
+dv work on the box.
+
+And you can tell how much
+the energy in the box
+
+should change for
+a given pressure.
+
+And we'll do this
+more carefully later,
+
+but to have the energy
+not change at all
+
+requires a pressure, which
+is the negative of the energy
+
+density.
+
+So we know how much acceleration
+the dark energy causes.
+
+We know to reasonable
+accuracy and we
+
+assume it's true
+that the pressure is
+
+equal to minus the
+energy density.
+
+And that's all you need to know
+to calculate how much of it
+
+you need to account for
+that much acceleration.
+
+And that's how it's done.
+
+Any other questions?
+
+OK next thing we want to
+do is to actually solve
+
+this equation for
+the easiest case.
+
+We'll solve it in general
+later, but the easiest case
+
+to solve it is the case
+of the critical case.
+
+We only have a few
+minutes, but it only
+
+takes a few minutes to solve
+the equation for this case.
+
+It should be over here.
+
+So for the critical case,
+it's the case E is equal to 0.
+
+And therefore, we
+just have a dot
+
+squared is equal to a
+constant divided by a.
+
+And it won't really
+matter for us
+
+right now what this constant is.
+
+So I don't even have
+to keep track of it.
+
+I'll just write it
+as const, C-O-N-S-T.
+
+And I'll take the square
+root of this equation
+
+because it's easier
+to know what a dot is
+
+than to know what a is.
+
+Easier to make use of
+knowing what a dot is.
+
+So I can rewrite that equation
+as a dot, which I'll now
+
+write as da dt, to be a little
+more explicit about what we're
+
+talking about, is equal to a
+constant over a to the 1/2.
+
+So this now is the k
+equals 0 evolution.
+
+So this is just the
+same Friedmann equation
+
+rewritten for the
+special case k equals 0.
+
+And now I'm just
+going to perform
+
+the amazingly complicated
+manipulation of multiplying
+
+both sides of the
+equation by a to the half.
+
+So we have a to the half.
+
+I'm also going to
+multiply by dt.
+
+So a to the half da will be
+equal to a constant times dt.
+
+And now we can just
+integrate both sides
+
+as an indefinite integral.
+
+And integrating both sides
+as an indefinite integral,
+
+the left-hand side
+becomes-- go back over here.
+
+2/3 a to the 3/2 is
+equal to a constant times
+
+t plus an arbitrary other
+constant of integration.
+
+This is the most
+general equation,
+
+which when differentiated
+gives you this.
+
+And now, this
+equation can be solved
+
+to tell us what a is
+as a function of t.
+
+But before I do that, I'm going
+to say something about c prime
+
+here.
+
+c prime is allowed
+by the integration.
+
+But remember that when we
+defined our scale of t,
+
+we just started at
+some arbitrary time,
+
+ti, which we didn't
+even specify.
+
+So there's no
+particular significance
+
+to the origin of
+time in the equations
+
+that we've written so far.
+
+So we're perfectly free to
+shift the origin of time
+
+by just redefining our clocks.
+
+Cosmic time,
+remember, is defined
+
+in a way which makes it
+uniform throughout the universe
+
+by our construction.
+
+But we haven't said anything yet
+about how to start cosmic time.
+
+But now, we have a
+good way to start it.
+
+In this model,
+there is going to be
+
+a time at which a
+is going to go to 0.
+
+No matter what we
+choose for c prime here,
+
+there will be some t which will
+make the right-hand side 0.
+
+And therefore, a 0.
+
+And that's the instant
+of the Big Bang.
+
+That's when everything starts.
+a never gets smaller than 0.
+
+So it's very natural
+to take that to be
+
+defined to be the 0 of time.
+
+So that's what
+we're going to do.
+
+So we're going to define t
+equals 0 to be when a of t
+
+equals 0.
+
+That's just a
+choice of the origin
+
+of time, which you're
+certainly allowed
+
+to do without contradicting
+anything else that we've said.
+
+And that means we're just
+setting c prime equal to 0.
+
+So that when that's 0, that's 0.
+
+So this implies
+c prime equals 0.
+
+And that then
+implies-- we could take
+
+the 2/3 power of this equation.
+
+And I told you we don't really
+care what that constant is.
+
+So therefore, we
+don't really care
+
+about what that constant is.
+
+What we get is that a is
+equal to some constant,
+
+not necessarily related
+to any of the constants
+
+we've said so far.
+
+Although, you can
+calculate how it is.
+
+But some constant times
+t to the 2/3 power.
+
+Or equivalently,
+you could just write
+
+a is proportional to
+t to the 2/3, which
+
+has the same content.
+
+Now, you might think
+you'd want to know
+
+what the constant of
+proportionality is.
+
+But remember, the constant
+of proportionality
+
+just depends on the
+definition of the notch.
+
+If you want to define the
+notch so that a is equal to 1
+
+today, then you would
+care what the constant is.
+
+If you're willing to just leave
+the definition of the notch
+
+arbitrary, then you don't
+care what the constant is.
+
+And that's the case that
+I'll be doing, actually.
+
+I will not define
+a to be 1 today.
+
+The definition of the
+notch is just arbitrary
+
+as far as the equations
+that I'll be writing.
+
+And therefore, it will
+be sufficient to know
+
+that a is just proportional
+to t to the 2/3
+
+for the flat universe case,
+for the critical density case.
+
+And that's where
+we'll stop today.
+
+And this actually pretty
+really covers everything
+
+through lecture notes three,
+which is the same material that
+
+will be covered on
+the quiz next week.
+
+[INAUDIBLE] does not
+seem to have shown up,
+
+but we'll assume that probably
+the review session will
+
+be next Monday night at 7:30.
+
+I will check it out and
+get back to you by email.
\ No newline at end of file
diff --git a/mJ54DfN95Zo.txt b/mJ54DfN95Zo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d5e6f1602a8a4c1d233f67174ca27e3875037fa2
--- /dev/null
+++ b/mJ54DfN95Zo.txt
@@ -0,0 +1,9411 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
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+will help MIT OpenCourseWare continue to
+ 
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+will help MIT OpenCourseWare continue to
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+offer high quality educational resources
+ 
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+for free
+to make a donation or to view additional
+
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+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay guys we're actually slightly ahead
+
+ align:start position:0%
+okay guys we're actually slightly ahead
+ 
+
+ align:start position:0%
+okay guys we're actually slightly ahead
+of where I thought we'd be at this point
+
+ align:start position:0%
+of where I thought we'd be at this point
+ 
+
+ align:start position:0%
+of where I thought we'd be at this point
+so I'm only gonna spend about half of
+
+ align:start position:0%
+so I'm only gonna spend about half of
+ 
+
+ align:start position:0%
+so I'm only gonna spend about half of
+today's lecture finishing up some new
+
+ align:start position:0%
+today's lecture finishing up some new
+ 
+
+ align:start position:0%
+today's lecture finishing up some new
+material on mass parabolas and stability
+
+ align:start position:0%
+material on mass parabolas and stability
+ 
+
+ align:start position:0%
+material on mass parabolas and stability
+I also got a comment in through the
+
+ align:start position:0%
+I also got a comment in through the
+ 
+
+ align:start position:0%
+I also got a comment in through the
+anonymous box that said please leave a
+
+ align:start position:0%
+anonymous box that said please leave a
+ 
+
+ align:start position:0%
+anonymous box that said please leave a
+little bit of time after class for
+
+ align:start position:0%
+little bit of time after class for
+ 
+
+ align:start position:0%
+little bit of time after class for
+questions so you can get them out right
+
+ align:start position:0%
+questions so you can get them out right
+ 
+
+ align:start position:0%
+questions so you can get them out right
+away and because I'm usually running off
+
+ align:start position:0%
+away and because I'm usually running off
+ 
+
+ align:start position:0%
+away and because I'm usually running off
+the teach some other class at like the
+
+ align:start position:0%
+the teach some other class at like the
+ 
+
+ align:start position:0%
+the teach some other class at like the
+IDC or some other building so from now
+
+ align:start position:0%
+IDC or some other building so from now
+ 
+
+ align:start position:0%
+IDC or some other building so from now
+on I'll try and leave about five minutes
+
+ align:start position:0%
+on I'll try and leave about five minutes
+ 
+
+ align:start position:0%
+on I'll try and leave about five minutes
+at the end of class for questions on
+
+ align:start position:0%
+at the end of class for questions on
+ 
+
+ align:start position:0%
+at the end of class for questions on
+today's material and we'll make up with
+
+ align:start position:0%
+today's material and we'll make up with
+ 
+
+ align:start position:0%
+today's material and we'll make up with
+it with the second half hour or 25
+
+ align:start position:0%
+it with the second half hour or 25
+ 
+
+ align:start position:0%
+it with the second half hour or 25
+minutes of this class being for all the
+
+ align:start position:0%
+minutes of this class being for all the
+ 
+
+ align:start position:0%
+minutes of this class being for all the
+questions on the material so far in the
+
+ align:start position:0%
+questions on the material so far in the
+ 
+
+ align:start position:0%
+questions on the material so far in the
+first two weeks but first I wanted to
+
+ align:start position:0%
+first two weeks but first I wanted to
+ 
+
+ align:start position:0%
+first two weeks but first I wanted to
+give a quick review of where we were
+
+ align:start position:0%
+give a quick review of where we were
+ 
+
+ align:start position:0%
+give a quick review of where we were
+Wednesday and launch back into math
+
+ align:start position:0%
+Wednesday and launch back into math
+ 
+
+ align:start position:0%
+Wednesday and launch back into math
+parabolas which are ways of looking at
+
+ align:start position:0%
+parabolas which are ways of looking at
+ 
+
+ align:start position:0%
+parabolas which are ways of looking at
+nuclear stability in relative numbers
+
+ align:start position:0%
+nuclear stability in relative numbers
+ 
+
+ align:start position:0%
+nuclear stability in relative numbers
+and even or oddness of nuclei so you saw
+
+ align:start position:0%
+and even or oddness of nuclei so you saw
+ 
+
+ align:start position:0%
+and even or oddness of nuclei so you saw
+last time we intuitively derived the
+
+ align:start position:0%
+last time we intuitively derived the
+ 
+
+ align:start position:0%
+last time we intuitively derived the
+semi empirical mass formula as a sum of
+
+ align:start position:0%
+semi empirical mass formula as a sum of
+ 
+
+ align:start position:0%
+semi empirical mass formula as a sum of
+volume surface Coulomb asymmetry and
+
+ align:start position:0%
+volume surface Coulomb asymmetry and
+ 
+
+ align:start position:0%
+volume surface Coulomb asymmetry and
+pairing or whether things are even even
+
+ align:start position:0%
+pairing or whether things are even even
+ 
+
+ align:start position:0%
+pairing or whether things are even even
+or odd even terms with the coefficients
+
+ align:start position:0%
+or odd even terms with the coefficients
+ 
+
+ align:start position:0%
+or odd even terms with the coefficients
+in MeV gleaned from data and the forms
+
+ align:start position:0%
+in MeV gleaned from data and the forms
+ 
+
+ align:start position:0%
+in MeV gleaned from data and the forms
+of the and the exponents right here
+
+ align:start position:0%
+of the and the exponents right here
+ 
+
+ align:start position:0%
+of the and the exponents right here
+gleaned from intuition here we assume
+
+ align:start position:0%
+gleaned from intuition here we assume
+ 
+
+ align:start position:0%
+gleaned from intuition here we assume
+that the nucleus can be thought of like
+
+ align:start position:0%
+that the nucleus can be thought of like
+ 
+
+ align:start position:0%
+that the nucleus can be thought of like
+a big drop of liquid with some charged
+
+ align:start position:0%
+a big drop of liquid with some charged
+ 
+
+ align:start position:0%
+a big drop of liquid with some charged
+particles in it and so the droplet
+
+ align:start position:0%
+particles in it and so the droplet
+ 
+
+ align:start position:0%
+particles in it and so the droplet
+should become more stable the more
+
+ align:start position:0%
+should become more stable the more
+ 
+
+ align:start position:0%
+should become more stable the more
+nuclei there are or the nor nucleons
+
+ align:start position:0%
+nuclei there are or the nor nucleons
+ 
+
+ align:start position:0%
+nuclei there are or the nor nucleons
+there are but then you have some more
+
+ align:start position:0%
+there are but then you have some more
+ 
+
+ align:start position:0%
+there are but then you have some more
+outside on the surface that aren't
+
+ align:start position:0%
+outside on the surface that aren't
+ 
+
+ align:start position:0%
+outside on the surface that aren't
+bonded to the others all of the protons
+
+ align:start position:0%
+bonded to the others all of the protons
+ 
+
+ align:start position:0%
+bonded to the others all of the protons
+are repelling each other over linear
+
+ align:start position:0%
+are repelling each other over linear
+ 
+
+ align:start position:0%
+are repelling each other over linear
+length scales because the radius of this
+
+ align:start position:0%
+length scales because the radius of this
+ 
+
+ align:start position:0%
+length scales because the radius of this
+liquid drop would scale like a to the
+
+ align:start position:0%
+liquid drop would scale like a to the
+ 
+
+ align:start position:0%
+liquid drop would scale like a to the
+one third there's an asymmetry term
+
+ align:start position:0%
+one third there's an asymmetry term
+ 
+
+ align:start position:0%
+one third there's an asymmetry term
+which means if the neutrons and protons
+
+ align:start position:0%
+which means if the neutrons and protons
+ 
+
+ align:start position:0%
+which means if the neutrons and protons
+are out of balance there's going to be
+
+ align:start position:0%
+are out of balance there's going to be
+ 
+
+ align:start position:0%
+are out of balance there's going to be
+some some less binding energy and then
+
+ align:start position:0%
+some some less binding energy and then
+ 
+
+ align:start position:0%
+some some less binding energy and then
+there's this extra part that tells you
+
+ align:start position:0%
+there's this extra part that tells you
+ 
+
+ align:start position:0%
+there's this extra part that tells you
+whether the nuclei are even even or odd
+
+ align:start position:0%
+whether the nuclei are even even or odd
+ 
+
+ align:start position:0%
+whether the nuclei are even even or odd
+odd and this works pretty well if you
+
+ align:start position:0%
+odd and this works pretty well if you
+ 
+
+ align:start position:0%
+odd and this works pretty well if you
+remember we looked at theory versus
+
+ align:start position:0%
+remember we looked at theory versus
+ 
+
+ align:start position:0%
+remember we looked at theory versus
+experiment where all the red points here
+
+ align:start position:0%
+experiment where all the red points here
+ 
+
+ align:start position:0%
+experiment where all the red points here
+are theoretical predictions and all the
+
+ align:start position:0%
+are theoretical predictions and all the
+ 
+
+ align:start position:0%
+are theoretical predictions and all the
+black points are experimental
+
+ align:start position:0%
+black points are experimental
+ 
+
+ align:start position:0%
+black points are experimental
+predictions and for the most part they
+
+ align:start position:0%
+predictions and for the most part they
+ 
+
+ align:start position:0%
+predictions and for the most part they
+look spot-on it generates the classic
+
+ align:start position:0%
+look spot-on it generates the classic
+ 
+
+ align:start position:0%
+look spot-on it generates the classic
+binding energy per nucleon curve that
+
+ align:start position:0%
+binding energy per nucleon curve that
+ 
+
+ align:start position:0%
+binding energy per nucleon curve that
+you see in the textbook and can predict
+
+ align:start position:0%
+you see in the textbook and can predict
+ 
+
+ align:start position:0%
+you see in the textbook and can predict
+from the semi empirical mass formula
+
+ align:start position:0%
+from the semi empirical mass formula
+ 
+
+ align:start position:0%
+from the semi empirical mass formula
+zooming in and correcting for let's say
+
+ align:start position:0%
+zooming in and correcting for let's say
+ 
+
+ align:start position:0%
+zooming in and correcting for let's say
+just getting absolute values of errors
+
+ align:start position:0%
+just getting absolute values of errors
+ 
+
+ align:start position:0%
+just getting absolute values of errors
+you can see that except for the very
+
+ align:start position:0%
+you can see that except for the very
+ 
+
+ align:start position:0%
+you can see that except for the very
+small nuclei and a few Peaks which we
+
+ align:start position:0%
+small nuclei and a few Peaks which we
+ 
+
+ align:start position:0%
+small nuclei and a few Peaks which we
+explained by looking even closer the
+
+ align:start position:0%
+explained by looking even closer the
+ 
+
+ align:start position:0%
+explained by looking even closer the
+formula well it predicts nuclear
+
+ align:start position:0%
+formula well it predicts nuclear
+ 
+
+ align:start position:0%
+formula well it predicts nuclear
+stability quite well on average again
+
+ align:start position:0%
+stability quite well on average again
+ 
+
+ align:start position:0%
+stability quite well on average again
+this line right here if there's a dot
+
+ align:start position:0%
+this line right here if there's a dot
+ 
+
+ align:start position:0%
+this line right here if there's a dot
+that lies on this blue line it means
+
+ align:start position:0%
+that lies on this blue line it means
+ 
+
+ align:start position:0%
+that lies on this blue line it means
+that theory and experiment agree and a
+
+ align:start position:0%
+that theory and experiment agree and a
+ 
+
+ align:start position:0%
+that theory and experiment agree and a
+deviation by ofyou mev here and they are
+
+ align:start position:0%
+deviation by ofyou mev here and they are
+ 
+
+ align:start position:0%
+deviation by ofyou mev here and they are
+not too bad but we started also looking
+
+ align:start position:0%
+not too bad but we started also looking
+ 
+
+ align:start position:0%
+not too bad but we started also looking
+at different nuclear stability trends
+
+ align:start position:0%
+at different nuclear stability trends
+ 
+
+ align:start position:0%
+at different nuclear stability trends
+and we noticed that for odd mass number
+
+ align:start position:0%
+and we noticed that for odd mass number
+ 
+
+ align:start position:0%
+and we noticed that for odd mass number
+nuclei there is usually only one or
+
+ align:start position:0%
+nuclei there is usually only one or
+ 
+
+ align:start position:0%
+nuclei there is usually only one or
+sometimes none stable isotopes per Z
+
+ align:start position:0%
+sometimes none stable isotopes per Z
+ 
+
+ align:start position:0%
+sometimes none stable isotopes per Z
+whereas for even once there's quite a
+
+ align:start position:0%
+whereas for even once there's quite a
+ 
+
+ align:start position:0%
+whereas for even once there's quite a
+few more and we're going to be now
+
+ align:start position:0%
+few more and we're going to be now
+ 
+
+ align:start position:0%
+few more and we're going to be now
+linking up the stability of nuclei
+
+ align:start position:0%
+linking up the stability of nuclei
+ 
+
+ align:start position:0%
+linking up the stability of nuclei
+versus what mode of decay they will take
+
+ align:start position:0%
+versus what mode of decay they will take
+ 
+
+ align:start position:0%
+versus what mode of decay they will take
+in order to find a more stable
+
+ align:start position:0%
+in order to find a more stable
+ 
+
+ align:start position:0%
+in order to find a more stable
+configuration we looked quickly at the
+
+ align:start position:0%
+configuration we looked quickly at the
+ 
+
+ align:start position:0%
+configuration we looked quickly at the
+number of stable nuclei with even and
+
+ align:start position:0%
+number of stable nuclei with even and
+ 
+
+ align:start position:0%
+number of stable nuclei with even and
+odd Z and noted that this these places
+
+ align:start position:0%
+odd Z and noted that this these places
+ 
+
+ align:start position:0%
+odd Z and noted that this these places
+right here where there are no stable
+
+ align:start position:0%
+right here where there are no stable
+ 
+
+ align:start position:0%
+right here where there are no stable
+nuclei correspond to technetium and
+
+ align:start position:0%
+nuclei correspond to technetium and
+ 
+
+ align:start position:0%
+nuclei correspond to technetium and
+promethium there's no periodic table on
+
+ align:start position:0%
+promethium there's no periodic table on
+ 
+
+ align:start position:0%
+promethium there's no periodic table on
+the back of this wall but behind my back
+
+ align:start position:0%
+the back of this wall but behind my back
+ 
+
+ align:start position:0%
+the back of this wall but behind my back
+on the other wall there's that periodic
+
+ align:start position:0%
+on the other wall there's that periodic
+ 
+
+ align:start position:0%
+on the other wall there's that periodic
+table where you can see the two elements
+
+ align:start position:0%
+table where you can see the two elements
+ 
+
+ align:start position:0%
+table where you can see the two elements
+that are fairly light with no stable
+
+ align:start position:0%
+that are fairly light with no stable
+ 
+
+ align:start position:0%
+that are fairly light with no stable
+isotopes that's what those correspond to
+
+ align:start position:0%
+isotopes that's what those correspond to
+ 
+
+ align:start position:0%
+isotopes that's what those correspond to
+and the peaks correspond to what we call
+
+ align:start position:0%
+and the peaks correspond to what we call
+ 
+
+ align:start position:0%
+and the peaks correspond to what we call
+magic numbers or numbers of protons or
+
+ align:start position:0%
+magic numbers or numbers of protons or
+ 
+
+ align:start position:0%
+magic numbers or numbers of protons or
+neutrons where all available States some
+
+ align:start position:0%
+neutrons where all available States some
+ 
+
+ align:start position:0%
+neutrons where all available States some
+energy are pretty much filled and this
+
+ align:start position:0%
+energy are pretty much filled and this
+ 
+
+ align:start position:0%
+energy are pretty much filled and this
+goes for both protons and neutrons so
+
+ align:start position:0%
+goes for both protons and neutrons so
+ 
+
+ align:start position:0%
+goes for both protons and neutrons so
+something with a magic number for both n
+
+ align:start position:0%
+something with a magic number for both n
+ 
+
+ align:start position:0%
+something with a magic number for both n
+number of neutrons and Z number of
+
+ align:start position:0%
+number of neutrons and Z number of
+ 
+
+ align:start position:0%
+number of neutrons and Z number of
+protons is going to be exceptionally
+
+ align:start position:0%
+protons is going to be exceptionally
+ 
+
+ align:start position:0%
+protons is going to be exceptionally
+stable and we'll see how that's used as
+
+ align:start position:0%
+stable and we'll see how that's used as
+ 
+
+ align:start position:0%
+stable and we'll see how that's used as
+a tool to synthesize the super-heavy
+
+ align:start position:0%
+a tool to synthesize the super-heavy
+ 
+
+ align:start position:0%
+a tool to synthesize the super-heavy
+elements that we believe should exist
+
+ align:start position:0%
+elements that we believe should exist
+ 
+
+ align:start position:0%
+elements that we believe should exist
+and finally we got into these mass
+
+ align:start position:0%
+and finally we got into these mass
+ 
+
+ align:start position:0%
+and finally we got into these mass
+parabolas I found this to be a
+
+ align:start position:0%
+parabolas I found this to be a
+ 
+
+ align:start position:0%
+parabolas I found this to be a
+particularly difficult concept to just
+
+ align:start position:0%
+particularly difficult concept to just
+ 
+
+ align:start position:0%
+particularly difficult concept to just
+get mathematically if you remember we
+
+ align:start position:0%
+get mathematically if you remember we
+ 
+
+ align:start position:0%
+get mathematically if you remember we
+wrote out the semi empirical mass
+
+ align:start position:0%
+wrote out the semi empirical mass
+ 
+
+ align:start position:0%
+wrote out the semi empirical mass
+formula and said if you take the
+
+ align:start position:0%
+formula and said if you take the
+ 
+
+ align:start position:0%
+formula and said if you take the
+derivative with respect to Z as we did
+
+ align:start position:0%
+derivative with respect to Z as we did
+ 
+
+ align:start position:0%
+derivative with respect to Z as we did
+it you would get the most stable z for a
+
+ align:start position:0%
+it you would get the most stable z for a
+ 
+
+ align:start position:0%
+it you would get the most stable z for a
+given a and we started graphing for a
+
+ align:start position:0%
+given a and we started graphing for a
+ 
+
+ align:start position:0%
+given a and we started graphing for a
+equals 93 where naya beum is stable that
+
+ align:start position:0%
+equals 93 where naya beum is stable that
+ 
+
+ align:start position:0%
+equals 93 where naya beum is stable that
+was just the one I had on the brain from
+
+ align:start position:0%
+was just the one I had on the brain from
+ 
+
+ align:start position:0%
+was just the one I had on the brain from
+some failures in lab earlier this week
+
+ align:start position:0%
+some failures in lab earlier this week
+ 
+
+ align:start position:0%
+some failures in lab earlier this week
+we started plotting where those nuclei
+
+ align:start position:0%
+we started plotting where those nuclei
+ 
+
+ align:start position:0%
+we started plotting where those nuclei
+what is at the the relative masses are
+
+ align:start position:0%
+what is at the the relative masses are
+ 
+
+ align:start position:0%
+what is at the the relative masses are
+for a fixed a so let's regenerate
+
+ align:start position:0%
+for a fixed a so let's regenerate
+ 
+
+ align:start position:0%
+for a fixed a so let's regenerate
+that one right now because we were a
+
+ align:start position:0%
+that one right now because we were a
+ 
+
+ align:start position:0%
+that one right now because we were a
+little fast at the end of last lecture
+
+ align:start position:0%
+little fast at the end of last lecture
+ 
+
+ align:start position:0%
+little fast at the end of last lecture
+then I want to generate one for a equals
+
+ align:start position:0%
+then I want to generate one for a equals
+ 
+
+ align:start position:0%
+then I want to generate one for a equals
+40 and you'll see something kind of
+
+ align:start position:0%
+40 and you'll see something kind of
+ 
+
+ align:start position:0%
+40 and you'll see something kind of
+curious I'm going to leave this up here
+
+ align:start position:0%
+curious I'm going to leave this up here
+ 
+
+ align:start position:0%
+curious I'm going to leave this up here
+for a sec if you notice for odd a nuclei
+
+ align:start position:0%
+for a sec if you notice for odd a nuclei
+ 
+
+ align:start position:0%
+for a sec if you notice for odd a nuclei
+there's only one parabola whereas for
+
+ align:start position:0%
+there's only one parabola whereas for
+ 
+
+ align:start position:0%
+there's only one parabola whereas for
+even a there are two why that is we're
+
+ align:start position:0%
+even a there are two why that is we're
+ 
+
+ align:start position:0%
+even a there are two why that is we're
+gonna see when we look at the table of
+
+ align:start position:0%
+gonna see when we look at the table of
+ 
+
+ align:start position:0%
+gonna see when we look at the table of
+nuclides but notice this nucleus right
+
+ align:start position:0%
+nuclides but notice this nucleus right
+ 
+
+ align:start position:0%
+nuclides but notice this nucleus right
+here can decay by either positron
+
+ align:start position:0%
+here can decay by either positron
+ 
+
+ align:start position:0%
+here can decay by either positron
+emission or beta emission to get to a
+
+ align:start position:0%
+emission or beta emission to get to a
+ 
+
+ align:start position:0%
+emission or beta emission to get to a
+more stable form and there are many real
+
+ align:start position:0%
+more stable form and there are many real
+ 
+
+ align:start position:0%
+more stable form and there are many real
+examples and I'm going to show you how
+
+ align:start position:0%
+examples and I'm going to show you how
+ 
+
+ align:start position:0%
+examples and I'm going to show you how
+to find them so let's start off by going
+
+ align:start position:0%
+to find them so let's start off by going
+ 
+
+ align:start position:0%
+to find them so let's start off by going
+back to the table of nuclides finding
+
+ align:start position:0%
+back to the table of nuclides finding
+ 
+
+ align:start position:0%
+back to the table of nuclides finding
+niobium 93 just go up one more chunk and
+
+ align:start position:0%
+niobium 93 just go up one more chunk and
+ 
+
+ align:start position:0%
+niobium 93 just go up one more chunk and
+there we are
+
+ align:start position:0%
+there we are
+ 
+
+ align:start position:0%
+there we are
+Niobe M 93 is a stable isotope and if
+
+ align:start position:0%
+Niobe M 93 is a stable isotope and if
+ 
+
+ align:start position:0%
+Niobe M 93 is a stable isotope and if
+you want to see where it came from you
+
+ align:start position:0%
+you want to see where it came from you
+ 
+
+ align:start position:0%
+you want to see where it came from you
+can scroll down a little bit and see
+
+ align:start position:0%
+can scroll down a little bit and see
+ 
+
+ align:start position:0%
+can scroll down a little bit and see
+it's possible parent nuclides right here
+
+ align:start position:0%
+it's possible parent nuclides right here
+ 
+
+ align:start position:0%
+it's possible parent nuclides right here
+so let's say that niobium will draw
+
+ align:start position:0%
+so let's say that niobium will draw
+ 
+
+ align:start position:0%
+so let's say that niobium will draw
+right there is stable we'll put it at
+
+ align:start position:0%
+right there is stable we'll put it at
+ 
+
+ align:start position:0%
+right there is stable we'll put it at
+the bottom of this parabola and let's
+
+ align:start position:0%
+the bottom of this parabola and let's
+ 
+
+ align:start position:0%
+the bottom of this parabola and let's
+work down in Z so we'll move to
+
+ align:start position:0%
+work down in Z so we'll move to
+ 
+
+ align:start position:0%
+work down in Z so we'll move to
+zirconium zirconium 93 ostensively has a
+
+ align:start position:0%
+zirconium zirconium 93 ostensively has a
+ 
+
+ align:start position:0%
+zirconium zirconium 93 ostensively has a
+very similar atomic mass but if you
+
+ align:start position:0%
+very similar atomic mass but if you
+ 
+
+ align:start position:0%
+very similar atomic mass but if you
+remember that 93 amu is a rather poor
+
+ align:start position:0%
+remember that 93 amu is a rather poor
+ 
+
+ align:start position:0%
+remember that 93 amu is a rather poor
+approximation for the actual mass of all
+
+ align:start position:0%
+approximation for the actual mass of all
+ 
+
+ align:start position:0%
+approximation for the actual mass of all
+nuclei with a equals 93 in fact if you
+
+ align:start position:0%
+nuclei with a equals 93 in fact if you
+ 
+
+ align:start position:0%
+nuclei with a equals 93 in fact if you
+look very closely at the atomic masses
+
+ align:start position:0%
+look very closely at the atomic masses
+ 
+
+ align:start position:0%
+look very closely at the atomic masses
+zirconium 93 is 90 2.90 niobium 93 well
+
+ align:start position:0%
+zirconium 93 is 90 2.90 niobium 93 well
+ 
+
+ align:start position:0%
+zirconium 93 is 90 2.90 niobium 93 well
+it looks like we have to go all the way
+
+ align:start position:0%
+it looks like we have to go all the way
+ 
+
+ align:start position:0%
+it looks like we have to go all the way
+to another digit there 92.9 o6 you have
+
+ align:start position:0%
+to another digit there 92.9 o6 you have
+ 
+
+ align:start position:0%
+to another digit there 92.9 o6 you have
+to go to like even more digits ninety
+
+ align:start position:0%
+to go to like even more digits ninety
+ 
+
+ align:start position:0%
+to go to like even more digits ninety
+two point nine oh six three seventy five
+
+ align:start position:0%
+two point nine oh six three seventy five
+ 
+
+ align:start position:0%
+two point nine oh six three seventy five
+ninety two point nine oh six four
+
+ align:start position:0%
+ninety two point nine oh six four
+ 
+
+ align:start position:0%
+ninety two point nine oh six four
+seventy five so we go down in Z and
+
+ align:start position:0%
+seventy five so we go down in Z and
+ 
+
+ align:start position:0%
+seventy five so we go down in Z and
+we've actually gone up in mass by looks
+
+ align:start position:0%
+we've actually gone up in mass by looks
+ 
+
+ align:start position:0%
+we've actually gone up in mass by looks
+like the sixth or seventh digit in AMU
+
+ align:start position:0%
+like the sixth or seventh digit in AMU
+ 
+
+ align:start position:0%
+like the sixth or seventh digit in AMU
+if we go up in mass we go down in
+
+ align:start position:0%
+if we go up in mass we go down in
+ 
+
+ align:start position:0%
+if we go up in mass we go down in
+binding energy that tells us that
+
+ align:start position:0%
+binding energy that tells us that
+ 
+
+ align:start position:0%
+binding energy that tells us that
+there's something that's less stable and
+
+ align:start position:0%
+there's something that's less stable and
+ 
+
+ align:start position:0%
+there's something that's less stable and
+if you notice we went down by a very
+
+ align:start position:0%
+if you notice we went down by a very
+ 
+
+ align:start position:0%
+if you notice we went down by a very
+smaller or Wien up by a very small
+
+ align:start position:0%
+smaller or Wien up by a very small
+ 
+
+ align:start position:0%
+smaller or Wien up by a very small
+amount of mass notice also that it's
+
+ align:start position:0%
+amount of mass notice also that it's
+ 
+
+ align:start position:0%
+amount of mass notice also that it's
+beta decay energy is really really small
+
+ align:start position:0%
+beta decay energy is really really small
+ 
+
+ align:start position:0%
+beta decay energy is really really small
+ninety one kill electron volts so why
+
+ align:start position:0%
+ninety one kill electron volts so why
+ 
+
+ align:start position:0%
+ninety one kill electron volts so why
+don't we put zirconium
+
+ align:start position:0%
+don't we put zirconium
+ 
+
+ align:start position:0%
+don't we put zirconium
+just above and we note that that decay
+
+ align:start position:0%
+just above and we note that that decay
+ 
+
+ align:start position:0%
+just above and we note that that decay
+will happen by data where the beta let's
+
+ align:start position:0%
+will happen by data where the beta let's
+ 
+
+ align:start position:0%
+will happen by data where the beta let's
+say if we have an isotope with mass
+
+ align:start position:0%
+say if we have an isotope with mass
+ 
+
+ align:start position:0%
+say if we have an isotope with mass
+number a protons Z and let's just call
+
+ align:start position:0%
+number a protons Z and let's just call
+ 
+
+ align:start position:0%
+number a protons Z and let's just call
+it symbol question mark in beta decay we
+
+ align:start position:0%
+it symbol question mark in beta decay we
+ 
+
+ align:start position:0%
+it symbol question mark in beta decay we
+have the same a will have a different Z
+
+ align:start position:0%
+have the same a will have a different Z
+ 
+
+ align:start position:0%
+have the same a will have a different Z
+I'm gonna have to give these symbols
+
+ align:start position:0%
+I'm gonna have to give these symbols
+ 
+
+ align:start position:0%
+I'm gonna have to give these symbols
+let's call this parent and we'll call
+
+ align:start position:0%
+let's call this parent and we'll call
+ 
+
+ align:start position:0%
+let's call this parent and we'll call
+that daughter plus a beta plus an
+
+ align:start position:0%
+that daughter plus a beta plus an
+ 
+
+ align:start position:0%
+that daughter plus a beta plus an
+electron antineutrino and what has to
+
+ align:start position:0%
+electron antineutrino and what has to
+ 
+
+ align:start position:0%
+electron antineutrino and what has to
+happen to that Z in order for everything
+
+ align:start position:0%
+happen to that Z in order for everything
+ 
+
+ align:start position:0%
+happen to that Z in order for everything
+to be conserved it's the same reaction
+
+ align:start position:0%
+to be conserved it's the same reaction
+ 
+
+ align:start position:0%
+to be conserved it's the same reaction
+that we've gone here for I'm sorry for
+
+ align:start position:0%
+that we've gone here for I'm sorry for
+ 
+
+ align:start position:0%
+that we've gone here for I'm sorry for
+their code iam so you'd have to have one
+
+ align:start position:0%
+their code iam so you'd have to have one
+ 
+
+ align:start position:0%
+their code iam so you'd have to have one
+fewer proton to release one electron and
+
+ align:start position:0%
+fewer proton to release one electron and
+ 
+
+ align:start position:0%
+fewer proton to release one electron and
+so that becomes same a but different Z
+
+ align:start position:0%
+so that becomes same a but different Z
+ 
+
+ align:start position:0%
+so that becomes same a but different Z
+and this is the beta decay reaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's go back a little farther we'll
+
+ align:start position:0%
+let's go back a little farther we'll
+ 
+
+ align:start position:0%
+let's go back a little farther we'll
+look at the possible parent nuclide for
+
+ align:start position:0%
+look at the possible parent nuclide for
+ 
+
+ align:start position:0%
+look at the possible parent nuclide for
+anyone have a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see which direction are we going
+
+ align:start position:0%
+let's see which direction are we going
+ 
+
+ align:start position:0%
+let's see which direction are we going
+in Z here that goes to yet trium
+
+ align:start position:0%
+in Z here that goes to yet trium
+ 
+
+ align:start position:0%
+in Z here that goes to yet trium
+actually looks like it's going down oh
+
+ align:start position:0%
+actually looks like it's going down oh
+ 
+
+ align:start position:0%
+actually looks like it's going down oh
+yeah for beta decay I'm thinking I have
+
+ align:start position:0%
+yeah for beta decay I'm thinking I have
+ 
+
+ align:start position:0%
+yeah for beta decay I'm thinking I have
+the reaction backwards sorry
+
+ align:start position:0%
+the reaction backwards sorry
+ 
+
+ align:start position:0%
+the reaction backwards sorry
+need one more proton to account for the
+
+ align:start position:0%
+need one more proton to account for the
+ 
+
+ align:start position:0%
+need one more proton to account for the
+extra negative charge you're right okay
+
+ align:start position:0%
+extra negative charge you're right okay
+ 
+
+ align:start position:0%
+extra negative charge you're right okay
+yep I was thinking backwards because
+
+ align:start position:0%
+yep I was thinking backwards because
+ 
+
+ align:start position:0%
+yep I was thinking backwards because
+we're now climbing up the decay chain in
+
+ align:start position:0%
+we're now climbing up the decay chain in
+ 
+
+ align:start position:0%
+we're now climbing up the decay chain in
+reverse order so this could have come
+
+ align:start position:0%
+reverse order so this could have come
+ 
+
+ align:start position:0%
+reverse order so this could have come
+from yttrium 93 with a much higher
+
+ align:start position:0%
+from yttrium 93 with a much higher
+ 
+
+ align:start position:0%
+from yttrium 93 with a much higher
+energy of three MeV so let's put it reom
+
+ align:start position:0%
+energy of three MeV so let's put it reom
+ 
+
+ align:start position:0%
+energy of three MeV so let's put it reom
+right here that gives a beta decay and
+
+ align:start position:0%
+right here that gives a beta decay and
+ 
+
+ align:start position:0%
+right here that gives a beta decay and
+we'll just go one more back to strontium
+
+ align:start position:0%
+we'll just go one more back to strontium
+ 
+
+ align:start position:0%
+we'll just go one more back to strontium
+93 has an even higher beta decay energy
+
+ align:start position:0%
+93 has an even higher beta decay energy
+ 
+
+ align:start position:0%
+93 has an even higher beta decay energy
+so let's put that up here and let's take
+
+ align:start position:0%
+so let's put that up here and let's take
+ 
+
+ align:start position:0%
+so let's put that up here and let's take
+a look at its mass real quick the mass
+
+ align:start position:0%
+a look at its mass real quick the mass
+ 
+
+ align:start position:0%
+a look at its mass real quick the mass
+of strontium 93 92 point nine one four
+
+ align:start position:0%
+of strontium 93 92 point nine one four
+ 
+
+ align:start position:0%
+of strontium 93 92 point nine one four
+AMU if we go back to niobium 93 now it's
+
+ align:start position:0%
+AMU if we go back to niobium 93 now it's
+ 
+
+ align:start position:0%
+AMU if we go back to niobium 93 now it's
+noticeably different different to like
+
+ align:start position:0%
+noticeably different different to like
+ 
+
+ align:start position:0%
+noticeably different different to like
+four significant digits instead of six
+
+ align:start position:0%
+four significant digits instead of six
+ 
+
+ align:start position:0%
+four significant digits instead of six
+ninety two point nine one four versus
+
+ align:start position:0%
+ninety two point nine one four versus
+ 
+
+ align:start position:0%
+ninety two point nine one four versus
+ninety two point nine oh six and so that
+
+ align:start position:0%
+ninety two point nine oh six and so that
+ 
+
+ align:start position:0%
+ninety two point nine oh six and so that
+shows you that a tiny bit of mass and
+
+ align:start position:0%
+shows you that a tiny bit of mass and
+ 
+
+ align:start position:0%
+shows you that a tiny bit of mass and
+AMU corresponds to a pretty significant
+
+ align:start position:0%
+AMU corresponds to a pretty significant
+ 
+
+ align:start position:0%
+AMU corresponds to a pretty significant
+change in binding energy by that same
+
+ align:start position:0%
+change in binding energy by that same
+ 
+
+ align:start position:0%
+change in binding energy by that same
+conversion factor that we've been using
+
+ align:start position:0%
+conversion factor that we've been using
+ 
+
+ align:start position:0%
+conversion factor that we've been using
+everywhere nine thirty one point four
+
+ align:start position:0%
+everywhere nine thirty one point four
+ 
+
+ align:start position:0%
+everywhere nine thirty one point four
+nine
+
+ align:start position:0%
+nine
+ 
+
+ align:start position:0%
+nine
+AMU per big MeV
+
+ align:start position:0%
+AMU per big MeV
+ 
+
+ align:start position:0%
+AMU per big MeV
+yeah per C squared
+
+ align:start position:0%
+yeah per C squared
+ 
+
+ align:start position:0%
+yeah per C squared
+let's see yeah okay
+
+ align:start position:0%
+let's see yeah okay
+ 
+
+ align:start position:0%
+let's see yeah okay
+so let's go now in the other direction
+
+ align:start position:0%
+so let's go now in the other direction
+ 
+
+ align:start position:0%
+so let's go now in the other direction
+in the positron direction niobium can
+
+ align:start position:0%
+in the positron direction niobium can
+ 
+
+ align:start position:0%
+in the positron direction niobium can
+also be made by electron capture from
+
+ align:start position:0%
+also be made by electron capture from
+ 
+
+ align:start position:0%
+also be made by electron capture from
+molybdenum so let's put molybdenum right
+
+ align:start position:0%
+molybdenum so let's put molybdenum right
+ 
+
+ align:start position:0%
+molybdenum so let's put molybdenum right
+here let's say that around half an Emmy
+
+ align:start position:0%
+here let's say that around half an Emmy
+ 
+
+ align:start position:0%
+here let's say that around half an Emmy
+or what do we have here who was like
+
+ align:start position:0%
+or what do we have here who was like
+ 
+
+ align:start position:0%
+or what do we have here who was like
+half an MeV like that
+
+ align:start position:0%
+half an MeV like that
+ 
+
+ align:start position:0%
+half an MeV like that
+and let's see molybdenum 93 could have
+
+ align:start position:0%
+and let's see molybdenum 93 could have
+ 
+
+ align:start position:0%
+and let's see molybdenum 93 could have
+been made by electron capture from
+
+ align:start position:0%
+been made by electron capture from
+ 
+
+ align:start position:0%
+been made by electron capture from
+technetium 93 with an energy of three
+
+ align:start position:0%
+technetium 93 with an energy of three
+ 
+
+ align:start position:0%
+technetium 93 with an energy of three
+point two oh one MeV even more extreme
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll go back one more because
+
+ align:start position:0%
+and we'll go back one more because
+ 
+
+ align:start position:0%
+and we'll go back one more because
+there's a trend that I want you guys to
+
+ align:start position:0%
+there's a trend that I want you guys to
+ 
+
+ align:start position:0%
+there's a trend that I want you guys to
+be able to see and this could have come
+
+ align:start position:0%
+be able to see and this could have come
+ 
+
+ align:start position:0%
+be able to see and this could have come
+from electron capture from ruthenium I
+
+ align:start position:0%
+from electron capture from ruthenium I
+ 
+
+ align:start position:0%
+from electron capture from ruthenium I
+think I may have said rubidium last time
+
+ align:start position:0%
+think I may have said rubidium last time
+ 
+
+ align:start position:0%
+think I may have said rubidium last time
+but are you is ruthenium 93 and that 6.3
+
+ align:start position:0%
+but are you is ruthenium 93 and that 6.3
+ 
+
+ align:start position:0%
+but are you is ruthenium 93 and that 6.3
+MeV something like that and this is
+
+ align:start position:0%
+MeV something like that and this is
+ 
+
+ align:start position:0%
+MeV something like that and this is
+where we got to yesterday now I'd like
+
+ align:start position:0%
+where we got to yesterday now I'd like
+ 
+
+ align:start position:0%
+where we got to yesterday now I'd like
+us to take a closer look at the decay
+
+ align:start position:0%
+us to take a closer look at the decay
+ 
+
+ align:start position:0%
+us to take a closer look at the decay
+diagrams which tells us what possible
+
+ align:start position:0%
+diagrams which tells us what possible
+ 
+
+ align:start position:0%
+diagrams which tells us what possible
+decay reactions can happen in each of
+
+ align:start position:0%
+decay reactions can happen in each of
+ 
+
+ align:start position:0%
+decay reactions can happen in each of
+these reactions
+
+ align:start position:0%
+these reactions
+ 
+
+ align:start position:0%
+these reactions
+so let's since we're right here on the
+
+ align:start position:0%
+so let's since we're right here on the
+ 
+
+ align:start position:0%
+so let's since we're right here on the
+chart let's take a look at ruthenium
+
+ align:start position:0%
+chart let's take a look at ruthenium
+ 
+
+ align:start position:0%
+chart let's take a look at ruthenium
+turning into technetium by what it says
+
+ align:start position:0%
+turning into technetium by what it says
+ 
+
+ align:start position:0%
+turning into technetium by what it says
+electron capture so note that on the
+
+ align:start position:0%
+electron capture so note that on the
+ 
+
+ align:start position:0%
+electron capture so note that on the
+table you can click on electron capture
+
+ align:start position:0%
+table you can click on electron capture
+ 
+
+ align:start position:0%
+table you can click on electron capture
+and if it's highlighted then the decay
+
+ align:start position:0%
+and if it's highlighted then the decay
+ 
+
+ align:start position:0%
+and if it's highlighted then the decay
+diagrams are known it's not known for
+
+ align:start position:0%
+diagrams are known it's not known for
+ 
+
+ align:start position:0%
+diagrams are known it's not known for
+every isotope but for a lot of the ones
+
+ align:start position:0%
+every isotope but for a lot of the ones
+ 
+
+ align:start position:0%
+every isotope but for a lot of the ones
+you'll be dealing with it is and you get
+
+ align:start position:0%
+you'll be dealing with it is and you get
+ 
+
+ align:start position:0%
+you'll be dealing with it is and you get
+something I have to zoom out for a lot a
+
+ align:start position:0%
+something I have to zoom out for a lot a
+ 
+
+ align:start position:0%
+something I have to zoom out for a lot a
+lot of different decays what I want you
+
+ align:start position:0%
+lot of different decays what I want you
+ 
+
+ align:start position:0%
+lot of different decays what I want you
+to look at is this one here on the
+
+ align:start position:0%
+to look at is this one here on the
+ 
+
+ align:start position:0%
+to look at is this one here on the
+bottom that I'll zoom into that should
+
+ align:start position:0%
+bottom that I'll zoom into that should
+ 
+
+ align:start position:0%
+bottom that I'll zoom into that should
+be a little more visible so notice that
+
+ align:start position:0%
+be a little more visible so notice that
+ 
+
+ align:start position:0%
+be a little more visible so notice that
+if you want to go down the entire 6.4
+
+ align:start position:0%
+if you want to go down the entire 6.4
+ 
+
+ align:start position:0%
+if you want to go down the entire 6.4
+something MeV it usually proceeds by B+
+
+ align:start position:0%
+something MeV it usually proceeds by B+
+ 
+
+ align:start position:0%
+something MeV it usually proceeds by B+
+or positron decay by either method and
+
+ align:start position:0%
+or positron decay by either method and
+ 
+
+ align:start position:0%
+or positron decay by either method and
+as you go up the chain as these energy
+
+ align:start position:0%
+as you go up the chain as these energy
+ 
+
+ align:start position:0%
+as you go up the chain as these energy
+differences get smaller look what
+
+ align:start position:0%
+differences get smaller look what
+ 
+
+ align:start position:0%
+differences get smaller look what
+happens to the probability of getting
+
+ align:start position:0%
+happens to the probability of getting
+ 
+
+ align:start position:0%
+happens to the probability of getting
+positron decay it shrinks lower and
+
+ align:start position:0%
+positron decay it shrinks lower and
+ 
+
+ align:start position:0%
+positron decay it shrinks lower and
+lower and lower so they
+
+ align:start position:0%
+lower and lower so they
+ 
+
+ align:start position:0%
+lower and lower so they
+a trend that the larger the decay energy
+
+ align:start position:0%
+a trend that the larger the decay energy
+ 
+
+ align:start position:0%
+a trend that the larger the decay energy
+for this type of reaction the more
+
+ align:start position:0%
+for this type of reaction the more
+ 
+
+ align:start position:0%
+for this type of reaction the more
+likely you're going to get positron
+
+ align:start position:0%
+likely you're going to get positron
+ 
+
+ align:start position:0%
+likely you're going to get positron
+decay and in fact where we left off last
+
+ align:start position:0%
+decay and in fact where we left off last
+ 
+
+ align:start position:0%
+decay and in fact where we left off last
+time is in order to get positron decay
+
+ align:start position:0%
+time is in order to get positron decay
+ 
+
+ align:start position:0%
+time is in order to get positron decay
+the Q value of the reaction has to be at
+
+ align:start position:0%
+the Q value of the reaction has to be at
+ 
+
+ align:start position:0%
+the Q value of the reaction has to be at
+least 1.0 to 2 MeV better known as at
+
+ align:start position:0%
+least 1.0 to 2 MeV better known as at
+ 
+
+ align:start position:0%
+least 1.0 to 2 MeV better known as at
+least two times the rest mass of the
+
+ align:start position:0%
+least two times the rest mass of the
+ 
+
+ align:start position:0%
+least two times the rest mass of the
+electron because in this case to
+
+ align:start position:0%
+electron because in this case to
+ 
+
+ align:start position:0%
+electron because in this case to
+conserve charge and energy you shoot out
+
+ align:start position:0%
+conserve charge and energy you shoot out
+ 
+
+ align:start position:0%
+conserve charge and energy you shoot out
+a positron and you also have to inject
+
+ align:start position:0%
+a positron and you also have to inject
+ 
+
+ align:start position:0%
+a positron and you also have to inject
+an electron in order to conserve all the
+
+ align:start position:0%
+an electron in order to conserve all the
+ 
+
+ align:start position:0%
+an electron in order to conserve all the
+charge going on here so there you have
+
+ align:start position:0%
+charge going on here so there you have
+ 
+
+ align:start position:0%
+charge going on here so there you have
+it now let's look at the lower energy
+
+ align:start position:0%
+it now let's look at the lower energy
+ 
+
+ align:start position:0%
+it now let's look at the lower energy
+decay of technetium to molybdenum which
+
+ align:start position:0%
+decay of technetium to molybdenum which
+ 
+
+ align:start position:0%
+decay of technetium to molybdenum which
+had something like 3 MeV associated with
+
+ align:start position:0%
+had something like 3 MeV associated with
+ 
+
+ align:start position:0%
+had something like 3 MeV associated with
+it so we'll click on technetium and its
+
+ align:start position:0%
+it so we'll click on technetium and its
+ 
+
+ align:start position:0%
+it so we'll click on technetium and its
+energy is 3.2 MeV let's take a look at
+
+ align:start position:0%
+energy is 3.2 MeV let's take a look at
+ 
+
+ align:start position:0%
+energy is 3.2 MeV let's take a look at
+its electron capture significantly
+
+ align:start position:0%
+its electron capture significantly
+ 
+
+ align:start position:0%
+its electron capture significantly
+simpler already what do you notice about
+
+ align:start position:0%
+simpler already what do you notice about
+ 
+
+ align:start position:0%
+simpler already what do you notice about
+these positron to electron capture
+
+ align:start position:0%
+these positron to electron capture
+ 
+
+ align:start position:0%
+these positron to electron capture
+ratios anyone call it out indeed when
+
+ align:start position:0%
+ratios anyone call it out indeed when
+ 
+
+ align:start position:0%
+ratios anyone call it out indeed when
+the energy of the decay goes down notice
+
+ align:start position:0%
+the energy of the decay goes down notice
+ 
+
+ align:start position:0%
+the energy of the decay goes down notice
+that only these decays are allowed the
+
+ align:start position:0%
+that only these decays are allowed the
+ 
+
+ align:start position:0%
+that only these decays are allowed the
+electron capture suddenly becomes much
+
+ align:start position:0%
+electron capture suddenly becomes much
+ 
+
+ align:start position:0%
+electron capture suddenly becomes much
+more likely but notice that it does not
+
+ align:start position:0%
+more likely but notice that it does not
+ 
+
+ align:start position:0%
+more likely but notice that it does not
+let you go directly from 3.2 mu v to 0
+
+ align:start position:0%
+let you go directly from 3.2 mu v to 0
+ 
+
+ align:start position:0%
+let you go directly from 3.2 mu v to 0
+there's no allowable decay here so this
+
+ align:start position:0%
+there's no allowable decay here so this
+ 
+
+ align:start position:0%
+there's no allowable decay here so this
+is probably a change of that's 3.2
+
+ align:start position:0%
+is probably a change of that's 3.2
+ 
+
+ align:start position:0%
+is probably a change of that's 3.2
+that's 1.3 a little less than 2 MeV all
+
+ align:start position:0%
+that's 1.3 a little less than 2 MeV all
+ 
+
+ align:start position:0%
+that's 1.3 a little less than 2 MeV all
+of a sudden electron capture becomes
+
+ align:start position:0%
+of a sudden electron capture becomes
+ 
+
+ align:start position:0%
+of a sudden electron capture becomes
+much more likely but not at positron
+
+ align:start position:0%
+much more likely but not at positron
+ 
+
+ align:start position:0%
+much more likely but not at positron
+decay is not disallowed yet so we can
+
+ align:start position:0%
+decay is not disallowed yet so we can
+ 
+
+ align:start position:0%
+decay is not disallowed yet so we can
+say electron capture or positron decay
+
+ align:start position:0%
+say electron capture or positron decay
+ 
+
+ align:start position:0%
+say electron capture or positron decay
+right there everyone with me so far so
+
+ align:start position:0%
+right there everyone with me so far so
+ 
+
+ align:start position:0%
+right there everyone with me so far so
+let's go to the really low energy one
+
+ align:start position:0%
+let's go to the really low energy one
+ 
+
+ align:start position:0%
+let's go to the really low energy one
+will click on molybdenum 93 and see how
+
+ align:start position:0%
+will click on molybdenum 93 and see how
+ 
+
+ align:start position:0%
+will click on molybdenum 93 and see how
+it decays with an energy of 0.40 5 MeV
+
+ align:start position:0%
+it decays with an energy of 0.40 5 MeV
+ 
+
+ align:start position:0%
+it decays with an energy of 0.40 5 MeV
+to niobium anyone want to guess what's
+
+ align:start position:0%
+to niobium anyone want to guess what's
+ 
+
+ align:start position:0%
+to niobium anyone want to guess what's
+allowed
+
+ align:start position:0%
+allowed
+ 
+
+ align:start position:0%
+allowed
+electron capture only there's not enough
+
+ align:start position:0%
+electron capture only there's not enough
+ 
+
+ align:start position:0%
+electron capture only there's not enough
+energy for positron decay and indeed it
+
+ align:start position:0%
+energy for positron decay and indeed it
+ 
+
+ align:start position:0%
+energy for positron decay and indeed it
+draws funny because there's a metastable
+
+ align:start position:0%
+draws funny because there's a metastable
+ 
+
+ align:start position:0%
+draws funny because there's a metastable
+state but if you go scroll down here
+
+ align:start position:0%
+state but if you go scroll down here
+ 
+
+ align:start position:0%
+state but if you go scroll down here
+there are two pathways allowed both of
+
+ align:start position:0%
+there are two pathways allowed both of
+ 
+
+ align:start position:0%
+there are two pathways allowed both of
+which by electron capture decaying
+
+ align:start position:0%
+which by electron capture decaying
+ 
+
+ align:start position:0%
+which by electron capture decaying
+diagrams quite a bit simpler so we leave
+
+ align:start position:0%
+diagrams quite a bit simpler so we leave
+ 
+
+ align:start position:0%
+diagrams quite a bit simpler so we leave
+this one here by saying it can only
+
+ align:start position:0%
+this one here by saying it can only
+ 
+
+ align:start position:0%
+this one here by saying it can only
+decay by electron capture any questions
+
+ align:start position:0%
+decay by electron capture any questions
+ 
+
+ align:start position:0%
+decay by electron capture any questions
+on the odd a before we move on to the
+
+ align:start position:0%
+on the odd a before we move on to the
+ 
+
+ align:start position:0%
+on the odd a before we move on to the
+even which is a little more interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool okay let's move on to the even case
+
+ align:start position:0%
+cool okay let's move on to the even case
+ 
+
+ align:start position:0%
+cool okay let's move on to the even case
+so for here I'm going to go back to the
+
+ align:start position:0%
+so for here I'm going to go back to the
+ 
+
+ align:start position:0%
+so for here I'm going to go back to the
+overall picture of the table of nuclides
+
+ align:start position:0%
+overall picture of the table of nuclides
+ 
+
+ align:start position:0%
+overall picture of the table of nuclides
+click on around where I think
+
+ align:start position:0%
+click on around where I think
+ 
+
+ align:start position:0%
+click on around where I think
+potassium-40 is looks like I got there
+
+ align:start position:0%
+potassium-40 is looks like I got there
+ 
+
+ align:start position:0%
+potassium-40 is looks like I got there
+and I want to point out one of these
+
+ align:start position:0%
+and I want to point out one of these
+ 
+
+ align:start position:0%
+and I want to point out one of these
+features if you wanted to go under go
+
+ align:start position:0%
+features if you wanted to go under go
+ 
+
+ align:start position:0%
+features if you wanted to go under go
+decay change and maintain the same mass
+
+ align:start position:0%
+decay change and maintain the same mass
+ 
+
+ align:start position:0%
+decay change and maintain the same mass
+number that's diagonally from upper left
+
+ align:start position:0%
+number that's diagonally from upper left
+ 
+
+ align:start position:0%
+number that's diagonally from upper left
+to lower right see how all the isotopes
+
+ align:start position:0%
+to lower right see how all the isotopes
+ 
+
+ align:start position:0%
+to lower right see how all the isotopes
+here have a forty in front of them the
+
+ align:start position:0%
+here have a forty in front of them the
+ 
+
+ align:start position:0%
+here have a forty in front of them the
+really interesting part is as you cross
+
+ align:start position:0%
+really interesting part is as you cross
+ 
+
+ align:start position:0%
+really interesting part is as you cross
+this line you go from stable to unstable
+
+ align:start position:0%
+this line you go from stable to unstable
+ 
+
+ align:start position:0%
+this line you go from stable to unstable
+to stable to unstable again the colors
+
+ align:start position:0%
+to stable to unstable again the colors
+ 
+
+ align:start position:0%
+to stable to unstable again the colors
+here is dark blue represents stable and
+
+ align:start position:0%
+here is dark blue represents stable and
+ 
+
+ align:start position:0%
+here is dark blue represents stable and
+dark gray represents long lifetimes of
+
+ align:start position:0%
+dark gray represents long lifetimes of
+ 
+
+ align:start position:0%
+dark gray represents long lifetimes of
+over a hundred thousand years so this is
+
+ align:start position:0%
+over a hundred thousand years so this is
+ 
+
+ align:start position:0%
+over a hundred thousand years so this is
+one of the reasons you find potassium-40
+
+ align:start position:0%
+one of the reasons you find potassium-40
+ 
+
+ align:start position:0%
+one of the reasons you find potassium-40
+in the environment in fact point oh one
+
+ align:start position:0%
+in the environment in fact point oh one
+ 
+
+ align:start position:0%
+in the environment in fact point oh one
+one percent of all potassium in you and
+
+ align:start position:0%
+one percent of all potassium in you and
+ 
+
+ align:start position:0%
+one percent of all potassium in you and
+everything is potassium-40
+
+ align:start position:0%
+everything is potassium-40
+ 
+
+ align:start position:0%
+everything is potassium-40
+it's what's known as a primordial
+
+ align:start position:0%
+it's what's known as a primordial
+ 
+
+ align:start position:0%
+it's what's known as a primordial
+nuclide it's not stable but it's
+
+ align:start position:0%
+nuclide it's not stable but it's
+ 
+
+ align:start position:0%
+nuclide it's not stable but it's
+half-life is so long that there's still
+
+ align:start position:0%
+half-life is so long that there's still
+ 
+
+ align:start position:0%
+half-life is so long that there's still
+some left since the universe began or
+
+ align:start position:0%
+some left since the universe began or
+ 
+
+ align:start position:0%
+some left since the universe began or
+whatever supernova that formed earth got
+
+ align:start position:0%
+whatever supernova that formed earth got
+ 
+
+ align:start position:0%
+whatever supernova that formed earth got
+accumulated into the earth but notice it
+
+ align:start position:0%
+accumulated into the earth but notice it
+ 
+
+ align:start position:0%
+accumulated into the earth but notice it
+can come from it can decay by a couple
+
+ align:start position:0%
+can come from it can decay by a couple
+ 
+
+ align:start position:0%
+can come from it can decay by a couple
+of different methods so let's pick one
+
+ align:start position:0%
+of different methods so let's pick one
+ 
+
+ align:start position:0%
+of different methods so let's pick one
+of those stable isotopes calcium for T
+
+ align:start position:0%
+of those stable isotopes calcium for T
+ 
+
+ align:start position:0%
+of those stable isotopes calcium for T
+and put that as the bottom of the
+
+ align:start position:0%
+and put that as the bottom of the
+ 
+
+ align:start position:0%
+and put that as the bottom of the
+parabola on this diagram
+
+ align:start position:0%
+parabola on this diagram
+ 
+
+ align:start position:0%
+parabola on this diagram
+so we'll put calcium here and in a
+
+ align:start position:0%
+so we'll put calcium here and in a
+ 
+
+ align:start position:0%
+so we'll put calcium here and in a
+relative sense we'll put a calcium point
+
+ align:start position:0%
+relative sense we'll put a calcium point
+ 
+
+ align:start position:0%
+relative sense we'll put a calcium point
+right there for its total mass and it
+
+ align:start position:0%
+right there for its total mass and it
+ 
+
+ align:start position:0%
+right there for its total mass and it
+could have come from beta decay from
+
+ align:start position:0%
+could have come from beta decay from
+ 
+
+ align:start position:0%
+could have come from beta decay from
+potassium-40 or electron capture from
+
+ align:start position:0%
+potassium-40 or electron capture from
+ 
+
+ align:start position:0%
+potassium-40 or electron capture from
+scandium 4040
+
+ align:start position:0%
+scandium 4040
+ 
+
+ align:start position:0%
+scandium 4040
+it can beta-decay for about a 1.3 MeV so
+
+ align:start position:0%
+it can beta-decay for about a 1.3 MeV so
+ 
+
+ align:start position:0%
+it can beta-decay for about a 1.3 MeV so
+potassium it's right here let's say it
+
+ align:start position:0%
+potassium it's right here let's say it
+ 
+
+ align:start position:0%
+potassium it's right here let's say it
+could beta decay with about 1.3 MeV and
+
+ align:start position:0%
+could beta decay with about 1.3 MeV and
+ 
+
+ align:start position:0%
+could beta decay with about 1.3 MeV and
+we'll trace potassium back a little bit
+
+ align:start position:0%
+we'll trace potassium back a little bit
+ 
+
+ align:start position:0%
+we'll trace potassium back a little bit
+figure out where would it have come from
+
+ align:start position:0%
+figure out where would it have come from
+ 
+
+ align:start position:0%
+figure out where would it have come from
+interesting doesn't tell us okay forget
+
+ align:start position:0%
+interesting doesn't tell us okay forget
+ 
+
+ align:start position:0%
+interesting doesn't tell us okay forget
+that let's trace calcium back and say
+
+ align:start position:0%
+that let's trace calcium back and say
+ 
+
+ align:start position:0%
+that let's trace calcium back and say
+there's scandium 40 and scandium 40 can
+
+ align:start position:0%
+there's scandium 40 and scandium 40 can
+ 
+
+ align:start position:0%
+there's scandium 40 and scandium 40 can
+decay with Wow an enormous 14 point 3 2
+
+ align:start position:0%
+decay with Wow an enormous 14 point 3 2
+ 
+
+ align:start position:0%
+decay with Wow an enormous 14 point 3 2
+MeV let's put that like here anyone want
+
+ align:start position:0%
+MeV let's put that like here anyone want
+ 
+
+ align:start position:0%
+MeV let's put that like here anyone want
+to guess which mode electron capture or
+
+ align:start position:0%
+to guess which mode electron capture or
+ 
+
+ align:start position:0%
+to guess which mode electron capture or
+positrons much more likely probably
+
+ align:start position:0%
+positrons much more likely probably
+ 
+
+ align:start position:0%
+positrons much more likely probably
+positron let's take a look oh boy
+
+ align:start position:0%
+positron let's take a look oh boy
+ 
+
+ align:start position:0%
+positron let's take a look oh boy
+another complicated one but the whole
+
+ align:start position:0%
+another complicated one but the whole
+ 
+
+ align:start position:0%
+another complicated one but the whole
+way down positron positron positron for
+
+ align:start position:0%
+way down positron positron positron for
+ 
+
+ align:start position:0%
+way down positron positron positron for
+all the most likely decays you won't
+
+ align:start position:0%
+all the most likely decays you won't
+ 
+
+ align:start position:0%
+all the most likely decays you won't
+find a drawing too every single line I
+
+ align:start position:0%
+find a drawing too every single line I
+ 
+
+ align:start position:0%
+find a drawing too every single line I
+believe that they know that at some
+
+ align:start position:0%
+believe that they know that at some
+ 
+
+ align:start position:0%
+believe that they know that at some
+point drawing extra lines is futile and
+
+ align:start position:0%
+point drawing extra lines is futile and
+ 
+
+ align:start position:0%
+point drawing extra lines is futile and
+they just all overlap each other so I
+
+ align:start position:0%
+they just all overlap each other so I
+ 
+
+ align:start position:0%
+they just all overlap each other so I
+don't know exactly how the algorithm
+
+ align:start position:0%
+don't know exactly how the algorithm
+ 
+
+ align:start position:0%
+don't know exactly how the algorithm
+works but it does draw up to some number
+
+ align:start position:0%
+works but it does draw up to some number
+ 
+
+ align:start position:0%
+works but it does draw up to some number
+of possible decay chains if you want to
+
+ align:start position:0%
+of possible decay chains if you want to
+ 
+
+ align:start position:0%
+of possible decay chains if you want to
+see every single one they are tabulated
+
+ align:start position:0%
+see every single one they are tabulated
+ 
+
+ align:start position:0%
+see every single one they are tabulated
+in a very very long list down below I'm
+
+ align:start position:0%
+in a very very long list down below I'm
+ 
+
+ align:start position:0%
+in a very very long list down below I'm
+never going to ask you to do something
+
+ align:start position:0%
+never going to ask you to do something
+ 
+
+ align:start position:0%
+never going to ask you to do something
+with all of these because that would be
+
+ align:start position:0%
+with all of these because that would be
+ 
+
+ align:start position:0%
+with all of these because that would be
+insane unless it's a relatively simple
+
+ align:start position:0%
+insane unless it's a relatively simple
+ 
+
+ align:start position:0%
+insane unless it's a relatively simple
+decay like that has two or three
+
+ align:start position:0%
+decay like that has two or three
+ 
+
+ align:start position:0%
+decay like that has two or three
+possibilities and let's see this could
+
+ align:start position:0%
+possibilities and let's see this could
+ 
+
+ align:start position:0%
+possibilities and let's see this could
+have come from electron capture from
+
+ align:start position:0%
+have come from electron capture from
+ 
+
+ align:start position:0%
+have come from electron capture from
+titanium forty with eleven point six
+
+ align:start position:0%
+titanium forty with eleven point six
+ 
+
+ align:start position:0%
+titanium forty with eleven point six
+eight I'm easy Wow okay here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's titanium and let's go in the
+
+ align:start position:0%
+and there's titanium and let's go in the
+ 
+
+ align:start position:0%
+and there's titanium and let's go in the
+other direction so I do know that
+
+ align:start position:0%
+other direction so I do know that
+ 
+
+ align:start position:0%
+other direction so I do know that
+potassium-40
+
+ align:start position:0%
+potassium-40
+ 
+
+ align:start position:0%
+potassium-40
+can decay into argon-40 so let's jump
+
+ align:start position:0%
+can decay into argon-40 so let's jump
+ 
+
+ align:start position:0%
+can decay into argon-40 so let's jump
+there argon is a stable isotope too so
+
+ align:start position:0%
+there argon is a stable isotope too so
+ 
+
+ align:start position:0%
+there argon is a stable isotope too so
+potassium-40 can decay into argon-40 by
+
+ align:start position:0%
+potassium-40 can decay into argon-40 by
+ 
+
+ align:start position:0%
+potassium-40 can decay into argon-40 by
+electron capture okay good a more
+
+ align:start position:0%
+electron capture okay good a more
+ 
+
+ align:start position:0%
+electron capture okay good a more
+respectable 1.50 5 MeV is positron decay
+
+ align:start position:0%
+respectable 1.50 5 MeV is positron decay
+ 
+
+ align:start position:0%
+respectable 1.50 5 MeV is positron decay
+allowed yes why is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+/ 1.02 to mev yeah anyone had a question
+
+ align:start position:0%
+/ 1.02 to mev yeah anyone had a question
+ 
+
+ align:start position:0%
+/ 1.02 to mev yeah anyone had a question
+no okay
+
+ align:start position:0%
+no okay
+ 
+
+ align:start position:0%
+no okay
+so we've got kind of a kink in our math
+
+ align:start position:0%
+so we've got kind of a kink in our math
+ 
+
+ align:start position:0%
+so we've got kind of a kink in our math
+parabola yeah that's correct yep so once
+
+ align:start position:0%
+parabola yeah that's correct yep so once
+ 
+
+ align:start position:0%
+parabola yeah that's correct yep so once
+the Q value satisfied it is technically
+
+ align:start position:0%
+the Q value satisfied it is technically
+ 
+
+ align:start position:0%
+the Q value satisfied it is technically
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+but if you had something with the decay
+
+ align:start position:0%
+but if you had something with the decay
+ 
+
+ align:start position:0%
+but if you had something with the decay
+energy of like 1.0 to 3 MeV it would be
+
+ align:start position:0%
+energy of like 1.0 to 3 MeV it would be
+ 
+
+ align:start position:0%
+energy of like 1.0 to 3 MeV it would be
+exceedingly unlikely so in fact we can
+
+ align:start position:0%
+exceedingly unlikely so in fact we can
+ 
+
+ align:start position:0%
+exceedingly unlikely so in fact we can
+take a look at this this is I would say
+
+ align:start position:0%
+take a look at this this is I would say
+ 
+
+ align:start position:0%
+take a look at this this is I would say
+is also going to be on the exceedingly
+
+ align:start position:0%
+is also going to be on the exceedingly
+ 
+
+ align:start position:0%
+is also going to be on the exceedingly
+unlikely level and we can take a look so
+
+ align:start position:0%
+unlikely level and we can take a look so
+ 
+
+ align:start position:0%
+unlikely level and we can take a look so
+if we look at the decay diagram we know
+
+ align:start position:0%
+if we look at the decay diagram we know
+ 
+
+ align:start position:0%
+if we look at the decay diagram we know
+it makes positrons they're not even
+
+ align:start position:0%
+it makes positrons they're not even
+ 
+
+ align:start position:0%
+it makes positrons they're not even
+really listed interesting because so
+
+ align:start position:0%
+really listed interesting because so
+ 
+
+ align:start position:0%
+really listed interesting because so
+that process would not be allowed but
+
+ align:start position:0%
+that process would not be allowed but
+ 
+
+ align:start position:0%
+that process would not be allowed but
+this one because that's about 1.5 MeV
+
+ align:start position:0%
+this one because that's about 1.5 MeV
+ 
+
+ align:start position:0%
+this one because that's about 1.5 MeV
+should be allowed but since that branch
+
+ align:start position:0%
+should be allowed but since that branch
+ 
+
+ align:start position:0%
+should be allowed but since that branch
+ratio or the probability of that
+
+ align:start position:0%
+ratio or the probability of that
+ 
+
+ align:start position:0%
+ratio or the probability of that
+happening is already so low I wonder if
+
+ align:start position:0%
+happening is already so low I wonder if
+ 
+
+ align:start position:0%
+happening is already so low I wonder if
+it even says yep beta ray with a max or
+
+ align:start position:0%
+it even says yep beta ray with a max or
+ 
+
+ align:start position:0%
+it even says yep beta ray with a max or
+average energy of 482 point 8 MeV we're
+
+ align:start position:0%
+average energy of 482 point 8 MeV we're
+ 
+
+ align:start position:0%
+average energy of 482 point 8 MeV we're
+gonna go over why that energy is so low
+
+ align:start position:0%
+gonna go over why that energy is so low
+ 
+
+ align:start position:0%
+gonna go over why that energy is so low
+when we talk about decay next week with
+
+ align:start position:0%
+when we talk about decay next week with
+ 
+
+ align:start position:0%
+when we talk about decay next week with
+a relative intensity of something with a
+
+ align:start position:0%
+a relative intensity of something with a
+ 
+
+ align:start position:0%
+a relative intensity of something with a
+lot of zeros before the decimal place so
+
+ align:start position:0%
+lot of zeros before the decimal place so
+ 
+
+ align:start position:0%
+lot of zeros before the decimal place so
+there you go like you said energies near
+
+ align:start position:0%
+there you go like you said energies near
+ 
+
+ align:start position:0%
+there you go like you said energies near
+1.0 to 2 MeV slightly above it are
+
+ align:start position:0%
+1.0 to 2 MeV slightly above it are
+ 
+
+ align:start position:0%
+1.0 to 2 MeV slightly above it are
+extremely unlikely but possible and
+
+ align:start position:0%
+extremely unlikely but possible and
+ 
+
+ align:start position:0%
+extremely unlikely but possible and
+measurable cool and then let's see what
+
+ align:start position:0%
+measurable cool and then let's see what
+ 
+
+ align:start position:0%
+measurable cool and then let's see what
+could have made argon-40 could have been
+
+ align:start position:0%
+could have made argon-40 could have been
+ 
+
+ align:start position:0%
+could have made argon-40 could have been
+beta decay from chlorine 40 so chlorine
+
+ align:start position:0%
+beta decay from chlorine 40 so chlorine
+ 
+
+ align:start position:0%
+beta decay from chlorine 40 so chlorine
+maybe was here and I don't think I have
+
+ align:start position:0%
+maybe was here and I don't think I have
+ 
+
+ align:start position:0%
+maybe was here and I don't think I have
+to draw any more so we've got an
+
+ align:start position:0%
+to draw any more so we've got an
+ 
+
+ align:start position:0%
+to draw any more so we've got an
+funny-looking parabola with a kink in it
+
+ align:start position:0%
+funny-looking parabola with a kink in it
+ 
+
+ align:start position:0%
+funny-looking parabola with a kink in it
+because really you have two bass
+
+ align:start position:0%
+because really you have two bass
+ 
+
+ align:start position:0%
+because really you have two bass
+parabolas overlapping I'm gonna go back
+
+ align:start position:0%
+parabolas overlapping I'm gonna go back
+ 
+
+ align:start position:0%
+parabolas overlapping I'm gonna go back
+to the screen so that the diagram from
+
+ align:start position:0%
+to the screen so that the diagram from
+ 
+
+ align:start position:0%
+to the screen so that the diagram from
+the notes makes a little more sense what
+
+ align:start position:0%
+the notes makes a little more sense what
+ 
+
+ align:start position:0%
+the notes makes a little more sense what
+we've kind of traced out here is that
+
+ align:start position:0%
+we've kind of traced out here is that
+ 
+
+ align:start position:0%
+we've kind of traced out here is that
+there's two overlapping parabolas here
+
+ align:start position:0%
+there's two overlapping parabolas here
+ 
+
+ align:start position:0%
+there's two overlapping parabolas here
+there's the one with the what is it the
+
+ align:start position:0%
+there's the one with the what is it the
+ 
+
+ align:start position:0%
+there's the one with the what is it the
+odd Z and the even Z so there you go
+
+ align:start position:0%
+odd Z and the even Z so there you go
+ 
+
+ align:start position:0%
+odd Z and the even Z so there you go
+just like the one on here which i think
+
+ align:start position:0%
+just like the one on here which i think
+ 
+
+ align:start position:0%
+just like the one on here which i think
+is for a different mass number yep 102
+
+ align:start position:0%
+is for a different mass number yep 102
+ 
+
+ align:start position:0%
+is for a different mass number yep 102
+we get the same kind of behavior
+
+ align:start position:0%
+we get the same kind of behavior
+ 
+
+ align:start position:0%
+we get the same kind of behavior
+where things will mostly follow the
+
+ align:start position:0%
+where things will mostly follow the
+ 
+
+ align:start position:0%
+where things will mostly follow the
+lower-mass parabola but sometimes if
+
+ align:start position:0%
+lower-mass parabola but sometimes if
+ 
+
+ align:start position:0%
+lower-mass parabola but sometimes if
+something gets stuck here it can go
+
+ align:start position:0%
+something gets stuck here it can go
+ 
+
+ align:start position:0%
+something gets stuck here it can go
+either way to get more stable so I want
+
+ align:start position:0%
+either way to get more stable so I want
+ 
+
+ align:start position:0%
+either way to get more stable so I want
+to stop here for new stuff because this
+
+ align:start position:0%
+to stop here for new stuff because this
+ 
+
+ align:start position:0%
+to stop here for new stuff because this
+is precisely where I thought we'd be at
+
+ align:start position:0%
+is precisely where I thought we'd be at
+ 
+
+ align:start position:0%
+is precisely where I thought we'd be at
+the end of the week and in the next half
+
+ align:start position:0%
+the end of the week and in the next half
+ 
+
+ align:start position:0%
+the end of the week and in the next half
+an hour I'd like to open it up to
+
+ align:start position:0%
+an hour I'd like to open it up to
+ 
+
+ align:start position:0%
+an hour I'd like to open it up to
+questions or working things out together
+
+ align:start position:0%
+questions or working things out together
+ 
+
+ align:start position:0%
+questions or working things out together
+on the board or anything else you might
+
+ align:start position:0%
+on the board or anything else you might
+ 
+
+ align:start position:0%
+on the board or anything else you might
+have had yeah sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's going to go in whatever when
+
+ align:start position:0%
+it's going to go in whatever when
+ 
+
+ align:start position:0%
+it's going to go in whatever when
+whatever way makes it more stable so
+
+ align:start position:0%
+whatever way makes it more stable so
+ 
+
+ align:start position:0%
+whatever way makes it more stable so
+you're never going to have a nucleus is
+
+ align:start position:0%
+you're never going to have a nucleus is
+ 
+
+ align:start position:0%
+you're never going to have a nucleus is
+going to spontaneously gain mass in
+
+ align:start position:0%
+going to spontaneously gain mass in
+ 
+
+ align:start position:0%
+going to spontaneously gain mass in
+order to get to a different path you can
+
+ align:start position:0%
+order to get to a different path you can
+ 
+
+ align:start position:0%
+order to get to a different path you can
+only go down on the mass axis but let's
+
+ align:start position:0%
+only go down on the mass axis but let's
+ 
+
+ align:start position:0%
+only go down on the mass axis but let's
+say you happen to be starting here at
+
+ align:start position:0%
+say you happen to be starting here at
+ 
+
+ align:start position:0%
+say you happen to be starting here at
+potassium-40
+
+ align:start position:0%
+potassium-40
+ 
+
+ align:start position:0%
+potassium-40
+you can go down via either mechanism to
+
+ align:start position:0%
+you can go down via either mechanism to
+ 
+
+ align:start position:0%
+you can go down via either mechanism to
+the next mass parabola down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's quite if you're at argon you're
+
+ align:start position:0%
+that's quite if you're at argon you're
+ 
+
+ align:start position:0%
+that's quite if you're at argon you're
+stuck and in fact if you want to take a
+
+ align:start position:0%
+stuck and in fact if you want to take a
+ 
+
+ align:start position:0%
+stuck and in fact if you want to take a
+look what do I mean scientifically by
+
+ align:start position:0%
+look what do I mean scientifically by
+ 
+
+ align:start position:0%
+look what do I mean scientifically by
+stuck I mean stable argon-40 is a stable
+
+ align:start position:0%
+stuck I mean stable argon-40 is a stable
+ 
+
+ align:start position:0%
+stuck I mean stable argon-40 is a stable
+nucleus that comprises ninety nine point
+
+ align:start position:0%
+nucleus that comprises ninety nine point
+ 
+
+ align:start position:0%
+nucleus that comprises ninety nine point
+six percent of the argon so that's what
+
+ align:start position:0%
+six percent of the argon so that's what
+ 
+
+ align:start position:0%
+six percent of the argon so that's what
+I mean by stock is stable and if we look
+
+ align:start position:0%
+I mean by stock is stable and if we look
+ 
+
+ align:start position:0%
+I mean by stock is stable and if we look
+at the rest of the table of nuclides for
+
+ align:start position:0%
+at the rest of the table of nuclides for
+ 
+
+ align:start position:0%
+at the rest of the table of nuclides for
+similar looking places so let's hunt
+
+ align:start position:0%
+similar looking places so let's hunt
+ 
+
+ align:start position:0%
+similar looking places so let's hunt
+near potassium-40 so notice potassium-40
+
+ align:start position:0%
+near potassium-40 so notice potassium-40
+ 
+
+ align:start position:0%
+near potassium-40 so notice potassium-40
+right here has got stable isotopes to
+
+ align:start position:0%
+right here has got stable isotopes to
+ 
+
+ align:start position:0%
+right here has got stable isotopes to
+the upper left and the lower right if we
+
+ align:start position:0%
+the upper left and the lower right if we
+ 
+
+ align:start position:0%
+the upper left and the lower right if we
+look back over here manganese 54 same
+
+ align:start position:0%
+look back over here manganese 54 same
+ 
+
+ align:start position:0%
+look back over here manganese 54 same
+deal it's got a stable isotope to the
+
+ align:start position:0%
+deal it's got a stable isotope to the
+ 
+
+ align:start position:0%
+deal it's got a stable isotope to the
+upper left and a stable one to the lower
+
+ align:start position:0%
+upper left and a stable one to the lower
+ 
+
+ align:start position:0%
+upper left and a stable one to the lower
+right how much you want to bet that when
+
+ align:start position:0%
+right how much you want to bet that when
+ 
+
+ align:start position:0%
+right how much you want to bet that when
+we click on manganese 54 it's got two
+
+ align:start position:0%
+we click on manganese 54 it's got two
+ 
+
+ align:start position:0%
+we click on manganese 54 it's got two
+possible parent new clients I'm sorry
+
+ align:start position:0%
+possible parent new clients I'm sorry
+ 
+
+ align:start position:0%
+possible parent new clients I'm sorry
+two possible decay math methods so let's
+
+ align:start position:0%
+two possible decay math methods so let's
+ 
+
+ align:start position:0%
+two possible decay math methods so let's
+take a look manganese 54 can either
+
+ align:start position:0%
+take a look manganese 54 can either
+ 
+
+ align:start position:0%
+take a look manganese 54 can either
+electron capture and positron decay to
+
+ align:start position:0%
+electron capture and positron decay to
+ 
+
+ align:start position:0%
+electron capture and positron decay to
+chromium 54 or beta decay to iron 54
+
+ align:start position:0%
+chromium 54 or beta decay to iron 54
+ 
+
+ align:start position:0%
+chromium 54 or beta decay to iron 54
+let's take a look at one more to hammer
+
+ align:start position:0%
+let's take a look at one more to hammer
+ 
+
+ align:start position:0%
+let's take a look at one more to hammer
+the point home and I think that'll
+
+ align:start position:0%
+the point home and I think that'll
+ 
+
+ align:start position:0%
+the point home and I think that'll
+probably be enough cobalt 58 right near
+
+ align:start position:0%
+probably be enough cobalt 58 right near
+ 
+
+ align:start position:0%
+probably be enough cobalt 58 right near
+nickel 58 and iron 58 interesting that
+
+ align:start position:0%
+nickel 58 and iron 58 interesting that
+ 
+
+ align:start position:0%
+nickel 58 and iron 58 interesting that
+one's not allowed unless there's more
+
+ align:start position:0%
+one's not allowed unless there's more
+ 
+
+ align:start position:0%
+one's not allowed unless there's more
+down here so you can electron capture to
+
+ align:start position:0%
+down here so you can electron capture to
+ 
+
+ align:start position:0%
+down here so you can electron capture to
+iron 58 but there's no allowed decay to
+
+ align:start position:0%
+iron 58 but there's no allowed decay to
+ 
+
+ align:start position:0%
+iron 58 but there's no allowed decay to
+what was it nickel 58 okay let's look
+
+ align:start position:0%
+what was it nickel 58 okay let's look
+ 
+
+ align:start position:0%
+what was it nickel 58 okay let's look
+for more chlorine 36 has argon and
+
+ align:start position:0%
+for more chlorine 36 has argon and
+ 
+
+ align:start position:0%
+for more chlorine 36 has argon and
+sulfur on either side there it is
+
+ align:start position:0%
+sulfur on either side there it is
+ 
+
+ align:start position:0%
+sulfur on either side there it is
+beta-decay and electron capture and how
+
+ align:start position:0%
+beta-decay and electron capture and how
+ 
+
+ align:start position:0%
+beta-decay and electron capture and how
+much you want to bet there's basically
+
+ align:start position:0%
+much you want to bet there's basically
+ 
+
+ align:start position:0%
+much you want to bet there's basically
+never a positron here but basically not
+
+ align:start position:0%
+never a positron here but basically not
+ 
+
+ align:start position:0%
+never a positron here but basically not
+actually never so you get a positron
+
+ align:start position:0%
+actually never so you get a positron
+ 
+
+ align:start position:0%
+actually never so you get a positron
+0.01 percent of the time and electron
+
+ align:start position:0%
+0.01 percent of the time and electron
+ 
+
+ align:start position:0%
+0.01 percent of the time and electron
+capture one point eight nine percent of
+
+ align:start position:0%
+capture one point eight nine percent of
+ 
+
+ align:start position:0%
+capture one point eight nine percent of
+the time where's the other 98 and change
+
+ align:start position:0%
+the time where's the other 98 and change
+ 
+
+ align:start position:0%
+the time where's the other 98 and change
+percent right here in the beta decay so
+
+ align:start position:0%
+percent right here in the beta decay so
+ 
+
+ align:start position:0%
+percent right here in the beta decay so
+in this case chlorine 36 will
+
+ align:start position:0%
+in this case chlorine 36 will
+ 
+
+ align:start position:0%
+in this case chlorine 36 will
+preferentially beta decay if you also
+
+ align:start position:0%
+preferentially beta decay if you also
+ 
+
+ align:start position:0%
+preferentially beta decay if you also
+notice it's a let's see you don't know
+
+ align:start position:0%
+notice it's a let's see you don't know
+ 
+
+ align:start position:0%
+notice it's a let's see you don't know
+if that actually matters so but I'm
+
+ align:start position:0%
+if that actually matters so but I'm
+ 
+
+ align:start position:0%
+if that actually matters so but I'm
+gonna say it's more likely to beta decay
+
+ align:start position:0%
+gonna say it's more likely to beta decay
+ 
+
+ align:start position:0%
+gonna say it's more likely to beta decay
+so when you sum these up you get a
+
+ align:start position:0%
+so when you sum these up you get a
+ 
+
+ align:start position:0%
+so when you sum these up you get a
+hundred percent of the possible to case
+
+ align:start position:0%
+hundred percent of the possible to case
+ 
+
+ align:start position:0%
+hundred percent of the possible to case
+let's see how many energy levels there
+
+ align:start position:0%
+let's see how many energy levels there
+ 
+
+ align:start position:0%
+let's see how many energy levels there
+are there too hopefully not too many
+
+ align:start position:0%
+are there too hopefully not too many
+ 
+
+ align:start position:0%
+are there too hopefully not too many
+that qualifies as not too many yeah John
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they'll be due to those as well as some
+
+ align:start position:0%
+they'll be due to those as well as some
+ 
+
+ align:start position:0%
+they'll be due to those as well as some
+other processes which we're going to
+
+ align:start position:0%
+other processes which we're going to
+ 
+
+ align:start position:0%
+other processes which we're going to
+cover on decay but if you notice I've
+
+ align:start position:0%
+cover on decay but if you notice I've
+ 
+
+ align:start position:0%
+cover on decay but if you notice I've
+been giving you a lot of flash-forwards
+
+ align:start position:0%
+been giving you a lot of flash-forwards
+ 
+
+ align:start position:0%
+been giving you a lot of flash-forwards
+in this class we've introduced
+
+ align:start position:0%
+in this class we've introduced
+ 
+
+ align:start position:0%
+in this class we've introduced
+cross-sections as a thing that a
+
+ align:start position:0%
+cross-sections as a thing that a
+ 
+
+ align:start position:0%
+cross-sections as a thing that a
+proportionality constant between
+
+ align:start position:0%
+proportionality constant between
+ 
+
+ align:start position:0%
+proportionality constant between
+interaction probabilities we're going to
+
+ align:start position:0%
+interaction probabilities we're going to
+ 
+
+ align:start position:0%
+interaction probabilities we're going to
+hit them hard later I've also been kind
+
+ align:start position:0%
+hit them hard later I've also been kind
+ 
+
+ align:start position:0%
+hit them hard later I've also been kind
+of introducing or flash forwarding
+
+ align:start position:0%
+of introducing or flash forwarding
+ 
+
+ align:start position:0%
+of introducing or flash forwarding
+different methods of decay so there's
+
+ align:start position:0%
+different methods of decay so there's
+ 
+
+ align:start position:0%
+different methods of decay so there's
+also alpha decay
+
+ align:start position:0%
+also alpha decay
+ 
+
+ align:start position:0%
+also alpha decay
+there's also isomeric transition or
+
+ align:start position:0%
+there's also isomeric transition or
+ 
+
+ align:start position:0%
+there's also isomeric transition or
+gamma emission
+
+ align:start position:0%
+gamma emission
+ 
+
+ align:start position:0%
+gamma emission
+there's also spontaneous fission this is
+
+ align:start position:0%
+there's also spontaneous fission this is
+ 
+
+ align:start position:0%
+there's also spontaneous fission this is
+the whole basis behind how fission can
+
+ align:start position:0%
+the whole basis behind how fission can
+ 
+
+ align:start position:0%
+the whole basis behind how fission can
+get working without some sort of
+
+ align:start position:0%
+get working without some sort of
+ 
+
+ align:start position:0%
+get working without some sort of
+kick-starting elements so maybe now's a
+
+ align:start position:0%
+kick-starting elements so maybe now's a
+ 
+
+ align:start position:0%
+kick-starting elements so maybe now's a
+good time to show you let's go to
+
+ align:start position:0%
+good time to show you let's go to
+ 
+
+ align:start position:0%
+good time to show you let's go to
+uranium-235 and see how it decays a de
+
+ align:start position:0%
+uranium-235 and see how it decays a de
+ 
+
+ align:start position:0%
+uranium-235 and see how it decays a de
+ganar D undergoes alpha decay de thorium
+
+ align:start position:0%
+ganar D undergoes alpha decay de thorium
+ 
+
+ align:start position:0%
+ganar D undergoes alpha decay de thorium
+231 most of the time and if you look how
+
+ align:start position:0%
+231 most of the time and if you look how
+ 
+
+ align:start position:0%
+231 most of the time and if you look how
+it's no it's not terrible we can make
+
+ align:start position:0%
+it's no it's not terrible we can make
+ 
+
+ align:start position:0%
+it's no it's not terrible we can make
+sense of this it also undergoes SF which
+
+ align:start position:0%
+sense of this it also undergoes SF which
+ 
+
+ align:start position:0%
+sense of this it also undergoes SF which
+stands for a spontaneous fission so one
+
+ align:start position:0%
+stands for a spontaneous fission so one
+ 
+
+ align:start position:0%
+stands for a spontaneous fission so one
+out of every seven Lords it you know
+
+ align:start position:0%
+out of every seven Lords it you know
+ 
+
+ align:start position:0%
+out of every seven Lords it you know
+seven out of every billion times it will
+
+ align:start position:0%
+seven out of every billion times it will
+ 
+
+ align:start position:0%
+seven out of every billion times it will
+just spontaneously fizz into two fission
+
+ align:start position:0%
+just spontaneously fizz into two fission
+ 
+
+ align:start position:0%
+just spontaneously fizz into two fission
+products and this is why if you put
+
+ align:start position:0%
+products and this is why if you put
+ 
+
+ align:start position:0%
+products and this is why if you put
+enough uranium-235 together in one place
+
+ align:start position:0%
+enough uranium-235 together in one place
+ 
+
+ align:start position:0%
+enough uranium-235 together in one place
+you can make a critical reactor in
+
+ align:start position:0%
+you can make a critical reactor in
+ 
+
+ align:start position:0%
+you can make a critical reactor in
+reality you don't tend to want to put
+
+ align:start position:0%
+reality you don't tend to want to put
+ 
+
+ align:start position:0%
+reality you don't tend to want to put
+enough u-235 together to just
+
+ align:start position:0%
+enough u-235 together to just
+ 
+
+ align:start position:0%
+enough u-235 together to just
+spontaneously go critical we use other
+
+ align:start position:0%
+spontaneously go critical we use other
+ 
+
+ align:start position:0%
+spontaneously go critical we use other
+isotopes as Kickstarter's for example
+
+ align:start position:0%
+isotopes as Kickstarter's for example
+ 
+
+ align:start position:0%
+isotopes as Kickstarter's for example
+californium I think it's two fifty-two
+
+ align:start position:0%
+californium I think it's two fifty-two
+ 
+
+ align:start position:0%
+californium I think it's two fifty-two
+let's take a quick look there we go
+
+ align:start position:0%
+let's take a quick look there we go
+ 
+
+ align:start position:0%
+let's take a quick look there we go
+californium 252 undergo spontaneous
+
+ align:start position:0%
+californium 252 undergo spontaneous
+ 
+
+ align:start position:0%
+californium 252 undergo spontaneous
+fission three percent of the time it's
+
+ align:start position:0%
+fission three percent of the time it's
+ 
+
+ align:start position:0%
+fission three percent of the time it's
+even heavier even more unstable so there
+
+ align:start position:0%
+even heavier even more unstable so there
+ 
+
+ align:start position:0%
+even heavier even more unstable so there
+is a reactor called high fer or the high
+
+ align:start position:0%
+is a reactor called high fer or the high
+ 
+
+ align:start position:0%
+is a reactor called high fer or the high
+flux isotope reactor at Oak Ridge
+
+ align:start position:0%
+flux isotope reactor at Oak Ridge
+ 
+
+ align:start position:0%
+flux isotope reactor at Oak Ridge
+National Lab one of its main outputs is
+
+ align:start position:0%
+National Lab one of its main outputs is
+ 
+
+ align:start position:0%
+National Lab one of its main outputs is
+californium Kickstarter's for reactors
+
+ align:start position:0%
+californium Kickstarter's for reactors
+ 
+
+ align:start position:0%
+californium Kickstarter's for reactors
+so to get things going you put a little
+
+ align:start position:0%
+so to get things going you put a little
+ 
+
+ align:start position:0%
+so to get things going you put a little
+bit of californium in as a gigantic
+
+ align:start position:0%
+bit of californium in as a gigantic
+ 
+
+ align:start position:0%
+bit of californium in as a gigantic
+neutron source and then you don't really
+
+ align:start position:0%
+neutron source and then you don't really
+ 
+
+ align:start position:0%
+neutron source and then you don't really
+need it anymore once it gets going so
+
+ align:start position:0%
+need it anymore once it gets going so
+ 
+
+ align:start position:0%
+need it anymore once it gets going so
+it's one of the safer ways of starting
+
+ align:start position:0%
+it's one of the safer ways of starting
+ 
+
+ align:start position:0%
+it's one of the safer ways of starting
+up a reactor is put in a crazy neutron
+
+ align:start position:0%
+up a reactor is put in a crazy neutron
+ 
+
+ align:start position:0%
+up a reactor is put in a crazy neutron
+source and then once it gets going take
+
+ align:start position:0%
+source and then once it gets going take
+ 
+
+ align:start position:0%
+source and then once it gets going take
+it out or leave it in and burn it I'm
+
+ align:start position:0%
+it out or leave it in and burn it I'm
+ 
+
+ align:start position:0%
+it out or leave it in and burn it I'm
+not actually sure which one they do yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is when we get to now is a good time
+
+ align:start position:0%
+it is when we get to now is a good time
+ 
+
+ align:start position:0%
+it is when we get to now is a good time
+to introduce the super-heavy element
+
+ align:start position:0%
+to introduce the super-heavy element
+ 
+
+ align:start position:0%
+to introduce the super-heavy element
+since you asked so a lot of these older
+
+ align:start position:0%
+since you asked so a lot of these older
+ 
+
+ align:start position:0%
+since you asked so a lot of these older
+elements were named after all actually
+
+ align:start position:0%
+elements were named after all actually
+ 
+
+ align:start position:0%
+elements were named after all actually
+this is kind of a hobby of mine
+
+ align:start position:0%
+this is kind of a hobby of mine
+ 
+
+ align:start position:0%
+this is kind of a hobby of mine
+so I don't know if you guys saw the
+
+ align:start position:0%
+so I don't know if you guys saw the
+ 
+
+ align:start position:0%
+so I don't know if you guys saw the
+periodic table outside
+
+ align:start position:0%
+periodic table outside
+ 
+
+ align:start position:0%
+periodic table outside
+I collect elements because if you're
+
+ align:start position:0%
+I collect elements because if you're
+ 
+
+ align:start position:0%
+I collect elements because if you're
+gonna collect something you might as
+
+ align:start position:0%
+gonna collect something you might as
+ 
+
+ align:start position:0%
+gonna collect something you might as
+well collect everything that everything
+
+ align:start position:0%
+well collect everything that everything
+ 
+
+ align:start position:0%
+well collect everything that everything
+else is made of it's the same reason I
+
+ align:start position:0%
+else is made of it's the same reason I
+ 
+
+ align:start position:0%
+else is made of it's the same reason I
+went into nuclear energy
+
+ align:start position:0%
+went into nuclear energy
+ 
+
+ align:start position:0%
+went into nuclear energy
+I started off course 6 or 6/1
+
+ align:start position:0%
+I started off course 6 or 6/1
+ 
+
+ align:start position:0%
+I started off course 6 or 6/1
+specifically electrical and I was like
+
+ align:start position:0%
+specifically electrical and I was like
+ 
+
+ align:start position:0%
+specifically electrical and I was like
+well I could be designing like the next
+
+ align:start position:0%
+well I could be designing like the next
+ 
+
+ align:start position:0%
+well I could be designing like the next
+screen for a cell phone or we could
+
+ align:start position:0%
+screen for a cell phone or we could
+ 
+
+ align:start position:0%
+screen for a cell phone or we could
+solve the energy problem which is the
+
+ align:start position:0%
+solve the energy problem which is the
+ 
+
+ align:start position:0%
+solve the energy problem which is the
+problem all others are based off of so
+
+ align:start position:0%
+problem all others are based off of so
+ 
+
+ align:start position:0%
+problem all others are based off of so
+my whole life theme has been go to the
+
+ align:start position:0%
+my whole life theme has been go to the
+ 
+
+ align:start position:0%
+my whole life theme has been go to the
+source that's why I came here in high
+
+ align:start position:0%
+source that's why I came here in high
+ 
+
+ align:start position:0%
+source that's why I came here in high
+school and never left that's why I
+
+ align:start position:0%
+school and never left that's why I
+ 
+
+ align:start position:0%
+school and never left that's why I
+declared course 22 that's why I collect
+
+ align:start position:0%
+declared course 22 that's why I collect
+ 
+
+ align:start position:0%
+declared course 22 that's why I collect
+elements and probably is the reason for
+
+ align:start position:0%
+elements and probably is the reason for
+ 
+
+ align:start position:0%
+elements and probably is the reason for
+many other things which only a
+
+ align:start position:0%
+many other things which only a
+ 
+
+ align:start position:0%
+many other things which only a
+psychiatrist could diagnose but let's
+
+ align:start position:0%
+psychiatrist could diagnose but let's
+ 
+
+ align:start position:0%
+psychiatrist could diagnose but let's
+look at some of the other elements for
+
+ align:start position:0%
+look at some of the other elements for
+ 
+
+ align:start position:0%
+look at some of the other elements for
+example yttrium I think it has an
+
+ align:start position:0%
+example yttrium I think it has an
+ 
+
+ align:start position:0%
+example yttrium I think it has an
+isotope 40 anyone know no it doesn't
+
+ align:start position:0%
+isotope 40 anyone know no it doesn't
+ 
+
+ align:start position:0%
+isotope 40 anyone know no it doesn't
+have a 40 what about a 50 60 hundred
+
+ align:start position:0%
+have a 40 what about a 50 60 hundred
+ 
+
+ align:start position:0%
+have a 40 what about a 50 60 hundred
+whatever at least it knew that why was
+
+ align:start position:0%
+whatever at least it knew that why was
+ 
+
+ align:start position:0%
+whatever at least it knew that why was
+you a trio anyone know where this is
+
+ align:start position:0%
+you a trio anyone know where this is
+ 
+
+ align:start position:0%
+you a trio anyone know where this is
+coming from 89 seems high oh my god
+
+ align:start position:0%
+coming from 89 seems high oh my god
+ 
+
+ align:start position:0%
+coming from 89 seems high oh my god
+you're right okay gotcha you work with
+
+ align:start position:0%
+you're right okay gotcha you work with
+ 
+
+ align:start position:0%
+you're right okay gotcha you work with
+it awesome
+
+ align:start position:0%
+it awesome
+ 
+
+ align:start position:0%
+it awesome
+anyone know what this is all about get
+
+ align:start position:0%
+anyone know what this is all about get
+ 
+
+ align:start position:0%
+anyone know what this is all about get
+trium there's a town called Iturbi in
+
+ align:start position:0%
+trium there's a town called Iturbi in
+ 
+
+ align:start position:0%
+trium there's a town called Iturbi in
+sweden where large deposits of yttrium
+
+ align:start position:0%
+sweden where large deposits of yttrium
+ 
+
+ align:start position:0%
+sweden where large deposits of yttrium
+and ytterbium or YB tend to be found or
+
+ align:start position:0%
+and ytterbium or YB tend to be found or
+ 
+
+ align:start position:0%
+and ytterbium or YB tend to be found or
+DB name for dubnium so let's say the
+
+ align:start position:0%
+DB name for dubnium so let's say the
+ 
+
+ align:start position:0%
+DB name for dubnium so let's say the
+really basic elements tend to come from
+
+ align:start position:0%
+really basic elements tend to come from
+ 
+
+ align:start position:0%
+really basic elements tend to come from
+Latin F F stands for iron which actually
+
+ align:start position:0%
+Latin F F stands for iron which actually
+ 
+
+ align:start position:0%
+Latin F F stands for iron which actually
+stands for theorem led is plumbum gold
+
+ align:start position:0%
+stands for theorem led is plumbum gold
+ 
+
+ align:start position:0%
+stands for theorem led is plumbum gold
+as Orem silver AG is argenteum I don't
+
+ align:start position:0%
+as Orem silver AG is argenteum I don't
+ 
+
+ align:start position:0%
+as Orem silver AG is argenteum I don't
+know if I'm saying that right
+
+ align:start position:0%
+know if I'm saying that right
+ 
+
+ align:start position:0%
+know if I'm saying that right
+I never took Latin and I've never heard
+
+ align:start position:0%
+I never took Latin and I've never heard
+ 
+
+ align:start position:0%
+I never took Latin and I've never heard
+it spoken of course and then a lot of
+
+ align:start position:0%
+it spoken of course and then a lot of
+ 
+
+ align:start position:0%
+it spoken of course and then a lot of
+the heavier and heavier elements as we
+
+ align:start position:0%
+the heavier and heavier elements as we
+ 
+
+ align:start position:0%
+the heavier and heavier elements as we
+go our being named for more and more
+
+ align:start position:0%
+go our being named for more and more
+ 
+
+ align:start position:0%
+go our being named for more and more
+famous scientists or places where they
+
+ align:start position:0%
+famous scientists or places where they
+ 
+
+ align:start position:0%
+famous scientists or places where they
+tend to be made like dB I'm gonna guess
+
+ align:start position:0%
+tend to be made like dB I'm gonna guess
+ 
+
+ align:start position:0%
+tend to be made like dB I'm gonna guess
+264 a mass there oh nice for a doob nah
+
+ align:start position:0%
+264 a mass there oh nice for a doob nah
+ 
+
+ align:start position:0%
+264 a mass there oh nice for a doob nah
+in Russia that has got one of the few
+
+ align:start position:0%
+in Russia that has got one of the few
+ 
+
+ align:start position:0%
+in Russia that has got one of the few
+gigantic
+
+ align:start position:0%
+gigantic
+ 
+
+ align:start position:0%
+gigantic
+for heavy element colliders where
+
+ align:start position:0%
+for heavy element colliders where
+ 
+
+ align:start position:0%
+for heavy element colliders where
+they're constantly synthesizing and
+
+ align:start position:0%
+they're constantly synthesizing and
+ 
+
+ align:start position:0%
+they're constantly synthesizing and
+characterizing these super-heavy
+
+ align:start position:0%
+characterizing these super-heavy
+ 
+
+ align:start position:0%
+characterizing these super-heavy
+elements so finally they said you know
+
+ align:start position:0%
+elements so finally they said you know
+ 
+
+ align:start position:0%
+elements so finally they said you know
+what they've made enough of these in
+
+ align:start position:0%
+what they've made enough of these in
+ 
+
+ align:start position:0%
+what they've made enough of these in
+Dubna let's name one of the elements
+
+ align:start position:0%
+Dubna let's name one of the elements
+ 
+
+ align:start position:0%
+Dubna let's name one of the elements
+after them or SG seaborgium for glenn
+
+ align:start position:0%
+after them or SG seaborgium for glenn
+ 
+
+ align:start position:0%
+after them or SG seaborgium for glenn
+seaborg or n o nobelium for Alfred Nobel
+
+ align:start position:0%
+seaborg or n o nobelium for Alfred Nobel
+ 
+
+ align:start position:0%
+seaborg or n o nobelium for Alfred Nobel
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah do they intersect I've never seen a
+
+ align:start position:0%
+ah do they intersect I've never seen a
+ 
+
+ align:start position:0%
+ah do they intersect I've never seen a
+case where they intersect that would
+
+ align:start position:0%
+case where they intersect that would
+ 
+
+ align:start position:0%
+case where they intersect that would
+make for a crazy situation indeed
+
+ align:start position:0%
+make for a crazy situation indeed
+ 
+
+ align:start position:0%
+make for a crazy situation indeed
+however part of what the homework
+
+ align:start position:0%
+however part of what the homework
+ 
+
+ align:start position:0%
+however part of what the homework
+assignments about is to derive an
+
+ align:start position:0%
+assignments about is to derive an
+ 
+
+ align:start position:0%
+assignments about is to derive an
+analytical form for a mass parabola and
+
+ align:start position:0%
+analytical form for a mass parabola and
+ 
+
+ align:start position:0%
+analytical form for a mass parabola and
+then check the data to see how well it
+
+ align:start position:0%
+then check the data to see how well it
+ 
+
+ align:start position:0%
+then check the data to see how well it
+works so for any cases where you have an
+
+ align:start position:0%
+works so for any cases where you have an
+ 
+
+ align:start position:0%
+works so for any cases where you have an
+even mass number and you have either odd
+
+ align:start position:0%
+even mass number and you have either odd
+ 
+
+ align:start position:0%
+even mass number and you have either odd
+odd or even even nuclei you can check
+
+ align:start position:0%
+odd or even even nuclei you can check
+ 
+
+ align:start position:0%
+odd or even even nuclei you can check
+those equations analytically to see if
+
+ align:start position:0%
+those equations analytically to see if
+ 
+
+ align:start position:0%
+those equations analytically to see if
+they'll intersect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the top parabola for potassium-40
+
+ align:start position:0%
+so the top parabola for potassium-40
+ 
+
+ align:start position:0%
+so the top parabola for potassium-40
+let's take a quick look at how many
+
+ align:start position:0%
+let's take a quick look at how many
+ 
+
+ align:start position:0%
+let's take a quick look at how many
+protons and neutrons it has potassium
+
+ align:start position:0%
+protons and neutrons it has potassium
+ 
+
+ align:start position:0%
+protons and neutrons it has potassium
+has a proton number of 19 which means it
+
+ align:start position:0%
+has a proton number of 19 which means it
+ 
+
+ align:start position:0%
+has a proton number of 19 which means it
+has a neutron number of 21 so the top
+
+ align:start position:0%
+has a neutron number of 21 so the top
+ 
+
+ align:start position:0%
+has a neutron number of 21 so the top
+parabola is odd n and odd Z where the
+
+ align:start position:0%
+parabola is odd n and odd Z where the
+ 
+
+ align:start position:0%
+parabola is odd n and odd Z where the
+bottom one is even N and even C whereas
+
+ align:start position:0%
+bottom one is even N and even C whereas
+ 
+
+ align:start position:0%
+bottom one is even N and even C whereas
+for odd mass number nuclei it has to be
+
+ align:start position:0%
+for odd mass number nuclei it has to be
+ 
+
+ align:start position:0%
+for odd mass number nuclei it has to be
+either odd even or even odd else it
+
+ align:start position:0%
+either odd even or even odd else it
+ 
+
+ align:start position:0%
+either odd even or even odd else it
+would be even which is a funny sentence
+
+ align:start position:0%
+would be even which is a funny sentence
+ 
+
+ align:start position:0%
+would be even which is a funny sentence
+when you say it all out loud yeah so
+
+ align:start position:0%
+when you say it all out loud yeah so
+ 
+
+ align:start position:0%
+when you say it all out loud yeah so
+that's the idea here is that notice that
+
+ align:start position:0%
+that's the idea here is that notice that
+ 
+
+ align:start position:0%
+that's the idea here is that notice that
+the even even parabola tends to be
+
+ align:start position:0%
+the even even parabola tends to be
+ 
+
+ align:start position:0%
+the even even parabola tends to be
+further down all those nuclear magic
+
+ align:start position:0%
+further down all those nuclear magic
+ 
+
+ align:start position:0%
+further down all those nuclear magic
+numbers - 8 20 28 I'm not going to quote
+
+ align:start position:0%
+numbers - 8 20 28 I'm not going to quote
+ 
+
+ align:start position:0%
+numbers - 8 20 28 I'm not going to quote
+the rest those little ones I know all
+
+ align:start position:0%
+the rest those little ones I know all
+ 
+
+ align:start position:0%
+the rest those little ones I know all
+even numbers so any other questions on
+
+ align:start position:0%
+even numbers so any other questions on
+ 
+
+ align:start position:0%
+even numbers so any other questions on
+these math problems before we launch
+
+ align:start position:0%
+these math problems before we launch
+ 
+
+ align:start position:0%
+these math problems before we launch
+into super heavy elements yep uh-huh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analytically or experimentally which
+
+ align:start position:0%
+analytically or experimentally which
+ 
+
+ align:start position:0%
+analytically or experimentally which
+question so analytically analytically
+
+ align:start position:0%
+question so analytically analytically
+ 
+
+ align:start position:0%
+question so analytically analytically
+there should be some isotope of well not
+
+ align:start position:0%
+there should be some isotope of well not
+ 
+
+ align:start position:0%
+there should be some isotope of well not
+potassium that wouldn't be allowed so in
+
+ align:start position:0%
+potassium that wouldn't be allowed so in
+ 
+
+ align:start position:0%
+potassium that wouldn't be allowed so in
+this case the the stable element
+
+ align:start position:0%
+this case the the stable element
+ 
+
+ align:start position:0%
+this case the the stable element
+positions have got to kind of switch off
+
+ align:start position:0%
+positions have got to kind of switch off
+ 
+
+ align:start position:0%
+positions have got to kind of switch off
+shouldn't they so if that's potassium 40
+
+ align:start position:0%
+shouldn't they so if that's potassium 40
+ 
+
+ align:start position:0%
+shouldn't they so if that's potassium 40
+that would still have to be potassium
+
+ align:start position:0%
+that would still have to be potassium
+ 
+
+ align:start position:0%
+that would still have to be potassium
+you don't really have another choice
+
+ align:start position:0%
+you don't really have another choice
+ 
+
+ align:start position:0%
+you don't really have another choice
+there isn't really a position there is
+
+ align:start position:0%
+there isn't really a position there is
+ 
+
+ align:start position:0%
+there isn't really a position there is
+there analytically that's the
+
+ align:start position:0%
+there analytically that's the
+ 
+
+ align:start position:0%
+there analytically that's the
+interesting thing is that you can either
+
+ align:start position:0%
+interesting thing is that you can either
+ 
+
+ align:start position:0%
+interesting thing is that you can either
+be odd odd or even even for an even mass
+
+ align:start position:0%
+be odd odd or even even for an even mass
+ 
+
+ align:start position:0%
+be odd odd or even even for an even mass
+number but you can't just take off one
+
+ align:start position:0%
+number but you can't just take off one
+ 
+
+ align:start position:0%
+number but you can't just take off one
+Neutron from potassium-40 and then
+
+ align:start position:0%
+Neutron from potassium-40 and then
+ 
+
+ align:start position:0%
+Neutron from potassium-40 and then
+you've got potassium 39 then you're on a
+
+ align:start position:0%
+you've got potassium 39 then you're on a
+ 
+
+ align:start position:0%
+you've got potassium 39 then you're on a
+different mass number or if you exchange
+
+ align:start position:0%
+different mass number or if you exchange
+ 
+
+ align:start position:0%
+different mass number or if you exchange
+a proton and a neutron which you pretty
+
+ align:start position:0%
+a proton and a neutron which you pretty
+ 
+
+ align:start position:0%
+a proton and a neutron which you pretty
+much do in either of these directions
+
+ align:start position:0%
+much do in either of these directions
+ 
+
+ align:start position:0%
+much do in either of these directions
+there's no way to get straight down here
+
+ align:start position:0%
+there's no way to get straight down here
+ 
+
+ align:start position:0%
+there's no way to get straight down here
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fraud what proof sorry yeah let's go
+
+ align:start position:0%
+fraud what proof sorry yeah let's go
+ 
+
+ align:start position:0%
+fraud what proof sorry yeah let's go
+back to that slide just to make sure you
+
+ align:start position:0%
+back to that slide just to make sure you
+ 
+
+ align:start position:0%
+back to that slide just to make sure you
+mean the pairing term in the semi
+
+ align:start position:0%
+mean the pairing term in the semi
+ 
+
+ align:start position:0%
+mean the pairing term in the semi
+empirical mass formula yeah yeah
+
+ align:start position:0%
+empirical mass formula yeah yeah
+ 
+
+ align:start position:0%
+empirical mass formula yeah yeah
+so for aw dog nuclei and D Delta is
+
+ align:start position:0%
+so for aw dog nuclei and D Delta is
+ 
+
+ align:start position:0%
+so for aw dog nuclei and D Delta is
+negative which means lower binding
+
+ align:start position:0%
+negative which means lower binding
+ 
+
+ align:start position:0%
+negative which means lower binding
+energy which means higher mass and
+
+ align:start position:0%
+energy which means higher mass and
+ 
+
+ align:start position:0%
+energy which means higher mass and
+that's why we see it bump up on the mass
+
+ align:start position:0%
+that's why we see it bump up on the mass
+ 
+
+ align:start position:0%
+that's why we see it bump up on the mass
+right here yep and you have a second
+
+ align:start position:0%
+right here yep and you have a second
+ 
+
+ align:start position:0%
+right here yep and you have a second
+part of the question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah we can actually relate so we can
+
+ align:start position:0%
+ah we can actually relate so we can
+ 
+
+ align:start position:0%
+ah we can actually relate so we can
+relate the binding energy to the mass
+
+ align:start position:0%
+relate the binding energy to the mass
+ 
+
+ align:start position:0%
+relate the binding energy to the mass
+and the mass parabola analytically
+
+ align:start position:0%
+and the mass parabola analytically
+ 
+
+ align:start position:0%
+and the mass parabola analytically
+because the binding energy is equal to Z
+
+ align:start position:0%
+because the binding energy is equal to Z
+ 
+
+ align:start position:0%
+because the binding energy is equal to Z
+times protons plus n times mass of
+
+ align:start position:0%
+times protons plus n times mass of
+ 
+
+ align:start position:0%
+times protons plus n times mass of
+neutron minus the actual mass of that
+
+ align:start position:0%
+neutron minus the actual mass of that
+ 
+
+ align:start position:0%
+neutron minus the actual mass of that
+same nucleus a comma Z so they're
+
+ align:start position:0%
+same nucleus a comma Z so they're
+ 
+
+ align:start position:0%
+same nucleus a comma Z so they're
+actually directly related just
+
+ align:start position:0%
+actually directly related just
+ 
+
+ align:start position:0%
+actually directly related just
+negatively so something with a higher
+
+ align:start position:0%
+negatively so something with a higher
+ 
+
+ align:start position:0%
+negatively so something with a higher
+mass is going to have a low binding
+
+ align:start position:0%
+mass is going to have a low binding
+ 
+
+ align:start position:0%
+mass is going to have a low binding
+energy which means it's less bound and
+
+ align:start position:0%
+energy which means it's less bound and
+ 
+
+ align:start position:0%
+energy which means it's less bound and
+less stable and indeed the further up
+
+ align:start position:0%
+less stable and indeed the further up
+ 
+
+ align:start position:0%
+less stable and indeed the further up
+the mass scale we go the higher those
+
+ align:start position:0%
+the mass scale we go the higher those
+ 
+
+ align:start position:0%
+the mass scale we go the higher those
+beta or electron capture or positron
+
+ align:start position:0%
+beta or electron capture or positron
+ 
+
+ align:start position:0%
+beta or electron capture or positron
+energies are and there's another thing
+
+ align:start position:0%
+energies are and there's another thing
+ 
+
+ align:start position:0%
+energies are and there's another thing
+you can check to which is the half-life
+
+ align:start position:0%
+you can check to which is the half-life
+ 
+
+ align:start position:0%
+you can check to which is the half-life
+half-life is what we'll be talking about
+
+ align:start position:0%
+half-life is what we'll be talking about
+ 
+
+ align:start position:0%
+half-life is what we'll be talking about
+on Tuesday it's how long before an
+
+ align:start position:0%
+on Tuesday it's how long before an
+ 
+
+ align:start position:0%
+on Tuesday it's how long before an
+average amount of a substance has
+
+ align:start position:0%
+average amount of a substance has
+ 
+
+ align:start position:0%
+average amount of a substance has
+undergone radioactive decay so let's
+
+ align:start position:0%
+undergone radioactive decay so let's
+ 
+
+ align:start position:0%
+undergone radioactive decay so let's
+look at some of these isotopes and start
+
+ align:start position:0%
+look at some of these isotopes and start
+ 
+
+ align:start position:0%
+look at some of these isotopes and start
+looking at half-life trends as another
+
+ align:start position:0%
+looking at half-life trends as another
+ 
+
+ align:start position:0%
+looking at half-life trends as another
+measure of stability so potassium-40 has
+
+ align:start position:0%
+measure of stability so potassium-40 has
+ 
+
+ align:start position:0%
+measure of stability so potassium-40 has
+an exceptionally long half-life so it's
+
+ align:start position:0%
+an exceptionally long half-life so it's
+ 
+
+ align:start position:0%
+an exceptionally long half-life so it's
+relatively stable
+
+ align:start position:0%
+relatively stable
+ 
+
+ align:start position:0%
+relatively stable
+let's take a look not at either the
+
+ align:start position:0%
+let's take a look not at either the
+ 
+
+ align:start position:0%
+let's take a look not at either the
+stable isotopes but let's go up the mass
+
+ align:start position:0%
+stable isotopes but let's go up the mass
+ 
+
+ align:start position:0%
+stable isotopes but let's go up the mass
+parabola chain in one direction calcium
+
+ align:start position:0%
+parabola chain in one direction calcium
+ 
+
+ align:start position:0%
+parabola chain in one direction calcium
+for T scandium-46 can diem for T
+
+ align:start position:0%
+for T scandium-46 can diem for T
+ 
+
+ align:start position:0%
+for T scandium-46 can diem for T
+scandium 45 less than a second and it's
+
+ align:start position:0%
+scandium 45 less than a second and it's
+ 
+
+ align:start position:0%
+scandium 45 less than a second and it's
+got quite a high decay energy by
+
+ align:start position:0%
+got quite a high decay energy by
+ 
+
+ align:start position:0%
+got quite a high decay energy by
+whatever method you want to use let's go
+
+ align:start position:0%
+whatever method you want to use let's go
+ 
+
+ align:start position:0%
+whatever method you want to use let's go
+up to titanium for T anyone want to
+
+ align:start position:0%
+up to titanium for T anyone want to
+ 
+
+ align:start position:0%
+up to titanium for T anyone want to
+guess is eating the half-life is gonna
+
+ align:start position:0%
+guess is eating the half-life is gonna
+ 
+
+ align:start position:0%
+guess is eating the half-life is gonna
+go up or down let's see if the half-life
+
+ align:start position:0%
+go up or down let's see if the half-life
+ 
+
+ align:start position:0%
+go up or down let's see if the half-life
+goes down we know the decay energy goes
+
+ align:start position:0%
+goes down we know the decay energy goes
+ 
+
+ align:start position:0%
+goes down we know the decay energy goes
+up indeed half-life goes down from 182
+
+ align:start position:0%
+up indeed half-life goes down from 182
+ 
+
+ align:start position:0%
+up indeed half-life goes down from 182
+milliseconds to 50 milliseconds and
+
+ align:start position:0%
+milliseconds to 50 milliseconds and
+ 
+
+ align:start position:0%
+milliseconds to 50 milliseconds and
+let's say titanium forty could have come
+
+ align:start position:0%
+let's say titanium forty could have come
+ 
+
+ align:start position:0%
+let's say titanium forty could have come
+from Wow two proton decay from cr.42
+
+ align:start position:0%
+from Wow two proton decay from cr.42
+ 
+
+ align:start position:0%
+from Wow two proton decay from cr.42
+with a half-life of 350 nano seconds so
+
+ align:start position:0%
+with a half-life of 350 nano seconds so
+ 
+
+ align:start position:0%
+with a half-life of 350 nano seconds so
+as we go up the mass ladder and down the
+
+ align:start position:0%
+as we go up the mass ladder and down the
+ 
+
+ align:start position:0%
+as we go up the mass ladder and down the
+stability ladder the half-life decreases
+
+ align:start position:0%
+stability ladder the half-life decreases
+ 
+
+ align:start position:0%
+stability ladder the half-life decreases
+which kind of follows intuitively
+
+ align:start position:0%
+which kind of follows intuitively
+ 
+
+ align:start position:0%
+which kind of follows intuitively
+something that's exceptional
+
+ align:start position:0%
+something that's exceptional
+ 
+
+ align:start position:0%
+something that's exceptional
+Stables should have a half-life of
+
+ align:start position:0%
+Stables should have a half-life of
+ 
+
+ align:start position:0%
+Stables should have a half-life of
+infinity and something that's
+
+ align:start position:0%
+infinity and something that's
+ 
+
+ align:start position:0%
+infinity and something that's
+exceptionally unstable should just blow
+
+ align:start position:0%
+exceptionally unstable should just blow
+ 
+
+ align:start position:0%
+exceptionally unstable should just blow
+apart instantly like remember the first
+
+ align:start position:0%
+apart instantly like remember the first
+ 
+
+ align:start position:0%
+apart instantly like remember the first
+week of class we talked about helium for
+
+ align:start position:0%
+week of class we talked about helium for
+ 
+
+ align:start position:0%
+week of class we talked about helium for
+grabbing a neutron becoming helium 5 and
+
+ align:start position:0%
+grabbing a neutron becoming helium 5 and
+ 
+
+ align:start position:0%
+grabbing a neutron becoming helium 5 and
+instantaneously going back to helium 4
+
+ align:start position:0%
+instantaneously going back to helium 4
+ 
+
+ align:start position:0%
+instantaneously going back to helium 4
+if you look at helium 5 it's half-life
+
+ align:start position:0%
+if you look at helium 5 it's half-life
+ 
+
+ align:start position:0%
+if you look at helium 5 it's half-life
+is measured in MeV or 7 times 10 to the
+
+ align:start position:0%
+is measured in MeV or 7 times 10 to the
+ 
+
+ align:start position:0%
+is measured in MeV or 7 times 10 to the
+minus seventh femtoseconds so if helium
+
+ align:start position:0%
+minus seventh femtoseconds so if helium
+ 
+
+ align:start position:0%
+minus seventh femtoseconds so if helium
+4 absorbs a neutron it simply doesn't
+
+ align:start position:0%
+4 absorbs a neutron it simply doesn't
+ 
+
+ align:start position:0%
+4 absorbs a neutron it simply doesn't
+want it and gets rid of it in ten to the
+
+ align:start position:0%
+want it and gets rid of it in ten to the
+ 
+
+ align:start position:0%
+want it and gets rid of it in ten to the
+minus seven femtoseconds which would
+
+ align:start position:0%
+minus seven femtoseconds which would
+ 
+
+ align:start position:0%
+minus seven femtoseconds which would
+tell us that it's exceptionally unstable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I hope that's a long-winded answer to
+
+ align:start position:0%
+so I hope that's a long-winded answer to
+ 
+
+ align:start position:0%
+so I hope that's a long-winded answer to
+that question but what does it mean to
+
+ align:start position:0%
+that question but what does it mean to
+ 
+
+ align:start position:0%
+that question but what does it mean to
+go to be going up in the mass levels any
+
+ align:start position:0%
+go to be going up in the mass levels any
+ 
+
+ align:start position:0%
+go to be going up in the mass levels any
+other questions on mass parabolas or the
+
+ align:start position:0%
+other questions on mass parabolas or the
+ 
+
+ align:start position:0%
+other questions on mass parabolas or the
+liquid drop model or stability in
+
+ align:start position:0%
+liquid drop model or stability in
+ 
+
+ align:start position:0%
+liquid drop model or stability in
+general yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you're changing one neutron to a
+
+ align:start position:0%
+so if you're changing one neutron to a
+ 
+
+ align:start position:0%
+so if you're changing one neutron to a
+proton in each case you're switching
+
+ align:start position:0%
+proton in each case you're switching
+ 
+
+ align:start position:0%
+proton in each case you're switching
+back and forth from the odd odd to the
+
+ align:start position:0%
+back and forth from the odd odd to the
+ 
+
+ align:start position:0%
+back and forth from the odd odd to the
+even even mass parabolas so if I were to
+
+ align:start position:0%
+even even mass parabolas so if I were to
+ 
+
+ align:start position:0%
+even even mass parabolas so if I were to
+redraw these dots more to scale this
+
+ align:start position:0%
+redraw these dots more to scale this
+ 
+
+ align:start position:0%
+redraw these dots more to scale this
+would have to be on the odd odd and oh
+
+ align:start position:0%
+would have to be on the odd odd and oh
+ 
+
+ align:start position:0%
+would have to be on the odd odd and oh
+let me draw them a little better yep
+
+ align:start position:0%
+let me draw them a little better yep
+ 
+
+ align:start position:0%
+let me draw them a little better yep
+that's on the odd odd and that's on the
+
+ align:start position:0%
+that's on the odd odd and that's on the
+ 
+
+ align:start position:0%
+that's on the odd odd and that's on the
+even even yeah so excuse my poor drawing
+
+ align:start position:0%
+even even yeah so excuse my poor drawing
+ 
+
+ align:start position:0%
+even even yeah so excuse my poor drawing
+skills but if you're switching one
+
+ align:start position:0%
+skills but if you're switching one
+ 
+
+ align:start position:0%
+skills but if you're switching one
+proton to a neutron or vice versa by
+
+ align:start position:0%
+proton to a neutron or vice versa by
+ 
+
+ align:start position:0%
+proton to a neutron or vice versa by
+definition you're jumping back and forth
+
+ align:start position:0%
+definition you're jumping back and forth
+ 
+
+ align:start position:0%
+definition you're jumping back and forth
+between these parabolas that's a good
+
+ align:start position:0%
+between these parabolas that's a good
+ 
+
+ align:start position:0%
+between these parabolas that's a good
+question for clarification you had a
+
+ align:start position:0%
+question for clarification you had a
+ 
+
+ align:start position:0%
+question for clarification you had a
+question too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the semi-empirical I'm sorry the semi
+
+ align:start position:0%
+the semi-empirical I'm sorry the semi
+ 
+
+ align:start position:0%
+the semi-empirical I'm sorry the semi
+empirical mass formula is a good way to
+
+ align:start position:0%
+empirical mass formula is a good way to
+ 
+
+ align:start position:0%
+empirical mass formula is a good way to
+get an analytical guess at most of them
+
+ align:start position:0%
+get an analytical guess at most of them
+ 
+
+ align:start position:0%
+get an analytical guess at most of them
+if you want an exact answer always use
+
+ align:start position:0%
+if you want an exact answer always use
+ 
+
+ align:start position:0%
+if you want an exact answer always use
+the actual binding energy I would not
+
+ align:start position:0%
+the actual binding energy I would not
+ 
+
+ align:start position:0%
+the actual binding energy I would not
+say it's used much now except well
+
+ align:start position:0%
+say it's used much now except well
+ 
+
+ align:start position:0%
+say it's used much now except well
+that's gonna be one of your homework
+
+ align:start position:0%
+that's gonna be one of your homework
+ 
+
+ align:start position:0%
+that's gonna be one of your homework
+questions is this formula predicts that
+
+ align:start position:0%
+questions is this formula predicts that
+ 
+
+ align:start position:0%
+questions is this formula predicts that
+as you get heavier and heavier and
+
+ align:start position:0%
+as you get heavier and heavier and
+ 
+
+ align:start position:0%
+as you get heavier and heavier and
+heavier nuclei should just continuously
+
+ align:start position:0%
+heavier nuclei should just continuously
+ 
+
+ align:start position:0%
+heavier nuclei should just continuously
+get less stable and that was as of when
+
+ align:start position:0%
+get less stable and that was as of when
+ 
+
+ align:start position:0%
+get less stable and that was as of when
+this was derived let's say decades ago
+
+ align:start position:0%
+this was derived let's say decades ago
+ 
+
+ align:start position:0%
+this was derived let's say decades ago
+we now know something different is
+
+ align:start position:0%
+we now know something different is
+ 
+
+ align:start position:0%
+we now know something different is
+happening so if you look at the table of
+
+ align:start position:0%
+happening so if you look at the table of
+ 
+
+ align:start position:0%
+happening so if you look at the table of
+nuclides you can sort of see some swells
+
+ align:start position:0%
+nuclides you can sort of see some swells
+ 
+
+ align:start position:0%
+nuclides you can sort of see some swells
+in the number of black pixels until it
+
+ align:start position:0%
+in the number of black pixels until it
+ 
+
+ align:start position:0%
+in the number of black pixels until it
+cuts off and this region actually where
+
+ align:start position:0%
+cuts off and this region actually where
+ 
+
+ align:start position:0%
+cuts off and this region actually where
+we think super-heavy elements happen I
+
+ align:start position:0%
+we think super-heavy elements happen I
+ 
+
+ align:start position:0%
+we think super-heavy elements happen I
+want to jump to the actual table of
+
+ align:start position:0%
+want to jump to the actual table of
+ 
+
+ align:start position:0%
+want to jump to the actual table of
+nuclides which I'll say is our snapshot
+
+ align:start position:0%
+nuclides which I'll say is our snapshot
+ 
+
+ align:start position:0%
+nuclides which I'll say is our snapshot
+of knowledge today and go all the way to
+
+ align:start position:0%
+of knowledge today and go all the way to
+ 
+
+ align:start position:0%
+of knowledge today and go all the way to
+the top and our knowledge kind of cuts
+
+ align:start position:0%
+the top and our knowledge kind of cuts
+ 
+
+ align:start position:0%
+the top and our knowledge kind of cuts
+off at these elements which are for now
+
+ align:start position:0%
+off at these elements which are for now
+ 
+
+ align:start position:0%
+off at these elements which are for now
+temporarily named in a very uncreated
+
+ align:start position:0%
+temporarily named in a very uncreated
+ 
+
+ align:start position:0%
+temporarily named in a very uncreated
+way we don't even know anything about
+
+ align:start position:0%
+way we don't even know anything about
+ 
+
+ align:start position:0%
+way we don't even know anything about
+them uun probably going to have a proton
+
+ align:start position:0%
+them uun probably going to have a proton
+ 
+
+ align:start position:0%
+them uun probably going to have a proton
+number of what 110 I don't know what the
+
+ align:start position:0%
+number of what 110 I don't know what the
+ 
+
+ align:start position:0%
+number of what 110 I don't know what the
+prefixes are but you you you would be on
+
+ align:start position:0%
+prefixes are but you you you would be on
+ 
+
+ align:start position:0%
+prefixes are but you you you would be on
+one one one probably has 111 protons
+
+ align:start position:0%
+one one one probably has 111 protons
+ 
+
+ align:start position:0%
+one one one probably has 111 protons
+beyond here off the screen or probably
+
+ align:start position:0%
+beyond here off the screen or probably
+ 
+
+ align:start position:0%
+beyond here off the screen or probably
+up into the next room it's predicted
+
+ align:start position:0%
+up into the next room it's predicted
+ 
+
+ align:start position:0%
+up into the next room it's predicted
+that once you approach the next magic
+
+ align:start position:0%
+that once you approach the next magic
+ 
+
+ align:start position:0%
+that once you approach the next magic
+number in nuclei there should be an
+
+ align:start position:0%
+number in nuclei there should be an
+ 
+
+ align:start position:0%
+number in nuclei there should be an
+island of stability where and it may not
+
+ align:start position:0%
+island of stability where and it may not
+ 
+
+ align:start position:0%
+island of stability where and it may not
+necessarily be totally stable but the
+
+ align:start position:0%
+necessarily be totally stable but the
+ 
+
+ align:start position:0%
+necessarily be totally stable but the
+half-life should go up again and we
+
+ align:start position:0%
+half-life should go up again and we
+ 
+
+ align:start position:0%
+half-life should go up again and we
+should be able to synthesize super-heavy
+
+ align:start position:0%
+should be able to synthesize super-heavy
+ 
+
+ align:start position:0%
+should be able to synthesize super-heavy
+matter and if you actually graph Neutron
+
+ align:start position:0%
+matter and if you actually graph Neutron
+ 
+
+ align:start position:0%
+matter and if you actually graph Neutron
+number versus half-life so notice how we
+
+ align:start position:0%
+number versus half-life so notice how we
+ 
+
+ align:start position:0%
+number versus half-life so notice how we
+were looking at half-life as a measure
+
+ align:start position:0%
+were looking at half-life as a measure
+ 
+
+ align:start position:0%
+were looking at half-life as a measure
+of stability it starts to go up then
+
+ align:start position:0%
+of stability it starts to go up then
+ 
+
+ align:start position:0%
+of stability it starts to go up then
+comes down and then to the extent of our
+
+ align:start position:0%
+comes down and then to the extent of our
+ 
+
+ align:start position:0%
+comes down and then to the extent of our
+knowledge it is going back up again to
+
+ align:start position:0%
+knowledge it is going back up again to
+ 
+
+ align:start position:0%
+knowledge it is going back up again to
+the next predicted magic number so what
+
+ align:start position:0%
+the next predicted magic number so what
+ 
+
+ align:start position:0%
+the next predicted magic number so what
+we think should be happening is
+
+ align:start position:0%
+we think should be happening is
+ 
+
+ align:start position:0%
+we think should be happening is
+half-life should be continuously going
+
+ align:start position:0%
+half-life should be continuously going
+ 
+
+ align:start position:0%
+half-life should be continuously going
+up and yeah you had a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well whatever you want it's gonna be it
+
+ align:start position:0%
+well whatever you want it's gonna be it
+ 
+
+ align:start position:0%
+well whatever you want it's gonna be it
+should be dense as all heck because
+
+ align:start position:0%
+should be dense as all heck because
+ 
+
+ align:start position:0%
+should be dense as all heck because
+nuclear matters quite a bit denser than
+
+ align:start position:0%
+nuclear matters quite a bit denser than
+ 
+
+ align:start position:0%
+nuclear matters quite a bit denser than
+ordinary matter and quite a bit as quite
+
+ align:start position:0%
+ordinary matter and quite a bit as quite
+ 
+
+ align:start position:0%
+ordinary matter and quite a bit as quite
+an understatement
+
+ align:start position:0%
+an understatement
+ 
+
+ align:start position:0%
+an understatement
+so what would you do with super heavy
+
+ align:start position:0%
+so what would you do with super heavy
+ 
+
+ align:start position:0%
+so what would you do with super heavy
+matter a lot of it could be used to
+
+ align:start position:0%
+matter a lot of it could be used to
+ 
+
+ align:start position:0%
+matter a lot of it could be used to
+probe the structure of matter there's a
+
+ align:start position:0%
+probe the structure of matter there's a
+ 
+
+ align:start position:0%
+probe the structure of matter there's a
+lot about how the nucleus is constructed
+
+ align:start position:0%
+lot about how the nucleus is constructed
+ 
+
+ align:start position:0%
+lot about how the nucleus is constructed
+that we don't know and beyond the scope
+
+ align:start position:0%
+that we don't know and beyond the scope
+ 
+
+ align:start position:0%
+that we don't know and beyond the scope
+of this course would also be an
+
+ align:start position:0%
+of this course would also be an
+ 
+
+ align:start position:0%
+of this course would also be an
+understatement
+
+ align:start position:0%
+understatement
+ 
+
+ align:start position:0%
+understatement
+there's folks that are making their
+
+ align:start position:0%
+there's folks that are making their
+ 
+
+ align:start position:0%
+there's folks that are making their
+careers now and figuring out what are
+
+ align:start position:0%
+careers now and figuring out what are
+ 
+
+ align:start position:0%
+careers now and figuring out what are
+the forces between nucleons why do
+
+ align:start position:0%
+the forces between nucleons why do
+ 
+
+ align:start position:0%
+the forces between nucleons why do
+things spontaneously fizz at the rates
+
+ align:start position:0%
+things spontaneously fizz at the rates
+ 
+
+ align:start position:0%
+things spontaneously fizz at the rates
+that they do you'll even hit a little
+
+ align:start position:0%
+that they do you'll even hit a little
+ 
+
+ align:start position:0%
+that they do you'll even hit a little
+bit of this in 22:02
+
+ align:start position:0%
+bit of this in 22:02
+ 
+
+ align:start position:0%
+bit of this in 22:02
+when you can calculate the rough
+
+ align:start position:0%
+when you can calculate the rough
+ 
+
+ align:start position:0%
+when you can calculate the rough
+half-life for alpha decay using quantum
+
+ align:start position:0%
+half-life for alpha decay using quantum
+ 
+
+ align:start position:0%
+half-life for alpha decay using quantum
+tunneling through the potential barrier
+
+ align:start position:0%
+tunneling through the potential barrier
+ 
+
+ align:start position:0%
+tunneling through the potential barrier
+in a nucleus and so the more nuclei we
+
+ align:start position:0%
+in a nucleus and so the more nuclei we
+ 
+
+ align:start position:0%
+in a nucleus and so the more nuclei we
+have to mess around with the more data
+
+ align:start position:0%
+have to mess around with the more data
+ 
+
+ align:start position:0%
+have to mess around with the more data
+and real examples we have to study but
+
+ align:start position:0%
+and real examples we have to study but
+ 
+
+ align:start position:0%
+and real examples we have to study but
+practical applications well I could
+
+ align:start position:0%
+practical applications well I could
+ 
+
+ align:start position:0%
+practical applications well I could
+imagine we might find something denser
+
+ align:start position:0%
+imagine we might find something denser
+ 
+
+ align:start position:0%
+imagine we might find something denser
+than osmium osmium right now is a
+
+ align:start position:0%
+than osmium osmium right now is a
+ 
+
+ align:start position:0%
+than osmium osmium right now is a
+density of about 22 grams per cubic
+
+ align:start position:0%
+density of about 22 grams per cubic
+ 
+
+ align:start position:0%
+density of about 22 grams per cubic
+centimeter this stuff zirconium
+
+ align:start position:0%
+centimeter this stuff zirconium
+ 
+
+ align:start position:0%
+centimeter this stuff zirconium
+it's about 6.9 or so Steel's like eight
+
+ align:start position:0%
+it's about 6.9 or so Steel's like eight
+ 
+
+ align:start position:0%
+it's about 6.9 or so Steel's like eight
+LEDs like eleven Mercury's like nineteen
+
+ align:start position:0%
+LEDs like eleven Mercury's like nineteen
+ 
+
+ align:start position:0%
+LEDs like eleven Mercury's like nineteen
+via any of you ever played with liquid
+
+ align:start position:0%
+via any of you ever played with liquid
+ 
+
+ align:start position:0%
+via any of you ever played with liquid
+mercury before yeah this is a don't try
+
+ align:start position:0%
+mercury before yeah this is a don't try
+ 
+
+ align:start position:0%
+mercury before yeah this is a don't try
+this at home kids kind of moment my
+
+ align:start position:0%
+this at home kids kind of moment my
+ 
+
+ align:start position:0%
+this at home kids kind of moment my
+grandfather happened to be a dentist so
+
+ align:start position:0%
+grandfather happened to be a dentist so
+ 
+
+ align:start position:0%
+grandfather happened to be a dentist so
+we happen to have a lot of mercury to
+
+ align:start position:0%
+we happen to have a lot of mercury to
+ 
+
+ align:start position:0%
+we happen to have a lot of mercury to
+mess around with and it's like
+
+ align:start position:0%
+mess around with and it's like
+ 
+
+ align:start position:0%
+mess around with and it's like
+unintuitive ly heavy it's unbelievable a
+
+ align:start position:0%
+unintuitive ly heavy it's unbelievable a
+ 
+
+ align:start position:0%
+unintuitive ly heavy it's unbelievable a
+one-pound jar is about that big I think
+
+ align:start position:0%
+one-pound jar is about that big I think
+ 
+
+ align:start position:0%
+one-pound jar is about that big I think
+would be cool if we could time something
+
+ align:start position:0%
+would be cool if we could time something
+ 
+
+ align:start position:0%
+would be cool if we could time something
+even denser and then really really dense
+
+ align:start position:0%
+even denser and then really really dense
+ 
+
+ align:start position:0%
+even denser and then really really dense
+matter happens to make really really
+
+ align:start position:0%
+matter happens to make really really
+ 
+
+ align:start position:0%
+matter happens to make really really
+good photon shields gamma seen on the
+
+ align:start position:0%
+good photon shields gamma seen on the
+ 
+
+ align:start position:0%
+good photon shields gamma seen on the
+Star Trek thing I mean this in the
+
+ align:start position:0%
+Star Trek thing I mean this in the
+ 
+
+ align:start position:0%
+Star Trek thing I mean this in the
+actual nuclear physics sense is the best
+
+ align:start position:0%
+actual nuclear physics sense is the best
+ 
+
+ align:start position:0%
+actual nuclear physics sense is the best
+way to stop gamma rays for gamma
+
+ align:start position:0%
+way to stop gamma rays for gamma
+ 
+
+ align:start position:0%
+way to stop gamma rays for gamma
+shielding is just put more matter in
+
+ align:start position:0%
+shielding is just put more matter in
+ 
+
+ align:start position:0%
+shielding is just put more matter in
+front of it and if we find a denser
+
+ align:start position:0%
+front of it and if we find a denser
+ 
+
+ align:start position:0%
+front of it and if we find a denser
+state of matter that's earth stable you
+
+ align:start position:0%
+state of matter that's earth stable you
+ 
+
+ align:start position:0%
+state of matter that's earth stable you
+then have a smaller gamma shield so
+
+ align:start position:0%
+then have a smaller gamma shield so
+ 
+
+ align:start position:0%
+then have a smaller gamma shield so
+there are practical applications to in
+
+ align:start position:0%
+there are practical applications to in
+ 
+
+ align:start position:0%
+there are practical applications to in
+radiation shielding they also might make
+
+ align:start position:0%
+radiation shielding they also might make
+ 
+
+ align:start position:0%
+radiation shielding they also might make
+awesome nuclear fuel because you better
+
+ align:start position:0%
+awesome nuclear fuel because you better
+ 
+
+ align:start position:0%
+awesome nuclear fuel because you better
+believe they're gonna fizz like crazy so
+
+ align:start position:0%
+believe they're gonna fizz like crazy so
+ 
+
+ align:start position:0%
+believe they're gonna fizz like crazy so
+who knows maybe we can I don't think
+
+ align:start position:0%
+who knows maybe we can I don't think
+ 
+
+ align:start position:0%
+who knows maybe we can I don't think
+that would be cost-effective but it
+
+ align:start position:0%
+that would be cost-effective but it
+ 
+
+ align:start position:0%
+that would be cost-effective but it
+would probably work so the way they're
+
+ align:start position:0%
+would probably work so the way they're
+ 
+
+ align:start position:0%
+would probably work so the way they're
+doing this is actually slamming calcium
+
+ align:start position:0%
+doing this is actually slamming calcium
+ 
+
+ align:start position:0%
+doing this is actually slamming calcium
+48 nuclei
+
+ align:start position:0%
+48 nuclei
+ 
+
+ align:start position:0%
+48 nuclei
+into other super-heavy elements that
+
+ align:start position:0%
+into other super-heavy elements that
+ 
+
+ align:start position:0%
+into other super-heavy elements that
+have exceptionally long half-lives so if
+
+ align:start position:0%
+have exceptionally long half-lives so if
+ 
+
+ align:start position:0%
+have exceptionally long half-lives so if
+you can't read what the screen says this
+
+ align:start position:0%
+you can't read what the screen says this
+ 
+
+ align:start position:0%
+you can't read what the screen says this
+here is berkelium for berkeley with
+
+ align:start position:0%
+here is berkelium for berkeley with
+ 
+
+ align:start position:0%
+here is berkelium for berkeley with
+proton number 97 mass number 249 let's
+
+ align:start position:0%
+proton number 97 mass number 249 let's
+ 
+
+ align:start position:0%
+proton number 97 mass number 249 let's
+take a look at EK 249 which happens to
+
+ align:start position:0%
+take a look at EK 249 which happens to
+ 
+
+ align:start position:0%
+take a look at EK 249 which happens to
+be way beyond uranium so it's definitely
+
+ align:start position:0%
+be way beyond uranium so it's definitely
+ 
+
+ align:start position:0%
+be way beyond uranium so it's definitely
+not a stable isotope but it has a
+
+ align:start position:0%
+not a stable isotope but it has a
+ 
+
+ align:start position:0%
+not a stable isotope but it has a
+half-life of 320 days that means you can
+
+ align:start position:0%
+half-life of 320 days that means you can
+ 
+
+ align:start position:0%
+half-life of 320 days that means you can
+make a bunch of it chemically separated
+
+ align:start position:0%
+make a bunch of it chemically separated
+ 
+
+ align:start position:0%
+make a bunch of it chemically separated
+make it into a target and fire calcium
+
+ align:start position:0%
+make it into a target and fire calcium
+ 
+
+ align:start position:0%
+make it into a target and fire calcium
+48 nuclei into it anyone want to guess
+
+ align:start position:0%
+48 nuclei into it anyone want to guess
+ 
+
+ align:start position:0%
+48 nuclei into it anyone want to guess
+why do we use calcium 48 and I'll give
+
+ align:start position:0%
+why do we use calcium 48 and I'll give
+ 
+
+ align:start position:0%
+why do we use calcium 48 and I'll give
+you a hint and write the proton number
+
+ align:start position:0%
+you a hint and write the proton number
+ 
+
+ align:start position:0%
+you a hint and write the proton number
+for calcium the isotope that we use it's
+
+ align:start position:0%
+for calcium the isotope that we use it's
+ 
+
+ align:start position:0%
+for calcium the isotope that we use it's
+calcium 28 Coliseum 48 anyone want to
+
+ align:start position:0%
+calcium 28 Coliseum 48 anyone want to
+ 
+
+ align:start position:0%
+calcium 28 Coliseum 48 anyone want to
+take a guess why start here why not just
+
+ align:start position:0%
+take a guess why start here why not just
+ 
+
+ align:start position:0%
+take a guess why start here why not just
+smash to berkelium Xin to each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calcium 48 happens to be exceptionally
+
+ align:start position:0%
+calcium 48 happens to be exceptionally
+ 
+
+ align:start position:0%
+calcium 48 happens to be exceptionally
+stable because it's got two magic
+
+ align:start position:0%
+stable because it's got two magic
+ 
+
+ align:start position:0%
+stable because it's got two magic
+numbers it's proton number is twenty one
+
+ align:start position:0%
+numbers it's proton number is twenty one
+ 
+
+ align:start position:0%
+numbers it's proton number is twenty one
+of those peaks of stability and it's
+
+ align:start position:0%
+of those peaks of stability and it's
+ 
+
+ align:start position:0%
+of those peaks of stability and it's
+Neutron numbers 28 so start with
+
+ align:start position:0%
+Neutron numbers 28 so start with
+ 
+
+ align:start position:0%
+Neutron numbers 28 so start with
+something super stable something with a
+
+ align:start position:0%
+something super stable something with a
+ 
+
+ align:start position:0%
+something super stable something with a
+lot more binding energy to begin with
+
+ align:start position:0%
+lot more binding energy to begin with
+ 
+
+ align:start position:0%
+lot more binding energy to begin with
+and you maximize your chance of making
+
+ align:start position:0%
+and you maximize your chance of making
+ 
+
+ align:start position:0%
+and you maximize your chance of making
+something with more binding energy that
+
+ align:start position:0%
+something with more binding energy that
+ 
+
+ align:start position:0%
+something with more binding energy that
+won't just spontaneously disappear so
+
+ align:start position:0%
+won't just spontaneously disappear so
+ 
+
+ align:start position:0%
+won't just spontaneously disappear so
+there are reasons calcium 48 was chosen
+
+ align:start position:0%
+there are reasons calcium 48 was chosen
+ 
+
+ align:start position:0%
+there are reasons calcium 48 was chosen
+and not something heavier or lighter if
+
+ align:start position:0%
+and not something heavier or lighter if
+ 
+
+ align:start position:0%
+and not something heavier or lighter if
+we go back to that article you can see
+
+ align:start position:0%
+we go back to that article you can see
+ 
+
+ align:start position:0%
+we go back to that article you can see
+what happens here is you make some
+
+ align:start position:0%
+what happens here is you make some
+ 
+
+ align:start position:0%
+what happens here is you make some
+element 117 which has yet to be made and
+
+ align:start position:0%
+element 117 which has yet to be made and
+ 
+
+ align:start position:0%
+element 117 which has yet to be made and
+it undergoes alpha decay until it
+
+ align:start position:0%
+it undergoes alpha decay until it
+ 
+
+ align:start position:0%
+it undergoes alpha decay until it
+reaches some rather stable you know 17
+
+ align:start position:0%
+reaches some rather stable you know 17
+ 
+
+ align:start position:0%
+reaches some rather stable you know 17
+seconds that's pretty exceptional and if
+
+ align:start position:0%
+seconds that's pretty exceptional and if
+ 
+
+ align:start position:0%
+seconds that's pretty exceptional and if
+you notice the trends here as you decay
+
+ align:start position:0%
+you notice the trends here as you decay
+ 
+
+ align:start position:0%
+you notice the trends here as you decay
+the alpha energy steadily goes down and
+
+ align:start position:0%
+the alpha energy steadily goes down and
+ 
+
+ align:start position:0%
+the alpha energy steadily goes down and
+the half-life steadily goes up and so
+
+ align:start position:0%
+the half-life steadily goes up and so
+ 
+
+ align:start position:0%
+the half-life steadily goes up and so
+what you do is you make an super
+
+ align:start position:0%
+what you do is you make an super
+ 
+
+ align:start position:0%
+what you do is you make an super
+super-heavy element hoping that it will
+
+ align:start position:0%
+super-heavy element hoping that it will
+ 
+
+ align:start position:0%
+super-heavy element hoping that it will
+decay and rest in one of these islands
+
+ align:start position:0%
+decay and rest in one of these islands
+ 
+
+ align:start position:0%
+decay and rest in one of these islands
+of stability beyond the magic numbers
+
+ align:start position:0%
+of stability beyond the magic numbers
+ 
+
+ align:start position:0%
+of stability beyond the magic numbers
+that we know right now which I thought
+
+ align:start position:0%
+that we know right now which I thought
+ 
+
+ align:start position:0%
+that we know right now which I thought
+this was super cool because this is
+
+ align:start position:0%
+this was super cool because this is
+ 
+
+ align:start position:0%
+this was super cool because this is
+actually how
+
+ align:start position:0%
+actually how
+ 
+
+ align:start position:0%
+actually how
+opening now like new elements are made I
+
+ align:start position:0%
+opening now like new elements are made I
+ 
+
+ align:start position:0%
+opening now like new elements are made I
+think we've been seeing one a year or so
+
+ align:start position:0%
+think we've been seeing one a year or so
+ 
+
+ align:start position:0%
+think we've been seeing one a year or so
+for the past few years on average there
+
+ align:start position:0%
+for the past few years on average there
+ 
+
+ align:start position:0%
+for the past few years on average there
+might have been a year when there was
+
+ align:start position:0%
+might have been a year when there was
+ 
+
+ align:start position:0%
+might have been a year when there was
+more than one announced recently there's
+
+ align:start position:0%
+more than one announced recently there's
+ 
+
+ align:start position:0%
+more than one announced recently there's
+only a few places in the world doing
+
+ align:start position:0%
+only a few places in the world doing
+ 
+
+ align:start position:0%
+only a few places in the world doing
+them but you can start to already with
+
+ align:start position:0%
+them but you can start to already with
+ 
+
+ align:start position:0%
+them but you can start to already with
+two weeks of 2201 you can start to get a
+
+ align:start position:0%
+two weeks of 2201 you can start to get a
+ 
+
+ align:start position:0%
+two weeks of 2201 you can start to get a
+handle for why do they use the nuclei
+
+ align:start position:0%
+handle for why do they use the nuclei
+ 
+
+ align:start position:0%
+handle for why do they use the nuclei
+they do and then what sort of things are
+
+ align:start position:0%
+they do and then what sort of things are
+ 
+
+ align:start position:0%
+they do and then what sort of things are
+you looking for decays with lower and
+
+ align:start position:0%
+you looking for decays with lower and
+ 
+
+ align:start position:0%
+you looking for decays with lower and
+lower energy mean you're already
+
+ align:start position:0%
+lower energy mean you're already
+ 
+
+ align:start position:0%
+lower energy mean you're already
+starting to gets less steep on whatever
+
+ align:start position:0%
+starting to gets less steep on whatever
+ 
+
+ align:start position:0%
+starting to gets less steep on whatever
+imaginary mass parabola don't quite know
+
+ align:start position:0%
+imaginary mass parabola don't quite know
+ 
+
+ align:start position:0%
+imaginary mass parabola don't quite know
+how to draw this one because it's beyond
+
+ align:start position:0%
+how to draw this one because it's beyond
+ 
+
+ align:start position:0%
+how to draw this one because it's beyond
+anything we know and as the half-lives
+
+ align:start position:0%
+anything we know and as the half-lives
+ 
+
+ align:start position:0%
+anything we know and as the half-lives
+keep going up you can tell that it's
+
+ align:start position:0%
+keep going up you can tell that it's
+ 
+
+ align:start position:0%
+keep going up you can tell that it's
+reaching a measure of stability however
+
+ align:start position:0%
+reaching a measure of stability however
+ 
+
+ align:start position:0%
+reaching a measure of stability however
+to get you started on the homework for
+
+ align:start position:0%
+to get you started on the homework for
+ 
+
+ align:start position:0%
+to get you started on the homework for
+the open ended problem I think I'll
+
+ align:start position:0%
+the open ended problem I think I'll
+ 
+
+ align:start position:0%
+the open ended problem I think I'll
+bring it up right now so you guys can
+
+ align:start position:0%
+bring it up right now so you guys can
+ 
+
+ align:start position:0%
+bring it up right now so you guys can
+take a look so let's go to the stellar
+
+ align:start position:0%
+take a look so let's go to the stellar
+ 
+
+ align:start position:0%
+take a look so let's go to the stellar
+site
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hopefully it doesn't call me good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the problem set 2 this is the way I
+
+ align:start position:0%
+at the problem set 2 this is the way I
+ 
+
+ align:start position:0%
+at the problem set 2 this is the way I
+know that everyone's seen the pset 7
+
+ align:start position:0%
+know that everyone's seen the pset 7
+ 
+
+ align:start position:0%
+know that everyone's seen the pset 7
+days before it's due cuz I'm gonna put
+
+ align:start position:0%
+days before it's due cuz I'm gonna put
+ 
+
+ align:start position:0%
+days before it's due cuz I'm gonna put
+it up on the screen so you can see it
+
+ align:start position:0%
+it up on the screen so you can see it
+ 
+
+ align:start position:0%
+it up on the screen so you can see it
+all the way at the end predicting the
+
+ align:start position:0%
+all the way at the end predicting the
+ 
+
+ align:start position:0%
+all the way at the end predicting the
+island of stability does the semi
+
+ align:start position:0%
+island of stability does the semi
+ 
+
+ align:start position:0%
+island of stability does the semi
+empirical mass formula predict the
+
+ align:start position:0%
+empirical mass formula predict the
+ 
+
+ align:start position:0%
+empirical mass formula predict the
+island of stability well let's start you
+
+ align:start position:0%
+island of stability well let's start you
+ 
+
+ align:start position:0%
+island of stability well let's start you
+off with the easier part of the question
+
+ align:start position:0%
+off with the easier part of the question
+ 
+
+ align:start position:0%
+off with the easier part of the question
+which is yes or no and I'm gonna leave
+
+ align:start position:0%
+which is yes or no and I'm gonna leave
+ 
+
+ align:start position:0%
+which is yes or no and I'm gonna leave
+you to the why and the how if we graph
+
+ align:start position:0%
+you to the why and the how if we graph
+ 
+
+ align:start position:0%
+you to the why and the how if we graph
+binding energy per nucleon versus mass
+
+ align:start position:0%
+binding energy per nucleon versus mass
+ 
+
+ align:start position:0%
+binding energy per nucleon versus mass
+number the semi empirical mass formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+predicts something like this what
+
+ align:start position:0%
+predicts something like this what
+ 
+
+ align:start position:0%
+predicts something like this what
+happens as we go beyond the realm of
+
+ align:start position:0%
+happens as we go beyond the realm of
+ 
+
+ align:start position:0%
+happens as we go beyond the realm of
+known mass numbers anyone how should I
+
+ align:start position:0%
+known mass numbers anyone how should I
+ 
+
+ align:start position:0%
+known mass numbers anyone how should I
+extend this curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would you say Alex just keep going yeah
+
+ align:start position:0%
+would you say Alex just keep going yeah
+ 
+
+ align:start position:0%
+would you say Alex just keep going yeah
+does this predict an island of stability
+
+ align:start position:0%
+does this predict an island of stability
+ 
+
+ align:start position:0%
+does this predict an island of stability
+I don't think so
+
+ align:start position:0%
+I don't think so
+ 
+
+ align:start position:0%
+I don't think so
+so that's one of the few questions I'm
+
+ align:start position:0%
+so that's one of the few questions I'm
+ 
+
+ align:start position:0%
+so that's one of the few questions I'm
+asking you in this homework and it's up
+
+ align:start position:0%
+asking you in this homework and it's up
+ 
+
+ align:start position:0%
+asking you in this homework and it's up
+to you guys use your creativity again
+
+ align:start position:0%
+to you guys use your creativity again
+ 
+
+ align:start position:0%
+to you guys use your creativity again
+this is an open-ended problem I'm not
+
+ align:start position:0%
+this is an open-ended problem I'm not
+ 
+
+ align:start position:0%
+this is an open-ended problem I'm not
+looking for a specific answer I want to
+
+ align:start position:0%
+looking for a specific answer I want to
+ 
+
+ align:start position:0%
+looking for a specific answer I want to
+see how you think and how you would
+
+ align:start position:0%
+see how you think and how you would
+ 
+
+ align:start position:0%
+see how you think and how you would
+change this formula to account and
+
+ align:start position:0%
+change this formula to account and
+ 
+
+ align:start position:0%
+change this formula to account and
+actually predict the island of stability
+
+ align:start position:0%
+actually predict the island of stability
+ 
+
+ align:start position:0%
+actually predict the island of stability
+while still satisfying the mostly
+
+ align:start position:0%
+while still satisfying the mostly
+ 
+
+ align:start position:0%
+while still satisfying the mostly
+correct predictions from the elements we
+
+ align:start position:0%
+correct predictions from the elements we
+ 
+
+ align:start position:0%
+correct predictions from the elements we
+know so sorry go ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well yaar you're on the right track if
+
+ align:start position:0%
+well yaar you're on the right track if
+ 
+
+ align:start position:0%
+well yaar you're on the right track if
+you wanna make if you want to show
+
+ align:start position:0%
+you wanna make if you want to show
+ 
+
+ align:start position:0%
+you wanna make if you want to show
+stability you'd want it to maybe have a
+
+ align:start position:0%
+stability you'd want it to maybe have a
+ 
+
+ align:start position:0%
+stability you'd want it to maybe have a
+higher value right here higher binding
+
+ align:start position:0%
+higher value right here higher binding
+ 
+
+ align:start position:0%
+higher value right here higher binding
+energy per nucleon would correspond to a
+
+ align:start position:0%
+energy per nucleon would correspond to a
+ 
+
+ align:start position:0%
+energy per nucleon would correspond to a
+lower mass which would correspond to
+
+ align:start position:0%
+lower mass which would correspond to
+ 
+
+ align:start position:0%
+lower mass which would correspond to
+higher stability so how would you
+
+ align:start position:0%
+higher stability so how would you
+ 
+
+ align:start position:0%
+higher stability so how would you
+predict this island of stability and
+
+ align:start position:0%
+predict this island of stability and
+ 
+
+ align:start position:0%
+predict this island of stability and
+then more specifically how would you
+
+ align:start position:0%
+then more specifically how would you
+ 
+
+ align:start position:0%
+then more specifically how would you
+reconcile the misty inaccuracies in the
+
+ align:start position:0%
+reconcile the misty inaccuracies in the
+ 
+
+ align:start position:0%
+reconcile the misty inaccuracies in the
+semi empirical mass formula because we
+
+ align:start position:0%
+semi empirical mass formula because we
+ 
+
+ align:start position:0%
+semi empirical mass formula because we
+know it doesn't work very well for all
+
+ align:start position:0%
+know it doesn't work very well for all
+ 
+
+ align:start position:0%
+know it doesn't work very well for all
+cases there are some cases like right
+
+ align:start position:0%
+cases there are some cases like right
+ 
+
+ align:start position:0%
+cases there are some cases like right
+around here where it works great and
+
+ align:start position:0%
+around here where it works great and
+ 
+
+ align:start position:0%
+around here where it works great and
+there's some like right here and right
+
+ align:start position:0%
+there's some like right here and right
+ 
+
+ align:start position:0%
+there's some like right here and right
+here where it really doesn't and get
+
+ align:start position:0%
+here where it really doesn't and get
+ 
+
+ align:start position:0%
+here where it really doesn't and get
+things wrong by like ten MeV which is
+
+ align:start position:0%
+things wrong by like ten MeV which is
+ 
+
+ align:start position:0%
+things wrong by like ten MeV which is
+pretty significant you know that's like
+
+ align:start position:0%
+pretty significant you know that's like
+ 
+
+ align:start position:0%
+pretty significant you know that's like
+four digits on the mass scale like the
+
+ align:start position:0%
+four digits on the mass scale like the
+ 
+
+ align:start position:0%
+four digits on the mass scale like the
+fourth decimal place that's huge to a
+
+ align:start position:0%
+fourth decimal place that's huge to a
+ 
+
+ align:start position:0%
+fourth decimal place that's huge to a
+nuclear engineer so that's something to
+
+ align:start position:0%
+nuclear engineer so that's something to
+ 
+
+ align:start position:0%
+nuclear engineer so that's something to
+get thinking about and remember I did
+
+ align:start position:0%
+get thinking about and remember I did
+ 
+
+ align:start position:0%
+get thinking about and remember I did
+tell you that there will be some
+
+ align:start position:0%
+tell you that there will be some
+ 
+
+ align:start position:0%
+tell you that there will be some
+open-ended problems I'm gonna mark them
+
+ align:start position:0%
+open-ended problems I'm gonna mark them
+ 
+
+ align:start position:0%
+open-ended problems I'm gonna mark them
+as open-ended so you actually know we're
+
+ align:start position:0%
+as open-ended so you actually know we're
+ 
+
+ align:start position:0%
+as open-ended so you actually know we're
+not looking for a right or wrong answer
+
+ align:start position:0%
+not looking for a right or wrong answer
+ 
+
+ align:start position:0%
+not looking for a right or wrong answer
+this is one of those kinds of things
+
+ align:start position:0%
+this is one of those kinds of things
+ 
+
+ align:start position:0%
+this is one of those kinds of things
+where we want to see how you think and
+
+ align:start position:0%
+where we want to see how you think and
+ 
+
+ align:start position:0%
+where we want to see how you think and
+what do you think is missing there's
+
+ align:start position:0%
+what do you think is missing there's
+ 
+
+ align:start position:0%
+what do you think is missing there's
+other hard problems where we give you
+
+ align:start position:0%
+other hard problems where we give you
+ 
+
+ align:start position:0%
+other hard problems where we give you
+the answer because I'm not interested in
+
+ align:start position:0%
+the answer because I'm not interested in
+ 
+
+ align:start position:0%
+the answer because I'm not interested in
+you deriving some explainin expression
+
+ align:start position:0%
+you deriving some explainin expression
+ 
+
+ align:start position:0%
+you deriving some explainin expression
+and getting it right I'm interested in
+
+ align:start position:0%
+and getting it right I'm interested in
+ 
+
+ align:start position:0%
+and getting it right I'm interested in
+the derivation process what are the
+
+ align:start position:0%
+the derivation process what are the
+ 
+
+ align:start position:0%
+the derivation process what are the
+steps you choose what sort of
+
+ align:start position:0%
+steps you choose what sort of
+ 
+
+ align:start position:0%
+steps you choose what sort of
+assumptions do you make what sort of
+
+ align:start position:0%
+assumptions do you make what sort of
+ 
+
+ align:start position:0%
+assumptions do you make what sort of
+terms can you neglect and say that's in
+
+ align:start position:0%
+terms can you neglect and say that's in
+ 
+
+ align:start position:0%
+terms can you neglect and say that's in
+the ninth decimal place I'm going to
+
+ align:start position:0%
+the ninth decimal place I'm going to
+ 
+
+ align:start position:0%
+the ninth decimal place I'm going to
+forget it so in this case we give you
+
+ align:start position:0%
+forget it so in this case we give you
+ 
+
+ align:start position:0%
+forget it so in this case we give you
+the answer because we're going to grade
+
+ align:start position:0%
+the answer because we're going to grade
+ 
+
+ align:start position:0%
+the answer because we're going to grade
+you on the process
+
+ align:start position:0%
+you on the process
+ 
+
+ align:start position:0%
+you on the process
+and you can use the answer to check your
+
+ align:start position:0%
+and you can use the answer to check your
+ 
+
+ align:start position:0%
+and you can use the answer to check your
+process and see if you're on the right
+
+ align:start position:0%
+process and see if you're on the right
+ 
+
+ align:start position:0%
+process and see if you're on the right
+track or not for the skill building
+
+ align:start position:0%
+track or not for the skill building
+ 
+
+ align:start position:0%
+track or not for the skill building
+questions we actually do want you to
+
+ align:start position:0%
+questions we actually do want you to
+ 
+
+ align:start position:0%
+questions we actually do want you to
+come up with some sort of an answer like
+
+ align:start position:0%
+come up with some sort of an answer like
+ 
+
+ align:start position:0%
+come up with some sort of an answer like
+explaining the terms in the semi
+
+ align:start position:0%
+explaining the terms in the semi
+ 
+
+ align:start position:0%
+explaining the terms in the semi
+empirical mass formula or modifying an
+
+ align:start position:0%
+empirical mass formula or modifying an
+ 
+
+ align:start position:0%
+empirical mass formula or modifying an
+equation to calculate something else we
+
+ align:start position:0%
+equation to calculate something else we
+ 
+
+ align:start position:0%
+equation to calculate something else we
+will be looking for a right answer there
+
+ align:start position:0%
+will be looking for a right answer there
+ 
+
+ align:start position:0%
+will be looking for a right answer there
+but those are questions to make sure
+
+ align:start position:0%
+but those are questions to make sure
+ 
+
+ align:start position:0%
+but those are questions to make sure
+that you get the basics of the material
+
+ align:start position:0%
+that you get the basics of the material
+ 
+
+ align:start position:0%
+that you get the basics of the material
+if you can answer all of the questions
+
+ align:start position:0%
+if you can answer all of the questions
+ 
+
+ align:start position:0%
+if you can answer all of the questions
+in the first half of these P sets fairly
+
+ align:start position:0%
+in the first half of these P sets fairly
+ 
+
+ align:start position:0%
+in the first half of these P sets fairly
+quickly let's say in three or four hours
+
+ align:start position:0%
+quickly let's say in three or four hours
+ 
+
+ align:start position:0%
+quickly let's say in three or four hours
+you're totally on the right track the
+
+ align:start position:0%
+you're totally on the right track the
+ 
+
+ align:start position:0%
+you're totally on the right track the
+hard ones is because this is MIT and we
+
+ align:start position:0%
+hard ones is because this is MIT and we
+ 
+
+ align:start position:0%
+hard ones is because this is MIT and we
+want you to think beyond just knowing
+
+ align:start position:0%
+want you to think beyond just knowing
+ 
+
+ align:start position:0%
+want you to think beyond just knowing
+what's in the Turner book or the Yip
+
+ align:start position:0%
+what's in the Turner book or the Yip
+ 
+
+ align:start position:0%
+what's in the Turner book or the Yip
+book like I said you guys are the
+
+ align:start position:0%
+book like I said you guys are the
+ 
+
+ align:start position:0%
+book like I said you guys are the
+leaders of this field so any other
+
+ align:start position:0%
+leaders of this field so any other
+ 
+
+ align:start position:0%
+leaders of this field so any other
+questions on instability in general yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you say
+
+ align:start position:0%
+you say
+ 
+
+ align:start position:0%
+you say
+correct so that would be even N and even
+
+ align:start position:0%
+correct so that would be even N and even
+ 
+
+ align:start position:0%
+correct so that would be even N and even
+Z are on N and odd Z like in the reading
+
+ align:start position:0%
+Z are on N and odd Z like in the reading
+ 
+
+ align:start position:0%
+Z are on N and odd Z like in the reading
+and like on these mass parabolas yep any
+
+ align:start position:0%
+and like on these mass parabolas yep any
+ 
+
+ align:start position:0%
+and like on these mass parabolas yep any
+other questions yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a few roots so the question was
+
+ align:start position:0%
+there's a few roots so the question was
+ 
+
+ align:start position:0%
+there's a few roots so the question was
+is the only is the only reason people
+
+ align:start position:0%
+is the only is the only reason people
+ 
+
+ align:start position:0%
+is the only is the only reason people
+think they'll be super heavy elements
+
+ align:start position:0%
+think they'll be super heavy elements
+ 
+
+ align:start position:0%
+think they'll be super heavy elements
+because the mass increases right so in
+
+ align:start position:0%
+because the mass increases right so in
+ 
+
+ align:start position:0%
+because the mass increases right so in
+this case the the mass will always are
+
+ align:start position:0%
+this case the the mass will always are
+ 
+
+ align:start position:0%
+this case the the mass will always are
+you talking about now the total mass or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we have a few things to go on so
+
+ align:start position:0%
+okay we have a few things to go on so
+ 
+
+ align:start position:0%
+okay we have a few things to go on so
+all there are a number of different
+
+ align:start position:0%
+all there are a number of different
+ 
+
+ align:start position:0%
+all there are a number of different
+aspects of nuclear stability that are
+
+ align:start position:0%
+aspects of nuclear stability that are
+ 
+
+ align:start position:0%
+aspects of nuclear stability that are
+all pointing to the same conclusion one
+
+ align:start position:0%
+all pointing to the same conclusion one
+ 
+
+ align:start position:0%
+all pointing to the same conclusion one
+of them you can see on this graph here
+
+ align:start position:0%
+of them you can see on this graph here
+ 
+
+ align:start position:0%
+of them you can see on this graph here
+if you look at the alpha decay half-life
+
+ align:start position:0%
+if you look at the alpha decay half-life
+ 
+
+ align:start position:0%
+if you look at the alpha decay half-life
+as a function of Neutron number it
+
+ align:start position:0%
+as a function of Neutron number it
+ 
+
+ align:start position:0%
+as a function of Neutron number it
+doesn't just increase or decrease
+
+ align:start position:0%
+doesn't just increase or decrease
+ 
+
+ align:start position:0%
+doesn't just increase or decrease
+monotonically it swells up and down and
+
+ align:start position:0%
+monotonically it swells up and down and
+ 
+
+ align:start position:0%
+monotonically it swells up and down and
+it reaches a relative maximum near
+
+ align:start position:0%
+it reaches a relative maximum near
+ 
+
+ align:start position:0%
+it reaches a relative maximum near
+certain magic numbers we can confirm
+
+ align:start position:0%
+certain magic numbers we can confirm
+ 
+
+ align:start position:0%
+certain magic numbers we can confirm
+that with the lower mass nuclei it
+
+ align:start position:0%
+that with the lower mass nuclei it
+ 
+
+ align:start position:0%
+that with the lower mass nuclei it
+doesn't work for really low mass because
+
+ align:start position:0%
+doesn't work for really low mass because
+ 
+
+ align:start position:0%
+doesn't work for really low mass because
+tiny things don't tend to go under
+
+ align:start position:0%
+tiny things don't tend to go under
+ 
+
+ align:start position:0%
+tiny things don't tend to go under
+undergo alpha decay but there are
+
+ align:start position:0%
+undergo alpha decay but there are
+ 
+
+ align:start position:0%
+undergo alpha decay but there are
+patterns that were simply recognizing
+
+ align:start position:0%
+patterns that were simply recognizing
+ 
+
+ align:start position:0%
+patterns that were simply recognizing
+and saying well if this is the next
+
+ align:start position:0%
+and saying well if this is the next
+ 
+
+ align:start position:0%
+and saying well if this is the next
+magic number it should continue to
+
+ align:start position:0%
+magic number it should continue to
+ 
+
+ align:start position:0%
+magic number it should continue to
+increase and I should mention to this
+
+ align:start position:0%
+increase and I should mention to this
+ 
+
+ align:start position:0%
+increase and I should mention to this
+scale is logarithmic so the top right
+
+ align:start position:0%
+scale is logarithmic so the top right
+ 
+
+ align:start position:0%
+scale is logarithmic so the top right
+here is like 10 to the 4 seconds just so
+
+ align:start position:0%
+here is like 10 to the 4 seconds just so
+ 
+
+ align:start position:0%
+here is like 10 to the 4 seconds just so
+you know there are 86,400 seconds in
+
+ align:start position:0%
+you know there are 86,400 seconds in
+ 
+
+ align:start position:0%
+you know there are 86,400 seconds in
+what is it a day and 3 times 10 to the 7
+
+ align:start position:0%
+what is it a day and 3 times 10 to the 7
+ 
+
+ align:start position:0%
+what is it a day and 3 times 10 to the 7
+seconds in a year so if this graph let's
+
+ align:start position:0%
+seconds in a year so if this graph let's
+ 
+
+ align:start position:0%
+seconds in a year so if this graph let's
+say for Z 111 were to continue on its
+
+ align:start position:0%
+say for Z 111 were to continue on its
+ 
+
+ align:start position:0%
+say for Z 111 were to continue on its
+track it should reach like 10 to the 9
+
+ align:start position:0%
+track it should reach like 10 to the 9
+ 
+
+ align:start position:0%
+track it should reach like 10 to the 9
+or 10 to the 10 which could be like
+
+ align:start position:0%
+or 10 to the 10 which could be like
+ 
+
+ align:start position:0%
+or 10 to the 10 which could be like
+hundred year lifetimes or 100 year
+
+ align:start position:0%
+hundred year lifetimes or 100 year
+ 
+
+ align:start position:0%
+hundred year lifetimes or 100 year
+half-lives which means definitely you
+
+ align:start position:0%
+half-lives which means definitely you
+ 
+
+ align:start position:0%
+half-lives which means definitely you
+can chemically separate them and do
+
+ align:start position:0%
+can chemically separate them and do
+ 
+
+ align:start position:0%
+can chemically separate them and do
+things with them I don't know if they
+
+ align:start position:0%
+things with them I don't know if they
+ 
+
+ align:start position:0%
+things with them I don't know if they
+would be safe enough to deal with but we
+
+ align:start position:0%
+would be safe enough to deal with but we
+ 
+
+ align:start position:0%
+would be safe enough to deal with but we
+also don't really know what's going to
+
+ align:start position:0%
+also don't really know what's going to
+ 
+
+ align:start position:0%
+also don't really know what's going to
+happen you can see that there is some
+
+ align:start position:0%
+happen you can see that there is some
+ 
+
+ align:start position:0%
+happen you can see that there is some
+uncertainty and things don't always
+
+ align:start position:0%
+uncertainty and things don't always
+ 
+
+ align:start position:0%
+uncertainty and things don't always
+follow the trend even the error bars are
+
+ align:start position:0%
+follow the trend even the error bars are
+ 
+
+ align:start position:0%
+follow the trend even the error bars are
+outside the dashed lines but so we have
+
+ align:start position:0%
+outside the dashed lines but so we have
+ 
+
+ align:start position:0%
+outside the dashed lines but so we have
+this to go on we have the alpha decay
+
+ align:start position:0%
+this to go on we have the alpha decay
+ 
+
+ align:start position:0%
+this to go on we have the alpha decay
+half-life we also have the alpha decay
+
+ align:start position:0%
+half-life we also have the alpha decay
+ 
+
+ align:start position:0%
+half-life we also have the alpha decay
+energy as you approach an island of
+
+ align:start position:0%
+energy as you approach an island of
+ 
+
+ align:start position:0%
+energy as you approach an island of
+stability something that's more stable
+
+ align:start position:0%
+stability something that's more stable
+ 
+
+ align:start position:0%
+stability something that's more stable
+won't give off as much kinetic energy to
+
+ align:start position:0%
+won't give off as much kinetic energy to
+ 
+
+ align:start position:0%
+won't give off as much kinetic energy to
+its alpha particle there's also for the
+
+ align:start position:0%
+its alpha particle there's also for the
+ 
+
+ align:start position:0%
+its alpha particle there's also for the
+ones that you can actually measure that
+
+ align:start position:0%
+ones that you can actually measure that
+ 
+
+ align:start position:0%
+ones that you can actually measure that
+live long enough you can measure their
+
+ align:start position:0%
+live long enough you can measure their
+ 
+
+ align:start position:0%
+live long enough you can measure their
+mass-to-charge ratio and actually get a
+
+ align:start position:0%
+mass-to-charge ratio and actually get a
+ 
+
+ align:start position:0%
+mass-to-charge ratio and actually get a
+good picture of their actual mass so we
+
+ align:start position:0%
+good picture of their actual mass so we
+ 
+
+ align:start position:0%
+good picture of their actual mass so we
+would expect the mass defect to follow a
+
+ align:start position:0%
+would expect the mass defect to follow a
+ 
+
+ align:start position:0%
+would expect the mass defect to follow a
+certain trend as we go up the mass is
+
+ align:start position:0%
+certain trend as we go up the mass is
+ 
+
+ align:start position:0%
+certain trend as we go up the mass is
+always going to increase if you add more
+
+ align:start position:0%
+always going to increase if you add more
+ 
+
+ align:start position:0%
+always going to increase if you add more
+nucleons it's going to increase but the
+
+ align:start position:0%
+nucleons it's going to increase but the
+ 
+
+ align:start position:0%
+nucleons it's going to increase but the
+mass defect which is the real mass minus
+
+ align:start position:0%
+mass defect which is the real mass minus
+ 
+
+ align:start position:0%
+mass defect which is the real mass minus
+the atomic number mass if stability were
+
+ align:start position:0%
+the atomic number mass if stability were
+ 
+
+ align:start position:0%
+the atomic number mass if stability were
+to increase do you think the mass defect
+
+ align:start position:0%
+to increase do you think the mass defect
+ 
+
+ align:start position:0%
+to increase do you think the mass defect
+would increase or decrease with more
+
+ align:start position:0%
+would increase or decrease with more
+ 
+
+ align:start position:0%
+would increase or decrease with more
+stability let's take a quick look at
+
+ align:start position:0%
+stability let's take a quick look at
+ 
+
+ align:start position:0%
+stability let's take a quick look at
+this if a were to stay the same a
+
+ align:start position:0%
+this if a were to stay the same a
+ 
+
+ align:start position:0%
+this if a were to stay the same a
+shrinking real mass and remember lower
+
+ align:start position:0%
+shrinking real mass and remember lower
+ 
+
+ align:start position:0%
+shrinking real mass and remember lower
+mass means more stability would mean a
+
+ align:start position:0%
+mass means more stability would mean a
+ 
+
+ align:start position:0%
+mass means more stability would mean a
+higher or a lower mass defect I mean a
+
+ align:start position:0%
+higher or a lower mass defect I mean a
+ 
+
+ align:start position:0%
+higher or a lower mass defect I mean a
+lower mass defect or a lower excess mass
+
+ align:start position:0%
+lower mass defect or a lower excess mass
+ 
+
+ align:start position:0%
+lower mass defect or a lower excess mass
+as you'd call it so in this case you
+
+ align:start position:0%
+as you'd call it so in this case you
+ 
+
+ align:start position:0%
+as you'd call it so in this case you
+would expect the mass of the nucleus to
+
+ align:start position:0%
+would expect the mass of the nucleus to
+ 
+
+ align:start position:0%
+would expect the mass of the nucleus to
+be smaller than its a if it was going
+
+ align:start position:0%
+be smaller than its a if it was going
+ 
+
+ align:start position:0%
+be smaller than its a if it was going
+more stable and all of these trends work
+
+ align:start position:0%
+more stable and all of these trends work
+ 
+
+ align:start position:0%
+more stable and all of these trends work
+in the same direction which is saying
+
+ align:start position:0%
+in the same direction which is saying
+ 
+
+ align:start position:0%
+in the same direction which is saying
+okay so we have the Alpha energy we have
+
+ align:start position:0%
+okay so we have the Alpha energy we have
+ 
+
+ align:start position:0%
+okay so we have the Alpha energy we have
+the mass defect we have the half-life
+
+ align:start position:0%
+the mass defect we have the half-life
+ 
+
+ align:start position:0%
+the mass defect we have the half-life
+all pointing to the same thing that
+
+ align:start position:0%
+all pointing to the same thing that
+ 
+
+ align:start position:0%
+all pointing to the same thing that
+something should be more stable and we
+
+ align:start position:0%
+something should be more stable and we
+ 
+
+ align:start position:0%
+something should be more stable and we
+have some patterns to go on but our
+
+ align:start position:0%
+have some patterns to go on but our
+ 
+
+ align:start position:0%
+have some patterns to go on but our
+understandings kind of incomplete so yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoo good question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the question is if super-heavy
+
+ align:start position:0%
+so the question is if super-heavy
+ 
+
+ align:start position:0%
+so the question is if super-heavy
+elements exist do they exist out there
+
+ align:start position:0%
+elements exist do they exist out there
+ 
+
+ align:start position:0%
+elements exist do they exist out there
+in space I think there would be a couple
+
+ align:start position:0%
+in space I think there would be a couple
+ 
+
+ align:start position:0%
+in space I think there would be a couple
+places they would exist the source of
+
+ align:start position:0%
+places they would exist the source of
+ 
+
+ align:start position:0%
+places they would exist the source of
+most of the elements beyond iron is
+
+ align:start position:0%
+most of the elements beyond iron is
+ 
+
+ align:start position:0%
+most of the elements beyond iron is
+supernovas where a regular old fusion
+
+ align:start position:0%
+supernovas where a regular old fusion
+ 
+
+ align:start position:0%
+supernovas where a regular old fusion
+doesn't cut it anymore when you hit the
+
+ align:start position:0%
+doesn't cut it anymore when you hit the
+ 
+
+ align:start position:0%
+doesn't cut it anymore when you hit the
+maximum of this binding energy per
+
+ align:start position:0%
+maximum of this binding energy per
+ 
+
+ align:start position:0%
+maximum of this binding energy per
+nucleon curve you're at about iron-56
+
+ align:start position:0%
+nucleon curve you're at about iron-56
+ 
+
+ align:start position:0%
+nucleon curve you're at about iron-56
+that's why stars tend to form a core of
+
+ align:start position:0%
+that's why stars tend to form a core of
+ 
+
+ align:start position:0%
+that's why stars tend to form a core of
+iron before it goes really bad in
+
+ align:start position:0%
+iron before it goes really bad in
+ 
+
+ align:start position:0%
+iron before it goes really bad in
+whatever way it does for a star there
+
+ align:start position:0%
+whatever way it does for a star there
+ 
+
+ align:start position:0%
+whatever way it does for a star there
+are multiple ways when you get a
+
+ align:start position:0%
+are multiple ways when you get a
+ 
+
+ align:start position:0%
+are multiple ways when you get a
+supernova you have an insane explosion
+
+ align:start position:0%
+supernova you have an insane explosion
+ 
+
+ align:start position:0%
+supernova you have an insane explosion
+and the core gets compressed from the
+
+ align:start position:0%
+and the core gets compressed from the
+ 
+
+ align:start position:0%
+and the core gets compressed from the
+outside
+
+ align:start position:0%
+outside
+ 
+
+ align:start position:0%
+outside
+forcing fusion of heavy elements to
+
+ align:start position:0%
+forcing fusion of heavy elements to
+ 
+
+ align:start position:0%
+forcing fusion of heavy elements to
+happen that's because you're putting in
+
+ align:start position:0%
+happen that's because you're putting in
+ 
+
+ align:start position:0%
+happen that's because you're putting in
+extra kinetic energy so it's like you
+
+ align:start position:0%
+extra kinetic energy so it's like you
+ 
+
+ align:start position:0%
+extra kinetic energy so it's like you
+have an endothermic reaction where if Q
+
+ align:start position:0%
+have an endothermic reaction where if Q
+ 
+
+ align:start position:0%
+have an endothermic reaction where if Q
+is less than zero how do you make that
+
+ align:start position:0%
+is less than zero how do you make that
+ 
+
+ align:start position:0%
+is less than zero how do you make that
+reaction happen add kinetic energy which
+
+ align:start position:0%
+reaction happen add kinetic energy which
+ 
+
+ align:start position:0%
+reaction happen add kinetic energy which
+can come from a tremendous explosion
+
+ align:start position:0%
+can come from a tremendous explosion
+ 
+
+ align:start position:0%
+can come from a tremendous explosion
+outside of the outer regions of the star
+
+ align:start position:0%
+outside of the outer regions of the star
+ 
+
+ align:start position:0%
+outside of the outer regions of the star
+so who's to say that some of these
+
+ align:start position:0%
+so who's to say that some of these
+ 
+
+ align:start position:0%
+so who's to say that some of these
+super-heavy elements aren't formed in
+
+ align:start position:0%
+super-heavy elements aren't formed in
+ 
+
+ align:start position:0%
+super-heavy elements aren't formed in
+supernovas I think they would be but
+
+ align:start position:0%
+supernovas I think they would be but
+ 
+
+ align:start position:0%
+supernovas I think they would be but
+would they actually make it out to be
+
+ align:start position:0%
+would they actually make it out to be
+ 
+
+ align:start position:0%
+would they actually make it out to be
+part of earth and then let's say live
+
+ align:start position:0%
+part of earth and then let's say live
+ 
+
+ align:start position:0%
+part of earth and then let's say live
+the five billion years that Art's been
+
+ align:start position:0%
+the five billion years that Art's been
+ 
+
+ align:start position:0%
+the five billion years that Art's been
+around we don't know if their half-lives
+
+ align:start position:0%
+around we don't know if their half-lives
+ 
+
+ align:start position:0%
+around we don't know if their half-lives
+are long enough there very well may have
+
+ align:start position:0%
+are long enough there very well may have
+ 
+
+ align:start position:0%
+are long enough there very well may have
+been some five billion years ago or when
+
+ align:start position:0%
+been some five billion years ago or when
+ 
+
+ align:start position:0%
+been some five billion years ago or when
+the supernova was made but we haven't
+
+ align:start position:0%
+the supernova was made but we haven't
+ 
+
+ align:start position:0%
+the supernova was made but we haven't
+detected any here on earth so we know
+
+ align:start position:0%
+detected any here on earth so we know
+ 
+
+ align:start position:0%
+detected any here on earth so we know
+that they're not five billion years
+
+ align:start position:0%
+that they're not five billion years
+ 
+
+ align:start position:0%
+that they're not five billion years
+stable rather I wouldn't even need to
+
+ align:start position:0%
+stable rather I wouldn't even need to
+ 
+
+ align:start position:0%
+stable rather I wouldn't even need to
+say we know that but we have a pretty
+
+ align:start position:0%
+say we know that but we have a pretty
+ 
+
+ align:start position:0%
+say we know that but we have a pretty
+good idea
+
+ align:start position:0%
+good idea
+ 
+
+ align:start position:0%
+good idea
+that's a great question is like are they
+
+ align:start position:0%
+that's a great question is like are they
+ 
+
+ align:start position:0%
+that's a great question is like are they
+naturally made probably yeah any other
+
+ align:start position:0%
+naturally made probably yeah any other
+ 
+
+ align:start position:0%
+naturally made probably yeah any other
+questions I like these outside the
+
+ align:start position:0%
+questions I like these outside the
+ 
+
+ align:start position:0%
+questions I like these outside the
+material ones we can take things beyond
+
+ align:start position:0%
+material ones we can take things beyond
+ 
+
+ align:start position:0%
+material ones we can take things beyond
+our known universe start to explain them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/mNlOG7CFPEY.txt b/mNlOG7CFPEY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..45b8ca222e83685403334242222a7ee05f836339
--- /dev/null
+++ b/mNlOG7CFPEY.txt
@@ -0,0 +1,13635 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu thank you for the
+
+ align:start position:0%
+ocw.mit.edu thank you for the
+ 
+
+ align:start position:0%
+ocw.mit.edu thank you for the
+introduction I'm happy to be here today
+
+ align:start position:0%
+introduction I'm happy to be here today
+ 
+
+ align:start position:0%
+introduction I'm happy to be here today
+I hear at Spring break so I'm impressed
+
+ align:start position:0%
+I hear at Spring break so I'm impressed
+ 
+
+ align:start position:0%
+I hear at Spring break so I'm impressed
+that you're all here uh it doesn't feel
+
+ align:start position:0%
+that you're all here uh it doesn't feel
+ 
+
+ align:start position:0%
+that you're all here uh it doesn't feel
+much like spring outside but I'm sure
+
+ align:start position:0%
+much like spring outside but I'm sure
+ 
+
+ align:start position:0%
+much like spring outside but I'm sure
+hopefully it will in the next couple
+
+ align:start position:0%
+hopefully it will in the next couple
+ 
+
+ align:start position:0%
+hopefully it will in the next couple
+weeks um so uh priia and I are going to
+
+ align:start position:0%
+weeks um so uh priia and I are going to
+ 
+
+ align:start position:0%
+weeks um so uh priia and I are going to
+talk a bit about uh what we've been
+
+ align:start position:0%
+talk a bit about uh what we've been
+ 
+
+ align:start position:0%
+talk a bit about uh what we've been
+working on in regards to checklist so
+
+ align:start position:0%
+working on in regards to checklist so
+ 
+
+ align:start position:0%
+working on in regards to checklist so
+it's a little bit uh I think it's a
+
+ align:start position:0%
+it's a little bit uh I think it's a
+ 
+
+ align:start position:0%
+it's a little bit uh I think it's a
+little bit different from some of the
+
+ align:start position:0%
+little bit different from some of the
+ 
+
+ align:start position:0%
+little bit different from some of the
+technology discussions you've have in
+
+ align:start position:0%
+technology discussions you've have in
+ 
+
+ align:start position:0%
+technology discussions you've have in
+the past but I think the similarity is
+
+ align:start position:0%
+the past but I think the similarity is
+ 
+
+ align:start position:0%
+the past but I think the similarity is
+in that we bring uh the idea of bringing
+
+ align:start position:0%
+in that we bring uh the idea of bringing
+ 
+
+ align:start position:0%
+in that we bring uh the idea of bringing
+Innovations and also implementing
+
+ align:start position:0%
+Innovations and also implementing
+ 
+
+ align:start position:0%
+Innovations and also implementing
+Innovations in poor areas and so I want
+
+ align:start position:0%
+Innovations in poor areas and so I want
+ 
+
+ align:start position:0%
+Innovations in poor areas and so I want
+to start off by just giving a brief
+
+ align:start position:0%
+to start off by just giving a brief
+ 
+
+ align:start position:0%
+to start off by just giving a brief
+story so uh about a month ago I went to
+
+ align:start position:0%
+story so uh about a month ago I went to
+ 
+
+ align:start position:0%
+story so uh about a month ago I went to
+Zambia we we one of our pilot sites is
+
+ align:start position:0%
+Zambia we we one of our pilot sites is
+ 
+
+ align:start position:0%
+Zambia we we one of our pilot sites is
+in Zambia and as we were flying to
+
+ align:start position:0%
+in Zambia and as we were flying to
+ 
+
+ align:start position:0%
+in Zambia and as we were flying to
+Zambia we stopped through Washington DC
+
+ align:start position:0%
+Zambia we stopped through Washington DC
+ 
+
+ align:start position:0%
+Zambia we stopped through Washington DC
+and um as we were coming down to the
+
+ align:start position:0%
+and um as we were coming down to the
+ 
+
+ align:start position:0%
+and um as we were coming down to the
+runway could watch the runway everything
+
+ align:start position:0%
+runway could watch the runway everything
+ 
+
+ align:start position:0%
+runway could watch the runway everything
+was going very well and right before we
+
+ align:start position:0%
+was going very well and right before we
+ 
+
+ align:start position:0%
+was going very well and right before we
+were about to land we took off again as
+
+ align:start position:0%
+were about to land we took off again as
+ 
+
+ align:start position:0%
+were about to land we took off again as
+we were going up we turned sharply to
+
+ align:start position:0%
+we were going up we turned sharply to
+ 
+
+ align:start position:0%
+we were going up we turned sharply to
+the left and then we just hit a whole
+
+ align:start position:0%
+the left and then we just hit a whole
+ 
+
+ align:start position:0%
+the left and then we just hit a whole
+bunch of turbulence we started the
+
+ align:start position:0%
+bunch of turbulence we started the
+ 
+
+ align:start position:0%
+bunch of turbulence we started the
+person next to me actually threw up I
+
+ align:start position:0%
+person next to me actually threw up I
+ 
+
+ align:start position:0%
+person next to me actually threw up I
+almost thought I was going to throw up
+
+ align:start position:0%
+almost thought I was going to throw up
+ 
+
+ align:start position:0%
+almost thought I was going to throw up
+uh uh despite all that we started making
+
+ align:start position:0%
+uh uh despite all that we started making
+ 
+
+ align:start position:0%
+uh uh despite all that we started making
+another approach to the to the runway as
+
+ align:start position:0%
+another approach to the to the runway as
+ 
+
+ align:start position:0%
+another approach to the to the runway as
+we were coming down to the runway uh we
+
+ align:start position:0%
+we were coming down to the runway uh we
+ 
+
+ align:start position:0%
+we were coming down to the runway uh we
+made another sharp turn to the left and
+
+ align:start position:0%
+made another sharp turn to the left and
+ 
+
+ align:start position:0%
+made another sharp turn to the left and
+then landed and as we were landing
+
+ align:start position:0%
+then landed and as we were landing
+ 
+
+ align:start position:0%
+then landed and as we were landing
+outside our window we saw these fire
+
+ align:start position:0%
+outside our window we saw these fire
+ 
+
+ align:start position:0%
+outside our window we saw these fire
+trucks kind of lined up right along the
+
+ align:start position:0%
+trucks kind of lined up right along the
+ 
+
+ align:start position:0%
+trucks kind of lined up right along the
+side of the runway and so uh following
+
+ align:start position:0%
+side of the runway and so uh following
+ 
+
+ align:start position:0%
+side of the runway and so uh following
+that the the captain got on the intercom
+
+ align:start position:0%
+that the the captain got on the intercom
+ 
+
+ align:start position:0%
+that the the captain got on the intercom
+and said sorry we had this disruption we
+
+ align:start position:0%
+and said sorry we had this disruption we
+ 
+
+ align:start position:0%
+and said sorry we had this disruption we
+had some trouble with our landing gear
+
+ align:start position:0%
+had some trouble with our landing gear
+ 
+
+ align:start position:0%
+had some trouble with our landing gear
+uh but we used our checklists and
+
+ align:start position:0%
+uh but we used our checklists and
+ 
+
+ align:start position:0%
+uh but we used our checklists and
+everything was fine everything was safe
+
+ align:start position:0%
+everything was fine everything was safe
+ 
+
+ align:start position:0%
+everything was fine everything was safe
+and so uh I give that story because
+
+ align:start position:0%
+and so uh I give that story because
+ 
+
+ align:start position:0%
+and so uh I give that story because
+checklists began kind of being used for
+
+ align:start position:0%
+checklists began kind of being used for
+ 
+
+ align:start position:0%
+checklists began kind of being used for
+safety in the aviation industry so if
+
+ align:start position:0%
+safety in the aviation industry so if
+ 
+
+ align:start position:0%
+safety in the aviation industry so if
+you go back several decades before um
+
+ align:start position:0%
+you go back several decades before um
+ 
+
+ align:start position:0%
+you go back several decades before um
+Pilots were noticing that they were
+
+ align:start position:0%
+Pilots were noticing that they were
+ 
+
+ align:start position:0%
+Pilots were noticing that they were
+involved with very risk a very risky and
+
+ align:start position:0%
+involved with very risk a very risky and
+ 
+
+ align:start position:0%
+involved with very risk a very risky and
+very complex um system and a complex
+
+ align:start position:0%
+very complex um system and a complex
+ 
+
+ align:start position:0%
+very complex um system and a complex
+procedure that had very little margin
+
+ align:start position:0%
+procedure that had very little margin
+ 
+
+ align:start position:0%
+procedure that had very little margin
+for error and for that reason they
+
+ align:start position:0%
+for error and for that reason they
+ 
+
+ align:start position:0%
+for error and for that reason they
+developed these checklists to help not
+
+ align:start position:0%
+developed these checklists to help not
+ 
+
+ align:start position:0%
+developed these checklists to help not
+only remind them but also to help them
+
+ align:start position:0%
+only remind them but also to help them
+ 
+
+ align:start position:0%
+only remind them but also to help them
+use uh tools that may not be um may not
+
+ align:start position:0%
+use uh tools that may not be um may not
+ 
+
+ align:start position:0%
+use uh tools that may not be um may not
+be found used very frequently and so
+
+ align:start position:0%
+be found used very frequently and so
+ 
+
+ align:start position:0%
+be found used very frequently and so
+that we see that in surgery as well if
+
+ align:start position:0%
+that we see that in surgery as well if
+ 
+
+ align:start position:0%
+that we see that in surgery as well if
+you think of a surgical procedure it's
+
+ align:start position:0%
+you think of a surgical procedure it's
+ 
+
+ align:start position:0%
+you think of a surgical procedure it's
+very complex you have very many
+
+ align:start position:0%
+very complex you have very many
+ 
+
+ align:start position:0%
+very complex you have very many
+different procedures uh very me very
+
+ align:start position:0%
+different procedures uh very me very
+ 
+
+ align:start position:0%
+different procedures uh very me very
+different steps throughout that uh but
+
+ align:start position:0%
+different steps throughout that uh but
+ 
+
+ align:start position:0%
+different steps throughout that uh but
+the commonality throughout the whole
+
+ align:start position:0%
+the commonality throughout the whole
+ 
+
+ align:start position:0%
+the commonality throughout the whole
+thing is there's a lot of risk involved
+
+ align:start position:0%
+thing is there's a lot of risk involved
+ 
+
+ align:start position:0%
+thing is there's a lot of risk involved
+with with
+
+ align:start position:0%
+with with
+ 
+
+ align:start position:0%
+with with
+operating and so some might say it's not
+
+ align:start position:0%
+operating and so some might say it's not
+ 
+
+ align:start position:0%
+operating and so some might say it's not
+as difficult as Landing a plane in the
+
+ align:start position:0%
+as difficult as Landing a plane in the
+ 
+
+ align:start position:0%
+as difficult as Landing a plane in the
+Hudson but I think it probably is just
+
+ align:start position:0%
+Hudson but I think it probably is just
+ 
+
+ align:start position:0%
+Hudson but I think it probably is just
+as difficult and so I wanted to start
+
+ align:start position:0%
+as difficult and so I wanted to start
+ 
+
+ align:start position:0%
+as difficult and so I wanted to start
+off give you a little background about
+
+ align:start position:0%
+off give you a little background about
+ 
+
+ align:start position:0%
+off give you a little background about
+what the safe surgery checklist is all
+
+ align:start position:0%
+what the safe surgery checklist is all
+ 
+
+ align:start position:0%
+what the safe surgery checklist is all
+about so a couple years ago the who uh
+
+ align:start position:0%
+about so a couple years ago the who uh
+ 
+
+ align:start position:0%
+about so a couple years ago the who uh
+was considering kind of its aims and in
+
+ align:start position:0%
+was considering kind of its aims and in
+ 
+
+ align:start position:0%
+was considering kind of its aims and in
+considering uh different diseases in the
+
+ align:start position:0%
+considering uh different diseases in the
+ 
+
+ align:start position:0%
+considering uh different diseases in the
+world and so as they took a look at
+
+ align:start position:0%
+world and so as they took a look at
+ 
+
+ align:start position:0%
+world and so as they took a look at
+surgery they found that surgery was
+
+ align:start position:0%
+surgery they found that surgery was
+ 
+
+ align:start position:0%
+surgery they found that surgery was
+actually very prevalent in the in the
+
+ align:start position:0%
+actually very prevalent in the in the
+ 
+
+ align:start position:0%
+actually very prevalent in the in the
+world uh it's estimated about 234
+
+ align:start position:0%
+world uh it's estimated about 234
+ 
+
+ align:start position:0%
+world uh it's estimated about 234
+million procedures are done a year and
+
+ align:start position:0%
+million procedures are done a year and
+ 
+
+ align:start position:0%
+million procedures are done a year and
+this outnumbers the am the number of
+
+ align:start position:0%
+this outnumbers the am the number of
+ 
+
+ align:start position:0%
+this outnumbers the am the number of
+child births as well as a number of new
+
+ align:start position:0%
+child births as well as a number of new
+ 
+
+ align:start position:0%
+child births as well as a number of new
+HIV cases a year and so as a result this
+
+ align:start position:0%
+HIV cases a year and so as a result this
+ 
+
+ align:start position:0%
+HIV cases a year and so as a result this
+focus in looking at surgery developed
+
+ align:start position:0%
+focus in looking at surgery developed
+ 
+
+ align:start position:0%
+focus in looking at surgery developed
+and during this time it was also noted
+
+ align:start position:0%
+and during this time it was also noted
+ 
+
+ align:start position:0%
+and during this time it was also noted
+that a lot of complications that arise
+
+ align:start position:0%
+that a lot of complications that arise
+ 
+
+ align:start position:0%
+that a lot of complications that arise
+from surgery um there were a lot of
+
+ align:start position:0%
+from surgery um there were a lot of
+ 
+
+ align:start position:0%
+from surgery um there were a lot of
+complications that AR Rose from surgery
+
+ align:start position:0%
+complications that AR Rose from surgery
+ 
+
+ align:start position:0%
+complications that AR Rose from surgery
+and in addition to that many of these
+
+ align:start position:0%
+and in addition to that many of these
+ 
+
+ align:start position:0%
+and in addition to that many of these
+were preventable so it's estimated about
+
+ align:start position:0%
+were preventable so it's estimated about
+ 
+
+ align:start position:0%
+were preventable so it's estimated about
+7 million disabling complications were
+
+ align:start position:0%
+7 million disabling complications were
+ 
+
+ align:start position:0%
+7 million disabling complications were
+wi occur a year and in addition to that
+
+ align:start position:0%
+wi occur a year and in addition to that
+ 
+
+ align:start position:0%
+wi occur a year and in addition to that
+about a million of those complications
+
+ align:start position:0%
+about a million of those complications
+ 
+
+ align:start position:0%
+about a million of those complications
+result in death and so that's a lot of
+
+ align:start position:0%
+result in death and so that's a lot of
+ 
+
+ align:start position:0%
+result in death and so that's a lot of
+death that's a lot of
+
+ align:start position:0%
+death that's a lot of
+ 
+
+ align:start position:0%
+death that's a lot of
+complications uh if you look at these
+
+ align:start position:0%
+complications uh if you look at these
+ 
+
+ align:start position:0%
+complications uh if you look at these
+complications it was also ES about 50%
+
+ align:start position:0%
+complications it was also ES about 50%
+ 
+
+ align:start position:0%
+complications it was also ES about 50%
+of these complications were preventable
+
+ align:start position:0%
+of these complications were preventable
+ 
+
+ align:start position:0%
+of these complications were preventable
+uh if you think about wrong site surgery
+
+ align:start position:0%
+uh if you think about wrong site surgery
+ 
+
+ align:start position:0%
+uh if you think about wrong site surgery
+you think well that seems very how could
+
+ align:start position:0%
+you think well that seems very how could
+ 
+
+ align:start position:0%
+you think well that seems very how could
+that ever happened but it's estimated
+
+ align:start position:0%
+that ever happened but it's estimated
+ 
+
+ align:start position:0%
+that ever happened but it's estimated
+about 1500
+
+ align:start position:0%
+about 1500
+ 
+
+ align:start position:0%
+about 1500
+2500 cases of wrong site surgery
+
+ align:start position:0%
+2500 cases of wrong site surgery
+ 
+
+ align:start position:0%
+2500 cases of wrong site surgery
+happened a year in fact my
+
+ align:start position:0%
+happened a year in fact my
+ 
+
+ align:start position:0%
+happened a year in fact my
+grandmother-in-law I guess you'd say uh
+
+ align:start position:0%
+grandmother-in-law I guess you'd say uh
+ 
+
+ align:start position:0%
+grandmother-in-law I guess you'd say uh
+was having carpal tunnel surgery maybe
+
+ align:start position:0%
+was having carpal tunnel surgery maybe
+ 
+
+ align:start position:0%
+was having carpal tunnel surgery maybe
+about five years ago and they actually
+
+ align:start position:0%
+about five years ago and they actually
+ 
+
+ align:start position:0%
+about five years ago and they actually
+did it on the wrong hand wrong wrist and
+
+ align:start position:0%
+did it on the wrong hand wrong wrist and
+ 
+
+ align:start position:0%
+did it on the wrong hand wrong wrist and
+nothing bad happened to her you know it
+
+ align:start position:0%
+nothing bad happened to her you know it
+ 
+
+ align:start position:0%
+nothing bad happened to her you know it
+was she was fine but at the same time it
+
+ align:start position:0%
+was she was fine but at the same time it
+ 
+
+ align:start position:0%
+was she was fine but at the same time it
+required her to go back to surgery again
+
+ align:start position:0%
+required her to go back to surgery again
+ 
+
+ align:start position:0%
+required her to go back to surgery again
+it was embarrassment for the surgeon
+
+ align:start position:0%
+it was embarrassment for the surgeon
+ 
+
+ align:start position:0%
+it was embarrassment for the surgeon
+embarrassment for everyone involved in
+
+ align:start position:0%
+embarrassment for everyone involved in
+ 
+
+ align:start position:0%
+embarrassment for everyone involved in
+addition that was was costly and so
+
+ align:start position:0%
+addition that was was costly and so
+ 
+
+ align:start position:0%
+addition that was was costly and so
+these things happen uh they're not they
+
+ align:start position:0%
+these things happen uh they're not they
+ 
+
+ align:start position:0%
+these things happen uh they're not they
+they're infrequent but they
+
+ align:start position:0%
+they're infrequent but they
+ 
+
+ align:start position:0%
+they're infrequent but they
+happen uh in addition to that if you uh
+
+ align:start position:0%
+happen uh in addition to that if you uh
+ 
+
+ align:start position:0%
+happen uh in addition to that if you uh
+consider essential modering in the
+
+ align:start position:0%
+consider essential modering in the
+ 
+
+ align:start position:0%
+consider essential modering in the
+operating rooms it's estimated that
+
+ align:start position:0%
+operating rooms it's estimated that
+ 
+
+ align:start position:0%
+operating rooms it's estimated that
+about 82% of incidents that occur in
+
+ align:start position:0%
+about 82% of incidents that occur in
+ 
+
+ align:start position:0%
+about 82% of incidents that occur in
+anesthesia can be prevented by having
+
+ align:start position:0%
+anesthesia can be prevented by having
+ 
+
+ align:start position:0%
+anesthesia can be prevented by having
+just basic monitoring systems for
+
+ align:start position:0%
+just basic monitoring systems for
+ 
+
+ align:start position:0%
+just basic monitoring systems for
+example kgs uh blood pressure monitoring
+
+ align:start position:0%
+example kgs uh blood pressure monitoring
+ 
+
+ align:start position:0%
+example kgs uh blood pressure monitoring
+or oxygen monitoring uh antibiotics
+
+ align:start position:0%
+or oxygen monitoring uh antibiotics
+ 
+
+ align:start position:0%
+or oxygen monitoring uh antibiotics
+which also are very uh not very commonly
+
+ align:start position:0%
+which also are very uh not very commonly
+ 
+
+ align:start position:0%
+which also are very uh not very commonly
+used in the developing world uh it's
+
+ align:start position:0%
+used in the developing world uh it's
+ 
+
+ align:start position:0%
+used in the developing world uh it's
+been shown that if antibo are given
+
+ align:start position:0%
+been shown that if antibo are given
+ 
+
+ align:start position:0%
+been shown that if antibo are given
+within an hour of the incision you can
+
+ align:start position:0%
+within an hour of the incision you can
+ 
+
+ align:start position:0%
+within an hour of the incision you can
+reduce the rate of surgical in infection
+
+ align:start position:0%
+reduce the rate of surgical in infection
+ 
+
+ align:start position:0%
+reduce the rate of surgical in infection
+Risk by about
+
+ align:start position:0%
+Risk by about
+ 
+
+ align:start position:0%
+Risk by about
+50% and so one of the things that we've
+
+ align:start position:0%
+50% and so one of the things that we've
+ 
+
+ align:start position:0%
+50% and so one of the things that we've
+we came to think of is that uh really in
+
+ align:start position:0%
+we came to think of is that uh really in
+ 
+
+ align:start position:0%
+we came to think of is that uh really in
+hospitals currently hospitals do most of
+
+ align:start position:0%
+hospitals currently hospitals do most of
+ 
+
+ align:start position:0%
+hospitals currently hospitals do most of
+the things most of the right things most
+
+ align:start position:0%
+the things most of the right things most
+ 
+
+ align:start position:0%
+the things most of the right things most
+of the time for most of their patients
+
+ align:start position:0%
+of the time for most of their patients
+ 
+
+ align:start position:0%
+of the time for most of their patients
+but what we were trying to do was find a
+
+ align:start position:0%
+but what we were trying to do was find a
+ 
+
+ align:start position:0%
+but what we were trying to do was find a
+way in which we can uh
+
+ align:start position:0%
+way in which we can uh
+ 
+
+ align:start position:0%
+way in which we can uh
+help uh hospitals and help providers do
+
+ align:start position:0%
+help uh hospitals and help providers do
+ 
+
+ align:start position:0%
+help uh hospitals and help providers do
+all the things all the right things to
+
+ align:start position:0%
+all the things all the right things to
+ 
+
+ align:start position:0%
+all the things all the right things to
+all their patients all the time and so
+
+ align:start position:0%
+all their patients all the time and so
+ 
+
+ align:start position:0%
+all their patients all the time and so
+that's where checklist came the idea for
+
+ align:start position:0%
+that's where checklist came the idea for
+ 
+
+ align:start position:0%
+that's where checklist came the idea for
+developing a checklist
+
+ align:start position:0%
+developing a checklist
+ 
+
+ align:start position:0%
+developing a checklist
+came and so what I'd like to talk about
+
+ align:start position:0%
+came and so what I'd like to talk about
+ 
+
+ align:start position:0%
+came and so what I'd like to talk about
+today is talk about firstly the surgical
+
+ align:start position:0%
+today is talk about firstly the surgical
+ 
+
+ align:start position:0%
+today is talk about firstly the surgical
+safety checklist and the pilot study
+
+ align:start position:0%
+safety checklist and the pilot study
+ 
+
+ align:start position:0%
+safety checklist and the pilot study
+associated with that that was published
+
+ align:start position:0%
+associated with that that was published
+ 
+
+ align:start position:0%
+associated with that that was published
+back in 2009 and then talk about what
+
+ align:start position:0%
+back in 2009 and then talk about what
+ 
+
+ align:start position:0%
+back in 2009 and then talk about what
+I've been working with directly is
+
+ align:start position:0%
+I've been working with directly is
+ 
+
+ align:start position:0%
+I've been working with directly is
+looking at the surgical safety checklist
+
+ align:start position:0%
+looking at the surgical safety checklist
+ 
+
+ align:start position:0%
+looking at the surgical safety checklist
+imp pulse o symmetry in resource limited
+
+ align:start position:0%
+imp pulse o symmetry in resource limited
+ 
+
+ align:start position:0%
+imp pulse o symmetry in resource limited
+areas and so anyone has anyone here does
+
+ align:start position:0%
+areas and so anyone has anyone here does
+ 
+
+ align:start position:0%
+areas and so anyone has anyone here does
+anyone here a physician we ask the
+
+ align:start position:0%
+anyone here a physician we ask the
+ 
+
+ align:start position:0%
+anyone here a physician we ask the
+Physicians to raise their hands Okay so
+
+ align:start position:0%
+Physicians to raise their hands Okay so
+ 
+
+ align:start position:0%
+Physicians to raise their hands Okay so
+we've got a couple anyone here a
+
+ align:start position:0%
+we've got a couple anyone here a
+ 
+
+ align:start position:0%
+we've got a couple anyone here a
+surgeon okay anyone here ever been opera
+
+ align:start position:0%
+surgeon okay anyone here ever been opera
+ 
+
+ align:start position:0%
+surgeon okay anyone here ever been opera
+on Okay so we've got a lot of people
+
+ align:start position:0%
+on Okay so we've got a lot of people
+ 
+
+ align:start position:0%
+on Okay so we've got a lot of people
+who've been opera on so I'm going to
+
+ align:start position:0%
+who've been opera on so I'm going to
+ 
+
+ align:start position:0%
+who've been opera on so I'm going to
+bring you into the operating room so
+
+ align:start position:0%
+bring you into the operating room so
+ 
+
+ align:start position:0%
+bring you into the operating room so
+this is a little glamorous here this is
+
+ align:start position:0%
+this is a little glamorous here this is
+ 
+
+ align:start position:0%
+this is a little glamorous here this is
+a this is as you recognize ER so this is
+
+ align:start position:0%
+a this is as you recognize ER so this is
+ 
+
+ align:start position:0%
+a this is as you recognize ER so this is
+one of the nicer uh operating rooms in
+
+ align:start position:0%
+one of the nicer uh operating rooms in
+ 
+
+ align:start position:0%
+one of the nicer uh operating rooms in
+the world but I just want you to I just
+
+ align:start position:0%
+the world but I just want you to I just
+ 
+
+ align:start position:0%
+the world but I just want you to I just
+want you to take a look at what's going
+
+ align:start position:0%
+want you to take a look at what's going
+ 
+
+ align:start position:0%
+want you to take a look at what's going
+on here and so to preface this this is
+
+ align:start position:0%
+on here and so to preface this this is
+ 
+
+ align:start position:0%
+on here and so to preface this this is
+uh a kidney transplant uh I believe
+
+ align:start position:0%
+uh a kidney transplant uh I believe
+ 
+
+ align:start position:0%
+uh a kidney transplant uh I believe
+Carter is undergoing a kidney transplant
+
+ align:start position:0%
+Carter is undergoing a kidney transplant
+ 
+
+ align:start position:0%
+Carter is undergoing a kidney transplant
+and so they're using the surgical safety
+
+ align:start position:0%
+and so they're using the surgical safety
+ 
+
+ align:start position:0%
+and so they're using the surgical safety
+checklist so this is an opportunity for
+
+ align:start position:0%
+checklist so this is an opportunity for
+ 
+
+ align:start position:0%
+checklist so this is an opportunity for
+you to be exposed to it then afterwards
+
+ align:start position:0%
+you to be exposed to it then afterwards
+ 
+
+ align:start position:0%
+you to be exposed to it then afterwards
+I'll talk a little bit about different
+
+ align:start position:0%
+I'll talk a little bit about different
+ 
+
+ align:start position:0%
+I'll talk a little bit about different
+parts of it and how it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works that's not too far from what
+
+ align:start position:0%
+works that's not too far from what
+ 
+
+ align:start position:0%
+works that's not too far from what
+happens in the operating room I don't
+
+ align:start position:0%
+happens in the operating room I don't
+ 
+
+ align:start position:0%
+happens in the operating room I don't
+know if any as we mentioned before some
+
+ align:start position:0%
+know if any as we mentioned before some
+ 
+
+ align:start position:0%
+know if any as we mentioned before some
+of you have uh been in medicine but they
+
+ align:start position:0%
+of you have uh been in medicine but they
+ 
+
+ align:start position:0%
+of you have uh been in medicine but they
+operate in theaters surgeons can often
+
+ align:start position:0%
+operate in theaters surgeons can often
+ 
+
+ align:start position:0%
+operate in theaters surgeons can often
+be very um pushy there is often a very
+
+ align:start position:0%
+be very um pushy there is often a very
+ 
+
+ align:start position:0%
+be very um pushy there is often a very
+strict hierarchy you know the the the
+
+ align:start position:0%
+strict hierarchy you know the the the
+ 
+
+ align:start position:0%
+strict hierarchy you know the the the
+the attending surgeon is basically in
+
+ align:start position:0%
+the attending surgeon is basically in
+ 
+
+ align:start position:0%
+the attending surgeon is basically in
+command of the whole operating theater
+
+ align:start position:0%
+command of the whole operating theater
+ 
+
+ align:start position:0%
+command of the whole operating theater
+people as the interns or the nurses may
+
+ align:start position:0%
+people as the interns or the nurses may
+ 
+
+ align:start position:0%
+people as the interns or the nurses may
+have difficult time speaking up so these
+
+ align:start position:0%
+have difficult time speaking up so these
+ 
+
+ align:start position:0%
+have difficult time speaking up so these
+are some of the challenges that happen
+
+ align:start position:0%
+are some of the challenges that happen
+ 
+
+ align:start position:0%
+are some of the challenges that happen
+here so I want to open up to you all
+
+ align:start position:0%
+here so I want to open up to you all
+ 
+
+ align:start position:0%
+here so I want to open up to you all
+what do you
+
+ align:start position:0%
+what do you
+ 
+
+ align:start position:0%
+what do you
+think what are you what are your
+
+ align:start position:0%
+think what are you what are your
+ 
+
+ align:start position:0%
+think what are you what are your
+thoughts about what what happened here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I was glad I wasn't the
+
+ align:start position:0%
+I was glad I wasn't the
+ 
+
+ align:start position:0%
+I was glad I wasn't the
+patient okay
+
+ align:start position:0%
+patient okay
+ 
+
+ align:start position:0%
+patient okay
+why because when I saw you know people
+
+ align:start position:0%
+why because when I saw you know people
+ 
+
+ align:start position:0%
+why because when I saw you know people
+arguing and fighting you know to nervous
+
+ align:start position:0%
+arguing and fighting you know to nervous
+ 
+
+ align:start position:0%
+arguing and fighting you know to nervous
+right can you imagine an environment
+
+ align:start position:0%
+right can you imagine an environment
+ 
+
+ align:start position:0%
+right can you imagine an environment
+where these people are are working
+
+ align:start position:0%
+where these people are are working
+ 
+
+ align:start position:0%
+where these people are are working
+together but not really getting along
+
+ align:start position:0%
+together but not really getting along
+ 
+
+ align:start position:0%
+together but not really getting along
+you think they can really work together
+
+ align:start position:0%
+you think they can really work together
+ 
+
+ align:start position:0%
+you think they can really work together
+very well probably
+
+ align:start position:0%
+very well probably
+ 
+
+ align:start position:0%
+very well probably
+not any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thoughts so I'll I'll start off with a
+
+ align:start position:0%
+thoughts so I'll I'll start off with a
+ 
+
+ align:start position:0%
+thoughts so I'll I'll start off with a
+couple so there are a couple points so
+
+ align:start position:0%
+couple so there are a couple points so
+ 
+
+ align:start position:0%
+couple so there are a couple points so
+one of the the hopes through development
+
+ align:start position:0%
+one of the the hopes through development
+ 
+
+ align:start position:0%
+one of the the hopes through development
+of this checklist was that was to help
+
+ align:start position:0%
+of this checklist was that was to help
+ 
+
+ align:start position:0%
+of this checklist was that was to help
+improve teamwork or communication in the
+
+ align:start position:0%
+improve teamwork or communication in the
+ 
+
+ align:start position:0%
+improve teamwork or communication in the
+operating room and so um you know the
+
+ align:start position:0%
+operating room and so um you know the
+ 
+
+ align:start position:0%
+operating room and so um you know the
+the the introduction of the different
+
+ align:start position:0%
+the the introduction of the different
+ 
+
+ align:start position:0%
+the the introduction of the different
+team members uh that was important so
+
+ align:start position:0%
+team members uh that was important so
+ 
+
+ align:start position:0%
+team members uh that was important so
+that everyone knew who was in the in the
+
+ align:start position:0%
+that everyone knew who was in the in the
+ 
+
+ align:start position:0%
+that everyone knew who was in the in the
+operating room uh there were also
+
+ align:start position:0%
+operating room uh there were also
+ 
+
+ align:start position:0%
+operating room uh there were also
+discussion we'll go I'll show you the
+
+ align:start position:0%
+discussion we'll go I'll show you the
+ 
+
+ align:start position:0%
+discussion we'll go I'll show you the
+checklist later but there are also
+
+ align:start position:0%
+checklist later but there are also
+ 
+
+ align:start position:0%
+checklist later but there are also
+points there that talk about sharing
+
+ align:start position:0%
+points there that talk about sharing
+ 
+
+ align:start position:0%
+points there that talk about sharing
+information about what were the
+
+ align:start position:0%
+information about what were the
+ 
+
+ align:start position:0%
+information about what were the
+important or critical events to
+
+ align:start position:0%
+important or critical events to
+ 
+
+ align:start position:0%
+important or critical events to
+anticipate you heard uh Dr Bon talked
+
+ align:start position:0%
+anticipate you heard uh Dr Bon talked
+ 
+
+ align:start position:0%
+anticipate you heard uh Dr Bon talked
+about the blood loss how much blood loss
+
+ align:start position:0%
+about the blood loss how much blood loss
+ 
+
+ align:start position:0%
+about the blood loss how much blood loss
+what kind of supplies are needed all
+
+ align:start position:0%
+what kind of supplies are needed all
+ 
+
+ align:start position:0%
+what kind of supplies are needed all
+these things are meant to improve the
+
+ align:start position:0%
+these things are meant to improve the
+ 
+
+ align:start position:0%
+these things are meant to improve the
+communication so that events like this
+
+ align:start position:0%
+communication so that events like this
+ 
+
+ align:start position:0%
+communication so that events like this
+even though they may be rare that they
+
+ align:start position:0%
+even though they may be rare that they
+ 
+
+ align:start position:0%
+even though they may be rare that they
+can be prepared for um so communication
+
+ align:start position:0%
+can be prepared for um so communication
+ 
+
+ align:start position:0%
+can be prepared for um so communication
+teamwork also other things such as
+
+ align:start position:0%
+teamwork also other things such as
+ 
+
+ align:start position:0%
+teamwork also other things such as
+standards of care so places such as this
+
+ align:start position:0%
+standards of care so places such as this
+ 
+
+ align:start position:0%
+standards of care so places such as this
+uh pulse oximeters or oxygen monitoring
+
+ align:start position:0%
+uh pulse oximeters or oxygen monitoring
+ 
+
+ align:start position:0%
+uh pulse oximeters or oxygen monitoring
+is always literally always present but
+
+ align:start position:0%
+is always literally always present but
+ 
+
+ align:start position:0%
+is always literally always present but
+other places that we'll talk about later
+
+ align:start position:0%
+other places that we'll talk about later
+ 
+
+ align:start position:0%
+other places that we'll talk about later
+on they're not very common and so having
+
+ align:start position:0%
+on they're not very common and so having
+ 
+
+ align:start position:0%
+on they're not very common and so having
+them available was another point of this
+
+ align:start position:0%
+them available was another point of this
+ 
+
+ align:start position:0%
+them available was another point of this
+checklist for The Who to say these are
+
+ align:start position:0%
+checklist for The Who to say these are
+ 
+
+ align:start position:0%
+checklist for The Who to say these are
+standards that we would like
+
+ align:start position:0%
+standards that we would like
+ 
+
+ align:start position:0%
+standards that we would like
+internationally for people to to make uh
+
+ align:start position:0%
+internationally for people to to make uh
+ 
+
+ align:start position:0%
+internationally for people to to make uh
+their own is there a comment over here
+
+ align:start position:0%
+their own is there a comment over here
+ 
+
+ align:start position:0%
+their own is there a comment over here
+anyone
+
+ align:start position:0%
+anyone
+ 
+
+ align:start position:0%
+anyone
+else okay so this is a little dramatic
+
+ align:start position:0%
+else okay so this is a little dramatic
+ 
+
+ align:start position:0%
+else okay so this is a little dramatic
+but you know here because they had the
+
+ align:start position:0%
+but you know here because they had the
+ 
+
+ align:start position:0%
+but you know here because they had the
+reperfusion solution they were able to
+
+ align:start position:0%
+reperfusion solution they were able to
+ 
+
+ align:start position:0%
+reperfusion solution they were able to
+help preserve that kidney and they were
+
+ align:start position:0%
+help preserve that kidney and they were
+ 
+
+ align:start position:0%
+help preserve that kidney and they were
+able to flush it with a reperfusion
+
+ align:start position:0%
+able to flush it with a reperfusion
+ 
+
+ align:start position:0%
+able to flush it with a reperfusion
+solution and reimplant the kidney so um
+
+ align:start position:0%
+solution and reimplant the kidney so um
+ 
+
+ align:start position:0%
+solution and reimplant the kidney so um
+sure had the append last summer really
+
+ align:start position:0%
+sure had the append last summer really
+ 
+
+ align:start position:0%
+sure had the append last summer really
+in a one of the hospital yeah and uh
+
+ align:start position:0%
+in a one of the hospital yeah and uh
+ 
+
+ align:start position:0%
+in a one of the hospital yeah and uh
+they all got up befor hand checklist
+
+ align:start position:0%
+they all got up befor hand checklist
+ 
+
+ align:start position:0%
+they all got up befor hand checklist
+they bow to the checklist
+
+ align:start position:0%
+they bow to the checklist
+ 
+
+ align:start position:0%
+they bow to the checklist
+great that's very good yeah you know
+
+ align:start position:0%
+great that's very good yeah you know
+ 
+
+ align:start position:0%
+great that's very good yeah you know
+it's uh we'll talk about this a little
+
+ align:start position:0%
+it's uh we'll talk about this a little
+ 
+
+ align:start position:0%
+it's uh we'll talk about this a little
+later this the checklist is not uh a
+
+ align:start position:0%
+later this the checklist is not uh a
+ 
+
+ align:start position:0%
+later this the checklist is not uh a
+huge Technologic Innovation it's
+
+ align:start position:0%
+huge Technologic Innovation it's
+ 
+
+ align:start position:0%
+huge Technologic Innovation it's
+something that people have been using
+
+ align:start position:0%
+something that people have been using
+ 
+
+ align:start position:0%
+something that people have been using
+checklist in their mind for hundreds of
+
+ align:start position:0%
+checklist in their mind for hundreds of
+ 
+
+ align:start position:0%
+checklist in their mind for hundreds of
+years but it's really the formalization
+
+ align:start position:0%
+years but it's really the formalization
+ 
+
+ align:start position:0%
+years but it's really the formalization
+of the checklist and some uh a lot of
+
+ align:start position:0%
+of the checklist and some uh a lot of
+ 
+
+ align:start position:0%
+of the checklist and some uh a lot of
+thinking put into what items going to
+
+ align:start position:0%
+thinking put into what items going to
+ 
+
+ align:start position:0%
+thinking put into what items going to
+the checklist that's really been
+
+ align:start position:0%
+the checklist that's really been
+ 
+
+ align:start position:0%
+the checklist that's really been
+somewhat novel here so this is a this is
+
+ align:start position:0%
+somewhat novel here so this is a this is
+ 
+
+ align:start position:0%
+somewhat novel here so this is a this is
+a picture of the surgical safety
+
+ align:start position:0%
+a picture of the surgical safety
+ 
+
+ align:start position:0%
+a picture of the surgical safety
+checklist as it stands uh I think it's a
+
+ align:start position:0%
+checklist as it stands uh I think it's a
+ 
+
+ align:start position:0%
+checklist as it stands uh I think it's a
+second version that the who has
+
+ align:start position:0%
+second version that the who has
+ 
+
+ align:start position:0%
+second version that the who has
+published and so it really is made up of
+
+ align:start position:0%
+published and so it really is made up of
+ 
+
+ align:start position:0%
+published and so it really is made up of
+three different portions there's uh
+
+ align:start position:0%
+three different portions there's uh
+ 
+
+ align:start position:0%
+three different portions there's uh
+they're called pause points so the first
+
+ align:start position:0%
+they're called pause points so the first
+ 
+
+ align:start position:0%
+they're called pause points so the first
+pause point is before the patient goes
+
+ align:start position:0%
+pause point is before the patient goes
+ 
+
+ align:start position:0%
+pause point is before the patient goes
+to sleep or before the induction of
+
+ align:start position:0%
+to sleep or before the induction of
+ 
+
+ align:start position:0%
+to sleep or before the induction of
+anesthesia the second pause point is
+
+ align:start position:0%
+anesthesia the second pause point is
+ 
+
+ align:start position:0%
+anesthesia the second pause point is
+before the incision of skin and the
+
+ align:start position:0%
+before the incision of skin and the
+ 
+
+ align:start position:0%
+before the incision of skin and the
+third pause point is right before the
+
+ align:start position:0%
+third pause point is right before the
+ 
+
+ align:start position:0%
+third pause point is right before the
+patient leaves a room and so these were
+
+ align:start position:0%
+patient leaves a room and so these were
+ 
+
+ align:start position:0%
+patient leaves a room and so these were
+thought to be three critical points
+
+ align:start position:0%
+thought to be three critical points
+ 
+
+ align:start position:0%
+thought to be three critical points
+points in the operation where we could
+
+ align:start position:0%
+points in the operation where we could
+ 
+
+ align:start position:0%
+points in the operation where we could
+have time to stop and also where if we
+
+ align:start position:0%
+have time to stop and also where if we
+ 
+
+ align:start position:0%
+have time to stop and also where if we
+pause to do these things we could
+
+ align:start position:0%
+pause to do these things we could
+ 
+
+ align:start position:0%
+pause to do these things we could
+prevent
+
+ align:start position:0%
+prevent
+ 
+
+ align:start position:0%
+prevent
+complications uh if you go through here
+
+ align:start position:0%
+complications uh if you go through here
+ 
+
+ align:start position:0%
+complications uh if you go through here
+um the the checklist is to be meant is
+
+ align:start position:0%
+um the the checklist is to be meant is
+ 
+
+ align:start position:0%
+um the the checklist is to be meant is
+meant to be used by all members of the
+
+ align:start position:0%
+meant to be used by all members of the
+ 
+
+ align:start position:0%
+meant to be used by all members of the
+team surgeons and anesthetists as well
+
+ align:start position:0%
+team surgeons and anesthetists as well
+ 
+
+ align:start position:0%
+team surgeons and anesthetists as well
+as nurses and so uh there are different
+
+ align:start position:0%
+as nurses and so uh there are different
+ 
+
+ align:start position:0%
+as nurses and so uh there are different
+portions that kind of focus on different
+
+ align:start position:0%
+portions that kind of focus on different
+ 
+
+ align:start position:0%
+portions that kind of focus on different
+groups but in general all portions can
+
+ align:start position:0%
+groups but in general all portions can
+ 
+
+ align:start position:0%
+groups but in general all portions can
+be done with all parts of the team I'm a
+
+ align:start position:0%
+be done with all parts of the team I'm a
+ 
+
+ align:start position:0%
+be done with all parts of the team I'm a
+little surprised if this is uh coming
+
+ align:start position:0%
+little surprised if this is uh coming
+ 
+
+ align:start position:0%
+little surprised if this is uh coming
+from the who um
+
+ align:start position:0%
+from the who um
+ 
+
+ align:start position:0%
+from the who um
+is is it is it clear that these
+
+ align:start position:0%
+is is it is it clear that these
+ 
+
+ align:start position:0%
+is is it is it clear that these
+checklists are um more stand the right
+
+ align:start position:0%
+checklists are um more stand the right
+ 
+
+ align:start position:0%
+checklists are um more stand the right
+thing for all International situations
+
+ align:start position:0%
+thing for all International situations
+ 
+
+ align:start position:0%
+thing for all International situations
+um that's a good question so there was a
+
+ align:start position:0%
+um that's a good question so there was a
+ 
+
+ align:start position:0%
+um that's a good question so there was a
+lot of debate about what exactly to
+
+ align:start position:0%
+lot of debate about what exactly to
+ 
+
+ align:start position:0%
+lot of debate about what exactly to
+include on the checklist as you can
+
+ align:start position:0%
+include on the checklist as you can
+ 
+
+ align:start position:0%
+include on the checklist as you can
+imagine a a operating room here in
+
+ align:start position:0%
+imagine a a operating room here in
+ 
+
+ align:start position:0%
+imagine a a operating room here in
+Boston is very different from one in
+
+ align:start position:0%
+Boston is very different from one in
+ 
+
+ align:start position:0%
+Boston is very different from one in
+luaka Zambia and they have very
+
+ align:start position:0%
+luaka Zambia and they have very
+ 
+
+ align:start position:0%
+luaka Zambia and they have very
+different needs as well as very
+
+ align:start position:0%
+different needs as well as very
+ 
+
+ align:start position:0%
+different needs as well as very
+different cultures and so a lot of uh
+
+ align:start position:0%
+different cultures and so a lot of uh
+ 
+
+ align:start position:0%
+different cultures and so a lot of uh
+work was done to make them uh
+
+ align:start position:0%
+work was done to make them uh
+ 
+
+ align:start position:0%
+work was done to make them uh
+generalizable and so you see there are
+
+ align:start position:0%
+generalizable and so you see there are
+ 
+
+ align:start position:0%
+generalizable and so you see there are
+some things that here are used in Boston
+
+ align:start position:0%
+some things that here are used in Boston
+ 
+
+ align:start position:0%
+some things that here are used in Boston
+that aren't necessarily used in Zambia
+
+ align:start position:0%
+that aren't necessarily used in Zambia
+ 
+
+ align:start position:0%
+that aren't necessarily used in Zambia
+and there's some things used in Zambia
+
+ align:start position:0%
+and there's some things used in Zambia
+ 
+
+ align:start position:0%
+and there's some things used in Zambia
+that aren't used here and so I you can't
+
+ align:start position:0%
+that aren't used here and so I you can't
+ 
+
+ align:start position:0%
+that aren't used here and so I you can't
+I don't actually have it on this slide I
+
+ align:start position:0%
+I don't actually have it on this slide I
+ 
+
+ align:start position:0%
+I don't actually have it on this slide I
+think prya has it on her slides but uh
+
+ align:start position:0%
+think prya has it on her slides but uh
+ 
+
+ align:start position:0%
+think prya has it on her slides but uh
+one of the points of this is was this is
+
+ align:start position:0%
+one of the points of this is was this is
+ 
+
+ align:start position:0%
+one of the points of this is was this is
+a framework for people to use and uh
+
+ align:start position:0%
+a framework for people to use and uh
+ 
+
+ align:start position:0%
+a framework for people to use and uh
+people were encouraged to modify as they
+
+ align:start position:0%
+people were encouraged to modify as they
+ 
+
+ align:start position:0%
+people were encouraged to modify as they
+as they needed for their own specific
+
+ align:start position:0%
+as they needed for their own specific
+ 
+
+ align:start position:0%
+as they needed for their own specific
+sites so to move backwards so what was
+
+ align:start position:0%
+sites so to move backwards so what was
+ 
+
+ align:start position:0%
+sites so to move backwards so what was
+who's interest in this so who is a large
+
+ align:start position:0%
+who's interest in this so who is a large
+ 
+
+ align:start position:0%
+who's interest in this so who is a large
+uh multi- intern ational organization
+
+ align:start position:0%
+uh multi- intern ational organization
+ 
+
+ align:start position:0%
+uh multi- intern ational organization
+and if you're thinking like they are
+
+ align:start position:0%
+and if you're thinking like they are
+ 
+
+ align:start position:0%
+and if you're thinking like they are
+what they wanted was something that was
+
+ align:start position:0%
+what they wanted was something that was
+ 
+
+ align:start position:0%
+what they wanted was something that was
+applicable to All Nations something that
+
+ align:start position:0%
+applicable to All Nations something that
+ 
+
+ align:start position:0%
+applicable to All Nations something that
+was cheap and something that was easy to
+
+ align:start position:0%
+was cheap and something that was easy to
+ 
+
+ align:start position:0%
+was cheap and something that was easy to
+use I if you look at most of their
+
+ align:start position:0%
+use I if you look at most of their
+ 
+
+ align:start position:0%
+use I if you look at most of their
+interventions uh they kind of Follow
+
+ align:start position:0%
+interventions uh they kind of Follow
+ 
+
+ align:start position:0%
+interventions uh they kind of Follow
+That same model A lot of it is
+
+ align:start position:0%
+That same model A lot of it is
+ 
+
+ align:start position:0%
+That same model A lot of it is
+information based a lot of it is uh
+
+ align:start position:0%
+information based a lot of it is uh
+ 
+
+ align:start position:0%
+information based a lot of it is uh
+disseminating information as well and so
+
+ align:start position:0%
+disseminating information as well and so
+ 
+
+ align:start position:0%
+disseminating information as well and so
+this is another way you know all you
+
+ align:start position:0%
+this is another way you know all you
+ 
+
+ align:start position:0%
+this is another way you know all you
+have to do is print on a piece of paper
+
+ align:start position:0%
+have to do is print on a piece of paper
+ 
+
+ align:start position:0%
+have to do is print on a piece of paper
+send it in email and there are these uh
+
+ align:start position:0%
+send it in email and there are these uh
+ 
+
+ align:start position:0%
+send it in email and there are these uh
+you kind of have you've given them the
+
+ align:start position:0%
+you kind of have you've given them the
+ 
+
+ align:start position:0%
+you kind of have you've given them the
+framework um the difficult part is
+
+ align:start position:0%
+framework um the difficult part is
+ 
+
+ align:start position:0%
+framework um the difficult part is
+actually implementing and we'll get to
+
+ align:start position:0%
+actually implementing and we'll get to
+ 
+
+ align:start position:0%
+actually implementing and we'll get to
+that point a little later that's a good
+
+ align:start position:0%
+that point a little later that's a good
+ 
+
+ align:start position:0%
+that point a little later that's a good
+question again I forgot to mention the
+
+ align:start position:0%
+question again I forgot to mention the
+ 
+
+ align:start position:0%
+question again I forgot to mention the
+very beginning that if you do have
+
+ align:start position:0%
+very beginning that if you do have
+ 
+
+ align:start position:0%
+very beginning that if you do have
+questions please feel free to to to
+
+ align:start position:0%
+questions please feel free to to to
+ 
+
+ align:start position:0%
+questions please feel free to to to
+raise your hands and
+
+ align:start position:0%
+raise your hands and
+ 
+
+ align:start position:0%
+raise your hands and
+interrupt um so this is a little bit
+
+ align:start position:0%
+interrupt um so this is a little bit
+ 
+
+ align:start position:0%
+interrupt um so this is a little bit
+background about the checklist and you
+
+ align:start position:0%
+background about the checklist and you
+ 
+
+ align:start position:0%
+background about the checklist and you
+can see the items there are only 19
+
+ align:start position:0%
+can see the items there are only 19
+ 
+
+ align:start position:0%
+can see the items there are only 19
+items um one of the concerns was that
+
+ align:start position:0%
+items um one of the concerns was that
+ 
+
+ align:start position:0%
+items um one of the concerns was that
+that using the checklist would really
+
+ align:start position:0%
+that using the checklist would really
+ 
+
+ align:start position:0%
+that using the checklist would really
+delay the the operation or increase the
+
+ align:start position:0%
+delay the the operation or increase the
+ 
+
+ align:start position:0%
+delay the the operation or increase the
+time it would take to operate and it
+
+ align:start position:0%
+time it would take to operate and it
+ 
+
+ align:start position:0%
+time it would take to operate and it
+only takes about two or three minutes
+
+ align:start position:0%
+only takes about two or three minutes
+ 
+
+ align:start position:0%
+only takes about two or three minutes
+for the whole entire checklist to be
+
+ align:start position:0%
+for the whole entire checklist to be
+ 
+
+ align:start position:0%
+for the whole entire checklist to be
+used um and so for that you know for for
+
+ align:start position:0%
+used um and so for that you know for for
+ 
+
+ align:start position:0%
+used um and so for that you know for for
+the amount of time it takes it's really
+
+ align:start position:0%
+the amount of time it takes it's really
+ 
+
+ align:start position:0%
+the amount of time it takes it's really
+minimal compared to the length of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case the che specific to that patient
+
+ align:start position:0%
+case the che specific to that patient
+ 
+
+ align:start position:0%
+case the che specific to that patient
+and that operation this is more General
+
+ align:start position:0%
+and that operation this is more General
+ 
+
+ align:start position:0%
+and that operation this is more General
+so is it is that the standard that this
+
+ align:start position:0%
+so is it is that the standard that this
+ 
+
+ align:start position:0%
+so is it is that the standard that this
+one is just general the CP was uh so the
+
+ align:start position:0%
+one is just general the CP was uh so the
+ 
+
+ align:start position:0%
+one is just general the CP was uh so the
+clip was actually pretty accurate um so
+
+ align:start position:0%
+clip was actually pretty accurate um so
+ 
+
+ align:start position:0%
+clip was actually pretty accurate um so
+they do a specific yeah so they ask what
+
+ align:start position:0%
+they do a specific yeah so they ask what
+ 
+
+ align:start position:0%
+they do a specific yeah so they ask what
+procedure is going on they talk as you
+
+ align:start position:0%
+procedure is going on they talk as you
+ 
+
+ align:start position:0%
+procedure is going on they talk as you
+can see uh the first question is you
+
+ align:start position:0%
+can see uh the first question is you
+ 
+
+ align:start position:0%
+can see uh the first question is you
+know has a patient identity site
+
+ align:start position:0%
+know has a patient identity site
+ 
+
+ align:start position:0%
+know has a patient identity site
+procedure and consent been uh confirmed
+
+ align:start position:0%
+procedure and consent been uh confirmed
+ 
+
+ align:start position:0%
+procedure and consent been uh confirmed
+and so uh it's known to the team what
+
+ align:start position:0%
+and so uh it's known to the team what
+ 
+
+ align:start position:0%
+and so uh it's known to the team what
+the procedure was I think that there may
+
+ align:start position:0%
+the procedure was I think that there may
+ 
+
+ align:start position:0%
+the procedure was I think that there may
+have been a couple
+
+ align:start position:0%
+have been a couple
+ 
+
+ align:start position:0%
+have been a couple
+um uh I think if I remember correctly in
+
+ align:start position:0%
+um uh I think if I remember correctly in
+ 
+
+ align:start position:0%
+um uh I think if I remember correctly in
+the in the video clip they they didn't
+
+ align:start position:0%
+the in the video clip they they didn't
+ 
+
+ align:start position:0%
+the in the video clip they they didn't
+deviate too much from what we were using
+
+ align:start position:0%
+deviate too much from what we were using
+ 
+
+ align:start position:0%
+deviate too much from what we were using
+they didn't show all the different parts
+
+ align:start position:0%
+they didn't show all the different parts
+ 
+
+ align:start position:0%
+they didn't show all the different parts
+of it but uh the parts that they used
+
+ align:start position:0%
+of it but uh the parts that they used
+ 
+
+ align:start position:0%
+of it but uh the parts that they used
+didn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deviate okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh you might ask so does this little
+
+ align:start position:0%
+so uh you might ask so does this little
+ 
+
+ align:start position:0%
+so uh you might ask so does this little
+piece of paper really
+
+ align:start position:0%
+piece of paper really
+ 
+
+ align:start position:0%
+piece of paper really
+work uh how how can we really know that
+
+ align:start position:0%
+work uh how how can we really know that
+ 
+
+ align:start position:0%
+work uh how how can we really know that
+bringing this piece of paper into
+
+ align:start position:0%
+bringing this piece of paper into
+ 
+
+ align:start position:0%
+bringing this piece of paper into
+different operating rooms that what kind
+
+ align:start position:0%
+different operating rooms that what kind
+ 
+
+ align:start position:0%
+different operating rooms that what kind
+of effect does this have and so the who
+
+ align:start position:0%
+of effect does this have and so the who
+ 
+
+ align:start position:0%
+of effect does this have and so the who
+before they were a before they put their
+
+ align:start position:0%
+before they were a before they put their
+ 
+
+ align:start position:0%
+before they were a before they put their
+stamp of approval on this document they
+
+ align:start position:0%
+stamp of approval on this document they
+ 
+
+ align:start position:0%
+stamp of approval on this document they
+wanted us to test it and so uh firstly
+
+ align:start position:0%
+wanted us to test it and so uh firstly
+ 
+
+ align:start position:0%
+wanted us to test it and so uh firstly
+the the concept was developed uh
+
+ align:start position:0%
+the the concept was developed uh
+ 
+
+ align:start position:0%
+the the concept was developed uh
+multiple rounds of
+
+ align:start position:0%
+multiple rounds of
+ 
+
+ align:start position:0%
+multiple rounds of
+uh revision with uh International
+
+ align:start position:0%
+uh revision with uh International
+ 
+
+ align:start position:0%
+uh revision with uh International
+consultations were were done to to decid
+
+ align:start position:0%
+consultations were were done to to decid
+ 
+
+ align:start position:0%
+consultations were were done to to decid
+on what items to keep on the checklist
+
+ align:start position:0%
+on what items to keep on the checklist
+ 
+
+ align:start position:0%
+on what items to keep on the checklist
+and then it was decided to do a pilot
+
+ align:start position:0%
+and then it was decided to do a pilot
+ 
+
+ align:start position:0%
+and then it was decided to do a pilot
+study so this pilot study involved eight
+
+ align:start position:0%
+study so this pilot study involved eight
+ 
+
+ align:start position:0%
+study so this pilot study involved eight
+different sites uh in very different
+
+ align:start position:0%
+different sites uh in very different
+ 
+
+ align:start position:0%
+different sites uh in very different
+settings you had settings in Seattle
+
+ align:start position:0%
+settings you had settings in Seattle
+ 
+
+ align:start position:0%
+settings you had settings in Seattle
+Washington as well as Tanzania all the
+
+ align:start position:0%
+Washington as well as Tanzania all the
+ 
+
+ align:start position:0%
+Washington as well as Tanzania all the
+way to India and so these were very
+
+ align:start position:0%
+way to India and so these were very
+ 
+
+ align:start position:0%
+way to India and so these were very
+diverse very different populations very
+
+ align:start position:0%
+diverse very different populations very
+ 
+
+ align:start position:0%
+diverse very different populations very
+different settings very different income
+
+ align:start position:0%
+different settings very different income
+ 
+
+ align:start position:0%
+different settings very different income
+levels and they were testing all these
+
+ align:start position:0%
+levels and they were testing all these
+ 
+
+ align:start position:0%
+levels and they were testing all these
+different sites
+
+ align:start position:0%
+different sites
+ 
+
+ align:start position:0%
+different sites
+and so the punch line is that they were
+
+ align:start position:0%
+and so the punch line is that they were
+ 
+
+ align:start position:0%
+and so the punch line is that they were
+found to reduce uh more post-operative
+
+ align:start position:0%
+found to reduce uh more post-operative
+ 
+
+ align:start position:0%
+found to reduce uh more post-operative
+complications by almost nearly a third
+
+ align:start position:0%
+complications by almost nearly a third
+ 
+
+ align:start position:0%
+complications by almost nearly a third
+and so um to break it down even more uh
+
+ align:start position:0%
+and so um to break it down even more uh
+ 
+
+ align:start position:0%
+and so um to break it down even more uh
+death was decreased from 1.5% as a whole
+
+ align:start position:0%
+death was decreased from 1.5% as a whole
+ 
+
+ align:start position:0%
+death was decreased from 1.5% as a whole
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+0.8% complications were decreased by
+
+ align:start position:0%
+0.8% complications were decreased by
+ 
+
+ align:start position:0%
+0.8% complications were decreased by
+nearly uh 40% seral site infection was
+
+ align:start position:0%
+nearly uh 40% seral site infection was
+ 
+
+ align:start position:0%
+nearly uh 40% seral site infection was
+also decreased by almost 50% and
+
+ align:start position:0%
+also decreased by almost 50% and
+ 
+
+ align:start position:0%
+also decreased by almost 50% and
+unplanned return to the O operating room
+
+ align:start position:0%
+unplanned return to the O operating room
+ 
+
+ align:start position:0%
+unplanned return to the O operating room
+decreased from 2.4 to 1.8% all of which
+
+ align:start position:0%
+decreased from 2.4 to 1.8% all of which
+ 
+
+ align:start position:0%
+decreased from 2.4 to 1.8% all of which
+were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+significant um in addition you might ask
+
+ align:start position:0%
+significant um in addition you might ask
+ 
+
+ align:start position:0%
+significant um in addition you might ask
+well does this really work in uh High
+
+ align:start position:0%
+well does this really work in uh High
+ 
+
+ align:start position:0%
+well does this really work in uh High
+income countries for example here in
+
+ align:start position:0%
+income countries for example here in
+ 
+
+ align:start position:0%
+income countries for example here in
+Boston if we were to use this where we
+
+ align:start position:0%
+Boston if we were to use this where we
+ 
+
+ align:start position:0%
+Boston if we were to use this where we
+already have relatively high standards
+
+ align:start position:0%
+already have relatively high standards
+ 
+
+ align:start position:0%
+already have relatively high standards
+of care are we really seeing a uh impact
+
+ align:start position:0%
+of care are we really seeing a uh impact
+ 
+
+ align:start position:0%
+of care are we really seeing a uh impact
+by using these pretty basic uh
+
+ align:start position:0%
+by using these pretty basic uh
+ 
+
+ align:start position:0%
+by using these pretty basic uh
+principles a lot of these principles are
+
+ align:start position:0%
+principles a lot of these principles are
+ 
+
+ align:start position:0%
+principles a lot of these principles are
+already used in a lot of operating rooms
+
+ align:start position:0%
+already used in a lot of operating rooms
+ 
+
+ align:start position:0%
+already used in a lot of operating rooms
+and so how much of this will really what
+
+ align:start position:0%
+and so how much of this will really what
+ 
+
+ align:start position:0%
+and so how much of this will really what
+kind of effect and so we we've broken it
+
+ align:start position:0%
+kind of effect and so we we've broken it
+ 
+
+ align:start position:0%
+kind of effect and so we we've broken it
+down to high income and low and middle
+
+ align:start position:0%
+down to high income and low and middle
+ 
+
+ align:start position:0%
+down to high income and low and middle
+inome countries and um we see a
+
+ align:start position:0%
+inome countries and um we see a
+ 
+
+ align:start position:0%
+inome countries and um we see a
+difference in complications that's
+
+ align:start position:0%
+difference in complications that's
+ 
+
+ align:start position:0%
+difference in complications that's
+statistically significant in regards to
+
+ align:start position:0%
+statistically significant in regards to
+ 
+
+ align:start position:0%
+statistically significant in regards to
+change in death rates uh we don't see
+
+ align:start position:0%
+change in death rates uh we don't see
+ 
+
+ align:start position:0%
+change in death rates uh we don't see
+statistical statistical significance in
+
+ align:start position:0%
+statistical statistical significance in
+ 
+
+ align:start position:0%
+statistical statistical significance in
+high income regions but there's a trend
+
+ align:start position:0%
+high income regions but there's a trend
+ 
+
+ align:start position:0%
+high income regions but there's a trend
+towards uh improvement from 0.9% to 6%
+
+ align:start position:0%
+towards uh improvement from 0.9% to 6%
+ 
+
+ align:start position:0%
+towards uh improvement from 0.9% to 6%
+and so one of the difficulties is
+
+ align:start position:0%
+and so one of the difficulties is
+ 
+
+ align:start position:0%
+and so one of the difficulties is
+there's so so few uh deaths in these
+
+ align:start position:0%
+there's so so few uh deaths in these
+ 
+
+ align:start position:0%
+there's so so few uh deaths in these
+high income countries that if we
+
+ align:start position:0%
+high income countries that if we
+ 
+
+ align:start position:0%
+high income countries that if we
+actually had larger numbers we may we
+
+ align:start position:0%
+actually had larger numbers we may we
+ 
+
+ align:start position:0%
+actually had larger numbers we may we
+may be able to show a significant
+
+ align:start position:0%
+may be able to show a significant
+ 
+
+ align:start position:0%
+may be able to show a significant
+difference and so this is kind of where
+
+ align:start position:0%
+difference and so this is kind of where
+ 
+
+ align:start position:0%
+difference and so this is kind of where
+we're at now so these studies were
+
+ align:start position:0%
+we're at now so these studies were
+ 
+
+ align:start position:0%
+we're at now so these studies were
+published in 2009 the the pilots were
+
+ align:start position:0%
+published in 2009 the the pilots were
+ 
+
+ align:start position:0%
+published in 2009 the the pilots were
+done in 2008 and then as we are now all
+
+ align:start position:0%
+done in 2008 and then as we are now all
+ 
+
+ align:start position:0%
+done in 2008 and then as we are now all
+these gold crosses are areas where the
+
+ align:start position:0%
+these gold crosses are areas where the
+ 
+
+ align:start position:0%
+these gold crosses are areas where the
+checklist is being actively used and so
+
+ align:start position:0%
+checklist is being actively used and so
+ 
+
+ align:start position:0%
+checklist is being actively used and so
+you can see it spans all across all the
+
+ align:start position:0%
+you can see it spans all across all the
+ 
+
+ align:start position:0%
+you can see it spans all across all the
+continents except for Antarctica we
+
+ align:start position:0%
+continents except for Antarctica we
+ 
+
+ align:start position:0%
+continents except for Antarctica we
+don't have one there yet uh but in
+
+ align:start position:0%
+don't have one there yet uh but in
+ 
+
+ align:start position:0%
+don't have one there yet uh but in
+multiple countries multiple languages
+
+ align:start position:0%
+multiple countries multiple languages
+ 
+
+ align:start position:0%
+multiple countries multiple languages
+multiple settings and so it's being used
+
+ align:start position:0%
+multiple settings and so it's being used
+ 
+
+ align:start position:0%
+multiple settings and so it's being used
+worldwide um I saw a question over here
+
+ align:start position:0%
+worldwide um I saw a question over here
+ 
+
+ align:start position:0%
+worldwide um I saw a question over here
+um have you or has anyone at any point
+
+ align:start position:0%
+um have you or has anyone at any point
+ 
+
+ align:start position:0%
+um have you or has anyone at any point
+uh analyzed
+
+ align:start position:0%
+uh analyzed
+ 
+
+ align:start position:0%
+uh analyzed
+items on the check list might be most
+
+ align:start position:0%
+items on the check list might be most
+ 
+
+ align:start position:0%
+items on the check list might be most
+critical to so that's a good point so so
+
+ align:start position:0%
+critical to so that's a good point so so
+ 
+
+ align:start position:0%
+critical to so that's a good point so so
+a lot of these complications are
+
+ align:start position:0%
+a lot of these complications are
+ 
+
+ align:start position:0%
+a lot of these complications are
+infectious complications so we saw
+
+ align:start position:0%
+infectious complications so we saw
+ 
+
+ align:start position:0%
+infectious complications so we saw
+before um surgical sight infection a lot
+
+ align:start position:0%
+before um surgical sight infection a lot
+ 
+
+ align:start position:0%
+before um surgical sight infection a lot
+of these surgical sight infections were
+
+ align:start position:0%
+of these surgical sight infections were
+ 
+
+ align:start position:0%
+of these surgical sight infections were
+also if you had any of these
+
+ align:start position:0%
+also if you had any of these
+ 
+
+ align:start position:0%
+also if you had any of these
+complications a lot of them were
+
+ align:start position:0%
+complications a lot of them were
+ 
+
+ align:start position:0%
+complications a lot of them were
+surgical sight infections pneumonias
+
+ align:start position:0%
+surgical sight infections pneumonias
+ 
+
+ align:start position:0%
+surgical sight infections pneumonias
+things that were considered infectious
+
+ align:start position:0%
+things that were considered infectious
+ 
+
+ align:start position:0%
+things that were considered infectious
+and so um it's uh we we've done some
+
+ align:start position:0%
+and so um it's uh we we've done some
+ 
+
+ align:start position:0%
+and so um it's uh we we've done some
+subanalysis and it so looks like that
+
+ align:start position:0%
+subanalysis and it so looks like that
+ 
+
+ align:start position:0%
+subanalysis and it so looks like that
+there has been changes in the Infectious
+
+ align:start position:0%
+there has been changes in the Infectious
+ 
+
+ align:start position:0%
+there has been changes in the Infectious
+complications as well as the
+
+ align:start position:0%
+complications as well as the
+ 
+
+ align:start position:0%
+complications as well as the
+non-infectious complications so U one of
+
+ align:start position:0%
+non-infectious complications so U one of
+ 
+
+ align:start position:0%
+non-infectious complications so U one of
+the criticisms we've had is that well
+
+ align:start position:0%
+the criticisms we've had is that well
+ 
+
+ align:start position:0%
+the criticisms we've had is that well
+all this is because you're uh asking
+
+ align:start position:0%
+all this is because you're uh asking
+ 
+
+ align:start position:0%
+all this is because you're uh asking
+people to give antibiotics on time you
+
+ align:start position:0%
+people to give antibiotics on time you
+ 
+
+ align:start position:0%
+people to give antibiotics on time you
+know something that's not being done
+
+ align:start position:0%
+know something that's not being done
+ 
+
+ align:start position:0%
+know something that's not being done
+very frequently sure that that may be a
+
+ align:start position:0%
+very frequently sure that that may be a
+ 
+
+ align:start position:0%
+very frequently sure that that may be a
+large component of it but I think that
+
+ align:start position:0%
+large component of it but I think that
+ 
+
+ align:start position:0%
+large component of it but I think that
+in addition to that um uh there are
+
+ align:start position:0%
+in addition to that um uh there are
+ 
+
+ align:start position:0%
+in addition to that um uh there are
+other parts of the checklist that are uh
+
+ align:start position:0%
+other parts of the checklist that are uh
+ 
+
+ align:start position:0%
+other parts of the checklist that are uh
+contributing to the effect I think
+
+ align:start position:0%
+contributing to the effect I think
+ 
+
+ align:start position:0%
+contributing to the effect I think
+antibiotics are playing a huge part of
+
+ align:start position:0%
+antibiotics are playing a huge part of
+ 
+
+ align:start position:0%
+antibiotics are playing a huge part of
+it I think some of the monitoring
+
+ align:start position:0%
+it I think some of the monitoring
+ 
+
+ align:start position:0%
+it I think some of the monitoring
+devices that we are encouraging people
+
+ align:start position:0%
+devices that we are encouraging people
+ 
+
+ align:start position:0%
+devices that we are encouraging people
+to use through the checklist are are are
+
+ align:start position:0%
+to use through the checklist are are are
+ 
+
+ align:start position:0%
+to use through the checklist are are are
+um contributing to the effect as well so
+
+ align:start position:0%
+um contributing to the effect as well so
+ 
+
+ align:start position:0%
+um contributing to the effect as well so
+it's possible maybe with five items on
+
+ align:start position:0%
+it's possible maybe with five items on
+ 
+
+ align:start position:0%
+it's possible maybe with five items on
+the checklist you can get 95% of the
+
+ align:start position:0%
+the checklist you can get 95% of the
+ 
+
+ align:start position:0%
+the checklist you can get 95% of the
+results not that that's good or bad just
+
+ align:start position:0%
+results not that that's good or bad just
+ 
+
+ align:start position:0%
+results not that that's good or bad just
+I think you're I think that may be right
+
+ align:start position:0%
+I think you're I think that may be right
+ 
+
+ align:start position:0%
+I think you're I think that may be right
+uh but I think there's probably more of
+
+ align:start position:0%
+uh but I think there's probably more of
+ 
+
+ align:start position:0%
+uh but I think there's probably more of
+kind of a the teamwork communication bit
+
+ align:start position:0%
+kind of a the teamwork communication bit
+ 
+
+ align:start position:0%
+kind of a the teamwork communication bit
+that's going into it so you know if you
+
+ align:start position:0%
+that's going into it so you know if you
+ 
+
+ align:start position:0%
+that's going into it so you know if you
+look at unplanned return to the
+
+ align:start position:0%
+look at unplanned return to the
+ 
+
+ align:start position:0%
+look at unplanned return to the
+operation operating room I don't know
+
+ align:start position:0%
+operation operating room I don't know
+ 
+
+ align:start position:0%
+operation operating room I don't know
+exactly what part of the check
+
+ align:start position:0%
+exactly what part of the check
+ 
+
+ align:start position:0%
+exactly what part of the check
+contributes to that you know what part
+
+ align:start position:0%
+contributes to that you know what part
+ 
+
+ align:start position:0%
+contributes to that you know what part
+of this of these 19 items really
+
+ align:start position:0%
+of this of these 19 items really
+ 
+
+ align:start position:0%
+of this of these 19 items really
+prevents the need to go back to the
+
+ align:start position:0%
+prevents the need to go back to the
+ 
+
+ align:start position:0%
+prevents the need to go back to the
+operating room don't really know but
+
+ align:start position:0%
+operating room don't really know but
+ 
+
+ align:start position:0%
+operating room don't really know but
+what it does suggest is maybe we're
+
+ align:start position:0%
+what it does suggest is maybe we're
+ 
+
+ align:start position:0%
+what it does suggest is maybe we're
+doing the operations better uh in
+
+ align:start position:0%
+doing the operations better uh in
+ 
+
+ align:start position:0%
+doing the operations better uh in
+general and so it's maybe some of that
+
+ align:start position:0%
+general and so it's maybe some of that
+ 
+
+ align:start position:0%
+general and so it's maybe some of that
+and this is something that's very
+
+ align:start position:0%
+and this is something that's very
+ 
+
+ align:start position:0%
+and this is something that's very
+difficult to capture scientifically but
+
+ align:start position:0%
+difficult to capture scientifically but
+ 
+
+ align:start position:0%
+difficult to capture scientifically but
+I think there's there there's something
+
+ align:start position:0%
+I think there's there there's something
+ 
+
+ align:start position:0%
+I think there's there there's something
+else behind the checklist than just the
+
+ align:start position:0%
+else behind the checklist than just the
+ 
+
+ align:start position:0%
+else behind the checklist than just the
+items on the checklist it's actually the
+
+ align:start position:0%
+items on the checklist it's actually the
+ 
+
+ align:start position:0%
+items on the checklist it's actually the
+process of using this and I think in my
+
+ align:start position:0%
+process of using this and I think in my
+ 
+
+ align:start position:0%
+process of using this and I think in my
+experience
+
+ align:start position:0%
+experience
+ 
+
+ align:start position:0%
+experience
+it's actually this idea of uh we want to
+
+ align:start position:0%
+it's actually this idea of uh we want to
+ 
+
+ align:start position:0%
+it's actually this idea of uh we want to
+use this we're interested in quality
+
+ align:start position:0%
+use this we're interested in quality
+ 
+
+ align:start position:0%
+use this we're interested in quality
+improvement and so therefore uh that
+
+ align:start position:0%
+improvement and so therefore uh that
+ 
+
+ align:start position:0%
+improvement and so therefore uh that
+kind of culture that's changed by using
+
+ align:start position:0%
+kind of culture that's changed by using
+ 
+
+ align:start position:0%
+kind of culture that's changed by using
+this type of Tool uh is what kind of
+
+ align:start position:0%
+this type of Tool uh is what kind of
+ 
+
+ align:start position:0%
+this type of Tool uh is what kind of
+adds to that that effect I think this
+
+ align:start position:0%
+adds to that that effect I think this
+ 
+
+ align:start position:0%
+adds to that that effect I think this
+goes a lot towards uh some of the
+
+ align:start position:0%
+goes a lot towards uh some of the
+ 
+
+ align:start position:0%
+goes a lot towards uh some of the
+technologies that you've talked about
+
+ align:start position:0%
+technologies that you've talked about
+ 
+
+ align:start position:0%
+technologies that you've talked about
+here uh Technologies are great uh and
+
+ align:start position:0%
+here uh Technologies are great uh and
+ 
+
+ align:start position:0%
+here uh Technologies are great uh and
+they do help uh but really you need the
+
+ align:start position:0%
+they do help uh but really you need the
+ 
+
+ align:start position:0%
+they do help uh but really you need the
+people using them to have an interest in
+
+ align:start position:0%
+people using them to have an interest in
+ 
+
+ align:start position:0%
+people using them to have an interest in
+them you need the people who are using
+
+ align:start position:0%
+them you need the people who are using
+ 
+
+ align:start position:0%
+them you need the people who are using
+them to want to improve and so that kind
+
+ align:start position:0%
+them to want to improve and so that kind
+ 
+
+ align:start position:0%
+them to want to improve and so that kind
+of catalyst I think makes a big
+
+ align:start position:0%
+of catalyst I think makes a big
+ 
+
+ align:start position:0%
+of catalyst I think makes a big
+difference go here in you don't think
+
+ align:start position:0%
+difference go here in you don't think
+ 
+
+ align:start position:0%
+difference go here in you don't think
+you'll getv approval for Le one
+
+ align:start position:0%
+you'll getv approval for Le one
+ 
+
+ align:start position:0%
+you'll getv approval for Le one
+out uh I think we could um I think we
+
+ align:start position:0%
+out uh I think we could um I think we
+ 
+
+ align:start position:0%
+out uh I think we could um I think we
+could if you leave a portion out yeah I
+
+ align:start position:0%
+could if you leave a portion out yeah I
+ 
+
+ align:start position:0%
+could if you leave a portion out yeah I
+think you'd have to leave 19 portions
+
+ align:start position:0%
+think you'd have to leave 19 portions
+ 
+
+ align:start position:0%
+think you'd have to leave 19 portions
+out or just do 19 separate experiments
+
+ align:start position:0%
+out or just do 19 separate experiments
+ 
+
+ align:start position:0%
+out or just do 19 separate experiments
+but um uh we could I'll go here and then
+
+ align:start position:0%
+but um uh we could I'll go here and then
+ 
+
+ align:start position:0%
+but um uh we could I'll go here and then
+here are you seeing a difference in how
+
+ align:start position:0%
+here are you seeing a difference in how
+ 
+
+ align:start position:0%
+here are you seeing a difference in how
+receptive people are depending on their
+
+ align:start position:0%
+receptive people are depending on their
+ 
+
+ align:start position:0%
+receptive people are depending on their
+age
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ad being more to this we are certainly
+
+ align:start position:0%
+ad being more to this we are certainly
+ 
+
+ align:start position:0%
+ad being more to this we are certainly
+seeing a difference in uh the I guess
+
+ align:start position:0%
+seeing a difference in uh the I guess
+ 
+
+ align:start position:0%
+seeing a difference in uh the I guess
+the buyin
+
+ align:start position:0%
+the buyin
+ 
+
+ align:start position:0%
+the buyin
+into uh the checklist and you've
+
+ align:start position:0%
+into uh the checklist and you've
+ 
+
+ align:start position:0%
+into uh the checklist and you've
+probably read about some of this you
+
+ align:start position:0%
+probably read about some of this you
+ 
+
+ align:start position:0%
+probably read about some of this you
+know you have your laggards you have
+
+ align:start position:0%
+know you have your laggards you have
+ 
+
+ align:start position:0%
+know you have your laggards you have
+your early adopters and you have kind of
+
+ align:start position:0%
+your early adopters and you have kind of
+ 
+
+ align:start position:0%
+your early adopters and you have kind of
+the people in between and so we
+
+ align:start position:0%
+the people in between and so we
+ 
+
+ align:start position:0%
+the people in between and so we
+certainly have a lot of early adopters
+
+ align:start position:0%
+certainly have a lot of early adopters
+ 
+
+ align:start position:0%
+certainly have a lot of early adopters
+but in a lot of these hospitals
+
+ align:start position:0%
+but in a lot of these hospitals
+ 
+
+ align:start position:0%
+but in a lot of these hospitals
+especially in some of these limited
+
+ align:start position:0%
+especially in some of these limited
+ 
+
+ align:start position:0%
+especially in some of these limited
+resource areas there are a lot of
+
+ align:start position:0%
+resource areas there are a lot of
+ 
+
+ align:start position:0%
+resource areas there are a lot of
+laggards who are are comfortable with
+
+ align:start position:0%
+laggards who are are comfortable with
+ 
+
+ align:start position:0%
+laggards who are are comfortable with
+what they're doing they are don't want
+
+ align:start position:0%
+what they're doing they are don't want
+ 
+
+ align:start position:0%
+what they're doing they are don't want
+to change and uh and in general it seems
+
+ align:start position:0%
+to change and uh and in general it seems
+ 
+
+ align:start position:0%
+to change and uh and in general it seems
+that people who are beginning their
+
+ align:start position:0%
+that people who are beginning their
+ 
+
+ align:start position:0%
+that people who are beginning their
+training and may have more kind of fear
+
+ align:start position:0%
+training and may have more kind of fear
+ 
+
+ align:start position:0%
+training and may have more kind of fear
+in the operating room they're the people
+
+ align:start position:0%
+in the operating room they're the people
+ 
+
+ align:start position:0%
+in the operating room they're the people
+who seem to to grasp onto these tools
+
+ align:start position:0%
+who seem to to grasp onto these tools
+ 
+
+ align:start position:0%
+who seem to to grasp onto these tools
+more I just thinking that it's an
+
+ align:start position:0%
+more I just thinking that it's an
+ 
+
+ align:start position:0%
+more I just thinking that it's an
+example where we've talked before about
+
+ align:start position:0%
+example where we've talked before about
+ 
+
+ align:start position:0%
+example where we've talked before about
+being able to collect data accurately in
+
+ align:start position:0%
+being able to collect data accurately in
+ 
+
+ align:start position:0%
+being able to collect data accurately in
+clinical settings as being one of the
+
+ align:start position:0%
+clinical settings as being one of the
+ 
+
+ align:start position:0%
+clinical settings as being one of the
+most important things you can do with
+
+ align:start position:0%
+most important things you can do with
+ 
+
+ align:start position:0%
+most important things you can do with
+the information system because that
+
+ align:start position:0%
+the information system because that
+ 
+
+ align:start position:0%
+the information system because that
+gives you some of the background data
+
+ align:start position:0%
+gives you some of the background data
+ 
+
+ align:start position:0%
+gives you some of the background data
+that lets you answer one of these
+
+ align:start position:0%
+that lets you answer one of these
+ 
+
+ align:start position:0%
+that lets you answer one of these
+questions so you you know what are the
+
+ align:start position:0%
+questions so you you know what are the
+ 
+
+ align:start position:0%
+questions so you you know what are the
+ethics of doing a you know Le one out
+
+ align:start position:0%
+ethics of doing a you know Le one out
+ 
+
+ align:start position:0%
+ethics of doing a you know Le one out
+type of study which you know is
+
+ align:start position:0%
+type of study which you know is
+ 
+
+ align:start position:0%
+type of study which you know is
+certainly one of the more definitive
+
+ align:start position:0%
+certainly one of the more definitive
+ 
+
+ align:start position:0%
+certainly one of the more definitive
+ways of doing this if you knew more
+
+ align:start position:0%
+ways of doing this if you knew more
+ 
+
+ align:start position:0%
+ways of doing this if you knew more
+about the nature Publications more about
+
+ align:start position:0%
+about the nature Publications more about
+ 
+
+ align:start position:0%
+about the nature Publications more about
+the kind of things that were going on
+
+ align:start position:0%
+the kind of things that were going on
+ 
+
+ align:start position:0%
+the kind of things that were going on
+with routine cical cases with with a a
+
+ align:start position:0%
+with routine cical cases with with a a
+ 
+
+ align:start position:0%
+with routine cical cases with with a a
+simple but you know useful core data set
+
+ align:start position:0%
+simple but you know useful core data set
+ 
+
+ align:start position:0%
+simple but you know useful core data set
+then I think that would be much very
+
+ align:start position:0%
+then I think that would be much very
+ 
+
+ align:start position:0%
+then I think that would be much very
+much easier to to look at this and see
+
+ align:start position:0%
+much easier to to look at this and see
+ 
+
+ align:start position:0%
+much easier to to look at this and see
+whether you actually want to revise the
+
+ align:start position:0%
+whether you actually want to revise the
+ 
+
+ align:start position:0%
+whether you actually want to revise the
+chck in other ways adding something
+
+ align:start position:0%
+chck in other ways adding something
+ 
+
+ align:start position:0%
+chck in other ways adding something
+right I I think that's a key point you
+
+ align:start position:0%
+right I I think that's a key point you
+ 
+
+ align:start position:0%
+right I I think that's a key point you
+know data collection we'll get I I'll
+
+ align:start position:0%
+know data collection we'll get I I'll
+ 
+
+ align:start position:0%
+know data collection we'll get I I'll
+have a couple slides later on to talk
+
+ align:start position:0%
+have a couple slides later on to talk
+ 
+
+ align:start position:0%
+have a couple slides later on to talk
+about the importance of data collection
+
+ align:start position:0%
+about the importance of data collection
+ 
+
+ align:start position:0%
+about the importance of data collection
+but uh it certainly is uh helps you
+
+ align:start position:0%
+but uh it certainly is uh helps you
+ 
+
+ align:start position:0%
+but uh it certainly is uh helps you
+understand what's going on here a lot
+
+ align:start position:0%
+understand what's going on here a lot
+ 
+
+ align:start position:0%
+understand what's going on here a lot
+better I just wanted to respond to
+
+ align:start position:0%
+better I just wanted to respond to
+ 
+
+ align:start position:0%
+better I just wanted to respond to
+questions one about an item the check
+
+ align:start position:0%
+questions one about an item the check
+ 
+
+ align:start position:0%
+questions one about an item the check
+and two sort of attrition Factor perhaps
+
+ align:start position:0%
+and two sort of attrition Factor perhaps
+ 
+
+ align:start position:0%
+and two sort of attrition Factor perhaps
+we just have to wait for the to go
+
+ align:start position:0%
+we just have to wait for the to go
+ 
+
+ align:start position:0%
+we just have to wait for the to go
+and actually if you looked at the um
+
+ align:start position:0%
+and actually if you looked at the um
+ 
+
+ align:start position:0%
+and actually if you looked at the um
+Korean I think it was Korean a they had
+
+ align:start position:0%
+Korean I think it was Korean a they had
+ 
+
+ align:start position:0%
+Korean I think it was Korean a they had
+they had Che in place pilot have been
+
+ align:start position:0%
+they had Che in place pilot have been
+ 
+
+ align:start position:0%
+they had Che in place pilot have been
+around since the 1930s and they were
+
+ align:start position:0%
+around since the 1930s and they were
+ 
+
+ align:start position:0%
+around since the 1930s and they were
+having lots of accidents and when they
+
+ align:start position:0%
+having lots of accidents and when they
+ 
+
+ align:start position:0%
+having lots of accidents and when they
+analyed
+
+ align:start position:0%
+analyed
+ 
+
+ align:start position:0%
+analyed
+long story short thing americ go over to
+
+ align:start position:0%
+long story short thing americ go over to
+ 
+
+ align:start position:0%
+long story short thing americ go over to
+Korea and say well what's going
+
+ align:start position:0%
+Korea and say well what's going
+ 
+
+ align:start position:0%
+Korea and say well what's going
+on and his solution was I think you
+
+ align:start position:0%
+on and his solution was I think you
+ 
+
+ align:start position:0%
+on and his solution was I think you
+should speak
+
+ align:start position:0%
+should speak
+ 
+
+ align:start position:0%
+should speak
+English that's your solution to our
+
+ align:start position:0%
+English that's your solution to our
+ 
+
+ align:start position:0%
+English that's your solution to our
+accidents you know you arrogant person
+
+ align:start position:0%
+accidents you know you arrogant person
+ 
+
+ align:start position:0%
+accidents you know you arrogant person
+and he said no what's happening is
+
+ align:start position:0%
+and he said no what's happening is
+ 
+
+ align:start position:0%
+and he said no what's happening is
+you're bringing your culture into the
+
+ align:start position:0%
+you're bringing your culture into the
+ 
+
+ align:start position:0%
+you're bringing your culture into the
+CIT of your language and the culture is
+
+ align:start position:0%
+CIT of your language and the culture is
+ 
+
+ align:start position:0%
+CIT of your language and the culture is
+very hierarchical so the pilot is the
+
+ align:start position:0%
+very hierarchical so the pilot is the
+ 
+
+ align:start position:0%
+very hierarchical so the pilot is the
+old one he's experienc and the co-pilot
+
+ align:start position:0%
+old one he's experienc and the co-pilot
+ 
+
+ align:start position:0%
+old one he's experienc and the co-pilot
+even though he's supposed to be able to
+
+ align:start position:0%
+even though he's supposed to be able to
+ 
+
+ align:start position:0%
+even though he's supposed to be able to
+correct him can't because well you know
+
+ align:start position:0%
+correct him can't because well you know
+ 
+
+ align:start position:0%
+correct him can't because well you know
+old and if you just speak English you're
+
+ align:start position:0%
+old and if you just speak English you're
+ 
+
+ align:start position:0%
+old and if you just speak English you're
+changing the culture in the and
+
+ align:start position:0%
+changing the culture in the and
+ 
+
+ align:start position:0%
+changing the culture in the and
+it's that empowering the younger persons
+
+ align:start position:0%
+it's that empowering the younger persons
+ 
+
+ align:start position:0%
+it's that empowering the younger persons
+it's empowering the nurses in the who
+
+ align:start position:0%
+it's empowering the nurses in the who
+ 
+
+ align:start position:0%
+it's empowering the nurses in the who
+you know it's been shown who won't say
+
+ align:start position:0%
+you know it's been shown who won't say
+ 
+
+ align:start position:0%
+you know it's been shown who won't say
+see said to Happ they say kind of
+
+ align:start position:0%
+see said to Happ they say kind of
+ 
+
+ align:start position:0%
+see said to Happ they say kind of
+whisper surge just didn't hear so I
+
+ align:start position:0%
+whisper surge just didn't hear so I
+ 
+
+ align:start position:0%
+whisper surge just didn't hear so I
+think that teamwork and culture
+
+ align:start position:0%
+think that teamwork and culture
+ 
+
+ align:start position:0%
+think that teamwork and culture
+component is critical to the checklist
+
+ align:start position:0%
+component is critical to the checklist
+ 
+
+ align:start position:0%
+component is critical to the checklist
+and it's really critical to the people
+
+ align:start position:0%
+and it's really critical to the people
+ 
+
+ align:start position:0%
+and it's really critical to the people
+who aren't empowered um because it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good question go ahead the
+
+ align:start position:0%
+good question go ahead the
+ 
+
+ align:start position:0%
+good question go ahead the
+issues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+supp
+
+ align:start position:0%
+supp
+ 
+
+ align:start position:0%
+supp
+yeah um so the you know uh in general in
+
+ align:start position:0%
+yeah um so the you know uh in general in
+ 
+
+ align:start position:0%
+yeah um so the you know uh in general in
+my experience so the uh the
+
+ align:start position:0%
+my experience so the uh the
+ 
+
+ align:start position:0%
+my experience so the uh the
+institution do you mean you mean as a as
+
+ align:start position:0%
+institution do you mean you mean as a as
+ 
+
+ align:start position:0%
+institution do you mean you mean as a as
+a hospital as a whole what would be the
+
+ align:start position:0%
+a hospital as a whole what would be the
+ 
+
+ align:start position:0%
+a hospital as a whole what would be the
+so in general I I found that people are
+
+ align:start position:0%
+so in general I I found that people are
+ 
+
+ align:start position:0%
+so in general I I found that people are
+really supportive of this from admin
+
+ align:start position:0%
+really supportive of this from admin
+ 
+
+ align:start position:0%
+really supportive of this from admin
+ative point of view it costs very little
+
+ align:start position:0%
+ative point of view it costs very little
+ 
+
+ align:start position:0%
+ative point of view it costs very little
+uh all you have to do is ask the
+
+ align:start position:0%
+uh all you have to do is ask the
+ 
+
+ align:start position:0%
+uh all you have to do is ask the
+surgeons nurses anesthesiologists to do
+
+ align:start position:0%
+surgeons nurses anesthesiologists to do
+ 
+
+ align:start position:0%
+surgeons nurses anesthesiologists to do
+it and so but that's been the challenge
+
+ align:start position:0%
+it and so but that's been the challenge
+ 
+
+ align:start position:0%
+it and so but that's been the challenge
+finding uh ways to ask people to change
+
+ align:start position:0%
+finding uh ways to ask people to change
+ 
+
+ align:start position:0%
+finding uh ways to ask people to change
+the culture of the of the practice there
+
+ align:start position:0%
+the culture of the of the practice there
+ 
+
+ align:start position:0%
+the culture of the of the practice there
+and so really uh the idea of accepting
+
+ align:start position:0%
+and so really uh the idea of accepting
+ 
+
+ align:start position:0%
+and so really uh the idea of accepting
+it seems easy but actually practicing it
+
+ align:start position:0%
+it seems easy but actually practicing it
+ 
+
+ align:start position:0%
+it seems easy but actually practicing it
+seems
+
+ align:start position:0%
+seems
+ 
+
+ align:start position:0%
+seems
+difficult and so kind of getting Buy in
+
+ align:start position:0%
+difficult and so kind of getting Buy in
+ 
+
+ align:start position:0%
+difficult and so kind of getting Buy in
+from all your laggards all and really
+
+ align:start position:0%
+from all your laggards all and really
+ 
+
+ align:start position:0%
+from all your laggards all and really
+all it takes is a couple people to
+
+ align:start position:0%
+all it takes is a couple people to
+ 
+
+ align:start position:0%
+all it takes is a couple people to
+badmouth it to make it a a a difficult
+
+ align:start position:0%
+badmouth it to make it a a a difficult
+ 
+
+ align:start position:0%
+badmouth it to make it a a a difficult
+experience are there places with kind of
+
+ align:start position:0%
+experience are there places with kind of
+ 
+
+ align:start position:0%
+experience are there places with kind of
+institutional incentives for using the
+
+ align:start position:0%
+institutional incentives for using the
+ 
+
+ align:start position:0%
+institutional incentives for using the
+checklist so there are and I'm G to talk
+
+ align:start position:0%
+checklist so there are and I'm G to talk
+ 
+
+ align:start position:0%
+checklist so there are and I'm G to talk
+a little bit about one of those places
+
+ align:start position:0%
+a little bit about one of those places
+ 
+
+ align:start position:0%
+a little bit about one of those places
+and I I'll I'll uh I would say there are
+
+ align:start position:0%
+and I I'll I'll uh I would say there are
+ 
+
+ align:start position:0%
+and I I'll I'll uh I would say there are
+some places that are very used to having
+
+ align:start position:0%
+some places that are very used to having
+ 
+
+ align:start position:0%
+some places that are very used to having
+top down Direction and so in one of the
+
+ align:start position:0%
+top down Direction and so in one of the
+ 
+
+ align:start position:0%
+top down Direction and so in one of the
+countries I uh I'm going to talk about
+
+ align:start position:0%
+countries I uh I'm going to talk about
+ 
+
+ align:start position:0%
+countries I uh I'm going to talk about
+mdova they're a East former Soviet Union
+
+ align:start position:0%
+mdova they're a East former Soviet Union
+ 
+
+ align:start position:0%
+mdova they're a East former Soviet Union
+uh country uh and they're kind of used
+
+ align:start position:0%
+uh country uh and they're kind of used
+ 
+
+ align:start position:0%
+uh country uh and they're kind of used
+to the dictum comes from the top and we
+
+ align:start position:0%
+to the dictum comes from the top and we
+ 
+
+ align:start position:0%
+to the dictum comes from the top and we
+do what they say whereas in Zambia which
+
+ align:start position:0%
+do what they say whereas in Zambia which
+ 
+
+ align:start position:0%
+do what they say whereas in Zambia which
+I'll talk about a little later we're
+
+ align:start position:0%
+I'll talk about a little later we're
+ 
+
+ align:start position:0%
+I'll talk about a little later we're
+having a difficult time there because um
+
+ align:start position:0%
+having a difficult time there because um
+ 
+
+ align:start position:0%
+having a difficult time there because um
+even though that's the case there is a
+
+ align:start position:0%
+even though that's the case there is a
+ 
+
+ align:start position:0%
+even though that's the case there is a
+lot of uh uh this hierarchy thing is uh
+
+ align:start position:0%
+lot of uh uh this hierarchy thing is uh
+ 
+
+ align:start position:0%
+lot of uh uh this hierarchy thing is uh
+I don't know there's just a lot of
+
+ align:start position:0%
+I don't know there's just a lot of
+ 
+
+ align:start position:0%
+I don't know there's just a lot of
+bureaucracy there and so it doesn't seem
+
+ align:start position:0%
+bureaucracy there and so it doesn't seem
+ 
+
+ align:start position:0%
+bureaucracy there and so it doesn't seem
+to be moving as as as uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smoothly uh so this is uh one of our
+
+ align:start position:0%
+smoothly uh so this is uh one of our
+ 
+
+ align:start position:0%
+smoothly uh so this is uh one of our
+checklists that we're using in the
+
+ align:start position:0%
+checklists that we're using in the
+ 
+
+ align:start position:0%
+checklists that we're using in the
+University teaching Hospital in laka
+
+ align:start position:0%
+University teaching Hospital in laka
+ 
+
+ align:start position:0%
+University teaching Hospital in laka
+Zambia and I'm going to move now to
+
+ align:start position:0%
+Zambia and I'm going to move now to
+ 
+
+ align:start position:0%
+Zambia and I'm going to move now to
+we've talked about the checklist as a
+
+ align:start position:0%
+we've talked about the checklist as a
+ 
+
+ align:start position:0%
+we've talked about the checklist as a
+whole kind of briefly now I'm going to
+
+ align:start position:0%
+whole kind of briefly now I'm going to
+ 
+
+ align:start position:0%
+whole kind of briefly now I'm going to
+move to kind of limited resource areas
+
+ align:start position:0%
+move to kind of limited resource areas
+ 
+
+ align:start position:0%
+move to kind of limited resource areas
+or or lower middle inome lower income
+
+ align:start position:0%
+or or lower middle inome lower income
+ 
+
+ align:start position:0%
+or or lower middle inome lower income
+countries and so uh as I mentioned there
+
+ align:start position:0%
+countries and so uh as I mentioned there
+ 
+
+ align:start position:0%
+countries and so uh as I mentioned there
+are 19 items these are all the same 19
+
+ align:start position:0%
+are 19 items these are all the same 19
+ 
+
+ align:start position:0%
+are 19 items these are all the same 19
+items but one of the difficulties with
+
+ align:start position:0%
+items but one of the difficulties with
+ 
+
+ align:start position:0%
+items but one of the difficulties with
+this is if the who wants to support this
+
+ align:start position:0%
+this is if the who wants to support this
+ 
+
+ align:start position:0%
+this is if the who wants to support this
+what do you do about these this portion
+
+ align:start position:0%
+what do you do about these this portion
+ 
+
+ align:start position:0%
+what do you do about these this portion
+here PSO symmetry so uh puls oximeter is
+
+ align:start position:0%
+here PSO symmetry so uh puls oximeter is
+ 
+
+ align:start position:0%
+here PSO symmetry so uh puls oximeter is
+a is a uh technology developed in the
+
+ align:start position:0%
+a is a uh technology developed in the
+ 
+
+ align:start position:0%
+a is a uh technology developed in the
+80s uh that is used to measure oxygen
+
+ align:start position:0%
+80s uh that is used to measure oxygen
+ 
+
+ align:start position:0%
+80s uh that is used to measure oxygen
+saturation or the level of oxygen in the
+
+ align:start position:0%
+saturation or the level of oxygen in the
+ 
+
+ align:start position:0%
+saturation or the level of oxygen in the
+blood and so when you're under general
+
+ align:start position:0%
+blood and so when you're under general
+ 
+
+ align:start position:0%
+blood and so when you're under general
+anesthesia uh you're sedated and you may
+
+ align:start position:0%
+anesthesia uh you're sedated and you may
+ 
+
+ align:start position:0%
+anesthesia uh you're sedated and you may
+not breathe as well and so as a result
+
+ align:start position:0%
+not breathe as well and so as a result
+ 
+
+ align:start position:0%
+not breathe as well and so as a result
+your oxygen level decreases if your
+
+ align:start position:0%
+your oxygen level decreases if your
+ 
+
+ align:start position:0%
+your oxygen level decreases if your
+oxygen level is low enough you can have
+
+ align:start position:0%
+oxygen level is low enough you can have
+ 
+
+ align:start position:0%
+oxygen level is low enough you can have
+your your heart can stop you can have
+
+ align:start position:0%
+your your heart can stop you can have
+ 
+
+ align:start position:0%
+your your heart can stop you can have
+other uh injuries as well some people
+
+ align:start position:0%
+other uh injuries as well some people
+ 
+
+ align:start position:0%
+other uh injuries as well some people
+might say that your um your ability to
+
+ align:start position:0%
+might say that your um your ability to
+ 
+
+ align:start position:0%
+might say that your um your ability to
+heal your wounds or your your profusion
+
+ align:start position:0%
+heal your wounds or your your profusion
+ 
+
+ align:start position:0%
+heal your wounds or your your profusion
+to different parts of your body is is is
+
+ align:start position:0%
+to different parts of your body is is is
+ 
+
+ align:start position:0%
+to different parts of your body is is is
+worse and so uh these little boxes I
+
+ align:start position:0%
+worse and so uh these little boxes I
+ 
+
+ align:start position:0%
+worse and so uh these little boxes I
+have a picture um actually that's not
+
+ align:start position:0%
+have a picture um actually that's not
+ 
+
+ align:start position:0%
+have a picture um actually that's not
+the picture I want but they're they're
+
+ align:start position:0%
+the picture I want but they're they're
+ 
+
+ align:start position:0%
+the picture I want but they're they're
+quite expensive in the United States if
+
+ align:start position:0%
+quite expensive in the United States if
+ 
+
+ align:start position:0%
+quite expensive in the United States if
+you're if you were to buy one it's about
+
+ align:start position:0%
+you're if you were to buy one it's about
+ 
+
+ align:start position:0%
+you're if you were to buy one it's about
+$1,200 per unit so if you can imagine in
+
+ align:start position:0%
+$1,200 per unit so if you can imagine in
+ 
+
+ align:start position:0%
+$1,200 per unit so if you can imagine in
+the this teaching hospital that has 12
+
+ align:start position:0%
+the this teaching hospital that has 12
+ 
+
+ align:start position:0%
+the this teaching hospital that has 12
+operating rooms uh to buy 12 of them is
+
+ align:start position:0%
+operating rooms uh to buy 12 of them is
+ 
+
+ align:start position:0%
+operating rooms uh to buy 12 of them is
+quite a significant resource intense
+
+ align:start position:0%
+quite a significant resource intense
+ 
+
+ align:start position:0%
+quite a significant resource intense
+task for them to do and so the who um
+
+ align:start position:0%
+task for them to do and so the who um
+ 
+
+ align:start position:0%
+task for them to do and so the who um
+what we set out to do is to show that
+
+ align:start position:0%
+what we set out to do is to show that
+ 
+
+ align:start position:0%
+what we set out to do is to show that
+poock symmetry was actually something
+
+ align:start position:0%
+poock symmetry was actually something
+ 
+
+ align:start position:0%
+poock symmetry was actually something
+that was important to for Ministries and
+
+ align:start position:0%
+that was important to for Ministries and
+ 
+
+ align:start position:0%
+that was important to for Ministries and
+for uh countries to consider how to make
+
+ align:start position:0%
+for uh countries to consider how to make
+ 
+
+ align:start position:0%
+for uh countries to consider how to make
+these more accessible for their for
+
+ align:start position:0%
+these more accessible for their for
+ 
+
+ align:start position:0%
+these more accessible for their for
+their uh countries in addition to that
+
+ align:start position:0%
+their uh countries in addition to that
+ 
+
+ align:start position:0%
+their uh countries in addition to that
+the who is has uh worked as a
+
+ align:start position:0%
+the who is has uh worked as a
+ 
+
+ align:start position:0%
+the who is has uh worked as a
+procurement uh body to procure uh drugs
+
+ align:start position:0%
+procurement uh body to procure uh drugs
+ 
+
+ align:start position:0%
+procurement uh body to procure uh drugs
+as well as devices and so the thought
+
+ align:start position:0%
+as well as devices and so the thought
+ 
+
+ align:start position:0%
+as well as devices and so the thought
+was if we can show that this is actually
+
+ align:start position:0%
+was if we can show that this is actually
+ 
+
+ align:start position:0%
+was if we can show that this is actually
+a very important thing that this package
+
+ align:start position:0%
+a very important thing that this package
+ 
+
+ align:start position:0%
+a very important thing that this package
+of the checklist and pulso symmetry
+
+ align:start position:0%
+of the checklist and pulso symmetry
+ 
+
+ align:start position:0%
+of the checklist and pulso symmetry
+would be worth the who investing their
+
+ align:start position:0%
+would be worth the who investing their
+ 
+
+ align:start position:0%
+would be worth the who investing their
+their time and efforts into developing a
+
+ align:start position:0%
+their time and efforts into developing a
+ 
+
+ align:start position:0%
+their time and efforts into developing a
+procurement of these to to provide for
+
+ align:start position:0%
+procurement of these to to provide for
+ 
+
+ align:start position:0%
+procurement of these to to provide for
+low-income countries and so this is a
+
+ align:start position:0%
+low-income countries and so this is a
+ 
+
+ align:start position:0%
+low-income countries and so this is a
+picture of the one of the new o Suites
+
+ align:start position:0%
+picture of the one of the new o Suites
+ 
+
+ align:start position:0%
+picture of the one of the new o Suites
+in the bring Woman's Hospital very nice
+
+ align:start position:0%
+in the bring Woman's Hospital very nice
+ 
+
+ align:start position:0%
+in the bring Woman's Hospital very nice
+you can see the the flat screen TVs you
+
+ align:start position:0%
+you can see the the flat screen TVs you
+ 
+
+ align:start position:0%
+you can see the the flat screen TVs you
+can get uh there Bose speakers in there
+
+ align:start position:0%
+can get uh there Bose speakers in there
+ 
+
+ align:start position:0%
+can get uh there Bose speakers in there
+so if you want some music you can listen
+
+ align:start position:0%
+so if you want some music you can listen
+ 
+
+ align:start position:0%
+so if you want some music you can listen
+to music while you're operating so
+
+ align:start position:0%
+to music while you're operating so
+ 
+
+ align:start position:0%
+to music while you're operating so
+they're very nice operating Suites uh
+
+ align:start position:0%
+they're very nice operating Suites uh
+ 
+
+ align:start position:0%
+they're very nice operating Suites uh
+bringing women's and so they're if you
+
+ align:start position:0%
+bringing women's and so they're if you
+ 
+
+ align:start position:0%
+bringing women's and so they're if you
+look in the back wall all those are
+
+ align:start position:0%
+look in the back wall all those are
+ 
+
+ align:start position:0%
+look in the back wall all those are
+supplies there's all the different types
+
+ align:start position:0%
+supplies there's all the different types
+ 
+
+ align:start position:0%
+supplies there's all the different types
+of sutures all the sponges all the
+
+ align:start position:0%
+of sutures all the sponges all the
+ 
+
+ align:start position:0%
+of sutures all the sponges all the
+little gadgets you would ever want this
+
+ align:start position:0%
+little gadgets you would ever want this
+ 
+
+ align:start position:0%
+little gadgets you would ever want this
+is in Zambia a little different if you
+
+ align:start position:0%
+is in Zambia a little different if you
+ 
+
+ align:start position:0%
+is in Zambia a little different if you
+can see the anesthesia machine up in the
+
+ align:start position:0%
+can see the anesthesia machine up in the
+ 
+
+ align:start position:0%
+can see the anesthesia machine up in the
+top left it's basically a tubing in a
+
+ align:start position:0%
+top left it's basically a tubing in a
+ 
+
+ align:start position:0%
+top left it's basically a tubing in a
+little bag that you you know you you you
+
+ align:start position:0%
+little bag that you you know you you you
+ 
+
+ align:start position:0%
+little bag that you you know you you you
+squeeze uh this is the operting room
+
+ align:start position:0%
+squeeze uh this is the operting room
+ 
+
+ align:start position:0%
+squeeze uh this is the operting room
+table not as comfortable as the other
+
+ align:start position:0%
+table not as comfortable as the other
+ 
+
+ align:start position:0%
+table not as comfortable as the other
+one uh equipments uh available maybe a
+
+ align:start position:0%
+one uh equipments uh available maybe a
+ 
+
+ align:start position:0%
+one uh equipments uh available maybe a
+couple sponges couple uh sutures that's
+
+ align:start position:0%
+couple sponges couple uh sutures that's
+ 
+
+ align:start position:0%
+couple sponges couple uh sutures that's
+about it um so it's it's a very
+
+ align:start position:0%
+about it um so it's it's a very
+ 
+
+ align:start position:0%
+about it um so it's it's a very
+different uh setting moving to Eastern
+
+ align:start position:0%
+different uh setting moving to Eastern
+ 
+
+ align:start position:0%
+different uh setting moving to Eastern
+Europe This is mdova maybe a little bit
+
+ align:start position:0%
+Europe This is mdova maybe a little bit
+ 
+
+ align:start position:0%
+Europe This is mdova maybe a little bit
+more developed and a little bit more
+
+ align:start position:0%
+more developed and a little bit more
+ 
+
+ align:start position:0%
+more developed and a little bit more
+equipment there uh but if you actually
+
+ align:start position:0%
+equipment there uh but if you actually
+ 
+
+ align:start position:0%
+equipment there uh but if you actually
+look closely the equipment it's all very
+
+ align:start position:0%
+look closely the equipment it's all very
+ 
+
+ align:start position:0%
+look closely the equipment it's all very
+old it's all reused uh if you can look
+
+ align:start position:0%
+old it's all reused uh if you can look
+ 
+
+ align:start position:0%
+old it's all reused uh if you can look
+at some of the
+
+ align:start position:0%
+at some of the
+ 
+
+ align:start position:0%
+at some of the
+laparoscopic uh devices there which I
+
+ align:start position:0%
+laparoscopic uh devices there which I
+ 
+
+ align:start position:0%
+laparoscopic uh devices there which I
+was surprised to see laparoscopy there
+
+ align:start position:0%
+was surprised to see laparoscopy there
+ 
+
+ align:start position:0%
+was surprised to see laparoscopy there
+but they're all things that are
+
+ align:start position:0%
+but they're all things that are
+ 
+
+ align:start position:0%
+but they're all things that are
+generally disposable in the United
+
+ align:start position:0%
+generally disposable in the United
+ 
+
+ align:start position:0%
+generally disposable in the United
+States use once but they use multiple
+
+ align:start position:0%
+States use once but they use multiple
+ 
+
+ align:start position:0%
+States use once but they use multiple
+times and something that you never
+
+ align:start position:0%
+times and something that you never
+ 
+
+ align:start position:0%
+times and something that you never
+really see here there's two patients in
+
+ align:start position:0%
+really see here there's two patients in
+ 
+
+ align:start position:0%
+really see here there's two patients in
+the same room and this they have 12
+
+ align:start position:0%
+the same room and this they have 12
+ 
+
+ align:start position:0%
+the same room and this they have 12
+operating rooms there are 22 beds or
+
+ align:start position:0%
+operating rooms there are 22 beds or
+ 
+
+ align:start position:0%
+operating rooms there are 22 beds or
+operating tables so most of their
+
+ align:start position:0%
+operating tables so most of their
+ 
+
+ align:start position:0%
+operating tables so most of their
+operating rooms have multiple tables and
+
+ align:start position:0%
+operating rooms have multiple tables and
+ 
+
+ align:start position:0%
+operating rooms have multiple tables and
+you can imagine kind of how crowded and
+
+ align:start position:0%
+you can imagine kind of how crowded and
+ 
+
+ align:start position:0%
+you can imagine kind of how crowded and
+how disorganized things are as well as
+
+ align:start position:0%
+how disorganized things are as well as
+ 
+
+ align:start position:0%
+how disorganized things are as well as
+infectious risk you have this many
+
+ align:start position:0%
+infectious risk you have this many
+ 
+
+ align:start position:0%
+infectious risk you have this many
+people coming in and out moving around
+
+ align:start position:0%
+people coming in and out moving around
+ 
+
+ align:start position:0%
+people coming in and out moving around
+uh and if you can think of some of the
+
+ align:start position:0%
+uh and if you can think of some of the
+ 
+
+ align:start position:0%
+uh and if you can think of some of the
+errors that can happen here think of the
+
+ align:start position:0%
+errors that can happen here think of the
+ 
+
+ align:start position:0%
+errors that can happen here think of the
+noise that's going on here if someone
+
+ align:start position:0%
+noise that's going on here if someone
+ 
+
+ align:start position:0%
+noise that's going on here if someone
+needs something well I didn't hear you
+
+ align:start position:0%
+needs something well I didn't hear you
+ 
+
+ align:start position:0%
+needs something well I didn't hear you
+because so- and so is yelling over here
+
+ align:start position:0%
+because so- and so is yelling over here
+ 
+
+ align:start position:0%
+because so- and so is yelling over here
+there's just uh it's just a different
+
+ align:start position:0%
+there's just uh it's just a different
+ 
+
+ align:start position:0%
+there's just uh it's just a different
+place and so what we wanted to show is
+
+ align:start position:0%
+place and so what we wanted to show is
+ 
+
+ align:start position:0%
+place and so what we wanted to show is
+in these limited these poor uh regions
+
+ align:start position:0%
+in these limited these poor uh regions
+ 
+
+ align:start position:0%
+in these limited these poor uh regions
+that we could actually implement the
+
+ align:start position:0%
+that we could actually implement the
+ 
+
+ align:start position:0%
+that we could actually implement the
+checklist on a hospital wide basis in
+
+ align:start position:0%
+checklist on a hospital wide basis in
+ 
+
+ align:start position:0%
+checklist on a hospital wide basis in
+addition to that we wanted to show that
+
+ align:start position:0%
+addition to that we wanted to show that
+ 
+
+ align:start position:0%
+addition to that we wanted to show that
+we could actually affect change and we
+
+ align:start position:0%
+we could actually affect change and we
+ 
+
+ align:start position:0%
+we could actually affect change and we
+could bring in these PEX SYM show
+
+ align:start position:0%
+could bring in these PEX SYM show
+ 
+
+ align:start position:0%
+could bring in these PEX SYM show
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+so I'm going to move along quickly uh
+
+ align:start position:0%
+so I'm going to move along quickly uh
+ 
+
+ align:start position:0%
+so I'm going to move along quickly uh
+this is a picture of a pulse oximeter it
+
+ align:start position:0%
+this is a picture of a pulse oximeter it
+ 
+
+ align:start position:0%
+this is a picture of a pulse oximeter it
+shows heart rate as well as oxygen
+
+ align:start position:0%
+shows heart rate as well as oxygen
+ 
+
+ align:start position:0%
+shows heart rate as well as oxygen
+saturation and uh in a study in the
+
+ align:start position:0%
+saturation and uh in a study in the
+ 
+
+ align:start position:0%
+saturation and uh in a study in the
+lanet was published last year um
+
+ align:start position:0%
+lanet was published last year um
+ 
+
+ align:start position:0%
+lanet was published last year um
+evidence showed that in highum countries
+
+ align:start position:0%
+evidence showed that in highum countries
+ 
+
+ align:start position:0%
+evidence showed that in highum countries
+virtually all operating rooms have pulse
+
+ align:start position:0%
+virtually all operating rooms have pulse
+ 
+
+ align:start position:0%
+virtually all operating rooms have pulse
+Symmetry and it's an international
+
+ align:start position:0%
+Symmetry and it's an international
+ 
+
+ align:start position:0%
+Symmetry and it's an international
+standard if you look at all the
+
+ align:start position:0%
+standard if you look at all the
+ 
+
+ align:start position:0%
+standard if you look at all the
+countries that have standards of
+
+ align:start position:0%
+countries that have standards of
+ 
+
+ align:start position:0%
+countries that have standards of
+anesthetic monitoring they're on all the
+
+ align:start position:0%
+anesthetic monitoring they're on all the
+ 
+
+ align:start position:0%
+anesthetic monitoring they're on all the
+monitoring standards um so it's an
+
+ align:start position:0%
+monitoring standards um so it's an
+ 
+
+ align:start position:0%
+monitoring standards um so it's an
+international standard of monitoring
+
+ align:start position:0%
+international standard of monitoring
+ 
+
+ align:start position:0%
+international standard of monitoring
+care but in low-income countries they're
+
+ align:start position:0%
+care but in low-income countries they're
+ 
+
+ align:start position:0%
+care but in low-income countries they're
+absent from more than 50% of those
+
+ align:start position:0%
+absent from more than 50% of those
+ 
+
+ align:start position:0%
+absent from more than 50% of those
+operating rooms and so so our aims were
+
+ align:start position:0%
+operating rooms and so so our aims were
+ 
+
+ align:start position:0%
+operating rooms and so so our aims were
+basically to see if we could bring the
+
+ align:start position:0%
+basically to see if we could bring the
+ 
+
+ align:start position:0%
+basically to see if we could bring the
+checklist in and the PO SYM and show
+
+ align:start position:0%
+checklist in and the PO SYM and show
+ 
+
+ align:start position:0%
+checklist in and the PO SYM and show
+that there was a difference and then to
+
+ align:start position:0%
+that there was a difference and then to
+ 
+
+ align:start position:0%
+that there was a difference and then to
+show the effect of pox symmetry training
+
+ align:start position:0%
+show the effect of pox symmetry training
+ 
+
+ align:start position:0%
+show the effect of pox symmetry training
+and show a trend in Improvement in
+
+ align:start position:0%
+and show a trend in Improvement in
+ 
+
+ align:start position:0%
+and show a trend in Improvement in
+hypoxemia over time and so in addition
+
+ align:start position:0%
+hypoxemia over time and so in addition
+ 
+
+ align:start position:0%
+hypoxemia over time and so in addition
+to these um eight sites we added three
+
+ align:start position:0%
+to these um eight sites we added three
+ 
+
+ align:start position:0%
+to these um eight sites we added three
+more sites one in Honduras one in mova
+
+ align:start position:0%
+more sites one in Honduras one in mova
+ 
+
+ align:start position:0%
+more sites one in Honduras one in mova
+and one in Zambia I'm going to talk
+
+ align:start position:0%
+and one in Zambia I'm going to talk
+ 
+
+ align:start position:0%
+and one in Zambia I'm going to talk
+about mdova and Zambia today because
+
+ align:start position:0%
+about mdova and Zambia today because
+ 
+
+ align:start position:0%
+about mdova and Zambia today because
+we're furthest along there we're still
+
+ align:start position:0%
+we're furthest along there we're still
+ 
+
+ align:start position:0%
+we're furthest along there we're still
+working with Honduras we don't have too
+
+ align:start position:0%
+working with Honduras we don't have too
+ 
+
+ align:start position:0%
+working with Honduras we don't have too
+much information from there yet but uh
+
+ align:start position:0%
+much information from there yet but uh
+ 
+
+ align:start position:0%
+much information from there yet but uh
+speaking about the implementation plan
+
+ align:start position:0%
+speaking about the implementation plan
+ 
+
+ align:start position:0%
+speaking about the implementation plan
+so we this is kind of the schema that we
+
+ align:start position:0%
+so we this is kind of the schema that we
+ 
+
+ align:start position:0%
+so we this is kind of the schema that we
+use to implement it's very basic um
+
+ align:start position:0%
+use to implement it's very basic um
+ 
+
+ align:start position:0%
+use to implement it's very basic um
+there's a lot more detail that goes
+
+ align:start position:0%
+there's a lot more detail that goes
+ 
+
+ align:start position:0%
+there's a lot more detail that goes
+along with it but this is the basic
+
+ align:start position:0%
+along with it but this is the basic
+ 
+
+ align:start position:0%
+along with it but this is the basic
+principles were we wanted a local team
+
+ align:start position:0%
+principles were we wanted a local team
+ 
+
+ align:start position:0%
+principles were we wanted a local team
+to be the implementation team someone a
+
+ align:start position:0%
+to be the implementation team someone a
+ 
+
+ align:start position:0%
+to be the implementation team someone a
+local team to really take charge we
+
+ align:start position:0%
+local team to really take charge we
+ 
+
+ align:start position:0%
+local team to really take charge we
+wanted to provide didactic education as
+
+ align:start position:0%
+wanted to provide didactic education as
+ 
+
+ align:start position:0%
+wanted to provide didactic education as
+well as demonstration we encouraged
+
+ align:start position:0%
+well as demonstration we encouraged
+ 
+
+ align:start position:0%
+well as demonstration we encouraged
+roleplay and then we did coaching and
+
+ align:start position:0%
+roleplay and then we did coaching and
+ 
+
+ align:start position:0%
+roleplay and then we did coaching and
+feedback and so the the thought was at
+
+ align:start position:0%
+feedback and so the the thought was at
+ 
+
+ align:start position:0%
+feedback and so the the thought was at
+the who the the School of Public Health
+
+ align:start position:0%
+the who the the School of Public Health
+ 
+
+ align:start position:0%
+the who the the School of Public Health
+and the World Federation site of
+
+ align:start position:0%
+and the World Federation site of
+ 
+
+ align:start position:0%
+and the World Federation site of
+anesthesiologist we would provide
+
+ align:start position:0%
+anesthesiologist we would provide
+ 
+
+ align:start position:0%
+anesthesiologist we would provide
+oversight to the local implementation as
+
+ align:start position:0%
+oversight to the local implementation as
+ 
+
+ align:start position:0%
+oversight to the local implementation as
+well as the local Administration and
+
+ align:start position:0%
+well as the local Administration and
+ 
+
+ align:start position:0%
+well as the local Administration and
+then they would then take this and teach
+
+ align:start position:0%
+then they would then take this and teach
+ 
+
+ align:start position:0%
+then they would then take this and teach
+it to their operating room staff and
+
+ align:start position:0%
+it to their operating room staff and
+ 
+
+ align:start position:0%
+it to their operating room staff and
+hopefully we'd find change and along
+
+ align:start position:0%
+hopefully we'd find change and along
+ 
+
+ align:start position:0%
+hopefully we'd find change and along
+this kind of the backbone of all this
+
+ align:start position:0%
+this kind of the backbone of all this
+ 
+
+ align:start position:0%
+this kind of the backbone of all this
+was data collection in order to to prove
+
+ align:start position:0%
+was data collection in order to to prove
+ 
+
+ align:start position:0%
+was data collection in order to to prove
+the things we wanted to show we needed
+
+ align:start position:0%
+the things we wanted to show we needed
+ 
+
+ align:start position:0%
+the things we wanted to show we needed
+to have robust data collection and so
+
+ align:start position:0%
+to have robust data collection and so
+ 
+
+ align:start position:0%
+to have robust data collection and so
+through uh funding through the who we
+
+ align:start position:0%
+through uh funding through the who we
+ 
+
+ align:start position:0%
+through uh funding through the who we
+were able to pay for data collectors in
+
+ align:start position:0%
+were able to pay for data collectors in
+ 
+
+ align:start position:0%
+were able to pay for data collectors in
+all these different
+
+ align:start position:0%
+all these different
+ 
+
+ align:start position:0%
+all these different
+areas uh and so this is just a
+
+ align:start position:0%
+areas uh and so this is just a
+ 
+
+ align:start position:0%
+areas uh and so this is just a
+demonstration of how the local
+
+ align:start position:0%
+demonstration of how the local
+ 
+
+ align:start position:0%
+demonstration of how the local
+implementation team taught uh I'll get
+
+ align:start position:0%
+implementation team taught uh I'll get
+ 
+
+ align:start position:0%
+implementation team taught uh I'll get
+you in just a minute so in we we had
+
+ align:start position:0%
+you in just a minute so in we we had
+ 
+
+ align:start position:0%
+you in just a minute so in we we had
+demonstrations as well as right in the
+
+ align:start position:0%
+demonstrations as well as right in the
+ 
+
+ align:start position:0%
+demonstrations as well as right in the
+operating room teaching on how to use a
+
+ align:start position:0%
+operating room teaching on how to use a
+ 
+
+ align:start position:0%
+operating room teaching on how to use a
+checklist we have these big posters
+
+ align:start position:0%
+checklist we have these big posters
+ 
+
+ align:start position:0%
+checklist we have these big posters
+placed on the wall and this is a local
+
+ align:start position:0%
+placed on the wall and this is a local
+ 
+
+ align:start position:0%
+placed on the wall and this is a local
+anesthesiologist teaching nurses about
+
+ align:start position:0%
+anesthesiologist teaching nurses about
+ 
+
+ align:start position:0%
+anesthesiologist teaching nurses about
+the checklist and this here is a surgeon
+
+ align:start position:0%
+the checklist and this here is a surgeon
+ 
+
+ align:start position:0%
+the checklist and this here is a surgeon
+teaching uh the anestis how to use a
+
+ align:start position:0%
+teaching uh the anestis how to use a
+ 
+
+ align:start position:0%
+teaching uh the anestis how to use a
+checklist quick question here the total
+
+ align:start position:0%
+checklist quick question here the total
+ 
+
+ align:start position:0%
+checklist quick question here the total
+budget for this uh so it's uh it's about
+
+ align:start position:0%
+budget for this uh so it's uh it's about
+ 
+
+ align:start position:0%
+budget for this uh so it's uh it's about
+30,000 per site so not 30,000 per site
+
+ align:start position:0%
+30,000 per site so not 30,000 per site
+ 
+
+ align:start position:0%
+30,000 per site so not 30,000 per site
+correct and so you might think that's a
+
+ align:start position:0%
+correct and so you might think that's a
+ 
+
+ align:start position:0%
+correct and so you might think that's a
+lot that's a lot to me but um if you
+
+ align:start position:0%
+lot that's a lot to me but um if you
+ 
+
+ align:start position:0%
+lot that's a lot to me but um if you
+consider the amount of uh data
+
+ align:start position:0%
+consider the amount of uh data
+ 
+
+ align:start position:0%
+consider the amount of uh data
+collection that occurred and and uh the
+
+ align:start position:0%
+collection that occurred and and uh the
+ 
+
+ align:start position:0%
+collection that occurred and and uh the
+resources used it was actually as
+
+ align:start position:0%
+resources used it was actually as
+ 
+
+ align:start position:0%
+resources used it was actually as
+studies go quite a lowbudget
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+study and so these are some of the
+
+ align:start position:0%
+study and so these are some of the
+ 
+
+ align:start position:0%
+study and so these are some of the
+results we see in Moldova this is just
+
+ align:start position:0%
+results we see in Moldova this is just
+ 
+
+ align:start position:0%
+results we see in Moldova this is just
+one of the sites we haven't quite seen
+
+ align:start position:0%
+one of the sites we haven't quite seen
+ 
+
+ align:start position:0%
+one of the sites we haven't quite seen
+significant differences in death yet and
+
+ align:start position:0%
+significant differences in death yet and
+ 
+
+ align:start position:0%
+significant differences in death yet and
+mortality but there's a trend from 4% to
+
+ align:start position:0%
+mortality but there's a trend from 4% to
+ 
+
+ align:start position:0%
+mortality but there's a trend from 4% to
+3.6% complication rates have gone down
+
+ align:start position:0%
+3.6% complication rates have gone down
+ 
+
+ align:start position:0%
+3.6% complication rates have gone down
+by almost 60% surgical s infection also
+
+ align:start position:0%
+by almost 60% surgical s infection also
+ 
+
+ align:start position:0%
+by almost 60% surgical s infection also
+almost about 60% % pneumonia has
+
+ align:start position:0%
+almost about 60% % pneumonia has
+ 
+
+ align:start position:0%
+almost about 60% % pneumonia has
+decreased by almost uh from 4.7 to 2.9%
+
+ align:start position:0%
+decreased by almost uh from 4.7 to 2.9%
+ 
+
+ align:start position:0%
+decreased by almost uh from 4.7 to 2.9%
+and unplanned intubation has also
+
+ align:start position:0%
+and unplanned intubation has also
+ 
+
+ align:start position:0%
+and unplanned intubation has also
+decreased and so some of this I think
+
+ align:start position:0%
+decreased and so some of this I think
+ 
+
+ align:start position:0%
+decreased and so some of this I think
+we've seen before any complications cgal
+
+ align:start position:0%
+we've seen before any complications cgal
+ 
+
+ align:start position:0%
+we've seen before any complications cgal
+site infections but things that are a
+
+ align:start position:0%
+site infections but things that are a
+ 
+
+ align:start position:0%
+site infections but things that are a
+little bit different that I think are
+
+ align:start position:0%
+little bit different that I think are
+ 
+
+ align:start position:0%
+little bit different that I think are
+added by the pulse sumers are the need
+
+ align:start position:0%
+added by the pulse sumers are the need
+ 
+
+ align:start position:0%
+added by the pulse sumers are the need
+to the prevention of unplanned
+
+ align:start position:0%
+to the prevention of unplanned
+ 
+
+ align:start position:0%
+to the prevention of unplanned
+intubations as well as maybe maybe
+
+ align:start position:0%
+intubations as well as maybe maybe
+ 
+
+ align:start position:0%
+intubations as well as maybe maybe
+pneumonia uh but I think um we're seeing
+
+ align:start position:0%
+pneumonia uh but I think um we're seeing
+ 
+
+ align:start position:0%
+pneumonia uh but I think um we're seeing
+the same thing we're seeing a reduction
+
+ align:start position:0%
+the same thing we're seeing a reduction
+ 
+
+ align:start position:0%
+the same thing we're seeing a reduction
+in complications overall by using the
+
+ align:start position:0%
+in complications overall by using the
+ 
+
+ align:start position:0%
+in complications overall by using the
+checklist
+
+ align:start position:0%
+checklist
+ 
+
+ align:start position:0%
+checklist
+uh here's a uh some figure a figure
+
+ align:start position:0%
+uh here's a uh some figure a figure
+ 
+
+ align:start position:0%
+uh here's a uh some figure a figure
+showing the the uh decrease in hypoxemic
+
+ align:start position:0%
+showing the the uh decrease in hypoxemic
+ 
+
+ align:start position:0%
+showing the the uh decrease in hypoxemic
+episodes per thousand oximetry hours so
+
+ align:start position:0%
+episodes per thousand oximetry hours so
+ 
+
+ align:start position:0%
+episodes per thousand oximetry hours so
+the bars in blue are periods where
+
+ align:start position:0%
+the bars in blue are periods where
+ 
+
+ align:start position:0%
+the bars in blue are periods where
+someone's oxygen level is just marginal
+
+ align:start position:0%
+someone's oxygen level is just marginal
+ 
+
+ align:start position:0%
+someone's oxygen level is just marginal
+from less than
+
+ align:start position:0%
+from less than
+ 
+
+ align:start position:0%
+from less than
+90 uh and you can see this sharp
+
+ align:start position:0%
+90 uh and you can see this sharp
+ 
+
+ align:start position:0%
+90 uh and you can see this sharp
+decrease from the early period to the
+
+ align:start position:0%
+decrease from the early period to the
+ 
+
+ align:start position:0%
+decrease from the early period to the
+middle period and then again just a
+
+ align:start position:0%
+middle period and then again just a
+ 
+
+ align:start position:0%
+middle period and then again just a
+little bit more from the late period the
+
+ align:start position:0%
+little bit more from the late period the
+ 
+
+ align:start position:0%
+little bit more from the late period the
+other thing we wanted to catch was to
+
+ align:start position:0%
+other thing we wanted to catch was to
+ 
+
+ align:start position:0%
+other thing we wanted to catch was to
+see well if people are having low oxygen
+
+ align:start position:0%
+see well if people are having low oxygen
+ 
+
+ align:start position:0%
+see well if people are having low oxygen
+levels uh what if they're are we
+
+ align:start position:0%
+levels uh what if they're are we
+ 
+
+ align:start position:0%
+levels uh what if they're are we
+preventing the the severity of the those
+
+ align:start position:0%
+preventing the the severity of the those
+ 
+
+ align:start position:0%
+preventing the the severity of the those
+low uh low oxygen levels uh so we looked
+
+ align:start position:0%
+low uh low oxygen levels uh so we looked
+ 
+
+ align:start position:0%
+low uh low oxygen levels uh so we looked
+at four minutes as well so if someone's
+
+ align:start position:0%
+at four minutes as well so if someone's
+ 
+
+ align:start position:0%
+at four minutes as well so if someone's
+having a a greater than 4 minute period
+
+ align:start position:0%
+having a a greater than 4 minute period
+ 
+
+ align:start position:0%
+having a a greater than 4 minute period
+of hypoxia that would be what we
+
+ align:start position:0%
+of hypoxia that would be what we
+ 
+
+ align:start position:0%
+of hypoxia that would be what we
+consider severe episode and so those
+
+ align:start position:0%
+consider severe episode and so those
+ 
+
+ align:start position:0%
+consider severe episode and so those
+have also gone down so not only we've
+
+ align:start position:0%
+have also gone down so not only we've
+ 
+
+ align:start position:0%
+have also gone down so not only we've
+been able to decrease the amount of
+
+ align:start position:0%
+been able to decrease the amount of
+ 
+
+ align:start position:0%
+been able to decrease the amount of
+hypoxemia in general but also the
+
+ align:start position:0%
+hypoxemia in general but also the
+ 
+
+ align:start position:0%
+hypoxemia in general but also the
+severity of the hyp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hypoxemia how does it differ from we
+
+ align:start position:0%
+hypoxemia how does it differ from we
+ 
+
+ align:start position:0%
+hypoxemia how does it differ from we
+have the United States you know I uh so
+
+ align:start position:0%
+have the United States you know I uh so
+ 
+
+ align:start position:0%
+have the United States you know I uh so
+the number of
+
+ align:start position:0%
+the number of
+ 
+
+ align:start position:0%
+the number of
+hypoxemia I don't have the numbers right
+
+ align:start position:0%
+hypoxemia I don't have the numbers right
+ 
+
+ align:start position:0%
+hypoxemia I don't have the numbers right
+off the top of my head but it's less
+
+ align:start position:0%
+off the top of my head but it's less
+ 
+
+ align:start position:0%
+off the top of my head but it's less
+than 1% really for uh and I don't I
+
+ align:start position:0%
+than 1% really for uh and I don't I
+ 
+
+ align:start position:0%
+than 1% really for uh and I don't I
+don't have it broken
+
+ align:start position:0%
+don't have it broken
+ 
+
+ align:start position:0%
+don't have it broken
+down so I would say that the rate of
+
+ align:start position:0%
+down so I would say that the rate of
+ 
+
+ align:start position:0%
+down so I would say that the rate of
+hypoxemia is twice that of here in the
+
+ align:start position:0%
+hypoxemia is twice that of here in the
+ 
+
+ align:start position:0%
+hypoxemia is twice that of here in the
+United States there there's a recent
+
+ align:start position:0%
+United States there there's a recent
+ 
+
+ align:start position:0%
+United States there there's a recent
+study that looked at um actually the MGH
+
+ align:start position:0%
+study that looked at um actually the MGH
+ 
+
+ align:start position:0%
+study that looked at um actually the MGH
+and a tertiary Hospital in Auckland New
+
+ align:start position:0%
+and a tertiary Hospital in Auckland New
+ 
+
+ align:start position:0%
+and a tertiary Hospital in Auckland New
+Zealand and so we considering those as
+
+ align:start position:0%
+Zealand and so we considering those as
+ 
+
+ align:start position:0%
+Zealand and so we considering those as
+high income countries their rates of
+
+ align:start position:0%
+high income countries their rates of
+ 
+
+ align:start position:0%
+high income countries their rates of
+hypoxemia were about half of what we see
+
+ align:start position:0%
+hypoxemia were about half of what we see
+ 
+
+ align:start position:0%
+hypoxemia were about half of what we see
+here in mdova
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so this is the schema we're hoping
+
+ align:start position:0%
+and so this is the schema we're hoping
+ 
+
+ align:start position:0%
+and so this is the schema we're hoping
+to show that check we know that
+
+ align:start position:0%
+to show that check we know that
+ 
+
+ align:start position:0%
+to show that check we know that
+checklist can save lives we know that
+
+ align:start position:0%
+checklist can save lives we know that
+ 
+
+ align:start position:0%
+checklist can save lives we know that
+puls symmetry is essential to Safe
+
+ align:start position:0%
+puls symmetry is essential to Safe
+ 
+
+ align:start position:0%
+puls symmetry is essential to Safe
+surgery uh implementation we hope we've
+
+ align:start position:0%
+surgery uh implementation we hope we've
+ 
+
+ align:start position:0%
+surgery uh implementation we hope we've
+shown that they can implementation of
+
+ align:start position:0%
+shown that they can implementation of
+ 
+
+ align:start position:0%
+shown that they can implementation of
+this this package uh improves outcomes
+
+ align:start position:0%
+this this package uh improves outcomes
+ 
+
+ align:start position:0%
+this this package uh improves outcomes
+and then lastly um we hope that this can
+
+ align:start position:0%
+and then lastly um we hope that this can
+ 
+
+ align:start position:0%
+and then lastly um we hope that this can
+become a universal
+
+ align:start position:0%
+become a universal
+ 
+
+ align:start position:0%
+become a universal
+standard so we're going to move on uh
+
+ align:start position:0%
+standard so we're going to move on uh
+ 
+
+ align:start position:0%
+standard so we're going to move on uh
+thank you very
+
+ align:start position:0%
+thank you very
+ 
+
+ align:start position:0%
+thank you very
+much long if you for
+
+ align:start position:0%
+much long if you for
+ 
+
+ align:start position:0%
+much long if you for
+how long
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do yeah it's a it's a machine that they
+
+ align:start position:0%
+do yeah it's a it's a machine that they
+ 
+
+ align:start position:0%
+do yeah it's a it's a machine that they
+can use till till it breaks uh but we uh
+
+ align:start position:0%
+can use till till it breaks uh but we uh
+ 
+
+ align:start position:0%
+can use till till it breaks uh but we uh
+we didn't feel like it was right to take
+
+ align:start position:0%
+we didn't feel like it was right to take
+ 
+
+ align:start position:0%
+we didn't feel like it was right to take
+them there and take them away so we've
+
+ align:start position:0%
+them there and take them away so we've
+ 
+
+ align:start position:0%
+them there and take them away so we've
+all the sites we've gone to are are
+
+ align:start position:0%
+all the sites we've gone to are are
+ 
+
+ align:start position:0%
+all the sites we've gone to are are
+we've left the oximeters there with
+
+ align:start position:0%
+we've left the oximeters there with
+ 
+
+ align:start position:0%
+we've left the oximeters there with
+replacement probes for them to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use so Alvin talked about his experience
+
+ align:start position:0%
+use so Alvin talked about his experience
+ 
+
+ align:start position:0%
+use so Alvin talked about his experience
+of the use of safe surgery checklist and
+
+ align:start position:0%
+of the use of safe surgery checklist and
+ 
+
+ align:start position:0%
+of the use of safe surgery checklist and
+surgery and then also the implementation
+
+ align:start position:0%
+surgery and then also the implementation
+ 
+
+ align:start position:0%
+surgery and then also the implementation
+and what you'll notice on his first
+
+ align:start position:0%
+and what you'll notice on his first
+ 
+
+ align:start position:0%
+and what you'll notice on his first
+slide it said the who safe surgery
+
+ align:start position:0%
+slide it said the who safe surgery
+ 
+
+ align:start position:0%
+slide it said the who safe surgery
+checklist and we quickly realize that
+
+ align:start position:0%
+checklist and we quickly realize that
+ 
+
+ align:start position:0%
+checklist and we quickly realize that
+you can't just drop checklists over
+
+ align:start position:0%
+you can't just drop checklists over
+ 
+
+ align:start position:0%
+you can't just drop checklists over
+subsaharan Africa and Asia and hope
+
+ align:start position:0%
+subsaharan Africa and Asia and hope
+ 
+
+ align:start position:0%
+subsaharan Africa and Asia and hope
+that'll function and have the impact and
+
+ align:start position:0%
+that'll function and have the impact and
+ 
+
+ align:start position:0%
+that'll function and have the impact and
+so you'll see on my slide it says the
+
+ align:start position:0%
+so you'll see on my slide it says the
+ 
+
+ align:start position:0%
+so you'll see on my slide it says the
+safe child birth checklist program
+
+ align:start position:0%
+safe child birth checklist program
+ 
+
+ align:start position:0%
+safe child birth checklist program
+because as you all know having the
+
+ align:start position:0%
+because as you all know having the
+ 
+
+ align:start position:0%
+because as you all know having the
+technology on its own isn't going to
+
+ align:start position:0%
+technology on its own isn't going to
+ 
+
+ align:start position:0%
+technology on its own isn't going to
+work you need to have some kind of
+
+ align:start position:0%
+work you need to have some kind of
+ 
+
+ align:start position:0%
+work you need to have some kind of
+supportive element however skinny that
+
+ align:start position:0%
+supportive element however skinny that
+ 
+
+ align:start position:0%
+supportive element however skinny that
+element is
+
+ align:start position:0%
+element is
+ 
+
+ align:start position:0%
+element is
+so I'm going to take us to a different
+
+ align:start position:0%
+so I'm going to take us to a different
+ 
+
+ align:start position:0%
+so I'm going to take us to a different
+scenario and I'm actually going to focus
+
+ align:start position:0%
+scenario and I'm actually going to focus
+ 
+
+ align:start position:0%
+scenario and I'm actually going to focus
+on the early stages because when we came
+
+ align:start position:0%
+on the early stages because when we came
+ 
+
+ align:start position:0%
+on the early stages because when we came
+when I entered there was no checklist we
+
+ align:start position:0%
+when I entered there was no checklist we
+ 
+
+ align:start position:0%
+when I entered there was no checklist we
+had to actually create the checklist so
+
+ align:start position:0%
+had to actually create the checklist so
+ 
+
+ align:start position:0%
+had to actually create the checklist so
+I'm going to talk about the development
+
+ align:start position:0%
+I'm going to talk about the development
+ 
+
+ align:start position:0%
+I'm going to talk about the development
+of the checklist bit more than the
+
+ align:start position:0%
+of the checklist bit more than the
+ 
+
+ align:start position:0%
+of the checklist bit more than the
+implementation of it so what are the
+
+ align:start position:0%
+implementation of it so what are the
+ 
+
+ align:start position:0%
+implementation of it so what are the
+principles the purpose is to ensure that
+
+ align:start position:0%
+principles the purpose is to ensure that
+ 
+
+ align:start position:0%
+principles the purpose is to ensure that
+essential care practices are reliably
+
+ align:start position:0%
+essential care practices are reliably
+ 
+
+ align:start position:0%
+essential care practices are reliably
+performed that's doing the right thing
+
+ align:start position:0%
+performed that's doing the right thing
+ 
+
+ align:start position:0%
+performed that's doing the right thing
+to the right patient at the right time
+
+ align:start position:0%
+to the right patient at the right time
+ 
+
+ align:start position:0%
+to the right patient at the right time
+every single time it has to be
+
+ align:start position:0%
+every single time it has to be
+ 
+
+ align:start position:0%
+every single time it has to be
+evidence-based so there is nothing
+
+ align:start position:0%
+evidence-based so there is nothing
+ 
+
+ align:start position:0%
+evidence-based so there is nothing
+nothing new on any of these checklists
+
+ align:start position:0%
+nothing new on any of these checklists
+ 
+
+ align:start position:0%
+nothing new on any of these checklists
+The Innovation is the tool so you're
+
+ align:start position:0%
+The Innovation is the tool so you're
+ 
+
+ align:start position:0%
+The Innovation is the tool so you're
+actually providing good care at the
+
+ align:start position:0%
+actually providing good care at the
+ 
+
+ align:start position:0%
+actually providing good care at the
+bedside it's not the items on the
+
+ align:start position:0%
+bedside it's not the items on the
+ 
+
+ align:start position:0%
+bedside it's not the items on the
+checklist and that's important for
+
+ align:start position:0%
+checklist and that's important for
+ 
+
+ align:start position:0%
+checklist and that's important for
+acceptability later on in the process
+
+ align:start position:0%
+acceptability later on in the process
+ 
+
+ align:start position:0%
+acceptability later on in the process
+then succinct and simple everyone wants
+
+ align:start position:0%
+then succinct and simple everyone wants
+ 
+
+ align:start position:0%
+then succinct and simple everyone wants
+to add items onto the checklist the more
+
+ align:start position:0%
+to add items onto the checklist the more
+ 
+
+ align:start position:0%
+to add items onto the checklist the more
+items you add on the longer it takes and
+
+ align:start position:0%
+items you add on the longer it takes and
+ 
+
+ align:start position:0%
+items you add on the longer it takes and
+the field that we're working in high
+
+ align:start position:0%
+the field that we're working in high
+ 
+
+ align:start position:0%
+the field that we're working in high
+burden sort of in the developing World
+
+ align:start position:0%
+burden sort of in the developing World
+ 
+
+ align:start position:0%
+burden sort of in the developing World
+they already have a shortage of
+
+ align:start position:0%
+they already have a shortage of
+ 
+
+ align:start position:0%
+they already have a shortage of
+healthcare workers they don't have time
+
+ align:start position:0%
+healthcare workers they don't have time
+ 
+
+ align:start position:0%
+healthcare workers they don't have time
+so everything on it must be absolutely
+
+ align:start position:0%
+so everything on it must be absolutely
+ 
+
+ align:start position:0%
+so everything on it must be absolutely
+mandatory and affects mortality or
+
+ align:start position:0%
+mandatory and affects mortality or
+ 
+
+ align:start position:0%
+mandatory and affects mortality or
+severe
+
+ align:start position:0%
+severe
+ 
+
+ align:start position:0%
+severe
+morbidity and it's a bedside tool you
+
+ align:start position:0%
+morbidity and it's a bedside tool you
+ 
+
+ align:start position:0%
+morbidity and it's a bedside tool you
+want something to be easy to use at the
+
+ align:start position:0%
+want something to be easy to use at the
+ 
+
+ align:start position:0%
+want something to be easy to use at the
+bedside broad applicability you ask that
+
+ align:start position:0%
+bedside broad applicability you ask that
+ 
+
+ align:start position:0%
+bedside broad applicability you ask that
+question you know is this for Africa is
+
+ align:start position:0%
+question you know is this for Africa is
+ 
+
+ align:start position:0%
+question you know is this for Africa is
+this for the US um it's important for
+
+ align:start position:0%
+this for the US um it's important for
+ 
+
+ align:start position:0%
+this for the US um it's important for
+scale up that every item is essential
+
+ align:start position:0%
+scale up that every item is essential
+ 
+
+ align:start position:0%
+scale up that every item is essential
+and therefore should be done all over
+
+ align:start position:0%
+and therefore should be done all over
+ 
+
+ align:start position:0%
+and therefore should be done all over
+the world so when we were in the middle
+
+ align:start position:0%
+the world so when we were in the middle
+ 
+
+ align:start position:0%
+the world so when we were in the middle
+of the development the other person
+
+ align:start position:0%
+of the development the other person
+ 
+
+ align:start position:0%
+of the development the other person
+that's working with me is a
+
+ align:start position:0%
+that's working with me is a
+ 
+
+ align:start position:0%
+that's working with me is a
+neonatologist and um he his wife was
+
+ align:start position:0%
+neonatologist and um he his wife was
+ 
+
+ align:start position:0%
+neonatologist and um he his wife was
+having his first baby at Beth Israel
+
+ align:start position:0%
+having his first baby at Beth Israel
+ 
+
+ align:start position:0%
+having his first baby at Beth Israel
+very good Hospital in Boston and he'd
+
+ align:start position:0%
+very good Hospital in Boston and he'd
+ 
+
+ align:start position:0%
+very good Hospital in Boston and he'd
+forgotten about it throughout the whole
+
+ align:start position:0%
+forgotten about it throughout the whole
+ 
+
+ align:start position:0%
+forgotten about it throughout the whole
+process of having the baby because he
+
+ align:start position:0%
+process of having the baby because he
+ 
+
+ align:start position:0%
+process of having the baby because he
+was so traumatized but then at the end
+
+ align:start position:0%
+was so traumatized but then at the end
+ 
+
+ align:start position:0%
+was so traumatized but then at the end
+he was like oh I have the checklist took
+
+ align:start position:0%
+he was like oh I have the checklist took
+ 
+
+ align:start position:0%
+he was like oh I have the checklist took
+it out the back of his pocket I was like
+
+ align:start position:0%
+it out the back of his pocket I was like
+ 
+
+ align:start position:0%
+it out the back of his pocket I was like
+okay so have they done the things that
+
+ align:start position:0%
+okay so have they done the things that
+ 
+
+ align:start position:0%
+okay so have they done the things that
+they should have done after delivery and
+
+ align:start position:0%
+they should have done after delivery and
+ 
+
+ align:start position:0%
+they should have done after delivery and
+no they hadn't they' missed two items
+
+ align:start position:0%
+no they hadn't they' missed two items
+ 
+
+ align:start position:0%
+no they hadn't they' missed two items
+one was they hadn't got the
+
+ align:start position:0%
+one was they hadn't got the
+ 
+
+ align:start position:0%
+one was they hadn't got the
+breastfeeding going within an hour which
+
+ align:start position:0%
+breastfeeding going within an hour which
+ 
+
+ align:start position:0%
+breastfeeding going within an hour which
+we know should be done and second they
+
+ align:start position:0%
+we know should be done and second they
+ 
+
+ align:start position:0%
+we know should be done and second they
+hadn't checked the temperature of the
+
+ align:start position:0%
+hadn't checked the temperature of the
+ 
+
+ align:start position:0%
+hadn't checked the temperature of the
+baby his baby was hypothermic had a
+
+ align:start position:0%
+baby his baby was hypothermic had a
+ 
+
+ align:start position:0%
+baby his baby was hypothermic had a
+lower temperature than it should have
+
+ align:start position:0%
+lower temperature than it should have
+ 
+
+ align:start position:0%
+lower temperature than it should have
+and it's fine we're in America put it on
+
+ align:start position:0%
+and it's fine we're in America put it on
+ 
+
+ align:start position:0%
+and it's fine we're in America put it on
+the heat be fine but that wouldn't have
+
+ align:start position:0%
+the heat be fine but that wouldn't have
+ 
+
+ align:start position:0%
+the heat be fine but that wouldn't have
+happened in Africa um so it should be
+
+ align:start position:0%
+happened in Africa um so it should be
+ 
+
+ align:start position:0%
+happened in Africa um so it should be
+applicable all over and then the
+
+ align:start position:0%
+applicable all over and then the
+ 
+
+ align:start position:0%
+applicable all over and then the
+capacity for measurable impact like you
+
+ align:start position:0%
+capacity for measurable impact like you
+ 
+
+ align:start position:0%
+capacity for measurable impact like you
+said if you can't prove meaningful
+
+ align:start position:0%
+said if you can't prove meaningful
+ 
+
+ align:start position:0%
+said if you can't prove meaningful
+change you won't build program support
+
+ align:start position:0%
+change you won't build program support
+ 
+
+ align:start position:0%
+change you won't build program support
+especially in medical areas where people
+
+ align:start position:0%
+especially in medical areas where people
+ 
+
+ align:start position:0%
+especially in medical areas where people
+want to know what they're doing has an
+
+ align:start position:0%
+want to know what they're doing has an
+ 
+
+ align:start position:0%
+want to know what they're doing has an
+Evidence base show me the numbers yeah
+
+ align:start position:0%
+Evidence base show me the numbers yeah
+ 
+
+ align:start position:0%
+Evidence base show me the numbers yeah
+and so you have to be able to measure
+
+ align:start position:0%
+and so you have to be able to measure
+ 
+
+ align:start position:0%
+and so you have to be able to measure
+what um impact you're having it's not
+
+ align:start position:0%
+what um impact you're having it's not
+ 
+
+ align:start position:0%
+what um impact you're having it's not
+comprehensive this checklist is not to
+
+ align:start position:0%
+comprehensive this checklist is not to
+ 
+
+ align:start position:0%
+comprehensive this checklist is not to
+prevent every conceivable patient harm
+
+ align:start position:0%
+prevent every conceivable patient harm
+ 
+
+ align:start position:0%
+prevent every conceivable patient harm
+it's focused on the Big Bang you know
+
+ align:start position:0%
+it's focused on the Big Bang you know
+ 
+
+ align:start position:0%
+it's focused on the Big Bang you know
+the mortality and the severe morbidity
+
+ align:start position:0%
+the mortality and the severe morbidity
+ 
+
+ align:start position:0%
+the mortality and the severe morbidity
+and it's not a protocol or guideline so
+
+ align:start position:0%
+and it's not a protocol or guideline so
+ 
+
+ align:start position:0%
+and it's not a protocol or guideline so
+people were like oh okay so this is what
+
+ align:start position:0%
+people were like oh okay so this is what
+ 
+
+ align:start position:0%
+people were like oh okay so this is what
+I do to deliver a baby no no you need to
+
+ align:start position:0%
+I do to deliver a baby no no you need to
+ 
+
+ align:start position:0%
+I do to deliver a baby no no you need to
+have training and you need to be able to
+
+ align:start position:0%
+have training and you need to be able to
+ 
+
+ align:start position:0%
+have training and you need to be able to
+know what to do so it's a bit like a
+
+ align:start position:0%
+know what to do so it's a bit like a
+ 
+
+ align:start position:0%
+know what to do so it's a bit like a
+shopping list you give your know partner
+
+ align:start position:0%
+shopping list you give your know partner
+ 
+
+ align:start position:0%
+shopping list you give your know partner
+a shopping list go and get tomatoes you
+
+ align:start position:0%
+a shopping list go and get tomatoes you
+ 
+
+ align:start position:0%
+a shopping list go and get tomatoes you
+don't tell them how to pick the tomatoes
+
+ align:start position:0%
+don't tell them how to pick the tomatoes
+ 
+
+ align:start position:0%
+don't tell them how to pick the tomatoes
+you just say I need some tomatoes and
+
+ align:start position:0%
+you just say I need some tomatoes and
+ 
+
+ align:start position:0%
+you just say I need some tomatoes and
+same with the pilot checklist you can't
+
+ align:start position:0%
+same with the pilot checklist you can't
+ 
+
+ align:start position:0%
+same with the pilot checklist you can't
+say oh well you don't need pilot
+
+ align:start position:0%
+say oh well you don't need pilot
+ 
+
+ align:start position:0%
+say oh well you don't need pilot
+training they're just
+
+ align:start position:0%
+training they're just
+ 
+
+ align:start position:0%
+training they're just
+reminders so we've sort of got a a bit
+
+ align:start position:0%
+reminders so we've sort of got a a bit
+ 
+
+ align:start position:0%
+reminders so we've sort of got a a bit
+of a schema on checklist development and
+
+ align:start position:0%
+of a schema on checklist development and
+ 
+
+ align:start position:0%
+of a schema on checklist development and
+then checklist testing and so it's
+
+ align:start position:0%
+then checklist testing and so it's
+ 
+
+ align:start position:0%
+then checklist testing and so it's
+assembling the evidence on critical
+
+ align:start position:0%
+assembling the evidence on critical
+ 
+
+ align:start position:0%
+assembling the evidence on critical
+omissions that will lead to harm then
+
+ align:start position:0%
+omissions that will lead to harm then
+ 
+
+ align:start position:0%
+omissions that will lead to harm then
+identifying the pause points and
+
+ align:start position:0%
+identifying the pause points and
+ 
+
+ align:start position:0%
+identifying the pause points and
+actually drafting the checklist items
+
+ align:start position:0%
+actually drafting the checklist items
+ 
+
+ align:start position:0%
+actually drafting the checklist items
+this actually Boeing and the aviation
+
+ align:start position:0%
+this actually Boeing and the aviation
+ 
+
+ align:start position:0%
+this actually Boeing and the aviation
+industry spend a lot of time on this and
+
+ align:start position:0%
+industry spend a lot of time on this and
+ 
+
+ align:start position:0%
+industry spend a lot of time on this and
+we got them to help us both with the
+
+ align:start position:0%
+we got them to help us both with the
+ 
+
+ align:start position:0%
+we got them to help us both with the
+safe surgery checklist and with the safe
+
+ align:start position:0%
+safe surgery checklist and with the safe
+ 
+
+ align:start position:0%
+safe surgery checklist and with the safe
+child birth checklist and this guy his
+
+ align:start position:0%
+child birth checklist and this guy his
+ 
+
+ align:start position:0%
+child birth checklist and this guy his
+name is Dan Borman this is his sort of
+
+ align:start position:0%
+name is Dan Borman this is his sort of
+ 
+
+ align:start position:0%
+name is Dan Borman this is his sort of
+what he does in life he's like this has
+
+ align:start position:0%
+what he does in life he's like this has
+ 
+
+ align:start position:0%
+what he does in life he's like this has
+to be the font this should be the size
+
+ align:start position:0%
+to be the font this should be the size
+ 
+
+ align:start position:0%
+to be the font this should be the size
+put your action item at the front of the
+
+ align:start position:0%
+put your action item at the front of the
+ 
+
+ align:start position:0%
+put your action item at the front of the
+sentence and all these things matter he
+
+ align:start position:0%
+sentence and all these things matter he
+ 
+
+ align:start position:0%
+sentence and all these things matter he
+like when people are doing this quickly
+
+ align:start position:0%
+like when people are doing this quickly
+ 
+
+ align:start position:0%
+like when people are doing this quickly
+they your wording needs to be
+
+ align:start position:0%
+they your wording needs to be
+ 
+
+ align:start position:0%
+they your wording needs to be
+perfect and then the next process which
+
+ align:start position:0%
+perfect and then the next process which
+ 
+
+ align:start position:0%
+perfect and then the next process which
+is an iterative process getting experts
+
+ align:start position:0%
+is an iterative process getting experts
+ 
+
+ align:start position:0%
+is an iterative process getting experts
+and field users it's actually pretty
+
+ align:start position:0%
+and field users it's actually pretty
+ 
+
+ align:start position:0%
+and field users it's actually pretty
+painful um but it's hugely important for
+
+ align:start position:0%
+painful um but it's hugely important for
+ 
+
+ align:start position:0%
+painful um but it's hugely important for
+scale up later on so quick story on this
+
+ align:start position:0%
+scale up later on so quick story on this
+ 
+
+ align:start position:0%
+scale up later on so quick story on this
+um we had an international consultation
+
+ align:start position:0%
+um we had an international consultation
+ 
+
+ align:start position:0%
+um we had an international consultation
+because it's a who thing so you have to
+
+ align:start position:0%
+because it's a who thing so you have to
+ 
+
+ align:start position:0%
+because it's a who thing so you have to
+have international consultation who's
+
+ align:start position:0%
+have international consultation who's
+ 
+
+ align:start position:0%
+have international consultation who's
+who of Safe child birth in in the room
+
+ align:start position:0%
+who of Safe child birth in in the room
+ 
+
+ align:start position:0%
+who of Safe child birth in in the room
+the first comment was that the neologist
+
+ align:start position:0%
+the first comment was that the neologist
+ 
+
+ align:start position:0%
+the first comment was that the neologist
+and the obstetrician sat there and said
+
+ align:start position:0%
+and the obstetrician sat there and said
+ 
+
+ align:start position:0%
+and the obstetrician sat there and said
+we've never been in the same room for an
+
+ align:start position:0%
+we've never been in the same room for an
+ 
+
+ align:start position:0%
+we've never been in the same room for an
+intervention day one of baby has always
+
+ align:start position:0%
+intervention day one of baby has always
+ 
+
+ align:start position:0%
+intervention day one of baby has always
+been argued over the Obstetricians will
+
+ align:start position:0%
+been argued over the Obstetricians will
+ 
+
+ align:start position:0%
+been argued over the Obstetricians will
+say it's mine and the neologist say it's
+
+ align:start position:0%
+say it's mine and the neologist say it's
+ 
+
+ align:start position:0%
+say it's mine and the neologist say it's
+mine and they've just never come
+
+ align:start position:0%
+mine and they've just never come
+ 
+
+ align:start position:0%
+mine and they've just never come
+together um which to being a surgeon
+
+ align:start position:0%
+together um which to being a surgeon
+ 
+
+ align:start position:0%
+together um which to being a surgeon
+like what the hell's going on here um
+
+ align:start position:0%
+like what the hell's going on here um
+ 
+
+ align:start position:0%
+like what the hell's going on here um
+and then he sat there and I really like
+
+ align:start position:0%
+and then he sat there and I really like
+ 
+
+ align:start position:0%
+and then he sat there and I really like
+the way he navigated the process there
+
+ align:start position:0%
+the way he navigated the process there
+ 
+
+ align:start position:0%
+the way he navigated the process there
+was controversy over everything you know
+
+ align:start position:0%
+was controversy over everything you know
+ 
+
+ align:start position:0%
+was controversy over everything you know
+one academic said no for PPH we should
+
+ align:start position:0%
+one academic said no for PPH we should
+ 
+
+ align:start position:0%
+one academic said no for PPH we should
+be doing this and someone else said this
+
+ align:start position:0%
+be doing this and someone else said this
+ 
+
+ align:start position:0%
+be doing this and someone else said this
+and like oh my God I have two days and
+
+ align:start position:0%
+and like oh my God I have two days and
+ 
+
+ align:start position:0%
+and like oh my God I have two days and
+we need to have a draft checklist at the
+
+ align:start position:0%
+we need to have a draft checklist at the
+ 
+
+ align:start position:0%
+we need to have a draft checklist at the
+end but I said you know what's going on
+
+ align:start position:0%
+end but I said you know what's going on
+ 
+
+ align:start position:0%
+end but I said you know what's going on
+like we're not really seeming to get
+
+ align:start position:0%
+like we're not really seeming to get
+ 
+
+ align:start position:0%
+like we're not really seeming to get
+anywhere and he said prya we have to
+
+ align:start position:0%
+anywhere and he said prya we have to
+ 
+
+ align:start position:0%
+anywhere and he said prya we have to
+have the controversial topics coming out
+
+ align:start position:0%
+have the controversial topics coming out
+ 
+
+ align:start position:0%
+have the controversial topics coming out
+now because you don't want them coming
+
+ align:start position:0%
+now because you don't want them coming
+ 
+
+ align:start position:0%
+now because you don't want them coming
+out halfway through your testing and I
+
+ align:start position:0%
+out halfway through your testing and I
+ 
+
+ align:start position:0%
+out halfway through your testing and I
+think that's critical like know your
+
+ align:start position:0%
+think that's critical like know your
+ 
+
+ align:start position:0%
+think that's critical like know your
+landscape whichever intervention
+
+ align:start position:0%
+landscape whichever intervention
+ 
+
+ align:start position:0%
+landscape whichever intervention
+Innovation you're creating and it was
+
+ align:start position:0%
+Innovation you're creating and it was
+ 
+
+ align:start position:0%
+Innovation you're creating and it was
+really important for buying the other
+
+ align:start position:0%
+really important for buying the other
+ 
+
+ align:start position:0%
+really important for buying the other
+thing was that yes we had all the
+
+ align:start position:0%
+thing was that yes we had all the
+ 
+
+ align:start position:0%
+thing was that yes we had all the
+academics but we also had field users we
+
+ align:start position:0%
+academics but we also had field users we
+ 
+
+ align:start position:0%
+academics but we also had field users we
+had the midwives from Kenya and Tanzania
+
+ align:start position:0%
+had the midwives from Kenya and Tanzania
+ 
+
+ align:start position:0%
+had the midwives from Kenya and Tanzania
+Etc and when the academics were fighting
+
+ align:start position:0%
+Etc and when the academics were fighting
+ 
+
+ align:start position:0%
+Etc and when the academics were fighting
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+myi and then they were saying well maybe
+
+ align:start position:0%
+myi and then they were saying well maybe
+ 
+
+ align:start position:0%
+myi and then they were saying well maybe
+we shouldn't have a checklist you know
+
+ align:start position:0%
+we shouldn't have a checklist you know
+ 
+
+ align:start position:0%
+we shouldn't have a checklist you know
+we can't really decide what should be on
+
+ align:start position:0%
+we can't really decide what should be on
+ 
+
+ align:start position:0%
+we can't really decide what should be on
+the checklist I remember the Kenyan
+
+ align:start position:0%
+the checklist I remember the Kenyan
+ 
+
+ align:start position:0%
+the checklist I remember the Kenyan
+Midwife stood up and said just this
+
+ align:start position:0%
+Midwife stood up and said just this
+ 
+
+ align:start position:0%
+Midwife stood up and said just this
+draft this like draft prototype number
+
+ align:start position:0%
+draft this like draft prototype number
+ 
+
+ align:start position:0%
+draft this like draft prototype number
+one can I photocopy it and take it
+
+ align:start position:0%
+one can I photocopy it and take it
+ 
+
+ align:start position:0%
+one can I photocopy it and take it
+because this will make a real difference
+
+ align:start position:0%
+because this will make a real difference
+ 
+
+ align:start position:0%
+because this will make a real difference
+and actually this happened over the
+
+ align:start position:0%
+and actually this happened over the
+ 
+
+ align:start position:0%
+and actually this happened over the
+process you know we had a WebEx later on
+
+ align:start position:0%
+process you know we had a WebEx later on
+ 
+
+ align:start position:0%
+process you know we had a WebEx later on
+in the process and again it was midwives
+
+ align:start position:0%
+in the process and again it was midwives
+ 
+
+ align:start position:0%
+in the process and again it was midwives
+on the front line saying I don't really
+
+ align:start position:0%
+on the front line saying I don't really
+ 
+
+ align:start position:0%
+on the front line saying I don't really
+care about the minui I just want to
+
+ align:start position:0%
+care about the minui I just want to
+ 
+
+ align:start position:0%
+care about the minui I just want to
+start using this because I know it will
+
+ align:start position:0%
+start using this because I know it will
+ 
+
+ align:start position:0%
+start using this because I know it will
+make a
+
+ align:start position:0%
+make a
+ 
+
+ align:start position:0%
+make a
+difference so the next stage now this
+
+ align:start position:0%
+difference so the next stage now this
+ 
+
+ align:start position:0%
+difference so the next stage now this
+was squashed for the safe surgery they
+
+ align:start position:0%
+was squashed for the safe surgery they
+ 
+
+ align:start position:0%
+was squashed for the safe surgery they
+had eight sites and they sort of did the
+
+ align:start position:0%
+had eight sites and they sort of did the
+ 
+
+ align:start position:0%
+had eight sites and they sort of did the
+pilot study for the safe child birth we
+
+ align:start position:0%
+pilot study for the safe child birth we
+ 
+
+ align:start position:0%
+pilot study for the safe child birth we
+uh separated it so we have a pilot study
+
+ align:start position:0%
+uh separated it so we have a pilot study
+ 
+
+ align:start position:0%
+uh separated it so we have a pilot study
+which I'll talk about briefly if I can
+
+ align:start position:0%
+which I'll talk about briefly if I can
+ 
+
+ align:start position:0%
+which I'll talk about briefly if I can
+get rid of the frog in my throat in
+
+ align:start position:0%
+get rid of the frog in my throat in
+ 
+
+ align:start position:0%
+get rid of the frog in my throat in
+India which is just one Center and then
+
+ align:start position:0%
+India which is just one Center and then
+ 
+
+ align:start position:0%
+India which is just one Center and then
+we're moving on to the randomized
+
+ align:start position:0%
+we're moving on to the randomized
+ 
+
+ align:start position:0%
+we're moving on to the randomized
+control trial because academics want the
+
+ align:start position:0%
+control trial because academics want the
+ 
+
+ align:start position:0%
+control trial because academics want the
+randomized control trial to prove that
+
+ align:start position:0%
+randomized control trial to prove that
+ 
+
+ align:start position:0%
+randomized control trial to prove that
+it has an impact on mortality so we see
+
+ align:start position:0%
+it has an impact on mortality so we see
+ 
+
+ align:start position:0%
+it has an impact on mortality so we see
+as the first step is is there
+
+ align:start position:0%
+as the first step is is there
+ 
+
+ align:start position:0%
+as the first step is is there
+Improvement in processes and then the
+
+ align:start position:0%
+Improvement in processes and then the
+ 
+
+ align:start position:0%
+Improvement in processes and then the
+second step is does this Improvement in
+
+ align:start position:0%
+second step is does this Improvement in
+ 
+
+ align:start position:0%
+second step is does this Improvement in
+process lead to reduced number of deaths
+
+ align:start position:0%
+process lead to reduced number of deaths
+ 
+
+ align:start position:0%
+process lead to reduced number of deaths
+now dissemination seems to be falling
+
+ align:start position:0%
+now dissemination seems to be falling
+ 
+
+ align:start position:0%
+now dissemination seems to be falling
+off the slide but actually it's where
+
+ align:start position:0%
+off the slide but actually it's where
+ 
+
+ align:start position:0%
+off the slide but actually it's where
+who sits and I think dissemination is
+
+ align:start position:0%
+who sits and I think dissemination is
+ 
+
+ align:start position:0%
+who sits and I think dissemination is
+something you need to think about right
+
+ align:start position:0%
+something you need to think about right
+ 
+
+ align:start position:0%
+something you need to think about right
+at the beginning of your process and
+
+ align:start position:0%
+at the beginning of your process and
+ 
+
+ align:start position:0%
+at the beginning of your process and
+through the process I've been thinking
+
+ align:start position:0%
+through the process I've been thinking
+ 
+
+ align:start position:0%
+through the process I've been thinking
+why did we start working with wh
+
+ align:start position:0%
+why did we start working with wh
+ 
+
+ align:start position:0%
+why did we start working with wh
+actually they are critical for when the
+
+ align:start position:0%
+actually they are critical for when the
+ 
+
+ align:start position:0%
+actually they are critical for when the
+tools been proven to disseminate across
+
+ align:start position:0%
+tools been proven to disseminate across
+ 
+
+ align:start position:0%
+tools been proven to disseminate across
+the world and so even though it was
+
+ align:start position:0%
+the world and so even though it was
+ 
+
+ align:start position:0%
+the world and so even though it was
+painful working with them at times they
+
+ align:start position:0%
+painful working with them at times they
+ 
+
+ align:start position:0%
+painful working with them at times they
+are now crucial for getting the message
+
+ align:start position:0%
+are now crucial for getting the message
+ 
+
+ align:start position:0%
+are now crucial for getting the message
+out um and if anyone has ideas for where
+
+ align:start position:0%
+out um and if anyone has ideas for where
+ 
+
+ align:start position:0%
+out um and if anyone has ideas for where
+we can put the safe child with checklist
+
+ align:start position:0%
+we can put the safe child with checklist
+ 
+
+ align:start position:0%
+we can put the safe child with checklist
+in terms of a good program then let me
+
+ align:start position:0%
+in terms of a good program then let me
+ 
+
+ align:start position:0%
+in terms of a good program then let me
+know because er's ended um so we're
+
+ align:start position:0%
+know because er's ended um so we're
+ 
+
+ align:start position:0%
+know because er's ended um so we're
+thinking of the next soap opera so I
+
+ align:start position:0%
+thinking of the next soap opera so I
+ 
+
+ align:start position:0%
+thinking of the next soap opera so I
+just want to talk about a few points
+
+ align:start position:0%
+just want to talk about a few points
+ 
+
+ align:start position:0%
+just want to talk about a few points
+this is a safe surgery checklist this is
+
+ align:start position:0%
+this is a safe surgery checklist this is
+ 
+
+ align:start position:0%
+this is a safe surgery checklist this is
+the PO point when you're identifying the
+
+ align:start position:0%
+the PO point when you're identifying the
+ 
+
+ align:start position:0%
+the PO point when you're identifying the
+pause points there have to be natural
+
+ align:start position:0%
+pause points there have to be natural
+ 
+
+ align:start position:0%
+pause points there have to be natural
+breaks in your clinical workflow so you
+
+ align:start position:0%
+breaks in your clinical workflow so you
+ 
+
+ align:start position:0%
+breaks in your clinical workflow so you
+want them I mean the safe surgery was
+
+ align:start position:0%
+want them I mean the safe surgery was
+ 
+
+ align:start position:0%
+want them I mean the safe surgery was
+perfect like when people get together
+
+ align:start position:0%
+perfect like when people get together
+ 
+
+ align:start position:0%
+perfect like when people get together
+and they're about to start a case you're
+
+ align:start position:0%
+and they're about to start a case you're
+ 
+
+ align:start position:0%
+and they're about to start a case you're
+already sort of talking and chatting
+
+ align:start position:0%
+already sort of talking and chatting
+ 
+
+ align:start position:0%
+already sort of talking and chatting
+pick up a checklist at the end when the
+
+ align:start position:0%
+pick up a checklist at the end when the
+ 
+
+ align:start position:0%
+pick up a checklist at the end when the
+patient leaves natural pause Point pick
+
+ align:start position:0%
+patient leaves natural pause Point pick
+ 
+
+ align:start position:0%
+patient leaves natural pause Point pick
+up the checklist for child birth there
+
+ align:start position:0%
+up the checklist for child birth there
+ 
+
+ align:start position:0%
+up the checklist for child birth there
+was a little bit of anxiety over where
+
+ align:start position:0%
+was a little bit of anxiety over where
+ 
+
+ align:start position:0%
+was a little bit of anxiety over where
+we were going to create these natural
+
+ align:start position:0%
+we were going to create these natural
+ 
+
+ align:start position:0%
+we were going to create these natural
+breaks and the reason it's important to
+
+ align:start position:0%
+breaks and the reason it's important to
+ 
+
+ align:start position:0%
+breaks and the reason it's important to
+be natural you don't want too much
+
+ align:start position:0%
+be natural you don't want too much
+ 
+
+ align:start position:0%
+be natural you don't want too much
+Behavior change happening so you want
+
+ align:start position:0%
+Behavior change happening so you want
+ 
+
+ align:start position:0%
+Behavior change happening so you want
+people to feel like it's completely
+
+ align:start position:0%
+people to feel like it's completely
+ 
+
+ align:start position:0%
+people to feel like it's completely
+normal to then have to pick up the
+
+ align:start position:0%
+normal to then have to pick up the
+ 
+
+ align:start position:0%
+normal to then have to pick up the
+checklist and do
+
+ align:start position:0%
+checklist and do
+ 
+
+ align:start position:0%
+checklist and do
+something um CR missions these are
+
+ align:start position:0%
+something um CR missions these are
+ 
+
+ align:start position:0%
+something um CR missions these are
+things that if you don't do you will
+
+ align:start position:0%
+things that if you don't do you will
+ 
+
+ align:start position:0%
+things that if you don't do you will
+cause severe harm and they make up your
+
+ align:start position:0%
+cause severe harm and they make up your
+ 
+
+ align:start position:0%
+cause severe harm and they make up your
+checklist items as we spoke about every
+
+ align:start position:0%
+checklist items as we spoke about every
+ 
+
+ align:start position:0%
+checklist items as we spoke about every
+single one of our checklists says this
+
+ align:start position:0%
+single one of our checklists says this
+ 
+
+ align:start position:0%
+single one of our checklists says this
+checklist is not intended to be
+
+ align:start position:0%
+checklist is not intended to be
+ 
+
+ align:start position:0%
+checklist is not intended to be
+comprehensive additions and
+
+ align:start position:0%
+comprehensive additions and
+ 
+
+ align:start position:0%
+comprehensive additions and
+modifications to fit local practice are
+
+ align:start position:0%
+modifications to fit local practice are
+ 
+
+ align:start position:0%
+modifications to fit local practice are
+encouraged that's not just about
+
+ align:start position:0%
+encouraged that's not just about
+ 
+
+ align:start position:0%
+encouraged that's not just about
+humility actually we realize that local
+
+ align:start position:0%
+humility actually we realize that local
+ 
+
+ align:start position:0%
+humility actually we realize that local
+ownership is really important so they
+
+ align:start position:0%
+ownership is really important so they
+ 
+
+ align:start position:0%
+ownership is really important so they
+don't want some tool from America being
+
+ align:start position:0%
+don't want some tool from America being
+ 
+
+ align:start position:0%
+don't want some tool from America being
+landed in Zambia and saying use this
+
+ align:start position:0%
+landed in Zambia and saying use this
+ 
+
+ align:start position:0%
+landed in Zambia and saying use this
+you'll be great because we know
+
+ align:start position:0%
+you'll be great because we know
+ 
+
+ align:start position:0%
+you'll be great because we know
+everything thing they want to be able to
+
+ align:start position:0%
+everything thing they want to be able to
+ 
+
+ align:start position:0%
+everything thing they want to be able to
+modify and say well we need to tweak
+
+ align:start position:0%
+modify and say well we need to tweak
+ 
+
+ align:start position:0%
+modify and say well we need to tweak
+this or this is
+
+ align:start position:0%
+this or this is
+ 
+
+ align:start position:0%
+this or this is
+important it has to be a Control process
+
+ align:start position:0%
+important it has to be a Control process
+ 
+
+ align:start position:0%
+important it has to be a Control process
+because what's on the checklist is
+
+ align:start position:0%
+because what's on the checklist is
+ 
+
+ align:start position:0%
+because what's on the checklist is
+evidence-based you know it's taken a
+
+ align:start position:0%
+evidence-based you know it's taken a
+ 
+
+ align:start position:0%
+evidence-based you know it's taken a
+long time to agree and so we actually
+
+ align:start position:0%
+long time to agree and so we actually
+ 
+
+ align:start position:0%
+long time to agree and so we actually
+now have a bit of a process on how you
+
+ align:start position:0%
+now have a bit of a process on how you
+ 
+
+ align:start position:0%
+now have a bit of a process on how you
+decide what comes on and off and
+
+ align:start position:0%
+decide what comes on and off and
+ 
+
+ align:start position:0%
+decide what comes on and off and
+generally you'll find people want add
+
+ align:start position:0%
+generally you'll find people want add
+ 
+
+ align:start position:0%
+generally you'll find people want add
+Lots on so we have a bit of a rule you
+
+ align:start position:0%
+Lots on so we have a bit of a rule you
+ 
+
+ align:start position:0%
+Lots on so we have a bit of a rule you
+can add one off you probably need to
+
+ align:start position:0%
+can add one off you probably need to
+ 
+
+ align:start position:0%
+can add one off you probably need to
+take one off um the other thing is does
+
+ align:start position:0%
+take one off um the other thing is does
+ 
+
+ align:start position:0%
+take one off um the other thing is does
+it actually impact mortality so for
+
+ align:start position:0%
+it actually impact mortality so for
+ 
+
+ align:start position:0%
+it actually impact mortality so for
+child birth everyone's like we want to
+
+ align:start position:0%
+child birth everyone's like we want to
+ 
+
+ align:start position:0%
+child birth everyone's like we want to
+put pomy on like so that's like a cut
+
+ align:start position:0%
+put pomy on like so that's like a cut
+ 
+
+ align:start position:0%
+put pomy on like so that's like a cut
+instead of tearing and like well is that
+
+ align:start position:0%
+instead of tearing and like well is that
+ 
+
+ align:start position:0%
+instead of tearing and like well is that
+actually going to prevent deaths no okay
+
+ align:start position:0%
+actually going to prevent deaths no okay
+ 
+
+ align:start position:0%
+actually going to prevent deaths no okay
+perhaps we won't put it on the checklist
+
+ align:start position:0%
+perhaps we won't put it on the checklist
+ 
+
+ align:start position:0%
+perhaps we won't put it on the checklist
+but it is important to get their local
+
+ align:start position:0%
+but it is important to get their local
+ 
+
+ align:start position:0%
+but it is important to get their local
+bind and for them to feel it's their
+
+ align:start position:0%
+bind and for them to feel it's their
+ 
+
+ align:start position:0%
+bind and for them to feel it's their
+tool and then we spoke a little bit
+
+ align:start position:0%
+tool and then we spoke a little bit
+ 
+
+ align:start position:0%
+tool and then we spoke a little bit
+about this it's that magical ingredient
+
+ align:start position:0%
+about this it's that magical ingredient
+ 
+
+ align:start position:0%
+about this it's that magical ingredient
+so processes like giving antibiotics are
+
+ align:start position:0%
+so processes like giving antibiotics are
+ 
+
+ align:start position:0%
+so processes like giving antibiotics are
+important in the developing world
+
+ align:start position:0%
+important in the developing world
+ 
+
+ align:start position:0%
+important in the developing world
+because they're not doing it most of
+
+ align:start position:0%
+because they're not doing it most of
+ 
+
+ align:start position:0%
+because they're not doing it most of
+these processes people are doing in the
+
+ align:start position:0%
+these processes people are doing in the
+ 
+
+ align:start position:0%
+these processes people are doing in the
+developed world and yet there was still
+
+ align:start position:0%
+developed world and yet there was still
+ 
+
+ align:start position:0%
+developed world and yet there was still
+difference and there I think it's that
+
+ align:start position:0%
+difference and there I think it's that
+ 
+
+ align:start position:0%
+difference and there I think it's that
+oh that's very kind thank you I love MIT
+
+ align:start position:0%
+oh that's very kind thank you I love MIT
+ 
+
+ align:start position:0%
+oh that's very kind thank you I love MIT
+um uh this is where I mean my sister's
+
+ align:start position:0%
+um uh this is where I mean my sister's
+ 
+
+ align:start position:0%
+um uh this is where I mean my sister's
+uh trained to be a pilot and her second
+
+ align:start position:0%
+uh trained to be a pilot and her second
+ 
+
+ align:start position:0%
+uh trained to be a pilot and her second
+lecture was she got handed this book on
+
+ align:start position:0%
+lecture was she got handed this book on
+ 
+
+ align:start position:0%
+lecture was she got handed this book on
+human
+
+ align:start position:0%
+human
+ 
+
+ align:start position:0%
+human
+factors and I picked it up it's
+
+ align:start position:0%
+factors and I picked it up it's
+ 
+
+ align:start position:0%
+factors and I picked it up it's
+something you've discussed and I was
+
+ align:start position:0%
+something you've discussed and I was
+ 
+
+ align:start position:0%
+something you've discussed and I was
+like oh this is great and she looked at
+
+ align:start position:0%
+like oh this is great and she looked at
+ 
+
+ align:start position:0%
+like oh this is great and she looked at
+me and went hang on a minute you're
+
+ align:start position:0%
+me and went hang on a minute you're
+ 
+
+ align:start position:0%
+me and went hang on a minute you're
+making life death decisions all the time
+
+ align:start position:0%
+making life death decisions all the time
+ 
+
+ align:start position:0%
+making life death decisions all the time
+have you not read this book on human
+
+ align:start position:0%
+have you not read this book on human
+ 
+
+ align:start position:0%
+have you not read this book on human
+factors and I was like uh no actually we
+
+ align:start position:0%
+factors and I was like uh no actually we
+ 
+
+ align:start position:0%
+factors and I was like uh no actually we
+were just told you go to medal School
+
+ align:start position:0%
+were just told you go to medal School
+ 
+
+ align:start position:0%
+were just told you go to medal School
+you read your books you do good training
+
+ align:start position:0%
+you read your books you do good training
+ 
+
+ align:start position:0%
+you read your books you do good training
+and you're God and everything will be
+
+ align:start position:0%
+and you're God and everything will be
+ 
+
+ align:start position:0%
+and you're God and everything will be
+fine and she was like oh right and she
+
+ align:start position:0%
+fine and she was like oh right and she
+ 
+
+ align:start position:0%
+fine and she was like oh right and she
+said what about crew Resource Management
+
+ align:start position:0%
+said what about crew Resource Management
+ 
+
+ align:start position:0%
+said what about crew Resource Management
+I was like what's that she says well
+
+ align:start position:0%
+I was like what's that she says well
+ 
+
+ align:start position:0%
+I was like what's that she says well
+when we go into the cockpit we have
+
+ align:start position:0%
+when we go into the cockpit we have
+ 
+
+ align:start position:0%
+when we go into the cockpit we have
+moments to create an effective team and
+
+ align:start position:0%
+moments to create an effective team and
+ 
+
+ align:start position:0%
+moments to create an effective team and
+the effective team is important not when
+
+ align:start position:0%
+the effective team is important not when
+ 
+
+ align:start position:0%
+the effective team is important not when
+the flight's going well it's important
+
+ align:start position:0%
+the flight's going well it's important
+ 
+
+ align:start position:0%
+the flight's going well it's important
+when there's an emergency and I had I'm
+
+ align:start position:0%
+when there's an emergency and I had I'm
+ 
+
+ align:start position:0%
+when there's an emergency and I had I'm
+an OB obstetrician and I remember doing
+
+ align:start position:0%
+an OB obstetrician and I remember doing
+ 
+
+ align:start position:0%
+an OB obstetrician and I remember doing
+this procedure where I needed blood in
+
+ align:start position:0%
+this procedure where I needed blood in
+ 
+
+ align:start position:0%
+this procedure where I needed blood in
+the middle of the case and I yell No One
+
+ align:start position:0%
+the middle of the case and I yell No One
+ 
+
+ align:start position:0%
+the middle of the case and I yell No One
+Ever Knows who the millions of people
+
+ align:start position:0%
+Ever Knows who the millions of people
+ 
+
+ align:start position:0%
+Ever Knows who the millions of people
+are in theater right so I yell off to
+
+ align:start position:0%
+are in theater right so I yell off to
+ 
+
+ align:start position:0%
+are in theater right so I yell off to
+this woman go get me blood and 20
+
+ align:start position:0%
+this woman go get me blood and 20
+ 
+
+ align:start position:0%
+this woman go get me blood and 20
+minutes later I'm like where's the blood
+
+ align:start position:0%
+minutes later I'm like where's the blood
+ 
+
+ align:start position:0%
+minutes later I'm like where's the blood
+getting angry that the blood hasn't
+
+ align:start position:0%
+getting angry that the blood hasn't
+ 
+
+ align:start position:0%
+getting angry that the blood hasn't
+arrived and I look at her she's like I'm
+
+ align:start position:0%
+arrived and I look at her she's like I'm
+ 
+
+ align:start position:0%
+arrived and I look at her she's like I'm
+just an observer I don't know where the
+
+ align:start position:0%
+just an observer I don't know where the
+ 
+
+ align:start position:0%
+just an observer I don't know where the
+blood is I was like oh I really should
+
+ align:start position:0%
+blood is I was like oh I really should
+ 
+
+ align:start position:0%
+blood is I was like oh I really should
+know who was my like circulating nurse
+
+ align:start position:0%
+know who was my like circulating nurse
+ 
+
+ align:start position:0%
+know who was my like circulating nurse
+and that's the M magical ingredient
+
+ align:start position:0%
+and that's the M magical ingredient
+ 
+
+ align:start position:0%
+and that's the M magical ingredient
+behind this they sort of confirm who you
+
+ align:start position:0%
+behind this they sort of confirm who you
+ 
+
+ align:start position:0%
+behind this they sort of confirm who you
+are let's all sit together the other
+
+ align:start position:0%
+are let's all sit together the other
+ 
+
+ align:start position:0%
+are let's all sit together the other
+component when with the checklist was
+
+ align:start position:0%
+component when with the checklist was
+ 
+
+ align:start position:0%
+component when with the checklist was
+the briefing like you all got together
+
+ align:start position:0%
+the briefing like you all got together
+ 
+
+ align:start position:0%
+the briefing like you all got together
+and discussed the cases of the day so I
+
+ align:start position:0%
+and discussed the cases of the day so I
+ 
+
+ align:start position:0%
+and discussed the cases of the day so I
+come from the UK it was mandated across
+
+ align:start position:0%
+come from the UK it was mandated across
+ 
+
+ align:start position:0%
+come from the UK it was mandated across
+hospitals someone was talking about
+
+ align:start position:0%
+hospitals someone was talking about
+ 
+
+ align:start position:0%
+hospitals someone was talking about
+institutional support but everyone had
+
+ align:start position:0%
+institutional support but everyone had
+ 
+
+ align:start position:0%
+institutional support but everyone had
+to do it and people were like oh God
+
+ align:start position:0%
+to do it and people were like oh God
+ 
+
+ align:start position:0%
+to do it and people were like oh God
+this is going to be such a nightmare but
+
+ align:start position:0%
+this is going to be such a nightmare but
+ 
+
+ align:start position:0%
+this is going to be such a nightmare but
+the briefing really helped so we one of
+
+ align:start position:0%
+the briefing really helped so we one of
+ 
+
+ align:start position:0%
+the briefing really helped so we one of
+the incentives we used is we timed our
+
+ align:start position:0%
+the incentives we used is we timed our
+ 
+
+ align:start position:0%
+the incentives we used is we timed our
+day so if I had six operations normally
+
+ align:start position:0%
+day so if I had six operations normally
+ 
+
+ align:start position:0%
+day so if I had six operations normally
+that would start at 9:00 with faf in
+
+ align:start position:0%
+that would start at 9:00 with faf in
+ 
+
+ align:start position:0%
+that would start at 9:00 with faf in
+between and finish at 6:30 an hour and a
+
+ align:start position:0%
+between and finish at 6:30 an hour and a
+ 
+
+ align:start position:0%
+between and finish at 6:30 an hour and a
+half after everyone should have left we
+
+ align:start position:0%
+half after everyone should have left we
+ 
+
+ align:start position:0%
+half after everyone should have left we
+started timing the day and recording it
+
+ align:start position:0%
+started timing the day and recording it
+ 
+
+ align:start position:0%
+started timing the day and recording it
+and we we were reducing the time because
+
+ align:start position:0%
+and we we were reducing the time because
+ 
+
+ align:start position:0%
+and we we were reducing the time because
+there was less sort of you know messing
+
+ align:start position:0%
+there was less sort of you know messing
+ 
+
+ align:start position:0%
+there was less sort of you know messing
+around between cases so the nurses were
+
+ align:start position:0%
+around between cases so the nurses were
+ 
+
+ align:start position:0%
+around between cases so the nurses were
+able to leave an hour earlier so there
+
+ align:start position:0%
+able to leave an hour earlier so there
+ 
+
+ align:start position:0%
+able to leave an hour earlier so there
+there's a lot to be said for that
+
+ align:start position:0%
+there's a lot to be said for that
+ 
+
+ align:start position:0%
+there's a lot to be said for that
+teamwork communication component that we
+
+ align:start position:0%
+teamwork communication component that we
+ 
+
+ align:start position:0%
+teamwork communication component that we
+can't really
+
+ align:start position:0%
+can't really
+ 
+
+ align:start position:0%
+can't really
+measure so as I said our challenge was
+
+ align:start position:0%
+measure so as I said our challenge was
+ 
+
+ align:start position:0%
+measure so as I said our challenge was
+mdgs four and five we know that we're
+
+ align:start position:0%
+mdgs four and five we know that we're
+ 
+
+ align:start position:0%
+mdgs four and five we know that we're
+having all this mortality and we know
+
+ align:start position:0%
+having all this mortality and we know
+ 
+
+ align:start position:0%
+having all this mortality and we know
+the causes and what's really sad is that
+
+ align:start position:0%
+the causes and what's really sad is that
+ 
+
+ align:start position:0%
+the causes and what's really sad is that
+we have proven interventions that are
+
+ align:start position:0%
+we have proven interventions that are
+ 
+
+ align:start position:0%
+we have proven interventions that are
+inexpensive and who has been trying to
+
+ align:start position:0%
+inexpensive and who has been trying to
+ 
+
+ align:start position:0%
+inexpensive and who has been trying to
+deliver these effectively four decades
+
+ align:start position:0%
+deliver these effectively four decades
+ 
+
+ align:start position:0%
+deliver these effectively four decades
+and we've been totally unable to get
+
+ align:start position:0%
+and we've been totally unable to get
+ 
+
+ align:start position:0%
+and we've been totally unable to get
+them to the bedside
+
+ align:start position:0%
+them to the bedside
+ 
+
+ align:start position:0%
+them to the bedside
+reliably it's a slightly different
+
+ align:start position:0%
+reliably it's a slightly different
+ 
+
+ align:start position:0%
+reliably it's a slightly different
+challenge to the safe surgery checklist
+
+ align:start position:0%
+challenge to the safe surgery checklist
+ 
+
+ align:start position:0%
+challenge to the safe surgery checklist
+so 99% of our burden of disease is in
+
+ align:start position:0%
+so 99% of our burden of disease is in
+ 
+
+ align:start position:0%
+so 99% of our burden of disease is in
+the developing world and why that's
+
+ align:start position:0%
+the developing world and why that's
+ 
+
+ align:start position:0%
+the developing world and why that's
+important is it's got to be very
+
+ align:start position:0%
+important is it's got to be very
+ 
+
+ align:start position:0%
+important is it's got to be very
+succinct these uh caregivers don't have
+
+ align:start position:0%
+succinct these uh caregivers don't have
+ 
+
+ align:start position:0%
+succinct these uh caregivers don't have
+excess time and second we can't have
+
+ align:start position:0%
+excess time and second we can't have
+ 
+
+ align:start position:0%
+excess time and second we can't have
+like intense Supply requirements because
+
+ align:start position:0%
+like intense Supply requirements because
+ 
+
+ align:start position:0%
+like intense Supply requirements because
+they probably won't have the resources
+
+ align:start position:0%
+they probably won't have the resources
+ 
+
+ align:start position:0%
+they probably won't have the resources
+there consistently available again we
+
+ align:start position:0%
+there consistently available again we
+ 
+
+ align:start position:0%
+there consistently available again we
+don't have surge that have had some kind
+
+ align:start position:0%
+don't have surge that have had some kind
+ 
+
+ align:start position:0%
+don't have surge that have had some kind
+of training some of the caregivers in
+
+ align:start position:0%
+of training some of the caregivers in
+ 
+
+ align:start position:0%
+of training some of the caregivers in
+these places have just been taught how
+
+ align:start position:0%
+these places have just been taught how
+ 
+
+ align:start position:0%
+these places have just been taught how
+to do some deliveries in the last six
+
+ align:start position:0%
+to do some deliveries in the last six
+ 
+
+ align:start position:0%
+to do some deliveries in the last six
+months or minimal training so again it
+
+ align:start position:0%
+months or minimal training so again it
+ 
+
+ align:start position:0%
+months or minimal training so again it
+had to be a slightly different tool the
+
+ align:start position:0%
+had to be a slightly different tool the
+ 
+
+ align:start position:0%
+had to be a slightly different tool the
+high risk period that you want to cover
+
+ align:start position:0%
+high risk period that you want to cover
+ 
+
+ align:start position:0%
+high risk period that you want to cover
+with the checklist well ours could cover
+
+ align:start position:0%
+with the checklist well ours could cover
+ 
+
+ align:start position:0%
+with the checklist well ours could cover
+weeks you know days to weeks someone
+
+ align:start position:0%
+weeks you know days to weeks someone
+ 
+
+ align:start position:0%
+weeks you know days to weeks someone
+comes in on a Monday by the time they've
+
+ align:start position:0%
+comes in on a Monday by the time they've
+ 
+
+ align:start position:0%
+comes in on a Monday by the time they've
+delivered and they're being discharged
+
+ align:start position:0%
+delivered and they're being discharged
+ 
+
+ align:start position:0%
+delivered and they're being discharged
+it could be sort of 5 days later it
+
+ align:start position:0%
+it could be sort of 5 days later it
+ 
+
+ align:start position:0%
+it could be sort of 5 days later it
+covers many rooms it covers multiple
+
+ align:start position:0%
+covers many rooms it covers multiple
+ 
+
+ align:start position:0%
+covers many rooms it covers multiple
+caregivers and it could be across
+
+ align:start position:0%
+caregivers and it could be across
+ 
+
+ align:start position:0%
+caregivers and it could be across
+facilities like someone gets referred so
+
+ align:start position:0%
+facilities like someone gets referred so
+ 
+
+ align:start position:0%
+facilities like someone gets referred so
+how is this checklist going to cover all
+
+ align:start position:0%
+how is this checklist going to cover all
+ 
+
+ align:start position:0%
+how is this checklist going to cover all
+these situations and we don't have an
+
+ align:start position:0%
+these situations and we don't have an
+ 
+
+ align:start position:0%
+these situations and we don't have an
+obvious team structure to work with in
+
+ align:start position:0%
+obvious team structure to work with in
+ 
+
+ align:start position:0%
+obvious team structure to work with in
+some situations you'll just have the one
+
+ align:start position:0%
+some situations you'll just have the one
+ 
+
+ align:start position:0%
+some situations you'll just have the one
+Midwife in the little health facility so
+
+ align:start position:0%
+Midwife in the little health facility so
+ 
+
+ align:start position:0%
+Midwife in the little health facility so
+put those in Reds because they were
+
+ align:start position:0%
+put those in Reds because they were
+ 
+
+ align:start position:0%
+put those in Reds because they were
+challenges some people felt the next one
+
+ align:start position:0%
+challenges some people felt the next one
+ 
+
+ align:start position:0%
+challenges some people felt the next one
+should be a challenge the woman's well
+
+ align:start position:0%
+should be a challenge the woman's well
+ 
+
+ align:start position:0%
+should be a challenge the woman's well
+you know pregnancy isn't a disease and
+
+ align:start position:0%
+you know pregnancy isn't a disease and
+ 
+
+ align:start position:0%
+you know pregnancy isn't a disease and
+she's awake what does that mean do we
+
+ align:start position:0%
+she's awake what does that mean do we
+ 
+
+ align:start position:0%
+she's awake what does that mean do we
+just bypass her or do we include her in
+
+ align:start position:0%
+just bypass her or do we include her in
+ 
+
+ align:start position:0%
+just bypass her or do we include her in
+the team I've put it in Orange because I
+
+ align:start position:0%
+the team I've put it in Orange because I
+ 
+
+ align:start position:0%
+the team I've put it in Orange because I
+actually think it's a benefit and then
+
+ align:start position:0%
+actually think it's a benefit and then
+ 
+
+ align:start position:0%
+actually think it's a benefit and then
+the advantage we had is that we've
+
+ align:start position:0%
+the advantage we had is that we've
+ 
+
+ align:start position:0%
+the advantage we had is that we've
+actually got a good evidence base for
+
+ align:start position:0%
+actually got a good evidence base for
+ 
+
+ align:start position:0%
+actually got a good evidence base for
+Safe child birth compared to safe
+
+ align:start position:0%
+Safe child birth compared to safe
+ 
+
+ align:start position:0%
+Safe child birth compared to safe
+surgery don't worry about the detail the
+
+ align:start position:0%
+surgery don't worry about the detail the
+ 
+
+ align:start position:0%
+surgery don't worry about the detail the
+reason I brought the slide up is we used
+
+ align:start position:0%
+reason I brought the slide up is we used
+ 
+
+ align:start position:0%
+reason I brought the slide up is we used
+every single source of information we
+
+ align:start position:0%
+every single source of information we
+ 
+
+ align:start position:0%
+every single source of information we
+could find published unpublished
+
+ align:start position:0%
+could find published unpublished
+ 
+
+ align:start position:0%
+could find published unpublished
+literature opinion getting experts
+
+ align:start position:0%
+literature opinion getting experts
+ 
+
+ align:start position:0%
+literature opinion getting experts
+together and it was all to ensure that
+
+ align:start position:0%
+together and it was all to ensure that
+ 
+
+ align:start position:0%
+together and it was all to ensure that
+there wasn't something that we hadn't
+
+ align:start position:0%
+there wasn't something that we hadn't
+ 
+
+ align:start position:0%
+there wasn't something that we hadn't
+covered that would come up later on in
+
+ align:start position:0%
+covered that would come up later on in
+ 
+
+ align:start position:0%
+covered that would come up later on in
+the progam uh process of forming this
+
+ align:start position:0%
+the progam uh process of forming this
+ 
+
+ align:start position:0%
+the progam uh process of forming this
+checklist so how do you decide on your
+
+ align:start position:0%
+checklist so how do you decide on your
+ 
+
+ align:start position:0%
+checklist so how do you decide on your
+highrisk period Well we were sort of
+
+ align:start position:0%
+highrisk period Well we were sort of
+ 
+
+ align:start position:0%
+highrisk period Well we were sort of
+given that it's the 24-hour highrisk
+
+ align:start position:0%
+given that it's the 24-hour highrisk
+ 
+
+ align:start position:0%
+given that it's the 24-hour highrisk
+period where you know from admission to
+
+ align:start position:0%
+period where you know from admission to
+ 
+
+ align:start position:0%
+period where you know from admission to
+discharge
+
+ align:start position:0%
+discharge
+ 
+
+ align:start position:0%
+discharge
+um but how do you decide on your pause
+
+ align:start position:0%
+um but how do you decide on your pause
+ 
+
+ align:start position:0%
+um but how do you decide on your pause
+points as I said pause point one and
+
+ align:start position:0%
+points as I said pause point one and
+ 
+
+ align:start position:0%
+points as I said pause point one and
+four were quite easy and then yeah go
+
+ align:start position:0%
+four were quite easy and then yeah go
+ 
+
+ align:start position:0%
+four were quite easy and then yeah go
+ahead where are The Debs ah so the
+
+ align:start position:0%
+ahead where are The Debs ah so the
+ 
+
+ align:start position:0%
+ahead where are The Debs ah so the
+highest number of deaths are actually
+
+ align:start position:0%
+highest number of deaths are actually
+ 
+
+ align:start position:0%
+highest number of deaths are actually
+from uh at delivery so labor to delivery
+
+ align:start position:0%
+from uh at delivery so labor to delivery
+ 
+
+ align:start position:0%
+from uh at delivery so labor to delivery
+and then um postpartum so the first 48
+
+ align:start position:0%
+and then um postpartum so the first 48
+ 
+
+ align:start position:0%
+and then um postpartum so the first 48
+Hours um so that's why we said right
+
+ align:start position:0%
+Hours um so that's why we said right
+ 
+
+ align:start position:0%
+Hours um so that's why we said right
+we'll cover admission to discharge it
+
+ align:start position:0%
+we'll cover admission to discharge it
+ 
+
+ align:start position:0%
+we'll cover admission to discharge it
+doesn't cover the 48 hour so we cover
+
+ align:start position:0%
+doesn't cover the 48 hour so we cover
+ 
+
+ align:start position:0%
+doesn't cover the 48 hour so we cover
+all the way from dischar uh any
+
+ align:start position:0%
+all the way from dischar uh any
+ 
+
+ align:start position:0%
+all the way from dischar uh any
+discharge from facilities so so actually
+
+ align:start position:0%
+discharge from facilities so so actually
+ 
+
+ align:start position:0%
+discharge from facilities so so actually
+the tool covers if someone's discharged
+
+ align:start position:0%
+the tool covers if someone's discharged
+ 
+
+ align:start position:0%
+the tool covers if someone's discharged
+within 6 hours it'll only cover that if
+
+ align:start position:0%
+within 6 hours it'll only cover that if
+ 
+
+ align:start position:0%
+within 6 hours it'll only cover that if
+someone's discharged within a week we
+
+ align:start position:0%
+someone's discharged within a week we
+ 
+
+ align:start position:0%
+someone's discharged within a week we
+cover the whole
+
+ align:start position:0%
+cover the whole
+ 
+
+ align:start position:0%
+cover the whole
+week um and the two middle pause points
+
+ align:start position:0%
+week um and the two middle pause points
+ 
+
+ align:start position:0%
+week um and the two middle pause points
+were the sort of fudge Factor now
+
+ align:start position:0%
+were the sort of fudge Factor now
+ 
+
+ align:start position:0%
+were the sort of fudge Factor now
+ideally you'd have a pause point one
+
+ align:start position:0%
+ideally you'd have a pause point one
+ 
+
+ align:start position:0%
+ideally you'd have a pause point one
+minute after delivery because that's
+
+ align:start position:0%
+minute after delivery because that's
+ 
+
+ align:start position:0%
+minute after delivery because that's
+where you want the oxytocin to be given
+
+ align:start position:0%
+where you want the oxytocin to be given
+ 
+
+ align:start position:0%
+where you want the oxytocin to be given
+to prevent Hemorrhage but one minute
+
+ align:start position:0%
+to prevent Hemorrhage but one minute
+ 
+
+ align:start position:0%
+to prevent Hemorrhage but one minute
+someone's got gloves on and they're in
+
+ align:start position:0%
+someone's got gloves on and they're in
+ 
+
+ align:start position:0%
+someone's got gloves on and they're in
+the midst of stuff they're not going to
+
+ align:start position:0%
+the midst of stuff they're not going to
+ 
+
+ align:start position:0%
+the midst of stuff they're not going to
+pick up a
+
+ align:start position:0%
+pick up a
+ 
+
+ align:start position:0%
+pick up a
+checklist and the other time you'd want
+
+ align:start position:0%
+checklist and the other time you'd want
+ 
+
+ align:start position:0%
+checklist and the other time you'd want
+a checklist is actually every time me do
+
+ align:start position:0%
+a checklist is actually every time me do
+ 
+
+ align:start position:0%
+a checklist is actually every time me do
+an examination during labor but then our
+
+ align:start position:0%
+an examination during labor but then our
+ 
+
+ align:start position:0%
+an examination during labor but then our
+checklist would be really long and so
+
+ align:start position:0%
+checklist would be really long and so
+ 
+
+ align:start position:0%
+checklist would be really long and so
+again the checklist would SN so there is
+
+ align:start position:0%
+again the checklist would SN so there is
+ 
+
+ align:start position:0%
+again the checklist would SN so there is
+a compromise and what's actually going
+
+ align:start position:0%
+a compromise and what's actually going
+ 
+
+ align:start position:0%
+a compromise and what's actually going
+to be effectively
+
+ align:start position:0%
+to be effectively
+ 
+
+ align:start position:0%
+to be effectively
+implemented again it's not about the
+
+ align:start position:0%
+implemented again it's not about the
+ 
+
+ align:start position:0%
+implemented again it's not about the
+details people say I'm going to fall I'm
+
+ align:start position:0%
+details people say I'm going to fall I'm
+ 
+
+ align:start position:0%
+details people say I'm going to fall I'm
+going to make a checklist and then I'm
+
+ align:start position:0%
+going to make a checklist and then I'm
+ 
+
+ align:start position:0%
+going to make a checklist and then I'm
+going to tral it next week this took two
+
+ align:start position:0%
+going to tral it next week this took two
+ 
+
+ align:start position:0%
+going to tral it next week this took two
+years and yes a lot of this is because
+
+ align:start position:0%
+years and yes a lot of this is because
+ 
+
+ align:start position:0%
+years and yes a lot of this is because
+we were working with who we wanted to
+
+ align:start position:0%
+we were working with who we wanted to
+ 
+
+ align:start position:0%
+we were working with who we wanted to
+get the acceptability worldwide
+
+ align:start position:0%
+get the acceptability worldwide
+ 
+
+ align:start position:0%
+get the acceptability worldwide
+acceptability of everyone and all that
+
+ align:start position:0%
+acceptability of everyone and all that
+ 
+
+ align:start position:0%
+acceptability of everyone and all that
+takes a long time and I'm not saying it
+
+ align:start position:0%
+takes a long time and I'm not saying it
+ 
+
+ align:start position:0%
+takes a long time and I'm not saying it
+has to to take two years to make a
+
+ align:start position:0%
+has to to take two years to make a
+ 
+
+ align:start position:0%
+has to to take two years to make a
+checklist I'm just saying that if you
+
+ align:start position:0%
+checklist I'm just saying that if you
+ 
+
+ align:start position:0%
+checklist I'm just saying that if you
+want that acceptability across the board
+
+ align:start position:0%
+want that acceptability across the board
+ 
+
+ align:start position:0%
+want that acceptability across the board
+and you are thinking of worldwide Global
+
+ align:start position:0%
+and you are thinking of worldwide Global
+ 
+
+ align:start position:0%
+and you are thinking of worldwide Global
+scaleup then it's a long
+
+ align:start position:0%
+scaleup then it's a long
+ 
+
+ align:start position:0%
+scaleup then it's a long
+process and this is the who's who of
+
+ align:start position:0%
+process and this is the who's who of
+ 
+
+ align:start position:0%
+process and this is the who's who of
+Safe child birth and everyone we spoke
+
+ align:start position:0%
+Safe child birth and everyone we spoke
+ 
+
+ align:start position:0%
+Safe child birth and everyone we spoke
+to their network was wide all the red
+
+ align:start position:0%
+to their network was wide all the red
+ 
+
+ align:start position:0%
+to their network was wide all the red
+dots they either have research going on
+
+ align:start position:0%
+dots they either have research going on
+ 
+
+ align:start position:0%
+dots they either have research going on
+there they've worked there they have
+
+ align:start position:0%
+there they've worked there they have
+ 
+
+ align:start position:0%
+there they've worked there they have
+contacts there and we the green dots
+
+ align:start position:0%
+contacts there and we the green dots
+ 
+
+ align:start position:0%
+contacts there and we the green dots
+represent where we did usability
+
+ align:start position:0%
+represent where we did usability
+ 
+
+ align:start position:0%
+represent where we did usability
+feedback so it wasn't testing we said to
+
+ align:start position:0%
+feedback so it wasn't testing we said to
+ 
+
+ align:start position:0%
+feedback so it wasn't testing we said to
+these people please take this tool try
+
+ align:start position:0%
+these people please take this tool try
+ 
+
+ align:start position:0%
+these people please take this tool try
+it on one or two deliveries so ihi is
+
+ align:start position:0%
+it on one or two deliveries so ihi is
+ 
+
+ align:start position:0%
+it on one or two deliveries so ihi is
+all about starting small we did that in
+
+ align:start position:0%
+all about starting small we did that in
+ 
+
+ align:start position:0%
+all about starting small we did that in
+the sort of crafting method we said okay
+
+ align:start position:0%
+the sort of crafting method we said okay
+ 
+
+ align:start position:0%
+the sort of crafting method we said okay
+you take this and then we'll have a call
+
+ align:start position:0%
+you take this and then we'll have a call
+ 
+
+ align:start position:0%
+you take this and then we'll have a call
+with you and you change and the
+
+ align:start position:0%
+with you and you change and the
+ 
+
+ align:start position:0%
+with you and you change and the
+checklist however you want and so at the
+
+ align:start position:0%
+checklist however you want and so at the
+ 
+
+ align:start position:0%
+checklist however you want and so at the
+end we had sort of 11 checklists and
+
+ align:start position:0%
+end we had sort of 11 checklists and
+ 
+
+ align:start position:0%
+end we had sort of 11 checklists and
+then we were going to combine
+
+ align:start position:0%
+then we were going to combine
+ 
+
+ align:start position:0%
+then we were going to combine
+them and this is what happened there's
+
+ align:start position:0%
+them and this is what happened there's
+ 
+
+ align:start position:0%
+them and this is what happened there's
+it's a two-sided checklist what it's
+
+ align:start position:0%
+it's a two-sided checklist what it's
+ 
+
+ align:start position:0%
+it's a two-sided checklist what it's
+four pause points the first is the two
+
+ align:start position:0%
+four pause points the first is the two
+ 
+
+ align:start position:0%
+four pause points the first is the two
+one before delivery and at the end on
+
+ align:start position:0%
+one before delivery and at the end on
+ 
+
+ align:start position:0%
+one before delivery and at the end on
+the other side is the two puse points
+
+ align:start position:0%
+the other side is the two puse points
+ 
+
+ align:start position:0%
+the other side is the two puse points
+after
+
+ align:start position:0%
+after
+ 
+
+ align:start position:0%
+after
+delivery and what I just wanted to show
+
+ align:start position:0%
+delivery and what I just wanted to show
+ 
+
+ align:start position:0%
+delivery and what I just wanted to show
+you on this is this is revision 67 and
+
+ align:start position:0%
+you on this is this is revision 67 and
+ 
+
+ align:start position:0%
+you on this is this is revision 67 and
+I'm sure by the time it gets onto who
+
+ align:start position:0%
+I'm sure by the time it gets onto who
+ 
+
+ align:start position:0%
+I'm sure by the time it gets onto who
+website it'll be 88 or
+
+ align:start position:0%
+website it'll be 88 or
+ 
+
+ align:start position:0%
+website it'll be 88 or
+something and what I wanted to show you
+
+ align:start position:0%
+something and what I wanted to show you
+ 
+
+ align:start position:0%
+something and what I wanted to show you
+on this is two differences between um
+
+ align:start position:0%
+on this is two differences between um
+ 
+
+ align:start position:0%
+on this is two differences between um
+this one and the safe surgery because of
+
+ align:start position:0%
+this one and the safe surgery because of
+ 
+
+ align:start position:0%
+this one and the safe surgery because of
+what we're dealing with so I told you
+
+ align:start position:0%
+what we're dealing with so I told you
+ 
+
+ align:start position:0%
+what we're dealing with so I told you
+about the variability of the caregiver
+
+ align:start position:0%
+about the variability of the caregiver
+ 
+
+ align:start position:0%
+about the variability of the caregiver
+you can say does a mother need to start
+
+ align:start position:0%
+you can say does a mother need to start
+ 
+
+ align:start position:0%
+you can say does a mother need to start
+antibiotics
+
+ align:start position:0%
+antibiotics
+ 
+
+ align:start position:0%
+antibiotics
+I don't know cuz you don't you can't
+
+ align:start position:0%
+I don't know cuz you don't you can't
+ 
+
+ align:start position:0%
+I don't know cuz you don't you can't
+rely on their training so in America
+
+ align:start position:0%
+rely on their training so in America
+ 
+
+ align:start position:0%
+rely on their training so in America
+we'd hope to get rid of the second
+
+ align:start position:0%
+we'd hope to get rid of the second
+ 
+
+ align:start position:0%
+we'd hope to get rid of the second
+column because they don't need to be
+
+ align:start position:0%
+column because they don't need to be
+ 
+
+ align:start position:0%
+column because they don't need to be
+told when to do things but for these
+
+ align:start position:0%
+told when to do things but for these
+ 
+
+ align:start position:0%
+told when to do things but for these
+settings it was crucial that we gave
+
+ align:start position:0%
+settings it was crucial that we gave
+ 
+
+ align:start position:0%
+settings it was crucial that we gave
+them the criteria and we were really
+
+ align:start position:0%
+them the criteria and we were really
+ 
+
+ align:start position:0%
+them the criteria and we were really
+anxious like oh the font's small Boeing
+
+ align:start position:0%
+anxious like oh the font's small Boeing
+ 
+
+ align:start position:0%
+anxious like oh the font's small Boeing
+didn't like it you know there's way too
+
+ align:start position:0%
+didn't like it you know there's way too
+ 
+
+ align:start position:0%
+didn't like it you know there's way too
+much stuff on the checklist the feedback
+
+ align:start position:0%
+much stuff on the checklist the feedback
+ 
+
+ align:start position:0%
+much stuff on the checklist the feedback
+we got was that was critical and
+
+ align:start position:0%
+we got was that was critical and
+ 
+
+ align:start position:0%
+we got was that was critical and
+actually in the modification stage that
+
+ align:start position:0%
+actually in the modification stage that
+ 
+
+ align:start position:0%
+actually in the modification stage that
+ended up being a fabulous training tool
+
+ align:start position:0%
+ended up being a fabulous training tool
+ 
+
+ align:start position:0%
+ended up being a fabulous training tool
+because when they discussed the criteria
+
+ align:start position:0%
+because when they discussed the criteria
+ 
+
+ align:start position:0%
+because when they discussed the criteria
+for things
+
+ align:start position:0%
+for things
+ 
+
+ align:start position:0%
+for things
+like oh I didn't know that and why did
+
+ align:start position:0%
+like oh I didn't know that and why did
+ 
+
+ align:start position:0%
+like oh I didn't know that and why did
+we do this and actually The Midwives
+
+ align:start position:0%
+we do this and actually The Midwives
+ 
+
+ align:start position:0%
+we do this and actually The Midwives
+were learning as they were discussing
+
+ align:start position:0%
+were learning as they were discussing
+ 
+
+ align:start position:0%
+were learning as they were discussing
+the checklist the second component in
+
+ align:start position:0%
+the checklist the second component in
+ 
+
+ align:start position:0%
+the checklist the second component in
+oval is that's how we decided to include
+
+ align:start position:0%
+oval is that's how we decided to include
+ 
+
+ align:start position:0%
+oval is that's how we decided to include
+the mother and her birth companion we
+
+ align:start position:0%
+the mother and her birth companion we
+ 
+
+ align:start position:0%
+the mother and her birth companion we
+actually said right you're member of
+
+ align:start position:0%
+actually said right you're member of
+ 
+
+ align:start position:0%
+actually said right you're member of
+this team we're going to tell you these
+
+ align:start position:0%
+this team we're going to tell you these
+ 
+
+ align:start position:0%
+this team we're going to tell you these
+are the danger signs that you should be
+
+ align:start position:0%
+are the danger signs that you should be
+ 
+
+ align:start position:0%
+are the danger signs that you should be
+calling the healthcare worker for it's
+
+ align:start position:0%
+calling the healthcare worker for it's
+ 
+
+ align:start position:0%
+calling the healthcare worker for it's
+not like in England where you have one
+
+ align:start position:0%
+not like in England where you have one
+ 
+
+ align:start position:0%
+not like in England where you have one
+Midwife you know to one patient you have
+
+ align:start position:0%
+Midwife you know to one patient you have
+ 
+
+ align:start position:0%
+Midwife you know to one patient you have
+one Midwife to sometimes 25 patients
+
+ align:start position:0%
+one Midwife to sometimes 25 patients
+ 
+
+ align:start position:0%
+one Midwife to sometimes 25 patients
+delivering well let them be part of the
+
+ align:start position:0%
+delivering well let them be part of the
+ 
+
+ align:start position:0%
+delivering well let them be part of the
+process why don't you call us when you
+
+ align:start position:0%
+process why don't you call us when you
+ 
+
+ align:start position:0%
+process why don't you call us when you
+need us and that was
+
+ align:start position:0%
+need us and that was
+ 
+
+ align:start position:0%
+need us and that was
+informed so I'm going to take you to
+
+ align:start position:0%
+informed so I'm going to take you to
+ 
+
+ align:start position:0%
+informed so I'm going to take you to
+four hours from Goa lovely weather um a
+
+ align:start position:0%
+four hours from Goa lovely weather um a
+ 
+
+ align:start position:0%
+four hours from Goa lovely weather um a
+rural Health Center called Goot it's the
+
+ align:start position:0%
+rural Health Center called Goot it's the
+ 
+
+ align:start position:0%
+rural Health Center called Goot it's the
+levels in India sort of Primary Health
+
+ align:start position:0%
+levels in India sort of Primary Health
+ 
+
+ align:start position:0%
+levels in India sort of Primary Health
+Center then a community health center
+
+ align:start position:0%
+Center then a community health center
+ 
+
+ align:start position:0%
+Center then a community health center
+than a district hospital and this was
+
+ align:start position:0%
+than a district hospital and this was
+ 
+
+ align:start position:0%
+than a district hospital and this was
+like an upgraded Community Health Center
+
+ align:start position:0%
+like an upgraded Community Health Center
+ 
+
+ align:start position:0%
+like an upgraded Community Health Center
+about 4,000 deliveries a year one or two
+
+ align:start position:0%
+about 4,000 deliveries a year one or two
+ 
+
+ align:start position:0%
+about 4,000 deliveries a year one or two
+obss depending on whether they felt like
+
+ align:start position:0%
+obss depending on whether they felt like
+ 
+
+ align:start position:0%
+obss depending on whether they felt like
+coming in and majority of the nurses
+
+ align:start position:0%
+coming in and majority of the nurses
+ 
+
+ align:start position:0%
+coming in and majority of the nurses
+doing the deliveries but they rotate
+
+ align:start position:0%
+doing the deliveries but they rotate
+ 
+
+ align:start position:0%
+doing the deliveries but they rotate
+around the hospital so they're not just
+
+ align:start position:0%
+around the hospital so they're not just
+ 
+
+ align:start position:0%
+around the hospital so they're not just
+OB Patric nurses they've never had
+
+ align:start position:0%
+OB Patric nurses they've never had
+ 
+
+ align:start position:0%
+OB Patric nurses they've never had
+quality improvement they've never been
+
+ align:start position:0%
+quality improvement they've never been
+ 
+
+ align:start position:0%
+quality improvement they've never been
+touched by research they just keep
+
+ align:start position:0%
+touched by research they just keep
+ 
+
+ align:start position:0%
+touched by research they just keep
+trying to do the work that they can and
+
+ align:start position:0%
+trying to do the work that they can and
+ 
+
+ align:start position:0%
+trying to do the work that they can and
+this is the classic scene corridors full
+
+ align:start position:0%
+this is the classic scene corridors full
+ 
+
+ align:start position:0%
+this is the classic scene corridors full
+of people the doctor in there has got to
+
+ align:start position:0%
+of people the doctor in there has got to
+ 
+
+ align:start position:0%
+of people the doctor in there has got to
+see these people in the next hour um
+
+ align:start position:0%
+see these people in the next hour um
+ 
+
+ align:start position:0%
+see these people in the next hour um
+because he's got three-hour clinic and
+
+ align:start position:0%
+because he's got three-hour clinic and
+ 
+
+ align:start position:0%
+because he's got three-hour clinic and
+there this is about a third of the
+
+ align:start position:0%
+there this is about a third of the
+ 
+
+ align:start position:0%
+there this is about a third of the
+patients they have a supplies board
+
+ align:start position:0%
+patients they have a supplies board
+ 
+
+ align:start position:0%
+patients they have a supplies board
+which they update in the mornings and
+
+ align:start position:0%
+which they update in the mornings and
+ 
+
+ align:start position:0%
+which they update in the mornings and
+unsurprisingly the two things that are
+
+ align:start position:0%
+unsurprisingly the two things that are
+ 
+
+ align:start position:0%
+unsurprisingly the two things that are
+really important to prevent bleeding
+
+ align:start position:0%
+really important to prevent bleeding
+ 
+
+ align:start position:0%
+really important to prevent bleeding
+after Labor they don't have
+
+ align:start position:0%
+after Labor they don't have
+ 
+
+ align:start position:0%
+after Labor they don't have
+the preeclampsia patient highrisk
+
+ align:start position:0%
+the preeclampsia patient highrisk
+ 
+
+ align:start position:0%
+the preeclampsia patient highrisk
+patient here would be in high dependency
+
+ align:start position:0%
+patient here would be in high dependency
+ 
+
+ align:start position:0%
+patient here would be in high dependency
+unit with lots of monitors she's in the
+
+ align:start position:0%
+unit with lots of monitors she's in the
+ 
+
+ align:start position:0%
+unit with lots of monitors she's in the
+corridor and they actually do have a
+
+ align:start position:0%
+corridor and they actually do have a
+ 
+
+ align:start position:0%
+corridor and they actually do have a
+fetal monitor it just hasn't worked for
+
+ align:start position:0%
+fetal monitor it just hasn't worked for
+ 
+
+ align:start position:0%
+fetal monitor it just hasn't worked for
+3 years it's being used as a shelf and
+
+ align:start position:0%
+3 years it's being used as a shelf and
+ 
+
+ align:start position:0%
+3 years it's being used as a shelf and
+I'm slightly anxious about that
+
+ align:start position:0%
+I'm slightly anxious about that
+ 
+
+ align:start position:0%
+I'm slightly anxious about that
+uncovered needle because it's probably
+
+ align:start position:0%
+uncovered needle because it's probably
+ 
+
+ align:start position:0%
+uncovered needle because it's probably
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+reused what were the objectives so the
+
+ align:start position:0%
+reused what were the objectives so the
+ 
+
+ align:start position:0%
+reused what were the objectives so the
+objectives were actually looking at
+
+ align:start position:0%
+objectives were actually looking at
+ 
+
+ align:start position:0%
+objectives were actually looking at
+processes we know that these
+
+ align:start position:0%
+processes we know that these
+ 
+
+ align:start position:0%
+processes we know that these
+interventions will reduce mortality who
+
+ align:start position:0%
+interventions will reduce mortality who
+ 
+
+ align:start position:0%
+interventions will reduce mortality who
+has done all that research can we get
+
+ align:start position:0%
+has done all that research can we get
+ 
+
+ align:start position:0%
+has done all that research can we get
+the healthcare providers to
+
+ align:start position:0%
+the healthcare providers to
+ 
+
+ align:start position:0%
+the healthcare providers to
+reliably deliver these interventions to
+
+ align:start position:0%
+reliably deliver these interventions to
+ 
+
+ align:start position:0%
+reliably deliver these interventions to
+every single woman that comes
+
+ align:start position:0%
+every single woman that comes
+ 
+
+ align:start position:0%
+every single woman that comes
+through and so it was a really simple
+
+ align:start position:0%
+through and so it was a really simple
+ 
+
+ align:start position:0%
+through and so it was a really simple
+pre-post um we wanted the intervention
+
+ align:start position:0%
+pre-post um we wanted the intervention
+ 
+
+ align:start position:0%
+pre-post um we wanted the intervention
+thing to be really skinny so it was a
+
+ align:start position:0%
+thing to be really skinny so it was a
+ 
+
+ align:start position:0%
+thing to be really skinny so it was a
+one-day launch because ideally what I'd
+
+ align:start position:0%
+one-day launch because ideally what I'd
+ 
+
+ align:start position:0%
+one-day launch because ideally what I'd
+like to see is someone can download the
+
+ align:start position:0%
+like to see is someone can download the
+ 
+
+ align:start position:0%
+like to see is someone can download the
+checklist you know have a bit of a video
+
+ align:start position:0%
+checklist you know have a bit of a video
+ 
+
+ align:start position:0%
+checklist you know have a bit of a video
+have a manual and run with it so it was
+
+ align:start position:0%
+have a manual and run with it so it was
+ 
+
+ align:start position:0%
+have a manual and run with it so it was
+one day launch and then four days sort
+
+ align:start position:0%
+one day launch and then four days sort
+ 
+
+ align:start position:0%
+one day launch and then four days sort
+of supportive we weren't there for the
+
+ align:start position:0%
+of supportive we weren't there for the
+ 
+
+ align:start position:0%
+of supportive we weren't there for the
+four days we got the um one of our
+
+ align:start position:0%
+four days we got the um one of our
+ 
+
+ align:start position:0%
+four days we got the um one of our
+implementing people to sort of support
+
+ align:start position:0%
+implementing people to sort of support
+ 
+
+ align:start position:0%
+implementing people to sort of support
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+and the implementing person was anst
+
+ align:start position:0%
+and the implementing person was anst
+ 
+
+ align:start position:0%
+and the implementing person was anst
+full-time anst she's been there for 20
+
+ align:start position:0%
+full-time anst she's been there for 20
+ 
+
+ align:start position:0%
+full-time anst she's been there for 20
+years so she's credible um people like
+
+ align:start position:0%
+years so she's credible um people like
+ 
+
+ align:start position:0%
+years so she's credible um people like
+her but also respect her she did this on
+
+ align:start position:0%
+her but also respect her she did this on
+ 
+
+ align:start position:0%
+her but also respect her she did this on
+top of her usual workload so we weren't
+
+ align:start position:0%
+top of her usual workload so we weren't
+ 
+
+ align:start position:0%
+top of her usual workload so we weren't
+sort of drafting more Workforce in and
+
+ align:start position:0%
+sort of drafting more Workforce in and
+ 
+
+ align:start position:0%
+sort of drafting more Workforce in and
+she led the launch day we trained her
+
+ align:start position:0%
+she led the launch day we trained her
+ 
+
+ align:start position:0%
+she led the launch day we trained her
+for a day and she led it she explained
+
+ align:start position:0%
+for a day and she led it she explained
+ 
+
+ align:start position:0%
+for a day and she led it she explained
+the why so she got the nurses to share
+
+ align:start position:0%
+the why so she got the nurses to share
+ 
+
+ align:start position:0%
+the why so she got the nurses to share
+stories of you know what's happening the
+
+ align:start position:0%
+stories of you know what's happening the
+ 
+
+ align:start position:0%
+stories of you know what's happening the
+adverse outcomes near misses she then
+
+ align:start position:0%
+adverse outcomes near misses she then
+ 
+
+ align:start position:0%
+adverse outcomes near misses she then
+shared some basic Baseline data so we
+
+ align:start position:0%
+shared some basic Baseline data so we
+ 
+
+ align:start position:0%
+shared some basic Baseline data so we
+could have just shared all our Baseline
+
+ align:start position:0%
+could have just shared all our Baseline
+ 
+
+ align:start position:0%
+could have just shared all our Baseline
+data we' collected it for 3 months but
+
+ align:start position:0%
+data we' collected it for 3 months but
+ 
+
+ align:start position:0%
+data we' collected it for 3 months but
+we said well that's not feasible you
+
+ align:start position:0%
+we said well that's not feasible you
+ 
+
+ align:start position:0%
+we said well that's not feasible you
+know they're not going to be able to
+
+ align:start position:0%
+know they're not going to be able to
+ 
+
+ align:start position:0%
+know they're not going to be able to
+collect that data in these kind of
+
+ align:start position:0%
+collect that data in these kind of
+ 
+
+ align:start position:0%
+collect that data in these kind of
+settings so she just shared a few items
+
+ align:start position:0%
+settings so she just shared a few items
+ 
+
+ align:start position:0%
+settings so she just shared a few items
+and then did the modification process so
+
+ align:start position:0%
+and then did the modification process so
+ 
+
+ align:start position:0%
+and then did the modification process so
+sat down with them and said what do you
+
+ align:start position:0%
+sat down with them and said what do you
+ 
+
+ align:start position:0%
+sat down with them and said what do you
+think let's go through the items it was
+
+ align:start position:0%
+think let's go through the items it was
+ 
+
+ align:start position:0%
+think let's go through the items it was
+a bit of a training session and then the
+
+ align:start position:0%
+a bit of a training session and then the
+ 
+
+ align:start position:0%
+a bit of a training session and then the
+video for the safe surgery they' made
+
+ align:start position:0%
+video for the safe surgery they' made
+ 
+
+ align:start position:0%
+video for the safe surgery they' made
+the video at Brigham and they
+
+ align:start position:0%
+the video at Brigham and they
+ 
+
+ align:start position:0%
+the video at Brigham and they
+transported it and what we decided was
+
+ align:start position:0%
+transported it and what we decided was
+ 
+
+ align:start position:0%
+transported it and what we decided was
+that we would make it on site and it's
+
+ align:start position:0%
+that we would make it on site and it's
+ 
+
+ align:start position:0%
+that we would make it on site and it's
+sort of based on the Chinese proverb you
+
+ align:start position:0%
+sort of based on the Chinese proverb you
+ 
+
+ align:start position:0%
+sort of based on the Chinese proverb you
+know tell tell me and I'll forget show
+
+ align:start position:0%
+know tell tell me and I'll forget show
+ 
+
+ align:start position:0%
+know tell tell me and I'll forget show
+me and I'll remember involve me and I'll
+
+ align:start position:0%
+me and I'll remember involve me and I'll
+ 
+
+ align:start position:0%
+me and I'll remember involve me and I'll
+understand and you could see the bulbs
+
+ align:start position:0%
+understand and you could see the bulbs
+ 
+
+ align:start position:0%
+understand and you could see the bulbs
+going on so the chief medical officer
+
+ align:start position:0%
+going on so the chief medical officer
+ 
+
+ align:start position:0%
+going on so the chief medical officer
+who was supposed to be our local
+
+ align:start position:0%
+who was supposed to be our local
+ 
+
+ align:start position:0%
+who was supposed to be our local
+institutional leader he sort of we're
+
+ align:start position:0%
+institutional leader he sort of we're
+ 
+
+ align:start position:0%
+institutional leader he sort of we're
+making the video with him and he's like
+
+ align:start position:0%
+making the video with him and he's like
+ 
+
+ align:start position:0%
+making the video with him and he's like
+so what do I have to do I was like you
+
+ align:start position:0%
+so what do I have to do I was like you
+ 
+
+ align:start position:0%
+so what do I have to do I was like you
+have to ask the question you know is
+
+ align:start position:0%
+have to ask the question you know is
+ 
+
+ align:start position:0%
+have to ask the question you know is
+oxytocin ready and he's said is oxytocin
+
+ align:start position:0%
+oxytocin ready and he's said is oxytocin
+ 
+
+ align:start position:0%
+oxytocin ready and he's said is oxytocin
+ready can I start the operation no you
+
+ align:start position:0%
+ready can I start the operation no you
+ 
+
+ align:start position:0%
+ready can I start the operation no you
+need to wait for the response and you
+
+ align:start position:0%
+need to wait for the response and you
+ 
+
+ align:start position:0%
+need to wait for the response and you
+could see the sort of light was going on
+
+ align:start position:0%
+could see the sort of light was going on
+ 
+
+ align:start position:0%
+could see the sort of light was going on
+as we were making this video and at the
+
+ align:start position:0%
+as we were making this video and at the
+ 
+
+ align:start position:0%
+as we were making this video and at the
+end he was like wow this is great and
+
+ align:start position:0%
+end he was like wow this is great and
+ 
+
+ align:start position:0%
+end he was like wow this is great and
+then we drafted two two very sort of
+
+ align:start position:0%
+then we drafted two two very sort of
+ 
+
+ align:start position:0%
+then we drafted two two very sort of
+low-level nurses and just brought them
+
+ align:start position:0%
+low-level nurses and just brought them
+ 
+
+ align:start position:0%
+low-level nurses and just brought them
+in we're like right all you have to do
+
+ align:start position:0%
+in we're like right all you have to do
+ 
+
+ align:start position:0%
+in we're like right all you have to do
+is read this checklist go through and
+
+ align:start position:0%
+is read this checklist go through and
+ 
+
+ align:start position:0%
+is read this checklist go through and
+we're just videoing you and I heard
+
+ align:start position:0%
+we're just videoing you and I heard
+ 
+
+ align:start position:0%
+we're just videoing you and I heard
+afterwards he said this checklist is
+
+ align:start position:0%
+afterwards he said this checklist is
+ 
+
+ align:start position:0%
+afterwards he said this checklist is
+really easy I mean I had no training
+
+ align:start position:0%
+really easy I mean I had no training
+ 
+
+ align:start position:0%
+really easy I mean I had no training
+they called me in they videoed me and I
+
+ align:start position:0%
+they called me in they videoed me and I
+ 
+
+ align:start position:0%
+they called me in they videoed me and I
+don't think we're going to have a
+
+ align:start position:0%
+don't think we're going to have a
+ 
+
+ align:start position:0%
+don't think we're going to have a
+problem so it it was actually really
+
+ align:start position:0%
+problem so it it was actually really
+ 
+
+ align:start position:0%
+problem so it it was actually really
+useful doing the video on site and then
+
+ align:start position:0%
+useful doing the video on site and then
+ 
+
+ align:start position:0%
+useful doing the video on site and then
+the other thing that Alvin mentioned was
+
+ align:start position:0%
+the other thing that Alvin mentioned was
+ 
+
+ align:start position:0%
+the other thing that Alvin mentioned was
+role plays I really really think role
+
+ align:start position:0%
+role plays I really really think role
+ 
+
+ align:start position:0%
+role plays I really really think role
+plays for something like this is
+
+ align:start position:0%
+plays for something like this is
+ 
+
+ align:start position:0%
+plays for something like this is
+critical because that's when they un
+
+ align:start position:0%
+critical because that's when they un
+ 
+
+ align:start position:0%
+critical because that's when they un
+understand what's happening and adults
+
+ align:start position:0%
+understand what's happening and adults
+ 
+
+ align:start position:0%
+understand what's happening and adults
+don't want to be sitting like you guys
+
+ align:start position:0%
+don't want to be sitting like you guys
+ 
+
+ align:start position:0%
+don't want to be sitting like you guys
+are sitting listening to me like adults
+
+ align:start position:0%
+are sitting listening to me like adults
+ 
+
+ align:start position:0%
+are sitting listening to me like adults
+want to be on the ground doing stuff and
+
+ align:start position:0%
+want to be on the ground doing stuff and
+ 
+
+ align:start position:0%
+want to be on the ground doing stuff and
+so that's when they really got to
+
+ align:start position:0%
+so that's when they really got to
+ 
+
+ align:start position:0%
+so that's when they really got to
+understand what was uh what the
+
+ align:start position:0%
+understand what was uh what the
+ 
+
+ align:start position:0%
+understand what was uh what the
+checklist was about and so I sort of
+
+ align:start position:0%
+checklist was about and so I sort of
+ 
+
+ align:start position:0%
+checklist was about and so I sort of
+made this like little pyramid so yes the
+
+ align:start position:0%
+made this like little pyramid so yes the
+ 
+
+ align:start position:0%
+made this like little pyramid so yes the
+safe child birth checklist is really the
+
+ align:start position:0%
+safe child birth checklist is really the
+ 
+
+ align:start position:0%
+safe child birth checklist is really the
+main component but the program bit is
+
+ align:start position:0%
+main component but the program bit is
+ 
+
+ align:start position:0%
+main component but the program bit is
+your implementing person so your child
+
+ align:start position:0%
+your implementing person so your child
+ 
+
+ align:start position:0%
+your implementing person so your child
+improve child birth Improvement
+
+ align:start position:0%
+improve child birth Improvement
+ 
+
+ align:start position:0%
+improve child birth Improvement
+coordinator and then we didn't have a
+
+ align:start position:0%
+coordinator and then we didn't have a
+ 
+
+ align:start position:0%
+coordinator and then we didn't have a
+teamwork component on our checklist
+
+ align:start position:0%
+teamwork component on our checklist
+ 
+
+ align:start position:0%
+teamwork component on our checklist
+there wasn't any introduce yourself and
+
+ align:start position:0%
+there wasn't any introduce yourself and
+ 
+
+ align:start position:0%
+there wasn't any introduce yourself and
+we realized that that was critical from
+
+ align:start position:0%
+we realized that that was critical from
+ 
+
+ align:start position:0%
+we realized that that was critical from
+the safe surgery so we said I'll tell
+
+ align:start position:0%
+the safe surgery so we said I'll tell
+ 
+
+ align:start position:0%
+the safe surgery so we said I'll tell
+you what why don't you just get all the
+
+ align:start position:0%
+you what why don't you just get all the
+ 
+
+ align:start position:0%
+you what why don't you just get all the
+labor people together in your facility
+
+ align:start position:0%
+labor people together in your facility
+ 
+
+ align:start position:0%
+labor people together in your facility
+once a day get them to introduce
+
+ align:start position:0%
+once a day get them to introduce
+ 
+
+ align:start position:0%
+once a day get them to introduce
+themselves and just motivate them to use
+
+ align:start position:0%
+themselves and just motivate them to use
+ 
+
+ align:start position:0%
+themselves and just motivate them to use
+the checklist and I thought she wasn't
+
+ align:start position:0%
+the checklist and I thought she wasn't
+ 
+
+ align:start position:0%
+the checklist and I thought she wasn't
+going to do it she thought the idea was
+
+ align:start position:0%
+going to do it she thought the idea was
+ 
+
+ align:start position:0%
+going to do it she thought the idea was
+absolutely rubbish why do I want to know
+
+ align:start position:0%
+absolutely rubbish why do I want to know
+ 
+
+ align:start position:0%
+absolutely rubbish why do I want to know
+the names of the nurses that are doing
+
+ align:start position:0%
+the names of the nurses that are doing
+ 
+
+ align:start position:0%
+the names of the nurses that are doing
+the deliveries at the end she said it
+
+ align:start position:0%
+the deliveries at the end she said it
+ 
+
+ align:start position:0%
+the deliveries at the end she said it
+was fabulous because when she was going
+
+ align:start position:0%
+was fabulous because when she was going
+ 
+
+ align:start position:0%
+was fabulous because when she was going
+home she knew what was going on she said
+
+ align:start position:0%
+home she knew what was going on she said
+ 
+
+ align:start position:0%
+home she knew what was going on she said
+it was the best way of knowing like
+
+ align:start position:0%
+it was the best way of knowing like
+ 
+
+ align:start position:0%
+it was the best way of knowing like
+getting a really quick safety assessment
+
+ align:start position:0%
+getting a really quick safety assessment
+ 
+
+ align:start position:0%
+getting a really quick safety assessment
+of the day like what who with the high
+
+ align:start position:0%
+of the day like what who with the high
+ 
+
+ align:start position:0%
+of the day like what who with the high
+risk patients so I think it's an aspect
+
+ align:start position:0%
+risk patients so I think it's an aspect
+ 
+
+ align:start position:0%
+risk patients so I think it's an aspect
+that she's going to take on now the
+
+ align:start position:0%
+that she's going to take on now the
+ 
+
+ align:start position:0%
+that she's going to take on now the
+study's ended I've only circled these
+
+ align:start position:0%
+study's ended I've only circled these
+ 
+
+ align:start position:0%
+study's ended I've only circled these
+two bits because we actually used um uh
+
+ align:start position:0%
+two bits because we actually used um uh
+ 
+
+ align:start position:0%
+two bits because we actually used um uh
+observers to collect data so we didn't
+
+ align:start position:0%
+observers to collect data so we didn't
+ 
+
+ align:start position:0%
+observers to collect data so we didn't
+want to have like the people who
+
+ align:start position:0%
+want to have like the people who
+ 
+
+ align:start position:0%
+want to have like the people who
+actually using the checklist sort of
+
+ align:start position:0%
+actually using the checklist sort of
+ 
+
+ align:start position:0%
+actually using the checklist sort of
+saying yes we used it and this is what
+
+ align:start position:0%
+saying yes we used it and this is what
+ 
+
+ align:start position:0%
+saying yes we used it and this is what
+we did so we actually drafted in five
+
+ align:start position:0%
+we did so we actually drafted in five
+ 
+
+ align:start position:0%
+we did so we actually drafted in five
+very Junior people to actually observe
+
+ align:start position:0%
+very Junior people to actually observe
+ 
+
+ align:start position:0%
+very Junior people to actually observe
+what they were
+
+ align:start position:0%
+what they were
+ 
+
+ align:start position:0%
+what they were
+doing quickly on the results every
+
+ align:start position:0%
+doing quickly on the results every
+ 
+
+ align:start position:0%
+doing quickly on the results every
+single essential standard that was on
+
+ align:start position:0%
+single essential standard that was on
+ 
+
+ align:start position:0%
+single essential standard that was on
+the checklist improved moved a lot and
+
+ align:start position:0%
+the checklist improved moved a lot and
+ 
+
+ align:start position:0%
+the checklist improved moved a lot and
+I'll show you the graphs and then
+
+ align:start position:0%
+I'll show you the graphs and then
+ 
+
+ align:start position:0%
+I'll show you the graphs and then
+overall they were probably delivering 10
+
+ align:start position:0%
+overall they were probably delivering 10
+ 
+
+ align:start position:0%
+overall they were probably delivering 10
+out the 29 essential standards on
+
+ align:start position:0%
+out the 29 essential standards on
+ 
+
+ align:start position:0%
+out the 29 essential standards on
+average before and afterwards they were
+
+ align:start position:0%
+average before and afterwards they were
+ 
+
+ align:start position:0%
+average before and afterwards they were
+delivering 25 out the 29 standards
+
+ align:start position:0%
+delivering 25 out the 29 standards
+ 
+
+ align:start position:0%
+delivering 25 out the 29 standards
+reliably and even though the study
+
+ align:start position:0%
+reliably and even though the study
+ 
+
+ align:start position:0%
+reliably and even though the study
+wasn't powered for mortality there was a
+
+ align:start position:0%
+wasn't powered for mortality there was a
+ 
+
+ align:start position:0%
+wasn't powered for mortality there was a
+significant drop in the fresh still
+
+ align:start position:0%
+significant drop in the fresh still
+ 
+
+ align:start position:0%
+significant drop in the fresh still
+birth probably because they would
+
+ align:start position:0%
+birth probably because they would
+ 
+
+ align:start position:0%
+birth probably because they would
+actually monitoring the fetus during
+
+ align:start position:0%
+actually monitoring the fetus during
+ 
+
+ align:start position:0%
+actually monitoring the fetus during
+labor and this is some of the fuzzy
+
+ align:start position:0%
+labor and this is some of the fuzzy
+ 
+
+ align:start position:0%
+labor and this is some of the fuzzy
+stuff that's I say fuzzy CU I'm not
+
+ align:start position:0%
+stuff that's I say fuzzy CU I'm not
+ 
+
+ align:start position:0%
+stuff that's I say fuzzy CU I'm not
+quality ative researcher but I went out
+
+ align:start position:0%
+quality ative researcher but I went out
+ 
+
+ align:start position:0%
+quality ative researcher but I went out
+and we were doing interviews and um they
+
+ align:start position:0%
+and we were doing interviews and um they
+ 
+
+ align:start position:0%
+and we were doing interviews and um they
+were talking about how the S the actual
+
+ align:start position:0%
+were talking about how the S the actual
+ 
+
+ align:start position:0%
+were talking about how the S the actual
+checklist as a catalyst for change that
+
+ align:start position:0%
+checklist as a catalyst for change that
+ 
+
+ align:start position:0%
+checklist as a catalyst for change that
+we don't you know it's not what we
+
+ align:start position:0%
+we don't you know it's not what we
+ 
+
+ align:start position:0%
+we don't you know it's not what we
+measure and we don't expect so before I
+
+ align:start position:0%
+measure and we don't expect so before I
+ 
+
+ align:start position:0%
+measure and we don't expect so before I
+told you like the oxytocin and the drugs
+
+ align:start position:0%
+told you like the oxytocin and the drugs
+ 
+
+ align:start position:0%
+told you like the oxytocin and the drugs
+weren't available well there's something
+
+ align:start position:0%
+weren't available well there's something
+ 
+
+ align:start position:0%
+weren't available well there's something
+about being on the checklist that helps
+
+ align:start position:0%
+about being on the checklist that helps
+ 
+
+ align:start position:0%
+about being on the checklist that helps
+the institution say well oh okay these
+
+ align:start position:0%
+the institution say well oh okay these
+ 
+
+ align:start position:0%
+the institution say well oh okay these
+are really important items we're going
+
+ align:start position:0%
+are really important items we're going
+ 
+
+ align:start position:0%
+are really important items we're going
+to focus on these and the availability
+
+ align:start position:0%
+to focus on these and the availability
+ 
+
+ align:start position:0%
+to focus on these and the availability
+increases then they've instituted
+
+ align:start position:0%
+increases then they've instituted
+ 
+
+ align:start position:0%
+increases then they've instituted
+different changes is like well she said
+
+ align:start position:0%
+different changes is like well she said
+ 
+
+ align:start position:0%
+different changes is like well she said
+well you want us to do a check 1 hour
+
+ align:start position:0%
+well you want us to do a check 1 hour
+ 
+
+ align:start position:0%
+well you want us to do a check 1 hour
+after birth but the woman's all over the
+
+ align:start position:0%
+after birth but the woman's all over the
+ 
+
+ align:start position:0%
+after birth but the woman's all over the
+hospital at that point so they shifted
+
+ align:start position:0%
+hospital at that point so they shifted
+ 
+
+ align:start position:0%
+hospital at that point so they shifted
+things around this was just a nurse on
+
+ align:start position:0%
+things around this was just a nurse on
+ 
+
+ align:start position:0%
+things around this was just a nurse on
+the ground she said I'm just going to
+
+ align:start position:0%
+the ground she said I'm just going to
+ 
+
+ align:start position:0%
+the ground she said I'm just going to
+create a bay and there every woman who
+
+ align:start position:0%
+create a bay and there every woman who
+ 
+
+ align:start position:0%
+create a bay and there every woman who
+delivers is going to go there she's
+
+ align:start position:0%
+delivers is going to go there she's
+ 
+
+ align:start position:0%
+delivers is going to go there she's
+going to have her checklist done her
+
+ align:start position:0%
+going to have her checklist done her
+ 
+
+ align:start position:0%
+going to have her checklist done her
+check done at now and then she'll move
+
+ align:start position:0%
+check done at now and then she'll move
+ 
+
+ align:start position:0%
+check done at now and then she'll move
+to the postnatal um Wards and you know
+
+ align:start position:0%
+to the postnatal um Wards and you know
+ 
+
+ align:start position:0%
+to the postnatal um Wards and you know
+wherever she's going to go so there were
+
+ align:start position:0%
+wherever she's going to go so there were
+ 
+
+ align:start position:0%
+wherever she's going to go so there were
+lots of little changes that happened to
+
+ align:start position:0%
+lots of little changes that happened to
+ 
+
+ align:start position:0%
+lots of little changes that happened to
+enable the checklist to be effectively
+
+ align:start position:0%
+enable the checklist to be effectively
+ 
+
+ align:start position:0%
+enable the checklist to be effectively
+delivered so it's sort of like
+
+ align:start position:0%
+delivered so it's sort of like
+ 
+
+ align:start position:0%
+delivered so it's sort of like
+operations management but they LED on
+
+ align:start position:0%
+operations management but they LED on
+ 
+
+ align:start position:0%
+operations management but they LED on
+that that the second thing I noticed
+
+ align:start position:0%
+that that the second thing I noticed
+ 
+
+ align:start position:0%
+that that the second thing I noticed
+when I was out there and the nurses said
+
+ align:start position:0%
+when I was out there and the nurses said
+ 
+
+ align:start position:0%
+when I was out there and the nurses said
+was the patients started asking whether
+
+ align:start position:0%
+was the patients started asking whether
+ 
+
+ align:start position:0%
+was the patients started asking whether
+this facility had become a private
+
+ align:start position:0%
+this facility had become a private
+ 
+
+ align:start position:0%
+this facility had become a private
+facility because they noticed that their
+
+ align:start position:0%
+facility because they noticed that their
+ 
+
+ align:start position:0%
+facility because they noticed that their
+care was improving and would they have
+
+ align:start position:0%
+care was improving and would they have
+ 
+
+ align:start position:0%
+care was improving and would they have
+to pay more and it was a great feedback
+
+ align:start position:0%
+to pay more and it was a great feedback
+ 
+
+ align:start position:0%
+to pay more and it was a great feedback
+mechanism because that made the nurses
+
+ align:start position:0%
+mechanism because that made the nurses
+ 
+
+ align:start position:0%
+mechanism because that made the nurses
+happier and at the end of the day you
+
+ align:start position:0%
+happier and at the end of the day you
+ 
+
+ align:start position:0%
+happier and at the end of the day you
+want to provide good care but when your
+
+ align:start position:0%
+want to provide good care but when your
+ 
+
+ align:start position:0%
+want to provide good care but when your
+workloads crazy you're just providing
+
+ align:start position:0%
+workloads crazy you're just providing
+ 
+
+ align:start position:0%
+workloads crazy you're just providing
+whatever and now they had this check
+
+ align:start position:0%
+whatever and now they had this check
+ 
+
+ align:start position:0%
+whatever and now they had this check
+they said this is great we do this and
+
+ align:start position:0%
+they said this is great we do this and
+ 
+
+ align:start position:0%
+they said this is great we do this and
+we provide good care and the patients
+
+ align:start position:0%
+we provide good care and the patients
+ 
+
+ align:start position:0%
+we provide good care and the patients
+are loving us and they were giving a few
+
+ align:start position:0%
+are loving us and they were giving a few
+ 
+
+ align:start position:0%
+are loving us and they were giving a few
+extra Rupees at the end you know backand
+
+ align:start position:0%
+extra Rupees at the end you know backand
+ 
+
+ align:start position:0%
+extra Rupees at the end you know backand
+deals and the ex the other thing was
+
+ align:start position:0%
+deals and the ex the other thing was
+ 
+
+ align:start position:0%
+deals and the ex the other thing was
+that the checklist was beginning to be
+
+ align:start position:0%
+that the checklist was beginning to be
+ 
+
+ align:start position:0%
+that the checklist was beginning to be
+used as a Handover tool so normally if
+
+ align:start position:0%
+used as a Handover tool so normally if
+ 
+
+ align:start position:0%
+used as a Handover tool so normally if
+they did a bit of a tag team it' be like
+
+ align:start position:0%
+they did a bit of a tag team it' be like
+ 
+
+ align:start position:0%
+they did a bit of a tag team it' be like
+okay woman in labor had three children
+
+ align:start position:0%
+okay woman in labor had three children
+ 
+
+ align:start position:0%
+okay woman in labor had three children
+before buy them off to lunch and now
+
+ align:start position:0%
+before buy them off to lunch and now
+ 
+
+ align:start position:0%
+before buy them off to lunch and now
+they were saying oh actually no I did
+
+ align:start position:0%
+they were saying oh actually no I did
+ 
+
+ align:start position:0%
+they were saying oh actually no I did
+check that and actually High she's got
+
+ align:start position:0%
+check that and actually High she's got
+ 
+
+ align:start position:0%
+check that and actually High she's got
+high blood pressure and I think she
+
+ align:start position:0%
+high blood pressure and I think she
+ 
+
+ align:start position:0%
+high blood pressure and I think she
+might be at risk of bleeding so even
+
+ align:start position:0%
+might be at risk of bleeding so even
+ 
+
+ align:start position:0%
+might be at risk of bleeding so even
+their communication was improving and
+
+ align:start position:0%
+their communication was improving and
+ 
+
+ align:start position:0%
+their communication was improving and
+these are changes that you don't really
+
+ align:start position:0%
+these are changes that you don't really
+ 
+
+ align:start position:0%
+these are changes that you don't really
+expect but happen because you've
+
+ align:start position:0%
+expect but happen because you've
+ 
+
+ align:start position:0%
+expect but happen because you've
+introduced an innovation I don't want
+
+ align:start position:0%
+introduced an innovation I don't want
+ 
+
+ align:start position:0%
+introduced an innovation I don't want
+you to look at any of the detail on
+
+ align:start position:0%
+you to look at any of the detail on
+ 
+
+ align:start position:0%
+you to look at any of the detail on
+apart from dark blue is pre and light
+
+ align:start position:0%
+apart from dark blue is pre and light
+ 
+
+ align:start position:0%
+apart from dark blue is pre and light
+blue is post and you can see that some
+
+ align:start position:0%
+blue is post and you can see that some
+ 
+
+ align:start position:0%
+blue is post and you can see that some
+have drastically improved hand hygiene I
+
+ align:start position:0%
+have drastically improved hand hygiene I
+ 
+
+ align:start position:0%
+have drastically improved hand hygiene I
+wash your hands with soap and water and
+
+ align:start position:0%
+wash your hands with soap and water and
+ 
+
+ align:start position:0%
+wash your hands with soap and water and
+use gloves 3% before 99% after I mean
+
+ align:start position:0%
+use gloves 3% before 99% after I mean
+ 
+
+ align:start position:0%
+use gloves 3% before 99% after I mean
+some of the things they were doing fine
+
+ align:start position:0%
+some of the things they were doing fine
+ 
+
+ align:start position:0%
+some of the things they were doing fine
+before but even though statistically
+
+ align:start position:0%
+before but even though statistically
+ 
+
+ align:start position:0%
+before but even though statistically
+improved every single item improved
+
+ align:start position:0%
+improved every single item improved
+ 
+
+ align:start position:0%
+improved every single item improved
+hugely and people say well that's fair
+
+ align:start position:0%
+hugely and people say well that's fair
+ 
+
+ align:start position:0%
+hugely and people say well that's fair
+enough but what about sustainability
+
+ align:start position:0%
+enough but what about sustainability
+ 
+
+ align:start position:0%
+enough but what about sustainability
+you're in a study environment so I went
+
+ align:start position:0%
+you're in a study environment so I went
+ 
+
+ align:start position:0%
+you're in a study environment so I went
+3 weeks later after the study and um
+
+ align:start position:0%
+3 weeks later after the study and um
+ 
+
+ align:start position:0%
+3 weeks later after the study and um
+we'd said we wouldn't provide checklist
+
+ align:start position:0%
+we'd said we wouldn't provide checklist
+ 
+
+ align:start position:0%
+we'd said we wouldn't provide checklist
+like if they wanted the checklist they
+
+ align:start position:0%
+like if they wanted the checklist they
+ 
+
+ align:start position:0%
+like if they wanted the checklist they
+the institution had to buy them but the
+
+ align:start position:0%
+the institution had to buy them but the
+ 
+
+ align:start position:0%
+the institution had to buy them but the
+chief medical officer was away and it's
+
+ align:start position:0%
+chief medical officer was away and it's
+ 
+
+ align:start position:0%
+chief medical officer was away and it's
+a very centralized process and um so
+
+ align:start position:0%
+a very centralized process and um so
+ 
+
+ align:start position:0%
+a very centralized process and um so
+there were no checklists I said oh what
+
+ align:start position:0%
+there were no checklists I said oh what
+ 
+
+ align:start position:0%
+there were no checklists I said oh what
+have you been doing and I said well for
+
+ align:start position:0%
+have you been doing and I said well for
+ 
+
+ align:start position:0%
+have you been doing and I said well for
+the first week we use posters but we
+
+ align:start position:0%
+the first week we use posters but we
+ 
+
+ align:start position:0%
+the first week we use posters but we
+really think it's about the piece of
+
+ align:start position:0%
+really think it's about the piece of
+ 
+
+ align:start position:0%
+really think it's about the piece of
+paper and I said so what have you done
+
+ align:start position:0%
+paper and I said so what have you done
+ 
+
+ align:start position:0%
+paper and I said so what have you done
+and they said well we just pulled our
+
+ align:start position:0%
+and they said well we just pulled our
+ 
+
+ align:start position:0%
+and they said well we just pulled our
+money we had a little bit of money saved
+
+ align:start position:0%
+money we had a little bit of money saved
+ 
+
+ align:start position:0%
+money we had a little bit of money saved
+up and every nurse gave I don't know
+
+ align:start position:0%
+up and every nurse gave I don't know
+ 
+
+ align:start position:0%
+up and every nurse gave I don't know
+must have been like 10 rupees or
+
+ align:start position:0%
+must have been like 10 rupees or
+ 
+
+ align:start position:0%
+must have been like 10 rupees or
+something and they went to the Xerox
+
+ align:start position:0%
+something and they went to the Xerox
+ 
+
+ align:start position:0%
+something and they went to the Xerox
+Center and photocopy checklists for
+
+ align:start position:0%
+Center and photocopy checklists for
+ 
+
+ align:start position:0%
+Center and photocopy checklists for
+themselves they said we might get the
+
+ align:start position:0%
+themselves they said we might get the
+ 
+
+ align:start position:0%
+themselves they said we might get the
+money back we might not but we're
+
+ align:start position:0%
+money back we might not but we're
+ 
+
+ align:start position:0%
+money back we might not but we're
+providing better care this way I like
+
+ align:start position:0%
+providing better care this way I like
+ 
+
+ align:start position:0%
+providing better care this way I like
+wow and they don't get paid a lot and
+
+ align:start position:0%
+wow and they don't get paid a lot and
+ 
+
+ align:start position:0%
+wow and they don't get paid a lot and
+they're putting their own money towards
+
+ align:start position:0%
+they're putting their own money towards
+ 
+
+ align:start position:0%
+they're putting their own money towards
+something that's
+
+ align:start position:0%
+something that's
+ 
+
+ align:start position:0%
+something that's
+acceptability um and next steps so yes
+
+ align:start position:0%
+acceptability um and next steps so yes
+ 
+
+ align:start position:0%
+acceptability um and next steps so yes
+there's the randomized control trial um
+
+ align:start position:0%
+there's the randomized control trial um
+ 
+
+ align:start position:0%
+there's the randomized control trial um
+but lots of people are saying well do we
+
+ align:start position:0%
+but lots of people are saying well do we
+ 
+
+ align:start position:0%
+but lots of people are saying well do we
+really have to wait for three years
+
+ align:start position:0%
+really have to wait for three years
+ 
+
+ align:start position:0%
+really have to wait for three years
+before we get this checklist out like
+
+ align:start position:0%
+before we get this checklist out like
+ 
+
+ align:start position:0%
+before we get this checklist out like
+what's the harm I looked at the cesarian
+
+ align:start position:0%
+what's the harm I looked at the cesarian
+ 
+
+ align:start position:0%
+what's the harm I looked at the cesarian
+section rates they're not going up
+
+ align:start position:0%
+section rates they're not going up
+ 
+
+ align:start position:0%
+section rates they're not going up
+you're not going to cause death and it's
+
+ align:start position:0%
+you're not going to cause death and it's
+ 
+
+ align:start position:0%
+you're not going to cause death and it's
+a question and it's a question for you
+
+ align:start position:0%
+a question and it's a question for you
+ 
+
+ align:start position:0%
+a question and it's a question for you
+guys and it's a question for the field
+
+ align:start position:0%
+guys and it's a question for the field
+ 
+
+ align:start position:0%
+guys and it's a question for the field
+like do we have to wait for the RCT
+
+ align:start position:0%
+like do we have to wait for the RCT
+ 
+
+ align:start position:0%
+like do we have to wait for the RCT
+before simple Innovations like this are
+
+ align:start position:0%
+before simple Innovations like this are
+ 
+
+ align:start position:0%
+before simple Innovations like this are
+rolled out oh sorry randomized control
+
+ align:start position:0%
+rolled out oh sorry randomized control
+ 
+
+ align:start position:0%
+rolled out oh sorry randomized control
+Tri so it's like you know the big
+
+ align:start position:0%
+Tri so it's like you know the big
+ 
+
+ align:start position:0%
+Tri so it's like you know the big
+shebang that the academics like well I
+
+ align:start position:0%
+shebang that the academics like well I
+ 
+
+ align:start position:0%
+shebang that the academics like well I
+don't know I don't know the answer to
+
+ align:start position:0%
+don't know I don't know the answer to
+ 
+
+ align:start position:0%
+don't know I don't know the answer to
+this and I I I think there is um an
+
+ align:start position:0%
+this and I I I think there is um an
+ 
+
+ align:start position:0%
+this and I I I think there is um an
+argument to be had and then the use of
+
+ align:start position:0%
+argument to be had and then the use of
+ 
+
+ align:start position:0%
+argument to be had and then the use of
+technology and again it's something that
+
+ align:start position:0%
+technology and again it's something that
+ 
+
+ align:start position:0%
+technology and again it's something that
+you can answer better than us I actually
+
+ align:start position:0%
+you can answer better than us I actually
+ 
+
+ align:start position:0%
+you can answer better than us I actually
+think that yes the checklist could be
+
+ align:start position:0%
+think that yes the checklist could be
+ 
+
+ align:start position:0%
+think that yes the checklist could be
+put on a mobile phone like yes that's
+
+ align:start position:0%
+put on a mobile phone like yes that's
+ 
+
+ align:start position:0%
+put on a mobile phone like yes that's
+one thing but you know I think there's
+
+ align:start position:0%
+one thing but you know I think there's
+ 
+
+ align:start position:0%
+one thing but you know I think there's
+more than that like could it be used for
+
+ align:start position:0%
+more than that like could it be used for
+ 
+
+ align:start position:0%
+more than that like could it be used for
+data collect ction could it be used for
+
+ align:start position:0%
+data collect ction could it be used for
+ 
+
+ align:start position:0%
+data collect ction could it be used for
+training like where does technology fit
+
+ align:start position:0%
+training like where does technology fit
+ 
+
+ align:start position:0%
+training like where does technology fit
+in with these Innovations and it's a
+
+ align:start position:0%
+in with these Innovations and it's a
+ 
+
+ align:start position:0%
+in with these Innovations and it's a
+thing that hasn't been sort of
+
+ align:start position:0%
+thing that hasn't been sort of
+ 
+
+ align:start position:0%
+thing that hasn't been sort of
+considered in you know the to g day
+
+ align:start position:0%
+considered in you know the to g day
+ 
+
+ align:start position:0%
+considered in you know the to g day
+group and I think it's you know I'm sure
+
+ align:start position:0%
+group and I think it's you know I'm sure
+ 
+
+ align:start position:0%
+group and I think it's you know I'm sure
+Leo's thought about this like how do we
+
+ align:start position:0%
+Leo's thought about this like how do we
+ 
+
+ align:start position:0%
+Leo's thought about this like how do we
+start using innov technology to support
+
+ align:start position:0%
+start using innov technology to support
+ 
+
+ align:start position:0%
+start using innov technology to support
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+Innovations so that's a quick run
+
+ align:start position:0%
+Innovations so that's a quick run
+ 
+
+ align:start position:0%
+Innovations so that's a quick run
+through the safe child with checklist
\ No newline at end of file
diff --git a/mhLI51d9LDc.txt b/mhLI51d9LDc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5e6df7975a6d3026ce728725c491a9eccd1d1bfb
--- /dev/null
+++ b/mhLI51d9LDc.txt
@@ -0,0 +1,7600 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+okay uh so this is a fun lecture this is
+
+ align:start position:0%
+okay uh so this is a fun lecture this is
+ 
+
+ align:start position:0%
+okay uh so this is a fun lecture this is
+the lecture where understanding uh the
+
+ align:start position:0%
+the lecture where understanding uh the
+ 
+
+ align:start position:0%
+the lecture where understanding uh the
+gradient which we did last time
+
+ align:start position:0%
+gradient which we did last time
+ 
+
+ align:start position:0%
+gradient which we did last time
+the Divergence that we almost completed
+
+ align:start position:0%
+the Divergence that we almost completed
+ 
+
+ align:start position:0%
+the Divergence that we almost completed
+those two pieces now come together into
+
+ align:start position:0%
+those two pieces now come together into
+ 
+
+ align:start position:0%
+those two pieces now come together into
+the Lassa equation and it's just things
+
+ align:start position:0%
+the Lassa equation and it's just things
+ 
+
+ align:start position:0%
+the Lassa equation and it's just things
+work in a fantastic way so I enjoy this
+
+ align:start position:0%
+work in a fantastic way so I enjoy this
+ 
+
+ align:start position:0%
+work in a fantastic way so I enjoy this
+one so the the result will be that we've
+
+ align:start position:0%
+one so the the result will be that we've
+ 
+
+ align:start position:0%
+one so the the result will be that we've
+have the potential function U that we've
+
+ align:start position:0%
+have the potential function U that we've
+ 
+
+ align:start position:0%
+have the potential function U that we've
+spoken about and take its gradient then
+
+ align:start position:0%
+spoken about and take its gradient then
+ 
+
+ align:start position:0%
+spoken about and take its gradient then
+now is coming a stream function s that's
+
+ align:start position:0%
+now is coming a stream function s that's
+ 
+
+ align:start position:0%
+now is coming a stream function s that's
+connected with the Divergence when the
+
+ align:start position:0%
+connected with the Divergence when the
+ 
+
+ align:start position:0%
+connected with the Divergence when the
+Divergence is zero that there's a
+
+ align:start position:0%
+Divergence is zero that there's a
+ 
+
+ align:start position:0%
+Divergence is zero that there's a
+something called a stream function s and
+
+ align:start position:0%
+something called a stream function s and
+ 
+
+ align:start position:0%
+something called a stream function s and
+these the connections between those two
+
+ align:start position:0%
+these the connections between those two
+ 
+
+ align:start position:0%
+these the connections between those two
+functions U and S are are crucial and
+
+ align:start position:0%
+functions U and S are are crucial and
+ 
+
+ align:start position:0%
+functions U and S are are crucial and
+and and connecting uh gradient to
+
+ align:start position:0%
+and and connecting uh gradient to
+ 
+
+ align:start position:0%
+and and connecting uh gradient to
+Divergence will take us to ll's equation
+
+ align:start position:0%
+Divergence will take us to ll's equation
+ 
+
+ align:start position:0%
+Divergence will take us to ll's equation
+and then you'll see the special special
+
+ align:start position:0%
+and then you'll see the special special
+ 
+
+ align:start position:0%
+and then you'll see the special special
+role of X Plus i y in in 2D so this is
+
+ align:start position:0%
+role of X Plus i y in in 2D so this is
+ 
+
+ align:start position:0%
+role of X Plus i y in in 2D so this is
+in two Dimensions okay so let me begin
+
+ align:start position:0%
+in two Dimensions okay so let me begin
+ 
+
+ align:start position:0%
+in two Dimensions okay so let me begin
+with with the Divergence this is the
+
+ align:start position:0%
+with with the Divergence this is the
+ 
+
+ align:start position:0%
+with with the Divergence this is the
+Divergence of w of
+
+ align:start position:0%
+Divergence of w of
+ 
+
+ align:start position:0%
+Divergence of w of
+course and uh solve
+
+ align:start position:0%
+course and uh solve
+ 
+
+ align:start position:0%
+course and uh solve
+it as just as we wanted to solve Kirk's
+
+ align:start position:0%
+it as just as we wanted to solve Kirk's
+ 
+
+ align:start position:0%
+it as just as we wanted to solve Kirk's
+current law a transpose W equals z so
+
+ align:start position:0%
+current law a transpose W equals z so
+ 
+
+ align:start position:0%
+current law a transpose W equals z so
+now in the continuous case we want to
+
+ align:start position:0%
+now in the continuous case we want to
+ 
+
+ align:start position:0%
+now in the continuous case we want to
+find solutions to the we want to find
+
+ align:start position:0%
+find solutions to the we want to find
+ 
+
+ align:start position:0%
+find solutions to the we want to find
+Divergence free Fields Source free
+
+ align:start position:0%
+Divergence free Fields Source free
+ 
+
+ align:start position:0%
+Divergence free Fields Source free
+Fields you could say that's about the
+
+ align:start position:0%
+Fields you could say that's about the
+ 
+
+ align:start position:0%
+Fields you could say that's about the
+best word we have Divergence free
+
+ align:start position:0%
+best word we have Divergence free
+ 
+
+ align:start position:0%
+best word we have Divergence free
+meaning there is no Divergence the the
+
+ align:start position:0%
+meaning there is no Divergence the the
+ 
+
+ align:start position:0%
+meaning there is no Divergence the the
+the okay so what have we got here we've
+
+ align:start position:0%
+the okay so what have we got here we've
+ 
+
+ align:start position:0%
+the okay so what have we got here we've
+got one equation in two
+
+ align:start position:0%
+got one equation in two
+ 
+
+ align:start position:0%
+got one equation in two
+unknowns last time with the gradient
+
+ align:start position:0%
+unknowns last time with the gradient
+ 
+
+ align:start position:0%
+unknowns last time with the gradient
+business we had two equations for you
+
+ align:start position:0%
+business we had two equations for you
+ 
+
+ align:start position:0%
+business we had two equations for you
+and only that one unknown now we've got
+
+ align:start position:0%
+and only that one unknown now we've got
+ 
+
+ align:start position:0%
+and only that one unknown now we've got
+one equation two unknowns because we're
+
+ align:start position:0%
+one equation two unknowns because we're
+ 
+
+ align:start position:0%
+one equation two unknowns because we're
+looking at the transpose so now I want
+
+ align:start position:0%
+looking at the transpose so now I want
+ 
+
+ align:start position:0%
+looking at the transpose so now I want
+so there should be a lot of solutions
+
+ align:start position:0%
+so there should be a lot of solutions
+ 
+
+ align:start position:0%
+so there should be a lot of solutions
+right if you give me a W1 then probably
+
+ align:start position:0%
+right if you give me a W1 then probably
+ 
+
+ align:start position:0%
+right if you give me a W1 then probably
+I'll be able to find a W2 but there's a
+
+ align:start position:0%
+I'll be able to find a W2 but there's a
+ 
+
+ align:start position:0%
+I'll be able to find a W2 but there's a
+neat way to describe the solutions to
+
+ align:start position:0%
+neat way to describe the solutions to
+ 
+
+ align:start position:0%
+neat way to describe the solutions to
+that equation the Divergence free Fields
+
+ align:start position:0%
+that equation the Divergence free Fields
+ 
+
+ align:start position:0%
+that equation the Divergence free Fields
+it's to introduce something called a
+
+ align:start position:0%
+it's to introduce something called a
+ 
+
+ align:start position:0%
+it's to introduce something called a
+source function a stream function sorry
+
+ align:start position:0%
+source function a stream function sorry
+ 
+
+ align:start position:0%
+source function a stream function sorry
+stream
+
+ align:start position:0%
+stream
+ 
+
+ align:start position:0%
+stream
+function okay and now the idea will be
+
+ align:start position:0%
+function okay and now the idea will be
+ 
+
+ align:start position:0%
+function okay and now the idea will be
+that if I let so I'll try let me try I
+
+ align:start position:0%
+that if I let so I'll try let me try I
+ 
+
+ align:start position:0%
+that if I let so I'll try let me try I
+take any function s ofx and Y any
+
+ align:start position:0%
+take any function s ofx and Y any
+ 
+
+ align:start position:0%
+take any function s ofx and Y any
+function whatever so now I try
+
+ align:start position:0%
+function whatever so now I try
+ 
+
+ align:start position:0%
+function whatever so now I try
+let
+
+ align:start position:0%
+let
+ 
+
+ align:start position:0%
+let
+W1 be DS Dy so so my maybe I should say
+
+ align:start position:0%
+W1 be DS Dy so so my maybe I should say
+ 
+
+ align:start position:0%
+W1 be DS Dy so so my maybe I should say
+yeah maybe I should go this way I'm I'm
+
+ align:start position:0%
+yeah maybe I should go this way I'm I'm
+ 
+
+ align:start position:0%
+yeah maybe I should go this way I'm I'm
+I'm looking for Solutions okay so I take
+
+ align:start position:0%
+I'm looking for Solutions okay so I take
+ 
+
+ align:start position:0%
+I'm looking for Solutions okay so I take
+any function s i take its y derivative
+
+ align:start position:0%
+any function s i take its y derivative
+ 
+
+ align:start position:0%
+any function s i take its y derivative
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+W1 and you can tell me what W2 has to be
+
+ align:start position:0%
+W1 and you can tell me what W2 has to be
+ 
+
+ align:start position:0%
+W1 and you can tell me what W2 has to be
+so let me see so so uh if if W1 is D sdy
+
+ align:start position:0%
+so let me see so so uh if if W1 is D sdy
+ 
+
+ align:start position:0%
+so let me see so so uh if if W1 is D sdy
+this will be what this will be the
+
+ align:start position:0%
+this will be what this will be the
+ 
+
+ align:start position:0%
+this will be what this will be the
+second the X derivative of the Y
+
+ align:start position:0%
+second the X derivative of the Y
+ 
+
+ align:start position:0%
+second the X derivative of the Y
+derivative right if W1 is the Y
+
+ align:start position:0%
+derivative right if W1 is the Y
+ 
+
+ align:start position:0%
+derivative right if W1 is the Y
+derivative then when I take the X
+
+ align:start position:0%
+derivative then when I take the X
+ 
+
+ align:start position:0%
+derivative then when I take the X
+derivative I've got this cross
+
+ align:start position:0%
+derivative I've got this cross
+ 
+
+ align:start position:0%
+derivative I've got this cross
+derivative so what would be the smart
+
+ align:start position:0%
+derivative so what would be the smart
+ 
+
+ align:start position:0%
+derivative so what would be the smart
+choice for W2 so I'll say then then W2
+
+ align:start position:0%
+choice for W2 so I'll say then then W2
+ 
+
+ align:start position:0%
+choice for W2 so I'll say then then W2
+will be what what will the now I've sort
+
+ align:start position:0%
+will be what what will the now I've sort
+ 
+
+ align:start position:0%
+will be what what will the now I've sort
+of said what W1 is what's the W2 that
+
+ align:start position:0%
+of said what W1 is what's the W2 that
+ 
+
+ align:start position:0%
+of said what W1 is what's the W2 that
+goes with it well it's whatever it takes
+
+ align:start position:0%
+goes with it well it's whatever it takes
+ 
+
+ align:start position:0%
+goes with it well it's whatever it takes
+to cancel this I want this to be in
+
+ align:start position:0%
+to cancel this I want this to be in
+ 
+
+ align:start position:0%
+to cancel this I want this to be in
+other words I want it to be get zero so
+
+ align:start position:0%
+other words I want it to be get zero so
+ 
+
+ align:start position:0%
+other words I want it to be get zero so
+this should be the second derivative of
+
+ align:start position:0%
+this should be the second derivative of
+ 
+
+ align:start position:0%
+this should be the second derivative of
+s and what am I going to put now Dy DX
+
+ align:start position:0%
+s and what am I going to put now Dy DX
+ 
+
+ align:start position:0%
+s and what am I going to put now Dy DX
+I'm using the same very crucial fact
+
+ align:start position:0%
+I'm using the same very crucial fact
+ 
+
+ align:start position:0%
+I'm using the same very crucial fact
+that the cross derivative can be in
+
+ align:start position:0%
+that the cross derivative can be in
+ 
+
+ align:start position:0%
+that the cross derivative can be in
+either order so what do I see for
+
+ align:start position:0%
+either order so what do I see for
+ 
+
+ align:start position:0%
+either order so what do I see for
+W2 do you see what W2 is this is
+
+ align:start position:0%
+W2 do you see what W2 is this is
+ 
+
+ align:start position:0%
+W2 do you see what W2 is this is
+supposed to match that that there's a
+
+ align:start position:0%
+supposed to match that that there's a
+ 
+
+ align:start position:0%
+supposed to match that that there's a
+minus sign W2 is
+
+ align:start position:0%
+minus sign W2 is
+ 
+
+ align:start position:0%
+minus sign W2 is
+What minus
+
+ align:start position:0%
+What minus
+ 
+
+ align:start position:0%
+What minus
+DSD X right minus DS DX that's that's
+
+ align:start position:0%
+DSD X right minus DS DX that's that's
+ 
+
+ align:start position:0%
+DSD X right minus DS DX that's that's
+the minus DS DX if if I take any
+
+ align:start position:0%
+the minus DS DX if if I take any
+ 
+
+ align:start position:0%
+the minus DS DX if if I take any
+function S I let W1 be its y derivative
+
+ align:start position:0%
+function S I let W1 be its y derivative
+ 
+
+ align:start position:0%
+function S I let W1 be its y derivative
+and W2 be its minus its X derivative
+
+ align:start position:0%
+and W2 be its minus its X derivative
+ 
+
+ align:start position:0%
+and W2 be its minus its X derivative
+then the Divergence will be zero because
+
+ align:start position:0%
+then the Divergence will be zero because
+ 
+
+ align:start position:0%
+then the Divergence will be zero because
+it'll I'll have the SEC the cross
+
+ align:start position:0%
+it'll I'll have the SEC the cross
+ 
+
+ align:start position:0%
+it'll I'll have the SEC the cross
+derivative minus the cross derivative of
+
+ align:start position:0%
+derivative minus the cross derivative of
+ 
+
+ align:start position:0%
+derivative minus the cross derivative of
+course that'll be zero so these will be
+
+ align:start position:0%
+course that'll be zero so these will be
+ 
+
+ align:start position:0%
+course that'll be zero so these will be
+my w1s my W's W1 W2 coming from s so I
+
+ align:start position:0%
+my w1s my W's W1 W2 coming from s so I
+ 
+
+ align:start position:0%
+my w1s my W's W1 W2 coming from s so I
+have what I expect with two unknowns
+
+ align:start position:0%
+have what I expect with two unknowns
+ 
+
+ align:start position:0%
+have what I expect with two unknowns
+only one equation I've got lots of
+
+ align:start position:0%
+only one equation I've got lots of
+ 
+
+ align:start position:0%
+only one equation I've got lots of
+solutions I create any function s and
+
+ align:start position:0%
+solutions I create any function s and
+ 
+
+ align:start position:0%
+solutions I create any function s and
+that will be one so that's a a stream
+
+ align:start position:0%
+that will be one so that's a a stream
+ 
+
+ align:start position:0%
+that will be one so that's a a stream
+function and it has a physical meaning
+
+ align:start position:0%
+function and it has a physical meaning
+ 
+
+ align:start position:0%
+function and it has a physical meaning
+so we get to see it and it has a
+
+ align:start position:0%
+so we get to see it and it has a
+ 
+
+ align:start position:0%
+so we get to see it and it has a
+fantastic connection to the potential
+
+ align:start position:0%
+fantastic connection to the potential
+ 
+
+ align:start position:0%
+fantastic connection to the potential
+when when so up to now so this is now
+
+ align:start position:0%
+when when so up to now so this is now
+ 
+
+ align:start position:0%
+when when so up to now so this is now
+the moment the Pieces come together up
+
+ align:start position:0%
+the moment the Pieces come together up
+ 
+
+ align:start position:0%
+the moment the Pieces come together up
+to now we had the Divergence and the
+
+ align:start position:0%
+to now we had the Divergence and the
+ 
+
+ align:start position:0%
+to now we had the Divergence and the
+gradient separately so up to now what we
+
+ align:start position:0%
+gradient separately so up to now what we
+ 
+
+ align:start position:0%
+gradient separately so up to now what we
+had was we started with a potential U
+
+ align:start position:0%
+had was we started with a potential U
+ 
+
+ align:start position:0%
+had was we started with a potential U
+and we went to v i I called it V for
+
+ align:start position:0%
+and we went to v i I called it V for
+ 
+
+ align:start position:0%
+and we went to v i I called it V for
+this application DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dy okay and now over on this side I had
+
+ align:start position:0%
+Dy okay and now over on this side I had
+ 
+
+ align:start position:0%
+Dy okay and now over on this side I had
+the Divergence of w equals z
+
+ align:start position:0%
+the Divergence of w equals z
+ 
+
+ align:start position:0%
+the Divergence of w equals z
+and that led me to W being what we've
+
+ align:start position:0%
+and that led me to W being what we've
+ 
+
+ align:start position:0%
+and that led me to W being what we've
+just said D
+
+ align:start position:0%
+just said D
+ 
+
+ align:start position:0%
+just said D
+sdy and minus
+
+ align:start position:0%
+sdy and minus
+ 
+
+ align:start position:0%
+sdy and minus
+dsdx okay two separate pictures
+
+ align:start position:0%
+dsdx okay two separate pictures
+ 
+
+ align:start position:0%
+dsdx okay two separate pictures
+now we're going to connect the framework
+
+ align:start position:0%
+now we're going to connect the framework
+ 
+
+ align:start position:0%
+now we're going to connect the framework
+going to give the connection between V
+
+ align:start position:0%
+going to give the connection between V
+ 
+
+ align:start position:0%
+going to give the connection between V
+and W and the connection will be the
+
+ align:start position:0%
+and W and the connection will be the
+ 
+
+ align:start position:0%
+and W and the connection will be the
+easiest possible they'll be equal so the
+
+ align:start position:0%
+easiest possible they'll be equal so the
+ 
+
+ align:start position:0%
+easiest possible they'll be equal so the
+C in our framework is the identity
+
+ align:start position:0%
+C in our framework is the identity
+ 
+
+ align:start position:0%
+C in our framework is the identity
+I want to say I want to look at the our
+
+ align:start position:0%
+I want to say I want to look at the our
+ 
+
+ align:start position:0%
+I want to say I want to look at the our
+framework when C is C is the
+
+ align:start position:0%
+framework when C is C is the
+ 
+
+ align:start position:0%
+framework when C is C is the
+identity so V and W are the same in
+
+ align:start position:0%
+identity so V and W are the same in
+ 
+
+ align:start position:0%
+identity so V and W are the same in
+other words what equation do we get then
+
+ align:start position:0%
+other words what equation do we get then
+ 
+
+ align:start position:0%
+other words what equation do we get then
+we started with u we take the gradient
+
+ align:start position:0%
+we started with u we take the gradient
+ 
+
+ align:start position:0%
+we started with u we take the gradient
+of U that's V we go over here and we
+
+ align:start position:0%
+of U that's V we go over here and we
+ 
+
+ align:start position:0%
+of U that's V we go over here and we
+still have the gradient of U because now
+
+ align:start position:0%
+still have the gradient of U because now
+ 
+
+ align:start position:0%
+still have the gradient of U because now
+it's this was this is the V and now it's
+
+ align:start position:0%
+it's this was this is the V and now it's
+ 
+
+ align:start position:0%
+it's this was this is the V and now it's
+also the W and then we take the what do
+
+ align:start position:0%
+also the W and then we take the what do
+ 
+
+ align:start position:0%
+also the W and then we take the what do
+we take minus the diver
+
+ align:start position:0%
+we take minus the diver
+ 
+
+ align:start position:0%
+we take minus the diver
+of the gradient of U equals let's say F
+
+ align:start position:0%
+of the gradient of U equals let's say F
+ 
+
+ align:start position:0%
+of the gradient of U equals let's say F
+should we say F to make something happen
+
+ align:start position:0%
+should we say F to make something happen
+ 
+
+ align:start position:0%
+should we say F to make something happen
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+zero uh I'll say zero I'll say
+
+ align:start position:0%
+zero uh I'll say zero I'll say
+ 
+
+ align:start position:0%
+zero uh I'll say zero I'll say
+zero yeah because zero is the one that
+
+ align:start position:0%
+zero yeah because zero is the one that
+ 
+
+ align:start position:0%
+zero yeah because zero is the one that
+gives ll's equation the official name
+
+ align:start position:0%
+gives ll's equation the official name
+ 
+
+ align:start position:0%
+gives ll's equation the official name
+would be that's ll's equation do you
+
+ align:start position:0%
+would be that's ll's equation do you
+ 
+
+ align:start position:0%
+would be that's ll's equation do you
+recognize
+
+ align:start position:0%
+recognize
+ 
+
+ align:start position:0%
+recognize
+it we better write it out properly the
+
+ align:start position:0%
+it we better write it out properly the
+ 
+
+ align:start position:0%
+it we better write it out properly the
+Divergence of the gradient is the lassan
+
+ align:start position:0%
+Divergence of the gradient is the lassan
+ 
+
+ align:start position:0%
+Divergence of the gradient is the lassan
+so so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+llas famous
+
+ align:start position:0%
+llas famous
+ 
+
+ align:start position:0%
+llas famous
+equation steady state type of equation
+
+ align:start position:0%
+equation steady state type of equation
+ 
+
+ align:start position:0%
+equation steady state type of equation
+it goes with steady state problems let's
+
+ align:start position:0%
+it goes with steady state problems let's
+ 
+
+ align:start position:0%
+it goes with steady state problems let's
+just figure out what this is we've got
+
+ align:start position:0%
+just figure out what this is we've got
+ 
+
+ align:start position:0%
+just figure out what this is we've got
+so w
+
+ align:start position:0%
+so w
+ 
+
+ align:start position:0%
+so w
+is since these are the same W is now DX
+
+ align:start position:0%
+is since these are the same W is now DX
+ 
+
+ align:start position:0%
+is since these are the same W is now DX
+duud y it's the gradient now what
+
+ align:start position:0%
+duud y it's the gradient now what
+ 
+
+ align:start position:0%
+duud y it's the gradient now what
+happens do you see what happens when I
+
+ align:start position:0%
+happens do you see what happens when I
+ 
+
+ align:start position:0%
+happens do you see what happens when I
+take the Divergence of the gradient the
+
+ align:start position:0%
+take the Divergence of the gradient the
+ 
+
+ align:start position:0%
+take the Divergence of the gradient the
+Divergence of this W what what's the
+
+ align:start position:0%
+Divergence of this W what what's the
+ 
+
+ align:start position:0%
+Divergence of this W what what's the
+what I just want to write that equation
+
+ align:start position:0%
+what I just want to write that equation
+ 
+
+ align:start position:0%
+what I just want to write that equation
+out it's
+
+ align:start position:0%
+out it's
+ 
+
+ align:start position:0%
+out it's
+crucial I need
+
+ align:start position:0%
+crucial I need
+ 
+
+ align:start position:0%
+crucial I need
+a brilliant colors and lights shining
+
+ align:start position:0%
+a brilliant colors and lights shining
+ 
+
+ align:start position:0%
+a brilliant colors and lights shining
+now for this uh what goes in there
+
+ align:start position:0%
+now for this uh what goes in there
+ 
+
+ align:start position:0%
+now for this uh what goes in there
+because I want to take the Divergence of
+
+ align:start position:0%
+because I want to take the Divergence of
+ 
+
+ align:start position:0%
+because I want to take the Divergence of
+the gradient so what does that mean I
+
+ align:start position:0%
+the gradient so what does that mean I
+ 
+
+ align:start position:0%
+the gradient so what does that mean I
+take the X derivative of the first
+
+ align:start position:0%
+take the X derivative of the first
+ 
+
+ align:start position:0%
+take the X derivative of the first
+component plus the Y derivative of the
+
+ align:start position:0%
+component plus the Y derivative of the
+ 
+
+ align:start position:0%
+component plus the Y derivative of the
+second component the minus sign is not
+
+ align:start position:0%
+second component the minus sign is not
+ 
+
+ align:start position:0%
+second component the minus sign is not
+going to matter with a zero on the right
+
+ align:start position:0%
+going to matter with a zero on the right
+ 
+
+ align:start position:0%
+going to matter with a zero on the right
+hand side I could cancel the minus so
+
+ align:start position:0%
+hand side I could cancel the minus so
+ 
+
+ align:start position:0%
+hand side I could cancel the minus so
+but let me say it again the Divergence
+
+ align:start position:0%
+but let me say it again the Divergence
+ 
+
+ align:start position:0%
+but let me say it again the Divergence
+is it applies to a vector I've got a
+
+ align:start position:0%
+is it applies to a vector I've got a
+ 
+
+ align:start position:0%
+is it applies to a vector I've got a
+vector I take the X component of the
+
+ align:start position:0%
+vector I take the X component of the
+ 
+
+ align:start position:0%
+vector I take the X component of the
+first of W1 so that'll give me DC U
+
+ align:start position:0%
+first of W1 so that'll give me DC U
+ 
+
+ align:start position:0%
+first of W1 so that'll give me DC U
+dx2 and I take the Y derivative I should
+
+ align:start position:0%
+dx2 and I take the Y derivative I should
+ 
+
+ align:start position:0%
+dx2 and I take the Y derivative I should
+have said derivative y derivative of the
+
+ align:start position:0%
+have said derivative y derivative of the
+ 
+
+ align:start position:0%
+have said derivative y derivative of the
+second component and the Y derivative of
+
+ align:start position:0%
+second component and the Y derivative of
+ 
+
+ align:start position:0%
+second component and the Y derivative of
+that is DC u d
+
+ align:start position:0%
+that is DC u d
+ 
+
+ align:start position:0%
+that is DC u d
+y^2 and I get zero so that's lass's
+
+ align:start position:0%
+y^2 and I get zero so that's lass's
+ 
+
+ align:start position:0%
+y^2 and I get zero so that's lass's
+equation you see that the whole idea is
+
+ align:start position:0%
+equation you see that the whole idea is
+ 
+
+ align:start position:0%
+equation you see that the whole idea is
+lass's equation in in in working with
+
+ align:start position:0%
+lass's equation in in in working with
+ 
+
+ align:start position:0%
+lass's equation in in in working with
+Lassa equation we have three elements
+
+ align:start position:0%
+Lassa equation we have three elements
+ 
+
+ align:start position:0%
+Lassa equation we have three elements
+here the gradient comes in the
+
+ align:start position:0%
+here the gradient comes in the
+ 
+
+ align:start position:0%
+here the gradient comes in the
+Divergence comes in and equality comes
+
+ align:start position:0%
+Divergence comes in and equality comes
+ 
+
+ align:start position:0%
+Divergence comes in and equality comes
+in a more General
+
+ align:start position:0%
+in a more General
+ 
+
+ align:start position:0%
+in a more General
+would you like to see a more General lus
+
+ align:start position:0%
+would you like to see a more General lus
+ 
+
+ align:start position:0%
+would you like to see a more General lus
+equation well a more General Pon
+
+ align:start position:0%
+equation well a more General Pon
+ 
+
+ align:start position:0%
+equation well a more General Pon
+equation so let me underneath La let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+write you got the pronunciation the
+
+ align:start position:0%
+write you got the pronunciation the
+ 
+
+ align:start position:0%
+write you got the pronunciation the
+brilliant French pronunciation there of
+
+ align:start position:0%
+brilliant French pronunciation there of
+ 
+
+ align:start position:0%
+brilliant French pronunciation there of
+P that was my best I can't improve on
+
+ align:start position:0%
+P that was my best I can't improve on
+ 
+
+ align:start position:0%
+P that was my best I can't improve on
+that one okay so it comes in when
+
+ align:start position:0%
+that one okay so it comes in when
+ 
+
+ align:start position:0%
+that one okay so it comes in when
+there's a right hand side so the normal
+
+ align:start position:0%
+there's a right hand side so the normal
+ 
+
+ align:start position:0%
+there's a right hand side so the normal
+P equation is second der with respect to
+
+ align:start position:0%
+P equation is second der with respect to
+ 
+
+ align:start position:0%
+P equation is second der with respect to
+X second deriva with respect to Y well
+
+ align:start position:0%
+X second deriva with respect to Y well
+ 
+
+ align:start position:0%
+X second deriva with respect to Y well
+actually our should should have a minus
+
+ align:start position:0%
+actually our should should have a minus
+ 
+
+ align:start position:0%
+actually our should should have a minus
+there really should be a minus there
+
+ align:start position:0%
+there really should be a minus there
+ 
+
+ align:start position:0%
+there really should be a minus there
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+to you remember why the minus is there
+
+ align:start position:0%
+to you remember why the minus is there
+ 
+
+ align:start position:0%
+to you remember why the minus is there
+the minus is there to make the whole
+
+ align:start position:0%
+the minus is there to make the whole
+ 
+
+ align:start position:0%
+the minus is there to make the whole
+thing positive I mean right that sounds
+
+ align:start position:0%
+thing positive I mean right that sounds
+ 
+
+ align:start position:0%
+thing positive I mean right that sounds
+crazy that the minus makes it positive
+
+ align:start position:0%
+crazy that the minus makes it positive
+ 
+
+ align:start position:0%
+crazy that the minus makes it positive
+but these second derivatives are
+
+ align:start position:0%
+but these second derivatives are
+ 
+
+ align:start position:0%
+but these second derivatives are
+negative definite as always and the
+
+ align:start position:0%
+negative definite as always and the
+ 
+
+ align:start position:0%
+negative definite as always and the
+minus makes some positive definite so I
+
+ align:start position:0%
+minus makes some positive definite so I
+ 
+
+ align:start position:0%
+minus makes some positive definite so I
+don't remember whether maybe I maybe I
+
+ align:start position:0%
+don't remember whether maybe I maybe I
+ 
+
+ align:start position:0%
+don't remember whether maybe I maybe I
+often include the minus over here equal
+
+ align:start position:0%
+often include the minus over here equal
+ 
+
+ align:start position:0%
+often include the minus over here equal
+f of x and y so there's a source plus
+
+ align:start position:0%
+f of x and y so there's a source plus
+ 
+
+ align:start position:0%
+f of x and y so there's a source plus
+all has a source term llas
+
+ align:start position:0%
+all has a source term llas
+ 
+
+ align:start position:0%
+all has a source term llas
+doesn't and and just while I'm talking
+
+ align:start position:0%
+doesn't and and just while I'm talking
+ 
+
+ align:start position:0%
+doesn't and and just while I'm talking
+about this framework if there was a c of
+
+ align:start position:0%
+about this framework if there was a c of
+ 
+
+ align:start position:0%
+about this framework if there was a c of
+X and Y so this would be uh or I'll put
+
+ align:start position:0%
+X and Y so this would be uh or I'll put
+ 
+
+ align:start position:0%
+X and Y so this would be uh or I'll put
+or uh the more General one would be the
+
+ align:start position:0%
+or uh the more General one would be the
+ 
+
+ align:start position:0%
+or uh the more General one would be the
+X derivative because I'm taking the
+
+ align:start position:0%
+X derivative because I'm taking the
+ 
+
+ align:start position:0%
+X derivative because I'm taking the
+Divergence of a c of X and y du U
+
+ align:start position:0%
+Divergence of a c of X and y du U
+ 
+
+ align:start position:0%
+Divergence of a c of X and y du U
+DX and the Y derivative of a c so you
+
+ align:start position:0%
+DX and the Y derivative of a c so you
+ 
+
+ align:start position:0%
+DX and the Y derivative of a c so you
+see the difference I'm now allowing a
+
+ align:start position:0%
+see the difference I'm now allowing a
+ 
+
+ align:start position:0%
+see the difference I'm now allowing a
+some variable
+
+ align:start position:0%
+some variable
+ 
+
+ align:start position:0%
+some variable
+conductivity
+
+ align:start position:0%
+conductivity
+ 
+
+ align:start position:0%
+conductivity
+variable uh whatever this variable
+
+ align:start position:0%
+variable uh whatever this variable
+ 
+
+ align:start position:0%
+variable uh whatever this variable
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+duy equals F again so that would be the
+
+ align:start position:0%
+duy equals F again so that would be the
+ 
+
+ align:start position:0%
+duy equals F again so that would be the
+more General one I don't think we plan
+
+ align:start position:0%
+more General one I don't think we plan
+ 
+
+ align:start position:0%
+more General one I don't think we plan
+to study that in well that's not the
+
+ align:start position:0%
+to study that in well that's not the
+ 
+
+ align:start position:0%
+to study that in well that's not the
+most General I could get have more and
+
+ align:start position:0%
+most General I could get have more and
+ 
+
+ align:start position:0%
+most General I could get have more and
+more things there but that's that shows
+
+ align:start position:0%
+more things there but that's that shows
+ 
+
+ align:start position:0%
+more things there but that's that shows
+you a variable
+
+ align:start position:0%
+you a variable
+ 
+
+ align:start position:0%
+you a variable
+material yeah that material is variable
+
+ align:start position:0%
+material yeah that material is variable
+ 
+
+ align:start position:0%
+material yeah that material is variable
+I would use the word what what word
+
+ align:start position:0%
+I would use the word what what word
+ 
+
+ align:start position:0%
+I would use the word what what word
+would I use it doesn't depend on the
+
+ align:start position:0%
+would I use it doesn't depend on the
+ 
+
+ align:start position:0%
+would I use it doesn't depend on the
+direction I I'm using the same C of XY y
+
+ align:start position:0%
+direction I I'm using the same C of XY y
+ 
+
+ align:start position:0%
+direction I I'm using the same C of XY y
+in the X Direction and the y direction
+
+ align:start position:0%
+in the X Direction and the y direction
+ 
+
+ align:start position:0%
+in the X Direction and the y direction
+therefore in all directions and I didn't
+
+ align:start position:0%
+therefore in all directions and I didn't
+ 
+
+ align:start position:0%
+therefore in all directions and I didn't
+come prepared with that word what's the
+
+ align:start position:0%
+come prepared with that word what's the
+ 
+
+ align:start position:0%
+come prepared with that word what's the
+word for when it doesn't depend on the
+
+ align:start position:0%
+word for when it doesn't depend on the
+ 
+
+ align:start position:0%
+word for when it doesn't depend on the
+direction I isotropic thanks isotropic
+
+ align:start position:0%
+direction I isotropic thanks isotropic
+ 
+
+ align:start position:0%
+direction I isotropic thanks isotropic
+so that's isotropic right so that's
+
+ align:start position:0%
+so that's isotropic right so that's
+ 
+
+ align:start position:0%
+so that's isotropic right so that's
+really our framework
+
+ align:start position:0%
+really our framework
+ 
+
+ align:start position:0%
+really our framework
+there at least for isotropic materials
+
+ align:start position:0%
+there at least for isotropic materials
+ 
+
+ align:start position:0%
+there at least for isotropic materials
+and then we could have more General with
+
+ align:start position:0%
+and then we could have more General with
+ 
+
+ align:start position:0%
+and then we could have more General with
+an isotropic materials that would be fun
+
+ align:start position:0%
+an isotropic materials that would be fun
+ 
+
+ align:start position:0%
+an isotropic materials that would be fun
+too all of those things are fun but
+
+ align:start position:0%
+too all of those things are fun but
+ 
+
+ align:start position:0%
+too all of those things are fun but
+lasses equation is the most fun of all
+
+ align:start position:0%
+lasses equation is the most fun of all
+ 
+
+ align:start position:0%
+lasses equation is the most fun of all
+so let me take F to be zero C to be one
+
+ align:start position:0%
+so let me take F to be zero C to be one
+ 
+
+ align:start position:0%
+so let me take F to be zero C to be one
+get back up to lass's equation and
+
+ align:start position:0%
+get back up to lass's equation and
+ 
+
+ align:start position:0%
+get back up to lass's equation and
+uh begin to make
+
+ align:start position:0%
+uh begin to make
+ 
+
+ align:start position:0%
+uh begin to make
+connections begin to make connections
+
+ align:start position:0%
+connections begin to make connections
+ 
+
+ align:start position:0%
+connections begin to make connections
+okay the beautiful connection the
+
+ align:start position:0%
+okay the beautiful connection the
+ 
+
+ align:start position:0%
+okay the beautiful connection the
+beautiful connection is the one right
+
+ align:start position:0%
+beautiful connection is the one right
+ 
+
+ align:start position:0%
+beautiful connection is the one right
+here when V and U are the same when V
+
+ align:start position:0%
+here when V and U are the same when V
+ 
+
+ align:start position:0%
+here when V and U are the same when V
+and W are the same then I just read off
+
+ align:start position:0%
+and W are the same then I just read off
+ 
+
+ align:start position:0%
+and W are the same then I just read off
+if V is the same as W then how is the
+
+ align:start position:0%
+if V is the same as W then how is the
+ 
+
+ align:start position:0%
+if V is the same as W then how is the
+potential function which is on the left
+
+ align:start position:0%
+potential function which is on the left
+ 
+
+ align:start position:0%
+potential function which is on the left
+side connected to the stream function
+
+ align:start position:0%
+side connected to the stream function
+ 
+
+ align:start position:0%
+side connected to the stream function
+which is coming from anytime div w is z
+
+ align:start position:0%
+which is coming from anytime div w is z
+ 
+
+ align:start position:0%
+which is coming from anytime div w is z
+I've got a stream function in 2D here
+
+ align:start position:0%
+I've got a stream function in 2D here
+ 
+
+ align:start position:0%
+I've got a stream function in 2D here
+the connection is just those two match
+
+ align:start position:0%
+the connection is just those two match
+ 
+
+ align:start position:0%
+the connection is just those two match
+DX is the same as DS
+
+ align:start position:0%
+DX is the same as DS
+ 
+
+ align:start position:0%
+DX is the same as DS
+Dy and
+
+ align:start position:0%
+Dy and
+ 
+
+ align:start position:0%
+Dy and
+dudy is the same as minus dsdx you see
+
+ align:start position:0%
+dudy is the same as minus dsdx you see
+ 
+
+ align:start position:0%
+dudy is the same as minus dsdx you see
+what the two sides of our world are
+
+ align:start position:0%
+what the two sides of our world are
+ 
+
+ align:start position:0%
+what the two sides of our world are
+coming together this is we're dealing
+
+ align:start position:0%
+coming together this is we're dealing
+ 
+
+ align:start position:0%
+coming together this is we're dealing
+with flows that are
+
+ align:start position:0%
+with flows that are
+ 
+
+ align:start position:0%
+with flows that are
+both gradient flows they come from a
+
+ align:start position:0%
+both gradient flows they come from a
+ 
+
+ align:start position:0%
+both gradient flows they come from a
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+potential and they're also there so I
+
+ align:start position:0%
+potential and they're also there so I
+ 
+
+ align:start position:0%
+potential and they're also there so I
+you could often say potential flows I
+
+ align:start position:0%
+you could often say potential flows I
+ 
+
+ align:start position:0%
+you could often say potential flows I
+see the word ideal flows coming in these
+
+ align:start position:0%
+see the word ideal flows coming in these
+ 
+
+ align:start position:0%
+see the word ideal flows coming in these
+are very special flows you know
+
+ align:start position:0%
+are very special flows you know
+ 
+
+ align:start position:0%
+are very special flows you know
+so uh Arrow couldn't work entirely with
+
+ align:start position:0%
+so uh Arrow couldn't work entirely with
+ 
+
+ align:start position:0%
+so uh Arrow couldn't work entirely with
+these flows of course these are such
+
+ align:start position:0%
+these flows of course these are such
+ 
+
+ align:start position:0%
+these flows of course these are such
+ideal flows that you know proper
+
+ align:start position:0%
+ideal flows that you know proper
+ 
+
+ align:start position:0%
+ideal flows that you know proper
+aerodynamics you got shocks you've got
+
+ align:start position:0%
+aerodynamics you got shocks you've got
+ 
+
+ align:start position:0%
+aerodynamics you got shocks you've got
+all sorts of stuff going on but in a
+
+ align:start position:0%
+all sorts of stuff going on but in a
+ 
+
+ align:start position:0%
+all sorts of stuff going on but in a
+region of where everything's beautiful
+
+ align:start position:0%
+region of where everything's beautiful
+ 
+
+ align:start position:0%
+region of where everything's beautiful
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+you get back to this set total steady
+
+ align:start position:0%
+you get back to this set total steady
+ 
+
+ align:start position:0%
+you get back to this set total steady
+state steady flow steady potential flow
+
+ align:start position:0%
+state steady flow steady potential flow
+ 
+
+ align:start position:0%
+state steady flow steady potential flow
+we've got those
+
+ align:start position:0%
+we've got those
+ 
+
+ align:start position:0%
+we've got those
+equations that connect you on one side
+
+ align:start position:0%
+equations that connect you on one side
+ 
+
+ align:start position:0%
+equations that connect you on one side
+with the with the Divergence business
+
+ align:start position:0%
+with the with the Divergence business
+ 
+
+ align:start position:0%
+with the with the Divergence business
+the stream function on the other side so
+
+ align:start position:0%
+the stream function on the other side so
+ 
+
+ align:start position:0%
+the stream function on the other side so
+I just want to so I want to focus on
+
+ align:start position:0%
+I just want to so I want to focus on
+ 
+
+ align:start position:0%
+I just want to so I want to focus on
+these actually I mean so the heart of
+
+ align:start position:0%
+these actually I mean so the heart of
+ 
+
+ align:start position:0%
+these actually I mean so the heart of
+ll's equation is in there yeah okay uh
+
+ align:start position:0%
+ll's equation is in there yeah okay uh
+ 
+
+ align:start position:0%
+ll's equation is in there yeah okay uh
+first do you know the names of those
+
+ align:start position:0%
+first do you know the names of those
+ 
+
+ align:start position:0%
+first do you know the names of those
+those two two guys I shouldn't call them
+
+ align:start position:0%
+those two two guys I shouldn't call them
+ 
+
+ align:start position:0%
+those two two guys I shouldn't call them
+guys they're the greatest mathematicians
+
+ align:start position:0%
+guys they're the greatest mathematicians
+ 
+
+ align:start position:0%
+guys they're the greatest mathematicians
+ever or maybe after gals uh do you know
+
+ align:start position:0%
+ever or maybe after gals uh do you know
+ 
+
+ align:start position:0%
+ever or maybe after gals uh do you know
+whose names are associated with with
+
+ align:start position:0%
+whose names are associated with with
+ 
+
+ align:start position:0%
+whose names are associated with with
+these those two
+
+ align:start position:0%
+these those two
+ 
+
+ align:start position:0%
+these those two
+equations well lrange was great I'm not
+
+ align:start position:0%
+equations well lrange was great I'm not
+ 
+
+ align:start position:0%
+equations well lrange was great I'm not
+saying anything about lrange but he
+
+ align:start position:0%
+saying anything about lrange but he
+ 
+
+ align:start position:0%
+saying anything about lrange but he
+didn't do this so two one French and one
+
+ align:start position:0%
+didn't do this so two one French and one
+ 
+
+ align:start position:0%
+didn't do this so two one French and one
+German uh so the French guy's name is is
+
+ align:start position:0%
+German uh so the French guy's name is is
+ 
+
+ align:start position:0%
+German uh so the French guy's name is is
+Koshi
+
+ align:start position:0%
+Koshi
+ 
+
+ align:start position:0%
+Koshi
+and the German is so these are the Koshi
+
+ align:start position:0%
+and the German is so these are the Koshi
+ 
+
+ align:start position:0%
+and the German is so these are the Koshi
+and the German is really fantastic guy
+
+ align:start position:0%
+and the German is really fantastic guy
+ 
+
+ align:start position:0%
+and the German is really fantastic guy
+uh anybody know his
+
+ align:start position:0%
+uh anybody know his
+ 
+
+ align:start position:0%
+uh anybody know his
+name Koshi reman yeah the other name is
+
+ align:start position:0%
+name Koshi reman yeah the other name is
+ 
+
+ align:start position:0%
+name Koshi reman yeah the other name is
+reman Koshi reman
+
+ align:start position:0%
+reman Koshi reman
+ 
+
+ align:start position:0%
+reman Koshi reman
+equations that connect the two pieces U
+
+ align:start position:0%
+equations that connect the two pieces U
+ 
+
+ align:start position:0%
+equations that connect the two pieces U
+and S and and they're the subject of an
+
+ align:start position:0%
+and S and and they're the subject of an
+ 
+
+ align:start position:0%
+and S and and they're the subject of an
+enormous theory that we'll just touch on
+
+ align:start position:0%
+enormous theory that we'll just touch on
+ 
+
+ align:start position:0%
+enormous theory that we'll just touch on
+here okay and we'll see them Gra ially
+
+ align:start position:0%
+here okay and we'll see them Gra ially
+ 
+
+ align:start position:0%
+here okay and we'll see them Gra ially
+and we'll find Solutions yeah so so this
+
+ align:start position:0%
+and we'll find Solutions yeah so so this
+ 
+
+ align:start position:0%
+and we'll find Solutions yeah so so this
+is one way to pose our problem notice
+
+ align:start position:0%
+is one way to pose our problem notice
+ 
+
+ align:start position:0%
+is one way to pose our problem notice
+something here so does so I think that
+
+ align:start position:0%
+something here so does so I think that
+ 
+
+ align:start position:0%
+something here so does so I think that
+if we have these equations the solution
+
+ align:start position:0%
+if we have these equations the solution
+ 
+
+ align:start position:0%
+if we have these equations the solution
+you should satisfy the pla's equation
+
+ align:start position:0%
+you should satisfy the pla's equation
+ 
+
+ align:start position:0%
+you should satisfy the pla's equation
+because that'll this equality will take
+
+ align:start position:0%
+because that'll this equality will take
+ 
+
+ align:start position:0%
+because that'll this equality will take
+us around the loop uh so do I do you see
+
+ align:start position:0%
+us around the loop uh so do I do you see
+ 
+
+ align:start position:0%
+us around the loop uh so do I do you see
+that if if I could solve these two
+
+ align:start position:0%
+that if if I could solve these two
+ 
+
+ align:start position:0%
+that if if I could solve these two
+here's the point I'm going to get ll's
+
+ align:start position:0%
+here's the point I'm going to get ll's
+ 
+
+ align:start position:0%
+here's the point I'm going to get ll's
+equation solved by you
+
+ align:start position:0%
+equation solved by you
+ 
+
+ align:start position:0%
+equation solved by you
+lass's equation will also be solved by S
+
+ align:start position:0%
+lass's equation will also be solved by S
+ 
+
+ align:start position:0%
+lass's equation will also be solved by S
+the stream function so what's going to
+
+ align:start position:0%
+the stream function so what's going to
+ 
+
+ align:start position:0%
+the stream function so what's going to
+happen is I get two solutions a pair of
+
+ align:start position:0%
+happen is I get two solutions a pair of
+ 
+
+ align:start position:0%
+happen is I get two solutions a pair of
+solutions lasses equation the solutions
+
+ align:start position:0%
+solutions lasses equation the solutions
+ 
+
+ align:start position:0%
+solutions lasses equation the solutions
+to that come in pairs U and S so to so
+
+ align:start position:0%
+to that come in pairs U and S so to so
+ 
+
+ align:start position:0%
+to that come in pairs U and S so to so
+we get them two at a time and they're
+
+ align:start position:0%
+we get them two at a time and they're
+ 
+
+ align:start position:0%
+we get them two at a time and they're
+connected in this remarkable way so why
+
+ align:start position:0%
+connected in this remarkable way so why
+ 
+
+ align:start position:0%
+connected in this remarkable way so why
+let's see can you see that you will
+
+ align:start position:0%
+let's see can you see that you will
+ 
+
+ align:start position:0%
+let's see can you see that you will
+satisfy that this is the key to
+
+ align:start position:0%
+satisfy that this is the key to
+ 
+
+ align:start position:0%
+satisfy that this is the key to
+everything does you s satisfy the pl's
+
+ align:start position:0%
+everything does you s satisfy the pl's
+ 
+
+ align:start position:0%
+everything does you s satisfy the pl's
+equation sure I take the X derivative of
+
+ align:start position:0%
+equation sure I take the X derivative of
+ 
+
+ align:start position:0%
+equation sure I take the X derivative of
+that and I add to the Y derivative of
+
+ align:start position:0%
+that and I add to the Y derivative of
+ 
+
+ align:start position:0%
+that and I add to the Y derivative of
+that do you see it works the X
+
+ align:start position:0%
+that do you see it works the X
+ 
+
+ align:start position:0%
+that do you see it works the X
+derivative of this plus the Y derivative
+
+ align:start position:0%
+derivative of this plus the Y derivative
+ 
+
+ align:start position:0%
+derivative of this plus the Y derivative
+of this is exactly the cancellation of
+
+ align:start position:0%
+of this is exactly the cancellation of
+ 
+
+ align:start position:0%
+of this is exactly the cancellation of
+the cross that I wanted so I do these I
+
+ align:start position:0%
+the cross that I wanted so I do these I
+ 
+
+ align:start position:0%
+the cross that I wanted so I do these I
+I combine those into the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus so I
+
+ align:start position:0%
+plus so I
+ 
+
+ align:start position:0%
+plus so I
+just say that go through that verbally
+
+ align:start position:0%
+just say that go through that verbally
+ 
+
+ align:start position:0%
+just say that go through that verbally
+again I take the X derivative of this
+
+ align:start position:0%
+again I take the X derivative of this
+ 
+
+ align:start position:0%
+again I take the X derivative of this
+which which gives me the cross
+
+ align:start position:0%
+which which gives me the cross
+ 
+
+ align:start position:0%
+which which gives me the cross
+derivative of s this ask me to take the
+
+ align:start position:0%
+derivative of s this ask me to take the
+ 
+
+ align:start position:0%
+derivative of s this ask me to take the
+Y derivative so I get the cross
+
+ align:start position:0%
+Y derivative so I get the cross
+ 
+
+ align:start position:0%
+Y derivative so I get the cross
+derivative again with the minus sign
+
+ align:start position:0%
+derivative again with the minus sign
+ 
+
+ align:start position:0%
+derivative again with the minus sign
+they add to zero I I just want to point
+
+ align:start position:0%
+they add to zero I I just want to point
+ 
+
+ align:start position:0%
+they add to zero I I just want to point
+out that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also s satisfies Theos equation can can
+
+ align:start position:0%
+also s satisfies Theos equation can can
+ 
+
+ align:start position:0%
+also s satisfies Theos equation can can
+we do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one I I claim that also the stream
+
+ align:start position:0%
+one I I claim that also the stream
+ 
+
+ align:start position:0%
+one I I claim that also the stream
+function solves L plastus equation
+
+ align:start position:0%
+function solves L plastus equation
+ 
+
+ align:start position:0%
+function solves L plastus equation
+because we want the X derivative of dsdx
+
+ align:start position:0%
+because we want the X derivative of dsdx
+ 
+
+ align:start position:0%
+because we want the X derivative of dsdx
+so DS DX is minus this do you see what's
+
+ align:start position:0%
+so DS DX is minus this do you see what's
+ 
+
+ align:start position:0%
+so DS DX is minus this do you see what's
+happening when I take the X derivative
+
+ align:start position:0%
+happening when I take the X derivative
+ 
+
+ align:start position:0%
+happening when I take the X derivative
+of DS DX I get minus the cross
+
+ align:start position:0%
+of DS DX I get minus the cross
+ 
+
+ align:start position:0%
+of DS DX I get minus the cross
+derivative of
+
+ align:start position:0%
+derivative of
+ 
+
+ align:start position:0%
+derivative of
+U for the this guy it's the Y derivative
+
+ align:start position:0%
+U for the this guy it's the Y derivative
+ 
+
+ align:start position:0%
+U for the this guy it's the Y derivative
+of this which is plus the cross
+
+ align:start position:0%
+of this which is plus the cross
+ 
+
+ align:start position:0%
+of this which is plus the cross
+derivative of U they cancel so yeah U
+
+ align:start position:0%
+derivative of U they cancel so yeah U
+ 
+
+ align:start position:0%
+derivative of U they cancel so yeah U
+and S are just together oh Let's find
+
+ align:start position:0%
+and S are just together oh Let's find
+ 
+
+ align:start position:0%
+and S are just together oh Let's find
+let's let's find some solutions they're
+
+ align:start position:0%
+let's let's find some solutions they're
+ 
+
+ align:start position:0%
+let's let's find some solutions they're
+they're great to find yeah and then draw
+
+ align:start position:0%
+they're great to find yeah and then draw
+ 
+
+ align:start position:0%
+they're great to find yeah and then draw
+them okay can I find some solutions to L
+
+ align:start position:0%
+them okay can I find some solutions to L
+ 
+
+ align:start position:0%
+them okay can I find some solutions to L
+pla's equation uh and I'm going to find
+
+ align:start position:0%
+pla's equation uh and I'm going to find
+ 
+
+ align:start position:0%
+pla's equation uh and I'm going to find
+them in pairs so I'm going to have a
+
+ align:start position:0%
+them in pairs so I'm going to have a
+ 
+
+ align:start position:0%
+them in pairs so I'm going to have a
+list of
+
+ align:start position:0%
+list of
+ 
+
+ align:start position:0%
+list of
+U's and their corresponding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s's
+
+ align:start position:0%
+s's
+ 
+
+ align:start position:0%
+s's
+okay that's these are solutions to lass
+
+ align:start position:0%
+okay that's these are solutions to lass
+ 
+
+ align:start position:0%
+okay that's these are solutions to lass
+these are solve lasses equation so we've
+
+ align:start position:0%
+these are solve lasses equation so we've
+ 
+
+ align:start position:0%
+these are solve lasses equation so we've
+got lass's equation in our minds
+
+ align:start position:0%
+got lass's equation in our minds
+ 
+
+ align:start position:0%
+got lass's equation in our minds
+actually they they furthermore they
+
+ align:start position:0%
+actually they they furthermore they
+ 
+
+ align:start position:0%
+actually they they furthermore they
+solve remon because they're going to be
+
+ align:start position:0%
+solve remon because they're going to be
+ 
+
+ align:start position:0%
+solve remon because they're going to be
+connected by our Koshi remon equations
+
+ align:start position:0%
+connected by our Koshi remon equations
+ 
+
+ align:start position:0%
+connected by our Koshi remon equations
+so so solve LL and Koshi
+
+ align:start position:0%
+so so solve LL and Koshi
+ 
+
+ align:start position:0%
+so so solve LL and Koshi
+Rema okay suppose I take U of x yal
+
+ align:start position:0%
+Rema okay suppose I take U of x yal
+ 
+
+ align:start position:0%
+Rema okay suppose I take U of x yal
+x i I'm going to start with an easy
+
+ align:start position:0%
+x i I'm going to start with an easy
+ 
+
+ align:start position:0%
+x i I'm going to start with an easy
+solution you that certainly solves Lassa
+
+ align:start position:0%
+solution you that certainly solves Lassa
+ 
+
+ align:start position:0%
+solution you that certainly solves Lassa
+equation you got Lassa equation in mind
+
+ align:start position:0%
+equation you got Lassa equation in mind
+ 
+
+ align:start position:0%
+equation you got Lassa equation in mind
+let me let me write it up here again uxx
+
+ align:start position:0%
+let me let me write it up here again uxx
+ 
+
+ align:start position:0%
+let me let me write it up here again uxx
+plus u y yal z
+
+ align:start position:0%
+plus u y yal z
+ 
+
+ align:start position:0%
+plus u y yal z
+I I take the chance to write it again to
+
+ align:start position:0%
+I I take the chance to write it again to
+ 
+
+ align:start position:0%
+I I take the chance to write it again to
+use to do it in this little bit shorter
+
+ align:start position:0%
+use to do it in this little bit shorter
+ 
+
+ align:start position:0%
+use to do it in this little bit shorter
+notation just subscripts instead of
+
+ align:start position:0%
+notation just subscripts instead of
+ 
+
+ align:start position:0%
+notation just subscripts instead of
+partials and also s XX plus s y yal z
+
+ align:start position:0%
+partials and also s XX plus s y yal z
+ 
+
+ align:start position:0%
+partials and also s XX plus s y yal z
+but most of
+
+ align:start position:0%
+but most of
+ 
+
+ align:start position:0%
+but most of
+all the the koshian that connects the
+
+ align:start position:0%
+all the the koshian that connects the
+ 
+
+ align:start position:0%
+all the the koshian that connects the
+two well does you equal x solve thees
+
+ align:start position:0%
+two well does you equal x solve thees
+ 
+
+ align:start position:0%
+two well does you equal x solve thees
+equation of course it does the second X
+
+ align:start position:0%
+equation of course it does the second X
+ 
+
+ align:start position:0%
+equation of course it does the second X
+derivative if the function is X is zero
+
+ align:start position:0%
+derivative if the function is X is zero
+ 
+
+ align:start position:0%
+derivative if the function is X is zero
+and the second y derivative is very very
+
+ align:start position:0%
+and the second y derivative is very very
+ 
+
+ align:start position:0%
+and the second y derivative is very very
+zero okay so what's s what's the s that
+
+ align:start position:0%
+zero okay so what's s what's the s that
+ 
+
+ align:start position:0%
+zero okay so what's s what's the s that
+goes with it it'll be simple too it's
+
+ align:start position:0%
+goes with it it'll be simple too it's
+ 
+
+ align:start position:0%
+goes with it it'll be simple too it's
+supposed to so the S so U is X right I'm
+
+ align:start position:0%
+supposed to so the S so U is X right I'm
+ 
+
+ align:start position:0%
+supposed to so the S so U is X right I'm
+taking starting with this x well so du
+
+ align:start position:0%
+taking starting with this x well so du
+ 
+
+ align:start position:0%
+taking starting with this x well so du
+DX is one so what do you figure s
+
+ align:start position:0%
+DX is one so what do you figure s
+ 
+
+ align:start position:0%
+DX is one so what do you figure s
+is if if if du DX see U is just X itself
+
+ align:start position:0%
+is if if if du DX see U is just X itself
+ 
+
+ align:start position:0%
+is if if if du DX see U is just X itself
+so DX is only a one that derivative was
+
+ align:start position:0%
+so DX is only a one that derivative was
+ 
+
+ align:start position:0%
+so DX is only a one that derivative was
+easy what's then DS Dy is supposed to be
+
+ align:start position:0%
+easy what's then DS Dy is supposed to be
+ 
+
+ align:start position:0%
+easy what's then DS Dy is supposed to be
+one and d s DX is supposed to be zero I
+
+ align:start position:0%
+one and d s DX is supposed to be zero I
+ 
+
+ align:start position:0%
+one and d s DX is supposed to be zero I
+guess do you see what s
+
+ align:start position:0%
+guess do you see what s
+ 
+
+ align:start position:0%
+guess do you see what s
+is y s is y s is y of course that solves
+
+ align:start position:0%
+is y s is y s is y of course that solves
+ 
+
+ align:start position:0%
+is y s is y s is y of course that solves
+lus equation to and it solves Koshi Rema
+
+ align:start position:0%
+lus equation to and it solves Koshi Rema
+ 
+
+ align:start position:0%
+lus equation to and it solves Koshi Rema
+and the X derivative of this is the Y
+
+ align:start position:0%
+and the X derivative of this is the Y
+ 
+
+ align:start position:0%
+and the X derivative of this is the Y
+derivative of that 1 equal 1 and the Y
+
+ align:start position:0%
+derivative of that 1 equal 1 and the Y
+ 
+
+ align:start position:0%
+derivative of that 1 equal 1 and the Y
+derivative of that is minus the X
+
+ align:start position:0%
+derivative of that is minus the X
+ 
+
+ align:start position:0%
+derivative of that is minus the X
+derivative of that 0 equals 0 okay so
+
+ align:start position:0%
+derivative of that 0 equals 0 okay so
+ 
+
+ align:start position:0%
+derivative of that 0 equals 0 okay so
+that's an easy one let me I'm going to
+
+ align:start position:0%
+that's an easy one let me I'm going to
+ 
+
+ align:start position:0%
+that's an easy one let me I'm going to
+go up a level I want to take a second
+
+ align:start position:0%
+go up a level I want to take a second
+ 
+
+ align:start position:0%
+go up a level I want to take a second
+degree so my next guy in the list will
+
+ align:start position:0%
+degree so my next guy in the list will
+ 
+
+ align:start position:0%
+degree so my next guy in the list will
+be a pair it's a list of pairs will be
+
+ align:start position:0%
+be a pair it's a list of pairs will be
+ 
+
+ align:start position:0%
+be a pair it's a list of pairs will be
+x^2 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y^2 first of all it better not be on
+
+ align:start position:0%
+y^2 first of all it better not be on
+ 
+
+ align:start position:0%
+y^2 first of all it better not be on
+that list unless it solves Theo's
+
+ align:start position:0%
+that list unless it solves Theo's
+ 
+
+ align:start position:0%
+that list unless it solves Theo's
+equation and then if it is we'll find an
+
+ align:start position:0%
+equation and then if it is we'll find an
+ 
+
+ align:start position:0%
+equation and then if it is we'll find an
+S so what's the plug it in mentally can
+
+ align:start position:0%
+S so what's the plug it in mentally can
+ 
+
+ align:start position:0%
+S so what's the plug it in mentally can
+you plug this into the plaza equation
+
+ align:start position:0%
+you plug this into the plaza equation
+ 
+
+ align:start position:0%
+you plug this into the plaza equation
+what's the second X derivative of this
+
+ align:start position:0%
+what's the second X derivative of this
+ 
+
+ align:start position:0%
+what's the second X derivative of this
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+two right x x brings down a two what's
+
+ align:start position:0%
+two right x x brings down a two what's
+ 
+
+ align:start position:0%
+two right x x brings down a two what's
+the second y
+
+ align:start position:0%
+the second y
+ 
+
+ align:start position:0%
+the second y
+derivative the minus two from this term
+
+ align:start position:0%
+derivative the minus two from this term
+ 
+
+ align:start position:0%
+derivative the minus two from this term
+and then put them into the pluses
+
+ align:start position:0%
+and then put them into the pluses
+ 
+
+ align:start position:0%
+and then put them into the pluses
+equation 2 minus 2 correct zero all
+
+ align:start position:0%
+equation 2 minus 2 correct zero all
+ 
+
+ align:start position:0%
+equation 2 minus 2 correct zero all
+right now I'm looking for the s that
+
+ align:start position:0%
+right now I'm looking for the s that
+ 
+
+ align:start position:0%
+right now I'm looking for the s that
+goes with it the other one in the pair
+
+ align:start position:0%
+goes with it the other one in the pair
+ 
+
+ align:start position:0%
+goes with it the other one in the pair
+okay so what what maybe I better think
+
+ align:start position:0%
+okay so what what maybe I better think
+ 
+
+ align:start position:0%
+okay so what what maybe I better think
+through what so this is supposed to give
+
+ align:start position:0%
+through what so this is supposed to give
+ 
+
+ align:start position:0%
+through what so this is supposed to give
+me the S du DX so so let me I'm copying
+
+ align:start position:0%
+me the S du DX so so let me I'm copying
+ 
+
+ align:start position:0%
+me the S du DX so so let me I'm copying
+the let me
+
+ align:start position:0%
+the let me
+ 
+
+ align:start position:0%
+the let me
+copy Koshi Rema here so we can just
+
+ align:start position:0%
+copy Koshi Rema here so we can just
+ 
+
+ align:start position:0%
+copy Koshi Rema here so we can just
+focus entirely on that board so Dux this
+
+ align:start position:0%
+focus entirely on that board so Dux this
+ 
+
+ align:start position:0%
+focus entirely on that board so Dux this
+is 2x in my
+
+ align:start position:0%
+is 2x in my
+ 
+
+ align:start position:0%
+is 2x in my
+example du Dy is minus
+
+ align:start position:0%
+example du Dy is minus
+ 
+
+ align:start position:0%
+example du Dy is minus
+2y so what am I learning DS Dy should be
+
+ align:start position:0%
+2y so what am I learning DS Dy should be
+ 
+
+ align:start position:0%
+2y so what am I learning DS Dy should be
+2 X DS DX should be 2 y because I have
+
+ align:start position:0%
+2 X DS DX should be 2 y because I have
+ 
+
+ align:start position:0%
+2 X DS DX should be 2 y because I have
+minus signs both there what's s do you
+
+ align:start position:0%
+minus signs both there what's s do you
+ 
+
+ align:start position:0%
+minus signs both there what's s do you
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+s the the Y derivative is 2x the X
+
+ align:start position:0%
+s the the Y derivative is 2x the X
+ 
+
+ align:start position:0%
+s the the Y derivative is 2x the X
+derivative is 2 Y and that stream
+
+ align:start position:0%
+derivative is 2 Y and that stream
+ 
+
+ align:start position:0%
+derivative is 2 Y and that stream
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+2 X Y right
+
+ align:start position:0%
+2 X Y right
+ 
+
+ align:start position:0%
+2 X Y right
+2xy because the X derivative of this is
+
+ align:start position:0%
+2xy because the X derivative of this is
+ 
+
+ align:start position:0%
+2xy because the X derivative of this is
+2 y and the Y derivative of this is 2X
+
+ align:start position:0%
+2 y and the Y derivative of this is 2X
+ 
+
+ align:start position:0%
+2 y and the Y derivative of this is 2X
+and we've saw we saw 2x y last time also
+
+ align:start position:0%
+and we've saw we saw 2x y last time also
+ 
+
+ align:start position:0%
+and we've saw we saw 2x y last time also
+and of course it solves the pl's
+
+ align:start position:0%
+and of course it solves the pl's
+ 
+
+ align:start position:0%
+and of course it solves the pl's
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+easily plug that in the second
+
+ align:start position:0%
+easily plug that in the second
+ 
+
+ align:start position:0%
+easily plug that in the second
+derivative is zero the second X
+
+ align:start position:0%
+derivative is zero the second X
+ 
+
+ align:start position:0%
+derivative is zero the second X
+derivative is zero like y derivative is
+
+ align:start position:0%
+derivative is zero like y derivative is
+ 
+
+ align:start position:0%
+derivative is zero like y derivative is
+zero everything so that's a
+
+ align:start position:0%
+zero everything so that's a
+ 
+
+ align:start position:0%
+zero everything so that's a
+pair this is this is a nice
+
+ align:start position:0%
+pair this is this is a nice
+ 
+
+ align:start position:0%
+pair this is this is a nice
+pair uh do you want to shoot for third
+
+ align:start position:0%
+pair uh do you want to shoot for third
+ 
+
+ align:start position:0%
+pair uh do you want to shoot for third
+degree
+
+ align:start position:0%
+degree
+ 
+
+ align:start position:0%
+degree
+we could maybe figure out third degree
+
+ align:start position:0%
+we could maybe figure out third degree
+ 
+
+ align:start position:0%
+we could maybe figure out third degree
+just by jiggling it after that we're
+
+ align:start position:0%
+just by jiggling it after that we're
+ 
+
+ align:start position:0%
+just by jiggling it after that we're
+going to need an idea yeah to get up to
+
+ align:start position:0%
+going to need an idea yeah to get up to
+ 
+
+ align:start position:0%
+going to need an idea yeah to get up to
+fourth degree let me let me try third
+
+ align:start position:0%
+fourth degree let me let me try third
+ 
+
+ align:start position:0%
+fourth degree let me let me try third
+degree cubics now so I'm looking first I
+
+ align:start position:0%
+degree cubics now so I'm looking first I
+ 
+
+ align:start position:0%
+degree cubics now so I'm looking first I
+just want to get somebody here so it's
+
+ align:start position:0%
+just want to get somebody here so it's
+ 
+
+ align:start position:0%
+just want to get somebody here so it's
+some X
+
+ align:start position:0%
+some X
+ 
+
+ align:start position:0%
+some X
+cub and then I'm going to need some more
+
+ align:start position:0%
+cub and then I'm going to need some more
+ 
+
+ align:start position:0%
+cub and then I'm going to need some more
+stuff because X Cub by itself certainly
+
+ align:start position:0%
+stuff because X Cub by itself certainly
+ 
+
+ align:start position:0%
+stuff because X Cub by itself certainly
+won't
+
+ align:start position:0%
+won't
+ 
+
+ align:start position:0%
+won't
+work I'm I need something more and I
+
+ align:start position:0%
+work I'm I need something more and I
+ 
+
+ align:start position:0%
+work I'm I need something more and I
+want to plug it into lasses equation and
+
+ align:start position:0%
+want to plug it into lasses equation and
+ 
+
+ align:start position:0%
+want to plug it into lasses equation and
+figure out what should I what should it
+
+ align:start position:0%
+figure out what should I what should it
+ 
+
+ align:start position:0%
+figure out what should I what should it
+be okay so what when I plug this into
+
+ align:start position:0%
+be okay so what when I plug this into
+ 
+
+ align:start position:0%
+be okay so what when I plug this into
+lasses equation what do I get so let me
+
+ align:start position:0%
+lasses equation what do I get so let me
+ 
+
+ align:start position:0%
+lasses equation what do I get so let me
+here let me do ll's equation over here
+
+ align:start position:0%
+here let me do ll's equation over here
+ 
+
+ align:start position:0%
+here let me do ll's equation over here
+for the for the to try to get the U of
+
+ align:start position:0%
+for the for the to try to get the U of
+ 
+
+ align:start position:0%
+for the for the to try to get the U of
+degree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 so what's uxx so
+
+ align:start position:0%
+3 so what's uxx so
+ 
+
+ align:start position:0%
+3 so what's uxx so
+far 6X right bring down a we get 3x SAR
+
+ align:start position:0%
+far 6X right bring down a we get 3x SAR
+ 
+
+ align:start position:0%
+far 6X right bring down a we get 3x SAR
+then we get 6X so I've got a
+
+ align:start position:0%
+then we get 6X so I've got a
+ 
+
+ align:start position:0%
+then we get 6X so I've got a
+6X and I'm looking for so u y y should
+
+ align:start position:0%
+6X and I'm looking for so u y y should
+ 
+
+ align:start position:0%
+6X and I'm looking for so u y y should
+be minus 6X to cancel that so what do I
+
+ align:start position:0%
+be minus 6X to cancel that so what do I
+ 
+
+ align:start position:0%
+be minus 6X to cancel that so what do I
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+there what do I need I need a minus I'm
+
+ align:start position:0%
+there what do I need I need a minus I'm
+ 
+
+ align:start position:0%
+there what do I need I need a minus I'm
+sure of that uh so the second y
+
+ align:start position:0%
+sure of that uh so the second y
+ 
+
+ align:start position:0%
+sure of that uh so the second y
+derivative should be this 6X deel what
+
+ align:start position:0%
+derivative should be this 6X deel what
+ 
+
+ align:start position:0%
+derivative should be this 6X deel what
+do I want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3x y^2 that sounds good let me write it
+
+ align:start position:0%
+3x y^2 that sounds good let me write it
+ 
+
+ align:start position:0%
+3x y^2 that sounds good let me write it
+down and see if it is good okay the
+
+ align:start position:0%
+down and see if it is good okay the
+ 
+
+ align:start position:0%
+down and see if it is good okay the
+second y derivative yes we'll bring down
+
+ align:start position:0%
+second y derivative yes we'll bring down
+ 
+
+ align:start position:0%
+second y derivative yes we'll bring down
+a two and then the then the Y's will
+
+ align:start position:0%
+a two and then the then the Y's will
+ 
+
+ align:start position:0%
+a two and then the then the Y's will
+disappear and I'll have the minus 6X
+
+ align:start position:0%
+disappear and I'll have the minus 6X
+ 
+
+ align:start position:0%
+disappear and I'll have the minus 6X
+golden okay that's great that's
+
+ align:start position:0%
+golden okay that's great that's
+ 
+
+ align:start position:0%
+golden okay that's great that's
+great is that correct I mean it's great
+
+ align:start position:0%
+great is that correct I mean it's great
+ 
+
+ align:start position:0%
+great is that correct I mean it's great
+but is it right yes yes okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you have faith that there's another
+
+ align:start position:0%
+now you have faith that there's another
+ 
+
+ align:start position:0%
+now you have faith that there's another
+one well yeah there is another one I
+
+ align:start position:0%
+one well yeah there is another one I
+ 
+
+ align:start position:0%
+one well yeah there is another one I
+mean right there's Koshi Rema never let
+
+ align:start position:0%
+mean right there's Koshi Rema never let
+ 
+
+ align:start position:0%
+mean right there's Koshi Rema never let
+us down there's a there will be a s
+
+ align:start position:0%
+us down there's a there will be a s
+ 
+
+ align:start position:0%
+us down there's a there will be a s
+that'll go with that that'll solve the
+
+ align:start position:0%
+that'll go with that that'll solve the
+ 
+
+ align:start position:0%
+that'll go with that that'll solve the
+Koshi reman equations and it'll look
+
+ align:start position:0%
+Koshi reman equations and it'll look
+ 
+
+ align:start position:0%
+Koshi reman equations and it'll look
+like it and I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think I think and and sort of I just
+
+ align:start position:0%
+think I think and and sort of I just
+ 
+
+ align:start position:0%
+think I think and and sort of I just
+sort of reverse X and Y to get another
+
+ align:start position:0%
+sort of reverse X and Y to get another
+ 
+
+ align:start position:0%
+sort of reverse X and Y to get another
+one because if I exchange X and Y I'm
+
+ align:start position:0%
+one because if I exchange X and Y I'm
+ 
+
+ align:start position:0%
+one because if I exchange X and Y I'm
+still okay with lass's equation I think
+
+ align:start position:0%
+still okay with lass's equation I think
+ 
+
+ align:start position:0%
+still okay with lass's equation I think
+I I think something like 3 y x^2 - y
+
+ align:start position:0%
+I I think something like 3 y x^2 - y
+ 
+
+ align:start position:0%
+I I think something like 3 y x^2 - y
+cubed you know if that worked then this
+
+ align:start position:0%
+cubed you know if that worked then this
+ 
+
+ align:start position:0%
+cubed you know if that worked then this
+one should work
+
+ align:start position:0%
+one should work
+ 
+
+ align:start position:0%
+one should work
+too because I've just switched X and Y
+
+ align:start position:0%
+too because I've just switched X and Y
+ 
+
+ align:start position:0%
+too because I've just switched X and Y
+and uh I think it it'll work right here
+
+ align:start position:0%
+and uh I think it it'll work right here
+ 
+
+ align:start position:0%
+and uh I think it it'll work right here
+the second X derivative will be 6 Y and
+
+ align:start position:0%
+the second X derivative will be 6 Y and
+ 
+
+ align:start position:0%
+the second X derivative will be 6 Y and
+the second y derivative will be minus 6
+
+ align:start position:0%
+the second y derivative will be minus 6
+ 
+
+ align:start position:0%
+the second y derivative will be minus 6
+Y and that's I think that's good okay so
+
+ align:start position:0%
+Y and that's I think that's good okay so
+ 
+
+ align:start position:0%
+Y and that's I think that's good okay so
+we so we've got
+
+ align:start position:0%
+we so we've got
+ 
+
+ align:start position:0%
+we so we've got
+let's put this list on hold for a moment
+
+ align:start position:0%
+let's put this list on hold for a moment
+ 
+
+ align:start position:0%
+let's put this list on hold for a moment
+something's obviously there's some
+
+ align:start position:0%
+something's obviously there's some
+ 
+
+ align:start position:0%
+something's obviously there's some
+pattern here that we've got to
+
+ align:start position:0%
+pattern here that we've got to
+ 
+
+ align:start position:0%
+pattern here that we've got to
+locate can I put it on hold for a moment
+
+ align:start position:0%
+locate can I put it on hold for a moment
+ 
+
+ align:start position:0%
+locate can I put it on hold for a moment
+and take for example the graph of this
+
+ align:start position:0%
+and take for example the graph of this
+ 
+
+ align:start position:0%
+and take for example the graph of this
+one and I want to draw the pictures
+
+ align:start position:0%
+one and I want to draw the pictures
+ 
+
+ align:start position:0%
+one and I want to draw the pictures
+before I
+
+ align:start position:0%
+before I
+ 
+
+ align:start position:0%
+before I
+get a complete list I want to draw the
+
+ align:start position:0%
+get a complete list I want to draw the
+ 
+
+ align:start position:0%
+get a complete list I want to draw the
+pictures of these functions and what do
+
+ align:start position:0%
+pictures of these functions and what do
+ 
+
+ align:start position:0%
+pictures of these functions and what do
+I mean by pictures I mean uh draw the so
+
+ align:start position:0%
+I mean by pictures I mean uh draw the so
+ 
+
+ align:start position:0%
+I mean by pictures I mean uh draw the so
+now I'm taking the U to be x^2 - y^2 and
+
+ align:start position:0%
+now I'm taking the U to be x^2 - y^2 and
+ 
+
+ align:start position:0%
+now I'm taking the U to be x^2 - y^2 and
+the S to be
+
+ align:start position:0%
+the S to be
+ 
+
+ align:start position:0%
+the S to be
+2xy and I want to draw the those I want
+
+ align:start position:0%
+2xy and I want to draw the those I want
+ 
+
+ align:start position:0%
+2xy and I want to draw the those I want
+to draw the vector field of the
+
+ align:start position:0%
+to draw the vector field of the
+ 
+
+ align:start position:0%
+to draw the vector field of the
+gradients of those guys okay so this is
+
+ align:start position:0%
+gradients of those guys okay so this is
+ 
+
+ align:start position:0%
+gradients of those guys okay so this is
+the U I want to draw the equ this is the
+
+ align:start position:0%
+the U I want to draw the equ this is the
+ 
+
+ align:start position:0%
+the U I want to draw the equ this is the
+potential x^2 minus y^2 so what are the
+
+ align:start position:0%
+potential x^2 minus y^2 so what are the
+ 
+
+ align:start position:0%
+potential x^2 minus y^2 so what are the
+equip potential curves so this is now
+
+ align:start position:0%
+equip potential curves so this is now
+ 
+
+ align:start position:0%
+equip potential curves so this is now
+I'm drawing the flow and to draw the
+
+ align:start position:0%
+I'm drawing the flow and to draw the
+ 
+
+ align:start position:0%
+I'm drawing the flow and to draw the
+flow I draw the curves on which the
+
+ align:start position:0%
+flow I draw the curves on which the
+ 
+
+ align:start position:0%
+flow I draw the curves on which the
+potential is a
+
+ align:start position:0%
+potential is a
+ 
+
+ align:start position:0%
+potential is a
+constant x^2 - y^2 equal constant so
+
+ align:start position:0%
+constant x^2 - y^2 equal constant so
+ 
+
+ align:start position:0%
+constant x^2 - y^2 equal constant so
+what kind of a curve is x^2 - y^2 equal
+
+ align:start position:0%
+what kind of a curve is x^2 - y^2 equal
+ 
+
+ align:start position:0%
+what kind of a curve is x^2 - y^2 equal
+constant it's a hyperbola it's a
+
+ align:start position:0%
+constant it's a hyperbola it's a
+ 
+
+ align:start position:0%
+constant it's a hyperbola it's a
+hyperbola so let me put in so x^2 - y^2
+
+ align:start position:0%
+hyperbola so let me put in so x^2 - y^2
+ 
+
+ align:start position:0%
+hyperbola so let me put in so x^2 - y^2
+equal Let's Take One For example what
+
+ align:start position:0%
+equal Let's Take One For example what
+ 
+
+ align:start position:0%
+equal Let's Take One For example what
+what as as one constant so so x = 1 will
+
+ align:start position:0%
+what as as one constant so so x = 1 will
+ 
+
+ align:start position:0%
+what as as one constant so so x = 1 will
+be on the curve when Y is zero and then
+
+ align:start position:0%
+be on the curve when Y is zero and then
+ 
+
+ align:start position:0%
+be on the curve when Y is zero and then
+what else will be on the curve if x is a
+
+ align:start position:0%
+what else will be on the curve if x is a
+ 
+
+ align:start position:0%
+what else will be on the curve if x is a
+little bigger like two yeah what what's
+
+ align:start position:0%
+little bigger like two yeah what what's
+ 
+
+ align:start position:0%
+little bigger like two yeah what what's
+see if suppose so so here is one Zer
+
+ align:start position:0%
+see if suppose so so here is one Zer
+ 
+
+ align:start position:0%
+see if suppose so so here is one Zer
+that point
+
+ align:start position:0%
+that point
+ 
+
+ align:start position:0%
+that point
+is certainly x^2 - y^2 is one for that
+
+ align:start position:0%
+is certainly x^2 - y^2 is one for that
+ 
+
+ align:start position:0%
+is certainly x^2 - y^2 is one for that
+suppose I go out to xal 2 What should y
+
+ align:start position:0%
+suppose I go out to xal 2 What should y
+ 
+
+ align:start position:0%
+suppose I go out to xal 2 What should y
+be then to make this right to where
+
+ align:start position:0%
+be then to make this right to where
+ 
+
+ align:start position:0%
+be then to make this right to where
+where's the curve going when X is two
+
+ align:start position:0%
+where's the curve going when X is two
+ 
+
+ align:start position:0%
+where's the curve going when X is two
+what what is
+
+ align:start position:0%
+what what is
+ 
+
+ align:start position:0%
+what what is
+y squ < TK of 3 up plus plus or minus so
+
+ align:start position:0%
+y squ < TK of 3 up plus plus or minus so
+ 
+
+ align:start position:0%
+y squ < TK of 3 up plus plus or minus so
+< TK 3 is something like this up or down
+
+ align:start position:0%
+< TK 3 is something like this up or down
+ 
+
+ align:start position:0%
+< TK 3 is something like this up or down
+it's a it's a
+
+ align:start position:0%
+it's a it's a
+ 
+
+ align:start position:0%
+it's a it's a
+curve like
+
+ align:start position:0%
+curve like
+ 
+
+ align:start position:0%
+curve like
+so it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hyperbola that's that's and now if I
+
+ align:start position:0%
+hyperbola that's that's and now if I
+ 
+
+ align:start position:0%
+hyperbola that's that's and now if I
+change one change change C to four let's
+
+ align:start position:0%
+change one change change C to four let's
+ 
+
+ align:start position:0%
+change one change change C to four let's
+say then it'll go through two Z and
+
+ align:start position:0%
+say then it'll go through two Z and
+ 
+
+ align:start position:0%
+say then it'll go through two Z and
+it'll go up this
+
+ align:start position:0%
+it'll go up this
+ 
+
+ align:start position:0%
+it'll go up this
+way and if I change X to something very
+
+ align:start position:0%
+way and if I change X to something very
+ 
+
+ align:start position:0%
+way and if I change X to something very
+small uh it'll still oh do you know what
+
+ align:start position:0%
+small uh it'll still oh do you know what
+ 
+
+ align:start position:0%
+small uh it'll still oh do you know what
+the there's a
+
+ align:start position:0%
+the there's a
+ 
+
+ align:start position:0%
+the there's a
+word a Greek word ASM tootes oh yeah
+
+ align:start position:0%
+word a Greek word ASM tootes oh yeah
+ 
+
+ align:start position:0%
+word a Greek word ASM tootes oh yeah
+what do I get if the ASM toote is when
+
+ align:start position:0%
+what do I get if the ASM toote is when
+ 
+
+ align:start position:0%
+what do I get if the ASM toote is when
+this is zero yeah when when that is zero
+
+ align:start position:0%
+this is zero yeah when when that is zero
+ 
+
+ align:start position:0%
+this is zero yeah when when that is zero
+what's what's my curve what what what
+
+ align:start position:0%
+what's what's my curve what what what
+ 
+
+ align:start position:0%
+what's what's my curve what what what
+are X and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y they'll be the same X will be y or
+
+ align:start position:0%
+Y they'll be the same X will be y or
+ 
+
+ align:start position:0%
+Y they'll be the same X will be y or
+minus y I'll be on that straight line or
+
+ align:start position:0%
+minus y I'll be on that straight line or
+ 
+
+ align:start position:0%
+minus y I'll be on that straight line or
+on this straight line so all the other
+
+ align:start position:0%
+on this straight line so all the other
+ 
+
+ align:start position:0%
+on this straight line so all the other
+all these other hyperbolas are kind of
+
+ align:start position:0%
+all these other hyperbolas are kind of
+ 
+
+ align:start position:0%
+all these other hyperbolas are kind of
+asymptotic whatever the word is uh right
+
+ align:start position:0%
+asymptotic whatever the word is uh right
+ 
+
+ align:start position:0%
+asymptotic whatever the word is uh right
+you see them as a bunch of
+
+ align:start position:0%
+you see them as a bunch of
+ 
+
+ align:start position:0%
+you see them as a bunch of
+hyperbolas uh and
+
+ align:start position:0%
+hyperbolas uh and
+ 
+
+ align:start position:0%
+hyperbolas uh and
+actually more
+
+ align:start position:0%
+actually more
+ 
+
+ align:start position:0%
+actually more
+hyperbolas well yeah
+
+ align:start position:0%
+hyperbolas well yeah
+ 
+
+ align:start position:0%
+hyperbolas well yeah
+think let's see when back when I had a
+
+ align:start position:0%
+think let's see when back when I had a
+ 
+
+ align:start position:0%
+think let's see when back when I had a
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+there I took X and Y to be positive and
+
+ align:start position:0%
+there I took X and Y to be positive and
+ 
+
+ align:start position:0%
+there I took X and Y to be positive and
+I got that
+
+ align:start position:0%
+I got that
+ 
+
+ align:start position:0%
+I got that
+hyperbola but I could have since I'm
+
+ align:start position:0%
+hyperbola but I could have since I'm
+ 
+
+ align:start position:0%
+hyperbola but I could have since I'm
+squaring them there also these
+
+ align:start position:0%
+squaring them there also these
+ 
+
+ align:start position:0%
+squaring them there also these
+hyperbolas are
+
+ align:start position:0%
+hyperbolas are
+ 
+
+ align:start position:0%
+hyperbolas are
+here so the these same guys are are uh
+
+ align:start position:0%
+here so the these same guys are are uh
+ 
+
+ align:start position:0%
+here so the these same guys are are uh
+on that side of the
+
+ align:start position:0%
+on that side of the
+ 
+
+ align:start position:0%
+on that side of the
+picture those are the equip potentials
+
+ align:start position:0%
+picture those are the equip potentials
+ 
+
+ align:start position:0%
+picture those are the equip potentials
+so these are the equip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potentials
+
+ align:start position:0%
+potentials
+ 
+
+ align:start position:0%
+potentials
+okay now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me draw
+
+ align:start position:0%
+let me draw
+ 
+
+ align:start position:0%
+let me draw
+s so those will be the
+
+ align:start position:0%
+s so those will be the
+ 
+
+ align:start position:0%
+s so those will be the
+equ no I don't want to say equist stream
+
+ align:start position:0%
+equ no I don't want to say equist stream
+ 
+
+ align:start position:0%
+equ no I don't want to say equist stream
+functions that's
+
+ align:start position:0%
+functions that's
+ 
+
+ align:start position:0%
+functions that's
+awkward so now I want to draw s equal
+
+ align:start position:0%
+awkward so now I want to draw s equal
+ 
+
+ align:start position:0%
+awkward so now I want to draw s equal
+constant like one or
+
+ align:start position:0%
+constant like one or
+ 
+
+ align:start position:0%
+constant like one or
+whatever so this was this was I've drawn
+
+ align:start position:0%
+whatever so this was this was I've drawn
+ 
+
+ align:start position:0%
+whatever so this was this was I've drawn
+this with a whole lot of constants and
+
+ align:start position:0%
+this with a whole lot of constants and
+ 
+
+ align:start position:0%
+this with a whole lot of constants and
+now I want to draw the other guys what
+
+ align:start position:0%
+now I want to draw the other guys what
+ 
+
+ align:start position:0%
+now I want to draw the other guys what
+do those curves look
+
+ align:start position:0%
+do those curves look
+ 
+
+ align:start position:0%
+do those curves look
+like and what's their
+
+ align:start position:0%
+like and what's their
+ 
+
+ align:start position:0%
+like and what's their
+name a curve on which the stream
+
+ align:start position:0%
+name a curve on which the stream
+ 
+
+ align:start position:0%
+name a curve on which the stream
+function is a constant is has the nice
+
+ align:start position:0%
+function is a constant is has the nice
+ 
+
+ align:start position:0%
+function is a constant is has the nice
+name stream line so now I'm going to
+
+ align:start position:0%
+name stream line so now I'm going to
+ 
+
+ align:start position:0%
+name stream line so now I'm going to
+draw the
+
+ align:start position:0%
+draw the
+ 
+
+ align:start position:0%
+draw the
+streamlines and what are the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+streamlines the streamlines will be the
+
+ align:start position:0%
+streamlines the streamlines will be the
+ 
+
+ align:start position:0%
+streamlines the streamlines will be the
+curves that the actual material flows if
+
+ align:start position:0%
+curves that the actual material flows if
+ 
+
+ align:start position:0%
+curves that the actual material flows if
+you drop a leaf into this flow it will
+
+ align:start position:0%
+you drop a leaf into this flow it will
+ 
+
+ align:start position:0%
+you drop a leaf into this flow it will
+and you watch it it'll flow along a
+
+ align:start position:0%
+and you watch it it'll flow along a
+ 
+
+ align:start position:0%
+and you watch it it'll flow along a
+streamline and we can draw those lines
+
+ align:start position:0%
+streamline and we can draw those lines
+ 
+
+ align:start position:0%
+streamline and we can draw those lines
+so what are those uh 2x y = 1 or the
+
+ align:start position:0%
+so what are those uh 2x y = 1 or the
+ 
+
+ align:start position:0%
+so what are those uh 2x y = 1 or the
+equation Y = 1 over
+
+ align:start position:0%
+equation Y = 1 over
+ 
+
+ align:start position:0%
+equation Y = 1 over
+2x that's also a hyperbola right that's
+
+ align:start position:0%
+2x that's also a hyperbola right that's
+ 
+
+ align:start position:0%
+2x that's also a hyperbola right that's
+also a hyperbola this is a fantastic
+
+ align:start position:0%
+also a hyperbola this is a fantastic
+ 
+
+ align:start position:0%
+also a hyperbola this is a fantastic
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+um in which the we have two sets of
+
+ align:start position:0%
+um in which the we have two sets of
+ 
+
+ align:start position:0%
+um in which the we have two sets of
+hyperbolas it just we're second degree
+
+ align:start position:0%
+hyperbolas it just we're second degree
+ 
+
+ align:start position:0%
+hyperbolas it just we're second degree
+that's why we're getting two hyperbolas
+
+ align:start position:0%
+that's why we're getting two hyperbolas
+ 
+
+ align:start position:0%
+that's why we're getting two hyperbolas
+when I I'm not going to tackle drawing
+
+ align:start position:0%
+when I I'm not going to tackle drawing
+ 
+
+ align:start position:0%
+when I I'm not going to tackle drawing
+matl could do it draw the equip
+
+ align:start position:0%
+matl could do it draw the equip
+ 
+
+ align:start position:0%
+matl could do it draw the equip
+potentials and the streamlines for this
+
+ align:start position:0%
+potentials and the streamlines for this
+ 
+
+ align:start position:0%
+potentials and the streamlines for this
+guy oh let's I'm willing to tackle this
+
+ align:start position:0%
+guy oh let's I'm willing to tackle this
+ 
+
+ align:start position:0%
+guy oh let's I'm willing to tackle this
+one um what are the equip potentials and
+
+ align:start position:0%
+one um what are the equip potentials and
+ 
+
+ align:start position:0%
+one um what are the equip potentials and
+the streamlines for the for the easiest
+
+ align:start position:0%
+the streamlines for the for the easiest
+ 
+
+ align:start position:0%
+the streamlines for the for the easiest
+one in the list
+
+ align:start position:0%
+one in the list
+ 
+
+ align:start position:0%
+one in the list
+there can I just draw that one because
+
+ align:start position:0%
+there can I just draw that one because
+ 
+
+ align:start position:0%
+there can I just draw that one because
+it makes a point very clear that that
+
+ align:start position:0%
+it makes a point very clear that that
+ 
+
+ align:start position:0%
+it makes a point very clear that that
+we'll see when we draw these okay so
+
+ align:start position:0%
+we'll see when we draw these okay so
+ 
+
+ align:start position:0%
+we'll see when we draw these okay so
+what's
+
+ align:start position:0%
+what's
+ 
+
+ align:start position:0%
+what's
+the what's the picture the corresponding
+
+ align:start position:0%
+the what's the picture the corresponding
+ 
+
+ align:start position:0%
+the what's the picture the corresponding
+picture what here's the XY plane again
+
+ align:start position:0%
+picture what here's the XY plane again
+ 
+
+ align:start position:0%
+picture what here's the XY plane again
+what are the equip potentials for this
+
+ align:start position:0%
+what are the equip potentials for this
+ 
+
+ align:start position:0%
+what are the equip potentials for this
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+pair and the
+
+ align:start position:0%
+pair and the
+ 
+
+ align:start position:0%
+pair and the
+streamlines the equip potentials are x
+
+ align:start position:0%
+streamlines the equip potentials are x
+ 
+
+ align:start position:0%
+streamlines the equip potentials are x
+equal constant what are those those are
+
+ align:start position:0%
+equal constant what are those those are
+ 
+
+ align:start position:0%
+equal constant what are those those are
+lines vertical lines so the equip
+
+ align:start position:0%
+lines vertical lines so the equip
+ 
+
+ align:start position:0%
+lines vertical lines so the equip
+potentials are just vertical lines equ
+
+ align:start position:0%
+potentials are just vertical lines equ
+ 
+
+ align:start position:0%
+potentials are just vertical lines equ
+potentials x equal a
+
+ align:start position:0%
+potentials x equal a
+ 
+
+ align:start position:0%
+potentials x equal a
+constant and what are the
+
+ align:start position:0%
+constant and what are the
+ 
+
+ align:start position:0%
+constant and what are the
+streamlines horizontal lines streamlines
+
+ align:start position:0%
+streamlines horizontal lines streamlines
+ 
+
+ align:start position:0%
+streamlines horizontal lines streamlines
+go this way and what's the great point
+
+ align:start position:0%
+go this way and what's the great point
+ 
+
+ align:start position:0%
+go this way and what's the great point
+about these These are the streamlines s
+
+ align:start position:0%
+about these These are the streamlines s
+ 
+
+ align:start position:0%
+about these These are the streamlines s
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+constant and of course what do you
+
+ align:start position:0%
+constant and of course what do you
+ 
+
+ align:start position:0%
+constant and of course what do you
+notice
+
+ align:start position:0%
+notice
+ 
+
+ align:start position:0%
+notice
+here they're
+
+ align:start position:0%
+here they're
+ 
+
+ align:start position:0%
+here they're
+perpendicular the streamlines are
+
+ align:start position:0%
+perpendicular the streamlines are
+ 
+
+ align:start position:0%
+perpendicular the streamlines are
+perpendicular to the equip
+
+ align:start position:0%
+perpendicular to the equip
+ 
+
+ align:start position:0%
+perpendicular to the equip
+potentials and why it's because the you
+
+ align:start position:0%
+potentials and why it's because the you
+ 
+
+ align:start position:0%
+potentials and why it's because the you
+remember we talked about what does the D
+
+ align:start position:0%
+remember we talked about what does the D
+ 
+
+ align:start position:0%
+remember we talked about what does the D
+what does the gradient mean where which
+
+ align:start position:0%
+what does the gradient mean where which
+ 
+
+ align:start position:0%
+what does the gradient mean where which
+way does the gradient point it points
+
+ align:start position:0%
+way does the gradient point it points
+ 
+
+ align:start position:0%
+way does the gradient point it points
+perpendicular to these equip potentials
+
+ align:start position:0%
+perpendicular to these equip potentials
+ 
+
+ align:start position:0%
+perpendicular to these equip potentials
+and in this case there all these equip
+
+ align:start position:0%
+and in this case there all these equip
+ 
+
+ align:start position:0%
+and in this case there all these equip
+potentials are parallel and the perpend
+
+ align:start position:0%
+potentials are parallel and the perpend
+ 
+
+ align:start position:0%
+potentials are parallel and the perpend
+and the perpendicular lines are the
+
+ align:start position:0%
+and the perpendicular lines are the
+ 
+
+ align:start position:0%
+and the perpendicular lines are the
+stream lines and they're all
+
+ align:start position:0%
+stream lines and they're all
+ 
+
+ align:start position:0%
+stream lines and they're all
+parallel now over
+
+ align:start position:0%
+parallel now over
+ 
+
+ align:start position:0%
+parallel now over
+here we haven't got straight lines but
+
+ align:start position:0%
+here we haven't got straight lines but
+ 
+
+ align:start position:0%
+here we haven't got straight lines but
+we still have the beautiful figure the
+
+ align:start position:0%
+we still have the beautiful figure the
+ 
+
+ align:start position:0%
+we still have the beautiful figure the
+if I now now I'm ready to tackle I'll
+
+ align:start position:0%
+if I now now I'm ready to tackle I'll
+ 
+
+ align:start position:0%
+if I now now I'm ready to tackle I'll
+draw these curves they're hyper
+
+ align:start position:0%
+draw these curves they're hyper
+ 
+
+ align:start position:0%
+draw these curves they're hyper
+like y = 1 2x yal if I just make that y
+
+ align:start position:0%
+like y = 1 2x yal if I just make that y
+ 
+
+ align:start position:0%
+like y = 1 2x yal if I just make that y
+= 1 2x that's a line that comes down
+
+ align:start position:0%
+= 1 2x that's a line that comes down
+ 
+
+ align:start position:0%
+= 1 2x that's a line that comes down
+this way let me try to draw
+
+ align:start position:0%
+this way let me try to draw
+ 
+
+ align:start position:0%
+this way let me try to draw
+it I'll do use Dash lines of
+
+ align:start position:0%
+it I'll do use Dash lines of
+ 
+
+ align:start position:0%
+it I'll do use Dash lines of
+course as X gets bigger y gets
+
+ align:start position:0%
+course as X gets bigger y gets
+ 
+
+ align:start position:0%
+course as X gets bigger y gets
+smaller but never you know y never makes
+
+ align:start position:0%
+smaller but never you know y never makes
+ 
+
+ align:start position:0%
+smaller but never you know y never makes
+it to zero because if y was Zero I
+
+ align:start position:0%
+it to zero because if y was Zero I
+ 
+
+ align:start position:0%
+it to zero because if y was Zero I
+couldn't no X would work so that and
+
+ align:start position:0%
+couldn't no X would work so that and
+ 
+
+ align:start position:0%
+couldn't no X would work so that and
+then but if if if I change that one to a
+
+ align:start position:0%
+then but if if if I change that one to a
+ 
+
+ align:start position:0%
+then but if if if I change that one to a
+four I've got a bigger I've got this is
+
+ align:start position:0%
+four I've got a bigger I've got this is
+ 
+
+ align:start position:0%
+four I've got a bigger I've got this is
+coming out here if I change that to a to
+
+ align:start position:0%
+coming out here if I change that to a to
+ 
+
+ align:start position:0%
+coming out here if I change that to a to
+something very small I'll get somebody
+
+ align:start position:0%
+something very small I'll get somebody
+ 
+
+ align:start position:0%
+something very small I'll get somebody
+I'll get one that's coming these are
+
+ align:start position:0%
+I'll get one that's coming these are
+ 
+
+ align:start position:0%
+I'll get one that's coming these are
+going do you see how the picture Works
+
+ align:start position:0%
+going do you see how the picture Works
+ 
+
+ align:start position:0%
+going do you see how the picture Works
+they these are all right
+
+ align:start position:0%
+they these are all right
+ 
+
+ align:start position:0%
+they these are all right
+angles that's the great thing right
+
+ align:start position:0%
+angles that's the great thing right
+ 
+
+ align:start position:0%
+angles that's the great thing right
+angles 90°
+
+ align:start position:0%
+angles 90°
+ 
+
+ align:start position:0%
+angles 90°
+angles the the between the streamlines
+
+ align:start position:0%
+angles the the between the streamlines
+ 
+
+ align:start position:0%
+angles the the between the streamlines
+and the equip potentials you you may
+
+ align:start position:0%
+and the equip potentials you you may
+ 
+
+ align:start position:0%
+and the equip potentials you you may
+have seen this before and now I'm just
+
+ align:start position:0%
+have seen this before and now I'm just
+ 
+
+ align:start position:0%
+have seen this before and now I'm just
+want to ask you why why are those 90
+
+ align:start position:0%
+want to ask you why why are those 90
+ 
+
+ align:start position:0%
+want to ask you why why are those 90
+degrees we we kind of see it physically
+
+ align:start position:0%
+degrees we we kind of see it physically
+ 
+
+ align:start position:0%
+degrees we we kind of see it physically
+that the gradient is the you know the
+
+ align:start position:0%
+that the gradient is the you know the
+ 
+
+ align:start position:0%
+that the gradient is the you know the
+flow is in the gradient Direction and we
+
+ align:start position:0%
+flow is in the gradient Direction and we
+ 
+
+ align:start position:0%
+flow is in the gradient Direction and we
+know that gradients are always
+
+ align:start position:0%
+know that gradients are always
+ 
+
+ align:start position:0%
+know that gradients are always
+perpendicular to equip potential lines
+
+ align:start position:0%
+perpendicular to equip potential lines
+ 
+
+ align:start position:0%
+perpendicular to equip potential lines
+the gradient of any curve the gradient
+
+ align:start position:0%
+the gradient of any curve the gradient
+ 
+
+ align:start position:0%
+the gradient of any curve the gradient
+of any function is perpendicular to the
+
+ align:start position:0%
+of any function is perpendicular to the
+ 
+
+ align:start position:0%
+of any function is perpendicular to the
+level curves that's that's all we're
+
+ align:start position:0%
+level curves that's that's all we're
+ 
+
+ align:start position:0%
+level curves that's that's all we're
+seeing here but we're seeing this these
+
+ align:start position:0%
+seeing here but we're seeing this these
+ 
+
+ align:start position:0%
+seeing here but we're seeing this these
+two fantastic uh families of Curves
+
+ align:start position:0%
+two fantastic uh families of Curves
+ 
+
+ align:start position:0%
+two fantastic uh families of Curves
+equip potentials perpendicular to
+
+ align:start position:0%
+equip potentials perpendicular to
+ 
+
+ align:start position:0%
+equip potentials perpendicular to
+streamlines and the reason they're
+
+ align:start position:0%
+streamlines and the reason they're
+ 
+
+ align:start position:0%
+streamlines and the reason they're
+perpendicular is Koshi reman Koshi reman
+
+ align:start position:0%
+perpendicular is Koshi reman Koshi reman
+ 
+
+ align:start position:0%
+perpendicular is Koshi reman Koshi reman
+is telling us they're
+
+ align:start position:0%
+is telling us they're
+ 
+
+ align:start position:0%
+is telling us they're
+perpendicular because the gradient
+
+ align:start position:0%
+perpendicular because the gradient
+ 
+
+ align:start position:0%
+perpendicular because the gradient
+yeah you see that they're perpendicular
+
+ align:start position:0%
+yeah you see that they're perpendicular
+ 
+
+ align:start position:0%
+yeah you see that they're perpendicular
+is may be overkilled to to try to give a
+
+ align:start position:0%
+is may be overkilled to to try to give a
+ 
+
+ align:start position:0%
+is may be overkilled to to try to give a
+proof
+
+ align:start position:0%
+proof
+ 
+
+ align:start position:0%
+proof
+this the the gradient of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U what I want to say is
+
+ align:start position:0%
+U what I want to say is
+ 
+
+ align:start position:0%
+U what I want to say is
+that the gradient of U is a 90° rotation
+
+ align:start position:0%
+that the gradient of U is a 90° rotation
+ 
+
+ align:start position:0%
+that the gradient of U is a 90° rotation
+of the gradient of s let me put it that
+
+ align:start position:0%
+of the gradient of s let me put it that
+ 
+
+ align:start position:0%
+of the gradient of s let me put it that
+way the gradient of s the gradient of
+
+ align:start position:0%
+way the gradient of s the gradient of
+ 
+
+ align:start position:0%
+way the gradient of s the gradient of
+U rotate
+
+ align:start position:0%
+U rotate
+ 
+
+ align:start position:0%
+U rotate
+90°
+
+ align:start position:0%
+90°
+ 
+
+ align:start position:0%
+90°
+rotate gradient of U by 90 by 90° pi
+
+ align:start position:0%
+rotate gradient of U by 90 by 90° pi
+ 
+
+ align:start position:0%
+rotate gradient of U by 90 by 90° pi
+over two and you get S you get grad
+
+ align:start position:0%
+over two and you get S you get grad
+ 
+
+ align:start position:0%
+over two and you get S you get grad
+s that's what these equations say that
+
+ align:start position:0%
+s that's what these equations say that
+ 
+
+ align:start position:0%
+s that's what these equations say that
+if if I take the gradient of
+
+ align:start position:0%
+if if I take the gradient of
+ 
+
+ align:start position:0%
+if if I take the gradient of
+U yeah let let me try to do that so I
+
+ align:start position:0%
+U yeah let let me try to do that so I
+ 
+
+ align:start position:0%
+U yeah let let me try to do that so I
+take the gradient of U that's D udx dud
+
+ align:start position:0%
+take the gradient of U that's D udx dud
+ 
+
+ align:start position:0%
+take the gradient of U that's D udx dud
+Dy so if I have a vector in 2D Dux D Dy
+
+ align:start position:0%
+Dy so if I have a vector in 2D Dux D Dy
+ 
+
+ align:start position:0%
+Dy so if I have a vector in 2D Dux D Dy
+and I want to find I want to rotate a
+
+ align:start position:0%
+and I want to find I want to rotate a
+ 
+
+ align:start position:0%
+and I want to find I want to rotate a
+vector by
+
+ align:start position:0%
+vector by
+ 
+
+ align:start position:0%
+vector by
+90° what what's the result suppose I
+
+ align:start position:0%
+90° what what's the result suppose I
+ 
+
+ align:start position:0%
+90° what what's the result suppose I
+have a vector
+
+ align:start position:0%
+have a vector
+ 
+
+ align:start position:0%
+have a vector
+ab and I'm looking to rotate it what's
+
+ align:start position:0%
+ab and I'm looking to rotate it what's
+ 
+
+ align:start position:0%
+ab and I'm looking to rotate it what's
+the vector that goes that way if that
+
+ align:start position:0%
+the vector that goes that way if that
+ 
+
+ align:start position:0%
+the vector that goes that way if that
+Vector is AB that Vector should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what you you may not have done this but
+
+ align:start position:0%
+what you you may not have done this but
+ 
+
+ align:start position:0%
+what you you may not have done this but
+it's it's worth just noticing because
+
+ align:start position:0%
+it's it's worth just noticing because
+ 
+
+ align:start position:0%
+it's it's worth just noticing because
+and you won't forget it it's got to have
+
+ align:start position:0%
+and you won't forget it it's got to have
+ 
+
+ align:start position:0%
+and you won't forget it it's got to have
+a zero dotproduct right so I'm looking
+
+ align:start position:0%
+a zero dotproduct right so I'm looking
+ 
+
+ align:start position:0%
+a zero dotproduct right so I'm looking
+for a vector here
+
+ align:start position:0%
+for a vector here
+ 
+
+ align:start position:0%
+for a vector here
+this went out a and up B I'm looking for
+
+ align:start position:0%
+this went out a and up B I'm looking for
+ 
+
+ align:start position:0%
+this went out a and up B I'm looking for
+a vector there that's perpendicular to
+
+ align:start position:0%
+a vector there that's perpendicular to
+ 
+
+ align:start position:0%
+a vector there that's perpendicular to
+this Vector so what should it do it yeah
+
+ align:start position:0%
+this Vector so what should it do it yeah
+ 
+
+ align:start position:0%
+this Vector so what should it do it yeah
+what what am I going to put
+
+ align:start position:0%
+what what am I going to put
+ 
+
+ align:start position:0%
+what what am I going to put
+there a b and what am I going to
+
+ align:start position:0%
+there a b and what am I going to
+ 
+
+ align:start position:0%
+there a b and what am I going to
+put oh no it it went backwards sorry
+
+ align:start position:0%
+put oh no it it went backwards sorry
+ 
+
+ align:start position:0%
+put oh no it it went backwards sorry
+when I put there I should have put minus
+
+ align:start position:0%
+when I put there I should have put minus
+ 
+
+ align:start position:0%
+when I put there I should have put minus
+B and and what goes there a yeah that's
+
+ align:start position:0%
+B and and what goes there a yeah that's
+ 
+
+ align:start position:0%
+B and and what goes there a yeah that's
+the that's the perpendicular one
+
+ align:start position:0%
+the that's the perpendicular one
+ 
+
+ align:start position:0%
+the that's the perpendicular one
+right if if that's the 90° rotation and
+
+ align:start position:0%
+right if if that's the 90° rotation and
+ 
+
+ align:start position:0%
+right if if that's the 90° rotation and
+that's what Koshi reman is doing for us
+
+ align:start position:0%
+that's what Koshi reman is doing for us
+ 
+
+ align:start position:0%
+that's what Koshi reman is doing for us
+I take the gradient that's I take this
+
+ align:start position:0%
+I take the gradient that's I take this
+ 
+
+ align:start position:0%
+I take the gradient that's I take this
+Vector now I rotate by 90° means I
+
+ align:start position:0%
+Vector now I rotate by 90° means I
+ 
+
+ align:start position:0%
+Vector now I rotate by 90° means I
+reverse these reverse a sign and I've
+
+ align:start position:0%
+reverse these reverse a sign and I've
+ 
+
+ align:start position:0%
+reverse these reverse a sign and I've
+got the gradient of s or minus the
+
+ align:start position:0%
+got the gradient of s or minus the
+ 
+
+ align:start position:0%
+got the gradient of s or minus the
+gradient of s I won't say whether the
+
+ align:start position:0%
+gradient of s I won't say whether the
+ 
+
+ align:start position:0%
+gradient of s I won't say whether the
+rotation is n Plus 90 degrees or minus
+
+ align:start position:0%
+rotation is n Plus 90 degrees or minus
+ 
+
+ align:start position:0%
+rotation is n Plus 90 degrees or minus
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+degrees this can remain an exercise to
+
+ align:start position:0%
+degrees this can remain an exercise to
+ 
+
+ align:start position:0%
+degrees this can remain an exercise to
+to uh to see it
+
+ align:start position:0%
+to uh to see it
+ 
+
+ align:start position:0%
+to uh to see it
+uh slowly and clearly I I I'm happy if
+
+ align:start position:0%
+uh slowly and clearly I I I'm happy if
+ 
+
+ align:start position:0%
+uh slowly and clearly I I I'm happy if
+you see it in the picture there and of
+
+ align:start position:0%
+you see it in the picture there and of
+ 
+
+ align:start position:0%
+you see it in the picture there and of
+course you saw it in this picture
+
+ align:start position:0%
+course you saw it in this picture
+ 
+
+ align:start position:0%
+course you saw it in this picture
+here so this is a moment then to take a
+
+ align:start position:0%
+here so this is a moment then to take a
+ 
+
+ align:start position:0%
+here so this is a moment then to take a
+little pause because we've got 10
+
+ align:start position:0%
+little pause because we've got 10
+ 
+
+ align:start position:0%
+little pause because we've got 10
+minutes for the great event uh we've got
+
+ align:start position:0%
+minutes for the great event uh we've got
+ 
+
+ align:start position:0%
+minutes for the great event uh we've got
+the general idea the U equal constants
+
+ align:start position:0%
+the general idea the U equal constants
+ 
+
+ align:start position:0%
+the general idea the U equal constants
+and the S equal constant these two
+
+ align:start position:0%
+and the S equal constant these two
+ 
+
+ align:start position:0%
+and the S equal constant these two
+families of perpendicular curves one
+
+ align:start position:0%
+families of perpendicular curves one
+ 
+
+ align:start position:0%
+families of perpendicular curves one
+telling us where level level sets for
+
+ align:start position:0%
+telling us where level level sets for
+ 
+
+ align:start position:0%
+telling us where level level sets for
+the potential the other telling us the
+
+ align:start position:0%
+the potential the other telling us the
+ 
+
+ align:start position:0%
+the potential the other telling us the
+direction of the flow the flow goes
+
+ align:start position:0%
+direction of the flow the flow goes
+ 
+
+ align:start position:0%
+direction of the flow the flow goes
+perpendicular to those level sets it's
+
+ align:start position:0%
+perpendicular to those level sets it's
+ 
+
+ align:start position:0%
+perpendicular to those level sets it's
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+wonderful and now I would like
+
+ align:start position:0%
+wonderful and now I would like
+ 
+
+ align:start position:0%
+wonderful and now I would like
+to get
+
+ align:start position:0%
+to get
+ 
+
+ align:start position:0%
+to get
+a get the pattern that's going on here
+
+ align:start position:0%
+a get the pattern that's going on here
+ 
+
+ align:start position:0%
+a get the pattern that's going on here
+and complete that
+
+ align:start position:0%
+and complete that
+ 
+
+ align:start position:0%
+and complete that
+list
+
+ align:start position:0%
+list
+ 
+
+ align:start position:0%
+list
+okay well that pattern like comes out of
+
+ align:start position:0%
+okay well that pattern like comes out of
+ 
+
+ align:start position:0%
+okay well that pattern like comes out of
+the blue I have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+admit you might sort of recognize that
+
+ align:start position:0%
+admit you might sort of recognize that
+ 
+
+ align:start position:0%
+admit you might sort of recognize that
+that something here's obviously stuff to
+
+ align:start position:0%
+that something here's obviously stuff to
+ 
+
+ align:start position:0%
+that something here's obviously stuff to
+the first Power here we've squared
+
+ align:start position:0%
+the first Power here we've squared
+ 
+
+ align:start position:0%
+the first Power here we've squared
+something to get here here we've cubed
+
+ align:start position:0%
+something to get here here we've cubed
+ 
+
+ align:start position:0%
+something to get here here we've cubed
+something do you you you sort of
+
+ align:start position:0%
+something do you you you sort of
+ 
+
+ align:start position:0%
+something do you you you sort of
+recognize these numbers one 331 or one
+
+ align:start position:0%
+recognize these numbers one 331 or one
+ 
+
+ align:start position:0%
+recognize these numbers one 331 or one
+minus 3 whatever that's we're we're
+
+ align:start position:0%
+minus 3 whatever that's we're we're
+ 
+
+ align:start position:0%
+minus 3 whatever that's we're we're
+we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah we're taking powers of something
+
+ align:start position:0%
+uh yeah we're taking powers of something
+ 
+
+ align:start position:0%
+uh yeah we're taking powers of something
+and that something
+
+ align:start position:0%
+and that something
+ 
+
+ align:start position:0%
+and that something
+is the what comes out of the blue
+
+ align:start position:0%
+is the what comes out of the blue
+ 
+
+ align:start position:0%
+is the what comes out of the blue
+it's this quantity X Plus i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y complex variables everything here was
+
+ align:start position:0%
+y complex variables everything here was
+ 
+
+ align:start position:0%
+y complex variables everything here was
+real until this moment and then I'm
+
+ align:start position:0%
+real until this moment and then I'm
+ 
+
+ align:start position:0%
+real until this moment and then I'm
+saying that the complex number I the the
+
+ align:start position:0%
+saying that the complex number I the the
+ 
+
+ align:start position:0%
+saying that the complex number I the the
+the imaginary number I the square root
+
+ align:start position:0%
+the imaginary number I the square root
+ 
+
+ align:start position:0%
+the imaginary number I the square root
+of minus one which of course it just
+
+ align:start position:0%
+of minus one which of course it just
+ 
+
+ align:start position:0%
+of minus one which of course it just
+whatever I mean it's not a real number
+
+ align:start position:0%
+whatever I mean it's not a real number
+ 
+
+ align:start position:0%
+whatever I mean it's not a real number
+but it has the property whenever we see
+
+ align:start position:0%
+but it has the property whenever we see
+ 
+
+ align:start position:0%
+but it has the property whenever we see
+i^ s we write minus one so then we know
+
+ align:start position:0%
+i^ s we write minus one so then we know
+ 
+
+ align:start position:0%
+i^ s we write minus one so then we know
+how to deal with it okay sort of anyway
+
+ align:start position:0%
+how to deal with it okay sort of anyway
+ 
+
+ align:start position:0%
+how to deal with it okay sort of anyway
+so that complex number I'll call
+
+ align:start position:0%
+so that complex number I'll call
+ 
+
+ align:start position:0%
+so that complex number I'll call
+Z and here's what I
+
+ align:start position:0%
+Z and here's what I
+ 
+
+ align:start position:0%
+Z and here's what I
+think I think
+
+ align:start position:0%
+think I think
+ 
+
+ align:start position:0%
+think I think
+that these two pieces are the real and
+
+ align:start position:0%
+that these two pieces are the real and
+ 
+
+ align:start position:0%
+that these two pieces are the real and
+the imaginary parts of
+
+ align:start position:0%
+the imaginary parts of
+ 
+
+ align:start position:0%
+the imaginary parts of
+Z now these two pieces are the the real
+
+ align:start position:0%
+Z now these two pieces are the the real
+ 
+
+ align:start position:0%
+Z now these two pieces are the the real
+and the imaginary parts
+
+ align:start position:0%
+and the imaginary parts
+ 
+
+ align:start position:0%
+and the imaginary parts
+of z
+
+ align:start position:0%
+of z
+ 
+
+ align:start position:0%
+of z
+s these two pieces will be the real part
+
+ align:start position:0%
+s these two pieces will be the real part
+ 
+
+ align:start position:0%
+s these two pieces will be the real part
+and the imaginary part of z cubed and if
+
+ align:start position:0%
+and the imaginary part of z cubed and if
+ 
+
+ align:start position:0%
+and the imaginary part of z cubed and if
+you we check that and then we begin to
+
+ align:start position:0%
+you we check that and then we begin to
+ 
+
+ align:start position:0%
+you we check that and then we begin to
+see why should these satisfy thees
+
+ align:start position:0%
+see why should these satisfy thees
+ 
+
+ align:start position:0%
+see why should these satisfy thees
+equation we'll have the whole pattern
+
+ align:start position:0%
+equation we'll have the whole pattern
+ 
+
+ align:start position:0%
+equation we'll have the whole pattern
+it'll just be X+ i y to fourth power
+
+ align:start position:0%
+it'll just be X+ i y to fourth power
+ 
+
+ align:start position:0%
+it'll just be X+ i y to fourth power
+fifth power sixth power we can make a
+
+ align:start position:0%
+fifth power sixth power we can make a
+ 
+
+ align:start position:0%
+fifth power sixth power we can make a
+complete infinite list of pairs of
+
+ align:start position:0%
+complete infinite list of pairs of
+ 
+
+ align:start position:0%
+complete infinite list of pairs of
+solutions to lass's equation so can I
+
+ align:start position:0%
+solutions to lass's equation so can I
+ 
+
+ align:start position:0%
+solutions to lass's equation so can I
+just see let me just check what I said
+
+ align:start position:0%
+just see let me just check what I said
+ 
+
+ align:start position:0%
+just see let me just check what I said
+about uh the squares first how how do
+
+ align:start position:0%
+about uh the squares first how how do
+ 
+
+ align:start position:0%
+about uh the squares first how how do
+you do X+ i y squar because that's what
+
+ align:start position:0%
+you do X+ i y squar because that's what
+ 
+
+ align:start position:0%
+you do X+ i y squar because that's what
+I believe we're seeing in the in the
+
+ align:start position:0%
+I believe we're seeing in the in the
+ 
+
+ align:start position:0%
+I believe we're seeing in the in the
+quadratic list so I I claim that if I
+
+ align:start position:0%
+quadratic list so I I claim that if I
+ 
+
+ align:start position:0%
+quadratic list so I I claim that if I
+take x + I y^ 2 just just do it normally
+
+ align:start position:0%
+take x + I y^ 2 just just do it normally
+ 
+
+ align:start position:0%
+take x + I y^ 2 just just do it normally
+I get x2 and I get two I i x y and I get
+
+ align:start position:0%
+I get x2 and I get two I i x y and I get
+ 
+
+ align:start position:0%
+I get x2 and I get two I i x y and I get
+i^ 2 y^ 2
+
+ align:start position:0%
+i^ 2 y^ 2
+ 
+
+ align:start position:0%
+i^ 2 y^ 2
+right I just squared it following normal
+
+ align:start position:0%
+right I just squared it following normal
+ 
+
+ align:start position:0%
+right I just squared it following normal
+algebra rules now what's the real part
+
+ align:start position:0%
+algebra rules now what's the real part
+ 
+
+ align:start position:0%
+algebra rules now what's the real part
+what's the real part of this X+ I y^
+
+ align:start position:0%
+what's the real part of this X+ I y^
+ 
+
+ align:start position:0%
+what's the real part of this X+ I y^
+2 X2 this is
+
+ align:start position:0%
+2 X2 this is
+ 
+
+ align:start position:0%
+2 X2 this is
+real and this is real because i^ s is
+
+ align:start position:0%
+real and this is real because i^ s is
+ 
+
+ align:start position:0%
+real and this is real because i^ s is
+minus1 this is minus y^2 that's our
+
+ align:start position:0%
+minus1 this is minus y^2 that's our
+ 
+
+ align:start position:0%
+minus1 this is minus y^2 that's our
+that's our guy and the imaginary part
+
+ align:start position:0%
+that's our guy and the imaginary part
+ 
+
+ align:start position:0%
+that's our guy and the imaginary part
+is 2xy that's what multi the imaginary
+
+ align:start position:0%
+is 2xy that's what multi the imaginary
+ 
+
+ align:start position:0%
+is 2xy that's what multi the imaginary
+part is the part that multiplies I so by
+
+ align:start position:0%
+part is the part that multiplies I so by
+ 
+
+ align:start position:0%
+part is the part that multiplies I so by
+some magic that we'll we'll next time is
+
+ align:start position:0%
+some magic that we'll we'll next time is
+ 
+
+ align:start position:0%
+some magic that we'll we'll next time is
+the the the fun of exploring this magic
+
+ align:start position:0%
+the the the fun of exploring this magic
+ 
+
+ align:start position:0%
+the the the fun of exploring this magic
+we've get we get solutions to a real
+
+ align:start position:0%
+we've get we get solutions to a real
+ 
+
+ align:start position:0%
+we've get we get solutions to a real
+equation we get two solutions to a real
+
+ align:start position:0%
+equation we get two solutions to a real
+ 
+
+ align:start position:0%
+equation we get two solutions to a real
+equation by working with this complex
+
+ align:start position:0%
+equation by working with this complex
+ 
+
+ align:start position:0%
+equation by working with this complex
+thing X Plus i y and taking things like
+
+ align:start position:0%
+thing X Plus i y and taking things like
+ 
+
+ align:start position:0%
+thing X Plus i y and taking things like
+now if I go to X Plus y
+
+ align:start position:0%
+now if I go to X Plus y
+ 
+
+ align:start position:0%
+now if I go to X Plus y
+cubed well let me just say it'll
+
+ align:start position:0%
+cubed well let me just say it'll
+ 
+
+ align:start position:0%
+cubed well let me just say it'll
+work we'll have uh yeah you remember
+
+ align:start position:0%
+work we'll have uh yeah you remember
+ 
+
+ align:start position:0%
+work we'll have uh yeah you remember
+when it's like you know if you Cube
+
+ align:start position:0%
+when it's like you know if you Cube
+ 
+
+ align:start position:0%
+when it's like you know if you Cube
+something you're going to see 1331
+
+ align:start position:0%
+something you're going to see 1331
+ 
+
+ align:start position:0%
+something you're going to see 1331
+you'll have an X cub and a 3 X2 i y and
+
+ align:start position:0%
+you'll have an X cub and a 3 X2 i y and
+ 
+
+ align:start position:0%
+you'll have an X cub and a 3 X2 i y and
+a 3X i y
+
+ align:start position:0%
+a 3X i y
+ 
+
+ align:start position:0%
+a 3X i y
+twice and an i and a one of the i y
+
+ align:start position:0%
+twice and an i and a one of the i y
+ 
+
+ align:start position:0%
+twice and an i and a one of the i y
+cubed
+
+ align:start position:0%
+cubed
+ 
+
+ align:start position:0%
+cubed
+and then you look to see what part is
+
+ align:start position:0%
+and then you look to see what part is
+ 
+
+ align:start position:0%
+and then you look to see what part is
+real and you say x Cub is real and i^2
+
+ align:start position:0%
+real and you say x Cub is real and i^2
+ 
+
+ align:start position:0%
+real and you say x Cub is real and i^2
+is the minus so I have minus 3x y^2
+
+ align:start position:0%
+is the minus so I have minus 3x y^2
+ 
+
+ align:start position:0%
+is the minus so I have minus 3x y^2
+golden and you look for what part is
+
+ align:start position:0%
+golden and you look for what part is
+ 
+
+ align:start position:0%
+golden and you look for what part is
+imaginary and you see the 3x^2 Y and you
+
+ align:start position:0%
+imaginary and you see the 3x^2 Y and you
+ 
+
+ align:start position:0%
+imaginary and you see the 3x^2 Y and you
+see the I cubed so what's I
+
+ align:start position:0%
+see the I cubed so what's I
+ 
+
+ align:start position:0%
+see the I cubed so what's I
+cubed is minus I so that's an imaginary
+
+ align:start position:0%
+cubed is minus I so that's an imaginary
+ 
+
+ align:start position:0%
+cubed is minus I so that's an imaginary
+term with a minus that we we wanted so
+
+ align:start position:0%
+term with a minus that we we wanted so
+ 
+
+ align:start position:0%
+term with a minus that we we wanted so
+now we've got the whole thing we've
+
+ align:start position:0%
+now we've got the whole thing we've
+ 
+
+ align:start position:0%
+now we've got the whole thing we've
+we've got solutions to thees equation
+
+ align:start position:0%
+we've got solutions to thees equation
+ 
+
+ align:start position:0%
+we've got solutions to thees equation
+coming
+
+ align:start position:0%
+coming
+ 
+
+ align:start position:0%
+coming
+from all the powers and that yeah this
+
+ align:start position:0%
+from all the powers and that yeah this
+ 
+
+ align:start position:0%
+from all the powers and that yeah this
+is this is now the moment to to
+
+ align:start position:0%
+is this is now the moment to to
+ 
+
+ align:start position:0%
+is this is now the moment to to
+celebrate right because we've got we've
+
+ align:start position:0%
+celebrate right because we've got we've
+ 
+
+ align:start position:0%
+celebrate right because we've got we've
+got a giant family of solutions to llas
+
+ align:start position:0%
+got a giant family of solutions to llas
+ 
+
+ align:start position:0%
+got a giant family of solutions to llas
+equation uh we've got all the we've got
+
+ align:start position:0%
+equation uh we've got all the we've got
+ 
+
+ align:start position:0%
+equation uh we've got all the we've got
+the real parts so U is the real part of
+
+ align:start position:0%
+the real parts so U is the real part of
+ 
+
+ align:start position:0%
+the real parts so U is the real part of
+X Plus i y to any power
+
+ align:start position:0%
+X Plus i y to any power
+ 
+
+ align:start position:0%
+X Plus i y to any power
+and S will be the imaginary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part and I claim that just as we held
+
+ align:start position:0%
+part and I claim that just as we held
+ 
+
+ align:start position:0%
+part and I claim that just as we held
+for n equal 1 2 3 for every n these will
+
+ align:start position:0%
+for n equal 1 2 3 for every n these will
+ 
+
+ align:start position:0%
+for n equal 1 2 3 for every n these will
+be solutions to the plas equation
+
+ align:start position:0%
+be solutions to the plas equation
+ 
+
+ align:start position:0%
+be solutions to the plas equation
+they'll not only that they'll be
+
+ align:start position:0%
+they'll not only that they'll be
+ 
+
+ align:start position:0%
+they'll not only that they'll be
+connected by Koshi remon so they'll be
+
+ align:start position:0%
+connected by Koshi remon so they'll be
+ 
+
+ align:start position:0%
+connected by Koshi remon so they'll be
+uh the the potential and the stream
+
+ align:start position:0%
+uh the the potential and the stream
+ 
+
+ align:start position:0%
+uh the the potential and the stream
+function for for a for a flow and uh and
+
+ align:start position:0%
+function for for a for a flow and uh and
+ 
+
+ align:start position:0%
+function for for a for a flow and uh and
+we've got lots of
+
+ align:start position:0%
+we've got lots of
+ 
+
+ align:start position:0%
+we've got lots of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+and well we got even more because we
+
+ align:start position:0%
+and well we got even more because we
+ 
+
+ align:start position:0%
+and well we got even more because we
+have linear equation here so what are we
+
+ align:start position:0%
+have linear equation here so what are we
+ 
+
+ align:start position:0%
+have linear equation here so what are we
+allowed to do if we have solutions to a
+
+ align:start position:0%
+allowed to do if we have solutions to a
+ 
+
+ align:start position:0%
+allowed to do if we have solutions to a
+linear equation what are we allowed to
+
+ align:start position:0%
+linear equation what are we allowed to
+ 
+
+ align:start position:0%
+linear equation what are we allowed to
+do with those solutions to get more
+
+ align:start position:0%
+do with those solutions to get more
+ 
+
+ align:start position:0%
+do with those solutions to get more
+solutions combine
+
+ align:start position:0%
+solutions combine
+ 
+
+ align:start position:0%
+solutions combine
+them I can take any combination of these
+
+ align:start position:0%
+them I can take any combination of these
+ 
+
+ align:start position:0%
+them I can take any combination of these
+guys I can take or so and or I don't
+
+ align:start position:0%
+guys I can take or so and or I don't
+ 
+
+ align:start position:0%
+guys I can take or so and or I don't
+know which should put or
+
+ align:start position:0%
+know which should put or
+ 
+
+ align:start position:0%
+know which should put or
+and uh the real part of any combination
+
+ align:start position:0%
+and uh the real part of any combination
+ 
+
+ align:start position:0%
+and uh the real part of any combination
+of these so I could take a
+
+ align:start position:0%
+of these so I could take a
+ 
+
+ align:start position:0%
+of these so I could take a
+combination of I can take coefficients
+
+ align:start position:0%
+combination of I can take coefficients
+ 
+
+ align:start position:0%
+combination of I can take coefficients
+CK or CN maybe I should say
+
+ align:start position:0%
+CK or CN maybe I should say
+ 
+
+ align:start position:0%
+CK or CN maybe I should say
+CN x + i y to the
+
+ align:start position:0%
+CN x + i y to the
+ 
+
+ align:start position:0%
+CN x + i y to the
+N so if I take a combination of
+
+ align:start position:0%
+N so if I take a combination of
+ 
+
+ align:start position:0%
+N so if I take a combination of
+solutions with with coefficients CN I
+
+ align:start position:0%
+solutions with with coefficients CN I
+ 
+
+ align:start position:0%
+solutions with with coefficients CN I
+still have Solutions and what will be
+
+ align:start position:0%
+still have Solutions and what will be
+ 
+
+ align:start position:0%
+still have Solutions and what will be
+the twin solution or the the the uh the
+
+ align:start position:0%
+the twin solution or the the the uh the
+ 
+
+ align:start position:0%
+the twin solution or the the the uh the
+stream function that goes with this U so
+
+ align:start position:0%
+stream function that goes with this U so
+ 
+
+ align:start position:0%
+stream function that goes with this U so
+this is another U this is a one this is
+
+ align:start position:0%
+this is another U this is a one this is
+ 
+
+ align:start position:0%
+this is another U this is a one this is
+a really virtually a complete family of
+
+ align:start position:0%
+a really virtually a complete family of
+ 
+
+ align:start position:0%
+a really virtually a complete family of
+use because we have all these
+
+ align:start position:0%
+use because we have all these
+ 
+
+ align:start position:0%
+use because we have all these
+coefficients to choose and what will be
+
+ align:start position:0%
+coefficients to choose and what will be
+ 
+
+ align:start position:0%
+coefficients to choose and what will be
+the S so I what's the corresponding s
+
+ align:start position:0%
+the S so I what's the corresponding s
+ 
+
+ align:start position:0%
+the S so I what's the corresponding s
+then it's the imaginary part
+
+ align:start position:0%
+then it's the imaginary part
+ 
+
+ align:start position:0%
+then it's the imaginary part
+of what the same
+
+ align:start position:0%
+of what the same
+ 
+
+ align:start position:0%
+of what the same
+thing the same we're just taking that
+
+ align:start position:0%
+thing the same we're just taking that
+ 
+
+ align:start position:0%
+thing the same we're just taking that
+same combination of
+
+ align:start position:0%
+same combination of
+ 
+
+ align:start position:0%
+same combination of
+the of the uh of the special ones so the
+
+ align:start position:0%
+the of the uh of the special ones so the
+ 
+
+ align:start position:0%
+the of the uh of the special ones so the
+special ones were X Plus i y to the nth
+
+ align:start position:0%
+special ones were X Plus i y to the nth
+ 
+
+ align:start position:0%
+special ones were X Plus i y to the nth
+and the combinations are those yeah
+
+ align:start position:0%
+and the combinations are those yeah
+ 
+
+ align:start position:0%
+and the combinations are those yeah
+that's these are fantastic Solutions and
+
+ align:start position:0%
+that's these are fantastic Solutions and
+ 
+
+ align:start position:0%
+that's these are fantastic Solutions and
+now since I blessed with two more
+
+ align:start position:0%
+now since I blessed with two more
+ 
+
+ align:start position:0%
+now since I blessed with two more
+minutes I get to
+
+ align:start position:0%
+minutes I get to
+ 
+
+ align:start position:0%
+minutes I get to
+make them much easier because well
+
+ align:start position:0%
+make them much easier because well
+ 
+
+ align:start position:0%
+make them much easier because well
+already when I got up to X Cube and Y
+
+ align:start position:0%
+already when I got up to X Cube and Y
+ 
+
+ align:start position:0%
+already when I got up to X Cube and Y
+Cube they they're looking messy you say
+
+ align:start position:0%
+Cube they they're looking messy you say
+ 
+
+ align:start position:0%
+Cube they they're looking messy you say
+h you say okay great to have all these
+
+ align:start position:0%
+h you say okay great to have all these
+ 
+
+ align:start position:0%
+h you say okay great to have all these
+Solutions but how am I going to use them
+
+ align:start position:0%
+Solutions but how am I going to use them
+ 
+
+ align:start position:0%
+Solutions but how am I going to use them
+you know they're they're they're they're
+
+ align:start position:0%
+you know they're they're they're they're
+ 
+
+ align:start position:0%
+you know they're they're they're they're
+uh uh getting more and more complicated
+
+ align:start position:0%
+uh uh getting more and more complicated
+ 
+
+ align:start position:0%
+uh uh getting more and more complicated
+as an increases but switch to Polar
+
+ align:start position:0%
+as an increases but switch to Polar
+ 
+
+ align:start position:0%
+as an increases but switch to Polar
+coordinates make the same list in polar
+
+ align:start position:0%
+coordinates make the same list in polar
+ 
+
+ align:start position:0%
+coordinates make the same list in polar
+coordinates so again I'm just going to
+
+ align:start position:0%
+coordinates so again I'm just going to
+ 
+
+ align:start position:0%
+coordinates so again I'm just going to
+list the same guys in polar coordinates
+
+ align:start position:0%
+list the same guys in polar coordinates
+ 
+
+ align:start position:0%
+list the same guys in polar coordinates
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta then you'll see the then the
+
+ align:start position:0%
+Theta then you'll see the then the
+ 
+
+ align:start position:0%
+Theta then you'll see the then the
+pattern really jumps out so what is x in
+
+ align:start position:0%
+pattern really jumps out so what is x in
+ 
+
+ align:start position:0%
+pattern really jumps out so what is x in
+polar
+
+ align:start position:0%
+polar
+ 
+
+ align:start position:0%
+polar
+coordinates you if I switch from XY
+
+ align:start position:0%
+coordinates you if I switch from XY
+ 
+
+ align:start position:0%
+coordinates you if I switch from XY
+rectangular coordinates to R Theta polar
+
+ align:start position:0%
+rectangular coordinates to R Theta polar
+ 
+
+ align:start position:0%
+rectangular coordinates to R Theta polar
+coordinates X is R cos Theta and Y
+
+ align:start position:0%
+coordinates X is R cos Theta and Y
+ 
+
+ align:start position:0%
+coordinates X is R cos Theta and Y
+is R sin Theta okay well so so far done
+
+ align:start position:0%
+is R sin Theta okay well so so far done
+ 
+
+ align:start position:0%
+is R sin Theta okay well so so far done
+any easier X and Y looked fine but let
+
+ align:start position:0%
+any easier X and Y looked fine but let
+ 
+
+ align:start position:0%
+any easier X and Y looked fine but let
+me go to the second second one so this
+
+ align:start position:0%
+me go to the second second one so this
+ 
+
+ align:start position:0%
+me go to the second second one so this
+is now R 2 cos 2 Theta right minus this
+
+ align:start position:0%
+is now R 2 cos 2 Theta right minus this
+ 
+
+ align:start position:0%
+is now R 2 cos 2 Theta right minus this
+is r s sin s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+trigonometry comes in I have r^ 2 cos 2
+
+ align:start position:0%
+trigonometry comes in I have r^ 2 cos 2
+ 
+
+ align:start position:0%
+trigonometry comes in I have r^ 2 cos 2
+Theta minus r^ 2 sin 2 Theta I want to I
+
+ align:start position:0%
+Theta minus r^ 2 sin 2 Theta I want to I
+ 
+
+ align:start position:0%
+Theta minus r^ 2 sin 2 Theta I want to I
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+simplify that so it's got an R
+
+ align:start position:0%
+simplify that so it's got an R
+ 
+
+ align:start position:0%
+simplify that so it's got an R
+2 and it's got a COS 2 thet minus sin 2
+
+ align:start position:0%
+2 and it's got a COS 2 thet minus sin 2
+ 
+
+ align:start position:0%
+2 and it's got a COS 2 thet minus sin 2
+thet anybody remember that cosine of 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta and this
+
+ align:start position:0%
+Theta and this
+ 
+
+ align:start position:0%
+Theta and this
+one well what do you think it's
+
+ align:start position:0%
+one well what do you think it's
+ 
+
+ align:start position:0%
+one well what do you think it's
+coming what do you think is coming here
+
+ align:start position:0%
+coming what do you think is coming here
+ 
+
+ align:start position:0%
+coming what do you think is coming here
+I have two R cos Theta * R sin Theta I
+
+ align:start position:0%
+I have two R cos Theta * R sin Theta I
+ 
+
+ align:start position:0%
+I have two R cos Theta * R sin Theta I
+have two I've got an r s again
+
+ align:start position:0%
+have two I've got an r s again
+ 
+
+ align:start position:0%
+have two I've got an r s again
+time 2 cos Theta sin Theta so what's 2
+
+ align:start position:0%
+time 2 cos Theta sin Theta so what's 2
+ 
+
+ align:start position:0%
+time 2 cos Theta sin Theta so what's 2
+cos Theta sin Theta sin 2 Theta you get
+
+ align:start position:0%
+cos Theta sin Theta sin 2 Theta you get
+ 
+
+ align:start position:0%
+cos Theta sin Theta sin 2 Theta you get
+it sin 2 Theta and you
+
+ align:start position:0%
+it sin 2 Theta and you
+ 
+
+ align:start position:0%
+it sin 2 Theta and you
+know what's coming next right you know
+
+ align:start position:0%
+know what's coming next right you know
+ 
+
+ align:start position:0%
+know what's coming next right you know
+that now the whole family in polar
+
+ align:start position:0%
+that now the whole family in polar
+ 
+
+ align:start position:0%
+that now the whole family in polar
+coordinates what's the what's the N
+
+ align:start position:0%
+coordinates what's the what's the N
+ 
+
+ align:start position:0%
+coordinates what's the what's the N
+power what's the N what's the N we can
+
+ align:start position:0%
+power what's the N what's the N we can
+ 
+
+ align:start position:0%
+power what's the N what's the N we can
+now write down the nth one in this list
+
+ align:start position:0%
+now write down the nth one in this list
+ 
+
+ align:start position:0%
+now write down the nth one in this list
+it is R to the nth or the nth
+
+ align:start position:0%
+it is R to the nth or the nth
+ 
+
+ align:start position:0%
+it is R to the nth or the nth
+R to the N
+
+ align:start position:0%
+R to the N
+ 
+
+ align:start position:0%
+R to the N
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+cos n Theta and R to the n s in Theta is
+
+ align:start position:0%
+cos n Theta and R to the n s in Theta is
+ 
+
+ align:start position:0%
+cos n Theta and R to the n s in Theta is
+it so those are the those are the uh
+
+ align:start position:0%
+it so those are the those are the uh
+ 
+
+ align:start position:0%
+it so those are the those are the uh
+twins the the U and the s that we get if
+
+ align:start position:0%
+twins the the U and the s that we get if
+ 
+
+ align:start position:0%
+twins the the U and the s that we get if
+we write if we use polar
+
+ align:start position:0%
+we write if we use polar
+ 
+
+ align:start position:0%
+we write if we use polar
+coordinates so that's uh just terrific
+
+ align:start position:0%
+coordinates so that's uh just terrific
+ 
+
+ align:start position:0%
+coordinates so that's uh just terrific
+now we have a whole lot of solutions to
+
+ align:start position:0%
+now we have a whole lot of solutions to
+ 
+
+ align:start position:0%
+now we have a whole lot of solutions to
+the ples equation
+
+ align:start position:0%
+the ples equation
+ 
+
+ align:start position:0%
+the ples equation
+and we have don't forget all
+
+ align:start position:0%
+and we have don't forget all
+ 
+
+ align:start position:0%
+and we have don't forget all
+combinations of
+
+ align:start position:0%
+combinations of
+ 
+
+ align:start position:0%
+combinations of
+them and we're really ready to go so
+
+ align:start position:0%
+them and we're really ready to go so
+ 
+
+ align:start position:0%
+them and we're really ready to go so
+when so Friday we'll be solving the ples
+
+ align:start position:0%
+when so Friday we'll be solving the ples
+ 
+
+ align:start position:0%
+when so Friday we'll be solving the ples
+equation by in the cases that we can do
+
+ align:start position:0%
+equation by in the cases that we can do
+ 
+
+ align:start position:0%
+equation by in the cases that we can do
+it by pencil and paper by chalk and then
+
+ align:start position:0%
+it by pencil and paper by chalk and then
+ 
+
+ align:start position:0%
+it by pencil and paper by chalk and then
+after that comes solving Theus equation
+
+ align:start position:0%
+after that comes solving Theus equation
+ 
+
+ align:start position:0%
+after that comes solving Theus equation
+by finite differences and finite
+
+ align:start position:0%
+by finite differences and finite
+ 
+
+ align:start position:0%
+by finite differences and finite
+elements okay
\ No newline at end of file
diff --git a/nPJRjMh9evk.txt b/nPJRjMh9evk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a86eb14a252cdc4394d01c71a0ceeefa045644f1
--- /dev/null
+++ b/nPJRjMh9evk.txt
@@ -0,0 +1,7203 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modeling and now we're going to start to
+
+ align:start position:0%
+modeling and now we're going to start to
+ 
+
+ align:start position:0%
+modeling and now we're going to start to
+see how it's done so this is the outline
+
+ align:start position:0%
+see how it's done so this is the outline
+ 
+
+ align:start position:0%
+see how it's done so this is the outline
+of today's lecture because we're going
+
+ align:start position:0%
+of today's lecture because we're going
+ 
+
+ align:start position:0%
+of today's lecture because we're going
+to cover a lot
+
+ align:start position:0%
+to cover a lot
+ 
+
+ align:start position:0%
+to cover a lot
+um I don't mind covering a lot here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's covered well in the text as well so
+
+ align:start position:0%
+it's covered well in the text as well so
+ 
+
+ align:start position:0%
+it's covered well in the text as well so
+this is basically a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know I'm I'm being a tour guide here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to start by introducing
+
+ align:start position:0%
+so we're going to start by introducing
+ 
+
+ align:start position:0%
+so we're going to start by introducing
+the ideal solution model
+
+ align:start position:0%
+the ideal solution model
+ 
+
+ align:start position:0%
+the ideal solution model
+then we're going to talk about non
+
+ align:start position:0%
+then we're going to talk about non
+ 
+
+ align:start position:0%
+then we're going to talk about non
+ideal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution models
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to talk about two particular
+
+ align:start position:0%
+we're going to talk about two particular
+ 
+
+ align:start position:0%
+we're going to talk about two particular
+types of non-ideal solution models
+
+ align:start position:0%
+types of non-ideal solution models
+ 
+
+ align:start position:0%
+types of non-ideal solution models
+dilute solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+and regular solution model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I hope folks are ahead of me
+
+ align:start position:0%
+and I hope folks are ahead of me
+ 
+
+ align:start position:0%
+and I hope folks are ahead of me
+um and I've read chapter eight in the
+
+ align:start position:0%
+um and I've read chapter eight in the
+ 
+
+ align:start position:0%
+um and I've read chapter eight in the
+book and if you have uh it will help
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's talk about first ideal gas
+
+ align:start position:0%
+okay so let's talk about first ideal gas
+ 
+
+ align:start position:0%
+okay so let's talk about first ideal gas
+Solutions we've already done this
+
+ align:start position:0%
+Solutions we've already done this
+ 
+
+ align:start position:0%
+Solutions we've already done this
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+we've already done this ideal gas
+
+ align:start position:0%
+we've already done this ideal gas
+ 
+
+ align:start position:0%
+we've already done this ideal gas
+Solutions
+
+ align:start position:0%
+Solutions
+ 
+
+ align:start position:0%
+Solutions
+right we have pure
+
+ align:start position:0%
+right we have pure
+ 
+
+ align:start position:0%
+right we have pure
+a at temperature pressure
+
+ align:start position:0%
+a at temperature pressure
+ 
+
+ align:start position:0%
+a at temperature pressure
+and some volume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we have Pier B at some temperature and
+
+ align:start position:0%
+we have Pier B at some temperature and
+ 
+
+ align:start position:0%
+we have Pier B at some temperature and
+pressure same temperature same pressure
+
+ align:start position:0%
+pressure same temperature same pressure
+ 
+
+ align:start position:0%
+pressure same temperature same pressure
+and in general a different volume
+
+ align:start position:0%
+and in general a different volume
+ 
+
+ align:start position:0%
+and in general a different volume
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we mix them
+
+ align:start position:0%
+we mix them
+ 
+
+ align:start position:0%
+we mix them
+and if these are ideal gases PV equals
+
+ align:start position:0%
+and if these are ideal gases PV equals
+ 
+
+ align:start position:0%
+and if these are ideal gases PV equals
+nrt tells us
+
+ align:start position:0%
+nrt tells us
+ 
+
+ align:start position:0%
+nrt tells us
+that we get a and b
+
+ align:start position:0%
+that we get a and b
+ 
+
+ align:start position:0%
+that we get a and b
+at the same temperature same pressure
+
+ align:start position:0%
+at the same temperature same pressure
+ 
+
+ align:start position:0%
+at the same temperature same pressure
+and a total volume that is simply the
+
+ align:start position:0%
+and a total volume that is simply the
+ 
+
+ align:start position:0%
+and a total volume that is simply the
+sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the two volumes
+
+ align:start position:0%
+of the two volumes
+ 
+
+ align:start position:0%
+of the two volumes
+so this is for ideal gases
+
+ align:start position:0%
+so this is for ideal gases
+ 
+
+ align:start position:0%
+so this is for ideal gases
+all right so we know this and we've seen
+
+ align:start position:0%
+all right so we know this and we've seen
+ 
+
+ align:start position:0%
+all right so we know this and we've seen
+that we can model this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process this process of making the
+
+ align:start position:0%
+process this process of making the
+ 
+
+ align:start position:0%
+process this process of making the
+mixture
+
+ align:start position:0%
+mixture
+ 
+
+ align:start position:0%
+mixture
+as an isothermal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an isothermal expansion for each gas so
+
+ align:start position:0%
+an isothermal expansion for each gas so
+ 
+
+ align:start position:0%
+an isothermal expansion for each gas so
+we've seen this and this is the result
+
+ align:start position:0%
+we've seen this and this is the result
+ 
+
+ align:start position:0%
+we've seen this and this is the result
+we got
+
+ align:start position:0%
+we got
+ 
+
+ align:start position:0%
+we got
+isothermal change and chemical potential
+
+ align:start position:0%
+isothermal change and chemical potential
+ 
+
+ align:start position:0%
+isothermal change and chemical potential
+is molar Gibbs tree energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means
+
+ align:start position:0%
+that means
+ 
+
+ align:start position:0%
+that means
+the total change
+
+ align:start position:0%
+the total change
+ 
+
+ align:start position:0%
+the total change
+and the chemical potential of each
+
+ align:start position:0%
+and the chemical potential of each
+ 
+
+ align:start position:0%
+and the chemical potential of each
+component throughout this process
+
+ align:start position:0%
+component throughout this process
+ 
+
+ align:start position:0%
+component throughout this process
+is going to be the integral of its
+
+ align:start position:0%
+is going to be the integral of its
+ 
+
+ align:start position:0%
+is going to be the integral of its
+partial pressure times V
+
+ align:start position:0%
+partial pressure times V
+ 
+
+ align:start position:0%
+partial pressure times V
+and making this a little bit more
+
+ align:start position:0%
+and making this a little bit more
+ 
+
+ align:start position:0%
+and making this a little bit more
+explicit this is from P to P sub I
+
+ align:start position:0%
+explicit this is from P to P sub I
+ 
+
+ align:start position:0%
+explicit this is from P to P sub I
+d p
+
+ align:start position:0%
+d p
+ 
+
+ align:start position:0%
+d p
+Ummy variable RT
+
+ align:start position:0%
+Ummy variable RT
+ 
+
+ align:start position:0%
+Ummy variable RT
+over p
+
+ align:start position:0%
+over p
+ 
+
+ align:start position:0%
+over p
+and this equals RT Ln partial pressure
+
+ align:start position:0%
+and this equals RT Ln partial pressure
+ 
+
+ align:start position:0%
+and this equals RT Ln partial pressure
+of I over the total pressure we've
+
+ align:start position:0%
+of I over the total pressure we've
+ 
+
+ align:start position:0%
+of I over the total pressure we've
+we already worked on this we derived
+
+ align:start position:0%
+we already worked on this we derived
+ 
+
+ align:start position:0%
+we already worked on this we derived
+this already and this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the change of chemical potential
+
+ align:start position:0%
+this is the change of chemical potential
+ 
+
+ align:start position:0%
+this is the change of chemical potential
+for isothermal expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here's the new part this is also
+
+ align:start position:0%
+and here's the new part this is also
+ 
+
+ align:start position:0%
+and here's the new part this is also
+Delta Mu of I
+
+ align:start position:0%
+Delta Mu of I
+ 
+
+ align:start position:0%
+Delta Mu of I
+for the mixing process well that's
+
+ align:start position:0%
+for the mixing process well that's
+ 
+
+ align:start position:0%
+for the mixing process well that's
+actually not new we use this in the
+
+ align:start position:0%
+actually not new we use this in the
+ 
+
+ align:start position:0%
+actually not new we use this in the
+previous unit on reacting gas systems
+
+ align:start position:0%
+previous unit on reacting gas systems
+ 
+
+ align:start position:0%
+previous unit on reacting gas systems
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+um we're gonna we're gonna really focus
+
+ align:start position:0%
+um we're gonna we're gonna really focus
+ 
+
+ align:start position:0%
+um we're gonna we're gonna really focus
+on this this is
+
+ align:start position:0%
+on this this is
+ 
+
+ align:start position:0%
+on this this is
+this Delta is now going to correspond
+
+ align:start position:0%
+this Delta is now going to correspond
+ 
+
+ align:start position:0%
+this Delta is now going to correspond
+to the mixing process
+
+ align:start position:0%
+to the mixing process
+ 
+
+ align:start position:0%
+to the mixing process
+so this is Delta for the mixing process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what is the Gibbs free energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of this mixing process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we know how to write that down now
+
+ align:start position:0%
+we know how to write that down now
+ 
+
+ align:start position:0%
+we know how to write that down now
+because we've sort of done the rudiments
+
+ align:start position:0%
+because we've sort of done the rudiments
+ 
+
+ align:start position:0%
+because we've sort of done the rudiments
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+solution modeling
+
+ align:start position:0%
+solution modeling
+ 
+
+ align:start position:0%
+solution modeling
+it's a sum
+
+ align:start position:0%
+it's a sum
+ 
+
+ align:start position:0%
+it's a sum
+weighted sum by molar mole fraction of
+
+ align:start position:0%
+weighted sum by molar mole fraction of
+ 
+
+ align:start position:0%
+weighted sum by molar mole fraction of
+the partial molar property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we just take from the previous board
+
+ align:start position:0%
+and we just take from the previous board
+ 
+
+ align:start position:0%
+and we just take from the previous board
+so what we're going to do is we we wrote
+
+ align:start position:0%
+so what we're going to do is we we wrote
+ 
+
+ align:start position:0%
+so what we're going to do is we we wrote
+down sorry about that we wrote down the
+
+ align:start position:0%
+down sorry about that we wrote down the
+ 
+
+ align:start position:0%
+down sorry about that we wrote down the
+partial molar properties the partial
+
+ align:start position:0%
+partial molar properties the partial
+ 
+
+ align:start position:0%
+partial molar properties the partial
+molar gives free energy that is the
+
+ align:start position:0%
+molar gives free energy that is the
+ 
+
+ align:start position:0%
+molar gives free energy that is the
+change of chemical potential with mixing
+
+ align:start position:0%
+change of chemical potential with mixing
+ 
+
+ align:start position:0%
+change of chemical potential with mixing
+and now we can write this using the sort
+
+ align:start position:0%
+and now we can write this using the sort
+ 
+
+ align:start position:0%
+and now we can write this using the sort
+of formalism that we already have seen
+
+ align:start position:0%
+of formalism that we already have seen
+ 
+
+ align:start position:0%
+of formalism that we already have seen
+so it's the sum of the mole fractions
+
+ align:start position:0%
+so it's the sum of the mole fractions
+ 
+
+ align:start position:0%
+so it's the sum of the mole fractions
+and the partial molar property and we
+
+ align:start position:0%
+and the partial molar property and we
+ 
+
+ align:start position:0%
+and the partial molar property and we
+just borrow from the previous slide this
+
+ align:start position:0%
+just borrow from the previous slide this
+ 
+
+ align:start position:0%
+just borrow from the previous slide this
+is x i r of t log P of I over p and
+
+ align:start position:0%
+is x i r of t log P of I over p and
+ 
+
+ align:start position:0%
+is x i r of t log P of I over p and
+we're going to use Dalton's rule to
+
+ align:start position:0%
+we're going to use Dalton's rule to
+ 
+
+ align:start position:0%
+we're going to use Dalton's rule to
+re-express the argument in the log as a
+
+ align:start position:0%
+re-express the argument in the log as a
+ 
+
+ align:start position:0%
+re-express the argument in the log as a
+mole fraction and so this is a solution
+
+ align:start position:0%
+mole fraction and so this is a solution
+ 
+
+ align:start position:0%
+mole fraction and so this is a solution
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+we've talked about solution models but
+
+ align:start position:0%
+we've talked about solution models but
+ 
+
+ align:start position:0%
+we've talked about solution models but
+we we haven't actually seen one written
+
+ align:start position:0%
+we we haven't actually seen one written
+ 
+
+ align:start position:0%
+we we haven't actually seen one written
+down mathematically before so this is
+
+ align:start position:0%
+down mathematically before so this is
+ 
+
+ align:start position:0%
+down mathematically before so this is
+one this is actually an important one so
+
+ align:start position:0%
+one this is actually an important one so
+ 
+
+ align:start position:0%
+one this is actually an important one so
+let's let's graph this and see what it
+
+ align:start position:0%
+let's let's graph this and see what it
+ 
+
+ align:start position:0%
+let's let's graph this and see what it
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+so I'm going to graph Delta G of mixing
+
+ align:start position:0%
+so I'm going to graph Delta G of mixing
+ 
+
+ align:start position:0%
+so I'm going to graph Delta G of mixing
+and the first thing is is that it's
+
+ align:start position:0%
+and the first thing is is that it's
+ 
+
+ align:start position:0%
+and the first thing is is that it's
+strictly negative
+
+ align:start position:0%
+strictly negative
+ 
+
+ align:start position:0%
+strictly negative
+and you can see that
+
+ align:start position:0%
+and you can see that
+ 
+
+ align:start position:0%
+and you can see that
+by the log expression both fractions are
+
+ align:start position:0%
+by the log expression both fractions are
+ 
+
+ align:start position:0%
+by the log expression both fractions are
+less than or equal to one
+
+ align:start position:0%
+less than or equal to one
+ 
+
+ align:start position:0%
+less than or equal to one
+so this this sum is less than or equal
+
+ align:start position:0%
+so this this sum is less than or equal
+ 
+
+ align:start position:0%
+so this this sum is less than or equal
+to zero and so
+
+ align:start position:0%
+to zero and so
+ 
+
+ align:start position:0%
+to zero and so
+um so that's that's an important thing
+
+ align:start position:0%
+um so that's that's an important thing
+ 
+
+ align:start position:0%
+um so that's that's an important thing
+to observe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have a family here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with increasing
+
+ align:start position:0%
+with increasing
+ 
+
+ align:start position:0%
+with increasing
+temp
+
+ align:start position:0%
+temp
+ 
+
+ align:start position:0%
+temp
+so the first thing to observe here is
+
+ align:start position:0%
+so the first thing to observe here is
+ 
+
+ align:start position:0%
+so the first thing to observe here is
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+there are very few parameters in this
+
+ align:start position:0%
+there are very few parameters in this
+ 
+
+ align:start position:0%
+there are very few parameters in this
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+this is the composition X of I
+
+ align:start position:0%
+this is the composition X of I
+ 
+
+ align:start position:0%
+this is the composition X of I
+and there's temperature and that's it so
+
+ align:start position:0%
+and there's temperature and that's it so
+ 
+
+ align:start position:0%
+and there's temperature and that's it so
+if I plotted the solution model versus
+
+ align:start position:0%
+if I plotted the solution model versus
+ 
+
+ align:start position:0%
+if I plotted the solution model versus
+composition I'm going to have a family
+
+ align:start position:0%
+composition I'm going to have a family
+ 
+
+ align:start position:0%
+composition I'm going to have a family
+of Curves in varying temperature
+
+ align:start position:0%
+of Curves in varying temperature
+ 
+
+ align:start position:0%
+of Curves in varying temperature
+and the way this is going to work is
+
+ align:start position:0%
+and the way this is going to work is
+ 
+
+ align:start position:0%
+and the way this is going to work is
+with increasing temperature Delta g mix
+
+ align:start position:0%
+with increasing temperature Delta g mix
+ 
+
+ align:start position:0%
+with increasing temperature Delta g mix
+gets more negative
+
+ align:start position:0%
+gets more negative
+ 
+
+ align:start position:0%
+gets more negative
+so we're going to note that
+
+ align:start position:0%
+so we're going to note that
+ 
+
+ align:start position:0%
+so we're going to note that
+note
+
+ align:start position:0%
+note
+ 
+
+ align:start position:0%
+note
+Delta G mixture
+
+ align:start position:0%
+Delta G mixture
+ 
+
+ align:start position:0%
+Delta G mixture
+is less than zero
+
+ align:start position:0%
+is less than zero
+ 
+
+ align:start position:0%
+is less than zero
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+D Squared
+
+ align:start position:0%
+D Squared
+ 
+
+ align:start position:0%
+D Squared
+Delta g mix
+
+ align:start position:0%
+Delta g mix
+ 
+
+ align:start position:0%
+Delta g mix
+dx2 squared
+
+ align:start position:0%
+dx2 squared
+ 
+
+ align:start position:0%
+dx2 squared
+is greater than zero
+
+ align:start position:0%
+is greater than zero
+ 
+
+ align:start position:0%
+is greater than zero
+everywhere
+
+ align:start position:0%
+everywhere
+ 
+
+ align:start position:0%
+everywhere
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that is it's negative and it's curved
+
+ align:start position:0%
+so that is it's negative and it's curved
+ 
+
+ align:start position:0%
+so that is it's negative and it's curved
+up everywhere
+
+ align:start position:0%
+up everywhere
+ 
+
+ align:start position:0%
+up everywhere
+and what we're going to see in a couple
+
+ align:start position:0%
+and what we're going to see in a couple
+ 
+
+ align:start position:0%
+and what we're going to see in a couple
+lectures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mathematically this ensures that the
+
+ align:start position:0%
+mathematically this ensures that the
+ 
+
+ align:start position:0%
+mathematically this ensures that the
+mixing is always spontaneous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which is good because we expect that to
+
+ align:start position:0%
+which is good because we expect that to
+ 
+
+ align:start position:0%
+which is good because we expect that to
+be the case for ideal gases mixing this
+
+ align:start position:0%
+be the case for ideal gases mixing this
+ 
+
+ align:start position:0%
+be the case for ideal gases mixing this
+goes back to the baby book right when
+
+ align:start position:0%
+goes back to the baby book right when
+ 
+
+ align:start position:0%
+goes back to the baby book right when
+you have these two populations of gas
+
+ align:start position:0%
+you have these two populations of gas
+ 
+
+ align:start position:0%
+you have these two populations of gas
+molecules and they don't interact with
+
+ align:start position:0%
+molecules and they don't interact with
+ 
+
+ align:start position:0%
+molecules and they don't interact with
+each other and you remove the barrier
+
+ align:start position:0%
+each other and you remove the barrier
+ 
+
+ align:start position:0%
+each other and you remove the barrier
+between them you expect them to mix
+
+ align:start position:0%
+between them you expect them to mix
+ 
+
+ align:start position:0%
+between them you expect them to mix
+spontaneously and that's what this map
+
+ align:start position:0%
+spontaneously and that's what this map
+ 
+
+ align:start position:0%
+spontaneously and that's what this map
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+enforcing
+
+ align:start position:0%
+enforcing
+ 
+
+ align:start position:0%
+enforcing
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so now what we're going to do is
+
+ align:start position:0%
+um so now what we're going to do is
+ 
+
+ align:start position:0%
+um so now what we're going to do is
+we're just going to abstract this a
+
+ align:start position:0%
+we're just going to abstract this a
+ 
+
+ align:start position:0%
+we're just going to abstract this a
+little bit and call everything we just
+
+ align:start position:0%
+little bit and call everything we just
+ 
+
+ align:start position:0%
+little bit and call everything we just
+did the ideal
+
+ align:start position:0%
+did the ideal
+ 
+
+ align:start position:0%
+did the ideal
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ideal solution model and we can
+
+ align:start position:0%
+the ideal solution model and we can
+ 
+
+ align:start position:0%
+the ideal solution model and we can
+write it down very compactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so this model it's motivated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motivated by or derived from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideal gas mixing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it approximates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a broader class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of real world systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is very typical in science you
+
+ align:start position:0%
+so this is very typical in science you
+ 
+
+ align:start position:0%
+so this is very typical in science you
+have some simple case you treat it as a
+
+ align:start position:0%
+have some simple case you treat it as a
+ 
+
+ align:start position:0%
+have some simple case you treat it as a
+model system
+
+ align:start position:0%
+model system
+ 
+
+ align:start position:0%
+model system
+you develop the model you study the
+
+ align:start position:0%
+you develop the model you study the
+ 
+
+ align:start position:0%
+you develop the model you study the
+model and then you say oh well maybe
+
+ align:start position:0%
+model and then you say oh well maybe
+ 
+
+ align:start position:0%
+model and then you say oh well maybe
+this model applies elsewhere maybe it
+
+ align:start position:0%
+this model applies elsewhere maybe it
+ 
+
+ align:start position:0%
+this model applies elsewhere maybe it
+does maybe it doesn't
+
+ align:start position:0%
+does maybe it doesn't
+ 
+
+ align:start position:0%
+does maybe it doesn't
+so here are some properties of the ideal
+
+ align:start position:0%
+so here are some properties of the ideal
+ 
+
+ align:start position:0%
+so here are some properties of the ideal
+solution model
+
+ align:start position:0%
+solution model
+ 
+
+ align:start position:0%
+solution model
+the partial molar entropy of mixing
+
+ align:start position:0%
+the partial molar entropy of mixing
+ 
+
+ align:start position:0%
+the partial molar entropy of mixing
+we can get this from the combined
+
+ align:start position:0%
+we can get this from the combined
+ 
+
+ align:start position:0%
+we can get this from the combined
+statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this derivative is really easy it's
+
+ align:start position:0%
+and this derivative is really easy it's
+ 
+
+ align:start position:0%
+and this derivative is really easy it's
+just a partial with temperature of this
+
+ align:start position:0%
+just a partial with temperature of this
+ 
+
+ align:start position:0%
+just a partial with temperature of this
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+and uh we have minus r
+
+ align:start position:0%
+and uh we have minus r
+ 
+
+ align:start position:0%
+and uh we have minus r
+l m x of I and this is everywhere
+
+ align:start position:0%
+l m x of I and this is everywhere
+ 
+
+ align:start position:0%
+l m x of I and this is everywhere
+positive that's good so entropy of
+
+ align:start position:0%
+positive that's good so entropy of
+ 
+
+ align:start position:0%
+positive that's good so entropy of
+mixing is positive
+
+ align:start position:0%
+mixing is positive
+ 
+
+ align:start position:0%
+mixing is positive
+another thing which we have the partial
+
+ align:start position:0%
+another thing which we have the partial
+ 
+
+ align:start position:0%
+another thing which we have the partial
+molar volume of mixing
+
+ align:start position:0%
+molar volume of mixing
+ 
+
+ align:start position:0%
+molar volume of mixing
+and again we get this from the combined
+
+ align:start position:0%
+and again we get this from the combined
+ 
+
+ align:start position:0%
+and again we get this from the combined
+statement going back to chapter 4 in the
+
+ align:start position:0%
+statement going back to chapter 4 in the
+ 
+
+ align:start position:0%
+statement going back to chapter 4 in the
+text
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+there's no pressure dependence here
+
+ align:start position:0%
+there's no pressure dependence here
+ 
+
+ align:start position:0%
+there's no pressure dependence here
+right there's no pressure dependence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this model so
+
+ align:start position:0%
+in this model so
+ 
+
+ align:start position:0%
+in this model so
+there's no volume of mixing that's good
+
+ align:start position:0%
+there's no volume of mixing that's good
+ 
+
+ align:start position:0%
+there's no volume of mixing that's good
+that's what we expected
+
+ align:start position:0%
+that's what we expected
+ 
+
+ align:start position:0%
+that's what we expected
+what about the enthalpy of mixing
+
+ align:start position:0%
+what about the enthalpy of mixing
+ 
+
+ align:start position:0%
+what about the enthalpy of mixing
+this is Delta Mu of I minus t
+
+ align:start position:0%
+this is Delta Mu of I minus t
+ 
+
+ align:start position:0%
+this is Delta Mu of I minus t
+Delta s of I
+
+ align:start position:0%
+Delta s of I
+ 
+
+ align:start position:0%
+Delta s of I
+going way back to the definition of our
+
+ align:start position:0%
+going way back to the definition of our
+ 
+
+ align:start position:0%
+going way back to the definition of our
+potentials and if you
+
+ align:start position:0%
+potentials and if you
+ 
+
+ align:start position:0%
+potentials and if you
+um write this out you see that zero
+
+ align:start position:0%
+um write this out you see that zero
+ 
+
+ align:start position:0%
+um write this out you see that zero
+and likewise the partial molar energy of
+
+ align:start position:0%
+and likewise the partial molar energy of
+ 
+
+ align:start position:0%
+and likewise the partial molar energy of
+mixing
+
+ align:start position:0%
+mixing
+ 
+
+ align:start position:0%
+mixing
+equals the partial molar enthalpy of
+
+ align:start position:0%
+equals the partial molar enthalpy of
+ 
+
+ align:start position:0%
+equals the partial molar enthalpy of
+mixing
+
+ align:start position:0%
+mixing
+ 
+
+ align:start position:0%
+mixing
+minus p and the partial molar volume of
+
+ align:start position:0%
+minus p and the partial molar volume of
+ 
+
+ align:start position:0%
+minus p and the partial molar volume of
+mixing and that's also zero
+
+ align:start position:0%
+mixing and that's also zero
+ 
+
+ align:start position:0%
+mixing and that's also zero
+so this is simply using the stuff which
+
+ align:start position:0%
+so this is simply using the stuff which
+ 
+
+ align:start position:0%
+so this is simply using the stuff which
+we did a couple of weeks ago
+
+ align:start position:0%
+we did a couple of weeks ago
+ 
+
+ align:start position:0%
+we did a couple of weeks ago
+definitions of these potentials
+
+ align:start position:0%
+definitions of these potentials
+ 
+
+ align:start position:0%
+definitions of these potentials
+and the combined statement of the first
+
+ align:start position:0%
+and the combined statement of the first
+ 
+
+ align:start position:0%
+and the combined statement of the first
+and second law and applying those
+
+ align:start position:0%
+and second law and applying those
+ 
+
+ align:start position:0%
+and second law and applying those
+operations to these quantities of mixing
+
+ align:start position:0%
+operations to these quantities of mixing
+ 
+
+ align:start position:0%
+operations to these quantities of mixing
+and I encourage you to work through
+
+ align:start position:0%
+and I encourage you to work through
+ 
+
+ align:start position:0%
+and I encourage you to work through
+these on your own and so the results
+
+ align:start position:0%
+these on your own and so the results
+ 
+
+ align:start position:0%
+these on your own and so the results
+here are are what we want that's what we
+
+ align:start position:0%
+here are are what we want that's what we
+ 
+
+ align:start position:0%
+here are are what we want that's what we
+want to see what the entropy increases
+
+ align:start position:0%
+want to see what the entropy increases
+ 
+
+ align:start position:0%
+want to see what the entropy increases
+on mixing so this is a process
+
+ align:start position:0%
+on mixing so this is a process
+ 
+
+ align:start position:0%
+on mixing so this is a process
+driven
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by entropy increase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is um you know we postulated that
+
+ align:start position:0%
+which is um you know we postulated that
+ 
+
+ align:start position:0%
+which is um you know we postulated that
+back in lecture one with the baby book
+
+ align:start position:0%
+back in lecture one with the baby book
+ 
+
+ align:start position:0%
+back in lecture one with the baby book
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+there is no volume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of mixing
+
+ align:start position:0%
+of mixing
+ 
+
+ align:start position:0%
+of mixing
+for ideal Solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the final volume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is some
+
+ align:start position:0%
+is some
+ 
+
+ align:start position:0%
+is some
+of pure component contributions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's good
+
+ align:start position:0%
+that's good
+ 
+
+ align:start position:0%
+that's good
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there are no interactions
+
+ align:start position:0%
+there are no interactions
+ 
+
+ align:start position:0%
+there are no interactions
+between molecules
+
+ align:start position:0%
+between molecules
+ 
+
+ align:start position:0%
+between molecules
+right that was a
+
+ align:start position:0%
+right that was a
+ 
+
+ align:start position:0%
+right that was a
+that was the foundation of the ideal gas
+
+ align:start position:0%
+that was the foundation of the ideal gas
+ 
+
+ align:start position:0%
+that was the foundation of the ideal gas
+molecule right
+
+ align:start position:0%
+molecule right
+ 
+
+ align:start position:0%
+molecule right
+no bonds
+
+ align:start position:0%
+no bonds
+ 
+
+ align:start position:0%
+no bonds
+made
+
+ align:start position:0%
+made
+ 
+
+ align:start position:0%
+made
+or broken
+
+ align:start position:0%
+or broken
+ 
+
+ align:start position:0%
+or broken
+by the mixing process
+
+ align:start position:0%
+by the mixing process
+ 
+
+ align:start position:0%
+by the mixing process
+no change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in enthalpy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we're seeing here is again what
+
+ align:start position:0%
+so what we're seeing here is again what
+ 
+
+ align:start position:0%
+so what we're seeing here is again what
+what we intuitively have have known now
+
+ align:start position:0%
+what we intuitively have have known now
+ 
+
+ align:start position:0%
+what we intuitively have have known now
+for weeks
+
+ align:start position:0%
+for weeks
+ 
+
+ align:start position:0%
+for weeks
+we're just seeing it in this
+
+ align:start position:0%
+we're just seeing it in this
+ 
+
+ align:start position:0%
+we're just seeing it in this
+formalism okay so this is the ideal
+
+ align:start position:0%
+formalism okay so this is the ideal
+ 
+
+ align:start position:0%
+formalism okay so this is the ideal
+solution model great let's move on
+
+ align:start position:0%
+solution model great let's move on
+ 
+
+ align:start position:0%
+solution model great let's move on
+I have a quick question sorry is there a
+
+ align:start position:0%
+I have a quick question sorry is there a
+ 
+
+ align:start position:0%
+I have a quick question sorry is there a
+reason why we write the bar for entropy
+
+ align:start position:0%
+reason why we write the bar for entropy
+ 
+
+ align:start position:0%
+reason why we write the bar for entropy
+enthalpy Etc but then we don't write the
+
+ align:start position:0%
+enthalpy Etc but then we don't write the
+ 
+
+ align:start position:0%
+enthalpy Etc but then we don't write the
+bar for the Muse for the the chemical
+
+ align:start position:0%
+bar for the Muse for the the chemical
+ 
+
+ align:start position:0%
+bar for the Muse for the the chemical
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah gives a special and the reason
+
+ align:start position:0%
+yeah gives a special and the reason
+ 
+
+ align:start position:0%
+yeah gives a special and the reason
+um the chemical potential is the partial
+
+ align:start position:0%
+um the chemical potential is the partial
+ 
+
+ align:start position:0%
+um the chemical potential is the partial
+molar gives free energy
+
+ align:start position:0%
+molar gives free energy
+ 
+
+ align:start position:0%
+molar gives free energy
+we don't have a special term for partial
+
+ align:start position:0%
+we don't have a special term for partial
+ 
+
+ align:start position:0%
+we don't have a special term for partial
+molar entropy partial molar volume
+
+ align:start position:0%
+molar entropy partial molar volume
+ 
+
+ align:start position:0%
+molar entropy partial molar volume
+partial molar H and partial molar U
+
+ align:start position:0%
+partial molar H and partial molar U
+ 
+
+ align:start position:0%
+partial molar H and partial molar U
+it's just historically there's not I
+
+ align:start position:0%
+it's just historically there's not I
+ 
+
+ align:start position:0%
+it's just historically there's not I
+mean you could imagine coming up with
+
+ align:start position:0%
+mean you could imagine coming up with
+ 
+
+ align:start position:0%
+mean you could imagine coming up with
+new words and using different Greek
+
+ align:start position:0%
+new words and using different Greek
+ 
+
+ align:start position:0%
+new words and using different Greek
+letters
+
+ align:start position:0%
+letters
+ 
+
+ align:start position:0%
+letters
+um but Gibbs is so important that the
+
+ align:start position:0%
+um but Gibbs is so important that the
+ 
+
+ align:start position:0%
+um but Gibbs is so important that the
+partial molar gives free energy has been
+
+ align:start position:0%
+partial molar gives free energy has been
+ 
+
+ align:start position:0%
+partial molar gives free energy has been
+named chemical potential and so it's
+
+ align:start position:0%
+named chemical potential and so it's
+ 
+
+ align:start position:0%
+named chemical potential and so it's
+special
+
+ align:start position:0%
+special
+ 
+
+ align:start position:0%
+special
+good question okay thank you yeah gives
+
+ align:start position:0%
+good question okay thank you yeah gives
+ 
+
+ align:start position:0%
+good question okay thank you yeah gives
+a special
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so what happens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if the molecules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do interact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happens if we're not mixing ideal
+
+ align:start position:0%
+what happens if we're not mixing ideal
+ 
+
+ align:start position:0%
+what happens if we're not mixing ideal
+gases
+
+ align:start position:0%
+gases
+ 
+
+ align:start position:0%
+gases
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we want to capture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the deviation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want to capture the deviation from
+
+ align:start position:0%
+we want to capture the deviation from
+ 
+
+ align:start position:0%
+we want to capture the deviation from
+the ideal model
+
+ align:start position:0%
+the ideal model
+ 
+
+ align:start position:0%
+the ideal model
+and what you're about to see is a very
+
+ align:start position:0%
+and what you're about to see is a very
+ 
+
+ align:start position:0%
+and what you're about to see is a very
+um familiar thermo thing
+
+ align:start position:0%
+um familiar thermo thing
+ 
+
+ align:start position:0%
+um familiar thermo thing
+which is more bookkeeping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your pattern recognition might start
+
+ align:start position:0%
+your pattern recognition might start
+ 
+
+ align:start position:0%
+your pattern recognition might start
+kicking in soon that this is a thermal
+
+ align:start position:0%
+kicking in soon that this is a thermal
+ 
+
+ align:start position:0%
+kicking in soon that this is a thermal
+thing this is what thermodynamics does
+
+ align:start position:0%
+thing this is what thermodynamics does
+ 
+
+ align:start position:0%
+thing this is what thermodynamics does
+we let
+
+ align:start position:0%
+we let
+ 
+
+ align:start position:0%
+we let
+Delta Mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals RT
+
+ align:start position:0%
+equals RT
+ 
+
+ align:start position:0%
+equals RT
+log of a of I
+
+ align:start position:0%
+log of a of I
+ 
+
+ align:start position:0%
+log of a of I
+I'm going to introduce that in a second
+
+ align:start position:0%
+I'm going to introduce that in a second
+ 
+
+ align:start position:0%
+I'm going to introduce that in a second
+equals RT log gamma of i x of I and just
+
+ align:start position:0%
+equals RT log gamma of i x of I and just
+ 
+
+ align:start position:0%
+equals RT log gamma of i x of I and just
+bear with me these are just definitions
+
+ align:start position:0%
+bear with me these are just definitions
+ 
+
+ align:start position:0%
+bear with me these are just definitions
+a i is being defined as the activity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and it's further defined by
+
+ align:start position:0%
+all right and it's further defined by
+ 
+
+ align:start position:0%
+all right and it's further defined by
+this product of gamma of I and X of I
+
+ align:start position:0%
+this product of gamma of I and X of I
+ 
+
+ align:start position:0%
+this product of gamma of I and X of I
+and Gamma of I is known as the activity
+
+ align:start position:0%
+and Gamma of I is known as the activity
+ 
+
+ align:start position:0%
+and Gamma of I is known as the activity
+coefficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of component I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and why do they do this to us right what
+
+ align:start position:0%
+and why do they do this to us right what
+ 
+
+ align:start position:0%
+and why do they do this to us right what
+is with all these terms
+
+ align:start position:0%
+is with all these terms
+ 
+
+ align:start position:0%
+is with all these terms
+if we rewrite Delta G of mixing in terms
+
+ align:start position:0%
+if we rewrite Delta G of mixing in terms
+ 
+
+ align:start position:0%
+if we rewrite Delta G of mixing in terms
+of these activities and activity
+
+ align:start position:0%
+of these activities and activity
+ 
+
+ align:start position:0%
+of these activities and activity
+coefficients let me just
+
+ align:start position:0%
+coefficients let me just
+ 
+
+ align:start position:0%
+coefficients let me just
+pull what we know to be the case this is
+
+ align:start position:0%
+pull what we know to be the case this is
+ 
+
+ align:start position:0%
+pull what we know to be the case this is
+X of I
+
+ align:start position:0%
+X of I
+ 
+
+ align:start position:0%
+X of I
+Delta Mu of I
+
+ align:start position:0%
+Delta Mu of I
+ 
+
+ align:start position:0%
+Delta Mu of I
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+product by X of I RT
+
+ align:start position:0%
+product by X of I RT
+ 
+
+ align:start position:0%
+product by X of I RT
+log gamma by X of I and we're going to
+
+ align:start position:0%
+log gamma by X of I and we're going to
+ 
+
+ align:start position:0%
+log gamma by X of I and we're going to
+use the property of the log function and
+
+ align:start position:0%
+use the property of the log function and
+ 
+
+ align:start position:0%
+use the property of the log function and
+we're going to see that this
+
+ align:start position:0%
+we're going to see that this
+ 
+
+ align:start position:0%
+we're going to see that this
+turns into
+
+ align:start position:0%
+turns into
+ 
+
+ align:start position:0%
+turns into
+X of i r t log X of I Plus
+
+ align:start position:0%
+X of i r t log X of I Plus
+ 
+
+ align:start position:0%
+X of i r t log X of I Plus
+X of I RT log gamma via so the reason
+
+ align:start position:0%
+X of I RT log gamma via so the reason
+ 
+
+ align:start position:0%
+X of I RT log gamma via so the reason
+why they do this to us is because when
+
+ align:start position:0%
+why they do this to us is because when
+ 
+
+ align:start position:0%
+why they do this to us is because when
+we model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Solutions in this particular way
+
+ align:start position:0%
+Solutions in this particular way
+ 
+
+ align:start position:0%
+Solutions in this particular way
+we have this neat separation between
+
+ align:start position:0%
+we have this neat separation between
+ 
+
+ align:start position:0%
+we have this neat separation between
+the uh ideal case
+
+ align:start position:0%
+the uh ideal case
+ 
+
+ align:start position:0%
+the uh ideal case
+and deviations from ideal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deviation
+
+ align:start position:0%
+deviation
+ 
+
+ align:start position:0%
+deviation
+for my deal
+
+ align:start position:0%
+for my deal
+ 
+
+ align:start position:0%
+for my deal
+and we can see that
+
+ align:start position:0%
+and we can see that
+ 
+
+ align:start position:0%
+and we can see that
+non ideal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Behavior
+
+ align:start position:0%
+Behavior
+ 
+
+ align:start position:0%
+Behavior
+is captured
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by gamma of I
+
+ align:start position:0%
+by gamma of I
+ 
+
+ align:start position:0%
+by gamma of I
+not equal
+
+ align:start position:0%
+not equal
+ 
+
+ align:start position:0%
+not equal
+to one
+
+ align:start position:0%
+to one
+ 
+
+ align:start position:0%
+to one
+so if you have ideal Solutions ideal
+
+ align:start position:0%
+so if you have ideal Solutions ideal
+ 
+
+ align:start position:0%
+so if you have ideal Solutions ideal
+Behavior
+
+ align:start position:0%
+Behavior
+ 
+
+ align:start position:0%
+Behavior
+the activity coefficients of all the
+
+ align:start position:0%
+the activity coefficients of all the
+ 
+
+ align:start position:0%
+the activity coefficients of all the
+components is one and this thing which
+
+ align:start position:0%
+components is one and this thing which
+ 
+
+ align:start position:0%
+components is one and this thing which
+we called activity is just equal to the
+
+ align:start position:0%
+we called activity is just equal to the
+ 
+
+ align:start position:0%
+we called activity is just equal to the
+mole fraction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if the solution does not behave
+
+ align:start position:0%
+and if the solution does not behave
+ 
+
+ align:start position:0%
+and if the solution does not behave
+ideally if it deviates
+
+ align:start position:0%
+ideally if it deviates
+ 
+
+ align:start position:0%
+ideally if it deviates
+we just dump that deviation into this
+
+ align:start position:0%
+we just dump that deviation into this
+ 
+
+ align:start position:0%
+we just dump that deviation into this
+term over here
+
+ align:start position:0%
+term over here
+ 
+
+ align:start position:0%
+term over here
+and we say it's captured by these
+
+ align:start position:0%
+and we say it's captured by these
+ 
+
+ align:start position:0%
+and we say it's captured by these
+activity coefficients being left not
+
+ align:start position:0%
+activity coefficients being left not
+ 
+
+ align:start position:0%
+activity coefficients being left not
+equal to one
+
+ align:start position:0%
+equal to one
+ 
+
+ align:start position:0%
+equal to one
+and uh we can figure out what they are
+
+ align:start position:0%
+and uh we can figure out what they are
+ 
+
+ align:start position:0%
+and uh we can figure out what they are
+later right so
+
+ align:start position:0%
+later right so
+ 
+
+ align:start position:0%
+later right so
+um again uh just a bookkeeping exercise
+
+ align:start position:0%
+um again uh just a bookkeeping exercise
+ 
+
+ align:start position:0%
+um again uh just a bookkeeping exercise
+at this point
+
+ align:start position:0%
+at this point
+ 
+
+ align:start position:0%
+at this point
+and also introducing essential terms now
+
+ align:start position:0%
+and also introducing essential terms now
+ 
+
+ align:start position:0%
+and also introducing essential terms now
+this um this activity
+
+ align:start position:0%
+this um this activity
+ 
+
+ align:start position:0%
+this um this activity
+uh if you're in course 10
+
+ align:start position:0%
+uh if you're in course 10
+ 
+
+ align:start position:0%
+uh if you're in course 10
+this is equal to fugacity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean that's not exactly true for gas
+
+ align:start position:0%
+I mean that's not exactly true for gas
+ 
+
+ align:start position:0%
+I mean that's not exactly true for gas
+City sort of activity in certain cases
+
+ align:start position:0%
+City sort of activity in certain cases
+ 
+
+ align:start position:0%
+City sort of activity in certain cases
+but anyway
+
+ align:start position:0%
+but anyway
+ 
+
+ align:start position:0%
+but anyway
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you've heard that term fugacity or
+
+ align:start position:0%
+if you've heard that term fugacity or
+ 
+
+ align:start position:0%
+if you've heard that term fugacity or
+you wondered what it was when you were
+
+ align:start position:0%
+you wondered what it was when you were
+ 
+
+ align:start position:0%
+you wondered what it was when you were
+reading the the Denby book um here
+
+ align:start position:0%
+reading the the Denby book um here
+ 
+
+ align:start position:0%
+reading the the Denby book um here
+effectively we have it it's the activity
+
+ align:start position:0%
+effectively we have it it's the activity
+ 
+
+ align:start position:0%
+effectively we have it it's the activity
+and um right okay so we now have this
+
+ align:start position:0%
+and um right okay so we now have this
+ 
+
+ align:start position:0%
+and um right okay so we now have this
+mathematical framework
+
+ align:start position:0%
+mathematical framework
+ 
+
+ align:start position:0%
+mathematical framework
+to capture non-ideal behavior and so
+
+ align:start position:0%
+to capture non-ideal behavior and so
+ 
+
+ align:start position:0%
+to capture non-ideal behavior and so
+what we're going to do next is
+
+ align:start position:0%
+what we're going to do next is
+ 
+
+ align:start position:0%
+what we're going to do next is
+introduce two solution models
+
+ align:start position:0%
+introduce two solution models
+ 
+
+ align:start position:0%
+introduce two solution models
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+for non-ideal Solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first one is going to be
+
+ align:start position:0%
+the first one is going to be
+ 
+
+ align:start position:0%
+the first one is going to be
+the dilute
+
+ align:start position:0%
+the dilute
+ 
+
+ align:start position:0%
+the dilute
+solution model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the dilute model
+
+ align:start position:0%
+okay so this is the dilute model
+ 
+
+ align:start position:0%
+okay so this is the dilute model
+it's based on some physical reasoning
+
+ align:start position:0%
+it's based on some physical reasoning
+ 
+
+ align:start position:0%
+it's based on some physical reasoning
+which is always a relief
+
+ align:start position:0%
+which is always a relief
+ 
+
+ align:start position:0%
+which is always a relief
+after all this math
+
+ align:start position:0%
+after all this math
+ 
+
+ align:start position:0%
+after all this math
+so we have
+
+ align:start position:0%
+so we have
+ 
+
+ align:start position:0%
+so we have
+solvent
+
+ align:start position:0%
+solvent
+ 
+
+ align:start position:0%
+solvent
+and solute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um what does dilute mean right not
+
+ align:start position:0%
+um what does dilute mean right not
+ 
+
+ align:start position:0%
+um what does dilute mean right not
+concentrated so these are the
+
+ align:start position:0%
+concentrated so these are the
+ 
+
+ align:start position:0%
+concentrated so these are the
+assumptions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to make two assumptions
+
+ align:start position:0%
+we're going to make two assumptions
+ 
+
+ align:start position:0%
+we're going to make two assumptions
+about these physical systems one
+
+ align:start position:0%
+about these physical systems one
+ 
+
+ align:start position:0%
+about these physical systems one
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+each solute molecule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is surrounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by solvent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and solute
+
+ align:start position:0%
+and solute
+ 
+
+ align:start position:0%
+and solute
+solute
+
+ align:start position:0%
+solute
+ 
+
+ align:start position:0%
+solute
+interactions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are negligible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so this has physical implications
+
+ align:start position:0%
+um so this has physical implications
+ 
+
+ align:start position:0%
+um so this has physical implications
+this is like
+
+ align:start position:0%
+this is like
+ 
+
+ align:start position:0%
+this is like
+um someone drops you in the middle of
+
+ align:start position:0%
+um someone drops you in the middle of
+ 
+
+ align:start position:0%
+um someone drops you in the middle of
+the woods very very very far
+
+ align:start position:0%
+the woods very very very far
+ 
+
+ align:start position:0%
+the woods very very very far
+uh from civilization
+
+ align:start position:0%
+uh from civilization
+ 
+
+ align:start position:0%
+uh from civilization
+and and you start acting the way you do
+
+ align:start position:0%
+and and you start acting the way you do
+ 
+
+ align:start position:0%
+and and you start acting the way you do
+when there's no one else around and
+
+ align:start position:0%
+when there's no one else around and
+ 
+
+ align:start position:0%
+when there's no one else around and
+there's not a chance of you running into
+
+ align:start position:0%
+there's not a chance of you running into
+ 
+
+ align:start position:0%
+there's not a chance of you running into
+somebody and however you act that's up
+
+ align:start position:0%
+somebody and however you act that's up
+ 
+
+ align:start position:0%
+somebody and however you act that's up
+to you but this is the point you are
+
+ align:start position:0%
+to you but this is the point you are
+ 
+
+ align:start position:0%
+to you but this is the point you are
+acting as if there's not another soul
+
+ align:start position:0%
+acting as if there's not another soul
+ 
+
+ align:start position:0%
+acting as if there's not another soul
+on Earth
+
+ align:start position:0%
+on Earth
+ 
+
+ align:start position:0%
+on Earth
+right you're in the middle of the woods
+
+ align:start position:0%
+right you're in the middle of the woods
+ 
+
+ align:start position:0%
+right you're in the middle of the woods
+and now let's say that somebody else
+
+ align:start position:0%
+and now let's say that somebody else
+ 
+
+ align:start position:0%
+and now let's say that somebody else
+gets dropped into the same Woods 10
+
+ align:start position:0%
+gets dropped into the same Woods 10
+ 
+
+ align:start position:0%
+gets dropped into the same Woods 10
+miles away
+
+ align:start position:0%
+miles away
+ 
+
+ align:start position:0%
+miles away
+all right that person will also act as
+
+ align:start position:0%
+all right that person will also act as
+ 
+
+ align:start position:0%
+all right that person will also act as
+if there's not another soul on Earth
+
+ align:start position:0%
+if there's not another soul on Earth
+ 
+
+ align:start position:0%
+if there's not another soul on Earth
+however they act
+
+ align:start position:0%
+however they act
+ 
+
+ align:start position:0%
+however they act
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if we populate the woods in this very
+
+ align:start position:0%
+if we populate the woods in this very
+ 
+
+ align:start position:0%
+if we populate the woods in this very
+dilute way where there's not anybody you
+
+ align:start position:0%
+dilute way where there's not anybody you
+ 
+
+ align:start position:0%
+dilute way where there's not anybody you
+know within miles and miles and miles of
+
+ align:start position:0%
+know within miles and miles and miles of
+ 
+
+ align:start position:0%
+know within miles and miles and miles of
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+then each individual person will act as
+
+ align:start position:0%
+then each individual person will act as
+ 
+
+ align:start position:0%
+then each individual person will act as
+if they're the only person in those
+
+ align:start position:0%
+if they're the only person in those
+ 
+
+ align:start position:0%
+if they're the only person in those
+woods
+
+ align:start position:0%
+woods
+ 
+
+ align:start position:0%
+woods
+until we get to a point when they start
+
+ align:start position:0%
+until we get to a point when they start
+ 
+
+ align:start position:0%
+until we get to a point when they start
+becoming aware of each other
+
+ align:start position:0%
+becoming aware of each other
+ 
+
+ align:start position:0%
+becoming aware of each other
+right and just as you might if it's for
+
+ align:start position:0%
+right and just as you might if it's for
+ 
+
+ align:start position:0%
+right and just as you might if it's for
+you in the woods if you started becoming
+
+ align:start position:0%
+you in the woods if you started becoming
+ 
+
+ align:start position:0%
+you in the woods if you started becoming
+aware of somebody else where before you
+
+ align:start position:0%
+aware of somebody else where before you
+ 
+
+ align:start position:0%
+aware of somebody else where before you
+didn't think there would be anyone else
+
+ align:start position:0%
+didn't think there would be anyone else
+ 
+
+ align:start position:0%
+didn't think there would be anyone else
+your behavior might change a little bit
+
+ align:start position:0%
+your behavior might change a little bit
+ 
+
+ align:start position:0%
+your behavior might change a little bit
+it's the same with dilute Solutions
+
+ align:start position:0%
+it's the same with dilute Solutions
+ 
+
+ align:start position:0%
+it's the same with dilute Solutions
+we're in the dilute limit when each
+
+ align:start position:0%
+we're in the dilute limit when each
+ 
+
+ align:start position:0%
+we're in the dilute limit when each
+solute is acting as if it's the only one
+
+ align:start position:0%
+solute is acting as if it's the only one
+ 
+
+ align:start position:0%
+solute is acting as if it's the only one
+completely surrounded by solvent and all
+
+ align:start position:0%
+completely surrounded by solvent and all
+ 
+
+ align:start position:0%
+completely surrounded by solvent and all
+of its thermodynamics are dominated by
+
+ align:start position:0%
+of its thermodynamics are dominated by
+ 
+
+ align:start position:0%
+of its thermodynamics are dominated by
+solute solvent interactions so that's
+
+ align:start position:0%
+solute solvent interactions so that's
+ 
+
+ align:start position:0%
+solute solvent interactions so that's
+the first assumption the second
+
+ align:start position:0%
+the first assumption the second
+ 
+
+ align:start position:0%
+the first assumption the second
+assumption is that
+
+ align:start position:0%
+assumption is that
+ 
+
+ align:start position:0%
+assumption is that
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+solvent
+
+ align:start position:0%
+solvent
+ 
+
+ align:start position:0%
+solvent
+molecule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is surrounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by pure solvent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Act
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+a pure substance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a little bit harder to
+
+ align:start position:0%
+so this is a little bit harder to
+ 
+
+ align:start position:0%
+so this is a little bit harder to
+justify
+
+ align:start position:0%
+justify
+ 
+
+ align:start position:0%
+justify
+and actually on the pset we ask you to
+
+ align:start position:0%
+and actually on the pset we ask you to
+ 
+
+ align:start position:0%
+and actually on the pset we ask you to
+uh take this and justify this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we don't put it that way we'll we'll
+
+ align:start position:0%
+we don't put it that way we'll we'll
+ 
+
+ align:start position:0%
+we don't put it that way we'll we'll
+cover that in you know three minutes but
+
+ align:start position:0%
+cover that in you know three minutes but
+ 
+
+ align:start position:0%
+cover that in you know three minutes but
+effectively what you're you're asked to
+
+ align:start position:0%
+effectively what you're you're asked to
+ 
+
+ align:start position:0%
+effectively what you're you're asked to
+show on the pizza is that given this
+
+ align:start position:0%
+show on the pizza is that given this
+ 
+
+ align:start position:0%
+show on the pizza is that given this
+this follows
+
+ align:start position:0%
+this follows
+ 
+
+ align:start position:0%
+this follows
+um so yeah there's some solvent
+
+ align:start position:0%
+um so yeah there's some solvent
+ 
+
+ align:start position:0%
+um so yeah there's some solvent
+molecules here that are near solute and
+
+ align:start position:0%
+molecules here that are near solute and
+ 
+
+ align:start position:0%
+molecules here that are near solute and
+yeah they know that they're soluble but
+
+ align:start position:0%
+yeah they know that they're soluble but
+ 
+
+ align:start position:0%
+yeah they know that they're soluble but
+if you averaged over all the solvent
+
+ align:start position:0%
+if you averaged over all the solvent
+ 
+
+ align:start position:0%
+if you averaged over all the solvent
+molecules the average solvent molecule
+
+ align:start position:0%
+molecules the average solvent molecule
+ 
+
+ align:start position:0%
+molecules the average solvent molecule
+is surrounded also by only solvent
+
+ align:start position:0%
+is surrounded also by only solvent
+ 
+
+ align:start position:0%
+is surrounded also by only solvent
+molecules so these are the physical
+
+ align:start position:0%
+molecules so these are the physical
+ 
+
+ align:start position:0%
+molecules so these are the physical
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+and um so here the mathematical
+
+ align:start position:0%
+and um so here the mathematical
+ 
+
+ align:start position:0%
+and um so here the mathematical
+implications of that so assumption
+
+ align:start position:0%
+implications of that so assumption
+ 
+
+ align:start position:0%
+implications of that so assumption
+number one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leads to
+
+ align:start position:0%
+leads to
+ 
+
+ align:start position:0%
+leads to
+something called Henry's law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Henry's law
+
+ align:start position:0%
+Henry's law
+ 
+
+ align:start position:0%
+Henry's law
+of the solute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's the following
+
+ align:start position:0%
+and that's the following
+ 
+
+ align:start position:0%
+and that's the following
+in the limit
+
+ align:start position:0%
+in the limit
+ 
+
+ align:start position:0%
+in the limit
+of mole fraction X2 going to zero
+
+ align:start position:0%
+of mole fraction X2 going to zero
+ 
+
+ align:start position:0%
+of mole fraction X2 going to zero
+so the second component here is the
+
+ align:start position:0%
+so the second component here is the
+ 
+
+ align:start position:0%
+so the second component here is the
+solute
+
+ align:start position:0%
+solute
+ 
+
+ align:start position:0%
+solute
+the activity
+
+ align:start position:0%
+the activity
+ 
+
+ align:start position:0%
+the activity
+of component two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approaches
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this quantity
+
+ align:start position:0%
+this quantity
+ 
+
+ align:start position:0%
+this quantity
+where gamma 2 naught is called Henry's
+
+ align:start position:0%
+where gamma 2 naught is called Henry's
+ 
+
+ align:start position:0%
+where gamma 2 naught is called Henry's
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this mathematical form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+results in
+
+ align:start position:0%
+results in
+ 
+
+ align:start position:0%
+results in
+what we want which is that
+
+ align:start position:0%
+what we want which is that
+ 
+
+ align:start position:0%
+what we want which is that
+thermodynamically each additional solute
+
+ align:start position:0%
+thermodynamically each additional solute
+ 
+
+ align:start position:0%
+thermodynamically each additional solute
+molecule thinks it's the only one in the
+
+ align:start position:0%
+molecule thinks it's the only one in the
+ 
+
+ align:start position:0%
+molecule thinks it's the only one in the
+forest okay
+
+ align:start position:0%
+forest okay
+ 
+
+ align:start position:0%
+forest okay
+assumption number two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has the following implication
+
+ align:start position:0%
+has the following implication
+ 
+
+ align:start position:0%
+has the following implication
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+Raul's law
+
+ align:start position:0%
+Raul's law
+ 
+
+ align:start position:0%
+Raul's law
+of the solvent
+
+ align:start position:0%
+of the solvent
+ 
+
+ align:start position:0%
+of the solvent
+and Raul's law of the solvent
+
+ align:start position:0%
+and Raul's law of the solvent
+ 
+
+ align:start position:0%
+and Raul's law of the solvent
+is that the limit of X1 going to one
+
+ align:start position:0%
+is that the limit of X1 going to one
+ 
+
+ align:start position:0%
+is that the limit of X1 going to one
+that is the solvent becoming
+
+ align:start position:0%
+that is the solvent becoming
+ 
+
+ align:start position:0%
+that is the solvent becoming
+increasingly concentrated the activity
+
+ align:start position:0%
+increasingly concentrated the activity
+ 
+
+ align:start position:0%
+increasingly concentrated the activity
+is simply equal to the mole fraction
+
+ align:start position:0%
+is simply equal to the mole fraction
+ 
+
+ align:start position:0%
+is simply equal to the mole fraction
+okay so these are Henry and her old I I
+
+ align:start position:0%
+okay so these are Henry and her old I I
+ 
+
+ align:start position:0%
+okay so these are Henry and her old I I
+don't know whether they were
+
+ align:start position:0%
+don't know whether they were
+ 
+
+ align:start position:0%
+don't know whether they were
+contemporaries whether they were BFFs or
+
+ align:start position:0%
+contemporaries whether they were BFFs or
+ 
+
+ align:start position:0%
+contemporaries whether they were BFFs or
+or whatnot and I have a really hard time
+
+ align:start position:0%
+or whatnot and I have a really hard time
+ 
+
+ align:start position:0%
+or whatnot and I have a really hard time
+remembering which one is which
+
+ align:start position:0%
+remembering which one is which
+ 
+
+ align:start position:0%
+remembering which one is which
+um just a note for the pset
+
+ align:start position:0%
+um just a note for the pset
+ 
+
+ align:start position:0%
+um just a note for the pset
+this can
+
+ align:start position:0%
+this can
+ 
+
+ align:start position:0%
+this can
+be derived
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from Henry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+via
+
+ align:start position:0%
+via
+ 
+
+ align:start position:0%
+via
+Gibbs do him integration
+
+ align:start position:0%
+Gibbs do him integration
+ 
+
+ align:start position:0%
+Gibbs do him integration
+which is discussed in detail
+
+ align:start position:0%
+which is discussed in detail
+ 
+
+ align:start position:0%
+which is discussed in detail
+in section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+8.2.3 okay so that's relevant for the
+
+ align:start position:0%
+8.2.3 okay so that's relevant for the
+ 
+
+ align:start position:0%
+8.2.3 okay so that's relevant for the
+preset
+
+ align:start position:0%
+preset
+ 
+
+ align:start position:0%
+preset
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're also out of the solvent and the
+
+ align:start position:0%
+we're also out of the solvent and the
+ 
+
+ align:start position:0%
+we're also out of the solvent and the
+result of the solute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let's plot how those look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+of activity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with composition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it could
+
+ align:start position:0%
+it could
+ 
+
+ align:start position:0%
+it could
+look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like this this is an example
+
+ align:start position:0%
+like this this is an example
+ 
+
+ align:start position:0%
+like this this is an example
+and I'm just going to copy
+
+ align:start position:0%
+and I'm just going to copy
+ 
+
+ align:start position:0%
+and I'm just going to copy
+this figure from the Hoff
+
+ align:start position:0%
+this figure from the Hoff
+ 
+
+ align:start position:0%
+this figure from the Hoff
+figure 8.4 because I think it's useful
+
+ align:start position:0%
+figure 8.4 because I think it's useful
+ 
+
+ align:start position:0%
+figure 8.4 because I think it's useful
+so I'm about to copy here
+
+ align:start position:0%
+so I'm about to copy here
+ 
+
+ align:start position:0%
+so I'm about to copy here
+all right so it could look like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I'm trying to plot here
+
+ align:start position:0%
+what I'm trying to plot here
+ 
+
+ align:start position:0%
+what I'm trying to plot here
+is as a function of X of 2
+
+ align:start position:0%
+is as a function of X of 2
+ 
+
+ align:start position:0%
+is as a function of X of 2
+the activity of the first component and
+
+ align:start position:0%
+the activity of the first component and
+ 
+
+ align:start position:0%
+the activity of the first component and
+the activity of the second line so this
+
+ align:start position:0%
+the activity of the second line so this
+ 
+
+ align:start position:0%
+the activity of the second line so this
+goes between zero and one this goes
+
+ align:start position:0%
+goes between zero and one this goes
+ 
+
+ align:start position:0%
+goes between zero and one this goes
+between zero and one
+
+ align:start position:0%
+between zero and one
+ 
+
+ align:start position:0%
+between zero and one
+this on this plot goes between zero and
+
+ align:start position:0%
+this on this plot goes between zero and
+ 
+
+ align:start position:0%
+this on this plot goes between zero and
+one it doesn't have to you can have two
+
+ align:start position:0%
+one it doesn't have to you can have two
+ 
+
+ align:start position:0%
+one it doesn't have to you can have two
+you can have activities greater than one
+
+ align:start position:0%
+you can have activities greater than one
+ 
+
+ align:start position:0%
+you can have activities greater than one
+but we're going to keep it simple here
+
+ align:start position:0%
+but we're going to keep it simple here
+ 
+
+ align:start position:0%
+but we're going to keep it simple here
+and so um the ideal solution model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that those are the ideal model
+
+ align:start position:0%
+is that those are the ideal model
+ 
+
+ align:start position:0%
+is that those are the ideal model
+slope
+
+ align:start position:0%
+slope
+ 
+
+ align:start position:0%
+slope
+minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideal
+
+ align:start position:0%
+ideal
+ 
+
+ align:start position:0%
+ideal
+slope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+ideal so the ideal solution model
+
+ align:start position:0%
+ideal so the ideal solution model
+ 
+
+ align:start position:0%
+ideal so the ideal solution model
+is um is like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Henry's law here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is going to have a slope not equal to
+
+ align:start position:0%
+is going to have a slope not equal to
+ 
+
+ align:start position:0%
+is going to have a slope not equal to
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+so this is a slope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of gamma one naught Henry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and similarly we can have
+
+ align:start position:0%
+and similarly we can have
+ 
+
+ align:start position:0%
+and similarly we can have
+some slope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gamma 2 naught and this is Henry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's Henry and the reality could be
+
+ align:start position:0%
+that's Henry and the reality could be
+ 
+
+ align:start position:0%
+that's Henry and the reality could be
+something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when X2
+
+ align:start position:0%
+when X2
+ 
+
+ align:start position:0%
+when X2
+is concentrated X1 is
+
+ align:start position:0%
+is concentrated X1 is
+ 
+
+ align:start position:0%
+is concentrated X1 is
+dilute
+
+ align:start position:0%
+dilute
+ 
+
+ align:start position:0%
+dilute
+and you start up Henry's law there and
+
+ align:start position:0%
+and you start up Henry's law there and
+ 
+
+ align:start position:0%
+and you start up Henry's law there and
+then it deviates and at some point you
+
+ align:start position:0%
+then it deviates and at some point you
+ 
+
+ align:start position:0%
+then it deviates and at some point you
+asymptote
+
+ align:start position:0%
+asymptote
+ 
+
+ align:start position:0%
+asymptote
+to Rule's law so this is this might this
+
+ align:start position:0%
+to Rule's law so this is this might this
+ 
+
+ align:start position:0%
+to Rule's law so this is this might this
+might be reality right there's lots of
+
+ align:start position:0%
+might be reality right there's lots of
+ 
+
+ align:start position:0%
+might be reality right there's lots of
+different ways that this can shake out
+
+ align:start position:0%
+different ways that this can shake out
+ 
+
+ align:start position:0%
+different ways that this can shake out
+but as drawn here and again you have
+
+ align:start position:0%
+but as drawn here and again you have
+ 
+
+ align:start position:0%
+but as drawn here and again you have
+for dilute X2 you start along Henry and
+
+ align:start position:0%
+for dilute X2 you start along Henry and
+ 
+
+ align:start position:0%
+for dilute X2 you start along Henry and
+then you at some point asymptote two
+
+ align:start position:0%
+then you at some point asymptote two
+ 
+
+ align:start position:0%
+then you at some point asymptote two
+Rebels
+
+ align:start position:0%
+Rebels
+ 
+
+ align:start position:0%
+Rebels
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+this this could be what you get
+
+ align:start position:0%
+this this could be what you get
+ 
+
+ align:start position:0%
+this this could be what you get
+all right Rhodes law Henry's law Henry's
+
+ align:start position:0%
+all right Rhodes law Henry's law Henry's
+ 
+
+ align:start position:0%
+all right Rhodes law Henry's law Henry's
+law rules and one implies the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that's dilute Solutions and
+
+ align:start position:0%
+all right so that's dilute Solutions and
+ 
+
+ align:start position:0%
+all right so that's dilute Solutions and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I ask you one problem on Data Solutions
+
+ align:start position:0%
+I ask you one problem on Data Solutions
+ 
+
+ align:start position:0%
+I ask you one problem on Data Solutions
+on the PSAT we're not going to spend a
+
+ align:start position:0%
+on the PSAT we're not going to spend a
+ 
+
+ align:start position:0%
+on the PSAT we're not going to spend a
+lot of time on the Solutions in this
+
+ align:start position:0%
+lot of time on the Solutions in this
+ 
+
+ align:start position:0%
+lot of time on the Solutions in this
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+the reason why we took this time these
+
+ align:start position:0%
+the reason why we took this time these
+ 
+
+ align:start position:0%
+the reason why we took this time these
+15 minutes of lecture and a little bit
+
+ align:start position:0%
+15 minutes of lecture and a little bit
+ 
+
+ align:start position:0%
+15 minutes of lecture and a little bit
+of time on the pset is to set you up for
+
+ align:start position:0%
+of time on the pset is to set you up for
+ 
+
+ align:start position:0%
+of time on the pset is to set you up for
+those of you who are going to do aqueous
+
+ align:start position:0%
+those of you who are going to do aqueous
+ 
+
+ align:start position:0%
+those of you who are going to do aqueous
+chemistry or electrochemistry
+
+ align:start position:0%
+chemistry or electrochemistry
+ 
+
+ align:start position:0%
+chemistry or electrochemistry
+um you you'll want to know this so
+
+ align:start position:0%
+um you you'll want to know this so
+ 
+
+ align:start position:0%
+um you you'll want to know this so
+that's that's why we did that
+
+ align:start position:0%
+that's that's why we did that
+ 
+
+ align:start position:0%
+that's that's why we did that
+um there is another type of solution to
+
+ align:start position:0%
+um there is another type of solution to
+ 
+
+ align:start position:0%
+um there is another type of solution to
+modeling which is much more useful for
+
+ align:start position:0%
+modeling which is much more useful for
+ 
+
+ align:start position:0%
+modeling which is much more useful for
+o2o
+
+ align:start position:0%
+o2o
+ 
+
+ align:start position:0%
+o2o
+and those are called regular solution
+
+ align:start position:0%
+and those are called regular solution
+ 
+
+ align:start position:0%
+and those are called regular solution
+models
+
+ align:start position:0%
+models
+ 
+
+ align:start position:0%
+models
+so these are models
+
+ align:start position:0%
+so these are models
+ 
+
+ align:start position:0%
+so these are models
+that we're going to spend the next
+
+ align:start position:0%
+that we're going to spend the next
+ 
+
+ align:start position:0%
+that we're going to spend the next
+couple lectures on at least the lectures
+
+ align:start position:0%
+couple lectures on at least the lectures
+ 
+
+ align:start position:0%
+couple lectures on at least the lectures
+that are new material
+
+ align:start position:0%
+that are new material
+ 
+
+ align:start position:0%
+that are new material
+and you spend more time on the PSAT Zone
+
+ align:start position:0%
+and you spend more time on the PSAT Zone
+ 
+
+ align:start position:0%
+and you spend more time on the PSAT Zone
+so regular solicitor models are like
+
+ align:start position:0%
+so regular solicitor models are like
+ 
+
+ align:start position:0%
+so regular solicitor models are like
+this we also start with some physical
+
+ align:start position:0%
+this we also start with some physical
+ 
+
+ align:start position:0%
+this we also start with some physical
+assumptions and then we develop the
+
+ align:start position:0%
+assumptions and then we develop the
+ 
+
+ align:start position:0%
+assumptions and then we develop the
+implications of that one
+
+ align:start position:0%
+implications of that one
+ 
+
+ align:start position:0%
+implications of that one
+the entropy of mixing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the entropy of mixing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is captured
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the ideal model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta s mix
+
+ align:start position:0%
+Delta s mix
+ 
+
+ align:start position:0%
+Delta s mix
+ideal that sort of gets a little bit
+
+ align:start position:0%
+ideal that sort of gets a little bit
+ 
+
+ align:start position:0%
+ideal that sort of gets a little bit
+fuzzy over there I'm sorry for that
+
+ align:start position:0%
+fuzzy over there I'm sorry for that
+ 
+
+ align:start position:0%
+fuzzy over there I'm sorry for that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so we're going to assume that the
+
+ align:start position:0%
+okay so we're going to assume that the
+ 
+
+ align:start position:0%
+okay so we're going to assume that the
+ideal model captures the entropy of
+
+ align:start position:0%
+ideal model captures the entropy of
+ 
+
+ align:start position:0%
+ideal model captures the entropy of
+mixing and as we'll see uh later when we
+
+ align:start position:0%
+mixing and as we'll see uh later when we
+ 
+
+ align:start position:0%
+mixing and as we'll see uh later when we
+do statistical thermodynamics we will
+
+ align:start position:0%
+do statistical thermodynamics we will
+ 
+
+ align:start position:0%
+do statistical thermodynamics we will
+show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is what's called configurational entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+configurational entropy is entropy
+
+ align:start position:0%
+configurational entropy is entropy
+ 
+
+ align:start position:0%
+configurational entropy is entropy
+associated with the spatial
+
+ align:start position:0%
+associated with the spatial
+ 
+
+ align:start position:0%
+associated with the spatial
+configuration of things
+
+ align:start position:0%
+configuration of things
+ 
+
+ align:start position:0%
+configuration of things
+and again you can recall the pictures in
+
+ align:start position:0%
+and again you can recall the pictures in
+ 
+
+ align:start position:0%
+and again you can recall the pictures in
+the baby book right mixed up in this
+
+ align:start position:0%
+the baby book right mixed up in this
+ 
+
+ align:start position:0%
+the baby book right mixed up in this
+represented by
+
+ align:start position:0%
+represented by
+ 
+
+ align:start position:0%
+represented by
+where things are in space
+
+ align:start position:0%
+where things are in space
+ 
+
+ align:start position:0%
+where things are in space
+so that's configurational activity
+
+ align:start position:0%
+so that's configurational activity
+ 
+
+ align:start position:0%
+so that's configurational activity
+that's the ideal model
+
+ align:start position:0%
+that's the ideal model
+ 
+
+ align:start position:0%
+that's the ideal model
+but we're also going to allow
+
+ align:start position:0%
+but we're also going to allow
+ 
+
+ align:start position:0%
+but we're also going to allow
+intermolecular interactions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intermolecular interactions are
+
+ align:start position:0%
+intermolecular interactions are
+ 
+
+ align:start position:0%
+intermolecular interactions are
+uh non-zero or finite
+
+ align:start position:0%
+uh non-zero or finite
+ 
+
+ align:start position:0%
+uh non-zero or finite
+exist there we have it what that means
+
+ align:start position:0%
+exist there we have it what that means
+ 
+
+ align:start position:0%
+exist there we have it what that means
+is going to be this
+
+ align:start position:0%
+is going to be this
+ 
+
+ align:start position:0%
+is going to be this
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this model when you make a mixture
+
+ align:start position:0%
+so in this model when you make a mixture
+ 
+
+ align:start position:0%
+so in this model when you make a mixture
+some bonds are made others are broken
+
+ align:start position:0%
+some bonds are made others are broken
+ 
+
+ align:start position:0%
+some bonds are made others are broken
+and there's going to be an energy cost
+
+ align:start position:0%
+and there's going to be an energy cost
+ 
+
+ align:start position:0%
+and there's going to be an energy cost
+to that so this is what we get we get
+
+ align:start position:0%
+to that so this is what we get we get
+ 
+
+ align:start position:0%
+to that so this is what we get we get
+Delta G of mixing
+
+ align:start position:0%
+Delta G of mixing
+ 
+
+ align:start position:0%
+Delta G of mixing
+equals Delta h of mixing General
+
+ align:start position:0%
+equals Delta h of mixing General
+ 
+
+ align:start position:0%
+equals Delta h of mixing General
+non-zero minus t Delta s mixing
+
+ align:start position:0%
+non-zero minus t Delta s mixing
+ 
+
+ align:start position:0%
+non-zero minus t Delta s mixing
+where this is ideal
+
+ align:start position:0%
+where this is ideal
+ 
+
+ align:start position:0%
+where this is ideal
+that's ideal
+
+ align:start position:0%
+that's ideal
+ 
+
+ align:start position:0%
+that's ideal
+and that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal to the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is um what's called a regular
+
+ align:start position:0%
+so this is um what's called a regular
+ 
+
+ align:start position:0%
+so this is um what's called a regular
+solution model
+
+ align:start position:0%
+solution model
+ 
+
+ align:start position:0%
+solution model
+and I'll give you one more
+
+ align:start position:0%
+and I'll give you one more
+ 
+
+ align:start position:0%
+and I'll give you one more
+piece of information
+
+ align:start position:0%
+piece of information
+ 
+
+ align:start position:0%
+piece of information
+which is the
+
+ align:start position:0%
+which is the
+ 
+
+ align:start position:0%
+which is the
+simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the simple regular model
+
+ align:start position:0%
+the simple regular model
+ 
+
+ align:start position:0%
+the simple regular model
+is the simplest case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of regular solution models
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for binary systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we can write it down really easily this
+
+ align:start position:0%
+we can write it down really easily this
+ 
+
+ align:start position:0%
+we can write it down really easily this
+is it Delta H mixing
+
+ align:start position:0%
+is it Delta H mixing
+ 
+
+ align:start position:0%
+is it Delta H mixing
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+a naught X1 X2
+
+ align:start position:0%
+a naught X1 X2
+ 
+
+ align:start position:0%
+a naught X1 X2
+so it's a model with one parameter
+
+ align:start position:0%
+so it's a model with one parameter
+ 
+
+ align:start position:0%
+so it's a model with one parameter
+it's a mixing term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameterized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by a naught which typically has units of
+
+ align:start position:0%
+by a naught which typically has units of
+ 
+
+ align:start position:0%
+by a naught which typically has units of
+joule per mole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if a naught is greater than zero this is
+
+ align:start position:0%
+if a naught is greater than zero this is
+ 
+
+ align:start position:0%
+if a naught is greater than zero this is
+an n
+
+ align:start position:0%
+an n
+ 
+
+ align:start position:0%
+an n
+endothermic mixing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right endothermic mixing we have to put
+
+ align:start position:0%
+right endothermic mixing we have to put
+ 
+
+ align:start position:0%
+right endothermic mixing we have to put
+in heat energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so maybe some bonds are broken right the
+
+ align:start position:0%
+so maybe some bonds are broken right the
+ 
+
+ align:start position:0%
+so maybe some bonds are broken right the
+molecules end up in a higher energy
+
+ align:start position:0%
+molecules end up in a higher energy
+ 
+
+ align:start position:0%
+molecules end up in a higher energy
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+in uh less than zero this is exothermic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so uh with that model for the
+
+ align:start position:0%
+okay and so uh with that model for the
+ 
+
+ align:start position:0%
+okay and so uh with that model for the
+enthalpy of mixing we have the full
+
+ align:start position:0%
+enthalpy of mixing we have the full
+ 
+
+ align:start position:0%
+enthalpy of mixing we have the full
+solution model which is a naught x 1 x 2
+
+ align:start position:0%
+solution model which is a naught x 1 x 2
+ 
+
+ align:start position:0%
+solution model which is a naught x 1 x 2
+plus r t some i x by natural log
+
+ align:start position:0%
+plus r t some i x by natural log
+ 
+
+ align:start position:0%
+plus r t some i x by natural log
+X of I
+
+ align:start position:0%
+X of I
+ 
+
+ align:start position:0%
+X of I
+okay so this is the simple regular model
+
+ align:start position:0%
+okay so this is the simple regular model
+ 
+
+ align:start position:0%
+okay so this is the simple regular model
+and we're going to spend some time on
+
+ align:start position:0%
+and we're going to spend some time on
+ 
+
+ align:start position:0%
+and we're going to spend some time on
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um you're spending some time on this on
+
+ align:start position:0%
+um you're spending some time on this on
+ 
+
+ align:start position:0%
+um you're spending some time on this on
+the pset
+
+ align:start position:0%
+the pset
+ 
+
+ align:start position:0%
+the pset
+um yeah we've got two parameters it's
+
+ align:start position:0%
+um yeah we've got two parameters it's
+ 
+
+ align:start position:0%
+um yeah we've got two parameters it's
+got enthalpy a mixing parameter and it's
+
+ align:start position:0%
+got enthalpy a mixing parameter and it's
+ 
+
+ align:start position:0%
+got enthalpy a mixing parameter and it's
+got temperature
+
+ align:start position:0%
+got temperature
+ 
+
+ align:start position:0%
+got temperature
+and from these two parameters you can
+
+ align:start position:0%
+and from these two parameters you can
+ 
+
+ align:start position:0%
+and from these two parameters you can
+generate a nice diversity of physical
+
+ align:start position:0%
+generate a nice diversity of physical
+ 
+
+ align:start position:0%
+generate a nice diversity of physical
+behavior and and we'll see that in the
+
+ align:start position:0%
+behavior and and we'll see that in the
+ 
+
+ align:start position:0%
+behavior and and we'll see that in the
+weeks ahead
+
+ align:start position:0%
+weeks ahead
+ 
+
+ align:start position:0%
+weeks ahead
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um today's lecture covered a lot of
+
+ align:start position:0%
+um today's lecture covered a lot of
+ 
+
+ align:start position:0%
+um today's lecture covered a lot of
+essential information
+
+ align:start position:0%
+essential information
+ 
+
+ align:start position:0%
+essential information
+and uh I went rather quickly so I have
+
+ align:start position:0%
+and uh I went rather quickly so I have
+ 
+
+ align:start position:0%
+and uh I went rather quickly so I have
+plenty of time for questions
+
+ align:start position:0%
+plenty of time for questions
+ 
+
+ align:start position:0%
+plenty of time for questions
+and I will keep the recording on for
+
+ align:start position:0%
+and I will keep the recording on for
+ 
+
+ align:start position:0%
+and I will keep the recording on for
+some time now
+
+ align:start position:0%
+some time now
+ 
+
+ align:start position:0%
+some time now
+and and then switch it off
+
+ align:start position:0%
+and and then switch it off
+ 
+
+ align:start position:0%
+and and then switch it off
+at at 10 55 and
+
+ align:start position:0%
+at at 10 55 and
+ 
+
+ align:start position:0%
+at at 10 55 and
+um before we start that I'll remind you
+
+ align:start position:0%
+um before we start that I'll remind you
+ 
+
+ align:start position:0%
+um before we start that I'll remind you
+my office hours have switched
+
+ align:start position:0%
+my office hours have switched
+ 
+
+ align:start position:0%
+my office hours have switched
+to Wednesday
+
+ align:start position:0%
+to Wednesday
+ 
+
+ align:start position:0%
+to Wednesday
+at 12 so that's in about an hour hour
+
+ align:start position:0%
+at 12 so that's in about an hour hour
+ 
+
+ align:start position:0%
+at 12 so that's in about an hour hour
+and 15 minutes from now
+
+ align:start position:0%
+and 15 minutes from now
+ 
+
+ align:start position:0%
+and 15 minutes from now
+officero switched to Wednesday at 12.
+
+ align:start position:0%
+officero switched to Wednesday at 12.
+ 
+
+ align:start position:0%
+officero switched to Wednesday at 12.
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there's a very slightly revised syllabus
+
+ align:start position:0%
+there's a very slightly revised syllabus
+ 
+
+ align:start position:0%
+there's a very slightly revised syllabus
+for Thermo
+
+ align:start position:0%
+for Thermo
+ 
+
+ align:start position:0%
+for Thermo
+none of the due dates change or anything
+
+ align:start position:0%
+none of the due dates change or anything
+ 
+
+ align:start position:0%
+none of the due dates change or anything
+like that it doesn't really change your
+
+ align:start position:0%
+like that it doesn't really change your
+ 
+
+ align:start position:0%
+like that it doesn't really change your
+life
+
+ align:start position:0%
+life
+ 
+
+ align:start position:0%
+life
+um substantially but it is a little bit
+
+ align:start position:0%
+um substantially but it is a little bit
+ 
+
+ align:start position:0%
+um substantially but it is a little bit
+of a more accurate view of where we're
+
+ align:start position:0%
+of a more accurate view of where we're
+ 
+
+ align:start position:0%
+of a more accurate view of where we're
+heading in the next couple lectures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the exam is Monday
+
+ align:start position:0%
+um the exam is Monday
+ 
+
+ align:start position:0%
+um the exam is Monday
+and it will cover unary phase diagrams
+
+ align:start position:0%
+and it will cover unary phase diagrams
+ 
+
+ align:start position:0%
+and it will cover unary phase diagrams
+and reacting ideal gas mixtures and the
+
+ align:start position:0%
+and reacting ideal gas mixtures and the
+ 
+
+ align:start position:0%
+and reacting ideal gas mixtures and the
+rudiments of Ideal Solutions
+
+ align:start position:0%
+rudiments of Ideal Solutions
+ 
+
+ align:start position:0%
+rudiments of Ideal Solutions
+but um none of this
+
+ align:start position:0%
+but um none of this
+ 
+
+ align:start position:0%
+but um none of this
+uh really involves solution and modeling
+
+ align:start position:0%
+uh really involves solution and modeling
+ 
+
+ align:start position:0%
+uh really involves solution and modeling
+apparatus that we're working on now
+
+ align:start position:0%
+apparatus that we're working on now
+ 
+
+ align:start position:0%
+apparatus that we're working on now
+um what that means is that the pizza
+
+ align:start position:0%
+um what that means is that the pizza
+ 
+
+ align:start position:0%
+um what that means is that the pizza
+that's due on Friday is only minimally
+
+ align:start position:0%
+that's due on Friday is only minimally
+ 
+
+ align:start position:0%
+that's due on Friday is only minimally
+covered on the exam so you can focus on
+
+ align:start position:0%
+covered on the exam so you can focus on
+ 
+
+ align:start position:0%
+covered on the exam so you can focus on
+slightly earlier material for the exam
+
+ align:start position:0%
+slightly earlier material for the exam
+ 
+
+ align:start position:0%
+slightly earlier material for the exam
+exam Monday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um we will get new Thermo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next Wednesday not this Wednesday but
+
+ align:start position:0%
+next Wednesday not this Wednesday but
+ 
+
+ align:start position:0%
+next Wednesday not this Wednesday but
+next Wednesday and what is that the 9th
+
+ align:start position:0%
+next Wednesday and what is that the 9th
+ 
+
+ align:start position:0%
+next Wednesday and what is that the 9th
+it's at the ninth
+
+ align:start position:0%
+it's at the ninth
+ 
+
+ align:start position:0%
+it's at the ninth
+right next Wednesday four nine
+
+ align:start position:0%
+right next Wednesday four nine
+ 
+
+ align:start position:0%
+right next Wednesday four nine
+um this Friday oh sorry next
+
+ align:start position:0%
+um this Friday oh sorry next
+ 
+
+ align:start position:0%
+um this Friday oh sorry next
+next Friday
+
+ align:start position:0%
+next Friday
+ 
+
+ align:start position:0%
+next Friday
+this Friday we're going to work some
+
+ align:start position:0%
+this Friday we're going to work some
+ 
+
+ align:start position:0%
+this Friday we're going to work some
+problems and then
+
+ align:start position:0%
+problems and then
+ 
+
+ align:start position:0%
+problems and then
+um I guess it will be new thermal but
+
+ align:start position:0%
+um I guess it will be new thermal but
+ 
+
+ align:start position:0%
+um I guess it will be new thermal but
+we're going to walk through the nurse
+
+ align:start position:0%
+we're going to walk through the nurse
+ 
+
+ align:start position:0%
+we're going to walk through the nurse
+equation just for your own curiosity and
+
+ align:start position:0%
+equation just for your own curiosity and
+ 
+
+ align:start position:0%
+equation just for your own curiosity and
+interest it won't be tested or covered
+
+ align:start position:0%
+interest it won't be tested or covered
+ 
+
+ align:start position:0%
+interest it won't be tested or covered
+formally in this class and then Monday
+
+ align:start position:0%
+formally in this class and then Monday
+ 
+
+ align:start position:0%
+formally in this class and then Monday
+is the exam and then Wednesday we're
+
+ align:start position:0%
+is the exam and then Wednesday we're
+ 
+
+ align:start position:0%
+is the exam and then Wednesday we're
+going to talk we're going to spend an
+
+ align:start position:0%
+going to talk we're going to spend an
+ 
+
+ align:start position:0%
+going to talk we're going to spend an
+hour talking about social implications
+
+ align:start position:0%
+hour talking about social implications
+ 
+
+ align:start position:0%
+hour talking about social implications
+of Material Science and so we won't
+
+ align:start position:0%
+of Material Science and so we won't
+ 
+
+ align:start position:0%
+of Material Science and so we won't
+really see new you know hardcore course
+
+ align:start position:0%
+really see new you know hardcore course
+ 
+
+ align:start position:0%
+really see new you know hardcore course
+content until next Friday
+
+ align:start position:0%
+content until next Friday
+ 
+
+ align:start position:0%
+content until next Friday
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay this is time for questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um can you explain the Delta h of mixing
+
+ align:start position:0%
+um can you explain the Delta h of mixing
+ 
+
+ align:start position:0%
+um can you explain the Delta h of mixing
+and like how you got that
+
+ align:start position:0%
+and like how you got that
+ 
+
+ align:start position:0%
+and like how you got that
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+um the way I got it is I just told you
+
+ align:start position:0%
+um the way I got it is I just told you
+ 
+
+ align:start position:0%
+um the way I got it is I just told you
+that's the model
+
+ align:start position:0%
+that's the model
+ 
+
+ align:start position:0%
+that's the model
+um it doesn't apparently come from
+
+ align:start position:0%
+um it doesn't apparently come from
+ 
+
+ align:start position:0%
+um it doesn't apparently come from
+anywhere
+
+ align:start position:0%
+anywhere
+ 
+
+ align:start position:0%
+anywhere
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+but I'm glad you have because we do have
+
+ align:start position:0%
+but I'm glad you have because we do have
+ 
+
+ align:start position:0%
+but I'm glad you have because we do have
+something called
+
+ align:start position:0%
+something called
+ 
+
+ align:start position:0%
+something called
+here let's do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the answer is that um you can say oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's empirical I made a bunch of
+
+ align:start position:0%
+it's empirical I made a bunch of
+ 
+
+ align:start position:0%
+it's empirical I made a bunch of
+measurements in this fit the data and
+
+ align:start position:0%
+measurements in this fit the data and
+ 
+
+ align:start position:0%
+measurements in this fit the data and
+historically that's that's probably the
+
+ align:start position:0%
+historically that's that's probably the
+ 
+
+ align:start position:0%
+historically that's that's probably the
+most accurate answer but it also comes
+
+ align:start position:0%
+most accurate answer but it also comes
+ 
+
+ align:start position:0%
+most accurate answer but it also comes
+from something called
+
+ align:start position:0%
+from something called
+ 
+
+ align:start position:0%
+from something called
+the Quasi chemical model and we are
+
+ align:start position:0%
+the Quasi chemical model and we are
+ 
+
+ align:start position:0%
+the Quasi chemical model and we are
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+I believe next Friday
+
+ align:start position:0%
+I believe next Friday
+ 
+
+ align:start position:0%
+I believe next Friday
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+start right here where we try to justify
+
+ align:start position:0%
+start right here where we try to justify
+ 
+
+ align:start position:0%
+start right here where we try to justify
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+as a preview what we do is we imagine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+green and red is never good red and blue
+
+ align:start position:0%
+green and red is never good red and blue
+ 
+
+ align:start position:0%
+green and red is never good red and blue
+is okay we imagine atoms or molecules
+
+ align:start position:0%
+is okay we imagine atoms or molecules
+ 
+
+ align:start position:0%
+is okay we imagine atoms or molecules
+on a lattice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm not drawing a nice lattice here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we imagine molecules on a lattice where
+
+ align:start position:0%
+we imagine molecules on a lattice where
+ 
+
+ align:start position:0%
+we imagine molecules on a lattice where
+we have two different components on the
+
+ align:start position:0%
+we have two different components on the
+ 
+
+ align:start position:0%
+we have two different components on the
+lattice
+
+ align:start position:0%
+lattice
+ 
+
+ align:start position:0%
+lattice
+and we say okay all the energy is
+
+ align:start position:0%
+and we say okay all the energy is
+ 
+
+ align:start position:0%
+and we say okay all the energy is
+nearest neighbor bonding so we have blue
+
+ align:start position:0%
+nearest neighbor bonding so we have blue
+ 
+
+ align:start position:0%
+nearest neighbor bonding so we have blue
+blue blue blue blue blue blue blue blue
+
+ align:start position:0%
+blue blue blue blue blue blue blue blue
+ 
+
+ align:start position:0%
+blue blue blue blue blue blue blue blue
+blue blue blue blue blue blue blue blue
+
+ align:start position:0%
+blue blue blue blue blue blue blue blue
+ 
+
+ align:start position:0%
+blue blue blue blue blue blue blue blue
+blue blue blue blue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a lot harder to save it so far
+
+ align:start position:0%
+this is a lot harder to save it so far
+ 
+
+ align:start position:0%
+this is a lot harder to save it so far
+and over again I would seem
+
+ align:start position:0%
+and over again I would seem
+ 
+
+ align:start position:0%
+and over again I would seem
+and oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we've got some blue red bottoms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and just for completeness let's say I
+
+ align:start position:0%
+and just for completeness let's say I
+ 
+
+ align:start position:0%
+and just for completeness let's say I
+have a red over there there's a red red
+
+ align:start position:0%
+have a red over there there's a red red
+ 
+
+ align:start position:0%
+have a red over there there's a red red
+one and what we're going to do is we're
+
+ align:start position:0%
+one and what we're going to do is we're
+ 
+
+ align:start position:0%
+one and what we're going to do is we're
+we're going to count up these bonds and
+
+ align:start position:0%
+we're going to count up these bonds and
+ 
+
+ align:start position:0%
+we're going to count up these bonds and
+we're going to do some combinatorics and
+
+ align:start position:0%
+we're going to do some combinatorics and
+ 
+
+ align:start position:0%
+we're going to do some combinatorics and
+we're going to end up with this
+
+ align:start position:0%
+we're going to end up with this
+ 
+
+ align:start position:0%
+we're going to end up with this
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+so it does come from somewhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I would be willing to bet a cup of
+
+ align:start position:0%
+I would be willing to bet a cup of
+ 
+
+ align:start position:0%
+I would be willing to bet a cup of
+coffee that historically comes from
+
+ align:start position:0%
+coffee that historically comes from
+ 
+
+ align:start position:0%
+coffee that historically comes from
+empirical data comes from data and
+
+ align:start position:0%
+empirical data comes from data and
+ 
+
+ align:start position:0%
+empirical data comes from data and
+fitting and people making reasonable
+
+ align:start position:0%
+fitting and people making reasonable
+ 
+
+ align:start position:0%
+fitting and people making reasonable
+guesses as to what empirical what model
+
+ align:start position:0%
+guesses as to what empirical what model
+ 
+
+ align:start position:0%
+guesses as to what empirical what model
+will empirically fit the data and then
+
+ align:start position:0%
+will empirically fit the data and then
+ 
+
+ align:start position:0%
+will empirically fit the data and then
+at some point somebody worked out this
+
+ align:start position:0%
+at some point somebody worked out this
+ 
+
+ align:start position:0%
+at some point somebody worked out this
+model and said oh this is neat this
+
+ align:start position:0%
+model and said oh this is neat this
+ 
+
+ align:start position:0%
+model and said oh this is neat this
+justifies this justifies what we've been
+
+ align:start position:0%
+justifies this justifies what we've been
+ 
+
+ align:start position:0%
+justifies this justifies what we've been
+using all these years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does that help
+
+ align:start position:0%
+does that help
+ 
+
+ align:start position:0%
+does that help
+yeah thank you
+
+ align:start position:0%
+yeah thank you
+ 
+
+ align:start position:0%
+yeah thank you
+how would you how would you how would
+
+ align:start position:0%
+how would you how would you how would
+ 
+
+ align:start position:0%
+how would you how would you how would
+you get that right how would you get
+
+ align:start position:0%
+you get that right how would you get
+ 
+
+ align:start position:0%
+you get that right how would you get
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+well you know you'd have a beaker
+
+ align:start position:0%
+well you know you'd have a beaker
+ 
+
+ align:start position:0%
+well you know you'd have a beaker
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+you would have inside of that beep it
+
+ align:start position:0%
+you would have inside of that beep it
+ 
+
+ align:start position:0%
+you would have inside of that beep it
+doesn't have to be a beaker right it can
+
+ align:start position:0%
+doesn't have to be a beaker right it can
+ 
+
+ align:start position:0%
+doesn't have to be a beaker right it can
+be a crucible or anything and inside of
+
+ align:start position:0%
+be a crucible or anything and inside of
+ 
+
+ align:start position:0%
+be a crucible or anything and inside of
+that you'd have another little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Beaker a crucible and this speaker would
+
+ align:start position:0%
+Beaker a crucible and this speaker would
+ 
+
+ align:start position:0%
+Beaker a crucible and this speaker would
+be full of something which has a large
+
+ align:start position:0%
+be full of something which has a large
+ 
+
+ align:start position:0%
+be full of something which has a large
+heat capacity
+
+ align:start position:0%
+heat capacity
+ 
+
+ align:start position:0%
+heat capacity
+like water
+
+ align:start position:0%
+like water
+ 
+
+ align:start position:0%
+like water
+and it's easy to measure the temperature
+
+ align:start position:0%
+and it's easy to measure the temperature
+ 
+
+ align:start position:0%
+and it's easy to measure the temperature
+of this thing so you've got a
+
+ align:start position:0%
+of this thing so you've got a
+ 
+
+ align:start position:0%
+of this thing so you've got a
+thermometer in there
+
+ align:start position:0%
+thermometer in there
+ 
+
+ align:start position:0%
+thermometer in there
+right so we've got a big thing of water
+
+ align:start position:0%
+right so we've got a big thing of water
+ 
+
+ align:start position:0%
+right so we've got a big thing of water
+and we've got a thermometer in there
+
+ align:start position:0%
+and we've got a thermometer in there
+ 
+
+ align:start position:0%
+and we've got a thermometer in there
+and what we're going to do
+
+ align:start position:0%
+and what we're going to do
+ 
+
+ align:start position:0%
+and what we're going to do
+is we're going to make mixtures so we're
+
+ align:start position:0%
+is we're going to make mixtures so we're
+ 
+
+ align:start position:0%
+is we're going to make mixtures so we're
+going to take sum of a
+
+ align:start position:0%
+going to take sum of a
+ 
+
+ align:start position:0%
+going to take sum of a
+and we're going to take some of B
+
+ align:start position:0%
+and we're going to take some of B
+ 
+
+ align:start position:0%
+and we're going to take some of B
+and we're going to add them to max out
+
+ align:start position:0%
+and we're going to add them to max out
+ 
+
+ align:start position:0%
+and we're going to add them to max out
+my colors here we're going to add them
+
+ align:start position:0%
+my colors here we're going to add them
+ 
+
+ align:start position:0%
+my colors here we're going to add them
+in in different quantities and we're
+
+ align:start position:0%
+in in different quantities and we're
+ 
+
+ align:start position:0%
+in in different quantities and we're
+going to end up with different solutions
+
+ align:start position:0%
+going to end up with different solutions
+ 
+
+ align:start position:0%
+going to end up with different solutions
+in this little beaker
+
+ align:start position:0%
+in this little beaker
+ 
+
+ align:start position:0%
+in this little beaker
+and we're going to measure the
+
+ align:start position:0%
+and we're going to measure the
+ 
+
+ align:start position:0%
+and we're going to measure the
+temperature rise right and so for every
+
+ align:start position:0%
+temperature rise right and so for every
+ 
+
+ align:start position:0%
+temperature rise right and so for every
+composition that I have right we're
+
+ align:start position:0%
+composition that I have right we're
+ 
+
+ align:start position:0%
+composition that I have right we're
+going to have something like this we're
+
+ align:start position:0%
+going to have something like this we're
+ 
+
+ align:start position:0%
+going to have something like this we're
+going to have X of a x of B and A
+
+ align:start position:0%
+going to have X of a x of B and A
+ 
+
+ align:start position:0%
+going to have X of a x of B and A
+temperature rise
+
+ align:start position:0%
+temperature rise
+ 
+
+ align:start position:0%
+temperature rise
+and we measure let's see 0.99 0.01 0.98
+
+ align:start position:0%
+and we measure let's see 0.99 0.01 0.98
+ 
+
+ align:start position:0%
+and we measure let's see 0.99 0.01 0.98
+we're doing a bunch of experiments right
+
+ align:start position:0%
+we're doing a bunch of experiments right
+ 
+
+ align:start position:0%
+we're doing a bunch of experiments right
+and I'm going to have numbers for
+
+ align:start position:0%
+and I'm going to have numbers for
+ 
+
+ align:start position:0%
+and I'm going to have numbers for
+temperature rise
+
+ align:start position:0%
+temperature rise
+ 
+
+ align:start position:0%
+temperature rise
+why does that help me well the
+
+ align:start position:0%
+why does that help me well the
+ 
+
+ align:start position:0%
+why does that help me well the
+temperature Rose in this uh in this big
+
+ align:start position:0%
+temperature Rose in this uh in this big
+ 
+
+ align:start position:0%
+temperature Rose in this uh in this big
+bath of water
+
+ align:start position:0%
+bath of water
+ 
+
+ align:start position:0%
+bath of water
+so I can estimate the heat evolved from
+
+ align:start position:0%
+so I can estimate the heat evolved from
+ 
+
+ align:start position:0%
+so I can estimate the heat evolved from
+this this mixing process because I know
+
+ align:start position:0%
+this this mixing process because I know
+ 
+
+ align:start position:0%
+this this mixing process because I know
+the capacity of water
+
+ align:start position:0%
+the capacity of water
+ 
+
+ align:start position:0%
+the capacity of water
+so the heat of all they're going to be
+
+ align:start position:0%
+so the heat of all they're going to be
+ 
+
+ align:start position:0%
+so the heat of all they're going to be
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+and then I can say oh well this is the
+
+ align:start position:0%
+and then I can say oh well this is the
+ 
+
+ align:start position:0%
+and then I can say oh well this is the
+constant pressure process
+
+ align:start position:0%
+constant pressure process
+ 
+
+ align:start position:0%
+constant pressure process
+so heat and enthalpy is about the same
+
+ align:start position:0%
+so heat and enthalpy is about the same
+ 
+
+ align:start position:0%
+so heat and enthalpy is about the same
+and okay I can model the the heat
+
+ align:start position:0%
+and okay I can model the the heat
+ 
+
+ align:start position:0%
+and okay I can model the the heat
+evolved as a function of composition
+
+ align:start position:0%
+evolved as a function of composition
+ 
+
+ align:start position:0%
+evolved as a function of composition
+and uh maybe it fits this functional
+
+ align:start position:0%
+and uh maybe it fits this functional
+ 
+
+ align:start position:0%
+and uh maybe it fits this functional
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+right that's how this actually would go
+
+ align:start position:0%
+right that's how this actually would go
+ 
+
+ align:start position:0%
+right that's how this actually would go
+that's how this actually does go when we
+
+ align:start position:0%
+that's how this actually does go when we
+ 
+
+ align:start position:0%
+that's how this actually does go when we
+do calorimetry in the lab this isn't you
+
+ align:start position:0%
+do calorimetry in the lab this isn't you
+ 
+
+ align:start position:0%
+do calorimetry in the lab this isn't you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+um like stuff relegated to you know the
+
+ align:start position:0%
+um like stuff relegated to you know the
+ 
+
+ align:start position:0%
+um like stuff relegated to you know the
+distant past I mean we do this every day
+
+ align:start position:0%
+distant past I mean we do this every day
+ 
+
+ align:start position:0%
+distant past I mean we do this every day
+in the lab
+
+ align:start position:0%
+in the lab
+ 
+
+ align:start position:0%
+in the lab
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+especially those that focus on
+
+ align:start position:0%
+especially those that focus on
+ 
+
+ align:start position:0%
+especially those that focus on
+thermochemistry and such things so
\ No newline at end of file
diff --git a/o57CTwt1-ck.txt b/o57CTwt1-ck.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a476c285d8ac8326d2ae4a304b69dd79387e2787
--- /dev/null
+++ b/o57CTwt1-ck.txt
@@ -0,0 +1,2627 @@
+align:start position:0%
+ 
+if we're going to make use of
+
+ align:start position:0%
+if we're going to make use of
+ 
+
+ align:start position:0%
+if we're going to make use of
+chebychev's bound and other results that
+
+ align:start position:0%
+chebychev's bound and other results that
+ 
+
+ align:start position:0%
+chebychev's bound and other results that
+depend on the variance we'll need some
+
+ align:start position:0%
+depend on the variance we'll need some
+ 
+
+ align:start position:0%
+depend on the variance we'll need some
+methods for calculating various variance
+
+ align:start position:0%
+methods for calculating various variance
+ 
+
+ align:start position:0%
+methods for calculating various variance
+in various circumstances so let's
+
+ align:start position:0%
+in various circumstances so let's
+ 
+
+ align:start position:0%
+in various circumstances so let's
+develop that here a basic place to begin
+
+ align:start position:0%
+develop that here a basic place to begin
+ 
+
+ align:start position:0%
+develop that here a basic place to begin
+is to ask about the indicator very about
+
+ align:start position:0%
+is to ask about the indicator very about
+ 
+
+ align:start position:0%
+is to ask about the indicator very about
+indicator variables and their variance
+
+ align:start position:0%
+indicator variables and their variance
+ 
+
+ align:start position:0%
+indicator variables and their variance
+remember I as an indicator variable
+
+ align:start position:0%
+remember I as an indicator variable
+ 
+
+ align:start position:0%
+remember I as an indicator variable
+means that it's zero one value it's also
+
+ align:start position:0%
+means that it's zero one value it's also
+ 
+
+ align:start position:0%
+means that it's zero one value it's also
+called a Bernoulli variable and if the
+
+ align:start position:0%
+called a Bernoulli variable and if the
+ 
+
+ align:start position:0%
+called a Bernoulli variable and if the
+probability that it equals one is pay
+
+ align:start position:0%
+probability that it equals one is pay
+ 
+
+ align:start position:0%
+probability that it equals one is pay
+that's also its expectation so we have
+
+ align:start position:0%
+that's also its expectation so we have
+ 
+
+ align:start position:0%
+that's also its expectation so we have
+an indicator variable with expectation
+
+ align:start position:0%
+an indicator variable with expectation
+ 
+
+ align:start position:0%
+an indicator variable with expectation
+of the indicator is pay and we're asking
+
+ align:start position:0%
+of the indicator is pay and we're asking
+ 
+
+ align:start position:0%
+of the indicator is pay and we're asking
+what's its variance which my definition
+
+ align:start position:0%
+what's its variance which my definition
+ 
+
+ align:start position:0%
+what's its variance which my definition
+is the expectation of I minus P squared
+
+ align:start position:0%
+is the expectation of I minus P squared
+ 
+
+ align:start position:0%
+is the expectation of I minus P squared
+well this is one of these sort of almost
+
+ align:start position:0%
+well this is one of these sort of almost
+ 
+
+ align:start position:0%
+well this is one of these sort of almost
+mechanical proofs that follows simply by
+
+ align:start position:0%
+mechanical proofs that follows simply by
+ 
+
+ align:start position:0%
+mechanical proofs that follows simply by
+algebra and linearity of expectation but
+
+ align:start position:0%
+algebra and linearity of expectation but
+ 
+
+ align:start position:0%
+algebra and linearity of expectation but
+let's walk through it step by step just
+
+ align:start position:0%
+let's walk through it step by step just
+ 
+
+ align:start position:0%
+let's walk through it step by step just
+to reassure you that that's all that's
+
+ align:start position:0%
+to reassure you that that's all that's
+ 
+
+ align:start position:0%
+to reassure you that that's all that's
+involved I would recommend against
+
+ align:start position:0%
+involved I would recommend against
+ 
+
+ align:start position:0%
+involved I would recommend against
+really trying to memorize this because
+
+ align:start position:0%
+really trying to memorize this because
+ 
+
+ align:start position:0%
+really trying to memorize this because
+it's I can never remember it anyway I
+
+ align:start position:0%
+it's I can never remember it anyway I
+ 
+
+ align:start position:0%
+it's I can never remember it anyway I
+just reprove it every time I need it and
+
+ align:start position:0%
+just reprove it every time I need it and
+ 
+
+ align:start position:0%
+just reprove it every time I need it and
+so let's see how the proof would go so
+
+ align:start position:0%
+so let's see how the proof would go so
+ 
+
+ align:start position:0%
+so let's see how the proof would go so
+step one would be to expand this I minus
+
+ align:start position:0%
+step one would be to expand this I minus
+ 
+
+ align:start position:0%
+step one would be to expand this I minus
+P squared algebraically so we're talking
+
+ align:start position:0%
+P squared algebraically so we're talking
+ 
+
+ align:start position:0%
+P squared algebraically so we're talking
+about the expectation of I squared minus
+
+ align:start position:0%
+about the expectation of I squared minus
+ 
+
+ align:start position:0%
+about the expectation of I squared minus
+two P I plus P squared now we can just
+
+ align:start position:0%
+two P I plus P squared now we can just
+ 
+
+ align:start position:0%
+two P I plus P squared now we can just
+apply linearity of expectation and I get
+
+ align:start position:0%
+apply linearity of expectation and I get
+ 
+
+ align:start position:0%
+apply linearity of expectation and I get
+the expectation of I squared minus two P
+
+ align:start position:0%
+the expectation of I squared minus two P
+ 
+
+ align:start position:0%
+the expectation of I squared minus two P
+times the expectation of I plus P
+
+ align:start position:0%
+times the expectation of I plus P
+ 
+
+ align:start position:0%
+times the expectation of I plus P
+squared of course the expectation of a
+
+ align:start position:0%
+squared of course the expectation of a
+ 
+
+ align:start position:0%
+squared of course the expectation of a
+constant is the constant so when I take
+
+ align:start position:0%
+constant is the constant so when I take
+ 
+
+ align:start position:0%
+constant is the constant so when I take
+expectation of P squared I get P squared
+
+ align:start position:0%
+expectation of P squared I get P squared
+ 
+
+ align:start position:0%
+expectation of P squared I get P squared
+but now look at this I squared is zero
+
+ align:start position:0%
+but now look at this I squared is zero
+ 
+
+ align:start position:0%
+but now look at this I squared is zero
+one value so in fact I squared is equal
+
+ align:start position:0%
+one value so in fact I squared is equal
+ 
+
+ align:start position:0%
+one value so in fact I squared is equal
+to I and the expectation of I has now
+
+ align:start position:0%
+to I and the expectation of I has now
+ 
+
+ align:start position:0%
+to I and the expectation of I has now
+appeared here that's P so this term
+
+ align:start position:0%
+appeared here that's P so this term
+ 
+
+ align:start position:0%
+appeared here that's P so this term
+simplifies to expectation of I and this
+
+ align:start position:0%
+simplifies to expectation of I and this
+ 
+
+ align:start position:0%
+simplifies to expectation of I and this
+term becomes two P times P plus P
+
+ align:start position:0%
+term becomes two P times P plus P
+ 
+
+ align:start position:0%
+term becomes two P times P plus P
+squared of course that expectation of I
+
+ align:start position:0%
+squared of course that expectation of I
+ 
+
+ align:start position:0%
+squared of course that expectation of I
+is a piece I got P minus two P squared
+
+ align:start position:0%
+is a piece I got P minus two P squared
+ 
+
+ align:start position:0%
+is a piece I got P minus two P squared
+plus P squared the P Squared's cancel
+
+ align:start position:0%
+plus P squared the P Squared's cancel
+ 
+
+ align:start position:0%
+plus P squared the P Squared's cancel
+and I get P minus P squared if you
+
+ align:start position:0%
+and I get P minus P squared if you
+ 
+
+ align:start position:0%
+and I get P minus P squared if you
+factor out pay that's P times one minus
+
+ align:start position:0%
+factor out pay that's P times one minus
+ 
+
+ align:start position:0%
+factor out pay that's P times one minus
+P or PQ which is the standard way that
+
+ align:start position:0%
+P or PQ which is the standard way that
+ 
+
+ align:start position:0%
+P or PQ which is the standard way that
+you write the variance of an indicator
+
+ align:start position:0%
+you write the variance of an indicator
+ 
+
+ align:start position:0%
+you write the variance of an indicator
+variable it's P times one minus P okay
+
+ align:start position:0%
+variable it's P times one minus P okay
+ 
+
+ align:start position:0%
+variable it's P times one minus P okay
+that was easy and again completely
+
+ align:start position:0%
+that was easy and again completely
+ 
+
+ align:start position:0%
+that was easy and again completely
+mechanical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a couple of other rules for
+
+ align:start position:0%
+there's a couple of other rules for
+ 
+
+ align:start position:0%
+there's a couple of other rules for
+calculating variance from of new
+
+ align:start position:0%
+calculating variance from of new
+ 
+
+ align:start position:0%
+calculating variance from of new
+variables from old ones that are basic
+
+ align:start position:0%
+variables from old ones that are basic
+ 
+
+ align:start position:0%
+variables from old ones that are basic
+like a nativity of expectation but it
+
+ align:start position:0%
+like a nativity of expectation but it
+ 
+
+ align:start position:0%
+like a nativity of expectation but it
+doesn't quite work so simply for
+
+ align:start position:0%
+doesn't quite work so simply for
+ 
+
+ align:start position:0%
+doesn't quite work so simply for
+variance so the first rule is that if
+
+ align:start position:0%
+variance so the first rule is that if
+ 
+
+ align:start position:0%
+variance so the first rule is that if
+you ask about the variance of a constant
+
+ align:start position:0%
+you ask about the variance of a constant
+ 
+
+ align:start position:0%
+you ask about the variance of a constant
+times R plus B that turns out to be the
+
+ align:start position:0%
+times R plus B that turns out to be the
+ 
+
+ align:start position:0%
+times R plus B that turns out to be the
+same as a squared times the variance of
+
+ align:start position:0%
+same as a squared times the variance of
+ 
+
+ align:start position:0%
+same as a squared times the variance of
+biti of our the B doesn't additive B
+
+ align:start position:0%
+biti of our the B doesn't additive B
+ 
+
+ align:start position:0%
+biti of our the B doesn't additive B
+doesn't matter and the because the
+
+ align:start position:0%
+doesn't matter and the because the
+ 
+
+ align:start position:0%
+doesn't matter and the because the
+variance is really the expectation of
+
+ align:start position:0%
+variance is really the expectation of
+ 
+
+ align:start position:0%
+variance is really the expectation of
+something squared when you get rid of
+
+ align:start position:0%
+something squared when you get rid of
+ 
+
+ align:start position:0%
+something squared when you get rid of
+that constant a you're factoring out an
+
+ align:start position:0%
+that constant a you're factoring out an
+ 
+
+ align:start position:0%
+that constant a you're factoring out an
+a squared and this is the rule that you
+
+ align:start position:0%
+a squared and this is the rule that you
+ 
+
+ align:start position:0%
+a squared and this is the rule that you
+get here okay another basic rule that's
+
+ align:start position:0%
+get here okay another basic rule that's
+ 
+
+ align:start position:0%
+get here okay another basic rule that's
+often convenient instead of working with
+
+ align:start position:0%
+often convenient instead of working with
+ 
+
+ align:start position:0%
+often convenient instead of working with
+variance in the form of the expectation
+
+ align:start position:0%
+variance in the form of the expectation
+ 
+
+ align:start position:0%
+variance in the form of the expectation
+of R minus mu squared is to say that
+
+ align:start position:0%
+of R minus mu squared is to say that
+ 
+
+ align:start position:0%
+of R minus mu squared is to say that
+it's the expectation of R squared minus
+
+ align:start position:0%
+it's the expectation of R squared minus
+ 
+
+ align:start position:0%
+it's the expectation of R squared minus
+the square of the expectation of R now
+
+ align:start position:0%
+the square of the expectation of R now
+ 
+
+ align:start position:0%
+the square of the expectation of R now
+this expression the square of the
+
+ align:start position:0%
+this expression the square of the
+ 
+
+ align:start position:0%
+this expression the square of the
+expectation of R comes up so often that
+
+ align:start position:0%
+expectation of R comes up so often that
+ 
+
+ align:start position:0%
+expectation of R comes up so often that
+there's a shorthand for it words that
+
+ align:start position:0%
+there's a shorthand for it words that
+ 
+
+ align:start position:0%
+there's a shorthand for it words that
+are writing parens you write e squared
+
+ align:start position:0%
+are writing parens you write e squared
+ 
+
+ align:start position:0%
+are writing parens you write e squared
+Lavar it just means the same as
+
+ align:start position:0%
+Lavar it just means the same as
+ 
+
+ align:start position:0%
+Lavar it just means the same as
+expectation of R squared and so much for
+
+ align:start position:0%
+expectation of R squared and so much for
+ 
+
+ align:start position:0%
+expectation of R squared and so much for
+the second rule which we'll use all the
+
+ align:start position:0%
+the second rule which we'll use all the
+ 
+
+ align:start position:0%
+the second rule which we'll use all the
+time because it's a convenient rule to
+
+ align:start position:0%
+time because it's a convenient rule to
+ 
+
+ align:start position:0%
+time because it's a convenient rule to
+have I'm going to prove the second one
+
+ align:start position:0%
+have I'm going to prove the second one
+ 
+
+ align:start position:0%
+have I'm going to prove the second one
+just begin to show you nothing to worry
+
+ align:start position:0%
+just begin to show you nothing to worry
+ 
+
+ align:start position:0%
+just begin to show you nothing to worry
+about you don't even have to remember
+
+ align:start position:0%
+about you don't even have to remember
+ 
+
+ align:start position:0%
+about you don't even have to remember
+how the proof goes because you can
+
+ align:start position:0%
+how the proof goes because you can
+ 
+
+ align:start position:0%
+how the proof goes because you can
+reconstruct it every time so this it's
+
+ align:start position:0%
+reconstruct it every time so this it's
+ 
+
+ align:start position:0%
+reconstruct it every time so this it's
+again simple proofs just by linearity of
+
+ align:start position:0%
+again simple proofs just by linearity of
+ 
+
+ align:start position:0%
+again simple proofs just by linearity of
+expectation and doing the algebra so the
+
+ align:start position:0%
+expectation and doing the algebra so the
+ 
+
+ align:start position:0%
+expectation and doing the algebra so the
+variance of R is by definition the
+
+ align:start position:0%
+variance of R is by definition the
+ 
+
+ align:start position:0%
+variance of R is by definition the
+expectation of R minus mu squared let's
+
+ align:start position:0%
+expectation of R minus mu squared let's
+ 
+
+ align:start position:0%
+expectation of R minus mu squared let's
+expand our minus mu squared it's the
+
+ align:start position:0%
+expand our minus mu squared it's the
+ 
+
+ align:start position:0%
+expand our minus mu squared it's the
+expectation of R squared minus 2 mu R
+
+ align:start position:0%
+expectation of R squared minus 2 mu R
+ 
+
+ align:start position:0%
+expectation of R squared minus 2 mu R
+plus mu squared now we apply linearity
+
+ align:start position:0%
+plus mu squared now we apply linearity
+ 
+
+ align:start position:0%
+plus mu squared now we apply linearity
+to that I get the expectation of R
+
+ align:start position:0%
+to that I get the expectation of R
+ 
+
+ align:start position:0%
+to that I get the expectation of R
+squared minus 2 mu expectation of R plus
+
+ align:start position:0%
+squared minus 2 mu expectation of R plus
+ 
+
+ align:start position:0%
+squared minus 2 mu expectation of R plus
+the expectation of MU squared if I'm
+
+ align:start position:0%
+the expectation of MU squared if I'm
+ 
+
+ align:start position:0%
+the expectation of MU squared if I'm
+really being completely mechanical about
+
+ align:start position:0%
+really being completely mechanical about
+ 
+
+ align:start position:0%
+really being completely mechanical about
+linearity of expectation an expectation
+
+ align:start position:0%
+linearity of expectation an expectation
+ 
+
+ align:start position:0%
+linearity of expectation an expectation
+of a constant mu squared is simply mu
+
+ align:start position:0%
+of a constant mu squared is simply mu
+ 
+
+ align:start position:0%
+of a constant mu squared is simply mu
+squared and here I've got the
+
+ align:start position:0%
+squared and here I've got the
+ 
+
+ align:start position:0%
+squared and here I've got the
+expectation off R that's mu again so I
+
+ align:start position:0%
+expectation off R that's mu again so I
+ 
+
+ align:start position:0%
+expectation off R that's mu again so I
+wind up with the expectation of R
+
+ align:start position:0%
+wind up with the expectation of R
+ 
+
+ align:start position:0%
+wind up with the expectation of R
+squared minus 2
+
+ align:start position:0%
+squared minus 2
+ 
+
+ align:start position:0%
+squared minus 2
+mumu plus R squared the this is 2 mu
+
+ align:start position:0%
+mumu plus R squared the this is 2 mu
+ 
+
+ align:start position:0%
+mumu plus R squared the this is 2 mu
+square minus 2 mu squared plus mu
+
+ align:start position:0%
+square minus 2 mu squared plus mu
+ 
+
+ align:start position:0%
+square minus 2 mu squared plus mu
+squared it lines up with minus mu
+
+ align:start position:0%
+squared it lines up with minus mu
+ 
+
+ align:start position:0%
+squared it lines up with minus mu
+squared and of course mu squared is the
+
+ align:start position:0%
+squared and of course mu squared is the
+ 
+
+ align:start position:0%
+squared and of course mu squared is the
+expectation squared of our food the
+
+ align:start position:0%
+expectation squared of our food the
+ 
+
+ align:start position:0%
+expectation squared of our food the
+formula again has claimed there's
+
+ align:start position:0%
+formula again has claimed there's
+ 
+
+ align:start position:0%
+formula again has claimed there's
+nothing interesting here just algebra
+
+ align:start position:0%
+nothing interesting here just algebra
+ 
+
+ align:start position:0%
+nothing interesting here just algebra
+and linearity of expectation and the
+
+ align:start position:0%
+and linearity of expectation and the
+ 
+
+ align:start position:0%
+and linearity of expectation and the
+first result about factoring out in a
+
+ align:start position:0%
+first result about factoring out in a
+ 
+
+ align:start position:0%
+first result about factoring out in a
+and squaring it follows from a similar
+
+ align:start position:0%
+and squaring it follows from a similar
+ 
+
+ align:start position:0%
+and squaring it follows from a similar
+proof which I'm not going to include
+
+ align:start position:0%
+proof which I'm not going to include
+ 
+
+ align:start position:0%
+proof which I'm not going to include
+here so let's look at the space station
+
+ align:start position:0%
+here so let's look at the space station
+ 
+
+ align:start position:0%
+here so let's look at the space station
+Mir again which we used as an example of
+
+ align:start position:0%
+Mir again which we used as an example of
+ 
+
+ align:start position:0%
+Mir again which we used as an example of
+calculating mean time to failure
+
+ align:start position:0%
+calculating mean time to failure
+ 
+
+ align:start position:0%
+calculating mean time to failure
+so the hypothesis that we're making is
+
+ align:start position:0%
+so the hypothesis that we're making is
+ 
+
+ align:start position:0%
+so the hypothesis that we're making is
+that with probability P the MIR space
+
+ align:start position:0%
+that with probability P the MIR space
+ 
+
+ align:start position:0%
+that with probability P the MIR space
+station will run into some huge space
+
+ align:start position:0%
+station will run into some huge space
+ 
+
+ align:start position:0%
+station will run into some huge space
+garbage and that will collaborate and
+
+ align:start position:0%
+garbage and that will collaborate and
+ 
+
+ align:start position:0%
+garbage and that will collaborate and
+the probability of that happening in any
+
+ align:start position:0%
+the probability of that happening in any
+ 
+
+ align:start position:0%
+the probability of that happening in any
+given hour is probability P so we know
+
+ align:start position:0%
+given hour is probability P so we know
+ 
+
+ align:start position:0%
+given hour is probability P so we know
+that that means that the expected number
+
+ align:start position:0%
+that that means that the expected number
+ 
+
+ align:start position:0%
+that that means that the expected number
+of hours for the MIR to fail is 1 over P
+
+ align:start position:0%
+of hours for the MIR to fail is 1 over P
+ 
+
+ align:start position:0%
+of hours for the MIR to fail is 1 over P
+that's the mean time to failure and what
+
+ align:start position:0%
+that's the mean time to failure and what
+ 
+
+ align:start position:0%
+that's the mean time to failure and what
+we're asking is what's the variance of F
+
+ align:start position:0%
+we're asking is what's the variance of F
+ 
+
+ align:start position:0%
+we're asking is what's the variance of F
+if F is the number of hours to failure
+
+ align:start position:0%
+if F is the number of hours to failure
+ 
+
+ align:start position:0%
+if F is the number of hours to failure
+what's variance of F well one way we can
+
+ align:start position:0%
+what's variance of F well one way we can
+ 
+
+ align:start position:0%
+what's variance of F well one way we can
+do to just plug in the definition of
+
+ align:start position:0%
+do to just plug in the definition of
+ 
+
+ align:start position:0%
+do to just plug in the definition of
+expectation and this will work the
+
+ align:start position:0%
+expectation and this will work the
+ 
+
+ align:start position:0%
+expectation and this will work the
+probability that the that it takes K
+
+ align:start position:0%
+probability that the that it takes K
+ 
+
+ align:start position:0%
+probability that the that it takes K
+hours to fail is we know the geometric
+
+ align:start position:0%
+hours to fail is we know the geometric
+ 
+
+ align:start position:0%
+hours to fail is we know the geometric
+distribution the probability of not
+
+ align:start position:0%
+distribution the probability of not
+ 
+
+ align:start position:0%
+distribution the probability of not
+failing for K minus 1 hours and failing
+
+ align:start position:0%
+failing for K minus 1 hours and failing
+ 
+
+ align:start position:0%
+failing for K minus 1 hours and failing
+after that Q to the K minus 1 times P so
+
+ align:start position:0%
+after that Q to the K minus 1 times P so
+ 
+
+ align:start position:0%
+after that Q to the K minus 1 times P so
+the variance of F using our previous
+
+ align:start position:0%
+the variance of F using our previous
+ 
+
+ align:start position:0%
+the variance of F using our previous
+formula about the expectation of F
+
+ align:start position:0%
+formula about the expectation of F
+ 
+
+ align:start position:0%
+formula about the expectation of F
+squared minus the expectation squared of
+
+ align:start position:0%
+squared minus the expectation squared of
+ 
+
+ align:start position:0%
+squared minus the expectation squared of
+F this becomes a minus 101 over P
+
+ align:start position:0%
+F this becomes a minus 101 over P
+ 
+
+ align:start position:0%
+F this becomes a minus 101 over P
+squared and we can forget about that we
+
+ align:start position:0%
+squared and we can forget about that we
+ 
+
+ align:start position:0%
+squared and we can forget about that we
+want to focus on calculating the
+
+ align:start position:0%
+want to focus on calculating the
+ 
+
+ align:start position:0%
+want to focus on calculating the
+expectation of F squared so F is 1 2 3
+
+ align:start position:0%
+expectation of F squared so F is 1 2 3
+ 
+
+ align:start position:0%
+expectation of F squared so F is 1 2 3
+and so on that means F square is 1 4 9 K
+
+ align:start position:0%
+and so on that means F square is 1 4 9 K
+ 
+
+ align:start position:0%
+and so on that means F square is 1 4 9 K
+square the point being that the only
+
+ align:start position:0%
+square the point being that the only
+ 
+
+ align:start position:0%
+square the point being that the only
+value is that F squared can take our
+
+ align:start position:0%
+value is that F squared can take our
+ 
+
+ align:start position:0%
+value is that F squared can take our
+squares so we don't have to worry about
+
+ align:start position:0%
+squares so we don't have to worry about
+ 
+
+ align:start position:0%
+squares so we don't have to worry about
+counting them in in the sum that defines
+
+ align:start position:0%
+counting them in in the sum that defines
+ 
+
+ align:start position:0%
+counting them in in the sum that defines
+the expectation so let's go look at that
+
+ align:start position:0%
+the expectation so let's go look at that
+ 
+
+ align:start position:0%
+the expectation so let's go look at that
+so the expectation of F squared is the
+
+ align:start position:0%
+so the expectation of F squared is the
+ 
+
+ align:start position:0%
+so the expectation of F squared is the
+sum over the possible value
+
+ align:start position:0%
+sum over the possible value
+ 
+
+ align:start position:0%
+sum over the possible value
+that FK squared can take namely the sum
+
+ align:start position:0%
+that FK squared can take namely the sum
+ 
+
+ align:start position:0%
+that FK squared can take namely the sum
+from k equals 1 to infinity of K squared
+
+ align:start position:0%
+from k equals 1 to infinity of K squared
+ 
+
+ align:start position:0%
+from k equals 1 to infinity of K squared
+times the probability that f squared is
+
+ align:start position:0%
+times the probability that f squared is
+ 
+
+ align:start position:0%
+times the probability that f squared is
+equal to K squared well of course the
+
+ align:start position:0%
+equal to K squared well of course the
+ 
+
+ align:start position:0%
+equal to K squared well of course the
+probability that f squared is equal to K
+
+ align:start position:0%
+probability that f squared is equal to K
+ 
+
+ align:start position:0%
+probability that f squared is equal to K
+squared is the same as the probability
+
+ align:start position:0%
+squared is the same as the probability
+ 
+
+ align:start position:0%
+squared is the same as the probability
+that F equals K so I can and we know
+
+ align:start position:0%
+that F equals K so I can and we know
+ 
+
+ align:start position:0%
+that F equals K so I can and we know
+what the probability of that F equals K
+
+ align:start position:0%
+what the probability of that F equals K
+ 
+
+ align:start position:0%
+what the probability of that F equals K
+is it's a geometric distribution so the
+
+ align:start position:0%
+is it's a geometric distribution so the
+ 
+
+ align:start position:0%
+is it's a geometric distribution so the
+probability that F equals K is Q to the
+
+ align:start position:0%
+probability that F equals K is Q to the
+ 
+
+ align:start position:0%
+probability that F equals K is Q to the
+K minus 1 times P if i factor out a P
+
+ align:start position:0%
+K minus 1 times P if i factor out a P
+ 
+
+ align:start position:0%
+K minus 1 times P if i factor out a P
+over Q this simplifies to the sum from k
+
+ align:start position:0%
+over Q this simplifies to the sum from k
+ 
+
+ align:start position:0%
+over Q this simplifies to the sum from k
+equals 0 to infinity of K squared Q to
+
+ align:start position:0%
+equals 0 to infinity of K squared Q to
+ 
+
+ align:start position:0%
+equals 0 to infinity of K squared Q to
+the K and this is a kind of sum that
+
+ align:start position:0%
+the K and this is a kind of sum that
+ 
+
+ align:start position:0%
+the K and this is a kind of sum that
+we've seen before and that it has a
+
+ align:start position:0%
+we've seen before and that it has a
+ 
+
+ align:start position:0%
+we've seen before and that it has a
+closed form and we could perfectly well
+
+ align:start position:0%
+closed form and we could perfectly well
+ 
+
+ align:start position:0%
+closed form and we could perfectly well
+calculate then the expectation of F
+
+ align:start position:0%
+calculate then the expectation of F
+ 
+
+ align:start position:0%
+calculate then the expectation of F
+squared by appealing to our generating
+
+ align:start position:0%
+squared by appealing to our generating
+ 
+
+ align:start position:0%
+squared by appealing to our generating
+function information to get a closed
+
+ align:start position:0%
+function information to get a closed
+ 
+
+ align:start position:0%
+function information to get a closed
+form for this and then remember to
+
+ align:start position:0%
+form for this and then remember to
+ 
+
+ align:start position:0%
+form for this and then remember to
+subtract 1 minus P squared because the
+
+ align:start position:0%
+subtract 1 minus P squared because the
+ 
+
+ align:start position:0%
+subtract 1 minus P squared because the
+variance is this term minus the square
+
+ align:start position:0%
+variance is this term minus the square
+ 
+
+ align:start position:0%
+variance is this term minus the square
+of the expectation of F but let's go
+
+ align:start position:0%
+of the expectation of F but let's go
+ 
+
+ align:start position:0%
+of the expectation of F but let's go
+another way and use the same technique
+
+ align:start position:0%
+another way and use the same technique
+ 
+
+ align:start position:0%
+another way and use the same technique
+of total expectation that we used before
+
+ align:start position:0%
+of total expectation that we used before
+ 
+
+ align:start position:0%
+of total expectation that we used before
+that is the expectation of F squared of
+
+ align:start position:0%
+that is the expectation of F squared of
+ 
+
+ align:start position:0%
+that is the expectation of F squared of
+the failure x squared is equal by the
+
+ align:start position:0%
+the failure x squared is equal by the
+ 
+
+ align:start position:0%
+the failure x squared is equal by the
+law of total probability so the
+
+ align:start position:0%
+law of total probability so the
+ 
+
+ align:start position:0%
+law of total probability so the
+expectation of F squared given that F is
+
+ align:start position:0%
+expectation of F squared given that F is
+ 
+
+ align:start position:0%
+expectation of F squared given that F is
+1 that is we fail after the on the first
+
+ align:start position:0%
+1 that is we fail after the on the first
+ 
+
+ align:start position:0%
+1 that is we fail after the on the first
+step times the probability that we fail
+
+ align:start position:0%
+step times the probability that we fail
+ 
+
+ align:start position:0%
+step times the probability that we fail
+on the first step plus the expectation
+
+ align:start position:0%
+on the first step plus the expectation
+ 
+
+ align:start position:0%
+on the first step plus the expectation
+of F squared given that we don't fail on
+
+ align:start position:0%
+of F squared given that we don't fail on
+ 
+
+ align:start position:0%
+of F squared given that we don't fail on
+the first step that F is greater than 1
+
+ align:start position:0%
+the first step that F is greater than 1
+ 
+
+ align:start position:0%
+the first step that F is greater than 1
+times the probability that F is greater
+
+ align:start position:0%
+times the probability that F is greater
+ 
+
+ align:start position:0%
+times the probability that F is greater
+than 1 now what's going to make this
+
+ align:start position:0%
+than 1 now what's going to make this
+ 
+
+ align:start position:0%
+than 1 now what's going to make this
+manageable is that this expression the
+
+ align:start position:0%
+manageable is that this expression the
+ 
+
+ align:start position:0%
+manageable is that this expression the
+expectation of F squared when F is
+
+ align:start position:0%
+expectation of F squared when F is
+ 
+
+ align:start position:0%
+expectation of F squared when F is
+greater than 1 will turn out to be
+
+ align:start position:0%
+greater than 1 will turn out to be
+ 
+
+ align:start position:0%
+greater than 1 will turn out to be
+something that we can easily convert
+
+ align:start position:0%
+something that we can easily convert
+ 
+
+ align:start position:0%
+something that we can easily convert
+into a non conditional probability and
+
+ align:start position:0%
+into a non conditional probability and
+ 
+
+ align:start position:0%
+into a non conditional probability and
+find a value for so the lemma that we're
+
+ align:start position:0%
+find a value for so the lemma that we're
+ 
+
+ align:start position:0%
+find a value for so the lemma that we're
+using here is the following when I'm
+
+ align:start position:0%
+using here is the following when I'm
+ 
+
+ align:start position:0%
+using here is the following when I'm
+thinking about mean time to failure if I
+
+ align:start position:0%
+thinking about mean time to failure if I
+ 
+
+ align:start position:0%
+thinking about mean time to failure if I
+think of any function whatsoever G of
+
+ align:start position:0%
+think of any function whatsoever G of
+ 
+
+ align:start position:0%
+think of any function whatsoever G of
+the mean time to failure and I'm
+
+ align:start position:0%
+the mean time to failure and I'm
+ 
+
+ align:start position:0%
+the mean time to failure and I'm
+interested in the expectation of G of F
+
+ align:start position:0%
+interested in the expectation of G of F
+ 
+
+ align:start position:0%
+interested in the expectation of G of F
+and I'm interested in the expectation of
+
+ align:start position:0%
+and I'm interested in the expectation of
+ 
+
+ align:start position:0%
+and I'm interested in the expectation of
+G of F given that F is greater than n
+
+ align:start position:0%
+G of F given that F is greater than n
+ 
+
+ align:start position:0%
+G of F given that F is greater than n
+that is it's already taken n steps to
+
+ align:start position:0%
+that is it's already taken n steps to
+ 
+
+ align:start position:0%
+that is it's already taken n steps to
+get where I am then the thing about the
+
+ align:start position:0%
+get where I am then the thing about the
+ 
+
+ align:start position:0%
+get where I am then the thing about the
+mean time to failure is that at any
+
+ align:start position:0%
+mean time to failure is that at any
+ 
+
+ align:start position:0%
+mean time to failure is that at any
+moment
+
+ align:start position:0%
+moment
+ 
+
+ align:start position:0%
+moment
+on what that you haven't failed you're
+
+ align:start position:0%
+on what that you haven't failed you're
+ 
+
+ align:start position:0%
+on what that you haven't failed you're
+starting off in essentially the same
+
+ align:start position:0%
+starting off in essentially the same
+ 
+
+ align:start position:0%
+starting off in essentially the same
+situation you were at the beginning in
+
+ align:start position:0%
+situation you were at the beginning in
+ 
+
+ align:start position:0%
+situation you were at the beginning in
+waiting for the next failure to occur
+
+ align:start position:0%
+waiting for the next failure to occur
+ 
+
+ align:start position:0%
+waiting for the next failure to occur
+and the probability of failing in one
+
+ align:start position:0%
+and the probability of failing in one
+ 
+
+ align:start position:0%
+and the probability of failing in one
+more step is the same probability is the
+
+ align:start position:0%
+more step is the same probability is the
+ 
+
+ align:start position:0%
+more step is the same probability is the
+same P and the probability of you're
+
+ align:start position:0%
+same P and the probability of you're
+ 
+
+ align:start position:0%
+same P and the probability of you're
+failing in two more steps is QP and
+
+ align:start position:0%
+failing in two more steps is QP and
+ 
+
+ align:start position:0%
+failing in two more steps is QP and
+three more steps is Q QP the only
+
+ align:start position:0%
+three more steps is Q QP the only
+ 
+
+ align:start position:0%
+three more steps is Q QP the only
+difference is that the value of F has
+
+ align:start position:0%
+difference is that the value of F has
+ 
+
+ align:start position:0%
+difference is that the value of F has
+been shifted by n it was in the ordinary
+
+ align:start position:0%
+been shifted by n it was in the ordinary
+ 
+
+ align:start position:0%
+been shifted by n it was in the ordinary
+case we start off with F equals zero and
+
+ align:start position:0%
+case we start off with F equals zero and
+ 
+
+ align:start position:0%
+case we start off with F equals zero and
+look at the probability that we failing
+
+ align:start position:0%
+look at the probability that we failing
+ 
+
+ align:start position:0%
+look at the probability that we failing
+one more step two more steps now we're
+
+ align:start position:0%
+one more step two more steps now we're
+ 
+
+ align:start position:0%
+one more step two more steps now we're
+starting off with F having the value F
+
+ align:start position:0%
+starting off with F having the value F
+ 
+
+ align:start position:0%
+starting off with F having the value F
+plus N and asking about the probability
+
+ align:start position:0%
+plus N and asking about the probability
+ 
+
+ align:start position:0%
+plus N and asking about the probability
+that it fails in the next step or the
+
+ align:start position:0%
+that it fails in the next step or the
+ 
+
+ align:start position:0%
+that it fails in the next step or the
+next step on the next step so the
+
+ align:start position:0%
+next step on the next step so the
+ 
+
+ align:start position:0%
+next step on the next step so the
+punchline is that the expectation of G
+
+ align:start position:0%
+punchline is that the expectation of G
+ 
+
+ align:start position:0%
+punchline is that the expectation of G
+of F given that F is greater than n is
+
+ align:start position:0%
+of F given that F is greater than n is
+ 
+
+ align:start position:0%
+of F given that F is greater than n is
+simply the expectation of G of F plus N
+
+ align:start position:0%
+simply the expectation of G of F plus N
+ 
+
+ align:start position:0%
+simply the expectation of G of F plus N
+and I'm gonna let you meditate that and
+
+ align:start position:0%
+and I'm gonna let you meditate that and
+ 
+
+ align:start position:0%
+and I'm gonna let you meditate that and
+not say any more about it but the
+
+ align:start position:0%
+not say any more about it but the
+ 
+
+ align:start position:0%
+not say any more about it but the
+punchline is the corollary that the
+
+ align:start position:0%
+punchline is the corollary that the
+ 
+
+ align:start position:0%
+punchline is the corollary that the
+expectation of F squared given that F is
+
+ align:start position:0%
+expectation of F squared given that F is
+ 
+
+ align:start position:0%
+expectation of F squared given that F is
+greater than 1 is simply the expectation
+
+ align:start position:0%
+greater than 1 is simply the expectation
+ 
+
+ align:start position:0%
+greater than 1 is simply the expectation
+of F plus 1 squared and that lets us go
+
+ align:start position:0%
+of F plus 1 squared and that lets us go
+ 
+
+ align:start position:0%
+of F plus 1 squared and that lets us go
+back and simplify this expression that
+
+ align:start position:0%
+back and simplify this expression that
+ 
+
+ align:start position:0%
+back and simplify this expression that
+we had from total expectation we now
+
+ align:start position:0%
+we had from total expectation we now
+ 
+
+ align:start position:0%
+we had from total expectation we now
+have here's the F expectation of F
+
+ align:start position:0%
+have here's the F expectation of F
+ 
+
+ align:start position:0%
+have here's the F expectation of F
+squared given that F is greater than 1
+
+ align:start position:0%
+squared given that F is greater than 1
+ 
+
+ align:start position:0%
+squared given that F is greater than 1
+and let's look at these other terms this
+
+ align:start position:0%
+and let's look at these other terms this
+ 
+
+ align:start position:0%
+and let's look at these other terms this
+is the expectation of F square given
+
+ align:start position:0%
+is the expectation of F square given
+ 
+
+ align:start position:0%
+is the expectation of F square given
+that F equals 1 well the expectation of
+
+ align:start position:0%
+that F equals 1 well the expectation of
+ 
+
+ align:start position:0%
+that F equals 1 well the expectation of
+F square given that F equals 1 is 1
+
+ align:start position:0%
+F square given that F equals 1 is 1
+ 
+
+ align:start position:0%
+F square given that F equals 1 is 1
+squared because we know what F is and
+
+ align:start position:0%
+squared because we know what F is and
+ 
+
+ align:start position:0%
+squared because we know what F is and
+that's the end of the story
+
+ align:start position:0%
+that's the end of the story
+ 
+
+ align:start position:0%
+that's the end of the story
+times the probability that F equals 1
+
+ align:start position:0%
+times the probability that F equals 1
+ 
+
+ align:start position:0%
+times the probability that F equals 1
+that's P the probability of failure on a
+
+ align:start position:0%
+that's P the probability of failure on a
+ 
+
+ align:start position:0%
+that's P the probability of failure on a
+given step this is the probability that
+
+ align:start position:0%
+given step this is the probability that
+ 
+
+ align:start position:0%
+given step this is the probability that
+F is greater than 1 which is Q that we
+
+ align:start position:0%
+F is greater than 1 which is Q that we
+ 
+
+ align:start position:0%
+F is greater than 1 which is Q that we
+didn't fail on the first step and we
+
+ align:start position:0%
+didn't fail on the first step and we
+ 
+
+ align:start position:0%
+didn't fail on the first step and we
+just figured out that this term is the
+
+ align:start position:0%
+just figured out that this term is the
+ 
+
+ align:start position:0%
+just figured out that this term is the
+expectation of the square of F of F plus
+
+ align:start position:0%
+expectation of the square of F of F plus
+ 
+
+ align:start position:0%
+expectation of the square of F of F plus
+1 so there's the 1 in the P and that
+
+ align:start position:0%
+1 so there's the 1 in the P and that
+ 
+
+ align:start position:0%
+1 so there's the 1 in the P and that
+becomes a Q and this is the expectation
+
+ align:start position:0%
+becomes a Q and this is the expectation
+ 
+
+ align:start position:0%
+becomes a Q and this is the expectation
+of F plus 1 squared now again I apply
+
+ align:start position:0%
+of F plus 1 squared now again I apply
+ 
+
+ align:start position:0%
+of F plus 1 squared now again I apply
+limit linearity I'm going to expand F
+
+ align:start position:0%
+limit linearity I'm going to expand F
+ 
+
+ align:start position:0%
+limit linearity I'm going to expand F
+plus 1 squared into F squared plus 2 F
+
+ align:start position:0%
+plus 1 squared into F squared plus 2 F
+ 
+
+ align:start position:0%
+plus 1 squared into F squared plus 2 F
+plus 1 and then apply linearity of
+
+ align:start position:0%
+plus 1 and then apply linearity of
+ 
+
+ align:start position:0%
+plus 1 and then apply linearity of
+expectation and I'm going to wind up
+
+ align:start position:0%
+expectation and I'm going to wind up
+ 
+
+ align:start position:0%
+expectation and I'm going to wind up
+with the expectation of F squared
+
+ align:start position:0%
+with the expectation of F squared
+ 
+
+ align:start position:0%
+with the expectation of F squared
+twice the expectation of F which
+
+ align:start position:0%
+twice the expectation of F which
+ 
+
+ align:start position:0%
+twice the expectation of F which
+remember is twice over two over P plus 1
+
+ align:start position:0%
+remember is twice over two over P plus 1
+ 
+
+ align:start position:0%
+remember is twice over two over P plus 1
+times the Q and now what I've got is a
+
+ align:start position:0%
+times the Q and now what I've got is a
+ 
+
+ align:start position:0%
+times the Q and now what I've got is a
+simple arithmetic equation between the
+
+ align:start position:0%
+simple arithmetic equation between the
+ 
+
+ align:start position:0%
+simple arithmetic equation between the
+expectation of F squared and some other
+
+ align:start position:0%
+expectation of F squared and some other
+ 
+
+ align:start position:0%
+expectation of F squared and some other
+arithmetic and the expectation of F
+
+ align:start position:0%
+arithmetic and the expectation of F
+ 
+
+ align:start position:0%
+arithmetic and the expectation of F
+squared it's easy to solve for the
+
+ align:start position:0%
+squared it's easy to solve for the
+ 
+
+ align:start position:0%
+squared it's easy to solve for the
+expectation of F squared
+
+ align:start position:0%
+expectation of F squared
+ 
+
+ align:start position:0%
+expectation of F squared
+and I'll spare you that elementary
+
+ align:start position:0%
+and I'll spare you that elementary
+ 
+
+ align:start position:0%
+and I'll spare you that elementary
+simplification but the punchline is when
+
+ align:start position:0%
+simplification but the punchline is when
+ 
+
+ align:start position:0%
+simplification but the punchline is when
+we also remember to subtract 1 over P
+
+ align:start position:0%
+we also remember to subtract 1 over P
+ 
+
+ align:start position:0%
+we also remember to subtract 1 over P
+squared because that was the expectation
+
+ align:start position:0%
+squared because that was the expectation
+ 
+
+ align:start position:0%
+squared because that was the expectation
+of the square of F of the expectation of
+
+ align:start position:0%
+of the square of F of the expectation of
+ 
+
+ align:start position:0%
+of the square of F of the expectation of
+F we come up with this punchline formula
+
+ align:start position:0%
+F we come up with this punchline formula
+ 
+
+ align:start position:0%
+F we come up with this punchline formula
+the variance of mean time to failure is
+
+ align:start position:0%
+the variance of mean time to failure is
+ 
+
+ align:start position:0%
+the variance of mean time to failure is
+1 over the probability of failure on a
+
+ align:start position:0%
+1 over the probability of failure on a
+ 
+
+ align:start position:0%
+1 over the probability of failure on a
+given step times 1 minus 1 over the
+
+ align:start position:0%
+given step times 1 minus 1 over the
+ 
+
+ align:start position:0%
+given step times 1 minus 1 over the
+times the probability 1 over the
+
+ align:start position:0%
+times the probability 1 over the
+ 
+
+ align:start position:0%
+times the probability 1 over the
+probability of a failure in the first
+
+ align:start position:0%
+probability of a failure in the first
+ 
+
+ align:start position:0%
+probability of a failure in the first
+step minus 1 all right let's just for
+
+ align:start position:0%
+step minus 1 all right let's just for
+ 
+
+ align:start position:0%
+step minus 1 all right let's just for
+practice and fun let's look at the space
+
+ align:start position:0%
+practice and fun let's look at the space
+ 
+
+ align:start position:0%
+practice and fun let's look at the space
+station Mir again suppose that I tell
+
+ align:start position:0%
+station Mir again suppose that I tell
+ 
+
+ align:start position:0%
+station Mir again suppose that I tell
+you that there's a 1 in 10,000 chance
+
+ align:start position:0%
+you that there's a 1 in 10,000 chance
+ 
+
+ align:start position:0%
+you that there's a 1 in 10,000 chance
+that in any given hour the mirrors gonna
+
+ align:start position:0%
+that in any given hour the mirrors gonna
+ 
+
+ align:start position:0%
+that in any given hour the mirrors gonna
+crash into some debris that's out there
+
+ align:start position:0%
+crash into some debris that's out there
+ 
+
+ align:start position:0%
+crash into some debris that's out there
+in orbit so the expectation of F is 10
+
+ align:start position:0%
+in orbit so the expectation of F is 10
+ 
+
+ align:start position:0%
+in orbit so the expectation of F is 10
+to the fourth about 10,000 hours and the
+
+ align:start position:0%
+to the fourth about 10,000 hours and the
+ 
+
+ align:start position:0%
+to the fourth about 10,000 hours and the
+Sigma is gonna be the variance of of F
+
+ align:start position:0%
+Sigma is gonna be the variance of of F
+ 
+
+ align:start position:0%
+Sigma is gonna be the variance of of F
+which is about one over one
+
+ align:start position:0%
+which is about one over one
+ 
+
+ align:start position:0%
+which is about one over one
+ten-thousandth then is 10,000 times
+
+ align:start position:0%
+ten-thousandth then is 10,000 times
+ 
+
+ align:start position:0%
+ten-thousandth then is 10,000 times
+10,000 minus one which is pretty close
+
+ align:start position:0%
+10,000 minus one which is pretty close
+ 
+
+ align:start position:0%
+10,000 minus one which is pretty close
+to 10,000 squared for the variance and
+
+ align:start position:0%
+to 10,000 squared for the variance and
+ 
+
+ align:start position:0%
+to 10,000 squared for the variance and
+then when I take the square root I get
+
+ align:start position:0%
+then when I take the square root I get
+ 
+
+ align:start position:0%
+then when I take the square root I get
+back to 10,000 so Sigma is just a tad
+
+ align:start position:0%
+back to 10,000 so Sigma is just a tad
+ 
+
+ align:start position:0%
+back to 10,000 so Sigma is just a tad
+less than than 10,000 it's 10 to the
+
+ align:start position:0%
+less than than 10,000 it's 10 to the
+ 
+
+ align:start position:0%
+less than than 10,000 it's 10 to the
+fourth so with those numbers I can apply
+
+ align:start position:0%
+fourth so with those numbers I can apply
+ 
+
+ align:start position:0%
+fourth so with those numbers I can apply
+the chebyshev theorem and conclude that
+
+ align:start position:0%
+the chebyshev theorem and conclude that
+ 
+
+ align:start position:0%
+the chebyshev theorem and conclude that
+the probability that the near lasts more
+
+ align:start position:0%
+the probability that the near lasts more
+ 
+
+ align:start position:0%
+the probability that the near lasts more
+than 4 times 10 to the 4th hours is less
+
+ align:start position:0%
+than 4 times 10 to the 4th hours is less
+ 
+
+ align:start position:0%
+than 4 times 10 to the 4th hours is less
+than one chance in 4 and if we translate
+
+ align:start position:0%
+than one chance in 4 and if we translate
+ 
+
+ align:start position:0%
+than one chance in 4 and if we translate
+that into years if it was really the
+
+ align:start position:0%
+that into years if it was really the
+ 
+
+ align:start position:0%
+that into years if it was really the
+case that there was a 1 in 10,000 chance
+
+ align:start position:0%
+case that there was a 1 in 10,000 chance
+ 
+
+ align:start position:0%
+case that there was a 1 in 10,000 chance
+of them--are being destroyed in any
+
+ align:start position:0%
+of them--are being destroyed in any
+ 
+
+ align:start position:0%
+of them--are being destroyed in any
+given hour and the probability that it
+
+ align:start position:0%
+given hour and the probability that it
+ 
+
+ align:start position:0%
+given hour and the probability that it
+lasts more than four point six years
+
+ align:start position:0%
+lasts more than four point six years
+ 
+
+ align:start position:0%
+lasts more than four point six years
+before destructing is less than 1/4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so another rule for calculating variance
+
+ align:start position:0%
+so another rule for calculating variance
+ 
+
+ align:start position:0%
+so another rule for calculating variance
+and then maybe the most important
+
+ align:start position:0%
+and then maybe the most important
+ 
+
+ align:start position:0%
+and then maybe the most important
+general one is that variance is additive
+
+ align:start position:0%
+general one is that variance is additive
+ 
+
+ align:start position:0%
+general one is that variance is additive
+that is the variance of a sum is the sum
+
+ align:start position:0%
+that is the variance of a sum is the sum
+ 
+
+ align:start position:0%
+that is the variance of a sum is the sum
+of the variances but unlike expectation
+
+ align:start position:0%
+of the variances but unlike expectation
+ 
+
+ align:start position:0%
+of the variances but unlike expectation
+where there's no other side condition
+
+ align:start position:0%
+where there's no other side condition
+ 
+
+ align:start position:0%
+where there's no other side condition
+and it does not in any way depend on
+
+ align:start position:0%
+and it does not in any way depend on
+ 
+
+ align:start position:0%
+and it does not in any way depend on
+independence it turns out that variance
+
+ align:start position:0%
+independence it turns out that variance
+ 
+
+ align:start position:0%
+independence it turns out that variance
+is additive only if the variables being
+
+ align:start position:0%
+is additive only if the variables being
+ 
+
+ align:start position:0%
+is additive only if the variables being
+added are pairwise independent now you
+
+ align:start position:0%
+added are pairwise independent now you
+ 
+
+ align:start position:0%
+added are pairwise independent now you
+might wonder where the pairwise came
+
+ align:start position:0%
+might wonder where the pairwise came
+ 
+
+ align:start position:0%
+might wonder where the pairwise came
+from and it's because variance is the
+
+ align:start position:0%
+from and it's because variance is the
+ 
+
+ align:start position:0%
+from and it's because variance is the
+square of an expectation so when you
+
+ align:start position:0%
+square of an expectation so when you
+ 
+
+ align:start position:0%
+square of an expectation so when you
+wind up multiplying out and doing the
+
+ align:start position:0%
+wind up multiplying out and doing the
+ 
+
+ align:start position:0%
+wind up multiplying out and doing the
+algebra you're just getting quadratic
+
+ align:start position:0%
+algebra you're just getting quadratic
+ 
+
+ align:start position:0%
+algebra you're just getting quadratic
+terms that you for variances of four
+
+ align:start position:0%
+terms that you for variances of four
+ 
+
+ align:start position:0%
+terms that you for variances of four
+expectations of RI times RJ and so you
+
+ align:start position:0%
+expectations of RI times RJ and so you
+ 
+
+ align:start position:0%
+expectations of RI times RJ and so you
+need to factor those into into
+
+ align:start position:0%
+need to factor those into into
+ 
+
+ align:start position:0%
+need to factor those into into
+expectation of our x expect our I times
+
+ align:start position:0%
+expectation of our x expect our I times
+ 
+
+ align:start position:0%
+expectation of our x expect our I times
+expectation of RJ which you only need
+
+ align:start position:0%
+expectation of RJ which you only need
+ 
+
+ align:start position:0%
+expectation of RJ which you only need
+pairwise independence for so that's a
+
+ align:start position:0%
+pairwise independence for so that's a
+ 
+
+ align:start position:0%
+pairwise independence for so that's a
+fast-talking through the algebra that
+
+ align:start position:0%
+fast-talking through the algebra that
+ 
+
+ align:start position:0%
+fast-talking through the algebra that
+I'm going to leave to you it's in the
+
+ align:start position:0%
+I'm going to leave to you it's in the
+ 
+
+ align:start position:0%
+I'm going to leave to you it's in the
+text and it's again one of these easy
+
+ align:start position:0%
+text and it's again one of these easy
+ 
+
+ align:start position:0%
+text and it's again one of these easy
+proofs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/o93axeQJqJ8.txt b/o93axeQJqJ8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7d95b3873cdadd743a4380cefb8bb97a70bf2dd3
--- /dev/null
+++ b/o93axeQJqJ8.txt
@@ -0,0 +1,1723 @@
+align:start position:0%
+ 
+okay well well you see spring has
+
+ align:start position:0%
+okay well well you see spring has
+ 
+
+ align:start position:0%
+okay well well you see spring has
+finally come to Boston my sweater is
+
+ align:start position:0%
+finally come to Boston my sweater is
+ 
+
+ align:start position:0%
+finally come to Boston my sweater is
+gone and uh it's April the 16th I think
+
+ align:start position:0%
+gone and uh it's April the 16th I think
+ 
+
+ align:start position:0%
+gone and uh it's April the 16th I think
+it's getting the late spring okay so
+
+ align:start position:0%
+it's getting the late spring okay so
+ 
+
+ align:start position:0%
+it's getting the late spring okay so
+today this video is the nice case
+
+ align:start position:0%
+today this video is the nice case
+ 
+
+ align:start position:0%
+today this video is the nice case
+constant coefficients linear equations
+
+ align:start position:0%
+constant coefficients linear equations
+ 
+
+ align:start position:0%
+constant coefficients linear equations
+and the right hand side is an
+
+ align:start position:0%
+and the right hand side is an
+ 
+
+ align:start position:0%
+and the right hand side is an
+exponential those are the best and we've
+
+ align:start position:0%
+exponential those are the best and we've
+ 
+
+ align:start position:0%
+exponential those are the best and we've
+seen that before in fact let me extend
+
+ align:start position:0%
+seen that before in fact let me extend
+ 
+
+ align:start position:0%
+seen that before in fact let me extend
+to from we saw it for first order
+
+ align:start position:0%
+to from we saw it for first order
+ 
+
+ align:start position:0%
+to from we saw it for first order
+equations here it is for second order
+
+ align:start position:0%
+equations here it is for second order
+ 
+
+ align:start position:0%
+equations here it is for second order
+equations and it could be an nth order
+
+ align:start position:0%
+equations and it could be an nth order
+ 
+
+ align:start position:0%
+equations and it could be an nth order
+equation we could have the nth
+
+ align:start position:0%
+equation we could have the nth
+ 
+
+ align:start position:0%
+equation we could have the nth
+derivative and all lower derivatives the
+
+ align:start position:0%
+derivative and all lower derivatives the
+ 
+
+ align:start position:0%
+derivative and all lower derivatives the
+first derivative the function itself
+
+ align:start position:0%
+first derivative the function itself
+ 
+
+ align:start position:0%
+first derivative the function itself
+zeroth derivative with coefficients
+
+ align:start position:0%
+zeroth derivative with coefficients
+ 
+
+ align:start position:0%
+zeroth derivative with coefficients
+constant coefficients equaling e to the
+
+ align:start position:0%
+constant coefficients equaling e to the
+ 
+
+ align:start position:0%
+constant coefficients equaling e to the
+St that's what makes it easy and what do
+
+ align:start position:0%
+St that's what makes it easy and what do
+ 
+
+ align:start position:0%
+St that's what makes it easy and what do
+we do when the right hand side is e to
+
+ align:start position:0%
+we do when the right hand side is e to
+ 
+
+ align:start position:0%
+we do when the right hand side is e to
+the St we look for a solution a multiple
+
+ align:start position:0%
+the St we look for a solution a multiple
+ 
+
+ align:start position:0%
+the St we look for a solution a multiple
+of e to the St capital y * e to the St
+
+ align:start position:0%
+of e to the St capital y * e to the St
+ 
+
+ align:start position:0%
+of e to the St capital y * e to the St
+that's going to work we just plug into
+
+ align:start position:0%
+that's going to work we just plug into
+ 
+
+ align:start position:0%
+that's going to work we just plug into
+the equation to find that transfer
+
+ align:start position:0%
+the equation to find that transfer
+ 
+
+ align:start position:0%
+the equation to find that transfer
+function capital Y can I just do that
+
+ align:start position:0%
+function capital Y can I just do that
+ 
+
+ align:start position:0%
+function capital Y can I just do that
+I'll do it for the big the INF degree
+
+ align:start position:0%
+I'll do it for the big the INF degree
+ 
+
+ align:start position:0%
+I'll do it for the big the INF degree
+why not so when I plug this in for y
+
+ align:start position:0%
+why not so when I plug this in for y
+ 
+
+ align:start position:0%
+why not so when I plug this in for y
+every derivative brings an S so there's
+
+ align:start position:0%
+every derivative brings an S so there's
+ 
+
+ align:start position:0%
+every derivative brings an S so there's
+the the capital Y is still there the
+
+ align:start position:0%
+the the capital Y is still there the
+ 
+
+ align:start position:0%
+the the capital Y is still there the
+exponential is going to be still there
+
+ align:start position:0%
+exponential is going to be still there
+ 
+
+ align:start position:0%
+exponential is going to be still there
+and then there all the s's that that
+
+ align:start position:0%
+and then there all the s's that that
+ 
+
+ align:start position:0%
+and then there all the s's that that
+come down from the derivatives n s's
+
+ align:start position:0%
+come down from the derivatives n s's
+ 
+
+ align:start position:0%
+come down from the derivatives n s's
+from the nth derivative 1 s from the
+
+ align:start position:0%
+from the nth derivative 1 s from the
+ 
+
+ align:start position:0%
+from the nth derivative 1 s from the
+first derivative no s from the constant
+
+ align:start position:0%
+first derivative no s from the constant
+ 
+
+ align:start position:0%
+first derivative no s from the constant
+term do you see that equation is exactly
+
+ align:start position:0%
+term do you see that equation is exactly
+ 
+
+ align:start position:0%
+term do you see that equation is exactly
+like what we had before with a S2 + b s
+
+ align:start position:0%
+like what we had before with a S2 + b s
+ 
+
+ align:start position:0%
+like what we had before with a S2 + b s
++ C we had quadratic equation the most
+
+ align:start position:0%
++ C we had quadratic equation the most
+ 
+
+ align:start position:0%
++ C we had quadratic equation the most
+important case now I'm including that
+
+ align:start position:0%
+important case now I'm including that
+ 
+
+ align:start position:0%
+important case now I'm including that
+with any any degree equation in degree
+
+ align:start position:0%
+with any any degree equation in degree
+ 
+
+ align:start position:0%
+with any any degree equation in degree
+equation okay and what's the solution
+
+ align:start position:0%
+equation okay and what's the solution
+ 
+
+ align:start position:0%
+equation okay and what's the solution
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+y because e to the St cancels e to the
+
+ align:start position:0%
+y because e to the St cancels e to the
+ 
+
+ align:start position:0%
+y because e to the St cancels e to the
+St that whole thing equals 1 I divide by
+
+ align:start position:0%
+St that whole thing equals 1 I divide by
+ 
+
+ align:start position:0%
+St that whole thing equals 1 I divide by
+this and I get y = 1 over that key
+
+ align:start position:0%
+this and I get y = 1 over that key
+ 
+
+ align:start position:0%
+this and I get y = 1 over that key
+polinomial it's a Nth Degree polinomial
+
+ align:start position:0%
+polinomial it's a Nth Degree polinomial
+ 
+
+ align:start position:0%
+polinomial it's a Nth Degree polinomial
+it's and the one over it is called the
+
+ align:start position:0%
+it's and the one over it is called the
+ 
+
+ align:start position:0%
+it's and the one over it is called the
+transfer function and uh it that
+
+ align:start position:0%
+transfer function and uh it that
+ 
+
+ align:start position:0%
+transfer function and uh it that
+transfer function transfers the input e
+
+ align:start position:0%
+transfer function transfers the input e
+ 
+
+ align:start position:0%
+transfer function transfers the input e
+to the St to the output y e to the St
+
+ align:start position:0%
+to the St to the output y e to the St
+ 
+
+ align:start position:0%
+to the St to the output y e to the St
+it's the it gives the exponential
+
+ align:start position:0%
+it's the it gives the exponential
+ 
+
+ align:start position:0%
+it's the it gives the exponential
+response very nice formula couldn't be
+
+ align:start position:0%
+response very nice formula couldn't be
+ 
+
+ align:start position:0%
+response very nice formula couldn't be
+better and you remember when for second
+
+ align:start position:0%
+better and you remember when for second
+ 
+
+ align:start position:0%
+better and you remember when for second
+degree equations our most important case
+
+ align:start position:0%
+degree equations our most important case
+ 
+
+ align:start position:0%
+degree equations our most important case
+is a S 2 b s + C okay that's the
+
+ align:start position:0%
+is a S 2 b s + C okay that's the
+ 
+
+ align:start position:0%
+is a S 2 b s + C okay that's the
+solution almost every time but one thing
+
+ align:start position:0%
+solution almost every time but one thing
+ 
+
+ align:start position:0%
+solution almost every time but one thing
+can go wrong one thing can go wrong
+
+ align:start position:0%
+can go wrong one thing can go wrong
+ 
+
+ align:start position:0%
+can go wrong one thing can go wrong
+suppose for the particular s the
+
+ align:start position:0%
+suppose for the particular s the
+ 
+
+ align:start position:0%
+suppose for the particular s the
+particular exponent in the in the
+
+ align:start position:0%
+particular exponent in the in the
+ 
+
+ align:start position:0%
+particular exponent in the in the
+forcing function suppose that s in the
+
+ align:start position:0%
+forcing function suppose that s in the
+ 
+
+ align:start position:0%
+forcing function suppose that s in the
+forcing function is also an one of the
+
+ align:start position:0%
+forcing function is also an one of the
+ 
+
+ align:start position:0%
+forcing function is also an one of the
+s's in the null Solutions you remember
+
+ align:start position:0%
+s's in the null Solutions you remember
+ 
+
+ align:start position:0%
+s's in the null Solutions you remember
+the null Solutions with the that there
+
+ align:start position:0%
+the null Solutions with the that there
+ 
+
+ align:start position:0%
+the null Solutions with the that there
+are two
+
+ align:start position:0%
+are two
+ 
+
+ align:start position:0%
+are two
+s's S1 and S2 that make this zero that
+
+ align:start position:0%
+s's S1 and S2 that make this zero that
+ 
+
+ align:start position:0%
+s's S1 and S2 that make this zero that
+make that zero those are the S1 and S2
+
+ align:start position:0%
+make that zero those are the S1 and S2
+ 
+
+ align:start position:0%
+make that zero those are the S1 and S2
+that go into the null
+
+ align:start position:0%
+that go into the null
+ 
+
+ align:start position:0%
+that go into the null
+Solutions now if the forcing s is one of
+
+ align:start position:0%
+Solutions now if the forcing s is one of
+ 
+
+ align:start position:0%
+Solutions now if the forcing s is one of
+those null solution
+
+ align:start position:0%
+those null solution
+ 
+
+ align:start position:0%
+those null solution
+s's we have a problem because this is 1
+
+ align:start position:0%
+s's we have a problem because this is 1
+ 
+
+ align:start position:0%
+s's we have a problem because this is 1
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+zero and we can't uh we haven't got an
+
+ align:start position:0%
+zero and we can't uh we haven't got an
+ 
+
+ align:start position:0%
+zero and we can't uh we haven't got an
+answer yet one over zero has no meaning
+
+ align:start position:0%
+answer yet one over zero has no meaning
+ 
+
+ align:start position:0%
+answer yet one over zero has no meaning
+so I have to this is called resonance
+
+ align:start position:0%
+so I have to this is called resonance
+ 
+
+ align:start position:0%
+so I have to this is called resonance
+resonance is when the forcing exponent
+
+ align:start position:0%
+resonance is when the forcing exponent
+ 
+
+ align:start position:0%
+resonance is when the forcing exponent
+is one of the null exponents that make
+
+ align:start position:0%
+is one of the null exponents that make
+ 
+
+ align:start position:0%
+is one of the null exponents that make
+this zero and there are two of those for
+
+ align:start position:0%
+this zero and there are two of those for
+ 
+
+ align:start position:0%
+this zero and there are two of those for
+for second order equations and there
+
+ align:start position:0%
+for second order equations and there
+ 
+
+ align:start position:0%
+for second order equations and there
+will be n
+
+ align:start position:0%
+will be n
+ 
+
+ align:start position:0%
+will be n
+different s's S1 S2 up to SN for nth
+
+ align:start position:0%
+different s's S1 S2 up to SN for nth
+ 
+
+ align:start position:0%
+different s's S1 S2 up to SN for nth
+degree equations those would be called
+
+ align:start position:0%
+degree equations those would be called
+ 
+
+ align:start position:0%
+degree equations those would be called
+those special s's I could also call them
+
+ align:start position:0%
+those special s's I could also call them
+ 
+
+ align:start position:0%
+those special s's I could also call them
+polls of the transfer function the
+
+ align:start position:0%
+polls of the transfer function the
+ 
+
+ align:start position:0%
+polls of the transfer function the
+transfer function has this in the
+
+ align:start position:0%
+transfer function has this in the
+ 
+
+ align:start position:0%
+transfer function has this in the
+denominator and when this is zero uh
+
+ align:start position:0%
+denominator and when this is zero uh
+ 
+
+ align:start position:0%
+denominator and when this is zero uh
+that identifies a pole so the S1 S2 to
+
+ align:start position:0%
+that identifies a pole so the S1 S2 to
+ 
+
+ align:start position:0%
+that identifies a pole so the S1 S2 to
+SN are the poles and we hope that this s
+
+ align:start position:0%
+SN are the poles and we hope that this s
+ 
+
+ align:start position:0%
+SN are the poles and we hope that this s
+is not one of those but it could be and
+
+ align:start position:0%
+is not one of those but it could be and
+ 
+
+ align:start position:0%
+is not one of those but it could be and
+if it is we need a new formula so that's
+
+ align:start position:0%
+if it is we need a new formula so that's
+ 
+
+ align:start position:0%
+if it is we need a new formula so that's
+the the only remaining case this is
+
+ align:start position:0%
+the the only remaining case this is
+ 
+
+ align:start position:0%
+the the only remaining case this is
+completely nice picture we just need
+
+ align:start position:0%
+completely nice picture we just need
+ 
+
+ align:start position:0%
+completely nice picture we just need
+this last case of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resonance when s equals say S1 kind I'll
+
+ align:start position:0%
+resonance when s equals say S1 kind I'll
+ 
+
+ align:start position:0%
+resonance when s equals say S1 kind I'll
+just pick S1 and when a I know that a S1
+
+ align:start position:0%
+just pick S1 and when a I know that a S1
+ 
+
+ align:start position:0%
+just pick S1 and when a I know that a S1
+2 + B S1 + C is
+
+ align:start position:0%
+2 + B S1 + C is
+ 
+
+ align:start position:0%
+2 + B S1 + C is
+zero so y would be 1 over Z and we can't
+
+ align:start position:0%
+zero so y would be 1 over Z and we can't
+ 
+
+ align:start position:0%
+zero so y would be 1 over Z and we can't
+live with that I've written here for the
+
+ align:start position:0%
+live with that I've written here for the
+ 
+
+ align:start position:0%
+live with that I've written here for the
+second degree equation same possibility
+
+ align:start position:0%
+second degree equation same possibility
+ 
+
+ align:start position:0%
+second degree equation same possibility
+for the N degree a ns1 to the N plus
+
+ align:start position:0%
+for the N degree a ns1 to the N plus
+ 
+
+ align:start position:0%
+for the N degree a ns1 to the N plus
+plus a0 equal 0 that would be a problem
+
+ align:start position:0%
+plus a0 equal 0 that would be a problem
+ 
+
+ align:start position:0%
+plus a0 equal 0 that would be a problem
+of resonance in the N equation this
+
+ align:start position:0%
+of resonance in the N equation this
+ 
+
+ align:start position:0%
+of resonance in the N equation this
+gives us resonance you see because you
+
+ align:start position:0%
+gives us resonance you see because you
+ 
+
+ align:start position:0%
+gives us resonance you see because you
+remember the null Solutions were e e to
+
+ align:start position:0%
+remember the null Solutions were e e to
+ 
+
+ align:start position:0%
+remember the null Solutions were e e to
+the s1t was a null
+
+ align:start position:0%
+the s1t was a null
+ 
+
+ align:start position:0%
+the s1t was a null
+solution if I plug in e to the S1 T the
+
+ align:start position:0%
+solution if I plug in e to the S1 T the
+ 
+
+ align:start position:0%
+solution if I plug in e to the S1 T the
+left side will give zero so I can't get
+
+ align:start position:0%
+left side will give zero so I can't get
+ 
+
+ align:start position:0%
+left side will give zero so I can't get
+a for equal to a forcing term on the
+
+ align:start position:0%
+a for equal to a forcing term on the
+ 
+
+ align:start position:0%
+a for equal to a forcing term on the
+right side I need a new solution what I
+
+ align:start position:0%
+right side I need a new solution what I
+ 
+
+ align:start position:0%
+right side I need a new solution what I
+need a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+new new y of
+
+ align:start position:0%
+new new y of
+ 
+
+ align:start position:0%
+new new y of
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+okay can I tell you what it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is and it comes it's a typical case of
+
+ align:start position:0%
+is and it comes it's a typical case of
+ 
+
+ align:start position:0%
+is and it comes it's a typical case of
+lal's rule from calculus when we
+
+ align:start position:0%
+lal's rule from calculus when we
+ 
+
+ align:start position:0%
+lal's rule from calculus when we
+approach this bad
+
+ align:start position:0%
+approach this bad
+ 
+
+ align:start position:0%
+approach this bad
+situation and we're getting a one over
+
+ align:start position:0%
+situation and we're getting a one over
+ 
+
+ align:start position:0%
+situation and we're getting a one over
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+but well you'll see a zero over zero and
+
+ align:start position:0%
+but well you'll see a zero over zero and
+ 
+
+ align:start position:0%
+but well you'll see a zero over zero and
+that's what Lal is aimed for okay so
+
+ align:start position:0%
+that's what Lal is aimed for okay so
+ 
+
+ align:start position:0%
+that's what Lal is aimed for okay so
+where do we start so we our y particular
+
+ align:start position:0%
+where do we start so we our y particular
+ 
+
+ align:start position:0%
+where do we start so we our y particular
+solution is this e to the s t
+
+ align:start position:0%
+solution is this e to the s t
+ 
+
+ align:start position:0%
+solution is this e to the s t
+over uh
+
+ align:start position:0%
+over uh
+ 
+
+ align:start position:0%
+over uh
+yeah e e to the
+
+ align:start position:0%
+yeah e e to the
+ 
+
+ align:start position:0%
+yeah e e to the
+St o over the the
+
+ align:start position:0%
+St o over the the
+ 
+
+ align:start position:0%
+St o over the the
+uh this A S 2 + b s +
+
+ align:start position:0%
+uh this A S 2 + b s +
+ 
+
+ align:start position:0%
+uh this A S 2 + b s +
+C right that's our particular solution
+
+ align:start position:0%
+C right that's our particular solution
+ 
+
+ align:start position:0%
+C right that's our particular solution
+if it works resonance is the case when
+
+ align:start position:0%
+if it works resonance is the case when
+ 
+
+ align:start position:0%
+if it works resonance is the case when
+this doesn't work because that's zero
+
+ align:start position:0%
+this doesn't work because that's zero
+ 
+
+ align:start position:0%
+this doesn't work because that's zero
+now that's a particular solution I'll
+
+ align:start position:0%
+now that's a particular solution I'll
+ 
+
+ align:start position:0%
+now that's a particular solution I'll
+subtract off a null solution I can do
+
+ align:start position:0%
+subtract off a null solution I can do
+ 
+
+ align:start position:0%
+subtract off a null solution I can do
+that I still have a solution so I'll
+
+ align:start position:0%
+that I still have a solution so I'll
+ 
+
+ align:start position:0%
+that I still have a solution so I'll
+subtract off e to the S1
+
+ align:start position:0%
+subtract off e to the S1
+ 
+
+ align:start position:0%
+subtract off e to the S1
+T So S1 is a is e to the s1t is a null
+
+ align:start position:0%
+T So S1 is a is e to the s1t is a null
+ 
+
+ align:start position:0%
+T So S1 is a is e to the s1t is a null
+solution this is what I would call a
+
+ align:start position:0%
+solution this is what I would call a
+ 
+
+ align:start position:0%
+solution this is what I would call a
+very particular solution it's very
+
+ align:start position:0%
+very particular solution it's very
+ 
+
+ align:start position:0%
+very particular solution it's very
+particular because at T equals 0 it's
+
+ align:start position:0%
+particular because at T equals 0 it's
+ 
+
+ align:start position:0%
+particular because at T equals 0 it's
+zero and so do you see that you see
+
+ align:start position:0%
+zero and so do you see that you see
+ 
+
+ align:start position:0%
+zero and so do you see that you see
+what's happening here the question
+
+ align:start position:0%
+what's happening here the question
+ 
+
+ align:start position:0%
+what's happening here the question
+resonance happens when s approaches S1
+
+ align:start position:0%
+resonance happens when s approaches S1
+ 
+
+ align:start position:0%
+resonance happens when s approaches S1
+resonance is s equal to Resonance itself
+
+ align:start position:0%
+resonance is s equal to Resonance itself
+ 
+
+ align:start position:0%
+resonance is s equal to Resonance itself
+is at the thing now we now we let s
+
+ align:start position:0%
+is at the thing now we now we let s
+ 
+
+ align:start position:0%
+is at the thing now we now we let s
+sneak up on
+
+ align:start position:0%
+sneak up on
+ 
+
+ align:start position:0%
+sneak up on
+S1 and we ask what happens to that
+
+ align:start position:0%
+S1 and we ask what happens to that
+ 
+
+ align:start position:0%
+S1 and we ask what happens to that
+formula you see we're sneaking up on
+
+ align:start position:0%
+formula you see we're sneaking up on
+ 
+
+ align:start position:0%
+formula you see we're sneaking up on
+resonance resonance in at resonance when
+
+ align:start position:0%
+resonance resonance in at resonance when
+ 
+
+ align:start position:0%
+resonance resonance in at resonance when
+s equals S1 that will be zero and that
+
+ align:start position:0%
+s equals S1 that will be zero and that
+ 
+
+ align:start position:0%
+s equals S1 that will be zero and that
+will be
+
+ align:start position:0%
+will be
+ 
+
+ align:start position:0%
+will be
+zero that's our
+
+ align:start position:0%
+zero that's our
+ 
+
+ align:start position:0%
+zero that's our
+problem so approach it and you end up
+
+ align:start position:0%
+problem so approach it and you end up
+ 
+
+ align:start position:0%
+problem so approach it and you end up
+with the derivative of this divided by
+
+ align:start position:0%
+with the derivative of this divided by
+ 
+
+ align:start position:0%
+with the derivative of this divided by
+the derivative of this do you remember l
+
+ align:start position:0%
+the derivative of this do you remember l
+ 
+
+ align:start position:0%
+the derivative of this do you remember l
+t it was a crazy rule in calculus but
+
+ align:start position:0%
+t it was a crazy rule in calculus but
+ 
+
+ align:start position:0%
+t it was a crazy rule in calculus but
+here it's actually needed so as s goes
+
+ align:start position:0%
+here it's actually needed so as s goes
+ 
+
+ align:start position:0%
+here it's actually needed so as s goes
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+S1 this goes to 0 over Z so I have to
+
+ align:start position:0%
+S1 this goes to 0 over Z so I have to
+ 
+
+ align:start position:0%
+S1 this goes to 0 over Z so I have to
+take derivative over derivative so let
+
+ align:start position:0%
+take derivative over derivative so let
+ 
+
+ align:start position:0%
+take derivative over derivative so let
+me write the answer
+
+ align:start position:0%
+me write the answer
+ 
+
+ align:start position:0%
+me write the answer
+y resonant can I call this the resonant
+
+ align:start position:0%
+y resonant can I call this the resonant
+ 
+
+ align:start position:0%
+y resonant can I call this the resonant
+solution when s equals S1 and what does
+
+ align:start position:0%
+solution when s equals S1 and what does
+ 
+
+ align:start position:0%
+solution when s equals S1 and what does
+it equal well s is I take the S
+
+ align:start position:0%
+it equal well s is I take the S
+ 
+
+ align:start position:0%
+it equal well s is I take the S
+derivative of this and divide by the S
+
+ align:start position:0%
+derivative of this and divide by the S
+ 
+
+ align:start position:0%
+derivative of this and divide by the S
+derivative of that derivative over
+
+ align:start position:0%
+derivative of that derivative over
+ 
+
+ align:start position:0%
+derivative of that derivative over
+derivative the S derivative of that is t
+
+ align:start position:0%
+derivative the S derivative of that is t
+ 
+
+ align:start position:0%
+derivative the S derivative of that is t
+e to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+St and the S derivative of this is 2 a s
+
+ align:start position:0%
+St and the S derivative of this is 2 a s
+ 
+
+ align:start position:0%
+St and the S derivative of this is 2 a s
++
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b and
+
+ align:start position:0%
+b and
+ 
+
+ align:start position:0%
+b and
+now I have derivative over derivative I
+
+ align:start position:0%
+now I have derivative over derivative I
+ 
+
+ align:start position:0%
+now I have derivative over derivative I
+can let s go to S1 so s goes to S1 this
+
+ align:start position:0%
+can let s go to S1 so s goes to S1 this
+ 
+
+ align:start position:0%
+can let s go to S1 so s goes to S1 this
+goes to S1 and I get an answer the right
+
+ align:start position:0%
+goes to S1 and I get an answer the right
+ 
+
+ align:start position:0%
+goes to S1 and I get an answer the right
+answer this is the correct
+
+ align:start position:0%
+answer this is the correct
+ 
+
+ align:start position:0%
+answer this is the correct
+solution and you notice everybody spots
+
+ align:start position:0%
+solution and you notice everybody spots
+ 
+
+ align:start position:0%
+solution and you notice everybody spots
+this T factor that t factor is a signal
+
+ align:start position:0%
+this T factor that t factor is a signal
+ 
+
+ align:start position:0%
+this T factor that t factor is a signal
+to everyone that we're in a special case
+
+ align:start position:0%
+to everyone that we're in a special case
+ 
+
+ align:start position:0%
+to everyone that we're in a special case
+when two things happen to be equal here
+
+ align:start position:0%
+when two things happen to be equal here
+ 
+
+ align:start position:0%
+when two things happen to be equal here
+the two things are the S and the S1 so
+
+ align:start position:0%
+the two things are the S and the S1 so
+ 
+
+ align:start position:0%
+the two things are the S and the S1 so
+that that will work so do you see the
+
+ align:start position:0%
+that that will work so do you see the
+ 
+
+ align:start position:0%
+that that will work so do you see the
+general picture it's always this t e to
+
+ align:start position:0%
+general picture it's always this t e to
+ 
+
+ align:start position:0%
+general picture it's always this t e to
+the s1t ab above and down below we have
+
+ align:start position:0%
+the s1t ab above and down below we have
+ 
+
+ align:start position:0%
+the s1t ab above and down below we have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+derivative of this polinomial at s equal
+
+ align:start position:0%
+derivative of this polinomial at s equal
+ 
+
+ align:start position:0%
+derivative of this polinomial at s equal
+S1 and now you know it's theoretically
+
+ align:start position:0%
+S1 and now you know it's theoretically
+ 
+
+ align:start position:0%
+S1 and now you know it's theoretically
+possible that we could have double
+
+ align:start position:0%
+possible that we could have double
+ 
+
+ align:start position:0%
+possible that we could have double
+resonance we would have double resonance
+
+ align:start position:0%
+resonance we would have double resonance
+ 
+
+ align:start position:0%
+resonance we would have double resonance
+if that thing is zero
+
+ align:start position:0%
+if that thing is zero
+ 
+
+ align:start position:0%
+if that thing is zero
+if not only if if S1 was a double root
+
+ align:start position:0%
+if not only if if S1 was a double root
+ 
+
+ align:start position:0%
+if not only if if S1 was a double root
+if S1 was a double root then well that's
+
+ align:start position:0%
+if S1 was a double root then well that's
+ 
+
+ align:start position:0%
+if S1 was a double root then well that's
+just absurd but it could happen then not
+
+ align:start position:0%
+just absurd but it could happen then not
+ 
+
+ align:start position:0%
+just absurd but it could happen then not
+only is that denominator zero but after
+
+ align:start position:0%
+only is that denominator zero but after
+ 
+
+ align:start position:0%
+only is that denominator zero but after
+L after one use of Lal so we have to
+
+ align:start position:0%
+L after one use of Lal so we have to
+ 
+
+ align:start position:0%
+L after one use of Lal so we have to
+drag Lal back from the hospital and and
+
+ align:start position:0%
+drag Lal back from the hospital and and
+ 
+
+ align:start position:0%
+drag Lal back from the hospital and and
+say do it again so we would have a
+
+ align:start position:0%
+say do it again so we would have a
+ 
+
+ align:start position:0%
+say do it again so we would have a
+second derivative I I won't write down
+
+ align:start position:0%
+second derivative I I won't write down
+ 
+
+ align:start position:0%
+second derivative I I won't write down
+that solution cuz it's pretty rare So
+
+ align:start position:0%
+that solution cuz it's pretty rare So
+ 
+
+ align:start position:0%
+that solution cuz it's pretty rare So
+what has this video done
+
+ align:start position:0%
+what has this video done
+ 
+
+ align:start position:0%
+what has this video done
+simply put on record the
+
+ align:start position:0%
+simply put on record the
+ 
+
+ align:start position:0%
+simply put on record the
+simplest uh case possible with a forcing
+
+ align:start position:0%
+simplest uh case possible with a forcing
+ 
+
+ align:start position:0%
+simplest uh case possible with a forcing
+function e to the
+
+ align:start position:0%
+function e to the
+ 
+
+ align:start position:0%
+function e to the
+St and above all we've identified this
+
+ align:start position:0%
+St and above all we've identified this
+ 
+
+ align:start position:0%
+St and above all we've identified this
+transfer function and let me just
+
+ align:start position:0%
+transfer function and let me just
+ 
+
+ align:start position:0%
+transfer function and let me just
+anticipate that if we another way to
+
+ align:start position:0%
+anticipate that if we another way to
+ 
+
+ align:start position:0%
+anticipate that if we another way to
+solve these
+
+ align:start position:0%
+solve these
+ 
+
+ align:start position:0%
+solve these
+equations instead of in the T domain we
+
+ align:start position:0%
+equations instead of in the T domain we
+ 
+
+ align:start position:0%
+equations instead of in the T domain we
+could go to the lass
+
+ align:start position:0%
+could go to the lass
+ 
+
+ align:start position:0%
+could go to the lass
+transform in the S domain we could solve
+
+ align:start position:0%
+transform in the S domain we could solve
+ 
+
+ align:start position:0%
+transform in the S domain we could solve
+it in the S domain and this is exactly
+
+ align:start position:0%
+it in the S domain and this is exactly
+ 
+
+ align:start position:0%
+it in the S domain and this is exactly
+what will meet when we take the lass
+
+ align:start position:0%
+what will meet when we take the lass
+ 
+
+ align:start position:0%
+what will meet when we take the lass
+transform that will be the llas
+
+ align:start position:0%
+transform that will be the llas
+ 
+
+ align:start position:0%
+transform that will be the llas
+transform which we have to uh deal with
+
+ align:start position:0%
+transform which we have to uh deal with
+ 
+
+ align:start position:0%
+transform which we have to uh deal with
+so uh that transfer function is a
+
+ align:start position:0%
+so uh that transfer function is a
+ 
+
+ align:start position:0%
+so uh that transfer function is a
+fundamental th this polom tells us uh
+
+ align:start position:0%
+fundamental th this polom tells us uh
+ 
+
+ align:start position:0%
+fundamental th this polom tells us uh
+its roots tell us the frequencies S1 S2
+
+ align:start position:0%
+its roots tell us the frequencies S1 S2
+ 
+
+ align:start position:0%
+its roots tell us the frequencies S1 S2
+in the null solution
+
+ align:start position:0%
+in the null solution
+ 
+
+ align:start position:0%
+in the null solution
+and then one over that tells us the
+
+ align:start position:0%
+and then one over that tells us the
+ 
+
+ align:start position:0%
+and then one over that tells us the
+right multiplier in the force
+
+ align:start position:0%
+right multiplier in the force
+ 
+
+ align:start position:0%
+right multiplier in the force
+solution so constant coefficients
+
+ align:start position:0%
+solution so constant coefficients
+ 
+
+ align:start position:0%
+solution so constant coefficients
+exponential forcing the best case
+
+ align:start position:0%
+exponential forcing the best case
+ 
+
+ align:start position:0%
+exponential forcing the best case
+possible thank you
\ No newline at end of file
diff --git a/oO5yP0cqEIw.txt b/oO5yP0cqEIw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3ed83e93788fd94a3e22233ed932fd571b916338
--- /dev/null
+++ b/oO5yP0cqEIw.txt
@@ -0,0 +1,331 @@
+align:start position:0%
+ 
+explosion. Here we use a laser with a
+
+ align:start position:0%
+explosion. Here we use a laser with a
+ 
+
+ align:start position:0%
+explosion. Here we use a laser with a
+wavelength of 650 nanometers. First take
+
+ align:start position:0%
+wavelength of 650 nanometers. First take
+ 
+
+ align:start position:0%
+wavelength of 650 nanometers. First take
+off the columnating lens of the laser.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Position the laser beam with close pin
+
+ align:start position:0%
+Position the laser beam with close pin
+ 
+
+ align:start position:0%
+Position the laser beam with close pin
+after you connect it to batteries. Have
+
+ align:start position:0%
+after you connect it to batteries. Have
+ 
+
+ align:start position:0%
+after you connect it to batteries. Have
+the laser warm up for two
+
+ align:start position:0%
+the laser warm up for two
+ 
+
+ align:start position:0%
+the laser warm up for two
+minutes. Turn off the light and you
+
+ align:start position:0%
+minutes. Turn off the light and you
+ 
+
+ align:start position:0%
+minutes. Turn off the light and you
+should see the bean spot. The area
+
+ align:start position:0%
+should see the bean spot. The area
+ 
+
+ align:start position:0%
+should see the bean spot. The area
+should be larger than your holographic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plate. Place your object in the middle
+
+ align:start position:0%
+plate. Place your object in the middle
+ 
+
+ align:start position:0%
+plate. Place your object in the middle
+of the beam. The object should be bright
+
+ align:start position:0%
+of the beam. The object should be bright
+ 
+
+ align:start position:0%
+of the beam. The object should be bright
+when illuminated with the red laser and
+
+ align:start position:0%
+when illuminated with the red laser and
+ 
+
+ align:start position:0%
+when illuminated with the red laser and
+it doesn't move or
+
+ align:start position:0%
+it doesn't move or
+ 
+
+ align:start position:0%
+it doesn't move or
+deform. You can place your holographic
+
+ align:start position:0%
+deform. You can place your holographic
+ 
+
+ align:start position:0%
+deform. You can place your holographic
+plate on the top of your object for 20
+
+ align:start position:0%
+plate on the top of your object for 20
+ 
+
+ align:start position:0%
+plate on the top of your object for 20
+seconds. Don't touch the table during
+
+ align:start position:0%
+seconds. Don't touch the table during
+ 
+
+ align:start position:0%
+seconds. Don't touch the table during
+exposure. Any vibration will affect the
+
+ align:start position:0%
+exposure. Any vibration will affect the
+ 
+
+ align:start position:0%
+exposure. Any vibration will affect the
+quality of interferent fringes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+developing and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drying. Here we have a developer, water
+
+ align:start position:0%
+drying. Here we have a developer, water
+ 
+
+ align:start position:0%
+drying. Here we have a developer, water
+for rinsing, bleach, water for more
+
+ align:start position:0%
+for rinsing, bleach, water for more
+ 
+
+ align:start position:0%
+for rinsing, bleach, water for more
+rinsing, alcohol for drying, and a place
+
+ align:start position:0%
+rinsing, alcohol for drying, and a place
+ 
+
+ align:start position:0%
+rinsing, alcohol for drying, and a place
+to dry your holographic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plate. Developing should be done in the
+
+ align:start position:0%
+plate. Developing should be done in the
+ 
+
+ align:start position:0%
+plate. Developing should be done in the
+dark to prevent a second exposure.
+
+ align:start position:0%
+dark to prevent a second exposure.
+ 
+
+ align:start position:0%
+dark to prevent a second exposure.
+Use your tweezers to dip the plate in
+
+ align:start position:0%
+Use your tweezers to dip the plate in
+ 
+
+ align:start position:0%
+Use your tweezers to dip the plate in
+the developer for 20 seconds until the
+
+ align:start position:0%
+the developer for 20 seconds until the
+ 
+
+ align:start position:0%
+the developer for 20 seconds until the
+plate turns black and rinse it in water
+
+ align:start position:0%
+plate turns black and rinse it in water
+ 
+
+ align:start position:0%
+plate turns black and rinse it in water
+for 1 minute.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Place a rinsed hologram into the
+
+ align:start position:0%
+Place a rinsed hologram into the
+ 
+
+ align:start position:0%
+Place a rinsed hologram into the
+bleaching solution. Agitating until the
+
+ align:start position:0%
+bleaching solution. Agitating until the
+ 
+
+ align:start position:0%
+bleaching solution. Agitating until the
+play is completed clear. It takes up to
+
+ align:start position:0%
+play is completed clear. It takes up to
+ 
+
+ align:start position:0%
+play is completed clear. It takes up to
+1 minute.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then rinse it in water for 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minute. Place the finished hologram in
+
+ align:start position:0%
+minute. Place the finished hologram in
+ 
+
+ align:start position:0%
+minute. Place the finished hologram in
+the wetting solution for 20 to 60
+
+ align:start position:0%
+the wetting solution for 20 to 60
+ 
+
+ align:start position:0%
+the wetting solution for 20 to 60
+seconds. It reduce the likelihood of
+
+ align:start position:0%
+seconds. It reduce the likelihood of
+ 
+
+ align:start position:0%
+seconds. It reduce the likelihood of
+water spots and have it dry for 10
+
+ align:start position:0%
+water spots and have it dry for 10
+ 
+
+ align:start position:0%
+water spots and have it dry for 10
+minutes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Testing view the hologram with
+
+ align:start position:0%
+Testing view the hologram with
+ 
+
+ align:start position:0%
+Testing view the hologram with
+incandescent light such as projector,
+
+ align:start position:0%
+incandescent light such as projector,
+ 
+
+ align:start position:0%
+incandescent light such as projector,
+flashlight, spotlight or LED in the sun.
\ No newline at end of file
diff --git a/pY9ol9So2Yw.txt b/pY9ol9So2Yw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5dd3cf2b4a6c9cf3fe73047f139a3e5d381f4f06
--- /dev/null
+++ b/pY9ol9So2Yw.txt
@@ -0,0 +1,3411 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: I'm going to spend
+most of time talking about
+
+chapters one, two, and three.
+
+A little bit talking about
+chapter four, because we've
+
+been doing so much with chapter
+four in the last
+
+couple of weeks that you
+probably remember that more.
+
+OK.
+
+The basics, which we started out
+with, and which you should
+
+never forget, is that any time
+you develop a probability
+
+model, you've got to specify
+what the sample space is and
+
+what the probability measure
+on that sample space is.
+
+And in practice, and in almost
+everything we've talked about
+
+so far, there's really a basic
+countable set of random
+
+variables which determine
+everything else.
+
+In other words, when you find
+the joint probability
+
+distribution on that set of
+random variables, that tells
+
+you everything else
+of interest.
+
+And a sample point or a sample
+path on that set of random
+
+variables is in a collection of
+sample values, one sample
+
+value for each random
+variable.
+
+It's very convenient, especially
+when you're in an
+
+exam and a little bit rushed,
+to confuse random variables
+
+with the sample values for
+the random variables.
+
+And that's fine.
+
+I just want to caution you
+again, and I've done this many
+
+times, that about half the
+mistakes that people make--
+
+half of the conceptual mistakes
+that people make
+
+doing problems and doing quizzes
+are connected with
+
+getting confused at some point
+about what's a random variable
+
+and what's a sample value
+of that random variable.
+
+And you start thinking about
+sample values as just numbers.
+
+And I do that too.
+
+It's convenient for thinking
+about things.
+
+But you have to know that that's
+not the whole story.
+
+Often, we have uncountable
+sets of random variables.
+
+Like in renewal processes, we
+have the counting renewal
+
+process, which typically has an
+uncountable set of random
+
+variables, a number of arrivals
+up to each time, t,
+
+where t is a continuous valued
+random variable.
+
+But in almost all of those
+cases, you can define things
+
+in terms of simpler sets of
+random variables, like the
+
+interarrival times,
+which are IID.
+
+Most of the processes we've
+talked about really have a
+
+pretty simple description if
+you look for the simplest
+
+description of them.
+
+If you have a sequence of
+IID random variables--
+
+which is what we have for
+Poisson and renewal processes,
+
+and what we have for Markov
+chains is not that much more
+
+complicated--
+
+the laws of large numbers are
+useful to specify what the
+
+long term behavior is.
+
+The sample time average is, as
+we all know by now, is the sum
+
+of the random variables
+divided by n.
+
+So it's a sample average
+of these quantities.
+
+The random variable, which has
+a main x bar, the expected
+
+value of x, that's
+almost obvious.
+
+You just take the expected value
+of s sub n, and it's n
+
+times the expected value of x
+divided by n, and you're done.
+
+And the variance, since these
+random variables are
+
+independent, you find that
+almost as easily.
+
+That has this very
+simple-minded
+
+distribution function.
+
+Remember, we usually work
+with distribution
+
+functions in this class.
+
+And often, the exercises are
+much easier when you do them
+
+in terms of the distribution
+function than if you use
+
+formulas you remember from
+elementary courses, which are
+
+specialized to--
+
+which are specialized to
+probability density and
+
+probability mass functions, and
+often have more special
+
+conditions on them than that.
+
+But anyway, the distribution
+function starts
+
+to look like this.
+
+As n gets bigger, you notice
+that what's happening is that
+
+you get a distribution which
+is scrunching in this way,
+
+which is starting to
+look smoother.
+
+The jumps in it gets smaller.
+
+And you start out with this
+thing which is kind of crazy.
+
+And by time, n is even 50.
+
+You get something which
+almost looks like a--
+
+I don't know how we tell
+the difference
+
+between those two things.
+
+I thought we could,
+but we can't.
+
+I certainly can't up there.
+
+But anyway, the one that's
+tightest in is the one
+
+for n equals 50.
+
+And what these laws of large
+numbers all say in some sense
+
+is that this distribution
+function gets crunched in
+
+towards an impulse
+at the mean.
+
+And then they say other more
+specialized things about how
+
+this happens, about sample
+paths and all of that.
+
+But the idea is that this
+distribution function is
+
+heading towards a
+unit impulse.
+
+The weak law of large numbers
+then says that if the expected
+
+value of the magnitude of x
+is less than infinity--
+
+and usually when we talk about
+random variables having a
+
+mean, that's exactly
+what we mean.
+
+If that condition is not
+satisfied, then we usually say
+
+that the random variable
+doesn't have a mean.
+
+And you'll see that every time
+you look at anything in
+
+probability theory.
+
+When people say the mean exists,
+that's what they
+
+always mean.
+
+And what the theorem says then
+is exactly what we were
+
+talking about before.
+
+The probability that the
+difference between s n over n,
+
+and the mean of x bar, the
+probability that it's greater
+
+than or equal to epsilon
+equals 0 in the limit.
+
+So it's saying that you put
+epsilon limits on that
+
+distribution function and let
+n get bigger and bigger, it
+
+goes to 1 and 0.
+
+It says the probability of s n
+over n, less than or equal to
+
+x, approaches a unit step as
+n approaches infinity.
+
+This says this is the condition
+for convergence in
+
+probability.
+
+What we're saying is that that
+also means convergence and
+
+distribution function, and
+distribution for this case.
+
+And then we also, when we got
+to renewal processes, we
+
+talked about the strong
+law of large numbers.
+
+And that says that the expected
+value of x is finite.
+
+Then this limit approaches
+x on a sample path basis.
+
+In other words, for every sample
+path, except this set
+
+of probability 0, this
+condition holds true.
+
+That doesn't seem like it's
+very different or very
+
+important for the time being.
+
+But when we started studying
+renewal processes, which is
+
+where we actually talked about
+this, we saw that in fact, it
+
+let us talk about this, which
+says that if you take any
+
+function of s n over n--
+
+in other words, a function
+of a real value--
+
+a function of a--
+
+a real valued function of a--
+
+a real valued function
+of a real value, yes.
+
+What you get is that
+same function
+
+applied to the mean here.
+
+And that's the thing
+which is so
+
+useful for renewal processes.
+
+And it's what usually makes
+the strong law of large
+
+numbers so much easier to
+use than the weak law.
+
+That's a plug for
+the strong law.
+
+There are many extensions of the
+week love telling how fast
+
+the convergence is.
+
+One thing you should always
+remember about the central
+
+limit theorem, is it really
+tells you something about the
+
+weak law of large numbers.
+
+It tells you how fast that
+convergence is and what the
+
+convergence looks like.
+
+It says that if the variance
+of this underlying random
+
+variable is finite, then this
+limit here is equal to the
+
+normal distribution function,
+the Gaussian at
+
+variance 1 and mean 0.
+
+And that becomes a little easier
+to see what it's saying
+
+if you look at it this way.
+
+It says probability that s
+n over n minus x bar--
+
+namely the difference between
+the sum and the mean which
+
+it's converging to--
+
+the probability that that's less
+than or equal to y sigma
+
+over square root of
+n is this normal
+
+Gaussian random variable.
+
+It says that as n gets bigger
+and bigger, this quantity here
+
+gets tighter and tighter.
+
+What it says in terms of the
+picture here, in terms of this
+
+picture, it says that as n gets
+bigger and bigger, this
+
+picture here scrunches down as
+1 over the square root of n.
+
+And it also becomes Gaussian.
+
+| it tells you exactly what
+kind of convergence you
+
+actually have here.
+
+Is not only saying that this
+does converge to a unit step.
+
+It says how it converges.
+
+And that's a nice thing,
+conceptually.
+
+You don't always need
+it in problems.
+
+But you need it for
+understanding what's going on.
+
+We're moving backwards,
+it seems.
+
+Now, 1, 2, Poisson processes.
+
+We talked about arrival
+processes.
+
+You'd almost think that all
+processes are arrival
+
+processes at this point.
+
+But any time you start to think
+about that, think of a
+
+Markov chain.
+
+And a Markov chain is not an
+arrival process, ordinarily.
+
+Some of them can be
+viewed that way.
+
+But most of them can't.
+
+An arrival processes
+is an increasing
+
+sequence of random variables.
+
+0 less than s1, which is the
+time of the first arrival, s2,
+
+which is a time of the second
+arrival, and so forth.
+
+Interarrival times are x1 equals
+s1, and x i equals s i
+
+minus s i minus 1.
+
+The picture, which you should
+have indelibly printed on the
+
+back of your brain someplace
+by this time, is
+
+this picture here.
+
+s1, s2, s3, are the times
+at which arrivals occur.
+
+These are random variables, so
+these arrivals come in at
+
+random times.
+
+x1, x2, x3 are the intervals
+between arrivals.
+
+And N of t is the number of
+arrivals that have occurred up
+
+until time t.
+
+So every time the t passes one
+of these arrival times, N of t
+
+pops up by one, pops up by one
+again, pops up by one again.
+
+The sample value
+pops up by one.
+
+Arrival process can model
+arrivals to a queue,
+
+departures from a queue,
+locations of breaks in an oil
+
+line, an enormous number
+of things.
+
+It's not just arrivals
+we're talking about.
+
+It's all of these other
+things, also.
+
+But it's something laid out on
+a one-dimensional axis where
+
+things happen at various
+places on that
+
+one-dimensional axis.
+
+So that's the way to view it.
+
+OK, same picture again.
+
+Process can be specified by the
+joint distribution of the
+
+arrival epochs or the
+interarrival times, and, in
+
+fact, of the counting process.
+
+If you see a sample path of
+the counting process, then
+
+from that you can determine the
+sample path of the arrival
+
+times and the sample path of
+the interarrival times.
+
+And since any set of these
+random variables specifies all
+
+three of these things, the
+three are all equivalent.
+
+OK, we have this important
+condition here.
+
+And I always sort of forget
+this, but when these arrivals
+
+are highly delayed, when there's
+a long period of time
+
+between each arrival, what that
+says is the accounting
+
+process is getting small.
+
+So big interarrival times
+corresponds to a small
+
+value of N of t.
+
+And you can see that in
+the picture here.
+
+If you spread out these
+arrivals, you make s1 all the
+
+way out here.
+
+Then N of t doesn't become
+1 until way out here.
+
+So N of t as a function of t is
+getting smaller as s sub n
+
+is getting larger.
+
+S sub n is the minimum of the
+set of t, such that N of t is
+
+greater than or equal to N.
+Sounds like a unpleasantly
+
+complicated expression.
+
+If any of you can find a simpler
+way to say it than
+
+that, I would be absolutely
+delighted to hear it.
+
+But I don't think there is.
+
+I think the simpler way to say
+it is this picture here.
+
+And the picture says it.
+
+And you can sort of figure out
+all those logical statements
+
+from the picture, which
+is intuitively a
+
+lot clearer, I think.
+
+So now, renewal processes is
+an arrival process with IID
+
+interarrival times.
+
+And a Poisson process is a
+renewal process where the
+
+interarrival random variables
+are exponential.
+
+So, Poisson process
+is a special
+
+case of renewal process.
+
+Why are these exponential
+interarrival
+
+arrival times so important?
+
+Well, it's because they're
+memoryless.
+
+And the memoryless property says
+that the probability that
+
+x is greater than t plus x is
+equal to the probability that
+
+it's greater than x times the
+probability that it's greater
+
+than t for all x and t greater
+than or equal to 0.
+
+This makes better sense if
+you say it conditionally.
+
+The probability that x is
+greater than t plus x, given
+
+that it's greater than t, is
+the same as the probability
+
+that x is greater that--
+
+capital X is greater
+than little x.
+
+This really gives you
+the memoryless
+
+property in a nutshell.
+
+It says if you're looking at
+this process as it evolves,
+
+and you see an arrival, and then
+you start looking for the
+
+next arrival, it says that no
+matter how long you've been
+
+looking, the distribution
+function, as the time to wait
+
+until the next arrival,
+is the same
+
+exponential random variable.
+
+So you never gain anything
+by waiting.
+
+You might as well
+be impatient.
+
+But it doesn't do any good
+to be impatient.
+
+Doesn't to any good to wait.
+
+It doesn't do any good
+to not wait.
+
+No matter what you do, this
+damn thing always takes an
+
+exponential amount
+of time to occur.
+
+OK, that's what it means
+to be memoryless.
+
+And the exponential is the only
+
+memoryless random variable.
+
+How about a geometric
+random variable?
+
+The geometric random variable
+is memoryless if you're only
+
+looking at integer times.
+
+Here we're talking about
+times on a continuum.
+
+That's what this says.
+
+Well, that's what this says.
+
+And if you look at discrete
+times, then a geometric random
+
+variable is memoryless also.
+
+We're given a Poisson
+of rate lambda.
+
+The interval from any given t
+greater than 0 until the first
+
+arrival after t is a
+random variable.
+
+Let's call it z1.
+
+We already said that that
+random variable was
+
+exponential.
+
+And it's independent of all
+arrivals which occur before
+
+that starting time t.
+
+So looking at any starting
+time t, doesn't make any
+
+difference what has happened
+back here.
+
+That's not only the
+last arrival, but
+
+all the other arrivals.
+
+The time until the next arrival
+is exponential.
+
+The time until each arrival
+after that is exponential
+
+also, which says that if you
+look at this process starting
+
+at time t, it's a Poisson
+process again, where all the
+
+times have to be shifted, of
+course, but it's a Poisson
+
+process starting at time t.
+
+The corresponding counting
+process, we can call it n
+
+tilde of t and tau, where tau is
+greater than or equal to t,
+
+where this is the number of
+arrivals in the original
+
+process up until time tau minus
+the number of arrivals
+
+up until time t.
+
+If you look at that difference,
+so many arrivals
+
+up until t, so many more
+up until time tau.
+
+You look at the difference
+between tau and t.
+
+The number of arrivals in that
+interval is the same Poisson
+
+distributing random
+variable again.
+
+So, it has the same
+distribution as N
+
+of tau minus t.
+
+And that's called the stationary
+increment property.
+
+It says that no matter where you
+start a Poisson process,
+
+it always looks exactly
+the same.
+
+It says that if you wait for one
+hour and start then, it's
+
+exactly the same as what
+it was before.
+
+If we had Poisson processes in
+the world, it wouldn't do any
+
+good to travel on certain days
+rather than other days.
+
+It wouldn't do any good to leave
+to drive home at one
+
+hour rather than another hour.
+
+You'd have the same travel
+all the time.
+
+It's all equal.
+
+It would be an awful world
+if it were stationary.
+
+The independent increment
+properties for counting
+
+process is that for all
+sequences of ordered times--
+
+0 less than t1 less than
+t2 up to t k--
+
+the random variables n of t1--
+
+and now we're talking about the
+number of arrivals between
+
+t1 and t2, the number
+of arrivals between
+
+n minus 1 and tn.
+
+These are all independent
+of each other.
+
+That's what this independent
+increment property says.
+
+And we see from what we've said
+about this memoryless
+
+property that the Poisson
+process does indeed have this
+
+independent increment
+property.
+
+Poisson processes have both the
+stationary and independent
+
+increment properties.
+
+And this looks like an immediate
+consequence of that.
+
+It's not.
+
+Remember, we had to struggle
+with this for a bit.
+
+But it says plus Poisson
+processes can be defined by
+
+the stationary and independent
+increment properties, plus
+
+either the Poisson PMF for N
+of t, or this incremental
+
+property, the probability that N
+tilde of t and t plus delta,
+
+and the number of arrivals
+between t and t plus delta,
+
+the probability that that's
+1 is equal to
+
+lambda times delta.
+
+In other words, this view of a
+Poisson process is the view
+
+that you get when you sort
+of forget about time.
+
+And you think of arrivals from
+outer space coming down and
+
+hitting on a line.
+
+And they hit on that
+line randomly.
+
+And each one of them
+is independent
+
+of every other one.
+
+And that's what you get if you
+wind up with a density of
+
+lambda arrivals per unit time.
+
+OK, we talked about all
+of that, of course.
+
+The probability distributions--
+
+there are many of them for
+a Poisson process.
+
+The Poisson process is
+remarkable in the sense that
+
+anything you want to find,
+there's generally a simple
+
+formula for it.
+
+If it's complicated, you're
+probably not looking at
+
+it the right way.
+
+So many things come out
+very, very simply.
+
+The probability--
+
+the joint probability
+distribution of all of the
+
+arrival times up until time N is
+an exponential just in the
+
+last one, which says that the
+intermediate arrival epochs
+
+are equally likely to be
+anywhere, just as long as they
+
+satisfy this ordering
+restriction, s1 less than s2.
+
+That's what this formula says.
+
+It says that the joint density
+of these arrival times doesn't
+
+depend on anything except the
+time of the last one.
+
+But it does depend on the fact
+that they're [INAUDIBLE].
+
+From that, you can find
+virtually everything else if
+
+you want to.
+
+That really is saying exactly
+the same thing as we were just
+
+saying a while ago.
+
+This is the viewpoint of looking
+at this line from
+
+outer space with arrivals coming
+in, coming in uniformly
+
+distributed over this line
+interval, and each of them
+
+independent of each other one.
+
+That's what you wind
+up saying.
+
+This density, then, of the
+n-th arrival, if you just
+
+integrate all this stuff, you
+get the Erlang formula.
+
+Probability of arrival n in
+t to t plus delta is--
+
+now this is the derivation that
+we went through before,
+
+going from Erlang to Poisson.
+
+You can go from Poisson to
+Erlang too, if you want to.
+
+But it's a little easier
+to go this way.
+
+The probability of arrival in
+t to t plus delta is the
+
+probability that n of t is
+equal to n minus 1 times
+
+lambda delta plus an o
+of delta, of course.
+
+And the probability that n of
+t is equal to n minus 1 from
+
+this formula here is going to be
+the density of when s sub n
+
+appears, divided by lambda.
+
+That's exactly what this
+formula here says.
+
+So that's just the Poisson
+distribution.
+
+We've been through
+that derivation.
+
+It's almost a derivation worth
+remembering, because it just
+
+appears so often.
+
+As you've seen from the problem
+sets we've done,
+
+almost every problem you can
+dream of, dealing with Poisson
+
+processes, the easy way to do
+them comes from this property
+
+of combining and splitting
+Poisson processes.
+
+It says if n1 of t, n2 of t,
+up to n sub k of t are
+
+independent Poisson
+processes--
+
+what do you mean by
+a process being
+
+independent of another process?
+
+Well, the process is specified
+by the interarrival times for
+
+that process.
+
+So what we're saying here is the
+interarrival times for the
+
+first process are independent
+of the interarrival times of
+
+the second process,
+independent of the
+
+interarrival times for the third
+process, and so forth.
+
+Again, this is a view of someone
+from outer space,
+
+throwing darts onto a line.
+
+And if you have multiple people
+throwing darts on a
+
+line, but they're all equally
+distributed, all uniformly
+
+distributed over the line,
+this is exactly
+
+the model you get.
+
+So we have two views here.
+
+The first one is to look at
+the arrival epochs that's
+
+generated from each process.
+
+And then combine all arrivals
+into one Poisson process.
+
+So we look at all these Poisson
+processes, and then
+
+take the sum of them, and we
+get a Poisson process.
+
+The other way to look at it--
+
+and going back and forth between
+these two views is the
+
+way you solve problems--
+
+you look at the combined
+sequence of
+
+arrival epochs first.
+
+And then for each arrival that
+comes in, you think of an IID
+
+random variable independent
+of all the other random
+
+variables, which decides for
+each arrival which of the
+
+sub-processes it goes to.
+
+So there's this hidden
+process--
+
+well, it's not hidden.
+
+You can see what it's doing
+from looking at all the
+
+sub-processes.
+
+And each arrival then is
+associated with the given
+
+sub-process, with the
+probability mass function
+
+lambda sub i over the
+sum of lambda sub j.
+
+So this is the workhorse
+of Poisson
+
+type queueing problems.
+
+You study queuing theory,
+every page, you
+
+see this thing used.
+
+If you look at Kleinrock's books
+on queueing, they're
+
+very nice books because they
+cover so many different
+
+queueing situations.
+
+You find him using this
+on every page.
+
+And he never tells you that he's
+using it, but that's what
+
+he's doing.
+
+So that's a useful
+thing to know.
+
+We then talked about conditional
+arrivals and order
+
+statistics.
+
+The conditional distribution
+of the N first arrivals--
+
+namely, s sub 1 s sub
+2 up to s sub n--
+
+given the number of arrivals in
+N of t is just n factorial
+
+over t to the n.
+
+Again, it doesn't depend on
+where these arrivals are.
+
+It's just a function which is
+independent of each arrival.
+
+It's the same kind of
+conditioning we had before.
+
+It's n factorial divided
+by t to the n.
+
+Because of the fact that if
+you order these random
+
+variables, t1 less than t2 less
+than t3, and so forth, up
+
+until time t, and then you say
+how many different ways can I
+
+arrange a set of numbers, each
+between 0 and t so that we
+
+have different orderings
+of them.
+
+And you can choose any one
+of the N to be the first.
+
+You can choose any one
+of the remaining n
+
+minus 1 to be the second.
+
+And that's where this is n
+factorial comes from here.
+
+And that, again we've
+been over.
+
+The probability that s1 is
+greater than tau, given that
+
+they're interarrivals in the
+overall interval t, comes from
+
+just looking at N uniformly
+distributed random variables
+
+between 0 and t.
+
+And then what do you do with
+those uniformly distributed
+
+random variables?
+
+Well, you ask the question,
+what's the probability that
+
+all of them occur
+after time tau?
+
+And that's just t minus tau
+divided by t raised to the
+
+n-th power.
+
+And see, all of these formulas
+just come from particular
+
+viewpoints about what's
+going on.
+
+You have a number
+of viewpoints.
+
+One of them is throwing
+darts at a line.
+
+One of them is having
+exponential
+
+interarrival times.
+
+One of them is these uniform
+interarrivals.
+
+It's only a very small
+number of tricks.
+
+And you just use them in
+various combinations.
+
+So the joint distribution of s1
+to s n, given N of t equals
+
+n, is the same as the joint
+distribution of N uniform
+
+random variables after
+they've been ordered.
+
+So let's go on to finite
+state Markov chains.
+
+Seems like we're covering an
+enormous amount of material in
+
+this course.
+
+And I think we are.
+
+But as I'm trying to say, as
+we go along, it's all--
+
+I mean, everything follows from
+a relatively small set of
+
+principles.
+
+Of course, it's harder to
+understand the small set of
+
+principles and how to apply them
+than it is to understand
+
+all the details.
+
+But that's--
+
+but on the other hand, if you
+understand the principles,
+
+then all those details,
+including the ones we haven't
+
+talked about, are easy
+to deal with.
+
+An integer-time stochastic
+process--
+
+x1, x2, x3, blah, blah, blah--
+
+is a Markov chain if for all n,
+namely the number of them
+
+that we're looking at--
+
+well--
+
+for all n, i, j, k, l, and so
+forth, the probability that
+
+the n-th of these random
+variables is equal to j, given
+
+what all of the others are-- and
+these are not ordered now.
+
+I mean, in a Markov chain,
+nothing is ordered.
+
+We're not talking about
+an arrival process.
+
+We're just talking about a frog
+jumping around on lily
+
+pads, if you arrange the lily
+pads in a linear way, if these
+
+are random variables.
+
+The probability that the n-th
+location is equal to j, given
+
+that the previous locations are
+i, k, back to m, is just
+
+some probability p sub
+i j, a conditional
+
+probability of j given i.
+
+In other words, once if you're
+looking at what happens at
+
+time n, once you know what
+happened at time n minus 1,
+
+everything else is
+of no concern.
+
+This process evolves by having
+a history of only one time
+
+unit, a little like the
+Poisson process.
+
+The Poisson process evolves
+by being totally
+
+independent of the past.
+
+Here, you put a little
+dependence in the past.
+
+But the dependence is only to
+look at the last thing that
+
+happened, and nothing before the
+last time that happened.
+
+So p sub i j depends
+only on i and j.
+
+And the initial probability mass
+function is arbitrary.
+
+Markov chain is finite-state if
+the sample space for each x
+
+i, as a finite set S. And the
+sample space S is usually
+
+taken to be integers
+1 up to M.
+
+In all these formulas we write,
+we're always summing
+
+from one to M. And the reason
+for that is we've assumed the
+
+states are 1, 2, 3, up to M.
+Sometimes it's more convenient
+
+to think of different
+state spaces.
+
+But all the formulas
+we use are based on
+
+this state space here.
+
+Markov up chain is completely
+described by these transition
+
+probabilities plus the initial
+probabilities.
+
+If you want to write down the
+probability of what x is this
+
+some time N given what was at
+some time 0, all you have to
+
+do is trace all the paths from
+0 out to N, add up the
+
+probabilities of all of those
+paths, and that tells you the
+
+probability you want.
+
+All probabilities and be
+calculated just from knowing
+
+what these transition
+probabilities are.
+
+Note that when we're dealing
+with Poisson processes, we
+
+defined everything in
+terms of how many--
+
+how many variables are there in
+defining a Poisson process?
+
+How many things do you have to
+specify before I know exactly
+
+what Poisson process
+I'm talking about?
+
+Only the Poisson rate.
+
+Only one parameter is necessary
+
+for a Poisson process.
+
+For a finite-state Markov
+process, you need a lot more.
+
+What you need is all of these
+values, p sub i j.
+
+If you sum p sub i j over
+j, you have to get 1.
+
+So that removes one of them.
+
+But as soon as you specify that
+transition matrix, you've
+
+specified everything.
+
+So there's nothing more to know
+
+about the Poisson process.
+
+There's only all these gruesome
+derivations that we
+
+go through.
+
+But everything is initially
+determined.
+
+Set of transition probabilities
+is usually
+
+viewed as the Markov chain.
+
+And the initial probabilities
+are usually viewed as just a
+
+parameter that we deal with.
+
+In other words, we--
+
+in other words, what we study
+is the particular Markov
+
+chain, whether it's recurrent,
+whether it's transient,
+
+whatever it is.
+
+How you break it up into
+classes, all of that stuff
+
+only depends on these transition
+probabilities and
+
+doesn't depend on
+where you start.
+
+Now, a finite-state Markov chain
+can be described either
+
+as a directed graph
+or as a matrix.
+
+I hope you've seen by this
+time that some things are
+
+easier to look at if you look at
+things in terms of a graph.
+
+Some things are easier to look
+at if you look at something
+
+like this matrix.
+
+And some problems can be solved
+by inspection, if you
+
+draw a graph of it.
+
+Some can be solved almost
+by inspection if
+
+you look at the matrix.
+
+If you're doing things by
+computer, usually computers
+
+deal with matrices more easily
+than with graphs.
+
+If you're dealing with a Markov
+chain with 100,000
+
+states, you're not going to
+look at the graph and
+
+determine very much from it,
+because it's typically going
+
+to be fairly complicated--
+
+unless it has some very
+simple structure.
+
+And sometimes that simple
+structure is determined.
+
+If it's something where
+you can only--
+
+where you have the states
+numbered from 1 to 100,000,
+
+and you can only go from state
+i to state i plus 1, or from
+
+state i to i plus 1, or
+i minus 1, then it
+
+becomes very simple.
+
+And you like to look at
+it as a graph again.
+
+But ordinarily, you don't
+like to do that.
+
+But the nice thing about this
+graph is that it tells you
+
+very simply and visually which
+transition probabilities are
+
+zero, and which transition
+probabilities are non-zero.
+
+And that's the thing that
+specifies which states are
+
+recurrent, which states are
+transient, and all of that.
+
+All of that kind of elementary
+analysis about a Markov chain
+
+all comes from looking at this
+graph and seeing whether you
+
+can get from one state to
+another state by some process.
+
+So let's move on from that.
+
+Talk about the classification
+of states.
+
+We started out with the
+idea of a walk and
+
+a path and a cycle.
+
+I'm not sure these terms are
+uniform throughout the field.
+
+But a walk is an ordered
+string of nodes, like
+
+i0, i1, up to i n.
+
+You can have repeated elements
+here, but you need a directed
+
+arc from i sub n minus
+1 to i sub m.
+
+Like for example, in this stupid
+Markov chain here--
+
+I mean, when you're drawing
+things is LaTeX, it's kind of
+
+hard to draw those nice
+little curves there.
+
+And because of that, when you
+once draw a Markov chain, you
+
+never want to change it.
+
+And that's why these nodes
+have a very small set of
+
+Markov chains in them.
+
+It's just to save me some work,
+drawing and drawing
+
+these diagrams.
+
+An example of a walk, as you
+start in 4, you take the self
+
+loop, go back to 4 at time 2.
+
+Then you go to state
+1 at time 3.
+
+Then you go to state
+2 at time 4.
+
+Then you go to stage
+3, time 5.
+
+And back to state 2 at time 6.
+
+You have repeated nodes there.
+
+You have repeated nodes
+separated here.
+
+Another example of a
+walk is 4, 1, 2, 3.
+
+Example of a path, the path
+can't have any repeated nodes.
+
+We'd like to look at paths,
+because if you're going to be
+
+able to get from one node to
+another node, and there's some
+
+walk that goes all around the
+place and gets to that final
+
+node, there's also path
+that goes there.
+
+If you look at the walk, you
+just leave that all the cycles
+
+along the way, and
+you get to the n.
+
+And a cycle, of course, which I
+didn't define, is something
+
+which starts at one node, goes
+through a path, and then
+
+finally comes back to the same
+node that it started at.
+
+And it doesn't make any
+difference for the cycle 2, 3,
+
+2 whether you call it
+2, 3, 2 or 3, 2, 3.
+
+That's the same cycle, and
+it's not even worth
+
+distinguishing between
+those two ideas.
+
+OK That's that.
+
+If there's a path from--
+
+where did I--
+
+node j is accessible from i,
+which we abbreviate as i
+
+has a path to j.
+
+If there's a walk from i to
+j, which means that p
+
+sup i j to the n--
+
+this is the transition
+probability, the probability
+
+that x sub n is equal to
+j, given that x sub
+
+0 is equal to i.
+
+And we use this all the time.
+
+If this is greater than zero
+for some n greater than 0.
+
+In other words, j is accessible
+from i if there's a
+
+path from i that goes to j.
+
+And trivially, if i go to j, and
+there's a path from j to
+
+k, then there has to be
+a path from i to k.
+
+If you've ever tried to make up
+a mapping program to find
+
+how to get from here to there,
+this is one of the most useful
+
+things you use.
+
+If there's a way to get here
+to there, and a way to get
+
+from here to there, then there's
+a way to get from here
+
+all the way to the end.
+
+And if you look up what most of
+these map programs do, you
+
+see that they overuse this
+enormously and they wind up
+
+taking you from here to there
+by some bizarre path just
+
+because it happens to go through
+some intermediate node
+
+on the way.
+
+So two nodes communicate--
+
+i double arrow j--
+
+if j is accessible from i, and
+if i is accessible from j.
+
+That means there's a path from
+i to j, and another path from
+
+j back to i, if you shorten
+them as much as you can.
+
+There's a cycle.
+
+It starts at i, goes through j,
+and comes back to i again.
+
+I didn't say that quite right,
+so delete that from what
+
+you've just heard.
+
+A class C of states as a
+non-empty set, such that i and
+
+j communicate for each
+i j in this class.
+
+But i does not communicate
+with j for each i and C--
+
+for i and C and j, not in C.
+
+The convenient way to think
+about this-- and I should have
+
+stated this as a theorem in
+the notes, because it's--
+
+I think it's something that
+we all use without even
+
+thinking about it.
+
+It says that the entire set of
+states, or the entire set of
+
+nodes in a graph, is partitioned
+into classes.
+
+The class C, containing, is i
+in union with all of the j's
+
+that communicate with i.
+
+So if you want to find this
+partition, you start out with
+
+an arbitrary node, you find all
+of the other nodes that it
+
+communicates with, and you
+find them by picking
+
+them one at a time.
+
+You pick all of the nodes
+for which p sub i j is
+
+greater than 0.
+
+Then you pick--
+
+and p sub j i is great--
+
+well-- blah.
+
+If you want to find the set of
+nodes that are accessible from
+
+i, you start out looking at i.
+
+You look at all the states
+which are accessible
+
+from i in one step.
+
+Then you look at all the steps,
+all of the states,
+
+which you can access from
+any one of those.
+
+Those are the states which are
+accessible in two states--
+
+in two steps, then in three
+steps, and so forth.
+
+So you find all the nodes that
+are accessible from node i.
+
+And then you turn around and
+do it the other way.
+
+And presto, you have all of
+these classes of states all
+
+very simply.
+
+For finite-state change, the
+state i is transient if
+
+there's a j in S such that
+i goes into j, but j
+
+does not go into i.
+
+In other words, if I'm a state
+i, and I can get to you, but
+
+you can't get back to me,
+then I'm transient.
+
+Because the way Markov chains
+work, we keep going from one
+
+step to the next step to the
+next step to the next step.
+
+And if I keep returning to
+myself, then eventually I'm
+
+going to go to you.
+
+And once I go to you, I'll
+never get back again.
+
+So because of that, these
+transient states are states
+
+where eventually you
+leave them and you
+
+never get back again.
+
+As soon as we start talking
+about countable state Markov
+
+chains, you'll see that
+this definition
+
+doesn't work anymore.
+
+You can--
+
+it is very possible to just
+wander away in a countable
+
+state Markov chain, and you
+never get back again that way.
+
+After you wander away too far,
+the probability of getting
+
+back gets smaller and smaller.
+
+You keep getting further
+and further away.
+
+The probability of returning
+gets smaller and smaller, so
+
+that you have transience
+that way also.
+
+But here, the situation is
+simpler for a finite-state
+
+Markov chain.
+
+And you can define transience if
+there's a j in S such that
+
+i goes into j, but j
+doesn't go into i.
+
+If i's not transient,
+then it's recurrent.
+
+Usually you define recurrence
+first and transience later,
+
+but it's a little simpler
+this way.
+
+All states in a class are
+transient, or all are
+
+recurrent, and a finite-state
+Markov chain contains at least
+
+one recurrent class.
+
+You did that in your homework.
+
+And you were surprised at how
+complicated it was to do it.
+
+I hope that after you wrote
+down a proof of this, you
+
+stopped and thought about what
+you were actually proving,
+
+which intuitively is something
+very, very simple.
+
+It's just looking at all of
+the transient classes.
+
+Starting at one transient
+class, you
+
+find if there's another--
+
+if there's another state you can
+get to from OK i which is
+
+also transient, and then you
+find if there's another state
+
+you get to from there which
+is also transient.
+
+And eventually, you have to come
+to a state from which you
+
+can't go to some other state,
+from which you can't get back.
+
+That was explaining it almost
+as badly as the problem
+
+statement explained it.
+
+And I hope that after you did
+the problem, even if you can't
+
+explain it to someone,
+you have an
+
+understanding of why it's true.
+
+It shouldn't be surprising
+after you do that.
+
+So the finite-state Markov chain
+contains at least one
+
+recurrent class.
+
+OK, the period of a state
+i as the greatest common
+
+denominator of n, such that
+p i n is greater than 0.
+
+Again, a very complicated
+definition for a
+
+simple kind of idea.
+
+Namely, you start out
+in a state i.
+
+You look at all of the times at
+which you can get back to
+
+state i again.
+
+If you find it that set of
+times has a period in it,
+
+namely, if every sequences of
+states is a multiple of some
+
+d, then you know that the state
+is periodic if d is
+
+greater than 1.
+
+And what you have to do is to
+find the largest such number.
+
+And that's the period
+of the state.
+
+All states in the same class
+have the same period.
+
+A recurring class with period
+d greater than one can be
+
+partitioned into sub-class--
+
+this is the best way
+of looking at
+
+periodic classes of states.
+
+If you have a periodic class of
+states, then you can always
+
+separate it into
+d sub-classes.
+
+And in such a set of
+sub-classes, transitions from
+
+S1 and the states in
+S1 only go to S2.
+
+Transitions from states
+in S2 only go to S3.
+
+Up to, transitions from S
+d only go back to S1.
+
+They have to go someplace,
+so they go back to S1.
+
+So as you cycle around, it takes
+d steps to cycle from 1
+
+back to 1 again.
+
+It takes d steps to cycle
+from 2 back to 2 again.
+
+So you can see the structure of
+the Markov chain and why,
+
+in fact, it does have to be--
+
+why that class has
+to be periodic.
+
+An ergodic class is a recurrent
+aperiodic class.
+
+In other words, it's a class
+where the period is equal to
+
+1, which means there really
+isn't any period.
+
+A Markov chain with only one
+class is ergodic if the class
+
+is ergodic.
+
+And the big theorem here--
+
+I mean, this is probably the
+most important theorem about
+
+finite-state Markov chains.
+
+You have an ergodic,
+finite-state Markov chain.
+
+Then the limit as n goes to
+infinity of the probability of
+
+arriving in state j after n
+steps, given that you started
+
+in state i, is just some
+function of j.
+
+In other words, when n gets very
+large, it doesn't depend
+
+on how large M is.
+
+It stays the same.
+
+It becomes independent of n.
+
+It doesn't depend on
+where you started.
+
+No matter where you start
+in a finite-state
+
+ergodic Markov chain.
+
+After a very long time, the
+probability of being in a
+
+state j is independent of where
+you started, and it's
+
+independent of how long
+you've been running.
+
+So that's a very strong
+kind of--
+
+it's a very strong kind
+of limit theorem.
+
+It's very much like the law of
+large numbers and all of these
+
+other things.
+
+I'm going to talk a little bit
+at the end about what that
+
+relationship really is.
+
+Except what it says is, after a
+long time, you're in steady
+
+state, which is why
+it's called the
+
+steady state theorem.
+
+Yes?
+
+AUDIENCE: Could you define the
+steady states for periodic
+
+changes [INAUDIBLE]?
+
+PROFESSOR: I try to avoid doing
+that because you have
+
+steady state probabilities.
+
+The steady state probabilities
+that you have are, you take--
+
+is if you have these
+sub-classes.
+
+Then you wind up with a steady
+state within each sub-class.
+
+If you assign a probability
+of the probability in the
+
+sub-class, divided by d, then
+you get what is the steady
+
+state probability.
+
+If you start out in that steady
+state, then you're in
+
+each sub-class with probability
+1 over d.
+
+And you shift to the next
+sub-class and you're still in
+
+steady state, because you have
+a probability, 1 over d, of
+
+being in each of those
+sub-classes to start with.
+
+You shift and you're still in
+one of the sub-classes with
+
+probability 1 over d.
+
+So there still is a steady
+state in that sense, but
+
+there's not a steady state
+in any nice sense.
+
+So anyway, that's
+the way it is.
+
+But you see, if you understand
+this theorem for ergodic
+
+finite state and Markov
+chains, and then you
+
+understand about periodic
+change and this set of
+
+sub-classes, you can
+see within each
+
+sub-class, if you look at--
+
+if you look at--
+
+if you look at time 0, time d,
+time 2d, times 3d and 4d, then
+
+whatever state you start in,
+you're going to be in the same
+
+class after d steps, the same
+class after 2d steps.
+
+You're going to have
+a transition
+
+matrix over d steps.
+
+And this theorem still applies
+to these sub-classes over
+
+periods of d.
+
+So the hard part of it
+is proving this.
+
+After you prove this, then you
+see that the same thing
+
+happens over each sub-class
+after that.
+
+That's a pretty major theorem.
+
+It's difficult to prove.
+
+A sub-step is to show that for
+an ergodic M state Markov
+
+chain, the probability of being
+in state j at time n,
+
+given that you're in state i at
+time 0, is positive for all
+
+i j, and all n greater than
+M minus 1 squared plus 1.
+
+It's very surprising that you
+have to go this many states--
+
+this many steps before you get
+to the point that all these
+
+transition probabilities
+are positive.
+
+You look at this particular kind
+of Markov chain in the
+
+homework, and I hope what you
+found out from it was that if
+
+you start, say, in state two,
+then at the next time, you
+
+have to be in 3.
+
+Next time, you have to be in
+4, you have to be in 5, you
+
+have to be in 6.
+
+In other words, the size of
+the set that you can be in
+
+after one step is just 1.
+
+One possible state here, one
+possible state here, one
+
+possible state here.
+
+The next step, you're in either
+1 or 2, and as you
+
+travel around, the size of the
+set of states you can be in at
+
+these different steps, is 2,
+until you get all the way
+
+around again.
+
+And then there's
+a way to get--
+
+when you get to state 6 again,
+the set of states enlarges.
+
+So finally you get up to a
+set of states, which is
+
+up to M minus 1.
+
+And that's why you get the M
+minus 1 squared here, plus 1.
+
+And this is the only Markov
+chain there is.
+
+You can have as many
+states going around
+
+here as you want to.
+
+But you have to have this
+structure at the end, where
+
+there's one special state and
+one way of circumventing it,
+
+which means there's one cycle
+of size M minus 1, and one
+
+cycle of size M. And that's the
+only way you can get it.
+
+And that's the only Markov chain
+that meets this bound
+
+with equality.
+
+In all other cases, you get this
+property much earlier.
+
+And often, you get it after just
+a linear amount of time.
+
+The other part of this major
+theorem that you reach steady
+
+state says, let P be
+greater than 0.
+
+In other words, let
+all the transition
+
+probabilities be positive.
+
+And then define some quantity
+alpha as a minimum of the
+
+transition probabilities.
+
+And then the theorem says, for
+all states j and all n greater
+
+than or equal to 1, the maximum
+over the initial
+
+states minus the minimum over
+the initial states of P sub i
+
+j to the n plus-- first step,
+that difference is less than
+
+or equal to the difference
+a the n-th step,
+
+times 1 minus 2 alpha.
+
+Now 1 minus 2 alpha is
+as a positive number.
+
+And this says that this maximum
+minus minimum is 1
+
+minus 2 alpha to the n, which
+says that the limit of the
+
+maximizing term is equal
+to the limit of
+
+the minimizing term.
+
+And what does that say?
+
+It says that everything in the
+middle gets squeezed together.
+
+And it says exactly what we want
+it to say, that the limit
+
+of P sub l j to the n is
+independent of l, after n gets
+
+very large.
+
+Because the maximum and
+the minimum get very
+
+close to each other.
+
+We also showed that [? our ?]
+approaches that limit
+
+exponentially.
+
+That's what this says.
+
+The exponent here is just this
+alpha, determined in that way.
+
+And the theorem for ergodic
+Markov chains then follows by
+
+just looking at successive h
+steps in the Markov chain when
+
+h is large enough so that all
+these transition probabilities
+
+are positive.
+
+So you go out far enough
+that all the transition
+
+probabilities are positive.
+
+And then you look at repetitions
+of that, and apply
+
+this theorem.
+
+And suddenly you have this
+general theorem,
+
+which is what we wanted.
+
+An ergodic unichain is a Markov
+up chain with one
+
+ergodic recurring class,
+plus perhaps a set
+
+of transient states.
+
+And most of the things we talk
+about in this course are for
+
+unichains, usually ergodic
+unichains, because if you have
+
+multiple recurrent classes,
+it just makes a mess.
+
+You wind up in this recurrent
+class, or
+
+this recurrent class.
+
+And aside from the question of
+which one you get to, you
+
+don't much care about it.
+
+And the theorem here is for an
+ergodic finite-state unichain.
+
+The limit of P sub i j to the
+n probability of being in
+
+state j at time n, given that
+you're in state i at time 0,
+
+is equal to pi sub j.
+
+In other words, this limit
+here exists for all i j.
+
+And the limit is independent
+of i.
+
+And it's independent of n
+as n gets big enough.
+
+And then also, we can choose
+this so that this set of
+
+probabilities here satisfies
+this, what's called the steady
+
+state condition, the sum
+of pi i times P sub i j
+
+is equal to pi j.
+
+In other words, if you start out
+in steady state, and you
+
+look at the probabilities of
+being in the different states
+
+at the next time unit, this is
+the probability of being in
+
+state j at time n plus 1, if
+this is the probability of
+
+being in state i at time n.
+
+So that condition
+gets satisfied.
+
+That condition is satisfied.
+
+You just stay in steady
+state forever.
+
+And pi i has to be positive for
+a recurrent i, and pi i is
+
+equal to 0 otherwise.
+
+So this is just a
+generalization
+
+of the ergodic theorem.
+
+And this is not what people
+refer to as the ergodic
+
+theorem, which is a much more
+general theorem than this.
+
+This is the ergodic theorem for
+the case of finite state
+
+Markov chains.
+
+You can restate this in matrix
+form as the limit of the
+
+matrix P to the n-th power.
+
+What I didn't mention here and
+what I probably didn't mention
+
+enough in the notes is
+that P sub i j--
+
+but also, if you take the matrix
+P times P time P, n
+
+times, namely, you take the
+matrix, P to the n.
+
+This says the P sub i j
+is the i j element.
+
+I'm sure all of you know that
+by now, because you've been
+
+using it all the time.
+
+And what this says here--
+
+what we've said before is that
+every row of this matrix, P to
+
+the n, is the same.
+
+Every row is equal to pi.
+
+P to the n tends to a matrix
+which is pi 1, pi 2,
+
+up to pi sub n.
+
+Pi 1, pi 2, up to pi sub n.
+
+Pi 1, pi 2, up to pi sub n.
+
+And the easiest way to express
+this is the vector e times pi,
+
+where e is transposed.
+
+In other words, if you take a
+column matrix, column 1, 1, 1,
+
+1, 1, and you multiply this by
+a row vector, pi 1 times pi
+
+sub n, what you get is, for this
+first row multiplied by
+
+this, this gives you--
+
+well, in fact, if you
+multiply this out,
+
+this is what you get.
+
+And if you've never gone through
+the trouble of seeing
+
+that this multiplication leads
+to this, please do it, because
+
+it's important to notice
+that correspondence.
+
+We got specific results by
+looking at the eigenvalues and
+
+eigenvectors of stochastic
+matrices.
+
+And a stochastic matrix is the
+matrix of a Markov chain.
+
+So some of these things
+are sort of obvious.
+
+Lambda is an eigenvalue of P, if
+and only if P minus lambda
+
+i is singular.
+
+This set of relationships
+is not obvious.
+
+This is obvious linear
+algebra.
+
+This is something that when
+you study eigenvalues and
+
+eigenvectors in linear algebra,
+you recognize that
+
+this is a summary of
+a lot of things.
+
+If and only if this determinant
+is equal to 0,
+
+which is true if and only if
+there's some vector nu for
+
+which P times nu equals lambda
+times nu for nu unequal to 0.
+
+And if and only if pi P equals
+lambda pi for some
+
+pi unequal to 0.
+
+In other words, if this
+determinant is equal to 0, it
+
+means that the matrix P minus
+lambda i is singular.
+
+If the matrix is singular, there
+has to be some solution
+
+to this equation here.
+
+There has to be some
+solution to this
+
+left eigenvector equation.
+
+Now, once you see this, you
+notice that e is always a
+
+right eigenvector of P. Every
+stochastic matrix in the world
+
+has the property that e is a
+right eigenvector of it.
+
+Why is that?
+
+Because all of the rows of a
+stochastic matrix sum to 1.
+
+If you start off in state i, the
+sum of the possible states
+
+you can be at in the next
+step is equal to 1.
+
+You have to go somewhere.
+
+So e is always a right
+eigenvector of P with
+
+eigenvalue 1.
+
+Since e is also is a right
+eigenvector of P with
+
+eigenvalue 1, we go up here.
+
+We look at these if and
+only if statements.
+
+We see, then, P must
+be singular.
+
+And then pi times P
+equals lambda pi.
+
+So no matter how many recurrent
+classes we have, no
+
+matter what periodicity we have
+in each of them, there's
+
+always a solution to pi
+times P equals pi.
+
+There's always at least one
+steady state vector.
+
+This determinant has an M-th
+degree polynomial in lambda.
+
+M-th degree polynomials
+have M roots.
+
+They aren't necessarily
+distinct.
+
+The multiplicity of an
+eigenvalue is the number roots
+
+of that value.
+
+And the multiplicity
+of lambda equals 1.
+
+How many different roots
+are there which have
+
+lambda equals 1?
+
+Well it turns out to be just
+the number of recurrent
+
+classes that you have.
+
+If you have a bunch of recurrent
+classes, within each
+
+recurring class, there's a
+solution to pi P equals pi,
+
+which is non-zero only one
+that recurrent class.
+
+Namely, you take this huge
+Markov chain and you say, I
+
+don't care about any
+of this except this
+
+one recurrent class.
+
+If we look at this one recurrent
+class, and solve for
+
+the steady state probability in
+that one recurrent class,
+
+then we get an eigenvector
+which is non-zero on that
+
+class, 0 everywhere else, that
+has an eigenvalue 1.
+
+And for every other recurrent
+class, we
+
+get the same situation.
+
+So the multiplicity of lambda
+equals 1 is equal to the
+
+number of recurrent classes.
+
+If you didn't get that proof
+on the fly, it gets
+
+proved in the notes.
+
+And if you don't get the proof,
+just remember that
+
+that's the way it is.
+
+For the special case where all
+M eigenvalues are distinct,
+
+the right eigenvectors are
+linearly independent.
+
+You remember that proof we went
+through that all of the
+
+left eigenvectors and all the
+right eigenvectors are all
+
+orthonormal to each other,
+or you can make them all
+
+orthonormal to each other?
+
+That says that if the right
+eigenvectors are linearly
+
+independent, you can represent
+them as the columns of an
+
+invertible matrix U.
+Then P times U is
+
+equal to U times lambda.
+
+What does this equations say?
+
+You split it up into a
+bunch of equations.
+
+P times U and we look at it as
+nu 1, nu 2, nu sub [? n ?].
+
+I guess better put the
+superscripts on it.
+
+If I take the matrix U and just
+view it as M different
+
+columns, then what this
+is saying is that
+
+this is equal to--
+
+nu 1, nu 2, nu M, times lambda
+1, lambda 2, up to lambda M.
+
+Now you multiply this out,
+and what do you get?
+
+You get nu 1 times lambda 1.
+
+You get a nu 2 times lambda 2
+for the second column, nu M
+
+times lambda M for the last
+column, and here you get P
+
+times nu 1 is equal to a nu 1
+times lambda 1, and so forth.
+
+So all this vector equation says
+is the same thing that
+
+these n M individual eigenvector
+equations say.
+
+It's just a more compact way
+of saying the same thing.
+
+And if these eigenvectors span
+this space, then this set of
+
+eigenvectors are linearly
+independent of each other.
+
+And when you look at the set of
+them, this matrix here has
+
+to have an inverse.
+
+So you can also express this
+as P equals this vector--
+
+this matrix of right
+eigenvectors times the
+
+diagonal matrix lambda, times
+the inverse of this matrix.
+
+Matrix U to the minus 1 turns
+out to have rows equal to the
+
+left eigenvectors.
+
+That's because these
+eigenvectors--
+
+that's because the right
+eigenvectors and the left
+
+eigenvectors are orthogonal
+to each other.
+
+When we then split up this
+matrix into a sum of M
+
+different matrices, each matrix
+having only one--
+
+and so forth.
+
+Then what you get--
+
+here's this--
+
+this nice equation here, which
+says that if all the
+
+eigenvalues are distinct, then
+you can always represent a
+
+stochastic matrix as the sum of
+lambda i times nu to the i
+
+times pi to the i.
+
+More importantly, if you take
+this equation here and look at
+
+P to the n, P to the n is U
+times lambda times U to the
+
+minus 1, times U times lambda
+times U to the minus 1, blah,
+
+blah, blah forever.
+
+Each U to the minus 1 cancels
+out with the following U. And
+
+you wind up with P to the n
+equals U times lambda to the
+
+n, U to the minus 1.
+
+Which says that P to the
+n is just a sum here.
+
+It's the sum of the eigenvalues
+to the n-th power
+
+times these pairs of
+eigenvectors here.
+
+So this is a general
+decomposition for P to the n.
+
+What we're interested in is what
+happens as n gets large.
+
+If we have a unit chain, we
+already know what happens as n
+
+gets large.
+
+We know that as n gets large,
+we wind up with just 1 times
+
+this eigenvector e times
+this eigenvector pi.
+
+Which says that all of the other
+eigenvalues have to go
+
+to 0, which says that the
+magnitude of these other
+
+eigenvalues are less than 1.
+
+So they're all going away.
+
+So the facts here are that all
+eigenvalues lambda have to
+
+satisfy the magnitude
+of lambda is less
+
+than or equal to 1.
+
+That's what I just argued.
+
+For each recurrent class C,
+there's one lambda equals 1,
+
+with a left side and vector
+equals the steady state on
+
+that recurrent class
+and 0 elsewhere.
+
+The right eigenvector nu
+satisfies the limit as n goes
+
+to infinity.
+
+So the probability that x sub n
+is in this recurring class,
+
+given that x sub 0 is equal
+to 0, is equal to the i-th
+
+component of that right
+eigenvector.
+
+In other words, if you have a
+Markov chain which has several
+
+recurrent classes, and you
+want to find out what the
+
+probability is, starting in the
+transient state, of going
+
+to one of those classes, this is
+what tells you that answer.
+
+This says that the probability
+that you go to a particular
+
+recurrent class C, given that
+you start off in a particular
+
+transient state i, is whatever
+that right eigenvector
+
+turns out to be.
+
+And you can solve that right
+eigenvector problem just as an
+
+M by M set of linear
+equations.
+
+So you can find the
+probabilities of going through
+
+each transient state just by
+solving that set of linear
+
+equations and finding those
+eigenvector equations.
+
+For each recurrent periodic
+class of period d, there are d
+
+eigenvalues equally spaced
+on the unit circle.
+
+There are no other eigenvalues
+with lambda equals 1-- with a
+
+magnitude of lambda equals 1.
+
+In other words, for each
+recurrent class, you get one
+
+eigenvalue that's equal to 1.
+
+If that recurrent class is
+periodic, you get a bunch of
+
+other eigenvalues put around
+the unit circle.
+
+And those are all the
+eigenvalues there are.
+
+Oh my God.
+
+It's--
+
+I thought I was talking
+quickly.
+
+But anyway, if the eigenvectors
+don't span the
+
+space, then P to the n is equal
+to U times this Jordan
+
+reform, U to the minus 1, where
+J is a Jordan form.
+
+What you saw in the homework
+when you looked at the--
+
+when you looked at the
+Markov chain--
+
+OK.
+
+This is one recurrent class
+with this one node in it.
+
+These two nodes are
+both transient.
+
+If you look at how long it takes
+to get from here over to
+
+there, those transition
+probabilities do not
+
+correspond to this
+equation here.
+
+Instead, P sub 1 2--
+
+P sub 2 3, the way I've
+drawn it here.
+
+P sub 1 3 is n times this
+eigenvalue, which
+
+is 1/2 in this case.
+
+And it doesn't correspond to
+this, which is why you need a
+
+Jordan form.
+
+I said that Jordan forms
+are excessively ugly.
+
+Jordan forms are really very
+classy and nice ways of
+
+dealing with a problem
+which is very ugly.
+
+So don't blame Jordan.
+
+Jordan simplified
+things for us.
+
+So that's roughly as far as we
+went with Markov chains.
+
+Renewal processes, we don't have
+to review them because
+
+you're already immediately
+familiar with them.
+
+I will do one thing next time
+with renewal classes and
+
+Markov chains, which is to
+explain to you why the
+
+expected amount of time to get
+from one state back to itself
+
+is equal to 1 over pi--
+
+1 over pi sub i.
+
+You did that in the homework.
+
+And it was an awful
+way to do it.
+
+And there's a nice
+way to do it.
+
+I'll talk about that next time.
\ No newline at end of file
diff --git a/pkNwvhEm1GQ.txt b/pkNwvhEm1GQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3f0628ae04425872f9322811a9c7e462d11cc70b
--- /dev/null
+++ b/pkNwvhEm1GQ.txt
@@ -0,0 +1,2230 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Today is our final
+clicker competition.
+
+The first question is up.
+
+And I would just like to go over
+the current standing for
+
+the clicker competition as we're
+getting started here.
+
+So, recitation 6 has two wins,
+and there are other
+
+recitations and have one win, so
+recitation 2, 3, 5, 7, and
+
+10 have one win.
+
+If any of those recitation wins
+today, we're going to go
+
+to a tie breaker to decide the
+overall recitation champion.
+
+There are also recitations 1, 4,
+9, and 11, who are looking
+
+for their first win.
+
+This is their last
+chance today.
+
+So, if they win today, they can
+not be overall champions,
+
+but they will have snacks,
+and they will assure that
+
+recitations 2, 3, 5, 7, and
+10 do not win the overall
+
+competition.
+
+So, you have a chance to
+foil those recitations.
+
+And if we need to go to a tie
+breaker, it will not be from
+
+current material, it's going
+to be past material or past
+
+things that were mentioned.
+
+So, just keep that in mind.
+
+All right, and for the overall
+winner, I just would like to
+
+show you what you will win, so
+members of the recitation will
+
+each get their own chemistry
+t-shirt, and at some schools,
+
+of course, you would look at
+this and say oh, they're on
+
+the varsity team, but at MIT,
+it means that you are
+
+associated with course 5.
+
+So, Department of Chemistry at
+Massachusetts Institute of
+
+Technology on the back, and we
+have different colors and
+
+different sizes.
+
+All right, so time to get
+started with the clicker
+
+competition.
+
+Go ahead and click in your
+first responses.
+
+OK, let's just take
+10 more seconds.
+
+All right.
+
+Big improvement from the first
+time we asked this question
+
+last class where it's about
+33%, now we're up to 89.
+
+And no, it is not temperature
+dependent.
+
+And we're going to be
+talking more about
+
+activation energy today.
+
+All right, so today we're going
+to finish up kinetics,
+
+and we're going to start with
+the material that we didn't
+
+quite get to at the
+end of last class.
+
+And I love this part, because
+I love it when we can think
+
+about what we learned before in
+a slightly different way.
+
+So, when I first started
+lecturing, I was talking about
+
+LeChatelier principle and, of
+course, encouraged students to
+
+sort of -- you know it's not too
+intuitive to MIT students,
+
+but LeChatelier's principle says
+that if you apply stress
+
+to a system, it tends to respond
+in such a way to
+
+minimize that stress.
+
+So it's all about minimizing
+stress, which is something
+
+that's hard to kind to imagine
+this time of year, a little
+
+easier to imagine activation
+energy barriers, a little hard
+
+to imagine minimizing stress.
+
+But we're back to talking
+about minimizing stress.
+
+And we talked about adding
+reagents and removing
+
+products, and we talked about
+how reactions will shift to
+
+respond to stresses.
+
+And one of the things we talked
+about is rationalizing
+
+the shift of reactions at
+equilibrium when temperature
+
+has changed.
+
+So, if you increase the
+temperature of a particular
+
+reaction, it tends to shift in
+the endothermic direction to
+
+remove that added heat
+from the reaction.
+
+So, that's what we learned
+before, but now we're going to
+
+think about this in a slightly
+different way.
+
+So we're going to think about
+this in terms of these
+
+reaction coordinate diagrams.
+So, on one axis we have p e
+
+plotted -- what does
+that stand for?
+
+Potential energy, right, so we
+have potential energy going up
+
+on both sides.
+
+And here we have a view of an
+endothermic reaction, and over
+
+here is an exothermic
+reaction.
+
+So, let's just take
+a look at this.
+
+For the endothermic reaction,
+we have reactants and
+
+products, we have a delta e
+between those, and we have a
+
+very large activation
+energy barrier
+
+for the forward direction.
+
+And, of course, for anything to
+react, there always has to
+
+be some barrier, you need some
+amount of critical energy,
+
+because as the molecules come
+close to each other, and if
+
+they're going to react and form
+some kind of product, you
+
+have to sort of distort bonds
+and sort of rearrange things,
+
+and that takes a certain
+amount of energy.
+
+So if they come together and
+they have that energy, they'll
+
+react and go on to products,
+if they don't they'll break
+
+apart and go back and
+be reactants.
+
+And how much temperature the
+system has, is more likely
+
+that they'll be able to react.
+
+So it's more likely, if there's
+high temperature, they
+
+could overcome this activation
+energy barrier.
+
+All right, so in an endothermic
+reaction, you have
+
+a big one in the forward
+direction, and a much smaller
+
+activation energy in the
+reverse direction.
+
+For exothermic reaction it's
+the reverse -- there's a
+
+smaller barrier for the forward
+direction, and a much
+
+larger barrier for the
+reverse direction.
+
+So, we can think about
+the sign of delta e.
+
+So delta e, this difference here
+which is related to delta
+
+h for liquids and solids, it's
+pretty much the same for gases
+
+is 1% or 2% different.
+
+So you have a positive value
+here, and you can get a
+
+positive delta e here if you
+have a big number for the
+
+forward activation energy
+barrier minus a small number
+
+for the reverse, so that's
+going to give
+
+you a positive number.
+
+For an exothermic reaction,
+delta e's going to be
+
+negative, and you get a negative
+number if you take a
+
+small number here for the
+forward activation energy, and
+
+subtract it from a larger number
+here for the reverse
+
+activation energy.
+
+And remember, this is one of the
+equations that we're not
+
+going to give you, you need to
+have that memorized because
+
+it's part of understanding
+what's going on in these
+
+diagrams.
+
+So now let's think about what
+increasing the temperature is
+
+going to do.
+
+So, it will help the molecules
+if the is temperatures
+
+increase, they'll have enough
+energy to overcome barriers.
+
+Now if the barriers are pretty
+small, then it's not very hard
+
+for the molecules to get over
+them, regardless of the
+
+temperature.
+
+But when the barrier is big,
+then temperature is going to
+
+make a big difference.
+
+And you can sort of think about
+this in your own life as
+
+you have a small assignment to
+do, you just jump in and do it
+
+and get it done and it's fine.
+
+But if it's a very, very large
+thing that you have to do, you
+
+often need to procrastinate
+longer before
+
+you start doing it.
+
+So, a small barrier's not so
+much of a problem, but if it's
+
+a big barrier, you need to
+increase that temperature to
+
+help the molecules get over
+the bigger barriers.
+
+So, let's think about what this
+means in terms of the
+
+direction that a reaction
+might shift.
+
+So, if you increase a
+temperature over here with an
+
+endothermic reaction, it makes
+it easier to overcome the
+
+bigger barrier.
+
+The forward reaction barrier
+is the bigger one, so
+
+increasing the temperature will
+help molecules get over
+
+that barrier.
+
+They're already doing fine with
+the reverse barrier, it's
+
+the forward barrier that we're
+having trouble with.
+
+So, if you increase the
+temperature, that's going to
+
+shift the equilibrium toward
+products, or it will shift the
+
+reaction in the endothermic
+direction.
+
+That's what we had learned
+before with LeChatelier's
+
+principle, but now there's a new
+way of thinking about why
+
+that is true.
+
+So, for an exothermic reaction,
+if you increase the
+
+temperature, that helps with
+the bigger barrier.
+
+Again, here the bigger barrier
+is for the reverse reaction.
+
+So, if you increase the
+temperature of an exothermic
+
+reaction, it's going to shift
+it toward reactants.
+
+More molecules can overcome that
+reverse barrier, and so
+
+you'll form more reactants,
+it'll shift toward reactants
+
+or it'll shift in the
+endothermic direction.
+
+Again, these are the same things
+that we already knew
+
+from LeChatelier, but it's a
+different way of thinking
+
+about why those things
+are true.
+
+So, a large activation energy
+barrier means that rate
+
+constants are very sensitive
+to temperature.
+
+And so, if you have a big
+activation energy barrier,
+
+increasing the temperature makes
+a big difference -- if
+
+it's a big barrier, then there's
+going to have a big
+
+difference if you have
+higher temperature.
+
+If it's a small barrier, then
+increasing the temperature
+
+doesn't make much
+of a difference.
+
+And so you can think about
+that in terms of these
+
+diagrams as well.
+
+So, now we're done with
+temperature and we're going to
+
+talk about catalysis and
+the use of catalysts.
+
+And so, if you remember there
+were factors affecting the
+
+reaction, and we've talked about
+everything on this list
+
+except for catalysts.
+
+So today we're going to
+talk about catalysts.
+
+So, a catalyst is a substance
+that speeds up a reaction, but
+
+it doesn't get consumed in the
+reaction, it doesn't undergo
+
+any permanent change itself.
+
+It's just added to speed
+up the reaction.
+
+So catalysts do not appear in
+the overall balanced equation.
+
+So let's look at what a catalyst
+is going to do, and
+
+we're going to look at in
+terms of these potential
+
+energy diagrams as well.
+
+So here we here we have a
+reaction, we're going from
+
+reactants down here
+to products.
+
+We have the delta e for the
+reaction, we have a forward
+
+activation energy barrier
+and a reverse one.
+
+So, up here, at the top, that's
+our barrier without a
+
+catalyst. This is the transition
+state or the
+
+activated complex up here, so
+you have to overcome the
+
+barrier, you form some kind of
+activated complex, which then,
+
+if there's enough energy to
+overcome that barrier, goes on
+
+to products.
+
+So when you add a catalyst
+what happens is
+
+it lowers this barrier.
+
+So, in the blue line
+here is the new
+
+activation energy barrier.
+
+This is the barrier with a
+catalyst, and so this would
+
+then be the new transition
+state with a catalyst.
+
+So when it lowers the barrier,
+it's going to lower the
+
+barrier for the forward
+reaction, so we have a new
+
+activation energy for the
+forward reaction, and we're
+
+going to have a new
+activation energy
+
+for the reverse direction.
+
+So catalysts work by reducing
+both the forward and the
+
+reverse activation
+energy barrier.
+
+And another way that you can
+say this is that they
+
+stabilize the activated
+complex or
+
+the transition state.
+
+So here you have an activated
+complex with a much higher
+
+potential energy without the
+catalysts, and by stabilizing,
+
+you lower in energy that
+transition state.
+
+So that's another way
+of expressing
+
+what a catalyst does.
+
+So, catalysts have no effect on
+the thermodynamics of the
+
+reaction, they affect the
+kinetics of the reaction, but
+
+they don't affect the
+
+thermodynamics of the reaction.
+
+And so, of course, when you
+think of thermodynamics, you
+
+often think of delta g.
+
+So, why don't you tell me what
+you think, what would happen
+
+about, so delta g is a state
+function, it's independent of
+
+path, and so therefore, what
+can you tell me about the
+
+equilibrium constant in the
+presence of a catalyst?
+
+OK, let's just take
+10 more seconds.
+
+Yup, very good.
+
+So, the equilibrium constant
+is not changed.
+
+The thermodynamics, which
+includes delta g and the
+
+equilibrium constant are not
+affected, the rates of the
+
+reaction are affected.
+
+All right, so opposite of a
+catalyst is an inhabitor, and
+
+we'll talk more about this at
+the end of class, so it would
+
+-- inhibitor is slow or
+sometimes stop the rate of the
+
+reaction, and one way that they
+do this is by increasing
+
+the activation energy.
+
+So let's consider types
+of catalysts now.
+
+You can have a homogeneous
+catalyst, which is in the same
+
+phase as the reaction that it's
+
+catalyzing as the reactants.
+
+An example of this is depletion
+of the ozone layer
+
+by chlorofluorocarbons.
+
+And so, this was one of the big
+environmental challenges
+
+that the U.S. has faced, whether
+it should ban these
+
+chlorofluorocarbons, and there
+was a lot of debate on what
+
+the data really was about what
+how much they affected the
+
+ozone layer.
+
+And I guess that debate is
+somewhat still going on,
+
+although I think most people now
+recognize that this is a
+
+serious problem and that
+legislation is really needed
+
+to help correct it.
+
+So that's an example.
+
+In this case they're all gases,
+so that's homogeneous
+
+catalyst, not a happy one.
+
+You could also have
+heterogeneous catalysts, which
+
+are a different phase.
+
+And here's another example
+that has to do with the
+
+environment.
+
+So a catalytic converter is an
+example of a heterogeneous
+
+catalyst. So here you have a
+solid metal surface, you can
+
+have palladium or platinum that
+will catalyze reactions
+
+with gases, and so they
+catalyze oxidation of
+
+hydrocarbons, carbon
+monoxide, also
+
+reduction of nitrogen oxide.
+
+So this is all to reduce
+pollution.
+
+So that's an example of a
+heterogeneous catalyst. And
+
+let me just show you a little
+movie of how that might work.
+
+So in this movie, in grey here
+we have a metal surface, and
+
+this metal surface can break
+the hydrogen bond of h 2.
+
+And so here, it is already
+broken, the h 2 bond, so
+
+there's a little hydrogen there
+and hydrogen there, and
+
+so that activates the
+hydrogen to react.
+
+And so, then we have ethene
+molecule come in, and oh,
+
+there goes the hydrogen, and oh,
+there goes the hydrogen,
+
+oh, there goes the other one
+and you can form ethane.
+
+So it speeds up the reaction
+by breaking the h 2 bond so
+
+it's more ready to react.
+
+That would be an example of a
+heterogeneous catalyst there.
+
+All right, and, of course, you
+may all have guessed that my
+
+favorite kind of catalysts
+are enzymes.
+
+They are the catalyst of life.
+
+And so, enzymes are made up of
+protein, or mostly protein
+
+molecules -- you can have an
+enzyme that's actually made of
+
+RNA, but most are protein
+molecules.
+
+And they're typically about
+20,000 grams per mole or more,
+
+and they're capable of carrying
+
+out specific reactions.
+
+And so, they're made up of amino
+acids, and just to take
+
+a quick look at that, an amino
+acid has an amino group and it
+
+has a carboxyl group, and it
+has what's called an alpha
+
+carbon that has a side chain on
+it, which is abbreviated r,
+
+and there are 20 different
+types of r.
+
+The simplest is just a hydrogen,
+you could also have
+
+a hydroxide, etc.
+
+And so, this makes up the
+alphabet of proteins, there
+
+are 20 different ones of these
+that get connected via a
+
+peptide bond.
+
+So at the end of this amino acid
+you'd stick on the amino
+
+group of another amino acid and
+form this peptide bond.
+
+And then you put together
+hundreds and hundreds of these
+
+to form an enzyme complex.
+
+And so, the long chain of amino
+acids folds up and forms
+
+a compact structure.
+
+So, in this particular picture,
+there are about 200
+
+amino acids in each of these
+colored units, so this is a
+
+tetramer, so there are four
+-- there's green,
+
+red, yellow and blue.
+
+And so, this is what's called
+a ribbon diagram.
+
+So, these ribbons, this is an
+alpha helix -- the beta
+
+strands are long.
+
+It traces out the position
+of the alpha carbons.
+
+And overall, this structure is
+about 90 angstroms by 70
+
+angstroms by 50 angstroms. Of
+course, 1 angstroms is 1 times
+
+10 the minus 10 meters.
+
+So these are fairly small.
+
+These protein molecules are,
+of course, in your body.
+
+And this particular one is
+an enzyme that makes an
+
+antibiotic, and that antibiotic
+is fosfomycin,
+
+shown here.
+
+And so, fosfomycin is used
+in antibiotic combination
+
+therapies to treat staph
+infections and other kinds of
+
+very difficult infections
+to treat.
+
+And so, I always talk about
+the things that I'm most
+
+concerned about.
+
+There are a lot of things that
+are big threats that I don't
+
+worry too much about.
+
+Antibiotic resistance
+is something I
+
+actually worry a lot about.
+
+I guess I go to too many
+meetings were they talk about
+
+problems. But the rate at
+which different kinds of
+
+bacteria are becoming resistant
+to antibiotics seems
+
+to be increasing.
+
+So it used to take a lot longer
+before a resistance
+
+would appear than it does now.
+
+And there really haven't been,
+I think since about 1980s or
+
+so, really new antibiotics.
+
+So, we're still using the same
+antibiotics that we have been,
+
+which causes more things to
+become immune or resistant to
+
+those antibiotics, and I think
+this is really dangerous.
+
+And there's not enough money in
+it for the pharmaceutical
+
+industry to really
+go after this.
+
+And it's not just a problem
+for biological warfare,
+
+although that is a possibility,
+but also in
+
+hospitals, you go in for some
+kind of surgery, you have to
+
+worry about the fact that even
+if the surgery goes great, you
+
+might get an infection that
+could really compromise your
+
+health in the hospital.
+
+And so, whether you have a heart
+problem, if you have
+
+cancer, you become immune
+compromised, there's a lot, a
+
+lot of cases where people end
+up not dying of cancer
+
+directly, they end up dying of
+the bacterial infection that
+
+can't be treated.
+
+So this is really
+a huge problem.
+
+So I always like to let you know
+all the possible problems
+
+that you can solve
+in your future.
+
+This is one that I think is
+particularly important, and I
+
+hope some of you will focus on
+this, because we really need
+
+different kinds of antibiotics,
+or we need to
+
+change the way we do medicine
+in this country so that
+
+resistance doesn't become
+as much of a
+
+problem as it has been.
+
+All right, so that enzyme made
+an antibiotic, so we like it,
+
+and let's talk about
+how that works.
+
+How that particular series of
+amino acids folds up to do
+
+that reaction.
+
+So now we have some new
+nomenclature, and sometimes
+
+when people get into the
+biochemistry world they get
+
+scared because there are all
+these words that they don't
+
+know what they mean.
+
+So most of them are not -- they
+are things that you can
+
+relate back to something
+you already know.
+
+So, we've been talking about
+reactants, and when you have a
+
+reactant with an enzyme, it's
+usually called a substrate.
+
+So this is just another name
+for a reactant molecule.
+
+And then substrates tend to
+bind in what we call the
+
+active site of the enzyme,
+which is the part of the
+
+enzyme that's going to
+do the chemistry.
+
+So those are two terms that
+you'll hear about in
+
+biochemistry.
+
+All right, so we have an enzyme,
+we'll call it e, it
+
+binds a substrate, we'll call
+that s, and then it forms an
+
+enzyme substrate complex,
+which we'll call an e s
+
+complex, for enzyme substrate.
+
+And then that enzyme substrate
+complex will go to enzyme and
+
+product, which we'll call p.
+
+And if you look in the
+state-of-the-art biochemistry
+
+books, these are the
+abbreviations you'll see in
+
+there as well.
+
+So, this pains me greatly to
+show this cartoon, because I
+
+spend my career determining
+3-dimensional structures of
+
+proteins, and so to describe
+it as a little squiggly is
+
+painful for me.
+
+But nonetheless, there you go.
+
+Also, the substrate is almost
+about as big as the enzyme.
+
+That is also usually not true.
+
+But nonetheless, here's
+a little cartoon.
+
+Here's our substrate binding to
+our enzyme, it's forming an
+
+e s complex.
+
+And then the enzyme is going
+to move the ears of the
+
+substrate around to
+form product, and
+
+now product is released.
+
+So, this is actually pretty
+simple in terms
+
+of writing a mechanism.
+
+And so, what we can do is write
+a mechanism the way that
+
+we have been writing
+a mechanism
+
+so far in this class.
+
+And so we're going to go through
+this, we're going to
+
+derive expression mostly to show
+you that all the things
+
+you've been learning are related
+to chemistry, they're
+
+also related to biochemistry.
+
+So, you already know a lot
+of biochemistry from just
+
+studying freshman chemistry
+in 511-1.
+
+All right, so we have 2 steps
+in our mechanism.
+
+We have enzyme binding
+substrate to form an
+
+intermediate enzyme substrate
+complex, which then goes on to
+
+form enzyme plus product
+in step 2.
+
+So the first step is reversible,
+the second step is
+
+not as drawn.
+
+All right, so now we can come up
+with the rates for each of
+
+the individual steps in this
+overall mechanism, and since
+
+they are elementary reactions
+or steps in an overall
+
+mechanism, we can write the rate
+laws directly from what
+
+we observe.
+
+So for the forward direction,
+we're going to
+
+have what rate constant?
+
+K 1 times the concentration
+of what?
+
+And?
+
+Yeah.
+
+So there we go.
+
+We have k 1 times the
+concentration of e and the
+
+concentration of s.
+
+See, you already knew how
+to do biochemistry.
+
+All right, so now at the rate of
+the reverse direction is --
+
+what's our rate constant?
+
+K minus 1 times e s.
+
+And then for step 2, we have
+what rate constant?
+
+K 2 times e s.
+
+All right, so now we can
+talk about the rate
+
+formation of product.
+
+And so you'll see this expressed
+as d concentration
+
+of p d t, so the change in
+product that's being formed
+
+and that's going to be equal
+to the second step
+
+here, k 2 times e s.
+
+But, as has been the case
+before, e s is an
+
+intermediate, and we need to
+solve our rate laws, our rate
+
+expressions, in terms
+of reactants or
+
+products and rate constants.
+
+So we need to solve for
+the intermediate.
+
+All right, so let's think
+about solving for the
+
+intermediate.
+
+And why don't you tell
+me how to do that.
+
+OK, let's just take
+10 more seconds.
+
+Very good.
+
+All right, so let's just
+take a look at
+
+why that is the case.
+
+So, when we solve for this, it's
+going to be equal to the
+
+formation of the intermediate,
+which happens in the first
+
+step with this rate that you
+told me, k 1 times the
+
+concentration of e s.
+
+And then we have the
+decomposition in the reverse
+
+of step one, so that's
+minus k minus 1 e s.
+
+And then we also have the
+consumption of the
+
+intermediate, which is -- so we
+have minus this step, which
+
+is k 2 times e s.
+
+So again, formation minus
+decomposition minus
+
+consumption.
+
+And now, we can use the steady
+state approximation.
+
+So the steady state
+approximation applies in
+
+biochemistry just as well as
+in all of your chemistry
+
+problems that you've done
+in this course.
+
+And so, the steady state
+approximation allows us to set
+
+that whole term equal to zero.
+
+So it says that the net rate of
+intermediate formation and
+
+decomposition and consumption is
+0, or you can express it as
+
+the rate of formation of the
+intermediate equals the rates
+
+of decomposition and consumption
+-- those are
+
+equivalent.
+
+So we can set all of
+this equal to zero.
+
+So again, the same as what
+we've done before.
+
+All right, so now we're going
+to have a slight change of
+
+what we've done before, and
+this has to do with the
+
+practical consideration.
+
+So you can solve for these
+in terms of reactants and
+
+products and rate constants,
+but it's actually easier to
+
+solve for e s in terms of your
+total enzyme rather than your
+
+free enzyme.
+
+So what we've had before is our
+free enzyme, but we often
+
+don't know how much enzyme is
+free, and by that we mean not
+
+bound to the substrate.
+
+And so, we know how much total
+enzyme we put in, but we might
+
+not know how much of
+that is unbound.
+
+So it's actually easier for the
+experimentalist to solve
+
+for things in terms
+of total enzyme.
+
+And so what we're going to do
+then is we're going to replace
+
+our free enzyme term with the
+following, total enzyme minus
+
+bound, and total enzyme
+minus the bound
+
+enzyme is the free enzyme.
+
+So we're going to do this change
+that makes it easier
+
+for the experimentalist.
+
+So here's the term we had
+before, but now we want to
+
+replace this term of e with
+e to 0 minus e s.
+
+So we're going to put that,
+here's the term e up here, so
+
+we're going to replace that
+with e 0 minus e s.
+
+And then we're going to multiply
+that out, so we get k
+
+1, e 0, s minus k 1, e s, and
+then the concentration of
+
+substrate here, and the rest
+of it is the same.
+
+So we got rid of our term e.
+
+So now we can solve for e s.
+
+So this is what we just had,
+and so we're going to
+
+rearrange so the e s terms are
+on one side, so we have an e s
+
+term here, here, and here.
+
+So all that is going to be on
+one side, and then this other
+
+term will be on the other
+side of the equation.
+
+So now we have moved all the e
+s terms over here, so we've
+
+got rid of the negative numbers,
+we've added them all
+
+to the other side, and then on
+this side we just have this k
+
+1 term left.
+
+Now we're going to pull
+out the e s terms. So,
+
+we'll solve for e s.
+
+We'll pull that out, that leaves
+us with k 1 times the
+
+concentration of s, k minus
+1, and then k 2.
+
+And now we're going to take this
+and divide by that term
+
+in parentheses, and so now we've
+solved for e s in terms
+
+of total enzyme substrate
+and our rate constants.
+
+All right, now we're going
+to do another thing
+
+that's a bit different.
+
+We're going to introduce a term
+in biochemistry, which is
+
+k m, also known as the
+Michaelis-Menten constant, and
+
+so k m is equal to the
+rate constant for the
+
+forward/reverse direction, k
+minus 1 plus k 2 over k 1.
+
+So we're going to now try to
+use this in our expression.
+
+So we're going to put this term
+in there, and so to have
+
+this term of k m in there,
+we need to have this
+
+divided by k 1.
+
+So we can do that, it's OK, as
+long as we divide everything
+
+by k 1, so we're going to divide
+the top by k 1, and
+
+this by k 1, and that by k 1.
+
+So now, we divide all by k 1,
+and so we have this top with k
+
+1, this term with k 1, and
+this with k 1, and
+
+that's our k m value.
+
+But now we can simplify this,
+we've got a lot of k 1's here,
+
+and so if we simplify this,
+we can cross out
+
+those k 1's over there.
+
+And we can also get rid of
+these k 1's over here.
+
+And that's going to leave
+us with a much simpler
+
+expression.
+
+So that's going to leave us with
+the total enzyme times
+
+substrate over substrate
+plus k m.
+
+And that looks a whole lot
+better than that other term
+
+that we had before.
+
+OK, so we can now take this and
+substitute it back into
+
+the expression we had earlier.
+
+So here we had the rate of
+product formation, k 2 times
+
+this intermediate, we solved
+for the intermediate using
+
+total enzyme and using
+this k m term.
+
+And now we just put all
+of this times k 2.
+
+And if you put all of that
+times k 2, you have this
+
+expression, which is the
+Michaelis-Menten equation.
+
+So the only difference of what
+you did before was that you
+
+solved in terms of total enzyme,
+and also, we have this
+
+new k m term.
+
+And so now we have an equation
+that's used in a lot of
+
+biochemistry research to think
+about enzyme kinetics.
+
+So let's think about enzyme
+kinetics for a minute.
+
+This is what a plot often looks
+like -- we are looking
+
+at the product formed by
+an enzyme versus the
+
+concentration of substrate.
+
+And it often goes up.
+
+It's pretty steep, and then
+it starts to level off.
+
+So let's think about what's
+happening here.
+
+So if you have low substrate,
+so that's way down here, not
+
+much substrate is available,
+adding more substrate will
+
+increase this rate
+significantly, you'll form a
+
+lot more product, it increases
+the rate of product formation.
+
+Because a lot of the
+enzyme is free and
+
+can react with substrate.
+
+So it goes up, but then the
+rate starts to level off.
+
+So when you got to higher
+substrate concentrations,
+
+adding more substrate does not
+affect the rate much, the rate
+
+is leveling off.
+
+And we say that the enzyme
+is saturated.
+
+All the enzyme that you have in
+there already has substrate
+
+going on, it's already
+doing the chemistry.
+
+So if you're throwing more at
+it, the enzyme can't bind that
+
+substrate, it's busy with a
+different substrate molecule.
+
+So all the active sites in the
+enzyme are full, and so not
+
+much happens.
+
+So this kind of graph
+is what you often
+
+see in enzyme kinetics.
+
+Now let's think about
+that in terms of our
+
+Michaelis-Menten equation.
+
+So let's think about conditions
+when there's a lot
+
+of substrate, when substrate
+is much greater than k m.
+
+So here we have substrate and
+k m on the bottom of our
+
+equation, and what's going to
+happen if this term is much,
+
+much bigger than
+this k m term?
+
+What happens to the k m term?
+
+It goes away.
+
+It's really small compared
+to this, it's kind of
+
+insignificant.
+
+So, if that happens, then you
+can cancel substrate as well.
+
+And so, that means that under
+conditions where substrate is
+
+much greater than k m, the rate
+is a much simpler term,
+
+it's just equal to k 2 times
+your total enzyme.
+
+And so this has a name, this is
+called Vmax or the maximum
+
+velocity of the reaction.
+
+So, under these conditions,
+when the substrate is much
+
+greater than that k m value,
+this expression simplifies and
+
+you get just k 2, your rate
+constant, times your total
+
+enzyme, and that'll give
+you the maximum
+
+velocity of the reaction.
+
+And so, that's just written
+again here.
+
+Vmax equals k 2 times total
+enzyme, and that equation will
+
+be given to you on an
+equation sheet.
+
+So what's happening?
+
+What's happening is that
+you're up here.
+
+So when substrate concentration
+is much greater
+
+than k m, then you're in these
+conditions, and you're at some
+
+maximum velocity.
+
+So the velocity will only go,
+the rate of the reaction will
+
+only go so fast, it will
+saturate, it'll level off up
+
+here, and so you can calculate
+that maximum
+
+rate of that reaction.
+
+Now let's consider what happens
+when your substrate
+
+concentration equals your k m.
+
+So down here, if k m is equal to
+substrate, then we're going
+
+to have two substrates
+down here.
+
+And so, we can write this, if
+they're equal, we can write
+
+this as substrate plus
+substrate, and then we can do
+
+some canceling.
+
+So this will be equal to 2
+substrates and then we can
+
+cancel that out, and so we get
+the rate of product formation
+
+under conditions where substrate
+equals k m of 1/2 k
+
+2 times the total enzyme
+concentration.
+
+And this is referred to
+the half maximal rate.
+
+Remember, the maximal rate was
+k 2 times this e knot, and so
+
+half of that is half the
+maximal rate here.
+
+So, the definition of k m is the
+concentration of substrate
+
+for which the rate
+is half maximal.
+
+So if your rate is half of the
+maximum rate, that substrate
+
+concentration that gives you
+half the maximum rate, is the
+
+value for k m.
+
+Substrate concentration equals
+k m at the half maximal rate.
+
+So let's just look at
+what that meant.
+
+So if this is Vmax up here, half
+of Vmax is here, half of
+
+that value, and the substrate
+concentration at half Vmax is
+
+equal to k m.
+
+So you can write those
+in on your diagram.
+
+Vmax is this velocity up here,
+half of that, when you're at
+
+half of the maximal rate,
+k m equals the substrate
+
+concentration.
+
+And there will be problems that
+you will work in your
+
+book very shortly, and often,
+the problems just have to do,
+
+they'll give you the information
+in words and the
+
+calculations can often
+be pretty simple.
+
+Sometimes it'll say, figure
+out what the k m for this
+
+reaction is.
+
+At this substrate concentration,
+the rate is
+
+half maximal.
+
+Well, at that substrate
+concentration, that's the k m.
+
+So, a lot of the problems are
+sort of word problems, they
+
+give you the information and
+you need to know what the
+
+definitions are.
+
+But let's try an example.
+
+So here in this example, we've
+talked about buffering in the
+
+blood, so the conversion of
+your ingredients that make
+
+your buffering agent in the
+blood, that can be catalyzed
+
+by an enzyme called
+carbonicanhydrase, and the
+
+following Michaelis-Menten
+constants are known, a k m is
+
+known, and a k 2 is known, and
+if you're doing experiment and
+
+you have a total concentration
+of your enzyme of 5 times 10
+
+to the minus 6 molar, then you
+should be able to figure out
+
+what the maximum rate of
+the reaction would be.
+
+So, why don't you go ahead
+and tell me what the
+
+maximum rate would be.
+
+OK, let's just take
+10 more seconds.
+
+Very good.
+
+Everyone's doing very
+good today.
+
+All right, so all you have to
+do, you have remember Vmax
+
+equals your total enzyme
+concentration times your k 2.
+
+And pretty much no one, hardly
+anyone was fooled
+
+by k m value there.
+
+All right, very good.
+
+So there are extra problems on
+enzyme kinetics posted on the
+
+extra problems posted
+on the Web.
+
+So there's a few there, so you
+can see the type of problems,
+
+again, they're like that,
+they're pretty simple.
+
+If you remember the definition
+of k m, and you'll be given
+
+the equation for Vmax, you
+should be able to handle the
+
+enzyme/kinetics problems
+pretty well.
+
+Often, also I'll ask questions
+like explain why at high
+
+substrate concentrations, the
+rate does not increase very
+
+much, or why the graph levels
+off, or I might ask you to
+
+draw the plot and tell me
+about low substrate
+
+concentrations, what's true
+there, and high substrate
+
+concentrations, what's true.
+
+So those are the types of
+questions you're going to get
+
+on enzyme kinetics, they're
+actually pretty simple.
+
+All right, so let's just talk
+briefly about enzyme
+
+inhibition.
+
+So the opposite of catalysis
+-- instead of binding a
+
+substrate, you'll bind
+an inhibitor.
+
+So often, these are actually
+pretty simple.
+
+An inhibitor sometimes will look
+a lot like a substrate or
+
+like a transition complex, and
+it'll blind to the enzyme.
+
+And when you have that inhibitor
+stuck in the active
+
+site, substrate physically can't
+bind, so it occupies the
+
+place that substrate goes,
+substrate will come in but it
+
+can't bind anywhere.
+
+So this is actually the
+mechanism by which a number of
+
+pharmaceuticals work.
+
+So, one thing that people who
+were designing enzyme
+
+inhibitors think about is the
+fact that enzymes do tend to
+
+stabilize a transition state
+in the reaction.
+
+So if you make an inhibitor that
+resembles a transition
+
+state, it should bind to the
+enzyme more tightly than
+
+either the reactants, the
+substrates, or the products.
+
+So, a lot of the pharmaceutical
+industry likes
+
+to try to figure out what the
+transition state might look
+
+like, and then try to make a
+molecule that looks like that
+
+transition state that hopefully
+will blind to the
+
+enzyme active site and prevent
+the enzyme from doing what
+
+it's supposed to do.
+
+So, just to kind of look back
+at this figure for a minute
+
+that you had earlier in your
+notes, so you have the
+
+transition state is often
+stabilized by a catalyst, and
+
+so an enzyme will also stabilize
+a transition state.
+
+So if you make your drug look
+like a transition state, it
+
+will hopefully bind
+very tightly.
+
+And so this is one of the sort
+of principles that's behind a
+
+lot of the pharmaceuticals that
+have made to treat HIV
+
+infections.
+
+So I mentioned last week we
+had world AIDS day, that
+
+understanding kinetics
+was actually very
+
+important in HIV research.
+
+And so, many of the
+pharmaceuticals that are given
+
+to HIV patients are what are
+called protease inhibitors.
+
+So they inhibit enzymes that are
+called proteases, and if
+
+you have ase at the end of the
+name that means it's an
+
+enzyme, and so protease means
+that it's an enzyme that
+
+cleaves proteins.
+
+It's a protein ase.
+
+And so, how do these
+enzymes work.
+
+Well, they cleave other
+proteins, they cleave peptide
+
+bonds, and so you often have
+some kind of either activated
+
+water or other hydroxide
+molecule that will attack here
+
+the carbonyl of a peptide
+bond, and it forms a
+
+tetrahedral intermediate, which
+then collapses and it
+
+cleaves that peptide bond.
+
+So the peptide bond is then
+broken, so that's what a
+
+protease does, and a
+protease inhibitor
+
+prevents that cleavage.
+
+So often, protease inhibitors
+look like tetrahedral
+
+intermediates, and so they'll
+bind to the protease active
+
+site and prevent the chemistry
+from occurring.
+
+So if it's a tetrahedral
+intermediate, what kind of
+
+angles should some
+pharmaceutical company be
+
+looking for in its compounds?
+
+109 .
+
+5, yes.
+
+So, molecules with this stable
+tetrahedral intermediate
+
+somewhere on the molecule could
+bind to the active site
+
+and prevent a catalysis.
+
+So, let me just show you one
+example of an improved HIV
+
+drug, and there it is.
+
+This is the tetrahedral site
+that binds at the active site
+
+of that enzyme, and the enzyme
+can't cleave this tetrahedral
+
+intermediate, and so this just
+binds, but the enzyme can't
+
+work on it, so it just sits
+there and prevents substrate
+
+from binding.
+
+So that's how a lot of
+these compounds work.
+
+And so, this is just a little
+picture of the enzyme active
+
+site and there's an inhibitor
+bound to the enzyme active
+
+site, and so a number of
+companies are working on
+
+trying to come up with better
+and better inhibitors that
+
+will sit in the HIV protease
+active site.
+
+So, knowledgeable of a reaction
+mechanism can lead to
+
+new therapeutic treatments.
+
+So, one question with this, with
+protease, there are a lot
+
+of proteases, not just the ones
+involved with HIV, and so
+
+one real problem is specificity
+and toxicity, so
+
+you want to have a drug that
+inhibits one enzyme and not
+
+all the enzymes in
+that category.
+
+So that's a big problem in the
+pharmaceutical industry.
+
+So, apparently, clicker results,
+we actually need to
+
+break a tie.
+
+But we can't do it now.
+
+OK, so Justin's section, woah!
+
+So, apparently we're having, we
+have the questions ready,
+
+but apparently they're
+not ready to be used
+
+right at the moment.
+
+So, we're going to use low tech
+here and indicate the
+
+results for today.
+
+And then on Wednesday, last
+day of class -- oh, my
+
+goodness, so close.
+
+Recitation 6, you were second.
+
+All right, so on Wednesday then,
+we're going to have the
+
+tie breaker, and review
+and evaluations.
\ No newline at end of file
diff --git a/qTGGSVjEBUw.txt b/qTGGSVjEBUw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..03cb80ece983366bd17553ad4bf363464fb26172
--- /dev/null
+++ b/qTGGSVjEBUw.txt
@@ -0,0 +1,14419 @@
+align:start position:0%
+ 
+good afternoon
+
+ align:start position:0%
+good afternoon
+ 
+
+ align:start position:0%
+good afternoon
+so with been studying properties of
+
+ align:start position:0%
+so with been studying properties of
+ 
+
+ align:start position:0%
+so with been studying properties of
+stable equilibrium
+
+ align:start position:0%
+stable equilibrium
+ 
+
+ align:start position:0%
+stable equilibrium
+States relations that can be extracted
+
+ align:start position:0%
+States relations that can be extracted
+ 
+
+ align:start position:0%
+States relations that can be extracted
+from the fundamental
+
+ align:start position:0%
+from the fundamental
+ 
+
+ align:start position:0%
+from the fundamental
+relation of any
+
+ align:start position:0%
+relation of any
+ 
+
+ align:start position:0%
+relation of any
+system and therefore if the system is
+
+ align:start position:0%
+system and therefore if the system is
+ 
+
+ align:start position:0%
+system and therefore if the system is
+for example a substance of a pure
+
+ align:start position:0%
+for example a substance of a pure
+ 
+
+ align:start position:0%
+for example a substance of a pure
+substance or mixtures of
+
+ align:start position:0%
+substance or mixtures of
+ 
+
+ align:start position:0%
+substance or mixtures of
+substances um yes it is a lot of um
+
+ align:start position:0%
+substances um yes it is a lot of um
+ 
+
+ align:start position:0%
+substances um yes it is a lot of um
+math and mathematical manipulations and
+
+ align:start position:0%
+math and mathematical manipulations and
+ 
+
+ align:start position:0%
+math and mathematical manipulations and
+today we'll have a little more of that
+
+ align:start position:0%
+today we'll have a little more of that
+ 
+
+ align:start position:0%
+today we'll have a little more of that
+uh then we we we stop about the
+
+ align:start position:0%
+uh then we we we stop about the
+ 
+
+ align:start position:0%
+uh then we we we stop about the
+mathematics at least for this part uh
+
+ align:start position:0%
+mathematics at least for this part uh
+ 
+
+ align:start position:0%
+mathematics at least for this part uh
+but I wanted
+
+ align:start position:0%
+but I wanted
+ 
+
+ align:start position:0%
+but I wanted
+to to stress the fact that
+
+ align:start position:0%
+to to stress the fact that
+ 
+
+ align:start position:0%
+to to stress the fact that
+we are extracting a lot of U information
+
+ align:start position:0%
+we are extracting a lot of U information
+ 
+
+ align:start position:0%
+we are extracting a lot of U information
+out of just the idea that there exists a
+
+ align:start position:0%
+out of just the idea that there exists a
+ 
+
+ align:start position:0%
+out of just the idea that there exists a
+fundamental relation for stable
+
+ align:start position:0%
+fundamental relation for stable
+ 
+
+ align:start position:0%
+fundamental relation for stable
+equilibrium States from which we can
+
+ align:start position:0%
+equilibrium States from which we can
+ 
+
+ align:start position:0%
+equilibrium States from which we can
+extract
+
+ align:start position:0%
+extract
+ 
+
+ align:start position:0%
+extract
+properties uh and it's precisely the
+
+ align:start position:0%
+properties uh and it's precisely the
+ 
+
+ align:start position:0%
+properties uh and it's precisely the
+mathematical M manipulations that is not
+
+ align:start position:0%
+mathematical M manipulations that is not
+ 
+
+ align:start position:0%
+mathematical M manipulations that is not
+just by itself but with proper physical
+
+ align:start position:0%
+just by itself but with proper physical
+ 
+
+ align:start position:0%
+just by itself but with proper physical
+interpretation and that's the important
+
+ align:start position:0%
+interpretation and that's the important
+ 
+
+ align:start position:0%
+interpretation and that's the important
+aspect it's not just the mathematics
+
+ align:start position:0%
+aspect it's not just the mathematics
+ 
+
+ align:start position:0%
+aspect it's not just the mathematics
+it's also to interpret the mathematics
+
+ align:start position:0%
+it's also to interpret the mathematics
+ 
+
+ align:start position:0%
+it's also to interpret the mathematics
+and then see what the useful part of it
+
+ align:start position:0%
+and then see what the useful part of it
+ 
+
+ align:start position:0%
+and then see what the useful part of it
+is it's from this that you can extract a
+
+ align:start position:0%
+is it's from this that you can extract a
+ 
+
+ align:start position:0%
+is it's from this that you can extract a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+information uh for example in
+
+ align:start position:0%
+information uh for example in
+ 
+
+ align:start position:0%
+information uh for example in
+um in
+
+ align:start position:0%
+um in
+ 
+
+ align:start position:0%
+um in
+economics manipulations of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort have earned uh the Nobel Prize to
+
+ align:start position:0%
+sort have earned uh the Nobel Prize to
+ 
+
+ align:start position:0%
+sort have earned uh the Nobel Prize to
+Paul Samuelson who was a professor here
+
+ align:start position:0%
+Paul Samuelson who was a professor here
+ 
+
+ align:start position:0%
+Paul Samuelson who was a professor here
+with MIT uh because you realize that
+
+ align:start position:0%
+with MIT uh because you realize that
+ 
+
+ align:start position:0%
+with MIT uh because you realize that
+essentially also in economics don't ask
+
+ align:start position:0%
+essentially also in economics don't ask
+ 
+
+ align:start position:0%
+essentially also in economics don't ask
+me what part of Economics but in any
+
+ align:start position:0%
+me what part of Economics but in any
+ 
+
+ align:start position:0%
+me what part of Economics but in any
+case in economics there are functions
+
+ align:start position:0%
+case in economics there are functions
+ 
+
+ align:start position:0%
+case in economics there are functions
+like that that can be manipulated by the
+
+ align:start position:0%
+like that that can be manipulated by the
+ 
+
+ align:start position:0%
+like that that can be manipulated by the
+tools that we are developing from which
+
+ align:start position:0%
+tools that we are developing from which
+ 
+
+ align:start position:0%
+tools that we are developing from which
+you can extract a lot of information
+
+ align:start position:0%
+you can extract a lot of information
+ 
+
+ align:start position:0%
+you can extract a lot of information
+about uh economics in that
+
+ align:start position:0%
+about uh economics in that
+ 
+
+ align:start position:0%
+about uh economics in that
+case so uh mathematics is a powerful uh
+
+ align:start position:0%
+case so uh mathematics is a powerful uh
+ 
+
+ align:start position:0%
+case so uh mathematics is a powerful uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+tool and way of that allows you to think
+
+ align:start position:0%
+tool and way of that allows you to think
+ 
+
+ align:start position:0%
+tool and way of that allows you to think
+straight so all right yes we've done the
+
+ align:start position:0%
+straight so all right yes we've done the
+ 
+
+ align:start position:0%
+straight so all right yes we've done the
+Leandra transform and uh we have applied
+
+ align:start position:0%
+Leandra transform and uh we have applied
+ 
+
+ align:start position:0%
+Leandra transform and uh we have applied
+it to derive uh uh the elal free energy
+
+ align:start position:0%
+it to derive uh uh the elal free energy
+ 
+
+ align:start position:0%
+it to derive uh uh the elal free energy
+the Gibs free energy the
+
+ align:start position:0%
+the Gibs free energy the
+ 
+
+ align:start position:0%
+the Gibs free energy the
+enthalpy and also this Oiler free
+
+ align:start position:0%
+enthalpy and also this Oiler free
+ 
+
+ align:start position:0%
+enthalpy and also this Oiler free
+energy that uh
+
+ align:start position:0%
+energy that uh
+ 
+
+ align:start position:0%
+energy that uh
+will return to to to also today and uh
+
+ align:start position:0%
+will return to to to also today and uh
+ 
+
+ align:start position:0%
+will return to to to also today and uh
+and the next
+
+ align:start position:0%
+and the next
+ 
+
+ align:start position:0%
+and the next
+time also we develop this Max
+
+ align:start position:0%
+time also we develop this Max
+ 
+
+ align:start position:0%
+time also we develop this Max
+coming from the second this the the
+
+ align:start position:0%
+coming from the second this the the
+ 
+
+ align:start position:0%
+coming from the second this the the
+reciprocity of the second order
+
+ align:start position:0%
+reciprocity of the second order
+ 
+
+ align:start position:0%
+reciprocity of the second order
+derivatives of the various
+
+ align:start position:0%
+derivatives of the various
+ 
+
+ align:start position:0%
+derivatives of the various
+functions today I want to introduce uh
+
+ align:start position:0%
+functions today I want to introduce uh
+ 
+
+ align:start position:0%
+functions today I want to introduce uh
+quickly or in the review quickly if
+
+ align:start position:0%
+quickly or in the review quickly if
+ 
+
+ align:start position:0%
+quickly or in the review quickly if
+you've seen it already the this um other
+
+ align:start position:0%
+you've seen it already the this um other
+ 
+
+ align:start position:0%
+you've seen it already the this um other
+tool which is the Jacobian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinants uh so if you have a system
+
+ align:start position:0%
+determinants uh so if you have a system
+ 
+
+ align:start position:0%
+determinants uh so if you have a system
+of two uh
+
+ align:start position:0%
+of two uh
+ 
+
+ align:start position:0%
+of two uh
+functions and you take the Matrix in
+
+ align:start position:0%
+functions and you take the Matrix in
+ 
+
+ align:start position:0%
+functions and you take the Matrix in
+which you put all the the partial
+
+ align:start position:0%
+which you put all the the partial
+ 
+
+ align:start position:0%
+which you put all the the partial
+derivatives in that fashion the
+
+ align:start position:0%
+derivatives in that fashion the
+ 
+
+ align:start position:0%
+derivatives in that fashion the
+determinant of that Matrix is called the
+
+ align:start position:0%
+determinant of that Matrix is called the
+ 
+
+ align:start position:0%
+determinant of that Matrix is called the
+Jacobian determinant The Matrix is the
+
+ align:start position:0%
+Jacobian determinant The Matrix is the
+ 
+
+ align:start position:0%
+Jacobian determinant The Matrix is the
+Jacobian and the determinant of the of
+
+ align:start position:0%
+Jacobian and the determinant of the of
+ 
+
+ align:start position:0%
+Jacobian and the determinant of the of
+the Jacobian is we call it
+
+ align:start position:0%
+the Jacobian is we call it
+ 
+
+ align:start position:0%
+the Jacobian is we call it
+the uh Jacobian anyway just for short
+
+ align:start position:0%
+the uh Jacobian anyway just for short
+ 
+
+ align:start position:0%
+the uh Jacobian anyway just for short
+and we use this uh symbol which
+
+ align:start position:0%
+and we use this uh symbol which
+ 
+
+ align:start position:0%
+and we use this uh symbol which
+resembles a partial because somehow it's
+
+ align:start position:0%
+resembles a partial because somehow it's
+ 
+
+ align:start position:0%
+resembles a partial because somehow it's
+it's a partial of a vector of of
+
+ align:start position:0%
+it's a partial of a vector of of
+ 
+
+ align:start position:0%
+it's a partial of a vector of of
+functions with respect to a vector of
+
+ align:start position:0%
+functions with respect to a vector of
+ 
+
+ align:start position:0%
+functions with respect to a vector of
+the uh independent
+
+ align:start position:0%
+the uh independent
+ 
+
+ align:start position:0%
+the uh independent
+variables and it has these properties
+
+ align:start position:0%
+variables and it has these properties
+ 
+
+ align:start position:0%
+variables and it has these properties
+which you can infer easily by uh the
+
+ align:start position:0%
+which you can infer easily by uh the
+ 
+
+ align:start position:0%
+which you can infer easily by uh the
+properties of determinants you exchange
+
+ align:start position:0%
+properties of determinants you exchange
+ 
+
+ align:start position:0%
+properties of determinants you exchange
+a row exchange a column you exchange the
+
+ align:start position:0%
+a row exchange a column you exchange the
+ 
+
+ align:start position:0%
+a row exchange a column you exchange the
+sign uh and uh so you can easily prove
+
+ align:start position:0%
+sign uh and uh so you can easily prove
+ 
+
+ align:start position:0%
+sign uh and uh so you can easily prove
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+relations you can also notice that if
+
+ align:start position:0%
+relations you can also notice that if
+ 
+
+ align:start position:0%
+relations you can also notice that if
+one of the functions like for example
+
+ align:start position:0%
+one of the functions like for example
+ 
+
+ align:start position:0%
+one of the functions like for example
+G is the uh is the is the simple
+
+ align:start position:0%
+G is the uh is the is the simple
+ 
+
+ align:start position:0%
+G is the uh is the is the simple
+function gals
+
+ align:start position:0%
+function gals
+ 
+
+ align:start position:0%
+function gals
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+then uh the second row is just the
+
+ align:start position:0%
+then uh the second row is just the
+ 
+
+ align:start position:0%
+then uh the second row is just the
+derivative of y with respect to X since
+
+ align:start position:0%
+derivative of y with respect to X since
+ 
+
+ align:start position:0%
+derivative of y with respect to X since
+Y and X are independent variables that's
+
+ align:start position:0%
+Y and X are independent variables that's
+ 
+
+ align:start position:0%
+Y and X are independent variables that's
+zero and this the derivative of y with
+
+ align:start position:0%
+zero and this the derivative of y with
+ 
+
+ align:start position:0%
+zero and this the derivative of y with
+respect to Y is one okay so that's zero
+
+ align:start position:0%
+respect to Y is one okay so that's zero
+ 
+
+ align:start position:0%
+respect to Y is one okay so that's zero
+and one which leaves for the determinant
+
+ align:start position:0%
+and one which leaves for the determinant
+ 
+
+ align:start position:0%
+and one which leaves for the determinant
+just this term here which is the partial
+
+ align:start position:0%
+just this term here which is the partial
+ 
+
+ align:start position:0%
+just this term here which is the partial
+derivative of of f with respect to
+
+ align:start position:0%
+derivative of of f with respect to
+ 
+
+ align:start position:0%
+derivative of of f with respect to
+X so this is a a useful identity because
+
+ align:start position:0%
+X so this is a a useful identity because
+ 
+
+ align:start position:0%
+X so this is a a useful identity because
+you can pass from partial derivatives
+
+ align:start position:0%
+you can pass from partial derivatives
+ 
+
+ align:start position:0%
+you can pass from partial derivatives
+that maybe you want to
+
+ align:start position:0%
+that maybe you want to
+ 
+
+ align:start position:0%
+that maybe you want to
+evaluate to an equivalent Jacobian and
+
+ align:start position:0%
+evaluate to an equivalent Jacobian and
+ 
+
+ align:start position:0%
+evaluate to an equivalent Jacobian and
+then we will see that we can manipulate
+
+ align:start position:0%
+then we will see that we can manipulate
+ 
+
+ align:start position:0%
+then we will see that we can manipulate
+that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+further of course if also f is equal to
+
+ align:start position:0%
+further of course if also f is equal to
+ 
+
+ align:start position:0%
+further of course if also f is equal to
+X then this the is
+
+ align:start position:0%
+X then this the is
+ 
+
+ align:start position:0%
+X then this the is
+becomes simply the entity I mean
+
+ align:start position:0%
+becomes simply the entity I mean
+ 
+
+ align:start position:0%
+becomes simply the entity I mean
+one okay the other theorem about zius is
+
+ align:start position:0%
+one okay the other theorem about zius is
+ 
+
+ align:start position:0%
+one okay the other theorem about zius is
+that if you consider a function of a
+
+ align:start position:0%
+that if you consider a function of a
+ 
+
+ align:start position:0%
+that if you consider a function of a
+single variable and you invert the
+
+ align:start position:0%
+single variable and you invert the
+ 
+
+ align:start position:0%
+single variable and you invert the
+function so you have f is a function of
+
+ align:start position:0%
+function so you have f is a function of
+ 
+
+ align:start position:0%
+function so you have f is a function of
+X and you invert it as X as a function
+
+ align:start position:0%
+X and you invert it as X as a function
+ 
+
+ align:start position:0%
+X and you invert it as X as a function
+of F you know that the derivative of
+
+ align:start position:0%
+of F you know that the derivative of
+ 
+
+ align:start position:0%
+of F you know that the derivative of
+this inverted function is equal to the
+
+ align:start position:0%
+this inverted function is equal to the
+ 
+
+ align:start position:0%
+this inverted function is equal to the
+inverse of the derivative of the
+
+ align:start position:0%
+inverse of the derivative of the
+ 
+
+ align:start position:0%
+inverse of the derivative of the
+original
+
+ align:start position:0%
+original
+ 
+
+ align:start position:0%
+original
+function and the equivalent for a system
+
+ align:start position:0%
+function and the equivalent for a system
+ 
+
+ align:start position:0%
+function and the equivalent for a system
+of uh um uh two functions of two
+
+ align:start position:0%
+of uh um uh two functions of two
+ 
+
+ align:start position:0%
+of uh um uh two functions of two
+variables is that
+
+ align:start position:0%
+variables is that
+ 
+
+ align:start position:0%
+variables is that
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+Jacobian of the inverted
+
+ align:start position:0%
+Jacobian of the inverted
+ 
+
+ align:start position:0%
+Jacobian of the inverted
+system when you solve the system this
+
+ align:start position:0%
+system when you solve the system this
+ 
+
+ align:start position:0%
+system when you solve the system this
+system of equations to put in evidence X
+
+ align:start position:0%
+system of equations to put in evidence X
+ 
+
+ align:start position:0%
+system of equations to put in evidence X
+and Y is a function on F of f and g so
+
+ align:start position:0%
+and Y is a function on F of f and g so
+ 
+
+ align:start position:0%
+and Y is a function on F of f and g so
+you change the independent
+
+ align:start position:0%
+you change the independent
+ 
+
+ align:start position:0%
+you change the independent
+variables uh and so you invert well the
+
+ align:start position:0%
+variables uh and so you invert well the
+ 
+
+ align:start position:0%
+variables uh and so you invert well the
+uh Jacobian of the invert system is
+
+ align:start position:0%
+uh Jacobian of the invert system is
+ 
+
+ align:start position:0%
+uh Jacobian of the invert system is
+equal to the inverse of the Jacobian of
+
+ align:start position:0%
+equal to the inverse of the Jacobian of
+ 
+
+ align:start position:0%
+equal to the inverse of the Jacobian of
+the original
+
+ align:start position:0%
+the original
+ 
+
+ align:start position:0%
+the original
+system and that also shows shows that if
+
+ align:start position:0%
+system and that also shows shows that if
+ 
+
+ align:start position:0%
+system and that also shows shows that if
+you prove if you um choose the function
+
+ align:start position:0%
+you prove if you um choose the function
+ 
+
+ align:start position:0%
+you prove if you um choose the function
+g y as
+
+ align:start position:0%
+g y as
+ 
+
+ align:start position:0%
+g y as
+before gals y as before you can uh prove
+
+ align:start position:0%
+before gals y as before you can uh prove
+ 
+
+ align:start position:0%
+before gals y as before you can uh prove
+by this relation the fact that the uh
+
+ align:start position:0%
+by this relation the fact that the uh
+ 
+
+ align:start position:0%
+by this relation the fact that the uh
+inverse I mean the partial derivative
+
+ align:start position:0%
+inverse I mean the partial derivative
+ 
+
+ align:start position:0%
+inverse I mean the partial derivative
+of the inverse with respect to F at fix
+
+ align:start position:0%
+of the inverse with respect to F at fix
+ 
+
+ align:start position:0%
+of the inverse with respect to F at fix
+Y is equal to the inverse of the
+
+ align:start position:0%
+Y is equal to the inverse of the
+ 
+
+ align:start position:0%
+Y is equal to the inverse of the
+original partial
+
+ align:start position:0%
+original partial
+ 
+
+ align:start position:0%
+original partial
+derivative so
+
+ align:start position:0%
+derivative so
+ 
+
+ align:start position:0%
+derivative so
+formally you see this is uh X over y a
+
+ align:start position:0%
+formally you see this is uh X over y a
+ 
+
+ align:start position:0%
+formally you see this is uh X over y a
+constant y let's read it Loosely well
+
+ align:start position:0%
+constant y let's read it Loosely well
+ 
+
+ align:start position:0%
+constant y let's read it Loosely well
+you can just uh put uh it uh consider
+
+ align:start position:0%
+you can just uh put uh it uh consider
+ 
+
+ align:start position:0%
+you can just uh put uh it uh consider
+the DX and the Dy consider it as a
+
+ align:start position:0%
+the DX and the Dy consider it as a
+ 
+
+ align:start position:0%
+the DX and the Dy consider it as a
+fraction and put it under a the
+
+ align:start position:0%
+fraction and put it under a the
+ 
+
+ align:start position:0%
+fraction and put it under a the
+denominator and you get this function
+
+ align:start position:0%
+denominator and you get this function
+ 
+
+ align:start position:0%
+denominator and you get this function
+and uh it is fair in other words it
+
+ align:start position:0%
+and uh it is fair in other words it
+ 
+
+ align:start position:0%
+and uh it is fair in other words it
+proves that you can do that easy uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+manipulation all right and the other
+
+ align:start position:0%
+manipulation all right and the other
+ 
+
+ align:start position:0%
+manipulation all right and the other
+item is that if you have a function f of
+
+ align:start position:0%
+item is that if you have a function f of
+ 
+
+ align:start position:0%
+item is that if you have a function f of
+x so X is your independent variable but
+
+ align:start position:0%
+x so X is your independent variable but
+ 
+
+ align:start position:0%
+x so X is your independent variable but
+but suppose you want to represent your
+
+ align:start position:0%
+but suppose you want to represent your
+ 
+
+ align:start position:0%
+but suppose you want to represent your
+independent variable as a in parametric
+
+ align:start position:0%
+independent variable as a in parametric
+ 
+
+ align:start position:0%
+independent variable as a in parametric
+form so you have so X is a function of
+
+ align:start position:0%
+form so you have so X is a function of
+ 
+
+ align:start position:0%
+form so you have so X is a function of
+another uh variable say a x of a so you
+
+ align:start position:0%
+another uh variable say a x of a so you
+ 
+
+ align:start position:0%
+another uh variable say a x of a so you
+substitute in the function and so you
+
+ align:start position:0%
+substitute in the function and so you
+ 
+
+ align:start position:0%
+substitute in the function and so you
+have a function of a function this is a
+
+ align:start position:0%
+have a function of a function this is a
+ 
+
+ align:start position:0%
+have a function of a function this is a
+function of a now a has become the
+
+ align:start position:0%
+function of a now a has become the
+ 
+
+ align:start position:0%
+function of a now a has become the
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+variable so the chain rule for
+
+ align:start position:0%
+variable so the chain rule for
+ 
+
+ align:start position:0%
+variable so the chain rule for
+derivatives says for for single
+
+ align:start position:0%
+derivatives says for for single
+ 
+
+ align:start position:0%
+derivatives says for for single
+variables that the derivative of f
+
+ align:start position:0%
+variables that the derivative of f
+ 
+
+ align:start position:0%
+variables that the derivative of f
+respect to a is the derivative of s with
+
+ align:start position:0%
+respect to a is the derivative of s with
+ 
+
+ align:start position:0%
+respect to a is the derivative of s with
+respect to x times the derivative of x
+
+ align:start position:0%
+respect to x times the derivative of x
+ 
+
+ align:start position:0%
+respect to x times the derivative of x
+with respect to a okay the
+
+ align:start position:0%
+with respect to a okay the
+ 
+
+ align:start position:0%
+with respect to a okay the
+equivalent for our system of two
+
+ align:start position:0%
+equivalent for our system of two
+ 
+
+ align:start position:0%
+equivalent for our system of two
+variables uh so when you change your
+
+ align:start position:0%
+variables uh so when you change your
+ 
+
+ align:start position:0%
+variables uh so when you change your
+system f and g uh in instead of as a
+
+ align:start position:0%
+system f and g uh in instead of as a
+ 
+
+ align:start position:0%
+system f and g uh in instead of as a
+function of X and Y but is a function of
+
+ align:start position:0%
+function of X and Y but is a function of
+ 
+
+ align:start position:0%
+function of X and Y but is a function of
+a and b so the X and Y are in turn
+
+ align:start position:0%
+a and b so the X and Y are in turn
+ 
+
+ align:start position:0%
+a and b so the X and Y are in turn
+functions of a and
+
+ align:start position:0%
+functions of a and
+ 
+
+ align:start position:0%
+functions of a and
+b um then you have a situation similar
+
+ align:start position:0%
+b um then you have a situation similar
+ 
+
+ align:start position:0%
+b um then you have a situation similar
+to that and the derivative actually the
+
+ align:start position:0%
+to that and the derivative actually the
+ 
+
+ align:start position:0%
+to that and the derivative actually the
+Jacobian of S and G with respect to the
+
+ align:start position:0%
+Jacobian of S and G with respect to the
+ 
+
+ align:start position:0%
+Jacobian of S and G with respect to the
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+variables you can is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to uh the Jacobian with respect to the
+
+ align:start position:0%
+to uh the Jacobian with respect to the
+ 
+
+ align:start position:0%
+to uh the Jacobian with respect to the
+old variables times the Jacobian of the
+
+ align:start position:0%
+old variables times the Jacobian of the
+ 
+
+ align:start position:0%
+old variables times the Jacobian of the
+new Vari of the old variables with
+
+ align:start position:0%
+new Vari of the old variables with
+ 
+
+ align:start position:0%
+new Vari of the old variables with
+respect to the old
+
+ align:start position:0%
+respect to the old
+ 
+
+ align:start position:0%
+respect to the old
+one and
+
+ align:start position:0%
+one and
+ 
+
+ align:start position:0%
+one and
+formally you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh write this result suppose you delete
+
+ align:start position:0%
+uh write this result suppose you delete
+ 
+
+ align:start position:0%
+uh write this result suppose you delete
+these two so you view
+
+ align:start position:0%
+these two so you view
+ 
+
+ align:start position:0%
+these two so you view
+this result is simply the Jacobian of f
+
+ align:start position:0%
+this result is simply the Jacobian of f
+ 
+
+ align:start position:0%
+this result is simply the Jacobian of f
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+a so you write it this way and then you
+
+ align:start position:0%
+a so you write it this way and then you
+ 
+
+ align:start position:0%
+a so you write it this way and then you
+have empty spaces here where you can put
+
+ align:start position:0%
+have empty spaces here where you can put
+ 
+
+ align:start position:0%
+have empty spaces here where you can put
+anything that cancels out so for example
+
+ align:start position:0%
+anything that cancels out so for example
+ 
+
+ align:start position:0%
+anything that cancels out so for example
+you can put the Jacobian of XY with
+
+ align:start position:0%
+you can put the Jacobian of XY with
+ 
+
+ align:start position:0%
+you can put the Jacobian of XY with
+respect to XY which is equal to one the
+
+ align:start position:0%
+respect to XY which is equal to one the
+ 
+
+ align:start position:0%
+respect to XY which is equal to one the
+identity we just proved it
+
+ align:start position:0%
+identity we just proved it
+ 
+
+ align:start position:0%
+identity we just proved it
+before and
+
+ align:start position:0%
+before and
+ 
+
+ align:start position:0%
+before and
+th uh the formal manipulation becomes uh
+
+ align:start position:0%
+th uh the formal manipulation becomes uh
+ 
+
+ align:start position:0%
+th uh the formal manipulation becomes uh
+uh easy now because uh then you
+
+ align:start position:0%
+uh easy now because uh then you
+ 
+
+ align:start position:0%
+uh easy now because uh then you
+interpret this one as the Jacobian of f
+
+ align:start position:0%
+interpret this one as the Jacobian of f
+ 
+
+ align:start position:0%
+interpret this one as the Jacobian of f
+with respect to XY and this is as the
+
+ align:start position:0%
+with respect to XY and this is as the
+ 
+
+ align:start position:0%
+with respect to XY and this is as the
+Jacobian of XY with respect to
+
+ align:start position:0%
+Jacobian of XY with respect to
+ 
+
+ align:start position:0%
+Jacobian of XY with respect to
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's give an example that brings
+
+ align:start position:0%
+okay let's give an example that brings
+ 
+
+ align:start position:0%
+okay let's give an example that brings
+us to a a a useful uh relation useful
+
+ align:start position:0%
+us to a a a useful uh relation useful
+ 
+
+ align:start position:0%
+us to a a a useful uh relation useful
+identity for two properties that are uh
+
+ align:start position:0%
+identity for two properties that are uh
+ 
+
+ align:start position:0%
+identity for two properties that are uh
+among the list that we have seen are
+
+ align:start position:0%
+among the list that we have seen are
+ 
+
+ align:start position:0%
+among the list that we have seen are
+measurable so
+
+ align:start position:0%
+measurable so
+ 
+
+ align:start position:0%
+measurable so
+take the
+
+ align:start position:0%
+take the
+ 
+
+ align:start position:0%
+take the
+S determinant the determinant of the S
+
+ align:start position:0%
+S determinant the determinant of the S
+ 
+
+ align:start position:0%
+S determinant the determinant of the S
+relation of the S Matrix of the
+
+ align:start position:0%
+relation of the S Matrix of the
+ 
+
+ align:start position:0%
+relation of the S Matrix of the
+fundamental relation with respect to
+
+ align:start position:0%
+fundamental relation with respect to
+ 
+
+ align:start position:0%
+fundamental relation with respect to
+entropy and volume so it's the Matrix of
+
+ align:start position:0%
+entropy and volume so it's the Matrix of
+ 
+
+ align:start position:0%
+entropy and volume so it's the Matrix of
+the second order derivatives of energy
+
+ align:start position:0%
+the second order derivatives of energy
+ 
+
+ align:start position:0%
+the second order derivatives of energy
+with respect to entropy and
+
+ align:start position:0%
+with respect to entropy and
+ 
+
+ align:start position:0%
+with respect to entropy and
+volume now since
+
+ align:start position:0%
+volume now since
+ 
+
+ align:start position:0%
+volume now since
+these second derivatives are derivatives
+
+ align:start position:0%
+these second derivatives are derivatives
+ 
+
+ align:start position:0%
+these second derivatives are derivatives
+of for example we remember that the
+
+ align:start position:0%
+of for example we remember that the
+ 
+
+ align:start position:0%
+of for example we remember that the
+derivative the first derivative of e
+
+ align:start position:0%
+derivative the first derivative of e
+ 
+
+ align:start position:0%
+derivative the first derivative of e
+with respect to S is the temperature you
+
+ align:start position:0%
+with respect to S is the temperature you
+ 
+
+ align:start position:0%
+with respect to S is the temperature you
+can also write them in this way
+
+ align:start position:0%
+can also write them in this way
+ 
+
+ align:start position:0%
+can also write them in this way
+in terms of
+
+ align:start position:0%
+in terms of
+ 
+
+ align:start position:0%
+in terms of
+the conjugate
+
+ align:start position:0%
+the conjugate
+ 
+
+ align:start position:0%
+the conjugate
+variables temperature for entropy minus
+
+ align:start position:0%
+variables temperature for entropy minus
+ 
+
+ align:start position:0%
+variables temperature for entropy minus
+the pressure for
+
+ align:start position:0%
+the pressure for
+ 
+
+ align:start position:0%
+the pressure for
+volume okay so this is just uh applying
+
+ align:start position:0%
+volume okay so this is just uh applying
+ 
+
+ align:start position:0%
+volume okay so this is just uh applying
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+definitions and then here you recognize
+
+ align:start position:0%
+definitions and then here you recognize
+ 
+
+ align:start position:0%
+definitions and then here you recognize
+that apart from the minus sign here that
+
+ align:start position:0%
+that apart from the minus sign here that
+ 
+
+ align:start position:0%
+that apart from the minus sign here that
+can be uh taken to outside of the
+
+ align:start position:0%
+can be uh taken to outside of the
+ 
+
+ align:start position:0%
+can be uh taken to outside of the
+determinant this is just the Coban of
+
+ align:start position:0%
+determinant this is just the Coban of
+ 
+
+ align:start position:0%
+determinant this is just the Coban of
+temperature and pressure versus uh with
+
+ align:start position:0%
+temperature and pressure versus uh with
+ 
+
+ align:start position:0%
+temperature and pressure versus uh with
+respect to S
+
+ align:start position:0%
+respect to S
+ 
+
+ align:start position:0%
+respect to S
+snv so now let's do this trick of
+
+ align:start position:0%
+snv so now let's do this trick of
+ 
+
+ align:start position:0%
+snv so now let's do this trick of
+Shifting the denominator leing the empty
+
+ align:start position:0%
+Shifting the denominator leing the empty
+ 
+
+ align:start position:0%
+Shifting the denominator leing the empty
+spaces and let's put here whatever we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want so I'll do it in two ways I put
+
+ align:start position:0%
+want so I'll do it in two ways I put
+ 
+
+ align:start position:0%
+want so I'll do it in two ways I put
+SNP here and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay and then I have I notice that
+
+ align:start position:0%
+there okay and then I have I notice that
+ 
+
+ align:start position:0%
+there okay and then I have I notice that
+I have chosen my uh I make it make my my
+
+ align:start position:0%
+I have chosen my uh I make it make my my
+ 
+
+ align:start position:0%
+I have chosen my uh I make it make my my
+choice so
+
+ align:start position:0%
+choice so
+ 
+
+ align:start position:0%
+choice so
+that uh in each of these determinant I
+
+ align:start position:0%
+that uh in each of these determinant I
+ 
+
+ align:start position:0%
+that uh in each of these determinant I
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+Jacobian there is a repeated U uh
+
+ align:start position:0%
+Jacobian there is a repeated U uh
+ 
+
+ align:start position:0%
+Jacobian there is a repeated U uh
+pressure above and
+
+ align:start position:0%
+pressure above and
+ 
+
+ align:start position:0%
+pressure above and
+below so that is the derivative of of t
+
+ align:start position:0%
+below so that is the derivative of of t
+ 
+
+ align:start position:0%
+below so that is the derivative of of t
+with respect to S at constant
+
+ align:start position:0%
+with respect to S at constant
+ 
+
+ align:start position:0%
+with respect to S at constant
+p and this other side has s which is
+
+ align:start position:0%
+p and this other side has s which is
+ 
+
+ align:start position:0%
+p and this other side has s which is
+repeated
+
+ align:start position:0%
+repeated
+ 
+
+ align:start position:0%
+repeated
+so that is the derivative of p with
+
+ align:start position:0%
+so that is the derivative of p with
+ 
+
+ align:start position:0%
+so that is the derivative of p with
+respect to V at constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s then if you look
+
+ align:start position:0%
+s then if you look
+ 
+
+ align:start position:0%
+s then if you look
+up and I have let me remind it
+
+ align:start position:0%
+up and I have let me remind it
+ 
+
+ align:start position:0%
+up and I have let me remind it
+here uh we Define the heat capacity at
+
+ align:start position:0%
+here uh we Define the heat capacity at
+ 
+
+ align:start position:0%
+here uh we Define the heat capacity at
+constant uh pressure a few days ago and
+
+ align:start position:0%
+constant uh pressure a few days ago and
+ 
+
+ align:start position:0%
+constant uh pressure a few days ago and
+and that was defined as the derivative
+
+ align:start position:0%
+and that was defined as the derivative
+ 
+
+ align:start position:0%
+and that was defined as the derivative
+of the enthalpy with respect to
+
+ align:start position:0%
+of the enthalpy with respect to
+ 
+
+ align:start position:0%
+of the enthalpy with respect to
+temperature at p
+
+ align:start position:0%
+temperature at p
+ 
+
+ align:start position:0%
+temperature at p
+but if you look at how the enal the
+
+ align:start position:0%
+but if you look at how the enal the
+ 
+
+ align:start position:0%
+but if you look at how the enal the
+differential for the enthalpy is if you
+
+ align:start position:0%
+differential for the enthalpy is if you
+ 
+
+ align:start position:0%
+differential for the enthalpy is if you
+keep p and N constant DH is equal to
+
+ align:start position:0%
+keep p and N constant DH is equal to
+ 
+
+ align:start position:0%
+keep p and N constant DH is equal to
+TDs so you can substitute the DH with
+
+ align:start position:0%
+TDs so you can substitute the DH with
+ 
+
+ align:start position:0%
+TDs so you can substitute the DH with
+the TDS
+
+ align:start position:0%
+the TDS
+ 
+
+ align:start position:0%
+the TDS
+here at constant pnn so CP or actually
+
+ align:start position:0%
+here at constant pnn so CP or actually
+ 
+
+ align:start position:0%
+here at constant pnn so CP or actually
+you see here that the derivative of s
+
+ align:start position:0%
+you see here that the derivative of s
+ 
+
+ align:start position:0%
+you see here that the derivative of s
+with respect to T at constant p is CP
+
+ align:start position:0%
+with respect to T at constant p is CP
+ 
+
+ align:start position:0%
+with respect to T at constant p is CP
+over t
+
+ align:start position:0%
+over t
+ 
+
+ align:start position:0%
+over t
+this derivative is therefore the inverse
+
+ align:start position:0%
+this derivative is therefore the inverse
+ 
+
+ align:start position:0%
+this derivative is therefore the inverse
+of CP over
+
+ align:start position:0%
+of CP over
+ 
+
+ align:start position:0%
+of CP over
+T why the inverse because we just Pro
+
+ align:start position:0%
+T why the inverse because we just Pro
+ 
+
+ align:start position:0%
+T why the inverse because we just Pro
+that uh uh this derivative here is equal
+
+ align:start position:0%
+that uh uh this derivative here is equal
+ 
+
+ align:start position:0%
+that uh uh this derivative here is equal
+to uh the inverse of its uh reciprocal
+
+ align:start position:0%
+to uh the inverse of its uh reciprocal
+ 
+
+ align:start position:0%
+to uh the inverse of its uh reciprocal
+so to
+
+ align:start position:0%
+so to
+ 
+
+ align:start position:0%
+so to
+speak also this other one we can
+
+ align:start position:0%
+speak also this other one we can
+ 
+
+ align:start position:0%
+speak also this other one we can
+recognize as one of the properties that
+
+ align:start position:0%
+recognize as one of the properties that
+ 
+
+ align:start position:0%
+recognize as one of the properties that
+we have defined or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+almost by it's it's
+
+ align:start position:0%
+almost by it's it's
+ 
+
+ align:start position:0%
+almost by it's it's
+the it's the derivative of V with
+
+ align:start position:0%
+the it's the derivative of V with
+ 
+
+ align:start position:0%
+the it's the derivative of V with
+respect to pressure with the minus in
+
+ align:start position:0%
+respect to pressure with the minus in
+ 
+
+ align:start position:0%
+respect to pressure with the minus in
+front so it's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compressibility actually the other day
+
+ align:start position:0%
+compressibility actually the other day
+ 
+
+ align:start position:0%
+compressibility actually the other day
+we defined the isothermal
+
+ align:start position:0%
+we defined the isothermal
+ 
+
+ align:start position:0%
+we defined the isothermal
+compressibility so when you compress a
+
+ align:start position:0%
+compressibility so when you compress a
+ 
+
+ align:start position:0%
+compressibility so when you compress a
+material at constant temperature but you
+
+ align:start position:0%
+material at constant temperature but you
+ 
+
+ align:start position:0%
+material at constant temperature but you
+could also compress it at constant
+
+ align:start position:0%
+could also compress it at constant
+ 
+
+ align:start position:0%
+could also compress it at constant
+entropy that defines the isentropic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compressibility and so here you
+
+ align:start position:0%
+compressibility and so here you
+ 
+
+ align:start position:0%
+compressibility and so here you
+recognize the inverse of the isentropic
+
+ align:start position:0%
+recognize the inverse of the isentropic
+ 
+
+ align:start position:0%
+recognize the inverse of the isentropic
+compressibility okay so first result is
+
+ align:start position:0%
+compressibility okay so first result is
+ 
+
+ align:start position:0%
+compressibility okay so first result is
+that that this uh since the determinant
+
+ align:start position:0%
+that that this uh since the determinant
+ 
+
+ align:start position:0%
+that that this uh since the determinant
+of the H determin of the H Matrix has uh
+
+ align:start position:0%
+of the H determin of the H Matrix has uh
+ 
+
+ align:start position:0%
+of the H determin of the H Matrix has uh
+to be non negative by the conditions of
+
+ align:start position:0%
+to be non negative by the conditions of
+ 
+
+ align:start position:0%
+to be non negative by the conditions of
+stability that we have uh already proved
+
+ align:start position:0%
+stability that we have uh already proved
+ 
+
+ align:start position:0%
+stability that we have uh already proved
+we have this
+
+ align:start position:0%
+we have this
+ 
+
+ align:start position:0%
+we have this
+inequality but that's not the main um
+
+ align:start position:0%
+inequality but that's not the main um
+ 
+
+ align:start position:0%
+inequality but that's not the main um
+object here I want to do now the same
+
+ align:start position:0%
+object here I want to do now the same
+ 
+
+ align:start position:0%
+object here I want to do now the same
+but by substituting here in the empty
+
+ align:start position:0%
+but by substituting here in the empty
+ 
+
+ align:start position:0%
+but by substituting here in the empty
+spaces another pair of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variables again in such a way that
+
+ align:start position:0%
+variables again in such a way that
+ 
+
+ align:start position:0%
+variables again in such a way that
+numerator and denominator have one same
+
+ align:start position:0%
+numerator and denominator have one same
+ 
+
+ align:start position:0%
+numerator and denominator have one same
+variable like here the temperature and
+
+ align:start position:0%
+variable like here the temperature and
+ 
+
+ align:start position:0%
+variable like here the temperature and
+here the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume then this becomes the partial of
+
+ align:start position:0%
+volume then this becomes the partial of
+ 
+
+ align:start position:0%
+volume then this becomes the partial of
+p with respect to volume at constant
+
+ align:start position:0%
+p with respect to volume at constant
+ 
+
+ align:start position:0%
+p with respect to volume at constant
+temperature and this becomes a partial
+
+ align:start position:0%
+temperature and this becomes a partial
+ 
+
+ align:start position:0%
+temperature and this becomes a partial
+of t with respect to s set constant V
+
+ align:start position:0%
+of t with respect to s set constant V
+ 
+
+ align:start position:0%
+of t with respect to s set constant V
+and by the
+
+ align:start position:0%
+and by the
+ 
+
+ align:start position:0%
+and by the
+same definitions that we just reviewed
+
+ align:start position:0%
+same definitions that we just reviewed
+ 
+
+ align:start position:0%
+same definitions that we just reviewed
+you can show that this is equal to T
+
+ align:start position:0%
+you can show that this is equal to T
+ 
+
+ align:start position:0%
+you can show that this is equal to T
+over the heat capacity at constant
+
+ align:start position:0%
+over the heat capacity at constant
+ 
+
+ align:start position:0%
+over the heat capacity at constant
+volume and this other is and this other
+
+ align:start position:0%
+volume and this other is and this other
+ 
+
+ align:start position:0%
+volume and this other is and this other
+is uh one over the volume times the
+
+ align:start position:0%
+is uh one over the volume times the
+ 
+
+ align:start position:0%
+is uh one over the volume times the
+isothermal compressibility also this
+
+ align:start position:0%
+isothermal compressibility also this
+ 
+
+ align:start position:0%
+isothermal compressibility also this
+group must be greater than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero but
+
+ align:start position:0%
+zero but
+ 
+
+ align:start position:0%
+zero but
+since they came from the manipulation of
+
+ align:start position:0%
+since they came from the manipulation of
+ 
+
+ align:start position:0%
+since they came from the manipulation of
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+stuff these groups must also be equal to
+
+ align:start position:0%
+stuff these groups must also be equal to
+ 
+
+ align:start position:0%
+stuff these groups must also be equal to
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+another and that by eliminating tnv
+
+ align:start position:0%
+another and that by eliminating tnv
+ 
+
+ align:start position:0%
+another and that by eliminating tnv
+which sort of cancel when you if you
+
+ align:start position:0%
+which sort of cancel when you if you
+ 
+
+ align:start position:0%
+which sort of cancel when you if you
+equate that to to
+
+ align:start position:0%
+equate that to to
+ 
+
+ align:start position:0%
+equate that to to
+this you obtain this result that the
+
+ align:start position:0%
+this you obtain this result that the
+ 
+
+ align:start position:0%
+this you obtain this result that the
+ratio of the heat
+
+ align:start position:0%
+ratio of the heat
+ 
+
+ align:start position:0%
+ratio of the heat
+capacities constant pressure and volume
+
+ align:start position:0%
+capacities constant pressure and volume
+ 
+
+ align:start position:0%
+capacities constant pressure and volume
+is equal to the ratio of the
+
+ align:start position:0%
+is equal to the ratio of the
+ 
+
+ align:start position:0%
+is equal to the ratio of the
+compressibilities
+
+ align:start position:0%
+compressibilities
+ 
+
+ align:start position:0%
+compressibilities
+temperature over entropy constant
+
+ align:start position:0%
+temperature over entropy constant
+ 
+
+ align:start position:0%
+temperature over entropy constant
+entropy temperature versus constant uh
+
+ align:start position:0%
+entropy temperature versus constant uh
+ 
+
+ align:start position:0%
+entropy temperature versus constant uh
+entropy for example if you
+
+ align:start position:0%
+entropy for example if you
+ 
+
+ align:start position:0%
+entropy for example if you
+remember like for
+
+ align:start position:0%
+remember like for
+ 
+
+ align:start position:0%
+remember like for
+air uh or for
+
+ align:start position:0%
+air uh or for
+ 
+
+ align:start position:0%
+air uh or for
+a diatomic um
+
+ align:start position:0%
+a diatomic um
+ 
+
+ align:start position:0%
+a diatomic um
+gas
+
+ align:start position:0%
+gas
+ 
+
+ align:start position:0%
+gas
+ER CP how much is CP over
+
+ align:start position:0%
+ER CP how much is CP over
+ 
+
+ align:start position:0%
+ER CP how much is CP over
+CV anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remembers for air
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+1.4 it it is a
+
+ align:start position:0%
+1.4 it it is a
+ 
+
+ align:start position:0%
+1.4 it it is a
+75th 7 over
+
+ align:start position:0%
+75th 7 over
+ 
+
+ align:start position:0%
+75th 7 over
+5 okay so that
+
+ align:start position:0%
+5 okay so that
+ 
+
+ align:start position:0%
+5 okay so that
+means that also the ratio of these
+
+ align:start position:0%
+means that also the ratio of these
+ 
+
+ align:start position:0%
+means that also the ratio of these
+compressibilities is 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over4 we will see uh uh in a while that
+
+ align:start position:0%
+over4 we will see uh uh in a while that
+ 
+
+ align:start position:0%
+over4 we will see uh uh in a while that
+this gives us this has some importance
+
+ align:start position:0%
+this gives us this has some importance
+ 
+
+ align:start position:0%
+this gives us this has some importance
+in in a practical application which is
+
+ align:start position:0%
+in in a practical application which is
+ 
+
+ align:start position:0%
+in in a practical application which is
+uh the airs Springs that are used in
+
+ align:start position:0%
+uh the airs Springs that are used in
+ 
+
+ align:start position:0%
+uh the airs Springs that are used in
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+uh transport U device I mean Transport
+
+ align:start position:0%
+uh transport U device I mean Transport
+ 
+
+ align:start position:0%
+uh transport U device I mean Transport
+Systems Like Trains uh trucks and cars
+
+ align:start position:0%
+Systems Like Trains uh trucks and cars
+ 
+
+ align:start position:0%
+Systems Like Trains uh trucks and cars
+and so on and even
+
+ align:start position:0%
+and so on and even
+ 
+
+ align:start position:0%
+and so on and even
+bicycles uh airs Springs okay
+
+ align:start position:0%
+bicycles uh airs Springs okay
+ 
+
+ align:start position:0%
+bicycles uh airs Springs okay
+so but before we get to that uh let's
+
+ align:start position:0%
+so but before we get to that uh let's
+ 
+
+ align:start position:0%
+so but before we get to that uh let's
+keep going with um another
+
+ align:start position:0%
+keep going with um another
+ 
+
+ align:start position:0%
+keep going with um another
+uh relation that uh we can
+
+ align:start position:0%
+uh relation that uh we can
+ 
+
+ align:start position:0%
+uh relation that uh we can
+prove by again using the properties of
+
+ align:start position:0%
+prove by again using the properties of
+ 
+
+ align:start position:0%
+prove by again using the properties of
+jacobians and here is
+
+ align:start position:0%
+jacobians and here is
+ 
+
+ align:start position:0%
+jacobians and here is
+a the situation in which you have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface for example a function of X Y
+
+ align:start position:0%
+surface for example a function of X Y
+ 
+
+ align:start position:0%
+surface for example a function of X Y
+and Z equal Zer represents a surface
+
+ align:start position:0%
+and Z equal Zer represents a surface
+ 
+
+ align:start position:0%
+and Z equal Zer represents a surface
+that you can represent in three
+
+ align:start position:0%
+that you can represent in three
+ 
+
+ align:start position:0%
+that you can represent in three
+dimensions XYZ so
+
+ align:start position:0%
+dimensions XYZ so
+ 
+
+ align:start position:0%
+dimensions XYZ so
+okay of course you can uh view that
+
+ align:start position:0%
+okay of course you can uh view that
+ 
+
+ align:start position:0%
+okay of course you can uh view that
+surface from various points of view by
+
+ align:start position:0%
+surface from various points of view by
+ 
+
+ align:start position:0%
+surface from various points of view by
+choosing what your base reference frame
+
+ align:start position:0%
+choosing what your base reference frame
+ 
+
+ align:start position:0%
+choosing what your base reference frame
+is and what the independent variable is
+
+ align:start position:0%
+is and what the independent variable is
+ 
+
+ align:start position:0%
+is and what the independent variable is
+so you can represent that uh surface
+
+ align:start position:0%
+so you can represent that uh surface
+ 
+
+ align:start position:0%
+so you can represent that uh surface
+also in these three alternative
+
+ align:start position:0%
+also in these three alternative
+ 
+
+ align:start position:0%
+also in these three alternative
+ways X is a function of X and why now
+
+ align:start position:0%
+ways X is a function of X and why now
+ 
+
+ align:start position:0%
+ways X is a function of X and why now
+you see what I'm saying if I uh if I
+
+ align:start position:0%
+you see what I'm saying if I uh if I
+ 
+
+ align:start position:0%
+you see what I'm saying if I uh if I
+have this
+
+ align:start position:0%
+have this
+ 
+
+ align:start position:0%
+have this
+uh surface here
+
+ align:start position:0%
+uh surface here
+ 
+
+ align:start position:0%
+uh surface here
+which is f of x y zal
+
+ align:start position:0%
+which is f of x y zal
+ 
+
+ align:start position:0%
+which is f of x y zal
+z uh I can represent it for suppose this
+
+ align:start position:0%
+z uh I can represent it for suppose this
+ 
+
+ align:start position:0%
+z uh I can represent it for suppose this
+is X Y and
+
+ align:start position:0%
+is X Y and
+ 
+
+ align:start position:0%
+is X Y and
+Z okay so this is
+
+ align:start position:0%
+Z okay so this is
+ 
+
+ align:start position:0%
+Z okay so this is
+also for every X and Y I have a value of
+
+ align:start position:0%
+also for every X and Y I have a value of
+ 
+
+ align:start position:0%
+also for every X and Y I have a value of
+Z so I can view it as a function of X of
+
+ align:start position:0%
+Z so I can view it as a function of X of
+ 
+
+ align:start position:0%
+Z so I can view it as a function of X of
+Z as a function of X and Y but I can
+
+ align:start position:0%
+Z as a function of X and Y but I can
+ 
+
+ align:start position:0%
+Z as a function of X and Y but I can
+also view it also uh from here I fix X I
+
+ align:start position:0%
+also view it also uh from here I fix X I
+ 
+
+ align:start position:0%
+also view it also uh from here I fix X I
+fix Z and that gives me a
+
+ align:start position:0%
+fix Z and that gives me a
+ 
+
+ align:start position:0%
+fix Z and that gives me a
+y so that's y function of uh Z and x and
+
+ align:start position:0%
+y so that's y function of uh Z and x and
+ 
+
+ align:start position:0%
+y so that's y function of uh Z and x and
+so on okay so these are alternative ways
+
+ align:start position:0%
+so on okay so these are alternative ways
+ 
+
+ align:start position:0%
+so on okay so these are alternative ways
+of representing in in thermodynamics the
+
+ align:start position:0%
+of representing in in thermodynamics the
+ 
+
+ align:start position:0%
+of representing in in thermodynamics the
+typical surface that is treated this way
+
+ align:start position:0%
+typical surface that is treated this way
+ 
+
+ align:start position:0%
+typical surface that is treated this way
+is the pvt relation so the the equation
+
+ align:start position:0%
+is the pvt relation so the the equation
+ 
+
+ align:start position:0%
+is the pvt relation so the the equation
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+state that particular
+
+ align:start position:0%
+state that particular
+ 
+
+ align:start position:0%
+state that particular
+equation uh that for a class of States
+
+ align:start position:0%
+equation uh that for a class of States
+ 
+
+ align:start position:0%
+equation uh that for a class of States
+like single phase
+
+ align:start position:0%
+like single phase
+ 
+
+ align:start position:0%
+like single phase
+States uh is equivalent to the uh
+
+ align:start position:0%
+States uh is equivalent to the uh
+ 
+
+ align:start position:0%
+States uh is equivalent to the uh
+fundamental
+
+ align:start position:0%
+fundamental
+ 
+
+ align:start position:0%
+fundamental
+relation and U and so it's useful
+
+ align:start position:0%
+relation and U and so it's useful
+ 
+
+ align:start position:0%
+relation and U and so it's useful
+because it's in terms of easily measur
+
+ align:start position:0%
+because it's in terms of easily measur
+ 
+
+ align:start position:0%
+because it's in terms of easily measur
+measurable properties like volume
+
+ align:start position:0%
+measurable properties like volume
+ 
+
+ align:start position:0%
+measurable properties like volume
+temperature and
+
+ align:start position:0%
+temperature and
+ 
+
+ align:start position:0%
+temperature and
+pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so here we do what do we
+
+ align:start position:0%
+okay all right so here we do what do we
+ 
+
+ align:start position:0%
+okay all right so here we do what do we
+do we take take essentially ratios of
+
+ align:start position:0%
+do we take take essentially ratios of
+ 
+
+ align:start position:0%
+do we take take essentially ratios of
+stuff that are equal to
+
+ align:start position:0%
+stuff that are equal to
+ 
+
+ align:start position:0%
+stuff that are equal to
+one or actually say minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so say x
+
+ align:start position:0%
+one so say x
+ 
+
+ align:start position:0%
+one so say x
+z uh and ZX the denominator by the
+
+ align:start position:0%
+z uh and ZX the denominator by the
+ 
+
+ align:start position:0%
+z uh and ZX the denominator by the
+properties of determinants that's equal
+
+ align:start position:0%
+properties of determinants that's equal
+ 
+
+ align:start position:0%
+properties of determinants that's equal
+to minus one if if I switch one uh one
+
+ align:start position:0%
+to minus one if if I switch one uh one
+ 
+
+ align:start position:0%
+to minus one if if I switch one uh one
+column it changes
+
+ align:start position:0%
+column it changes
+ 
+
+ align:start position:0%
+column it changes
+sign okay so I write this which are
+
+ align:start position:0%
+sign okay so I write this which are
+ 
+
+ align:start position:0%
+sign okay so I write this which are
+easy identities then I rearrange them in
+
+ align:start position:0%
+easy identities then I rearrange them in
+ 
+
+ align:start position:0%
+easy identities then I rearrange them in
+a in an in a more interesting way so
+
+ align:start position:0%
+a in an in a more interesting way so
+ 
+
+ align:start position:0%
+a in an in a more interesting way so
+that again I have the same variable uh
+
+ align:start position:0%
+that again I have the same variable uh
+ 
+
+ align:start position:0%
+that again I have the same variable uh
+numerator and denominator so for example
+
+ align:start position:0%
+numerator and denominator so for example
+ 
+
+ align:start position:0%
+numerator and denominator so for example
+this is the partial of X with respect to
+
+ align:start position:0%
+this is the partial of X with respect to
+ 
+
+ align:start position:0%
+this is the partial of X with respect to
+Y at constant Z this is the partial of X
+
+ align:start position:0%
+Y at constant Z this is the partial of X
+ 
+
+ align:start position:0%
+Y at constant Z this is the partial of X
+with respect I'm sorry y with respect to
+
+ align:start position:0%
+with respect I'm sorry y with respect to
+ 
+
+ align:start position:0%
+with respect I'm sorry y with respect to
+Z at constant X and this is partial of Z
+
+ align:start position:0%
+Z at constant X and this is partial of Z
+ 
+
+ align:start position:0%
+Z at constant X and this is partial of Z
+respect to x constant
+
+ align:start position:0%
+respect to x constant
+ 
+
+ align:start position:0%
+respect to x constant
+Y which is written here
+
+ align:start position:0%
+Y which is written here
+ 
+
+ align:start position:0%
+Y which is written here
+and if you multiply minus one three
+
+ align:start position:0%
+and if you multiply minus one three
+ 
+
+ align:start position:0%
+and if you multiply minus one three
+times you get minus one so this is
+
+ align:start position:0%
+times you get minus one so this is
+ 
+
+ align:start position:0%
+times you get minus one so this is
+called the cyc cyclic relation and if
+
+ align:start position:0%
+called the cyc cyclic relation and if
+ 
+
+ align:start position:0%
+called the cyc cyclic relation and if
+you apply it to
+
+ align:start position:0%
+you apply it to
+ 
+
+ align:start position:0%
+you apply it to
+the uh pvt relation equation of State
+
+ align:start position:0%
+the uh pvt relation equation of State
+ 
+
+ align:start position:0%
+the uh pvt relation equation of State
+here is what you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get and for example you could you could
+
+ align:start position:0%
+get and for example you could you could
+ 
+
+ align:start position:0%
+get and for example you could you could
+apply it you remember that the one of
+
+ align:start position:0%
+apply it you remember that the one of
+ 
+
+ align:start position:0%
+apply it you remember that the one of
+the Maxwell relations that we said could
+
+ align:start position:0%
+the Maxwell relations that we said could
+ 
+
+ align:start position:0%
+the Maxwell relations that we said could
+be useful to measure entropy because it
+
+ align:start position:0%
+be useful to measure entropy because it
+ 
+
+ align:start position:0%
+be useful to measure entropy because it
+has it gives a entropy
+
+ align:start position:0%
+has it gives a entropy
+ 
+
+ align:start position:0%
+has it gives a entropy
+changes that you can measure by
+
+ align:start position:0%
+changes that you can measure by
+ 
+
+ align:start position:0%
+changes that you can measure by
+measuring volume changes pressure
+
+ align:start position:0%
+measuring volume changes pressure
+ 
+
+ align:start position:0%
+measuring volume changes pressure
+changes temperature changes at constant
+
+ align:start position:0%
+changes temperature changes at constant
+ 
+
+ align:start position:0%
+changes temperature changes at constant
+temperature at constant volume so this
+
+ align:start position:0%
+temperature at constant volume so this
+ 
+
+ align:start position:0%
+temperature at constant volume so this
+is somehow uh the basis of a an
+
+ align:start position:0%
+is somehow uh the basis of a an
+ 
+
+ align:start position:0%
+is somehow uh the basis of a an
+instrument that you could call an
+
+ align:start position:0%
+instrument that you could call an
+ 
+
+ align:start position:0%
+instrument that you could call an
+entropy
+
+ align:start position:0%
+entropy
+ 
+
+ align:start position:0%
+entropy
+meter well by applying this cyclic
+
+ align:start position:0%
+meter well by applying this cyclic
+ 
+
+ align:start position:0%
+meter well by applying this cyclic
+relation and I'm not going to the
+
+ align:start position:0%
+relation and I'm not going to the
+ 
+
+ align:start position:0%
+relation and I'm not going to the
+details but I'll let you uh show
+
+ align:start position:0%
+details but I'll let you uh show
+ 
+
+ align:start position:0%
+details but I'll let you uh show
+that um you prove that this derivative
+
+ align:start position:0%
+that um you prove that this derivative
+ 
+
+ align:start position:0%
+that um you prove that this derivative
+is equal to the ratio of alpha p over
+
+ align:start position:0%
+is equal to the ratio of alpha p over
+ 
+
+ align:start position:0%
+is equal to the ratio of alpha p over
+Capa T so it's the
+
+ align:start position:0%
+Capa T so it's the
+ 
+
+ align:start position:0%
+Capa T so it's the
+um isobaric coefficient of expansion
+
+ align:start position:0%
+um isobaric coefficient of expansion
+ 
+
+ align:start position:0%
+um isobaric coefficient of expansion
+Alpha over the isothermal
+
+ align:start position:0%
+Alpha over the isothermal
+ 
+
+ align:start position:0%
+Alpha over the isothermal
+compressibility of your
+
+ align:start position:0%
+compressibility of your
+ 
+
+ align:start position:0%
+compressibility of your
+material for example for a
+
+ align:start position:0%
+material for example for a
+ 
+
+ align:start position:0%
+material for example for a
+gas I mean if I can write
+
+ align:start position:0%
+gas I mean if I can write
+ 
+
+ align:start position:0%
+gas I mean if I can write
+the ideal gas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relation you can view that as a as a v
+
+ align:start position:0%
+relation you can view that as a as a v
+ 
+
+ align:start position:0%
+relation you can view that as a as a v
+as a function of T and
+
+ align:start position:0%
+as a function of T and
+ 
+
+ align:start position:0%
+as a function of T and
+P and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N right so it's
+
+ align:start position:0%
+N right so it's
+ 
+
+ align:start position:0%
+N right so it's
+nrt over
+
+ align:start position:0%
+nrt over
+ 
+
+ align:start position:0%
+nrt over
+P so it's easy to compute for example
+
+ align:start position:0%
+P so it's easy to compute for example
+ 
+
+ align:start position:0%
+P so it's easy to compute for example
+Alpha
+
+ align:start position:0%
+Alpha
+ 
+
+ align:start position:0%
+Alpha
+p Alpha p is 1 / V the derivative of V
+
+ align:start position:0%
+p Alpha p is 1 / V the derivative of V
+ 
+
+ align:start position:0%
+p Alpha p is 1 / V the derivative of V
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+T at constant pressure so it's how much
+
+ align:start position:0%
+T at constant pressure so it's how much
+ 
+
+ align:start position:0%
+T at constant pressure so it's how much
+the uh uh the
+
+ align:start position:0%
+the uh uh the
+ 
+
+ align:start position:0%
+the uh uh the
+expansion for a given U increasing
+
+ align:start position:0%
+expansion for a given U increasing
+ 
+
+ align:start position:0%
+expansion for a given U increasing
+temperature all right so it's one / V
+
+ align:start position:0%
+temperature all right so it's one / V
+ 
+
+ align:start position:0%
+temperature all right so it's one / V
+the derivative of V of V with respect to
+
+ align:start position:0%
+the derivative of V of V with respect to
+ 
+
+ align:start position:0%
+the derivative of V of V with respect to
+T is easy it's
+
+ align:start position:0%
+T is easy it's
+ 
+
+ align:start position:0%
+T is easy it's
+NR over
+
+ align:start position:0%
+NR over
+ 
+
+ align:start position:0%
+NR over
+p and if you use that again this is 1 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T Capa
+
+ align:start position:0%
+T Capa
+ 
+
+ align:start position:0%
+T Capa
+T is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus 1 / V the derivative of V with
+
+ align:start position:0%
+minus 1 / V the derivative of V with
+ 
+
+ align:start position:0%
+minus 1 / V the derivative of V with
+respect to P at constant
+
+ align:start position:0%
+respect to P at constant
+ 
+
+ align:start position:0%
+respect to P at constant
+T all right we can also do that
+
+ align:start position:0%
+T all right we can also do that
+ 
+
+ align:start position:0%
+T all right we can also do that
+derivative uh the derivative of this
+
+ align:start position:0%
+derivative uh the derivative of this
+ 
+
+ align:start position:0%
+derivative uh the derivative of this
+with respect to p
+
+ align:start position:0%
+with respect to p
+ 
+
+ align:start position:0%
+with respect to p
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+nrt / p ^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 I apply that
+
+ align:start position:0%
+2 I apply that
+ 
+
+ align:start position:0%
+2 I apply that
+again and the minus goes away with the
+
+ align:start position:0%
+again and the minus goes away with the
+ 
+
+ align:start position:0%
+again and the minus goes away with the
+minus one V goes away I'm left with one
+
+ align:start position:0%
+minus one V goes away I'm left with one
+ 
+
+ align:start position:0%
+minus one V goes away I'm left with one
+/
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P so Alpha and Kappa for ideal gases are
+
+ align:start position:0%
+P so Alpha and Kappa for ideal gases are
+ 
+
+ align:start position:0%
+P so Alpha and Kappa for ideal gases are
+relatively simple
+
+ align:start position:0%
+relatively simple
+ 
+
+ align:start position:0%
+relatively simple
+and uh um and so this gives that that
+
+ align:start position:0%
+and uh um and so this gives that that
+ 
+
+ align:start position:0%
+and uh um and so this gives that that
+derivative here is equal to P /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T okay for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gas there is
+
+ align:start position:0%
+gas there is
+ 
+
+ align:start position:0%
+gas there is
+another interesting
+
+ align:start position:0%
+another interesting
+ 
+
+ align:start position:0%
+another interesting
+relation that you can prove
+
+ align:start position:0%
+relation that you can prove
+ 
+
+ align:start position:0%
+relation that you can prove
+not so easily but relatively uh
+
+ align:start position:0%
+not so easily but relatively uh
+ 
+
+ align:start position:0%
+not so easily but relatively uh
+straightforward by
+
+ align:start position:0%
+straightforward by
+ 
+
+ align:start position:0%
+straightforward by
+using uh
+
+ align:start position:0%
+using uh
+ 
+
+ align:start position:0%
+using uh
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jacobians it's the Mayer relation which
+
+ align:start position:0%
+jacobians it's the Mayer relation which
+ 
+
+ align:start position:0%
+jacobians it's the Mayer relation which
+relates CP CV Alpha p and Capa
+
+ align:start position:0%
+relates CP CV Alpha p and Capa
+ 
+
+ align:start position:0%
+relates CP CV Alpha p and Capa
+te and of course temperature and
+
+ align:start position:0%
+te and of course temperature and
+ 
+
+ align:start position:0%
+te and of course temperature and
+volume and here you see this is just the
+
+ align:start position:0%
+volume and here you see this is just the
+ 
+
+ align:start position:0%
+volume and here you see this is just the
+definition of CP
+
+ align:start position:0%
+definition of CP
+ 
+
+ align:start position:0%
+definition of CP
+we write this derivative in terms of a
+
+ align:start position:0%
+we write this derivative in terms of a
+ 
+
+ align:start position:0%
+we write this derivative in terms of a
+Jacobian with the with the property that
+
+ align:start position:0%
+Jacobian with the with the property that
+ 
+
+ align:start position:0%
+Jacobian with the with the property that
+is kept constant repeated numerator and
+
+ align:start position:0%
+is kept constant repeated numerator and
+ 
+
+ align:start position:0%
+is kept constant repeated numerator and
+do denominator then we shift leave the
+
+ align:start position:0%
+do denominator then we shift leave the
+ 
+
+ align:start position:0%
+do denominator then we shift leave the
+empty space and then we search and now
+
+ align:start position:0%
+empty space and then we search and now
+ 
+
+ align:start position:0%
+empty space and then we search and now
+the CH the choice of what to put there
+
+ align:start position:0%
+the CH the choice of what to put there
+ 
+
+ align:start position:0%
+the CH the choice of what to put there
+is sort of a smart you have to have some
+
+ align:start position:0%
+is sort of a smart you have to have some
+ 
+
+ align:start position:0%
+is sort of a smart you have to have some
+uh just trial and error or some
+
+ align:start position:0%
+uh just trial and error or some
+ 
+
+ align:start position:0%
+uh just trial and error or some
+experience on how to choose
+
+ align:start position:0%
+experience on how to choose
+ 
+
+ align:start position:0%
+experience on how to choose
+it but here if you for example we choose
+
+ align:start position:0%
+it but here if you for example we choose
+ 
+
+ align:start position:0%
+it but here if you for example we choose
+to to to select T and
+
+ align:start position:0%
+to to to select T and
+ 
+
+ align:start position:0%
+to to to select T and
+V the second one has a repeated um
+
+ align:start position:0%
+V the second one has a repeated um
+ 
+
+ align:start position:0%
+V the second one has a repeated um
+variable numerator denominator so it is
+
+ align:start position:0%
+variable numerator denominator so it is
+ 
+
+ align:start position:0%
+variable numerator denominator so it is
+a partial derivative and again we find
+
+ align:start position:0%
+a partial derivative and again we find
+ 
+
+ align:start position:0%
+a partial derivative and again we find
+that it's related to Capa T the first
+
+ align:start position:0%
+that it's related to Capa T the first
+ 
+
+ align:start position:0%
+that it's related to Capa T the first
+determinant has four different variables
+
+ align:start position:0%
+determinant has four different variables
+ 
+
+ align:start position:0%
+determinant has four different variables
+so we write it here in terms of its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definition and then these various
+
+ align:start position:0%
+definition and then these various
+ 
+
+ align:start position:0%
+definition and then these various
+entries can be recognized as
+
+ align:start position:0%
+entries can be recognized as
+ 
+
+ align:start position:0%
+entries can be recognized as
+those properties for example this is CV
+
+ align:start position:0%
+those properties for example this is CV
+ 
+
+ align:start position:0%
+those properties for example this is CV
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+um this we just prove this Alpha over
+
+ align:start position:0%
+um this we just prove this Alpha over
+ 
+
+ align:start position:0%
+um this we just prove this Alpha over
+Kappa
+
+ align:start position:0%
+Kappa
+ 
+
+ align:start position:0%
+Kappa
+T this is the same because of the
+
+ align:start position:0%
+T this is the same because of the
+ 
+
+ align:start position:0%
+T this is the same because of the
+symmetry of um of the S determinant and
+
+ align:start position:0%
+symmetry of um of the S determinant and
+ 
+
+ align:start position:0%
+symmetry of um of the S determinant and
+or because of the max relations which is
+
+ align:start position:0%
+or because of the max relations which is
+ 
+
+ align:start position:0%
+or because of the max relations which is
+the same and this is one over Capa T so
+
+ align:start position:0%
+the same and this is one over Capa T so
+ 
+
+ align:start position:0%
+the same and this is one over Capa T so
+now you compute the determinant you get
+
+ align:start position:0%
+now you compute the determinant you get
+ 
+
+ align:start position:0%
+now you compute the determinant you get
+that you place it here
+
+ align:start position:0%
+that you place it here
+ 
+
+ align:start position:0%
+that you place it here
+and out comes to my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relation okay yeah so what what's the my
+
+ align:start position:0%
+relation okay yeah so what what's the my
+ 
+
+ align:start position:0%
+relation okay yeah so what what's the my
+relation for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gas what's the relation between c c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CP and CV for a for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gas no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+water how about
+
+ align:start position:0%
+water how about
+ 
+
+ align:start position:0%
+water how about
+R the gas
+
+ align:start position:0%
+R the gas
+ 
+
+ align:start position:0%
+R the gas
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+usually you don't do heat
+
+ align:start position:0%
+usually you don't do heat
+ 
+
+ align:start position:0%
+usually you don't do heat
+capacities uh we we uh we you we do
+
+ align:start position:0%
+capacities uh we we uh we you we do
+ 
+
+ align:start position:0%
+capacities uh we we uh we you we do
+specific Heats so that's CP small C is
+
+ align:start position:0%
+specific Heats so that's CP small C is
+ 
+
+ align:start position:0%
+specific Heats so that's CP small C is
+Capital C over
+
+ align:start position:0%
+Capital C over
+ 
+
+ align:start position:0%
+Capital C over
+n and uh CV small C heat
+
+ align:start position:0%
+n and uh CV small C heat
+ 
+
+ align:start position:0%
+n and uh CV small C heat
+capacity I'm sorry specific heat is the
+
+ align:start position:0%
+capacity I'm sorry specific heat is the
+ 
+
+ align:start position:0%
+capacity I'm sorry specific heat is the
+CV over
+
+ align:start position:0%
+CV over
+ 
+
+ align:start position:0%
+CV over
+n and then the relation my relation is
+
+ align:start position:0%
+n and then the relation my relation is
+ 
+
+ align:start position:0%
+n and then the relation my relation is
+that CP equals CV plus the gas constant
+
+ align:start position:0%
+that CP equals CV plus the gas constant
+ 
+
+ align:start position:0%
+that CP equals CV plus the gas constant
+but let's prove it because we said that
+
+ align:start position:0%
+but let's prove it because we said that
+ 
+
+ align:start position:0%
+but let's prove it because we said that
+U uh we have it there so we have we have
+
+ align:start position:0%
+U uh we have it there so we have we have
+ 
+
+ align:start position:0%
+U uh we have it there so we have we have
+to compute V
+
+ align:start position:0%
+to compute V
+ 
+
+ align:start position:0%
+to compute V
+uh what is it the VT Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squ over Capa
+
+ align:start position:0%
+squ over Capa
+ 
+
+ align:start position:0%
+squ over Capa
+T all right which is this term here
+
+ align:start position:0%
+T all right which is this term here
+ 
+
+ align:start position:0%
+T all right which is this term here
+which is the difference between the two
+
+ align:start position:0%
+which is the difference between the two
+ 
+
+ align:start position:0%
+which is the difference between the two
+capacitors so Alpha so that's
+
+ align:start position:0%
+capacitors so Alpha so that's
+ 
+
+ align:start position:0%
+capacitors so Alpha so that's
+VT uh Alpha is 1 / T so got T squ
+
+ align:start position:0%
+VT uh Alpha is 1 / T so got T squ
+ 
+
+ align:start position:0%
+VT uh Alpha is 1 / T so got T squ
+here and Kappa is one over P so I got a
+
+ align:start position:0%
+here and Kappa is one over P so I got a
+ 
+
+ align:start position:0%
+here and Kappa is one over P so I got a
+p there
+
+ align:start position:0%
+p there
+ 
+
+ align:start position:0%
+p there
+so that goes with that and hopefully
+
+ align:start position:0%
+so that goes with that and hopefully
+ 
+
+ align:start position:0%
+so that goes with that and hopefully
+since PV is equal to an
+
+ align:start position:0%
+since PV is equal to an
+ 
+
+ align:start position:0%
+since PV is equal to an
+nrt divided by T gives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+NR I see a lot of rust in your minds
+
+ align:start position:0%
+NR I see a lot of rust in your minds
+ 
+
+ align:start position:0%
+NR I see a lot of rust in your minds
+about about previous thermal that's
+
+ align:start position:0%
+about about previous thermal that's
+ 
+
+ align:start position:0%
+about about previous thermal that's
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so done
+
+ align:start position:0%
+so done
+ 
+
+ align:start position:0%
+so done
+with these properties I want to go back
+
+ align:start position:0%
+with these properties I want to go back
+ 
+
+ align:start position:0%
+with these properties I want to go back
+to the subject of available
+
+ align:start position:0%
+to the subject of available
+ 
+
+ align:start position:0%
+to the subject of available
+energy you remember what we've done
+
+ align:start position:0%
+energy you remember what we've done
+ 
+
+ align:start position:0%
+energy you remember what we've done
+um I forget now if it was the previous
+
+ align:start position:0%
+um I forget now if it was the previous
+ 
+
+ align:start position:0%
+um I forget now if it was the previous
+lecture or the one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um available
+
+ align:start position:0%
+um available
+ 
+
+ align:start position:0%
+um available
+energy this is the setup in which I have
+
+ align:start position:0%
+energy this is the setup in which I have
+ 
+
+ align:start position:0%
+energy this is the setup in which I have
+a system and a
+
+ align:start position:0%
+a system and a
+ 
+
+ align:start position:0%
+a system and a
+reservoir and they undergo a a weight
+
+ align:start position:0%
+reservoir and they undergo a a weight
+ 
+
+ align:start position:0%
+reservoir and they undergo a a weight
+process and we know that if the process
+
+ align:start position:0%
+process and we know that if the process
+ 
+
+ align:start position:0%
+process and we know that if the process
+the weight process is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reversible uh we can
+
+ align:start position:0%
+reversible uh we can
+ 
+
+ align:start position:0%
+reversible uh we can
+extract uh the maximum amount of energy
+
+ align:start position:0%
+extract uh the maximum amount of energy
+ 
+
+ align:start position:0%
+extract uh the maximum amount of energy
+when the system ends in a in a mutual
+
+ align:start position:0%
+when the system ends in a in a mutual
+ 
+
+ align:start position:0%
+when the system ends in a in a mutual
+equilibrium state with the environment
+
+ align:start position:0%
+equilibrium state with the environment
+ 
+
+ align:start position:0%
+equilibrium state with the environment
+with the rest
+
+ align:start position:0%
+with the rest
+ 
+
+ align:start position:0%
+with the rest
+work here is instead we are going to
+
+ align:start position:0%
+work here is instead we are going to
+ 
+
+ align:start position:0%
+work here is instead we are going to
+adopt two different states two arbitrary
+
+ align:start position:0%
+adopt two different states two arbitrary
+ 
+
+ align:start position:0%
+adopt two different states two arbitrary
+States so initial and
+
+ align:start position:0%
+States so initial and
+ 
+
+ align:start position:0%
+States so initial and
+final and you ask yourself well if my
+
+ align:start position:0%
+final and you ask yourself well if my
+ 
+
+ align:start position:0%
+final and you ask yourself well if my
+system has to go from A1 to
+
+ align:start position:0%
+system has to go from A1 to
+ 
+
+ align:start position:0%
+system has to go from A1 to
+A2 and it has available the interaction
+
+ align:start position:0%
+A2 and it has available the interaction
+ 
+
+ align:start position:0%
+A2 and it has available the interaction
+with the this thermal
+
+ align:start position:0%
+with the this thermal
+ 
+
+ align:start position:0%
+with the this thermal
+Reservoir what is the maximum weight
+
+ align:start position:0%
+Reservoir what is the maximum weight
+ 
+
+ align:start position:0%
+Reservoir what is the maximum weight
+lifted it can
+
+ align:start position:0%
+lifted it can
+ 
+
+ align:start position:0%
+lifted it can
+do or if it cannot lift the weight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is the minimum weight
+
+ align:start position:0%
+what is the minimum weight
+ 
+
+ align:start position:0%
+what is the minimum weight
+lowering that is required so as to
+
+ align:start position:0%
+lowering that is required so as to
+ 
+
+ align:start position:0%
+lowering that is required so as to
+achieve that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change and we have seen that um all any
+
+ align:start position:0%
+change and we have seen that um all any
+ 
+
+ align:start position:0%
+change and we have seen that um all any
+I mean this class of problems what's the
+
+ align:start position:0%
+I mean this class of problems what's the
+ 
+
+ align:start position:0%
+I mean this class of problems what's the
+maximum work what's the minimum
+
+ align:start position:0%
+maximum work what's the minimum
+ 
+
+ align:start position:0%
+maximum work what's the minimum
+work are always solved by writing an
+
+ align:start position:0%
+work are always solved by writing an
+ 
+
+ align:start position:0%
+work are always solved by writing an
+energy balance
+
+ align:start position:0%
+energy balance
+ 
+
+ align:start position:0%
+energy balance
+an entropy
+
+ align:start position:0%
+an entropy
+ 
+
+ align:start position:0%
+an entropy
+balance and also inserting as much as we
+
+ align:start position:0%
+balance and also inserting as much as we
+ 
+
+ align:start position:0%
+balance and also inserting as much as we
+know about the properties of the systems
+
+ align:start position:0%
+know about the properties of the systems
+ 
+
+ align:start position:0%
+know about the properties of the systems
+involved in this case we have a
+
+ align:start position:0%
+involved in this case we have a
+ 
+
+ align:start position:0%
+involved in this case we have a
+reservoir for which we know the
+
+ align:start position:0%
+reservoir for which we know the
+ 
+
+ align:start position:0%
+reservoir for which we know the
+fundamental relation is this linear
+
+ align:start position:0%
+fundamental relation is this linear
+ 
+
+ align:start position:0%
+fundamental relation is this linear
+relationship between energy and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entropy and by the
+
+ align:start position:0%
+entropy and by the
+ 
+
+ align:start position:0%
+entropy and by the
+way uh usually in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh often I mean in in uh especially in
+
+ align:start position:0%
+uh often I mean in in uh especially in
+ 
+
+ align:start position:0%
+uh often I mean in in uh especially in
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+physics language what we call thermal
+
+ align:start position:0%
+physics language what we call thermal
+ 
+
+ align:start position:0%
+physics language what we call thermal
+Reservoir it's called The Heat
+
+ align:start position:0%
+Reservoir it's called The Heat
+ 
+
+ align:start position:0%
+Reservoir it's called The Heat
+buff okay now you realize that uh we
+
+ align:start position:0%
+buff okay now you realize that uh we
+ 
+
+ align:start position:0%
+buff okay now you realize that uh we
+defined uh uh the heat interaction so
+
+ align:start position:0%
+defined uh uh the heat interaction so
+ 
+
+ align:start position:0%
+defined uh uh the heat interaction so
+that keep from a to
+
+ align:start position:0%
+that keep from a to
+ 
+
+ align:start position:0%
+that keep from a to
+me uh so that
+
+ align:start position:0%
+me uh so that
+ 
+
+ align:start position:0%
+me uh so that
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the okay so that if you are I want how
+
+ align:start position:0%
+the okay so that if you are I want how
+ 
+
+ align:start position:0%
+the okay so that if you are I want how
+much entropy is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transferred you get it because the ratio
+
+ align:start position:0%
+transferred you get it because the ratio
+ 
+
+ align:start position:0%
+transferred you get it because the ratio
+between energy and entropy uh
+
+ align:start position:0%
+between energy and entropy uh
+ 
+
+ align:start position:0%
+between energy and entropy uh
+transferred in a heat interaction is
+
+ align:start position:0%
+transferred in a heat interaction is
+ 
+
+ align:start position:0%
+transferred in a heat interaction is
+equal to the temperature at which that
+
+ align:start position:0%
+equal to the temperature at which that
+ 
+
+ align:start position:0%
+equal to the temperature at which that
+transfer
+
+ align:start position:0%
+transfer
+ 
+
+ align:start position:0%
+transfer
+occurs
+
+ align:start position:0%
+occurs
+ 
+
+ align:start position:0%
+occurs
+okay now the
+
+ align:start position:0%
+okay now the
+ 
+
+ align:start position:0%
+okay now the
+reservoir you can write the fundamental
+
+ align:start position:0%
+reservoir you can write the fundamental
+ 
+
+ align:start position:0%
+reservoir you can write the fundamental
+relation for the reservoir
+
+ align:start position:0%
+relation for the reservoir
+ 
+
+ align:start position:0%
+relation for the reservoir
+uh this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so you
+
+ align:start position:0%
+way so you
+ 
+
+ align:start position:0%
+way so you
+see the why they call it heat buff
+
+ align:start position:0%
+see the why they call it heat buff
+ 
+
+ align:start position:0%
+see the why they call it heat buff
+because the uh heat Reservoir is ready
+
+ align:start position:0%
+because the uh heat Reservoir is ready
+ 
+
+ align:start position:0%
+because the uh heat Reservoir is ready
+to provide a heat interaction if you
+
+ align:start position:0%
+to provide a heat interaction if you
+ 
+
+ align:start position:0%
+to provide a heat interaction if you
+extract energy at its
+
+ align:start position:0%
+extract energy at its
+ 
+
+ align:start position:0%
+extract energy at its
+temperature uh then it provides also the
+
+ align:start position:0%
+temperature uh then it provides also the
+ 
+
+ align:start position:0%
+temperature uh then it provides also the
+entropy and in in the right ratio so
+
+ align:start position:0%
+entropy and in in the right ratio so
+ 
+
+ align:start position:0%
+entropy and in in the right ratio so
+that you have a heat interaction at the
+
+ align:start position:0%
+that you have a heat interaction at the
+ 
+
+ align:start position:0%
+that you have a heat interaction at the
+temperature of the
+
+ align:start position:0%
+temperature of the
+ 
+
+ align:start position:0%
+temperature of the
+reservoir so it's a heat buff in the
+
+ align:start position:0%
+reservoir so it's a heat buff in the
+ 
+
+ align:start position:0%
+reservoir so it's a heat buff in the
+sense that it can provide uh heat I mean
+
+ align:start position:0%
+sense that it can provide uh heat I mean
+ 
+
+ align:start position:0%
+sense that it can provide uh heat I mean
+so that's at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+justifies that's the reading of the ter
+
+ align:start position:0%
+justifies that's the reading of the ter
+ 
+
+ align:start position:0%
+justifies that's the reading of the ter
+that's the my justification of that
+
+ align:start position:0%
+that's the my justification of that
+ 
+
+ align:start position:0%
+that's the my justification of that
+language it is not a reservoir of heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+though in a in the sense that
+
+ align:start position:0%
+though in a in the sense that
+ 
+
+ align:start position:0%
+though in a in the sense that
+heat is not a a form of energy it is a
+
+ align:start position:0%
+heat is not a a form of energy it is a
+ 
+
+ align:start position:0%
+heat is not a a form of energy it is a
+form of energy
+
+ align:start position:0%
+form of energy
+ 
+
+ align:start position:0%
+form of energy
+transfer you cannot store heat you store
+
+ align:start position:0%
+transfer you cannot store heat you store
+ 
+
+ align:start position:0%
+transfer you cannot store heat you store
+energy okay you transfer energy in the
+
+ align:start position:0%
+energy okay you transfer energy in the
+ 
+
+ align:start position:0%
+energy okay you transfer energy in the
+form of heat when you have an
+
+ align:start position:0%
+form of heat when you have an
+ 
+
+ align:start position:0%
+form of heat when you have an
+interaction of that
+
+ align:start position:0%
+interaction of that
+ 
+
+ align:start position:0%
+interaction of that
+form so the language is is important and
+
+ align:start position:0%
+form so the language is is important and
+ 
+
+ align:start position:0%
+form so the language is is important and
+lose language is okay if you understand
+
+ align:start position:0%
+lose language is okay if you understand
+ 
+
+ align:start position:0%
+lose language is okay if you understand
+what you're doing if it is too loose and
+
+ align:start position:0%
+what you're doing if it is too loose and
+ 
+
+ align:start position:0%
+what you're doing if it is too loose and
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+assign to this language uh two popular
+
+ align:start position:0%
+assign to this language uh two popular
+ 
+
+ align:start position:0%
+assign to this language uh two popular
+meaning then you get a lot of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+confusion this is
+
+ align:start position:0%
+confusion this is
+ 
+
+ align:start position:0%
+confusion this is
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+I one of our objectives here is to try
+
+ align:start position:0%
+I one of our objectives here is to try
+ 
+
+ align:start position:0%
+I one of our objectives here is to try
+to be as careful as possible with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+language and by the way uh my
+
+ align:start position:0%
+language and by the way uh my
+ 
+
+ align:start position:0%
+language and by the way uh my
+um sincere congratulations for how good
+
+ align:start position:0%
+um sincere congratulations for how good
+ 
+
+ align:start position:0%
+um sincere congratulations for how good
+you're doing in your uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+homeworks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the the
+
+ align:start position:0%
+so the the
+ 
+
+ align:start position:0%
+so the the
+work that you by solving this system of
+
+ align:start position:0%
+work that you by solving this system of
+ 
+
+ align:start position:0%
+work that you by solving this system of
+equations we already said that we we
+
+ align:start position:0%
+equations we already said that we we
+ 
+
+ align:start position:0%
+equations we already said that we we
+find an expression for the
+
+ align:start position:0%
+find an expression for the
+ 
+
+ align:start position:0%
+find an expression for the
+work which is uh H which is a term
+
+ align:start position:0%
+work which is uh H which is a term
+ 
+
+ align:start position:0%
+work which is uh H which is a term
+related to irreversibility entropy
+
+ align:start position:0%
+related to irreversibility entropy
+ 
+
+ align:start position:0%
+related to irreversibility entropy
+produced by irreversibility which is not
+
+ align:start position:0%
+produced by irreversibility which is not
+ 
+
+ align:start position:0%
+produced by irreversibility which is not
+there if the process is reversible and
+
+ align:start position:0%
+there if the process is reversible and
+ 
+
+ align:start position:0%
+there if the process is reversible and
+that's typically the best you can do
+
+ align:start position:0%
+that's typically the best you can do
+ 
+
+ align:start position:0%
+that's typically the best you can do
+whether you have to spend energy or
+
+ align:start position:0%
+whether you have to spend energy or
+ 
+
+ align:start position:0%
+whether you have to spend energy or
+produce uh um mechanical energy
+
+ align:start position:0%
+produce uh um mechanical energy
+ 
+
+ align:start position:0%
+produce uh um mechanical energy
+uh you get the best always when you do
+
+ align:start position:0%
+uh you get the best always when you do
+ 
+
+ align:start position:0%
+uh you get the best always when you do
+it uh reversibly so if you have to
+
+ align:start position:0%
+it uh reversibly so if you have to
+ 
+
+ align:start position:0%
+it uh reversibly so if you have to
+extract energy if you can extract energy
+
+ align:start position:0%
+extract energy if you can extract energy
+ 
+
+ align:start position:0%
+extract energy if you can extract energy
+you extract the max you should do the
+
+ align:start position:0%
+you extract the max you should do the
+ 
+
+ align:start position:0%
+you extract the max you should do the
+reversable process if you have to spend
+
+ align:start position:0%
+reversable process if you have to spend
+ 
+
+ align:start position:0%
+reversable process if you have to spend
+energy in order to obtain uh a change of
+
+ align:start position:0%
+energy in order to obtain uh a change of
+ 
+
+ align:start position:0%
+energy in order to obtain uh a change of
+state for example heating up uh some
+
+ align:start position:0%
+state for example heating up uh some
+ 
+
+ align:start position:0%
+state for example heating up uh some
+water it's a a task that requires uh
+
+ align:start position:0%
+water it's a a task that requires uh
+ 
+
+ align:start position:0%
+water it's a a task that requires uh
+spending energy you can ask yourself
+
+ align:start position:0%
+spending energy you can ask yourself
+ 
+
+ align:start position:0%
+spending energy you can ask yourself
+what is the minimum uh uh work that you
+
+ align:start position:0%
+what is the minimum uh uh work that you
+ 
+
+ align:start position:0%
+what is the minimum uh uh work that you
+need to spend in order to heat up that
+
+ align:start position:0%
+need to spend in order to heat up that
+ 
+
+ align:start position:0%
+need to spend in order to heat up that
+uh that water
+
+ align:start position:0%
+uh that water
+ 
+
+ align:start position:0%
+uh that water
+and if you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh maybe when we do uh next time
+
+ align:start position:0%
+that uh maybe when we do uh next time
+ 
+
+ align:start position:0%
+that uh maybe when we do uh next time
+the review on aies uh we
+
+ align:start position:0%
+the review on aies uh we
+ 
+
+ align:start position:0%
+the review on aies uh we
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we will'll see our efficient certain
+
+ align:start position:0%
+we will'll see our efficient certain
+ 
+
+ align:start position:0%
+we will'll see our efficient certain
+ways we have to heat up
+
+ align:start position:0%
+ways we have to heat up
+ 
+
+ align:start position:0%
+ways we have to heat up
+water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+okay now the maximum the reversible work
+
+ align:start position:0%
+okay now the maximum the reversible work
+ 
+
+ align:start position:0%
+okay now the maximum the reversible work
+is the difference between the available
+
+ align:start position:0%
+is the difference between the available
+ 
+
+ align:start position:0%
+is the difference between the available
+energies of the two uh states of your
+
+ align:start position:0%
+energies of the two uh states of your
+ 
+
+ align:start position:0%
+energies of the two uh states of your
+system it's also the
+
+ align:start position:0%
+system it's also the
+ 
+
+ align:start position:0%
+system it's also the
+difference in this availability function
+
+ align:start position:0%
+difference in this availability function
+ 
+
+ align:start position:0%
+difference in this availability function
+gamma that is energy minus entropy
+
+ align:start position:0%
+gamma that is energy minus entropy
+ 
+
+ align:start position:0%
+gamma that is energy minus entropy
+multiplied by the temperature of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resare well called the availab canonical
+
+ align:start position:0%
+resare well called the availab canonical
+ 
+
+ align:start position:0%
+resare well called the availab canonical
+AV availability function and that we
+
+ align:start position:0%
+AV availability function and that we
+ 
+
+ align:start position:0%
+AV availability function and that we
+have seen that uh if you try to um
+
+ align:start position:0%
+have seen that uh if you try to um
+ 
+
+ align:start position:0%
+have seen that uh if you try to um
+represented
+
+ align:start position:0%
+represented
+ 
+
+ align:start position:0%
+represented
+graphically it acquires an absolute
+
+ align:start position:0%
+graphically it acquires an absolute
+ 
+
+ align:start position:0%
+graphically it acquires an absolute
+minimum uh at the state in which a
+
+ align:start position:0%
+minimum uh at the state in which a
+ 
+
+ align:start position:0%
+minimum uh at the state in which a
+system is in mutual equilibrium with the
+
+ align:start position:0%
+system is in mutual equilibrium with the
+ 
+
+ align:start position:0%
+system is in mutual equilibrium with the
+reservoir so uh we by by exploiting this
+
+ align:start position:0%
+reservoir so uh we by by exploiting this
+ 
+
+ align:start position:0%
+reservoir so uh we by by exploiting this
+this idea that this is a
+
+ align:start position:0%
+this idea that this is a
+ 
+
+ align:start position:0%
+this idea that this is a
+minimum uh
+
+ align:start position:0%
+minimum uh
+ 
+
+ align:start position:0%
+minimum uh
+we we extract information about for
+
+ align:start position:0%
+we we extract information about for
+ 
+
+ align:start position:0%
+we we extract information about for
+example the
+
+ align:start position:0%
+example the
+ 
+
+ align:start position:0%
+example the
+uh concavity of the
+
+ align:start position:0%
+uh concavity of the
+ 
+
+ align:start position:0%
+uh concavity of the
+fundamental relation
+
+ align:start position:0%
+fundamental relation
+ 
+
+ align:start position:0%
+fundamental relation
+By
+
+ align:start position:0%
+By
+ 
+
+ align:start position:0%
+By
+devising changes so you start from this
+
+ align:start position:0%
+devising changes so you start from this
+ 
+
+ align:start position:0%
+devising changes so you start from this
+uh Mutual equilibrium State and you move
+
+ align:start position:0%
+uh Mutual equilibrium State and you move
+ 
+
+ align:start position:0%
+uh Mutual equilibrium State and you move
+anywhere else in uh an available one of
+
+ align:start position:0%
+anywhere else in uh an available one of
+ 
+
+ align:start position:0%
+anywhere else in uh an available one of
+the possible states of your system a
+
+ align:start position:0%
+the possible states of your system a
+ 
+
+ align:start position:0%
+the possible states of your system a
+wherever you
+
+ align:start position:0%
+wherever you
+ 
+
+ align:start position:0%
+wherever you
+move gamma must
+
+ align:start position:0%
+move gamma must
+ 
+
+ align:start position:0%
+move gamma must
+increase and so for example we chose uh
+
+ align:start position:0%
+increase and so for example we chose uh
+ 
+
+ align:start position:0%
+increase and so for example we chose uh
+particular changes and we prove that uh
+
+ align:start position:0%
+particular changes and we prove that uh
+ 
+
+ align:start position:0%
+particular changes and we prove that uh
+with those particular changes just you
+
+ align:start position:0%
+with those particular changes just you
+ 
+
+ align:start position:0%
+with those particular changes just you
+can find that
+
+ align:start position:0%
+can find that
+ 
+
+ align:start position:0%
+can find that
+uh the second differential of the
+
+ align:start position:0%
+uh the second differential of the
+ 
+
+ align:start position:0%
+uh the second differential of the
+energy with respect to V and so fixed
+
+ align:start position:0%
+energy with respect to V and so fixed
+ 
+
+ align:start position:0%
+energy with respect to V and so fixed
+sorry fixed then and V the second
+
+ align:start position:0%
+sorry fixed then and V the second
+ 
+
+ align:start position:0%
+sorry fixed then and V the second
+differential so the concavity here is
+
+ align:start position:0%
+differential so the concavity here is
+ 
+
+ align:start position:0%
+differential so the concavity here is
+positive you can do it also from the
+
+ align:start position:0%
+positive you can do it also from the
+ 
+
+ align:start position:0%
+positive you can do it also from the
+other point of view so we say you find
+
+ align:start position:0%
+other point of view so we say you find
+ 
+
+ align:start position:0%
+other point of view so we say you find
+that the second differential of s with
+
+ align:start position:0%
+that the second differential of s with
+ 
+
+ align:start position:0%
+that the second differential of s with
+respect to uh at fixed vnn is negative
+
+ align:start position:0%
+respect to uh at fixed vnn is negative
+ 
+
+ align:start position:0%
+respect to uh at fixed vnn is negative
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now yeah we also apply that to prove uh
+
+ align:start position:0%
+now yeah we also apply that to prove uh
+ 
+
+ align:start position:0%
+now yeah we also apply that to prove uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but for example that the specific I mean
+
+ align:start position:0%
+but for example that the specific I mean
+ 
+
+ align:start position:0%
+but for example that the specific I mean
+the heat capacities are uh non-
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative and we
+
+ align:start position:0%
+negative and we
+ 
+
+ align:start position:0%
+negative and we
+proved the first part this is just the
+
+ align:start position:0%
+proved the first part this is just the
+ 
+
+ align:start position:0%
+proved the first part this is just the
+first part of the of the theorem by CH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Brown today we'll uh we'll do also a
+
+ align:start position:0%
+Brown today we'll uh we'll do also a
+ 
+
+ align:start position:0%
+Brown today we'll uh we'll do also a
+second part which is
+
+ align:start position:0%
+second part which is
+ 
+
+ align:start position:0%
+second part which is
+um even more
+
+ align:start position:0%
+um even more
+ 
+
+ align:start position:0%
+um even more
+interesting so the first part was any
+
+ align:start position:0%
+interesting so the first part was any
+ 
+
+ align:start position:0%
+interesting so the first part was any
+way that um if you if you perturb your
+
+ align:start position:0%
+way that um if you if you perturb your
+ 
+
+ align:start position:0%
+way that um if you if you perturb your
+the state of your system which is
+
+ align:start position:0%
+the state of your system which is
+ 
+
+ align:start position:0%
+the state of your system which is
+initially in mutual equilibrium with the
+
+ align:start position:0%
+initially in mutual equilibrium with the
+ 
+
+ align:start position:0%
+initially in mutual equilibrium with the
+res you put it off the mutual
+
+ align:start position:0%
+res you put it off the mutual
+ 
+
+ align:start position:0%
+res you put it off the mutual
+equilibrium by for example giving energy
+
+ align:start position:0%
+equilibrium by for example giving energy
+ 
+
+ align:start position:0%
+equilibrium by for example giving energy
+the system will
+
+ align:start position:0%
+the system will
+ 
+
+ align:start position:0%
+the system will
+react uh by increasing its temperature
+
+ align:start position:0%
+react uh by increasing its temperature
+ 
+
+ align:start position:0%
+react uh by increasing its temperature
+and the temperature as we know is the
+
+ align:start position:0%
+and the temperature as we know is the
+ 
+
+ align:start position:0%
+and the temperature as we know is the
+escaping tendency for energy so it
+
+ align:start position:0%
+escaping tendency for energy so it
+ 
+
+ align:start position:0%
+escaping tendency for energy so it
+increases its willingness to give away
+
+ align:start position:0%
+increases its willingness to give away
+ 
+
+ align:start position:0%
+increases its willingness to give away
+energy and since the reservoir is there
+
+ align:start position:0%
+energy and since the reservoir is there
+ 
+
+ align:start position:0%
+energy and since the reservoir is there
+uh it is It prepares uh the increasing
+
+ align:start position:0%
+uh it is It prepares uh the increasing
+ 
+
+ align:start position:0%
+uh it is It prepares uh the increasing
+in temperature
+
+ align:start position:0%
+in temperature
+ 
+
+ align:start position:0%
+in temperature
+prepares uh the for the for a heat
+
+ align:start position:0%
+prepares uh the for the for a heat
+ 
+
+ align:start position:0%
+prepares uh the for the for a heat
+interaction in which the system gives
+
+ align:start position:0%
+interaction in which the system gives
+ 
+
+ align:start position:0%
+interaction in which the system gives
+energy to the
+
+ align:start position:0%
+energy to the
+ 
+
+ align:start position:0%
+energy to the
+thereby
+
+ align:start position:0%
+thereby
+ 
+
+ align:start position:0%
+thereby
+contrasting the change with which you
+
+ align:start position:0%
+contrasting the change with which you
+ 
+
+ align:start position:0%
+contrasting the change with which you
+took it away from equilibrium it tries
+
+ align:start position:0%
+took it away from equilibrium it tries
+ 
+
+ align:start position:0%
+took it away from equilibrium it tries
+to spontaneously return to equilibrium
+
+ align:start position:0%
+to spontaneously return to equilibrium
+ 
+
+ align:start position:0%
+to spontaneously return to equilibrium
+by increasing its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature so that's one thing all
+
+ align:start position:0%
+temperature so that's one thing all
+ 
+
+ align:start position:0%
+temperature so that's one thing all
+right so to to see a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more uh let's broaden our
+
+ align:start position:0%
+more uh let's broaden our
+ 
+
+ align:start position:0%
+more uh let's broaden our
+class or category of systems that we
+
+ align:start position:0%
+class or category of systems that we
+ 
+
+ align:start position:0%
+class or category of systems that we
+call thermal reservoirs or say heat
+
+ align:start position:0%
+call thermal reservoirs or say heat
+ 
+
+ align:start position:0%
+call thermal reservoirs or say heat
+Buffs because in practice we often have
+
+ align:start position:0%
+Buffs because in practice we often have
+ 
+
+ align:start position:0%
+Buffs because in practice we often have
+also uh
+
+ align:start position:0%
+also uh
+ 
+
+ align:start position:0%
+also uh
+reservoirs that are variable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume
+
+ align:start position:0%
+volume
+ 
+
+ align:start position:0%
+volume
+often the atmosphere where we live the
+
+ align:start position:0%
+often the atmosphere where we live the
+ 
+
+ align:start position:0%
+often the atmosphere where we live the
+Environ is the environment and it's
+
+ align:start position:0%
+Environ is the environment and it's
+ 
+
+ align:start position:0%
+Environ is the environment and it's
+something that would accept a change in
+
+ align:start position:0%
+something that would accept a change in
+ 
+
+ align:start position:0%
+something that would accept a change in
+volume uh
+
+ align:start position:0%
+volume uh
+ 
+
+ align:start position:0%
+volume uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+without if you if if if the changeing
+
+ align:start position:0%
+without if you if if if the changeing
+ 
+
+ align:start position:0%
+without if you if if if the changeing
+volume is reasonably small and also the
+
+ align:start position:0%
+volume is reasonably small and also the
+ 
+
+ align:start position:0%
+volume is reasonably small and also the
+changes in
+
+ align:start position:0%
+changes in
+ 
+
+ align:start position:0%
+changes in
+energy are reasonably small uh you can
+
+ align:start position:0%
+energy are reasonably small uh you can
+ 
+
+ align:start position:0%
+energy are reasonably small uh you can
+add or subtract the volume and energy to
+
+ align:start position:0%
+add or subtract the volume and energy to
+ 
+
+ align:start position:0%
+add or subtract the volume and energy to
+the environment without changing its
+
+ align:start position:0%
+the environment without changing its
+ 
+
+ align:start position:0%
+the environment without changing its
+temperature and
+
+ align:start position:0%
+temperature and
+ 
+
+ align:start position:0%
+temperature and
+pressure so if the system is large
+
+ align:start position:0%
+pressure so if the system is large
+ 
+
+ align:start position:0%
+pressure so if the system is large
+enough like the air uh in the
+
+ align:start position:0%
+enough like the air uh in the
+ 
+
+ align:start position:0%
+enough like the air uh in the
+environment of of a town or the the the
+
+ align:start position:0%
+environment of of a town or the the the
+ 
+
+ align:start position:0%
+environment of of a town or the the the
+water in the sea or in the lake or in a
+
+ align:start position:0%
+water in the sea or in the lake or in a
+ 
+
+ align:start position:0%
+water in the sea or in the lake or in a
+river with respect to if it is if it is
+
+ align:start position:0%
+river with respect to if it is if it is
+ 
+
+ align:start position:0%
+river with respect to if it is if it is
+large enough with respect to the amounts
+
+ align:start position:0%
+large enough with respect to the amounts
+ 
+
+ align:start position:0%
+large enough with respect to the amounts
+of energies entropies and volume that
+
+ align:start position:0%
+of energies entropies and volume that
+ 
+
+ align:start position:0%
+of energies entropies and volume that
+you exchange then you may consider that
+
+ align:start position:0%
+you exchange then you may consider that
+ 
+
+ align:start position:0%
+you exchange then you may consider that
+as a as a thermal r word so A system
+
+ align:start position:0%
+as a as a thermal r word so A system
+ 
+
+ align:start position:0%
+as a as a thermal r word so A system
+that maintains
+
+ align:start position:0%
+that maintains
+ 
+
+ align:start position:0%
+that maintains
+fixed uh values of the temperature and
+
+ align:start position:0%
+fixed uh values of the temperature and
+ 
+
+ align:start position:0%
+fixed uh values of the temperature and
+the pressure in this case we
+
+ align:start position:0%
+the pressure in this case we
+ 
+
+ align:start position:0%
+the pressure in this case we
+consider system which has variable
+
+ align:start position:0%
+consider system which has variable
+ 
+
+ align:start position:0%
+consider system which has variable
+volume but still the amounts are
+
+ align:start position:0%
+volume but still the amounts are
+ 
+
+ align:start position:0%
+volume but still the amounts are
+fixed okay then the fundamental relation
+
+ align:start position:0%
+fixed okay then the fundamental relation
+ 
+
+ align:start position:0%
+fixed okay then the fundamental relation
+for a system is also um
+
+ align:start position:0%
+for a system is also um
+ 
+
+ align:start position:0%
+for a system is also um
+linear except that
+
+ align:start position:0%
+linear except that
+ 
+
+ align:start position:0%
+linear except that
+now okay before we had the uh energy
+
+ align:start position:0%
+now okay before we had the uh energy
+ 
+
+ align:start position:0%
+now okay before we had the uh energy
+entropy and this is the temperature
+
+ align:start position:0%
+entropy and this is the temperature
+ 
+
+ align:start position:0%
+entropy and this is the temperature
+TR now if we add volume as a possibility
+
+ align:start position:0%
+TR now if we add volume as a possibility
+ 
+
+ align:start position:0%
+TR now if we add volume as a possibility
+to change then okay let's see make to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then okay then we have an equation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh of the plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of which the slopes are
+
+ align:start position:0%
+of which the slopes are
+ 
+
+ align:start position:0%
+of which the slopes are
+TR when you take the slope at constant V
+
+ align:start position:0%
+TR when you take the slope at constant V
+ 
+
+ align:start position:0%
+TR when you take the slope at constant V
+and minus P when you take the slope at
+
+ align:start position:0%
+and minus P when you take the slope at
+ 
+
+ align:start position:0%
+and minus P when you take the slope at
+constant uh
+
+ align:start position:0%
+constant uh
+ 
+
+ align:start position:0%
+constant uh
+s so this is equation of a of a plane
+
+ align:start position:0%
+s so this is equation of a of a plane
+ 
+
+ align:start position:0%
+s so this is equation of a of a plane
+and that's the fundamental relation for
+
+ align:start position:0%
+and that's the fundamental relation for
+ 
+
+ align:start position:0%
+and that's the fundamental relation for
+that thermal Reservoir at variable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume so we ask the same question now
+
+ align:start position:0%
+volume so we ask the same question now
+ 
+
+ align:start position:0%
+volume so we ask the same question now
+okay what
+
+ align:start position:0%
+okay what
+ 
+
+ align:start position:0%
+okay what
+if I'm changing state for my
+
+ align:start position:0%
+if I'm changing state for my
+ 
+
+ align:start position:0%
+if I'm changing state for my
+system but it exchanges volume what it
+
+ align:start position:0%
+system but it exchanges volume what it
+ 
+
+ align:start position:0%
+system but it exchanges volume what it
+exchanges volume with the
+
+ align:start position:0%
+exchanges volume with the
+ 
+
+ align:start position:0%
+exchanges volume with the
+reservoir so maybe the system changes s
+
+ align:start position:0%
+reservoir so maybe the system changes s
+ 
+
+ align:start position:0%
+reservoir so maybe the system changes s
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+volume and where does it take that
+
+ align:start position:0%
+volume and where does it take that
+ 
+
+ align:start position:0%
+volume and where does it take that
+volume from the
+
+ align:start position:0%
+volume from the
+ 
+
+ align:start position:0%
+volume from the
+reservoir or where does it give it to
+
+ align:start position:0%
+reservoir or where does it give it to
+ 
+
+ align:start position:0%
+reservoir or where does it give it to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+reservoir you want to ask the maximum
+
+ align:start position:0%
+reservoir you want to ask the maximum
+ 
+
+ align:start position:0%
+reservoir you want to ask the maximum
+work or the minimum work requirement for
+
+ align:start position:0%
+work or the minimum work requirement for
+ 
+
+ align:start position:0%
+work or the minimum work requirement for
+doing that change well energy balance
+
+ align:start position:0%
+doing that change well energy balance
+ 
+
+ align:start position:0%
+doing that change well energy balance
+entropy balance fundamental relation for
+
+ align:start position:0%
+entropy balance fundamental relation for
+ 
+
+ align:start position:0%
+entropy balance fundamental relation for
+the reservoir and here you also have to
+
+ align:start position:0%
+the reservoir and here you also have to
+ 
+
+ align:start position:0%
+the reservoir and here you also have to
+do a volume balance because you have an
+
+ align:start position:0%
+do a volume balance because you have an
+ 
+
+ align:start position:0%
+do a volume balance because you have an
+additional variable that has to be kept
+
+ align:start position:0%
+additional variable that has to be kept
+ 
+
+ align:start position:0%
+additional variable that has to be kept
+uh fixed for the composite
+
+ align:start position:0%
+uh fixed for the composite
+ 
+
+ align:start position:0%
+uh fixed for the composite
+system the overall volume is
+
+ align:start position:0%
+system the overall volume is
+ 
+
+ align:start position:0%
+system the overall volume is
+concerned in order to have no other
+
+ align:start position:0%
+concerned in order to have no other
+ 
+
+ align:start position:0%
+concerned in order to have no other
+effect external
+
+ align:start position:0%
+effect external
+ 
+
+ align:start position:0%
+effect external
+effects like in a weight
+
+ align:start position:0%
+effects like in a weight
+ 
+
+ align:start position:0%
+effects like in a weight
+process okay
+
+ align:start position:0%
+process okay
+ 
+
+ align:start position:0%
+process okay
+so when you do the Sol when you solve
+
+ align:start position:0%
+so when you do the Sol when you solve
+ 
+
+ align:start position:0%
+so when you do the Sol when you solve
+this problem
+
+ align:start position:0%
+this problem
+ 
+
+ align:start position:0%
+this problem
+by eliminating the variables that um
+
+ align:start position:0%
+by eliminating the variables that um
+ 
+
+ align:start position:0%
+by eliminating the variables that um
+relate to the
+
+ align:start position:0%
+relate to the
+ 
+
+ align:start position:0%
+relate to the
+resir here's the
+
+ align:start position:0%
+resir here's the
+ 
+
+ align:start position:0%
+resir here's the
+result it's almost like before except
+
+ align:start position:0%
+result it's almost like before except
+ 
+
+ align:start position:0%
+result it's almost like before except
+that there is now an extra term here
+
+ align:start position:0%
+that there is now an extra term here
+ 
+
+ align:start position:0%
+that there is now an extra term here
+which is PR times the difference in
+
+ align:start position:0%
+which is PR times the difference in
+ 
+
+ align:start position:0%
+which is PR times the difference in
+volume of your system and again it's a
+
+ align:start position:0%
+volume of your system and again it's a
+ 
+
+ align:start position:0%
+volume of your system and again it's a
+reversible term minus
+
+ align:start position:0%
+reversible term minus
+ 
+
+ align:start position:0%
+reversible term minus
+a term related to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+irreversibility the reversible term can
+
+ align:start position:0%
+irreversibility the reversible term can
+ 
+
+ align:start position:0%
+irreversibility the reversible term can
+be seen as the difference in two
+
+ align:start position:0%
+be seen as the difference in two
+ 
+
+ align:start position:0%
+be seen as the difference in two
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+properties you could consider this as a
+
+ align:start position:0%
+properties you could consider this as a
+ 
+
+ align:start position:0%
+properties you could consider this as a
+definition of another property that we
+
+ align:start position:0%
+definition of another property that we
+ 
+
+ align:start position:0%
+definition of another property that we
+still call for short of names um
+
+ align:start position:0%
+still call for short of names um
+ 
+
+ align:start position:0%
+still call for short of names um
+available energy with respect to that
+
+ align:start position:0%
+available energy with respect to that
+ 
+
+ align:start position:0%
+available energy with respect to that
+particular Reservoir in that variable
+
+ align:start position:0%
+particular Reservoir in that variable
+ 
+
+ align:start position:0%
+particular Reservoir in that variable
+volume it's it's like the one
+
+ align:start position:0%
+volume it's it's like the one
+ 
+
+ align:start position:0%
+volume it's it's like the one
+before plus this additional P * Delta
+
+ align:start position:0%
+before plus this additional P * Delta
+ 
+
+ align:start position:0%
+before plus this additional P * Delta
+V and also this one if you as you notice
+
+ align:start position:0%
+V and also this one if you as you notice
+ 
+
+ align:start position:0%
+V and also this one if you as you notice
+may be written as a
+
+ align:start position:0%
+may be written as a
+ 
+
+ align:start position:0%
+may be written as a
+difference in an availability function e
+
+ align:start position:0%
+difference in an availability function e
+ 
+
+ align:start position:0%
+difference in an availability function e
+minus TRS plus P
+
+ align:start position:0%
+minus TRS plus P
+ 
+
+ align:start position:0%
+minus TRS plus P
+RV which we're going to call uh just
+
+ align:start position:0%
+RV which we're going to call uh just
+ 
+
+ align:start position:0%
+RV which we're going to call uh just
+with the name capital c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we may notice
+
+ align:start position:0%
+and we may notice
+ 
+
+ align:start position:0%
+and we may notice
+that this is
+
+ align:start position:0%
+that this is
+ 
+
+ align:start position:0%
+that this is
+not it looks like but it's not the GS
+
+ align:start position:0%
+not it looks like but it's not the GS
+ 
+
+ align:start position:0%
+not it looks like but it's not the GS
+free
+
+ align:start position:0%
+free
+ 
+
+ align:start position:0%
+free
+energy except when the system is in
+
+ align:start position:0%
+energy except when the system is in
+ 
+
+ align:start position:0%
+energy except when the system is in
+mutual equilibrium in the state of
+
+ align:start position:0%
+mutual equilibrium in the state of
+ 
+
+ align:start position:0%
+mutual equilibrium in the state of
+mutual equilibrium with the
+
+ align:start position:0%
+mutual equilibrium with the
+ 
+
+ align:start position:0%
+mutual equilibrium with the
+environment in that case TR is also the
+
+ align:start position:0%
+environment in that case TR is also the
+ 
+
+ align:start position:0%
+environment in that case TR is also the
+temperature of your system a and
+
+ align:start position:0%
+temperature of your system a and
+ 
+
+ align:start position:0%
+temperature of your system a and
+therefore this is the Gibs free energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whereas uh in any other
+
+ align:start position:0%
+whereas uh in any other
+ 
+
+ align:start position:0%
+whereas uh in any other
+state this TR this PR may not
+
+ align:start position:0%
+state this TR this PR may not
+ 
+
+ align:start position:0%
+state this TR this PR may not
+be the uh temperature of your system
+
+ align:start position:0%
+be the uh temperature of your system
+ 
+
+ align:start position:0%
+be the uh temperature of your system
+a and actually if the state is not an
+
+ align:start position:0%
+a and actually if the state is not an
+ 
+
+ align:start position:0%
+a and actually if the state is not an
+equilibrium State the temp the system a
+
+ align:start position:0%
+equilibrium State the temp the system a
+ 
+
+ align:start position:0%
+equilibrium State the temp the system a
+might not even have a temperature
+
+ align:start position:0%
+might not even have a temperature
+ 
+
+ align:start position:0%
+might not even have a temperature
+defined actually it does not if it is
+
+ align:start position:0%
+defined actually it does not if it is
+ 
+
+ align:start position:0%
+defined actually it does not if it is
+not stable equilibrium yet this
+
+ align:start position:0%
+not stable equilibrium yet this
+ 
+
+ align:start position:0%
+not stable equilibrium yet this
+availability function is
+
+ align:start position:0%
+availability function is
+ 
+
+ align:start position:0%
+availability function is
+defined and it gives
+
+ align:start position:0%
+defined and it gives
+ 
+
+ align:start position:0%
+defined and it gives
+you these answers to questions of
+
+ align:start position:0%
+you these answers to questions of
+ 
+
+ align:start position:0%
+you these answers to questions of
+minimum or maximum uh work to do or to
+
+ align:start position:0%
+minimum or maximum uh work to do or to
+ 
+
+ align:start position:0%
+minimum or maximum uh work to do or to
+uh to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+obtain yes exactly with the same
+
+ align:start position:0%
+obtain yes exactly with the same
+ 
+
+ align:start position:0%
+obtain yes exactly with the same
+procedure that we have done to
+
+ align:start position:0%
+procedure that we have done to
+ 
+
+ align:start position:0%
+procedure that we have done to
+obtain
+
+ align:start position:0%
+obtain
+ 
+
+ align:start position:0%
+obtain
+these conditions for the
+
+ align:start position:0%
+these conditions for the
+ 
+
+ align:start position:0%
+these conditions for the
+stability you can do it also here now I
+
+ align:start position:0%
+stability you can do it also here now I
+ 
+
+ align:start position:0%
+stability you can do it also here now I
+since I have several variables it's not
+
+ align:start position:0%
+since I have several variables it's not
+ 
+
+ align:start position:0%
+since I have several variables it's not
+uh I'm sorry let me go back one moment
+
+ align:start position:0%
+uh I'm sorry let me go back one moment
+ 
+
+ align:start position:0%
+uh I'm sorry let me go back one moment
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so you you should think of a
+
+ align:start position:0%
+okay so you you should think of a
+ 
+
+ align:start position:0%
+okay so you you should think of a
+similar procedure only in a
+
+ align:start position:0%
+similar procedure only in a
+ 
+
+ align:start position:0%
+similar procedure only in a
+three-dimensional setup in which you
+
+ align:start position:0%
+three-dimensional setup in which you
+ 
+
+ align:start position:0%
+three-dimensional setup in which you
+start from a mutual equilibrium state
+
+ align:start position:0%
+start from a mutual equilibrium state
+ 
+
+ align:start position:0%
+start from a mutual equilibrium state
+and you
+
+ align:start position:0%
+and you
+ 
+
+ align:start position:0%
+and you
+move away from it and then you apply the
+
+ align:start position:0%
+move away from it and then you apply the
+ 
+
+ align:start position:0%
+move away from it and then you apply the
+condition that gamma must
+
+ align:start position:0%
+condition that gamma must
+ 
+
+ align:start position:0%
+condition that gamma must
+increase if you move away now whereas
+
+ align:start position:0%
+increase if you move away now whereas
+ 
+
+ align:start position:0%
+increase if you move away now whereas
+here you could move
+
+ align:start position:0%
+here you could move
+ 
+
+ align:start position:0%
+here you could move
+away only on the e s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane in the new uh setup where also the
+
+ align:start position:0%
+plane in the new uh setup where also the
+ 
+
+ align:start position:0%
+plane in the new uh setup where also the
+Val volume is CH is uh is is is can be
+
+ align:start position:0%
+Val volume is CH is uh is is is can be
+ 
+
+ align:start position:0%
+Val volume is CH is uh is is is can be
+changed yes you can move
+
+ align:start position:0%
+changed yes you can move
+ 
+
+ align:start position:0%
+changed yes you can move
+at constant uh V or constant e or but
+
+ align:start position:0%
+at constant uh V or constant e or but
+ 
+
+ align:start position:0%
+at constant uh V or constant e or but
+you can also move in any other direction
+
+ align:start position:0%
+you can also move in any other direction
+ 
+
+ align:start position:0%
+you can also move in any other direction
+so you have more
+
+ align:start position:0%
+so you have more
+ 
+
+ align:start position:0%
+so you have more
+choices and whatever choice you make you
+
+ align:start position:0%
+choices and whatever choice you make you
+ 
+
+ align:start position:0%
+choices and whatever choice you make you
+still have to have this property to
+
+ align:start position:0%
+still have to have this property to
+ 
+
+ align:start position:0%
+still have to have this property to
+uh uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+increase so here I let you if you're
+
+ align:start position:0%
+increase so here I let you if you're
+ 
+
+ align:start position:0%
+increase so here I let you if you're
+interested watch the
+
+ align:start position:0%
+interested watch the
+ 
+
+ align:start position:0%
+interested watch the
+details I choose a a uh for example to
+
+ align:start position:0%
+details I choose a a uh for example to
+ 
+
+ align:start position:0%
+details I choose a a uh for example to
+move by changing the entropy and the
+
+ align:start position:0%
+move by changing the entropy and the
+ 
+
+ align:start position:0%
+move by changing the entropy and the
+volume keeping keeping the N fixed and
+
+ align:start position:0%
+volume keeping keeping the N fixed and
+ 
+
+ align:start position:0%
+volume keeping keeping the N fixed and
+it turns out that when you compute the
+
+ align:start position:0%
+it turns out that when you compute the
+ 
+
+ align:start position:0%
+it turns out that when you compute the
+change in the variable Fe it is exactly
+
+ align:start position:0%
+change in the variable Fe it is exactly
+ 
+
+ align:start position:0%
+change in the variable Fe it is exactly
+equal to a half the second differential
+
+ align:start position:0%
+equal to a half the second differential
+ 
+
+ align:start position:0%
+equal to a half the second differential
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+e uh and therefore you prove that this
+
+ align:start position:0%
+e uh and therefore you prove that this
+ 
+
+ align:start position:0%
+e uh and therefore you prove that this
+is greater than equal to
+
+ align:start position:0%
+is greater than equal to
+ 
+
+ align:start position:0%
+is greater than equal to
+zero or if I choose instead to change
+
+ align:start position:0%
+zero or if I choose instead to change
+ 
+
+ align:start position:0%
+zero or if I choose instead to change
+the energy and volume and therefore and
+
+ align:start position:0%
+the energy and volume and therefore and
+ 
+
+ align:start position:0%
+the energy and volume and therefore and
+to move along the stable equilibrium
+
+ align:start position:0%
+to move along the stable equilibrium
+ 
+
+ align:start position:0%
+to move along the stable equilibrium
+State curve so that the entropy is
+
+ align:start position:0%
+State curve so that the entropy is
+ 
+
+ align:start position:0%
+State curve so that the entropy is
+determined by the fundamental relation
+
+ align:start position:0%
+determined by the fundamental relation
+ 
+
+ align:start position:0%
+determined by the fundamental relation
+then Delta V becomes equal to minus the
+
+ align:start position:0%
+then Delta V becomes equal to minus the
+ 
+
+ align:start position:0%
+then Delta V becomes equal to minus the
+second differential of the
+
+ align:start position:0%
+second differential of the
+ 
+
+ align:start position:0%
+second differential of the
+entropy and since that must be greater
+
+ align:start position:0%
+entropy and since that must be greater
+ 
+
+ align:start position:0%
+entropy and since that must be greater
+than zero it it gives again that
+
+ align:start position:0%
+than zero it it gives again that
+ 
+
+ align:start position:0%
+than zero it it gives again that
+d2s is at fixed n now this
+
+ align:start position:0%
+d2s is at fixed n now this
+ 
+
+ align:start position:0%
+d2s is at fixed n now this
+d2s now
+
+ align:start position:0%
+d2s now
+ 
+
+ align:start position:0%
+d2s now
+if you want to represent
+
+ align:start position:0%
+if you want to represent
+ 
+
+ align:start position:0%
+if you want to represent
+it it's not just the second
+
+ align:start position:0%
+it it's not just the second
+ 
+
+ align:start position:0%
+it it's not just the second
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+uh because you
+
+ align:start position:0%
+uh because you
+ 
+
+ align:start position:0%
+uh because you
+see when we have D d2s at constant V and
+
+ align:start position:0%
+see when we have D d2s at constant V and
+ 
+
+ align:start position:0%
+see when we have D d2s at constant V and
+N this was equal to the second
+
+ align:start position:0%
+N this was equal to the second
+ 
+
+ align:start position:0%
+N this was equal to the second
+derivative of s with respect to
+
+ align:start position:0%
+derivative of s with respect to
+ 
+
+ align:start position:0%
+derivative of s with respect to
+e times the e s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this other
+
+ align:start position:0%
+but this other
+ 
+
+ align:start position:0%
+but this other
+d2s at constant n only you can vary both
+
+ align:start position:0%
+d2s at constant n only you can vary both
+ 
+
+ align:start position:0%
+d2s at constant n only you can vary both
+e and s
+
+ align:start position:0%
+e and s
+ 
+
+ align:start position:0%
+e and s
+then uh it's given by d2s with respect
+
+ align:start position:0%
+then uh it's given by d2s with respect
+ 
+
+ align:start position:0%
+then uh it's given by d2s with respect
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+e^2 time e
+
+ align:start position:0%
+e^2 time e
+ 
+
+ align:start position:0%
+e^2 time e
+squar plus twice the second derivative
+
+ align:start position:0%
+squar plus twice the second derivative
+ 
+
+ align:start position:0%
+squar plus twice the second derivative
+of s with respect to e and with respect
+
+ align:start position:0%
+of s with respect to e and with respect
+ 
+
+ align:start position:0%
+of s with respect to e and with respect
+to V times d e
+
+ align:start position:0%
+to V times d e
+ 
+
+ align:start position:0%
+to V times d e
+DV plus the second with respect to
+
+ align:start position:0%
+DV plus the second with respect to
+ 
+
+ align:start position:0%
+DV plus the second with respect to
+V twice times DV squ so it's a quadratic
+
+ align:start position:0%
+V twice times DV squ so it's a quadratic
+ 
+
+ align:start position:0%
+V twice times DV squ so it's a quadratic
+form which you can express also in terms
+
+ align:start position:0%
+form which you can express also in terms
+ 
+
+ align:start position:0%
+form which you can express also in terms
+of the uh in in in this form uh like
+
+ align:start position:0%
+of the uh in in in this form uh like
+ 
+
+ align:start position:0%
+of the uh in in in this form uh like
+using matrices D
+
+ align:start position:0%
+using matrices D
+ 
+
+ align:start position:0%
+using matrices D
+DV here you put the S determinant which
+
+ align:start position:0%
+DV here you put the S determinant which
+ 
+
+ align:start position:0%
+DV here you put the S determinant which
+is the determinant made up of the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivatives okay and this is
+
+ align:start position:0%
+derivatives okay and this is
+ 
+
+ align:start position:0%
+derivatives okay and this is
+equal and then you multiply this by this
+
+ align:start position:0%
+equal and then you multiply this by this
+ 
+
+ align:start position:0%
+equal and then you multiply this by this
+other Vector made up of two
+
+ align:start position:0%
+other Vector made up of two
+ 
+
+ align:start position:0%
+other Vector made up of two
+elements D and DV if you do matrix
+
+ align:start position:0%
+elements D and DV if you do matrix
+ 
+
+ align:start position:0%
+elements D and DV if you do matrix
+multiplication of of this let's be more
+
+ align:start position:0%
+multiplication of of this let's be more
+ 
+
+ align:start position:0%
+multiplication of of this let's be more
+uh elegant here uh you get the above
+
+ align:start position:0%
+uh elegant here uh you get the above
+ 
+
+ align:start position:0%
+uh elegant here uh you get the above
+result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the fact that this has to be
+
+ align:start position:0%
+okay and the fact that this has to be
+ 
+
+ align:start position:0%
+okay and the fact that this has to be
+negative for arbitrary so this has to
+
+ align:start position:0%
+negative for arbitrary so this has to
+ 
+
+ align:start position:0%
+negative for arbitrary so this has to
+be uh negative for arbitrary choice of
+
+ align:start position:0%
+be uh negative for arbitrary choice of
+ 
+
+ align:start position:0%
+be uh negative for arbitrary choice of
+your vector D DV which
+
+ align:start position:0%
+your vector D DV which
+ 
+
+ align:start position:0%
+your vector D DV which
+means no matter what direction you want
+
+ align:start position:0%
+means no matter what direction you want
+ 
+
+ align:start position:0%
+means no matter what direction you want
+to move uh uh
+
+ align:start position:0%
+to move uh uh
+ 
+
+ align:start position:0%
+to move uh uh
+this has to be
+
+ align:start position:0%
+this has to be
+ 
+
+ align:start position:0%
+this has to be
+negative that requires that the Matrix
+
+ align:start position:0%
+negative that requires that the Matrix
+ 
+
+ align:start position:0%
+negative that requires that the Matrix
+inside be no negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definite and the Matrix is non negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definite
+
+ align:start position:0%
+definite
+ 
+
+ align:start position:0%
+definite
+when I me I mean sorry sorry non
+
+ align:start position:0%
+when I me I mean sorry sorry non
+ 
+
+ align:start position:0%
+when I me I mean sorry sorry non
+positive non so it's it's negative
+
+ align:start position:0%
+positive non so it's it's negative
+ 
+
+ align:start position:0%
+positive non so it's it's negative
+semide definite okay so when is a matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's start with positive when is a
+
+ align:start position:0%
+uh let's start with positive when is a
+ 
+
+ align:start position:0%
+uh let's start with positive when is a
+matrix positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definite I have a matrix a 1 one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a12 and let's make it symmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this if it is positive semide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definite the diagonal entries must be
+
+ align:start position:0%
+definite the diagonal entries must be
+ 
+
+ align:start position:0%
+definite the diagonal entries must be
+non-
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative the
+
+ align:start position:0%
+negative the
+ 
+
+ align:start position:0%
+negative the
+determinant must be non- negative so a 1
+
+ align:start position:0%
+determinant must be non- negative so a 1
+ 
+
+ align:start position:0%
+determinant must be non- negative so a 1
+1 a22 minus
+
+ align:start position:0%
+1 a22 minus
+ 
+
+ align:start position:0%
+1 a22 minus
+a12 squared because it's a
+
+ align:start position:0%
+a12 squared because it's a
+ 
+
+ align:start position:0%
+a12 squared because it's a
+symmetric must be greater than equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero you want to make it uh uh if the
+
+ align:start position:0%
+zero you want to make it uh uh if the
+ 
+
+ align:start position:0%
+zero you want to make it uh uh if the
+Matrix instead of
+
+ align:start position:0%
+Matrix instead of
+ 
+
+ align:start position:0%
+Matrix instead of
+being positive semi-definite is negative
+
+ align:start position:0%
+being positive semi-definite is negative
+ 
+
+ align:start position:0%
+being positive semi-definite is negative
+semi-definite so this is less than or
+
+ align:start position:0%
+semi-definite so this is less than or
+ 
+
+ align:start position:0%
+semi-definite so this is less than or
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+entries on the diagonal should
+
+ align:start position:0%
+entries on the diagonal should
+ 
+
+ align:start position:0%
+entries on the diagonal should
+be non NE non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positive how about the
+
+ align:start position:0%
+positive how about the
+ 
+
+ align:start position:0%
+positive how about the
+determinant should I change the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign not for a 2X two
+
+ align:start position:0%
+sign not for a 2X two
+ 
+
+ align:start position:0%
+sign not for a 2X two
+Matrix because you see also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the more uh fundamental way uh property
+
+ align:start position:0%
+the more uh fundamental way uh property
+ 
+
+ align:start position:0%
+the more uh fundamental way uh property
+of of a non negative uh of a a nonos
+
+ align:start position:0%
+of of a non negative uh of a a nonos
+ 
+
+ align:start position:0%
+of of a non negative uh of a a nonos
+of of a negative semide definite Matrix
+
+ align:start position:0%
+of of a negative semide definite Matrix
+ 
+
+ align:start position:0%
+of of a negative semide definite Matrix
+is that it's igen values are
+
+ align:start position:0%
+is that it's igen values are
+ 
+
+ align:start position:0%
+is that it's igen values are
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+negative so it means let's say let's
+
+ align:start position:0%
+negative so it means let's say let's
+ 
+
+ align:start position:0%
+negative so it means let's say let's
+call them Lambda so Lambda 1 is less
+
+ align:start position:0%
+call them Lambda so Lambda 1 is less
+ 
+
+ align:start position:0%
+call them Lambda so Lambda 1 is less
+than zero Lambda 2 is less than zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for a 2x2 matrix the
+
+ align:start position:0%
+and for a 2x2 matrix the
+ 
+
+ align:start position:0%
+and for a 2x2 matrix the
+determinant is equal to the product of
+
+ align:start position:0%
+determinant is equal to the product of
+ 
+
+ align:start position:0%
+determinant is equal to the product of
+the two L values so this is also equal
+
+ align:start position:0%
+the two L values so this is also equal
+ 
+
+ align:start position:0%
+the two L values so this is also equal
+to Lambda 1 time Lambda 2 so if you
+
+ align:start position:0%
+to Lambda 1 time Lambda 2 so if you
+ 
+
+ align:start position:0%
+to Lambda 1 time Lambda 2 so if you
+multiply two negative numbers you get a
+
+ align:start position:0%
+multiply two negative numbers you get a
+ 
+
+ align:start position:0%
+multiply two negative numbers you get a
+positive number and so you
+
+ align:start position:0%
+positive number and so you
+ 
+
+ align:start position:0%
+positive number and so you
+get the determinant is greater than zero
+
+ align:start position:0%
+get the determinant is greater than zero
+ 
+
+ align:start position:0%
+get the determinant is greater than zero
+If instead you you add a 3 by 3x3 Matrix
+
+ align:start position:0%
+If instead you you add a 3 by 3x3 Matrix
+ 
+
+ align:start position:0%
+If instead you you add a 3 by 3x3 Matrix
+then you have three negative numbers
+
+ align:start position:0%
+then you have three negative numbers
+ 
+
+ align:start position:0%
+then you have three negative numbers
+that multiplied give the determinant in
+
+ align:start position:0%
+that multiplied give the determinant in
+ 
+
+ align:start position:0%
+that multiplied give the determinant in
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+case with an odd number of uh entries uh
+
+ align:start position:0%
+case with an odd number of uh entries uh
+ 
+
+ align:start position:0%
+case with an odd number of uh entries uh
+negative time negative time negative
+
+ align:start position:0%
+negative time negative time negative
+ 
+
+ align:start position:0%
+negative time negative time negative
+makes Nega right so the determinant of
+
+ align:start position:0%
+makes Nega right so the determinant of
+ 
+
+ align:start position:0%
+makes Nega right so the determinant of
+of of the uh
+
+ align:start position:0%
+of of the uh
+ 
+
+ align:start position:0%
+of of the uh
+semi uh of a negative semide definite
+
+ align:start position:0%
+semi uh of a negative semide definite
+ 
+
+ align:start position:0%
+semi uh of a negative semide definite
+Matrix is positive for odd number of uh
+
+ align:start position:0%
+Matrix is positive for odd number of uh
+ 
+
+ align:start position:0%
+Matrix is positive for odd number of uh
+rows and columns and uh negative for uh
+
+ align:start position:0%
+rows and columns and uh negative for uh
+ 
+
+ align:start position:0%
+rows and columns and uh negative for uh
+what did it say positive for even number
+
+ align:start position:0%
+what did it say positive for even number
+ 
+
+ align:start position:0%
+what did it say positive for even number
+and negative for odd
+
+ align:start position:0%
+and negative for odd
+ 
+
+ align:start position:0%
+and negative for odd
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we need that in a short
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+while here oh yeah let me just uh
+
+ align:start position:0%
+while here oh yeah let me just uh
+ 
+
+ align:start position:0%
+while here oh yeah let me just uh
+go back to like
+
+ align:start position:0%
+go back to like
+ 
+
+ align:start position:0%
+go back to like
+a a simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about all right suppose you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have you have vacuum so you have a
+
+ align:start position:0%
+have you have vacuum so you have a
+ 
+
+ align:start position:0%
+have you have vacuum so you have a
+piston you have a a
+
+ align:start position:0%
+piston you have a a
+ 
+
+ align:start position:0%
+piston you have a a
+container in which you manage to have
+
+ align:start position:0%
+container in which you manage to have
+ 
+
+ align:start position:0%
+container in which you manage to have
+nothing vacuum vacuum means no particles
+
+ align:start position:0%
+nothing vacuum vacuum means no particles
+ 
+
+ align:start position:0%
+nothing vacuum vacuum means no particles
+nothing
+
+ align:start position:0%
+nothing
+ 
+
+ align:start position:0%
+nothing
+okay so the question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is is that a
+
+ align:start position:0%
+is is that a
+ 
+
+ align:start position:0%
+is is that a
+situation and this vacuum is in a uh in
+
+ align:start position:0%
+situation and this vacuum is in a uh in
+ 
+
+ align:start position:0%
+situation and this vacuum is in a uh in
+an environment which I can
+
+ align:start position:0%
+an environment which I can
+ 
+
+ align:start position:0%
+an environment which I can
+model as a reservoir
+
+ align:start position:0%
+model as a reservoir
+ 
+
+ align:start position:0%
+model as a reservoir
+at pressure
+
+ align:start position:0%
+at pressure
+ 
+
+ align:start position:0%
+at pressure
+PR yeah also temperature TR but uh the
+
+ align:start position:0%
+PR yeah also temperature TR but uh the
+ 
+
+ align:start position:0%
+PR yeah also temperature TR but uh the
+temperature doesn't play much over Ro
+
+ align:start position:0%
+temperature doesn't play much over Ro
+ 
+
+ align:start position:0%
+temperature doesn't play much over Ro
+here so it's like I have this container
+
+ align:start position:0%
+here so it's like I have this container
+ 
+
+ align:start position:0%
+here so it's like I have this container
+in the environment here man I manage to
+
+ align:start position:0%
+in the environment here man I manage to
+ 
+
+ align:start position:0%
+in the environment here man I manage to
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+vacuum what's the minimum work required
+
+ align:start position:0%
+vacuum what's the minimum work required
+ 
+
+ align:start position:0%
+vacuum what's the minimum work required
+to make that
+
+ align:start position:0%
+to make that
+ 
+
+ align:start position:0%
+to make that
+vacuum or if I have that vacuum can I do
+
+ align:start position:0%
+vacuum or if I have that vacuum can I do
+ 
+
+ align:start position:0%
+vacuum or if I have that vacuum can I do
+something useful can I lift the weight
+
+ align:start position:0%
+something useful can I lift the weight
+ 
+
+ align:start position:0%
+something useful can I lift the weight
+what's the maximum uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lift well let's
+
+ align:start position:0%
+lift well let's
+ 
+
+ align:start position:0%
+lift well let's
+apply this formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here assume that we do things the best
+
+ align:start position:0%
+here assume that we do things the best
+ 
+
+ align:start position:0%
+here assume that we do things the best
+thermodynamic way so that means without
+
+ align:start position:0%
+thermodynamic way so that means without
+ 
+
+ align:start position:0%
+thermodynamic way so that means without
+generating entropy by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+irreversibility and suppose I want my
+
+ align:start position:0%
+irreversibility and suppose I want my
+ 
+
+ align:start position:0%
+irreversibility and suppose I want my
+initial state state one
+
+ align:start position:0%
+initial state state one
+ 
+
+ align:start position:0%
+initial state state one
+okay so let me say that I started with
+
+ align:start position:0%
+okay so let me say that I started with
+ 
+
+ align:start position:0%
+okay so let me say that I started with
+my piston down below
+
+ align:start position:0%
+my piston down below
+ 
+
+ align:start position:0%
+my piston down below
+here and now so this is my say State one
+
+ align:start position:0%
+here and now so this is my say State one
+ 
+
+ align:start position:0%
+here and now so this is my say State one
+and this is my state
+
+ align:start position:0%
+and this is my state
+ 
+
+ align:start position:0%
+and this is my state
+two and I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pull here I have the
+
+ align:start position:0%
+pull here I have the
+ 
+
+ align:start position:0%
+pull here I have the
+pressure of the
+
+ align:start position:0%
+pressure of the
+ 
+
+ align:start position:0%
+pressure of the
+environment so if I pull
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how much work do I have to do I have to
+
+ align:start position:0%
+how much work do I have to do I have to
+ 
+
+ align:start position:0%
+how much work do I have to do I have to
+the if you look at the piston on one
+
+ align:start position:0%
+the if you look at the piston on one
+ 
+
+ align:start position:0%
+the if you look at the piston on one
+side you have zero pressure because
+
+ align:start position:0%
+side you have zero pressure because
+ 
+
+ align:start position:0%
+side you have zero pressure because
+nothing here on the other side you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PR so if you if the the
+
+ align:start position:0%
+PR so if you if the the
+ 
+
+ align:start position:0%
+PR so if you if the the
+volume change is vs2 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V1 you can view that as
+
+ align:start position:0%
+V1 you can view that as
+ 
+
+ align:start position:0%
+V1 you can view that as
+a that's let's call X this
+
+ align:start position:0%
+a that's let's call X this
+ 
+
+ align:start position:0%
+a that's let's call X this
+uh the loc let's call Z the location of
+
+ align:start position:0%
+uh the loc let's call Z the location of
+ 
+
+ align:start position:0%
+uh the loc let's call Z the location of
+the of the weight I'm sorry of the
+
+ align:start position:0%
+the of the weight I'm sorry of the
+ 
+
+ align:start position:0%
+the of the weight I'm sorry of the
+piston and let's call Little a the area
+
+ align:start position:0%
+piston and let's call Little a the area
+ 
+
+ align:start position:0%
+piston and let's call Little a the area
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Piston
+
+ align:start position:0%
+Piston
+ 
+
+ align:start position:0%
+Piston
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+force that you have to apply is equal
+
+ align:start position:0%
+force that you have to apply is equal
+ 
+
+ align:start position:0%
+force that you have to apply is equal
+to the pressure times which is force per
+
+ align:start position:0%
+to the pressure times which is force per
+ 
+
+ align:start position:0%
+to the pressure times which is force per
+unit area times the area so that's the
+
+ align:start position:0%
+unit area times the area so that's the
+ 
+
+ align:start position:0%
+unit area times the area so that's the
+force the
+
+ align:start position:0%
+force the
+ 
+
+ align:start position:0%
+force the
+work is
+
+ align:start position:0%
+work is
+ 
+
+ align:start position:0%
+work is
+f time
+
+ align:start position:0%
+f time
+ 
+
+ align:start position:0%
+f time
+x Force I'm sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z
+
+ align:start position:0%
+Z
+ 
+
+ align:start position:0%
+Z
+right uh so that's p
+
+ align:start position:0%
+right uh so that's p
+ 
+
+ align:start position:0%
+right uh so that's p
+r time a
+
+ align:start position:0%
+r time a
+ 
+
+ align:start position:0%
+r time a
+z but a z is the volume so that's p r *
+
+ align:start position:0%
+z but a z is the volume so that's p r *
+ 
+
+ align:start position:0%
+z but a z is the volume so that's p r *
+V but actually it's V2 minus V1 because
+
+ align:start position:0%
+V but actually it's V2 minus V1 because
+ 
+
+ align:start position:0%
+V but actually it's V2 minus V1 because
+uh this is V2 and this is V1 is equal to
+
+ align:start position:0%
+uh this is V2 and this is V1 is equal to
+ 
+
+ align:start position:0%
+uh this is V2 and this is V1 is equal to
+zero in in our case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it seems that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work that you need to spend B in order
+
+ align:start position:0%
+work that you need to spend B in order
+ 
+
+ align:start position:0%
+work that you need to spend B in order
+to go from one to two in a reversible
+
+ align:start position:0%
+to go from one to two in a reversible
+ 
+
+ align:start position:0%
+to go from one to two in a reversible
+way is equal to
+
+ align:start position:0%
+way is equal to
+ 
+
+ align:start position:0%
+way is equal to
+that which is written
+
+ align:start position:0%
+that which is written
+ 
+
+ align:start position:0%
+that which is written
+here except that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now it has the wrong
+
+ align:start position:0%
+now it has the wrong
+ 
+
+ align:start position:0%
+now it has the wrong
+sign because this represents the work
+
+ align:start position:0%
+sign because this represents the work
+ 
+
+ align:start position:0%
+sign because this represents the work
+with the arrow out
+
+ align:start position:0%
+with the arrow out
+ 
+
+ align:start position:0%
+with the arrow out
+instead we are spend if we change the
+
+ align:start position:0%
+instead we are spend if we change the
+ 
+
+ align:start position:0%
+instead we are spend if we change the
+direction of the the arrow so me say
+
+ align:start position:0%
+direction of the the arrow so me say
+ 
+
+ align:start position:0%
+direction of the the arrow so me say
+that this is the work that I need to
+
+ align:start position:0%
+that this is the work that I need to
+ 
+
+ align:start position:0%
+that this is the work that I need to
+spend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and of course this I could also
+
+ align:start position:0%
+okay and of course this I could also
+ 
+
+ align:start position:0%
+okay and of course this I could also
+write at the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing by changing the arrow if I change
+
+ align:start position:0%
+thing by changing the arrow if I change
+ 
+
+ align:start position:0%
+thing by changing the arrow if I change
+the arrow I change also the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign
+
+ align:start position:0%
+sign
+ 
+
+ align:start position:0%
+sign
+okay so essentially the the the the
+
+ align:start position:0%
+okay so essentially the the the the
+ 
+
+ align:start position:0%
+okay so essentially the the the the
+minimum work to required to produce the
+
+ align:start position:0%
+minimum work to required to produce the
+ 
+
+ align:start position:0%
+minimum work to required to produce the
+vacuum is equal to the pressure of the
+
+ align:start position:0%
+vacuum is equal to the pressure of the
+ 
+
+ align:start position:0%
+vacuum is equal to the pressure of the
+environment times the volume of that
+
+ align:start position:0%
+environment times the volume of that
+ 
+
+ align:start position:0%
+environment times the volume of that
+vacuum that's an easy result we could
+
+ align:start position:0%
+vacuum that's an easy result we could
+ 
+
+ align:start position:0%
+vacuum that's an easy result we could
+have I mean we actually got to that
+
+ align:start position:0%
+have I mean we actually got to that
+ 
+
+ align:start position:0%
+have I mean we actually got to that
+result without all the complicated uh
+
+ align:start position:0%
+result without all the complicated uh
+ 
+
+ align:start position:0%
+result without all the complicated uh
+long story that we are telling
+
+ align:start position:0%
+long story that we are telling
+ 
+
+ align:start position:0%
+long story that we are telling
+but that's just
+
+ align:start position:0%
+but that's just
+ 
+
+ align:start position:0%
+but that's just
+to uh show what uh the consistency of
+
+ align:start position:0%
+to uh show what uh the consistency of
+ 
+
+ align:start position:0%
+to uh show what uh the consistency of
+this relation we what we what we know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's think of another kind of uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Reservoir which again can be uh
+
+ align:start position:0%
+Reservoir which again can be uh
+ 
+
+ align:start position:0%
+Reservoir which again can be uh
+typically is a typical model of the a
+
+ align:start position:0%
+typically is a typical model of the a
+ 
+
+ align:start position:0%
+typically is a typical model of the a
+environment or the or or some natural uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+environment so here is a particular
+
+ align:start position:0%
+environment so here is a particular
+ 
+
+ align:start position:0%
+environment so here is a particular
+Reservoir that can exchange through a
+
+ align:start position:0%
+Reservoir that can exchange through a
+ 
+
+ align:start position:0%
+Reservoir that can exchange through a
+semi perable membrane only one type of
+
+ align:start position:0%
+semi perable membrane only one type of
+ 
+
+ align:start position:0%
+semi perable membrane only one type of
+substance with your
+
+ align:start position:0%
+substance with your
+ 
+
+ align:start position:0%
+substance with your
+system we may we may call it the an
+
+ align:start position:0%
+system we may we may call it the an
+ 
+
+ align:start position:0%
+system we may we may call it the an
+osmotic Reservoir or a thermal Reservoir
+
+ align:start position:0%
+osmotic Reservoir or a thermal Reservoir
+ 
+
+ align:start position:0%
+osmotic Reservoir or a thermal Reservoir
+or we just not don't give any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+names but just Define it uh uh by just
+
+ align:start position:0%
+names but just Define it uh uh by just
+ 
+
+ align:start position:0%
+names but just Define it uh uh by just
+these words all
+
+ align:start position:0%
+these words all
+ 
+
+ align:start position:0%
+these words all
+right you run the same machine machery
+
+ align:start position:0%
+right you run the same machine machery
+ 
+
+ align:start position:0%
+right you run the same machine machery
+energy balance entropy balance now you
+
+ align:start position:0%
+energy balance entropy balance now you
+ 
+
+ align:start position:0%
+energy balance entropy balance now you
+also have to make a balance for the
+
+ align:start position:0%
+also have to make a balance for the
+ 
+
+ align:start position:0%
+also have to make a balance for the
+amounts of constituents of the kind of
+
+ align:start position:0%
+amounts of constituents of the kind of
+ 
+
+ align:start position:0%
+amounts of constituents of the kind of
+substance that can be uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transferred for example you
+
+ align:start position:0%
+transferred for example you
+ 
+
+ align:start position:0%
+transferred for example you
+can you may be
+
+ align:start position:0%
+can you may be
+ 
+
+ align:start position:0%
+can you may be
+interested in U you know some people are
+
+ align:start position:0%
+interested in U you know some people are
+ 
+
+ align:start position:0%
+interested in U you know some people are
+devising uh devising um methods or or U
+
+ align:start position:0%
+devising uh devising um methods or or U
+ 
+
+ align:start position:0%
+devising uh devising um methods or or U
+uh plants that want to extract CO2 from
+
+ align:start position:0%
+uh plants that want to extract CO2 from
+ 
+
+ align:start position:0%
+uh plants that want to extract CO2 from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+atmosphere right so you want to ask well
+
+ align:start position:0%
+atmosphere right so you want to ask well
+ 
+
+ align:start position:0%
+atmosphere right so you want to ask well
+what's the minimum amount of work I need
+
+ align:start position:0%
+what's the minimum amount of work I need
+ 
+
+ align:start position:0%
+what's the minimum amount of work I need
+to spend if I want to uh extract CO2
+
+ align:start position:0%
+to spend if I want to uh extract CO2
+ 
+
+ align:start position:0%
+to spend if I want to uh extract CO2
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+atmosphere because that minimum defines
+
+ align:start position:0%
+atmosphere because that minimum defines
+ 
+
+ align:start position:0%
+atmosphere because that minimum defines
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+target defines also the way in which you
+
+ align:start position:0%
+target defines also the way in which you
+ 
+
+ align:start position:0%
+target defines also the way in which you
+determine the efficiency the second low
+
+ align:start position:0%
+determine the efficiency the second low
+ 
+
+ align:start position:0%
+determine the efficiency the second low
+efficiency of that uh particular uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equipment and it's a question very
+
+ align:start position:0%
+equipment and it's a question very
+ 
+
+ align:start position:0%
+equipment and it's a question very
+similar to this one because one
+
+ align:start position:0%
+similar to this one because one
+ 
+
+ align:start position:0%
+similar to this one because one
+way one way to do
+
+ align:start position:0%
+way one way to do
+ 
+
+ align:start position:0%
+way one way to do
+that uh not saying it's the reversible
+
+ align:start position:0%
+that uh not saying it's the reversible
+ 
+
+ align:start position:0%
+that uh not saying it's the reversible
+way but I'm saying that one way to do it
+
+ align:start position:0%
+way but I'm saying that one way to do it
+ 
+
+ align:start position:0%
+way but I'm saying that one way to do it
+is first you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vacuum and
+
+ align:start position:0%
+vacuum and
+ 
+
+ align:start position:0%
+vacuum and
+then you open
+
+ align:start position:0%
+then you open
+ 
+
+ align:start position:0%
+then you open
+up the permeability of the Piston to C
+
+ align:start position:0%
+up the permeability of the Piston to C
+ 
+
+ align:start position:0%
+up the permeability of the Piston to C
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+CO2 and so CO2 will fill this
+
+ align:start position:0%
+CO2 and so CO2 will fill this
+ 
+
+ align:start position:0%
+CO2 and so CO2 will fill this
+region and you'll have just CO2 because
+
+ align:start position:0%
+region and you'll have just CO2 because
+ 
+
+ align:start position:0%
+region and you'll have just CO2 because
+the other parts the other mean O oxygen
+
+ align:start position:0%
+the other parts the other mean O oxygen
+ 
+
+ align:start position:0%
+the other parts the other mean O oxygen
+and nitrogen cannot go through uh this
+
+ align:start position:0%
+and nitrogen cannot go through uh this
+ 
+
+ align:start position:0%
+and nitrogen cannot go through uh this
+particular semi-permeable membrane and
+
+ align:start position:0%
+particular semi-permeable membrane and
+ 
+
+ align:start position:0%
+particular semi-permeable membrane and
+that way you have
+
+ align:start position:0%
+that way you have
+ 
+
+ align:start position:0%
+that way you have
+separated so one way is produce vacuum
+
+ align:start position:0%
+separated so one way is produce vacuum
+ 
+
+ align:start position:0%
+separated so one way is produce vacuum
+and we know how much it work it requires
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use a semi-perm membrane and there you
+
+ align:start position:0%
+use a semi-perm membrane and there you
+ 
+
+ align:start position:0%
+use a semi-perm membrane and there you
+have your your uh CO2 your CO2
+
+ align:start position:0%
+have your your uh CO2 your CO2
+ 
+
+ align:start position:0%
+have your your uh CO2 your CO2
+eventually will reach Mutual equilibrium
+
+ align:start position:0%
+eventually will reach Mutual equilibrium
+ 
+
+ align:start position:0%
+eventually will reach Mutual equilibrium
+with the reservoir and
+
+ align:start position:0%
+with the reservoir and
+ 
+
+ align:start position:0%
+with the reservoir and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh so if you at that stage I have
+
+ align:start position:0%
+uh so if you at that stage I have
+ 
+
+ align:start position:0%
+uh so if you at that stage I have
+blocked my piston cannot go up and down
+
+ align:start position:0%
+blocked my piston cannot go up and down
+ 
+
+ align:start position:0%
+blocked my piston cannot go up and down
+and I change Reservoir instead of having
+
+ align:start position:0%
+and I change Reservoir instead of having
+ 
+
+ align:start position:0%
+and I change Reservoir instead of having
+a reservoir at variable volume
+
+ align:start position:0%
+a reservoir at variable volume
+ 
+
+ align:start position:0%
+a reservoir at variable volume
+I have a reservoir at uh that can
+
+ align:start position:0%
+I have a reservoir at uh that can
+ 
+
+ align:start position:0%
+I have a reservoir at uh that can
+exchange that so at constant chemical
+
+ align:start position:0%
+exchange that so at constant chemical
+ 
+
+ align:start position:0%
+exchange that so at constant chemical
+potential of that substance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CO2
+
+ align:start position:0%
+CO2
+ 
+
+ align:start position:0%
+CO2
+okay uh the final state will be that
+
+ align:start position:0%
+okay uh the final state will be that
+ 
+
+ align:start position:0%
+okay uh the final state will be that
+instead of vacuum I will just have CO2
+
+ align:start position:0%
+instead of vacuum I will just have CO2
+ 
+
+ align:start position:0%
+instead of vacuum I will just have CO2
+pure let's say that this will have a
+
+ align:start position:0%
+pure let's say that this will have a
+ 
+
+ align:start position:0%
+pure let's say that this will have a
+chemical potential that we will
+
+ align:start position:0%
+chemical potential that we will
+ 
+
+ align:start position:0%
+chemical potential that we will
+call MU
+
+ align:start position:0%
+call MU
+ 
+
+ align:start position:0%
+call MU
+I and it will have a pressure that
+
+ align:start position:0%
+I and it will have a pressure that
+ 
+
+ align:start position:0%
+I and it will have a pressure that
+corresponds to what we
+
+ align:start position:0%
+corresponds to what we
+ 
+
+ align:start position:0%
+corresponds to what we
+defined when they are in mutual
+
+ align:start position:0%
+defined when they are in mutual
+ 
+
+ align:start position:0%
+defined when they are in mutual
+equilibrium equality of chemical
+
+ align:start position:0%
+equilibrium equality of chemical
+ 
+
+ align:start position:0%
+equilibrium equality of chemical
+potentials defines the partial
+
+ align:start position:0%
+potentials defines the partial
+ 
+
+ align:start position:0%
+potentials defines the partial
+pressure so the CO2 will be at the
+
+ align:start position:0%
+pressure so the CO2 will be at the
+ 
+
+ align:start position:0%
+pressure so the CO2 will be at the
+partial pressure that it has in air
+
+ align:start position:0%
+partial pressure that it has in air
+ 
+
+ align:start position:0%
+partial pressure that it has in air
+viewed as a
+
+ align:start position:0%
+viewed as a
+ 
+
+ align:start position:0%
+viewed as a
+mixture okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this second part of the process from
+
+ align:start position:0%
+this second part of the process from
+ 
+
+ align:start position:0%
+this second part of the process from
+when I after I made vacuum and I stop
+
+ align:start position:0%
+when I after I made vacuum and I stop
+ 
+
+ align:start position:0%
+when I after I made vacuum and I stop
+the piston and I open the pory uh the
+
+ align:start position:0%
+the piston and I open the pory uh the
+ 
+
+ align:start position:0%
+the piston and I open the pory uh the
+second part of the process is
+
+ align:start position:0%
+second part of the process is
+ 
+
+ align:start position:0%
+second part of the process is
+spontaneous because
+
+ align:start position:0%
+spontaneous because
+ 
+
+ align:start position:0%
+spontaneous because
+initially you are in non equilibrium
+
+ align:start position:0%
+initially you are in non equilibrium
+ 
+
+ align:start position:0%
+initially you are in non equilibrium
+State because here you have no CO2
+
+ align:start position:0%
+State because here you have no CO2
+ 
+
+ align:start position:0%
+State because here you have no CO2
+whereas in order for a equilibrium you
+
+ align:start position:0%
+whereas in order for a equilibrium you
+ 
+
+ align:start position:0%
+whereas in order for a equilibrium you
+need to have chemical potentials to be
+
+ align:start position:0%
+need to have chemical potentials to be
+ 
+
+ align:start position:0%
+need to have chemical potentials to be
+equal so this is an irreversible process
+
+ align:start position:0%
+equal so this is an irreversible process
+ 
+
+ align:start position:0%
+equal so this is an irreversible process
+there will be entropy produced by
+
+ align:start position:0%
+there will be entropy produced by
+ 
+
+ align:start position:0%
+there will be entropy produced by
+reversibility so this is not the best
+
+ align:start position:0%
+reversibility so this is not the best
+ 
+
+ align:start position:0%
+reversibility so this is not the best
+way to do it you could also evaluate how
+
+ align:start position:0%
+way to do it you could also evaluate how
+ 
+
+ align:start position:0%
+way to do it you could also evaluate how
+much is the efficiency if you could
+
+ align:start position:0%
+much is the efficiency if you could
+ 
+
+ align:start position:0%
+much is the efficiency if you could
+compare it with what's the minimum work
+
+ align:start position:0%
+compare it with what's the minimum work
+ 
+
+ align:start position:0%
+compare it with what's the minimum work
+that is required and the minimum work
+
+ align:start position:0%
+that is required and the minimum work
+ 
+
+ align:start position:0%
+that is required and the minimum work
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+required is given
+
+ align:start position:0%
+required is given
+ 
+
+ align:start position:0%
+required is given
+here by this formula here I'm Sorry by
+
+ align:start position:0%
+here by this formula here I'm Sorry by
+ 
+
+ align:start position:0%
+here by this formula here I'm Sorry by
+this formula
+
+ align:start position:0%
+this formula
+ 
+
+ align:start position:0%
+this formula
+here so there is again another
+
+ align:start position:0%
+here so there is again another
+ 
+
+ align:start position:0%
+here so there is again another
+um available energy
+
+ align:start position:0%
+um available energy
+ 
+
+ align:start position:0%
+um available energy
+function I'm sorry available energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property for this particular kind of
+
+ align:start position:0%
+property for this particular kind of
+ 
+
+ align:start position:0%
+property for this particular kind of
+osmotic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reservoirs the difference of which tells
+
+ align:start position:0%
+reservoirs the difference of which tells
+ 
+
+ align:start position:0%
+reservoirs the difference of which tells
+you the minimum or the maximum
+
+ align:start position:0%
+you the minimum or the maximum
+ 
+
+ align:start position:0%
+you the minimum or the maximum
+works for producing or or exploiting and
+
+ align:start position:0%
+works for producing or or exploiting and
+ 
+
+ align:start position:0%
+works for producing or or exploiting and
+the situation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll return later on uh to this
+
+ align:start position:0%
+so we'll return later on uh to this
+ 
+
+ align:start position:0%
+so we'll return later on uh to this
+question of minimum work for separating
+
+ align:start position:0%
+question of minimum work for separating
+ 
+
+ align:start position:0%
+question of minimum work for separating
+a substance from uh from from say the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atmosphere
+
+ align:start position:0%
+atmosphere
+ 
+
+ align:start position:0%
+atmosphere
+here this combination that appears in
+
+ align:start position:0%
+here this combination that appears in
+ 
+
+ align:start position:0%
+here this combination that appears in
+the expression for this new version of
+
+ align:start position:0%
+the expression for this new version of
+ 
+
+ align:start position:0%
+the expression for this new version of
+the available energy namely e minus TRS
+
+ align:start position:0%
+the available energy namely e minus TRS
+ 
+
+ align:start position:0%
+the available energy namely e minus TRS
+minus the chemical potential
+
+ align:start position:0%
+minus the chemical potential
+ 
+
+ align:start position:0%
+minus the chemical potential
+times the amount of that substance that
+
+ align:start position:0%
+times the amount of that substance that
+ 
+
+ align:start position:0%
+times the amount of that substance that
+is can cross between the system and the
+
+ align:start position:0%
+is can cross between the system and the
+ 
+
+ align:start position:0%
+is can cross between the system and the
+reservoir we may give it a name or not
+
+ align:start position:0%
+reservoir we may give it a name or not
+ 
+
+ align:start position:0%
+reservoir we may give it a name or not
+simply an availability
+
+ align:start position:0%
+simply an availability
+ 
+
+ align:start position:0%
+simply an availability
+function maybe we could call it osmotic
+
+ align:start position:0%
+function maybe we could call it osmotic
+ 
+
+ align:start position:0%
+function maybe we could call it osmotic
+availability function maybe we could use
+
+ align:start position:0%
+availability function maybe we could use
+ 
+
+ align:start position:0%
+availability function maybe we could use
+this letter or another letter uh it's
+
+ align:start position:0%
+this letter or another letter uh it's
+ 
+
+ align:start position:0%
+this letter or another letter uh it's
+just a matter of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choice as for for the other availability
+
+ align:start position:0%
+choice as for for the other availability
+ 
+
+ align:start position:0%
+choice as for for the other availability
+functions this also is
+
+ align:start position:0%
+functions this also is
+ 
+
+ align:start position:0%
+functions this also is
+minimum so also from this one you can
+
+ align:start position:0%
+minimum so also from this one you can
+ 
+
+ align:start position:0%
+minimum so also from this one you can
+derive by the
+
+ align:start position:0%
+derive by the
+ 
+
+ align:start position:0%
+derive by the
+same method as before same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+procedure conditions for stability of
+
+ align:start position:0%
+procedure conditions for stability of
+ 
+
+ align:start position:0%
+procedure conditions for stability of
+equilibrium for the second differential
+
+ align:start position:0%
+equilibrium for the second differential
+ 
+
+ align:start position:0%
+equilibrium for the second differential
+of the energy now it will be like uh uh
+
+ align:start position:0%
+of the energy now it will be like uh uh
+ 
+
+ align:start position:0%
+of the energy now it will be like uh uh
+this is but not with volume but with NI
+
+ align:start position:0%
+this is but not with volume but with NI
+ 
+
+ align:start position:0%
+this is but not with volume but with NI
+I uh that substitutes and that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the the the expression for this
+
+ align:start position:0%
+uh the the the expression for this
+ 
+
+ align:start position:0%
+uh the the the expression for this
+second order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentials and finally we could have
+
+ align:start position:0%
+differentials and finally we could have
+ 
+
+ align:start position:0%
+differentials and finally we could have
+a grand situation okay so Grand
+
+ align:start position:0%
+a grand situation okay so Grand
+ 
+
+ align:start position:0%
+a grand situation okay so Grand
+Reservoir
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um with which
+
+ align:start position:0%
+um with which
+ 
+
+ align:start position:0%
+um with which
+you can your system can exchange
+
+ align:start position:0%
+you can your system can exchange
+ 
+
+ align:start position:0%
+you can your system can exchange
+anything it
+
+ align:start position:0%
+anything it
+ 
+
+ align:start position:0%
+anything it
+wants amounts volume energy and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you have to run again the same
+
+ align:start position:0%
+okay so you have to run again the same
+ 
+
+ align:start position:0%
+okay so you have to run again the same
+Machinery energy balance entropy balance
+
+ align:start position:0%
+Machinery energy balance entropy balance
+ 
+
+ align:start position:0%
+Machinery energy balance entropy balance
+fundamental relation for the
+
+ align:start position:0%
+fundamental relation for the
+ 
+
+ align:start position:0%
+fundamental relation for the
+reservoir notice that PO in the previous
+
+ align:start position:0%
+reservoir notice that PO in the previous
+ 
+
+ align:start position:0%
+reservoir notice that PO in the previous
+case maybe I didn't emphasize it enough
+
+ align:start position:0%
+case maybe I didn't emphasize it enough
+ 
+
+ align:start position:0%
+case maybe I didn't emphasize it enough
+but what changes from Reservoir to
+
+ align:start position:0%
+but what changes from Reservoir to
+ 
+
+ align:start position:0%
+but what changes from Reservoir to
+Reservoir is the
+
+ align:start position:0%
+Reservoir is the
+ 
+
+ align:start position:0%
+Reservoir is the
+expression for the fundamental relation
+
+ align:start position:0%
+expression for the fundamental relation
+ 
+
+ align:start position:0%
+expression for the fundamental relation
+see these uh terms are
+
+ align:start position:0%
+see these uh terms are
+ 
+
+ align:start position:0%
+see these uh terms are
+new peculiar to this
+
+ align:start position:0%
+new peculiar to this
+ 
+
+ align:start position:0%
+new peculiar to this
+Reservoir that acts as a reservoir not
+
+ align:start position:0%
+Reservoir that acts as a reservoir not
+ 
+
+ align:start position:0%
+Reservoir that acts as a reservoir not
+only for exchanges of energy and entropy
+
+ align:start position:0%
+only for exchanges of energy and entropy
+ 
+
+ align:start position:0%
+only for exchanges of energy and entropy
+but also for if you change volume it
+
+ align:start position:0%
+but also for if you change volume it
+ 
+
+ align:start position:0%
+but also for if you change volume it
+doesn't change the pressure if you
+
+ align:start position:0%
+doesn't change the pressure if you
+ 
+
+ align:start position:0%
+doesn't change the pressure if you
+change the amounts it doesn't change the
+
+ align:start position:0%
+change the amounts it doesn't change the
+ 
+
+ align:start position:0%
+change the amounts it doesn't change the
+chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potentials and then you have to uh
+
+ align:start position:0%
+potentials and then you have to uh
+ 
+
+ align:start position:0%
+potentials and then you have to uh
+remember also to do the
+
+ align:start position:0%
+remember also to do the
+ 
+
+ align:start position:0%
+remember also to do the
+volume balance and the balance balances
+
+ align:start position:0%
+volume balance and the balance balances
+ 
+
+ align:start position:0%
+volume balance and the balance balances
+for all of the amounts of the various
+
+ align:start position:0%
+for all of the amounts of the various
+ 
+
+ align:start position:0%
+for all of the amounts of the various
+constituents that are
+
+ align:start position:0%
+constituents that are
+ 
+
+ align:start position:0%
+constituents that are
+conserved now chemical reactions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here again eliminate
+
+ align:start position:0%
+here again eliminate
+ 
+
+ align:start position:0%
+here again eliminate
+the terms that relate to
+
+ align:start position:0%
+the terms that relate to
+ 
+
+ align:start position:0%
+the terms that relate to
+the reservoir and you get this
+
+ align:start position:0%
+the reservoir and you get this
+ 
+
+ align:start position:0%
+the reservoir and you get this
+expression which is a
+
+ align:start position:0%
+expression which is a
+ 
+
+ align:start position:0%
+expression which is a
+another generalization of the available
+
+ align:start position:0%
+another generalization of the available
+ 
+
+ align:start position:0%
+another generalization of the available
+energy with respect to this completely
+
+ align:start position:0%
+energy with respect to this completely
+ 
+
+ align:start position:0%
+energy with respect to this completely
+open uh Reservoir and uh it's
+
+ align:start position:0%
+open uh Reservoir and uh it's
+ 
+
+ align:start position:0%
+open uh Reservoir and uh it's
+um this is the available energy the
+
+ align:start position:0%
+um this is the available energy the
+ 
+
+ align:start position:0%
+um this is the available energy the
+expression which can also be written as
+
+ align:start position:0%
+expression which can also be written as
+ 
+
+ align:start position:0%
+expression which can also be written as
+a difference in two
+
+ align:start position:0%
+a difference in two
+ 
+
+ align:start position:0%
+a difference in two
+values so the the work the maximum or
+
+ align:start position:0%
+values so the the work the maximum or
+ 
+
+ align:start position:0%
+values so the the work the maximum or
+minum the reversible work is the
+
+ align:start position:0%
+minum the reversible work is the
+ 
+
+ align:start position:0%
+minum the reversible work is the
+difference in the values of this new
+
+ align:start position:0%
+difference in the values of this new
+ 
+
+ align:start position:0%
+difference in the values of this new
+availability function which I like to
+
+ align:start position:0%
+availability function which I like to
+ 
+
+ align:start position:0%
+availability function which I like to
+call Oiler availability function for the
+
+ align:start position:0%
+call Oiler availability function for the
+ 
+
+ align:start position:0%
+call Oiler availability function for the
+reason I already explained uh the other
+
+ align:start position:0%
+reason I already explained uh the other
+ 
+
+ align:start position:0%
+reason I already explained uh the other
+time and that will be also clear uh
+
+ align:start position:0%
+time and that will be also clear uh
+ 
+
+ align:start position:0%
+time and that will be also clear uh
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+on so this e minus TRS plus PV minus mu
+
+ align:start position:0%
+on so this e minus TRS plus PV minus mu
+ 
+
+ align:start position:0%
+on so this e minus TRS plus PV minus mu
+RN this availability function is defined
+
+ align:start position:0%
+RN this availability function is defined
+ 
+
+ align:start position:0%
+RN this availability function is defined
+for all states equilibrium and non-e
+
+ align:start position:0%
+for all states equilibrium and non-e
+ 
+
+ align:start position:0%
+for all states equilibrium and non-e
+equilibrium when your system is
+
+ align:start position:0%
+equilibrium when your system is
+ 
+
+ align:start position:0%
+equilibrium when your system is
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+uh neutal equilibrium so so it is in the
+
+ align:start position:0%
+uh neutal equilibrium so so it is in the
+ 
+
+ align:start position:0%
+uh neutal equilibrium so so it is in the
+state at temperature TR pressure PR and
+
+ align:start position:0%
+state at temperature TR pressure PR and
+ 
+
+ align:start position:0%
+state at temperature TR pressure PR and
+with the chemical potential so complete
+
+ align:start position:0%
+with the chemical potential so complete
+ 
+
+ align:start position:0%
+with the chemical potential so complete
+equilibrium between system and
+
+ align:start position:0%
+equilibrium between system and
+ 
+
+ align:start position:0%
+equilibrium between system and
+Reservoir then this availability
+
+ align:start position:0%
+Reservoir then this availability
+ 
+
+ align:start position:0%
+Reservoir then this availability
+function we corresponds to that
+
+ align:start position:0%
+function we corresponds to that
+ 
+
+ align:start position:0%
+function we corresponds to that
+characteristic function that we called
+
+ align:start position:0%
+characteristic function that we called
+ 
+
+ align:start position:0%
+characteristic function that we called
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+oiler free energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I just reviewed at the beginning of
+
+ align:start position:0%
+that I just reviewed at the beginning of
+ 
+
+ align:start position:0%
+that I just reviewed at the beginning of
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+okay and from this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one this
+
+ align:start position:0%
+one this
+ 
+
+ align:start position:0%
+one this
+also is
+
+ align:start position:0%
+also is
+ 
+
+ align:start position:0%
+also is
+minimum at Mutual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium and you can do the same
+
+ align:start position:0%
+equilibrium and you can do the same
+ 
+
+ align:start position:0%
+equilibrium and you can do the same
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh to EXT ract
+
+ align:start position:0%
+uh to EXT ract
+ 
+
+ align:start position:0%
+uh to EXT ract
+conditions for stability this
+
+ align:start position:0%
+conditions for stability this
+ 
+
+ align:start position:0%
+conditions for stability this
+time this
+
+ align:start position:0%
+time this
+ 
+
+ align:start position:0%
+time this
+expression D2 e is with respect not to
+
+ align:start position:0%
+expression D2 e is with respect not to
+ 
+
+ align:start position:0%
+expression D2 e is with respect not to
+just two variables so this
+
+ align:start position:0%
+just two variables so this
+ 
+
+ align:start position:0%
+just two variables so this
+Matrix uh the S Matrix will not be just
+
+ align:start position:0%
+Matrix uh the S Matrix will not be just
+ 
+
+ align:start position:0%
+Matrix uh the S Matrix will not be just
+2 by two but will be uh 2 + r because y
+
+ align:start position:0%
+2 by two but will be uh 2 + r because y
+ 
+
+ align:start position:0%
+2 by two but will be uh 2 + r because y
+also also can change all the
+
+ align:start position:0%
+also also can change all the
+ 
+
+ align:start position:0%
+also also can change all the
+constituents and if the our constituents
+
+ align:start position:0%
+constituents and if the our constituents
+ 
+
+ align:start position:0%
+constituents and if the our constituents
+is like a 2X two 2+ R by 2+ R so it's
+
+ align:start position:0%
+is like a 2X two 2+ R by 2+ R so it's
+ 
+
+ align:start position:0%
+is like a 2X two 2+ R by 2+ R so it's
+this Matrix that we have already
+
+ align:start position:0%
+this Matrix that we have already
+ 
+
+ align:start position:0%
+this Matrix that we have already
+anticipated a while
+
+ align:start position:0%
+anticipated a while
+ 
+
+ align:start position:0%
+anticipated a while
+ago and uh this therefore
+
+ align:start position:0%
+ago and uh this therefore
+ 
+
+ align:start position:0%
+ago and uh this therefore
+proves uh I mean here the details here
+
+ align:start position:0%
+proves uh I mean here the details here
+ 
+
+ align:start position:0%
+proves uh I mean here the details here
+prove in more detail
+
+ align:start position:0%
+prove in more detail
+ 
+
+ align:start position:0%
+prove in more detail
+also these expression that we had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anticipated but you can also choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since now you you are you think that you
+
+ align:start position:0%
+since now you you are you think that you
+ 
+
+ align:start position:0%
+since now you you are you think that you
+are in a in a the mutual equilibrium
+
+ align:start position:0%
+are in a in a the mutual equilibrium
+ 
+
+ align:start position:0%
+are in a in a the mutual equilibrium
+State and then you can move your
+
+ align:start position:0%
+State and then you can move your
+ 
+
+ align:start position:0%
+State and then you can move your
+State uh in various
+
+ align:start position:0%
+State uh in various
+ 
+
+ align:start position:0%
+State uh in various
+directions and one
+
+ align:start position:0%
+directions and one
+ 
+
+ align:start position:0%
+directions and one
+way is that
+
+ align:start position:0%
+way is that
+ 
+
+ align:start position:0%
+way is that
+you choose another
+
+ align:start position:0%
+you choose another
+ 
+
+ align:start position:0%
+you choose another
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+that has still has the same temperature
+
+ align:start position:0%
+that has still has the same temperature
+ 
+
+ align:start position:0%
+that has still has the same temperature
+pressure of your reservo but you change
+
+ align:start position:0%
+pressure of your reservo but you change
+ 
+
+ align:start position:0%
+pressure of your reservo but you change
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+amount so you choose to move away from
+
+ align:start position:0%
+amount so you choose to move away from
+ 
+
+ align:start position:0%
+amount so you choose to move away from
+Mutual
+
+ align:start position:0%
+Mutual
+ 
+
+ align:start position:0%
+Mutual
+equilibrium because the conditions for
+
+ align:start position:0%
+equilibrium because the conditions for
+ 
+
+ align:start position:0%
+equilibrium because the conditions for
+Mutual equilibrium with res is not only
+
+ align:start position:0%
+Mutual equilibrium with res is not only
+ 
+
+ align:start position:0%
+Mutual equilibrium with res is not only
+now that it can exchange not only energy
+
+ align:start position:0%
+now that it can exchange not only energy
+ 
+
+ align:start position:0%
+now that it can exchange not only energy
+but also amounts it's not only the
+
+ align:start position:0%
+but also amounts it's not only the
+ 
+
+ align:start position:0%
+but also amounts it's not only the
+temperature equality it's also the
+
+ align:start position:0%
+temperature equality it's also the
+ 
+
+ align:start position:0%
+temperature equality it's also the
+pressure equality for the volume change
+
+ align:start position:0%
+pressure equality for the volume change
+ 
+
+ align:start position:0%
+pressure equality for the volume change
+and the chemical potentials or chemical
+
+ align:start position:0%
+and the chemical potentials or chemical
+ 
+
+ align:start position:0%
+and the chemical potentials or chemical
+potential so I can move away from Mutual
+
+ align:start position:0%
+potential so I can move away from Mutual
+ 
+
+ align:start position:0%
+potential so I can move away from Mutual
+equilibrium while keeping some of the
+
+ align:start position:0%
+equilibrium while keeping some of the
+ 
+
+ align:start position:0%
+equilibrium while keeping some of the
+mutual equilibrium conditions satisfied
+
+ align:start position:0%
+mutual equilibrium conditions satisfied
+ 
+
+ align:start position:0%
+mutual equilibrium conditions satisfied
+like same temperature and same pressure
+
+ align:start position:0%
+like same temperature and same pressure
+ 
+
+ align:start position:0%
+like same temperature and same pressure
+and moving only the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amounts if you do that and move along uh
+
+ align:start position:0%
+amounts if you do that and move along uh
+ 
+
+ align:start position:0%
+amounts if you do that and move along uh
+the stable equilibrium State surface
+
+ align:start position:0%
+the stable equilibrium State surface
+ 
+
+ align:start position:0%
+the stable equilibrium State surface
+constant temperature and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure uh the condition that Delta uh
+
+ align:start position:0%
+pressure uh the condition that Delta uh
+ 
+
+ align:start position:0%
+pressure uh the condition that Delta uh
+that that uh this um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oiler uh availability
+
+ align:start position:0%
+Oiler uh availability
+ 
+
+ align:start position:0%
+Oiler uh availability
+function must increase along that
+
+ align:start position:0%
+function must increase along that
+ 
+
+ align:start position:0%
+function must increase along that
+path turns out to be the change in this
+
+ align:start position:0%
+path turns out to be the change in this
+ 
+
+ align:start position:0%
+path turns out to be the change in this
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+side is uh equal to the second
+
+ align:start position:0%
+side is uh equal to the second
+ 
+
+ align:start position:0%
+side is uh equal to the second
+differential of the Gibs free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy you you can prove it by
+
+ align:start position:0%
+energy you you can prove it by
+ 
+
+ align:start position:0%
+energy you you can prove it by
+remembering that the
+
+ align:start position:0%
+remembering that the
+ 
+
+ align:start position:0%
+remembering that the
+the Gibs V energy is e minus s minus TR
+
+ align:start position:0%
+the Gibs V energy is e minus s minus TR
+ 
+
+ align:start position:0%
+the Gibs V energy is e minus s minus TR
+and here TR and PR remain remain
+
+ align:start position:0%
+and here TR and PR remain remain
+ 
+
+ align:start position:0%
+and here TR and PR remain remain
+constant so it it remains
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defined so this proves that um the
+
+ align:start position:0%
+defined so this proves that um the
+ 
+
+ align:start position:0%
+defined so this proves that um the
+Gibs free
+
+ align:start position:0%
+Gibs free
+ 
+
+ align:start position:0%
+Gibs free
+energy as a minimum if you move so the
+
+ align:start position:0%
+energy as a minimum if you move so the
+ 
+
+ align:start position:0%
+energy as a minimum if you move so the
+second differential is non negative yes
+
+ align:start position:0%
+second differential is non negative yes
+ 
+
+ align:start position:0%
+second differential is non negative yes
+it's is non negative h if you move at
+
+ align:start position:0%
+it's is non negative h if you move at
+ 
+
+ align:start position:0%
+it's is non negative h if you move at
+con if you change the composition at
+
+ align:start position:0%
+con if you change the composition at
+ 
+
+ align:start position:0%
+con if you change the composition at
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tnp if you keep only temperature fixed
+
+ align:start position:0%
+tnp if you keep only temperature fixed
+ 
+
+ align:start position:0%
+tnp if you keep only temperature fixed
+and change the volume instead of keeping
+
+ align:start position:0%
+and change the volume instead of keeping
+ 
+
+ align:start position:0%
+and change the volume instead of keeping
+the pressure constant you get a similar
+
+ align:start position:0%
+the pressure constant you get a similar
+ 
+
+ align:start position:0%
+the pressure constant you get a similar
+relation this is not the givs free
+
+ align:start position:0%
+relation this is not the givs free
+ 
+
+ align:start position:0%
+relation this is not the givs free
+energy it's the elol free
+
+ align:start position:0%
+energy it's the elol free
+ 
+
+ align:start position:0%
+energy it's the elol free
+energy at constant t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so remember that we have seen
+
+ align:start position:0%
+okay so remember that we have seen
+ 
+
+ align:start position:0%
+okay so remember that we have seen
+the that from these conditions here we
+
+ align:start position:0%
+the that from these conditions here we
+ 
+
+ align:start position:0%
+the that from these conditions here we
+obtain first part of the brown
+
+ align:start position:0%
+obtain first part of the brown
+ 
+
+ align:start position:0%
+obtain first part of the brown
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+yes another little piece of math sorry
+
+ align:start position:0%
+yes another little piece of math sorry
+ 
+
+ align:start position:0%
+yes another little piece of math sorry
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+but that will get us to the second part
+
+ align:start position:0%
+but that will get us to the second part
+ 
+
+ align:start position:0%
+but that will get us to the second part
+of the chatellier brown principle so it
+
+ align:start position:0%
+of the chatellier brown principle so it
+ 
+
+ align:start position:0%
+of the chatellier brown principle so it
+is which is a more General uh
+
+ align:start position:0%
+is which is a more General uh
+ 
+
+ align:start position:0%
+is which is a more General uh
+statement
+
+ align:start position:0%
+statement
+ 
+
+ align:start position:0%
+statement
+which requires a little um uh brush
+
+ align:start position:0%
+which requires a little um uh brush
+ 
+
+ align:start position:0%
+which requires a little um uh brush
+up or maybe first time you see
+
+ align:start position:0%
+up or maybe first time you see
+ 
+
+ align:start position:0%
+up or maybe first time you see
+math
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so let's say we have a function
+
+ align:start position:0%
+uh so let's say we have a function
+ 
+
+ align:start position:0%
+uh so let's say we have a function
+for of two variables I put also the the
+
+ align:start position:0%
+for of two variables I put also the the
+ 
+
+ align:start position:0%
+for of two variables I put also the the
+other Z here just to say that the z's
+
+ align:start position:0%
+other Z here just to say that the z's
+ 
+
+ align:start position:0%
+other Z here just to say that the z's
+are going to be constant so I have
+
+ align:start position:0%
+are going to be constant so I have
+ 
+
+ align:start position:0%
+are going to be constant so I have
+several variables but I
+
+ align:start position:0%
+several variables but I
+ 
+
+ align:start position:0%
+several variables but I
+keep a constant all except two of them
+
+ align:start position:0%
+keep a constant all except two of them
+ 
+
+ align:start position:0%
+keep a constant all except two of them
+which are X and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y and then for example I have that
+
+ align:start position:0%
+Y and then for example I have that
+ 
+
+ align:start position:0%
+Y and then for example I have that
+function I can write the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differential so that's the partial of a
+
+ align:start position:0%
+differential so that's the partial of a
+ 
+
+ align:start position:0%
+differential so that's the partial of a
+with respect to X
+
+ align:start position:0%
+with respect to X
+ 
+
+ align:start position:0%
+with respect to X
+time DX times the partial of a with
+
+ align:start position:0%
+time DX times the partial of a with
+ 
+
+ align:start position:0%
+time DX times the partial of a with
+respect to y * d y I'm going to use the
+
+ align:start position:0%
+respect to y * d y I'm going to use the
+ 
+
+ align:start position:0%
+respect to y * d y I'm going to use the
+notation comma X for partial with
+
+ align:start position:0%
+notation comma X for partial with
+ 
+
+ align:start position:0%
+notation comma X for partial with
+respect to X which is often used like in
+
+ align:start position:0%
+respect to X which is often used like in
+ 
+
+ align:start position:0%
+respect to X which is often used like in
+fluid mechanics so maybe you've seen it
+
+ align:start position:0%
+fluid mechanics so maybe you've seen it
+ 
+
+ align:start position:0%
+fluid mechanics so maybe you've seen it
+already or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elsewhere and for example comma X is the
+
+ align:start position:0%
+elsewhere and for example comma X is the
+ 
+
+ align:start position:0%
+elsewhere and for example comma X is the
+second derivative with respect to X
+
+ align:start position:0%
+second derivative with respect to X
+ 
+
+ align:start position:0%
+second derivative with respect to X
+twice uh comma XY is the derivative of
+
+ align:start position:0%
+twice uh comma XY is the derivative of
+ 
+
+ align:start position:0%
+twice uh comma XY is the derivative of
+uh with respect to X and with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y
+
+ align:start position:0%
+Y
+ 
+
+ align:start position:0%
+Y
+okay so this is the partial derivative
+
+ align:start position:0%
+okay so this is the partial derivative
+ 
+
+ align:start position:0%
+okay so this is the partial derivative
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+X and here's the full Glory of uh the um
+
+ align:start position:0%
+X and here's the full Glory of uh the um
+ 
+
+ align:start position:0%
+X and here's the full Glory of uh the um
+representation of that
+
+ align:start position:0%
+representation of that
+ 
+
+ align:start position:0%
+representation of that
+derivatives uh where where the subs as
+
+ align:start position:0%
+derivatives uh where where the subs as
+ 
+
+ align:start position:0%
+derivatives uh where where the subs as
+you remember mean the other variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the original function that you're
+
+ align:start position:0%
+of the original function that you're
+ 
+
+ align:start position:0%
+of the original function that you're
+taking the deriv the partial derivative
+
+ align:start position:0%
+taking the deriv the partial derivative
+ 
+
+ align:start position:0%
+taking the deriv the partial derivative
+of okay
+
+ align:start position:0%
+of okay
+ 
+
+ align:start position:0%
+of okay
+good then we
+
+ align:start position:0%
+good then we
+ 
+
+ align:start position:0%
+good then we
+have like we've seen there for d2s
+
+ align:start position:0%
+have like we've seen there for d2s
+ 
+
+ align:start position:0%
+have like we've seen there for d2s
+here's
+
+ align:start position:0%
+here's
+ 
+
+ align:start position:0%
+here's
+D2 of this variable
+
+ align:start position:0%
+D2 of this variable
+ 
+
+ align:start position:0%
+D2 of this variable
+a can think of s but it could be also
+
+ align:start position:0%
+a can think of s but it could be also
+ 
+
+ align:start position:0%
+a can think of s but it could be also
+others like the gifts fre energy or or
+
+ align:start position:0%
+others like the gifts fre energy or or
+ 
+
+ align:start position:0%
+others like the gifts fre energy or or
+the elos free energy or whatever you
+
+ align:start position:0%
+the elos free energy or whatever you
+ 
+
+ align:start position:0%
+the elos free energy or whatever you
+need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is the quadratic
+
+ align:start position:0%
+and this is the quadratic
+ 
+
+ align:start position:0%
+and this is the quadratic
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+that represents the explicit
+
+ align:start position:0%
+that represents the explicit
+ 
+
+ align:start position:0%
+that represents the explicit
+form of the
+
+ align:start position:0%
+form of the
+ 
+
+ align:start position:0%
+form of the
+uh second or
+
+ align:start position:0%
+uh second or
+ 
+
+ align:start position:0%
+uh second or
+differential okay so now that we have a
+
+ align:start position:0%
+differential okay so now that we have a
+ 
+
+ align:start position:0%
+differential okay so now that we have a
+quadratic
+
+ align:start position:0%
+quadratic
+ 
+
+ align:start position:0%
+quadratic
+form the trick is to put it in the
+
+ align:start position:0%
+form the trick is to put it in the
+ 
+
+ align:start position:0%
+form the trick is to put it in the
+so-called canonical form because you see
+
+ align:start position:0%
+so-called canonical form because you see
+ 
+
+ align:start position:0%
+so-called canonical form because you see
+this quadratic
+
+ align:start position:0%
+this quadratic
+ 
+
+ align:start position:0%
+this quadratic
+form has a square here a square there
+
+ align:start position:0%
+form has a square here a square there
+ 
+
+ align:start position:0%
+form has a square here a square there
+and then it has a product DX
+
+ align:start position:0%
+and then it has a product DX
+ 
+
+ align:start position:0%
+and then it has a product DX
+Dy this isn't doesn't have a a definite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign
+
+ align:start position:0%
+sign
+ 
+
+ align:start position:0%
+sign
+but let's try to rewrite this quadratic
+
+ align:start position:0%
+but let's try to rewrite this quadratic
+ 
+
+ align:start position:0%
+but let's try to rewrite this quadratic
+form into a form in which you have
+
+ align:start position:0%
+form into a form in which you have
+ 
+
+ align:start position:0%
+form into a form in which you have
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+squared and uh Dy squared so a
+
+ align:start position:0%
+squared and uh Dy squared so a
+ 
+
+ align:start position:0%
+squared and uh Dy squared so a
+combination of DX and Dy proper
+
+ align:start position:0%
+combination of DX and Dy proper
+ 
+
+ align:start position:0%
+combination of DX and Dy proper
+combinate if you choose a proper
+
+ align:start position:0%
+combinate if you choose a proper
+ 
+
+ align:start position:0%
+combinate if you choose a proper
+combination of DX and D
+
+ align:start position:0%
+combination of DX and D
+ 
+
+ align:start position:0%
+combination of DX and D
+y uh and this is the proper combination
+
+ align:start position:0%
+y uh and this is the proper combination
+ 
+
+ align:start position:0%
+y uh and this is the proper combination
+I already built in the the answer so you
+
+ align:start position:0%
+I already built in the the answer so you
+ 
+
+ align:start position:0%
+I already built in the the answer so you
+if you want to check it you just
+
+ align:start position:0%
+if you want to check it you just
+ 
+
+ align:start position:0%
+if you want to check it you just
+substitute if you if you take this
+
+ align:start position:0%
+substitute if you if you take this
+ 
+
+ align:start position:0%
+substitute if you if you take this
+expression and work it out you will
+
+ align:start position:0%
+expression and work it out you will
+ 
+
+ align:start position:0%
+expression and work it out you will
+prove to yourself that it's equivalent
+
+ align:start position:0%
+prove to yourself that it's equivalent
+ 
+
+ align:start position:0%
+prove to yourself that it's equivalent
+to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and this ratio this coefficient here
+
+ align:start position:0%
+one and this ratio this coefficient here
+ 
+
+ align:start position:0%
+one and this ratio this coefficient here
+is the ratio
+
+ align:start position:0%
+is the ratio
+ 
+
+ align:start position:0%
+is the ratio
+of uh the second derivative with respect
+
+ align:start position:0%
+of uh the second derivative with respect
+ 
+
+ align:start position:0%
+of uh the second derivative with respect
+to XY and divided by the second
+
+ align:start position:0%
+to XY and divided by the second
+ 
+
+ align:start position:0%
+to XY and divided by the second
+derivative respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xx and then you find if you substitute
+
+ align:start position:0%
+xx and then you find if you substitute
+ 
+
+ align:start position:0%
+xx and then you find if you substitute
+by comparison you find that what you
+
+ align:start position:0%
+by comparison you find that what you
+ 
+
+ align:start position:0%
+by comparison you find that what you
+need to put in front of the Dy squ is
+
+ align:start position:0%
+need to put in front of the Dy squ is
+ 
+
+ align:start position:0%
+need to put in front of the Dy squ is
+this Lambda which is not sorry that I
+
+ align:start position:0%
+this Lambda which is not sorry that I
+ 
+
+ align:start position:0%
+this Lambda which is not sorry that I
+used Lambda here it's not the a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values but this
+
+ align:start position:0%
+values but this
+ 
+
+ align:start position:0%
+values but this
+Lambda is given by this
+
+ align:start position:0%
+Lambda is given by this
+ 
+
+ align:start position:0%
+Lambda is given by this
+expression again terms of the
+
+ align:start position:0%
+expression again terms of the
+ 
+
+ align:start position:0%
+expression again terms of the
+original you can do it in this way where
+
+ align:start position:0%
+original you can do it in this way where
+ 
+
+ align:start position:0%
+original you can do it in this way where
+in your summation you get you keep the
+
+ align:start position:0%
+in your summation you get you keep the
+ 
+
+ align:start position:0%
+in your summation you get you keep the
+square of the Y squared or you can do it
+
+ align:start position:0%
+square of the Y squared or you can do it
+ 
+
+ align:start position:0%
+square of the Y squared or you can do it
+also in this other way this is another
+
+ align:start position:0%
+also in this other way this is another
+ 
+
+ align:start position:0%
+also in this other way this is another
+canonical form in which you keep the X
+
+ align:start position:0%
+canonical form in which you keep the X
+ 
+
+ align:start position:0%
+canonical form in which you keep the X
+squar they
+
+ align:start position:0%
+squar they
+ 
+
+ align:start position:0%
+squar they
+are two equivalent
+
+ align:start position:0%
+are two equivalent
+ 
+
+ align:start position:0%
+are two equivalent
+ways of course here the Lambda is
+
+ align:start position:0%
+ways of course here the Lambda is
+ 
+
+ align:start position:0%
+ways of course here the Lambda is
+different than the Lambda X is given by
+
+ align:start position:0%
+different than the Lambda X is given by
+ 
+
+ align:start position:0%
+different than the Lambda X is given by
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now do I have more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+now let's look at
+
+ align:start position:0%
+now let's look at
+ 
+
+ align:start position:0%
+now let's look at
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+suppose that our function a is such that
+
+ align:start position:0%
+suppose that our function a is such that
+ 
+
+ align:start position:0%
+suppose that our function a is such that
+it's uh second differential must be
+
+ align:start position:0%
+it's uh second differential must be
+ 
+
+ align:start position:0%
+it's uh second differential must be
+positive okay
+
+ align:start position:0%
+positive okay
+ 
+
+ align:start position:0%
+positive okay
+so positive
+
+ align:start position:0%
+so positive
+ 
+
+ align:start position:0%
+so positive
+means that this Matrix is positive
+
+ align:start position:0%
+means that this Matrix is positive
+ 
+
+ align:start position:0%
+means that this Matrix is positive
+definite or semide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definite and as as we remember yeah I
+
+ align:start position:0%
+definite and as as we remember yeah I
+ 
+
+ align:start position:0%
+definite and as as we remember yeah I
+took away the wrong so if we
+
+ align:start position:0%
+took away the wrong so if we
+ 
+
+ align:start position:0%
+took away the wrong so if we
+remember uh positive definite for a
+
+ align:start position:0%
+remember uh positive definite for a
+ 
+
+ align:start position:0%
+remember uh positive definite for a
+matrix imply
+
+ align:start position:0%
+matrix imply
+ 
+
+ align:start position:0%
+matrix imply
+all these things are
+
+ align:start position:0%
+all these things are
+ 
+
+ align:start position:0%
+all these things are
+positive or non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative so we have to have that
+
+ align:start position:0%
+negative so we have to have that
+ 
+
+ align:start position:0%
+negative so we have to have that
+axx is greater than
+
+ align:start position:0%
+axx is greater than
+ 
+
+ align:start position:0%
+axx is greater than
+zero and in fact here that's what I have
+
+ align:start position:0%
+zero and in fact here that's what I have
+ 
+
+ align:start position:0%
+zero and in fact here that's what I have
+written
+
+ align:start position:0%
+written
+ 
+
+ align:start position:0%
+written
+axx is greater than zero it's greater
+
+ align:start position:0%
+axx is greater than zero it's greater
+ 
+
+ align:start position:0%
+axx is greater than zero it's greater
+than something else is greater than zero
+
+ align:start position:0%
+than something else is greater than zero
+ 
+
+ align:start position:0%
+than something else is greater than zero
+and also a y I is greater than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+but here we have written also something
+
+ align:start position:0%
+but here we have written also something
+ 
+
+ align:start position:0%
+but here we have written also something
+more strong than
+
+ align:start position:0%
+more strong than
+ 
+
+ align:start position:0%
+more strong than
+that we have written that a XX or a y y
+
+ align:start position:0%
+that we have written that a XX or a y y
+ 
+
+ align:start position:0%
+that we have written that a XX or a y y
+is greater than
+
+ align:start position:0%
+is greater than
+ 
+
+ align:start position:0%
+is greater than
+Lambda let's
+
+ align:start position:0%
+Lambda let's
+ 
+
+ align:start position:0%
+Lambda let's
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+um the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda uh
+
+ align:start position:0%
+Lambda uh
+ 
+
+ align:start position:0%
+Lambda uh
+Tai yeah I can write it
+
+ align:start position:0%
+Tai yeah I can write it
+ 
+
+ align:start position:0%
+Tai yeah I can write it
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+um see for example Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y let me rewrite it uh this way uh it
+
+ align:start position:0%
+y let me rewrite it uh this way uh it
+ 
+
+ align:start position:0%
+y let me rewrite it uh this way uh it
+has that the
+
+ align:start position:0%
+has that the
+ 
+
+ align:start position:0%
+has that the
+denominator a xx
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squ and at the denominate I'm sorry at
+
+ align:start position:0%
+squ and at the denominate I'm sorry at
+ 
+
+ align:start position:0%
+squ and at the denominate I'm sorry at
+the yeah denominator there and numerator
+
+ align:start position:0%
+the yeah denominator there and numerator
+ 
+
+ align:start position:0%
+the yeah denominator there and numerator
+a XX time
+
+ align:start position:0%
+a XX time
+ 
+
+ align:start position:0%
+a XX time
+a y
+
+ align:start position:0%
+a y
+ 
+
+ align:start position:0%
+a y
+y minus a
+
+ align:start position:0%
+y minus a
+ 
+
+ align:start position:0%
+y minus a
+XY
+
+ align:start position:0%
+XY
+ 
+
+ align:start position:0%
+XY
+squar that is the
+
+ align:start position:0%
+squar that is the
+ 
+
+ align:start position:0%
+squar that is the
+determinant of the S
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numerator
+
+ align:start position:0%
+numerator
+ 
+
+ align:start position:0%
+numerator
+so since the Matrix is positive the
+
+ align:start position:0%
+so since the Matrix is positive the
+ 
+
+ align:start position:0%
+so since the Matrix is positive the
+numerator is positive the denominator is
+
+ align:start position:0%
+numerator is positive the denominator is
+ 
+
+ align:start position:0%
+numerator is positive the denominator is
+positive so this is also
+
+ align:start position:0%
+positive so this is also
+ 
+
+ align:start position:0%
+positive so this is also
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+okay so Lambda so this explains why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda uh you can do that for y but also
+
+ align:start position:0%
+Lambda uh you can do that for y but also
+ 
+
+ align:start position:0%
+Lambda uh you can do that for y but also
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+x uh the lambdas are also non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative and now you can also see here y
+
+ align:start position:0%
+negative and now you can also see here y
+ 
+
+ align:start position:0%
+negative and now you can also see here y
+Lambda uh for example Lambda
+
+ align:start position:0%
+Lambda uh for example Lambda
+ 
+
+ align:start position:0%
+Lambda uh for example Lambda
+Y is smaller than a y y because you look
+
+ align:start position:0%
+Y is smaller than a y y because you look
+ 
+
+ align:start position:0%
+Y is smaller than a y y because you look
+look here this is lamb this is a and
+
+ align:start position:0%
+look here this is lamb this is a and
+ 
+
+ align:start position:0%
+look here this is lamb this is a and
+then you subtract something
+
+ align:start position:0%
+then you subtract something
+ 
+
+ align:start position:0%
+then you subtract something
+positive so if if you from a you
+
+ align:start position:0%
+positive so if if you from a you
+ 
+
+ align:start position:0%
+positive so if if you from a you
+subtract something positive it means
+
+ align:start position:0%
+subtract something positive it means
+ 
+
+ align:start position:0%
+subtract something positive it means
+that Lambda is smaller than a i a y
+
+ align:start position:0%
+that Lambda is smaller than a i a y
+ 
+
+ align:start position:0%
+that Lambda is smaller than a i a y
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+okay all right so this is the
+
+ align:start position:0%
+okay all right so this is the
+ 
+
+ align:start position:0%
+okay all right so this is the
+mathematics that uh
+
+ align:start position:0%
+mathematics that uh
+ 
+
+ align:start position:0%
+mathematics that uh
+stands uh that supports that stands
+
+ align:start position:0%
+stands uh that supports that stands
+ 
+
+ align:start position:0%
+stands uh that supports that stands
+behind the um the next the The Brown
+
+ align:start position:0%
+behind the um the next the The Brown
+ 
+
+ align:start position:0%
+behind the um the next the The Brown
+principle that we're going to do in a
+
+ align:start position:0%
+principle that we're going to do in a
+ 
+
+ align:start position:0%
+principle that we're going to do in a
+second of course you can do exactly the
+
+ align:start position:0%
+second of course you can do exactly the
+ 
+
+ align:start position:0%
+second of course you can do exactly the
+same that I've done here
+
+ align:start position:0%
+same that I've done here
+ 
+
+ align:start position:0%
+same that I've done here
+for uh positive semide definite you can
+
+ align:start position:0%
+for uh positive semide definite you can
+ 
+
+ align:start position:0%
+for uh positive semide definite you can
+also do it for negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sem okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps help understanding uh
+
+ align:start position:0%
+steps help understanding uh
+ 
+
+ align:start position:0%
+steps help understanding uh
+the various steps on the previous
+
+ align:start position:0%
+the various steps on the previous
+ 
+
+ align:start position:0%
+the various steps on the previous
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slide and
+
+ align:start position:0%
+slide and
+ 
+
+ align:start position:0%
+slide and
+uh the bottom line is is here you can uh
+
+ align:start position:0%
+uh the bottom line is is here you can uh
+ 
+
+ align:start position:0%
+uh the bottom line is is here you can uh
+um rewrite that aou
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X it it this is equal to the
+
+ align:start position:0%
+X it it this is equal to the
+ 
+
+ align:start position:0%
+X it it this is equal to the
+partial of ax which is the conjugate
+
+ align:start position:0%
+partial of ax which is the conjugate
+ 
+
+ align:start position:0%
+partial of ax which is the conjugate
+potential to variable uh uh X so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah so suppose suppose our function
+
+ align:start position:0%
+um yeah so suppose suppose our function
+ 
+
+ align:start position:0%
+um yeah so suppose suppose our function
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+S and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S is a function of energy and so s e e
+
+ align:start position:0%
+S is a function of energy and so s e e
+ 
+
+ align:start position:0%
+S is a function of energy and so s e e
+which is the equivalent so our functions
+
+ align:start position:0%
+which is the equivalent so our functions
+ 
+
+ align:start position:0%
+which is the equivalent so our functions
+is the entropy and X variable is the
+
+ align:start position:0%
+is the entropy and X variable is the
+ 
+
+ align:start position:0%
+is the entropy and X variable is the
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+so s e e means partial of s with respect
+
+ align:start position:0%
+so s e e means partial of s with respect
+ 
+
+ align:start position:0%
+so s e e means partial of s with respect
+to e twice but since the partial of s
+
+ align:start position:0%
+to e twice but since the partial of s
+ 
+
+ align:start position:0%
+to e twice but since the partial of s
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+e is 1 / t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so this is equivalent also to the
+
+ align:start position:0%
+Okay so this is equivalent also to the
+ 
+
+ align:start position:0%
+Okay so this is equivalent also to the
+the you can write it
+
+ align:start position:0%
+the you can write it
+ 
+
+ align:start position:0%
+the you can write it
+as s comma e which is the inverse of the
+
+ align:start position:0%
+as s comma e which is the inverse of the
+ 
+
+ align:start position:0%
+as s comma e which is the inverse of the
+temperature the gain comma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e and of course you can do also the
+
+ align:start position:0%
+e and of course you can do also the
+ 
+
+ align:start position:0%
+e and of course you can do also the
+other uh like that so this is the
+
+ align:start position:0%
+other uh like that so this is the
+ 
+
+ align:start position:0%
+other uh like that so this is the
+meaning of partial of the a comma X
+
+ align:start position:0%
+meaning of partial of the a comma X
+ 
+
+ align:start position:0%
+meaning of partial of the a comma X
+again comma X done at constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y the point is
+
+ align:start position:0%
+y the point is
+ 
+
+ align:start position:0%
+y the point is
+that uh by doing this math here that I
+
+ align:start position:0%
+that uh by doing this math here that I
+ 
+
+ align:start position:0%
+that uh by doing this math here that I
+want to skip
+
+ align:start position:0%
+want to skip
+ 
+
+ align:start position:0%
+want to skip
+uh I have uh um I prove that the Lambda
+
+ align:start position:0%
+uh I have uh um I prove that the Lambda
+ 
+
+ align:start position:0%
+uh I have uh um I prove that the Lambda
+also the lambdas can be written as
+
+ align:start position:0%
+also the lambdas can be written as
+ 
+
+ align:start position:0%
+also the lambdas can be written as
+partials of um this potential so on the
+
+ align:start position:0%
+partials of um this potential so on the
+ 
+
+ align:start position:0%
+partials of um this potential so on the
+first derivative respect to X but not
+
+ align:start position:0%
+first derivative respect to X but not
+ 
+
+ align:start position:0%
+first derivative respect to X but not
+while keeping y constant y but but while
+
+ align:start position:0%
+while keeping y constant y but but while
+ 
+
+ align:start position:0%
+while keeping y constant y but but while
+keeping constant the other
+
+ align:start position:0%
+keeping constant the other
+ 
+
+ align:start position:0%
+keeping constant the other
+potential conjugated to
+
+ align:start position:0%
+potential conjugated to
+ 
+
+ align:start position:0%
+potential conjugated to
+Y okay
+
+ align:start position:0%
+Y okay
+ 
+
+ align:start position:0%
+Y okay
+so what changes in these two terms is
+
+ align:start position:0%
+so what changes in these two terms is
+ 
+
+ align:start position:0%
+so what changes in these two terms is
+what is kept constant here I keep
+
+ align:start position:0%
+what is kept constant here I keep
+ 
+
+ align:start position:0%
+what is kept constant here I keep
+constant y here I say I keep I keep
+
+ align:start position:0%
+constant y here I say I keep I keep
+ 
+
+ align:start position:0%
+constant y here I say I keep I keep
+constant the potential conjugated to
+
+ align:start position:0%
+constant the potential conjugated to
+ 
+
+ align:start position:0%
+constant the potential conjugated to
+Y and that's the
+
+ align:start position:0%
+Y and that's the
+ 
+
+ align:start position:0%
+Y and that's the
+key to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh to the the Practical uh consequences
+
+ align:start position:0%
+uh to the the Practical uh consequences
+ 
+
+ align:start position:0%
+uh to the the Practical uh consequences
+of these mathematics
+
+ align:start position:0%
+of these mathematics
+ 
+
+ align:start position:0%
+of these mathematics
+so for
+
+ align:start position:0%
+so for
+ 
+
+ align:start position:0%
+so for
+example let's change once more variable
+
+ align:start position:0%
+example let's change once more variable
+ 
+
+ align:start position:0%
+example let's change once more variable
+so that we you get uh a more confused
+
+ align:start position:0%
+so that we you get uh a more confused
+ 
+
+ align:start position:0%
+so that we you get uh a more confused
+but we just have five minutes so it's
+
+ align:start position:0%
+but we just have five minutes so it's
+ 
+
+ align:start position:0%
+but we just have five minutes so it's
+okay uh so we start from a function
+
+ align:start position:0%
+okay uh so we start from a function
+ 
+
+ align:start position:0%
+okay uh so we start from a function
+E from this fundamental relation this
+
+ align:start position:0%
+E from this fundamental relation this
+ 
+
+ align:start position:0%
+E from this fundamental relation this
+form of the fundamental
+
+ align:start position:0%
+form of the fundamental
+ 
+
+ align:start position:0%
+form of the fundamental
+relation keep the end fixed and look at
+
+ align:start position:0%
+relation keep the end fixed and look at
+ 
+
+ align:start position:0%
+relation keep the end fixed and look at
+what happens by applying what we've just
+
+ align:start position:0%
+what happens by applying what we've just
+ 
+
+ align:start position:0%
+what happens by applying what we've just
+seen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the train of inequalities that
+
+ align:start position:0%
+this is the train of inequalities that
+ 
+
+ align:start position:0%
+this is the train of inequalities that
+is implied by one of the forms by this
+
+ align:start position:0%
+is implied by one of the forms by this
+ 
+
+ align:start position:0%
+is implied by one of the forms by this
+form and by the second form is written
+
+ align:start position:0%
+form and by the second form is written
+ 
+
+ align:start position:0%
+form and by the second form is written
+here you can do the
+
+ align:start position:0%
+here you can do the
+ 
+
+ align:start position:0%
+here you can do the
+substitutions uh you see I put here what
+
+ align:start position:0%
+substitutions uh you see I put here what
+ 
+
+ align:start position:0%
+substitutions uh you see I put here what
+the variable X Y is what a subx a sub y
+
+ align:start position:0%
+the variable X Y is what a subx a sub y
+ 
+
+ align:start position:0%
+the variable X Y is what a subx a sub y
+called the temperature and the pressure
+
+ align:start position:0%
+called the temperature and the pressure
+ 
+
+ align:start position:0%
+called the temperature and the pressure
+in our case and here is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result now by the way by looking at
+
+ align:start position:0%
+result now by the way by looking at
+ 
+
+ align:start position:0%
+result now by the way by looking at
+these derivatives you find all friends
+
+ align:start position:0%
+these derivatives you find all friends
+ 
+
+ align:start position:0%
+these derivatives you find all friends
+and you can see that for example you can
+
+ align:start position:0%
+and you can see that for example you can
+ 
+
+ align:start position:0%
+and you can see that for example you can
+rewrite this as
+
+ align:start position:0%
+rewrite this as
+ 
+
+ align:start position:0%
+rewrite this as
+CP is greater than or equal to CV which
+
+ align:start position:0%
+CP is greater than or equal to CV which
+ 
+
+ align:start position:0%
+CP is greater than or equal to CV which
+is greater than equal to zero or that
+
+ align:start position:0%
+is greater than equal to zero or that
+ 
+
+ align:start position:0%
+is greater than equal to zero or that
+one the compressibility constant
+
+ align:start position:0%
+one the compressibility constant
+ 
+
+ align:start position:0%
+one the compressibility constant
+temperature is greater than a
+
+ align:start position:0%
+temperature is greater than a
+ 
+
+ align:start position:0%
+temperature is greater than a
+compressibility at constant
+
+ align:start position:0%
+compressibility at constant
+ 
+
+ align:start position:0%
+compressibility at constant
+entropy okay
+
+ align:start position:0%
+entropy okay
+ 
+
+ align:start position:0%
+entropy okay
+so what's the
+
+ align:start position:0%
+so what's the
+ 
+
+ align:start position:0%
+so what's the
+reading that the chatel brown
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does so what's the difference here
+
+ align:start position:0%
+does so what's the difference here
+ 
+
+ align:start position:0%
+does so what's the difference here
+between V the what is what is the
+
+ align:start position:0%
+between V the what is what is the
+ 
+
+ align:start position:0%
+between V the what is what is the
+difference between these two derivatives
+
+ align:start position:0%
+difference between these two derivatives
+ 
+
+ align:start position:0%
+difference between these two derivatives
+is what is kept
+
+ align:start position:0%
+is what is kept
+ 
+
+ align:start position:0%
+is what is kept
+constant I change the entropy and
+
+ align:start position:0%
+constant I change the entropy and
+ 
+
+ align:start position:0%
+constant I change the entropy and
+measure what temperature change
+
+ align:start position:0%
+measure what temperature change
+ 
+
+ align:start position:0%
+measure what temperature change
+occurs uh when I keep volume or when I
+
+ align:start position:0%
+occurs uh when I keep volume or when I
+ 
+
+ align:start position:0%
+occurs uh when I keep volume or when I
+keep uh pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixed you see
+
+ align:start position:0%
+fixed you see
+ 
+
+ align:start position:0%
+fixed you see
+volume
+
+ align:start position:0%
+volume
+ 
+
+ align:start position:0%
+volume
+is the original variable pressure is the
+
+ align:start position:0%
+is the original variable pressure is the
+ 
+
+ align:start position:0%
+is the original variable pressure is the
+conjugated potential it has to do with
+
+ align:start position:0%
+conjugated potential it has to do with
+ 
+
+ align:start position:0%
+conjugated potential it has to do with
+the tendency to escape uh to to to gain
+
+ align:start position:0%
+the tendency to escape uh to to to gain
+ 
+
+ align:start position:0%
+the tendency to escape uh to to to gain
+volume so minus pressure is the tendency
+
+ align:start position:0%
+volume so minus pressure is the tendency
+ 
+
+ align:start position:0%
+volume so minus pressure is the tendency
+to yield
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume so the the idea is that you know
+
+ align:start position:0%
+volume so the the idea is that you know
+ 
+
+ align:start position:0%
+volume so the the idea is that you know
+that the interpretation of these
+
+ align:start position:0%
+that the interpretation of these
+ 
+
+ align:start position:0%
+that the interpretation of these
+derivatives being positive is that the
+
+ align:start position:0%
+derivatives being positive is that the
+ 
+
+ align:start position:0%
+derivatives being positive is that the
+system uh reacts if you move it away
+
+ align:start position:0%
+system uh reacts if you move it away
+ 
+
+ align:start position:0%
+system uh reacts if you move it away
+from the mutual equilibrium state from
+
+ align:start position:0%
+from the mutual equilibrium state from
+ 
+
+ align:start position:0%
+from the mutual equilibrium state from
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+environment uh you add some entropy for
+
+ align:start position:0%
+environment uh you add some entropy for
+ 
+
+ align:start position:0%
+environment uh you add some entropy for
+example it will increase its temperature
+
+ align:start position:0%
+example it will increase its temperature
+ 
+
+ align:start position:0%
+example it will increase its temperature
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+positive so as to increase its uh
+
+ align:start position:0%
+positive so as to increase its uh
+ 
+
+ align:start position:0%
+positive so as to increase its uh
+uh tendency
+
+ align:start position:0%
+uh tendency
+ 
+
+ align:start position:0%
+uh tendency
+to return energy to contrast your change
+
+ align:start position:0%
+to return energy to contrast your change
+ 
+
+ align:start position:0%
+to return energy to contrast your change
+by giving energy giving energy away to
+
+ align:start position:0%
+by giving energy giving energy away to
+ 
+
+ align:start position:0%
+by giving energy giving energy away to
+your environment so the system responds
+
+ align:start position:0%
+your environment so the system responds
+ 
+
+ align:start position:0%
+your environment so the system responds
+by trying to uh spontaneously
+
+ align:start position:0%
+by trying to uh spontaneously
+ 
+
+ align:start position:0%
+by trying to uh spontaneously
+reestablish
+
+ align:start position:0%
+reestablish
+ 
+
+ align:start position:0%
+reestablish
+equilibrium but it does more
+
+ align:start position:0%
+equilibrium but it does more
+ 
+
+ align:start position:0%
+equilibrium but it does more
+so if you do it at constant volume than
+
+ align:start position:0%
+so if you do it at constant volume than
+ 
+
+ align:start position:0%
+so if you do it at constant volume than
+if you do it at constant pressure so the
+
+ align:start position:0%
+if you do it at constant pressure so the
+ 
+
+ align:start position:0%
+if you do it at constant pressure so the
+reaction of the system is
+
+ align:start position:0%
+reaction of the system is
+ 
+
+ align:start position:0%
+reaction of the system is
+stronger uh
+
+ align:start position:0%
+stronger uh
+ 
+
+ align:start position:0%
+stronger uh
+if if what so what's the difference the
+
+ align:start position:0%
+if if what so what's the difference the
+ 
+
+ align:start position:0%
+if if what so what's the difference the
+difference is that
+
+ align:start position:0%
+difference is that
+ 
+
+ align:start position:0%
+difference is that
+here the system as as a smaller reaction
+
+ align:start position:0%
+here the system as as a smaller reaction
+ 
+
+ align:start position:0%
+here the system as as a smaller reaction
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+keep keeping the pressure constant means
+
+ align:start position:0%
+keep keeping the pressure constant means
+ 
+
+ align:start position:0%
+keep keeping the pressure constant means
+means keeping your
+
+ align:start position:0%
+means keeping your
+ 
+
+ align:start position:0%
+means keeping your
+system uh in equilibrium with your res
+
+ align:start position:0%
+system uh in equilibrium with your res
+ 
+
+ align:start position:0%
+system uh in equilibrium with your res
+at least as for the condition that
+
+ align:start position:0%
+at least as for the condition that
+ 
+
+ align:start position:0%
+at least as for the condition that
+requires pressure equality so you're not
+
+ align:start position:0%
+requires pressure equality so you're not
+ 
+
+ align:start position:0%
+requires pressure equality so you're not
+touching that condition for Mutual
+
+ align:start position:0%
+touching that condition for Mutual
+ 
+
+ align:start position:0%
+touching that condition for Mutual
+equilibrium you're touching also some
+
+ align:start position:0%
+equilibrium you're touching also some
+ 
+
+ align:start position:0%
+equilibrium you're touching also some
+something else so if you if you do it
+
+ align:start position:0%
+something else so if you if you do it
+ 
+
+ align:start position:0%
+something else so if you if you do it
+there the system says all right well
+
+ align:start position:0%
+there the system says all right well
+ 
+
+ align:start position:0%
+there the system says all right well
+after all you're you're moving me away
+
+ align:start position:0%
+after all you're you're moving me away
+ 
+
+ align:start position:0%
+after all you're you're moving me away
+but not so much so its reaction is
+
+ align:start position:0%
+but not so much so its reaction is
+ 
+
+ align:start position:0%
+but not so much so its reaction is
+softer if you move it away so that also
+
+ align:start position:0%
+softer if you move it away so that also
+ 
+
+ align:start position:0%
+softer if you move it away so that also
+its pressure changes and therefore like
+
+ align:start position:0%
+its pressure changes and therefore like
+ 
+
+ align:start position:0%
+its pressure changes and therefore like
+you do when you keep the volume constant
+
+ align:start position:0%
+you do when you keep the volume constant
+ 
+
+ align:start position:0%
+you do when you keep the volume constant
+uh then it will U it will uh in in
+
+ align:start position:0%
+uh then it will U it will uh in in
+ 
+
+ align:start position:0%
+uh then it will U it will uh in in
+increase uh not
+
+ align:start position:0%
+increase uh not
+ 
+
+ align:start position:0%
+increase uh not
+only so essentially you are
+
+ align:start position:0%
+only so essentially you are
+ 
+
+ align:start position:0%
+only so essentially you are
+touching two conditions of Mutual
+
+ align:start position:0%
+touching two conditions of Mutual
+ 
+
+ align:start position:0%
+touching two conditions of Mutual
+equilibrium touching equality of
+
+ align:start position:0%
+equilibrium touching equality of
+ 
+
+ align:start position:0%
+equilibrium touching equality of
+temperature and touching equality of
+
+ align:start position:0%
+temperature and touching equality of
+ 
+
+ align:start position:0%
+temperature and touching equality of
+pressure and therefore the system reacts
+
+ align:start position:0%
+pressure and therefore the system reacts
+ 
+
+ align:start position:0%
+pressure and therefore the system reacts
+stronger wants more to come back to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium this is the uh this is the
+
+ align:start position:0%
+equilibrium this is the uh this is the
+ 
+
+ align:start position:0%
+equilibrium this is the uh this is the
+um uh the idea and since I wanted
+
+ align:start position:0%
+um uh the idea and since I wanted
+ 
+
+ align:start position:0%
+um uh the idea and since I wanted
+to to give me two more minutes I wanted
+
+ align:start position:0%
+to to give me two more minutes I wanted
+ 
+
+ align:start position:0%
+to to give me two more minutes I wanted
+to uh show you the uh
+
+ align:start position:0%
+to uh show you the uh
+ 
+
+ align:start position:0%
+to uh show you the uh
+application
+
+ align:start position:0%
+application
+ 
+
+ align:start position:0%
+application
+here you know uh this is an air spring
+
+ align:start position:0%
+here you know uh this is an air spring
+ 
+
+ align:start position:0%
+here you know uh this is an air spring
+so it's like a piston with air
+
+ align:start position:0%
+so it's like a piston with air
+ 
+
+ align:start position:0%
+so it's like a piston with air
+inside and it acts like a standard uh
+
+ align:start position:0%
+inside and it acts like a standard uh
+ 
+
+ align:start position:0%
+inside and it acts like a standard uh
+mechanical spring you can compute the
+
+ align:start position:0%
+mechanical spring you can compute the
+ 
+
+ align:start position:0%
+mechanical spring you can compute the
+spring
+
+ align:start position:0%
+spring
+ 
+
+ align:start position:0%
+spring
+constant and you here are the details
+
+ align:start position:0%
+constant and you here are the details
+ 
+
+ align:start position:0%
+constant and you here are the details
+it's kind of easy um mechanical
+
+ align:start position:0%
+it's kind of easy um mechanical
+ 
+
+ align:start position:0%
+it's kind of easy um mechanical
+engineering so to
+
+ align:start position:0%
+engineering so to
+ 
+
+ align:start position:0%
+engineering so to
+speak uh so the cake this uh K is the K
+
+ align:start position:0%
+speak uh so the cake this uh K is the K
+ 
+
+ align:start position:0%
+speak uh so the cake this uh K is the K
+the the spring constant that
+
+ align:start position:0%
+the the spring constant that
+ 
+
+ align:start position:0%
+the the spring constant that
+relates the increasing uh reaction or
+
+ align:start position:0%
+relates the increasing uh reaction or
+ 
+
+ align:start position:0%
+relates the increasing uh reaction or
+force of your spring to a change in its
+
+ align:start position:0%
+force of your spring to a change in its
+ 
+
+ align:start position:0%
+force of your spring to a change in its
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compression and this is also similar
+
+ align:start position:0%
+compression and this is also similar
+ 
+
+ align:start position:0%
+compression and this is also similar
+situation it this acts as a
+
+ align:start position:0%
+situation it this acts as a
+ 
+
+ align:start position:0%
+situation it this acts as a
+spring and you can
+
+ align:start position:0%
+spring and you can
+ 
+
+ align:start position:0%
+spring and you can
+compute uh DF over DX
+
+ align:start position:0%
+compute uh DF over DX
+ 
+
+ align:start position:0%
+compute uh DF over DX
+and uh if you do go down here you see
+
+ align:start position:0%
+and uh if you do go down here you see
+ 
+
+ align:start position:0%
+and uh if you do go down here you see
+it's related to how much the area little
+
+ align:start position:0%
+it's related to how much the area little
+ 
+
+ align:start position:0%
+it's related to how much the area little
+a of the Piston the
+
+ align:start position:0%
+a of the Piston the
+ 
+
+ align:start position:0%
+a of the Piston the
+volume and this thing as a denominator
+
+ align:start position:0%
+volume and this thing as a denominator
+ 
+
+ align:start position:0%
+volume and this thing as a denominator
+is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compressibility so you could have U so
+
+ align:start position:0%
+compressibility so you could have U so
+ 
+
+ align:start position:0%
+compressibility so you could have U so
+if you act your
+
+ align:start position:0%
+if you act your
+ 
+
+ align:start position:0%
+if you act your
+spring while keeping the temperature
+
+ align:start position:0%
+spring while keeping the temperature
+ 
+
+ align:start position:0%
+spring while keeping the temperature
+constant so if your spring uh is in
+
+ align:start position:0%
+constant so if your spring uh is in
+ 
+
+ align:start position:0%
+constant so if your spring uh is in
+contact with the th
+
+ align:start position:0%
+contact with the th
+ 
+
+ align:start position:0%
+contact with the th
+were and therefore it has the time to
+
+ align:start position:0%
+were and therefore it has the time to
+ 
+
+ align:start position:0%
+were and therefore it has the time to
+exchange energy to remain in mutual
+
+ align:start position:0%
+exchange energy to remain in mutual
+ 
+
+ align:start position:0%
+exchange energy to remain in mutual
+equilibrium which typically is when you
+
+ align:start position:0%
+equilibrium which typically is when you
+ 
+
+ align:start position:0%
+equilibrium which typically is when you
+push it but push it slow enough so that
+
+ align:start position:0%
+push it but push it slow enough so that
+ 
+
+ align:start position:0%
+push it but push it slow enough so that
+the system has time to uh exchange heat
+
+ align:start position:0%
+the system has time to uh exchange heat
+ 
+
+ align:start position:0%
+the system has time to uh exchange heat
+with the environment and remain in
+
+ align:start position:0%
+with the environment and remain in
+ 
+
+ align:start position:0%
+with the environment and remain in
+equilibrium then you get one spring
+
+ align:start position:0%
+equilibrium then you get one spring
+ 
+
+ align:start position:0%
+equilibrium then you get one spring
+constant If instead you push a spring
+
+ align:start position:0%
+constant If instead you push a spring
+ 
+
+ align:start position:0%
+constant If instead you push a spring
+fast like when the car goes on on a on a
+
+ align:start position:0%
+fast like when the car goes on on a on a
+ 
+
+ align:start position:0%
+fast like when the car goes on on a on a
+bump
+
+ align:start position:0%
+bump
+ 
+
+ align:start position:0%
+bump
+uh that the system doesn't have time to
+
+ align:start position:0%
+uh that the system doesn't have time to
+ 
+
+ align:start position:0%
+uh that the system doesn't have time to
+exchange energy or or heat and the
+
+ align:start position:0%
+exchange energy or or heat and the
+ 
+
+ align:start position:0%
+exchange energy or or heat and the
+entropy remains
+
+ align:start position:0%
+entropy remains
+ 
+
+ align:start position:0%
+entropy remains
+constant so that's the
+
+ align:start position:0%
+constant so that's the
+ 
+
+ align:start position:0%
+constant so that's the
+isothermal uh compress I'm sorry the
+
+ align:start position:0%
+isothermal uh compress I'm sorry the
+ 
+
+ align:start position:0%
+isothermal uh compress I'm sorry the
+isentropic compressibility that
+
+ align:start position:0%
+isentropic compressibility that
+ 
+
+ align:start position:0%
+isentropic compressibility that
+appears and so you see that the ratio of
+
+ align:start position:0%
+appears and so you see that the ratio of
+ 
+
+ align:start position:0%
+appears and so you see that the ratio of
+these two compress of these two uh spray
+
+ align:start position:0%
+these two compress of these two uh spray
+ 
+
+ align:start position:0%
+these two compress of these two uh spray
+constants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+equal to CP over C CV which for air is
+
+ align:start position:0%
+equal to CP over C CV which for air is
+ 
+
+ align:start position:0%
+equal to CP over C CV which for air is
+1.4 we just
+
+ align:start position:0%
+1.4 we just
+ 
+
+ align:start position:0%
+1.4 we just
+reviewed so that means that U if you act
+
+ align:start position:0%
+reviewed so that means that U if you act
+ 
+
+ align:start position:0%
+reviewed so that means that U if you act
+on the spring fast you get the spring
+
+ align:start position:0%
+on the spring fast you get the spring
+ 
+
+ align:start position:0%
+on the spring fast you get the spring
+constant that is 40% higher than if you
+
+ align:start position:0%
+constant that is 40% higher than if you
+ 
+
+ align:start position:0%
+constant that is 40% higher than if you
+act on the spring
+
+ align:start position:0%
+act on the spring
+ 
+
+ align:start position:0%
+act on the spring
+slow
+
+ align:start position:0%
+slow
+ 
+
+ align:start position:0%
+slow
+okay and these devices if you look up
+
+ align:start position:0%
+okay and these devices if you look up
+ 
+
+ align:start position:0%
+okay and these devices if you look up
+air Springs you see that there are uh
+
+ align:start position:0%
+air Springs you see that there are uh
+ 
+
+ align:start position:0%
+air Springs you see that there are uh
+it's an enormous business because as I
+
+ align:start position:0%
+it's an enormous business because as I
+ 
+
+ align:start position:0%
+it's an enormous business because as I
+said trains uh buses bicycles cars use
+
+ align:start position:0%
+said trains uh buses bicycles cars use
+ 
+
+ align:start position:0%
+said trains uh buses bicycles cars use
+spring constants combined also with The
+
+ align:start position:0%
+spring constants combined also with The
+ 
+
+ align:start position:0%
+spring constants combined also with The
+Dumping system to give you uh like um
+
+ align:start position:0%
+Dumping system to give you uh like um
+ 
+
+ align:start position:0%
+Dumping system to give you uh like um
+suspension systems that are uh allowed
+
+ align:start position:0%
+suspension systems that are uh allowed
+ 
+
+ align:start position:0%
+suspension systems that are uh allowed
+to absorb vibrations and make it uh more
+
+ align:start position:0%
+to absorb vibrations and make it uh more
+ 
+
+ align:start position:0%
+to absorb vibrations and make it uh more
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+comfortable Okay so sorry if I went a
+
+ align:start position:0%
+comfortable Okay so sorry if I went a
+ 
+
+ align:start position:0%
+comfortable Okay so sorry if I went a
+little bit uh late
\ No newline at end of file
diff --git a/qY0ixUWJx0g.txt b/qY0ixUWJx0g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..236dbddedc7211993971e30a1f6f8f59c5ff3a72
--- /dev/null
+++ b/qY0ixUWJx0g.txt
@@ -0,0 +1,460 @@
+PROFESSOR: Hello and
+welcome to the
+
+help session on pedigrees.
+
+Today, we will be working
+out a problem together.
+
+If you have not yet had a chance
+to work it on your own,
+
+please do so now, and
+return to this video
+
+when you are done.
+
+Now that you've had a chance to
+look at this problem, let's
+
+work it out together.
+
+The first part of this question
+asks, what is the
+
+mode of inheritance that is
+observed in this pedigree?
+
+So, we know that there are two
+main types of modes of
+
+inheritance.
+
+It can either be dominant
+or recessive.
+
+And from there it can either
+be autosomal or X-linked.
+
+If a disease follows a dominant
+inheritance pattern,
+
+generally, it must be present
+in every generation.
+
+So here we notice that the
+disease is present in the
+
+first generation, but it's not
+present in anyone in the
+
+second generation.
+
+However, then it reappears
+in the third generation.
+
+This suggests that the
+disease is recessive.
+
+So now, do we think
+this disease is
+
+autosomal or is it X-linked?
+
+So we look at the pedigree
+again, and upon closer
+
+inspection, we notice
+that the affected
+
+individuals are only males.
+
+This is a key characteristic
+of an
+
+X-linked recessive disease.
+
+However, we're also given more
+information that tells us that
+
+this individual here does not
+carry an allele associated
+
+with the affected phenotype.
+
+This rules out the possibility
+that this disease could be an
+
+autosomal recessive disease.
+
+Thus, the most likely mode of
+
+inheritance is X-linked recessive.
+
+Great, so moving on to the
+second part of this problem,
+
+we are asked to determine the
+genotypes of individuals
+
+number one and number three.
+
+So, if we look at this pedigree,
+we know individual
+
+one is female and not affected
+by the disease.
+
+Female individuals contain two
+X chromosomes, and since she
+
+is not affected she must contain
+at least one large R.
+
+So we'll call the allele
+associated with the
+
+disease small r.
+
+We do not yet know what her
+second X chromosome could be.
+
+It could be either another
+large R or it
+
+could be a small r.
+
+And she also would still not
+be affected by the disease.
+
+This male right here is affected
+by the disease.
+
+So he must have an
+X with a small r.
+
+Remember that males have one
+X chromosome and one Y
+
+chromosome.
+
+So now, making our way down to
+individual number three.
+
+Individual number three does
+not have the disease and is
+
+female, so again, must have
+two X chromosomes.
+
+One of the X chromosomes must
+come from her father and the
+
+other from her mother.
+
+The only X chromosome that her
+father can pass along to her
+
+is X small r.
+
+In order for her to not be
+affected with the disease, her
+
+other X chromosome must
+have a large R.
+
+She was able to get this
+genotype with her mother
+
+having either of these
+two genotypes.
+
+To make sure that both of these
+genotypes are possible
+
+for this mother, we need to
+examine her other children.
+
+Her son here is unaffected.
+
+So his genotype must have been
+X large R, Y. It's possible
+
+for him to get this genotype
+when the mother has either of
+
+these two genotypes.
+
+Similarly, this daughter could
+be unaffected just as this
+
+daughter was unaffected.
+
+So the mother can have either
+of these two genotypes.
+
+And we're unable to rule
+out one of them.
+
+So let me just write up
+the answer over here.
+
+All right, so far, so good.
+
+Next, we're asked to calculate
+the probability that
+
+individual A is affected.
+
+Individual A is over here at
+the bottom of the pedigree.
+
+In order for individual A to be
+affected, she must have the
+
+following genotype.
+
+The only way for her to get two
+little r's is for her to
+
+get one from her father and
+one from her mother.
+
+We know this is possible because
+her father is affected
+
+with the following genotype
+of Y, X small r.
+
+Her mother is not affected.
+
+So for her to get this small
+r, her mother must be a
+
+carrier for the disease,
+and have the genotype X
+
+large R, X small r.
+
+So in order to determine the
+probability that A is affected
+
+with both X small r's, we must
+also know the probability that
+
+her mother was a carrier
+for the disease.
+
+Let's call her mother
+individual C.
+
+So, we know the genotypes
+of her parents.
+
+Her mother was a carrier.
+
+And her father did not have the
+disease, so his genotype
+
+was Y with X large R. So to
+calculate the probability that
+
+individual C is a carrier for
+the disease, let's go back
+
+over here and draw out
+a Punnett square.
+
+On one side, we're going to
+write the genotype of her
+
+father, which was Y because
+he's a male.
+
+And then, he was not affected
+by the disease, so it was X
+
+with a large R. Her mother
+was a carrier.
+
+So she had one copy that was X
+large R, and one copy that was
+
+x little r.
+
+So next, we want to know
+the probability
+
+that she was a carrier.
+
+The only ways you can get
+females is by looking at this
+
+top row here.
+
+So, for now, we're going to
+ignore the bottom row.
+
+Of the two possible ways to
+generate a female, only one of
+
+them is a carrier.
+
+So there's a 50% chance that
+a female will be a carrier.
+
+So this is a 50% chance that
+individual C is a carrier,
+
+which we will denote with this
+half filled in circle.
+
+All right, so now that we know
+the probability that C was a
+
+carrier, we need to know the
+probability that her progeny,
+
+A, was affected with
+the disease.
+
+Again, looking back over here,
+her progeny needs to inherit
+
+the X small r from the
+mother and the X
+
+small r from the father.
+
+So, once again, we can draw
+a Punnett square to better
+
+understand this.
+
+Individual A's father
+was indeed
+
+affected by the disease.
+
+So his genotype was X small r
+and Y. Her mother, we just
+
+calculated the probability of
+her being a carrier, so she is
+
+X large R, X small r.
+
+Now, we're looking at individual
+A, who is a female,
+
+so again, we can ignore
+the bottom row because
+
+this will be males.
+
+Here are the progeny
+which are female.
+
+Of the two possibilities, only
+the one on the right, X small
+
+r, X small r is affected
+by the disease.
+
+So there is a 50% chance that
+A will be affected by the
+
+disease given that her mother
+is a carrier of the disease.
+
+Now to finish up this part of
+the problem, we need to
+
+multiply these two probabilities
+together because
+
+we're looking at the probability
+that C is a
+
+carrier, and the probability
+that A is
+
+affected with the disease.
+
+This gives us our answer
+of one fourth.
+
+All right, so, moving on to the
+last part of the problem.
+
+We need to calculate the
+probability that B is affected
+
+with the disease.
+
+So this isn't that hard now that
+we've drawn out all of
+
+these Punnett squares already.
+
+So, let's take a look back at
+our pedigree over here.
+
+If B is going to be affected
+with the disease, he must have
+
+the genotype Y, X
+with a small r.
+
+He gets the Y from his father
+and he must get this X with a
+
+small r from his mother.
+
+So again, we need the mother,
+C, to be a carrier.
+
+So let's go back to our Punnett
+squares over here.
+
+We know that there is
+a 50% chance that
+
+individual C is a carrier.
+
+Now we need to look at
+individual B being affected by
+
+the disease.
+
+So we can go ahead and fill
+in the bottom part of this
+
+Punnett square.
+
+So of these two males, that are
+possible, only one of them
+
+is affected with the disease.
+
+So again, there is a 50%
+probability that that child
+
+will be affected with
+the disease.
+
+Again, we are going
+to multiply these
+
+probabilities together.
+
+So the probability that the
+mother is a carrier, and that
+
+the son is affected with the
+disease, gives us one quarter.
+
+That concludes our problem
+on pedigrees.
+
+Thank you for joining us.
\ No newline at end of file
diff --git a/qw0pfuCu8q0.txt b/qw0pfuCu8q0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..246d2f33d405fe7812e3425d09ad52f2a4da00be
--- /dev/null
+++ b/qw0pfuCu8q0.txt
@@ -0,0 +1,9091 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common license. Your support
+
+ align:start position:0%
+a Creative Common license. Your support
+ 
+
+ align:start position:0%
+a Creative Common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's get started. Um, couple of
+
+ align:start position:0%
+Let's get started. Um, couple of
+ 
+
+ align:start position:0%
+Let's get started. Um, couple of
+announcements.
+
+ align:start position:0%
+announcements.
+ 
+
+ align:start position:0%
+announcements.
+Um reminder about the periodic table
+
+ align:start position:0%
+Um reminder about the periodic table
+ 
+
+ align:start position:0%
+Um reminder about the periodic table
+test which will uh be added next week on
+
+ align:start position:0%
+test which will uh be added next week on
+ 
+
+ align:start position:0%
+test which will uh be added next week on
+the 23rd. You can see the website if you
+
+ align:start position:0%
+the 23rd. You can see the website if you
+ 
+
+ align:start position:0%
+the 23rd. You can see the website if you
+want to download a a copy of this to
+
+ align:start position:0%
+want to download a a copy of this to
+ 
+
+ align:start position:0%
+want to download a a copy of this to
+practice on it. You're required only to
+
+ align:start position:0%
+practice on it. You're required only to
+ 
+
+ align:start position:0%
+practice on it. You're required only to
+put the one or two letter chemical
+
+ align:start position:0%
+put the one or two letter chemical
+ 
+
+ align:start position:0%
+put the one or two letter chemical
+abbreviation the symbol. Some people
+
+ align:start position:0%
+abbreviation the symbol. Some people
+ 
+
+ align:start position:0%
+abbreviation the symbol. Some people
+asked me if I wanted you to know the
+
+ align:start position:0%
+asked me if I wanted you to know the
+ 
+
+ align:start position:0%
+asked me if I wanted you to know the
+molecular weights and so on. And I um I
+
+ align:start position:0%
+molecular weights and so on. And I um I
+ 
+
+ align:start position:0%
+molecular weights and so on. And I um I
+thought that was a bit excessive. So, I
+
+ align:start position:0%
+thought that was a bit excessive. So, I
+ 
+
+ align:start position:0%
+thought that was a bit excessive. So, I
+think if you just know the symbols for
+
+ align:start position:0%
+think if you just know the symbols for
+ 
+
+ align:start position:0%
+think if you just know the symbols for
+the ones that are up there, that would
+
+ align:start position:0%
+the ones that are up there, that would
+ 
+
+ align:start position:0%
+the ones that are up there, that would
+be just that'd be just dandy. Um, here's
+
+ align:start position:0%
+be just that'd be just dandy. Um, here's
+ 
+
+ align:start position:0%
+be just that'd be just dandy. Um, here's
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh here's the lady's
+
+ align:start position:0%
+uh here's the lady's
+ 
+
+ align:start position:0%
+uh here's the lady's
+scarf. Very hot. Black. See trim lines
+
+ align:start position:0%
+scarf. Very hot. Black. See trim lines
+ 
+
+ align:start position:0%
+scarf. Very hot. Black. See trim lines
+and uh blue and gold. And it's got
+
+ align:start position:0%
+and uh blue and gold. And it's got
+ 
+
+ align:start position:0%
+and uh blue and gold. And it's got
+elements on it. Very hot. Very
+
+ align:start position:0%
+elements on it. Very hot. Very
+ 
+
+ align:start position:0%
+elements on it. Very hot. Very
+hot. There's a neck tie. Comparable
+
+ align:start position:0%
+hot. There's a neck tie. Comparable
+ 
+
+ align:start position:0%
+hot. There's a neck tie. Comparable
+fabric, comparable pattern. It's not
+
+ align:start position:0%
+fabric, comparable pattern. It's not
+ 
+
+ align:start position:0%
+fabric, comparable pattern. It's not
+geeky. This is very hot.
+
+ align:start position:0%
+geeky. This is very hot.
+ 
+
+ align:start position:0%
+geeky. This is very hot.
+You need you need this. You need this.
+
+ align:start position:0%
+You need you need this. You need this.
+ 
+
+ align:start position:0%
+You need you need this. You need this.
+Okay, let's get on with the lesson. Last
+
+ align:start position:0%
+Okay, let's get on with the lesson. Last
+ 
+
+ align:start position:0%
+Okay, let's get on with the lesson. Last
+day we looked at uh uh Rutherford Guyger
+
+ align:start position:0%
+day we looked at uh uh Rutherford Guyger
+ 
+
+ align:start position:0%
+day we looked at uh uh Rutherford Guyger
+Marsden and the experiment that they
+
+ align:start position:0%
+Marsden and the experiment that they
+ 
+
+ align:start position:0%
+Marsden and the experiment that they
+conducted on the gold foil and out of
+
+ align:start position:0%
+conducted on the gold foil and out of
+ 
+
+ align:start position:0%
+conducted on the gold foil and out of
+that came the uh recognition that
+
+ align:start position:0%
+that came the uh recognition that
+ 
+
+ align:start position:0%
+that came the uh recognition that
+Thompson's plum pudding model uh is not
+
+ align:start position:0%
+Thompson's plum pudding model uh is not
+ 
+
+ align:start position:0%
+Thompson's plum pudding model uh is not
+sustainable in the light of this
+
+ align:start position:0%
+sustainable in the light of this
+ 
+
+ align:start position:0%
+sustainable in the light of this
+evidence and instead Rutherford proposed
+
+ align:start position:0%
+evidence and instead Rutherford proposed
+ 
+
+ align:start position:0%
+evidence and instead Rutherford proposed
+something akin to a planetary system.
+
+ align:start position:0%
+something akin to a planetary system.
+ 
+
+ align:start position:0%
+something akin to a planetary system.
+And there's something uh I'd like you to
+
+ align:start position:0%
+And there's something uh I'd like you to
+ 
+
+ align:start position:0%
+And there's something uh I'd like you to
+be tuned into here. You know, people to
+
+ align:start position:0%
+be tuned into here. You know, people to
+ 
+
+ align:start position:0%
+be tuned into here. You know, people to
+this day are looking for a theory of
+
+ align:start position:0%
+this day are looking for a theory of
+ 
+
+ align:start position:0%
+this day are looking for a theory of
+everything. And there was something very
+
+ align:start position:0%
+everything. And there was something very
+ 
+
+ align:start position:0%
+everything. And there was something very
+appealing about the notion that the
+
+ align:start position:0%
+appealing about the notion that the
+ 
+
+ align:start position:0%
+appealing about the notion that the
+rules that govern the motion of heavenly
+
+ align:start position:0%
+rules that govern the motion of heavenly
+ 
+
+ align:start position:0%
+rules that govern the motion of heavenly
+bodies might be applicable down at uh
+
+ align:start position:0%
+bodies might be applicable down at uh
+ 
+
+ align:start position:0%
+bodies might be applicable down at uh
+atomic dimensions. So this is very uh
+
+ align:start position:0%
+atomic dimensions. So this is very uh
+ 
+
+ align:start position:0%
+atomic dimensions. So this is very uh
+you know cosmic you know there's a
+
+ align:start position:0%
+you know cosmic you know there's a
+ 
+
+ align:start position:0%
+you know cosmic you know there's a
+gestalt here. So uh we ended the day
+
+ align:start position:0%
+gestalt here. So uh we ended the day
+ 
+
+ align:start position:0%
+gestalt here. So uh we ended the day
+with Boore's model of the atom which
+
+ align:start position:0%
+with Boore's model of the atom which
+ 
+
+ align:start position:0%
+with Boore's model of the atom which
+derived from the conceptualization of
+
+ align:start position:0%
+derived from the conceptualization of
+ 
+
+ align:start position:0%
+derived from the conceptualization of
+Rutherford and this uh model is
+
+ align:start position:0%
+Rutherford and this uh model is
+ 
+
+ align:start position:0%
+Rutherford and this uh model is
+quantitative and I think I put up the
+
+ align:start position:0%
+quantitative and I think I put up the
+ 
+
+ align:start position:0%
+quantitative and I think I put up the
+postulates and what I'm going to do
+
+ align:start position:0%
+postulates and what I'm going to do
+ 
+
+ align:start position:0%
+postulates and what I'm going to do
+today is is go in some detail through
+
+ align:start position:0%
+today is is go in some detail through
+ 
+
+ align:start position:0%
+today is is go in some detail through
+the bore model. So let's do that. Um so
+
+ align:start position:0%
+the bore model. So let's do that. Um so
+ 
+
+ align:start position:0%
+the bore model. So let's do that. Um so
+I'm going to put up the uh most
+
+ align:start position:0%
+I'm going to put up the uh most
+ 
+
+ align:start position:0%
+I'm going to put up the uh most
+primitive version. It's a one electron
+
+ align:start position:0%
+primitive version. It's a one electron
+ 
+
+ align:start position:0%
+primitive version. It's a one electron
+atom. So it's got a nucleus at the
+
+ align:start position:0%
+atom. So it's got a nucleus at the
+ 
+
+ align:start position:0%
+atom. So it's got a nucleus at the
+center charged positively. This is where
+
+ align:start position:0%
+center charged positively. This is where
+ 
+
+ align:start position:0%
+center charged positively. This is where
+most of the mass resides and the
+
+ align:start position:0%
+most of the mass resides and the
+ 
+
+ align:start position:0%
+most of the mass resides and the
+positive charge resides. And orbiting
+
+ align:start position:0%
+positive charge resides. And orbiting
+ 
+
+ align:start position:0%
+positive charge resides. And orbiting
+around this is a lone electron out at
+
+ align:start position:0%
+around this is a lone electron out at
+ 
+
+ align:start position:0%
+around this is a lone electron out at
+some distance r. And I don't have to
+
+ align:start position:0%
+some distance r. And I don't have to
+ 
+
+ align:start position:0%
+some distance r. And I don't have to
+worry about these relative dimensions
+
+ align:start position:0%
+worry about these relative dimensions
+ 
+
+ align:start position:0%
+worry about these relative dimensions
+because we know from Marsen's
+
+ align:start position:0%
+because we know from Marsen's
+ 
+
+ align:start position:0%
+because we know from Marsen's
+calculations that on a on the length
+
+ align:start position:0%
+calculations that on a on the length
+ 
+
+ align:start position:0%
+calculations that on a on the length
+scale that I've shown here, these would
+
+ align:start position:0%
+scale that I've shown here, these would
+ 
+
+ align:start position:0%
+scale that I've shown here, these would
+be just tiny little dots. It's about
+
+ align:start position:0%
+be just tiny little dots. It's about
+ 
+
+ align:start position:0%
+be just tiny little dots. It's about
+10,000 to one. ratio of the nuclear
+
+ align:start position:0%
+10,000 to one. ratio of the nuclear
+ 
+
+ align:start position:0%
+10,000 to one. ratio of the nuclear
+dimension to the uh entire atomic
+
+ align:start position:0%
+dimension to the uh entire atomic
+ 
+
+ align:start position:0%
+dimension to the uh entire atomic
+dimension. And so we have a positive
+
+ align:start position:0%
+dimension. And so we have a positive
+ 
+
+ align:start position:0%
+dimension. And so we have a positive
+charge in the nucleus which is given by
+
+ align:start position:0%
+charge in the nucleus which is given by
+ 
+
+ align:start position:0%
+charge in the nucleus which is given by
+the number of protons. This would be a
+
+ align:start position:0%
+the number of protons. This would be a
+ 
+
+ align:start position:0%
+the number of protons. This would be a
+one electron atom. It could be hydrogen.
+
+ align:start position:0%
+one electron atom. It could be hydrogen.
+ 
+
+ align:start position:0%
+one electron atom. It could be hydrogen.
+It could be helium plus. It could be
+
+ align:start position:0%
+It could be helium plus. It could be
+ 
+
+ align:start position:0%
+It could be helium plus. It could be
+lithium double plus and so on. These are
+
+ align:start position:0%
+lithium double plus and so on. These are
+ 
+
+ align:start position:0%
+lithium double plus and so on. These are
+all one electron atoms and they're
+
+ align:start position:0%
+all one electron atoms and they're
+ 
+
+ align:start position:0%
+all one electron atoms and they're
+gas. It's gas single atom. So this will
+
+ align:start position:0%
+gas. It's gas single atom. So this will
+ 
+
+ align:start position:0%
+gas. It's gas single atom. So this will
+be Z times the elementary charge.
+
+ align:start position:0%
+be Z times the elementary charge.
+ 
+
+ align:start position:0%
+be Z times the elementary charge.
+Remember E represents the elementary
+
+ align:start position:0%
+Remember E represents the elementary
+ 
+
+ align:start position:0%
+Remember E represents the elementary
+charge not the charge on the electron.
+
+ align:start position:0%
+charge not the charge on the electron.
+ 
+
+ align:start position:0%
+charge not the charge on the electron.
+The charge on the electron is minus E.
+
+ align:start position:0%
+The charge on the electron is minus E.
+ 
+
+ align:start position:0%
+The charge on the electron is minus E.
+So this is Z * E in the center. And out
+
+ align:start position:0%
+So this is Z * E in the center. And out
+ 
+
+ align:start position:0%
+So this is Z * E in the center. And out
+here we have the charge on the electron
+
+ align:start position:0%
+here we have the charge on the electron
+ 
+
+ align:start position:0%
+here we have the charge on the electron
+as simply equal to E. So I'm going to
+
+ align:start position:0%
+as simply equal to E. So I'm going to
+ 
+
+ align:start position:0%
+as simply equal to E. So I'm going to
+highlight this by calling this Q1.
+
+ align:start position:0%
+highlight this by calling this Q1.
+ 
+
+ align:start position:0%
+highlight this by calling this Q1.
+Lowerase Q being the charge here on the
+
+ align:start position:0%
+Lowerase Q being the charge here on the
+ 
+
+ align:start position:0%
+Lowerase Q being the charge here on the
+uh nucleus and lowercase Q sub 2 is the
+
+ align:start position:0%
+uh nucleus and lowercase Q sub 2 is the
+ 
+
+ align:start position:0%
+uh nucleus and lowercase Q sub 2 is the
+charge on the electron and that is given
+
+ align:start position:0%
+charge on the electron and that is given
+ 
+
+ align:start position:0%
+charge on the electron and that is given
+by minus E minus E and um so the the
+
+ align:start position:0%
+by minus E minus E and um so the the
+ 
+
+ align:start position:0%
+by minus E minus E and um so the the
+other thing that we consider is the
+
+ align:start position:0%
+other thing that we consider is the
+ 
+
+ align:start position:0%
+other thing that we consider is the
+nucleuses being stationary. So we have
+
+ align:start position:0%
+nucleuses being stationary. So we have
+ 
+
+ align:start position:0%
+nucleuses being stationary. So we have
+an orbiting electron but a stationary
+
+ align:start position:0%
+an orbiting electron but a stationary
+ 
+
+ align:start position:0%
+an orbiting electron but a stationary
+nucleus. And Rutherford, whom I've
+
+ align:start position:0%
+nucleus. And Rutherford, whom I've
+ 
+
+ align:start position:0%
+nucleus. And Rutherford, whom I've
+already described to you as being uh a
+
+ align:start position:0%
+already described to you as being uh a
+ 
+
+ align:start position:0%
+already described to you as being uh a
+little bit colorful in his language, he
+
+ align:start position:0%
+little bit colorful in his language, he
+ 
+
+ align:start position:0%
+little bit colorful in his language, he
+backed up bore on this and he says, you
+
+ align:start position:0%
+backed up bore on this and he says, you
+ 
+
+ align:start position:0%
+backed up bore on this and he says, you
+know, when an elephant has fleas, it's
+
+ align:start position:0%
+know, when an elephant has fleas, it's
+ 
+
+ align:start position:0%
+know, when an elephant has fleas, it's
+the fleas that do the jumping. So that's
+
+ align:start position:0%
+the fleas that do the jumping. So that's
+ 
+
+ align:start position:0%
+the fleas that do the jumping. So that's
+why we don't worry about the motion of
+
+ align:start position:0%
+why we don't worry about the motion of
+ 
+
+ align:start position:0%
+why we don't worry about the motion of
+the nucleus because the ratio of masses
+
+ align:start position:0%
+the nucleus because the ratio of masses
+ 
+
+ align:start position:0%
+the nucleus because the ratio of masses
+is about 2,000 to1. So what I'm going to
+
+ align:start position:0%
+is about 2,000 to1. So what I'm going to
+ 
+
+ align:start position:0%
+is about 2,000 to1. So what I'm going to
+do is use these postulates and go
+
+ align:start position:0%
+do is use these postulates and go
+ 
+
+ align:start position:0%
+do is use these postulates and go
+through the basis for the bore model.
+
+ align:start position:0%
+through the basis for the bore model.
+ 
+
+ align:start position:0%
+through the basis for the bore model.
+The first thing we're going to do is uh
+
+ align:start position:0%
+The first thing we're going to do is uh
+ 
+
+ align:start position:0%
+The first thing we're going to do is uh
+describe the energy of the system. So
+
+ align:start position:0%
+describe the energy of the system. So
+ 
+
+ align:start position:0%
+describe the energy of the system. So
+the total energy of the system which
+
+ align:start position:0%
+the total energy of the system which
+ 
+
+ align:start position:0%
+the total energy of the system which
+we're going to get from postulate number
+
+ align:start position:0%
+we're going to get from postulate number
+ 
+
+ align:start position:0%
+we're going to get from postulate number
+four which says the energy of the
+
+ align:start position:0%
+four which says the energy of the
+ 
+
+ align:start position:0%
+four which says the energy of the
+electron which is the energy of the
+
+ align:start position:0%
+electron which is the energy of the
+ 
+
+ align:start position:0%
+electron which is the energy of the
+system is the sum of the kinetic and the
+
+ align:start position:0%
+system is the sum of the kinetic and the
+ 
+
+ align:start position:0%
+system is the sum of the kinetic and the
+potential energy. So let's write that.
+
+ align:start position:0%
+potential energy. So let's write that.
+ 
+
+ align:start position:0%
+potential energy. So let's write that.
+And I as I've reminded you at the end of
+
+ align:start position:0%
+And I as I've reminded you at the end of
+ 
+
+ align:start position:0%
+And I as I've reminded you at the end of
+last day the only reason I'm doing this
+
+ align:start position:0%
+last day the only reason I'm doing this
+ 
+
+ align:start position:0%
+last day the only reason I'm doing this
+for you right now is I want to elucidate
+
+ align:start position:0%
+for you right now is I want to elucidate
+ 
+
+ align:start position:0%
+for you right now is I want to elucidate
+the principles. It's not because I favor
+
+ align:start position:0%
+the principles. It's not because I favor
+ 
+
+ align:start position:0%
+the principles. It's not because I favor
+derivations in class. I've been teaching
+
+ align:start position:0%
+derivations in class. I've been teaching
+ 
+
+ align:start position:0%
+derivations in class. I've been teaching
+long enough to know that doing
+
+ align:start position:0%
+long enough to know that doing
+ 
+
+ align:start position:0%
+long enough to know that doing
+derivations in class is equivalent
+
+ align:start position:0%
+derivations in class is equivalent
+ 
+
+ align:start position:0%
+derivations in class is equivalent
+pouring ice water on the proceedings. So
+
+ align:start position:0%
+pouring ice water on the proceedings. So
+ 
+
+ align:start position:0%
+pouring ice water on the proceedings. So
+this I do this sparingly. So it's a
+
+ align:start position:0%
+this I do this sparingly. So it's a
+ 
+
+ align:start position:0%
+this I do this sparingly. So it's a
+Newtonian system from the mechanical
+
+ align:start position:0%
+Newtonian system from the mechanical
+ 
+
+ align:start position:0%
+Newtonian system from the mechanical
+standpoint. So this is going to be a
+
+ align:start position:0%
+standpoint. So this is going to be a
+ 
+
+ align:start position:0%
+standpoint. So this is going to be a
+half mv squared where this is the mass
+
+ align:start position:0%
+half mv squared where this is the mass
+ 
+
+ align:start position:0%
+half mv squared where this is the mass
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+electron and then the potential energy
+
+ align:start position:0%
+electron and then the potential energy
+ 
+
+ align:start position:0%
+electron and then the potential energy
+the energy is stored here due to the
+
+ align:start position:0%
+the energy is stored here due to the
+ 
+
+ align:start position:0%
+the energy is stored here due to the
+kulomic force of attraction between the
+
+ align:start position:0%
+kulomic force of attraction between the
+ 
+
+ align:start position:0%
+kulomic force of attraction between the
+electron and the nucleus. So in the most
+
+ align:start position:0%
+electron and the nucleus. So in the most
+ 
+
+ align:start position:0%
+electron and the nucleus. So in the most
+general form, Kulum's law is the product
+
+ align:start position:0%
+general form, Kulum's law is the product
+ 
+
+ align:start position:0%
+general form, Kulum's law is the product
+of the charges Q1 Q2 divided by their
+
+ align:start position:0%
+of the charges Q1 Q2 divided by their
+ 
+
+ align:start position:0%
+of the charges Q1 Q2 divided by their
+separation which is R. And in order to
+
+ align:start position:0%
+separation which is R. And in order to
+ 
+
+ align:start position:0%
+separation which is R. And in order to
+rationalize electrostatic units with
+
+ align:start position:0%
+rationalize electrostatic units with
+ 
+
+ align:start position:0%
+rationalize electrostatic units with
+mechanical units, we have to put a
+
+ align:start position:0%
+mechanical units, we have to put a
+ 
+
+ align:start position:0%
+mechanical units, we have to put a
+factor in here. Otherwise, the units
+
+ align:start position:0%
+factor in here. Otherwise, the units
+ 
+
+ align:start position:0%
+factor in here. Otherwise, the units
+that come out of this calculation won't
+
+ align:start position:0%
+that come out of this calculation won't
+ 
+
+ align:start position:0%
+that come out of this calculation won't
+dovetail with the units that come out of
+
+ align:start position:0%
+dovetail with the units that come out of
+ 
+
+ align:start position:0%
+dovetail with the units that come out of
+this calculation. And that factor is 4
+
+ align:start position:0%
+this calculation. And that factor is 4
+ 
+
+ align:start position:0%
+this calculation. And that factor is 4
+pi time epsilon0. epsilon0 is the
+
+ align:start position:0%
+pi time epsilon0. epsilon0 is the
+ 
+
+ align:start position:0%
+pi time epsilon0. epsilon0 is the
+permitivity of vacuum. And now we can
+
+ align:start position:0%
+permitivity of vacuum. And now we can
+ 
+
+ align:start position:0%
+permitivity of vacuum. And now we can
+plug in Q1 and Q2. We know that we've
+
+ align:start position:0%
+plug in Q1 and Q2. We know that we've
+ 
+
+ align:start position:0%
+plug in Q1 and Q2. We know that we've
+got half MV
+
+ align:start position:0%
+got half MV
+ 
+
+ align:start position:0%
+got half MV
+squared. And then Q1 is plus QE. Q2 is
+
+ align:start position:0%
+squared. And then Q1 is plus QE. Q2 is
+ 
+
+ align:start position:0%
+squared. And then Q1 is plus QE. Q2 is
+minus E. So then that will give us a net
+
+ align:start position:0%
+minus E. So then that will give us a net
+ 
+
+ align:start position:0%
+minus E. So then that will give us a net
+minus Z * the square of the elementary
+
+ align:start position:0%
+minus Z * the square of the elementary
+ 
+
+ align:start position:0%
+minus Z * the square of the elementary
+charge over 4 pi epsilon0 R. And I'm
+
+ align:start position:0%
+charge over 4 pi epsilon0 R. And I'm
+ 
+
+ align:start position:0%
+charge over 4 pi epsilon0 R. And I'm
+going to label this as equation one. And
+
+ align:start position:0%
+going to label this as equation one. And
+ 
+
+ align:start position:0%
+going to label this as equation one. And
+um so this is really this is a
+
+ align:start position:0%
+um so this is really this is a
+ 
+
+ align:start position:0%
+um so this is really this is a
+mechanical term if you like mechanical
+
+ align:start position:0%
+mechanical term if you like mechanical
+ 
+
+ align:start position:0%
+mechanical term if you like mechanical
+and this is
+
+ align:start position:0%
+and this is
+ 
+
+ align:start position:0%
+and this is
+electrostatic or
+
+ align:start position:0%
+electrostatic or
+ 
+
+ align:start position:0%
+electrostatic or
+kombic use different words for that. And
+
+ align:start position:0%
+kombic use different words for that. And
+ 
+
+ align:start position:0%
+kombic use different words for that. And
+where do we find these things? We can
+
+ align:start position:0%
+where do we find these things? We can
+ 
+
+ align:start position:0%
+where do we find these things? We can
+find values of all of these. If you look
+
+ align:start position:0%
+find values of all of these. If you look
+ 
+
+ align:start position:0%
+find values of all of these. If you look
+at your table of constants um if you
+
+ align:start position:0%
+at your table of constants um if you
+ 
+
+ align:start position:0%
+at your table of constants um if you
+look at your table of constants this is
+
+ align:start position:0%
+look at your table of constants this is
+ 
+
+ align:start position:0%
+look at your table of constants this is
+the table of constants in its entirety.
+
+ align:start position:0%
+the table of constants in its entirety.
+ 
+
+ align:start position:0%
+the table of constants in its entirety.
+But if you look up really close, there's
+
+ align:start position:0%
+But if you look up really close, there's
+ 
+
+ align:start position:0%
+But if you look up really close, there's
+uh the elementary charge E. There's the
+
+ align:start position:0%
+uh the elementary charge E. There's the
+ 
+
+ align:start position:0%
+uh the elementary charge E. There's the
+mass of the electron. All of these are
+
+ align:start position:0%
+mass of the electron. All of these are
+ 
+
+ align:start position:0%
+mass of the electron. All of these are
+given here. This is 9.11 time 10 - 31 kg
+
+ align:start position:0%
+given here. This is 9.11 time 10 - 31 kg
+ 
+
+ align:start position:0%
+given here. This is 9.11 time 10 - 31 kg
+is 1.6 * 10 - 19 kum. There's the
+
+ align:start position:0%
+is 1.6 * 10 - 19 kum. There's the
+ 
+
+ align:start position:0%
+is 1.6 * 10 - 19 kum. There's the
+permitivity of vacuum. It's all up
+
+ align:start position:0%
+permitivity of vacuum. It's all up
+ 
+
+ align:start position:0%
+permitivity of vacuum. It's all up
+there. Okay. So you have these at your
+
+ align:start position:0%
+there. Okay. So you have these at your
+ 
+
+ align:start position:0%
+there. Okay. So you have these at your
+uh disposal. Um so now let's do the next
+
+ align:start position:0%
+uh disposal. Um so now let's do the next
+ 
+
+ align:start position:0%
+uh disposal. Um so now let's do the next
+uh do the next step which is a force
+
+ align:start position:0%
+uh do the next step which is a force
+ 
+
+ align:start position:0%
+uh do the next step which is a force
+balance that comes out of postulate 3.
+
+ align:start position:0%
+balance that comes out of postulate 3.
+ 
+
+ align:start position:0%
+balance that comes out of postulate 3.
+Out of postulate 3 it says Newtonian
+
+ align:start position:0%
+Out of postulate 3 it says Newtonian
+ 
+
+ align:start position:0%
+Out of postulate 3 it says Newtonian
+mechanics applicable. So let's put a
+
+ align:start position:0%
+mechanics applicable. So let's put a
+ 
+
+ align:start position:0%
+mechanics applicable. So let's put a
+force balance. So I'm going to say if
+
+ align:start position:0%
+force balance. So I'm going to say if
+ 
+
+ align:start position:0%
+force balance. So I'm going to say if
+that electron is to stay in its orbit
+
+ align:start position:0%
+that electron is to stay in its orbit
+ 
+
+ align:start position:0%
+that electron is to stay in its orbit
+that is to say it doesn't flee the atom
+
+ align:start position:0%
+that is to say it doesn't flee the atom
+ 
+
+ align:start position:0%
+that is to say it doesn't flee the atom
+it doesn't collapse into the nucleus
+
+ align:start position:0%
+it doesn't collapse into the nucleus
+ 
+
+ align:start position:0%
+it doesn't collapse into the nucleus
+then the sum of the forces on the
+
+ align:start position:0%
+then the sum of the forces on the
+ 
+
+ align:start position:0%
+then the sum of the forces on the
+electron must be zero. No net force. No
+
+ align:start position:0%
+electron must be zero. No net force. No
+ 
+
+ align:start position:0%
+electron must be zero. No net force. No
+net force. And so that'll be the sum of
+
+ align:start position:0%
+net force. And so that'll be the sum of
+ 
+
+ align:start position:0%
+net force. And so that'll be the sum of
+a of a
+
+ align:start position:0%
+a of a
+ 
+
+ align:start position:0%
+a of a
+dynamic force plus a electrostatic or
+
+ align:start position:0%
+dynamic force plus a electrostatic or
+ 
+
+ align:start position:0%
+dynamic force plus a electrostatic or
+just to be pluralistic in our language
+
+ align:start position:0%
+just to be pluralistic in our language
+ 
+
+ align:start position:0%
+just to be pluralistic in our language
+kulomic force. And so you know from your
+
+ align:start position:0%
+kulomic force. And so you know from your
+ 
+
+ align:start position:0%
+kulomic force. And so you know from your
+Newtonian mechanics as you're learning
+
+ align:start position:0%
+Newtonian mechanics as you're learning
+ 
+
+ align:start position:0%
+Newtonian mechanics as you're learning
+in 801 the dynamic force here is m v ^2
+
+ align:start position:0%
+in 801 the dynamic force here is m v ^2
+ 
+
+ align:start position:0%
+in 801 the dynamic force here is m v ^2
+/ r again m is the mass of the electron.
+
+ align:start position:0%
+/ r again m is the mass of the electron.
+ 
+
+ align:start position:0%
+/ r again m is the mass of the electron.
+And now the force in its most general
+
+ align:start position:0%
+And now the force in its most general
+ 
+
+ align:start position:0%
+And now the force in its most general
+term is Q1 Q2 over 4 piepsilon0 which is
+
+ align:start position:0%
+term is Q1 Q2 over 4 piepsilon0 which is
+ 
+
+ align:start position:0%
+term is Q1 Q2 over 4 piepsilon0 which is
+the conversion factor R2. Force goes as
+
+ align:start position:0%
+the conversion factor R2. Force goes as
+ 
+
+ align:start position:0%
+the conversion factor R2. Force goes as
+1 / R squared. Energy goes as 1 / R. And
+
+ align:start position:0%
+1 / R squared. Energy goes as 1 / R. And
+ 
+
+ align:start position:0%
+1 / R squared. Energy goes as 1 / R. And
+if you ever get confused the way to
+
+ align:start position:0%
+if you ever get confused the way to
+ 
+
+ align:start position:0%
+if you ever get confused the way to
+remember these is that you know that uh
+
+ align:start position:0%
+remember these is that you know that uh
+ 
+
+ align:start position:0%
+remember these is that you know that uh
+energy is the integral of a force moving
+
+ align:start position:0%
+energy is the integral of a force moving
+ 
+
+ align:start position:0%
+energy is the integral of a force moving
+through a distance.
+
+ align:start position:0%
+through a distance.
+ 
+
+ align:start position:0%
+through a distance.
+Right? Energy energy is the integral of
+
+ align:start position:0%
+Right? Energy energy is the integral of
+ 
+
+ align:start position:0%
+Right? Energy energy is the integral of
+force moving through a distance. So the
+
+ align:start position:0%
+force moving through a distance. So the
+ 
+
+ align:start position:0%
+force moving through a distance. So the
+integral of 1 / r 2 gives you 1 / r. If
+
+ align:start position:0%
+integral of 1 / r 2 gives you 1 / r. If
+ 
+
+ align:start position:0%
+integral of 1 / r 2 gives you 1 / r. If
+you get them backwards, you'll integrate
+
+ align:start position:0%
+you get them backwards, you'll integrate
+ 
+
+ align:start position:0%
+you get them backwards, you'll integrate
+one over r, you'll get log r. That makes
+
+ align:start position:0%
+one over r, you'll get log r. That makes
+ 
+
+ align:start position:0%
+one over r, you'll get log r. That makes
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+sense. So there we are. And uh we plug
+
+ align:start position:0%
+sense. So there we are. And uh we plug
+ 
+
+ align:start position:0%
+sense. So there we are. And uh we plug
+in our values and we end up with m v ^2
+
+ align:start position:0%
+in our values and we end up with m v ^2
+ 
+
+ align:start position:0%
+in our values and we end up with m v ^2
+/ r minus z e^2 over 4 pi epsilon0 r 2.
+
+ align:start position:0%
+/ r minus z e^2 over 4 pi epsilon0 r 2.
+ 
+
+ align:start position:0%
+/ r minus z e^2 over 4 pi epsilon0 r 2.
+And I'm going to call this equation two.
+
+ align:start position:0%
+And I'm going to call this equation two.
+ 
+
+ align:start position:0%
+And I'm going to call this equation two.
+So that's our force balance. And then
+
+ align:start position:0%
+So that's our force balance. And then
+ 
+
+ align:start position:0%
+So that's our force balance. And then
+for the for the next piece of
+
+ align:start position:0%
+for the for the next piece of
+ 
+
+ align:start position:0%
+for the for the next piece of
+information, uh I'm going to go to
+
+ align:start position:0%
+information, uh I'm going to go to
+ 
+
+ align:start position:0%
+information, uh I'm going to go to
+postulate number five. And postulate
+
+ align:start position:0%
+postulate number five. And postulate
+ 
+
+ align:start position:0%
+postulate number five. And postulate
+number five is some of Boore's uh early
+
+ align:start position:0%
+number five is some of Boore's uh early
+ 
+
+ align:start position:0%
+number five is some of Boore's uh early
+genius. Boore says that the energy is
+
+ align:start position:0%
+genius. Boore says that the energy is
+ 
+
+ align:start position:0%
+genius. Boore says that the energy is
+quantized through its angular momentum.
+
+ align:start position:0%
+quantized through its angular momentum.
+ 
+
+ align:start position:0%
+quantized through its angular momentum.
+He's talking about the energy of an
+
+ align:start position:0%
+He's talking about the energy of an
+ 
+
+ align:start position:0%
+He's talking about the energy of an
+electron. No one until this time had
+
+ align:start position:0%
+electron. No one until this time had
+ 
+
+ align:start position:0%
+electron. No one until this time had
+suggested that a system would be
+
+ align:start position:0%
+suggested that a system would be
+ 
+
+ align:start position:0%
+suggested that a system would be
+subjected to
+
+ align:start position:0%
+subjected to
+ 
+
+ align:start position:0%
+subjected to
+quantization except for light. Plunk had
+
+ align:start position:0%
+quantization except for light. Plunk had
+ 
+
+ align:start position:0%
+quantization except for light. Plunk had
+already annunciated back in 1900 this E
+
+ align:start position:0%
+already annunciated back in 1900 this E
+ 
+
+ align:start position:0%
+already annunciated back in 1900 this E
+equals H new. In other words, that the
+
+ align:start position:0%
+equals H new. In other words, that the
+ 
+
+ align:start position:0%
+equals H new. In other words, that the
+photon has a quantum of energy H new. So
+
+ align:start position:0%
+photon has a quantum of energy H new. So
+ 
+
+ align:start position:0%
+photon has a quantum of energy H new. So
+quantization of radiation was already
+
+ align:start position:0%
+quantization of radiation was already
+ 
+
+ align:start position:0%
+quantization of radiation was already
+established as of about 1900. But no one
+
+ align:start position:0%
+established as of about 1900. But no one
+ 
+
+ align:start position:0%
+established as of about 1900. But no one
+dared no one dared say we've got this
+
+ align:start position:0%
+dared no one dared say we've got this
+ 
+
+ align:start position:0%
+dared no one dared say we've got this
+little planetary model. I've got an
+
+ align:start position:0%
+little planetary model. I've got an
+ 
+
+ align:start position:0%
+little planetary model. I've got an
+electron orbiting a central nucleus and
+
+ align:start position:0%
+electron orbiting a central nucleus and
+ 
+
+ align:start position:0%
+electron orbiting a central nucleus and
+I'm going to endow that electron with
+
+ align:start position:0%
+I'm going to endow that electron with
+ 
+
+ align:start position:0%
+I'm going to endow that electron with
+quantiz states. That was a big leap. And
+
+ align:start position:0%
+quantiz states. That was a big leap. And
+ 
+
+ align:start position:0%
+quantiz states. That was a big leap. And
+that was bore in postulate 5. So
+
+ align:start position:0%
+that was bore in postulate 5. So
+ 
+
+ align:start position:0%
+that was bore in postulate 5. So
+postulate 5 I'm just going to reproduce.
+
+ align:start position:0%
+postulate 5 I'm just going to reproduce.
+ 
+
+ align:start position:0%
+postulate 5 I'm just going to reproduce.
+So that's mvr which is its angular
+
+ align:start position:0%
+So that's mvr which is its angular
+ 
+
+ align:start position:0%
+So that's mvr which is its angular
+momentum does not take continuous
+
+ align:start position:0%
+momentum does not take continuous
+ 
+
+ align:start position:0%
+momentum does not take continuous
+values. It takes discrete values
+
+ align:start position:0%
+values. It takes discrete values
+ 
+
+ align:start position:0%
+values. It takes discrete values
+multiples of some integer n and the
+
+ align:start position:0%
+multiples of some integer n and the
+ 
+
+ align:start position:0%
+multiples of some integer n and the
+multiplication factor is the ratio of
+
+ align:start position:0%
+multiplication factor is the ratio of
+ 
+
+ align:start position:0%
+multiplication factor is the ratio of
+the plank constant divided by 2 pi where
+
+ align:start position:0%
+the plank constant divided by 2 pi where
+ 
+
+ align:start position:0%
+the plank constant divided by 2 pi where
+n takes one two three and so on. And I'm
+
+ align:start position:0%
+n takes one two three and so on. And I'm
+ 
+
+ align:start position:0%
+n takes one two three and so on. And I'm
+going to call this one equation three.
+
+ align:start position:0%
+going to call this one equation three.
+ 
+
+ align:start position:0%
+going to call this one equation three.
+So, I've got three equations and three
+
+ align:start position:0%
+So, I've got three equations and three
+ 
+
+ align:start position:0%
+So, I've got three equations and three
+unknowns. And I'm not going to take the
+
+ align:start position:0%
+unknowns. And I'm not going to take the
+ 
+
+ align:start position:0%
+unknowns. And I'm not going to take the
+time to solve it because I think that's
+
+ align:start position:0%
+time to solve it because I think that's
+ 
+
+ align:start position:0%
+time to solve it because I think that's
+a waste of class time. But those are the
+
+ align:start position:0%
+a waste of class time. But those are the
+ 
+
+ align:start position:0%
+a waste of class time. But those are the
+three unknowns. The radius of the orbit,
+
+ align:start position:0%
+three unknowns. The radius of the orbit,
+ 
+
+ align:start position:0%
+three unknowns. The radius of the orbit,
+the energy of the
+
+ align:start position:0%
+the energy of the
+ 
+
+ align:start position:0%
+the energy of the
+system, and the velocity of the
+
+ align:start position:0%
+system, and the velocity of the
+ 
+
+ align:start position:0%
+system, and the velocity of the
+electron. So, I'm just going to present
+
+ align:start position:0%
+electron. So, I'm just going to present
+ 
+
+ align:start position:0%
+electron. So, I'm just going to present
+you the solutions. Let's look first of
+
+ align:start position:0%
+you the solutions. Let's look first of
+ 
+
+ align:start position:0%
+you the solutions. Let's look first of
+all at the radius of the orbit. If you
+
+ align:start position:0%
+all at the radius of the orbit. If you
+ 
+
+ align:start position:0%
+all at the radius of the orbit. If you
+solve for r, you'll end up with this.
+
+ align:start position:0%
+solve for r, you'll end up with this.
+ 
+
+ align:start position:0%
+solve for r, you'll end up with this.
+This is the um permitivity of vacuum
+
+ align:start position:0%
+This is the um permitivity of vacuum
+ 
+
+ align:start position:0%
+This is the um permitivity of vacuum
+square of the plant constant time pi
+
+ align:start position:0%
+square of the plant constant time pi
+ 
+
+ align:start position:0%
+square of the plant constant time pi
+mass of the electron. I'm going to stop
+
+ align:start position:0%
+mass of the electron. I'm going to stop
+ 
+
+ align:start position:0%
+mass of the electron. I'm going to stop
+putting subscript e. It's the mass of
+
+ align:start position:0%
+putting subscript e. It's the mass of
+ 
+
+ align:start position:0%
+putting subscript e. It's the mass of
+the electron times the square of the
+
+ align:start position:0%
+the electron times the square of the
+ 
+
+ align:start position:0%
+the electron times the square of the
+elementary charge times n^2
+
+ align:start position:0%
+elementary charge times n^2
+ 
+
+ align:start position:0%
+elementary charge times n^2
+over z. Z is the proton number of
+
+ align:start position:0%
+over z. Z is the proton number of
+ 
+
+ align:start position:0%
+over z. Z is the proton number of
+protons in the nucleus. So what do I
+
+ align:start position:0%
+protons in the nucleus. So what do I
+ 
+
+ align:start position:0%
+protons in the nucleus. So what do I
+see? I see that r takes on discrete
+
+ align:start position:0%
+see? I see that r takes on discrete
+ 
+
+ align:start position:0%
+see? I see that r takes on discrete
+values. R is a function of N takes on
+
+ align:start position:0%
+values. R is a function of N takes on
+ 
+
+ align:start position:0%
+values. R is a function of N takes on
+discrete values and in fact it's a the
+
+ align:start position:0%
+discrete values and in fact it's a the
+ 
+
+ align:start position:0%
+discrete values and in fact it's a the
+the functionality is that of the square
+
+ align:start position:0%
+the functionality is that of the square
+ 
+
+ align:start position:0%
+the functionality is that of the square
+of this number times a constant times a
+
+ align:start position:0%
+of this number times a constant times a
+ 
+
+ align:start position:0%
+of this number times a constant times a
+constant. So this tells us that the
+
+ align:start position:0%
+constant. So this tells us that the
+ 
+
+ align:start position:0%
+constant. So this tells us that the
+radius of the electron orbit first of
+
+ align:start position:0%
+radius of the electron orbit first of
+ 
+
+ align:start position:0%
+radius of the electron orbit first of
+all there is more than one radius
+
+ align:start position:0%
+all there is more than one radius
+ 
+
+ align:start position:0%
+all there is more than one radius
+there's a plurality of values secondly
+
+ align:start position:0%
+there's a plurality of values secondly
+ 
+
+ align:start position:0%
+there's a plurality of values secondly
+that those values are discrete they're
+
+ align:start position:0%
+that those values are discrete they're
+ 
+
+ align:start position:0%
+that those values are discrete they're
+quantized and third it's nonlinear so if
+
+ align:start position:0%
+quantized and third it's nonlinear so if
+ 
+
+ align:start position:0%
+quantized and third it's nonlinear so if
+I look at something that goes as uh n
+
+ align:start position:0%
+I look at something that goes as uh n
+ 
+
+ align:start position:0%
+I look at something that goes as uh n
+squar if this is the edge of the nucleus
+
+ align:start position:0%
+squar if this is the edge of the nucleus
+ 
+
+ align:start position:0%
+squar if this is the edge of the nucleus
+here and if this is r1 it says when n
+
+ align:start position:0%
+here and if this is r1 it says when n
+ 
+
+ align:start position:0%
+here and if this is r1 it says when n
+goes to two the radius goes to four so
+
+ align:start position:0%
+goes to two the radius goes to four so
+ 
+
+ align:start position:0%
+goes to two the radius goes to four so
+this is let's say this is r1 this is r2
+
+ align:start position:0%
+this is let's say this is r1 this is r2
+ 
+
+ align:start position:0%
+this is let's say this is r1 this is r2
+and then this will be R3 and this will
+
+ align:start position:0%
+and then this will be R3 and this will
+ 
+
+ align:start position:0%
+and then this will be R3 and this will
+be R4 and even that's not the scale.
+
+ align:start position:0%
+be R4 and even that's not the scale.
+ 
+
+ align:start position:0%
+be R4 and even that's not the scale.
+Okay, so the the higher the N number the
+
+ align:start position:0%
+Okay, so the the higher the N number the
+ 
+
+ align:start position:0%
+Okay, so the the higher the N number the
+the greater the radius by uh by far and
+
+ align:start position:0%
+the greater the radius by uh by far and
+ 
+
+ align:start position:0%
+the greater the radius by uh by far and
+this applies to all one electron atoms.
+
+ align:start position:0%
+this applies to all one electron atoms.
+ 
+
+ align:start position:0%
+this applies to all one electron atoms.
+All one electron atoms. Um so let's look
+
+ align:start position:0%
+All one electron atoms. Um so let's look
+ 
+
+ align:start position:0%
+All one electron atoms. Um so let's look
+at the simplest case. Suppose we look at
+
+ align:start position:0%
+at the simplest case. Suppose we look at
+ 
+
+ align:start position:0%
+at the simplest case. Suppose we look at
+elemental hydrogen. So in case of
+
+ align:start position:0%
+elemental hydrogen. So in case of
+ 
+
+ align:start position:0%
+elemental hydrogen. So in case of
+elemental hydrogen Z will equal one. And
+
+ align:start position:0%
+elemental hydrogen Z will equal one. And
+ 
+
+ align:start position:0%
+elemental hydrogen Z will equal one. And
+then let's look at the lowest orbit n=
+
+ align:start position:0%
+then let's look at the lowest orbit n=
+ 
+
+ align:start position:0%
+then let's look at the lowest orbit n=
+1. That's the electron in its lowest
+
+ align:start position:0%
+1. That's the electron in its lowest
+ 
+
+ align:start position:0%
+1. That's the electron in its lowest
+orbit to the nucleus of atomic hydrogen.
+
+ align:start position:0%
+orbit to the nucleus of atomic hydrogen.
+ 
+
+ align:start position:0%
+orbit to the nucleus of atomic hydrogen.
+And this lowest orbit is termed the
+
+ align:start position:0%
+And this lowest orbit is termed the
+ 
+
+ align:start position:0%
+And this lowest orbit is termed the
+ground state. The ground
+
+ align:start position:0%
+ground state. The ground
+ 
+
+ align:start position:0%
+ground state. The ground
+state first floor. So if we put one here
+
+ align:start position:0%
+state first floor. So if we put one here
+ 
+
+ align:start position:0%
+state first floor. So if we put one here
+and one here, the value is simply given
+
+ align:start position:0%
+and one here, the value is simply given
+ 
+
+ align:start position:0%
+and one here, the value is simply given
+by this constant. And if you evaluate
+
+ align:start position:0%
+by this constant. And if you evaluate
+ 
+
+ align:start position:0%
+by this constant. And if you evaluate
+the constant you get that r1 is equal to
+
+ align:start position:0%
+the constant you get that r1 is equal to
+ 
+
+ align:start position:0%
+the constant you get that r1 is equal to
+5.29
+
+ align:start position:0%
+5.29
+ 
+
+ align:start position:0%
+5.29
+* 10us 11 m or
+
+ align:start position:0%
+* 10us 11 m or
+ 
+
+ align:start position:0%
+* 10us 11 m or
+0.529 angstroms. I like the angstrom.
+
+ align:start position:0%
+0.529 angstroms. I like the angstrom.
+ 
+
+ align:start position:0%
+0.529 angstroms. I like the angstrom.
+It's 10 the minus 10 m. It's not an SI
+
+ align:start position:0%
+It's 10 the minus 10 m. It's not an SI
+ 
+
+ align:start position:0%
+It's 10 the minus 10 m. It's not an SI
+unit because it's not a multiple of 10
+
+ align:start position:0%
+unit because it's not a multiple of 10
+ 
+
+ align:start position:0%
+unit because it's not a multiple of 10
+the 3. But I like the angstrom. I I I
+
+ align:start position:0%
+the 3. But I like the angstrom. I I I
+ 
+
+ align:start position:0%
+the 3. But I like the angstrom. I I I
+don't like the nanometer. I like the
+
+ align:start position:0%
+don't like the nanometer. I like the
+ 
+
+ align:start position:0%
+don't like the nanometer. I like the
+angstrom because atomic dimensions are
+
+ align:start position:0%
+angstrom because atomic dimensions are
+ 
+
+ align:start position:0%
+angstrom because atomic dimensions are
+conveniently measured by angstroms.
+
+ align:start position:0%
+conveniently measured by angstroms.
+ 
+
+ align:start position:0%
+conveniently measured by angstroms.
+And this is given a special symbol a
+
+ align:start position:0%
+And this is given a special symbol a
+ 
+
+ align:start position:0%
+And this is given a special symbol a
+knot. A knot. It's the value of the
+
+ align:start position:0%
+knot. A knot. It's the value of the
+ 
+
+ align:start position:0%
+knot. A knot. It's the value of the
+radius of the ground state electron
+
+ align:start position:0%
+radius of the ground state electron
+ 
+
+ align:start position:0%
+radius of the ground state electron
+orbit in atomic hydrogen. And this
+
+ align:start position:0%
+orbit in atomic hydrogen. And this
+ 
+
+ align:start position:0%
+orbit in atomic hydrogen. And this
+quantity is termed the bore radius. And
+
+ align:start position:0%
+quantity is termed the bore radius. And
+ 
+
+ align:start position:0%
+quantity is termed the bore radius. And
+you don't even have to look it up
+
+ align:start position:0%
+you don't even have to look it up
+ 
+
+ align:start position:0%
+you don't even have to look it up
+because it too is given on your on your
+
+ align:start position:0%
+because it too is given on your on your
+ 
+
+ align:start position:0%
+because it too is given on your on your
+table of constant. There's the plunk
+
+ align:start position:0%
+table of constant. There's the plunk
+ 
+
+ align:start position:0%
+table of constant. There's the plunk
+constant. It's number five. There's the
+
+ align:start position:0%
+constant. It's number five. There's the
+ 
+
+ align:start position:0%
+constant. It's number five. There's the
+bore radius down there. Number 24. So
+
+ align:start position:0%
+bore radius down there. Number 24. So
+ 
+
+ align:start position:0%
+bore radius down there. Number 24. So
+you just look that up and you know any
+
+ align:start position:0%
+you just look that up and you know any
+ 
+
+ align:start position:0%
+you just look that up and you know any
+anything else is going to be some some
+
+ align:start position:0%
+anything else is going to be some some
+ 
+
+ align:start position:0%
+anything else is going to be some some
+multiple of it. Um the other thing I'd
+
+ align:start position:0%
+multiple of it. Um the other thing I'd
+ 
+
+ align:start position:0%
+multiple of it. Um the other thing I'd
+like to draw your attention to is this
+
+ align:start position:0%
+like to draw your attention to is this
+ 
+
+ align:start position:0%
+like to draw your attention to is this
+that uh I can simplify this in the
+
+ align:start position:0%
+that uh I can simplify this in the
+ 
+
+ align:start position:0%
+that uh I can simplify this in the
+following manner. Say that Rn now that
+
+ align:start position:0%
+following manner. Say that Rn now that
+ 
+
+ align:start position:0%
+following manner. Say that Rn now that
+I've got a bore radius for this uh
+
+ align:start position:0%
+I've got a bore radius for this uh
+ 
+
+ align:start position:0%
+I've got a bore radius for this uh
+bracketed quantity. I can write that as
+
+ align:start position:0%
+bracketed quantity. I can write that as
+ 
+
+ align:start position:0%
+bracketed quantity. I can write that as
+the product of the bore radius for the
+
+ align:start position:0%
+the product of the bore radius for the
+ 
+
+ align:start position:0%
+the product of the bore radius for the
+value of the
+
+ align:start position:0%
+value of the
+ 
+
+ align:start position:0%
+value of the
+orbit in any one electron
+
+ align:start position:0%
+orbit in any one electron
+ 
+
+ align:start position:0%
+orbit in any one electron
+atom. Specify the quantum number
+
+ align:start position:0%
+atom. Specify the quantum number
+ 
+
+ align:start position:0%
+atom. Specify the quantum number
+n divide by z. So that's that's this
+
+ align:start position:0%
+n divide by z. So that's that's this
+ 
+
+ align:start position:0%
+n divide by z. So that's that's this
+rewritten in a much more compact
+
+ align:start position:0%
+rewritten in a much more compact
+ 
+
+ align:start position:0%
+rewritten in a much more compact
+notation because you have the value of
+
+ align:start position:0%
+notation because you have the value of
+ 
+
+ align:start position:0%
+notation because you have the value of
+this. And note that as z increases as
+
+ align:start position:0%
+this. And note that as z increases as
+ 
+
+ align:start position:0%
+this. And note that as z increases as
+the proton number increases the uh
+
+ align:start position:0%
+the proton number increases the uh
+ 
+
+ align:start position:0%
+the proton number increases the uh
+radius decreases for a given end number.
+
+ align:start position:0%
+radius decreases for a given end number.
+ 
+
+ align:start position:0%
+radius decreases for a given end number.
+So if you look at the ground state in
+
+ align:start position:0%
+So if you look at the ground state in
+ 
+
+ align:start position:0%
+So if you look at the ground state in
+two different systems, if you look at
+
+ align:start position:0%
+two different systems, if you look at
+ 
+
+ align:start position:0%
+two different systems, if you look at
+the ground state which is n equals 1.
+
+ align:start position:0%
+the ground state which is n equals 1.
+ 
+
+ align:start position:0%
+the ground state which is n equals 1.
+Think about this. If I increase the
+
+ align:start position:0%
+Think about this. If I increase the
+ 
+
+ align:start position:0%
+Think about this. If I increase the
+proton charge, the komic force of
+
+ align:start position:0%
+proton charge, the komic force of
+ 
+
+ align:start position:0%
+proton charge, the komic force of
+attraction is greater. And so therefore
+
+ align:start position:0%
+attraction is greater. And so therefore
+ 
+
+ align:start position:0%
+attraction is greater. And so therefore
+all other things being equal, the first
+
+ align:start position:0%
+all other things being equal, the first
+ 
+
+ align:start position:0%
+all other things being equal, the first
+orbit should be at a smaller distance.
+
+ align:start position:0%
+orbit should be at a smaller distance.
+ 
+
+ align:start position:0%
+orbit should be at a smaller distance.
+So this is making this is making
+
+ align:start position:0%
+So this is making this is making
+ 
+
+ align:start position:0%
+So this is making this is making
+physical sense. Okay. Now let's look at
+
+ align:start position:0%
+physical sense. Okay. Now let's look at
+ 
+
+ align:start position:0%
+physical sense. Okay. Now let's look at
+energy. Let's uh quantify the energy
+
+ align:start position:0%
+energy. Let's uh quantify the energy
+ 
+
+ align:start position:0%
+energy. Let's uh quantify the energy
+value. If you go through and solve for
+
+ align:start position:0%
+value. If you go through and solve for
+ 
+
+ align:start position:0%
+value. If you go through and solve for
+energy, you'll get this equation. E is
+
+ align:start position:0%
+energy, you'll get this equation. E is
+ 
+
+ align:start position:0%
+energy, you'll get this equation. E is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+minus mass of the electron time the
+
+ align:start position:0%
+minus mass of the electron time the
+ 
+
+ align:start position:0%
+minus mass of the electron time the
+elementary charge raised to the 4th
+
+ align:start position:0%
+elementary charge raised to the 4th
+ 
+
+ align:start position:0%
+elementary charge raised to the 4th
+power / e * the square of the
+
+ align:start position:0%
+power / e * the square of the
+ 
+
+ align:start position:0%
+power / e * the square of the
+permitivity of vacuum time the square of
+
+ align:start position:0%
+permitivity of vacuum time the square of
+ 
+
+ align:start position:0%
+permitivity of vacuum time the square of
+the plank
+
+ align:start position:0%
+the plank
+ 
+
+ align:start position:0%
+the plank
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+time z ^2 /
+
+ align:start position:0%
+time z ^2 /
+ 
+
+ align:start position:0%
+time z ^2 /
+n^2. So again we see that e is a
+
+ align:start position:0%
+n^2. So again we see that e is a
+ 
+
+ align:start position:0%
+n^2. So again we see that e is a
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+of n. You see the quantum condition by
+
+ align:start position:0%
+of n. You see the quantum condition by
+ 
+
+ align:start position:0%
+of n. You see the quantum condition by
+putting quantization into the angular
+
+ align:start position:0%
+putting quantization into the angular
+ 
+
+ align:start position:0%
+putting quantization into the angular
+momentum it's propagated through the
+
+ align:start position:0%
+momentum it's propagated through the
+ 
+
+ align:start position:0%
+momentum it's propagated through the
+entire system. Orbits dimensions are
+
+ align:start position:0%
+entire system. Orbits dimensions are
+ 
+
+ align:start position:0%
+entire system. Orbits dimensions are
+quantized. Energy is quantized. Velocity
+
+ align:start position:0%
+quantized. Energy is quantized. Velocity
+ 
+
+ align:start position:0%
+quantized. Energy is quantized. Velocity
+is quantized. Everything is quantized.
+
+ align:start position:0%
+is quantized. Everything is quantized.
+ 
+
+ align:start position:0%
+is quantized. Everything is quantized.
+So energy is quantized. It has a
+
+ align:start position:0%
+So energy is quantized. It has a
+ 
+
+ align:start position:0%
+So energy is quantized. It has a
+different n dependence. If I lump all of
+
+ align:start position:0%
+different n dependence. If I lump all of
+ 
+
+ align:start position:0%
+different n dependence. If I lump all of
+this together in some constant, I can
+
+ align:start position:0%
+this together in some constant, I can
+ 
+
+ align:start position:0%
+this together in some constant, I can
+then represent that formula as minus k *
+
+ align:start position:0%
+then represent that formula as minus k *
+ 
+
+ align:start position:0%
+then represent that formula as minus k *
+z
+
+ align:start position:0%
+z
+ 
+
+ align:start position:0%
+z
+^2 over n^2 where n again uh chooses
+
+ align:start position:0%
+^2 over n^2 where n again uh chooses
+ 
+
+ align:start position:0%
+^2 over n^2 where n again uh chooses
+integer values 1 2 3 and so on. And we
+
+ align:start position:0%
+integer values 1 2 3 and so on. And we
+ 
+
+ align:start position:0%
+integer values 1 2 3 and so on. And we
+can go through and and calculate the
+
+ align:start position:0%
+can go through and and calculate the
+ 
+
+ align:start position:0%
+can go through and and calculate the
+value of this quantity in parentheses.
+
+ align:start position:0%
+value of this quantity in parentheses.
+ 
+
+ align:start position:0%
+value of this quantity in parentheses.
+And when we do so we get the value 2.18
+
+ align:start position:0%
+And when we do so we get the value 2.18
+ 
+
+ align:start position:0%
+And when we do so we get the value 2.18
+* 10
+
+ align:start position:0%
+* 10
+ 
+
+ align:start position:0%
+* 10
+-18
+
+ align:start position:0%
+-18
+ 
+
+ align:start position:0%
+-18
+Jew. This is 10 -8 Jew for this one
+
+ align:start position:0%
+Jew. This is 10 -8 Jew for this one
+ 
+
+ align:start position:0%
+Jew. This is 10 -8 Jew for this one
+atom. So I'm going to draw attention to
+
+ align:start position:0%
+atom. So I'm going to draw attention to
+ 
+
+ align:start position:0%
+atom. So I'm going to draw attention to
+this. It's jewels per
+
+ align:start position:0%
+this. It's jewels per
+ 
+
+ align:start position:0%
+this. It's jewels per
+atom. Or if you multiply by Avagadro's
+
+ align:start position:0%
+atom. Or if you multiply by Avagadro's
+ 
+
+ align:start position:0%
+atom. Or if you multiply by Avagadro's
+number then you'll get jewels per mole.
+
+ align:start position:0%
+number then you'll get jewels per mole.
+ 
+
+ align:start position:0%
+number then you'll get jewels per mole.
+And if you do so, you'll end up with
+
+ align:start position:0%
+And if you do so, you'll end up with
+ 
+
+ align:start position:0%
+And if you do so, you'll end up with
+1.312
+
+ align:start position:0%
+1.312
+ 
+
+ align:start position:0%
+1.312
+megaj per mole for this quantity
+
+ align:start position:0%
+megaj per mole for this quantity
+ 
+
+ align:start position:0%
+megaj per mole for this quantity
+K. And and you can find that one too.
+
+ align:start position:0%
+K. And and you can find that one too.
+ 
+
+ align:start position:0%
+K. And and you can find that one too.
+That's on your that's on your chart. Uh
+
+ align:start position:0%
+That's on your that's on your chart. Uh
+ 
+
+ align:start position:0%
+That's on your that's on your chart. Uh
+if you multiply entry 23, which is 13.6
+
+ align:start position:0%
+if you multiply entry 23, which is 13.6
+ 
+
+ align:start position:0%
+if you multiply entry 23, which is 13.6
+electron volts, I'll show you what the
+
+ align:start position:0%
+electron volts, I'll show you what the
+ 
+
+ align:start position:0%
+electron volts, I'll show you what the
+electron volt is in a in a few minutes.
+
+ align:start position:0%
+electron volt is in a in a few minutes.
+ 
+
+ align:start position:0%
+electron volt is in a in a few minutes.
+So we'll just put it up here
+
+ align:start position:0%
+So we'll just put it up here
+ 
+
+ align:start position:0%
+So we'll just put it up here
+prematurely, but that's given in your
+
+ align:start position:0%
+prematurely, but that's given in your
+ 
+
+ align:start position:0%
+prematurely, but that's given in your
+chart. And then the conversion of jewels
+
+ align:start position:0%
+chart. And then the conversion of jewels
+ 
+
+ align:start position:0%
+chart. And then the conversion of jewels
+to electron volts is entry 42. So if you
+
+ align:start position:0%
+to electron volts is entry 42. So if you
+ 
+
+ align:start position:0%
+to electron volts is entry 42. So if you
+multiply those two together, you'll end
+
+ align:start position:0%
+multiply those two together, you'll end
+ 
+
+ align:start position:0%
+multiply those two together, you'll end
+up with with this quantity. And so um
+
+ align:start position:0%
+up with with this quantity. And so um
+ 
+
+ align:start position:0%
+up with with this quantity. And so um
+let's take a look at what that
+
+ align:start position:0%
+let's take a look at what that
+ 
+
+ align:start position:0%
+let's take a look at what that
+does in terms of uh uh graphical
+
+ align:start position:0%
+does in terms of uh uh graphical
+ 
+
+ align:start position:0%
+does in terms of uh uh graphical
+representation. I tried to give you a
+
+ align:start position:0%
+representation. I tried to give you a
+ 
+
+ align:start position:0%
+representation. I tried to give you a
+simple graphical representation of uh so
+
+ align:start position:0%
+simple graphical representation of uh so
+ 
+
+ align:start position:0%
+simple graphical representation of uh so
+that was cartisian space, right? When I
+
+ align:start position:0%
+that was cartisian space, right? When I
+ 
+
+ align:start position:0%
+that was cartisian space, right? When I
+plot r as as a distance out from the
+
+ align:start position:0%
+plot r as as a distance out from the
+ 
+
+ align:start position:0%
+plot r as as a distance out from the
+nucleus, that's sort of our
+
+ align:start position:0%
+nucleus, that's sort of our
+ 
+
+ align:start position:0%
+nucleus, that's sort of our
+simple-minded planetary model. So now
+
+ align:start position:0%
+simple-minded planetary model. So now
+ 
+
+ align:start position:0%
+simple-minded planetary model. So now
+let's look at energy. So energy I'm
+
+ align:start position:0%
+let's look at energy. So energy I'm
+ 
+
+ align:start position:0%
+let's look at energy. So energy I'm
+going to put energy in the following
+
+ align:start position:0%
+going to put energy in the following
+ 
+
+ align:start position:0%
+going to put energy in the following
+manner. See it's a conservative system.
+
+ align:start position:0%
+manner. See it's a conservative system.
+ 
+
+ align:start position:0%
+manner. See it's a conservative system.
+So all the energies are negative, right?
+
+ align:start position:0%
+So all the energies are negative, right?
+ 
+
+ align:start position:0%
+So all the energies are negative, right?
+That quantity in parenthesis I've got a
+
+ align:start position:0%
+That quantity in parenthesis I've got a
+ 
+
+ align:start position:0%
+That quantity in parenthesis I've got a
+mass which is a positive number.
+
+ align:start position:0%
+mass which is a positive number.
+ 
+
+ align:start position:0%
+mass which is a positive number.
+Something raised to the fourth power has
+
+ align:start position:0%
+Something raised to the fourth power has
+ 
+
+ align:start position:0%
+Something raised to the fourth power has
+got to be positive. Something raised to
+
+ align:start position:0%
+got to be positive. Something raised to
+ 
+
+ align:start position:0%
+got to be positive. Something raised to
+the second power it's got to be
+
+ align:start position:0%
+the second power it's got to be
+ 
+
+ align:start position:0%
+the second power it's got to be
+positive. So everything inside the
+
+ align:start position:0%
+positive. So everything inside the
+ 
+
+ align:start position:0%
+positive. So everything inside the
+parenthesis is positive. So minus a
+
+ align:start position:0%
+parenthesis is positive. So minus a
+ 
+
+ align:start position:0%
+parenthesis is positive. So minus a
+positive number. All the energies are
+
+ align:start position:0%
+positive number. All the energies are
+ 
+
+ align:start position:0%
+positive number. All the energies are
+negative because it's a bound system. So
+
+ align:start position:0%
+negative because it's a bound system. So
+ 
+
+ align:start position:0%
+negative because it's a bound system. So
+I start up
+
+ align:start position:0%
+I start up
+ 
+
+ align:start position:0%
+I start up
+here with n= 1 and uh over here this is
+
+ align:start position:0%
+here with n= 1 and uh over here this is
+ 
+
+ align:start position:0%
+here with n= 1 and uh over here this is
+the value of minus k and then if we go
+
+ align:start position:0%
+the value of minus k and then if we go
+ 
+
+ align:start position:0%
+the value of minus k and then if we go
+to n equals 2 what happens? We go to n=
+
+ align:start position:0%
+to n equals 2 what happens? We go to n=
+ 
+
+ align:start position:0%
+to n equals 2 what happens? We go to n=
+2 for a fixed value of z. Uh let's make
+
+ align:start position:0%
+2 for a fixed value of z. Uh let's make
+ 
+
+ align:start position:0%
+2 for a fixed value of z. Uh let's make
+this z equals 1. We'll do it for atomic
+
+ align:start position:0%
+this z equals 1. We'll do it for atomic
+ 
+
+ align:start position:0%
+this z equals 1. We'll do it for atomic
+hydrogen. So it's k over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4 and then we go to n= 3. This is not to
+
+ align:start position:0%
+4 and then we go to n= 3. This is not to
+ 
+
+ align:start position:0%
+4 and then we go to n= 3. This is not to
+scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but and so on. So this is what uh the
+
+ align:start position:0%
+but and so on. So this is what uh the
+ 
+
+ align:start position:0%
+but and so on. So this is what uh the
+energy level diagram looks like. This is
+
+ align:start position:0%
+energy level diagram looks like. This is
+ 
+
+ align:start position:0%
+energy level diagram looks like. This is
+for atomic hydrogen gas. And I'm going
+
+ align:start position:0%
+for atomic hydrogen gas. And I'm going
+ 
+
+ align:start position:0%
+for atomic hydrogen gas. And I'm going
+to put on here not to
+
+ align:start position:0%
+to put on here not to
+ 
+
+ align:start position:0%
+to put on here not to
+scale. There's some relative the notion
+
+ align:start position:0%
+scale. There's some relative the notion
+ 
+
+ align:start position:0%
+scale. There's some relative the notion
+that the that the energy gap between n=1
+
+ align:start position:0%
+that the that the energy gap between n=1
+ 
+
+ align:start position:0%
+that the that the energy gap between n=1
+and n=2 is greater than that for n= 2 to
+
+ align:start position:0%
+and n=2 is greater than that for n= 2 to
+ 
+
+ align:start position:0%
+and n=2 is greater than that for n= 2 to
+n= 3. That's correctly represented.
+
+ align:start position:0%
+n= 3. That's correctly represented.
+ 
+
+ align:start position:0%
+n= 3. That's correctly represented.
+These are definitely not equally spaced,
+
+ align:start position:0%
+These are definitely not equally spaced,
+ 
+
+ align:start position:0%
+These are definitely not equally spaced,
+but they should be even more uh
+
+ align:start position:0%
+but they should be even more uh
+ 
+
+ align:start position:0%
+but they should be even more uh
+disproportionate than I than I've shown
+
+ align:start position:0%
+disproportionate than I than I've shown
+ 
+
+ align:start position:0%
+disproportionate than I than I've shown
+it. Um, and finally up here we have n
+
+ align:start position:0%
+it. Um, and finally up here we have n
+ 
+
+ align:start position:0%
+it. Um, and finally up here we have n
+equals infinity. When n equals infinity,
+
+ align:start position:0%
+equals infinity. When n equals infinity,
+ 
+
+ align:start position:0%
+equals infinity. When n equals infinity,
+r equals infinity. And so the energy is
+
+ align:start position:0%
+r equals infinity. And so the energy is
+ 
+
+ align:start position:0%
+r equals infinity. And so the energy is
+zero because the electron is no longer
+
+ align:start position:0%
+zero because the electron is no longer
+ 
+
+ align:start position:0%
+zero because the electron is no longer
+bound. It's free. The electron has been
+
+ align:start position:0%
+bound. It's free. The electron has been
+ 
+
+ align:start position:0%
+bound. It's free. The electron has been
+liberated. This represents the uh free
+
+ align:start position:0%
+liberated. This represents the uh free
+ 
+
+ align:start position:0%
+liberated. This represents the uh free
+electron. It's no longer tethered to the
+
+ align:start position:0%
+electron. It's no longer tethered to the
+ 
+
+ align:start position:0%
+electron. It's no longer tethered to the
+nucleus. So there's no energy stored in
+
+ align:start position:0%
+nucleus. So there's no energy stored in
+ 
+
+ align:start position:0%
+nucleus. So there's no energy stored in
+the system and the the the the closer it
+
+ align:start position:0%
+the system and the the the the closer it
+ 
+
+ align:start position:0%
+the system and the the the the closer it
+gets to the nucleus the greater the
+
+ align:start position:0%
+gets to the nucleus the greater the
+ 
+
+ align:start position:0%
+gets to the nucleus the greater the
+amount of energy which means that you
+
+ align:start position:0%
+amount of energy which means that you
+ 
+
+ align:start position:0%
+amount of energy which means that you
+see this in the following manner. Uh
+
+ align:start position:0%
+see this in the following manner. Uh
+ 
+
+ align:start position:0%
+see this in the following manner. Uh
+this is called the ground state n equals
+
+ align:start position:0%
+this is called the ground state n equals
+ 
+
+ align:start position:0%
+this is called the ground state n equals
+1. I already mentioned that it's like
+
+ align:start position:0%
+1. I already mentioned that it's like
+ 
+
+ align:start position:0%
+1. I already mentioned that it's like
+the ground floor. I know some of you
+
+ align:start position:0%
+the ground floor. I know some of you
+ 
+
+ align:start position:0%
+the ground floor. I know some of you
+come from Europe and other parts of the
+
+ align:start position:0%
+come from Europe and other parts of the
+ 
+
+ align:start position:0%
+come from Europe and other parts of the
+world where they have uh the ground
+
+ align:start position:0%
+world where they have uh the ground
+ 
+
+ align:start position:0%
+world where they have uh the ground
+floor is the chos or some silly thing
+
+ align:start position:0%
+floor is the chos or some silly thing
+ 
+
+ align:start position:0%
+floor is the chos or some silly thing
+like this and you push the button on the
+
+ align:start position:0%
+like this and you push the button on the
+ 
+
+ align:start position:0%
+like this and you push the button on the
+elevator to one and you go up to the
+
+ align:start position:0%
+elevator to one and you go up to the
+ 
+
+ align:start position:0%
+elevator to one and you go up to the
+first floor. You are in America now and
+
+ align:start position:0%
+first floor. You are in America now and
+ 
+
+ align:start position:0%
+first floor. You are in America now and
+the international chemical community
+
+ align:start position:0%
+the international chemical community
+ 
+
+ align:start position:0%
+the international chemical community
+calls the ground state n equals 1 not n
+
+ align:start position:0%
+calls the ground state n equals 1 not n
+ 
+
+ align:start position:0%
+calls the ground state n equals 1 not n
+equals zero. So please observe the
+
+ align:start position:0%
+equals zero. So please observe the
+ 
+
+ align:start position:0%
+equals zero. So please observe the
+traditions of the international union of
+
+ align:start position:0%
+traditions of the international union of
+ 
+
+ align:start position:0%
+traditions of the international union of
+pure and applied chemistry not to
+
+ align:start position:0%
+pure and applied chemistry not to
+ 
+
+ align:start position:0%
+pure and applied chemistry not to
+mention Neil's bore. Okay. So this is
+
+ align:start position:0%
+mention Neil's bore. Okay. So this is
+ 
+
+ align:start position:0%
+mention Neil's bore. Okay. So this is
+ground state. These are the excited
+
+ align:start position:0%
+ground state. These are the excited
+ 
+
+ align:start position:0%
+ground state. These are the excited
+states. These are the excited states.
+
+ align:start position:0%
+states. These are the excited states.
+ 
+
+ align:start position:0%
+states. These are the excited states.
+And free electron at n equals infinity.
+
+ align:start position:0%
+And free electron at n equals infinity.
+ 
+
+ align:start position:0%
+And free electron at n equals infinity.
+And at this point we say that the the
+
+ align:start position:0%
+And at this point we say that the the
+ 
+
+ align:start position:0%
+And at this point we say that the the
+atom has
+
+ align:start position:0%
+atom has
+ 
+
+ align:start position:0%
+atom has
+become has become
+
+ align:start position:0%
+become has become
+ 
+
+ align:start position:0%
+become has become
+ionized ionized. That is to say the
+
+ align:start position:0%
+ionized ionized. That is to say the
+ 
+
+ align:start position:0%
+ionized ionized. That is to say the
+electron has been ejected. And so now we
+
+ align:start position:0%
+electron has been ejected. And so now we
+ 
+
+ align:start position:0%
+electron has been ejected. And so now we
+have net charge. And we can calculate
+
+ align:start position:0%
+have net charge. And we can calculate
+ 
+
+ align:start position:0%
+have net charge. And we can calculate
+the ionization energy. The ionization
+
+ align:start position:0%
+the ionization energy. The ionization
+ 
+
+ align:start position:0%
+the ionization energy. The ionization
+energy must then be nothing more than
+
+ align:start position:0%
+energy must then be nothing more than
+ 
+
+ align:start position:0%
+energy must then be nothing more than
+that's the energy to go from the ground
+
+ align:start position:0%
+that's the energy to go from the ground
+ 
+
+ align:start position:0%
+that's the energy to go from the ground
+state here from the ground state to n
+
+ align:start position:0%
+state here from the ground state to n
+ 
+
+ align:start position:0%
+state here from the ground state to n
+equals infinity. So that would be the
+
+ align:start position:0%
+equals infinity. So that would be the
+ 
+
+ align:start position:0%
+equals infinity. So that would be the
+energy at state infinity minus the
+
+ align:start position:0%
+energy at state infinity minus the
+ 
+
+ align:start position:0%
+energy at state infinity minus the
+energy of the ground state. Well the
+
+ align:start position:0%
+energy of the ground state. Well the
+ 
+
+ align:start position:0%
+energy of the ground state. Well the
+energy at infinity is zero and the
+
+ align:start position:0%
+energy at infinity is zero and the
+ 
+
+ align:start position:0%
+energy at infinity is zero and the
+energy in the ground state is minus k.
+
+ align:start position:0%
+energy in the ground state is minus k.
+ 
+
+ align:start position:0%
+energy in the ground state is minus k.
+So min - k is plus k. So k in fact is
+
+ align:start position:0%
+So min - k is plus k. So k in fact is
+ 
+
+ align:start position:0%
+So min - k is plus k. So k in fact is
+the ionization energy. And in fact if
+
+ align:start position:0%
+the ionization energy. And in fact if
+ 
+
+ align:start position:0%
+the ionization energy. And in fact if
+you go
+
+ align:start position:0%
+you go
+ 
+
+ align:start position:0%
+you go
+to if you go to the chart to your
+
+ align:start position:0%
+to if you go to the chart to your
+ 
+
+ align:start position:0%
+to if you go to the chart to your
+periodic table uh indeed there it is. So
+
+ align:start position:0%
+periodic table uh indeed there it is. So
+ 
+
+ align:start position:0%
+periodic table uh indeed there it is. So
+here, this is a a slightly different
+
+ align:start position:0%
+here, this is a a slightly different
+ 
+
+ align:start position:0%
+here, this is a a slightly different
+version from the one you have, but it's
+
+ align:start position:0%
+version from the one you have, but it's
+ 
+
+ align:start position:0%
+version from the one you have, but it's
+the same order. If you look on the
+
+ align:start position:0%
+the same order. If you look on the
+ 
+
+ align:start position:0%
+the same order. If you look on the
+periodic table, this is atomic hydrogen.
+
+ align:start position:0%
+periodic table, this is atomic hydrogen.
+ 
+
+ align:start position:0%
+periodic table, this is atomic hydrogen.
+And sure enough, there's
+
+ align:start position:0%
+And sure enough, there's
+ 
+
+ align:start position:0%
+And sure enough, there's
+13.598, which is this number here in
+
+ align:start position:0%
+13.598, which is this number here in
+ 
+
+ align:start position:0%
+13.598, which is this number here in
+electron volts. That's the ground state
+
+ align:start position:0%
+electron volts. That's the ground state
+ 
+
+ align:start position:0%
+electron volts. That's the ground state
+energy of atomic hydrogen. The other
+
+ align:start position:0%
+energy of atomic hydrogen. The other
+ 
+
+ align:start position:0%
+energy of atomic hydrogen. The other
+thing to note is look at the dependence
+
+ align:start position:0%
+thing to note is look at the dependence
+ 
+
+ align:start position:0%
+thing to note is look at the dependence
+upon Z.
+
+ align:start position:0%
+upon Z.
+ 
+
+ align:start position:0%
+upon Z.
+Suppose instead of hydrogen we
+
+ align:start position:0%
+Suppose instead of hydrogen we
+ 
+
+ align:start position:0%
+Suppose instead of hydrogen we
+considered lithium plus excuse me uh
+
+ align:start position:0%
+considered lithium plus excuse me uh
+ 
+
+ align:start position:0%
+considered lithium plus excuse me uh
+lithium 2+. Lithium 2+ is a is a one
+
+ align:start position:0%
+lithium 2+. Lithium 2+ is a is a one
+ 
+
+ align:start position:0%
+lithium 2+. Lithium 2+ is a is a one
+electron atom. Lithium has three
+
+ align:start position:0%
+electron atom. Lithium has three
+ 
+
+ align:start position:0%
+electron atom. Lithium has three
+electrons. If it loses two, one remains.
+
+ align:start position:0%
+electrons. If it loses two, one remains.
+ 
+
+ align:start position:0%
+electrons. If it loses two, one remains.
+What is this formula telling us? It's
+
+ align:start position:0%
+What is this formula telling us? It's
+ 
+
+ align:start position:0%
+What is this formula telling us? It's
+telling us that the ground state in
+
+ align:start position:0%
+telling us that the ground state in
+ 
+
+ align:start position:0%
+telling us that the ground state in
+lithium would be z. It would be nine
+
+ align:start position:0%
+lithium would be z. It would be nine
+ 
+
+ align:start position:0%
+lithium would be z. It would be nine
+times more intense. It' be nine times
+
+ align:start position:0%
+times more intense. It' be nine times
+ 
+
+ align:start position:0%
+times more intense. It' be nine times
+less. That is to say -9 is less than
+
+ align:start position:0%
+less. That is to say -9 is less than
+ 
+
+ align:start position:0%
+less. That is to say -9 is less than
+minus1. Okay. And that makes sense too
+
+ align:start position:0%
+minus1. Okay. And that makes sense too
+ 
+
+ align:start position:0%
+minus1. Okay. And that makes sense too
+because the positive3 pulling on minus1
+
+ align:start position:0%
+because the positive3 pulling on minus1
+ 
+
+ align:start position:0%
+because the positive3 pulling on minus1
+has a tighter binding energy than
+
+ align:start position:0%
+has a tighter binding energy than
+ 
+
+ align:start position:0%
+has a tighter binding energy than
+positive one pulling on minus1. So this
+
+ align:start position:0%
+positive one pulling on minus1. So this
+ 
+
+ align:start position:0%
+positive one pulling on minus1. So this
+drops by the square whereas the you saw
+
+ align:start position:0%
+drops by the square whereas the you saw
+ 
+
+ align:start position:0%
+drops by the square whereas the you saw
+how the the orbit goes. Um so just
+
+ align:start position:0%
+how the the orbit goes. Um so just
+ 
+
+ align:start position:0%
+how the the orbit goes. Um so just
+picking up on this ionization energy the
+
+ align:start position:0%
+picking up on this ionization energy the
+ 
+
+ align:start position:0%
+picking up on this ionization energy the
+ionization energy we can define as this
+
+ align:start position:0%
+ionization energy we can define as this
+ 
+
+ align:start position:0%
+ionization energy we can define as this
+is the minimum energy. This is the
+
+ align:start position:0%
+is the minimum energy. This is the
+ 
+
+ align:start position:0%
+is the minimum energy. This is the
+minimum energy to remove an electron.
+
+ align:start position:0%
+minimum energy to remove an electron.
+ 
+
+ align:start position:0%
+minimum energy to remove an electron.
+to remove an electron from the ground
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state from the ground state. Take out
+
+ align:start position:0%
+state from the ground state. Take out
+ 
+
+ align:start position:0%
+state from the ground state. Take out
+that ambiguity of an atom in the gas
+
+ align:start position:0%
+that ambiguity of an atom in the gas
+ 
+
+ align:start position:0%
+that ambiguity of an atom in the gas
+phase. All the things we're talking
+
+ align:start position:0%
+phase. All the things we're talking
+ 
+
+ align:start position:0%
+phase. All the things we're talking
+about here are with reference to the gas
+
+ align:start position:0%
+about here are with reference to the gas
+ 
+
+ align:start position:0%
+about here are with reference to the gas
+phase. Gas phase single atom. So we
+
+ align:start position:0%
+phase. Gas phase single atom. So we
+ 
+
+ align:start position:0%
+phase. Gas phase single atom. So we
+don't have to deal with work function or
+
+ align:start position:0%
+don't have to deal with work function or
+ 
+
+ align:start position:0%
+don't have to deal with work function or
+any kind of energies associated with
+
+ align:start position:0%
+any kind of energies associated with
+ 
+
+ align:start position:0%
+any kind of energies associated with
+some condensed form of matter. So we're
+
+ align:start position:0%
+some condensed form of matter. So we're
+ 
+
+ align:start position:0%
+some condensed form of matter. So we're
+really looking at uh this reaction here
+
+ align:start position:0%
+really looking at uh this reaction here
+ 
+
+ align:start position:0%
+really looking at uh this reaction here
+for ionization. It's H gas neutral goes
+
+ align:start position:0%
+for ionization. It's H gas neutral goes
+ 
+
+ align:start position:0%
+for ionization. It's H gas neutral goes
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+H+ in the gas phase plus the electron.
+
+ align:start position:0%
+H+ in the gas phase plus the electron.
+ 
+
+ align:start position:0%
+H+ in the gas phase plus the electron.
+Okay. And furthermore, we can have
+
+ align:start position:0%
+Okay. And furthermore, we can have
+ 
+
+ align:start position:0%
+Okay. And furthermore, we can have
+multiple ionization energies. If you
+
+ align:start position:0%
+multiple ionization energies. If you
+ 
+
+ align:start position:0%
+multiple ionization energies. If you
+have multiple electrons, we can lose
+
+ align:start position:0%
+have multiple electrons, we can lose
+ 
+
+ align:start position:0%
+have multiple electrons, we can lose
+them in sequence. So for example, I
+
+ align:start position:0%
+them in sequence. So for example, I
+ 
+
+ align:start position:0%
+them in sequence. So for example, I
+could look at the ionization of lithium.
+
+ align:start position:0%
+could look at the ionization of lithium.
+ 
+
+ align:start position:0%
+could look at the ionization of lithium.
+Again, lithium gas. lithium gas loses an
+
+ align:start position:0%
+Again, lithium gas. lithium gas loses an
+ 
+
+ align:start position:0%
+Again, lithium gas. lithium gas loses an
+electron to become lithium
+
+ align:start position:0%
+electron to become lithium
+ 
+
+ align:start position:0%
+electron to become lithium
+ion plus electron. I can then
+
+ align:start position:0%
+ion plus electron. I can then
+ 
+
+ align:start position:0%
+ion plus electron. I can then
+subsequently lose an electron from the
+
+ align:start position:0%
+subsequently lose an electron from the
+ 
+
+ align:start position:0%
+subsequently lose an electron from the
+lithium ion. So lithium ion loses an
+
+ align:start position:0%
+lithium ion. So lithium ion loses an
+ 
+
+ align:start position:0%
+lithium ion. So lithium ion loses an
+electron to become lithium
+
+ align:start position:0%
+electron to become lithium
+ 
+
+ align:start position:0%
+electron to become lithium
+2+ and the lithium 2+ still has an
+
+ align:start position:0%
+2+ and the lithium 2+ still has an
+ 
+
+ align:start position:0%
+2+ and the lithium 2+ still has an
+electron. Let's dnude lithium 2+. So
+
+ align:start position:0%
+electron. Let's dnude lithium 2+. So
+ 
+
+ align:start position:0%
+electron. Let's dnude lithium 2+. So
+lithium 2+ loses its electron to become
+
+ align:start position:0%
+lithium 2+ loses its electron to become
+ 
+
+ align:start position:0%
+lithium 2+ loses its electron to become
+just the this is the analogy to the
+
+ align:start position:0%
+just the this is the analogy to the
+ 
+
+ align:start position:0%
+just the this is the analogy to the
+alpha particle, right? This alpha
+
+ align:start position:0%
+alpha particle, right? This alpha
+ 
+
+ align:start position:0%
+alpha particle, right? This alpha
+particle was the helium nucleus. This is
+
+ align:start position:0%
+particle was the helium nucleus. This is
+ 
+
+ align:start position:0%
+particle was the helium nucleus. This is
+the lithium nucleus plus electron. So we
+
+ align:start position:0%
+the lithium nucleus plus electron. So we
+ 
+
+ align:start position:0%
+the lithium nucleus plus electron. So we
+call these first, second, third
+
+ align:start position:0%
+call these first, second, third
+ 
+
+ align:start position:0%
+call these first, second, third
+ionization energies in sequence. Right?
+
+ align:start position:0%
+ionization energies in sequence. Right?
+ 
+
+ align:start position:0%
+ionization energies in sequence. Right?
+This is this is the first
+
+ align:start position:0%
+This is this is the first
+ 
+
+ align:start position:0%
+This is this is the first
+ionization energy. This is the second
+
+ align:start position:0%
+ionization energy. This is the second
+ 
+
+ align:start position:0%
+ionization energy. This is the second
+ionization energy. That is to say the
+
+ align:start position:0%
+ionization energy. That is to say the
+ 
+
+ align:start position:0%
+ionization energy. That is to say the
+ionization energy of the
+
+ align:start position:0%
+ionization energy of the
+ 
+
+ align:start position:0%
+ionization energy of the
+second most electron. And this is the
+
+ align:start position:0%
+second most electron. And this is the
+ 
+
+ align:start position:0%
+second most electron. And this is the
+third ionization energy. Now where do we
+
+ align:start position:0%
+third ionization energy. Now where do we
+ 
+
+ align:start position:0%
+third ionization energy. Now where do we
+find these values? Well, if we look on
+
+ align:start position:0%
+find these values? Well, if we look on
+ 
+
+ align:start position:0%
+find these values? Well, if we look on
+the chart, the first ionization energy
+
+ align:start position:0%
+the chart, the first ionization energy
+ 
+
+ align:start position:0%
+the chart, the first ionization energy
+is what is reported in your periodic
+
+ align:start position:0%
+is what is reported in your periodic
+ 
+
+ align:start position:0%
+is what is reported in your periodic
+table. So, the first ionization energy
+
+ align:start position:0%
+table. So, the first ionization energy
+ 
+
+ align:start position:0%
+table. So, the first ionization energy
+of lithium is about
+
+ align:start position:0%
+of lithium is about
+ 
+
+ align:start position:0%
+of lithium is about
+5.4 electron volts per atom. So, we can
+
+ align:start position:0%
+5.4 electron volts per atom. So, we can
+ 
+
+ align:start position:0%
+5.4 electron volts per atom. So, we can
+get this uh from the periodic table.
+
+ align:start position:0%
+get this uh from the periodic table.
+ 
+
+ align:start position:0%
+get this uh from the periodic table.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+reported in periodic table and this is
+
+ align:start position:0%
+reported in periodic table and this is
+ 
+
+ align:start position:0%
+reported in periodic table and this is
+determined by measurement. This is
+
+ align:start position:0%
+determined by measurement. This is
+ 
+
+ align:start position:0%
+determined by measurement. This is
+determined by measurement.
+
+ align:start position:0%
+determined by measurement.
+ 
+
+ align:start position:0%
+determined by measurement.
+Uh, this one
+
+ align:start position:0%
+Uh, this one
+ 
+
+ align:start position:0%
+Uh, this one
+here can't do anything for you. I have
+
+ align:start position:0%
+here can't do anything for you. I have
+ 
+
+ align:start position:0%
+here can't do anything for you. I have
+to look that one up. What about this
+
+ align:start position:0%
+to look that one up. What about this
+ 
+
+ align:start position:0%
+to look that one up. What about this
+one? This one is calculable by the bore
+
+ align:start position:0%
+one? This one is calculable by the bore
+ 
+
+ align:start position:0%
+one? This one is calculable by the bore
+model because lithium 2+ is a one
+
+ align:start position:0%
+model because lithium 2+ is a one
+ 
+
+ align:start position:0%
+model because lithium 2+ is a one
+electron system. So, I just go through
+
+ align:start position:0%
+electron system. So, I just go through
+ 
+
+ align:start position:0%
+electron system. So, I just go through
+these equations. But be careful to put
+
+ align:start position:0%
+these equations. But be careful to put
+ 
+
+ align:start position:0%
+these equations. But be careful to put
+in Z= 3 and I can calculate this from
+
+ align:start position:0%
+in Z= 3 and I can calculate this from
+ 
+
+ align:start position:0%
+in Z= 3 and I can calculate this from
+bore
+
+ align:start position:0%
+bore
+ 
+
+ align:start position:0%
+bore
+model. Bore model. Let's say calculable.
+
+ align:start position:0%
+model. Bore model. Let's say calculable.
+ 
+
+ align:start position:0%
+model. Bore model. Let's say calculable.
+calculable by bore model and then
+
+ align:start position:0%
+calculable by bore model and then
+ 
+
+ align:start position:0%
+calculable by bore model and then
+remember Z equals 3. So, showing some
+
+ align:start position:0%
+remember Z equals 3. So, showing some
+ 
+
+ align:start position:0%
+remember Z equals 3. So, showing some
+versatility here. And let's see, we've
+
+ align:start position:0%
+versatility here. And let's see, we've
+ 
+
+ align:start position:0%
+versatility here. And let's see, we've
+talked about um radius, we've talked
+
+ align:start position:0%
+talked about um radius, we've talked
+ 
+
+ align:start position:0%
+talked about um radius, we've talked
+about energy. Let's talk about velocity.
+
+ align:start position:0%
+about energy. Let's talk about velocity.
+ 
+
+ align:start position:0%
+about energy. Let's talk about velocity.
+Just for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+completeness. Uh so the velocity is
+
+ align:start position:0%
+completeness. Uh so the velocity is
+ 
+
+ align:start position:0%
+completeness. Uh so the velocity is
+given by this uh product of the the
+
+ align:start position:0%
+given by this uh product of the the
+ 
+
+ align:start position:0%
+given by this uh product of the the
+quantum number n plank constant 2 pi
+
+ align:start position:0%
+quantum number n plank constant 2 pi
+ 
+
+ align:start position:0%
+quantum number n plank constant 2 pi
+mass of the electron time the radius of
+
+ align:start position:0%
+mass of the electron time the radius of
+ 
+
+ align:start position:0%
+mass of the electron time the radius of
+the orbit which itself is a function of
+
+ align:start position:0%
+the orbit which itself is a function of
+ 
+
+ align:start position:0%
+the orbit which itself is a function of
+n. We can make some substitutions here
+
+ align:start position:0%
+n. We can make some substitutions here
+ 
+
+ align:start position:0%
+n. We can make some substitutions here
+using some of the derivation on the
+
+ align:start position:0%
+using some of the derivation on the
+ 
+
+ align:start position:0%
+using some of the derivation on the
+previous board which will give us the
+
+ align:start position:0%
+previous board which will give us the
+ 
+
+ align:start position:0%
+previous board which will give us the
+plank constant / 2 pi mass of the
+
+ align:start position:0%
+plank constant / 2 pi mass of the
+ 
+
+ align:start position:0%
+plank constant / 2 pi mass of the
+electron times the bore
+
+ align:start position:0%
+electron times the bore
+ 
+
+ align:start position:0%
+electron times the bore
+radius. All of this times the ratio of Z
+
+ align:start position:0%
+radius. All of this times the ratio of Z
+ 
+
+ align:start position:0%
+radius. All of this times the ratio of Z
+over N where N equals 1 2 3
+
+ align:start position:0%
+over N where N equals 1 2 3
+ 
+
+ align:start position:0%
+over N where N equals 1 2 3
+so and we rarely look at velocity
+
+ align:start position:0%
+so and we rarely look at velocity
+ 
+
+ align:start position:0%
+so and we rarely look at velocity
+because we don't as you'll learn very
+
+ align:start position:0%
+because we don't as you'll learn very
+ 
+
+ align:start position:0%
+because we don't as you'll learn very
+quickly in 3091 we're not we're going to
+
+ align:start position:0%
+quickly in 3091 we're not we're going to
+ 
+
+ align:start position:0%
+quickly in 3091 we're not we're going to
+abandon this strict adherence to a
+
+ align:start position:0%
+abandon this strict adherence to a
+ 
+
+ align:start position:0%
+abandon this strict adherence to a
+planetary model pretty soon but it is
+
+ align:start position:0%
+planetary model pretty soon but it is
+ 
+
+ align:start position:0%
+planetary model pretty soon but it is
+interesting. Let's just for an order of
+
+ align:start position:0%
+interesting. Let's just for an order of
+ 
+
+ align:start position:0%
+interesting. Let's just for an order of
+magnitude say what happens um for ground
+
+ align:start position:0%
+magnitude say what happens um for ground
+ 
+
+ align:start position:0%
+magnitude say what happens um for ground
+state electron and atomic hydrogen. So
+
+ align:start position:0%
+state electron and atomic hydrogen. So
+ 
+
+ align:start position:0%
+state electron and atomic hydrogen. So
+we're going to put atomic hydrogen Z
+
+ align:start position:0%
+we're going to put atomic hydrogen Z
+ 
+
+ align:start position:0%
+we're going to put atomic hydrogen Z
+equals 1 ground state N= 1 that's just
+
+ align:start position:0%
+equals 1 ground state N= 1 that's just
+ 
+
+ align:start position:0%
+equals 1 ground state N= 1 that's just
+this quantity here. So let's find out.
+
+ align:start position:0%
+this quantity here. So let's find out.
+ 
+
+ align:start position:0%
+this quantity here. So let's find out.
+So V1 in atomic hydrogen. Is it fast? Is
+
+ align:start position:0%
+So V1 in atomic hydrogen. Is it fast? Is
+ 
+
+ align:start position:0%
+So V1 in atomic hydrogen. Is it fast? Is
+it slow? What's the number? Plug in the
+
+ align:start position:0%
+it slow? What's the number? Plug in the
+ 
+
+ align:start position:0%
+it slow? What's the number? Plug in the
+values. You get 2.18 *
+
+ align:start position:0%
+values. You get 2.18 *
+ 
+
+ align:start position:0%
+values. You get 2.18 *
+10us uh excuse me 10 + 6 m/s.
+
+ align:start position:0%
+10us uh excuse me 10 + 6 m/s.
+ 
+
+ align:start position:0%
+10us uh excuse me 10 + 6 m/s.
+10 plus 6 meters/s which is about 1% of
+
+ align:start position:0%
+10 plus 6 meters/s which is about 1% of
+ 
+
+ align:start position:0%
+10 plus 6 meters/s which is about 1% of
+the value of the speed of light 1% of
+
+ align:start position:0%
+the value of the speed of light 1% of
+ 
+
+ align:start position:0%
+the value of the speed of light 1% of
+the value of speed of light by the way C
+
+ align:start position:0%
+the value of speed of light by the way C
+ 
+
+ align:start position:0%
+the value of speed of light by the way C
+the value of speed of light in case you
+
+ align:start position:0%
+the value of speed of light in case you
+ 
+
+ align:start position:0%
+the value of speed of light in case you
+can't remember it is the number one
+
+ align:start position:0%
+can't remember it is the number one
+ 
+
+ align:start position:0%
+can't remember it is the number one
+entry in your in your table of constants
+
+ align:start position:0%
+entry in your in your table of constants
+ 
+
+ align:start position:0%
+entry in your in your table of constants
+so 1% of speed of light so I would say
+
+ align:start position:0%
+so 1% of speed of light so I would say
+ 
+
+ align:start position:0%
+so 1% of speed of light so I would say
+that's relatively fast that's a pun
+
+ align:start position:0%
+that's relatively fast that's a pun
+ 
+
+ align:start position:0%
+that's relatively fast that's a pun
+there think about this is a relatively
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fast yeah this is people have no sense
+
+ align:start position:0%
+fast yeah this is people have no sense
+ 
+
+ align:start position:0%
+fast yeah this is people have no sense
+of humor no sense of joy no sense of uh
+
+ align:start position:0%
+of humor no sense of joy no sense of uh
+ 
+
+ align:start position:0%
+of humor no sense of joy no sense of uh
+dev. You're so young. You've only been
+
+ align:start position:0%
+dev. You're so young. You've only been
+ 
+
+ align:start position:0%
+dev. You're so young. You've only been
+here a week and so jaded. You got four
+
+ align:start position:0%
+here a week and so jaded. You got four
+ 
+
+ align:start position:0%
+here a week and so jaded. You got four
+years to
+
+ align:start position:0%
+years to
+ 
+
+ align:start position:0%
+years to
+go. So where does C come from? How come
+
+ align:start position:0%
+go. So where does C come from? How come
+ 
+
+ align:start position:0%
+go. So where does C come from? How come
+the speed of light has the symbol C?
+
+ align:start position:0%
+the speed of light has the symbol C?
+ 
+
+ align:start position:0%
+the speed of light has the symbol C?
+Where is the symbol C? It comes from the
+
+ align:start position:0%
+Where is the symbol C? It comes from the
+ 
+
+ align:start position:0%
+Where is the symbol C? It comes from the
+Latin
+
+ align:start position:0%
+Latin
+ 
+
+ align:start position:0%
+Latin
+word caleritas, which means swiftness.
+
+ align:start position:0%
+word caleritas, which means swiftness.
+ 
+
+ align:start position:0%
+word caleritas, which means swiftness.
+We get the English word accelerate from
+
+ align:start position:0%
+We get the English word accelerate from
+ 
+
+ align:start position:0%
+We get the English word accelerate from
+the same root word. That's why that's
+
+ align:start position:0%
+the same root word. That's why that's
+ 
+
+ align:start position:0%
+the same root word. That's why that's
+why we have one. That's why we have C.
+
+ align:start position:0%
+why we have one. That's why we have C.
+ 
+
+ align:start position:0%
+why we have one. That's why we have C.
+All right. So we're in pretty good shape
+
+ align:start position:0%
+All right. So we're in pretty good shape
+ 
+
+ align:start position:0%
+All right. So we're in pretty good shape
+here. We've got a bore model. Bore
+
+ align:start position:0%
+here. We've got a bore model. Bore
+ 
+
+ align:start position:0%
+here. We've got a bore model. Bore
+model's quantitative. So, um, it makes
+
+ align:start position:0%
+model's quantitative. So, um, it makes
+ 
+
+ align:start position:0%
+model's quantitative. So, um, it makes
+predictions that can be tested. We've
+
+ align:start position:0%
+predictions that can be tested. We've
+ 
+
+ align:start position:0%
+predictions that can be tested. We've
+got energies. We got
+
+ align:start position:0%
+got energies. We got
+ 
+
+ align:start position:0%
+got energies. We got
+radi. So, is there any experimental
+
+ align:start position:0%
+radi. So, is there any experimental
+ 
+
+ align:start position:0%
+radi. So, is there any experimental
+evidence that can put this to the test?
+
+ align:start position:0%
+evidence that can put this to the test?
+ 
+
+ align:start position:0%
+evidence that can put this to the test?
+And the answer is yes. In the early
+
+ align:start position:0%
+And the answer is yes. In the early
+ 
+
+ align:start position:0%
+And the answer is yes. In the early
+1850s,
+
+ align:start position:0%
+1850s,
+ 
+
+ align:start position:0%
+1850s,
+um, Angstrom Angstrom up at the, uh,
+
+ align:start position:0%
+um, Angstrom Angstrom up at the, uh,
+ 
+
+ align:start position:0%
+um, Angstrom Angstrom up at the, uh,
+University of of Upsula in Sweden was
+
+ align:start position:0%
+University of of Upsula in Sweden was
+ 
+
+ align:start position:0%
+University of of Upsula in Sweden was
+conducting experiments on atomic
+
+ align:start position:0%
+conducting experiments on atomic
+ 
+
+ align:start position:0%
+conducting experiments on atomic
+hydrogen. He was doing experiments in a
+
+ align:start position:0%
+hydrogen. He was doing experiments in a
+ 
+
+ align:start position:0%
+hydrogen. He was doing experiments in a
+gas discharge tube. He had a tube with
+
+ align:start position:0%
+gas discharge tube. He had a tube with
+ 
+
+ align:start position:0%
+gas discharge tube. He had a tube with
+electrodes potted in it filled with
+
+ align:start position:0%
+electrodes potted in it filled with
+ 
+
+ align:start position:0%
+electrodes potted in it filled with
+atomic hydrogen and by applying a
+
+ align:start position:0%
+atomic hydrogen and by applying a
+ 
+
+ align:start position:0%
+atomic hydrogen and by applying a
+voltage he was able to get the gas to
+
+ align:start position:0%
+voltage he was able to get the gas to
+ 
+
+ align:start position:0%
+voltage he was able to get the gas to
+glow and then he analyzed the components
+
+ align:start position:0%
+glow and then he analyzed the components
+ 
+
+ align:start position:0%
+glow and then he analyzed the components
+of that radiation and this is what he
+
+ align:start position:0%
+of that radiation and this is what he
+ 
+
+ align:start position:0%
+of that radiation and this is what he
+found. First of all, let's take a look
+
+ align:start position:0%
+found. First of all, let's take a look
+ 
+
+ align:start position:0%
+found. First of all, let's take a look
+at his experiment. Uh there it is. This
+
+ align:start position:0%
+at his experiment. Uh there it is. This
+ 
+
+ align:start position:0%
+at his experiment. Uh there it is. This
+is he used the prism spectrograph to
+
+ align:start position:0%
+is he used the prism spectrograph to
+ 
+
+ align:start position:0%
+is he used the prism spectrograph to
+analyze his results. So what do we have
+
+ align:start position:0%
+analyze his results. So what do we have
+ 
+
+ align:start position:0%
+analyze his results. So what do we have
+here? Here's the gas discharge tube.
+
+ align:start position:0%
+here? Here's the gas discharge tube.
+ 
+
+ align:start position:0%
+here? Here's the gas discharge tube.
+This is the diagram taken right from
+
+ align:start position:0%
+This is the diagram taken right from
+ 
+
+ align:start position:0%
+This is the diagram taken right from
+your text. It's uh there's the two
+
+ align:start position:0%
+your text. It's uh there's the two
+ 
+
+ align:start position:0%
+your text. It's uh there's the two
+electrodes coming in and this is atomic
+
+ align:start position:0%
+electrodes coming in and this is atomic
+ 
+
+ align:start position:0%
+electrodes coming in and this is atomic
+hydrogen in the gas tube. And so if he
+
+ align:start position:0%
+hydrogen in the gas tube. And so if he
+ 
+
+ align:start position:0%
+hydrogen in the gas tube. And so if he
+gets the voltage high enough, this gas
+
+ align:start position:0%
+gets the voltage high enough, this gas
+ 
+
+ align:start position:0%
+gets the voltage high enough, this gas
+discharge tube will glow and the light
+
+ align:start position:0%
+discharge tube will glow and the light
+ 
+
+ align:start position:0%
+discharge tube will glow and the light
+will be going in all directions.
+
+ align:start position:0%
+will be going in all directions.
+ 
+
+ align:start position:0%
+will be going in all directions.
+Obviously, it's a glass tube. So he he
+
+ align:start position:0%
+Obviously, it's a glass tube. So he he
+ 
+
+ align:start position:0%
+Obviously, it's a glass tube. So he he
+wants to narrow the light. So he puts a
+
+ align:start position:0%
+wants to narrow the light. So he puts a
+ 
+
+ align:start position:0%
+wants to narrow the light. So he puts a
+couple of slits here and then he just
+
+ align:start position:0%
+couple of slits here and then he just
+ 
+
+ align:start position:0%
+couple of slits here and then he just
+takes that narrow column of light and he
+
+ align:start position:0%
+takes that narrow column of light and he
+ 
+
+ align:start position:0%
+takes that narrow column of light and he
+admits it to a prism. And what the prism
+
+ align:start position:0%
+admits it to a prism. And what the prism
+ 
+
+ align:start position:0%
+admits it to a prism. And what the prism
+does is it takes a tiny tiny difference
+
+ align:start position:0%
+does is it takes a tiny tiny difference
+ 
+
+ align:start position:0%
+does is it takes a tiny tiny difference
+in wavelength and refracts it through a
+
+ align:start position:0%
+in wavelength and refracts it through a
+ 
+
+ align:start position:0%
+in wavelength and refracts it through a
+different angle. And if the prism is of
+
+ align:start position:0%
+different angle. And if the prism is of
+ 
+
+ align:start position:0%
+different angle. And if the prism is of
+sufficient dimension that angle can be
+
+ align:start position:0%
+sufficient dimension that angle can be
+ 
+
+ align:start position:0%
+sufficient dimension that angle can be
+magnified and then further you put a
+
+ align:start position:0%
+magnified and then further you put a
+ 
+
+ align:start position:0%
+magnified and then further you put a
+some recording device which in those
+
+ align:start position:0%
+some recording device which in those
+ 
+
+ align:start position:0%
+some recording device which in those
+days was a photographic plate far across
+
+ align:start position:0%
+days was a photographic plate far across
+ 
+
+ align:start position:0%
+days was a photographic plate far across
+a room. So you take a tiny tiny angle
+
+ align:start position:0%
+a room. So you take a tiny tiny angle
+ 
+
+ align:start position:0%
+a room. So you take a tiny tiny angle
+and you go far enough across the room
+
+ align:start position:0%
+and you go far enough across the room
+ 
+
+ align:start position:0%
+and you go far enough across the room
+and now you get separation on the order
+
+ align:start position:0%
+and now you get separation on the order
+ 
+
+ align:start position:0%
+and now you get separation on the order
+of centimeters. and we record here. And
+
+ align:start position:0%
+of centimeters. and we record here. And
+ 
+
+ align:start position:0%
+of centimeters. and we record here. And
+this is the the blowup of what's on that
+
+ align:start position:0%
+this is the the blowup of what's on that
+ 
+
+ align:start position:0%
+this is the the blowup of what's on that
+photographic plate. And and this was
+
+ align:start position:0%
+photographic plate. And and this was
+ 
+
+ align:start position:0%
+photographic plate. And and this was
+painstaking work. Okay. What what you've
+
+ align:start position:0%
+painstaking work. Okay. What what you've
+ 
+
+ align:start position:0%
+painstaking work. Okay. What what you've
+got here is the photographic plate
+
+ align:start position:0%
+got here is the photographic plate
+ 
+
+ align:start position:0%
+got here is the photographic plate
+demonstrating a spread. First of all,
+
+ align:start position:0%
+demonstrating a spread. First of all,
+ 
+
+ align:start position:0%
+demonstrating a spread. First of all,
+that the the the glow is made up of
+
+ align:start position:0%
+that the the the glow is made up of
+ 
+
+ align:start position:0%
+that the the the glow is made up of
+constituents. There are distinct lines
+
+ align:start position:0%
+constituents. There are distinct lines
+ 
+
+ align:start position:0%
+constituents. There are distinct lines
+here. What what appears to the naked eye
+
+ align:start position:0%
+here. What what appears to the naked eye
+ 
+
+ align:start position:0%
+here. What what appears to the naked eye
+to be just glowing is actually
+
+ align:start position:0%
+to be just glowing is actually
+ 
+
+ align:start position:0%
+to be just glowing is actually
+superposition of different lines of
+
+ align:start position:0%
+superposition of different lines of
+ 
+
+ align:start position:0%
+superposition of different lines of
+distinct frequency. So you see this is
+
+ align:start position:0%
+distinct frequency. So you see this is
+ 
+
+ align:start position:0%
+distinct frequency. So you see this is
+quantized. It's
+
+ align:start position:0%
+quantized. It's
+ 
+
+ align:start position:0%
+quantized. It's
+quantized. And so he published his
+
+ align:start position:0%
+quantized. And so he published his
+ 
+
+ align:start position:0%
+quantized. And so he published his
+results around
+
+ align:start position:0%
+results around
+ 
+
+ align:start position:0%
+results around
+1853. And so they lay. So let's
+
+ align:start position:0%
+1853. And so they lay. So let's
+ 
+
+ align:start position:0%
+1853. And so they lay. So let's
+get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1853. Let's get
+
+ align:start position:0%
+1853. Let's get
+ 
+
+ align:start position:0%
+1853. Let's get
+Angstrom up on the board here since he
+
+ align:start position:0%
+Angstrom up on the board here since he
+ 
+
+ align:start position:0%
+Angstrom up on the board here since he
+did the
+
+ align:start position:0%
+did the
+ 
+
+ align:start position:0%
+did the
+work. He was upsell in Sweden. So he he
+
+ align:start position:0%
+work. He was upsell in Sweden. So he he
+ 
+
+ align:start position:0%
+work. He was upsell in Sweden. So he he
+measured the line spectra line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectra of atomic
+
+ align:start position:0%
+spectra of atomic
+ 
+
+ align:start position:0%
+spectra of atomic
+hydrogen. By the way, your your text has
+
+ align:start position:0%
+hydrogen. By the way, your your text has
+ 
+
+ align:start position:0%
+hydrogen. By the way, your your text has
+a glaring error. The the label above
+
+ align:start position:0%
+a glaring error. The the label above
+ 
+
+ align:start position:0%
+a glaring error. The the label above
+this figure refers to H2. Take a take
+
+ align:start position:0%
+this figure refers to H2. Take a take
+ 
+
+ align:start position:0%
+this figure refers to H2. Take a take
+the fattest marking pen you have,
+
+ align:start position:0%
+the fattest marking pen you have,
+ 
+
+ align:start position:0%
+the fattest marking pen you have,
+scratch that out, and replace it with
+
+ align:start position:0%
+scratch that out, and replace it with
+ 
+
+ align:start position:0%
+scratch that out, and replace it with
+atomic hydrogen. You do not get this
+
+ align:start position:0%
+atomic hydrogen. You do not get this
+ 
+
+ align:start position:0%
+atomic hydrogen. You do not get this
+line from from uh hydrogen uh molecular
+
+ align:start position:0%
+line from from uh hydrogen uh molecular
+ 
+
+ align:start position:0%
+line from from uh hydrogen uh molecular
+hydrogen. So we've got the line spectra
+
+ align:start position:0%
+hydrogen. So we've got the line spectra
+ 
+
+ align:start position:0%
+hydrogen. So we've got the line spectra
+lying out there in the literature and
+
+ align:start position:0%
+lying out there in the literature and
+ 
+
+ align:start position:0%
+lying out there in the literature and
+people read the literature. They read
+
+ align:start position:0%
+people read the literature. They read
+ 
+
+ align:start position:0%
+people read the literature. They read
+and one of the person one of the people
+
+ align:start position:0%
+and one of the person one of the people
+ 
+
+ align:start position:0%
+and one of the person one of the people
+that was reading this literature was a
+
+ align:start position:0%
+that was reading this literature was a
+ 
+
+ align:start position:0%
+that was reading this literature was a
+school teacher a high school teacher
+
+ align:start position:0%
+school teacher a high school teacher
+ 
+
+ align:start position:0%
+school teacher a high school teacher
+who's teaching uh mathematics in Basil
+
+ align:start position:0%
+who's teaching uh mathematics in Basil
+ 
+
+ align:start position:0%
+who's teaching uh mathematics in Basil
+in Switzerland. So this man
+
+ align:start position:0%
+in Switzerland. So this man
+ 
+
+ align:start position:0%
+in Switzerland. So this man
+was he also had the initials JJ as in JJ
+
+ align:start position:0%
+was he also had the initials JJ as in JJ
+ 
+
+ align:start position:0%
+was he also had the initials JJ as in JJ
+Thompson. This is JJ Balmer and JJ
+
+ align:start position:0%
+Thompson. This is JJ Balmer and JJ
+ 
+
+ align:start position:0%
+Thompson. This is JJ Balmer and JJ
+Balmer in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1885 playing with the numbers associated
+
+ align:start position:0%
+1885 playing with the numbers associated
+ 
+
+ align:start position:0%
+1885 playing with the numbers associated
+with the lines there. You notice how the
+
+ align:start position:0%
+with the lines there. You notice how the
+ 
+
+ align:start position:0%
+with the lines there. You notice how the
+lines are colored? Your book isn't
+
+ align:start position:0%
+lines are colored? Your book isn't
+ 
+
+ align:start position:0%
+lines are colored? Your book isn't
+colored. See, I colored them for you.
+
+ align:start position:0%
+colored. See, I colored them for you.
+ 
+
+ align:start position:0%
+colored. See, I colored them for you.
+You know, I care about you. I wanted to
+
+ align:start position:0%
+You know, I care about you. I wanted to
+ 
+
+ align:start position:0%
+You know, I care about you. I wanted to
+illustrate that there's representing
+
+ align:start position:0%
+illustrate that there's representing
+ 
+
+ align:start position:0%
+illustrate that there's representing
+different wavelengths in the visible,
+
+ align:start position:0%
+different wavelengths in the visible,
+ 
+
+ align:start position:0%
+different wavelengths in the visible,
+you know, and I and the doctor told me
+
+ align:start position:0%
+you know, and I and the doctor told me
+ 
+
+ align:start position:0%
+you know, and I and the doctor told me
+it's it's good for me to express my
+
+ align:start position:0%
+it's it's good for me to express my
+ 
+
+ align:start position:0%
+it's it's good for me to express my
+creative urges because it's so so I I
+
+ align:start position:0%
+creative urges because it's so so I I
+ 
+
+ align:start position:0%
+creative urges because it's so so I I
+got out my pen and and I did
+
+ align:start position:0%
+got out my pen and and I did
+ 
+
+ align:start position:0%
+got out my pen and and I did
+that. Where was I? Oh, so so what Balmer
+
+ align:start position:0%
+that. Where was I? Oh, so so what Balmer
+ 
+
+ align:start position:0%
+that. Where was I? Oh, so so what Balmer
+did Balmer he all he has is those four
+
+ align:start position:0%
+did Balmer he all he has is those four
+ 
+
+ align:start position:0%
+did Balmer he all he has is those four
+numbers. He's got the wavelengths of
+
+ align:start position:0%
+numbers. He's got the wavelengths of
+ 
+
+ align:start position:0%
+numbers. He's got the wavelengths of
+those four numbers and he's playing with
+
+ align:start position:0%
+those four numbers and he's playing with
+ 
+
+ align:start position:0%
+those four numbers and he's playing with
+those numbers. He's determined to make
+
+ align:start position:0%
+those numbers. He's determined to make
+ 
+
+ align:start position:0%
+those numbers. He's determined to make
+sense of those four numbers in some kind
+
+ align:start position:0%
+sense of those four numbers in some kind
+ 
+
+ align:start position:0%
+sense of those four numbers in some kind
+of a sequence and this is what he came
+
+ align:start position:0%
+of a sequence and this is what he came
+ 
+
+ align:start position:0%
+of a sequence and this is what he came
+up with finally he came up with the
+
+ align:start position:0%
+up with finally he came up with the
+ 
+
+ align:start position:0%
+up with finally he came up with the
+relationship
+
+ align:start position:0%
+relationship
+ 
+
+ align:start position:0%
+relationship
+that newbar which is called wave
+
+ align:start position:0%
+that newbar which is called wave
+ 
+
+ align:start position:0%
+that newbar which is called wave
+number wave number which in he found the
+
+ align:start position:0%
+number wave number which in he found the
+ 
+
+ align:start position:0%
+number wave number which in he found the
+reciprocal what he did he coined this
+
+ align:start position:0%
+reciprocal what he did he coined this
+ 
+
+ align:start position:0%
+reciprocal what he did he coined this
+but he found that by taking the
+
+ align:start position:0%
+but he found that by taking the
+ 
+
+ align:start position:0%
+but he found that by taking the
+reciprocal of the wavelengths you've got
+
+ align:start position:0%
+reciprocal of the wavelengths you've got
+ 
+
+ align:start position:0%
+reciprocal of the wavelengths you've got
+four numbers he took the reciprocals of
+
+ align:start position:0%
+four numbers he took the reciprocals of
+ 
+
+ align:start position:0%
+four numbers he took the reciprocals of
+those wavelengths he found that they fit
+
+ align:start position:0%
+those wavelengths he found that they fit
+ 
+
+ align:start position:0%
+those wavelengths he found that they fit
+Get a sequence, a numerical sequence 1 /
+
+ align:start position:0%
+Get a sequence, a numerical sequence 1 /
+ 
+
+ align:start position:0%
+Get a sequence, a numerical sequence 1 /
+2^2 - 1 /
+
+ align:start position:0%
+2^2 - 1 /
+ 
+
+ align:start position:0%
+2^2 - 1 /
+n^2 where n takes values 3 4 5 6 3 4 5
+
+ align:start position:0%
+n^2 where n takes values 3 4 5 6 3 4 5
+ 
+
+ align:start position:0%
+n^2 where n takes values 3 4 5 6 3 4 5
+6 and there's a constant out here and
+
+ align:start position:0%
+6 and there's a constant out here and
+ 
+
+ align:start position:0%
+6 and there's a constant out here and
+the constant if we redo it in in modern
+
+ align:start position:0%
+the constant if we redo it in in modern
+ 
+
+ align:start position:0%
+the constant if we redo it in in modern
+SI units would take on the value of 1.1
+
+ align:start position:0%
+SI units would take on the value of 1.1
+ 
+
+ align:start position:0%
+SI units would take on the value of 1.1
+* 10
+
+ align:start position:0%
+* 10
+ 
+
+ align:start position:0%
+* 10
+7th reciprocal
+
+ align:start position:0%
+7th reciprocal
+ 
+
+ align:start position:0%
+7th reciprocal
+meters 1.1 * 10 7th uh reciprocal
+
+ align:start position:0%
+meters 1.1 * 10 7th uh reciprocal
+ 
+
+ align:start position:0%
+meters 1.1 * 10 7th uh reciprocal
+meters.
+
+ align:start position:0%
+meters.
+ 
+
+ align:start position:0%
+meters.
+So how does this support the bore model?
+
+ align:start position:0%
+So how does this support the bore model?
+ 
+
+ align:start position:0%
+So how does this support the bore model?
+Well, in order to answer that question,
+
+ align:start position:0%
+Well, in order to answer that question,
+ 
+
+ align:start position:0%
+Well, in order to answer that question,
+I've got to give you a little more
+
+ align:start position:0%
+I've got to give you a little more
+ 
+
+ align:start position:0%
+I've got to give you a little more
+background information. First thing I do
+
+ align:start position:0%
+background information. First thing I do
+ 
+
+ align:start position:0%
+background information. First thing I do
+is give you the understanding of what's
+
+ align:start position:0%
+is give you the understanding of what's
+ 
+
+ align:start position:0%
+is give you the understanding of what's
+the physics of the uh gas discharge
+
+ align:start position:0%
+the physics of the uh gas discharge
+ 
+
+ align:start position:0%
+the physics of the uh gas discharge
+tube. So let's let's take a look inside
+
+ align:start position:0%
+tube. So let's let's take a look inside
+ 
+
+ align:start position:0%
+tube. So let's let's take a look inside
+that tube. So let me redraw it. I'm
+
+ align:start position:0%
+that tube. So let me redraw it. I'm
+ 
+
+ align:start position:0%
+that tube. So let me redraw it. I'm
+going to redraw it horizontally. So this
+
+ align:start position:0%
+going to redraw it horizontally. So this
+ 
+
+ align:start position:0%
+going to redraw it horizontally. So this
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+glass glass
+
+ align:start position:0%
+glass glass
+ 
+
+ align:start position:0%
+glass glass
+tube. There are some feedroughs here to
+
+ align:start position:0%
+tube. There are some feedroughs here to
+ 
+
+ align:start position:0%
+tube. There are some feedroughs here to
+allow electrodes to be potted. So this
+
+ align:start position:0%
+allow electrodes to be potted. So this
+ 
+
+ align:start position:0%
+allow electrodes to be potted. So this
+is this is these are gastight
+
+ align:start position:0%
+is this is these are gastight
+ 
+
+ align:start position:0%
+is this is these are gastight
+feedroughs. And these electrodes are
+
+ align:start position:0%
+feedroughs. And these electrodes are
+ 
+
+ align:start position:0%
+feedroughs. And these electrodes are
+then connected to a variable voltage
+
+ align:start position:0%
+then connected to a variable voltage
+ 
+
+ align:start position:0%
+then connected to a variable voltage
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+supply and it's possible to to change
+
+ align:start position:0%
+supply and it's possible to to change
+ 
+
+ align:start position:0%
+supply and it's possible to to change
+the voltage on this on the plates. And
+
+ align:start position:0%
+the voltage on this on the plates. And
+ 
+
+ align:start position:0%
+the voltage on this on the plates. And
+the way I've got this configured, uh,
+
+ align:start position:0%
+the way I've got this configured, uh,
+ 
+
+ align:start position:0%
+the way I've got this configured, uh,
+the left electrode is going to be
+
+ align:start position:0%
+the left electrode is going to be
+ 
+
+ align:start position:0%
+the left electrode is going to be
+charged negatively and the right
+
+ align:start position:0%
+charged negatively and the right
+ 
+
+ align:start position:0%
+charged negatively and the right
+electrode is going to be charged
+
+ align:start position:0%
+electrode is going to be charged
+ 
+
+ align:start position:0%
+electrode is going to be charged
+positively. So this will be the left
+
+ align:start position:0%
+positively. So this will be the left
+ 
+
+ align:start position:0%
+positively. So this will be the left
+electrode will be the cathode as I've
+
+ align:start position:0%
+electrode will be the cathode as I've
+ 
+
+ align:start position:0%
+electrode will be the cathode as I've
+configured it and the right electron the
+
+ align:start position:0%
+configured it and the right electron the
+ 
+
+ align:start position:0%
+configured it and the right electron the
+right electrode will be the anode. And
+
+ align:start position:0%
+right electrode will be the anode. And
+ 
+
+ align:start position:0%
+right electrode will be the anode. And
+um, what is inside the gas discharge
+
+ align:start position:0%
+um, what is inside the gas discharge
+ 
+
+ align:start position:0%
+um, what is inside the gas discharge
+tube is gas at low
+
+ align:start position:0%
+tube is gas at low
+ 
+
+ align:start position:0%
+tube is gas at low
+pressure. Gas at low pressure.
+
+ align:start position:0%
+pressure. Gas at low pressure.
+ 
+
+ align:start position:0%
+pressure. Gas at low pressure.
+As we increase the voltage, we get to a
+
+ align:start position:0%
+As we increase the voltage, we get to a
+ 
+
+ align:start position:0%
+As we increase the voltage, we get to a
+critical value at which it's possible to
+
+ align:start position:0%
+critical value at which it's possible to
+ 
+
+ align:start position:0%
+critical value at which it's possible to
+actually draw electrons across the gap.
+
+ align:start position:0%
+actually draw electrons across the gap.
+ 
+
+ align:start position:0%
+actually draw electrons across the gap.
+Electrons will actually boil off the
+
+ align:start position:0%
+Electrons will actually boil off the
+ 
+
+ align:start position:0%
+Electrons will actually boil off the
+cathode and accelerate across. You've
+
+ align:start position:0%
+cathode and accelerate across. You've
+ 
+
+ align:start position:0%
+cathode and accelerate across. You've
+got a positive electrode here and the
+
+ align:start position:0%
+got a positive electrode here and the
+ 
+
+ align:start position:0%
+got a positive electrode here and the
+electron is charged negatively. It will
+
+ align:start position:0%
+electron is charged negatively. It will
+ 
+
+ align:start position:0%
+electron is charged negatively. It will
+be drawn to the positive electrode. So,
+
+ align:start position:0%
+be drawn to the positive electrode. So,
+ 
+
+ align:start position:0%
+be drawn to the positive electrode. So,
+it will accelerate from rest, crash into
+
+ align:start position:0%
+it will accelerate from rest, crash into
+ 
+
+ align:start position:0%
+it will accelerate from rest, crash into
+the anode.
+
+ align:start position:0%
+the anode.
+ 
+
+ align:start position:0%
+the anode.
+So if we have nothing here, we see
+
+ align:start position:0%
+So if we have nothing here, we see
+ 
+
+ align:start position:0%
+So if we have nothing here, we see
+nothing. If we have too much gas in
+
+ align:start position:0%
+nothing. If we have too much gas in
+ 
+
+ align:start position:0%
+nothing. If we have too much gas in
+here, in other words, if the gas is at
+
+ align:start position:0%
+here, in other words, if the gas is at
+ 
+
+ align:start position:0%
+here, in other words, if the gas is at
+too high a pressure, the collisions with
+
+ align:start position:0%
+too high a pressure, the collisions with
+ 
+
+ align:start position:0%
+too high a pressure, the collisions with
+the gas molecules will consume the
+
+ align:start position:0%
+the gas molecules will consume the
+ 
+
+ align:start position:0%
+the gas molecules will consume the
+energy of the electrons and again, we'll
+
+ align:start position:0%
+energy of the electrons and again, we'll
+ 
+
+ align:start position:0%
+energy of the electrons and again, we'll
+see nothing. So if we get the the
+
+ align:start position:0%
+see nothing. So if we get the the
+ 
+
+ align:start position:0%
+see nothing. So if we get the the
+pressure in there just right, we'll
+
+ align:start position:0%
+pressure in there just right, we'll
+ 
+
+ align:start position:0%
+pressure in there just right, we'll
+allow for gas electron collisions, and
+
+ align:start position:0%
+allow for gas electron collisions, and
+ 
+
+ align:start position:0%
+allow for gas electron collisions, and
+then we get the the glow that ultimately
+
+ align:start position:0%
+then we get the the glow that ultimately
+ 
+
+ align:start position:0%
+then we get the the glow that ultimately
+was sent through the the slits.
+
+ align:start position:0%
+was sent through the the slits.
+ 
+
+ align:start position:0%
+was sent through the the slits.
+So that's
+
+ align:start position:0%
+So that's
+ 
+
+ align:start position:0%
+So that's
+the operation of the gas discharge tube.
+
+ align:start position:0%
+the operation of the gas discharge tube.
+ 
+
+ align:start position:0%
+the operation of the gas discharge tube.
+Now let's look at the physics. What's
+
+ align:start position:0%
+Now let's look at the physics. What's
+ 
+
+ align:start position:0%
+Now let's look at the physics. What's
+the energy of the electron? The energy
+
+ align:start position:0%
+the energy of the electron? The energy
+ 
+
+ align:start position:0%
+the energy of the electron? The energy
+of this electron accelerating from rest
+
+ align:start position:0%
+of this electron accelerating from rest
+ 
+
+ align:start position:0%
+of this electron accelerating from rest
+and crashing into the uh anode here.
+
+ align:start position:0%
+and crashing into the uh anode here.
+ 
+
+ align:start position:0%
+and crashing into the uh anode here.
+Well, it's going to be mechanical a half
+
+ align:start position:0%
+Well, it's going to be mechanical a half
+ 
+
+ align:start position:0%
+Well, it's going to be mechanical a half
+mv
+
+ align:start position:0%
+mv
+ 
+
+ align:start position:0%
+mv
+squared. And how about potential energy?
+
+ align:start position:0%
+squared. And how about potential energy?
+ 
+
+ align:start position:0%
+squared. And how about potential energy?
+It's it's not bound. It's a free
+
+ align:start position:0%
+It's it's not bound. It's a free
+ 
+
+ align:start position:0%
+It's it's not bound. It's a free
+electron. So there's no potential energy
+
+ align:start position:0%
+electron. So there's no potential energy
+ 
+
+ align:start position:0%
+electron. So there's no potential energy
+to be accounted for. So it's simply half
+
+ align:start position:0%
+to be accounted for. So it's simply half
+ 
+
+ align:start position:0%
+to be accounted for. So it's simply half
+MV^2. But I can equate the amount of
+
+ align:start position:0%
+MV^2. But I can equate the amount of
+ 
+
+ align:start position:0%
+MV^2. But I can equate the amount of
+energy, mechanical energy in the
+
+ align:start position:0%
+energy, mechanical energy in the
+ 
+
+ align:start position:0%
+energy, mechanical energy in the
+electron to the amount of electrical
+
+ align:start position:0%
+electron to the amount of electrical
+ 
+
+ align:start position:0%
+electron to the amount of electrical
+energy that was imparted through the
+
+ align:start position:0%
+energy that was imparted through the
+ 
+
+ align:start position:0%
+energy that was imparted through the
+electrodes. And the electrical energy is
+
+ align:start position:0%
+electrodes. And the electrical energy is
+ 
+
+ align:start position:0%
+electrodes. And the electrical energy is
+the product of the charge on the
+
+ align:start position:0%
+the product of the charge on the
+ 
+
+ align:start position:0%
+the product of the charge on the
+electrodes, excuse me, the charge on the
+
+ align:start position:0%
+electrodes, excuse me, the charge on the
+ 
+
+ align:start position:0%
+electrodes, excuse me, the charge on the
+electron times the voltage, which is the
+
+ align:start position:0%
+electron times the voltage, which is the
+ 
+
+ align:start position:0%
+electron times the voltage, which is the
+potential difference through which the
+
+ align:start position:0%
+potential difference through which the
+ 
+
+ align:start position:0%
+potential difference through which the
+electron was accelerated.
+
+ align:start position:0%
+electron was accelerated.
+ 
+
+ align:start position:0%
+electron was accelerated.
+And so this allows me to by increasing
+
+ align:start position:0%
+And so this allows me to by increasing
+ 
+
+ align:start position:0%
+And so this allows me to by increasing
+the voltage increase the energy on the
+
+ align:start position:0%
+the voltage increase the energy on the
+ 
+
+ align:start position:0%
+the voltage increase the energy on the
+electron. So you can see low voltage,
+
+ align:start position:0%
+electron. So you can see low voltage,
+ 
+
+ align:start position:0%
+electron. So you can see low voltage,
+low energy, high voltage, high energy.
+
+ align:start position:0%
+low energy, high voltage, high energy.
+ 
+
+ align:start position:0%
+low energy, high voltage, high energy.
+It's a linear function. And how about
+
+ align:start position:0%
+It's a linear function. And how about
+ 
+
+ align:start position:0%
+It's a linear function. And how about
+order of magnitude? Let's let's see
+
+ align:start position:0%
+order of magnitude? Let's let's see
+ 
+
+ align:start position:0%
+order of magnitude? Let's let's see
+suppose I took let's do everything unit.
+
+ align:start position:0%
+suppose I took let's do everything unit.
+ 
+
+ align:start position:0%
+suppose I took let's do everything unit.
+That's a good way. Let's say suppose I
+
+ align:start position:0%
+That's a good way. Let's say suppose I
+ 
+
+ align:start position:0%
+That's a good way. Let's say suppose I
+took what's the unit charge? The
+
+ align:start position:0%
+took what's the unit charge? The
+ 
+
+ align:start position:0%
+took what's the unit charge? The
+smallest charge I could put here would
+
+ align:start position:0%
+smallest charge I could put here would
+ 
+
+ align:start position:0%
+smallest charge I could put here would
+be 1.6 * 10 -19 kms. And what if I took
+
+ align:start position:0%
+be 1.6 * 10 -19 kms. And what if I took
+ 
+
+ align:start position:0%
+be 1.6 * 10 -19 kms. And what if I took
+a unit charge and I multiplied it times
+
+ align:start position:0%
+a unit charge and I multiplied it times
+ 
+
+ align:start position:0%
+a unit charge and I multiplied it times
+unit voltage 1 volt? Unit charge times
+
+ align:start position:0%
+unit voltage 1 volt? Unit charge times
+ 
+
+ align:start position:0%
+unit voltage 1 volt? Unit charge times
+unit voltage then would give me what? If
+
+ align:start position:0%
+unit voltage then would give me what? If
+ 
+
+ align:start position:0%
+unit voltage then would give me what? If
+I multiply these two what's the kum
+
+ align:start position:0%
+I multiply these two what's the kum
+ 
+
+ align:start position:0%
+I multiply these two what's the kum
+times a volt. You see here's the value
+
+ align:start position:0%
+times a volt. You see here's the value
+ 
+
+ align:start position:0%
+times a volt. You see here's the value
+of using SI units. SI units means
+
+ align:start position:0%
+of using SI units. SI units means
+ 
+
+ align:start position:0%
+of using SI units. SI units means
+everything goes in in SI. Everything
+
+ align:start position:0%
+everything goes in in SI. Everything
+ 
+
+ align:start position:0%
+everything goes in in SI. Everything
+comes out in SI. What's the energy unit
+
+ align:start position:0%
+comes out in SI. What's the energy unit
+ 
+
+ align:start position:0%
+comes out in SI. What's the energy unit
+in SI? The jewel. What is the unit of
+
+ align:start position:0%
+in SI? The jewel. What is the unit of
+ 
+
+ align:start position:0%
+in SI? The jewel. What is the unit of
+charge in Si? Kulom. What's the unit of
+
+ align:start position:0%
+charge in Si? Kulom. What's the unit of
+ 
+
+ align:start position:0%
+charge in Si? Kulom. What's the unit of
+potential difference? Volt with
+
+ align:start position:0%
+potential difference? Volt with
+ 
+
+ align:start position:0%
+potential difference? Volt with
+impunity. With impunity, if I use kulms
+
+ align:start position:0%
+impunity. With impunity, if I use kulms
+ 
+
+ align:start position:0%
+impunity. With impunity, if I use kulms
+here and volts here, I don't even think
+
+ align:start position:0%
+here and volts here, I don't even think
+ 
+
+ align:start position:0%
+here and volts here, I don't even think
+I write 1* 1.6. Even I can do that in my
+
+ align:start position:0%
+I write 1* 1.6. Even I can do that in my
+ 
+
+ align:start position:0%
+I write 1* 1.6. Even I can do that in my
+head. That's 1.6*
+
+ align:start position:0%
+head. That's 1.6*
+ 
+
+ align:start position:0%
+head. That's 1.6*
+10us19 and I write jewels. That's the
+
+ align:start position:0%
+10us19 and I write jewels. That's the
+ 
+
+ align:start position:0%
+10us19 and I write jewels. That's the
+power of having a rationalized system of
+
+ align:start position:0%
+power of having a rationalized system of
+ 
+
+ align:start position:0%
+power of having a rationalized system of
+units. So that's the good news. The bad
+
+ align:start position:0%
+units. So that's the good news. The bad
+ 
+
+ align:start position:0%
+units. So that's the good news. The bad
+news is I hate this number. Look it 1.6
+
+ align:start position:0%
+news is I hate this number. Look it 1.6
+ 
+
+ align:start position:0%
+news is I hate this number. Look it 1.6
+6 * 10 - 18. We got 2.18 * 10, excuse
+
+ align:start position:0%
+6 * 10 - 18. We got 2.18 * 10, excuse
+ 
+
+ align:start position:0%
+6 * 10 - 18. We got 2.18 * 10, excuse
+me, 1.6 * 10 - 19. 2.18 * 10 - 18. Yap
+
+ align:start position:0%
+me, 1.6 * 10 - 19. 2.18 * 10 - 18. Yap
+ 
+
+ align:start position:0%
+me, 1.6 * 10 - 19. 2.18 * 10 - 18. Yap
+yap yap yap yap. Can't we get simple
+
+ align:start position:0%
+yap yap yap yap. Can't we get simple
+ 
+
+ align:start position:0%
+yap yap yap yap. Can't we get simple
+numbers like three, seven? Whatever
+
+ align:start position:0%
+numbers like three, seven? Whatever
+ 
+
+ align:start position:0%
+numbers like three, seven? Whatever
+happened to good old numbers? So I have
+
+ align:start position:0%
+happened to good old numbers? So I have
+ 
+
+ align:start position:0%
+happened to good old numbers? So I have
+an idea. Why don't we why don't we
+
+ align:start position:0%
+an idea. Why don't we why don't we
+ 
+
+ align:start position:0%
+an idea. Why don't we why don't we
+define a new unit of energy that is
+
+ align:start position:0%
+define a new unit of energy that is
+ 
+
+ align:start position:0%
+define a new unit of energy that is
+nearer to what we have to measure? And
+
+ align:start position:0%
+nearer to what we have to measure? And
+ 
+
+ align:start position:0%
+nearer to what we have to measure? And
+that was done. So what people did is
+
+ align:start position:0%
+that was done. So what people did is
+ 
+
+ align:start position:0%
+that was done. So what people did is
+they said let's define a unit of energy
+
+ align:start position:0%
+they said let's define a unit of energy
+ 
+
+ align:start position:0%
+they said let's define a unit of energy
+that represents a unit charge
+
+ align:start position:0%
+that represents a unit charge
+ 
+
+ align:start position:0%
+that represents a unit charge
+accelerated across a unit potential
+
+ align:start position:0%
+accelerated across a unit potential
+ 
+
+ align:start position:0%
+accelerated across a unit potential
+difference and let's call that the
+
+ align:start position:0%
+difference and let's call that the
+ 
+
+ align:start position:0%
+difference and let's call that the
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+volt that's one electron volt the
+
+ align:start position:0%
+volt that's one electron volt the
+ 
+
+ align:start position:0%
+volt that's one electron volt the
+electron volt is not a unit of potential
+
+ align:start position:0%
+electron volt is not a unit of potential
+ 
+
+ align:start position:0%
+electron volt is not a unit of potential
+difference it's a unit of energy so now
+
+ align:start position:0%
+difference it's a unit of energy so now
+ 
+
+ align:start position:0%
+difference it's a unit of energy so now
+this is one eV so now you can see 2.18*
+
+ align:start position:0%
+this is one eV so now you can see 2.18*
+ 
+
+ align:start position:0%
+this is one eV so now you can see 2.18*
+10 - 18 jewels can be 13.6 6 EV. Now I I
+
+ align:start position:0%
+10 - 18 jewels can be 13.6 6 EV. Now I I
+ 
+
+ align:start position:0%
+10 - 18 jewels can be 13.6 6 EV. Now I I
+don't have to, you know, fill my head
+
+ align:start position:0%
+don't have to, you know, fill my head
+ 
+
+ align:start position:0%
+don't have to, you know, fill my head
+with a 2.18 * 10us
+
+ align:start position:0%
+with a 2.18 * 10us
+ 
+
+ align:start position:0%
+with a 2.18 * 10us
+18.6. That's a cool number. I can
+
+ align:start position:0%
+18.6. That's a cool number. I can
+ 
+
+ align:start position:0%
+18.6. That's a cool number. I can
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+that. All right. So that's how that
+
+ align:start position:0%
+that. All right. So that's how that
+ 
+
+ align:start position:0%
+that. All right. So that's how that
+works. By the way, um this is the
+
+ align:start position:0%
+works. By the way, um this is the
+ 
+
+ align:start position:0%
+works. By the way, um this is the
+cathode. And we have a beam. We have a
+
+ align:start position:0%
+cathode. And we have a beam. We have a
+ 
+
+ align:start position:0%
+cathode. And we have a beam. We have a
+beam. It's an electron
+
+ align:start position:0%
+beam. It's an electron
+ 
+
+ align:start position:0%
+beam. It's an electron
+beam. Electron beam. in in the in the
+
+ align:start position:0%
+beam. Electron beam. in in the in the
+ 
+
+ align:start position:0%
+beam. Electron beam. in in the in the
+1890s, the latter part of the 19th
+
+ align:start position:0%
+1890s, the latter part of the 19th
+ 
+
+ align:start position:0%
+1890s, the latter part of the 19th
+century, a very fashionable word was
+
+ align:start position:0%
+century, a very fashionable word was
+ 
+
+ align:start position:0%
+century, a very fashionable word was
+ray because it came from optics. You
+
+ align:start position:0%
+ray because it came from optics. You
+ 
+
+ align:start position:0%
+ray because it came from optics. You
+know, the rays rays of sunlight and so
+
+ align:start position:0%
+know, the rays rays of sunlight and so
+ 
+
+ align:start position:0%
+know, the rays rays of sunlight and so
+on. And in fact, even when we first
+
+ align:start position:0%
+on. And in fact, even when we first
+ 
+
+ align:start position:0%
+on. And in fact, even when we first
+started pulling synthetic fiber, the
+
+ align:start position:0%
+started pulling synthetic fiber, the
+ 
+
+ align:start position:0%
+started pulling synthetic fiber, the
+first synthetic fiber cellulose was
+
+ align:start position:0%
+first synthetic fiber cellulose was
+ 
+
+ align:start position:0%
+first synthetic fiber cellulose was
+referred to as rayon because it looked
+
+ align:start position:0%
+referred to as rayon because it looked
+ 
+
+ align:start position:0%
+referred to as rayon because it looked
+like a ray that was being pulled. So
+
+ align:start position:0%
+like a ray that was being pulled. So
+ 
+
+ align:start position:0%
+like a ray that was being pulled. So
+this rather than calling this an
+
+ align:start position:0%
+this rather than calling this an
+ 
+
+ align:start position:0%
+this rather than calling this an
+electron beam, this was called a cathode
+
+ align:start position:0%
+electron beam, this was called a cathode
+ 
+
+ align:start position:0%
+electron beam, this was called a cathode
+ray. This was called a cathode ray. And
+
+ align:start position:0%
+ray. This was called a cathode ray. And
+ 
+
+ align:start position:0%
+ray. This was called a cathode ray. And
+this is a tube at low pressure. And if I
+
+ align:start position:0%
+this is a tube at low pressure. And if I
+ 
+
+ align:start position:0%
+this is a tube at low pressure. And if I
+evacuate it, I have a cathode ray tube.
+
+ align:start position:0%
+evacuate it, I have a cathode ray tube.
+ 
+
+ align:start position:0%
+evacuate it, I have a cathode ray tube.
+And in fact, instead of having just a an
+
+ align:start position:0%
+And in fact, instead of having just a an
+ 
+
+ align:start position:0%
+And in fact, instead of having just a an
+electrode here, what I could do is I
+
+ align:start position:0%
+electrode here, what I could do is I
+ 
+
+ align:start position:0%
+electrode here, what I could do is I
+could have an electrode that's that's uh
+
+ align:start position:0%
+could have an electrode that's that's uh
+ 
+
+ align:start position:0%
+could have an electrode that's that's uh
+has that's hollow. And then I could put
+
+ align:start position:0%
+has that's hollow. And then I could put
+ 
+
+ align:start position:0%
+has that's hollow. And then I could put
+a flat end here, and I could put
+
+ align:start position:0%
+a flat end here, and I could put
+ 
+
+ align:start position:0%
+a flat end here, and I could put
+phosphorus here. And then I could put a
+
+ align:start position:0%
+phosphorus here. And then I could put a
+ 
+
+ align:start position:0%
+phosphorus here. And then I could put a
+couple of uh plates and I could raster
+
+ align:start position:0%
+couple of uh plates and I could raster
+ 
+
+ align:start position:0%
+couple of uh plates and I could raster
+the beam so that when I'm looking here,
+
+ align:start position:0%
+the beam so that when I'm looking here,
+ 
+
+ align:start position:0%
+the beam so that when I'm looking here,
+the beam goes back and forth about 80
+
+ align:start position:0%
+the beam goes back and forth about 80
+ 
+
+ align:start position:0%
+the beam goes back and forth about 80
+times a second and the phosphorus glow
+
+ align:start position:0%
+times a second and the phosphorus glow
+ 
+
+ align:start position:0%
+times a second and the phosphorus glow
+and I can be watching um uh science
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+documentary. All right. The other thing
+
+ align:start position:0%
+documentary. All right. The other thing
+ 
+
+ align:start position:0%
+documentary. All right. The other thing
+I have to teach you is matter energy
+
+ align:start position:0%
+I have to teach you is matter energy
+ 
+
+ align:start position:0%
+I have to teach you is matter energy
+interaction so that we can see how the
+
+ align:start position:0%
+interaction so that we can see how the
+ 
+
+ align:start position:0%
+interaction so that we can see how the
+Balmer
+
+ align:start position:0%
+Balmer
+ 
+
+ align:start position:0%
+Balmer
+series validates the bore model. So
+
+ align:start position:0%
+series validates the bore model. So
+ 
+
+ align:start position:0%
+series validates the bore model. So
+there's one more thing you need to know
+
+ align:start position:0%
+there's one more thing you need to know
+ 
+
+ align:start position:0%
+there's one more thing you need to know
+and I'm going to put up this energy
+
+ align:start position:0%
+and I'm going to put up this energy
+ 
+
+ align:start position:0%
+and I'm going to put up this energy
+level diagram again. So this is uh this
+
+ align:start position:0%
+level diagram again. So this is uh this
+ 
+
+ align:start position:0%
+level diagram again. So this is uh this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+infinity. Let's call this three 2 one.
+
+ align:start position:0%
+infinity. Let's call this three 2 one.
+ 
+
+ align:start position:0%
+infinity. Let's call this three 2 one.
+So this is E1 ground state E2 E3 and so
+
+ align:start position:0%
+So this is E1 ground state E2 E3 and so
+ 
+
+ align:start position:0%
+So this is E1 ground state E2 E3 and so
+on. This is zero.
+
+ align:start position:0%
+on. This is zero.
+ 
+
+ align:start position:0%
+on. This is zero.
+Okay, so let's let's look at the
+
+ align:start position:0%
+Okay, so let's let's look at the
+ 
+
+ align:start position:0%
+Okay, so let's let's look at the
+energetics of one of those electrons
+
+ align:start position:0%
+energetics of one of those electrons
+ 
+
+ align:start position:0%
+energetics of one of those electrons
+crashing into a hydrogen atom inside the
+
+ align:start position:0%
+crashing into a hydrogen atom inside the
+ 
+
+ align:start position:0%
+crashing into a hydrogen atom inside the
+gas tube. So here's here's an electron
+
+ align:start position:0%
+gas tube. So here's here's an electron
+ 
+
+ align:start position:0%
+gas tube. So here's here's an electron
+and I'm going to let this arrow somehow
+
+ align:start position:0%
+and I'm going to let this arrow somehow
+ 
+
+ align:start position:0%
+and I'm going to let this arrow somehow
+indicate the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um value of the incident energy and this
+
+ align:start position:0%
+um value of the incident energy and this
+ 
+
+ align:start position:0%
+um value of the incident energy and this
+is this is the this I'm saying electron
+
+ align:start position:0%
+is this is the this I'm saying electron
+ 
+
+ align:start position:0%
+is this is the this I'm saying electron
+but more generally it's applies to any
+
+ align:start position:0%
+but more generally it's applies to any
+ 
+
+ align:start position:0%
+but more generally it's applies to any
+incident particle later on we could do
+
+ align:start position:0%
+incident particle later on we could do
+ 
+
+ align:start position:0%
+incident particle later on we could do
+this with a proton we could do it with a
+
+ align:start position:0%
+this with a proton we could do it with a
+ 
+
+ align:start position:0%
+this with a proton we could do it with a
+um with a neutron uh we could do saw
+
+ align:start position:0%
+um with a neutron uh we could do saw
+ 
+
+ align:start position:0%
+um with a neutron uh we could do saw
+Rutherford used alpha particles we could
+
+ align:start position:0%
+Rutherford used alpha particles we could
+ 
+
+ align:start position:0%
+Rutherford used alpha particles we could
+use argon ion. There's all kinds of
+
+ align:start position:0%
+use argon ion. There's all kinds of
+ 
+
+ align:start position:0%
+use argon ion. There's all kinds of
+different ways of bombarding um in this
+
+ align:start position:0%
+different ways of bombarding um in this
+ 
+
+ align:start position:0%
+different ways of bombarding um in this
+case hydrogen gas. Now, if this incident
+
+ align:start position:0%
+case hydrogen gas. Now, if this incident
+ 
+
+ align:start position:0%
+case hydrogen gas. Now, if this incident
+energy is great enough, it'll take an
+
+ align:start position:0%
+energy is great enough, it'll take an
+ 
+
+ align:start position:0%
+energy is great enough, it'll take an
+electron out of the ground state and
+
+ align:start position:0%
+electron out of the ground state and
+ 
+
+ align:start position:0%
+electron out of the ground state and
+promote it. But the electron cannot
+
+ align:start position:0%
+promote it. But the electron cannot
+ 
+
+ align:start position:0%
+promote it. But the electron cannot
+reside anywhere except in one of these
+
+ align:start position:0%
+reside anywhere except in one of these
+ 
+
+ align:start position:0%
+reside anywhere except in one of these
+quantized states. So suppose suppose the
+
+ align:start position:0%
+quantized states. So suppose suppose the
+ 
+
+ align:start position:0%
+quantized states. So suppose suppose the
+E
+
+ align:start position:0%
+E
+ 
+
+ align:start position:0%
+E
+incident suppose E incident is greater
+
+ align:start position:0%
+incident suppose E incident is greater
+ 
+
+ align:start position:0%
+incident suppose E incident is greater
+than the energy in the transition going
+
+ align:start position:0%
+than the energy in the transition going
+ 
+
+ align:start position:0%
+than the energy in the transition going
+from ground state to N=2. What will
+
+ align:start position:0%
+from ground state to N=2. What will
+ 
+
+ align:start position:0%
+from ground state to N=2. What will
+happen? That energy will be absorbed by
+
+ align:start position:0%
+happen? That energy will be absorbed by
+ 
+
+ align:start position:0%
+happen? That energy will be absorbed by
+the hydrogen atom. The electron will
+
+ align:start position:0%
+the hydrogen atom. The electron will
+ 
+
+ align:start position:0%
+the hydrogen atom. The electron will
+rise from n=1 to n=2 and that amount of
+
+ align:start position:0%
+rise from n=1 to n=2 and that amount of
+ 
+
+ align:start position:0%
+rise from n=1 to n=2 and that amount of
+energy will be subtracted. And then over
+
+ align:start position:0%
+energy will be subtracted. And then over
+ 
+
+ align:start position:0%
+energy will be subtracted. And then over
+here this electron will continue. And
+
+ align:start position:0%
+here this electron will continue. And
+ 
+
+ align:start position:0%
+here this electron will continue. And
+I've purposely made the arrow shorter to
+
+ align:start position:0%
+I've purposely made the arrow shorter to
+ 
+
+ align:start position:0%
+I've purposely made the arrow shorter to
+indicate that it has been slowed because
+
+ align:start position:0%
+indicate that it has been slowed because
+ 
+
+ align:start position:0%
+indicate that it has been slowed because
+we're going to argue its mass didn't
+
+ align:start position:0%
+we're going to argue its mass didn't
+ 
+
+ align:start position:0%
+we're going to argue its mass didn't
+change. So the only way to change its
+
+ align:start position:0%
+change. So the only way to change its
+ 
+
+ align:start position:0%
+change. So the only way to change its
+energy is to change its velocity. So
+
+ align:start position:0%
+energy is to change its velocity. So
+ 
+
+ align:start position:0%
+energy is to change its velocity. So
+this will be now the the uh scattered.
+
+ align:start position:0%
+this will be now the the uh scattered.
+ 
+
+ align:start position:0%
+this will be now the the uh scattered.
+We call this it's scattered now. It's
+
+ align:start position:0%
+We call this it's scattered now. It's
+ 
+
+ align:start position:0%
+We call this it's scattered now. It's
+interacted. This is the scattered
+
+ align:start position:0%
+interacted. This is the scattered
+ 
+
+ align:start position:0%
+interacted. This is the scattered
+particle. But it doesn't end there. So
+
+ align:start position:0%
+particle. But it doesn't end there. So
+ 
+
+ align:start position:0%
+particle. But it doesn't end there. So
+how much energy is there? If this is let
+
+ align:start position:0%
+how much energy is there? If this is let
+ 
+
+ align:start position:0%
+how much energy is there? If this is let
+this represent the total energy of the
+
+ align:start position:0%
+this represent the total energy of the
+ 
+
+ align:start position:0%
+this represent the total energy of the
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+incident electron and if that's the
+
+ align:start position:0%
+incident electron and if that's the
+ 
+
+ align:start position:0%
+incident electron and if that's the
+energy to go from n equals 1 to n equals
+
+ align:start position:0%
+energy to go from n equals 1 to n equals
+ 
+
+ align:start position:0%
+energy to go from n equals 1 to n equals
+2 then this is the amount of energy
+
+ align:start position:0%
+2 then this is the amount of energy
+ 
+
+ align:start position:0%
+2 then this is the amount of energy
+that's going to be left as kinetic
+
+ align:start position:0%
+that's going to be left as kinetic
+ 
+
+ align:start position:0%
+that's going to be left as kinetic
+energy of the electron. It's like an
+
+ align:start position:0%
+energy of the electron. It's like an
+ 
+
+ align:start position:0%
+energy of the electron. It's like an
+elastic collision between billiard
+
+ align:start position:0%
+elastic collision between billiard
+ 
+
+ align:start position:0%
+elastic collision between billiard
+balls. You've seen these things but it
+
+ align:start position:0%
+balls. You've seen these things but it
+ 
+
+ align:start position:0%
+balls. You've seen these things but it
+doesn't end there because the electron
+
+ align:start position:0%
+doesn't end there because the electron
+ 
+
+ align:start position:0%
+doesn't end there because the electron
+is sitting up here at n equals 2 very
+
+ align:start position:0%
+is sitting up here at n equals 2 very
+ 
+
+ align:start position:0%
+is sitting up here at n equals 2 very
+nervous because there's a lower energy
+
+ align:start position:0%
+nervous because there's a lower energy
+ 
+
+ align:start position:0%
+nervous because there's a lower energy
+state and there's a colombic attraction
+
+ align:start position:0%
+state and there's a colombic attraction
+ 
+
+ align:start position:0%
+state and there's a colombic attraction
+of the nucleus. So what happens you know
+
+ align:start position:0%
+of the nucleus. So what happens you know
+ 
+
+ align:start position:0%
+of the nucleus. So what happens you know
+almost instantaneously after the
+
+ align:start position:0%
+almost instantaneously after the
+ 
+
+ align:start position:0%
+almost instantaneously after the
+collision the electron up here falls
+
+ align:start position:0%
+collision the electron up here falls
+ 
+
+ align:start position:0%
+collision the electron up here falls
+back down and when it falls back down
+
+ align:start position:0%
+back down and when it falls back down
+ 
+
+ align:start position:0%
+back down and when it falls back down
+that energy is given off and it's given
+
+ align:start position:0%
+that energy is given off and it's given
+ 
+
+ align:start position:0%
+that energy is given off and it's given
+off in the form of a
+
+ align:start position:0%
+off in the form of a
+ 
+
+ align:start position:0%
+off in the form of a
+photon. It's given off in the form of a
+
+ align:start position:0%
+photon. It's given off in the form of a
+ 
+
+ align:start position:0%
+photon. It's given off in the form of a
+photon. And what's the energy of that
+
+ align:start position:0%
+photon. And what's the energy of that
+ 
+
+ align:start position:0%
+photon. And what's the energy of that
+photon? Well the energy of the
+
+ align:start position:0%
+photon? Well the energy of the
+ 
+
+ align:start position:0%
+photon? Well the energy of the
+photon we know from plunk is H new which
+
+ align:start position:0%
+photon we know from plunk is H new which
+ 
+
+ align:start position:0%
+photon we know from plunk is H new which
+is H C over lambda.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now I've got lambdas associated with
+
+ align:start position:0%
+So now I've got lambdas associated with
+ 
+
+ align:start position:0%
+So now I've got lambdas associated with
+transitions between energy levels in
+
+ align:start position:0%
+transitions between energy levels in
+ 
+
+ align:start position:0%
+transitions between energy levels in
+atomic
+
+ align:start position:0%
+atomic
+ 
+
+ align:start position:0%
+atomic
+hydrogen. Gee, I wonder if I could come
+
+ align:start position:0%
+hydrogen. Gee, I wonder if I could come
+ 
+
+ align:start position:0%
+hydrogen. Gee, I wonder if I could come
+up with a set of
+
+ align:start position:0%
+up with a set of
+ 
+
+ align:start position:0%
+up with a set of
+transitions occurring inside atomic
+
+ align:start position:0%
+transitions occurring inside atomic
+ 
+
+ align:start position:0%
+transitions occurring inside atomic
+hydrogen that just might match what
+
+ align:start position:0%
+hydrogen that just might match what
+ 
+
+ align:start position:0%
+hydrogen that just might match what
+Angstrom measured back in 1853.
+
+ align:start position:0%
+Angstrom measured back in 1853.
+ 
+
+ align:start position:0%
+Angstrom measured back in 1853.
+So that's going to be the the challenge.
+
+ align:start position:0%
+So that's going to be the the challenge.
+ 
+
+ align:start position:0%
+So that's going to be the the challenge.
+That's going to be the challenge. The
+
+ align:start position:0%
+That's going to be the challenge. The
+ 
+
+ align:start position:0%
+That's going to be the challenge. The
+interesting thing here is
+
+ align:start position:0%
+interesting thing here is
+ 
+
+ align:start position:0%
+interesting thing here is
+that I can change the incident velocity
+
+ align:start position:0%
+that I can change the incident velocity
+ 
+
+ align:start position:0%
+that I can change the incident velocity
+continuously, right? This is
+
+ align:start position:0%
+continuously, right? This is
+ 
+
+ align:start position:0%
+continuously, right? This is
+continuously variable because I can vary
+
+ align:start position:0%
+continuously variable because I can vary
+ 
+
+ align:start position:0%
+continuously variable because I can vary
+voltage
+
+ align:start position:0%
+voltage
+ 
+
+ align:start position:0%
+voltage
+continuously. Change the voltage, I
+
+ align:start position:0%
+continuously. Change the voltage, I
+ 
+
+ align:start position:0%
+continuously. Change the voltage, I
+change the incident energy. What about
+
+ align:start position:0%
+change the incident energy. What about
+ 
+
+ align:start position:0%
+change the incident energy. What about
+the energy of the emitted photons? Are
+
+ align:start position:0%
+the energy of the emitted photons? Are
+ 
+
+ align:start position:0%
+the energy of the emitted photons? Are
+they continuously variable? No, they are
+
+ align:start position:0%
+they continuously variable? No, they are
+ 
+
+ align:start position:0%
+they continuously variable? No, they are
+discrete. They're discreet. And
+
+ align:start position:0%
+discrete. They're discreet. And
+ 
+
+ align:start position:0%
+discrete. They're discreet. And
+furthermore, they're characteristic of
+
+ align:start position:0%
+furthermore, they're characteristic of
+ 
+
+ align:start position:0%
+furthermore, they're characteristic of
+the target gas element. So, let's say I
+
+ align:start position:0%
+the target gas element. So, let's say I
+ 
+
+ align:start position:0%
+the target gas element. So, let's say I
+got up late and I'm racing to get to
+
+ align:start position:0%
+got up late and I'm racing to get to
+ 
+
+ align:start position:0%
+got up late and I'm racing to get to
+class and I just burst in now and I look
+
+ align:start position:0%
+class and I just burst in now and I look
+ 
+
+ align:start position:0%
+class and I just burst in now and I look
+up there and I go, that's atomic
+
+ align:start position:0%
+up there and I go, that's atomic
+ 
+
+ align:start position:0%
+up there and I go, that's atomic
+hydrogen. because only atomic hydrogen
+
+ align:start position:0%
+hydrogen. because only atomic hydrogen
+ 
+
+ align:start position:0%
+hydrogen. because only atomic hydrogen
+has that set of
+
+ align:start position:0%
+has that set of
+ 
+
+ align:start position:0%
+has that set of
+lines which means I could then take the
+
+ align:start position:0%
+lines which means I could then take the
+ 
+
+ align:start position:0%
+lines which means I could then take the
+spectra of gasphase species and use that
+
+ align:start position:0%
+spectra of gasphase species and use that
+ 
+
+ align:start position:0%
+spectra of gasphase species and use that
+information to
+
+ align:start position:0%
+information to
+ 
+
+ align:start position:0%
+information to
+identify. So this is now a technique of
+
+ align:start position:0%
+identify. So this is now a technique of
+ 
+
+ align:start position:0%
+identify. So this is now a technique of
+analysis. I could take an unknown gas
+
+ align:start position:0%
+analysis. I could take an unknown gas
+ 
+
+ align:start position:0%
+analysis. I could take an unknown gas
+and put it in and measure it and then
+
+ align:start position:0%
+and put it in and measure it and then
+ 
+
+ align:start position:0%
+and put it in and measure it and then
+say wow those are the lines that are
+
+ align:start position:0%
+say wow those are the lines that are
+ 
+
+ align:start position:0%
+say wow those are the lines that are
+characteristic of sodium. This gee, have
+
+ align:start position:0%
+characteristic of sodium. This gee, have
+ 
+
+ align:start position:0%
+characteristic of sodium. This gee, have
+you ever wondered how they know the
+
+ align:start position:0%
+you ever wondered how they know the
+ 
+
+ align:start position:0%
+you ever wondered how they know the
+composition of stars that are light
+
+ align:start position:0%
+composition of stars that are light
+ 
+
+ align:start position:0%
+composition of stars that are light
+years away? Do they get sample bottles
+
+ align:start position:0%
+years away? Do they get sample bottles
+ 
+
+ align:start position:0%
+years away? Do they get sample bottles
+coming in? How do they get that
+
+ align:start position:0%
+coming in? How do they get that
+ 
+
+ align:start position:0%
+coming in? How do they get that
+information? You What is a star if not
+
+ align:start position:0%
+information? You What is a star if not
+ 
+
+ align:start position:0%
+information? You What is a star if not
+just a giant gas bottle
+
+ align:start position:0%
+just a giant gas bottle
+ 
+
+ align:start position:0%
+just a giant gas bottle
+containerless? It's
+
+ align:start position:0%
+containerless? It's
+ 
+
+ align:start position:0%
+containerless? It's
+glowing. And why is it glowing? It's
+
+ align:start position:0%
+glowing. And why is it glowing? It's
+ 
+
+ align:start position:0%
+glowing. And why is it glowing? It's
+glowing because electrons are excited.
+
+ align:start position:0%
+glowing because electrons are excited.
+ 
+
+ align:start position:0%
+glowing because electrons are excited.
+and they're excited and they're jumping
+
+ align:start position:0%
+and they're excited and they're jumping
+ 
+
+ align:start position:0%
+and they're excited and they're jumping
+up and down and they're emitting, but
+
+ align:start position:0%
+up and down and they're emitting, but
+ 
+
+ align:start position:0%
+up and down and they're emitting, but
+they're just not emitting anything. I
+
+ align:start position:0%
+they're just not emitting anything. I
+ 
+
+ align:start position:0%
+they're just not emitting anything. I
+mean, why are some stars this color and
+
+ align:start position:0%
+mean, why are some stars this color and
+ 
+
+ align:start position:0%
+mean, why are some stars this color and
+some stars that color? Somebody painted
+
+ align:start position:0%
+some stars that color? Somebody painted
+ 
+
+ align:start position:0%
+some stars that color? Somebody painted
+them that way. They're different because
+
+ align:start position:0%
+them that way. They're different because
+ 
+
+ align:start position:0%
+them that way. They're different because
+they got different compositions. So, you
+
+ align:start position:0%
+they got different compositions. So, you
+ 
+
+ align:start position:0%
+they got different compositions. So, you
+could use this in order to identify the
+
+ align:start position:0%
+could use this in order to identify the
+ 
+
+ align:start position:0%
+could use this in order to identify the
+contents of
+
+ align:start position:0%
+contents of
+ 
+
+ align:start position:0%
+contents of
+stars, all of
+
+ align:start position:0%
+stars, all of
+ 
+
+ align:start position:0%
+stars, all of
+this.
+
+ align:start position:0%
+this.
+ 
+
+ align:start position:0%
+this.
+So, what did Boore do? I want to tell
+
+ align:start position:0%
+So, what did Boore do? I want to tell
+ 
+
+ align:start position:0%
+So, what did Boore do? I want to tell
+you a couple more Boore stories. Boore,
+
+ align:start position:0%
+you a couple more Boore stories. Boore,
+ 
+
+ align:start position:0%
+you a couple more Boore stories. Boore,
+the guy was great. Okay, so here's what
+
+ align:start position:0%
+the guy was great. Okay, so here's what
+ 
+
+ align:start position:0%
+the guy was great. Okay, so here's what
+happens. Here's a story. Capstone of
+
+ align:start position:0%
+happens. Here's a story. Capstone of
+ 
+
+ align:start position:0%
+happens. Here's a story. Capstone of
+Bor's work on the Balmer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula. Let me simply tell you that in
+
+ align:start position:0%
+formula. Let me simply tell you that in
+ 
+
+ align:start position:0%
+formula. Let me simply tell you that in
+time I'm going to show you that this
+
+ align:start position:0%
+time I'm going to show you that this
+ 
+
+ align:start position:0%
+time I'm going to show you that this
+formula is inconsistent with the bore
+
+ align:start position:0%
+formula is inconsistent with the bore
+ 
+
+ align:start position:0%
+formula is inconsistent with the bore
+model. You see that at the beginning of
+
+ align:start position:0%
+model. You see that at the beginning of
+ 
+
+ align:start position:0%
+model. You see that at the beginning of
+next lecture. So in 1896, Charles
+
+ align:start position:0%
+next lecture. So in 1896, Charles
+ 
+
+ align:start position:0%
+next lecture. So in 1896, Charles
+Pickering from Harvard found a series of
+
+ align:start position:0%
+Pickering from Harvard found a series of
+ 
+
+ align:start position:0%
+Pickering from Harvard found a series of
+lines in starlight which he attributed
+
+ align:start position:0%
+lines in starlight which he attributed
+ 
+
+ align:start position:0%
+lines in starlight which he attributed
+to hydrogen even though they did not fit
+
+ align:start position:0%
+to hydrogen even though they did not fit
+ 
+
+ align:start position:0%
+to hydrogen even though they did not fit
+Balmer. They were off by a factor
+
+ align:start position:0%
+Balmer. They were off by a factor
+ 
+
+ align:start position:0%
+Balmer. They were off by a factor
+of four. Now, what do you know about
+
+ align:start position:0%
+of four. Now, what do you know about
+ 
+
+ align:start position:0%
+of four. Now, what do you know about
+energy? Already from this class, if I
+
+ align:start position:0%
+energy? Already from this class, if I
+ 
+
+ align:start position:0%
+energy? Already from this class, if I
+told you that I gave you energies in
+
+ align:start position:0%
+told you that I gave you energies in
+ 
+
+ align:start position:0%
+told you that I gave you energies in
+some spectrum, but they were off by a
+
+ align:start position:0%
+some spectrum, but they were off by a
+ 
+
+ align:start position:0%
+some spectrum, but they were off by a
+factor of four, what would you
+
+ align:start position:0%
+factor of four, what would you
+ 
+
+ align:start position:0%
+factor of four, what would you
+think? It's
+
+ align:start position:0%
+think? It's
+ 
+
+ align:start position:0%
+think? It's
+probably maybe the Z is wrong. So, even
+
+ align:start position:0%
+probably maybe the Z is wrong. So, even
+ 
+
+ align:start position:0%
+probably maybe the Z is wrong. So, even
+though the lines were wrong, he says,
+
+ align:start position:0%
+though the lines were wrong, he says,
+ 
+
+ align:start position:0%
+though the lines were wrong, he says,
+"No, it's
+
+ align:start position:0%
+"No, it's
+ 
+
+ align:start position:0%
+"No, it's
+hydrogen." So, Bore says, "No, no, it's
+
+ align:start position:0%
+hydrogen." So, Bore says, "No, no, it's
+ 
+
+ align:start position:0%
+hydrogen." So, Bore says, "No, no, it's
+not hydrogen, it's helium. That star has
+
+ align:start position:0%
+not hydrogen, it's helium. That star has
+ 
+
+ align:start position:0%
+not hydrogen, it's helium. That star has
+got ionized helium. Helium plus Z equ= 2
+
+ align:start position:0%
+got ionized helium. Helium plus Z equ= 2
+ 
+
+ align:start position:0%
+got ionized helium. Helium plus Z equ= 2
+energy will be four times more intense.
+
+ align:start position:0%
+energy will be four times more intense.
+ 
+
+ align:start position:0%
+energy will be four times more intense.
+So Pickering was nasty so and he said ah
+
+ align:start position:0%
+So Pickering was nasty so and he said ah
+ 
+
+ align:start position:0%
+So Pickering was nasty so and he said ah
+you're wrong because in fact it's
+
+ align:start position:0%
+you're wrong because in fact it's
+ 
+
+ align:start position:0%
+you're wrong because in fact it's
+4.0016 and the six is greater than what
+
+ align:start position:0%
+4.0016 and the six is greater than what
+ 
+
+ align:start position:0%
+4.0016 and the six is greater than what
+I would have as experimental error. So
+
+ align:start position:0%
+I would have as experimental error. So
+ 
+
+ align:start position:0%
+I would have as experimental error. So
+your theory is wrong. So Boris says oh
+
+ align:start position:0%
+your theory is wrong. So Boris says oh
+ 
+
+ align:start position:0%
+your theory is wrong. So Boris says oh
+yeah. So he goes back and he redoes the
+
+ align:start position:0%
+yeah. So he goes back and he redoes the
+ 
+
+ align:start position:0%
+yeah. So he goes back and he redoes the
+calculation only in this case he says
+
+ align:start position:0%
+calculation only in this case he says
+ 
+
+ align:start position:0%
+calculation only in this case he says
+all right what I'm going to do is I'm
+
+ align:start position:0%
+all right what I'm going to do is I'm
+ 
+
+ align:start position:0%
+all right what I'm going to do is I'm
+going to redo the calculation for helium
+
+ align:start position:0%
+going to redo the calculation for helium
+ 
+
+ align:start position:0%
+going to redo the calculation for helium
+but I'm going to consider not just the
+
+ align:start position:0%
+but I'm going to consider not just the
+ 
+
+ align:start position:0%
+but I'm going to consider not just the
+mass of the electron but the reduced
+
+ align:start position:0%
+mass of the electron but the reduced
+ 
+
+ align:start position:0%
+mass of the electron but the reduced
+mass of the system. So I'll take into
+
+ align:start position:0%
+mass of the system. So I'll take into
+ 
+
+ align:start position:0%
+mass of the system. So I'll take into
+account that there is some contribution
+
+ align:start position:0%
+account that there is some contribution
+ 
+
+ align:start position:0%
+account that there is some contribution
+of both the nucleus and the electron and
+
+ align:start position:0%
+of both the nucleus and the electron and
+ 
+
+ align:start position:0%
+of both the nucleus and the electron and
+he gets you're you're absolutely right
+
+ align:start position:0%
+he gets you're you're absolutely right
+ 
+
+ align:start position:0%
+he gets you're you're absolutely right
+it's not four it's 4.00163
+
+ align:start position:0%
+it's not four it's 4.00163
+ 
+
+ align:start position:0%
+it's not four it's 4.00163
+0163 take that right so what you have is
+
+ align:start position:0%
+0163 take that right so what you have is
+ 
+
+ align:start position:0%
+0163 take that right so what you have is
+with a simple calculation five
+
+ align:start position:0%
+with a simple calculation five
+ 
+
+ align:start position:0%
+with a simple calculation five
+significant figures five significant
+
+ align:start position:0%
+significant figures five significant
+ 
+
+ align:start position:0%
+significant figures five significant
+figures that shut him
+
+ align:start position:0%
+figures that shut him
+ 
+
+ align:start position:0%
+figures that shut him
+up now to just show it doesn't end more
+
+ align:start position:0%
+up now to just show it doesn't end more
+ 
+
+ align:start position:0%
+up now to just show it doesn't end more
+more nonsense at Harvard this is Cecilia
+
+ align:start position:0%
+more nonsense at Harvard this is Cecilia
+ 
+
+ align:start position:0%
+more nonsense at Harvard this is Cecilia
+Payne first woman graduate student in
+
+ align:start position:0%
+Payne first woman graduate student in
+ 
+
+ align:start position:0%
+Payne first woman graduate student in
+astronomy first PhD in astronomy first
+
+ align:start position:0%
+astronomy first PhD in astronomy first
+ 
+
+ align:start position:0%
+astronomy first PhD in astronomy first
+woman to receive tenure at Harvard she
+
+ align:start position:0%
+woman to receive tenure at Harvard she
+ 
+
+ align:start position:0%
+woman to receive tenure at Harvard she
+was awarded tenure in 193 38 denied a
+
+ align:start position:0%
+was awarded tenure in 193 38 denied a
+ 
+
+ align:start position:0%
+was awarded tenure in 193 38 denied a
+professorship for 18 years. And when she
+
+ align:start position:0%
+professorship for 18 years. And when she
+ 
+
+ align:start position:0%
+professorship for 18 years. And when she
+presented her PhD thesis, she was the
+
+ align:start position:0%
+presented her PhD thesis, she was the
+ 
+
+ align:start position:0%
+presented her PhD thesis, she was the
+one that determined that the sun is made
+
+ align:start position:0%
+one that determined that the sun is made
+ 
+
+ align:start position:0%
+one that determined that the sun is made
+dominantly of hydrogen, not iron, the
+
+ align:start position:0%
+dominantly of hydrogen, not iron, the
+ 
+
+ align:start position:0%
+dominantly of hydrogen, not iron, the
+way most the old goats thought because
+
+ align:start position:0%
+way most the old goats thought because
+ 
+
+ align:start position:0%
+way most the old goats thought because
+the earth is made of iron. Heaven knows
+
+ align:start position:0%
+the earth is made of iron. Heaven knows
+ 
+
+ align:start position:0%
+the earth is made of iron. Heaven knows
+everything is made of the same stuff,
+
+ align:start position:0%
+everything is made of the same stuff,
+ 
+
+ align:start position:0%
+everything is made of the same stuff,
+right? All heavenly bodies, even though
+
+ align:start position:0%
+right? All heavenly bodies, even though
+ 
+
+ align:start position:0%
+right? All heavenly bodies, even though
+the sun is glowing and the earth isn't,
+
+ align:start position:0%
+the sun is glowing and the earth isn't,
+ 
+
+ align:start position:0%
+the sun is glowing and the earth isn't,
+but oh, they must be they must be made
+
+ align:start position:0%
+but oh, they must be they must be made
+ 
+
+ align:start position:0%
+but oh, they must be they must be made
+of the same thing. And after all, we're
+
+ align:start position:0%
+of the same thing. And after all, we're
+ 
+
+ align:start position:0%
+of the same thing. And after all, we're
+Harvard, so we know. So
+
+ align:start position:0%
+Harvard, so we know. So
+ 
+
+ align:start position:0%
+Harvard, so we know. So
+So here's what she did. She was
+
+ align:start position:0%
+So here's what she did. She was
+ 
+
+ align:start position:0%
+So here's what she did. She was
+festidious. Look at this. What do you
+
+ align:start position:0%
+festidious. Look at this. What do you
+ 
+
+ align:start position:0%
+festidious. Look at this. What do you
+see there? Well, you see iron, but you
+
+ align:start position:0%
+see there? Well, you see iron, but you
+ 
+
+ align:start position:0%
+see there? Well, you see iron, but you
+know, this is misspelled. So, yeah,
+
+ align:start position:0%
+know, this is misspelled. So, yeah,
+ 
+
+ align:start position:0%
+know, this is misspelled. So, yeah,
+you're making an excuses. Ah, the
+
+ align:start position:0%
+you're making an excuses. Ah, the
+ 
+
+ align:start position:0%
+you're making an excuses. Ah, the
+detector isn't working. You know, this
+
+ align:start position:0%
+detector isn't working. You know, this
+ 
+
+ align:start position:0%
+detector isn't working. You know, this
+is the noisy system. So, that's what
+
+ align:start position:0%
+is the noisy system. So, that's what
+ 
+
+ align:start position:0%
+is the noisy system. So, that's what
+everybody else is doing. But what
+
+ align:start position:0%
+everybody else is doing. But what
+ 
+
+ align:start position:0%
+everybody else is doing. But what
+Cecilia is doing is she's saying, I got
+
+ align:start position:0%
+Cecilia is doing is she's saying, I got
+ 
+
+ align:start position:0%
+Cecilia is doing is she's saying, I got
+to keep looking. I need a I need a
+
+ align:start position:0%
+to keep looking. I need a I need a
+ 
+
+ align:start position:0%
+to keep looking. I need a I need a
+consistent I need a consistent uh
+
+ align:start position:0%
+consistent I need a consistent uh
+ 
+
+ align:start position:0%
+consistent I need a consistent uh
+picture. So, this is what spectroscopy
+
+ align:start position:0%
+picture. So, this is what spectroscopy
+ 
+
+ align:start position:0%
+picture. So, this is what spectroscopy
+is. Spectroscopy is how you go and look
+
+ align:start position:0%
+is. Spectroscopy is how you go and look
+ 
+
+ align:start position:0%
+is. Spectroscopy is how you go and look
+at patterns, not just individual lines.
+
+ align:start position:0%
+at patterns, not just individual lines.
+ 
+
+ align:start position:0%
+at patterns, not just individual lines.
+So when she defended her thesis, she was
+
+ align:start position:0%
+So when she defended her thesis, she was
+ 
+
+ align:start position:0%
+So when she defended her thesis, she was
+forced to put this phrase in her thesis.
+
+ align:start position:0%
+forced to put this phrase in her thesis.
+ 
+
+ align:start position:0%
+forced to put this phrase in her thesis.
+The enormous abundance of hydrogen is
+
+ align:start position:0%
+The enormous abundance of hydrogen is
+ 
+
+ align:start position:0%
+The enormous abundance of hydrogen is
+almost certainly not
+
+ align:start position:0%
+almost certainly not
+ 
+
+ align:start position:0%
+almost certainly not
+real. Yeah. This is this is the way this
+
+ align:start position:0%
+real. Yeah. This is this is the way this
+ 
+
+ align:start position:0%
+real. Yeah. This is this is the way this
+is the way science welcomes newcomers.
+
+ align:start position:0%
+is the way science welcomes newcomers.
+ 
+
+ align:start position:0%
+is the way science welcomes newcomers.
+This is the way science on some
+
+ align:start position:0%
+This is the way science on some
+ 
+
+ align:start position:0%
+This is the way science on some
+occasions welcomes new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+findings just up the
+
+ align:start position:0%
+findings just up the
+ 
+
+ align:start position:0%
+findings just up the
+street. And I'm not talking about, you
+
+ align:start position:0%
+street. And I'm not talking about, you
+ 
+
+ align:start position:0%
+street. And I'm not talking about, you
+know, the 1600s. This was in the in the
+
+ align:start position:0%
+know, the 1600s. This was in the in the
+ 
+
+ align:start position:0%
+know, the 1600s. This was in the in the
+30s. So, this is a painting of her.
+
+ align:start position:0%
+30s. So, this is a painting of her.
+ 
+
+ align:start position:0%
+30s. So, this is a painting of her.
+Dudley Hersbach, who's a Harvard uh
+
+ align:start position:0%
+Dudley Hersbach, who's a Harvard uh
+ 
+
+ align:start position:0%
+Dudley Hersbach, who's a Harvard uh
+chemistry professor who has a Nobel
+
+ align:start position:0%
+chemistry professor who has a Nobel
+ 
+
+ align:start position:0%
+chemistry professor who has a Nobel
+Prize, uh had this painting hung at one
+
+ align:start position:0%
+Prize, uh had this painting hung at one
+ 
+
+ align:start position:0%
+Prize, uh had this painting hung at one
+of the halls, and it's a it's obviously
+
+ align:start position:0%
+of the halls, and it's a it's obviously
+ 
+
+ align:start position:0%
+of the halls, and it's a it's obviously
+referential to Vermeier's the
+
+ align:start position:0%
+referential to Vermeier's the
+ 
+
+ align:start position:0%
+referential to Vermeier's the
+astronomer.
+
+ align:start position:0%
+astronomer.
+ 
+
+ align:start position:0%
+astronomer.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+um, we've come a long way from the gas
+
+ align:start position:0%
+um, we've come a long way from the gas
+ 
+
+ align:start position:0%
+um, we've come a long way from the gas
+discharge tube to the heavens, but it
+
+ align:start position:0%
+discharge tube to the heavens, but it
+ 
+
+ align:start position:0%
+discharge tube to the heavens, but it
+shows you that with a little bit of
+
+ align:start position:0%
+shows you that with a little bit of
+ 
+
+ align:start position:0%
+shows you that with a little bit of
+understanding of quantization, you can
+
+ align:start position:0%
+understanding of quantization, you can
+ 
+
+ align:start position:0%
+understanding of quantization, you can
+go a long way. Okay, we'll see you
+
+ align:start position:0%
+go a long way. Okay, we'll see you
+ 
+
+ align:start position:0%
+go a long way. Okay, we'll see you
+Friday.
\ No newline at end of file
diff --git a/r4-cftqTcdI.txt b/r4-cftqTcdI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0facea0eb6dd161b6e95332d311672f2368337c4
--- /dev/null
+++ b/r4-cftqTcdI.txt
@@ -0,0 +1,12011 @@
+align:start position:0%
+ 
+all right welcome back to double-oh-six
+
+ align:start position:0%
+all right welcome back to double-oh-six
+ 
+
+ align:start position:0%
+all right welcome back to double-oh-six
+today we start a totally new section of
+
+ align:start position:0%
+today we start a totally new section of
+ 
+
+ align:start position:0%
+today we start a totally new section of
+the class
+
+ align:start position:0%
+the class
+ 
+
+ align:start position:0%
+the class
+up till now we've mostly been showing
+
+ align:start position:0%
+up till now we've mostly been showing
+ 
+
+ align:start position:0%
+up till now we've mostly been showing
+you really cool and powerful
+
+ align:start position:0%
+you really cool and powerful
+ 
+
+ align:start position:0%
+you really cool and powerful
+algorithms sorting algorithms graph
+
+ align:start position:0%
+algorithms sorting algorithms graph
+ 
+
+ align:start position:0%
+algorithms sorting algorithms graph
+algorithms data structures trees
+
+ align:start position:0%
+algorithms data structures trees
+ 
+
+ align:start position:0%
+algorithms data structures trees
+lots of good stuff that you can apply to
+
+ align:start position:0%
+lots of good stuff that you can apply to
+ 
+
+ align:start position:0%
+lots of good stuff that you can apply to
+solve tons of algorithmic problems
+
+ align:start position:0%
+solve tons of algorithmic problems
+ 
+
+ align:start position:0%
+solve tons of algorithmic problems
+either by reducing to the
+
+ align:start position:0%
+either by reducing to the
+ 
+
+ align:start position:0%
+either by reducing to the
+things data structures that we we showed
+
+ align:start position:0%
+things data structures that we we showed
+ 
+
+ align:start position:0%
+things data structures that we we showed
+you or reducing to the graph problems
+
+ align:start position:0%
+you or reducing to the graph problems
+ 
+
+ align:start position:0%
+you or reducing to the graph problems
+that we showed you
+
+ align:start position:0%
+that we showed you
+ 
+
+ align:start position:0%
+that we showed you
+or by modifying those algorithms a bit
+
+ align:start position:0%
+or by modifying those algorithms a bit
+ 
+
+ align:start position:0%
+or by modifying those algorithms a bit
+today we're going to start a
+
+ align:start position:0%
+today we're going to start a
+ 
+
+ align:start position:0%
+today we're going to start a
+new section on algorithmic design how to
+
+ align:start position:0%
+new section on algorithmic design how to
+ 
+
+ align:start position:0%
+new section on algorithmic design how to
+from scratch come up with a polynomial
+
+ align:start position:0%
+from scratch come up with a polynomial
+ 
+
+ align:start position:0%
+from scratch come up with a polynomial
+time algorithm to solve a problem
+
+ align:start position:0%
+time algorithm to solve a problem
+ 
+
+ align:start position:0%
+time algorithm to solve a problem
+so this is a and in particular we're
+
+ align:start position:0%
+so this is a and in particular we're
+ 
+
+ align:start position:0%
+so this is a and in particular we're
+going to talk about
+
+ align:start position:0%
+going to talk about
+ 
+
+ align:start position:0%
+going to talk about
+a algorithmic design paradigm called
+
+ align:start position:0%
+a algorithmic design paradigm called
+ 
+
+ align:start position:0%
+a algorithmic design paradigm called
+dynamic programming
+
+ align:start position:0%
+dynamic programming
+ 
+
+ align:start position:0%
+dynamic programming
+which is extremely powerful it's
+
+ align:start position:0%
+which is extremely powerful it's
+ 
+
+ align:start position:0%
+which is extremely powerful it's
+probably the most powerful algorithmic
+
+ align:start position:0%
+probably the most powerful algorithmic
+ 
+
+ align:start position:0%
+probably the most powerful algorithmic
+design paradigm very general
+
+ align:start position:0%
+design paradigm very general
+ 
+
+ align:start position:0%
+design paradigm very general
+can solve lots of problems it's a
+
+ align:start position:0%
+can solve lots of problems it's a
+ 
+
+ align:start position:0%
+can solve lots of problems it's a
+particular type of recursive algorithm
+
+ align:start position:0%
+particular type of recursive algorithm
+ 
+
+ align:start position:0%
+particular type of recursive algorithm
+design
+
+ align:start position:0%
+design
+ 
+
+ align:start position:0%
+design
+and in general this class
+
+ align:start position:0%
+and in general this class
+ 
+
+ align:start position:0%
+and in general this class
+all of algorithms is about recursive
+
+ align:start position:0%
+all of algorithms is about recursive
+ 
+
+ align:start position:0%
+all of algorithms is about recursive
+algorithm design
+
+ align:start position:0%
+algorithm design
+ 
+
+ align:start position:0%
+algorithm design
+at some level because we want to write
+
+ align:start position:0%
+at some level because we want to write
+ 
+
+ align:start position:0%
+at some level because we want to write
+constant size pieces of code
+
+ align:start position:0%
+constant size pieces of code
+ 
+
+ align:start position:0%
+constant size pieces of code
+that solve problems of arbitrary size we
+
+ align:start position:0%
+that solve problems of arbitrary size we
+ 
+
+ align:start position:0%
+that solve problems of arbitrary size we
+have some problem size
+
+ align:start position:0%
+have some problem size
+ 
+
+ align:start position:0%
+have some problem size
+n and we're trying to write you know 100
+
+ align:start position:0%
+n and we're trying to write you know 100
+ 
+
+ align:start position:0%
+n and we're trying to write you know 100
+lines of code or whatever some constant
+
+ align:start position:0%
+lines of code or whatever some constant
+ 
+
+ align:start position:0%
+lines of code or whatever some constant
+amount that doesn't depend on the
+
+ align:start position:0%
+amount that doesn't depend on the
+ 
+
+ align:start position:0%
+amount that doesn't depend on the
+problem size we have one algorithm that
+
+ align:start position:0%
+problem size we have one algorithm that
+ 
+
+ align:start position:0%
+problem size we have one algorithm that
+solves all
+
+ align:start position:0%
+solves all
+ 
+
+ align:start position:0%
+solves all
+instances of the problem and so we have
+
+ align:start position:0%
+instances of the problem and so we have
+ 
+
+ align:start position:0%
+instances of the problem and so we have
+to write code
+
+ align:start position:0%
+to write code
+ 
+
+ align:start position:0%
+to write code
+that is recursive or uses loops or
+
+ align:start position:0%
+that is recursive or uses loops or
+ 
+
+ align:start position:0%
+that is recursive or uses loops or
+somehow reuses the instructions that we
+
+ align:start position:0%
+somehow reuses the instructions that we
+ 
+
+ align:start position:0%
+somehow reuses the instructions that we
+give the computer
+
+ align:start position:0%
+give the computer
+ 
+
+ align:start position:0%
+give the computer
+and you may know you can convert any
+
+ align:start position:0%
+and you may know you can convert any
+ 
+
+ align:start position:0%
+and you may know you can convert any
+algorithm based on loops into an
+
+ align:start position:0%
+algorithm based on loops into an
+ 
+
+ align:start position:0%
+algorithm based on loops into an
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+using recursion and we're going to take
+
+ align:start position:0%
+using recursion and we're going to take
+ 
+
+ align:start position:0%
+using recursion and we're going to take
+the recursive view today
+
+ align:start position:0%
+the recursive view today
+ 
+
+ align:start position:0%
+the recursive view today
+in particular because it fits very well
+
+ align:start position:0%
+in particular because it fits very well
+ 
+
+ align:start position:0%
+in particular because it fits very well
+with our proof by induction
+
+ align:start position:0%
+with our proof by induction
+ 
+
+ align:start position:0%
+with our proof by induction
+technique which we've used throughout
+
+ align:start position:0%
+technique which we've used throughout
+ 
+
+ align:start position:0%
+technique which we've used throughout
+this class
+
+ align:start position:0%
+this class
+ 
+
+ align:start position:0%
+this class
+but also because it gives us some
+
+ align:start position:0%
+but also because it gives us some
+ 
+
+ align:start position:0%
+but also because it gives us some
+structure on how
+
+ align:start position:0%
+structure on how
+ 
+
+ align:start position:0%
+structure on how
+different subproblems relate in
+
+ align:start position:0%
+different subproblems relate in
+ 
+
+ align:start position:0%
+different subproblems relate in
+something called a sub problem graph
+
+ align:start position:0%
+something called a sub problem graph
+ 
+
+ align:start position:0%
+something called a sub problem graph
+that we'll be talking about today
+
+ align:start position:0%
+that we'll be talking about today
+ 
+
+ align:start position:0%
+that we'll be talking about today
+and so we're going to start out with in
+
+ align:start position:0%
+and so we're going to start out with in
+ 
+
+ align:start position:0%
+and so we're going to start out with in
+general how do we design recursive
+
+ align:start position:0%
+general how do we design recursive
+ 
+
+ align:start position:0%
+general how do we design recursive
+algorithms
+
+ align:start position:0%
+algorithms
+ 
+
+ align:start position:0%
+algorithms
+that's sort of the overall encompassing
+
+ align:start position:0%
+that's sort of the overall encompassing
+ 
+
+ align:start position:0%
+that's sort of the overall encompassing
+everything we have
+
+ align:start position:0%
+everything we have
+ 
+
+ align:start position:0%
+everything we have
+thought very hard to come up with a cool
+
+ align:start position:0%
+thought very hard to come up with a cool
+ 
+
+ align:start position:0%
+thought very hard to come up with a cool
+acronym for this paradigm
+
+ align:start position:0%
+acronym for this paradigm
+ 
+
+ align:start position:0%
+acronym for this paradigm
+which we invented called sort bot thanks
+
+ align:start position:0%
+which we invented called sort bot thanks
+ 
+
+ align:start position:0%
+which we invented called sort bot thanks
+jason
+
+ align:start position:0%
+jason
+ 
+
+ align:start position:0%
+jason
+and so we'll talk it's not actually for
+
+ align:start position:0%
+and so we'll talk it's not actually for
+ 
+
+ align:start position:0%
+and so we'll talk it's not actually for
+sorting it's just an acronym for
+
+ align:start position:0%
+sorting it's just an acronym for
+ 
+
+ align:start position:0%
+sorting it's just an acronym for
+subproblems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relations topological order base case
+
+ align:start position:0%
+relations topological order base case
+ 
+
+ align:start position:0%
+relations topological order base case
+original problem and time but it's an
+
+ align:start position:0%
+original problem and time but it's an
+ 
+
+ align:start position:0%
+original problem and time but it's an
+acronym that
+
+ align:start position:0%
+acronym that
+ 
+
+ align:start position:0%
+acronym that
+will help you remember all the steps you
+
+ align:start position:0%
+will help you remember all the steps you
+ 
+
+ align:start position:0%
+will help you remember all the steps you
+need in order to specify a recursive
+
+ align:start position:0%
+need in order to specify a recursive
+ 
+
+ align:start position:0%
+need in order to specify a recursive
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+and dynamic programming is going to
+
+ align:start position:0%
+and dynamic programming is going to
+ 
+
+ align:start position:0%
+and dynamic programming is going to
+build on this template
+
+ align:start position:0%
+build on this template
+ 
+
+ align:start position:0%
+build on this template
+by adding one new idea called
+
+ align:start position:0%
+by adding one new idea called
+ 
+
+ align:start position:0%
+by adding one new idea called
+memoization which is just the idea of
+
+ align:start position:0%
+memoization which is just the idea of
+ 
+
+ align:start position:0%
+memoization which is just the idea of
+reusing work that you've done before
+
+ align:start position:0%
+reusing work that you've done before
+ 
+
+ align:start position:0%
+reusing work that you've done before
+and that's going to let us solve tons of
+
+ align:start position:0%
+and that's going to let us solve tons of
+ 
+
+ align:start position:0%
+and that's going to let us solve tons of
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+and let's see i don't uh
+
+ align:start position:0%
+and let's see i don't uh
+ 
+
+ align:start position:0%
+and let's see i don't uh
+let's get into it so we'll start out
+
+ align:start position:0%
+let's get into it so we'll start out
+ 
+
+ align:start position:0%
+let's get into it so we'll start out
+today with sort bots so here is sort
+
+ align:start position:0%
+today with sort bots so here is sort
+ 
+
+ align:start position:0%
+today with sort bots so here is sort
+bot down the column here this is a
+
+ align:start position:0%
+bot down the column here this is a
+ 
+
+ align:start position:0%
+bot down the column here this is a
+recursive algorithm design paradigm
+
+ align:start position:0%
+recursive algorithm design paradigm
+ 
+
+ align:start position:0%
+recursive algorithm design paradigm
+and in general what we're going to do is
+
+ align:start position:0%
+and in general what we're going to do is
+ 
+
+ align:start position:0%
+and in general what we're going to do is
+take the problem that we actually want
+
+ align:start position:0%
+take the problem that we actually want
+ 
+
+ align:start position:0%
+take the problem that we actually want
+to solve
+
+ align:start position:0%
+to solve
+ 
+
+ align:start position:0%
+to solve
+and split it up into lots of possible
+
+ align:start position:0%
+and split it up into lots of possible
+ 
+
+ align:start position:0%
+and split it up into lots of possible
+sub problems
+
+ align:start position:0%
+sub problems
+ 
+
+ align:start position:0%
+sub problems
+and so the first part is to define what
+
+ align:start position:0%
+and so the first part is to define what
+ 
+
+ align:start position:0%
+and so the first part is to define what
+the heck are the sub problems in general
+
+ align:start position:0%
+the heck are the sub problems in general
+ 
+
+ align:start position:0%
+the heck are the sub problems in general
+we'll want some polynomial number of
+
+ align:start position:0%
+we'll want some polynomial number of
+ 
+
+ align:start position:0%
+we'll want some polynomial number of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+but it's pretty open-ended what these
+
+ align:start position:0%
+but it's pretty open-ended what these
+ 
+
+ align:start position:0%
+but it's pretty open-ended what these
+look like
+
+ align:start position:0%
+look like
+ 
+
+ align:start position:0%
+look like
+and the hardest part usually in
+
+ align:start position:0%
+and the hardest part usually in
+ 
+
+ align:start position:0%
+and the hardest part usually in
+deceptive defining a recursive algorithm
+
+ align:start position:0%
+deceptive defining a recursive algorithm
+ 
+
+ align:start position:0%
+deceptive defining a recursive algorithm
+is figuring out what the sub problems
+
+ align:start position:0%
+is figuring out what the sub problems
+ 
+
+ align:start position:0%
+is figuring out what the sub problems
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+usually they're related to the problem
+
+ align:start position:0%
+usually they're related to the problem
+ 
+
+ align:start position:0%
+usually they're related to the problem
+you want to solve often
+
+ align:start position:0%
+you want to solve often
+ 
+
+ align:start position:0%
+you want to solve often
+the problem you want to solve this is
+
+ align:start position:0%
+the problem you want to solve this is
+ 
+
+ align:start position:0%
+the problem you want to solve this is
+actually near the last step
+
+ align:start position:0%
+actually near the last step
+ 
+
+ align:start position:0%
+actually near the last step
+the original problem you're trying to
+
+ align:start position:0%
+the original problem you're trying to
+ 
+
+ align:start position:0%
+the original problem you're trying to
+solve is often one of these sub problems
+
+ align:start position:0%
+solve is often one of these sub problems
+ 
+
+ align:start position:0%
+solve is often one of these sub problems
+and then you use the smaller sub
+
+ align:start position:0%
+and then you use the smaller sub
+ 
+
+ align:start position:0%
+and then you use the smaller sub
+problems in order to build up
+
+ align:start position:0%
+problems in order to build up
+ 
+
+ align:start position:0%
+problems in order to build up
+the final original problem but sometimes
+
+ align:start position:0%
+the final original problem but sometimes
+ 
+
+ align:start position:0%
+the final original problem but sometimes
+at the end you need to
+
+ align:start position:0%
+at the end you need to
+ 
+
+ align:start position:0%
+at the end you need to
+take a bunch of sub problems and combine
+
+ align:start position:0%
+take a bunch of sub problems and combine
+ 
+
+ align:start position:0%
+take a bunch of sub problems and combine
+it into your original problem
+
+ align:start position:0%
+it into your original problem
+ 
+
+ align:start position:0%
+it into your original problem
+you can think one analogy you can think
+
+ align:start position:0%
+you can think one analogy you can think
+ 
+
+ align:start position:0%
+you can think one analogy you can think
+of here is divide and conquer algorithms
+
+ align:start position:0%
+of here is divide and conquer algorithms
+ 
+
+ align:start position:0%
+of here is divide and conquer algorithms
+which also had this kind of style but
+
+ align:start position:0%
+which also had this kind of style but
+ 
+
+ align:start position:0%
+which also had this kind of style but
+more generally we're going to relate
+
+ align:start position:0%
+more generally we're going to relate
+ 
+
+ align:start position:0%
+more generally we're going to relate
+different subproblem solutions with some
+
+ align:start position:0%
+different subproblem solutions with some
+ 
+
+ align:start position:0%
+different subproblem solutions with some
+recursive structure some recursive
+
+ align:start position:0%
+recursive structure some recursive
+ 
+
+ align:start position:0%
+recursive structure some recursive
+recurrence relation
+
+ align:start position:0%
+recurrence relation
+ 
+
+ align:start position:0%
+recurrence relation
+this is just a recursive algorithm that
+
+ align:start position:0%
+this is just a recursive algorithm that
+ 
+
+ align:start position:0%
+this is just a recursive algorithm that
+defines how to solve one problem in
+
+ align:start position:0%
+defines how to solve one problem in
+ 
+
+ align:start position:0%
+defines how to solve one problem in
+terms of smaller
+
+ align:start position:0%
+terms of smaller
+ 
+
+ align:start position:0%
+terms of smaller
+sub-problems for some notion of smaller
+
+ align:start position:0%
+sub-problems for some notion of smaller
+ 
+
+ align:start position:0%
+sub-problems for some notion of smaller
+and this is given by the topological
+
+ align:start position:0%
+and this is given by the topological
+ 
+
+ align:start position:0%
+and this is given by the topological
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+so if we think of the sub problems as a
+
+ align:start position:0%
+so if we think of the sub problems as a
+ 
+
+ align:start position:0%
+so if we think of the sub problems as a
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+and we draw an edge between
+
+ align:start position:0%
+and we draw an edge between
+ 
+
+ align:start position:0%
+and we draw an edge between
+so the vertices of the graph are sub
+
+ align:start position:0%
+so the vertices of the graph are sub
+ 
+
+ align:start position:0%
+so the vertices of the graph are sub
+problems the edges are the dependencies
+
+ align:start position:0%
+problems the edges are the dependencies
+ 
+
+ align:start position:0%
+problems the edges are the dependencies
+between those sub problems then what
+
+ align:start position:0%
+between those sub problems then what
+ 
+
+ align:start position:0%
+between those sub problems then what
+we'd like
+
+ align:start position:0%
+we'd like
+ 
+
+ align:start position:0%
+we'd like
+is the topological ordering the
+
+ align:start position:0%
+is the topological ordering the
+ 
+
+ align:start position:0%
+is the topological ordering the
+topological sort problem we talked about
+
+ align:start position:0%
+topological sort problem we talked about
+ 
+
+ align:start position:0%
+topological sort problem we talked about
+in the context of dfs or dag shortest
+
+ align:start position:0%
+in the context of dfs or dag shortest
+ 
+
+ align:start position:0%
+in the context of dfs or dag shortest
+paths
+
+ align:start position:0%
+paths
+ 
+
+ align:start position:0%
+paths
+uh what we would like is that this uh
+
+ align:start position:0%
+uh what we would like is that this uh
+ 
+
+ align:start position:0%
+uh what we would like is that this uh
+the sub problems and the calls the
+
+ align:start position:0%
+the sub problems and the calls the
+ 
+
+ align:start position:0%
+the sub problems and the calls the
+recursive calls between them in this
+
+ align:start position:0%
+recursive calls between them in this
+ 
+
+ align:start position:0%
+recursive calls between them in this
+recursive relation
+
+ align:start position:0%
+recursive relation
+ 
+
+ align:start position:0%
+recursive relation
+forms a dag we want it to be acyclic
+
+ align:start position:0%
+forms a dag we want it to be acyclic
+ 
+
+ align:start position:0%
+forms a dag we want it to be acyclic
+otherwise
+
+ align:start position:0%
+otherwise
+ 
+
+ align:start position:0%
+otherwise
+you have an infinite loop in your
+
+ align:start position:0%
+you have an infinite loop in your
+ 
+
+ align:start position:0%
+you have an infinite loop in your
+recursive calls if you have a cycle
+
+ align:start position:0%
+recursive calls if you have a cycle
+ 
+
+ align:start position:0%
+recursive calls if you have a cycle
+you're just go you'll never terminate
+
+ align:start position:0%
+you're just go you'll never terminate
+ 
+
+ align:start position:0%
+you're just go you'll never terminate
+and so to spec to make sure that our
+
+ align:start position:0%
+and so to spec to make sure that our
+ 
+
+ align:start position:0%
+and so to spec to make sure that our
+these dependencies between subproblems
+
+ align:start position:0%
+these dependencies between subproblems
+ 
+
+ align:start position:0%
+these dependencies between subproblems
+given by this recurrence relation
+
+ align:start position:0%
+given by this recurrence relation
+ 
+
+ align:start position:0%
+given by this recurrence relation
+is a cyclic uh one way to do that is to
+
+ align:start position:0%
+is a cyclic uh one way to do that is to
+ 
+
+ align:start position:0%
+is a cyclic uh one way to do that is to
+specify a topological order
+
+ align:start position:0%
+specify a topological order
+ 
+
+ align:start position:0%
+specify a topological order
+okay or you could prove it some other
+
+ align:start position:0%
+okay or you could prove it some other
+ 
+
+ align:start position:0%
+okay or you could prove it some other
+way but often it's just a for loop
+
+ align:start position:0%
+way but often it's just a for loop
+ 
+
+ align:start position:0%
+way but often it's just a for loop
+to say just do it in this order then of
+
+ align:start position:0%
+to say just do it in this order then of
+ 
+
+ align:start position:0%
+to say just do it in this order then of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+any recursive structure needs base cases
+
+ align:start position:0%
+any recursive structure needs base cases
+ 
+
+ align:start position:0%
+any recursive structure needs base cases
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's a useful step not to forget um we
+
+ align:start position:0%
+that's a useful step not to forget um we
+ 
+
+ align:start position:0%
+that's a useful step not to forget um we
+want to solve the original problem using
+
+ align:start position:0%
+want to solve the original problem using
+ 
+
+ align:start position:0%
+want to solve the original problem using
+these sub problems and then we analyze
+
+ align:start position:0%
+these sub problems and then we analyze
+ 
+
+ align:start position:0%
+these sub problems and then we analyze
+our running time
+
+ align:start position:0%
+our running time
+ 
+
+ align:start position:0%
+our running time
+at the end so six easy steps
+
+ align:start position:0%
+at the end so six easy steps
+ 
+
+ align:start position:0%
+at the end so six easy steps
+actually the hardest ones are these two
+
+ align:start position:0%
+actually the hardest ones are these two
+ 
+
+ align:start position:0%
+actually the hardest ones are these two
+which are interrelated
+
+ align:start position:0%
+which are interrelated
+ 
+
+ align:start position:0%
+which are interrelated
+and what we're going to see over the
+
+ align:start position:0%
+and what we're going to see over the
+ 
+
+ align:start position:0%
+and what we're going to see over the
+next four lectures this is the first of
+
+ align:start position:0%
+next four lectures this is the first of
+ 
+
+ align:start position:0%
+next four lectures this is the first of
+four lectures on dynamic programming
+
+ align:start position:0%
+four lectures on dynamic programming
+ 
+
+ align:start position:0%
+four lectures on dynamic programming
+is lots of examples of applying this
+
+ align:start position:0%
+is lots of examples of applying this
+ 
+
+ align:start position:0%
+is lots of examples of applying this
+paradigm over and over
+
+ align:start position:0%
+paradigm over and over
+ 
+
+ align:start position:0%
+paradigm over and over
+together with the memoization idea which
+
+ align:start position:0%
+together with the memoization idea which
+ 
+
+ align:start position:0%
+together with the memoization idea which
+we'll get to soon
+
+ align:start position:0%
+we'll get to soon
+ 
+
+ align:start position:0%
+we'll get to soon
+let's see an example first of an
+
+ align:start position:0%
+let's see an example first of an
+ 
+
+ align:start position:0%
+let's see an example first of an
+algorithm we've already seen which is
+
+ align:start position:0%
+algorithm we've already seen which is
+ 
+
+ align:start position:0%
+algorithm we've already seen which is
+merge sort
+
+ align:start position:0%
+merge sort
+ 
+
+ align:start position:0%
+merge sort
+so a divide and conquer algorithm
+
+ align:start position:0%
+so a divide and conquer algorithm
+ 
+
+ align:start position:0%
+so a divide and conquer algorithm
+phrased in this
+
+ align:start position:0%
+phrased in this
+ 
+
+ align:start position:0%
+phrased in this
+with this structure of sort bot so for
+
+ align:start position:0%
+with this structure of sort bot so for
+ 
+
+ align:start position:0%
+with this structure of sort bot so for
+the subproblems
+
+ align:start position:0%
+the subproblems
+ 
+
+ align:start position:0%
+the subproblems
+so original problem is to sort the
+
+ align:start position:0%
+so original problem is to sort the
+ 
+
+ align:start position:0%
+so original problem is to sort the
+elements of a
+
+ align:start position:0%
+elements of a
+ 
+
+ align:start position:0%
+elements of a
+and some sub problems that we solve
+
+ align:start position:0%
+and some sub problems that we solve
+ 
+
+ align:start position:0%
+and some sub problems that we solve
+along the way are sorting different
+
+ align:start position:0%
+along the way are sorting different
+ 
+
+ align:start position:0%
+along the way are sorting different
+subarrays of a so for every well not for
+
+ align:start position:0%
+subarrays of a so for every well not for
+ 
+
+ align:start position:0%
+subarrays of a so for every well not for
+every i and j but for some
+
+ align:start position:0%
+every i and j but for some
+ 
+
+ align:start position:0%
+every i and j but for some
+i and js we sort the items from
+
+ align:start position:0%
+i and js we sort the items from
+ 
+
+ align:start position:0%
+i and js we sort the items from
+i up to j minus 1. so i'm going to
+
+ align:start position:0%
+i up to j minus 1. so i'm going to
+ 
+
+ align:start position:0%
+i up to j minus 1. so i'm going to
+define that subproblem to be
+
+ align:start position:0%
+define that subproblem to be
+ 
+
+ align:start position:0%
+define that subproblem to be
+s of i j so this is something that i
+
+ align:start position:0%
+s of i j so this is something that i
+ 
+
+ align:start position:0%
+s of i j so this is something that i
+might want to solve
+
+ align:start position:0%
+might want to solve
+ 
+
+ align:start position:0%
+might want to solve
+the original problem that i want to
+
+ align:start position:0%
+the original problem that i want to
+ 
+
+ align:start position:0%
+the original problem that i want to
+solve is s of 0 comma n where n is the
+
+ align:start position:0%
+solve is s of 0 comma n where n is the
+ 
+
+ align:start position:0%
+solve is s of 0 comma n where n is the
+length of the array
+
+ align:start position:0%
+length of the array
+ 
+
+ align:start position:0%
+length of the array
+so that's what i actually care about in
+
+ align:start position:0%
+so that's what i actually care about in
+ 
+
+ align:start position:0%
+so that's what i actually care about in
+the end but we're going to solve that
+
+ align:start position:0%
+the end but we're going to solve that
+ 
+
+ align:start position:0%
+the end but we're going to solve that
+by writing it recursively in terms of
+
+ align:start position:0%
+by writing it recursively in terms of
+ 
+
+ align:start position:0%
+by writing it recursively in terms of
+sorting different
+
+ align:start position:0%
+sorting different
+ 
+
+ align:start position:0%
+sorting different
+subarrays as follows this is the
+
+ align:start position:0%
+subarrays as follows this is the
+ 
+
+ align:start position:0%
+subarrays as follows this is the
+recurrence relation
+
+ align:start position:0%
+recurrence relation
+ 
+
+ align:start position:0%
+recurrence relation
+i've written it very simply here of
+
+ align:start position:0%
+i've written it very simply here of
+ 
+
+ align:start position:0%
+i've written it very simply here of
+course there's a merge algorithm
+
+ align:start position:0%
+course there's a merge algorithm
+ 
+
+ align:start position:0%
+course there's a merge algorithm
+which is uh somewhat complicated but
+
+ align:start position:0%
+which is uh somewhat complicated but
+ 
+
+ align:start position:0%
+which is uh somewhat complicated but
+it's we we saw the two finger
+
+ align:start position:0%
+it's we we saw the two finger
+ 
+
+ align:start position:0%
+it's we we saw the two finger
+linear time merge algorithm given two
+
+ align:start position:0%
+linear time merge algorithm given two
+ 
+
+ align:start position:0%
+linear time merge algorithm given two
+sorted arrays so this is supposed to be
+
+ align:start position:0%
+sorted arrays so this is supposed to be
+ 
+
+ align:start position:0%
+sorted arrays so this is supposed to be
+the sorted array version of the items i
+
+ align:start position:0%
+the sorted array version of the items i
+ 
+
+ align:start position:0%
+the sorted array version of the items i
+through m
+
+ align:start position:0%
+through m
+ 
+
+ align:start position:0%
+through m
+m is the middle element between i and j
+
+ align:start position:0%
+m is the middle element between i and j
+ 
+
+ align:start position:0%
+m is the middle element between i and j
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the sorted array of the items from m up
+
+ align:start position:0%
+the sorted array of the items from m up
+ 
+
+ align:start position:0%
+the sorted array of the items from m up
+to j
+
+ align:start position:0%
+to j
+ 
+
+ align:start position:0%
+to j
+if we merge those that gives us the
+
+ align:start position:0%
+if we merge those that gives us the
+ 
+
+ align:start position:0%
+if we merge those that gives us the
+sorted array
+
+ align:start position:0%
+sorted array
+ 
+
+ align:start position:0%
+sorted array
+from i up to j and that's exactly what
+
+ align:start position:0%
+from i up to j and that's exactly what
+ 
+
+ align:start position:0%
+from i up to j and that's exactly what
+merge sort
+
+ align:start position:0%
+merge sort
+ 
+
+ align:start position:0%
+merge sort
+does so this is in general this relation
+
+ align:start position:0%
+does so this is in general this relation
+ 
+
+ align:start position:0%
+does so this is in general this relation
+is just some algorithm
+
+ align:start position:0%
+is just some algorithm
+ 
+
+ align:start position:0%
+is just some algorithm
+for if you if you're given the solutions
+
+ align:start position:0%
+for if you if you're given the solutions
+ 
+
+ align:start position:0%
+for if you if you're given the solutions
+to some smaller sub problems
+
+ align:start position:0%
+to some smaller sub problems
+ 
+
+ align:start position:0%
+to some smaller sub problems
+how do i solve uh the sub problem that i
+
+ align:start position:0%
+how do i solve uh the sub problem that i
+ 
+
+ align:start position:0%
+how do i solve uh the sub problem that i
+want to solve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we need to make sure that this
+
+ align:start position:0%
+and so we need to make sure that this
+ 
+
+ align:start position:0%
+and so we need to make sure that this
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+is bigger than the ones that we
+
+ align:start position:0%
+is bigger than the ones that we
+ 
+
+ align:start position:0%
+is bigger than the ones that we
+recursively call on
+
+ align:start position:0%
+recursively call on
+ 
+
+ align:start position:0%
+recursively call on
+and that we don't get an infinite cyclic
+
+ align:start position:0%
+and that we don't get an infinite cyclic
+ 
+
+ align:start position:0%
+and that we don't get an infinite cyclic
+group of recursions
+
+ align:start position:0%
+group of recursions
+ 
+
+ align:start position:0%
+group of recursions
+and here a valid topological order is to
+
+ align:start position:0%
+and here a valid topological order is to
+ 
+
+ align:start position:0%
+and here a valid topological order is to
+say solve these problems in order
+
+ align:start position:0%
+say solve these problems in order
+ 
+
+ align:start position:0%
+say solve these problems in order
+where j minus i the length of the
+
+ align:start position:0%
+where j minus i the length of the
+ 
+
+ align:start position:0%
+where j minus i the length of the
+subarray
+
+ align:start position:0%
+subarray
+ 
+
+ align:start position:0%
+subarray
+is increasing and then you can check
+
+ align:start position:0%
+is increasing and then you can check
+ 
+
+ align:start position:0%
+is increasing and then you can check
+because m
+
+ align:start position:0%
+because m
+ 
+
+ align:start position:0%
+because m
+is strictly between i and j as long as
+
+ align:start position:0%
+is strictly between i and j as long as
+ 
+
+ align:start position:0%
+is strictly between i and j as long as
+we're not in a base case
+
+ align:start position:0%
+we're not in a base case
+ 
+
+ align:start position:0%
+we're not in a base case
+then we know uh we can
+
+ align:start position:0%
+then we know uh we can
+ 
+
+ align:start position:0%
+then we know uh we can
+these subarrays will be smaller than
+
+ align:start position:0%
+these subarrays will be smaller than
+ 
+
+ align:start position:0%
+these subarrays will be smaller than
+this one and so this increasing order
+
+ align:start position:0%
+this one and so this increasing order
+ 
+
+ align:start position:0%
+this one and so this increasing order
+gives us a valid topological order
+
+ align:start position:0%
+gives us a valid topological order
+ 
+
+ align:start position:0%
+gives us a valid topological order
+on all of the problems all the sub
+
+ align:start position:0%
+on all of the problems all the sub
+ 
+
+ align:start position:0%
+on all of the problems all the sub
+problems uh we have a base case which is
+
+ align:start position:0%
+problems uh we have a base case which is
+ 
+
+ align:start position:0%
+problems uh we have a base case which is
+if we don't want to sort anything
+
+ align:start position:0%
+if we don't want to sort anything
+ 
+
+ align:start position:0%
+if we don't want to sort anything
+that's the empty array i already said
+
+ align:start position:0%
+that's the empty array i already said
+ 
+
+ align:start position:0%
+that's the empty array i already said
+the original problem and then running
+
+ align:start position:0%
+the original problem and then running
+ 
+
+ align:start position:0%
+the original problem and then running
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+is i mean there's no better way to solve
+
+ align:start position:0%
+is i mean there's no better way to solve
+ 
+
+ align:start position:0%
+is i mean there's no better way to solve
+it than
+
+ align:start position:0%
+it than
+ 
+
+ align:start position:0%
+it than
+the recurrence that we already saw how
+
+ align:start position:0%
+the recurrence that we already saw how
+ 
+
+ align:start position:0%
+the recurrence that we already saw how
+to solve so this is just another way to
+
+ align:start position:0%
+to solve so this is just another way to
+ 
+
+ align:start position:0%
+to solve so this is just another way to
+think of n log n merge sort
+
+ align:start position:0%
+think of n log n merge sort
+ 
+
+ align:start position:0%
+think of n log n merge sort
+in this labeled framework of sort bot
+
+ align:start position:0%
+in this labeled framework of sort bot
+ 
+
+ align:start position:0%
+in this labeled framework of sort bot
+let's get to another problem that does
+
+ align:start position:0%
+let's get to another problem that does
+ 
+
+ align:start position:0%
+let's get to another problem that does
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+fit recursion so well but we can
+
+ align:start position:0%
+fit recursion so well but we can
+ 
+
+ align:start position:0%
+fit recursion so well but we can
+make it better so this we're going to
+
+ align:start position:0%
+make it better so this we're going to
+ 
+
+ align:start position:0%
+make it better so this we're going to
+start with a very simple problem which
+
+ align:start position:0%
+start with a very simple problem which
+ 
+
+ align:start position:0%
+start with a very simple problem which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+computing fibonacci numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's really just a toy problem to
+
+ align:start position:0%
+it's really just a toy problem to
+ 
+
+ align:start position:0%
+it's really just a toy problem to
+illustrate a very powerful idea which is
+
+ align:start position:0%
+illustrate a very powerful idea which is
+ 
+
+ align:start position:0%
+illustrate a very powerful idea which is
+memoization
+
+ align:start position:0%
+memoization
+ 
+
+ align:start position:0%
+memoization
+so the problem i'm interested in is i'm
+
+ align:start position:0%
+so the problem i'm interested in is i'm
+ 
+
+ align:start position:0%
+so the problem i'm interested in is i'm
+given a particular number
+
+ align:start position:0%
+given a particular number
+ 
+
+ align:start position:0%
+given a particular number
+n and i want to compute
+
+ align:start position:0%
+n and i want to compute
+ 
+
+ align:start position:0%
+n and i want to compute
+the nth fibonacci number and in case you
+
+ align:start position:0%
+the nth fibonacci number and in case you
+ 
+
+ align:start position:0%
+the nth fibonacci number and in case you
+forgot
+
+ align:start position:0%
+forgot
+ 
+
+ align:start position:0%
+forgot
+the nth fibonacci number is given by
+
+ align:start position:0%
+the nth fibonacci number is given by
+ 
+
+ align:start position:0%
+the nth fibonacci number is given by
+this recurrence fn
+
+ align:start position:0%
+this recurrence fn
+ 
+
+ align:start position:0%
+this recurrence fn
+is fn minus one plus fn minus two with
+
+ align:start position:0%
+is fn minus one plus fn minus two with
+ 
+
+ align:start position:0%
+is fn minus one plus fn minus two with
+base case
+
+ align:start position:0%
+base case
+ 
+
+ align:start position:0%
+base case
+uh let's say f1 equals f2 equals one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we'd like to compute this this
+
+ align:start position:0%
+and so we'd like to compute this this
+ 
+
+ align:start position:0%
+and so we'd like to compute this this
+seems this is a recurrence
+
+ align:start position:0%
+seems this is a recurrence
+ 
+
+ align:start position:0%
+seems this is a recurrence
+so it seems very natural to write it as
+
+ align:start position:0%
+so it seems very natural to write it as
+ 
+
+ align:start position:0%
+so it seems very natural to write it as
+a recursive algorithm so let's try to do
+
+ align:start position:0%
+a recursive algorithm so let's try to do
+ 
+
+ align:start position:0%
+a recursive algorithm so let's try to do
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+we start with what are the sub-problems
+
+ align:start position:0%
+we start with what are the sub-problems
+ 
+
+ align:start position:0%
+we start with what are the sub-problems
+the obvious sub-problems
+
+ align:start position:0%
+the obvious sub-problems
+ 
+
+ align:start position:0%
+the obvious sub-problems
+are just the various fibonacci numbers
+
+ align:start position:0%
+are just the various fibonacci numbers
+ 
+
+ align:start position:0%
+are just the various fibonacci numbers
+fi for i between
+
+ align:start position:0%
+fi for i between
+ 
+
+ align:start position:0%
+fi for i between
+one and n
+
+ align:start position:0%
+one and n
+ 
+
+ align:start position:0%
+one and n
+so they're n of these sub problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool let's see we want a relation
+
+ align:start position:0%
+cool let's see we want a relation
+ 
+
+ align:start position:0%
+cool let's see we want a relation
+between them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well maybe i'll just to distinguish the
+
+ align:start position:0%
+well maybe i'll just to distinguish the
+ 
+
+ align:start position:0%
+well maybe i'll just to distinguish the
+problems from the fibonacci numbers
+
+ align:start position:0%
+problems from the fibonacci numbers
+ 
+
+ align:start position:0%
+problems from the fibonacci numbers
+let me write f of i this is a function
+
+ align:start position:0%
+let me write f of i this is a function
+ 
+
+ align:start position:0%
+let me write f of i this is a function
+an algorithm we're going to define and
+
+ align:start position:0%
+an algorithm we're going to define and
+ 
+
+ align:start position:0%
+an algorithm we're going to define and
+it's defined to be
+
+ align:start position:0%
+it's defined to be
+ 
+
+ align:start position:0%
+it's defined to be
+the goal we're trying to get is the i
+
+ align:start position:0%
+the goal we're trying to get is the i
+ 
+
+ align:start position:0%
+the goal we're trying to get is the i
+fibonacci number
+
+ align:start position:0%
+fibonacci number
+ 
+
+ align:start position:0%
+fibonacci number
+given i and then we can write
+
+ align:start position:0%
+given i and then we can write
+ 
+
+ align:start position:0%
+given i and then we can write
+the recurrence relation on these guys
+
+ align:start position:0%
+the recurrence relation on these guys
+ 
+
+ align:start position:0%
+the recurrence relation on these guys
+just uh
+
+ align:start position:0%
+just uh
+ 
+
+ align:start position:0%
+just uh
+f of i equals f of i minus 1
+
+ align:start position:0%
+f of i equals f of i minus 1
+ 
+
+ align:start position:0%
+f of i equals f of i minus 1
+plus f of i minus 2. so in other words
+
+ align:start position:0%
+plus f of i minus 2. so in other words
+ 
+
+ align:start position:0%
+plus f of i minus 2. so in other words
+recursively compute
+
+ align:start position:0%
+recursively compute
+ 
+
+ align:start position:0%
+recursively compute
+those fibonacci numbers then add them
+
+ align:start position:0%
+those fibonacci numbers then add them
+ 
+
+ align:start position:0%
+those fibonacci numbers then add them
+together that's an algorithm
+
+ align:start position:0%
+together that's an algorithm
+ 
+
+ align:start position:0%
+together that's an algorithm
+next is t for topological order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here of course we just want to compute
+
+ align:start position:0%
+here of course we just want to compute
+ 
+
+ align:start position:0%
+here of course we just want to compute
+these in order of increasing
+
+ align:start position:0%
+these in order of increasing
+ 
+
+ align:start position:0%
+these in order of increasing
+i from the base cases up
+
+ align:start position:0%
+i from the base cases up
+ 
+
+ align:start position:0%
+i from the base cases up
+another way i like to write this is as a
+
+ align:start position:0%
+another way i like to write this is as a
+ 
+
+ align:start position:0%
+another way i like to write this is as a
+for loop
+
+ align:start position:0%
+for loop
+ 
+
+ align:start position:0%
+for loop
+for i equals one to n
+
+ align:start position:0%
+for i equals one to n
+ 
+
+ align:start position:0%
+for i equals one to n
+maybe we'll see why but this gives an
+
+ align:start position:0%
+maybe we'll see why but this gives an
+ 
+
+ align:start position:0%
+maybe we'll see why but this gives an
+explicit order
+
+ align:start position:0%
+explicit order
+ 
+
+ align:start position:0%
+explicit order
+of to compute these sub-problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and all right base case is just the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the fibonacci numbers but i guess i
+
+ align:start position:0%
+as the fibonacci numbers but i guess i
+ 
+
+ align:start position:0%
+as the fibonacci numbers but i guess i
+should write parentheses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the original problem we want to solve is
+
+ align:start position:0%
+the original problem we want to solve is
+ 
+
+ align:start position:0%
+the original problem we want to solve is
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+n and the time
+
+ align:start position:0%
+n and the time
+ 
+
+ align:start position:0%
+n and the time
+all right here's where things get
+
+ align:start position:0%
+all right here's where things get
+ 
+
+ align:start position:0%
+all right here's where things get
+interesting or bad
+
+ align:start position:0%
+interesting or bad
+ 
+
+ align:start position:0%
+interesting or bad
+so what is the running time of this
+
+ align:start position:0%
+so what is the running time of this
+ 
+
+ align:start position:0%
+so what is the running time of this
+recursive algorithm
+
+ align:start position:0%
+recursive algorithm
+ 
+
+ align:start position:0%
+recursive algorithm
+as i've stated it so far the running
+
+ align:start position:0%
+as i've stated it so far the running
+ 
+
+ align:start position:0%
+as i've stated it so far the running
+time is
+
+ align:start position:0%
+time is
+ 
+
+ align:start position:0%
+time is
+given by a recurrence let's write the
+
+ align:start position:0%
+given by a recurrence let's write the
+ 
+
+ align:start position:0%
+given by a recurrence let's write the
+recurrence
+
+ align:start position:0%
+recurrence
+ 
+
+ align:start position:0%
+recurrence
+so in order to compute f of n uh
+
+ align:start position:0%
+so in order to compute f of n uh
+ 
+
+ align:start position:0%
+so in order to compute f of n uh
+i recursively compute f of i minus 1
+
+ align:start position:0%
+i recursively compute f of i minus 1
+ 
+
+ align:start position:0%
+i recursively compute f of i minus 1
+or f of n minus 1 here
+
+ align:start position:0%
+or f of n minus 1 here
+ 
+
+ align:start position:0%
+or f of n minus 1 here
+and i recursively compute f
+
+ align:start position:0%
+and i recursively compute f
+ 
+
+ align:start position:0%
+and i recursively compute f
+of n minus 2 so that will take t of n
+
+ align:start position:0%
+of n minus 2 so that will take t of n
+ 
+
+ align:start position:0%
+of n minus 2 so that will take t of n
+minus 2 this first step will take t of n
+
+ align:start position:0%
+minus 2 this first step will take t of n
+ 
+
+ align:start position:0%
+minus 2 this first step will take t of n
+minus 1.
+
+ align:start position:0%
+minus 1.
+ 
+
+ align:start position:0%
+minus 1.
+and now i need to solve this recurrence
+
+ align:start position:0%
+and now i need to solve this recurrence
+ 
+
+ align:start position:0%
+and now i need to solve this recurrence
+uh this is not a recurrence that falls
+
+ align:start position:0%
+uh this is not a recurrence that falls
+ 
+
+ align:start position:0%
+uh this is not a recurrence that falls
+to the master method it doesn't have a
+
+ align:start position:0%
+to the master method it doesn't have a
+ 
+
+ align:start position:0%
+to the master method it doesn't have a
+divided by so we have to think about it
+
+ align:start position:0%
+divided by so we have to think about it
+ 
+
+ align:start position:0%
+divided by so we have to think about it
+a little bit
+
+ align:start position:0%
+a little bit
+ 
+
+ align:start position:0%
+a little bit
+but we don't have to think about it too
+
+ align:start position:0%
+but we don't have to think about it too
+ 
+
+ align:start position:0%
+but we don't have to think about it too
+hard because this recurrence
+
+ align:start position:0%
+hard because this recurrence
+ 
+
+ align:start position:0%
+hard because this recurrence
+is the same as this recurrence which is
+
+ align:start position:0%
+is the same as this recurrence which is
+ 
+
+ align:start position:0%
+is the same as this recurrence which is
+the same as this recurrence i've written
+
+ align:start position:0%
+the same as this recurrence i've written
+ 
+
+ align:start position:0%
+the same as this recurrence i've written
+it three times now
+
+ align:start position:0%
+it three times now
+ 
+
+ align:start position:0%
+it three times now
+and so the solution to this is the nth
+
+ align:start position:0%
+and so the solution to this is the nth
+ 
+
+ align:start position:0%
+and so the solution to this is the nth
+fibonacci number
+
+ align:start position:0%
+fibonacci number
+ 
+
+ align:start position:0%
+fibonacci number
+uh oh sorry it's a little bit worse
+
+ align:start position:0%
+uh oh sorry it's a little bit worse
+ 
+
+ align:start position:0%
+uh oh sorry it's a little bit worse
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+in addition to those recursions i also
+
+ align:start position:0%
+in addition to those recursions i also
+ 
+
+ align:start position:0%
+in addition to those recursions i also
+spend constant time to do the addition
+
+ align:start position:0%
+spend constant time to do the addition
+ 
+
+ align:start position:0%
+spend constant time to do the addition
+maybe more than constant time but if we
+
+ align:start position:0%
+maybe more than constant time but if we
+ 
+
+ align:start position:0%
+maybe more than constant time but if we
+just count the number of additions we do
+
+ align:start position:0%
+just count the number of additions we do
+ 
+
+ align:start position:0%
+just count the number of additions we do
+it will be plus plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+additions
+
+ align:start position:0%
+additions
+ 
+
+ align:start position:0%
+additions
+okay but this is bigger than the nth
+
+ align:start position:0%
+okay but this is bigger than the nth
+ 
+
+ align:start position:0%
+okay but this is bigger than the nth
+fibonacci number
+
+ align:start position:0%
+fibonacci number
+ 
+
+ align:start position:0%
+fibonacci number
+and if you know anything about fibonacci
+
+ align:start position:0%
+and if you know anything about fibonacci
+ 
+
+ align:start position:0%
+and if you know anything about fibonacci
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+they grow exponentially they're about
+
+ align:start position:0%
+they grow exponentially they're about
+ 
+
+ align:start position:0%
+they grow exponentially they're about
+golden ratio to the n i'm wearing golden
+
+ align:start position:0%
+golden ratio to the n i'm wearing golden
+ 
+
+ align:start position:0%
+golden ratio to the n i'm wearing golden
+ratio in case you forgot the number
+
+ align:start position:0%
+ratio in case you forgot the number
+ 
+
+ align:start position:0%
+ratio in case you forgot the number
+so that's bad because golden ratio is
+
+ align:start position:0%
+so that's bad because golden ratio is
+ 
+
+ align:start position:0%
+so that's bad because golden ratio is
+bigger than one so this is exponential
+
+ align:start position:0%
+bigger than one so this is exponential
+ 
+
+ align:start position:0%
+bigger than one so this is exponential
+growth
+
+ align:start position:0%
+growth
+ 
+
+ align:start position:0%
+growth
+as we know especially in this time
+
+ align:start position:0%
+as we know especially in this time
+ 
+
+ align:start position:0%
+as we know especially in this time
+exponential growth is bad
+
+ align:start position:0%
+exponential growth is bad
+ 
+
+ align:start position:0%
+exponential growth is bad
+and algorithms exponential growth is bad
+
+ align:start position:0%
+and algorithms exponential growth is bad
+ 
+
+ align:start position:0%
+and algorithms exponential growth is bad
+because we can only solve very small
+
+ align:start position:0%
+because we can only solve very small
+ 
+
+ align:start position:0%
+because we can only solve very small
+problems with exponential growth very
+
+ align:start position:0%
+problems with exponential growth very
+ 
+
+ align:start position:0%
+problems with exponential growth very
+small n so this is a
+
+ align:start position:0%
+small n so this is a
+ 
+
+ align:start position:0%
+small n so this is a
+terrible way to compute the nth
+
+ align:start position:0%
+terrible way to compute the nth
+ 
+
+ align:start position:0%
+terrible way to compute the nth
+fibonacci number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so don't do this
+
+ align:start position:0%
+okay so don't do this
+ 
+
+ align:start position:0%
+okay so don't do this
+but there's a very tiny tweak to this
+
+ align:start position:0%
+but there's a very tiny tweak to this
+ 
+
+ align:start position:0%
+but there's a very tiny tweak to this
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+that makes it really good which is
+
+ align:start position:0%
+that makes it really good which is
+ 
+
+ align:start position:0%
+that makes it really good which is
+memoization and this is a big idea
+
+ align:start position:0%
+memoization and this is a big idea
+ 
+
+ align:start position:0%
+memoization and this is a big idea
+it is the big idea of dynamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+programming
+
+ align:start position:0%
+programming
+ 
+
+ align:start position:0%
+programming
+it's a funny word probably made up by a
+
+ align:start position:0%
+it's a funny word probably made up by a
+ 
+
+ align:start position:0%
+it's a funny word probably made up by a
+computer scientist
+
+ align:start position:0%
+computer scientist
+ 
+
+ align:start position:0%
+computer scientist
+um instead of memorization it's
+
+ align:start position:0%
+um instead of memorization it's
+ 
+
+ align:start position:0%
+um instead of memorization it's
+memoization
+
+ align:start position:0%
+memoization
+ 
+
+ align:start position:0%
+memoization
+because we're going to write things down
+
+ align:start position:0%
+because we're going to write things down
+ 
+
+ align:start position:0%
+because we're going to write things down
+in a memo pad is the idea
+
+ align:start position:0%
+in a memo pad is the idea
+ 
+
+ align:start position:0%
+in a memo pad is the idea
+and it's a very simple idea which is
+
+ align:start position:0%
+and it's a very simple idea which is
+ 
+
+ align:start position:0%
+and it's a very simple idea which is
+just remember
+
+ align:start position:0%
+just remember
+ 
+
+ align:start position:0%
+just remember
+and reuse solutions to sub-problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's draw the recursion tree
+
+ align:start position:0%
+so let's draw the recursion tree
+ 
+
+ align:start position:0%
+so let's draw the recursion tree
+for this recursive algorithm as we've
+
+ align:start position:0%
+for this recursive algorithm as we've
+ 
+
+ align:start position:0%
+for this recursive algorithm as we've
+done it so far
+
+ align:start position:0%
+done it so far
+ 
+
+ align:start position:0%
+done it so far
+so at the top we let me make a little
+
+ align:start position:0%
+so at the top we let me make a little
+ 
+
+ align:start position:0%
+so at the top we let me make a little
+bit of space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the top we are calling f of n
+
+ align:start position:0%
+at the top we are calling f of n
+ 
+
+ align:start position:0%
+at the top we are calling f of n
+and then that calls f of n minus 1
+
+ align:start position:0%
+and then that calls f of n minus 1
+ 
+
+ align:start position:0%
+and then that calls f of n minus 1
+and f of n minus two and it does an
+
+ align:start position:0%
+and f of n minus two and it does an
+ 
+
+ align:start position:0%
+and f of n minus two and it does an
+addition up here
+
+ align:start position:0%
+addition up here
+ 
+
+ align:start position:0%
+addition up here
+and then this calls f of n minus two
+
+ align:start position:0%
+and then this calls f of n minus two
+ 
+
+ align:start position:0%
+and then this calls f of n minus two
+and this calls f of n minus three
+
+ align:start position:0%
+and this calls f of n minus three
+ 
+
+ align:start position:0%
+and this calls f of n minus three
+this calls f of n minus three
+
+ align:start position:0%
+this calls f of n minus three
+ 
+
+ align:start position:0%
+this calls f of n minus three
+and this calls f of n minus 4.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and we notice that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this sub problem is the same as this sub
+
+ align:start position:0%
+this sub problem is the same as this sub
+ 
+
+ align:start position:0%
+this sub problem is the same as this sub
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+so to compute f of n minus 1 i need f of
+
+ align:start position:0%
+so to compute f of n minus 1 i need f of
+ 
+
+ align:start position:0%
+so to compute f of n minus 1 i need f of
+n minus 3 and also to compute f of n
+
+ align:start position:0%
+n minus 3 and also to compute f of n
+ 
+
+ align:start position:0%
+n minus 3 and also to compute f of n
+minus 2 i need f of n minus 3.
+
+ align:start position:0%
+minus 2 i need f of n minus 3.
+ 
+
+ align:start position:0%
+minus 2 i need f of n minus 3.
+so why are we computing it twice let's
+
+ align:start position:0%
+so why are we computing it twice let's
+ 
+
+ align:start position:0%
+so why are we computing it twice let's
+just do it once
+
+ align:start position:0%
+just do it once
+ 
+
+ align:start position:0%
+just do it once
+when we solve it let's write it in a
+
+ align:start position:0%
+when we solve it let's write it in a
+ 
+
+ align:start position:0%
+when we solve it let's write it in a
+table somewhere
+
+ align:start position:0%
+table somewhere
+ 
+
+ align:start position:0%
+table somewhere
+and then when we need it again we'll
+
+ align:start position:0%
+and then when we need it again we'll
+ 
+
+ align:start position:0%
+and then when we need it again we'll
+just reuse that value question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of n minus 2 is also shared so let me
+
+ align:start position:0%
+f of n minus 2 is also shared so let me
+ 
+
+ align:start position:0%
+f of n minus 2 is also shared so let me
+use a different
+
+ align:start position:0%
+use a different
+ 
+
+ align:start position:0%
+use a different
+symbol f of n minus 2 is already
+
+ align:start position:0%
+symbol f of n minus 2 is already
+ 
+
+ align:start position:0%
+symbol f of n minus 2 is already
+here so this was at the same level but
+
+ align:start position:0%
+here so this was at the same level but
+ 
+
+ align:start position:0%
+here so this was at the same level but
+we also get shared reuse
+
+ align:start position:0%
+we also get shared reuse
+ 
+
+ align:start position:0%
+we also get shared reuse
+between different levels in fact i
+
+ align:start position:0%
+between different levels in fact i
+ 
+
+ align:start position:0%
+between different levels in fact i
+wouldn't even call f of n minus 3
+
+ align:start position:0%
+wouldn't even call f of n minus 3
+ 
+
+ align:start position:0%
+wouldn't even call f of n minus 3
+because this whole part
+
+ align:start position:0%
+because this whole part
+ 
+
+ align:start position:0%
+because this whole part
+doesn't need to be computed a second
+
+ align:start position:0%
+doesn't need to be computed a second
+ 
+
+ align:start position:0%
+doesn't need to be computed a second
+time if i already computed it here
+
+ align:start position:0%
+time if i already computed it here
+ 
+
+ align:start position:0%
+time if i already computed it here
+it doesn't matter which one comes first
+
+ align:start position:0%
+it doesn't matter which one comes first
+ 
+
+ align:start position:0%
+it doesn't matter which one comes first
+let's say this one comes first once this
+
+ align:start position:0%
+let's say this one comes first once this
+ 
+
+ align:start position:0%
+let's say this one comes first once this
+is done
+
+ align:start position:0%
+is done
+ 
+
+ align:start position:0%
+is done
+i can write it down and reuse it over
+
+ align:start position:0%
+i can write it down and reuse it over
+ 
+
+ align:start position:0%
+i can write it down and reuse it over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay but actually and then in here we're
+
+ align:start position:0%
+okay but actually and then in here we're
+ 
+
+ align:start position:0%
+okay but actually and then in here we're
+going to call f of n minus 3
+
+ align:start position:0%
+going to call f of n minus 3
+ 
+
+ align:start position:0%
+going to call f of n minus 3
+so there's still a another computation
+
+ align:start position:0%
+so there's still a another computation
+ 
+
+ align:start position:0%
+so there's still a another computation
+of f of n minus 3.
+
+ align:start position:0%
+of f of n minus 3.
+ 
+
+ align:start position:0%
+of f of n minus 3.
+when that one's done i won't need to do
+
+ align:start position:0%
+when that one's done i won't need to do
+ 
+
+ align:start position:0%
+when that one's done i won't need to do
+any do this recursively
+
+ align:start position:0%
+any do this recursively
+ 
+
+ align:start position:0%
+any do this recursively
+okay so magically this is going to make
+
+ align:start position:0%
+okay so magically this is going to make
+ 
+
+ align:start position:0%
+okay so magically this is going to make
+this algorithm efficient with this
+
+ align:start position:0%
+this algorithm efficient with this
+ 
+
+ align:start position:0%
+this algorithm efficient with this
+very simple tweak let me write down the
+
+ align:start position:0%
+very simple tweak let me write down the
+ 
+
+ align:start position:0%
+very simple tweak let me write down the
+tweak more explicitly
+
+ align:start position:0%
+tweak more explicitly
+ 
+
+ align:start position:0%
+tweak more explicitly
+i won't write code here but
+
+ align:start position:0%
+i won't write code here but
+ 
+
+ align:start position:0%
+i won't write code here but
+just describe it as a data structure
+
+ align:start position:0%
+just describe it as a data structure
+ 
+
+ align:start position:0%
+just describe it as a data structure
+so we're going to maintain our good
+
+ align:start position:0%
+so we're going to maintain our good
+ 
+
+ align:start position:0%
+so we're going to maintain our good
+friend the dictionary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is abstract data type or interface
+
+ align:start position:0%
+which is abstract data type or interface
+ 
+
+ align:start position:0%
+which is abstract data type or interface
+we could use different data structures
+
+ align:start position:0%
+we could use different data structures
+ 
+
+ align:start position:0%
+we could use different data structures
+to do it but we're going to map
+
+ align:start position:0%
+to do it but we're going to map
+ 
+
+ align:start position:0%
+to do it but we're going to map
+sub problems to their solutions
+
+ align:start position:0%
+sub problems to their solutions
+ 
+
+ align:start position:0%
+sub problems to their solutions
+at least the ones that we've solved
+
+ align:start position:0%
+at least the ones that we've solved
+ 
+
+ align:start position:0%
+at least the ones that we've solved
+already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and usually we can do this with just a
+
+ align:start position:0%
+and usually we can do this with just a
+ 
+
+ align:start position:0%
+and usually we can do this with just a
+direct access array
+
+ align:start position:0%
+direct access array
+ 
+
+ align:start position:0%
+direct access array
+though you could use a hash table just
+
+ align:start position:0%
+though you could use a hash table just
+ 
+
+ align:start position:0%
+though you could use a hash table just
+get expected bounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh when we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+write the code for our recursive
+
+ align:start position:0%
+write the code for our recursive
+ 
+
+ align:start position:0%
+write the code for our recursive
+function so in general once we have a
+
+ align:start position:0%
+function so in general once we have a
+ 
+
+ align:start position:0%
+function so in general once we have a
+sort bot
+
+ align:start position:0%
+sort bot
+ 
+
+ align:start position:0%
+sort bot
+description we can turn this into code
+
+ align:start position:0%
+description we can turn this into code
+ 
+
+ align:start position:0%
+description we can turn this into code
+right we define
+
+ align:start position:0%
+right we define
+ 
+
+ align:start position:0%
+right we define
+f of i and it says am i in a base case
+
+ align:start position:0%
+f of i and it says am i in a base case
+ 
+
+ align:start position:0%
+f of i and it says am i in a base case
+if so return this
+
+ align:start position:0%
+if so return this
+ 
+
+ align:start position:0%
+if so return this
+otherwise do this recursive call that's
+
+ align:start position:0%
+otherwise do this recursive call that's
+ 
+
+ align:start position:0%
+otherwise do this recursive call that's
+our recursive algorithm
+
+ align:start position:0%
+our recursive algorithm
+ 
+
+ align:start position:0%
+our recursive algorithm
+but we're going to do a little more now
+
+ align:start position:0%
+but we're going to do a little more now
+ 
+
+ align:start position:0%
+but we're going to do a little more now
+at first we're going to check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whether this sub problem that we're
+
+ align:start position:0%
+whether this sub problem that we're
+ 
+
+ align:start position:0%
+whether this sub problem that we're
+trying to solve has already been solved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if so we return that stored solution
+
+ align:start position:0%
+and if so we return that stored solution
+ 
+
+ align:start position:0%
+and if so we return that stored solution
+that's the easy case but it might not
+
+ align:start position:0%
+that's the easy case but it might not
+ 
+
+ align:start position:0%
+that's the easy case but it might not
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we'll we'll compute it in the
+
+ align:start position:0%
+and then we'll we'll compute it in the
+ 
+
+ align:start position:0%
+and then we'll we'll compute it in the
+usual way
+
+ align:start position:0%
+usual way
+ 
+
+ align:start position:0%
+usual way
+so what the code then would look like to
+
+ align:start position:0%
+so what the code then would look like to
+ 
+
+ align:start position:0%
+so what the code then would look like to
+define
+
+ align:start position:0%
+define
+ 
+
+ align:start position:0%
+define
+f of i is first we check is i in our
+
+ align:start position:0%
+f of i is first we check is i in our
+ 
+
+ align:start position:0%
+f of i is first we check is i in our
+in our data structure this is usually
+
+ align:start position:0%
+in our data structure this is usually
+ 
+
+ align:start position:0%
+in our data structure this is usually
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+the memo
+
+ align:start position:0%
+the memo
+ 
+
+ align:start position:0%
+the memo
+so we say is this sub problem is i in my
+
+ align:start position:0%
+so we say is this sub problem is i in my
+ 
+
+ align:start position:0%
+so we say is this sub problem is i in my
+memo
+
+ align:start position:0%
+memo
+ 
+
+ align:start position:0%
+memo
+data structure if so just return memo of
+
+ align:start position:0%
+data structure if so just return memo of
+ 
+
+ align:start position:0%
+data structure if so just return memo of
+i done no recursion necessary
+
+ align:start position:0%
+i done no recursion necessary
+ 
+
+ align:start position:0%
+i done no recursion necessary
+otherwise check if i'm a base case if so
+
+ align:start position:0%
+otherwise check if i'm a base case if so
+ 
+
+ align:start position:0%
+otherwise check if i'm a base case if so
+done otherwise recurse so recursively
+
+ align:start position:0%
+done otherwise recurse so recursively
+ 
+
+ align:start position:0%
+done otherwise recurse so recursively
+call f of i minus 1 and f
+
+ align:start position:0%
+call f of i minus 1 and f
+ 
+
+ align:start position:0%
+call f of i minus 1 and f
+minus 2. and in this recursion we can
+
+ align:start position:0%
+minus 2. and in this recursion we can
+ 
+
+ align:start position:0%
+minus 2. and in this recursion we can
+see that after we call f of i minus 1
+
+ align:start position:0%
+see that after we call f of i minus 1
+ 
+
+ align:start position:0%
+see that after we call f of i minus 1
+in fact it will have already computed f
+
+ align:start position:0%
+in fact it will have already computed f
+ 
+
+ align:start position:0%
+in fact it will have already computed f
+of i minus 2. so while this call is
+
+ align:start position:0%
+of i minus 2. so while this call is
+ 
+
+ align:start position:0%
+of i minus 2. so while this call is
+recursive
+
+ align:start position:0%
+recursive
+ 
+
+ align:start position:0%
+recursive
+this one will immediately terminate
+
+ align:start position:0%
+this one will immediately terminate
+ 
+
+ align:start position:0%
+this one will immediately terminate
+because i minus 2 will already be in the
+
+ align:start position:0%
+because i minus 2 will already be in the
+ 
+
+ align:start position:0%
+because i minus 2 will already be in the
+memo table
+
+ align:start position:0%
+memo table
+ 
+
+ align:start position:0%
+memo table
+and so if you think about what happens
+
+ align:start position:0%
+and so if you think about what happens
+ 
+
+ align:start position:0%
+and so if you think about what happens
+in fact we'll just have recursion down
+
+ align:start position:0%
+in fact we'll just have recursion down
+ 
+
+ align:start position:0%
+in fact we'll just have recursion down
+the left branch
+
+ align:start position:0%
+the left branch
+ 
+
+ align:start position:0%
+the left branch
+of this thing and all the right branches
+
+ align:start position:0%
+of this thing and all the right branches
+ 
+
+ align:start position:0%
+of this thing and all the right branches
+will be free we can just look things up
+
+ align:start position:0%
+will be free we can just look things up
+ 
+
+ align:start position:0%
+will be free we can just look things up
+in the memo table
+
+ align:start position:0%
+in the memo table
+ 
+
+ align:start position:0%
+in the memo table
+so what is the overall running time for
+
+ align:start position:0%
+so what is the overall running time for
+ 
+
+ align:start position:0%
+so what is the overall running time for
+fibonacci
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this should be order n
+
+ align:start position:0%
+this should be order n
+ 
+
+ align:start position:0%
+this should be order n
+why is it order n this is number of
+
+ align:start position:0%
+why is it order n this is number of
+ 
+
+ align:start position:0%
+why is it order n this is number of
+additions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+come back to that in a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in general the way to analyze an
+
+ align:start position:0%
+in general the way to analyze an
+ 
+
+ align:start position:0%
+in general the way to analyze an
+algorithm like this that uses
+
+ align:start position:0%
+algorithm like this that uses
+ 
+
+ align:start position:0%
+algorithm like this that uses
+memorization is we just count
+
+ align:start position:0%
+memorization is we just count
+ 
+
+ align:start position:0%
+memorization is we just count
+how many different sub-problems are
+
+ align:start position:0%
+how many different sub-problems are
+ 
+
+ align:start position:0%
+how many different sub-problems are
+there because once we solve the
+
+ align:start position:0%
+there because once we solve the
+ 
+
+ align:start position:0%
+there because once we solve the
+sub-problem we will never solve it again
+
+ align:start position:0%
+sub-problem we will never solve it again
+ 
+
+ align:start position:0%
+sub-problem we will never solve it again
+that's the whole idea of a memo table so
+
+ align:start position:0%
+that's the whole idea of a memo table so
+ 
+
+ align:start position:0%
+that's the whole idea of a memo table so
+we will solve each sub-problem
+
+ align:start position:0%
+we will solve each sub-problem
+ 
+
+ align:start position:0%
+we will solve each sub-problem
+at most once and so we just need to
+
+ align:start position:0%
+at most once and so we just need to
+ 
+
+ align:start position:0%
+at most once and so we just need to
+count how much time does it take to
+
+ align:start position:0%
+count how much time does it take to
+ 
+
+ align:start position:0%
+count how much time does it take to
+solve
+
+ align:start position:0%
+solve
+ 
+
+ align:start position:0%
+solve
+every subproblem and here you can see
+
+ align:start position:0%
+every subproblem and here you can see
+ 
+
+ align:start position:0%
+every subproblem and here you can see
+it's constant
+
+ align:start position:0%
+it's constant
+ 
+
+ align:start position:0%
+it's constant
+either it's a base case and it takes
+
+ align:start position:0%
+either it's a base case and it takes
+ 
+
+ align:start position:0%
+either it's a base case and it takes
+constant time or
+
+ align:start position:0%
+constant time or
+ 
+
+ align:start position:0%
+constant time or
+we recursively call these things but
+
+ align:start position:0%
+we recursively call these things but
+ 
+
+ align:start position:0%
+we recursively call these things but
+those are different sub problems so
+
+ align:start position:0%
+those are different sub problems so
+ 
+
+ align:start position:0%
+those are different sub problems so
+we're going to count those later
+
+ align:start position:0%
+we're going to count those later
+ 
+
+ align:start position:0%
+we're going to count those later
+and then the work that's actually done
+
+ align:start position:0%
+and then the work that's actually done
+ 
+
+ align:start position:0%
+and then the work that's actually done
+by this recurrence is a single addition
+
+ align:start position:0%
+by this recurrence is a single addition
+ 
+
+ align:start position:0%
+by this recurrence is a single addition
+so in fact it's n additions to compute f
+
+ align:start position:0%
+so in fact it's n additions to compute f
+ 
+
+ align:start position:0%
+so in fact it's n additions to compute f
+n will be exactly n additions
+
+ align:start position:0%
+n will be exactly n additions
+ 
+
+ align:start position:0%
+n will be exactly n additions
+so it turns out to be very nice closed
+
+ align:start position:0%
+so it turns out to be very nice closed
+ 
+
+ align:start position:0%
+so it turns out to be very nice closed
+form in this case
+
+ align:start position:0%
+form in this case
+ 
+
+ align:start position:0%
+form in this case
+um it should be exactly n sub problems
+
+ align:start position:0%
+um it should be exactly n sub problems
+ 
+
+ align:start position:0%
+um it should be exactly n sub problems
+to compute f of n and because we start
+
+ align:start position:0%
+to compute f of n and because we start
+ 
+
+ align:start position:0%
+to compute f of n and because we start
+stop
+
+ align:start position:0%
+stop
+ 
+
+ align:start position:0%
+stop
+at one and each one has
+
+ align:start position:0%
+at one and each one has
+ 
+
+ align:start position:0%
+at one and each one has
+one addition involved i guess not the
+
+ align:start position:0%
+one addition involved i guess not the
+ 
+
+ align:start position:0%
+one addition involved i guess not the
+base case so maybe n minus two
+
+ align:start position:0%
+base case so maybe n minus two
+ 
+
+ align:start position:0%
+base case so maybe n minus two
+okay definitely order n uh
+
+ align:start position:0%
+okay definitely order n uh
+ 
+
+ align:start position:0%
+okay definitely order n uh
+now there's this one subtlety uh which
+
+ align:start position:0%
+now there's this one subtlety uh which
+ 
+
+ align:start position:0%
+now there's this one subtlety uh which
+let's forget about dynamic programming
+
+ align:start position:0%
+let's forget about dynamic programming
+ 
+
+ align:start position:0%
+let's forget about dynamic programming
+for a moment and go back to
+
+ align:start position:0%
+for a moment and go back to
+ 
+
+ align:start position:0%
+for a moment and go back to
+good old lecture one and two talking
+
+ align:start position:0%
+good old lecture one and two talking
+ 
+
+ align:start position:0%
+good old lecture one and two talking
+about the word ram model of computation
+
+ align:start position:0%
+about the word ram model of computation
+ 
+
+ align:start position:0%
+about the word ram model of computation
+um a question here that usually doesn't
+
+ align:start position:0%
+um a question here that usually doesn't
+ 
+
+ align:start position:0%
+um a question here that usually doesn't
+matter
+
+ align:start position:0%
+matter
+ 
+
+ align:start position:0%
+matter
+in this class usually we assume
+
+ align:start position:0%
+in this class usually we assume
+ 
+
+ align:start position:0%
+in this class usually we assume
+additions take constant time
+
+ align:start position:0%
+additions take constant time
+ 
+
+ align:start position:0%
+additions take constant time
+and we usually do that because it's
+
+ align:start position:0%
+and we usually do that because it's
+ 
+
+ align:start position:0%
+and we usually do that because it's
+usually true and in general our model is
+
+ align:start position:0%
+usually true and in general our model is
+ 
+
+ align:start position:0%
+usually true and in general our model is
+that w
+
+ align:start position:0%
+that w
+ 
+
+ align:start position:0%
+that w
+bit additions
+
+ align:start position:0%
+bit additions
+ 
+
+ align:start position:0%
+bit additions
+where w is our machine word size
+
+ align:start position:0%
+where w is our machine word size
+ 
+
+ align:start position:0%
+where w is our machine word size
+takes constant time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but for this problem and this problem
+
+ align:start position:0%
+but for this problem and this problem
+ 
+
+ align:start position:0%
+but for this problem and this problem
+only pretty much for fibonacci numbers
+
+ align:start position:0%
+only pretty much for fibonacci numbers
+ 
+
+ align:start position:0%
+only pretty much for fibonacci numbers
+i happen to know that the fibonacci
+
+ align:start position:0%
+i happen to know that the fibonacci
+ 
+
+ align:start position:0%
+i happen to know that the fibonacci
+numbers grow exponentially so to write
+
+ align:start position:0%
+numbers grow exponentially so to write
+ 
+
+ align:start position:0%
+numbers grow exponentially so to write
+them down
+
+ align:start position:0%
+them down
+ 
+
+ align:start position:0%
+them down
+actually requires uh theta n bits
+
+ align:start position:0%
+actually requires uh theta n bits
+ 
+
+ align:start position:0%
+actually requires uh theta n bits
+because they are some constant to the n
+
+ align:start position:0%
+because they are some constant to the n
+ 
+
+ align:start position:0%
+because they are some constant to the n
+power and so they're actually really big
+
+ align:start position:0%
+power and so they're actually really big
+ 
+
+ align:start position:0%
+power and so they're actually really big
+uh potential n is probably bigger than w
+
+ align:start position:0%
+uh potential n is probably bigger than w
+ 
+
+ align:start position:0%
+uh potential n is probably bigger than w
+usually you
+
+ align:start position:0%
+usually you
+ 
+
+ align:start position:0%
+usually you
+think of problems that are much bigger
+
+ align:start position:0%
+think of problems that are much bigger
+ 
+
+ align:start position:0%
+think of problems that are much bigger
+than 64 or whatever your word size
+
+ align:start position:0%
+than 64 or whatever your word size
+ 
+
+ align:start position:0%
+than 64 or whatever your word size
+happens to be
+
+ align:start position:0%
+happens to be
+ 
+
+ align:start position:0%
+happens to be
+we do assume that w is at least log n
+
+ align:start position:0%
+we do assume that w is at least log n
+ 
+
+ align:start position:0%
+we do assume that w is at least log n
+but n is
+
+ align:start position:0%
+but n is
+ 
+
+ align:start position:0%
+but n is
+probably bigger than w might be bigger
+
+ align:start position:0%
+probably bigger than w might be bigger
+ 
+
+ align:start position:0%
+probably bigger than w might be bigger
+or smaller we don't know
+
+ align:start position:0%
+or smaller we don't know
+ 
+
+ align:start position:0%
+or smaller we don't know
+and in general to do an n bit addition
+
+ align:start position:0%
+and in general to do an n bit addition
+ 
+
+ align:start position:0%
+and in general to do an n bit addition
+these are n bit additions
+
+ align:start position:0%
+these are n bit additions
+ 
+
+ align:start position:0%
+these are n bit additions
+is going to take a ceiling of n over w
+
+ align:start position:0%
+is going to take a ceiling of n over w
+ 
+
+ align:start position:0%
+is going to take a ceiling of n over w
+time so in the end we will spend
+
+ align:start position:0%
+time so in the end we will spend
+ 
+
+ align:start position:0%
+time so in the end we will spend
+this times n because we have to do that
+
+ align:start position:0%
+this times n because we have to do that
+ 
+
+ align:start position:0%
+this times n because we have to do that
+many of them which
+
+ align:start position:0%
+many of them which
+ 
+
+ align:start position:0%
+many of them which
+is n plus n squared over w
+
+ align:start position:0%
+is n plus n squared over w
+ 
+
+ align:start position:0%
+is n plus n squared over w
+time so a bit of a weird running time
+
+ align:start position:0%
+time so a bit of a weird running time
+ 
+
+ align:start position:0%
+time so a bit of a weird running time
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it's polynomial whereas this original
+
+ align:start position:0%
+it's polynomial whereas this original
+ 
+
+ align:start position:0%
+it's polynomial whereas this original
+recursive algorithm was exponential
+
+ align:start position:0%
+recursive algorithm was exponential
+ 
+
+ align:start position:0%
+recursive algorithm was exponential
+here using this one simple idea of just
+
+ align:start position:0%
+here using this one simple idea of just
+ 
+
+ align:start position:0%
+here using this one simple idea of just
+remembering the work we've done suddenly
+
+ align:start position:0%
+remembering the work we've done suddenly
+ 
+
+ align:start position:0%
+remembering the work we've done suddenly
+this exponential time algorithm becomes
+
+ align:start position:0%
+this exponential time algorithm becomes
+ 
+
+ align:start position:0%
+this exponential time algorithm becomes
+polynomial
+
+ align:start position:0%
+polynomial
+ 
+
+ align:start position:0%
+polynomial
+why because we have few sub-problems we
+
+ align:start position:0%
+why because we have few sub-problems we
+ 
+
+ align:start position:0%
+why because we have few sub-problems we
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+n sub-problems
+
+ align:start position:0%
+n sub-problems
+ 
+
+ align:start position:0%
+n sub-problems
+for each subproblem we could write a
+
+ align:start position:0%
+for each subproblem we could write a
+ 
+
+ align:start position:0%
+for each subproblem we could write a
+recurrence relation that if we already
+
+ align:start position:0%
+recurrence relation that if we already
+ 
+
+ align:start position:0%
+recurrence relation that if we already
+knew
+
+ align:start position:0%
+knew
+ 
+
+ align:start position:0%
+knew
+the solutions to smaller sub-problems we
+
+ align:start position:0%
+the solutions to smaller sub-problems we
+ 
+
+ align:start position:0%
+the solutions to smaller sub-problems we
+could compute
+
+ align:start position:0%
+could compute
+ 
+
+ align:start position:0%
+could compute
+this bigger problem very efficiently
+
+ align:start position:0%
+this bigger problem very efficiently
+ 
+
+ align:start position:0%
+this bigger problem very efficiently
+this happened to be constant time
+
+ align:start position:0%
+this happened to be constant time
+ 
+
+ align:start position:0%
+this happened to be constant time
+or constant additions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n over w time but as long as this is
+
+ align:start position:0%
+n over w time but as long as this is
+ 
+
+ align:start position:0%
+n over w time but as long as this is
+polynomial
+
+ align:start position:0%
+polynomial
+ 
+
+ align:start position:0%
+polynomial
+and this is polynomial we're happy
+
+ align:start position:0%
+and this is polynomial we're happy
+ 
+
+ align:start position:0%
+and this is polynomial we're happy
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+we we have this nice formula that the
+
+ align:start position:0%
+we we have this nice formula that the
+ 
+
+ align:start position:0%
+we we have this nice formula that the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+it takes is at most the sum over all sub
+
+ align:start position:0%
+it takes is at most the sum over all sub
+ 
+
+ align:start position:0%
+it takes is at most the sum over all sub
+problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the relation time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i'm referring to subproblems the
+
+ align:start position:0%
+okay so i'm referring to subproblems the
+ 
+
+ align:start position:0%
+okay so i'm referring to subproblems the
+number of them and the time it takes to
+
+ align:start position:0%
+number of them and the time it takes to
+ 
+
+ align:start position:0%
+number of them and the time it takes to
+evaluate this ignoring the recursive
+
+ align:start position:0%
+evaluate this ignoring the recursive
+ 
+
+ align:start position:0%
+evaluate this ignoring the recursive
+calls that's important this is the
+
+ align:start position:0%
+calls that's important this is the
+ 
+
+ align:start position:0%
+calls that's important this is the
+uh non-recursive part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the notes i call this non-recursive
+
+ align:start position:0%
+in the notes i call this non-recursive
+ 
+
+ align:start position:0%
+in the notes i call this non-recursive
+work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this formula gives us a way to bound
+
+ align:start position:0%
+so this formula gives us a way to bound
+ 
+
+ align:start position:0%
+so this formula gives us a way to bound
+the running time
+
+ align:start position:0%
+the running time
+ 
+
+ align:start position:0%
+the running time
+of one of these algorithms if we use
+
+ align:start position:0%
+of one of these algorithms if we use
+ 
+
+ align:start position:0%
+of one of these algorithms if we use
+memoization
+
+ align:start position:0%
+memoization
+ 
+
+ align:start position:0%
+memoization
+without memoization this is not true
+
+ align:start position:0%
+without memoization this is not true
+ 
+
+ align:start position:0%
+without memoization this is not true
+fibonacci took exponential time
+
+ align:start position:0%
+fibonacci took exponential time
+ 
+
+ align:start position:0%
+fibonacci took exponential time
+but if we add memoization we know that
+
+ align:start position:0%
+but if we add memoization we know that
+ 
+
+ align:start position:0%
+but if we add memoization we know that
+we only solve each sub problem once
+
+ align:start position:0%
+we only solve each sub problem once
+ 
+
+ align:start position:0%
+we only solve each sub problem once
+and so we just need to see for each one
+
+ align:start position:0%
+and so we just need to see for each one
+ 
+
+ align:start position:0%
+and so we just need to see for each one
+how much did it cost me to compute it
+
+ align:start position:0%
+how much did it cost me to compute it
+ 
+
+ align:start position:0%
+how much did it cost me to compute it
+assuming all the recursion work is free
+
+ align:start position:0%
+assuming all the recursion work is free
+ 
+
+ align:start position:0%
+assuming all the recursion work is free
+because that's already taken into
+
+ align:start position:0%
+because that's already taken into
+ 
+
+ align:start position:0%
+because that's already taken into
+account by the summation
+
+ align:start position:0%
+account by the summation
+ 
+
+ align:start position:0%
+account by the summation
+so in particular this summation is at
+
+ align:start position:0%
+so in particular this summation is at
+ 
+
+ align:start position:0%
+so in particular this summation is at
+most the number of sub-problems
+
+ align:start position:0%
+most the number of sub-problems
+ 
+
+ align:start position:0%
+most the number of sub-problems
+times the time per sub-problem which in
+
+ align:start position:0%
+times the time per sub-problem which in
+ 
+
+ align:start position:0%
+times the time per sub-problem which in
+this case is order n
+
+ align:start position:0%
+this case is order n
+ 
+
+ align:start position:0%
+this case is order n
+we could try to apply that analysis to
+
+ align:start position:0%
+we could try to apply that analysis to
+ 
+
+ align:start position:0%
+we could try to apply that analysis to
+merge sort because
+
+ align:start position:0%
+merge sort because
+ 
+
+ align:start position:0%
+merge sort because
+after all this is also a recursive
+
+ align:start position:0%
+after all this is also a recursive
+ 
+
+ align:start position:0%
+after all this is also a recursive
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+it happens to not benefit from
+
+ align:start position:0%
+it happens to not benefit from
+ 
+
+ align:start position:0%
+it happens to not benefit from
+memoization but we could throw in
+
+ align:start position:0%
+memoization but we could throw in
+ 
+
+ align:start position:0%
+memoization but we could throw in
+memorization it wouldn't hurt us
+
+ align:start position:0%
+memorization it wouldn't hurt us
+ 
+
+ align:start position:0%
+memorization it wouldn't hurt us
+but if you think about the call graph
+
+ align:start position:0%
+but if you think about the call graph
+ 
+
+ align:start position:0%
+but if you think about the call graph
+here which is like
+
+ align:start position:0%
+here which is like
+ 
+
+ align:start position:0%
+here which is like
+s of zero n which calls s
+
+ align:start position:0%
+s of zero n which calls s
+ 
+
+ align:start position:0%
+s of zero n which calls s
+of n of zero n over two
+
+ align:start position:0%
+of n of zero n over two
+ 
+
+ align:start position:0%
+of n of zero n over two
+and s of n over two n
+
+ align:start position:0%
+and s of n over two n
+ 
+
+ align:start position:0%
+and s of n over two n
+and so on it has the same picture but
+
+ align:start position:0%
+and so on it has the same picture but
+ 
+
+ align:start position:0%
+and so on it has the same picture but
+there's actually
+
+ align:start position:0%
+there's actually
+ 
+
+ align:start position:0%
+there's actually
+no common substructure here you'll never
+
+ align:start position:0%
+no common substructure here you'll never
+ 
+
+ align:start position:0%
+no common substructure here you'll never
+see a repeated sub-problem because
+
+ align:start position:0%
+see a repeated sub-problem because
+ 
+
+ align:start position:0%
+see a repeated sub-problem because
+this range is completely disjoint from
+
+ align:start position:0%
+this range is completely disjoint from
+ 
+
+ align:start position:0%
+this range is completely disjoint from
+this range
+
+ align:start position:0%
+this range
+ 
+
+ align:start position:0%
+this range
+but you could throw in memorization and
+
+ align:start position:0%
+but you could throw in memorization and
+ 
+
+ align:start position:0%
+but you could throw in memorization and
+try to analyze in the same way and say
+
+ align:start position:0%
+try to analyze in the same way and say
+ 
+
+ align:start position:0%
+try to analyze in the same way and say
+well how many sub problems are there
+
+ align:start position:0%
+well how many sub problems are there
+ 
+
+ align:start position:0%
+well how many sub problems are there
+well looks like there's there's n
+
+ align:start position:0%
+well looks like there's there's n
+ 
+
+ align:start position:0%
+well looks like there's there's n
+choices for i
+
+ align:start position:0%
+choices for i
+ 
+
+ align:start position:0%
+choices for i
+and not quite n choices but
+
+ align:start position:0%
+and not quite n choices but
+ 
+
+ align:start position:0%
+and not quite n choices but
+in general it's at most n squared
+
+ align:start position:0%
+in general it's at most n squared
+ 
+
+ align:start position:0%
+in general it's at most n squared
+different choices in fact it's the
+
+ align:start position:0%
+different choices in fact it's the
+ 
+
+ align:start position:0%
+different choices in fact it's the
+triangular number
+
+ align:start position:0%
+triangular number
+ 
+
+ align:start position:0%
+triangular number
+sum of i equals 1 to n of i
+
+ align:start position:0%
+sum of i equals 1 to n of i
+ 
+
+ align:start position:0%
+sum of i equals 1 to n of i
+different possible choices for i and j
+
+ align:start position:0%
+different possible choices for i and j
+ 
+
+ align:start position:0%
+different possible choices for i and j
+but this is theta n squared
+
+ align:start position:0%
+but this is theta n squared
+ 
+
+ align:start position:0%
+but this is theta n squared
+sub problems which seems not so good
+
+ align:start position:0%
+sub problems which seems not so good
+ 
+
+ align:start position:0%
+sub problems which seems not so good
+and then how much time are we spending
+
+ align:start position:0%
+and then how much time are we spending
+ 
+
+ align:start position:0%
+and then how much time are we spending
+for per sub problem well
+
+ align:start position:0%
+for per sub problem well
+ 
+
+ align:start position:0%
+for per sub problem well
+to solve s of i j we have to merge
+
+ align:start position:0%
+to solve s of i j we have to merge
+ 
+
+ align:start position:0%
+to solve s of i j we have to merge
+about that many elements we know merge
+
+ align:start position:0%
+about that many elements we know merge
+ 
+
+ align:start position:0%
+about that many elements we know merge
+takes linear time and so this takes
+
+ align:start position:0%
+takes linear time and so this takes
+ 
+
+ align:start position:0%
+takes linear time and so this takes
+uh theta j minus i time
+
+ align:start position:0%
+uh theta j minus i time
+ 
+
+ align:start position:0%
+uh theta j minus i time
+to evaluate and so
+
+ align:start position:0%
+to evaluate and so
+ 
+
+ align:start position:0%
+to evaluate and so
+uh what we'd like to do is sum over all
+
+ align:start position:0%
+uh what we'd like to do is sum over all
+ 
+
+ align:start position:0%
+uh what we'd like to do is sum over all
+the sub-problems
+
+ align:start position:0%
+the sub-problems
+ 
+
+ align:start position:0%
+the sub-problems
+of j minus i this is the uh not
+
+ align:start position:0%
+of j minus i this is the uh not
+ 
+
+ align:start position:0%
+of j minus i this is the uh not
+triangular number but the tetrahedral
+
+ align:start position:0%
+triangular number but the tetrahedral
+ 
+
+ align:start position:0%
+triangular number but the tetrahedral
+number i guess
+
+ align:start position:0%
+number i guess
+ 
+
+ align:start position:0%
+number i guess
+and so we end up that the running time
+
+ align:start position:0%
+and so we end up that the running time
+ 
+
+ align:start position:0%
+and so we end up that the running time
+is at most
+
+ align:start position:0%
+is at most
+ 
+
+ align:start position:0%
+is at most
+n cubed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great um so it's true that n log n is
+
+ align:start position:0%
+great um so it's true that n log n is
+ 
+
+ align:start position:0%
+great um so it's true that n log n is
+less than or equal to n cubed
+
+ align:start position:0%
+less than or equal to n cubed
+ 
+
+ align:start position:0%
+less than or equal to n cubed
+but obviously not terribly useful this
+
+ align:start position:0%
+but obviously not terribly useful this
+ 
+
+ align:start position:0%
+but obviously not terribly useful this
+algorithm by the way we already know
+
+ align:start position:0%
+algorithm by the way we already know
+ 
+
+ align:start position:0%
+algorithm by the way we already know
+how to analyze it is indeed n log n and
+
+ align:start position:0%
+how to analyze it is indeed n log n and
+ 
+
+ align:start position:0%
+how to analyze it is indeed n log n and
+the running time turns out to be
+
+ align:start position:0%
+the running time turns out to be
+ 
+
+ align:start position:0%
+the running time turns out to be
+theta n log n so
+
+ align:start position:0%
+theta n log n so
+ 
+
+ align:start position:0%
+theta n log n so
+sometimes this is this equation is not
+
+ align:start position:0%
+sometimes this is this equation is not
+ 
+
+ align:start position:0%
+sometimes this is this equation is not
+what you want to use
+
+ align:start position:0%
+what you want to use
+ 
+
+ align:start position:0%
+what you want to use
+but often it's good enough and
+
+ align:start position:0%
+but often it's good enough and
+ 
+
+ align:start position:0%
+but often it's good enough and
+especially if you just want to get a
+
+ align:start position:0%
+especially if you just want to get a
+ 
+
+ align:start position:0%
+especially if you just want to get a
+polynomial upper bound and then you can
+
+ align:start position:0%
+polynomial upper bound and then you can
+ 
+
+ align:start position:0%
+polynomial upper bound and then you can
+try to optimize it later
+
+ align:start position:0%
+try to optimize it later
+ 
+
+ align:start position:0%
+try to optimize it later
+this will give you a polynomial upper
+
+ align:start position:0%
+this will give you a polynomial upper
+ 
+
+ align:start position:0%
+this will give you a polynomial upper
+bound as long as the number of
+
+ align:start position:0%
+bound as long as the number of
+ 
+
+ align:start position:0%
+bound as long as the number of
+subproblems is polynomial
+
+ align:start position:0%
+subproblems is polynomial
+ 
+
+ align:start position:0%
+subproblems is polynomial
+and the time per subproblem is
+
+ align:start position:0%
+and the time per subproblem is
+ 
+
+ align:start position:0%
+and the time per subproblem is
+polynomial and indeed
+
+ align:start position:0%
+polynomial and indeed
+ 
+
+ align:start position:0%
+polynomial and indeed
+n cubed is polynomial it's not a great
+
+ align:start position:0%
+n cubed is polynomial it's not a great
+ 
+
+ align:start position:0%
+n cubed is polynomial it's not a great
+polynomial but
+
+ align:start position:0%
+polynomial but
+ 
+
+ align:start position:0%
+polynomial but
+this is a an alternate way to analyze
+
+ align:start position:0%
+this is a an alternate way to analyze
+ 
+
+ align:start position:0%
+this is a an alternate way to analyze
+merge sort obviously
+
+ align:start position:0%
+merge sort obviously
+ 
+
+ align:start position:0%
+merge sort obviously
+don't do this for merge sort but it
+
+ align:start position:0%
+don't do this for merge sort but it
+ 
+
+ align:start position:0%
+don't do this for merge sort but it
+illustrates the
+
+ align:start position:0%
+illustrates the
+ 
+
+ align:start position:0%
+illustrates the
+technique good so far
+
+ align:start position:0%
+technique good so far
+ 
+
+ align:start position:0%
+technique good so far
+any questions all right
+
+ align:start position:0%
+any questions all right
+ 
+
+ align:start position:0%
+any questions all right
+uh let me remember where we are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool so the next thing i'd like to do is
+
+ align:start position:0%
+cool so the next thing i'd like to do is
+ 
+
+ align:start position:0%
+cool so the next thing i'd like to do is
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+show you one more algorithm that we've
+
+ align:start position:0%
+show you one more algorithm that we've
+ 
+
+ align:start position:0%
+show you one more algorithm that we've
+already seen in this class that fits
+
+ align:start position:0%
+already seen in this class that fits
+ 
+
+ align:start position:0%
+already seen in this class that fits
+very nicely into this structure
+
+ align:start position:0%
+very nicely into this structure
+ 
+
+ align:start position:0%
+very nicely into this structure
+arguably is a dynamic program and that
+
+ align:start position:0%
+arguably is a dynamic program and that
+ 
+
+ align:start position:0%
+arguably is a dynamic program and that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+uh dag shortest paths oh so just to
+
+ align:start position:0%
+uh dag shortest paths oh so just to
+ 
+
+ align:start position:0%
+uh dag shortest paths oh so just to
+close the loop here
+
+ align:start position:0%
+close the loop here
+ 
+
+ align:start position:0%
+close the loop here
+when i say dynamic programming i mean
+
+ align:start position:0%
+when i say dynamic programming i mean
+ 
+
+ align:start position:0%
+when i say dynamic programming i mean
+recursion with memoization
+
+ align:start position:0%
+recursion with memoization
+ 
+
+ align:start position:0%
+recursion with memoization
+i mean we take we we
+
+ align:start position:0%
+i mean we take we we
+ 
+
+ align:start position:0%
+i mean we take we we
+write a recursive piece of code which is
+
+ align:start position:0%
+write a recursive piece of code which is
+ 
+
+ align:start position:0%
+write a recursive piece of code which is
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+def f of some args um
+
+ align:start position:0%
+def f of some args um
+ 
+
+ align:start position:0%
+def f of some args um
+some you know sub-problem specification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we check is the sub-problem uh
+
+ align:start position:0%
+we check is the sub-problem uh
+ 
+
+ align:start position:0%
+we check is the sub-problem uh
+in the memo table if so
+
+ align:start position:0%
+in the memo table if so
+ 
+
+ align:start position:0%
+in the memo table if so
+uh return
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+memo of subproblem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and otherwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check if it's a base case if and solve
+
+ align:start position:0%
+check if it's a base case if and solve
+ 
+
+ align:start position:0%
+check if it's a base case if and solve
+it if it's a base case and otherwise
+
+ align:start position:0%
+it if it's a base case and otherwise
+ 
+
+ align:start position:0%
+it if it's a base case and otherwise
+write the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recurrence recurse via
+
+ align:start position:0%
+recurrence recurse via
+ 
+
+ align:start position:0%
+recurrence recurse via
+relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and set the memo table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the subproblem to be one of those
+
+ align:start position:0%
+of the subproblem to be one of those
+ 
+
+ align:start position:0%
+of the subproblem to be one of those
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+okay so this is the generic dynamic
+
+ align:start position:0%
+okay so this is the generic dynamic
+ 
+
+ align:start position:0%
+okay so this is the generic dynamic
+program
+
+ align:start position:0%
+program
+ 
+
+ align:start position:0%
+program
+and implicitly i'm writing fibonacci
+
+ align:start position:0%
+and implicitly i'm writing fibonacci
+ 
+
+ align:start position:0%
+and implicitly i'm writing fibonacci
+in that way and all of the dynamic
+
+ align:start position:0%
+in that way and all of the dynamic
+ 
+
+ align:start position:0%
+in that way and all of the dynamic
+programs have this implicit structure
+
+ align:start position:0%
+programs have this implicit structure
+ 
+
+ align:start position:0%
+programs have this implicit structure
+where i start with a memo table which is
+
+ align:start position:0%
+where i start with a memo table which is
+ 
+
+ align:start position:0%
+where i start with a memo table which is
+empty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i always just check if i'm in the
+
+ align:start position:0%
+and i always just check if i'm in the
+ 
+
+ align:start position:0%
+and i always just check if i'm in the
+memo table
+
+ align:start position:0%
+memo table
+ 
+
+ align:start position:0%
+memo table
+if i am i return it otherwise i compute
+
+ align:start position:0%
+if i am i return it otherwise i compute
+ 
+
+ align:start position:0%
+if i am i return it otherwise i compute
+according to this recursive relation
+
+ align:start position:0%
+according to this recursive relation
+ 
+
+ align:start position:0%
+according to this recursive relation
+by recursively calling f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's it so this is every dp
+
+ align:start position:0%
+and that's it so this is every dp
+ 
+
+ align:start position:0%
+and that's it so this is every dp
+algorithm is going to have that
+
+ align:start position:0%
+algorithm is going to have that
+ 
+
+ align:start position:0%
+algorithm is going to have that
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+and it's just using recursion and
+
+ align:start position:0%
+and it's just using recursion and
+ 
+
+ align:start position:0%
+and it's just using recursion and
+memorization together
+
+ align:start position:0%
+memorization together
+ 
+
+ align:start position:0%
+memorization together
+okay so now let's apply that technique
+
+ align:start position:0%
+okay so now let's apply that technique
+ 
+
+ align:start position:0%
+okay so now let's apply that technique
+to think about the dag shortest paths
+
+ align:start position:0%
+to think about the dag shortest paths
+ 
+
+ align:start position:0%
+to think about the dag shortest paths
+problem the problem was i give you a dag
+
+ align:start position:0%
+problem the problem was i give you a dag
+ 
+
+ align:start position:0%
+problem the problem was i give you a dag
+i give you a source vertex
+
+ align:start position:0%
+i give you a source vertex
+ 
+
+ align:start position:0%
+i give you a source vertex
+s single source shortest paths compute
+
+ align:start position:0%
+s single source shortest paths compute
+ 
+
+ align:start position:0%
+s single source shortest paths compute
+the shortest path weight
+
+ align:start position:0%
+the shortest path weight
+ 
+
+ align:start position:0%
+the shortest path weight
+from s to every vertex that's the goal
+
+ align:start position:0%
+from s to every vertex that's the goal
+ 
+
+ align:start position:0%
+from s to every vertex that's the goal
+of the problem
+
+ align:start position:0%
+of the problem
+ 
+
+ align:start position:0%
+of the problem
+and we saw a way to solve that which is
+
+ align:start position:0%
+and we saw a way to solve that which is
+ 
+
+ align:start position:0%
+and we saw a way to solve that which is
+dag relaxation i'm going to show you a
+
+ align:start position:0%
+dag relaxation i'm going to show you a
+ 
+
+ align:start position:0%
+dag relaxation i'm going to show you a
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+way which turns out to be basically the
+
+ align:start position:0%
+way which turns out to be basically the
+ 
+
+ align:start position:0%
+way which turns out to be basically the
+same but upside down
+
+ align:start position:0%
+same but upside down
+ 
+
+ align:start position:0%
+same but upside down
+or flipped left to right depending which
+
+ align:start position:0%
+or flipped left to right depending which
+ 
+
+ align:start position:0%
+or flipped left to right depending which
+way you
+
+ align:start position:0%
+way you
+ 
+
+ align:start position:0%
+way you
+direct your edges so
+
+ align:start position:0%
+direct your edges so
+ 
+
+ align:start position:0%
+direct your edges so
+what are our sub problems well here
+
+ align:start position:0%
+what are our sub problems well here
+ 
+
+ align:start position:0%
+what are our sub problems well here
+actually they're kind of spelled out for
+
+ align:start position:0%
+actually they're kind of spelled out for
+ 
+
+ align:start position:0%
+actually they're kind of spelled out for
+us we want to compute delta of sv for
+
+ align:start position:0%
+us we want to compute delta of sv for
+ 
+
+ align:start position:0%
+us we want to compute delta of sv for
+all v
+
+ align:start position:0%
+all v
+ 
+
+ align:start position:0%
+all v
+so that is uh size of these sub-problems
+
+ align:start position:0%
+so that is uh size of these sub-problems
+ 
+
+ align:start position:0%
+so that is uh size of these sub-problems
+that turns out to be enough for this
+
+ align:start position:0%
+that turns out to be enough for this
+ 
+
+ align:start position:0%
+that turns out to be enough for this
+overall problem and the original problem
+
+ align:start position:0%
+overall problem and the original problem
+ 
+
+ align:start position:0%
+overall problem and the original problem
+we want to solve
+
+ align:start position:0%
+we want to solve
+ 
+
+ align:start position:0%
+we want to solve
+is all of the sub problems we solve all
+
+ align:start position:0%
+is all of the sub problems we solve all
+ 
+
+ align:start position:0%
+is all of the sub problems we solve all
+the sub problems we're done
+
+ align:start position:0%
+the sub problems we're done
+ 
+
+ align:start position:0%
+the sub problems we're done
+and then we have uh i think we wrote
+
+ align:start position:0%
+and then we have uh i think we wrote
+ 
+
+ align:start position:0%
+and then we have uh i think we wrote
+this at some point during
+
+ align:start position:0%
+this at some point during
+ 
+
+ align:start position:0%
+this at some point during
+the dag shortest paths lecture we have a
+
+ align:start position:0%
+the dag shortest paths lecture we have a
+ 
+
+ align:start position:0%
+the dag shortest paths lecture we have a
+recursive relation saying that
+
+ align:start position:0%
+recursive relation saying that
+ 
+
+ align:start position:0%
+recursive relation saying that
+the the shortest way to get from s to v
+
+ align:start position:0%
+the the shortest way to get from s to v
+ 
+
+ align:start position:0%
+the the shortest way to get from s to v
+is the minimum
+
+ align:start position:0%
+is the minimum
+ 
+
+ align:start position:0%
+is the minimum
+of the shortest path to get to some
+
+ align:start position:0%
+of the shortest path to get to some
+ 
+
+ align:start position:0%
+of the shortest path to get to some
+vertex u
+
+ align:start position:0%
+vertex u
+ 
+
+ align:start position:0%
+vertex u
+plus the weight of the edge from u to v
+
+ align:start position:0%
+plus the weight of the edge from u to v
+ 
+
+ align:start position:0%
+plus the weight of the edge from u to v
+why because if we look at a vertex v
+
+ align:start position:0%
+why because if we look at a vertex v
+ 
+
+ align:start position:0%
+why because if we look at a vertex v
+unless we started there we came from
+
+ align:start position:0%
+unless we started there we came from
+ 
+
+ align:start position:0%
+unless we started there we came from
+somewhere
+
+ align:start position:0%
+somewhere
+ 
+
+ align:start position:0%
+somewhere
+and so we can consider all of the
+
+ align:start position:0%
+and so we can consider all of the
+ 
+
+ align:start position:0%
+and so we can consider all of the
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+choices for the previous vertex u and
+
+ align:start position:0%
+choices for the previous vertex u and
+ 
+
+ align:start position:0%
+choices for the previous vertex u and
+if you start at s and get to v you must
+
+ align:start position:0%
+if you start at s and get to v you must
+ 
+
+ align:start position:0%
+if you start at s and get to v you must
+go through one of them
+
+ align:start position:0%
+go through one of them
+ 
+
+ align:start position:0%
+go through one of them
+and so this is finding the best way
+
+ align:start position:0%
+and so this is finding the best way
+ 
+
+ align:start position:0%
+and so this is finding the best way
+among all the choices of you
+
+ align:start position:0%
+among all the choices of you
+ 
+
+ align:start position:0%
+among all the choices of you
+uh what's the best way to get to you and
+
+ align:start position:0%
+uh what's the best way to get to you and
+ 
+
+ align:start position:0%
+uh what's the best way to get to you and
+then take the edge from u to v
+
+ align:start position:0%
+then take the edge from u to v
+ 
+
+ align:start position:0%
+then take the edge from u to v
+for all edges uv and this is adjacency
+
+ align:start position:0%
+for all edges uv and this is adjacency
+ 
+
+ align:start position:0%
+for all edges uv and this is adjacency
+minus we don't usually think of that
+
+ align:start position:0%
+minus we don't usually think of that
+ 
+
+ align:start position:0%
+minus we don't usually think of that
+usually we look at adjacency plus the
+
+ align:start position:0%
+usually we look at adjacency plus the
+ 
+
+ align:start position:0%
+usually we look at adjacency plus the
+outgoing edges this is the incoming
+
+ align:start position:0%
+outgoing edges this is the incoming
+ 
+
+ align:start position:0%
+outgoing edges this is the incoming
+edges
+
+ align:start position:0%
+edges
+ 
+
+ align:start position:0%
+edges
+and so u is an incoming uv is an
+
+ align:start position:0%
+and so u is an incoming uv is an
+ 
+
+ align:start position:0%
+and so u is an incoming uv is an
+incoming edge into v
+
+ align:start position:0%
+incoming edge into v
+ 
+
+ align:start position:0%
+incoming edge into v
+okay if we take that minimum and of
+
+ align:start position:0%
+okay if we take that minimum and of
+ 
+
+ align:start position:0%
+okay if we take that minimum and of
+course the possible there
+
+ align:start position:0%
+course the possible there
+ 
+
+ align:start position:0%
+course the possible there
+there is no way to get to v and so i'll
+
+ align:start position:0%
+there is no way to get to v and so i'll
+ 
+
+ align:start position:0%
+there is no way to get to v and so i'll
+also throw infinity into this set
+
+ align:start position:0%
+also throw infinity into this set
+ 
+
+ align:start position:0%
+also throw infinity into this set
+take the min of that set that will give
+
+ align:start position:0%
+take the min of that set that will give
+ 
+
+ align:start position:0%
+take the min of that set that will give
+me the shortest path weight
+
+ align:start position:0%
+me the shortest path weight
+ 
+
+ align:start position:0%
+me the shortest path weight
+in an acyclic graph from s to v and
+
+ align:start position:0%
+in an acyclic graph from s to v and
+ 
+
+ align:start position:0%
+in an acyclic graph from s to v and
+great this is recursive right this was a
+
+ align:start position:0%
+great this is recursive right this was a
+ 
+
+ align:start position:0%
+great this is recursive right this was a
+sub problem
+
+ align:start position:0%
+sub problem
+ 
+
+ align:start position:0%
+sub problem
+these are sub problems which are smaller
+
+ align:start position:0%
+these are sub problems which are smaller
+ 
+
+ align:start position:0%
+these are sub problems which are smaller
+i guess there's no clear notion of
+
+ align:start position:0%
+i guess there's no clear notion of
+ 
+
+ align:start position:0%
+i guess there's no clear notion of
+smaller here
+
+ align:start position:0%
+smaller here
+ 
+
+ align:start position:0%
+smaller here
+except we already know the clear notion
+
+ align:start position:0%
+except we already know the clear notion
+ 
+
+ align:start position:0%
+except we already know the clear notion
+of smaller is
+
+ align:start position:0%
+of smaller is
+ 
+
+ align:start position:0%
+of smaller is
+the topological order of our dag
+
+ align:start position:0%
+the topological order of our dag
+ 
+
+ align:start position:0%
+the topological order of our dag
+because our graph is acyclic we know it
+
+ align:start position:0%
+because our graph is acyclic we know it
+ 
+
+ align:start position:0%
+because our graph is acyclic we know it
+has a topological order we know how to
+
+ align:start position:0%
+has a topological order we know how to
+ 
+
+ align:start position:0%
+has a topological order we know how to
+compute it with dfs
+
+ align:start position:0%
+compute it with dfs
+ 
+
+ align:start position:0%
+compute it with dfs
+and so that guarantees uh there's a
+
+ align:start position:0%
+and so that guarantees uh there's a
+ 
+
+ align:start position:0%
+and so that guarantees uh there's a
+topological order to compute these
+
+ align:start position:0%
+topological order to compute these
+ 
+
+ align:start position:0%
+topological order to compute these
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+and in fact the the relationship
+
+ align:start position:0%
+and in fact the the relationship
+ 
+
+ align:start position:0%
+and in fact the the relationship
+between problems is exactly
+
+ align:start position:0%
+between problems is exactly
+ 
+
+ align:start position:0%
+between problems is exactly
+the given graph g in order to compute
+
+ align:start position:0%
+the given graph g in order to compute
+ 
+
+ align:start position:0%
+the given graph g in order to compute
+the shortest path weight from
+
+ align:start position:0%
+the shortest path weight from
+ 
+
+ align:start position:0%
+the shortest path weight from
+s to v i need to know the shortest
+
+ align:start position:0%
+s to v i need to know the shortest
+ 
+
+ align:start position:0%
+s to v i need to know the shortest
+pathway from s to all of the incoming
+
+ align:start position:0%
+pathway from s to all of the incoming
+ 
+
+ align:start position:0%
+pathway from s to all of the incoming
+vertices
+
+ align:start position:0%
+vertices
+ 
+
+ align:start position:0%
+vertices
+to v and so this is uh i guess
+
+ align:start position:0%
+to v and so this is uh i guess
+ 
+
+ align:start position:0%
+to v and so this is uh i guess
+in the call graph this vertex calls this
+
+ align:start position:0%
+in the call graph this vertex calls this
+ 
+
+ align:start position:0%
+in the call graph this vertex calls this
+vertex
+
+ align:start position:0%
+vertex
+ 
+
+ align:start position:0%
+vertex
+but i'll direct the edge this way to say
+
+ align:start position:0%
+but i'll direct the edge this way to say
+ 
+
+ align:start position:0%
+but i'll direct the edge this way to say
+that this vertex
+
+ align:start position:0%
+that this vertex
+ 
+
+ align:start position:0%
+that this vertex
+requires uh this vertex needs to be
+
+ align:start position:0%
+requires uh this vertex needs to be
+ 
+
+ align:start position:0%
+requires uh this vertex needs to be
+computed before this one
+
+ align:start position:0%
+computed before this one
+ 
+
+ align:start position:0%
+computed before this one
+and so then i can compute them in a
+
+ align:start position:0%
+and so then i can compute them in a
+ 
+
+ align:start position:0%
+and so then i can compute them in a
+topological order
+
+ align:start position:0%
+topological order
+ 
+
+ align:start position:0%
+topological order
+okay we have a base case which is delta
+
+ align:start position:0%
+okay we have a base case which is delta
+ 
+
+ align:start position:0%
+okay we have a base case which is delta
+of ss equals zero
+
+ align:start position:0%
+of ss equals zero
+ 
+
+ align:start position:0%
+of ss equals zero
+and the running time is again we can use
+
+ align:start position:0%
+and the running time is again we can use
+ 
+
+ align:start position:0%
+and the running time is again we can use
+this formula and say let's just sum over
+
+ align:start position:0%
+this formula and say let's just sum over
+ 
+
+ align:start position:0%
+this formula and say let's just sum over
+all the sub-problems
+
+ align:start position:0%
+all the sub-problems
+ 
+
+ align:start position:0%
+all the sub-problems
+of the non-recursive work in our
+
+ align:start position:0%
+of the non-recursive work in our
+ 
+
+ align:start position:0%
+of the non-recursive work in our
+recurrence relation
+
+ align:start position:0%
+recurrence relation
+ 
+
+ align:start position:0%
+recurrence relation
+and so it's computing this min if i gave
+
+ align:start position:0%
+and so it's computing this min if i gave
+ 
+
+ align:start position:0%
+and so it's computing this min if i gave
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+these deltas for free and i gave you
+
+ align:start position:0%
+these deltas for free and i gave you
+ 
+
+ align:start position:0%
+these deltas for free and i gave you
+these weights which we know
+
+ align:start position:0%
+these weights which we know
+ 
+
+ align:start position:0%
+these weights which we know
+from our weight data structure how long
+
+ align:start position:0%
+from our weight data structure how long
+ 
+
+ align:start position:0%
+from our weight data structure how long
+does it take to compute this min well
+
+ align:start position:0%
+does it take to compute this min well
+ 
+
+ align:start position:0%
+does it take to compute this min well
+however many things there are and how
+
+ align:start position:0%
+however many things there are and how
+ 
+
+ align:start position:0%
+however many things there are and how
+many numbers were
+
+ align:start position:0%
+many numbers were
+ 
+
+ align:start position:0%
+many numbers were
+were mining which is the size of the
+
+ align:start position:0%
+were mining which is the size of the
+ 
+
+ align:start position:0%
+were mining which is the size of the
+incoming adjacency list
+
+ align:start position:0%
+incoming adjacency list
+ 
+
+ align:start position:0%
+incoming adjacency list
+plus one for that infinity and so if you
+
+ align:start position:0%
+plus one for that infinity and so if you
+ 
+
+ align:start position:0%
+plus one for that infinity and so if you
+compute this sum
+
+ align:start position:0%
+compute this sum
+ 
+
+ align:start position:0%
+compute this sum
+sum of incoming edges to every vertex
+
+ align:start position:0%
+sum of incoming edges to every vertex
+ 
+
+ align:start position:0%
+sum of incoming edges to every vertex
+that's all the edges
+
+ align:start position:0%
+that's all the edges
+ 
+
+ align:start position:0%
+that's all the edges
+so this is v plus e okay so
+
+ align:start position:0%
+so this is v plus e okay so
+ 
+
+ align:start position:0%
+so this is v plus e okay so
+in fact this algorithm is
+
+ align:start position:0%
+in fact this algorithm is
+ 
+
+ align:start position:0%
+in fact this algorithm is
+morally the same algorithm is the one
+
+ align:start position:0%
+morally the same algorithm is the one
+ 
+
+ align:start position:0%
+morally the same algorithm is the one
+that we saw in the dag shortest path
+
+ align:start position:0%
+that we saw in the dag shortest path
+ 
+
+ align:start position:0%
+that we saw in the dag shortest path
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+which was computer topological order
+
+ align:start position:0%
+which was computer topological order
+ 
+
+ align:start position:0%
+which was computer topological order
+and process vertices in that order
+
+ align:start position:0%
+and process vertices in that order
+ 
+
+ align:start position:0%
+and process vertices in that order
+and relax edges going out from
+
+ align:start position:0%
+and relax edges going out from
+ 
+
+ align:start position:0%
+and relax edges going out from
+vertices so here uh so in
+
+ align:start position:0%
+vertices so here uh so in
+ 
+
+ align:start position:0%
+vertices so here uh so in
+in that algorithm we would have uh tried
+
+ align:start position:0%
+in that algorithm we would have uh tried
+ 
+
+ align:start position:0%
+in that algorithm we would have uh tried
+to relax this edge
+
+ align:start position:0%
+to relax this edge
+ 
+
+ align:start position:0%
+to relax this edge
+if if there's a better path to v and the
+
+ align:start position:0%
+if if there's a better path to v and the
+ 
+
+ align:start position:0%
+if if there's a better path to v and the
+first one certainly is better than
+
+ align:start position:0%
+first one certainly is better than
+ 
+
+ align:start position:0%
+first one certainly is better than
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+so the first one we relax uh indeed
+
+ align:start position:0%
+so the first one we relax uh indeed
+ 
+
+ align:start position:0%
+so the first one we relax uh indeed
+uh the next edge if this is a if this
+
+ align:start position:0%
+uh the next edge if this is a if this
+ 
+
+ align:start position:0%
+uh the next edge if this is a if this
+gave a better path from s to v then we
+
+ align:start position:0%
+gave a better path from s to v then we
+ 
+
+ align:start position:0%
+gave a better path from s to v then we
+would relax that edge and update the
+
+ align:start position:0%
+would relax that edge and update the
+ 
+
+ align:start position:0%
+would relax that edge and update the
+weight here
+
+ align:start position:0%
+weight here
+ 
+
+ align:start position:0%
+weight here
+and do the same here in the end we're
+
+ align:start position:0%
+and do the same here in the end we're
+ 
+
+ align:start position:0%
+and do the same here in the end we're
+just computing this min
+
+ align:start position:0%
+just computing this min
+ 
+
+ align:start position:0%
+just computing this min
+in the relaxation algorithm but doing it
+
+ align:start position:0%
+in the relaxation algorithm but doing it
+ 
+
+ align:start position:0%
+in the relaxation algorithm but doing it
+step by step in the in the relaxation
+
+ align:start position:0%
+step by step in the in the relaxation
+ 
+
+ align:start position:0%
+step by step in the in the relaxation
+algorithm tag relaxation
+
+ align:start position:0%
+algorithm tag relaxation
+ 
+
+ align:start position:0%
+algorithm tag relaxation
+we for each incoming edge to v
+
+ align:start position:0%
+we for each incoming edge to v
+ 
+
+ align:start position:0%
+we for each incoming edge to v
+we update d of v if it's better
+
+ align:start position:0%
+we update d of v if it's better
+ 
+
+ align:start position:0%
+we update d of v if it's better
+and so if you if you repeatedly update
+
+ align:start position:0%
+and so if you if you repeatedly update
+ 
+
+ align:start position:0%
+and so if you if you repeatedly update
+if you're better that ends up computing
+
+ align:start position:0%
+if you're better that ends up computing
+ 
+
+ align:start position:0%
+if you're better that ends up computing
+a min
+
+ align:start position:0%
+a min
+ 
+
+ align:start position:0%
+a min
+okay so this is the same algorithm just
+
+ align:start position:0%
+okay so this is the same algorithm just
+ 
+
+ align:start position:0%
+okay so this is the same algorithm just
+kind of flipped backwards
+
+ align:start position:0%
+kind of flipped backwards
+ 
+
+ align:start position:0%
+kind of flipped backwards
+uh a funny thing although we wrote down
+
+ align:start position:0%
+uh a funny thing although we wrote down
+ 
+
+ align:start position:0%
+uh a funny thing although we wrote down
+the topological order
+
+ align:start position:0%
+the topological order
+ 
+
+ align:start position:0%
+the topological order
+of the subproblem graph here is the
+
+ align:start position:0%
+of the subproblem graph here is the
+ 
+
+ align:start position:0%
+of the subproblem graph here is the
+topological order of g because
+
+ align:start position:0%
+topological order of g because
+ 
+
+ align:start position:0%
+topological order of g because
+the sub-problem graph is g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the algorithm doesn't actually have to
+
+ align:start position:0%
+the algorithm doesn't actually have to
+ 
+
+ align:start position:0%
+the algorithm doesn't actually have to
+compute one it's doing it
+
+ align:start position:0%
+compute one it's doing it
+ 
+
+ align:start position:0%
+compute one it's doing it
+automatically for free if you think
+
+ align:start position:0%
+automatically for free if you think
+ 
+
+ align:start position:0%
+automatically for free if you think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+this algorithm a generic
+
+ align:start position:0%
+this algorithm a generic
+ 
+
+ align:start position:0%
+this algorithm a generic
+dp algorithm which is check whether
+
+ align:start position:0%
+dp algorithm which is check whether
+ 
+
+ align:start position:0%
+dp algorithm which is check whether
+we're in a memo table if so return
+
+ align:start position:0%
+we're in a memo table if so return
+ 
+
+ align:start position:0%
+we're in a memo table if so return
+otherwise recurse or base case
+
+ align:start position:0%
+otherwise recurse or base case
+ 
+
+ align:start position:0%
+otherwise recurse or base case
+this actually is a depth for search
+
+ align:start position:0%
+this actually is a depth for search
+ 
+
+ align:start position:0%
+this actually is a depth for search
+through the sub-problem graph
+
+ align:start position:0%
+through the sub-problem graph
+ 
+
+ align:start position:0%
+through the sub-problem graph
+technically through the reverse of the
+
+ align:start position:0%
+technically through the reverse of the
+ 
+
+ align:start position:0%
+technically through the reverse of the
+subproblem graph
+
+ align:start position:0%
+subproblem graph
+ 
+
+ align:start position:0%
+subproblem graph
+if i draw an edge
+
+ align:start position:0%
+if i draw an edge
+ 
+
+ align:start position:0%
+if i draw an edge
+so from small
+
+ align:start position:0%
+so from small
+ 
+
+ align:start position:0%
+so from small
+to big so
+
+ align:start position:0%
+to big so
+ 
+
+ align:start position:0%
+to big so
+if i'm just saying i orient the edges
+
+ align:start position:0%
+if i'm just saying i orient the edges
+ 
+
+ align:start position:0%
+if i'm just saying i orient the edges
+from my smaller sub problems to the ones
+
+ align:start position:0%
+from my smaller sub problems to the ones
+ 
+
+ align:start position:0%
+from my smaller sub problems to the ones
+that need it
+
+ align:start position:0%
+that need it
+ 
+
+ align:start position:0%
+that need it
+then i'm actually definitely searching
+
+ align:start position:0%
+then i'm actually definitely searching
+ 
+
+ align:start position:0%
+then i'm actually definitely searching
+backwards in this graph
+
+ align:start position:0%
+backwards in this graph
+ 
+
+ align:start position:0%
+backwards in this graph
+because the bigger problem calls the
+
+ align:start position:0%
+because the bigger problem calls the
+ 
+
+ align:start position:0%
+because the bigger problem calls the
+smaller problem
+
+ align:start position:0%
+smaller problem
+ 
+
+ align:start position:0%
+smaller problem
+and the memo table is serving as the
+
+ align:start position:0%
+and the memo table is serving as the
+ 
+
+ align:start position:0%
+and the memo table is serving as the
+have i visited this vertex
+
+ align:start position:0%
+have i visited this vertex
+ 
+
+ align:start position:0%
+have i visited this vertex
+already check in dfs so this is actually
+
+ align:start position:0%
+already check in dfs so this is actually
+ 
+
+ align:start position:0%
+already check in dfs so this is actually
+a dfs algorithm
+
+ align:start position:0%
+a dfs algorithm
+ 
+
+ align:start position:0%
+a dfs algorithm
+plus we're doing some computation
+
+ align:start position:0%
+plus we're doing some computation
+ 
+
+ align:start position:0%
+plus we're doing some computation
+to actually solve the sub problems we
+
+ align:start position:0%
+to actually solve the sub problems we
+ 
+
+ align:start position:0%
+to actually solve the sub problems we
+care about
+
+ align:start position:0%
+care about
+ 
+
+ align:start position:0%
+care about
+so implicit in this algorithm we are
+
+ align:start position:0%
+so implicit in this algorithm we are
+ 
+
+ align:start position:0%
+so implicit in this algorithm we are
+doing a dfs and at
+
+ align:start position:0%
+doing a dfs and at
+ 
+
+ align:start position:0%
+doing a dfs and at
+the same time we're doing this shortest
+
+ align:start position:0%
+the same time we're doing this shortest
+ 
+
+ align:start position:0%
+the same time we're doing this shortest
+path computation
+
+ align:start position:0%
+path computation
+ 
+
+ align:start position:0%
+path computation
+uh in the finishing order of that dfs
+
+ align:start position:0%
+uh in the finishing order of that dfs
+ 
+
+ align:start position:0%
+uh in the finishing order of that dfs
+traversal
+
+ align:start position:0%
+traversal
+ 
+
+ align:start position:0%
+traversal
+because all the edges are backwards this
+
+ align:start position:0%
+because all the edges are backwards this
+ 
+
+ align:start position:0%
+because all the edges are backwards this
+is the same as the reverse finishing
+
+ align:start position:0%
+is the same as the reverse finishing
+ 
+
+ align:start position:0%
+is the same as the reverse finishing
+order if the graph is forwards so in the
+
+ align:start position:0%
+order if the graph is forwards so in the
+ 
+
+ align:start position:0%
+order if the graph is forwards so in the
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+we're computing a topological order
+
+ align:start position:0%
+we're computing a topological order
+ 
+
+ align:start position:0%
+we're computing a topological order
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh dynamic programming includes in it
+
+ align:start position:0%
+uh dynamic programming includes in it
+ 
+
+ align:start position:0%
+uh dynamic programming includes in it
+uh depth first search oh a lot of words
+
+ align:start position:0%
+uh depth first search oh a lot of words
+ 
+
+ align:start position:0%
+uh depth first search oh a lot of words
+but it's kind of cool that this
+
+ align:start position:0%
+but it's kind of cool that this
+ 
+
+ align:start position:0%
+but it's kind of cool that this
+framework just solves dag shortest paths
+
+ align:start position:0%
+framework just solves dag shortest paths
+ 
+
+ align:start position:0%
+framework just solves dag shortest paths
+without
+
+ align:start position:0%
+without
+ 
+
+ align:start position:0%
+without
+much work i mean we we did a lot of work
+
+ align:start position:0%
+much work i mean we we did a lot of work
+ 
+
+ align:start position:0%
+much work i mean we we did a lot of work
+in shorts paths to prove that this
+
+ align:start position:0%
+in shorts paths to prove that this
+ 
+
+ align:start position:0%
+in shorts paths to prove that this
+relation is true
+
+ align:start position:0%
+relation is true
+ 
+
+ align:start position:0%
+relation is true
+but once you know it's true the
+
+ align:start position:0%
+but once you know it's true the
+ 
+
+ align:start position:0%
+but once you know it's true the
+algorithm part is
+
+ align:start position:0%
+algorithm part is
+ 
+
+ align:start position:0%
+algorithm part is
+is pretty much free you just write down
+
+ align:start position:0%
+is pretty much free you just write down
+ 
+
+ align:start position:0%
+is pretty much free you just write down
+sort bot and you're done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this brings us to
+
+ align:start position:0%
+okay this brings us to
+ 
+
+ align:start position:0%
+okay this brings us to
+in general at this point we have seen
+
+ align:start position:0%
+in general at this point we have seen
+ 
+
+ align:start position:0%
+in general at this point we have seen
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+examples of dynamic programming i guess
+
+ align:start position:0%
+examples of dynamic programming i guess
+ 
+
+ align:start position:0%
+examples of dynamic programming i guess
+technically merge sort
+
+ align:start position:0%
+technically merge sort
+ 
+
+ align:start position:0%
+technically merge sort
+you can think of as a dynamic program
+
+ align:start position:0%
+you can think of as a dynamic program
+ 
+
+ align:start position:0%
+you can think of as a dynamic program
+but it doesn't actually reuse anything
+
+ align:start position:0%
+but it doesn't actually reuse anything
+ 
+
+ align:start position:0%
+but it doesn't actually reuse anything
+so it's not interesting
+
+ align:start position:0%
+so it's not interesting
+ 
+
+ align:start position:0%
+so it's not interesting
+and indeed that gave us a really bad
+
+ align:start position:0%
+and indeed that gave us a really bad
+ 
+
+ align:start position:0%
+and indeed that gave us a really bad
+bound we've definitely seen bag shortest
+
+ align:start position:0%
+bound we've definitely seen bag shortest
+ 
+
+ align:start position:0%
+bound we've definitely seen bag shortest
+paths
+
+ align:start position:0%
+paths
+ 
+
+ align:start position:0%
+paths
+and fibonacci numbers as two interesting
+
+ align:start position:0%
+and fibonacci numbers as two interesting
+ 
+
+ align:start position:0%
+and fibonacci numbers as two interesting
+examples
+
+ align:start position:0%
+examples
+ 
+
+ align:start position:0%
+examples
+and what the next remainder of this
+
+ align:start position:0%
+and what the next remainder of this
+ 
+
+ align:start position:0%
+and what the next remainder of this
+lecture and the next three lectures are
+
+ align:start position:0%
+lecture and the next three lectures are
+ 
+
+ align:start position:0%
+lecture and the next three lectures are
+going to be about
+
+ align:start position:0%
+going to be about
+ 
+
+ align:start position:0%
+going to be about
+is more and more examples of dynamic
+
+ align:start position:0%
+is more and more examples of dynamic
+ 
+
+ align:start position:0%
+is more and more examples of dynamic
+programming and how you can use it to
+
+ align:start position:0%
+programming and how you can use it to
+ 
+
+ align:start position:0%
+programming and how you can use it to
+solve
+
+ align:start position:0%
+solve
+ 
+
+ align:start position:0%
+solve
+increasingly general problems so far
+
+ align:start position:0%
+increasingly general problems so far
+ 
+
+ align:start position:0%
+increasingly general problems so far
+we've just solved an easy problem
+
+ align:start position:0%
+we've just solved an easy problem
+ 
+
+ align:start position:0%
+we've just solved an easy problem
+and a problem we already knew how to
+
+ align:start position:0%
+and a problem we already knew how to
+ 
+
+ align:start position:0%
+and a problem we already knew how to
+solve let's go to a new problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is bowling bowling is popular in
+
+ align:start position:0%
+which is bowling bowling is popular in
+ 
+
+ align:start position:0%
+which is bowling bowling is popular in
+boston
+
+ align:start position:0%
+boston
+ 
+
+ align:start position:0%
+boston
+this boston likes to play candlepin
+
+ align:start position:0%
+this boston likes to play candlepin
+ 
+
+ align:start position:0%
+this boston likes to play candlepin
+bowling which is a bit unusual
+
+ align:start position:0%
+bowling which is a bit unusual
+ 
+
+ align:start position:0%
+bowling which is a bit unusual
+uh today we're going to play an even
+
+ align:start position:0%
+uh today we're going to play an even
+ 
+
+ align:start position:0%
+uh today we're going to play an even
+more unusual bowling game
+
+ align:start position:0%
+more unusual bowling game
+ 
+
+ align:start position:0%
+more unusual bowling game
+one that i made up based on a bowling
+
+ align:start position:0%
+one that i made up based on a bowling
+ 
+
+ align:start position:0%
+one that i made up based on a bowling
+game
+
+ align:start position:0%
+game
+ 
+
+ align:start position:0%
+game
+that henry dudeny made up in 1908
+
+ align:start position:0%
+that henry dudeny made up in 1908
+ 
+
+ align:start position:0%
+that henry dudeny made up in 1908
+so ancient bowling i might call it
+
+ align:start position:0%
+so ancient bowling i might call it
+ 
+
+ align:start position:0%
+so ancient bowling i might call it
+or i think linear bowling is what i
+
+ align:start position:0%
+or i think linear bowling is what i
+ 
+
+ align:start position:0%
+or i think linear bowling is what i
+might call it i'll just call it bowling
+
+ align:start position:0%
+might call it i'll just call it bowling
+ 
+
+ align:start position:0%
+might call it i'll just call it bowling
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and now i'm going to attempt to draw a
+
+ align:start position:0%
+and now i'm going to attempt to draw a
+ 
+
+ align:start position:0%
+and now i'm going to attempt to draw a
+bowling pin not bad
+
+ align:start position:0%
+bowling pin not bad
+ 
+
+ align:start position:0%
+bowling pin not bad
+that might get progressively worse so
+
+ align:start position:0%
+that might get progressively worse so
+ 
+
+ align:start position:0%
+that might get progressively worse so
+imagine
+
+ align:start position:0%
+imagine
+ 
+
+ align:start position:0%
+imagine
+n identical bowling pins please pretend
+
+ align:start position:0%
+n identical bowling pins please pretend
+ 
+
+ align:start position:0%
+n identical bowling pins please pretend
+these are identical
+
+ align:start position:0%
+these are identical
+ 
+
+ align:start position:0%
+these are identical
+and i have a ball which is
+
+ align:start position:0%
+and i have a ball which is
+ 
+
+ align:start position:0%
+and i have a ball which is
+approximately the same size as a bowling
+
+ align:start position:0%
+approximately the same size as a bowling
+ 
+
+ align:start position:0%
+approximately the same size as a bowling
+pin these bowling pins are
+
+ align:start position:0%
+pin these bowling pins are
+ 
+
+ align:start position:0%
+pin these bowling pins are
+pretty close together i should have left
+
+ align:start position:0%
+pretty close together i should have left
+ 
+
+ align:start position:0%
+pretty close together i should have left
+a little gap here
+
+ align:start position:0%
+a little gap here
+ 
+
+ align:start position:0%
+a little gap here
+and you're a really good bowler now
+
+ align:start position:0%
+and you're a really good bowler now
+ 
+
+ align:start position:0%
+and you're a really good bowler now
+unfortunately these bowling
+
+ align:start position:0%
+unfortunately these bowling
+ 
+
+ align:start position:0%
+unfortunately these bowling
+pins are on a line and you're bowling
+
+ align:start position:0%
+pins are on a line and you're bowling
+ 
+
+ align:start position:0%
+pins are on a line and you're bowling
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+way down at infinity so when you bowl
+
+ align:start position:0%
+way down at infinity so when you bowl
+ 
+
+ align:start position:0%
+way down at infinity so when you bowl
+um you can only hit one pin or two pins
+
+ align:start position:0%
+um you can only hit one pin or two pins
+ 
+
+ align:start position:0%
+um you can only hit one pin or two pins
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+zero pins but probably you want to hit
+
+ align:start position:0%
+zero pins but probably you want to hit
+ 
+
+ align:start position:0%
+zero pins but probably you want to hit
+some pins uh so if you
+
+ align:start position:0%
+some pins uh so if you
+ 
+
+ align:start position:0%
+some pins uh so if you
+pull straight at a pin you will just hit
+
+ align:start position:0%
+pull straight at a pin you will just hit
+ 
+
+ align:start position:0%
+pull straight at a pin you will just hit
+that one pin
+
+ align:start position:0%
+that one pin
+ 
+
+ align:start position:0%
+that one pin
+and if you bowl in the middle between
+
+ align:start position:0%
+and if you bowl in the middle between
+ 
+
+ align:start position:0%
+and if you bowl in the middle between
+two pins
+
+ align:start position:0%
+two pins
+ 
+
+ align:start position:0%
+two pins
+you will knock down that's a ball sorry
+
+ align:start position:0%
+you will knock down that's a ball sorry
+ 
+
+ align:start position:0%
+you will knock down that's a ball sorry
+you will knock down
+
+ align:start position:0%
+you will knock down
+ 
+
+ align:start position:0%
+you will knock down
+two pins okay this is your model of
+
+ align:start position:0%
+two pins okay this is your model of
+ 
+
+ align:start position:0%
+two pins okay this is your model of
+bowling
+
+ align:start position:0%
+bowling
+ 
+
+ align:start position:0%
+bowling
+model of computation now what makes this
+
+ align:start position:0%
+model of computation now what makes this
+ 
+
+ align:start position:0%
+model of computation now what makes this
+interesting is that the pins have values
+
+ align:start position:0%
+interesting is that the pins have values
+ 
+
+ align:start position:0%
+interesting is that the pins have values
+pin i has value
+
+ align:start position:0%
+pin i has value
+ 
+
+ align:start position:0%
+pin i has value
+yeah this is obviously a toy problem uh
+
+ align:start position:0%
+yeah this is obviously a toy problem uh
+ 
+
+ align:start position:0%
+yeah this is obviously a toy problem uh
+though this problem this type of bowling
+
+ align:start position:0%
+though this problem this type of bowling
+ 
+
+ align:start position:0%
+though this problem this type of bowling
+does go back to 1908
+
+ align:start position:0%
+does go back to 1908
+ 
+
+ align:start position:0%
+does go back to 1908
+it was also a toy problem in that
+
+ align:start position:0%
+it was also a toy problem in that
+ 
+
+ align:start position:0%
+it was also a toy problem in that
+setting so each of these
+
+ align:start position:0%
+setting so each of these
+ 
+
+ align:start position:0%
+setting so each of these
+uh bowling pins has some number on it
+
+ align:start position:0%
+uh bowling pins has some number on it
+ 
+
+ align:start position:0%
+uh bowling pins has some number on it
+let's say one nine nine
+
+ align:start position:0%
+let's say one nine nine
+ 
+
+ align:start position:0%
+let's say one nine nine
+let me do a slightly more interesting
+
+ align:start position:0%
+let me do a slightly more interesting
+ 
+
+ align:start position:0%
+let me do a slightly more interesting
+example maybe another one here
+
+ align:start position:0%
+example maybe another one here
+ 
+
+ align:start position:0%
+example maybe another one here
+uh and a two
+
+ align:start position:0%
+uh and a two
+ 
+
+ align:start position:0%
+uh and a two
+and a five and a five something like
+
+ align:start position:0%
+and a five and a five something like
+ 
+
+ align:start position:0%
+and a five and a five something like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay uh or maybe make a little more
+
+ align:start position:0%
+okay uh or maybe make a little more
+ 
+
+ align:start position:0%
+okay uh or maybe make a little more
+interesting let's put some negative
+
+ align:start position:0%
+interesting let's put some negative
+ 
+
+ align:start position:0%
+interesting let's put some negative
+numbers on here
+
+ align:start position:0%
+numbers on here
+ 
+
+ align:start position:0%
+numbers on here
+okay and the model uh so you're at the
+
+ align:start position:0%
+okay and the model uh so you're at the
+ 
+
+ align:start position:0%
+okay and the model uh so you're at the
+carnival bowling
+
+ align:start position:0%
+carnival bowling
+ 
+
+ align:start position:0%
+carnival bowling
+each pin has different potentially
+
+ align:start position:0%
+each pin has different potentially
+ 
+
+ align:start position:0%
+each pin has different potentially
+different values
+
+ align:start position:0%
+different values
+ 
+
+ align:start position:0%
+different values
+and the model is if you hit
+
+ align:start position:0%
+and the model is if you hit
+ 
+
+ align:start position:0%
+and the model is if you hit
+one pin i
+
+ align:start position:0%
+one pin i
+ 
+
+ align:start position:0%
+one pin i
+then you get vi points
+
+ align:start position:0%
+then you get vi points
+ 
+
+ align:start position:0%
+then you get vi points
+so that's straightforward to make it
+
+ align:start position:0%
+so that's straightforward to make it
+ 
+
+ align:start position:0%
+so that's straightforward to make it
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+when you hit two pins you get the
+
+ align:start position:0%
+when you hit two pins you get the
+ 
+
+ align:start position:0%
+when you hit two pins you get the
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+so if i hit two pins it's always i and i
+
+ align:start position:0%
+so if i hit two pins it's always i and i
+ 
+
+ align:start position:0%
+so if i hit two pins it's always i and i
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+for some i you get vi times vi plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points this is the
+
+ align:start position:0%
+points this is the
+ 
+
+ align:start position:0%
+points this is the
+the game you're playing and it doesn't
+
+ align:start position:0%
+the game you're playing and it doesn't
+ 
+
+ align:start position:0%
+the game you're playing and it doesn't
+really matter that this is a product
+
+ align:start position:0%
+really matter that this is a product
+ 
+
+ align:start position:0%
+really matter that this is a product
+uh product is just some weird function
+
+ align:start position:0%
+uh product is just some weird function
+ 
+
+ align:start position:0%
+uh product is just some weird function
+that's hard to
+
+ align:start position:0%
+that's hard to
+ 
+
+ align:start position:0%
+that's hard to
+imagine if you stare at this long enough
+
+ align:start position:0%
+imagine if you stare at this long enough
+ 
+
+ align:start position:0%
+imagine if you stare at this long enough
+you should convince yourself that the
+
+ align:start position:0%
+you should convince yourself that the
+ 
+
+ align:start position:0%
+you should convince yourself that the
+optimal solution is probably to
+
+ align:start position:0%
+optimal solution is probably to
+ 
+
+ align:start position:0%
+optimal solution is probably to
+so for each of these numbers i could
+
+ align:start position:0%
+so for each of these numbers i could
+ 
+
+ align:start position:0%
+so for each of these numbers i could
+leave it singleton or pair it with its
+
+ align:start position:0%
+leave it singleton or pair it with its
+ 
+
+ align:start position:0%
+leave it singleton or pair it with its
+left neighbor or pair it with its right
+
+ align:start position:0%
+left neighbor or pair it with its right
+ 
+
+ align:start position:0%
+left neighbor or pair it with its right
+neighbor but the pairings can't overlap
+
+ align:start position:0%
+neighbor but the pairings can't overlap
+ 
+
+ align:start position:0%
+neighbor but the pairings can't overlap
+because once i hit a pin
+
+ align:start position:0%
+because once i hit a pin
+ 
+
+ align:start position:0%
+because once i hit a pin
+it's gone it's knocked over and it
+
+ align:start position:0%
+it's gone it's knocked over and it
+ 
+
+ align:start position:0%
+it's gone it's knocked over and it
+disappears
+
+ align:start position:0%
+disappears
+ 
+
+ align:start position:0%
+disappears
+so because of these nines which are very
+
+ align:start position:0%
+so because of these nines which are very
+ 
+
+ align:start position:0%
+so because of these nines which are very
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+value what i'd probably like to do is
+
+ align:start position:0%
+value what i'd probably like to do is
+ 
+
+ align:start position:0%
+value what i'd probably like to do is
+hit both of them together so pair them
+
+ align:start position:0%
+hit both of them together so pair them
+ 
+
+ align:start position:0%
+hit both of them together so pair them
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+because 9 times 9 is 81 that's really
+
+ align:start position:0%
+because 9 times 9 is 81 that's really
+ 
+
+ align:start position:0%
+because 9 times 9 is 81 that's really
+big much better than hitting them
+
+ align:start position:0%
+big much better than hitting them
+ 
+
+ align:start position:0%
+big much better than hitting them
+individually or hitting 9 times 1 or 9
+
+ align:start position:0%
+individually or hitting 9 times 1 or 9
+ 
+
+ align:start position:0%
+individually or hitting 9 times 1 or 9
+times 2.
+
+ align:start position:0%
+times 2.
+ 
+
+ align:start position:0%
+times 2.
+one and one is kind of funny because
+
+ align:start position:0%
+one and one is kind of funny because
+ 
+
+ align:start position:0%
+one and one is kind of funny because
+it's actually better to hit them
+
+ align:start position:0%
+it's actually better to hit them
+ 
+
+ align:start position:0%
+it's actually better to hit them
+individually
+
+ align:start position:0%
+individually
+ 
+
+ align:start position:0%
+individually
+that will give you two points whereas if
+
+ align:start position:0%
+that will give you two points whereas if
+ 
+
+ align:start position:0%
+that will give you two points whereas if
+i pair them up i only get one point
+
+ align:start position:0%
+i pair them up i only get one point
+ 
+
+ align:start position:0%
+i pair them up i only get one point
+two and minus five that seems bad
+
+ align:start position:0%
+two and minus five that seems bad
+ 
+
+ align:start position:0%
+two and minus five that seems bad
+negative ten points my goal is to
+
+ align:start position:0%
+negative ten points my goal is to
+ 
+
+ align:start position:0%
+negative ten points my goal is to
+maximize score
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you have to hit all the pins
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say no you don't have to hit all
+
+ align:start position:0%
+let's say no you don't have to hit all
+ 
+
+ align:start position:0%
+let's say no you don't have to hit all
+the pins so i could skip the minus fives
+
+ align:start position:0%
+the pins so i could skip the minus fives
+ 
+
+ align:start position:0%
+the pins so i could skip the minus fives
+but in fact here uh because they're
+
+ align:start position:0%
+but in fact here uh because they're
+ 
+
+ align:start position:0%
+but in fact here uh because they're
+adjacent minus five times minus five is
+
+ align:start position:0%
+adjacent minus five times minus five is
+ 
+
+ align:start position:0%
+adjacent minus five times minus five is
+good that's 25 points
+
+ align:start position:0%
+good that's 25 points
+ 
+
+ align:start position:0%
+good that's 25 points
+so uh the optimal solution for this
+
+ align:start position:0%
+so uh the optimal solution for this
+ 
+
+ align:start position:0%
+so uh the optimal solution for this
+particular instance
+
+ align:start position:0%
+particular instance
+ 
+
+ align:start position:0%
+particular instance
+are to hit all the pins these positive
+
+ align:start position:0%
+are to hit all the pins these positive
+ 
+
+ align:start position:0%
+are to hit all the pins these positive
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+these together these together if i added
+
+ align:start position:0%
+these together these together if i added
+ 
+
+ align:start position:0%
+these together these together if i added
+for example another pin of minus three
+
+ align:start position:0%
+for example another pin of minus three
+ 
+
+ align:start position:0%
+for example another pin of minus three
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+i would choose not to hit that pin good
+
+ align:start position:0%
+i would choose not to hit that pin good
+ 
+
+ align:start position:0%
+i would choose not to hit that pin good
+question so
+
+ align:start position:0%
+question so
+ 
+
+ align:start position:0%
+question so
+you just play until you are tired when
+
+ align:start position:0%
+you just play until you are tired when
+ 
+
+ align:start position:0%
+you just play until you are tired when
+you decide to stop playing
+
+ align:start position:0%
+you decide to stop playing
+ 
+
+ align:start position:0%
+you decide to stop playing
+how can i maximize your score there are
+
+ align:start position:0%
+how can i maximize your score there are
+ 
+
+ align:start position:0%
+how can i maximize your score there are
+many variations this game
+
+ align:start position:0%
+many variations this game
+ 
+
+ align:start position:0%
+many variations this game
+all of them basically any variation
+
+ align:start position:0%
+all of them basically any variation
+ 
+
+ align:start position:0%
+all of them basically any variation
+not literally every variation but many
+
+ align:start position:0%
+not literally every variation but many
+ 
+
+ align:start position:0%
+not literally every variation but many
+many variations of this problem can all
+
+ align:start position:0%
+many variations of this problem can all
+ 
+
+ align:start position:0%
+many variations of this problem can all
+be solved
+
+ align:start position:0%
+be solved
+ 
+
+ align:start position:0%
+be solved
+quickly with dynamic programming but
+
+ align:start position:0%
+quickly with dynamic programming but
+ 
+
+ align:start position:0%
+quickly with dynamic programming but
+let's solve this particular one
+
+ align:start position:0%
+let's solve this particular one
+ 
+
+ align:start position:0%
+let's solve this particular one
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we're really in algorithmic
+
+ align:start position:0%
+so now we're really in algorithmic
+ 
+
+ align:start position:0%
+so now we're really in algorithmic
+design mode
+
+ align:start position:0%
+design mode
+ 
+
+ align:start position:0%
+design mode
+we need to think about sort bot
+
+ align:start position:0%
+we need to think about sort bot
+ 
+
+ align:start position:0%
+we need to think about sort bot
+and in particular we need to think about
+
+ align:start position:0%
+and in particular we need to think about
+ 
+
+ align:start position:0%
+and in particular we need to think about
+what would the subproblems be
+
+ align:start position:0%
+what would the subproblems be
+ 
+
+ align:start position:0%
+what would the subproblems be
+here and at this point we don't have a
+
+ align:start position:0%
+here and at this point we don't have a
+ 
+
+ align:start position:0%
+here and at this point we don't have a
+lot of of help so i should probably give
+
+ align:start position:0%
+lot of of help so i should probably give
+ 
+
+ align:start position:0%
+lot of of help so i should probably give
+you some tools
+
+ align:start position:0%
+you some tools
+ 
+
+ align:start position:0%
+you some tools
+if i want to solve a problem like this
+
+ align:start position:0%
+if i want to solve a problem like this
+ 
+
+ align:start position:0%
+if i want to solve a problem like this
+the input
+
+ align:start position:0%
+the input
+ 
+
+ align:start position:0%
+the input
+is a sequence of numbers right it's a
+
+ align:start position:0%
+is a sequence of numbers right it's a
+ 
+
+ align:start position:0%
+is a sequence of numbers right it's a
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+data structure maybe it's an array of
+
+ align:start position:0%
+data structure maybe it's an array of
+ 
+
+ align:start position:0%
+data structure maybe it's an array of
+numbers which is this v
+
+ align:start position:0%
+numbers which is this v
+ 
+
+ align:start position:0%
+numbers which is this v
+v array
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's see
+
+ align:start position:0%
+and let's see
+ 
+
+ align:start position:0%
+and let's see
+um a general tool for subproblem design
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which will cover most of the problems
+
+ align:start position:0%
+which will cover most of the problems
+ 
+
+ align:start position:0%
+which will cover most of the problems
+maybe all of the problems that we
+
+ align:start position:0%
+maybe all of the problems that we
+ 
+
+ align:start position:0%
+maybe all of the problems that we
+see in this class for dynamic
+
+ align:start position:0%
+see in this class for dynamic
+ 
+
+ align:start position:0%
+see in this class for dynamic
+programming
+
+ align:start position:0%
+programming
+ 
+
+ align:start position:0%
+programming
+here's a trick if
+
+ align:start position:0%
+here's a trick if
+ 
+
+ align:start position:0%
+here's a trick if
+your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+input is a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's some good sub problems to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+uh we could do all prefixes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's call the sequence x
+
+ align:start position:0%
+so let's call the sequence x
+ 
+
+ align:start position:0%
+so let's call the sequence x
+so we could do x prefix means up to a
+
+ align:start position:0%
+so we could do x prefix means up to a
+ 
+
+ align:start position:0%
+so we could do x prefix means up to a
+given i for all i
+
+ align:start position:0%
+given i for all i
+ 
+
+ align:start position:0%
+given i for all i
+we could do all the suffixes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x from i onward for all i
+
+ align:start position:0%
+x from i onward for all i
+ 
+
+ align:start position:0%
+x from i onward for all i
+or we could do substrings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which are the consecutive items from i
+
+ align:start position:0%
+which are the consecutive items from i
+ 
+
+ align:start position:0%
+which are the consecutive items from i
+to j
+
+ align:start position:0%
+to j
+ 
+
+ align:start position:0%
+to j
+i don't write subsequence here
+
+ align:start position:0%
+i don't write subsequence here
+ 
+
+ align:start position:0%
+i don't write subsequence here
+subsequence means you can emit items in
+
+ align:start position:0%
+subsequence means you can emit items in
+ 
+
+ align:start position:0%
+subsequence means you can emit items in
+the middle
+
+ align:start position:0%
+the middle
+ 
+
+ align:start position:0%
+the middle
+so substring you have to start at some
+
+ align:start position:0%
+so substring you have to start at some
+ 
+
+ align:start position:0%
+so substring you have to start at some
+position and do all the things up to j
+
+ align:start position:0%
+position and do all the things up to j
+ 
+
+ align:start position:0%
+position and do all the things up to j
+uh so these are nice easy to express in
+
+ align:start position:0%
+uh so these are nice easy to express in
+ 
+
+ align:start position:0%
+uh so these are nice easy to express in
+python notation
+
+ align:start position:0%
+python notation
+ 
+
+ align:start position:0%
+python notation
+and these are great because they're
+
+ align:start position:0%
+and these are great because they're
+ 
+
+ align:start position:0%
+and these are great because they're
+polynomial right if i have n
+
+ align:start position:0%
+polynomial right if i have n
+ 
+
+ align:start position:0%
+polynomial right if i have n
+things if the length of my sequence x is
+
+ align:start position:0%
+things if the length of my sequence x is
+ 
+
+ align:start position:0%
+things if the length of my sequence x is
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+then there are n sequences n prefixes
+
+ align:start position:0%
+then there are n sequences n prefixes
+ 
+
+ align:start position:0%
+then there are n sequences n prefixes
+technically n plus one so
+
+ align:start position:0%
+technically n plus one so
+ 
+
+ align:start position:0%
+technically n plus one so
+let's do theta n prefixes they're theta
+
+ align:start position:0%
+let's do theta n prefixes they're theta
+ 
+
+ align:start position:0%
+let's do theta n prefixes they're theta
+and suffixes
+
+ align:start position:0%
+and suffixes
+ 
+
+ align:start position:0%
+and suffixes
+and they're theta and squared
+
+ align:start position:0%
+and they're theta and squared
+ 
+
+ align:start position:0%
+and they're theta and squared
+substrings because there's n roughly n
+
+ align:start position:0%
+substrings because there's n roughly n
+ 
+
+ align:start position:0%
+substrings because there's n roughly n
+choices for i and j
+
+ align:start position:0%
+choices for i and j
+ 
+
+ align:start position:0%
+choices for i and j
+separately sorry
+
+ align:start position:0%
+separately sorry
+ 
+
+ align:start position:0%
+separately sorry
+subsequences good right i didn't write
+
+ align:start position:0%
+subsequences good right i didn't write
+ 
+
+ align:start position:0%
+subsequences good right i didn't write
+subsequences because in fact there are
+
+ align:start position:0%
+subsequences because in fact there are
+ 
+
+ align:start position:0%
+subsequences because in fact there are
+exponentially many subsequences right
+
+ align:start position:0%
+exponentially many subsequences right
+ 
+
+ align:start position:0%
+exponentially many subsequences right
+it's 2 to the n
+
+ align:start position:0%
+it's 2 to the n
+ 
+
+ align:start position:0%
+it's 2 to the n
+for every item i could choose it or not
+
+ align:start position:0%
+for every item i could choose it or not
+ 
+
+ align:start position:0%
+for every item i could choose it or not
+so i don't want to parametrize i don't
+
+ align:start position:0%
+so i don't want to parametrize i don't
+ 
+
+ align:start position:0%
+so i don't want to parametrize i don't
+want my sub problems to be sub sequences
+
+ align:start position:0%
+want my sub problems to be sub sequences
+ 
+
+ align:start position:0%
+want my sub problems to be sub sequences
+because that's
+
+ align:start position:0%
+because that's
+ 
+
+ align:start position:0%
+because that's
+guaranteed well then you're guaranteed
+
+ align:start position:0%
+guaranteed well then you're guaranteed
+ 
+
+ align:start position:0%
+guaranteed well then you're guaranteed
+to get an exponential number of
+
+ align:start position:0%
+to get an exponential number of
+ 
+
+ align:start position:0%
+to get an exponential number of
+sub-problems which is bad
+
+ align:start position:0%
+sub-problems which is bad
+ 
+
+ align:start position:0%
+sub-problems which is bad
+we'd like to bound the number of
+
+ align:start position:0%
+we'd like to bound the number of
+ 
+
+ align:start position:0%
+we'd like to bound the number of
+sub-problems by a polynomial
+
+ align:start position:0%
+sub-problems by a polynomial
+ 
+
+ align:start position:0%
+sub-problems by a polynomial
+so these are three natural ways to get
+
+ align:start position:0%
+so these are three natural ways to get
+ 
+
+ align:start position:0%
+so these are three natural ways to get
+uh polynomial bounds
+
+ align:start position:0%
+uh polynomial bounds
+ 
+
+ align:start position:0%
+uh polynomial bounds
+now prefixes and suffixes are obviously
+
+ align:start position:0%
+now prefixes and suffixes are obviously
+ 
+
+ align:start position:0%
+now prefixes and suffixes are obviously
+better because there's fewer of them
+
+ align:start position:0%
+better because there's fewer of them
+ 
+
+ align:start position:0%
+better because there's fewer of them
+linear instead of quadratic and usually
+
+ align:start position:0%
+linear instead of quadratic and usually
+ 
+
+ align:start position:0%
+linear instead of quadratic and usually
+almost every problem you'll encounter
+
+ align:start position:0%
+almost every problem you'll encounter
+ 
+
+ align:start position:0%
+almost every problem you'll encounter
+prefixes and suffixes are equally good
+
+ align:start position:0%
+prefixes and suffixes are equally good
+ 
+
+ align:start position:0%
+prefixes and suffixes are equally good
+it doesn't really matter which one you
+
+ align:start position:0%
+it doesn't really matter which one you
+ 
+
+ align:start position:0%
+it doesn't really matter which one you
+choose
+
+ align:start position:0%
+choose
+ 
+
+ align:start position:0%
+choose
+so maybe you like to think of well we'll
+
+ align:start position:0%
+so maybe you like to think of well we'll
+ 
+
+ align:start position:0%
+so maybe you like to think of well we'll
+get to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's you just choose whichever is more
+
+ align:start position:0%
+it's you just choose whichever is more
+ 
+
+ align:start position:0%
+it's you just choose whichever is more
+comfortable for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but sometimes it's not enough and we'll
+
+ align:start position:0%
+but sometimes it's not enough and we'll
+ 
+
+ align:start position:0%
+but sometimes it's not enough and we'll
+have to go to substrings that won't be
+
+ align:start position:0%
+have to go to substrings that won't be
+ 
+
+ align:start position:0%
+have to go to substrings that won't be
+for another lecture or two
+
+ align:start position:0%
+for another lecture or two
+ 
+
+ align:start position:0%
+for another lecture or two
+okay today i claim that prefixes or
+
+ align:start position:0%
+okay today i claim that prefixes or
+ 
+
+ align:start position:0%
+okay today i claim that prefixes or
+suffixes
+
+ align:start position:0%
+suffixes
+ 
+
+ align:start position:0%
+suffixes
+are uh enough to solve the bowling
+
+ align:start position:0%
+are uh enough to solve the bowling
+ 
+
+ align:start position:0%
+are uh enough to solve the bowling
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+so what we're going to do is think about
+
+ align:start position:0%
+so what we're going to do is think about
+ 
+
+ align:start position:0%
+so what we're going to do is think about
+i prefer suffixes usually
+
+ align:start position:0%
+i prefer suffixes usually
+ 
+
+ align:start position:0%
+i prefer suffixes usually
+because i like to work from left to
+
+ align:start position:0%
+because i like to work from left to
+ 
+
+ align:start position:0%
+because i like to work from left to
+right from the beginning to the end
+
+ align:start position:0%
+right from the beginning to the end
+ 
+
+ align:start position:0%
+right from the beginning to the end
+so we're going to think of a suffix of
+
+ align:start position:0%
+so we're going to think of a suffix of
+ 
+
+ align:start position:0%
+so we're going to think of a suffix of
+the bowling pins
+
+ align:start position:0%
+the bowling pins
+ 
+
+ align:start position:0%
+the bowling pins
+and so what is the sub problem on a
+
+ align:start position:0%
+and so what is the sub problem on a
+ 
+
+ align:start position:0%
+and so what is the sub problem on a
+suffix well
+
+ align:start position:0%
+suffix well
+ 
+
+ align:start position:0%
+suffix well
+a natural version is just to solve the
+
+ align:start position:0%
+a natural version is just to solve the
+ 
+
+ align:start position:0%
+a natural version is just to solve the
+original problem
+
+ align:start position:0%
+original problem
+ 
+
+ align:start position:0%
+original problem
+bowling how do i maximize my score if
+
+ align:start position:0%
+bowling how do i maximize my score if
+ 
+
+ align:start position:0%
+bowling how do i maximize my score if
+all i were given were these pins
+
+ align:start position:0%
+all i were given were these pins
+ 
+
+ align:start position:0%
+all i were given were these pins
+suppose the pins to the left of i didn't
+
+ align:start position:0%
+suppose the pins to the left of i didn't
+ 
+
+ align:start position:0%
+suppose the pins to the left of i didn't
+exist
+
+ align:start position:0%
+exist
+ 
+
+ align:start position:0%
+exist
+how would i maximize my score on the
+
+ align:start position:0%
+how would i maximize my score on the
+ 
+
+ align:start position:0%
+how would i maximize my score on the
+remaining pins or for this suffix
+
+ align:start position:0%
+remaining pins or for this suffix
+ 
+
+ align:start position:0%
+remaining pins or for this suffix
+given these four pins what would i do
+
+ align:start position:0%
+given these four pins what would i do
+ 
+
+ align:start position:0%
+given these four pins what would i do
+and there's some weird sub problems here
+
+ align:start position:0%
+and there's some weird sub problems here
+ 
+
+ align:start position:0%
+and there's some weird sub problems here
+right if i just gave you the last pin
+
+ align:start position:0%
+right if i just gave you the last pin
+ 
+
+ align:start position:0%
+right if i just gave you the last pin
+what would you do
+
+ align:start position:0%
+what would you do
+ 
+
+ align:start position:0%
+what would you do
+nothing that's clearly different from
+
+ align:start position:0%
+nothing that's clearly different from
+ 
+
+ align:start position:0%
+nothing that's clearly different from
+what i would do globally here
+
+ align:start position:0%
+what i would do globally here
+ 
+
+ align:start position:0%
+what i would do globally here
+but i claim if i can solve all suffixes
+
+ align:start position:0%
+but i claim if i can solve all suffixes
+ 
+
+ align:start position:0%
+but i claim if i can solve all suffixes
+i can solve my original problem because
+
+ align:start position:0%
+i can solve my original problem because
+ 
+
+ align:start position:0%
+i can solve my original problem because
+one of the suffixes is the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+so let's do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort bot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for bowling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's our dynamic program uh the sub
+
+ align:start position:0%
+so here's our dynamic program uh the sub
+ 
+
+ align:start position:0%
+so here's our dynamic program uh the sub
+problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are suffixes so um
+
+ align:start position:0%
+are suffixes so um
+ 
+
+ align:start position:0%
+are suffixes so um
+all right b of i is the maximum score we
+
+ align:start position:0%
+all right b of i is the maximum score we
+ 
+
+ align:start position:0%
+all right b of i is the maximum score we
+could get
+
+ align:start position:0%
+could get
+ 
+
+ align:start position:0%
+could get
+possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with our starting
+
+ align:start position:0%
+with our starting
+ 
+
+ align:start position:0%
+with our starting
+if we started a game with pins
+
+ align:start position:0%
+if we started a game with pins
+ 
+
+ align:start position:0%
+if we started a game with pins
+um i i plus one up to
+
+ align:start position:0%
+um i i plus one up to
+ 
+
+ align:start position:0%
+um i i plus one up to
+n minus one okay which is a suffix of
+
+ align:start position:0%
+n minus one okay which is a suffix of
+ 
+
+ align:start position:0%
+n minus one okay which is a suffix of
+the pins
+
+ align:start position:0%
+the pins
+ 
+
+ align:start position:0%
+the pins
+very important whenever you write a
+
+ align:start position:0%
+very important whenever you write a
+ 
+
+ align:start position:0%
+very important whenever you write a
+dynamic program to define what your
+
+ align:start position:0%
+dynamic program to define what your
+ 
+
+ align:start position:0%
+dynamic program to define what your
+sub-problems are don't just say how to
+
+ align:start position:0%
+sub-problems are don't just say how to
+ 
+
+ align:start position:0%
+sub-problems are don't just say how to
+compute them
+
+ align:start position:0%
+compute them
+ 
+
+ align:start position:0%
+compute them
+but first say what is the goal of the
+
+ align:start position:0%
+but first say what is the goal of the
+ 
+
+ align:start position:0%
+but first say what is the goal of the
+subproblem this is a common mistake to
+
+ align:start position:0%
+subproblem this is a common mistake to
+ 
+
+ align:start position:0%
+subproblem this is a common mistake to
+forget
+
+ align:start position:0%
+forget
+ 
+
+ align:start position:0%
+forget
+to state what you're trying to do so now
+
+ align:start position:0%
+to state what you're trying to do so now
+ 
+
+ align:start position:0%
+to state what you're trying to do so now
+i have to find
+
+ align:start position:0%
+i have to find
+ 
+
+ align:start position:0%
+i have to find
+b of i um now what is the
+
+ align:start position:0%
+b of i um now what is the
+ 
+
+ align:start position:0%
+b of i um now what is the
+original thing i'm trying to solve i
+
+ align:start position:0%
+original thing i'm trying to solve i
+ 
+
+ align:start position:0%
+original thing i'm trying to solve i
+like to you can you can also put in sort
+
+ align:start position:0%
+like to you can you can also put in sort
+ 
+
+ align:start position:0%
+like to you can you can also put in sort
+by you could put the o
+
+ align:start position:0%
+by you could put the o
+ 
+
+ align:start position:0%
+by you could put the o
+earlier also then it's actually spell
+
+ align:start position:0%
+earlier also then it's actually spell
+ 
+
+ align:start position:0%
+earlier also then it's actually spell
+sort so why don't i do that for fun
+
+ align:start position:0%
+sort so why don't i do that for fun
+ 
+
+ align:start position:0%
+sort so why don't i do that for fun
+the original problem we're trying to
+
+ align:start position:0%
+the original problem we're trying to
+ 
+
+ align:start position:0%
+the original problem we're trying to
+solve is b
+
+ align:start position:0%
+solve is b
+ 
+
+ align:start position:0%
+solve is b
+of zero right because that is all of the
+
+ align:start position:0%
+of zero right because that is all of the
+ 
+
+ align:start position:0%
+of zero right because that is all of the
+pins the suffix starting at zero is
+
+ align:start position:0%
+pins the suffix starting at zero is
+ 
+
+ align:start position:0%
+pins the suffix starting at zero is
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+so if we can solve that we're done next
+
+ align:start position:0%
+so if we can solve that we're done next
+ 
+
+ align:start position:0%
+so if we can solve that we're done next
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+r for relate this
+
+ align:start position:0%
+r for relate this
+ 
+
+ align:start position:0%
+r for relate this
+is the test of did i get the sub
+
+ align:start position:0%
+is the test of did i get the sub
+ 
+
+ align:start position:0%
+is the test of did i get the sub
+problems right is whether i can write
+
+ align:start position:0%
+problems right is whether i can write
+ 
+
+ align:start position:0%
+problems right is whether i can write
+a recurrence relation so let's try to do
+
+ align:start position:0%
+a recurrence relation so let's try to do
+ 
+
+ align:start position:0%
+a recurrence relation so let's try to do
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+we want to compute b of i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have pin i here
+
+ align:start position:0%
+so we have pin i here
+ 
+
+ align:start position:0%
+so we have pin i here
+and then the remaining pins
+
+ align:start position:0%
+and then the remaining pins
+ 
+
+ align:start position:0%
+and then the remaining pins
+and the big idea here is to just think
+
+ align:start position:0%
+and the big idea here is to just think
+ 
+
+ align:start position:0%
+and the big idea here is to just think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+the nice thing about suffixes is if i
+
+ align:start position:0%
+the nice thing about suffixes is if i
+ 
+
+ align:start position:0%
+the nice thing about suffixes is if i
+take off something from the beginning
+
+ align:start position:0%
+take off something from the beginning
+ 
+
+ align:start position:0%
+take off something from the beginning
+i still have a suffix remember my goal
+
+ align:start position:0%
+i still have a suffix remember my goal
+ 
+
+ align:start position:0%
+i still have a suffix remember my goal
+is to take this sub problem which is
+
+ align:start position:0%
+is to take this sub problem which is
+ 
+
+ align:start position:0%
+is to take this sub problem which is
+the suffix starting at i and reduce it
+
+ align:start position:0%
+the suffix starting at i and reduce it
+ 
+
+ align:start position:0%
+the suffix starting at i and reduce it
+to a smaller sub problem which means a
+
+ align:start position:0%
+to a smaller sub problem which means a
+ 
+
+ align:start position:0%
+to a smaller sub problem which means a
+smaller suffix
+
+ align:start position:0%
+smaller suffix
+ 
+
+ align:start position:0%
+smaller suffix
+so i'd like to clip off a couple one or
+
+ align:start position:0%
+so i'd like to clip off a couple one or
+ 
+
+ align:start position:0%
+so i'd like to clip off a couple one or
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+items here and then the remaining
+
+ align:start position:0%
+items here and then the remaining
+ 
+
+ align:start position:0%
+items here and then the remaining
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+will be one of my sub problems i'll be
+
+ align:start position:0%
+will be one of my sub problems i'll be
+ 
+
+ align:start position:0%
+will be one of my sub problems i'll be
+able to recursively call b of something
+
+ align:start position:0%
+able to recursively call b of something
+ 
+
+ align:start position:0%
+able to recursively call b of something
+smaller than i
+
+ align:start position:0%
+smaller than i
+ 
+
+ align:start position:0%
+smaller than i
+or sorry b of something larger than i
+
+ align:start position:0%
+or sorry b of something larger than i
+ 
+
+ align:start position:0%
+or sorry b of something larger than i
+will be a smaller subsequence because
+
+ align:start position:0%
+will be a smaller subsequence because
+ 
+
+ align:start position:0%
+will be a smaller subsequence because
+we're starting later
+
+ align:start position:0%
+we're starting later
+ 
+
+ align:start position:0%
+we're starting later
+okay so what could i do well the idea is
+
+ align:start position:0%
+okay so what could i do well the idea is
+ 
+
+ align:start position:0%
+okay so what could i do well the idea is
+to just look at pin eye and think
+
+ align:start position:0%
+to just look at pin eye and think
+ 
+
+ align:start position:0%
+to just look at pin eye and think
+what what could i do to pin i i could
+
+ align:start position:0%
+what what could i do to pin i i could
+ 
+
+ align:start position:0%
+what what could i do to pin i i could
+not hit it ever with a ball i could skip
+
+ align:start position:0%
+not hit it ever with a ball i could skip
+ 
+
+ align:start position:0%
+not hit it ever with a ball i could skip
+it that's one option what would be my
+
+ align:start position:0%
+it that's one option what would be my
+ 
+
+ align:start position:0%
+it that's one option what would be my
+score then
+
+ align:start position:0%
+score then
+ 
+
+ align:start position:0%
+score then
+well i if i skip pin i
+
+ align:start position:0%
+well i if i skip pin i
+ 
+
+ align:start position:0%
+well i if i skip pin i
+that leaves the remaining pins which is
+
+ align:start position:0%
+that leaves the remaining pins which is
+ 
+
+ align:start position:0%
+that leaves the remaining pins which is
+just a smaller suffix
+
+ align:start position:0%
+just a smaller suffix
+ 
+
+ align:start position:0%
+just a smaller suffix
+so that is uh b of i plus one
+
+ align:start position:0%
+so that is uh b of i plus one
+ 
+
+ align:start position:0%
+so that is uh b of i plus one
+i'm going to write a max out here
+
+ align:start position:0%
+i'm going to write a max out here
+ 
+
+ align:start position:0%
+i'm going to write a max out here
+because i'd like to maximize my score
+
+ align:start position:0%
+because i'd like to maximize my score
+ 
+
+ align:start position:0%
+because i'd like to maximize my score
+and one of the options is
+
+ align:start position:0%
+and one of the options is
+ 
+
+ align:start position:0%
+and one of the options is
+forget about pin i just solve the rest
+
+ align:start position:0%
+forget about pin i just solve the rest
+ 
+
+ align:start position:0%
+forget about pin i just solve the rest
+another option is i
+
+ align:start position:0%
+another option is i
+ 
+
+ align:start position:0%
+another option is i
+throw a ball and i exactly hit pin i
+
+ align:start position:0%
+throw a ball and i exactly hit pin i
+ 
+
+ align:start position:0%
+throw a ball and i exactly hit pin i
+that's a thing i could do and it would
+
+ align:start position:0%
+that's a thing i could do and it would
+ 
+
+ align:start position:0%
+that's a thing i could do and it would
+it would leave exactly the same
+
+ align:start position:0%
+it would leave exactly the same
+ 
+
+ align:start position:0%
+it would leave exactly the same
+remainder
+
+ align:start position:0%
+remainder
+ 
+
+ align:start position:0%
+remainder
+so another option is b of i plus 1
+
+ align:start position:0%
+so another option is b of i plus 1
+ 
+
+ align:start position:0%
+so another option is b of i plus 1
+plus v i uh why would i prefer this over
+
+ align:start position:0%
+plus v i uh why would i prefer this over
+ 
+
+ align:start position:0%
+plus v i uh why would i prefer this over
+this well if v i is negative
+
+ align:start position:0%
+this well if v i is negative
+ 
+
+ align:start position:0%
+this well if v i is negative
+i'd prefer this but if u is positive
+
+ align:start position:0%
+i'd prefer this but if u is positive
+ 
+
+ align:start position:0%
+i'd prefer this but if u is positive
+i'd actually prefer this over that okay
+
+ align:start position:0%
+i'd actually prefer this over that okay
+ 
+
+ align:start position:0%
+i'd actually prefer this over that okay
+so you're going to figure out which is
+
+ align:start position:0%
+so you're going to figure out which is
+ 
+
+ align:start position:0%
+so you're going to figure out which is
+which is better just locally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then there's another thing i can do
+
+ align:start position:0%
+but then there's another thing i can do
+ 
+
+ align:start position:0%
+but then there's another thing i can do
+which is maybe i hit this pin
+
+ align:start position:0%
+which is maybe i hit this pin
+ 
+
+ align:start position:0%
+which is maybe i hit this pin
+in a pair with some other pin now
+
+ align:start position:0%
+in a pair with some other pin now
+ 
+
+ align:start position:0%
+in a pair with some other pin now
+there's no pin to the left of this one
+
+ align:start position:0%
+there's no pin to the left of this one
+ 
+
+ align:start position:0%
+there's no pin to the left of this one
+we're assuming we only have the suffix
+
+ align:start position:0%
+we're assuming we only have the suffix
+ 
+
+ align:start position:0%
+we're assuming we only have the suffix
+and so the only other thing i can do is
+
+ align:start position:0%
+and so the only other thing i can do is
+ 
+
+ align:start position:0%
+and so the only other thing i can do is
+throw a ball and hit
+
+ align:start position:0%
+throw a ball and hit
+ 
+
+ align:start position:0%
+throw a ball and hit
+i together with i plus one and then i
+
+ align:start position:0%
+i together with i plus one and then i
+ 
+
+ align:start position:0%
+i together with i plus one and then i
+get the product
+
+ align:start position:0%
+get the product
+ 
+
+ align:start position:0%
+get the product
+now what pins remain i plus two on still
+
+ align:start position:0%
+now what pins remain i plus two on still
+ 
+
+ align:start position:0%
+now what pins remain i plus two on still
+a suffix
+
+ align:start position:0%
+a suffix
+ 
+
+ align:start position:0%
+a suffix
+so if i remove one or two items of
+
+ align:start position:0%
+so if i remove one or two items of
+ 
+
+ align:start position:0%
+so if i remove one or two items of
+course i still get a suffix
+
+ align:start position:0%
+course i still get a suffix
+ 
+
+ align:start position:0%
+course i still get a suffix
+in this case b of i plus two and then
+
+ align:start position:0%
+in this case b of i plus two and then
+ 
+
+ align:start position:0%
+in this case b of i plus two and then
+the number of
+
+ align:start position:0%
+the number of
+ 
+
+ align:start position:0%
+the number of
+points that i add on are vi times vi
+
+ align:start position:0%
+points that i add on are vi times vi
+ 
+
+ align:start position:0%
+points that i add on are vi times vi
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+so this is a max of three things
+
+ align:start position:0%
+so this is a max of three things
+ 
+
+ align:start position:0%
+so this is a max of three things
+so how long does it take me to compute
+
+ align:start position:0%
+so how long does it take me to compute
+ 
+
+ align:start position:0%
+so how long does it take me to compute
+it i claim
+
+ align:start position:0%
+it i claim
+ 
+
+ align:start position:0%
+it i claim
+constant time if i don't count the time
+
+ align:start position:0%
+constant time if i don't count the time
+ 
+
+ align:start position:0%
+constant time if i don't count the time
+it takes to compute these other
+
+ align:start position:0%
+it takes to compute these other
+ 
+
+ align:start position:0%
+it takes to compute these other
+subproblems which are smaller
+
+ align:start position:0%
+subproblems which are smaller
+ 
+
+ align:start position:0%
+subproblems which are smaller
+because they are smaller suffixes
+
+ align:start position:0%
+because they are smaller suffixes
+ 
+
+ align:start position:0%
+because they are smaller suffixes
+further to the right
+
+ align:start position:0%
+further to the right
+ 
+
+ align:start position:0%
+further to the right
+uh then i'm doing you know a couple of
+
+ align:start position:0%
+uh then i'm doing you know a couple of
+ 
+
+ align:start position:0%
+uh then i'm doing you know a couple of
+additions product
+
+ align:start position:0%
+additions product
+ 
+
+ align:start position:0%
+additions product
+max these are all nice numbers they will
+
+ align:start position:0%
+max these are all nice numbers they will
+ 
+
+ align:start position:0%
+max these are all nice numbers they will
+assume that they live in a w
+
+ align:start position:0%
+assume that they live in a w
+ 
+
+ align:start position:0%
+assume that they live in a w
+bit word um because they're only doing
+
+ align:start position:0%
+bit word um because they're only doing
+ 
+
+ align:start position:0%
+bit word um because they're only doing
+constant size products that's good
+
+ align:start position:0%
+constant size products that's good
+ 
+
+ align:start position:0%
+constant size products that's good
+uh so this takes constant constant
+
+ align:start position:0%
+uh so this takes constant constant
+ 
+
+ align:start position:0%
+uh so this takes constant constant
+non-recursive work
+
+ align:start position:0%
+non-recursive work
+ 
+
+ align:start position:0%
+non-recursive work
+how many sub-problems are but suffixes
+
+ align:start position:0%
+how many sub-problems are but suffixes
+ 
+
+ align:start position:0%
+how many sub-problems are but suffixes
+so it's a linear number of sub-problems
+
+ align:start position:0%
+so it's a linear number of sub-problems
+ 
+
+ align:start position:0%
+so it's a linear number of sub-problems
+and so the time i'm going to end up
+
+ align:start position:0%
+and so the time i'm going to end up
+ 
+
+ align:start position:0%
+and so the time i'm going to end up
+needing
+
+ align:start position:0%
+needing
+ 
+
+ align:start position:0%
+needing
+is the number of sub-problems n times
+
+ align:start position:0%
+is the number of sub-problems n times
+ 
+
+ align:start position:0%
+is the number of sub-problems n times
+the non-recursive work i do per sub
+
+ align:start position:0%
+the non-recursive work i do per sub
+ 
+
+ align:start position:0%
+the non-recursive work i do per sub
+problem which is constant
+
+ align:start position:0%
+problem which is constant
+ 
+
+ align:start position:0%
+problem which is constant
+and so this is linear time
+
+ align:start position:0%
+and so this is linear time
+ 
+
+ align:start position:0%
+and so this is linear time
+great now i didn't finish sort bot so
+
+ align:start position:0%
+great now i didn't finish sort bot so
+ 
+
+ align:start position:0%
+great now i didn't finish sort bot so
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+another t which is to make sure that
+
+ align:start position:0%
+another t which is to make sure that
+ 
+
+ align:start position:0%
+another t which is to make sure that
+there is a topological order
+
+ align:start position:0%
+there is a topological order
+ 
+
+ align:start position:0%
+there is a topological order
+and that is in decreasing i order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or i might write that as a for loop
+
+ align:start position:0%
+or i might write that as a for loop
+ 
+
+ align:start position:0%
+or i might write that as a for loop
+for i equals n n minus 1.
+
+ align:start position:0%
+for i equals n n minus 1.
+ 
+
+ align:start position:0%
+for i equals n n minus 1.
+this is the order that i would compute
+
+ align:start position:0%
+this is the order that i would compute
+ 
+
+ align:start position:0%
+this is the order that i would compute
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+my problems because the suffix starting
+
+ align:start position:0%
+my problems because the suffix starting
+ 
+
+ align:start position:0%
+my problems because the suffix starting
+at n is the empty suffix
+
+ align:start position:0%
+at n is the empty suffix
+ 
+
+ align:start position:0%
+at n is the empty suffix
+the suffix starting at zero that's the
+
+ align:start position:0%
+the suffix starting at zero that's the
+ 
+
+ align:start position:0%
+the suffix starting at zero that's the
+one i actually want to compute that's
+
+ align:start position:0%
+one i actually want to compute that's
+ 
+
+ align:start position:0%
+one i actually want to compute that's
+the final suffix i should be computing
+
+ align:start position:0%
+the final suffix i should be computing
+ 
+
+ align:start position:0%
+the final suffix i should be computing
+and then we have a b for base case
+
+ align:start position:0%
+and then we have a b for base case
+ 
+
+ align:start position:0%
+and then we have a b for base case
+which is that first case b of n
+
+ align:start position:0%
+which is that first case b of n
+ 
+
+ align:start position:0%
+which is that first case b of n
+equals uh zero
+
+ align:start position:0%
+equals uh zero
+ 
+
+ align:start position:0%
+equals uh zero
+because there's no pins so i don't get
+
+ align:start position:0%
+because there's no pins so i don't get
+ 
+
+ align:start position:0%
+because there's no pins so i don't get
+any points
+
+ align:start position:0%
+any points
+ 
+
+ align:start position:0%
+any points
+sad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is it we just take these
+
+ align:start position:0%
+okay so this is it we just take these
+ 
+
+ align:start position:0%
+okay so this is it we just take these
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+plug them into this recursive memoized
+
+ align:start position:0%
+plug them into this recursive memoized
+ 
+
+ align:start position:0%
+plug them into this recursive memoized
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+and we have a linear time algorithm i
+
+ align:start position:0%
+and we have a linear time algorithm i
+ 
+
+ align:start position:0%
+and we have a linear time algorithm i
+want to briefly mention
+
+ align:start position:0%
+want to briefly mention
+ 
+
+ align:start position:0%
+want to briefly mention
+a different way you could plug together
+
+ align:start position:0%
+a different way you could plug together
+ 
+
+ align:start position:0%
+a different way you could plug together
+those pieces which is called bottom up
+
+ align:start position:0%
+those pieces which is called bottom up
+ 
+
+ align:start position:0%
+those pieces which is called bottom up
+dp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is uh let's do it for this example
+
+ align:start position:0%
+which is uh let's do it for this example
+ 
+
+ align:start position:0%
+which is uh let's do it for this example
+so if i have um
+
+ align:start position:0%
+so if i have um
+ 
+
+ align:start position:0%
+so if i have um
+let's see let me start with the base
+
+ align:start position:0%
+let's see let me start with the base
+ 
+
+ align:start position:0%
+let's see let me start with the base
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+b of n equals zero but now it's an
+
+ align:start position:0%
+b of n equals zero but now it's an
+ 
+
+ align:start position:0%
+b of n equals zero but now it's an
+assignment
+
+ align:start position:0%
+assignment
+ 
+
+ align:start position:0%
+assignment
+and i'm going to do the for loop from
+
+ align:start position:0%
+and i'm going to do the for loop from
+ 
+
+ align:start position:0%
+and i'm going to do the for loop from
+the topological order for i equals
+
+ align:start position:0%
+the topological order for i equals
+ 
+
+ align:start position:0%
+the topological order for i equals
+m n minus 1 to 0.
+
+ align:start position:0%
+m n minus 1 to 0.
+ 
+
+ align:start position:0%
+m n minus 1 to 0.
+now i'm going to do the relation b of i
+
+ align:start position:0%
+now i'm going to do the relation b of i
+ 
+
+ align:start position:0%
+now i'm going to do the relation b of i
+equals max of b of i plus 1
+
+ align:start position:0%
+equals max of b of i plus 1
+ 
+
+ align:start position:0%
+equals max of b of i plus 1
+and b of i plus uh
+
+ align:start position:0%
+and b of i plus uh
+ 
+
+ align:start position:0%
+and b of i plus uh
+1 plus v i and v of i plus 2
+
+ align:start position:0%
+1 plus v i and v of i plus 2
+ 
+
+ align:start position:0%
+1 plus v i and v of i plus 2
+plus v i v i plus 1.
+
+ align:start position:0%
+plus v i v i plus 1.
+ 
+
+ align:start position:0%
+plus v i v i plus 1.
+technically this only works if i is
+
+ align:start position:0%
+technically this only works if i is
+ 
+
+ align:start position:0%
+technically this only works if i is
+strictly less than n minus 1.
+
+ align:start position:0%
+strictly less than n minus 1.
+ 
+
+ align:start position:0%
+strictly less than n minus 1.
+so i should have an if i is less than n
+
+ align:start position:0%
+so i should have an if i is less than n
+ 
+
+ align:start position:0%
+so i should have an if i is less than n
+minus 1 for that last part
+
+ align:start position:0%
+minus 1 for that last part
+ 
+
+ align:start position:0%
+minus 1 for that last part
+because i can only do i can only hit two
+
+ align:start position:0%
+because i can only do i can only hit two
+ 
+
+ align:start position:0%
+because i can only do i can only hit two
+pins if there's at least two pins left
+
+ align:start position:0%
+pins if there's at least two pins left
+ 
+
+ align:start position:0%
+pins if there's at least two pins left
+and then return
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b of zero so what i just did is a
+
+ align:start position:0%
+b of zero so what i just did is a
+ 
+
+ align:start position:0%
+b of zero so what i just did is a
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+from this sort bot template into
+
+ align:start position:0%
+from this sort bot template into
+ 
+
+ align:start position:0%
+from this sort bot template into
+a non-recursive algorithm a for loop
+
+ align:start position:0%
+a non-recursive algorithm a for loop
+ 
+
+ align:start position:0%
+a non-recursive algorithm a for loop
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+where i wrote my base case first then i
+
+ align:start position:0%
+where i wrote my base case first then i
+ 
+
+ align:start position:0%
+where i wrote my base case first then i
+did my
+
+ align:start position:0%
+did my
+ 
+
+ align:start position:0%
+did my
+topological order then i did my
+
+ align:start position:0%
+topological order then i did my
+ 
+
+ align:start position:0%
+topological order then i did my
+relation then at the end i did my base
+
+ align:start position:0%
+relation then at the end i did my base
+ 
+
+ align:start position:0%
+relation then at the end i did my base
+not base case the original problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and provided you can write your
+
+ align:start position:0%
+and provided you can write your
+ 
+
+ align:start position:0%
+and provided you can write your
+topological order as some for loops
+
+ align:start position:0%
+topological order as some for loops
+ 
+
+ align:start position:0%
+topological order as some for loops
+this is actually a great way to write
+
+ align:start position:0%
+this is actually a great way to write
+ 
+
+ align:start position:0%
+this is actually a great way to write
+down a dp as code if i were going to
+
+ align:start position:0%
+down a dp as code if i were going to
+ 
+
+ align:start position:0%
+down a dp as code if i were going to
+implement this algorithm i would write
+
+ align:start position:0%
+implement this algorithm i would write
+ 
+
+ align:start position:0%
+implement this algorithm i would write
+it this way because this is super fast
+
+ align:start position:0%
+it this way because this is super fast
+ 
+
+ align:start position:0%
+it this way because this is super fast
+no recursive calls
+
+ align:start position:0%
+no recursive calls
+ 
+
+ align:start position:0%
+no recursive calls
+just one for loop in fact this is almost
+
+ align:start position:0%
+just one for loop in fact this is almost
+ 
+
+ align:start position:0%
+just one for loop in fact this is almost
+a trivial algorithm it's amazing that
+
+ align:start position:0%
+a trivial algorithm it's amazing that
+ 
+
+ align:start position:0%
+a trivial algorithm it's amazing that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+solves the bowling problem
+
+ align:start position:0%
+solves the bowling problem
+ 
+
+ align:start position:0%
+solves the bowling problem
+it's in some sense considering every
+
+ align:start position:0%
+it's in some sense considering every
+ 
+
+ align:start position:0%
+it's in some sense considering every
+possible strategy i could
+
+ align:start position:0%
+possible strategy i could
+ 
+
+ align:start position:0%
+possible strategy i could
+for bowling these pins what we're using
+
+ align:start position:0%
+for bowling these pins what we're using
+ 
+
+ align:start position:0%
+for bowling these pins what we're using
+is what we like to call
+
+ align:start position:0%
+is what we like to call
+ 
+
+ align:start position:0%
+is what we like to call
+local brute force where when we think
+
+ align:start position:0%
+local brute force where when we think
+ 
+
+ align:start position:0%
+local brute force where when we think
+about pin
+
+ align:start position:0%
+about pin
+ 
+
+ align:start position:0%
+about pin
+i we look at all of the possible things
+
+ align:start position:0%
+i we look at all of the possible things
+ 
+
+ align:start position:0%
+i we look at all of the possible things
+i could do to pin i
+
+ align:start position:0%
+i could do to pin i
+ 
+
+ align:start position:0%
+i could do to pin i
+here there's really only three options
+
+ align:start position:0%
+here there's really only three options
+ 
+
+ align:start position:0%
+here there's really only three options
+of what i could do
+
+ align:start position:0%
+of what i could do
+ 
+
+ align:start position:0%
+of what i could do
+now normally if i if i tried all the
+
+ align:start position:0%
+now normally if i if i tried all the
+ 
+
+ align:start position:0%
+now normally if i if i tried all the
+options for pin i
+
+ align:start position:0%
+options for pin i
+ 
+
+ align:start position:0%
+options for pin i
+and then all the options for i plus 1
+
+ align:start position:0%
+and then all the options for i plus 1
+ 
+
+ align:start position:0%
+and then all the options for i plus 1
+and i plus 2 and so on that would be
+
+ align:start position:0%
+and i plus 2 and so on that would be
+ 
+
+ align:start position:0%
+and i plus 2 and so on that would be
+exponential it'd be 3 times 3 times 3
+
+ align:start position:0%
+exponential it'd be 3 times 3 times 3
+ 
+
+ align:start position:0%
+exponential it'd be 3 times 3 times 3
+that's bad but because i can reuse these
+
+ align:start position:0%
+that's bad but because i can reuse these
+ 
+
+ align:start position:0%
+that's bad but because i can reuse these
+sub problems
+
+ align:start position:0%
+sub problems
+ 
+
+ align:start position:0%
+sub problems
+it turns out to only be linear time it's
+
+ align:start position:0%
+it turns out to only be linear time it's
+ 
+
+ align:start position:0%
+it turns out to only be linear time it's
+almost like
+
+ align:start position:0%
+almost like
+ 
+
+ align:start position:0%
+almost like
+magic dp
+
+ align:start position:0%
+magic dp
+ 
+
+ align:start position:0%
+magic dp
+dp dp is essentially an idea of
+
+ align:start position:0%
+dp dp is essentially an idea of
+ 
+
+ align:start position:0%
+dp dp is essentially an idea of
+using local brute force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and by defining a small number of sub
+
+ align:start position:0%
+and by defining a small number of sub
+ 
+
+ align:start position:0%
+and by defining a small number of sub
+problems up front and
+
+ align:start position:0%
+problems up front and
+ 
+
+ align:start position:0%
+problems up front and
+as long as i stay within those sub
+
+ align:start position:0%
+as long as i stay within those sub
+ 
+
+ align:start position:0%
+as long as i stay within those sub
+problems as long as i'm always recursing
+
+ align:start position:0%
+problems as long as i'm always recursing
+ 
+
+ align:start position:0%
+problems as long as i'm always recursing
+into this polynomial space
+
+ align:start position:0%
+into this polynomial space
+ 
+
+ align:start position:0%
+into this polynomial space
+i end up only doing polynomial work even
+
+ align:start position:0%
+i end up only doing polynomial work even
+ 
+
+ align:start position:0%
+i end up only doing polynomial work even
+though i'm in some sense exploring
+
+ align:start position:0%
+though i'm in some sense exploring
+ 
+
+ align:start position:0%
+though i'm in some sense exploring
+exponentially many options
+
+ align:start position:0%
+exponentially many options
+ 
+
+ align:start position:0%
+exponentially many options
+and it's it's because what i do for this
+
+ align:start position:0%
+and it's it's because what i do for this
+ 
+
+ align:start position:0%
+and it's it's because what i do for this
+pin doesn't depend
+
+ align:start position:0%
+pin doesn't depend
+ 
+
+ align:start position:0%
+pin doesn't depend
+too much to what i do to a pin much
+
+ align:start position:0%
+too much to what i do to a pin much
+ 
+
+ align:start position:0%
+too much to what i do to a pin much
+later and there's a lot of intuition
+
+ align:start position:0%
+later and there's a lot of intuition
+ 
+
+ align:start position:0%
+later and there's a lot of intuition
+going on here for what
+
+ align:start position:0%
+going on here for what
+ 
+
+ align:start position:0%
+going on here for what
+uh when dp works but we're going to see
+
+ align:start position:0%
+uh when dp works but we're going to see
+ 
+
+ align:start position:0%
+uh when dp works but we're going to see
+a lot more examples of that
+
+ align:start position:0%
+a lot more examples of that
+ 
+
+ align:start position:0%
+a lot more examples of that
+coming up and i just want to mention
+
+ align:start position:0%
+coming up and i just want to mention
+ 
+
+ align:start position:0%
+coming up and i just want to mention
+that the intuition for how to write a
+
+ align:start position:0%
+that the intuition for how to write a
+ 
+
+ align:start position:0%
+that the intuition for how to write a
+recurrence like this
+
+ align:start position:0%
+recurrence like this
+ 
+
+ align:start position:0%
+recurrence like this
+is to think about in the case of
+
+ align:start position:0%
+is to think about in the case of
+ 
+
+ align:start position:0%
+is to think about in the case of
+suffixes you always want to think about
+
+ align:start position:0%
+suffixes you always want to think about
+ 
+
+ align:start position:0%
+suffixes you always want to think about
+the first item
+
+ align:start position:0%
+the first item
+ 
+
+ align:start position:0%
+the first item
+or maybe the first couple items the case
+
+ align:start position:0%
+or maybe the first couple items the case
+ 
+
+ align:start position:0%
+or maybe the first couple items the case
+of prefixes you always think about the
+
+ align:start position:0%
+of prefixes you always think about the
+ 
+
+ align:start position:0%
+of prefixes you always think about the
+last item
+
+ align:start position:0%
+last item
+ 
+
+ align:start position:0%
+last item
+and for sub strings it's could be any
+
+ align:start position:0%
+and for sub strings it's could be any
+ 
+
+ align:start position:0%
+and for sub strings it's could be any
+item maybe in the middle
+
+ align:start position:0%
+item maybe in the middle
+ 
+
+ align:start position:0%
+item maybe in the middle
+if i remove an item from the middle of
+
+ align:start position:0%
+if i remove an item from the middle of
+ 
+
+ align:start position:0%
+if i remove an item from the middle of
+the substring i get two substrings so i
+
+ align:start position:0%
+the substring i get two substrings so i
+ 
+
+ align:start position:0%
+the substring i get two substrings so i
+can recurse
+
+ align:start position:0%
+can recurse
+ 
+
+ align:start position:0%
+can recurse
+here or in general what we want to do is
+
+ align:start position:0%
+here or in general what we want to do is
+ 
+
+ align:start position:0%
+here or in general what we want to do is
+identify
+
+ align:start position:0%
+identify
+ 
+
+ align:start position:0%
+identify
+some feature of the solution that if we
+
+ align:start position:0%
+some feature of the solution that if we
+ 
+
+ align:start position:0%
+some feature of the solution that if we
+knew that feature
+
+ align:start position:0%
+knew that feature
+ 
+
+ align:start position:0%
+knew that feature
+we would be done we would reduce to a
+
+ align:start position:0%
+we would be done we would reduce to a
+ 
+
+ align:start position:0%
+we would be done we would reduce to a
+smaller sub problem
+
+ align:start position:0%
+smaller sub problem
+ 
+
+ align:start position:0%
+smaller sub problem
+in this case we just say well what are
+
+ align:start position:0%
+in this case we just say well what are
+ 
+
+ align:start position:0%
+in this case we just say well what are
+the possible things i could do
+
+ align:start position:0%
+the possible things i could do
+ 
+
+ align:start position:0%
+the possible things i could do
+to the first pin there are three options
+
+ align:start position:0%
+to the first pin there are three options
+ 
+
+ align:start position:0%
+to the first pin there are three options
+if i knew which option it was i would be
+
+ align:start position:0%
+if i knew which option it was i would be
+ 
+
+ align:start position:0%
+if i knew which option it was i would be
+done i could recurse and do my addition
+
+ align:start position:0%
+done i could recurse and do my addition
+ 
+
+ align:start position:0%
+done i could recurse and do my addition
+now i don't know which thing i want to
+
+ align:start position:0%
+now i don't know which thing i want to
+ 
+
+ align:start position:0%
+now i don't know which thing i want to
+do so just try them all
+
+ align:start position:0%
+do so just try them all
+ 
+
+ align:start position:0%
+do so just try them all
+and take the max and if you're
+
+ align:start position:0%
+and take the max and if you're
+ 
+
+ align:start position:0%
+and take the max and if you're
+maximizing you take the max if you're
+
+ align:start position:0%
+maximizing you take the max if you're
+ 
+
+ align:start position:0%
+maximizing you take the max if you're
+minimizing you take them in
+
+ align:start position:0%
+minimizing you take them in
+ 
+
+ align:start position:0%
+minimizing you take them in
+sometimes you take an or or an and there
+
+ align:start position:0%
+sometimes you take an or or an and there
+ 
+
+ align:start position:0%
+sometimes you take an or or an and there
+might be some combination function
+
+ align:start position:0%
+might be some combination function
+ 
+
+ align:start position:0%
+might be some combination function
+for optimization problems where you're
+
+ align:start position:0%
+for optimization problems where you're
+ 
+
+ align:start position:0%
+for optimization problems where you're
+trying to maximize or minimize something
+
+ align:start position:0%
+trying to maximize or minimize something
+ 
+
+ align:start position:0%
+trying to maximize or minimize something
+like shortest paths we're trying to
+
+ align:start position:0%
+like shortest paths we're trying to
+ 
+
+ align:start position:0%
+like shortest paths we're trying to
+minimize we put them in here
+
+ align:start position:0%
+minimize we put them in here
+ 
+
+ align:start position:0%
+minimize we put them in here
+so usually it's min or max and this is
+
+ align:start position:0%
+so usually it's min or max and this is
+ 
+
+ align:start position:0%
+so usually it's min or max and this is
+extremely powerful
+
+ align:start position:0%
+extremely powerful
+ 
+
+ align:start position:0%
+extremely powerful
+uh all you need to do the hard part is
+
+ align:start position:0%
+uh all you need to do the hard part is
+ 
+
+ align:start position:0%
+uh all you need to do the hard part is
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+inspired design part where you say
+
+ align:start position:0%
+inspired design part where you say
+ 
+
+ align:start position:0%
+inspired design part where you say
+what do i need to know that would let me
+
+ align:start position:0%
+what do i need to know that would let me
+ 
+
+ align:start position:0%
+what do i need to know that would let me
+solve my problem
+
+ align:start position:0%
+solve my problem
+ 
+
+ align:start position:0%
+solve my problem
+if you can identify that and the number
+
+ align:start position:0%
+if you can identify that and the number
+ 
+
+ align:start position:0%
+if you can identify that and the number
+of choices for what you need to know
+
+ align:start position:0%
+of choices for what you need to know
+ 
+
+ align:start position:0%
+of choices for what you need to know
+is polynomial then you will be able to
+
+ align:start position:0%
+is polynomial then you will be able to
+ 
+
+ align:start position:0%
+is polynomial then you will be able to
+get a polynomial dynamic program that's
+
+ align:start position:0%
+get a polynomial dynamic program that's
+ 
+
+ align:start position:0%
+get a polynomial dynamic program that's
+the intuition we'll see a lot more
+
+ align:start position:0%
+the intuition we'll see a lot more
+ 
+
+ align:start position:0%
+the intuition we'll see a lot more
+examples
+
+ align:start position:0%
+examples
+ 
+
+ align:start position:0%
+examples
+in the next three lectures
\ No newline at end of file
diff --git a/r5pXu1PAUkI.txt b/r5pXu1PAUkI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3aa041119ab1f0b1e58bd13ffa6924d57a2320fc
--- /dev/null
+++ b/r5pXu1PAUkI.txt
@@ -0,0 +1,3087 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: If you guys
+want me to cover anything
+
+in particular, is
+there anything you
+
+didn't understand in lecture?
+
+In the last section, I
+covered the recursion trees
+
+because they will
+be on the Pset,
+
+and people said they
+were a bit unclear,
+
+so we can do that and cover less
+of the stuff that I have here.
+
+Or if there's anything else,
+you can tell me what you want.
+
+So there I cover recursion
+trees because someone said, hey,
+
+can you go over that again?
+
+Is there any pain points?
+
+No?
+
+OK.
+
+So then I'm going to
+give you the same choice
+
+that I gave to people
+last time, and that
+
+is we can go over
+recursion trees again,
+
+but if I do that, then I
+won't have time to go over
+
+the code for deleting a node
+from a binary search tree.
+
+So we'll go through
+the theory and you guys
+
+will have to go through
+the code on your own.
+
+But instead, we'll go
+over recursion trees again
+
+and remember how you
+solve a recurrence using
+
+recursion trees.
+
+The alternative is
+we don't do that
+
+and we complete
+the deletions part.
+
+AUDIENCE: I feel like
+covering deletions,
+
+since we didn't do that in
+lecture, that would probably
+
+be more helpful.
+
+PROFESSOR: Let's take a vote.
+
+Who wants to do deletions
+in painstaking detail?
+
+So deletions and not recursion?
+
+Who wants to do recursion
+trees and not deletion?
+
+AUDIENCE: It's about equal.
+
+PROFESSOR: It's equal
+and nobody cares.
+
+I'm really sad.
+
+AUDIENCE: Let's do
+both in half detail.
+
+PROFESSOR: OK, sure.
+
+Who remembers merge sort?
+
+What does merge sort
+do really quick?
+
+AUDIENCE: It takes some
+sort of unsorted array,
+
+splits it in half, and
+then continually splits it,
+
+and then once it finally
+gets to the point
+
+where you have arrays of two
+elements, then it sorts them,
+
+and then sorts those,
+and then sorts those.
+
+It's a fun thing.
+
+And then it merges [INAUDIBLE].
+
+PROFESSOR: That's so much code.
+
+I don't like to write much code
+because for every line of code
+
+that you write, you
+might have a bug in it,
+
+so I like to write less code.
+
+So the way I do it is when I
+get to an array size of one
+
+element, I know
+it's already sorted.
+
+So merge sort.
+
+You have an array,
+it's unsorted.
+
+Split it into two halves,
+call merge sort on each half,
+
+assume that magically, they're
+going to come back sorted,
+
+and then you merge
+the sorted halves.
+
+How much time does merging take?
+
+OK.
+
+So the recursion for the
+running time of merge sort?
+
+AUDIENCE: Why does
+it take n time?
+
+Just too large?
+
+AUDIENCE: Isn't it
+the finger thing where
+
+you take each element,
+and you're like, this one,
+
+is that greater or less than,
+then you put it in the array.
+
+So you get--
+
+PROFESSOR: Please take my
+word for it that it's order n.
+
+AUDIENCE: I'll explain it
+and then I'll be confused.
+
+PROFESSOR: OK, so order n.
+
+What's the recursion?
+
+Don't give me the
+solution because then I
+
+can't do the trees anymore,
+so give me the recursion
+
+before it's solved.
+
+Give me the recurrence formula.
+
+So it starts with T of N, right?
+
+AUDIENCE: It starts with
+N over 2 plus N, I think.
+
+PROFESSOR: Perfect.
+
+So you take the array,
+you split it into two,
+
+you call merge sort on the
+two halves of the arrays.
+
+So you call merge sort twice.
+
+That's why you have a 2 here.
+
+The 2 matters.
+
+Without it, you get
+a different answer.
+
+And when you call it,
+the arrays that you
+
+give it are half the
+size, and then merge
+
+takes order and time.
+
+Splitting depends on what you're
+using to store your arrays.
+
+Can be constant time or it
+can be order N. So the time
+
+won't change because of split.
+
+How do we solve this recurrence?
+
+The recursion tree
+method says that we're
+
+going to draw a call graph.
+
+So we start out
+with a call to merge
+
+sort with an array
+of size N. Then
+
+it's going to call
+merge sort again,
+
+but after the array is split.
+
+So it's going to call merge
+sort twice, size is N over 2.
+
+This guy gets an array of
+N over 2, calls merge sort.
+
+Two arrays, sizes
+N over 4, N over 4.
+
+This does the same.
+
+So this goes on forever and ever
+and ever until at some point
+
+we reach our base case.
+
+So we're going to
+have a bunch of calls
+
+here where the array size is?
+
+What's our base case?
+
+1.
+
+Excellent.
+
+So this is the call graph
+for merge sort, and let's
+
+put the base case here so we
+know what we're talking about.
+
+T of 1 is theta 1.
+
+Now inside the
+nodes, we're going
+
+to put the cost for each
+call without counting
+
+the sub-call, so
+the children here.
+
+That's this guy here,
+except instead of order N,
+
+I will write CN.
+
+Remember how sometimes
+we use CN instead
+
+of the order of notation?
+
+The reason we do that is if I
+put in the asymptotic notation,
+
+then we're going to be
+tempted to sum them up.
+
+You're allowed to sum terms
+using asymptotic notation as
+
+long as there's a
+finite number of them,
+
+but here, it turns out there's
+an infinite number of them.
+
+Also, if you go this way,
+you can never go wrong.
+
+You always get the
+right answer, so that's
+
+why we switch from
+order N to CN.
+
+In order to merge sort
+an array of size N,
+
+we're going to merge sort
+two arrays of size N over 2
+
+and then spend CN time
+on doing the merge.
+
+What are the costs here?
+
+To sort an array
+of N over 2, what's
+
+the cost outside
+the cost to merge?
+
+AUDIENCE: C of N over 2.
+
+PROFESSOR: Perfect.
+
+C times N over 2.
+
+C times N over 2.
+
+How about here?
+
+AUDIENCE: C times N over 4.
+
+PROFESSOR: Perfect.
+
+CN over 4.
+
+My nodes are really ugly.
+
+I should have drawn them
+like this from the beginning.
+
+CN over 4.
+
+There you go.
+
+How about down here?
+
+AUDIENCE: C of N
+over 2 to the i.
+
+PROFESSOR: You're
+going on step ahead.
+
+We'll do that right next.
+
+AUDIENCE: C of N
+over log N, right?
+
+Because they're
+log N levels, so--
+
+PROFESSOR: Let's not worry
+about the number of levels.
+
+You're ruining my steps.
+
+I was going to get to
+that two steps after this.
+
+AUDIENCE: Is it just C?
+
+PROFESSOR: Yep.
+
+So array size is 1, right?
+
+So the cost is C. C, C,
+C, C. OK, you guys got it
+
+if you're thinking
+of levels already.
+
+The next thing I
+want to do is I want
+
+to figure out how many
+levels I have in this tree.
+
+Why do I care about that?
+
+The answer for T of N is the
+sum of all these costs in here
+
+because the cost of merge
+sorting an array of size N
+
+is the merge sort plus the costs
+for sorting the two arrays.
+
+And the nodes here keep
+track of all the time spent
+
+in recursive sub-calls, so if
+we can add up everything up,
+
+we have the answer to T of
+N. It turns out the easiest
+
+way to do that is to sum
+up the cost at each level
+
+because the costs are
+this guy copied over here.
+
+For a level, they
+tend to be the same,
+
+so it's reasonably
+easy to add them up,
+
+except in order to be
+able to add those up,
+
+you have to know how
+many levels you have.
+
+So how do I know how
+many levels I have?
+
+Someone already told me log
+N. How do I get to that log N?
+
+So when I get to the
+bottommost level,
+
+the number has to be 1, the
+number next to the node,
+
+because that's my base case.
+
+When I have a one element
+array, it's sorted, I'm done.
+
+I return.
+
+So I can say that
+for each level,
+
+the number next to the node is
+something as a function of L.
+
+Here, I'm going to
+say that this is
+
+N over 1, which is N
+over 2 to the 0 power.
+
+And this is N over 2, so it's
+N over 2 to the first power.
+
+This is N over 2 to the
+second, and so on and so forth.
+
+It might not be obvious if
+you only have two levels.
+
+I don't want to draw
+a lot on the board
+
+because I don't have a lot
+of space and I'd get my nodes
+
+all messed into each other.
+
+If it takes more than two levels
+to see the pattern, go for it.
+
+Expand for three levels,
+four levels, five levels,
+
+whatever it takes to get it
+right on a Pset or on a test.
+
+So you see the pattern,
+then you write the formula
+
+for the node size at the level.
+
+And assuming this
+pattern holds, we
+
+see that the size of a
+node at level l, the size
+
+is 2 N over 2 to the l minus 1.
+
+Fair enough?
+
+You can say N over 2
+to the l, and forget
+
+that there's a minus 1, and then
+the asymptotics will save you,
+
+so it's no big deal, but
+this is the real number.
+
+So that means that at the
+bottommost level, at level l,
+
+this size is going to be 1.
+
+N over 2 to the l
+minus 1 equals 1.
+
+So now this is an equation,
+so I can solve for l.
+
+I pull this on the right side,
+N equals 2 to the l minus 1,
+
+so l minus 1 equals-- anyone?
+
+The inverse of an exponential?
+
+AUDIENCE: I wasn't
+paying attention.
+
+Sorry.
+
+AUDIENCE: Log N.
+
+PROFESSOR: The inverse of an
+exponential is a logarithm.
+
+Keep that in mind for
+solving 6.006 problems.
+
+l minus 1 is log N so l is
+log n plus 1, roughly log n.
+
+I could use log n plus 1
+and go through the math.
+
+It's a bit more painful
+and, because we're
+
+using asymptotics, it
+doesn't really matter.
+
+So now we know how
+many levels we have.
+
+Let's see what's the
+cost at the level.
+
+So all the calls
+at a certain level,
+
+what's the sum of the costs?
+
+For this level, what's the cost?
+
+CN.
+
+And That was the easy question.
+
+Just the root, right?
+
+How about this level?
+
+Because I have two nodes, the
+cost in each node is CN over 2.
+
+How about this level?
+
+Four levels, each
+level CN over 4.
+
+How about the bottom level?
+
+AUDIENCE: CN.
+
+PROFESSOR: Why is it CN?
+
+AUDIENCE: Because there
+are N arrays of size 1.
+
+PROFESSOR: N arrays of size 1.
+
+Excellent.
+
+A cute argument I heard once
+is you start out with N,
+
+you split it into N
+over 2 and N over 2.
+
+Then you split this guy
+in N over 4, N over 4,
+
+so this is like
+conservation of mass.
+
+If you start with N and here,
+you don't end up with N total,
+
+then you lost some element
+somewhere on the way.
+
+So CN.
+
+CN, CN, CN, CN.
+
+I think I see a pattern.
+
+I think it's reasonable to say
+that for every level, it's CN.
+
+And if you write the
+proof, you can prove that
+
+by using math instead
+of waving hands.
+
+So CN times the number
+of levels, right?
+
+The answer for this guy
+is C of N is CN times l.
+
+What's l?
+
+AUDIENCE: N log N.
+
+PROFESSOR: Roughly.
+
+OK So order of N
+log N. C becomes
+
+order of, l is order of
+log N, N stays the same.
+
+Any questions?
+
+Are people getting it or
+did I confuse you even more?
+
+AUDIENCE: We got it.
+
+PROFESSOR: OK, sweet.
+
+Thank you for the encouragement.
+
+So this gets you through
+problem one of Pset 2.
+
+So in this case, the
+tree is nicely balanced.
+
+The cost at each
+level is the same.
+
+When [INAUDIBLE] talked about
+recursion trees in lectures,
+
+he showed two more
+trees, one where
+
+pretty much all the cost was up
+here-- the cost of the children
+
+was negligible-- and one
+tree where all the cost was
+
+concentrated here, so the
+cost of all the inner nodes
+
+was negligible and the leaves
+were doing all the real work.
+
+So don't be scared if your
+costs aren't the same.
+
+Just sum them up and you'll
+get to the right answer.
+
+Now I'm going to talk
+about binary search trees,
+
+except I will make a five
+minute general talk about data
+
+structures before I do that.
+
+So we use the term
+"data structures."
+
+I think we covered
+it well, and I
+
+want to give you
+a couple of tips
+
+for dealing with them on Pset 1.
+
+A data structure is
+a bunch of algorithms
+
+that help you store and
+then retrieve information.
+
+You have two types
+of algorithms.
+
+You have queries,
+and you have updates.
+
+You start out with an
+empty data structure,
+
+like an empty binary search
+tree or an empty list,
+
+and then you throw
+some data at it.
+
+That's when you update it.
+
+Then you ask it some questions,
+and that's when you query it.
+
+Then maybe you throw more data
+at it, so you do more updates,
+
+and you ask more questions,
+so you do more queries.
+
+What are the queries
+and the updates
+
+for the binary search trees
+that we talked about in lecture?
+
+AUDIENCE: A query
+would be like, what's
+
+your right child,
+what's your left child?
+
+PROFESSOR: So that's for a node.
+
+AUDIENCE: What are
+you looking for?
+
+PROFESSOR: I'm
+looking for something
+
+for the entire infrastructure.
+
+So for the entire
+tree, what's a question
+
+that you would ask the tree?
+
+PROFESSOR: Max.
+
+PROFESSOR: OK.
+
+Min.
+
+AUDIENCE: Next larger.
+
+PROFESSOR: Next larger.
+
+Are you looking at the nodes?
+
+AUDIENCE: Is there an are
+you balanced question?
+
+PROFESSOR: Well, I would say
+that the most popular operation
+
+in a binary search
+tree is Search, which
+
+looks for-- we call
+it Find in the code
+
+because most code
+implementations call it Find
+
+nowadays, but
+binary search tree.
+
+What are you going to do in it?
+
+You search for a value.
+
+That's why it has the
+Search in binary search.
+
+So queries are operations where
+you ask questions to the data
+
+structure and it doesn't change.
+
+How about updates?
+
+What did we learn for updates?
+
+AUDIENCE: Insert.
+
+PROFESSOR: Excellent.
+
+So Insert was
+covered in lecture,
+
+and we're doing Delete today.
+
+So data structures
+have this property
+
+that's called the
+representation invariant, RI,
+
+or Rep Invariant.
+
+Actually, before I get
+there, the rep invariant
+
+says that the data in
+the data structures
+
+is organized in this
+way, and as long
+
+as it's organized in this way,
+the data structure functions
+
+correctly.
+
+Can someone guess
+for a sorted array
+
+what's the
+representation invariant?
+
+AUDIENCE: It can mean sorted.
+
+PROFESSOR: Yeah.
+
+A sorted array should be sorted.
+
+Sounds like a very
+good rep invariant.
+
+So the elements should
+be stored an array.
+
+Every element should be smaller
+than any element after it.
+
+And as long as the rep
+invariant holds, so as long
+
+as elements are stored in
+the right way in the data
+
+structure, the queries will
+return the right results.
+
+If the rep invariant
+doesn't hold,
+
+then God knows what's
+going to happen.
+
+What can you do
+in a storage array
+
+as long as the rep
+invariant holds?
+
+Sorted array.
+
+What's the reason why I
+would have a sorted array?
+
+What can I do that's
+fast in a sorted array?
+
+AUDIENCE: Min and Max.
+
+PROFESSOR: I can
+do that very fast.
+
+That's good.
+
+What's the running time?
+
+AUDIENCE: A constant.
+
+PROFESSOR: Perfect.
+
+Min you look at the beginning,
+Max you look at the end.
+
+Yes?
+
+AUDIENCE: Binary search.
+
+PROFESSOR: Binary search.
+
+That's the other
+reason for that.
+
+So binary search
+runs in order log
+
+N time, doesn't have to
+look at most of the array,
+
+tells you whether an
+element is there are not.
+
+Now, what if the
+array is unsorted?
+
+Will the algorithm work?
+
+It might say
+something isn't there
+
+when it actually is there.
+
+You can do binary search
+on a non-sorted array.
+
+So if the rep
+invariant doesn't hold,
+
+your queries might give
+you a wrong answer.
+
+How about updates?
+
+How do you search
+something in a sorted list?
+
+AUDIENCE: You find
+where it should go
+
+and you move everything.
+
+PROFESSOR: Yep.
+
+So you have to move
+everything, make room for it,
+
+and put it there so
+that the array is still
+
+sorted at the end.
+
+You can't just append
+things at the end,
+
+even though that would be
+faster and lazier and less code.
+
+When you do an update
+to a data structure,
+
+you have to make sure that
+the rep invariant still
+
+holds at the end.
+
+Sort of a correctness proof
+for an update algorithm
+
+says that if the rep invariant
+holds at the beginning,
+
+the rep invariant is
+guaranteed to hold at the end.
+
+Why do we care about
+this rep invariant stuff?
+
+Suppose you have a problem,
+say on the next Pset, that
+
+asks you to find the place
+that's slow in your code
+
+and then speed it up.
+
+And suppose you recognize
+the data structure there,
+
+and you say that's
+inefficient, and you
+
+want to implement another
+data structure that
+
+would be more efficient.
+
+You're going to implement it.
+
+You might have
+bugs in an update.
+
+How do you find the bugs?
+
+Queries give you
+the wrong answers.
+
+You might do queries a long
+time after you do updates,
+
+and you're not going to
+know which update failed.
+
+The right way to do this
+is you implement the method
+
+called Check RI-- that's
+what I call it-- so
+
+check the representation
+invariant.
+
+And that method walks through
+the entire data structure
+
+and make sure that the
+rep invariant holds,
+
+and if it doesn't, it
+raises an exception
+
+because you know that whatever
+you try to do from there
+
+is not going to work, so
+there's no reason to keep going.
+
+So at the end of every
+update, you add a call
+
+to this Check RI
+method until you're
+
+sure that your code is correct.
+
+And after you're done
+debugging your code,
+
+you remove this method
+and you submit the code.
+
+Why do I want to
+remove the method?
+
+It might be painfully slow
+and inefficient, much slower
+
+than the actual
+queries and updates.
+
+For example, let's take a heap.
+
+Do people remember
+heaps from lecture?
+
+What's the query for a heap?
+
+Say you have a max heap.
+
+What's a query?
+
+AUDIENCE: Where's the max?
+
+PROFESSOR: OK, cool.
+
+So for a max heap, a
+query would be max.
+
+Running time?
+
+AUDIENCE: Constant.
+
+PROFESSOR: Perfect.
+
+Constant.
+
+What do you do?
+
+Look at the top?
+
+AUDIENCE: Yeah, exactly.
+
+PROFESSOR: OK.
+
+Sweet.
+
+So what are the two popular
+updates in a max heap?
+
+AUDIENCE: There would
+be Insert as well.
+
+PROFESSOR: OK.
+
+Insert.
+
+And did we teach
+you general delete?
+
+Usually Extract Max is simpler.
+
+That's all you need.
+
+What's the running
+time for Insert?
+
+Do people remember heaps?
+
+AUDIENCE: I think it was per
+N, but I'm not completely sure.
+
+PROFESSOR: Anyone else?
+
+It's not.
+
+Life would be bad
+if it would be N.
+
+AUDIENCE: N squared?
+
+PROFESSOR: No.
+
+It's better than N, so you
+guys are doing a binary search
+
+over the few running times
+that I gave you earlier.
+
+AUDIENCE: [INAUDIBLE]
+add to the N,
+
+and then you compare your
+neighbor, and then you
+
+[INAUDIBLE].
+
+AUDIENCE: If it's an
+array, there isn't--
+
+PROFESSOR: So conceptually,
+a heap looks like this.
+
+And yeah, it becomes
+an array eventually,
+
+but let's look at it this way.
+
+It is a full binary tree.
+
+Binary tree means that each
+node has at most two children,
+
+and full means that every
+level except for the last level
+
+is completely populated.
+
+So every internal node
+has exactly two children,
+
+and in here, every node
+except for some nodes
+
+and then some nodes
+after it will not have.
+
+Everything to the left
+is fully populated,
+
+and then at some point,
+you stop having children.
+
+It turns out that this is
+easy to store in an array,
+
+but I will not go over that.
+
+Instead, I want to
+go over inserting.
+
+What's the rep
+invariant for a heap?
+
+AUDIENCE: The max
+in the top, right?
+
+Well, for max heap, and
+then the two children
+
+are less than the next node.
+
+PROFESSOR: All right.
+
+So the guy here has to be
+bigger than these guys,
+
+then the guy here has to
+be bigger than these guys,
+
+and so on and so forth.
+
+And if you use
+induction, you can
+
+prove that if this
+is bigger than this,
+
+it has to be bigger than
+these guys, and bigger
+
+than these guys, and bigger
+than everything, and it's a max.
+
+That's the reason why we
+have that rep invariant.
+
+So the way we insert
+a node is we add it
+
+at the bottom, the only
+place where we could add it.
+
+And then if this guy is
+bigger than this guy,
+
+the rep invariant is
+violated, so we swap them
+
+in order to fix that.
+
+Now the guy is here.
+
+If this is bigger than
+this, we do another swap.
+
+If this is bigger than
+this, we do another swap.
+
+So you're going to go from the
+bottom of the heap potentially
+
+all the way up to the root.
+
+So the running time
+of insert is order
+
+of the height of the heap.
+
+Now, the heap is a
+full binary tree.
+
+I said "full."
+
+I keep saying "full."
+
+The reason I care about full
+is that the full binary tree
+
+is guaranteed to have a
+height of log N. It's always
+
+log N, where N is
+the number of nodes.
+
+So inserting in a
+heap takes log N.
+
+AUDIENCE: I have a question.
+
+Didn't they say that
+because it's in an array,
+
+then to find it-- oh no, I
+guess because you can still
+
+do the swaps.
+
+PROFESSOR: You can
+still do the swaps
+
+when you have it
+serialized in an array.
+
+You know that given
+an item's index,
+
+the parent is that
+index divided by 2.
+
+So you add an element
+at the end of the array,
+
+and then you know
+what the parent is,
+
+and then you keep swapping
+and swapping and swapping
+
+towards the [INAUDIBLE].
+
+AUDIENCE: You don't
+ever have to put it in
+
+and shift everything over.
+
+You're only swapping.
+
+PROFESSOR: Yep.
+
+You only swap.
+
+That's important.
+
+Thanks for asking.
+
+That's important.
+
+So log N. Extract max,
+take my word for it,
+
+also log N. What's the
+running time for checking
+
+the invariant in a heap?
+
+So to make sure that this guy is
+a heap, if I had numbers here,
+
+what would you have to do?
+
+AUDIENCE: You'd have
+to look at every node.
+
+PROFESSOR: Yep.
+
+So running time?
+
+AUDIENCE: Theta of N.
+
+PROFESSOR: Yep.
+
+So if I'm going to
+submit code for a heap
+
+where the operations
+are our order of log N,
+
+or order 1, but then each
+of these calls Check RI,
+
+that's going to be
+painfully slow because I'm
+
+making the updates be
+order N instead of log N.
+
+So you're putting Check
+RI calls in every update.
+
+You debug your code.
+
+When you make sure it's
+correct, you remove those,
+
+and then you submit the Pset.
+
+Make sense?
+
+Sweet.
+
+And we looked a little bit
+at heaps, which is good.
+
+Binary search trees.
+
+So a binary tree is a
+tree where every node
+
+has at most two children.
+
+When we code this up, we
+represent a node as a Python
+
+object, and for a node, we
+keep track of the left child,
+
+of the right child, parent,
+and then this is a hollow tree.
+
+It's not very useful.
+
+This becomes useful when you
+start putting keys in the nodes
+
+so that you can find them and
+do other things with them.
+
+So each node has a key.
+
+Let me draw a
+binary search tree.
+
+Can people see this?
+
+So this is a binary tree.
+
+Can someone say something a
+bit more specific about it?
+
+AUDIENCE: It's unbalanced.
+
+PROFESSOR: OK.
+
+It's imbalanced.
+
+So that means that
+finding things all the way
+
+at the bottom is
+going to be expensive.
+
+What else?
+
+So I said it's a binary tree.
+
+Give me something more specific.
+
+So binary tree just means that
+every node has two children.
+
+There's a bit more
+structure in this guy.
+
+So if I look at the
+root, if I look at 23,
+
+all the nodes to the
+left are smaller.
+
+All the nodes to the
+right are bigger.
+
+Now, if I look at 8, all the
+nodes to the left are smaller,
+
+all the nodes to the
+right are greater.
+
+This additional rep invariant
+defines a binary search tree.
+
+This is what we
+talked about in class.
+
+BST.
+
+Why would I want to
+have this rep invariant?
+
+It sounds like a pain
+to maintain nodes
+
+with all these
+ordering constraints.
+
+What's the advantage
+of doing that?
+
+AUDIENCE: Search is fast.
+
+PROFESSOR: Yep.
+
+Search is fast.
+
+How do I do search?
+
+If you're looking
+for 42 or for 16,
+
+you'd be like, oh,
+it's less than 23.
+
+I'll get on this path.
+
+PROFESSOR: So start at the root,
+compare my key to the root.
+
+If it's smaller, go left.
+
+If it's bigger, go right.
+
+Then keep doing that
+until I arrive somewhere
+
+or until I arrive at a dead
+end if I'm looking for 14.
+
+This is a lot like
+binary search.
+
+Binary search in an array,
+you look at the middle.
+
+If your key is smaller, go left.
+
+If your key is
+bigger, then go right.
+
+Let's look at the
+code for a little bit.
+
+Look at the BST Node
+Class, and you'll
+
+see that it has the fields
+that we have up here.
+
+And look at the Find method,
+and this is pretty much
+
+the binary search code.
+
+Lines 8 and 9 have the return
+condition when you're happy
+
+and you found the key,
+and then line 10 compares
+
+the key that you're looking
+for with the key in the node
+
+that you're at, and then lines
+11, 14, 16, and 19 are pretty
+
+much copy pasted,
+except one of them
+
+deals with the left
+case, the other one
+
+deals with the right case.
+
+What is the running
+time for Find?
+
+AUDIENCE: Wouldn't
+it be log N, right?
+
+PROFESSOR: I wish.
+
+If this is all you have
+to do to get log N,
+
+then I would have to
+write a lot less code.
+
+So not quite log N. We will
+have to go through next lecture
+
+to get to log N. Until then,
+what's the running time?
+
+AUDIENCE: Order h.
+
+PROFESSOR: Yep.
+
+So you told me at the
+beginning it's unbalanced.
+
+AUDIENCE: Yeah.
+
+PROFESSOR: So then it's
+not going to be fast.
+
+OK, so order h.
+
+The reason why we care
+about h, and the reason
+
+we don't say order
+N, is because next
+
+lecture after we learn
+how to balance a tree,
+
+there's some magic that you can
+do to these binary search trees
+
+to guarantee that the
+height is order of log N.
+
+And then we'll go through all
+the running times that we have
+
+and replace h with log N.
+
+Now, it happens that in this
+case, if you would have told
+
+me order N, I couldn't argue
+with you because worst case,
+
+searches are order N. Can
+someone give me a binary search
+
+tree that exposes
+this degenerate case?
+
+Yes?
+
+AUDIENCE: If it's
+completely unbalanced
+
+and every node is greater
+than the parent nodes.
+
+PROFESSOR: So give me some
+inserts that create it.
+
+AUDIENCE: Insert 5.
+
+PROFESSOR: 5.
+
+AUDIENCE: Insert 10.
+
+PROFESSOR: 10.
+
+AUDIENCE: Insert 15.
+
+PROFESSOR: 15.
+
+AUDIENCE: Insert 20.
+
+PROFESSOR: Yep.
+
+And I could keep going.
+
+I could say, 1, 2, 3, 4, 5.
+
+I could say 5, 10, 15.
+
+As long as these keep
+growing, this is basically
+
+going to be a list,
+so searching is
+
+order N. This is
+a degenerate case.
+
+Turns out it doesn't happen
+too often in practice.
+
+If you have random data, the
+height will be roughly log N.
+
+But in order to avoid
+those degenerate cases,
+
+we'll be doing balanced
+trees later on.
+
+So we covered Find.
+
+We know it's order h.
+
+How do you insert,
+really quickly?
+
+AUDIENCE: Do you
+mean in searching
+
+when it's balanced
+or unbalanced?
+
+PROFESSOR: This guy.
+
+So the trees look
+exactly the same.
+
+If it's balanced, it's
+going to look more
+
+like that than like this.
+
+Actually, this is balanced.
+
+This is perfectly unbalanced.
+
+This is somewhere in the middle.
+
+If it's balanced, it's just
+going to look more like this,
+
+but it's still a
+binary search tree.
+
+How would you insert a node?
+
+Yes?
+
+AUDIENCE: Can't you
+start at the root
+
+and find your way down, and
+then the first open child
+
+that you see that's applicable
+to your element, state it then?
+
+PROFESSOR: Yep.
+
+So if I wanted to insert
+14, which way do I go?
+
+AUDIENCE: So you'd look
+at 23, and you'd say,
+
+it's less than 23, go left.
+
+You'd look at 8.
+
+You'd say, it's greater than 8.
+
+You'd go right.
+
+Look at 16.
+
+You'd say it's less,
+so you go left.
+
+15, it's less.
+
+Then you have an open spot
+so you stick it there.
+
+PROFESSOR: Excellent.
+
+Thank you.
+
+Yes?
+
+AUDIENCE: I have a question.
+
+What if we want to insert 5?
+
+Then--
+
+PROFESSOR: So if you
+want to insert who?
+
+AUDIENCE: 5.
+
+Or actually no, we can't.
+
+I'm thinking, is there any case
+in which need to move a node?
+
+PROFESSOR: How
+would you insert 5?
+
+Let's see.
+
+What would you do for 5?
+
+AUDIENCE: For 5, then we'd
+insert it to the right of 4,
+
+right?
+
+PROFESSOR: Smaller,
+smaller, greater, 5.
+
+Right?
+
+AUDIENCE: So there would
+be no case in which we'd
+
+need to swap nodes or something?
+
+PROFESSOR: No.
+
+You're thinking ahead.
+
+We'll talk about that a little
+later when we get to deleting.
+
+As long as you follow a path in
+the tree, the path that finding
+
+would get you to, as soon
+as you hit a dead end,
+
+that's where your node belongs.
+
+Because you know next time
+you're going to search for it,
+
+the search is going to follow
+that path and find the node.
+
+Yes?
+
+AUDIENCE: If you have values
+are the same, like two
+
+nodes at the same
+number, does it
+
+matter which side you put it on?
+
+PROFESSOR: You don't.
+
+AUDIENCE: Oh, I see.
+
+It's more like you would only
+have four 1's in the tree.
+
+PROFESSOR: Yes.
+
+So if you're trying to
+store keys and values,
+
+then what you'd
+have to do if you
+
+want to allow multiple
+values for the same key
+
+is you have a linked
+list going off
+
+of this, which node
+becomes an array of values
+
+aside from the key.
+
+Smart question.
+
+Thank you.
+
+That trips you up every
+time you do actual code,
+
+so that's the right
+question to ask yourself
+
+when you're implementing this.
+
+Will I have duplicates?
+
+How do I handle them?
+
+We don't.
+
+We take the easy way out.
+
+So if you look at
+Insert, on the next page,
+
+you will see that the code
+is pretty much the Find code
+
+copy pasted, except
+when Self Left is None
+
+or Self Right is None,
+instead of returning,
+
+it creates a new node.
+
+Does that make sense to people?
+
+All right.
+
+So Delete is going to be the
+hardest operation for today.
+
+Before we do that, let's
+do a warm up operation.
+
+Let's say I want to implement
+Find Next Larger, also called
+
+Successor in some
+implementations.
+
+So I have a node.
+
+Say I have node 8, and I
+want to find the next key
+
+in the tree that's
+strictly larger than 8
+
+but smaller than anything else.
+
+So if I would take these nodes
+and write them down in order,
+
+I want to find the element
+that would go right after it.
+
+How do I do that?
+
+Don't cheat.
+
+Don't look at the code, or make
+my life easier and do searches.
+
+AUDIENCE: Go down
+one to the right,
+
+and you try to get down
+left as far as you can.
+
+PROFESSOR: OK.
+
+Very good.
+
+So I have a node, and it
+has some subtree here,
+
+so I can go to the right here,
+I can go all the way left.
+
+We have an operation
+that does this,
+
+and it's called Min for a tree.
+
+In order to find the minimum
+in a binary search tree,
+
+you keep going left.
+
+For example, in this case,
+you get 4, which is good.
+
+So the way you would code
+this up is if you have Min,
+
+you go to the right
+if you can, and then
+
+you call Min on the subtree.
+
+And you can see that lines
+3 and 4 do exactly that.
+
+Good guess.
+
+But you can line
+1 says case one,
+
+so you have the right
+answer for one case.
+
+Now we have to handle
+more difficult cases.
+
+What if instead, I go
+down a bunch of nodes,
+
+and I want to find the successor
+for this guy, for example,
+
+and there's nothing here.
+
+What do I do?
+
+So if I want to find the
+successor for 8, what do I do?
+
+Sorry.
+
+It has an answer.
+
+What if I want to find
+the successor for 4?
+
+AUDIENCE: Go up one.
+
+PROFESSOR: OK.
+
+Go up one.
+
+Why does that work?
+
+AUDIENCE: You know it's
+going to be greater.
+
+PROFESSOR: So I'm
+going up right.
+
+So I know that everything here
+is guaranteed to be smaller,
+
+everything here is guaranteed
+to be greater than this guy.
+
+This guy is up right, so this
+is guaranteed to be greater
+
+than this, and
+everything here is
+
+guaranteed to be greater than
+this, and so on and so forth
+
+for the entire tree.
+
+So if I go up right, I'm happy.
+
+I definitely found my answer.
+
+Now, what if I have something
+that looks like this,
+
+and I want to find the
+successor for this guy?
+
+AUDIENCE: There is none.
+
+PROFESSOR: In this
+case, there is none
+
+if there's nothing else here.
+
+What if I have this,
+but then I have this?
+
+So I came down this way.
+
+AUDIENCE: Are you saying you're
+calling on that last node?
+
+PROFESSOR: Yep.
+
+AUDIENCE: Find the larger?
+
+I guess you'd just
+trace back up.
+
+PROFESSOR: And where do I stop?
+
+AUDIENCE: It affects the tree,
+so you go up one from there.
+
+You don't stop there.
+
+PROFESSOR: Why
+can't I stop here?
+
+AUDIENCE: Because you know
+that that-- not necessarily.
+
+AUDIENCE: You know that
+everything in that long branch
+
+right there is less than
+that node [INAUDIBLE].
+
+PROFESSOR: This is to
+the left of this guy,
+
+so this guy has to be
+greater than everything here,
+
+and then you can repeat the
+argument that we had before.
+
+So here, we could
+stop right away
+
+because we could branch left.
+
+In this case, you have
+to go up until you're
+
+able to go left and up.
+
+If you get to the root,
+then what happened?
+
+Then we're in this case,
+and you have no successor.
+
+So take a look at the code.
+
+The next larger,
+lines 1 through 9.
+
+Case two, 6 through
+8, does exactly that.
+
+If I can't go to my right
+and find the tree there,
+
+then I go up through
+my parent chain,
+
+and as long as I have
+to go up to the left,
+
+so as long as I'm the
+right child of my parent,
+
+I have to keep going.
+
+The moment I find the parent
+where I'm the left child,
+
+I stop.
+
+That's my successor.
+
+What if I would have to find
+the predecessor instead?
+
+So the element that's
+smaller than me
+
+but bigger than everything
+else in the tree.
+
+What would I do?
+
+AUDIENCE: It's
+just the opposite.
+
+PROFESSOR: Just the opposite.
+
+So how do I do the opposite?
+
+AUDIENCE: You can take the
+max of the left side tree,
+
+or traverse up, and
+if that's less than--
+
+PROFESSOR: OK, so if I
+have a left subtree, fine.
+
+Call max on it and get
+the rightmost node there.
+
+If not, I go up,
+and when do I stop?
+
+When I go left or right?
+
+AUDIENCE: You'd
+have to go right.
+
+Is that right?
+
+PROFESSOR: Yep.
+
+So last time, in this
+case, when I was going up,
+
+if I was going left,
+I had to keep going,
+
+and the moment I went right,
+I was happy and I stopped.
+
+What if I want to
+find the predecessor?
+
+It's the opposite, right?
+
+So I will go this way, and
+the moment I can go this way,
+
+I'm done.
+
+How do you do this in code?
+
+Slightly tricky.
+
+Just slightly, I promise.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: It's hard.
+
+What I would do is
+copy paste the code,
+
+replace "left" with "right"
+everywhere, and replace "min"
+
+with "max."
+
+You get it done.
+
+So we talked about how the
+tree is symmetric, right?
+
+So every time, instead of
+saying "left," you say "right,"
+
+and instead of saying
+"min," you say "max."
+
+That's how you do this.
+
+How do we do deletions?
+
+So suppose I'm in this tree
+and I want to delete 15.
+
+What do I do?
+
+AUDIENCE: Kill it.
+
+PROFESSOR: Kill it.
+
+Very good.
+
+What if I want to delete 16?
+
+What do I do?
+
+AUDIENCE: You need to
+put 15 where 16 is.
+
+PROFESSOR: OK.
+
+So I would put 15 here.
+
+So I had 16.
+
+Suppose I have a big tree here.
+
+Actually, let's go
+for an easier case.
+
+Let's say I have this tree here.
+
+So you're here, you
+have a big tree here,
+
+you don't have
+anything here, and you
+
+want to delete this guy.
+
+AUDIENCE: You know
+that everything less
+
+than the top node is
+going to be less than it,
+
+so you can just move that up.
+
+PROFESSOR: Everything
+less than this guy is also
+
+going to be less than this guy.
+
+So you're saying move
+the whole tree up.
+
+AUDIENCE: Yep.
+
+PROFESSOR: So the
+way we do that is
+
+we'd take this node's left
+link and make it point here,
+
+and take this guy's parent
+link and make it point here,
+
+and this guy sort of goes away.
+
+So we have two
+cases for deleting.
+
+We have if you're a
+leaf, we'll take you out.
+
+Sorry.
+
+I got confused.
+
+If you have one
+child and that child
+
+is in the same direction as your
+parent, then you can do this.
+
+What if you have one child,
+but it's a zigzag like this?
+
+What do you do?
+
+AUDIENCE: It's still greater
+than, so you do the same thing.
+
+PROFESSOR: Exactly.
+
+Same thing.
+
+Just change this guy, change
+this guy, and I'm happy.
+
+So it doesn't matter if you have
+a zigzag or a straight line.
+
+It might help you think
+about it to convince yourself
+
+that the code is correct, but in
+the end, you do the same thing.
+
+Now, what if I want
+to delete node 8?
+
+So what if I have a nasty case
+where I want to delete this guy
+
+and it has children both on
+the left and on the right?
+
+AUDIENCE: You have to take
+8, compare it to its parent
+
+and compare it to
+its right child,
+
+and see which one
+is greater in order
+
+to figure out which node
+gets replaced in its spot.
+
+PROFESSOR: OK.
+
+So there is replacing
+that's going to happen.
+
+The answer is really tricky.
+
+I always forget
+this when coding.
+
+Try to understand it,
+and if it doesn't work,
+
+refer to the textbook.
+
+When you forget it, because
+you will, refer to the textbook
+
+or to the internet.
+
+So what you do is I can't just
+magically replace this node
+
+with one of the subtrees,
+but we talked right
+
+before this about Next Greater,
+so finding a node's successor.
+
+If this node has both a left
+subtree and a right subtree,
+
+then I know that if I
+call Find Successor on it,
+
+I'm going to go
+somewhere inside here,
+
+and I'm going to find a node
+somewhere in here all the way
+
+to the left that is
+this guy's successor.
+
+So what I'm going
+to do is I'm going
+
+to delete this node instead, and
+then I'm going to take its key
+
+and put it up here.
+
+So if I want to delete 8, what
+I do is I find its successor,
+
+then I delete it, then I take
+the 15 that was here-- you
+
+can see it, right?
+
+It's still there.
+
+Put it here.
+
+So the reason this works
+is that everything here
+
+is greater than this guy.
+
+Everything here is
+smaller than this guy.
+
+This is the next node that's
+greater than this guy,
+
+but everything else
+is bigger than it,
+
+right, because we wanted
+it to be a successor.
+
+So if I take this value
+and I put it up here,
+
+everything in here is still
+going to be greater than it.
+
+This is a successor of this
+guy, so everything here
+
+is still going to be
+smaller than the successor.
+
+Great.
+
+In order to do a delete,
+I find the successor,
+
+and then I call Delete on it.
+
+How do I know that
+this will end?
+
+How do I know that
+I'm not going to go
+
+into a loop that runs forever?
+
+AUDIENCE: Because it's not--
+
+AUDIENCE: It's acyclic, right?
+
+PROFESSOR: OK.
+
+First answer, good.
+
+Eventually, worst case, I'm
+going to get to the maximum,
+
+and then not going on have to
+delete the successor anymore.
+
+Now, another thing
+to note here is
+
+that if this guy is the
+successor of this guy,
+
+it can't have anything on the
+left, because if it would,
+
+then whatever is down here
+has to be bigger than this,
+
+and whatever's to
+the left of this node
+
+has to be smaller than this.
+
+But we said that this is
+the successor of this,
+
+so there's nothing here.
+
+So this will be one of the easy
+cases that we talked about.
+
+The successor
+either has no kids,
+
+or it has only one
+child, only one subtree.
+
+So then I can delete it
+using one of the easy cases.
+
+So in fact, worst case that
+happens in a delete is my node
+
+has two subtrees.
+
+Then I find the successor that's
+only going to have one subtree,
+
+I change my links
+there, and I'm done.
+
+What is the running
+time for Delete?
+
+AUDIENCE: Is it order h,
+because you should do it
+
+all the way down to the
+bottom of the tree, right?
+
+PROFESSOR: You have
+the right answer.
+
+Let's see why it's order h.
+
+It has to be order h, right?
+
+Otherwise, the tree
+would be too slow.
+
+If it's order N, then it's bad.
+
+So why would Delete be order h?
+
+This was a heap, right,
+so I can't use this.
+
+I'm going to write
+"delete" here again.
+
+So the first thing you do is
+you have to search for the key,
+
+right?
+
+That's order h.
+
+Now, if it's a happy case,
+if it's case one or two,
+
+you change some links
+and you're done.
+
+What's the time for that?
+
+AUDIENCE: Constant.
+
+PROFESSOR: Constant.
+
+So happy case, order h for sure.
+
+Now sad case.
+
+If you have two
+children, what do you
+
+have to do after you realize
+that you have two subtrees?
+
+AUDIENCE: Find the successor.
+
+PROFESSOR: OK.
+
+What's the running time
+for finding a successor?
+
+AUDIENCE: Order h.
+
+PROFESSOR: Order h.
+
+Once I find the
+successor, what do I do?
+
+Call Delete on that,
+and what happens?
+
+It's a happy case or a sad case?
+
+AUDIENCE: It's a happy case.
+
+PROFESSOR: Happy case,
+a few links get swapped,
+
+constant time.
+
+So worst case, order
+h plus order h.
+
+Order h.
+
+So insertions are order
+h, deletions are order h.
+
+AUDIENCE: The first one.
+
+Because the second one is
+from finding the successor.
+
+What is the first one for?
+
+PROFESSOR: Finding the
+node for a key in the tree.
+
+So if I say Delete 8,
+then you have to find 8.
+
+If I give you the node,
+then you don't have that.
+
+Good question.
+
+It's a good question.
+
+Thank you.
+
+So that's insertion.
+
+That's deletion.
+
+Let's look at the
+code for Delete.
+
+Looks kind of long.
+
+So lines through 21,
+happy case or sad case?
+
+Try to do it by
+looking at the "if"
+
+instead of looking
+at the comments.
+
+So lines through 21 for Delete.
+
+AUDIENCE: On this tree?
+
+Which tree, because
+there are two deletes?
+
+PROFESSOR: Oh really?
+
+Sorry.
+
+Why do we have two deletes?
+
+AUDIENCE: There's BST Delete and
+then there's BST Node Delete.
+
+PROFESSOR: So BST Delete.
+
+Finds the node, and then
+calls Delete on the node.
+
+And then if the node
+is a tree's root,
+
+then it updates the tree's root.
+
+So let's look at
+the nodes delete.
+
+Oh, I see.
+
+I think I was looking
+at the wrong one.
+
+Thank you.
+
+My Delete was much
+longer than yours.
+
+So lines 3 through 12,
+happy case or sad case?
+
+Look at the "if" on
+line 3 and tell me,
+
+what case is it going for?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: If it doesn't
+have a left child
+
+or it doesn't have
+a right child,
+
+is that the happy
+case or the sad case?
+
+AUDIENCE: Happy.
+
+PROFESSOR: Happy case.
+
+So lines 4 through 12
+handle the happy case.
+
+Lines 14 through 16
+handle the sad case.
+
+Do lines 14 through
+16 make sense?
+
+Find the successor,
+then swap the keys,
+
+then delete that successor.
+
+Now, lines 4 through
+11 are pretty much what
+
+we talked about here, except I
+can't draw arrows on the board
+
+and instead I have to
+change left and right links.
+
+Line 4 has to see if we're a
+left child or a right child,
+
+and then lines 5 through 7 and
+9 through 11 are pretty much
+
+copy paste, swap
+left with right.
+
+And they changed the links
+like we changed them here.
+
+Do we have any
+questions on Deletes?
+
+AUDIENCE: So if the
+successor had a right child,
+
+then all you do, you just do
+the workaround thing where
+
+you just--
+
+PROFESSOR: Yep.
+
+So the case that it
+doesn't have two children.
+
+As long as it doesn't
+have both children,
+
+you're in the happy case and
+you can do some link swapping.
+
+Are you guys burned out already?
+
+Fair enough.
+
+I left a part out.
+
+What I left out is how
+to augment a binary tree.
+
+So binary trees by default
+can answer the question,
+
+what's the minimum node
+in a tree in order h.
+
+You go all the way to the
+left, you find the minimum.
+
+That's the minimum.
+
+It turns out that if you make
+a node a little bit fatter,
+
+so if instead of storing, say,
+23 in this node, I store 23,
+
+and I store the fact that the
+minimum in my left subtree
+
+is 4, then it turns out that
+I can answer the question
+
+in constant time,
+what's the minimum?
+
+Oh gee, if you store
+the minimum here,
+
+of course you can retrieve
+it in constant time, right?
+
+The hard part is, how do you
+handle insertions and updates
+
+in the same time?
+
+So the idea is that
+if I have a node
+
+and I have a function here,
+say the minimum of everything,
+
+if I have two children,
+here they're 15 and 42,
+
+and say the minimum
+in this tree is 4
+
+and the minimum in this tree is.
+
+So if I already computed
+the function for these guys,
+
+how do I compute the
+function for this?
+
+AUDIENCE: [INAUDIBLE]
+and compare it?
+
+PROFESSOR: Yep.
+
+Take the minimum of
+these two guys, right?
+
+There are some special cases
+if you don't have a child.
+
+If you don't have a left
+child, then you're the minimum.
+
+But you write down
+those special cases,
+
+and you can compute
+this in how much time?
+
+AUDIENCE: Order h, right?
+
+PROFESSOR: What if I
+already computed the answer
+
+for the children?
+
+How much time does
+it take to compute
+
+the answer for a single node?
+
+AUDIENCE: Constant.
+
+PROFESSOR: Constant.
+
+OK.
+
+AUDIENCE: For a tree, though.
+
+PROFESSOR: For a
+tree, it's order h.
+
+Yeah.
+
+You're getting ahead.
+
+You're rushing me.
+
+You're not letting me finish.
+
+AUDIENCE: Are you saying that
+we store the minimum value?
+
+PROFESSOR: So for every--
+
+AUDIENCE: Each node
+has a field that
+
+says what the minimum
+value is in that tree.
+
+PROFESSOR: Yep, exactly.
+
+So for each node, what's
+the minimum in the subtree.
+
+So if I add a node here,
+suppose I add three
+
+and I had my minimums,
+what changed?
+
+This subtree changed,
+this subtree changed,
+
+this subtree changed, and
+then this subtree changed.
+
+So I have to update the
+minimums here, here, here, here.
+
+Nothing else changed.
+
+Outside the path where
+I did the Insert,
+
+nothing changed, so I don't
+have to update anything.
+
+So what I do is after
+the Insert, I go back up
+
+and I re-compute the values.
+
+So here, I'll have 3.
+
+I go back up 3, 3, 3.
+
+AUDIENCE: You could when
+you're passing down, though.
+
+When you're going
+down that column,
+
+you can just compare
+it on the way down.
+
+You don't have to
+go back up, right?
+
+PROFESSOR: Yep.
+
+So the advantage of doing
+it the way I'm saying it
+
+is that you can have other
+functions instead of minimum.
+
+As long as you can
+compute the function
+
+inside the parent
+in constant time
+
+using the function
+from the children,
+
+it makes sense to compute the
+function on the children first.
+
+There's an obvious function
+that I can't tell you
+
+because that's on the Pset,
+but when you see the next Pset,
+
+you'll see what I mean.
+
+So if you have a
+function where you
+
+know the result for the children
+and you can compute the result
+
+for the parent in constant time,
+then after you do the Insert,
+
+you go up on the path and
+you re-compute the function.
+
+When you delete, what do you do?
+
+AUDIENCE: Same thing.
+
+PROFESSOR: Same thing.
+
+If this goes away, then this
+subtree changed, and then
+
+if there would be
+something else here,
+
+then this subtree changed,
+but nothing else changed.
+
+So whenever you do an Insert
+or a Delete, all you have to do
+
+is go back up the
+path to the parent
+
+and re-compute the function
+that you're trying to compute.
+
+And that's tree augmentation.
+
+Does this make sense somewhat?
+
+That's it.
+
+So what you'll find
+in lecture notes
+
+is a harder way of doing
+it that works for minimum,
+
+but what I told you
+works for everything.
+
+So don't tell people I told you
+how to do this for everything.
+
+Sure nobody's going to know.
\ No newline at end of file
diff --git a/rL25BoFW1V4.txt b/rL25BoFW1V4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a094a2cbe6455f4bbed7b3fa3c97d45d62c5532b
--- /dev/null
+++ b/rL25BoFW1V4.txt
@@ -0,0 +1,6795 @@
+align:start position:0%
+ 
+my name is David Sue I'm a professor of
+
+ align:start position:0%
+my name is David Sue I'm a professor of
+ 
+
+ align:start position:0%
+my name is David Sue I'm a professor of
+urban studies and planning at MIT this
+
+ align:start position:0%
+urban studies and planning at MIT this
+ 
+
+ align:start position:0%
+urban studies and planning at MIT this
+is another installment of my class on
+
+ align:start position:0%
+is another installment of my class on
+ 
+
+ align:start position:0%
+is another installment of my class on
+Urban Energy Systems and policy thank
+
+ align:start position:0%
+Urban Energy Systems and policy thank
+ 
+
+ align:start position:0%
+Urban Energy Systems and policy thank
+you for joining me today we're going to
+
+ align:start position:0%
+you for joining me today we're going to
+ 
+
+ align:start position:0%
+you for joining me today we're going to
+give the third lecture on transportation
+
+ align:start position:0%
+give the third lecture on transportation
+ 
+
+ align:start position:0%
+give the third lecture on transportation
+and I'm going to talk about
+
+ align:start position:0%
+and I'm going to talk about
+ 
+
+ align:start position:0%
+and I'm going to talk about
+Transportation Systems in the first
+
+ align:start position:0%
+Transportation Systems in the first
+ 
+
+ align:start position:0%
+Transportation Systems in the first
+lecture we talked about Transportation
+
+ align:start position:0%
+lecture we talked about Transportation
+ 
+
+ align:start position:0%
+lecture we talked about Transportation
+Technologies personal transport
+
+ align:start position:0%
+Technologies personal transport
+ 
+
+ align:start position:0%
+Technologies personal transport
+standpoint we use that to build up our
+
+ align:start position:0%
+standpoint we use that to build up our
+ 
+
+ align:start position:0%
+standpoint we use that to build up our
+understanding of the Technologies
+
+ align:start position:0%
+understanding of the Technologies
+ 
+
+ align:start position:0%
+understanding of the Technologies
+involved in the last class I talked
+
+ align:start position:0%
+involved in the last class I talked
+ 
+
+ align:start position:0%
+involved in the last class I talked
+about uh policy analysis and how to
+
+ align:start position:0%
+about uh policy analysis and how to
+ 
+
+ align:start position:0%
+about uh policy analysis and how to
+analyze Transportation Systems we talked
+
+ align:start position:0%
+analyze Transportation Systems we talked
+ 
+
+ align:start position:0%
+analyze Transportation Systems we talked
+about it mostly on an equity basis today
+
+ align:start position:0%
+about it mostly on an equity basis today
+ 
+
+ align:start position:0%
+about it mostly on an equity basis today
+I want to talk about about an efficiency
+
+ align:start position:0%
+I want to talk about about an efficiency
+ 
+
+ align:start position:0%
+I want to talk about about an efficiency
+basis and use efficiency to talk about
+
+ align:start position:0%
+basis and use efficiency to talk about
+ 
+
+ align:start position:0%
+basis and use efficiency to talk about
+what cities can do what cities can do to
+
+ align:start position:0%
+what cities can do what cities can do to
+ 
+
+ align:start position:0%
+what cities can do what cities can do to
+affect a transportation system that is
+
+ align:start position:0%
+affect a transportation system that is
+ 
+
+ align:start position:0%
+affect a transportation system that is
+governed at the local level but also the
+
+ align:start position:0%
+governed at the local level but also the
+ 
+
+ align:start position:0%
+governed at the local level but also the
+regional state and federal level also
+
+ align:start position:0%
+regional state and federal level also
+ 
+
+ align:start position:0%
+regional state and federal level also
+so the materials for today are on the
+
+ align:start position:0%
+so the materials for today are on the
+ 
+
+ align:start position:0%
+so the materials for today are on the
+syllabus I'm going to spend most of my
+
+ align:start position:0%
+syllabus I'm going to spend most of my
+ 
+
+ align:start position:0%
+syllabus I'm going to spend most of my
+time talking about that fourth bullet
+
+ align:start position:0%
+time talking about that fourth bullet
+ 
+
+ align:start position:0%
+time talking about that fourth bullet
+point which was not a reading I signed
+
+ align:start position:0%
+point which was not a reading I signed
+ 
+
+ align:start position:0%
+point which was not a reading I signed
+for this class it's a report by
+
+ align:start position:0%
+for this class it's a report by
+ 
+
+ align:start position:0%
+for this class it's a report by
+Cambridge systematics and the Urban Land
+
+ align:start position:0%
+Cambridge systematics and the Urban Land
+ 
+
+ align:start position:0%
+Cambridge systematics and the Urban Land
+Institute it's titled moving cooler and
+
+ align:start position:0%
+Institute it's titled moving cooler and
+ 
+
+ align:start position:0%
+Institute it's titled moving cooler and
+Analysis of Transportation strategies
+
+ align:start position:0%
+Analysis of Transportation strategies
+ 
+
+ align:start position:0%
+Analysis of Transportation strategies
+for reducing greenhouse gas missions
+
+ align:start position:0%
+for reducing greenhouse gas missions
+ 
+
+ align:start position:0%
+for reducing greenhouse gas missions
+I'll tell you a little bit why I didn't
+
+ align:start position:0%
+I'll tell you a little bit why I didn't
+ 
+
+ align:start position:0%
+I'll tell you a little bit why I didn't
+assign it as a reading but at the same
+
+ align:start position:0%
+assign it as a reading but at the same
+ 
+
+ align:start position:0%
+assign it as a reading but at the same
+time I'll spend most of this lecture
+
+ align:start position:0%
+time I'll spend most of this lecture
+ 
+
+ align:start position:0%
+time I'll spend most of this lecture
+talking about it so you won't
+
+ align:start position:0%
+talking about it so you won't
+ 
+
+ align:start position:0%
+talking about it so you won't
+necessarily find these um uh this
+
+ align:start position:0%
+necessarily find these um uh this
+ 
+
+ align:start position:0%
+necessarily find these um uh this
+lecture or it's not part of our sign
+
+ align:start position:0%
+lecture or it's not part of our sign
+ 
+
+ align:start position:0%
+lecture or it's not part of our sign
+reading but I encourage you to listen to
+
+ align:start position:0%
+reading but I encourage you to listen to
+ 
+
+ align:start position:0%
+reading but I encourage you to listen to
+the video lecture because there's things
+
+ align:start position:0%
+the video lecture because there's things
+ 
+
+ align:start position:0%
+the video lecture because there's things
+I want to pull out of that lecture for
+
+ align:start position:0%
+I want to pull out of that lecture for
+ 
+
+ align:start position:0%
+I want to pull out of that lecture for
+class discussion on
+
+ align:start position:0%
+class discussion on
+ 
+
+ align:start position:0%
+class discussion on
+Thursday just to remind you what can
+
+ align:start position:0%
+Thursday just to remind you what can
+ 
+
+ align:start position:0%
+Thursday just to remind you what can
+cities do why is that an important
+
+ align:start position:0%
+cities do why is that an important
+ 
+
+ align:start position:0%
+cities do why is that an important
+question I'll remind you that we're
+
+ align:start position:0%
+question I'll remind you that we're
+ 
+
+ align:start position:0%
+question I'll remind you that we're
+focusing on cities because of population
+
+ align:start position:0%
+focusing on cities because of population
+ 
+
+ align:start position:0%
+focusing on cities because of population
+majority of human beings globally and in
+
+ align:start position:0%
+majority of human beings globally and in
+ 
+
+ align:start position:0%
+majority of human beings globally and in
+almost all countries or almost all
+
+ align:start position:0%
+almost all countries or almost all
+ 
+
+ align:start position:0%
+almost all countries or almost all
+regions of the world live in cities with
+
+ align:start position:0%
+regions of the world live in cities with
+ 
+
+ align:start position:0%
+regions of the world live in cities with
+that population we have a very high
+
+ align:start position:0%
+that population we have a very high
+ 
+
+ align:start position:0%
+that population we have a very high
+degree of economic activity and of
+
+ align:start position:0%
+degree of economic activity and of
+ 
+
+ align:start position:0%
+degree of economic activity and of
+course cities are centers of consumption
+
+ align:start position:0%
+course cities are centers of consumption
+ 
+
+ align:start position:0%
+course cities are centers of consumption
+while we do have cities that produce
+
+ align:start position:0%
+while we do have cities that produce
+ 
+
+ align:start position:0%
+while we do have cities that produce
+energy and materials and goods in
+
+ align:start position:0%
+energy and materials and goods in
+ 
+
+ align:start position:0%
+energy and materials and goods in
+general in urban areas we consume things
+
+ align:start position:0%
+general in urban areas we consume things
+ 
+
+ align:start position:0%
+general in urban areas we consume things
+from the outside like food like
+
+ align:start position:0%
+from the outside like food like
+ 
+
+ align:start position:0%
+from the outside like food like
+materials like fuels and so our cities
+
+ align:start position:0%
+materials like fuels and so our cities
+ 
+
+ align:start position:0%
+materials like fuels and so our cities
+are centers of consumption not
+
+ align:start position:0%
+are centers of consumption not
+ 
+
+ align:start position:0%
+are centers of consumption not
+production and so we have to think about
+
+ align:start position:0%
+production and so we have to think about
+ 
+
+ align:start position:0%
+production and so we have to think about
+the role of cities in reducing
+
+ align:start position:0%
+the role of cities in reducing
+ 
+
+ align:start position:0%
+the role of cities in reducing
+consumption to achieve our
+
+ align:start position:0%
+consumption to achieve our
+ 
+
+ align:start position:0%
+consumption to achieve our
+decarbonization goals this raises
+
+ align:start position:0%
+decarbonization goals this raises
+ 
+
+ align:start position:0%
+decarbonization goals this raises
+questions about how we are going to make
+
+ align:start position:0%
+questions about how we are going to make
+ 
+
+ align:start position:0%
+questions about how we are going to make
+the necessary changes in cities we know
+
+ align:start position:0%
+the necessary changes in cities we know
+ 
+
+ align:start position:0%
+the necessary changes in cities we know
+that cities are composed of land use and
+
+ align:start position:0%
+that cities are composed of land use and
+ 
+
+ align:start position:0%
+that cities are composed of land use and
+built environment I've just made the
+
+ align:start position:0%
+built environment I've just made the
+ 
+
+ align:start position:0%
+built environment I've just made the
+point to you that cities are connected
+
+ align:start position:0%
+point to you that cities are connected
+ 
+
+ align:start position:0%
+point to you that cities are connected
+to outside areas basically all outside
+
+ align:start position:0%
+to outside areas basically all outside
+ 
+
+ align:start position:0%
+to outside areas basically all outside
+areas we import materials foods and fuel
+
+ align:start position:0%
+areas we import materials foods and fuel
+ 
+
+ align:start position:0%
+areas we import materials foods and fuel
+into cities so how do we think about
+
+ align:start position:0%
+into cities so how do we think about
+ 
+
+ align:start position:0%
+into cities so how do we think about
+changing cities or what can cities do in
+
+ align:start position:0%
+changing cities or what can cities do in
+ 
+
+ align:start position:0%
+changing cities or what can cities do in
+a larger transportation
+
+ align:start position:0%
+a larger transportation
+ 
+
+ align:start position:0%
+a larger transportation
+system and we also know that while urban
+
+ align:start position:0%
+system and we also know that while urban
+ 
+
+ align:start position:0%
+system and we also know that while urban
+life seems very fast-paced we also know
+
+ align:start position:0%
+life seems very fast-paced we also know
+ 
+
+ align:start position:0%
+life seems very fast-paced we also know
+that buildings and the shape of cities
+
+ align:start position:0%
+that buildings and the shape of cities
+ 
+
+ align:start position:0%
+that buildings and the shape of cities
+are relatively long lived durable and
+
+ align:start position:0%
+are relatively long lived durable and
+ 
+
+ align:start position:0%
+are relatively long lived durable and
+seemingly slow to change so the question
+
+ align:start position:0%
+seemingly slow to change so the question
+ 
+
+ align:start position:0%
+seemingly slow to change so the question
+is can we make changes as the urban
+
+ align:start position:0%
+is can we make changes as the urban
+ 
+
+ align:start position:0%
+is can we make changes as the urban
+scale fast enough or broadly enough
+
+ align:start position:0%
+scale fast enough or broadly enough
+ 
+
+ align:start position:0%
+scale fast enough or broadly enough
+who's going to do it and how are we
+
+ align:start position:0%
+who's going to do it and how are we
+ 
+
+ align:start position:0%
+who's going to do it and how are we
+going to make these changes and of
+
+ align:start position:0%
+going to make these changes and of
+ 
+
+ align:start position:0%
+going to make these changes and of
+course from efficiency perspective we
+
+ align:start position:0%
+course from efficiency perspective we
+ 
+
+ align:start position:0%
+course from efficiency perspective we
+have to ask what should we do first to
+
+ align:start position:0%
+have to ask what should we do first to
+ 
+
+ align:start position:0%
+have to ask what should we do first to
+try to achieve better enviral
+
+ align:start position:0%
+try to achieve better enviral
+ 
+
+ align:start position:0%
+try to achieve better enviral
+sustainability or
+
+ align:start position:0%
+sustainability or
+ 
+
+ align:start position:0%
+sustainability or
+decarbonization and I just want to
+
+ align:start position:0%
+decarbonization and I just want to
+ 
+
+ align:start position:0%
+decarbonization and I just want to
+emphasize that a lot of the
+
+ align:start position:0%
+emphasize that a lot of the
+ 
+
+ align:start position:0%
+emphasize that a lot of the
+characteristics we are concerned about
+
+ align:start position:0%
+characteristics we are concerned about
+ 
+
+ align:start position:0%
+characteristics we are concerned about
+cities or why we think cities are hard
+
+ align:start position:0%
+cities or why we think cities are hard
+ 
+
+ align:start position:0%
+cities or why we think cities are hard
+to change quickly are similar
+
+ align:start position:0%
+to change quickly are similar
+ 
+
+ align:start position:0%
+to change quickly are similar
+characteristics to infrastructure to put
+
+ align:start position:0%
+characteristics to infrastructure to put
+ 
+
+ align:start position:0%
+characteristics to infrastructure to put
+it simply infrastructure is really big
+
+ align:start position:0%
+it simply infrastructure is really big
+ 
+
+ align:start position:0%
+it simply infrastructure is really big
+it is also longlived durable and
+
+ align:start position:0%
+it is also longlived durable and
+ 
+
+ align:start position:0%
+it is also longlived durable and
+seemingly slow to change infrastructure
+
+ align:start position:0%
+seemingly slow to change infrastructure
+ 
+
+ align:start position:0%
+seemingly slow to change infrastructure
+is really expensive it's composed of a
+
+ align:start position:0%
+is really expensive it's composed of a
+ 
+
+ align:start position:0%
+is really expensive it's composed of a
+lot of assets and investment it's often
+
+ align:start position:0%
+lot of assets and investment it's often
+ 
+
+ align:start position:0%
+lot of assets and investment it's often
+debt financed over long periods of
+
+ align:start position:0%
+debt financed over long periods of
+ 
+
+ align:start position:0%
+debt financed over long periods of
+time it's debt finan over long periods
+
+ align:start position:0%
+time it's debt finan over long periods
+ 
+
+ align:start position:0%
+time it's debt finan over long periods
+of time because infrastructure is
+
+ align:start position:0%
+of time because infrastructure is
+ 
+
+ align:start position:0%
+of time because infrastructure is
+assumed to operate in a fairly
+
+ align:start position:0%
+assumed to operate in a fairly
+ 
+
+ align:start position:0%
+assumed to operate in a fairly
+continuous basis we move large volumes
+
+ align:start position:0%
+continuous basis we move large volumes
+ 
+
+ align:start position:0%
+continuous basis we move large volumes
+of things we have continuous operations
+
+ align:start position:0%
+of things we have continuous operations
+ 
+
+ align:start position:0%
+of things we have continuous operations
+and they connect to Global Systems and
+
+ align:start position:0%
+and they connect to Global Systems and
+ 
+
+ align:start position:0%
+and they connect to Global Systems and
+in other words our supply chains that we
+
+ align:start position:0%
+in other words our supply chains that we
+ 
+
+ align:start position:0%
+in other words our supply chains that we
+have seen stressed over the last couple
+
+ align:start position:0%
+have seen stressed over the last couple
+ 
+
+ align:start position:0%
+have seen stressed over the last couple
+years we know that infrastructure
+
+ align:start position:0%
+years we know that infrastructure
+ 
+
+ align:start position:0%
+years we know that infrastructure
+physically has very large Footprints and
+
+ align:start position:0%
+physically has very large Footprints and
+ 
+
+ align:start position:0%
+physically has very large Footprints and
+areas and impact and we know that we
+
+ align:start position:0%
+areas and impact and we know that we
+ 
+
+ align:start position:0%
+areas and impact and we know that we
+have environmental justice concerns the
+
+ align:start position:0%
+have environmental justice concerns the
+ 
+
+ align:start position:0%
+have environmental justice concerns the
+Buller article I think quite
+
+ align:start position:0%
+Buller article I think quite
+ 
+
+ align:start position:0%
+Buller article I think quite
+convincingly argues that infrastructure
+
+ align:start position:0%
+convincingly argues that infrastructure
+ 
+
+ align:start position:0%
+convincingly argues that infrastructure
+such as transportation is often cited
+
+ align:start position:0%
+such as transportation is often cited
+ 
+
+ align:start position:0%
+such as transportation is often cited
+apologies for that misspelling there
+
+ align:start position:0%
+apologies for that misspelling there
+ 
+
+ align:start position:0%
+apologies for that misspelling there
+cited near poor and minority communities
+
+ align:start position:0%
+cited near poor and minority communities
+ 
+
+ align:start position:0%
+cited near poor and minority communities
+the article examines why but also
+
+ align:start position:0%
+the article examines why but also
+ 
+
+ align:start position:0%
+the article examines why but also
+examines why the environmental burdens
+
+ align:start position:0%
+examines why the environmental burdens
+ 
+
+ align:start position:0%
+examines why the environmental burdens
+of these infrastructures are often
+
+ align:start position:0%
+of these infrastructures are often
+ 
+
+ align:start position:0%
+of these infrastructures are often
+nearly quite often cited your poor and
+
+ align:start position:0%
+nearly quite often cited your poor and
+ 
+
+ align:start position:0%
+nearly quite often cited your poor and
+minority
+
+ align:start position:0%
+minority
+ 
+
+ align:start position:0%
+minority
+communities one last thing I want to
+
+ align:start position:0%
+communities one last thing I want to
+ 
+
+ align:start position:0%
+communities one last thing I want to
+talk about before we talk about
+
+ align:start position:0%
+talk about before we talk about
+ 
+
+ align:start position:0%
+talk about before we talk about
+analyzing systems and understanding what
+
+ align:start position:0%
+analyzing systems and understanding what
+ 
+
+ align:start position:0%
+analyzing systems and understanding what
+cities can do is the concept of energy
+
+ align:start position:0%
+cities can do is the concept of energy
+ 
+
+ align:start position:0%
+cities can do is the concept of energy
+density we know that energy can be
+
+ align:start position:0%
+density we know that energy can be
+ 
+
+ align:start position:0%
+density we know that energy can be
+measured in terms of the sheer amount of
+
+ align:start position:0%
+measured in terms of the sheer amount of
+ 
+
+ align:start position:0%
+measured in terms of the sheer amount of
+energy but more useful for certain kinds
+
+ align:start position:0%
+energy but more useful for certain kinds
+ 
+
+ align:start position:0%
+energy but more useful for certain kinds
+of systems it's good to analyze certain
+
+ align:start position:0%
+of systems it's good to analyze certain
+ 
+
+ align:start position:0%
+of systems it's good to analyze certain
+metrics so in terms of weight we might
+
+ align:start position:0%
+metrics so in terms of weight we might
+ 
+
+ align:start position:0%
+metrics so in terms of weight we might
+think about how much energy certain
+
+ align:start position:0%
+think about how much energy certain
+ 
+
+ align:start position:0%
+think about how much energy certain
+Technologies store like kilowatt hours
+
+ align:start position:0%
+Technologies store like kilowatt hours
+ 
+
+ align:start position:0%
+Technologies store like kilowatt hours
+per kilogram critical applications are
+
+ align:start position:0%
+per kilogram critical applications are
+ 
+
+ align:start position:0%
+per kilogram critical applications are
+planes cars and ebikes because we know
+
+ align:start position:0%
+planes cars and ebikes because we know
+ 
+
+ align:start position:0%
+planes cars and ebikes because we know
+the batteries themselves or the fuel
+
+ align:start position:0%
+the batteries themselves or the fuel
+ 
+
+ align:start position:0%
+the batteries themselves or the fuel
+tank is a really large portion of the
+
+ align:start position:0%
+tank is a really large portion of the
+ 
+
+ align:start position:0%
+tank is a really large portion of the
+vehicle weight itself it's hard to keep
+
+ align:start position:0%
+vehicle weight itself it's hard to keep
+ 
+
+ align:start position:0%
+vehicle weight itself it's hard to keep
+planes in the air you know a heavy car
+
+ align:start position:0%
+planes in the air you know a heavy car
+ 
+
+ align:start position:0%
+planes in the air you know a heavy car
+or heavy bicycle doesn't perform
+
+ align:start position:0%
+or heavy bicycle doesn't perform
+ 
+
+ align:start position:0%
+or heavy bicycle doesn't perform
+similarly to a lighter bicycle or
+
+ align:start position:0%
+similarly to a lighter bicycle or
+ 
+
+ align:start position:0%
+similarly to a lighter bicycle or
+lighter car we can also measure things
+
+ align:start position:0%
+lighter car we can also measure things
+ 
+
+ align:start position:0%
+lighter car we can also measure things
+in terms of energy required to ship a
+
+ align:start position:0%
+in terms of energy required to ship a
+ 
+
+ align:start position:0%
+in terms of energy required to ship a
+certain amount of weight kilowatt hours
+
+ align:start position:0%
+certain amount of weight kilowatt hours
+ 
+
+ align:start position:0%
+certain amount of weight kilowatt hours
+per ton that matters for planes but also
+
+ align:start position:0%
+per ton that matters for planes but also
+ 
+
+ align:start position:0%
+per ton that matters for planes but also
+ships trucks and trains we can measure
+
+ align:start position:0%
+ships trucks and trains we can measure
+ 
+
+ align:start position:0%
+ships trucks and trains we can measure
+energy in terms of kilowatt hours per
+
+ align:start position:0%
+energy in terms of kilowatt hours per
+ 
+
+ align:start position:0%
+energy in terms of kilowatt hours per
+liter of volume terms of the fuel tank
+
+ align:start position:0%
+liter of volume terms of the fuel tank
+ 
+
+ align:start position:0%
+liter of volume terms of the fuel tank
+planes cars trucks you know that the
+
+ align:start position:0%
+planes cars trucks you know that the
+ 
+
+ align:start position:0%
+planes cars trucks you know that the
+fuel tank is not a small portion of the
+
+ align:start position:0%
+fuel tank is not a small portion of the
+ 
+
+ align:start position:0%
+fuel tank is not a small portion of the
+vehicle volume and of course we can
+
+ align:start position:0%
+vehicle volume and of course we can
+ 
+
+ align:start position:0%
+vehicle volume and of course we can
+measure how much Freight volume we can
+
+ align:start position:0%
+measure how much Freight volume we can
+ 
+
+ align:start position:0%
+measure how much Freight volume we can
+move for large amounts of Commodities in
+
+ align:start position:0%
+move for large amounts of Commodities in
+ 
+
+ align:start position:0%
+move for large amounts of Commodities in
+Planes ships trucks and trains we can
+
+ align:start position:0%
+Planes ships trucks and trains we can
+ 
+
+ align:start position:0%
+Planes ships trucks and trains we can
+measure energy in terms of land area for
+
+ align:start position:0%
+measure energy in terms of land area for
+ 
+
+ align:start position:0%
+measure energy in terms of land area for
+example the kilowatt hours produced per
+
+ align:start position:0%
+example the kilowatt hours produced per
+ 
+
+ align:start position:0%
+example the kilowatt hours produced per
+acre let's say biomass we we're going to
+
+ align:start position:0%
+acre let's say biomass we we're going to
+ 
+
+ align:start position:0%
+acre let's say biomass we we're going to
+need biomass to produce liquid fuels and
+
+ align:start position:0%
+need biomass to produce liquid fuels and
+ 
+
+ align:start position:0%
+need biomass to produce liquid fuels and
+hydrogen or kilowatt hours per acre to
+
+ align:start position:0%
+hydrogen or kilowatt hours per acre to
+ 
+
+ align:start position:0%
+hydrogen or kilowatt hours per acre to
+generate solar and wind produce
+
+ align:start position:0%
+generate solar and wind produce
+ 
+
+ align:start position:0%
+generate solar and wind produce
+electricity and finally there's the
+
+ align:start position:0%
+electricity and finally there's the
+ 
+
+ align:start position:0%
+electricity and finally there's the
+energy density of energy dens density
+
+ align:start position:0%
+energy density of energy dens density
+ 
+
+ align:start position:0%
+energy density of energy dens density
+per per money or kilowatt hours per
+
+ align:start position:0%
+per per money or kilowatt hours per
+ 
+
+ align:start position:0%
+per per money or kilowatt hours per
+dollar we obviously need to know that
+
+ align:start position:0%
+dollar we obviously need to know that
+ 
+
+ align:start position:0%
+dollar we obviously need to know that
+for pretty much everything to deploy
+
+ align:start position:0%
+for pretty much everything to deploy
+ 
+
+ align:start position:0%
+for pretty much everything to deploy
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+Technologies this bring things to the
+
+ align:start position:0%
+Technologies this bring things to the
+ 
+
+ align:start position:0%
+Technologies this bring things to the
+moving cooler strategies report it was
+
+ align:start position:0%
+moving cooler strategies report it was
+ 
+
+ align:start position:0%
+moving cooler strategies report it was
+written in 2009 it was written by this
+
+ align:start position:0%
+written in 2009 it was written by this
+ 
+
+ align:start position:0%
+written in 2009 it was written by this
+entire group of different agencies and
+
+ align:start position:0%
+entire group of different agencies and
+ 
+
+ align:start position:0%
+entire group of different agencies and
+environmental groups ranging from the
+
+ align:start position:0%
+environmental groups ranging from the
+ 
+
+ align:start position:0%
+environmental groups ranging from the
+American public transportation
+
+ align:start position:0%
+American public transportation
+ 
+
+ align:start position:0%
+American public transportation
+Association the intelligent
+
+ align:start position:0%
+Association the intelligent
+ 
+
+ align:start position:0%
+Association the intelligent
+Transportation Society of America and
+
+ align:start position:0%
+Transportation Society of America and
+ 
+
+ align:start position:0%
+Transportation Society of America and
+the Shell Oil Company to the
+
+ align:start position:0%
+the Shell Oil Company to the
+ 
+
+ align:start position:0%
+the Shell Oil Company to the
+environmental defense fund the Federal
+
+ align:start position:0%
+environmental defense fund the Federal
+ 
+
+ align:start position:0%
+environmental defense fund the Federal
+Highway Administration Federal Transit
+
+ align:start position:0%
+Highway Administration Federal Transit
+ 
+
+ align:start position:0%
+Highway Administration Federal Transit
+Administration and the US envir
+
+ align:start position:0%
+Administration and the US envir
+ 
+
+ align:start position:0%
+Administration and the US envir
+Protection Agency and a few other groups
+
+ align:start position:0%
+Protection Agency and a few other groups
+ 
+
+ align:start position:0%
+Protection Agency and a few other groups
+and agencies the key point is that this
+
+ align:start position:0%
+and agencies the key point is that this
+ 
+
+ align:start position:0%
+and agencies the key point is that this
+is actually a fairly unusual report it
+
+ align:start position:0%
+is actually a fairly unusual report it
+ 
+
+ align:start position:0%
+is actually a fairly unusual report it
+was meant to bring together a lot of
+
+ align:start position:0%
+was meant to bring together a lot of
+ 
+
+ align:start position:0%
+was meant to bring together a lot of
+disperate groups to think about how to
+
+ align:start position:0%
+disperate groups to think about how to
+ 
+
+ align:start position:0%
+disperate groups to think about how to
+reduce greenhous gas emissions in the
+
+ align:start position:0%
+reduce greenhous gas emissions in the
+ 
+
+ align:start position:0%
+reduce greenhous gas emissions in the
+transportation system which is very much
+
+ align:start position:0%
+transportation system which is very much
+ 
+
+ align:start position:0%
+transportation system which is very much
+tied up to tied up with our urban life
+
+ align:start position:0%
+tied up to tied up with our urban life
+ 
+
+ align:start position:0%
+tied up to tied up with our urban life
+which is why the Urban Land Institute
+
+ align:start position:0%
+which is why the Urban Land Institute
+ 
+
+ align:start position:0%
+which is why the Urban Land Institute
+helped convene this report and
+
+ align:start position:0%
+helped convene this report and
+ 
+
+ align:start position:0%
+helped convene this report and
+workshop and it's important to note why
+
+ align:start position:0%
+workshop and it's important to note why
+ 
+
+ align:start position:0%
+workshop and it's important to note why
+I guess I didn't assign it as weing this
+
+ align:start position:0%
+I guess I didn't assign it as weing this
+ 
+
+ align:start position:0%
+I guess I didn't assign it as weing this
+year I've assigned it in previous years
+
+ align:start position:0%
+year I've assigned it in previous years
+ 
+
+ align:start position:0%
+year I've assigned it in previous years
+it's a 2009 report and honestly it gets
+
+ align:start position:0%
+it's a 2009 report and honestly it gets
+ 
+
+ align:start position:0%
+it's a 2009 report and honestly it gets
+very technical in places so I decided
+
+ align:start position:0%
+very technical in places so I decided
+ 
+
+ align:start position:0%
+very technical in places so I decided
+not to assign it this year but I want to
+
+ align:start position:0%
+not to assign it this year but I want to
+ 
+
+ align:start position:0%
+not to assign it this year but I want to
+highlight some of the findings in this
+
+ align:start position:0%
+highlight some of the findings in this
+ 
+
+ align:start position:0%
+highlight some of the findings in this
+video lecture it's important to note
+
+ align:start position:0%
+video lecture it's important to note
+ 
+
+ align:start position:0%
+video lecture it's important to note
+what this report does have that makes it
+
+ align:start position:0%
+what this report does have that makes it
+ 
+
+ align:start position:0%
+what this report does have that makes it
+a really good report it does have a
+
+ align:start position:0%
+a really good report it does have a
+ 
+
+ align:start position:0%
+a really good report it does have a
+consideration of telor or less work days
+
+ align:start position:0%
+consideration of telor or less work days
+ 
+
+ align:start position:0%
+consideration of telor or less work days
+at the office now we know after two
+
+ align:start position:0%
+at the office now we know after two
+ 
+
+ align:start position:0%
+at the office now we know after two
+years of Zoom this is possible and
+
+ align:start position:0%
+years of Zoom this is possible and
+ 
+
+ align:start position:0%
+years of Zoom this is possible and
+perhaps even preferable now it does
+
+ align:start position:0%
+perhaps even preferable now it does
+ 
+
+ align:start position:0%
+perhaps even preferable now it does
+include changes in vehicle technology
+
+ align:start position:0%
+include changes in vehicle technology
+ 
+
+ align:start position:0%
+include changes in vehicle technology
+fuel technology travel activity vehicle
+
+ align:start position:0%
+fuel technology travel activity vehicle
+ 
+
+ align:start position:0%
+fuel technology travel activity vehicle
+system operations and crucially codes
+
+ align:start position:0%
+system operations and crucially codes
+ 
+
+ align:start position:0%
+system operations and crucially codes
+all different modes of transportation
+
+ align:start position:0%
+all different modes of transportation
+ 
+
+ align:start position:0%
+all different modes of transportation
+passenger modes Transit modes Freight
+
+ align:start position:0%
+passenger modes Transit modes Freight
+ 
+
+ align:start position:0%
+passenger modes Transit modes Freight
+modes shipping modes and Aviation modes
+
+ align:start position:0%
+modes shipping modes and Aviation modes
+ 
+
+ align:start position:0%
+modes shipping modes and Aviation modes
+what it doesn't have it's a 2009 report
+
+ align:start position:0%
+what it doesn't have it's a 2009 report
+ 
+
+ align:start position:0%
+what it doesn't have it's a 2009 report
+but it doesn't actually have shared
+
+ align:start position:0%
+but it doesn't actually have shared
+ 
+
+ align:start position:0%
+but it doesn't actually have shared
+Vehicles zip car was the business model
+
+ align:start position:0%
+Vehicles zip car was the business model
+ 
+
+ align:start position:0%
+Vehicles zip car was the business model
+where you could share vehicles in your
+
+ align:start position:0%
+where you could share vehicles in your
+ 
+
+ align:start position:0%
+where you could share vehicles in your
+neighborhood I think it's since been
+
+ align:start position:0%
+neighborhood I think it's since been
+ 
+
+ align:start position:0%
+neighborhood I think it's since been
+bought by Herz and I'm not sure if Herz
+
+ align:start position:0%
+bought by Herz and I'm not sure if Herz
+ 
+
+ align:start position:0%
+bought by Herz and I'm not sure if Herz
+still offers the vehicle based shared
+
+ align:start position:0%
+still offers the vehicle based shared
+ 
+
+ align:start position:0%
+still offers the vehicle based shared
+vehicles uh the report only written 2009
+
+ align:start position:0%
+vehicles uh the report only written 2009
+ 
+
+ align:start position:0%
+vehicles uh the report only written 2009
+which is the same year that Uber starts
+
+ align:start position:0%
+which is the same year that Uber starts
+ 
+
+ align:start position:0%
+which is the same year that Uber starts
+ride sharing and lift follows three
+
+ align:start position:0%
+ride sharing and lift follows three
+ 
+
+ align:start position:0%
+ride sharing and lift follows three
+years later it doesn't include
+
+ align:start position:0%
+years later it doesn't include
+ 
+
+ align:start position:0%
+years later it doesn't include
+autonomous vehicles they arguably
+
+ align:start position:0%
+autonomous vehicles they arguably
+ 
+
+ align:start position:0%
+autonomous vehicles they arguably
+autonomous vehicles may be a few more
+
+ align:start position:0%
+autonomous vehicles may be a few more
+ 
+
+ align:start position:0%
+autonomous vehicles may be a few more
+years off than we think they are but it
+
+ align:start position:0%
+years off than we think they are but it
+ 
+
+ align:start position:0%
+years off than we think they are but it
+also doesn't include the fact that
+
+ align:start position:0%
+also doesn't include the fact that
+ 
+
+ align:start position:0%
+also doesn't include the fact that
+electric vehicle costs have greatly
+
+ align:start position:0%
+electric vehicle costs have greatly
+ 
+
+ align:start position:0%
+electric vehicle costs have greatly
+decreased and we're seeing increases in
+
+ align:start position:0%
+decreased and we're seeing increases in
+ 
+
+ align:start position:0%
+decreased and we're seeing increases in
+micro Mobility like scooters electric
+
+ align:start position:0%
+micro Mobility like scooters electric
+ 
+
+ align:start position:0%
+micro Mobility like scooters electric
+bikes it doesn't include bike sharing
+
+ align:start position:0%
+bikes it doesn't include bike sharing
+ 
+
+ align:start position:0%
+bikes it doesn't include bike sharing
+which was started in Amsterdam in
+
+ align:start position:0%
+which was started in Amsterdam in
+ 
+
+ align:start position:0%
+which was started in Amsterdam in
+1965 was deployed at Portland Oregon in
+
+ align:start position:0%
+1965 was deployed at Portland Oregon in
+ 
+
+ align:start position:0%
+1965 was deployed at Portland Oregon in
+1995 and dockless bikes started being
+
+ align:start position:0%
+1995 and dockless bikes started being
+ 
+
+ align:start position:0%
+1995 and dockless bikes started being
+deployed in
+
+ align:start position:0%
+deployed in
+ 
+
+ align:start position:0%
+deployed in
+1998 so this report has good aspect also
+
+ align:start position:0%
+1998 so this report has good aspect also
+ 
+
+ align:start position:0%
+1998 so this report has good aspect also
+lacks other
+
+ align:start position:0%
+lacks other
+ 
+
+ align:start position:0%
+lacks other
+aspects it also considers performance
+
+ align:start position:0%
+aspects it also considers performance
+ 
+
+ align:start position:0%
+aspects it also considers performance
+outcomes it does look at greenhouse gas
+
+ align:start position:0%
+outcomes it does look at greenhouse gas
+ 
+
+ align:start position:0%
+outcomes it does look at greenhouse gas
+reductions it looks at the
+
+ align:start position:0%
+reductions it looks at the
+ 
+
+ align:start position:0%
+reductions it looks at the
+implementation costs which is important
+
+ align:start position:0%
+implementation costs which is important
+ 
+
+ align:start position:0%
+implementation costs which is important
+it looks at the change in vehicle costs
+
+ align:start position:0%
+it looks at the change in vehicle costs
+ 
+
+ align:start position:0%
+it looks at the change in vehicle costs
+required to achieve these performance
+
+ align:start position:0%
+required to achieve these performance
+ 
+
+ align:start position:0%
+required to achieve these performance
+outcomes and it looks at Equity effects
+
+ align:start position:0%
+outcomes and it looks at Equity effects
+ 
+
+ align:start position:0%
+outcomes and it looks at Equity effects
+it doesn't look necessarily look at
+
+ align:start position:0%
+it doesn't look necessarily look at
+ 
+
+ align:start position:0%
+it doesn't look necessarily look at
+travel times one of the reasons why we
+
+ align:start position:0%
+travel times one of the reasons why we
+ 
+
+ align:start position:0%
+travel times one of the reasons why we
+care about Transportation like in the
+
+ align:start position:0%
+care about Transportation like in the
+ 
+
+ align:start position:0%
+care about Transportation like in the
+graph before we care about how fast
+
+ align:start position:0%
+graph before we care about how fast
+ 
+
+ align:start position:0%
+graph before we care about how fast
+these modes are even if they use
+
+ align:start position:0%
+these modes are even if they use
+ 
+
+ align:start position:0%
+these modes are even if they use
+different amounts of energy it does not
+
+ align:start position:0%
+different amounts of energy it does not
+ 
+
+ align:start position:0%
+different amounts of energy it does not
+I think look at what positive which is
+
+ align:start position:0%
+I think look at what positive which is
+ 
+
+ align:start position:0%
+I think look at what positive which is
+if we were expand options reduce
+
+ align:start position:0%
+if we were expand options reduce
+ 
+
+ align:start position:0%
+if we were expand options reduce
+congestions or enable greater
+
+ align:start position:0%
+congestions or enable greater
+ 
+
+ align:start position:0%
+congestions or enable greater
+accessibility it doesn't look at
+
+ align:start position:0%
+accessibility it doesn't look at
+ 
+
+ align:start position:0%
+accessibility it doesn't look at
+improving safety which is something we
+
+ align:start position:0%
+improving safety which is something we
+ 
+
+ align:start position:0%
+improving safety which is something we
+care about in our let's say our vision
+
+ align:start position:0%
+care about in our let's say our vision
+ 
+
+ align:start position:0%
+care about in our let's say our vision
+zero plans and it does does not include
+
+ align:start position:0%
+zero plans and it does does not include
+ 
+
+ align:start position:0%
+zero plans and it does does not include
+improvements in livability equity
+
+ align:start position:0%
+improvements in livability equity
+ 
+
+ align:start position:0%
+improvements in livability equity
+improve local market quality and enhance
+
+ align:start position:0%
+improve local market quality and enhance
+ 
+
+ align:start position:0%
+improve local market quality and enhance
+public health for example I don't think
+
+ align:start position:0%
+public health for example I don't think
+ 
+
+ align:start position:0%
+public health for example I don't think
+it considers the impacts of air
+
+ align:start position:0%
+it considers the impacts of air
+ 
+
+ align:start position:0%
+it considers the impacts of air
+pollution on asthma or chronic pulmonary
+
+ align:start position:0%
+pollution on asthma or chronic pulmonary
+ 
+
+ align:start position:0%
+pollution on asthma or chronic pulmonary
+heart disease which we know are really
+
+ align:start position:0%
+heart disease which we know are really
+ 
+
+ align:start position:0%
+heart disease which we know are really
+big impacts of our transportation system
+
+ align:start position:0%
+big impacts of our transportation system
+ 
+
+ align:start position:0%
+big impacts of our transportation system
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+but the most important thing about this
+
+ align:start position:0%
+but the most important thing about this
+ 
+
+ align:start position:0%
+but the most important thing about this
+from a policy perspective for cities is
+
+ align:start position:0%
+from a policy perspective for cities is
+ 
+
+ align:start position:0%
+from a policy perspective for cities is
+that it does include many different
+
+ align:start position:0%
+that it does include many different
+ 
+
+ align:start position:0%
+that it does include many different
+strategies that cities can Implement in
+
+ align:start position:0%
+strategies that cities can Implement in
+ 
+
+ align:start position:0%
+strategies that cities can Implement in
+various ways it includes many kinds of
+
+ align:start position:0%
+various ways it includes many kinds of
+ 
+
+ align:start position:0%
+various ways it includes many kinds of
+pricing and taxes ranging from parking
+
+ align:start position:0%
+pricing and taxes ranging from parking
+ 
+
+ align:start position:0%
+pricing and taxes ranging from parking
+pricing to Road or congestion pricing it
+
+ align:start position:0%
+pricing to Road or congestion pricing it
+ 
+
+ align:start position:0%
+pricing to Road or congestion pricing it
+includes land use and smart growth
+
+ align:start position:0%
+includes land use and smart growth
+ 
+
+ align:start position:0%
+includes land use and smart growth
+policies includes non-motorized
+
+ align:start position:0%
+policies includes non-motorized
+ 
+
+ align:start position:0%
+policies includes non-motorized
+Transportation includes improvements to
+
+ align:start position:0%
+Transportation includes improvements to
+ 
+
+ align:start position:0%
+Transportation includes improvements to
+public transportation includes ride
+
+ align:start position:0%
+public transportation includes ride
+ 
+
+ align:start position:0%
+public transportation includes ride
+sharing and car sharing and other
+
+ align:start position:0%
+sharing and car sharing and other
+ 
+
+ align:start position:0%
+sharing and car sharing and other
+community strategies I think they're
+
+ align:start position:0%
+community strategies I think they're
+ 
+
+ align:start position:0%
+community strategies I think they're
+referring mostly to car pooling not to
+
+ align:start position:0%
+referring mostly to car pooling not to
+ 
+
+ align:start position:0%
+referring mostly to car pooling not to
+ride hailing services but you can
+
+ align:start position:0%
+ride hailing services but you can
+ 
+
+ align:start position:0%
+ride hailing services but you can
+imagine that some of those results might
+
+ align:start position:0%
+imagine that some of those results might
+ 
+
+ align:start position:0%
+imagine that some of those results might
+extend to ride hailing Services includes
+
+ align:start position:0%
+extend to ride hailing Services includes
+ 
+
+ align:start position:0%
+extend to ride hailing Services includes
+regulatory strategies operational and
+
+ align:start position:0%
+regulatory strategies operational and
+ 
+
+ align:start position:0%
+regulatory strategies operational and
+intelligent Transportation strategies
+
+ align:start position:0%
+intelligent Transportation strategies
+ 
+
+ align:start position:0%
+intelligent Transportation strategies
+things that are probably have expanded
+
+ align:start position:0%
+things that are probably have expanded
+ 
+
+ align:start position:0%
+things that are probably have expanded
+in the last 13 years since the report
+
+ align:start position:0%
+in the last 13 years since the report
+ 
+
+ align:start position:0%
+in the last 13 years since the report
+was written because the growth of
+
+ align:start position:0%
+was written because the growth of
+ 
+
+ align:start position:0%
+was written because the growth of
+telecomunications infrastructure I just
+
+ align:start position:0%
+telecomunications infrastructure I just
+ 
+
+ align:start position:0%
+telecomunications infrastructure I just
+to put this in perspective this report
+
+ align:start position:0%
+to put this in perspective this report
+ 
+
+ align:start position:0%
+to put this in perspective this report
+was written one year after the iPhone
+
+ align:start position:0%
+was written one year after the iPhone
+ 
+
+ align:start position:0%
+was written one year after the iPhone
+was introduced and yet we probably all
+
+ align:start position:0%
+was introduced and yet we probably all
+ 
+
+ align:start position:0%
+was introduced and yet we probably all
+use various mapping applications on our
+
+ align:start position:0%
+use various mapping applications on our
+ 
+
+ align:start position:0%
+use various mapping applications on our
+phones every day now to figure out the
+
+ align:start position:0%
+phones every day now to figure out the
+ 
+
+ align:start position:0%
+phones every day now to figure out the
+quickest way to a certain place or to
+
+ align:start position:0%
+quickest way to a certain place or to
+ 
+
+ align:start position:0%
+quickest way to a certain place or to
+work and finally capacity expansion
+
+ align:start position:0%
+work and finally capacity expansion
+ 
+
+ align:start position:0%
+work and finally capacity expansion
+bottleneck relief multimodal great
+
+ align:start position:0%
+bottleneck relief multimodal great
+ 
+
+ align:start position:0%
+bottleneck relief multimodal great
+sector strategies I would argue are
+
+ align:start position:0%
+sector strategies I would argue are
+ 
+
+ align:start position:0%
+sector strategies I would argue are
+things that as urban planners we don't
+
+ align:start position:0%
+things that as urban planners we don't
+ 
+
+ align:start position:0%
+things that as urban planners we don't
+look at very
+
+ align:start position:0%
+look at very
+ 
+
+ align:start position:0%
+look at very
+often it also considers expanded uh
+
+ align:start position:0%
+often it also considers expanded uh
+ 
+
+ align:start position:0%
+often it also considers expanded uh
+different levels of deployment expanded
+
+ align:start position:0%
+different levels of deployment expanded
+ 
+
+ align:start position:0%
+different levels of deployment expanded
+hear practice focuses mostly on major
+
+ align:start position:0%
+hear practice focuses mostly on major
+ 
+
+ align:start position:0%
+hear practice focuses mostly on major
+Metro areas an aggressive level of
+
+ align:start position:0%
+Metro areas an aggressive level of
+ 
+
+ align:start position:0%
+Metro areas an aggressive level of
+deployment does this sooner and more
+
+ align:start position:0%
+deployment does this sooner and more
+ 
+
+ align:start position:0%
+deployment does this sooner and more
+broadly geographically deployed through
+
+ align:start position:0%
+broadly geographically deployed through
+ 
+
+ align:start position:0%
+broadly geographically deployed through
+smaller or Med mediumsized metral areas
+
+ align:start position:0%
+smaller or Med mediumsized metral areas
+ 
+
+ align:start position:0%
+smaller or Med mediumsized metral areas
+and a maximum effort assumes we have a
+
+ align:start position:0%
+and a maximum effort assumes we have a
+ 
+
+ align:start position:0%
+and a maximum effort assumes we have a
+maximum National regional and local
+
+ align:start position:0%
+maximum National regional and local
+ 
+
+ align:start position:0%
+maximum National regional and local
+focus on trying to reduce green gas
+
+ align:start position:0%
+focus on trying to reduce green gas
+ 
+
+ align:start position:0%
+focus on trying to reduce green gas
+emissions finally they they categorize
+
+ align:start position:0%
+emissions finally they they categorize
+ 
+
+ align:start position:0%
+emissions finally they they categorize
+these things into two different strategy
+
+ align:start position:0%
+these things into two different strategy
+ 
+
+ align:start position:0%
+these things into two different strategy
+bundles they look at near-term early
+
+ align:start position:0%
+bundles they look at near-term early
+ 
+
+ align:start position:0%
+bundles they look at near-term early
+results they look at long-term maximum
+
+ align:start position:0%
+results they look at long-term maximum
+ 
+
+ align:start position:0%
+results they look at long-term maximum
+results they look at land use Transit
+
+ align:start position:0%
+results they look at land use Transit
+ 
+
+ align:start position:0%
+results they look at land use Transit
+and a non-motorized bundle and they look
+
+ align:start position:0%
+and a non-motorized bundle and they look
+ 
+
+ align:start position:0%
+and a non-motorized bundle and they look
+at a system driver a system and Driver
+
+ align:start position:0%
+at a system driver a system and Driver
+ 
+
+ align:start position:0%
+at a system driver a system and Driver
+efficiency bundle a bundle that improves
+
+ align:start position:0%
+efficiency bundle a bundle that improves
+ 
+
+ align:start position:0%
+efficiency bundle a bundle that improves
+Transportation facilities themselves and
+
+ align:start position:0%
+Transportation facilities themselves and
+ 
+
+ align:start position:0%
+Transportation facilities themselves and
+finally and importantly a lowcost Bund
+
+ align:start position:0%
+finally and importantly a lowcost Bund
+ 
+
+ align:start position:0%
+finally and importantly a lowcost Bund
+looking at what are the lowest cost
+
+ align:start position:0%
+looking at what are the lowest cost
+ 
+
+ align:start position:0%
+looking at what are the lowest cost
+things we can do to reduce greenhouse
+
+ align:start position:0%
+things we can do to reduce greenhouse
+ 
+
+ align:start position:0%
+things we can do to reduce greenhouse
+gas
+
+ align:start position:0%
+gas
+ 
+
+ align:start position:0%
+gas
+emissions so if you look at some of the
+
+ align:start position:0%
+emissions so if you look at some of the
+ 
+
+ align:start position:0%
+emissions so if you look at some of the
+results they measure things against the
+
+ align:start position:0%
+results they measure things against the
+ 
+
+ align:start position:0%
+results they measure things against the
+study Baseline they do a sensitivity
+
+ align:start position:0%
+study Baseline they do a sensitivity
+ 
+
+ align:start position:0%
+study Baseline they do a sensitivity
+analysis according to different kinds of
+
+ align:start position:0%
+analysis according to different kinds of
+ 
+
+ align:start position:0%
+analysis according to different kinds of
+assumptions around fuel prices vehicle
+
+ align:start position:0%
+assumptions around fuel prices vehicle
+ 
+
+ align:start position:0%
+assumptions around fuel prices vehicle
+miles traveled Obama administration
+
+ align:start position:0%
+miles traveled Obama administration
+ 
+
+ align:start position:0%
+miles traveled Obama administration
+proposal at the time crucially though
+
+ align:start position:0%
+proposal at the time crucially though
+ 
+
+ align:start position:0%
+proposal at the time crucially though
+and this is something that always found
+
+ align:start position:0%
+and this is something that always found
+ 
+
+ align:start position:0%
+and this is something that always found
+a little depressing when I taught this
+
+ align:start position:0%
+a little depressing when I taught this
+ 
+
+ align:start position:0%
+a little depressing when I taught this
+report in class is that if you look at
+
+ align:start position:0%
+report in class is that if you look at
+ 
+
+ align:start position:0%
+report in class is that if you look at
+the six strategy bundles at the maximum
+
+ align:start position:0%
+the six strategy bundles at the maximum
+ 
+
+ align:start position:0%
+the six strategy bundles at the maximum
+and aggressive deployment levels you can
+
+ align:start position:0%
+and aggressive deployment levels you can
+ 
+
+ align:start position:0%
+and aggressive deployment levels you can
+see that the most Max the maximum range
+
+ align:start position:0%
+see that the most Max the maximum range
+ 
+
+ align:start position:0%
+see that the most Max the maximum range
+of full National regional and local
+
+ align:start position:0%
+of full National regional and local
+ 
+
+ align:start position:0%
+of full National regional and local
+effort only gets this to about a 24%
+
+ align:start position:0%
+effort only gets this to about a 24%
+ 
+
+ align:start position:0%
+effort only gets this to about a 24%
+reduction in V GRE gas emissions the
+
+ align:start position:0%
+reduction in V GRE gas emissions the
+ 
+
+ align:start position:0%
+reduction in V GRE gas emissions the
+report was written in 2009 they had a 4%
+
+ align:start position:0%
+report was written in 2009 they had a 4%
+ 
+
+ align:start position:0%
+report was written in 2009 they had a 4%
+decline already baked in I assume
+
+ align:start position:0%
+decline already baked in I assume
+ 
+
+ align:start position:0%
+decline already baked in I assume
+largely from vehicle efficiency
+
+ align:start position:0%
+largely from vehicle efficiency
+ 
+
+ align:start position:0%
+largely from vehicle efficiency
+standards but if we do everything in the
+
+ align:start position:0%
+standards but if we do everything in the
+ 
+
+ align:start position:0%
+standards but if we do everything in the
+report that they analyze which we'll
+
+ align:start position:0%
+report that they analyze which we'll
+ 
+
+ align:start position:0%
+report that they analyze which we'll
+talk more about you only get to a 24%
+
+ align:start position:0%
+talk more about you only get to a 24%
+ 
+
+ align:start position:0%
+talk more about you only get to a 24%
+reduction of course a 24% reduction in
+
+ align:start position:0%
+reduction of course a 24% reduction in
+ 
+
+ align:start position:0%
+reduction of course a 24% reduction in
+transcation which is about 30% % of our
+
+ align:start position:0%
+transcation which is about 30% % of our
+ 
+
+ align:start position:0%
+transcation which is about 30% % of our
+total greenhous gas missions is not
+
+ align:start position:0%
+total greenhous gas missions is not
+ 
+
+ align:start position:0%
+total greenhous gas missions is not
+nothing that's about a seven or 8%
+
+ align:start position:0%
+nothing that's about a seven or 8%
+ 
+
+ align:start position:0%
+nothing that's about a seven or 8%
+reduction in our total greenhous gas
+
+ align:start position:0%
+reduction in our total greenhous gas
+ 
+
+ align:start position:0%
+reduction in our total greenhous gas
+missions by 2050 but obviously a small
+
+ align:start position:0%
+missions by 2050 but obviously a small
+ 
+
+ align:start position:0%
+missions by 2050 but obviously a small
+drop in the bucket towards where we need
+
+ align:start position:0%
+drop in the bucket towards where we need
+ 
+
+ align:start position:0%
+drop in the bucket towards where we need
+to go in
+
+ align:start position:0%
+to go in
+ 
+
+ align:start position:0%
+to go in
+2050 but and if we just maybe highlight
+
+ align:start position:0%
+2050 but and if we just maybe highlight
+ 
+
+ align:start position:0%
+2050 but and if we just maybe highlight
+that again you can see that the maximum
+
+ align:start position:0%
+that again you can see that the maximum
+ 
+
+ align:start position:0%
+that again you can see that the maximum
+level deployment reduces millions of
+
+ align:start position:0%
+level deployment reduces millions of
+ 
+
+ align:start position:0%
+level deployment reduces millions of
+barrels per year by 11 maybe 110 to 470
+
+ align:start position:0%
+barrels per year by 11 maybe 110 to 470
+ 
+
+ align:start position:0%
+barrels per year by 11 maybe 110 to 470
+million barrels per year but the
+
+ align:start position:0%
+million barrels per year but the
+ 
+
+ align:start position:0%
+million barrels per year but the
+consumption in the US is 5.7 million
+
+ align:start position:0%
+consumption in the US is 5.7 million
+ 
+
+ align:start position:0%
+consumption in the US is 5.7 million
+barrels per day so in other this range
+
+ align:start position:0%
+barrels per day so in other this range
+ 
+
+ align:start position:0%
+barrels per day so in other this range
+is only about 19 or 82 days per year in
+
+ align:start position:0%
+is only about 19 or 82 days per year in
+ 
+
+ align:start position:0%
+is only about 19 or 82 days per year in
+the transportation system alone these
+
+ align:start position:0%
+the transportation system alone these
+ 
+
+ align:start position:0%
+the transportation system alone these
+assumptions of course could have changed
+
+ align:start position:0%
+assumptions of course could have changed
+ 
+
+ align:start position:0%
+assumptions of course could have changed
+in the last 13 year last 13 years but I
+
+ align:start position:0%
+in the last 13 year last 13 years but I
+ 
+
+ align:start position:0%
+in the last 13 year last 13 years but I
+think this just highlights that you know
+
+ align:start position:0%
+think this just highlights that you know
+ 
+
+ align:start position:0%
+think this just highlights that you know
+transportation is a really hard to
+
+ align:start position:0%
+transportation is a really hard to
+ 
+
+ align:start position:0%
+transportation is a really hard to
+decarbonize
+
+ align:start position:0%
+decarbonize
+ 
+
+ align:start position:0%
+decarbonize
+sector now there's one point that I want
+
+ align:start position:0%
+sector now there's one point that I want
+ 
+
+ align:start position:0%
+sector now there's one point that I want
+to make about all of these different
+
+ align:start position:0%
+to make about all of these different
+ 
+
+ align:start position:0%
+to make about all of these different
+strategies and I think it's an important
+
+ align:start position:0%
+strategies and I think it's an important
+ 
+
+ align:start position:0%
+strategies and I think it's an important
+point to make which is we can have these
+
+ align:start position:0%
+point to make which is we can have these
+ 
+
+ align:start position:0%
+point to make which is we can have these
+six different approaches to trying to
+
+ align:start position:0%
+six different approaches to trying to
+ 
+
+ align:start position:0%
+six different approaches to trying to
+reduce our greenhouse gas assumptions in
+
+ align:start position:0%
+reduce our greenhouse gas assumptions in
+ 
+
+ align:start position:0%
+reduce our greenhouse gas assumptions in
+this First Column they all have varying
+
+ align:start position:0%
+this First Column they all have varying
+ 
+
+ align:start position:0%
+this First Column they all have varying
+degrees of greenhouse gas reduction they
+
+ align:start position:0%
+degrees of greenhouse gas reduction they
+ 
+
+ align:start position:0%
+degrees of greenhouse gas reduction they
+also have positive implementation costs
+
+ align:start position:0%
+also have positive implementation costs
+ 
+
+ align:start position:0%
+also have positive implementation costs
+you can see they cost different amounts
+
+ align:start position:0%
+you can see they cost different amounts
+ 
+
+ align:start position:0%
+you can see they cost different amounts
+the U System and Driver efficiency
+
+ align:start position:0%
+the U System and Driver efficiency
+ 
+
+ align:start position:0%
+the U System and Driver efficiency
+perhaps efforts are relatively expensive
+
+ align:start position:0%
+perhaps efforts are relatively expensive
+ 
+
+ align:start position:0%
+perhaps efforts are relatively expensive
+the long-term maximum results and
+
+ align:start position:0%
+the long-term maximum results and
+ 
+
+ align:start position:0%
+the long-term maximum results and
+facility pricing are relatively
+
+ align:start position:0%
+facility pricing are relatively
+ 
+
+ align:start position:0%
+facility pricing are relatively
+expensive but the point is all the
+
+ align:start position:0%
+expensive but the point is all the
+ 
+
+ align:start position:0%
+expensive but the point is all the
+implementation costs are positive but
+
+ align:start position:0%
+implementation costs are positive but
+ 
+
+ align:start position:0%
+implementation costs are positive but
+the changes in vehicle costs are all
+
+ align:start position:0%
+the changes in vehicle costs are all
+ 
+
+ align:start position:0%
+the changes in vehicle costs are all
+negative and much larger which is to say
+
+ align:start position:0%
+negative and much larger which is to say
+ 
+
+ align:start position:0%
+negative and much larger which is to say
+that vehicle costs in footnote B says
+
+ align:start position:0%
+that vehicle costs in footnote B says
+ 
+
+ align:start position:0%
+that vehicle costs in footnote B says
+it's the estimated cumul reduction the
+
+ align:start position:0%
+it's the estimated cumul reduction the
+ 
+
+ align:start position:0%
+it's the estimated cumul reduction the
+cost of owning and operating vehicles
+
+ align:start position:0%
+cost of owning and operating vehicles
+ 
+
+ align:start position:0%
+cost of owning and operating vehicles
+from a societal perspective which would
+
+ align:start position:0%
+from a societal perspective which would
+ 
+
+ align:start position:0%
+from a societal perspective which would
+result in reduction in vehicle miles
+
+ align:start position:0%
+result in reduction in vehicle miles
+ 
+
+ align:start position:0%
+result in reduction in vehicle miles
+travel and fuel consumption in other
+
+ align:start position:0%
+travel and fuel consumption in other
+ 
+
+ align:start position:0%
+travel and fuel consumption in other
+words even though the implementation
+
+ align:start position:0%
+words even though the implementation
+ 
+
+ align:start position:0%
+words even though the implementation
+cost for all these strategies is
+
+ align:start position:0%
+cost for all these strategies is
+ 
+
+ align:start position:0%
+cost for all these strategies is
+positive the change in vehicle cost is
+
+ align:start position:0%
+positive the change in vehicle cost is
+ 
+
+ align:start position:0%
+positive the change in vehicle cost is
+negative and much larger which means if
+
+ align:start position:0%
+negative and much larger which means if
+ 
+
+ align:start position:0%
+negative and much larger which means if
+you take the implementation cost minus
+
+ align:start position:0%
+you take the implementation cost minus
+ 
+
+ align:start position:0%
+you take the implementation cost minus
+vehicle costs you can see in almost all
+
+ align:start position:0%
+vehicle costs you can see in almost all
+ 
+
+ align:start position:0%
+vehicle costs you can see in almost all
+these cases five out of six cases we
+
+ align:start position:0%
+these cases five out of six cases we
+ 
+
+ align:start position:0%
+these cases five out of six cases we
+actually save a lot of money over the
+
+ align:start position:0%
+actually save a lot of money over the
+ 
+
+ align:start position:0%
+actually save a lot of money over the
+forecast for these different strategies
+
+ align:start position:0%
+forecast for these different strategies
+ 
+
+ align:start position:0%
+forecast for these different strategies
+this is that the aggressive level
+
+ align:start position:0%
+this is that the aggressive level
+ 
+
+ align:start position:0%
+this is that the aggressive level
+deployment if you look at maximum level
+
+ align:start position:0%
+deployment if you look at maximum level
+ 
+
+ align:start position:0%
+deployment if you look at maximum level
+of deployment again five out of these
+
+ align:start position:0%
+of deployment again five out of these
+ 
+
+ align:start position:0%
+of deployment again five out of these
+six strategies are actually negative
+
+ align:start position:0%
+six strategies are actually negative
+ 
+
+ align:start position:0%
+six strategies are actually negative
+cost so if we look at the greenhouse gas
+
+ align:start position:0%
+cost so if we look at the greenhouse gas
+ 
+
+ align:start position:0%
+cost so if we look at the greenhouse gas
+reductions that results they actually
+
+ align:start position:0%
+reductions that results they actually
+ 
+
+ align:start position:0%
+reductions that results they actually
+have a negative cost per ton which is to
+
+ align:start position:0%
+have a negative cost per ton which is to
+ 
+
+ align:start position:0%
+have a negative cost per ton which is to
+say that not only do you save money you
+
+ align:start position:0%
+say that not only do you save money you
+ 
+
+ align:start position:0%
+say that not only do you save money you
+can also reduce greenhouse gas emissions
+
+ align:start position:0%
+can also reduce greenhouse gas emissions
+ 
+
+ align:start position:0%
+can also reduce greenhouse gas emissions
+and that's true for five out of the six
+
+ align:start position:0%
+and that's true for five out of the six
+ 
+
+ align:start position:0%
+and that's true for five out of the six
+strategies at the aggressive deployment
+
+ align:start position:0%
+strategies at the aggressive deployment
+ 
+
+ align:start position:0%
+strategies at the aggressive deployment
+level and it's true for four out of the
+
+ align:start position:0%
+level and it's true for four out of the
+ 
+
+ align:start position:0%
+level and it's true for four out of the
+six strategies at the maximum deployment
+
+ align:start position:0%
+six strategies at the maximum deployment
+ 
+
+ align:start position:0%
+six strategies at the maximum deployment
+level this is not taking into account
+
+ align:start position:0%
+level this is not taking into account
+ 
+
+ align:start position:0%
+level this is not taking into account
+the cost of actually reducing carbon or
+
+ align:start position:0%
+the cost of actually reducing carbon or
+ 
+
+ align:start position:0%
+the cost of actually reducing carbon or
+the social cost of carbon for example
+
+ align:start position:0%
+the social cost of carbon for example
+ 
+
+ align:start position:0%
+the social cost of carbon for example
+the net cost of reducing a ton of gas
+
+ align:start position:0%
+the net cost of reducing a ton of gas
+ 
+
+ align:start position:0%
+the net cost of reducing a ton of gas
+gas emissions in the near-term or early
+
+ align:start position:0%
+gas emissions in the near-term or early
+ 
+
+ align:start position:0%
+gas emissions in the near-term or early
+results is negative $410 per ton at
+
+ align:start position:0%
+results is negative $410 per ton at
+ 
+
+ align:start position:0%
+results is negative $410 per ton at
+maximum deployment level which means
+
+ align:start position:0%
+maximum deployment level which means
+ 
+
+ align:start position:0%
+maximum deployment level which means
+that we would actually save $400 for
+
+ align:start position:0%
+that we would actually save $400 for
+ 
+
+ align:start position:0%
+that we would actually save $400 for
+every ton of greenhous gas emissions we
+
+ align:start position:0%
+every ton of greenhous gas emissions we
+ 
+
+ align:start position:0%
+every ton of greenhous gas emissions we
+saving that's not even including
+
+ align:start position:0%
+saving that's not even including
+ 
+
+ align:start position:0%
+saving that's not even including
+including the $51 the federal government
+
+ align:start position:0%
+including the $51 the federal government
+ 
+
+ align:start position:0%
+including the $51 the federal government
+says every ton of gas emissions cost us
+
+ align:start position:0%
+says every ton of gas emissions cost us
+ 
+
+ align:start position:0%
+says every ton of gas emissions cost us
+or the $150 that the most recent studies
+
+ align:start position:0%
+or the $150 that the most recent studies
+ 
+
+ align:start position:0%
+or the $150 that the most recent studies
+say is the social cost of carbon so this
+
+ align:start position:0%
+say is the social cost of carbon so this
+ 
+
+ align:start position:0%
+say is the social cost of carbon so this
+is to say that we should try to do the
+
+ align:start position:0%
+is to say that we should try to do the
+ 
+
+ align:start position:0%
+is to say that we should try to do the
+negative cost stuff because we're going
+
+ align:start position:0%
+negative cost stuff because we're going
+ 
+
+ align:start position:0%
+negative cost stuff because we're going
+to do greenhous gas missions and save
+
+ align:start position:0%
+to do greenhous gas missions and save
+ 
+
+ align:start position:0%
+to do greenhous gas missions and save
+ourselves money in fuel
+
+ align:start position:0%
+ourselves money in fuel
+ 
+
+ align:start position:0%
+ourselves money in fuel
+anyways just to show you this
+
+ align:start position:0%
+anyways just to show you this
+ 
+
+ align:start position:0%
+anyways just to show you this
+graphically this is for the near-term
+
+ align:start position:0%
+graphically this is for the near-term
+ 
+
+ align:start position:0%
+graphically this is for the near-term
+early results bundle aggressive
+
+ align:start position:0%
+early results bundle aggressive
+ 
+
+ align:start position:0%
+early results bundle aggressive
+deployment it cost about 20 billion doll
+
+ align:start position:0%
+deployment it cost about 20 billion doll
+ 
+
+ align:start position:0%
+deployment it cost about 20 billion doll
+in 2008 to implement between 2008 2050
+
+ align:start position:0%
+in 2008 to implement between 2008 2050
+ 
+
+ align:start position:0%
+in 2008 to implement between 2008 2050
+but you can see the vehicle cost savings
+
+ align:start position:0%
+but you can see the vehicle cost savings
+ 
+
+ align:start position:0%
+but you can see the vehicle cost savings
+work that at their high point they're
+
+ align:start position:0%
+work that at their high point they're
+ 
+
+ align:start position:0%
+work that at their high point they're
+about five times more than the original
+
+ align:start position:0%
+about five times more than the original
+ 
+
+ align:start position:0%
+about five times more than the original
+the implementation cost that year and
+
+ align:start position:0%
+the implementation cost that year and
+ 
+
+ align:start position:0%
+the implementation cost that year and
+even at their lowest point in 2050 there
+
+ align:start position:0%
+even at their lowest point in 2050 there
+ 
+
+ align:start position:0%
+even at their lowest point in 2050 there
+are four times the implementation cost
+
+ align:start position:0%
+are four times the implementation cost
+ 
+
+ align:start position:0%
+are four times the implementation cost
+this isst to say if we make policy
+
+ align:start position:0%
+this isst to say if we make policy
+ 
+
+ align:start position:0%
+this isst to say if we make policy
+changes and change infrastructure we can
+
+ align:start position:0%
+changes and change infrastructure we can
+ 
+
+ align:start position:0%
+changes and change infrastructure we can
+reduce greenhouse gas emissions and save
+
+ align:start position:0%
+reduce greenhouse gas emissions and save
+ 
+
+ align:start position:0%
+reduce greenhouse gas emissions and save
+money in the long term throughout almost
+
+ align:start position:0%
+money in the long term throughout almost
+ 
+
+ align:start position:0%
+money in the long term throughout almost
+the entire life of this bundle and if
+
+ align:start position:0%
+the entire life of this bundle and if
+ 
+
+ align:start position:0%
+the entire life of this bundle and if
+you look at what that bundle is supposed
+
+ align:start position:0%
+you look at what that bundle is supposed
+ 
+
+ align:start position:0%
+you look at what that bundle is supposed
+of you can see that there's different
+
+ align:start position:0%
+of you can see that there's different
+ 
+
+ align:start position:0%
+of you can see that there's different
+categories this composed of Park pricing
+
+ align:start position:0%
+categories this composed of Park pricing
+ 
+
+ align:start position:0%
+categories this composed of Park pricing
+strategies for example a price on
+
+ align:start position:0%
+strategies for example a price on
+ 
+
+ align:start position:0%
+strategies for example a price on
+parking in Central Business districts
+
+ align:start position:0%
+parking in Central Business districts
+ 
+
+ align:start position:0%
+parking in Central Business districts
+a price on parking for free private
+
+ align:start position:0%
+a price on parking for free private
+ 
+
+ align:start position:0%
+a price on parking for free private
+parking residential parking permits and
+
+ align:start position:0%
+parking residential parking permits and
+ 
+
+ align:start position:0%
+parking residential parking permits and
+congestion pricing public transportation
+
+ align:start position:0%
+congestion pricing public transportation
+ 
+
+ align:start position:0%
+congestion pricing public transportation
+strategies we have commuting strategies
+
+ align:start position:0%
+strategies we have commuting strategies
+ 
+
+ align:start position:0%
+strategies we have commuting strategies
+we regulatory strategies system
+
+ align:start position:0%
+we regulatory strategies system
+ 
+
+ align:start position:0%
+we regulatory strategies system
+operation strategies and multim modal
+
+ align:start position:0%
+operation strategies and multim modal
+ 
+
+ align:start position:0%
+operation strategies and multim modal
+Freight strategies all these things
+
+ align:start position:0%
+Freight strategies all these things
+ 
+
+ align:start position:0%
+Freight strategies all these things
+together get us a 14% decrease in Prenos
+
+ align:start position:0%
+together get us a 14% decrease in Prenos
+ 
+
+ align:start position:0%
+together get us a 14% decrease in Prenos
+gas emissions from just the near-term
+
+ align:start position:0%
+gas emissions from just the near-term
+ 
+
+ align:start position:0%
+gas emissions from just the near-term
+early results bundle but also crucially
+
+ align:start position:0%
+early results bundle but also crucially
+ 
+
+ align:start position:0%
+early results bundle but also crucially
+it is saving us money in this bundle
+
+ align:start position:0%
+it is saving us money in this bundle
+ 
+
+ align:start position:0%
+it is saving us money in this bundle
+throughout the lifetime of the bundle if
+
+ align:start position:0%
+throughout the lifetime of the bundle if
+ 
+
+ align:start position:0%
+throughout the lifetime of the bundle if
+we do the longterm our maximum results
+
+ align:start position:0%
+we do the longterm our maximum results
+ 
+
+ align:start position:0%
+we do the longterm our maximum results
+bundle at aggressive levels of
+
+ align:start position:0%
+bundle at aggressive levels of
+ 
+
+ align:start position:0%
+bundle at aggressive levels of
+deployment you can see that our vehicle
+
+ align:start position:0%
+deployment you can see that our vehicle
+ 
+
+ align:start position:0%
+deployment you can see that our vehicle
+C our implementation costs start off
+
+ align:start position:0%
+C our implementation costs start off
+ 
+
+ align:start position:0%
+C our implementation costs start off
+much higher around $80 billion was taper
+
+ align:start position:0%
+much higher around $80 billion was taper
+ 
+
+ align:start position:0%
+much higher around $80 billion was taper
+down to $60 billion a year in 2050 but
+
+ align:start position:0%
+down to $60 billion a year in 2050 but
+ 
+
+ align:start position:0%
+down to $60 billion a year in 2050 but
+our vehicle cost savings are still
+
+ align:start position:0%
+our vehicle cost savings are still
+ 
+
+ align:start position:0%
+our vehicle cost savings are still
+almost a factor of two or three higher
+
+ align:start position:0%
+almost a factor of two or three higher
+ 
+
+ align:start position:0%
+almost a factor of two or three higher
+than with notation costs which is to say
+
+ align:start position:0%
+than with notation costs which is to say
+ 
+
+ align:start position:0%
+than with notation costs which is to say
+that we are going to save money through
+
+ align:start position:0%
+that we are going to save money through
+ 
+
+ align:start position:0%
+that we are going to save money through
+lifetime of this analysis and you can
+
+ align:start position:0%
+lifetime of this analysis and you can
+ 
+
+ align:start position:0%
+lifetime of this analysis and you can
+see that to get to our maximum level of
+
+ align:start position:0%
+see that to get to our maximum level of
+ 
+
+ align:start position:0%
+see that to get to our maximum level of
+deployment that's our 24% reduction we
+
+ align:start position:0%
+deployment that's our 24% reduction we
+ 
+
+ align:start position:0%
+deployment that's our 24% reduction we
+have to do many more things over the
+
+ align:start position:0%
+have to do many more things over the
+ 
+
+ align:start position:0%
+have to do many more things over the
+long term to get our maximum results
+
+ align:start position:0%
+long term to get our maximum results
+ 
+
+ align:start position:0%
+long term to get our maximum results
+I'll let you dive into the report to
+
+ align:start position:0%
+I'll let you dive into the report to
+ 
+
+ align:start position:0%
+I'll let you dive into the report to
+understand what some of these policies
+
+ align:start position:0%
+understand what some of these policies
+ 
+
+ align:start position:0%
+understand what some of these policies
+are but all these policies are things
+
+ align:start position:0%
+are but all these policies are things
+ 
+
+ align:start position:0%
+are but all these policies are things
+that you can work on in your
+
+ align:start position:0%
+that you can work on in your
+ 
+
+ align:start position:0%
+that you can work on in your
+careers if you look at the uh same
+
+ align:start position:0%
+careers if you look at the uh same
+ 
+
+ align:start position:0%
+careers if you look at the uh same
+bundle in terms of the graphics you can
+
+ align:start position:0%
+bundle in terms of the graphics you can
+ 
+
+ align:start position:0%
+bundle in terms of the graphics you can
+see that it starts off I think this one
+
+ align:start position:0%
+see that it starts off I think this one
+ 
+
+ align:start position:0%
+see that it starts off I think this one
+might actually be repeated from before
+
+ align:start position:0%
+might actually be repeated from before
+ 
+
+ align:start position:0%
+might actually be repeated from before
+apologies but the crucial thing is
+
+ align:start position:0%
+apologies but the crucial thing is
+ 
+
+ align:start position:0%
+apologies but the crucial thing is
+here's all the uh strategy that comprise
+
+ align:start position:0%
+here's all the uh strategy that comprise
+ 
+
+ align:start position:0%
+here's all the uh strategy that comprise
+this bundle and you can see the land use
+
+ align:start position:0%
+this bundle and you can see the land use
+ 
+
+ align:start position:0%
+this bundle and you can see the land use
+Transit nonmotorized transation bundle
+
+ align:start position:0%
+Transit nonmotorized transation bundle
+ 
+
+ align:start position:0%
+Transit nonmotorized transation bundle
+which is something that planners focus
+
+ align:start position:0%
+which is something that planners focus
+ 
+
+ align:start position:0%
+which is something that planners focus
+on quite a bit the implementation costs
+
+ align:start position:0%
+on quite a bit the implementation costs
+ 
+
+ align:start position:0%
+on quite a bit the implementation costs
+are slightly higher than our near-term
+
+ align:start position:0%
+are slightly higher than our near-term
+ 
+
+ align:start position:0%
+are slightly higher than our near-term
+results but again our vehicle cost
+
+ align:start position:0%
+results but again our vehicle cost
+ 
+
+ align:start position:0%
+results but again our vehicle cost
+savings are roughly two or three times
+
+ align:start position:0%
+savings are roughly two or three times
+ 
+
+ align:start position:0%
+savings are roughly two or three times
+what our implementation costs are and
+
+ align:start position:0%
+what our implementation costs are and
+ 
+
+ align:start position:0%
+what our implementation costs are and
+you can see that there are many things
+
+ align:start position:0%
+you can see that there are many things
+ 
+
+ align:start position:0%
+you can see that there are many things
+that urban planners love ranging from
+
+ align:start position:0%
+that urban planners love ranging from
+ 
+
+ align:start position:0%
+that urban planners love ranging from
+pricing strategies transportation to
+
+ align:start position:0%
+pricing strategies transportation to
+ 
+
+ align:start position:0%
+pricing strategies transportation to
+land use and smart growth strategies to
+
+ align:start position:0%
+land use and smart growth strategies to
+ 
+
+ align:start position:0%
+land use and smart growth strategies to
+public transportation strategies to
+
+ align:start position:0%
+public transportation strategies to
+ 
+
+ align:start position:0%
+public transportation strategies to
+regulatory strategies and so on so this
+
+ align:start position:0%
+regulatory strategies and so on so this
+ 
+
+ align:start position:0%
+regulatory strategies and so on so this
+brings me to the idea of marginal
+
+ align:start position:0%
+brings me to the idea of marginal
+ 
+
+ align:start position:0%
+brings me to the idea of marginal
+abatement this is a very famous graph
+
+ align:start position:0%
+abatement this is a very famous graph
+ 
+
+ align:start position:0%
+abatement this is a very famous graph
+done in 2008 by McKenzie McKenzie didn't
+
+ align:start position:0%
+done in 2008 by McKenzie McKenzie didn't
+ 
+
+ align:start position:0%
+done in 2008 by McKenzie McKenzie didn't
+invent the marginal abatement cost curve
+
+ align:start position:0%
+invent the marginal abatement cost curve
+ 
+
+ align:start position:0%
+invent the marginal abatement cost curve
+but they certainly popularized it in a
+
+ align:start position:0%
+but they certainly popularized it in a
+ 
+
+ align:start position:0%
+but they certainly popularized it in a
+2008 report that was studying the cost
+
+ align:start position:0%
+2008 report that was studying the cost
+ 
+
+ align:start position:0%
+2008 report that was studying the cost
+to reduce greenhouse gas emissions
+
+ align:start position:0%
+to reduce greenhouse gas emissions
+ 
+
+ align:start position:0%
+to reduce greenhouse gas emissions
+across the US economy arguably that 2008
+
+ align:start position:0%
+across the US economy arguably that 2008
+ 
+
+ align:start position:0%
+across the US economy arguably that 2008
+report by McKenzie inspired the moving
+
+ align:start position:0%
+report by McKenzie inspired the moving
+ 
+
+ align:start position:0%
+report by McKenzie inspired the moving
+Pooler report in 2009 but the key thing
+
+ align:start position:0%
+Pooler report in 2009 but the key thing
+ 
+
+ align:start position:0%
+Pooler report in 2009 but the key thing
+is here is that what you do is you graph
+
+ align:start position:0%
+is here is that what you do is you graph
+ 
+
+ align:start position:0%
+is here is that what you do is you graph
+on the horizontal axis the potential
+
+ align:start position:0%
+on the horizontal axis the potential
+ 
+
+ align:start position:0%
+on the horizontal axis the potential
+Savings in terms of gigatons of carbon
+
+ align:start position:0%
+Savings in terms of gigatons of carbon
+ 
+
+ align:start position:0%
+Savings in terms of gigatons of carbon
+dioxide equivalent per year the width of
+
+ align:start position:0%
+dioxide equivalent per year the width of
+ 
+
+ align:start position:0%
+dioxide equivalent per year the width of
+each of these bars tells you how much
+
+ align:start position:0%
+each of these bars tells you how much
+ 
+
+ align:start position:0%
+each of these bars tells you how much
+potential is associated with each of
+
+ align:start position:0%
+potential is associated with each of
+ 
+
+ align:start position:0%
+potential is associated with each of
+these different Technologies or policies
+
+ align:start position:0%
+these different Technologies or policies
+ 
+
+ align:start position:0%
+these different Technologies or policies
+crucial thing here is on the vertical
+
+ align:start position:0%
+crucial thing here is on the vertical
+ 
+
+ align:start position:0%
+crucial thing here is on the vertical
+axis you can see that some things cost
+
+ align:start position:0%
+axis you can see that some things cost
+ 
+
+ align:start position:0%
+axis you can see that some things cost
+money to reduce a ton of greenhouse gas
+
+ align:start position:0%
+money to reduce a ton of greenhouse gas
+ 
+
+ align:start position:0%
+money to reduce a ton of greenhouse gas
+missions and some things like our moving
+
+ align:start position:0%
+missions and some things like our moving
+ 
+
+ align:start position:0%
+missions and some things like our moving
+pool report are negative you actually
+
+ align:start position:0%
+pool report are negative you actually
+ 
+
+ align:start position:0%
+pool report are negative you actually
+save money and you reduce greenhouse gas
+
+ align:start position:0%
+save money and you reduce greenhouse gas
+ 
+
+ align:start position:0%
+save money and you reduce greenhouse gas
+emissions my unsolicited career advice
+
+ align:start position:0%
+emissions my unsolicited career advice
+ 
+
+ align:start position:0%
+emissions my unsolicited career advice
+to all of you is that you want to be on
+
+ align:start position:0%
+to all of you is that you want to be on
+ 
+
+ align:start position:0%
+to all of you is that you want to be on
+the left hand side of this curve the
+
+ align:start position:0%
+the left hand side of this curve the
+ 
+
+ align:start position:0%
+the left hand side of this curve the
+left hand side of the curve are all
+
+ align:start position:0%
+left hand side of the curve are all
+ 
+
+ align:start position:0%
+left hand side of the curve are all
+things that are essentially free for
+
+ align:start position:0%
+things that are essentially free for
+ 
+
+ align:start position:0%
+things that are essentially free for
+people and they achieve our
+
+ align:start position:0%
+people and they achieve our
+ 
+
+ align:start position:0%
+people and they achieve our
+environmental goals so it is much easier
+
+ align:start position:0%
+environmental goals so it is much easier
+ 
+
+ align:start position:0%
+environmental goals so it is much easier
+to sell let's say changes in commercial
+
+ align:start position:0%
+to sell let's say changes in commercial
+ 
+
+ align:start position:0%
+to sell let's say changes in commercial
+buildings and residential buildings and
+
+ align:start position:0%
+buildings and residential buildings and
+ 
+
+ align:start position:0%
+buildings and residential buildings and
+fuel economy packages then it will be to
+
+ align:start position:0%
+fuel economy packages then it will be to
+ 
+
+ align:start position:0%
+fuel economy packages then it will be to
+do things like solar concentrating solar
+
+ align:start position:0%
+do things like solar concentrating solar
+ 
+
+ align:start position:0%
+do things like solar concentrating solar
+concentrating solar power solar CSP
+
+ align:start position:0%
+concentrating solar power solar CSP
+ 
+
+ align:start position:0%
+concentrating solar power solar CSP
+which is a very Hot Topic in 2008 but
+
+ align:start position:0%
+which is a very Hot Topic in 2008 but
+ 
+
+ align:start position:0%
+which is a very Hot Topic in 2008 but
+we've proven over the last 10 years that
+
+ align:start position:0%
+we've proven over the last 10 years that
+ 
+
+ align:start position:0%
+we've proven over the last 10 years that
+those costs have never gone down as much
+
+ align:start position:0%
+those costs have never gone down as much
+ 
+
+ align:start position:0%
+those costs have never gone down as much
+as solar panels have this is probably
+
+ align:start position:0%
+as solar panels have this is probably
+ 
+
+ align:start position:0%
+as solar panels have this is probably
+out of date distributed solar PV has
+
+ align:start position:0%
+out of date distributed solar PV has
+ 
+
+ align:start position:0%
+out of date distributed solar PV has
+become much cheaper
+
+ align:start position:0%
+become much cheaper
+ 
+
+ align:start position:0%
+become much cheaper
+but you know even if you compare this
+
+ align:start position:0%
+but you know even if you compare this
+ 
+
+ align:start position:0%
+but you know even if you compare this
+solar distributed PV is relatively
+
+ align:start position:0%
+solar distributed PV is relatively
+ 
+
+ align:start position:0%
+solar distributed PV is relatively
+expensive compared to utility scale what
+
+ align:start position:0%
+expensive compared to utility scale what
+ 
+
+ align:start position:0%
+expensive compared to utility scale what
+will TS but of course those things are
+
+ align:start position:0%
+will TS but of course those things are
+ 
+
+ align:start position:0%
+will TS but of course those things are
+still more expensive than residential
+
+ align:start position:0%
+still more expensive than residential
+ 
+
+ align:start position:0%
+still more expensive than residential
+water heaters not the sexiest topic but
+
+ align:start position:0%
+water heaters not the sexiest topic but
+ 
+
+ align:start position:0%
+water heaters not the sexiest topic but
+a place where you can actually have
+
+ align:start position:0%
+a place where you can actually have
+ 
+
+ align:start position:0%
+a place where you can actually have
+significant impact it has a negative
+
+ align:start position:0%
+significant impact it has a negative
+ 
+
+ align:start position:0%
+significant impact it has a negative
+cost and has a significant potential
+
+ align:start position:0%
+cost and has a significant potential
+ 
+
+ align:start position:0%
+cost and has a significant potential
+combined heat and Power Residential
+
+ align:start position:0%
+combined heat and Power Residential
+ 
+
+ align:start position:0%
+combined heat and Power Residential
+Building lighting these are fundamental
+
+ align:start position:0%
+Building lighting these are fundamental
+ 
+
+ align:start position:0%
+Building lighting these are fundamental
+changes we can make in buildings which
+
+ align:start position:0%
+changes we can make in buildings which
+ 
+
+ align:start position:0%
+changes we can make in buildings which
+we'll talk about in the next few
+
+ align:start position:0%
+we'll talk about in the next few
+ 
+
+ align:start position:0%
+we'll talk about in the next few
+lectures the point of this is that you
+
+ align:start position:0%
+lectures the point of this is that you
+ 
+
+ align:start position:0%
+lectures the point of this is that you
+can be time do things that have negative
+
+ align:start position:0%
+can be time do things that have negative
+ 
+
+ align:start position:0%
+can be time do things that have negative
+cost and reduced green gas emissions
+
+ align:start position:0%
+cost and reduced green gas emissions
+ 
+
+ align:start position:0%
+cost and reduced green gas emissions
+which is something we can analyze from
+
+ align:start position:0%
+which is something we can analyze from
+ 
+
+ align:start position:0%
+which is something we can analyze from
+the moving cooler report if you look at
+
+ align:start position:0%
+the moving cooler report if you look at
+ 
+
+ align:start position:0%
+the moving cooler report if you look at
+the moving cooler report on the around
+
+ align:start position:0%
+the moving cooler report on the around
+ 
+
+ align:start position:0%
+the moving cooler report on the around
+page 47 or so you can see different
+
+ align:start position:0%
+page 47 or so you can see different
+ 
+
+ align:start position:0%
+page 47 or so you can see different
+categories of how much potential there
+
+ align:start position:0%
+categories of how much potential there
+ 
+
+ align:start position:0%
+categories of how much potential there
+is to reduce greous gas emissions this
+
+ align:start position:0%
+is to reduce greous gas emissions this
+ 
+
+ align:start position:0%
+is to reduce greous gas emissions this
+is the at expanded aggressive and
+
+ align:start position:0%
+is the at expanded aggressive and
+ 
+
+ align:start position:0%
+is the at expanded aggressive and
+maximum levels and you can see on a
+
+ align:start position:0%
+maximum levels and you can see on a
+ 
+
+ align:start position:0%
+maximum levels and you can see on a
+categorized basis that pricing
+
+ align:start position:0%
+categorized basis that pricing
+ 
+
+ align:start position:0%
+categorized basis that pricing
+strategies are basically as much as
+
+ align:start position:0%
+strategies are basically as much as
+ 
+
+ align:start position:0%
+strategies are basically as much as
+everything else put together however on
+
+ align:start position:0%
+everything else put together however on
+ 
+
+ align:start position:0%
+everything else put together however on
+a per unit basis or on a cost basis you
+
+ align:start position:0%
+a per unit basis or on a cost basis you
+ 
+
+ align:start position:0%
+a per unit basis or on a cost basis you
+can also see that the negative costs are
+
+ align:start position:0%
+can also see that the negative costs are
+ 
+
+ align:start position:0%
+can also see that the negative costs are
+R our public transportation strategies
+
+ align:start position:0%
+R our public transportation strategies
+ 
+
+ align:start position:0%
+R our public transportation strategies
+as we talked about in class are
+
+ align:start position:0%
+as we talked about in class are
+ 
+
+ align:start position:0%
+as we talked about in class are
+relatively expensive they don't always
+
+ align:start position:0%
+relatively expensive they don't always
+ 
+
+ align:start position:0%
+relatively expensive they don't always
+recover they don't have Fair box
+
+ align:start position:0%
+recover they don't have Fair box
+ 
+
+ align:start position:0%
+recover they don't have Fair box
+recovery or they don't recover their
+
+ align:start position:0%
+recovery or they don't recover their
+ 
+
+ align:start position:0%
+recovery or they don't recover their
+full cost Through the Fair box but we
+
+ align:start position:0%
+full cost Through the Fair box but we
+ 
+
+ align:start position:0%
+full cost Through the Fair box but we
+might invest in public transportation as
+
+ align:start position:0%
+might invest in public transportation as
+ 
+
+ align:start position:0%
+might invest in public transportation as
+a public good it also has benefits in
+
+ align:start position:0%
+a public good it also has benefits in
+ 
+
+ align:start position:0%
+a public good it also has benefits in
+livability and safety and access the
+
+ align:start position:0%
+livability and safety and access the
+ 
+
+ align:start position:0%
+livability and safety and access the
+things that this report doesn't
+
+ align:start position:0%
+things that this report doesn't
+ 
+
+ align:start position:0%
+things that this report doesn't
+necessarily include but it's also worth
+
+ align:start position:0%
+necessarily include but it's also worth
+ 
+
+ align:start position:0%
+necessarily include but it's also worth
+noting there's lots of other things we
+
+ align:start position:0%
+noting there's lots of other things we
+ 
+
+ align:start position:0%
+noting there's lots of other things we
+can do that essentially have a negative
+
+ align:start position:0%
+can do that essentially have a negative
+ 
+
+ align:start position:0%
+can do that essentially have a negative
+economic cost they probably have
+
+ align:start position:0%
+economic cost they probably have
+ 
+
+ align:start position:0%
+economic cost they probably have
+beneficial costs in terms of uh safety
+
+ align:start position:0%
+beneficial costs in terms of uh safety
+ 
+
+ align:start position:0%
+beneficial costs in terms of uh safety
+and health they're just not included in
+
+ align:start position:0%
+and health they're just not included in
+ 
+
+ align:start position:0%
+and health they're just not included in
+this report so everything here in red
+
+ align:start position:0%
+this report so everything here in red
+ 
+
+ align:start position:0%
+this report so everything here in red
+and almost all levels of deployment is a
+
+ align:start position:0%
+and almost all levels of deployment is a
+ 
+
+ align:start position:0%
+and almost all levels of deployment is a
+negative cost and a reduce gas emission
+
+ align:start position:0%
+negative cost and a reduce gas emission
+ 
+
+ align:start position:0%
+negative cost and a reduce gas emission
+this is a cost of um a a cost of
+
+ align:start position:0%
+this is a cost of um a a cost of
+ 
+
+ align:start position:0%
+this is a cost of um a a cost of
+reducing a ton of greous gas emissions
+
+ align:start position:0%
+reducing a ton of greous gas emissions
+ 
+
+ align:start position:0%
+reducing a ton of greous gas emissions
+you can see that in the data analysis I
+
+ align:start position:0%
+you can see that in the data analysis I
+ 
+
+ align:start position:0%
+you can see that in the data analysis I
+look at the total reduction divided by
+
+ align:start position:0%
+look at the total reduction divided by
+ 
+
+ align:start position:0%
+look at the total reduction divided by
+the net
+
+ align:start position:0%
+the net
+ 
+
+ align:start position:0%
+the net
+cost and if we break it down into the
+
+ align:start position:0%
+cost and if we break it down into the
+ 
+
+ align:start position:0%
+cost and if we break it down into the
+very strategies you can see that the
+
+ align:start position:0%
+very strategies you can see that the
+ 
+
+ align:start position:0%
+very strategies you can see that the
+category of system operations and
+
+ align:start position:0%
+category of system operations and
+ 
+
+ align:start position:0%
+category of system operations and
+management is composed of active traffic
+
+ align:start position:0%
+management is composed of active traffic
+ 
+
+ align:start position:0%
+management is composed of active traffic
+management integrated Corridor
+
+ align:start position:0%
+management integrated Corridor
+ 
+
+ align:start position:0%
+management integrated Corridor
+management signal control management
+
+ align:start position:0%
+management signal control management
+ 
+
+ align:start position:0%
+management signal control management
+these all have a the maximum level
+
+ align:start position:0%
+these all have a the maximum level
+ 
+
+ align:start position:0%
+these all have a the maximum level
+deployment a cost to reduce a metric ton
+
+ align:start position:0%
+deployment a cost to reduce a metric ton
+ 
+
+ align:start position:0%
+deployment a cost to reduce a metric ton
+of carbon dioxide equivalent these are
+
+ align:start position:0%
+of carbon dioxide equivalent these are
+ 
+
+ align:start position:0%
+of carbon dioxide equivalent these are
+all positive
+
+ align:start position:0%
+all positive
+ 
+
+ align:start position:0%
+all positive
+costs you can see that if we move one
+
+ align:start position:0%
+costs you can see that if we move one
+ 
+
+ align:start position:0%
+costs you can see that if we move one
+page down you can see lots of other the
+
+ align:start position:0%
+page down you can see lots of other the
+ 
+
+ align:start position:0%
+page down you can see lots of other the
+things have negative costs I would argue
+
+ align:start position:0%
+things have negative costs I would argue
+ 
+
+ align:start position:0%
+things have negative costs I would argue
+you negative costs are the things that
+
+ align:start position:0%
+you negative costs are the things that
+ 
+
+ align:start position:0%
+you negative costs are the things that
+should be easiest to sell in your career
+
+ align:start position:0%
+should be easiest to sell in your career
+ 
+
+ align:start position:0%
+should be easiest to sell in your career
+and of course if you look at something
+
+ align:start position:0%
+and of course if you look at something
+ 
+
+ align:start position:0%
+and of course if you look at something
+that is not very glamorous Incident
+
+ align:start position:0%
+that is not very glamorous Incident
+ 
+
+ align:start position:0%
+that is not very glamorous Incident
+Management Incident Management looks
+
+ align:start position:0%
+Management Incident Management looks
+ 
+
+ align:start position:0%
+Management Incident Management looks
+like on a per cost basis basically
+
+ align:start position:0%
+like on a per cost basis basically
+ 
+
+ align:start position:0%
+like on a per cost basis basically
+almost the equivalent of everything else
+
+ align:start position:0%
+almost the equivalent of everything else
+ 
+
+ align:start position:0%
+almost the equivalent of everything else
+put together so I would argue that this
+
+ align:start position:0%
+put together so I would argue that this
+ 
+
+ align:start position:0%
+put together so I would argue that this
+is the first thing we should be doing to
+
+ align:start position:0%
+is the first thing we should be doing to
+ 
+
+ align:start position:0%
+is the first thing we should be doing to
+try to reduce greenos gas
+
+ align:start position:0%
+try to reduce greenos gas
+ 
+
+ align:start position:0%
+try to reduce greenos gas
+emissions if we look at the expanded
+
+ align:start position:0%
+emissions if we look at the expanded
+ 
+
+ align:start position:0%
+emissions if we look at the expanded
+aggressive and maximum levels of effort
+
+ align:start position:0%
+aggressive and maximum levels of effort
+ 
+
+ align:start position:0%
+aggressive and maximum levels of effort
+just to talk about that a little bit
+
+ align:start position:0%
+just to talk about that a little bit
+ 
+
+ align:start position:0%
+just to talk about that a little bit
+more expanding current practice is
+
+ align:start position:0%
+more expanding current practice is
+ 
+
+ align:start position:0%
+more expanding current practice is
+basically in large urban areas that
+
+ align:start position:0%
+basically in large urban areas that
+ 
+
+ align:start position:0%
+basically in large urban areas that
+already have Transit medium area
+
+ align:start position:0%
+already have Transit medium area
+ 
+
+ align:start position:0%
+already have Transit medium area
+medium urban areas that have Transit and
+
+ align:start position:0%
+medium urban areas that have Transit and
+ 
+
+ align:start position:0%
+medium urban areas that have Transit and
+small areas that have Transit already
+
+ align:start position:0%
+small areas that have Transit already
+ 
+
+ align:start position:0%
+small areas that have Transit already
+and then in the future we'll try to
+
+ align:start position:0%
+and then in the future we'll try to
+ 
+
+ align:start position:0%
+and then in the future we'll try to
+improve the large urban areas medium
+
+ align:start position:0%
+improve the large urban areas medium
+ 
+
+ align:start position:0%
+improve the large urban areas medium
+urban areas and small urban areas in bit
+
+ align:start position:0%
+urban areas and small urban areas in bit
+ 
+
+ align:start position:0%
+urban areas and small urban areas in bit
+if we want to be more aggressive we'll
+
+ align:start position:0%
+if we want to be more aggressive we'll
+ 
+
+ align:start position:0%
+if we want to be more aggressive we'll
+start doing this faster for all these
+
+ align:start position:0%
+start doing this faster for all these
+ 
+
+ align:start position:0%
+start doing this faster for all these
+categories and bring them up in time and
+
+ align:start position:0%
+categories and bring them up in time and
+ 
+
+ align:start position:0%
+categories and bring them up in time and
+a maximum effort would have been to
+
+ align:start position:0%
+a maximum effort would have been to
+ 
+
+ align:start position:0%
+a maximum effort would have been to
+start 10 years ago in 2010 or so to try
+
+ align:start position:0%
+start 10 years ago in 2010 or so to try
+ 
+
+ align:start position:0%
+start 10 years ago in 2010 or so to try
+to do all of our Metro areas or all of
+
+ align:start position:0%
+to do all of our Metro areas or all of
+ 
+
+ align:start position:0%
+to do all of our Metro areas or all of
+our urban areas with these TR ation
+
+ align:start position:0%
+our urban areas with these TR ation
+ 
+
+ align:start position:0%
+our urban areas with these TR ation
+interventions to I finally got around to
+
+ align:start position:0%
+interventions to I finally got around to
+ 
+
+ align:start position:0%
+interventions to I finally got around to
+making a marginal bait cost curve from
+
+ align:start position:0%
+making a marginal bait cost curve from
+ 
+
+ align:start position:0%
+making a marginal bait cost curve from
+the moving Pooler report itself you can
+
+ align:start position:0%
+the moving Pooler report itself you can
+ 
+
+ align:start position:0%
+the moving Pooler report itself you can
+see we have these nine different
+
+ align:start position:0%
+see we have these nine different
+ 
+
+ align:start position:0%
+see we have these nine different
+categories of strategy types I think
+
+ align:start position:0%
+categories of strategy types I think
+ 
+
+ align:start position:0%
+categories of strategy types I think
+this very thin sliver over here is
+
+ align:start position:0%
+this very thin sliver over here is
+ 
+
+ align:start position:0%
+this very thin sliver over here is
+probably the Incident Management I
+
+ align:start position:0%
+probably the Incident Management I
+ 
+
+ align:start position:0%
+probably the Incident Management I
+mentioned before and you can see the
+
+ align:start position:0%
+mentioned before and you can see the
+ 
+
+ align:start position:0%
+mentioned before and you can see the
+system operations and management
+
+ align:start position:0%
+system operations and management
+ 
+
+ align:start position:0%
+system operations and management
+strategies are relatively cost effective
+
+ align:start position:0%
+strategies are relatively cost effective
+ 
+
+ align:start position:0%
+strategies are relatively cost effective
+they're negative cost but have fairly
+
+ align:start position:0%
+they're negative cost but have fairly
+ 
+
+ align:start position:0%
+they're negative cost but have fairly
+large potential you can see that much of
+
+ align:start position:0%
+large potential you can see that much of
+ 
+
+ align:start position:0%
+large potential you can see that much of
+our negative potential here is composed
+
+ align:start position:0%
+our negative potential here is composed
+ 
+
+ align:start position:0%
+our negative potential here is composed
+of pricing strategies which is going to
+
+ align:start position:0%
+of pricing strategies which is going to
+ 
+
+ align:start position:0%
+of pricing strategies which is going to
+be very politically very difficult but
+
+ align:start position:0%
+be very politically very difficult but
+ 
+
+ align:start position:0%
+be very politically very difficult but
+worthwhile but we can also get a lot of
+
+ align:start position:0%
+worthwhile but we can also get a lot of
+ 
+
+ align:start position:0%
+worthwhile but we can also get a lot of
+changes uh in our transportation system
+
+ align:start position:0%
+changes uh in our transportation system
+ 
+
+ align:start position:0%
+changes uh in our transportation system
+emissions simply by changing our
+
+ align:start position:0%
+emissions simply by changing our
+ 
+
+ align:start position:0%
+emissions simply by changing our
+regulatory strategies and I'll let you
+
+ align:start position:0%
+regulatory strategies and I'll let you
+ 
+
+ align:start position:0%
+regulatory strategies and I'll let you
+look at the report to see what those are
+
+ align:start position:0%
+look at the report to see what those are
+ 
+
+ align:start position:0%
+look at the report to see what those are
+uh we do love uh our land use and smart
+
+ align:start position:0%
+uh we do love uh our land use and smart
+ 
+
+ align:start position:0%
+uh we do love uh our land use and smart
+growth strategies it's a very small box
+
+ align:start position:0%
+growth strategies it's a very small box
+ 
+
+ align:start position:0%
+growth strategies it's a very small box
+here and public transportation
+
+ align:start position:0%
+here and public transportation
+ 
+
+ align:start position:0%
+here and public transportation
+strategies as I said before tend to have
+
+ align:start position:0%
+strategies as I said before tend to have
+ 
+
+ align:start position:0%
+strategies as I said before tend to have
+a positive cost but actually do reduce
+
+ align:start position:0%
+a positive cost but actually do reduce
+ 
+
+ align:start position:0%
+a positive cost but actually do reduce
+gas emissions but you can see that all
+
+ align:start position:0%
+gas emissions but you can see that all
+ 
+
+ align:start position:0%
+gas emissions but you can see that all
+the things we often talk about as urban
+
+ align:start position:0%
+the things we often talk about as urban
+ 
+
+ align:start position:0%
+the things we often talk about as urban
+planners are relatively small and
+
+ align:start position:0%
+planners are relatively small and
+ 
+
+ align:start position:0%
+planners are relatively small and
+potential there are lots of things we
+
+ align:start position:0%
+potential there are lots of things we
+ 
+
+ align:start position:0%
+potential there are lots of things we
+can do over here in pricing strategy and
+
+ align:start position:0%
+can do over here in pricing strategy and
+ 
+
+ align:start position:0%
+can do over here in pricing strategy and
+Regulatory measures that I would argue
+
+ align:start position:0%
+Regulatory measures that I would argue
+ 
+
+ align:start position:0%
+Regulatory measures that I would argue
+we don't talk about enough in urban
+
+ align:start position:0%
+we don't talk about enough in urban
+ 
+
+ align:start position:0%
+we don't talk about enough in urban
+planning HOV carpol man poool communting
+
+ align:start position:0%
+planning HOV carpol man poool communting
+ 
+
+ align:start position:0%
+planning HOV carpol man poool communting
+strategies this blue box right here at
+
+ align:start position:0%
+strategies this blue box right here at
+ 
+
+ align:start position:0%
+strategies this blue box right here at
+all if we go to an aggressive level I've
+
+ align:start position:0%
+all if we go to an aggressive level I've
+ 
+
+ align:start position:0%
+all if we go to an aggressive level I've
+replotted this with the social cost of
+
+ align:start position:0%
+replotted this with the social cost of
+ 
+
+ align:start position:0%
+replotted this with the social cost of
+carbon at
+
+ align:start position:0%
+carbon at
+ 
+
+ align:start position:0%
+carbon at
+$150 per million metric sorry $150 per
+
+ align:start position:0%
+$150 per million metric sorry $150 per
+ 
+
+ align:start position:0%
+$150 per million metric sorry $150 per
+metric ton of carbon di equival
+
+ align:start position:0%
+metric ton of carbon di equival
+ 
+
+ align:start position:0%
+metric ton of carbon di equival
+you can see that in almost every case
+
+ align:start position:0%
+you can see that in almost every case
+ 
+
+ align:start position:0%
+you can see that in almost every case
+everything is cheaper than letting
+
+ align:start position:0%
+everything is cheaper than letting
+ 
+
+ align:start position:0%
+everything is cheaper than letting
+greenhouse gas emissions continue
+
+ align:start position:0%
+greenhouse gas emissions continue
+ 
+
+ align:start position:0%
+greenhouse gas emissions continue
+unchecked or everything is cheaper than
+
+ align:start position:0%
+unchecked or everything is cheaper than
+ 
+
+ align:start position:0%
+unchecked or everything is cheaper than
+climate change so from a social cost to
+
+ align:start position:0%
+climate change so from a social cost to
+ 
+
+ align:start position:0%
+climate change so from a social cost to
+car perspective we should just make all
+
+ align:start position:0%
+car perspective we should just make all
+ 
+
+ align:start position:0%
+car perspective we should just make all
+these Transportation efforts as soon as
+
+ align:start position:0%
+these Transportation efforts as soon as
+ 
+
+ align:start position:0%
+these Transportation efforts as soon as
+possible and of course at the maximum
+
+ align:start position:0%
+possible and of course at the maximum
+ 
+
+ align:start position:0%
+possible and of course at the maximum
+level you can see that the maximum level
+
+ align:start position:0%
+level you can see that the maximum level
+ 
+
+ align:start position:0%
+level you can see that the maximum level
+some things I think that's Incident
+
+ align:start position:0%
+some things I think that's Incident
+ 
+
+ align:start position:0%
+some things I think that's Incident
+Management is incredibly beneficial from
+
+ align:start position:0%
+Management is incredibly beneficial from
+ 
+
+ align:start position:0%
+Management is incredibly beneficial from
+a cost perspective and a greenhouse Gap
+
+ align:start position:0%
+a cost perspective and a greenhouse Gap
+ 
+
+ align:start position:0%
+a cost perspective and a greenhouse Gap
+Val perspective but pretty much
+
+ align:start position:0%
+Val perspective but pretty much
+ 
+
+ align:start position:0%
+Val perspective but pretty much
+everything else here is small and the
+
+ align:start position:0%
+everything else here is small and the
+ 
+
+ align:start position:0%
+everything else here is small and the
+point is at the maximum level everything
+
+ align:start position:0%
+point is at the maximum level everything
+ 
+
+ align:start position:0%
+point is at the maximum level everything
+is less than social cost toart again a
+
+ align:start position:0%
+is less than social cost toart again a
+ 
+
+ align:start position:0%
+is less than social cost toart again a
+good argument for trying to reduce
+
+ align:start position:0%
+good argument for trying to reduce
+ 
+
+ align:start position:0%
+good argument for trying to reduce
+greenos gas emissions
+
+ align:start position:0%
+greenos gas emissions
+ 
+
+ align:start position:0%
+greenos gas emissions
+anyways just to bring us back to the
+
+ align:start position:0%
+anyways just to bring us back to the
+ 
+
+ align:start position:0%
+anyways just to bring us back to the
+Daniel Sperling identity I said before
+
+ align:start position:0%
+Daniel Sperling identity I said before
+ 
+
+ align:start position:0%
+Daniel Sperling identity I said before
+this is I want to highlight the
+
+ align:start position:0%
+this is I want to highlight the
+ 
+
+ align:start position:0%
+this is I want to highlight the
+different parts of the system and how to
+
+ align:start position:0%
+different parts of the system and how to
+ 
+
+ align:start position:0%
+different parts of the system and how to
+break down system there's Mobility the
+
+ align:start position:0%
+break down system there's Mobility the
+ 
+
+ align:start position:0%
+break down system there's Mobility the
+demand we have for transportation
+
+ align:start position:0%
+demand we have for transportation
+ 
+
+ align:start position:0%
+demand we have for transportation
+vehicle miles traveled there's the
+
+ align:start position:0%
+vehicle miles traveled there's the
+ 
+
+ align:start position:0%
+vehicle miles traveled there's the
+vehicle Energy Efficiency and there's
+
+ align:start position:0%
+vehicle Energy Efficiency and there's
+ 
+
+ align:start position:0%
+vehicle Energy Efficiency and there's
+the carbon intensity of the energy
+
+ align:start position:0%
+the carbon intensity of the energy
+ 
+
+ align:start position:0%
+the carbon intensity of the energy
+itself re has gas emissions per unit of
+
+ align:start position:0%
+itself re has gas emissions per unit of
+ 
+
+ align:start position:0%
+itself re has gas emissions per unit of
+energy and that is what gives us greenos
+
+ align:start position:0%
+energy and that is what gives us greenos
+ 
+
+ align:start position:0%
+energy and that is what gives us greenos
+gas emissions the reason why I say that
+
+ align:start position:0%
+gas emissions the reason why I say that
+ 
+
+ align:start position:0%
+gas emissions the reason why I say that
+is because if you look at the existing
+
+ align:start position:0%
+is because if you look at the existing
+ 
+
+ align:start position:0%
+is because if you look at the existing
+sanki diagram you can see that in the US
+
+ align:start position:0%
+sanki diagram you can see that in the US
+ 
+
+ align:start position:0%
+sanki diagram you can see that in the US
+now we have a very small fraction of
+
+ align:start position:0%
+now we have a very small fraction of
+ 
+
+ align:start position:0%
+now we have a very small fraction of
+hydrogen production and almost entirely
+
+ align:start position:0%
+hydrogen production and almost entirely
+ 
+
+ align:start position:0%
+hydrogen production and almost entirely
+goes to Industry almost all of our
+
+ align:start position:0%
+goes to Industry almost all of our
+ 
+
+ align:start position:0%
+goes to Industry almost all of our
+transportation energy comes from liquid
+
+ align:start position:0%
+transportation energy comes from liquid
+ 
+
+ align:start position:0%
+transportation energy comes from liquid
+fuels petroleum and petroleum
+
+ align:start position:0%
+fuels petroleum and petroleum
+ 
+
+ align:start position:0%
+fuels petroleum and petroleum
+sources but if we want to reach a fully
+
+ align:start position:0%
+sources but if we want to reach a fully
+ 
+
+ align:start position:0%
+sources but if we want to reach a fully
+decarbonized economy this is the
+
+ align:start position:0%
+decarbonized economy this is the
+ 
+
+ align:start position:0%
+decarbonized economy this is the
+Williams 2020 paper for 100% renewable
+
+ align:start position:0%
+Williams 2020 paper for 100% renewable
+ 
+
+ align:start position:0%
+Williams 2020 paper for 100% renewable
+energy Matrix it basically forecast that
+
+ align:start position:0%
+energy Matrix it basically forecast that
+ 
+
+ align:start position:0%
+energy Matrix it basically forecast that
+Transportation will come from liquid
+
+ align:start position:0%
+Transportation will come from liquid
+ 
+
+ align:start position:0%
+Transportation will come from liquid
+fuels that are derived from originally
+
+ align:start position:0%
+fuels that are derived from originally
+ 
+
+ align:start position:0%
+fuels that are derived from originally
+from hydrogen and from that hydrogen or
+
+ align:start position:0%
+from hydrogen and from that hydrogen or
+ 
+
+ align:start position:0%
+from hydrogen and from that hydrogen or
+renewable resources like solar and wind
+
+ align:start position:0%
+renewable resources like solar and wind
+ 
+
+ align:start position:0%
+renewable resources like solar and wind
+how are we going to get there and what
+
+ align:start position:0%
+how are we going to get there and what
+ 
+
+ align:start position:0%
+how are we going to get there and what
+does that mean the MIT team led by
+
+ align:start position:0%
+does that mean the MIT team led by
+ 
+
+ align:start position:0%
+does that mean the MIT team led by
+Steven Barrett and in AO Astro and Bill
+
+ align:start position:0%
+Steven Barrett and in AO Astro and Bill
+ 
+
+ align:start position:0%
+Steven Barrett and in AO Astro and Bill
+Green in chemical engineering put
+
+ align:start position:0%
+Green in chemical engineering put
+ 
+
+ align:start position:0%
+Green in chemical engineering put
+together a proposal for the climate
+
+ align:start position:0%
+together a proposal for the climate
+ 
+
+ align:start position:0%
+together a proposal for the climate
+Grand Challenge that called the tough
+
+ align:start position:0%
+Grand Challenge that called the tough
+ 
+
+ align:start position:0%
+Grand Challenge that called the tough
+decarbonize Transportation initiative in
+
+ align:start position:0%
+decarbonize Transportation initiative in
+ 
+
+ align:start position:0%
+decarbonize Transportation initiative in
+2021 and the key finding from these
+
+ align:start position:0%
+2021 and the key finding from these
+ 
+
+ align:start position:0%
+2021 and the key finding from these
+system engineers and from these chemical
+
+ align:start position:0%
+system engineers and from these chemical
+ 
+
+ align:start position:0%
+system engineers and from these chemical
+Engineers was that we're going to need
+
+ align:start position:0%
+Engineers was that we're going to need
+ 
+
+ align:start position:0%
+Engineers was that we're going to need
+new vehicles new fuels and entirely new
+
+ align:start position:0%
+new vehicles new fuels and entirely new
+ 
+
+ align:start position:0%
+new vehicles new fuels and entirely new
+hydrogen system in order of decarbonized
+
+ align:start position:0%
+hydrogen system in order of decarbonized
+ 
+
+ align:start position:0%
+hydrogen system in order of decarbonized
+transportation for low greenhouse gas
+
+ align:start position:0%
+transportation for low greenhouse gas
+ 
+
+ align:start position:0%
+transportation for low greenhouse gas
+carbon based fuels the main challenge is
+
+ align:start position:0%
+carbon based fuels the main challenge is
+ 
+
+ align:start position:0%
+carbon based fuels the main challenge is
+the huge scale of fuel production needed
+
+ align:start position:0%
+the huge scale of fuel production needed
+ 
+
+ align:start position:0%
+the huge scale of fuel production needed
+all of our low greenhouse gas fuel
+
+ align:start position:0%
+all of our low greenhouse gas fuel
+ 
+
+ align:start position:0%
+all of our low greenhouse gas fuel
+options even biofuels depend on a huge
+
+ align:start position:0%
+options even biofuels depend on a huge
+ 
+
+ align:start position:0%
+options even biofuels depend on a huge
+scale production of low greenhous gas
+
+ align:start position:0%
+scale production of low greenhous gas
+ 
+
+ align:start position:0%
+scale production of low greenhous gas
+hydrogen and the cost of low greenhous
+
+ align:start position:0%
+hydrogen and the cost of low greenhous
+ 
+
+ align:start position:0%
+hydrogen and the cost of low greenhous
+gas hydrogen is often largest part of
+
+ align:start position:0%
+gas hydrogen is often largest part of
+ 
+
+ align:start position:0%
+gas hydrogen is often largest part of
+the cost of the finished low gas gas
+
+ align:start position:0%
+the cost of the finished low gas gas
+ 
+
+ align:start position:0%
+the cost of the finished low gas gas
+emitting
+
+ align:start position:0%
+emitting
+ 
+
+ align:start position:0%
+emitting
+Fuel and they find a number of key
+
+ align:start position:0%
+Fuel and they find a number of key
+ 
+
+ align:start position:0%
+Fuel and they find a number of key
+findings in the executive summary first
+
+ align:start position:0%
+findings in the executive summary first
+ 
+
+ align:start position:0%
+findings in the executive summary first
+longdistance vehicles in the tough to
+
+ align:start position:0%
+longdistance vehicles in the tough to
+ 
+
+ align:start position:0%
+longdistance vehicles in the tough to
+decarbonized Transportation sectors
+
+ align:start position:0%
+decarbonized Transportation sectors
+ 
+
+ align:start position:0%
+decarbonized Transportation sectors
+Aviation shipping and trucks all those
+
+ align:start position:0%
+Aviation shipping and trucks all those
+ 
+
+ align:start position:0%
+Aviation shipping and trucks all those
+long-distance Vehicles carry their own
+
+ align:start position:0%
+long-distance Vehicles carry their own
+ 
+
+ align:start position:0%
+long-distance Vehicles carry their own
+energy so the energy density is crucial
+
+ align:start position:0%
+energy so the energy density is crucial
+ 
+
+ align:start position:0%
+energy so the energy density is crucial
+the more weight and more volume of a
+
+ align:start position:0%
+the more weight and more volume of a
+ 
+
+ align:start position:0%
+the more weight and more volume of a
+fuel or battery you carry reduces the
+
+ align:start position:0%
+fuel or battery you carry reduces the
+ 
+
+ align:start position:0%
+fuel or battery you carry reduces the
+payload VI for the vehicle which is the
+
+ align:start position:0%
+payload VI for the vehicle which is the
+ 
+
+ align:start position:0%
+payload VI for the vehicle which is the
+purpose of the trip in and of itself the
+
+ align:start position:0%
+purpose of the trip in and of itself the
+ 
+
+ align:start position:0%
+purpose of the trip in and of itself the
+Alternatives we have hydrocarbons are
+
+ align:start position:0%
+Alternatives we have hydrocarbons are
+ 
+
+ align:start position:0%
+Alternatives we have hydrocarbons are
+two to 30 times heavier and require
+
+ align:start position:0%
+two to 30 times heavier and require
+ 
+
+ align:start position:0%
+two to 30 times heavier and require
+greater
+
+ align:start position:0%
+greater
+ 
+
+ align:start position:0%
+greater
+volumes they also point out a major
+
+ align:start position:0%
+volumes they also point out a major
+ 
+
+ align:start position:0%
+volumes they also point out a major
+challenge is going to be the scale of
+
+ align:start position:0%
+challenge is going to be the scale of
+ 
+
+ align:start position:0%
+challenge is going to be the scale of
+achieving this fuel infrastructure today
+
+ align:start position:0%
+achieving this fuel infrastructure today
+ 
+
+ align:start position:0%
+achieving this fuel infrastructure today
+only fossil fuels are available at the
+
+ align:start position:0%
+only fossil fuels are available at the
+ 
+
+ align:start position:0%
+only fossil fuels are available at the
+huge scale needed about a billion tons
+
+ align:start position:0%
+huge scale needed about a billion tons
+ 
+
+ align:start position:0%
+huge scale needed about a billion tons
+per year and realistically only a few
+
+ align:start position:0%
+per year and realistically only a few
+ 
+
+ align:start position:0%
+per year and realistically only a few
+low carbon alternatives to reach needed
+
+ align:start position:0%
+low carbon alternatives to reach needed
+ 
+
+ align:start position:0%
+low carbon alternatives to reach needed
+scale by
+
+ align:start position:0%
+scale by
+ 
+
+ align:start position:0%
+scale by
+2050 existing vehicles are all designed
+
+ align:start position:0%
+2050 existing vehicles are all designed
+ 
+
+ align:start position:0%
+2050 existing vehicles are all designed
+to use hydrocarbon fuels so we either
+
+ align:start position:0%
+to use hydrocarbon fuels so we either
+ 
+
+ align:start position:0%
+to use hydrocarbon fuels so we either
+need a carbon fuel that doesn't increase
+
+ align:start position:0%
+need a carbon fuel that doesn't increase
+ 
+
+ align:start position:0%
+need a carbon fuel that doesn't increase
+P gas emissions a quote unquote drop
+
+ align:start position:0%
+P gas emissions a quote unquote drop
+ 
+
+ align:start position:0%
+P gas emissions a quote unquote drop
+Fuel and we make a liquid fuel like
+
+ align:start position:0%
+Fuel and we make a liquid fuel like
+ 
+
+ align:start position:0%
+Fuel and we make a liquid fuel like
+gasoline from renewable resources like
+
+ align:start position:0%
+gasoline from renewable resources like
+ 
+
+ align:start position:0%
+gasoline from renewable resources like
+solar and wind instead of pulling it out
+
+ align:start position:0%
+solar and wind instead of pulling it out
+ 
+
+ align:start position:0%
+solar and wind instead of pulling it out
+of the ground and we're also going to
+
+ align:start position:0%
+of the ground and we're also going to
+ 
+
+ align:start position:0%
+of the ground and we're also going to
+need new vehicles or we need new
+
+ align:start position:0%
+need new vehicles or we need new
+ 
+
+ align:start position:0%
+need new vehicles or we need new
+vehicles to use new fuels those vehicle
+
+ align:start position:0%
+vehicles to use new fuels those vehicle
+ 
+
+ align:start position:0%
+vehicles to use new fuels those vehicle
+lifetimes are long 20 to 30 years and
+
+ align:start position:0%
+lifetimes are long 20 to 30 years and
+ 
+
+ align:start position:0%
+lifetimes are long 20 to 30 years and
+new vehicle development is very slow so
+
+ align:start position:0%
+new vehicle development is very slow so
+ 
+
+ align:start position:0%
+new vehicle development is very slow so
+if we want to achieve decarbonization by
+
+ align:start position:0%
+if we want to achieve decarbonization by
+ 
+
+ align:start position:0%
+if we want to achieve decarbonization by
+2050 we need to start develop the new
+
+ align:start position:0%
+2050 we need to start develop the new
+ 
+
+ align:start position:0%
+2050 we need to start develop the new
+vehicles now the good news as you know
+
+ align:start position:0%
+vehicles now the good news as you know
+ 
+
+ align:start position:0%
+vehicles now the good news as you know
+from the news we have many new vehicles
+
+ align:start position:0%
+from the news we have many new vehicles
+ 
+
+ align:start position:0%
+from the news we have many new vehicles
+many new uh trucks being developed now
+
+ align:start position:0%
+many new uh trucks being developed now
+ 
+
+ align:start position:0%
+many new uh trucks being developed now
+we probably arguably have fewer options
+
+ align:start position:0%
+we probably arguably have fewer options
+ 
+
+ align:start position:0%
+we probably arguably have fewer options
+for shipping and Aviation though
+
+ align:start position:0%
+for shipping and Aviation though
+ 
+
+ align:start position:0%
+for shipping and Aviation though
+shipping is one sector that seems to be
+
+ align:start position:0%
+shipping is one sector that seems to be
+ 
+
+ align:start position:0%
+shipping is one sector that seems to be
+quite engaged in reducing its greenhouse
+
+ align:start position:0%
+quite engaged in reducing its greenhouse
+ 
+
+ align:start position:0%
+quite engaged in reducing its greenhouse
+gas emissions the cost of the fuel
+
+ align:start position:0%
+gas emissions the cost of the fuel
+ 
+
+ align:start position:0%
+gas emissions the cost of the fuel
+itself is a significant part of the
+
+ align:start position:0%
+itself is a significant part of the
+ 
+
+ align:start position:0%
+itself is a significant part of the
+total cost of transportation services
+
+ align:start position:0%
+total cost of transportation services
+ 
+
+ align:start position:0%
+total cost of transportation services
+this the fuels for the sector currently
+
+ align:start position:0%
+this the fuels for the sector currently
+ 
+
+ align:start position:0%
+this the fuels for the sector currently
+cost about a trillion dollars per year
+
+ align:start position:0%
+cost about a trillion dollars per year
+ 
+
+ align:start position:0%
+cost about a trillion dollars per year
+and expensive infrastructure adds
+
+ align:start position:0%
+and expensive infrastructure adds
+ 
+
+ align:start position:0%
+and expensive infrastructure adds
+additional cost so if we want to build a
+
+ align:start position:0%
+additional cost so if we want to build a
+ 
+
+ align:start position:0%
+additional cost so if we want to build a
+new fuel infrastructure we're going to
+
+ align:start position:0%
+new fuel infrastructure we're going to
+ 
+
+ align:start position:0%
+new fuel infrastructure we're going to
+need new infrastructure and we're going
+
+ align:start position:0%
+need new infrastructure and we're going
+ 
+
+ align:start position:0%
+need new infrastructure and we're going
+to have to achieve that on a toost
+
+ align:start position:0%
+to have to achieve that on a toost
+ 
+
+ align:start position:0%
+to have to achieve that on a toost
+competitive basis
+
+ align:start position:0%
+competitive basis
+ 
+
+ align:start position:0%
+competitive basis
+and of course there's the practicalities
+
+ align:start position:0%
+and of course there's the practicalities
+ 
+
+ align:start position:0%
+and of course there's the practicalities
+of fuel instructor room temperature
+
+ align:start position:0%
+of fuel instructor room temperature
+ 
+
+ align:start position:0%
+of fuel instructor room temperature
+liquids are much easier to distribute
+
+ align:start position:0%
+liquids are much easier to distribute
+ 
+
+ align:start position:0%
+liquids are much easier to distribute
+and store than gases or solids fast
+
+ align:start position:0%
+and store than gases or solids fast
+ 
+
+ align:start position:0%
+and store than gases or solids fast
+refueling and recharging is important
+
+ align:start position:0%
+refueling and recharging is important
+ 
+
+ align:start position:0%
+refueling and recharging is important
+for some vehicles and a very practical
+
+ align:start position:0%
+for some vehicles and a very practical
+ 
+
+ align:start position:0%
+for some vehicles and a very practical
+level that new fuel has to be available
+
+ align:start position:0%
+level that new fuel has to be available
+ 
+
+ align:start position:0%
+level that new fuel has to be available
+at 800 ports 177,000 airports and more
+
+ align:start position:0%
+at 800 ports 177,000 airports and more
+ 
+
+ align:start position:0%
+at 800 ports 177,000 airports and more
+than 100,000 truck stops in the
+
+ align:start position:0%
+than 100,000 truck stops in the
+ 
+
+ align:start position:0%
+than 100,000 truck stops in the
+US another summary slide from these
+
+ align:start position:0%
+US another summary slide from these
+ 
+
+ align:start position:0%
+US another summary slide from these
+sectors that this team identified as
+
+ align:start position:0%
+sectors that this team identified as
+ 
+
+ align:start position:0%
+sectors that this team identified as
+tough to decarbonize trucking shipping
+
+ align:start position:0%
+tough to decarbonize trucking shipping
+ 
+
+ align:start position:0%
+tough to decarbonize trucking shipping
+and Aviation they all constit about one
+
+ align:start position:0%
+and Aviation they all constit about one
+ 
+
+ align:start position:0%
+and Aviation they all constit about one
+to one 1.25 gigatons per year that's
+
+ align:start position:0%
+to one 1.25 gigatons per year that's
+ 
+
+ align:start position:0%
+to one 1.25 gigatons per year that's
+about 3.25 gigatons a year about one10
+
+ align:start position:0%
+about 3.25 gigatons a year about one10
+ 
+
+ align:start position:0%
+about 3.25 gigatons a year about one10
+of all of the greous gas emissions for
+
+ align:start position:0%
+of all of the greous gas emissions for
+ 
+
+ align:start position:0%
+of all of the greous gas emissions for
+the world you can see that all these
+
+ align:start position:0%
+the world you can see that all these
+ 
+
+ align:start position:0%
+the world you can see that all these
+vehicles have very different vehicle
+
+ align:start position:0%
+vehicles have very different vehicle
+ 
+
+ align:start position:0%
+vehicles have very different vehicle
+intensity of greenhous gas emissions per
+
+ align:start position:0%
+intensity of greenhous gas emissions per
+ 
+
+ align:start position:0%
+intensity of greenhous gas emissions per
+use the engines themselves are different
+
+ align:start position:0%
+use the engines themselves are different
+ 
+
+ align:start position:0%
+use the engines themselves are different
+they use different fuels and they have
+
+ align:start position:0%
+they use different fuels and they have
+ 
+
+ align:start position:0%
+they use different fuels and they have
+very different power requirements it
+
+ align:start position:0%
+very different power requirements it
+ 
+
+ align:start position:0%
+very different power requirements it
+requires a lot more power to lift a
+
+ align:start position:0%
+requires a lot more power to lift a
+ 
+
+ align:start position:0%
+requires a lot more power to lift a
+plane into the air than it does to move
+
+ align:start position:0%
+plane into the air than it does to move
+ 
+
+ align:start position:0%
+plane into the air than it does to move
+a truck along a road or ship through
+
+ align:start position:0%
+a truck along a road or ship through
+ 
+
+ align:start position:0%
+a truck along a road or ship through
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+the state of electrification is that
+
+ align:start position:0%
+the state of electrification is that
+ 
+
+ align:start position:0%
+the state of electrification is that
+Trucking we can achieve at relatively
+
+ align:start position:0%
+Trucking we can achieve at relatively
+ 
+
+ align:start position:0%
+Trucking we can achieve at relatively
+high cost it looks very challenging for
+
+ align:start position:0%
+high cost it looks very challenging for
+ 
+
+ align:start position:0%
+high cost it looks very challenging for
+shipping and for Aviation and space been
+
+ align:start position:0%
+shipping and for Aviation and space been
+ 
+
+ align:start position:0%
+shipping and for Aviation and space been
+deemed barely impossible over large
+
+ align:start position:0%
+deemed barely impossible over large
+ 
+
+ align:start position:0%
+deemed barely impossible over large
+distances because the batteries
+
+ align:start position:0%
+distances because the batteries
+ 
+
+ align:start position:0%
+distances because the batteries
+themselves weigh so much they would
+
+ align:start position:0%
+themselves weigh so much they would
+ 
+
+ align:start position:0%
+themselves weigh so much they would
+displace the passengers or simply way
+
+ align:start position:0%
+displace the passengers or simply way
+ 
+
+ align:start position:0%
+displace the passengers or simply way
+too much for the plane at all fuel cell
+
+ align:start position:0%
+too much for the plane at all fuel cell
+ 
+
+ align:start position:0%
+too much for the plane at all fuel cell
+options where we use a chemical battery
+
+ align:start position:0%
+options where we use a chemical battery
+ 
+
+ align:start position:0%
+options where we use a chemical battery
+a relatively high cost for Trucking and
+
+ align:start position:0%
+a relatively high cost for Trucking and
+ 
+
+ align:start position:0%
+a relatively high cost for Trucking and
+shipping not possible for Aviation if
+
+ align:start position:0%
+shipping not possible for Aviation if
+ 
+
+ align:start position:0%
+shipping not possible for Aviation if
+you summarize these things we have a few
+
+ align:start position:0%
+you summarize these things we have a few
+ 
+
+ align:start position:0%
+you summarize these things we have a few
+different viable path ways that we have
+
+ align:start position:0%
+different viable path ways that we have
+ 
+
+ align:start position:0%
+different viable path ways that we have
+to focus in on we have many different
+
+ align:start position:0%
+to focus in on we have many different
+ 
+
+ align:start position:0%
+to focus in on we have many different
+viable Pathways for Trucking we have a
+
+ align:start position:0%
+viable Pathways for Trucking we have a
+ 
+
+ align:start position:0%
+viable Pathways for Trucking we have a
+few options for shpping carbon based
+
+ align:start position:0%
+few options for shpping carbon based
+ 
+
+ align:start position:0%
+few options for shpping carbon based
+fuels ammonia or hydrogen and for
+
+ align:start position:0%
+fuels ammonia or hydrogen and for
+ 
+
+ align:start position:0%
+fuels ammonia or hydrogen and for
+Aviation we need the energy density of
+
+ align:start position:0%
+Aviation we need the energy density of
+ 
+
+ align:start position:0%
+Aviation we need the energy density of
+carbon based fuels they have low weight
+
+ align:start position:0%
+carbon based fuels they have low weight
+ 
+
+ align:start position:0%
+carbon based fuels they have low weight
+and low volume compared to how much
+
+ align:start position:0%
+and low volume compared to how much
+ 
+
+ align:start position:0%
+and low volume compared to how much
+energy carbon based fuel packed in so we
+
+ align:start position:0%
+energy carbon based fuel packed in so we
+ 
+
+ align:start position:0%
+energy carbon based fuel packed in so we
+need to think about Aviation fuels that
+
+ align:start position:0%
+need to think about Aviation fuels that
+ 
+
+ align:start position:0%
+need to think about Aviation fuels that
+will be low carbon in order to continue
+
+ align:start position:0%
+will be low carbon in order to continue
+ 
+
+ align:start position:0%
+will be low carbon in order to continue
+flying this is to point out that again
+
+ align:start position:0%
+flying this is to point out that again
+ 
+
+ align:start position:0%
+flying this is to point out that again
+if you look at the moving cooler report
+
+ align:start position:0%
+if you look at the moving cooler report
+ 
+
+ align:start position:0%
+if you look at the moving cooler report
+you look at these tough to decarbonized
+
+ align:start position:0%
+you look at these tough to decarbonized
+ 
+
+ align:start position:0%
+you look at these tough to decarbonized
+Transportation sectors urban planners
+
+ align:start position:0%
+Transportation sectors urban planners
+ 
+
+ align:start position:0%
+Transportation sectors urban planners
+can do a lot they have jurisdiction they
+
+ align:start position:0%
+can do a lot they have jurisdiction they
+ 
+
+ align:start position:0%
+can do a lot they have jurisdiction they
+have authority to help plan new
+
+ align:start position:0%
+have authority to help plan new
+ 
+
+ align:start position:0%
+have authority to help plan new
+infrastructure they have authority to
+
+ align:start position:0%
+infrastructure they have authority to
+ 
+
+ align:start position:0%
+infrastructure they have authority to
+plan great infrastructure which we don't
+
+ align:start position:0%
+plan great infrastructure which we don't
+ 
+
+ align:start position:0%
+plan great infrastructure which we don't
+look at very often but I would argue to
+
+ align:start position:0%
+look at very often but I would argue to
+ 
+
+ align:start position:0%
+look at very often but I would argue to
+you that this is kind of an unexplored
+
+ align:start position:0%
+you that this is kind of an unexplored
+ 
+
+ align:start position:0%
+you that this is kind of an unexplored
+area for urban planners to try to affect
\ No newline at end of file
diff --git a/r_AGxxITsbQ.txt b/r_AGxxITsbQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7898c2fa7e773c2e686cdd597d76877bf7578754
--- /dev/null
+++ b/r_AGxxITsbQ.txt
@@ -0,0 +1,10659 @@
+align:start position:0%
+ 
+So now uh let's let's talk about the uh
+
+ align:start position:0%
+So now uh let's let's talk about the uh
+ 
+
+ align:start position:0%
+So now uh let's let's talk about the uh
+let's talk about first the different uh
+
+ align:start position:0%
+let's talk about first the different uh
+ 
+
+ align:start position:0%
+let's talk about first the different uh
+concepts uh that we have talked about in
+
+ align:start position:0%
+concepts uh that we have talked about in
+ 
+
+ align:start position:0%
+concepts uh that we have talked about in
+class and then get and then in the end
+
+ align:start position:0%
+class and then get and then in the end
+ 
+
+ align:start position:0%
+class and then get and then in the end
+I'll get to just some example of some
+
+ align:start position:0%
+I'll get to just some example of some
+ 
+
+ align:start position:0%
+I'll get to just some example of some
+problems that you might face on the mid.
+
+ align:start position:0%
+problems that you might face on the mid.
+ 
+
+ align:start position:0%
+problems that you might face on the mid.
+So the first is this that if you take a
+
+ align:start position:0%
+So the first is this that if you take a
+ 
+
+ align:start position:0%
+So the first is this that if you take a
+subset
+
+ align:start position:0%
+subset
+ 
+
+ align:start position:0%
+subset
+of Rn uh to say that a is bounded from
+
+ align:start position:0%
+of Rn uh to say that a is bounded from
+ 
+
+ align:start position:0%
+of Rn uh to say that a is bounded from
+above.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This just means that there exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m such that for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a in a a here is less than equal to a.
+
+ align:start position:0%
+a in a a here is less than equal to a.
+ 
+
+ align:start position:0%
+a in a a here is less than equal to a.
+This is what it means to be bounded from
+
+ align:start position:0%
+This is what it means to be bounded from
+ 
+
+ align:start position:0%
+This is what it means to be bounded from
+about from a subset, right? And now the
+
+ align:start position:0%
+about from a subset, right? And now the
+ 
+
+ align:start position:0%
+about from a subset, right? And now the
+there's a list of about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this is a number uh so so m here is a
+
+ align:start position:0%
+um this is a number uh so so m here is a
+ 
+
+ align:start position:0%
+um this is a number uh so so m here is a
+least
+
+ align:start position:0%
+least
+ 
+
+ align:start position:0%
+least
+so m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a least upper bound.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If
+
+ align:start position:0%
+If
+ 
+
+ align:start position:0%
+If
+uh um if uh m is an upper bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's call it m
+
+ align:start position:0%
+let's call it m
+ 
+
+ align:start position:0%
+let's call it m
+uh uh is
+
+ align:start position:0%
+uh uh is
+ 
+
+ align:start position:0%
+uh uh is
+bigger equal
+
+ align:start position:0%
+bigger equal
+ 
+
+ align:start position:0%
+bigger equal
+to it. So this is what it means to be a
+
+ align:start position:0%
+to it. So this is what it means to be a
+ 
+
+ align:start position:0%
+to it. So this is what it means to be a
+least up
+
+ align:start position:0%
+least up
+ 
+
+ align:start position:0%
+least up
+and so the least up bounds. So so the
+
+ align:start position:0%
+and so the least up bounds. So so the
+ 
+
+ align:start position:0%
+and so the least up bounds. So so the
+least upper bounds is this is what we
+
+ align:start position:0%
+least upper bounds is this is what we
+ 
+
+ align:start position:0%
+least upper bounds is this is what we
+denote by super.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And similarly, similarly form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for lower bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh and in
+
+ align:start position:0%
+and uh and in
+ 
+
+ align:start position:0%
+and uh and in
+right and the real numbers have this
+
+ align:start position:0%
+right and the real numbers have this
+ 
+
+ align:start position:0%
+right and the real numbers have this
+property that if I set this bounded from
+
+ align:start position:0%
+property that if I set this bounded from
+ 
+
+ align:start position:0%
+property that if I set this bounded from
+above then it has a then there is a
+
+ align:start position:0%
+above then it has a then there is a
+ 
+
+ align:start position:0%
+above then it has a then there is a
+least upper bound.
+
+ align:start position:0%
+least upper bound.
+ 
+
+ align:start position:0%
+least upper bound.
+uh and likewise for uh assets that is
+
+ align:start position:0%
+uh and likewise for uh assets that is
+ 
+
+ align:start position:0%
+uh and likewise for uh assets that is
+below.
+
+ align:start position:0%
+below.
+ 
+
+ align:start position:0%
+below.
+Okay, so that was soup and we'll get to
+
+ align:start position:0%
+Okay, so that was soup and we'll get to
+ 
+
+ align:start position:0%
+Okay, so that was soup and we'll get to
+this mean soup and make uh I'll just
+
+ align:start position:0%
+this mean soup and make uh I'll just
+ 
+
+ align:start position:0%
+this mean soup and make uh I'll just
+review that a little bit later also.
+
+ align:start position:0%
+review that a little bit later also.
+ 
+
+ align:start position:0%
+review that a little bit later also.
+Uh but that's another important thing.
+
+ align:start position:0%
+Uh but that's another important thing.
+ 
+
+ align:start position:0%
+Uh but that's another important thing.
+Uh a sequence. So another key uh concept
+
+ align:start position:0%
+Uh a sequence. So another key uh concept
+ 
+
+ align:start position:0%
+Uh a sequence. So another key uh concept
+in this class is sequence
+
+ align:start position:0%
+in this class is sequence
+ 
+
+ align:start position:0%
+in this class is sequence
+and we let's begin with a sequence of
+
+ align:start position:0%
+and we let's begin with a sequence of
+ 
+
+ align:start position:0%
+and we let's begin with a sequence of
+real numbers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So this is a map
+
+ align:start position:0%
+So this is a map
+ 
+
+ align:start position:0%
+So this is a map
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+positive integers
+
+ align:start position:0%
+positive integers
+ 
+
+ align:start position:0%
+positive integers
+into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again it denotes so the image. So if
+
+ align:start position:0%
+and again it denotes so the image. So if
+ 
+
+ align:start position:0%
+and again it denotes so the image. So if
+you're looking at uh the image of some n
+
+ align:start position:0%
+you're looking at uh the image of some n
+ 
+
+ align:start position:0%
+you're looking at uh the image of some n
+we typically denote this by a n or by a
+
+ align:start position:0%
+we typically denote this by a n or by a
+ 
+
+ align:start position:0%
+we typically denote this by a n or by a
+n or xn or something like that
+
+ align:start position:0%
+n or xn or something like that
+ 
+
+ align:start position:0%
+n or xn or something like that
+where we use the subscript
+
+ align:start position:0%
+where we use the subscript
+ 
+
+ align:start position:0%
+where we use the subscript
+but it's just the image under this map.
+
+ align:start position:0%
+but it's just the image under this map.
+ 
+
+ align:start position:0%
+but it's just the image under this map.
+So that's a sequence. So for each
+
+ align:start position:0%
+So that's a sequence. So for each
+ 
+
+ align:start position:0%
+So that's a sequence. So for each
+positive integer you get a real number.
+
+ align:start position:0%
+positive integer you get a real number.
+ 
+
+ align:start position:0%
+positive integer you get a real number.
+Then um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then for a sequence one of the first
+
+ align:start position:0%
+then for a sequence one of the first
+ 
+
+ align:start position:0%
+then for a sequence one of the first
+things you are interested in is
+
+ align:start position:0%
+things you are interested in is
+ 
+
+ align:start position:0%
+things you are interested in is
+convergence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if you have so if this here is a
+
+ align:start position:0%
+So if you have so if this here is a
+ 
+
+ align:start position:0%
+So if you have so if this here is a
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+that xn converts to some x here. This
+
+ align:start position:0%
+that xn converts to some x here. This
+ 
+
+ align:start position:0%
+that xn converts to some x here. This
+here just means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh epsilon greater than zero they exist.
+
+ align:start position:0%
+uh epsilon greater than zero they exist.
+ 
+
+ align:start position:0%
+uh epsilon greater than zero they exist.
+I I will use this symbol. I haven't used
+
+ align:start position:0%
+I I will use this symbol. I haven't used
+ 
+
+ align:start position:0%
+I I will use this symbol. I haven't used
+it until now but it's so hard not to use
+
+ align:start position:0%
+it until now but it's so hard not to use
+ 
+
+ align:start position:0%
+it until now but it's so hard not to use
+it. This means they exist.
+
+ align:start position:0%
+it. This means they exist.
+ 
+
+ align:start position:0%
+it. This means they exist.
+It's not on
+
+ align:start position:0%
+It's not on
+ 
+
+ align:start position:0%
+It's not on
+but it's a totally standard symbol. So
+
+ align:start position:0%
+but it's a totally standard symbol. So
+ 
+
+ align:start position:0%
+but it's a totally standard symbol. So
+they exist.
+
+ align:start position:0%
+they exist.
+ 
+
+ align:start position:0%
+they exist.
+uh capital n such that
+
+ align:start position:0%
+uh capital n such that
+ 
+
+ align:start position:0%
+uh capital n such that
+if little n is bigger equal to capital n
+
+ align:start position:0%
+if little n is bigger equal to capital n
+ 
+
+ align:start position:0%
+if little n is bigger equal to capital n
+then uh xn - x
+
+ align:start position:0%
+then uh xn - x
+ 
+
+ align:start position:0%
+then uh xn - x
+small.
+
+ align:start position:0%
+small.
+ 
+
+ align:start position:0%
+small.
+So this is what it means for a sequence
+
+ align:start position:0%
+So this is what it means for a sequence
+ 
+
+ align:start position:0%
+So this is what it means for a sequence
+to convert
+
+ align:start position:0%
+to convert
+ 
+
+ align:start position:0%
+to convert
+to x sequence x to convert to x and you
+
+ align:start position:0%
+to x sequence x to convert to x and you
+ 
+
+ align:start position:0%
+to x sequence x to convert to x and you
+write like this or you can write xn and
+
+ align:start position:0%
+write like this or you can write xn and
+ 
+
+ align:start position:0%
+write like this or you can write xn and
+then the limit here as n go to infinity=
+
+ align:start position:0%
+then the limit here as n go to infinity=
+ 
+
+ align:start position:0%
+then the limit here as n go to infinity=
+both of these
+
+ align:start position:0%
+both of these
+ 
+
+ align:start position:0%
+both of these
+are standard use.
+
+ align:start position:0%
+are standard use.
+ 
+
+ align:start position:0%
+are standard use.
+So and then also if a seage is not
+
+ align:start position:0%
+So and then also if a seage is not
+ 
+
+ align:start position:0%
+So and then also if a seage is not
+convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is not convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+then we say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is diver.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So sequence is either convergent or it's
+
+ align:start position:0%
+So sequence is either convergent or it's
+ 
+
+ align:start position:0%
+So sequence is either convergent or it's
+divergent.
+
+ align:start position:0%
+divergent.
+ 
+
+ align:start position:0%
+divergent.
+Um and then you there's this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+useful property.
+
+ align:start position:0%
+useful property.
+ 
+
+ align:start position:0%
+useful property.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So a lema
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if x
+
+ align:start position:0%
+if x
+ 
+
+ align:start position:0%
+if x
+is convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then the set
+
+ align:start position:0%
+Then the set
+ 
+
+ align:start position:0%
+Then the set
+this as a set this here is a bounce set.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, we talk about that.
+
+ align:start position:0%
+Okay, we talk about that.
+ 
+
+ align:start position:0%
+Okay, we talk about that.
+And then another thing about sequences
+
+ align:start position:0%
+And then another thing about sequences
+ 
+
+ align:start position:0%
+And then another thing about sequences
+is that the algebraic processes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of sequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what are the algebraic properties
+
+ align:start position:0%
+and what are the algebraic properties
+ 
+
+ align:start position:0%
+and what are the algebraic properties
+they are that if you take two sequences
+
+ align:start position:0%
+they are that if you take two sequences
+ 
+
+ align:start position:0%
+they are that if you take two sequences
+a n and bn and let's say that a n
+
+ align:start position:0%
+a n and bn and let's say that a n
+ 
+
+ align:start position:0%
+a n and bn and let's say that a n
+converts to a and bn convert to b then
+
+ align:start position:0%
+converts to a and bn convert to b then
+ 
+
+ align:start position:0%
+converts to a and bn convert to b then
+the algebraic and c and c is just a
+
+ align:start position:0%
+the algebraic and c and c is just a
+ 
+
+ align:start position:0%
+the algebraic and c and c is just a
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then you have that sort of and often
+
+ align:start position:0%
+Then you have that sort of and often
+ 
+
+ align:start position:0%
+Then you have that sort of and often
+when you combine what I did there is one
+
+ align:start position:0%
+when you combine what I did there is one
+ 
+
+ align:start position:0%
+when you combine what I did there is one
+and two before you combine you're
+
+ align:start position:0%
+and two before you combine you're
+ 
+
+ align:start position:0%
+and two before you combine you're
+looking at a n + c * bn this here
+
+ align:start position:0%
+looking at a n + c * bn this here
+ 
+
+ align:start position:0%
+looking at a n + c * bn this here
+converts to a c * b
+
+ align:start position:0%
+converts to a c * b
+ 
+
+ align:start position:0%
+converts to a c * b
+this is the first and this when I state
+
+ align:start position:0%
+this is the first and this when I state
+ 
+
+ align:start position:0%
+this is the first and this when I state
+it like this it actually combine two of
+
+ align:start position:0%
+it like this it actually combine two of
+ 
+
+ align:start position:0%
+it like this it actually combine two of
+the one properties that we talked about
+
+ align:start position:0%
+the one properties that we talked about
+ 
+
+ align:start position:0%
+the one properties that we talked about
+earlier
+
+ align:start position:0%
+earlier
+ 
+
+ align:start position:0%
+earlier
+uh the second one is that a n * B n will
+
+ align:start position:0%
+uh the second one is that a n * B n will
+ 
+
+ align:start position:0%
+uh the second one is that a n * B n will
+converge to a * b.
+
+ align:start position:0%
+converge to a * b.
+ 
+
+ align:start position:0%
+converge to a * b.
+Third property is that if uh if a n if
+
+ align:start position:0%
+Third property is that if uh if a n if
+ 
+
+ align:start position:0%
+Third property is that if uh if a n if
+these here are not equal to zero and the
+
+ align:start position:0%
+these here are not equal to zero and the
+ 
+
+ align:start position:0%
+these here are not equal to zero and the
+limit here is not equal to zero then 1 /
+
+ align:start position:0%
+limit here is not equal to zero then 1 /
+ 
+
+ align:start position:0%
+limit here is not equal to zero then 1 /
+a n converts to 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so of course this last one
+
+ align:start position:0%
+And so of course this last one
+ 
+
+ align:start position:0%
+And so of course this last one
+you know this one implies in particular
+
+ align:start position:0%
+you know this one implies in particular
+ 
+
+ align:start position:0%
+you know this one implies in particular
+of course that also bn / a n converse to
+
+ align:start position:0%
+of course that also bn / a n converse to
+ 
+
+ align:start position:0%
+of course that also bn / a n converse to
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+this is just because this property here
+
+ align:start position:0%
+this is just because this property here
+ 
+
+ align:start position:0%
+this is just because this property here
+combined with property two that will
+
+ align:start position:0%
+combined with property two that will
+ 
+
+ align:start position:0%
+combined with property two that will
+give you this
+
+ align:start position:0%
+give you this
+ 
+
+ align:start position:0%
+give you this
+okay so that's
+
+ align:start position:0%
+okay so that's
+ 
+
+ align:start position:0%
+okay so that's
+the algebraic properties uh of limits
+
+ align:start position:0%
+the algebraic properties uh of limits
+ 
+
+ align:start position:0%
+the algebraic properties uh of limits
+um then you have um the concept of a
+
+ align:start position:0%
+um then you have um the concept of a
+ 
+
+ align:start position:0%
+um then you have um the concept of a
+subsequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So a subsequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we are imagining that we have a
+
+ align:start position:0%
+So we are imagining that we have a
+ 
+
+ align:start position:0%
+So we are imagining that we have a
+sequence and often we don't go all the
+
+ align:start position:0%
+sequence and often we don't go all the
+ 
+
+ align:start position:0%
+sequence and often we don't go all the
+way back like this but but a sequence
+
+ align:start position:0%
+way back like this but but a sequence
+ 
+
+ align:start position:0%
+way back like this but but a sequence
+again is is a map from the positive
+
+ align:start position:0%
+again is is a map from the positive
+ 
+
+ align:start position:0%
+again is is a map from the positive
+integer into R and we know the image of
+
+ align:start position:0%
+integer into R and we know the image of
+ 
+
+ align:start position:0%
+integer into R and we know the image of
+N like typically like Xn
+
+ align:start position:0%
+N like typically like Xn
+ 
+
+ align:start position:0%
+N like typically like Xn
+then a subsequence of this sequence and
+
+ align:start position:0%
+then a subsequence of this sequence and
+ 
+
+ align:start position:0%
+then a subsequence of this sequence and
+this is typically denoted something like
+
+ align:start position:0%
+this is typically denoted something like
+ 
+
+ align:start position:0%
+this is typically denoted something like
+this where you have a further subscript
+
+ align:start position:0%
+this where you have a further subscript
+ 
+
+ align:start position:0%
+this where you have a further subscript
+And this is and this is important again
+
+ align:start position:0%
+And this is and this is important again
+ 
+
+ align:start position:0%
+And this is and this is important again
+that this is like equal to f of g of k
+
+ align:start position:0%
+that this is like equal to f of g of k
+ 
+
+ align:start position:0%
+that this is like equal to f of g of k
+where g here and this is the really
+
+ align:start position:0%
+where g here and this is the really
+ 
+
+ align:start position:0%
+where g here and this is the really
+important property that g is a map from
+
+ align:start position:0%
+important property that g is a map from
+ 
+
+ align:start position:0%
+important property that g is a map from
+the positive integers into the positive
+
+ align:start position:0%
+the positive integers into the positive
+ 
+
+ align:start position:0%
+the positive integers into the positive
+integers and the really important is
+
+ align:start position:0%
+integers and the really important is
+ 
+
+ align:start position:0%
+integers and the really important is
+that g here is strictly increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so strictly increasing guarantee you
+
+ align:start position:0%
+And so strictly increasing guarantee you
+ 
+
+ align:start position:0%
+And so strictly increasing guarantee you
+that these numbers here is taken in the
+
+ align:start position:0%
+that these numbers here is taken in the
+ 
+
+ align:start position:0%
+that these numbers here is taken in the
+same order as in the original sequence
+
+ align:start position:0%
+same order as in the original sequence
+ 
+
+ align:start position:0%
+same order as in the original sequence
+but you may skip a bunch right I mean
+
+ align:start position:0%
+but you may skip a bunch right I mean
+ 
+
+ align:start position:0%
+but you may skip a bunch right I mean
+you know you take one and then you may
+
+ align:start position:0%
+you know you take one and then you may
+ 
+
+ align:start position:0%
+you know you take one and then you may
+skip a bunch and then you take another
+
+ align:start position:0%
+skip a bunch and then you take another
+ 
+
+ align:start position:0%
+skip a bunch and then you take another
+one and then you may skip more but it's
+
+ align:start position:0%
+one and then you may skip more but it's
+ 
+
+ align:start position:0%
+one and then you may skip more but it's
+in the same order and that's what
+
+ align:start position:0%
+in the same order and that's what
+ 
+
+ align:start position:0%
+in the same order and that's what
+increasing this guinea
+
+ align:start position:0%
+increasing this guinea
+ 
+
+ align:start position:0%
+increasing this guinea
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+and and then you have
+
+ align:start position:0%
+and and then you have
+ 
+
+ align:start position:0%
+and and then you have
+then you have this property.
+
+ align:start position:0%
+then you have this property.
+ 
+
+ align:start position:0%
+then you have this property.
+So you have this theorem
+
+ align:start position:0%
+So you have this theorem
+ 
+
+ align:start position:0%
+So you have this theorem
+that a sequence xn is converged
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if and only if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or all subsequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And one of these two was one of the two
+
+ align:start position:0%
+And one of these two was one of the two
+ 
+
+ align:start position:0%
+And one of these two was one of the two
+directions for this was trivial because
+
+ align:start position:0%
+directions for this was trivial because
+ 
+
+ align:start position:0%
+directions for this was trivial because
+if you have a um
+
+ align:start position:0%
+if you have a um
+ 
+
+ align:start position:0%
+if you have a um
+because because if you take a sequence
+
+ align:start position:0%
+because because if you take a sequence
+ 
+
+ align:start position:0%
+because because if you take a sequence
+then it is if you're thinking about this
+
+ align:start position:0%
+then it is if you're thinking about this
+ 
+
+ align:start position:0%
+then it is if you're thinking about this
+map here G as being the identity
+
+ align:start position:0%
+map here G as being the identity
+ 
+
+ align:start position:0%
+map here G as being the identity
+that's so that will give you a
+
+ align:start position:0%
+that's so that will give you a
+ 
+
+ align:start position:0%
+that's so that will give you a
+subsequence but that really is the
+
+ align:start position:0%
+subsequence but that really is the
+ 
+
+ align:start position:0%
+subsequence but that really is the
+original sequence, right? So the
+
+ align:start position:0%
+original sequence, right? So the
+ 
+
+ align:start position:0%
+original sequence, right? So the
+original sequence is a subsequence of
+
+ align:start position:0%
+original sequence is a subsequence of
+ 
+
+ align:start position:0%
+original sequence is a subsequence of
+itself. So if all subsequences are
+
+ align:start position:0%
+itself. So if all subsequences are
+ 
+
+ align:start position:0%
+itself. So if all subsequences are
+convergent, well then in particular the
+
+ align:start position:0%
+convergent, well then in particular the
+ 
+
+ align:start position:0%
+convergent, well then in particular the
+sequence itself is convergent. So one of
+
+ align:start position:0%
+sequence itself is convergent. So one of
+ 
+
+ align:start position:0%
+sequence itself is convergent. So one of
+those two directions was trivial.
+
+ align:start position:0%
+those two directions was trivial.
+ 
+
+ align:start position:0%
+those two directions was trivial.
+Okay. Now then we had these two theorems
+
+ align:start position:0%
+Okay. Now then we had these two theorems
+ 
+
+ align:start position:0%
+Okay. Now then we had these two theorems
+and they were right by then. So you know
+
+ align:start position:0%
+and they were right by then. So you know
+ 
+
+ align:start position:0%
+and they were right by then. So you know
+the like the sing the sort of the
+
+ align:start position:0%
+the like the sing the sort of the
+ 
+
+ align:start position:0%
+the like the sing the sort of the
+singing mathematics is a sinks built on
+
+ align:start position:0%
+singing mathematics is a sinks built on
+ 
+
+ align:start position:0%
+singing mathematics is a sinks built on
+each other right and hopefully like each
+
+ align:start position:0%
+each other right and hopefully like each
+ 
+
+ align:start position:0%
+each other right and hopefully like each
+step is fairly trivial but you build
+
+ align:start position:0%
+step is fairly trivial but you build
+ 
+
+ align:start position:0%
+step is fairly trivial but you build
+step by step and then you end up with
+
+ align:start position:0%
+step by step and then you end up with
+ 
+
+ align:start position:0%
+step by step and then you end up with
+something highly non-trivial right? So
+
+ align:start position:0%
+something highly non-trivial right? So
+ 
+
+ align:start position:0%
+something highly non-trivial right? So
+this here was was pretty trivial but
+
+ align:start position:0%
+this here was was pretty trivial but
+ 
+
+ align:start position:0%
+this here was was pretty trivial but
+then we used it later on to prove
+
+ align:start position:0%
+then we used it later on to prove
+ 
+
+ align:start position:0%
+then we used it later on to prove
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+non-trivial. So this was this model from
+
+ align:start position:0%
+non-trivial. So this was this model from
+ 
+
+ align:start position:0%
+non-trivial. So this was this model from
+convergence theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it has two there was two versions of
+
+ align:start position:0%
+and it has two there was two versions of
+ 
+
+ align:start position:0%
+and it has two there was two versions of
+this. you had a sequence xm
+
+ align:start position:0%
+this. you had a sequence xm
+ 
+
+ align:start position:0%
+this. you had a sequence xm
+and and xm was increasing.
+
+ align:start position:0%
+and and xm was increasing.
+ 
+
+ align:start position:0%
+and and xm was increasing.
+So that means that the next element is
+
+ align:start position:0%
+So that means that the next element is
+ 
+
+ align:start position:0%
+So that means that the next element is
+bigger equal to the previous element. If
+
+ align:start position:0%
+bigger equal to the previous element. If
+ 
+
+ align:start position:0%
+bigger equal to the previous element. If
+this here was the case, then XN is
+
+ align:start position:0%
+this here was the case, then XN is
+ 
+
+ align:start position:0%
+this here was the case, then XN is
+convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if and only if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh XM is is bound.
+
+ align:start position:0%
+uh XM is is bound.
+ 
+
+ align:start position:0%
+uh XM is is bound.
+If the sequence is bound
+
+ align:start position:0%
+If the sequence is bound
+ 
+
+ align:start position:0%
+If the sequence is bound
+and uh the soup
+
+ align:start position:0%
+and uh the soup
+ 
+
+ align:start position:0%
+and uh the soup
+of the exam
+
+ align:start position:0%
+of the exam
+ 
+
+ align:start position:0%
+of the exam
+this here is is is
+
+ align:start position:0%
+this here is is is
+ 
+
+ align:start position:0%
+this here is is is
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second pro the second verse. of this is
+
+ align:start position:0%
+second pro the second verse. of this is
+ 
+
+ align:start position:0%
+second pro the second verse. of this is
+if you have a monot. So instead of being
+
+ align:start position:0%
+if you have a monot. So instead of being
+ 
+
+ align:start position:0%
+if you have a monot. So instead of being
+increasing it's now decreasing. So the
+
+ align:start position:0%
+increasing it's now decreasing. So the
+ 
+
+ align:start position:0%
+increasing it's now decreasing. So the
+next element is smaller equal to the
+
+ align:start position:0%
+next element is smaller equal to the
+ 
+
+ align:start position:0%
+next element is smaller equal to the
+previous element.
+
+ align:start position:0%
+previous element.
+ 
+
+ align:start position:0%
+previous element.
+And then similarly uh the sequence uh xn
+
+ align:start position:0%
+And then similarly uh the sequence uh xn
+ 
+
+ align:start position:0%
+And then similarly uh the sequence uh xn
+is convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if and only if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X is found from below
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+below and in this case and if it is part
+
+ align:start position:0%
+below and in this case and if it is part
+ 
+
+ align:start position:0%
+below and in this case and if it is part
+from below then the limit here
+
+ align:start position:0%
+from below then the limit here
+ 
+
+ align:start position:0%
+from below then the limit here
+is of XN.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that was the monitor
+
+ align:start position:0%
+Okay. So that was the monitor
+ 
+
+ align:start position:0%
+Okay. So that was the monitor
+convergence there and it has these two
+
+ align:start position:0%
+convergence there and it has these two
+ 
+
+ align:start position:0%
+convergence there and it has these two
+versions the increasing version and the
+
+ align:start position:0%
+versions the increasing version and the
+ 
+
+ align:start position:0%
+versions the increasing version and the
+decreasing version.
+
+ align:start position:0%
+decreasing version.
+ 
+
+ align:start position:0%
+decreasing version.
+Then
+
+ align:start position:0%
+Then
+ 
+
+ align:start position:0%
+Then
+another important concept
+
+ align:start position:0%
+another important concept
+ 
+
+ align:start position:0%
+another important concept
+was that of the precence
+
+ align:start position:0%
+was that of the precence
+ 
+
+ align:start position:0%
+was that of the precence
+and the use the the the
+
+ align:start position:0%
+and the use the the the
+ 
+
+ align:start position:0%
+and the use the the the
+reason why sequence is useful even for
+
+ align:start position:0%
+reason why sequence is useful even for
+ 
+
+ align:start position:0%
+reason why sequence is useful even for
+the real numbers right I mean you know
+
+ align:start position:0%
+the real numbers right I mean you know
+ 
+
+ align:start position:0%
+the real numbers right I mean you know
+later on we generalize these concepts
+
+ align:start position:0%
+later on we generalize these concepts
+ 
+
+ align:start position:0%
+later on we generalize these concepts
+there was obvious generalization of of
+
+ align:start position:0%
+there was obvious generalization of of
+ 
+
+ align:start position:0%
+there was obvious generalization of of
+the concept of convergence but also of
+
+ align:start position:0%
+the concept of convergence but also of
+ 
+
+ align:start position:0%
+the concept of convergence but also of
+that of being a cruise sequence to
+
+ align:start position:0%
+that of being a cruise sequence to
+ 
+
+ align:start position:0%
+that of being a cruise sequence to
+metric spaces
+
+ align:start position:0%
+metric spaces
+ 
+
+ align:start position:0%
+metric spaces
+But even for the real numbers C
+
+ align:start position:0%
+But even for the real numbers C
+ 
+
+ align:start position:0%
+But even for the real numbers C
+sequence,
+
+ align:start position:0%
+sequence,
+ 
+
+ align:start position:0%
+sequence,
+you know, you might be interested in
+
+ align:start position:0%
+you know, you might be interested in
+ 
+
+ align:start position:0%
+you know, you might be interested in
+whether a sequence is convergent. But
+
+ align:start position:0%
+whether a sequence is convergent. But
+ 
+
+ align:start position:0%
+whether a sequence is convergent. But
+sometimes it's much easier to prove that
+
+ align:start position:0%
+sometimes it's much easier to prove that
+ 
+
+ align:start position:0%
+sometimes it's much easier to prove that
+it's a C sequence than to prove that it
+
+ align:start position:0%
+it's a C sequence than to prove that it
+ 
+
+ align:start position:0%
+it's a C sequence than to prove that it
+actually is convergent. And so if you
+
+ align:start position:0%
+actually is convergent. And so if you
+ 
+
+ align:start position:0%
+actually is convergent. And so if you
+don't really care about what the limit
+
+ align:start position:0%
+don't really care about what the limit
+ 
+
+ align:start position:0%
+don't really care about what the limit
+is, then it's often uh easier to prove
+
+ align:start position:0%
+is, then it's often uh easier to prove
+ 
+
+ align:start position:0%
+is, then it's often uh easier to prove
+that it's a co
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So cushy sequence.
+
+ align:start position:0%
+So cushy sequence.
+ 
+
+ align:start position:0%
+So cushy sequence.
+So you have a sequence again. We're
+
+ align:start position:0%
+So you have a sequence again. We're
+ 
+
+ align:start position:0%
+So you have a sequence again. We're
+still in in the real numbers.
+
+ align:start position:0%
+still in in the real numbers.
+ 
+
+ align:start position:0%
+still in in the real numbers.
+And this is a cushy sequence. It just
+
+ align:start position:0%
+And this is a cushy sequence. It just
+ 
+
+ align:start position:0%
+And this is a cushy sequence. It just
+means that for all and now I will use
+
+ align:start position:0%
+means that for all and now I will use
+ 
+
+ align:start position:0%
+means that for all and now I will use
+also this here. This symbol just means
+
+ align:start position:0%
+also this here. This symbol just means
+ 
+
+ align:start position:0%
+also this here. This symbol just means
+for all and that's also a standard
+
+ align:start position:0%
+for all and that's also a standard
+ 
+
+ align:start position:0%
+for all and that's also a standard
+symbol. It's a inverted a
+
+ align:start position:0%
+symbol. It's a inverted a
+ 
+
+ align:start position:0%
+symbol. It's a inverted a
+for all epsilon greater than zero there
+
+ align:start position:0%
+for all epsilon greater than zero there
+ 
+
+ align:start position:0%
+for all epsilon greater than zero there
+exist again this here the inver you know
+
+ align:start position:0%
+exist again this here the inver you know
+ 
+
+ align:start position:0%
+exist again this here the inver you know
+inverted e there exist
+
+ align:start position:0%
+inverted e there exist
+ 
+
+ align:start position:0%
+inverted e there exist
+delta there sorry there exist capital n
+
+ align:start position:0%
+delta there sorry there exist capital n
+ 
+
+ align:start position:0%
+delta there sorry there exist capital n
+um such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if little n and little m are bigger than
+
+ align:start position:0%
+if little n and little m are bigger than
+ 
+
+ align:start position:0%
+if little n and little m are bigger than
+capital n Then those two elements are
+
+ align:start position:0%
+capital n Then those two elements are
+ 
+
+ align:start position:0%
+capital n Then those two elements are
+bunched
+
+ align:start position:0%
+bunched
+ 
+
+ align:start position:0%
+bunched
+epsilon close together.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is what it means
+
+ align:start position:0%
+This is what it means
+ 
+
+ align:start position:0%
+This is what it means
+for a sequence to be precise sequence
+
+ align:start position:0%
+for a sequence to be precise sequence
+ 
+
+ align:start position:0%
+for a sequence to be precise sequence
+that the tail of the sequence lies very
+
+ align:start position:0%
+that the tail of the sequence lies very
+ 
+
+ align:start position:0%
+that the tail of the sequence lies very
+very close together.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me skip uh in my notes I have
+
+ align:start position:0%
+let me skip uh in my notes I have
+ 
+
+ align:start position:0%
+let me skip uh in my notes I have
+something about contracting that but
+
+ align:start position:0%
+something about contracting that but
+ 
+
+ align:start position:0%
+something about contracting that but
+actually there won't be anything about
+
+ align:start position:0%
+actually there won't be anything about
+ 
+
+ align:start position:0%
+actually there won't be anything about
+contracting that so I'll skip that
+
+ align:start position:0%
+contracting that so I'll skip that
+ 
+
+ align:start position:0%
+contracting that so I'll skip that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+let me uh let me look at let me now next
+
+ align:start position:0%
+let me uh let me look at let me now next
+ 
+
+ align:start position:0%
+let me uh let me look at let me now next
+talk about the
+
+ align:start position:0%
+talk about the
+ 
+
+ align:start position:0%
+talk about the
+convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Put some wires right there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also let me just remind you that again
+
+ align:start position:0%
+also let me just remind you that again
+ 
+
+ align:start position:0%
+also let me just remind you that again
+on the midterm so there are these five
+
+ align:start position:0%
+on the midterm so there are these five
+ 
+
+ align:start position:0%
+on the midterm so there are these five
+main problems then there's a six bonus
+
+ align:start position:0%
+main problems then there's a six bonus
+ 
+
+ align:start position:0%
+main problems then there's a six bonus
+problems but make sure that you uh if
+
+ align:start position:0%
+problems but make sure that you uh if
+ 
+
+ align:start position:0%
+problems but make sure that you uh if
+you know it doesn't matter which one you
+
+ align:start position:0%
+you know it doesn't matter which one you
+ 
+
+ align:start position:0%
+you know it doesn't matter which one you
+do so you might as well uh start like
+
+ align:start position:0%
+do so you might as well uh start like
+ 
+
+ align:start position:0%
+do so you might as well uh start like
+with the ones that seems easiest
+
+ align:start position:0%
+with the ones that seems easiest
+ 
+
+ align:start position:0%
+with the ones that seems easiest
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh and you can see anyway say exactly
+
+ align:start position:0%
+uh and you can see anyway say exactly
+ 
+
+ align:start position:0%
+uh and you can see anyway say exactly
+how many points each of them give. So
+
+ align:start position:0%
+how many points each of them give. So
+ 
+
+ align:start position:0%
+how many points each of them give. So
+you can uh if you don't have you know
+
+ align:start position:0%
+you can uh if you don't have you know
+ 
+
+ align:start position:0%
+you can uh if you don't have you know
+enough time to finish all of this you
+
+ align:start position:0%
+enough time to finish all of this you
+ 
+
+ align:start position:0%
+enough time to finish all of this you
+can make sure to try to optimize.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So what is the cushy convergence
+
+ align:start position:0%
+Okay. So what is the cushy convergence
+ 
+
+ align:start position:0%
+Okay. So what is the cushy convergence
+theorem? So again we are in R sorry uh
+
+ align:start position:0%
+theorem? So again we are in R sorry uh
+ 
+
+ align:start position:0%
+theorem? So again we are in R sorry uh
+and uh and we have and so the CI
+
+ align:start position:0%
+and uh and we have and so the CI
+ 
+
+ align:start position:0%
+and uh and we have and so the CI
+convergence is the
+
+ align:start position:0%
+convergence is the
+ 
+
+ align:start position:0%
+convergence is the
+let's say that if XM is a C sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh XM is converted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's a pushy convers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and and this trans we talk about
+
+ align:start position:0%
+and and and this trans we talk about
+ 
+
+ align:start position:0%
+and and and this trans we talk about
+that. So like the concepts if you when
+
+ align:start position:0%
+that. So like the concepts if you when
+ 
+
+ align:start position:0%
+that. So like the concepts if you when
+we in a minute review metric spaces then
+
+ align:start position:0%
+we in a minute review metric spaces then
+ 
+
+ align:start position:0%
+we in a minute review metric spaces then
+convergence sequence that makes sense in
+
+ align:start position:0%
+convergence sequence that makes sense in
+ 
+
+ align:start position:0%
+convergence sequence that makes sense in
+a metric space could see sequence makes
+
+ align:start position:0%
+a metric space could see sequence makes
+ 
+
+ align:start position:0%
+a metric space could see sequence makes
+sense in a metric space
+
+ align:start position:0%
+sense in a metric space
+ 
+
+ align:start position:0%
+sense in a metric space
+um but it's not and the statement of
+
+ align:start position:0%
+um but it's not and the statement of
+ 
+
+ align:start position:0%
+um but it's not and the statement of
+this theorem makes sense in a metric
+
+ align:start position:0%
+this theorem makes sense in a metric
+ 
+
+ align:start position:0%
+this theorem makes sense in a metric
+space but it's not always that it holds
+
+ align:start position:0%
+space but it's not always that it holds
+ 
+
+ align:start position:0%
+space but it's not always that it holds
+it holds in on but it doesn't hold in a
+
+ align:start position:0%
+it holds in on but it doesn't hold in a
+ 
+
+ align:start position:0%
+it holds in on but it doesn't hold in a
+general metric space. The possum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statement of that
+
+ align:start position:0%
+statement of that
+ 
+
+ align:start position:0%
+statement of that
+also makes sense in a general metric
+
+ align:start position:0%
+also makes sense in a general metric
+ 
+
+ align:start position:0%
+also makes sense in a general metric
+space but it doesn't hold in a general
+
+ align:start position:0%
+space but it doesn't hold in a general
+ 
+
+ align:start position:0%
+space but it doesn't hold in a general
+metric space. So these are again these
+
+ align:start position:0%
+metric space. So these are again these
+ 
+
+ align:start position:0%
+metric space. So these are again these
+are things about the real numbers.
+
+ align:start position:0%
+are things about the real numbers.
+ 
+
+ align:start position:0%
+are things about the real numbers.
+I mean they they extend to more than the
+
+ align:start position:0%
+I mean they they extend to more than the
+ 
+
+ align:start position:0%
+I mean they they extend to more than the
+real number but you have to for other
+
+ align:start position:0%
+real number but you have to for other
+ 
+
+ align:start position:0%
+real number but you have to for other
+spaces you have to kind of prove it
+
+ align:start position:0%
+spaces you have to kind of prove it
+ 
+
+ align:start position:0%
+spaces you have to kind of prove it
+individually right.
+
+ align:start position:0%
+individually right.
+ 
+
+ align:start position:0%
+individually right.
+So banana bias theorem say that if xn is
+
+ align:start position:0%
+So banana bias theorem say that if xn is
+ 
+
+ align:start position:0%
+So banana bias theorem say that if xn is
+a bounded sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+uh xn has
+
+ align:start position:0%
+uh xn has
+ 
+
+ align:start position:0%
+uh xn has
+a convergent subsequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that's simp.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um the next thing is the next thing I
+
+ align:start position:0%
+Um the next thing is the next thing I
+ 
+
+ align:start position:0%
+Um the next thing is the next thing I
+want to review is what it means for a
+
+ align:start position:0%
+want to review is what it means for a
+ 
+
+ align:start position:0%
+want to review is what it means for a
+function to be continuous. So continuity
+
+ align:start position:0%
+function to be continuous. So continuity
+ 
+
+ align:start position:0%
+function to be continuous. So continuity
+is another important property. It's
+
+ align:start position:0%
+is another important property. It's
+ 
+
+ align:start position:0%
+is another important property. It's
+closely tied together with this sequence
+
+ align:start position:0%
+closely tied together with this sequence
+ 
+
+ align:start position:0%
+closely tied together with this sequence
+and we'll get to that in just a minute.
+
+ align:start position:0%
+and we'll get to that in just a minute.
+ 
+
+ align:start position:0%
+and we'll get to that in just a minute.
+So if you take a
+
+ align:start position:0%
+So if you take a
+ 
+
+ align:start position:0%
+So if you take a
+if you take and you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+if you have a function let's say on R
+
+ align:start position:0%
+if you have a function let's say on R
+ 
+
+ align:start position:0%
+if you have a function let's say on R
+but it could be defined on a subset of
+
+ align:start position:0%
+but it could be defined on a subset of
+ 
+
+ align:start position:0%
+but it could be defined on a subset of
+R. So if you have a function like this
+
+ align:start position:0%
+R. So if you have a function like this
+ 
+
+ align:start position:0%
+R. So if you have a function like this
+then we say that f here
+
+ align:start position:0%
+then we say that f here
+ 
+
+ align:start position:0%
+then we say that f here
+is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0
+
+ align:start position:0%
+at x0
+ 
+
+ align:start position:0%
+at x0
+if for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh it's continuous at x0
+
+ align:start position:0%
+uh it's continuous at x0
+ 
+
+ align:start position:0%
+uh it's continuous at x0
+if for all u epsilon greater zero there
+
+ align:start position:0%
+if for all u epsilon greater zero there
+ 
+
+ align:start position:0%
+if for all u epsilon greater zero there
+exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta greater than zero such that
+
+ align:start position:0%
+delta greater than zero such that
+ 
+
+ align:start position:0%
+delta greater than zero such that
+if uh x - x0
+
+ align:start position:0%
+if uh x - x0
+ 
+
+ align:start position:0%
+if uh x - x0
+is smaller than delta then the images
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smaller than epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so that what it means for a function
+
+ align:start position:0%
+um so that what it means for a function
+ 
+
+ align:start position:0%
+um so that what it means for a function
+to be continuous and there was this
+
+ align:start position:0%
+to be continuous and there was this
+ 
+
+ align:start position:0%
+to be continuous and there was this
+this theorem or lema
+
+ align:start position:0%
+this theorem or lema
+ 
+
+ align:start position:0%
+this theorem or lema
+that was that tied things together. So
+
+ align:start position:0%
+that was that tied things together. So
+ 
+
+ align:start position:0%
+that was that tied things together. So
+lema
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh f is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at x0
+
+ align:start position:0%
+at x0
+ 
+
+ align:start position:0%
+at x0
+and xn
+
+ align:start position:0%
+and xn
+ 
+
+ align:start position:0%
+and xn
+converge to x0
+
+ align:start position:0%
+converge to x0
+ 
+
+ align:start position:0%
+converge to x0
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+then then
+
+ align:start position:0%
+then then
+ 
+
+ align:start position:0%
+then then
+the images
+
+ align:start position:0%
+the images
+ 
+
+ align:start position:0%
+the images
+of this sequence. So that's another
+
+ align:start position:0%
+of this sequence. So that's another
+ 
+
+ align:start position:0%
+of this sequence. So that's another
+sequence convert.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we prove this even in a metric space
+
+ align:start position:0%
+So we prove this even in a metric space
+ 
+
+ align:start position:0%
+So we prove this even in a metric space
+but we're still not.
+
+ align:start position:0%
+but we're still not.
+ 
+
+ align:start position:0%
+but we're still not.
+Okay. And so
+
+ align:start position:0%
+Okay. And so
+ 
+
+ align:start position:0%
+Okay. And so
+uh right and then we had the algebraic
+
+ align:start position:0%
+uh right and then we had the algebraic
+ 
+
+ align:start position:0%
+uh right and then we had the algebraic
+properties of functions and they were
+
+ align:start position:0%
+properties of functions and they were
+ 
+
+ align:start position:0%
+properties of functions and they were
+very similar to this. So let me just
+
+ align:start position:0%
+very similar to this. So let me just
+ 
+
+ align:start position:0%
+very similar to this. So let me just
+review them. So algebraic properties of
+
+ align:start position:0%
+review them. So algebraic properties of
+ 
+
+ align:start position:0%
+review them. So algebraic properties of
+continuous functions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So imagine that you have f and g
+
+ align:start position:0%
+So imagine that you have f and g
+ 
+
+ align:start position:0%
+So imagine that you have f and g
+are continuous functions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Everything is defined on r.
+
+ align:start position:0%
+Everything is defined on r.
+ 
+
+ align:start position:0%
+Everything is defined on r.
+C here is a constant.
+
+ align:start position:0%
+C here is a constant.
+ 
+
+ align:start position:0%
+C here is a constant.
+Well then property one that correspond
+
+ align:start position:0%
+Well then property one that correspond
+ 
+
+ align:start position:0%
+Well then property one that correspond
+to that property one here is that this
+
+ align:start position:0%
+to that property one here is that this
+ 
+
+ align:start position:0%
+to that property one here is that this
+function plus C * this function here
+
+ align:start position:0%
+function plus C * this function here
+ 
+
+ align:start position:0%
+function plus C * this function here
+this here is also continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then two is that if this function
+
+ align:start position:0%
+and then two is that if this function
+ 
+
+ align:start position:0%
+and then two is that if this function
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is never equal to zero
+
+ align:start position:0%
+is never equal to zero
+ 
+
+ align:start position:0%
+is never equal to zero
+then one over this function again is is
+
+ align:start position:0%
+then one over this function again is is
+ 
+
+ align:start position:0%
+then one over this function again is is
+also continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then sorry that was not that should
+
+ align:start position:0%
+and then sorry that was not that should
+ 
+
+ align:start position:0%
+and then sorry that was not that should
+sorry I should not make that the second
+
+ align:start position:0%
+sorry I should not make that the second
+ 
+
+ align:start position:0%
+sorry I should not make that the second
+I should make that the third property
+
+ align:start position:0%
+I should make that the third property
+ 
+
+ align:start position:0%
+I should make that the third property
+sorry that f *
+
+ align:start position:0%
+sorry that f *
+ 
+
+ align:start position:0%
+sorry that f *
+is also continuous and then the third
+
+ align:start position:0%
+is also continuous and then the third
+ 
+
+ align:start position:0%
+is also continuous and then the third
+property would be that f is not equal to
+
+ align:start position:0%
+property would be that f is not equal to
+ 
+
+ align:start position:0%
+property would be that f is not equal to
+z correspond to it then this function
+
+ align:start position:0%
+z correspond to it then this function
+ 
+
+ align:start position:0%
+z correspond to it then this function
+here is also contin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Again I divided it up when I did it
+
+ align:start position:0%
+and Again I divided it up when I did it
+ 
+
+ align:start position:0%
+and Again I divided it up when I did it
+I divided up into four steps because I
+
+ align:start position:0%
+I divided up into four steps because I
+ 
+
+ align:start position:0%
+I divided up into four steps because I
+separated this out as two steps.
+
+ align:start position:0%
+separated this out as two steps.
+ 
+
+ align:start position:0%
+separated this out as two steps.
+Okay. And so from this one we got that
+
+ align:start position:0%
+Okay. And so from this one we got that
+ 
+
+ align:start position:0%
+Okay. And so from this one we got that
+right just because then we proved that
+
+ align:start position:0%
+right just because then we proved that
+ 
+
+ align:start position:0%
+right just because then we proved that
+the constant function was continuous and
+
+ align:start position:0%
+the constant function was continuous and
+ 
+
+ align:start position:0%
+the constant function was continuous and
+the linear function the function f ofx=
+
+ align:start position:0%
+the linear function the function f ofx=
+ 
+
+ align:start position:0%
+the linear function the function f ofx=
+to x is continuous. Once we have that
+
+ align:start position:0%
+to x is continuous. Once we have that
+ 
+
+ align:start position:0%
+to x is continuous. Once we have that
+then we then we just use one and two.
+
+ align:start position:0%
+then we then we just use one and two.
+ 
+
+ align:start position:0%
+then we then we just use one and two.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> To prove that all all uh polomials is
+
+ align:start position:0%
+>> To prove that all all uh polomials is
+ 
+
+ align:start position:0%
+>> To prove that all all uh polomials is
+continuous. And then if we bring in
+
+ align:start position:0%
+continuous. And then if we bring in
+ 
+
+ align:start position:0%
+continuous. And then if we bring in
+three then we have this with all
+
+ align:start position:0%
+three then we have this with all
+ 
+
+ align:start position:0%
+three then we have this with all
+rational functions are continuous except
+
+ align:start position:0%
+rational functions are continuous except
+ 
+
+ align:start position:0%
+rational functions are continuous except
+of course where the denominator vanishes
+
+ align:start position:0%
+of course where the denominator vanishes
+ 
+
+ align:start position:0%
+of course where the denominator vanishes
+by.
+
+ align:start position:0%
+by.
+ 
+
+ align:start position:0%
+by.
+Okay. So, so that was how you sort of
+
+ align:start position:0%
+Okay. So, so that was how you sort of
+ 
+
+ align:start position:0%
+Okay. So, so that was how you sort of
+built uh continuous functions from non
+
+ align:start position:0%
+built uh continuous functions from non
+ 
+
+ align:start position:0%
+built uh continuous functions from non
+continuous functions.
+
+ align:start position:0%
+continuous functions.
+ 
+
+ align:start position:0%
+continuous functions.
+Um then we proved the extreme value and
+
+ align:start position:0%
+Um then we proved the extreme value and
+ 
+
+ align:start position:0%
+Um then we proved the extreme value and
+the intermediate values theorem. We had
+
+ align:start position:0%
+the intermediate values theorem. We had
+ 
+
+ align:start position:0%
+the intermediate values theorem. We had
+these two zero and they were proved. So
+
+ align:start position:0%
+these two zero and they were proved. So
+ 
+
+ align:start position:0%
+these two zero and they were proved. So
+one way to prove it that we did last
+
+ align:start position:0%
+one way to prove it that we did last
+ 
+
+ align:start position:0%
+one way to prove it that we did last
+time was to use this lemon that tie
+
+ align:start position:0%
+time was to use this lemon that tie
+ 
+
+ align:start position:0%
+time was to use this lemon that tie
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+um that tie together continuity and
+
+ align:start position:0%
+um that tie together continuity and
+ 
+
+ align:start position:0%
+um that tie together continuity and
+sequences.
+
+ align:start position:0%
+sequences.
+ 
+
+ align:start position:0%
+sequences.
+And so we had the extreme values there
+
+ align:start position:0%
+And so we had the extreme values there
+ 
+
+ align:start position:0%
+And so we had the extreme values there
+and this just say that if you have a
+
+ align:start position:0%
+and this just say that if you have a
+ 
+
+ align:start position:0%
+and this just say that if you have a
+function but now it's crucial
+
+ align:start position:0%
+function but now it's crucial
+ 
+
+ align:start position:0%
+function but now it's crucial
+that this here is a bounded interval and
+
+ align:start position:0%
+that this here is a bounded interval and
+ 
+
+ align:start position:0%
+that this here is a bounded interval and
+the end points are included in this. So
+
+ align:start position:0%
+the end points are included in this. So
+ 
+
+ align:start position:0%
+the end points are included in this. So
+if you have a function like this and
+
+ align:start position:0%
+if you have a function like this and
+ 
+
+ align:start position:0%
+if you have a function like this and
+this function is continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the soup and the in over the set
+
+ align:start position:0%
+then the soup and the in over the set
+ 
+
+ align:start position:0%
+then the soup and the in over the set
+here is achieved. So max or if you go
+
+ align:start position:0%
+here is achieved. So max or if you go
+ 
+
+ align:start position:0%
+here is achieved. So max or if you go
+the max of f and min of
+
+ align:start position:0%
+the max of f and min of
+ 
+
+ align:start position:0%
+the max of f and min of
+of f are achieved.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in particular the function is bounded.
+
+ align:start position:0%
+in particular the function is bounded.
+ 
+
+ align:start position:0%
+in particular the function is bounded.
+So I just state it like this little
+
+ align:start position:0%
+So I just state it like this little
+ 
+
+ align:start position:0%
+So I just state it like this little
+brief like that. So that was the extreme
+
+ align:start position:0%
+brief like that. So that was the extreme
+ 
+
+ align:start position:0%
+brief like that. So that was the extreme
+value theorem. The intermediate value
+
+ align:start position:0%
+value theorem. The intermediate value
+ 
+
+ align:start position:0%
+value theorem. The intermediate value
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+it say that if you have a function
+
+ align:start position:0%
+it say that if you have a function
+ 
+
+ align:start position:0%
+it say that if you have a function
+imagine that starting off here and it
+
+ align:start position:0%
+imagine that starting off here and it
+ 
+
+ align:start position:0%
+imagine that starting off here and it
+ending there. So this is like the
+
+ align:start position:0%
+ending there. So this is like the
+ 
+
+ align:start position:0%
+ending there. So this is like the
+function the intermediate value shall
+
+ align:start position:0%
+function the intermediate value shall
+ 
+
+ align:start position:0%
+function the intermediate value shall
+say that everything in between these two
+
+ align:start position:0%
+say that everything in between these two
+ 
+
+ align:start position:0%
+say that everything in between these two
+is also the image of something right. So
+
+ align:start position:0%
+is also the image of something right. So
+ 
+
+ align:start position:0%
+is also the image of something right. So
+if let's say that f of a smaller than f
+
+ align:start position:0%
+if let's say that f of a smaller than f
+ 
+
+ align:start position:0%
+if let's say that f of a smaller than f
+of b
+
+ align:start position:0%
+of b
+ 
+
+ align:start position:0%
+of b
+then n y here is between f of a and f of
+
+ align:start position:0%
+then n y here is between f of a and f of
+ 
+
+ align:start position:0%
+then n y here is between f of a and f of
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+then there exist
+
+ align:start position:0%
+then there exist
+ 
+
+ align:start position:0%
+then there exist
+x between a and b
+
+ align:start position:0%
+x between a and b
+ 
+
+ align:start position:0%
+x between a and b
+so that f of x
+
+ align:start position:0%
+so that f of x
+ 
+
+ align:start position:0%
+so that f of x
+is equal to one. Again the functions
+
+ align:start position:0%
+is equal to one. Again the functions
+ 
+
+ align:start position:0%
+is equal to one. Again the functions
+we're talking about are continuous right
+
+ align:start position:0%
+we're talking about are continuous right
+ 
+
+ align:start position:0%
+we're talking about are continuous right
+and they're defined on this inter
+
+ align:start position:0%
+and they're defined on this inter
+ 
+
+ align:start position:0%
+and they're defined on this inter
+this inter
+
+ align:start position:0%
+this inter
+ 
+
+ align:start position:0%
+this inter
+okay so that was those two themselium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and then they used uh And then he
+
+ align:start position:0%
+right and then they used uh And then he
+ 
+
+ align:start position:0%
+right and then they used uh And then he
+used how sequences and continuous
+
+ align:start position:0%
+used how sequences and continuous
+ 
+
+ align:start position:0%
+used how sequences and continuous
+functions was tied together. The Banana
+
+ align:start position:0%
+functions was tied together. The Banana
+ 
+
+ align:start position:0%
+functions was tied together. The Banana
+bias theorem is using something about
+
+ align:start position:0%
+bias theorem is using something about
+ 
+
+ align:start position:0%
+bias theorem is using something about
+the real numbers are ordered and like
+
+ align:start position:0%
+the real numbers are ordered and like
+ 
+
+ align:start position:0%
+the real numbers are ordered and like
+this will soup and if uh uh you know you
+
+ align:start position:0%
+this will soup and if uh uh you know you
+ 
+
+ align:start position:0%
+this will soup and if uh uh you know you
+have the least upper bound property and
+
+ align:start position:0%
+have the least upper bound property and
+ 
+
+ align:start position:0%
+have the least upper bound property and
+the greatest lower bound property,
+
+ align:start position:0%
+the greatest lower bound property,
+ 
+
+ align:start position:0%
+the greatest lower bound property,
+right? So
+
+ align:start position:0%
+right? So
+ 
+
+ align:start position:0%
+right? So
+okay now another thing. So there was so
+
+ align:start position:0%
+okay now another thing. So there was so
+ 
+
+ align:start position:0%
+okay now another thing. So there was so
+we tal about so like some of the
+
+ align:start position:0%
+we tal about so like some of the
+ 
+
+ align:start position:0%
+we tal about so like some of the
+highlights is like the in terms of
+
+ align:start position:0%
+highlights is like the in terms of
+ 
+
+ align:start position:0%
+highlights is like the in terms of
+concepts are sequences and continuity of
+
+ align:start position:0%
+concepts are sequences and continuity of
+ 
+
+ align:start position:0%
+concepts are sequences and continuity of
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+and then various properties that follow
+
+ align:start position:0%
+and then various properties that follow
+ 
+
+ align:start position:0%
+and then various properties that follow
+from this. Then another thing is
+
+ align:start position:0%
+from this. Then another thing is
+ 
+
+ align:start position:0%
+from this. Then another thing is
+sequence series.
+
+ align:start position:0%
+sequence series.
+ 
+
+ align:start position:0%
+sequence series.
+So that's another key property
+
+ align:start position:0%
+So that's another key property
+ 
+
+ align:start position:0%
+So that's another key property
+key concept.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So series is where you started with a
+
+ align:start position:0%
+So series is where you started with a
+ 
+
+ align:start position:0%
+So series is where you started with a
+sequence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+serious.
+
+ align:start position:0%
+serious.
+ 
+
+ align:start position:0%
+serious.
+So you started with so this here is a
+
+ align:start position:0%
+So you started with so this here is a
+ 
+
+ align:start position:0%
+So you started with so this here is a
+sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now you form another
+
+ align:start position:0%
+and now you form another
+ 
+
+ align:start position:0%
+and now you form another
+sequence sn but here you sum it and it
+
+ align:start position:0%
+sequence sn but here you sum it and it
+ 
+
+ align:start position:0%
+sequence sn but here you sum it and it
+could start wherever you want to start
+
+ align:start position:0%
+could start wherever you want to start
+ 
+
+ align:start position:0%
+could start wherever you want to start
+it let's say start from zero you're
+
+ align:start position:0%
+it let's say start from zero you're
+ 
+
+ align:start position:0%
+it let's say start from zero you're
+summing the first in this case it would
+
+ align:start position:0%
+summing the first in this case it would
+ 
+
+ align:start position:0%
+summing the first in this case it would
+be because you're starting at zero
+
+ align:start position:0%
+be because you're starting at zero
+ 
+
+ align:start position:0%
+be because you're starting at zero
+you're summing the first n + one
+
+ align:start position:0%
+you're summing the first n + one
+ 
+
+ align:start position:0%
+you're summing the first n + one
+so ai this is A z +
+
+ align:start position:0%
+so ai this is A z +
+ 
+
+ align:start position:0%
+so ai this is A z +
+a n is like n + one in this case, but
+
+ align:start position:0%
+a n is like n + one in this case, but
+ 
+
+ align:start position:0%
+a n is like n + one in this case, but
+you don't have to start at zero. You
+
+ align:start position:0%
+you don't have to start at zero. You
+ 
+
+ align:start position:0%
+you don't have to start at zero. You
+start at one, it would be the first n
+
+ align:start position:0%
+start at one, it would be the first n
+ 
+
+ align:start position:0%
+start at one, it would be the first n
+numbers.
+
+ align:start position:0%
+numbers.
+ 
+
+ align:start position:0%
+numbers.
+So you're looking at so a series is
+
+ align:start position:0%
+So you're looking at so a series is
+ 
+
+ align:start position:0%
+So you're looking at so a series is
+really kind of the same thing, but you
+
+ align:start position:0%
+really kind of the same thing, but you
+ 
+
+ align:start position:0%
+really kind of the same thing, but you
+think about it a little bit different,
+
+ align:start position:0%
+think about it a little bit different,
+ 
+
+ align:start position:0%
+think about it a little bit different,
+but really the same thing as a sequence
+
+ align:start position:0%
+but really the same thing as a sequence
+ 
+
+ align:start position:0%
+but really the same thing as a sequence
+where you starting with a sequence and
+
+ align:start position:0%
+where you starting with a sequence and
+ 
+
+ align:start position:0%
+where you starting with a sequence and
+then you form a new sequence.
+
+ align:start position:0%
+then you form a new sequence.
+ 
+
+ align:start position:0%
+then you form a new sequence.
+And then the the key question here is so
+
+ align:start position:0%
+And then the the key question here is so
+ 
+
+ align:start position:0%
+And then the the key question here is so
+key question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the serious conversion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conversion,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? And um so that's a key question
+
+ align:start position:0%
+right? And um so that's a key question
+ 
+
+ align:start position:0%
+right? And um so that's a key question
+and if it is convergent and you often
+
+ align:start position:0%
+and if it is convergent and you often
+ 
+
+ align:start position:0%
+and if it is convergent and you often
+the series is often written like this
+
+ align:start position:0%
+the series is often written like this
+ 
+
+ align:start position:0%
+the series is often written like this
+and so this is so this here will
+
+ align:start position:0%
+and so this is so this here will
+ 
+
+ align:start position:0%
+and so this is so this here will
+symbolize the series and if the series
+
+ align:start position:0%
+symbolize the series and if the series
+ 
+
+ align:start position:0%
+symbolize the series and if the series
+is convergent it will also symbolize the
+
+ align:start position:0%
+is convergent it will also symbolize the
+ 
+
+ align:start position:0%
+is convergent it will also symbolize the
+limit. So it has two meanings. Okay.
+
+ align:start position:0%
+limit. So it has two meanings. Okay.
+ 
+
+ align:start position:0%
+limit. So it has two meanings. Okay.
+Um but you can but even if it's not
+
+ align:start position:0%
+Um but you can but even if it's not
+ 
+
+ align:start position:0%
+Um but you can but even if it's not
+convergent then it well but if it's not
+
+ align:start position:0%
+convergent then it well but if it's not
+ 
+
+ align:start position:0%
+convergent then it well but if it's not
+convergent you would just write down and
+
+ align:start position:0%
+convergent you would just write down and
+ 
+
+ align:start position:0%
+convergent you would just write down and
+you think about this as as as a series.
+
+ align:start position:0%
+you think about this as as as a series.
+ 
+
+ align:start position:0%
+you think about this as as as a series.
+Now there are some series that are
+
+ align:start position:0%
+Now there are some series that are
+ 
+
+ align:start position:0%
+Now there are some series that are
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+you know important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and they can then be used to
+
+ align:start position:0%
+and and they can then be used to
+ 
+
+ align:start position:0%
+and and they can then be used to
+determine whether or not other series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let me just review them. And the most
+
+ align:start position:0%
+So let me just review them. And the most
+ 
+
+ align:start position:0%
+So let me just review them. And the most
+important of all is the geometric
+
+ align:start position:0%
+important of all is the geometric
+ 
+
+ align:start position:0%
+important of all is the geometric
+series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the geometric series is the series
+
+ align:start position:0%
+And the geometric series is the series
+ 
+
+ align:start position:0%
+And the geometric series is the series
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+C to the N=
+
+ align:start position:0%
+C to the N=
+ 
+
+ align:start position:0%
+C to the N=
+to Z to infinity.
+
+ align:start position:0%
+to Z to infinity.
+ 
+
+ align:start position:0%
+to Z to infinity.
+This is C is just some fixed number,
+
+ align:start position:0%
+This is C is just some fixed number,
+ 
+
+ align:start position:0%
+This is C is just some fixed number,
+real number. And you're looking at this
+
+ align:start position:0%
+real number. And you're looking at this
+ 
+
+ align:start position:0%
+real number. And you're looking at this
+and this is called this is the geometric
+
+ align:start position:0%
+and this is called this is the geometric
+ 
+
+ align:start position:0%
+and this is called this is the geometric
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+and this is is convergent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh if
+
+ align:start position:0%
+uh if
+ 
+
+ align:start position:0%
+uh if
+the absolute value of C is less than one
+
+ align:start position:0%
+the absolute value of C is less than one
+ 
+
+ align:start position:0%
+the absolute value of C is less than one
+and divergent otherwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if it is convergent when
+
+ align:start position:0%
+and if it is convergent when
+ 
+
+ align:start position:0%
+and if it is convergent when
+when C here in absolute value is less
+
+ align:start position:0%
+when C here in absolute value is less
+ 
+
+ align:start position:0%
+when C here in absolute value is less
+than one then this here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is = 1us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but remember two things one is that when
+
+ align:start position:0%
+but remember two things one is that when
+ 
+
+ align:start position:0%
+but remember two things one is that when
+you actually want to evaluate the sum
+
+ align:start position:0%
+you actually want to evaluate the sum
+ 
+
+ align:start position:0%
+you actually want to evaluate the sum
+it's crucial where you starting if I
+
+ align:start position:0%
+it's crucial where you starting if I
+ 
+
+ align:start position:0%
+it's crucial where you starting if I
+started at one then it's not anymore
+
+ align:start position:0%
+started at one then it's not anymore
+ 
+
+ align:start position:0%
+started at one then it's not anymore
+equal to this but you have to subtract
+
+ align:start position:0%
+equal to this but you have to subtract
+ 
+
+ align:start position:0%
+equal to this but you have to subtract
+the first element right that was missing
+
+ align:start position:0%
+the first element right that was missing
+ 
+
+ align:start position:0%
+the first element right that was missing
+so it's really for convergence it
+
+ align:start position:0%
+so it's really for convergence it
+ 
+
+ align:start position:0%
+so it's really for convergence it
+doesn't matter where you start but for
+
+ align:start position:0%
+doesn't matter where you start but for
+ 
+
+ align:start position:0%
+doesn't matter where you start but for
+the limits it's it's it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's one thing and the other thing is
+
+ align:start position:0%
+That's one thing and the other thing is
+ 
+
+ align:start position:0%
+That's one thing and the other thing is
+uh is like when you again we talk about
+
+ align:start position:0%
+uh is like when you again we talk about
+ 
+
+ align:start position:0%
+uh is like when you again we talk about
+this that when you're given a series
+
+ align:start position:0%
+this that when you're given a series
+ 
+
+ align:start position:0%
+this that when you're given a series
+even before there's any question the
+
+ align:start position:0%
+even before there's any question the
+ 
+
+ align:start position:0%
+even before there's any question the
+first thing when you have a series the
+
+ align:start position:0%
+first thing when you have a series the
+ 
+
+ align:start position:0%
+first thing when you have a series the
+first thing you look at is does this a
+
+ align:start position:0%
+first thing you look at is does this a
+ 
+
+ align:start position:0%
+first thing you look at is does this a
+end convert to zero or not right if a
+
+ align:start position:0%
+end convert to zero or not right if a
+ 
+
+ align:start position:0%
+end convert to zero or not right if a
+end does not go to zero well the series
+
+ align:start position:0%
+end does not go to zero well the series
+ 
+
+ align:start position:0%
+end does not go to zero well the series
+is not going to converge there's no need
+
+ align:start position:0%
+is not going to converge there's no need
+ 
+
+ align:start position:0%
+is not going to converge there's no need
+to apply any fancy test right and and
+
+ align:start position:0%
+to apply any fancy test right and and
+ 
+
+ align:start position:0%
+to apply any fancy test right and and
+for a series it's it's always the
+
+ align:start position:0%
+for a series it's it's always the
+ 
+
+ align:start position:0%
+for a series it's it's always the
+question is always whether it's
+
+ align:start position:0%
+question is always whether it's
+ 
+
+ align:start position:0%
+question is always whether it's
+convergent or not.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that's so that's a geometric
+
+ align:start position:0%
+Okay. So that's so that's a geometric
+ 
+
+ align:start position:0%
+Okay. So that's so that's a geometric
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+and then there are two other series that
+
+ align:start position:0%
+and then there are two other series that
+ 
+
+ align:start position:0%
+and then there are two other series that
+we talked about and let me just you know
+
+ align:start position:0%
+we talked about and let me just you know
+ 
+
+ align:start position:0%
+we talked about and let me just you know
+that not only talked about but we also
+
+ align:start position:0%
+that not only talked about but we also
+ 
+
+ align:start position:0%
+that not only talked about but we also
+determined whether or not they were
+
+ align:start position:0%
+determined whether or not they were
+ 
+
+ align:start position:0%
+determined whether or not they were
+converging and they were used then we
+
+ align:start position:0%
+converging and they were used then we
+ 
+
+ align:start position:0%
+converging and they were used then we
+used them to determine whether other
+
+ align:start position:0%
+used them to determine whether other
+ 
+
+ align:start position:0%
+used them to determine whether other
+series were convergent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But but the again the most important of
+
+ align:start position:0%
+But but the again the most important of
+ 
+
+ align:start position:0%
+But but the again the most important of
+all of them is the geometric series.
+
+ align:start position:0%
+all of them is the geometric series.
+ 
+
+ align:start position:0%
+all of them is the geometric series.
+That's the one that we use to determine
+
+ align:start position:0%
+That's the one that we use to determine
+ 
+
+ align:start position:0%
+That's the one that we use to determine
+whether power series in general was
+
+ align:start position:0%
+whether power series in general was
+ 
+
+ align:start position:0%
+whether power series in general was
+converging or not. But there are two
+
+ align:start position:0%
+converging or not. But there are two
+ 
+
+ align:start position:0%
+converging or not. But there are two
+other that are worth mentioning. One is
+
+ align:start position:0%
+other that are worth mentioning. One is
+ 
+
+ align:start position:0%
+other that are worth mentioning. One is
+the harmonic series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The harmonic series is the series
+
+ align:start position:0%
+The harmonic series is the series
+ 
+
+ align:start position:0%
+The harmonic series is the series
+1 / n.
+
+ align:start position:0%
+1 / n.
+ 
+
+ align:start position:0%
+1 / n.
+So this here is diverg.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's call this second
+
+ align:start position:0%
+So let's call this second
+ 
+
+ align:start position:0%
+So let's call this second
+and then there is like a
+
+ align:start position:0%
+and then there is like a
+ 
+
+ align:start position:0%
+and then there is like a
+closely related. Let's call it two and a
+
+ align:start position:0%
+closely related. Let's call it two and a
+ 
+
+ align:start position:0%
+closely related. Let's call it two and a
+half.
+
+ align:start position:0%
+half.
+ 
+
+ align:start position:0%
+half.
+That's called the alternating.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the alternating was that the it was
+
+ align:start position:0%
+So the alternating was that the it was
+ 
+
+ align:start position:0%
+So the alternating was that the it was
+like the harmonic series but the sign of
+
+ align:start position:0%
+like the harmonic series but the sign of
+ 
+
+ align:start position:0%
+like the harmonic series but the sign of
+it was alternating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this here is actually converging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then so there's one two two and a
+
+ align:start position:0%
+and then so there's one two two and a
+ 
+
+ align:start position:0%
+and then so there's one two two and a
+half and then there's three
+
+ align:start position:0%
+half and then there's three
+ 
+
+ align:start position:0%
+half and then there's three
+uh three and that's uh that's the series
+
+ align:start position:0%
+uh three and that's uh that's the series
+ 
+
+ align:start position:0%
+uh three and that's uh that's the series
+this series. Here we this year and this
+
+ align:start position:0%
+this series. Here we this year and this
+ 
+
+ align:start position:0%
+this series. Here we this year and this
+year was converging.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The only one where we determine what the
+
+ align:start position:0%
+The only one where we determine what the
+ 
+
+ align:start position:0%
+The only one where we determine what the
+sum was was actually the geometric
+
+ align:start position:0%
+sum was was actually the geometric
+ 
+
+ align:start position:0%
+sum was was actually the geometric
+series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that's like some key series.
+
+ align:start position:0%
+Okay. So that's like some key series.
+ 
+
+ align:start position:0%
+Okay. So that's like some key series.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there are
+
+ align:start position:0%
+then there are
+ 
+
+ align:start position:0%
+then there are
+then there's when you have a series
+
+ align:start position:0%
+then there's when you have a series
+ 
+
+ align:start position:0%
+then there's when you have a series
+there was one concept that proved to be
+
+ align:start position:0%
+there was one concept that proved to be
+ 
+
+ align:start position:0%
+there was one concept that proved to be
+quite useful and that's was the concept
+
+ align:start position:0%
+quite useful and that's was the concept
+ 
+
+ align:start position:0%
+quite useful and that's was the concept
+of absolute
+
+ align:start position:0%
+of absolute
+ 
+
+ align:start position:0%
+of absolute
+convergence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you're looking at a series
+
+ align:start position:0%
+and so you're looking at a series
+ 
+
+ align:start position:0%
+and so you're looking at a series
+and absolute convergence was
+
+ align:start position:0%
+and absolute convergence was
+ 
+
+ align:start position:0%
+and absolute convergence was
+that this sum here
+
+ align:start position:0%
+that this sum here
+ 
+
+ align:start position:0%
+that this sum here
+was was converging. So this here is
+
+ align:start position:0%
+was was converging. So this here is
+ 
+
+ align:start position:0%
+was was converging. So this here is
+absolute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convergent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If this series where you just the a
+
+ align:start position:0%
+If this series where you just the a
+ 
+
+ align:start position:0%
+If this series where you just the a
+replaced by the absolute value is
+
+ align:start position:0%
+replaced by the absolute value is
+ 
+
+ align:start position:0%
+replaced by the absolute value is
+convergent. Okay. So of course a non-
+
+ align:start position:0%
+convergent. Okay. So of course a non-
+ 
+
+ align:start position:0%
+convergent. Okay. So of course a non-
+negative for non for a series of non-
+
+ align:start position:0%
+negative for non for a series of non-
+ 
+
+ align:start position:0%
+negative for non for a series of non-
+negative numbers it's automatically if
+
+ align:start position:0%
+negative numbers it's automatically if
+ 
+
+ align:start position:0%
+negative numbers it's automatically if
+it's convergence it's automatically
+
+ align:start position:0%
+it's convergence it's automatically
+ 
+
+ align:start position:0%
+it's convergence it's automatically
+absolute convergent.
+
+ align:start position:0%
+absolute convergent.
+ 
+
+ align:start position:0%
+absolute convergent.
+And like we talked about it a little bit
+
+ align:start position:0%
+And like we talked about it a little bit
+ 
+
+ align:start position:0%
+And like we talked about it a little bit
+that that one of the things about an
+
+ align:start position:0%
+that that one of the things about an
+ 
+
+ align:start position:0%
+that that one of the things about an
+absolute convergent is that you could
+
+ align:start position:0%
+absolute convergent is that you could
+ 
+
+ align:start position:0%
+absolute convergent is that you could
+kind of reorder the value of summing
+
+ align:start position:0%
+kind of reorder the value of summing
+ 
+
+ align:start position:0%
+kind of reorder the value of summing
+things and it wouldn't matter for the
+
+ align:start position:0%
+things and it wouldn't matter for the
+ 
+
+ align:start position:0%
+things and it wouldn't matter for the
+limit.
+
+ align:start position:0%
+limit.
+ 
+
+ align:start position:0%
+limit.
+But if it's not absolute convergent that
+
+ align:start position:0%
+But if it's not absolute convergent that
+ 
+
+ align:start position:0%
+But if it's not absolute convergent that
+really matters we thought about it. We
+
+ align:start position:0%
+really matters we thought about it. We
+ 
+
+ align:start position:0%
+really matters we thought about it. We
+didn't really prove anything there but I
+
+ align:start position:0%
+didn't really prove anything there but I
+ 
+
+ align:start position:0%
+didn't really prove anything there but I
+think it was kind of clear you can do
+
+ align:start position:0%
+think it was kind of clear you can do
+ 
+
+ align:start position:0%
+think it was kind of clear you can do
+this.
+
+ align:start position:0%
+this.
+ 
+
+ align:start position:0%
+this.
+One thing where we used it was that when
+
+ align:start position:0%
+One thing where we used it was that when
+ 
+
+ align:start position:0%
+One thing where we used it was that when
+we look at product of series
+
+ align:start position:0%
+we look at product of series
+ 
+
+ align:start position:0%
+we look at product of series
+then the product of series was
+
+ align:start position:0%
+then the product of series was
+ 
+
+ align:start position:0%
+then the product of series was
+convergent if each of them was absolute
+
+ align:start position:0%
+convergent if each of them was absolute
+ 
+
+ align:start position:0%
+convergent if each of them was absolute
+convergence and there you saw that we
+
+ align:start position:0%
+convergence and there you saw that we
+ 
+
+ align:start position:0%
+convergence and there you saw that we
+estimated some remainder term and there
+
+ align:start position:0%
+estimated some remainder term and there
+ 
+
+ align:start position:0%
+estimated some remainder term and there
+was really kind of key that that we had
+
+ align:start position:0%
+was really kind of key that that we had
+ 
+
+ align:start position:0%
+was really kind of key that that we had
+absolute convergence. Okay.
+
+ align:start position:0%
+absolute convergence. Okay.
+ 
+
+ align:start position:0%
+absolute convergence. Okay.
+So anyway, so absolute convergence is an
+
+ align:start position:0%
+So anyway, so absolute convergence is an
+ 
+
+ align:start position:0%
+So anyway, so absolute convergence is an
+important uh you know it's it's it's for
+
+ align:start position:0%
+important uh you know it's it's it's for
+ 
+
+ align:start position:0%
+important uh you know it's it's it's for
+a series it's a it's a stronger property
+
+ align:start position:0%
+a series it's a it's a stronger property
+ 
+
+ align:start position:0%
+a series it's a it's a stronger property
+than convergence. So absolute
+
+ align:start position:0%
+than convergence. So absolute
+ 
+
+ align:start position:0%
+than convergence. So absolute
+convergence implies convergence. Maybe I
+
+ align:start position:0%
+convergence implies convergence. Maybe I
+ 
+
+ align:start position:0%
+convergence implies convergence. Maybe I
+should write this as a theorem. So we
+
+ align:start position:0%
+should write this as a theorem. So we
+ 
+
+ align:start position:0%
+should write this as a theorem. So we
+had that theorem. So absolute conversion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's not it's it's stronger.
+
+ align:start position:0%
+but it's not it's it's stronger.
+ 
+
+ align:start position:0%
+but it's not it's it's stronger.
+general.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And now then we had some tests.
+
+ align:start position:0%
+Okay. And now then we had some tests.
+ 
+
+ align:start position:0%
+Okay. And now then we had some tests.
+Then we had some tests and so we had uh
+
+ align:start position:0%
+Then we had some tests and so we had uh
+ 
+
+ align:start position:0%
+Then we had some tests and so we had uh
+we talked in particular about
+
+ align:start position:0%
+we talked in particular about
+ 
+
+ align:start position:0%
+we talked in particular about
+there was a few other tests that we
+
+ align:start position:0%
+there was a few other tests that we
+ 
+
+ align:start position:0%
+there was a few other tests that we
+talked about but but I didn't
+
+ align:start position:0%
+talked about but but I didn't
+ 
+
+ align:start position:0%
+talked about but but I didn't
+um I mean they're not actually going to
+
+ align:start position:0%
+um I mean they're not actually going to
+ 
+
+ align:start position:0%
+um I mean they're not actually going to
+be on the victim uh and and some of them
+
+ align:start position:0%
+be on the victim uh and and some of them
+ 
+
+ align:start position:0%
+be on the victim uh and and some of them
+we get back to this one here won't be on
+
+ align:start position:0%
+we get back to this one here won't be on
+ 
+
+ align:start position:0%
+we get back to this one here won't be on
+the victim alternating but we talked
+
+ align:start position:0%
+the victim alternating but we talked
+ 
+
+ align:start position:0%
+the victim alternating but we talked
+about how to prove the convergence right
+
+ align:start position:0%
+about how to prove the convergence right
+ 
+
+ align:start position:0%
+about how to prove the convergence right
+and the important and and when we talk
+
+ align:start position:0%
+and the important and and when we talk
+ 
+
+ align:start position:0%
+and the important and and when we talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that we discovered that this thing here
+
+ align:start position:0%
+that we discovered that this thing here
+ 
+
+ align:start position:0%
+that we discovered that this thing here
+that there was a stronger statement that
+
+ align:start position:0%
+that there was a stronger statement that
+ 
+
+ align:start position:0%
+that there was a stronger statement that
+if you have alternating and the a were
+
+ align:start position:0%
+if you have alternating and the a were
+ 
+
+ align:start position:0%
+if you have alternating and the a were
+all non negative and these guys was
+
+ align:start position:0%
+all non negative and these guys was
+ 
+
+ align:start position:0%
+all non negative and these guys was
+decreasing goes decreasing down to zero
+
+ align:start position:0%
+decreasing goes decreasing down to zero
+ 
+
+ align:start position:0%
+decreasing goes decreasing down to zero
+then actually any alternating sequence
+
+ align:start position:0%
+then actually any alternating sequence
+ 
+
+ align:start position:0%
+then actually any alternating sequence
+like that would be would be converging
+
+ align:start position:0%
+like that would be would be converging
+ 
+
+ align:start position:0%
+like that would be would be converging
+anyway but but but the test we really
+
+ align:start position:0%
+anyway but but but the test we really
+ 
+
+ align:start position:0%
+anyway but but but the test we really
+talked about was three test. One of them
+
+ align:start position:0%
+talked about was three test. One of them
+ 
+
+ align:start position:0%
+talked about was three test. One of them
+had two parts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then then in a minute we'll talk
+
+ align:start position:0%
+and then then in a minute we'll talk
+ 
+
+ align:start position:0%
+and then then in a minute we'll talk
+about how we apply them to power series
+
+ align:start position:0%
+about how we apply them to power series
+ 
+
+ align:start position:0%
+about how we apply them to power series
+which one. So we had some tests
+
+ align:start position:0%
+which one. So we had some tests
+ 
+
+ align:start position:0%
+which one. So we had some tests
+to determine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whether or not the series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or not as serious
+
+ align:start position:0%
+or not as serious
+ 
+
+ align:start position:0%
+or not as serious
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is convergence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So what are the tests? So there
+
+ align:start position:0%
+Okay. So what are the tests? So there
+ 
+
+ align:start position:0%
+Okay. So what are the tests? So there
+are the comparison test.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let me just first write down the test.
+
+ align:start position:0%
+Let me just first write down the test.
+ 
+
+ align:start position:0%
+Let me just first write down the test.
+So the comparison test and there was two
+
+ align:start position:0%
+So the comparison test and there was two
+ 
+
+ align:start position:0%
+So the comparison test and there was two
+versions. Version A and version B.
+
+ align:start position:0%
+versions. Version A and version B.
+ 
+
+ align:start position:0%
+versions. Version A and version B.
+Then there was the ratio test.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then there was the root test.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ratio test and the root test they
+
+ align:start position:0%
+the ratio test and the root test they
+ 
+
+ align:start position:0%
+the ratio test and the root test they
+are both offsprings of the geometric
+
+ align:start position:0%
+are both offsprings of the geometric
+ 
+
+ align:start position:0%
+are both offsprings of the geometric
+series right in both of these you got
+
+ align:start position:0%
+series right in both of these you got
+ 
+
+ align:start position:0%
+series right in both of these you got
+let's just talk about these first uh the
+
+ align:start position:0%
+let's just talk about these first uh the
+ 
+
+ align:start position:0%
+let's just talk about these first uh the
+ratio test was looking at this
+
+ align:start position:0%
+ratio test was looking at this
+ 
+
+ align:start position:0%
+ratio test was looking at this
+ratio of a n a divided by a n a n + 1 /
+
+ align:start position:0%
+ratio of a n a divided by a n a n + 1 /
+ 
+
+ align:start position:0%
+ratio of a n a divided by a n a n + 1 /
+a n so you are implicitly assuming
+
+ align:start position:0%
+a n so you are implicitly assuming
+ 
+
+ align:start position:0%
+a n so you are implicitly assuming
+that the a does not vanish not zero.
+
+ align:start position:0%
+that the a does not vanish not zero.
+ 
+
+ align:start position:0%
+that the a does not vanish not zero.
+Right? So you can form this ratio and
+
+ align:start position:0%
+Right? So you can form this ratio and
+ 
+
+ align:start position:0%
+Right? So you can form this ratio and
+then if this limit here as n goes to
+
+ align:start position:0%
+then if this limit here as n goes to
+ 
+
+ align:start position:0%
+then if this limit here as n goes to
+infinity if this limit here is less than
+
+ align:start position:0%
+infinity if this limit here is less than
+ 
+
+ align:start position:0%
+infinity if this limit here is less than
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+then then uh the ratio test say that uh
+
+ align:start position:0%
+then then uh the ratio test say that uh
+ 
+
+ align:start position:0%
+then then uh the ratio test say that uh
+the series was convergent.
+
+ align:start position:0%
+the series was convergent.
+ 
+
+ align:start position:0%
+the series was convergent.
+If the ratio was bigger than one then
+
+ align:start position:0%
+If the ratio was bigger than one then
+ 
+
+ align:start position:0%
+If the ratio was bigger than one then
+this ordinary element a n would not even
+
+ align:start position:0%
+this ordinary element a n would not even
+ 
+
+ align:start position:0%
+this ordinary element a n would not even
+go to zero. Right? So this here is so
+
+ align:start position:0%
+go to zero. Right? So this here is so
+ 
+
+ align:start position:0%
+go to zero. Right? So this here is so
+that in this case here maybe maybe I'll
+
+ align:start position:0%
+that in this case here maybe maybe I'll
+ 
+
+ align:start position:0%
+that in this case here maybe maybe I'll
+write it over here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So for the ratio test,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the ratio test, you assume that a
+
+ align:start position:0%
+for the ratio test, you assume that a
+ 
+
+ align:start position:0%
+for the ratio test, you assume that a
+none of the a
+
+ align:start position:0%
+none of the a
+ 
+
+ align:start position:0%
+none of the a
+and you're looking at a n + one / n.
+
+ align:start position:0%
+and you're looking at a n + one / n.
+ 
+
+ align:start position:0%
+and you're looking at a n + one / n.
+And if this limit here,
+
+ align:start position:0%
+And if this limit here,
+ 
+
+ align:start position:0%
+And if this limit here,
+let's call this limit, let's assume that
+
+ align:start position:0%
+let's call this limit, let's assume that
+ 
+
+ align:start position:0%
+let's call this limit, let's assume that
+the limit exists. Of course, it may not
+
+ align:start position:0%
+the limit exists. Of course, it may not
+ 
+
+ align:start position:0%
+the limit exists. Of course, it may not
+exist, right? But if the limit existed.
+
+ align:start position:0%
+exist, right? But if the limit existed.
+ 
+
+ align:start position:0%
+exist, right? But if the limit existed.
+So if if C here is less than one, right?
+
+ align:start position:0%
+So if if C here is less than one, right?
+ 
+
+ align:start position:0%
+So if if C here is less than one, right?
+It's always not negative. These are non
+
+ align:start position:0%
+It's always not negative. These are non
+ 
+
+ align:start position:0%
+It's always not negative. These are non
+negative numbers. See is is less than
+
+ align:start position:0%
+negative numbers. See is is less than
+ 
+
+ align:start position:0%
+negative numbers. See is is less than
+one, then the series is converted.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If this C here is strictly bigger than
+
+ align:start position:0%
+If this C here is strictly bigger than
+ 
+
+ align:start position:0%
+If this C here is strictly bigger than
+one, this implies that the series
+
+ align:start position:0%
+one, this implies that the series
+ 
+
+ align:start position:0%
+one, this implies that the series
+is diverted.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And if the C was equal to one then it's
+
+ align:start position:0%
+And if the C was equal to one then it's
+ 
+
+ align:start position:0%
+And if the C was equal to one then it's
+unclear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so unclear which means that further
+
+ align:start position:0%
+and so unclear which means that further
+ 
+
+ align:start position:0%
+and so unclear which means that further
+test are needed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so now
+
+ align:start position:0%
+And so now
+ 
+
+ align:start position:0%
+And so now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so that's the ratio test and the root
+
+ align:start position:0%
+so that's the ratio test and the root
+ 
+
+ align:start position:0%
+so that's the ratio test and the root
+test was similar.
+
+ align:start position:0%
+test was similar.
+ 
+
+ align:start position:0%
+test was similar.
+the root test where so you're looking at
+
+ align:start position:0%
+the root test where so you're looking at
+ 
+
+ align:start position:0%
+the root test where so you're looking at
+the AM you take the so this is the root
+
+ align:start position:0%
+the AM you take the so this is the root
+ 
+
+ align:start position:0%
+the AM you take the so this is the root
+test and again this is tested by
+
+ align:start position:0%
+test and again this is tested by
+ 
+
+ align:start position:0%
+test and again this is tested by
+comparing it to the geometric series so
+
+ align:start position:0%
+comparing it to the geometric series so
+ 
+
+ align:start position:0%
+comparing it to the geometric series so
+the root test
+
+ align:start position:0%
+the root test
+ 
+
+ align:start position:0%
+the root test
+so you take the am
+
+ align:start position:0%
+so you take the am
+ 
+
+ align:start position:0%
+so you take the am
+take the nth root of this
+
+ align:start position:0%
+take the nth root of this
+ 
+
+ align:start position:0%
+take the nth root of this
+and you're looking at the limit here and
+
+ align:start position:0%
+and you're looking at the limit here and
+ 
+
+ align:start position:0%
+and you're looking at the limit here and
+we actually looked at the name soup.
+
+ align:start position:0%
+we actually looked at the name soup.
+ 
+
+ align:start position:0%
+we actually looked at the name soup.
+I write in the new soup. Reason why I
+
+ align:start position:0%
+I write in the new soup. Reason why I
+ 
+
+ align:start position:0%
+I write in the new soup. Reason why I
+want the new soup is
+
+ align:start position:0%
+want the new soup is
+ 
+
+ align:start position:0%
+want the new soup is
+that I want to make sure it's later on I
+
+ align:start position:0%
+that I want to make sure it's later on I
+ 
+
+ align:start position:0%
+that I want to make sure it's later on I
+want to apply more generally. Okay. So I
+
+ align:start position:0%
+want to apply more generally. Okay. So I
+ 
+
+ align:start position:0%
+want to apply more generally. Okay. So I
+have uh so if the loom soup here was um
+
+ align:start position:0%
+have uh so if the loom soup here was um
+ 
+
+ align:start position:0%
+have uh so if the loom soup here was um
+was less than one is called soup. It's
+
+ align:start position:0%
+was less than one is called soup. It's
+ 
+
+ align:start position:0%
+was less than one is called soup. It's
+called C. If if C here is less than one
+
+ align:start position:0%
+called C. If if C here is less than one
+ 
+
+ align:start position:0%
+called C. If if C here is less than one
+then uh series is convergence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+True. If the C is bigger than one series
+
+ align:start position:0%
+True. If the C is bigger than one series
+ 
+
+ align:start position:0%
+True. If the C is bigger than one series
+is divergent. This fails the most basic
+
+ align:start position:0%
+is divergent. This fails the most basic
+ 
+
+ align:start position:0%
+is divergent. This fails the most basic
+test divergence.
+
+ align:start position:0%
+test divergence.
+ 
+
+ align:start position:0%
+test divergence.
+And again uh three if C is equal to one
+
+ align:start position:0%
+And again uh three if C is equal to one
+ 
+
+ align:start position:0%
+And again uh three if C is equal to one
+then it's unclear for test or leave it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That was the that was those two tests.
+
+ align:start position:0%
+That was the that was those two tests.
+ 
+
+ align:start position:0%
+That was the that was those two tests.
+The comparison tests, let's get back to
+
+ align:start position:0%
+The comparison tests, let's get back to
+ 
+
+ align:start position:0%
+The comparison tests, let's get back to
+that. The comparison test had two parts
+
+ align:start position:0%
+that. The comparison test had two parts
+ 
+
+ align:start position:0%
+that. The comparison test had two parts
+that you had suppose you had a n and bn.
+
+ align:start position:0%
+that you had suppose you had a n and bn.
+ 
+
+ align:start position:0%
+that you had suppose you had a n and bn.
+The first part is this statement that if
+
+ align:start position:0%
+The first part is this statement that if
+ 
+
+ align:start position:0%
+The first part is this statement that if
+you have two series, one based on the a
+
+ align:start position:0%
+you have two series, one based on the a
+ 
+
+ align:start position:0%
+you have two series, one based on the a
+series based on the bn. If you have this
+
+ align:start position:0%
+series based on the bn. If you have this
+ 
+
+ align:start position:0%
+series based on the bn. If you have this
+if BN
+
+ align:start position:0%
+if BN
+ 
+
+ align:start position:0%
+if BN
+so this if if this
+
+ align:start position:0%
+so this if if this
+ 
+
+ align:start position:0%
+so this if if this
+is converted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then it fires like this it's converted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and this is sometimes used both
+
+ align:start position:0%
+right and this is sometimes used both
+ 
+
+ align:start position:0%
+right and this is sometimes used both
+exactly like this and it's also
+
+ align:start position:0%
+exactly like this and it's also
+ 
+
+ align:start position:0%
+exactly like this and it's also
+sometimes used where you know that this
+
+ align:start position:0%
+sometimes used where you know that this
+ 
+
+ align:start position:0%
+sometimes used where you know that this
+one here is divergent and so you
+
+ align:start position:0%
+one here is divergent and so you
+ 
+
+ align:start position:0%
+one here is divergent and so you
+conclude that this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The other part of the comparison test
+
+ align:start position:0%
+The other part of the comparison test
+ 
+
+ align:start position:0%
+The other part of the comparison test
+was if you had the limit here if this
+
+ align:start position:0%
+was if you had the limit here if this
+ 
+
+ align:start position:0%
+was if you had the limit here if this
+limit here exist and it was some L
+
+ align:start position:0%
+limit here exist and it was some L
+ 
+
+ align:start position:0%
+limit here exist and it was some L
+then actually it it say that let's say L
+
+ align:start position:0%
+then actually it it say that let's say L
+ 
+
+ align:start position:0%
+then actually it it say that let's say L
+here is not equal to Z
+
+ align:start position:0%
+here is not equal to Z
+ 
+
+ align:start position:0%
+here is not equal to Z
+then then uh then um then um If
+
+ align:start position:0%
+then then uh then um then um If
+ 
+
+ align:start position:0%
+then then uh then um then um If
+if one of them is converging the other
+
+ align:start position:0%
+if one of them is converging the other
+ 
+
+ align:start position:0%
+if one of them is converging the other
+one is also converging. So
+
+ align:start position:0%
+one is also converging. So
+ 
+
+ align:start position:0%
+one is also converging. So
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+is converted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and vice versa is actually equivalent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So those were the three tests that we
+
+ align:start position:0%
+So those were the three tests that we
+ 
+
+ align:start position:0%
+So those were the three tests that we
+really went through. There was a few
+
+ align:start position:0%
+really went through. There was a few
+ 
+
+ align:start position:0%
+really went through. There was a few
+other tests like again this alternating
+
+ align:start position:0%
+other tests like again this alternating
+ 
+
+ align:start position:0%
+other tests like again this alternating
+series test that sort of proved but it's
+
+ align:start position:0%
+series test that sort of proved but it's
+ 
+
+ align:start position:0%
+series test that sort of proved but it's
+not being unmet and you will be trapped
+
+ align:start position:0%
+not being unmet and you will be trapped
+ 
+
+ align:start position:0%
+not being unmet and you will be trapped
+to this later.
+
+ align:start position:0%
+to this later.
+ 
+
+ align:start position:0%
+to this later.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Um are there like patterns of like when
+
+ align:start position:0%
+>> Um are there like patterns of like when
+ 
+
+ align:start position:0%
+>> Um are there like patterns of like when
+we should apply which tests?
+
+ align:start position:0%
+we should apply which tests?
+ 
+
+ align:start position:0%
+we should apply which tests?
+>> Yeah. No. And I want to get to this
+
+ align:start position:0%
+>> Yeah. No. And I want to get to this
+ 
+
+ align:start position:0%
+>> Yeah. No. And I want to get to this
+um I want to get to this in just a
+
+ align:start position:0%
+um I want to get to this in just a
+ 
+
+ align:start position:0%
+um I want to get to this in just a
+second.
+
+ align:start position:0%
+second.
+ 
+
+ align:start position:0%
+second.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+let me let me just say a couple of words
+
+ align:start position:0%
+let me let me just say a couple of words
+ 
+
+ align:start position:0%
+let me let me just say a couple of words
+first and then let let me jump to some
+
+ align:start position:0%
+first and then let let me jump to some
+ 
+
+ align:start position:0%
+first and then let let me jump to some
+of the examples of problems and then
+
+ align:start position:0%
+of the examples of problems and then
+ 
+
+ align:start position:0%
+of the examples of problems and then
+I'll come back and I'll review a little
+
+ align:start position:0%
+I'll come back and I'll review a little
+ 
+
+ align:start position:0%
+I'll come back and I'll review a little
+more. So uh but let's just talk about
+
+ align:start position:0%
+more. So uh but let's just talk about
+ 
+
+ align:start position:0%
+more. So uh but let's just talk about
+power shares.
+
+ align:start position:0%
+power shares.
+ 
+
+ align:start position:0%
+power shares.
+Um maybe maybe a little
+
+ align:start position:0%
+Um maybe maybe a little
+ 
+
+ align:start position:0%
+Um maybe maybe a little
+whether uh just now when you were asking
+
+ align:start position:0%
+whether uh just now when you were asking
+ 
+
+ align:start position:0%
+whether uh just now when you were asking
+the question
+
+ align:start position:0%
+the question
+ 
+
+ align:start position:0%
+the question
+uh no this this just review the power
+
+ align:start position:0%
+uh no this this just review the power
+ 
+
+ align:start position:0%
+uh no this this just review the power
+series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So a power series was a series but it
+
+ align:start position:0%
+So a power series was a series but it
+ 
+
+ align:start position:0%
+So a power series was a series but it
+was something that also defined a
+
+ align:start position:0%
+was something that also defined a
+ 
+
+ align:start position:0%
+was something that also defined a
+function right and so you take so you
+
+ align:start position:0%
+function right and so you take so you
+ 
+
+ align:start position:0%
+function right and so you take so you
+have a you have a u
+
+ align:start position:0%
+have a you have a u
+ 
+
+ align:start position:0%
+have a you have a u
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+see power series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have a sequence a
+
+ align:start position:0%
+so you have a sequence a
+ 
+
+ align:start position:0%
+so you have a sequence a
+and then you think for each x but x but
+
+ align:start position:0%
+and then you think for each x but x but
+ 
+
+ align:start position:0%
+and then you think for each x but x but
+x is being fixed you form a series
+
+ align:start position:0%
+x is being fixed you form a series
+ 
+
+ align:start position:0%
+x is being fixed you form a series
+and this is the series that you form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so for each x you can ask is this
+
+ align:start position:0%
+and so for each x you can ask is this
+ 
+
+ align:start position:0%
+and so for each x you can ask is this
+series convergent or not right this here
+
+ align:start position:0%
+series convergent or not right this here
+ 
+
+ align:start position:0%
+series convergent or not right this here
+is called a power series
+
+ align:start position:0%
+is called a power series
+ 
+
+ align:start position:0%
+is called a power series
+and uh and the the key point for a power
+
+ align:start position:0%
+and uh and the the key point for a power
+ 
+
+ align:start position:0%
+and uh and the the key point for a power
+series is uh again of course whether or
+
+ align:start position:0%
+series is uh again of course whether or
+ 
+
+ align:start position:0%
+series is uh again of course whether or
+not this is convergence
+
+ align:start position:0%
+not this is convergence
+ 
+
+ align:start position:0%
+not this is convergence
+and this give rise to the radius of
+
+ align:start position:0%
+and this give rise to the radius of
+ 
+
+ align:start position:0%
+and this give rise to the radius of
+convergence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so the radius of convergence was
+
+ align:start position:0%
+And so the radius of convergence was
+ 
+
+ align:start position:0%
+And so the radius of convergence was
+that we defined we looked at at le
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the nth root
+
+ align:start position:0%
+of the nth root
+ 
+
+ align:start position:0%
+of the nth root
+of a n like that.
+
+ align:start position:0%
+of a n like that.
+ 
+
+ align:start position:0%
+of a n like that.
+Right? And we looked at when this thing
+
+ align:start position:0%
+Right? And we looked at when this thing
+ 
+
+ align:start position:0%
+Right? And we looked at when this thing
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh if this thing here is uh right so we
+
+ align:start position:0%
+uh if this thing here is uh right so we
+ 
+
+ align:start position:0%
+uh if this thing here is uh right so we
+define this thing here
+
+ align:start position:0%
+define this thing here
+ 
+
+ align:start position:0%
+define this thing here
+and so we get this thing here and then
+
+ align:start position:0%
+and so we get this thing here and then
+ 
+
+ align:start position:0%
+and so we get this thing here and then
+we define the radius of convergence. So
+
+ align:start position:0%
+we define the radius of convergence. So
+ 
+
+ align:start position:0%
+we define the radius of convergence. So
+the radius of conver
+
+ align:start position:0%
+the radius of conver
+ 
+
+ align:start position:0%
+the radius of conver
+of convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is r and the r is 1 /
+
+ align:start position:0%
+this is r and the r is 1 /
+ 
+
+ align:start position:0%
+this is r and the r is 1 /
+This should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there was an understanding in this.
+
+ align:start position:0%
+but there was an understanding in this.
+ 
+
+ align:start position:0%
+but there was an understanding in this.
+The understanding is that if this number
+
+ align:start position:0%
+The understanding is that if this number
+ 
+
+ align:start position:0%
+The understanding is that if this number
+here this number here you this one of
+
+ align:start position:0%
+here this number here you this one of
+ 
+
+ align:start position:0%
+here this number here you this one of
+potential could be infinite. Right?
+
+ align:start position:0%
+potential could be infinite. Right?
+ 
+
+ align:start position:0%
+potential could be infinite. Right?
+If it was infinite it meant that this
+
+ align:start position:0%
+If it was infinite it meant that this
+ 
+
+ align:start position:0%
+If it was infinite it meant that this
+thing here was zero.
+
+ align:start position:0%
+thing here was zero.
+ 
+
+ align:start position:0%
+thing here was zero.
+Right? If this one here is is infinity,
+
+ align:start position:0%
+Right? If this one here is is infinity,
+ 
+
+ align:start position:0%
+Right? If this one here is is infinity,
+if this here is zero, then this here
+
+ align:start position:0%
+if this here is zero, then this here
+ 
+
+ align:start position:0%
+if this here is zero, then this here
+would be infinity.
+
+ align:start position:0%
+would be infinity.
+ 
+
+ align:start position:0%
+would be infinity.
+Okay, so that's so that's like a
+
+ align:start position:0%
+Okay, so that's so that's like a
+ 
+
+ align:start position:0%
+Okay, so that's so that's like a
+convention in this particular case,
+
+ align:start position:0%
+convention in this particular case,
+ 
+
+ align:start position:0%
+convention in this particular case,
+right? I mean, usually we don't want to
+
+ align:start position:0%
+right? I mean, usually we don't want to
+ 
+
+ align:start position:0%
+right? I mean, usually we don't want to
+divide by zero that kind of stuff, but
+
+ align:start position:0%
+divide by zero that kind of stuff, but
+ 
+
+ align:start position:0%
+divide by zero that kind of stuff, but
+this is convention in this particular
+
+ align:start position:0%
+this is convention in this particular
+ 
+
+ align:start position:0%
+this is convention in this particular
+case.
+
+ align:start position:0%
+case.
+ 
+
+ align:start position:0%
+case.
+And so using this radius of convergence,
+
+ align:start position:0%
+And so using this radius of convergence,
+ 
+
+ align:start position:0%
+And so using this radius of convergence,
+we saw that if you take a power series,
+
+ align:start position:0%
+we saw that if you take a power series,
+ 
+
+ align:start position:0%
+we saw that if you take a power series,
+if you have any power shares like this,
+
+ align:start position:0%
+if you have any power shares like this,
+ 
+
+ align:start position:0%
+if you have any power shares like this,
+there have any power shares like this,
+
+ align:start position:0%
+there have any power shares like this,
+ 
+
+ align:start position:0%
+there have any power shares like this,
+it's going to be if this here is R and
+
+ align:start position:0%
+it's going to be if this here is R and
+ 
+
+ align:start position:0%
+it's going to be if this here is R and
+again R could be zero or it could be
+
+ align:start position:0%
+again R could be zero or it could be
+ 
+
+ align:start position:0%
+again R could be zero or it could be
+infinity, right? But if this is R. So I
+
+ align:start position:0%
+infinity, right? But if this is R. So I
+ 
+
+ align:start position:0%
+infinity, right? But if this is R. So I
+should write this minus
+
+ align:start position:0%
+should write this minus
+ 
+
+ align:start position:0%
+should write this minus
+then the for x in between for x not
+
+ align:start position:0%
+then the for x in between for x not
+ 
+
+ align:start position:0%
+then the for x in between for x not
+including the end point but in between
+
+ align:start position:0%
+including the end point but in between
+ 
+
+ align:start position:0%
+including the end point but in between
+the series is converging right the power
+
+ align:start position:0%
+the series is converging right the power
+ 
+
+ align:start position:0%
+the series is converging right the power
+series is converging and outside here
+
+ align:start position:0%
+series is converging and outside here
+ 
+
+ align:start position:0%
+series is converging and outside here
+it's it's diverging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outside it's diverging here it's
+
+ align:start position:0%
+outside it's diverging here it's
+ 
+
+ align:start position:0%
+outside it's diverging here it's
+converting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and at those two points here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+further test are needed right so this is
+
+ align:start position:0%
+further test are needed right so this is
+ 
+
+ align:start position:0%
+further test are needed right so this is
+always this picture so this come back to
+
+ align:start position:0%
+always this picture so this come back to
+ 
+
+ align:start position:0%
+always this picture so this come back to
+your question about you know which test
+
+ align:start position:0%
+your question about you know which test
+ 
+
+ align:start position:0%
+your question about you know which test
+I mean of course you can use any test
+
+ align:start position:0%
+I mean of course you can use any test
+ 
+
+ align:start position:0%
+I mean of course you can use any test
+you want but when I you know like if
+
+ align:start position:0%
+you want but when I you know like if
+ 
+
+ align:start position:0%
+you want but when I you know like if
+you're looking at a series you can use
+
+ align:start position:0%
+you're looking at a series you can use
+ 
+
+ align:start position:0%
+you're looking at a series you can use
+whatever test you want but if it was a
+
+ align:start position:0%
+whatever test you want but if it was a
+ 
+
+ align:start position:0%
+whatever test you want but if it was a
+power series you already know that
+
+ align:start position:0%
+power series you already know that
+ 
+
+ align:start position:0%
+power series you already know that
+there's some integral around here where
+
+ align:start position:0%
+there's some integral around here where
+ 
+
+ align:start position:0%
+there's some integral around here where
+it's convergent and then there's a
+
+ align:start position:0%
+it's convergent and then there's a
+ 
+
+ align:start position:0%
+it's convergent and then there's a
+question about the end points, right?
+
+ align:start position:0%
+question about the end points, right?
+ 
+
+ align:start position:0%
+question about the end points, right?
+And so um okay, so now let's look at
+
+ align:start position:0%
+And so um okay, so now let's look at
+ 
+
+ align:start position:0%
+And so um okay, so now let's look at
+let's look at some examples of this
+
+ align:start position:0%
+let's look at some examples of this
+ 
+
+ align:start position:0%
+let's look at some examples of this
+and suppose you look at
+
+ align:start position:0%
+and suppose you look at
+ 
+
+ align:start position:0%
+and suppose you look at
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's usually not too hard to use either
+
+ align:start position:0%
+it's usually not too hard to use either
+ 
+
+ align:start position:0%
+it's usually not too hard to use either
+either the roof
+
+ align:start position:0%
+either the roof
+ 
+
+ align:start position:0%
+either the roof
+to to use either um
+
+ align:start position:0%
+to to use either um
+ 
+
+ align:start position:0%
+to to use either um
+the this here was based on the root test
+
+ align:start position:0%
+the this here was based on the root test
+ 
+
+ align:start position:0%
+the this here was based on the root test
+to either use the root test or the ratio
+
+ align:start position:0%
+to either use the root test or the ratio
+ 
+
+ align:start position:0%
+to either use the root test or the ratio
+test for power but but you can take
+
+ align:start position:0%
+test for power but but you can take
+ 
+
+ align:start position:0%
+test for power but but you can take
+advantage of it sometimes slightly
+
+ align:start position:0%
+advantage of it sometimes slightly
+ 
+
+ align:start position:0%
+advantage of it sometimes slightly
+easier. So let's look at two examples
+
+ align:start position:0%
+easier. So let's look at two examples
+ 
+
+ align:start position:0%
+easier. So let's look at two examples
+here. So suppose that
+
+ align:start position:0%
+here. So suppose that
+ 
+
+ align:start position:0%
+here. So suppose that
+that you ask to find the the radius of
+
+ align:start position:0%
+that you ask to find the the radius of
+ 
+
+ align:start position:0%
+that you ask to find the the radius of
+convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the power sh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then let's say that this is n to the
+
+ align:start position:0%
+and then let's say that this is n to the
+ 
+
+ align:start position:0%
+and then let's say that this is n to the
+fifth power x.
+
+ align:start position:0%
+fifth power x.
+ 
+
+ align:start position:0%
+fifth power x.
+So suppose that you are this is a power
+
+ align:start position:0%
+So suppose that you are this is a power
+ 
+
+ align:start position:0%
+So suppose that you are this is a power
+series you're given
+
+ align:start position:0%
+series you're given
+ 
+
+ align:start position:0%
+series you're given
+and you want to find the radius of
+
+ align:start position:0%
+and you want to find the radius of
+ 
+
+ align:start position:0%
+and you want to find the radius of
+convergence right you can either just
+
+ align:start position:0%
+convergence right you can either just
+ 
+
+ align:start position:0%
+convergence right you can either just
+form you know do
+
+ align:start position:0%
+form you know do
+ 
+
+ align:start position:0%
+form you know do
+plug it into this test right or you can
+
+ align:start position:0%
+plug it into this test right or you can
+ 
+
+ align:start position:0%
+plug it into this test right or you can
+just say okay we just apply we know that
+
+ align:start position:0%
+just say okay we just apply we know that
+ 
+
+ align:start position:0%
+just say okay we just apply we know that
+it's some interval and I just want to
+
+ align:start position:0%
+it's some interval and I just want to
+ 
+
+ align:start position:0%
+it's some interval and I just want to
+see for which x does this here converge
+
+ align:start position:0%
+see for which x does this here converge
+ 
+
+ align:start position:0%
+see for which x does this here converge
+so if I looked in this case you might
+
+ align:start position:0%
+so if I looked in this case you might
+ 
+
+ align:start position:0%
+so if I looked in this case you might
+find it slightly easier to do the the
+
+ align:start position:0%
+find it slightly easier to do the the
+ 
+
+ align:start position:0%
+find it slightly easier to do the the
+root test. So if you're looking at the n
+
+ align:start position:0%
+root test. So if you're looking at the n
+ 
+
+ align:start position:0%
+root test. So if you're looking at the n
++ one elements in this series the n
+
+ align:start position:0%
++ one elements in this series the n
+ 
+
+ align:start position:0%
++ one elements in this series the n
+elements sorry the n elements would be
+
+ align:start position:0%
+elements sorry the n elements would be
+ 
+
+ align:start position:0%
+elements sorry the n elements would be
+this to the fifth power think about x as
+
+ align:start position:0%
+this to the fifth power think about x as
+ 
+
+ align:start position:0%
+this to the fifth power think about x as
+being fixed right and you're asking for
+
+ align:start position:0%
+being fixed right and you're asking for
+ 
+
+ align:start position:0%
+being fixed right and you're asking for
+which and then you want to for given x
+
+ align:start position:0%
+which and then you want to for given x
+ 
+
+ align:start position:0%
+which and then you want to for given x
+you want to determine whether the series
+
+ align:start position:0%
+you want to determine whether the series
+ 
+
+ align:start position:0%
+you want to determine whether the series
+this series here is convergent right
+
+ align:start position:0%
+this series here is convergent right
+ 
+
+ align:start position:0%
+this series here is convergent right
+so if you using the root test you would
+
+ align:start position:0%
+so if you using the root test you would
+ 
+
+ align:start position:0%
+so if you using the root test you would
+look at this one here and you might find
+
+ align:start position:0%
+look at this one here and you might find
+ 
+
+ align:start position:0%
+look at this one here and you might find
+in this case slightly easier to use the
+
+ align:start position:0%
+in this case slightly easier to use the
+ 
+
+ align:start position:0%
+in this case slightly easier to use the
+root test.
+
+ align:start position:0%
+root test.
+ 
+
+ align:start position:0%
+root test.
+So if you're looking at this, this thing
+
+ align:start position:0%
+So if you're looking at this, this thing
+ 
+
+ align:start position:0%
+So if you're looking at this, this thing
+here is now n + 1
+
+ align:start position:0%
+here is now n + 1
+ 
+
+ align:start position:0%
+here is now n + 1
+to the 5th power * x to the n + 1
+
+ align:start position:0%
+to the 5th power * x to the n + 1
+ 
+
+ align:start position:0%
+to the 5th power * x to the n + 1
+/ n 5th power * x to the n. Right?
+
+ align:start position:0%
+/ n 5th power * x to the n. Right?
+ 
+
+ align:start position:0%
+/ n 5th power * x to the n. Right?
+That's a ratio.
+
+ align:start position:0%
+That's a ratio.
+ 
+
+ align:start position:0%
+That's a ratio.
+And so of course you can write this in
+
+ align:start position:0%
+And so of course you can write this in
+ 
+
+ align:start position:0%
+And so of course you can write this in
+here. This is like x n + 1 * by itself
+
+ align:start position:0%
+here. This is like x n + 1 * by itself
+ 
+
+ align:start position:0%
+here. This is like x n + 1 * by itself
+five times
+
+ align:start position:0%
+five times
+ 
+
+ align:start position:0%
+five times
+divided by n * by itself five times and
+
+ align:start position:0%
+divided by n * by itself five times and
+ 
+
+ align:start position:0%
+divided by n * by itself five times and
+then this thing here you can write as x
+
+ align:start position:0%
+then this thing here you can write as x
+ 
+
+ align:start position:0%
+then this thing here you can write as x
+to the n * x
+
+ align:start position:0%
+to the n * x
+ 
+
+ align:start position:0%
+to the n * x
+uh over x to the n.
+
+ align:start position:0%
+uh over x to the n.
+ 
+
+ align:start position:0%
+uh over x to the n.
+So you see this thing here you can then
+
+ align:start position:0%
+So you see this thing here you can then
+ 
+
+ align:start position:0%
+So you see this thing here you can then
+think about as n + 1 / n
+
+ align:start position:0%
+think about as n + 1 / n
+ 
+
+ align:start position:0%
+think about as n + 1 / n
+to the fifth power
+
+ align:start position:0%
+to the fifth power
+ 
+
+ align:start position:0%
+to the fifth power
+um and and time sorry time x right
+
+ align:start position:0%
+um and and time sorry time x right
+ 
+
+ align:start position:0%
+um and and time sorry time x right
+and I can write this in here in the
+
+ align:start position:0%
+and I can write this in here in the
+ 
+
+ align:start position:0%
+and I can write this in here in the
+usual way if you want you can write it
+
+ align:start position:0%
+usual way if you want you can write it
+ 
+
+ align:start position:0%
+usual way if you want you can write it
+as 1 + 1 / n I'm dividing by n in both
+
+ align:start position:0%
+as 1 + 1 / n I'm dividing by n in both
+ 
+
+ align:start position:0%
+as 1 + 1 / n I'm dividing by n in both
+denominator and denominator so you can
+
+ align:start position:0%
+denominator and denominator so you can
+ 
+
+ align:start position:0%
+denominator and denominator so you can
+write it like this to the fifth power *
+
+ align:start position:0%
+write it like this to the fifth power *
+ 
+
+ align:start position:0%
+write it like this to the fifth power *
+x.
+
+ align:start position:0%
+x.
+ 
+
+ align:start position:0%
+x.
+And so now
+
+ align:start position:0%
+And so now
+ 
+
+ align:start position:0%
+And so now
+the root test it's asking
+
+ align:start position:0%
+the root test it's asking
+ 
+
+ align:start position:0%
+the root test it's asking
+it's asking whether this the absolute
+
+ align:start position:0%
+it's asking whether this the absolute
+ 
+
+ align:start position:0%
+it's asking whether this the absolute
+value of this root test would be then
+
+ align:start position:0%
+value of this root test would be then
+ 
+
+ align:start position:0%
+value of this root test would be then
+asking if the limit here of x n + one
+
+ align:start position:0%
+asking if the limit here of x n + one
+ 
+
+ align:start position:0%
+asking if the limit here of x n + one
+sorry n + 1
+
+ align:start position:0%
+sorry n + 1
+ 
+
+ align:start position:0%
+sorry n + 1
+if this here has a limit
+
+ align:start position:0%
+if this here has a limit
+ 
+
+ align:start position:0%
+if this here has a limit
+and then it's asking you if that limit
+
+ align:start position:0%
+and then it's asking you if that limit
+ 
+
+ align:start position:0%
+and then it's asking you if that limit
+is less than one if it has a limit and
+
+ align:start position:0%
+is less than one if it has a limit and
+ 
+
+ align:start position:0%
+is less than one if it has a limit and
+the limit is less than one when the
+
+ align:start position:0%
+the limit is less than one when the
+ 
+
+ align:start position:0%
+the limit is less than one when the
+series is converting and it's diverse
+
+ align:start position:0%
+series is converting and it's diverse
+ 
+
+ align:start position:0%
+series is converting and it's diverse
+one. But in this case, this thing here
+
+ align:start position:0%
+one. But in this case, this thing here
+ 
+
+ align:start position:0%
+one. But in this case, this thing here
+this ratio here
+
+ align:start position:0%
+this ratio here
+ 
+
+ align:start position:0%
+this ratio here
+is 1 + 1
+
+ align:start position:0%
+is 1 + 1
+ 
+
+ align:start position:0%
+is 1 + 1
+to the 5th power * x
+
+ align:start position:0%
+to the 5th power * x
+ 
+
+ align:start position:0%
+to the 5th power * x
+that this is all non negative. So the
+
+ align:start position:0%
+that this is all non negative. So the
+ 
+
+ align:start position:0%
+that this is all non negative. So the
+absolute value just go over here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The algebraic property of the limit say
+
+ align:start position:0%
+The algebraic property of the limit say
+ 
+
+ align:start position:0%
+The algebraic property of the limit say
+that this this one here goes to zero and
+
+ align:start position:0%
+that this this one here goes to zero and
+ 
+
+ align:start position:0%
+that this this one here goes to zero and
+so raised to the fifth power still go to
+
+ align:start position:0%
+so raised to the fifth power still go to
+ 
+
+ align:start position:0%
+so raised to the fifth power still go to
+zero right it's multiply bunch of
+
+ align:start position:0%
+zero right it's multiply bunch of
+ 
+
+ align:start position:0%
+zero right it's multiply bunch of
+sequences five times together that go to
+
+ align:start position:0%
+sequences five times together that go to
+ 
+
+ align:start position:0%
+sequences five times together that go to
+zero to one so so this here this goes to
+
+ align:start position:0%
+zero to one so so this here this goes to
+ 
+
+ align:start position:0%
+zero to one so so this here this goes to
+one and so even raised to fifth power
+
+ align:start position:0%
+one and so even raised to fifth power
+ 
+
+ align:start position:0%
+one and so even raised to fifth power
+still go to one so this here goes to to
+
+ align:start position:0%
+still go to one so this here goes to to
+ 
+
+ align:start position:0%
+still go to one so this here goes to to
+the norm of x right and so the ratio
+
+ align:start position:0%
+the norm of x right and so the ratio
+ 
+
+ align:start position:0%
+the norm of x right and so the ratio
+test would be that if x so ratio test
+
+ align:start position:0%
+test would be that if x so ratio test
+ 
+
+ align:start position:0%
+test would be that if x so ratio test
+gives you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that if this norm here is less than
+
+ align:start position:0%
+is that if this norm here is less than
+ 
+
+ align:start position:0%
+is that if this norm here is less than
+one then this series is convergent.
+
+ align:start position:0%
+one then this series is convergent.
+ 
+
+ align:start position:0%
+one then this series is convergent.
+If the norm here is bigger than one the
+
+ align:start position:0%
+If the norm here is bigger than one the
+ 
+
+ align:start position:0%
+If the norm here is bigger than one the
+ratio is divergent
+
+ align:start position:0%
+ratio is divergent
+ 
+
+ align:start position:0%
+ratio is divergent
+and it's unclear if the norm is equal to
+
+ align:start position:0%
+and it's unclear if the norm is equal to
+ 
+
+ align:start position:0%
+and it's unclear if the norm is equal to
+one. So in other words you see that the
+
+ align:start position:0%
+one. So in other words you see that the
+ 
+
+ align:start position:0%
+one. So in other words you see that the
+ratio test here gives you directly that
+
+ align:start position:0%
+ratio test here gives you directly that
+ 
+
+ align:start position:0%
+ratio test here gives you directly that
+the radius of convergence is one. Right?
+
+ align:start position:0%
+the radius of convergence is one. Right?
+ 
+
+ align:start position:0%
+the radius of convergence is one. Right?
+So and and of course you could apply the
+
+ align:start position:0%
+So and and of course you could apply the
+ 
+
+ align:start position:0%
+So and and of course you could apply the
+root test, right?
+
+ align:start position:0%
+root test, right?
+ 
+
+ align:start position:0%
+root test, right?
+The root test is great on this here.
+
+ align:start position:0%
+The root test is great on this here.
+ 
+
+ align:start position:0%
+The root test is great on this here.
+It's ah it's a little bit more know I
+
+ align:start position:0%
+It's ah it's a little bit more know I
+ 
+
+ align:start position:0%
+It's ah it's a little bit more know I
+mean you have to do a little bit more
+
+ align:start position:0%
+mean you have to do a little bit more
+ 
+
+ align:start position:0%
+mean you have to do a little bit more
+argument. It's not very hard but it
+
+ align:start position:0%
+argument. It's not very hard but it
+ 
+
+ align:start position:0%
+argument. It's not very hard but it
+actually in this case the root ratio
+
+ align:start position:0%
+actually in this case the root ratio
+ 
+
+ align:start position:0%
+actually in this case the root ratio
+test would be easier to it would be less
+
+ align:start position:0%
+test would be easier to it would be less
+ 
+
+ align:start position:0%
+test would be easier to it would be less
+to argue than in the root test.
+
+ align:start position:0%
+to argue than in the root test.
+ 
+
+ align:start position:0%
+to argue than in the root test.
+Let's do one more example of this.
+
+ align:start position:0%
+Let's do one more example of this.
+ 
+
+ align:start position:0%
+Let's do one more example of this.
+So maybe I'll just switch a little bit
+
+ align:start position:0%
+So maybe I'll just switch a little bit
+ 
+
+ align:start position:0%
+So maybe I'll just switch a little bit
+to and then I'll come back and review
+
+ align:start position:0%
+to and then I'll come back and review
+ 
+
+ align:start position:0%
+to and then I'll come back and review
+some more stuff. I will um I'll just
+
+ align:start position:0%
+some more stuff. I will um I'll just
+ 
+
+ align:start position:0%
+some more stuff. I will um I'll just
+talk about a few of the problems that I
+
+ align:start position:0%
+talk about a few of the problems that I
+ 
+
+ align:start position:0%
+talk about a few of the problems that I
+added to the end of my review notes
+
+ align:start position:0%
+added to the end of my review notes
+ 
+
+ align:start position:0%
+added to the end of my review notes
+again. I post this with these problems.
+
+ align:start position:0%
+again. I post this with these problems.
+ 
+
+ align:start position:0%
+again. I post this with these problems.
+Um and and obviously they are I mean
+
+ align:start position:0%
+Um and and obviously they are I mean
+ 
+
+ align:start position:0%
+Um and and obviously they are I mean
+it's not exactly problems on the met but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Also another thing I want to say
+
+ align:start position:0%
+Okay. Also another thing I want to say
+ 
+
+ align:start position:0%
+Okay. Also another thing I want to say
+is that uh that the the homework uh is
+
+ align:start position:0%
+is that uh that the the homework uh is
+ 
+
+ align:start position:0%
+is that uh that the the homework uh is
+graded up to an including four. So I
+
+ align:start position:0%
+graded up to an including four. So I
+ 
+
+ align:start position:0%
+graded up to an including four. So I
+wasn't actually aware of over the
+
+ align:start position:0%
+wasn't actually aware of over the
+ 
+
+ align:start position:0%
+wasn't actually aware of over the
+weekend. It was supposed to be handed
+
+ align:start position:0%
+weekend. It was supposed to be handed
+ 
+
+ align:start position:0%
+weekend. It was supposed to be handed
+back within latest a week of when you
+
+ align:start position:0%
+back within latest a week of when you
+ 
+
+ align:start position:0%
+back within latest a week of when you
+handed it in and I just discovered it
+
+ align:start position:0%
+handed it in and I just discovered it
+ 
+
+ align:start position:0%
+handed it in and I just discovered it
+over the weekend that it was uh some of
+
+ align:start position:0%
+over the weekend that it was uh some of
+ 
+
+ align:start position:0%
+over the weekend that it was uh some of
+them were late. So, but I it's fixed uh
+
+ align:start position:0%
+them were late. So, but I it's fixed uh
+ 
+
+ align:start position:0%
+them were late. So, but I it's fixed uh
+you know I'm I'm not the grader. There's
+
+ align:start position:0%
+you know I'm I'm not the grader. There's
+ 
+
+ align:start position:0%
+you know I'm I'm not the grader. There's
+two ways that are grading and a greater
+
+ align:start position:0%
+two ways that are grading and a greater
+ 
+
+ align:start position:0%
+two ways that are grading and a greater
+um but it's all fixed now. So the first
+
+ align:start position:0%
+um but it's all fixed now. So the first
+ 
+
+ align:start position:0%
+um but it's all fixed now. So the first
+four are are you know you can review
+
+ align:start position:0%
+four are are you know you can review
+ 
+
+ align:start position:0%
+four are are you know you can review
+those also for the lecture.
+
+ align:start position:0%
+those also for the lecture.
+ 
+
+ align:start position:0%
+those also for the lecture.
+Okay. So the other the other series or
+
+ align:start position:0%
+Okay. So the other the other series or
+ 
+
+ align:start position:0%
+Okay. So the other the other series or
+power series I want to look at is that
+
+ align:start position:0%
+power series I want to look at is that
+ 
+
+ align:start position:0%
+power series I want to look at is that
+so again what is the radius
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the thing about power series the nice
+
+ align:start position:0%
+the thing about power series the nice
+ 
+
+ align:start position:0%
+the thing about power series the nice
+thing about power series is that you
+
+ align:start position:0%
+thing about power series is that you
+ 
+
+ align:start position:0%
+thing about power series is that you
+know power series also test about series
+
+ align:start position:0%
+know power series also test about series
+ 
+
+ align:start position:0%
+know power series also test about series
+right so it's like you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what is the radius of convergence?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now the series it's a slightly
+
+ align:start position:0%
+And now the series it's a slightly
+ 
+
+ align:start position:0%
+And now the series it's a slightly
+different series. It's this series here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And so now let me again I mean you
+
+ align:start position:0%
+Okay. And so now let me again I mean you
+ 
+
+ align:start position:0%
+Okay. And so now let me again I mean you
+could apply the root test. The root test
+
+ align:start position:0%
+could apply the root test. The root test
+ 
+
+ align:start position:0%
+could apply the root test. The root test
+is the one that sort of just give you a
+
+ align:start position:0%
+is the one that sort of just give you a
+ 
+
+ align:start position:0%
+is the one that sort of just give you a
+answer. It always give you an answer,
+
+ align:start position:0%
+answer. It always give you an answer,
+ 
+
+ align:start position:0%
+answer. It always give you an answer,
+but you know it you may have to work
+
+ align:start position:0%
+but you know it you may have to work
+ 
+
+ align:start position:0%
+but you know it you may have to work
+harder to find the nth root. So, and
+
+ align:start position:0%
+harder to find the nth root. So, and
+ 
+
+ align:start position:0%
+harder to find the nth root. So, and
+sometimes it's just easier to use the
+
+ align:start position:0%
+sometimes it's just easier to use the
+ 
+
+ align:start position:0%
+sometimes it's just easier to use the
+ratio test. So, let's use the ratio test
+
+ align:start position:0%
+ratio test. So, let's use the ratio test
+ 
+
+ align:start position:0%
+ratio test. So, let's use the ratio test
+again. So, a n here is n to the 5th
+
+ align:start position:0%
+again. So, a n here is n to the 5th
+ 
+
+ align:start position:0%
+again. So, a n here is n to the 5th
+power x^ n / n factorial.
+
+ align:start position:0%
+power x^ n / n factorial.
+ 
+
+ align:start position:0%
+power x^ n / n factorial.
+So if you're looking at a n + 1 / a n,
+
+ align:start position:0%
+So if you're looking at a n + 1 / a n,
+ 
+
+ align:start position:0%
+So if you're looking at a n + 1 / a n,
+maybe I should maybe let me write over
+
+ align:start position:0%
+maybe I should maybe let me write over
+ 
+
+ align:start position:0%
+maybe I should maybe let me write over
+here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if I'm looking at at a n + one a n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then I have uh n + 1
+
+ align:start position:0%
+so then I have uh n + 1
+ 
+
+ align:start position:0%
+so then I have uh n + 1
+to the 3 power
+
+ align:start position:0%
+to the 3 power
+ 
+
+ align:start position:0%
+to the 3 power
+uh * x to the power n + 1
+
+ align:start position:0%
+uh * x to the power n + 1
+ 
+
+ align:start position:0%
+uh * x to the power n + 1
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over n + 1
+
+ align:start position:0%
+over n + 1
+ 
+
+ align:start position:0%
+over n + 1
+that is a n + one and then I have to
+
+ align:start position:0%
+that is a n + one and then I have to
+ 
+
+ align:start position:0%
+that is a n + one and then I have to
+divide by this. But when I divide by a
+
+ align:start position:0%
+divide by this. But when I divide by a
+ 
+
+ align:start position:0%
+divide by this. But when I divide by a
+fraction, it's like multiplying by
+
+ align:start position:0%
+fraction, it's like multiplying by
+ 
+
+ align:start position:0%
+fraction, it's like multiplying by
+the inverse of this. So like this in
+
+ align:start position:0%
+the inverse of this. So like this in
+ 
+
+ align:start position:0%
+the inverse of this. So like this in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+x to the n power like that.
+
+ align:start position:0%
+x to the n power like that.
+ 
+
+ align:start position:0%
+x to the n power like that.
+And so again I can what I again I can uh
+
+ align:start position:0%
+And so again I can what I again I can uh
+ 
+
+ align:start position:0%
+And so again I can what I again I can uh
+I can write this in here as um so if I
+
+ align:start position:0%
+I can write this in here as um so if I
+ 
+
+ align:start position:0%
+I can write this in here as um so if I
+just do like I did before I would have n
+
+ align:start position:0%
+just do like I did before I would have n
+ 
+
+ align:start position:0%
+just do like I did before I would have n
++ one over n to the fifth power that's
+
+ align:start position:0%
++ one over n to the fifth power that's
+ 
+
+ align:start position:0%
++ one over n to the fifth power that's
+when I take this one here and that one
+
+ align:start position:0%
+when I take this one here and that one
+ 
+
+ align:start position:0%
+when I take this one here and that one
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+then I have when I take those two
+
+ align:start position:0%
+then I have when I take those two
+ 
+
+ align:start position:0%
+then I have when I take those two
+together I can get rid of the n here and
+
+ align:start position:0%
+together I can get rid of the n here and
+ 
+
+ align:start position:0%
+together I can get rid of the n here and
+I just get x
+
+ align:start position:0%
+I just get x
+ 
+
+ align:start position:0%
+I just get x
+and then when I look at the ratio of
+
+ align:start position:0%
+and then when I look at the ratio of
+ 
+
+ align:start position:0%
+and then when I look at the ratio of
+these two this one here n + one
+
+ align:start position:0%
+these two this one here n + one
+ 
+
+ align:start position:0%
+these two this one here n + one
+factorial you can think about that as n
+
+ align:start position:0%
+factorial you can think about that as n
+ 
+
+ align:start position:0%
+factorial you can think about that as n
++ one and then times n factorial.
+
+ align:start position:0%
++ one and then times n factorial.
+ 
+
+ align:start position:0%
++ one and then times n factorial.
+So this n factorial cancel out with that
+
+ align:start position:0%
+So this n factorial cancel out with that
+ 
+
+ align:start position:0%
+So this n factorial cancel out with that
+and you're left with n + one. So this is
+
+ align:start position:0%
+and you're left with n + one. So this is
+ 
+
+ align:start position:0%
+and you're left with n + one. So this is
+what you get
+
+ align:start position:0%
+what you get
+ 
+
+ align:start position:0%
+what you get
+and this one here just writing it as we
+
+ align:start position:0%
+and this one here just writing it as we
+ 
+
+ align:start position:0%
+and this one here just writing it as we
+did before dividing this fraction by 1 /
+
+ align:start position:0%
+did before dividing this fraction by 1 /
+ 
+
+ align:start position:0%
+did before dividing this fraction by 1 /
+n in both uh denominator and denominator
+
+ align:start position:0%
+n in both uh denominator and denominator
+ 
+
+ align:start position:0%
+n in both uh denominator and denominator
+and getting this ring here
+
+ align:start position:0%
+and getting this ring here
+ 
+
+ align:start position:0%
+and getting this ring here
+5 * x n
+
+ align:start position:0%
+5 * x n
+ 
+
+ align:start position:0%
+5 * x n
+and now you see that if and this here I
+
+ align:start position:0%
+and now you see that if and this here I
+ 
+
+ align:start position:0%
+and now you see that if and this here I
+guess it should have been absolute value
+
+ align:start position:0%
+guess it should have been absolute value
+ 
+
+ align:start position:0%
+guess it should have been absolute value
+of So it's absolute value on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that.
+
+ align:start position:0%
+like that.
+ 
+
+ align:start position:0%
+like that.
+This one here converts to one.
+
+ align:start position:0%
+This one here converts to one.
+ 
+
+ align:start position:0%
+This one here converts to one.
+This one is just x and this converts to
+
+ align:start position:0%
+This one is just x and this converts to
+ 
+
+ align:start position:0%
+This one is just x and this converts to
+x. And then this here goes to infinity.
+
+ align:start position:0%
+x. And then this here goes to infinity.
+ 
+
+ align:start position:0%
+x. And then this here goes to infinity.
+So the ratio here goes to zero. Right?
+
+ align:start position:0%
+So the ratio here goes to zero. Right?
+ 
+
+ align:start position:0%
+So the ratio here goes to zero. Right?
+I'm using the algebraic property of
+
+ align:start position:0%
+I'm using the algebraic property of
+ 
+
+ align:start position:0%
+I'm using the algebraic property of
+limits. So this is converted to zero.
+
+ align:start position:0%
+limits. So this is converted to zero.
+ 
+
+ align:start position:0%
+limits. So this is converted to zero.
+And so you see that it does have a
+
+ align:start position:0%
+And so you see that it does have a
+ 
+
+ align:start position:0%
+And so you see that it does have a
+limit. So the ratio test apply because
+
+ align:start position:0%
+limit. So the ratio test apply because
+ 
+
+ align:start position:0%
+limit. So the ratio test apply because
+that limit is zero for all x. It's going
+
+ align:start position:0%
+that limit is zero for all x. It's going
+ 
+
+ align:start position:0%
+that limit is zero for all x. It's going
+to be converged for all x. So the radius
+
+ align:start position:0%
+to be converged for all x. So the radius
+ 
+
+ align:start position:0%
+to be converged for all x. So the radius
+of convergence in this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course on the midterm don't just
+
+ align:start position:0%
+and of course on the midterm don't just
+ 
+
+ align:start position:0%
+and of course on the midterm don't just
+say that the radius of convergence is
+
+ align:start position:0%
+say that the radius of convergence is
+ 
+
+ align:start position:0%
+say that the radius of convergence is
+infinite explain this thing here and the
+
+ align:start position:0%
+infinite explain this thing here and the
+ 
+
+ align:start position:0%
+infinite explain this thing here and the
+more detailed the better right because
+
+ align:start position:0%
+more detailed the better right because
+ 
+
+ align:start position:0%
+more detailed the better right because
+even if there's some typos you would
+
+ align:start position:0%
+even if there's some typos you would
+ 
+
+ align:start position:0%
+even if there's some typos you would
+definitely get you should definitely get
+
+ align:start position:0%
+definitely get you should definitely get
+ 
+
+ align:start position:0%
+definitely get you should definitely get
+I mean I'm not great in mid either But
+
+ align:start position:0%
+I mean I'm not great in mid either But
+ 
+
+ align:start position:0%
+I mean I'm not great in mid either But
+you you definitely should get positive,
+
+ align:start position:0%
+you you definitely should get positive,
+ 
+
+ align:start position:0%
+you you definitely should get positive,
+right? Yeah.
+
+ align:start position:0%
+right? Yeah.
+ 
+
+ align:start position:0%
+right? Yeah.
+>> So to get R, is it always like you
+
+ align:start position:0%
+>> So to get R, is it always like you
+ 
+
+ align:start position:0%
+>> So to get R, is it always like you
+divide by the limb soup? Cuz like is the
+
+ align:start position:0%
+divide by the limb soup? Cuz like is the
+ 
+
+ align:start position:0%
+divide by the limb soup? Cuz like is the
+thing on the bottom board the limb soup
+
+ align:start position:0%
+thing on the bottom board the limb soup
+ 
+
+ align:start position:0%
+thing on the bottom board the limb soup
+or just the
+
+ align:start position:0%
+or just the
+ 
+
+ align:start position:0%
+or just the
+>> Yeah. So
+
+ align:start position:0%
+>> Yeah. So
+ 
+
+ align:start position:0%
+>> Yeah. So
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+when you take just a complete general sh
+
+ align:start position:0%
+when you take just a complete general sh
+ 
+
+ align:start position:0%
+when you take just a complete general sh
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+then um you then the radius of
+
+ align:start position:0%
+then um you then the radius of
+ 
+
+ align:start position:0%
+then um you then the radius of
+convergence is by definition this this
+
+ align:start position:0%
+convergence is by definition this this
+ 
+
+ align:start position:0%
+convergence is by definition this this
+is related to you. You asked this
+
+ align:start position:0%
+is related to you. You asked this
+ 
+
+ align:start position:0%
+is related to you. You asked this
+question a couple of times ago that
+
+ align:start position:0%
+question a couple of times ago that
+ 
+
+ align:start position:0%
+question a couple of times ago that
+because we started with the RA ratio
+
+ align:start position:0%
+because we started with the RA ratio
+ 
+
+ align:start position:0%
+because we started with the RA ratio
+test. We did that before we did the root
+
+ align:start position:0%
+test. We did that before we did the root
+ 
+
+ align:start position:0%
+test. We did that before we did the root
+test and you were noting that the in the
+
+ align:start position:0%
+test and you were noting that the in the
+ 
+
+ align:start position:0%
+test and you were noting that the in the
+ratio test you always comparing an
+
+ align:start position:0%
+ratio test you always comparing an
+ 
+
+ align:start position:0%
+ratio test you always comparing an
+element to the previous one, right? And
+
+ align:start position:0%
+element to the previous one, right? And
+ 
+
+ align:start position:0%
+element to the previous one, right? And
+so but in and in general, right, the
+
+ align:start position:0%
+so but in and in general, right, the
+ 
+
+ align:start position:0%
+so but in and in general, right, the
+series can be convergent even though the
+
+ align:start position:0%
+series can be convergent even though the
+ 
+
+ align:start position:0%
+series can be convergent even though the
+next element is slightly larger than the
+
+ align:start position:0%
+next element is slightly larger than the
+ 
+
+ align:start position:0%
+next element is slightly larger than the
+previous. If that keep happening, it's
+
+ align:start position:0%
+previous. If that keep happening, it's
+ 
+
+ align:start position:0%
+previous. If that keep happening, it's
+not convergent. But it could happen a
+
+ align:start position:0%
+not convergent. But it could happen a
+ 
+
+ align:start position:0%
+not convergent. But it could happen a
+few times and then it go really down,
+
+ align:start position:0%
+few times and then it go really down,
+ 
+
+ align:start position:0%
+few times and then it go really down,
+right? And that's fine, right? And so
+
+ align:start position:0%
+right? And that's fine, right? And so
+ 
+
+ align:start position:0%
+right? And that's fine, right? And so
+that's why like the the the the
+
+ align:start position:0%
+that's why like the the the the
+ 
+
+ align:start position:0%
+that's why like the the the the
+root test, right, gives you this general
+
+ align:start position:0%
+root test, right, gives you this general
+ 
+
+ align:start position:0%
+root test, right, gives you this general
+result about that is always right. It
+
+ align:start position:0%
+result about that is always right. It
+ 
+
+ align:start position:0%
+result about that is always right. It
+always work. It doesn't assume that a
+
+ align:start position:0%
+always work. It doesn't assume that a
+ 
+
+ align:start position:0%
+always work. It doesn't assume that a
+end not zero etc. right in any part for
+
+ align:start position:0%
+end not zero etc. right in any part for
+ 
+
+ align:start position:0%
+end not zero etc. right in any part for
+any particular and and it really should
+
+ align:start position:0%
+any particular and and it really should
+ 
+
+ align:start position:0%
+any particular and and it really should
+be in suk right and then it's like
+
+ align:start position:0%
+be in suk right and then it's like
+ 
+
+ align:start position:0%
+be in suk right and then it's like
+defined it's also you know it's a number
+
+ align:start position:0%
+defined it's also you know it's a number
+ 
+
+ align:start position:0%
+defined it's also you know it's a number
+that's always defined
+
+ align:start position:0%
+that's always defined
+ 
+
+ align:start position:0%
+that's always defined
+um and it it's and again you know the
+
+ align:start position:0%
+um and it it's and again you know the
+ 
+
+ align:start position:0%
+um and it it's and again you know the
+way it's stated here the way the proof
+
+ align:start position:0%
+way it's stated here the way the proof
+ 
+
+ align:start position:0%
+way it's stated here the way the proof
+goes is it's not comparing two uh
+
+ align:start position:0%
+goes is it's not comparing two uh
+ 
+
+ align:start position:0%
+goes is it's not comparing two uh
+consecutive a
+
+ align:start position:0%
+consecutive a
+ 
+
+ align:start position:0%
+consecutive a
+um in any particular example the root
+
+ align:start position:0%
+um in any particular example the root
+ 
+
+ align:start position:0%
+um in any particular example the root
+test may not be the easiest way to
+
+ align:start position:0%
+test may not be the easiest way to
+ 
+
+ align:start position:0%
+test may not be the easiest way to
+argue. Often if you can for a power
+
+ align:start position:0%
+argue. Often if you can for a power
+ 
+
+ align:start position:0%
+argue. Often if you can for a power
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+almost always I would say if if it
+
+ align:start position:0%
+almost always I would say if if it
+ 
+
+ align:start position:0%
+almost always I would say if if it
+almost in a power sense it's almost
+
+ align:start position:0%
+almost in a power sense it's almost
+ 
+
+ align:start position:0%
+almost in a power sense it's almost
+always easier to use the ratio test but
+
+ align:start position:0%
+always easier to use the ratio test but
+ 
+
+ align:start position:0%
+always easier to use the ratio test but
+it require that power shares has some
+
+ align:start position:0%
+it require that power shares has some
+ 
+
+ align:start position:0%
+it require that power shares has some
+nice property for this to apply.
+
+ align:start position:0%
+nice property for this to apply.
+ 
+
+ align:start position:0%
+nice property for this to apply.
+>> Yeah. So the reason you know that r is
+
+ align:start position:0%
+>> Yeah. So the reason you know that r is
+ 
+
+ align:start position:0%
+>> Yeah. So the reason you know that r is
+infinity for that example because you
+
+ align:start position:0%
+infinity for that example because you
+ 
+
+ align:start position:0%
+infinity for that example because you
+know for all x
+
+ align:start position:0%
+know for all x
+ 
+
+ align:start position:0%
+know for all x
+>> so in this example here
+
+ align:start position:0%
+>> so in this example here
+ 
+
+ align:start position:0%
+>> so in this example here
+yeah this guy is infinity which means
+
+ align:start position:0%
+yeah this guy is infinity which means
+ 
+
+ align:start position:0%
+yeah this guy is infinity which means
+that this thing here would be zero yeah
+
+ align:start position:0%
+that this thing here would be zero yeah
+ 
+
+ align:start position:0%
+that this thing here would be zero yeah
+>> but you like you know it's very
+
+ align:start position:0%
+>> but you like you know it's very
+ 
+
+ align:start position:0%
+>> but you like you know it's very
+>> but I didn't actually calculate you see
+
+ align:start position:0%
+>> but I didn't actually calculate you see
+ 
+
+ align:start position:0%
+>> but I didn't actually calculate you see
+I didn't calculate the end booth in this
+
+ align:start position:0%
+I didn't calculate the end booth in this
+ 
+
+ align:start position:0%
+I didn't calculate the end booth in this
+example but if I had calculated I would
+
+ align:start position:0%
+example but if I had calculated I would
+ 
+
+ align:start position:0%
+example but if I had calculated I would
+actually it's not very hard to calculate
+
+ align:start position:0%
+actually it's not very hard to calculate
+ 
+
+ align:start position:0%
+actually it's not very hard to calculate
+but it needs some small tricks and So
+
+ align:start position:0%
+but it needs some small tricks and So
+ 
+
+ align:start position:0%
+but it needs some small tricks and So
+and we have yeah which we haven't talked
+
+ align:start position:0%
+and we have yeah which we haven't talked
+ 
+
+ align:start position:0%
+and we have yeah which we haven't talked
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+but so that's why like
+
+ align:start position:0%
+but so that's why like
+ 
+
+ align:start position:0%
+but so that's why like
+let me talk about a few other things and
+
+ align:start position:0%
+let me talk about a few other things and
+ 
+
+ align:start position:0%
+let me talk about a few other things and
+then I mean so again I mean you you know
+
+ align:start position:0%
+then I mean so again I mean you you know
+ 
+
+ align:start position:0%
+then I mean so again I mean you you know
+I I didn't necess I don't think I can
+
+ align:start position:0%
+I I didn't necess I don't think I can
+ 
+
+ align:start position:0%
+I I didn't necess I don't think I can
+probably review all what I what I hadn't
+
+ align:start position:0%
+probably review all what I what I hadn't
+ 
+
+ align:start position:0%
+probably review all what I what I hadn't
+my review notes but let me just talk
+
+ align:start position:0%
+my review notes but let me just talk
+ 
+
+ align:start position:0%
+my review notes but let me just talk
+about a few of the problems that I had
+
+ align:start position:0%
+about a few of the problems that I had
+ 
+
+ align:start position:0%
+about a few of the problems that I had
+but again
+
+ align:start position:0%
+but again
+ 
+
+ align:start position:0%
+but again
+so the things I Let me just quickly
+
+ align:start position:0%
+so the things I Let me just quickly
+ 
+
+ align:start position:0%
+so the things I Let me just quickly
+mention the things I I I may or may not
+
+ align:start position:0%
+mention the things I I I may or may not
+ 
+
+ align:start position:0%
+mention the things I I I may or may not
+get to that I have in my review notes.
+
+ align:start position:0%
+get to that I have in my review notes.
+ 
+
+ align:start position:0%
+get to that I have in my review notes.
+So I had also
+
+ align:start position:0%
+So I had also
+ 
+
+ align:start position:0%
+So I had also
+poverty you know what is le what is le
+
+ align:start position:0%
+poverty you know what is le what is le
+ 
+
+ align:start position:0%
+poverty you know what is le what is le
+and so definitely review that also talk
+
+ align:start position:0%
+and so definitely review that also talk
+ 
+
+ align:start position:0%
+and so definitely review that also talk
+about the radius convergence
+
+ align:start position:0%
+about the radius convergence
+ 
+
+ align:start position:0%
+about the radius convergence
+um and maybe this is all and then talk a
+
+ align:start position:0%
+um and maybe this is all and then talk a
+ 
+
+ align:start position:0%
+um and maybe this is all and then talk a
+little bit about the power series for
+
+ align:start position:0%
+little bit about the power series for
+ 
+
+ align:start position:0%
+little bit about the power series for
+the exponential functions but again all
+
+ align:start position:0%
+the exponential functions but again all
+ 
+
+ align:start position:0%
+the exponential functions but again all
+the stuff we did on the power series for
+
+ align:start position:0%
+the stuff we did on the power series for
+ 
+
+ align:start position:0%
+the stuff we did on the power series for
+the exponential functions
+
+ align:start position:0%
+the exponential functions
+ 
+
+ align:start position:0%
+the exponential functions
+And you know at this point we have
+
+ align:start position:0%
+And you know at this point we have
+ 
+
+ align:start position:0%
+And you know at this point we have
+established it. This is like um it's
+
+ align:start position:0%
+established it. This is like um it's
+ 
+
+ align:start position:0%
+established it. This is like um it's
+more like uh I mean there won't be
+
+ align:start position:0%
+more like uh I mean there won't be
+ 
+
+ align:start position:0%
+more like uh I mean there won't be
+anything particular about I mean the
+
+ align:start position:0%
+anything particular about I mean the
+ 
+
+ align:start position:0%
+anything particular about I mean the
+exponential function itself could be on
+
+ align:start position:0%
+exponential function itself could be on
+ 
+
+ align:start position:0%
+exponential function itself could be on
+the uh midterm but it's not like you
+
+ align:start position:0%
+the uh midterm but it's not like you
+ 
+
+ align:start position:0%
+the uh midterm but it's not like you
+would have to prove the properties of
+
+ align:start position:0%
+would have to prove the properties of
+ 
+
+ align:start position:0%
+would have to prove the properties of
+the exponential function. This property
+
+ align:start position:0%
+the exponential function. This property
+ 
+
+ align:start position:0%
+the exponential function. This property
+that it has property that the
+
+ align:start position:0%
+that it has property that the
+ 
+
+ align:start position:0%
+that it has property that the
+exponential function of x + y is like
+
+ align:start position:0%
+exponential function of x + y is like
+ 
+
+ align:start position:0%
+exponential function of x + y is like
+the product of that kind of stuff. It's
+
+ align:start position:0%
+the product of that kind of stuff. It's
+ 
+
+ align:start position:0%
+the product of that kind of stuff. It's
+not on the midterm. Okay. So, I didn't
+
+ align:start position:0%
+not on the midterm. Okay. So, I didn't
+ 
+
+ align:start position:0%
+not on the midterm. Okay. So, I didn't
+so it's not part of this review.
+
+ align:start position:0%
+so it's not part of this review.
+ 
+
+ align:start position:0%
+so it's not part of this review.
+The other thing that I probably won't
+
+ align:start position:0%
+The other thing that I probably won't
+ 
+
+ align:start position:0%
+The other thing that I probably won't
+get to because I in a minute I'll just
+
+ align:start position:0%
+get to because I in a minute I'll just
+ 
+
+ align:start position:0%
+get to because I in a minute I'll just
+turn to these other problems is that
+
+ align:start position:0%
+turn to these other problems is that
+ 
+
+ align:start position:0%
+turn to these other problems is that
+metric spaces definitely review metric
+
+ align:start position:0%
+metric spaces definitely review metric
+ 
+
+ align:start position:0%
+metric spaces definitely review metric
+spaces. Uh it was in the last lecture.
+
+ align:start position:0%
+spaces. Uh it was in the last lecture.
+ 
+
+ align:start position:0%
+spaces. Uh it was in the last lecture.
+So, you know there's a bunch of you know
+
+ align:start position:0%
+So, you know there's a bunch of you know
+ 
+
+ align:start position:0%
+So, you know there's a bunch of you know
+like there's three properties for metric
+
+ align:start position:0%
+like there's three properties for metric
+ 
+
+ align:start position:0%
+like there's three properties for metric
+space. The distance should be non-
+
+ align:start position:0%
+space. The distance should be non-
+ 
+
+ align:start position:0%
+space. The distance should be non-
+negative. It should be symmetric and the
+
+ align:start position:0%
+negative. It should be symmetric and the
+ 
+
+ align:start position:0%
+negative. It should be symmetric and the
+distance between two points should be
+
+ align:start position:0%
+distance between two points should be
+ 
+
+ align:start position:0%
+distance between two points should be
+zero if and only if those point are the
+
+ align:start position:0%
+zero if and only if those point are the
+ 
+
+ align:start position:0%
+zero if and only if those point are the
+same. And then the crucial the crucial
+
+ align:start position:0%
+same. And then the crucial the crucial
+ 
+
+ align:start position:0%
+same. And then the crucial the crucial
+property in the metric space and that's
+
+ align:start position:0%
+property in the metric space and that's
+ 
+
+ align:start position:0%
+property in the metric space and that's
+like the powerful property is the
+
+ align:start position:0%
+like the powerful property is the
+ 
+
+ align:start position:0%
+like the powerful property is the
+triangle.
+
+ align:start position:0%
+triangle.
+ 
+
+ align:start position:0%
+triangle.
+Okay. And so there was a few examples
+
+ align:start position:0%
+Okay. And so there was a few examples
+ 
+
+ align:start position:0%
+Okay. And so there was a few examples
+and review those examples. I I there in
+
+ align:start position:0%
+and review those examples. I I there in
+ 
+
+ align:start position:0%
+and review those examples. I I there in
+my review notes like the most important
+
+ align:start position:0%
+my review notes like the most important
+ 
+
+ align:start position:0%
+my review notes like the most important
+example I would say this the French
+
+ align:start position:0%
+example I would say this the French
+ 
+
+ align:start position:0%
+example I would say this the French
+world metric is kind of uh you know
+
+ align:start position:0%
+world metric is kind of uh you know
+ 
+
+ align:start position:0%
+world metric is kind of uh you know
+crazy uh metric that's not one of the
+
+ align:start position:0%
+crazy uh metric that's not one of the
+ 
+
+ align:start position:0%
+crazy uh metric that's not one of the
+important ones so I just in just the
+
+ align:start position:0%
+important ones so I just in just the
+ 
+
+ align:start position:0%
+important ones so I just in just the
+most important ones and then there's
+
+ align:start position:0%
+most important ones and then there's
+ 
+
+ align:start position:0%
+most important ones and then there's
+this with what does it mean to be
+
+ align:start position:0%
+this with what does it mean to be
+ 
+
+ align:start position:0%
+this with what does it mean to be
+convergent in a metric space and what
+
+ align:start position:0%
+convergent in a metric space and what
+ 
+
+ align:start position:0%
+convergent in a metric space and what
+does it mean to be a C sequence
+
+ align:start position:0%
+does it mean to be a C sequence
+ 
+
+ align:start position:0%
+does it mean to be a C sequence
+and so now let's get to a couple of the
+
+ align:start position:0%
+and so now let's get to a couple of the
+ 
+
+ align:start position:0%
+and so now let's get to a couple of the
+other uh problems that I suggested that
+
+ align:start position:0%
+other uh problems that I suggested that
+ 
+
+ align:start position:0%
+other uh problems that I suggested that
+you look at
+
+ align:start position:0%
+you look at
+ 
+
+ align:start position:0%
+you look at
+u and so
+
+ align:start position:0%
+u and so
+ 
+
+ align:start position:0%
+u and so
+so here are two other problems
+
+ align:start position:0%
+so here are two other problems
+ 
+
+ align:start position:0%
+so here are two other problems
+u and again you know I won't get to
+
+ align:start position:0%
+u and again you know I won't get to
+ 
+
+ align:start position:0%
+u and again you know I won't get to
+there's also problems about message
+
+ align:start position:0%
+there's also problems about message
+ 
+
+ align:start position:0%
+there's also problems about message
+bases and you should definitely look at
+
+ align:start position:0%
+bases and you should definitely look at
+ 
+
+ align:start position:0%
+bases and you should definitely look at
+it but I I don't have the time
+
+ align:start position:0%
+it but I I don't have the time
+ 
+
+ align:start position:0%
+it but I I don't have the time
+even though it's relevant for the mum uh
+
+ align:start position:0%
+even though it's relevant for the mum uh
+ 
+
+ align:start position:0%
+even though it's relevant for the mum uh
+I just have to pick some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all of all of the problems that I I I
+
+ align:start position:0%
+all of all of the problems that I I I
+ 
+
+ align:start position:0%
+all of all of the problems that I I I
+have four problems here. All of these
+
+ align:start position:0%
+have four problems here. All of these
+ 
+
+ align:start position:0%
+have four problems here. All of these
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+okay. So now uh suppose you take suppose
+
+ align:start position:0%
+okay. So now uh suppose you take suppose
+ 
+
+ align:start position:0%
+okay. So now uh suppose you take suppose
+you take a sequence. So I have a
+
+ align:start position:0%
+you take a sequence. So I have a
+ 
+
+ align:start position:0%
+you take a sequence. So I have a
+sequence here xn and so often a sequence
+
+ align:start position:0%
+sequence here xn and so often a sequence
+ 
+
+ align:start position:0%
+sequence here xn and so often a sequence
+is defined recursively.
+
+ align:start position:0%
+is defined recursively.
+ 
+
+ align:start position:0%
+is defined recursively.
+So recursive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so recursively defined
+
+ align:start position:0%
+so recursively defined
+ 
+
+ align:start position:0%
+so recursively defined
+sequences.
+
+ align:start position:0%
+sequences.
+ 
+
+ align:start position:0%
+sequences.
+So what does it mean? It means that
+
+ align:start position:0%
+So what does it mean? It means that
+ 
+
+ align:start position:0%
+So what does it mean? It means that
+typically you have the first one is
+
+ align:start position:0%
+typically you have the first one is
+ 
+
+ align:start position:0%
+typically you have the first one is
+defined to be whatever and then the next
+
+ align:start position:0%
+defined to be whatever and then the next
+ 
+
+ align:start position:0%
+defined to be whatever and then the next
+one is defined from the previous one.
+
+ align:start position:0%
+one is defined from the previous one.
+ 
+
+ align:start position:0%
+one is defined from the previous one.
+And so the one I was suggesting
+
+ align:start position:0%
+And so the one I was suggesting
+ 
+
+ align:start position:0%
+And so the one I was suggesting
+looking at here is that you said this
+
+ align:start position:0%
+looking at here is that you said this
+ 
+
+ align:start position:0%
+looking at here is that you said this
+here the first one.
+
+ align:start position:0%
+here the first one.
+ 
+
+ align:start position:0%
+here the first one.
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and then actually let me let me
+
+ align:start position:0%
+right and then actually let me let me
+ 
+
+ align:start position:0%
+right and then actually let me let me
+and then the next one let me just do
+
+ align:start position:0%
+and then the next one let me just do
+ 
+
+ align:start position:0%
+and then the next one let me just do
+this one here. It's actually simpler
+
+ align:start position:0%
+this one here. It's actually simpler
+ 
+
+ align:start position:0%
+this one here. It's actually simpler
+than what I have in my notes, but maybe
+
+ align:start position:0%
+than what I have in my notes, but maybe
+ 
+
+ align:start position:0%
+than what I have in my notes, but maybe
+that one. But but I just want to So the
+
+ align:start position:0%
+that one. But but I just want to So the
+ 
+
+ align:start position:0%
+that one. But but I just want to So the
+next one is defined to be xn.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And so then uh right. So now uh the
+
+ align:start position:0%
+And so then uh right. So now uh the
+ 
+
+ align:start position:0%
+And so then uh right. So now uh the
+question will be uh for what
+
+ align:start position:0%
+question will be uh for what
+ 
+
+ align:start position:0%
+question will be uh for what
+for what
+
+ align:start position:0%
+for what
+ 
+
+ align:start position:0%
+for what
+a does this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have a limit the sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have a limit
+
+ align:start position:0%
+have a limit
+ 
+
+ align:start position:0%
+have a limit
+and so you see that in this case we only
+
+ align:start position:0%
+and so you see that in this case we only
+ 
+
+ align:start position:0%
+and so you see that in this case we only
+have four minutes left so I only say few
+
+ align:start position:0%
+have four minutes left so I only say few
+ 
+
+ align:start position:0%
+have four minutes left so I only say few
+but this is also it just you do I just
+
+ align:start position:0%
+but this is also it just you do I just
+ 
+
+ align:start position:0%
+but this is also it just you do I just
+wanted you to review what it means like
+
+ align:start position:0%
+wanted you to review what it means like
+ 
+
+ align:start position:0%
+wanted you to review what it means like
+for a sequence to be defined recursively
+
+ align:start position:0%
+for a sequence to be defined recursively
+ 
+
+ align:start position:0%
+for a sequence to be defined recursively
+okay and so you see that in this is
+
+ align:start position:0%
+okay and so you see that in this is
+ 
+
+ align:start position:0%
+okay and so you see that in this is
+right. You have you have that this thing
+
+ align:start position:0%
+right. You have you have that this thing
+ 
+
+ align:start position:0%
+right. You have you have that this thing
+here. It is going down. It's actually
+
+ align:start position:0%
+here. It is going down. It's actually
+ 
+
+ align:start position:0%
+here. It is going down. It's actually
+going down. It it even could go down by
+
+ align:start position:0%
+going down. It it even could go down by
+ 
+
+ align:start position:0%
+going down. It it even could go down by
+a fraction. But now it's like if you're
+
+ align:start position:0%
+a fraction. But now it's like if you're
+ 
+
+ align:start position:0%
+a fraction. But now it's like if you're
+looking at this thing here, if you're
+
+ align:start position:0%
+looking at this thing here, if you're
+ 
+
+ align:start position:0%
+looking at this thing here, if you're
+looking at XN, this here is definitely
+
+ align:start position:0%
+looking at XN, this here is definitely
+ 
+
+ align:start position:0%
+looking at XN, this here is definitely
+going to converge. Whatever you start
+
+ align:start position:0%
+going to converge. Whatever you start
+ 
+
+ align:start position:0%
+going to converge. Whatever you start
+with.
+
+ align:start position:0%
+with.
+ 
+
+ align:start position:0%
+with.
+So I claim that you will always get
+
+ align:start position:0%
+So I claim that you will always get
+ 
+
+ align:start position:0%
+So I claim that you will always get
+that you will always get that xn here
+
+ align:start position:0%
+that you will always get that xn here
+ 
+
+ align:start position:0%
+that you will always get that xn here
+converted to zero
+
+ align:start position:0%
+converted to zero
+ 
+
+ align:start position:0%
+converted to zero
+and it's just you see that if you when
+
+ align:start position:0%
+and it's just you see that if you when
+ 
+
+ align:start position:0%
+and it's just you see that if you when
+you have something recursively
+
+ align:start position:0%
+you have something recursively
+ 
+
+ align:start position:0%
+you have something recursively
+it's often can pay to just write out the
+
+ align:start position:0%
+it's often can pay to just write out the
+ 
+
+ align:start position:0%
+it's often can pay to just write out the
+few first few terms. So you have x and a
+
+ align:start position:0%
+few first few terms. So you have x and a
+ 
+
+ align:start position:0%
+few first few terms. So you have x and a
+x2 is equal to uh a over uh y a is also
+
+ align:start position:0%
+x2 is equal to uh a over uh y a is also
+ 
+
+ align:start position:0%
+x2 is equal to uh a over uh y a is also
+a right because it's the previous one. H
+
+ align:start position:0%
+a right because it's the previous one. H
+ 
+
+ align:start position:0%
+a right because it's the previous one. H
+x2
+
+ align:start position:0%
+x2
+ 
+
+ align:start position:0%
+x2
+is now uh a / 2 x4
+
+ align:start position:0%
+is now uh a / 2 x4
+ 
+
+ align:start position:0%
+is now uh a / 2 x4
+is then uh a / 2 / 3. So this is a / 6,
+
+ align:start position:0%
+is then uh a / 2 / 3. So this is a / 6,
+ 
+
+ align:start position:0%
+is then uh a / 2 / 3. So this is a / 6,
+right? and so on, right? And so if you
+
+ align:start position:0%
+right? and so on, right? And so if you
+ 
+
+ align:start position:0%
+right? and so on, right? And so if you
+continue like this, you will see that
+
+ align:start position:0%
+continue like this, you will see that
+ 
+
+ align:start position:0%
+continue like this, you will see that
+they get that it's like a divided by
+
+ align:start position:0%
+they get that it's like a divided by
+ 
+
+ align:start position:0%
+they get that it's like a divided by
+some larger and larger number, right?
+
+ align:start position:0%
+some larger and larger number, right?
+ 
+
+ align:start position:0%
+some larger and larger number, right?
+And but you have to of course write it
+
+ align:start position:0%
+And but you have to of course write it
+ 
+
+ align:start position:0%
+And but you have to of course write it
+nicely out as a proof, right? But this
+
+ align:start position:0%
+nicely out as a proof, right? But this
+ 
+
+ align:start position:0%
+nicely out as a proof, right? But this
+is so this is proving that. But again,
+
+ align:start position:0%
+is so this is proving that. But again,
+ 
+
+ align:start position:0%
+is so this is proving that. But again,
+you know, this here, if you just did
+
+ align:start position:0%
+you know, this here, if you just did
+ 
+
+ align:start position:0%
+you know, this here, if you just did
+what I did, that would not be enough to
+
+ align:start position:0%
+what I did, that would not be enough to
+ 
+
+ align:start position:0%
+what I did, that would not be enough to
+get full credit, right? So definitely
+
+ align:start position:0%
+get full credit, right? So definitely
+ 
+
+ align:start position:0%
+get full credit, right? So definitely
+write out the other thing in the last
+
+ align:start position:0%
+write out the other thing in the last
+ 
+
+ align:start position:0%
+write out the other thing in the last
+minute here. The other thing uh
+
+ align:start position:0%
+minute here. The other thing uh
+ 
+
+ align:start position:0%
+minute here. The other thing uh
+uh the other
+
+ align:start position:0%
+uh the other
+ 
+
+ align:start position:0%
+uh the other
+thing here for my example here we look
+
+ align:start position:0%
+thing here for my example here we look
+ 
+
+ align:start position:0%
+thing here for my example here we look
+suppose you take a series like this and
+
+ align:start position:0%
+suppose you take a series like this and
+ 
+
+ align:start position:0%
+suppose you take a series like this and
+suppose that a yeah here was less than 1
+
+ align:start position:0%
+suppose that a yeah here was less than 1
+ 
+
+ align:start position:0%
+suppose that a yeah here was less than 1
+/ n²
+
+ align:start position:0%
+/ n²
+ 
+
+ align:start position:0%
+/ n²
+and then the question could be is this
+
+ align:start position:0%
+and then the question could be is this
+ 
+
+ align:start position:0%
+and then the question could be is this
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+is the series because you knew this but
+
+ align:start position:0%
+is the series because you knew this but
+ 
+
+ align:start position:0%
+is the series because you knew this but
+that's all you know is the is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convergent or divergent
+
+ align:start position:0%
+convergent or divergent
+ 
+
+ align:start position:0%
+convergent or divergent
+or divergent,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? And and and and then I say in the
+
+ align:start position:0%
+right? And and and and then I say in the
+ 
+
+ align:start position:0%
+right? And and and and then I say in the
+notes here, I mean in the in the review
+
+ align:start position:0%
+notes here, I mean in the in the review
+ 
+
+ align:start position:0%
+notes here, I mean in the in the review
+here, right? that if either you should
+
+ align:start position:0%
+here, right? that if either you should
+ 
+
+ align:start position:0%
+here, right? that if either you should
+prove that for all such series it's
+
+ align:start position:0%
+prove that for all such series it's
+ 
+
+ align:start position:0%
+prove that for all such series it's
+convergent or if that's not the case you
+
+ align:start position:0%
+convergent or if that's not the case you
+ 
+
+ align:start position:0%
+convergent or if that's not the case you
+should give an example of a series with
+
+ align:start position:0%
+should give an example of a series with
+ 
+
+ align:start position:0%
+should give an example of a series with
+this property that is divergent because
+
+ align:start position:0%
+this property that is divergent because
+ 
+
+ align:start position:0%
+this property that is divergent because
+obviously if all the a was zero it would
+
+ align:start position:0%
+obviously if all the a was zero it would
+ 
+
+ align:start position:0%
+obviously if all the a was zero it would
+be convergence right but it still could
+
+ align:start position:0%
+be convergence right but it still could
+ 
+
+ align:start position:0%
+be convergence right but it still could
+be another series with a end that
+
+ align:start position:0%
+be another series with a end that
+ 
+
+ align:start position:0%
+be another series with a end that
+property that was divergent right but in
+
+ align:start position:0%
+property that was divergent right but in
+ 
+
+ align:start position:0%
+property that was divergent right but in
+this case it is going to be convergence.
+
+ align:start position:0%
+this case it is going to be convergence.
+ 
+
+ align:start position:0%
+this case it is going to be convergence.
+And why is it convergent? Because that
+
+ align:start position:0%
+And why is it convergent? Because that
+ 
+
+ align:start position:0%
+And why is it convergent? Because that
+this series here is convergence, right?
+
+ align:start position:0%
+this series here is convergence, right?
+ 
+
+ align:start position:0%
+this series here is convergence, right?
+But we've already seen. So this here
+
+ align:start position:0%
+But we've already seen. So this here
+ 
+
+ align:start position:0%
+But we've already seen. So this here
+would be like the simple comparison test
+
+ align:start position:0%
+would be like the simple comparison test
+ 
+
+ align:start position:0%
+would be like the simple comparison test
+like the first comparison test.
+
+ align:start position:0%
+like the first comparison test.
+ 
+
+ align:start position:0%
+like the first comparison test.
+Okay. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um right. So these are just like
+
+ align:start position:0%
+um right. So these are just like
+ 
+
+ align:start position:0%
+um right. So these are just like
+examples of things you should be
+
+ align:start position:0%
+examples of things you should be
+ 
+
+ align:start position:0%
+examples of things you should be
+reviewing. Right? They are this like
+
+ align:start position:0%
+reviewing. Right? They are this like
+ 
+
+ align:start position:0%
+reviewing. Right? They are this like
+these sinks here, the two sinks to the
+
+ align:start position:0%
+these sinks here, the two sinks to the
+ 
+
+ align:start position:0%
+these sinks here, the two sinks to the
+end that like this one here like this is
+
+ align:start position:0%
+end that like this one here like this is
+ 
+
+ align:start position:0%
+end that like this one here like this is
+super fast. So don't expect it to be
+
+ align:start position:0%
+super fast. So don't expect it to be
+ 
+
+ align:start position:0%
+super fast. So don't expect it to be
+quite as fast on the m but it just give
+
+ align:start position:0%
+quite as fast on the m but it just give
+ 
+
+ align:start position:0%
+quite as fast on the m but it just give
+you it just give you an idea of what you
+
+ align:start position:0%
+you it just give you an idea of what you
+ 
+
+ align:start position:0%
+you it just give you an idea of what you
+should be doing. Okay.
\ No newline at end of file
diff --git a/rei6tud0Tsg.txt b/rei6tud0Tsg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b43ccde0121badedc82517ac81db8c5dcab6d035
--- /dev/null
+++ b/rei6tud0Tsg.txt
@@ -0,0 +1,3757 @@
+NARRATOR: The following content
+is provided under a
+
+Creative Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: To take up the topic
+of quantization, you
+
+remember we're talking about
+source coding in the first
+
+part of the course, channel
+coding in the
+
+last 2/3 of the course.
+
+Source coding, like all, is
+divided into three parts.
+
+If you have waveforms, such
+as speech, you start
+
+out with the waveform.
+
+The typical way to encode
+waveforms is you first either
+
+sample the waveform or
+you expand it in
+
+some kind of expansion.
+
+When you do that, you wind up
+with a sequence of numbers.
+
+You put the sequence of numbers
+into a quantizer, and
+
+the quantizer reduces that
+to a discrete alphabet.
+
+You put the discrete symbols
+into the discrete encoder.
+
+You pass it through a reliable
+binary channel.
+
+What is a reliable
+binary channel?
+
+It's a layered view of any old
+channel in the world, OK?
+
+In other words, the way that
+discrete channels work these
+
+days is that, in almost all
+cases, what goes into them is
+
+a binary stream of signals, and
+what comes out of them is
+
+a binary stream of symbols, and
+the output is essentially
+
+the same z-input.
+
+That's the whole purpose of
+how you design digital
+
+channels, and they work
+over analog media and
+
+all sorts of things.
+
+OK, so discrete encoders and
+discrete decoders are really a
+
+valid topic to study
+in their own.
+
+I mean, you have text and stuff
+like that, which is
+
+discrete to start with, so
+there's a general topic of how
+
+do you encode discrete things?
+
+We've pretty much answered that
+problem, at least in an
+
+abstract sense, and the main
+point there is you find the
+
+entropy of that discrete
+sequence, the entropy per
+
+symbol, and then you find ways
+of encoding that discrete
+
+source in such a way that the
+number of bits per symbol is
+
+approximately equal
+to that entropy.
+
+We know you can't do any
+better than that.
+
+You can't do an encoding, which
+is uniquely decodable,
+
+which you can get out of with
+the original symbols again,
+
+with anything less
+than the entropy.
+
+So at least we know roughly what
+the answer to that is.
+
+We even know some classy schemes
+like the Lempel-Ziv
+
+algorithm, which will in fact
+operate without even knowing
+
+anything about what the
+probabilities are.
+
+So we sort of understand this
+block here at this point.
+
+And we could start with this
+next, or we could start with
+
+this next, and unlike the
+electrician here, we're going
+
+to move in sequence and look at
+this next and this third.
+
+There's another reason
+for that.
+
+When we get into this question,
+we will be talking
+
+about what do you do
+with waveforms?
+
+How do you deal with
+waveforms?
+
+It's what you've been studying
+probably since the sixth
+
+grade, and you're all
+familiar with it.
+
+You do integration and
+things like that.
+
+You know how to work
+with functions.
+
+What we're going to do with
+functions in this course is a
+
+little bit different than
+what you're used to.
+
+It's quite a bit different than
+what you learned in your
+
+Signals and Systems course, and
+you'll find out why as we
+
+move along.
+
+But we have to understand this
+business of how to deal with
+
+waveforms, both in terms of this
+block, which is the final
+
+block we'll study in source
+coding, and also in terms of
+
+how to deal with channels
+because in real channels,
+
+generally what you transmit
+is a waveform.
+
+What the noise does to you is to
+add a waveform or, in some
+
+sense, multiply what you put
+in by something else.
+
+And all of that is
+waveform stuff.
+
+And all of information theory
+and all of digital
+
+communication is based
+on thinking bits.
+
+So somehow or other, we have to
+become very facile in going
+
+from waveforms to bits.
+
+Now I've been around the
+professional communities of
+
+both communication and
+information theory for
+
+a long, long time.
+
+There is one fundamental problem
+that gives everyone
+
+problems because information
+theory texts do not deal with
+
+it and communication texts
+do not deal with it.
+
+And that problem is how do you
+go from one to the other,
+
+which seems like it ought
+to be an easy thing.
+
+It's not as easy as it looks,
+and therefore, we're going to
+
+spent quite a bit
+of time on that.
+
+In fact, I passed out lectures
+6 and 7 today, which in
+
+previous years I've done in two
+separate lectures because
+
+quantization is a problem
+that looks important.
+
+We'll see that it's not quite
+as important as it looks.
+
+And I guess the other thing is,
+I mean, at different times
+
+you have to teach different
+things or you get stale on it.
+
+And I've just finished writing
+some fairly nice notes, I
+
+think, on this question of how
+do you go from waveforms to
+
+numbers and how do you go from
+numbers to waveforms.
+
+And I want to spend a little
+more time on that this year
+
+than I did last year.
+
+I want to spend, therefore,
+a little less time on
+
+quantization, so that next time,
+we will briefly review
+
+what we've done today on
+quantization, but we will
+
+essentially just compress
+those two
+
+lectures all into one.
+
+In dealing with waveforms,
+we're going to learn some
+
+interesting and kind
+of cool things.
+
+Like for those of you who
+really don't -- are not
+
+interested in mathematics, you
+know that people study things
+
+like the theory of real
+variables and functional
+
+analysis and all of these neat
+things, which are very, in a
+
+sense, advanced mathematics.
+
+They're all based on measure
+theory, and you're going to
+
+find out a little bit about
+measure theory here.
+
+Not an awful lot, but just
+enough to know why one has to
+
+deal with those questions
+because the major results in
+
+dealing with waveforms and
+samples really can't be stated
+
+in any other form than
+in a somewhat
+
+measure-theoretic form.
+
+So we're going to find just
+enough about that so we can
+
+understand what those
+issues are about.
+
+So that's why next time we're
+going to start dealing with
+
+the waveform issues.
+
+OK, so today, we're dealing with
+these quantizer issues
+
+and how do you take a sequence
+of numbers, turn them into a
+
+sequence of symbols
+at the other end?
+
+How do you take a sequence
+of symbols, turn
+
+them back into numbers?
+
+So when you convert real numbers
+to binary strings, you
+
+need a mapping from the
+set of real numbers
+
+to a discrete alphabet.
+
+And we're typically going to
+have a mapping from the set of
+
+real numbers into a finite
+discrete alphabet.
+
+Now what's the first obvious
+thing that you notice when you
+
+have a mapping that goes from an
+infinite set of things into
+
+a finite set of things?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: What?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Not really.
+
+It's a much simpler
+idea than that.
+
+How are you going to get back?
+
+I mean, usually when you map
+something into something else,
+
+you would like to
+get back again.
+
+When you map an infinite set
+into a finite set, how are you
+
+going to get back?
+
+AUDIENCE: You're not.
+
+PROFESSOR: You're not.
+
+Good!
+
+There's not any way in hell
+that you're ever going
+
+to get back, OK?
+
+So, in other words, what
+you've done here is to
+
+deliberately introduce some
+distortion into the picture.
+
+You've introduced distortion
+because you have no choice.
+
+If you want to turn numbers into
+bits, you can't get back
+
+to the exact numbers again.
+
+So you can only get back to some
+approximation of what the
+
+numbers are.
+
+But anyway, this process of
+doing this is called scalar
+
+quantization, if we're mapping
+from the set of real numbers
+
+to a discrete alphabet.
+
+If instead you want to convert
+real n-tuples into sequences
+
+of discrete symbols, in other
+words, into a finite alphabet,
+
+you call that vector
+quantization because you can
+
+view n real numbers, a sequence
+of n real numbers as
+
+a vector within coordinates
+and within components.
+
+And I'm not doing anything
+fancy with vectors here.
+
+You just look at an n-tuple
+of numbers as a vector.
+
+OK, so scalar quantization is
+going to encode each term of
+
+the source sequence
+separately.
+
+And vector quantization is first
+going to segment this
+
+sequence of numbers into blocks
+of n numbers each, and
+
+then it's going to find a way
+of encoding those n-blocks
+
+into discrete symbols.
+
+Does this sound a little bit
+like what we've already done
+
+in dealing with discrete
+sources?
+
+Yeah, it's exactly
+the same thing.
+
+I mean, we started out by
+mapping individual symbols
+
+into bit sequences, and then we
+said, gee, we can also map
+
+n-blocks of those symbols into
+bits, and we said, gee, this
+
+is the same problem again.
+
+There's nothing different,
+nothing new.
+
+And it's the same thing here
+almost except here the
+
+properties of the real numbers
+are important.
+
+Why are the properties of the
+real numbers important?
+
+Why can't we just look
+at this as symbols?
+
+Well, because, since we can't
+do this mapping in an
+
+invertable way, you have to deal
+with the fact that you
+
+have distortion here.
+
+There's no other way
+to think about it.
+
+There is distortion.
+
+You might as well face it.
+
+If you try to cover it
+up, it just comes
+
+up to kick you later.
+
+So we face it right in the
+beginning, and that's why we
+
+deal with these things
+as numbers.
+
+So let's look at a simple
+example of what a scalar
+
+quantizer is going to do.
+
+Basically, what we have to do
+is to map the line R, mainly
+
+the set of real numbers, into
+M different regions, which
+
+we'll call R1 up to R sub M.
+And in this picture here,
+
+here's R1, here's R2, here's R3,
+here's R4, R5 and R6, and
+
+that's all the regions
+we have.
+
+You'll notice one of the things
+that that does is it
+
+takes an enormous set of
+numbers, namely all these
+
+numbers less than this,
+and match them all
+
+into the same symbol.
+
+So you might wind up with a
+fair amount of distortion
+
+there, no matter how you
+measure distortion.
+
+All these outliers here all
+get mapped into a6, and
+
+everything in the middle gets
+mapped somehow into these
+
+intermediate values.
+
+But every source value now in
+the region R sub j, we're
+
+going to map into a
+representation point a sub j.
+
+So everything in R1 is going
+to be mapped into a1.
+
+Everything in R2 is going
+to get mapped
+
+into a2 and so forth.
+
+Is this a general way to map
+R into a set of M symbols?
+
+Is there anything else I ought
+to be thinking about?
+
+Well, here, these regions here
+have a very special property.
+
+Namely, each region
+is an interval.
+
+And we might say to ourselves,
+well, maybe we shouldn't map
+
+points into intervals.
+
+But aside from the fact that
+we've chosen intervals here,
+
+this is a perfectly general
+way to represent a mapping
+
+from the real numbers into
+a discrete set of things.
+
+Namely, when you're doing a
+mapping from the real numbers
+
+into a discrete set of things,
+there's some set of real
+
+numbers that get mapped
+into a1, and that by
+
+definition is called R1.
+
+There's some set of numbers
+which get mapped into a2.
+
+That by definition is called
+R2 and so forth.
+
+So aside from the fact that
+these intervals with these
+
+regions in this picture happen
+to be intervals, this is a
+
+perfectly general mapping from
+R into a discrete alphabet.
+
+So since I've decided I'm
+going to look at scalar
+
+quantizers first, this is a
+completely general view of
+
+what a scalar quantizer is.
+
+You tell me how many
+quantization regions you want,
+
+namely how big the alphabet is
+that you're mapping things
+
+into, and then your only problem
+is how do you choose
+
+these regions and how
+do you choose the
+
+representation points?
+
+OK, one new thing here: Before,
+we said when you have
+
+a set of symbols a1 up to
+a6, it doesn't matter
+
+what you call them.
+
+They're just six symbols.
+
+Here it makes a difference what
+you call them because
+
+here they are representing
+real numbers and they are
+
+representing real numbers
+because when you map some real
+
+number on the real line into one
+of these letters here, the
+
+distortion is u minus a sub j.
+
+If you're mapping u into a sub
+j, then you get a distortion,
+
+which is this difference here.
+
+I haven't said yet what I am
+interested in as far as
+
+distortion is concerned.
+
+Am I interested in squared
+distortion, cubed distortion,
+
+absolute magnitude
+of distortion?
+
+I haven't answered that
+question yet.
+
+But there is a distortion here,
+and somehow that has to
+
+be important.
+
+We have to come to grips with
+what we call a distortion and
+
+somehow how big that distortion
+is going to be.
+
+So our problem here is somehow
+to trade off between
+
+distortion and number
+of points.
+
+As we make the number of
+points bigger, we can
+
+presumably make the distortion
+smaller in some sense,
+
+although the distortion is
+always going to be very big
+
+from these really big negative
+numbers and from really big
+
+positive numbers.
+
+But aside from that, we just
+have a problem of how do you
+
+choose the regions?
+
+How do you choose the points?
+
+OK, I've sort of forgotten
+about the problem that we
+
+started with.
+
+And the problem that we started
+with was to have a
+
+source where the source was
+a sequence of numbers.
+
+And when we're talking about
+sources, we're talking about
+
+something stochastic.
+
+We need a probability measure
+on these real numbers that
+
+we're encoding.
+
+If we knew what they were, there
+wouldn't be any need to
+
+encode them.
+
+I mean, if we knew and the
+receiver knew, there would be
+
+no need to encode them.
+
+The receiver would just print
+out what they were or store
+
+them or do whatever
+the receiver
+
+wants to do with them.
+
+OK, so we're going to view the
+source value u with the sample
+
+value of some random variable
+capital U. And more generally,
+
+since we have a sequence, we're
+going to consider a
+
+source sequence to be U1, U2, U3
+and so forth, or you could
+
+consider it a bi-infinite
+sequence, starting at U minus
+
+infinity and working
+its way up forever.
+
+And then we're going to have
+some sort of model,
+
+statistical model, for this
+sequence of random variables.
+
+Our typical model for these is
+to assume that we have a
+
+memoryless source.
+
+In other words, U1, U2, U3 are
+independent, identically
+
+distributed, random variables.
+
+That's the model we'll use until
+we get smarter and start
+
+to think of something else.
+
+OK, so now each of these source
+values we're going to
+
+map into some representation
+point a sub j.
+
+That's what defines
+the quantizer.
+
+And now since a sub j is a
+sample value of a random
+
+variable U, a sub j is going to
+be a sample value of some
+
+random variable V. OK, in other
+words, the probabilities
+
+of these different sample
+values is going to be
+
+determined by the set of U's
+that math into that a sub j.
+
+So we have a source sequence
+U1, U2, blah, blah, blah.
+
+We have a representation
+sequence V1, V2, blah, blah,
+
+blah, which is defined by if U
+sub k is in R sub j, then Vk
+
+is equal to a sub j.
+
+Point of confusion here: It's
+not confusing now, but it will
+
+be confusing at some
+point to you.
+
+When you're talking about
+sources, you really need two
+
+indices that you're talking
+about all the time.
+
+OK, one of them is
+how to represent
+
+different elements in time.
+
+Here we're using k as a way of
+keeping track of what element
+
+in time we're talking about.
+
+We're also talking about a
+discrete alphabet, which has a
+
+certain number of elements in
+it, which is completely
+
+independent of time.
+
+Namely, we've just described
+the quantizer as something
+
+which maps real numbers
+into sample values.
+
+It has nothing to do
+with time at all.
+
+We're going to use that same
+thing again and again and
+
+again, and we're using
+the subscript j
+
+to talk about that.
+
+When you write out problem
+solutions, you are going to
+
+find that it's incredibly
+difficult sometimes to write
+
+sentences which distinguish
+about whether you're talking
+
+about one element out of an
+alphabet or one element out of
+
+a time sequence.
+
+And everybody has that trouble,
+and you read most of
+
+the literature in information
+theory or communication
+
+theory, and you can't sort out
+most of the time what people
+
+are talking about because
+they're doing that.
+
+I recommend to you using an
+element and an alphabet to
+
+talk about this sort of thing,
+what a sub j is or an element
+
+and a time sequence to
+keep track of things
+
+at different times.
+
+It's a nice way of keeping
+them straight.
+
+OK, so anyway, for a scalar
+quantizer, we're going to be
+
+able to just look at a single
+random variable U, which is a
+
+continuous-valued random
+variable, which takes values
+
+anywhere on the real line and
+maps it into a single element
+
+in this discrete alphabet, which
+is the set a1 up to a6
+
+that we were talking
+about here.
+
+So a scalar quantizer then is
+just a map of this form, OK?
+
+So the only thing we need for a
+scalar quantizer, we can now
+
+forget about time and talk about
+how do you choose the
+
+regions, how do you choose the
+representation points?
+
+OK, and there's a nice
+algorithm there.
+
+Again, one of these things,
+which if you were the first
+
+person to think about it, easy
+way to become famous.
+
+You might not stay famous, but
+you can get famous initially.
+
+Anyway, we're almost always
+interested in the mean squared
+
+error or the mean squared
+distortion, MSD or MSE, which
+
+is the expected value of U minus
+V. U is this real-valued
+
+random variable.
+
+V is the discrete random
+variable into which it maps.
+
+We have the distortion between
+U and V, which is U minus V.
+
+We now have the expected value
+of that squared distortion.
+
+Why is everybody interested in
+squared distortion instead of
+
+magnitude distortion
+or something else?
+
+In many engineering problems,
+you should be more interested
+
+in magnitude distortion.
+
+Sometimes you're much more
+interested in fourth-moment
+
+distortion or some other
+strange thing.
+
+Why do we always use mean
+squared distortion?
+
+And why do we use mean-squared
+everything throughout almost
+
+everything we do in
+communication?
+
+I'll tell you the reason now.
+
+We'll come back and talk about
+it more a number of times.
+
+It's because this quantization
+problem that we're talking
+
+about is almost always a
+subproblem of this problem,
+
+where you're dealing with
+waveforms, where you take the
+
+waveform and you sample the
+waveform, where you take the
+
+waveform, and you turn the
+waveform into some expansion.
+
+When you find the mean-squared
+distortion in a quantizer, it
+
+turns out that that maps in
+a beautiful way into the
+
+mean-squared distortion
+between waveforms.
+
+If you deal with magnitudes or
+with anything else in the
+
+world, all of that beauty
+goes away, OK?
+
+In other words, whenever you
+want to go from waveforms to
+
+numbers, the one thing which
+remains invariant, which
+
+remains nice all the way
+through, is this mean-square
+
+distortion, mean-square
+value, OK?
+
+In other words, if you want
+to layer this problem into
+
+looking at this problem
+separately from looking at
+
+this problem, almost the only
+way you can do it that makes
+
+sense is to worry about mean
+square distortion rather than
+
+some other kind of distortion.
+
+So even though as engineers
+we might be interested in
+
+something else, we almost always
+stick to that because
+
+that's the thing that we can
+deal with most nicely.
+
+I mean, as engineers, we're like
+the drunk who dropped his
+
+wallet on a dark street, and
+he's searching for it, and
+
+somebody comes along.
+
+And here he is underneath a
+beautiful light where he can
+
+see everything.
+
+Somebody asks him what he's
+looking for you, and he says
+
+he's looking for his wallet.
+
+The guy looks down and says,
+well, there's no wallet there.
+
+The drunk says I know.
+
+I dropped it over there, but
+it's dark over there.
+
+So we use mean square
+distortion in
+
+exactly the same sense.
+
+It isn't necessarily the problem
+we're interested in,
+
+but it's a problem where we
+can see things clearly.
+
+So given that we're interested
+in the mean square distortion
+
+of a scalar quantizer, an
+interesting analytical problem
+
+that we can play with is for a
+given probability density on
+
+this real random variable, and
+we're assuming we have a
+
+probability density and a given
+alphabet size M, the
+
+problem is how do you choose
+these regions and how do you
+
+choose these representation
+points in such a way as to
+
+minimize the mean square
+error, OK?
+
+So, in other words, we've taken
+a big sort of messy
+
+amorphous engineering problem,
+and we said, OK, we're going
+
+to deal with mean square error,
+and OK, we're going to
+
+deal with scalar quantizers, and
+OK, we're going to fix a
+
+number of quantization levels,
+so we've made all those
+
+choices to start with.
+
+We still have this interesting
+problem of how do you choose
+
+the right regions?
+
+How do you choose the
+right sample points?
+
+And that turns out to
+be a simple problem.
+
+I wouldn't talk about
+if it wasn't simple.
+
+And we'll break it into
+subproblems, and the
+
+subproblems are really simple.
+
+The first subproblem is if I
+tell you what representation
+
+points I want to use, namely,
+in this picture here, I say
+
+OK, I want to use these
+representation points.
+
+And then I ask you, how are
+you going to choose the
+
+regions in an optimal way to
+minimize mean square error?
+
+Well, you think about that for
+awhile, and you think about it
+
+in a number of ways.
+
+When you think about it in just
+the right way, the answer
+
+becomes obvious.
+
+And the answer is, let me not
+think about the regions here,
+
+but let me think about a
+particular value that comes
+
+out of the source.
+
+Let me think, how should I
+construct a rule for how to
+
+take outputs from this
+source and map them
+
+into some number here.
+
+So if I get some output from
+the source u, I say, OK,
+
+what's the distortion
+between u and a1?
+
+It's u minus a1.
+
+And the magnitude of that is the
+magnitude of u minus a1.
+
+The square of it is the square
+of u minus a1, and then say,
+
+OK, let me compare that
+with u minus a2.
+
+Let me compare it with u
+minus a3 and so forth.
+
+Let me choose the smallest
+of those things.
+
+What's the smallest stuff
+for any given u?
+
+Suppose I have a u which
+happens to be
+
+right there, for example.
+
+What's the closest
+representation point?
+
+Well, a3 is obviously
+closer than a2.
+
+And in fact for any point in
+here, which is closer to a3
+
+than it is to a2, we're
+going to choose a3.
+
+Now what's the set of points
+which are closer to a3 than
+
+they are to a2?
+
+Well, you put a line here right
+between a2 and a3, OK?
+
+When you put that line right
+between a2 and a3, everything
+
+on this side is closer to a3 and
+everything on this side is
+
+closer to a2.
+
+So the answer is,
+in fact, simple,
+
+once you see the answer.
+
+And the answer is, given these
+points, we simply construct
+
+bisectors between them, namely,
+bisectors with --
+
+halfway between a1 and
+a2, we call that b1.
+
+Halfway between a2 and a3, we
+call that b2, and those are
+
+the separators between
+the regions, OK?
+
+In other words, what we wind
+up doing is we define the
+
+region R sub j, the set of
+things which get mapped into a
+
+sub j as the region which is
+bounded by bj minus 1 is the
+
+average of aj and aj minus 1,
+and bj is the average of aj
+
+and aj plus 1, where I've
+already ordered the points a
+
+sub j going from left
+to right, OK?
+
+And that also tells us that the
+minimum mean square error
+
+regions have got to
+be intervals.
+
+There is no reason at all to
+ever pick regions which are
+
+not intervals because, as soon
+as you start to solve this
+
+problem for any given set of
+representation points, you
+
+wind up with intervals.
+
+So if you ever think of using
+things that are not intervals
+
+for this mean square error
+problem, then as soon as you
+
+look at this, you say, well,
+aha, that can't be the best
+
+thing to do.
+
+I will make my regions
+intervals.
+
+I will therefore simplify the
+whole problem, and I'll also
+
+improve it.
+
+And when you can both simplify
+things and improve them at the
+
+same time, it usually is worth
+doing it unless you're dealing
+
+with standards bodies or
+something, and then
+
+all bets are off.
+
+OK, so this one part of
+the problem is easy.
+
+If we know what the
+representation points are, we
+
+can solve the problem.
+
+OK, we have a second problem,
+which is just
+
+the opposite problem.
+
+Suppose then that somebody gives
+you the interval regions
+
+and asks you, OK, if I give you
+these interval regions,
+
+how are you going to choose the
+representation points to
+
+minimize the mean
+square error?
+
+And analytically that's harder,
+but conceptually, it's
+
+just about as easy.
+
+And let's look at it and see
+if we can understand it.
+
+Somebody gives us this region
+here, R sub 2, and says, OK,
+
+where should we put
+the point a sub 2?
+
+Well, anybody have any
+clues as to where
+
+you want to put it?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: What?
+
+AUDIENCE: At the midpoint?
+
+PROFESSOR: At the midpoint.
+
+It sounds like a reasonable
+thing, but
+
+it's not quite right.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: What?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: It depends on the
+probability density, yes.
+
+If you have a probability
+density, which is highly
+
+weighted over on -- let's see,
+was I talking about R2 or R3?
+
+Well, it doesn't make
+any difference.
+
+We'll talk about R2.
+
+If I have a probability density,
+which looks like
+
+this, then I want a2 to be
+closer to the left-hand side
+
+than to the right-hand side.
+
+I want it to be a little bit
+weighted towards here because
+
+that's more important
+in choosing
+
+the mean square error.
+
+OK, if you didn't have any of
+this stuff, and I said how do
+
+I choose this to minimize the
+mean square error, what's your
+
+answer then?
+
+If I just have one region and
+I want to minimize the mean
+
+square error, what do you do?
+
+Anybody who doesn't know should
+go back and study
+
+elementary probability theory
+because this is almost day one
+
+of elementary probability theory
+when you start to study
+
+what random variables
+are all about.
+
+And the next thing you start
+to look at is things like
+
+variance and second moment.
+
+And what I'm asking you here
+is, how do you choose a2 in
+
+order to minimize the second
+moment of U, whatever it is in
+
+here, minus a2?
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: I want to take
+the expectation of U
+
+over the region R2.
+
+In other words, to say it more
+technically, I want to take
+
+the expectation of the
+conditional random variable U,
+
+conditional on being
+in R2, OK?
+
+And all of you could figure that
+out yourselves, if you
+
+sat down quietly and thought
+about it for five minutes.
+
+If you got frightened about it
+and started looking it up in a
+
+book or something, it
+would take you about
+
+two hours to do it.
+
+But if you just asked
+yourselves, how do I do it?
+
+You'll come up with the right
+answer very, very soon, OK?
+
+So subproblem 2 says let's
+look at the conditional
+
+density of U in this
+region R sub j.
+
+I'll call the conditional
+density -- well, the
+
+conditional density, given that
+you're in this region,
+
+is, in fact, the real density
+divided by the probability of
+
+being in that interval, OK?
+
+So we'll call that the
+conditional density.
+
+And I'll let U of j be the
+random variable, which has
+
+this density.
+
+In other words, this isn't
+a random variable on the
+
+probability space that we
+started to deal with it.
+
+It's sort of a phony
+random variable.
+
+But, in fact, it's the
+intuitive thing that
+
+you think of, OK?
+
+In other words, if this is
+exactly what you were thinking
+
+of, you probably wouldn't have
+called this a separate random
+
+variable, OK?
+
+So this is a random variable
+with this density.
+
+The expected value of U of j
+minus a of j quantity squared,
+
+as you all know, is sigma
+squared of U of j plus the
+
+expected value a U of j minus a
+sub j quantity squared, OK?
+
+How do you minimize this?
+
+Well, you're stuck with this.
+
+This term, you minimize it by
+making a sub j equal to the
+
+expected value of
+U of j, which is
+
+exactly what you said.
+
+Namely, you set a of j to be the
+conditional mean of U of j
+
+conditional on being
+in the center.
+
+It's harder to say
+mathematically than
+
+it is to see it.
+
+But, in fact, the intuitive
+idea is exactly right.
+
+Namely, you condition your
+random variable on being in
+
+that interval, and then what you
+want to do is choose the
+
+mean within that interval, which
+is exactly the sort of
+
+thing we were thinking
+about here.
+
+When I drew this curve here, if
+I scale it, this, in fact,
+
+is the density of
+u conditional on
+
+being in R sub j.
+
+And now all I'm trying to do
+is choose the point here,
+
+which happens to be
+the mean which
+
+minimizes this second moment.
+
+The second moment, in fact,
+is this mean square error.
+
+So, bingo!
+
+That's the second problem.
+
+Well, how do you put the
+two problems together?
+
+Well, you can put it together
+in two ways.
+
+One of them is to say, OK, well
+then, clearly an optimal
+
+scalar quantizer has to
+satisfy both of these
+
+conditions.
+
+Namely, the endpoints of the
+regions have to be the
+
+midpoints of the representation
+points, and the
+
+representation points have to
+be the conditional means of
+
+the points within a region
+that you start with.
+
+And then you say, OK, how
+do I solve that problem?
+
+Well, if you're a computer
+scientist, and sometimes it's
+
+good to be a computer scientist,
+you say, well, I
+
+don't know how to solve the
+problem, but generating an
+
+algorithm to solve the problem
+is almost trivial.
+
+I start out with some
+arbitrary set of
+
+representation points.
+
+That should be a capital M
+because that's the number of
+
+points I'm allowed to use.
+
+Then the next step in the
+algorithm is I choose these
+
+separation points to be b sub j
+is the midpoint between the
+
+a's for each of these values.
+
+Then as soon as I get these
+midpoints, I have a set of
+
+intervals, and my next step is
+to say set a sub j is equal to
+
+the expected value of this
+conditional random variable U
+
+of j where R sub j is now this
+new interval for 1 less than
+
+or equal to j less than
+or equal to M minus 1.
+
+This means it's open
+on the left side.
+
+This means it's closed on the
+right side, and since it's a
+
+probability density, it doesn't
+make any difference
+
+what it is.
+
+I just wanted to give you an
+explicit rule for what to do
+
+with probability zero when you
+happen to wind up on that
+
+special point.
+
+OK, and then you iterate on
+2 and 3 until you get a
+
+negligible improvement.
+
+And then you ask, of course,
+well, if I got a negligible
+
+improvement this time, maybe
+I'll get a bigger
+
+improvement next time.
+
+And that, of course, is true.
+
+And you then say, well, it's
+possible that after I can't
+
+get any improvement anymore,
+I still don't
+
+have the optimal solution.
+
+And that, of course,
+is true also.
+
+But at least you have an
+algorithm which makes sense
+
+and which, each time you try
+it, you do a little better
+
+than you did before.
+
+Now, this mean square error for
+any choice of regions and
+
+any choice of representation
+points is going to be
+
+nonnegative because
+it's an expected
+
+value of squared terms.
+
+The algorithm is nonincreasing
+with iterations.
+
+In other words, the algorithm
+is going down all the time.
+
+So you have zero down here.
+
+You have an algorithm which is
+marching you down toward zero.
+
+It's not going to get to zero,
+but it has to reach a minimum.
+
+That's a major theorem in
+analysis, but you don't need
+
+any major theorems in analysis
+to see this.
+
+You have a set of numbers, which
+are decreasing all the
+
+time, and they're bounded
+underneath.
+
+After awhile, you have to get
+to some point, and you don't
+
+go any further.
+
+So it has a limit.
+
+So that's nice.
+
+So you have an algorithm
+which has to converge.
+
+It can't keep on going.
+
+Well, it can keep on going
+forever, but it keeps going on
+
+forever with smaller and
+smaller improvements.
+
+So eventually, you might as well
+stop because you're not
+
+getting anywhere.
+
+OK, well, those conditions
+that we stated, the way a
+
+mathematician would say this, is
+these Lloyd-Max conditions
+
+are necessary but not
+sufficient, OK?
+
+In other words, any solution
+to this problem that we're
+
+looking at has to have
+the property that the
+
+representation points are the
+conditional means of the
+
+intervals and the interval
+boundaries are the midpoints
+
+between the representation
+points.
+
+But that isn't necessarily
+enough.
+
+Here's a simple example of
+where it's not enough.
+
+Suppose you have a probability
+density, which is running
+
+along almost zero, jumps up to
+a big value, almost zero,
+
+jumps up to a big value, jumps
+up to a big value.
+
+This intentionally is wider than
+this and wider than this.
+
+In other words, there's a lot
+more probability over here
+
+than there is here
+or there is here.
+
+And you're unlucky, and you
+start out somehow with points
+
+like a1 and a2, and you start
+out with regions like R1 --
+
+well, yeah, you want to start
+out with points, a1 and a2.
+
+So you start out with a point
+a1, which is way over here,
+
+and a point a2, which is
+not too far over here.
+
+And your algorithm then says
+pick the midpoint b1.
+
+Here the algorithm is
+particularly simple because,
+
+since we're only using two
+regions, all you need is one
+
+separator point.
+
+So we wind up with b1 here,
+which is halfway
+
+between a1 and a2.
+
+a1 happens to be right in the
+middle of that big interval
+
+there, and there's hardly
+anything else here.
+
+So a1 just stays there as the
+conditional mean, given that
+
+you're on this side.
+
+And a2 stays as the conditional
+mean, given that
+
+you're over here, which means
+that a2 is a little closer
+
+this big region than it is
+to this region, but a2 is
+
+perfectly happy there.
+
+And we go back and
+we iterate again.
+
+And we haven't changed b1, we
+haven't changed a1, we haven't
+
+changed a2, and therefore, the
+algorithm sticks there.
+
+Well, that's not surprising.
+
+I mean, you know that there are
+many problems where you
+
+try to minimize things by
+differentiating or all the
+
+different tricks you have for
+minimizing things, and you
+
+very often find local minima.
+
+People call algorithms like this
+hill-climbing algorithms.
+
+They should call them
+valley-finding algorithms
+
+because we're sitting
+at someplace.
+
+We try to find a better place.
+
+So we wind up moving
+down into the
+
+valley further and further.
+
+Of course, if it's a real
+geographical area, you finally
+
+wind up at the river.
+
+You then move down the river,
+you wind up in the
+
+ocean and all that.
+
+But let's forgot about that.
+
+Let's just assume that there
+aren't rivers or anything.
+
+That we just have some arbitrary
+geographical area.
+
+We wind up in the bottom of a
+valley, and we say, OK, are we
+
+at the minimum or not?
+
+Well, with hill climbing, you
+can take a pair of binoculars,
+
+and you look around to see if
+there's any higher peak
+
+someplace else.
+
+With valley seeking,
+you can't do that.
+
+We're sitting there at the
+bottom of the valley, and we
+
+have no idea whether there's a
+better valley somewhere else
+
+or not, OK?
+
+So that's the trouble with
+hill-climbing algorithms or
+
+valley-seeking algorithms.
+
+And that's exactly what
+this algorithm does.
+
+This is called the Lloyd-Max
+algorithm because a guy by the
+
+name of Lloyd at Bell Labs
+discovered it, I think in '57.
+
+A guy by the name of Joel
+Max discovered it again.
+
+He was at MIT in 1960, and
+because all the information
+
+theorists around were at MIT at
+that time, they called it
+
+the Max algorithm
+for many years.
+
+And then somebody discovered
+that Lloyd had done it three
+
+years earlier.
+
+Lloyd never even published it.
+
+So it became the Lloyd-Max
+algorithm.
+
+And now there's somebody else
+who did it even earlier, I
+
+think, so we should probably
+take Max's name off it.
+
+But anyway, sometime when I
+revise the notes, I will give
+
+the whole story of that.
+
+But I hope you see that
+this algorithm
+
+is no big deal anyway.
+
+It was just people fortunately
+looking at the question at the
+
+right time before too many other
+people had looked at it.
+
+And Max unfortunately
+looked at it.
+
+He was in a valley.
+
+He didn't see all the other
+people had looked at it.
+
+But he became famous.
+
+He had his moment of time and
+then sunk gradually into
+
+oblivion except when once
+in awhile we call it the
+
+Lloyd-Max algorithm.
+
+Most people call it the Lloyd
+algorithm, though, and I
+
+really should also.
+
+OK, vector quantization:
+We talked about vector
+
+quantization a little bit.
+
+It's the idea of segmenting the
+source outputs before you
+
+try to do the encoding.
+
+So we ask is scalar quantization
+going to be the
+
+right approach?
+
+To answer that question, we want
+to look at quantizing two
+
+sample values jointly and
+drawing pictures.
+
+Incidentally, what's the
+simplest way of quantizing
+
+that you can think of?
+
+And what do people who do simple
+things call quantizers?
+
+Ever hear of an
+analog-to-digital converter?
+
+That's what a quantizer is.
+
+And an analog-to-digital
+converter, the way that
+
+everybody does it, is scalar.
+
+So that says that either the
+people who implement things
+
+are very stupid, or there's
+something pretty good about
+
+scalar quantization.
+
+But anyway, since this is a
+course trying to find better
+
+ways of doing things, we ought
+to investigate whether it is
+
+better to use vector
+quantizers and
+
+what they result in.
+
+OK, well, the first thing that
+we can do is look at
+
+quantizing two samples.
+
+In other words, when you want
+to generalize a problem to
+
+vectors, I find it better to
+generalize it to two vectors
+
+first and see what
+goes on there.
+
+And one possible approach is to
+use a rectangular grid of
+
+quantization regions.
+
+And as I'll show you in the
+next slide, that really is
+
+just a camouflaged scalar
+quantizer again.
+
+So you have a two-dimensional
+region corresponding to two
+
+real samples.
+
+So you've got two real
+numbers, U1 and U2.
+
+You're trying to map them into
+a finite set of sample values
+
+of representation points.
+
+Since you're going to be
+interested in the distortion
+
+between U1 and U2, between the
+vector U1, U2, and your
+
+representation vector, a1,
+a2, these points, these
+
+representation points, are going
+to be two-dimensional
+
+points also.
+
+So if you start out by saying
+let's put these points on a
+
+rectangular grid, well, we can
+then look at it, and we say,
+
+well, given the points, how
+do we choose the regions?
+
+You see, it's exactly
+the same problem
+
+that you solved before.
+
+If I give you the points and
+then I ask you, well, if we
+
+get a vector U1, U2 that's
+there, what do we map it to?
+
+Well, we map it to the closest
+thing, which means if we want
+
+to find these regions, we set
+up these perpendicular
+
+bisectors halfway between the
+representation points.
+
+So all of this is looking very
+rectangular now because we
+
+started out with these
+points rectangular.
+
+These lines are rectangular, and
+now I say, well, is this
+
+really any different from
+a scalar quantizer?
+
+And, of course, it isn't because
+for this particular
+
+vector quantizer, I can first
+ask the question, OK, here's
+
+U1, which is something
+in this direction.
+
+How do I find regions
+for that?
+
+Well, for U1, I just establish
+these regions here.
+
+And then I say, OK, let's
+look at U2 next.
+
+And then I look at things in
+this direction, and I wind up
+
+in saying, OK, that's all
+there is to the problem.
+
+I have a scalar quantizer
+again.
+
+Everything that I said
+before works.
+
+Now if you're a theoretician,
+you go one step further, and
+
+you say, what this tells me is
+that vector quantizers cannot
+
+be any worse than scalar
+quantizers.
+
+Because, in fact, a vector
+quantizer has a -- or at least
+
+a vector quantizer in two
+dimensions -- has a scalar
+
+quantizer --
+
+has two scalar quantizers
+as a special case.
+
+And therefore, the amount of
+square distortion that I wind
+
+up with in the vector case,
+I can always get that --
+
+whatever I can do with the
+scalar quantizer, I can do
+
+just as well with a vector
+quantizer by choosing it, in
+
+fact, to be rectangular
+like this.
+
+And you can also get some
+intuitive ideas that if
+
+instead of having IID random
+variables, if U1 and U2 are
+
+very heavily correlated somehow
+so that they're very
+
+close together, I mean, you
+sort of get an engineering
+
+view of what you want to do.
+
+You want to take this
+rectangular picture here.
+
+You want to skew it
+around that way.
+
+And you want to have lots of
+points going this way and not
+
+too many points going this way
+because almost everything is
+
+going this way, and
+there's not much
+
+going on in that direction.
+
+So you got some pictures
+of what you want to do.
+
+These regions here, a little bit
+of terminology, are called
+
+Voronoi regions.
+
+Anytime you start out with a
+set of points and you put
+
+perpendicular bisectors in
+between those points, halfway
+
+between the points, you call the
+regions that you wind up
+
+with Voronoi regions.
+
+So, in fact, part of this
+Lloyd-Max algorithm,
+
+generalized at two dimensions,
+says given any set of points,
+
+the regions ought to be the
+Voronoi regions for them.
+
+So that's that first subproblem
+generalized at two
+
+dimensions.
+
+And if you have an arbitrary
+set of points, the Voronoi
+
+regions look sort of
+like this, OK?
+
+And I've only drawn it for the
+center point because, well,
+
+there aren't enough points to
+do anything more than that.
+
+So anything in this region gets
+mapped into this point.
+
+Anything in this semi-infinite
+region gets mapped into this
+
+point and so forth.
+
+So even in two dimensions,
+this part of the
+
+algorithm is simple.
+
+When you start out with the
+regions, with almost the same
+
+argument that we used before,
+you can see that the mean
+
+square error is going to be
+minimized by using conditional
+
+means for the representation
+points.
+
+I mean, that's done in
+detail in the notes.
+
+It's just algebra to do that.
+
+It's sort of intuitive that
+the same thing ought to
+
+happen, and in fact, it does.
+
+So you can still find
+a local minimum by
+
+this Lloyd-Max algorithm.
+
+If you're unhappy with the
+fact that the Lloyd-Max
+
+algorithm doesn't always work
+in one dimension, be content
+
+with the fact that it's far
+worse in two dimensions, and
+
+it gets worse and worse as you
+go to higher numbers of
+
+dimensions.
+
+So it is a local minimum,
+but not
+
+necessarily the best thing.
+
+OK, well, about that time, and
+let's go forward for maybe 10
+
+years from 1957 and '60 when
+people were inventing the
+
+Lloyd-Max algorithm and where
+they thought that quantization
+
+was a really neat academic
+problem, and many people were
+
+writing theses on it and having
+lots of fun with it.
+
+And then eventually, they
+started to realize that when
+
+you try to solve that problem
+and find the minimum, it
+
+really is just a very
+ugly problem.
+
+At least it looks like a very
+ugly problem with everything
+
+that anybody knows after
+having worked on it
+
+for a very long time.
+
+So not many people work
+on this anymore.
+
+So we stop and say, well, we
+really don't want to go too
+
+far on this because it's ugly.
+
+But then we stop and think.
+
+I mean, anytime you get stuck
+on a problem, you ought to
+
+stop and ask, well, am
+I really looking
+
+at the right problem?
+
+Now why am I or why am I not
+looking at the right problem?
+
+And remember where
+we started off.
+
+We started off with this kind
+of layered solution, which
+
+said we were going to quantize
+these things into a finite
+
+alphabet and then
+we were going to
+
+discrete code them, OK?
+
+And here what we've been
+doing for awhile,
+
+and none of you objected.
+
+Of course, it's hard to object
+at 9:30 in the morning.
+
+You just listen and you -- but
+you should have objected.
+
+You should have said why in hell
+am I choosing the number
+
+of quantization levels
+to minimize over?
+
+What should I be minimizing
+over?
+
+I should be trying to find the
+minimum mean square error
+
+conditional on the entropy
+of this output alphabet.
+
+Because the entropy of the
+output alphabet is what
+
+determines what I can accomplish
+by discrete coding.
+
+That's a slightly phony problem
+because I'm insisting,
+
+now at least to start with, that
+the quantizer is a scalar
+
+quantizer, and by using coding
+here, I'm allowing memory in
+
+the coding process.
+
+But it's not that phony
+because, in fact, this
+
+quantization job is a real
+mess, and this job
+
+is very, very easy.
+
+And, in fact, when you think
+about it a little bit, you
+
+say, OK, how do people really
+do this if they're trying to
+
+implement things?
+
+And how would you go about
+implementing something like
+
+this entire problem that
+we're talking about?
+
+What would you do if you
+had to implement it?
+
+Well, you're probably afraid to
+say it, but you would use
+
+digital signal processing,
+wouldn't you?
+
+I mean, the first thing you
+would try to do is to get rid
+
+of all these analog values, and
+you would try to turn them
+
+into discrete values, so that
+you would really, after you
+
+somehow find this sequence of
+numbers here, you would go
+
+through a quantizer and quantize
+these numbers very,
+
+very finely.
+
+You would think of them as real
+numbers, and then you
+
+would do some kind of discrete
+coding, and you would wind up
+
+with something.
+
+And then you would say, ah, I
+have quantized these things
+
+very, very finely.
+
+And we'll see that when you
+quantize it very, very finely,
+
+what you're going to wind up
+with, which is almost optimal,
+
+is a uniform scalar quantizer,
+which is just what a
+
+garden-variety analog-to-digital
+converter
+
+does for you, OK?
+
+But then you say, aha!
+
+What I can't do at that moment,
+I don't have enough
+
+bits to represent what this very
+fine quantizer has done.
+
+So then I think of this
+quantization as real numbers.
+
+I go through the same process
+again, and I think of then
+
+quantizing the real numbers
+to the number of
+
+bits I really want.
+
+Anybody catch what
+I just said?
+
+I'm saying you do this
+in two steps.
+
+The first step is a very fine
+quantization, strictly for
+
+implementation purposes and
+for no other reason.
+
+And at that point, you
+have bits to process.
+
+You do digital-signal
+processing, but you think of
+
+those bits as representing
+numbers, OK?
+
+In other words, as far as your
+thoughts are concerned, you're
+
+not dealing with the
+quantization errors that
+
+occurred here at all.
+
+You're just thinking
+of real numbers.
+
+And at that point, you try to
+design conceptually what it is
+
+you want to do in this
+process of quantizing
+
+and discrete coding.
+
+And you then go back to looking
+at these things as
+
+numbers again, and you quantize
+them again, and you
+
+discrete encode them again in
+whatever way makes sense.
+
+So you do one thing strictly for
+implementation purposes.
+
+You do the other thing for
+conceptual purposes.
+
+Then you put them together into
+something that works.
+
+And that's the way engineers
+operate all the time, I think.
+
+At least they did when I was
+more active doing real
+
+engineering.
+
+OK, so that's that.
+
+But anyway, it says finding a
+minimum mean square error
+
+quantizer for fixed M isn't the
+right problem that we're
+
+interested in.
+
+If you're going to have
+quantization followed by
+
+discrete coding, the quantizer
+should minimize mean square
+
+error for fixed representation
+point entropy.
+
+In other words, I'd
+want to find these
+
+representation points.
+
+It's important what the
+numerical values of the
+
+representation points are for
+mean square error, but I'm not
+
+interested in how many
+of them I have.
+
+What I'm interested in is
+the entropy of them.
+
+OK, so the quantizer should
+minimize mean square error for
+
+a fixed representation
+point entropy.
+
+I would like some algorithm,
+which goes through and changes
+
+my representation points,
+including perhaps changing the
+
+number of representation
+points as a
+
+way of reducing entropy.
+
+OK, sometimes you can get more
+representation points by
+
+having them out where there's
+virtually no probability, and
+
+therefore they don't happen very
+often, but when they do
+
+happen, they sure save
+you an awful lot
+
+of mean square error.
+
+So you can wind up with things
+using many, many more
+
+quantization points than you
+would think you would want
+
+because that's the optimal
+thing to do.
+
+OK, when you're given the
+regions, if we try to say what
+
+happens to the Lloyd-Max
+algorithm then, the
+
+representation points
+should still be
+
+the conditional means.
+
+Why?
+
+Anybody figure out why we want
+to solve the problem that way?
+
+If I've already figured out what
+the region should the --
+
+well, before, when I told you
+what the regions were, you
+
+told me that you wanted to make
+the representation points
+
+the conditional means.
+
+Now if I make the representation
+points
+
+something other than the
+conditional means, what's
+
+going to happen to
+the entropy?
+
+The entropy stays the same.
+
+The entropy has nothing
+to do with what
+
+you call these symbols.
+
+I can move where they are, but
+they still have the same
+
+probability because they still
+occur whenever you wind up in
+
+that region.
+
+And therefore, the entropy
+doesn't change, and therefore,
+
+the same rule holds.
+
+But now the peculiar thing is
+you don't want to make the
+
+representation regions Voronoi
+regions anymore.
+
+In other words, sometimes you
+want to make a region much
+
+closer to one point than
+to the other point.
+
+And why do you want
+to do that?
+
+Because you'd like to make these
+probabilities of the
+
+points as unequal as you can
+because you're trying to
+
+reduce entropy.
+
+And you can reduce entropy by
+making things have different
+
+probabilities.
+
+OK, so that's where we
+wind up with that.
+
+I would like to say there's
+a nice algorithm
+
+to solve this problem.
+
+There isn't.
+
+It's an incredibly
+ugly problem.
+
+You might think it makes sense
+to use a Lagrange multiplier
+
+approach and try to minimize
+some linear combination of
+
+entropy and mean square error.
+
+I've never been able
+to make it work.
+
+So anyway, let's go on.
+
+When we want to look at a
+high-rate quantizer, which is
+
+what we very often want, you
+can do a very simple
+
+approximation.
+
+And the simple approximation
+makes the problem much easier,
+
+and it gives you an
+added benefit.
+
+There's something called
+differential entropy.
+
+And differential entropy is the
+same as ordinary entropy,
+
+except instead of dealing with
+probabilities, it deals with
+
+probability densities.
+
+And you look at this, and you
+say, well, that's virtually
+
+the same thing, and it looks
+like the same thing.
+
+And to most physicists, most
+physicists look at something
+
+like this, and physicists who
+are into statistical mechanics
+
+say, oh, of course that's
+the same thing.
+
+There's no fundamental
+difference between a
+
+differential entropy
+and a real entropy.
+
+And you say, well, but
+they're all these
+
+scaling issues there.
+
+And they say, blah, that's
+not important.
+
+And they're right, because once
+you understand it, it's
+
+not important.
+
+But let's look and see what the
+similarities and what the
+
+differences are.
+
+And I'll think in terms of, in
+fact, a quantization problem,
+
+where I'm taking this
+continuous-valued random
+
+variable with density, and I'm
+quantizing it into a set of
+
+discrete points.
+
+And I want to say what's the
+difference between this
+
+differential entropy here and
+this discrete entropy, which
+
+we sort of understand by now.
+
+Well, things that are the same
+-- the first thing that's the
+
+same is the differential entropy
+is still the expected
+
+value of minus the logarithm
+of the probability density.
+
+OK, we found that that was
+useful before when we were
+
+trying to understand
+the entropy.
+
+It's the expected value
+of a log pmf.
+
+Now the differential entropy is
+expected value of a log pdf
+
+instead of pmf.
+
+And the entropy of two random
+variables, U1 and U2, if
+
+they're independent, is just the
+differential entropy of U1
+
+plus the differential
+entropy of U2.
+
+How do I see that?
+
+You just write it down.
+
+You write down these
+joint densities.
+
+You write down this.
+
+The logarithm of the joint
+density for IID splits into a
+
+product of densities.
+
+A log of a product is
+the sum of the logs.
+
+It's the same as the
+argument before.
+
+In other words, it's not only
+that this is the same as the
+
+answer that we got before,
+but the argument
+
+is exactly the same.
+
+And the other thing, the next
+thing is if you shift this
+
+density here.
+
+If I have a density, which is
+going along here and I shift
+
+it over to here and have a
+density over there, the
+
+entropy is the same again.
+
+Because this entropy is just
+fundamentally not -- it
+
+doesn't have to do with where
+you happen to be.
+
+It has to do with what these
+probability densities are.
+
+And you can stick that shift
+into here, and if you're very
+
+good at doing calculus, you can,
+in fact, see that when
+
+you put a shift in here, you
+still get the same entropy.
+
+I couldn't do that at this
+point, but I'm sure that all
+
+of you can.
+
+And I can do it if
+I spent enough
+
+time thinking it through.
+
+It would just take me longer
+than most of you.
+
+OK, so all of these things
+are still true.
+
+There a couple of
+very disturbing
+
+differences, though.
+
+And the first difference
+is that h of U
+
+is not scale invariant.
+
+And, in fact, if it were
+scale invariant, it
+
+would be totally useless.
+
+The fact that it's not scale
+invariant turns out to be very
+
+important when you try
+to understand it, OK?
+
+In other words, if you stretch
+this probability density by
+
+some quantity a, then your
+probability density, which
+
+looks like this, shifts
+like this.
+
+It shifts down and
+it shifts out.
+
+So the log of the
+pmf gets bigger.
+
+The pmf itself is just
+sort of spread out.
+
+It does what you would
+expect it to do, and
+
+that works very nicely.
+
+But the log of the pmf has this
+extra term which comes in
+
+here, which is a factor of a.
+
+And it turns out you can just
+factor that factor of a out,
+
+and you wind up with the
+differential entropy of a
+
+scaled random variable U is
+equal to the differential
+
+entropy of the original U plus
+log of a, which might be
+
+minus log of a.
+
+I'm not sure which it is.
+
+I'll write down plus
+or minus log of a.
+
+It's one or the other.
+
+I don't care at this point.
+
+All I'm interested
+in is that you
+
+recognize that it's different.
+
+An even more disturbing point
+is this differential entropy
+
+can be negative.
+
+It can be negative
+or positive.
+
+It can do whatever
+it wants to do.
+
+And so we're left with a sort
+of a peculiar thing.
+
+But we say, well, all right,
+that's the way it is.
+
+The physicists had
+to deal with that
+
+for many, many years.
+
+And the physicists, who think
+about it all the time, deal
+
+with it and say it's
+not very important.
+
+So we'll say, OK, we'll go along
+with this unless asked:
+
+What happens if we try to build
+a uniform high-rate
+
+scalar quantizer, which is
+exactly what you would do for
+
+implementation purposes
+anyway.
+
+So how does this work?
+
+You pick a little tiny delta.
+
+You have all these
+regions here.
+
+And by uniform, I mean you make
+all the regions the same.
+
+I mean, conceptually, this might
+mean having accountably
+
+infinite number of regions.
+
+Let's not worry about that
+for the time being.
+
+And you have points in here,
+which are the conditional
+
+means of the regions.
+
+Well, if I assume that delta is
+small, then the probability
+
+density of u is almost constant
+within a region, if
+
+it really is a density.
+
+And I can define an average
+value of f of u within each
+
+region in the following way.
+
+It's easier to see what it is
+graphically if I have a
+
+density here, which runs
+along like this.
+
+And within each region, I will
+choose f-bar of u to be a
+
+piecewise constant version of
+this density, which might be
+
+like that, OK?
+
+Now that's just analytical
+stuff to make
+
+things come out right.
+
+If you read the notes about how
+to do this, you find out
+
+that this quantity is important
+analytically to
+
+trace through what's going on.
+
+I think for the level that we're
+at now, it's fine to
+
+just say, OK, this is the same
+as this, if we make the
+
+quantization very small.
+
+I mean, at some point in this
+argument, you want to go
+
+through and say, OK, what do
+I mean by approximate?
+
+Is the approximation close?
+
+How does the approximation
+become better as I make delta
+
+smaller, and all of
+these questions.
+
+But let's just now say, OK, this
+is the same as that, and
+
+I'd like to find out how well
+this uniform high-rate scalar
+
+quantizer does.
+
+So my high-rate approximation
+is that this average density
+
+is the same as the true
+density and for
+
+all possible u.
+
+So conditional on u and Rj,
+this quantity is constant.
+
+It's constant and equal to 1
+over delta, and the actual
+
+density is approximately
+equal to 1 over delta.
+
+What's that mean?
+
+It means that the mean square
+error in one of these
+
+quantization regions is our
+usual delta squared over 12,
+
+which is the mean square error
+of a uniform density in a
+
+region from minus delta over
+2 to plus delta over 2.
+
+So that's the mean
+square error.
+
+You can't do anything
+with that.
+
+You're stuck with it.
+
+The next question is
+what is the entropy
+
+as a quantizer output?
+
+I'm sorry, I'm giving a typical
+MIT lecture today,
+
+which people have characterized
+as a fire hose,
+
+and it's because I want to get
+done with this material today.
+
+I think if you read the notes
+afterwards, you've got a
+
+pretty good picture of
+what's going on.
+
+We are not going to have
+an enormous number
+
+of problems on this.
+
+It's not something we're
+stressing so I want to get you
+
+to have some idea of what
+this is all about.
+
+This slide is probably the most
+important slide because
+
+it tells you what this
+differential
+
+entropy really is.
+
+OK, I'm going to look at the
+probabilities of each of these
+
+discrete points now. p sub j
+is the probability that the
+
+quantizer will get the
+point a sub j.
+
+In other words, it is the
+probability of the
+
+region R sub j.
+
+And that's just the integral
+of the probability density
+
+over the j-th region.
+
+Namely, it's the probability of
+being in that j-th region.
+
+p sub j is also equal to this
+average value times delta.
+
+OK, so I look at what
+the entropy is of
+
+the high-rate quantizer.
+
+It's the sum of minus
+pj log pj.
+
+I translate that pj is
+equal to this, so I
+
+have a sum over j.
+
+I have an integral minus a fU of
+u, which is that, times log
+
+And now I'll use this quantity
+instead of this quantity.
+
+f-bar of u times delta du.
+
+OK, in other words, these
+probabilities are scaled by
+
+delta, which is what I was
+telling you before.
+
+That's the crucial thing here.
+
+As you make delta smaller and
+smaller, the probabilities of
+
+the intervals go down
+with delta.
+
+OK, so I break this up
+into two terms now.
+
+I take out the log of delta,
+which is integrated over fU.
+
+I have this quantity left.
+
+This quantity is approximately
+equal to the density, and what
+
+I wind up with is that the
+actual entropy of the
+
+quantized version is equal to
+the differential entropy minus
+
+the log of delta at high rate.
+
+OK, that's the only way I know
+to interpret differential
+
+entropy that makes any sense,
+OK, in other words, usually
+
+when you think of integrals,
+you think of them
+
+in a Riemann sense.
+
+You think of breaking up the
+interval into lots of very
+
+thin slices with delta, and then
+you integrate things by
+
+adding up things, and that
+integral then is then a sum.
+
+It's the same as this
+kind of sum.
+
+And the integral that you wind
+up with when you're dealing
+
+with a log of the pmf, you
+get this extra delta
+
+sticking in there, OK?
+
+So this entropy is this phony
+thing minus log of delta.
+
+As I quantize more and
+more finely, this
+
+entropy keeps going up.
+
+It goes up because when delta is
+very, very small, minus log
+
+delta is a large number.
+
+So as delta gets smaller and
+smaller, this entropy heads
+
+off towards infinity.
+
+And in fact, you would expect
+that because if you take a
+
+real number, which has a
+distribution which is -- well,
+
+anything just between minus 1
+and plus 1, for example, and I
+
+want to represent it very, very
+well if it's uniformly
+
+distributed there, the better
+I try to represent it, the
+
+more bits it takes.
+
+That's what this is saying.
+
+This thing is changing as I try
+to represent things better
+
+and better.
+
+This quantity here is just some
+funny thing that deals
+
+with the shape of the
+probability density and
+
+nothing else.
+
+It essentially has a scale
+factor built into it because
+
+the probability density has a
+scale factor built into it.
+
+A probability density is
+probability per unit length.
+
+And therefore, this kind of
+entropy has to have that unit
+
+length coming in here somehow,
+and that's the
+
+way it comes in.
+
+That's the way it is.
+
+So to summarize all of that, and
+I'm sure you haven't quite
+
+understood all of it, but if
+you do efficient discrete
+
+coding at the end of the whole
+thing, the number of bits per
+
+sample, namely, per number
+coming into the quantizer that
+
+you need, is H of V, OK?
+
+With this uniform quantizer,
+which produces an entropy of
+
+the symbols H of V, then you
+L-bar bits per symbol to
+
+represent that.
+
+That's the result that
+we had before.
+
+This quantity H of V depends
+only on delta and h of U.
+
+Namely, h of U is equal to
+H of V plus log delta.
+
+So, in other words,
+analytically, the only thing
+
+you have to worry about
+is what is this
+
+differential entropy?
+
+You can't interpret what it is,
+but you can calculate it.
+
+And once you calculate it,
+this tells you what this
+
+entropy is for every
+choice of delta so
+
+long as delta is small.
+
+It says that when you get to the
+point where delta is small
+
+and the probability density is
+essentially constant over a
+
+region, if I want to make delta
+half as big as it was
+
+before, then I'm going to wind
+up with twice as many
+
+quantization regions.
+
+They're all going to
+be only half as
+
+probable as the ones before.
+
+It's going to take me
+one extra bit to
+
+represent that, OK?
+
+Namely, this one extra bit for
+each of these old regions is
+
+going to tell me whether I'm on
+the right side or the left
+
+side of that old quantization
+region to talk about the new
+
+quantization region.
+
+So this all make sense, OK?
+
+Namely, the only thing that's
+happening as you make the
+
+quantization finer and finer is
+that you have these extra
+
+bits coming in, which are sort
+of telling you what the fine
+
+structure is.
+
+And little h of U already has
+built into it the overall
+
+shape of the thing.
+
+OK, now I've added one thing
+more here, which I haven't
+
+talked about at all.
+
+This uniform scalar quantizer
+in fact becomes optimal as
+
+delta become small.
+
+And that's not obvious;
+it's not intuitive.
+
+There's an argument
+in the text that
+
+shows why that is true.
+
+It uses a Lagrange multiplier
+to do it.
+
+I guess there's a certain
+elegance to it.
+
+I mean, after years of thinking
+about it, I would
+
+say, yeah, it's pretty likely
+that it's true if I didn't
+
+have the mathematics
+to know it's true.
+
+But, in fact, it's a very
+interesting result.
+
+It says that what you do with
+classical a to z converters,
+
+if you're going to have very
+fine quantization, is, in
+
+fact, the right thing to do.
\ No newline at end of file
diff --git a/rzD4knm4--I.txt b/rzD4knm4--I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e2b9d63a9cb20178bc614f1c7f32fd577909b7ed
--- /dev/null
+++ b/rzD4knm4--I.txt
@@ -0,0 +1,571 @@
+align:start position:0%
+ 
+hi this is Tanya from the publication
+
+ align:start position:0%
+hi this is Tanya from the publication
+ 
+
+ align:start position:0%
+hi this is Tanya from the publication
+team at MIT opencourseware I'd like to
+
+ align:start position:0%
+team at MIT opencourseware I'd like to
+ 
+
+ align:start position:0%
+team at MIT opencourseware I'd like to
+show you a course called toy product
+
+ align:start position:0%
+show you a course called toy product
+ 
+
+ align:start position:0%
+show you a course called toy product
+design in this class students work in
+
+ align:start position:0%
+design in this class students work in
+ 
+
+ align:start position:0%
+design in this class students work in
+small teams to design and prototype new
+
+ align:start position:0%
+small teams to design and prototype new
+ 
+
+ align:start position:0%
+small teams to design and prototype new
+toys all of this takes place in the MIT
+
+ align:start position:0%
+toys all of this takes place in the MIT
+ 
+
+ align:start position:0%
+toys all of this takes place in the MIT
+toy lab which was founded in 2004 by
+
+ align:start position:0%
+toy lab which was founded in 2004 by
+ 
+
+ align:start position:0%
+toy lab which was founded in 2004 by
+Professor David Wallace I worked with
+
+ align:start position:0%
+Professor David Wallace I worked with
+ 
+
+ align:start position:0%
+Professor David Wallace I worked with
+graduate student Barry cudgerowitz on
+
+ align:start position:0%
+graduate student Barry cudgerowitz on
+ 
+
+ align:start position:0%
+graduate student Barry cudgerowitz on
+this course site he developed and
+
+ align:start position:0%
+this course site he developed and
+ 
+
+ align:start position:0%
+this course site he developed and
+teaches the class
+
+ align:start position:0%
+teaches the class
+ 
+
+ align:start position:0%
+teaches the class
+in the project section you'll see all of
+
+ align:start position:0%
+in the project section you'll see all of
+ 
+
+ align:start position:0%
+in the project section you'll see all of
+the things students have developed let's
+
+ align:start position:0%
+the things students have developed let's
+ 
+
+ align:start position:0%
+the things students have developed let's
+take a look at 2006 where the theme was
+
+ align:start position:0%
+take a look at 2006 where the theme was
+ 
+
+ align:start position:0%
+take a look at 2006 where the theme was
+toys to promote good dental hygiene
+
+ align:start position:0%
+toys to promote good dental hygiene
+ 
+
+ align:start position:0%
+toys to promote good dental hygiene
+here's r2d tooth he's the work of the
+
+ align:start position:0%
+here's r2d tooth he's the work of the
+ 
+
+ align:start position:0%
+here's r2d tooth he's the work of the
+red team
+
+ align:start position:0%
+red team
+ 
+
+ align:start position:0%
+red team
+they call it the ultimate robotic dental
+
+ align:start position:0%
+they call it the ultimate robotic dental
+ 
+
+ align:start position:0%
+they call it the ultimate robotic dental
+hygiene sync top assistant
+
+ align:start position:0%
+hygiene sync top assistant
+ 
+
+ align:start position:0%
+hygiene sync top assistant
+you can see that R2 holds a lightsaber
+
+ align:start position:0%
+you can see that R2 holds a lightsaber
+ 
+
+ align:start position:0%
+you can see that R2 holds a lightsaber
+toothbrush that lights up when you use
+
+ align:start position:0%
+toothbrush that lights up when you use
+ 
+
+ align:start position:0%
+toothbrush that lights up when you use
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+students worked with mentors from a
+
+ align:start position:0%
+students worked with mentors from a
+ 
+
+ align:start position:0%
+students worked with mentors from a
+local toy company and a dental hygienist
+
+ align:start position:0%
+local toy company and a dental hygienist
+ 
+
+ align:start position:0%
+local toy company and a dental hygienist
+from MIT medical to develop their ideas
+
+ align:start position:0%
+from MIT medical to develop their ideas
+ 
+
+ align:start position:0%
+from MIT medical to develop their ideas
+they also visited students at a local
+
+ align:start position:0%
+they also visited students at a local
+ 
+
+ align:start position:0%
+they also visited students at a local
+school to get feedback on their
+
+ align:start position:0%
+school to get feedback on their
+ 
+
+ align:start position:0%
+school to get feedback on their
+preliminary designs
+
+ align:start position:0%
+preliminary designs
+ 
+
+ align:start position:0%
+preliminary designs
+the theme for 2007 was toys that could
+
+ align:start position:0%
+the theme for 2007 was toys that could
+ 
+
+ align:start position:0%
+the theme for 2007 was toys that could
+be inexpensively manufactured in Brazil
+
+ align:start position:0%
+be inexpensively manufactured in Brazil
+ 
+
+ align:start position:0%
+be inexpensively manufactured in Brazil
+here's Eggman and Friends a collection
+
+ align:start position:0%
+here's Eggman and Friends a collection
+ 
+
+ align:start position:0%
+here's Eggman and Friends a collection
+of six egg-shaped tops that have a
+
+ align:start position:0%
+of six egg-shaped tops that have a
+ 
+
+ align:start position:0%
+of six egg-shaped tops that have a
+special power when you spin them such as
+
+ align:start position:0%
+special power when you spin them such as
+ 
+
+ align:start position:0%
+special power when you spin them such as
+singing each egg comes in a special egg
+
+ align:start position:0%
+singing each egg comes in a special egg
+ 
+
+ align:start position:0%
+singing each egg comes in a special egg
+carton with a lightning bolt lock
+
+ align:start position:0%
+carton with a lightning bolt lock
+ 
+
+ align:start position:0%
+carton with a lightning bolt lock
+of course it's not all just fun and play
+
+ align:start position:0%
+of course it's not all just fun and play
+ 
+
+ align:start position:0%
+of course it's not all just fun and play
+in addition to working in the toy lab
+
+ align:start position:0%
+in addition to working in the toy lab
+ 
+
+ align:start position:0%
+in addition to working in the toy lab
+students attend lectures and complete
+
+ align:start position:0%
+students attend lectures and complete
+ 
+
+ align:start position:0%
+students attend lectures and complete
+reading assignments to learn about
+
+ align:start position:0%
+reading assignments to learn about
+ 
+
+ align:start position:0%
+reading assignments to learn about
+things like ergonomics and safety
+
+ align:start position:0%
+things like ergonomics and safety
+ 
+
+ align:start position:0%
+things like ergonomics and safety
+half of the total grade is based on
+
+ align:start position:0%
+half of the total grade is based on
+ 
+
+ align:start position:0%
+half of the total grade is based on
+individual work and the other half is
+
+ align:start position:0%
+individual work and the other half is
+ 
+
+ align:start position:0%
+individual work and the other half is
+based on teamwork
+
+ align:start position:0%
+based on teamwork
+ 
+
+ align:start position:0%
+based on teamwork
+each team has to come up with three
+
+ align:start position:0%
+each team has to come up with three
+ 
+
+ align:start position:0%
+each team has to come up with three
+sketch models then select two for
+
+ align:start position:0%
+sketch models then select two for
+ 
+
+ align:start position:0%
+sketch models then select two for
+mock-up designs
+
+ align:start position:0%
+mock-up designs
+ 
+
+ align:start position:0%
+mock-up designs
+finally each team takes one of its ideas
+
+ align:start position:0%
+finally each team takes one of its ideas
+ 
+
+ align:start position:0%
+finally each team takes one of its ideas
+all the way to completion
+
+ align:start position:0%
+all the way to completion
+ 
+
+ align:start position:0%
+all the way to completion
+students are provided with many
+
+ align:start position:0%
+students are provided with many
+ 
+
+ align:start position:0%
+students are provided with many
+resources to guide them and stimulate
+
+ align:start position:0%
+resources to guide them and stimulate
+ 
+
+ align:start position:0%
+resources to guide them and stimulate
+ideas and we've included them on the
+
+ align:start position:0%
+ideas and we've included them on the
+ 
+
+ align:start position:0%
+ideas and we've included them on the
+site
+
+ align:start position:0%
+site
+ 
+
+ align:start position:0%
+site
+at the end of the course students
+
+ align:start position:0%
+at the end of the course students
+ 
+
+ align:start position:0%
+at the end of the course students
+present their prototypes at the
+
+ align:start position:0%
+present their prototypes at the
+ 
+
+ align:start position:0%
+present their prototypes at the
+playsentations an event where they
+
+ align:start position:0%
+playsentations an event where they
+ 
+
+ align:start position:0%
+playsentations an event where they
+present their work to toy designers
+
+ align:start position:0%
+present their work to toy designers
+ 
+
+ align:start position:0%
+present their work to toy designers
+Engineers elementary schools children
+
+ align:start position:0%
+Engineers elementary schools children
+ 
+
+ align:start position:0%
+Engineers elementary schools children
+and the MIT community
+
+ align:start position:0%
+and the MIT community
+ 
+
+ align:start position:0%
+and the MIT community
+by the way ocw's site for toy product
+
+ align:start position:0%
+by the way ocw's site for toy product
+ 
+
+ align:start position:0%
+by the way ocw's site for toy product
+design can be downloaded for use offline
+
+ align:start position:0%
+design can be downloaded for use offline
+ 
+
+ align:start position:0%
+design can be downloaded for use offline
+the link and instructions are right here
+
+ align:start position:0%
+the link and instructions are right here
+ 
+
+ align:start position:0%
+the link and instructions are right here
+I enjoyed working on this course and I
+
+ align:start position:0%
+I enjoyed working on this course and I
+ 
+
+ align:start position:0%
+I enjoyed working on this course and I
+hope you'll enjoy exploring it
+
+ align:start position:0%
+hope you'll enjoy exploring it
+ 
+
+ align:start position:0%
+hope you'll enjoy exploring it
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can explore more courses like this
+
+ align:start position:0%
+you can explore more courses like this
+ 
+
+ align:start position:0%
+you can explore more courses like this
+one at
+
+ align:start position:0%
+one at
+ 
+
+ align:start position:0%
+one at
+ocw.mit.edu or get email updates from
+
+ align:start position:0%
+ocw.mit.edu or get email updates from
+ 
+
+ align:start position:0%
+ocw.mit.edu or get email updates from
+MIT opencourseware by subscribing to our
+
+ align:start position:0%
+MIT opencourseware by subscribing to our
+ 
+
+ align:start position:0%
+MIT opencourseware by subscribing to our
+monthly newsletter we hope you'll help
+
+ align:start position:0%
+monthly newsletter we hope you'll help
+ 
+
+ align:start position:0%
+monthly newsletter we hope you'll help
+us keep going and growing by making a
+
+ align:start position:0%
+us keep going and growing by making a
+ 
+
+ align:start position:0%
+us keep going and growing by making a
+donation at
+
+ align:start position:0%
+donation at
+ 
+
+ align:start position:0%
+donation at
+ocw.mit.edu donate
\ No newline at end of file
diff --git a/s8dZi6eqsJU.txt b/s8dZi6eqsJU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..14ecaa970fb4cc4bf7b992fb952c1e80057ec4fa
--- /dev/null
+++ b/s8dZi6eqsJU.txt
@@ -0,0 +1,4243 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I'm Arvin and this is Micah and we
+
+ align:start position:0%
+So I'm Arvin and this is Micah and we
+ 
+
+ align:start position:0%
+So I'm Arvin and this is Micah and we
+work together on a framework for
+
+ align:start position:0%
+work together on a framework for
+ 
+
+ align:start position:0%
+work together on a framework for
+flexible stream processing on the cell.
+
+ align:start position:0%
+flexible stream processing on the cell.
+ 
+
+ align:start position:0%
+flexible stream processing on the cell.
+So we were also oriented towards an
+
+ align:start position:0%
+So we were also oriented towards an
+ 
+
+ align:start position:0%
+So we were also oriented towards an
+application which is in this case is
+
+ align:start position:0%
+application which is in this case is
+ 
+
+ align:start position:0%
+application which is in this case is
+software radio and we use this
+
+ align:start position:0%
+software radio and we use this
+ 
+
+ align:start position:0%
+software radio and we use this
+application as a case study. Where's the
+
+ align:start position:0%
+application as a case study. Where's the
+ 
+
+ align:start position:0%
+application as a case study. Where's the
+mic? Okay, I'll try and speak as loud as
+
+ align:start position:0%
+mic? Okay, I'll try and speak as loud as
+ 
+
+ align:start position:0%
+mic? Okay, I'll try and speak as loud as
+I can. So our project was about flexible
+
+ align:start position:0%
+I can. So our project was about flexible
+ 
+
+ align:start position:0%
+I can. So our project was about flexible
+flexible stream processing framework for
+
+ align:start position:0%
+flexible stream processing framework for
+ 
+
+ align:start position:0%
+flexible stream processing framework for
+the cell and we used the software radio
+
+ align:start position:0%
+the cell and we used the software radio
+ 
+
+ align:start position:0%
+the cell and we used the software radio
+as an as a case study essentially of an
+
+ align:start position:0%
+as an as a case study essentially of an
+ 
+
+ align:start position:0%
+as an as a case study essentially of an
+application we could build using this
+
+ align:start position:0%
+application we could build using this
+ 
+
+ align:start position:0%
+application we could build using this
+framework. The motivation for our
+
+ align:start position:0%
+framework. The motivation for our
+ 
+
+ align:start position:0%
+framework. The motivation for our
+project is essentially what we've been
+
+ align:start position:0%
+project is essentially what we've been
+ 
+
+ align:start position:0%
+project is essentially what we've been
+discussing in class. It's been
+
+ align:start position:0%
+discussing in class. It's been
+ 
+
+ align:start position:0%
+discussing in class. It's been
+reiterated. The cell isn't easy to
+
+ align:start position:0%
+reiterated. The cell isn't easy to
+ 
+
+ align:start position:0%
+reiterated. The cell isn't easy to
+program. There's no shared memory.
+
+ align:start position:0%
+program. There's no shared memory.
+ 
+
+ align:start position:0%
+program. There's no shared memory.
+There's just message passing which is
+
+ align:start position:0%
+There's just message passing which is
+ 
+
+ align:start position:0%
+There's just message passing which is
+quite messy. You have to explicitly
+
+ align:start position:0%
+quite messy. You have to explicitly
+ 
+
+ align:start position:0%
+quite messy. You have to explicitly
+paralyze your programs if you want to
+
+ align:start position:0%
+paralyze your programs if you want to
+ 
+
+ align:start position:0%
+paralyze your programs if you want to
+write them as say custom C programs.
+
+ align:start position:0%
+write them as say custom C programs.
+ 
+
+ align:start position:0%
+write them as say custom C programs.
+Some of the groups have described the
+
+ align:start position:0%
+Some of the groups have described the
+ 
+
+ align:start position:0%
+Some of the groups have described the
+challenges they faced when doing that.
+
+ align:start position:0%
+challenges they faced when doing that.
+ 
+
+ align:start position:0%
+challenges they faced when doing that.
+Extracting parallelism can be tricky.
+
+ align:start position:0%
+Extracting parallelism can be tricky.
+ 
+
+ align:start position:0%
+Extracting parallelism can be tricky.
+For example, if you want to do
+
+ align:start position:0%
+For example, if you want to do
+ 
+
+ align:start position:0%
+For example, if you want to do
+pipelining, then on the SPEs, you have
+
+ align:start position:0%
+pipelining, then on the SPEs, you have
+ 
+
+ align:start position:0%
+pipelining, then on the SPEs, you have
+to predict what addresses you're going
+
+ align:start position:0%
+to predict what addresses you're going
+ 
+
+ align:start position:0%
+to predict what addresses you're going
+to require and set up the DMA so that
+
+ align:start position:0%
+to require and set up the DMA so that
+ 
+
+ align:start position:0%
+to require and set up the DMA so that
+those addresses are fetched in advance.
+
+ align:start position:0%
+those addresses are fetched in advance.
+ 
+
+ align:start position:0%
+those addresses are fetched in advance.
+And as Bill mentioned in his talk in
+
+ align:start position:0%
+And as Bill mentioned in his talk in
+ 
+
+ align:start position:0%
+And as Bill mentioned in his talk in
+class, stream programming can help
+
+ align:start position:0%
+class, stream programming can help
+ 
+
+ align:start position:0%
+class, stream programming can help
+alleviate some of these issues for some
+
+ align:start position:0%
+alleviate some of these issues for some
+ 
+
+ align:start position:0%
+alleviate some of these issues for some
+applications like software radio where
+
+ align:start position:0%
+applications like software radio where
+ 
+
+ align:start position:0%
+applications like software radio where
+the applications fit naturally into the
+
+ align:start position:0%
+the applications fit naturally into the
+ 
+
+ align:start position:0%
+the applications fit naturally into the
+streaming model. So what we tried to do
+
+ align:start position:0%
+streaming model. So what we tried to do
+ 
+
+ align:start position:0%
+streaming model. So what we tried to do
+for our project was build a lightweight
+
+ align:start position:0%
+for our project was build a lightweight
+ 
+
+ align:start position:0%
+for our project was build a lightweight
+as lightweight as possible because the
+
+ align:start position:0%
+as lightweight as possible because the
+ 
+
+ align:start position:0%
+as lightweight as possible because the
+code has to fit on the SPEs
+
+ align:start position:0%
+code has to fit on the SPEs
+ 
+
+ align:start position:0%
+code has to fit on the SPEs
+but as expressive as possible as well so
+
+ align:start position:0%
+but as expressive as possible as well so
+ 
+
+ align:start position:0%
+but as expressive as possible as well so
+as to simplify life for developers. The
+
+ align:start position:0%
+as to simplify life for developers. The
+ 
+
+ align:start position:0%
+as to simplify life for developers. The
+streaming framework which is targeted
+
+ align:start position:0%
+streaming framework which is targeted
+ 
+
+ align:start position:0%
+streaming framework which is targeted
+specifically at signal processing
+
+ align:start position:0%
+specifically at signal processing
+ 
+
+ align:start position:0%
+specifically at signal processing
+applications. So this is based on the
+
+ align:start position:0%
+applications. So this is based on the
+ 
+
+ align:start position:0%
+applications. So this is based on the
+data model at least is based on a
+
+ align:start position:0%
+data model at least is based on a
+ 
+
+ align:start position:0%
+data model at least is based on a
+research project that I have worked on
+
+ align:start position:0%
+research project that I have worked on
+ 
+
+ align:start position:0%
+research project that I have worked on
+in the past which is wave scope
+
+ align:start position:0%
+in the past which is wave scope
+ 
+
+ align:start position:0%
+in the past which is wave scope
+streaming database management system is
+
+ align:start position:0%
+streaming database management system is
+ 
+
+ align:start position:0%
+streaming database management system is
+a research project in the database
+
+ align:start position:0%
+a research project in the database
+ 
+
+ align:start position:0%
+a research project in the database
+group. The data model is essentially an
+
+ align:start position:0%
+group. The data model is essentially an
+ 
+
+ align:start position:0%
+group. The data model is essentially an
+extension of the streaming model to
+
+ align:start position:0%
+extension of the streaming model to
+ 
+
+ align:start position:0%
+extension of the streaming model to
+handle larger blocks of data so as to
+
+ align:start position:0%
+handle larger blocks of data so as to
+ 
+
+ align:start position:0%
+handle larger blocks of data so as to
+process them better. For example,
+
+ align:start position:0%
+process them better. For example,
+ 
+
+ align:start position:0%
+process them better. For example,
+several signal processing operators like
+
+ align:start position:0%
+several signal processing operators like
+ 
+
+ align:start position:0%
+several signal processing operators like
+the fast 4 year transform need to do
+
+ align:start position:0%
+the fast 4 year transform need to do
+ 
+
+ align:start position:0%
+the fast 4 year transform need to do
+multiple passes over their data and
+
+ align:start position:0%
+multiple passes over their data and
+ 
+
+ align:start position:0%
+multiple passes over their data and
+therefore trying to treat streams on a
+
+ align:start position:0%
+therefore trying to treat streams on a
+ 
+
+ align:start position:0%
+therefore trying to treat streams on a
+sample by sample basis leads to high
+
+ align:start position:0%
+sample by sample basis leads to high
+ 
+
+ align:start position:0%
+sample by sample basis leads to high
+cost scheduling overhead as well as
+
+ align:start position:0%
+cost scheduling overhead as well as
+ 
+
+ align:start position:0%
+cost scheduling overhead as well as
+inefficiency.
+
+ align:start position:0%
+inefficiency.
+ 
+
+ align:start position:0%
+inefficiency.
+So that's what the data model does and
+
+ align:start position:0%
+So that's what the data model does and
+ 
+
+ align:start position:0%
+So that's what the data model does and
+we tried to port this data model over to
+
+ align:start position:0%
+we tried to port this data model over to
+ 
+
+ align:start position:0%
+we tried to port this data model over to
+the cell processor and see how well we
+
+ align:start position:0%
+the cell processor and see how well we
+ 
+
+ align:start position:0%
+the cell processor and see how well we
+could exploit the features of the cell
+
+ align:start position:0%
+could exploit the features of the cell
+ 
+
+ align:start position:0%
+could exploit the features of the cell
+processor in particular the high onchip
+
+ align:start position:0%
+processor in particular the high onchip
+ 
+
+ align:start position:0%
+processor in particular the high onchip
+bandwidth between the SPEs to do
+
+ align:start position:0%
+bandwidth between the SPEs to do
+ 
+
+ align:start position:0%
+bandwidth between the SPEs to do
+streaming. So our case study was as you
+
+ align:start position:0%
+streaming. So our case study was as you
+ 
+
+ align:start position:0%
+streaming. So our case study was as you
+mentioned a simple software radio
+
+ align:start position:0%
+mentioned a simple software radio
+ 
+
+ align:start position:0%
+mentioned a simple software radio
+application it's really simple uses uh
+
+ align:start position:0%
+application it's really simple uses uh
+ 
+
+ align:start position:0%
+application it's really simple uses uh
+incoherent um demodulation as well as
+
+ align:start position:0%
+incoherent um demodulation as well as
+ 
+
+ align:start position:0%
+incoherent um demodulation as well as
+just simple amplitude shift key
+
+ align:start position:0%
+just simple amplitude shift key
+ 
+
+ align:start position:0%
+just simple amplitude shift key
+modulation.
+
+ align:start position:0%
+modulation.
+ 
+
+ align:start position:0%
+modulation.
+As I said, the main goals of our
+
+ align:start position:0%
+As I said, the main goals of our
+ 
+
+ align:start position:0%
+As I said, the main goals of our
+framework are to simplify life and
+
+ align:start position:0%
+framework are to simplify life and
+ 
+
+ align:start position:0%
+framework are to simplify life and
+automate as much parallelism as
+
+ align:start position:0%
+automate as much parallelism as
+ 
+
+ align:start position:0%
+automate as much parallelism as
+possible. Try and extract pipeline
+
+ align:start position:0%
+possible. Try and extract pipeline
+ 
+
+ align:start position:0%
+possible. Try and extract pipeline
+parallelism, data parallelism, some of
+
+ align:start position:0%
+parallelism, data parallelism, some of
+ 
+
+ align:start position:0%
+parallelism, data parallelism, some of
+the kinds of parallelism bill mentioned.
+
+ align:start position:0%
+the kinds of parallelism bill mentioned.
+ 
+
+ align:start position:0%
+the kinds of parallelism bill mentioned.
+The kind of parallelism we were able to
+
+ align:start position:0%
+The kind of parallelism we were able to
+ 
+
+ align:start position:0%
+The kind of parallelism we were able to
+finally implement. So far, it's only
+
+ align:start position:0%
+finally implement. So far, it's only
+ 
+
+ align:start position:0%
+finally implement. So far, it's only
+pipeline parallelism, but as future
+
+ align:start position:0%
+pipeline parallelism, but as future
+ 
+
+ align:start position:0%
+pipeline parallelism, but as future
+work, we'd be interested in the other
+
+ align:start position:0%
+work, we'd be interested in the other
+ 
+
+ align:start position:0%
+work, we'd be interested in the other
+kinds of parallelism as well. More about
+
+ align:start position:0%
+kinds of parallelism as well. More about
+ 
+
+ align:start position:0%
+kinds of parallelism as well. More about
+it as I go on. So, in our in the
+
+ align:start position:0%
+it as I go on. So, in our in the
+ 
+
+ align:start position:0%
+it as I go on. So, in our in the
+framework, we at least implemented the
+
+ align:start position:0%
+framework, we at least implemented the
+ 
+
+ align:start position:0%
+framework, we at least implemented the
+programming model is quite simple. The
+
+ align:start position:0%
+programming model is quite simple. The
+ 
+
+ align:start position:0%
+programming model is quite simple. The
+basic execution unit is what we call an
+
+ align:start position:0%
+basic execution unit is what we call an
+ 
+
+ align:start position:0%
+basic execution unit is what we call an
+operator. It's analogist to what in
+
+ align:start position:0%
+operator. It's analogist to what in
+ 
+
+ align:start position:0%
+operator. It's analogist to what in
+stream it would be called a work
+
+ align:start position:0%
+stream it would be called a work
+ 
+
+ align:start position:0%
+stream it would be called a work
+function or what in glue radio which is
+
+ align:start position:0%
+function or what in glue radio which is
+ 
+
+ align:start position:0%
+function or what in glue radio which is
+a framework for building software radios
+
+ align:start position:0%
+a framework for building software radios
+ 
+
+ align:start position:0%
+a framework for building software radios
+would be called a block. So these
+
+ align:start position:0%
+would be called a block. So these
+ 
+
+ align:start position:0%
+would be called a block. So these
+operators can be any arbitrary C++
+
+ align:start position:0%
+operators can be any arbitrary C++
+ 
+
+ align:start position:0%
+operators can be any arbitrary C++
+classes with state and they implement uh
+
+ align:start position:0%
+classes with state and they implement uh
+ 
+
+ align:start position:0%
+classes with state and they implement uh
+an iterate method which the developer
+
+ align:start position:0%
+an iterate method which the developer
+ 
+
+ align:start position:0%
+an iterate method which the developer
+has to overload in order to process a
+
+ align:start position:0%
+has to overload in order to process a
+ 
+
+ align:start position:0%
+has to overload in order to process a
+block of data. Uh the waves scope data
+
+ align:start position:0%
+block of data. Uh the waves scope data
+ 
+
+ align:start position:0%
+block of data. Uh the waves scope data
+model also provides a library for
+
+ align:start position:0%
+model also provides a library for
+ 
+
+ align:start position:0%
+model also provides a library for
+managing memory and passing blocks of
+
+ align:start position:0%
+managing memory and passing blocks of
+ 
+
+ align:start position:0%
+managing memory and passing blocks of
+signal data between these operators.
+
+ align:start position:0%
+signal data between these operators.
+ 
+
+ align:start position:0%
+signal data between these operators.
+Applications in this model are built by
+
+ align:start position:0%
+Applications in this model are built by
+ 
+
+ align:start position:0%
+Applications in this model are built by
+chaining operators together. So this is
+
+ align:start position:0%
+chaining operators together. So this is
+ 
+
+ align:start position:0%
+chaining operators together. So this is
+a snippet of some of the code we wrote
+
+ align:start position:0%
+a snippet of some of the code we wrote
+ 
+
+ align:start position:0%
+a snippet of some of the code we wrote
+for the software radio roughly. U so you
+
+ align:start position:0%
+for the software radio roughly. U so you
+ 
+
+ align:start position:0%
+for the software radio roughly. U so you
+create a box let's say a fur filter
+
+ align:start position:0%
+create a box let's say a fur filter
+ 
+
+ align:start position:0%
+create a box let's say a fur filter
+which processes elements of type float
+
+ align:start position:0%
+which processes elements of type float
+ 
+
+ align:start position:0%
+which processes elements of type float
+and then it takes in some arguments
+
+ align:start position:0%
+and then it takes in some arguments
+ 
+
+ align:start position:0%
+and then it takes in some arguments
+initialize the filters parameters and so
+
+ align:start position:0%
+initialize the filters parameters and so
+ 
+
+ align:start position:0%
+initialize the filters parameters and so
+on. You want to create a white noise
+
+ align:start position:0%
+on. You want to create a white noise
+ 
+
+ align:start position:0%
+on. You want to create a white noise
+generator and hook up the filter to the
+
+ align:start position:0%
+generator and hook up the filter to the
+ 
+
+ align:start position:0%
+generator and hook up the filter to the
+white noise generator. We use this to
+
+ align:start position:0%
+white noise generator. We use this to
+ 
+
+ align:start position:0%
+white noise generator. We use this to
+simulate a simple channel whis channel.
+
+ align:start position:0%
+simulate a simple channel whis channel.
+ 
+
+ align:start position:0%
+simulate a simple channel whis channel.
+So I'll just describe the components of
+
+ align:start position:0%
+So I'll just describe the components of
+ 
+
+ align:start position:0%
+So I'll just describe the components of
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+framework. Uh we have a lightweight
+
+ align:start position:0%
+framework. Uh we have a lightweight
+ 
+
+ align:start position:0%
+framework. Uh we have a lightweight
+scheduleuler on both the PPE as well as
+
+ align:start position:0%
+scheduleuler on both the PPE as well as
+ 
+
+ align:start position:0%
+scheduleuler on both the PPE as well as
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+SPEs. Uh right now it uses a static
+
+ align:start position:0%
+SPEs. Uh right now it uses a static
+ 
+
+ align:start position:0%
+SPEs. Uh right now it uses a static
+operator mapping in the sense that you
+
+ align:start position:0%
+operator mapping in the sense that you
+ 
+
+ align:start position:0%
+operator mapping in the sense that you
+have to specify a static configuration
+
+ align:start position:0%
+have to specify a static configuration
+ 
+
+ align:start position:0%
+have to specify a static configuration
+file where you say this operator name
+
+ align:start position:0%
+file where you say this operator name
+ 
+
+ align:start position:0%
+file where you say this operator name
+will run on this SP SPU number. But uh
+
+ align:start position:0%
+will run on this SP SPU number. But uh
+ 
+
+ align:start position:0%
+will run on this SP SPU number. But uh
+we've we've not completely implemented
+
+ align:start position:0%
+we've we've not completely implemented
+ 
+
+ align:start position:0%
+we've we've not completely implemented
+dynamically reconfiguring it at runtime
+
+ align:start position:0%
+dynamically reconfiguring it at runtime
+ 
+
+ align:start position:0%
+dynamically reconfiguring it at runtime
+and we haven't yet seen the need for
+
+ align:start position:0%
+and we haven't yet seen the need for
+ 
+
+ align:start position:0%
+and we haven't yet seen the need for
+doing that. So it it wouldn't be too
+
+ align:start position:0%
+doing that. So it it wouldn't be too
+ 
+
+ align:start position:0%
+doing that. So it it wouldn't be too
+hard to add if needed, but right now you
+
+ align:start position:0%
+hard to add if needed, but right now you
+ 
+
+ align:start position:0%
+hard to add if needed, but right now you
+can easily shuffle around the operator
+
+ align:start position:0%
+can easily shuffle around the operator
+ 
+
+ align:start position:0%
+can easily shuffle around the operator
+mapping by tweaking the configuration
+
+ align:start position:0%
+mapping by tweaking the configuration
+ 
+
+ align:start position:0%
+mapping by tweaking the configuration
+file. Signal blocks as I said were
+
+ align:start position:0%
+file. Signal blocks as I said were
+ 
+
+ align:start position:0%
+file. Signal blocks as I said were
+adapted from wave scope. Uh they use
+
+ align:start position:0%
+adapted from wave scope. Uh they use
+ 
+
+ align:start position:0%
+adapted from wave scope. Uh they use
+reference counting and avoid in-memory
+
+ align:start position:0%
+reference counting and avoid in-memory
+ 
+
+ align:start position:0%
+reference counting and avoid in-memory
+copies which can be quite expensive
+
+ align:start position:0%
+copies which can be quite expensive
+ 
+
+ align:start position:0%
+copies which can be quite expensive
+especially on the cell. Uh they also
+
+ align:start position:0%
+especially on the cell. Uh they also
+ 
+
+ align:start position:0%
+especially on the cell. Uh they also
+provide a convenient API to manipulate
+
+ align:start position:0%
+provide a convenient API to manipulate
+ 
+
+ align:start position:0%
+provide a convenient API to manipulate
+signals. So you don't have to do much of
+
+ align:start position:0%
+signals. So you don't have to do much of
+ 
+
+ align:start position:0%
+signals. So you don't have to do much of
+the memory management yourself or debug
+
+ align:start position:0%
+the memory management yourself or debug
+ 
+
+ align:start position:0%
+the memory management yourself or debug
+any of the hard problems to do with
+
+ align:start position:0%
+any of the hard problems to do with
+ 
+
+ align:start position:0%
+any of the hard problems to do with
+memory management. uh we also ported
+
+ align:start position:0%
+memory management. uh we also ported
+ 
+
+ align:start position:0%
+memory management. uh we also ported
+this library to ensure that data is
+
+ align:start position:0%
+this library to ensure that data is
+ 
+
+ align:start position:0%
+this library to ensure that data is
+aligned for you automatically and
+
+ align:start position:0%
+aligned for you automatically and
+ 
+
+ align:start position:0%
+aligned for you automatically and
+transported
+
+ align:start position:0%
+transported
+ 
+
+ align:start position:0%
+transported
+uh via cues. So one of the major things
+
+ align:start position:0%
+uh via cues. So one of the major things
+ 
+
+ align:start position:0%
+uh via cues. So one of the major things
+we had to implement was a queuing
+
+ align:start position:0%
+we had to implement was a queuing
+ 
+
+ align:start position:0%
+we had to implement was a queuing
+library and a remote heap management.
+
+ align:start position:0%
+library and a remote heap management.
+ 
+
+ align:start position:0%
+library and a remote heap management.
+What amounted essentially to a remote
+
+ align:start position:0%
+What amounted essentially to a remote
+ 
+
+ align:start position:0%
+What amounted essentially to a remote
+heap management library? So in some
+
+ align:start position:0%
+heap management library? So in some
+ 
+
+ align:start position:0%
+heap management library? So in some
+sense we faced a choice here. We could
+
+ align:start position:0%
+sense we faced a choice here. We could
+ 
+
+ align:start position:0%
+sense we faced a choice here. We could
+either have the PPE control and allocate
+
+ align:start position:0%
+either have the PPE control and allocate
+ 
+
+ align:start position:0%
+either have the PPE control and allocate
+memory statically and make all the
+
+ align:start position:0%
+memory statically and make all the
+ 
+
+ align:start position:0%
+memory statically and make all the
+decisions about what memory is allocated
+
+ align:start position:0%
+decisions about what memory is allocated
+ 
+
+ align:start position:0%
+decisions about what memory is allocated
+where or we could have the SPS manage it
+
+ align:start position:0%
+where or we could have the SPS manage it
+ 
+
+ align:start position:0%
+where or we could have the SPS manage it
+themselves. We decided to go for the
+
+ align:start position:0%
+themselves. We decided to go for the
+ 
+
+ align:start position:0%
+themselves. We decided to go for the
+latter uh partly because it was more
+
+ align:start position:0%
+latter uh partly because it was more
+ 
+
+ align:start position:0%
+latter uh partly because it was more
+dynamic and also because we weren't sure
+
+ align:start position:0%
+dynamic and also because we weren't sure
+ 
+
+ align:start position:0%
+dynamic and also because we weren't sure
+what the implications of all the control
+
+ align:start position:0%
+what the implications of all the control
+ 
+
+ align:start position:0%
+what the implications of all the control
+flow passing through the PPE were for
+
+ align:start position:0%
+flow passing through the PPE were for
+ 
+
+ align:start position:0%
+flow passing through the PPE were for
+this. So we chose the second approach
+
+ align:start position:0%
+this. So we chose the second approach
+ 
+
+ align:start position:0%
+this. So we chose the second approach
+which is autonomous memory management.
+
+ align:start position:0%
+which is autonomous memory management.
+ 
+
+ align:start position:0%
+which is autonomous memory management.
+So when an SP sends a streaming data
+
+ align:start position:0%
+So when an SP sends a streaming data
+ 
+
+ align:start position:0%
+So when an SP sends a streaming data
+element to another SP, it can it doesn't
+
+ align:start position:0%
+element to another SP, it can it doesn't
+ 
+
+ align:start position:0%
+element to another SP, it can it doesn't
+have to actually explicitly request the
+
+ align:start position:0%
+have to actually explicitly request the
+ 
+
+ align:start position:0%
+have to actually explicitly request the
+other SP for allocating memory. It has a
+
+ align:start position:0%
+other SP for allocating memory. It has a
+ 
+
+ align:start position:0%
+other SP for allocating memory. It has a
+remote heap interface so that it can
+
+ align:start position:0%
+remote heap interface so that it can
+ 
+
+ align:start position:0%
+remote heap interface so that it can
+directly allocate data and write to the
+
+ align:start position:0%
+directly allocate data and write to the
+ 
+
+ align:start position:0%
+directly allocate data and write to the
+SP. This is currently of fixed size. Um
+
+ align:start position:0%
+SP. This is currently of fixed size. Um
+ 
+
+ align:start position:0%
+SP. This is currently of fixed size. Um
+but it could be improved by using this
+
+ align:start position:0%
+but it could be improved by using this
+ 
+
+ align:start position:0%
+but it could be improved by using this
+heap to share a bunch of cues. Right now
+
+ align:start position:0%
+heap to share a bunch of cues. Right now
+ 
+
+ align:start position:0%
+heap to share a bunch of cues. Right now
+we have one remote heap for each que uh
+
+ align:start position:0%
+we have one remote heap for each que uh
+ 
+
+ align:start position:0%
+we have one remote heap for each que uh
+between operators on different SPEs.
+
+ align:start position:0%
+between operators on different SPEs.
+ 
+
+ align:start position:0%
+between operators on different SPEs.
+Uh so our system automatically handles
+
+ align:start position:0%
+Uh so our system automatically handles
+ 
+
+ align:start position:0%
+Uh so our system automatically handles
+pipelining and streaming data from SP to
+
+ align:start position:0%
+pipelining and streaming data from SP to
+ 
+
+ align:start position:0%
+pipelining and streaming data from SP to
+SP using the DMA
+
+ align:start position:0%
+SP using the DMA
+ 
+
+ align:start position:0%
+SP using the DMA
+API. So Micah will take over from here
+
+ align:start position:0%
+API. So Micah will take over from here
+ 
+
+ align:start position:0%
+API. So Micah will take over from here
+and describe the software radio
+
+ align:start position:0%
+and describe the software radio
+ 
+
+ align:start position:0%
+and describe the software radio
+implementation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+briefly. Either stay on the side where
+
+ align:start position:0%
+briefly. Either stay on the side where
+ 
+
+ align:start position:0%
+briefly. Either stay on the side where
+the phone is or move from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So, so our software radio implementation
+
+ align:start position:0%
+So, so our software radio implementation
+ 
+
+ align:start position:0%
+So, so our software radio implementation
+is is relatively simple. Um, we weren't
+
+ align:start position:0%
+is is relatively simple. Um, we weren't
+ 
+
+ align:start position:0%
+is is relatively simple. Um, we weren't
+we weren't pushing on that too hard,
+
+ align:start position:0%
+we weren't pushing on that too hard,
+ 
+
+ align:start position:0%
+we weren't pushing on that too hard,
+especially because it took the vast
+
+ align:start position:0%
+especially because it took the vast
+ 
+
+ align:start position:0%
+especially because it took the vast
+majority of our time just to get the
+
+ align:start position:0%
+majority of our time just to get the
+ 
+
+ align:start position:0%
+majority of our time just to get the
+framework to work. Um, saving the
+
+ align:start position:0%
+framework to work. Um, saving the
+ 
+
+ align:start position:0%
+framework to work. Um, saving the
+programmer trouble meant that we
+
+ align:start position:0%
+programmer trouble meant that we
+ 
+
+ align:start position:0%
+programmer trouble meant that we
+inherited a lot of trouble ourselves.
+
+ align:start position:0%
+inherited a lot of trouble ourselves.
+ 
+
+ align:start position:0%
+inherited a lot of trouble ourselves.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+um, it breaks down into about 25 boxes.
+
+ align:start position:0%
+um, it breaks down into about 25 boxes.
+ 
+
+ align:start position:0%
+um, it breaks down into about 25 boxes.
+um which which we took in our config
+
+ align:start position:0%
+um which which we took in our config
+ 
+
+ align:start position:0%
+um which which we took in our config
+file which is manually map mapped to
+
+ align:start position:0%
+file which is manually map mapped to
+ 
+
+ align:start position:0%
+file which is manually map mapped to
+mapped to the to the SPEs um about about
+
+ align:start position:0%
+mapped to the to the SPEs um about about
+ 
+
+ align:start position:0%
+mapped to the to the SPEs um about about
+3,000 lines of code most of which is
+
+ align:start position:0%
+3,000 lines of code most of which is
+ 
+
+ align:start position:0%
+3,000 lines of code most of which is
+most of which is framework
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so I guess if it were to put together
+
+ align:start position:0%
+um so I guess if it were to put together
+ 
+
+ align:start position:0%
+um so I guess if it were to put together
+we'd have a nice diagram to show you I
+
+ align:start position:0%
+we'd have a nice diagram to show you I
+ 
+
+ align:start position:0%
+we'd have a nice diagram to show you I
+will there's enough time I'll try to
+
+ align:start position:0%
+will there's enough time I'll try to
+ 
+
+ align:start position:0%
+will there's enough time I'll try to
+draw a quick diagram on the chalkboard
+
+ align:start position:0%
+draw a quick diagram on the chalkboard
+ 
+
+ align:start position:0%
+draw a quick diagram on the chalkboard
+um so we're simul we're simulating both
+
+ align:start position:0%
+um so we're simul we're simulating both
+ 
+
+ align:start position:0%
+um so we're simul we're simulating both
+sender receiver and a channel. Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so that this is so the the the
+
+ align:start position:0%
+so so that this is so the the the
+ 
+
+ align:start position:0%
+so so that this is so the the the
+computation in question looks something
+
+ align:start position:0%
+computation in question looks something
+ 
+
+ align:start position:0%
+computation in question looks something
+like you have a a bit
+
+ align:start position:0%
+like you have a a bit
+ 
+
+ align:start position:0%
+like you have a a bit
+stream. You need to take these and
+
+ align:start position:0%
+stream. You need to take these and
+ 
+
+ align:start position:0%
+stream. You need to take these and
+convert them into some
+
+ align:start position:0%
+convert them into some
+ 
+
+ align:start position:0%
+convert them into some
+Can you can you read anything? Yeah. All
+
+ align:start position:0%
+Can you can you read anything? Yeah. All
+ 
+
+ align:start position:0%
+Can you can you read anything? Yeah. All
+right.
+
+ align:start position:0%
+right.
+ 
+
+ align:start position:0%
+right.
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lovely. All right. Um so you take stream
+
+ align:start position:0%
+Lovely. All right. Um so you take stream
+ 
+
+ align:start position:0%
+Lovely. All right. Um so you take stream
+of bits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in.
+
+ align:start position:0%
+in.
+ 
+
+ align:start position:0%
+in.
+Um take bits um basically sort of sort
+
+ align:start position:0%
+Um take bits um basically sort of sort
+ 
+
+ align:start position:0%
+Um take bits um basically sort of sort
+of use a lookup mechanism to convert it
+
+ align:start position:0%
+of use a lookup mechanism to convert it
+ 
+
+ align:start position:0%
+of use a lookup mechanism to convert it
+to an analog waveform. Um and filter
+
+ align:start position:0%
+to an analog waveform. Um and filter
+ 
+
+ align:start position:0%
+to an analog waveform. Um and filter
+that to produce something that has a
+
+ align:start position:0%
+that to produce something that has a
+ 
+
+ align:start position:0%
+that to produce something that has a
+narrower
+
+ align:start position:0%
+narrower
+ 
+
+ align:start position:0%
+narrower
+spectrum.
+
+ align:start position:0%
+spectrum.
+ 
+
+ align:start position:0%
+spectrum.
+Um I'm running out of space here. Mix
+
+ align:start position:0%
+Um I'm running out of space here. Mix
+ 
+
+ align:start position:0%
+Um I'm running out of space here. Mix
+that multiply that against the sine
+
+ align:start position:0%
+that multiply that against the sine
+ 
+
+ align:start position:0%
+that multiply that against the sine
+wave modulation. Um and so you get you
+
+ align:start position:0%
+wave modulation. Um and so you get you
+ 
+
+ align:start position:0%
+wave modulation. Um and so you get you
+know you've probably seen pictures of
+
+ align:start position:0%
+know you've probably seen pictures of
+ 
+
+ align:start position:0%
+know you've probably seen pictures of
+this. It's um in it's very much like AM.
+
+ align:start position:0%
+this. It's um in it's very much like AM.
+ 
+
+ align:start position:0%
+this. It's um in it's very much like AM.
+It's basically binary AM is the scheme
+
+ align:start position:0%
+It's basically binary AM is the scheme
+ 
+
+ align:start position:0%
+It's basically binary AM is the scheme
+we use. It's one of the simplest things
+
+ align:start position:0%
+we use. It's one of the simplest things
+ 
+
+ align:start position:0%
+we use. It's one of the simplest things
+you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do. Okay.
+
+ align:start position:0%
+do. Okay.
+ 
+
+ align:start position:0%
+do. Okay.
+Um then this is sent to a simulated
+
+ align:start position:0%
+Um then this is sent to a simulated
+ 
+
+ align:start position:0%
+Um then this is sent to a simulated
+channel which is a random fur filter
+
+ align:start position:0%
+channel which is a random fur filter
+ 
+
+ align:start position:0%
+channel which is a random fur filter
+finite impulse response. So it's basic
+
+ align:start position:0%
+finite impulse response. So it's basic
+ 
+
+ align:start position:0%
+finite impulse response. So it's basic
+what that means is basically it's taking
+
+ align:start position:0%
+what that means is basically it's taking
+ 
+
+ align:start position:0%
+what that means is basically it's taking
+the copies of the input at different
+
+ align:start position:0%
+the copies of the input at different
+ 
+
+ align:start position:0%
+the copies of the input at different
+time offsets with random random
+
+ align:start position:0%
+time offsets with random random
+ 
+
+ align:start position:0%
+time offsets with random random
+coefficients and just summing them up.
+
+ align:start position:0%
+coefficients and just summing them up.
+ 
+
+ align:start position:0%
+coefficients and just summing them up.
+It's a huge multiply add multiply add
+
+ align:start position:0%
+It's a huge multiply add multiply add
+ 
+
+ align:start position:0%
+It's a huge multiply add multiply add
+combination.
+
+ align:start position:0%
+combination.
+ 
+
+ align:start position:0%
+combination.
+So 80 this is 80
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+taps and add some Gaussian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+noise. Um and then this we take over and
+
+ align:start position:0%
+noise. Um and then this we take over and
+ 
+
+ align:start position:0%
+noise. Um and then this we take over and
+then try to figure out what we put in in
+
+ align:start position:0%
+then try to figure out what we put in in
+ 
+
+ align:start position:0%
+then try to figure out what we put in in
+the first place.
+
+ align:start position:0%
+the first place.
+ 
+
+ align:start position:0%
+the first place.
+Um so a bunch of filtering
+
+ align:start position:0%
+Um so a bunch of filtering
+ 
+
+ align:start position:0%
+Um so a bunch of filtering
+uh again through more more finite
+
+ align:start position:0%
+uh again through more more finite
+ 
+
+ align:start position:0%
+uh again through more more finite
+impulse response filtering. Um, we have
+
+ align:start position:0%
+impulse response filtering. Um, we have
+ 
+
+ align:start position:0%
+impulse response filtering. Um, we have
+to there's a little a closed loop that
+
+ align:start position:0%
+to there's a little a closed loop that
+ 
+
+ align:start position:0%
+to there's a little a closed loop that
+tries to estimate the signal amplitude
+
+ align:start position:0%
+tries to estimate the signal amplitude
+ 
+
+ align:start position:0%
+tries to estimate the signal amplitude
+and correct for it. That's called
+
+ align:start position:0%
+and correct for it. That's called
+ 
+
+ align:start position:0%
+and correct for it. That's called
+automatic gain control to sort of keep
+
+ align:start position:0%
+automatic gain control to sort of keep
+ 
+
+ align:start position:0%
+automatic gain control to sort of keep
+it constant.
+
+ align:start position:0%
+it constant.
+ 
+
+ align:start position:0%
+it constant.
+Um, and I'm probably getting things
+
+ align:start position:0%
+Um, and I'm probably getting things
+ 
+
+ align:start position:0%
+Um, and I'm probably getting things
+these things a little out of order.
+
+ align:start position:0%
+these things a little out of order.
+ 
+
+ align:start position:0%
+these things a little out of order.
+Um, we we square the signal to we this
+
+ align:start position:0%
+Um, we we square the signal to we this
+ 
+
+ align:start position:0%
+Um, we we square the signal to we this
+is the incoherent de modulation part. We
+
+ align:start position:0%
+is the incoherent de modulation part. We
+ 
+
+ align:start position:0%
+is the incoherent de modulation part. We
+square the signal to get rid of the
+
+ align:start position:0%
+square the signal to get rid of the
+ 
+
+ align:start position:0%
+square the signal to get rid of the
+carrier.
+
+ align:start position:0%
+carrier.
+ 
+
+ align:start position:0%
+carrier.
+Um, automated gain control
+
+ align:start position:0%
+Um, automated gain control
+ 
+
+ align:start position:0%
+Um, automated gain control
+filtering. There's another loop. Um,
+
+ align:start position:0%
+filtering. There's another loop. Um,
+ 
+
+ align:start position:0%
+filtering. There's another loop. Um,
+this is called a phase lock loop. The
+
+ align:start position:0%
+this is called a phase lock loop. The
+ 
+
+ align:start position:0%
+this is called a phase lock loop. The
+idea is try to match a sine wave to some
+
+ align:start position:0%
+idea is try to match a sine wave to some
+ 
+
+ align:start position:0%
+idea is try to match a sine wave to some
+to some to some input signal. Um, so I
+
+ align:start position:0%
+to some to some input signal. Um, so I
+ 
+
+ align:start position:0%
+to some to some input signal. Um, so I
+don't explain it very well. Um, it's
+
+ align:start position:0%
+don't explain it very well. Um, it's
+ 
+
+ align:start position:0%
+don't explain it very well. Um, it's
+basically a lock in type of detector.
+
+ align:start position:0%
+basically a lock in type of detector.
+ 
+
+ align:start position:0%
+basically a lock in type of detector.
+The idea is to lock into the phase of
+
+ align:start position:0%
+The idea is to lock into the phase of
+ 
+
+ align:start position:0%
+The idea is to lock into the phase of
+some periodic thing. This is for
+
+ align:start position:0%
+some periodic thing. This is for
+ 
+
+ align:start position:0%
+some periodic thing. This is for
+recovering when do you sample? Because
+
+ align:start position:0%
+recovering when do you sample? Because
+ 
+
+ align:start position:0%
+recovering when do you sample? Because
+you've got this messy waveform. You got
+
+ align:start position:0%
+you've got this messy waveform. You got
+ 
+
+ align:start position:0%
+you've got this messy waveform. You got
+to know when when to look and say, okay,
+
+ align:start position:0%
+to know when when to look and say, okay,
+ 
+
+ align:start position:0%
+to know when when to look and say, okay,
+is it high? Is it low to get a bit out?
+
+ align:start position:0%
+is it high? Is it low to get a bit out?
+ 
+
+ align:start position:0%
+is it high? Is it low to get a bit out?
+Yeah, that's I think that gives the
+
+ align:start position:0%
+Yeah, that's I think that gives the
+ 
+
+ align:start position:0%
+Yeah, that's I think that gives the
+picture. I'm probably boring everybody.
+
+ align:start position:0%
+picture. I'm probably boring everybody.
+ 
+
+ align:start position:0%
+picture. I'm probably boring everybody.
+So, here's a picture. Here's a picture
+
+ align:start position:0%
+So, here's a picture. Here's a picture
+ 
+
+ align:start position:0%
+So, here's a picture. Here's a picture
+generated from the system. Um the red
+
+ align:start position:0%
+generated from the system. Um the red
+ 
+
+ align:start position:0%
+generated from the system. Um the red
+line So, the green line is the data in
+
+ align:start position:0%
+line So, the green line is the data in
+ 
+
+ align:start position:0%
+line So, the green line is the data in
+um you know, high low one. Uh the red
+
+ align:start position:0%
+um you know, high low one. Uh the red
+ 
+
+ align:start position:0%
+um you know, high low one. Uh the red
+line is the analog signal out right
+
+ align:start position:0%
+line is the analog signal out right
+ 
+
+ align:start position:0%
+line is the analog signal out right
+before it's supposed to decide what the
+
+ align:start position:0%
+before it's supposed to decide what the
+ 
+
+ align:start position:0%
+before it's supposed to decide what the
+heck the input was. So, this is after
+
+ align:start position:0%
+heck the input was. So, this is after
+ 
+
+ align:start position:0%
+heck the input was. So, this is after
+this is after um this is after squaring
+
+ align:start position:0%
+this is after um this is after squaring
+ 
+
+ align:start position:0%
+this is after um this is after squaring
+and filtering and automatic gain control
+
+ align:start position:0%
+and filtering and automatic gain control
+ 
+
+ align:start position:0%
+and filtering and automatic gain control
+and all that. Um the little blips um are
+
+ align:start position:0%
+and all that. Um the little blips um are
+ 
+
+ align:start position:0%
+and all that. Um the little blips um are
+actually because we used we used a
+
+ align:start position:0%
+actually because we used we used a
+ 
+
+ align:start position:0%
+actually because we used we used a
+modulation called alternate mark
+
+ align:start position:0%
+modulation called alternate mark
+ 
+
+ align:start position:0%
+modulation called alternate mark
+inversion. It just basically flips every
+
+ align:start position:0%
+inversion. It just basically flips every
+ 
+
+ align:start position:0%
+inversion. It just basically flips every
+one. That's why it's blipping instead of
+
+ align:start position:0%
+one. That's why it's blipping instead of
+ 
+
+ align:start position:0%
+one. That's why it's blipping instead of
+being constant. It's just a convenient
+
+ align:start position:0%
+being constant. It's just a convenient
+ 
+
+ align:start position:0%
+being constant. It's just a convenient
+trick. And then the little blue daggers
+
+ align:start position:0%
+trick. And then the little blue daggers
+ 
+
+ align:start position:0%
+trick. And then the little blue daggers
+are the results of the phase lock loop
+
+ align:start position:0%
+are the results of the phase lock loop
+ 
+
+ align:start position:0%
+are the results of the phase lock loop
+to try and recover when to sample.
+
+ align:start position:0%
+to try and recover when to sample.
+ 
+
+ align:start position:0%
+to try and recover when to sample.
+They're kind of off, but they're kind of
+
+ align:start position:0%
+They're kind of off, but they're kind of
+ 
+
+ align:start position:0%
+They're kind of off, but they're kind of
+right. And so if you take the little
+
+ align:start position:0%
+right. And so if you take the little
+ 
+
+ align:start position:0%
+right. And so if you take the little
+blue blue blip, if the red line is above
+
+ align:start position:0%
+blue blue blip, if the red line is above
+ 
+
+ align:start position:0%
+blue blue blip, if the red line is above
+zero, it's a one. And if it's below
+
+ align:start position:0%
+zero, it's a one. And if it's below
+ 
+
+ align:start position:0%
+zero, it's a one. And if it's below
+zero, it's a zero. Um
+
+ align:start position:0%
+zero, it's a zero. Um
+ 
+
+ align:start position:0%
+zero, it's a zero. Um
+And that's how you get your bits
+
+ align:start position:0%
+And that's how you get your bits
+ 
+
+ align:start position:0%
+And that's how you get your bits
+out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+so this was hard to get
+
+ align:start position:0%
+so this was hard to get
+ 
+
+ align:start position:0%
+so this was hard to get
+right mostly because of the framework
+
+ align:start position:0%
+right mostly because of the framework
+ 
+
+ align:start position:0%
+right mostly because of the framework
+issues.
+
+ align:start position:0%
+issues.
+ 
+
+ align:start position:0%
+issues.
+Um so we you know implementing
+
+ align:start position:0%
+Um so we you know implementing
+ 
+
+ align:start position:0%
+Um so we you know implementing
+implementing distributed objects on a
+
+ align:start position:0%
+implementing distributed objects on a
+ 
+
+ align:start position:0%
+implementing distributed objects on a
+system without real shared memory um is
+
+ align:start position:0%
+system without real shared memory um is
+ 
+
+ align:start position:0%
+system without real shared memory um is
+hard because you have to serialize
+
+ align:start position:0%
+hard because you have to serialize
+ 
+
+ align:start position:0%
+hard because you have to serialize
+everything into a stream of bits and
+
+ align:start position:0%
+everything into a stream of bits and
+ 
+
+ align:start position:0%
+everything into a stream of bits and
+deserialize.
+
+ align:start position:0%
+deserialize.
+ 
+
+ align:start position:0%
+deserialize.
+Um so it really makes pi out of any
+
+ align:start position:0%
+Um so it really makes pi out of any
+ 
+
+ align:start position:0%
+Um so it really makes pi out of any
+existing object-oriented code. Um we we
+
+ align:start position:0%
+existing object-oriented code. Um we we
+ 
+
+ align:start position:0%
+existing object-oriented code. Um we we
+did quite a bit of work to get um to get
+
+ align:start position:0%
+did quite a bit of work to get um to get
+ 
+
+ align:start position:0%
+did quite a bit of work to get um to get
+sort of decent lock free almost zero
+
+ align:start position:0%
+sort of decent lock free almost zero
+ 
+
+ align:start position:0%
+sort of decent lock free almost zero
+copy. Another day or so we probably
+
+ align:start position:0%
+copy. Another day or so we probably
+ 
+
+ align:start position:0%
+copy. Another day or so we probably
+would have gotten zero copy. um transfer
+
+ align:start position:0%
+would have gotten zero copy. um transfer
+ 
+
+ align:start position:0%
+would have gotten zero copy. um transfer
+transfer streaming of the data from
+
+ align:start position:0%
+transfer streaming of the data from
+ 
+
+ align:start position:0%
+transfer streaming of the data from
+place to place. Um and we had to keep
+
+ align:start position:0%
+place to place. Um and we had to keep
+ 
+
+ align:start position:0%
+place to place. Um and we had to keep
+the code footprint low.
+
+ align:start position:0%
+the code footprint low.
+ 
+
+ align:start position:0%
+the code footprint low.
+Um C++ is bloated. Uh we don't have an
+
+ align:start position:0%
+Um C++ is bloated. Uh we don't have an
+ 
+
+ align:start position:0%
+Um C++ is bloated. Uh we don't have an
+overlay system yet to sort of you know
+
+ align:start position:0%
+overlay system yet to sort of you know
+ 
+
+ align:start position:0%
+overlay system yet to sort of you know
+if if a SPE is not running a particular
+
+ align:start position:0%
+if if a SPE is not running a particular
+ 
+
+ align:start position:0%
+if if a SPE is not running a particular
+box. It still has to have the code for
+
+ align:start position:0%
+box. It still has to have the code for
+ 
+
+ align:start position:0%
+box. It still has to have the code for
+it because we don't have you know we
+
+ align:start position:0%
+it because we don't have you know we
+ 
+
+ align:start position:0%
+it because we don't have you know we
+don't have any infrastructure for some
+
+ align:start position:0%
+don't have any infrastructure for some
+ 
+
+ align:start position:0%
+don't have any infrastructure for some
+that yeah it's pretty messy. So all the
+
+ align:start position:0%
+that yeah it's pretty messy. So all the
+ 
+
+ align:start position:0%
+that yeah it's pretty messy. So all the
+code is on all the SPDs. Um so code
+
+ align:start position:0%
+code is on all the SPDs. Um so code
+ 
+
+ align:start position:0%
+code is on all the SPDs. Um so code
+bloat is particular issue and XLC has
+
+ align:start position:0%
+bloat is particular issue and XLC has
+ 
+
+ align:start position:0%
+bloat is particular issue and XLC has
+this particular penchant for runtime
+
+ align:start position:0%
+this particular penchant for runtime
+ 
+
+ align:start position:0%
+this particular penchant for runtime
+type information and exception handling.
+
+ align:start position:0%
+type information and exception handling.
+ 
+
+ align:start position:0%
+type information and exception handling.
+Um incredible amount of voodoo is
+
+ align:start position:0%
+Um incredible amount of voodoo is
+ 
+
+ align:start position:0%
+Um incredible amount of voodoo is
+necessary to get them out to get them
+
+ align:start position:0%
+necessary to get them out to get them
+ 
+
+ align:start position:0%
+necessary to get them out to get them
+and that 70k of useless bloat out of
+
+ align:start position:0%
+and that 70k of useless bloat out of
+ 
+
+ align:start position:0%
+and that 70k of useless bloat out of
+there.
+
+ align:start position:0%
+there.
+ 
+
+ align:start position:0%
+there.
+Um but but we pretty much have the it
+
+ align:start position:0%
+Um but but we pretty much have the it
+ 
+
+ align:start position:0%
+Um but but we pretty much have the it
+works but not always. So we did manage
+
+ align:start position:0%
+works but not always. So we did manage
+ 
+
+ align:start position:0%
+works but not always. So we did manage
+to get it running long enough to make
+
+ align:start position:0%
+to get it running long enough to make
+ 
+
+ align:start position:0%
+to get it running long enough to make
+some measurements. But yeah, we did get
+
+ align:start position:0%
+some measurements. But yeah, we did get
+ 
+
+ align:start position:0%
+some measurements. But yeah, we did get
+we did get some decent data out. Um
+
+ align:start position:0%
+we did get some decent data out. Um
+ 
+
+ align:start position:0%
+we did get some decent data out. Um
+running on the PPU only we can run about
+
+ align:start position:0%
+running on the PPU only we can run about
+ 
+
+ align:start position:0%
+running on the PPU only we can run about
+170,000 samples per second through um
+
+ align:start position:0%
+170,000 samples per second through um
+ 
+
+ align:start position:0%
+170,000 samples per second through um
+and by with the scheduling file that
+
+ align:start position:0%
+and by with the scheduling file that
+ 
+
+ align:start position:0%
+and by with the scheduling file that
+sort of kind of rule of thumb we just
+
+ align:start position:0%
+sort of kind of rule of thumb we just
+ 
+
+ align:start position:0%
+sort of kind of rule of thumb we just
+sort of roughly said okay that looks
+
+ align:start position:0%
+sort of roughly said okay that looks
+ 
+
+ align:start position:0%
+sort of roughly said okay that looks
+about this big we'll throw it on this
+
+ align:start position:0%
+about this big we'll throw it on this
+ 
+
+ align:start position:0%
+about this big we'll throw it on this
+SP.
+
+ align:start position:0%
+SP.
+ 
+
+ align:start position:0%
+SP.
+We got roughly four times that using
+
+ align:start position:0%
+We got roughly four times that using
+ 
+
+ align:start position:0%
+We got roughly four times that using
+five SPEs. The post is a little large
+
+ align:start position:0%
+five SPEs. The post is a little large
+ 
+
+ align:start position:0%
+five SPEs. The post is a little large
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+Um, yeah, we're we we had to really had
+
+ align:start position:0%
+Um, yeah, we're we we had to really had
+ 
+
+ align:start position:0%
+Um, yeah, we're we we had to really had
+to push down things like our Q. We we
+
+ align:start position:0%
+to push down things like our Q. We we
+ 
+
+ align:start position:0%
+to push down things like our Q. We we
+just didn't have enough memory. It
+
+ align:start position:0%
+just didn't have enough memory. It
+ 
+
+ align:start position:0%
+just didn't have enough memory. It
+sucked. Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah, basically just said that
+
+ align:start position:0%
+yeah, basically just said that
+ 
+
+ align:start position:0%
+yeah, basically just said that
+performance, I guess. Um, so interesting
+
+ align:start position:0%
+performance, I guess. Um, so interesting
+ 
+
+ align:start position:0%
+performance, I guess. Um, so interesting
+interesting performance behavior. We
+
+ align:start position:0%
+interesting performance behavior. We
+ 
+
+ align:start position:0%
+interesting performance behavior. We
+found that the SPEs are ridiculously
+
+ align:start position:0%
+found that the SPEs are ridiculously
+ 
+
+ align:start position:0%
+found that the SPEs are ridiculously
+underutilized. Um, there may be most of
+
+ align:start position:0%
+underutilized. Um, there may be most of
+ 
+
+ align:start position:0%
+underutilized. Um, there may be most of
+the algorithms are quite a bit zippier
+
+ align:start position:0%
+the algorithms are quite a bit zippier
+ 
+
+ align:start position:0%
+the algorithms are quite a bit zippier
+on the SPEs. Um and so you know they're
+
+ align:start position:0%
+on the SPEs. Um and so you know they're
+ 
+
+ align:start position:0%
+on the SPEs. Um and so you know they're
+maybe running about a third of the time
+
+ align:start position:0%
+maybe running about a third of the time
+ 
+
+ align:start position:0%
+maybe running about a third of the time
+or and the rest of the time just waiting
+
+ align:start position:0%
+or and the rest of the time just waiting
+ 
+
+ align:start position:0%
+or and the rest of the time just waiting
+for input and then the PPE um which is
+
+ align:start position:0%
+for input and then the PPE um which is
+ 
+
+ align:start position:0%
+for input and then the PPE um which is
+doing only a tiny amount of the
+
+ align:start position:0%
+doing only a tiny amount of the
+ 
+
+ align:start position:0%
+doing only a tiny amount of the
+computation basically just feeding in
+
+ align:start position:0%
+computation basically just feeding in
+ 
+
+ align:start position:0%
+computation basically just feeding in
+and sucking it out is spending half of
+
+ align:start position:0%
+and sucking it out is spending half of
+ 
+
+ align:start position:0%
+and sucking it out is spending half of
+its time all busy and the other half of
+
+ align:start position:0%
+its time all busy and the other half of
+ 
+
+ align:start position:0%
+its time all busy and the other half of
+the time stuck in flow control um
+
+ align:start position:0%
+the time stuck in flow control um
+ 
+
+ align:start position:0%
+the time stuck in flow control um
+waiting for Q space which
+
+ align:start position:0%
+waiting for Q space which
+ 
+
+ align:start position:0%
+waiting for Q space which
+is we our flow control algorithm sucks
+
+ align:start position:0%
+is we our flow control algorithm sucks
+ 
+
+ align:start position:0%
+is we our flow control algorithm sucks
+and better with time but so but it seems
+
+ align:start position:0%
+and better with time but so but it seems
+ 
+
+ align:start position:0%
+and better with time but so but it seems
+like you should be able to quite a bit
+
+ align:start position:0%
+like you should be able to quite a bit
+ 
+
+ align:start position:0%
+like you should be able to quite a bit
+better than we did um with a bit more
+
+ align:start position:0%
+better than we did um with a bit more
+ 
+
+ align:start position:0%
+better than we did um with a bit more
+work. Um I
+
+ align:start position:0%
+work. Um I
+ 
+
+ align:start position:0%
+work. Um I
+guess
+
+ align:start position:0%
+guess
+ 
+
+ align:start position:0%
+guess
+so we need to cut down on the code
+
+ align:start position:0%
+so we need to cut down on the code
+ 
+
+ align:start position:0%
+so we need to cut down on the code
+footprint. Um and once we have a little
+
+ align:start position:0%
+footprint. Um and once we have a little
+ 
+
+ align:start position:0%
+footprint. Um and once we have a little
+bit of breathing room, we can and get
+
+ align:start position:0%
+bit of breathing room, we can and get
+ 
+
+ align:start position:0%
+bit of breathing room, we can and get
+rid of the nasty race bugs and such. We
+
+ align:start position:0%
+rid of the nasty race bugs and such. We
+ 
+
+ align:start position:0%
+rid of the nasty race bugs and such. We
+can finally investigate what was our
+
+ align:start position:0%
+can finally investigate what was our
+ 
+
+ align:start position:0%
+can finally investigate what was our
+sort of original pie in the sky goal of
+
+ align:start position:0%
+sort of original pie in the sky goal of
+ 
+
+ align:start position:0%
+sort of original pie in the sky goal of
+automatically deciding what goes where.
+
+ align:start position:0%
+automatically deciding what goes where.
+ 
+
+ align:start position:0%
+automatically deciding what goes where.
+um you know doing me taking measurements
+
+ align:start position:0%
+um you know doing me taking measurements
+ 
+
+ align:start position:0%
+um you know doing me taking measurements
+of the performance and then feeding that
+
+ align:start position:0%
+of the performance and then feeding that
+ 
+
+ align:start position:0%
+of the performance and then feeding that
+back into to producing a better
+
+ align:start position:0%
+back into to producing a better
+ 
+
+ align:start position:0%
+back into to producing a better
+placement of operators
+
+ align:start position:0%
+placement of operators
+ 
+
+ align:start position:0%
+placement of operators
+um and uh applying data parallelism by
+
+ align:start position:0%
+um and uh applying data parallelism by
+ 
+
+ align:start position:0%
+um and uh applying data parallelism by
+instantiating operators on multiple SP
+
+ align:start position:0%
+instantiating operators on multiple SP
+ 
+
+ align:start position:0%
+instantiating operators on multiple SP
+multiple different SPEs and splitting
+
+ align:start position:0%
+multiple different SPEs and splitting
+ 
+
+ align:start position:0%
+multiple different SPEs and splitting
+the data stream
+
+ align:start position:0%
+the data stream
+ 
+
+ align:start position:0%
+the data stream
+um and just doing more. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since your PB is only at 40%
+
+ align:start position:0%
+since your PB is only at 40%
+ 
+
+ align:start position:0%
+since your PB is only at 40%
+utilization, could you put actual work
+
+ align:start position:0%
+utilization, could you put actual work
+ 
+
+ align:start position:0%
+utilization, could you put actual work
+on there? We did put some work on there.
+
+ align:start position:0%
+on there? We did put some work on there.
+ 
+
+ align:start position:0%
+on there? We did put some work on there.
+Actually, we put work on there because
+
+ align:start position:0%
+Actually, we put work on there because
+ 
+
+ align:start position:0%
+Actually, we put work on there because
+we couldn't fit all the boxes, the code
+
+ align:start position:0%
+we couldn't fit all the boxes, the code
+ 
+
+ align:start position:0%
+we couldn't fit all the boxes, the code
+for all the boxes into the SPES. So we
+
+ align:start position:0%
+for all the boxes into the SPES. So we
+ 
+
+ align:start position:0%
+for all the boxes into the SPES. So we
+we sort of strategically put a few
+
+ align:start position:0%
+we sort of strategically put a few
+ 
+
+ align:start position:0%
+we sort of strategically put a few
+things at the beginning, a few things at
+
+ align:start position:0%
+things at the beginning, a few things at
+ 
+
+ align:start position:0%
+things at the beginning, a few things at
+the end, which weren't supposed to be
+
+ align:start position:0%
+the end, which weren't supposed to be
+ 
+
+ align:start position:0%
+the end, which weren't supposed to be
+very computationally intensive, and yet
+
+ align:start position:0%
+very computationally intensive, and yet
+ 
+
+ align:start position:0%
+very computationally intensive, and yet
+they managed to take up half the CPU.
+
+ align:start position:0%
+they managed to take up half the CPU.
+ 
+
+ align:start position:0%
+they managed to take up half the CPU.
+Now the issue the issue with the other
+
+ align:start position:0%
+Now the issue the issue with the other
+ 
+
+ align:start position:0%
+Now the issue the issue with the other
+half of the CPU is that it's actually in
+
+ align:start position:0%
+half of the CPU is that it's actually in
+ 
+
+ align:start position:0%
+half of the CPU is that it's actually in
+inside an inner loop deep recursive in
+
+ align:start position:0%
+inside an inner loop deep recursive in
+ 
+
+ align:start position:0%
+inside an inner loop deep recursive in
+blocking because basically our back
+
+ align:start position:0%
+blocking because basically our back
+ 
+
+ align:start position:0%
+blocking because basically our back
+pressure isn't online yet. So if it if
+
+ align:start position:0%
+pressure isn't online yet. So if it if
+ 
+
+ align:start position:0%
+pressure isn't online yet. So if it if
+if it tries to emit something to a queue
+
+ align:start position:0%
+if it tries to emit something to a queue
+ 
+
+ align:start position:0%
+if it tries to emit something to a queue
+and that queue is full just stops and it
+
+ align:start position:0%
+and that queue is full just stops and it
+ 
+
+ align:start position:0%
+and that queue is full just stops and it
+really could be running a whole bunch of
+
+ align:start position:0%
+really could be running a whole bunch of
+ 
+
+ align:start position:0%
+really could be running a whole bunch of
+other stuff but it's not smart enough to
+
+ align:start position:0%
+other stuff but it's not smart enough to
+ 
+
+ align:start position:0%
+other stuff but it's not smart enough to
+do that yet.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Everything being everything being unlike
+
+ align:start position:0%
+Everything being everything being unlike
+ 
+
+ align:start position:0%
+Everything being everything being unlike
+sort of a model like stream it
+
+ align:start position:0%
+sort of a model like stream it
+ 
+
+ align:start position:0%
+sort of a model like stream it
+everything here is sort of asynchronous
+
+ align:start position:0%
+everything here is sort of asynchronous
+ 
+
+ align:start position:0%
+everything here is sort of asynchronous
+and code driven or sort of the SPs they
+
+ align:start position:0%
+and code driven or sort of the SPs they
+ 
+
+ align:start position:0%
+and code driven or sort of the SPs they
+can decide on the fly how much to emit
+
+ align:start position:0%
+can decide on the fly how much to emit
+ 
+
+ align:start position:0%
+can decide on the fly how much to emit
+um the programmer doesn't have to
+
+ align:start position:0%
+um the programmer doesn't have to
+ 
+
+ align:start position:0%
+um the programmer doesn't have to
+declare anything but it means everything
+
+ align:start position:0%
+declare anything but it means everything
+ 
+
+ align:start position:0%
+declare anything but it means everything
+is asynchronous um and so you can raise
+
+ align:start position:0%
+is asynchronous um and so you can raise
+ 
+
+ align:start position:0%
+is asynchronous um and so you can raise
+the issues or but in this application do
+
+ align:start position:0%
+the issues or but in this application do
+ 
+
+ align:start position:0%
+the issues or but in this application do
+you find any dynamic rates in this
+
+ align:start position:0%
+you find any dynamic rates in this
+ 
+
+ align:start position:0%
+you find any dynamic rates in this
+application there's not much it's a very
+
+ align:start position:0%
+application there's not much it's a very
+ 
+
+ align:start position:0%
+application there's not much it's a very
+simple application if we actually went
+
+ align:start position:0%
+simple application if we actually went
+ 
+
+ align:start position:0%
+simple application if we actually went
+to packetization
+
+ align:start position:0%
+to packetization
+ 
+
+ align:start position:0%
+to packetization
+um error correction, compression, things
+
+ align:start position:0%
+um error correction, compression, things
+ 
+
+ align:start position:0%
+um error correction, compression, things
+like that. Probably see a lot more of
+
+ align:start position:0%
+like that. Probably see a lot more of
+ 
+
+ align:start position:0%
+like that. Probably see a lot more of
+that. But yeah, this this is definitely
+
+ align:start position:0%
+that. But yeah, this this is definitely
+ 
+
+ align:start position:0%
+that. But yeah, this this is definitely
+underutilized in sort of the synchronous
+
+ align:start position:0%
+underutilized in sort of the synchronous
+ 
+
+ align:start position:0%
+underutilized in sort of the synchronous
+capabilities of the system.
+
+ align:start position:0%
+capabilities of the system.
+ 
+
+ align:start position:0%
+capabilities of the system.
+In the case of radio, wouldn't it be
+
+ align:start position:0%
+In the case of radio, wouldn't it be
+ 
+
+ align:start position:0%
+In the case of radio, wouldn't it be
+okay to drop maybe a frame or two of
+
+ align:start position:0%
+okay to drop maybe a frame or two of
+ 
+
+ align:start position:0%
+okay to drop maybe a frame or two of
+audio data just because you you know
+
+ align:start position:0%
+audio data just because you you know
+ 
+
+ align:start position:0%
+audio data just because you you know
+you're spending so much time waiting?
+
+ align:start position:0%
+you're spending so much time waiting?
+ 
+
+ align:start position:0%
+you're spending so much time waiting?
+It'd be better just, you know, relieve
+
+ align:start position:0%
+It'd be better just, you know, relieve
+ 
+
+ align:start position:0%
+It'd be better just, you know, relieve
+the pressure on the cues by just
+
+ align:start position:0%
+the pressure on the cues by just
+ 
+
+ align:start position:0%
+the pressure on the cues by just
+dropping some frames that are necessary
+
+ align:start position:0%
+dropping some frames that are necessary
+ 
+
+ align:start position:0%
+dropping some frames that are necessary
+interpolating it in the end. try to fix
+
+ align:start position:0%
+interpolating it in the end. try to fix
+ 
+
+ align:start position:0%
+interpolating it in the end. try to fix
+it up. It might well be. We decided not
+
+ align:start position:0%
+it up. It might well be. We decided not
+ 
+
+ align:start position:0%
+it up. It might well be. We decided not
+to do that as a part of the framework um
+
+ align:start position:0%
+to do that as a part of the framework um
+ 
+
+ align:start position:0%
+to do that as a part of the framework um
+because of a policy decision and we
+
+ align:start position:0%
+because of a policy decision and we
+ 
+
+ align:start position:0%
+because of a policy decision and we
+didn't want to make that for all
+
+ align:start position:0%
+didn't want to make that for all
+ 
+
+ align:start position:0%
+didn't want to make that for all
+possible applications. But if you figure
+
+ align:start position:0%
+possible applications. But if you figure
+ 
+
+ align:start position:0%
+possible applications. But if you figure
+out a good way to expose that, that
+
+ align:start position:0%
+out a good way to expose that, that
+ 
+
+ align:start position:0%
+out a good way to expose that, that
+definitely would be an option. Just drop
+
+ align:start position:0%
+definitely would be an option. Just drop
+ 
+
+ align:start position:0%
+definitely would be an option. Just drop
+a few packets, drop a few samples. Yeah.
+
+ align:start position:0%
+a few packets, drop a few samples. Yeah.
+ 
+
+ align:start position:0%
+a few packets, drop a few samples. Yeah.
+So, what about buffer sizes? You declare
+
+ align:start position:0%
+So, what about buffer sizes? You declare
+ 
+
+ align:start position:0%
+So, what about buffer sizes? You declare
+the buffer size as well? Uh yeah. Well,
+
+ align:start position:0%
+the buffer size as well? Uh yeah. Well,
+ 
+
+ align:start position:0%
+the buffer size as well? Uh yeah. Well,
+the way we have it now is actually
+
+ align:start position:0%
+the way we have it now is actually
+ 
+
+ align:start position:0%
+the way we have it now is actually
+there's just a pound defined info that
+
+ align:start position:0%
+there's just a pound defined info that
+ 
+
+ align:start position:0%
+there's just a pound defined info that
+says all buffers are this size. Okay.
+
+ align:start position:0%
+says all buffers are this size. Okay.
+ 
+
+ align:start position:0%
+says all buffers are this size. Okay.
+any double buffering in there or uh you
+
+ align:start position:0%
+any double buffering in there or uh you
+ 
+
+ align:start position:0%
+any double buffering in there or uh you
+don't need it. Well, actually the way it
+
+ align:start position:0%
+don't need it. Well, actually the way it
+ 
+
+ align:start position:0%
+don't need it. Well, actually the way it
+works is that there's there's this sort
+
+ align:start position:0%
+works is that there's there's this sort
+ 
+
+ align:start position:0%
+works is that there's there's this sort
+of this remote heap input Q and an
+
+ align:start position:0%
+of this remote heap input Q and an
+ 
+
+ align:start position:0%
+of this remote heap input Q and an
+upstream SP just DMAS things in as it
+
+ align:start position:0%
+upstream SP just DMAS things in as it
+ 
+
+ align:start position:0%
+upstream SP just DMAS things in as it
+feels like and then the the downstream
+
+ align:start position:0%
+feels like and then the the downstream
+ 
+
+ align:start position:0%
+feels like and then the the downstream
+SP looks is is there something here?
+
+ align:start position:0%
+SP looks is is there something here?
+ 
+
+ align:start position:0%
+SP looks is is there something here?
+Grab it, use it. So it it just it just
+
+ align:start position:0%
+Grab it, use it. So it it just it just
+ 
+
+ align:start position:0%
+Grab it, use it. So it it just it just
+it just sort of works however much
+
+ align:start position:0%
+it just sort of works however much
+ 
+
+ align:start position:0%
+it just sort of works however much
+buffering there's buffer and sort of
+
+ align:start position:0%
+buffering there's buffer and sort of
+ 
+
+ align:start position:0%
+buffering there's buffer and sort of
+manage to get that lock free. Yeah.
+
+ align:start position:0%
+manage to get that lock free. Yeah.
+ 
+
+ align:start position:0%
+manage to get that lock free. Yeah.
+Yeah. So that's that's that's an that's
+
+ align:start position:0%
+Yeah. So that's that's that's an that's
+ 
+
+ align:start position:0%
+Yeah. So that's that's that's an that's
+a benefit of the asynchronous approach.
+
+ align:start position:0%
+a benefit of the asynchronous approach.
+ 
+
+ align:start position:0%
+a benefit of the asynchronous approach.
+It just sort of works if you have enough
+
+ align:start position:0%
+It just sort of works if you have enough
+ 
+
+ align:start position:0%
+It just sort of works if you have enough
+memory, which we don't.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Your cues are tiny.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Any other questions? Mom's angrily
+
+ align:start position:0%
+Any other questions? Mom's angrily
+ 
+
+ align:start position:0%
+Any other questions? Mom's angrily
+telling me that his connection dropped,
+
+ align:start position:0%
+telling me that his connection dropped,
+ 
+
+ align:start position:0%
+telling me that his connection dropped,
+but he's not the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, I I see it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How do you do that?
+
+ align:start position:0%
+How do you do that?
+ 
+
+ align:start position:0%
+How do you do that?
+Yeah. Hold on. Just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other questions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Did you want to do the demo?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh what did you do to get
+
+ align:start position:0%
+Uh what did you do to get
+ 
+
+ align:start position:0%
+Uh what did you do to get
+How did we manage to get ourselves race
+
+ align:start position:0%
+How did we manage to get ourselves race
+ 
+
+ align:start position:0%
+How did we manage to get ourselves race
+conditions?
+
+ align:start position:0%
+conditions?
+ 
+
+ align:start position:0%
+conditions?
+Um well it's a mix of the fact that all
+
+ align:start position:0%
+Um well it's a mix of the fact that all
+ 
+
+ align:start position:0%
+Um well it's a mix of the fact that all
+the SPUs can essentially operate as
+
+ align:start position:0%
+the SPUs can essentially operate as
+ 
+
+ align:start position:0%
+the SPUs can essentially operate as
+independent threads and are sort of
+
+ align:start position:0%
+independent threads and are sort of
+ 
+
+ align:start position:0%
+independent threads and are sort of
+asynchronously dmaing things to each
+
+ align:start position:0%
+asynchronously dmaing things to each
+ 
+
+ align:start position:0%
+asynchronously dmaing things to each
+other and some somewhat poor arch you
+
+ align:start position:0%
+other and some somewhat poor arch you
+ 
+
+ align:start position:0%
+other and some somewhat poor arch you
+know sort of legacy driven architectural
+
+ align:start position:0%
+know sort of legacy driven architectural
+ 
+
+ align:start position:0%
+know sort of legacy driven architectural
+decisions on the way the ppu code works
+
+ align:start position:0%
+decisions on the way the ppu code works
+ 
+
+ align:start position:0%
+decisions on the way the ppu code works
+um because we we ported a lot of code
+
+ align:start position:0%
+um because we we ported a lot of code
+ 
+
+ align:start position:0%
+um because we we ported a lot of code
+from the wave scope platform wasn't
+
+ align:start position:0%
+from the wave scope platform wasn't
+ 
+
+ align:start position:0%
+from the wave scope platform wasn't
+fairly well backed yeah and and that was
+
+ align:start position:0%
+fairly well backed yeah and and that was
+ 
+
+ align:start position:0%
+fairly well backed yeah and and that was
+intended to be multi-threaded with
+
+ align:start position:0%
+intended to be multi-threaded with
+ 
+
+ align:start position:0%
+intended to be multi-threaded with
+pthreads which you know in our in our
+
+ align:start position:0%
+pthreads which you know in our in our
+ 
+
+ align:start position:0%
+pthreads which you know in our in our
+original naive before we actually
+
+ align:start position:0%
+original naive before we actually
+ 
+
+ align:start position:0%
+original naive before we actually
+started the class um impression, we
+
+ align:start position:0%
+started the class um impression, we
+ 
+
+ align:start position:0%
+started the class um impression, we
+thought we were just going to port the
+
+ align:start position:0%
+thought we were just going to port the
+ 
+
+ align:start position:0%
+thought we were just going to port the
+whole thing and use Bthreads on the
+
+ align:start position:0%
+whole thing and use Bthreads on the
+ 
+
+ align:start position:0%
+whole thing and use Bthreads on the
+cell, which of course is not possible.
+
+ align:start position:0%
+cell, which of course is not possible.
+ 
+
+ align:start position:0%
+cell, which of course is not possible.
+Um so there were some still some
+
+ align:start position:0%
+Um so there were some still some
+ 
+
+ align:start position:0%
+Um so there were some still some
+threaded components in there. Um and we
+
+ align:start position:0%
+threaded components in there. Um and we
+ 
+
+ align:start position:0%
+threaded components in there. Um and we
+introduced a lot of bugs trying to port
+
+ align:start position:0%
+introduced a lot of bugs trying to port
+ 
+
+ align:start position:0%
+introduced a lot of bugs trying to port
+the thing.
+
+ align:start position:0%
+the thing.
+ 
+
+ align:start position:0%
+the thing.
+Um see if I can see another subtle
+
+ align:start position:0%
+Um see if I can see another subtle
+ 
+
+ align:start position:0%
+Um see if I can see another subtle
+surprising thing was the fact that we
+
+ align:start position:0%
+surprising thing was the fact that we
+ 
+
+ align:start position:0%
+surprising thing was the fact that we
+had to replace array constructors in
+
+ align:start position:0%
+had to replace array constructors in
+ 
+
+ align:start position:0%
+had to replace array constructors in
+order to eliminate RTI and it was just a
+
+ align:start position:0%
+order to eliminate RTI and it was just a
+ 
+
+ align:start position:0%
+order to eliminate RTI and it was just a
+big deal. We had to get rid of new, we
+
+ align:start position:0%
+big deal. We had to get rid of new, we
+ 
+
+ align:start position:0%
+big deal. We had to get rid of new, we
+had to get rid of delete, we had to get
+
+ align:start position:0%
+had to get rid of delete, we had to get
+ 
+
+ align:start position:0%
+had to get rid of delete, we had to get
+rid of array constructors, we had to get
+
+ align:start position:0%
+rid of array constructors, we had to get
+ 
+
+ align:start position:0%
+rid of array constructors, we had to get
+rid of pure vual functions and virtual
+
+ align:start position:0%
+rid of pure vual functions and virtual
+ 
+
+ align:start position:0%
+rid of pure vual functions and virtual
+destructors. It was a mess. But I guess
+
+ align:start position:0%
+destructors. It was a mess. But I guess
+ 
+
+ align:start position:0%
+destructors. It was a mess. But I guess
+one I guess there's one more piffy thing
+
+ align:start position:0%
+one I guess there's one more piffy thing
+ 
+
+ align:start position:0%
+one I guess there's one more piffy thing
+I can say about race conditions is um
+
+ align:start position:0%
+I can say about race conditions is um
+ 
+
+ align:start position:0%
+I can say about race conditions is um
+it's incredible how many subtle race
+
+ align:start position:0%
+it's incredible how many subtle race
+ 
+
+ align:start position:0%
+it's incredible how many subtle race
+conditions and bugs we found in the
+
+ align:start position:0%
+conditions and bugs we found in the
+ 
+
+ align:start position:0%
+conditions and bugs we found in the
+queueing the remote heap and queuing
+
+ align:start position:0%
+queueing the remote heap and queuing
+ 
+
+ align:start position:0%
+queueing the remote heap and queuing
+library. Um because there's one one it's
+
+ align:start position:0%
+library. Um because there's one one it's
+ 
+
+ align:start position:0%
+library. Um because there's one one it's
+it's a log free it's a log free
+
+ align:start position:0%
+it's a log free it's a log free
+ 
+
+ align:start position:0%
+it's a log free it's a log free
+asynchronous data structure. um there
+
+ align:start position:0%
+asynchronous data structure. um there
+ 
+
+ align:start position:0%
+asynchronous data structure. um there
+are two two threads but two two SPUs
+
+ align:start position:0%
+are two two threads but two two SPUs
+ 
+
+ align:start position:0%
+are two two threads but two two SPUs
+reading and writing from it at the same
+
+ align:start position:0%
+reading and writing from it at the same
+ 
+
+ align:start position:0%
+reading and writing from it at the same
+time and there's all sorts of little
+
+ align:start position:0%
+time and there's all sorts of little
+ 
+
+ align:start position:0%
+time and there's all sorts of little
+subtleties where if you get it a little
+
+ align:start position:0%
+subtleties where if you get it a little
+ 
+
+ align:start position:0%
+subtleties where if you get it a little
+bit wrong you end up with one of the Q
+
+ align:start position:0%
+bit wrong you end up with one of the Q
+ 
+
+ align:start position:0%
+bit wrong you end up with one of the Q
+pointers overrunning the other guy and
+
+ align:start position:0%
+pointers overrunning the other guy and
+ 
+
+ align:start position:0%
+pointers overrunning the other guy and
+you have basically dangling pointers and
+
+ align:start position:0%
+you have basically dangling pointers and
+ 
+
+ align:start position:0%
+you have basically dangling pointers and
+things like that. Um at least three or
+
+ align:start position:0%
+things like that. Um at least three or
+ 
+
+ align:start position:0%
+things like that. Um at least three or
+four times we spent a few hours until we
+
+ align:start position:0%
+four times we spent a few hours until we
+ 
+
+ align:start position:0%
+four times we spent a few hours until we
+discovered that was the cause of
+
+ align:start position:0%
+discovered that was the cause of
+ 
+
+ align:start position:0%
+discovered that was the cause of
+mysterious behavior.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I
+
+ align:start position:0%
+Okay, I
+ 
+
+ align:start position:0%
+Okay, I
+[Applause]
\ No newline at end of file
diff --git a/t2PkbsWjG80.txt b/t2PkbsWjG80.txt
new file mode 100644
index 0000000000000000000000000000000000000000..47e374e92e09e709465537257cea6c2b70134196
--- /dev/null
+++ b/t2PkbsWjG80.txt
@@ -0,0 +1,1139 @@
+align:start position:0%
+ 
+we would now like to calculate the
+
+ align:start position:0%
+we would now like to calculate the
+ 
+
+ align:start position:0%
+we would now like to calculate the
+potential function for a universal law
+
+ align:start position:0%
+potential function for a universal law
+ 
+
+ align:start position:0%
+potential function for a universal law
+of gravity so let's set up a coordinate
+
+ align:start position:0%
+of gravity so let's set up a coordinate
+ 
+
+ align:start position:0%
+of gravity so let's set up a coordinate
+system first and in this case we're
+
+ align:start position:0%
+system first and in this case we're
+ 
+
+ align:start position:0%
+system first and in this case we're
+going to make a very special case
+
+ align:start position:0%
+going to make a very special case
+ 
+
+ align:start position:0%
+going to make a very special case
+although the general result doesn't
+
+ align:start position:0%
+although the general result doesn't
+ 
+
+ align:start position:0%
+although the general result doesn't
+depend on that so suppose we have a
+
+ align:start position:0%
+depend on that so suppose we have a
+ 
+
+ align:start position:0%
+depend on that so suppose we have a
+planet of radius RP and we have a small
+
+ align:start position:0%
+planet of radius RP and we have a small
+ 
+
+ align:start position:0%
+planet of radius RP and we have a small
+object and initially our object is a
+
+ align:start position:0%
+object and initially our object is a
+ 
+
+ align:start position:0%
+object and initially our object is a
+distance R away from the planet this is
+
+ align:start position:0%
+distance R away from the planet this is
+ 
+
+ align:start position:0%
+distance R away from the planet this is
+our initial state and the planet has
+
+ align:start position:0%
+our initial state and the planet has
+ 
+
+ align:start position:0%
+our initial state and the planet has
+mass of the planet and our small object
+
+ align:start position:0%
+mass of the planet and our small object
+ 
+
+ align:start position:0%
+mass of the planet and our small object
+has mass and and this object is moving
+
+ align:start position:0%
+has mass and and this object is moving
+ 
+
+ align:start position:0%
+has mass and and this object is moving
+of course orbits really aren't like that
+
+ align:start position:0%
+of course orbits really aren't like that
+ 
+
+ align:start position:0%
+of course orbits really aren't like that
+so we should be a little bit more
+
+ align:start position:0%
+so we should be a little bit more
+ 
+
+ align:start position:0%
+so we should be a little bit more
+careful but our orbit might be some type
+
+ align:start position:0%
+careful but our orbit might be some type
+ 
+
+ align:start position:0%
+careful but our orbit might be some type
+of hyperbolic section conic section and
+
+ align:start position:0%
+of hyperbolic section conic section and
+ 
+
+ align:start position:0%
+of hyperbolic section conic section and
+the orbit over here is at some final
+
+ align:start position:0%
+the orbit over here is at some final
+ 
+
+ align:start position:0%
+the orbit over here is at some final
+position did and our eyes the distance
+
+ align:start position:0%
+position did and our eyes the distance
+ 
+
+ align:start position:0%
+position did and our eyes the distance
+from the object to the center of the
+
+ align:start position:0%
+from the object to the center of the
+ 
+
+ align:start position:0%
+from the object to the center of the
+planet as our final is now let's just
+
+ align:start position:0%
+planet as our final is now let's just
+ 
+
+ align:start position:0%
+planet as our final is now let's just
+because there's a central point in this
+
+ align:start position:0%
+because there's a central point in this
+ 
+
+ align:start position:0%
+because there's a central point in this
+problem the natural coordinate system to
+
+ align:start position:0%
+problem the natural coordinate system to
+ 
+
+ align:start position:0%
+problem the natural coordinate system to
+use is polar coordinates in the plane
+
+ align:start position:0%
+use is polar coordinates in the plane
+ 
+
+ align:start position:0%
+use is polar coordinates in the plane
+and let's just imagine that at this
+
+ align:start position:0%
+and let's just imagine that at this
+ 
+
+ align:start position:0%
+and let's just imagine that at this
+moment we have the universal force of
+
+ align:start position:0%
+moment we have the universal force of
+ 
+
+ align:start position:0%
+moment we have the universal force of
+gravity here's our object and it's being
+
+ align:start position:0%
+gravity here's our object and it's being
+ 
+
+ align:start position:0%
+gravity here's our object and it's being
+displaced a distance s so our coordinate
+
+ align:start position:0%
+displaced a distance s so our coordinate
+ 
+
+ align:start position:0%
+displaced a distance s so our coordinate
+system is polar
+
+ align:start position:0%
+system is polar
+ 
+
+ align:start position:0%
+system is polar
+let's call R hat this way and theta hat
+
+ align:start position:0%
+let's call R hat this way and theta hat
+ 
+
+ align:start position:0%
+let's call R hat this way and theta hat
+that way and let's blow up our little
+
+ align:start position:0%
+that way and let's blow up our little
+ 
+
+ align:start position:0%
+that way and let's blow up our little
+displacement in terms of our coordinate
+
+ align:start position:0%
+displacement in terms of our coordinate
+ 
+
+ align:start position:0%
+displacement in terms of our coordinate
+system just so that we see what's
+
+ align:start position:0%
+system just so that we see what's
+ 
+
+ align:start position:0%
+system just so that we see what's
+happening so our displacement had a
+
+ align:start position:0%
+happening so our displacement had a
+ 
+
+ align:start position:0%
+happening so our displacement had a
+let's imagine that our little DS vector
+
+ align:start position:0%
+let's imagine that our little DS vector
+ 
+
+ align:start position:0%
+let's imagine that our little DS vector
+is pointing like this and our center
+
+ align:start position:0%
+is pointing like this and our center
+ 
+
+ align:start position:0%
+is pointing like this and our center
+point here we have the R hat pointing
+
+ align:start position:0%
+point here we have the R hat pointing
+ 
+
+ align:start position:0%
+point here we have the R hat pointing
+radially outward and the theta hat
+
+ align:start position:0%
+radially outward and the theta hat
+ 
+
+ align:start position:0%
+radially outward and the theta hat
+pointing towards the center now to
+
+ align:start position:0%
+pointing towards the center now to
+ 
+
+ align:start position:0%
+pointing towards the center now to
+exaggerate this picture if this is R
+
+ align:start position:0%
+exaggerate this picture if this is R
+ 
+
+ align:start position:0%
+exaggerate this picture if this is R
+then the arc length here is Rd theta and
+
+ align:start position:0%
+then the arc length here is Rd theta and
+ 
+
+ align:start position:0%
+then the arc length here is Rd theta and
+the difference
+
+ align:start position:0%
+the difference
+ 
+
+ align:start position:0%
+the difference
+as the object moves from one point here
+
+ align:start position:0%
+as the object moves from one point here
+ 
+
+ align:start position:0%
+as the object moves from one point here
+to a closer point towards the center
+
+ align:start position:0%
+to a closer point towards the center
+ 
+
+ align:start position:0%
+to a closer point towards the center
+will be D R and so our D s vector we can
+
+ align:start position:0%
+will be D R and so our D s vector we can
+ 
+
+ align:start position:0%
+will be D R and so our D s vector we can
+write as a radial piece R hat now I
+
+ align:start position:0%
+write as a radial piece R hat now I
+ 
+
+ align:start position:0%
+write as a radial piece R hat now I
+don't put a sign in there because only
+
+ align:start position:0%
+don't put a sign in there because only
+ 
+
+ align:start position:0%
+don't put a sign in there because only
+the endpoints of my integral will tell
+
+ align:start position:0%
+the endpoints of my integral will tell
+ 
+
+ align:start position:0%
+the endpoints of my integral will tell
+me whether I was going towards the
+
+ align:start position:0%
+me whether I was going towards the
+ 
+
+ align:start position:0%
+me whether I was going towards the
+planet or away from the planet and our D
+
+ align:start position:0%
+planet or away from the planet and our D
+ 
+
+ align:start position:0%
+planet or away from the planet and our D
+theta theta hat and our gravitational
+
+ align:start position:0%
+theta theta hat and our gravitational
+ 
+
+ align:start position:0%
+theta theta hat and our gravitational
+force is minus G mass mass of the planet
+
+ align:start position:0%
+force is minus G mass mass of the planet
+ 
+
+ align:start position:0%
+force is minus G mass mass of the planet
+over the distance squared R hat so now
+
+ align:start position:0%
+over the distance squared R hat so now
+ 
+
+ align:start position:0%
+over the distance squared R hat so now
+what we see is that when we take the dot
+
+ align:start position:0%
+what we see is that when we take the dot
+ 
+
+ align:start position:0%
+what we see is that when we take the dot
+product of these two forces our hat down
+
+ align:start position:0%
+product of these two forces our hat down
+ 
+
+ align:start position:0%
+product of these two forces our hat down
+our hat is one in polar coordinates why
+
+ align:start position:0%
+our hat is one in polar coordinates why
+ 
+
+ align:start position:0%
+our hat is one in polar coordinates why
+is that the case our hat dot R hat is
+
+ align:start position:0%
+is that the case our hat dot R hat is
+ 
+
+ align:start position:0%
+is that the case our hat dot R hat is
+one because these vectors are purpose of
+
+ align:start position:0%
+one because these vectors are purpose of
+ 
+
+ align:start position:0%
+one because these vectors are purpose of
+the same direction the angle between
+
+ align:start position:0%
+the same direction the angle between
+ 
+
+ align:start position:0%
+the same direction the angle between
+them is zero and remember that any two
+
+ align:start position:0%
+them is zero and remember that any two
+ 
+
+ align:start position:0%
+them is zero and remember that any two
+vectors that are perpendicular have dot
+
+ align:start position:0%
+vectors that are perpendicular have dot
+ 
+
+ align:start position:0%
+vectors that are perpendicular have dot
+product zero R hat and beta hat are
+
+ align:start position:0%
+product zero R hat and beta hat are
+ 
+
+ align:start position:0%
+product zero R hat and beta hat are
+perpendicular and so R hat dot R hat is
+
+ align:start position:0%
+perpendicular and so R hat dot R hat is
+ 
+
+ align:start position:0%
+perpendicular and so R hat dot R hat is
+1 R hat dot theta hat is 0 so we only
+
+ align:start position:0%
+1 R hat dot theta hat is 0 so we only
+ 
+
+ align:start position:0%
+1 R hat dot theta hat is 0 so we only
+get minus g-m P R squared D R and that's
+
+ align:start position:0%
+get minus g-m P R squared D R and that's
+ 
+
+ align:start position:0%
+get minus g-m P R squared D R and that's
+the first step in calculating our
+
+ align:start position:0%
+the first step in calculating our
+ 
+
+ align:start position:0%
+the first step in calculating our
+potential difference because you of our
+
+ align:start position:0%
+potential difference because you of our
+ 
+
+ align:start position:0%
+potential difference because you of our
+final minus you of our initial by
+
+ align:start position:0%
+final minus you of our initial by
+ 
+
+ align:start position:0%
+final minus you of our initial by
+definition is minus the work done in
+
+ align:start position:0%
+definition is minus the work done in
+ 
+
+ align:start position:0%
+definition is minus the work done in
+going from the initial state to the
+
+ align:start position:0%
+going from the initial state to the
+ 
+
+ align:start position:0%
+going from the initial state to the
+final state which are described by these
+
+ align:start position:0%
+final state which are described by these
+ 
+
+ align:start position:0%
+final state which are described by these
+parameters our initial in our final of F
+
+ align:start position:0%
+parameters our initial in our final of F
+ 
+
+ align:start position:0%
+parameters our initial in our final of F
+gravitational dot d s and now we have
+
+ align:start position:0%
+gravitational dot d s and now we have
+ 
+
+ align:start position:0%
+gravitational dot d s and now we have
+actually minus sign in the definition
+
+ align:start position:0%
+actually minus sign in the definition
+ 
+
+ align:start position:0%
+actually minus sign in the definition
+another minus sign coming from the dot
+
+ align:start position:0%
+another minus sign coming from the dot
+ 
+
+ align:start position:0%
+another minus sign coming from the dot
+product and let's make this our
+
+ align:start position:0%
+product and let's make this our
+ 
+
+ align:start position:0%
+product and let's make this our
+integration variable our prime our
+
+ align:start position:0%
+integration variable our prime our
+ 
+
+ align:start position:0%
+integration variable our prime our
+initial R prime equals our final and
+
+ align:start position:0%
+initial R prime equals our final and
+ 
+
+ align:start position:0%
+initial R prime equals our final and
+there's going to be a third minus sign
+
+ align:start position:0%
+there's going to be a third minus sign
+ 
+
+ align:start position:0%
+there's going to be a third minus sign
+because the integral of D RR prime
+
+ align:start position:0%
+because the integral of D RR prime
+ 
+
+ align:start position:0%
+because the integral of D RR prime
+squared is minus one over R prime so
+
+ align:start position:0%
+squared is minus one over R prime so
+ 
+
+ align:start position:0%
+squared is minus one over R prime so
+there'll be three minus signs one from
+
+ align:start position:0%
+there'll be three minus signs one from
+ 
+
+ align:start position:0%
+there'll be three minus signs one from
+the definition one from the scalar
+
+ align:start position:0%
+the definition one from the scalar
+ 
+
+ align:start position:0%
+the definition one from the scalar
+product and one from the integration and
+
+ align:start position:0%
+product and one from the integration and
+ 
+
+ align:start position:0%
+product and one from the integration and
+so we get our final
+
+ align:start position:0%
+so we get our final
+ 
+
+ align:start position:0%
+so we get our final
+- our initial equals three minus signs
+
+ align:start position:0%
+- our initial equals three minus signs
+ 
+
+ align:start position:0%
+- our initial equals three minus signs
+give an overall minus sign G M and
+
+ align:start position:0%
+give an overall minus sign G M and
+ 
+
+ align:start position:0%
+give an overall minus sign G M and
+planet one over our final minus one over
+
+ align:start position:0%
+planet one over our final minus one over
+ 
+
+ align:start position:0%
+planet one over our final minus one over
+our initial so this is the change in
+
+ align:start position:0%
+our initial so this is the change in
+ 
+
+ align:start position:0%
+our initial so this is the change in
+gravitational potential energy as my
+
+ align:start position:0%
+gravitational potential energy as my
+ 
+
+ align:start position:0%
+gravitational potential energy as my
+small object goes from some initial
+
+ align:start position:0%
+small object goes from some initial
+ 
+
+ align:start position:0%
+small object goes from some initial
+state to some final state what about the
+
+ align:start position:0%
+state to some final state what about the
+ 
+
+ align:start position:0%
+state to some final state what about the
+potential function where should we
+
+ align:start position:0%
+potential function where should we
+ 
+
+ align:start position:0%
+potential function where should we
+choose our reference point now so our
+
+ align:start position:0%
+choose our reference point now so our
+ 
+
+ align:start position:0%
+choose our reference point now so our
+reference state here is a little bit
+
+ align:start position:0%
+reference state here is a little bit
+ 
+
+ align:start position:0%
+reference state here is a little bit
+unusual and it will be at infinity and
+
+ align:start position:0%
+unusual and it will be at infinity and
+ 
+
+ align:start position:0%
+unusual and it will be at infinity and
+we'll choose as a potential for our
+
+ align:start position:0%
+we'll choose as a potential for our
+ 
+
+ align:start position:0%
+we'll choose as a potential for our
+reference potential to be zero at
+
+ align:start position:0%
+reference potential to be zero at
+ 
+
+ align:start position:0%
+reference potential to be zero at
+infinity that means when our imagine an
+
+ align:start position:0%
+infinity that means when our imagine an
+ 
+
+ align:start position:0%
+infinity that means when our imagine an
+initial state very very far away from
+
+ align:start position:0%
+initial state very very far away from
+ 
+
+ align:start position:0%
+initial state very very far away from
+the planet and we'll take as a final
+
+ align:start position:0%
+the planet and we'll take as a final
+ 
+
+ align:start position:0%
+the planet and we'll take as a final
+state an arbitrary state just where the
+
+ align:start position:0%
+state an arbitrary state just where the
+ 
+
+ align:start position:0%
+state an arbitrary state just where the
+object is some distance R from the
+
+ align:start position:0%
+object is some distance R from the
+ 
+
+ align:start position:0%
+object is some distance R from the
+planet now we have to be a little bit
+
+ align:start position:0%
+planet now we have to be a little bit
+ 
+
+ align:start position:0%
+planet now we have to be a little bit
+careful because in this calculation are
+
+ align:start position:0%
+careful because in this calculation are
+ 
+
+ align:start position:0%
+careful because in this calculation are
+always our final state must always be
+
+ align:start position:0%
+always our final state must always be
+ 
+
+ align:start position:0%
+always our final state must always be
+outside the planet when the reasons for
+
+ align:start position:0%
+outside the planet when the reasons for
+ 
+
+ align:start position:0%
+outside the planet when the reasons for
+that is subtle but the gravitational
+
+ align:start position:0%
+that is subtle but the gravitational
+ 
+
+ align:start position:0%
+that is subtle but the gravitational
+force inside the planet is no longer
+
+ align:start position:0%
+force inside the planet is no longer
+ 
+
+ align:start position:0%
+force inside the planet is no longer
+minus G m1 m2 over R squared so our
+
+ align:start position:0%
+minus G m1 m2 over R squared so our
+ 
+
+ align:start position:0%
+minus G m1 m2 over R squared so our
+analysis only applies for our bigger
+
+ align:start position:0%
+analysis only applies for our bigger
+ 
+
+ align:start position:0%
+analysis only applies for our bigger
+than our planet and if we put these
+
+ align:start position:0%
+than our planet and if we put these
+ 
+
+ align:start position:0%
+than our planet and if we put these
+values for R and infinity in here we get
+
+ align:start position:0%
+values for R and infinity in here we get
+ 
+
+ align:start position:0%
+values for R and infinity in here we get
+U of R minus the potential at our
+
+ align:start position:0%
+U of R minus the potential at our
+ 
+
+ align:start position:0%
+U of R minus the potential at our
+reference point which will be 0 equals
+
+ align:start position:0%
+reference point which will be 0 equals
+ 
+
+ align:start position:0%
+reference point which will be 0 equals
+minus g-m and P and here's the reason
+
+ align:start position:0%
+minus g-m and P and here's the reason
+ 
+
+ align:start position:0%
+minus g-m and P and here's the reason
+why we choose that reference point 1
+
+ align:start position:0%
+why we choose that reference point 1
+ 
+
+ align:start position:0%
+why we choose that reference point 1
+over our arbitrary state is just minus 1
+
+ align:start position:0%
+over our arbitrary state is just minus 1
+ 
+
+ align:start position:0%
+over our arbitrary state is just minus 1
+over 1 over R but 1 over infinity if we
+
+ align:start position:0%
+over 1 over R but 1 over infinity if we
+ 
+
+ align:start position:0%
+over 1 over R but 1 over infinity if we
+use the initial state as the reference
+
+ align:start position:0%
+use the initial state as the reference
+ 
+
+ align:start position:0%
+use the initial state as the reference
+point 1 over infinity is 0 so that's
+
+ align:start position:0%
+point 1 over infinity is 0 so that's
+ 
+
+ align:start position:0%
+point 1 over infinity is 0 so that's
+minus 0 and so what we get is that the
+
+ align:start position:0%
+minus 0 and so what we get is that the
+ 
+
+ align:start position:0%
+minus 0 and so what we get is that the
+potential function is equal to our
+
+ align:start position:0%
+potential function is equal to our
+ 
+
+ align:start position:0%
+potential function is equal to our
+reference potential plot actually minus
+
+ align:start position:0%
+reference potential plot actually minus
+ 
+
+ align:start position:0%
+reference potential plot actually minus
+g-m mass of the planet over R for R
+
+ align:start position:0%
+g-m mass of the planet over R for R
+ 
+
+ align:start position:0%
+g-m mass of the planet over R for R
+bigger than our
+
+ align:start position:0%
+bigger than our
+ 
+
+ align:start position:0%
+bigger than our
+reference and that is the potential
+
+ align:start position:0%
+reference and that is the potential
+ 
+
+ align:start position:0%
+reference and that is the potential
+function for the gravitational problem
+
+ align:start position:0%
+function for the gravitational problem
+ 
+
+ align:start position:0%
+function for the gravitational problem
+but now remember we're choosing that to
+
+ align:start position:0%
+but now remember we're choosing that to
+ 
+
+ align:start position:0%
+but now remember we're choosing that to
+be our reference point and so the real
+
+ align:start position:0%
+be our reference point and so the real
+ 
+
+ align:start position:0%
+be our reference point and so the real
+conclusion is U of R equals minus g-m
+
+ align:start position:0%
+conclusion is U of R equals minus g-m
+ 
+
+ align:start position:0%
+conclusion is U of R equals minus g-m
+and planet over R with you at infinity
+
+ align:start position:0%
+and planet over R with you at infinity
+ 
+
+ align:start position:0%
+and planet over R with you at infinity
+equal to zero now let's just finish this
+
+ align:start position:0%
+equal to zero now let's just finish this
+ 
+
+ align:start position:0%
+equal to zero now let's just finish this
+by saying in words precisely what this
+
+ align:start position:0%
+by saying in words precisely what this
+ 
+
+ align:start position:0%
+by saying in words precisely what this
+means so if I start my system at
+
+ align:start position:0%
+means so if I start my system at
+ 
+
+ align:start position:0%
+means so if I start my system at
+infinity and I end my system a distance
+
+ align:start position:0%
+infinity and I end my system a distance
+ 
+
+ align:start position:0%
+infinity and I end my system a distance
+R away from the planet and I calculate
+
+ align:start position:0%
+R away from the planet and I calculate
+ 
+
+ align:start position:0%
+R away from the planet and I calculate
+the work done by the gravitational force
+
+ align:start position:0%
+the work done by the gravitational force
+ 
+
+ align:start position:0%
+the work done by the gravitational force
+in going from infinity to a distance R
+
+ align:start position:0%
+in going from infinity to a distance R
+ 
+
+ align:start position:0%
+in going from infinity to a distance R
+away from the planet I take a minus that
+
+ align:start position:0%
+away from the planet I take a minus that
+ 
+
+ align:start position:0%
+away from the planet I take a minus that
+sign so the negative of the
+
+ align:start position:0%
+sign so the negative of the
+ 
+
+ align:start position:0%
+sign so the negative of the
+gravitational work then that's what that
+
+ align:start position:0%
+gravitational work then that's what that
+ 
+
+ align:start position:0%
+gravitational work then that's what that
+number corresponds to
\ No newline at end of file
diff --git a/tMr9XH64rtM.txt b/tMr9XH64rtM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8b0abb3afd7aaa511a16094b1004469d6eb84a4e
--- /dev/null
+++ b/tMr9XH64rtM.txt
@@ -0,0 +1,345 @@
+PROFESSOR: Now, onward.
+
+Transcription.
+
+So, we've got DNA, we'll do two,
+three, probably three by
+
+now, transcription.
+
+So we have DNA goes to DNA.
+
+DNA makes RNA, RNA
+makes protein.
+
+This, by the way, gets the
+name the central dogma of
+
+molecular biology.
+
+Due to Francis Crick, and as
+an aside, Francis actually
+
+never said DNA goes to
+RNA goes to protein.
+
+What he said was nucleic
+acids go to protein.
+
+The information flows from
+nucleic acids to proteins.
+
+He never actually said DNA goes
+to RNA goes to protein,
+
+and that's an important point.
+
+And we'll come to it at some
+point, probably next time.
+
+So, transcription.
+
+Here's my genome.
+
+Here's my double helix.
+
+I'm going to stop wrapping
+around itself, just because
+
+it's tedious.
+
+And here's a chunk of DNA
+that encodes a gene.
+
+Maybe it's a gene that makes
+our enzyme for arginine
+
+biosynthesis.
+
+Remember, we had our arginine
+genes and all that.
+
+But what happens is it has a
+starting point, it has a
+
+stopping point.
+
+Five prime to three prime.
+
+What happens is there is a
+signal in the DNA that the
+
+cell knows how to read
+called a promoter.
+
+And under certain circumstances,
+this promoter
+
+invites an enzyme to sit down,
+and the enzyme starts copying.
+
+Which direction does
+this enzyme go?
+
+Five prime to three prime.
+
+They all go five prime
+to three prime.
+
+But it makes RNA.
+
+Okay?
+
+And then it gets to certain
+point, and it stops copying.
+
+This process of copying is
+called transcription, because
+
+it's just a direct
+transcribing.
+
+So what's the difference
+between DNA and RNA?
+
+Two differences.
+
+One, this is two prime
+deoxyribose.
+
+This is ribose.
+
+It's not two prime deoxy.
+
+It's truly ribose.
+
+The other difference, where DNA
+has T, RNA, has U, uracil.
+
+The difference, what's the
+difference between T and U?
+
+The difference is
+a methyl group.
+
+It's a methyl group in an
+unimportant position for the
+
+base paring.
+
+It doesn't matter.
+
+It has an extra methyl group.
+
+You can look it up
+in your book.
+
+So for all practical purposes,
+you, in thinking about
+
+polymerization and five prime
+to three prime, and
+
+everything, could imagine the
+DNA and RNA are the same basic
+
+structure, because it's got one
+little methyl group that
+
+distinguishes T and U. And it's
+got a hydroxyl on the two
+
+prime position in the carbon,
+in the sugar, which actually
+
+isn't anything we use.
+
+We never use the two prime.
+
+So none of what I've told you is
+affected by t versus u, or
+
+deoxyribose versus ribose.
+
+Now, it turns out it does
+make a difference
+
+in the overall structure.
+
+It's harder to base pair with
+the ribose there as opposed to
+
+the deoxyribose because they
+stack differently, et cetera.
+
+It makes a difference
+to the cell.
+
+RNA is less stable, all
+sorts of things.
+
+But for your practical purposes,
+apart from having to
+
+know that it's T versus U, and
+deoxyribose versus ribose, you
+
+won't see in this course
+actually see any real strong
+
+reasons why it matters, but it
+does matter to the cell.
+
+All right.
+
+So this enzyme comes along, and
+it copies a segment of the
+
+DNA, starting at a promoter.
+
+It knows which strand it's on.
+
+Remember, this is stranded.
+
+It's not like it's going
+back this way.
+
+It has a directionality to it.
+
+And in reaches what's called a
+transcriptional stop signal.
+
+Transcriptional stop, which is a
+certain sequence in the DNA,
+
+and it comes to an end.
+
+And it makes an RNA transcript,
+
+which then floats away.
+
+Which we'll talk
+next time, gets
+
+translated into a protein.
+
+And how do you think
+this works?
+
+It takes nucleotides, RNA
+nucleotides here, with their
+
+triphosphates, and sticks them
+on, just like we saw with DNA.
+
+And it makes a polymer of RNA.
+
+And the enzyme is called
+RNA polymerase, right?
+
+This is all pretty
+logical stuff.
+
+RNA polymerase comes along
+and does that.
+
+So we get RNA polymerase.
+
+Now, when I am a cell, and this
+is my genome, I have a
+
+gene that goes this way.
+
+Here's its promoter, here's
+its transcriptional stop.
+
+I could also have a gene
+that goes this way.
+
+Here's its promoter, here's
+its transcriptional stop.
+
+Directionality could go
+in either direction.
+
+RNA polymerase comes along, and
+with the help of friends,
+
+knows where to start.
+
+Those friends could be other
+proteins that are sitting down
+
+there that RNA polymerase
+likes to associate with.
+
+And which strand is
+being transcribed?
+
+The bottom strand, or
+the top strand?
+
+Matters.
+
+You get a different single
+stranded RNA.
+
+So RNA, when it floats off,
+is single stranded.
+
+This is going to make a single
+stranded RNA that, five prime
+
+to three prime RNA that is
+complimentary to, matching to,
+
+the bottom.
+
+This guy, however, will make an
+RNA that is complimentary
+
+to the top.
+
+Much of the business of running
+your cell is figuring
+
+out which genes you should
+be transcribing into RNA.
+
+It turns out your liver is
+making different transcripts.
+
+It's transcribing different
+segments of your genome than
+
+say, a muscle cell.
+
+Than say, a brain cell.
+
+All of that machinery of
+figuring out how one genome
+
+gets read out in different ways
+by RNA polymerase is the
+
+problem of gene regulation.
+
+And we will talk about that
+in a little while.
+
+What we're going to talk about
+next time is how that RNA
+
+transcript gets translated
+into a protein.
+
+And you guys probably,
+again, all know this.
+
+But nonetheless, we'll talk
+a little bit about it.
+
+And then we'll talk about some
+variations on that theme.
+
+Until next time.
\ No newline at end of file
diff --git a/tkglOK3ZEsI.txt b/tkglOK3ZEsI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..55d4b067c3629fd1b0e080308f8300d5261d9781
--- /dev/null
+++ b/tkglOK3ZEsI.txt
@@ -0,0 +1,12200 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so last time
+
+ align:start position:0%
+so so last time
+ 
+
+ align:start position:0%
+so so last time
+we started talking about the following
+
+ align:start position:0%
+we started talking about the following
+ 
+
+ align:start position:0%
+we started talking about the following
+process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e plus e minus
+
+ align:start position:0%
+e plus e minus
+ 
+
+ align:start position:0%
+e plus e minus
+so electron voltage on the scatter
+
+ align:start position:0%
+so electron voltage on the scatter
+ 
+
+ align:start position:0%
+so electron voltage on the scatter
+and then they will allow it and then
+
+ align:start position:0%
+and then they will allow it and then
+ 
+
+ align:start position:0%
+and then they will allow it and then
+they create some other particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so B and B Bar some feral particles
+
+ align:start position:0%
+okay so B and B Bar some feral particles
+ 
+
+ align:start position:0%
+okay so B and B Bar some feral particles
+okay can be can be different kind of
+
+ align:start position:0%
+okay can be can be different kind of
+ 
+
+ align:start position:0%
+okay can be can be different kind of
+things so if we draw the function
+
+ align:start position:0%
+things so if we draw the function
+ 
+
+ align:start position:0%
+things so if we draw the function
+diagram with the time going up
+
+ align:start position:0%
+diagram with the time going up
+ 
+
+ align:start position:0%
+diagram with the time going up
+and then then the uh then the process
+
+ align:start position:0%
+and then then the uh then the process
+ 
+
+ align:start position:0%
+and then then the uh then the process
+will be like falling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the um so the initial particle
+
+ align:start position:0%
+so the um so the initial particle
+ 
+
+ align:start position:0%
+so the um so the initial particle
+so this is the E minus and this is e
+
+ align:start position:0%
+so this is the E minus and this is e
+ 
+
+ align:start position:0%
+so this is the E minus and this is e
+plus and then we have
+
+ align:start position:0%
+plus and then we have
+ 
+
+ align:start position:0%
+plus and then we have
+B and B Bar okay
+
+ align:start position:0%
+B and B Bar okay
+ 
+
+ align:start position:0%
+B and B Bar okay
+so we can um
+
+ align:start position:0%
+so we can um
+ 
+
+ align:start position:0%
+so we can um
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so such a process
+
+ align:start position:0%
+so such a process
+ 
+
+ align:start position:0%
+so such a process
+is a very important Discovery machine
+
+ align:start position:0%
+is a very important Discovery machine
+ 
+
+ align:start position:0%
+is a very important Discovery machine
+for new particles
+
+ align:start position:0%
+for new particles
+ 
+
+ align:start position:0%
+for new particles
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um very important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me just mention two examples here
+
+ align:start position:0%
+so let me just mention two examples here
+ 
+
+ align:start position:0%
+so let me just mention two examples here
+so in 1974
+
+ align:start position:0%
+so in 1974
+ 
+
+ align:start position:0%
+so in 1974
+to 1976
+
+ align:start position:0%
+to 1976
+ 
+
+ align:start position:0%
+to 1976
+at Slack
+
+ align:start position:0%
+at Slack
+ 
+
+ align:start position:0%
+at Slack
+so slack is called Stanford linear
+
+ align:start position:0%
+so slack is called Stanford linear
+ 
+
+ align:start position:0%
+so slack is called Stanford linear
+acceleration Center so they have a
+
+ align:start position:0%
+acceleration Center so they have a
+ 
+
+ align:start position:0%
+acceleration Center so they have a
+electron Collider
+
+ align:start position:0%
+electron Collider
+ 
+
+ align:start position:0%
+electron Collider
+and so there they first discovered the
+
+ align:start position:0%
+and so there they first discovered the
+ 
+
+ align:start position:0%
+and so there they first discovered the
+towel
+
+ align:start position:0%
+towel
+ 
+
+ align:start position:0%
+towel
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and this top particle
+
+ align:start position:0%
+okay and this top particle
+ 
+
+ align:start position:0%
+okay and this top particle
+with mass is the 1.8 gev Okay so
+
+ align:start position:0%
+with mass is the 1.8 gev Okay so
+ 
+
+ align:start position:0%
+with mass is the 1.8 gev Okay so
+when they
+
+ align:start position:0%
+when they
+ 
+
+ align:start position:0%
+when they
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you or when your total energy is
+
+ align:start position:0%
+when you or when your total energy is
+ 
+
+ align:start position:0%
+when you or when your total energy is
+greater than this one twice the one
+
+ align:start position:0%
+greater than this one twice the one
+ 
+
+ align:start position:0%
+greater than this one twice the one
+point in the GV then you can in
+
+ align:start position:0%
+point in the GV then you can in
+ 
+
+ align:start position:0%
+point in the GV then you can in
+principle create the pair created this
+
+ align:start position:0%
+principle create the pair created this
+ 
+
+ align:start position:0%
+principle create the pair created this
+top part Tau plus and Tall menus
+
+ align:start position:0%
+top part Tau plus and Tall menus
+ 
+
+ align:start position:0%
+top part Tau plus and Tall menus
+and another example
+
+ align:start position:0%
+and another example
+ 
+
+ align:start position:0%
+and another example
+is in 1974
+
+ align:start position:0%
+is in 1974
+ 
+
+ align:start position:0%
+is in 1974
+again at the slack
+
+ align:start position:0%
+again at the slack
+ 
+
+ align:start position:0%
+again at the slack
+and the E plus e minus
+
+ align:start position:0%
+and the E plus e minus
+ 
+
+ align:start position:0%
+and the E plus e minus
+goes to CC Bar
+
+ align:start position:0%
+goes to CC Bar
+ 
+
+ align:start position:0%
+goes to CC Bar
+so C is the chunk Park here
+
+ align:start position:0%
+so C is the chunk Park here
+ 
+
+ align:start position:0%
+so C is the chunk Park here
+okay it's the time clock here so what
+
+ align:start position:0%
+okay it's the time clock here so what
+ 
+
+ align:start position:0%
+okay it's the time clock here so what
+they observed is the bump state of the
+
+ align:start position:0%
+they observed is the bump state of the
+ 
+
+ align:start position:0%
+they observed is the bump state of the
+CC Bar called JSI
+
+ align:start position:0%
+CC Bar called JSI
+ 
+
+ align:start position:0%
+CC Bar called JSI
+so under the mass of the JSI is about
+
+ align:start position:0%
+so under the mass of the JSI is about
+ 
+
+ align:start position:0%
+so under the mass of the JSI is about
+3.1 Kev
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3.1 guv
+
+ align:start position:0%
+3.1 guv
+ 
+
+ align:start position:0%
+3.1 guv
+so so this JSI uh so so this particle
+
+ align:start position:0%
+so so this JSI uh so so this particle
+ 
+
+ align:start position:0%
+so so this JSI uh so so this particle
+was discovered
+
+ align:start position:0%
+was discovered
+ 
+
+ align:start position:0%
+was discovered
+at the same time
+
+ align:start position:0%
+at the same time
+ 
+
+ align:start position:0%
+at the same time
+at Brookhaven
+
+ align:start position:0%
+at Brookhaven
+ 
+
+ align:start position:0%
+at Brookhaven
+by through the proton quite through the
+
+ align:start position:0%
+by through the proton quite through the
+ 
+
+ align:start position:0%
+by through the proton quite through the
+conditioning of the protons by by our
+
+ align:start position:0%
+conditioning of the protons by by our
+ 
+
+ align:start position:0%
+conditioning of the protons by by our
+own colleagues Samuel team
+
+ align:start position:0%
+own colleagues Samuel team
+ 
+
+ align:start position:0%
+own colleagues Samuel team
+and then they both get the Bell price in
+
+ align:start position:0%
+and then they both get the Bell price in
+ 
+
+ align:start position:0%
+and then they both get the Bell price in
+1975 I think okay
+
+ align:start position:0%
+1975 I think okay
+ 
+
+ align:start position:0%
+1975 I think okay
+so uh uh there was actually a funny
+
+ align:start position:0%
+so uh uh there was actually a funny
+ 
+
+ align:start position:0%
+so uh uh there was actually a funny
+story regarding the discovery of this
+
+ align:start position:0%
+story regarding the discovery of this
+ 
+
+ align:start position:0%
+story regarding the discovery of this
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+so uh so at Brookhaven they
+
+ align:start position:0%
+so uh so at Brookhaven they
+ 
+
+ align:start position:0%
+so uh so at Brookhaven they
+they cried the protons on the abyss
+
+ align:start position:0%
+they cried the protons on the abyss
+ 
+
+ align:start position:0%
+they cried the protons on the abyss
+fixed Target so that is a much massier
+
+ align:start position:0%
+fixed Target so that is a much massier
+ 
+
+ align:start position:0%
+fixed Target so that is a much massier
+machine
+
+ align:start position:0%
+machine
+ 
+
+ align:start position:0%
+machine
+because proton contain lots of uh yeah
+
+ align:start position:0%
+because proton contain lots of uh yeah
+ 
+
+ align:start position:0%
+because proton contain lots of uh yeah
+contain quarks and plurals and so
+
+ align:start position:0%
+contain quarks and plurals and so
+ 
+
+ align:start position:0%
+contain quarks and plurals and so
+um yeah it's
+
+ align:start position:0%
+um yeah it's
+ 
+
+ align:start position:0%
+um yeah it's
+restoring interactions so so uh if you
+
+ align:start position:0%
+restoring interactions so so uh if you
+ 
+
+ align:start position:0%
+restoring interactions so so uh if you
+create the highness yeah if your client
+
+ align:start position:0%
+create the highness yeah if your client
+ 
+
+ align:start position:0%
+create the highness yeah if your client
+had high enough energy you can create
+
+ align:start position:0%
+had high enough energy you can create
+ 
+
+ align:start position:0%
+had high enough energy you can create
+any uh any particles but since you move
+
+ align:start position:0%
+any uh any particles but since you move
+ 
+
+ align:start position:0%
+any uh any particles but since you move
+in strong interactions and strong
+
+ align:start position:0%
+in strong interactions and strong
+ 
+
+ align:start position:0%
+in strong interactions and strong
+interaction have many many particles so
+
+ align:start position:0%
+interaction have many many particles so
+ 
+
+ align:start position:0%
+interaction have many many particles so
+the pro so the client at Brookhaven is
+
+ align:start position:0%
+the pro so the client at Brookhaven is
+ 
+
+ align:start position:0%
+the pro so the client at Brookhaven is
+very very messy
+
+ align:start position:0%
+very very messy
+ 
+
+ align:start position:0%
+very very messy
+okay so in order to find the new
+
+ align:start position:0%
+okay so in order to find the new
+ 
+
+ align:start position:0%
+okay so in order to find the new
+particles it's very very difficult okay
+
+ align:start position:0%
+particles it's very very difficult okay
+ 
+
+ align:start position:0%
+particles it's very very difficult okay
+but but they manage find this new
+
+ align:start position:0%
+but but they manage find this new
+ 
+
+ align:start position:0%
+but but they manage find this new
+particle at Brookhaven
+
+ align:start position:0%
+particle at Brookhaven
+ 
+
+ align:start position:0%
+particle at Brookhaven
+and but Sameer thing was
+
+ align:start position:0%
+and but Sameer thing was
+ 
+
+ align:start position:0%
+and but Sameer thing was
+uh famously
+
+ align:start position:0%
+uh famously
+ 
+
+ align:start position:0%
+uh famously
+extraordinary meticulous okay so he
+
+ align:start position:0%
+extraordinary meticulous okay so he
+ 
+
+ align:start position:0%
+extraordinary meticulous okay so he
+wanted to be absolutely right okay so he
+
+ align:start position:0%
+wanted to be absolutely right okay so he
+ 
+
+ align:start position:0%
+wanted to be absolutely right okay so he
+was checking and checking
+
+ align:start position:0%
+was checking and checking
+ 
+
+ align:start position:0%
+was checking and checking
+so during one of the yeah so this is a
+
+ align:start position:0%
+so during one of the yeah so this is a
+ 
+
+ align:start position:0%
+so during one of the yeah so this is a
+rumor so so the rumor said that during
+
+ align:start position:0%
+rumor so so the rumor said that during
+ 
+
+ align:start position:0%
+rumor so so the rumor said that during
+the one of the check-in process
+
+ align:start position:0%
+the one of the check-in process
+ 
+
+ align:start position:0%
+the one of the check-in process
+and somehow
+
+ align:start position:0%
+and somehow
+ 
+
+ align:start position:0%
+and somehow
+the room was private
+
+ align:start position:0%
+the room was private
+ 
+
+ align:start position:0%
+the room was private
+that he discovered a new particle
+
+ align:start position:0%
+that he discovered a new particle
+ 
+
+ align:start position:0%
+that he discovered a new particle
+and so the person was still in the
+
+ align:start position:0%
+and so the person was still in the
+ 
+
+ align:start position:0%
+and so the person was still in the
+experiment at the slack then caught him
+
+ align:start position:0%
+experiment at the slack then caught him
+ 
+
+ align:start position:0%
+experiment at the slack then caught him
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+even the rumor of the rumor even yeah so
+
+ align:start position:0%
+even the rumor of the rumor even yeah so
+ 
+
+ align:start position:0%
+even the rumor of the rumor even yeah so
+uh so so the news leaked it even leaked
+
+ align:start position:0%
+uh so so the news leaked it even leaked
+ 
+
+ align:start position:0%
+uh so so the news leaked it even leaked
+the energy scale of the particle they
+
+ align:start position:0%
+the energy scale of the particle they
+ 
+
+ align:start position:0%
+the energy scale of the particle they
+found okay
+
+ align:start position:0%
+found okay
+ 
+
+ align:start position:0%
+found okay
+and then the person was doing the
+
+ align:start position:0%
+and then the person was doing the
+ 
+
+ align:start position:0%
+and then the person was doing the
+visitor at the slack and then called the
+
+ align:start position:0%
+visitor at the slack and then called the
+ 
+
+ align:start position:0%
+visitor at the slack and then called the
+same thing he said oh uh uh uh I heard
+
+ align:start position:0%
+same thing he said oh uh uh uh I heard
+ 
+
+ align:start position:0%
+same thing he said oh uh uh uh I heard
+you have found a new particle
+
+ align:start position:0%
+you have found a new particle
+ 
+
+ align:start position:0%
+you have found a new particle
+no no I didn't
+
+ align:start position:0%
+no no I didn't
+ 
+
+ align:start position:0%
+no no I didn't
+yeah because he didn't want to have the
+
+ align:start position:0%
+yeah because he didn't want to have the
+ 
+
+ align:start position:0%
+yeah because he didn't want to have the
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+yeah actually it's not very good because
+
+ align:start position:0%
+yeah actually it's not very good because
+ 
+
+ align:start position:0%
+yeah actually it's not very good because
+I'm recorded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I recorded so so I think this uh maybe
+
+ align:start position:0%
+I recorded so so I think this uh maybe
+ 
+
+ align:start position:0%
+I recorded so so I think this uh maybe
+it's not the good spread rumors
+
+ align:start position:0%
+it's not the good spread rumors
+ 
+
+ align:start position:0%
+it's not the good spread rumors
+it is not recorded actually I can tell
+
+ align:start position:0%
+it is not recorded actually I can tell
+ 
+
+ align:start position:0%
+it is not recorded actually I can tell
+the story uh yeah anyway so so so
+
+ align:start position:0%
+the story uh yeah anyway so so so
+ 
+
+ align:start position:0%
+the story uh yeah anyway so so so
+accordingly and then then then
+
+ align:start position:0%
+accordingly and then then then
+ 
+
+ align:start position:0%
+accordingly and then then then
+the a rich eater and they say oh you
+
+ align:start position:0%
+the a rich eater and they say oh you
+ 
+
+ align:start position:0%
+the a rich eater and they say oh you
+didn't find the particle that I can
+
+ align:start position:0%
+didn't find the particle that I can
+ 
+
+ align:start position:0%
+didn't find the particle that I can
+Discover it
+
+ align:start position:0%
+Discover it
+ 
+
+ align:start position:0%
+Discover it
+because they already knew the energy
+
+ align:start position:0%
+because they already knew the energy
+ 
+
+ align:start position:0%
+because they already knew the energy
+scale they already heard the role model
+
+ align:start position:0%
+scale they already heard the role model
+ 
+
+ align:start position:0%
+scale they already heard the role model
+energy scale and this is a very very
+
+ align:start position:0%
+energy scale and this is a very very
+ 
+
+ align:start position:0%
+energy scale and this is a very very
+clean machine
+
+ align:start position:0%
+clean machine
+ 
+
+ align:start position:0%
+clean machine
+so electron positive and declined the
+
+ align:start position:0%
+so electron positive and declined the
+ 
+
+ align:start position:0%
+so electron positive and declined the
+only energy created and so you don't
+
+ align:start position:0%
+only energy created and so you don't
+ 
+
+ align:start position:0%
+only energy created and so you don't
+create a lot of chunks and if you add to
+
+ align:start position:0%
+create a lot of chunks and if you add to
+ 
+
+ align:start position:0%
+create a lot of chunks and if you add to
+the right energy you can immediately
+
+ align:start position:0%
+the right energy you can immediately
+ 
+
+ align:start position:0%
+the right energy you can immediately
+find the new particle you don't need to
+
+ align:start position:0%
+find the new particle you don't need to
+ 
+
+ align:start position:0%
+find the new particle you don't need to
+do much work and so they put the the
+
+ align:start position:0%
+do much work and so they put the the
+ 
+
+ align:start position:0%
+do much work and so they put the the
+machine at that energy immediately new
+
+ align:start position:0%
+machine at that energy immediately new
+ 
+
+ align:start position:0%
+machine at that energy immediately new
+particle was discovered
+
+ align:start position:0%
+particle was discovered
+ 
+
+ align:start position:0%
+particle was discovered
+okay and so they uh they were um yeah so
+
+ align:start position:0%
+okay and so they uh they were um yeah so
+ 
+
+ align:start position:0%
+okay and so they uh they were um yeah so
+they were avoided Nobel Prize jointly
+
+ align:start position:0%
+they were avoided Nobel Prize jointly
+ 
+
+ align:start position:0%
+they were avoided Nobel Prize jointly
+um anyway so so this was a important
+
+ align:start position:0%
+um anyway so so this was a important
+ 
+
+ align:start position:0%
+um anyway so so this was a important
+discovery
+
+ align:start position:0%
+discovery
+ 
+
+ align:start position:0%
+discovery
+because the because before that people
+
+ align:start position:0%
+because the because before that people
+ 
+
+ align:start position:0%
+because the because before that people
+didn't believe quarks exist okay even
+
+ align:start position:0%
+didn't believe quarks exist okay even
+ 
+
+ align:start position:0%
+didn't believe quarks exist okay even
+though people didn't quite believe the
+
+ align:start position:0%
+though people didn't quite believe the
+ 
+
+ align:start position:0%
+though people didn't quite believe the
+clock existed even though they're there
+
+ align:start position:0%
+clock existed even though they're there
+ 
+
+ align:start position:0%
+clock existed even though they're there
+are many models Etc and there are lots
+
+ align:start position:0%
+are many models Etc and there are lots
+ 
+
+ align:start position:0%
+are many models Etc and there are lots
+of other evidences but this was the
+
+ align:start position:0%
+of other evidences but this was the
+ 
+
+ align:start position:0%
+of other evidences but this was the
+first uh uh uh uh the the the first uh
+
+ align:start position:0%
+first uh uh uh uh the the the first uh
+ 
+
+ align:start position:0%
+first uh uh uh uh the the the first uh
+yeah because sea Clark is very strongly
+
+ align:start position:0%
+yeah because sea Clark is very strongly
+ 
+
+ align:start position:0%
+yeah because sea Clark is very strongly
+uh it is very heavy and so see and the C
+
+ align:start position:0%
+uh it is very heavy and so see and the C
+ 
+
+ align:start position:0%
+uh it is very heavy and so see and the C
+bar the the band not very strongly and
+
+ align:start position:0%
+bar the the band not very strongly and
+ 
+
+ align:start position:0%
+bar the the band not very strongly and
+so this is the first evidence a direct
+
+ align:start position:0%
+so this is the first evidence a direct
+ 
+
+ align:start position:0%
+so this is the first evidence a direct
+evidence actually clock existence and so
+
+ align:start position:0%
+evidence actually clock existence and so
+ 
+
+ align:start position:0%
+evidence actually clock existence and so
+this actually shocked the community so
+
+ align:start position:0%
+this actually shocked the community so
+ 
+
+ align:start position:0%
+this actually shocked the community so
+this was discovered in in October so
+
+ align:start position:0%
+this was discovered in in October so
+ 
+
+ align:start position:0%
+this was discovered in in October so
+they call it October Revolution and uh
+
+ align:start position:0%
+they call it October Revolution and uh
+ 
+
+ align:start position:0%
+they call it October Revolution and uh
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+so uh um yeah played a very important
+
+ align:start position:0%
+so uh um yeah played a very important
+ 
+
+ align:start position:0%
+so uh um yeah played a very important
+role in in understand yeah for people to
+
+ align:start position:0%
+role in in understand yeah for people to
+ 
+
+ align:start position:0%
+role in in understand yeah for people to
+accept the existence of clocks
+
+ align:start position:0%
+accept the existence of clocks
+ 
+
+ align:start position:0%
+accept the existence of clocks
+anyway so
+
+ align:start position:0%
+anyway so
+ 
+
+ align:start position:0%
+anyway so
+in particular by looking at
+
+ align:start position:0%
+in particular by looking at
+ 
+
+ align:start position:0%
+in particular by looking at
+the more General process
+
+ align:start position:0%
+the more General process
+ 
+
+ align:start position:0%
+the more General process
+so this goes to hydrons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you just Collide them and then you
+
+ align:start position:0%
+okay you just Collide them and then you
+ 
+
+ align:start position:0%
+okay you just Collide them and then you
+look at it's going to hydrons you can
+
+ align:start position:0%
+look at it's going to hydrons you can
+ 
+
+ align:start position:0%
+look at it's going to hydrons you can
+actually can show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the clock has three colors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay make sure I have crop I have three
+
+ align:start position:0%
+okay make sure I have crop I have three
+ 
+
+ align:start position:0%
+okay make sure I have crop I have three
+colors
+
+ align:start position:0%
+colors
+ 
+
+ align:start position:0%
+colors
+and uh yeah so we will we will see that
+
+ align:start position:0%
+and uh yeah so we will we will see that
+ 
+
+ align:start position:0%
+and uh yeah so we will we will see that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so before doing that let's uh first
+
+ align:start position:0%
+so so before doing that let's uh first
+ 
+
+ align:start position:0%
+so so before doing that let's uh first
+have to do a calculation
+
+ align:start position:0%
+have to do a calculation
+ 
+
+ align:start position:0%
+have to do a calculation
+okay so so we have to calculate this
+
+ align:start position:0%
+okay so so we have to calculate this
+ 
+
+ align:start position:0%
+okay so so we have to calculate this
+explicitly
+
+ align:start position:0%
+explicitly
+ 
+
+ align:start position:0%
+explicitly
+well let me see I get my page a little
+
+ align:start position:0%
+well let me see I get my page a little
+ 
+
+ align:start position:0%
+well let me see I get my page a little
+bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay yeah so so first we have to
+
+ align:start position:0%
+right okay yeah so so first we have to
+ 
+
+ align:start position:0%
+right okay yeah so so first we have to
+do a calculation we have to calculate
+
+ align:start position:0%
+do a calculation we have to calculate
+ 
+
+ align:start position:0%
+do a calculation we have to calculate
+this process okay
+
+ align:start position:0%
+this process okay
+ 
+
+ align:start position:0%
+this process okay
+so so uh so after we have calculating
+
+ align:start position:0%
+so so uh so after we have calculating
+ 
+
+ align:start position:0%
+so so uh so after we have calculating
+this then then it's obvious that how
+
+ align:start position:0%
+this then then it's obvious that how
+ 
+
+ align:start position:0%
+this then then it's obvious that how
+that the uh this can tell us why the
+
+ align:start position:0%
+that the uh this can tell us why the
+ 
+
+ align:start position:0%
+that the uh this can tell us why the
+clock has three colors okay
+
+ align:start position:0%
+clock has three colors okay
+ 
+
+ align:start position:0%
+clock has three colors okay
+okay yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so so indeed for the so that's why
+
+ align:start position:0%
+yeah so so indeed for the so that's why
+ 
+
+ align:start position:0%
+yeah so so indeed for the so that's why
+for many years uh if you look at the
+
+ align:start position:0%
+for many years uh if you look at the
+ 
+
+ align:start position:0%
+for many years uh if you look at the
+proton the neutron and the pair they're
+
+ align:start position:0%
+proton the neutron and the pair they're
+ 
+
+ align:start position:0%
+proton the neutron and the pair they're
+very tightly bound and so so
+
+ align:start position:0%
+very tightly bound and so so
+ 
+
+ align:start position:0%
+very tightly bound and so so
+even though there were models about the
+
+ align:start position:0%
+even though there were models about the
+ 
+
+ align:start position:0%
+even though there were models about the
+clocks inside there so it's not quite uh
+
+ align:start position:0%
+clocks inside there so it's not quite uh
+ 
+
+ align:start position:0%
+clocks inside there so it's not quite uh
+uh yeah but but in the CKC a very uh
+
+ align:start position:0%
+uh yeah but but in the CKC a very uh
+ 
+
+ align:start position:0%
+uh yeah but but in the CKC a very uh
+heavy and so so they form a weekly Bond
+
+ align:start position:0%
+heavy and so so they form a weekly Bond
+ 
+
+ align:start position:0%
+heavy and so so they form a weekly Bond
+State and uh and so in the sense that
+
+ align:start position:0%
+State and uh and so in the sense that
+ 
+
+ align:start position:0%
+State and uh and so in the sense that
+you're looking at the uh uh yeah so here
+
+ align:start position:0%
+you're looking at the uh uh yeah so here
+ 
+
+ align:start position:0%
+you're looking at the uh uh yeah so here
+it's in the sense you can look at the C
+
+ align:start position:0%
+it's in the sense you can look at the C
+ 
+
+ align:start position:0%
+it's in the sense you can look at the C
+clock yeah yeah because it's a very
+
+ align:start position:0%
+clock yeah yeah because it's a very
+ 
+
+ align:start position:0%
+clock yeah yeah because it's a very
+weakly Bond state of the CNC one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+just say uh you can probe with the yeah
+
+ align:start position:0%
+just say uh you can probe with the yeah
+ 
+
+ align:start position:0%
+just say uh you can probe with the yeah
+you can essentially you can probe with
+
+ align:start position:0%
+you can essentially you can probe with
+ 
+
+ align:start position:0%
+you can essentially you can probe with
+the internal structure much easier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this Village
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like the most important machine like
+
+ align:start position:0%
+like the most important machine like
+ 
+
+ align:start position:0%
+like the most important machine like
+yeah yeah it is quite big big election
+
+ align:start position:0%
+yeah yeah it is quite big big election
+ 
+
+ align:start position:0%
+yeah yeah it is quite big big election
+Crider is more difficult because you
+
+ align:start position:0%
+Crider is more difficult because you
+ 
+
+ align:start position:0%
+Crider is more difficult because you
+have to build a straight line
+
+ align:start position:0%
+have to build a straight line
+ 
+
+ align:start position:0%
+have to build a straight line
+and because the electron have a much
+
+ align:start position:0%
+and because the electron have a much
+ 
+
+ align:start position:0%
+and because the electron have a much
+stronger single Singleton radiation if
+
+ align:start position:0%
+stronger single Singleton radiation if
+ 
+
+ align:start position:0%
+stronger single Singleton radiation if
+they are moving in the circle and so
+
+ align:start position:0%
+they are moving in the circle and so
+ 
+
+ align:start position:0%
+they are moving in the circle and so
+that lose a lot of energy and so that's
+
+ align:start position:0%
+that lose a lot of energy and so that's
+ 
+
+ align:start position:0%
+that lose a lot of energy and so that's
+the inaction clitor they should build a
+
+ align:start position:0%
+the inaction clitor they should build a
+ 
+
+ align:start position:0%
+the inaction clitor they should build a
+strong a straight line but straight nine
+
+ align:start position:0%
+strong a straight line but straight nine
+ 
+
+ align:start position:0%
+strong a straight line but straight nine
+you cannot have very high energy a
+
+ align:start position:0%
+you cannot have very high energy a
+ 
+
+ align:start position:0%
+you cannot have very high energy a
+require very long distance
+
+ align:start position:0%
+require very long distance
+ 
+
+ align:start position:0%
+require very long distance
+so that's why uh normally people build
+
+ align:start position:0%
+so that's why uh normally people build
+ 
+
+ align:start position:0%
+so that's why uh normally people build
+they build the the proton glider
+
+ align:start position:0%
+they build the the proton glider
+ 
+
+ align:start position:0%
+they build the the proton glider
+is easier
+
+ align:start position:0%
+is easier
+ 
+
+ align:start position:0%
+is easier
+and yeah it's easier to to get higher
+
+ align:start position:0%
+and yeah it's easier to to get higher
+ 
+
+ align:start position:0%
+and yeah it's easier to to get higher
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+and but but the last generation of the
+
+ align:start position:0%
+and but but the last generation of the
+ 
+
+ align:start position:0%
+and but but the last generation of the
+accelerator of the ahc people are
+
+ align:start position:0%
+accelerator of the ahc people are
+ 
+
+ align:start position:0%
+accelerator of the ahc people are
+talking about building an electron
+
+ align:start position:0%
+talking about building an electron
+ 
+
+ align:start position:0%
+talking about building an electron
+glider again yeah
+
+ align:start position:0%
+glider again yeah
+ 
+
+ align:start position:0%
+glider again yeah
+um yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so now let's try to calculate this
+
+ align:start position:0%
+good so now let's try to calculate this
+ 
+
+ align:start position:0%
+good so now let's try to calculate this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so and essentially we need to calculate
+
+ align:start position:0%
+so and essentially we need to calculate
+ 
+
+ align:start position:0%
+so and essentially we need to calculate
+this diagram
+
+ align:start position:0%
+this diagram
+ 
+
+ align:start position:0%
+this diagram
+and yeah this diagram is very easy we
+
+ align:start position:0%
+and yeah this diagram is very easy we
+ 
+
+ align:start position:0%
+and yeah this diagram is very easy we
+need to calculate the cross section
+
+ align:start position:0%
+need to calculate the cross section
+ 
+
+ align:start position:0%
+need to calculate the cross section
+corresponding to this so so let me just
+
+ align:start position:0%
+corresponding to this so so let me just
+ 
+
+ align:start position:0%
+corresponding to this so so let me just
+label our a label so this is e minus say
+
+ align:start position:0%
+label our a label so this is e minus say
+ 
+
+ align:start position:0%
+label our a label so this is e minus say
+this is e plus so this would be B and
+
+ align:start position:0%
+this is e plus so this would be B and
+ 
+
+ align:start position:0%
+this is e plus so this would be B and
+this will be P bar
+
+ align:start position:0%
+this will be P bar
+ 
+
+ align:start position:0%
+this will be P bar
+so let me enable the momentum so here
+
+ align:start position:0%
+so let me enable the momentum so here
+ 
+
+ align:start position:0%
+so let me enable the momentum so here
+let's take P1 R1
+
+ align:start position:0%
+let's take P1 R1
+ 
+
+ align:start position:0%
+let's take P1 R1
+and then this would be P2
+
+ align:start position:0%
+and then this would be P2
+ 
+
+ align:start position:0%
+and then this would be P2
+R2 bar
+
+ align:start position:0%
+R2 bar
+ 
+
+ align:start position:0%
+R2 bar
+so to tell you this is the antiparticle
+
+ align:start position:0%
+so to tell you this is the antiparticle
+ 
+
+ align:start position:0%
+so to tell you this is the antiparticle
+and so this one is k1 S1
+
+ align:start position:0%
+and so this one is k1 S1
+ 
+
+ align:start position:0%
+and so this one is k1 S1
+and this one is K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so so the amplitude for this will be
+
+ align:start position:0%
+and so so the amplitude for this will be
+ 
+
+ align:start position:0%
+and so so the amplitude for this will be
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+but the cross section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now suppose we consider
+
+ align:start position:0%
+so so now suppose we consider
+ 
+
+ align:start position:0%
+so so now suppose we consider
+unpolarized process
+
+ align:start position:0%
+unpolarized process
+ 
+
+ align:start position:0%
+unpolarized process
+as we discussed last time
+
+ align:start position:0%
+as we discussed last time
+ 
+
+ align:start position:0%
+as we discussed last time
+that the cross section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah say the sigma the Omega should be
+
+ align:start position:0%
+yeah say the sigma the Omega should be
+ 
+
+ align:start position:0%
+yeah say the sigma the Omega should be
+proportional
+
+ align:start position:0%
+proportional
+ 
+
+ align:start position:0%
+proportional
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the spin
+
+ align:start position:0%
+the spin
+ 
+
+ align:start position:0%
+the spin
+so we should
+
+ align:start position:0%
+so we should
+ 
+
+ align:start position:0%
+so we should
+sum over
+
+ align:start position:0%
+sum over
+ 
+
+ align:start position:0%
+sum over
+the value States sum over the
+
+ align:start position:0%
+the value States sum over the
+ 
+
+ align:start position:0%
+the value States sum over the
+presentation of the follow States
+
+ align:start position:0%
+presentation of the follow States
+ 
+
+ align:start position:0%
+presentation of the follow States
+because we don't measure individual
+
+ align:start position:0%
+because we don't measure individual
+ 
+
+ align:start position:0%
+because we don't measure individual
+prioritizations but we also should
+
+ align:start position:0%
+prioritizations but we also should
+ 
+
+ align:start position:0%
+prioritizations but we also should
+average over the polarization of the
+
+ align:start position:0%
+average over the polarization of the
+ 
+
+ align:start position:0%
+average over the polarization of the
+initial States
+
+ align:start position:0%
+initial States
+ 
+
+ align:start position:0%
+initial States
+so so so the result as we discussed at
+
+ align:start position:0%
+so so so the result as we discussed at
+ 
+
+ align:start position:0%
+so so so the result as we discussed at
+the end of last lecture you say you need
+
+ align:start position:0%
+the end of last lecture you say you need
+ 
+
+ align:start position:0%
+the end of last lecture you say you need
+to take one quarter count from the
+
+ align:start position:0%
+to take one quarter count from the
+ 
+
+ align:start position:0%
+to take one quarter count from the
+average over the spin
+
+ align:start position:0%
+average over the spin
+ 
+
+ align:start position:0%
+average over the spin
+so these two initial particles
+
+ align:start position:0%
+so these two initial particles
+ 
+
+ align:start position:0%
+so these two initial particles
+and and then
+
+ align:start position:0%
+and and then
+ 
+
+ align:start position:0%
+and and then
+the sum of spins of all the particles
+
+ align:start position:0%
+the sum of spins of all the particles
+ 
+
+ align:start position:0%
+the sum of spins of all the particles
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh uh uh um
+
+ align:start position:0%
+okay and uh uh uh um
+ 
+
+ align:start position:0%
+okay and uh uh uh um
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um okay so so so so so that's the thing
+
+ align:start position:0%
+um okay so so so so so that's the thing
+ 
+
+ align:start position:0%
+um okay so so so so so that's the thing
+we need to so let's just try to First
+
+ align:start position:0%
+we need to so let's just try to First
+ 
+
+ align:start position:0%
+we need to so let's just try to First
+compute the m
+
+ align:start position:0%
+compute the m
+ 
+
+ align:start position:0%
+compute the m
+so m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is given by
+
+ align:start position:0%
+is given by
+ 
+
+ align:start position:0%
+is given by
+okay so we just follow our rule
+
+ align:start position:0%
+okay so we just follow our rule
+ 
+
+ align:start position:0%
+okay so we just follow our rule
+so you look you follow the formionic
+
+ align:start position:0%
+so you look you follow the formionic
+ 
+
+ align:start position:0%
+so you look you follow the formionic
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+okay so so here there's a vertex
+
+ align:start position:0%
+okay so so here there's a vertex
+ 
+
+ align:start position:0%
+okay so so here there's a vertex
+so here there's a gamma
+
+ align:start position:0%
+so here there's a gamma
+ 
+
+ align:start position:0%
+so here there's a gamma
+so each vertex gives you a minus i e
+
+ align:start position:0%
+so each vertex gives you a minus i e
+ 
+
+ align:start position:0%
+so each vertex gives you a minus i e
+comma mu okay
+
+ align:start position:0%
+comma mu okay
+ 
+
+ align:start position:0%
+comma mu okay
+so if you follow this one okay then we
+
+ align:start position:0%
+so if you follow this one okay then we
+ 
+
+ align:start position:0%
+so if you follow this one okay then we
+get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V bar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R2
+
+ align:start position:0%
+R2
+ 
+
+ align:start position:0%
+R2
+P2
+
+ align:start position:0%
+P2
+ 
+
+ align:start position:0%
+P2
+the minus IE gamma mu
+
+ align:start position:0%
+the minus IE gamma mu
+ 
+
+ align:start position:0%
+the minus IE gamma mu
+and U R1 P1 okay
+
+ align:start position:0%
+and U R1 P1 okay
+ 
+
+ align:start position:0%
+and U R1 P1 okay
+so this is coming from this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+we start from here
+
+ align:start position:0%
+we start from here
+ 
+
+ align:start position:0%
+we start from here
+so this would be the um
+
+ align:start position:0%
+so this would be the um
+ 
+
+ align:start position:0%
+so this would be the um
+the U yeah yeah also we have this
+
+ align:start position:0%
+the U yeah yeah also we have this
+ 
+
+ align:start position:0%
+the U yeah yeah also we have this
+propagator let me just write down the
+
+ align:start position:0%
+propagator let me just write down the
+ 
+
+ align:start position:0%
+propagator let me just write down the
+propagator
+
+ align:start position:0%
+propagator
+ 
+
+ align:start position:0%
+propagator
+for the photon
+
+ align:start position:0%
+for the photon
+ 
+
+ align:start position:0%
+for the photon
+so let's take PSI equal to 1 h
+
+ align:start position:0%
+so let's take PSI equal to 1 h
+ 
+
+ align:start position:0%
+so let's take PSI equal to 1 h
+colon the larynx cage with PSI equal to
+
+ align:start position:0%
+colon the larynx cage with PSI equal to
+ 
+
+ align:start position:0%
+colon the larynx cage with PSI equal to
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and then and then it follows this nine
+
+ align:start position:0%
+and then and then it follows this nine
+ 
+
+ align:start position:0%
+and then and then it follows this nine
+so here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then we will have
+
+ align:start position:0%
+okay and then we will have
+ 
+
+ align:start position:0%
+okay and then we will have
+U Bar as one
+
+ align:start position:0%
+U Bar as one
+ 
+
+ align:start position:0%
+U Bar as one
+K1
+
+ align:start position:0%
+K1
+ 
+
+ align:start position:0%
+K1
+and minus IE comma Nu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V S2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K2
+
+ align:start position:0%
+K2
+ 
+
+ align:start position:0%
+K2
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is the full amplitude
+
+ align:start position:0%
+so this is the full amplitude
+ 
+
+ align:start position:0%
+so this is the full amplitude
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so this is a lumber
+
+ align:start position:0%
+so this is a lumber
+ 
+
+ align:start position:0%
+so this is a lumber
+okay so this is a number because this is
+
+ align:start position:0%
+okay so this is a number because this is
+ 
+
+ align:start position:0%
+okay so this is a number because this is
+a row vector
+
+ align:start position:0%
+a row vector
+ 
+
+ align:start position:0%
+a row vector
+this is a matrix and this is a column
+
+ align:start position:0%
+this is a matrix and this is a column
+ 
+
+ align:start position:0%
+this is a matrix and this is a column
+Vector okay so this will be a number and
+
+ align:start position:0%
+Vector okay so this will be a number and
+ 
+
+ align:start position:0%
+Vector okay so this will be a number and
+similarly this will be a number and then
+
+ align:start position:0%
+similarly this will be a number and then
+ 
+
+ align:start position:0%
+similarly this will be a number and then
+the MU Nu in this is a contraction with
+
+ align:start position:0%
+the MU Nu in this is a contraction with
+ 
+
+ align:start position:0%
+the MU Nu in this is a contraction with
+the propagator of the photon okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so actually uh if I want to be precise
+
+ align:start position:0%
+so actually uh if I want to be precise
+ 
+
+ align:start position:0%
+so actually uh if I want to be precise
+there's actually a factor of I here okay
+
+ align:start position:0%
+there's actually a factor of I here okay
+ 
+
+ align:start position:0%
+there's actually a factor of I here okay
+yeah but but this Factor Y is not
+
+ align:start position:0%
+yeah but but this Factor Y is not
+ 
+
+ align:start position:0%
+yeah but but this Factor Y is not
+important because
+
+ align:start position:0%
+important because
+ 
+
+ align:start position:0%
+important because
+and then the queue
+
+ align:start position:0%
+and then the queue
+ 
+
+ align:start position:0%
+and then the queue
+so the Q is the momentum of the photon
+
+ align:start position:0%
+so the Q is the momentum of the photon
+ 
+
+ align:start position:0%
+so the Q is the momentum of the photon
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so the Q should be the sum of the
+
+ align:start position:0%
+so the Q should be the sum of the
+ 
+
+ align:start position:0%
+so the Q should be the sum of the
+initial momentum okay so Q
+
+ align:start position:0%
+initial momentum okay so Q
+ 
+
+ align:start position:0%
+initial momentum okay so Q
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+should be equal to P1 plus P2
+
+ align:start position:0%
+should be equal to P1 plus P2
+ 
+
+ align:start position:0%
+should be equal to P1 plus P2
+and also this means that the Q Square
+
+ align:start position:0%
+and also this means that the Q Square
+ 
+
+ align:start position:0%
+and also this means that the Q Square
+is equal to minus s
+
+ align:start position:0%
+is equal to minus s
+ 
+
+ align:start position:0%
+is equal to minus s
+okay remember s is defined to be the
+
+ align:start position:0%
+okay remember s is defined to be the
+ 
+
+ align:start position:0%
+okay remember s is defined to be the
+minus P1 plus P2 Square
+
+ align:start position:0%
+minus P1 plus P2 Square
+ 
+
+ align:start position:0%
+minus P1 plus P2 Square
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now we can write this
+
+ align:start position:0%
+so now we can write this
+ 
+
+ align:start position:0%
+so now we can write this
+amplitude using the shorthand location
+
+ align:start position:0%
+amplitude using the shorthand location
+ 
+
+ align:start position:0%
+amplitude using the shorthand location
+so so if I forget all these momentum
+
+ align:start position:0%
+so so if I forget all these momentum
+ 
+
+ align:start position:0%
+so so if I forget all these momentum
+dependence and then this is
+
+ align:start position:0%
+dependence and then this is
+ 
+
+ align:start position:0%
+dependence and then this is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+minus IE Square
+
+ align:start position:0%
+minus IE Square
+ 
+
+ align:start position:0%
+minus IE Square
+divided by S okay if you cancel all the
+
+ align:start position:0%
+divided by S okay if you cancel all the
+ 
+
+ align:start position:0%
+divided by S okay if you cancel all the
+I's and then we have two terms V bar R2
+
+ align:start position:0%
+I's and then we have two terms V bar R2
+ 
+
+ align:start position:0%
+I's and then we have two terms V bar R2
+comma Nu
+
+ align:start position:0%
+comma Nu
+ 
+
+ align:start position:0%
+comma Nu
+and U are one
+
+ align:start position:0%
+and U are one
+ 
+
+ align:start position:0%
+and U are one
+and the U Bar S1 comma Nu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b s cubed
+
+ align:start position:0%
+b s cubed
+ 
+
+ align:start position:0%
+b s cubed
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now we need to
+
+ align:start position:0%
+and now we need to
+ 
+
+ align:start position:0%
+and now we need to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then what we need to do is we do to
+
+ align:start position:0%
+then what we need to do is we do to
+ 
+
+ align:start position:0%
+then what we need to do is we do to
+square it
+
+ align:start position:0%
+square it
+ 
+
+ align:start position:0%
+square it
+and sum over all the spin
+
+ align:start position:0%
+and sum over all the spin
+ 
+
+ align:start position:0%
+and sum over all the spin
+and then we plug then we plug the
+
+ align:start position:0%
+and then we plug then we plug the
+ 
+
+ align:start position:0%
+and then we plug then we plug the
+resulting expression into the formula we
+
+ align:start position:0%
+resulting expression into the formula we
+ 
+
+ align:start position:0%
+resulting expression into the formula we
+derived for the cross-section V uh
+
+ align:start position:0%
+derived for the cross-section V uh
+ 
+
+ align:start position:0%
+derived for the cross-section V uh
+derived last time okay
+
+ align:start position:0%
+derived last time okay
+ 
+
+ align:start position:0%
+derived last time okay
+so uh uh so the so the whole calculation
+
+ align:start position:0%
+so uh uh so the so the whole calculation
+ 
+
+ align:start position:0%
+so uh uh so the so the whole calculation
+is a little bit tedious okay but but I
+
+ align:start position:0%
+is a little bit tedious okay but but I
+ 
+
+ align:start position:0%
+is a little bit tedious okay but but I
+think we should at least go through one
+
+ align:start position:0%
+think we should at least go through one
+ 
+
+ align:start position:0%
+think we should at least go through one
+such calculation
+
+ align:start position:0%
+such calculation
+ 
+
+ align:start position:0%
+such calculation
+because this is the uh
+
+ align:start position:0%
+because this is the uh
+ 
+
+ align:start position:0%
+because this is the uh
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+uh um yeah prime example okay of QED
+
+ align:start position:0%
+uh um yeah prime example okay of QED
+ 
+
+ align:start position:0%
+uh um yeah prime example okay of QED
+calculation so so each of us should at
+
+ align:start position:0%
+calculation so so each of us should at
+ 
+
+ align:start position:0%
+calculation so so each of us should at
+least see
+
+ align:start position:0%
+least see
+ 
+
+ align:start position:0%
+least see
+once in our life okay so so we will do
+
+ align:start position:0%
+once in our life okay so so we will do
+ 
+
+ align:start position:0%
+once in our life okay so so we will do
+it explicitly here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hmm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh okay yeah yeah also uh uh uh uh here
+
+ align:start position:0%
+oh okay yeah yeah also uh uh uh uh here
+ 
+
+ align:start position:0%
+oh okay yeah yeah also uh uh uh uh here
+because the Q square is never equal to
+
+ align:start position:0%
+because the Q square is never equal to
+ 
+
+ align:start position:0%
+because the Q square is never equal to
+zero and so we don't need to care about
+
+ align:start position:0%
+zero and so we don't need to care about
+ 
+
+ align:start position:0%
+zero and so we don't need to care about
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so now let's do the square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's do the square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Square we just Square this term and
+
+ align:start position:0%
+so Square we just Square this term and
+ 
+
+ align:start position:0%
+so Square we just Square this term and
+square this term okay
+
+ align:start position:0%
+square this term okay
+ 
+
+ align:start position:0%
+square this term okay
+so when we Square this term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so we also Square this term so here
+
+ align:start position:0%
+so so we also Square this term so here
+ 
+
+ align:start position:0%
+so so we also Square this term so here
+we just get the e to the power 4 divided
+
+ align:start position:0%
+we just get the e to the power 4 divided
+ 
+
+ align:start position:0%
+we just get the e to the power 4 divided
+by S Square
+
+ align:start position:0%
+by S Square
+ 
+
+ align:start position:0%
+by S Square
+and when we Square this term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we just get another uh yeah so
+
+ align:start position:0%
+we just get another uh yeah so
+ 
+
+ align:start position:0%
+we just get another uh yeah so
+so this is gamma Nu comma mu so we if we
+
+ align:start position:0%
+so this is gamma Nu comma mu so we if we
+ 
+
+ align:start position:0%
+so this is gamma Nu comma mu so we if we
+Square it then we get another term
+
+ align:start position:0%
+Square it then we get another term
+ 
+
+ align:start position:0%
+Square it then we get another term
+okay so so we just copy this term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let me just copy here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you are one
+
+ align:start position:0%
+you are one
+ 
+
+ align:start position:0%
+you are one
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah when we scaled we get a lot of copy
+
+ align:start position:0%
+yeah when we scaled we get a lot of copy
+ 
+
+ align:start position:0%
+yeah when we scaled we get a lot of copy
+of this and so let me just write it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah sorry
+
+ align:start position:0%
+yeah sorry
+ 
+
+ align:start position:0%
+yeah sorry
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so we take the compressed conjugate okay
+
+ align:start position:0%
+so we take the compressed conjugate okay
+ 
+
+ align:start position:0%
+so we take the compressed conjugate okay
+so when we take the complex we need to
+
+ align:start position:0%
+so when we take the complex we need to
+ 
+
+ align:start position:0%
+so when we take the complex we need to
+take the modulus that means we need to
+
+ align:start position:0%
+take the modulus that means we need to
+ 
+
+ align:start position:0%
+take the modulus that means we need to
+multiply this
+
+ align:start position:0%
+multiply this
+ 
+
+ align:start position:0%
+multiply this
+which is on compressed conjugates okay
+
+ align:start position:0%
+which is on compressed conjugates okay
+ 
+
+ align:start position:0%
+which is on compressed conjugates okay
+and the complex conjugate of these
+
+ align:start position:0%
+and the complex conjugate of these
+ 
+
+ align:start position:0%
+and the complex conjugate of these
+is given by U Bar R1
+
+ align:start position:0%
+is given by U Bar R1
+ 
+
+ align:start position:0%
+is given by U Bar R1
+then comma Nu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and VR2
+
+ align:start position:0%
+and VR2
+ 
+
+ align:start position:0%
+and VR2
+and then times
+
+ align:start position:0%
+and then times
+ 
+
+ align:start position:0%
+and then times
+this one and its times
+
+ align:start position:0%
+this one and its times
+ 
+
+ align:start position:0%
+this one and its times
+its compressed conjugate and so we have
+
+ align:start position:0%
+its compressed conjugate and so we have
+ 
+
+ align:start position:0%
+its compressed conjugate and so we have
+u s one bar
+
+ align:start position:0%
+u s one bar
+ 
+
+ align:start position:0%
+u s one bar
+common view
+
+ align:start position:0%
+common view
+ 
+
+ align:start position:0%
+common view
+vs2
+
+ align:start position:0%
+vs2
+ 
+
+ align:start position:0%
+vs2
+and vs2 Bar
+
+ align:start position:0%
+and vs2 Bar
+ 
+
+ align:start position:0%
+and vs2 Bar
+comma Nu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S1 Okay so
+
+ align:start position:0%
+S1 Okay so
+ 
+
+ align:start position:0%
+S1 Okay so
+so this is original copy
+
+ align:start position:0%
+so this is original copy
+ 
+
+ align:start position:0%
+so this is original copy
+with the build contracts with this new
+
+ align:start position:0%
+with the build contracts with this new
+ 
+
+ align:start position:0%
+with the build contracts with this new
+and this is a complex conjugate with
+
+ align:start position:0%
+and this is a complex conjugate with
+ 
+
+ align:start position:0%
+and this is a complex conjugate with
+this new contract with this new okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this looks like a mass
+
+ align:start position:0%
+so this looks like a mass
+ 
+
+ align:start position:0%
+so this looks like a mass
+okay this is nuclex the big Mass
+
+ align:start position:0%
+okay this is nuclex the big Mass
+ 
+
+ align:start position:0%
+okay this is nuclex the big Mass
+and the 1000 actually there's a a series
+
+ align:start position:0%
+and the 1000 actually there's a a series
+ 
+
+ align:start position:0%
+and the 1000 actually there's a a series
+of beautiful tricks we can use to
+
+ align:start position:0%
+of beautiful tricks we can use to
+ 
+
+ align:start position:0%
+of beautiful tricks we can use to
+calculate this quantity okay so solidity
+
+ align:start position:0%
+calculate this quantity okay so solidity
+ 
+
+ align:start position:0%
+calculate this quantity okay so solidity
+you say oh
+
+ align:start position:0%
+you say oh
+ 
+
+ align:start position:0%
+you say oh
+to calculate this thing I have to plug
+
+ align:start position:0%
+to calculate this thing I have to plug
+ 
+
+ align:start position:0%
+to calculate this thing I have to plug
+in the individual
+
+ align:start position:0%
+in the individual
+ 
+
+ align:start position:0%
+in the individual
+wave functions for this uh V and U Etc
+
+ align:start position:0%
+wave functions for this uh V and U Etc
+ 
+
+ align:start position:0%
+wave functions for this uh V and U Etc
+okay we we worked out before but
+
+ align:start position:0%
+okay we we worked out before but
+ 
+
+ align:start position:0%
+okay we we worked out before but
+fortunately actually you don't need to
+
+ align:start position:0%
+fortunately actually you don't need to
+ 
+
+ align:start position:0%
+fortunately actually you don't need to
+do it okay so so we can actually go
+
+ align:start position:0%
+do it okay so so we can actually go
+ 
+
+ align:start position:0%
+do it okay so so we can actually go
+through a a series tricks and that we
+
+ align:start position:0%
+through a a series tricks and that we
+ 
+
+ align:start position:0%
+through a a series tricks and that we
+don't have to do it
+
+ align:start position:0%
+don't have to do it
+ 
+
+ align:start position:0%
+don't have to do it
+so the first trick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that this is a number
+
+ align:start position:0%
+is that this is a number
+ 
+
+ align:start position:0%
+is that this is a number
+okay since this is a number
+
+ align:start position:0%
+okay since this is a number
+ 
+
+ align:start position:0%
+okay since this is a number
+I can put the trace outside of it okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because the trace of a number is just a
+
+ align:start position:0%
+because the trace of a number is just a
+ 
+
+ align:start position:0%
+because the trace of a number is just a
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now if you now remember the trades
+
+ align:start position:0%
+and now if you now remember the trades
+ 
+
+ align:start position:0%
+and now if you now remember the trades
+have this cyclic properties
+
+ align:start position:0%
+have this cyclic properties
+ 
+
+ align:start position:0%
+have this cyclic properties
+okay so it's a recycling property so I
+
+ align:start position:0%
+okay so it's a recycling property so I
+ 
+
+ align:start position:0%
+okay so it's a recycling property so I
+can actually move this
+
+ align:start position:0%
+can actually move this
+ 
+
+ align:start position:0%
+can actually move this
+to there okay so so I can move it
+
+ align:start position:0%
+to there okay so so I can move it
+ 
+
+ align:start position:0%
+to there okay so so I can move it
+so so now I can write it as equal to 4 S
+
+ align:start position:0%
+so so now I can write it as equal to 4 S
+ 
+
+ align:start position:0%
+so so now I can write it as equal to 4 S
+Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can just move this to this so that the
+
+ align:start position:0%
+I can just move this to this so that the
+ 
+
+ align:start position:0%
+I can just move this to this so that the
+two R2 come together okay so if you have
+
+ align:start position:0%
+two R2 come together okay so if you have
+ 
+
+ align:start position:0%
+two R2 come together okay so if you have
+a v r Cube
+
+ align:start position:0%
+a v r Cube
+ 
+
+ align:start position:0%
+a v r Cube
+V bar R2
+
+ align:start position:0%
+V bar R2
+ 
+
+ align:start position:0%
+V bar R2
+R2 comma mu
+
+ align:start position:0%
+R2 comma mu
+ 
+
+ align:start position:0%
+R2 comma mu
+and U R1 U power R1
+
+ align:start position:0%
+and U R1 U power R1
+ 
+
+ align:start position:0%
+and U R1 U power R1
+times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+similarly I put this us to the other
+
+ align:start position:0%
+similarly I put this us to the other
+ 
+
+ align:start position:0%
+similarly I put this us to the other
+side US1
+
+ align:start position:0%
+side US1
+ 
+
+ align:start position:0%
+side US1
+if r s one
+
+ align:start position:0%
+if r s one
+ 
+
+ align:start position:0%
+if r s one
+comma mu
+
+ align:start position:0%
+comma mu
+ 
+
+ align:start position:0%
+comma mu
+sorry I missed
+
+ align:start position:0%
+sorry I missed
+ 
+
+ align:start position:0%
+sorry I missed
+use the Gamma New
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry did I
+
+ align:start position:0%
+sorry did I
+ 
+
+ align:start position:0%
+sorry did I
+so I put this oh sorry no no
+
+ align:start position:0%
+so I put this oh sorry no no
+ 
+
+ align:start position:0%
+so I put this oh sorry no no
+sorry I just missed that one
+
+ align:start position:0%
+sorry I just missed that one
+ 
+
+ align:start position:0%
+sorry I just missed that one
+bar R1 comma nuke
+
+ align:start position:0%
+bar R1 comma nuke
+ 
+
+ align:start position:0%
+bar R1 comma nuke
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and it's similarly with that so so I
+
+ align:start position:0%
+and it's similarly with that so so I
+ 
+
+ align:start position:0%
+and it's similarly with that so so I
+have U Bar is one command
+
+ align:start position:0%
+have U Bar is one command
+ 
+
+ align:start position:0%
+have U Bar is one command
+mu
+
+ align:start position:0%
+mu
+ 
+
+ align:start position:0%
+mu
+and then we have vs2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V bar is two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I guess that
+
+ align:start position:0%
+so I guess that
+ 
+
+ align:start position:0%
+so I guess that
+so the reason I do that
+
+ align:start position:0%
+so the reason I do that
+ 
+
+ align:start position:0%
+so the reason I do that
+so so now in this form now this is a
+
+ align:start position:0%
+so so now in this form now this is a
+ 
+
+ align:start position:0%
+so so now in this form now this is a
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+okay now this is a now this is a column
+
+ align:start position:0%
+okay now this is a now this is a column
+ 
+
+ align:start position:0%
+okay now this is a now this is a column
+this is a row
+
+ align:start position:0%
+this is a row
+ 
+
+ align:start position:0%
+this is a row
+and this is a matrix and this is column
+
+ align:start position:0%
+and this is a matrix and this is column
+ 
+
+ align:start position:0%
+and this is a matrix and this is column
+and this is row so so this is a matrix
+
+ align:start position:0%
+and this is row so so this is a matrix
+ 
+
+ align:start position:0%
+and this is row so so this is a matrix
+times a matrix and times a matrix and
+
+ align:start position:0%
+times a matrix and times a matrix and
+ 
+
+ align:start position:0%
+times a matrix and times a matrix and
+times a matrix okay and then you take
+
+ align:start position:0%
+times a matrix okay and then you take
+ 
+
+ align:start position:0%
+times a matrix okay and then you take
+the trace and then you get number okay
+
+ align:start position:0%
+the trace and then you get number okay
+ 
+
+ align:start position:0%
+the trace and then you get number okay
+similarly with things here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we need to sum over all the
+
+ align:start position:0%
+and then we need to sum over all the
+ 
+
+ align:start position:0%
+and then we need to sum over all the
+spins okay remember we did actually when
+
+ align:start position:0%
+spins okay remember we did actually when
+ 
+
+ align:start position:0%
+spins okay remember we did actually when
+we sum all the spins we means we sum
+
+ align:start position:0%
+we sum all the spins we means we sum
+ 
+
+ align:start position:0%
+we sum all the spins we means we sum
+over all possible with some other R2 R1
+
+ align:start position:0%
+over all possible with some other R2 R1
+ 
+
+ align:start position:0%
+over all possible with some other R2 R1
+S1 and S2 okay
+
+ align:start position:0%
+S1 and S2 okay
+ 
+
+ align:start position:0%
+S1 and S2 okay
+so now we can use a trick which we uh we
+
+ align:start position:0%
+so now we can use a trick which we uh we
+ 
+
+ align:start position:0%
+so now we can use a trick which we uh we
+had when we discussed the direct
+
+ align:start position:0%
+had when we discussed the direct
+ 
+
+ align:start position:0%
+had when we discussed the direct
+Spinners okay so now recall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now recall
+
+ align:start position:0%
+now recall
+ 
+
+ align:start position:0%
+now recall
+for unshare spinners
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means don't satisfy the equation motion
+
+ align:start position:0%
+means don't satisfy the equation motion
+ 
+
+ align:start position:0%
+means don't satisfy the equation motion
+okay those all the unshell spindles okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they satisfy the following sum over R if
+
+ align:start position:0%
+they satisfy the following sum over R if
+ 
+
+ align:start position:0%
+they satisfy the following sum over R if
+you sum over all the r of the U
+
+ align:start position:0%
+you sum over all the r of the U
+ 
+
+ align:start position:0%
+you sum over all the r of the U
+u r p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u r bar p
+
+ align:start position:0%
+u r bar p
+ 
+
+ align:start position:0%
+u r bar p
+that give you I I P slash plus m
+
+ align:start position:0%
+that give you I I P slash plus m
+ 
+
+ align:start position:0%
+that give you I I P slash plus m
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and when you sum over V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the minus I minus is
+
+ align:start position:0%
+with the minus I minus is
+ 
+
+ align:start position:0%
+with the minus I minus is
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now we can now we see we have if
+
+ align:start position:0%
+so so now we can now we see we have if
+ 
+
+ align:start position:0%
+so so now we can now we see we have if
+we sum over spin then we have these
+
+ align:start position:0%
+we sum over spin then we have these
+ 
+
+ align:start position:0%
+we sum over spin then we have these
+combinations
+
+ align:start position:0%
+combinations
+ 
+
+ align:start position:0%
+combinations
+now we can use those formulas okay now
+
+ align:start position:0%
+now we can use those formulas okay now
+ 
+
+ align:start position:0%
+now we can use those formulas okay now
+we can use those formulas
+
+ align:start position:0%
+we can use those formulas
+ 
+
+ align:start position:0%
+we can use those formulas
+so now we find
+
+ align:start position:0%
+so now we find
+ 
+
+ align:start position:0%
+so now we find
+one quarter
+
+ align:start position:0%
+one quarter
+ 
+
+ align:start position:0%
+one quarter
+when we sum all the all the indices
+
+ align:start position:0%
+when we sum all the all the indices
+ 
+
+ align:start position:0%
+when we sum all the all the indices
+R1 R2 S1 S2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the M Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+then we just get the uh
+
+ align:start position:0%
+then we just get the uh
+ 
+
+ align:start position:0%
+then we just get the uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so we get E4
+
+ align:start position:0%
+so we get E4
+ 
+
+ align:start position:0%
+so we get E4
+divided by 4s squared
+
+ align:start position:0%
+divided by 4s squared
+ 
+
+ align:start position:0%
+divided by 4s squared
+and then we just
+
+ align:start position:0%
+and then we just
+ 
+
+ align:start position:0%
+and then we just
+apply those formulas into here okay so
+
+ align:start position:0%
+apply those formulas into here okay so
+ 
+
+ align:start position:0%
+apply those formulas into here okay so
+we get
+
+ align:start position:0%
+we get
+ 
+
+ align:start position:0%
+we get
+Trace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus I P2 slash
+
+ align:start position:0%
+minus I P2 slash
+ 
+
+ align:start position:0%
+minus I P2 slash
+plus m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so m is the mass of the initial particle
+
+ align:start position:0%
+so m is the mass of the initial particle
+ 
+
+ align:start position:0%
+so m is the mass of the initial particle
+and I take the M Prime of the particle
+
+ align:start position:0%
+and I take the M Prime of the particle
+ 
+
+ align:start position:0%
+and I take the M Prime of the particle
+mass of the fellow particle
+
+ align:start position:0%
+mass of the fellow particle
+ 
+
+ align:start position:0%
+mass of the fellow particle
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+so the E plus minus of mass m and b
+
+ align:start position:0%
+so the E plus minus of mass m and b
+ 
+
+ align:start position:0%
+so the E plus minus of mass m and b
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then I have this then this times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then this comma mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so this is still inside this bracket
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ip1 slash plus m
+
+ align:start position:0%
+ip1 slash plus m
+ 
+
+ align:start position:0%
+ip1 slash plus m
+comma Nu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I have Trace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ik1 smash
+
+ align:start position:0%
+ik1 smash
+ 
+
+ align:start position:0%
+ik1 smash
+plus M Prime
+
+ align:start position:0%
+plus M Prime
+ 
+
+ align:start position:0%
+plus M Prime
+gamma
+
+ align:start position:0%
+gamma
+ 
+
+ align:start position:0%
+gamma
+mu
+
+ align:start position:0%
+mu
+ 
+
+ align:start position:0%
+mu
+and the minus I K2
+
+ align:start position:0%
+and the minus I K2
+ 
+
+ align:start position:0%
+and the minus I K2
+slash plus M Prime
+
+ align:start position:0%
+slash plus M Prime
+ 
+
+ align:start position:0%
+slash plus M Prime
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I just when I do this so the spin sum
+
+ align:start position:0%
+so I just when I do this so the spin sum
+ 
+
+ align:start position:0%
+so I just when I do this so the spin sum
+is crucial okay for this simplification
+
+ align:start position:0%
+is crucial okay for this simplification
+ 
+
+ align:start position:0%
+is crucial okay for this simplification
+when I sum over spins
+
+ align:start position:0%
+when I sum over spins
+ 
+
+ align:start position:0%
+when I sum over spins
+and then without using
+
+ align:start position:0%
+and then without using
+ 
+
+ align:start position:0%
+and then without using
+explicit expression of those uh u and v
+
+ align:start position:0%
+explicit expression of those uh u and v
+ 
+
+ align:start position:0%
+explicit expression of those uh u and v
+we can write all of them just in terms
+
+ align:start position:0%
+we can write all of them just in terms
+ 
+
+ align:start position:0%
+we can write all of them just in terms
+of P slash and the K slash Etc okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions on this
+
+ align:start position:0%
+any questions on this
+ 
+
+ align:start position:0%
+any questions on this
+and now we can evaluate the trace
+
+ align:start position:0%
+and now we can evaluate the trace
+ 
+
+ align:start position:0%
+and now we can evaluate the trace
+okay so imagine the trace
+
+ align:start position:0%
+okay so imagine the trace
+ 
+
+ align:start position:0%
+okay so imagine the trace
+now we need to use the wireless formula
+
+ align:start position:0%
+now we need to use the wireless formula
+ 
+
+ align:start position:0%
+now we need to use the wireless formula
+I think some of them we have done in
+
+ align:start position:0%
+I think some of them we have done in
+ 
+
+ align:start position:0%
+I think some of them we have done in
+your preset
+
+ align:start position:0%
+your preset
+ 
+
+ align:start position:0%
+your preset
+he said now recall
+
+ align:start position:0%
+he said now recall
+ 
+
+ align:start position:0%
+he said now recall
+so this is the place all those
+
+ align:start position:0%
+so this is the place all those
+ 
+
+ align:start position:0%
+so this is the place all those
+exercises they become useful
+
+ align:start position:0%
+exercises they become useful
+ 
+
+ align:start position:0%
+exercises they become useful
+so comma mu so here yeah if you look at
+
+ align:start position:0%
+so comma mu so here yeah if you look at
+ 
+
+ align:start position:0%
+so comma mu so here yeah if you look at
+the structure of these terms
+
+ align:start position:0%
+the structure of these terms
+ 
+
+ align:start position:0%
+the structure of these terms
+so here this is p slash so there's one
+
+ align:start position:0%
+so here this is p slash so there's one
+ 
+
+ align:start position:0%
+so here this is p slash so there's one
+gamma Matrix here
+
+ align:start position:0%
+gamma Matrix here
+ 
+
+ align:start position:0%
+gamma Matrix here
+and there's another gamma Matrix here
+
+ align:start position:0%
+and there's another gamma Matrix here
+ 
+
+ align:start position:0%
+and there's another gamma Matrix here
+and here p is actually the gamma Matrix
+
+ align:start position:0%
+and here p is actually the gamma Matrix
+ 
+
+ align:start position:0%
+and here p is actually the gamma Matrix
+here there's another gamma Matrix so at
+
+ align:start position:0%
+here there's another gamma Matrix so at
+ 
+
+ align:start position:0%
+here there's another gamma Matrix so at
+the most we can have the product of the
+
+ align:start position:0%
+the most we can have the product of the
+ 
+
+ align:start position:0%
+the most we can have the product of the
+four gamma matrices inside the trace
+
+ align:start position:0%
+four gamma matrices inside the trace
+ 
+
+ align:start position:0%
+four gamma matrices inside the trace
+and also depend on the product we can
+
+ align:start position:0%
+and also depend on the product we can
+ 
+
+ align:start position:0%
+and also depend on the product we can
+have four
+
+ align:start position:0%
+have four
+ 
+
+ align:start position:0%
+have four
+three and two okay uh three and two
+
+ align:start position:0%
+three and two okay uh three and two
+ 
+
+ align:start position:0%
+three and two okay uh three and two
+so so we need to uh for this purpose we
+
+ align:start position:0%
+so so we need to uh for this purpose we
+ 
+
+ align:start position:0%
+so so we need to uh for this purpose we
+lead to the uh those formulas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are the product of the form
+
+ align:start position:0%
+what are the product of the form
+ 
+
+ align:start position:0%
+what are the product of the form
+government Matrix is inside the integral
+
+ align:start position:0%
+government Matrix is inside the integral
+ 
+
+ align:start position:0%
+government Matrix is inside the integral
+so so this is just given by
+
+ align:start position:0%
+so so this is just given by
+ 
+
+ align:start position:0%
+so so this is just given by
+it's a mule
+
+ align:start position:0%
+it's a mule
+ 
+
+ align:start position:0%
+it's a mule
+need a number row
+
+ align:start position:0%
+need a number row
+ 
+
+ align:start position:0%
+need a number row
+Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+it's a new Lambda
+
+ align:start position:0%
+it's a new Lambda
+ 
+
+ align:start position:0%
+it's a new Lambda
+Madness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and also if you have three gamma
+
+ align:start position:0%
+and also if you have three gamma
+ 
+
+ align:start position:0%
+and also if you have three gamma
+matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you know the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+good and if I have two gamma matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you know what is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right it's four years
+
+ align:start position:0%
+that's right it's four years
+ 
+
+ align:start position:0%
+that's right it's four years
+okay so you can just apply those
+
+ align:start position:0%
+okay so you can just apply those
+ 
+
+ align:start position:0%
+okay so you can just apply those
+formulas to here
+
+ align:start position:0%
+formulas to here
+ 
+
+ align:start position:0%
+formulas to here
+okay so I will not
+
+ align:start position:0%
+okay so I will not
+ 
+
+ align:start position:0%
+okay so I will not
+do the calculation explicitly
+
+ align:start position:0%
+do the calculation explicitly
+ 
+
+ align:start position:0%
+do the calculation explicitly
+so you can just
+
+ align:start position:0%
+so you can just
+ 
+
+ align:start position:0%
+so you can just
+plug them in
+
+ align:start position:0%
+plug them in
+ 
+
+ align:start position:0%
+plug them in
+and then then it's mechanical you can
+
+ align:start position:0%
+and then then it's mechanical you can
+ 
+
+ align:start position:0%
+and then then it's mechanical you can
+just calculate it
+
+ align:start position:0%
+just calculate it
+ 
+
+ align:start position:0%
+just calculate it
+and then you find
+
+ align:start position:0%
+and then you find
+ 
+
+ align:start position:0%
+and then you find
+one over four
+
+ align:start position:0%
+one over four
+ 
+
+ align:start position:0%
+one over four
+sum over spin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M Square
+
+ align:start position:0%
+M Square
+ 
+
+ align:start position:0%
+M Square
+is equal to let me write down the answer
+
+ align:start position:0%
+is equal to let me write down the answer
+ 
+
+ align:start position:0%
+is equal to let me write down the answer
+so even though this answer is slightly
+
+ align:start position:0%
+so even though this answer is slightly
+ 
+
+ align:start position:0%
+so even though this answer is slightly
+long but I think it's instructive to
+
+ align:start position:0%
+long but I think it's instructive to
+ 
+
+ align:start position:0%
+long but I think it's instructive to
+write it down so that you see it so if
+
+ align:start position:0%
+write it down so that you see it so if
+ 
+
+ align:start position:0%
+write it down so that you see it so if
+you when you plug all this in
+
+ align:start position:0%
+you when you plug all this in
+ 
+
+ align:start position:0%
+you when you plug all this in
+and the to the algebra
+
+ align:start position:0%
+and the to the algebra
+ 
+
+ align:start position:0%
+and the to the algebra
+and you find that the expression can be
+
+ align:start position:0%
+and you find that the expression can be
+ 
+
+ align:start position:0%
+and you find that the expression can be
+written as this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K1 dot p
+
+ align:start position:0%
+K1 dot p
+ 
+
+ align:start position:0%
+K1 dot p
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+K2 dot P2
+
+ align:start position:0%
+K2 dot P2
+ 
+
+ align:start position:0%
+K2 dot P2
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+P1 dot K2
+
+ align:start position:0%
+P1 dot K2
+ 
+
+ align:start position:0%
+P1 dot K2
+and PQ dot K1
+
+ align:start position:0%
+and PQ dot K1
+ 
+
+ align:start position:0%
+and PQ dot K1
+the minus
+
+ align:start position:0%
+the minus
+ 
+
+ align:start position:0%
+the minus
+M Square
+
+ align:start position:0%
+M Square
+ 
+
+ align:start position:0%
+M Square
+K1 dot KQ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus M squared
+
+ align:start position:0%
+minus M squared
+ 
+
+ align:start position:0%
+minus M squared
+P1 dot P2
+
+ align:start position:0%
+P1 dot P2
+ 
+
+ align:start position:0%
+P1 dot P2
+M Prime squared sorry here should be M
+
+ align:start position:0%
+M Prime squared sorry here should be M
+ 
+
+ align:start position:0%
+M Prime squared sorry here should be M
+Times Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus 2m Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we discussed before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the uh the amplitude Square must be
+
+ align:start position:0%
+that the uh the amplitude Square must be
+ 
+
+ align:start position:0%
+that the uh the amplitude Square must be
+a low end scalar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scalar and so you see it explicitly here
+
+ align:start position:0%
+scalar and so you see it explicitly here
+ 
+
+ align:start position:0%
+scalar and so you see it explicitly here
+so it only involves either M square m
+
+ align:start position:0%
+so it only involves either M square m
+ 
+
+ align:start position:0%
+so it only involves either M square m
+Prime square or the product third
+
+ align:start position:0%
+Prime square or the product third
+ 
+
+ align:start position:0%
+Prime square or the product third
+product of initial and final momentum
+
+ align:start position:0%
+product of initial and final momentum
+ 
+
+ align:start position:0%
+product of initial and final momentum
+okay and uh you see all kind of
+
+ align:start position:0%
+okay and uh you see all kind of
+ 
+
+ align:start position:0%
+okay and uh you see all kind of
+combination of the uh initial and final
+
+ align:start position:0%
+combination of the uh initial and final
+ 
+
+ align:start position:0%
+combination of the uh initial and final
+momentum appearing here
+
+ align:start position:0%
+momentum appearing here
+ 
+
+ align:start position:0%
+momentum appearing here
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+so it's convention
+
+ align:start position:0%
+so it's convention
+ 
+
+ align:start position:0%
+so it's convention
+so as we mentioned before actually if
+
+ align:start position:0%
+so as we mentioned before actually if
+ 
+
+ align:start position:0%
+so as we mentioned before actually if
+you look at all these different uh adult
+
+ align:start position:0%
+you look at all these different uh adult
+ 
+
+ align:start position:0%
+you look at all these different uh adult
+products between Indonesia and fellow
+
+ align:start position:0%
+products between Indonesia and fellow
+ 
+
+ align:start position:0%
+products between Indonesia and fellow
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+actually for
+
+ align:start position:0%
+actually for
+ 
+
+ align:start position:0%
+actually for
+because of the moment because of the
+
+ align:start position:0%
+because of the moment because of the
+ 
+
+ align:start position:0%
+because of the moment because of the
+momentum connivation
+
+ align:start position:0%
+momentum connivation
+ 
+
+ align:start position:0%
+momentum connivation
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+actually there are only two
+
+ align:start position:0%
+actually there are only two
+ 
+
+ align:start position:0%
+actually there are only two
+the renting warrant okay
+
+ align:start position:0%
+the renting warrant okay
+ 
+
+ align:start position:0%
+the renting warrant okay
+so so would be convenient
+
+ align:start position:0%
+so so would be convenient
+ 
+
+ align:start position:0%
+so so would be convenient
+to to write this all this in terms of
+
+ align:start position:0%
+to to write this all this in terms of
+ 
+
+ align:start position:0%
+to to write this all this in terms of
+those two uh a Lawrence environment okay
+
+ align:start position:0%
+those two uh a Lawrence environment okay
+ 
+
+ align:start position:0%
+those two uh a Lawrence environment okay
+so so that's the S2 2 of the Stu
+
+ align:start position:0%
+so so that's the S2 2 of the Stu
+ 
+
+ align:start position:0%
+so so that's the S2 2 of the Stu
+variables we defined previously okay so
+
+ align:start position:0%
+variables we defined previously okay so
+ 
+
+ align:start position:0%
+variables we defined previously okay so
+it's often just to use Stu at the same
+
+ align:start position:0%
+it's often just to use Stu at the same
+ 
+
+ align:start position:0%
+it's often just to use Stu at the same
+time so so so we just yeah okay so so
+
+ align:start position:0%
+time so so so we just yeah okay so so
+ 
+
+ align:start position:0%
+time so so so we just yeah okay so so
+now if you write them in terms of Base
+
+ align:start position:0%
+now if you write them in terms of Base
+ 
+
+ align:start position:0%
+now if you write them in terms of Base
+to you
+
+ align:start position:0%
+to you
+ 
+
+ align:start position:0%
+to you
+and then you find for example yeah let
+
+ align:start position:0%
+and then you find for example yeah let
+ 
+
+ align:start position:0%
+and then you find for example yeah let
+me just give you some example for
+
+ align:start position:0%
+me just give you some example for
+ 
+
+ align:start position:0%
+me just give you some example for
+example 2K1
+
+ align:start position:0%
+example 2K1
+ 
+
+ align:start position:0%
+example 2K1
+P1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this can be written as t
+
+ align:start position:0%
+so this can be written as t
+ 
+
+ align:start position:0%
+so this can be written as t
+minus M Square minus n Prime squared
+
+ align:start position:0%
+minus M Square minus n Prime squared
+ 
+
+ align:start position:0%
+minus M Square minus n Prime squared
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+which is the same
+
+ align:start position:0%
+which is the same
+ 
+
+ align:start position:0%
+which is the same
+as 2k2 dot P2
+
+ align:start position:0%
+as 2k2 dot P2
+ 
+
+ align:start position:0%
+as 2k2 dot P2
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and uh 2K1
+
+ align:start position:0%
+and uh 2K1
+ 
+
+ align:start position:0%
+and uh 2K1
+dot P2 then it's actually equal to two
+
+ align:start position:0%
+dot P2 then it's actually equal to two
+ 
+
+ align:start position:0%
+dot P2 then it's actually equal to two
+K2 dot P1
+
+ align:start position:0%
+K2 dot P1
+ 
+
+ align:start position:0%
+K2 dot P1
+then you go to U minus M Square minus M
+
+ align:start position:0%
+then you go to U minus M Square minus M
+ 
+
+ align:start position:0%
+then you go to U minus M Square minus M
+Prime squared
+
+ align:start position:0%
+Prime squared
+ 
+
+ align:start position:0%
+Prime squared
+and then since related to the initial
+
+ align:start position:0%
+and then since related to the initial
+ 
+
+ align:start position:0%
+and then since related to the initial
+momentum then related to the S equal to
+
+ align:start position:0%
+momentum then related to the S equal to
+ 
+
+ align:start position:0%
+momentum then related to the S equal to
+S minus two M Square
+
+ align:start position:0%
+S minus two M Square
+ 
+
+ align:start position:0%
+S minus two M Square
+the minus K1 K2
+
+ align:start position:0%
+the minus K1 K2
+ 
+
+ align:start position:0%
+the minus K1 K2
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so you just apply those equations in
+
+ align:start position:0%
+so so you just apply those equations in
+ 
+
+ align:start position:0%
+so so you just apply those equations in
+here then you can write them in terms of
+
+ align:start position:0%
+here then you can write them in terms of
+ 
+
+ align:start position:0%
+here then you can write them in terms of
+Stu variables and then you find
+
+ align:start position:0%
+Stu variables and then you find
+ 
+
+ align:start position:0%
+Stu variables and then you find
+with one over sum over spin
+
+ align:start position:0%
+with one over sum over spin
+ 
+
+ align:start position:0%
+with one over sum over spin
+M square is equal to the following
+
+ align:start position:0%
+M square is equal to the following
+ 
+
+ align:start position:0%
+M square is equal to the following
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+2 e to the power 4
+
+ align:start position:0%
+2 e to the power 4
+ 
+
+ align:start position:0%
+2 e to the power 4
+Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T minus
+
+ align:start position:0%
+T minus
+ 
+
+ align:start position:0%
+T minus
+M Square
+
+ align:start position:0%
+M Square
+ 
+
+ align:start position:0%
+M Square
+Prime squared squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus u minus M Square minus n Prime
+
+ align:start position:0%
+plus u minus M Square minus n Prime
+ 
+
+ align:start position:0%
+plus u minus M Square minus n Prime
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+of 2s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so recall that
+
+ align:start position:0%
+so recall that
+ 
+
+ align:start position:0%
+so recall that
+S Plus t plus u equal to 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can eliminate one of them okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this concludes the calculation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the scattering amplitude
+
+ align:start position:0%
+of the scattering amplitude
+ 
+
+ align:start position:0%
+of the scattering amplitude
+okay so that's the expression you get
+
+ align:start position:0%
+okay so that's the expression you get
+ 
+
+ align:start position:0%
+okay so that's the expression you get
+okay and you see that it's all expressed
+
+ align:start position:0%
+okay and you see that it's all expressed
+ 
+
+ align:start position:0%
+okay and you see that it's all expressed
+in terms of this s2u okay
+
+ align:start position:0%
+in terms of this s2u okay
+ 
+
+ align:start position:0%
+in terms of this s2u okay
+can be expressed nicely in terms of
+
+ align:start position:0%
+can be expressed nicely in terms of
+ 
+
+ align:start position:0%
+can be expressed nicely in terms of
+these Stu variables
+
+ align:start position:0%
+these Stu variables
+ 
+
+ align:start position:0%
+these Stu variables
+any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so now let's calculate the cross action
+
+ align:start position:0%
+so now let's calculate the cross action
+ 
+
+ align:start position:0%
+so now let's calculate the cross action
+and our goal we to calculate the total
+
+ align:start position:0%
+and our goal we to calculate the total
+ 
+
+ align:start position:0%
+and our goal we to calculate the total
+cross section okay
+
+ align:start position:0%
+cross section okay
+ 
+
+ align:start position:0%
+cross section okay
+and so for this purpose let's do the
+
+ align:start position:0%
+and so for this purpose let's do the
+ 
+
+ align:start position:0%
+and so for this purpose let's do the
+center of Mass frame okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's go to the consider the center
+
+ align:start position:0%
+so let's go to the consider the center
+ 
+
+ align:start position:0%
+so let's go to the consider the center
+of Mass frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the simplest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so remember in the center of Mass frame
+
+ align:start position:0%
+so remember in the center of Mass frame
+ 
+
+ align:start position:0%
+so remember in the center of Mass frame
+we um
+
+ align:start position:0%
+we um
+ 
+
+ align:start position:0%
+we um
+so so so first we need to um
+
+ align:start position:0%
+so so so first we need to um
+ 
+
+ align:start position:0%
+so so so first we need to um
+yeah so remember the certain mesh frame
+
+ align:start position:0%
+yeah so remember the certain mesh frame
+ 
+
+ align:start position:0%
+yeah so remember the certain mesh frame
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+that the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+the sigma
+
+ align:start position:0%
+the sigma
+ 
+
+ align:start position:0%
+the sigma
+the Omega cm
+
+ align:start position:0%
+the Omega cm
+ 
+
+ align:start position:0%
+the Omega cm
+is given by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let me check my formula suddenly I
+
+ align:start position:0%
+yeah let me check my formula suddenly I
+ 
+
+ align:start position:0%
+yeah let me check my formula suddenly I
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's given by
+
+ align:start position:0%
+so it's given by
+ 
+
+ align:start position:0%
+so it's given by
+say the m
+
+ align:start position:0%
+say the m
+ 
+
+ align:start position:0%
+say the m
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+divided by p c m Prime
+
+ align:start position:0%
+divided by p c m Prime
+ 
+
+ align:start position:0%
+divided by p c m Prime
+divided by
+
+ align:start position:0%
+divided by
+ 
+
+ align:start position:0%
+divided by
+6 4 64 pi squared
+
+ align:start position:0%
+6 4 64 pi squared
+ 
+
+ align:start position:0%
+6 4 64 pi squared
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+p c Prime
+
+ align:start position:0%
+p c Prime
+ 
+
+ align:start position:0%
+p c Prime
+okay so PCM Prime is the momentum in the
+
+ align:start position:0%
+okay so PCM Prime is the momentum in the
+ 
+
+ align:start position:0%
+okay so PCM Prime is the momentum in the
+for the final particles and PCM is the
+
+ align:start position:0%
+for the final particles and PCM is the
+ 
+
+ align:start position:0%
+for the final particles and PCM is the
+momentum in the center of Mass frame for
+
+ align:start position:0%
+momentum in the center of Mass frame for
+ 
+
+ align:start position:0%
+momentum in the center of Mass frame for
+the initial particles okay
+
+ align:start position:0%
+the initial particles okay
+ 
+
+ align:start position:0%
+the initial particles okay
+so so now let's we also need to find the
+
+ align:start position:0%
+so so now let's we also need to find the
+ 
+
+ align:start position:0%
+so so now let's we also need to find the
+PCM Etc okay
+
+ align:start position:0%
+PCM Etc okay
+ 
+
+ align:start position:0%
+PCM Etc okay
+we we also need to express the m
+
+ align:start position:0%
+we we also need to express the m
+ 
+
+ align:start position:0%
+we we also need to express the m
+the amplitude in terms of the Central
+
+ align:start position:0%
+the amplitude in terms of the Central
+ 
+
+ align:start position:0%
+the amplitude in terms of the Central
+Mass script okay
+
+ align:start position:0%
+Mass script okay
+ 
+
+ align:start position:0%
+Mass script okay
+so so in the center of Mass frame
+
+ align:start position:0%
+so so in the center of Mass frame
+ 
+
+ align:start position:0%
+so so in the center of Mass frame
+then we have the P1
+
+ align:start position:0%
+then we have the P1
+ 
+
+ align:start position:0%
+then we have the P1
+would be say e
+
+ align:start position:0%
+would be say e
+ 
+
+ align:start position:0%
+would be say e
+PCM
+
+ align:start position:0%
+PCM
+ 
+
+ align:start position:0%
+PCM
+okay the P2
+
+ align:start position:0%
+okay the P2
+ 
+
+ align:start position:0%
+okay the P2
+will be equal to the same e but the
+
+ align:start position:0%
+will be equal to the same e but the
+ 
+
+ align:start position:0%
+will be equal to the same e but the
+minus PCM
+
+ align:start position:0%
+minus PCM
+ 
+
+ align:start position:0%
+minus PCM
+okay the high but the same e because
+
+ align:start position:0%
+okay the high but the same e because
+ 
+
+ align:start position:0%
+okay the high but the same e because
+they have the same mass
+
+ align:start position:0%
+they have the same mass
+ 
+
+ align:start position:0%
+they have the same mass
+okay the same similarly K1
+
+ align:start position:0%
+okay the same similarly K1
+ 
+
+ align:start position:0%
+okay the same similarly K1
+would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PCMS
+
+ align:start position:0%
+PCMS
+ 
+
+ align:start position:0%
+PCMS
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+and K2
+
+ align:start position:0%
+and K2
+ 
+
+ align:start position:0%
+and K2
+would be e Prime
+
+ align:start position:0%
+would be e Prime
+ 
+
+ align:start position:0%
+would be e Prime
+PCM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+from energy conservation immediately
+
+ align:start position:0%
+from energy conservation immediately
+ 
+
+ align:start position:0%
+from energy conservation immediately
+concludes that e must be equal to e
+
+ align:start position:0%
+concludes that e must be equal to e
+ 
+
+ align:start position:0%
+concludes that e must be equal to e
+Prime okay so a second forget about e
+
+ align:start position:0%
+Prime okay so a second forget about e
+ 
+
+ align:start position:0%
+Prime okay so a second forget about e
+Prime okay
+
+ align:start position:0%
+Prime okay
+ 
+
+ align:start position:0%
+Prime okay
+because the total energy would be QE and
+
+ align:start position:0%
+because the total energy would be QE and
+ 
+
+ align:start position:0%
+because the total energy would be QE and
+the final energy will also be 2E so so e
+
+ align:start position:0%
+the final energy will also be 2E so so e
+ 
+
+ align:start position:0%
+the final energy will also be 2E so so e
+have to be equal to e Prime
+
+ align:start position:0%
+have to be equal to e Prime
+ 
+
+ align:start position:0%
+have to be equal to e Prime
+and then we can find
+
+ align:start position:0%
+and then we can find
+ 
+
+ align:start position:0%
+and then we can find
+and so e
+
+ align:start position:0%
+and so e
+ 
+
+ align:start position:0%
+and so e
+would be equal to one half square root S
+
+ align:start position:0%
+would be equal to one half square root S
+ 
+
+ align:start position:0%
+would be equal to one half square root S
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this is the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or s
+
+ align:start position:0%
+or s
+ 
+
+ align:start position:0%
+or s
+is equal to 4G squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because of the P1 plus P2 is just 2E
+
+ align:start position:0%
+because of the P1 plus P2 is just 2E
+ 
+
+ align:start position:0%
+because of the P1 plus P2 is just 2E
+okay you square it become 4G squared
+
+ align:start position:0%
+okay you square it become 4G squared
+ 
+
+ align:start position:0%
+okay you square it become 4G squared
+and then we find that the PCM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+then s divided by 4 minus M squared
+
+ align:start position:0%
+then s divided by 4 minus M squared
+ 
+
+ align:start position:0%
+then s divided by 4 minus M squared
+and the PCM
+
+ align:start position:0%
+and the PCM
+ 
+
+ align:start position:0%
+and the PCM
+param Square
+
+ align:start position:0%
+param Square
+ 
+
+ align:start position:0%
+param Square
+equal to S equal to 4
+
+ align:start position:0%
+equal to S equal to 4
+ 
+
+ align:start position:0%
+equal to S equal to 4
+s divided by 4
+
+ align:start position:0%
+s divided by 4
+ 
+
+ align:start position:0%
+s divided by 4
+minus S Prime squared okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah because they have the same mass I
+
+ align:start position:0%
+yeah because they have the same mass I
+ 
+
+ align:start position:0%
+yeah because they have the same mass I
+had to go there momentum over there to
+
+ align:start position:0%
+had to go there momentum over there to
+ 
+
+ align:start position:0%
+had to go there momentum over there to
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+in the center of Mass frame and they
+
+ align:start position:0%
+in the center of Mass frame and they
+ 
+
+ align:start position:0%
+in the center of Mass frame and they
+have the same mass
+
+ align:start position:0%
+have the same mass
+ 
+
+ align:start position:0%
+have the same mass
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a violation process you always
+
+ align:start position:0%
+it's a violation process you always
+ 
+
+ align:start position:0%
+it's a violation process you always
+create the particle animals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so you can similarly Express the T
+
+ align:start position:0%
+so so you can similarly Express the T
+ 
+
+ align:start position:0%
+so so you can similarly Express the T
+okay you can similarly Express the T and
+
+ align:start position:0%
+okay you can similarly Express the T and
+ 
+
+ align:start position:0%
+okay you can similarly Express the T and
+U in terms of the this uh send a center
+
+ align:start position:0%
+U in terms of the this uh send a center
+ 
+
+ align:start position:0%
+U in terms of the this uh send a center
+of mass the momentum Etc okay and uh so
+
+ align:start position:0%
+of mass the momentum Etc okay and uh so
+ 
+
+ align:start position:0%
+of mass the momentum Etc okay and uh so
+I will uh you can just do that okay so
+
+ align:start position:0%
+I will uh you can just do that okay so
+ 
+
+ align:start position:0%
+I will uh you can just do that okay so
+let me just uh uh write down the final
+
+ align:start position:0%
+let me just uh uh write down the final
+ 
+
+ align:start position:0%
+let me just uh uh write down the final
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+let me just write down the value on so
+
+ align:start position:0%
+let me just write down the value on so
+ 
+
+ align:start position:0%
+let me just write down the value on so
+you can also rewrite one quarter
+
+ align:start position:0%
+you can also rewrite one quarter
+ 
+
+ align:start position:0%
+you can also rewrite one quarter
+some spin
+
+ align:start position:0%
+some spin
+ 
+
+ align:start position:0%
+some spin
+M Square equal to
+
+ align:start position:0%
+M Square equal to
+ 
+
+ align:start position:0%
+M Square equal to
+in terms of the center of mass and then
+
+ align:start position:0%
+in terms of the center of mass and then
+ 
+
+ align:start position:0%
+in terms of the center of mass and then
+you can write the
+
+ align:start position:0%
+you can write the
+ 
+
+ align:start position:0%
+you can write the
+um and then you find is equal to e to
+
+ align:start position:0%
+um and then you find is equal to e to
+ 
+
+ align:start position:0%
+um and then you find is equal to e to
+the power 4
+
+ align:start position:0%
+the power 4
+ 
+
+ align:start position:0%
+the power 4
+1 plus
+
+ align:start position:0%
+1 plus
+ 
+
+ align:start position:0%
+1 plus
+M squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the under the uh the Theta is
+
+ align:start position:0%
+okay and the under the uh the Theta is
+ 
+
+ align:start position:0%
+okay and the under the uh the Theta is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+so you have the scattering of the
+
+ align:start position:0%
+so you have the scattering of the
+ 
+
+ align:start position:0%
+so you have the scattering of the
+initial particle with PCM
+
+ align:start position:0%
+initial particle with PCM
+ 
+
+ align:start position:0%
+initial particle with PCM
+and then you have the final particle
+
+ align:start position:0%
+and then you have the final particle
+ 
+
+ align:start position:0%
+and then you have the final particle
+with the PCM Prime
+
+ align:start position:0%
+with the PCM Prime
+ 
+
+ align:start position:0%
+with the PCM Prime
+and so this angle is set okay
+
+ align:start position:0%
+and so this angle is set okay
+ 
+
+ align:start position:0%
+and so this angle is set okay
+this angle is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the Theta comes from when you
+
+ align:start position:0%
+and so the Theta comes from when you
+ 
+
+ align:start position:0%
+and so the Theta comes from when you
+calculate using the uh using the
+
+ align:start position:0%
+calculate using the uh using the
+ 
+
+ align:start position:0%
+calculate using the uh using the
+involving key and U okay
+
+ align:start position:0%
+involving key and U okay
+ 
+
+ align:start position:0%
+involving key and U okay
+moving here
+
+ align:start position:0%
+moving here
+ 
+
+ align:start position:0%
+moving here
+and so now you have now we have
+
+ align:start position:0%
+and so now you have now we have
+ 
+
+ align:start position:0%
+and so now you have now we have
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+so we have the PCM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's all in terms of s
+
+ align:start position:0%
+it's all in terms of s
+ 
+
+ align:start position:0%
+it's all in terms of s
+and then your your amplitude is also
+
+ align:start position:0%
+and then your your amplitude is also
+ 
+
+ align:start position:0%
+and then your your amplitude is also
+expressed in terms of the uh either s or
+
+ align:start position:0%
+expressed in terms of the uh either s or
+ 
+
+ align:start position:0%
+expressed in terms of the uh either s or
+E Yeah e is also the S and then we have
+
+ align:start position:0%
+E Yeah e is also the S and then we have
+ 
+
+ align:start position:0%
+E Yeah e is also the S and then we have
+the Theta okay
+
+ align:start position:0%
+the Theta okay
+ 
+
+ align:start position:0%
+the Theta okay
+then we have the Theta
+
+ align:start position:0%
+then we have the Theta
+ 
+
+ align:start position:0%
+then we have the Theta
+so so this is so you just plug the whole
+
+ align:start position:0%
+so so this is so you just plug the whole
+ 
+
+ align:start position:0%
+so so this is so you just plug the whole
+thing into here
+
+ align:start position:0%
+thing into here
+ 
+
+ align:start position:0%
+thing into here
+okay just plug the whole thing into here
+
+ align:start position:0%
+okay just plug the whole thing into here
+ 
+
+ align:start position:0%
+okay just plug the whole thing into here
+and then you find the total
+
+ align:start position:0%
+and then you find the total
+ 
+
+ align:start position:0%
+and then you find the total
+cross-section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's just the
+
+ align:start position:0%
+okay it's just the
+ 
+
+ align:start position:0%
+okay it's just the
+the sigma
+
+ align:start position:0%
+the sigma
+ 
+
+ align:start position:0%
+the sigma
+the Omega
+
+ align:start position:0%
+the Omega
+ 
+
+ align:start position:0%
+the Omega
+it's in the Mass frame
+
+ align:start position:0%
+it's in the Mass frame
+ 
+
+ align:start position:0%
+it's in the Mass frame
+and then sine Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+5 okay nothing here depends on Phi so
+
+ align:start position:0%
+5 okay nothing here depends on Phi so
+ 
+
+ align:start position:0%
+5 okay nothing here depends on Phi so
+the Phi integral you can just down
+
+ align:start position:0%
+the Phi integral you can just down
+ 
+
+ align:start position:0%
+the Phi integral you can just down
+attributory and then you just need to do
+
+ align:start position:0%
+attributory and then you just need to do
+ 
+
+ align:start position:0%
+attributory and then you just need to do
+the Theta integral and then you have
+
+ align:start position:0%
+the Theta integral and then you have
+ 
+
+ align:start position:0%
+the Theta integral and then you have
+this okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so again uh let me just write down
+
+ align:start position:0%
+so so again uh let me just write down
+ 
+
+ align:start position:0%
+so so again uh let me just write down
+the final answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the end you get
+
+ align:start position:0%
+so in the end you get
+ 
+
+ align:start position:0%
+so in the end you get
+4 pi
+
+ align:start position:0%
+4 pi
+ 
+
+ align:start position:0%
+4 pi
+Alpha Square
+
+ align:start position:0%
+Alpha Square
+ 
+
+ align:start position:0%
+Alpha Square
+divided by S
+
+ align:start position:0%
+divided by S
+ 
+
+ align:start position:0%
+divided by S
+so the alpha is to find structure
+
+ align:start position:0%
+so the alpha is to find structure
+ 
+
+ align:start position:0%
+so the alpha is to find structure
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah so the alpha
+
+ align:start position:0%
+um yeah so the alpha
+ 
+
+ align:start position:0%
+um yeah so the alpha
+here's e squared divided by 4 pi
+
+ align:start position:0%
+here's e squared divided by 4 pi
+ 
+
+ align:start position:0%
+here's e squared divided by 4 pi
+is defined structure constant
+
+ align:start position:0%
+is defined structure constant
+ 
+
+ align:start position:0%
+is defined structure constant
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this is four Pi Alpha squares 3s
+
+ align:start position:0%
+this is four Pi Alpha squares 3s
+ 
+
+ align:start position:0%
+this is four Pi Alpha squares 3s
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+y minus
+
+ align:start position:0%
+y minus
+ 
+
+ align:start position:0%
+y minus
+Prime squared divided by E Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+M squared divided by E squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the hosting times
+
+ align:start position:0%
+and the hosting times
+ 
+
+ align:start position:0%
+and the hosting times
+1 plus
+
+ align:start position:0%
+1 plus
+ 
+
+ align:start position:0%
+1 plus
+M Square divided by 2E squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one plus and Prime squared divided
+
+ align:start position:0%
+and one plus and Prime squared divided
+ 
+
+ align:start position:0%
+and one plus and Prime squared divided
+by 2E squared
+
+ align:start position:0%
+by 2E squared
+ 
+
+ align:start position:0%
+by 2E squared
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a final answer okay
+
+ align:start position:0%
+so this is a final answer okay
+ 
+
+ align:start position:0%
+so this is a final answer okay
+and this is also you can compare with
+
+ align:start position:0%
+and this is also you can compare with
+ 
+
+ align:start position:0%
+and this is also you can compare with
+experiments
+
+ align:start position:0%
+experiments
+ 
+
+ align:start position:0%
+experiments
+okay so this is also you can compare
+
+ align:start position:0%
+okay so this is also you can compare
+ 
+
+ align:start position:0%
+okay so this is also you can compare
+experience
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if you look at this answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's almost completely symmetric in
+
+ align:start position:0%
+it's almost completely symmetric in
+ 
+
+ align:start position:0%
+it's almost completely symmetric in
+terms of n and n Prime
+
+ align:start position:0%
+terms of n and n Prime
+ 
+
+ align:start position:0%
+terms of n and n Prime
+okay except that for this ratio and the
+
+ align:start position:0%
+okay except that for this ratio and the
+ 
+
+ align:start position:0%
+okay except that for this ratio and the
+m is downstairs and M Prime is upstairs
+
+ align:start position:0%
+m is downstairs and M Prime is upstairs
+ 
+
+ align:start position:0%
+m is downstairs and M Prime is upstairs
+okay otherwise it's the uh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this m Prime is upstairs of course
+
+ align:start position:0%
+so so this m Prime is upstairs of course
+ 
+
+ align:start position:0%
+so so this m Prime is upstairs of course
+it's the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great yeah so so this factor is key
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you have to have such kind of
+
+ align:start position:0%
+okay you have to have such kind of
+ 
+
+ align:start position:0%
+okay you have to have such kind of
+factor in the upstairs
+
+ align:start position:0%
+factor in the upstairs
+ 
+
+ align:start position:0%
+factor in the upstairs
+because when e you have to be e to be
+
+ align:start position:0%
+because when e you have to be e to be
+ 
+
+ align:start position:0%
+because when e you have to be e to be
+greater than M Prime Square in order to
+
+ align:start position:0%
+greater than M Prime Square in order to
+ 
+
+ align:start position:0%
+greater than M Prime Square in order to
+produce the particle
+
+ align:start position:0%
+produce the particle
+ 
+
+ align:start position:0%
+produce the particle
+okay if the if your energy is not big
+
+ align:start position:0%
+okay if the if your energy is not big
+ 
+
+ align:start position:0%
+okay if the if your energy is not big
+enough to produce uh uh in order to
+
+ align:start position:0%
+enough to produce uh uh in order to
+ 
+
+ align:start position:0%
+enough to produce uh uh in order to
+produce B and B Bar your energy at least
+
+ align:start position:0%
+produce B and B Bar your energy at least
+ 
+
+ align:start position:0%
+produce B and B Bar your energy at least
+so each so the uh so the so the uh each
+
+ align:start position:0%
+so each so the uh so the so the uh each
+ 
+
+ align:start position:0%
+so each so the uh so the so the uh each
+e has to be large enough to be the
+
+ align:start position:0%
+e has to be large enough to be the
+ 
+
+ align:start position:0%
+e has to be large enough to be the
+greater than uh than M okay because the
+
+ align:start position:0%
+greater than uh than M okay because the
+ 
+
+ align:start position:0%
+greater than uh than M okay because the
+uh your QE total energy must be greater
+
+ align:start position:0%
+uh your QE total energy must be greater
+ 
+
+ align:start position:0%
+uh your QE total energy must be greater
+than 2 m Prime
+
+ align:start position:0%
+than 2 m Prime
+ 
+
+ align:start position:0%
+than 2 m Prime
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so you see that when uh uh uh when e
+
+ align:start position:0%
+and so you see that when uh uh uh when e
+ 
+
+ align:start position:0%
+and so you see that when uh uh uh when e
+is smaller than uh M Prime and when e
+
+ align:start position:0%
+is smaller than uh M Prime and when e
+ 
+
+ align:start position:0%
+is smaller than uh M Prime and when e
+equal to n Prime and then this Factor
+
+ align:start position:0%
+equal to n Prime and then this Factor
+ 
+
+ align:start position:0%
+equal to n Prime and then this Factor
+becomes zero and then the cross-section
+
+ align:start position:0%
+becomes zero and then the cross-section
+ 
+
+ align:start position:0%
+becomes zero and then the cross-section
+becomes zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now let's consider some specific
+
+ align:start position:0%
+so now let's consider some specific
+ 
+
+ align:start position:0%
+so now let's consider some specific
+cases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now let's consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e plus e minus going to muon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+the next
+
+ align:start position:0%
+the next
+ 
+
+ align:start position:0%
+the next
+massive laptop after the electron
+
+ align:start position:0%
+massive laptop after the electron
+ 
+
+ align:start position:0%
+massive laptop after the electron
+okay so in this case
+
+ align:start position:0%
+okay so in this case
+ 
+
+ align:start position:0%
+okay so in this case
+say m e
+
+ align:start position:0%
+say m e
+ 
+
+ align:start position:0%
+say m e
+M Square will be m e squared
+
+ align:start position:0%
+M Square will be m e squared
+ 
+
+ align:start position:0%
+M Square will be m e squared
+and the m m Prime Square will be mu
+
+ align:start position:0%
+and the m m Prime Square will be mu
+ 
+
+ align:start position:0%
+and the m m Prime Square will be mu
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the MU or mass is 207 Mev
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+100s
+
+ align:start position:0%
+100s
+ 
+
+ align:start position:0%
+100s
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+actually I didn't code number so so mu
+
+ align:start position:0%
+actually I didn't code number so so mu
+ 
+
+ align:start position:0%
+actually I didn't code number so so mu
+and mass is 207
+
+ align:start position:0%
+and mass is 207
+ 
+
+ align:start position:0%
+and mass is 207
+times and the mass of the electron
+
+ align:start position:0%
+times and the mass of the electron
+ 
+
+ align:start position:0%
+times and the mass of the electron
+okay so do you do anybody remember the
+
+ align:start position:0%
+okay so do you do anybody remember the
+ 
+
+ align:start position:0%
+okay so do you do anybody remember the
+electron Mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hmm
+
+ align:start position:0%
+hmm
+ 
+
+ align:start position:0%
+hmm
+yeah that's right yeah yeah 0.5
+
+ align:start position:0%
+yeah that's right yeah yeah 0.5
+ 
+
+ align:start position:0%
+yeah that's right yeah yeah 0.5
+1 did you say one
+
+ align:start position:0%
+1 did you say one
+ 
+
+ align:start position:0%
+1 did you say one
+yeah yeah it's 511 Kev yeah
+
+ align:start position:0%
+yeah yeah it's 511 Kev yeah
+ 
+
+ align:start position:0%
+yeah yeah it's 511 Kev yeah
+uh 0.511 or Meb and the muon is the 207
+
+ align:start position:0%
+uh 0.511 or Meb and the muon is the 207
+ 
+
+ align:start position:0%
+uh 0.511 or Meb and the muon is the 207
+times the mass of the electron
+
+ align:start position:0%
+times the mass of the electron
+ 
+
+ align:start position:0%
+times the mass of the electron
+so when you so if you want to create the
+
+ align:start position:0%
+so when you so if you want to create the
+ 
+
+ align:start position:0%
+so when you so if you want to create the
+MU arm
+
+ align:start position:0%
+MU arm
+ 
+
+ align:start position:0%
+MU arm
+then the initial total energy okay so
+
+ align:start position:0%
+then the initial total energy okay so
+ 
+
+ align:start position:0%
+then the initial total energy okay so
+that so the so the s
+
+ align:start position:0%
+that so the so the s
+ 
+
+ align:start position:0%
+that so the so the s
+so the square root S which is 2E
+
+ align:start position:0%
+so the square root S which is 2E
+ 
+
+ align:start position:0%
+so the square root S which is 2E
+have to be greater than the 2 and mu
+
+ align:start position:0%
+have to be greater than the 2 and mu
+ 
+
+ align:start position:0%
+have to be greater than the 2 and mu
+okay so that means that the E has to be
+
+ align:start position:0%
+okay so that means that the E has to be
+ 
+
+ align:start position:0%
+okay so that means that the E has to be
+greater than mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then this is much much larger than
+
+ align:start position:0%
+and then this is much much larger than
+ 
+
+ align:start position:0%
+and then this is much much larger than
+electron Mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is about 200 times larger than
+
+ align:start position:0%
+so this is about 200 times larger than
+ 
+
+ align:start position:0%
+so this is about 200 times larger than
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+so that means actually that the
+
+ align:start position:0%
+so that means actually that the
+ 
+
+ align:start position:0%
+so that means actually that the
+for All Purpose that you can just relax
+
+ align:start position:0%
+for All Purpose that you can just relax
+ 
+
+ align:start position:0%
+for All Purpose that you can just relax
+the electron Mass
+
+ align:start position:0%
+the electron Mass
+ 
+
+ align:start position:0%
+the electron Mass
+okay and so uh so this ratio is a huge
+
+ align:start position:0%
+okay and so uh so this ratio is a huge
+ 
+
+ align:start position:0%
+okay and so uh so this ratio is a huge
+uh so this ratio is 10.
+
+ align:start position:0%
+uh so this ratio is 10.
+ 
+
+ align:start position:0%
+uh so this ratio is 10.
+okay uh
+
+ align:start position:0%
+okay uh
+ 
+
+ align:start position:0%
+okay uh
+it's tiny so we can treat the
+
+ align:start position:0%
+it's tiny so we can treat the
+ 
+
+ align:start position:0%
+it's tiny so we can treat the
+essentially electron as messages
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I just not well defined yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+no you you don't even yeah in this case
+
+ align:start position:0%
+no you you don't even yeah in this case
+ 
+
+ align:start position:0%
+no you you don't even yeah in this case
+you don't even go to that so so
+
+ align:start position:0%
+you don't even go to that so so
+ 
+
+ align:start position:0%
+you don't even go to that so so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so in the case that the um
+
+ align:start position:0%
+so in the case that the um
+ 
+
+ align:start position:0%
+so in the case that the um
+uh yeah uh let me see so so in the case
+
+ align:start position:0%
+uh yeah uh let me see so so in the case
+ 
+
+ align:start position:0%
+uh yeah uh let me see so so in the case
+that the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let me think a little bit
+
+ align:start position:0%
+uh let me think a little bit
+ 
+
+ align:start position:0%
+uh let me think a little bit
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so yeah for this case of course it's not
+
+ align:start position:0%
+so yeah for this case of course it's not
+ 
+
+ align:start position:0%
+so yeah for this case of course it's not
+very defined but in the office case
+
+ align:start position:0%
+very defined but in the office case
+ 
+
+ align:start position:0%
+very defined but in the office case
+let's imagine if you have the two very
+
+ align:start position:0%
+let's imagine if you have the two very
+ 
+
+ align:start position:0%
+let's imagine if you have the two very
+massive particles to collide to create
+
+ align:start position:0%
+massive particles to collide to create
+ 
+
+ align:start position:0%
+massive particles to collide to create
+say lighter particle and then in that
+
+ align:start position:0%
+say lighter particle and then in that
+ 
+
+ align:start position:0%
+say lighter particle and then in that
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+um yeah actually I don't remember the
+
+ align:start position:0%
+um yeah actually I don't remember the
+ 
+
+ align:start position:0%
+um yeah actually I don't remember the
+answer from my top of my head yeah it's
+
+ align:start position:0%
+answer from my top of my head yeah it's
+ 
+
+ align:start position:0%
+answer from my top of my head yeah it's
+a good question I will uh try to find it
+
+ align:start position:0%
+a good question I will uh try to find it
+ 
+
+ align:start position:0%
+a good question I will uh try to find it
+afterwards
+
+ align:start position:0%
+afterwards
+ 
+
+ align:start position:0%
+afterwards
+any other questions
+
+ align:start position:0%
+any other questions
+ 
+
+ align:start position:0%
+any other questions
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so in this case
+
+ align:start position:0%
+so in this case
+ 
+
+ align:start position:0%
+so in this case
+so when the when the electron mass is
+
+ align:start position:0%
+so when the when the electron mass is
+ 
+
+ align:start position:0%
+so when the when the electron mass is
+much larger than when the uh the mirror
+
+ align:start position:0%
+much larger than when the uh the mirror
+ 
+
+ align:start position:0%
+much larger than when the uh the mirror
+message might not do the electron Mass
+
+ align:start position:0%
+message might not do the electron Mass
+ 
+
+ align:start position:0%
+message might not do the electron Mass
+and then the um
+
+ align:start position:0%
+and then the um
+ 
+
+ align:start position:0%
+and then the um
+then the beacon set
+
+ align:start position:0%
+then the beacon set
+ 
+
+ align:start position:0%
+then the beacon set
+essentially me equal to zero
+
+ align:start position:0%
+essentially me equal to zero
+ 
+
+ align:start position:0%
+essentially me equal to zero
+okay and in this case the formula
+
+ align:start position:0%
+okay and in this case the formula
+ 
+
+ align:start position:0%
+okay and in this case the formula
+becomes simpler
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then in this case it becomes similar
+
+ align:start position:0%
+and then in this case it becomes similar
+ 
+
+ align:start position:0%
+and then in this case it becomes similar
+the downstairs equal just equal to one
+
+ align:start position:0%
+the downstairs equal just equal to one
+ 
+
+ align:start position:0%
+the downstairs equal just equal to one
+and uh and this Factor also become what
+
+ align:start position:0%
+and uh and this Factor also become what
+ 
+
+ align:start position:0%
+and uh and this Factor also become what
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this Factor also become one
+
+ align:start position:0%
+this Factor also become one
+ 
+
+ align:start position:0%
+this Factor also become one
+so then there are two interesting
+
+ align:start position:0%
+so then there are two interesting
+ 
+
+ align:start position:0%
+so then there are two interesting
+regimes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are two interesting regimes
+
+ align:start position:0%
+there are two interesting regimes
+ 
+
+ align:start position:0%
+there are two interesting regimes
+so the first is you just need the
+
+ align:start position:0%
+so the first is you just need the
+ 
+
+ align:start position:0%
+so the first is you just need the
+threshold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay just near the threshold means that
+
+ align:start position:0%
+okay just near the threshold means that
+ 
+
+ align:start position:0%
+okay just near the threshold means that
+the PCM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime is much much smaller than mu
+
+ align:start position:0%
+Prime is much much smaller than mu
+ 
+
+ align:start position:0%
+Prime is much much smaller than mu
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so in this regime then the E would be
+
+ align:start position:0%
+so in this regime then the E would be
+ 
+
+ align:start position:0%
+so in this regime then the E would be
+approximately just a mu
+
+ align:start position:0%
+approximately just a mu
+ 
+
+ align:start position:0%
+approximately just a mu
+okay and then s will be approximately
+
+ align:start position:0%
+okay and then s will be approximately
+ 
+
+ align:start position:0%
+okay and then s will be approximately
+just for a mu squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now if you just look at that
+
+ align:start position:0%
+so so now if you just look at that
+ 
+
+ align:start position:0%
+so so now if you just look at that
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah so so let's look at that expression
+
+ align:start position:0%
+yeah so so let's look at that expression
+ 
+
+ align:start position:0%
+yeah so so let's look at that expression
+then you find
+
+ align:start position:0%
+then you find
+ 
+
+ align:start position:0%
+then you find
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+then you find that the total the
+
+ align:start position:0%
+then you find that the total the
+ 
+
+ align:start position:0%
+then you find that the total the
+differential cross action
+
+ align:start position:0%
+differential cross action
+ 
+
+ align:start position:0%
+differential cross action
+is equal to Alpha Square
+
+ align:start position:0%
+is equal to Alpha Square
+ 
+
+ align:start position:0%
+is equal to Alpha Square
+to eight
+
+ align:start position:0%
+to eight
+ 
+
+ align:start position:0%
+to eight
+mu squared
+
+ align:start position:0%
+mu squared
+ 
+
+ align:start position:0%
+mu squared
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+PCM Prime
+
+ align:start position:0%
+PCM Prime
+ 
+
+ align:start position:0%
+PCM Prime
+divided by Nu
+
+ align:start position:0%
+divided by Nu
+ 
+
+ align:start position:0%
+divided by Nu
+plus higher all the corrections okay so
+
+ align:start position:0%
+plus higher all the corrections okay so
+ 
+
+ align:start position:0%
+plus higher all the corrections okay so
+you expand in in PCM divided by mu okay
+
+ align:start position:0%
+you expand in in PCM divided by mu okay
+ 
+
+ align:start position:0%
+you expand in in PCM divided by mu okay
+PCM Prime divided by m u and the total
+
+ align:start position:0%
+PCM Prime divided by m u and the total
+ 
+
+ align:start position:0%
+PCM Prime divided by m u and the total
+cross-section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just give them by pi Alpha Square
+
+ align:start position:0%
+just give them by pi Alpha Square
+ 
+
+ align:start position:0%
+just give them by pi Alpha Square
+2 mu squared
+
+ align:start position:0%
+2 mu squared
+ 
+
+ align:start position:0%
+2 mu squared
+and PCM
+
+ align:start position:0%
+and PCM
+ 
+
+ align:start position:0%
+and PCM
+Prime right there
+
+ align:start position:0%
+Prime right there
+ 
+
+ align:start position:0%
+Prime right there
+okay so so you hear you see explicitly
+
+ align:start position:0%
+okay so so you hear you see explicitly
+ 
+
+ align:start position:0%
+okay so so you hear you see explicitly
+that when you reach the threshold
+
+ align:start position:0%
+that when you reach the threshold
+ 
+
+ align:start position:0%
+that when you reach the threshold
+the reach the threshold because when
+
+ align:start position:0%
+the reach the threshold because when
+ 
+
+ align:start position:0%
+the reach the threshold because when
+this quantity goes to zero
+
+ align:start position:0%
+this quantity goes to zero
+ 
+
+ align:start position:0%
+this quantity goes to zero
+okay so when this quantity goes to zero
+
+ align:start position:0%
+okay so when this quantity goes to zero
+ 
+
+ align:start position:0%
+okay so when this quantity goes to zero
+and then you uh uh yeah
+
+ align:start position:0%
+and then you uh uh yeah
+ 
+
+ align:start position:0%
+and then you uh uh yeah
+yeah and then you uh um
+
+ align:start position:0%
+yeah and then you uh um
+ 
+
+ align:start position:0%
+yeah and then you uh um
+at the course I can go to do okay
+
+ align:start position:0%
+at the course I can go to do okay
+ 
+
+ align:start position:0%
+at the course I can go to do okay
+so another regime of Interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the actual relativistic regime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the actual optimistic regime so in this
+
+ align:start position:0%
+the actual optimistic regime so in this
+ 
+
+ align:start position:0%
+the actual optimistic regime so in this
+in this case which we can take e to be
+
+ align:start position:0%
+in this case which we can take e to be
+ 
+
+ align:start position:0%
+in this case which we can take e to be
+much much both the me and mu
+
+ align:start position:0%
+much much both the me and mu
+ 
+
+ align:start position:0%
+much much both the me and mu
+so also much greater than mu okay so of
+
+ align:start position:0%
+so also much greater than mu okay so of
+ 
+
+ align:start position:0%
+so also much greater than mu okay so of
+course it's already much greater than me
+
+ align:start position:0%
+course it's already much greater than me
+ 
+
+ align:start position:0%
+course it's already much greater than me
+so in this case then then we can uh yeah
+
+ align:start position:0%
+so in this case then then we can uh yeah
+ 
+
+ align:start position:0%
+so in this case then then we can uh yeah
+you can just hear
+
+ align:start position:0%
+you can just hear
+ 
+
+ align:start position:0%
+you can just hear
+uh uh uh uh you can just you simply take
+
+ align:start position:0%
+uh uh uh uh you can just you simply take
+ 
+
+ align:start position:0%
+uh uh uh uh you can just you simply take
+the both Mass to be zero in this case
+
+ align:start position:0%
+the both Mass to be zero in this case
+ 
+
+ align:start position:0%
+the both Mass to be zero in this case
+and then you find in this case
+
+ align:start position:0%
+and then you find in this case
+ 
+
+ align:start position:0%
+and then you find in this case
+that the sigma
+
+ align:start position:0%
+that the sigma
+ 
+
+ align:start position:0%
+that the sigma
+the Omega CM because you can given by
+
+ align:start position:0%
+the Omega CM because you can given by
+ 
+
+ align:start position:0%
+the Omega CM because you can given by
+Alpha Square divided by 4s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then you can find the total
+
+ align:start position:0%
+and then you can find the total
+ 
+
+ align:start position:0%
+and then you can find the total
+cross-section
+
+ align:start position:0%
+cross-section
+ 
+
+ align:start position:0%
+cross-section
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can find the total cross-section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4 Pi Alpha Square
+
+ align:start position:0%
+4 Pi Alpha Square
+ 
+
+ align:start position:0%
+4 Pi Alpha Square
+divided by 3x okay
+
+ align:start position:0%
+divided by 3x okay
+ 
+
+ align:start position:0%
+divided by 3x okay
+so now this final formula is very simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you could
+
+ align:start position:0%
+so you could
+ 
+
+ align:start position:0%
+so you could
+have written down this formula without
+
+ align:start position:0%
+have written down this formula without
+ 
+
+ align:start position:0%
+have written down this formula without
+doing any calculation
+
+ align:start position:0%
+doing any calculation
+ 
+
+ align:start position:0%
+doing any calculation
+of course up to the prefactor
+
+ align:start position:0%
+of course up to the prefactor
+ 
+
+ align:start position:0%
+of course up to the prefactor
+just on dimensional graph okay so in the
+
+ align:start position:0%
+just on dimensional graph okay so in the
+ 
+
+ align:start position:0%
+just on dimensional graph okay so in the
+archerativistic regime
+
+ align:start position:0%
+archerativistic regime
+ 
+
+ align:start position:0%
+archerativistic regime
+then essentially you can neglect both
+
+ align:start position:0%
+then essentially you can neglect both
+ 
+
+ align:start position:0%
+then essentially you can neglect both
+the mass of the initial particle and the
+
+ align:start position:0%
+the mass of the initial particle and the
+ 
+
+ align:start position:0%
+the mass of the initial particle and the
+final product
+
+ align:start position:0%
+final product
+ 
+
+ align:start position:0%
+final product
+and then in this the the in this whole
+
+ align:start position:0%
+and then in this the the in this whole
+ 
+
+ align:start position:0%
+and then in this the the in this whole
+process if the initial particles message
+
+ align:start position:0%
+process if the initial particles message
+ 
+
+ align:start position:0%
+process if the initial particles message
+and the final particle is massless and
+
+ align:start position:0%
+and the final particle is massless and
+ 
+
+ align:start position:0%
+and the final particle is massless and
+then for for this whole process the only
+
+ align:start position:0%
+then for for this whole process the only
+ 
+
+ align:start position:0%
+then for for this whole process the only
+scale is what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the only scale is s okay that's the only
+
+ align:start position:0%
+the only scale is s okay that's the only
+ 
+
+ align:start position:0%
+the only scale is s okay that's the only
+scale so the only scale is s
+
+ align:start position:0%
+scale so the only scale is s
+ 
+
+ align:start position:0%
+scale so the only scale is s
+and essentially and then that means and
+
+ align:start position:0%
+and essentially and then that means and
+ 
+
+ align:start position:0%
+and essentially and then that means and
+this should have Dimension
+
+ align:start position:0%
+this should have Dimension
+ 
+
+ align:start position:0%
+this should have Dimension
+area Okay and then that means that there
+
+ align:start position:0%
+area Okay and then that means that there
+ 
+
+ align:start position:0%
+area Okay and then that means that there
+should be one over s
+
+ align:start position:0%
+should be one over s
+ 
+
+ align:start position:0%
+should be one over s
+okay and then Alpha Square just comes
+
+ align:start position:0%
+okay and then Alpha Square just comes
+ 
+
+ align:start position:0%
+okay and then Alpha Square just comes
+from because we have two vertex okay
+
+ align:start position:0%
+from because we have two vertex okay
+ 
+
+ align:start position:0%
+from because we have two vertex okay
+and a from a tree level or process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so if you draw the plot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Say Say often we feature the total
+
+ align:start position:0%
+Say Say often we feature the total
+ 
+
+ align:start position:0%
+Say Say often we feature the total
+cross-section times s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so s times the total cross-section as a
+
+ align:start position:0%
+so s times the total cross-section as a
+ 
+
+ align:start position:0%
+so s times the total cross-section as a
+function of the square root S
+
+ align:start position:0%
+function of the square root S
+ 
+
+ align:start position:0%
+function of the square root S
+then this threshold is at 2 mu 2 mu
+
+ align:start position:0%
+then this threshold is at 2 mu 2 mu
+ 
+
+ align:start position:0%
+then this threshold is at 2 mu 2 mu
+and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then uh here it goes zero like a
+
+ align:start position:0%
+and then uh here it goes zero like a
+ 
+
+ align:start position:0%
+and then uh here it goes zero like a
+square root
+
+ align:start position:0%
+square root
+ 
+
+ align:start position:0%
+square root
+and then you are going to say approach
+
+ align:start position:0%
+and then you are going to say approach
+ 
+
+ align:start position:0%
+and then you are going to say approach
+your const approach your constant this
+
+ align:start position:0%
+your const approach your constant this
+ 
+
+ align:start position:0%
+your const approach your constant this
+is 4 pi
+
+ align:start position:0%
+is 4 pi
+ 
+
+ align:start position:0%
+is 4 pi
+of a square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so you have a curve like this
+
+ align:start position:0%
+okay so so you have a curve like this
+ 
+
+ align:start position:0%
+okay so so you have a curve like this
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's consider
+
+ align:start position:0%
+so now let's consider
+ 
+
+ align:start position:0%
+so now let's consider
+now let's consider using this process
+
+ align:start position:0%
+now let's consider using this process
+ 
+
+ align:start position:0%
+now let's consider using this process
+to show that actually the the quarks
+
+ align:start position:0%
+to show that actually the the quarks
+ 
+
+ align:start position:0%
+to show that actually the the quarks
+have three colors okay
+
+ align:start position:0%
+have three colors okay
+ 
+
+ align:start position:0%
+have three colors okay
+the clock says three colors
+
+ align:start position:0%
+the clock says three colors
+ 
+
+ align:start position:0%
+the clock says three colors
+so for this purpose let's consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e plus minus E plus e minus
+
+ align:start position:0%
+e plus minus E plus e minus
+ 
+
+ align:start position:0%
+e plus minus E plus e minus
+goes to hydrogens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this simile is a very complicated
+
+ align:start position:0%
+so so this simile is a very complicated
+ 
+
+ align:start position:0%
+so so this simile is a very complicated
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+okay similarly this is a very
+
+ align:start position:0%
+okay similarly this is a very
+ 
+
+ align:start position:0%
+okay similarly this is a very
+complicated process
+
+ align:start position:0%
+complicated process
+ 
+
+ align:start position:0%
+complicated process
+it's because the uh
+
+ align:start position:0%
+it's because the uh
+ 
+
+ align:start position:0%
+it's because the uh
+so suppose say suppose if you have e
+
+ align:start position:0%
+so suppose say suppose if you have e
+ 
+
+ align:start position:0%
+so suppose say suppose if you have e
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+you create a clock and the anti-clock
+
+ align:start position:0%
+you create a clock and the anti-clock
+ 
+
+ align:start position:0%
+you create a clock and the anti-clock
+pair
+
+ align:start position:0%
+pair
+ 
+
+ align:start position:0%
+pair
+but remember the clocks
+
+ align:start position:0%
+but remember the clocks
+ 
+
+ align:start position:0%
+but remember the clocks
+they're they're confined
+
+ align:start position:0%
+they're they're confined
+ 
+
+ align:start position:0%
+they're they're confined
+okay so so we don't observe individual
+
+ align:start position:0%
+okay so so we don't observe individual
+ 
+
+ align:start position:0%
+okay so so we don't observe individual
+clocks it's because the qcd is shown
+
+ align:start position:0%
+clocks it's because the qcd is shown
+ 
+
+ align:start position:0%
+clocks it's because the qcd is shown
+interacting and so the clocks are
+
+ align:start position:0%
+interacting and so the clocks are
+ 
+
+ align:start position:0%
+interacting and so the clocks are
+confined inside the proton parents Etc
+
+ align:start position:0%
+confined inside the proton parents Etc
+ 
+
+ align:start position:0%
+confined inside the proton parents Etc
+and so so in this process
+
+ align:start position:0%
+and so so in this process
+ 
+
+ align:start position:0%
+and so so in this process
+so even though originally created the
+
+ align:start position:0%
+so even though originally created the
+ 
+
+ align:start position:0%
+so even though originally created the
+clock
+
+ align:start position:0%
+clock
+ 
+
+ align:start position:0%
+clock
+but each individual clock and anti-clock
+
+ align:start position:0%
+but each individual clock and anti-clock
+ 
+
+ align:start position:0%
+but each individual clock and anti-clock
+they cannot survive either on their own
+
+ align:start position:0%
+they cannot survive either on their own
+ 
+
+ align:start position:0%
+they cannot survive either on their own
+so so they will so their presence will
+
+ align:start position:0%
+so so they will so their presence will
+ 
+
+ align:start position:0%
+so so they will so their presence will
+polarize the vacuum create many other
+
+ align:start position:0%
+polarize the vacuum create many other
+ 
+
+ align:start position:0%
+polarize the vacuum create many other
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+and so so what happens is that you uh
+
+ align:start position:0%
+and so so what happens is that you uh
+ 
+
+ align:start position:0%
+and so so what happens is that you uh
+you create uh so each of them will
+
+ align:start position:0%
+you create uh so each of them will
+ 
+
+ align:start position:0%
+you create uh so each of them will
+create a lot of particles along with
+
+ align:start position:0%
+create a lot of particles along with
+ 
+
+ align:start position:0%
+create a lot of particles along with
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+okay so in the end it's a complicated
+
+ align:start position:0%
+okay so in the end it's a complicated
+ 
+
+ align:start position:0%
+okay so in the end it's a complicated
+product You observe many hydrogens okay
+
+ align:start position:0%
+product You observe many hydrogens okay
+ 
+
+ align:start position:0%
+product You observe many hydrogens okay
+You observe many hydraulics
+
+ align:start position:0%
+You observe many hydraulics
+ 
+
+ align:start position:0%
+You observe many hydraulics
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do we in our in any hope to be able
+
+ align:start position:0%
+how do we in our in any hope to be able
+ 
+
+ align:start position:0%
+how do we in our in any hope to be able
+to understand this process just by
+
+ align:start position:0%
+to understand this process just by
+ 
+
+ align:start position:0%
+to understand this process just by
+imagining this very complicated product
+
+ align:start position:0%
+imagining this very complicated product
+ 
+
+ align:start position:0%
+imagining this very complicated product
+because this product can have protons
+
+ align:start position:0%
+because this product can have protons
+ 
+
+ align:start position:0%
+because this product can have protons
+neutrons ions can also have other cells
+
+ align:start position:0%
+neutrons ions can also have other cells
+ 
+
+ align:start position:0%
+neutrons ions can also have other cells
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then this is a very complicated
+
+ align:start position:0%
+and then this is a very complicated
+ 
+
+ align:start position:0%
+and then this is a very complicated
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+but now the key is the following
+
+ align:start position:0%
+but now the key is the following
+ 
+
+ align:start position:0%
+but now the key is the following
+but now the key is the following
+
+ align:start position:0%
+but now the key is the following
+ 
+
+ align:start position:0%
+but now the key is the following
+indeed if you look at the question
+
+ align:start position:0%
+indeed if you look at the question
+ 
+
+ align:start position:0%
+indeed if you look at the question
+of going to each individual hydrant is
+
+ align:start position:0%
+of going to each individual hydrant is
+ 
+
+ align:start position:0%
+of going to each individual hydrant is
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+but if you consider in a so-called
+
+ align:start position:0%
+but if you consider in a so-called
+ 
+
+ align:start position:0%
+but if you consider in a so-called
+include inclusive
+
+ align:start position:0%
+include inclusive
+ 
+
+ align:start position:0%
+include inclusive
+process which goes to all possible
+
+ align:start position:0%
+process which goes to all possible
+ 
+
+ align:start position:0%
+process which goes to all possible
+hydrons in this process okay
+
+ align:start position:0%
+hydrons in this process okay
+ 
+
+ align:start position:0%
+hydrons in this process okay
+and then that probability just given by
+
+ align:start position:0%
+and then that probability just given by
+ 
+
+ align:start position:0%
+and then that probability just given by
+the total cross-section
+
+ align:start position:0%
+the total cross-section
+ 
+
+ align:start position:0%
+the total cross-section
+okay remember the total cosine just
+
+ align:start position:0%
+okay remember the total cosine just
+ 
+
+ align:start position:0%
+okay remember the total cosine just
+matches the total probability
+
+ align:start position:0%
+matches the total probability
+ 
+
+ align:start position:0%
+matches the total probability
+to create say to create such particles
+
+ align:start position:0%
+to create say to create such particles
+ 
+
+ align:start position:0%
+to create say to create such particles
+and and then when they are created and
+
+ align:start position:0%
+and and then when they are created and
+ 
+
+ align:start position:0%
+and and then when they are created and
+then they they go through a complicated
+
+ align:start position:0%
+then they they go through a complicated
+ 
+
+ align:start position:0%
+then they they go through a complicated
+process but that process is unitary
+
+ align:start position:0%
+process but that process is unitary
+ 
+
+ align:start position:0%
+process but that process is unitary
+we're not uh will be uh uh uh say or
+
+ align:start position:0%
+we're not uh will be uh uh uh say or
+ 
+
+ align:start position:0%
+we're not uh will be uh uh uh say or
+probability why to go to all possible
+
+ align:start position:0%
+probability why to go to all possible
+ 
+
+ align:start position:0%
+probability why to go to all possible
+fellow fellow products so if we include
+
+ align:start position:0%
+fellow fellow products so if we include
+ 
+
+ align:start position:0%
+fellow fellow products so if we include
+the cross-section go into all possible
+
+ align:start position:0%
+the cross-section go into all possible
+ 
+
+ align:start position:0%
+the cross-section go into all possible
+value product and so that probability
+
+ align:start position:0%
+value product and so that probability
+ 
+
+ align:start position:0%
+value product and so that probability
+just captured by the total cost Act
+
+ align:start position:0%
+just captured by the total cost Act
+ 
+
+ align:start position:0%
+just captured by the total cost Act
+so the total closed section before this
+
+ align:start position:0%
+so the total closed section before this
+ 
+
+ align:start position:0%
+so the total closed section before this
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+okay for the
+
+ align:start position:0%
+okay for the
+ 
+
+ align:start position:0%
+okay for the
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+e plus E minor is going to equivalent
+
+ align:start position:0%
+e plus E minor is going to equivalent
+ 
+
+ align:start position:0%
+e plus E minor is going to equivalent
+and then just including the total total
+
+ align:start position:0%
+and then just including the total total
+ 
+
+ align:start position:0%
+and then just including the total total
+cross-section
+
+ align:start position:0%
+cross-section
+ 
+
+ align:start position:0%
+cross-section
+so inclusive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all hydrogen
+
+ align:start position:0%
+for all hydrogen
+ 
+
+ align:start position:0%
+for all hydrogen
+product okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this way we can actually measure this
+
+ align:start position:0%
+so this way we can actually measure this
+ 
+
+ align:start position:0%
+so this way we can actually measure this
+process okay
+
+ align:start position:0%
+process okay
+ 
+
+ align:start position:0%
+process okay
+indirectly okay even though you don't
+
+ align:start position:0%
+indirectly okay even though you don't
+ 
+
+ align:start position:0%
+indirectly okay even though you don't
+directly measure the clocks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so now let's calculate the total
+
+ align:start position:0%
+so now let's calculate the total
+ 
+
+ align:start position:0%
+so now let's calculate the total
+cross-section
+
+ align:start position:0%
+cross-section
+ 
+
+ align:start position:0%
+cross-section
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now let's calculate the total
+
+ align:start position:0%
+so now let's calculate the total
+ 
+
+ align:start position:0%
+so now let's calculate the total
+cross-action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now we we also don't have a choice
+
+ align:start position:0%
+and now we we also don't have a choice
+ 
+
+ align:start position:0%
+and now we we also don't have a choice
+which Quark will be uh uh reproduced so
+
+ align:start position:0%
+which Quark will be uh uh reproduced so
+ 
+
+ align:start position:0%
+which Quark will be uh uh reproduced so
+we need to sum over
+
+ align:start position:0%
+we need to sum over
+ 
+
+ align:start position:0%
+we need to sum over
+the total cross-action
+
+ align:start position:0%
+the total cross-action
+ 
+
+ align:start position:0%
+the total cross-action
+for E plus e minus
+
+ align:start position:0%
+for E plus e minus
+ 
+
+ align:start position:0%
+for E plus e minus
+goes to say different kind of clocks
+
+ align:start position:0%
+goes to say different kind of clocks
+ 
+
+ align:start position:0%
+goes to say different kind of clocks
+so I equals one into different types of
+
+ align:start position:0%
+so I equals one into different types of
+ 
+
+ align:start position:0%
+so I equals one into different types of
+clocks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh so so each of them we can just
+
+ align:start position:0%
+and uh so so each of them we can just
+ 
+
+ align:start position:0%
+and uh so so each of them we can just
+write it down using our formula
+
+ align:start position:0%
+write it down using our formula
+ 
+
+ align:start position:0%
+write it down using our formula
+so the only difference okay the only
+
+ align:start position:0%
+so the only difference okay the only
+ 
+
+ align:start position:0%
+so the only difference okay the only
+difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the same diagram applies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the only difference is that the clock
+
+ align:start position:0%
+the only difference is that the clock
+ 
+
+ align:start position:0%
+the only difference is that the clock
+have different charge from the electron
+
+ align:start position:0%
+have different charge from the electron
+ 
+
+ align:start position:0%
+have different charge from the electron
+so here is ie
+
+ align:start position:0%
+so here is ie
+ 
+
+ align:start position:0%
+so here is ie
+comma mu
+
+ align:start position:0%
+comma mu
+ 
+
+ align:start position:0%
+comma mu
+here we should use the charge for the
+
+ align:start position:0%
+here we should use the charge for the
+ 
+
+ align:start position:0%
+here we should use the charge for the
+clock
+
+ align:start position:0%
+clock
+ 
+
+ align:start position:0%
+clock
+okay so that would be i q e
+
+ align:start position:0%
+okay so that would be i q e
+ 
+
+ align:start position:0%
+okay so that would be i q e
+gamma mu okay Q would be the Quark of
+
+ align:start position:0%
+gamma mu okay Q would be the Quark of
+ 
+
+ align:start position:0%
+gamma mu okay Q would be the Quark of
+the charge compared to the uh the charge
+
+ align:start position:0%
+the charge compared to the uh the charge
+ 
+
+ align:start position:0%
+the charge compared to the uh the charge
+of the electron okay
+
+ align:start position:0%
+of the electron okay
+ 
+
+ align:start position:0%
+of the electron okay
+so so then then what we get
+
+ align:start position:0%
+so so then then what we get
+ 
+
+ align:start position:0%
+so so then then what we get
+okay so so suppose
+
+ align:start position:0%
+okay so so suppose
+ 
+
+ align:start position:0%
+okay so so suppose
+Qi is the the charge for the clock Qi
+
+ align:start position:0%
+Qi is the the charge for the clock Qi
+ 
+
+ align:start position:0%
+Qi is the the charge for the clock Qi
+and then and then and then this gives
+
+ align:start position:0%
+and then and then and then this gives
+ 
+
+ align:start position:0%
+and then and then and then this gives
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+so this total is going to all hydrons
+
+ align:start position:0%
+so this total is going to all hydrons
+ 
+
+ align:start position:0%
+so this total is going to all hydrons
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+two four hydraulics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this could be given by
+
+ align:start position:0%
+so this could be given by
+ 
+
+ align:start position:0%
+so this could be given by
+sum over different sum over the number
+
+ align:start position:0%
+sum over different sum over the number
+ 
+
+ align:start position:0%
+sum over different sum over the number
+of colors
+
+ align:start position:0%
+of colors
+ 
+
+ align:start position:0%
+of colors
+okay and C is the number of colors for
+
+ align:start position:0%
+okay and C is the number of colors for
+ 
+
+ align:start position:0%
+okay and C is the number of colors for
+each clock
+
+ align:start position:0%
+each clock
+ 
+
+ align:start position:0%
+each clock
+and then then the I will be the flavor
+
+ align:start position:0%
+and then then the I will be the flavor
+ 
+
+ align:start position:0%
+and then then the I will be the flavor
+now the I is the flavor of quark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say whether it's the uh you crack or D
+
+ align:start position:0%
+say whether it's the uh you crack or D
+ 
+
+ align:start position:0%
+say whether it's the uh you crack or D
+Quark or Charm clock Etc and NC is the
+
+ align:start position:0%
+Quark or Charm clock Etc and NC is the
+ 
+
+ align:start position:0%
+Quark or Charm clock Etc and NC is the
+number of colors
+
+ align:start position:0%
+number of colors
+ 
+
+ align:start position:0%
+number of colors
+and then you have Qi Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you have Sigma e plus e minus
+
+ align:start position:0%
+and then you have Sigma e plus e minus
+ 
+
+ align:start position:0%
+and then you have Sigma e plus e minus
+2 mu plus mu minus
+
+ align:start position:0%
+2 mu plus mu minus
+ 
+
+ align:start position:0%
+2 mu plus mu minus
+okay the rest is the same
+
+ align:start position:0%
+okay the rest is the same
+ 
+
+ align:start position:0%
+okay the rest is the same
+so for each type of Quark this is
+
+ align:start position:0%
+so for each type of Quark this is
+ 
+
+ align:start position:0%
+so for each type of Quark this is
+exactly the same you just replace IQ
+
+ align:start position:0%
+exactly the same you just replace IQ
+ 
+
+ align:start position:0%
+exactly the same you just replace IQ
+this vertex by iqi and then you get the
+
+ align:start position:0%
+this vertex by iqi and then you get the
+ 
+
+ align:start position:0%
+this vertex by iqi and then you get the
+QI Square okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no that's a very complicated process
+
+ align:start position:0%
+no no that's a very complicated process
+ 
+
+ align:start position:0%
+no no that's a very complicated process
+we cannot uh yeah yeah that's a very
+
+ align:start position:0%
+we cannot uh yeah yeah that's a very
+ 
+
+ align:start position:0%
+we cannot uh yeah yeah that's a very
+complicated process it's a it's a huge
+
+ align:start position:0%
+complicated process it's a it's a huge
+ 
+
+ align:start position:0%
+complicated process it's a it's a huge
+uh it's a huge field yeah
+
+ align:start position:0%
+uh it's a huge field yeah
+ 
+
+ align:start position:0%
+uh it's a huge field yeah
+to study that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no you just measure you just match all
+
+ align:start position:0%
+no you just measure you just match all
+ 
+
+ align:start position:0%
+no you just measure you just match all
+possible products right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no that's the only thing you can produce
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no no no no no no no as I said
+
+ align:start position:0%
+no no no no no no no no as I said
+ 
+
+ align:start position:0%
+no no no no no no no no as I said
+earlier we only need to worry about this
+
+ align:start position:0%
+earlier we only need to worry about this
+ 
+
+ align:start position:0%
+earlier we only need to worry about this
+process and then this process into
+
+ align:start position:0%
+process and then this process into
+ 
+
+ align:start position:0%
+process and then this process into
+hydrons is complicated
+
+ align:start position:0%
+hydrons is complicated
+ 
+
+ align:start position:0%
+hydrons is complicated
+but this happens with probability one
+
+ align:start position:0%
+but this happens with probability one
+ 
+
+ align:start position:0%
+but this happens with probability one
+okay and so if we calculate this
+
+ align:start position:0%
+okay and so if we calculate this
+ 
+
+ align:start position:0%
+okay and so if we calculate this
+probability then we know the total
+
+ align:start position:0%
+probability then we know the total
+ 
+
+ align:start position:0%
+probability then we know the total
+probability to here yeah yeah
+
+ align:start position:0%
+probability to here yeah yeah
+ 
+
+ align:start position:0%
+probability to here yeah yeah
+yeah because this happens with
+
+ align:start position:0%
+yeah because this happens with
+ 
+
+ align:start position:0%
+yeah because this happens with
+probability one
+
+ align:start position:0%
+probability one
+ 
+
+ align:start position:0%
+probability one
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+indeed that can happen but this is the
+
+ align:start position:0%
+indeed that can happen but this is the
+ 
+
+ align:start position:0%
+indeed that can happen but this is the
+leading process
+
+ align:start position:0%
+leading process
+ 
+
+ align:start position:0%
+leading process
+yeah this is the leading process
+
+ align:start position:0%
+yeah this is the leading process
+ 
+
+ align:start position:0%
+yeah this is the leading process
+yeah so this is the leading
+
+ align:start position:0%
+yeah so this is the leading
+ 
+
+ align:start position:0%
+yeah so this is the leading
+approximation yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so now
+
+ align:start position:0%
+okay so so now
+ 
+
+ align:start position:0%
+okay so so now
+you're just given by this formula
+
+ align:start position:0%
+you're just given by this formula
+ 
+
+ align:start position:0%
+you're just given by this formula
+because uh you just multiply the QI
+
+ align:start position:0%
+because uh you just multiply the QI
+ 
+
+ align:start position:0%
+because uh you just multiply the QI
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+to the to the total cross-section of the
+
+ align:start position:0%
+to the to the total cross-section of the
+ 
+
+ align:start position:0%
+to the to the total cross-section of the
+E plus image to Mu arm and then you sum
+
+ align:start position:0%
+E plus image to Mu arm and then you sum
+ 
+
+ align:start position:0%
+E plus image to Mu arm and then you sum
+all the all the flavors and times the
+
+ align:start position:0%
+all the all the flavors and times the
+ 
+
+ align:start position:0%
+all the all the flavors and times the
+number of the color
+
+ align:start position:0%
+number of the color
+ 
+
+ align:start position:0%
+number of the color
+okay the times the number of color
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because the each
+
+ align:start position:0%
+because the each
+ 
+
+ align:start position:0%
+because the each
+or different colors have the same charge
+
+ align:start position:0%
+or different colors have the same charge
+ 
+
+ align:start position:0%
+or different colors have the same charge
+okay or different color have same charge
+
+ align:start position:0%
+okay or different color have same charge
+ 
+
+ align:start position:0%
+okay or different color have same charge
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we can define a ratio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the same for everybody
+
+ align:start position:0%
+so this is the same for everybody
+ 
+
+ align:start position:0%
+so this is the same for everybody
+so this just factorized
+
+ align:start position:0%
+so this just factorized
+ 
+
+ align:start position:0%
+so this just factorized
+so we can define a ratio
+
+ align:start position:0%
+so we can define a ratio
+ 
+
+ align:start position:0%
+so we can define a ratio
+called the quantity code r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is defined by
+
+ align:start position:0%
+is defined by
+ 
+
+ align:start position:0%
+is defined by
+Sigma e plus e minus those two hydrons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divided by Sigma e plus e minus goes to
+
+ align:start position:0%
+divided by Sigma e plus e minus goes to
+ 
+
+ align:start position:0%
+divided by Sigma e plus e minus goes to
+Mu
+
+ align:start position:0%
+Mu
+ 
+
+ align:start position:0%
+Mu
+plus mu Mass
+
+ align:start position:0%
+plus mu Mass
+ 
+
+ align:start position:0%
+plus mu Mass
+and this is just given by Sum and C
+
+ align:start position:0%
+and this is just given by Sum and C
+ 
+
+ align:start position:0%
+and this is just given by Sum and C
+pounds some over eye flavor and the QI
+
+ align:start position:0%
+pounds some over eye flavor and the QI
+ 
+
+ align:start position:0%
+pounds some over eye flavor and the QI
+Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this eye of course
+
+ align:start position:0%
+and this eye of course
+ 
+
+ align:start position:0%
+and this eye of course
+you should only sum over I which Allowed
+
+ align:start position:0%
+you should only sum over I which Allowed
+ 
+
+ align:start position:0%
+you should only sum over I which Allowed
+by your energy okay
+
+ align:start position:0%
+by your energy okay
+ 
+
+ align:start position:0%
+by your energy okay
+those cracks which are too heavy will
+
+ align:start position:0%
+those cracks which are too heavy will
+ 
+
+ align:start position:0%
+those cracks which are too heavy will
+not be created by your energy you're not
+
+ align:start position:0%
+not be created by your energy you're not
+ 
+
+ align:start position:0%
+not be created by your energy you're not
+including the sun okay
+
+ align:start position:0%
+including the sun okay
+ 
+
+ align:start position:0%
+including the sun okay
+so a flavor of quarks allowed
+
+ align:start position:0%
+so a flavor of quarks allowed
+ 
+
+ align:start position:0%
+so a flavor of quarks allowed
+by NH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+initial image
+
+ align:start position:0%
+initial image
+ 
+
+ align:start position:0%
+initial image
+okay if the quarks are too heavy then of
+
+ align:start position:0%
+okay if the quarks are too heavy then of
+ 
+
+ align:start position:0%
+okay if the quarks are too heavy then of
+course you cannot create them
+
+ align:start position:0%
+course you cannot create them
+ 
+
+ align:start position:0%
+course you cannot create them
+so now let's list
+
+ align:start position:0%
+so now let's list
+ 
+
+ align:start position:0%
+so now let's list
+now let's list the the clocks we know
+
+ align:start position:0%
+now let's list the the clocks we know
+ 
+
+ align:start position:0%
+now let's list the the clocks we know
+the process uh I will not do the
+
+ align:start position:0%
+the process uh I will not do the
+ 
+
+ align:start position:0%
+the process uh I will not do the
+final one so we have U clock D Quark
+
+ align:start position:0%
+final one so we have U clock D Quark
+ 
+
+ align:start position:0%
+final one so we have U clock D Quark
+strange Croc Chunk rock bottom clock and
+
+ align:start position:0%
+strange Croc Chunk rock bottom clock and
+ 
+
+ align:start position:0%
+strange Croc Chunk rock bottom clock and
+then there's a top clock the top clock
+
+ align:start position:0%
+then there's a top clock the top clock
+ 
+
+ align:start position:0%
+then there's a top clock the top clock
+is very heavy and its process will be um
+
+ align:start position:0%
+is very heavy and its process will be um
+ 
+
+ align:start position:0%
+is very heavy and its process will be um
+will be communicated so let's not worry
+
+ align:start position:0%
+will be communicated so let's not worry
+ 
+
+ align:start position:0%
+will be communicated so let's not worry
+about that
+
+ align:start position:0%
+about that
+ 
+
+ align:start position:0%
+about that
+so so then the charge for each of them
+
+ align:start position:0%
+so so then the charge for each of them
+ 
+
+ align:start position:0%
+so so then the charge for each of them
+so this is two-thirds
+
+ align:start position:0%
+so this is two-thirds
+ 
+
+ align:start position:0%
+so this is two-thirds
+so this is minus one third this is minus
+
+ align:start position:0%
+so this is minus one third this is minus
+ 
+
+ align:start position:0%
+so this is minus one third this is minus
+one third
+
+ align:start position:0%
+one third
+ 
+
+ align:start position:0%
+one third
+this is two thirds
+
+ align:start position:0%
+this is two thirds
+ 
+
+ align:start position:0%
+this is two thirds
+this is minus one set okay
+
+ align:start position:0%
+this is minus one set okay
+ 
+
+ align:start position:0%
+this is minus one set okay
+and then the mass twice of the mass
+
+ align:start position:0%
+and then the mass twice of the mass
+ 
+
+ align:start position:0%
+and then the mass twice of the mass
+so I just give you some rough number so
+
+ align:start position:0%
+so I just give you some rough number so
+ 
+
+ align:start position:0%
+so I just give you some rough number so
+you would be about a few Mev okay so so
+
+ align:start position:0%
+you would be about a few Mev okay so so
+ 
+
+ align:start position:0%
+you would be about a few Mev okay so so
+this is a few Meb
+
+ align:start position:0%
+this is a few Meb
+ 
+
+ align:start position:0%
+this is a few Meb
+so this again is a few Mev
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so so so the strange will become
+
+ align:start position:0%
+and so so so the strange will become
+ 
+
+ align:start position:0%
+and so so so the strange will become
+strange is heavier twice is 1 9 PMB
+
+ align:start position:0%
+strange is heavier twice is 1 9 PMB
+ 
+
+ align:start position:0%
+strange is heavier twice is 1 9 PMB
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the charm
+
+ align:start position:0%
+and the charm
+ 
+
+ align:start position:0%
+and the charm
+the threshold is about 3.1 GV
+
+ align:start position:0%
+the threshold is about 3.1 GV
+ 
+
+ align:start position:0%
+the threshold is about 3.1 GV
+and the threshold for the bottom clock
+
+ align:start position:0%
+and the threshold for the bottom clock
+ 
+
+ align:start position:0%
+and the threshold for the bottom clock
+is about the line point five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+let's consider the value of r
+
+ align:start position:0%
+let's consider the value of r
+ 
+
+ align:start position:0%
+let's consider the value of r
+as a function of energy okay
+
+ align:start position:0%
+as a function of energy okay
+ 
+
+ align:start position:0%
+as a function of energy okay
+so then if you consider for s
+
+ align:start position:0%
+so then if you consider for s
+ 
+
+ align:start position:0%
+so then if you consider for s
+smaller than
+
+ align:start position:0%
+smaller than
+ 
+
+ align:start position:0%
+smaller than
+the the the uh uh the the charm says 3gb
+
+ align:start position:0%
+the the the uh uh the the charm says 3gb
+ 
+
+ align:start position:0%
+the the the uh uh the the charm says 3gb
+so in this case we can just produce
+
+ align:start position:0%
+so in this case we can just produce
+ 
+
+ align:start position:0%
+so in this case we can just produce
+UDS okay
+
+ align:start position:0%
+UDS okay
+ 
+
+ align:start position:0%
+UDS okay
+so in this case we have r equal to
+
+ align:start position:0%
+so in this case we have r equal to
+ 
+
+ align:start position:0%
+so in this case we have r equal to
+and see
+
+ align:start position:0%
+and see
+ 
+
+ align:start position:0%
+and see
+then times
+
+ align:start position:0%
+then times
+ 
+
+ align:start position:0%
+then times
+say this
+
+ align:start position:0%
+say this
+ 
+
+ align:start position:0%
+say this
+so this one two thirds and two one third
+
+ align:start position:0%
+so this one two thirds and two one third
+ 
+
+ align:start position:0%
+so this one two thirds and two one third
+so we have two three square plus twice
+
+ align:start position:0%
+so we have two three square plus twice
+ 
+
+ align:start position:0%
+so we have two three square plus twice
+Point third Square minus one so it's
+
+ align:start position:0%
+Point third Square minus one so it's
+ 
+
+ align:start position:0%
+Point third Square minus one so it's
+good okay
+
+ align:start position:0%
+good okay
+ 
+
+ align:start position:0%
+good okay
+so this is give you NC
+
+ align:start position:0%
+so this is give you NC
+ 
+
+ align:start position:0%
+so this is give you NC
+times two thirds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then for
+
+ align:start position:0%
+and then for
+ 
+
+ align:start position:0%
+and then for
+we would other others you cannot create
+
+ align:start position:0%
+we would other others you cannot create
+ 
+
+ align:start position:0%
+we would other others you cannot create
+okay and for square root S
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say between
+
+ align:start position:0%
+say between
+ 
+
+ align:start position:0%
+say between
+3G V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and the line 0.5
+
+ align:start position:0%
+and and the line 0.5
+ 
+
+ align:start position:0%
+and and the line 0.5
+GV the threshold for producing the the
+
+ align:start position:0%
+GV the threshold for producing the the
+ 
+
+ align:start position:0%
+GV the threshold for producing the the
+bottom clock
+
+ align:start position:0%
+bottom clock
+ 
+
+ align:start position:0%
+bottom clock
+and then you can now you can create the
+
+ align:start position:0%
+and then you can now you can create the
+ 
+
+ align:start position:0%
+and then you can now you can create the
+charm clock
+
+ align:start position:0%
+charm clock
+ 
+
+ align:start position:0%
+charm clock
+so you just add another one third
+
+ align:start position:0%
+so you just add another one third
+ 
+
+ align:start position:0%
+so you just add another one third
+so and then now R become
+
+ align:start position:0%
+so and then now R become
+ 
+
+ align:start position:0%
+so and then now R become
+and c times 10 divided by 9. okay just
+
+ align:start position:0%
+and c times 10 divided by 9. okay just
+ 
+
+ align:start position:0%
+and c times 10 divided by 9. okay just
+add another two third Square here
+
+ align:start position:0%
+add another two third Square here
+ 
+
+ align:start position:0%
+add another two third Square here
+and then for now if you have square root
+
+ align:start position:0%
+and then for now if you have square root
+ 
+
+ align:start position:0%
+and then for now if you have square root
+S
+
+ align:start position:0%
+S
+ 
+
+ align:start position:0%
+S
+greater than 9.5 GB
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then R now you can create the Bottom now
+
+ align:start position:0%
+then R now you can create the Bottom now
+ 
+
+ align:start position:0%
+then R now you can create the Bottom now
+okay so you add another one third Square
+
+ align:start position:0%
+okay so you add another one third Square
+ 
+
+ align:start position:0%
+okay so you add another one third Square
+so this r equal to q and c times
+
+ align:start position:0%
+so this r equal to q and c times
+ 
+
+ align:start position:0%
+so this r equal to q and c times
+10 divided by 9
+
+ align:start position:0%
+10 divided by 9
+ 
+
+ align:start position:0%
+10 divided by 9
+plus another one third Square
+
+ align:start position:0%
+plus another one third Square
+ 
+
+ align:start position:0%
+plus another one third Square
+so they'll give you
+
+ align:start position:0%
+so they'll give you
+ 
+
+ align:start position:0%
+so they'll give you
+see 11 divided
+
+ align:start position:0%
+see 11 divided
+ 
+
+ align:start position:0%
+see 11 divided
+so now if you plot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the r as a function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say for square root S
+
+ align:start position:0%
+say for square root S
+ 
+
+ align:start position:0%
+say for square root S
+as measured by experiments
+
+ align:start position:0%
+as measured by experiments
+ 
+
+ align:start position:0%
+as measured by experiments
+okay so so you should see your Threshold
+
+ align:start position:0%
+okay so so you should see your Threshold
+ 
+
+ align:start position:0%
+okay so so you should see your Threshold
+at three
+
+ align:start position:0%
+at three
+ 
+
+ align:start position:0%
+at three
+a lot of threshold around the 10
+
+ align:start position:0%
+a lot of threshold around the 10
+ 
+
+ align:start position:0%
+a lot of threshold around the 10
+okay yeah 9.5 say around 10 okay
+
+ align:start position:0%
+okay yeah 9.5 say around 10 okay
+ 
+
+ align:start position:0%
+okay yeah 9.5 say around 10 okay
+and then you see something like this
+
+ align:start position:0%
+and then you see something like this
+ 
+
+ align:start position:0%
+and then you see something like this
+yeah I'm just showing roughly okay you
+
+ align:start position:0%
+yeah I'm just showing roughly okay you
+ 
+
+ align:start position:0%
+yeah I'm just showing roughly okay you
+create something
+
+ align:start position:0%
+create something
+ 
+
+ align:start position:0%
+create something
+and then you
+
+ align:start position:0%
+and then you
+ 
+
+ align:start position:0%
+and then you
+something and then you have a large
+
+ align:start position:0%
+something and then you have a large
+ 
+
+ align:start position:0%
+something and then you have a large
+threshold and then you have a lot of
+
+ align:start position:0%
+threshold and then you have a lot of
+ 
+
+ align:start position:0%
+threshold and then you have a lot of
+stretch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it turns out the first nine is
+
+ align:start position:0%
+so it turns out the first nine is
+ 
+
+ align:start position:0%
+so it turns out the first nine is
+precisely at the two
+
+ align:start position:0%
+precisely at the two
+ 
+
+ align:start position:0%
+precisely at the two
+yeah I have to say precisely it's just
+
+ align:start position:0%
+yeah I have to say precisely it's just
+ 
+
+ align:start position:0%
+yeah I have to say precisely it's just
+say up to some Arrow bar okay and the
+
+ align:start position:0%
+say up to some Arrow bar okay and the
+ 
+
+ align:start position:0%
+say up to some Arrow bar okay and the
+other one is about say a little bit more
+
+ align:start position:0%
+other one is about say a little bit more
+ 
+
+ align:start position:0%
+other one is about say a little bit more
+than three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little bit more than three and then
+
+ align:start position:0%
+a little bit more than three and then
+ 
+
+ align:start position:0%
+a little bit more than three and then
+the four is one here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so if you compare with these numbers
+
+ align:start position:0%
+so if you compare with these numbers
+ 
+
+ align:start position:0%
+so if you compare with these numbers
+and you conclude that NC is actually
+
+ align:start position:0%
+and you conclude that NC is actually
+ 
+
+ align:start position:0%
+and you conclude that NC is actually
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+yeah in C3 okay to be compatible with
+
+ align:start position:0%
+yeah in C3 okay to be compatible with
+ 
+
+ align:start position:0%
+yeah in C3 okay to be compatible with
+this experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+going to high jumps yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+so so this way
+
+ align:start position:0%
+so so this way
+ 
+
+ align:start position:0%
+so so this way
+so this is a very nice
+
+ align:start position:0%
+so this is a very nice
+ 
+
+ align:start position:0%
+so this is a very nice
+simple uh uh uh even though this is a
+
+ align:start position:0%
+simple uh uh uh even though this is a
+ 
+
+ align:start position:0%
+simple uh uh uh even though this is a
+very simple process
+
+ align:start position:0%
+very simple process
+ 
+
+ align:start position:0%
+very simple process
+but actually uh uh have very important
+
+ align:start position:0%
+but actually uh uh have very important
+ 
+
+ align:start position:0%
+but actually uh uh have very important
+physical implications okay and uh in
+
+ align:start position:0%
+physical implications okay and uh in
+ 
+
+ align:start position:0%
+physical implications okay and uh in
+fact quite profound physical
+
+ align:start position:0%
+fact quite profound physical
+ 
+
+ align:start position:0%
+fact quite profound physical
+implications
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we only have a few minutes left
+
+ align:start position:0%
+so we only have a few minutes left
+ 
+
+ align:start position:0%
+so we only have a few minutes left
+so let's
+
+ align:start position:0%
+so let's
+ 
+
+ align:start position:0%
+so let's
+say a few words regarding the
+
+ align:start position:0%
+say a few words regarding the
+ 
+
+ align:start position:0%
+say a few words regarding the
+next topic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's again consider this
+
+ align:start position:0%
+okay so let's again consider this
+ 
+
+ align:start position:0%
+okay so let's again consider this
+process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of e plus
+
+ align:start position:0%
+of e plus
+ 
+
+ align:start position:0%
+of e plus
+E minor is going to Mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay go into mu
+
+ align:start position:0%
+okay go into mu
+ 
+
+ align:start position:0%
+okay go into mu
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so we have
+
+ align:start position:0%
+so we have
+ 
+
+ align:start position:0%
+so we have
+again this diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose this is P1 P2
+
+ align:start position:0%
+so suppose this is P1 P2
+ 
+
+ align:start position:0%
+so suppose this is P1 P2
+and the K1
+
+ align:start position:0%
+and the K1
+ 
+
+ align:start position:0%
+and the K1
+the K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when we draw this diagram we take the
+
+ align:start position:0%
+so when we draw this diagram we take the
+ 
+
+ align:start position:0%
+so when we draw this diagram we take the
+time as going above so these are the
+
+ align:start position:0%
+time as going above so these are the
+ 
+
+ align:start position:0%
+time as going above so these are the
+initial State these are the final States
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if we view this diagram sideways
+
+ align:start position:0%
+so now if we view this diagram sideways
+ 
+
+ align:start position:0%
+so now if we view this diagram sideways
+so if we view in this direction
+
+ align:start position:0%
+so if we view in this direction
+ 
+
+ align:start position:0%
+so if we view in this direction
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if you try to think that the time go
+
+ align:start position:0%
+so if you try to think that the time go
+ 
+
+ align:start position:0%
+so if you try to think that the time go
+into right direction say if you try to
+
+ align:start position:0%
+into right direction say if you try to
+ 
+
+ align:start position:0%
+into right direction say if you try to
+view it sideways
+
+ align:start position:0%
+view it sideways
+ 
+
+ align:start position:0%
+view it sideways
+and then then in this case we'll view
+
+ align:start position:0%
+and then then in this case we'll view
+ 
+
+ align:start position:0%
+and then then in this case we'll view
+the sideway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and now this become my initial
+
+ align:start position:0%
+okay and now this become my initial
+ 
+
+ align:start position:0%
+okay and now this become my initial
+state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the initial State and this is
+
+ align:start position:0%
+so this is the initial State and this is
+ 
+
+ align:start position:0%
+so this is the initial State and this is
+still initial state
+
+ align:start position:0%
+still initial state
+ 
+
+ align:start position:0%
+still initial state
+let me see um oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one second let me see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then this is the initial State and
+
+ align:start position:0%
+and then this is the initial State and
+ 
+
+ align:start position:0%
+and then this is the initial State and
+this is the uh uh initial State
+
+ align:start position:0%
+this is the uh uh initial State
+ 
+
+ align:start position:0%
+this is the uh uh initial State
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let me show the arrow this way okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it doesn't matter let's do the iron
+
+ align:start position:0%
+yeah it doesn't matter let's do the iron
+ 
+
+ align:start position:0%
+yeah it doesn't matter let's do the iron
+this way so so that this is the uh this
+
+ align:start position:0%
+this way so so that this is the uh this
+ 
+
+ align:start position:0%
+this way so so that this is the uh this
+is the MU this is the MU plus okay
+
+ align:start position:0%
+is the MU this is the MU plus okay
+ 
+
+ align:start position:0%
+is the MU this is the MU plus okay
+so so this is and now let's view this
+
+ align:start position:0%
+so so this is and now let's view this
+ 
+
+ align:start position:0%
+so so this is and now let's view this
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+and now this is nuke you have initial
+
+ align:start position:0%
+and now this is nuke you have initial
+ 
+
+ align:start position:0%
+and now this is nuke you have initial
+initial electron and then you have
+
+ align:start position:0%
+initial electron and then you have
+ 
+
+ align:start position:0%
+initial electron and then you have
+initial muon okay and then
+
+ align:start position:0%
+initial muon okay and then
+ 
+
+ align:start position:0%
+initial muon okay and then
+this become a process e minus plus mu
+
+ align:start position:0%
+this become a process e minus plus mu
+ 
+
+ align:start position:0%
+this become a process e minus plus mu
+minus going to e minus and mu minus
+
+ align:start position:0%
+minus going to e minus and mu minus
+ 
+
+ align:start position:0%
+minus going to e minus and mu minus
+okay because this is the final particle
+
+ align:start position:0%
+okay because this is the final particle
+ 
+
+ align:start position:0%
+okay because this is the final particle
+now going out would be the particle and
+
+ align:start position:0%
+now going out would be the particle and
+ 
+
+ align:start position:0%
+now going out would be the particle and
+this fellow particle going out would be
+
+ align:start position:0%
+this fellow particle going out would be
+ 
+
+ align:start position:0%
+this fellow particle going out would be
+a particle and then then the final will
+
+ align:start position:0%
+a particle and then then the final will
+ 
+
+ align:start position:0%
+a particle and then then the final will
+be the electron and the muon okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and then and then you get the process
+
+ align:start position:0%
+so and then and then you get the process
+ 
+
+ align:start position:0%
+so and then and then you get the process
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+that means the diagram when you view the
+
+ align:start position:0%
+that means the diagram when you view the
+ 
+
+ align:start position:0%
+that means the diagram when you view the
+sideways then you have a diagram like
+
+ align:start position:0%
+sideways then you have a diagram like
+ 
+
+ align:start position:0%
+sideways then you have a diagram like
+this if I choose using our again time
+
+ align:start position:0%
+this if I choose using our again time
+ 
+
+ align:start position:0%
+this if I choose using our again time
+going to up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then this is like that
+
+ align:start position:0%
+then this is like that
+ 
+
+ align:start position:0%
+then this is like that
+now this is e minus E minus mu minus
+
+ align:start position:0%
+now this is e minus E minus mu minus
+ 
+
+ align:start position:0%
+now this is e minus E minus mu minus
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now you wonder
+
+ align:start position:0%
+so now you wonder
+ 
+
+ align:start position:0%
+so now you wonder
+whether there's some relation
+
+ align:start position:0%
+whether there's some relation
+ 
+
+ align:start position:0%
+whether there's some relation
+between these two process okay
+
+ align:start position:0%
+between these two process okay
+ 
+
+ align:start position:0%
+between these two process okay
+whether there's some a relation between
+
+ align:start position:0%
+whether there's some a relation between
+ 
+
+ align:start position:0%
+whether there's some a relation between
+this process we do from you just
+
+ align:start position:0%
+this process we do from you just
+ 
+
+ align:start position:0%
+this process we do from you just
+exchange initial state to the final
+
+ align:start position:0%
+exchange initial state to the final
+ 
+
+ align:start position:0%
+exchange initial state to the final
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+so it turns out actually there's a very
+
+ align:start position:0%
+so it turns out actually there's a very
+ 
+
+ align:start position:0%
+so it turns out actually there's a very
+nice relation between them okay if you
+
+ align:start position:0%
+nice relation between them okay if you
+ 
+
+ align:start position:0%
+nice relation between them okay if you
+know one of them you can try to use the
+
+ align:start position:0%
+know one of them you can try to use the
+ 
+
+ align:start position:0%
+know one of them you can try to use the
+other uh can help you deduce the other
+
+ align:start position:0%
+other uh can help you deduce the other
+ 
+
+ align:start position:0%
+other uh can help you deduce the other
+which uh or or we are running out of
+
+ align:start position:0%
+which uh or or we are running out of
+ 
+
+ align:start position:0%
+which uh or or we are running out of
+time so we will do it the next time okay
\ No newline at end of file
diff --git a/tpaE_C8rqf8.txt b/tpaE_C8rqf8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b9f16ac099ced211cb9ca847791ad7ad3a6716a7
--- /dev/null
+++ b/tpaE_C8rqf8.txt
@@ -0,0 +1,859 @@
+align:start position:0%
+ 
+we now continue with our example and
+
+ align:start position:0%
+we now continue with our example and
+ 
+
+ align:start position:0%
+we now continue with our example and
+turn to the performance evaluation
+
+ align:start position:0%
+turn to the performance evaluation
+ 
+
+ align:start position:0%
+turn to the performance evaluation
+question as you recall we have a theta
+
+ align:start position:0%
+question as you recall we have a theta
+ 
+
+ align:start position:0%
+question as you recall we have a theta
+that has a certain prior distribution
+
+ align:start position:0%
+that has a certain prior distribution
+ 
+
+ align:start position:0%
+that has a certain prior distribution
+were given a model for the observations
+
+ align:start position:0%
+were given a model for the observations
+ 
+
+ align:start position:0%
+were given a model for the observations
+we came up with a joint distribution for
+
+ align:start position:0%
+we came up with a joint distribution for
+ 
+
+ align:start position:0%
+we came up with a joint distribution for
+X and theta which was uniform on this
+
+ align:start position:0%
+X and theta which was uniform on this
+ 
+
+ align:start position:0%
+X and theta which was uniform on this
+particular shape and we found that the
+
+ align:start position:0%
+particular shape and we found that the
+ 
+
+ align:start position:0%
+particular shape and we found that the
+least mean square system ATAR namely the
+
+ align:start position:0%
+least mean square system ATAR namely the
+ 
+
+ align:start position:0%
+least mean square system ATAR namely the
+conditional expectation of theta given
+
+ align:start position:0%
+conditional expectation of theta given
+ 
+
+ align:start position:0%
+conditional expectation of theta given
+any particular value of x is given by
+
+ align:start position:0%
+any particular value of x is given by
+ 
+
+ align:start position:0%
+any particular value of x is given by
+this particular piecewise linear
+
+ align:start position:0%
+this particular piecewise linear
+ 
+
+ align:start position:0%
+this particular piecewise linear
+function now let us look at the
+
+ align:start position:0%
+function now let us look at the
+ 
+
+ align:start position:0%
+function now let us look at the
+performance of this estimator we judge
+
+ align:start position:0%
+performance of this estimator we judge
+ 
+
+ align:start position:0%
+performance of this estimator we judge
+the performance given any particular
+
+ align:start position:0%
+the performance given any particular
+ 
+
+ align:start position:0%
+the performance given any particular
+value of x by looking at the
+
+ align:start position:0%
+value of x by looking at the
+ 
+
+ align:start position:0%
+value of x by looking at the
+corresponding mean squared error which
+
+ align:start position:0%
+corresponding mean squared error which
+ 
+
+ align:start position:0%
+corresponding mean squared error which
+is the square of the distance between
+
+ align:start position:0%
+is the square of the distance between
+ 
+
+ align:start position:0%
+is the square of the distance between
+the unknown parameter and the estimate
+
+ align:start position:0%
+the unknown parameter and the estimate
+ 
+
+ align:start position:0%
+the unknown parameter and the estimate
+with which we came up and as we have
+
+ align:start position:0%
+with which we came up and as we have
+ 
+
+ align:start position:0%
+with which we came up and as we have
+discussed this is the same as the
+
+ align:start position:0%
+discussed this is the same as the
+ 
+
+ align:start position:0%
+discussed this is the same as the
+variance of theta but in the conditional
+
+ align:start position:0%
+variance of theta but in the conditional
+ 
+
+ align:start position:0%
+variance of theta but in the conditional
+universe where X has been observed
+
+ align:start position:0%
+universe where X has been observed
+ 
+
+ align:start position:0%
+universe where X has been observed
+it's the variance of the conditional
+
+ align:start position:0%
+it's the variance of the conditional
+ 
+
+ align:start position:0%
+it's the variance of the conditional
+distribution of theta as we have
+
+ align:start position:0%
+distribution of theta as we have
+ 
+
+ align:start position:0%
+distribution of theta as we have
+discussed if I tell you that X takes on
+
+ align:start position:0%
+discussed if I tell you that X takes on
+ 
+
+ align:start position:0%
+discussed if I tell you that X takes on
+this particular value theta is uniform
+
+ align:start position:0%
+this particular value theta is uniform
+ 
+
+ align:start position:0%
+this particular value theta is uniform
+on this interval therefore the
+
+ align:start position:0%
+on this interval therefore the
+ 
+
+ align:start position:0%
+on this interval therefore the
+conditional variance of theta is the
+
+ align:start position:0%
+conditional variance of theta is the
+ 
+
+ align:start position:0%
+conditional variance of theta is the
+variance of a uniform on an interval of
+
+ align:start position:0%
+variance of a uniform on an interval of
+ 
+
+ align:start position:0%
+variance of a uniform on an interval of
+this particular length now we know that
+
+ align:start position:0%
+this particular length now we know that
+ 
+
+ align:start position:0%
+this particular length now we know that
+the variance of a uniform on an interval
+
+ align:start position:0%
+the variance of a uniform on an interval
+ 
+
+ align:start position:0%
+the variance of a uniform on an interval
+from A to B is equal to B minus a
+
+ align:start position:0%
+from A to B is equal to B minus a
+ 
+
+ align:start position:0%
+from A to B is equal to B minus a
+squared divided by 12 in this particular
+
+ align:start position:0%
+squared divided by 12 in this particular
+ 
+
+ align:start position:0%
+squared divided by 12 in this particular
+instance the interval has length 2
+
+ align:start position:0%
+instance the interval has length 2
+ 
+
+ align:start position:0%
+instance the interval has length 2
+therefore we have 2 squared divided by
+
+ align:start position:0%
+therefore we have 2 squared divided by
+ 
+
+ align:start position:0%
+therefore we have 2 squared divided by
+12 so the variance is equal to one-third
+
+ align:start position:0%
+12 so the variance is equal to one-third
+ 
+
+ align:start position:0%
+12 so the variance is equal to one-third
+this is what we get when the picture is
+
+ align:start position:0%
+this is what we get when the picture is
+ 
+
+ align:start position:0%
+this is what we get when the picture is
+of this type on the other hand if X
+
+ align:start position:0%
+of this type on the other hand if X
+ 
+
+ align:start position:0%
+of this type on the other hand if X
+falls in this range then this interval
+
+ align:start position:0%
+falls in this range then this interval
+ 
+
+ align:start position:0%
+falls in this range then this interval
+on which theta is now constrained to
+
+ align:start position:0%
+on which theta is now constrained to
+ 
+
+ align:start position:0%
+on which theta is now constrained to
+live has a smaller length and we're
+
+ align:start position:0%
+live has a smaller length and we're
+ 
+
+ align:start position:0%
+live has a smaller length and we're
+going to get a different variance so in
+
+ align:start position:0%
+going to get a different variance so in
+ 
+
+ align:start position:0%
+going to get a different variance so in
+order to keep track let us come up with
+
+ align:start position:0%
+order to keep track let us come up with
+ 
+
+ align:start position:0%
+order to keep track let us come up with
+a plot when x is between 5 & 9
+
+ align:start position:0%
+a plot when x is between 5 & 9
+ 
+
+ align:start position:0%
+a plot when x is between 5 & 9
+theta has a conditioned distribution
+
+ align:start position:0%
+theta has a conditioned distribution
+ 
+
+ align:start position:0%
+theta has a conditioned distribution
+which is uniform on an interval of
+
+ align:start position:0%
+which is uniform on an interval of
+ 
+
+ align:start position:0%
+which is uniform on an interval of
+length 2 and the variance of 1/3 and
+
+ align:start position:0%
+length 2 and the variance of 1/3 and
+ 
+
+ align:start position:0%
+length 2 and the variance of 1/3 and
+therefore the variance is constant takes
+
+ align:start position:0%
+therefore the variance is constant takes
+ 
+
+ align:start position:0%
+therefore the variance is constant takes
+this value at the extreme case when X is
+
+ align:start position:0%
+this value at the extreme case when X is
+ 
+
+ align:start position:0%
+this value at the extreme case when X is
+equal to 3 then this interval has zero
+
+ align:start position:0%
+equal to 3 then this interval has zero
+ 
+
+ align:start position:0%
+equal to 3 then this interval has zero
+lengths in fact we have perfect
+
+ align:start position:0%
+lengths in fact we have perfect
+ 
+
+ align:start position:0%
+lengths in fact we have perfect
+certainty about the value of theta if X
+
+ align:start position:0%
+certainty about the value of theta if X
+ 
+
+ align:start position:0%
+certainty about the value of theta if X
+is equal to 3 then we know that theta is
+
+ align:start position:0%
+is equal to 3 then we know that theta is
+ 
+
+ align:start position:0%
+is equal to 3 then we know that theta is
+equal to 4 there is no uncertainty
+
+ align:start position:0%
+equal to 4 there is no uncertainty
+ 
+
+ align:start position:0%
+equal to 4 there is no uncertainty
+there's zero variance what happens in
+
+ align:start position:0%
+there's zero variance what happens in
+ 
+
+ align:start position:0%
+there's zero variance what happens in
+between and as we increase X moving away
+
+ align:start position:0%
+between and as we increase X moving away
+ 
+
+ align:start position:0%
+between and as we increase X moving away
+from 3 the length of this interval
+
+ align:start position:0%
+from 3 the length of this interval
+ 
+
+ align:start position:0%
+from 3 the length of this interval
+increases linearly with X and this means
+
+ align:start position:0%
+increases linearly with X and this means
+ 
+
+ align:start position:0%
+increases linearly with X and this means
+that the variance increases
+
+ align:start position:0%
+that the variance increases
+ 
+
+ align:start position:0%
+that the variance increases
+quadratically with X so we have a
+
+ align:start position:0%
+quadratically with X so we have a
+ 
+
+ align:start position:0%
+quadratically with X so we have a
+quadratic that starts at 0 and rises to
+
+ align:start position:0%
+quadratic that starts at 0 and rises to
+ 
+
+ align:start position:0%
+quadratic that starts at 0 and rises to
+this value and by symmetric argument
+
+ align:start position:0%
+this value and by symmetric argument
+ 
+
+ align:start position:0%
+this value and by symmetric argument
+on the other side we also get a function
+
+ align:start position:0%
+on the other side we also get a function
+ 
+
+ align:start position:0%
+on the other side we also get a function
+which is 0 at 11 and which rises
+
+ align:start position:0%
+which is 0 at 11 and which rises
+ 
+
+ align:start position:0%
+which is 0 at 11 and which rises
+quadratically as X gets reduced from 11
+
+ align:start position:0%
+quadratically as X gets reduced from 11
+ 
+
+ align:start position:0%
+quadratically as X gets reduced from 11
+to 9 so this is a complete plot of the
+
+ align:start position:0%
+to 9 so this is a complete plot of the
+ 
+
+ align:start position:0%
+to 9 so this is a complete plot of the
+conditional variance of theta as a
+
+ align:start position:0%
+conditional variance of theta as a
+ 
+
+ align:start position:0%
+conditional variance of theta as a
+function of the particular observation
+
+ align:start position:0%
+function of the particular observation
+ 
+
+ align:start position:0%
+function of the particular observation
+that we have obtained we notice that
+
+ align:start position:0%
+that we have obtained we notice that
+ 
+
+ align:start position:0%
+that we have obtained we notice that
+some X's are more favorable than others
+
+ align:start position:0%
+some X's are more favorable than others
+ 
+
+ align:start position:0%
+some X's are more favorable than others
+an observation equal to 3 is extremely
+
+ align:start position:0%
+an observation equal to 3 is extremely
+ 
+
+ align:start position:0%
+an observation equal to 3 is extremely
+favorable because it tells us
+
+ align:start position:0%
+favorable because it tells us
+ 
+
+ align:start position:0%
+favorable because it tells us
+unambiguously the value of theta but
+
+ align:start position:0%
+unambiguously the value of theta but
+ 
+
+ align:start position:0%
+unambiguously the value of theta but
+other choices of X other possible
+
+ align:start position:0%
+other choices of X other possible
+ 
+
+ align:start position:0%
+other choices of X other possible
+observations we lead to more uncertainty
+
+ align:start position:0%
+observations we lead to more uncertainty
+ 
+
+ align:start position:0%
+observations we lead to more uncertainty
+in theta and this is reflected in this
+
+ align:start position:0%
+in theta and this is reflected in this
+ 
+
+ align:start position:0%
+in theta and this is reflected in this
+diagram in case we're now interested in
+
+ align:start position:0%
+diagram in case we're now interested in
+ 
+
+ align:start position:0%
+diagram in case we're now interested in
+the overall mean squared error then we
+
+ align:start position:0%
+the overall mean squared error then we
+ 
+
+ align:start position:0%
+the overall mean squared error then we
+have to calculate the average of this
+
+ align:start position:0%
+have to calculate the average of this
+ 
+
+ align:start position:0%
+have to calculate the average of this
+conditional variance where the average
+
+ align:start position:0%
+conditional variance where the average
+ 
+
+ align:start position:0%
+conditional variance where the average
+is taken over all values of X this is
+
+ align:start position:0%
+is taken over all values of X this is
+ 
+
+ align:start position:0%
+is taken over all values of X this is
+going to be an integral of the
+
+ align:start position:0%
+going to be an integral of the
+ 
+
+ align:start position:0%
+going to be an integral of the
+conditional variance of theta integrated
+
+ align:start position:0%
+conditional variance of theta integrated
+ 
+
+ align:start position:0%
+conditional variance of theta integrated
+over all possibilities for X but of
+
+ align:start position:0%
+over all possibilities for X but of
+ 
+
+ align:start position:0%
+over all possibilities for X but of
+course each possibility of X has to be
+
+ align:start position:0%
+course each possibility of X has to be
+ 
+
+ align:start position:0%
+course each possibility of X has to be
+weighted
+
+ align:start position:0%
+weighted
+ 
+
+ align:start position:0%
+weighted
+according to the corresponding
+
+ align:start position:0%
+according to the corresponding
+ 
+
+ align:start position:0%
+according to the corresponding
+probability or in this case probability
+
+ align:start position:0%
+probability or in this case probability
+ 
+
+ align:start position:0%
+probability or in this case probability
+density function of X what is the PDF of
+
+ align:start position:0%
+density function of X what is the PDF of
+ 
+
+ align:start position:0%
+density function of X what is the PDF of
+X it is not given to us but it is
+
+ align:start position:0%
+X it is not given to us but it is
+ 
+
+ align:start position:0%
+X it is not given to us but it is
+something that can be easily determined
+
+ align:start position:0%
+something that can be easily determined
+ 
+
+ align:start position:0%
+something that can be easily determined
+from what we have already done
+
+ align:start position:0%
+from what we have already done
+ 
+
+ align:start position:0%
+from what we have already done
+we know the Joint Distribution of theta
+
+ align:start position:0%
+we know the Joint Distribution of theta
+ 
+
+ align:start position:0%
+we know the Joint Distribution of theta
+and X and whenever we know the joint we
+
+ align:start position:0%
+and X and whenever we know the joint we
+ 
+
+ align:start position:0%
+and X and whenever we know the joint we
+can also find the marginal so once we
+
+ align:start position:0%
+can also find the marginal so once we
+ 
+
+ align:start position:0%
+can also find the marginal so once we
+find the marginal PDF of X then we can
+
+ align:start position:0%
+find the marginal PDF of X then we can
+ 
+
+ align:start position:0%
+find the marginal PDF of X then we can
+plug it in multiplied by this function
+
+ align:start position:0%
+plug it in multiplied by this function
+ 
+
+ align:start position:0%
+plug it in multiplied by this function
+that we have already obtained carry out
+
+ align:start position:0%
+that we have already obtained carry out
+ 
+
+ align:start position:0%
+that we have already obtained carry out
+the integration and we will end up with
+
+ align:start position:0%
+the integration and we will end up with
+ 
+
+ align:start position:0%
+the integration and we will end up with
+a numerical value since it is an average
+
+ align:start position:0%
+a numerical value since it is an average
+ 
+
+ align:start position:0%
+a numerical value since it is an average
+of what we have here it's going to end
+
+ align:start position:0%
+of what we have here it's going to end
+ 
+
+ align:start position:0%
+of what we have here it's going to end
+up being some number between 0 and 1/3
+
+ align:start position:0%
+up being some number between 0 and 1/3
+ 
+
+ align:start position:0%
+up being some number between 0 and 1/3
+it's the average of these values and
+
+ align:start position:0%
+it's the average of these values and
+ 
+
+ align:start position:0%
+it's the average of these values and
+closer to 1/3 rather than to 0 and this
+
+ align:start position:0%
+closer to 1/3 rather than to 0 and this
+ 
+
+ align:start position:0%
+closer to 1/3 rather than to 0 and this
+would complete the way that the
+
+ align:start position:0%
+would complete the way that the
+ 
+
+ align:start position:0%
+would complete the way that the
+performance of a particular estimator
+
+ align:start position:0%
+performance of a particular estimator
+ 
+
+ align:start position:0%
+performance of a particular estimator
+gets evaluated
\ No newline at end of file
diff --git a/turMcLH-o_o.txt b/turMcLH-o_o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fd0655f1c12315aaacb7fea4579acaf0524d76ce
--- /dev/null
+++ b/turMcLH-o_o.txt
@@ -0,0 +1,16939 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common license. Your support
+
+ align:start position:0%
+a Creative Common license. Your support
+ 
+
+ align:start position:0%
+a Creative Common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+My name is David Hart for those of you
+
+ align:start position:0%
+My name is David Hart for those of you
+ 
+
+ align:start position:0%
+My name is David Hart for those of you
+who I haven't met yet. And uh uh I'm
+
+ align:start position:0%
+who I haven't met yet. And uh uh I'm
+ 
+
+ align:start position:0%
+who I haven't met yet. And uh uh I'm
+filling in for for Dwayne Bonding today
+
+ align:start position:0%
+filling in for for Dwayne Bonding today
+ 
+
+ align:start position:0%
+filling in for for Dwayne Bonding today
+or sitting in or or guest lecturing
+
+ align:start position:0%
+or sitting in or or guest lecturing
+ 
+
+ align:start position:0%
+or sitting in or or guest lecturing
+whichever you want to call. You're a co-
+
+ align:start position:0%
+whichever you want to call. You're a co-
+ 
+
+ align:start position:0%
+whichever you want to call. You're a co-
+lecturer. Oh yeah, I'm a co- lecturer.
+
+ align:start position:0%
+lecturer. Oh yeah, I'm a co- lecturer.
+ 
+
+ align:start position:0%
+lecturer. Oh yeah, I'm a co- lecturer.
+Yeah. Yeah, that's right. No, I'm guest
+
+ align:start position:0%
+Yeah. Yeah, that's right. No, I'm guest
+ 
+
+ align:start position:0%
+Yeah. Yeah, that's right. No, I'm guest
+lecturing because well, you know the
+
+ align:start position:0%
+lecturing because well, you know the
+ 
+
+ align:start position:0%
+lecturing because well, you know the
+story. So uh uh I think my role today is
+
+ align:start position:0%
+story. So uh uh I think my role today is
+ 
+
+ align:start position:0%
+story. So uh uh I think my role today is
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh in some ways repeat what uh Dwayne
+
+ align:start position:0%
+uh in some ways repeat what uh Dwayne
+ 
+
+ align:start position:0%
+uh in some ways repeat what uh Dwayne
+Bonding has talked about in the first
+
+ align:start position:0%
+Bonding has talked about in the first
+ 
+
+ align:start position:0%
+Bonding has talked about in the first
+two lectures from a little bit more of a
+
+ align:start position:0%
+two lectures from a little bit more of a
+ 
+
+ align:start position:0%
+two lectures from a little bit more of a
+mechanical engineering perspective. But
+
+ align:start position:0%
+mechanical engineering perspective. But
+ 
+
+ align:start position:0%
+mechanical engineering perspective. But
+I'm going to also throw in some things.
+
+ align:start position:0%
+I'm going to also throw in some things.
+ 
+
+ align:start position:0%
+I'm going to also throw in some things.
+Um, you might just say a personal
+
+ align:start position:0%
+Um, you might just say a personal
+ 
+
+ align:start position:0%
+Um, you might just say a personal
+perspective on the problem. Um, and uh,
+
+ align:start position:0%
+perspective on the problem. Um, and uh,
+ 
+
+ align:start position:0%
+perspective on the problem. Um, and uh,
+uh, I I've got too much to try and do in
+
+ align:start position:0%
+uh, I I've got too much to try and do in
+ 
+
+ align:start position:0%
+uh, I I've got too much to try and do in
+one lecture, but that's sort of typical
+
+ align:start position:0%
+one lecture, but that's sort of typical
+ 
+
+ align:start position:0%
+one lecture, but that's sort of typical
+of me anyway. Uh, but the notes are on
+
+ align:start position:0%
+of me anyway. Uh, but the notes are on
+ 
+
+ align:start position:0%
+of me anyway. Uh, but the notes are on
+the on the web if you want for the
+
+ align:start position:0%
+the on the web if you want for the
+ 
+
+ align:start position:0%
+the on the web if you want for the
+things I have to skip over. Um, now the
+
+ align:start position:0%
+things I have to skip over. Um, now the
+ 
+
+ align:start position:0%
+things I have to skip over. Um, now the
+first part of the lecture is to to
+
+ align:start position:0%
+first part of the lecture is to to
+ 
+
+ align:start position:0%
+first part of the lecture is to to
+notice this scene. And this is someone
+
+ align:start position:0%
+notice this scene. And this is someone
+ 
+
+ align:start position:0%
+notice this scene. And this is someone
+was pointing out to me the other day
+
+ align:start position:0%
+was pointing out to me the other day
+ 
+
+ align:start position:0%
+was pointing out to me the other day
+said, "You must be tough for you this
+
+ align:start position:0%
+said, "You must be tough for you this
+ 
+
+ align:start position:0%
+said, "You must be tough for you this
+summer because you go between these
+
+ align:start position:0%
+summer because you go between these
+ 
+
+ align:start position:0%
+summer because you go between these
+these this winter because you go between
+
+ align:start position:0%
+these this winter because you go between
+ 
+
+ align:start position:0%
+these this winter because you go between
+these extreme environments." So I found
+
+ align:start position:0%
+these extreme environments." So I found
+ 
+
+ align:start position:0%
+these extreme environments." So I found
+this picture of sort of what I'll call a
+
+ align:start position:0%
+this picture of sort of what I'll call a
+ 
+
+ align:start position:0%
+this picture of sort of what I'll call a
+tree tunnel. Does anybody know where
+
+ align:start position:0%
+tree tunnel. Does anybody know where
+ 
+
+ align:start position:0%
+tree tunnel. Does anybody know where
+this picture was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+taken in January?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It wasn't at MIT. It's a little washed
+
+ align:start position:0%
+It wasn't at MIT. It's a little washed
+ 
+
+ align:start position:0%
+It wasn't at MIT. It's a little washed
+out so you can't see what these these
+
+ align:start position:0%
+out so you can't see what these these
+ 
+
+ align:start position:0%
+out so you can't see what these these
+things are off in the distance.
+
+ align:start position:0%
+things are off in the distance.
+ 
+
+ align:start position:0%
+things are off in the distance.
+If you saw those, you'd probably know in
+
+ align:start position:0%
+If you saw those, you'd probably know in
+ 
+
+ align:start position:0%
+If you saw those, you'd probably know in
+an instant if you know
+
+ align:start position:0%
+an instant if you know
+ 
+
+ align:start position:0%
+an instant if you know
+anybody in Singapore know what that
+
+ align:start position:0%
+anybody in Singapore know what that
+ 
+
+ align:start position:0%
+anybody in Singapore know what that
+picture might be
+
+ align:start position:0%
+picture might be
+ 
+
+ align:start position:0%
+picture might be
+taken. Oh, come
+
+ align:start position:0%
+taken. Oh, come
+ 
+
+ align:start position:0%
+taken. Oh, come
+on. All right. Where do you think this
+
+ align:start position:0%
+on. All right. Where do you think this
+ 
+
+ align:start position:0%
+on. All right. Where do you think this
+picture was taken?
+
+ align:start position:0%
+picture was taken?
+ 
+
+ align:start position:0%
+picture was taken?
+Not. All right. Okay. So, here's a tree
+
+ align:start position:0%
+Not. All right. Okay. So, here's a tree
+ 
+
+ align:start position:0%
+Not. All right. Okay. So, here's a tree
+tunnel in Actton, Massachusetts in
+
+ align:start position:0%
+tunnel in Actton, Massachusetts in
+ 
+
+ align:start position:0%
+tunnel in Actton, Massachusetts in
+January. And here's a tree tunnel in on
+
+ align:start position:0%
+January. And here's a tree tunnel in on
+ 
+
+ align:start position:0%
+January. And here's a tree tunnel in on
+Sentosa Island in Singapore in January.
+
+ align:start position:0%
+Sentosa Island in Singapore in January.
+ 
+
+ align:start position:0%
+Sentosa Island in Singapore in January.
+Just about the same time, same kind of
+
+ align:start position:0%
+Just about the same time, same kind of
+ 
+
+ align:start position:0%
+Just about the same time, same kind of
+view. The difference is that those are
+
+ align:start position:0%
+view. The difference is that those are
+ 
+
+ align:start position:0%
+view. The difference is that those are
+probably the second largest collection
+
+ align:start position:0%
+probably the second largest collection
+ 
+
+ align:start position:0%
+probably the second largest collection
+of container ships in the world.
+
+ align:start position:0%
+of container ships in the world.
+ 
+
+ align:start position:0%
+of container ships in the world.
+Something like that, which is the main
+
+ align:start position:0%
+Something like that, which is the main
+ 
+
+ align:start position:0%
+Something like that, which is the main
+uh landscape feature off of that coast
+
+ align:start position:0%
+uh landscape feature off of that coast
+ 
+
+ align:start position:0%
+uh landscape feature off of that coast
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Singapore. Okay, just to let everybody
+
+ align:start position:0%
+Singapore. Okay, just to let everybody
+ 
+
+ align:start position:0%
+Singapore. Okay, just to let everybody
+know what the other side is is enjoying
+
+ align:start position:0%
+know what the other side is is enjoying
+ 
+
+ align:start position:0%
+know what the other side is is enjoying
+on their
+
+ align:start position:0%
+on their
+ 
+
+ align:start position:0%
+on their
+weekends. So, um here's what I want to
+
+ align:start position:0%
+weekends. So, um here's what I want to
+ 
+
+ align:start position:0%
+weekends. So, um here's what I want to
+uh try to do today. Okay, I want to uh
+
+ align:start position:0%
+uh try to do today. Okay, I want to uh
+ 
+
+ align:start position:0%
+uh try to do today. Okay, I want to uh
+go back and talk a little bit more about
+
+ align:start position:0%
+go back and talk a little bit more about
+ 
+
+ align:start position:0%
+go back and talk a little bit more about
+process definitions from the point of
+
+ align:start position:0%
+process definitions from the point of
+ 
+
+ align:start position:0%
+process definitions from the point of
+view of geometric change of an object.
+
+ align:start position:0%
+view of geometric change of an object.
+ 
+
+ align:start position:0%
+view of geometric change of an object.
+And I think Dwayne has already talked
+
+ align:start position:0%
+And I think Dwayne has already talked
+ 
+
+ align:start position:0%
+And I think Dwayne has already talked
+about this a fair amount, but I want to
+
+ align:start position:0%
+about this a fair amount, but I want to
+ 
+
+ align:start position:0%
+about this a fair amount, but I want to
+relate it to that model or that view of
+
+ align:start position:0%
+relate it to that model or that view of
+ 
+
+ align:start position:0%
+relate it to that model or that view of
+processes to a couple key mechanical
+
+ align:start position:0%
+processes to a couple key mechanical
+ 
+
+ align:start position:0%
+processes to a couple key mechanical
+processes uh as examples. And then
+
+ align:start position:0%
+processes uh as examples. And then
+ 
+
+ align:start position:0%
+processes uh as examples. And then
+something that we always do is talk
+
+ align:start position:0%
+something that we always do is talk
+ 
+
+ align:start position:0%
+something that we always do is talk
+about this taxonomy for control. It's
+
+ align:start position:0%
+about this taxonomy for control. It's
+ 
+
+ align:start position:0%
+about this taxonomy for control. It's
+it's a framework. It's it's all these
+
+ align:start position:0%
+it's a framework. It's it's all these
+ 
+
+ align:start position:0%
+it's a framework. It's it's all these
+these rather uh abstract terms that uh
+
+ align:start position:0%
+these rather uh abstract terms that uh
+ 
+
+ align:start position:0%
+these rather uh abstract terms that uh
+say here's a way for you to think about
+
+ align:start position:0%
+say here's a way for you to think about
+ 
+
+ align:start position:0%
+say here's a way for you to think about
+every process that's ever been invented
+
+ align:start position:0%
+every process that's ever been invented
+ 
+
+ align:start position:0%
+every process that's ever been invented
+and try to understand how it relates to
+
+ align:start position:0%
+and try to understand how it relates to
+ 
+
+ align:start position:0%
+and try to understand how it relates to
+some other process with respect to
+
+ align:start position:0%
+some other process with respect to
+ 
+
+ align:start position:0%
+some other process with respect to
+things that affect how we control the
+
+ align:start position:0%
+things that affect how we control the
+ 
+
+ align:start position:0%
+things that affect how we control the
+process. So that's our taxonomy for
+
+ align:start position:0%
+process. So that's our taxonomy for
+ 
+
+ align:start position:0%
+process. So that's our taxonomy for
+control. And then we go through a couple
+
+ align:start position:0%
+control. And then we go through a couple
+ 
+
+ align:start position:0%
+control. And then we go through a couple
+mechanical examples. I'll use the
+
+ align:start position:0%
+mechanical examples. I'll use the
+ 
+
+ align:start position:0%
+mechanical examples. I'll use the
+process of simple machining, a turning
+
+ align:start position:0%
+process of simple machining, a turning
+ 
+
+ align:start position:0%
+process of simple machining, a turning
+process, a bending process, and a
+
+ align:start position:0%
+process, a bending process, and a
+ 
+
+ align:start position:0%
+process, a bending process, and a
+molding process. Um we used to have a
+
+ align:start position:0%
+molding process. Um we used to have a
+ 
+
+ align:start position:0%
+molding process. Um we used to have a
+lab in in the course that we did. Uh in
+
+ align:start position:0%
+lab in in the course that we did. Uh in
+ 
+
+ align:start position:0%
+lab in in the course that we did. Uh in
+fact the guys in Singapore did it this
+
+ align:start position:0%
+fact the guys in Singapore did it this
+ 
+
+ align:start position:0%
+fact the guys in Singapore did it this
+summer as part of their summer
+
+ align:start position:0%
+summer as part of their summer
+ 
+
+ align:start position:0%
+summer as part of their summer
+orientation. They actually did this lab
+
+ align:start position:0%
+orientation. They actually did this lab
+ 
+
+ align:start position:0%
+orientation. They actually did this lab
+where they they went through and made
+
+ align:start position:0%
+where they they went through and made
+ 
+
+ align:start position:0%
+where they they went through and made
+parts using these three
+
+ align:start position:0%
+parts using these three
+ 
+
+ align:start position:0%
+parts using these three
+processes and we studied the process
+
+ align:start position:0%
+processes and we studied the process
+ 
+
+ align:start position:0%
+processes and we studied the process
+control aspects of that. And they're
+
+ align:start position:0%
+control aspects of that. And they're
+ 
+
+ align:start position:0%
+control aspects of that. And they're
+simple enough they're they're they're
+
+ align:start position:0%
+simple enough they're they're they're
+ 
+
+ align:start position:0%
+simple enough they're they're they're
+ubiquitous processes but they also can
+
+ align:start position:0%
+ubiquitous processes but they also can
+ 
+
+ align:start position:0%
+ubiquitous processes but they also can
+be reduced uh to some simple enough
+
+ align:start position:0%
+be reduced uh to some simple enough
+ 
+
+ align:start position:0%
+be reduced uh to some simple enough
+concepts that you can try to understand
+
+ align:start position:0%
+concepts that you can try to understand
+ 
+
+ align:start position:0%
+concepts that you can try to understand
+this this idea of the origins of
+
+ align:start position:0%
+this this idea of the origins of
+ 
+
+ align:start position:0%
+this this idea of the origins of
+variation. Why did things vary? Instead
+
+ align:start position:0%
+variation. Why did things vary? Instead
+ 
+
+ align:start position:0%
+variation. Why did things vary? Instead
+of it being a purely um uh uh random
+
+ align:start position:0%
+of it being a purely um uh uh random
+ 
+
+ align:start position:0%
+of it being a purely um uh uh random
+event instead of sort of throwing up
+
+ align:start position:0%
+event instead of sort of throwing up
+ 
+
+ align:start position:0%
+event instead of sort of throwing up
+your hands and saying I have no idea why
+
+ align:start position:0%
+your hands and saying I have no idea why
+ 
+
+ align:start position:0%
+your hands and saying I have no idea why
+anything happened. Let's just model it
+
+ align:start position:0%
+anything happened. Let's just model it
+ 
+
+ align:start position:0%
+anything happened. Let's just model it
+as a random process. We say no, let's
+
+ align:start position:0%
+as a random process. We say no, let's
+ 
+
+ align:start position:0%
+as a random process. We say no, let's
+try to see if we can separate those
+
+ align:start position:0%
+try to see if we can separate those
+ 
+
+ align:start position:0%
+try to see if we can separate those
+things that have a clear cause which we
+
+ align:start position:0%
+things that have a clear cause which we
+ 
+
+ align:start position:0%
+things that have a clear cause which we
+may or may not be able to control and
+
+ align:start position:0%
+may or may not be able to control and
+ 
+
+ align:start position:0%
+may or may not be able to control and
+those things that we just don't know
+
+ align:start position:0%
+those things that we just don't know
+ 
+
+ align:start position:0%
+those things that we just don't know
+about. Okay. And then scrambling at the
+
+ align:start position:0%
+about. Okay. And then scrambling at the
+ 
+
+ align:start position:0%
+about. Okay. And then scrambling at the
+end I'll try to get to this concept of
+
+ align:start position:0%
+end I'll try to get to this concept of
+ 
+
+ align:start position:0%
+end I'll try to get to this concept of
+uh states and properties. And this is
+
+ align:start position:0%
+uh states and properties. And this is
+ 
+
+ align:start position:0%
+uh states and properties. And this is
+again this is more of a framework issue
+
+ align:start position:0%
+again this is more of a framework issue
+ 
+
+ align:start position:0%
+again this is more of a framework issue
+but it is uh an issue of looking at any
+
+ align:start position:0%
+but it is uh an issue of looking at any
+ 
+
+ align:start position:0%
+but it is uh an issue of looking at any
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+uh looking at all the different factors
+
+ align:start position:0%
+uh looking at all the different factors
+ 
+
+ align:start position:0%
+uh looking at all the different factors
+that enter into the outcome of the
+
+ align:start position:0%
+that enter into the outcome of the
+ 
+
+ align:start position:0%
+that enter into the outcome of the
+process and just parsing it really uh
+
+ align:start position:0%
+process and just parsing it really uh
+ 
+
+ align:start position:0%
+process and just parsing it really uh
+into four areas and this idea
+
+ align:start position:0%
+into four areas and this idea
+ 
+
+ align:start position:0%
+into four areas and this idea
+of what we'll end up calling
+
+ align:start position:0%
+of what we'll end up calling
+ 
+
+ align:start position:0%
+of what we'll end up calling
+thermodynamic states those things that
+
+ align:start position:0%
+thermodynamic states those things that
+ 
+
+ align:start position:0%
+thermodynamic states those things that
+are kind of transit come and go and
+
+ align:start position:0%
+are kind of transit come and go and
+ 
+
+ align:start position:0%
+are kind of transit come and go and
+properties those things that are
+
+ align:start position:0%
+properties those things that are
+ 
+
+ align:start position:0%
+properties those things that are
+inherent in the process and then we'll
+
+ align:start position:0%
+inherent in the process and then we'll
+ 
+
+ align:start position:0%
+inherent in the process and then we'll
+separate the process into the equipment
+
+ align:start position:0%
+separate the process into the equipment
+ 
+
+ align:start position:0%
+separate the process into the equipment
+that executes the process which kind of
+
+ align:start position:0%
+that executes the process which kind of
+ 
+
+ align:start position:0%
+that executes the process which kind of
+stays there day after day and year after
+
+ align:start position:0%
+stays there day after day and year after
+ 
+
+ align:start position:0%
+stays there day after day and year after
+year and the material that you're uh
+
+ align:start position:0%
+year and the material that you're uh
+ 
+
+ align:start position:0%
+year and the material that you're uh
+changing as part of the process and of
+
+ align:start position:0%
+changing as part of the process and of
+ 
+
+ align:start position:0%
+changing as part of the process and of
+course that changes on every cycle of
+
+ align:start position:0%
+course that changes on every cycle of
+ 
+
+ align:start position:0%
+course that changes on every cycle of
+the process and those that distinction
+
+ align:start position:0%
+the process and those that distinction
+ 
+
+ align:start position:0%
+the process and those that distinction
+between the two is extremely
+
+ align:start position:0%
+between the two is extremely
+ 
+
+ align:start position:0%
+between the two is extremely
+important. So here's the model you've
+
+ align:start position:0%
+important. So here's the model you've
+ 
+
+ align:start position:0%
+important. So here's the model you've
+already seen and um the first part of
+
+ align:start position:0%
+already seen and um the first part of
+ 
+
+ align:start position:0%
+already seen and um the first part of
+this is to notice that uh we've taken
+
+ align:start position:0%
+this is to notice that uh we've taken
+ 
+
+ align:start position:0%
+this is to notice that uh we've taken
+the manufacturing process and said well
+
+ align:start position:0%
+the manufacturing process and said well
+ 
+
+ align:start position:0%
+the manufacturing process and said well
+again uh there are these two elements to
+
+ align:start position:0%
+again uh there are these two elements to
+ 
+
+ align:start position:0%
+again uh there are these two elements to
+it. There's the material
+
+ align:start position:0%
+it. There's the material
+ 
+
+ align:start position:0%
+it. There's the material
+um which is again sort of coming and
+
+ align:start position:0%
+um which is again sort of coming and
+ 
+
+ align:start position:0%
+um which is again sort of coming and
+going and by its very nature the fact
+
+ align:start position:0%
+going and by its very nature the fact
+ 
+
+ align:start position:0%
+going and by its very nature the fact
+that every time you run the process
+
+ align:start position:0%
+that every time you run the process
+ 
+
+ align:start position:0%
+that every time you run the process
+there's a new piece of material in there
+
+ align:start position:0%
+there's a new piece of material in there
+ 
+
+ align:start position:0%
+there's a new piece of material in there
+that's going to have a different
+
+ align:start position:0%
+that's going to have a different
+ 
+
+ align:start position:0%
+that's going to have a different
+characteristic for its variability than
+
+ align:start position:0%
+characteristic for its variability than
+ 
+
+ align:start position:0%
+characteristic for its variability than
+the equipment which again is you know
+
+ align:start position:0%
+the equipment which again is you know
+ 
+
+ align:start position:0%
+the equipment which again is you know
+unless you buy disposable equipment um
+
+ align:start position:0%
+unless you buy disposable equipment um
+ 
+
+ align:start position:0%
+unless you buy disposable equipment um
+you generally keep around for uh years
+
+ align:start position:0%
+you generally keep around for uh years
+ 
+
+ align:start position:0%
+you generally keep around for uh years
+and then there's an interaction between
+
+ align:start position:0%
+and then there's an interaction between
+ 
+
+ align:start position:0%
+and then there's an interaction between
+the two and that interaction
+
+ align:start position:0%
+the two and that interaction
+ 
+
+ align:start position:0%
+the two and that interaction
+uh if you really want to abstract it is
+
+ align:start position:0%
+uh if you really want to abstract it is
+ 
+
+ align:start position:0%
+uh if you really want to abstract it is
+a uh could be called a directed energy
+
+ align:start position:0%
+a uh could be called a directed energy
+ 
+
+ align:start position:0%
+a uh could be called a directed energy
+exchange. It always takes some energy to
+
+ align:start position:0%
+exchange. It always takes some energy to
+ 
+
+ align:start position:0%
+exchange. It always takes some energy to
+cause the material to change. And what
+
+ align:start position:0%
+cause the material to change. And what
+ 
+
+ align:start position:0%
+cause the material to change. And what
+are you trying to change? You're trying
+
+ align:start position:0%
+are you trying to change? You're trying
+ 
+
+ align:start position:0%
+are you trying to change? You're trying
+to change its
+
+ align:start position:0%
+to change its
+ 
+
+ align:start position:0%
+to change its
+geometry. Usually only its geometry.
+
+ align:start position:0%
+geometry. Usually only its geometry.
+ 
+
+ align:start position:0%
+geometry. Usually only its geometry.
+Often properties change as a result of
+
+ align:start position:0%
+Often properties change as a result of
+ 
+
+ align:start position:0%
+Often properties change as a result of
+that. Or sometimes you're changing
+
+ align:start position:0%
+that. Or sometimes you're changing
+ 
+
+ align:start position:0%
+that. Or sometimes you're changing
+properties like a hardening process or
+
+ align:start position:0%
+properties like a hardening process or
+ 
+
+ align:start position:0%
+properties like a hardening process or
+ion implantation something like that.
+
+ align:start position:0%
+ion implantation something like that.
+ 
+
+ align:start position:0%
+ion implantation something like that.
+You're taking one material and through
+
+ align:start position:0%
+You're taking one material and through
+ 
+
+ align:start position:0%
+You're taking one material and through
+this pl pro process transforming it in
+
+ align:start position:0%
+this pl pro process transforming it in
+ 
+
+ align:start position:0%
+this pl pro process transforming it in
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+way. And um again just just to to remind
+
+ align:start position:0%
+way. And um again just just to to remind
+ 
+
+ align:start position:0%
+way. And um again just just to to remind
+you we have this simple functional
+
+ align:start position:0%
+you we have this simple functional
+ 
+
+ align:start position:0%
+you we have this simple functional
+relationship that says well guess what
+
+ align:start position:0%
+relationship that says well guess what
+ 
+
+ align:start position:0%
+relationship that says well guess what
+the output is a function of all the
+
+ align:start position:0%
+the output is a function of all the
+ 
+
+ align:start position:0%
+the output is a function of all the
+inputs. That's really all it's saying
+
+ align:start position:0%
+inputs. That's really all it's saying
+ 
+
+ align:start position:0%
+inputs. That's really all it's saying
+and and defining it right now saying
+
+ align:start position:0%
+and and defining it right now saying
+ 
+
+ align:start position:0%
+and and defining it right now saying
+that the outputs is some are some vector
+
+ align:start position:0%
+that the outputs is some are some vector
+ 
+
+ align:start position:0%
+that the outputs is some are some vector
+or the outputs can be described as a
+
+ align:start position:0%
+or the outputs can be described as a
+ 
+
+ align:start position:0%
+or the outputs can be described as a
+vector which has all of the relevant
+
+ align:start position:0%
+vector which has all of the relevant
+ 
+
+ align:start position:0%
+vector which has all of the relevant
+geometry and property characteristics of
+
+ align:start position:0%
+geometry and property characteristics of
+ 
+
+ align:start position:0%
+geometry and property characteristics of
+the process. So it would be dimensions,
+
+ align:start position:0%
+the process. So it would be dimensions,
+ 
+
+ align:start position:0%
+the process. So it would be dimensions,
+material properties, things like that.
+
+ align:start position:0%
+material properties, things like that.
+ 
+
+ align:start position:0%
+material properties, things like that.
+um and process parameters using a really
+
+ align:start position:0%
+um and process parameters using a really
+ 
+
+ align:start position:0%
+um and process parameters using a really
+generic word for those input variables
+
+ align:start position:0%
+generic word for those input variables
+ 
+
+ align:start position:0%
+generic word for those input variables
+because I'm going to distinguish between
+
+ align:start position:0%
+because I'm going to distinguish between
+ 
+
+ align:start position:0%
+because I'm going to distinguish between
+inputs and uh parameters a little bit
+
+ align:start position:0%
+inputs and uh parameters a little bit
+ 
+
+ align:start position:0%
+inputs and uh parameters a little bit
+later. Uh and just saying that there's
+
+ align:start position:0%
+later. Uh and just saying that there's
+ 
+
+ align:start position:0%
+later. Uh and just saying that there's
+some functional relationship between the
+
+ align:start position:0%
+some functional relationship between the
+ 
+
+ align:start position:0%
+some functional relationship between the
+two and of course here's the functional
+
+ align:start position:0%
+two and of course here's the functional
+ 
+
+ align:start position:0%
+two and of course here's the functional
+relationship all that all that stuff
+
+ align:start position:0%
+relationship all that all that stuff
+ 
+
+ align:start position:0%
+relationship all that all that stuff
+that's in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there. Okay. So
+
+ align:start position:0%
+there. Okay. So
+ 
+
+ align:start position:0%
+there. Okay. So
+um if if we just focus for a moment on
+
+ align:start position:0%
+um if if we just focus for a moment on
+ 
+
+ align:start position:0%
+um if if we just focus for a moment on
+processes where geometry change is the
+
+ align:start position:0%
+processes where geometry change is the
+ 
+
+ align:start position:0%
+processes where geometry change is the
+most uh important one and and I don't
+
+ align:start position:0%
+most uh important one and and I don't
+ 
+
+ align:start position:0%
+most uh important one and and I don't
+know speaking from my perspective on
+
+ align:start position:0%
+know speaking from my perspective on
+ 
+
+ align:start position:0%
+know speaking from my perspective on
+this class that's going to be 100% of
+
+ align:start position:0%
+this class that's going to be 100% of
+ 
+
+ align:start position:0%
+this class that's going to be 100% of
+what I talk about and I think when we
+
+ align:start position:0%
+what I talk about and I think when we
+ 
+
+ align:start position:0%
+what I talk about and I think when we
+get into semiconductors is a little bit
+
+ align:start position:0%
+get into semiconductors is a little bit
+ 
+
+ align:start position:0%
+get into semiconductors is a little bit
+more on on uh material modification but
+
+ align:start position:0%
+more on on uh material modification but
+ 
+
+ align:start position:0%
+more on on uh material modification but
+I think certainly most of the stuff
+
+ align:start position:0%
+I think certainly most of the stuff
+ 
+
+ align:start position:0%
+I think certainly most of the stuff
+you've seen has been on a manufacturing
+
+ align:start position:0%
+you've seen has been on a manufacturing
+ 
+
+ align:start position:0%
+you've seen has been on a manufacturing
+process meaning we change the geometry
+
+ align:start position:0%
+process meaning we change the geometry
+ 
+
+ align:start position:0%
+process meaning we change the geometry
+um you know what causes the output to
+
+ align:start position:0%
+um you know what causes the output to
+ 
+
+ align:start position:0%
+um you know what causes the output to
+change? Well, there's there's a directed
+
+ align:start position:0%
+change? Well, there's there's a directed
+ 
+
+ align:start position:0%
+change? Well, there's there's a directed
+energy exchange with the equipment.
+
+ align:start position:0%
+energy exchange with the equipment.
+ 
+
+ align:start position:0%
+energy exchange with the equipment.
+Okay. And that energy exchange can take
+
+ align:start position:0%
+Okay. And that energy exchange can take
+ 
+
+ align:start position:0%
+Okay. And that energy exchange can take
+the form of any of of the relevant forms
+
+ align:start position:0%
+the form of any of of the relevant forms
+ 
+
+ align:start position:0%
+the form of any of of the relevant forms
+of energy. So, we could have a
+
+ align:start position:0%
+of energy. So, we could have a
+ 
+
+ align:start position:0%
+of energy. So, we could have a
+mechanical exchange where you impose a
+
+ align:start position:0%
+mechanical exchange where you impose a
+ 
+
+ align:start position:0%
+mechanical exchange where you impose a
+force or a displacement on something. We
+
+ align:start position:0%
+force or a displacement on something. We
+ 
+
+ align:start position:0%
+force or a displacement on something. We
+can have an electrical change where you
+
+ align:start position:0%
+can have an electrical change where you
+ 
+
+ align:start position:0%
+can have an electrical change where you
+run a current through something or or uh
+
+ align:start position:0%
+run a current through something or or uh
+ 
+
+ align:start position:0%
+run a current through something or or uh
+have an electric arc something like
+
+ align:start position:0%
+have an electric arc something like
+ 
+
+ align:start position:0%
+have an electric arc something like
+that. It could be thermal and certainly
+
+ align:start position:0%
+that. It could be thermal and certainly
+ 
+
+ align:start position:0%
+that. It could be thermal and certainly
+there are many of processes where uh
+
+ align:start position:0%
+there are many of processes where uh
+ 
+
+ align:start position:0%
+there are many of processes where uh
+transfer of heat is the is the key way
+
+ align:start position:0%
+transfer of heat is the is the key way
+ 
+
+ align:start position:0%
+transfer of heat is the is the key way
+that you change a geometry and certainly
+
+ align:start position:0%
+that you change a geometry and certainly
+ 
+
+ align:start position:0%
+that you change a geometry and certainly
+it could be chemical. Think of an
+
+ align:start position:0%
+it could be chemical. Think of an
+ 
+
+ align:start position:0%
+it could be chemical. Think of an
+etching process or anything like that.
+
+ align:start position:0%
+etching process or anything like that.
+ 
+
+ align:start position:0%
+etching process or anything like that.
+All of these energies directed the
+
+ align:start position:0%
+All of these energies directed the
+ 
+
+ align:start position:0%
+All of these energies directed the
+correct way
+
+ align:start position:0%
+correct way
+ 
+
+ align:start position:0%
+correct way
+uh can be thought of as um uh geometry
+
+ align:start position:0%
+uh can be thought of as um uh geometry
+ 
+
+ align:start position:0%
+uh can be thought of as um uh geometry
+change mechanisms. Now how do we direct
+
+ align:start position:0%
+change mechanisms. Now how do we direct
+ 
+
+ align:start position:0%
+change mechanisms. Now how do we direct
+this energy?
+
+ align:start position:0%
+this energy?
+ 
+
+ align:start position:0%
+this energy?
+You know, if I if I just say say, you
+
+ align:start position:0%
+You know, if I if I just say say, you
+ 
+
+ align:start position:0%
+You know, if I if I just say say, you
+know, I've got I've got some thermal
+
+ align:start position:0%
+know, I've got I've got some thermal
+ 
+
+ align:start position:0%
+know, I've got I've got some thermal
+energy sitting around. You know, how do
+
+ align:start position:0%
+energy sitting around. You know, how do
+ 
+
+ align:start position:0%
+energy sitting around. You know, how do
+I make sure it goes to the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place? That's the goal. In effect,
+
+ align:start position:0%
+place? That's the goal. In effect,
+ 
+
+ align:start position:0%
+place? That's the goal. In effect,
+that's the goal of the equipment. That's
+
+ align:start position:0%
+that's the goal of the equipment. That's
+ 
+
+ align:start position:0%
+that's the goal of the equipment. That's
+why this one little thing, which which
+
+ align:start position:0%
+why this one little thing, which which
+ 
+
+ align:start position:0%
+why this one little thing, which which
+my thermodynamics friends would go crazy
+
+ align:start position:0%
+my thermodynamics friends would go crazy
+ 
+
+ align:start position:0%
+my thermodynamics friends would go crazy
+with, but but calling energy a vector
+
+ align:start position:0%
+with, but but calling energy a vector
+ 
+
+ align:start position:0%
+with, but but calling energy a vector
+quantity.
+
+ align:start position:0%
+quantity.
+ 
+
+ align:start position:0%
+quantity.
+Um, it matters where you put the energy,
+
+ align:start position:0%
+Um, it matters where you put the energy,
+ 
+
+ align:start position:0%
+Um, it matters where you put the energy,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+If I want to if I want to take this bar
+
+ align:start position:0%
+If I want to if I want to take this bar
+ 
+
+ align:start position:0%
+If I want to if I want to take this bar
+and maybe do something to the center of
+
+ align:start position:0%
+and maybe do something to the center of
+ 
+
+ align:start position:0%
+and maybe do something to the center of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+thermally and I've got a thermal energy
+
+ align:start position:0%
+thermally and I've got a thermal energy
+ 
+
+ align:start position:0%
+thermally and I've got a thermal energy
+source out here called a piece of
+
+ align:start position:0%
+source out here called a piece of
+ 
+
+ align:start position:0%
+source out here called a piece of
+equipment, maybe a torch or something
+
+ align:start position:0%
+equipment, maybe a torch or something
+ 
+
+ align:start position:0%
+equipment, maybe a torch or something
+like that. How do I make sure it goes to
+
+ align:start position:0%
+like that. How do I make sure it goes to
+ 
+
+ align:start position:0%
+like that. How do I make sure it goes to
+the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place? Equipment material.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's this is one of my easy
+
+ align:start position:0%
+It's this is one of my easy
+ 
+
+ align:start position:0%
+It's this is one of my easy
+questions. I I make sure I hold it in
+
+ align:start position:0%
+questions. I I make sure I hold it in
+ 
+
+ align:start position:0%
+questions. I I make sure I hold it in
+place, right? Yeah. Go ahead. Go ahead,
+
+ align:start position:0%
+place, right? Yeah. Go ahead. Go ahead,
+ 
+
+ align:start position:0%
+place, right? Yeah. Go ahead. Go ahead,
+Z. So I I guess by ways of relative
+
+ align:start position:0%
+Z. So I I guess by ways of relative
+ 
+
+ align:start position:0%
+Z. So I I guess by ways of relative
+positioning, these two are in the
+
+ align:start position:0%
+positioning, these two are in the
+ 
+
+ align:start position:0%
+positioning, these two are in the
+correct positions. Yeah. I mean, if if I
+
+ align:start position:0%
+correct positions. Yeah. I mean, if if I
+ 
+
+ align:start position:0%
+correct positions. Yeah. I mean, if if I
+had like a point source, a laser or or
+
+ align:start position:0%
+had like a point source, a laser or or
+ 
+
+ align:start position:0%
+had like a point source, a laser or or
+an arc or something like that. Laser is
+
+ align:start position:0%
+an arc or something like that. Laser is
+ 
+
+ align:start position:0%
+an arc or something like that. Laser is
+a better example. and I needed to do
+
+ align:start position:0%
+a better example. and I needed to do
+ 
+
+ align:start position:0%
+a better example. and I needed to do
+something right here maybe uh uh
+
+ align:start position:0%
+something right here maybe uh uh
+ 
+
+ align:start position:0%
+something right here maybe uh uh
+thermally deform this or or join it or
+
+ align:start position:0%
+thermally deform this or or join it or
+ 
+
+ align:start position:0%
+thermally deform this or or join it or
+something like that then the key would
+
+ align:start position:0%
+something like that then the key would
+ 
+
+ align:start position:0%
+something like that then the key would
+be how both the value of that energy and
+
+ align:start position:0%
+be how both the value of that energy and
+ 
+
+ align:start position:0%
+be how both the value of that energy and
+uh where I put it. So location would be
+
+ align:start position:0%
+uh where I put it. So location would be
+ 
+
+ align:start position:0%
+uh where I put it. So location would be
+would be uh really important. So that's
+
+ align:start position:0%
+would be uh really important. So that's
+ 
+
+ align:start position:0%
+would be uh really important. So that's
+one way of thinking of the concept of a
+
+ align:start position:0%
+one way of thinking of the concept of a
+ 
+
+ align:start position:0%
+one way of thinking of the concept of a
+directed energy source. If I want to
+
+ align:start position:0%
+directed energy source. If I want to
+ 
+
+ align:start position:0%
+directed energy source. If I want to
+bend this piece of sheet metal, which
+
+ align:start position:0%
+bend this piece of sheet metal, which
+ 
+
+ align:start position:0%
+bend this piece of sheet metal, which
+was originally flat, um, you know, and I
+
+ align:start position:0%
+was originally flat, um, you know, and I
+ 
+
+ align:start position:0%
+was originally flat, um, you know, and I
+have a a displacement device, it's
+
+ align:start position:0%
+have a a displacement device, it's
+ 
+
+ align:start position:0%
+have a a displacement device, it's
+probably probably a good idea for me to
+
+ align:start position:0%
+probably probably a good idea for me to
+ 
+
+ align:start position:0%
+probably probably a good idea for me to
+put that displacement device in the
+
+ align:start position:0%
+put that displacement device in the
+ 
+
+ align:start position:0%
+put that displacement device in the
+middle, not over here, and to have that
+
+ align:start position:0%
+middle, not over here, and to have that
+ 
+
+ align:start position:0%
+middle, not over here, and to have that
+displacement device have a certain shape
+
+ align:start position:0%
+displacement device have a certain shape
+ 
+
+ align:start position:0%
+displacement device have a certain shape
+um, to get what I
+
+ align:start position:0%
+um, to get what I
+ 
+
+ align:start position:0%
+um, to get what I
+want. Think about this one for a second.
+
+ align:start position:0%
+want. Think about this one for a second.
+ 
+
+ align:start position:0%
+want. Think about this one for a second.
+This one, I don't know if you can see
+
+ align:start position:0%
+This one, I don't know if you can see
+ 
+
+ align:start position:0%
+This one, I don't know if you can see
+this. Let me try my document camera.
+
+ align:start position:0%
+this. Let me try my document camera.
+ 
+
+ align:start position:0%
+this. Let me try my document camera.
+Come on, doc. There we
+
+ align:start position:0%
+Come on, doc. There we
+ 
+
+ align:start position:0%
+Come on, doc. There we
+go. Um, this is an injection molded
+
+ align:start position:0%
+go. Um, this is an injection molded
+ 
+
+ align:start position:0%
+go. Um, this is an injection molded
+part. It's from a precision
+
+ align:start position:0%
+part. It's from a precision
+ 
+
+ align:start position:0%
+part. It's from a precision
+yo-yo. And,
+
+ align:start position:0%
+yo-yo. And,
+ 
+
+ align:start position:0%
+yo-yo. And,
+uh, how do I make what's the energy
+
+ align:start position:0%
+uh, how do I make what's the energy
+ 
+
+ align:start position:0%
+uh, how do I make what's the energy
+we're talking about
+
+ align:start position:0%
+we're talking about
+ 
+
+ align:start position:0%
+we're talking about
+there? This was injection molded. I
+
+ align:start position:0%
+there? This was injection molded. I
+ 
+
+ align:start position:0%
+there? This was injection molded. I
+think most of you here have had some
+
+ align:start position:0%
+think most of you here have had some
+ 
+
+ align:start position:0%
+think most of you here have had some
+hands-on experience with injection
+
+ align:start position:0%
+hands-on experience with injection
+ 
+
+ align:start position:0%
+hands-on experience with injection
+molding. If you haven't, I'll haven't,
+
+ align:start position:0%
+molding. If you haven't, I'll haven't,
+ 
+
+ align:start position:0%
+molding. If you haven't, I'll haven't,
+I'll explain it in a few minutes. But
+
+ align:start position:0%
+I'll explain it in a few minutes. But
+ 
+
+ align:start position:0%
+I'll explain it in a few minutes. But
+um where's my directed energy source
+
+ align:start position:0%
+um where's my directed energy source
+ 
+
+ align:start position:0%
+um where's my directed energy source
+there? Or if you're having trouble think
+
+ align:start position:0%
+there? Or if you're having trouble think
+ 
+
+ align:start position:0%
+there? Or if you're having trouble think
+getting your head around that, how did I
+
+ align:start position:0%
+getting your head around that, how did I
+ 
+
+ align:start position:0%
+getting your head around that, how did I
+come up with that shape?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Heat and pressure. Well, I had heat and
+
+ align:start position:0%
+Heat and pressure. Well, I had heat and
+ 
+
+ align:start position:0%
+Heat and pressure. Well, I had heat and
+pressure to to put the liquid plastic in
+
+ align:start position:0%
+pressure to to put the liquid plastic in
+ 
+
+ align:start position:0%
+pressure to to put the liquid plastic in
+there.
+
+ align:start position:0%
+there.
+ 
+
+ align:start position:0%
+there.
+Okay. That kind of filled the mold. But
+
+ align:start position:0%
+Okay. That kind of filled the mold. But
+ 
+
+ align:start position:0%
+Okay. That kind of filled the mold. But
+what determined the shape? Yeah, the
+
+ align:start position:0%
+what determined the shape? Yeah, the
+ 
+
+ align:start position:0%
+what determined the shape? Yeah, the
+mold. And what's the directed energy in
+
+ align:start position:0%
+mold. And what's the directed energy in
+ 
+
+ align:start position:0%
+mold. And what's the directed energy in
+this case? If if if I'm saying the
+
+ align:start position:0%
+this case? If if if I'm saying the
+ 
+
+ align:start position:0%
+this case? If if if I'm saying the
+directed energy leads to the shape of
+
+ align:start position:0%
+directed energy leads to the shape of
+ 
+
+ align:start position:0%
+directed energy leads to the shape of
+the part, you know, the geometry
+
+ align:start position:0%
+the part, you know, the geometry
+ 
+
+ align:start position:0%
+the part, you know, the geometry
+changees,
+
+ align:start position:0%
+changees,
+ 
+
+ align:start position:0%
+changees,
+pardon me, the mill cutting forces from
+
+ align:start position:0%
+pardon me, the mill cutting forces from
+ 
+
+ align:start position:0%
+pardon me, the mill cutting forces from
+whatever bit used to cut the metal. Uh
+
+ align:start position:0%
+whatever bit used to cut the metal. Uh
+ 
+
+ align:start position:0%
+whatever bit used to cut the metal. Uh
+we're talking about plastic molding
+
+ align:start position:0%
+we're talking about plastic molding
+ 
+
+ align:start position:0%
+we're talking about plastic molding
+right now, right? But to make the Oh, to
+
+ align:start position:0%
+right now, right? But to make the Oh, to
+ 
+
+ align:start position:0%
+right now, right? But to make the Oh, to
+make the mold. Um yeah, I see where
+
+ align:start position:0%
+make the mold. Um yeah, I see where
+ 
+
+ align:start position:0%
+make the mold. Um yeah, I see where
+you're going with that. But I'm thinking
+
+ align:start position:0%
+you're going with that. But I'm thinking
+ 
+
+ align:start position:0%
+you're going with that. But I'm thinking
+about just the molding process. The
+
+ align:start position:0%
+about just the molding process. The
+ 
+
+ align:start position:0%
+about just the molding process. The
+tooling the tooling somehow was
+
+ align:start position:0%
+tooling the tooling somehow was
+ 
+
+ align:start position:0%
+tooling the tooling somehow was
+magically there. I think that the energy
+
+ align:start position:0%
+magically there. I think that the energy
+ 
+
+ align:start position:0%
+magically there. I think that the energy
+of the surface. So everywhere where we
+
+ align:start position:0%
+of the surface. So everywhere where we
+ 
+
+ align:start position:0%
+of the surface. So everywhere where we
+have surface we direct energy. Exactly.
+
+ align:start position:0%
+have surface we direct energy. Exactly.
+ 
+
+ align:start position:0%
+have surface we direct energy. Exactly.
+So now the the the one big distinction
+
+ align:start position:0%
+So now the the the one big distinction
+ 
+
+ align:start position:0%
+So now the the the one big distinction
+between these two is that here it was
+
+ align:start position:0%
+between these two is that here it was
+ 
+
+ align:start position:0%
+between these two is that here it was
+pretty clear that I had a um a pretty
+
+ align:start position:0%
+pretty clear that I had a um a pretty
+ 
+
+ align:start position:0%
+pretty clear that I had a um a pretty
+localized uh source of
+
+ align:start position:0%
+localized uh source of
+ 
+
+ align:start position:0%
+localized uh source of
+energy. And of course the case of
+
+ align:start position:0%
+energy. And of course the case of
+ 
+
+ align:start position:0%
+energy. And of course the case of
+heating this would be the same or as
+
+ align:start position:0%
+heating this would be the same or as
+ 
+
+ align:start position:0%
+heating this would be the same or as
+you'll see later turning it with a with
+
+ align:start position:0%
+you'll see later turning it with a with
+ 
+
+ align:start position:0%
+you'll see later turning it with a with
+a with a
+
+ align:start position:0%
+a with a
+ 
+
+ align:start position:0%
+a with a
+a point say a pointed tool. um here
+
+ align:start position:0%
+a point say a pointed tool. um here
+ 
+
+ align:start position:0%
+a point say a pointed tool. um here
+everything's happening everywhere at
+
+ align:start position:0%
+everything's happening everywhere at
+ 
+
+ align:start position:0%
+everything's happening everywhere at
+once and the direction the the if you
+
+ align:start position:0%
+once and the direction the the if you
+ 
+
+ align:start position:0%
+once and the direction the the if you
+will the spatial aspect of it is imbued
+
+ align:start position:0%
+will the spatial aspect of it is imbued
+ 
+
+ align:start position:0%
+will the spatial aspect of it is imbued
+not by how I position something but by
+
+ align:start position:0%
+not by how I position something but by
+ 
+
+ align:start position:0%
+not by how I position something but by
+uh the shape of the tool. So you start
+
+ align:start position:0%
+uh the shape of the tool. So you start
+ 
+
+ align:start position:0%
+uh the shape of the tool. So you start
+to see that there kind of two extremes
+
+ align:start position:0%
+to see that there kind of two extremes
+ 
+
+ align:start position:0%
+to see that there kind of two extremes
+here. There's the case where this
+
+ align:start position:0%
+here. There's the case where this
+ 
+
+ align:start position:0%
+here. There's the case where this
+geometry is determined
+
+ align:start position:0%
+geometry is determined
+ 
+
+ align:start position:0%
+geometry is determined
+primarily by a spatial distribution of
+
+ align:start position:0%
+primarily by a spatial distribution of
+ 
+
+ align:start position:0%
+primarily by a spatial distribution of
+energy exchange which is a little bit
+
+ align:start position:0%
+energy exchange which is a little bit
+ 
+
+ align:start position:0%
+energy exchange which is a little bit
+stretching it a little bit here but a
+
+ align:start position:0%
+stretching it a little bit here but a
+ 
+
+ align:start position:0%
+stretching it a little bit here but a
+shaped tool and as Simon said everything
+
+ align:start position:0%
+shaped tool and as Simon said everything
+ 
+
+ align:start position:0%
+shaped tool and as Simon said everything
+happens everywhere at the same time.
+
+ align:start position:0%
+happens everywhere at the same time.
+ 
+
+ align:start position:0%
+happens everywhere at the same time.
+Okay. Whereas in this case things are
+
+ align:start position:0%
+Okay. Whereas in this case things are
+ 
+
+ align:start position:0%
+Okay. Whereas in this case things are
+thing the things are changing over
+
+ align:start position:0%
+thing the things are changing over
+ 
+
+ align:start position:0%
+thing the things are changing over
+time and uh thing quite different things
+
+ align:start position:0%
+time and uh thing quite different things
+ 
+
+ align:start position:0%
+time and uh thing quite different things
+happening at different places and in
+
+ align:start position:0%
+happening at different places and in
+ 
+
+ align:start position:0%
+happening at different places and in
+more extreme case again which I'll get
+
+ align:start position:0%
+more extreme case again which I'll get
+ 
+
+ align:start position:0%
+more extreme case again which I'll get
+to later is if if I'm coming in here
+
+ align:start position:0%
+to later is if if I'm coming in here
+ 
+
+ align:start position:0%
+to later is if if I'm coming in here
+with some sort of a point source let's
+
+ align:start position:0%
+with some sort of a point source let's
+ 
+
+ align:start position:0%
+with some sort of a point source let's
+say heating it or applying a force here
+
+ align:start position:0%
+say heating it or applying a force here
+ 
+
+ align:start position:0%
+say heating it or applying a force here
+there's nothing happening out here it's
+
+ align:start position:0%
+there's nothing happening out here it's
+ 
+
+ align:start position:0%
+there's nothing happening out here it's
+all happening right here and the net
+
+ align:start position:0%
+all happening right here and the net
+ 
+
+ align:start position:0%
+all happening right here and the net
+shape that I get has a lot more to do
+
+ align:start position:0%
+shape that I get has a lot more to do
+ 
+
+ align:start position:0%
+shape that I get has a lot more to do
+with how I move that interaction
+
+ align:start position:0%
+with how I move that interaction
+ 
+
+ align:start position:0%
+with how I move that interaction
+port, otherwise known as a tool, uh,
+
+ align:start position:0%
+port, otherwise known as a tool, uh,
+ 
+
+ align:start position:0%
+port, otherwise known as a tool, uh,
+than it does with the tool shape. Tool
+
+ align:start position:0%
+than it does with the tool shape. Tool
+ 
+
+ align:start position:0%
+than it does with the tool shape. Tool
+shape is important, but it's of
+
+ align:start position:0%
+shape is important, but it's of
+ 
+
+ align:start position:0%
+shape is important, but it's of
+secondary importance.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Okay. They're supposed to go away
+
+ align:start position:0%
+Okay. Okay. They're supposed to go away
+ 
+
+ align:start position:0%
+Okay. Okay. They're supposed to go away
+now. There we go. Okay. Well, they
+
+ align:start position:0%
+now. There we go. Okay. Well, they
+ 
+
+ align:start position:0%
+now. There we go. Okay. Well, they
+didn't go away. It's good to see you
+
+ align:start position:0%
+didn't go away. It's good to see you
+ 
+
+ align:start position:0%
+didn't go away. It's good to see you
+guys. Okay. So, um, now we talk about it
+
+ align:start position:0%
+guys. Okay. So, um, now we talk about it
+ 
+
+ align:start position:0%
+guys. Okay. So, um, now we talk about it
+and we say,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um, it's about geometry change, and I've
+
+ align:start position:0%
+um, it's about geometry change, and I've
+ 
+
+ align:start position:0%
+um, it's about geometry change, and I've
+kind of thrown out some some different
+
+ align:start position:0%
+kind of thrown out some some different
+ 
+
+ align:start position:0%
+kind of thrown out some some different
+ones here. How do you change the shape
+
+ align:start position:0%
+ones here. How do you change the shape
+ 
+
+ align:start position:0%
+ones here. How do you change the shape
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+anything? All right. Well, we already
+
+ align:start position:0%
+anything? All right. Well, we already
+ 
+
+ align:start position:0%
+anything? All right. Well, we already
+talked about one. It's pretty obvious.
+
+ align:start position:0%
+talked about one. It's pretty obvious.
+ 
+
+ align:start position:0%
+talked about one. It's pretty obvious.
+Take out a knife and and a piece of wood
+
+ align:start position:0%
+Take out a knife and and a piece of wood
+ 
+
+ align:start position:0%
+Take out a knife and and a piece of wood
+and you can change its shape by removing
+
+ align:start position:0%
+and you can change its shape by removing
+ 
+
+ align:start position:0%
+and you can change its shape by removing
+wood chips. Okay. Whiddling. That's your
+
+ align:start position:0%
+wood chips. Okay. Whiddling. That's your
+ 
+
+ align:start position:0%
+wood chips. Okay. Whiddling. That's your
+basic basic shaping technique. Well,
+
+ align:start position:0%
+basic basic shaping technique. Well,
+ 
+
+ align:start position:0%
+basic basic shaping technique. Well,
+that's that's essentially uh one of the
+
+ align:start position:0%
+that's that's essentially uh one of the
+ 
+
+ align:start position:0%
+that's that's essentially uh one of the
+most common ways of making anything. You
+
+ align:start position:0%
+most common ways of making anything. You
+ 
+
+ align:start position:0%
+most common ways of making anything. You
+know, we etch away uh silicon. U we
+
+ align:start position:0%
+know, we etch away uh silicon. U we
+ 
+
+ align:start position:0%
+know, we etch away uh silicon. U we
+machine away
+
+ align:start position:0%
+machine away
+ 
+
+ align:start position:0%
+machine away
+material. Um we can uh oxidize and burn
+
+ align:start position:0%
+material. Um we can uh oxidize and burn
+ 
+
+ align:start position:0%
+material. Um we can uh oxidize and burn
+things off. We can uh uh do it in a
+
+ align:start position:0%
+things off. We can uh uh do it in a
+ 
+
+ align:start position:0%
+things off. We can uh uh do it in a
+number of different ways. Okay. So,
+
+ align:start position:0%
+number of different ways. Okay. So,
+ 
+
+ align:start position:0%
+number of different ways. Okay. So,
+removal of material is obviously one way
+
+ align:start position:0%
+removal of material is obviously one way
+ 
+
+ align:start position:0%
+removal of material is obviously one way
+of doing things. Okay. Pretty obvious
+
+ align:start position:0%
+of doing things. Okay. Pretty obvious
+ 
+
+ align:start position:0%
+of doing things. Okay. Pretty obvious
+one. How else can I change the shape of
+
+ align:start position:0%
+one. How else can I change the shape of
+ 
+
+ align:start position:0%
+one. How else can I change the shape of
+something?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+add material. I can add material to it.
+
+ align:start position:0%
+add material. I can add material to it.
+ 
+
+ align:start position:0%
+add material. I can add material to it.
+Yeah, I can or or join or something like
+
+ align:start position:0%
+Yeah, I can or or join or something like
+ 
+
+ align:start position:0%
+Yeah, I can or or join or something like
+that. So, I can and can reform uh
+
+ align:start position:0%
+that. So, I can and can reform uh
+ 
+
+ align:start position:0%
+that. So, I can and can reform uh
+things. Okay. How else?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can deform the material like this.
+
+ align:start position:0%
+I can deform the material like this.
+ 
+
+ align:start position:0%
+I can deform the material like this.
+This started out it's it's a fixed piece
+
+ align:start position:0%
+This started out it's it's a fixed piece
+ 
+
+ align:start position:0%
+This started out it's it's a fixed piece
+of material. I didn't add or subtract
+
+ align:start position:0%
+of material. I didn't add or subtract
+ 
+
+ align:start position:0%
+of material. I didn't add or subtract
+anything to it, but I changed the shape
+
+ align:start position:0%
+anything to it, but I changed the shape
+ 
+
+ align:start position:0%
+anything to it, but I changed the shape
+by bending
+
+ align:start position:0%
+by bending
+ 
+
+ align:start position:0%
+by bending
+it. How else? Let me see what I've got
+
+ align:start position:0%
+it. How else? Let me see what I've got
+ 
+
+ align:start position:0%
+it. How else? Let me see what I've got
+here. Okay. plastic deformation of the
+
+ align:start position:0%
+here. Okay. plastic deformation of the
+ 
+
+ align:start position:0%
+here. Okay. plastic deformation of the
+material. So a constant volume, constant
+
+ align:start position:0%
+material. So a constant volume, constant
+ 
+
+ align:start position:0%
+material. So a constant volume, constant
+mass process. The first case you're
+
+ align:start position:0%
+mass process. The first case you're
+ 
+
+ align:start position:0%
+mass process. The first case you're
+throwing material
+
+ align:start position:0%
+throwing material
+ 
+
+ align:start position:0%
+throwing material
+away, adding material, which I think is
+
+ align:start position:0%
+away, adding material, which I think is
+ 
+
+ align:start position:0%
+away, adding material, which I think is
+what people were already talking about.
+
+ align:start position:0%
+what people were already talking about.
+ 
+
+ align:start position:0%
+what people were already talking about.
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+then so uh one one of my famous
+
+ align:start position:0%
+then so uh one one of my famous
+ 
+
+ align:start position:0%
+then so uh one one of my famous
+professors here at MIT called this
+
+ align:start position:0%
+professors here at MIT called this
+ 
+
+ align:start position:0%
+professors here at MIT called this
+machining and negative machining. So
+
+ align:start position:0%
+machining and negative machining. So
+ 
+
+ align:start position:0%
+machining and negative machining. So
+it's kind of another way of thinking of
+
+ align:start position:0%
+it's kind of another way of thinking of
+ 
+
+ align:start position:0%
+it's kind of another way of thinking of
+it, but adding material, subtracting
+
+ align:start position:0%
+it, but adding material, subtracting
+ 
+
+ align:start position:0%
+it, but adding material, subtracting
+material. the the ultimate manufacturing
+
+ align:start position:0%
+material. the the ultimate manufacturing
+ 
+
+ align:start position:0%
+material. the the ultimate manufacturing
+tool would be one that you know took
+
+ align:start position:0%
+tool would be one that you know took
+ 
+
+ align:start position:0%
+tool would be one that you know took
+from here and gave to there and that
+
+ align:start position:0%
+from here and gave to there and that
+ 
+
+ align:start position:0%
+from here and gave to there and that
+sort of thing. Um what else? There's one
+
+ align:start position:0%
+sort of thing. Um what else? There's one
+ 
+
+ align:start position:0%
+sort of thing. Um what else? There's one
+other where does this where does this
+
+ align:start position:0%
+other where does this where does this
+ 
+
+ align:start position:0%
+other where does this where does this
+fit in? It doesn't fit any of those.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, you guys took 2810, right? So you
+
+ align:start position:0%
+Yeah, you guys took 2810, right? So you
+ 
+
+ align:start position:0%
+Yeah, you guys took 2810, right? So you
+probably already covered this, but yes,
+
+ align:start position:0%
+probably already covered this, but yes,
+ 
+
+ align:start position:0%
+probably already covered this, but yes,
+formation of material. So uh where you
+
+ align:start position:0%
+formation of material. So uh where you
+ 
+
+ align:start position:0%
+formation of material. So uh where you
+uh go from uh a liquid or vapor state,
+
+ align:start position:0%
+uh go from uh a liquid or vapor state,
+ 
+
+ align:start position:0%
+uh go from uh a liquid or vapor state,
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+solidifies against some energy exchange
+
+ align:start position:0%
+solidifies against some energy exchange
+ 
+
+ align:start position:0%
+solidifies against some energy exchange
+medium or form tool and you come up with
+
+ align:start position:0%
+medium or form tool and you come up with
+ 
+
+ align:start position:0%
+medium or form tool and you come up with
+that shape. Okay. What else? That's only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four. This is every manufacturing
+
+ align:start position:0%
+four. This is every manufacturing
+ 
+
+ align:start position:0%
+four. This is every manufacturing
+process in the world in the universe.
+
+ align:start position:0%
+process in the world in the universe.
+ 
+
+ align:start position:0%
+process in the world in the universe.
+Well, it's kind of under addition, but
+
+ align:start position:0%
+Well, it's kind of under addition, but
+ 
+
+ align:start position:0%
+Well, it's kind of under addition, but
+actually growing material
+
+ align:start position:0%
+actually growing material
+ 
+
+ align:start position:0%
+actually growing material
+biological process like a silicon
+
+ align:start position:0%
+biological process like a silicon
+ 
+
+ align:start position:0%
+biological process like a silicon
+crystal. Okay, good. We'll call that
+
+ align:start position:0%
+crystal. Okay, good. We'll call that
+ 
+
+ align:start position:0%
+crystal. Okay, good. We'll call that
+addition.
+
+ align:start position:0%
+addition.
+ 
+
+ align:start position:0%
+addition.
+It ruins my punch line if we
+
+ align:start position:0%
+It ruins my punch line if we
+ 
+
+ align:start position:0%
+It ruins my punch line if we
+don't. Any others?
+
+ align:start position:0%
+don't. Any others?
+ 
+
+ align:start position:0%
+don't. Any others?
+Well, I mean the the the point is that
+
+ align:start position:0%
+Well, I mean the the the point is that
+ 
+
+ align:start position:0%
+Well, I mean the the the point is that
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um again it's it is a matter of
+
+ align:start position:0%
+um again it's it is a matter of
+ 
+
+ align:start position:0%
+um again it's it is a matter of
+definitions and you could cut this more
+
+ align:start position:0%
+definitions and you could cut this more
+ 
+
+ align:start position:0%
+definitions and you could cut this more
+finely, but this pretty nicely
+
+ align:start position:0%
+finely, but this pretty nicely
+ 
+
+ align:start position:0%
+finely, but this pretty nicely
+characterizes every manufacturing
+
+ align:start position:0%
+characterizes every manufacturing
+ 
+
+ align:start position:0%
+characterizes every manufacturing
+process with respect to geometry change.
+
+ align:start position:0%
+process with respect to geometry change.
+ 
+
+ align:start position:0%
+process with respect to geometry change.
+We could have a parallel set for uh
+
+ align:start position:0%
+We could have a parallel set for uh
+ 
+
+ align:start position:0%
+We could have a parallel set for uh
+property changes, thermodynamic changes
+
+ align:start position:0%
+property changes, thermodynamic changes
+ 
+
+ align:start position:0%
+property changes, thermodynamic changes
+and you know implantation changes,
+
+ align:start position:0%
+and you know implantation changes,
+ 
+
+ align:start position:0%
+and you know implantation changes,
+atomic changes, so forth and so on. But
+
+ align:start position:0%
+atomic changes, so forth and so on. But
+ 
+
+ align:start position:0%
+atomic changes, so forth and so on. But
+uh for this it seems to cover pretty
+
+ align:start position:0%
+uh for this it seems to cover pretty
+ 
+
+ align:start position:0%
+uh for this it seems to cover pretty
+much everything. So if you look at a
+
+ align:start position:0%
+much everything. So if you look at a
+ 
+
+ align:start position:0%
+much everything. So if you look at a
+manufacturing process or you look at
+
+ align:start position:0%
+manufacturing process or you look at
+ 
+
+ align:start position:0%
+manufacturing process or you look at
+something going on in a factory and say
+
+ align:start position:0%
+something going on in a factory and say
+ 
+
+ align:start position:0%
+something going on in a factory and say
+is this a manufacturing process one of
+
+ align:start position:0%
+is this a manufacturing process one of
+ 
+
+ align:start position:0%
+is this a manufacturing process one of
+these things should be going on if it's
+
+ align:start position:0%
+these things should be going on if it's
+ 
+
+ align:start position:0%
+these things should be going on if it's
+a geometry change uh
+
+ align:start position:0%
+a geometry change uh
+ 
+
+ align:start position:0%
+a geometry change uh
+process. So um what controls the
+
+ align:start position:0%
+process. So um what controls the
+ 
+
+ align:start position:0%
+process. So um what controls the
+geometry change as you said lo the the
+
+ align:start position:0%
+geometry change as you said lo the the
+ 
+
+ align:start position:0%
+geometry change as you said lo the the
+local location and intensity of the
+
+ align:start position:0%
+local location and intensity of the
+ 
+
+ align:start position:0%
+local location and intensity of the
+energy exchange. So we already talked
+
+ align:start position:0%
+energy exchange. So we already talked
+ 
+
+ align:start position:0%
+energy exchange. So we already talked
+about this for turning and here's just a
+
+ align:start position:0%
+about this for turning and here's just a
+ 
+
+ align:start position:0%
+about this for turning and here's just a
+schematic of a simple turning. Uh this
+
+ align:start position:0%
+schematic of a simple turning. Uh this
+ 
+
+ align:start position:0%
+schematic of a simple turning. Uh this
+is actually the experiment we used to do
+
+ align:start position:0%
+is actually the experiment we used to do
+ 
+
+ align:start position:0%
+is actually the experiment we used to do
+where you just or you guys actually did
+
+ align:start position:0%
+where you just or you guys actually did
+ 
+
+ align:start position:0%
+where you just or you guys actually did
+it again where you just come in
+
+ align:start position:0%
+it again where you just come in
+ 
+
+ align:start position:0%
+it again where you just come in
+so-called orthogonal turning and you
+
+ align:start position:0%
+so-called orthogonal turning and you
+ 
+
+ align:start position:0%
+so-called orthogonal turning and you
+come in and reduce the diameter of this
+
+ align:start position:0%
+come in and reduce the diameter of this
+ 
+
+ align:start position:0%
+come in and reduce the diameter of this
+stock. Um and you know more formally we
+
+ align:start position:0%
+stock. Um and you know more formally we
+ 
+
+ align:start position:0%
+stock. Um and you know more formally we
+would say this is the location of the
+
+ align:start position:0%
+would say this is the location of the
+ 
+
+ align:start position:0%
+would say this is the location of the
+maximum shear stress. You you take bring
+
+ align:start position:0%
+maximum shear stress. You you take bring
+ 
+
+ align:start position:0%
+maximum shear stress. You you take bring
+in a tool and the the material is
+
+ align:start position:0%
+in a tool and the the material is
+ 
+
+ align:start position:0%
+in a tool and the the material is
+spinning in this case and there's
+
+ align:start position:0%
+spinning in this case and there's
+ 
+
+ align:start position:0%
+spinning in this case and there's
+essentially no stresses on it. Then you
+
+ align:start position:0%
+essentially no stresses on it. Then you
+ 
+
+ align:start position:0%
+essentially no stresses on it. Then you
+come in with a tool and start applying a
+
+ align:start position:0%
+come in with a tool and start applying a
+ 
+
+ align:start position:0%
+come in with a tool and start applying a
+significant force over a very limited
+
+ align:start position:0%
+significant force over a very limited
+ 
+
+ align:start position:0%
+significant force over a very limited
+area in such a way as to create a
+
+ align:start position:0%
+area in such a way as to create a
+ 
+
+ align:start position:0%
+area in such a way as to create a
+critical shear stress and the material
+
+ align:start position:0%
+critical shear stress and the material
+ 
+
+ align:start position:0%
+critical shear stress and the material
+decides to uh
+
+ align:start position:0%
+decides to uh
+ 
+
+ align:start position:0%
+decides to uh
+leave. Okay. And where you so in an
+
+ align:start position:0%
+leave. Okay. And where you so in an
+ 
+
+ align:start position:0%
+leave. Okay. And where you so in an
+abstract sense I can think of machining
+
+ align:start position:0%
+abstract sense I can think of machining
+ 
+
+ align:start position:0%
+abstract sense I can think of machining
+as locating a maximum a very
+
+ align:start position:0%
+as locating a maximum a very
+ 
+
+ align:start position:0%
+as locating a maximum a very
+concentrated maximal shear stress point
+
+ align:start position:0%
+concentrated maximal shear stress point
+ 
+
+ align:start position:0%
+concentrated maximal shear stress point
+at different places in such a way as to
+
+ align:start position:0%
+at different places in such a way as to
+ 
+
+ align:start position:0%
+at different places in such a way as to
+as to at that location make the material
+
+ align:start position:0%
+as to at that location make the material
+ 
+
+ align:start position:0%
+as to at that location make the material
+disassociate with it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Yeah. So, we already talked about
+
+ align:start position:0%
+Okay. Yeah. So, we already talked about
+ 
+
+ align:start position:0%
+Okay. Yeah. So, we already talked about
+this one. Heat transfer at the mold
+
+ align:start position:0%
+this one. Heat transfer at the mold
+ 
+
+ align:start position:0%
+this one. Heat transfer at the mold
+surface and injection molding.
+
+ align:start position:0%
+surface and injection molding.
+ 
+
+ align:start position:0%
+surface and injection molding.
+Um, yeah. This is this is Oops. So, uh,
+
+ align:start position:0%
+Um, yeah. This is this is Oops. So, uh,
+ 
+
+ align:start position:0%
+Um, yeah. This is this is Oops. So, uh,
+another extreme of of um interaction to
+
+ align:start position:0%
+another extreme of of um interaction to
+ 
+
+ align:start position:0%
+another extreme of of um interaction to
+give you an idea that there's more than
+
+ align:start position:0%
+give you an idea that there's more than
+ 
+
+ align:start position:0%
+give you an idea that there's more than
+one way to remove material. And
+
+ align:start position:0%
+one way to remove material. And
+ 
+
+ align:start position:0%
+one way to remove material. And
+everybody, certainly anybody with a
+
+ align:start position:0%
+everybody, certainly anybody with a
+ 
+
+ align:start position:0%
+everybody, certainly anybody with a
+mechanical engineering education, any
+
+ align:start position:0%
+mechanical engineering education, any
+ 
+
+ align:start position:0%
+mechanical engineering education, any
+sort of shop or manufacturing experience
+
+ align:start position:0%
+sort of shop or manufacturing experience
+ 
+
+ align:start position:0%
+sort of shop or manufacturing experience
+says, "Oh, yeah, machining." That's it.
+
+ align:start position:0%
+says, "Oh, yeah, machining." That's it.
+ 
+
+ align:start position:0%
+says, "Oh, yeah, machining." That's it.
+And that's how you remove material. But
+
+ align:start position:0%
+And that's how you remove material. But
+ 
+
+ align:start position:0%
+And that's how you remove material. But
+of course, uh, we remove material in a
+
+ align:start position:0%
+of course, uh, we remove material in a
+ 
+
+ align:start position:0%
+of course, uh, we remove material in a
+lot of different ways. And of course,
+
+ align:start position:0%
+lot of different ways. And of course,
+ 
+
+ align:start position:0%
+lot of different ways. And of course,
+anybody from a doubly or semiconductor
+
+ align:start position:0%
+anybody from a doubly or semiconductor
+ 
+
+ align:start position:0%
+anybody from a doubly or semiconductor
+background says, "Oh yeah, removal,
+
+ align:start position:0%
+background says, "Oh yeah, removal,
+ 
+
+ align:start position:0%
+background says, "Oh yeah, removal,
+that's chemical etching or something
+
+ align:start position:0%
+that's chemical etching or something
+ 
+
+ align:start position:0%
+that's chemical etching or something
+like that." Um, and that's true also.
+
+ align:start position:0%
+like that." Um, and that's true also.
+ 
+
+ align:start position:0%
+like that." Um, and that's true also.
+But, uh, then you have many things these
+
+ align:start position:0%
+But, uh, then you have many things these
+ 
+
+ align:start position:0%
+But, uh, then you have many things these
+beam type processes which are, uh, very
+
+ align:start position:0%
+beam type processes which are, uh, very
+ 
+
+ align:start position:0%
+beam type processes which are, uh, very
+important for a lot of different
+
+ align:start position:0%
+important for a lot of different
+ 
+
+ align:start position:0%
+important for a lot of different
+processes. But you know, think of the
+
+ align:start position:0%
+processes. But you know, think of the
+ 
+
+ align:start position:0%
+processes. But you know, think of the
+the extreme case of a process where
+
+ align:start position:0%
+the extreme case of a process where
+ 
+
+ align:start position:0%
+the extreme case of a process where
+things are very localized and you're
+
+ align:start position:0%
+things are very localized and you're
+ 
+
+ align:start position:0%
+things are very localized and you're
+just doing some something
+
+ align:start position:0%
+just doing some something
+ 
+
+ align:start position:0%
+just doing some something
+uh in a very small region and then you
+
+ align:start position:0%
+uh in a very small region and then you
+ 
+
+ align:start position:0%
+uh in a very small region and then you
+move that region around. The part might
+
+ align:start position:0%
+move that region around. The part might
+ 
+
+ align:start position:0%
+move that region around. The part might
+be something like laser uh processing
+
+ align:start position:0%
+be something like laser uh processing
+ 
+
+ align:start position:0%
+be something like laser uh processing
+laser beams using a laser beam to cut
+
+ align:start position:0%
+laser beams using a laser beam to cut
+ 
+
+ align:start position:0%
+laser beams using a laser beam to cut
+and moving it. This this is uh meant to
+
+ align:start position:0%
+and moving it. This this is uh meant to
+ 
+
+ align:start position:0%
+and moving it. This this is uh meant to
+be a a picture of a robot moving it
+
+ align:start position:0%
+be a a picture of a robot moving it
+ 
+
+ align:start position:0%
+be a a picture of a robot moving it
+around. So the robot is very important
+
+ align:start position:0%
+around. So the robot is very important
+ 
+
+ align:start position:0%
+around. So the robot is very important
+in this case because it's providing the
+
+ align:start position:0%
+in this case because it's providing the
+ 
+
+ align:start position:0%
+in this case because it's providing the
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+um and moving the uh the laser tool. And
+
+ align:start position:0%
+um and moving the uh the laser tool. And
+ 
+
+ align:start position:0%
+um and moving the uh the laser tool. And
+of course this has been taken to extreme
+
+ align:start position:0%
+of course this has been taken to extreme
+ 
+
+ align:start position:0%
+of course this has been taken to extreme
+with um these phentoc lasers which can
+
+ align:start position:0%
+with um these phentoc lasers which can
+ 
+
+ align:start position:0%
+with um these phentoc lasers which can
+affect uh at at any given instant will
+
+ align:start position:0%
+affect uh at at any given instant will
+ 
+
+ align:start position:0%
+affect uh at at any given instant will
+only ablate material in I don't know
+
+ align:start position:0%
+only ablate material in I don't know
+ 
+
+ align:start position:0%
+only ablate material in I don't know
+what submicron areas. So you can you can
+
+ align:start position:0%
+what submicron areas. So you can you can
+ 
+
+ align:start position:0%
+what submicron areas. So you can you can
+really localize it if you want
+
+ align:start position:0%
+really localize it if you want
+ 
+
+ align:start position:0%
+really localize it if you want
+to. And then um you know you've got
+
+ align:start position:0%
+to. And then um you know you've got
+ 
+
+ align:start position:0%
+to. And then um you know you've got
+you've got other things like this like a
+
+ align:start position:0%
+you've got other things like this like a
+ 
+
+ align:start position:0%
+you've got other things like this like a
+CVD process where what you're actually
+
+ align:start position:0%
+CVD process where what you're actually
+ 
+
+ align:start position:0%
+CVD process where what you're actually
+doing is locating uh a chemical reaction
+
+ align:start position:0%
+doing is locating uh a chemical reaction
+ 
+
+ align:start position:0%
+doing is locating uh a chemical reaction
+across the entire surface of something.
+
+ align:start position:0%
+across the entire surface of something.
+ 
+
+ align:start position:0%
+across the entire surface of something.
+And again that's that's that location is
+
+ align:start position:0%
+And again that's that's that location is
+ 
+
+ align:start position:0%
+And again that's that's that location is
+determined primarily by what whatever
+
+ align:start position:0%
+determined primarily by what whatever
+ 
+
+ align:start position:0%
+determined primarily by what whatever
+substrate it is you're trying to coat.
+
+ align:start position:0%
+substrate it is you're trying to coat.
+ 
+
+ align:start position:0%
+substrate it is you're trying to coat.
+In this case we're trying trying to
+
+ align:start position:0%
+In this case we're trying trying to
+ 
+
+ align:start position:0%
+In this case we're trying trying to
+coat.
+
+ align:start position:0%
+coat.
+ 
+
+ align:start position:0%
+coat.
+Um, but just to throw this out, if I
+
+ align:start position:0%
+Um, but just to throw this out, if I
+ 
+
+ align:start position:0%
+Um, but just to throw this out, if I
+have, you know, a nice clean uniform
+
+ align:start position:0%
+have, you know, a nice clean uniform
+ 
+
+ align:start position:0%
+have, you know, a nice clean uniform
+substrate, even with, well, let's just
+
+ align:start position:0%
+substrate, even with, well, let's just
+ 
+
+ align:start position:0%
+substrate, even with, well, let's just
+take a flat one, just a flat disc, and I
+
+ align:start position:0%
+take a flat one, just a flat disc, and I
+ 
+
+ align:start position:0%
+take a flat one, just a flat disc, and I
+need to coat it with a chemical vapor
+
+ align:start position:0%
+need to coat it with a chemical vapor
+ 
+
+ align:start position:0%
+need to coat it with a chemical vapor
+deposition process. So, I've got this
+
+ align:start position:0%
+deposition process. So, I've got this
+ 
+
+ align:start position:0%
+deposition process. So, I've got this
+vapor, and it's going to deposit and um,
+
+ align:start position:0%
+vapor, and it's going to deposit and um,
+ 
+
+ align:start position:0%
+vapor, and it's going to deposit and um,
+solidify on the surface. Um, what's
+
+ align:start position:0%
+solidify on the surface. Um, what's
+ 
+
+ align:start position:0%
+solidify on the surface. Um, what's
+going to determine the final geometry of
+
+ align:start position:0%
+going to determine the final geometry of
+ 
+
+ align:start position:0%
+going to determine the final geometry of
+that surface, of that coating of the
+
+ align:start position:0%
+that surface, of that coating of the
+ 
+
+ align:start position:0%
+that surface, of that coating of the
+surface?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, let's Yeah. Well, let's let's
+
+ align:start position:0%
+Well, let's Yeah. Well, let's let's
+ 
+
+ align:start position:0%
+Well, let's Yeah. Well, let's let's
+assume this is just sort of this
+
+ align:start position:0%
+assume this is just sort of this
+ 
+
+ align:start position:0%
+assume this is just sort of this
+chamber filled with with vapor and then
+
+ align:start position:0%
+chamber filled with with vapor and then
+ 
+
+ align:start position:0%
+chamber filled with with vapor and then
+you introduce this in there.
+
+ align:start position:0%
+you introduce this in there.
+ 
+
+ align:start position:0%
+you introduce this in there.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Time certainly is a big big part of it.
+
+ align:start position:0%
+Time certainly is a big big part of it.
+ 
+
+ align:start position:0%
+Time certainly is a big big part of it.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+topology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the topology of the of the of the
+
+ align:start position:0%
+the topology of the of the of the
+ 
+
+ align:start position:0%
+the topology of the of the of the
+substrate and and I'll just throw in the
+
+ align:start position:0%
+substrate and and I'll just throw in the
+ 
+
+ align:start position:0%
+substrate and and I'll just throw in the
+other is that and because I I want to
+
+ align:start position:0%
+other is that and because I I want to
+ 
+
+ align:start position:0%
+other is that and because I I want to
+make the point that with any of these
+
+ align:start position:0%
+make the point that with any of these
+ 
+
+ align:start position:0%
+make the point that with any of these
+these processes that
+
+ align:start position:0%
+these processes that
+ 
+
+ align:start position:0%
+these processes that
+occur with a distribution sort of
+
+ align:start position:0%
+occur with a distribution sort of
+ 
+
+ align:start position:0%
+occur with a distribution sort of
+simultaneously the ones that Simon was
+
+ align:start position:0%
+simultaneously the ones that Simon was
+ 
+
+ align:start position:0%
+simultaneously the ones that Simon was
+talking about earlier
+
+ align:start position:0%
+talking about earlier
+ 
+
+ align:start position:0%
+talking about earlier
+um there there's always this uh concern
+
+ align:start position:0%
+um there there's always this uh concern
+ 
+
+ align:start position:0%
+um there there's always this uh concern
+that you don't have uniform spatial
+
+ align:start position:0%
+that you don't have uniform spatial
+ 
+
+ align:start position:0%
+that you don't have uniform spatial
+distribution so what I was getting at is
+
+ align:start position:0%
+distribution so what I was getting at is
+ 
+
+ align:start position:0%
+distribution so what I was getting at is
+there was no intention of having
+
+ align:start position:0%
+there was no intention of having
+ 
+
+ align:start position:0%
+there was no intention of having
+directed vapor um density or anything
+
+ align:start position:0%
+directed vapor um density or anything
+ 
+
+ align:start position:0%
+directed vapor um density or anything
+like that. The idea is I've got this
+
+ align:start position:0%
+like that. The idea is I've got this
+ 
+
+ align:start position:0%
+like that. The idea is I've got this
+uniform cloud of uh
+
+ align:start position:0%
+uniform cloud of uh
+ 
+
+ align:start position:0%
+uniform cloud of uh
+vapor and it's reacting with the
+
+ align:start position:0%
+vapor and it's reacting with the
+ 
+
+ align:start position:0%
+vapor and it's reacting with the
+surface. So why might it
+
+ align:start position:0%
+surface. So why might it
+ 
+
+ align:start position:0%
+surface. So why might it
+vary spatially? Not it's certainly going
+
+ align:start position:0%
+vary spatially? Not it's certainly going
+ 
+
+ align:start position:0%
+vary spatially? Not it's certainly going
+to vary over time because it takes time
+
+ align:start position:0%
+to vary over time because it takes time
+ 
+
+ align:start position:0%
+to vary over time because it takes time
+for this stuff to solidify. But it's
+
+ align:start position:0%
+for this stuff to solidify. But it's
+ 
+
+ align:start position:0%
+for this stuff to solidify. But it's
+also going to vary spatially because who
+
+ align:start position:0%
+also going to vary spatially because who
+ 
+
+ align:start position:0%
+also going to vary spatially because who
+said it's uniform? Okay. And one of the
+
+ align:start position:0%
+said it's uniform? Okay. And one of the
+ 
+
+ align:start position:0%
+said it's uniform? Okay. And one of the
+things you want to think about when
+
+ align:start position:0%
+things you want to think about when
+ 
+
+ align:start position:0%
+things you want to think about when
+we're talking about manufacturing is
+
+ align:start position:0%
+we're talking about manufacturing is
+ 
+
+ align:start position:0%
+we're talking about manufacturing is
+always sort of question any any
+
+ align:start position:0%
+always sort of question any any
+ 
+
+ align:start position:0%
+always sort of question any any
+statement of uh uh uniformity or
+
+ align:start position:0%
+statement of uh uh uniformity or
+ 
+
+ align:start position:0%
+statement of uh uh uniformity or
+constancy or things like that because um
+
+ align:start position:0%
+constancy or things like that because um
+ 
+
+ align:start position:0%
+constancy or things like that because um
+uh in inevitably there will be
+
+ align:start position:0%
+uh in inevitably there will be
+ 
+
+ align:start position:0%
+uh in inevitably there will be
+variations because the the topography of
+
+ align:start position:0%
+variations because the the topography of
+ 
+
+ align:start position:0%
+variations because the the topography of
+the of the uh substrate might change. uh
+
+ align:start position:0%
+the of the uh substrate might change. uh
+ 
+
+ align:start position:0%
+the of the uh substrate might change. uh
+who knows and in fact it does happen
+
+ align:start position:0%
+who knows and in fact it does happen
+ 
+
+ align:start position:0%
+who knows and in fact it does happen
+especi especially as you go to larger
+
+ align:start position:0%
+especi especially as you go to larger
+ 
+
+ align:start position:0%
+especi especially as you go to larger
+and larger wafers you get important
+
+ align:start position:0%
+and larger wafers you get important
+ 
+
+ align:start position:0%
+and larger wafers you get important
+variations in the chamber temperature
+
+ align:start position:0%
+variations in the chamber temperature
+ 
+
+ align:start position:0%
+variations in the chamber temperature
+variations you could get concentration
+
+ align:start position:0%
+variations you could get concentration
+ 
+
+ align:start position:0%
+variations you could get concentration
+variations all these kinds of things can
+
+ align:start position:0%
+variations all these kinds of things can
+ 
+
+ align:start position:0%
+variations all these kinds of things can
+uh cause
+
+ align:start position:0%
+uh cause
+ 
+
+ align:start position:0%
+uh cause
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+um one other that I'll mention because I
+
+ align:start position:0%
+um one other that I'll mention because I
+ 
+
+ align:start position:0%
+um one other that I'll mention because I
+I showed this this piece of sheet metal
+
+ align:start position:0%
+I showed this this piece of sheet metal
+ 
+
+ align:start position:0%
+I showed this this piece of sheet metal
+and talked about it as a concentrated
+
+ align:start position:0%
+and talked about it as a concentrated
+ 
+
+ align:start position:0%
+and talked about it as a concentrated
+u energy exchange here's another example
+
+ align:start position:0%
+u energy exchange here's another example
+ 
+
+ align:start position:0%
+u energy exchange here's another example
+of a non-conentrated energy exchange
+
+ align:start position:0%
+of a non-conentrated energy exchange
+ 
+
+ align:start position:0%
+of a non-conentrated energy exchange
+This is a large piece of sheet metal.
+
+ align:start position:0%
+This is a large piece of sheet metal.
+ 
+
+ align:start position:0%
+This is a large piece of sheet metal.
+This dimension here is about 6 feet uh
+
+ align:start position:0%
+This dimension here is about 6 feet uh
+ 
+
+ align:start position:0%
+This dimension here is about 6 feet uh
+aerospace manufacturing and uh it's
+
+ align:start position:0%
+aerospace manufacturing and uh it's
+ 
+
+ align:start position:0%
+aerospace manufacturing and uh it's
+being pulled across this tool and
+
+ align:start position:0%
+being pulled across this tool and
+ 
+
+ align:start position:0%
+being pulled across this tool and
+deformed into here. I actually have a a
+
+ align:start position:0%
+deformed into here. I actually have a a
+ 
+
+ align:start position:0%
+deformed into here. I actually have a a
+sort of video of this which I couldn't
+
+ align:start position:0%
+sort of video of this which I couldn't
+ 
+
+ align:start position:0%
+sort of video of this which I couldn't
+find but you can see it being pulled
+
+ align:start position:0%
+find but you can see it being pulled
+ 
+
+ align:start position:0%
+find but you can see it being pulled
+down to the tool and because of the
+
+ align:start position:0%
+down to the tool and because of the
+ 
+
+ align:start position:0%
+down to the tool and because of the
+reflections of the light you can see
+
+ align:start position:0%
+reflections of the light you can see
+ 
+
+ align:start position:0%
+reflections of the light you can see
+that there's not a single portion of
+
+ align:start position:0%
+that there's not a single portion of
+ 
+
+ align:start position:0%
+that there's not a single portion of
+this p piece large piece of metal that
+
+ align:start position:0%
+this p piece large piece of metal that
+ 
+
+ align:start position:0%
+this p piece large piece of metal that
+isn't being changed at any instant in
+
+ align:start position:0%
+isn't being changed at any instant in
+ 
+
+ align:start position:0%
+isn't being changed at any instant in
+time. So clearly this is this is
+
+ align:start position:0%
+time. So clearly this is this is
+ 
+
+ align:start position:0%
+time. So clearly this is this is
+everything happening everywhere all at
+
+ align:start position:0%
+everything happening everywhere all at
+ 
+
+ align:start position:0%
+everything happening everywhere all at
+once. Uh and we're in effect we're
+
+ align:start position:0%
+once. Uh and we're in effect we're
+ 
+
+ align:start position:0%
+once. Uh and we're in effect we're
+pulling it across a a shaped tool. So in
+
+ align:start position:0%
+pulling it across a a shaped tool. So in
+ 
+
+ align:start position:0%
+pulling it across a a shaped tool. So in
+the end we're we're imposing this
+
+ align:start position:0%
+the end we're we're imposing this
+ 
+
+ align:start position:0%
+the end we're we're imposing this
+displacement field on
+
+ align:start position:0%
+displacement field on
+ 
+
+ align:start position:0%
+displacement field on
+it. Okay. So this gets us to this
+
+ align:start position:0%
+it. Okay. So this gets us to this
+ 
+
+ align:start position:0%
+it. Okay. So this gets us to this
+concept of the
+
+ align:start position:0%
+concept of the
+ 
+
+ align:start position:0%
+concept of the
+taxonomy. You can see that that you know
+
+ align:start position:0%
+taxonomy. You can see that that you know
+ 
+
+ align:start position:0%
+taxonomy. You can see that that you know
+been kind of ranging widely over a
+
+ align:start position:0%
+been kind of ranging widely over a
+ 
+
+ align:start position:0%
+been kind of ranging widely over a
+number of different processes either uh
+
+ align:start position:0%
+number of different processes either uh
+ 
+
+ align:start position:0%
+number of different processes either uh
+directly or by implication.
+
+ align:start position:0%
+directly or by implication.
+ 
+
+ align:start position:0%
+directly or by implication.
+uh and we want to kind of draw some
+
+ align:start position:0%
+uh and we want to kind of draw some
+ 
+
+ align:start position:0%
+uh and we want to kind of draw some
+conclusions from this. So the first is
+
+ align:start position:0%
+conclusions from this. So the first is
+ 
+
+ align:start position:0%
+conclusions from this. So the first is
+that there are two extremes to these
+
+ align:start position:0%
+that there are two extremes to these
+ 
+
+ align:start position:0%
+that there are two extremes to these
+interactions.
+
+ align:start position:0%
+interactions.
+ 
+
+ align:start position:0%
+interactions.
+the so-called serial interaction and you
+
+ align:start position:0%
+the so-called serial interaction and you
+ 
+
+ align:start position:0%
+the so-called serial interaction and you
+know schematically here it's best
+
+ align:start position:0%
+know schematically here it's best
+ 
+
+ align:start position:0%
+know schematically here it's best
+described as you know my phentoc
+
+ align:start position:0%
+described as you know my phentoc
+ 
+
+ align:start position:0%
+described as you know my phentoc
+laser a infantessimally small area of
+
+ align:start position:0%
+laser a infantessimally small area of
+ 
+
+ align:start position:0%
+laser a infantessimally small area of
+interaction over the over the large area
+
+ align:start position:0%
+interaction over the over the large area
+ 
+
+ align:start position:0%
+interaction over the over the large area
+so that at any instant I'm only
+
+ align:start position:0%
+so that at any instant I'm only
+ 
+
+ align:start position:0%
+so that at any instant I'm only
+affecting a small part of the material
+
+ align:start position:0%
+affecting a small part of the material
+ 
+
+ align:start position:0%
+affecting a small part of the material
+but then I I move it I have a time
+
+ align:start position:0%
+but then I I move it I have a time
+ 
+
+ align:start position:0%
+but then I I move it I have a time
+history of this and that's what
+
+ align:start position:0%
+history of this and that's what
+ 
+
+ align:start position:0%
+history of this and that's what
+determines the geometry now of course in
+
+ align:start position:0%
+determines the geometry now of course in
+ 
+
+ align:start position:0%
+determines the geometry now of course in
+a real process even with the phentoc
+
+ align:start position:0%
+a real process even with the phentoc
+ 
+
+ align:start position:0%
+a real process even with the phentoc
+laser if get to small enough um there
+
+ align:start position:0%
+laser if get to small enough um there
+ 
+
+ align:start position:0%
+laser if get to small enough um there
+are spatially distributed effects and as
+
+ align:start position:0%
+are spatially distributed effects and as
+ 
+
+ align:start position:0%
+are spatially distributed effects and as
+I go to larger and larger tools uh this
+
+ align:start position:0%
+I go to larger and larger tools uh this
+ 
+
+ align:start position:0%
+I go to larger and larger tools uh this
+gets uh worse and
+
+ align:start position:0%
+gets uh worse and
+ 
+
+ align:start position:0%
+gets uh worse and
+worse. But if we make a definition that
+
+ align:start position:0%
+worse. But if we make a definition that
+ 
+
+ align:start position:0%
+worse. But if we make a definition that
+the area of the interaction of the
+
+ align:start position:0%
+the area of the interaction of the
+ 
+
+ align:start position:0%
+the area of the interaction of the
+energy interaction is small compared to
+
+ align:start position:0%
+energy interaction is small compared to
+ 
+
+ align:start position:0%
+energy interaction is small compared to
+the total area that I want to
+
+ align:start position:0%
+the total area that I want to
+ 
+
+ align:start position:0%
+the total area that I want to
+change then it's clearly what we'll call
+
+ align:start position:0%
+change then it's clearly what we'll call
+ 
+
+ align:start position:0%
+change then it's clearly what we'll call
+a serial process.
+
+ align:start position:0%
+a serial process.
+ 
+
+ align:start position:0%
+a serial process.
+Um, if the opposite is true, if the area
+
+ align:start position:0%
+Um, if the opposite is true, if the area
+ 
+
+ align:start position:0%
+Um, if the opposite is true, if the area
+of that interaction is on the order of
+
+ align:start position:0%
+of that interaction is on the order of
+ 
+
+ align:start position:0%
+of that interaction is on the order of
+the total area that I'm trying to
+
+ align:start position:0%
+the total area that I'm trying to
+ 
+
+ align:start position:0%
+the total area that I'm trying to
+change, and again, the icon for that
+
+ align:start position:0%
+change, and again, the icon for that
+ 
+
+ align:start position:0%
+change, and again, the icon for that
+would be a, you know, stamping out a car
+
+ align:start position:0%
+would be a, you know, stamping out a car
+ 
+
+ align:start position:0%
+would be a, you know, stamping out a car
+hood or something like that. The area of
+
+ align:start position:0%
+hood or something like that. The area of
+ 
+
+ align:start position:0%
+hood or something like that. The area of
+interaction is the same as the uh area
+
+ align:start position:0%
+interaction is the same as the uh area
+ 
+
+ align:start position:0%
+interaction is the same as the uh area
+that I'm trying to change. Same with
+
+ align:start position:0%
+that I'm trying to change. Same with
+ 
+
+ align:start position:0%
+that I'm trying to change. Same with
+this part. The area of interaction is
+
+ align:start position:0%
+this part. The area of interaction is
+ 
+
+ align:start position:0%
+this part. The area of interaction is
+the entire area. Then we have uh a
+
+ align:start position:0%
+the entire area. Then we have uh a
+ 
+
+ align:start position:0%
+the entire area. Then we have uh a
+parallel process.
+
+ align:start position:0%
+parallel process.
+ 
+
+ align:start position:0%
+parallel process.
+we run into a couple interesting uh
+
+ align:start position:0%
+we run into a couple interesting uh
+ 
+
+ align:start position:0%
+we run into a couple interesting uh
+variants on that.
+
+ align:start position:0%
+variants on that.
+ 
+
+ align:start position:0%
+variants on that.
+Um if we
+
+ align:start position:0%
+Um if we
+ 
+
+ align:start position:0%
+Um if we
+take a very common
+
+ align:start position:0%
+take a very common
+ 
+
+ align:start position:0%
+take a very common
+process rolling to get you know to get
+
+ align:start position:0%
+process rolling to get you know to get
+ 
+
+ align:start position:0%
+process rolling to get you know to get
+um to create sheet or just plate uh
+
+ align:start position:0%
+um to create sheet or just plate uh
+ 
+
+ align:start position:0%
+um to create sheet or just plate uh
+reductions you know I'm coming in with
+
+ align:start position:0%
+reductions you know I'm coming in with
+ 
+
+ align:start position:0%
+reductions you know I'm coming in with
+material that looks like this. I'm
+
+ align:start position:0%
+material that looks like this. I'm
+ 
+
+ align:start position:0%
+material that looks like this. I'm
+coming out with a material that's much
+
+ align:start position:0%
+coming out with a material that's much
+ 
+
+ align:start position:0%
+coming out with a material that's much
+thinner.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, where does this fit in this taxonomy
+
+ align:start position:0%
+Um, where does this fit in this taxonomy
+ 
+
+ align:start position:0%
+Um, where does this fit in this taxonomy
+here? This part of the taxonomy, is it a
+
+ align:start position:0%
+here? This part of the taxonomy, is it a
+ 
+
+ align:start position:0%
+here? This part of the taxonomy, is it a
+serial process or a a parallel process?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Serial.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Okay. So we have 50% of the
+
+ align:start position:0%
+Okay. Okay. So we have 50% of the
+ 
+
+ align:start position:0%
+Okay. Okay. So we have 50% of the
+electorate going for serial. This might
+
+ align:start position:0%
+electorate going for serial. This might
+ 
+
+ align:start position:0%
+electorate going for serial. This might
+be Democratic uh primary parallel 50%
+
+ align:start position:0%
+be Democratic uh primary parallel 50%
+ 
+
+ align:start position:0%
+be Democratic uh primary parallel 50%
+saying parallel. Guess it goes to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+superdelegates. Okay. You guys you guys
+
+ align:start position:0%
+superdelegates. Okay. You guys you guys
+ 
+
+ align:start position:0%
+superdelegates. Okay. You guys you guys
+in Singapore and to you guys want to you
+
+ align:start position:0%
+in Singapore and to you guys want to you
+ 
+
+ align:start position:0%
+in Singapore and to you guys want to you
+want to break the tie here? What is it?
+
+ align:start position:0%
+want to break the tie here? What is it?
+ 
+
+ align:start position:0%
+want to break the tie here? What is it?
+Serial or parallel?
+
+ align:start position:0%
+Serial or parallel?
+ 
+
+ align:start position:0%
+Serial or parallel?
+I think it's parallel. Okay. So 51% for
+
+ align:start position:0%
+I think it's parallel. Okay. So 51% for
+ 
+
+ align:start position:0%
+I think it's parallel. Okay. So 51% for
+uh parallel. Anybody? Anybody there say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+serial? We have some Yeah, we still we
+
+ align:start position:0%
+serial? We have some Yeah, we still we
+ 
+
+ align:start position:0%
+serial? We have some Yeah, we still we
+got some cereals here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H Yeah, now we're getting to it. Okay,
+
+ align:start position:0%
+H Yeah, now we're getting to it. Okay,
+ 
+
+ align:start position:0%
+H Yeah, now we're getting to it. Okay,
+it depends. If I had drawn this in
+
+ align:start position:0%
+it depends. If I had drawn this in
+ 
+
+ align:start position:0%
+it depends. If I had drawn this in
+2D like
+
+ align:start position:0%
+2D like
+ 
+
+ align:start position:0%
+2D like
+this and maybe maybe sort of drawn it in
+
+ align:start position:0%
+this and maybe maybe sort of drawn it in
+ 
+
+ align:start position:0%
+this and maybe maybe sort of drawn it in
+extreme and didn't even show this
+
+ align:start position:0%
+extreme and didn't even show this
+ 
+
+ align:start position:0%
+extreme and didn't even show this
+necking just kind of showed it doing
+
+ align:start position:0%
+necking just kind of showed it doing
+ 
+
+ align:start position:0%
+necking just kind of showed it doing
+this then you'd you'd be pretty tempted
+
+ align:start position:0%
+this then you'd you'd be pretty tempted
+ 
+
+ align:start position:0%
+this then you'd you'd be pretty tempted
+to say oh that's a serial process
+
+ align:start position:0%
+to say oh that's a serial process
+ 
+
+ align:start position:0%
+to say oh that's a serial process
+because all the action is right here.
+
+ align:start position:0%
+because all the action is right here.
+ 
+
+ align:start position:0%
+because all the action is right here.
+Look at this huge area that I'm
+
+ align:start position:0%
+Look at this huge area that I'm
+ 
+
+ align:start position:0%
+Look at this huge area that I'm
+affecting and all the action is right
+
+ align:start position:0%
+affecting and all the action is right
+ 
+
+ align:start position:0%
+affecting and all the action is right
+there. If I draw it in in in uh uh front
+
+ align:start position:0%
+there. If I draw it in in in uh uh front
+ 
+
+ align:start position:0%
+there. If I draw it in in in uh uh front
+end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+view and I here's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material, you'd look at that say, "Oh,
+
+ align:start position:0%
+material, you'd look at that say, "Oh,
+ 
+
+ align:start position:0%
+material, you'd look at that say, "Oh,
+that's parallel. Everything's happening
+
+ align:start position:0%
+that's parallel. Everything's happening
+ 
+
+ align:start position:0%
+that's parallel. Everything's happening
+everywhere at the same time." Okay, so
+
+ align:start position:0%
+everywhere at the same time." Okay, so
+ 
+
+ align:start position:0%
+everywhere at the same time." Okay, so
+just a cautionary tale. It's it's it's
+
+ align:start position:0%
+just a cautionary tale. It's it's it's
+ 
+
+ align:start position:0%
+just a cautionary tale. It's it's it's
+it's not either or, it's neither nor.
+
+ align:start position:0%
+it's not either or, it's neither nor.
+ 
+
+ align:start position:0%
+it's not either or, it's neither nor.
+Okay. uh uh it's it's sort of
+
+ align:start position:0%
+Okay. uh uh it's it's sort of
+ 
+
+ align:start position:0%
+Okay. uh uh it's it's sort of
+prepundonderance of if you will. So
+
+ align:start position:0%
+prepundonderance of if you will. So
+ 
+
+ align:start position:0%
+prepundonderance of if you will. So
+um this this is a good example of of why
+
+ align:start position:0%
+um this this is a good example of of why
+ 
+
+ align:start position:0%
+um this this is a good example of of why
+they're actually important even though
+
+ align:start position:0%
+they're actually important even though
+ 
+
+ align:start position:0%
+they're actually important even though
+it's mixed on here. And I'm going to
+
+ align:start position:0%
+it's mixed on here. And I'm going to
+ 
+
+ align:start position:0%
+it's mixed on here. And I'm going to
+jump ahead to the sort of who cares,
+
+ align:start position:0%
+jump ahead to the sort of who cares,
+ 
+
+ align:start position:0%
+jump ahead to the sort of who cares,
+which may not have a satisfactory answer
+
+ align:start position:0%
+which may not have a satisfactory answer
+ 
+
+ align:start position:0%
+which may not have a satisfactory answer
+today, but the who cares is um if I'm
+
+ align:start position:0%
+today, but the who cares is um if I'm
+ 
+
+ align:start position:0%
+today, but the who cares is um if I'm
+running in this case the Alcoa,
+
+ align:start position:0%
+running in this case the Alcoa,
+ 
+
+ align:start position:0%
+running in this case the Alcoa,
+Tennessee, that's a that's a real town.
+
+ align:start position:0%
+Tennessee, that's a that's a real town.
+ 
+
+ align:start position:0%
+Tennessee, that's a that's a real town.
+The Alcoa,
+
+ align:start position:0%
+The Alcoa,
+ 
+
+ align:start position:0%
+The Alcoa,
+Tennessee cold rolling mill that makes
+
+ align:start position:0%
+Tennessee cold rolling mill that makes
+ 
+
+ align:start position:0%
+Tennessee cold rolling mill that makes
+all their beer can stock. Um, and I'm
+
+ align:start position:0%
+all their beer can stock. Um, and I'm
+ 
+
+ align:start position:0%
+all their beer can stock. Um, and I'm
+really concerned about extremely good
+
+ align:start position:0%
+really concerned about extremely good
+ 
+
+ align:start position:0%
+really concerned about extremely good
+thickness control because when it goes
+
+ align:start position:0%
+thickness control because when it goes
+ 
+
+ align:start position:0%
+thickness control because when it goes
+into the high-speed canning machines,
+
+ align:start position:0%
+into the high-speed canning machines,
+ 
+
+ align:start position:0%
+into the high-speed canning machines,
+that thickness has to be right on,
+
+ align:start position:0%
+that thickness has to be right on,
+ 
+
+ align:start position:0%
+that thickness has to be right on,
+otherwise the walls will tear or it
+
+ align:start position:0%
+otherwise the walls will tear or it
+ 
+
+ align:start position:0%
+otherwise the walls will tear or it
+won't form
+
+ align:start position:0%
+won't form
+ 
+
+ align:start position:0%
+won't form
+properly. What do I control? Just
+
+ align:start position:0%
+properly. What do I control? Just
+ 
+
+ align:start position:0%
+properly. What do I control? Just
+intuitively, what would I control to
+
+ align:start position:0%
+intuitively, what would I control to
+ 
+
+ align:start position:0%
+intuitively, what would I control to
+affect the
+
+ align:start position:0%
+affect the
+ 
+
+ align:start position:0%
+affect the
+geometry parameter called thickness?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Distance between the rolls. Yeah. Okay.
+
+ align:start position:0%
+Distance between the rolls. Yeah. Okay.
+ 
+
+ align:start position:0%
+Distance between the rolls. Yeah. Okay.
+So I control the thickness by
+
+ align:start position:0%
+So I control the thickness by
+ 
+
+ align:start position:0%
+So I control the thickness by
+controlling let's say this this this
+
+ align:start position:0%
+controlling let's say this this this
+ 
+
+ align:start position:0%
+controlling let's say this this this
+distance right
+
+ align:start position:0%
+distance right
+ 
+
+ align:start position:0%
+distance right
+here,
+
+ align:start position:0%
+here,
+ 
+
+ align:start position:0%
+here,
+right? Which thickness does that
+
+ align:start position:0%
+right? Which thickness does that
+ 
+
+ align:start position:0%
+right? Which thickness does that
+control? Does it control this thickness
+
+ align:start position:0%
+control? Does it control this thickness
+ 
+
+ align:start position:0%
+control? Does it control this thickness
+right here or this one here or that one
+
+ align:start position:0%
+right here or this one here or that one
+ 
+
+ align:start position:0%
+right here or this one here or that one
+there? Or maybe that one there or that
+
+ align:start position:0%
+there? Or maybe that one there or that
+ 
+
+ align:start position:0%
+there? Or maybe that one there or that
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there? All you can Yeah. All you're
+
+ align:start position:0%
+there? All you can Yeah. All you're
+ 
+
+ align:start position:0%
+there? All you can Yeah. All you're
+doing there's one display there's one
+
+ align:start position:0%
+doing there's one display there's one
+ 
+
+ align:start position:0%
+doing there's one display there's one
+spacing there. You all right? Right. And
+
+ align:start position:0%
+spacing there. You all right? Right. And
+ 
+
+ align:start position:0%
+spacing there. You all right? Right. And
+if I if you say, "Oh, yeah. It's exactly
+
+ align:start position:0%
+if I if you say, "Oh, yeah. It's exactly
+ 
+
+ align:start position:0%
+if I if you say, "Oh, yeah. It's exactly
+right here." And then I I make little
+
+ align:start position:0%
+right here." And then I I make little
+ 
+
+ align:start position:0%
+right here." And then I I make little
+discs and make my cans for the material
+
+ align:start position:0%
+discs and make my cans for the material
+ 
+
+ align:start position:0%
+discs and make my cans for the material
+over here. Who's to say it's going to be
+
+ align:start position:0%
+over here. Who's to say it's going to be
+ 
+
+ align:start position:0%
+over here. Who's to say it's going to be
+right? So even in this case, I've
+
+ align:start position:0%
+right? So even in this case, I've
+ 
+
+ align:start position:0%
+right? So even in this case, I've
+actually got a mixed problem here and a
+
+ align:start position:0%
+actually got a mixed problem here and a
+ 
+
+ align:start position:0%
+actually got a mixed problem here and a
+mixed control problem. So yeah, here's a
+
+ align:start position:0%
+mixed control problem. So yeah, here's a
+ 
+
+ align:start position:0%
+mixed control problem. So yeah, here's a
+case where displacement, you know, this
+
+ align:start position:0%
+case where displacement, you know, this
+ 
+
+ align:start position:0%
+case where displacement, you know, this
+trajectory we're talking about, just
+
+ align:start position:0%
+trajectory we're talking about, just
+ 
+
+ align:start position:0%
+trajectory we're talking about, just
+like uh this deal, you want to think of
+
+ align:start position:0%
+like uh this deal, you want to think of
+ 
+
+ align:start position:0%
+like uh this deal, you want to think of
+it that way. I'm directing the energy
+
+ align:start position:0%
+it that way. I'm directing the energy
+ 
+
+ align:start position:0%
+it that way. I'm directing the energy
+source by displacing
+
+ align:start position:0%
+source by displacing
+ 
+
+ align:start position:0%
+source by displacing
+it. That's part of it. But then how do I
+
+ align:start position:0%
+it. That's part of it. But then how do I
+ 
+
+ align:start position:0%
+it. That's part of it. But then how do I
+change the the the
+
+ align:start position:0%
+change the the the
+ 
+
+ align:start position:0%
+change the the the
+um thickness distribution, the parallel
+
+ align:start position:0%
+um thickness distribution, the parallel
+ 
+
+ align:start position:0%
+um thickness distribution, the parallel
+part of the process? Well, I'd actually
+
+ align:start position:0%
+part of the process? Well, I'd actually
+ 
+
+ align:start position:0%
+part of the process? Well, I'd actually
+probably have to change the shape of the
+
+ align:start position:0%
+probably have to change the shape of the
+ 
+
+ align:start position:0%
+probably have to change the shape of the
+rolls,
+
+ align:start position:0%
+rolls,
+ 
+
+ align:start position:0%
+rolls,
+right? You can do a little bit. They
+
+ align:start position:0%
+right? You can do a little bit. They
+ 
+
+ align:start position:0%
+right? You can do a little bit. They
+actually do both sides and that does
+
+ align:start position:0%
+actually do both sides and that does
+ 
+
+ align:start position:0%
+actually do both sides and that does
+help. But let's say I do both sides. So
+
+ align:start position:0%
+help. But let's say I do both sides. So
+ 
+
+ align:start position:0%
+help. But let's say I do both sides. So
+this is exactly right. This is exactly
+
+ align:start position:0%
+this is exactly right. This is exactly
+ 
+
+ align:start position:0%
+this is exactly right. This is exactly
+right. And the middle looks like this,
+
+ align:start position:0%
+right. And the middle looks like this,
+ 
+
+ align:start position:0%
+right. And the middle looks like this,
+which is not uncommon. It becomes fatter
+
+ align:start position:0%
+which is not uncommon. It becomes fatter
+ 
+
+ align:start position:0%
+which is not uncommon. It becomes fatter
+in the middle. What do you do?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, but I don't want to do that. Yes,
+
+ align:start position:0%
+Yeah, but I don't want to do that. Yes,
+ 
+
+ align:start position:0%
+Yeah, but I don't want to do that. Yes,
+you would change the rolls and and in
+
+ align:start position:0%
+you would change the rolls and and in
+ 
+
+ align:start position:0%
+you would change the rolls and and in
+fact, what they do is they build rolls
+
+ align:start position:0%
+fact, what they do is they build rolls
+ 
+
+ align:start position:0%
+fact, what they do is they build rolls
+with a little bit of a camber in them
+
+ align:start position:0%
+with a little bit of a camber in them
+ 
+
+ align:start position:0%
+with a little bit of a camber in them
+because, you know, the center is going
+
+ align:start position:0%
+because, you know, the center is going
+ 
+
+ align:start position:0%
+because, you know, the center is going
+to deflect up a little bit, so you put
+
+ align:start position:0%
+to deflect up a little bit, so you put
+ 
+
+ align:start position:0%
+to deflect up a little bit, so you put
+some camber into it. Believe it or not,
+
+ align:start position:0%
+some camber into it. Believe it or not,
+ 
+
+ align:start position:0%
+some camber into it. Believe it or not,
+at Alcoa, that's still not good enough.
+
+ align:start position:0%
+at Alcoa, that's still not good enough.
+ 
+
+ align:start position:0%
+at Alcoa, that's still not good enough.
+This stuff is very precise. I think that
+
+ align:start position:0%
+This stuff is very precise. I think that
+ 
+
+ align:start position:0%
+This stuff is very precise. I think that
+I I shouldn't quote the tolerances, but
+
+ align:start position:0%
+I I shouldn't quote the tolerances, but
+ 
+
+ align:start position:0%
+I I shouldn't quote the tolerances, but
+it's it's on the order of uh in in my
+
+ align:start position:0%
+it's it's on the order of uh in in my
+ 
+
+ align:start position:0%
+it's it's on the order of uh in in my
+newly converted SI brain, I think it's
+
+ align:start position:0%
+newly converted SI brain, I think it's
+ 
+
+ align:start position:0%
+newly converted SI brain, I think it's
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+be 15 microns, you know, fra it's it it
+
+ align:start position:0%
+be 15 microns, you know, fra it's it it
+ 
+
+ align:start position:0%
+be 15 microns, you know, fra it's it it
+could be in the 10,000 several 10,000 of
+
+ align:start position:0%
+could be in the 10,000 several 10,000 of
+ 
+
+ align:start position:0%
+could be in the 10,000 several 10,000 of
+an inch in terms of thickness tolerance.
+
+ align:start position:0%
+an inch in terms of thickness tolerance.
+ 
+
+ align:start position:0%
+an inch in terms of thickness tolerance.
+It's not very thick stuff to begin with.
+
+ align:start position:0%
+It's not very thick stuff to begin with.
+ 
+
+ align:start position:0%
+It's not very thick stuff to begin with.
+So like locally heated through heat.
+
+ align:start position:0%
+So like locally heated through heat.
+ 
+
+ align:start position:0%
+So like locally heated through heat.
+Yeah. In fact, that's what done what is
+
+ align:start position:0%
+Yeah. In fact, that's what done what is
+ 
+
+ align:start position:0%
+Yeah. In fact, that's what done what is
+done to get small displacements to be
+
+ align:start position:0%
+done to get small displacements to be
+ 
+
+ align:start position:0%
+done to get small displacements to be
+able to actually arbitrarily not
+
+ align:start position:0%
+able to actually arbitrarily not
+ 
+
+ align:start position:0%
+able to actually arbitrarily not
+arbitrarily but to put you know some
+
+ align:start position:0%
+arbitrarily but to put you know some
+ 
+
+ align:start position:0%
+arbitrarily but to put you know some
+different profiles on that you locally
+
+ align:start position:0%
+different profiles on that you locally
+ 
+
+ align:start position:0%
+different profiles on that you locally
+heat it or cool
+
+ align:start position:0%
+heat it or cool
+ 
+
+ align:start position:0%
+heat it or cool
+it in response to feedback to actually
+
+ align:start position:0%
+it in response to feedback to actually
+ 
+
+ align:start position:0%
+it in response to feedback to actually
+slowly move the tool locally a little
+
+ align:start position:0%
+slowly move the tool locally a little
+ 
+
+ align:start position:0%
+slowly move the tool locally a little
+bit fatter here a little bit less. You
+
+ align:start position:0%
+bit fatter here a little bit less. You
+ 
+
+ align:start position:0%
+bit fatter here a little bit less. You
+can imagine if you only need, you know,
+
+ align:start position:0%
+can imagine if you only need, you know,
+ 
+
+ align:start position:0%
+can imagine if you only need, you know,
+10 micron, something like that, doesn't
+
+ align:start position:0%
+10 micron, something like that, doesn't
+ 
+
+ align:start position:0%
+10 micron, something like that, doesn't
+take a lot of heat. And yes, indeed,
+
+ align:start position:0%
+take a lot of heat. And yes, indeed,
+ 
+
+ align:start position:0%
+take a lot of heat. And yes, indeed,
+you're going to say, "Oh, how localized
+
+ align:start position:0%
+you're going to say, "Oh, how localized
+ 
+
+ align:start position:0%
+you're going to say, "Oh, how localized
+can that be?" And that's the trade
+
+ align:start position:0%
+can that be?" And that's the trade
+ 
+
+ align:start position:0%
+can that be?" And that's the trade
+secret they won't tell anybody about.
+
+ align:start position:0%
+secret they won't tell anybody about.
+ 
+
+ align:start position:0%
+secret they won't tell anybody about.
+But um yeah, so in this particular case,
+
+ align:start position:0%
+But um yeah, so in this particular case,
+ 
+
+ align:start position:0%
+But um yeah, so in this particular case,
+notice these two different modes of
+
+ align:start position:0%
+notice these two different modes of
+ 
+
+ align:start position:0%
+notice these two different modes of
+uh uh two different modes of interaction
+
+ align:start position:0%
+uh uh two different modes of interaction
+ 
+
+ align:start position:0%
+uh uh two different modes of interaction
+lead to two different ways of
+
+ align:start position:0%
+lead to two different ways of
+ 
+
+ align:start position:0%
+lead to two different ways of
+controlling it. In one case, it's very
+
+ align:start position:0%
+controlling it. In one case, it's very
+ 
+
+ align:start position:0%
+controlling it. In one case, it's very
+simple. I'm going to buy a servo system.
+
+ align:start position:0%
+simple. I'm going to buy a servo system.
+ 
+
+ align:start position:0%
+simple. I'm going to buy a servo system.
+It's going to be really good. it's going
+
+ align:start position:0%
+It's going to be really good. it's going
+ 
+
+ align:start position:0%
+It's going to be really good. it's going
+to be very stiff and I'm going to say
+
+ align:start position:0%
+to be very stiff and I'm going to say
+ 
+
+ align:start position:0%
+to be very stiff and I'm going to say
+make that 2000 of an inch gap and you
+
+ align:start position:0%
+make that 2000 of an inch gap and you
+ 
+
+ align:start position:0%
+make that 2000 of an inch gap and you
+get 2,000 of an inch gap. In the other
+
+ align:start position:0%
+get 2,000 of an inch gap. In the other
+ 
+
+ align:start position:0%
+get 2,000 of an inch gap. In the other
+case, it's like oh my gosh, you know, uh
+
+ align:start position:0%
+case, it's like oh my gosh, you know, uh
+ 
+
+ align:start position:0%
+case, it's like oh my gosh, you know, uh
+I've got to change this spatial
+
+ align:start position:0%
+I've got to change this spatial
+ 
+
+ align:start position:0%
+I've got to change this spatial
+distribution somehow. The extreme case
+
+ align:start position:0%
+distribution somehow. The extreme case
+ 
+
+ align:start position:0%
+distribution somehow. The extreme case
+is to shut the thing down, put in a new
+
+ align:start position:0%
+is to shut the thing down, put in a new
+ 
+
+ align:start position:0%
+is to shut the thing down, put in a new
+set of roles and the other is to come up
+
+ align:start position:0%
+set of roles and the other is to come up
+ 
+
+ align:start position:0%
+set of roles and the other is to come up
+with some clever way of deforming it.
+
+ align:start position:0%
+with some clever way of deforming it.
+ 
+
+ align:start position:0%
+with some clever way of deforming it.
+Okay, so why do we worry about the two
+
+ align:start position:0%
+Okay, so why do we worry about the two
+ 
+
+ align:start position:0%
+Okay, so why do we worry about the two
+modes of interaction? It leads directly
+
+ align:start position:0%
+modes of interaction? It leads directly
+ 
+
+ align:start position:0%
+modes of interaction? It leads directly
+to how we would ever find the knobs on
+
+ align:start position:0%
+to how we would ever find the knobs on
+ 
+
+ align:start position:0%
+to how we would ever find the knobs on
+the machine to change what we're doing.
+
+ align:start position:0%
+the machine to change what we're doing.
+ 
+
+ align:start position:0%
+the machine to change what we're doing.
+Now that will become most
+
+ align:start position:0%
+Now that will become most
+ 
+
+ align:start position:0%
+Now that will become most
+important in the last part of the class
+
+ align:start position:0%
+important in the last part of the class
+ 
+
+ align:start position:0%
+important in the last part of the class
+when we talk about process optimization
+
+ align:start position:0%
+when we talk about process optimization
+ 
+
+ align:start position:0%
+when we talk about process optimization
+and you're saying what can I do you know
+
+ align:start position:0%
+and you're saying what can I do you know
+ 
+
+ align:start position:0%
+and you're saying what can I do you know
+what can I actually change on a process
+
+ align:start position:0%
+what can I actually change on a process
+ 
+
+ align:start position:0%
+what can I actually change on a process
+what can I
+
+ align:start position:0%
+what can I
+ 
+
+ align:start position:0%
+what can I
+change real time millisecond what can I
+
+ align:start position:0%
+change real time millisecond what can I
+ 
+
+ align:start position:0%
+change real time millisecond what can I
+change maybe in this case this is a this
+
+ align:start position:0%
+change maybe in this case this is a this
+ 
+
+ align:start position:0%
+change maybe in this case this is a this
+is an unusual example what can I change
+
+ align:start position:0%
+is an unusual example what can I change
+ 
+
+ align:start position:0%
+is an unusual example what can I change
+on on a you know a frequent basis but in
+
+ align:start position:0%
+on on a you know a frequent basis but in
+ 
+
+ align:start position:0%
+on on a you know a frequent basis but in
+most cases the major change you do with
+
+ align:start position:0%
+most cases the major change you do with
+ 
+
+ align:start position:0%
+most cases the major change you do with
+tooling and things like this is on a
+
+ align:start position:0%
+tooling and things like this is on a
+ 
+
+ align:start position:0%
+tooling and things like this is on a
+you know, hourly shift, yearly basis.
+
+ align:start position:0%
+you know, hourly shift, yearly basis.
+ 
+
+ align:start position:0%
+you know, hourly shift, yearly basis.
+So, your ability to affect the output
+
+ align:start position:0%
+So, your ability to affect the output
+ 
+
+ align:start position:0%
+So, your ability to affect the output
+once you've kind of literally cast it in
+
+ align:start position:0%
+once you've kind of literally cast it in
+ 
+
+ align:start position:0%
+once you've kind of literally cast it in
+stone uh is is greatly uh changed by
+
+ align:start position:0%
+stone uh is is greatly uh changed by
+ 
+
+ align:start position:0%
+stone uh is is greatly uh changed by
+whether it's a parallel or ser or serial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. All right. Okay. So, just just to
+
+ align:start position:0%
+Okay. All right. Okay. So, just just to
+ 
+
+ align:start position:0%
+Okay. All right. Okay. So, just just to
+to summarize this again. So for this
+
+ align:start position:0%
+to summarize this again. So for this
+ 
+
+ align:start position:0%
+to summarize this again. So for this
+lumped or serial case um the time
+
+ align:start position:0%
+lumped or serial case um the time
+ 
+
+ align:start position:0%
+lumped or serial case um the time
+trajectory of that interaction port is
+
+ align:start position:0%
+trajectory of that interaction port is
+ 
+
+ align:start position:0%
+trajectory of that interaction port is
+one of the most important things. So
+
+ align:start position:0%
+one of the most important things. So
+ 
+
+ align:start position:0%
+one of the most important things. So
+robotic
+
+ align:start position:0%
+robotic
+ 
+
+ align:start position:0%
+robotic
+manufacturing which was all the rage for
+
+ align:start position:0%
+manufacturing which was all the rage for
+ 
+
+ align:start position:0%
+manufacturing which was all the rage for
+many a year until we found out it wasn't
+
+ align:start position:0%
+many a year until we found out it wasn't
+ 
+
+ align:start position:0%
+many a year until we found out it wasn't
+really such a thing to be rageful about.
+
+ align:start position:0%
+really such a thing to be rageful about.
+ 
+
+ align:start position:0%
+really such a thing to be rageful about.
+Um it it works for a limited class of
+
+ align:start position:0%
+Um it it works for a limited class of
+ 
+
+ align:start position:0%
+Um it it works for a limited class of
+processes pretty well, but uh and your
+
+ align:start position:0%
+processes pretty well, but uh and your
+ 
+
+ align:start position:0%
+processes pretty well, but uh and your
+your classic CNC machine, the CNC
+
+ align:start position:0%
+your classic CNC machine, the CNC
+ 
+
+ align:start position:0%
+your classic CNC machine, the CNC
+machine of the 60s, which sort of got
+
+ align:start position:0%
+machine of the 60s, which sort of got
+ 
+
+ align:start position:0%
+machine of the 60s, which sort of got
+generalized in the 70s and and put
+
+ align:start position:0%
+generalized in the 70s and and put
+ 
+
+ align:start position:0%
+generalized in the 70s and and put
+everywhere essentially means, if you
+
+ align:start position:0%
+everywhere essentially means, if you
+ 
+
+ align:start position:0%
+everywhere essentially means, if you
+want to put in the terminology what
+
+ align:start position:0%
+want to put in the terminology what
+ 
+
+ align:start position:0%
+want to put in the terminology what
+we're talking about today, usually means
+
+ align:start position:0%
+we're talking about today, usually means
+ 
+
+ align:start position:0%
+we're talking about today, usually means
+the ability to control
+
+ align:start position:0%
+the ability to control
+ 
+
+ align:start position:0%
+the ability to control
+trajectories in a very repeatable way.
+
+ align:start position:0%
+trajectories in a very repeatable way.
+ 
+
+ align:start position:0%
+trajectories in a very repeatable way.
+So it's not just the ability a machine
+
+ align:start position:0%
+So it's not just the ability a machine
+ 
+
+ align:start position:0%
+So it's not just the ability a machine
+that can follow a trajectory, it's also
+
+ align:start position:0%
+that can follow a trajectory, it's also
+ 
+
+ align:start position:0%
+that can follow a trajectory, it's also
+the ability to generate the trajectory
+
+ align:start position:0%
+the ability to generate the trajectory
+ 
+
+ align:start position:0%
+the ability to generate the trajectory
+and things like that. And then in this
+
+ align:start position:0%
+and things like that. And then in this
+ 
+
+ align:start position:0%
+and things like that. And then in this
+distributed distri I've used two
+
+ align:start position:0%
+distributed distri I've used two
+ 
+
+ align:start position:0%
+distributed distri I've used two
+different terms here, but distributed or
+
+ align:start position:0%
+different terms here, but distributed or
+ 
+
+ align:start position:0%
+different terms here, but distributed or
+parallel case it's more than anything
+
+ align:start position:0%
+parallel case it's more than anything
+ 
+
+ align:start position:0%
+parallel case it's more than anything
+it's the shape of the energy
+
+ align:start position:0%
+it's the shape of the energy
+ 
+
+ align:start position:0%
+it's the shape of the energy
+distributor. You know patterns, molds,
+
+ align:start position:0%
+distributor. You know patterns, molds,
+ 
+
+ align:start position:0%
+distributor. You know patterns, molds,
+masks, heat distributions, things like
+
+ align:start position:0%
+masks, heat distributions, things like
+ 
+
+ align:start position:0%
+masks, heat distributions, things like
+that. I think we've seen enough
+
+ align:start position:0%
+that. I think we've seen enough
+ 
+
+ align:start position:0%
+that. I think we've seen enough
+examples. We're sick of these
+
+ align:start position:0%
+examples. We're sick of these
+ 
+
+ align:start position:0%
+examples. We're sick of these
+now. Uh oh yeah. Well, you'll see this
+
+ align:start position:0%
+now. Uh oh yeah. Well, you'll see this
+ 
+
+ align:start position:0%
+now. Uh oh yeah. Well, you'll see this
+in a moment, but a lot of the uh
+
+ align:start position:0%
+in a moment, but a lot of the uh
+ 
+
+ align:start position:0%
+in a moment, but a lot of the uh
+so-called um rapid prototyping methods
+
+ align:start position:0%
+so-called um rapid prototyping methods
+ 
+
+ align:start position:0%
+so-called um rapid prototyping methods
+that that popped up in the '9s or solid
+
+ align:start position:0%
+that that popped up in the '9s or solid
+ 
+
+ align:start position:0%
+that that popped up in the '9s or solid
+free form fabrication as it's sometimes
+
+ align:start position:0%
+free form fabrication as it's sometimes
+ 
+
+ align:start position:0%
+free form fabrication as it's sometimes
+as the government likes to call it um
+
+ align:start position:0%
+as the government likes to call it um
+ 
+
+ align:start position:0%
+as the government likes to call it um
+stereoiththography sort of the first big
+
+ align:start position:0%
+stereoiththography sort of the first big
+ 
+
+ align:start position:0%
+stereoiththography sort of the first big
+one on that 3D printing developed here
+
+ align:start position:0%
+one on that 3D printing developed here
+ 
+
+ align:start position:0%
+one on that 3D printing developed here
+um are serial processes and they figured
+
+ align:start position:0%
+um are serial processes and they figured
+ 
+
+ align:start position:0%
+um are serial processes and they figured
+out how to put down in they turn out to
+
+ align:start position:0%
+out how to put down in they turn out to
+ 
+
+ align:start position:0%
+out how to put down in they turn out to
+be usually serial edition type
+
+ align:start position:0%
+be usually serial edition type
+ 
+
+ align:start position:0%
+be usually serial edition type
+processes. is they figured out how to
+
+ align:start position:0%
+processes. is they figured out how to
+ 
+
+ align:start position:0%
+processes. is they figured out how to
+put a dot of material down at a time uh
+
+ align:start position:0%
+put a dot of material down at a time uh
+ 
+
+ align:start position:0%
+put a dot of material down at a time uh
+to build up uh to build up a structure
+
+ align:start position:0%
+to build up uh to build up a structure
+ 
+
+ align:start position:0%
+to build up uh to build up a structure
+and that that dot itself was cohesive
+
+ align:start position:0%
+and that that dot itself was cohesive
+ 
+
+ align:start position:0%
+and that that dot itself was cohesive
+enough that if you put it down it stayed
+
+ align:start position:0%
+enough that if you put it down it stayed
+ 
+
+ align:start position:0%
+enough that if you put it down it stayed
+there and you didn't need anything to
+
+ align:start position:0%
+there and you didn't need anything to
+ 
+
+ align:start position:0%
+there and you didn't need anything to
+hold it.
+
+ align:start position:0%
+hold it.
+ 
+
+ align:start position:0%
+hold it.
+Um and I'll talk more about that in just
+
+ align:start position:0%
+Um and I'll talk more about that in just
+ 
+
+ align:start position:0%
+Um and I'll talk more about that in just
+a moment. But I think we've kind of
+
+ align:start position:0%
+a moment. But I think we've kind of
+ 
+
+ align:start position:0%
+a moment. But I think we've kind of
+talked about you know these are all
+
+ align:start position:0%
+talked about you know these are all
+ 
+
+ align:start position:0%
+talked about you know these are all
+these are all interesting examples. So
+
+ align:start position:0%
+these are all interesting examples. So
+ 
+
+ align:start position:0%
+these are all interesting examples. So
+if we talk about a taxonomy to kind of
+
+ align:start position:0%
+if we talk about a taxonomy to kind of
+ 
+
+ align:start position:0%
+if we talk about a taxonomy to kind of
+bring together the uh the um energy
+
+ align:start position:0%
+bring together the uh the um energy
+ 
+
+ align:start position:0%
+bring together the uh the um energy
+source if you will or for the um
+
+ align:start position:0%
+source if you will or for the um
+ 
+
+ align:start position:0%
+source if you will or for the um
+geometry change the way we apply it
+
+ align:start position:0%
+geometry change the way we apply it
+ 
+
+ align:start position:0%
+geometry change the way we apply it
+um and a couple other things that'll
+
+ align:start position:0%
+um and a couple other things that'll
+ 
+
+ align:start position:0%
+um and a couple other things that'll
+come up in just a second then we can uh
+
+ align:start position:0%
+come up in just a second then we can uh
+ 
+
+ align:start position:0%
+come up in just a second then we can uh
+and I I think I've said why for the for
+
+ align:start position:0%
+and I I think I've said why for the for
+ 
+
+ align:start position:0%
+and I I think I've said why for the for
+the mode uh you know the change mode why
+
+ align:start position:0%
+the mode uh you know the change mode why
+ 
+
+ align:start position:0%
+the mode uh you know the change mode why
+oh actually I haven't I'm sorry about
+
+ align:start position:0%
+oh actually I haven't I'm sorry about
+ 
+
+ align:start position:0%
+oh actually I haven't I'm sorry about
+that Why does it matter? Let me go back
+
+ align:start position:0%
+that Why does it matter? Let me go back
+ 
+
+ align:start position:0%
+that Why does it matter? Let me go back
+to this. I think I won't bother with the
+
+ align:start position:0%
+to this. I think I won't bother with the
+ 
+
+ align:start position:0%
+to this. I think I won't bother with the
+slides. What I called mode before was
+
+ align:start position:0%
+slides. What I called mode before was
+ 
+
+ align:start position:0%
+slides. What I called mode before was
+really my energy source. Why does it
+
+ align:start position:0%
+really my energy source. Why does it
+ 
+
+ align:start position:0%
+really my energy source. Why does it
+matter matter whether I'm
+
+ align:start position:0%
+matter matter whether I'm
+ 
+
+ align:start position:0%
+matter matter whether I'm
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+mechanical,
+
+ align:start position:0%
+mechanical,
+ 
+
+ align:start position:0%
+mechanical,
+electrical, thermal or chemical as my
+
+ align:start position:0%
+electrical, thermal or chemical as my
+ 
+
+ align:start position:0%
+electrical, thermal or chemical as my
+change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+agent? What difference does that make?
+
+ align:start position:0%
+agent? What difference does that make?
+ 
+
+ align:start position:0%
+agent? What difference does that make?
+It's just energy,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? And again, back to to lecture
+
+ align:start position:0%
+right? And again, back to to lecture
+ 
+
+ align:start position:0%
+right? And again, back to to lecture
+one, what do we care about in a process?
+
+ align:start position:0%
+one, what do we care about in a process?
+ 
+
+ align:start position:0%
+one, what do we care about in a process?
+Quality number one in this class, but
+
+ align:start position:0%
+Quality number one in this class, but
+ 
+
+ align:start position:0%
+Quality number one in this class, but
+also we worry about rate and we worry
+
+ align:start position:0%
+also we worry about rate and we worry
+ 
+
+ align:start position:0%
+also we worry about rate and we worry
+about cost, we worry about flexibility.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So with respect
+
+ align:start position:0%
+So with respect
+ 
+
+ align:start position:0%
+So with respect
+to which
+
+ align:start position:0%
+to which
+ 
+
+ align:start position:0%
+to which
+energy mode is involved, what difference
+
+ align:start position:0%
+energy mode is involved, what difference
+ 
+
+ align:start position:0%
+energy mode is involved, what difference
+does it make in this in
+
+ align:start position:0%
+does it make in this in
+ 
+
+ align:start position:0%
+does it make in this in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+consideration? Simon, please. Or the way
+
+ align:start position:0%
+consideration? Simon, please. Or the way
+ 
+
+ align:start position:0%
+consideration? Simon, please. Or the way
+we can control the process, we need to
+
+ align:start position:0%
+we can control the process, we need to
+ 
+
+ align:start position:0%
+we can control the process, we need to
+know what energy is involved so we can
+
+ align:start position:0%
+know what energy is involved so we can
+ 
+
+ align:start position:0%
+know what energy is involved so we can
+change. Yeah, sure.
+
+ align:start position:0%
+change. Yeah, sure.
+ 
+
+ align:start position:0%
+change. Yeah, sure.
+Absolutely. So I I would control these
+
+ align:start position:0%
+Absolutely. So I I would control these
+ 
+
+ align:start position:0%
+Absolutely. So I I would control these
+in different ways, right? Uh but let's
+
+ align:start position:0%
+in different ways, right? Uh but let's
+ 
+
+ align:start position:0%
+in different ways, right? Uh but let's
+assume I can do that. I I know how to
+
+ align:start position:0%
+assume I can do that. I I know how to
+ 
+
+ align:start position:0%
+assume I can do that. I I know how to
+control mechanical energy. You know, I
+
+ align:start position:0%
+control mechanical energy. You know, I
+ 
+
+ align:start position:0%
+control mechanical energy. You know, I
+can change forces and displacements and
+
+ align:start position:0%
+can change forces and displacements and
+ 
+
+ align:start position:0%
+can change forces and displacements and
+velocities, electrical, you know,
+
+ align:start position:0%
+velocities, electrical, you know,
+ 
+
+ align:start position:0%
+velocities, electrical, you know,
+currents and voltages. Thermal, I can I
+
+ align:start position:0%
+currents and voltages. Thermal, I can I
+ 
+
+ align:start position:0%
+currents and voltages. Thermal, I can I
+can, you know, that's a little bit
+
+ align:start position:0%
+can, you know, that's a little bit
+ 
+
+ align:start position:0%
+can, you know, that's a little bit
+different. I can certainly control
+
+ align:start position:0%
+different. I can certainly control
+ 
+
+ align:start position:0%
+different. I can certainly control
+temperatures. I can also try to control
+
+ align:start position:0%
+temperatures. I can also try to control
+ 
+
+ align:start position:0%
+temperatures. I can also try to control
+their distributions. I can sometimes
+
+ align:start position:0%
+their distributions. I can sometimes
+ 
+
+ align:start position:0%
+their distributions. I can sometimes
+control heat flux is a little bit harder
+
+ align:start position:0%
+control heat flux is a little bit harder
+ 
+
+ align:start position:0%
+control heat flux is a little bit harder
+to do. And chemical, I can control
+
+ align:start position:0%
+to do. And chemical, I can control
+ 
+
+ align:start position:0%
+to do. And chemical, I can control
+concentrations and temperatures and and
+
+ align:start position:0%
+concentrations and temperatures and and
+ 
+
+ align:start position:0%
+concentrations and temperatures and and
+maybe reaction rates as a result of
+
+ align:start position:0%
+maybe reaction rates as a result of
+ 
+
+ align:start position:0%
+maybe reaction rates as a result of
+that. Yeah. matter of size if you're
+
+ align:start position:0%
+that. Yeah. matter of size if you're
+ 
+
+ align:start position:0%
+that. Yeah. matter of size if you're
+affecting a large area or smaller wafer
+
+ align:start position:0%
+affecting a large area or smaller wafer
+ 
+
+ align:start position:0%
+affecting a large area or smaller wafer
+versus a big stack of door for uh yeah
+
+ align:start position:0%
+versus a big stack of door for uh yeah
+ 
+
+ align:start position:0%
+versus a big stack of door for uh yeah
+that's a
+
+ align:start position:0%
+that's a
+ 
+
+ align:start position:0%
+that's a
+um I thought you were going someplace
+
+ align:start position:0%
+um I thought you were going someplace
+ 
+
+ align:start position:0%
+um I thought you were going someplace
+else with that but yes there is a there
+
+ align:start position:0%
+else with that but yes there is a there
+ 
+
+ align:start position:0%
+else with that but yes there is a there
+is a size scaling but what the example
+
+ align:start position:0%
+is a size scaling but what the example
+ 
+
+ align:start position:0%
+is a size scaling but what the example
+you gave actually though a
+
+ align:start position:0%
+you gave actually though a
+ 
+
+ align:start position:0%
+you gave actually though a
+wafer on in terms of the relative size
+
+ align:start position:0%
+wafer on in terms of the relative size
+ 
+
+ align:start position:0%
+wafer on in terms of the relative size
+of the of the the features that I care
+
+ align:start position:0%
+of the of the the features that I care
+ 
+
+ align:start position:0%
+of the of the the features that I care
+about um is actually huge when you think
+
+ align:start position:0%
+about um is actually huge when you think
+ 
+
+ align:start position:0%
+about um is actually huge when you think
+about a wafer compared to a tiny
+
+ align:start position:0%
+about a wafer compared to a tiny
+ 
+
+ align:start position:0%
+about a wafer compared to a tiny
+submicron line and then I think about a
+
+ align:start position:0%
+submicron line and then I think about a
+ 
+
+ align:start position:0%
+submicron line and then I think about a
+car hood with a little, you know, little
+
+ align:start position:0%
+car hood with a little, you know, little
+ 
+
+ align:start position:0%
+car hood with a little, you know, little
+feature in the middle. The wafer is
+
+ align:start position:0%
+feature in the middle. The wafer is
+ 
+
+ align:start position:0%
+feature in the middle. The wafer is
+actually bigger.
+
+ align:start position:0%
+actually bigger.
+ 
+
+ align:start position:0%
+actually bigger.
+Speaking of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the changes.
+
+ align:start position:0%
+the changes.
+ 
+
+ align:start position:0%
+the changes.
+Yeah. Yeah. Yeah. Yeah. Okay. I think I
+
+ align:start position:0%
+Yeah. Yeah. Yeah. Yeah. Okay. I think I
+ 
+
+ align:start position:0%
+Yeah. Yeah. Yeah. Yeah. Okay. I think I
+think you're getting what to what I what
+
+ align:start position:0%
+think you're getting what to what I what
+ 
+
+ align:start position:0%
+think you're getting what to what I what
+I wanted to do. Let me let me see if I
+
+ align:start position:0%
+I wanted to do. Let me let me see if I
+ 
+
+ align:start position:0%
+I wanted to do. Let me let me see if I
+get any more here and then we'll see.
+
+ align:start position:0%
+get any more here and then we'll see.
+ 
+
+ align:start position:0%
+get any more here and then we'll see.
+The rates are definitely different.
+
+ align:start position:0%
+The rates are definitely different.
+ 
+
+ align:start position:0%
+The rates are definitely different.
+faster than
+
+ align:start position:0%
+faster than
+ 
+
+ align:start position:0%
+faster than
+Yeah. Yeah. Believe it or not, when you
+
+ align:start position:0%
+Yeah. Yeah. Believe it or not, when you
+ 
+
+ align:start position:0%
+Yeah. Yeah. Believe it or not, when you
+think about this, you know, you always
+
+ align:start position:0%
+think about this, you know, you always
+ 
+
+ align:start position:0%
+think about this, you know, you always
+think of electrical, oh, that's that's
+
+ align:start position:0%
+think of electrical, oh, that's that's
+ 
+
+ align:start position:0%
+think of electrical, oh, that's that's
+the gigahertz range, right? And all that
+
+ align:start position:0%
+the gigahertz range, right? And all that
+ 
+
+ align:start position:0%
+the gigahertz range, right? And all that
+kind of stuff. And that's true. If all
+
+ align:start position:0%
+kind of stuff. And that's true. If all
+ 
+
+ align:start position:0%
+kind of stuff. And that's true. If all
+you need to do move is move electrons,
+
+ align:start position:0%
+you need to do move is move electrons,
+ 
+
+ align:start position:0%
+you need to do move is move electrons,
+but we have to move material around
+
+ align:start position:0%
+but we have to move material around
+ 
+
+ align:start position:0%
+but we have to move material around
+here. So, this tends to be very fast. If
+
+ align:start position:0%
+here. So, this tends to be very fast. If
+ 
+
+ align:start position:0%
+here. So, this tends to be very fast. If
+I apply a mechanical load to something,
+
+ align:start position:0%
+I apply a mechanical load to something,
+ 
+
+ align:start position:0%
+I apply a mechanical load to something,
+uh, I can modulate that load pretty fast
+
+ align:start position:0%
+uh, I can modulate that load pretty fast
+ 
+
+ align:start position:0%
+uh, I can modulate that load pretty fast
+these days if I want to. And how long
+
+ align:start position:0%
+these days if I want to. And how long
+ 
+
+ align:start position:0%
+these days if I want to. And how long
+when I when I when when I bring a tool
+
+ align:start position:0%
+when I when I when when I bring a tool
+ 
+
+ align:start position:0%
+when I when I when when I bring a tool
+into a a piece of sheet metal like this,
+
+ align:start position:0%
+into a a piece of sheet metal like this,
+ 
+
+ align:start position:0%
+into a a piece of sheet metal like this,
+how long does it take for this to
+
+ align:start position:0%
+how long does it take for this to
+ 
+
+ align:start position:0%
+how long does it take for this to
+react? Well, essentially at the kinds of
+
+ align:start position:0%
+react? Well, essentially at the kinds of
+ 
+
+ align:start position:0%
+react? Well, essentially at the kinds of
+time scales we're talking about, it
+
+ align:start position:0%
+time scales we're talking about, it
+ 
+
+ align:start position:0%
+time scales we're talking about, it
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+instantaneously. Compare that to how
+
+ align:start position:0%
+instantaneously. Compare that to how
+ 
+
+ align:start position:0%
+instantaneously. Compare that to how
+long it takes to etch something or do
+
+ align:start position:0%
+long it takes to etch something or do
+ 
+
+ align:start position:0%
+long it takes to etch something or do
+certain deposition processes. We're
+
+ align:start position:0%
+certain deposition processes. We're
+ 
+
+ align:start position:0%
+certain deposition processes. We're
+doing these nickelplated
+
+ align:start position:0%
+doing these nickelplated
+ 
+
+ align:start position:0%
+doing these nickelplated
+uh micron scale tools. I just saw a
+
+ align:start position:0%
+uh micron scale tools. I just saw a
+ 
+
+ align:start position:0%
+uh micron scale tools. I just saw a
+presentation last night. you know, three
+
+ align:start position:0%
+presentation last night. you know, three
+ 
+
+ align:start position:0%
+presentation last night. you know, three
+days to make a tool with 50 micron
+
+ align:start position:0%
+days to make a tool with 50 micron
+ 
+
+ align:start position:0%
+days to make a tool with 50 micron
+features on it, you know, that's not
+
+ align:start position:0%
+features on it, you know, that's not
+ 
+
+ align:start position:0%
+features on it, you know, that's not
+what you'd call smoking. Um, so pretty
+
+ align:start position:0%
+what you'd call smoking. Um, so pretty
+ 
+
+ align:start position:0%
+what you'd call smoking. Um, so pretty
+low stuff. So rate that we we could
+
+ align:start position:0%
+low stuff. So rate that we we could
+ 
+
+ align:start position:0%
+low stuff. So rate that we we could
+argue different things. You can have
+
+ align:start position:0%
+argue different things. You can have
+ 
+
+ align:start position:0%
+argue different things. You can have
+fast chemical stuff and so forth and so
+
+ align:start position:0%
+fast chemical stuff and so forth and so
+ 
+
+ align:start position:0%
+fast chemical stuff and so forth and so
+on, but in general there's a speed issue
+
+ align:start position:0%
+on, but in general there's a speed issue
+ 
+
+ align:start position:0%
+on, but in general there's a speed issue
+here. What
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else? That's rate. What about quality?
+
+ align:start position:0%
+else? That's rate. What about quality?
+ 
+
+ align:start position:0%
+else? That's rate. What about quality?
+tolerance is or also side effects of
+
+ align:start position:0%
+tolerance is or also side effects of
+ 
+
+ align:start position:0%
+tolerance is or also side effects of
+Yeah, side effects. I like that. Yeah.
+
+ align:start position:0%
+Yeah, side effects. I like that. Yeah.
+ 
+
+ align:start position:0%
+Yeah, side effects. I like that. Yeah.
+Say a little bit more about side
+
+ align:start position:0%
+Say a little bit more about side
+ 
+
+ align:start position:0%
+Say a little bit more about side
+effects. Well, you got the theoretical
+
+ align:start position:0%
+effects. Well, you got the theoretical
+ 
+
+ align:start position:0%
+effects. Well, you got the theoretical
+maybe I want to cut a perfect square.
+
+ align:start position:0%
+maybe I want to cut a perfect square.
+ 
+
+ align:start position:0%
+maybe I want to cut a perfect square.
+The tool is not going to cut perfectly
+
+ align:start position:0%
+The tool is not going to cut perfectly
+ 
+
+ align:start position:0%
+The tool is not going to cut perfectly
+square edges, right? Depending on what
+
+ align:start position:0%
+square edges, right? Depending on what
+ 
+
+ align:start position:0%
+square edges, right? Depending on what
+process I use, it may have undercutting
+
+ align:start position:0%
+process I use, it may have undercutting
+ 
+
+ align:start position:0%
+process I use, it may have undercutting
+or rounded edges. Absolutely.
+
+ align:start position:0%
+or rounded edges. Absolutely.
+ 
+
+ align:start position:0%
+or rounded edges. Absolutely.
+Absolutely. So, there there's a there's
+
+ align:start position:0%
+Absolutely. So, there there's a there's
+ 
+
+ align:start position:0%
+Absolutely. So, there there's a there's
+a there's something here inherently
+
+ align:start position:0%
+a there's something here inherently
+ 
+
+ align:start position:0%
+a there's something here inherently
+related to quality. Two at least two
+
+ align:start position:0%
+related to quality. Two at least two
+ 
+
+ align:start position:0%
+related to quality. Two at least two
+things that I can think of. One of them
+
+ align:start position:0%
+things that I can think of. One of them
+ 
+
+ align:start position:0%
+things that I can think of. One of them
+is related to what I'll call uh
+
+ align:start position:0%
+is related to what I'll call uh
+ 
+
+ align:start position:0%
+is related to what I'll call uh
+uh diffusivity in in the general sense
+
+ align:start position:0%
+uh diffusivity in in the general sense
+ 
+
+ align:start position:0%
+uh diffusivity in in the general sense
+not just purely in the thermal sense. If
+
+ align:start position:0%
+not just purely in the thermal sense. If
+ 
+
+ align:start position:0%
+not just purely in the thermal sense. If
+I apply a load to something
+
+ align:start position:0%
+I apply a load to something
+ 
+
+ align:start position:0%
+I apply a load to something
+uh as as you're saying if I apply a load
+
+ align:start position:0%
+uh as as you're saying if I apply a load
+ 
+
+ align:start position:0%
+uh as as you're saying if I apply a load
+to something even with a point tool you
+
+ align:start position:0%
+to something even with a point tool you
+ 
+
+ align:start position:0%
+to something even with a point tool you
+know there's a stress field that
+
+ align:start position:0%
+know there's a stress field that
+ 
+
+ align:start position:0%
+know there's a stress field that
+develops in it and that sort of thing
+
+ align:start position:0%
+develops in it and that sort of thing
+ 
+
+ align:start position:0%
+develops in it and that sort of thing
+and I you can this will be a little bit
+
+ align:start position:0%
+and I you can this will be a little bit
+ 
+
+ align:start position:0%
+and I you can this will be a little bit
+fille but I can make an argument that
+
+ align:start position:0%
+fille but I can make an argument that
+ 
+
+ align:start position:0%
+fille but I can make an argument that
+says okay if I apply that load to here
+
+ align:start position:0%
+says okay if I apply that load to here
+ 
+
+ align:start position:0%
+says okay if I apply that load to here
+it diffuses and so I I wanted to put the
+
+ align:start position:0%
+it diffuses and so I I wanted to put the
+ 
+
+ align:start position:0%
+it diffuses and so I I wanted to put the
+load in in a in a in a tiny point but it
+
+ align:start position:0%
+load in in a in a in a tiny point but it
+ 
+
+ align:start position:0%
+load in in a in a in a tiny point but it
+actually spread out and so I didn't get
+
+ align:start position:0%
+actually spread out and so I didn't get
+ 
+
+ align:start position:0%
+actually spread out and so I didn't get
+exactly what we want. How about if I put
+
+ align:start position:0%
+exactly what we want. How about if I put
+ 
+
+ align:start position:0%
+exactly what we want. How about if I put
+a thermal source in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there? Yeah. And and the worst part is
+
+ align:start position:0%
+there? Yeah. And and the worst part is
+ 
+
+ align:start position:0%
+there? Yeah. And and the worst part is
+not only does it does it dissipate, it
+
+ align:start position:0%
+not only does it does it dissipate, it
+ 
+
+ align:start position:0%
+not only does it does it dissipate, it
+just keeps dissipating. You know, it
+
+ align:start position:0%
+just keeps dissipating. You know, it
+ 
+
+ align:start position:0%
+just keeps dissipating. You know, it
+probably never reaches equilibrium. So,
+
+ align:start position:0%
+probably never reaches equilibrium. So,
+ 
+
+ align:start position:0%
+probably never reaches equilibrium. So,
+it's really going How about chemical uh
+
+ align:start position:0%
+it's really going How about chemical uh
+ 
+
+ align:start position:0%
+it's really going How about chemical uh
+a chemical reaction. You
+
+ align:start position:0%
+a chemical reaction. You
+ 
+
+ align:start position:0%
+a chemical reaction. You
+know, you know, one of the one of the
+
+ align:start position:0%
+know, you know, one of the one of the
+ 
+
+ align:start position:0%
+know, you know, one of the one of the
+problems we have with that, of course,
+
+ align:start position:0%
+problems we have with that, of course,
+ 
+
+ align:start position:0%
+problems we have with that, of course,
+is the if you do thick etching, you have
+
+ align:start position:0%
+is the if you do thick etching, you have
+ 
+
+ align:start position:0%
+is the if you do thick etching, you have
+undercutting because it don't go there,
+
+ align:start position:0%
+undercutting because it don't go there,
+ 
+
+ align:start position:0%
+undercutting because it don't go there,
+but it's going there. You know, it wants
+
+ align:start position:0%
+but it's going there. You know, it wants
+ 
+
+ align:start position:0%
+but it's going there. You know, it wants
+to go everywhere and other things like
+
+ align:start position:0%
+to go everywhere and other things like
+ 
+
+ align:start position:0%
+to go everywhere and other things like
+that. So, again, you have different
+
+ align:start position:0%
+that. So, again, you have different
+ 
+
+ align:start position:0%
+that. So, again, you have different
+diffusion characteristics here depending
+
+ align:start position:0%
+diffusion characteristics here depending
+ 
+
+ align:start position:0%
+diffusion characteristics here depending
+on what's uh going on. So your ability
+
+ align:start position:0%
+on what's uh going on. So your ability
+ 
+
+ align:start position:0%
+on what's uh going on. So your ability
+to control the shape to get a minimum
+
+ align:start position:0%
+to control the shape to get a minimum
+ 
+
+ align:start position:0%
+to control the shape to get a minimum
+feature size to get a level of precision
+
+ align:start position:0%
+feature size to get a level of precision
+ 
+
+ align:start position:0%
+feature size to get a level of precision
+will vary depending on what you have
+
+ align:start position:0%
+will vary depending on what you have
+ 
+
+ align:start position:0%
+will vary depending on what you have
+here. Um and what else do you think is
+
+ align:start position:0%
+here. Um and what else do you think is
+ 
+
+ align:start position:0%
+here. Um and what else do you think is
+important to quality? Obviously my
+
+ align:start position:0%
+important to quality? Obviously my
+ 
+
+ align:start position:0%
+important to quality? Obviously my
+ability to
+
+ align:start position:0%
+ability to
+ 
+
+ align:start position:0%
+ability to
+um sort of direct things exactly where I
+
+ align:start position:0%
+um sort of direct things exactly where I
+ 
+
+ align:start position:0%
+um sort of direct things exactly where I
+want them to be is important. What else
+
+ align:start position:0%
+want them to be is important. What else
+ 
+
+ align:start position:0%
+want them to be is important. What else
+do you think is important to quality? Um
+
+ align:start position:0%
+do you think is important to quality? Um
+ 
+
+ align:start position:0%
+do you think is important to quality? Um
+how about um repeatability?
+
+ align:start position:0%
+how about um repeatability?
+ 
+
+ align:start position:0%
+how about um repeatability?
+Yeah. Sort of the how how um well I can
+
+ align:start position:0%
+Yeah. Sort of the how how um well I can
+ 
+
+ align:start position:0%
+Yeah. Sort of the how how um well I can
+repeatedly apply this energy and have
+
+ align:start position:0%
+repeatedly apply this energy and have
+ 
+
+ align:start position:0%
+repeatedly apply this energy and have
+the same thing happen. Yeah. And that
+
+ align:start position:0%
+the same thing happen. Yeah. And that
+ 
+
+ align:start position:0%
+the same thing happen. Yeah. And that
+will vary uh again depending on the
+
+ align:start position:0%
+will vary uh again depending on the
+ 
+
+ align:start position:0%
+will vary uh again depending on the
+nature of the interfaces here. You know
+
+ align:start position:0%
+nature of the interfaces here. You know
+ 
+
+ align:start position:0%
+nature of the interfaces here. You know
+for example um if thermal conductivity
+
+ align:start position:0%
+for example um if thermal conductivity
+ 
+
+ align:start position:0%
+for example um if thermal conductivity
+is a big part of it and you're
+
+ align:start position:0%
+is a big part of it and you're
+ 
+
+ align:start position:0%
+is a big part of it and you're
+continually bringing new material into
+
+ align:start position:0%
+continually bringing new material into
+ 
+
+ align:start position:0%
+continually bringing new material into
+contact with an old tool it could be a
+
+ align:start position:0%
+contact with an old tool it could be a
+ 
+
+ align:start position:0%
+contact with an old tool it could be a
+different heat transfer coefficient
+
+ align:start position:0%
+different heat transfer coefficient
+ 
+
+ align:start position:0%
+different heat transfer coefficient
+every time. Um, in mechanical cases, if
+
+ align:start position:0%
+every time. Um, in mechanical cases, if
+ 
+
+ align:start position:0%
+every time. Um, in mechanical cases, if
+I'm always coming back with the same
+
+ align:start position:0%
+I'm always coming back with the same
+ 
+
+ align:start position:0%
+I'm always coming back with the same
+tool except for long-term wear, maybe
+
+ align:start position:0%
+tool except for long-term wear, maybe
+ 
+
+ align:start position:0%
+tool except for long-term wear, maybe
+it's a little bit more uh maybe it's a
+
+ align:start position:0%
+it's a little bit more uh maybe it's a
+ 
+
+ align:start position:0%
+it's a little bit more uh maybe it's a
+little bit more
+
+ align:start position:0%
+little bit more
+ 
+
+ align:start position:0%
+little bit more
+repeatable.
+
+ align:start position:0%
+repeatable.
+ 
+
+ align:start position:0%
+repeatable.
+Um, there's one other aspect to it. Now,
+
+ align:start position:0%
+Um, there's one other aspect to it. Now,
+ 
+
+ align:start position:0%
+Um, there's one other aspect to it. Now,
+now think a little bit more about where
+
+ align:start position:0%
+now think a little bit more about where
+ 
+
+ align:start position:0%
+now think a little bit more about where
+we're going with the class with things
+
+ align:start position:0%
+we're going with the class with things
+ 
+
+ align:start position:0%
+we're going with the class with things
+like statistical process control, which
+
+ align:start position:0%
+like statistical process control, which
+ 
+
+ align:start position:0%
+like statistical process control, which
+says, let's find out things that are not
+
+ align:start position:0%
+says, let's find out things that are not
+ 
+
+ align:start position:0%
+says, let's find out things that are not
+quite right with the process and fix
+
+ align:start position:0%
+quite right with the process and fix
+ 
+
+ align:start position:0%
+quite right with the process and fix
+them, and that will improve our quality.
+
+ align:start position:0%
+them, and that will improve our quality.
+ 
+
+ align:start position:0%
+them, and that will improve our quality.
+and and then in uh the more active
+
+ align:start position:0%
+and and then in uh the more active
+ 
+
+ align:start position:0%
+and and then in uh the more active
+process optimization stuff where we say
+
+ align:start position:0%
+process optimization stuff where we say
+ 
+
+ align:start position:0%
+process optimization stuff where we say
+let's adjust things until they're really
+
+ align:start position:0%
+let's adjust things until they're really
+ 
+
+ align:start position:0%
+let's adjust things until they're really
+right. And then we actually at the end
+
+ align:start position:0%
+right. And then we actually at the end
+ 
+
+ align:start position:0%
+right. And then we actually at the end
+we'll talk a little bit about active
+
+ align:start position:0%
+we'll talk a little bit about active
+ 
+
+ align:start position:0%
+we'll talk a little bit about active
+control where you're continually
+
+ align:start position:0%
+control where you're continually
+ 
+
+ align:start position:0%
+control where you're continually
+adjusting. But think of it this
+
+ align:start position:0%
+adjusting. But think of it this
+ 
+
+ align:start position:0%
+adjusting. But think of it this
+way because this is where you you you
+
+ align:start position:0%
+way because this is where you you you
+ 
+
+ align:start position:0%
+way because this is where you you you
+will be thinking about this. Here's the
+
+ align:start position:0%
+will be thinking about this. Here's the
+ 
+
+ align:start position:0%
+will be thinking about this. Here's the
+process. I just measured its result.
+
+ align:start position:0%
+process. I just measured its result.
+ 
+
+ align:start position:0%
+process. I just measured its result.
+It's not good
+
+ align:start position:0%
+It's not good
+ 
+
+ align:start position:0%
+It's not good
+enough. I need to improve its quality
+
+ align:start position:0%
+enough. I need to improve its quality
+ 
+
+ align:start position:0%
+enough. I need to improve its quality
+and I can't go buy a new machine.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So don't So I have to have the ability
+
+ align:start position:0%
+So don't So I have to have the ability
+ 
+
+ align:start position:0%
+So don't So I have to have the ability
+to adjust something, right? I have to
+
+ align:start position:0%
+to adjust something, right? I have to
+ 
+
+ align:start position:0%
+to adjust something, right? I have to
+have the ability to change something. So
+
+ align:start position:0%
+have the ability to change something. So
+ 
+
+ align:start position:0%
+have the ability to change something. So
+think about what it takes to change
+
+ align:start position:0%
+think about what it takes to change
+ 
+
+ align:start position:0%
+think about what it takes to change
+these just as I was saying before with
+
+ align:start position:0%
+these just as I was saying before with
+ 
+
+ align:start position:0%
+these just as I was saying before with
+the rolling pace in the uh in that.
+
+ align:start position:0%
+the rolling pace in the uh in that.
+ 
+
+ align:start position:0%
+the rolling pace in the uh in that.
+Yeah, go ahead. I think for some
+
+ align:start position:0%
+Yeah, go ahead. I think for some
+ 
+
+ align:start position:0%
+Yeah, go ahead. I think for some
+mechanical uh process, it's easier to
+
+ align:start position:0%
+mechanical uh process, it's easier to
+ 
+
+ align:start position:0%
+mechanical uh process, it's easier to
+stop, but for the chemical thermal uh if
+
+ align:start position:0%
+stop, but for the chemical thermal uh if
+ 
+
+ align:start position:0%
+stop, but for the chemical thermal uh if
+you uh even you you know the problem,
+
+ align:start position:0%
+you uh even you you know the problem,
+ 
+
+ align:start position:0%
+you uh even you you know the problem,
+you can hard to stop the process. It's
+
+ align:start position:0%
+you can hard to stop the process. It's
+ 
+
+ align:start position:0%
+you can hard to stop the process. It's
+hard to stop it. I mean, I'm not trying
+
+ align:start position:0%
+hard to stop it. I mean, I'm not trying
+ 
+
+ align:start position:0%
+hard to stop it. I mean, I'm not trying
+to come up with winners and losers here,
+
+ align:start position:0%
+to come up with winners and losers here,
+ 
+
+ align:start position:0%
+to come up with winners and losers here,
+uh, because they all have advantages and
+
+ align:start position:0%
+uh, because they all have advantages and
+ 
+
+ align:start position:0%
+uh, because they all have advantages and
+disadvantages, but you're absolutely
+
+ align:start position:0%
+disadvantages, but you're absolutely
+ 
+
+ align:start position:0%
+disadvantages, but you're absolutely
+right. There are big differences, right?
+
+ align:start position:0%
+right. There are big differences, right?
+ 
+
+ align:start position:0%
+right. There are big differences, right?
+If if, for example, there's a time
+
+ align:start position:0%
+If if, for example, there's a time
+ 
+
+ align:start position:0%
+If if, for example, there's a time
+aspect to it mechanically, and I can
+
+ align:start position:0%
+aspect to it mechanically, and I can
+ 
+
+ align:start position:0%
+aspect to it mechanically, and I can
+pull that force off and it it goes away.
+
+ align:start position:0%
+pull that force off and it it goes away.
+ 
+
+ align:start position:0%
+pull that force off and it it goes away.
+There's not there's a wave that goes
+
+ align:start position:0%
+There's not there's a wave that goes
+ 
+
+ align:start position:0%
+There's not there's a wave that goes
+through the material, but it it it goes
+
+ align:start position:0%
+through the material, but it it it goes
+ 
+
+ align:start position:0%
+through the material, but it it it goes
+at at sonic rates. You know, uh, the
+
+ align:start position:0%
+at at sonic rates. You know, uh, the
+ 
+
+ align:start position:0%
+at at sonic rates. You know, uh, the
+thermal could take a long time to change
+
+ align:start position:0%
+thermal could take a long time to change
+ 
+
+ align:start position:0%
+thermal could take a long time to change
+anything there. And certainly the
+
+ align:start position:0%
+anything there. And certainly the
+ 
+
+ align:start position:0%
+anything there. And certainly the
+chemical um uh depending on scale could
+
+ align:start position:0%
+chemical um uh depending on scale could
+ 
+
+ align:start position:0%
+chemical um uh depending on scale could
+be like that too. Okay. So it is
+
+ align:start position:0%
+be like that too. Okay. So it is
+ 
+
+ align:start position:0%
+be like that too. Okay. So it is
+important to know what these different
+
+ align:start position:0%
+important to know what these different
+ 
+
+ align:start position:0%
+important to know what these different
+energy sources are if only to say
+
+ align:start position:0%
+energy sources are if only to say
+ 
+
+ align:start position:0%
+energy sources are if only to say
+okay these types of things are more
+
+ align:start position:0%
+okay these types of things are more
+ 
+
+ align:start position:0%
+okay these types of things are more
+important when you're really faced with
+
+ align:start position:0%
+important when you're really faced with
+ 
+
+ align:start position:0%
+important when you're really faced with
+the decision of what's the best I could
+
+ align:start position:0%
+the decision of what's the best I could
+ 
+
+ align:start position:0%
+the decision of what's the best I could
+ever expect this process to do. I've
+
+ align:start position:0%
+ever expect this process to do. I've
+ 
+
+ align:start position:0%
+ever expect this process to do. I've
+I've worked I've done SPC I've done
+
+ align:start position:0%
+I've worked I've done SPC I've done
+ 
+
+ align:start position:0%
+I've worked I've done SPC I've done
+process optimization. There's a
+
+ align:start position:0%
+process optimization. There's a
+ 
+
+ align:start position:0%
+process optimization. There's a
+fundamental limitation because it uses
+
+ align:start position:0%
+fundamental limitation because it uses
+ 
+
+ align:start position:0%
+fundamental limitation because it uses
+mechanical energy. I'll never be able to
+
+ align:start position:0%
+mechanical energy. I'll never be able to
+ 
+
+ align:start position:0%
+mechanical energy. I'll never be able to
+do the following or or so on.
+
+ align:start position:0%
+do the following or or so on.
+ 
+
+ align:start position:0%
+do the following or or so on.
+Okay, so you have these types of things
+
+ align:start position:0%
+Okay, so you have these types of things
+ 
+
+ align:start position:0%
+Okay, so you have these types of things
+interacting with how we apply them. Um,
+
+ align:start position:0%
+interacting with how we apply them. Um,
+ 
+
+ align:start position:0%
+interacting with how we apply them. Um,
+and of course it it's you could say it's
+
+ align:start position:0%
+and of course it it's you could say it's
+ 
+
+ align:start position:0%
+and of course it it's you could say it's
+impossible to use all these in all their
+
+ align:start position:0%
+impossible to use all these in all their
+ 
+
+ align:start position:0%
+impossible to use all these in all their
+different ways, but actually that's not
+
+ align:start position:0%
+different ways, but actually that's not
+ 
+
+ align:start position:0%
+different ways, but actually that's not
+entirely true.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+so kind of said all that. So let's go
+
+ align:start position:0%
+so kind of said all that. So let's go
+ 
+
+ align:start position:0%
+so kind of said all that. So let's go
+on. Now this eye chart um is an attempt
+
+ align:start position:0%
+on. Now this eye chart um is an attempt
+ 
+
+ align:start position:0%
+on. Now this eye chart um is an attempt
+to take this entire taxonomy and then
+
+ align:start position:0%
+to take this entire taxonomy and then
+ 
+
+ align:start position:0%
+to take this entire taxonomy and then
+just populate it. uh this chart with
+
+ align:start position:0%
+just populate it. uh this chart with
+ 
+
+ align:start position:0%
+just populate it. uh this chart with
+um some
+
+ align:start position:0%
+um some
+ 
+
+ align:start position:0%
+um some
+examples, you know, and some of these
+
+ align:start position:0%
+examples, you know, and some of these
+ 
+
+ align:start position:0%
+examples, you know, and some of these
+are are are no-brainers and some of them
+
+ align:start position:0%
+are are are no-brainers and some of them
+ 
+
+ align:start position:0%
+are are are no-brainers and some of them
+could be a little bit controversial. But
+
+ align:start position:0%
+could be a little bit controversial. But
+ 
+
+ align:start position:0%
+could be a little bit controversial. But
+so what this says is, you know, across
+
+ align:start position:0%
+so what this says is, you know, across
+ 
+
+ align:start position:0%
+so what this says is, you know, across
+here, this is the the removal mode of
+
+ align:start position:0%
+here, this is the the removal mode of
+ 
+
+ align:start position:0%
+here, this is the the removal mode of
+transformation and here's a addition and
+
+ align:start position:0%
+transformation and here's a addition and
+ 
+
+ align:start position:0%
+transformation and here's a addition and
+here's formation and here's deformation
+
+ align:start position:0%
+here's formation and here's deformation
+ 
+
+ align:start position:0%
+here's formation and here's deformation
+and in each case then it's divided in
+
+ align:start position:0%
+and in each case then it's divided in
+ 
+
+ align:start position:0%
+and in each case then it's divided in
+half with serial and parallel and then
+
+ align:start position:0%
+half with serial and parallel and then
+ 
+
+ align:start position:0%
+half with serial and parallel and then
+four different energy sources. So you
+
+ align:start position:0%
+four different energy sources. So you
+ 
+
+ align:start position:0%
+four different energy sources. So you
+look at each one and say okay where
+
+ align:start position:0%
+look at each one and say okay where
+ 
+
+ align:start position:0%
+look at each one and say okay where
+where's my favorite process you know so
+
+ align:start position:0%
+where's my favorite process you know so
+ 
+
+ align:start position:0%
+where's my favorite process you know so
+serial
+
+ align:start position:0%
+serial
+ 
+
+ align:start position:0%
+serial
+removal mechanical cutting grinding
+
+ align:start position:0%
+removal mechanical cutting grinding
+ 
+
+ align:start position:0%
+removal mechanical cutting grinding
+brooing polishing water jet right water
+
+ align:start position:0%
+brooing polishing water jet right water
+ 
+
+ align:start position:0%
+brooing polishing water jet right water
+jet is mechanical it's be fluid
+
+ align:start position:0%
+jet is mechanical it's be fluid
+ 
+
+ align:start position:0%
+jet is mechanical it's be fluid
+mechanical but it's mechanical
+
+ align:start position:0%
+mechanical but it's mechanical
+ 
+
+ align:start position:0%
+mechanical but it's mechanical
+electrical serial wire EDM take a single
+
+ align:start position:0%
+electrical serial wire EDM take a single
+ 
+
+ align:start position:0%
+electrical serial wire EDM take a single
+skinny little wire drill a hole
+
+ align:start position:0%
+skinny little wire drill a hole
+ 
+
+ align:start position:0%
+skinny little wire drill a hole
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+that put a whole bunch of them together
+
+ align:start position:0%
+that put a whole bunch of them together
+ 
+
+ align:start position:0%
+that put a whole bunch of them together
+do it all at once say with a with a
+
+ align:start position:0%
+do it all at once say with a with a
+ 
+
+ align:start position:0%
+do it all at once say with a with a
+formed electrode code. Now, it's
+
+ align:start position:0%
+formed electrode code. Now, it's
+ 
+
+ align:start position:0%
+formed electrode code. Now, it's
+parallel EDM. Um,
+
+ align:start position:0%
+parallel EDM. Um,
+ 
+
+ align:start position:0%
+parallel EDM. Um,
+photoiththography with a with an with a
+
+ align:start position:0%
+photoiththography with a with an with a
+ 
+
+ align:start position:0%
+photoiththography with a with an with a
+wet etch, if you want to think of it
+
+ align:start position:0%
+wet etch, if you want to think of it
+ 
+
+ align:start position:0%
+wet etch, if you want to think of it
+that way, is basically a parallel
+
+ align:start position:0%
+that way, is basically a parallel
+ 
+
+ align:start position:0%
+that way, is basically a parallel
+process. It's it's etching everywhere at
+
+ align:start position:0%
+process. It's it's etching everywhere at
+ 
+
+ align:start position:0%
+process. It's it's etching everywhere at
+once, but you just happen to put a mask
+
+ align:start position:0%
+once, but you just happen to put a mask
+ 
+
+ align:start position:0%
+once, but you just happen to put a mask
+in a few places. That's your tool. So,
+
+ align:start position:0%
+in a few places. That's your tool. So,
+ 
+
+ align:start position:0%
+in a few places. That's your tool. So,
+that it can't or I'm sorry, resist.
+
+ align:start position:0%
+that it can't or I'm sorry, resist.
+ 
+
+ align:start position:0%
+that it can't or I'm sorry, resist.
+Um, uh, I think Dwayne has already
+
+ align:start position:0%
+Um, uh, I think Dwayne has already
+ 
+
+ align:start position:0%
+Um, uh, I think Dwayne has already
+talked about chemical mechanical
+
+ align:start position:0%
+talked about chemical mechanical
+ 
+
+ align:start position:0%
+talked about chemical mechanical
+polishing, which I'm told by the experts
+
+ align:start position:0%
+polishing, which I'm told by the experts
+ 
+
+ align:start position:0%
+polishing, which I'm told by the experts
+in the field is really mechanical
+
+ align:start position:0%
+in the field is really mechanical
+ 
+
+ align:start position:0%
+in the field is really mechanical
+polishing, right? So, if we take the C
+
+ align:start position:0%
+polishing, right? So, if we take the C
+ 
+
+ align:start position:0%
+polishing, right? So, if we take the C
+off of there, then CMP is a mechanical
+
+ align:start position:0%
+off of there, then CMP is a mechanical
+ 
+
+ align:start position:0%
+off of there, then CMP is a mechanical
+parallel process. If it's chemical
+
+ align:start position:0%
+parallel process. If it's chemical
+ 
+
+ align:start position:0%
+parallel process. If it's chemical
+mechanical process, then I guess it has
+
+ align:start position:0%
+mechanical process, then I guess it has
+ 
+
+ align:start position:0%
+mechanical process, then I guess it has
+to show up in both of them. Which is it?
+
+ align:start position:0%
+to show up in both of them. Which is it?
+ 
+
+ align:start position:0%
+to show up in both of them. Which is it?
+Is it both? The chemistry softens the
+
+ align:start position:0%
+Is it both? The chemistry softens the
+ 
+
+ align:start position:0%
+Is it both? The chemistry softens the
+surface enough.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. But the chemical by itself would
+
+ align:start position:0%
+Okay. But the chemical by itself would
+ 
+
+ align:start position:0%
+Okay. But the chemical by itself would
+not remove any material. Okay.
+
+ align:start position:0%
+not remove any material. Okay.
+ 
+
+ align:start position:0%
+not remove any material. Okay.
+Chemically assisted mechanical
+
+ align:start position:0%
+Chemically assisted mechanical
+ 
+
+ align:start position:0%
+Chemically assisted mechanical
+processing. Okay. And strangely enough,
+
+ align:start position:0%
+processing. Okay. And strangely enough,
+ 
+
+ align:start position:0%
+processing. Okay. And strangely enough,
+the brazing by itself would not remove
+
+ align:start position:0%
+the brazing by itself would not remove
+ 
+
+ align:start position:0%
+the brazing by itself would not remove
+any material any at all.
+
+ align:start position:0%
+any material any at all.
+ 
+
+ align:start position:0%
+any material any at all.
+Interesting.
+
+ align:start position:0%
+Interesting.
+ 
+
+ align:start position:0%
+Interesting.
+Okay. Well, that's actually an example
+
+ align:start position:0%
+Okay. Well, that's actually an example
+ 
+
+ align:start position:0%
+Okay. Well, that's actually an example
+here of where the chemical part is
+
+ align:start position:0%
+here of where the chemical part is
+ 
+
+ align:start position:0%
+here of where the chemical part is
+actually affecting
+
+ align:start position:0%
+actually affecting
+ 
+
+ align:start position:0%
+actually affecting
+properties. Not unusual. So this is
+
+ align:start position:0%
+properties. Not unusual. So this is
+ 
+
+ align:start position:0%
+properties. Not unusual. So this is
+still true if I'm only talking about the
+
+ align:start position:0%
+still true if I'm only talking about the
+ 
+
+ align:start position:0%
+still true if I'm only talking about the
+uh the the uh rem
+
+ align:start position:0%
+uh the the uh rem
+ 
+
+ align:start position:0%
+uh the the uh rem
+uh the geometry change part of it. Yeah.
+
+ align:start position:0%
+uh the geometry change part of it. Yeah.
+ 
+
+ align:start position:0%
+uh the geometry change part of it. Yeah.
+Um there's a bunch of other ones here.
+
+ align:start position:0%
+Um there's a bunch of other ones here.
+ 
+
+ align:start position:0%
+Um there's a bunch of other ones here.
+One of the interesting things is uh if
+
+ align:start position:0%
+One of the interesting things is uh if
+ 
+
+ align:start position:0%
+One of the interesting things is uh if
+you come over here to something like hot
+
+ align:start position:0%
+you come over here to something like hot
+ 
+
+ align:start position:0%
+you come over here to something like hot
+isostatic pressing a powder metal powder
+
+ align:start position:0%
+isostatic pressing a powder metal powder
+ 
+
+ align:start position:0%
+isostatic pressing a powder metal powder
+metallurgy or powder ceramic process
+
+ align:start position:0%
+metallurgy or powder ceramic process
+ 
+
+ align:start position:0%
+metallurgy or powder ceramic process
+where you take you know uniform powders
+
+ align:start position:0%
+where you take you know uniform powders
+ 
+
+ align:start position:0%
+where you take you know uniform powders
+and compress them in a mold. So that's
+
+ align:start position:0%
+and compress them in a mold. So that's
+ 
+
+ align:start position:0%
+and compress them in a mold. So that's
+obviously an addition process. And then
+
+ align:start position:0%
+obviously an addition process. And then
+ 
+
+ align:start position:0%
+obviously an addition process. And then
+I cinch them and then I do other stuff
+
+ align:start position:0%
+I cinch them and then I do other stuff
+ 
+
+ align:start position:0%
+I cinch them and then I do other stuff
+to it. And I do it all at once in a in a
+
+ align:start position:0%
+to it. And I do it all at once in a in a
+ 
+
+ align:start position:0%
+to it. And I do it all at once in a in a
+in a form tool, a can. Um, and I'm all
+
+ align:start position:0%
+in a form tool, a can. Um, and I'm all
+ 
+
+ align:start position:0%
+in a form tool, a can. Um, and I'm all
+set.
+
+ align:start position:0%
+set.
+ 
+
+ align:start position:0%
+set.
+Um, that's clearly clearly clearly a
+
+ align:start position:0%
+Um, that's clearly clearly clearly a
+ 
+
+ align:start position:0%
+Um, that's clearly clearly clearly a
+parallel process and the result depends
+
+ align:start position:0%
+parallel process and the result depends
+ 
+
+ align:start position:0%
+parallel process and the result depends
+primarily on the shape of the can.
+
+ align:start position:0%
+primarily on the shape of the can.
+ 
+
+ align:start position:0%
+primarily on the shape of the can.
+Um then uh Ellie Saxs at MIT kind of
+
+ align:start position:0%
+Um then uh Ellie Saxs at MIT kind of
+ 
+
+ align:start position:0%
+Um then uh Ellie Saxs at MIT kind of
+invented this process called 3D
+
+ align:start position:0%
+invented this process called 3D
+ 
+
+ align:start position:0%
+invented this process called 3D
+printing. And if you look at 3D
+
+ align:start position:0%
+printing. And if you look at 3D
+ 
+
+ align:start position:0%
+printing. And if you look at 3D
+printing, it's it's not exactly this,
+
+ align:start position:0%
+printing, it's it's not exactly this,
+ 
+
+ align:start position:0%
+printing, it's it's not exactly this,
+but it's essentially the same as saying,
+
+ align:start position:0%
+but it's essentially the same as saying,
+ 
+
+ align:start position:0%
+but it's essentially the same as saying,
+okay, I'm going to uh put down each
+
+ align:start position:0%
+okay, I'm going to uh put down each
+ 
+
+ align:start position:0%
+okay, I'm going to uh put down each
+piece of that powder one piece at a
+
+ align:start position:0%
+piece of that powder one piece at a
+ 
+
+ align:start position:0%
+piece of that powder one piece at a
+time. He does it by joining the powder
+
+ align:start position:0%
+time. He does it by joining the powder
+ 
+
+ align:start position:0%
+time. He does it by joining the powder
+one drop at a time. He puts a binder on
+
+ align:start position:0%
+one drop at a time. He puts a binder on
+ 
+
+ align:start position:0%
+one drop at a time. He puts a binder on
+it. Instead of binding it all at once,
+
+ align:start position:0%
+it. Instead of binding it all at once,
+ 
+
+ align:start position:0%
+it. Instead of binding it all at once,
+he puts a drop down at a time. It's an
+
+ align:start position:0%
+he puts a drop down at a time. It's an
+ 
+
+ align:start position:0%
+he puts a drop down at a time. It's an
+inkjet type process. Um, now it becomes
+
+ align:start position:0%
+inkjet type process. Um, now it becomes
+ 
+
+ align:start position:0%
+inkjet type process. Um, now it becomes
+a serial process. And think about the
+
+ align:start position:0%
+a serial process. And think about the
+ 
+
+ align:start position:0%
+a serial process. And think about the
+difference between these two processes.
+
+ align:start position:0%
+difference between these two processes.
+ 
+
+ align:start position:0%
+difference between these two processes.
+You know, if I've got this big press
+
+ align:start position:0%
+You know, if I've got this big press
+ 
+
+ align:start position:0%
+You know, if I've got this big press
+that has to push this this powder into a
+
+ align:start position:0%
+that has to push this this powder into a
+ 
+
+ align:start position:0%
+that has to push this this powder into a
+green compact, um, big piece of
+
+ align:start position:0%
+green compact, um, big piece of
+ 
+
+ align:start position:0%
+green compact, um, big piece of
+equipment, got to have an expensive
+
+ align:start position:0%
+equipment, got to have an expensive
+ 
+
+ align:start position:0%
+equipment, got to have an expensive
+tool. Whereas this 3D printing, you
+
+ align:start position:0%
+tool. Whereas this 3D printing, you
+ 
+
+ align:start position:0%
+tool. Whereas this 3D printing, you
+know, it's a desktop thing. There are
+
+ align:start position:0%
+know, it's a desktop thing. There are
+ 
+
+ align:start position:0%
+know, it's a desktop thing. There are
+desktop versions of it. Desktop thing.
+
+ align:start position:0%
+desktop versions of it. Desktop thing.
+ 
+
+ align:start position:0%
+desktop versions of it. Desktop thing.
+All I have to do is type in a a CAD
+
+ align:start position:0%
+All I have to do is type in a a CAD
+ 
+
+ align:start position:0%
+All I have to do is type in a a CAD
+file. It does a section
+
+ align:start position:0%
+file. It does a section
+ 
+
+ align:start position:0%
+file. It does a section
+file of it. It creates this thing and
+
+ align:start position:0%
+file of it. It creates this thing and
+ 
+
+ align:start position:0%
+file of it. It creates this thing and
+I've got essentially equivalent parts.
+
+ align:start position:0%
+I've got essentially equivalent parts.
+ 
+
+ align:start position:0%
+I've got essentially equivalent parts.
+Not exactly equivalent, centrally
+
+ align:start position:0%
+Not exactly equivalent, centrally
+ 
+
+ align:start position:0%
+Not exactly equivalent, centrally
+equivalent parts. So clearly this serial
+
+ align:start position:0%
+equivalent parts. So clearly this serial
+ 
+
+ align:start position:0%
+equivalent parts. So clearly this serial
+process is much more
+
+ align:start position:0%
+process is much more
+ 
+
+ align:start position:0%
+process is much more
+flexible. Really great. And I
+
+ align:start position:0%
+flexible. Really great. And I
+ 
+
+ align:start position:0%
+flexible. Really great. And I
+probably can control the quality better
+
+ align:start position:0%
+probably can control the quality better
+ 
+
+ align:start position:0%
+probably can control the quality better
+because if it's not quite right, I just
+
+ align:start position:0%
+because if it's not quite right, I just
+ 
+
+ align:start position:0%
+because if it's not quite right, I just
+change the program a little bit. Right?
+
+ align:start position:0%
+change the program a little bit. Right?
+ 
+
+ align:start position:0%
+change the program a little bit. Right?
+It was a little bit too wide. The last
+
+ align:start position:0%
+It was a little bit too wide. The last
+ 
+
+ align:start position:0%
+It was a little bit too wide. The last
+one I made, I said, "Well, let's let's
+
+ align:start position:0%
+one I made, I said, "Well, let's let's
+ 
+
+ align:start position:0%
+one I made, I said, "Well, let's let's
+reprogram the geometry and bring it in a
+
+ align:start position:0%
+reprogram the geometry and bring it in a
+ 
+
+ align:start position:0%
+reprogram the geometry and bring it in a
+little bit." And it just doesn't.
+
+ align:start position:0%
+little bit." And it just doesn't.
+ 
+
+ align:start position:0%
+little bit." And it just doesn't.
+Whereas, if I'm doing the hot isoatic
+
+ align:start position:0%
+Whereas, if I'm doing the hot isoatic
+ 
+
+ align:start position:0%
+Whereas, if I'm doing the hot isoatic
+pressing, I've got this big expensive
+
+ align:start position:0%
+pressing, I've got this big expensive
+ 
+
+ align:start position:0%
+pressing, I've got this big expensive
+tool and it's not quite right and I
+
+ align:start position:0%
+tool and it's not quite right and I
+ 
+
+ align:start position:0%
+tool and it's not quite right and I
+can't heat it and cool it like I did
+
+ align:start position:0%
+can't heat it and cool it like I did
+ 
+
+ align:start position:0%
+can't heat it and cool it like I did
+with the the uh the rolls on the
+
+ align:start position:0%
+with the the uh the rolls on the
+ 
+
+ align:start position:0%
+with the the uh the rolls on the
+aluminum. I'm kind of stuck with it.
+
+ align:start position:0%
+aluminum. I'm kind of stuck with it.
+ 
+
+ align:start position:0%
+aluminum. I'm kind of stuck with it.
+Right. So, why would anybody do HIP when
+
+ align:start position:0%
+Right. So, why would anybody do HIP when
+ 
+
+ align:start position:0%
+Right. So, why would anybody do HIP when
+you've got 3D printing?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rate and cost. Absolutely. You know, you
+
+ align:start position:0%
+Rate and cost. Absolutely. You know, you
+ 
+
+ align:start position:0%
+Rate and cost. Absolutely. You know, you
+do the high hot isostatic pressing in
+
+ align:start position:0%
+do the high hot isostatic pressing in
+ 
+
+ align:start position:0%
+do the high hot isostatic pressing in
+minutes, seconds, that sort of thing.
+
+ align:start position:0%
+minutes, seconds, that sort of thing.
+ 
+
+ align:start position:0%
+minutes, seconds, that sort of thing.
+these again the the 3D printing the fast
+
+ align:start position:0%
+these again the the 3D printing the fast
+ 
+
+ align:start position:0%
+these again the the 3D printing the fast
+ones are going to take you minutes to uh
+
+ align:start position:0%
+ones are going to take you minutes to uh
+ 
+
+ align:start position:0%
+ones are going to take you minutes to uh
+to hours and it's volume dependent
+
+ align:start position:0%
+to hours and it's volume dependent
+ 
+
+ align:start position:0%
+to hours and it's volume dependent
+whereas with the hip it's much much less
+
+ align:start position:0%
+whereas with the hip it's much much less
+ 
+
+ align:start position:0%
+whereas with the hip it's much much less
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+um in general why does anybody do
+
+ align:start position:0%
+um in general why does anybody do
+ 
+
+ align:start position:0%
+um in general why does anybody do
+parallel processing because it's really
+
+ align:start position:0%
+parallel processing because it's really
+ 
+
+ align:start position:0%
+parallel processing because it's really
+fast and the example I always like to
+
+ align:start position:0%
+fast and the example I always like to
+ 
+
+ align:start position:0%
+fast and the example I always like to
+give is imagine if if someone took a
+
+ align:start position:0%
+give is imagine if if someone took a
+ 
+
+ align:start position:0%
+give is imagine if if someone took a
+block of uh steel or better yet
+
+ align:start position:0%
+block of uh steel or better yet
+ 
+
+ align:start position:0%
+block of uh steel or better yet
+aluminum and said okay I'm going to make
+
+ align:start position:0%
+aluminum and said okay I'm going to make
+ 
+
+ align:start position:0%
+aluminum and said okay I'm going to make
+all the body panels for your car the
+
+ align:start position:0%
+all the body panels for your car the
+ 
+
+ align:start position:0%
+all the body panels for your car the
+thin little body panels with my machine
+
+ align:start position:0%
+thin little body panels with my machine
+ 
+
+ align:start position:0%
+thin little body panels with my machine
+tool over
+
+ align:start position:0%
+tool over
+ 
+
+ align:start position:0%
+tool over
+here. You know, just imagine that what
+
+ align:start position:0%
+here. You know, just imagine that what
+ 
+
+ align:start position:0%
+here. You know, just imagine that what
+that what it would take to to build that
+
+ align:start position:0%
+that what it would take to to build that
+ 
+
+ align:start position:0%
+that what it would take to to build that
+as opposed to uh going to a high-speed
+
+ align:start position:0%
+as opposed to uh going to a high-speed
+ 
+
+ align:start position:0%
+as opposed to uh going to a high-speed
+modern high-speed stamping shop. Has
+
+ align:start position:0%
+modern high-speed stamping shop. Has
+ 
+
+ align:start position:0%
+modern high-speed stamping shop. Has
+anybody seen automobile body stamping
+
+ align:start position:0%
+anybody seen automobile body stamping
+ 
+
+ align:start position:0%
+anybody seen automobile body stamping
+going on? Yeah. How long does it take to
+
+ align:start position:0%
+going on? Yeah. How long does it take to
+ 
+
+ align:start position:0%
+going on? Yeah. How long does it take to
+make side panel for a car with like
+
+ align:start position:0%
+make side panel for a car with like
+ 
+
+ align:start position:0%
+make side panel for a car with like
+integral door frames and all that other
+
+ align:start position:0%
+integral door frames and all that other
+ 
+
+ align:start position:0%
+integral door frames and all that other
+stuff? Each given operation probably
+
+ align:start position:0%
+stuff? Each given operation probably
+ 
+
+ align:start position:0%
+stuff? Each given operation probably
+takes about two seconds. there's there's
+
+ align:start position:0%
+takes about two seconds. there's there's
+ 
+
+ align:start position:0%
+takes about two seconds. there's there's
+multiple stages. So maybe we'll give it
+
+ align:start position:0%
+multiple stages. So maybe we'll give it
+ 
+
+ align:start position:0%
+multiple stages. So maybe we'll give it
+10 seconds by the time it's done, you
+
+ align:start position:0%
+10 seconds by the time it's done, you
+ 
+
+ align:start position:0%
+10 seconds by the time it's done, you
+know, but blank metal in one end and
+
+ align:start position:0%
+know, but blank metal in one end and
+ 
+
+ align:start position:0%
+know, but blank metal in one end and
+these huge complex structures coming out
+
+ align:start position:0%
+these huge complex structures coming out
+ 
+
+ align:start position:0%
+these huge complex structures coming out
+the other end at incredible rates. Uh
+
+ align:start position:0%
+the other end at incredible rates. Uh
+ 
+
+ align:start position:0%
+the other end at incredible rates. Uh
+you're not going to do that with a
+
+ align:start position:0%
+you're not going to do that with a
+ 
+
+ align:start position:0%
+you're not going to do that with a
+serial process. Uh although I will say
+
+ align:start position:0%
+serial process. Uh although I will say
+ 
+
+ align:start position:0%
+serial process. Uh although I will say
+they've done some things with laser
+
+ align:start position:0%
+they've done some things with laser
+ 
+
+ align:start position:0%
+they've done some things with laser
+cutting and laser welding where that
+
+ align:start position:0%
+cutting and laser welding where that
+ 
+
+ align:start position:0%
+cutting and laser welding where that
+thing really whips along. Uh but uh it's
+
+ align:start position:0%
+thing really whips along. Uh but uh it's
+ 
+
+ align:start position:0%
+thing really whips along. Uh but uh it's
+it's still got a ways to go and it's
+
+ align:start position:0%
+it's still got a ways to go and it's
+ 
+
+ align:start position:0%
+it's still got a ways to go and it's
+much more costly. So all these things uh
+
+ align:start position:0%
+much more costly. So all these things uh
+ 
+
+ align:start position:0%
+much more costly. So all these things uh
+do matter and they uh they come in
+
+ align:start position:0%
+do matter and they uh they come in
+ 
+
+ align:start position:0%
+do matter and they uh they come in
+different ways. Oh. Um, just because I I
+
+ align:start position:0%
+different ways. Oh. Um, just because I I
+ 
+
+ align:start position:0%
+different ways. Oh. Um, just because I I
+always uh like to do this
+
+ align:start position:0%
+always uh like to do this
+ 
+
+ align:start position:0%
+always uh like to do this
+stereoliththography. How does that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work? It's a rapid It it was the
+
+ align:start position:0%
+work? It's a rapid It it was the
+ 
+
+ align:start position:0%
+work? It's a rapid It it was the
+original I think the original rapid
+
+ align:start position:0%
+original I think the original rapid
+ 
+
+ align:start position:0%
+original I think the original rapid
+prototyping process. Anybody know what
+
+ align:start position:0%
+prototyping process. Anybody know what
+ 
+
+ align:start position:0%
+prototyping process. Anybody know what
+stereo uh what's the is what's the trade
+
+ align:start position:0%
+stereo uh what's the is what's the trade
+ 
+
+ align:start position:0%
+stereo uh what's the is what's the trade
+name for that now? That's the most
+
+ align:start position:0%
+name for that now? That's the most
+ 
+
+ align:start position:0%
+name for that now? That's the most
+commercial of them. There's a machine
+
+ align:start position:0%
+commercial of them. There's a machine
+ 
+
+ align:start position:0%
+commercial of them. There's a machine
+right down the far end of this hallway
+
+ align:start position:0%
+right down the far end of this hallway
+ 
+
+ align:start position:0%
+right down the far end of this hallway
+in the architecture department that's an
+
+ align:start position:0%
+in the architecture department that's an
+ 
+
+ align:start position:0%
+in the architecture department that's an
+STL machine. Um stereoiththography. Ah,
+
+ align:start position:0%
+STL machine. Um stereoiththography. Ah,
+ 
+
+ align:start position:0%
+STL machine. Um stereoiththography. Ah,
+I guess it's become pass. Yeah, Adam.
+
+ align:start position:0%
+I guess it's become pass. Yeah, Adam.
+ 
+
+ align:start position:0%
+I guess it's become pass. Yeah, Adam.
+It's just I don't know what the liquid
+
+ align:start position:0%
+It's just I don't know what the liquid
+ 
+
+ align:start position:0%
+It's just I don't know what the liquid
+is, but you select that liquid material.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, as I as I That's right. There
+
+ align:start position:0%
+Yeah, as I as I That's right. There
+ 
+
+ align:start position:0%
+Yeah, as I as I That's right. There
+there are these photocurable
+
+ align:start position:0%
+there are these photocurable
+ 
+
+ align:start position:0%
+there are these photocurable
+polymers that will be in a liquid state
+
+ align:start position:0%
+polymers that will be in a liquid state
+ 
+
+ align:start position:0%
+polymers that will be in a liquid state
+at room temperature and with just
+
+ align:start position:0%
+at room temperature and with just
+ 
+
+ align:start position:0%
+at room temperature and with just
+regular light on them. But if you hit
+
+ align:start position:0%
+regular light on them. But if you hit
+ 
+
+ align:start position:0%
+regular light on them. But if you hit
+them with the right wavelength light,
+
+ align:start position:0%
+them with the right wavelength light,
+ 
+
+ align:start position:0%
+them with the right wavelength light,
+they will polymerize. you know, they're
+
+ align:start position:0%
+they will polymerize. you know, they're
+ 
+
+ align:start position:0%
+they will polymerize. you know, they're
+UV curable polymers that that are used
+
+ align:start position:0%
+UV curable polymers that that are used
+ 
+
+ align:start position:0%
+UV curable polymers that that are used
+for a lot of things, uh, like contact
+
+ align:start position:0%
+for a lot of things, uh, like contact
+ 
+
+ align:start position:0%
+for a lot of things, uh, like contact
+lenses and things like that. Um, but,
+
+ align:start position:0%
+lenses and things like that. Um, but,
+ 
+
+ align:start position:0%
+lenses and things like that. Um, but,
+uh, this particular case, what they said
+
+ align:start position:0%
+uh, this particular case, what they said
+ 
+
+ align:start position:0%
+uh, this particular case, what they said
+is, well, instead of putting it in a
+
+ align:start position:0%
+is, well, instead of putting it in a
+ 
+
+ align:start position:0%
+is, well, instead of putting it in a
+mold and flashing it with UV light
+
+ align:start position:0%
+mold and flashing it with UV light
+ 
+
+ align:start position:0%
+mold and flashing it with UV light
+everywhere, what if we put a little tiny
+
+ align:start position:0%
+everywhere, what if we put a little tiny
+ 
+
+ align:start position:0%
+everywhere, what if we put a little tiny
+spot of UV light on it? Will it form a
+
+ align:start position:0%
+spot of UV light on it? Will it form a
+ 
+
+ align:start position:0%
+spot of UV light on it? Will it form a
+little ball of of polymer? And the
+
+ align:start position:0%
+little ball of of polymer? And the
+ 
+
+ align:start position:0%
+little ball of of polymer? And the
+answer was sort of, yeah. Uh, so they
+
+ align:start position:0%
+answer was sort of, yeah. Uh, so they
+ 
+
+ align:start position:0%
+answer was sort of, yeah. Uh, so they
+have a you have this bath, I think.
+
+ align:start position:0%
+have a you have this bath, I think.
+ 
+
+ align:start position:0%
+have a you have this bath, I think.
+Again, I I I haven't walked by there
+
+ align:start position:0%
+Again, I I I haven't walked by there
+ 
+
+ align:start position:0%
+Again, I I I haven't walked by there
+this month, but there used to be in one
+
+ align:start position:0%
+this month, but there used to be in one
+ 
+
+ align:start position:0%
+this month, but there used to be in one
+of these glasswalled classrooms down
+
+ align:start position:0%
+of these glasswalled classrooms down
+ 
+
+ align:start position:0%
+of these glasswalled classrooms down
+here at the far end of the fourth floor
+
+ align:start position:0%
+here at the far end of the fourth floor
+ 
+
+ align:start position:0%
+here at the far end of the fourth floor
+in in the architecture department this
+
+ align:start position:0%
+in in the architecture department this
+ 
+
+ align:start position:0%
+in in the architecture department this
+white box with a clear window in it. And
+
+ align:start position:0%
+white box with a clear window in it. And
+ 
+
+ align:start position:0%
+white box with a clear window in it. And
+it's kind of lit up and there's usually
+
+ align:start position:0%
+it's kind of lit up and there's usually
+ 
+
+ align:start position:0%
+it's kind of lit up and there's usually
+something going on in there. And what
+
+ align:start position:0%
+something going on in there. And what
+ 
+
+ align:start position:0%
+something going on in there. And what
+you'll see is is a bath of nearly
+
+ align:start position:0%
+you'll see is is a bath of nearly
+ 
+
+ align:start position:0%
+you'll see is is a bath of nearly
+colorless liquid with a platin on it.
+
+ align:start position:0%
+colorless liquid with a platin on it.
+ 
+
+ align:start position:0%
+colorless liquid with a platin on it.
+And the platin starts at the top with a
+
+ align:start position:0%
+And the platin starts at the top with a
+ 
+
+ align:start position:0%
+And the platin starts at the top with a
+very thin layer of of uh fluid on it.
+
+ align:start position:0%
+very thin layer of of uh fluid on it.
+ 
+
+ align:start position:0%
+very thin layer of of uh fluid on it.
+And this laser, usually not visible, but
+
+ align:start position:0%
+And this laser, usually not visible, but
+ 
+
+ align:start position:0%
+And this laser, usually not visible, but
+this laser will be dancing across the
+
+ align:start position:0%
+this laser will be dancing across the
+ 
+
+ align:start position:0%
+this laser will be dancing across the
+surface tracing an outline. And that
+
+ align:start position:0%
+surface tracing an outline. And that
+ 
+
+ align:start position:0%
+surface tracing an outline. And that
+outline will will become solid. And once
+
+ align:start position:0%
+outline will will become solid. And once
+ 
+
+ align:start position:0%
+outline will will become solid. And once
+it's polymerized, it'll move it down and
+
+ align:start position:0%
+it's polymerized, it'll move it down and
+ 
+
+ align:start position:0%
+it's polymerized, it'll move it down and
+it'll do it again. So it's it's
+
+ align:start position:0%
+it'll do it again. So it's it's
+ 
+
+ align:start position:0%
+it'll do it again. So it's it's
+basically reacting causing a chemical
+
+ align:start position:0%
+basically reacting causing a chemical
+ 
+
+ align:start position:0%
+basically reacting causing a chemical
+reaction or in this case a
+
+ align:start position:0%
+reaction or in this case a
+ 
+
+ align:start position:0%
+reaction or in this case a
+polymerization reaction at a very small
+
+ align:start position:0%
+polymerization reaction at a very small
+ 
+
+ align:start position:0%
+polymerization reaction at a very small
+area by by hitting it with the right
+
+ align:start position:0%
+area by by hitting it with the right
+ 
+
+ align:start position:0%
+area by by hitting it with the right
+amount of activation
+
+ align:start position:0%
+amount of activation
+ 
+
+ align:start position:0%
+amount of activation
+energy. Okay. So that's uh
+
+ align:start position:0%
+energy. Okay. So that's uh
+ 
+
+ align:start position:0%
+energy. Okay. So that's uh
+stereoiththography. That would be a
+
+ align:start position:0%
+stereoiththography. That would be a
+ 
+
+ align:start position:0%
+stereoiththography. That would be a
+serial
+
+ align:start position:0%
+serial
+ 
+
+ align:start position:0%
+serial
+chemical formation process. You're going
+
+ align:start position:0%
+chemical formation process. You're going
+ 
+
+ align:start position:0%
+chemical formation process. You're going
+from liquid to
+
+ align:start position:0%
+from liquid to
+ 
+
+ align:start position:0%
+from liquid to
+solid.
+
+ align:start position:0%
+solid.
+ 
+
+ align:start position:0%
+solid.
+Um, we also do, in fact, I I was here
+
+ align:start position:0%
+Um, we also do, in fact, I I was here
+ 
+
+ align:start position:0%
+Um, we also do, in fact, I I was here
+last night listening to a PhD thesis
+
+ align:start position:0%
+last night listening to a PhD thesis
+ 
+
+ align:start position:0%
+last night listening to a PhD thesis
+from Singapore where what they did is
+
+ align:start position:0%
+from Singapore where what they did is
+ 
+
+ align:start position:0%
+from Singapore where what they did is
+they took a mold, poured UV curable
+
+ align:start position:0%
+they took a mold, poured UV curable
+ 
+
+ align:start position:0%
+they took a mold, poured UV curable
+polymer on it, flashed it with with a UV
+
+ align:start position:0%
+polymer on it, flashed it with with a UV
+ 
+
+ align:start position:0%
+polymer on it, flashed it with with a UV
+lamp over the whole thing for
+
+ align:start position:0%
+lamp over the whole thing for
+ 
+
+ align:start position:0%
+lamp over the whole thing for
+about about 30 seconds or something, I
+
+ align:start position:0%
+about about 30 seconds or something, I
+ 
+
+ align:start position:0%
+about about 30 seconds or something, I
+think, and then pulled it apart. Okay.
+
+ align:start position:0%
+think, and then pulled it apart. Okay.
+ 
+
+ align:start position:0%
+think, and then pulled it apart. Okay.
+And it was all about the mold, the mold
+
+ align:start position:0%
+And it was all about the mold, the mold
+ 
+
+ align:start position:0%
+And it was all about the mold, the mold
+quality and and filling and that sort of
+
+ align:start position:0%
+quality and and filling and that sort of
+ 
+
+ align:start position:0%
+quality and and filling and that sort of
+thing. So, um, and it's all about, you
+
+ align:start position:0%
+thing. So, um, and it's all about, you
+ 
+
+ align:start position:0%
+thing. So, um, and it's all about, you
+know, 90% of her thesis was about, well,
+
+ align:start position:0%
+know, 90% of her thesis was about, well,
+ 
+
+ align:start position:0%
+know, 90% of her thesis was about, well,
+not 90%, a good percentage of her thesis
+
+ align:start position:0%
+not 90%, a good percentage of her thesis
+ 
+
+ align:start position:0%
+not 90%, a good percentage of her thesis
+was about making the molds and how well
+
+ align:start position:0%
+was about making the molds and how well
+ 
+
+ align:start position:0%
+was about making the molds and how well
+could I extract this thing from the
+
+ align:start position:0%
+could I extract this thing from the
+ 
+
+ align:start position:0%
+could I extract this thing from the
+mold. So physically the same material,
+
+ align:start position:0%
+mold. So physically the same material,
+ 
+
+ align:start position:0%
+mold. So physically the same material,
+the same process, but in this case a
+
+ align:start position:0%
+the same process, but in this case a
+ 
+
+ align:start position:0%
+the same process, but in this case a
+really good example of going from a
+
+ align:start position:0%
+really good example of going from a
+ 
+
+ align:start position:0%
+really good example of going from a
+directed energy source that was a point
+
+ align:start position:0%
+directed energy source that was a point
+ 
+
+ align:start position:0%
+directed energy source that was a point
+to a directed energy source source that
+
+ align:start position:0%
+to a directed energy source source that
+ 
+
+ align:start position:0%
+to a directed energy source source that
+was really this entire surface. So I
+
+ align:start position:0%
+was really this entire surface. So I
+ 
+
+ align:start position:0%
+was really this entire surface. So I
+guess my point is and now I guess it's
+
+ align:start position:0%
+guess my point is and now I guess it's
+ 
+
+ align:start position:0%
+guess my point is and now I guess it's
+it's getting a little bit dated but when
+
+ align:start position:0%
+it's getting a little bit dated but when
+ 
+
+ align:start position:0%
+it's getting a little bit dated but when
+when uh these uh rapid prototyping
+
+ align:start position:0%
+when uh these uh rapid prototyping
+ 
+
+ align:start position:0%
+when uh these uh rapid prototyping
+processes were all the rage it was
+
+ align:start position:0%
+processes were all the rage it was
+ 
+
+ align:start position:0%
+processes were all the rage it was
+interesting to notice that on this
+
+ align:start position:0%
+interesting to notice that on this
+ 
+
+ align:start position:0%
+interesting to notice that on this
+taxonomy they simply were the fact that
+
+ align:start position:0%
+taxonomy they simply were the fact that
+ 
+
+ align:start position:0%
+taxonomy they simply were the fact that
+that some people realized and it's been
+
+ align:start position:0%
+that some people realized and it's been
+ 
+
+ align:start position:0%
+that some people realized and it's been
+done for a lot of different things not
+
+ align:start position:0%
+done for a lot of different things not
+ 
+
+ align:start position:0%
+done for a lot of different things not
+just these but people realized that I
+
+ align:start position:0%
+just these but people realized that I
+ 
+
+ align:start position:0%
+just these but people realized that I
+can take a parallel process and if I
+
+ align:start position:0%
+can take a parallel process and if I
+ 
+
+ align:start position:0%
+can take a parallel process and if I
+serialize it it all of a sudden becomes
+
+ align:start position:0%
+serialize it it all of a sudden becomes
+ 
+
+ align:start position:0%
+serialize it it all of a sudden becomes
+a rapid free form uh method doesn't need
+
+ align:start position:0%
+a rapid free form uh method doesn't need
+ 
+
+ align:start position:0%
+a rapid free form uh method doesn't need
+any tooling. And so you've got that
+
+ align:start position:0%
+any tooling. And so you've got that
+ 
+
+ align:start position:0%
+any tooling. And so you've got that
+example. You've got uh what turns out to
+
+ align:start position:0%
+example. You've got uh what turns out to
+ 
+
+ align:start position:0%
+example. You've got uh what turns out to
+be uh I guess I'd call it it's like sort
+
+ align:start position:0%
+be uh I guess I'd call it it's like sort
+ 
+
+ align:start position:0%
+be uh I guess I'd call it it's like sort
+of like a reaction molding parallel
+
+ align:start position:0%
+of like a reaction molding parallel
+ 
+
+ align:start position:0%
+of like a reaction molding parallel
+reaction process to a serial reaction
+
+ align:start position:0%
+reaction process to a serial reaction
+ 
+
+ align:start position:0%
+reaction process to a serial reaction
+process. There's also um this you know
+
+ align:start position:0%
+process. There's also um this you know
+ 
+
+ align:start position:0%
+process. There's also um this you know
+with powdered metals you can center them
+
+ align:start position:0%
+with powdered metals you can center them
+ 
+
+ align:start position:0%
+with powdered metals you can center them
+thermally to get the shape. And when
+
+ align:start position:0%
+thermally to get the shape. And when
+ 
+
+ align:start position:0%
+thermally to get the shape. And when
+people decided they could cinder it
+
+ align:start position:0%
+people decided they could cinder it
+ 
+
+ align:start position:0%
+people decided they could cinder it
+locally with a laser, you could take a
+
+ align:start position:0%
+locally with a laser, you could take a
+ 
+
+ align:start position:0%
+locally with a laser, you could take a
+powder of of metal and zap it with a
+
+ align:start position:0%
+powder of of metal and zap it with a
+ 
+
+ align:start position:0%
+powder of of metal and zap it with a
+laser and just get things to center to
+
+ align:start position:0%
+laser and just get things to center to
+ 
+
+ align:start position:0%
+laser and just get things to center to
+each other uh locally. Okay. So they got
+
+ align:start position:0%
+each other uh locally. Okay. So they got
+ 
+
+ align:start position:0%
+each other uh locally. Okay. So they got
+they they changed the whole equation on
+
+ align:start position:0%
+they they changed the whole equation on
+ 
+
+ align:start position:0%
+they they changed the whole equation on
+how the process is controlled which has
+
+ align:start position:0%
+how the process is controlled which has
+ 
+
+ align:start position:0%
+how the process is controlled which has
+effects on all these different uh
+
+ align:start position:0%
+effects on all these different uh
+ 
+
+ align:start position:0%
+effects on all these different uh
+things.
+
+ align:start position:0%
+things.
+ 
+
+ align:start position:0%
+things.
+Last thing, because we're not going to
+
+ align:start position:0%
+Last thing, because we're not going to
+ 
+
+ align:start position:0%
+Last thing, because we're not going to
+talk about it much for the rest of the
+
+ align:start position:0%
+talk about it much for the rest of the
+ 
+
+ align:start position:0%
+talk about it much for the rest of the
+term, but because it's an extremely has
+
+ align:start position:0%
+term, but because it's an extremely has
+ 
+
+ align:start position:0%
+term, but because it's an extremely has
+been an extremely important part of
+
+ align:start position:0%
+been an extremely important part of
+ 
+
+ align:start position:0%
+been an extremely important part of
+manufacturing, interestingly fading in
+
+ align:start position:0%
+manufacturing, interestingly fading in
+ 
+
+ align:start position:0%
+manufacturing, interestingly fading in
+recent years for good and sufficient
+
+ align:start position:0%
+recent years for good and sufficient
+ 
+
+ align:start position:0%
+recent years for good and sufficient
+reasons, is flexibility.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What do you
+
+ align:start position:0%
+What do you
+ 
+
+ align:start position:0%
+What do you
+think about if I if I were to go to
+
+ align:start position:0%
+think about if I if I were to go to
+ 
+
+ align:start position:0%
+think about if I if I were to go to
+different corners of this taxonomy and
+
+ align:start position:0%
+different corners of this taxonomy and
+ 
+
+ align:start position:0%
+different corners of this taxonomy and
+say, "All
+
+ align:start position:0%
+say, "All
+ 
+
+ align:start position:0%
+say, "All
+right, so let's put a flexibility
+
+ align:start position:0%
+right, so let's put a flexibility
+ 
+
+ align:start position:0%
+right, so let's put a flexibility
+overlay on
+
+ align:start position:0%
+overlay on
+ 
+
+ align:start position:0%
+overlay on
+this." And we'll talk about um you know,
+
+ align:start position:0%
+this." And we'll talk about um you know,
+ 
+
+ align:start position:0%
+this." And we'll talk about um you know,
+flexibility here, I guess. Well, two two
+
+ align:start position:0%
+flexibility here, I guess. Well, two two
+ 
+
+ align:start position:0%
+flexibility here, I guess. Well, two two
+common ways of looking at flexibility
+
+ align:start position:0%
+common ways of looking at flexibility
+ 
+
+ align:start position:0%
+common ways of looking at flexibility
+are sort of product flexibility. So, in
+
+ align:start position:0%
+are sort of product flexibility. So, in
+ 
+
+ align:start position:0%
+are sort of product flexibility. So, in
+our case, it's going to be geometry
+
+ align:start position:0%
+our case, it's going to be geometry
+ 
+
+ align:start position:0%
+our case, it's going to be geometry
+flexibility, geometry and material
+
+ align:start position:0%
+flexibility, geometry and material
+ 
+
+ align:start position:0%
+flexibility, geometry and material
+flexibility. Um and the other would be
+
+ align:start position:0%
+flexibility. Um and the other would be
+ 
+
+ align:start position:0%
+flexibility. Um and the other would be
+sort of quantity flexibility, ability to
+
+ align:start position:0%
+sort of quantity flexibility, ability to
+ 
+
+ align:start position:0%
+sort of quantity flexibility, ability to
+um uh vary the capacity or output of
+
+ align:start position:0%
+um uh vary the capacity or output of
+ 
+
+ align:start position:0%
+um uh vary the capacity or output of
+something without having quite a big
+
+ align:start position:0%
+something without having quite a big
+ 
+
+ align:start position:0%
+something without having quite a big
+cost variances. But let's do the first
+
+ align:start position:0%
+cost variances. But let's do the first
+ 
+
+ align:start position:0%
+cost variances. But let's do the first
+one. We won't get into that second one.
+
+ align:start position:0%
+one. We won't get into that second one.
+ 
+
+ align:start position:0%
+one. We won't get into that second one.
+for flexibility of this process to work
+
+ align:start position:0%
+for flexibility of this process to work
+ 
+
+ align:start position:0%
+for flexibility of this process to work
+with different materials and different
+
+ align:start position:0%
+with different materials and different
+ 
+
+ align:start position:0%
+with different materials and different
+shapes. Obviously, the the the extreme
+
+ align:start position:0%
+shapes. Obviously, the the the extreme
+ 
+
+ align:start position:0%
+shapes. Obviously, the the the extreme
+example of flexibility is every part's
+
+ align:start position:0%
+example of flexibility is every part's
+ 
+
+ align:start position:0%
+example of flexibility is every part's
+different and and there's no every
+
+ align:start position:0%
+different and and there's no every
+ 
+
+ align:start position:0%
+different and and there's no every
+part's different and the setup time is
+
+ align:start position:0%
+part's different and the setup time is
+ 
+
+ align:start position:0%
+part's different and the setup time is
+zero. Okay? So mass production
+
+ align:start position:0%
+zero. Okay? So mass production
+ 
+
+ align:start position:0%
+zero. Okay? So mass production
+rates, mass production cost savings, but
+
+ align:start position:0%
+rates, mass production cost savings, but
+ 
+
+ align:start position:0%
+rates, mass production cost savings, but
+custom
+
+ align:start position:0%
+custom
+ 
+
+ align:start position:0%
+custom
+uh custom uh part capability somewhere
+
+ align:start position:0%
+uh custom uh part capability somewhere
+ 
+
+ align:start position:0%
+uh custom uh part capability somewhere
+these all lie somewhere in between
+
+ align:start position:0%
+these all lie somewhere in between
+ 
+
+ align:start position:0%
+these all lie somewhere in between
+there. But if I look at this broadly,
+
+ align:start position:0%
+there. But if I look at this broadly,
+ 
+
+ align:start position:0%
+there. But if I look at this broadly,
+what do you think is the most
+
+ align:start position:0%
+what do you think is the most
+ 
+
+ align:start position:0%
+what do you think is the most
+flexible or what what most flexible or
+
+ align:start position:0%
+flexible or what what most flexible or
+ 
+
+ align:start position:0%
+flexible or what what most flexible or
+more flexible? If I look at the
+
+ align:start position:0%
+more flexible? If I look at the
+ 
+
+ align:start position:0%
+more flexible? If I look at the
+taxonomy, what area would you look at
+
+ align:start position:0%
+taxonomy, what area would you look at
+ 
+
+ align:start position:0%
+taxonomy, what area would you look at
+for for high flexibility?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+serial processes and why
+
+ align:start position:0%
+serial processes and why
+ 
+
+ align:start position:0%
+serial processes and why
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess I guess it gives you more
+
+ align:start position:0%
+guess I guess it gives you more
+ 
+
+ align:start position:0%
+guess I guess it gives you more
+flexibility in
+
+ align:start position:0%
+flexibility in
+ 
+
+ align:start position:0%
+flexibility in
+terms I guess feature by feature and
+
+ align:start position:0%
+terms I guess feature by feature and
+ 
+
+ align:start position:0%
+terms I guess feature by feature and
+also part by part. Yeah, I mean exactly.
+
+ align:start position:0%
+also part by part. Yeah, I mean exactly.
+ 
+
+ align:start position:0%
+also part by part. Yeah, I mean exactly.
+I mean think think of again the the
+
+ align:start position:0%
+I mean think think of again the the
+ 
+
+ align:start position:0%
+I mean think think of again the the
+ubiquous example is a uh um I'm trying
+
+ align:start position:0%
+ubiquous example is a uh um I'm trying
+ 
+
+ align:start position:0%
+ubiquous example is a uh um I'm trying
+to think of
+
+ align:start position:0%
+to think of
+ 
+
+ align:start position:0%
+to think of
+of some
+
+ align:start position:0%
+of some
+ 
+
+ align:start position:0%
+of some
+consumer oriented parts of this but um I
+
+ align:start position:0%
+consumer oriented parts of this but um I
+ 
+
+ align:start position:0%
+consumer oriented parts of this but um I
+mean I'm not coming up with them but
+
+ align:start position:0%
+mean I'm not coming up with them but
+ 
+
+ align:start position:0%
+mean I'm not coming up with them but
+yeah a machine tool let's say you know
+
+ align:start position:0%
+yeah a machine tool let's say you know
+ 
+
+ align:start position:0%
+yeah a machine tool let's say you know
+take a machine tool with an endmill and
+
+ align:start position:0%
+take a machine tool with an endmill and
+ 
+
+ align:start position:0%
+take a machine tool with an endmill and
+it can write your name in a piece of
+
+ align:start position:0%
+it can write your name in a piece of
+ 
+
+ align:start position:0%
+it can write your name in a piece of
+plastic
+
+ align:start position:0%
+plastic
+ 
+
+ align:start position:0%
+plastic
+right there's no once I programmed your
+
+ align:start position:0%
+right there's no once I programmed your
+ 
+
+ align:start position:0%
+right there's no once I programmed your
+name in there and then your name and
+
+ align:start position:0%
+name in there and then your name and
+ 
+
+ align:start position:0%
+name in there and then your name and
+then your name and you know there's
+
+ align:start position:0%
+then your name and you know there's
+ 
+
+ align:start position:0%
+then your name and you know there's
+absolutely no overhead to me switching
+
+ align:start position:0%
+absolutely no overhead to me switching
+ 
+
+ align:start position:0%
+absolutely no overhead to me switching
+because all I have to change is the
+
+ align:start position:0%
+because all I have to change is the
+ 
+
+ align:start position:0%
+because all I have to change is the
+trajectory of the tool and that nowadays
+
+ align:start position:0%
+trajectory of the tool and that nowadays
+ 
+
+ align:start position:0%
+trajectory of the tool and that nowadays
+with CNC control that's a zero cost
+
+ align:start position:0%
+with CNC control that's a zero cost
+ 
+
+ align:start position:0%
+with CNC control that's a zero cost
+changeover. There's a minimal cost in
+
+ align:start position:0%
+changeover. There's a minimal cost in
+ 
+
+ align:start position:0%
+changeover. There's a minimal cost in
+creating the programs and for simple
+
+ align:start position:0%
+creating the programs and for simple
+ 
+
+ align:start position:0%
+creating the programs and for simple
+things like that. So yeah, obviously
+
+ align:start position:0%
+things like that. So yeah, obviously
+ 
+
+ align:start position:0%
+things like that. So yeah, obviously
+something that is purely
+
+ align:start position:0%
+something that is purely
+ 
+
+ align:start position:0%
+something that is purely
+serial makes a big difference. And I'm
+
+ align:start position:0%
+serial makes a big difference. And I'm
+ 
+
+ align:start position:0%
+serial makes a big difference. And I'm
+going to add one other thing because I
+
+ align:start position:0%
+going to add one other thing because I
+ 
+
+ align:start position:0%
+going to add one other thing because I
+if if I hurry up, I'll get at least to
+
+ align:start position:0%
+if if I hurry up, I'll get at least to
+ 
+
+ align:start position:0%
+if if I hurry up, I'll get at least to
+mention
+
+ align:start position:0%
+mention
+ 
+
+ align:start position:0%
+mention
+this. I'll make the case that cutting
+
+ align:start position:0%
+this. I'll make the case that cutting
+ 
+
+ align:start position:0%
+this. I'll make the case that cutting
+metal mechanically
+
+ align:start position:0%
+metal mechanically
+ 
+
+ align:start position:0%
+metal mechanically
+um is is maybe the purest form of
+
+ align:start position:0%
+um is is maybe the purest form of
+ 
+
+ align:start position:0%
+um is is maybe the purest form of
+geometry transformation. pure geometry
+
+ align:start position:0%
+geometry transformation. pure geometry
+ 
+
+ align:start position:0%
+geometry transformation. pure geometry
+transformation with no side
+
+ align:start position:0%
+transformation with no side
+ 
+
+ align:start position:0%
+transformation with no side
+effects. Okay. So that also makes it
+
+ align:start position:0%
+effects. Okay. So that also makes it
+ 
+
+ align:start position:0%
+effects. Okay. So that also makes it
+very flexible in that sense. Uh you know
+
+ align:start position:0%
+very flexible in that sense. Uh you know
+ 
+
+ align:start position:0%
+very flexible in that sense. Uh you know
+it's it's almost as if yeah all I have
+
+ align:start position:0%
+it's it's almost as if yeah all I have
+ 
+
+ align:start position:0%
+it's it's almost as if yeah all I have
+to do is reprogram the trajectory and
+
+ align:start position:0%
+to do is reprogram the trajectory and
+ 
+
+ align:start position:0%
+to do is reprogram the trajectory and
+nothing else changes and everything's
+
+ align:start position:0%
+nothing else changes and everything's
+ 
+
+ align:start position:0%
+nothing else changes and everything's
+fine. Um so we'll we'll start from that
+
+ align:start position:0%
+fine. Um so we'll we'll start from that
+ 
+
+ align:start position:0%
+fine. Um so we'll we'll start from that
+and then we move to to
+
+ align:start position:0%
+and then we move to to
+ 
+
+ align:start position:0%
+and then we move to to
+other other changes here. Um let's go to
+
+ align:start position:0%
+other other changes here. Um let's go to
+ 
+
+ align:start position:0%
+other other changes here. Um let's go to
+uh deformation serial deformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bending. Okay. Going to bend this
+
+ align:start position:0%
+bending. Okay. Going to bend this
+ 
+
+ align:start position:0%
+bending. Okay. Going to bend this
+three-point bending.
+
+ align:start position:0%
+three-point bending.
+ 
+
+ align:start position:0%
+three-point bending.
+Um I'm calling it serial because most of
+
+ align:start position:0%
+Um I'm calling it serial because most of
+ 
+
+ align:start position:0%
+Um I'm calling it serial because most of
+the action is happening right here. And
+
+ align:start position:0%
+the action is happening right here. And
+ 
+
+ align:start position:0%
+the action is happening right here. And
+I'm not using form tools. You can even
+
+ align:start position:0%
+I'm not using form tools. You can even
+ 
+
+ align:start position:0%
+I'm not using form tools. You can even
+think of this as using knife edge tools
+
+ align:start position:0%
+think of this as using knife edge tools
+ 
+
+ align:start position:0%
+think of this as using knife edge tools
+and I would get sort of this same shape.
+
+ align:start position:0%
+and I would get sort of this same shape.
+ 
+
+ align:start position:0%
+and I would get sort of this same shape.
+And the main thing that determines this
+
+ align:start position:0%
+And the main thing that determines this
+ 
+
+ align:start position:0%
+And the main thing that determines this
+shape, the main thing is how far I push
+
+ align:start position:0%
+shape, the main thing is how far I push
+ 
+
+ align:start position:0%
+shape, the main thing is how far I push
+down in the middle, right? Okay. So,
+
+ align:start position:0%
+down in the middle, right? Okay. So,
+ 
+
+ align:start position:0%
+down in the middle, right? Okay. So,
+that's pretty
+
+ align:start position:0%
+that's pretty
+ 
+
+ align:start position:0%
+that's pretty
+flexible. I mean, if you know, if I want
+
+ align:start position:0%
+flexible. I mean, if you know, if I want
+ 
+
+ align:start position:0%
+flexible. I mean, if you know, if I want
+45 degrees, I just take it down less. If
+
+ align:start position:0%
+45 degrees, I just take it down less. If
+ 
+
+ align:start position:0%
+45 degrees, I just take it down less. If
+I go down farther, it takes down take it
+
+ align:start position:0%
+I go down farther, it takes down take it
+ 
+
+ align:start position:0%
+I go down farther, it takes down take it
+down more. But, as can be shown, and
+
+ align:start position:0%
+down more. But, as can be shown, and
+ 
+
+ align:start position:0%
+down more. But, as can be shown, and
+it's it is in the notes, but we probably
+
+ align:start position:0%
+it's it is in the notes, but we probably
+ 
+
+ align:start position:0%
+it's it is in the notes, but we probably
+won't have time to go through it. As can
+
+ align:start position:0%
+won't have time to go through it. As can
+ 
+
+ align:start position:0%
+won't have time to go through it. As can
+be shown, it makes a huge
+
+ align:start position:0%
+be shown, it makes a huge
+ 
+
+ align:start position:0%
+be shown, it makes a huge
+difference what this material
+
+ align:start position:0%
+difference what this material
+ 
+
+ align:start position:0%
+difference what this material
+is and what the underlying machine
+
+ align:start position:0%
+is and what the underlying machine
+ 
+
+ align:start position:0%
+is and what the underlying machine
+structure looks like. And it also, and
+
+ align:start position:0%
+structure looks like. And it also, and
+ 
+
+ align:start position:0%
+structure looks like. And it also, and
+this really kind of gets us to the next
+
+ align:start position:0%
+this really kind of gets us to the next
+ 
+
+ align:start position:0%
+this really kind of gets us to the next
+the next theme here, it also depends
+
+ align:start position:0%
+the next theme here, it also depends
+ 
+
+ align:start position:0%
+the next theme here, it also depends
+very strongly on the uniformity of this
+
+ align:start position:0%
+very strongly on the uniformity of this
+ 
+
+ align:start position:0%
+very strongly on the uniformity of this
+material. So make the statement that
+
+ align:start position:0%
+material. So make the statement that
+ 
+
+ align:start position:0%
+material. So make the statement that
+that the natural variations out of an
+
+ align:start position:0%
+that the natural variations out of an
+ 
+
+ align:start position:0%
+that the natural variations out of an
+aluminum
+
+ align:start position:0%
+aluminum
+ 
+
+ align:start position:0%
+aluminum
+mill, maybe not the Alcoa Tennessee
+
+ align:start position:0%
+mill, maybe not the Alcoa Tennessee
+ 
+
+ align:start position:0%
+mill, maybe not the Alcoa Tennessee
+mill, but the other ones uh of aluminum
+
+ align:start position:0%
+mill, but the other ones uh of aluminum
+ 
+
+ align:start position:0%
+mill, but the other ones uh of aluminum
+is enough that it can completely
+
+ align:start position:0%
+is enough that it can completely
+ 
+
+ align:start position:0%
+is enough that it can completely
+confound precise control of a process
+
+ align:start position:0%
+confound precise control of a process
+ 
+
+ align:start position:0%
+confound precise control of a process
+like this. The natural variation of a
+
+ align:start position:0%
+like this. The natural variation of a
+ 
+
+ align:start position:0%
+like this. The natural variation of a
+piece of aluminum like this that I'm
+
+ align:start position:0%
+piece of aluminum like this that I'm
+ 
+
+ align:start position:0%
+piece of aluminum like this that I'm
+going to turn just doesn't make any
+
+ align:start position:0%
+going to turn just doesn't make any
+ 
+
+ align:start position:0%
+going to turn just doesn't make any
+difference. Sure, if I put a different
+
+ align:start position:0%
+difference. Sure, if I put a different
+ 
+
+ align:start position:0%
+difference. Sure, if I put a different
+alloy in or I sneak in steel or titanium
+
+ align:start position:0%
+alloy in or I sneak in steel or titanium
+ 
+
+ align:start position:0%
+alloy in or I sneak in steel or titanium
+instead of aluminum, yeah, that's a
+
+ align:start position:0%
+instead of aluminum, yeah, that's a
+ 
+
+ align:start position:0%
+instead of aluminum, yeah, that's a
+that's a big mess up. But,
+
+ align:start position:0%
+that's a big mess up. But,
+ 
+
+ align:start position:0%
+that's a big mess up. But,
+um, if I just say, well, you know, uh,
+
+ align:start position:0%
+um, if I just say, well, you know, uh,
+ 
+
+ align:start position:0%
+um, if I just say, well, you know, uh,
+here here's a piece of aluminum. We we
+
+ align:start position:0%
+here here's a piece of aluminum. We we
+ 
+
+ align:start position:0%
+here here's a piece of aluminum. We we
+did it in this mill over here and it
+
+ align:start position:0%
+did it in this mill over here and it
+ 
+
+ align:start position:0%
+did it in this mill over here and it
+came out with the
+
+ align:start position:0%
+came out with the
+ 
+
+ align:start position:0%
+came out with the
+following properties. You know, it it's
+
+ align:start position:0%
+following properties. You know, it it's
+ 
+
+ align:start position:0%
+following properties. You know, it it's
+elasticity, it's its yield strength,
+
+ align:start position:0%
+elasticity, it's its yield strength,
+ 
+
+ align:start position:0%
+elasticity, it's its yield strength,
+it's its strain hardening
+
+ align:start position:0%
+it's its strain hardening
+ 
+
+ align:start position:0%
+it's its strain hardening
+characteristics. And then I get
+
+ align:start position:0%
+characteristics. And then I get
+ 
+
+ align:start position:0%
+characteristics. And then I get
+supposedly the same material from a
+
+ align:start position:0%
+supposedly the same material from a
+ 
+
+ align:start position:0%
+supposedly the same material from a
+different mill, and they're 10%
+
+ align:start position:0%
+different mill, and they're 10%
+ 
+
+ align:start position:0%
+different mill, and they're 10%
+different. Not the elasticity by the
+
+ align:start position:0%
+different. Not the elasticity by the
+ 
+
+ align:start position:0%
+different. Not the elasticity by the
+way, but all the others. Uh 10%
+
+ align:start position:0%
+way, but all the others. Uh 10%
+ 
+
+ align:start position:0%
+way, but all the others. Uh 10%
+different. Huge difference
+
+ align:start position:0%
+different. Huge difference
+ 
+
+ align:start position:0%
+different. Huge difference
+here. Virtually no difference for the
+
+ align:start position:0%
+here. Virtually no difference for the
+ 
+
+ align:start position:0%
+here. Virtually no difference for the
+machining. So there's an inherent
+
+ align:start position:0%
+machining. So there's an inherent
+ 
+
+ align:start position:0%
+machining. So there's an inherent
+sensitivity of the processes to that.
+
+ align:start position:0%
+sensitivity of the processes to that.
+ 
+
+ align:start position:0%
+sensitivity of the processes to that.
+So if I look just at this purely serial
+
+ align:start position:0%
+So if I look just at this purely serial
+ 
+
+ align:start position:0%
+So if I look just at this purely serial
+parallel thing, yeah, serial is better
+
+ align:start position:0%
+parallel thing, yeah, serial is better
+ 
+
+ align:start position:0%
+parallel thing, yeah, serial is better
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+parallel. I think we can show in general
+
+ align:start position:0%
+parallel. I think we can show in general
+ 
+
+ align:start position:0%
+parallel. I think we can show in general
+that removal tends to be the least
+
+ align:start position:0%
+that removal tends to be the least
+ 
+
+ align:start position:0%
+that removal tends to be the least
+sensitive to material properties, tends
+
+ align:start position:0%
+sensitive to material properties, tends
+ 
+
+ align:start position:0%
+sensitive to material properties, tends
+to be the least sensitive to all these
+
+ align:start position:0%
+to be the least sensitive to all these
+ 
+
+ align:start position:0%
+to be the least sensitive to all these
+things. So, you know, serial removal
+
+ align:start position:0%
+things. So, you know, serial removal
+ 
+
+ align:start position:0%
+things. So, you know, serial removal
+kind of wins in most cases in terms of
+
+ align:start position:0%
+kind of wins in most cases in terms of
+ 
+
+ align:start position:0%
+kind of wins in most cases in terms of
+flexibility.
+
+ align:start position:0%
+flexibility.
+ 
+
+ align:start position:0%
+flexibility.
+Um, deformation is generally a killer in
+
+ align:start position:0%
+Um, deformation is generally a killer in
+ 
+
+ align:start position:0%
+Um, deformation is generally a killer in
+terms of flexibility for these regions
+
+ align:start position:0%
+terms of flexibility for these regions
+ 
+
+ align:start position:0%
+terms of flexibility for these regions
+that we've talked about. And, uh, in
+
+ align:start position:0%
+that we've talked about. And, uh, in
+ 
+
+ align:start position:0%
+that we've talked about. And, uh, in
+many cases, well, certainly anything
+
+ align:start position:0%
+many cases, well, certainly anything
+ 
+
+ align:start position:0%
+many cases, well, certainly anything
+that involves a uh, parallel energy
+
+ align:start position:0%
+that involves a uh, parallel energy
+ 
+
+ align:start position:0%
+that involves a uh, parallel energy
+exchange sort of starts off behind the
+
+ align:start position:0%
+exchange sort of starts off behind the
+ 
+
+ align:start position:0%
+exchange sort of starts off behind the
+eightball with respect to flexibility.
+
+ align:start position:0%
+eightball with respect to flexibility.
+ 
+
+ align:start position:0%
+eightball with respect to flexibility.
+Simon, what about the chemical vapor
+
+ align:start position:0%
+Simon, what about the chemical vapor
+ 
+
+ align:start position:0%
+Simon, what about the chemical vapor
+deposition? I mean, they throw in all
+
+ align:start position:0%
+deposition? I mean, they throw in all
+ 
+
+ align:start position:0%
+deposition? I mean, they throw in all
+sorts of parts and they come out with
+
+ align:start position:0%
+sorts of parts and they come out with
+ 
+
+ align:start position:0%
+sorts of parts and they come out with
+the the coating and I mean there is no
+
+ align:start position:0%
+the the coating and I mean there is no
+ 
+
+ align:start position:0%
+the the coating and I mean there is no
+dependency on that's a that's a very
+
+ align:start position:0%
+dependency on that's a that's a very
+ 
+
+ align:start position:0%
+dependency on that's a that's a very
+good point that's a that's a really good
+
+ align:start position:0%
+good point that's a that's a really good
+ 
+
+ align:start position:0%
+good point that's a that's a really good
+point and I think uh I'm glad you raised
+
+ align:start position:0%
+point and I think uh I'm glad you raised
+ 
+
+ align:start position:0%
+point and I think uh I'm glad you raised
+that uh I hadn't thought about that but
+
+ align:start position:0%
+that uh I hadn't thought about that but
+ 
+
+ align:start position:0%
+that uh I hadn't thought about that but
+um a process like this some of these
+
+ align:start position:0%
+um a process like this some of these
+ 
+
+ align:start position:0%
+um a process like this some of these
+addition processes any sort of a plating
+
+ align:start position:0%
+addition processes any sort of a plating
+ 
+
+ align:start position:0%
+addition processes any sort of a plating
+or coating process um where you put
+
+ align:start position:0%
+or coating process um where you put
+ 
+
+ align:start position:0%
+or coating process um where you put
+stuff into a liquid or or vapor
+
+ align:start position:0%
+stuff into a liquid or or vapor
+ 
+
+ align:start position:0%
+stuff into a liquid or or vapor
+uh bath Um, yeah, it doesn't care about
+
+ align:start position:0%
+uh bath Um, yeah, it doesn't care about
+ 
+
+ align:start position:0%
+uh bath Um, yeah, it doesn't care about
+the shape, does it? In I mean, it it at
+
+ align:start position:0%
+the shape, does it? In I mean, it it at
+ 
+
+ align:start position:0%
+the shape, does it? In I mean, it it at
+a microscopic level it might, but yeah,
+
+ align:start position:0%
+a microscopic level it might, but yeah,
+ 
+
+ align:start position:0%
+a microscopic level it might, but yeah,
+it doesn't. That's a good point. So, in
+
+ align:start position:0%
+it doesn't. That's a good point. So, in
+ 
+
+ align:start position:0%
+it doesn't. That's a good point. So, in
+terms of geometry,
+
+ align:start position:0%
+terms of geometry,
+ 
+
+ align:start position:0%
+terms of geometry,
+um, which is, you know, there's the
+
+ align:start position:0%
+um, which is, you know, there's the
+ 
+
+ align:start position:0%
+um, which is, you know, there's the
+underlying geometry of the substrate
+
+ align:start position:0%
+underlying geometry of the substrate
+ 
+
+ align:start position:0%
+underlying geometry of the substrate
+plus whatever thickness you add, um, to
+
+ align:start position:0%
+plus whatever thickness you add, um, to
+ 
+
+ align:start position:0%
+plus whatever thickness you add, um, to
+my knowledge, if I have a big big piece
+
+ align:start position:0%
+my knowledge, if I have a big big piece
+ 
+
+ align:start position:0%
+my knowledge, if I have a big big piece
+over here and right next to it a little
+
+ align:start position:0%
+over here and right next to it a little
+ 
+
+ align:start position:0%
+over here and right next to it a little
+piece over here, another one over here,
+
+ align:start position:0%
+piece over here, another one over here,
+ 
+
+ align:start position:0%
+piece over here, another one over here,
+they're independent of each other, so
+
+ align:start position:0%
+they're independent of each other, so
+ 
+
+ align:start position:0%
+they're independent of each other, so
+they all deposit at the same rate unless
+
+ align:start position:0%
+they all deposit at the same rate unless
+ 
+
+ align:start position:0%
+they all deposit at the same rate unless
+you do something really dumb. Yeah, it's
+
+ align:start position:0%
+you do something really dumb. Yeah, it's
+ 
+
+ align:start position:0%
+you do something really dumb. Yeah, it's
+a good point. Good point. I don't know
+
+ align:start position:0%
+a good point. Good point. I don't know
+ 
+
+ align:start position:0%
+a good point. Good point. I don't know
+how to I don't know how to pull that
+
+ align:start position:0%
+how to I don't know how to pull that
+ 
+
+ align:start position:0%
+how to I don't know how to pull that
+out. But uh in in that
+
+ align:start position:0%
+out. But uh in in that
+ 
+
+ align:start position:0%
+out. But uh in in that
+sense, well to relate it to what we said
+
+ align:start position:0%
+sense, well to relate it to what we said
+ 
+
+ align:start position:0%
+sense, well to relate it to what we said
+before, the energy
+
+ align:start position:0%
+before, the energy
+ 
+
+ align:start position:0%
+before, the energy
+exchange area is determined by the shape
+
+ align:start position:0%
+exchange area is determined by the shape
+ 
+
+ align:start position:0%
+exchange area is determined by the shape
+of the substrate, not the shape of the
+
+ align:start position:0%
+of the substrate, not the shape of the
+ 
+
+ align:start position:0%
+of the substrate, not the shape of the
+tool. And so in a situation like that,
+
+ align:start position:0%
+tool. And so in a situation like that,
+ 
+
+ align:start position:0%
+tool. And so in a situation like that,
+the shape of the substrate, if it's
+
+ align:start position:0%
+the shape of the substrate, if it's
+ 
+
+ align:start position:0%
+the shape of the substrate, if it's
+right, and I can change it each time I
+
+ align:start position:0%
+right, and I can change it each time I
+ 
+
+ align:start position:0%
+right, and I can change it each time I
+put it in, I get high flexibility with
+
+ align:start position:0%
+put it in, I get high flexibility with
+ 
+
+ align:start position:0%
+put it in, I get high flexibility with
+that. Yeah, good point. Good point.
+
+ align:start position:0%
+that. Yeah, good point. Good point.
+ 
+
+ align:start position:0%
+that. Yeah, good point. Good point.
+have to remember
+
+ align:start position:0%
+have to remember
+ 
+
+ align:start position:0%
+have to remember
+that. Okay, enough enough on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+taxonomy. Okay, now uh the last thing I
+
+ align:start position:0%
+taxonomy. Okay, now uh the last thing I
+ 
+
+ align:start position:0%
+taxonomy. Okay, now uh the last thing I
+want to talk about is um what goes
+
+ align:start position:0%
+want to talk about is um what goes
+ 
+
+ align:start position:0%
+want to talk about is um what goes
+wrong. We've been talking about so far,
+
+ align:start position:0%
+wrong. We've been talking about so far,
+ 
+
+ align:start position:0%
+wrong. We've been talking about so far,
+we've made some reference to it. We've
+
+ align:start position:0%
+we've made some reference to it. We've
+ 
+
+ align:start position:0%
+we've made some reference to it. We've
+been talking about so far is is how to
+
+ align:start position:0%
+been talking about so far is is how to
+ 
+
+ align:start position:0%
+been talking about so far is is how to
+make major changes. you know, I want to
+
+ align:start position:0%
+make major changes. you know, I want to
+ 
+
+ align:start position:0%
+make major changes. you know, I want to
+go from a from uh uh you know, this
+
+ align:start position:0%
+go from a from uh uh you know, this
+ 
+
+ align:start position:0%
+go from a from uh uh you know, this
+diameter down to half that diameter.
+
+ align:start position:0%
+diameter down to half that diameter.
+ 
+
+ align:start position:0%
+diameter down to half that diameter.
+Well, I have to push this in. I have to
+
+ align:start position:0%
+Well, I have to push this in. I have to
+ 
+
+ align:start position:0%
+Well, I have to push this in. I have to
+make chips and and you know, I have to
+
+ align:start position:0%
+make chips and and you know, I have to
+ 
+
+ align:start position:0%
+make chips and and you know, I have to
+push this down so far. But what I want
+
+ align:start position:0%
+push this down so far. But what I want
+ 
+
+ align:start position:0%
+push this down so far. But what I want
+to talk about is why isn't this always
+
+ align:start position:0%
+to talk about is why isn't this always
+ 
+
+ align:start position:0%
+to talk about is why isn't this always
+come out to the to the same angle every
+
+ align:start position:0%
+come out to the to the same angle every
+ 
+
+ align:start position:0%
+come out to the to the same angle every
+time? Why is the the third part out of
+
+ align:start position:0%
+time? Why is the the third part out of
+ 
+
+ align:start position:0%
+time? Why is the the third part out of
+the run of 50 different from the 24th
+
+ align:start position:0%
+the run of 50 different from the 24th
+ 
+
+ align:start position:0%
+the run of 50 different from the 24th
+part? You know, that sort of thing. and
+
+ align:start position:0%
+part? You know, that sort of thing. and
+ 
+
+ align:start position:0%
+part? You know, that sort of thing. and
+why when I when I machine this is it not
+
+ align:start position:0%
+why when I when I machine this is it not
+ 
+
+ align:start position:0%
+why when I when I machine this is it not
+the same diameter
+
+ align:start position:0%
+the same diameter
+ 
+
+ align:start position:0%
+the same diameter
+everywhere. Um, and so it it gets into
+
+ align:start position:0%
+everywhere. Um, and so it it gets into
+ 
+
+ align:start position:0%
+everywhere. Um, and so it it gets into
+looking at um the sources of
+
+ align:start position:0%
+looking at um the sources of
+ 
+
+ align:start position:0%
+looking at um the sources of
+variation. And by by our definition of a
+
+ align:start position:0%
+variation. And by by our definition of a
+ 
+
+ align:start position:0%
+variation. And by by our definition of a
+process parameter, we're going to say,
+
+ align:start position:0%
+process parameter, we're going to say,
+ 
+
+ align:start position:0%
+process parameter, we're going to say,
+well, it it Oops. Oh, don't do
+
+ align:start position:0%
+well, it it Oops. Oh, don't do
+ 
+
+ align:start position:0%
+well, it it Oops. Oh, don't do
+that. I'll say yes. But what did I
+
+ align:start position:0%
+that. I'll say yes. But what did I
+ 
+
+ align:start position:0%
+that. I'll say yes. But what did I
+do?
+
+ align:start position:0%
+do?
+ 
+
+ align:start position:0%
+do?
+Push
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by our definition of Oh, I see. by our
+
+ align:start position:0%
+by our definition of Oh, I see. by our
+ 
+
+ align:start position:0%
+by our definition of Oh, I see. by our
+definition of of this it's it's all
+
+ align:start position:0%
+definition of of this it's it's all
+ 
+
+ align:start position:0%
+definition of of this it's it's all
+wrapped
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up somehow well in the end it's all it's
+
+ align:start position:0%
+up somehow well in the end it's all it's
+ 
+
+ align:start position:0%
+up somehow well in the end it's all it's
+all wrapped up in this this functional
+
+ align:start position:0%
+all wrapped up in this this functional
+ 
+
+ align:start position:0%
+all wrapped up in this this functional
+relationship but primarily through these
+
+ align:start position:0%
+relationship but primarily through these
+ 
+
+ align:start position:0%
+relationship but primarily through these
+process parameters okay so we're going
+
+ align:start position:0%
+process parameters okay so we're going
+ 
+
+ align:start position:0%
+process parameters okay so we're going
+to use those to try and understand so so
+
+ align:start position:0%
+to use those to try and understand so so
+ 
+
+ align:start position:0%
+to use those to try and understand so so
+let's break down these these process
+
+ align:start position:0%
+let's break down these these process
+ 
+
+ align:start position:0%
+let's break down these these process
+parameters in a little bit more of um a
+
+ align:start position:0%
+parameters in a little bit more of um a
+ 
+
+ align:start position:0%
+parameters in a little bit more of um a
+u a logical fashion
+
+ align:start position:0%
+u a logical fashion
+ 
+
+ align:start position:0%
+u a logical fashion
+um and I'm going to do it in the
+
+ align:start position:0%
+um and I'm going to do it in the
+ 
+
+ align:start position:0%
+um and I'm going to do it in the
+following way with the following
+
+ align:start position:0%
+following way with the following
+ 
+
+ align:start position:0%
+following way with the following
+definitions. First of all, we're going
+
+ align:start position:0%
+definitions. First of all, we're going
+ 
+
+ align:start position:0%
+definitions. First of all, we're going
+to have alphas associated with the
+
+ align:start position:0%
+to have alphas associated with the
+ 
+
+ align:start position:0%
+to have alphas associated with the
+equipment and then we're going to have
+
+ align:start position:0%
+equipment and then we're going to have
+ 
+
+ align:start position:0%
+equipment and then we're going to have
+alphas associate let me go back here
+
+ align:start position:0%
+alphas associate let me go back here
+ 
+
+ align:start position:0%
+alphas associate let me go back here
+actually need my picture. So, we're
+
+ align:start position:0%
+actually need my picture. So, we're
+ 
+
+ align:start position:0%
+actually need my picture. So, we're
+going to have these parameters
+
+ align:start position:0%
+going to have these parameters
+ 
+
+ align:start position:0%
+going to have these parameters
+associated just with the
+
+ align:start position:0%
+associated just with the
+ 
+
+ align:start position:0%
+associated just with the
+equipment. And I think I've already
+
+ align:start position:0%
+equipment. And I think I've already
+ 
+
+ align:start position:0%
+equipment. And I think I've already
+explained why we want to distinguish
+
+ align:start position:0%
+explained why we want to distinguish
+ 
+
+ align:start position:0%
+explained why we want to distinguish
+between the two, you know. So, now we're
+
+ align:start position:0%
+between the two, you know. So, now we're
+ 
+
+ align:start position:0%
+between the two, you know. So, now we're
+talking about properties, variables,
+
+ align:start position:0%
+talking about properties, variables,
+ 
+
+ align:start position:0%
+talking about properties, variables,
+things I can adjust, things that happen
+
+ align:start position:0%
+things I can adjust, things that happen
+ 
+
+ align:start position:0%
+things I can adjust, things that happen
+that are staying with that piece of iron
+
+ align:start position:0%
+that are staying with that piece of iron
+ 
+
+ align:start position:0%
+that are staying with that piece of iron
+that's bolted down to the factory floor.
+
+ align:start position:0%
+that's bolted down to the factory floor.
+ 
+
+ align:start position:0%
+that's bolted down to the factory floor.
+And then a similar set, but
+
+ align:start position:0%
+And then a similar set, but
+ 
+
+ align:start position:0%
+And then a similar set, but
+for the stuff that goes in and out of
+
+ align:start position:0%
+for the stuff that goes in and out of
+ 
+
+ align:start position:0%
+for the stuff that goes in and out of
+the machine or that flows through the
+
+ align:start position:0%
+the machine or that flows through the
+ 
+
+ align:start position:0%
+the machine or that flows through the
+machine, it doesn't go in and out. So,
+
+ align:start position:0%
+machine, it doesn't go in and out. So,
+ 
+
+ align:start position:0%
+machine, it doesn't go in and out. So,
+that's why we distinguish between them.
+
+ align:start position:0%
+that's why we distinguish between them.
+ 
+
+ align:start position:0%
+that's why we distinguish between them.
+So let's just focus uh um I don't know
+
+ align:start position:0%
+So let's just focus uh um I don't know
+ 
+
+ align:start position:0%
+So let's just focus uh um I don't know
+let's focus on the machine on the
+
+ align:start position:0%
+let's focus on the machine on the
+ 
+
+ align:start position:0%
+let's focus on the machine on the
+equipment. If I think of two broad
+
+ align:start position:0%
+equipment. If I think of two broad
+ 
+
+ align:start position:0%
+equipment. If I think of two broad
+classifications of a machine well let's
+
+ align:start position:0%
+classifications of a machine well let's
+ 
+
+ align:start position:0%
+classifications of a machine well let's
+see try this exercise. I think
+
+ align:start position:0%
+see try this exercise. I think
+ 
+
+ align:start position:0%
+see try this exercise. I think
+everybody's familiar with a machine
+
+ align:start position:0%
+everybody's familiar with a machine
+ 
+
+ align:start position:0%
+everybody's familiar with a machine
+tool. I got a simple lathe. It's sitting
+
+ align:start position:0%
+tool. I got a simple lathe. It's sitting
+ 
+
+ align:start position:0%
+tool. I got a simple lathe. It's sitting
+here in front of us. Um and it's not
+
+ align:start position:0%
+here in front of us. Um and it's not
+ 
+
+ align:start position:0%
+here in front of us. Um and it's not
+doing a thing. It's not moving. It's not
+
+ align:start position:0%
+doing a thing. It's not moving. It's not
+ 
+
+ align:start position:0%
+doing a thing. It's not moving. It's not
+even plugged in.
+
+ align:start position:0%
+even plugged in.
+ 
+
+ align:start position:0%
+even plugged in.
+What what alphas what characteristics
+
+ align:start position:0%
+What what alphas what characteristics
+ 
+
+ align:start position:0%
+What what alphas what characteristics
+can you tell me about it just by looking
+
+ align:start position:0%
+can you tell me about it just by looking
+ 
+
+ align:start position:0%
+can you tell me about it just by looking
+at it? It's not
+
+ align:start position:0%
+at it? It's not
+ 
+
+ align:start position:0%
+at it? It's not
+moving. What might you if you were to
+
+ align:start position:0%
+moving. What might you if you were to
+ 
+
+ align:start position:0%
+moving. What might you if you were to
+describe it from an engineering point of
+
+ align:start position:0%
+describe it from an engineering point of
+ 
+
+ align:start position:0%
+describe it from an engineering point of
+view? What are the kinds of things you'd
+
+ align:start position:0%
+view? What are the kinds of things you'd
+ 
+
+ align:start position:0%
+view? What are the kinds of things you'd
+worry about on it?
+
+ align:start position:0%
+worry about on it?
+ 
+
+ align:start position:0%
+worry about on it?
+Stiffness. How stiff is it? Does it
+
+ align:start position:0%
+Stiffness. How stiff is it? Does it
+ 
+
+ align:start position:0%
+Stiffness. How stiff is it? Does it
+deform?
+
+ align:start position:0%
+deform?
+ 
+
+ align:start position:0%
+deform?
+Yeah, that's a that's almost it. That's
+
+ align:start position:0%
+Yeah, that's a that's almost it. That's
+ 
+
+ align:start position:0%
+Yeah, that's a that's almost it. That's
+a good one right there. Stiffness.
+
+ align:start position:0%
+a good one right there. Stiffness.
+ 
+
+ align:start position:0%
+a good one right there. Stiffness.
+Straightness.
+
+ align:start position:0%
+Straightness.
+ 
+
+ align:start position:0%
+Straightness.
+um uh some details of other you know
+
+ align:start position:0%
+um uh some details of other you know
+ 
+
+ align:start position:0%
+um uh some details of other you know
+mechanical characteristics of it. How
+
+ align:start position:0%
+mechanical characteristics of it. How
+ 
+
+ align:start position:0%
+mechanical characteristics of it. How
+about thermal expansion? Yeah, thermal
+
+ align:start position:0%
+about thermal expansion? Yeah, thermal
+ 
+
+ align:start position:0%
+about thermal expansion? Yeah, thermal
+expansion coefficient. Very important
+
+ align:start position:0%
+expansion coefficient. Very important
+ 
+
+ align:start position:0%
+expansion coefficient. Very important
+stuff. All those things that basically
+
+ align:start position:0%
+stuff. All those things that basically
+ 
+
+ align:start position:0%
+stuff. All those things that basically
+go into is is the structure and where
+
+ align:start position:0%
+go into is is the structure and where
+ 
+
+ align:start position:0%
+go into is is the structure and where
+I'm going to direct that energy source
+
+ align:start position:0%
+I'm going to direct that energy source
+ 
+
+ align:start position:0%
+I'm going to direct that energy source
+where I think it's going to be. Okay. Um
+
+ align:start position:0%
+where I think it's going to be. Okay. Um
+ 
+
+ align:start position:0%
+where I think it's going to be. Okay. Um
+now I turn it on. It starts moving and I
+
+ align:start position:0%
+now I turn it on. It starts moving and I
+ 
+
+ align:start position:0%
+now I turn it on. It starts moving and I
+start
+
+ align:start position:0%
+start
+ 
+
+ align:start position:0%
+start
+machining. Forget about the chips and
+
+ align:start position:0%
+machining. Forget about the chips and
+ 
+
+ align:start position:0%
+machining. Forget about the chips and
+all that other stuff, but just the
+
+ align:start position:0%
+all that other stuff, but just the
+ 
+
+ align:start position:0%
+all that other stuff, but just the
+machine itself. What are you gonna What
+
+ align:start position:0%
+machine itself. What are you gonna What
+ 
+
+ align:start position:0%
+machine itself. What are you gonna What
+other characteristics of the machine are
+
+ align:start position:0%
+other characteristics of the machine are
+ 
+
+ align:start position:0%
+other characteristics of the machine are
+you now going to worry about?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The turning speed. Yeah, the turning
+
+ align:start position:0%
+The turning speed. Yeah, the turning
+ 
+
+ align:start position:0%
+The turning speed. Yeah, the turning
+speed. Exactly. The speed. What else?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Accuracy of that rotation. Yeah.
+
+ align:start position:0%
+Accuracy of that rotation. Yeah.
+ 
+
+ align:start position:0%
+Accuracy of that rotation. Yeah.
+Accuracy of the rotation. Yeah. Okay.
+
+ align:start position:0%
+Accuracy of the rotation. Yeah. Okay.
+ 
+
+ align:start position:0%
+Accuracy of the rotation. Yeah. Okay.
+Yep. But now we got the turning speed.
+
+ align:start position:0%
+Yep. But now we got the turning speed.
+ 
+
+ align:start position:0%
+Yep. But now we got the turning speed.
+All right. Now, okay. What's the
+
+ align:start position:0%
+All right. Now, okay. What's the
+ 
+
+ align:start position:0%
+All right. Now, okay. What's the
+difference from the machine's point of
+
+ align:start position:0%
+difference from the machine's point of
+ 
+
+ align:start position:0%
+difference from the machine's point of
+view? If I've got the tool and I'm
+
+ align:start position:0%
+view? If I've got the tool and I'm
+ 
+
+ align:start position:0%
+view? If I've got the tool and I'm
+coming along, I think you guys can see
+
+ align:start position:0%
+coming along, I think you guys can see
+ 
+
+ align:start position:0%
+coming along, I think you guys can see
+this. If I'm coming along like this,
+
+ align:start position:0%
+this. If I'm coming along like this,
+ 
+
+ align:start position:0%
+this. If I'm coming along like this,
+right now I'm characterizing the machine
+
+ align:start position:0%
+right now I'm characterizing the machine
+ 
+
+ align:start position:0%
+right now I'm characterizing the machine
+and now I'm characterizing the machine.
+
+ align:start position:0%
+and now I'm characterizing the machine.
+ 
+
+ align:start position:0%
+and now I'm characterizing the machine.
+I'm I've hit the material and I'm
+
+ align:start position:0%
+I'm I've hit the material and I'm
+ 
+
+ align:start position:0%
+I'm I've hit the material and I'm
+starting to machine. What's the
+
+ align:start position:0%
+starting to machine. What's the
+ 
+
+ align:start position:0%
+starting to machine. What's the
+difference between when I'm here and
+
+ align:start position:0%
+difference between when I'm here and
+ 
+
+ align:start position:0%
+difference between when I'm here and
+when I'm here?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H you skipped something. Go ahead. I
+
+ align:start position:0%
+H you skipped something. Go ahead. I
+ 
+
+ align:start position:0%
+H you skipped something. Go ahead. I
+think Yeah. Yeah. You talked about the
+
+ align:start position:0%
+think Yeah. Yeah. You talked about the
+ 
+
+ align:start position:0%
+think Yeah. Yeah. You talked about the
+speed. So I have a the speed a speed
+
+ align:start position:0%
+speed. So I have a the speed a speed
+ 
+
+ align:start position:0%
+speed. So I have a the speed a speed
+here and I have a rotation speed. But if
+
+ align:start position:0%
+here and I have a rotation speed. But if
+ 
+
+ align:start position:0%
+here and I have a rotation speed. But if
+there's no force like you know there's
+
+ align:start position:0%
+there's no force like you know there's
+ 
+
+ align:start position:0%
+there's no force like you know there's
+no power there's no nothing no nothing
+
+ align:start position:0%
+no power there's no nothing no nothing
+ 
+
+ align:start position:0%
+no power there's no nothing no nothing
+much happening. It's good grammar. Um
+
+ align:start position:0%
+much happening. It's good grammar. Um
+ 
+
+ align:start position:0%
+much happening. It's good grammar. Um
+but if if I come along here all of a
+
+ align:start position:0%
+but if if I come along here all of a
+ 
+
+ align:start position:0%
+but if if I come along here all of a
+sudden the force changes. So as a
+
+ align:start position:0%
+sudden the force changes. So as a
+ 
+
+ align:start position:0%
+sudden the force changes. So as a
+minimum you've got these two sets of
+
+ align:start position:0%
+minimum you've got these two sets of
+ 
+
+ align:start position:0%
+minimum you've got these two sets of
+variables. You've got you know how stiff
+
+ align:start position:0%
+variables. You've got you know how stiff
+ 
+
+ align:start position:0%
+variables. You've got you know how stiff
+is the machine? How does it react to
+
+ align:start position:0%
+is the machine? How does it react to
+ 
+
+ align:start position:0%
+is the machine? How does it react to
+things like forces? um how straight is
+
+ align:start position:0%
+things like forces? um how straight is
+ 
+
+ align:start position:0%
+things like forces? um how straight is
+the machine if I move this way relative
+
+ align:start position:0%
+the machine if I move this way relative
+ 
+
+ align:start position:0%
+the machine if I move this way relative
+to the axis of rotation that's your
+
+ align:start position:0%
+to the axis of rotation that's your
+ 
+
+ align:start position:0%
+to the axis of rotation that's your
+accuracy thing you know is it that way
+
+ align:start position:0%
+accuracy thing you know is it that way
+ 
+
+ align:start position:0%
+accuracy thing you know is it that way
+and those are properties that they're
+
+ align:start position:0%
+and those are properties that they're
+ 
+
+ align:start position:0%
+and those are properties that they're
+not independent of of whether it's
+
+ align:start position:0%
+not independent of of whether it's
+ 
+
+ align:start position:0%
+not independent of of whether it's
+moving or not but you know you kind of
+
+ align:start position:0%
+moving or not but you know you kind of
+ 
+
+ align:start position:0%
+moving or not but you know you kind of
+look at it and you say and it's the
+
+ align:start position:0%
+look at it and you say and it's the
+ 
+
+ align:start position:0%
+look at it and you say and it's the
+basic characteristic of the machine and
+
+ align:start position:0%
+basic characteristic of the machine and
+ 
+
+ align:start position:0%
+basic characteristic of the machine and
+then you've got these transient ones
+
+ align:start position:0%
+then you've got these transient ones
+ 
+
+ align:start position:0%
+then you've got these transient ones
+that are only related to the energy
+
+ align:start position:0%
+that are only related to the energy
+ 
+
+ align:start position:0%
+that are only related to the energy
+exchange so you'd agree that if there's
+
+ align:start position:0%
+exchange so you'd agree that if there's
+ 
+
+ align:start position:0%
+exchange so you'd agree that if there's
+no force there's no energy exchange but
+
+ align:start position:0%
+no force there's no energy exchange but
+ 
+
+ align:start position:0%
+no force there's no energy exchange but
+as soon as I have a force and a velocity
+
+ align:start position:0%
+as soon as I have a force and a velocity
+ 
+
+ align:start position:0%
+as soon as I have a force and a velocity
+I'm putting mechanical power into that
+
+ align:start position:0%
+I'm putting mechanical power into that
+ 
+
+ align:start position:0%
+I'm putting mechanical power into that
+thing and something's going to happen.
+
+ align:start position:0%
+thing and something's going to happen.
+ 
+
+ align:start position:0%
+thing and something's going to happen.
+Okay. So from that we can actually say
+
+ align:start position:0%
+Okay. So from that we can actually say
+ 
+
+ align:start position:0%
+Okay. So from that we can actually say
+okay there are two types of variables.
+
+ align:start position:0%
+okay there are two types of variables.
+ 
+
+ align:start position:0%
+okay there are two types of variables.
+Think of these sort of ones that are
+
+ align:start position:0%
+Think of these sort of ones that are
+ 
+
+ align:start position:0%
+Think of these sort of ones that are
+intrinsic variables that characterize
+
+ align:start position:0%
+intrinsic variables that characterize
+ 
+
+ align:start position:0%
+intrinsic variables that characterize
+the basic properties of the machine. And
+
+ align:start position:0%
+the basic properties of the machine. And
+ 
+
+ align:start position:0%
+the basic properties of the machine. And
+you know if we if we were doing applied
+
+ align:start position:0%
+you know if we if we were doing applied
+ 
+
+ align:start position:0%
+you know if we if we were doing applied
+mechanics we'd say those are the
+
+ align:start position:0%
+mechanics we'd say those are the
+ 
+
+ align:start position:0%
+mechanics we'd say those are the
+constitutive properties of the material
+
+ align:start position:0%
+constitutive properties of the material
+ 
+
+ align:start position:0%
+constitutive properties of the material
+of the material or their constitutive
+
+ align:start position:0%
+of the material or their constitutive
+ 
+
+ align:start position:0%
+of the material or their constitutive
+properties of our machine. And then
+
+ align:start position:0%
+properties of our machine. And then
+ 
+
+ align:start position:0%
+properties of our machine. And then
+there are the energy states, how things
+
+ align:start position:0%
+there are the energy states, how things
+ 
+
+ align:start position:0%
+there are the energy states, how things
+change over time as the as the energy
+
+ align:start position:0%
+change over time as the as the energy
+ 
+
+ align:start position:0%
+change over time as the as the energy
+waxes and wanes and interchanges and
+
+ align:start position:0%
+waxes and wanes and interchanges and
+ 
+
+ align:start position:0%
+waxes and wanes and interchanges and
+things like that. And those are useful
+
+ align:start position:0%
+things like that. And those are useful
+ 
+
+ align:start position:0%
+things like that. And those are useful
+divisions because for example, how
+
+ align:start position:0%
+divisions because for example, how
+ 
+
+ align:start position:0%
+divisions because for example, how
+easily can I change the stiffness of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+machine? Can be done. Could buy a new
+
+ align:start position:0%
+machine? Can be done. Could buy a new
+ 
+
+ align:start position:0%
+machine? Can be done. Could buy a new
+one. I could go in and put in some more
+
+ align:start position:0%
+one. I could go in and put in some more
+ 
+
+ align:start position:0%
+one. I could go in and put in some more
+supports, you know, and that kind of
+
+ align:start position:0%
+supports, you know, and that kind of
+ 
+
+ align:start position:0%
+supports, you know, and that kind of
+stuff. Or I can take some away and make
+
+ align:start position:0%
+stuff. Or I can take some away and make
+ 
+
+ align:start position:0%
+stuff. Or I can take some away and make
+it less stiff.
+
+ align:start position:0%
+it less stiff.
+ 
+
+ align:start position:0%
+it less stiff.
+um kind of hard. Yeah. Depends a lot on
+
+ align:start position:0%
+um kind of hard. Yeah. Depends a lot on
+ 
+
+ align:start position:0%
+um kind of hard. Yeah. Depends a lot on
+where I
+
+ align:start position:0%
+where I
+ 
+
+ align:start position:0%
+where I
+have I have like a mill. I can take the
+
+ align:start position:0%
+have I have like a mill. I can take the
+ 
+
+ align:start position:0%
+have I have like a mill. I can take the
+table out very far and reduce the
+
+ align:start position:0%
+table out very far and reduce the
+ 
+
+ align:start position:0%
+table out very far and reduce the
+stiffness. Oh yeah. Yeah. Yeah. Yeah.
+
+ align:start position:0%
+stiffness. Oh yeah. Yeah. Yeah. Yeah.
+ 
+
+ align:start position:0%
+stiffness. Oh yeah. Yeah. Yeah. Yeah.
+Within right with stiffness is not a
+
+ align:start position:0%
+Within right with stiffness is not a
+ 
+
+ align:start position:0%
+Within right with stiffness is not a
+single quantity. You're right. I can
+
+ align:start position:0%
+single quantity. You're right. I can
+ 
+
+ align:start position:0%
+single quantity. You're right. I can
+find stiffer regions and less stiff
+
+ align:start position:0%
+find stiffer regions and less stiff
+ 
+
+ align:start position:0%
+find stiffer regions and less stiff
+regions. But I guess what I'm saying is
+
+ align:start position:0%
+regions. But I guess what I'm saying is
+ 
+
+ align:start position:0%
+regions. But I guess what I'm saying is
+if you need to elevate the stiffness of
+
+ align:start position:0%
+if you need to elevate the stiffness of
+ 
+
+ align:start position:0%
+if you need to elevate the stiffness of
+the whole, you know, there's no
+
+ align:start position:0%
+the whole, you know, there's no
+ 
+
+ align:start position:0%
+the whole, you know, there's no
+acceptable spot in it. What do you do?
+
+ align:start position:0%
+acceptable spot in it. What do you do?
+ 
+
+ align:start position:0%
+acceptable spot in it. What do you do?
+You know, you have to go you have to
+
+ align:start position:0%
+You know, you have to go you have to
+ 
+
+ align:start position:0%
+You know, you have to go you have to
+change the iron. I have to go in and
+
+ align:start position:0%
+change the iron. I have to go in and
+ 
+
+ align:start position:0%
+change the iron. I have to go in and
+make a a change. It's not something that
+
+ align:start position:0%
+make a a change. It's not something that
+ 
+
+ align:start position:0%
+make a a change. It's not something that
+we would call really at this case a
+
+ align:start position:0%
+we would call really at this case a
+ 
+
+ align:start position:0%
+we would call really at this case a
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+variable. On the other hand, if I need
+
+ align:start position:0%
+variable. On the other hand, if I need
+ 
+
+ align:start position:0%
+variable. On the other hand, if I need
+to change
+
+ align:start position:0%
+to change
+ 
+
+ align:start position:0%
+to change
+the speed at which I'm
+
+ align:start position:0%
+the speed at which I'm
+ 
+
+ align:start position:0%
+the speed at which I'm
+cutting, just change the speed at which
+
+ align:start position:0%
+cutting, just change the speed at which
+ 
+
+ align:start position:0%
+cutting, just change the speed at which
+I'm cutting and it changes. Okay. So, uh
+
+ align:start position:0%
+I'm cutting and it changes. Okay. So, uh
+ 
+
+ align:start position:0%
+I'm cutting and it changes. Okay. So, uh
+again, there's a there's an important
+
+ align:start position:0%
+again, there's a there's an important
+ 
+
+ align:start position:0%
+again, there's a there's an important
+distinction between uh between those two
+
+ align:start position:0%
+distinction between uh between those two
+ 
+
+ align:start position:0%
+distinction between uh between those two
+and our ability to know them as well as
+
+ align:start position:0%
+and our ability to know them as well as
+ 
+
+ align:start position:0%
+and our ability to know them as well as
+to control them is is vastly different.
+
+ align:start position:0%
+to control them is is vastly different.
+ 
+
+ align:start position:0%
+to control them is is vastly different.
+Now, the same thing holds true for this
+
+ align:start position:0%
+Now, the same thing holds true for this
+ 
+
+ align:start position:0%
+Now, the same thing holds true for this
+this this uh piece of piece of sheet
+
+ align:start position:0%
+this this uh piece of piece of sheet
+ 
+
+ align:start position:0%
+this this uh piece of piece of sheet
+metal, you know, in its undeformed
+
+ align:start position:0%
+metal, you know, in its undeformed
+ 
+
+ align:start position:0%
+metal, you know, in its undeformed
+state. This is really hard stuff. It's
+
+ align:start position:0%
+state. This is really hard stuff. It's
+ 
+
+ align:start position:0%
+state. This is really hard stuff. It's
+like butter. Okay. Um, how would you
+
+ align:start position:0%
+like butter. Okay. Um, how would you
+ 
+
+ align:start position:0%
+like butter. Okay. Um, how would you
+characterize if I just put this piece of
+
+ align:start position:0%
+characterize if I just put this piece of
+ 
+
+ align:start position:0%
+characterize if I just put this piece of
+sheet metal down here? How would you
+
+ align:start position:0%
+sheet metal down here? How would you
+ 
+
+ align:start position:0%
+sheet metal down here? How would you
+characterize it?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, please. Yield strength. Yield
+
+ align:start position:0%
+Yeah, please. Yield strength. Yield
+ 
+
+ align:start position:0%
+Yeah, please. Yield strength. Yield
+strength extremely important. Anything
+
+ align:start position:0%
+strength extremely important. Anything
+ 
+
+ align:start position:0%
+strength extremely important. Anything
+else?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Go ahead, Adam. Elasticity. Yeah,
+
+ align:start position:0%
+Go ahead, Adam. Elasticity. Yeah,
+ 
+
+ align:start position:0%
+Go ahead, Adam. Elasticity. Yeah,
+elasticity. Thickness. Thickness.
+
+ align:start position:0%
+elasticity. Thickness. Thickness.
+ 
+
+ align:start position:0%
+elasticity. Thickness. Thickness.
+Temperature.
+
+ align:start position:0%
+Temperature.
+ 
+
+ align:start position:0%
+Temperature.
+Temperature. Actually, that's not I'm
+
+ align:start position:0%
+Temperature. Actually, that's not I'm
+ 
+
+ align:start position:0%
+Temperature. Actually, that's not I'm
+I'm going to disagree with you on that.
+
+ align:start position:0%
+I'm going to disagree with you on that.
+ 
+
+ align:start position:0%
+I'm going to disagree with you on that.
+No. Why does temperature matter? Because
+
+ align:start position:0%
+No. Why does temperature matter? Because
+ 
+
+ align:start position:0%
+No. Why does temperature matter? Because
+it changes the dimension. Okay. So that
+
+ align:start position:0%
+it changes the dimension. Okay. So that
+ 
+
+ align:start position:0%
+it changes the dimension. Okay. So that
+so there's a thermal expansion
+
+ align:start position:0%
+so there's a thermal expansion
+ 
+
+ align:start position:0%
+so there's a thermal expansion
+characteristic on this. Okay, that's
+
+ align:start position:0%
+characteristic on this. Okay, that's
+ 
+
+ align:start position:0%
+characteristic on this. Okay, that's
+what I that's very important point for
+
+ align:start position:0%
+what I that's very important point for
+ 
+
+ align:start position:0%
+what I that's very important point for
+the when I say characterizing this you
+
+ align:start position:0%
+the when I say characterizing this you
+ 
+
+ align:start position:0%
+the when I say characterizing this you
+don't characterize it by its
+
+ align:start position:0%
+don't characterize it by its
+ 
+
+ align:start position:0%
+don't characterize it by its
+temperature. You characterize it by its
+
+ align:start position:0%
+temperature. You characterize it by its
+ 
+
+ align:start position:0%
+temperature. You characterize it by its
+reaction to
+
+ align:start position:0%
+reaction to
+ 
+
+ align:start position:0%
+reaction to
+temperature. I don't characterize it by
+
+ align:start position:0%
+temperature. I don't characterize it by
+ 
+
+ align:start position:0%
+temperature. I don't characterize it by
+its stress or strain. I characterize it
+
+ align:start position:0%
+its stress or strain. I characterize it
+ 
+
+ align:start position:0%
+its stress or strain. I characterize it
+by its reaction to stress or strain. So
+
+ align:start position:0%
+by its reaction to stress or strain. So
+ 
+
+ align:start position:0%
+by its reaction to stress or strain. So
+those are all again very clearly for a
+
+ align:start position:0%
+those are all again very clearly for a
+ 
+
+ align:start position:0%
+those are all again very clearly for a
+piece of metal it is constitutive
+
+ align:start position:0%
+piece of metal it is constitutive
+ 
+
+ align:start position:0%
+piece of metal it is constitutive
+properties and we could also worry about
+
+ align:start position:0%
+properties and we could also worry about
+ 
+
+ align:start position:0%
+properties and we could also worry about
+its chemical reactivity and all this
+
+ align:start position:0%
+its chemical reactivity and all this
+ 
+
+ align:start position:0%
+its chemical reactivity and all this
+other stuff but it's inherent
+
+ align:start position:0%
+other stuff but it's inherent
+ 
+
+ align:start position:0%
+other stuff but it's inherent
+characteristic of it which describes how
+
+ align:start position:0%
+characteristic of it which describes how
+ 
+
+ align:start position:0%
+characteristic of it which describes how
+it reacts
+
+ align:start position:0%
+it reacts
+ 
+
+ align:start position:0%
+it reacts
+to impinging energy. Okay. So the
+
+ align:start position:0%
+to impinging energy. Okay. So the
+ 
+
+ align:start position:0%
+to impinging energy. Okay. So the
+mechanical energy I put in
+
+ align:start position:0%
+mechanical energy I put in
+ 
+
+ align:start position:0%
+mechanical energy I put in
+here combined with its elasticity, its
+
+ align:start position:0%
+here combined with its elasticity, its
+ 
+
+ align:start position:0%
+here combined with its elasticity, its
+yield stress and other things determines
+
+ align:start position:0%
+yield stress and other things determines
+ 
+
+ align:start position:0%
+yield stress and other things determines
+how far it bends. Okay. And how it
+
+ align:start position:0%
+how far it bends. Okay. And how it
+ 
+
+ align:start position:0%
+how far it bends. Okay. And how it
+bends. So we distinguish between the
+
+ align:start position:0%
+bends. So we distinguish between the
+ 
+
+ align:start position:0%
+bends. So we distinguish between the
+two. Again, um so when this when this
+
+ align:start position:0%
+two. Again, um so when this when this
+ 
+
+ align:start position:0%
+two. Again, um so when this when this
+baby's sitting here waiting to be bent,
+
+ align:start position:0%
+baby's sitting here waiting to be bent,
+ 
+
+ align:start position:0%
+baby's sitting here waiting to be bent,
+it's got its constituive properties. As
+
+ align:start position:0%
+it's got its constituive properties. As
+ 
+
+ align:start position:0%
+it's got its constituive properties. As
+it's being bent, it's now bearing
+
+ align:start position:0%
+it's being bent, it's now bearing
+ 
+
+ align:start position:0%
+it's being bent, it's now bearing
+uh uh external loads uh and
+
+ align:start position:0%
+uh uh external loads uh and
+ 
+
+ align:start position:0%
+uh uh external loads uh and
+displacements. It's stressing and
+
+ align:start position:0%
+displacements. It's stressing and
+ 
+
+ align:start position:0%
+displacements. It's stressing and
+straining. Um and uh that's a
+
+ align:start position:0%
+straining. Um and uh that's a
+ 
+
+ align:start position:0%
+straining. Um and uh that's a
+transangent state, right? It's an energy
+
+ align:start position:0%
+transangent state, right? It's an energy
+ 
+
+ align:start position:0%
+transangent state, right? It's an energy
+transfer. And those are two different
+
+ align:start position:0%
+transfer. And those are two different
+ 
+
+ align:start position:0%
+transfer. And those are two different
+things. They're both important to
+
+ align:start position:0%
+things. They're both important to
+ 
+
+ align:start position:0%
+things. They're both important to
+determining what comes out here because,
+
+ align:start position:0%
+determining what comes out here because,
+ 
+
+ align:start position:0%
+determining what comes out here because,
+you know, if I said, "Okay, go back to
+
+ align:start position:0%
+you know, if I said, "Okay, go back to
+ 
+
+ align:start position:0%
+you know, if I said, "Okay, go back to
+your computers or your textbooks and
+
+ align:start position:0%
+your computers or your textbooks and
+ 
+
+ align:start position:0%
+your computers or your textbooks and
+give me an analysis of how what it takes
+
+ align:start position:0%
+give me an analysis of how what it takes
+ 
+
+ align:start position:0%
+give me an analysis of how what it takes
+to get this shape." You're going to need
+
+ align:start position:0%
+to get this shape." You're going to need
+ 
+
+ align:start position:0%
+to get this shape." You're going to need
+to know the characteristics of the
+
+ align:start position:0%
+to know the characteristics of the
+ 
+
+ align:start position:0%
+to know the characteristics of the
+material, stiffness, yield, stress, that
+
+ align:start position:0%
+material, stiffness, yield, stress, that
+ 
+
+ align:start position:0%
+material, stiffness, yield, stress, that
+sort of thing. You're also going to need
+
+ align:start position:0%
+sort of thing. You're also going to need
+ 
+
+ align:start position:0%
+sort of thing. You're also going to need
+to know what forces and displacements I
+
+ align:start position:0%
+to know what forces and displacements I
+ 
+
+ align:start position:0%
+to know what forces and displacements I
+put into it, which will tell you what
+
+ align:start position:0%
+put into it, which will tell you what
+ 
+
+ align:start position:0%
+put into it, which will tell you what
+happened internally to this thing. What
+
+ align:start position:0%
+happened internally to this thing. What
+ 
+
+ align:start position:0%
+happened internally to this thing. What
+stresses and strains did it did it have?
+
+ align:start position:0%
+stresses and strains did it did it have?
+ 
+
+ align:start position:0%
+stresses and strains did it did it have?
+Okay. Same thing with this
+
+ align:start position:0%
+Okay. Same thing with this
+ 
+
+ align:start position:0%
+Okay. Same thing with this
+You know, I needed to know what the the
+
+ align:start position:0%
+You know, I needed to know what the the
+ 
+
+ align:start position:0%
+You know, I needed to know what the the
+characteristic of the polymer was. How
+
+ align:start position:0%
+characteristic of the polymer was. How
+ 
+
+ align:start position:0%
+characteristic of the polymer was. How
+did it react to temperature? What was it
+
+ align:start position:0%
+did it react to temperature? What was it
+ 
+
+ align:start position:0%
+did it react to temperature? What was it
+its viscosity with temperature? What's
+
+ align:start position:0%
+its viscosity with temperature? What's
+ 
+
+ align:start position:0%
+its viscosity with temperature? What's
+its heat transfer characteristics? And
+
+ align:start position:0%
+its heat transfer characteristics? And
+ 
+
+ align:start position:0%
+its heat transfer characteristics? And
+then I needed to know what temperature
+
+ align:start position:0%
+then I needed to know what temperature
+ 
+
+ align:start position:0%
+then I needed to know what temperature
+it was, what pressure it saw, and what
+
+ align:start position:0%
+it was, what pressure it saw, and what
+ 
+
+ align:start position:0%
+it was, what pressure it saw, and what
+the heat transfer characteristics of the
+
+ align:start position:0%
+the heat transfer characteristics of the
+ 
+
+ align:start position:0%
+the heat transfer characteristics of the
+mold were. Okay. So, what does this all
+
+ align:start position:0%
+mold were. Okay. So, what does this all
+ 
+
+ align:start position:0%
+mold were. Okay. So, what does this all
+lead
+
+ align:start position:0%
+lead
+ 
+
+ align:start position:0%
+lead
+to? These four babies. Two two major
+
+ align:start position:0%
+to? These four babies. Two two major
+ 
+
+ align:start position:0%
+to? These four babies. Two two major
+things. States and properties. Okay.
+
+ align:start position:0%
+things. States and properties. Okay.
+ 
+
+ align:start position:0%
+things. States and properties. Okay.
+States and properties. energy
+
+ align:start position:0%
+States and properties. energy
+ 
+
+ align:start position:0%
+States and properties. energy
+states, transient things, things that
+
+ align:start position:0%
+states, transient things, things that
+ 
+
+ align:start position:0%
+states, transient things, things that
+don't hang around, things that are just
+
+ align:start position:0%
+don't hang around, things that are just
+ 
+
+ align:start position:0%
+don't hang around, things that are just
+there to accomplish what we wanted to
+
+ align:start position:0%
+there to accomplish what we wanted to
+ 
+
+ align:start position:0%
+there to accomplish what we wanted to
+accomplish and then they go away and
+
+ align:start position:0%
+accomplish and then they go away and
+ 
+
+ align:start position:0%
+accomplish and then they go away and
+properties which if you will, we can
+
+ align:start position:0%
+properties which if you will, we can
+ 
+
+ align:start position:0%
+properties which if you will, we can
+change them, but they kind of are there
+
+ align:start position:0%
+change them, but they kind of are there
+ 
+
+ align:start position:0%
+change them, but they kind of are there
+when we begin and they're still there
+
+ align:start position:0%
+when we begin and they're still there
+ 
+
+ align:start position:0%
+when we begin and they're still there
+when we're done.
+
+ align:start position:0%
+when we're done.
+ 
+
+ align:start position:0%
+when we're done.
+Okay? Um, and are are more inherent to
+
+ align:start position:0%
+Okay? Um, and are are more inherent to
+ 
+
+ align:start position:0%
+Okay? Um, and are are more inherent to
+either the the the equipment itself, the
+
+ align:start position:0%
+either the the the equipment itself, the
+ 
+
+ align:start position:0%
+either the the the equipment itself, the
+m essentially the material of the
+
+ align:start position:0%
+m essentially the material of the
+ 
+
+ align:start position:0%
+m essentially the material of the
+equipment or inherent to the to the
+
+ align:start position:0%
+equipment or inherent to the to the
+ 
+
+ align:start position:0%
+equipment or inherent to the to the
+material itself.
+
+ align:start position:0%
+material itself.
+ 
+
+ align:start position:0%
+material itself.
+Um so when we talk about energy states
+
+ align:start position:0%
+Um so when we talk about energy states
+ 
+
+ align:start position:0%
+Um so when we talk about energy states
+this one is is can be made much more
+
+ align:start position:0%
+this one is is can be made much more
+ 
+
+ align:start position:0%
+this one is is can be made much more
+precise than we have time to do here and
+
+ align:start position:0%
+precise than we have time to do here and
+ 
+
+ align:start position:0%
+precise than we have time to do here and
+uh those of us who who are students of
+
+ align:start position:0%
+uh those of us who who are students of
+ 
+
+ align:start position:0%
+uh those of us who who are students of
+uh system dynamics in the mechanical in
+
+ align:start position:0%
+uh system dynamics in the mechanical in
+ 
+
+ align:start position:0%
+uh system dynamics in the mechanical in
+the in the not in the in the um Sturman
+
+ align:start position:0%
+the in the not in the in the um Sturman
+ 
+
+ align:start position:0%
+the in the not in the in the um Sturman
+sense but in the uh in the painter and
+
+ align:start position:0%
+sense but in the uh in the painter and
+ 
+
+ align:start position:0%
+sense but in the uh in the painter and
+and Richardson sense of uh system
+
+ align:start position:0%
+and Richardson sense of uh system
+ 
+
+ align:start position:0%
+and Richardson sense of uh system
+dynamics. uh understand that you can
+
+ align:start position:0%
+dynamics. uh understand that you can
+ 
+
+ align:start position:0%
+dynamics. uh understand that you can
+really do a good job of describing the
+
+ align:start position:0%
+really do a good job of describing the
+ 
+
+ align:start position:0%
+really do a good job of describing the
+world by simply talking about uh energy
+
+ align:start position:0%
+world by simply talking about uh energy
+ 
+
+ align:start position:0%
+world by simply talking about uh energy
+or power and constitutive relationships
+
+ align:start position:0%
+or power and constitutive relationships
+ 
+
+ align:start position:0%
+or power and constitutive relationships
+and you can model any thing as how it
+
+ align:start position:0%
+and you can model any thing as how it
+ 
+
+ align:start position:0%
+and you can model any thing as how it
+reacts to these to these things. So
+
+ align:start position:0%
+reacts to these to these things. So
+ 
+
+ align:start position:0%
+reacts to these to these things. So
+that's really what we've done here. The
+
+ align:start position:0%
+that's really what we've done here. The
+ 
+
+ align:start position:0%
+that's really what we've done here. The
+equipment provides or absorbs either
+
+ align:start position:0%
+equipment provides or absorbs either
+ 
+
+ align:start position:0%
+equipment provides or absorbs either
+either provides or absorbs some form of
+
+ align:start position:0%
+either provides or absorbs some form of
+ 
+
+ align:start position:0%
+either provides or absorbs some form of
+energy, force, velocity, pressure, flow,
+
+ align:start position:0%
+energy, force, velocity, pressure, flow,
+ 
+
+ align:start position:0%
+energy, force, velocity, pressure, flow,
+force displacement,
+
+ align:start position:0%
+force displacement,
+ 
+
+ align:start position:0%
+force displacement,
+uh that sort of thing, voltage, current,
+
+ align:start position:0%
+uh that sort of thing, voltage, current,
+ 
+
+ align:start position:0%
+uh that sort of thing, voltage, current,
+heat transfer, u heat flow. Um, and
+
+ align:start position:0%
+heat transfer, u heat flow. Um, and
+ 
+
+ align:start position:0%
+heat transfer, u heat flow. Um, and
+those are the things that
+
+ align:start position:0%
+those are the things that
+ 
+
+ align:start position:0%
+those are the things that
+determine specifically what's what what
+
+ align:start position:0%
+determine specifically what's what what
+ 
+
+ align:start position:0%
+determine specifically what's what what
+happens in the interaction between these
+
+ align:start position:0%
+happens in the interaction between these
+ 
+
+ align:start position:0%
+happens in the interaction between these
+two. And then the properties which is
+
+ align:start position:0%
+two. And then the properties which is
+ 
+
+ align:start position:0%
+two. And then the properties which is
+sort of like what's going to happen when
+
+ align:start position:0%
+sort of like what's going to happen when
+ 
+
+ align:start position:0%
+sort of like what's going to happen when
+that energy is transferred are all these
+
+ align:start position:0%
+that energy is transferred are all these
+ 
+
+ align:start position:0%
+that energy is transferred are all these
+things we've talked about modulus of
+
+ align:start position:0%
+things we've talked about modulus of
+ 
+
+ align:start position:0%
+things we've talked about modulus of
+elasticity plastic flow properties
+
+ align:start position:0%
+elasticity plastic flow properties
+ 
+
+ align:start position:0%
+elasticity plastic flow properties
+viscosity sort of almost the same thing
+
+ align:start position:0%
+viscosity sort of almost the same thing
+ 
+
+ align:start position:0%
+viscosity sort of almost the same thing
+resistance inductance capacitance
+
+ align:start position:0%
+resistance inductance capacitance
+ 
+
+ align:start position:0%
+resistance inductance capacitance
+chemical reactivity heat transfer
+
+ align:start position:0%
+chemical reactivity heat transfer
+ 
+
+ align:start position:0%
+chemical reactivity heat transfer
+coefficients okay thermal diffusivities
+
+ align:start position:0%
+coefficients okay thermal diffusivities
+ 
+
+ align:start position:0%
+coefficients okay thermal diffusivities
+um intensive constituive properties plus
+
+ align:start position:0%
+um intensive constituive properties plus
+ 
+
+ align:start position:0%
+um intensive constituive properties plus
+because someone mentioned this before
+
+ align:start position:0%
+because someone mentioned this before
+ 
+
+ align:start position:0%
+because someone mentioned this before
+someone mentioned thickness of this
+
+ align:start position:0%
+someone mentioned thickness of this
+ 
+
+ align:start position:0%
+someone mentioned thickness of this
+extremely important so are the other two
+
+ align:start position:0%
+extremely important so are the other two
+ 
+
+ align:start position:0%
+extremely important so are the other two
+dimensions these dimensions are
+
+ align:start position:0%
+dimensions these dimensions are
+ 
+
+ align:start position:0%
+dimensions these dimensions are
+important and these dimensions are
+
+ align:start position:0%
+important and these dimensions are
+ 
+
+ align:start position:0%
+important and these dimensions are
+important and so it turns out the the
+
+ align:start position:0%
+important and so it turns out the the
+ 
+
+ align:start position:0%
+important and so it turns out the the
+object of our all our affection is
+
+ align:start position:0%
+object of our all our affection is
+ 
+
+ align:start position:0%
+object of our all our affection is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+um the geometry in the end right so it's
+
+ align:start position:0%
+um the geometry in the end right so it's
+ 
+
+ align:start position:0%
+um the geometry in the end right so it's
+a sort of an extensive property of the
+
+ align:start position:0%
+a sort of an extensive property of the
+ 
+
+ align:start position:0%
+a sort of an extensive property of the
+material but we also have to worry about
+
+ align:start position:0%
+material but we also have to worry about
+ 
+
+ align:start position:0%
+material but we also have to worry about
+the geometry before and after and we
+
+ align:start position:0%
+the geometry before and after and we
+ 
+
+ align:start position:0%
+the geometry before and after and we
+worry about the geometry of uh obviously
+
+ align:start position:0%
+worry about the geometry of uh obviously
+ 
+
+ align:start position:0%
+worry about the geometry of uh obviously
+the geometry of the machine is important
+
+ align:start position:0%
+the geometry of the machine is important
+ 
+
+ align:start position:0%
+the geometry of the machine is important
+you know is it straight is it square
+
+ align:start position:0%
+you know is it straight is it square
+ 
+
+ align:start position:0%
+you know is it straight is it square
+that sort of
+
+ align:start position:0%
+that sort of
+ 
+
+ align:start position:0%
+that sort of
+okay so uh let me finish up by just
+
+ align:start position:0%
+okay so uh let me finish up by just
+ 
+
+ align:start position:0%
+okay so uh let me finish up by just
+saying that we can have this
+
+ align:start position:0%
+saying that we can have this
+ 
+
+ align:start position:0%
+saying that we can have this
+model and then talk about and and why
+
+ align:start position:0%
+model and then talk about and and why
+ 
+
+ align:start position:0%
+model and then talk about and and why
+did I bother doing this? I mean, it's
+
+ align:start position:0%
+did I bother doing this? I mean, it's
+ 
+
+ align:start position:0%
+did I bother doing this? I mean, it's
+it's kind of fun. It's it's uh
+
+ align:start position:0%
+it's kind of fun. It's it's uh
+ 
+
+ align:start position:0%
+it's kind of fun. It's it's uh
+intellectually stimulating a little bit,
+
+ align:start position:0%
+intellectually stimulating a little bit,
+ 
+
+ align:start position:0%
+intellectually stimulating a little bit,
+but I think there's one real benefit to
+
+ align:start position:0%
+but I think there's one real benefit to
+ 
+
+ align:start position:0%
+but I think there's one real benefit to
+it, which is to understand why things
+
+ align:start position:0%
+it, which is to understand why things
+ 
+
+ align:start position:0%
+it, which is to understand why things
+vary.
+
+ align:start position:0%
+vary.
+ 
+
+ align:start position:0%
+vary.
+So if I take if I just say all right I'm
+
+ align:start position:0%
+So if I take if I just say all right I'm
+ 
+
+ align:start position:0%
+So if I take if I just say all right I'm
+going to subdivide all of by the way all
+
+ align:start position:0%
+going to subdivide all of by the way all
+ 
+
+ align:start position:0%
+going to subdivide all of by the way all
+all four of these
+
+ align:start position:0%
+all four of these
+ 
+
+ align:start position:0%
+all four of these
+things are subdivisions of this this
+
+ align:start position:0%
+things are subdivisions of this this
+ 
+
+ align:start position:0%
+things are subdivisions of this this
+vector alpha that I that we said is is
+
+ align:start position:0%
+vector alpha that I that we said is is
+ 
+
+ align:start position:0%
+vector alpha that I that we said is is
+what makes everything happen. Okay. So
+
+ align:start position:0%
+what makes everything happen. Okay. So
+ 
+
+ align:start position:0%
+what makes everything happen. Okay. So
+I've got alpha and then I'm going to
+
+ align:start position:0%
+I've got alpha and then I'm going to
+ 
+
+ align:start position:0%
+I've got alpha and then I'm going to
+divide that into what I'll call
+
+ align:start position:0%
+divide that into what I'll call
+ 
+
+ align:start position:0%
+divide that into what I'll call
+equipment states equipment properties
+
+ align:start position:0%
+equipment states equipment properties
+ 
+
+ align:start position:0%
+equipment states equipment properties
+material states and material properties.
+
+ align:start position:0%
+material states and material properties.
+ 
+
+ align:start position:0%
+material states and material properties.
+And why do I bother to do that? Well, in
+
+ align:start position:0%
+And why do I bother to do that? Well, in
+ 
+
+ align:start position:0%
+And why do I bother to do that? Well, in
+end, I'll give you the punch line
+
+ align:start position:0%
+end, I'll give you the punch line
+ 
+
+ align:start position:0%
+end, I'll give you the punch line
+because we're just about out of time. Is
+
+ align:start position:0%
+because we're just about out of time. Is
+ 
+
+ align:start position:0%
+because we're just about out of time. Is
+some of
+
+ align:start position:0%
+some of
+ 
+
+ align:start position:0%
+some of
+these are really easy to control, to
+
+ align:start position:0%
+these are really easy to control, to
+ 
+
+ align:start position:0%
+these are really easy to control, to
+keep fixed, and to basically know
+
+ align:start position:0%
+keep fixed, and to basically know
+ 
+
+ align:start position:0%
+keep fixed, and to basically know
+deterministically. Most of
+
+ align:start position:0%
+deterministically. Most of
+ 
+
+ align:start position:0%
+deterministically. Most of
+them certain certain categories are
+
+ align:start position:0%
+them certain certain categories are
+ 
+
+ align:start position:0%
+them certain certain categories are
+really hard to do that with. As an
+
+ align:start position:0%
+really hard to do that with. As an
+ 
+
+ align:start position:0%
+really hard to do that with. As an
+example, material
+
+ align:start position:0%
+example, material
+ 
+
+ align:start position:0%
+example, material
+properties again material property of
+
+ align:start position:0%
+properties again material property of
+ 
+
+ align:start position:0%
+properties again material property of
+this. How well do I know the properties
+
+ align:start position:0%
+this. How well do I know the properties
+ 
+
+ align:start position:0%
+this. How well do I know the properties
+of this bar of aluminum or this this
+
+ align:start position:0%
+of this bar of aluminum or this this
+ 
+
+ align:start position:0%
+of this bar of aluminum or this this
+hunk of plastic? Well, you know, I can
+
+ align:start position:0%
+hunk of plastic? Well, you know, I can
+ 
+
+ align:start position:0%
+hunk of plastic? Well, you know, I can
+do some tests and do this kind of stuff,
+
+ align:start position:0%
+do some tests and do this kind of stuff,
+ 
+
+ align:start position:0%
+do some tests and do this kind of stuff,
+but again, it can be shown that that
+
+ align:start position:0%
+but again, it can be shown that that
+ 
+
+ align:start position:0%
+but again, it can be shown that that
+these can be highly variable,
+
+ align:start position:0%
+these can be highly variable,
+ 
+
+ align:start position:0%
+these can be highly variable,
+particularly as I go from this bar to
+
+ align:start position:0%
+particularly as I go from this bar to
+ 
+
+ align:start position:0%
+particularly as I go from this bar to
+that bar to that bar. So, we're going to
+
+ align:start position:0%
+that bar to that bar. So, we're going to
+ 
+
+ align:start position:0%
+that bar to that bar. So, we're going to
+be able to argue that unless you spend a
+
+ align:start position:0%
+be able to argue that unless you spend a
+ 
+
+ align:start position:0%
+be able to argue that unless you spend a
+lot of time upstream eliminating
+
+ align:start position:0%
+lot of time upstream eliminating
+ 
+
+ align:start position:0%
+lot of time upstream eliminating
+variations like in in the unless you do
+
+ align:start position:0%
+variations like in in the unless you do
+ 
+
+ align:start position:0%
+variations like in in the unless you do
+really good process control on the
+
+ align:start position:0%
+really good process control on the
+ 
+
+ align:start position:0%
+really good process control on the
+casting and and u turning or casting and
+
+ align:start position:0%
+casting and and u turning or casting and
+ 
+
+ align:start position:0%
+casting and and u turning or casting and
+and rolling and other processes that go
+
+ align:start position:0%
+and rolling and other processes that go
+ 
+
+ align:start position:0%
+and rolling and other processes that go
+into this this will have variable
+
+ align:start position:0%
+into this this will have variable
+ 
+
+ align:start position:0%
+into this this will have variable
+properties. So this tends to be material
+
+ align:start position:0%
+properties. So this tends to be material
+ 
+
+ align:start position:0%
+properties. So this tends to be material
+properties tends to be uh
+
+ align:start position:0%
+properties tends to be uh
+ 
+
+ align:start position:0%
+properties tends to be uh
+variable and as a result depending on
+
+ align:start position:0%
+variable and as a result depending on
+ 
+
+ align:start position:0%
+variable and as a result depending on
+the process
+
+ align:start position:0%
+the process
+ 
+
+ align:start position:0%
+the process
+mechanics has a huge effect on what um
+
+ align:start position:0%
+mechanics has a huge effect on what um
+ 
+
+ align:start position:0%
+mechanics has a huge effect on what um
+what your result can be unless there
+
+ align:start position:0%
+what your result can be unless there
+ 
+
+ align:start position:0%
+what your result can be unless there
+there are some wonderful processes out
+
+ align:start position:0%
+there are some wonderful processes out
+ 
+
+ align:start position:0%
+there are some wonderful processes out
+there again like I said like machining
+
+ align:start position:0%
+there again like I said like machining
+ 
+
+ align:start position:0%
+there again like I said like machining
+that say yeah I don't really care I'm
+
+ align:start position:0%
+that say yeah I don't really care I'm
+ 
+
+ align:start position:0%
+that say yeah I don't really care I'm
+I'm very insensitive to that
+
+ align:start position:0%
+I'm very insensitive to that
+ 
+
+ align:start position:0%
+I'm very insensitive to that
+um equipment properties properties.
+
+ align:start position:0%
+um equipment properties properties.
+ 
+
+ align:start position:0%
+um equipment properties properties.
+Okay. Equipment properties. So, the
+
+ align:start position:0%
+Okay. Equipment properties. So, the
+ 
+
+ align:start position:0%
+Okay. Equipment properties. So, the
+stiffness of the machine, you know, uh
+
+ align:start position:0%
+stiffness of the machine, you know, uh
+ 
+
+ align:start position:0%
+stiffness of the machine, you know, uh
+the the temperature in a reaction
+
+ align:start position:0%
+the the temperature in a reaction
+ 
+
+ align:start position:0%
+the the temperature in a reaction
+chamber, other things like that. I'm
+
+ align:start position:0%
+chamber, other things like that. I'm
+ 
+
+ align:start position:0%
+chamber, other things like that. I'm
+sorry, not temperature uh sorry, the uh
+
+ align:start position:0%
+sorry, not temperature uh sorry, the uh
+ 
+
+ align:start position:0%
+sorry, not temperature uh sorry, the uh
+the thermal insulation in a in a uh in a
+
+ align:start position:0%
+the thermal insulation in a in a uh in a
+ 
+
+ align:start position:0%
+the thermal insulation in a in a uh in a
+in an oven, something like
+
+ align:start position:0%
+in an oven, something like
+ 
+
+ align:start position:0%
+in an oven, something like
+that. Okay. Um within limits, of course,
+
+ align:start position:0%
+that. Okay. Um within limits, of course,
+ 
+
+ align:start position:0%
+that. Okay. Um within limits, of course,
+there's some uncertainty there. It's not
+
+ align:start position:0%
+there's some uncertainty there. It's not
+ 
+
+ align:start position:0%
+there's some uncertainty there. It's not
+just variable. I I should say variable
+
+ align:start position:0%
+just variable. I I should say variable
+ 
+
+ align:start position:0%
+just variable. I I should say variable
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+uh uncertain. either one is as a source
+
+ align:start position:0%
+uh uncertain. either one is as a source
+ 
+
+ align:start position:0%
+uh uncertain. either one is as a source
+of uncertainty or variation for us.
+
+ align:start position:0%
+of uncertainty or variation for us.
+ 
+
+ align:start position:0%
+of uncertainty or variation for us.
+Um, equipment properties. Well, again,
+
+ align:start position:0%
+Um, equipment properties. Well, again,
+ 
+
+ align:start position:0%
+Um, equipment properties. Well, again,
+if I pay a lot, if I'm careful with the
+
+ align:start position:0%
+if I pay a lot, if I'm careful with the
+ 
+
+ align:start position:0%
+if I pay a lot, if I'm careful with the
+machine, if it doesn't degrade a lot
+
+ align:start position:0%
+machine, if it doesn't degrade a lot
+ 
+
+ align:start position:0%
+machine, if it doesn't degrade a lot
+over time, then I'm in good shape.
+
+ align:start position:0%
+over time, then I'm in good shape.
+ 
+
+ align:start position:0%
+over time, then I'm in good shape.
+Machines degrade over time. So, tool
+
+ align:start position:0%
+Machines degrade over time. So, tool
+ 
+
+ align:start position:0%
+Machines degrade over time. So, tool
+wear is a degradation in an equipment
+
+ align:start position:0%
+wear is a degradation in an equipment
+ 
+
+ align:start position:0%
+wear is a degradation in an equipment
+property, right? It's an expected
+
+ align:start position:0%
+property, right? It's an expected
+ 
+
+ align:start position:0%
+property, right? It's an expected
+dimension that's actually changing over
+
+ align:start position:0%
+dimension that's actually changing over
+ 
+
+ align:start position:0%
+dimension that's actually changing over
+time. So this can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable over many cases long times.
+
+ align:start position:0%
+variable over many cases long times.
+ 
+
+ align:start position:0%
+variable over many cases long times.
+That's a maintenance issue as much as
+
+ align:start position:0%
+That's a maintenance issue as much as
+ 
+
+ align:start position:0%
+That's a maintenance issue as much as
+anything else. But again, it's within a
+
+ align:start position:0%
+anything else. But again, it's within a
+ 
+
+ align:start position:0%
+anything else. But again, it's within a
+question of how good the machine is. If
+
+ align:start position:0%
+question of how good the machine is. If
+ 
+
+ align:start position:0%
+question of how good the machine is. If
+you build a a machine with very sloppy
+
+ align:start position:0%
+you build a a machine with very sloppy
+ 
+
+ align:start position:0%
+you build a a machine with very sloppy
+bearings, a sloppy bearing is basically
+
+ align:start position:0%
+bearings, a sloppy bearing is basically
+ 
+
+ align:start position:0%
+bearings, a sloppy bearing is basically
+a noise generator, right? You just don't
+
+ align:start position:0%
+a noise generator, right? You just don't
+ 
+
+ align:start position:0%
+a noise generator, right? You just don't
+know where things are. If you build a
+
+ align:start position:0%
+know where things are. If you build a
+ 
+
+ align:start position:0%
+know where things are. If you build a
+machine that is supposed to distribute a
+
+ align:start position:0%
+machine that is supposed to distribute a
+ 
+
+ align:start position:0%
+machine that is supposed to distribute a
+vapor, it's got a a a some sort of a a
+
+ align:start position:0%
+vapor, it's got a a a some sort of a a
+ 
+
+ align:start position:0%
+vapor, it's got a a a some sort of a a
+vapor handling system that's supposed to
+
+ align:start position:0%
+vapor handling system that's supposed to
+ 
+
+ align:start position:0%
+vapor handling system that's supposed to
+distribute it evenly, but it clogs
+
+ align:start position:0%
+distribute it evenly, but it clogs
+ 
+
+ align:start position:0%
+distribute it evenly, but it clogs
+easily or something like that or it just
+
+ align:start position:0%
+easily or something like that or it just
+ 
+
+ align:start position:0%
+easily or something like that or it just
+wasn't designed properly, then um you've
+
+ align:start position:0%
+wasn't designed properly, then um you've
+ 
+
+ align:start position:0%
+wasn't designed properly, then um you've
+got bad properties could cause
+
+ align:start position:0%
+got bad properties could cause
+ 
+
+ align:start position:0%
+got bad properties could cause
+variability.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um equipment
+
+ align:start position:0%
+um equipment
+ 
+
+ align:start position:0%
+um equipment
+states, forces, pressures, temperatures,
+
+ align:start position:0%
+states, forces, pressures, temperatures,
+ 
+
+ align:start position:0%
+states, forces, pressures, temperatures,
+flows,
+
+ align:start position:0%
+flows,
+ 
+
+ align:start position:0%
+flows,
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+velocities. What do you think about
+
+ align:start position:0%
+velocities. What do you think about
+ 
+
+ align:start position:0%
+velocities. What do you think about
+those in terms of our ability to control
+
+ align:start position:0%
+those in terms of our ability to control
+ 
+
+ align:start position:0%
+those in terms of our ability to control
+those and eliminate uncertainty? Good,
+
+ align:start position:0%
+those and eliminate uncertainty? Good,
+ 
+
+ align:start position:0%
+those and eliminate uncertainty? Good,
+bad, or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indifferent?
+
+ align:start position:0%
+indifferent?
+ 
+
+ align:start position:0%
+indifferent?
+Good. We have a vote for good.
+
+ align:start position:0%
+Good. We have a vote for good.
+ 
+
+ align:start position:0%
+Good. We have a vote for good.
+on any I would I would opine that any
+
+ align:start position:0%
+on any I would I would opine that any
+ 
+
+ align:start position:0%
+on any I would I would opine that any
+machine built in the past 20 years at
+
+ align:start position:0%
+machine built in the past 20 years at
+ 
+
+ align:start position:0%
+machine built in the past 20 years at
+least it's really good and that if you
+
+ align:start position:0%
+least it's really good and that if you
+ 
+
+ align:start position:0%
+least it's really good and that if you
+will is the victory of of CNC type
+
+ align:start position:0%
+will is the victory of of CNC type
+ 
+
+ align:start position:0%
+will is the victory of of CNC type
+controls of computer controls one of the
+
+ align:start position:0%
+controls of computer controls one of the
+ 
+
+ align:start position:0%
+controls of computer controls one of the
+biggest things is that this is now very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minimal minimal
+
+ align:start position:0%
+minimal minimal
+ 
+
+ align:start position:0%
+minimal minimal
+variation or uncertainty I know
+
+ align:start position:0%
+variation or uncertainty I know
+ 
+
+ align:start position:0%
+variation or uncertainty I know
+exactly you know if I if I have a good
+
+ align:start position:0%
+exactly you know if I if I have a good
+ 
+
+ align:start position:0%
+exactly you know if I if I have a good
+servo and I say go to this velocity it
+
+ align:start position:0%
+servo and I say go to this velocity it
+ 
+
+ align:start position:0%
+servo and I say go to this velocity it
+goes to that velocity
+
+ align:start position:0%
+goes to that velocity
+ 
+
+ align:start position:0%
+goes to that velocity
+If I have a good temperature regulator
+
+ align:start position:0%
+If I have a good temperature regulator
+ 
+
+ align:start position:0%
+If I have a good temperature regulator
+and I say go to this temperature, it'll
+
+ align:start position:0%
+and I say go to this temperature, it'll
+ 
+
+ align:start position:0%
+and I say go to this temperature, it'll
+hold that within easily within a degree
+
+ align:start position:0%
+hold that within easily within a degree
+ 
+
+ align:start position:0%
+hold that within easily within a degree
+and in some extreme cases a lot less
+
+ align:start position:0%
+and in some extreme cases a lot less
+ 
+
+ align:start position:0%
+and in some extreme cases a lot less
+than that. So with particularly with the
+
+ align:start position:0%
+than that. So with particularly with the
+ 
+
+ align:start position:0%
+than that. So with particularly with the
+use of active control, we've made that
+
+ align:start position:0%
+use of active control, we've made that
+ 
+
+ align:start position:0%
+use of active control, we've made that
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+good. So the last
+
+ align:start position:0%
+good. So the last
+ 
+
+ align:start position:0%
+good. So the last
+one and and I would say
+
+ align:start position:0%
+one and and I would say
+ 
+
+ align:start position:0%
+one and and I would say
+uncontrollable. In other words, not only
+
+ align:start position:0%
+uncontrollable. In other words, not only
+ 
+
+ align:start position:0%
+uncontrollable. In other words, not only
+is it it not variable, I can actually
+
+ align:start position:0%
+is it it not variable, I can actually
+ 
+
+ align:start position:0%
+is it it not variable, I can actually
+tell you what I want it to be.
+
+ align:start position:0%
+tell you what I want it to be.
+ 
+
+ align:start position:0%
+tell you what I want it to be.
+So I'm going to skip discussion of the
+
+ align:start position:0%
+So I'm going to skip discussion of the
+ 
+
+ align:start position:0%
+So I'm going to skip discussion of the
+material states except to say that
+
+ align:start position:0%
+material states except to say that
+ 
+
+ align:start position:0%
+material states except to say that
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+always in some ways they're always
+
+ align:start position:0%
+always in some ways they're always
+ 
+
+ align:start position:0%
+always in some ways they're always
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+often well let's say they are
+
+ align:start position:0%
+often well let's say they are
+ 
+
+ align:start position:0%
+often well let's say they are
+variable and hard to
+
+ align:start position:0%
+variable and hard to
+ 
+
+ align:start position:0%
+variable and hard to
+know and I'll give you my one favorite
+
+ align:start position:0%
+know and I'll give you my one favorite
+ 
+
+ align:start position:0%
+know and I'll give you my one favorite
+example of that. Let's say that I have a
+
+ align:start position:0%
+example of that. Let's say that I have a
+ 
+
+ align:start position:0%
+example of that. Let's say that I have a
+polymer that needs to be at a certain
+
+ align:start position:0%
+polymer that needs to be at a certain
+ 
+
+ align:start position:0%
+polymer that needs to be at a certain
+temperature to do what it's supposed to
+
+ align:start position:0%
+temperature to do what it's supposed to
+ 
+
+ align:start position:0%
+temperature to do what it's supposed to
+do. Typical way of doing that would be
+
+ align:start position:0%
+do. Typical way of doing that would be
+ 
+
+ align:start position:0%
+do. Typical way of doing that would be
+put it in an oven and let it sit in that
+
+ align:start position:0%
+put it in an oven and let it sit in that
+ 
+
+ align:start position:0%
+put it in an oven and let it sit in that
+oven. Okay? So the oven has certain
+
+ align:start position:0%
+oven. Okay? So the oven has certain
+ 
+
+ align:start position:0%
+oven. Okay? So the oven has certain
+properties that you know makes it keep
+
+ align:start position:0%
+properties that you know makes it keep
+ 
+
+ align:start position:0%
+properties that you know makes it keep
+uniform temperature and it has a really
+
+ align:start position:0%
+uniform temperature and it has a really
+ 
+
+ align:start position:0%
+uniform temperature and it has a really
+good temperature control on it. So if I
+
+ align:start position:0%
+good temperature control on it. So if I
+ 
+
+ align:start position:0%
+good temperature control on it. So if I
+say heat this to 100 C, it's right there
+
+ align:start position:0%
+say heat this to 100 C, it's right there
+ 
+
+ align:start position:0%
+say heat this to 100 C, it's right there
+at 100 C. So I've got this heated air
+
+ align:start position:0%
+at 100 C. So I've got this heated air
+ 
+
+ align:start position:0%
+at 100 C. So I've got this heated air
+and it's at 100 C. I take a piece of
+
+ align:start position:0%
+and it's at 100 C. I take a piece of
+ 
+
+ align:start position:0%
+and it's at 100 C. I take a piece of
+polymer and I put it in there. Um, and I
+
+ align:start position:0%
+polymer and I put it in there. Um, and I
+ 
+
+ align:start position:0%
+polymer and I put it in there. Um, and I
+wait sufficiently long that it's at
+
+ align:start position:0%
+wait sufficiently long that it's at
+ 
+
+ align:start position:0%
+wait sufficiently long that it's at
+equilibrium and the polymer is now at
+
+ align:start position:0%
+equilibrium and the polymer is now at
+ 
+
+ align:start position:0%
+equilibrium and the polymer is now at
+100 C. And then I pull it out and put it
+
+ align:start position:0%
+100 C. And then I pull it out and put it
+ 
+
+ align:start position:0%
+100 C. And then I pull it out and put it
+in a forming machine. something like
+
+ align:start position:0%
+in a forming machine. something like
+ 
+
+ align:start position:0%
+in a forming machine. something like
+that. Um, what's the temperature of the
+
+ align:start position:0%
+that. Um, what's the temperature of the
+ 
+
+ align:start position:0%
+that. Um, what's the temperature of the
+polymer when I formed it? That's a state
+
+ align:start position:0%
+polymer when I formed it? That's a state
+ 
+
+ align:start position:0%
+polymer when I formed it? That's a state
+of the polymer, right? It's a
+
+ align:start position:0%
+of the polymer, right? It's a
+ 
+
+ align:start position:0%
+of the polymer, right? It's a
+thermodynamic state of the polymer. I
+
+ align:start position:0%
+thermodynamic state of the polymer. I
+ 
+
+ align:start position:0%
+thermodynamic state of the polymer. I
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+know. Unless I measure it, I don't know.
+
+ align:start position:0%
+know. Unless I measure it, I don't know.
+ 
+
+ align:start position:0%
+know. Unless I measure it, I don't know.
+I'm not controlling it anymore. Now,
+
+ align:start position:0%
+I'm not controlling it anymore. Now,
+ 
+
+ align:start position:0%
+I'm not controlling it anymore. Now,
+there are also cases, and this is true,
+
+ align:start position:0%
+there are also cases, and this is true,
+ 
+
+ align:start position:0%
+there are also cases, and this is true,
+I think, in the semiconductor world now
+
+ align:start position:0%
+I think, in the semiconductor world now
+ 
+
+ align:start position:0%
+I think, in the semiconductor world now
+more than anything else, is that if I
+
+ align:start position:0%
+more than anything else, is that if I
+ 
+
+ align:start position:0%
+more than anything else, is that if I
+want to control a temperature, for
+
+ align:start position:0%
+want to control a temperature, for
+ 
+
+ align:start position:0%
+want to control a temperature, for
+example, I don't measure the temperature
+
+ align:start position:0%
+example, I don't measure the temperature
+ 
+
+ align:start position:0%
+example, I don't measure the temperature
+of the oven or or the chamber. I measure
+
+ align:start position:0%
+of the oven or or the chamber. I measure
+ 
+
+ align:start position:0%
+of the oven or or the chamber. I measure
+the temperature of the thing that I'm
+
+ align:start position:0%
+the temperature of the thing that I'm
+ 
+
+ align:start position:0%
+the temperature of the thing that I'm
+going to uh make. And uh uh an example
+
+ align:start position:0%
+going to uh make. And uh uh an example
+ 
+
+ align:start position:0%
+going to uh make. And uh uh an example
+of that is in fact the machine that this
+
+ align:start position:0%
+of that is in fact the machine that this
+ 
+
+ align:start position:0%
+of that is in fact the machine that this
+was made on, if you guys have used this,
+
+ align:start position:0%
+was made on, if you guys have used this,
+ 
+
+ align:start position:0%
+was made on, if you guys have used this,
+the angle down in building 35, um you
+
+ align:start position:0%
+the angle down in building 35, um you
+ 
+
+ align:start position:0%
+the angle down in building 35, um you
+control the temperature usually on this
+
+ align:start position:0%
+control the temperature usually on this
+ 
+
+ align:start position:0%
+control the temperature usually on this
+process by controlling the nozzle
+
+ align:start position:0%
+process by controlling the nozzle
+ 
+
+ align:start position:0%
+process by controlling the nozzle
+temperature and the barrel temperature.
+
+ align:start position:0%
+temperature and the barrel temperature.
+ 
+
+ align:start position:0%
+temperature and the barrel temperature.
+And you say, "Oh, well that's the
+
+ align:start position:0%
+And you say, "Oh, well that's the
+ 
+
+ align:start position:0%
+And you say, "Oh, well that's the
+temperature of the polymer." But what
+
+ align:start position:0%
+temperature of the polymer." But what
+ 
+
+ align:start position:0%
+temperature of the polymer." But what
+really matters is the temperature of the
+
+ align:start position:0%
+really matters is the temperature of the
+ 
+
+ align:start position:0%
+really matters is the temperature of the
+polymer in the mold, which you never
+
+ align:start position:0%
+polymer in the mold, which you never
+ 
+
+ align:start position:0%
+polymer in the mold, which you never
+measure, right? But there's actually a
+
+ align:start position:0%
+measure, right? But there's actually a
+ 
+
+ align:start position:0%
+measure, right? But there's actually a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+temperature sensor in the mold that you
+
+ align:start position:0%
+temperature sensor in the mold that you
+ 
+
+ align:start position:0%
+temperature sensor in the mold that you
+can uh measure that and there's also a
+
+ align:start position:0%
+can uh measure that and there's also a
+ 
+
+ align:start position:0%
+can uh measure that and there's also a
+pressure sensor in the mold. So you
+
+ align:start position:0%
+pressure sensor in the mold. So you
+ 
+
+ align:start position:0%
+pressure sensor in the mold. So you
+could you could if you wanted to
+
+ align:start position:0%
+could you could if you wanted to
+ 
+
+ align:start position:0%
+could you could if you wanted to
+actually measure the pressure on this.
+
+ align:start position:0%
+actually measure the pressure on this.
+ 
+
+ align:start position:0%
+actually measure the pressure on this.
+Okay, but it's hard to do. So this tends
+
+ align:start position:0%
+Okay, but it's hard to do. So this tends
+ 
+
+ align:start position:0%
+Okay, but it's hard to do. So this tends
+to be it's knowable but sort of
+
+ align:start position:0%
+to be it's knowable but sort of
+ 
+
+ align:start position:0%
+to be it's knowable but sort of
+expensive to do. So here's here's the
+
+ align:start position:0%
+expensive to do. So here's here's the
+ 
+
+ align:start position:0%
+expensive to do. So here's here's the
+moral of the story. biggest source of
+
+ align:start position:0%
+moral of the story. biggest source of
+ 
+
+ align:start position:0%
+moral of the story. biggest source of
+variation tends to be material
+
+ align:start position:0%
+variation tends to be material
+ 
+
+ align:start position:0%
+variation tends to be material
+uncertainties just inherent in the
+
+ align:start position:0%
+uncertainties just inherent in the
+ 
+
+ align:start position:0%
+uncertainties just inherent in the
+material and if you will the coupling
+
+ align:start position:0%
+material and if you will the coupling
+ 
+
+ align:start position:0%
+material and if you will the coupling
+between this energy source and how well
+
+ align:start position:0%
+between this energy source and how well
+ 
+
+ align:start position:0%
+between this energy source and how well
+it actually gets into the the material
+
+ align:start position:0%
+it actually gets into the the material
+ 
+
+ align:start position:0%
+it actually gets into the the material
+through sort of an uncertain interface.
+
+ align:start position:0%
+through sort of an uncertain interface.
+ 
+
+ align:start position:0%
+through sort of an uncertain interface.
+So all of these things here these three
+
+ align:start position:0%
+So all of these things here these three
+ 
+
+ align:start position:0%
+So all of these things here these three
+are your sources of variation typically
+
+ align:start position:0%
+are your sources of variation typically
+ 
+
+ align:start position:0%
+are your sources of variation typically
+in differenting measures. This is the
+
+ align:start position:0%
+in differenting measures. This is the
+ 
+
+ align:start position:0%
+in differenting measures. This is the
+one saving grace you're going to
+
+ align:start position:0%
+one saving grace you're going to
+ 
+
+ align:start position:0%
+one saving grace you're going to
+actually control way back at the
+
+ align:start position:0%
+actually control way back at the
+ 
+
+ align:start position:0%
+actually control way back at the
+beginning of the process. you're going
+
+ align:start position:0%
+beginning of the process. you're going
+ 
+
+ align:start position:0%
+beginning of the process. you're going
+to control uh equipment states. So when
+
+ align:start position:0%
+to control uh equipment states. So when
+ 
+
+ align:start position:0%
+to control uh equipment states. So when
+it's all said and done, what we
+
+ align:start position:0%
+it's all said and done, what we
+ 
+
+ align:start position:0%
+it's all said and done, what we
+manipulate here are typically not
+
+ align:start position:0%
+manipulate here are typically not
+ 
+
+ align:start position:0%
+manipulate here are typically not
+always, but typically equipment
+
+ align:start position:0%
+always, but typically equipment
+ 
+
+ align:start position:0%
+always, but typically equipment
+states, right? And our ability to do
+
+ align:start position:0%
+states, right? And our ability to do
+ 
+
+ align:start position:0%
+states, right? And our ability to do
+that has a lot and and how well I can
+
+ align:start position:0%
+that has a lot and and how well I can
+ 
+
+ align:start position:0%
+that has a lot and and how well I can
+change an equipment state to get a a
+
+ align:start position:0%
+change an equipment state to get a a
+ 
+
+ align:start position:0%
+change an equipment state to get a a
+change the sensitivity of the process
+
+ align:start position:0%
+change the sensitivity of the process
+ 
+
+ align:start position:0%
+change the sensitivity of the process
+has a lot to do with what I can do with
+
+ align:start position:0%
+has a lot to do with what I can do with
+ 
+
+ align:start position:0%
+has a lot to do with what I can do with
+its control. And the rest of the lecture
+
+ align:start position:0%
+its control. And the rest of the lecture
+ 
+
+ align:start position:0%
+its control. And the rest of the lecture
+which is in the notes is going through
+
+ align:start position:0%
+which is in the notes is going through
+ 
+
+ align:start position:0%
+which is in the notes is going through
+these three processes I've talked about
+
+ align:start position:0%
+these three processes I've talked about
+ 
+
+ align:start position:0%
+these three processes I've talked about
+and kind of addressing those issues. So
+
+ align:start position:0%
+and kind of addressing those issues. So
+ 
+
+ align:start position:0%
+and kind of addressing those issues. So
+if you have a chance take a look at the
+
+ align:start position:0%
+if you have a chance take a look at the
+ 
+
+ align:start position:0%
+if you have a chance take a look at the
+rest of those. Okay. Okay. Thank you. Uh
+
+ align:start position:0%
+rest of those. Okay. Okay. Thank you. Uh
+ 
+
+ align:start position:0%
+rest of those. Okay. Okay. Thank you. Uh
+thank you all and I won't see you next
+
+ align:start position:0%
+thank you all and I won't see you next
+ 
+
+ align:start position:0%
+thank you all and I won't see you next
+time. He will.
\ No newline at end of file
diff --git a/ufU6b7OHb8M.txt b/ufU6b7OHb8M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..af7106929ac2ffca4be6d96b8a6dc6f1459709c7
--- /dev/null
+++ b/ufU6b7OHb8M.txt
@@ -0,0 +1,8107 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a creative common license. Your support
+
+ align:start position:0%
+a creative common license. Your support
+ 
+
+ align:start position:0%
+a creative common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hello and welcome.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Today we're starting the second half of
+
+ align:start position:0%
+Today we're starting the second half of
+ 
+
+ align:start position:0%
+Today we're starting the second half of
+the class. In the second half of the
+
+ align:start position:0%
+the class. In the second half of the
+ 
+
+ align:start position:0%
+the class. In the second half of the
+class, we'll focus on methods that will
+
+ align:start position:0%
+class, we'll focus on methods that will
+ 
+
+ align:start position:0%
+class, we'll focus on methods that will
+generally be be described as forier
+
+ align:start position:0%
+generally be be described as forier
+ 
+
+ align:start position:0%
+generally be be described as forier
+methods.
+
+ align:start position:0%
+methods.
+ 
+
+ align:start position:0%
+methods.
+And those methods are revolve around
+
+ align:start position:0%
+And those methods are revolve around
+ 
+
+ align:start position:0%
+And those methods are revolve around
+thinking about signals
+
+ align:start position:0%
+thinking about signals
+ 
+
+ align:start position:0%
+thinking about signals
+as being uh sums of sine waves. So we've
+
+ align:start position:0%
+as being uh sums of sine waves. So we've
+ 
+
+ align:start position:0%
+as being uh sums of sine waves. So we've
+previously thought about how you can
+
+ align:start position:0%
+previously thought about how you can
+ 
+
+ align:start position:0%
+previously thought about how you can
+think about a system
+
+ align:start position:0%
+think about a system
+ 
+
+ align:start position:0%
+think about a system
+by thinking about how it responds to
+
+ align:start position:0%
+by thinking about how it responds to
+ 
+
+ align:start position:0%
+by thinking about how it responds to
+sine waves. So this is closely related.
+
+ align:start position:0%
+sine waves. So this is closely related.
+ 
+
+ align:start position:0%
+sine waves. So this is closely related.
+Now instead of thinking about a system
+
+ align:start position:0%
+Now instead of thinking about a system
+ 
+
+ align:start position:0%
+Now instead of thinking about a system
+as how by how it uh processes sound by
+
+ align:start position:0%
+as how by how it uh processes sound by
+ 
+
+ align:start position:0%
+as how by how it uh processes sound by
+how it processes sine waves rather we'll
+
+ align:start position:0%
+how it processes sine waves rather we'll
+ 
+
+ align:start position:0%
+how it processes sine waves rather we'll
+think about signals
+
+ align:start position:0%
+think about signals
+ 
+
+ align:start position:0%
+think about signals
+as being composed of sine waves. So
+
+ align:start position:0%
+as being composed of sine waves. So
+ 
+
+ align:start position:0%
+as being composed of sine waves. So
+that's sort of the idea and today we'll
+
+ align:start position:0%
+that's sort of the idea and today we'll
+ 
+
+ align:start position:0%
+that's sort of the idea and today we'll
+do the very simplest kind of
+
+ align:start position:0%
+do the very simplest kind of
+ 
+
+ align:start position:0%
+do the very simplest kind of
+representation which is a 4A series. Um
+
+ align:start position:0%
+representation which is a 4A series. Um
+ 
+
+ align:start position:0%
+representation which is a 4A series. Um
+the importance of that's going to be our
+
+ align:start position:0%
+the importance of that's going to be our
+ 
+
+ align:start position:0%
+the importance of that's going to be our
+first encounter with how you can think
+
+ align:start position:0%
+first encounter with how you can think
+ 
+
+ align:start position:0%
+first encounter with how you can think
+about complicated signals
+
+ align:start position:0%
+about complicated signals
+ 
+
+ align:start position:0%
+about complicated signals
+as sums of signs and cosiness but also
+
+ align:start position:0%
+as sums of signs and cosiness but also
+ 
+
+ align:start position:0%
+as sums of signs and cosiness but also
+we'll get a new representation for a
+
+ align:start position:0%
+we'll get a new representation for a
+ 
+
+ align:start position:0%
+we'll get a new representation for a
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+that will be generally useful called a
+
+ align:start position:0%
+that will be generally useful called a
+ 
+
+ align:start position:0%
+that will be generally useful called a
+filter. So that's the two agenda items
+
+ align:start position:0%
+filter. So that's the two agenda items
+ 
+
+ align:start position:0%
+filter. So that's the two agenda items
+for today roughly. The first half is on
+
+ align:start position:0%
+for today roughly. The first half is on
+ 
+
+ align:start position:0%
+for today roughly. The first half is on
+the um for a uh series representations
+
+ align:start position:0%
+the um for a uh series representations
+ 
+
+ align:start position:0%
+the um for a uh series representations
+for a signal. The second half is on
+
+ align:start position:0%
+for a signal. The second half is on
+ 
+
+ align:start position:0%
+for a signal. The second half is on
+thinking about systems as filters which
+
+ align:start position:0%
+thinking about systems as filters which
+ 
+
+ align:start position:0%
+thinking about systems as filters which
+is a direct consequence of the first. So
+
+ align:start position:0%
+is a direct consequence of the first. So
+ 
+
+ align:start position:0%
+is a direct consequence of the first. So
+the first idea is just how why should we
+
+ align:start position:0%
+the first idea is just how why should we
+ 
+
+ align:start position:0%
+the first idea is just how why should we
+even think that you can think about
+
+ align:start position:0%
+even think that you can think about
+ 
+
+ align:start position:0%
+even think that you can think about
+signals in terms of sine waves. Well,
+
+ align:start position:0%
+signals in terms of sine waves. Well,
+ 
+
+ align:start position:0%
+signals in terms of sine waves. Well,
+there's very simple examples of that.
+
+ align:start position:0%
+there's very simple examples of that.
+ 
+
+ align:start position:0%
+there's very simple examples of that.
+Some signals are just very naturally
+
+ align:start position:0%
+Some signals are just very naturally
+ 
+
+ align:start position:0%
+Some signals are just very naturally
+described that way. One class of those
+
+ align:start position:0%
+described that way. One class of those
+ 
+
+ align:start position:0%
+described that way. One class of those
+are the ones whose entire frequency
+
+ align:start position:0%
+are the ones whose entire frequency
+ 
+
+ align:start position:0%
+are the ones whose entire frequency
+content are harmonics.
+
+ align:start position:0%
+content are harmonics.
+ 
+
+ align:start position:0%
+content are harmonics.
+Just a bit of jargon. We'll think about
+
+ align:start position:0%
+Just a bit of jargon. We'll think about
+ 
+
+ align:start position:0%
+Just a bit of jargon. We'll think about
+harmonics of omega kn harmonics of some
+
+ align:start position:0%
+harmonics of omega kn harmonics of some
+ 
+
+ align:start position:0%
+harmonics of omega kn harmonics of some
+frequency say 1 khertz
+
+ align:start position:0%
+frequency say 1 khertz
+ 
+
+ align:start position:0%
+frequency say 1 khertz
+then we'll have the first harmonic
+
+ align:start position:0%
+then we'll have the first harmonic
+ 
+
+ align:start position:0%
+then we'll have the first harmonic
+that's another name for the fundamental
+
+ align:start position:0%
+that's another name for the fundamental
+ 
+
+ align:start position:0%
+that's another name for the fundamental
+that's 1 kHz and for example second
+
+ align:start position:0%
+that's 1 kHz and for example second
+ 
+
+ align:start position:0%
+that's 1 kHz and for example second
+harmonic would be some component at
+
+ align:start position:0%
+harmonic would be some component at
+ 
+
+ align:start position:0%
+harmonic would be some component at
+twice the frequency third harmonic three
+
+ align:start position:0%
+twice the frequency third harmonic three
+ 
+
+ align:start position:0%
+twice the frequency third harmonic three
+times the frequency zero harmonic for
+
+ align:start position:0%
+times the frequency zero harmonic for
+ 
+
+ align:start position:0%
+times the frequency zero harmonic for
+the completely obliv so the so for no
+
+ align:start position:0%
+the completely obliv so the so for no
+ 
+
+ align:start position:0%
+the completely obliv so the so for no
+good reason at all we'll call the zero
+
+ align:start position:0%
+good reason at all we'll call the zero
+ 
+
+ align:start position:0%
+good reason at all we'll call the zero
+earth harmonic the DC term meaning
+
+ align:start position:0%
+earth harmonic the DC term meaning
+ 
+
+ align:start position:0%
+earth harmonic the DC term meaning
+direct current which is neither direct
+
+ align:start position:0%
+direct current which is neither direct
+ 
+
+ align:start position:0%
+direct current which is neither direct
+nor has anything to do with current but
+
+ align:start position:0%
+nor has anything to do with current but
+ 
+
+ align:start position:0%
+nor has anything to do with current but
+we will use that jargon because
+
+ align:start position:0%
+we will use that jargon because
+ 
+
+ align:start position:0%
+we will use that jargon because
+everybody else does so that's just
+
+ align:start position:0%
+everybody else does so that's just
+ 
+
+ align:start position:0%
+everybody else does so that's just
+jargon
+
+ align:start position:0%
+jargon
+ 
+
+ align:start position:0%
+jargon
+what I want to think about though at a
+
+ align:start position:0%
+what I want to think about though at a
+ 
+
+ align:start position:0%
+what I want to think about though at a
+deeper level is what what kinds of
+
+ align:start position:0%
+deeper level is what what kinds of
+ 
+
+ align:start position:0%
+deeper level is what what kinds of
+signals should we expect have a good
+
+ align:start position:0%
+signals should we expect have a good
+ 
+
+ align:start position:0%
+signals should we expect have a good
+representation
+
+ align:start position:0%
+representation
+ 
+
+ align:start position:0%
+representation
+in terms of sums of signs and cosiness
+
+ align:start position:0%
+in terms of sums of signs and cosiness
+ 
+
+ align:start position:0%
+in terms of sums of signs and cosiness
+and one very easy kind of uh signal that
+
+ align:start position:0%
+and one very easy kind of uh signal that
+ 
+
+ align:start position:0%
+and one very easy kind of uh signal that
+you can think about is mu signals that
+
+ align:start position:0%
+you can think about is mu signals that
+ 
+
+ align:start position:0%
+you can think about is mu signals that
+we associate with musical instruments
+
+ align:start position:0%
+we associate with musical instruments
+ 
+
+ align:start position:0%
+we associate with musical instruments
+So, think about the sounds that these
+
+ align:start position:0%
+So, think about the sounds that these
+ 
+
+ align:start position:0%
+So, think about the sounds that these
+instruments generate. And I'll play some
+
+ align:start position:0%
+instruments generate. And I'll play some
+ 
+
+ align:start position:0%
+instruments generate. And I'll play some
+audio. And while I'm playing it, what
+
+ align:start position:0%
+audio. And while I'm playing it, what
+ 
+
+ align:start position:0%
+audio. And while I'm playing it, what
+you're supposed to be doing is thinking
+
+ align:start position:0%
+you're supposed to be doing is thinking
+ 
+
+ align:start position:0%
+you're supposed to be doing is thinking
+about what's the cues that this sounds
+
+ align:start position:0%
+about what's the cues that this sounds
+ 
+
+ align:start position:0%
+about what's the cues that this sounds
+like a sum of harmonics.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the idea so using the things that we
+
+ align:start position:0%
+So the idea so using the things that we
+ 
+
+ align:start position:0%
+So the idea so using the things that we
+we'll go over today in lecture I can use
+
+ align:start position:0%
+we'll go over today in lecture I can use
+ 
+
+ align:start position:0%
+we'll go over today in lecture I can use
+I can write a Python program which I did
+
+ align:start position:0%
+I can write a Python program which I did
+ 
+
+ align:start position:0%
+I can write a Python program which I did
+to analyze each of those sounds
+
+ align:start position:0%
+to analyze each of those sounds
+ 
+
+ align:start position:0%
+to analyze each of those sounds
+to expose its harmonic structure.
+
+ align:start position:0%
+to expose its harmonic structure.
+ 
+
+ align:start position:0%
+to expose its harmonic structure.
+And here's the results. So for k= 0 DC 1
+
+ align:start position:0%
+And here's the results. So for k= 0 DC 1
+ 
+
+ align:start position:0%
+And here's the results. So for k= 0 DC 1
+the fundamental two the second harmonic
+
+ align:start position:0%
+the fundamental two the second harmonic
+ 
+
+ align:start position:0%
+the fundamental two the second harmonic
+third harmonic fourth harmonic the
+
+ align:start position:0%
+third harmonic fourth harmonic the
+ 
+
+ align:start position:0%
+third harmonic fourth harmonic the
+lengths of the bars represent the
+
+ align:start position:0%
+lengths of the bars represent the
+ 
+
+ align:start position:0%
+lengths of the bars represent the
+magnitudes how much energy well roughly
+
+ align:start position:0%
+magnitudes how much energy well roughly
+ 
+
+ align:start position:0%
+magnitudes how much energy well roughly
+energy how much signal is present at
+
+ align:start position:0%
+energy how much signal is present at
+ 
+
+ align:start position:0%
+energy how much signal is present at
+those harmonic frequencies as a function
+
+ align:start position:0%
+those harmonic frequencies as a function
+ 
+
+ align:start position:0%
+those harmonic frequencies as a function
+of harmonic number k for each of the
+
+ align:start position:0%
+of harmonic number k for each of the
+ 
+
+ align:start position:0%
+of harmonic number k for each of the
+different instruments. And just like uh
+
+ align:start position:0%
+different instruments. And just like uh
+ 
+
+ align:start position:0%
+different instruments. And just like uh
+the time waveforms have a signature,
+
+ align:start position:0%
+the time waveforms have a signature,
+ 
+
+ align:start position:0%
+the time waveforms have a signature,
+there was a characteristic shape. In
+
+ align:start position:0%
+there was a characteristic shape. In
+ 
+
+ align:start position:0%
+there was a characteristic shape. In
+fact, if I go on, here's the
+
+ align:start position:0%
+fact, if I go on, here's the
+ 
+
+ align:start position:0%
+fact, if I go on, here's the
+characteristic shape. That's an actual
+
+ align:start position:0%
+characteristic shape. That's an actual
+ 
+
+ align:start position:0%
+characteristic shape. That's an actual
+waveform taken from the audio clip that
+
+ align:start position:0%
+waveform taken from the audio clip that
+ 
+
+ align:start position:0%
+waveform taken from the audio clip that
+I played. That's a clip from the piano.
+
+ align:start position:0%
+I played. That's a clip from the piano.
+ 
+
+ align:start position:0%
+I played. That's a clip from the piano.
+This is a clip of the same time duration
+
+ align:start position:0%
+This is a clip of the same time duration
+ 
+
+ align:start position:0%
+This is a clip of the same time duration
+from the violin. Uh a clip of the same
+
+ align:start position:0%
+from the violin. Uh a clip of the same
+ 
+
+ align:start position:0%
+from the violin. Uh a clip of the same
+time duration from the bassoon.
+
+ align:start position:0%
+time duration from the bassoon.
+ 
+
+ align:start position:0%
+time duration from the bassoon.
+And here are the harmonic structures
+
+ align:start position:0%
+And here are the harmonic structures
+ 
+
+ align:start position:0%
+And here are the harmonic structures
+for those different sounds. And you can
+
+ align:start position:0%
+for those different sounds. And you can
+ 
+
+ align:start position:0%
+for those different sounds. And you can
+see the harmonic structures look very
+
+ align:start position:0%
+see the harmonic structures look very
+ 
+
+ align:start position:0%
+see the harmonic structures look very
+different, right? So, uh, not much DC, a
+
+ align:start position:0%
+different, right? So, uh, not much DC, a
+ 
+
+ align:start position:0%
+different, right? So, uh, not much DC, a
+fair amount of fundamental, a lot of
+
+ align:start position:0%
+fair amount of fundamental, a lot of
+ 
+
+ align:start position:0%
+fair amount of fundamental, a lot of
+second,
+
+ align:start position:0%
+second,
+ 
+
+ align:start position:0%
+second,
+uh, a lot of fundamental, not much
+
+ align:start position:0%
+uh, a lot of fundamental, not much
+ 
+
+ align:start position:0%
+uh, a lot of fundamental, not much
+second,
+
+ align:start position:0%
+second,
+ 
+
+ align:start position:0%
+second,
+not much fundamental. That's kind of
+
+ align:start position:0%
+not much fundamental. That's kind of
+ 
+
+ align:start position:0%
+not much fundamental. That's kind of
+interesting. The bassoon is special in
+
+ align:start position:0%
+interesting. The bassoon is special in
+ 
+
+ align:start position:0%
+interesting. The bassoon is special in
+this class because there's not much
+
+ align:start position:0%
+this class because there's not much
+ 
+
+ align:start position:0%
+this class because there's not much
+fundamental, but there's a lot of
+
+ align:start position:0%
+fundamental, but there's a lot of
+ 
+
+ align:start position:0%
+fundamental, but there's a lot of
+second.
+
+ align:start position:0%
+second.
+ 
+
+ align:start position:0%
+second.
+So now think about comparing these two
+
+ align:start position:0%
+So now think about comparing these two
+ 
+
+ align:start position:0%
+So now think about comparing these two
+and listen to them again.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what what I want you to try to think
+
+ align:start position:0%
+So what what I want you to try to think
+ 
+
+ align:start position:0%
+So what what I want you to try to think
+about and it's kind of hard. Think about
+
+ align:start position:0%
+about and it's kind of hard. Think about
+ 
+
+ align:start position:0%
+about and it's kind of hard. Think about
+how it is that the harmonic structure is
+
+ align:start position:0%
+how it is that the harmonic structure is
+ 
+
+ align:start position:0%
+how it is that the harmonic structure is
+playing a role in determining the the
+
+ align:start position:0%
+playing a role in determining the the
+ 
+
+ align:start position:0%
+playing a role in determining the the
+tamber
+
+ align:start position:0%
+tamber
+ 
+
+ align:start position:0%
+tamber
+of the sound that you're hearing. Okay,
+
+ align:start position:0%
+of the sound that you're hearing. Okay,
+ 
+
+ align:start position:0%
+of the sound that you're hearing. Okay,
+so that's kind of the motivation. Um,
+
+ align:start position:0%
+so that's kind of the motivation. Um,
+ 
+
+ align:start position:0%
+so that's kind of the motivation. Um,
+another motivation is that thinking
+
+ align:start position:0%
+another motivation is that thinking
+ 
+
+ align:start position:0%
+another motivation is that thinking
+about signals in terms of their harmonic
+
+ align:start position:0%
+about signals in terms of their harmonic
+ 
+
+ align:start position:0%
+about signals in terms of their harmonic
+structure can provide important insights
+
+ align:start position:0%
+structure can provide important insights
+ 
+
+ align:start position:0%
+structure can provide important insights
+into the signals. And so for example in
+
+ align:start position:0%
+into the signals. And so for example in
+ 
+
+ align:start position:0%
+into the signals. And so for example in
+music the harmonic structure is what
+
+ align:start position:0%
+music the harmonic structure is what
+ 
+
+ align:start position:0%
+music the harmonic structure is what
+determines uh um consonants and
+
+ align:start position:0%
+determines uh um consonants and
+ 
+
+ align:start position:0%
+determines uh um consonants and
+dissonance
+
+ align:start position:0%
+dissonance
+ 
+
+ align:start position:0%
+dissonance
+dissonance. So uh I'm going to play two
+
+ align:start position:0%
+dissonance. So uh I'm going to play two
+ 
+
+ align:start position:0%
+dissonance. So uh I'm going to play two
+tone two u two different notes that are
+
+ align:start position:0%
+tone two u two different notes that are
+ 
+
+ align:start position:0%
+tone two u two different notes that are
+related by an octave shift by a fifth
+
+ align:start position:0%
+related by an octave shift by a fifth
+ 
+
+ align:start position:0%
+related by an octave shift by a fifth
+shift and uh adjacent notes in in the
+
+ align:start position:0%
+shift and uh adjacent notes in in the
+ 
+
+ align:start position:0%
+shift and uh adjacent notes in in the
+semmitone scale.
+
+ align:start position:0%
+semmitone scale.
+ 
+
+ align:start position:0%
+semmitone scale.
+And below it, I've illustrated the
+
+ align:start position:0%
+And below it, I've illustrated the
+ 
+
+ align:start position:0%
+And below it, I've illustrated the
+harmonic structure for the uh D and for
+
+ align:start position:0%
+harmonic structure for the uh D and for
+ 
+
+ align:start position:0%
+harmonic structure for the uh D and for
+D prime. Okay, so an octave above means
+
+ align:start position:0%
+D prime. Okay, so an octave above means
+ 
+
+ align:start position:0%
+D prime. Okay, so an octave above means
+that the first harmonic, the fundamental
+
+ align:start position:0%
+that the first harmonic, the fundamental
+ 
+
+ align:start position:0%
+that the first harmonic, the fundamental
+of this guy corresponds to the second
+
+ align:start position:0%
+of this guy corresponds to the second
+ 
+
+ align:start position:0%
+of this guy corresponds to the second
+harmonic of this guy. The second to the
+
+ align:start position:0%
+harmonic of this guy. The second to the
+ 
+
+ align:start position:0%
+harmonic of this guy. The second to the
+fourth, etc. There's some relationship
+
+ align:start position:0%
+fourth, etc. There's some relationship
+ 
+
+ align:start position:0%
+fourth, etc. There's some relationship
+for the fifths illustrated here. And
+
+ align:start position:0%
+for the fifths illustrated here. And
+ 
+
+ align:start position:0%
+for the fifths illustrated here. And
+there's a different illust there's a
+
+ align:start position:0%
+there's a different illust there's a
+ 
+
+ align:start position:0%
+there's a different illust there's a
+different relationship here. So what I
+
+ align:start position:0%
+different relationship here. So what I
+ 
+
+ align:start position:0%
+different relationship here. So what I
+want you to do is hear the difference
+
+ align:start position:0%
+want you to do is hear the difference
+ 
+
+ align:start position:0%
+want you to do is hear the difference
+between those six sounds and again think
+
+ align:start position:0%
+between those six sounds and again think
+ 
+
+ align:start position:0%
+between those six sounds and again think
+about uh not only the time waveform but
+
+ align:start position:0%
+about uh not only the time waveform but
+ 
+
+ align:start position:0%
+about uh not only the time waveform but
+also how their harmonics relate.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, um, dissonance has something to do,
+
+ align:start position:0%
+So, um, dissonance has something to do,
+ 
+
+ align:start position:0%
+So, um, dissonance has something to do,
+well, consonants has something to do
+
+ align:start position:0%
+well, consonants has something to do
+ 
+
+ align:start position:0%
+well, consonants has something to do
+with the overlap
+
+ align:start position:0%
+with the overlap
+ 
+
+ align:start position:0%
+with the overlap
+of the harmonic structure and dissonance
+
+ align:start position:0%
+of the harmonic structure and dissonance
+ 
+
+ align:start position:0%
+of the harmonic structure and dissonance
+has something to do with the lack of
+
+ align:start position:0%
+has something to do with the lack of
+ 
+
+ align:start position:0%
+has something to do with the lack of
+overlap
+
+ align:start position:0%
+overlap
+ 
+
+ align:start position:0%
+overlap
+of the harmonic content. So the point
+
+ align:start position:0%
+of the harmonic content. So the point
+ 
+
+ align:start position:0%
+of the harmonic content. So the point
+just being that you we can we can get
+
+ align:start position:0%
+just being that you we can we can get
+ 
+
+ align:start position:0%
+just being that you we can we can get
+some mileage out of thinking about
+
+ align:start position:0%
+some mileage out of thinking about
+ 
+
+ align:start position:0%
+some mileage out of thinking about
+signals
+
+ align:start position:0%
+signals
+ 
+
+ align:start position:0%
+signals
+according to their harmonic
+
+ align:start position:0%
+according to their harmonic
+ 
+
+ align:start position:0%
+according to their harmonic
+decomposition. So that's kind of the uh
+
+ align:start position:0%
+decomposition. So that's kind of the uh
+ 
+
+ align:start position:0%
+decomposition. So that's kind of the uh
+introduction.
+
+ align:start position:0%
+introduction.
+ 
+
+ align:start position:0%
+introduction.
+How should we think about that? What
+
+ align:start position:0%
+How should we think about that? What
+ 
+
+ align:start position:0%
+How should we think about that? What
+kinds of signals ought to be
+
+ align:start position:0%
+kinds of signals ought to be
+ 
+
+ align:start position:0%
+kinds of signals ought to be
+representable
+
+ align:start position:0%
+representable
+ 
+
+ align:start position:0%
+representable
+by their harmonic structure? Okay. Well,
+
+ align:start position:0%
+by their harmonic structure? Okay. Well,
+ 
+
+ align:start position:0%
+by their harmonic structure? Okay. Well,
+if you just draw a picture in the time
+
+ align:start position:0%
+if you just draw a picture in the time
+ 
+
+ align:start position:0%
+if you just draw a picture in the time
+domain and think about a fundamental,
+
+ align:start position:0%
+domain and think about a fundamental,
+ 
+
+ align:start position:0%
+domain and think about a fundamental,
+what would it look like in the time
+
+ align:start position:0%
+what would it look like in the time
+ 
+
+ align:start position:0%
+what would it look like in the time
+domain? What would the signal look like?
+
+ align:start position:0%
+domain? What would the signal look like?
+ 
+
+ align:start position:0%
+domain? What would the signal look like?
+What would the second harmonic look
+
+ align:start position:0%
+What would the second harmonic look
+ 
+
+ align:start position:0%
+What would the second harmonic look
+like? Well, that's a that's a signal
+
+ align:start position:0%
+like? Well, that's a that's a signal
+ 
+
+ align:start position:0%
+like? Well, that's a that's a signal
+whose frequency is twice as big.
+
+ align:start position:0%
+whose frequency is twice as big.
+ 
+
+ align:start position:0%
+whose frequency is twice as big.
+If the frequency is twice as big, the
+
+ align:start position:0%
+If the frequency is twice as big, the
+ 
+
+ align:start position:0%
+If the frequency is twice as big, the
+period is half as big. So, there's now
+
+ align:start position:0%
+period is half as big. So, there's now
+ 
+
+ align:start position:0%
+period is half as big. So, there's now
+two periods of the blue guy
+
+ align:start position:0%
+two periods of the blue guy
+ 
+
+ align:start position:0%
+two periods of the blue guy
+in the same time interval as one period
+
+ align:start position:0%
+in the same time interval as one period
+ 
+
+ align:start position:0%
+in the same time interval as one period
+of the red guy.
+
+ align:start position:0%
+of the red guy.
+ 
+
+ align:start position:0%
+of the red guy.
+Okay. So the relationship of frequencies
+
+ align:start position:0%
+Okay. So the relationship of frequencies
+ 
+
+ align:start position:0%
+Okay. So the relationship of frequencies
+in the harmonics has a relationship in
+
+ align:start position:0%
+in the harmonics has a relationship in
+ 
+
+ align:start position:0%
+in the harmonics has a relationship in
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and it's proportion or it's inversely
+
+ align:start position:0%
+and it's proportion or it's inversely
+ 
+
+ align:start position:0%
+and it's proportion or it's inversely
+proportional. Okay. So if you think
+
+ align:start position:0%
+proportional. Okay. So if you think
+ 
+
+ align:start position:0%
+proportional. Okay. So if you think
+about uh fundamental second third fourth
+
+ align:start position:0%
+about uh fundamental second third fourth
+ 
+
+ align:start position:0%
+about uh fundamental second third fourth
+fifth fundamental second third fourth
+
+ align:start position:0%
+fifth fundamental second third fourth
+ 
+
+ align:start position:0%
+fifth fundamental second third fourth
+fifth there's a relationship between in
+
+ align:start position:0%
+fifth there's a relationship between in
+ 
+
+ align:start position:0%
+fifth there's a relationship between in
+time of the periods.
+
+ align:start position:0%
+time of the periods.
+ 
+
+ align:start position:0%
+time of the periods.
+And one thing that should be clear is
+
+ align:start position:0%
+And one thing that should be clear is
+ 
+
+ align:start position:0%
+And one thing that should be clear is
+that the these harmonics are all
+
+ align:start position:0%
+that the these harmonics are all
+ 
+
+ align:start position:0%
+that the these harmonics are all
+periodic in the period of the
+
+ align:start position:0%
+periodic in the period of the
+ 
+
+ align:start position:0%
+periodic in the period of the
+fundamental.
+
+ align:start position:0%
+fundamental.
+ 
+
+ align:start position:0%
+fundamental.
+So one thing that you can think about by
+
+ align:start position:0%
+So one thing that you can think about by
+ 
+
+ align:start position:0%
+So one thing that you can think about by
+thinking about the time representation
+
+ align:start position:0%
+thinking about the time representation
+ 
+
+ align:start position:0%
+thinking about the time representation
+of what harmonic signals ought to look
+
+ align:start position:0%
+of what harmonic signals ought to look
+ 
+
+ align:start position:0%
+of what harmonic signals ought to look
+like, periodic signals
+
+ align:start position:0%
+like, periodic signals
+ 
+
+ align:start position:0%
+like, periodic signals
+are sort of our only candidates.
+
+ align:start position:0%
+are sort of our only candidates.
+ 
+
+ align:start position:0%
+are sort of our only candidates.
+All of the harmonics
+
+ align:start position:0%
+All of the harmonics
+ 
+
+ align:start position:0%
+All of the harmonics
+of a fundamental have the same are are
+
+ align:start position:0%
+of a fundamental have the same are are
+ 
+
+ align:start position:0%
+of a fundamental have the same are are
+periodic in capital T the period of the
+
+ align:start position:0%
+periodic in capital T the period of the
+ 
+
+ align:start position:0%
+periodic in capital T the period of the
+fundamental. So it's going to be hard to
+
+ align:start position:0%
+fundamental. So it's going to be hard to
+ 
+
+ align:start position:0%
+fundamental. So it's going to be hard to
+generate a signal by a sum of harmonics
+
+ align:start position:0%
+generate a signal by a sum of harmonics
+ 
+
+ align:start position:0%
+generate a signal by a sum of harmonics
+that doesn't have that periodicity.
+
+ align:start position:0%
+that doesn't have that periodicity.
+ 
+
+ align:start position:0%
+that doesn't have that periodicity.
+Right? So we should be expecting a
+
+ align:start position:0%
+Right? So we should be expecting a
+ 
+
+ align:start position:0%
+Right? So we should be expecting a
+relationship between signals that can be
+
+ align:start position:0%
+relationship between signals that can be
+ 
+
+ align:start position:0%
+relationship between signals that can be
+represented by a sum of harmonics
+
+ align:start position:0%
+represented by a sum of harmonics
+ 
+
+ align:start position:0%
+represented by a sum of harmonics
+and periodic signals.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we would not expect an aperiodic
+
+ align:start position:0%
+So we would not expect an aperiodic
+ 
+
+ align:start position:0%
+So we would not expect an aperiodic
+signal to be represented this way. The
+
+ align:start position:0%
+signal to be represented this way. The
+ 
+
+ align:start position:0%
+signal to be represented this way. The
+the counter question is should we be
+
+ align:start position:0%
+the counter question is should we be
+ 
+
+ align:start position:0%
+the counter question is should we be
+expecting that all periodic signals can
+
+ align:start position:0%
+expecting that all periodic signals can
+ 
+
+ align:start position:0%
+expecting that all periodic signals can
+be represented this way or some periodic
+
+ align:start position:0%
+be represented this way or some periodic
+ 
+
+ align:start position:0%
+be represented this way or some periodic
+signals or some very special class? Is
+
+ align:start position:0%
+signals or some very special class? Is
+ 
+
+ align:start position:0%
+signals or some very special class? Is
+it a big class or a small class? How do
+
+ align:start position:0%
+it a big class or a small class? How do
+ 
+
+ align:start position:0%
+it a big class or a small class? How do
+we think about that? And historically
+
+ align:start position:0%
+we think about that? And historically
+ 
+
+ align:start position:0%
+we think about that? And historically
+that's been a hard question. And by the
+
+ align:start position:0%
+that's been a hard question. And by the
+ 
+
+ align:start position:0%
+that's been a hard question. And by the
+end of the hour I I hope that you all
+
+ align:start position:0%
+end of the hour I I hope that you all
+ 
+
+ align:start position:0%
+end of the hour I I hope that you all
+understand why it was a hard question.
+
+ align:start position:0%
+understand why it was a hard question.
+ 
+
+ align:start position:0%
+understand why it was a hard question.
+uh people like Furier, you might
+
+ align:start position:0%
+uh people like Furier, you might
+ 
+
+ align:start position:0%
+uh people like Furier, you might
+imagine, advocated the notion
+
+ align:start position:0%
+imagine, advocated the notion
+ 
+
+ align:start position:0%
+imagine, advocated the notion
+that you can make a meaningful harmonic
+
+ align:start position:0%
+that you can make a meaningful harmonic
+ 
+
+ align:start position:0%
+that you can make a meaningful harmonic
+uh representation for a very wide class
+
+ align:start position:0%
+uh representation for a very wide class
+ 
+
+ align:start position:0%
+uh representation for a very wide class
+of signals. Forier claimed basically
+
+ align:start position:0%
+of signals. Forier claimed basically
+ 
+
+ align:start position:0%
+of signals. Forier claimed basically
+everything anything that was periodic
+
+ align:start position:0%
+everything anything that was periodic
+ 
+
+ align:start position:0%
+everything anything that was periodic
+could be represented in terms of a sum
+
+ align:start position:0%
+could be represented in terms of a sum
+ 
+
+ align:start position:0%
+could be represented in terms of a sum
+of harmonics. Other people thought that
+
+ align:start position:0%
+of harmonics. Other people thought that
+ 
+
+ align:start position:0%
+of harmonics. Other people thought that
+was preposterous.
+
+ align:start position:0%
+was preposterous.
+ 
+
+ align:start position:0%
+was preposterous.
+uh in a widely reported public rebuke of
+
+ align:start position:0%
+uh in a widely reported public rebuke of
+ 
+
+ align:start position:0%
+uh in a widely reported public rebuke of
+uh furier lrange said this is ridiculous
+
+ align:start position:0%
+uh furier lrange said this is ridiculous
+ 
+
+ align:start position:0%
+uh furier lrange said this is ridiculous
+because every harmonic is a continuous
+
+ align:start position:0%
+because every harmonic is a continuous
+ 
+
+ align:start position:0%
+because every harmonic is a continuous
+function of time
+
+ align:start position:0%
+function of time
+ 
+
+ align:start position:0%
+function of time
+and you can easily manufacture a
+
+ align:start position:0%
+and you can easily manufacture a
+ 
+
+ align:start position:0%
+and you can easily manufacture a
+periodic signal that's a discontinuous
+
+ align:start position:0%
+periodic signal that's a discontinuous
+ 
+
+ align:start position:0%
+periodic signal that's a discontinuous
+function of time
+
+ align:start position:0%
+function of time
+ 
+
+ align:start position:0%
+function of time
+so for example a square wave
+
+ align:start position:0%
+so for example a square wave
+ 
+
+ align:start position:0%
+so for example a square wave
+how on earth argued lrange how on earth
+
+ align:start position:0%
+how on earth argued lrange how on earth
+ 
+
+ align:start position:0%
+how on earth argued lrange how on earth
+would you represent
+
+ align:start position:0%
+would you represent
+ 
+
+ align:start position:0%
+would you represent
+a discontinuous function by a sum of
+
+ align:start position:0%
+a discontinuous function by a sum of
+ 
+
+ align:start position:0%
+a discontinuous function by a sum of
+continuous functions. That makes no
+
+ align:start position:0%
+continuous functions. That makes no
+ 
+
+ align:start position:0%
+continuous functions. That makes no
+sense, right? So, um what what we will
+
+ align:start position:0%
+sense, right? So, um what what we will
+ 
+
+ align:start position:0%
+sense, right? So, um what what we will
+want to do in the course of the hour is
+
+ align:start position:0%
+want to do in the course of the hour is
+ 
+
+ align:start position:0%
+want to do in the course of the hour is
+think about does that or doesn't that
+
+ align:start position:0%
+think about does that or doesn't that
+ 
+
+ align:start position:0%
+think about does that or doesn't that
+make sense and it'll turn out the answer
+
+ align:start position:0%
+make sense and it'll turn out the answer
+ 
+
+ align:start position:0%
+make sense and it'll turn out the answer
+is kind of complicated
+
+ align:start position:0%
+is kind of complicated
+ 
+
+ align:start position:0%
+is kind of complicated
+and so we can sort of forgive both sides
+
+ align:start position:0%
+and so we can sort of forgive both sides
+ 
+
+ align:start position:0%
+and so we can sort of forgive both sides
+for having sort of u argued with each
+
+ align:start position:0%
+for having sort of u argued with each
+ 
+
+ align:start position:0%
+for having sort of u argued with each
+other because the answer is not
+
+ align:start position:0%
+other because the answer is not
+ 
+
+ align:start position:0%
+other because the answer is not
+completely obvious.
+
+ align:start position:0%
+completely obvious.
+ 
+
+ align:start position:0%
+completely obvious.
+For the time being, I'm going to just
+
+ align:start position:0%
+For the time being, I'm going to just
+ 
+
+ align:start position:0%
+For the time being, I'm going to just
+assume that the answer is yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that it makes sense to try to make a
+
+ align:start position:0%
+that it makes sense to try to make a
+ 
+
+ align:start position:0%
+that it makes sense to try to make a
+harmonic representation of a signal that
+
+ align:start position:0%
+harmonic representation of a signal that
+ 
+
+ align:start position:0%
+harmonic representation of a signal that
+might even be discontinuous. I'm going
+
+ align:start position:0%
+might even be discontinuous. I'm going
+ 
+
+ align:start position:0%
+might even be discontinuous. I'm going
+to assume periodic. Let's try and the
+
+ align:start position:0%
+to assume periodic. Let's try and the
+ 
+
+ align:start position:0%
+to assume periodic. Let's try and the
+question will be does that make any
+
+ align:start position:0%
+question will be does that make any
+ 
+
+ align:start position:0%
+question will be does that make any
+sense?
+
+ align:start position:0%
+sense?
+ 
+
+ align:start position:0%
+sense?
+So there's a there's a little bit of
+
+ align:start position:0%
+So there's a there's a little bit of
+ 
+
+ align:start position:0%
+So there's a there's a little bit of
+math there's a mathematical foundation
+
+ align:start position:0%
+math there's a mathematical foundation
+ 
+
+ align:start position:0%
+math there's a mathematical foundation
+that makes understanding these forier
+
+ align:start position:0%
+that makes understanding these forier
+ 
+
+ align:start position:0%
+that makes understanding these forier
+series very easy. The idea is uh has two
+
+ align:start position:0%
+series very easy. The idea is uh has two
+ 
+
+ align:start position:0%
+series very easy. The idea is uh has two
+parts. First off, if you have a
+
+ align:start position:0%
+parts. First off, if you have a
+ 
+
+ align:start position:0%
+parts. First off, if you have a
+sinosoidally varying signal here at
+
+ align:start position:0%
+sinosoidally varying signal here at
+ 
+
+ align:start position:0%
+sinosoidally varying signal here at
+frequency k omega kn, the kith harmonic,
+
+ align:start position:0%
+frequency k omega kn, the kith harmonic,
+ 
+
+ align:start position:0%
+frequency k omega kn, the kith harmonic,
+if you were to multiply the kith
+
+ align:start position:0%
+if you were to multiply the kith
+ 
+
+ align:start position:0%
+if you were to multiply the kith
+harmonic times the elf harmonic,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a signal of frequency k omega times a
+
+ align:start position:0%
+a signal of frequency k omega times a
+ 
+
+ align:start position:0%
+a signal of frequency k omega times a
+signal of frequency l omega, you get a
+
+ align:start position:0%
+signal of frequency l omega, you get a
+ 
+
+ align:start position:0%
+signal of frequency l omega, you get a
+new harmonic, the k plus one. That's a
+
+ align:start position:0%
+new harmonic, the k plus one. That's a
+ 
+
+ align:start position:0%
+new harmonic, the k plus one. That's a
+simple property of the way the product
+
+ align:start position:0%
+simple property of the way the product
+ 
+
+ align:start position:0%
+simple property of the way the product
+of two exponents you you add the
+
+ align:start position:0%
+of two exponents you you add the
+ 
+
+ align:start position:0%
+of two exponents you you add the
+exponents when you take the product of
+
+ align:start position:0%
+exponents when you take the product of
+ 
+
+ align:start position:0%
+exponents when you take the product of
+of two exponentials.
+
+ align:start position:0%
+of two exponentials.
+ 
+
+ align:start position:0%
+of two exponentials.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So that makes it very easy to think
+
+ align:start position:0%
+So that makes it very easy to think
+ 
+
+ align:start position:0%
+So that makes it very easy to think
+about harmonic structure because there's
+
+ align:start position:0%
+about harmonic structure because there's
+ 
+
+ align:start position:0%
+about harmonic structure because there's
+a simple relationship for for generating
+
+ align:start position:0%
+a simple relationship for for generating
+ 
+
+ align:start position:0%
+a simple relationship for for generating
+one harmonic signal in time from another
+
+ align:start position:0%
+one harmonic signal in time from another
+ 
+
+ align:start position:0%
+one harmonic signal in time from another
+harmonic signal in time.
+
+ align:start position:0%
+harmonic signal in time.
+ 
+
+ align:start position:0%
+harmonic signal in time.
+The second thing that makes uh harmonics
+
+ align:start position:0%
+The second thing that makes uh harmonics
+ 
+
+ align:start position:0%
+The second thing that makes uh harmonics
+easy to uh think about mathematically is
+
+ align:start position:0%
+easy to uh think about mathematically is
+ 
+
+ align:start position:0%
+easy to uh think about mathematically is
+that if you integrate over a period,
+
+ align:start position:0%
+that if you integrate over a period,
+ 
+
+ align:start position:0%
+that if you integrate over a period,
+we'll do this so often that we'll
+
+ align:start position:0%
+we'll do this so often that we'll
+ 
+
+ align:start position:0%
+we'll do this so often that we'll
+abbreviate it this way because if you
+
+ align:start position:0%
+abbreviate it this way because if you
+ 
+
+ align:start position:0%
+abbreviate it this way because if you
+have a signal that's periodic, it really
+
+ align:start position:0%
+have a signal that's periodic, it really
+ 
+
+ align:start position:0%
+have a signal that's periodic, it really
+doesn't matter which period you choose
+
+ align:start position:0%
+doesn't matter which period you choose
+ 
+
+ align:start position:0%
+doesn't matter which period you choose
+to do the integral over. If you had a a
+
+ align:start position:0%
+to do the integral over. If you had a a
+ 
+
+ align:start position:0%
+to do the integral over. If you had a a
+signal that was periodic in say capital
+
+ align:start position:0%
+signal that was periodic in say capital
+ 
+
+ align:start position:0%
+signal that was periodic in say capital
+T and integrated it between zero and T,
+
+ align:start position:0%
+T and integrated it between zero and T,
+ 
+
+ align:start position:0%
+T and integrated it between zero and T,
+and if it's periodic, you should be able
+
+ align:start position:0%
+and if it's periodic, you should be able
+ 
+
+ align:start position:0%
+and if it's periodic, you should be able
+to shift that window anywhere you like
+
+ align:start position:0%
+to shift that window anywhere you like
+ 
+
+ align:start position:0%
+to shift that window anywhere you like
+and you should get the same thing.
+
+ align:start position:0%
+and you should get the same thing.
+ 
+
+ align:start position:0%
+and you should get the same thing.
+So we'll not worry about whether it goes
+
+ align:start position:0%
+So we'll not worry about whether it goes
+ 
+
+ align:start position:0%
+So we'll not worry about whether it goes
+from zero to capital t or from 1 to
+
+ align:start position:0%
+from zero to capital t or from 1 to
+ 
+
+ align:start position:0%
+from zero to capital t or from 1 to
+capital t + one. We won't worry about
+
+ align:start position:0%
+capital t + one. We won't worry about
+ 
+
+ align:start position:0%
+capital t + one. We won't worry about
+that. We'll just say integrate over the
+
+ align:start position:0%
+that. We'll just say integrate over the
+ 
+
+ align:start position:0%
+that. We'll just say integrate over the
+period t. If you integrate over the
+
+ align:start position:0%
+period t. If you integrate over the
+ 
+
+ align:start position:0%
+period t. If you integrate over the
+period t any harmonic signal
+
+ align:start position:0%
+period t any harmonic signal
+ 
+
+ align:start position:0%
+period t any harmonic signal
+then there's only two possible answers.
+
+ align:start position:0%
+then there's only two possible answers.
+ 
+
+ align:start position:0%
+then there's only two possible answers.
+So if you integrate e to the j k omega t
+
+ align:start position:0%
+So if you integrate e to the j k omega t
+ 
+
+ align:start position:0%
+So if you integrate e to the j k omega t
+over u one period of omega kn
+
+ align:start position:0%
+over u one period of omega kn
+ 
+
+ align:start position:0%
+over u one period of omega kn
+there will be k periods in there.
+
+ align:start position:0%
+there will be k periods in there.
+ 
+
+ align:start position:0%
+there will be k periods in there.
+So if k is a number other than zero
+
+ align:start position:0%
+So if k is a number other than zero
+ 
+
+ align:start position:0%
+So if k is a number other than zero
+you'll have complete periods of a sine
+
+ align:start position:0%
+you'll have complete periods of a sine
+ 
+
+ align:start position:0%
+you'll have complete periods of a sine
+wave. So the answer of the integral the
+
+ align:start position:0%
+wave. So the answer of the integral the
+ 
+
+ align:start position:0%
+wave. So the answer of the integral the
+average value over that period is zero.
+
+ align:start position:0%
+average value over that period is zero.
+ 
+
+ align:start position:0%
+average value over that period is zero.
+The only time you'll ever get something
+
+ align:start position:0%
+The only time you'll ever get something
+ 
+
+ align:start position:0%
+The only time you'll ever get something
+that's non zero is if k were zero.
+
+ align:start position:0%
+that's non zero is if k were zero.
+ 
+
+ align:start position:0%
+that's non zero is if k were zero.
+If k were zero. If it were DC,
+
+ align:start position:0%
+If k were zero. If it were DC,
+ 
+
+ align:start position:0%
+If k were zero. If it were DC,
+then e to the 0 is one. The integral of
+
+ align:start position:0%
+then e to the 0 is one. The integral of
+ 
+
+ align:start position:0%
+then e to the 0 is one. The integral of
+one over a period, regardless of what
+
+ align:start position:0%
+one over a period, regardless of what
+ 
+
+ align:start position:0%
+one over a period, regardless of what
+period you pick up, the integral of one
+
+ align:start position:0%
+period you pick up, the integral of one
+ 
+
+ align:start position:0%
+period you pick up, the integral of one
+over a period is capital t.
+
+ align:start position:0%
+over a period is capital t.
+ 
+
+ align:start position:0%
+over a period is capital t.
+So it becomes so two things. It's easy
+
+ align:start position:0%
+So it becomes so two things. It's easy
+ 
+
+ align:start position:0%
+So it becomes so two things. It's easy
+to figure out the product of two
+
+ align:start position:0%
+to figure out the product of two
+ 
+
+ align:start position:0%
+to figure out the product of two
+harmonic signals. It's just a different
+
+ align:start position:0%
+harmonic signals. It's just a different
+ 
+
+ align:start position:0%
+harmonic signals. It's just a different
+harmonic. And uh integrals over a period
+
+ align:start position:0%
+harmonic. And uh integrals over a period
+ 
+
+ align:start position:0%
+harmonic. And uh integrals over a period
+are easy with that basis. Then it's easy
+
+ align:start position:0%
+are easy with that basis. Then it's easy
+ 
+
+ align:start position:0%
+are easy with that basis. Then it's easy
+to say how let's imagine that some
+
+ align:start position:0%
+to say how let's imagine that some
+ 
+
+ align:start position:0%
+to say how let's imagine that some
+arbitrary periodic signal which we can
+
+ align:start position:0%
+arbitrary periodic signal which we can
+ 
+
+ align:start position:0%
+arbitrary periodic signal which we can
+always write this way x of t if it's
+
+ align:start position:0%
+always write this way x of t if it's
+ 
+
+ align:start position:0%
+always write this way x of t if it's
+periodic could also be written x of t
+
+ align:start position:0%
+periodic could also be written x of t
+ 
+
+ align:start position:0%
+periodic could also be written x of t
+plus capital t if x if x of t is
+
+ align:start position:0%
+plus capital t if x if x of t is
+ 
+
+ align:start position:0%
+plus capital t if x if x of t is
+periodic in capital t. Let's assume that
+
+ align:start position:0%
+periodic in capital t. Let's assume that
+ 
+
+ align:start position:0%
+periodic in capital t. Let's assume that
+that can be written as a sum of
+
+ align:start position:0%
+that can be written as a sum of
+ 
+
+ align:start position:0%
+that can be written as a sum of
+harmonics.
+
+ align:start position:0%
+harmonics.
+ 
+
+ align:start position:0%
+harmonics.
+So a sum k= minus infinity to infinity
+
+ align:start position:0%
+So a sum k= minus infinity to infinity
+ 
+
+ align:start position:0%
+So a sum k= minus infinity to infinity
+of some amount of e to the j omega kt.
+
+ align:start position:0%
+of some amount of e to the j omega kt.
+ 
+
+ align:start position:0%
+of some amount of e to the j omega kt.
+Why do I have the minus k's in there?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I've asked this question about six
+
+ align:start position:0%
+Okay, I've asked this question about six
+ 
+
+ align:start position:0%
+Okay, I've asked this question about six
+times.
+
+ align:start position:0%
+times.
+ 
+
+ align:start position:0%
+times.
+Why do I have a minus case in there?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Precisely.
+
+ align:start position:0%
+Precisely.
+ 
+
+ align:start position:0%
+Precisely.
+We like Oilers's equation. We like
+
+ align:start position:0%
+We like Oilers's equation. We like
+ 
+
+ align:start position:0%
+We like Oilers's equation. We like
+complex numbers. We don't like cosiness
+
+ align:start position:0%
+complex numbers. We don't like cosiness
+ 
+
+ align:start position:0%
+complex numbers. We don't like cosiness
+and signs. And we can convert SS and
+
+ align:start position:0%
+and signs. And we can convert SS and
+ 
+
+ align:start position:0%
+and signs. And we can convert SS and
+cosiness into complex exponentials using
+
+ align:start position:0%
+cosiness into complex exponentials using
+ 
+
+ align:start position:0%
+cosiness into complex exponentials using
+Oilers's formula. And any everything's
+
+ align:start position:0%
+Oilers's formula. And any everything's
+ 
+
+ align:start position:0%
+Oilers's formula. And any everything's
+very easy, right? So we use minus K for
+
+ align:start position:0%
+very easy, right? So we use minus K for
+ 
+
+ align:start position:0%
+very easy, right? So we use minus K for
+the same reason that we use minus omega
+
+ align:start position:0%
+the same reason that we use minus omega
+ 
+
+ align:start position:0%
+the same reason that we use minus omega
+in previous representations.
+
+ align:start position:0%
+in previous representations.
+ 
+
+ align:start position:0%
+in previous representations.
+So imagine that we can write x of t some
+
+ align:start position:0%
+So imagine that we can write x of t some
+ 
+
+ align:start position:0%
+So imagine that we can write x of t some
+generic periodic signal as a sum of
+
+ align:start position:0%
+generic periodic signal as a sum of
+ 
+
+ align:start position:0%
+generic periodic signal as a sum of
+harmonics.
+
+ align:start position:0%
+harmonics.
+ 
+
+ align:start position:0%
+harmonics.
+Then let's use those principles that we
+
+ align:start position:0%
+Then let's use those principles that we
+ 
+
+ align:start position:0%
+Then let's use those principles that we
+talked about before. If that can be
+
+ align:start position:0%
+talked about before. If that can be
+ 
+
+ align:start position:0%
+talked about before. If that can be
+represented as a sum, I can sift out the
+
+ align:start position:0%
+represented as a sum, I can sift out the
+ 
+
+ align:start position:0%
+represented as a sum, I can sift out the
+one of interest
+
+ align:start position:0%
+one of interest
+ 
+
+ align:start position:0%
+one of interest
+by multiplying x of t times e to the
+
+ align:start position:0%
+by multiplying x of t times e to the
+ 
+
+ align:start position:0%
+by multiplying x of t times e to the
+minus j l omega. We'll see in a minute
+
+ align:start position:0%
+minus j l omega. We'll see in a minute
+ 
+
+ align:start position:0%
+minus j l omega. We'll see in a minute
+what I mean by sift out and why I'm
+
+ align:start position:0%
+what I mean by sift out and why I'm
+ 
+
+ align:start position:0%
+what I mean by sift out and why I'm
+using minus instead of plus.
+
+ align:start position:0%
+using minus instead of plus.
+ 
+
+ align:start position:0%
+using minus instead of plus.
+If you were to run this integral over a
+
+ align:start position:0%
+If you were to run this integral over a
+ 
+
+ align:start position:0%
+If you were to run this integral over a
+period
+
+ align:start position:0%
+period
+ 
+
+ align:start position:0%
+period
+and imagine for the moment that all the
+
+ align:start position:0%
+and imagine for the moment that all the
+ 
+
+ align:start position:0%
+and imagine for the moment that all the
+sums are well behaved so nothing
+
+ align:start position:0%
+sums are well behaved so nothing
+ 
+
+ align:start position:0%
+sums are well behaved so nothing
+explodes and so all the convergence
+
+ align:start position:0%
+explodes and so all the convergence
+ 
+
+ align:start position:0%
+explodes and so all the convergence
+issues are are trivial. If I if the
+
+ align:start position:0%
+issues are are trivial. If I if the
+ 
+
+ align:start position:0%
+issues are are trivial. If I if the
+convergence issues were trivial then I
+
+ align:start position:0%
+convergence issues were trivial then I
+ 
+
+ align:start position:0%
+convergence issues were trivial then I
+could swap the sum in the integral.
+
+ align:start position:0%
+could swap the sum in the integral.
+ 
+
+ align:start position:0%
+could swap the sum in the integral.
+If I did that, then I would end up with
+
+ align:start position:0%
+If I did that, then I would end up with
+ 
+
+ align:start position:0%
+If I did that, then I would end up with
+a sum of a bunch of different ks. But
+
+ align:start position:0%
+a sum of a bunch of different ks. But
+ 
+
+ align:start position:0%
+a sum of a bunch of different ks. But
+for each one, I'd be taking some
+
+ align:start position:0%
+for each one, I'd be taking some
+ 
+
+ align:start position:0%
+for each one, I'd be taking some
+harmonic
+
+ align:start position:0%
+harmonic
+ 
+
+ align:start position:0%
+harmonic
+times the minus l har harmonic.
+
+ align:start position:0%
+times the minus l har harmonic.
+ 
+
+ align:start position:0%
+times the minus l har harmonic.
+And that's going to give me zero when I
+
+ align:start position:0%
+And that's going to give me zero when I
+ 
+
+ align:start position:0%
+And that's going to give me zero when I
+integrate over a period except when k
+
+ align:start position:0%
+integrate over a period except when k
+ 
+
+ align:start position:0%
+integrate over a period except when k
+equals l.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If k equals l, then I'm going to get
+
+ align:start position:0%
+If k equals l, then I'm going to get
+ 
+
+ align:start position:0%
+If k equals l, then I'm going to get
+capital t. So the net effect of doing
+
+ align:start position:0%
+capital t. So the net effect of doing
+ 
+
+ align:start position:0%
+capital t. So the net effect of doing
+this is to to generate T A L. It sifts
+
+ align:start position:0%
+this is to to generate T A L. It sifts
+ 
+
+ align:start position:0%
+this is to to generate T A L. It sifts
+out one of those coefficients.
+
+ align:start position:0%
+out one of those coefficients.
+ 
+
+ align:start position:0%
+out one of those coefficients.
+Well, that's nice. That means that if I
+
+ align:start position:0%
+Well, that's nice. That means that if I
+ 
+
+ align:start position:0%
+Well, that's nice. That means that if I
+assume I can write the signal this way,
+
+ align:start position:0%
+assume I can write the signal this way,
+ 
+
+ align:start position:0%
+assume I can write the signal this way,
+then I can sift out the kith
+
+ align:start position:0%
+then I can sift out the kith
+ 
+
+ align:start position:0%
+then I can sift out the kith
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+by integrating against minus the kith
+
+ align:start position:0%
+by integrating against minus the kith
+ 
+
+ align:start position:0%
+by integrating against minus the kith
+and divide by t because of the
+
+ align:start position:0%
+and divide by t because of the
+ 
+
+ align:start position:0%
+and divide by t because of the
+normalization because if you integrate
+
+ align:start position:0%
+normalization because if you integrate
+ 
+
+ align:start position:0%
+normalization because if you integrate
+one over a period, you get capital t.
+
+ align:start position:0%
+one over a period, you get capital t.
+ 
+
+ align:start position:0%
+one over a period, you get capital t.
+And that tells me then that if this were
+
+ align:start position:0%
+And that tells me then that if this were
+ 
+
+ align:start position:0%
+And that tells me then that if this were
+true, this is how you'd find the
+
+ align:start position:0%
+true, this is how you'd find the
+ 
+
+ align:start position:0%
+true, this is how you'd find the
+coefficient.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that leads to what we call a set of
+
+ align:start position:0%
+So that leads to what we call a set of
+ 
+
+ align:start position:0%
+So that leads to what we call a set of
+uh analysis and synthesis equations.
+
+ align:start position:0%
+uh analysis and synthesis equations.
+ 
+
+ align:start position:0%
+uh analysis and synthesis equations.
+So that if X can be represented this
+
+ align:start position:0%
+So that if X can be represented this
+ 
+
+ align:start position:0%
+So that if X can be represented this
+way, if we can synthesize
+
+ align:start position:0%
+way, if we can synthesize
+ 
+
+ align:start position:0%
+way, if we can synthesize
+a periodic signal X by adding together a
+
+ align:start position:0%
+a periodic signal X by adding together a
+ 
+
+ align:start position:0%
+a periodic signal X by adding together a
+bunch of harmonic components with a
+
+ align:start position:0%
+bunch of harmonic components with a
+ 
+
+ align:start position:0%
+bunch of harmonic components with a
+suitable waiting factor. The waiting
+
+ align:start position:0%
+suitable waiting factor. The waiting
+ 
+
+ align:start position:0%
+suitable waiting factor. The waiting
+factor a subk certainly has a different
+
+ align:start position:0%
+factor a subk certainly has a different
+ 
+
+ align:start position:0%
+factor a subk certainly has a different
+magnitude just like those musical tones
+
+ align:start position:0%
+magnitude just like those musical tones
+ 
+
+ align:start position:0%
+magnitude just like those musical tones
+that I played at the beginning, those
+
+ align:start position:0%
+that I played at the beginning, those
+ 
+
+ align:start position:0%
+that I played at the beginning, those
+musical notes. All the different ks had
+
+ align:start position:0%
+musical notes. All the different ks had
+ 
+
+ align:start position:0%
+musical notes. All the different ks had
+different amplitudes. They also have
+
+ align:start position:0%
+different amplitudes. They also have
+ 
+
+ align:start position:0%
+different amplitudes. They also have
+different phases. A subk can be a
+
+ align:start position:0%
+different phases. A subk can be a
+ 
+
+ align:start position:0%
+different phases. A subk can be a
+complex number. We like complex numbers.
+
+ align:start position:0%
+complex number. We like complex numbers.
+ 
+
+ align:start position:0%
+complex number. We like complex numbers.
+Complex numbers are easy.
+
+ align:start position:0%
+Complex numbers are easy.
+ 
+
+ align:start position:0%
+Complex numbers are easy.
+So uh if we can represent x by a sum of
+
+ align:start position:0%
+So uh if we can represent x by a sum of
+ 
+
+ align:start position:0%
+So uh if we can represent x by a sum of
+harmonics complex complex valued
+
+ align:start position:0%
+harmonics complex complex valued
+ 
+
+ align:start position:0%
+harmonics complex complex valued
+s uh so weighted by a complex number
+
+ align:start position:0%
+s uh so weighted by a complex number
+ 
+
+ align:start position:0%
+s uh so weighted by a complex number
+then we can sift out what those weight
+
+ align:start position:0%
+then we can sift out what those weight
+ 
+
+ align:start position:0%
+then we can sift out what those weight
+factors were by running the analysis
+
+ align:start position:0%
+factors were by running the analysis
+ 
+
+ align:start position:0%
+factors were by running the analysis
+equation. we can analyze the signal to
+
+ align:start position:0%
+equation. we can analyze the signal to
+ 
+
+ align:start position:0%
+equation. we can analyze the signal to
+figure out how much of the case
+
+ align:start position:0%
+figure out how much of the case
+ 
+
+ align:start position:0%
+figure out how much of the case
+component is there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the strategy then is assume that all
+
+ align:start position:0%
+So the strategy then is assume that all
+ 
+
+ align:start position:0%
+So the strategy then is assume that all
+works.
+
+ align:start position:0%
+works.
+ 
+
+ align:start position:0%
+works.
+That is to say let's take an ugly signal
+
+ align:start position:0%
+That is to say let's take an ugly signal
+ 
+
+ align:start position:0%
+That is to say let's take an ugly signal
+of the type that caused controversy back
+
+ align:start position:0%
+of the type that caused controversy back
+ 
+
+ align:start position:0%
+of the type that caused controversy back
+in the mid 1800s.
+
+ align:start position:0%
+in the mid 1800s.
+ 
+
+ align:start position:0%
+in the mid 1800s.
+Let's take a controversial signal like a
+
+ align:start position:0%
+Let's take a controversial signal like a
+ 
+
+ align:start position:0%
+Let's take a controversial signal like a
+square wave. Assume it all works and
+
+ align:start position:0%
+square wave. Assume it all works and
+ 
+
+ align:start position:0%
+square wave. Assume it all works and
+figure out what the AKs would have had
+
+ align:start position:0%
+figure out what the AKs would have had
+ 
+
+ align:start position:0%
+figure out what the AKs would have had
+to be. and then we'll figure out whether
+
+ align:start position:0%
+to be. and then we'll figure out whether
+ 
+
+ align:start position:0%
+to be. and then we'll figure out whether
+that made any sense.
+
+ align:start position:0%
+that made any sense.
+ 
+
+ align:start position:0%
+that made any sense.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+uh if this thing were to be represented
+
+ align:start position:0%
+uh if this thing were to be represented
+ 
+
+ align:start position:0%
+uh if this thing were to be represented
+by a forier series by a a sum of
+
+ align:start position:0%
+by a forier series by a a sum of
+ 
+
+ align:start position:0%
+by a forier series by a a sum of
+harmonic components,
+
+ align:start position:0%
+harmonic components,
+ 
+
+ align:start position:0%
+harmonic components,
+how many of these statements would be
+
+ align:start position:0%
+how many of these statements would be
+ 
+
+ align:start position:0%
+how many of these statements would be
+true about those harmonic amplitudes?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, as you start to write, look toward
+
+ align:start position:0%
+So, as you start to write, look toward
+ 
+
+ align:start position:0%
+So, as you start to write, look toward
+your neighbor and say hi.
+
+ align:start position:0%
+your neighbor and say hi.
+ 
+
+ align:start position:0%
+your neighbor and say hi.
+Then write and figure out the answer.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, how many of those statements
+
+ align:start position:0%
+Okay. So, how many of those statements
+ 
+
+ align:start position:0%
+Okay. So, how many of those statements
+are true? Raise your hand with a number
+
+ align:start position:0%
+are true? Raise your hand with a number
+ 
+
+ align:start position:0%
+are true? Raise your hand with a number
+of fingers between zero and five would
+
+ align:start position:0%
+of fingers between zero and five would
+ 
+
+ align:start position:0%
+of fingers between zero and five would
+seem good limits.
+
+ align:start position:0%
+seem good limits.
+ 
+
+ align:start position:0%
+seem good limits.
+How many statements are true?
+
+ align:start position:0%
+How many statements are true?
+ 
+
+ align:start position:0%
+How many statements are true?
+Okay, we got about 40% correct. So,
+
+ align:start position:0%
+Okay, we got about 40% correct. So,
+ 
+
+ align:start position:0%
+Okay, we got about 40% correct. So,
+that's a little under half. What do I do
+
+ align:start position:0%
+that's a little under half. What do I do
+ 
+
+ align:start position:0%
+that's a little under half. What do I do
+first?
+
+ align:start position:0%
+first?
+ 
+
+ align:start position:0%
+first?
+If I want to figure this out, what would
+
+ align:start position:0%
+If I want to figure this out, what would
+ 
+
+ align:start position:0%
+If I want to figure this out, what would
+I do to try to figure out? So, statement
+
+ align:start position:0%
+I do to try to figure out? So, statement
+ 
+
+ align:start position:0%
+I do to try to figure out? So, statement
+one, a subk is zero if k is even. Should
+
+ align:start position:0%
+one, a subk is zero if k is even. Should
+ 
+
+ align:start position:0%
+one, a subk is zero if k is even. Should
+that be true or false? How do I think
+
+ align:start position:0%
+that be true or false? How do I think
+ 
+
+ align:start position:0%
+that be true or false? How do I think
+about that?
+
+ align:start position:0%
+about that?
+ 
+
+ align:start position:0%
+about that?
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Square wave is odd. Okay, that sounds
+
+ align:start position:0%
+Square wave is odd. Okay, that sounds
+ 
+
+ align:start position:0%
+Square wave is odd. Okay, that sounds
+good. So, what's how's that help me?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, I might want to have only uh odd
+
+ align:start position:0%
+So, I might want to have only uh odd
+ 
+
+ align:start position:0%
+So, I might want to have only uh odd
+terms. How do I tell how many terms in
+
+ align:start position:0%
+terms. How do I tell how many terms in
+ 
+
+ align:start position:0%
+terms. How do I tell how many terms in
+the forier decomposition are odd and
+
+ align:start position:0%
+the forier decomposition are odd and
+ 
+
+ align:start position:0%
+the forier decomposition are odd and
+even?
+
+ align:start position:0%
+even?
+ 
+
+ align:start position:0%
+even?
+What is the forier decomposition? So
+
+ align:start position:0%
+What is the forier decomposition? So
+ 
+
+ align:start position:0%
+What is the forier decomposition? So
+let's start by just writing some
+
+ align:start position:0%
+let's start by just writing some
+ 
+
+ align:start position:0%
+let's start by just writing some
+definition, right? So I want to say that
+
+ align:start position:0%
+definition, right? So I want to say that
+ 
+
+ align:start position:0%
+definition, right? So I want to say that
+x of t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is let's see I have a period of one.
+
+ align:start position:0%
+is let's see I have a period of one.
+ 
+
+ align:start position:0%
+is let's see I have a period of one.
+That's the same as x of t + one, right?
+
+ align:start position:0%
+That's the same as x of t + one, right?
+ 
+
+ align:start position:0%
+That's the same as x of t + one, right?
+And I want to write this as some sort of
+
+ align:start position:0%
+And I want to write this as some sort of
+ 
+
+ align:start position:0%
+And I want to write this as some sort of
+a forier thing. So what do I write next?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? I want to say I want to say that
+
+ align:start position:0%
+Right? I want to say I want to say that
+ 
+
+ align:start position:0%
+Right? I want to say I want to say that
+this signal can be represented by some
+
+ align:start position:0%
+this signal can be represented by some
+ 
+
+ align:start position:0%
+this signal can be represented by some
+sum of something. Right? And I'm going
+
+ align:start position:0%
+sum of something. Right? And I'm going
+ 
+
+ align:start position:0%
+sum of something. Right? And I'm going
+to have to put some weights in.
+
+ align:start position:0%
+to have to put some weights in.
+ 
+
+ align:start position:0%
+to have to put some weights in.
+And I'm going to want something like e
+
+ align:start position:0%
+And I'm going to want something like e
+ 
+
+ align:start position:0%
+And I'm going to want something like e
+to the minus j 2 pi kt by t something
+
+ align:start position:0%
+to the minus j 2 pi kt by t something
+ 
+
+ align:start position:0%
+to the minus j 2 pi kt by t something
+like that.
+
+ align:start position:0%
+like that.
+ 
+
+ align:start position:0%
+like that.
+And I'm going to need a whole bunch of
+
+ align:start position:0%
+And I'm going to need a whole bunch of
+ 
+
+ align:start position:0%
+And I'm going to need a whole bunch of
+these.
+
+ align:start position:0%
+these.
+ 
+
+ align:start position:0%
+these.
+Where does even and odd show up?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if I were to rewrite this as ss and
+
+ align:start position:0%
+So if I were to rewrite this as ss and
+ 
+
+ align:start position:0%
+So if I were to rewrite this as ss and
+cosiness, right? So I could rewrite this
+
+ align:start position:0%
+cosiness, right? So I could rewrite this
+ 
+
+ align:start position:0%
+cosiness, right? So I could rewrite this
+in terms of some signs and some
+
+ align:start position:0%
+in terms of some signs and some
+ 
+
+ align:start position:0%
+in terms of some signs and some
+cosiness,
+
+ align:start position:0%
+cosiness,
+ 
+
+ align:start position:0%
+cosiness,
+then then the decomposition into even
+
+ align:start position:0%
+then then the decomposition into even
+ 
+
+ align:start position:0%
+then then the decomposition into even
+and odd is easier. That's correct.
+
+ align:start position:0%
+and odd is easier. That's correct.
+ 
+
+ align:start position:0%
+and odd is easier. That's correct.
+How do I So let's get back to this one.
+
+ align:start position:0%
+How do I So let's get back to this one.
+ 
+
+ align:start position:0%
+How do I So let's get back to this one.
+How do I think about this one now? Uh so
+
+ align:start position:0%
+How do I think about this one now? Uh so
+ 
+
+ align:start position:0%
+How do I think about this one now? Uh so
+I want k to be even.
+
+ align:start position:0%
+I want k to be even.
+ 
+
+ align:start position:0%
+I want k to be even.
+What does K even correspond to?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, let's assume I don't know what K
+
+ align:start position:0%
+Okay, let's assume I don't know what K
+ 
+
+ align:start position:0%
+Okay, let's assume I don't know what K
+even How do I do this if I don't know
+
+ align:start position:0%
+even How do I do this if I don't know
+ 
+
+ align:start position:0%
+even How do I do this if I don't know
+anything? How do I just uh grunt through
+
+ align:start position:0%
+anything? How do I just uh grunt through
+ 
+
+ align:start position:0%
+anything? How do I just uh grunt through
+it?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+just do the integral. Exactly. So, what
+
+ align:start position:0%
+just do the integral. Exactly. So, what
+ 
+
+ align:start position:0%
+just do the integral. Exactly. So, what
+I'd like to do is say that uh a subk is
+
+ align:start position:0%
+I'd like to do is say that uh a subk is
+ 
+
+ align:start position:0%
+I'd like to do is say that uh a subk is
+one of So, assuming everything works,
+
+ align:start position:0%
+one of So, assuming everything works,
+ 
+
+ align:start position:0%
+one of So, assuming everything works,
+right? Assuming everything works, then a
+
+ align:start position:0%
+right? Assuming everything works, then a
+ 
+
+ align:start position:0%
+right? Assuming everything works, then a
+subk should be the integral over t
+
+ align:start position:0%
+subk should be the integral over t
+ 
+
+ align:start position:0%
+subk should be the integral over t
+weighted by 1 / t x of t e to the minus
+
+ align:start position:0%
+weighted by 1 / t x of t e to the minus
+ 
+
+ align:start position:0%
+weighted by 1 / t x of t e to the minus
+j 2 pi kt over t. I put a I should have
+
+ align:start position:0%
+j 2 pi kt over t. I put a I should have
+ 
+
+ align:start position:0%
+j 2 pi kt over t. I put a I should have
+put a plus there.
+
+ align:start position:0%
+put a plus there.
+ 
+
+ align:start position:0%
+put a plus there.
+Um I want the minus sign in one of the
+
+ align:start position:0%
+Um I want the minus sign in one of the
+ 
+
+ align:start position:0%
+Um I want the minus sign in one of the
+formulas and not in the other one. Okay.
+
+ align:start position:0%
+formulas and not in the other one. Okay.
+ 
+
+ align:start position:0%
+formulas and not in the other one. Okay.
+And if you just think about that that uh
+
+ align:start position:0%
+And if you just think about that that uh
+ 
+
+ align:start position:0%
+And if you just think about that that uh
+integral, it's not very hard.
+
+ align:start position:0%
+integral, it's not very hard.
+ 
+
+ align:start position:0%
+integral, it's not very hard.
+So I want this kind of thing. Capital T
+
+ align:start position:0%
+So I want this kind of thing. Capital T
+ 
+
+ align:start position:0%
+So I want this kind of thing. Capital T
+is one, right?
+
+ align:start position:0%
+is one, right?
+ 
+
+ align:start position:0%
+is one, right?
+So I get two pieces. The piece that
+
+ align:start position:0%
+So I get two pieces. The piece that
+ 
+
+ align:start position:0%
+So I get two pieces. The piece that
+corresponds to the minus a half and plus
+
+ align:start position:0%
+corresponds to the minus a half and plus
+ 
+
+ align:start position:0%
+corresponds to the minus a half and plus
+a half.
+
+ align:start position:0%
+a half.
+ 
+
+ align:start position:0%
+a half.
+And when I integrate them, I get
+
+ align:start position:0%
+And when I integrate them, I get
+ 
+
+ align:start position:0%
+And when I integrate them, I get
+something that's a little bit Well, no,
+
+ align:start position:0%
+something that's a little bit Well, no,
+ 
+
+ align:start position:0%
+something that's a little bit Well, no,
+it's pretty straightforward, right? So
+
+ align:start position:0%
+it's pretty straightforward, right? So
+ 
+
+ align:start position:0%
+it's pretty straightforward, right? So
+you integrate this thing, the one over
+
+ align:start position:0%
+you integrate this thing, the one over
+ 
+
+ align:start position:0%
+you integrate this thing, the one over
+minus, so the minus J2 pi K flips into
+
+ align:start position:0%
+minus, so the minus J2 pi K flips into
+ 
+
+ align:start position:0%
+minus, so the minus J2 pi K flips into
+the bottom. Uh the half turns it into J
+
+ align:start position:0%
+the bottom. Uh the half turns it into J
+ 
+
+ align:start position:0%
+the bottom. Uh the half turns it into J
+4 pi K blah blah blah. You get four
+
+ align:start position:0%
+4 pi K blah blah blah. You get four
+ 
+
+ align:start position:0%
+4 pi K blah blah blah. You get four
+pieces. two pieces. The these two pieces
+
+ align:start position:0%
+pieces. two pieces. The these two pieces
+ 
+
+ align:start position:0%
+pieces. two pieces. The these two pieces
+correspond to one. They sum to two. So
+
+ align:start position:0%
+correspond to one. They sum to two. So
+ 
+
+ align:start position:0%
+correspond to one. They sum to two. So
+you get that.
+
+ align:start position:0%
+you get that.
+ 
+
+ align:start position:0%
+you get that.
+The point is that it's a pretty simple
+
+ align:start position:0%
+The point is that it's a pretty simple
+ 
+
+ align:start position:0%
+The point is that it's a pretty simple
+it's a pretty simple transformation
+
+ align:start position:0%
+it's a pretty simple transformation
+ 
+
+ align:start position:0%
+it's a pretty simple transformation
+to think about the square wave turning
+
+ align:start position:0%
+to think about the square wave turning
+ 
+
+ align:start position:0%
+to think about the square wave turning
+into a sequence of amplitudes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if you choose um let's see. So if you
+
+ align:start position:0%
+So if you choose um let's see. So if you
+ 
+
+ align:start position:0%
+So if you choose um let's see. So if you
+choose uh k to be even then I've got uh
+
+ align:start position:0%
+choose uh k to be even then I've got uh
+ 
+
+ align:start position:0%
+choose uh k to be even then I've got uh
+an integer multiple of 2 pi
+
+ align:start position:0%
+an integer multiple of 2 pi
+ 
+
+ align:start position:0%
+an integer multiple of 2 pi
+right if k were even then I would have
+
+ align:start position:0%
+right if k were even then I would have
+ 
+
+ align:start position:0%
+right if k were even then I would have
+uh an integer multiple of 2 pi e to the
+
+ align:start position:0%
+uh an integer multiple of 2 pi e to the
+ 
+
+ align:start position:0%
+uh an integer multiple of 2 pi e to the
+integer multiple of 2 pi flips around to
+
+ align:start position:0%
+integer multiple of 2 pi flips around to
+ 
+
+ align:start position:0%
+integer multiple of 2 pi flips around to
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+as does the minus one that kills this
+
+ align:start position:0%
+as does the minus one that kills this
+ 
+
+ align:start position:0%
+as does the minus one that kills this
+stuff.
+
+ align:start position:0%
+stuff.
+ 
+
+ align:start position:0%
+stuff.
+Okay, so that's where the K even and K
+
+ align:start position:0%
+Okay, so that's where the K even and K
+ 
+
+ align:start position:0%
+Okay, so that's where the K even and K
+odd comes from.
+
+ align:start position:0%
+odd comes from.
+ 
+
+ align:start position:0%
+odd comes from.
+So the point is that there's a simple
+
+ align:start position:0%
+So the point is that there's a simple
+ 
+
+ align:start position:0%
+So the point is that there's a simple
+way to to just crank through it and we
+
+ align:start position:0%
+way to to just crank through it and we
+ 
+
+ align:start position:0%
+way to to just crank through it and we
+get a a simple representation. So we get
+
+ align:start position:0%
+get a a simple representation. So we get
+ 
+
+ align:start position:0%
+get a a simple representation. So we get
+that AK is um 1 over J pi K
+
+ align:start position:0%
+that AK is um 1 over J pi K
+ 
+
+ align:start position:0%
+that AK is um 1 over J pi K
+uh K odd
+
+ align:start position:0%
+uh K odd
+ 
+
+ align:start position:0%
+uh K odd
+zero otherwise.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And then we can just sort of t run
+
+ align:start position:0%
+Okay. And then we can just sort of t run
+ 
+
+ align:start position:0%
+Okay. And then we can just sort of t run
+down through the list. We'll see in a
+
+ align:start position:0%
+down through the list. We'll see in a
+ 
+
+ align:start position:0%
+down through the list. We'll see in a
+minute why this particular list of
+
+ align:start position:0%
+minute why this particular list of
+ 
+
+ align:start position:0%
+minute why this particular list of
+properties is interesting. So a a subk
+
+ align:start position:0%
+properties is interesting. So a a subk
+ 
+
+ align:start position:0%
+properties is interesting. So a a subk
+is zero if k is even. Yep. Right.
+
+ align:start position:0%
+is zero if k is even. Yep. Right.
+ 
+
+ align:start position:0%
+is zero if k is even. Yep. Right.
+Ak is real. Nope. There's a j in it.
+
+ align:start position:0%
+Ak is real. Nope. There's a j in it.
+ 
+
+ align:start position:0%
+Ak is real. Nope. There's a j in it.
+Uh a k magnitude decreases with k
+
+ align:start position:0%
+Uh a k magnitude decreases with k
+ 
+
+ align:start position:0%
+Uh a k magnitude decreases with k
+square. Nope. Decreases with k.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh there's an infinite number of nonzero
+
+ align:start position:0%
+Uh there's an infinite number of nonzero
+ 
+
+ align:start position:0%
+Uh there's an infinite number of nonzero
+terms. Yep. Right. K goes to infinity.
+
+ align:start position:0%
+terms. Yep. Right. K goes to infinity.
+ 
+
+ align:start position:0%
+terms. Yep. Right. K goes to infinity.
+All of the above obvious. Okay. The
+
+ align:start position:0%
+All of the above obvious. Okay. The
+ 
+
+ align:start position:0%
+All of the above obvious. Okay. The
+point is it's simple to do and you end
+
+ align:start position:0%
+point is it's simple to do and you end
+ 
+
+ align:start position:0%
+point is it's simple to do and you end
+up representing the the uh
+
+ align:start position:0%
+up representing the the uh
+ 
+
+ align:start position:0%
+up representing the the uh
+time waveform
+
+ align:start position:0%
+time waveform
+ 
+
+ align:start position:0%
+time waveform
+by just a sequence of numbers.
+
+ align:start position:0%
+by just a sequence of numbers.
+ 
+
+ align:start position:0%
+by just a sequence of numbers.
+How big is the fundamental? How big is
+
+ align:start position:0%
+How big is the fundamental? How big is
+ 
+
+ align:start position:0%
+How big is the fundamental? How big is
+the second harmonic? How big is the
+
+ align:start position:0%
+the second harmonic? How big is the
+ 
+
+ align:start position:0%
+the second harmonic? How big is the
+third harmonic? Etc.
+
+ align:start position:0%
+third harmonic? Etc.
+ 
+
+ align:start position:0%
+third harmonic? Etc.
+There's some more math that makes things
+
+ align:start position:0%
+There's some more math that makes things
+ 
+
+ align:start position:0%
+There's some more math that makes things
+even easier.
+
+ align:start position:0%
+even easier.
+ 
+
+ align:start position:0%
+even easier.
+There are ways of thinking about
+
+ align:start position:0%
+There are ways of thinking about
+ 
+
+ align:start position:0%
+There are ways of thinking about
+operations in time
+
+ align:start position:0%
+operations in time
+ 
+
+ align:start position:0%
+operations in time
+as equivalent operations in harmonics.
+
+ align:start position:0%
+as equivalent operations in harmonics.
+ 
+
+ align:start position:0%
+as equivalent operations in harmonics.
+That makes the idea even more powerful
+
+ align:start position:0%
+That makes the idea even more powerful
+ 
+
+ align:start position:0%
+That makes the idea even more powerful
+because what we are developing is an
+
+ align:start position:0%
+because what we are developing is an
+ 
+
+ align:start position:0%
+because what we are developing is an
+alternative representation for signals.
+
+ align:start position:0%
+alternative representation for signals.
+ 
+
+ align:start position:0%
+alternative representation for signals.
+So same as we had multiple
+
+ align:start position:0%
+So same as we had multiple
+ 
+
+ align:start position:0%
+So same as we had multiple
+representations for systems,
+
+ align:start position:0%
+representations for systems,
+ 
+
+ align:start position:0%
+representations for systems,
+differential equations, block diagrams,
+
+ align:start position:0%
+differential equations, block diagrams,
+ 
+
+ align:start position:0%
+differential equations, block diagrams,
+h of t, h of s, h of r, bod plots, all
+
+ align:start position:0%
+h of t, h of s, h of r, bod plots, all
+ 
+
+ align:start position:0%
+h of t, h of s, h of r, bod plots, all
+those different representations of
+
+ align:start position:0%
+those different representations of
+ 
+
+ align:start position:0%
+those different representations of
+signal of systems. This represents an
+
+ align:start position:0%
+signal of systems. This represents an
+ 
+
+ align:start position:0%
+signal of systems. This represents an
+alternative representation of a signal.
+
+ align:start position:0%
+alternative representation of a signal.
+ 
+
+ align:start position:0%
+alternative representation of a signal.
+We think about it being represented in
+
+ align:start position:0%
+We think about it being represented in
+ 
+
+ align:start position:0%
+We think about it being represented in
+time or we will we think about it being
+
+ align:start position:0%
+time or we will we think about it being
+ 
+
+ align:start position:0%
+time or we will we think about it being
+represented in harmonics or eventually
+
+ align:start position:0%
+represented in harmonics or eventually
+ 
+
+ align:start position:0%
+represented in harmonics or eventually
+we'll call that frequency. So we'll
+
+ align:start position:0%
+we'll call that frequency. So we'll
+ 
+
+ align:start position:0%
+we'll call that frequency. So we'll
+think about signals being represented in
+
+ align:start position:0%
+think about signals being represented in
+ 
+
+ align:start position:0%
+think about signals being represented in
+time or frequency. And you can think
+
+ align:start position:0%
+time or frequency. And you can think
+ 
+
+ align:start position:0%
+time or frequency. And you can think
+about operations in time having a
+
+ align:start position:0%
+about operations in time having a
+ 
+
+ align:start position:0%
+about operations in time having a
+corresponding operation in frequency.
+
+ align:start position:0%
+corresponding operation in frequency.
+ 
+
+ align:start position:0%
+corresponding operation in frequency.
+So illustrated here, if a signal is
+
+ align:start position:0%
+So illustrated here, if a signal is
+ 
+
+ align:start position:0%
+So illustrated here, if a signal is
+differentiated in time, the 4A
+
+ align:start position:0%
+differentiated in time, the 4A
+ 
+
+ align:start position:0%
+differentiated in time, the 4A
+coefficients are multiplied by J 2 pi
+
+ align:start position:0%
+coefficients are multiplied by J 2 pi
+ 
+
+ align:start position:0%
+coefficients are multiplied by J 2 pi
+over T K. Okay. Well, that's easy. If we
+
+ align:start position:0%
+over T K. Okay. Well, that's easy. If we
+ 
+
+ align:start position:0%
+over T K. Okay. Well, that's easy. If we
+assume for the moment that we can
+
+ align:start position:0%
+assume for the moment that we can
+ 
+
+ align:start position:0%
+assume for the moment that we can
+represent X as this kind of a sum,
+
+ align:start position:0%
+represent X as this kind of a sum,
+ 
+
+ align:start position:0%
+represent X as this kind of a sum,
+differentiation is linear. The
+
+ align:start position:0%
+differentiation is linear. The
+ 
+
+ align:start position:0%
+differentiation is linear. The
+derivative of a sum is a sum of the
+
+ align:start position:0%
+derivative of a sum is a sum of the
+ 
+
+ align:start position:0%
+derivative of a sum is a sum of the
+derivatives. the derivative of sine
+
+ align:start position:0%
+derivatives. the derivative of sine
+ 
+
+ align:start position:0%
+derivatives. the derivative of sine
+waves easy and we end up with with the
+
+ align:start position:0%
+waves easy and we end up with with the
+ 
+
+ align:start position:0%
+waves easy and we end up with with the
+idea that if you knew the a subks
+
+ align:start position:0%
+idea that if you knew the a subks
+ 
+
+ align:start position:0%
+idea that if you knew the a subks
+then you can easily formulate the the u
+
+ align:start position:0%
+then you can easily formulate the the u
+ 
+
+ align:start position:0%
+then you can easily formulate the the u
+series representation
+
+ align:start position:0%
+series representation
+ 
+
+ align:start position:0%
+series representation
+for the harmonic structure by just
+
+ align:start position:0%
+for the harmonic structure by just
+ 
+
+ align:start position:0%
+for the harmonic structure by just
+multiplying each of the aks by the power
+
+ align:start position:0%
+multiplying each of the aks by the power
+ 
+
+ align:start position:0%
+multiplying each of the aks by the power
+of the exponent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that gives us a way of thinking
+
+ align:start position:0%
+Okay, so that gives us a way of thinking
+ 
+
+ align:start position:0%
+Okay, so that gives us a way of thinking
+about signals in time
+
+ align:start position:0%
+about signals in time
+ 
+
+ align:start position:0%
+about signals in time
+as being represented in frequency.
+
+ align:start position:0%
+as being represented in frequency.
+ 
+
+ align:start position:0%
+as being represented in frequency.
+So here's an illustration of that.
+
+ align:start position:0%
+So here's an illustration of that.
+ 
+
+ align:start position:0%
+So here's an illustration of that.
+Imagine that we have a a triangle wave
+
+ align:start position:0%
+Imagine that we have a a triangle wave
+ 
+
+ align:start position:0%
+Imagine that we have a a triangle wave
+rather than a square wave.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Answer the same questions and be aware
+
+ align:start position:0%
+Answer the same questions and be aware
+ 
+
+ align:start position:0%
+Answer the same questions and be aware
+that it's a trick.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+By trick I mean you could use the
+
+ align:start position:0%
+By trick I mean you could use the
+ 
+
+ align:start position:0%
+By trick I mean you could use the
+obvious approach which is one we just
+
+ align:start position:0%
+obvious approach which is one we just
+ 
+
+ align:start position:0%
+obvious approach which is one we just
+did or you could use some insight from
+
+ align:start position:0%
+did or you could use some insight from
+ 
+
+ align:start position:0%
+did or you could use some insight from
+the last slide and do it in one step.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, how many of these statements are
+
+ align:start position:0%
+So, how many of these statements are
+ 
+
+ align:start position:0%
+So, how many of these statements are
+true?
+
+ align:start position:0%
+true?
+ 
+
+ align:start position:0%
+true?
+Everybody raise your hand. raise a
+
+ align:start position:0%
+Everybody raise your hand. raise a
+ 
+
+ align:start position:0%
+Everybody raise your hand. raise a
+number of fingers
+
+ align:start position:0%
+number of fingers
+ 
+
+ align:start position:0%
+number of fingers
+equal to the U number of correct
+
+ align:start position:0%
+equal to the U number of correct
+ 
+
+ align:start position:0%
+equal to the U number of correct
+statements. We've got complete switch of
+
+ align:start position:0%
+statements. We've got complete switch of
+ 
+
+ align:start position:0%
+statements. We've got complete switch of
+who's right and still 40% correct.
+
+ align:start position:0%
+who's right and still 40% correct.
+ 
+
+ align:start position:0%
+who's right and still 40% correct.
+That's phenomenal.
+
+ align:start position:0%
+That's phenomenal.
+ 
+
+ align:start position:0%
+That's phenomenal.
+So, uh we could just go through the
+
+ align:start position:0%
+So, uh we could just go through the
+ 
+
+ align:start position:0%
+So, uh we could just go through the
+list. What's the trick?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So close. So integral. Exactly. Right.
+
+ align:start position:0%
+So close. So integral. Exactly. Right.
+ 
+
+ align:start position:0%
+So close. So integral. Exactly. Right.
+This signal is the integral of the
+
+ align:start position:0%
+This signal is the integral of the
+ 
+
+ align:start position:0%
+This signal is the integral of the
+previous signal. Right.
+
+ align:start position:0%
+previous signal. Right.
+ 
+
+ align:start position:0%
+previous signal. Right.
+So that means that we ought to be able
+
+ align:start position:0%
+So that means that we ought to be able
+ 
+
+ align:start position:0%
+So that means that we ought to be able
+to there's some kind of a simple
+
+ align:start position:0%
+to there's some kind of a simple
+ 
+
+ align:start position:0%
+to there's some kind of a simple
+relationship between this series and the
+
+ align:start position:0%
+relationship between this series and the
+ 
+
+ align:start position:0%
+relationship between this series and the
+series that represents that one. What
+
+ align:start position:0%
+series that represents that one. What
+ 
+
+ align:start position:0%
+series that represents that one. What
+should I do to this one to make it look
+
+ align:start position:0%
+should I do to this one to make it look
+ 
+
+ align:start position:0%
+should I do to this one to make it look
+like that one?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Divide by J2 K precisely.
+
+ align:start position:0%
+Divide by J2 K precisely.
+ 
+
+ align:start position:0%
+Divide by J2 K precisely.
+So um I can think about the bks being
+
+ align:start position:0%
+So um I can think about the bks being
+ 
+
+ align:start position:0%
+So um I can think about the bks being
+the aks
+
+ align:start position:0%
+the aks
+ 
+
+ align:start position:0%
+the aks
+but then I have to worry about the
+
+ align:start position:0%
+but then I have to worry about the
+ 
+
+ align:start position:0%
+but then I have to worry about the
+representation for differentiation or
+
+ align:start position:0%
+representation for differentiation or
+ 
+
+ align:start position:0%
+representation for differentiation or
+here integration
+
+ align:start position:0%
+here integration
+ 
+
+ align:start position:0%
+here integration
+in the frequency domain. In the
+
+ align:start position:0%
+in the frequency domain. In the
+ 
+
+ align:start position:0%
+in the frequency domain. In the
+frequency domain integration
+
+ align:start position:0%
+frequency domain integration
+ 
+
+ align:start position:0%
+frequency domain integration
+corresponds to dividing by uh J2 pi k.
+
+ align:start position:0%
+corresponds to dividing by uh J2 pi k.
+ 
+
+ align:start position:0%
+corresponds to dividing by uh J2 pi k.
+So now uh if I think about the list of
+
+ align:start position:0%
+So now uh if I think about the list of
+ 
+
+ align:start position:0%
+So now uh if I think about the list of
+questions uh is b zero for k even? Yeah,
+
+ align:start position:0%
+questions uh is b zero for k even? Yeah,
+ 
+
+ align:start position:0%
+questions uh is b zero for k even? Yeah,
+it was before. It is now
+
+ align:start position:0%
+it was before. It is now
+ 
+
+ align:start position:0%
+it was before. It is now
+because all we're doing is changing the
+
+ align:start position:0%
+because all we're doing is changing the
+ 
+
+ align:start position:0%
+because all we're doing is changing the
+the weights. And if the weights started
+
+ align:start position:0%
+the weights. And if the weights started
+ 
+
+ align:start position:0%
+the weights. And if the weights started
+out zero and we're multiplying by
+
+ align:start position:0%
+out zero and we're multiplying by
+ 
+
+ align:start position:0%
+out zero and we're multiplying by
+something, we can't get it to be
+
+ align:start position:0%
+something, we can't get it to be
+ 
+
+ align:start position:0%
+something, we can't get it to be
+different from zero.
+
+ align:start position:0%
+different from zero.
+ 
+
+ align:start position:0%
+different from zero.
+Uh, is it real valued? Well, now it is
+
+ align:start position:0%
+Uh, is it real valued? Well, now it is
+ 
+
+ align:start position:0%
+Uh, is it real valued? Well, now it is
+because I had a J time J.
+
+ align:start position:0%
+because I had a J time J.
+ 
+
+ align:start position:0%
+because I had a J time J.
+So now they are real real valued.
+
+ align:start position:0%
+So now they are real real valued.
+ 
+
+ align:start position:0%
+So now they are real real valued.
+Uh, does it decrease with K square? Now
+
+ align:start position:0%
+Uh, does it decrease with K square? Now
+ 
+
+ align:start position:0%
+Uh, does it decrease with K square? Now
+it does because I got one of the K's
+
+ align:start position:0%
+it does because I got one of the K's
+ 
+
+ align:start position:0%
+it does because I got one of the K's
+from the differentiation operator and
+
+ align:start position:0%
+from the differentiation operator and
+ 
+
+ align:start position:0%
+from the differentiation operator and
+the other K from over here.
+
+ align:start position:0%
+the other K from over here.
+ 
+
+ align:start position:0%
+the other K from over here.
+uh infinite number. Of course, the old
+
+ align:start position:0%
+uh infinite number. Of course, the old
+ 
+
+ align:start position:0%
+uh infinite number. Of course, the old
+one did too. All of the above. Yes.
+
+ align:start position:0%
+one did too. All of the above. Yes.
+ 
+
+ align:start position:0%
+one did too. All of the above. Yes.
+Okay. So, that was just supposed to be a
+
+ align:start position:0%
+Okay. So, that was just supposed to be a
+ 
+
+ align:start position:0%
+Okay. So, that was just supposed to be a
+simple exercise in in how to run the
+
+ align:start position:0%
+simple exercise in in how to run the
+ 
+
+ align:start position:0%
+simple exercise in in how to run the
+formulas, how to do this stuff um from a
+
+ align:start position:0%
+formulas, how to do this stuff um from a
+ 
+
+ align:start position:0%
+formulas, how to do this stuff um from a
+purely mechanical point of view. Now, I
+
+ align:start position:0%
+purely mechanical point of view. Now, I
+ 
+
+ align:start position:0%
+purely mechanical point of view. Now, I
+want to think about the bigger question.
+
+ align:start position:0%
+want to think about the bigger question.
+ 
+
+ align:start position:0%
+want to think about the bigger question.
+Does any of this make any sense?
+
+ align:start position:0%
+Does any of this make any sense?
+ 
+
+ align:start position:0%
+Does any of this make any sense?
+And the answers were concocted to help
+
+ align:start position:0%
+And the answers were concocted to help
+ 
+
+ align:start position:0%
+And the answers were concocted to help
+me make sense of that. The questions,
+
+ align:start position:0%
+me make sense of that. The questions,
+ 
+
+ align:start position:0%
+me make sense of that. The questions,
+the check yourselves were concocted so
+
+ align:start position:0%
+the check yourselves were concocted so
+ 
+
+ align:start position:0%
+the check yourselves were concocted so
+that if we think about the answer that
+
+ align:start position:0%
+that if we think about the answer that
+ 
+
+ align:start position:0%
+that if we think about the answer that
+came out, we'll have some insight into
+
+ align:start position:0%
+came out, we'll have some insight into
+ 
+
+ align:start position:0%
+came out, we'll have some insight into
+why we think it works and why it was
+
+ align:start position:0%
+why we think it works and why it was
+ 
+
+ align:start position:0%
+why we think it works and why it was
+controversial 150 years ago.
+
+ align:start position:0%
+controversial 150 years ago.
+ 
+
+ align:start position:0%
+controversial 150 years ago.
+So let's do the simple case first. Even
+
+ align:start position:0%
+So let's do the simple case first. Even
+ 
+
+ align:start position:0%
+So let's do the simple case first. Even
+Lrange wouldn't have any trouble with
+
+ align:start position:0%
+Lrange wouldn't have any trouble with
+ 
+
+ align:start position:0%
+Lrange wouldn't have any trouble with
+this way. Well, maybe he would have had
+
+ align:start position:0%
+this way. Well, maybe he would have had
+ 
+
+ align:start position:0%
+this way. Well, maybe he would have had
+a little trouble. I guess he would have
+
+ align:start position:0%
+a little trouble. I guess he would have
+ 
+
+ align:start position:0%
+a little trouble. I guess he would have
+had a little trouble. So, Lrange had the
+
+ align:start position:0%
+had a little trouble. So, Lrange had the
+ 
+
+ align:start position:0%
+had a little trouble. So, Lrange had the
+problem with Forier that Forier was
+
+ align:start position:0%
+problem with Forier that Forier was
+ 
+
+ align:start position:0%
+problem with Forier that Forier was
+making these outrageous claims that any
+
+ align:start position:0%
+making these outrageous claims that any
+ 
+
+ align:start position:0%
+making these outrageous claims that any
+periodic function should have a Forier
+
+ align:start position:0%
+periodic function should have a Forier
+ 
+
+ align:start position:0%
+periodic function should have a Forier
+decomposition and if you have uh
+
+ align:start position:0%
+decomposition and if you have uh
+ 
+
+ align:start position:0%
+decomposition and if you have uh
+discontinuous function and if all the
+
+ align:start position:0%
+discontinuous function and if all the
+ 
+
+ align:start position:0%
+discontinuous function and if all the
+basis functions are continuous, how
+
+ align:start position:0%
+basis functions are continuous, how
+ 
+
+ align:start position:0%
+basis functions are continuous, how
+could that make any sense, right? This
+
+ align:start position:0%
+could that make any sense, right? This
+ 
+
+ align:start position:0%
+could that make any sense, right? This
+doesn't have any discontinuities, but it
+
+ align:start position:0%
+doesn't have any discontinuities, but it
+ 
+
+ align:start position:0%
+doesn't have any discontinuities, but it
+does have slope discontinuities.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's sort of the same thing, right? If
+
+ align:start position:0%
+That's sort of the same thing, right? If
+ 
+
+ align:start position:0%
+That's sort of the same thing, right? If
+you have a slope discontinuity and
+
+ align:start position:0%
+you have a slope discontinuity and
+ 
+
+ align:start position:0%
+you have a slope discontinuity and
+you're trying to make u you're trying to
+
+ align:start position:0%
+you're trying to make u you're trying to
+ 
+
+ align:start position:0%
+you're trying to make u you're trying to
+represent the signal by a sum of signals
+
+ align:start position:0%
+represent the signal by a sum of signals
+ 
+
+ align:start position:0%
+represent the signal by a sum of signals
+none of whom have slope discontinuities
+
+ align:start position:0%
+none of whom have slope discontinuities
+ 
+
+ align:start position:0%
+none of whom have slope discontinuities
+that's kind of the same kind of problem.
+
+ align:start position:0%
+that's kind of the same kind of problem.
+ 
+
+ align:start position:0%
+that's kind of the same kind of problem.
+One way we can think about it is to
+
+ align:start position:0%
+One way we can think about it is to
+ 
+
+ align:start position:0%
+One way we can think about it is to
+think about how the approximation gets
+
+ align:start position:0%
+think about how the approximation gets
+ 
+
+ align:start position:0%
+think about how the approximation gets
+better or fails to get better as we add
+
+ align:start position:0%
+better or fails to get better as we add
+ 
+
+ align:start position:0%
+better or fails to get better as we add
+terms. So this is the base function.
+
+ align:start position:0%
+terms. So this is the base function.
+ 
+
+ align:start position:0%
+terms. So this is the base function.
+This is how the signal that we would
+
+ align:start position:0%
+This is how the signal that we would
+ 
+
+ align:start position:0%
+This is how the signal that we would
+like to represent harmonically. If we
+
+ align:start position:0%
+like to represent harmonically. If we
+ 
+
+ align:start position:0%
+like to represent harmonically. If we
+just think about the first nonzero term,
+
+ align:start position:0%
+just think about the first nonzero term,
+ 
+
+ align:start position:0%
+just think about the first nonzero term,
+the first nonzero term is the
+
+ align:start position:0%
+the first nonzero term is the
+ 
+
+ align:start position:0%
+the first nonzero term is the
+fundamental. It actually is not bad,
+
+ align:start position:0%
+fundamental. It actually is not bad,
+ 
+
+ align:start position:0%
+fundamental. It actually is not bad,
+right? If we were willing to accept
+
+ align:start position:0%
+right? If we were willing to accept
+ 
+
+ align:start position:0%
+right? If we were willing to accept
+errors about this big, it would be okay.
+
+ align:start position:0%
+errors about this big, it would be okay.
+ 
+
+ align:start position:0%
+errors about this big, it would be okay.
+Okay. Well, but somehow it doesn't
+
+ align:start position:0%
+Okay. Well, but somehow it doesn't
+ 
+
+ align:start position:0%
+Okay. Well, but somehow it doesn't
+capture much trianguliness,
+
+ align:start position:0%
+capture much trianguliness,
+ 
+
+ align:start position:0%
+capture much trianguliness,
+right? it sort of doesn't look much like
+
+ align:start position:0%
+right? it sort of doesn't look much like
+ 
+
+ align:start position:0%
+right? it sort of doesn't look much like
+even though so the one term sort of
+
+ align:start position:0%
+even though so the one term sort of
+ 
+
+ align:start position:0%
+even though so the one term sort of
+catches a lot of the deviation but it
+
+ align:start position:0%
+catches a lot of the deviation but it
+ 
+
+ align:start position:0%
+catches a lot of the deviation but it
+doesn't capture the the triangle aspect
+
+ align:start position:0%
+doesn't capture the the triangle aspect
+ 
+
+ align:start position:0%
+doesn't capture the the triangle aspect
+if you add another term the next nonzero
+
+ align:start position:0%
+if you add another term the next nonzero
+ 
+
+ align:start position:0%
+if you add another term the next nonzero
+term is the third one so if you write
+
+ align:start position:0%
+term is the third one so if you write
+ 
+
+ align:start position:0%
+term is the third one so if you write
+the sum of the first term the k equals 1
+
+ align:start position:0%
+the sum of the first term the k equals 1
+ 
+
+ align:start position:0%
+the sum of the first term the k equals 1
+term and the k= 3 term you get this
+
+ align:start position:0%
+term and the k= 3 term you get this
+ 
+
+ align:start position:0%
+term and the k= 3 term you get this
+waveform
+
+ align:start position:0%
+waveform
+ 
+
+ align:start position:0%
+waveform
+notice that the effect of that was to
+
+ align:start position:0%
+notice that the effect of that was to
+ 
+
+ align:start position:0%
+notice that the effect of that was to
+creep it toward the underlying signal if
+
+ align:start position:0%
+creep it toward the underlying signal if
+ 
+
+ align:start position:0%
+creep it toward the underlying signal if
+you add another term Five, seven, nine.
+
+ align:start position:0%
+you add another term Five, seven, nine.
+ 
+
+ align:start position:0%
+you add another term Five, seven, nine.
+It's getting closer, closer, closer.
+
+ align:start position:0%
+It's getting closer, closer, closer.
+ 
+
+ align:start position:0%
+It's getting closer, closer, closer.
+19 because I got bored making the
+
+ align:start position:0%
+19 because I got bored making the
+ 
+
+ align:start position:0%
+19 because I got bored making the
+figures, right? So, I skipped a bunch.
+
+ align:start position:0%
+figures, right? So, I skipped a bunch.
+ 
+
+ align:start position:0%
+figures, right? So, I skipped a bunch.
+29 because I skipped a bunch.
+
+ align:start position:0%
+29 because I skipped a bunch.
+ 
+
+ align:start position:0%
+29 because I skipped a bunch.
+39. You can see that what's happening is
+
+ align:start position:0%
+39. You can see that what's happening is
+ 
+
+ align:start position:0%
+39. You can see that what's happening is
+that we as we add more and more of those
+
+ align:start position:0%
+that we as we add more and more of those
+ 
+
+ align:start position:0%
+that we as we add more and more of those
+terms, by the time we've got up to
+
+ align:start position:0%
+terms, by the time we've got up to
+ 
+
+ align:start position:0%
+terms, by the time we've got up to
+number 39, it's pretty good. So, that
+
+ align:start position:0%
+number 39, it's pretty good. So, that
+ 
+
+ align:start position:0%
+number 39, it's pretty good. So, that
+probably from your seat, it's not
+
+ align:start position:0%
+probably from your seat, it's not
+ 
+
+ align:start position:0%
+probably from your seat, it's not
+altogether apparent that they're
+
+ align:start position:0%
+altogether apparent that they're
+ 
+
+ align:start position:0%
+altogether apparent that they're
+different. They're still different,
+
+ align:start position:0%
+different. They're still different,
+ 
+
+ align:start position:0%
+different. They're still different,
+right? But you can see that there's a
+
+ align:start position:0%
+right? But you can see that there's a
+ 
+
+ align:start position:0%
+right? But you can see that there's a
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+in which the approximation is converging
+
+ align:start position:0%
+in which the approximation is converging
+ 
+
+ align:start position:0%
+in which the approximation is converging
+toward the underlying signal.
+
+ align:start position:0%
+toward the underlying signal.
+ 
+
+ align:start position:0%
+toward the underlying signal.
+That's good. So that's a sense in which
+
+ align:start position:0%
+That's good. So that's a sense in which
+ 
+
+ align:start position:0%
+That's good. So that's a sense in which
+there's a convergence between the signal
+
+ align:start position:0%
+there's a convergence between the signal
+ 
+
+ align:start position:0%
+there's a convergence between the signal
+and its forier representation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A different kind of thing happens here.
+
+ align:start position:0%
+A different kind of thing happens here.
+ 
+
+ align:start position:0%
+A different kind of thing happens here.
+Now let's do the square wave.
+
+ align:start position:0%
+Now let's do the square wave.
+ 
+
+ align:start position:0%
+Now let's do the square wave.
+If we put in the first term of the
+
+ align:start position:0%
+If we put in the first term of the
+ 
+
+ align:start position:0%
+If we put in the first term of the
+forier representation, which is the
+
+ align:start position:0%
+forier representation, which is the
+ 
+
+ align:start position:0%
+forier representation, which is the
+fundamental, we get a sine wave
+
+ align:start position:0%
+fundamental, we get a sine wave
+ 
+
+ align:start position:0%
+fundamental, we get a sine wave
+approximation, which is a little worse
+
+ align:start position:0%
+approximation, which is a little worse
+ 
+
+ align:start position:0%
+approximation, which is a little worse
+perhaps for a square wave than it was
+
+ align:start position:0%
+perhaps for a square wave than it was
+ 
+
+ align:start position:0%
+perhaps for a square wave than it was
+for a triangle wave.
+
+ align:start position:0%
+for a triangle wave.
+ 
+
+ align:start position:0%
+for a triangle wave.
+put in the third, fifth, 7th, 9th,
+
+ align:start position:0%
+put in the third, fifth, 7th, 9th,
+ 
+
+ align:start position:0%
+put in the third, fifth, 7th, 9th,
+19th. So that's the So I threw in five
+
+ align:start position:0%
+19th. So that's the So I threw in five
+ 
+
+ align:start position:0%
+19th. So that's the So I threw in five
+again.
+
+ align:start position:0%
+again.
+ 
+
+ align:start position:0%
+again.
+29,
+
+ align:start position:0%
+29,
+ 
+
+ align:start position:0%
+29,
+39.
+
+ align:start position:0%
+39.
+ 
+
+ align:start position:0%
+39.
+It's not doing as well. What's not doing
+
+ align:start position:0%
+It's not doing as well. What's not doing
+ 
+
+ align:start position:0%
+It's not doing as well. What's not doing
+as well?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right. So we go one one term partial sum
+
+ align:start position:0%
+Right. So we go one one term partial sum
+ 
+
+ align:start position:0%
+Right. So we go one one term partial sum
+two three four five
+
+ align:start position:0%
+two three four five
+ 
+
+ align:start position:0%
+two three four five
+20 uh 10 15 20
+
+ align:start position:0%
+20 uh 10 15 20
+ 
+
+ align:start position:0%
+20 uh 10 15 20
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really quick transitions not able to
+
+ align:start position:0%
+really quick transitions not able to
+ 
+
+ align:start position:0%
+really quick transitions not able to
+handle the really quick transition it's
+
+ align:start position:0%
+handle the really quick transition it's
+ 
+
+ align:start position:0%
+handle the really quick transition it's
+kind of like Lrange said right how are
+
+ align:start position:0%
+kind of like Lrange said right how are
+ 
+
+ align:start position:0%
+kind of like Lrange said right how are
+you going to make a discontinuous
+
+ align:start position:0%
+you going to make a discontinuous
+ 
+
+ align:start position:0%
+you going to make a discontinuous
+function out of a sum of continuous ones
+
+ align:start position:0%
+function out of a sum of continuous ones
+ 
+
+ align:start position:0%
+function out of a sum of continuous ones
+right it's
+
+ align:start position:0%
+right it's
+ 
+
+ align:start position:0%
+right it's
+In fact, um this is called Gibbs
+
+ align:start position:0%
+In fact, um this is called Gibbs
+ 
+
+ align:start position:0%
+In fact, um this is called Gibbs
+phenomena after the guy who sort of
+
+ align:start position:0%
+phenomena after the guy who sort of
+ 
+
+ align:start position:0%
+phenomena after the guy who sort of
+formulated the mathematics of this.
+
+ align:start position:0%
+formulated the mathematics of this.
+ 
+
+ align:start position:0%
+formulated the mathematics of this.
+There's even in the limit, no matter how
+
+ align:start position:0%
+There's even in the limit, no matter how
+ 
+
+ align:start position:0%
+There's even in the limit, no matter how
+many terms you put into the sum,
+
+ align:start position:0%
+many terms you put into the sum,
+ 
+
+ align:start position:0%
+many terms you put into the sum,
+the worstcase deviation is about 9%.
+
+ align:start position:0%
+the worstcase deviation is about 9%.
+ 
+
+ align:start position:0%
+the worstcase deviation is about 9%.
+You can't get rid of it. So in some
+
+ align:start position:0%
+You can't get rid of it. So in some
+ 
+
+ align:start position:0%
+You can't get rid of it. So in some
+sense,
+
+ align:start position:0%
+sense,
+ 
+
+ align:start position:0%
+sense,
+Lrange is right. Right. You can't put
+
+ align:start position:0%
+Lrange is right. Right. You can't put
+ 
+
+ align:start position:0%
+Lrange is right. Right. You can't put
+enough terms in there so that it
+
+ align:start position:0%
+enough terms in there so that it
+ 
+
+ align:start position:0%
+enough terms in there so that it
+converges everywhere.
+
+ align:start position:0%
+converges everywhere.
+ 
+
+ align:start position:0%
+converges everywhere.
+Okay. So the problem then becomes that
+
+ align:start position:0%
+Okay. So the problem then becomes that
+ 
+
+ align:start position:0%
+Okay. So the problem then becomes that
+we can't really think about convergence
+
+ align:start position:0%
+we can't really think about convergence
+ 
+
+ align:start position:0%
+we can't really think about convergence
+in the familiar ways we like to think
+
+ align:start position:0%
+in the familiar ways we like to think
+ 
+
+ align:start position:0%
+in the familiar ways we like to think
+about convergence. Convergence at a
+
+ align:start position:0%
+about convergence. Convergence at a
+ 
+
+ align:start position:0%
+about convergence. Convergence at a
+point is not a good way to think about
+
+ align:start position:0%
+point is not a good way to think about
+ 
+
+ align:start position:0%
+point is not a good way to think about
+it because there's always a point that
+
+ align:start position:0%
+it because there's always a point that
+ 
+
+ align:start position:0%
+it because there's always a point that
+deviates a lot.
+
+ align:start position:0%
+deviates a lot.
+ 
+
+ align:start position:0%
+deviates a lot.
+And in fact in signal processing we have
+
+ align:start position:0%
+And in fact in signal processing we have
+ 
+
+ align:start position:0%
+And in fact in signal processing we have
+lots of other ways we think about
+
+ align:start position:0%
+lots of other ways we think about
+ 
+
+ align:start position:0%
+lots of other ways we think about
+convergence if you think about so in
+
+ align:start position:0%
+convergence if you think about so in
+ 
+
+ align:start position:0%
+convergence if you think about so in
+addition to being 9% overshoot the Gibbs
+
+ align:start position:0%
+addition to being 9% overshoot the Gibbs
+ 
+
+ align:start position:0%
+addition to being 9% overshoot the Gibbs
+phenomenon
+
+ align:start position:0%
+phenomenon
+ 
+
+ align:start position:0%
+phenomenon
+what else do you see as the trend as you
+
+ align:start position:0%
+what else do you see as the trend as you
+ 
+
+ align:start position:0%
+what else do you see as the trend as you
+increase the number of terms in the
+
+ align:start position:0%
+increase the number of terms in the
+ 
+
+ align:start position:0%
+increase the number of terms in the
+partial sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in addition to converging and staying
+
+ align:start position:0%
+in addition to converging and staying
+ 
+
+ align:start position:0%
+in addition to converging and staying
+sort of the same height eight.
+
+ align:start position:0%
+sort of the same height eight.
+ 
+
+ align:start position:0%
+sort of the same height eight.
+What else happened as I added terms to
+
+ align:start position:0%
+What else happened as I added terms to
+ 
+
+ align:start position:0%
+What else happened as I added terms to
+the partial sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got skinnier.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The deviations got crammed toward the
+
+ align:start position:0%
+The deviations got crammed toward the
+ 
+
+ align:start position:0%
+The deviations got crammed toward the
+transition point.
+
+ align:start position:0%
+transition point.
+ 
+
+ align:start position:0%
+transition point.
+And if I keep adding them, they'll get
+
+ align:start position:0%
+And if I keep adding them, they'll get
+ 
+
+ align:start position:0%
+And if I keep adding them, they'll get
+crammed more and more in there.
+
+ align:start position:0%
+crammed more and more in there.
+ 
+
+ align:start position:0%
+crammed more and more in there.
+And it's not like an impulse, right? The
+
+ align:start position:0%
+And it's not like an impulse, right? The
+ 
+
+ align:start position:0%
+And it's not like an impulse, right? The
+height didn't get bigger. The width got
+
+ align:start position:0%
+height didn't get bigger. The width got
+ 
+
+ align:start position:0%
+height didn't get bigger. The width got
+smaller.
+
+ align:start position:0%
+smaller.
+ 
+
+ align:start position:0%
+smaller.
+Had the height got bigger, we'd have
+
+ align:start position:0%
+Had the height got bigger, we'd have
+ 
+
+ align:start position:0%
+Had the height got bigger, we'd have
+been in trouble
+
+ align:start position:0%
+been in trouble
+ 
+
+ align:start position:0%
+been in trouble
+because then we would have said it
+
+ align:start position:0%
+because then we would have said it
+ 
+
+ align:start position:0%
+because then we would have said it
+deviates from the square wave by having
+
+ align:start position:0%
+deviates from the square wave by having
+ 
+
+ align:start position:0%
+deviates from the square wave by having
+an impulse at the transition. It doesn't
+
+ align:start position:0%
+an impulse at the transition. It doesn't
+ 
+
+ align:start position:0%
+an impulse at the transition. It doesn't
+have an impulse. The height staying the
+
+ align:start position:0%
+have an impulse. The height staying the
+ 
+
+ align:start position:0%
+have an impulse. The height staying the
+same, the width is smashing towards
+
+ align:start position:0%
+same, the width is smashing towards
+ 
+
+ align:start position:0%
+same, the width is smashing towards
+zero. The energy in that signal is
+
+ align:start position:0%
+zero. The energy in that signal is
+ 
+
+ align:start position:0%
+zero. The energy in that signal is
+getting smaller and smaller. So we like
+
+ align:start position:0%
+getting smaller and smaller. So we like
+ 
+
+ align:start position:0%
+getting smaller and smaller. So we like
+to think about so a different way to
+
+ align:start position:0%
+to think about so a different way to
+ 
+
+ align:start position:0%
+to think about so a different way to
+think about convergence is how big is
+
+ align:start position:0%
+think about convergence is how big is
+ 
+
+ align:start position:0%
+think about convergence is how big is
+the energy difference between the two
+
+ align:start position:0%
+the energy difference between the two
+ 
+
+ align:start position:0%
+the energy difference between the two
+signals.
+
+ align:start position:0%
+signals.
+ 
+
+ align:start position:0%
+signals.
+In that sense, this converges in 4A's
+
+ align:start position:0%
+In that sense, this converges in 4A's
+ 
+
+ align:start position:0%
+In that sense, this converges in 4A's
+right.
+
+ align:start position:0%
+right.
+ 
+
+ align:start position:0%
+right.
+As you add terms, the energy difference
+
+ align:start position:0%
+As you add terms, the energy difference
+ 
+
+ align:start position:0%
+As you add terms, the energy difference
+between the two signals goes to zero.
+
+ align:start position:0%
+between the two signals goes to zero.
+ 
+
+ align:start position:0%
+between the two signals goes to zero.
+That's the that's the modern way of
+
+ align:start position:0%
+That's the that's the modern way of
+ 
+
+ align:start position:0%
+That's the that's the modern way of
+thinking about the controversy. Right?
+
+ align:start position:0%
+thinking about the controversy. Right?
+ 
+
+ align:start position:0%
+thinking about the controversy. Right?
+There is an issue, right? If we choose
+
+ align:start position:0%
+There is an issue, right? If we choose
+ 
+
+ align:start position:0%
+There is an issue, right? If we choose
+to think about convergence in terms of
+
+ align:start position:0%
+to think about convergence in terms of
+ 
+
+ align:start position:0%
+to think about convergence in terms of
+uh energy difference, then we can
+
+ align:start position:0%
+uh energy difference, then we can
+ 
+
+ align:start position:0%
+uh energy difference, then we can
+resolve the problem. That's what we'll
+
+ align:start position:0%
+resolve the problem. That's what we'll
+ 
+
+ align:start position:0%
+resolve the problem. That's what we'll
+do.
+
+ align:start position:0%
+do.
+ 
+
+ align:start position:0%
+do.
+That's the reason in lots of the things
+
+ align:start position:0%
+That's the reason in lots of the things
+ 
+
+ align:start position:0%
+That's the reason in lots of the things
+that we talk about, we haven't been too
+
+ align:start position:0%
+that we talk about, we haven't been too
+ 
+
+ align:start position:0%
+that we talk about, we haven't been too
+worried about single points being off of
+
+ align:start position:0%
+worried about single points being off of
+ 
+
+ align:start position:0%
+worried about single points being off of
+curves.
+
+ align:start position:0%
+curves.
+ 
+
+ align:start position:0%
+curves.
+That's come up in some of the homeworks
+
+ align:start position:0%
+That's come up in some of the homeworks
+ 
+
+ align:start position:0%
+That's come up in some of the homeworks
+that we don't really care too much that
+
+ align:start position:0%
+that we don't really care too much that
+ 
+
+ align:start position:0%
+that we don't really care too much that
+say you have a function that is one
+
+ align:start position:0%
+say you have a function that is one
+ 
+
+ align:start position:0%
+say you have a function that is one
+everywhere except one point.
+
+ align:start position:0%
+everywhere except one point.
+ 
+
+ align:start position:0%
+everywhere except one point.
+There's no energy difference between the
+
+ align:start position:0%
+There's no energy difference between the
+ 
+
+ align:start position:0%
+There's no energy difference between the
+signal that differs by one point and the
+
+ align:start position:0%
+signal that differs by one point and the
+ 
+
+ align:start position:0%
+signal that differs by one point and the
+original,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? has a finite height, but there's
+
+ align:start position:0%
+right? has a finite height, but there's
+ 
+
+ align:start position:0%
+right? has a finite height, but there's
+zero width, so there's no energy
+
+ align:start position:0%
+zero width, so there's no energy
+ 
+
+ align:start position:0%
+zero width, so there's no energy
+difference. So we So that's the reason
+
+ align:start position:0%
+difference. So we So that's the reason
+ 
+
+ align:start position:0%
+difference. So we So that's the reason
+we haven't been so worried about that
+
+ align:start position:0%
+we haven't been so worried about that
+ 
+
+ align:start position:0%
+we haven't been so worried about that
+because we we use this kind of a
+
+ align:start position:0%
+because we we use this kind of a
+ 
+
+ align:start position:0%
+because we we use this kind of a
+definition of equality. They're equal if
+
+ align:start position:0%
+definition of equality. They're equal if
+ 
+
+ align:start position:0%
+definition of equality. They're equal if
+there's no energy difference between
+
+ align:start position:0%
+there's no energy difference between
+ 
+
+ align:start position:0%
+there's no energy difference between
+them.
+
+ align:start position:0%
+them.
+ 
+
+ align:start position:0%
+them.
+Okay? And using that kind of a way of
+
+ align:start position:0%
+Okay? And using that kind of a way of
+ 
+
+ align:start position:0%
+Okay? And using that kind of a way of
+thinking about things, we get to write
+
+ align:start position:0%
+thinking about things, we get to write
+ 
+
+ align:start position:0%
+thinking about things, we get to write
+FRA uh decompositions, harmonic
+
+ align:start position:0%
+FRA uh decompositions, harmonic
+ 
+
+ align:start position:0%
+FRA uh decompositions, harmonic
+decompositions for a wide range of
+
+ align:start position:0%
+decompositions for a wide range of
+ 
+
+ align:start position:0%
+decompositions for a wide range of
+signals, not all of them, right? for EA
+
+ align:start position:0%
+signals, not all of them, right? for EA
+ 
+
+ align:start position:0%
+signals, not all of them, right? for EA
+exaggerated
+
+ align:start position:0%
+exaggerated
+ 
+
+ align:start position:0%
+exaggerated
+but for a wide range of signals in fact
+
+ align:start position:0%
+but for a wide range of signals in fact
+ 
+
+ align:start position:0%
+but for a wide range of signals in fact
+with the definition we will typically
+
+ align:start position:0%
+with the definition we will typically
+ 
+
+ align:start position:0%
+with the definition we will typically
+use is signals with finite energy
+
+ align:start position:0%
+use is signals with finite energy
+ 
+
+ align:start position:0%
+use is signals with finite energy
+we'll be able to do this
+
+ align:start position:0%
+we'll be able to do this
+ 
+
+ align:start position:0%
+we'll be able to do this
+so now what I want to do is the last
+
+ align:start position:0%
+so now what I want to do is the last
+ 
+
+ align:start position:0%
+so now what I want to do is the last
+part of this lecture I want to introduce
+
+ align:start position:0%
+part of this lecture I want to introduce
+ 
+
+ align:start position:0%
+part of this lecture I want to introduce
+how thinking about a signal in terms of
+
+ align:start position:0%
+how thinking about a signal in terms of
+ 
+
+ align:start position:0%
+how thinking about a signal in terms of
+its harmonic structure lets us think
+
+ align:start position:0%
+its harmonic structure lets us think
+ 
+
+ align:start position:0%
+its harmonic structure lets us think
+about systems differently
+
+ align:start position:0%
+about systems differently
+ 
+
+ align:start position:0%
+about systems differently
+so here the idea is we previously
+
+ align:start position:0%
+so here the idea is we previously
+ 
+
+ align:start position:0%
+so here the idea is we previously
+thought about systems as frequency
+
+ align:start position:0%
+thought about systems as frequency
+ 
+
+ align:start position:0%
+thought about systems as frequency
+responses. In a frequency response, we
+
+ align:start position:0%
+responses. In a frequency response, we
+ 
+
+ align:start position:0%
+responses. In a frequency response, we
+use the igen function property. You put
+
+ align:start position:0%
+use the igen function property. You put
+ 
+
+ align:start position:0%
+use the igen function property. You put
+in an igen function, one of these
+
+ align:start position:0%
+in an igen function, one of these
+ 
+
+ align:start position:0%
+in an igen function, one of these
+complex exponentials, you get out the
+
+ align:start position:0%
+complex exponentials, you get out the
+ 
+
+ align:start position:0%
+complex exponentials, you get out the
+same complex exponential if the system
+
+ align:start position:0%
+same complex exponential if the system
+ 
+
+ align:start position:0%
+same complex exponential if the system
+is linear time invariant.
+
+ align:start position:0%
+is linear time invariant.
+ 
+
+ align:start position:0%
+is linear time invariant.
+And the igen value is the value of the
+
+ align:start position:0%
+And the igen value is the value of the
+ 
+
+ align:start position:0%
+And the igen value is the value of the
+system function evaluated the frequency
+
+ align:start position:0%
+system function evaluated the frequency
+ 
+
+ align:start position:0%
+system function evaluated the frequency
+of interest. We've done that before.
+
+ align:start position:0%
+of interest. We've done that before.
+ 
+
+ align:start position:0%
+of interest. We've done that before.
+The neat thing that happens if you think
+
+ align:start position:0%
+The neat thing that happens if you think
+ 
+
+ align:start position:0%
+The neat thing that happens if you think
+about for series is that you can break
+
+ align:start position:0%
+about for series is that you can break
+ 
+
+ align:start position:0%
+about for series is that you can break
+down the input into a a sum of discrete
+
+ align:start position:0%
+down the input into a a sum of discrete
+ 
+
+ align:start position:0%
+down the input into a a sum of discrete
+parts. the first harmonic, the zero
+
+ align:start position:0%
+parts. the first harmonic, the zero
+ 
+
+ align:start position:0%
+parts. the first harmonic, the zero
+harmonic, the second harmonic, the third
+
+ align:start position:0%
+harmonic, the second harmonic, the third
+ 
+
+ align:start position:0%
+harmonic, the second harmonic, the third
+harmonic. And now each one of those
+
+ align:start position:0%
+harmonic. And now each one of those
+ 
+
+ align:start position:0%
+harmonic. And now each one of those
+parts was an igen function. And each one
+
+ align:start position:0%
+parts was an igen function. And each one
+ 
+
+ align:start position:0%
+parts was an igen function. And each one
+of those parts gets preferentially
+
+ align:start position:0%
+of those parts gets preferentially
+ 
+
+ align:start position:0%
+of those parts gets preferentially
+amplified
+
+ align:start position:0%
+amplified
+ 
+
+ align:start position:0%
+amplified
+andor time delayed according to the the
+
+ align:start position:0%
+andor time delayed according to the the
+ 
+
+ align:start position:0%
+andor time delayed according to the the
+um frequency response idea for the
+
+ align:start position:0%
+um frequency response idea for the
+ 
+
+ align:start position:0%
+um frequency response idea for the
+system.
+
+ align:start position:0%
+system.
+ 
+
+ align:start position:0%
+system.
+That lets us think about the effect of a
+
+ align:start position:0%
+That lets us think about the effect of a
+ 
+
+ align:start position:0%
+That lets us think about the effect of a
+system is to filter the input. So the
+
+ align:start position:0%
+system is to filter the input. So the
+ 
+
+ align:start position:0%
+system is to filter the input. So the
+system u the idea in a filter is that
+
+ align:start position:0%
+system u the idea in a filter is that
+ 
+
+ align:start position:0%
+system u the idea in a filter is that
+systems do not LTI systems linear time
+
+ align:start position:0%
+systems do not LTI systems linear time
+ 
+
+ align:start position:0%
+systems do not LTI systems linear time
+invariant systems the same kind of
+
+ align:start position:0%
+invariant systems the same kind of
+ 
+
+ align:start position:0%
+invariant systems the same kind of
+systems that we've been thinking about
+
+ align:start position:0%
+systems that we've been thinking about
+ 
+
+ align:start position:0%
+systems that we've been thinking about
+all along so far linear time invariant
+
+ align:start position:0%
+all along so far linear time invariant
+ 
+
+ align:start position:0%
+all along so far linear time invariant
+systems cannot create new frequencies.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you put some frequency in that's the
+
+ align:start position:0%
+If you put some frequency in that's the
+ 
+
+ align:start position:0%
+If you put some frequency in that's the
+frequency that comes out. We've already
+
+ align:start position:0%
+frequency that comes out. We've already
+ 
+
+ align:start position:0%
+frequency that comes out. We've already
+seen that when we talked about frequency
+
+ align:start position:0%
+seen that when we talked about frequency
+ 
+
+ align:start position:0%
+seen that when we talked about frequency
+response.
+
+ align:start position:0%
+response.
+ 
+
+ align:start position:0%
+response.
+They can only scale the magnitude and
+
+ align:start position:0%
+They can only scale the magnitude and
+ 
+
+ align:start position:0%
+They can only scale the magnitude and
+shift the phase. They can't make new
+
+ align:start position:0%
+shift the phase. They can't make new
+ 
+
+ align:start position:0%
+shift the phase. They can't make new
+frequencies. All they can do is change
+
+ align:start position:0%
+frequencies. All they can do is change
+ 
+
+ align:start position:0%
+frequencies. All they can do is change
+the amplitude and the phase. And that's
+
+ align:start position:0%
+the amplitude and the phase. And that's
+ 
+
+ align:start position:0%
+the amplitude and the phase. And that's
+a very interesting way to think about a
+
+ align:start position:0%
+a very interesting way to think about a
+ 
+
+ align:start position:0%
+a very interesting way to think about a
+system. Think about a lowass filter.
+
+ align:start position:0%
+system. Think about a lowass filter.
+ 
+
+ align:start position:0%
+system. Think about a lowass filter.
+Think about a system whose input is
+
+ align:start position:0%
+Think about a system whose input is
+ 
+
+ align:start position:0%
+Think about a system whose input is
+little VI and whose output is little VO.
+
+ align:start position:0%
+little VI and whose output is little VO.
+ 
+
+ align:start position:0%
+little VI and whose output is little VO.
+You all know how to characterize that a
+
+ align:start position:0%
+You all know how to characterize that a
+ 
+
+ align:start position:0%
+You all know how to characterize that a
+gazillion ways. You would know how to
+
+ align:start position:0%
+gazillion ways. You would know how to
+ 
+
+ align:start position:0%
+gazillion ways. You would know how to
+write a differential equation for that.
+
+ align:start position:0%
+write a differential equation for that.
+ 
+
+ align:start position:0%
+write a differential equation for that.
+Nod your head. Yes. Yes. Yes. You would
+
+ align:start position:0%
+Nod your head. Yes. Yes. Yes. You would
+ 
+
+ align:start position:0%
+Nod your head. Yes. Yes. Yes. You would
+know how to write that as a differential
+
+ align:start position:0%
+know how to write that as a differential
+ 
+
+ align:start position:0%
+know how to write that as a differential
+equation. You'd be able to write a
+
+ align:start position:0%
+equation. You'd be able to write a
+ 
+
+ align:start position:0%
+equation. You'd be able to write a
+system function. you'll be able to do a
+
+ align:start position:0%
+system function. you'll be able to do a
+ 
+
+ align:start position:0%
+system function. you'll be able to do a
+frequency response, a bodie plot, all
+
+ align:start position:0%
+frequency response, a bodie plot, all
+ 
+
+ align:start position:0%
+frequency response, a bodie plot, all
+those sorts of things.
+
+ align:start position:0%
+those sorts of things.
+ 
+
+ align:start position:0%
+those sorts of things.
+That's fine. What I want to do is think
+
+ align:start position:0%
+That's fine. What I want to do is think
+ 
+
+ align:start position:0%
+That's fine. What I want to do is think
+about it instead as a filter.
+
+ align:start position:0%
+about it instead as a filter.
+ 
+
+ align:start position:0%
+about it instead as a filter.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+imagine the bodie plot, right? Bodie
+
+ align:start position:0%
+imagine the bodie plot, right? Bodie
+ 
+
+ align:start position:0%
+imagine the bodie plot, right? Bodie
+plot's good, right? U so imagine the
+
+ align:start position:0%
+plot's good, right? U so imagine the
+ 
+
+ align:start position:0%
+plot's good, right? U so imagine the
+bodie plot representation for the uh RC
+
+ align:start position:0%
+bodie plot representation for the uh RC
+ 
+
+ align:start position:0%
+bodie plot representation for the uh RC
+lowass filter. You get uh so the RCC low
+
+ align:start position:0%
+lowass filter. You get uh so the RCC low
+ 
+
+ align:start position:0%
+lowass filter. You get uh so the RCC low
+pass filter has a single pole. The pole
+
+ align:start position:0%
+pass filter has a single pole. The pole
+ 
+
+ align:start position:0%
+pass filter has a single pole. The pole
+is at the frequency one over RC minus
+
+ align:start position:0%
+is at the frequency one over RC minus
+ 
+
+ align:start position:0%
+is at the frequency one over RC minus
+one over RC.
+
+ align:start position:0%
+one over RC.
+ 
+
+ align:start position:0%
+one over RC.
+Bodie plot looks like so magnitude has
+
+ align:start position:0%
+Bodie plot looks like so magnitude has
+ 
+
+ align:start position:0%
+Bodie plot looks like so magnitude has
+an asmtote at low frequencies that is a
+
+ align:start position:0%
+an asmtote at low frequencies that is a
+ 
+
+ align:start position:0%
+an asmtote at low frequencies that is a
+constant. At high frequencies it's
+
+ align:start position:0%
+constant. At high frequencies it's
+ 
+
+ align:start position:0%
+constant. At high frequencies it's
+sloping with minus1 or as we would say
+
+ align:start position:0%
+sloping with minus1 or as we would say
+ 
+
+ align:start position:0%
+sloping with minus1 or as we would say
+minus 20 dB per decade
+
+ align:start position:0%
+minus 20 dB per decade
+ 
+
+ align:start position:0%
+minus 20 dB per decade
+and it has some sort of phase response
+
+ align:start position:0%
+and it has some sort of phase response
+ 
+
+ align:start position:0%
+and it has some sort of phase response
+right low frequencies phase is zero.
+
+ align:start position:0%
+right low frequencies phase is zero.
+ 
+
+ align:start position:0%
+right low frequencies phase is zero.
+High frequencies the phase lags by pi
+
+ align:start position:0%
+High frequencies the phase lags by pi
+ 
+
+ align:start position:0%
+High frequencies the phase lags by pi
+over two.
+
+ align:start position:0%
+over two.
+ 
+
+ align:start position:0%
+over two.
+But now let's think about exciting it
+
+ align:start position:0%
+But now let's think about exciting it
+ 
+
+ align:start position:0%
+But now let's think about exciting it
+with a square wave. Square wave is what
+
+ align:start position:0%
+with a square wave. Square wave is what
+ 
+
+ align:start position:0%
+with a square wave. Square wave is what
+we've been thinking about.
+
+ align:start position:0%
+we've been thinking about.
+ 
+
+ align:start position:0%
+we've been thinking about.
+Square wave has a harmonic structure
+
+ align:start position:0%
+Square wave has a harmonic structure
+ 
+
+ align:start position:0%
+Square wave has a harmonic structure
+that falls with K.
+
+ align:start position:0%
+that falls with K.
+ 
+
+ align:start position:0%
+that falls with K.
+So if we represent K= 1 3 5 7 9 on a log
+
+ align:start position:0%
+So if we represent K= 1 3 5 7 9 on a log
+ 
+
+ align:start position:0%
+So if we represent K= 1 3 5 7 9 on a log
+scale
+
+ align:start position:0%
+scale
+ 
+
+ align:start position:0%
+scale
+falling with K is a linear slope. So
+
+ align:start position:0%
+falling with K is a linear slope. So
+ 
+
+ align:start position:0%
+falling with K is a linear slope. So
+this linear decrease in amplitude height
+
+ align:start position:0%
+this linear decrease in amplitude height
+ 
+
+ align:start position:0%
+this linear decrease in amplitude height
+is the reciprocal over here. It's the
+
+ align:start position:0%
+is the reciprocal over here. It's the
+ 
+
+ align:start position:0%
+is the reciprocal over here. It's the
+idea of a log, right?
+
+ align:start position:0%
+idea of a log, right?
+ 
+
+ align:start position:0%
+idea of a log, right?
+So we can represent the signal the
+
+ align:start position:0%
+So we can represent the signal the
+ 
+
+ align:start position:0%
+So we can represent the signal the
+square wave by this amplitude spectrum.
+
+ align:start position:0%
+square wave by this amplitude spectrum.
+ 
+
+ align:start position:0%
+square wave by this amplitude spectrum.
+How big are the components at all the
+
+ align:start position:0%
+How big are the components at all the
+ 
+
+ align:start position:0%
+How big are the components at all the
+different frequencies? Well, there's
+
+ align:start position:0%
+different frequencies? Well, there's
+ 
+
+ align:start position:0%
+different frequencies? Well, there's
+only a discrete number of them. There's
+
+ align:start position:0%
+only a discrete number of them. There's
+ 
+
+ align:start position:0%
+only a discrete number of them. There's
+the what? The k= 1 1, the k= 31, the k=
+
+ align:start position:0%
+the what? The k= 1 1, the k= 31, the k=
+ 
+
+ align:start position:0%
+the what? The k= 1 1, the k= 31, the k=
+5, 1, etc. each one represented by a
+
+ align:start position:0%
+5, 1, etc. each one represented by a
+ 
+
+ align:start position:0%
+5, 1, etc. each one represented by a
+straight line. And they all have phase
+
+ align:start position:0%
+straight line. And they all have phase
+ 
+
+ align:start position:0%
+straight line. And they all have phase
+of minus pi over two because of the j.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now if you were to choose the base
+
+ align:start position:0%
+Now if you were to choose the base
+ 
+
+ align:start position:0%
+Now if you were to choose the base
+frequency for the square wave so that 2
+
+ align:start position:0%
+frequency for the square wave so that 2
+ 
+
+ align:start position:0%
+frequency for the square wave so that 2
+pi over capital t
+
+ align:start position:0%
+pi over capital t
+ 
+
+ align:start position:0%
+pi over capital t
+omega kn is small compared to the cutff
+
+ align:start position:0%
+omega kn is small compared to the cutff
+ 
+
+ align:start position:0%
+omega kn is small compared to the cutff
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+for the lowass filter.
+
+ align:start position:0%
+for the lowass filter.
+ 
+
+ align:start position:0%
+for the lowass filter.
+What would be the effect on these
+
+ align:start position:0%
+What would be the effect on these
+ 
+
+ align:start position:0%
+What would be the effect on these
+amplitudes
+
+ align:start position:0%
+amplitudes
+ 
+
+ align:start position:0%
+amplitudes
+of this filter?
+
+ align:start position:0%
+of this filter?
+ 
+
+ align:start position:0%
+of this filter?
+Well, the magnitude is one. So if you go
+
+ align:start position:0%
+Well, the magnitude is one. So if you go
+ 
+
+ align:start position:0%
+Well, the magnitude is one. So if you go
+to arbitrarily low frequencies,
+
+ align:start position:0%
+to arbitrarily low frequencies,
+ 
+
+ align:start position:0%
+to arbitrarily low frequencies,
+the magnitude is arbitrarily close to
+
+ align:start position:0%
+the magnitude is arbitrarily close to
+ 
+
+ align:start position:0%
+the magnitude is arbitrarily close to
+one. The phase is arbitrarily close to
+
+ align:start position:0%
+one. The phase is arbitrarily close to
+ 
+
+ align:start position:0%
+one. The phase is arbitrarily close to
+to pi over two. What would happen?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Excuse me. The phase would be
+
+ align:start position:0%
+Excuse me. The phase would be
+ 
+
+ align:start position:0%
+Excuse me. The phase would be
+arbitrarily close to zero. Sorry, I'm
+
+ align:start position:0%
+arbitrarily close to zero. Sorry, I'm
+ 
+
+ align:start position:0%
+arbitrarily close to zero. Sorry, I'm
+supposed to be going to very low
+
+ align:start position:0%
+supposed to be going to very low
+ 
+
+ align:start position:0%
+supposed to be going to very low
+frequencies. If I go to very low
+
+ align:start position:0%
+frequencies. If I go to very low
+ 
+
+ align:start position:0%
+frequencies. If I go to very low
+frequencies, the phase is zero.
+
+ align:start position:0%
+frequencies, the phase is zero.
+ 
+
+ align:start position:0%
+frequencies, the phase is zero.
+If the amplitude is arbitrarily close to
+
+ align:start position:0%
+If the amplitude is arbitrarily close to
+ 
+
+ align:start position:0%
+If the amplitude is arbitrarily close to
+one, the the phase is arbitrarily close
+
+ align:start position:0%
+one, the the phase is arbitrarily close
+ 
+
+ align:start position:0%
+one, the the phase is arbitrarily close
+to zero. And if the input is represented
+
+ align:start position:0%
+to zero. And if the input is represented
+ 
+
+ align:start position:0%
+to zero. And if the input is represented
+by the red lines, what's the output
+
+ align:start position:0%
+by the red lines, what's the output
+ 
+
+ align:start position:0%
+by the red lines, what's the output
+represented by?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Same red lines, right? Each red line is
+
+ align:start position:0%
+Same red lines, right? Each red line is
+ 
+
+ align:start position:0%
+Same red lines, right? Each red line is
+multiplied by one at angle zero.
+
+ align:start position:0%
+multiplied by one at angle zero.
+ 
+
+ align:start position:0%
+multiplied by one at angle zero.
+So the output has the same shape as the
+
+ align:start position:0%
+So the output has the same shape as the
+ 
+
+ align:start position:0%
+So the output has the same shape as the
+input.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If however I shift the period
+
+ align:start position:0%
+If however I shift the period
+ 
+
+ align:start position:0%
+If however I shift the period
+to be shorter so that omega kn is higher
+
+ align:start position:0%
+to be shorter so that omega kn is higher
+ 
+
+ align:start position:0%
+to be shorter so that omega kn is higher
+then I can have some of the higher
+
+ align:start position:0%
+then I can have some of the higher
+ 
+
+ align:start position:0%
+then I can have some of the higher
+frequencies fall into the region of
+
+ align:start position:0%
+frequencies fall into the region of
+ 
+
+ align:start position:0%
+frequencies fall into the region of
+sloping magnitude.
+
+ align:start position:0%
+sloping magnitude.
+ 
+
+ align:start position:0%
+sloping magnitude.
+I can have some of the phases fall into
+
+ align:start position:0%
+I can have some of the phases fall into
+ 
+
+ align:start position:0%
+I can have some of the phases fall into
+the region where the phase is minus pi /
+
+ align:start position:0%
+the region where the phase is minus pi /
+ 
+
+ align:start position:0%
+the region where the phase is minus pi /
+2.
+
+ align:start position:0%
+2.
+ 
+
+ align:start position:0%
+2.
+The way to think about it is the
+
+ align:start position:0%
+The way to think about it is the
+ 
+
+ align:start position:0%
+The way to think about it is the
+fundamental is still going through the
+
+ align:start position:0%
+fundamental is still going through the
+ 
+
+ align:start position:0%
+fundamental is still going through the
+place with unity gain phase of zero. The
+
+ align:start position:0%
+place with unity gain phase of zero. The
+ 
+
+ align:start position:0%
+place with unity gain phase of zero. The
+basic shape is determined by the
+
+ align:start position:0%
+basic shape is determined by the
+ 
+
+ align:start position:0%
+basic shape is determined by the
+fundamental. The basic shape comes
+
+ align:start position:0%
+fundamental. The basic shape comes
+ 
+
+ align:start position:0%
+fundamental. The basic shape comes
+through.
+
+ align:start position:0%
+through.
+ 
+
+ align:start position:0%
+through.
+But now the high frequencies are being
+
+ align:start position:0%
+But now the high frequencies are being
+ 
+
+ align:start position:0%
+But now the high frequencies are being
+altered and their phase relationship is
+
+ align:start position:0%
+altered and their phase relationship is
+ 
+
+ align:start position:0%
+altered and their phase relationship is
+being altered and that's why the shape
+
+ align:start position:0%
+being altered and that's why the shape
+ 
+
+ align:start position:0%
+being altered and that's why the shape
+is different.
+
+ align:start position:0%
+is different.
+ 
+
+ align:start position:0%
+is different.
+If you go to still higher frequencies,
+
+ align:start position:0%
+If you go to still higher frequencies,
+ 
+
+ align:start position:0%
+If you go to still higher frequencies,
+more of the components are filtered.
+
+ align:start position:0%
+more of the components are filtered.
+ 
+
+ align:start position:0%
+more of the components are filtered.
+Each component gets sent through the
+
+ align:start position:0%
+Each component gets sent through the
+ 
+
+ align:start position:0%
+Each component gets sent through the
+frequency response and its amplitude and
+
+ align:start position:0%
+frequency response and its amplitude and
+ 
+
+ align:start position:0%
+frequency response and its amplitude and
+phase are modified appropriately. And if
+
+ align:start position:0%
+phase are modified appropriately. And if
+ 
+
+ align:start position:0%
+phase are modified appropriately. And if
+you go to extremely high frequencies,
+
+ align:start position:0%
+you go to extremely high frequencies,
+ 
+
+ align:start position:0%
+you go to extremely high frequencies,
+then all of the magnitudes
+
+ align:start position:0%
+then all of the magnitudes
+ 
+
+ align:start position:0%
+then all of the magnitudes
+are multiplied by the sloping down line.
+
+ align:start position:0%
+are multiplied by the sloping down line.
+ 
+
+ align:start position:0%
+are multiplied by the sloping down line.
+We turn K convergence, we turn the
+
+ align:start position:0%
+We turn K convergence, we turn the
+ 
+
+ align:start position:0%
+We turn K convergence, we turn the
+reciprocal in K into a reciprocal on K
+
+ align:start position:0%
+reciprocal in K into a reciprocal on K
+ 
+
+ align:start position:0%
+reciprocal in K into a reciprocal on K
+squ. Where have we seen that before?
+
+ align:start position:0%
+squ. Where have we seen that before?
+ 
+
+ align:start position:0%
+squ. Where have we seen that before?
+That was the decomposition for the
+
+ align:start position:0%
+That was the decomposition for the
+ 
+
+ align:start position:0%
+That was the decomposition for the
+triangle wave. So the answer comes out
+
+ align:start position:0%
+triangle wave. So the answer comes out
+ 
+
+ align:start position:0%
+triangle wave. So the answer comes out
+looking like a triangle wave.
+
+ align:start position:0%
+looking like a triangle wave.
+ 
+
+ align:start position:0%
+looking like a triangle wave.
+The point being that in addition to
+
+ align:start position:0%
+The point being that in addition to
+ 
+
+ align:start position:0%
+The point being that in addition to
+thinking about how the system works in
+
+ align:start position:0%
+thinking about how the system works in
+ 
+
+ align:start position:0%
+thinking about how the system works in
+terms of feeding frequencies through it,
+
+ align:start position:0%
+terms of feeding frequencies through it,
+ 
+
+ align:start position:0%
+terms of feeding frequencies through it,
+now we think about how signals work by
+
+ align:start position:0%
+now we think about how signals work by
+ 
+
+ align:start position:0%
+now we think about how signals work by
+breaking them up into frequency parts
+
+ align:start position:0%
+breaking them up into frequency parts
+ 
+
+ align:start position:0%
+breaking them up into frequency parts
+and the whole system then is reduced to
+
+ align:start position:0%
+and the whole system then is reduced to
+ 
+
+ align:start position:0%
+and the whole system then is reduced to
+how does the system modify that
+
+ align:start position:0%
+how does the system modify that
+ 
+
+ align:start position:0%
+how does the system modify that
+component. So that gives rise to the
+
+ align:start position:0%
+component. So that gives rise to the
+ 
+
+ align:start position:0%
+component. So that gives rise to the
+idea of thinking about the fil the
+
+ align:start position:0%
+idea of thinking about the fil the
+ 
+
+ align:start position:0%
+idea of thinking about the fil the
+system as a filter. Systems LTI systems
+
+ align:start position:0%
+system as a filter. Systems LTI systems
+ 
+
+ align:start position:0%
+system as a filter. Systems LTI systems
+do not generate new frequencies. All
+
+ align:start position:0%
+do not generate new frequencies. All
+ 
+
+ align:start position:0%
+do not generate new frequencies. All
+they do is modify the amplitude and
+
+ align:start position:0%
+they do is modify the amplitude and
+ 
+
+ align:start position:0%
+they do is modify the amplitude and
+phase of existing frequencies. If you
+
+ align:start position:0%
+phase of existing frequencies. If you
+ 
+
+ align:start position:0%
+phase of existing frequencies. If you
+enumerate all the existing frequencies,
+
+ align:start position:0%
+enumerate all the existing frequencies,
+ 
+
+ align:start position:0%
+enumerate all the existing frequencies,
+you can just go through them one by one
+
+ align:start position:0%
+you can just go through them one by one
+ 
+
+ align:start position:0%
+you can just go through them one by one
+and figure out how they come out. And
+
+ align:start position:0%
+and figure out how they come out. And
+ 
+
+ align:start position:0%
+and figure out how they come out. And
+that's an equivalent way of thinking
+
+ align:start position:0%
+that's an equivalent way of thinking
+ 
+
+ align:start position:0%
+that's an equivalent way of thinking
+about an LTI system. And that's the kind
+
+ align:start position:0%
+about an LTI system. And that's the kind
+ 
+
+ align:start position:0%
+about an LTI system. And that's the kind
+of a focus that we'll use in the
+
+ align:start position:0%
+of a focus that we'll use in the
+ 
+
+ align:start position:0%
+of a focus that we'll use in the
+remaining part of the course.
+
+ align:start position:0%
+remaining part of the course.
+ 
+
+ align:start position:0%
+remaining part of the course.
+Okay. Thanks.
\ No newline at end of file
diff --git a/uiG6KY0Cqd8.txt b/uiG6KY0Cqd8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..84e65aa826559e9f4869f4f08cfe06a2dadaf830
--- /dev/null
+++ b/uiG6KY0Cqd8.txt
@@ -0,0 +1,18323 @@
+align:start position:0%
+ 
+uh let's start
+
+ align:start position:0%
+uh let's start
+ 
+
+ align:start position:0%
+uh let's start
+this should be
+
+ align:start position:0%
+this should be
+ 
+
+ align:start position:0%
+this should be
+a fun diversion from
+
+ align:start position:0%
+a fun diversion from
+ 
+
+ align:start position:0%
+a fun diversion from
+other things we're doing
+
+ align:start position:0%
+other things we're doing
+ 
+
+ align:start position:0%
+other things we're doing
+we'll
+
+ align:start position:0%
+we'll
+ 
+
+ align:start position:0%
+we'll
+develop methods that are useful in
+
+ align:start position:0%
+develop methods that are useful in
+ 
+
+ align:start position:0%
+develop methods that are useful in
+photogrammetry and
+
+ align:start position:0%
+photogrammetry and
+ 
+
+ align:start position:0%
+photogrammetry and
+robotics
+
+ align:start position:0%
+robotics
+ 
+
+ align:start position:0%
+robotics
+in particular dealing with
+
+ align:start position:0%
+in particular dealing with
+ 
+
+ align:start position:0%
+ 
+rotation which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has some strange properties
+
+ align:start position:0%
+has some strange properties
+ 
+
+ align:start position:0%
+has some strange properties
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+in the case of translation things are
+
+ align:start position:0%
+in the case of translation things are
+ 
+
+ align:start position:0%
+in the case of translation things are
+commutative if i go
+
+ align:start position:0%
+commutative if i go
+ 
+
+ align:start position:0%
+commutative if i go
+5 meters in x and 10 meters in y i end
+
+ align:start position:0%
+5 meters in x and 10 meters in y i end
+ 
+
+ align:start position:0%
+5 meters in x and 10 meters in y i end
+up in the same place as if i go
+
+ align:start position:0%
+up in the same place as if i go
+ 
+
+ align:start position:0%
+up in the same place as if i go
+10 meters in y and 5 meters in x
+
+ align:start position:0%
+10 meters in y and 5 meters in x
+ 
+
+ align:start position:0%
+10 meters in y and 5 meters in x
+this is not the case with rotation and
+
+ align:start position:0%
+this is not the case with rotation and
+ 
+
+ align:start position:0%
+this is not the case with rotation and
+to illustrate i suppose that
+
+ align:start position:0%
+to illustrate i suppose that
+ 
+
+ align:start position:0%
+to illustrate i suppose that
+this is the x-axis and this is the
+
+ align:start position:0%
+this is the x-axis and this is the
+ 
+
+ align:start position:0%
+this is the x-axis and this is the
+y-axis so i'm going to take
+
+ align:start position:0%
+y-axis so i'm going to take
+ 
+
+ align:start position:0%
+y-axis so i'm going to take
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+this eraser and rotate it uh 90 degrees
+
+ align:start position:0%
+this eraser and rotate it uh 90 degrees
+ 
+
+ align:start position:0%
+this eraser and rotate it uh 90 degrees
+about the x-axis like that
+
+ align:start position:0%
+about the x-axis like that
+ 
+
+ align:start position:0%
+about the x-axis like that
+and then 90 degrees about the y-axis and
+
+ align:start position:0%
+and then 90 degrees about the y-axis and
+ 
+
+ align:start position:0%
+and then 90 degrees about the y-axis and
+i end up there and i take the
+
+ align:start position:0%
+i end up there and i take the
+ 
+
+ align:start position:0%
+i end up there and i take the
+equivalent eraser and i rotate it uh 90
+
+ align:start position:0%
+equivalent eraser and i rotate it uh 90
+ 
+
+ align:start position:0%
+equivalent eraser and i rotate it uh 90
+degrees about the y-axis
+
+ align:start position:0%
+degrees about the y-axis
+ 
+
+ align:start position:0%
+degrees about the y-axis
+and then 90 degrees about the x-axis and
+
+ align:start position:0%
+and then 90 degrees about the x-axis and
+ 
+
+ align:start position:0%
+and then 90 degrees about the x-axis and
+i'm there so
+
+ align:start position:0%
+i'm there so
+ 
+
+ align:start position:0%
+i'm there so
+fortunately that worked so they're not
+
+ align:start position:0%
+fortunately that worked so they're not
+ 
+
+ align:start position:0%
+fortunately that worked so they're not
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+and so it's not commutative so it's a
+
+ align:start position:0%
+and so it's not commutative so it's a
+ 
+
+ align:start position:0%
+and so it's not commutative so it's a
+little bit more difficult to deal with
+
+ align:start position:0%
+little bit more difficult to deal with
+ 
+
+ align:start position:0%
+little bit more difficult to deal with
+particularly when it comes to
+
+ align:start position:0%
+particularly when it comes to
+ 
+
+ align:start position:0%
+particularly when it comes to
+least squares problems and
+
+ align:start position:0%
+least squares problems and
+ 
+
+ align:start position:0%
+least squares problems and
+fitting of
+
+ align:start position:0%
+fitting of
+ 
+
+ align:start position:0%
+fitting of
+data to observations
+
+ align:start position:0%
+data to observations
+ 
+
+ align:start position:0%
+data to observations
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here's an outline of what we're going to
+
+ align:start position:0%
+here's an outline of what we're going to
+ 
+
+ align:start position:0%
+here's an outline of what we're going to
+be talking about
+
+ align:start position:0%
+be talking about
+ 
+
+ align:start position:0%
+be talking about
+properties of rotation
+
+ align:start position:0%
+properties of rotation
+ 
+
+ align:start position:0%
+properties of rotation
+different representation for rotations
+
+ align:start position:0%
+different representation for rotations
+ 
+
+ align:start position:0%
+different representation for rotations
+and in particular the one we're going to
+
+ align:start position:0%
+and in particular the one we're going to
+ 
+
+ align:start position:0%
+and in particular the one we're going to
+pick which is
+
+ align:start position:0%
+pick which is
+ 
+
+ align:start position:0%
+pick which is
+hamilton hamilton's quaternions
+
+ align:start position:0%
+hamilton hamilton's quaternions
+ 
+
+ align:start position:0%
+hamilton hamilton's quaternions
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+they're more general but if we restrict
+
+ align:start position:0%
+they're more general but if we restrict
+ 
+
+ align:start position:0%
+they're more general but if we restrict
+attention to unit quaternions they map
+
+ align:start position:0%
+attention to unit quaternions they map
+ 
+
+ align:start position:0%
+attention to unit quaternions they map
+directly onto rotations in three space
+
+ align:start position:0%
+directly onto rotations in three space
+ 
+
+ align:start position:0%
+directly onto rotations in three space
+they allow us to talk about a space of
+
+ align:start position:0%
+they allow us to talk about a space of
+ 
+
+ align:start position:0%
+they allow us to talk about a space of
+rotation so for translation obviously
+
+ align:start position:0%
+rotation so for translation obviously
+ 
+
+ align:start position:0%
+rotation so for translation obviously
+you know three space is our space of
+
+ align:start position:0%
+you know three space is our space of
+ 
+
+ align:start position:0%
+you know three space is our space of
+translations
+
+ align:start position:0%
+translations
+ 
+
+ align:start position:0%
+translations
+and if we do some optimization
+
+ align:start position:0%
+and if we do some optimization
+ 
+
+ align:start position:0%
+and if we do some optimization
+that's the space we're searching in
+
+ align:start position:0%
+that's the space we're searching in
+ 
+
+ align:start position:0%
+that's the space we're searching in
+that's the space we tessellate that's
+
+ align:start position:0%
+that's the space we tessellate that's
+ 
+
+ align:start position:0%
+that's the space we tessellate that's
+the space where um
+
+ align:start position:0%
+the space where um
+ 
+
+ align:start position:0%
+the space where um
+we get our answers whereas uh it's not
+
+ align:start position:0%
+we get our answers whereas uh it's not
+ 
+
+ align:start position:0%
+we get our answers whereas uh it's not
+so obvious with rotation you know what
+
+ align:start position:0%
+so obvious with rotation you know what
+ 
+
+ align:start position:0%
+so obvious with rotation you know what
+say you want to take an average of force
+
+ align:start position:0%
+say you want to take an average of force
+ 
+
+ align:start position:0%
+say you want to take an average of force
+on a seat belt over all possible
+
+ align:start position:0%
+on a seat belt over all possible
+ 
+
+ align:start position:0%
+on a seat belt over all possible
+orientations of a car
+
+ align:start position:0%
+orientations of a car
+ 
+
+ align:start position:0%
+orientations of a car
+that's something that you know if it was
+
+ align:start position:0%
+that's something that you know if it was
+ 
+
+ align:start position:0%
+that's something that you know if it was
+translation it'd be trivial you just
+
+ align:start position:0%
+translation it'd be trivial you just
+ 
+
+ align:start position:0%
+translation it'd be trivial you just
+integrate over some volume of space
+
+ align:start position:0%
+integrate over some volume of space
+ 
+
+ align:start position:0%
+integrate over some volume of space
+divide by its volume and you're done
+
+ align:start position:0%
+divide by its volume and you're done
+ 
+
+ align:start position:0%
+divide by its volume and you're done
+so that that's something we'll be able
+
+ align:start position:0%
+so that that's something we'll be able
+ 
+
+ align:start position:0%
+so that that's something we'll be able
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+applications are for us mostly in
+
+ align:start position:0%
+applications are for us mostly in
+ 
+
+ align:start position:0%
+applications are for us mostly in
+photogrammetry although they're
+
+ align:start position:0%
+photogrammetry although they're
+ 
+
+ align:start position:0%
+photogrammetry although they're
+very important in robotics and graphics
+
+ align:start position:0%
+very important in robotics and graphics
+ 
+
+ align:start position:0%
+very important in robotics and graphics
+and um control of spacecraft so we'll
+
+ align:start position:0%
+and um control of spacecraft so we'll
+ 
+
+ align:start position:0%
+and um control of spacecraft so we'll
+talk about some of that
+
+ align:start position:0%
+talk about some of that
+ 
+
+ align:start position:0%
+talk about some of that
+and in particular uh using this we're
+
+ align:start position:0%
+and in particular uh using this we're
+ 
+
+ align:start position:0%
+and in particular uh using this we're
+going to develop a closed form solution
+
+ align:start position:0%
+going to develop a closed form solution
+ 
+
+ align:start position:0%
+going to develop a closed form solution
+to the problem that we
+
+ align:start position:0%
+to the problem that we
+ 
+
+ align:start position:0%
+to the problem that we
+started talking about last time which is
+
+ align:start position:0%
+started talking about last time which is
+ 
+
+ align:start position:0%
+started talking about last time which is
+you know either measurements in two
+
+ align:start position:0%
+you know either measurements in two
+ 
+
+ align:start position:0%
+you know either measurements in two
+different coordinate system of the same
+
+ align:start position:0%
+different coordinate system of the same
+ 
+
+ align:start position:0%
+different coordinate system of the same
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+or measurements in one coordinate system
+
+ align:start position:0%
+or measurements in one coordinate system
+ 
+
+ align:start position:0%
+or measurements in one coordinate system
+of two objects or one object that moved
+
+ align:start position:0%
+of two objects or one object that moved
+ 
+
+ align:start position:0%
+of two objects or one object that moved
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+and just for fun at the end we'll
+
+ align:start position:0%
+and just for fun at the end we'll
+ 
+
+ align:start position:0%
+and just for fun at the end we'll
+briefly talk about
+
+ align:start position:0%
+briefly talk about
+ 
+
+ align:start position:0%
+briefly talk about
+division algebras
+
+ align:start position:0%
+division algebras
+ 
+
+ align:start position:0%
+division algebras
+and space time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so here are some of the things i
+
+ align:start position:0%
+and so here are some of the things i
+ 
+
+ align:start position:0%
+and so here are some of the things i
+mentioned where we need to
+
+ align:start position:0%
+mentioned where we need to
+ 
+
+ align:start position:0%
+mentioned where we need to
+have a good representation for rotation
+
+ align:start position:0%
+have a good representation for rotation
+ 
+
+ align:start position:0%
+have a good representation for rotation
+obviously in machine vision for
+
+ align:start position:0%
+obviously in machine vision for
+ 
+
+ align:start position:0%
+obviously in machine vision for
+recognition and for determining the
+
+ align:start position:0%
+recognition and for determining the
+ 
+
+ align:start position:0%
+recognition and for determining the
+orientation of an object in space for
+
+ align:start position:0%
+orientation of an object in space for
+ 
+
+ align:start position:0%
+orientation of an object in space for
+the robot arm to
+
+ align:start position:0%
+the robot arm to
+ 
+
+ align:start position:0%
+the robot arm to
+and so on so
+
+ align:start position:0%
+and so on so
+ 
+
+ align:start position:0%
+and so on so
+you know down to protein folding
+
+ align:start position:0%
+you know down to protein folding
+ 
+
+ align:start position:0%
+you know down to protein folding
+cryo micros electron microscopy
+
+ align:start position:0%
+cryo micros electron microscopy
+ 
+
+ align:start position:0%
+cryo micros electron microscopy
+we all need a good representation for
+
+ align:start position:0%
+we all need a good representation for
+ 
+
+ align:start position:0%
+we all need a good representation for
+rotation there
+
+ align:start position:0%
+rotation there
+ 
+
+ align:start position:0%
+rotation there
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in particular with
+
+ align:start position:0%
+in particular with
+ 
+
+ align:start position:0%
+in particular with
+robotic situations we're dealing with
+
+ align:start position:0%
+robotic situations we're dealing with
+ 
+
+ align:start position:0%
+robotic situations we're dealing with
+motions in space
+
+ align:start position:0%
+motions in space
+ 
+
+ align:start position:0%
+motions in space
+euclidean motions which
+
+ align:start position:0%
+euclidean motions which
+ 
+
+ align:start position:0%
+euclidean motions which
+can be decomposed into translations and
+
+ align:start position:0%
+can be decomposed into translations and
+ 
+
+ align:start position:0%
+can be decomposed into translations and
+rotations
+
+ align:start position:0%
+rotations
+ 
+
+ align:start position:0%
+rotations
+and the euclidean motions have the
+
+ align:start position:0%
+and the euclidean motions have the
+ 
+
+ align:start position:0%
+and the euclidean motions have the
+property that they preserve distances
+
+ align:start position:0%
+property that they preserve distances
+ 
+
+ align:start position:0%
+property that they preserve distances
+between points they preserve angles
+
+ align:start position:0%
+between points they preserve angles
+ 
+
+ align:start position:0%
+between points they preserve angles
+between lines and they preserve
+
+ align:start position:0%
+between lines and they preserve
+ 
+
+ align:start position:0%
+between lines and they preserve
+handedness which sometimes we forget but
+
+ align:start position:0%
+handedness which sometimes we forget but
+ 
+
+ align:start position:0%
+handedness which sometimes we forget but
+if we don't put that in then we're going
+
+ align:start position:0%
+if we don't put that in then we're going
+ 
+
+ align:start position:0%
+if we don't put that in then we're going
+to get
+
+ align:start position:0%
+to get
+ 
+
+ align:start position:0%
+to get
+reflections
+
+ align:start position:0%
+reflections
+ 
+
+ align:start position:0%
+reflections
+as you know most of the biologically
+
+ align:start position:0%
+as you know most of the biologically
+ 
+
+ align:start position:0%
+as you know most of the biologically
+important uh chemicals exist in in one
+
+ align:start position:0%
+important uh chemicals exist in in one
+ 
+
+ align:start position:0%
+important uh chemicals exist in in one
+particular form the mirror image form
+
+ align:start position:0%
+particular form the mirror image form
+ 
+
+ align:start position:0%
+particular form the mirror image form
+doesn't work and so it's you know kind
+
+ align:start position:0%
+doesn't work and so it's you know kind
+ 
+
+ align:start position:0%
+doesn't work and so it's you know kind
+of important to preserve-handedness
+
+ align:start position:0%
+of important to preserve-handedness
+ 
+
+ align:start position:0%
+of important to preserve-handedness
+uh put together those mean that we
+
+ align:start position:0%
+uh put together those mean that we
+ 
+
+ align:start position:0%
+uh put together those mean that we
+preserve dot products and we preserve uh
+
+ align:start position:0%
+preserve dot products and we preserve uh
+ 
+
+ align:start position:0%
+preserve dot products and we preserve uh
+triple products and we're leaving out
+
+ align:start position:0%
+triple products and we're leaving out
+ 
+
+ align:start position:0%
+triple products and we're leaving out
+by doing this transformations of free
+
+ align:start position:0%
+by doing this transformations of free
+ 
+
+ align:start position:0%
+by doing this transformations of free
+space that you know would otherwise be
+
+ align:start position:0%
+space that you know would otherwise be
+ 
+
+ align:start position:0%
+space that you know would otherwise be
+perfectly reasonable
+
+ align:start position:0%
+perfectly reasonable
+ 
+
+ align:start position:0%
+perfectly reasonable
+such as reflections and skewing and
+
+ align:start position:0%
+such as reflections and skewing and
+ 
+
+ align:start position:0%
+such as reflections and skewing and
+scaling we'll talk a little bit about
+
+ align:start position:0%
+scaling we'll talk a little bit about
+ 
+
+ align:start position:0%
+scaling we'll talk a little bit about
+scaling but
+
+ align:start position:0%
+scaling but
+ 
+
+ align:start position:0%
+scaling but
+mostly for the moment we leave it out
+
+ align:start position:0%
+mostly for the moment we leave it out
+ 
+
+ align:start position:0%
+mostly for the moment we leave it out
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+rotations first euler's theorem
+
+ align:start position:0%
+rotations first euler's theorem
+ 
+
+ align:start position:0%
+rotations first euler's theorem
+any rotation of a rigid object has the
+
+ align:start position:0%
+any rotation of a rigid object has the
+ 
+
+ align:start position:0%
+any rotation of a rigid object has the
+property that there is a line that is
+
+ align:start position:0%
+property that there is a line that is
+ 
+
+ align:start position:0%
+property that there is a line that is
+not changed that's the axis
+
+ align:start position:0%
+not changed that's the axis
+ 
+
+ align:start position:0%
+not changed that's the axis
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+there's the parallel axis theorem which
+
+ align:start position:0%
+there's the parallel axis theorem which
+ 
+
+ align:start position:0%
+there's the parallel axis theorem which
+says that
+
+ align:start position:0%
+says that
+ 
+
+ align:start position:0%
+says that
+any rotation
+
+ align:start position:0%
+any rotation
+ 
+
+ align:start position:0%
+any rotation
+about any axis is equivalent to a
+
+ align:start position:0%
+about any axis is equivalent to a
+ 
+
+ align:start position:0%
+about any axis is equivalent to a
+rotation about an axis through the
+
+ align:start position:0%
+rotation about an axis through the
+ 
+
+ align:start position:0%
+rotation about an axis through the
+origin
+
+ align:start position:0%
+origin
+ 
+
+ align:start position:0%
+origin
+plus a translation
+
+ align:start position:0%
+plus a translation
+ 
+
+ align:start position:0%
+plus a translation
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+for us it's going to be very convenient
+
+ align:start position:0%
+for us it's going to be very convenient
+ 
+
+ align:start position:0%
+for us it's going to be very convenient
+to separate translation and rotation
+
+ align:start position:0%
+to separate translation and rotation
+ 
+
+ align:start position:0%
+to separate translation and rotation
+this way that when we talk about
+
+ align:start position:0%
+this way that when we talk about
+ 
+
+ align:start position:0%
+this way that when we talk about
+rotation that we're going to recover
+
+ align:start position:0%
+rotation that we're going to recover
+ 
+
+ align:start position:0%
+rotation that we're going to recover
+we're just going to talk about rotation
+
+ align:start position:0%
+we're just going to talk about rotation
+ 
+
+ align:start position:0%
+we're just going to talk about rotation
+about an axis through the origin because
+
+ align:start position:0%
+about an axis through the origin because
+ 
+
+ align:start position:0%
+about an axis through the origin because
+we deal with the translation separately
+
+ align:start position:0%
+we deal with the translation separately
+ 
+
+ align:start position:0%
+we deal with the translation separately
+and because of the parallel axis theorem
+
+ align:start position:0%
+and because of the parallel axis theorem
+ 
+
+ align:start position:0%
+and because of the parallel axis theorem
+we can do that then if we figure out how
+
+ align:start position:0%
+we can do that then if we figure out how
+ 
+
+ align:start position:0%
+we can do that then if we figure out how
+a sphere rotates
+
+ align:start position:0%
+a sphere rotates
+ 
+
+ align:start position:0%
+a sphere rotates
+we basically figured out how everything
+
+ align:start position:0%
+we basically figured out how everything
+ 
+
+ align:start position:0%
+we basically figured out how everything
+rotates because we can and that sort of
+
+ align:start position:0%
+rotates because we can and that sort of
+ 
+
+ align:start position:0%
+rotates because we can and that sort of
+simplifies thing we can just think of
+
+ align:start position:0%
+simplifies thing we can just think of
+ 
+
+ align:start position:0%
+simplifies thing we can just think of
+sphere rotating in space and all the
+
+ align:start position:0%
+sphere rotating in space and all the
+ 
+
+ align:start position:0%
+sphere rotating in space and all the
+possible ways that can happen and that
+
+ align:start position:0%
+possible ways that can happen and that
+ 
+
+ align:start position:0%
+possible ways that can happen and that
+then corresponds to
+
+ align:start position:0%
+then corresponds to
+ 
+
+ align:start position:0%
+then corresponds to
+rotation of space
+
+ align:start position:0%
+rotation of space
+ 
+
+ align:start position:0%
+rotation of space
+when we talk about attitude we basically
+
+ align:start position:0%
+when we talk about attitude we basically
+ 
+
+ align:start position:0%
+when we talk about attitude we basically
+mean orientation we mean orientation
+
+ align:start position:0%
+mean orientation we mean orientation
+ 
+
+ align:start position:0%
+mean orientation we mean orientation
+relative to some standard so for example
+
+ align:start position:0%
+relative to some standard so for example
+ 
+
+ align:start position:0%
+relative to some standard so for example
+we might have models
+
+ align:start position:0%
+we might have models
+ 
+
+ align:start position:0%
+we might have models
+as we had when we're talking about the
+
+ align:start position:0%
+as we had when we're talking about the
+ 
+
+ align:start position:0%
+as we had when we're talking about the
+patents except now in 3d
+
+ align:start position:0%
+patents except now in 3d
+ 
+
+ align:start position:0%
+patents except now in 3d
+and they'll be in some preferred
+
+ align:start position:0%
+and they'll be in some preferred
+ 
+
+ align:start position:0%
+and they'll be in some preferred
+coordinate system and when we talk about
+
+ align:start position:0%
+coordinate system and when we talk about
+ 
+
+ align:start position:0%
+coordinate system and when we talk about
+locating that object we're talking about
+
+ align:start position:0%
+locating that object we're talking about
+ 
+
+ align:start position:0%
+locating that object we're talking about
+finding its position in space and
+
+ align:start position:0%
+finding its position in space and
+ 
+
+ align:start position:0%
+finding its position in space and
+finding its rotation relative to that
+
+ align:start position:0%
+finding its rotation relative to that
+ 
+
+ align:start position:0%
+finding its rotation relative to that
+reference rotation
+
+ align:start position:0%
+reference rotation
+ 
+
+ align:start position:0%
+reference rotation
+so by the way
+
+ align:start position:0%
+so by the way
+ 
+
+ align:start position:0%
+so by the way
+this is going to be on stellar
+
+ align:start position:0%
+this is going to be on stellar
+ 
+
+ align:start position:0%
+this is going to be on stellar
+this whole presentation
+
+ align:start position:0%
+this whole presentation
+ 
+
+ align:start position:0%
+this whole presentation
+then there's a
+
+ align:start position:0%
+then there's a
+ 
+
+ align:start position:0%
+then there's a
+four-page blurb that summarizes
+
+ align:start position:0%
+four-page blurb that summarizes
+ 
+
+ align:start position:0%
+four-page blurb that summarizes
+everything you want to know about
+
+ align:start position:0%
+everything you want to know about
+ 
+
+ align:start position:0%
+everything you want to know about
+quaternions
+
+ align:start position:0%
+quaternions
+ 
+
+ align:start position:0%
+quaternions
+or maybe not
+
+ align:start position:0%
+or maybe not
+ 
+
+ align:start position:0%
+or maybe not
+maybe everything you need for this
+
+ align:start position:0%
+maybe everything you need for this
+ 
+
+ align:start position:0%
+maybe everything you need for this
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+degrees of freedom so we talked about
+
+ align:start position:0%
+degrees of freedom so we talked about
+ 
+
+ align:start position:0%
+degrees of freedom so we talked about
+this last time that there happened to be
+
+ align:start position:0%
+this last time that there happened to be
+ 
+
+ align:start position:0%
+this last time that there happened to be
+three degrees of freedom to rotation and
+
+ align:start position:0%
+three degrees of freedom to rotation and
+ 
+
+ align:start position:0%
+three degrees of freedom to rotation and
+that can be slightly confusing
+
+ align:start position:0%
+that can be slightly confusing
+ 
+
+ align:start position:0%
+that can be slightly confusing
+what's interesting is that rotational
+
+ align:start position:0%
+what's interesting is that rotational
+ 
+
+ align:start position:0%
+what's interesting is that rotational
+velocity is much easier
+
+ align:start position:0%
+velocity is much easier
+ 
+
+ align:start position:0%
+velocity is much easier
+angular velocity all we need is a vector
+
+ align:start position:0%
+angular velocity all we need is a vector
+ 
+
+ align:start position:0%
+angular velocity all we need is a vector
+that gives us the axis
+
+ align:start position:0%
+that gives us the axis
+ 
+
+ align:start position:0%
+that gives us the axis
+and a rate
+
+ align:start position:0%
+and a rate
+ 
+
+ align:start position:0%
+and a rate
+so many radians per second and if we
+
+ align:start position:0%
+so many radians per second and if we
+ 
+
+ align:start position:0%
+so many radians per second and if we
+take the axis and multiply it by the
+
+ align:start position:0%
+take the axis and multiply it by the
+ 
+
+ align:start position:0%
+take the axis and multiply it by the
+rate we have a three vector
+
+ align:start position:0%
+rate we have a three vector
+ 
+
+ align:start position:0%
+rate we have a three vector
+and those three vectors add just like
+
+ align:start position:0%
+and those three vectors add just like
+ 
+
+ align:start position:0%
+and those three vectors add just like
+translations so if you're spinning
+
+ align:start position:0%
+translations so if you're spinning
+ 
+
+ align:start position:0%
+translations so if you're spinning
+around the x-axis at you know one radian
+
+ align:start position:0%
+around the x-axis at you know one radian
+ 
+
+ align:start position:0%
+around the x-axis at you know one radian
+per second you're spinning about the
+
+ align:start position:0%
+per second you're spinning about the
+ 
+
+ align:start position:0%
+per second you're spinning about the
+y-axis at one radian per second then
+
+ align:start position:0%
+y-axis at one radian per second then
+ 
+
+ align:start position:0%
+y-axis at one radian per second then
+you're spinning about the one one zero
+
+ align:start position:0%
+you're spinning about the one one zero
+ 
+
+ align:start position:0%
+you're spinning about the one one zero
+axis you know so it's very easy to just
+
+ align:start position:0%
+axis you know so it's very easy to just
+ 
+
+ align:start position:0%
+axis you know so it's very easy to just
+add these up
+
+ align:start position:0%
+add these up
+ 
+
+ align:start position:0%
+add these up
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+of course that can change so now you've
+
+ align:start position:0%
+of course that can change so now you've
+ 
+
+ align:start position:0%
+of course that can change so now you've
+moved a little bit and the next time
+
+ align:start position:0%
+moved a little bit and the next time
+ 
+
+ align:start position:0%
+moved a little bit and the next time
+instance the axis will be different so
+
+ align:start position:0%
+instance the axis will be different so
+ 
+
+ align:start position:0%
+instance the axis will be different so
+but instantaneously rotational velocity
+
+ align:start position:0%
+but instantaneously rotational velocity
+ 
+
+ align:start position:0%
+but instantaneously rotational velocity
+is very easy
+
+ align:start position:0%
+is very easy
+ 
+
+ align:start position:0%
+is very easy
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+for those of you who know about these
+
+ align:start position:0%
+for those of you who know about these
+ 
+
+ align:start position:0%
+for those of you who know about these
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+corresponds to you know the the lee
+
+ align:start position:0%
+corresponds to you know the the lee
+ 
+
+ align:start position:0%
+corresponds to you know the the lee
+algebra versus the lead group
+
+ align:start position:0%
+algebra versus the lead group
+ 
+
+ align:start position:0%
+algebra versus the lead group
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+rotational velocities are the algebra it
+
+ align:start position:0%
+rotational velocities are the algebra it
+ 
+
+ align:start position:0%
+rotational velocities are the algebra it
+has all the nice properties of an
+
+ align:start position:0%
+has all the nice properties of an
+ 
+
+ align:start position:0%
+has all the nice properties of an
+algebra
+
+ align:start position:0%
+algebra
+ 
+
+ align:start position:0%
+algebra
+the rotations which are sort of the
+
+ align:start position:0%
+the rotations which are sort of the
+ 
+
+ align:start position:0%
+the rotations which are sort of the
+integral of that don't they don't have
+
+ align:start position:0%
+integral of that don't they don't have
+ 
+
+ align:start position:0%
+integral of that don't they don't have
+quite those nice properties
+
+ align:start position:0%
+quite those nice properties
+ 
+
+ align:start position:0%
+quite those nice properties
+poisson's formula tells you what the
+
+ align:start position:0%
+poisson's formula tells you what the
+ 
+
+ align:start position:0%
+poisson's formula tells you what the
+velocity is of some point uh when
+
+ align:start position:0%
+velocity is of some point uh when
+ 
+
+ align:start position:0%
+velocity is of some point uh when
+there's a known rotational veloci um
+
+ align:start position:0%
+there's a known rotational veloci um
+ 
+
+ align:start position:0%
+there's a known rotational veloci um
+right rotational velocity so omega
+
+ align:start position:0%
+right rotational velocity so omega
+ 
+
+ align:start position:0%
+right rotational velocity so omega
+is that vector
+
+ align:start position:0%
+is that vector
+ 
+
+ align:start position:0%
+is that vector
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+axis of which is the axis of the
+
+ align:start position:0%
+axis of which is the axis of the
+ 
+
+ align:start position:0%
+axis of which is the axis of the
+direction of which is the axis of
+
+ align:start position:0%
+direction of which is the axis of
+ 
+
+ align:start position:0%
+direction of which is the axis of
+rotation and the magnitude of it is the
+
+ align:start position:0%
+rotation and the magnitude of it is the
+ 
+
+ align:start position:0%
+rotation and the magnitude of it is the
+rate of rotation and then if we have
+
+ align:start position:0%
+rate of rotation and then if we have
+ 
+
+ align:start position:0%
+rate of rotation and then if we have
+some point r we just take that cross
+
+ align:start position:0%
+some point r we just take that cross
+ 
+
+ align:start position:0%
+some point r we just take that cross
+product to figure out what the velocity
+
+ align:start position:0%
+product to figure out what the velocity
+ 
+
+ align:start position:0%
+product to figure out what the velocity
+is and obviously
+
+ align:start position:0%
+is and obviously
+ 
+
+ align:start position:0%
+is and obviously
+it's going to be perpendicular to r and
+
+ align:start position:0%
+it's going to be perpendicular to r and
+ 
+
+ align:start position:0%
+it's going to be perpendicular to r and
+it's going to be perpendicular to omega
+
+ align:start position:0%
+it's going to be perpendicular to omega
+ 
+
+ align:start position:0%
+it's going to be perpendicular to omega
+and you can you know get its direction
+
+ align:start position:0%
+and you can you know get its direction
+ 
+
+ align:start position:0%
+and you can you know get its direction
+by using the right hand rule
+
+ align:start position:0%
+by using the right hand rule
+ 
+
+ align:start position:0%
+by using the right hand rule
+so rotational velocity is simpler they
+
+ align:start position:0%
+so rotational velocity is simpler they
+ 
+
+ align:start position:0%
+so rotational velocity is simpler they
+add
+
+ align:start position:0%
+add
+ 
+
+ align:start position:0%
+add
+and we just saw finite finite rotations
+
+ align:start position:0%
+and we just saw finite finite rotations
+ 
+
+ align:start position:0%
+and we just saw finite finite rotations
+don't commute and we talked last time
+
+ align:start position:0%
+don't commute and we talked last time
+ 
+
+ align:start position:0%
+don't commute and we talked last time
+about how they're
+
+ align:start position:0%
+about how they're
+ 
+
+ align:start position:0%
+about how they're
+n times n minus one over two degrees of
+
+ align:start position:0%
+n times n minus one over two degrees of
+ 
+
+ align:start position:0%
+n times n minus one over two degrees of
+freedom
+
+ align:start position:0%
+freedom
+ 
+
+ align:start position:0%
+freedom
+and for n equals three that happens to
+
+ align:start position:0%
+and for n equals three that happens to
+ 
+
+ align:start position:0%
+and for n equals three that happens to
+give you three
+
+ align:start position:0%
+give you three
+ 
+
+ align:start position:0%
+give you three
+so often we talk about rotation about
+
+ align:start position:0%
+so often we talk about rotation about
+ 
+
+ align:start position:0%
+so often we talk about rotation about
+axes like i just did rotation about the
+
+ align:start position:0%
+axes like i just did rotation about the
+ 
+
+ align:start position:0%
+axes like i just did rotation about the
+x-axis rotation about the y-axis
+
+ align:start position:0%
+x-axis rotation about the y-axis
+ 
+
+ align:start position:0%
+x-axis rotation about the y-axis
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if you follow that
+
+ align:start position:0%
+if you follow that
+ 
+
+ align:start position:0%
+if you follow that
+view then you might think that in
+
+ align:start position:0%
+view then you might think that in
+ 
+
+ align:start position:0%
+view then you might think that in
+n-dimensions rotation is n-dimensional
+
+ align:start position:0%
+n-dimensions rotation is n-dimensional
+ 
+
+ align:start position:0%
+n-dimensions rotation is n-dimensional
+and therefore it is better to think
+
+ align:start position:0%
+and therefore it is better to think
+ 
+
+ align:start position:0%
+and therefore it is better to think
+about rotation as rotation preserving
+
+ align:start position:0%
+about rotation as rotation preserving
+ 
+
+ align:start position:0%
+about rotation as rotation preserving
+certain planes
+
+ align:start position:0%
+certain planes
+ 
+
+ align:start position:0%
+certain planes
+so for example we can preserve the x y
+
+ align:start position:0%
+so for example we can preserve the x y
+ 
+
+ align:start position:0%
+so for example we can preserve the x y
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+uh we can rotate in such a way that the
+
+ align:start position:0%
+uh we can rotate in such a way that the
+ 
+
+ align:start position:0%
+uh we can rotate in such a way that the
+x y plane is not changed the things in
+
+ align:start position:0%
+x y plane is not changed the things in
+ 
+
+ align:start position:0%
+x y plane is not changed the things in
+the x y plane are moved into x y plane
+
+ align:start position:0%
+the x y plane are moved into x y plane
+ 
+
+ align:start position:0%
+the x y plane are moved into x y plane
+somewhere else
+
+ align:start position:0%
+somewhere else
+ 
+
+ align:start position:0%
+somewhere else
+uh y z plane and z x plane also three
+
+ align:start position:0%
+uh y z plane and z x plane also three
+ 
+
+ align:start position:0%
+uh y z plane and z x plane also three
+but that one works because in in 2d
+
+ align:start position:0%
+but that one works because in in 2d
+ 
+
+ align:start position:0%
+but that one works because in in 2d
+we only have the xy plane one degree of
+
+ align:start position:0%
+we only have the xy plane one degree of
+ 
+
+ align:start position:0%
+we only have the xy plane one degree of
+freedom
+
+ align:start position:0%
+freedom
+ 
+
+ align:start position:0%
+freedom
+and in 4d we have
+
+ align:start position:0%
+and in 4d we have
+ 
+
+ align:start position:0%
+and in 4d we have
+six combinations and that's the number
+
+ align:start position:0%
+six combinations and that's the number
+ 
+
+ align:start position:0%
+six combinations and that's the number
+of degrees of freedom of rotation in 4d
+
+ align:start position:0%
+of degrees of freedom of rotation in 4d
+ 
+
+ align:start position:0%
+of degrees of freedom of rotation in 4d
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so before we go further
+
+ align:start position:0%
+so before we go further
+ 
+
+ align:start position:0%
+so before we go further
+here's a
+
+ align:start position:0%
+here's a
+ 
+
+ align:start position:0%
+here's a
+interesting thing that we will exploit
+
+ align:start position:0%
+interesting thing that we will exploit
+ 
+
+ align:start position:0%
+interesting thing that we will exploit
+and also it's a
+
+ align:start position:0%
+and also it's a
+ 
+
+ align:start position:0%
+and also it's a
+kind of preview of a method we'll use
+
+ align:start position:0%
+kind of preview of a method we'll use
+ 
+
+ align:start position:0%
+kind of preview of a method we'll use
+which is uh
+
+ align:start position:0%
+which is uh
+ 
+
+ align:start position:0%
+which is uh
+you know cross products cross products
+
+ align:start position:0%
+you know cross products cross products
+ 
+
+ align:start position:0%
+you know cross products cross products
+as i mentioned are kind of confusing
+
+ align:start position:0%
+as i mentioned are kind of confusing
+ 
+
+ align:start position:0%
+as i mentioned are kind of confusing
+because you take the product of two
+
+ align:start position:0%
+because you take the product of two
+ 
+
+ align:start position:0%
+because you take the product of two
+vectors and you get another vector
+
+ align:start position:0%
+vectors and you get another vector
+ 
+
+ align:start position:0%
+vectors and you get another vector
+which isn't quite right but it happens
+
+ align:start position:0%
+which isn't quite right but it happens
+ 
+
+ align:start position:0%
+which isn't quite right but it happens
+to have three
+
+ align:start position:0%
+to have three
+ 
+
+ align:start position:0%
+to have three
+degrees of freedom so we represent it as
+
+ align:start position:0%
+degrees of freedom so we represent it as
+ 
+
+ align:start position:0%
+degrees of freedom so we represent it as
+a vector
+
+ align:start position:0%
+a vector
+ 
+
+ align:start position:0%
+a vector
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+again that's a coincidence
+
+ align:start position:0%
+again that's a coincidence
+ 
+
+ align:start position:0%
+again that's a coincidence
+what is it well it's perpendicular to
+
+ align:start position:0%
+what is it well it's perpendicular to
+ 
+
+ align:start position:0%
+what is it well it's perpendicular to
+the two vectors you started with
+
+ align:start position:0%
+the two vectors you started with
+ 
+
+ align:start position:0%
+the two vectors you started with
+and so in
+
+ align:start position:0%
+and so in
+ 
+
+ align:start position:0%
+and so in
+higher dimensional space if you take
+
+ align:start position:0%
+higher dimensional space if you take
+ 
+
+ align:start position:0%
+higher dimensional space if you take
+if you say you know what are the things
+
+ align:start position:0%
+if you say you know what are the things
+ 
+
+ align:start position:0%
+if you say you know what are the things
+that are perpendicular to two vectors
+
+ align:start position:0%
+that are perpendicular to two vectors
+ 
+
+ align:start position:0%
+that are perpendicular to two vectors
+well they're not going to be a vector
+
+ align:start position:0%
+well they're not going to be a vector
+ 
+
+ align:start position:0%
+well they're not going to be a vector
+there's going to be a whole subspace
+
+ align:start position:0%
+there's going to be a whole subspace
+ 
+
+ align:start position:0%
+there's going to be a whole subspace
+so the generalization of a cross product
+
+ align:start position:0%
+so the generalization of a cross product
+ 
+
+ align:start position:0%
+so the generalization of a cross product
+would be something more complicated like
+
+ align:start position:0%
+would be something more complicated like
+ 
+
+ align:start position:0%
+would be something more complicated like
+uh one way to generalize it in an
+
+ align:start position:0%
+uh one way to generalize it in an
+ 
+
+ align:start position:0%
+uh one way to generalize it in an
+n-dimensional space is it's that vector
+
+ align:start position:0%
+n-dimensional space is it's that vector
+ 
+
+ align:start position:0%
+n-dimensional space is it's that vector
+that's perpendicular to n minus one
+
+ align:start position:0%
+that's perpendicular to n minus one
+ 
+
+ align:start position:0%
+that's perpendicular to n minus one
+other vectors well here n minus one
+
+ align:start position:0%
+other vectors well here n minus one
+ 
+
+ align:start position:0%
+other vectors well here n minus one
+happens to be two so
+
+ align:start position:0%
+happens to be two so
+ 
+
+ align:start position:0%
+happens to be two so
+that's where we get our cross product
+
+ align:start position:0%
+that's where we get our cross product
+ 
+
+ align:start position:0%
+that's where we get our cross product
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+actually very convenient
+
+ align:start position:0%
+actually very convenient
+ 
+
+ align:start position:0%
+actually very convenient
+for certain operations
+
+ align:start position:0%
+for certain operations
+ 
+
+ align:start position:0%
+for certain operations
+particularly matrix vector operations to
+
+ align:start position:0%
+particularly matrix vector operations to
+ 
+
+ align:start position:0%
+particularly matrix vector operations to
+represent the cross product in this way
+
+ align:start position:0%
+represent the cross product in this way
+ 
+
+ align:start position:0%
+represent the cross product in this way
+where we
+
+ align:start position:0%
+where we
+ 
+
+ align:start position:0%
+where we
+uh take the skew symmetric matrix
+
+ align:start position:0%
+uh take the skew symmetric matrix
+ 
+
+ align:start position:0%
+uh take the skew symmetric matrix
+and we can represent a cross b by
+
+ align:start position:0%
+and we can represent a cross b by
+ 
+
+ align:start position:0%
+and we can represent a cross b by
+multiplying that
+
+ align:start position:0%
+multiplying that
+ 
+
+ align:start position:0%
+multiplying that
+skew symmetric matrix by b
+
+ align:start position:0%
+skew symmetric matrix by b
+ 
+
+ align:start position:0%
+skew symmetric matrix by b
+and it has the right degrees of freedom
+
+ align:start position:0%
+and it has the right degrees of freedom
+ 
+
+ align:start position:0%
+and it has the right degrees of freedom
+right because a has three degrees of
+
+ align:start position:0%
+right because a has three degrees of
+ 
+
+ align:start position:0%
+right because a has three degrees of
+freedom
+
+ align:start position:0%
+freedom
+ 
+
+ align:start position:0%
+freedom
+a skew-symmetric matrix has zero on the
+
+ align:start position:0%
+a skew-symmetric matrix has zero on the
+ 
+
+ align:start position:0%
+a skew-symmetric matrix has zero on the
+diagonal and
+
+ align:start position:0%
+diagonal and
+ 
+
+ align:start position:0%
+diagonal and
+the off-diagonal symmetric so you again
+
+ align:start position:0%
+the off-diagonal symmetric so you again
+ 
+
+ align:start position:0%
+the off-diagonal symmetric so you again
+have three degrees of freedom so
+
+ align:start position:0%
+have three degrees of freedom so
+ 
+
+ align:start position:0%
+have three degrees of freedom so
+that seems like a reasonable isomorphism
+
+ align:start position:0%
+that seems like a reasonable isomorphism
+ 
+
+ align:start position:0%
+that seems like a reasonable isomorphism
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then once you've done that you've gotten
+
+ align:start position:0%
+then once you've done that you've gotten
+ 
+
+ align:start position:0%
+then once you've done that you've gotten
+rid of this weird thing the cross
+
+ align:start position:0%
+rid of this weird thing the cross
+ 
+
+ align:start position:0%
+rid of this weird thing the cross
+product and you have something that you
+
+ align:start position:0%
+product and you have something that you
+ 
+
+ align:start position:0%
+product and you have something that you
+can manipulate in combination with other
+
+ align:start position:0%
+can manipulate in combination with other
+ 
+
+ align:start position:0%
+can manipulate in combination with other
+vectors and matrices
+
+ align:start position:0%
+vectors and matrices
+ 
+
+ align:start position:0%
+vectors and matrices
+now of course why did we pick a to
+
+ align:start position:0%
+now of course why did we pick a to
+ 
+
+ align:start position:0%
+now of course why did we pick a to
+expand as the matrix we could equally
+
+ align:start position:0%
+expand as the matrix we could equally
+ 
+
+ align:start position:0%
+expand as the matrix we could equally
+well have picked b
+
+ align:start position:0%
+well have picked b
+ 
+
+ align:start position:0%
+well have picked b
+and have written it this way equally
+
+ align:start position:0%
+and have written it this way equally
+ 
+
+ align:start position:0%
+and have written it this way equally
+valid uh and you'll notice this matrix
+
+ align:start position:0%
+valid uh and you'll notice this matrix
+ 
+
+ align:start position:0%
+valid uh and you'll notice this matrix
+is uh you know
+
+ align:start position:0%
+is uh you know
+ 
+
+ align:start position:0%
+is uh you know
+transpose or negate that version of of
+
+ align:start position:0%
+transpose or negate that version of of
+ 
+
+ align:start position:0%
+transpose or negate that version of of
+that matrix
+
+ align:start position:0%
+that matrix
+ 
+
+ align:start position:0%
+that matrix
+so the matrix for b
+
+ align:start position:0%
+so the matrix for b
+ 
+
+ align:start position:0%
+so the matrix for b
+so it's order dependent and we know that
+
+ align:start position:0%
+so it's order dependent and we know that
+ 
+
+ align:start position:0%
+so it's order dependent and we know that
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+cross products don't don't commute so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there are loads of representations
+
+ align:start position:0%
+okay there are loads of representations
+ 
+
+ align:start position:0%
+okay there are loads of representations
+for rotation which tells you that
+
+ align:start position:0%
+for rotation which tells you that
+ 
+
+ align:start position:0%
+for rotation which tells you that
+there's a problem you know with
+
+ align:start position:0%
+there's a problem you know with
+ 
+
+ align:start position:0%
+there's a problem you know with
+translation we just have x y z be done
+
+ align:start position:0%
+translation we just have x y z be done
+ 
+
+ align:start position:0%
+translation we just have x y z be done
+with it
+
+ align:start position:0%
+with it
+ 
+
+ align:start position:0%
+with it
+um so one uh one notation that's very
+
+ align:start position:0%
+um so one uh one notation that's very
+ 
+
+ align:start position:0%
+um so one uh one notation that's very
+useful is um axis and angle so we have
+
+ align:start position:0%
+useful is um axis and angle so we have
+ 
+
+ align:start position:0%
+useful is um axis and angle so we have
+an axis which can be given as a unit
+
+ align:start position:0%
+an axis which can be given as a unit
+ 
+
+ align:start position:0%
+an axis which can be given as a unit
+vector and we have a
+
+ align:start position:0%
+vector and we have a
+ 
+
+ align:start position:0%
+vector and we have a
+number of degrees that we rotate or
+
+ align:start position:0%
+number of degrees that we rotate or
+ 
+
+ align:start position:0%
+number of degrees that we rotate or
+radians that we rotate through so that's
+
+ align:start position:0%
+radians that we rotate through so that's
+ 
+
+ align:start position:0%
+radians that we rotate through so that's
+three degrees of freedom because the
+
+ align:start position:0%
+three degrees of freedom because the
+ 
+
+ align:start position:0%
+three degrees of freedom because the
+unit vector only has two and plus the
+
+ align:start position:0%
+unit vector only has two and plus the
+ 
+
+ align:start position:0%
+unit vector only has two and plus the
+angle gives us 3.
+
+ align:start position:0%
+angle gives us 3.
+ 
+
+ align:start position:0%
+angle gives us 3.
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+sometimes
+
+ align:start position:0%
+sometimes
+ 
+
+ align:start position:0%
+sometimes
+we can derive other notations from that
+
+ align:start position:0%
+we can derive other notations from that
+ 
+
+ align:start position:0%
+we can derive other notations from that
+one of them is the gibbs vector which
+
+ align:start position:0%
+one of them is the gibbs vector which
+ 
+
+ align:start position:0%
+one of them is the gibbs vector which
+tries to combine those two
+
+ align:start position:0%
+tries to combine those two
+ 
+
+ align:start position:0%
+tries to combine those two
+you know into a single thing so this
+
+ align:start position:0%
+you know into a single thing so this
+ 
+
+ align:start position:0%
+you know into a single thing so this
+this is sort of inconvenient in a way
+
+ align:start position:0%
+this is sort of inconvenient in a way
+ 
+
+ align:start position:0%
+this is sort of inconvenient in a way
+because you've got a three vector which
+
+ align:start position:0%
+because you've got a three vector which
+ 
+
+ align:start position:0%
+because you've got a three vector which
+happens to be unit vector and then you
+
+ align:start position:0%
+happens to be unit vector and then you
+ 
+
+ align:start position:0%
+happens to be unit vector and then you
+have this thing
+
+ align:start position:0%
+have this thing
+ 
+
+ align:start position:0%
+have this thing
+so the gibbs vector
+
+ align:start position:0%
+so the gibbs vector
+ 
+
+ align:start position:0%
+so the gibbs vector
+is a vector and and it turns out that
+
+ align:start position:0%
+is a vector and and it turns out that
+ 
+
+ align:start position:0%
+is a vector and and it turns out that
+you don't want to just multiply by theta
+
+ align:start position:0%
+you don't want to just multiply by theta
+ 
+
+ align:start position:0%
+you don't want to just multiply by theta
+that doesn't give you uh nice algebraic
+
+ align:start position:0%
+that doesn't give you uh nice algebraic
+ 
+
+ align:start position:0%
+that doesn't give you uh nice algebraic
+properties uh it's much better and plus
+
+ align:start position:0%
+properties uh it's much better and plus
+ 
+
+ align:start position:0%
+properties uh it's much better and plus
+you know theta wraps around 2 pi so that
+
+ align:start position:0%
+you know theta wraps around 2 pi so that
+ 
+
+ align:start position:0%
+you know theta wraps around 2 pi so that
+doesn't really make much sense anyway
+
+ align:start position:0%
+doesn't really make much sense anyway
+ 
+
+ align:start position:0%
+doesn't really make much sense anyway
+and gibbs found out that you can get
+
+ align:start position:0%
+and gibbs found out that you can get
+ 
+
+ align:start position:0%
+and gibbs found out that you can get
+some useful properties by taking tan
+
+ align:start position:0%
+some useful properties by taking tan
+ 
+
+ align:start position:0%
+some useful properties by taking tan
+theta over two so now you have a vector
+
+ align:start position:0%
+theta over two so now you have a vector
+ 
+
+ align:start position:0%
+theta over two so now you have a vector
+it's no longer a unit vector so it has
+
+ align:start position:0%
+it's no longer a unit vector so it has
+ 
+
+ align:start position:0%
+it's no longer a unit vector so it has
+three components so it has the right
+
+ align:start position:0%
+three components so it has the right
+ 
+
+ align:start position:0%
+three components so it has the right
+number of degrees of freedom
+
+ align:start position:0%
+number of degrees of freedom
+ 
+
+ align:start position:0%
+number of degrees of freedom
+only bad thing is
+
+ align:start position:0%
+only bad thing is
+ 
+
+ align:start position:0%
+only bad thing is
+it blows up at theta equals pi right
+
+ align:start position:0%
+it blows up at theta equals pi right
+ 
+
+ align:start position:0%
+it blows up at theta equals pi right
+because tan of pi over 2 is infinite
+
+ align:start position:0%
+because tan of pi over 2 is infinite
+ 
+
+ align:start position:0%
+because tan of pi over 2 is infinite
+uh and theta over pi so is that a
+
+ align:start position:0%
+uh and theta over pi so is that a
+ 
+
+ align:start position:0%
+uh and theta over pi so is that a
+problem well you know rotating through
+
+ align:start position:0%
+problem well you know rotating through
+ 
+
+ align:start position:0%
+problem well you know rotating through
+180 degrees that's a perfectly
+
+ align:start position:0%
+180 degrees that's a perfectly
+ 
+
+ align:start position:0%
+180 degrees that's a perfectly
+reasonable thing to do so it's not like
+
+ align:start position:0%
+reasonable thing to do so it's not like
+ 
+
+ align:start position:0%
+reasonable thing to do so it's not like
+we want to exclude that because it's not
+
+ align:start position:0%
+we want to exclude that because it's not
+ 
+
+ align:start position:0%
+we want to exclude that because it's not
+a reasonable thing to do so that is a
+
+ align:start position:0%
+a reasonable thing to do so that is a
+ 
+
+ align:start position:0%
+a reasonable thing to do so that is a
+problem and it's very similar to you
+
+ align:start position:0%
+problem and it's very similar to you
+ 
+
+ align:start position:0%
+problem and it's very similar to you
+know y equals mx plus c when when the
+
+ align:start position:0%
+know y equals mx plus c when when the
+ 
+
+ align:start position:0%
+know y equals mx plus c when when the
+line happens to be perpendicular up
+
+ align:start position:0%
+line happens to be perpendicular up
+ 
+
+ align:start position:0%
+line happens to be perpendicular up
+parallel to the y axis
+
+ align:start position:0%
+parallel to the y axis
+ 
+
+ align:start position:0%
+parallel to the y axis
+then we have euler angles
+
+ align:start position:0%
+then we have euler angles
+ 
+
+ align:start position:0%
+then we have euler angles
+and there's a classic uh
+
+ align:start position:0%
+and there's a classic uh
+ 
+
+ align:start position:0%
+and there's a classic uh
+text in mechanical engineering by by
+
+ align:start position:0%
+text in mechanical engineering by by
+ 
+
+ align:start position:0%
+text in mechanical engineering by by
+gold
+
+ align:start position:0%
+gold
+ 
+
+ align:start position:0%
+gold
+uh which explains about euler angles
+
+ align:start position:0%
+uh which explains about euler angles
+ 
+
+ align:start position:0%
+uh which explains about euler angles
+basically you know you rotate about x
+
+ align:start position:0%
+basically you know you rotate about x
+ 
+
+ align:start position:0%
+basically you know you rotate about x
+you rotate about y rotate about z
+
+ align:start position:0%
+you rotate about y rotate about z
+ 
+
+ align:start position:0%
+you rotate about y rotate about z
+if you're in an airplane
+
+ align:start position:0%
+if you're in an airplane
+ 
+
+ align:start position:0%
+if you're in an airplane
+you have roll which is rotation about
+
+ align:start position:0%
+you have roll which is rotation about
+ 
+
+ align:start position:0%
+you have roll which is rotation about
+the axis length long axis of the plane
+
+ align:start position:0%
+the axis length long axis of the plane
+ 
+
+ align:start position:0%
+the axis length long axis of the plane
+then you have pitch which is
+
+ align:start position:0%
+then you have pitch which is
+ 
+
+ align:start position:0%
+then you have pitch which is
+going up or down and then you have your
+
+ align:start position:0%
+going up or down and then you have your
+ 
+
+ align:start position:0%
+going up or down and then you have your
+which is going left and right
+
+ align:start position:0%
+which is going left and right
+ 
+
+ align:start position:0%
+which is going left and right
+so it's
+
+ align:start position:0%
+so it's
+ 
+
+ align:start position:0%
+so it's
+very convenient to think about that but
+
+ align:start position:0%
+very convenient to think about that but
+ 
+
+ align:start position:0%
+very convenient to think about that but
+as you know
+
+ align:start position:0%
+as you know
+ 
+
+ align:start position:0%
+as you know
+the result will depend on the order so
+
+ align:start position:0%
+the result will depend on the order so
+ 
+
+ align:start position:0%
+the result will depend on the order so
+yeah if you have very small angles of
+
+ align:start position:0%
+yeah if you have very small angles of
+ 
+
+ align:start position:0%
+yeah if you have very small angles of
+roll pitch and yaw which is a
+
+ align:start position:0%
+roll pitch and yaw which is a
+ 
+
+ align:start position:0%
+roll pitch and yaw which is a
+comfortable airplane flight
+
+ align:start position:0%
+comfortable airplane flight
+ 
+
+ align:start position:0%
+comfortable airplane flight
+it probably doesn't matter a lot because
+
+ align:start position:0%
+it probably doesn't matter a lot because
+ 
+
+ align:start position:0%
+it probably doesn't matter a lot because
+you get pretty much the same result if
+
+ align:start position:0%
+you get pretty much the same result if
+ 
+
+ align:start position:0%
+you get pretty much the same result if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+compose them in different orders but if
+
+ align:start position:0%
+compose them in different orders but if
+ 
+
+ align:start position:0%
+compose them in different orders but if
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+large angles like 90 degrees you know
+
+ align:start position:0%
+large angles like 90 degrees you know
+ 
+
+ align:start position:0%
+large angles like 90 degrees you know
+it's definitely not going to work
+
+ align:start position:0%
+it's definitely not going to work
+ 
+
+ align:start position:0%
+it's definitely not going to work
+so that means if you define euler angles
+
+ align:start position:0%
+so that means if you define euler angles
+ 
+
+ align:start position:0%
+so that means if you define euler angles
+you've got to do several things one of
+
+ align:start position:0%
+you've got to do several things one of
+ 
+
+ align:start position:0%
+you've got to do several things one of
+them is you have to define the order of
+
+ align:start position:0%
+them is you have to define the order of
+ 
+
+ align:start position:0%
+them is you have to define the order of
+operations you know does the x-axis come
+
+ align:start position:0%
+operations you know does the x-axis come
+ 
+
+ align:start position:0%
+operations you know does the x-axis come
+first and so on
+
+ align:start position:0%
+first and so on
+ 
+
+ align:start position:0%
+first and so on
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+other rotations about the new axes after
+
+ align:start position:0%
+other rotations about the new axes after
+ 
+
+ align:start position:0%
+other rotations about the new axes after
+you rotate or about the original axes
+
+ align:start position:0%
+you rotate or about the original axes
+ 
+
+ align:start position:0%
+you rotate or about the original axes
+anyway as a result of this as google
+
+ align:start position:0%
+anyway as a result of this as google
+ 
+
+ align:start position:0%
+anyway as a result of this as google
+points out there are 24 different
+
+ align:start position:0%
+points out there are 24 different
+ 
+
+ align:start position:0%
+points out there are 24 different
+definitions for euler angle and there
+
+ align:start position:0%
+definitions for euler angle and there
+ 
+
+ align:start position:0%
+definitions for euler angle and there
+hasn't been an international meeting to
+
+ align:start position:0%
+hasn't been an international meeting to
+ 
+
+ align:start position:0%
+hasn't been an international meeting to
+say you know thou shalt use this one so
+
+ align:start position:0%
+say you know thou shalt use this one so
+ 
+
+ align:start position:0%
+say you know thou shalt use this one so
+it's it's pretty confusing
+
+ align:start position:0%
+it's it's pretty confusing
+ 
+
+ align:start position:0%
+it's it's pretty confusing
+then we have of course orthonormal
+
+ align:start position:0%
+then we have of course orthonormal
+ 
+
+ align:start position:0%
+then we have of course orthonormal
+matrices which i'm sure you're all very
+
+ align:start position:0%
+matrices which i'm sure you're all very
+ 
+
+ align:start position:0%
+matrices which i'm sure you're all very
+familiar with and they have these two
+
+ align:start position:0%
+familiar with and they have these two
+ 
+
+ align:start position:0%
+familiar with and they have these two
+constraints on them
+
+ align:start position:0%
+constraints on them
+ 
+
+ align:start position:0%
+constraints on them
+and then this one is a kind of exotic
+
+ align:start position:0%
+and then this one is a kind of exotic
+ 
+
+ align:start position:0%
+and then this one is a kind of exotic
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+represents a rotation matrix in an
+
+ align:start position:0%
+represents a rotation matrix in an
+ 
+
+ align:start position:0%
+represents a rotation matrix in an
+exponential form so what does this mean
+
+ align:start position:0%
+exponential form so what does this mean
+ 
+
+ align:start position:0%
+exponential form so what does this mean
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+here this capital omega is that three by
+
+ align:start position:0%
+here this capital omega is that three by
+ 
+
+ align:start position:0%
+here this capital omega is that three by
+three skew symmetric matrix that you get
+
+ align:start position:0%
+three skew symmetric matrix that you get
+ 
+
+ align:start position:0%
+three skew symmetric matrix that you get
+for cross product
+
+ align:start position:0%
+for cross product
+ 
+
+ align:start position:0%
+for cross product
+and so what does it mean to have
+
+ align:start position:0%
+and so what does it mean to have
+ 
+
+ align:start position:0%
+and so what does it mean to have
+exponential with a matrix in the
+
+ align:start position:0%
+exponential with a matrix in the
+ 
+
+ align:start position:0%
+exponential with a matrix in the
+exponent well you just use the formula
+
+ align:start position:0%
+exponent well you just use the formula
+ 
+
+ align:start position:0%
+exponent well you just use the formula
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+e to the x except now x is the matrix
+
+ align:start position:0%
+e to the x except now x is the matrix
+ 
+
+ align:start position:0%
+e to the x except now x is the matrix
+instead of uh scalar so you're going to
+
+ align:start position:0%
+instead of uh scalar so you're going to
+ 
+
+ align:start position:0%
+instead of uh scalar so you're going to
+end up with you know 1 plus
+
+ align:start position:0%
+end up with you know 1 plus
+ 
+
+ align:start position:0%
+end up with you know 1 plus
+x plus
+
+ align:start position:0%
+x plus
+ 
+
+ align:start position:0%
+x plus
+1 half x squared and so on where x now
+
+ align:start position:0%
+1 half x squared and so on where x now
+ 
+
+ align:start position:0%
+1 half x squared and so on where x now
+is a matrix so you can make this work
+
+ align:start position:0%
+is a matrix so you can make this work
+ 
+
+ align:start position:0%
+is a matrix so you can make this work
+but we won't uh pursue this it's
+
+ align:start position:0%
+but we won't uh pursue this it's
+ 
+
+ align:start position:0%
+but we won't uh pursue this it's
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the and the others so here's another one
+
+ align:start position:0%
+the and the others so here's another one
+ 
+
+ align:start position:0%
+the and the others so here's another one
+uh stereography
+
+ align:start position:0%
+uh stereography
+ 
+
+ align:start position:0%
+uh stereography
+so there are lots of projections of the
+
+ align:start position:0%
+so there are lots of projections of the
+ 
+
+ align:start position:0%
+so there are lots of projections of the
+sphere and you know there's a whole
+
+ align:start position:0%
+sphere and you know there's a whole
+ 
+
+ align:start position:0%
+sphere and you know there's a whole
+cottage industry dating back hundreds of
+
+ align:start position:0%
+cottage industry dating back hundreds of
+ 
+
+ align:start position:0%
+cottage industry dating back hundreds of
+years because people found it necessary
+
+ align:start position:0%
+years because people found it necessary
+ 
+
+ align:start position:0%
+years because people found it necessary
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+take the spherical or almost spherical
+
+ align:start position:0%
+take the spherical or almost spherical
+ 
+
+ align:start position:0%
+take the spherical or almost spherical
+earth and map it onto a plane so they
+
+ align:start position:0%
+earth and map it onto a plane so they
+ 
+
+ align:start position:0%
+earth and map it onto a plane so they
+could sell maps and so there are lots of
+
+ align:start position:0%
+could sell maps and so there are lots of
+ 
+
+ align:start position:0%
+could sell maps and so there are lots of
+these one of them
+
+ align:start position:0%
+these one of them
+ 
+
+ align:start position:0%
+these one of them
+is conformal that is it preserves angles
+
+ align:start position:0%
+is conformal that is it preserves angles
+ 
+
+ align:start position:0%
+is conformal that is it preserves angles
+and uh it's called stereography
+
+ align:start position:0%
+and uh it's called stereography
+ 
+
+ align:start position:0%
+and uh it's called stereography
+and as we said a rotation of a sphere
+
+ align:start position:0%
+and as we said a rotation of a sphere
+ 
+
+ align:start position:0%
+and as we said a rotation of a sphere
+induces rotation of the space so uh we
+
+ align:start position:0%
+induces rotation of the space so uh we
+ 
+
+ align:start position:0%
+induces rotation of the space so uh we
+can take a sphere map it onto the plane
+
+ align:start position:0%
+can take a sphere map it onto the plane
+ 
+
+ align:start position:0%
+can take a sphere map it onto the plane
+then mush things around in the plane and
+
+ align:start position:0%
+then mush things around in the plane and
+ 
+
+ align:start position:0%
+then mush things around in the plane and
+map them back onto the sphere
+
+ align:start position:0%
+map them back onto the sphere
+ 
+
+ align:start position:0%
+map them back onto the sphere
+and if we mush things around just the
+
+ align:start position:0%
+and if we mush things around just the
+ 
+
+ align:start position:0%
+and if we mush things around just the
+right way in the plane
+
+ align:start position:0%
+right way in the plane
+ 
+
+ align:start position:0%
+right way in the plane
+uh then we actually have induced the
+
+ align:start position:0%
+uh then we actually have induced the
+ 
+
+ align:start position:0%
+uh then we actually have induced the
+rotation on the sphere
+
+ align:start position:0%
+rotation on the sphere
+ 
+
+ align:start position:0%
+rotation on the sphere
+we'll look at a picture of that again
+
+ align:start position:0%
+we'll look at a picture of that again
+ 
+
+ align:start position:0%
+we'll look at a picture of that again
+we're not going to use that but it's
+
+ align:start position:0%
+we're not going to use that but it's
+ 
+
+ align:start position:0%
+we're not going to use that but it's
+kind of amusing
+
+ align:start position:0%
+kind of amusing
+ 
+
+ align:start position:0%
+kind of amusing
+the thing you do in the plane is to
+
+ align:start position:0%
+the thing you do in the plane is to
+ 
+
+ align:start position:0%
+the thing you do in the plane is to
+treat the plane as a complex plane and
+
+ align:start position:0%
+treat the plane as a complex plane and
+ 
+
+ align:start position:0%
+treat the plane as a complex plane and
+do some
+
+ align:start position:0%
+do some
+ 
+
+ align:start position:0%
+do some
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+homogeneous transformation on that
+
+ align:start position:0%
+homogeneous transformation on that
+ 
+
+ align:start position:0%
+homogeneous transformation on that
+and then of course physicists you know
+
+ align:start position:0%
+and then of course physicists you know
+ 
+
+ align:start position:0%
+and then of course physicists you know
+have to invent their own stuff
+
+ align:start position:0%
+have to invent their own stuff
+ 
+
+ align:start position:0%
+have to invent their own stuff
+so there's a type of two by two complex
+
+ align:start position:0%
+so there's a type of two by two complex
+ 
+
+ align:start position:0%
+so there's a type of two by two complex
+matrix that can be used to represent
+
+ align:start position:0%
+matrix that can be used to represent
+ 
+
+ align:start position:0%
+matrix that can be used to represent
+rotation that paulie came up with
+
+ align:start position:0%
+rotation that paulie came up with
+ 
+
+ align:start position:0%
+rotation that paulie came up with
+the same man who's famous for saying
+
+ align:start position:0%
+the same man who's famous for saying
+ 
+
+ align:start position:0%
+the same man who's famous for saying
+you know that paper isn't even wrong
+
+ align:start position:0%
+you know that paper isn't even wrong
+ 
+
+ align:start position:0%
+you know that paper isn't even wrong
+as a criticism of one of his colleagues
+
+ align:start position:0%
+as a criticism of one of his colleagues
+ 
+
+ align:start position:0%
+as a criticism of one of his colleagues
+so uh two by two complex numbers that
+
+ align:start position:0%
+so uh two by two complex numbers that
+ 
+
+ align:start position:0%
+so uh two by two complex numbers that
+sounds like eight degrees of freedom
+
+ align:start position:0%
+sounds like eight degrees of freedom
+ 
+
+ align:start position:0%
+sounds like eight degrees of freedom
+uh well they're not just any they have
+
+ align:start position:0%
+uh well they're not just any they have
+ 
+
+ align:start position:0%
+uh well they're not just any they have
+to be hermitian
+
+ align:start position:0%
+to be hermitian
+ 
+
+ align:start position:0%
+to be hermitian
+and they have to be unitary so it turns
+
+ align:start position:0%
+and they have to be unitary so it turns
+ 
+
+ align:start position:0%
+and they have to be unitary so it turns
+out that after you do that the only
+
+ align:start position:0%
+out that after you do that the only
+ 
+
+ align:start position:0%
+out that after you do that the only
+three degrees of freedom left
+
+ align:start position:0%
+three degrees of freedom left
+ 
+
+ align:start position:0%
+three degrees of freedom left
+then we get the euler parameters
+
+ align:start position:0%
+then we get the euler parameters
+ 
+
+ align:start position:0%
+then we get the euler parameters
+sometimes also called
+
+ align:start position:0%
+sometimes also called
+ 
+
+ align:start position:0%
+sometimes also called
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+gonzales parameters rodriguez parameters
+
+ align:start position:0%
+gonzales parameters rodriguez parameters
+ 
+
+ align:start position:0%
+gonzales parameters rodriguez parameters
+excuse me
+
+ align:start position:0%
+excuse me
+ 
+
+ align:start position:0%
+excuse me
+and then we get to unit quaternions now
+
+ align:start position:0%
+and then we get to unit quaternions now
+ 
+
+ align:start position:0%
+and then we get to unit quaternions now
+of course there's a relation between all
+
+ align:start position:0%
+of course there's a relation between all
+ 
+
+ align:start position:0%
+of course there's a relation between all
+of them and in fact uh
+
+ align:start position:0%
+of them and in fact uh
+ 
+
+ align:start position:0%
+of them and in fact uh
+it's important to be able to convert
+
+ align:start position:0%
+it's important to be able to convert
+ 
+
+ align:start position:0%
+it's important to be able to convert
+between them
+
+ align:start position:0%
+between them
+ 
+
+ align:start position:0%
+between them
+and uh we'll do some of that and it's a
+
+ align:start position:0%
+and uh we'll do some of that and it's a
+ 
+
+ align:start position:0%
+and uh we'll do some of that and it's a
+little bit like
+
+ align:start position:0%
+little bit like
+ 
+
+ align:start position:0%
+little bit like
+many other problems where
+
+ align:start position:0%
+many other problems where
+ 
+
+ align:start position:0%
+many other problems where
+you're trying to solve something and it
+
+ align:start position:0%
+you're trying to solve something and it
+ 
+
+ align:start position:0%
+you're trying to solve something and it
+turns out if you have the right
+
+ align:start position:0%
+turns out if you have the right
+ 
+
+ align:start position:0%
+turns out if you have the right
+representation
+
+ align:start position:0%
+representation
+ 
+
+ align:start position:0%
+representation
+the answer is easy and so often the
+
+ align:start position:0%
+the answer is easy and so often the
+ 
+
+ align:start position:0%
+the answer is easy and so often the
+problem then ends up being the
+
+ align:start position:0%
+problem then ends up being the
+ 
+
+ align:start position:0%
+problem then ends up being the
+conversion and so then you find that
+
+ align:start position:0%
+conversion and so then you find that
+ 
+
+ align:start position:0%
+conversion and so then you find that
+well the conversion is complex just like
+
+ align:start position:0%
+well the conversion is complex just like
+ 
+
+ align:start position:0%
+well the conversion is complex just like
+you know in the trivial case we could
+
+ align:start position:0%
+you know in the trivial case we could
+ 
+
+ align:start position:0%
+you know in the trivial case we could
+have polar coordinates versus cartesian
+
+ align:start position:0%
+have polar coordinates versus cartesian
+ 
+
+ align:start position:0%
+have polar coordinates versus cartesian
+coordinates and maybe the answer in the
+
+ align:start position:0%
+coordinates and maybe the answer in the
+ 
+
+ align:start position:0%
+coordinates and maybe the answer in the
+car in polar coordinates is trivial but
+
+ align:start position:0%
+car in polar coordinates is trivial but
+ 
+
+ align:start position:0%
+car in polar coordinates is trivial but
+it's not in cartesian coordinates and
+
+ align:start position:0%
+it's not in cartesian coordinates and
+ 
+
+ align:start position:0%
+it's not in cartesian coordinates and
+then you're left with a conversion well
+
+ align:start position:0%
+then you're left with a conversion well
+ 
+
+ align:start position:0%
+then you're left with a conversion well
+in that case the conversion's not too
+
+ align:start position:0%
+in that case the conversion's not too
+ 
+
+ align:start position:0%
+in that case the conversion's not too
+hard but
+
+ align:start position:0%
+hard but
+ 
+
+ align:start position:0%
+hard but
+here sometimes it is
+
+ align:start position:0%
+here sometimes it is
+ 
+
+ align:start position:0%
+here sometimes it is
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+uh let's start with that this is
+
+ align:start position:0%
+uh let's start with that this is
+ 
+
+ align:start position:0%
+uh let's start with that this is
+rodriguez rodriguez was a
+
+ align:start position:0%
+rodriguez rodriguez was a
+ 
+
+ align:start position:0%
+rodriguez rodriguez was a
+banker
+
+ align:start position:0%
+banker
+ 
+
+ align:start position:0%
+banker
+in paris and apparently he found banking
+
+ align:start position:0%
+in paris and apparently he found banking
+ 
+
+ align:start position:0%
+in paris and apparently he found banking
+a fairly boring profession because he
+
+ align:start position:0%
+a fairly boring profession because he
+ 
+
+ align:start position:0%
+a fairly boring profession because he
+spent his nights doing math and so this
+
+ align:start position:0%
+spent his nights doing math and so this
+ 
+
+ align:start position:0%
+spent his nights doing math and so this
+is one of his results basically um the
+
+ align:start position:0%
+is one of his results basically um the
+ 
+
+ align:start position:0%
+is one of his results basically um the
+operations we're going to want to do uh
+
+ align:start position:0%
+operations we're going to want to do uh
+ 
+
+ align:start position:0%
+operations we're going to want to do uh
+two one operation is take a vector and
+
+ align:start position:0%
+two one operation is take a vector and
+ 
+
+ align:start position:0%
+two one operation is take a vector and
+rotate it or find out what that vector
+
+ align:start position:0%
+rotate it or find out what that vector
+ 
+
+ align:start position:0%
+rotate it or find out what that vector
+is in a rotated coordinate system
+
+ align:start position:0%
+is in a rotated coordinate system
+ 
+
+ align:start position:0%
+is in a rotated coordinate system
+equivalent problem the other one is
+
+ align:start position:0%
+equivalent problem the other one is
+ 
+
+ align:start position:0%
+equivalent problem the other one is
+composing rotations we've rotated a
+
+ align:start position:0%
+composing rotations we've rotated a
+ 
+
+ align:start position:0%
+composing rotations we've rotated a
+little bit in this around this axis now
+
+ align:start position:0%
+little bit in this around this axis now
+ 
+
+ align:start position:0%
+little bit in this around this axis now
+we're going to rotate about another axis
+
+ align:start position:0%
+we're going to rotate about another axis
+ 
+
+ align:start position:0%
+we're going to rotate about another axis
+what is the overall result and that
+
+ align:start position:0%
+what is the overall result and that
+ 
+
+ align:start position:0%
+what is the overall result and that
+turns out to be you know non-trivial so
+
+ align:start position:0%
+turns out to be you know non-trivial so
+ 
+
+ align:start position:0%
+turns out to be you know non-trivial so
+this here
+
+ align:start position:0%
+this here
+ 
+
+ align:start position:0%
+this here
+is addressing that first problem so we
+
+ align:start position:0%
+is addressing that first problem so we
+ 
+
+ align:start position:0%
+is addressing that first problem so we
+have a vector r
+
+ align:start position:0%
+have a vector r
+ 
+
+ align:start position:0%
+have a vector r
+and we have an axis of rotation that's
+
+ align:start position:0%
+and we have an axis of rotation that's
+ 
+
+ align:start position:0%
+and we have an axis of rotation that's
+uh here you know vertical
+
+ align:start position:0%
+uh here you know vertical
+ 
+
+ align:start position:0%
+uh here you know vertical
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we're going to rotate through an angle
+
+ align:start position:0%
+we're going to rotate through an angle
+ 
+
+ align:start position:0%
+we're going to rotate through an angle
+theta about that axis and that will take
+
+ align:start position:0%
+theta about that axis and that will take
+ 
+
+ align:start position:0%
+theta about that axis and that will take
+us to a new position
+
+ align:start position:0%
+us to a new position
+ 
+
+ align:start position:0%
+us to a new position
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+prime and the question is you know how
+
+ align:start position:0%
+prime and the question is you know how
+ 
+
+ align:start position:0%
+prime and the question is you know how
+do you compute r prime
+
+ align:start position:0%
+do you compute r prime
+ 
+
+ align:start position:0%
+do you compute r prime
+well if we first convert it to a 2d
+
+ align:start position:0%
+well if we first convert it to a 2d
+ 
+
+ align:start position:0%
+well if we first convert it to a 2d
+problem you know in this plane indicated
+
+ align:start position:0%
+problem you know in this plane indicated
+ 
+
+ align:start position:0%
+problem you know in this plane indicated
+by this ellipse then it's very easy
+
+ align:start position:0%
+by this ellipse then it's very easy
+ 
+
+ align:start position:0%
+by this ellipse then it's very easy
+because we just take this vector
+
+ align:start position:0%
+because we just take this vector
+ 
+
+ align:start position:0%
+because we just take this vector
+and that vector and combine them in a
+
+ align:start position:0%
+and that vector and combine them in a
+ 
+
+ align:start position:0%
+and that vector and combine them in a
+weighted fashion
+
+ align:start position:0%
+weighted fashion
+ 
+
+ align:start position:0%
+weighted fashion
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+dotted vector is
+
+ align:start position:0%
+dotted vector is
+ 
+
+ align:start position:0%
+dotted vector is
+this vector times cosine theta plus this
+
+ align:start position:0%
+this vector times cosine theta plus this
+ 
+
+ align:start position:0%
+this vector times cosine theta plus this
+vector times sine theta
+
+ align:start position:0%
+vector times sine theta
+ 
+
+ align:start position:0%
+vector times sine theta
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you can see how when theta is zero the
+
+ align:start position:0%
+you can see how when theta is zero the
+ 
+
+ align:start position:0%
+you can see how when theta is zero the
+dotted vector will be equal to this one
+
+ align:start position:0%
+dotted vector will be equal to this one
+ 
+
+ align:start position:0%
+dotted vector will be equal to this one
+and when theta is equal to one uh pi
+
+ align:start position:0%
+and when theta is equal to one uh pi
+ 
+
+ align:start position:0%
+and when theta is equal to one uh pi
+over two it'll be equal to this vector
+
+ align:start position:0%
+over two it'll be equal to this vector
+ 
+
+ align:start position:0%
+over two it'll be equal to this vector
+and all the way along it retains its its
+
+ align:start position:0%
+and all the way along it retains its its
+ 
+
+ align:start position:0%
+and all the way along it retains its its
+length and so on so in 2d rotation as we
+
+ align:start position:0%
+length and so on so in 2d rotation as we
+ 
+
+ align:start position:0%
+length and so on so in 2d rotation as we
+know is very simple then and like
+
+ align:start position:0%
+know is very simple then and like
+ 
+
+ align:start position:0%
+know is very simple then and like
+mathematicians want to often do we
+
+ align:start position:0%
+mathematicians want to often do we
+ 
+
+ align:start position:0%
+mathematicians want to often do we
+reduce a complicated problem to a
+
+ align:start position:0%
+reduce a complicated problem to a
+ 
+
+ align:start position:0%
+reduce a complicated problem to a
+simpler one we already know how to solve
+
+ align:start position:0%
+simpler one we already know how to solve
+ 
+
+ align:start position:0%
+simpler one we already know how to solve
+but that's in this plane and so we first
+
+ align:start position:0%
+but that's in this plane and so we first
+ 
+
+ align:start position:0%
+but that's in this plane and so we first
+have to figure out what what these two
+
+ align:start position:0%
+have to figure out what what these two
+ 
+
+ align:start position:0%
+have to figure out what what these two
+vectors are that we are combining using
+
+ align:start position:0%
+vectors are that we are combining using
+ 
+
+ align:start position:0%
+vectors are that we are combining using
+cosine and sine and so first of all this
+
+ align:start position:0%
+cosine and sine and so first of all this
+ 
+
+ align:start position:0%
+cosine and sine and so first of all this
+one here so how do we get that one well
+
+ align:start position:0%
+one here so how do we get that one well
+ 
+
+ align:start position:0%
+one here so how do we get that one well
+we take r and we subtract out
+
+ align:start position:0%
+we take r and we subtract out
+ 
+
+ align:start position:0%
+we take r and we subtract out
+this vector
+
+ align:start position:0%
+this vector
+ 
+
+ align:start position:0%
+this vector
+right and the difference is going to be
+
+ align:start position:0%
+right and the difference is going to be
+ 
+
+ align:start position:0%
+right and the difference is going to be
+this vector here
+
+ align:start position:0%
+this vector here
+ 
+
+ align:start position:0%
+this vector here
+well um that means that we need to know
+
+ align:start position:0%
+well um that means that we need to know
+ 
+
+ align:start position:0%
+well um that means that we need to know
+what this vector is well that's just
+
+ align:start position:0%
+what this vector is well that's just
+ 
+
+ align:start position:0%
+what this vector is well that's just
+projecting r onto omega and since omega
+
+ align:start position:0%
+projecting r onto omega and since omega
+ 
+
+ align:start position:0%
+projecting r onto omega and since omega
+is the unit vector it's very easy
+
+ align:start position:0%
+is the unit vector it's very easy
+ 
+
+ align:start position:0%
+is the unit vector it's very easy
+there's a formula
+
+ align:start position:0%
+there's a formula
+ 
+
+ align:start position:0%
+there's a formula
+and so therefore this vector is r minus
+
+ align:start position:0%
+and so therefore this vector is r minus
+ 
+
+ align:start position:0%
+and so therefore this vector is r minus
+that thing
+
+ align:start position:0%
+that thing
+ 
+
+ align:start position:0%
+that thing
+and then finally we need to know what
+
+ align:start position:0%
+and then finally we need to know what
+ 
+
+ align:start position:0%
+and then finally we need to know what
+this vector is and basically that vector
+
+ align:start position:0%
+this vector is and basically that vector
+ 
+
+ align:start position:0%
+this vector is and basically that vector
+has to be perpendicular to omega
+
+ align:start position:0%
+has to be perpendicular to omega
+ 
+
+ align:start position:0%
+has to be perpendicular to omega
+and it has to be perpendicular to this
+
+ align:start position:0%
+and it has to be perpendicular to this
+ 
+
+ align:start position:0%
+and it has to be perpendicular to this
+because in this plane it's pi over two
+
+ align:start position:0%
+because in this plane it's pi over two
+ 
+
+ align:start position:0%
+because in this plane it's pi over two
+away from that vector right so by taking
+
+ align:start position:0%
+away from that vector right so by taking
+ 
+
+ align:start position:0%
+away from that vector right so by taking
+the cross product of uh of um uh
+
+ align:start position:0%
+the cross product of uh of um uh
+ 
+
+ align:start position:0%
+the cross product of uh of um uh
+let's see this this thing here with this
+
+ align:start position:0%
+let's see this this thing here with this
+ 
+
+ align:start position:0%
+let's see this this thing here with this
+thing here we end up with after
+
+ align:start position:0%
+thing here we end up with after
+ 
+
+ align:start position:0%
+thing here we end up with after
+simplification just omega cross r and it
+
+ align:start position:0%
+simplification just omega cross r and it
+ 
+
+ align:start position:0%
+simplification just omega cross r and it
+makes sense because it's going to be
+
+ align:start position:0%
+makes sense because it's going to be
+ 
+
+ align:start position:0%
+makes sense because it's going to be
+perpendicular to r and it's going to be
+
+ align:start position:0%
+perpendicular to r and it's going to be
+ 
+
+ align:start position:0%
+perpendicular to r and it's going to be
+perpendicular to omega anyway you put
+
+ align:start position:0%
+perpendicular to omega anyway you put
+ 
+
+ align:start position:0%
+perpendicular to omega anyway you put
+all of those things together you get
+
+ align:start position:0%
+all of those things together you get
+ 
+
+ align:start position:0%
+all of those things together you get
+this formula so r prime the the vector
+
+ align:start position:0%
+this formula so r prime the the vector
+ 
+
+ align:start position:0%
+this formula so r prime the the vector
+after rotation is cosine theta r the
+
+ align:start position:0%
+after rotation is cosine theta r the
+ 
+
+ align:start position:0%
+after rotation is cosine theta r the
+vector before rotation uh plus uh these
+
+ align:start position:0%
+vector before rotation uh plus uh these
+ 
+
+ align:start position:0%
+vector before rotation uh plus uh these
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+and you know you can see that rotation's
+
+ align:start position:0%
+and you know you can see that rotation's
+ 
+
+ align:start position:0%
+and you know you can see that rotation's
+not quite that trivial so
+
+ align:start position:0%
+not quite that trivial so
+ 
+
+ align:start position:0%
+not quite that trivial so
+anyway so uh we'll
+
+ align:start position:0%
+anyway so uh we'll
+ 
+
+ align:start position:0%
+anyway so uh we'll
+so axis and angle is a useful notation
+
+ align:start position:0%
+so axis and angle is a useful notation
+ 
+
+ align:start position:0%
+so axis and angle is a useful notation
+and it's often a good way to visualize
+
+ align:start position:0%
+and it's often a good way to visualize
+ 
+
+ align:start position:0%
+and it's often a good way to visualize
+things you know it's easy to say okay
+
+ align:start position:0%
+things you know it's easy to say okay
+ 
+
+ align:start position:0%
+things you know it's easy to say okay
+we're rotating about the x-axis through
+
+ align:start position:0%
+we're rotating about the x-axis through
+ 
+
+ align:start position:0%
+we're rotating about the x-axis through
+90 degrees easy to understand what it is
+
+ align:start position:0%
+90 degrees easy to understand what it is
+ 
+
+ align:start position:0%
+90 degrees easy to understand what it is
+what's the disadvantage the disadvantage
+
+ align:start position:0%
+what's the disadvantage the disadvantage
+ 
+
+ align:start position:0%
+what's the disadvantage the disadvantage
+is if it composition if you have two
+
+ align:start position:0%
+is if it composition if you have two
+ 
+
+ align:start position:0%
+is if it composition if you have two
+rotations given as axes and angle
+
+ align:start position:0%
+rotations given as axes and angle
+ 
+
+ align:start position:0%
+rotations given as axes and angle
+how do you combine them into a single we
+
+ align:start position:0%
+how do you combine them into a single we
+ 
+
+ align:start position:0%
+how do you combine them into a single we
+know by euler's theorem there's a single
+
+ align:start position:0%
+know by euler's theorem there's a single
+ 
+
+ align:start position:0%
+know by euler's theorem there's a single
+rotation that uh represents the
+
+ align:start position:0%
+rotation that uh represents the
+ 
+
+ align:start position:0%
+rotation that uh represents the
+combination
+
+ align:start position:0%
+combination
+ 
+
+ align:start position:0%
+combination
+but how do you combine them well it
+
+ align:start position:0%
+but how do you combine them well it
+ 
+
+ align:start position:0%
+but how do you combine them well it
+turns out
+
+ align:start position:0%
+turns out
+ 
+
+ align:start position:0%
+turns out
+what i would do is convert both of these
+
+ align:start position:0%
+what i would do is convert both of these
+ 
+
+ align:start position:0%
+what i would do is convert both of these
+to some other form like
+
+ align:start position:0%
+to some other form like
+ 
+
+ align:start position:0%
+to some other form like
+orthonormal matrices multiply the normal
+
+ align:start position:0%
+orthonormal matrices multiply the normal
+ 
+
+ align:start position:0%
+orthonormal matrices multiply the normal
+matrices go back to this form so so
+
+ align:start position:0%
+matrices go back to this form so so
+ 
+
+ align:start position:0%
+matrices go back to this form so so
+that's a disadvantage there is no it's
+
+ align:start position:0%
+that's a disadvantage there is no it's
+ 
+
+ align:start position:0%
+that's a disadvantage there is no it's
+you can rotate vectors that's the one
+
+ align:start position:0%
+you can rotate vectors that's the one
+ 
+
+ align:start position:0%
+you can rotate vectors that's the one
+operation we want it's hard to do uh
+
+ align:start position:0%
+operation we want it's hard to do uh
+ 
+
+ align:start position:0%
+operation we want it's hard to do uh
+composition of rotation so
+
+ align:start position:0%
+composition of rotation so
+ 
+
+ align:start position:0%
+composition of rotation so
+uh okay well i will skip this this is
+
+ align:start position:0%
+uh okay well i will skip this this is
+ 
+
+ align:start position:0%
+uh okay well i will skip this this is
+the exponential
+
+ align:start position:0%
+the exponential
+ 
+
+ align:start position:0%
+the exponential
+the algebra view of things and
+
+ align:start position:0%
+the algebra view of things and
+ 
+
+ align:start position:0%
+the algebra view of things and
+that too let's forget that i just wanted
+
+ align:start position:0%
+that too let's forget that i just wanted
+ 
+
+ align:start position:0%
+that too let's forget that i just wanted
+to point uh
+
+ align:start position:0%
+to point uh
+ 
+
+ align:start position:0%
+to point uh
+this one which we mentioned
+
+ align:start position:0%
+this one which we mentioned
+ 
+
+ align:start position:0%
+this one which we mentioned
+so here the idea is that here's our
+
+ align:start position:0%
+so here the idea is that here's our
+ 
+
+ align:start position:0%
+so here the idea is that here's our
+sphere that we're going to rotate and we
+
+ align:start position:0%
+sphere that we're going to rotate and we
+ 
+
+ align:start position:0%
+sphere that we're going to rotate and we
+project it onto a plane which happens to
+
+ align:start position:0%
+project it onto a plane which happens to
+ 
+
+ align:start position:0%
+project it onto a plane which happens to
+be tangent at the north pole
+
+ align:start position:0%
+be tangent at the north pole
+ 
+
+ align:start position:0%
+be tangent at the north pole
+and this projection if your center of
+
+ align:start position:0%
+and this projection if your center of
+ 
+
+ align:start position:0%
+and this projection if your center of
+projection is the south pole so you go
+
+ align:start position:0%
+projection is the south pole so you go
+ 
+
+ align:start position:0%
+projection is the south pole so you go
+from the south pole to a point on the
+
+ align:start position:0%
+from the south pole to a point on the
+ 
+
+ align:start position:0%
+from the south pole to a point on the
+surface and that
+
+ align:start position:0%
+surface and that
+ 
+
+ align:start position:0%
+surface and that
+then extend that line until it hits that
+
+ align:start position:0%
+then extend that line until it hits that
+ 
+
+ align:start position:0%
+then extend that line until it hits that
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+and you'll see a couple of things one of
+
+ align:start position:0%
+and you'll see a couple of things one of
+ 
+
+ align:start position:0%
+and you'll see a couple of things one of
+them is you can map the whole sphere
+
+ align:start position:0%
+them is you can map the whole sphere
+ 
+
+ align:start position:0%
+them is you can map the whole sphere
+onto a plane
+
+ align:start position:0%
+onto a plane
+ 
+
+ align:start position:0%
+onto a plane
+well except the south pole right
+
+ align:start position:0%
+well except the south pole right
+ 
+
+ align:start position:0%
+well except the south pole right
+the other one you can see is
+
+ align:start position:0%
+the other one you can see is
+ 
+
+ align:start position:0%
+the other one you can see is
+areas are going to be distorted right
+
+ align:start position:0%
+areas are going to be distorted right
+ 
+
+ align:start position:0%
+areas are going to be distorted right
+because if we're dealing with
+
+ align:start position:0%
+because if we're dealing with
+ 
+
+ align:start position:0%
+because if we're dealing with
+say alaska up here it's going to be
+
+ align:start position:0%
+say alaska up here it's going to be
+ 
+
+ align:start position:0%
+say alaska up here it's going to be
+mapped onto the plane without much
+
+ align:start position:0%
+mapped onto the plane without much
+ 
+
+ align:start position:0%
+mapped onto the plane without much
+magnification but if we're looking at
+
+ align:start position:0%
+magnification but if we're looking at
+ 
+
+ align:start position:0%
+magnification but if we're looking at
+australia you know it's going to come
+
+ align:start position:0%
+australia you know it's going to come
+ 
+
+ align:start position:0%
+australia you know it's going to come
+out way over here it's going to be huge
+
+ align:start position:0%
+out way over here it's going to be huge
+ 
+
+ align:start position:0%
+out way over here it's going to be huge
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this particular map projection
+
+ align:start position:0%
+this particular map projection
+ 
+
+ align:start position:0%
+this particular map projection
+is actually
+
+ align:start position:0%
+is actually
+ 
+
+ align:start position:0%
+is actually
+used for the polar regions because most
+
+ align:start position:0%
+used for the polar regions because most
+ 
+
+ align:start position:0%
+used for the polar regions because most
+of the other map projections don't work
+
+ align:start position:0%
+of the other map projections don't work
+ 
+
+ align:start position:0%
+of the other map projections don't work
+very well there
+
+ align:start position:0%
+very well there
+ 
+
+ align:start position:0%
+very well there
+but it does have that feature and why is
+
+ align:start position:0%
+but it does have that feature and why is
+ 
+
+ align:start position:0%
+but it does have that feature and why is
+it liked so much well because it doesn't
+
+ align:start position:0%
+it liked so much well because it doesn't
+ 
+
+ align:start position:0%
+it liked so much well because it doesn't
+distort shapes
+
+ align:start position:0%
+distort shapes
+ 
+
+ align:start position:0%
+distort shapes
+so and it preserves angles most now all
+
+ align:start position:0%
+so and it preserves angles most now all
+ 
+
+ align:start position:0%
+so and it preserves angles most now all
+other projections have the property that
+
+ align:start position:0%
+other projections have the property that
+ 
+
+ align:start position:0%
+other projections have the property that
+they will distort shapes they will
+
+ align:start position:0%
+they will distort shapes they will
+ 
+
+ align:start position:0%
+they will distort shapes they will
+distort areas you have your choice you
+
+ align:start position:0%
+distort areas you have your choice you
+ 
+
+ align:start position:0%
+distort areas you have your choice you
+know you can pick
+
+ align:start position:0%
+know you can pick
+ 
+
+ align:start position:0%
+know you can pick
+projections that preserve area you can
+
+ align:start position:0%
+projections that preserve area you can
+ 
+
+ align:start position:0%
+projections that preserve area you can
+pick projections that preserve shape
+
+ align:start position:0%
+pick projections that preserve shape
+ 
+
+ align:start position:0%
+pick projections that preserve shape
+angles
+
+ align:start position:0%
+angles
+ 
+
+ align:start position:0%
+angles
+but you can't do both
+
+ align:start position:0%
+but you can't do both
+ 
+
+ align:start position:0%
+but you can't do both
+okay so uh we start off we take our
+
+ align:start position:0%
+okay so uh we start off we take our
+ 
+
+ align:start position:0%
+okay so uh we start off we take our
+sphere we project it onto this pla map
+
+ align:start position:0%
+sphere we project it onto this pla map
+ 
+
+ align:start position:0%
+sphere we project it onto this pla map
+this plane which is the complex plane
+
+ align:start position:0%
+this plane which is the complex plane
+ 
+
+ align:start position:0%
+this plane which is the complex plane
+then in that complex plane we do this
+
+ align:start position:0%
+then in that complex plane we do this
+ 
+
+ align:start position:0%
+then in that complex plane we do this
+operation so z is a complex variable
+
+ align:start position:0%
+operation so z is a complex variable
+ 
+
+ align:start position:0%
+operation so z is a complex variable
+coordinate in this plane
+
+ align:start position:0%
+coordinate in this plane
+ 
+
+ align:start position:0%
+coordinate in this plane
+and z prime is its new position
+
+ align:start position:0%
+and z prime is its new position
+ 
+
+ align:start position:0%
+and z prime is its new position
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a b c d are
+
+ align:start position:0%
+and a b c d are
+ 
+
+ align:start position:0%
+and a b c d are
+complex numbers
+
+ align:start position:0%
+complex numbers
+ 
+
+ align:start position:0%
+complex numbers
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+everything in that plane is going to get
+
+ align:start position:0%
+everything in that plane is going to get
+ 
+
+ align:start position:0%
+everything in that plane is going to get
+moved around and now we project it back
+
+ align:start position:0%
+moved around and now we project it back
+ 
+
+ align:start position:0%
+moved around and now we project it back
+on the sphere and the amazing thing is
+
+ align:start position:0%
+on the sphere and the amazing thing is
+ 
+
+ align:start position:0%
+on the sphere and the amazing thing is
+that the pattern on the sphere is just a
+
+ align:start position:0%
+that the pattern on the sphere is just a
+ 
+
+ align:start position:0%
+that the pattern on the sphere is just a
+rotated version of what it was before
+
+ align:start position:0%
+rotated version of what it was before
+ 
+
+ align:start position:0%
+rotated version of what it was before
+and therefore we can think of rotation
+
+ align:start position:0%
+and therefore we can think of rotation
+ 
+
+ align:start position:0%
+and therefore we can think of rotation
+or in three space
+
+ align:start position:0%
+or in three space
+ 
+
+ align:start position:0%
+or in three space
+instead in terms of some operation in
+
+ align:start position:0%
+instead in terms of some operation in
+ 
+
+ align:start position:0%
+instead in terms of some operation in
+the complex plane which is pretty
+
+ align:start position:0%
+the complex plane which is pretty
+ 
+
+ align:start position:0%
+the complex plane which is pretty
+amazing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's yet another representation
+
+ align:start position:0%
+so that's yet another representation
+ 
+
+ align:start position:0%
+so that's yet another representation
+okay so what are the desirable
+
+ align:start position:0%
+okay so what are the desirable
+ 
+
+ align:start position:0%
+okay so what are the desirable
+properties we already mentioned some of
+
+ align:start position:0%
+properties we already mentioned some of
+ 
+
+ align:start position:0%
+properties we already mentioned some of
+them we we need to be able to rotate
+
+ align:start position:0%
+them we we need to be able to rotate
+ 
+
+ align:start position:0%
+them we we need to be able to rotate
+vectors or equivalently rotate
+
+ align:start position:0%
+vectors or equivalently rotate
+ 
+
+ align:start position:0%
+vectors or equivalently rotate
+coordinate systems we but also we need
+
+ align:start position:0%
+coordinate systems we but also we need
+ 
+
+ align:start position:0%
+coordinate systems we but also we need
+to be able to compose rotations
+
+ align:start position:0%
+to be able to compose rotations
+ 
+
+ align:start position:0%
+to be able to compose rotations
+we would like to have an intuitive
+
+ align:start position:0%
+we would like to have an intuitive
+ 
+
+ align:start position:0%
+we would like to have an intuitive
+representation you know like axis and
+
+ align:start position:0%
+representation you know like axis and
+ 
+
+ align:start position:0%
+representation you know like axis and
+angle sort of intuitive it's easy to
+
+ align:start position:0%
+angle sort of intuitive it's easy to
+ 
+
+ align:start position:0%
+angle sort of intuitive it's easy to
+understand what that is whereas you look
+
+ align:start position:0%
+understand what that is whereas you look
+ 
+
+ align:start position:0%
+understand what that is whereas you look
+at a rotational matrix you look at the
+
+ align:start position:0%
+at a rotational matrix you look at the
+ 
+
+ align:start position:0%
+at a rotational matrix you look at the
+numbers you know
+
+ align:start position:0%
+numbers you know
+ 
+
+ align:start position:0%
+numbers you know
+what do they mean
+
+ align:start position:0%
+what do they mean
+ 
+
+ align:start position:0%
+what do they mean
+i don't know you you multiply a vector
+
+ align:start position:0%
+i don't know you you multiply a vector
+ 
+
+ align:start position:0%
+i don't know you you multiply a vector
+and see what happens but the numbers
+
+ align:start position:0%
+and see what happens but the numbers
+ 
+
+ align:start position:0%
+and see what happens but the numbers
+don't directly mean anything
+
+ align:start position:0%
+don't directly mean anything
+ 
+
+ align:start position:0%
+don't directly mean anything
+if you know a little bit more about it
+
+ align:start position:0%
+if you know a little bit more about it
+ 
+
+ align:start position:0%
+if you know a little bit more about it
+you say well if i look at the trace
+
+ align:start position:0%
+you say well if i look at the trace
+ 
+
+ align:start position:0%
+you say well if i look at the trace
+with the sum of diagonal elements it's i
+
+ align:start position:0%
+with the sum of diagonal elements it's i
+ 
+
+ align:start position:0%
+with the sum of diagonal elements it's i
+don't know
+
+ align:start position:0%
+don't know
+ 
+
+ align:start position:0%
+don't know
+2 times 1 minus the cosine of the angle
+
+ align:start position:0%
+2 times 1 minus the cosine of the angle
+ 
+
+ align:start position:0%
+2 times 1 minus the cosine of the angle
+of rotation but it's not very intuitive
+
+ align:start position:0%
+of rotation but it's not very intuitive
+ 
+
+ align:start position:0%
+of rotation but it's not very intuitive
+then is it redundant well orthonormal
+
+ align:start position:0%
+then is it redundant well orthonormal
+ 
+
+ align:start position:0%
+then is it redundant well orthonormal
+matrices are a prime example of
+
+ align:start position:0%
+matrices are a prime example of
+ 
+
+ align:start position:0%
+matrices are a prime example of
+something that's definitely not
+
+ align:start position:0%
+something that's definitely not
+ 
+
+ align:start position:0%
+something that's definitely not
+redundant
+
+ align:start position:0%
+redundant
+ 
+
+ align:start position:0%
+redundant
+because we have nine numbers to
+
+ align:start position:0%
+because we have nine numbers to
+ 
+
+ align:start position:0%
+because we have nine numbers to
+represent three things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's a very good point so so
+
+ align:start position:0%
+right that's a very good point so so
+ 
+
+ align:start position:0%
+right that's a very good point so so
+much for my story about it not being
+
+ align:start position:0%
+much for my story about it not being
+ 
+
+ align:start position:0%
+much for my story about it not being
+intuitive
+
+ align:start position:0%
+intuitive
+ 
+
+ align:start position:0%
+intuitive
+well if you think about rotating uh the
+
+ align:start position:0%
+well if you think about rotating uh the
+ 
+
+ align:start position:0%
+well if you think about rotating uh the
+x-axis
+
+ align:start position:0%
+x-axis
+ 
+
+ align:start position:0%
+x-axis
+ie one zero zero multiply the matrix by
+
+ align:start position:0%
+ie one zero zero multiply the matrix by
+ 
+
+ align:start position:0%
+ie one zero zero multiply the matrix by
+that you get the first column
+
+ align:start position:0%
+that you get the first column
+ 
+
+ align:start position:0%
+that you get the first column
+so uh as he's pointing out the first
+
+ align:start position:0%
+so uh as he's pointing out the first
+ 
+
+ align:start position:0%
+so uh as he's pointing out the first
+column is a significant vector it's what
+
+ align:start position:0%
+column is a significant vector it's what
+ 
+
+ align:start position:0%
+column is a significant vector it's what
+happens to the x-axis second column is
+
+ align:start position:0%
+happens to the x-axis second column is
+ 
+
+ align:start position:0%
+happens to the x-axis second column is
+what happens to the y-axis
+
+ align:start position:0%
+what happens to the y-axis
+ 
+
+ align:start position:0%
+what happens to the y-axis
+third column is what happens to the
+
+ align:start position:0%
+third column is what happens to the
+ 
+
+ align:start position:0%
+third column is what happens to the
+z-axis so
+
+ align:start position:0%
+z-axis so
+ 
+
+ align:start position:0%
+z-axis so
+you can understand the rotation matrix
+
+ align:start position:0%
+you can understand the rotation matrix
+ 
+
+ align:start position:0%
+you can understand the rotation matrix
+that way
+
+ align:start position:0%
+that way
+ 
+
+ align:start position:0%
+that way
+and similarly you can talk about the the
+
+ align:start position:0%
+and similarly you can talk about the the
+ 
+
+ align:start position:0%
+and similarly you can talk about the the
+rows going in the other direction
+
+ align:start position:0%
+rows going in the other direction
+ 
+
+ align:start position:0%
+rows going in the other direction
+but you know you wouldn't know the axis
+
+ align:start position:0%
+but you know you wouldn't know the axis
+ 
+
+ align:start position:0%
+but you know you wouldn't know the axis
+of rotation or the angle of rotation so
+
+ align:start position:0%
+of rotation or the angle of rotation so
+ 
+
+ align:start position:0%
+of rotation or the angle of rotation so
+but yes that's a good point okay
+
+ align:start position:0%
+but yes that's a good point okay
+ 
+
+ align:start position:0%
+but yes that's a good point okay
+redundant so let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis an angle well axis an angle is kind
+
+ align:start position:0%
+axis an angle well axis an angle is kind
+ 
+
+ align:start position:0%
+axis an angle well axis an angle is kind
+of redundant because if we have a vector
+
+ align:start position:0%
+of redundant because if we have a vector
+ 
+
+ align:start position:0%
+of redundant because if we have a vector
+it has three components plus an angle is
+
+ align:start position:0%
+it has three components plus an angle is
+ 
+
+ align:start position:0%
+it has three components plus an angle is
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+gibbs vector is not redundant because
+
+ align:start position:0%
+gibbs vector is not redundant because
+ 
+
+ align:start position:0%
+gibbs vector is not redundant because
+we've
+
+ align:start position:0%
+we've
+ 
+
+ align:start position:0%
+we've
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+multiplied the vector by the tangent of
+
+ align:start position:0%
+multiplied the vector by the tangent of
+ 
+
+ align:start position:0%
+multiplied the vector by the tangent of
+theta over two
+
+ align:start position:0%
+theta over two
+ 
+
+ align:start position:0%
+theta over two
+but we don't want singularities
+
+ align:start position:0%
+but we don't want singularities
+ 
+
+ align:start position:0%
+but we don't want singularities
+gibbs vector has a singularity so
+
+ align:start position:0%
+gibbs vector has a singularity so
+ 
+
+ align:start position:0%
+gibbs vector has a singularity so
+we'd also like it to be computationally
+
+ align:start position:0%
+we'd also like it to be computationally
+ 
+
+ align:start position:0%
+we'd also like it to be computationally
+efficient
+
+ align:start position:0%
+efficient
+ 
+
+ align:start position:0%
+efficient
+and we'll get into that a little bit and
+
+ align:start position:0%
+and we'll get into that a little bit and
+ 
+
+ align:start position:0%
+and we'll get into that a little bit and
+we want to be able to do lots of things
+
+ align:start position:0%
+we want to be able to do lots of things
+ 
+
+ align:start position:0%
+we want to be able to do lots of things
+for example interpolate orientation so
+
+ align:start position:0%
+for example interpolate orientation so
+ 
+
+ align:start position:0%
+for example interpolate orientation so
+in graphics
+
+ align:start position:0%
+in graphics
+ 
+
+ align:start position:0%
+in graphics
+we might often have
+
+ align:start position:0%
+we might often have
+ 
+
+ align:start position:0%
+we might often have
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+person performing some
+
+ align:start position:0%
+person performing some
+ 
+
+ align:start position:0%
+person performing some
+dance or action in the world
+
+ align:start position:0%
+dance or action in the world
+ 
+
+ align:start position:0%
+dance or action in the world
+and we would like the artist to only
+
+ align:start position:0%
+and we would like the artist to only
+ 
+
+ align:start position:0%
+and we would like the artist to only
+have to specify certain distinct points
+
+ align:start position:0%
+have to specify certain distinct points
+ 
+
+ align:start position:0%
+have to specify certain distinct points
+rather than you know every frame
+
+ align:start position:0%
+rather than you know every frame
+ 
+
+ align:start position:0%
+rather than you know every frame
+and so we'll need to interpolate well if
+
+ align:start position:0%
+and so we'll need to interpolate well if
+ 
+
+ align:start position:0%
+and so we'll need to interpolate well if
+that person is rotating how do we
+
+ align:start position:0%
+that person is rotating how do we
+ 
+
+ align:start position:0%
+that person is rotating how do we
+interpolate how do you do a partial
+
+ align:start position:0%
+interpolate how do you do a partial
+ 
+
+ align:start position:0%
+interpolate how do you do a partial
+rotation
+
+ align:start position:0%
+rotation
+ 
+
+ align:start position:0%
+rotation
+and so you know you might say well half
+
+ align:start position:0%
+and so you know you might say well half
+ 
+
+ align:start position:0%
+and so you know you might say well half
+a rotation that's the square root of the
+
+ align:start position:0%
+a rotation that's the square root of the
+ 
+
+ align:start position:0%
+a rotation that's the square root of the
+rotation matrix
+
+ align:start position:0%
+rotation matrix
+ 
+
+ align:start position:0%
+rotation matrix
+right because if you multiply that by
+
+ align:start position:0%
+right because if you multiply that by
+ 
+
+ align:start position:0%
+right because if you multiply that by
+itself you get the rotation matrix but
+
+ align:start position:0%
+itself you get the rotation matrix but
+ 
+
+ align:start position:0%
+itself you get the rotation matrix but
+what how do you get the square root of a
+
+ align:start position:0%
+what how do you get the square root of a
+ 
+
+ align:start position:0%
+what how do you get the square root of a
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's something another thing we might
+
+ align:start position:0%
+that's something another thing we might
+ 
+
+ align:start position:0%
+that's something another thing we might
+want to do is get averages of ranges of
+
+ align:start position:0%
+want to do is get averages of ranges of
+ 
+
+ align:start position:0%
+want to do is get averages of ranges of
+rotation
+
+ align:start position:0%
+rotation
+ 
+
+ align:start position:0%
+rotation
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+for us a big deal is going to be
+
+ align:start position:0%
+for us a big deal is going to be
+ 
+
+ align:start position:0%
+for us a big deal is going to be
+optimization we're going to try and fit
+
+ align:start position:0%
+optimization we're going to try and fit
+ 
+
+ align:start position:0%
+optimization we're going to try and fit
+coordinate system we're going to try and
+
+ align:start position:0%
+coordinate system we're going to try and
+ 
+
+ align:start position:0%
+coordinate system we're going to try and
+fit measurements to
+
+ align:start position:0%
+fit measurements to
+ 
+
+ align:start position:0%
+fit measurements to
+models and in that case we need to be
+
+ align:start position:0%
+models and in that case we need to be
+ 
+
+ align:start position:0%
+models and in that case we need to be
+able to do things like take a derivative
+
+ align:start position:0%
+able to do things like take a derivative
+ 
+
+ align:start position:0%
+able to do things like take a derivative
+and set the result equal to zero well
+
+ align:start position:0%
+and set the result equal to zero well
+ 
+
+ align:start position:0%
+and set the result equal to zero well
+the derivative with respect to a
+
+ align:start position:0%
+the derivative with respect to a
+ 
+
+ align:start position:0%
+the derivative with respect to a
+rotational matrix that you know doesn't
+
+ align:start position:0%
+rotational matrix that you know doesn't
+ 
+
+ align:start position:0%
+rotational matrix that you know doesn't
+make a lot of sense
+
+ align:start position:0%
+make a lot of sense
+ 
+
+ align:start position:0%
+make a lot of sense
+what is it well something with nine
+
+ align:start position:0%
+what is it well something with nine
+ 
+
+ align:start position:0%
+what is it well something with nine
+components but you know how do you
+
+ align:start position:0%
+components but you know how do you
+ 
+
+ align:start position:0%
+components but you know how do you
+enforce the constraints
+
+ align:start position:0%
+enforce the constraints
+ 
+
+ align:start position:0%
+enforce the constraints
+then in some cases where we can't get a
+
+ align:start position:0%
+then in some cases where we can't get a
+ 
+
+ align:start position:0%
+then in some cases where we can't get a
+closed form solution
+
+ align:start position:0%
+closed form solution
+ 
+
+ align:start position:0%
+closed form solution
+we might want to sample that space and
+
+ align:start position:0%
+we might want to sample that space and
+ 
+
+ align:start position:0%
+we might want to sample that space and
+you know try to try
+
+ align:start position:0%
+you know try to try
+ 
+
+ align:start position:0%
+you know try to try
+some subsid but we'd like to sample the
+
+ align:start position:0%
+some subsid but we'd like to sample the
+ 
+
+ align:start position:0%
+some subsid but we'd like to sample the
+space in an efficient way which means we
+
+ align:start position:0%
+space in an efficient way which means we
+ 
+
+ align:start position:0%
+space in an efficient way which means we
+want to sample it uniformly so if it was
+
+ align:start position:0%
+want to sample it uniformly so if it was
+ 
+
+ align:start position:0%
+want to sample it uniformly so if it was
+a translation space we just you know
+
+ align:start position:0%
+a translation space we just you know
+ 
+
+ align:start position:0%
+a translation space we just you know
+chop up space into
+
+ align:start position:0%
+chop up space into
+ 
+
+ align:start position:0%
+chop up space into
+voxels
+
+ align:start position:0%
+voxels
+ 
+
+ align:start position:0%
+voxels
+equally spaced
+
+ align:start position:0%
+equally spaced
+ 
+
+ align:start position:0%
+equally spaced
+and we'd be done or if we
+
+ align:start position:0%
+and we'd be done or if we
+ 
+
+ align:start position:0%
+and we'd be done or if we
+go into for a random sampling we could
+
+ align:start position:0%
+go into for a random sampling we could
+ 
+
+ align:start position:0%
+go into for a random sampling we could
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+generate a random x between the range
+
+ align:start position:0%
+generate a random x between the range
+ 
+
+ align:start position:0%
+generate a random x between the range
+and the random y between the certain in
+
+ align:start position:0%
+and the random y between the certain in
+ 
+
+ align:start position:0%
+and the random y between the certain in
+a certain range and the z in a certain
+
+ align:start position:0%
+a certain range and the z in a certain
+ 
+
+ align:start position:0%
+a certain range and the z in a certain
+range but how do you do that for
+
+ align:start position:0%
+range but how do you do that for
+ 
+
+ align:start position:0%
+range but how do you do that for
+rotations now if you did it in euler
+
+ align:start position:0%
+rotations now if you did it in euler
+ 
+
+ align:start position:0%
+rotations now if you did it in euler
+angles you could say okay well i'll take
+
+ align:start position:0%
+angles you could say okay well i'll take
+ 
+
+ align:start position:0%
+angles you could say okay well i'll take
+the first angle
+
+ align:start position:0%
+the first angle
+ 
+
+ align:start position:0%
+the first angle
+between minus 90 and plus 90 and then
+
+ align:start position:0%
+between minus 90 and plus 90 and then
+ 
+
+ align:start position:0%
+between minus 90 and plus 90 and then
+the second angle and so on and you get
+
+ align:start position:0%
+the second angle and so on and you get
+ 
+
+ align:start position:0%
+the second angle and so on and you get
+into a non-uniform sampling of the space
+
+ align:start position:0%
+into a non-uniform sampling of the space
+ 
+
+ align:start position:0%
+into a non-uniform sampling of the space
+for example you know much easier example
+
+ align:start position:0%
+for example you know much easier example
+ 
+
+ align:start position:0%
+for example you know much easier example
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+on the sphere
+
+ align:start position:0%
+on the sphere
+ 
+
+ align:start position:0%
+on the sphere
+we can use latitude and longitude as
+
+ align:start position:0%
+we can use latitude and longitude as
+ 
+
+ align:start position:0%
+we can use latitude and longitude as
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+but if you use that to control your
+
+ align:start position:0%
+but if you use that to control your
+ 
+
+ align:start position:0%
+but if you use that to control your
+sampling you're going to sample much
+
+ align:start position:0%
+sampling you're going to sample much
+ 
+
+ align:start position:0%
+sampling you're going to sample much
+more closely near the two poles right so
+
+ align:start position:0%
+more closely near the two poles right so
+ 
+
+ align:start position:0%
+more closely near the two poles right so
+that's um
+
+ align:start position:0%
+that's um
+ 
+
+ align:start position:0%
+that's um
+you know one more add one more dimension
+
+ align:start position:0%
+you know one more add one more dimension
+ 
+
+ align:start position:0%
+you know one more add one more dimension
+and you get the problem for uh rotations
+
+ align:start position:0%
+and you get the problem for uh rotations
+ 
+
+ align:start position:0%
+and you get the problem for uh rotations
+so the idea of having a space of no
+
+ align:start position:0%
+so the idea of having a space of no
+ 
+
+ align:start position:0%
+so the idea of having a space of no
+rotations is very
+
+ align:start position:0%
+rotations is very
+ 
+
+ align:start position:0%
+rotations is very
+attractive because then we can
+
+ align:start position:0%
+attractive because then we can
+ 
+
+ align:start position:0%
+attractive because then we can
+tessellate that space we can sample it
+
+ align:start position:0%
+tessellate that space we can sample it
+ 
+
+ align:start position:0%
+tessellate that space we can sample it
+uniformly or randomly we can compute
+
+ align:start position:0%
+uniformly or randomly we can compute
+ 
+
+ align:start position:0%
+uniformly or randomly we can compute
+averages or whatever
+
+ align:start position:0%
+averages or whatever
+ 
+
+ align:start position:0%
+averages or whatever
+so here are some of the problems we
+
+ align:start position:0%
+so here are some of the problems we
+ 
+
+ align:start position:0%
+so here are some of the problems we
+already talked about
+
+ align:start position:0%
+already talked about
+ 
+
+ align:start position:0%
+already talked about
+you know the orthonormal matrices
+
+ align:start position:0%
+you know the orthonormal matrices
+ 
+
+ align:start position:0%
+you know the orthonormal matrices
+they're redundant and the constraints
+
+ align:start position:0%
+they're redundant and the constraints
+ 
+
+ align:start position:0%
+they're redundant and the constraints
+are complicated
+
+ align:start position:0%
+are complicated
+ 
+
+ align:start position:0%
+are complicated
+euler angles don't make it easy to
+
+ align:start position:0%
+euler angles don't make it easy to
+ 
+
+ align:start position:0%
+euler angles don't make it easy to
+compose rotations just as with angle and
+
+ align:start position:0%
+compose rotations just as with angle and
+ 
+
+ align:start position:0%
+compose rotations just as with angle and
+axis notation best thing you can do is
+
+ align:start position:0%
+axis notation best thing you can do is
+ 
+
+ align:start position:0%
+axis notation best thing you can do is
+convert it to orthonormal matrix and
+
+ align:start position:0%
+convert it to orthonormal matrix and
+ 
+
+ align:start position:0%
+convert it to orthonormal matrix and
+multiply
+
+ align:start position:0%
+multiply
+ 
+
+ align:start position:0%
+multiply
+and then there's gimbal lock
+
+ align:start position:0%
+and then there's gimbal lock
+ 
+
+ align:start position:0%
+and then there's gimbal lock
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i know you're all too young for this but
+
+ align:start position:0%
+i know you're all too young for this but
+ 
+
+ align:start position:0%
+i know you're all too young for this but
+there was a time when man went to the
+
+ align:start position:0%
+there was a time when man went to the
+ 
+
+ align:start position:0%
+there was a time when man went to the
+moon which was a very exciting time and
+
+ align:start position:0%
+moon which was a very exciting time and
+ 
+
+ align:start position:0%
+moon which was a very exciting time and
+when you listened on television
+
+ align:start position:0%
+when you listened on television
+ 
+
+ align:start position:0%
+when you listened on television
+and you ignored the stupid commentators
+
+ align:start position:0%
+and you ignored the stupid commentators
+ 
+
+ align:start position:0%
+and you ignored the stupid commentators
+that were talking over the
+
+ align:start position:0%
+that were talking over the
+ 
+
+ align:start position:0%
+that were talking over the
+communication from the cabin you'd hear
+
+ align:start position:0%
+communication from the cabin you'd hear
+ 
+
+ align:start position:0%
+communication from the cabin you'd hear
+them talk about
+
+ align:start position:0%
+them talk about
+ 
+
+ align:start position:0%
+them talk about
+approaching gimbal lock so what was that
+
+ align:start position:0%
+approaching gimbal lock so what was that
+ 
+
+ align:start position:0%
+approaching gimbal lock so what was that
+well they draper lab built their
+
+ align:start position:0%
+well they draper lab built their
+ 
+
+ align:start position:0%
+well they draper lab built their
+navigation system
+
+ align:start position:0%
+navigation system
+ 
+
+ align:start position:0%
+navigation system
+and it had gyroscopes in it and
+
+ align:start position:0%
+and it had gyroscopes in it and
+ 
+
+ align:start position:0%
+and it had gyroscopes in it and
+gyroscopes basically
+
+ align:start position:0%
+gyroscopes basically
+ 
+
+ align:start position:0%
+gyroscopes basically
+have three
+
+ align:start position:0%
+have three
+ 
+
+ align:start position:0%
+have three
+that type of gyroscope has three axes
+
+ align:start position:0%
+that type of gyroscope has three axes
+ 
+
+ align:start position:0%
+that type of gyroscope has three axes
+and it has a
+
+ align:start position:0%
+and it has a
+ 
+
+ align:start position:0%
+and it has a
+part that is spinning at high speed and
+
+ align:start position:0%
+part that is spinning at high speed and
+ 
+
+ align:start position:0%
+part that is spinning at high speed and
+wants to continue spinning around that
+
+ align:start position:0%
+wants to continue spinning around that
+ 
+
+ align:start position:0%
+wants to continue spinning around that
+axis and then the
+
+ align:start position:0%
+axis and then the
+ 
+
+ align:start position:0%
+axis and then the
+the cage basically
+
+ align:start position:0%
+the cage basically
+ 
+
+ align:start position:0%
+the cage basically
+allows the spacecraft to rotate about
+
+ align:start position:0%
+allows the spacecraft to rotate about
+ 
+
+ align:start position:0%
+allows the spacecraft to rotate about
+that fixed direction
+
+ align:start position:0%
+that fixed direction
+ 
+
+ align:start position:0%
+that fixed direction
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+as with euler angles
+
+ align:start position:0%
+as with euler angles
+ 
+
+ align:start position:0%
+as with euler angles
+you can get to a situation where two of
+
+ align:start position:0%
+you can get to a situation where two of
+ 
+
+ align:start position:0%
+you can get to a situation where two of
+the axes line up and then you've lost
+
+ align:start position:0%
+the axes line up and then you've lost
+ 
+
+ align:start position:0%
+the axes line up and then you've lost
+the degree of freedom and if you move
+
+ align:start position:0%
+the degree of freedom and if you move
+ 
+
+ align:start position:0%
+the degree of freedom and if you move
+through that point you've basically lost
+
+ align:start position:0%
+through that point you've basically lost
+ 
+
+ align:start position:0%
+through that point you've basically lost
+your orientation in space so they were
+
+ align:start position:0%
+your orientation in space so they were
+ 
+
+ align:start position:0%
+your orientation in space so they were
+carefully instructed not to
+
+ align:start position:0%
+carefully instructed not to
+ 
+
+ align:start position:0%
+carefully instructed not to
+go through that point because their
+
+ align:start position:0%
+go through that point because their
+ 
+
+ align:start position:0%
+go through that point because their
+automated systems wouldn't wouldn't work
+
+ align:start position:0%
+automated systems wouldn't wouldn't work
+ 
+
+ align:start position:0%
+automated systems wouldn't wouldn't work
+correctly and so
+
+ align:start position:0%
+correctly and so
+ 
+
+ align:start position:0%
+correctly and so
+that's exactly the problem with euler
+
+ align:start position:0%
+that's exactly the problem with euler
+ 
+
+ align:start position:0%
+that's exactly the problem with euler
+angles that when you rotate one of them
+
+ align:start position:0%
+angles that when you rotate one of them
+ 
+
+ align:start position:0%
+angles that when you rotate one of them
+through 90 degrees it lines up with the
+
+ align:start position:0%
+through 90 degrees it lines up with the
+ 
+
+ align:start position:0%
+through 90 degrees it lines up with the
+next one and you've lost the degree of
+
+ align:start position:0%
+next one and you've lost the degree of
+ 
+
+ align:start position:0%
+next one and you've lost the degree of
+freedom
+
+ align:start position:0%
+freedom
+ 
+
+ align:start position:0%
+freedom
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+by the way how do you solve it well
+
+ align:start position:0%
+by the way how do you solve it well
+ 
+
+ align:start position:0%
+by the way how do you solve it well
+the easiest way is have four axes
+
+ align:start position:0%
+the easiest way is have four axes
+ 
+
+ align:start position:0%
+the easiest way is have four axes
+and in that case unfortunately you can
+
+ align:start position:0%
+and in that case unfortunately you can
+ 
+
+ align:start position:0%
+and in that case unfortunately you can
+no longer treat it as a passive system
+
+ align:start position:0%
+no longer treat it as a passive system
+ 
+
+ align:start position:0%
+no longer treat it as a passive system
+you have to have an active system that
+
+ align:start position:0%
+you have to have an active system that
+ 
+
+ align:start position:0%
+you have to have an active system that
+drives the axis so that you never have
+
+ align:start position:0%
+drives the axis so that you never have
+ 
+
+ align:start position:0%
+drives the axis so that you never have
+two of them line up anyway
+
+ align:start position:0%
+two of them line up anyway
+ 
+
+ align:start position:0%
+two of them line up anyway
+euler angles gibbs vector had that
+
+ align:start position:0%
+euler angles gibbs vector had that
+ 
+
+ align:start position:0%
+euler angles gibbs vector had that
+singularity
+
+ align:start position:0%
+singularity
+ 
+
+ align:start position:0%
+singularity
+uh acts as an angle has the problem of
+
+ align:start position:0%
+uh acts as an angle has the problem of
+ 
+
+ align:start position:0%
+uh acts as an angle has the problem of
+the composing rotations and then of
+
+ align:start position:0%
+the composing rotations and then of
+ 
+
+ align:start position:0%
+the composing rotations and then of
+course we don't have a clear idea of
+
+ align:start position:0%
+course we don't have a clear idea of
+ 
+
+ align:start position:0%
+course we don't have a clear idea of
+what is the space of rotations
+
+ align:start position:0%
+what is the space of rotations
+ 
+
+ align:start position:0%
+what is the space of rotations
+so we get to hamilton
+
+ align:start position:0%
+so we get to hamilton
+ 
+
+ align:start position:0%
+so we get to hamilton
+who lived in dublin ireland
+
+ align:start position:0%
+who lived in dublin ireland
+ 
+
+ align:start position:0%
+who lived in dublin ireland
+and he was fascinated by
+
+ align:start position:0%
+and he was fascinated by
+ 
+
+ align:start position:0%
+and he was fascinated by
+algebraic couples so the view is that we
+
+ align:start position:0%
+algebraic couples so the view is that we
+ 
+
+ align:start position:0%
+algebraic couples so the view is that we
+think of complex numbers as pairs of
+
+ align:start position:0%
+think of complex numbers as pairs of
+ 
+
+ align:start position:0%
+think of complex numbers as pairs of
+reals and can we somehow
+
+ align:start position:0%
+reals and can we somehow
+ 
+
+ align:start position:0%
+reals and can we somehow
+generalize that
+
+ align:start position:0%
+generalize that
+ 
+
+ align:start position:0%
+generalize that
+and you want to have a nice algebra you
+
+ align:start position:0%
+and you want to have a nice algebra you
+ 
+
+ align:start position:0%
+and you want to have a nice algebra you
+want to be able to add subtract multiply
+
+ align:start position:0%
+want to be able to add subtract multiply
+ 
+
+ align:start position:0%
+want to be able to add subtract multiply
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+very important you want to be able to
+
+ align:start position:0%
+very important you want to be able to
+ 
+
+ align:start position:0%
+very important you want to be able to
+divide
+
+ align:start position:0%
+divide
+ 
+
+ align:start position:0%
+divide
+you i mean you can do all sorts of
+
+ align:start position:0%
+you i mean you can do all sorts of
+ 
+
+ align:start position:0%
+you i mean you can do all sorts of
+wonderful things but if you if you can
+
+ align:start position:0%
+wonderful things but if you if you can
+ 
+
+ align:start position:0%
+wonderful things but if you if you can
+do that then you can solve equations you
+
+ align:start position:0%
+do that then you can solve equations you
+ 
+
+ align:start position:0%
+do that then you can solve equations you
+know by subtracting
+
+ align:start position:0%
+know by subtracting
+ 
+
+ align:start position:0%
+know by subtracting
+cross multiplying doing all those things
+
+ align:start position:0%
+cross multiplying doing all those things
+ 
+
+ align:start position:0%
+cross multiplying doing all those things
+we're used to
+
+ align:start position:0%
+we're used to
+ 
+
+ align:start position:0%
+we're used to
+and so uh there was a lot of interest in
+
+ align:start position:0%
+and so uh there was a lot of interest in
+ 
+
+ align:start position:0%
+and so uh there was a lot of interest in
+physics particularly in dealing with
+
+ align:start position:0%
+physics particularly in dealing with
+ 
+
+ align:start position:0%
+physics particularly in dealing with
+vectors in space well they weren't
+
+ align:start position:0%
+vectors in space well they weren't
+ 
+
+ align:start position:0%
+vectors in space well they weren't
+called vectors but dealing with points
+
+ align:start position:0%
+called vectors but dealing with points
+ 
+
+ align:start position:0%
+called vectors but dealing with points
+in space and so the natural thing was
+
+ align:start position:0%
+in space and so the natural thing was
+ 
+
+ align:start position:0%
+in space and so the natural thing was
+you know let's go from real numbers to
+
+ align:start position:0%
+you know let's go from real numbers to
+ 
+
+ align:start position:0%
+you know let's go from real numbers to
+complex numbers to triples
+
+ align:start position:0%
+complex numbers to triples
+ 
+
+ align:start position:0%
+complex numbers to triples
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then what can we do with the triples
+
+ align:start position:0%
+then what can we do with the triples
+ 
+
+ align:start position:0%
+then what can we do with the triples
+well you can multiply them and of course
+
+ align:start position:0%
+well you can multiply them and of course
+ 
+
+ align:start position:0%
+well you can multiply them and of course
+the dot products not much use for this
+
+ align:start position:0%
+the dot products not much use for this
+ 
+
+ align:start position:0%
+the dot products not much use for this
+purpose because it's a scalar
+
+ align:start position:0%
+purpose because it's a scalar
+ 
+
+ align:start position:0%
+purpose because it's a scalar
+cross product well the trouble is if
+
+ align:start position:0%
+cross product well the trouble is if
+ 
+
+ align:start position:0%
+cross product well the trouble is if
+you've got a cross b
+
+ align:start position:0%
+you've got a cross b
+ 
+
+ align:start position:0%
+you've got a cross b
+you know c equals a cross b can you say
+
+ align:start position:0%
+you know c equals a cross b can you say
+ 
+
+ align:start position:0%
+you know c equals a cross b can you say
+uh a equals c divided by b uh no so you
+
+ align:start position:0%
+uh a equals c divided by b uh no so you
+ 
+
+ align:start position:0%
+uh a equals c divided by b uh no so you
+know so that was his problem and it
+
+ align:start position:0%
+know so that was his problem and it
+ 
+
+ align:start position:0%
+know so that was his problem and it
+really uh puzzled him for for quite a
+
+ align:start position:0%
+really uh puzzled him for for quite a
+ 
+
+ align:start position:0%
+really uh puzzled him for for quite a
+while
+
+ align:start position:0%
+while
+ 
+
+ align:start position:0%
+while
+and he'd he trained his children to
+
+ align:start position:0%
+and he'd he trained his children to
+ 
+
+ align:start position:0%
+and he'd he trained his children to
+every morning he came down for breakfast
+
+ align:start position:0%
+every morning he came down for breakfast
+ 
+
+ align:start position:0%
+every morning he came down for breakfast
+to ask him uh papa can you multiply
+
+ align:start position:0%
+to ask him uh papa can you multiply
+ 
+
+ align:start position:0%
+to ask him uh papa can you multiply
+triplets yet
+
+ align:start position:0%
+triplets yet
+ 
+
+ align:start position:0%
+triplets yet
+which were these vectors
+
+ align:start position:0%
+which were these vectors
+ 
+
+ align:start position:0%
+which were these vectors
+we later call vectors
+
+ align:start position:0%
+we later call vectors
+ 
+
+ align:start position:0%
+we later call vectors
+and then uh on this fateful day
+
+ align:start position:0%
+and then uh on this fateful day
+ 
+
+ align:start position:0%
+and then uh on this fateful day
+uh he
+
+ align:start position:0%
+uh he
+ 
+
+ align:start position:0%
+uh he
+he's he got it
+
+ align:start position:0%
+he's he got it
+ 
+
+ align:start position:0%
+he's he got it
+and he went with his wife on his usual
+
+ align:start position:0%
+and he went with his wife on his usual
+ 
+
+ align:start position:0%
+and he went with his wife on his usual
+sunday stroll through
+
+ align:start position:0%
+sunday stroll through
+ 
+
+ align:start position:0%
+sunday stroll through
+dublin
+
+ align:start position:0%
+dublin
+ 
+
+ align:start position:0%
+dublin
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+he committed a criminal act on the
+
+ align:start position:0%
+he committed a criminal act on the
+ 
+
+ align:start position:0%
+he committed a criminal act on the
+bridge he engraved in graffiti the basic
+
+ align:start position:0%
+bridge he engraved in graffiti the basic
+ 
+
+ align:start position:0%
+bridge he engraved in graffiti the basic
+equation you need to solve this problem
+
+ align:start position:0%
+equation you need to solve this problem
+ 
+
+ align:start position:0%
+equation you need to solve this problem
+without explanation just the formula
+
+ align:start position:0%
+without explanation just the formula
+ 
+
+ align:start position:0%
+without explanation just the formula
+and then later when he described it he's
+
+ align:start position:0%
+and then later when he described it he's
+ 
+
+ align:start position:0%
+and then later when he described it he's
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+and here they dawned on me the notion
+
+ align:start position:0%
+and here they dawned on me the notion
+ 
+
+ align:start position:0%
+and here they dawned on me the notion
+that we must admit in some sense a
+
+ align:start position:0%
+that we must admit in some sense a
+ 
+
+ align:start position:0%
+that we must admit in some sense a
+fourth dimension of space for the
+
+ align:start position:0%
+fourth dimension of space for the
+ 
+
+ align:start position:0%
+fourth dimension of space for the
+purpose of calculating with triples an
+
+ align:start position:0%
+purpose of calculating with triples an
+ 
+
+ align:start position:0%
+purpose of calculating with triples an
+electric circuit seemed to close and a
+
+ align:start position:0%
+electric circuit seemed to close and a
+ 
+
+ align:start position:0%
+electric circuit seemed to close and a
+spark flashed forth remember it was 1843
+
+ align:start position:0%
+spark flashed forth remember it was 1843
+ 
+
+ align:start position:0%
+spark flashed forth remember it was 1843
+so you know there's a lot of excitement
+
+ align:start position:0%
+so you know there's a lot of excitement
+ 
+
+ align:start position:0%
+so you know there's a lot of excitement
+about electric stuff but long before
+
+ align:start position:0%
+about electric stuff but long before
+ 
+
+ align:start position:0%
+about electric stuff but long before
+tesla and edison
+
+ align:start position:0%
+tesla and edison
+ 
+
+ align:start position:0%
+tesla and edison
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the key thing was that he decided you
+
+ align:start position:0%
+the key thing was that he decided you
+ 
+
+ align:start position:0%
+the key thing was that he decided you
+can't do it with three there's no way to
+
+ align:start position:0%
+can't do it with three there's no way to
+ 
+
+ align:start position:0%
+can't do it with three there's no way to
+do it with three but you can do it with
+
+ align:start position:0%
+do it with three but you can do it with
+ 
+
+ align:start position:0%
+do it with three but you can do it with
+four and so
+
+ align:start position:0%
+four and so
+ 
+
+ align:start position:0%
+four and so
+then he wrote a book which is basically
+
+ align:start position:0%
+then he wrote a book which is basically
+ 
+
+ align:start position:0%
+then he wrote a book which is basically
+incomprehensible it's like 800 pages of
+
+ align:start position:0%
+incomprehensible it's like 800 pages of
+ 
+
+ align:start position:0%
+incomprehensible it's like 800 pages of
+heavy math but we'll simplify it a lot
+
+ align:start position:0%
+heavy math but we'll simplify it a lot
+ 
+
+ align:start position:0%
+heavy math but we'll simplify it a lot
+so the insight was you can't do it with
+
+ align:start position:0%
+so the insight was you can't do it with
+ 
+
+ align:start position:0%
+so the insight was you can't do it with
+three components and then he took his q
+
+ align:start position:0%
+three components and then he took his q
+ 
+
+ align:start position:0%
+three components and then he took his q
+from complex numbers where we introduced
+
+ align:start position:0%
+from complex numbers where we introduced
+ 
+
+ align:start position:0%
+from complex numbers where we introduced
+a quote imaginary number and
+
+ align:start position:0%
+a quote imaginary number and
+ 
+
+ align:start position:0%
+a quote imaginary number and
+he said well maybe if we have more of
+
+ align:start position:0%
+he said well maybe if we have more of
+ 
+
+ align:start position:0%
+he said well maybe if we have more of
+them you know maybe there are other
+
+ align:start position:0%
+them you know maybe there are other
+ 
+
+ align:start position:0%
+them you know maybe there are other
+things when you square them they become
+
+ align:start position:0%
+things when you square them they become
+ 
+
+ align:start position:0%
+things when you square them they become
+minus one and so that was his key
+
+ align:start position:0%
+minus one and so that was his key
+ 
+
+ align:start position:0%
+minus one and so that was his key
+insight he used
+
+ align:start position:0%
+insight he used
+ 
+
+ align:start position:0%
+insight he used
+the notation i j k
+
+ align:start position:0%
+the notation i j k
+ 
+
+ align:start position:0%
+the notation i j k
+such that i squared and j squared and k
+
+ align:start position:0%
+such that i squared and j squared and k
+ 
+
+ align:start position:0%
+such that i squared and j squared and k
+squared are minus one and then very
+
+ align:start position:0%
+squared are minus one and then very
+ 
+
+ align:start position:0%
+squared are minus one and then very
+importantly he added this i j k equals
+
+ align:start position:0%
+importantly he added this i j k equals
+ 
+
+ align:start position:0%
+importantly he added this i j k equals
+minus one and this is what he engraved
+
+ align:start position:0%
+minus one and this is what he engraved
+ 
+
+ align:start position:0%
+minus one and this is what he engraved
+in the bridge
+
+ align:start position:0%
+in the bridge
+ 
+
+ align:start position:0%
+in the bridge
+and it's still there although heavily
+
+ align:start position:0%
+and it's still there although heavily
+ 
+
+ align:start position:0%
+and it's still there although heavily
+worn by mathematicians touching it to
+
+ align:start position:0%
+worn by mathematicians touching it to
+ 
+
+ align:start position:0%
+worn by mathematicians touching it to
+see if they can get the inside from
+
+ align:start position:0%
+see if they can get the inside from
+ 
+
+ align:start position:0%
+see if they can get the inside from
+uh anyway
+
+ align:start position:0%
+uh anyway
+ 
+
+ align:start position:0%
+uh anyway
+from those you can get everything else
+
+ align:start position:0%
+from those you can get everything else
+ 
+
+ align:start position:0%
+from those you can get everything else
+for example if you want to know what i j
+
+ align:start position:0%
+for example if you want to know what i j
+ 
+
+ align:start position:0%
+for example if you want to know what i j
+is well you just multiply i j k by k and
+
+ align:start position:0%
+is well you just multiply i j k by k and
+ 
+
+ align:start position:0%
+is well you just multiply i j k by k and
+you get k squared which is minus one so
+
+ align:start position:0%
+you get k squared which is minus one so
+ 
+
+ align:start position:0%
+you get k squared which is minus one so
+it's going to be minus one times you
+
+ align:start position:0%
+it's going to be minus one times you
+ 
+
+ align:start position:0%
+it's going to be minus one times you
+know and so on to get k
+
+ align:start position:0%
+know and so on to get k
+ 
+
+ align:start position:0%
+know and so on to get k
+so these others are all subsidiary he
+
+ align:start position:0%
+so these others are all subsidiary he
+ 
+
+ align:start position:0%
+so these others are all subsidiary he
+didn't bother engraving them he just
+
+ align:start position:0%
+didn't bother engraving them he just
+ 
+
+ align:start position:0%
+didn't bother engraving them he just
+took the uh
+
+ align:start position:0%
+took the uh
+ 
+
+ align:start position:0%
+took the uh
+important the multiplication is not
+
+ align:start position:0%
+important the multiplication is not
+ 
+
+ align:start position:0%
+important the multiplication is not
+commutative so you know i j is k j i is
+
+ align:start position:0%
+commutative so you know i j is k j i is
+ 
+
+ align:start position:0%
+commutative so you know i j is k j i is
+minus k and um
+
+ align:start position:0%
+minus k and um
+ 
+
+ align:start position:0%
+minus k and um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+that sort of corresponds to cross
+
+ align:start position:0%
+that sort of corresponds to cross
+ 
+
+ align:start position:0%
+that sort of corresponds to cross
+products so this kind of suggests a
+
+ align:start position:0%
+products so this kind of suggests a
+ 
+
+ align:start position:0%
+products so this kind of suggests a
+connection with
+
+ align:start position:0%
+connection with
+ 
+
+ align:start position:0%
+connection with
+vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so there are lots of different ways
+
+ align:start position:0%
+and so there are lots of different ways
+ 
+
+ align:start position:0%
+and so there are lots of different ways
+of thinking about quaternions
+
+ align:start position:0%
+of thinking about quaternions
+ 
+
+ align:start position:0%
+of thinking about quaternions
+one is just simply as a real part and
+
+ align:start position:0%
+one is just simply as a real part and
+ 
+
+ align:start position:0%
+one is just simply as a real part and
+three different flavors of imaginary
+
+ align:start position:0%
+three different flavors of imaginary
+ 
+
+ align:start position:0%
+three different flavors of imaginary
+parts rather than just one imaginary
+
+ align:start position:0%
+parts rather than just one imaginary
+ 
+
+ align:start position:0%
+parts rather than just one imaginary
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+but then you can take these three and
+
+ align:start position:0%
+but then you can take these three and
+ 
+
+ align:start position:0%
+but then you can take these three and
+think of them as a vector in space
+
+ align:start position:0%
+think of them as a vector in space
+ 
+
+ align:start position:0%
+think of them as a vector in space
+and treat the whole thing as a scalar q
+
+ align:start position:0%
+and treat the whole thing as a scalar q
+ 
+
+ align:start position:0%
+and treat the whole thing as a scalar q
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+plus this vector and use this notation
+
+ align:start position:0%
+plus this vector and use this notation
+ 
+
+ align:start position:0%
+plus this vector and use this notation
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+has a scalar comma vector part
+
+ align:start position:0%
+has a scalar comma vector part
+ 
+
+ align:start position:0%
+has a scalar comma vector part
+or you can just write it as a four
+
+ align:start position:0%
+or you can just write it as a four
+ 
+
+ align:start position:0%
+or you can just write it as a four
+vector a thing with four components
+
+ align:start position:0%
+vector a thing with four components
+ 
+
+ align:start position:0%
+vector a thing with four components
+so uh i use this notation with a little
+
+ align:start position:0%
+so uh i use this notation with a little
+ 
+
+ align:start position:0%
+so uh i use this notation with a little
+circle over it to denote a quaternion
+
+ align:start position:0%
+circle over it to denote a quaternion
+ 
+
+ align:start position:0%
+circle over it to denote a quaternion
+it's not standard so don't get confused
+
+ align:start position:0%
+it's not standard so don't get confused
+ 
+
+ align:start position:0%
+it's not standard so don't get confused
+by that but
+
+ align:start position:0%
+by that but
+ 
+
+ align:start position:0%
+by that but
+when i'm writing stuff it's very
+
+ align:start position:0%
+when i'm writing stuff it's very
+ 
+
+ align:start position:0%
+when i'm writing stuff it's very
+important for me to distinguish the
+
+ align:start position:0%
+important for me to distinguish the
+ 
+
+ align:start position:0%
+important for me to distinguish the
+scalar the vector and the quaternion so
+
+ align:start position:0%
+scalar the vector and the quaternion so
+ 
+
+ align:start position:0%
+scalar the vector and the quaternion so
+i use the little circle to denote that
+
+ align:start position:0%
+i use the little circle to denote that
+ 
+
+ align:start position:0%
+i use the little circle to denote that
+another way of thinking about
+
+ align:start position:0%
+another way of thinking about
+ 
+
+ align:start position:0%
+another way of thinking about
+quaternions is as four by four matrices
+
+ align:start position:0%
+quaternions is as four by four matrices
+ 
+
+ align:start position:0%
+quaternions is as four by four matrices
+and that brings us back to that
+
+ align:start position:0%
+and that brings us back to that
+ 
+
+ align:start position:0%
+and that brings us back to that
+isomorphism we had that was useful for
+
+ align:start position:0%
+isomorphism we had that was useful for
+ 
+
+ align:start position:0%
+isomorphism we had that was useful for
+cross products there will be an
+
+ align:start position:0%
+cross products there will be an
+ 
+
+ align:start position:0%
+cross products there will be an
+isomorphism
+
+ align:start position:0%
+isomorphism
+ 
+
+ align:start position:0%
+isomorphism
+of quaternions with 4x4 matrices
+
+ align:start position:0%
+of quaternions with 4x4 matrices
+ 
+
+ align:start position:0%
+of quaternions with 4x4 matrices
+that allows us to do
+
+ align:start position:0%
+that allows us to do
+ 
+
+ align:start position:0%
+that allows us to do
+multiplication and yet another way
+
+ align:start position:0%
+multiplication and yet another way
+ 
+
+ align:start position:0%
+multiplication and yet another way
+is to think of a complex composite of
+
+ align:start position:0%
+is to think of a complex composite of
+ 
+
+ align:start position:0%
+is to think of a complex composite of
+two complex numbers so you know complex
+
+ align:start position:0%
+two complex numbers so you know complex
+ 
+
+ align:start position:0%
+two complex numbers so you know complex
+numbers are real plus i times a real now
+
+ align:start position:0%
+numbers are real plus i times a real now
+ 
+
+ align:start position:0%
+numbers are real plus i times a real now
+imagine that you replace the real with
+
+ align:start position:0%
+imagine that you replace the real with
+ 
+
+ align:start position:0%
+imagine that you replace the real with
+complex numbers you've got something
+
+ align:start position:0%
+complex numbers you've got something
+ 
+
+ align:start position:0%
+complex numbers you've got something
+with four components because you've got
+
+ align:start position:0%
+with four components because you've got
+ 
+
+ align:start position:0%
+with four components because you've got
+to be careful because you've got two
+
+ align:start position:0%
+to be careful because you've got two
+ 
+
+ align:start position:0%
+to be careful because you've got two
+different types of imaginary things
+
+ align:start position:0%
+different types of imaginary things
+ 
+
+ align:start position:0%
+different types of imaginary things
+that's actually a way we aren't going to
+
+ align:start position:0%
+that's actually a way we aren't going to
+ 
+
+ align:start position:0%
+that's actually a way we aren't going to
+use but it's a way that leads you to
+
+ align:start position:0%
+use but it's a way that leads you to
+ 
+
+ align:start position:0%
+use but it's a way that leads you to
+other things for example you can
+
+ align:start position:0%
+other things for example you can
+ 
+
+ align:start position:0%
+other things for example you can
+use that idea again and now you get
+
+ align:start position:0%
+use that idea again and now you get
+ 
+
+ align:start position:0%
+use that idea again and now you get
+instead of four components eight
+
+ align:start position:0%
+instead of four components eight
+ 
+
+ align:start position:0%
+instead of four components eight
+and then again you can get sixteen
+
+ align:start position:0%
+and then again you can get sixteen
+ 
+
+ align:start position:0%
+and then again you can get sixteen
+components so you can build these
+
+ align:start position:0%
+components so you can build these
+ 
+
+ align:start position:0%
+components so you can build these
+algebras that have uh you know one two
+
+ align:start position:0%
+algebras that have uh you know one two
+ 
+
+ align:start position:0%
+algebras that have uh you know one two
+four eight sixteen components and they
+
+ align:start position:0%
+four eight sixteen components and they
+ 
+
+ align:start position:0%
+four eight sixteen components and they
+get weirder and weirder we're gonna
+
+ align:start position:0%
+get weirder and weirder we're gonna
+ 
+
+ align:start position:0%
+get weirder and weirder we're gonna
+stick with four that's as far as we need
+
+ align:start position:0%
+stick with four that's as far as we need
+ 
+
+ align:start position:0%
+stick with four that's as far as we need
+to go
+
+ align:start position:0%
+to go
+ 
+
+ align:start position:0%
+to go
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+here's the view of multiplication using
+
+ align:start position:0%
+here's the view of multiplication using
+ 
+
+ align:start position:0%
+here's the view of multiplication using
+uh hamilton's uh basic uh uh explanation
+
+ align:start position:0%
+uh hamilton's uh basic uh uh explanation
+ 
+
+ align:start position:0%
+uh hamilton's uh basic uh uh explanation
+of how to multiply these things
+
+ align:start position:0%
+of how to multiply these things
+ 
+
+ align:start position:0%
+of how to multiply these things
+here two quaternions we're gonna
+
+ align:start position:0%
+here two quaternions we're gonna
+ 
+
+ align:start position:0%
+here two quaternions we're gonna
+multiply them and obviously we're gonna
+
+ align:start position:0%
+multiply them and obviously we're gonna
+ 
+
+ align:start position:0%
+multiply them and obviously we're gonna
+get 16 terms and then you know j times k
+
+ align:start position:0%
+get 16 terms and then you know j times k
+ 
+
+ align:start position:0%
+get 16 terms and then you know j times k
+is minus i
+
+ align:start position:0%
+is minus i
+ 
+
+ align:start position:0%
+is minus i
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so we can gather them up as again a
+
+ align:start position:0%
+and so we can gather them up as again a
+ 
+
+ align:start position:0%
+and so we can gather them up as again a
+scalar part
+
+ align:start position:0%
+scalar part
+ 
+
+ align:start position:0%
+scalar part
+and then these three um
+
+ align:start position:0%
+and then these three um
+ 
+
+ align:start position:0%
+and then these three um
+uh imaginary parts
+
+ align:start position:0%
+uh imaginary parts
+ 
+
+ align:start position:0%
+uh imaginary parts
+and that's you know that's the
+
+ align:start position:0%
+and that's you know that's the
+ 
+
+ align:start position:0%
+and that's you know that's the
+bottom baseline truth but it's kind of
+
+ align:start position:0%
+bottom baseline truth but it's kind of
+ 
+
+ align:start position:0%
+bottom baseline truth but it's kind of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+too detailed it's kind of hard to
+
+ align:start position:0%
+too detailed it's kind of hard to
+ 
+
+ align:start position:0%
+too detailed it's kind of hard to
+uh keep remember that
+
+ align:start position:0%
+uh keep remember that
+ 
+
+ align:start position:0%
+uh keep remember that
+and it's uh for us who are now remember
+
+ align:start position:0%
+and it's uh for us who are now remember
+ 
+
+ align:start position:0%
+and it's uh for us who are now remember
+this was before vectors
+
+ align:start position:0%
+this was before vectors
+ 
+
+ align:start position:0%
+this was before vectors
+but today we're all into vectors and
+
+ align:start position:0%
+but today we're all into vectors and
+ 
+
+ align:start position:0%
+but today we're all into vectors and
+scalars so in that notation it's a lot
+
+ align:start position:0%
+scalars so in that notation it's a lot
+ 
+
+ align:start position:0%
+scalars so in that notation it's a lot
+easier to write it this way so here's a
+
+ align:start position:0%
+easier to write it this way so here's a
+ 
+
+ align:start position:0%
+easier to write it this way so here's a
+quaternion p a quaternion q we multiply
+
+ align:start position:0%
+quaternion p a quaternion q we multiply
+ 
+
+ align:start position:0%
+quaternion p a quaternion q we multiply
+them together and we get this quaternion
+
+ align:start position:0%
+them together and we get this quaternion
+ 
+
+ align:start position:0%
+them together and we get this quaternion
+and the scalar part of it is just the
+
+ align:start position:0%
+and the scalar part of it is just the
+ 
+
+ align:start position:0%
+and the scalar part of it is just the
+scalar parts multiplied minus the dot
+
+ align:start position:0%
+scalar parts multiplied minus the dot
+ 
+
+ align:start position:0%
+scalar parts multiplied minus the dot
+product of the vector parts and so on
+
+ align:start position:0%
+product of the vector parts and so on
+ 
+
+ align:start position:0%
+product of the vector parts and so on
+and it's non-commutative why because it
+
+ align:start position:0%
+and it's non-commutative why because it
+ 
+
+ align:start position:0%
+and it's non-commutative why because it
+includes this cross product at the end
+
+ align:start position:0%
+includes this cross product at the end
+ 
+
+ align:start position:0%
+includes this cross product at the end
+here so if we if we interchange these
+
+ align:start position:0%
+here so if we if we interchange these
+ 
+
+ align:start position:0%
+here so if we if we interchange these
+two we're going to get q cross p which
+
+ align:start position:0%
+two we're going to get q cross p which
+ 
+
+ align:start position:0%
+two we're going to get q cross p which
+is of course minus p cross
+
+ align:start position:0%
+is of course minus p cross
+ 
+
+ align:start position:0%
+is of course minus p cross
+okay so this is actually a way we're
+
+ align:start position:0%
+okay so this is actually a way we're
+ 
+
+ align:start position:0%
+okay so this is actually a way we're
+going to use it
+
+ align:start position:0%
+going to use it
+ 
+
+ align:start position:0%
+going to use it
+just it's much more compact than this
+
+ align:start position:0%
+just it's much more compact than this
+ 
+
+ align:start position:0%
+just it's much more compact than this
+uh here's another notation that's
+
+ align:start position:0%
+uh here's another notation that's
+ 
+
+ align:start position:0%
+uh here's another notation that's
+sometimes uh very useful and this is
+
+ align:start position:0%
+sometimes uh very useful and this is
+ 
+
+ align:start position:0%
+sometimes uh very useful and this is
+analogous to the isomorphism we had
+
+ align:start position:0%
+analogous to the isomorphism we had
+ 
+
+ align:start position:0%
+analogous to the isomorphism we had
+between vectors and skew symmetric three
+
+ align:start position:0%
+between vectors and skew symmetric three
+ 
+
+ align:start position:0%
+between vectors and skew symmetric three
+by three matrices here we have
+
+ align:start position:0%
+by three matrices here we have
+ 
+
+ align:start position:0%
+by three matrices here we have
+isomorphism between a quaternion and a
+
+ align:start position:0%
+isomorphism between a quaternion and a
+ 
+
+ align:start position:0%
+isomorphism between a quaternion and a
+four by four
+
+ align:start position:0%
+four by four
+ 
+
+ align:start position:0%
+four by four
+uh matrix which happens to be orthogonal
+
+ align:start position:0%
+uh matrix which happens to be orthogonal
+ 
+
+ align:start position:0%
+uh matrix which happens to be orthogonal
+and if the quaternion is a unit
+
+ align:start position:0%
+and if the quaternion is a unit
+ 
+
+ align:start position:0%
+and if the quaternion is a unit
+quaternion it's also a unit
+
+ align:start position:0%
+quaternion it's also a unit
+ 
+
+ align:start position:0%
+quaternion it's also a unit
+normal so this actually in our case is
+
+ align:start position:0%
+normal so this actually in our case is
+ 
+
+ align:start position:0%
+normal so this actually in our case is
+typically a orthonormal four by four
+
+ align:start position:0%
+typically a orthonormal four by four
+ 
+
+ align:start position:0%
+typically a orthonormal four by four
+matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so this multiplication up here can
+
+ align:start position:0%
+and so this multiplication up here can
+ 
+
+ align:start position:0%
+and so this multiplication up here can
+be written as this product of a matrix
+
+ align:start position:0%
+be written as this product of a matrix
+ 
+
+ align:start position:0%
+be written as this product of a matrix
+times a vector and there's quite a bit
+
+ align:start position:0%
+times a vector and there's quite a bit
+ 
+
+ align:start position:0%
+times a vector and there's quite a bit
+of structure to this you can see you
+
+ align:start position:0%
+of structure to this you can see you
+ 
+
+ align:start position:0%
+of structure to this you can see you
+know the first column is just the
+
+ align:start position:0%
+know the first column is just the
+ 
+
+ align:start position:0%
+know the first column is just the
+quaternion p
+
+ align:start position:0%
+quaternion p
+ 
+
+ align:start position:0%
+quaternion p
+and then you can see that it's sort of
+
+ align:start position:0%
+and then you can see that it's sort of
+ 
+
+ align:start position:0%
+and then you can see that it's sort of
+skew symmetric except for the diagonal
+
+ align:start position:0%
+skew symmetric except for the diagonal
+ 
+
+ align:start position:0%
+skew symmetric except for the diagonal
+which would be zero if it was skew
+
+ align:start position:0%
+which would be zero if it was skew
+ 
+
+ align:start position:0%
+which would be zero if it was skew
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so uh we can write the product of
+
+ align:start position:0%
+and so uh we can write the product of
+ 
+
+ align:start position:0%
+and so uh we can write the product of
+two quaternions
+
+ align:start position:0%
+two quaternions
+ 
+
+ align:start position:0%
+two quaternions
+uh in that form so we can write p q so
+
+ align:start position:0%
+uh in that form so we can write p q so
+ 
+
+ align:start position:0%
+uh in that form so we can write p q so
+this is just like cross product you know
+
+ align:start position:0%
+this is just like cross product you know
+ 
+
+ align:start position:0%
+this is just like cross product you know
+where we said a cross b is some matrix
+
+ align:start position:0%
+where we said a cross b is some matrix
+ 
+
+ align:start position:0%
+where we said a cross b is some matrix
+times b similarly here p q can be
+
+ align:start position:0%
+times b similarly here p q can be
+ 
+
+ align:start position:0%
+times b similarly here p q can be
+written as this matrix times q and the
+
+ align:start position:0%
+written as this matrix times q and the
+ 
+
+ align:start position:0%
+written as this matrix times q and the
+matrix looks like this
+
+ align:start position:0%
+matrix looks like this
+ 
+
+ align:start position:0%
+matrix looks like this
+and the matrix is orthogonal and it's
+
+ align:start position:0%
+and the matrix is orthogonal and it's
+ 
+
+ align:start position:0%
+and the matrix is orthogonal and it's
+normal if it's a unit quaternion
+
+ align:start position:0%
+normal if it's a unit quaternion
+ 
+
+ align:start position:0%
+normal if it's a unit quaternion
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if we get rid of p0 then it's skew
+
+ align:start position:0%
+if we get rid of p0 then it's skew
+ 
+
+ align:start position:0%
+if we get rid of p0 then it's skew
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+and again just as with cross products we
+
+ align:start position:0%
+and again just as with cross products we
+ 
+
+ align:start position:0%
+and again just as with cross products we
+have the choice of either expanding the
+
+ align:start position:0%
+have the choice of either expanding the
+ 
+
+ align:start position:0%
+have the choice of either expanding the
+first part into a matrix or the second
+
+ align:start position:0%
+first part into a matrix or the second
+ 
+
+ align:start position:0%
+first part into a matrix or the second
+part so here's the other version
+
+ align:start position:0%
+part so here's the other version
+ 
+
+ align:start position:0%
+part so here's the other version
+where now we've
+
+ align:start position:0%
+where now we've
+ 
+
+ align:start position:0%
+where now we've
+turned q into a four by four matrix and
+
+ align:start position:0%
+turned q into a four by four matrix and
+ 
+
+ align:start position:0%
+turned q into a four by four matrix and
+this four by four matrix looks a lot
+
+ align:start position:0%
+this four by four matrix looks a lot
+ 
+
+ align:start position:0%
+this four by four matrix looks a lot
+like this one the first column is pretty
+
+ align:start position:0%
+like this one the first column is pretty
+ 
+
+ align:start position:0%
+like this one the first column is pretty
+much the same the first row is pretty
+
+ align:start position:0%
+much the same the first row is pretty
+ 
+
+ align:start position:0%
+much the same the first row is pretty
+much the same what's different is this
+
+ align:start position:0%
+much the same what's different is this
+ 
+
+ align:start position:0%
+much the same what's different is this
+three by three sub matrix is flipped
+
+ align:start position:0%
+three by three sub matrix is flipped
+ 
+
+ align:start position:0%
+three by three sub matrix is flipped
+it's it's a transpose
+
+ align:start position:0%
+it's it's a transpose
+ 
+
+ align:start position:0%
+it's it's a transpose
+so they're very similar but and this
+
+ align:start position:0%
+so they're very similar but and this
+ 
+
+ align:start position:0%
+so they're very similar but and this
+corresponds again to the fact that
+
+ align:start position:0%
+corresponds again to the fact that
+ 
+
+ align:start position:0%
+corresponds again to the fact that
+multiplication is non-commutative if
+
+ align:start position:0%
+multiplication is non-commutative if
+ 
+
+ align:start position:0%
+multiplication is non-commutative if
+those two pieces were the same then this
+
+ align:start position:0%
+those two pieces were the same then this
+ 
+
+ align:start position:0%
+those two pieces were the same then this
+whole operation would have been
+
+ align:start position:0%
+whole operation would have been
+ 
+
+ align:start position:0%
+whole operation would have been
+commutative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+now that we've got you know the basics
+
+ align:start position:0%
+now that we've got you know the basics
+ 
+
+ align:start position:0%
+now that we've got you know the basics
+and different ways of representing it uh
+
+ align:start position:0%
+and different ways of representing it uh
+ 
+
+ align:start position:0%
+and different ways of representing it uh
+it's easy to prove some of these uh
+
+ align:start position:0%
+it's easy to prove some of these uh
+ 
+
+ align:start position:0%
+it's easy to prove some of these uh
+basic results so first of all
+
+ align:start position:0%
+basic results so first of all
+ 
+
+ align:start position:0%
+basic results so first of all
+it's clear that it's not commutative and
+
+ align:start position:0%
+it's clear that it's not commutative and
+ 
+
+ align:start position:0%
+it's clear that it's not commutative and
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it you know that's why we're talking
+
+ align:start position:0%
+it you know that's why we're talking
+ 
+
+ align:start position:0%
+it you know that's why we're talking
+about it we wouldn't be talking about it
+
+ align:start position:0%
+about it we wouldn't be talking about it
+ 
+
+ align:start position:0%
+about it we wouldn't be talking about it
+because commutative gives them there's
+
+ align:start position:0%
+because commutative gives them there's
+ 
+
+ align:start position:0%
+because commutative gives them there's
+no way that it can represent rotation uh
+
+ align:start position:0%
+no way that it can represent rotation uh
+ 
+
+ align:start position:0%
+no way that it can represent rotation uh
+it's associative and that's not too hard
+
+ align:start position:0%
+it's associative and that's not too hard
+ 
+
+ align:start position:0%
+it's associative and that's not too hard
+to prove just use the formula for
+
+ align:start position:0%
+to prove just use the formula for
+ 
+
+ align:start position:0%
+to prove just use the formula for
+multiplication it's just a bit of messy
+
+ align:start position:0%
+multiplication it's just a bit of messy
+ 
+
+ align:start position:0%
+multiplication it's just a bit of messy
+algebra
+
+ align:start position:0%
+algebra
+ 
+
+ align:start position:0%
+algebra
+then we define a conjugate and the
+
+ align:start position:0%
+then we define a conjugate and the
+ 
+
+ align:start position:0%
+then we define a conjugate and the
+conjugate in analogy with complex
+
+ align:start position:0%
+conjugate in analogy with complex
+ 
+
+ align:start position:0%
+conjugate in analogy with complex
+numbers just means you negate the
+
+ align:start position:0%
+numbers just means you negate the
+ 
+
+ align:start position:0%
+numbers just means you negate the
+imaginary part
+
+ align:start position:0%
+imaginary part
+ 
+
+ align:start position:0%
+imaginary part
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+the next result you can get is that the
+
+ align:start position:0%
+the next result you can get is that the
+ 
+
+ align:start position:0%
+the next result you can get is that the
+conjugate of a product is the product of
+
+ align:start position:0%
+conjugate of a product is the product of
+ 
+
+ align:start position:0%
+conjugate of a product is the product of
+the conjugates in reverse order which is
+
+ align:start position:0%
+the conjugates in reverse order which is
+ 
+
+ align:start position:0%
+the conjugates in reverse order which is
+just like uh matrix multiplication
+
+ align:start position:0%
+just like uh matrix multiplication
+ 
+
+ align:start position:0%
+just like uh matrix multiplication
+a b all transposed is b transpose a
+
+ align:start position:0%
+a b all transposed is b transpose a
+ 
+
+ align:start position:0%
+a b all transposed is b transpose a
+transpose so there there's some
+
+ align:start position:0%
+transpose so there there's some
+ 
+
+ align:start position:0%
+transpose so there there's some
+analogies here and you you know if you
+
+ align:start position:0%
+analogies here and you you know if you
+ 
+
+ align:start position:0%
+analogies here and you you know if you
+into physics you'll realize that you
+
+ align:start position:0%
+into physics you'll realize that you
+ 
+
+ align:start position:0%
+into physics you'll realize that you
+know different heroes of physics had
+
+ align:start position:0%
+know different heroes of physics had
+ 
+
+ align:start position:0%
+know different heroes of physics had
+different uh
+
+ align:start position:0%
+different uh
+ 
+
+ align:start position:0%
+different uh
+ways of approaching quantum physics and
+
+ align:start position:0%
+ways of approaching quantum physics and
+ 
+
+ align:start position:0%
+ways of approaching quantum physics and
+some of them like to do it with a sort
+
+ align:start position:0%
+some of them like to do it with a sort
+ 
+
+ align:start position:0%
+some of them like to do it with a sort
+of complex number view and some of them
+
+ align:start position:0%
+of complex number view and some of them
+ 
+
+ align:start position:0%
+of complex number view and some of them
+like to do it with a matrix view and you
+
+ align:start position:0%
+like to do it with a matrix view and you
+ 
+
+ align:start position:0%
+like to do it with a matrix view and you
+can find that they're kind of equivalent
+
+ align:start position:0%
+can find that they're kind of equivalent
+ 
+
+ align:start position:0%
+can find that they're kind of equivalent
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so uh i've done a little of that and i'm
+
+ align:start position:0%
+so uh i've done a little of that and i'm
+ 
+
+ align:start position:0%
+so uh i've done a little of that and i'm
+going to do more of it
+
+ align:start position:0%
+going to do more of it
+ 
+
+ align:start position:0%
+going to do more of it
+and the main reason is that we can get a
+
+ align:start position:0%
+and the main reason is that we can get a
+ 
+
+ align:start position:0%
+and the main reason is that we can get a
+closed form solution because we can
+
+ align:start position:0%
+closed form solution because we can
+ 
+
+ align:start position:0%
+closed form solution because we can
+differentiate with respect to a
+
+ align:start position:0%
+differentiate with respect to a
+ 
+
+ align:start position:0%
+differentiate with respect to a
+quaternion we can't differentiate with
+
+ align:start position:0%
+quaternion we can't differentiate with
+ 
+
+ align:start position:0%
+quaternion we can't differentiate with
+respect to orthonormal matrix so that's
+
+ align:start position:0%
+respect to orthonormal matrix so that's
+ 
+
+ align:start position:0%
+respect to orthonormal matrix so that's
+kind of the main reason
+
+ align:start position:0%
+kind of the main reason
+ 
+
+ align:start position:0%
+kind of the main reason
+but there are these subsidiary reasons
+
+ align:start position:0%
+but there are these subsidiary reasons
+ 
+
+ align:start position:0%
+but there are these subsidiary reasons
+like if you can't get a closed form
+
+ align:start position:0%
+like if you can't get a closed form
+ 
+
+ align:start position:0%
+like if you can't get a closed form
+solution you can do a search in the
+
+ align:start position:0%
+solution you can do a search in the
+ 
+
+ align:start position:0%
+solution you can do a search in the
+space of rotations
+
+ align:start position:0%
+space of rotations
+ 
+
+ align:start position:0%
+space of rotations
+and you can sample that space
+
+ align:start position:0%
+and you can sample that space
+ 
+
+ align:start position:0%
+and you can sample that space
+efficiently either
+
+ align:start position:0%
+efficiently either
+ 
+
+ align:start position:0%
+efficiently either
+uniformly or randomly
+
+ align:start position:0%
+uniformly or randomly
+ 
+
+ align:start position:0%
+uniformly or randomly
+once you've got the notion of a space of
+
+ align:start position:0%
+once you've got the notion of a space of
+ 
+
+ align:start position:0%
+once you've got the notion of a space of
+rotation which is the case with
+
+ align:start position:0%
+rotation which is the case with
+ 
+
+ align:start position:0%
+rotation which is the case with
+quaternions
+
+ align:start position:0%
+quaternions
+ 
+
+ align:start position:0%
+quaternions
+okay so the few other
+
+ align:start position:0%
+okay so the few other
+ 
+
+ align:start position:0%
+okay so the few other
+dot product well the dot product you
+
+ align:start position:0%
+dot product well the dot product you
+ 
+
+ align:start position:0%
+dot product well the dot product you
+know if we think of it as a four vector
+
+ align:start position:0%
+know if we think of it as a four vector
+ 
+
+ align:start position:0%
+know if we think of it as a four vector
+it's just the ordinary dot product of a
+
+ align:start position:0%
+it's just the ordinary dot product of a
+ 
+
+ align:start position:0%
+it's just the ordinary dot product of a
+four vector if we think of it in terms
+
+ align:start position:0%
+four vector if we think of it in terms
+ 
+
+ align:start position:0%
+four vector if we think of it in terms
+of scalar and vector well then it's the
+
+ align:start position:0%
+of scalar and vector well then it's the
+ 
+
+ align:start position:0%
+of scalar and vector well then it's the
+product of the scalars plus the dot
+
+ align:start position:0%
+product of the scalars plus the dot
+ 
+
+ align:start position:0%
+product of the scalars plus the dot
+product of the vectors
+
+ align:start position:0%
+product of the vectors
+ 
+
+ align:start position:0%
+product of the vectors
+but you know underneath it's just q 0
+
+ align:start position:0%
+but you know underneath it's just q 0
+ 
+
+ align:start position:0%
+but you know underneath it's just q 0
+squared plus q x squared plus
+
+ align:start position:0%
+squared plus q x squared plus
+ 
+
+ align:start position:0%
+squared plus q x squared plus
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+p 0 q 0 plus p x q x etc
+
+ align:start position:0%
+p 0 q 0 plus p x q x etc
+ 
+
+ align:start position:0%
+p 0 q 0 plus p x q x etc
+and therefore there's a norm we can
+
+ align:start position:0%
+and therefore there's a norm we can
+ 
+
+ align:start position:0%
+and therefore there's a norm we can
+define a norm
+
+ align:start position:0%
+define a norm
+ 
+
+ align:start position:0%
+define a norm
+and this is the perhaps the most
+
+ align:start position:0%
+and this is the perhaps the most
+ 
+
+ align:start position:0%
+and this is the perhaps the most
+important if we multiply
+
+ align:start position:0%
+important if we multiply
+ 
+
+ align:start position:0%
+important if we multiply
+q by its conjugate
+
+ align:start position:0%
+q by its conjugate
+ 
+
+ align:start position:0%
+q by its conjugate
+it turns out we get a real quantity
+
+ align:start position:0%
+it turns out we get a real quantity
+ 
+
+ align:start position:0%
+it turns out we get a real quantity
+there's no imaginary part
+
+ align:start position:0%
+there's no imaginary part
+ 
+
+ align:start position:0%
+there's no imaginary part
+and it's it's this
+
+ align:start position:0%
+and it's it's this
+ 
+
+ align:start position:0%
+and it's it's this
+uh it's uh the dot product of q
+
+ align:start position:0%
+uh it's uh the dot product of q
+ 
+
+ align:start position:0%
+uh it's uh the dot product of q
+with itself times e where e is this
+
+ align:start position:0%
+with itself times e where e is this
+ 
+
+ align:start position:0%
+with itself times e where e is this
+quaternion that
+
+ align:start position:0%
+quaternion that
+ 
+
+ align:start position:0%
+quaternion that
+has a scalar it's a scalar one and i
+
+ align:start position:0%
+has a scalar it's a scalar one and i
+ 
+
+ align:start position:0%
+has a scalar it's a scalar one and i
+could have just written one there but
+
+ align:start position:0%
+could have just written one there but
+ 
+
+ align:start position:0%
+could have just written one there but
+that looks sort of funny so i invented
+
+ align:start position:0%
+that looks sort of funny so i invented
+ 
+
+ align:start position:0%
+that looks sort of funny so i invented
+this symbol
+
+ align:start position:0%
+this symbol
+ 
+
+ align:start position:0%
+this symbol
+which is a quaternion that has
+
+ align:start position:0%
+which is a quaternion that has
+ 
+
+ align:start position:0%
+which is a quaternion that has
+no vector part
+
+ align:start position:0%
+no vector part
+ 
+
+ align:start position:0%
+no vector part
+and why is this important well if you
+
+ align:start position:0%
+and why is this important well if you
+ 
+
+ align:start position:0%
+and why is this important well if you
+can do that then you have division
+
+ align:start position:0%
+can do that then you have division
+ 
+
+ align:start position:0%
+can do that then you have division
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the multiplicative inverse is is this
+
+ align:start position:0%
+the multiplicative inverse is is this
+ 
+
+ align:start position:0%
+the multiplicative inverse is is this
+and that was the problem with the
+
+ align:start position:0%
+and that was the problem with the
+ 
+
+ align:start position:0%
+and that was the problem with the
+triplets there was no way of defining an
+
+ align:start position:0%
+triplets there was no way of defining an
+ 
+
+ align:start position:0%
+triplets there was no way of defining an
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+and here here we can define an inverse
+
+ align:start position:0%
+and here here we can define an inverse
+ 
+
+ align:start position:0%
+and here here we can define an inverse
+well except for q equals 0 but then
+
+ align:start position:0%
+well except for q equals 0 but then
+ 
+
+ align:start position:0%
+well except for q equals 0 but then
+that's always a problem so
+
+ align:start position:0%
+that's always a problem so
+ 
+
+ align:start position:0%
+that's always a problem so
+and so this means for example that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can
+
+ align:start position:0%
+we can
+ 
+
+ align:start position:0%
+we can
+get the inverse of a rotation very
+
+ align:start position:0%
+get the inverse of a rotation very
+ 
+
+ align:start position:0%
+get the inverse of a rotation very
+easily first of all in the rotation
+
+ align:start position:0%
+easily first of all in the rotation
+ 
+
+ align:start position:0%
+easily first of all in the rotation
+we're going to be dealing with unit
+
+ align:start position:0%
+we're going to be dealing with unit
+ 
+
+ align:start position:0%
+we're going to be dealing with unit
+quaternions so q dot q is 1. so in the
+
+ align:start position:0%
+quaternions so q dot q is 1. so in the
+ 
+
+ align:start position:0%
+quaternions so q dot q is 1. so in the
+case of that
+
+ align:start position:0%
+case of that
+ 
+
+ align:start position:0%
+case of that
+unit quaternion representation the
+
+ align:start position:0%
+unit quaternion representation the
+ 
+
+ align:start position:0%
+unit quaternion representation the
+inverse is just the conjugate
+
+ align:start position:0%
+inverse is just the conjugate
+ 
+
+ align:start position:0%
+inverse is just the conjugate
+sort of like in the case of orthonormal
+
+ align:start position:0%
+sort of like in the case of orthonormal
+ 
+
+ align:start position:0%
+sort of like in the case of orthonormal
+matrices the inverse is just the
+
+ align:start position:0%
+matrices the inverse is just the
+ 
+
+ align:start position:0%
+matrices the inverse is just the
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+okay and then a few other sort of minor
+
+ align:start position:0%
+okay and then a few other sort of minor
+ 
+
+ align:start position:0%
+okay and then a few other sort of minor
+properties and you can just take those
+
+ align:start position:0%
+properties and you can just take those
+ 
+
+ align:start position:0%
+properties and you can just take those
+on faith or you can check them by doing
+
+ align:start position:0%
+on faith or you can check them by doing
+ 
+
+ align:start position:0%
+on faith or you can check them by doing
+the multiplications so the dot product
+
+ align:start position:0%
+the multiplications so the dot product
+ 
+
+ align:start position:0%
+the multiplications so the dot product
+of uh products is the product of dot
+
+ align:start position:0%
+of uh products is the product of dot
+ 
+
+ align:start position:0%
+of uh products is the product of dot
+products all surprising that
+
+ align:start position:0%
+products all surprising that
+ 
+
+ align:start position:0%
+products all surprising that
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+this first line is the
+
+ align:start position:0%
+this first line is the
+ 
+
+ align:start position:0%
+this first line is the
+special case of the second line which is
+
+ align:start position:0%
+special case of the second line which is
+ 
+
+ align:start position:0%
+special case of the second line which is
+more useful in calculations
+
+ align:start position:0%
+more useful in calculations
+ 
+
+ align:start position:0%
+more useful in calculations
+and then this this one's pretty handy so
+
+ align:start position:0%
+and then this this one's pretty handy so
+ 
+
+ align:start position:0%
+and then this this one's pretty handy so
+what's happened here well sometimes we
+
+ align:start position:0%
+what's happened here well sometimes we
+ 
+
+ align:start position:0%
+what's happened here well sometimes we
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+quaternion on one side we'd like to move
+
+ align:start position:0%
+quaternion on one side we'd like to move
+ 
+
+ align:start position:0%
+quaternion on one side we'd like to move
+it to the other side of a dot product
+
+ align:start position:0%
+it to the other side of a dot product
+ 
+
+ align:start position:0%
+it to the other side of a dot product
+and it turns out we can do that as long
+
+ align:start position:0%
+and it turns out we can do that as long
+ 
+
+ align:start position:0%
+and it turns out we can do that as long
+as we conjugate it
+
+ align:start position:0%
+as we conjugate it
+ 
+
+ align:start position:0%
+as we conjugate it
+so we've moved the cube from the left
+
+ align:start position:0%
+so we've moved the cube from the left
+ 
+
+ align:start position:0%
+so we've moved the cube from the left
+side of the dot to the right side of the
+
+ align:start position:0%
+side of the dot to the right side of the
+ 
+
+ align:start position:0%
+side of the dot to the right side of the
+dot and
+
+ align:start position:0%
+dot and
+ 
+
+ align:start position:0%
+dot and
+just conjugated it and it's easy to
+
+ align:start position:0%
+just conjugated it and it's easy to
+ 
+
+ align:start position:0%
+just conjugated it and it's easy to
+prove that you just multiply by you know
+
+ align:start position:0%
+prove that you just multiply by you know
+ 
+
+ align:start position:0%
+prove that you just multiply by you know
+cube conjugate and so on
+
+ align:start position:0%
+cube conjugate and so on
+ 
+
+ align:start position:0%
+cube conjugate and so on
+okay so uh so we're going to use unit
+
+ align:start position:0%
+okay so uh so we're going to use unit
+ 
+
+ align:start position:0%
+okay so uh so we're going to use unit
+quaternaries to represent rotation and
+
+ align:start position:0%
+quaternaries to represent rotation and
+ 
+
+ align:start position:0%
+quaternaries to represent rotation and
+we'll see right now how that's related
+
+ align:start position:0%
+we'll see right now how that's related
+ 
+
+ align:start position:0%
+we'll see right now how that's related
+to the other notations for rotation but
+
+ align:start position:0%
+to the other notations for rotation but
+ 
+
+ align:start position:0%
+to the other notations for rotation but
+we're dealing with vectors so what about
+
+ align:start position:0%
+we're dealing with vectors so what about
+ 
+
+ align:start position:0%
+we're dealing with vectors so what about
+vectors well we'll need to have a
+
+ align:start position:0%
+vectors well we'll need to have a
+ 
+
+ align:start position:0%
+vectors well we'll need to have a
+quaternion way of representing vectors
+
+ align:start position:0%
+quaternion way of representing vectors
+ 
+
+ align:start position:0%
+quaternion way of representing vectors
+and of course
+
+ align:start position:0%
+and of course
+ 
+
+ align:start position:0%
+and of course
+it's obvious we just leave out the
+
+ align:start position:0%
+it's obvious we just leave out the
+ 
+
+ align:start position:0%
+it's obvious we just leave out the
+scalar part conversely if we wanted to
+
+ align:start position:0%
+scalar part conversely if we wanted to
+ 
+
+ align:start position:0%
+scalar part conversely if we wanted to
+represent a scalar we could just leave
+
+ align:start position:0%
+represent a scalar we could just leave
+ 
+
+ align:start position:0%
+represent a scalar we could just leave
+out the vector part
+
+ align:start position:0%
+out the vector part
+ 
+
+ align:start position:0%
+out the vector part
+okay so we're going to convert our
+
+ align:start position:0%
+okay so we're going to convert our
+ 
+
+ align:start position:0%
+okay so we're going to convert our
+vectors in 3d to these funny uh
+
+ align:start position:0%
+vectors in 3d to these funny uh
+ 
+
+ align:start position:0%
+vectors in 3d to these funny uh
+quaternions purely imaginary quaternions
+
+ align:start position:0%
+quaternions purely imaginary quaternions
+ 
+
+ align:start position:0%
+quaternions purely imaginary quaternions
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+manipulate them in that space and then
+
+ align:start position:0%
+manipulate them in that space and then
+ 
+
+ align:start position:0%
+manipulate them in that space and then
+bring them back into the into 3d
+
+ align:start position:0%
+bring them back into the into 3d
+ 
+
+ align:start position:0%
+bring them back into the into 3d
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+for this special case only of these
+
+ align:start position:0%
+for this special case only of these
+ 
+
+ align:start position:0%
+for this special case only of these
+types of quaternions
+
+ align:start position:0%
+types of quaternions
+ 
+
+ align:start position:0%
+types of quaternions
+there's lots of interesting properties
+
+ align:start position:0%
+there's lots of interesting properties
+ 
+
+ align:start position:0%
+there's lots of interesting properties
+first of all the conjugate of course is
+
+ align:start position:0%
+first of all the conjugate of course is
+ 
+
+ align:start position:0%
+first of all the conjugate of course is
+just negating it because conjugate means
+
+ align:start position:0%
+just negating it because conjugate means
+ 
+
+ align:start position:0%
+just negating it because conjugate means
+negating the imaginary part
+
+ align:start position:0%
+negating the imaginary part
+ 
+
+ align:start position:0%
+negating the imaginary part
+the dot product is just the dot product
+
+ align:start position:0%
+the dot product is just the dot product
+ 
+
+ align:start position:0%
+the dot product is just the dot product
+so this is the dot product of the
+
+ align:start position:0%
+so this is the dot product of the
+ 
+
+ align:start position:0%
+so this is the dot product of the
+quaternions this is the dot product of
+
+ align:start position:0%
+quaternions this is the dot product of
+ 
+
+ align:start position:0%
+quaternions this is the dot product of
+the corresponding vectors and since the
+
+ align:start position:0%
+the corresponding vectors and since the
+ 
+
+ align:start position:0%
+the corresponding vectors and since the
+scalar part is zero you know it's
+
+ align:start position:0%
+scalar part is zero you know it's
+ 
+
+ align:start position:0%
+scalar part is zero you know it's
+obvious that this is the case so we can
+
+ align:start position:0%
+obvious that this is the case so we can
+ 
+
+ align:start position:0%
+obvious that this is the case so we can
+easily compute dot products uh if we
+
+ align:start position:0%
+easily compute dot products uh if we
+ 
+
+ align:start position:0%
+easily compute dot products uh if we
+multiply two of these special
+
+ align:start position:0%
+multiply two of these special
+ 
+
+ align:start position:0%
+multiply two of these special
+quaternions we get this funny thing
+
+ align:start position:0%
+quaternions we get this funny thing
+ 
+
+ align:start position:0%
+quaternions we get this funny thing
+it has the dot product in it and the
+
+ align:start position:0%
+it has the dot product in it and the
+ 
+
+ align:start position:0%
+it has the dot product in it and the
+cross product
+
+ align:start position:0%
+cross product
+ 
+
+ align:start position:0%
+cross product
+and this is why some critics of this
+
+ align:start position:0%
+and this is why some critics of this
+ 
+
+ align:start position:0%
+and this is why some critics of this
+notation uh called it a hermaphrodite
+
+ align:start position:0%
+notation uh called it a hermaphrodite
+ 
+
+ align:start position:0%
+notation uh called it a hermaphrodite
+monster you know it's got both sexes
+
+ align:start position:0%
+monster you know it's got both sexes
+ 
+
+ align:start position:0%
+monster you know it's got both sexes
+built into it dot products and cross
+
+ align:start position:0%
+built into it dot products and cross
+ 
+
+ align:start position:0%
+built into it dot products and cross
+products and they they thought this was
+
+ align:start position:0%
+products and they they thought this was
+ 
+
+ align:start position:0%
+products and they they thought this was
+a disadvantage well
+
+ align:start position:0%
+a disadvantage well
+ 
+
+ align:start position:0%
+a disadvantage well
+for some purposes is actually an
+
+ align:start position:0%
+for some purposes is actually an
+ 
+
+ align:start position:0%
+for some purposes is actually an
+advantage then if we take the product of
+
+ align:start position:0%
+advantage then if we take the product of
+ 
+
+ align:start position:0%
+advantage then if we take the product of
+r and s and take the dot with t
+
+ align:start position:0%
+r and s and take the dot with t
+ 
+
+ align:start position:0%
+r and s and take the dot with t
+uh we get the triple product rst and the
+
+ align:start position:0%
+uh we get the triple product rst and the
+ 
+
+ align:start position:0%
+uh we get the triple product rst and the
+triple products often pretty useful
+
+ align:start position:0%
+triple products often pretty useful
+ 
+
+ align:start position:0%
+triple products often pretty useful
+aside from computing volumes or
+
+ align:start position:0%
+aside from computing volumes or
+ 
+
+ align:start position:0%
+aside from computing volumes or
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+and again this is very simple to prove
+
+ align:start position:0%
+and again this is very simple to prove
+ 
+
+ align:start position:0%
+and again this is very simple to prove
+you know once you have a zero scalar
+
+ align:start position:0%
+you know once you have a zero scalar
+ 
+
+ align:start position:0%
+you know once you have a zero scalar
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+then all you're going to get is the
+
+ align:start position:0%
+then all you're going to get is the
+ 
+
+ align:start position:0%
+then all you're going to get is the
+vector part of t dotted with
+
+ align:start position:0%
+vector part of t dotted with
+ 
+
+ align:start position:0%
+vector part of t dotted with
+this thing r cross s
+
+ align:start position:0%
+this thing r cross s
+ 
+
+ align:start position:0%
+this thing r cross s
+and of course that's just you know r
+
+ align:start position:0%
+and of course that's just you know r
+ 
+
+ align:start position:0%
+and of course that's just you know r
+cross s dot t that's the triple product
+
+ align:start position:0%
+cross s dot t that's the triple product
+ 
+
+ align:start position:0%
+cross s dot t that's the triple product
+rst
+
+ align:start position:0%
+rst
+ 
+
+ align:start position:0%
+rst
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's how we represent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors
+
+ align:start position:0%
+vectors
+ 
+
+ align:start position:0%
+vectors
+okay scalars yeah we can do that
+
+ align:start position:0%
+okay scalars yeah we can do that
+ 
+
+ align:start position:0%
+okay scalars yeah we can do that
+finally we get to rotation so how do we
+
+ align:start position:0%
+finally we get to rotation so how do we
+ 
+
+ align:start position:0%
+finally we get to rotation so how do we
+do rotation well it turns out that a
+
+ align:start position:0%
+do rotation well it turns out that a
+ 
+
+ align:start position:0%
+do rotation well it turns out that a
+simple product of a quaternion with
+
+ align:start position:0%
+simple product of a quaternion with
+ 
+
+ align:start position:0%
+simple product of a quaternion with
+another quaternion won't do it because
+
+ align:start position:0%
+another quaternion won't do it because
+ 
+
+ align:start position:0%
+another quaternion won't do it because
+it takes us out of 3d into 4d
+
+ align:start position:0%
+it takes us out of 3d into 4d
+ 
+
+ align:start position:0%
+it takes us out of 3d into 4d
+we need an operation that takes us back
+
+ align:start position:0%
+we need an operation that takes us back
+ 
+
+ align:start position:0%
+we need an operation that takes us back
+into 3d
+
+ align:start position:0%
+into 3d
+ 
+
+ align:start position:0%
+into 3d
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+this is a little bit like
+
+ align:start position:0%
+this is a little bit like
+ 
+
+ align:start position:0%
+this is a little bit like
+you can do rotation in the plane by
+
+ align:start position:0%
+you can do rotation in the plane by
+ 
+
+ align:start position:0%
+you can do rotation in the plane by
+doing some operation that takes you out
+
+ align:start position:0%
+doing some operation that takes you out
+ 
+
+ align:start position:0%
+doing some operation that takes you out
+into three space but then you have to
+
+ align:start position:0%
+into three space but then you have to
+ 
+
+ align:start position:0%
+into three space but then you have to
+have another part of the operation that
+
+ align:start position:0%
+have another part of the operation that
+ 
+
+ align:start position:0%
+have another part of the operation that
+takes you back into the plane now in a
+
+ align:start position:0%
+takes you back into the plane now in a
+ 
+
+ align:start position:0%
+takes you back into the plane now in a
+rotated form so this is like that if we
+
+ align:start position:0%
+rotated form so this is like that if we
+ 
+
+ align:start position:0%
+rotated form so this is like that if we
+multiply two quaternions we're basically
+
+ align:start position:0%
+multiply two quaternions we're basically
+ 
+
+ align:start position:0%
+multiply two quaternions we're basically
+doing an operation of rotation in four
+
+ align:start position:0%
+doing an operation of rotation in four
+ 
+
+ align:start position:0%
+doing an operation of rotation in four
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+and now we need to find a
+
+ align:start position:0%
+and now we need to find a
+ 
+
+ align:start position:0%
+and now we need to find a
+operation that
+
+ align:start position:0%
+operation that
+ 
+
+ align:start position:0%
+operation that
+doesn't undo that but takes us back into
+
+ align:start position:0%
+doesn't undo that but takes us back into
+ 
+
+ align:start position:0%
+doesn't undo that but takes us back into
+free space and this is
+
+ align:start position:0%
+free space and this is
+ 
+
+ align:start position:0%
+free space and this is
+exactly what what happens here so we
+
+ align:start position:0%
+exactly what what happens here so we
+ 
+
+ align:start position:0%
+exactly what what happens here so we
+take our vector r turn it into a
+
+ align:start position:0%
+take our vector r turn it into a
+ 
+
+ align:start position:0%
+take our vector r turn it into a
+quaternion with zero scalar part then we
+
+ align:start position:0%
+quaternion with zero scalar part then we
+ 
+
+ align:start position:0%
+quaternion with zero scalar part then we
+pre-multiply by q and post-multiply by q
+
+ align:start position:0%
+pre-multiply by q and post-multiply by q
+ 
+
+ align:start position:0%
+pre-multiply by q and post-multiply by q
+conjugate and magically we're back in
+
+ align:start position:0%
+conjugate and magically we're back in
+ 
+
+ align:start position:0%
+conjugate and magically we're back in
+the in the real world so that this
+
+ align:start position:0%
+the in the real world so that this
+ 
+
+ align:start position:0%
+the in the real world so that this
+quaternion r prime has a zero scalar
+
+ align:start position:0%
+quaternion r prime has a zero scalar
+ 
+
+ align:start position:0%
+quaternion r prime has a zero scalar
+part and so this is how we're going to
+
+ align:start position:0%
+part and so this is how we're going to
+ 
+
+ align:start position:0%
+part and so this is how we're going to
+do rotation
+
+ align:start position:0%
+do rotation
+ 
+
+ align:start position:0%
+do rotation
+now there are many different ways of
+
+ align:start position:0%
+now there are many different ways of
+ 
+
+ align:start position:0%
+now there are many different ways of
+analyzing this one is to use that trick
+
+ align:start position:0%
+analyzing this one is to use that trick
+ 
+
+ align:start position:0%
+analyzing this one is to use that trick
+we had of
+
+ align:start position:0%
+we had of
+ 
+
+ align:start position:0%
+we had of
+representing quaternion multiplication
+
+ align:start position:0%
+representing quaternion multiplication
+ 
+
+ align:start position:0%
+representing quaternion multiplication
+as multiplication of four by four
+
+ align:start position:0%
+as multiplication of four by four
+ 
+
+ align:start position:0%
+as multiplication of four by four
+matrices and a four vector right so we
+
+ align:start position:0%
+matrices and a four vector right so we
+ 
+
+ align:start position:0%
+matrices and a four vector right so we
+take these first two
+
+ align:start position:0%
+take these first two
+ 
+
+ align:start position:0%
+take these first two
+and turn them into that
+
+ align:start position:0%
+and turn them into that
+ 
+
+ align:start position:0%
+and turn them into that
+and then we take the second uh
+
+ align:start position:0%
+and then we take the second uh
+ 
+
+ align:start position:0%
+and then we take the second uh
+multiplication and this time we turn the
+
+ align:start position:0%
+multiplication and this time we turn the
+ 
+
+ align:start position:0%
+multiplication and this time we turn the
+q
+
+ align:start position:0%
+q
+ 
+
+ align:start position:0%
+q
+conjugate into a matrix this matrix over
+
+ align:start position:0%
+conjugate into a matrix this matrix over
+ 
+
+ align:start position:0%
+conjugate into a matrix this matrix over
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+this operation is actually equivalent to
+
+ align:start position:0%
+this operation is actually equivalent to
+ 
+
+ align:start position:0%
+this operation is actually equivalent to
+that operation and what is this this is
+
+ align:start position:0%
+that operation and what is this this is
+ 
+
+ align:start position:0%
+that operation and what is this this is
+a four by four matrix is a product of
+
+ align:start position:0%
+a four by four matrix is a product of
+ 
+
+ align:start position:0%
+a four by four matrix is a product of
+two four by four matrices and if you
+
+ align:start position:0%
+two four by four matrices and if you
+ 
+
+ align:start position:0%
+two four by four matrices and if you
+multiply them out you get this
+
+ align:start position:0%
+multiply them out you get this
+ 
+
+ align:start position:0%
+multiply them out you get this
+and this uh the most interesting
+
+ align:start position:0%
+and this uh the most interesting
+ 
+
+ align:start position:0%
+and this uh the most interesting
+property of this is that the first row
+
+ align:start position:0%
+property of this is that the first row
+ 
+
+ align:start position:0%
+property of this is that the first row
+and the first column are mostly zeros
+
+ align:start position:0%
+and the first column are mostly zeros
+ 
+
+ align:start position:0%
+and the first column are mostly zeros
+and the result is that if you have a
+
+ align:start position:0%
+and the result is that if you have a
+ 
+
+ align:start position:0%
+and the result is that if you have a
+vector in 3d
+
+ align:start position:0%
+vector in 3d
+ 
+
+ align:start position:0%
+vector in 3d
+which has a zero part scalar part and
+
+ align:start position:0%
+which has a zero part scalar part and
+ 
+
+ align:start position:0%
+which has a zero part scalar part and
+multiplied by this
+
+ align:start position:0%
+multiplied by this
+ 
+
+ align:start position:0%
+multiplied by this
+there'll be no zero scalar part right
+
+ align:start position:0%
+there'll be no zero scalar part right
+ 
+
+ align:start position:0%
+there'll be no zero scalar part right
+because you're multiplying this by zero
+
+ align:start position:0%
+because you're multiplying this by zero
+ 
+
+ align:start position:0%
+because you're multiplying this by zero
+and then you're adding all of these
+
+ align:start position:0%
+and then you're adding all of these
+ 
+
+ align:start position:0%
+and then you're adding all of these
+zeros multiplied by whatever and you get
+
+ align:start position:0%
+zeros multiplied by whatever and you get
+ 
+
+ align:start position:0%
+zeros multiplied by whatever and you get
+zero so so uh all this is proved so far
+
+ align:start position:0%
+zero so so uh all this is proved so far
+ 
+
+ align:start position:0%
+zero so so uh all this is proved so far
+is that this operation will in fact get
+
+ align:start position:0%
+is that this operation will in fact get
+ 
+
+ align:start position:0%
+is that this operation will in fact get
+you back into 3d so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+by the way this sub matrix is also and
+
+ align:start position:0%
+by the way this sub matrix is also and
+ 
+
+ align:start position:0%
+by the way this sub matrix is also and
+this actually is our three by three
+
+ align:start position:0%
+this actually is our three by three
+ 
+
+ align:start position:0%
+this actually is our three by three
+orthonormal rotational matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's the
+
+ align:start position:0%
+okay so that's the
+ 
+
+ align:start position:0%
+okay so that's the
+equation we're going to use for rotation
+
+ align:start position:0%
+equation we're going to use for rotation
+ 
+
+ align:start position:0%
+equation we're going to use for rotation
+and this is the scalar part we can
+
+ align:start position:0%
+and this is the scalar part we can
+ 
+
+ align:start position:0%
+and this is the scalar part we can
+compute the scalar part and if the
+
+ align:start position:0%
+compute the scalar part and if the
+ 
+
+ align:start position:0%
+compute the scalar part and if the
+scalar part of the original vector is 0
+
+ align:start position:0%
+scalar part of the original vector is 0
+ 
+
+ align:start position:0%
+scalar part of the original vector is 0
+we get 0 for the scalar part of the new
+
+ align:start position:0%
+we get 0 for the scalar part of the new
+ 
+
+ align:start position:0%
+we get 0 for the scalar part of the new
+vector the vector part can be computed
+
+ align:start position:0%
+vector the vector part can be computed
+ 
+
+ align:start position:0%
+vector the vector part can be computed
+this way so if you don't want to you
+
+ align:start position:0%
+this way so if you don't want to you
+ 
+
+ align:start position:0%
+this way so if you don't want to you
+know jump into the ocean of quaternions
+
+ align:start position:0%
+know jump into the ocean of quaternions
+ 
+
+ align:start position:0%
+know jump into the ocean of quaternions
+you can do everything using scalars and
+
+ align:start position:0%
+you can do everything using scalars and
+ 
+
+ align:start position:0%
+you can do everything using scalars and
+vectors here's the formula
+
+ align:start position:0%
+vectors here's the formula
+ 
+
+ align:start position:0%
+vectors here's the formula
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know just dot products and cross
+
+ align:start position:0%
+you know just dot products and cross
+ 
+
+ align:start position:0%
+you know just dot products and cross
+products very easy
+
+ align:start position:0%
+products very easy
+ 
+
+ align:start position:0%
+products very easy
+when we uh
+
+ align:start position:0%
+when we uh
+ 
+
+ align:start position:0%
+when we uh
+use this operation
+
+ align:start position:0%
+use this operation
+ 
+
+ align:start position:0%
+use this operation
+we can easily well with a bit of algebra
+
+ align:start position:0%
+we can easily well with a bit of algebra
+ 
+
+ align:start position:0%
+we can easily well with a bit of algebra
+we can prove that it preserves dot
+
+ align:start position:0%
+we can prove that it preserves dot
+ 
+
+ align:start position:0%
+we can prove that it preserves dot
+products right you just take this
+
+ align:start position:0%
+products right you just take this
+ 
+
+ align:start position:0%
+products right you just take this
+formula apply it to r and then apply it
+
+ align:start position:0%
+formula apply it to r and then apply it
+ 
+
+ align:start position:0%
+formula apply it to r and then apply it
+to s take the dot product and you get r
+
+ align:start position:0%
+to s take the dot product and you get r
+ 
+
+ align:start position:0%
+to s take the dot product and you get r
+dot s
+
+ align:start position:0%
+dot s
+ 
+
+ align:start position:0%
+dot s
+and so it preserves dot product
+
+ align:start position:0%
+and so it preserves dot product
+ 
+
+ align:start position:0%
+and so it preserves dot product
+uh similarly it preserves triple
+
+ align:start position:0%
+uh similarly it preserves triple
+ 
+
+ align:start position:0%
+uh similarly it preserves triple
+products remember we had this special
+
+ align:start position:0%
+products remember we had this special
+ 
+
+ align:start position:0%
+products remember we had this special
+form that this multiplication gave us a
+
+ align:start position:0%
+form that this multiplication gave us a
+ 
+
+ align:start position:0%
+form that this multiplication gave us a
+triple product of the vector uh the
+
+ align:start position:0%
+triple product of the vector uh the
+ 
+
+ align:start position:0%
+triple product of the vector uh the
+underlying vectors
+
+ align:start position:0%
+underlying vectors
+ 
+
+ align:start position:0%
+underlying vectors
+well it preserves triple products so so
+
+ align:start position:0%
+well it preserves triple products so so
+ 
+
+ align:start position:0%
+well it preserves triple products so so
+that's it it's a
+
+ align:start position:0%
+that's it it's a
+ 
+
+ align:start position:0%
+that's it it's a
+rotation right it preserves dot products
+
+ align:start position:0%
+rotation right it preserves dot products
+ 
+
+ align:start position:0%
+rotation right it preserves dot products
+it preserves triple products
+
+ align:start position:0%
+it preserves triple products
+ 
+
+ align:start position:0%
+it preserves triple products
+so that's good
+
+ align:start position:0%
+so that's good
+ 
+
+ align:start position:0%
+so that's good
+we don't know yet what rotation but but
+
+ align:start position:0%
+we don't know yet what rotation but but
+ 
+
+ align:start position:0%
+we don't know yet what rotation but but
+we know it has to be a rotation because
+
+ align:start position:0%
+we know it has to be a rotation because
+ 
+
+ align:start position:0%
+we know it has to be a rotation because
+it preserves length and angles and it
+
+ align:start position:0%
+it preserves length and angles and it
+ 
+
+ align:start position:0%
+it preserves length and angles and it
+preserves handedness
+
+ align:start position:0%
+preserves handedness
+ 
+
+ align:start position:0%
+preserves handedness
+and then the other thing we were talking
+
+ align:start position:0%
+and then the other thing we were talking
+ 
+
+ align:start position:0%
+and then the other thing we were talking
+about was not just rotating a vector but
+
+ align:start position:0%
+about was not just rotating a vector but
+ 
+
+ align:start position:0%
+about was not just rotating a vector but
+composing rotations we wanted that to be
+
+ align:start position:0%
+composing rotations we wanted that to be
+ 
+
+ align:start position:0%
+composing rotations we wanted that to be
+easy well uh so suppose we first rotate
+
+ align:start position:0%
+easy well uh so suppose we first rotate
+ 
+
+ align:start position:0%
+easy well uh so suppose we first rotate
+uh we take our vector r we rotate it
+
+ align:start position:0%
+uh we take our vector r we rotate it
+ 
+
+ align:start position:0%
+uh we take our vector r we rotate it
+using q
+
+ align:start position:0%
+using q
+ 
+
+ align:start position:0%
+using q
+and then we take the result and we
+
+ align:start position:0%
+and then we take the result and we
+ 
+
+ align:start position:0%
+and then we take the result and we
+rotate it using p
+
+ align:start position:0%
+rotate it using p
+ 
+
+ align:start position:0%
+rotate it using p
+so we we write this and because these
+
+ align:start position:0%
+so we we write this and because these
+ 
+
+ align:start position:0%
+so we we write this and because these
+operations are associative i can rewrite
+
+ align:start position:0%
+operations are associative i can rewrite
+ 
+
+ align:start position:0%
+operations are associative i can rewrite
+it this way
+
+ align:start position:0%
+it this way
+ 
+
+ align:start position:0%
+it this way
+and that tells you oh
+
+ align:start position:0%
+and that tells you oh
+ 
+
+ align:start position:0%
+and that tells you oh
+composition of rotation is just
+
+ align:start position:0%
+composition of rotation is just
+ 
+
+ align:start position:0%
+composition of rotation is just
+multiplication of quaternions very easy
+
+ align:start position:0%
+multiplication of quaternions very easy
+ 
+
+ align:start position:0%
+multiplication of quaternions very easy
+and actually computationally efficient
+
+ align:start position:0%
+and actually computationally efficient
+ 
+
+ align:start position:0%
+and actually computationally efficient
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+which is very different from axes in
+
+ align:start position:0%
+which is very different from axes in
+ 
+
+ align:start position:0%
+which is very different from axes in
+angle notation or euler angles
+
+ align:start position:0%
+angle notation or euler angles
+ 
+
+ align:start position:0%
+angle notation or euler angles
+where it's very hard to compose
+
+ align:start position:0%
+where it's very hard to compose
+ 
+
+ align:start position:0%
+where it's very hard to compose
+rotations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we need to figure out what rotation
+
+ align:start position:0%
+then we need to figure out what rotation
+ 
+
+ align:start position:0%
+then we need to figure out what rotation
+is it
+
+ align:start position:0%
+is it
+ 
+
+ align:start position:0%
+is it
+or if we have specified rotation in some
+
+ align:start position:0%
+or if we have specified rotation in some
+ 
+
+ align:start position:0%
+or if we have specified rotation in some
+other form how do we turn it into
+
+ align:start position:0%
+other form how do we turn it into
+ 
+
+ align:start position:0%
+other form how do we turn it into
+quaternion
+
+ align:start position:0%
+quaternion
+ 
+
+ align:start position:0%
+quaternion
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+this is the formula we just
+
+ align:start position:0%
+this is the formula we just
+ 
+
+ align:start position:0%
+this is the formula we just
+sort of derived on the previous page
+
+ align:start position:0%
+sort of derived on the previous page
+ 
+
+ align:start position:0%
+sort of derived on the previous page
+and here's rodriguez's formula remember
+
+ align:start position:0%
+and here's rodriguez's formula remember
+ 
+
+ align:start position:0%
+and here's rodriguez's formula remember
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+a while back and then if we identify
+
+ align:start position:0%
+a while back and then if we identify
+ 
+
+ align:start position:0%
+a while back and then if we identify
+corresponding pairs first thing you
+
+ align:start position:0%
+corresponding pairs first thing you
+ 
+
+ align:start position:0%
+corresponding pairs first thing you
+notice is that q the vector part is
+
+ align:start position:0%
+notice is that q the vector part is
+ 
+
+ align:start position:0%
+notice is that q the vector part is
+parallel to omega so the vector part of
+
+ align:start position:0%
+parallel to omega so the vector part of
+ 
+
+ align:start position:0%
+parallel to omega so the vector part of
+the quaternion is in the direction of
+
+ align:start position:0%
+the quaternion is in the direction of
+ 
+
+ align:start position:0%
+the quaternion is in the direction of
+the axis
+
+ align:start position:0%
+the axis
+ 
+
+ align:start position:0%
+the axis
+sort of makes sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we can actually prove that easily
+
+ align:start position:0%
+and we can actually prove that easily
+ 
+
+ align:start position:0%
+and we can actually prove that easily
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if you plug um
+
+ align:start position:0%
+if you plug um
+ 
+
+ align:start position:0%
+if you plug um
+if you plug q in here for r
+
+ align:start position:0%
+if you plug q in here for r
+ 
+
+ align:start position:0%
+if you plug q in here for r
+what happens well this part drops out
+
+ align:start position:0%
+what happens well this part drops out
+ 
+
+ align:start position:0%
+what happens well this part drops out
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+you know q cross q is 0.
+
+ align:start position:0%
+you know q cross q is 0.
+ 
+
+ align:start position:0%
+you know q cross q is 0.
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+this becomes q dot q times q
+
+ align:start position:0%
+this becomes q dot q times q
+ 
+
+ align:start position:0%
+this becomes q dot q times q
+and this becomes something times q
+
+ align:start position:0%
+and this becomes something times q
+ 
+
+ align:start position:0%
+and this becomes something times q
+so what
+
+ align:start position:0%
+so what
+ 
+
+ align:start position:0%
+so what
+the whole thing
+
+ align:start position:0%
+the whole thing
+ 
+
+ align:start position:0%
+the whole thing
+both of these are vectors in the q
+
+ align:start position:0%
+both of these are vectors in the q
+ 
+
+ align:start position:0%
+both of these are vectors in the q
+direction so r prime is going to be in
+
+ align:start position:0%
+direction so r prime is going to be in
+ 
+
+ align:start position:0%
+direction so r prime is going to be in
+the q direction so uh very easy to show
+
+ align:start position:0%
+the q direction so uh very easy to show
+ 
+
+ align:start position:0%
+the q direction so uh very easy to show
+that q becomes q
+
+ align:start position:0%
+that q becomes q
+ 
+
+ align:start position:0%
+that q becomes q
+you know and that's
+
+ align:start position:0%
+you know and that's
+ 
+
+ align:start position:0%
+you know and that's
+euler's
+
+ align:start position:0%
+euler's
+ 
+
+ align:start position:0%
+euler's
+axis theorem
+
+ align:start position:0%
+axis theorem
+ 
+
+ align:start position:0%
+axis theorem
+so it's very easy to see that the vector
+
+ align:start position:0%
+so it's very easy to see that the vector
+ 
+
+ align:start position:0%
+so it's very easy to see that the vector
+part is parallel to the
+
+ align:start position:0%
+part is parallel to the
+ 
+
+ align:start position:0%
+part is parallel to the
+axis of rotation we don't know yet how
+
+ align:start position:0%
+axis of rotation we don't know yet how
+ 
+
+ align:start position:0%
+axis of rotation we don't know yet how
+long it's supposed to be
+
+ align:start position:0%
+long it's supposed to be
+ 
+
+ align:start position:0%
+long it's supposed to be
+and we don't know what the angle is
+
+ align:start position:0%
+and we don't know what the angle is
+ 
+
+ align:start position:0%
+and we don't know what the angle is
+but anyway uh leave out some of this the
+
+ align:start position:0%
+but anyway uh leave out some of this the
+ 
+
+ align:start position:0%
+but anyway uh leave out some of this the
+conclusion is this is our representation
+
+ align:start position:0%
+conclusion is this is our representation
+ 
+
+ align:start position:0%
+conclusion is this is our representation
+a conversion so if we know
+
+ align:start position:0%
+a conversion so if we know
+ 
+
+ align:start position:0%
+a conversion so if we know
+axis and angle we can compute the uh
+
+ align:start position:0%
+axis and angle we can compute the uh
+ 
+
+ align:start position:0%
+axis and angle we can compute the uh
+quaternion
+
+ align:start position:0%
+quaternion
+ 
+
+ align:start position:0%
+quaternion
+so that's one of the conversions between
+
+ align:start position:0%
+so that's one of the conversions between
+ 
+
+ align:start position:0%
+so that's one of the conversions between
+the you know we have eight different
+
+ align:start position:0%
+the you know we have eight different
+ 
+
+ align:start position:0%
+the you know we have eight different
+ways of representing it so there are
+
+ align:start position:0%
+ways of representing it so there are
+ 
+
+ align:start position:0%
+ways of representing it so there are
+eight times seven
+
+ align:start position:0%
+eight times seven
+ 
+
+ align:start position:0%
+eight times seven
+56 different conversions we could
+
+ align:start position:0%
+56 different conversions we could
+ 
+
+ align:start position:0%
+56 different conversions we could
+possibly do but we're not going to do
+
+ align:start position:0%
+possibly do but we're not going to do
+ 
+
+ align:start position:0%
+possibly do but we're not going to do
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+so this is one the other one we saw
+
+ align:start position:0%
+so this is one the other one we saw
+ 
+
+ align:start position:0%
+so this is one the other one we saw
+earlier
+
+ align:start position:0%
+earlier
+ 
+
+ align:start position:0%
+earlier
+where we can we produce the orthonormal
+
+ align:start position:0%
+where we can we produce the orthonormal
+ 
+
+ align:start position:0%
+where we can we produce the orthonormal
+matrix that's another important one
+
+ align:start position:0%
+matrix that's another important one
+ 
+
+ align:start position:0%
+matrix that's another important one
+because we use orthonormal matrices all
+
+ align:start position:0%
+because we use orthonormal matrices all
+ 
+
+ align:start position:0%
+because we use orthonormal matrices all
+the time we need to be able to go back
+
+ align:start position:0%
+the time we need to be able to go back
+ 
+
+ align:start position:0%
+the time we need to be able to go back
+and forth between axis and angle which
+
+ align:start position:0%
+and forth between axis and angle which
+ 
+
+ align:start position:0%
+and forth between axis and angle which
+is this formula
+
+ align:start position:0%
+is this formula
+ 
+
+ align:start position:0%
+is this formula
+and between orthogonal matrix and that
+
+ align:start position:0%
+and between orthogonal matrix and that
+ 
+
+ align:start position:0%
+and between orthogonal matrix and that
+was that previous formula
+
+ align:start position:0%
+was that previous formula
+ 
+
+ align:start position:0%
+was that previous formula
+uh there so there are two things about
+
+ align:start position:0%
+uh there so there are two things about
+ 
+
+ align:start position:0%
+uh there so there are two things about
+this one of them this is a unit
+
+ align:start position:0%
+this one of them this is a unit
+ 
+
+ align:start position:0%
+this one of them this is a unit
+quaternion you easily prove you you know
+
+ align:start position:0%
+quaternion you easily prove you you know
+ 
+
+ align:start position:0%
+quaternion you easily prove you you know
+take its dot product with itself and you
+
+ align:start position:0%
+take its dot product with itself and you
+ 
+
+ align:start position:0%
+take its dot product with itself and you
+get cos squared theta over two plus sine
+
+ align:start position:0%
+get cos squared theta over two plus sine
+ 
+
+ align:start position:0%
+get cos squared theta over two plus sine
+squared theta over two so
+
+ align:start position:0%
+squared theta over two so
+ 
+
+ align:start position:0%
+squared theta over two so
+so that's one thing so we're not talking
+
+ align:start position:0%
+so that's one thing so we're not talking
+ 
+
+ align:start position:0%
+so that's one thing so we're not talking
+about arbitrary quaternions just unit
+
+ align:start position:0%
+about arbitrary quaternions just unit
+ 
+
+ align:start position:0%
+about arbitrary quaternions just unit
+quaternions and then the other thing
+
+ align:start position:0%
+quaternions and then the other thing
+ 
+
+ align:start position:0%
+quaternions and then the other thing
+that's a little bit uh annoying is that
+
+ align:start position:0%
+that's a little bit uh annoying is that
+ 
+
+ align:start position:0%
+that's a little bit uh annoying is that
+minus q is the same rotation as plus q
+
+ align:start position:0%
+minus q is the same rotation as plus q
+ 
+
+ align:start position:0%
+minus q is the same rotation as plus q
+y well imagine you plug minus q into
+
+ align:start position:0%
+y well imagine you plug minus q into
+ 
+
+ align:start position:0%
+y well imagine you plug minus q into
+this formula the minuses just multi
+
+ align:start position:0%
+this formula the minuses just multi
+ 
+
+ align:start position:0%
+this formula the minuses just multi
+disappear
+
+ align:start position:0%
+disappear
+ 
+
+ align:start position:0%
+disappear
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what does this mean it means that if we
+
+ align:start position:0%
+what does this mean it means that if we
+ 
+
+ align:start position:0%
+what does this mean it means that if we
+think of the sphere
+
+ align:start position:0%
+think of the sphere
+ 
+
+ align:start position:0%
+think of the sphere
+as representing the space of rotation
+
+ align:start position:0%
+as representing the space of rotation
+ 
+
+ align:start position:0%
+as representing the space of rotation
+opposite points are actually the same
+
+ align:start position:0%
+opposite points are actually the same
+ 
+
+ align:start position:0%
+opposite points are actually the same
+rotation
+
+ align:start position:0%
+rotation
+ 
+
+ align:start position:0%
+rotation
+so it's you know
+
+ align:start position:0%
+so it's you know
+ 
+
+ align:start position:0%
+so it's you know
+it's very nice to think of a sphere in
+
+ align:start position:0%
+it's very nice to think of a sphere in
+ 
+
+ align:start position:0%
+it's very nice to think of a sphere in
+four dimensions as the space of rotation
+
+ align:start position:0%
+four dimensions as the space of rotation
+ 
+
+ align:start position:0%
+four dimensions as the space of rotation
+and then we can produce ways of sampling
+
+ align:start position:0%
+and then we can produce ways of sampling
+ 
+
+ align:start position:0%
+and then we can produce ways of sampling
+that space and taking integrals and take
+
+ align:start position:0%
+that space and taking integrals and take
+ 
+
+ align:start position:0%
+that space and taking integrals and take
+computing averages and so on but you
+
+ align:start position:0%
+computing averages and so on but you
+ 
+
+ align:start position:0%
+computing averages and so on but you
+have to keep in mind that you really
+
+ align:start position:0%
+have to keep in mind that you really
+ 
+
+ align:start position:0%
+have to keep in mind that you really
+only want half the sphere because the
+
+ align:start position:0%
+only want half the sphere because the
+ 
+
+ align:start position:0%
+only want half the sphere because the
+opposite side the reflected side
+
+ align:start position:0%
+opposite side the reflected side
+ 
+
+ align:start position:0%
+opposite side the reflected side
+represents the same rotations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and typical points are identified so we
+
+ align:start position:0%
+and typical points are identified so we
+ 
+
+ align:start position:0%
+and typical points are identified so we
+use we're going to use this in
+
+ align:start position:0%
+use we're going to use this in
+ 
+
+ align:start position:0%
+use we're going to use this in
+photogrammetry and uh in particular
+
+ align:start position:0%
+photogrammetry and uh in particular
+ 
+
+ align:start position:0%
+photogrammetry and uh in particular
+in absolute orientation
+
+ align:start position:0%
+in absolute orientation
+ 
+
+ align:start position:0%
+in absolute orientation
+we already talked about that and this is
+
+ align:start position:0%
+we already talked about that and this is
+ 
+
+ align:start position:0%
+we already talked about that and this is
+from last lecture so we got
+
+ align:start position:0%
+from last lecture so we got
+ 
+
+ align:start position:0%
+from last lecture so we got
+points in space
+
+ align:start position:0%
+points in space
+ 
+
+ align:start position:0%
+points in space
+identified measured in two coordinate
+
+ align:start position:0%
+identified measured in two coordinate
+ 
+
+ align:start position:0%
+identified measured in two coordinate
+systems we want to know the
+
+ align:start position:0%
+systems we want to know the
+ 
+
+ align:start position:0%
+systems we want to know the
+coordinate transformation between those
+
+ align:start position:0%
+coordinate transformation between those
+ 
+
+ align:start position:0%
+coordinate transformation between those
+two systems
+
+ align:start position:0%
+two systems
+ 
+
+ align:start position:0%
+two systems
+and it's dual to the other problem where
+
+ align:start position:0%
+and it's dual to the other problem where
+ 
+
+ align:start position:0%
+and it's dual to the other problem where
+we have the same coordinate system but
+
+ align:start position:0%
+we have the same coordinate system but
+ 
+
+ align:start position:0%
+we have the same coordinate system but
+we have two objects so we have one
+
+ align:start position:0%
+we have two objects so we have one
+ 
+
+ align:start position:0%
+we have two objects so we have one
+object moving
+
+ align:start position:0%
+object moving
+ 
+
+ align:start position:0%
+object moving
+and we modeled it this way where
+
+ align:start position:0%
+and we modeled it this way where
+ 
+
+ align:start position:0%
+and we modeled it this way where
+coordinates in the left system are
+
+ align:start position:0%
+coordinates in the left system are
+ 
+
+ align:start position:0%
+coordinates in the left system are
+rotated and translated to produce
+
+ align:start position:0%
+rotated and translated to produce
+ 
+
+ align:start position:0%
+rotated and translated to produce
+coordinates in the right coordinate
+
+ align:start position:0%
+coordinates in the right coordinate
+ 
+
+ align:start position:0%
+coordinates in the right coordinate
+system and we want the best fit rotation
+
+ align:start position:0%
+system and we want the best fit rotation
+ 
+
+ align:start position:0%
+system and we want the best fit rotation
+and translation meaning we want to
+
+ align:start position:0%
+and translation meaning we want to
+ 
+
+ align:start position:0%
+and translation meaning we want to
+minimize some error
+
+ align:start position:0%
+minimize some error
+ 
+
+ align:start position:0%
+minimize some error
+and what we're given are a bunch of
+
+ align:start position:0%
+and what we're given are a bunch of
+ 
+
+ align:start position:0%
+and what we're given are a bunch of
+corresponding points measured in the two
+
+ align:start position:0%
+corresponding points measured in the two
+ 
+
+ align:start position:0%
+corresponding points measured in the two
+coordinate system
+
+ align:start position:0%
+coordinate system
+ 
+
+ align:start position:0%
+coordinate system
+left left and right
+
+ align:start position:0%
+left left and right
+ 
+
+ align:start position:0%
+left left and right
+and then we talked about this mechanical
+
+ align:start position:0%
+and then we talked about this mechanical
+ 
+
+ align:start position:0%
+and then we talked about this mechanical
+this physical analog
+
+ align:start position:0%
+this physical analog
+ 
+
+ align:start position:0%
+this physical analog
+uh that we want a min we want to make
+
+ align:start position:0%
+uh that we want a min we want to make
+ 
+
+ align:start position:0%
+uh that we want a min we want to make
+these errors small and so one way to do
+
+ align:start position:0%
+these errors small and so one way to do
+ 
+
+ align:start position:0%
+these errors small and so one way to do
+it is to have these springs
+
+ align:start position:0%
+it is to have these springs
+ 
+
+ align:start position:0%
+it is to have these springs
+which have energy proportional to the
+
+ align:start position:0%
+which have energy proportional to the
+ 
+
+ align:start position:0%
+which have energy proportional to the
+distance squared
+
+ align:start position:0%
+distance squared
+ 
+
+ align:start position:0%
+distance squared
+and the energy total energy in those
+
+ align:start position:0%
+and the energy total energy in those
+ 
+
+ align:start position:0%
+and the energy total energy in those
+springs is the sum of squares of errors
+
+ align:start position:0%
+springs is the sum of squares of errors
+ 
+
+ align:start position:0%
+springs is the sum of squares of errors
+and the system wants to minimize that so
+
+ align:start position:0%
+and the system wants to minimize that so
+ 
+
+ align:start position:0%
+and the system wants to minimize that so
+that's the physical model
+
+ align:start position:0%
+that's the physical model
+ 
+
+ align:start position:0%
+that's the physical model
+of how it finds the rotation and
+
+ align:start position:0%
+of how it finds the rotation and
+ 
+
+ align:start position:0%
+of how it finds the rotation and
+transcend translation
+
+ align:start position:0%
+transcend translation
+ 
+
+ align:start position:0%
+transcend translation
+so then we
+
+ align:start position:0%
+so then we
+ 
+
+ align:start position:0%
+so then we
+we did this so
+
+ align:start position:0%
+we did this so
+ 
+
+ align:start position:0%
+we did this so
+this is the error term right because if
+
+ align:start position:0%
+this is the error term right because if
+ 
+
+ align:start position:0%
+this is the error term right because if
+i take the left coordinate and i rotate
+
+ align:start position:0%
+i take the left coordinate and i rotate
+ 
+
+ align:start position:0%
+i take the left coordinate and i rotate
+and translate it i i get this and that
+
+ align:start position:0%
+and translate it i i get this and that
+ 
+
+ align:start position:0%
+and translate it i i get this and that
+should be equal to the right coordinate
+
+ align:start position:0%
+should be equal to the right coordinate
+ 
+
+ align:start position:0%
+should be equal to the right coordinate
+when i subtract them i get the remaining
+
+ align:start position:0%
+when i subtract them i get the remaining
+ 
+
+ align:start position:0%
+when i subtract them i get the remaining
+error i square that i add all of those
+
+ align:start position:0%
+error i square that i add all of those
+ 
+
+ align:start position:0%
+error i square that i add all of those
+errors
+
+ align:start position:0%
+errors
+ 
+
+ align:start position:0%
+errors
+then first step let's find the
+
+ align:start position:0%
+then first step let's find the
+ 
+
+ align:start position:0%
+then first step let's find the
+translation and we did this last time
+
+ align:start position:0%
+translation and we did this last time
+ 
+
+ align:start position:0%
+translation and we did this last time
+one way to do it which is not the way we
+
+ align:start position:0%
+one way to do it which is not the way we
+ 
+
+ align:start position:0%
+one way to do it which is not the way we
+did it in class is just differentiate
+
+ align:start position:0%
+did it in class is just differentiate
+ 
+
+ align:start position:0%
+did it in class is just differentiate
+with respect to the translation r0 and
+
+ align:start position:0%
+with respect to the translation r0 and
+ 
+
+ align:start position:0%
+with respect to the translation r0 and
+this is uh
+
+ align:start position:0%
+this is uh
+ 
+
+ align:start position:0%
+this is uh
+you know this notation this is the norm
+
+ align:start position:0%
+you know this notation this is the norm
+ 
+
+ align:start position:0%
+you know this notation this is the norm
+which is really the dot product of this
+
+ align:start position:0%
+which is really the dot product of this
+ 
+
+ align:start position:0%
+which is really the dot product of this
+thing with itself if we differentiate it
+
+ align:start position:0%
+thing with itself if we differentiate it
+ 
+
+ align:start position:0%
+thing with itself if we differentiate it
+we get twice this
+
+ align:start position:0%
+we get twice this
+ 
+
+ align:start position:0%
+we get twice this
+and we set that equal to zero and then
+
+ align:start position:0%
+and we set that equal to zero and then
+ 
+
+ align:start position:0%
+and we set that equal to zero and then
+we can split so we have a sum of
+
+ align:start position:0%
+we can split so we have a sum of
+ 
+
+ align:start position:0%
+we can split so we have a sum of
+three terms we can split that into
+
+ align:start position:0%
+three terms we can split that into
+ 
+
+ align:start position:0%
+three terms we can split that into
+uh three sums right so for example of
+
+ align:start position:0%
+uh three sums right so for example of
+ 
+
+ align:start position:0%
+uh three sums right so for example of
+course we get rid of the two that's not
+
+ align:start position:0%
+course we get rid of the two that's not
+ 
+
+ align:start position:0%
+course we get rid of the two that's not
+very interesting
+
+ align:start position:0%
+very interesting
+ 
+
+ align:start position:0%
+very interesting
+and we get this and and final result was
+
+ align:start position:0%
+and we get this and and final result was
+ 
+
+ align:start position:0%
+and we get this and and final result was
+just that
+
+ align:start position:0%
+just that
+ 
+
+ align:start position:0%
+just that
+uh the translation is what takes the
+
+ align:start position:0%
+uh the translation is what takes the
+ 
+
+ align:start position:0%
+uh the translation is what takes the
+centroid in the left system
+
+ align:start position:0%
+centroid in the left system
+ 
+
+ align:start position:0%
+centroid in the left system
+after rotation
+
+ align:start position:0%
+after rotation
+ 
+
+ align:start position:0%
+after rotation
+into the centroid of the right system so
+
+ align:start position:0%
+into the centroid of the right system so
+ 
+
+ align:start position:0%
+into the centroid of the right system so
+so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kind of intuitive and nice it says that
+
+ align:start position:0%
+kind of intuitive and nice it says that
+ 
+
+ align:start position:0%
+kind of intuitive and nice it says that
+you know whatever your transformation is
+
+ align:start position:0%
+you know whatever your transformation is
+ 
+
+ align:start position:0%
+you know whatever your transformation is
+it should map the centroid of this point
+
+ align:start position:0%
+it should map the centroid of this point
+ 
+
+ align:start position:0%
+it should map the centroid of this point
+cloud into the centroid of that point
+
+ align:start position:0%
+cloud into the centroid of that point
+ 
+
+ align:start position:0%
+cloud into the centroid of that point
+cloud and one of the nice features of it
+
+ align:start position:0%
+cloud and one of the nice features of it
+ 
+
+ align:start position:0%
+cloud and one of the nice features of it
+is that you don't even need
+
+ align:start position:0%
+is that you don't even need
+ 
+
+ align:start position:0%
+is that you don't even need
+correspondences
+
+ align:start position:0%
+correspondences
+ 
+
+ align:start position:0%
+correspondences
+you just compute the centroid of those
+
+ align:start position:0%
+you just compute the centroid of those
+ 
+
+ align:start position:0%
+you just compute the centroid of those
+clouds so for this part uh you don't
+
+ align:start position:0%
+clouds so for this part uh you don't
+ 
+
+ align:start position:0%
+clouds so for this part uh you don't
+need to know which point in that cloud
+
+ align:start position:0%
+need to know which point in that cloud
+ 
+
+ align:start position:0%
+need to know which point in that cloud
+corresponds to which point in the other
+
+ align:start position:0%
+corresponds to which point in the other
+ 
+
+ align:start position:0%
+corresponds to which point in the other
+cloud
+
+ align:start position:0%
+cloud
+ 
+
+ align:start position:0%
+cloud
+and of course right now we can't get the
+
+ align:start position:0%
+and of course right now we can't get the
+ 
+
+ align:start position:0%
+and of course right now we can't get the
+answer because we don't know r
+
+ align:start position:0%
+answer because we don't know r
+ 
+
+ align:start position:0%
+answer because we don't know r
+but this is the formula that we're going
+
+ align:start position:0%
+but this is the formula that we're going
+ 
+
+ align:start position:0%
+but this is the formula that we're going
+to come back to at the end to get the
+
+ align:start position:0%
+to come back to at the end to get the
+ 
+
+ align:start position:0%
+to come back to at the end to get the
+translation
+
+ align:start position:0%
+translation
+ 
+
+ align:start position:0%
+translation
+and so at that point we can
+
+ align:start position:0%
+and so at that point we can
+ 
+
+ align:start position:0%
+and so at that point we can
+at that point we can move the origin to
+
+ align:start position:0%
+at that point we can move the origin to
+ 
+
+ align:start position:0%
+at that point we can move the origin to
+the centroid
+
+ align:start position:0%
+the centroid
+ 
+
+ align:start position:0%
+the centroid
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+add a dash to the r's indicating they're
+
+ align:start position:0%
+add a dash to the r's indicating they're
+ 
+
+ align:start position:0%
+add a dash to the r's indicating they're
+now measured with respect to the
+
+ align:start position:0%
+now measured with respect to the
+ 
+
+ align:start position:0%
+now measured with respect to the
+centroid so
+
+ align:start position:0%
+centroid so
+ 
+
+ align:start position:0%
+centroid so
+when we do that the formula simplifies
+
+ align:start position:0%
+when we do that the formula simplifies
+ 
+
+ align:start position:0%
+when we do that the formula simplifies
+this now that we're minimizing this
+
+ align:start position:0%
+this now that we're minimizing this
+ 
+
+ align:start position:0%
+this now that we're minimizing this
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+where these
+
+ align:start position:0%
+where these
+ 
+
+ align:start position:0%
+where these
+r prime and r r prime and r l prime are
+
+ align:start position:0%
+r prime and r r prime and r l prime are
+ 
+
+ align:start position:0%
+r prime and r r prime and r l prime are
+defined in terms of uh coordinates with
+
+ align:start position:0%
+defined in terms of uh coordinates with
+ 
+
+ align:start position:0%
+defined in terms of uh coordinates with
+respect to the center we subtract out
+
+ align:start position:0%
+respect to the center we subtract out
+ 
+
+ align:start position:0%
+respect to the center we subtract out
+the centroid subtract out the centroid
+
+ align:start position:0%
+the centroid subtract out the centroid
+ 
+
+ align:start position:0%
+the centroid subtract out the centroid
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and okay then we take this and we
+
+ align:start position:0%
+and okay then we take this and we
+ 
+
+ align:start position:0%
+and okay then we take this and we
+multiply this out again the norm squared
+
+ align:start position:0%
+multiply this out again the norm squared
+ 
+
+ align:start position:0%
+multiply this out again the norm squared
+is just the dot product of this thing
+
+ align:start position:0%
+is just the dot product of this thing
+ 
+
+ align:start position:0%
+is just the dot product of this thing
+with itself so think of it written out
+
+ align:start position:0%
+with itself so think of it written out
+ 
+
+ align:start position:0%
+with itself so think of it written out
+that way then when you multiply out you
+
+ align:start position:0%
+that way then when you multiply out you
+ 
+
+ align:start position:0%
+that way then when you multiply out you
+get four terms you gather them up and
+
+ align:start position:0%
+get four terms you gather them up and
+ 
+
+ align:start position:0%
+get four terms you gather them up and
+you you get this
+
+ align:start position:0%
+you you get this
+ 
+
+ align:start position:0%
+you you get this
+and here we use one little trick which
+
+ align:start position:0%
+and here we use one little trick which
+ 
+
+ align:start position:0%
+and here we use one little trick which
+is that we noted that the length of a
+
+ align:start position:0%
+is that we noted that the length of a
+ 
+
+ align:start position:0%
+is that we noted that the length of a
+vector is not changed by rotation so
+
+ align:start position:0%
+vector is not changed by rotation so
+ 
+
+ align:start position:0%
+vector is not changed by rotation so
+over here we we really get r
+
+ align:start position:0%
+over here we we really get r
+ 
+
+ align:start position:0%
+over here we we really get r
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+the left vector squared
+
+ align:start position:0%
+the left vector squared
+ 
+
+ align:start position:0%
+the left vector squared
+but we know that after rotation it's the
+
+ align:start position:0%
+but we know that after rotation it's the
+ 
+
+ align:start position:0%
+but we know that after rotation it's the
+same length so we just
+
+ align:start position:0%
+same length so we just
+ 
+
+ align:start position:0%
+same length so we just
+replace it
+
+ align:start position:0%
+replace it
+ 
+
+ align:start position:0%
+replace it
+okay and at that point these two things
+
+ align:start position:0%
+okay and at that point these two things
+ 
+
+ align:start position:0%
+okay and at that point these two things
+are fixed they're given by the data
+
+ align:start position:0%
+are fixed they're given by the data
+ 
+
+ align:start position:0%
+are fixed they're given by the data
+they're not going to depend on the
+
+ align:start position:0%
+they're not going to depend on the
+ 
+
+ align:start position:0%
+they're not going to depend on the
+rotation you pick so forget about them
+
+ align:start position:0%
+rotation you pick so forget about them
+ 
+
+ align:start position:0%
+rotation you pick so forget about them
+we need to focus on this middle term
+
+ align:start position:0%
+we need to focus on this middle term
+ 
+
+ align:start position:0%
+we need to focus on this middle term
+it's the only one we have control over
+
+ align:start position:0%
+it's the only one we have control over
+ 
+
+ align:start position:0%
+it's the only one we have control over
+we can change r
+
+ align:start position:0%
+we can change r
+ 
+
+ align:start position:0%
+we can change r
+but it has a minus sign so we're trying
+
+ align:start position:0%
+but it has a minus sign so we're trying
+ 
+
+ align:start position:0%
+but it has a minus sign so we're trying
+to minimize something so that means we
+
+ align:start position:0%
+to minimize something so that means we
+ 
+
+ align:start position:0%
+to minimize something so that means we
+want to maximize uh this term
+
+ align:start position:0%
+want to maximize uh this term
+ 
+
+ align:start position:0%
+want to maximize uh this term
+and that that's where we got to last
+
+ align:start position:0%
+and that that's where we got to last
+ 
+
+ align:start position:0%
+and that that's where we got to last
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and now i was explaining it in terms of
+
+ align:start position:0%
+and now i was explaining it in terms of
+ 
+
+ align:start position:0%
+and now i was explaining it in terms of
+uh see the sea urchin analogy where
+
+ align:start position:0%
+uh see the sea urchin analogy where
+ 
+
+ align:start position:0%
+uh see the sea urchin analogy where
+we've got these spines and we're trying
+
+ align:start position:0%
+we've got these spines and we're trying
+ 
+
+ align:start position:0%
+we've got these spines and we're trying
+to get them to
+
+ align:start position:0%
+to get them to
+ 
+
+ align:start position:0%
+to get them to
+um be as lined up as close as possible
+
+ align:start position:0%
+um be as lined up as close as possible
+ 
+
+ align:start position:0%
+um be as lined up as close as possible
+so that their dot product is as large as
+
+ align:start position:0%
+so that their dot product is as large as
+ 
+
+ align:start position:0%
+so that their dot product is as large as
+possible the dot product of
+
+ align:start position:0%
+possible the dot product of
+ 
+
+ align:start position:0%
+possible the dot product of
+corresponding point now we need
+
+ align:start position:0%
+corresponding point now we need
+ 
+
+ align:start position:0%
+corresponding point now we need
+correspondences
+
+ align:start position:0%
+correspondences
+ 
+
+ align:start position:0%
+correspondences
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is a classic problem in spacecraft
+
+ align:start position:0%
+this is a classic problem in spacecraft
+ 
+
+ align:start position:0%
+this is a classic problem in spacecraft
+attitude control
+
+ align:start position:0%
+attitude control
+ 
+
+ align:start position:0%
+attitude control
+you have the direction to
+
+ align:start position:0%
+you have the direction to
+ 
+
+ align:start position:0%
+you have the direction to
+stars in your cameras
+
+ align:start position:0%
+stars in your cameras
+ 
+
+ align:start position:0%
+stars in your cameras
+and you're trying to
+
+ align:start position:0%
+and you're trying to
+ 
+
+ align:start position:0%
+and you're trying to
+line them up with the catalog directions
+
+ align:start position:0%
+line them up with the catalog directions
+ 
+
+ align:start position:0%
+line them up with the catalog directions
+and of course you want to make the
+
+ align:start position:0%
+and of course you want to make the
+ 
+
+ align:start position:0%
+and of course you want to make the
+and it's a good analogy because in this
+
+ align:start position:0%
+and it's a good analogy because in this
+ 
+
+ align:start position:0%
+and it's a good analogy because in this
+case we don't care about the length we
+
+ align:start position:0%
+case we don't care about the length we
+ 
+
+ align:start position:0%
+case we don't care about the length we
+don't have the length we don't know how
+
+ align:start position:0%
+don't have the length we don't know how
+ 
+
+ align:start position:0%
+don't have the length we don't know how
+we from the camera we have no idea how
+
+ align:start position:0%
+we from the camera we have no idea how
+ 
+
+ align:start position:0%
+we from the camera we have no idea how
+far away the stars are and we don't care
+
+ align:start position:0%
+far away the stars are and we don't care
+ 
+
+ align:start position:0%
+far away the stars are and we don't care
+and if we move sideways actually that
+
+ align:start position:0%
+and if we move sideways actually that
+ 
+
+ align:start position:0%
+and if we move sideways actually that
+direction doesn't change because in
+
+ align:start position:0%
+direction doesn't change because in
+ 
+
+ align:start position:0%
+direction doesn't change because in
+comparison to the distance to the stars
+
+ align:start position:0%
+comparison to the distance to the stars
+ 
+
+ align:start position:0%
+comparison to the distance to the stars
+our own motion is microscopic
+
+ align:start position:0%
+our own motion is microscopic
+ 
+
+ align:start position:0%
+our own motion is microscopic
+so uh this would be the thing you want
+
+ align:start position:0%
+so uh this would be the thing you want
+ 
+
+ align:start position:0%
+so uh this would be the thing you want
+to maximize in in that case
+
+ align:start position:0%
+to maximize in in that case
+ 
+
+ align:start position:0%
+to maximize in in that case
+but how do you do it well you know
+
+ align:start position:0%
+but how do you do it well you know
+ 
+
+ align:start position:0%
+but how do you do it well you know
+we're sort of tuned to using calculus to
+
+ align:start position:0%
+we're sort of tuned to using calculus to
+ 
+
+ align:start position:0%
+we're sort of tuned to using calculus to
+solve all these problems just
+
+ align:start position:0%
+solve all these problems just
+ 
+
+ align:start position:0%
+solve all these problems just
+differentiate with respect to the
+
+ align:start position:0%
+differentiate with respect to the
+ 
+
+ align:start position:0%
+differentiate with respect to the
+unknown
+
+ align:start position:0%
+unknown
+ 
+
+ align:start position:0%
+unknown
+transformation but you know what does it
+
+ align:start position:0%
+transformation but you know what does it
+ 
+
+ align:start position:0%
+transformation but you know what does it
+mean to differentiate with respect to r
+
+ align:start position:0%
+mean to differentiate with respect to r
+ 
+
+ align:start position:0%
+mean to differentiate with respect to r
+now i'm sort of making fun of it but you
+
+ align:start position:0%
+now i'm sort of making fun of it but you
+ 
+
+ align:start position:0%
+now i'm sort of making fun of it but you
+can actually pursue this further
+
+ align:start position:0%
+can actually pursue this further
+ 
+
+ align:start position:0%
+can actually pursue this further
+what you need to do is not just
+
+ align:start position:0%
+what you need to do is not just
+ 
+
+ align:start position:0%
+what you need to do is not just
+differentiate with respect to r but
+
+ align:start position:0%
+differentiate with respect to r but
+ 
+
+ align:start position:0%
+differentiate with respect to r but
+impose all of those constraints that i
+
+ align:start position:0%
+impose all of those constraints that i
+ 
+
+ align:start position:0%
+impose all of those constraints that i
+talked about and you can do that it just
+
+ align:start position:0%
+talked about and you can do that it just
+ 
+
+ align:start position:0%
+talked about and you can do that it just
+gets messy you know you have to impose
+
+ align:start position:0%
+gets messy you know you have to impose
+ 
+
+ align:start position:0%
+gets messy you know you have to impose
+that r transpose r is the identity and
+
+ align:start position:0%
+that r transpose r is the identity and
+ 
+
+ align:start position:0%
+that r transpose r is the identity and
+you have the the determinant of r is
+
+ align:start position:0%
+you have the the determinant of r is
+ 
+
+ align:start position:0%
+you have the the determinant of r is
+plus one that's the hard one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's not do it that way
+
+ align:start position:0%
+okay so let's not do it that way
+ 
+
+ align:start position:0%
+okay so let's not do it that way
+let's use our newfangled
+
+ align:start position:0%
+let's use our newfangled
+ 
+
+ align:start position:0%
+let's use our newfangled
+quaternion notation so here we have a
+
+ align:start position:0%
+quaternion notation so here we have a
+ 
+
+ align:start position:0%
+quaternion notation so here we have a
+dot product of two vectors and we can
+
+ align:start position:0%
+dot product of two vectors and we can
+ 
+
+ align:start position:0%
+dot product of two vectors and we can
+express that here as the dot product of
+
+ align:start position:0%
+express that here as the dot product of
+ 
+
+ align:start position:0%
+express that here as the dot product of
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+quaternions with zero scalar part
+
+ align:start position:0%
+quaternions with zero scalar part
+ 
+
+ align:start position:0%
+quaternions with zero scalar part
+right so we we map this
+
+ align:start position:0%
+right so we we map this
+ 
+
+ align:start position:0%
+right so we we map this
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+l i prime
+
+ align:start position:0%
+l i prime
+ 
+
+ align:start position:0%
+l i prime
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+a quaternion r l i prime
+
+ align:start position:0%
+a quaternion r l i prime
+ 
+
+ align:start position:0%
+a quaternion r l i prime
+and we map this
+
+ align:start position:0%
+and we map this
+ 
+
+ align:start position:0%
+and we map this
+r r i prime into this quaternion and
+
+ align:start position:0%
+r r i prime into this quaternion and
+ 
+
+ align:start position:0%
+r r i prime into this quaternion and
+it's all you've done is add the zero
+
+ align:start position:0%
+it's all you've done is add the zero
+ 
+
+ align:start position:0%
+it's all you've done is add the zero
+scalar part is you know i've also
+
+ align:start position:0%
+scalar part is you know i've also
+ 
+
+ align:start position:0%
+scalar part is you know i've also
+flipped them around because you know dot
+
+ align:start position:0%
+flipped them around because you know dot
+ 
+
+ align:start position:0%
+flipped them around because you know dot
+products commute so i can do that
+
+ align:start position:0%
+products commute so i can do that
+ 
+
+ align:start position:0%
+products commute so i can do that
+okay and this is where i use that trick
+
+ align:start position:0%
+okay and this is where i use that trick
+ 
+
+ align:start position:0%
+okay and this is where i use that trick
+remember i said that sometimes you want
+
+ align:start position:0%
+remember i said that sometimes you want
+ 
+
+ align:start position:0%
+remember i said that sometimes you want
+to move something from one side of a dot
+
+ align:start position:0%
+to move something from one side of a dot
+ 
+
+ align:start position:0%
+to move something from one side of a dot
+product to the other
+
+ align:start position:0%
+product to the other
+ 
+
+ align:start position:0%
+product to the other
+here i've taken this
+
+ align:start position:0%
+here i've taken this
+ 
+
+ align:start position:0%
+here i've taken this
+quaternion flipped it to the other side
+
+ align:start position:0%
+quaternion flipped it to the other side
+ 
+
+ align:start position:0%
+quaternion flipped it to the other side
+but i had to conjugate it
+
+ align:start position:0%
+but i had to conjugate it
+ 
+
+ align:start position:0%
+but i had to conjugate it
+now it's already conjugated so conjugate
+
+ align:start position:0%
+now it's already conjugated so conjugate
+ 
+
+ align:start position:0%
+now it's already conjugated so conjugate
+of the conjugate is the thing itself so
+
+ align:start position:0%
+of the conjugate is the thing itself so
+ 
+
+ align:start position:0%
+of the conjugate is the thing itself so
+i get this expression
+
+ align:start position:0%
+i get this expression
+ 
+
+ align:start position:0%
+i get this expression
+and then i make use of the uh property
+
+ align:start position:0%
+and then i make use of the uh property
+ 
+
+ align:start position:0%
+and then i make use of the uh property
+that i can write this quaternion product
+
+ align:start position:0%
+that i can write this quaternion product
+ 
+
+ align:start position:0%
+that i can write this quaternion product
+as a matrix times vector and i can write
+
+ align:start position:0%
+as a matrix times vector and i can write
+ 
+
+ align:start position:0%
+as a matrix times vector and i can write
+this as a matrix times vector so i get
+
+ align:start position:0%
+this as a matrix times vector so i get
+ 
+
+ align:start position:0%
+this as a matrix times vector so i get
+so i get that
+
+ align:start position:0%
+so i get that
+ 
+
+ align:start position:0%
+so i get that
+and then i make use of the fact that a
+
+ align:start position:0%
+and then i make use of the fact that a
+ 
+
+ align:start position:0%
+and then i make use of the fact that a
+dot product is just the left thing
+
+ align:start position:0%
+dot product is just the left thing
+ 
+
+ align:start position:0%
+dot product is just the left thing
+transposed multiplied by the right thing
+
+ align:start position:0%
+transposed multiplied by the right thing
+ 
+
+ align:start position:0%
+transposed multiplied by the right thing
+and then finally i can pull out the q
+
+ align:start position:0%
+and then finally i can pull out the q
+ 
+
+ align:start position:0%
+and then finally i can pull out the q
+so so this is important i can
+
+ align:start position:0%
+so so this is important i can
+ 
+
+ align:start position:0%
+so so this is important i can
+you know separate out the cube on both
+
+ align:start position:0%
+you know separate out the cube on both
+ 
+
+ align:start position:0%
+you know separate out the cube on both
+sides so it doesn't it doesn't vary with
+
+ align:start position:0%
+sides so it doesn't it doesn't vary with
+ 
+
+ align:start position:0%
+sides so it doesn't it doesn't vary with
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+and so i end up with this
+
+ align:start position:0%
+and so i end up with this
+ 
+
+ align:start position:0%
+and so i end up with this
+product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is where all my data is all my
+
+ align:start position:0%
+so this is where all my data is all my
+ 
+
+ align:start position:0%
+so this is where all my data is all my
+measurements are buried in here this is
+
+ align:start position:0%
+measurements are buried in here this is
+ 
+
+ align:start position:0%
+measurements are buried in here this is
+a four by four matrix that i get from my
+
+ align:start position:0%
+a four by four matrix that i get from my
+ 
+
+ align:start position:0%
+a four by four matrix that i get from my
+measurements and now all i want to do is
+
+ align:start position:0%
+measurements and now all i want to do is
+ 
+
+ align:start position:0%
+measurements and now all i want to do is
+make this thing as large as possible
+
+ align:start position:0%
+make this thing as large as possible
+ 
+
+ align:start position:0%
+make this thing as large as possible
+well you know uh not quite
+
+ align:start position:0%
+well you know uh not quite
+ 
+
+ align:start position:0%
+well you know uh not quite
+because i can make this as large as i
+
+ align:start position:0%
+because i can make this as large as i
+ 
+
+ align:start position:0%
+because i can make this as large as i
+like by making q large right
+
+ align:start position:0%
+like by making q large right
+ 
+
+ align:start position:0%
+like by making q large right
+so i have to be careful to impose that
+
+ align:start position:0%
+so i have to be careful to impose that
+ 
+
+ align:start position:0%
+so i have to be careful to impose that
+constraint and so that's
+
+ align:start position:0%
+constraint and so that's
+ 
+
+ align:start position:0%
+constraint and so that's
+uh so quaternions are not a redundant
+
+ align:start position:0%
+uh so quaternions are not a redundant
+ 
+
+ align:start position:0%
+uh so quaternions are not a redundant
+representation because they have four
+
+ align:start position:0%
+representation because they have four
+ 
+
+ align:start position:0%
+representation because they have four
+degree four numbers
+
+ align:start position:0%
+degree four numbers
+ 
+
+ align:start position:0%
+degree four numbers
+and you have to impose this extra
+
+ align:start position:0%
+and you have to impose this extra
+ 
+
+ align:start position:0%
+and you have to impose this extra
+constraint okay and then the different
+
+ align:start position:0%
+constraint okay and then the different
+ 
+
+ align:start position:0%
+constraint okay and then the different
+ways of doing this so first of all
+
+ align:start position:0%
+ways of doing this so first of all
+ 
+
+ align:start position:0%
+ways of doing this so first of all
+let's see what is n well n is again
+
+ align:start position:0%
+let's see what is n well n is again
+ 
+
+ align:start position:0%
+let's see what is n well n is again
+got from the data
+
+ align:start position:0%
+got from the data
+ 
+
+ align:start position:0%
+got from the data
+and there are two ways to do this if you
+
+ align:start position:0%
+and there are two ways to do this if you
+ 
+
+ align:start position:0%
+and there are two ways to do this if you
+know about lagrange multipliers you can
+
+ align:start position:0%
+know about lagrange multipliers you can
+ 
+
+ align:start position:0%
+know about lagrange multipliers you can
+add another term that imposes the
+
+ align:start position:0%
+add another term that imposes the
+ 
+
+ align:start position:0%
+add another term that imposes the
+constraint so the constraint is that q
+
+ align:start position:0%
+constraint so the constraint is that q
+ 
+
+ align:start position:0%
+constraint so the constraint is that q
+dot q equals one
+
+ align:start position:0%
+dot q equals one
+ 
+
+ align:start position:0%
+dot q equals one
+or minus one minus q dot q equals zero
+
+ align:start position:0%
+or minus one minus q dot q equals zero
+ 
+
+ align:start position:0%
+or minus one minus q dot q equals zero
+so you can impose that way and we'll do
+
+ align:start position:0%
+so you can impose that way and we'll do
+ 
+
+ align:start position:0%
+so you can impose that way and we'll do
+it another way that doesn't involve
+
+ align:start position:0%
+it another way that doesn't involve
+ 
+
+ align:start position:0%
+it another way that doesn't involve
+needing to know about lagrange
+
+ align:start position:0%
+needing to know about lagrange
+ 
+
+ align:start position:0%
+needing to know about lagrange
+multipliers
+
+ align:start position:0%
+multipliers
+ 
+
+ align:start position:0%
+multipliers
+anyway in either method we can now
+
+ align:start position:0%
+anyway in either method we can now
+ 
+
+ align:start position:0%
+anyway in either method we can now
+differentiate with respect to q which is
+
+ align:start position:0%
+differentiate with respect to q which is
+ 
+
+ align:start position:0%
+differentiate with respect to q which is
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+amazing we can differentiate with
+
+ align:start position:0%
+amazing we can differentiate with
+ 
+
+ align:start position:0%
+amazing we can differentiate with
+respect to rotation of course in the
+
+ align:start position:0%
+respect to rotation of course in the
+ 
+
+ align:start position:0%
+respect to rotation of course in the
+case of translation you know no one's
+
+ align:start position:0%
+case of translation you know no one's
+ 
+
+ align:start position:0%
+case of translation you know no one's
+surprised you can differentiate with
+
+ align:start position:0%
+surprised you can differentiate with
+ 
+
+ align:start position:0%
+surprised you can differentiate with
+respect to translation or position but
+
+ align:start position:0%
+respect to translation or position but
+ 
+
+ align:start position:0%
+respect to translation or position but
+for rotation that's quite something
+
+ align:start position:0%
+for rotation that's quite something
+ 
+
+ align:start position:0%
+for rotation that's quite something
+if we do
+
+ align:start position:0%
+if we do
+ 
+
+ align:start position:0%
+if we do
+we get this and this is just using the
+
+ align:start position:0%
+we get this and this is just using the
+ 
+
+ align:start position:0%
+we get this and this is just using the
+ordinary rules for
+
+ align:start position:0%
+ordinary rules for
+ 
+
+ align:start position:0%
+ordinary rules for
+differentiation of a dot product and
+
+ align:start position:0%
+differentiation of a dot product and
+ 
+
+ align:start position:0%
+differentiation of a dot product and
+differentiation of a matrix times a
+
+ align:start position:0%
+differentiation of a matrix times a
+ 
+
+ align:start position:0%
+differentiation of a matrix times a
+vector which by the way are in the
+
+ align:start position:0%
+vector which by the way are in the
+ 
+
+ align:start position:0%
+vector which by the way are in the
+appendix of the book which by the way is
+
+ align:start position:0%
+appendix of the book which by the way is
+ 
+
+ align:start position:0%
+appendix of the book which by the way is
+on stellar so if you need to refresh
+
+ align:start position:0%
+on stellar so if you need to refresh
+ 
+
+ align:start position:0%
+on stellar so if you need to refresh
+your memory about differentiating with
+
+ align:start position:0%
+your memory about differentiating with
+ 
+
+ align:start position:0%
+your memory about differentiating with
+respect to a vector it's all there
+
+ align:start position:0%
+respect to a vector it's all there
+ 
+
+ align:start position:0%
+respect to a vector it's all there
+and so what does this say well this says
+
+ align:start position:0%
+and so what does this say well this says
+ 
+
+ align:start position:0%
+and so what does this say well this says
+that nq equals lambda q
+
+ align:start position:0%
+that nq equals lambda q
+ 
+
+ align:start position:0%
+that nq equals lambda q
+well that should remind you of stuff
+
+ align:start position:0%
+well that should remind you of stuff
+ 
+
+ align:start position:0%
+well that should remind you of stuff
+we've done before right it's an
+
+ align:start position:0%
+we've done before right it's an
+ 
+
+ align:start position:0%
+we've done before right it's an
+eigenvector
+
+ align:start position:0%
+eigenvector
+ 
+
+ align:start position:0%
+eigenvector
+so q has to be an eigenvector and lambda
+
+ align:start position:0%
+so q has to be an eigenvector and lambda
+ 
+
+ align:start position:0%
+so q has to be an eigenvector and lambda
+is the eigenvalue
+
+ align:start position:0%
+is the eigenvalue
+ 
+
+ align:start position:0%
+is the eigenvalue
+and since we want to make this as large
+
+ align:start position:0%
+and since we want to make this as large
+ 
+
+ align:start position:0%
+and since we want to make this as large
+as possible we pick the eigenvector that
+
+ align:start position:0%
+as possible we pick the eigenvector that
+ 
+
+ align:start position:0%
+as possible we pick the eigenvector that
+corresponds to the largest eigen which
+
+ align:start position:0%
+corresponds to the largest eigen which
+ 
+
+ align:start position:0%
+corresponds to the largest eigen which
+is sort of unusual in the past we've
+
+ align:start position:0%
+is sort of unusual in the past we've
+ 
+
+ align:start position:0%
+is sort of unusual in the past we've
+always wanted to minimize something we
+
+ align:start position:0%
+always wanted to minimize something we
+ 
+
+ align:start position:0%
+always wanted to minimize something we
+wanted the smallest
+
+ align:start position:0%
+wanted the smallest
+ 
+
+ align:start position:0%
+wanted the smallest
+eigenvalue here because of that sine
+
+ align:start position:0%
+eigenvalue here because of that sine
+ 
+
+ align:start position:0%
+eigenvalue here because of that sine
+flip we want the largest one
+
+ align:start position:0%
+flip we want the largest one
+ 
+
+ align:start position:0%
+flip we want the largest one
+and what is it the eigenvector of it's a
+
+ align:start position:0%
+and what is it the eigenvector of it's a
+ 
+
+ align:start position:0%
+and what is it the eigenvector of it's a
+four by four real symmetric matrix
+
+ align:start position:0%
+four by four real symmetric matrix
+ 
+
+ align:start position:0%
+four by four real symmetric matrix
+which is constructed from the data
+
+ align:start position:0%
+which is constructed from the data
+ 
+
+ align:start position:0%
+which is constructed from the data
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+so a couple of notes on that so one of
+
+ align:start position:0%
+so a couple of notes on that so one of
+ 
+
+ align:start position:0%
+so a couple of notes on that so one of
+them is
+
+ align:start position:0%
+them is
+ 
+
+ align:start position:0%
+them is
+you know we said for a two by four two
+
+ align:start position:0%
+you know we said for a two by four two
+ 
+
+ align:start position:0%
+you know we said for a two by four two
+by two matrix we actually explicitly
+
+ align:start position:0%
+by two matrix we actually explicitly
+ 
+
+ align:start position:0%
+by two matrix we actually explicitly
+gave the eigenvalues and eigenvectors
+
+ align:start position:0%
+gave the eigenvalues and eigenvectors
+ 
+
+ align:start position:0%
+gave the eigenvalues and eigenvectors
+because we know how to solve quadratics
+
+ align:start position:0%
+because we know how to solve quadratics
+ 
+
+ align:start position:0%
+because we know how to solve quadratics
+and i mentioned last time that for 3x3
+
+ align:start position:0%
+and i mentioned last time that for 3x3
+ 
+
+ align:start position:0%
+and i mentioned last time that for 3x3
+it can be done because the
+
+ align:start position:0%
+it can be done because the
+ 
+
+ align:start position:0%
+it can be done because the
+characteristic equation is a cubic
+
+ align:start position:0%
+characteristic equation is a cubic
+ 
+
+ align:start position:0%
+characteristic equation is a cubic
+polynomial in lambda and and someone
+
+ align:start position:0%
+polynomial in lambda and and someone
+ 
+
+ align:start position:0%
+polynomial in lambda and and someone
+knows how to solve cubics in closed form
+
+ align:start position:0%
+knows how to solve cubics in closed form
+ 
+
+ align:start position:0%
+knows how to solve cubics in closed form
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+by the way this used to be
+
+ align:start position:0%
+by the way this used to be
+ 
+
+ align:start position:0%
+by the way this used to be
+a big game particularly amongst the
+
+ align:start position:0%
+a big game particularly amongst the
+ 
+
+ align:start position:0%
+a big game particularly amongst the
+italian mathematicians you know they
+
+ align:start position:0%
+italian mathematicians you know they
+ 
+
+ align:start position:0%
+italian mathematicians you know they
+would this was these problems were real
+
+ align:start position:0%
+would this was these problems were real
+ 
+
+ align:start position:0%
+would this was these problems were real
+puzzled to them and they were very proud
+
+ align:start position:0%
+puzzled to them and they were very proud
+ 
+
+ align:start position:0%
+puzzled to them and they were very proud
+when they saw them you know correctly so
+
+ align:start position:0%
+when they saw them you know correctly so
+ 
+
+ align:start position:0%
+when they saw them you know correctly so
+but there was uh there wasn't the same
+
+ align:start position:0%
+but there was uh there wasn't the same
+ 
+
+ align:start position:0%
+but there was uh there wasn't the same
+sort of modern you know publication and
+
+ align:start position:0%
+sort of modern you know publication and
+ 
+
+ align:start position:0%
+sort of modern you know publication and
+tenure and whatever it's like you've
+
+ align:start position:0%
+tenure and whatever it's like you've
+ 
+
+ align:start position:0%
+tenure and whatever it's like you've
+solved this tough problem and you know
+
+ align:start position:0%
+solved this tough problem and you know
+ 
+
+ align:start position:0%
+solved this tough problem and you know
+you're very proud of it what do you do
+
+ align:start position:0%
+you're very proud of it what do you do
+ 
+
+ align:start position:0%
+you're very proud of it what do you do
+with it you don't want to just give it
+
+ align:start position:0%
+with it you don't want to just give it
+ 
+
+ align:start position:0%
+with it you don't want to just give it
+away and yet you want to be able to say
+
+ align:start position:0%
+away and yet you want to be able to say
+ 
+
+ align:start position:0%
+away and yet you want to be able to say
+later you know i got that 10 years ago
+
+ align:start position:0%
+later you know i got that 10 years ago
+ 
+
+ align:start position:0%
+later you know i got that 10 years ago
+so they'd come up with all these weird
+
+ align:start position:0%
+so they'd come up with all these weird
+ 
+
+ align:start position:0%
+so they'd come up with all these weird
+ways of coding and coding their solution
+
+ align:start position:0%
+ways of coding and coding their solution
+ 
+
+ align:start position:0%
+ways of coding and coding their solution
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+like in a story or as a sort of parable
+
+ align:start position:0%
+like in a story or as a sort of parable
+ 
+
+ align:start position:0%
+like in a story or as a sort of parable
+or some sort of other mathematics and
+
+ align:start position:0%
+or some sort of other mathematics and
+ 
+
+ align:start position:0%
+or some sort of other mathematics and
+then later on you know ferrari who was
+
+ align:start position:0%
+then later on you know ferrari who was
+ 
+
+ align:start position:0%
+then later on you know ferrari who was
+one of the guys who did this could say
+
+ align:start position:0%
+one of the guys who did this could say
+ 
+
+ align:start position:0%
+one of the guys who did this could say
+that oh i solved this years before
+
+ align:start position:0%
+that oh i solved this years before
+ 
+
+ align:start position:0%
+that oh i solved this years before
+cardano who is another guy because look
+
+ align:start position:0%
+cardano who is another guy because look
+ 
+
+ align:start position:0%
+cardano who is another guy because look
+at that poem i wrote it tells you how to
+
+ align:start position:0%
+at that poem i wrote it tells you how to
+ 
+
+ align:start position:0%
+at that poem i wrote it tells you how to
+do this so anyway
+
+ align:start position:0%
+do this so anyway
+ 
+
+ align:start position:0%
+do this so anyway
+they discovered how to solve cubics
+
+ align:start position:0%
+they discovered how to solve cubics
+ 
+
+ align:start position:0%
+they discovered how to solve cubics
+here we're going to have a quartic right
+
+ align:start position:0%
+here we're going to have a quartic right
+ 
+
+ align:start position:0%
+here we're going to have a quartic right
+because it's four by four it's going to
+
+ align:start position:0%
+because it's four by four it's going to
+ 
+
+ align:start position:0%
+because it's four by four it's going to
+be fourth order and guess what
+
+ align:start position:0%
+be fourth order and guess what
+ 
+
+ align:start position:0%
+be fourth order and guess what
+they have closed form solutions and
+
+ align:start position:0%
+they have closed form solutions and
+ 
+
+ align:start position:0%
+they have closed form solutions and
+those italian mathematicians and others
+
+ align:start position:0%
+those italian mathematicians and others
+ 
+
+ align:start position:0%
+those italian mathematicians and others
+figured out how to how to do do it
+
+ align:start position:0%
+figured out how to how to do do it
+ 
+
+ align:start position:0%
+figured out how to how to do do it
+basically how do you do any of these
+
+ align:start position:0%
+basically how do you do any of these
+ 
+
+ align:start position:0%
+basically how do you do any of these
+things well the usual trick you try and
+
+ align:start position:0%
+things well the usual trick you try and
+ 
+
+ align:start position:0%
+things well the usual trick you try and
+find a way of reducing third order to
+
+ align:start position:0%
+find a way of reducing third order to
+ 
+
+ align:start position:0%
+find a way of reducing third order to
+second order because you know how to do
+
+ align:start position:0%
+second order because you know how to do
+ 
+
+ align:start position:0%
+second order because you know how to do
+second order
+
+ align:start position:0%
+second order
+ 
+
+ align:start position:0%
+second order
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+quartics
+
+ align:start position:0%
+quartics
+ 
+
+ align:start position:0%
+quartics
+first step is reduce it to a cubic solve
+
+ align:start position:0%
+first step is reduce it to a cubic solve
+ 
+
+ align:start position:0%
+first step is reduce it to a cubic solve
+the cubic and then the rest is easy
+
+ align:start position:0%
+the cubic and then the rest is easy
+ 
+
+ align:start position:0%
+the cubic and then the rest is easy
+and so uh can you solve fifth order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+okay so it's good that some of you know
+
+ align:start position:0%
+okay so it's good that some of you know
+ 
+
+ align:start position:0%
+okay so it's good that some of you know
+that that's it you can't now of course
+
+ align:start position:0%
+that that's it you can't now of course
+ 
+
+ align:start position:0%
+that that's it you can't now of course
+today with computers we can always
+
+ align:start position:0%
+today with computers we can always
+ 
+
+ align:start position:0%
+today with computers we can always
+numerically solve any of these but
+
+ align:start position:0%
+numerically solve any of these but
+ 
+
+ align:start position:0%
+numerically solve any of these but
+if you want to
+
+ align:start position:0%
+if you want to
+ 
+
+ align:start position:0%
+if you want to
+have a quote closed form solution
+
+ align:start position:0%
+have a quote closed form solution
+ 
+
+ align:start position:0%
+have a quote closed form solution
+you know then you do need to know that
+
+ align:start position:0%
+you know then you do need to know that
+ 
+
+ align:start position:0%
+you know then you do need to know that
+you can solve one two three four but
+
+ align:start position:0%
+you can solve one two three four but
+ 
+
+ align:start position:0%
+you can solve one two three four but
+that's it then higher order you can't
+
+ align:start position:0%
+that's it then higher order you can't
+ 
+
+ align:start position:0%
+that's it then higher order you can't
+solve in closed form using addition
+
+ align:start position:0%
+solve in closed form using addition
+ 
+
+ align:start position:0%
+solve in closed form using addition
+subtraction multiplication and square
+
+ align:start position:0%
+subtraction multiplication and square
+ 
+
+ align:start position:0%
+subtraction multiplication and square
+roots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this matrix down here
+
+ align:start position:0%
+this matrix down here
+ 
+
+ align:start position:0%
+this matrix down here
+it look is more familiar to you than n
+
+ align:start position:0%
+it look is more familiar to you than n
+ 
+
+ align:start position:0%
+it look is more familiar to you than n
+that's because this is simply the diatic
+
+ align:start position:0%
+that's because this is simply the diatic
+ 
+
+ align:start position:0%
+that's because this is simply the diatic
+product of the vector in the left
+
+ align:start position:0%
+product of the vector in the left
+ 
+
+ align:start position:0%
+product of the vector in the left
+coordinate system and the vector in the
+
+ align:start position:0%
+coordinate system and the vector in the
+ 
+
+ align:start position:0%
+coordinate system and the vector in the
+right coordinate system so this is a
+
+ align:start position:0%
+right coordinate system so this is a
+ 
+
+ align:start position:0%
+right coordinate system so this is a
+three by three each of these is a three
+
+ align:start position:0%
+three by three each of these is a three
+ 
+
+ align:start position:0%
+three by three each of these is a three
+by three matrix
+
+ align:start position:0%
+by three matrix
+ 
+
+ align:start position:0%
+by three matrix
+that's a dyadic product and you just
+
+ align:start position:0%
+that's a dyadic product and you just
+ 
+
+ align:start position:0%
+that's a dyadic product and you just
+keep on going stepping through your
+
+ align:start position:0%
+keep on going stepping through your
+ 
+
+ align:start position:0%
+keep on going stepping through your
+point pairs and adding them up and you
+
+ align:start position:0%
+point pairs and adding them up and you
+ 
+
+ align:start position:0%
+point pairs and adding them up and you
+get a three by three matrix
+
+ align:start position:0%
+get a three by three matrix
+ 
+
+ align:start position:0%
+get a three by three matrix
+which is not symmetric um
+
+ align:start position:0%
+which is not symmetric um
+ 
+
+ align:start position:0%
+which is not symmetric um
+and so it has nine independent
+
+ align:start position:0%
+and so it has nine independent
+ 
+
+ align:start position:0%
+and so it has nine independent
+quantities
+
+ align:start position:0%
+quantities
+ 
+
+ align:start position:0%
+quantities
+and let's think about n
+
+ align:start position:0%
+and let's think about n
+ 
+
+ align:start position:0%
+and let's think about n
+well uh n um
+
+ align:start position:0%
+well uh n um
+ 
+
+ align:start position:0%
+well uh n um
+is four by four so it has 16 so so how
+
+ align:start position:0%
+is four by four so it has 16 so so how
+ 
+
+ align:start position:0%
+is four by four so it has 16 so so how
+does that work
+
+ align:start position:0%
+does that work
+ 
+
+ align:start position:0%
+does that work
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it turns out that uh n is rather special
+
+ align:start position:0%
+it turns out that uh n is rather special
+ 
+
+ align:start position:0%
+it turns out that uh n is rather special
+it turns out n is symmetric and and uh
+
+ align:start position:0%
+it turns out n is symmetric and and uh
+ 
+
+ align:start position:0%
+it turns out n is symmetric and and uh
+it turns out that it's not that easy to
+
+ align:start position:0%
+it turns out that it's not that easy to
+ 
+
+ align:start position:0%
+it turns out that it's not that easy to
+prove and
+
+ align:start position:0%
+prove and
+ 
+
+ align:start position:0%
+prove and
+the one mistake in this paper was that
+
+ align:start position:0%
+the one mistake in this paper was that
+ 
+
+ align:start position:0%
+the one mistake in this paper was that
+um i think i said something like it's
+
+ align:start position:0%
+um i think i said something like it's
+ 
+
+ align:start position:0%
+um i think i said something like it's
+obvious that it's symmetric but
+
+ align:start position:0%
+obvious that it's symmetric but
+ 
+
+ align:start position:0%
+obvious that it's symmetric but
+it takes some anyway it's symmetric so
+
+ align:start position:0%
+it takes some anyway it's symmetric so
+ 
+
+ align:start position:0%
+it takes some anyway it's symmetric so
+that means four by four symmetric we've
+
+ align:start position:0%
+that means four by four symmetric we've
+ 
+
+ align:start position:0%
+that means four by four symmetric we've
+got uh four on the diagonal and then we
+
+ align:start position:0%
+got uh four on the diagonal and then we
+ 
+
+ align:start position:0%
+got uh four on the diagonal and then we
+have um
+
+ align:start position:0%
+have um
+ 
+
+ align:start position:0%
+have um
+six more no ten we have ten independent
+
+ align:start position:0%
+six more no ten we have ten independent
+ 
+
+ align:start position:0%
+six more no ten we have ten independent
+so it's not sixteen but it's ten but
+
+ align:start position:0%
+so it's not sixteen but it's ten but
+ 
+
+ align:start position:0%
+so it's not sixteen but it's ten but
+it's still it's still too many right
+
+ align:start position:0%
+it's still it's still too many right
+ 
+
+ align:start position:0%
+it's still it's still too many right
+because we only have 9 in m well it
+
+ align:start position:0%
+because we only have 9 in m well it
+ 
+
+ align:start position:0%
+because we only have 9 in m well it
+turns out that this matrix is very
+
+ align:start position:0%
+turns out that this matrix is very
+ 
+
+ align:start position:0%
+turns out that this matrix is very
+special because
+
+ align:start position:0%
+special because
+ 
+
+ align:start position:0%
+special because
+the determinant the characteristic
+
+ align:start position:0%
+the determinant the characteristic
+ 
+
+ align:start position:0%
+the determinant the characteristic
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+up here has some has this important
+
+ align:start position:0%
+up here has some has this important
+ 
+
+ align:start position:0%
+up here has some has this important
+property that
+
+ align:start position:0%
+property that
+ 
+
+ align:start position:0%
+property that
+that cubic term is zero which actually
+
+ align:start position:0%
+that cubic term is zero which actually
+ 
+
+ align:start position:0%
+that cubic term is zero which actually
+makes it easier to reduce it to a cubic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so n is a symmetric four by four matrix
+
+ align:start position:0%
+so n is a symmetric four by four matrix
+ 
+
+ align:start position:0%
+so n is a symmetric four by four matrix
+with a trace of zero so that means we've
+
+ align:start position:0%
+with a trace of zero so that means we've
+ 
+
+ align:start position:0%
+with a trace of zero so that means we've
+got ten minus one is nine so that so now
+
+ align:start position:0%
+got ten minus one is nine so that so now
+ 
+
+ align:start position:0%
+got ten minus one is nine so that so now
+it matches
+
+ align:start position:0%
+it matches
+ 
+
+ align:start position:0%
+it matches
+m has nine independent values okay we
+
+ align:start position:0%
+m has nine independent values okay we
+ 
+
+ align:start position:0%
+m has nine independent values okay we
+don't need to really know and if you're
+
+ align:start position:0%
+don't need to really know and if you're
+ 
+
+ align:start position:0%
+don't need to really know and if you're
+actually gonna implement this you might
+
+ align:start position:0%
+actually gonna implement this you might
+ 
+
+ align:start position:0%
+actually gonna implement this you might
+want to know this but
+
+ align:start position:0%
+want to know this but
+ 
+
+ align:start position:0%
+want to know this but
+just to know that you can compute all
+
+ align:start position:0%
+just to know that you can compute all
+ 
+
+ align:start position:0%
+just to know that you can compute all
+the coefficients of the characteristic
+
+ align:start position:0%
+the coefficients of the characteristic
+ 
+
+ align:start position:0%
+the coefficients of the characteristic
+equation and then you go off and solve
+
+ align:start position:0%
+equation and then you go off and solve
+ 
+
+ align:start position:0%
+equation and then you go off and solve
+your quotient
+
+ align:start position:0%
+your quotient
+ 
+
+ align:start position:0%
+your quotient
+so the main application is going to be
+
+ align:start position:0%
+so the main application is going to be
+ 
+
+ align:start position:0%
+so the main application is going to be
+absolute orientation
+
+ align:start position:0%
+absolute orientation
+ 
+
+ align:start position:0%
+absolute orientation
+but it also has lots of other
+
+ align:start position:0%
+but it also has lots of other
+ 
+
+ align:start position:0%
+but it also has lots of other
+applications that we you know already
+
+ align:start position:0%
+applications that we you know already
+ 
+
+ align:start position:0%
+applications that we you know already
+talked about
+
+ align:start position:0%
+talked about
+ 
+
+ align:start position:0%
+talked about
+and in
+
+ align:start position:0%
+and in
+ 
+
+ align:start position:0%
+and in
+if you go over to draper lab where they
+
+ align:start position:0%
+if you go over to draper lab where they
+ 
+
+ align:start position:0%
+if you go over to draper lab where they
+do all this uh spacecraft control
+
+ align:start position:0%
+do all this uh spacecraft control
+ 
+
+ align:start position:0%
+do all this uh spacecraft control
+you'll find people who uh know about
+
+ align:start position:0%
+you'll find people who uh know about
+ 
+
+ align:start position:0%
+you'll find people who uh know about
+quaternions because that's what's used
+
+ align:start position:0%
+quaternions because that's what's used
+ 
+
+ align:start position:0%
+quaternions because that's what's used
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+desirable properties so we had this
+
+ align:start position:0%
+desirable properties so we had this
+ 
+
+ align:start position:0%
+desirable properties so we had this
+table let's see how we're doing
+
+ align:start position:0%
+table let's see how we're doing
+ 
+
+ align:start position:0%
+table let's see how we're doing
+ability to rotate vectors yes we q r q
+
+ align:start position:0%
+ability to rotate vectors yes we q r q
+ 
+
+ align:start position:0%
+ability to rotate vectors yes we q r q
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+ability compose rotations yes p times q
+
+ align:start position:0%
+ability compose rotations yes p times q
+ 
+
+ align:start position:0%
+ability compose rotations yes p times q
+is the composition
+
+ align:start position:0%
+is the composition
+ 
+
+ align:start position:0%
+is the composition
+intuitive non-redundant representation
+
+ align:start position:0%
+intuitive non-redundant representation
+ 
+
+ align:start position:0%
+intuitive non-redundant representation
+well it's almost non-redundant it has
+
+ align:start position:0%
+well it's almost non-redundant it has
+ 
+
+ align:start position:0%
+well it's almost non-redundant it has
+four numbers to represent three degrees
+
+ align:start position:0%
+four numbers to represent three degrees
+ 
+
+ align:start position:0%
+four numbers to represent three degrees
+of freedom
+
+ align:start position:0%
+of freedom
+ 
+
+ align:start position:0%
+of freedom
+and but the redundancy is very simple
+
+ align:start position:0%
+and but the redundancy is very simple
+ 
+
+ align:start position:0%
+and but the redundancy is very simple
+it's just the unit unit quaternion uh is
+
+ align:start position:0%
+it's just the unit unit quaternion uh is
+ 
+
+ align:start position:0%
+it's just the unit unit quaternion uh is
+it intuitive
+
+ align:start position:0%
+it intuitive
+ 
+
+ align:start position:0%
+it intuitive
+you know one part the the vector part is
+
+ align:start position:0%
+you know one part the the vector part is
+ 
+
+ align:start position:0%
+you know one part the the vector part is
+in the direction of the axis that sort
+
+ align:start position:0%
+in the direction of the axis that sort
+ 
+
+ align:start position:0%
+in the direction of the axis that sort
+of intuitive
+
+ align:start position:0%
+of intuitive
+ 
+
+ align:start position:0%
+of intuitive
+computational efficiency we haven't
+
+ align:start position:0%
+computational efficiency we haven't
+ 
+
+ align:start position:0%
+computational efficiency we haven't
+talked about that yet you know how does
+
+ align:start position:0%
+talked about that yet you know how does
+ 
+
+ align:start position:0%
+talked about that yet you know how does
+it compare with matrix operations
+
+ align:start position:0%
+it compare with matrix operations
+ 
+
+ align:start position:0%
+it compare with matrix operations
+uh can we do things like interpolate
+
+ align:start position:0%
+uh can we do things like interpolate
+ 
+
+ align:start position:0%
+uh can we do things like interpolate
+orientations yes
+
+ align:start position:0%
+orientations yes
+ 
+
+ align:start position:0%
+orientations yes
+you know suppose that you have um
+
+ align:start position:0%
+you know suppose that you have um
+ 
+
+ align:start position:0%
+you know suppose that you have um
+your artist has the ballerina doing a
+
+ align:start position:0%
+your artist has the ballerina doing a
+ 
+
+ align:start position:0%
+your artist has the ballerina doing a
+turn and got it got her in this position
+
+ align:start position:0%
+turn and got it got her in this position
+ 
+
+ align:start position:0%
+turn and got it got her in this position
+and then in that position
+
+ align:start position:0%
+and then in that position
+ 
+
+ align:start position:0%
+and then in that position
+uh rotate it
+
+ align:start position:0%
+uh rotate it
+ 
+
+ align:start position:0%
+uh rotate it
+how do you do all the in-betweening
+
+ align:start position:0%
+how do you do all the in-betweening
+ 
+
+ align:start position:0%
+how do you do all the in-betweening
+do you take the initial rotation matrix
+
+ align:start position:0%
+do you take the initial rotation matrix
+ 
+
+ align:start position:0%
+do you take the initial rotation matrix
+and the final rotation matrix takes some
+
+ align:start position:0%
+and the final rotation matrix takes some
+ 
+
+ align:start position:0%
+and the final rotation matrix takes some
+sort of weighted average
+
+ align:start position:0%
+sort of weighted average
+ 
+
+ align:start position:0%
+sort of weighted average
+well that's not going to be orthonormal
+
+ align:start position:0%
+well that's not going to be orthonormal
+ 
+
+ align:start position:0%
+well that's not going to be orthonormal
+so here it's trivial
+
+ align:start position:0%
+so here it's trivial
+ 
+
+ align:start position:0%
+so here it's trivial
+right you just
+
+ align:start position:0%
+right you just
+ 
+
+ align:start position:0%
+right you just
+take that angle suppose that the
+
+ align:start position:0%
+take that angle suppose that the
+ 
+
+ align:start position:0%
+take that angle suppose that the
+rotation is about an axis through an
+
+ align:start position:0%
+rotation is about an axis through an
+ 
+
+ align:start position:0%
+rotation is about an axis through an
+angle of 90 degrees you just split it up
+
+ align:start position:0%
+angle of 90 degrees you just split it up
+ 
+
+ align:start position:0%
+angle of 90 degrees you just split it up
+into however many frames you need and
+
+ align:start position:0%
+into however many frames you need and
+ 
+
+ align:start position:0%
+into however many frames you need and
+compute the quaternion
+
+ align:start position:0%
+compute the quaternion
+ 
+
+ align:start position:0%
+compute the quaternion
+correspondingly
+
+ align:start position:0%
+correspondingly
+ 
+
+ align:start position:0%
+correspondingly
+we can take averages of a range of
+
+ align:start position:0%
+we can take averages of a range of
+ 
+
+ align:start position:0%
+we can take averages of a range of
+rotations if you want to know
+
+ align:start position:0%
+rotations if you want to know
+ 
+
+ align:start position:0%
+rotations if you want to know
+the average loading on the seat belt as
+
+ align:start position:0%
+the average loading on the seat belt as
+ 
+
+ align:start position:0%
+the average loading on the seat belt as
+your car is tumbling in all possible
+
+ align:start position:0%
+your car is tumbling in all possible
+ 
+
+ align:start position:0%
+your car is tumbling in all possible
+orientations you can easily do that
+
+ align:start position:0%
+orientations you can easily do that
+ 
+
+ align:start position:0%
+orientations you can easily do that
+and we can
+
+ align:start position:0%
+and we can
+ 
+
+ align:start position:0%
+and we can
+take the derivative as we saw so we can
+
+ align:start position:0%
+take the derivative as we saw so we can
+ 
+
+ align:start position:0%
+take the derivative as we saw so we can
+do optimizations least squares
+
+ align:start position:0%
+do optimizations least squares
+ 
+
+ align:start position:0%
+do optimizations least squares
+if if there's no closed form solution we
+
+ align:start position:0%
+if if there's no closed form solution we
+ 
+
+ align:start position:0%
+if if there's no closed form solution we
+at least have a way of sampling that
+
+ align:start position:0%
+at least have a way of sampling that
+ 
+
+ align:start position:0%
+at least have a way of sampling that
+space of possibilities in a uniform or
+
+ align:start position:0%
+space of possibilities in a uniform or
+ 
+
+ align:start position:0%
+space of possibilities in a uniform or
+random way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh okay well let's see how late is it
+
+ align:start position:0%
+oh okay well let's see how late is it
+ 
+
+ align:start position:0%
+oh okay well let's see how late is it
+well let's do a couple more things
+
+ align:start position:0%
+well let's do a couple more things
+ 
+
+ align:start position:0%
+well let's do a couple more things
+okay so this is where we're going to go
+
+ align:start position:0%
+okay so this is where we're going to go
+ 
+
+ align:start position:0%
+okay so this is where we're going to go
+after absolute orientation this is
+
+ align:start position:0%
+after absolute orientation this is
+ 
+
+ align:start position:0%
+after absolute orientation this is
+relative orientation and this is kind of
+
+ align:start position:0%
+relative orientation and this is kind of
+ 
+
+ align:start position:0%
+relative orientation and this is kind of
+uh more
+
+ align:start position:0%
+uh more
+ 
+
+ align:start position:0%
+uh more
+so absolute orientation is very
+
+ align:start position:0%
+so absolute orientation is very
+ 
+
+ align:start position:0%
+so absolute orientation is very
+important for photogrammetry you know
+
+ align:start position:0%
+important for photogrammetry you know
+ 
+
+ align:start position:0%
+important for photogrammetry you know
+making topographic maps from aerial
+
+ align:start position:0%
+making topographic maps from aerial
+ 
+
+ align:start position:0%
+making topographic maps from aerial
+photographs but in terms of
+
+ align:start position:0%
+photographs but in terms of
+ 
+
+ align:start position:0%
+photographs but in terms of
+understanding human vision you know one
+
+ align:start position:0%
+understanding human vision you know one
+ 
+
+ align:start position:0%
+understanding human vision you know one
+of a dozen depth cues is binocular
+
+ align:start position:0%
+of a dozen depth cues is binocular
+ 
+
+ align:start position:0%
+of a dozen depth cues is binocular
+stereo and so relative orientation there
+
+ align:start position:0%
+stereo and so relative orientation there
+ 
+
+ align:start position:0%
+stereo and so relative orientation there
+is more important and so that's the
+
+ align:start position:0%
+is more important and so that's the
+ 
+
+ align:start position:0%
+is more important and so that's the
+problem of we've got two eyes
+
+ align:start position:0%
+problem of we've got two eyes
+ 
+
+ align:start position:0%
+problem of we've got two eyes
+and the eyes don't get depth uh they
+
+ align:start position:0%
+and the eyes don't get depth uh they
+ 
+
+ align:start position:0%
+and the eyes don't get depth uh they
+only get directions so we have the
+
+ align:start position:0%
+only get directions so we have the
+ 
+
+ align:start position:0%
+only get directions so we have the
+directions in each of those coordinate
+
+ align:start position:0%
+directions in each of those coordinate
+ 
+
+ align:start position:0%
+directions in each of those coordinate
+systems two points out in the world
+
+ align:start position:0%
+systems two points out in the world
+ 
+
+ align:start position:0%
+systems two points out in the world
+and are shown five and it turns out five
+
+ align:start position:0%
+and are shown five and it turns out five
+ 
+
+ align:start position:0%
+and are shown five and it turns out five
+is the minimum number you need to solve
+
+ align:start position:0%
+is the minimum number you need to solve
+ 
+
+ align:start position:0%
+is the minimum number you need to solve
+this problem and your problem is to find
+
+ align:start position:0%
+this problem and your problem is to find
+ 
+
+ align:start position:0%
+this problem and your problem is to find
+out what that baseline is and what the
+
+ align:start position:0%
+out what that baseline is and what the
+ 
+
+ align:start position:0%
+out what that baseline is and what the
+relative orientation of this coordinate
+
+ align:start position:0%
+relative orientation of this coordinate
+ 
+
+ align:start position:0%
+relative orientation of this coordinate
+system is relative to that in other
+
+ align:start position:0%
+system is relative to that in other
+ 
+
+ align:start position:0%
+system is relative to that in other
+words
+
+ align:start position:0%
+words
+ 
+
+ align:start position:0%
+words
+we have a translation and we're going to
+
+ align:start position:0%
+we have a translation and we're going to
+ 
+
+ align:start position:0%
+we have a translation and we're going to
+have a rotation
+
+ align:start position:0%
+have a rotation
+ 
+
+ align:start position:0%
+have a rotation
+so in that respect it's the same problem
+
+ align:start position:0%
+so in that respect it's the same problem
+ 
+
+ align:start position:0%
+so in that respect it's the same problem
+it's just that our data now is not as
+
+ align:start position:0%
+it's just that our data now is not as
+ 
+
+ align:start position:0%
+it's just that our data now is not as
+good but for in absolute orientation we
+
+ align:start position:0%
+good but for in absolute orientation we
+ 
+
+ align:start position:0%
+good but for in absolute orientation we
+actually know 3d coordinates of all of
+
+ align:start position:0%
+actually know 3d coordinates of all of
+ 
+
+ align:start position:0%
+actually know 3d coordinates of all of
+these points and that makes it possible
+
+ align:start position:0%
+these points and that makes it possible
+ 
+
+ align:start position:0%
+these points and that makes it possible
+to get a closed form solution here we
+
+ align:start position:0%
+to get a closed form solution here we
+ 
+
+ align:start position:0%
+to get a closed form solution here we
+only know the directions so that's the
+
+ align:start position:0%
+only know the directions so that's the
+ 
+
+ align:start position:0%
+only know the directions so that's the
+problem we're going to solve after
+
+ align:start position:0%
+problem we're going to solve after
+ 
+
+ align:start position:0%
+problem we're going to solve after
+absolute orientation
+
+ align:start position:0%
+absolute orientation
+ 
+
+ align:start position:0%
+absolute orientation
+um then you know if you're trying to
+
+ align:start position:0%
+um then you know if you're trying to
+ 
+
+ align:start position:0%
+um then you know if you're trying to
+describe the kinematics of a robot
+
+ align:start position:0%
+describe the kinematics of a robot
+ 
+
+ align:start position:0%
+describe the kinematics of a robot
+manipulator
+
+ align:start position:0%
+manipulator
+ 
+
+ align:start position:0%
+manipulator
+well these days people are lazy you just
+
+ align:start position:0%
+well these days people are lazy you just
+ 
+
+ align:start position:0%
+well these days people are lazy you just
+buy it and the software does all that
+
+ align:start position:0%
+buy it and the software does all that
+ 
+
+ align:start position:0%
+buy it and the software does all that
+for you but you know in the old days
+
+ align:start position:0%
+for you but you know in the old days
+ 
+
+ align:start position:0%
+for you but you know in the old days
+uh you know we had to walk in the snow
+
+ align:start position:0%
+uh you know we had to walk in the snow
+ 
+
+ align:start position:0%
+uh you know we had to walk in the snow
+there was no bus well in the old days
+
+ align:start position:0%
+there was no bus well in the old days
+ 
+
+ align:start position:0%
+there was no bus well in the old days
+you actually had to understand the
+
+ align:start position:0%
+you actually had to understand the
+ 
+
+ align:start position:0%
+you actually had to understand the
+geometry of these devices and that means
+
+ align:start position:0%
+geometry of these devices and that means
+ 
+
+ align:start position:0%
+geometry of these devices and that means
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+as you go through each link you are
+
+ align:start position:0%
+as you go through each link you are
+ 
+
+ align:start position:0%
+as you go through each link you are
+doing a translation and a rotation and
+
+ align:start position:0%
+doing a translation and a rotation and
+ 
+
+ align:start position:0%
+doing a translation and a rotation and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if you want to avoid problems with
+
+ align:start position:0%
+if you want to avoid problems with
+ 
+
+ align:start position:0%
+if you want to avoid problems with
+coordinate systems lining up
+
+ align:start position:0%
+coordinate systems lining up
+ 
+
+ align:start position:0%
+coordinate systems lining up
+particularly in the wrist
+
+ align:start position:0%
+particularly in the wrist
+ 
+
+ align:start position:0%
+particularly in the wrist
+then quaternions are a good way to
+
+ align:start position:0%
+then quaternions are a good way to
+ 
+
+ align:start position:0%
+then quaternions are a good way to
+represent the rotation so in the wrist
+
+ align:start position:0%
+represent the rotation so in the wrist
+ 
+
+ align:start position:0%
+represent the rotation so in the wrist
+for example you can imagine that if this
+
+ align:start position:0%
+for example you can imagine that if this
+ 
+
+ align:start position:0%
+for example you can imagine that if this
+part now comes up there'll be a time
+
+ align:start position:0%
+part now comes up there'll be a time
+ 
+
+ align:start position:0%
+part now comes up there'll be a time
+where this axis in here is parallel to
+
+ align:start position:0%
+where this axis in here is parallel to
+ 
+
+ align:start position:0%
+where this axis in here is parallel to
+that axis and you've lost the degree of
+
+ align:start position:0%
+that axis and you've lost the degree of
+ 
+
+ align:start position:0%
+that axis and you've lost the degree of
+freedom so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh computational issues now i guess
+
+ align:start position:0%
+uh computational issues now i guess
+ 
+
+ align:start position:0%
+uh computational issues now i guess
+these days computers are pretty fast so
+
+ align:start position:0%
+these days computers are pretty fast so
+ 
+
+ align:start position:0%
+these days computers are pretty fast so
+we don't worry about this as much but if
+
+ align:start position:0%
+we don't worry about this as much but if
+ 
+
+ align:start position:0%
+we don't worry about this as much but if
+you have to do this for every point in
+
+ align:start position:0%
+you have to do this for every point in
+ 
+
+ align:start position:0%
+you have to do this for every point in
+some object in your graphics
+
+ align:start position:0%
+some object in your graphics
+ 
+
+ align:start position:0%
+some object in your graphics
+representation this this could be an
+
+ align:start position:0%
+representation this this could be an
+ 
+
+ align:start position:0%
+representation this this could be an
+issue
+
+ align:start position:0%
+issue
+ 
+
+ align:start position:0%
+issue
+so let's see how expensive it is so
+
+ align:start position:0%
+so let's see how expensive it is so
+ 
+
+ align:start position:0%
+so let's see how expensive it is so
+again the two things we want to do
+
+ align:start position:0%
+again the two things we want to do
+ 
+
+ align:start position:0%
+again the two things we want to do
+compose rotations and rotate vectors so
+
+ align:start position:0%
+compose rotations and rotate vectors so
+ 
+
+ align:start position:0%
+compose rotations and rotate vectors so
+for composition we know it's just
+
+ align:start position:0%
+for composition we know it's just
+ 
+
+ align:start position:0%
+for composition we know it's just
+multiplying two quaternions and if you
+
+ align:start position:0%
+multiplying two quaternions and if you
+ 
+
+ align:start position:0%
+multiplying two quaternions and if you
+do it the naive way just you following
+
+ align:start position:0%
+do it the naive way just you following
+ 
+
+ align:start position:0%
+do it the naive way just you following
+that formula you get 16 multipliers and
+
+ align:start position:0%
+that formula you get 16 multipliers and
+ 
+
+ align:start position:0%
+that formula you get 16 multipliers and
+12 adds
+
+ align:start position:0%
+12 adds
+ 
+
+ align:start position:0%
+12 adds
+and if you do this with the orthonormal
+
+ align:start position:0%
+and if you do this with the orthonormal
+ 
+
+ align:start position:0%
+and if you do this with the orthonormal
+matrix of course it's a 3x3 matrix
+
+ align:start position:0%
+matrix of course it's a 3x3 matrix
+ 
+
+ align:start position:0%
+matrix of course it's a 3x3 matrix
+product which is 27 multipliers and 18
+
+ align:start position:0%
+product which is 27 multipliers and 18
+ 
+
+ align:start position:0%
+product which is 27 multipliers and 18
+adds so we we win definitely win here
+
+ align:start position:0%
+adds so we we win definitely win here
+ 
+
+ align:start position:0%
+adds so we we win definitely win here
+let's go to rotating a vector so we use
+
+ align:start position:0%
+let's go to rotating a vector so we use
+ 
+
+ align:start position:0%
+let's go to rotating a vector so we use
+this formula
+
+ align:start position:0%
+this formula
+ 
+
+ align:start position:0%
+this formula
+and we can expand out the part we want
+
+ align:start position:0%
+and we can expand out the part we want
+ 
+
+ align:start position:0%
+and we can expand out the part we want
+which is the vector part
+
+ align:start position:0%
+which is the vector part
+ 
+
+ align:start position:0%
+which is the vector part
+22 multiplies 16 ads
+
+ align:start position:0%
+22 multiplies 16 ads
+ 
+
+ align:start position:0%
+22 multiplies 16 ads
+compare the matrix per oops
+
+ align:start position:0%
+compare the matrix per oops
+ 
+
+ align:start position:0%
+compare the matrix per oops
+9 multipliers and 6 ads so here we lose
+
+ align:start position:0%
+9 multipliers and 6 ads so here we lose
+ 
+
+ align:start position:0%
+9 multipliers and 6 ads so here we lose
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+this can be rewritten in this form which
+
+ align:start position:0%
+this can be rewritten in this form which
+ 
+
+ align:start position:0%
+this can be rewritten in this form which
+has the advantage that you compute the
+
+ align:start position:0%
+has the advantage that you compute the
+ 
+
+ align:start position:0%
+has the advantage that you compute the
+qr once and you use it in two different
+
+ align:start position:0%
+qr once and you use it in two different
+ 
+
+ align:start position:0%
+qr once and you use it in two different
+places and you get it down to 15
+
+ align:start position:0%
+places and you get it down to 15
+ 
+
+ align:start position:0%
+places and you get it down to 15
+multipliers and 12 ads
+
+ align:start position:0%
+multipliers and 12 ads
+ 
+
+ align:start position:0%
+multipliers and 12 ads
+and this is naive stuff you know people
+
+ align:start position:0%
+and this is naive stuff you know people
+ 
+
+ align:start position:0%
+and this is naive stuff you know people
+that get serious about this go further
+
+ align:start position:0%
+that get serious about this go further
+ 
+
+ align:start position:0%
+that get serious about this go further
+for example with a three by three matrix
+
+ align:start position:0%
+for example with a three by three matrix
+ 
+
+ align:start position:0%
+for example with a three by three matrix
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+they don't represent it as three by
+
+ align:start position:0%
+they don't represent it as three by
+ 
+
+ align:start position:0%
+they don't represent it as three by
+three matrix at most you take the first
+
+ align:start position:0%
+three matrix at most you take the first
+ 
+
+ align:start position:0%
+three matrix at most you take the first
+two rows because the other one's
+
+ align:start position:0%
+two rows because the other one's
+ 
+
+ align:start position:0%
+two rows because the other one's
+implicit it's a cross product and so
+
+ align:start position:0%
+implicit it's a cross product and so
+ 
+
+ align:start position:0%
+implicit it's a cross product and so
+both so um you know you could have a
+
+ align:start position:0%
+both so um you know you could have a
+ 
+
+ align:start position:0%
+both so um you know you could have a
+competition where you just keep on going
+
+ align:start position:0%
+competition where you just keep on going
+ 
+
+ align:start position:0%
+competition where you just keep on going
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+on both sides
+
+ align:start position:0%
+on both sides
+ 
+
+ align:start position:0%
+on both sides
+and they end up uh being similar
+
+ align:start position:0%
+and they end up uh being similar
+ 
+
+ align:start position:0%
+and they end up uh being similar
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but with the advantage for composition
+
+ align:start position:0%
+but with the advantage for composition
+ 
+
+ align:start position:0%
+but with the advantage for composition
+going to quaternions and the advantage
+
+ align:start position:0%
+going to quaternions and the advantage
+ 
+
+ align:start position:0%
+going to quaternions and the advantage
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+rotating vectors going to um
+
+ align:start position:0%
+rotating vectors going to um
+ 
+
+ align:start position:0%
+rotating vectors going to um
+orthonormal
+
+ align:start position:0%
+orthonormal
+ 
+
+ align:start position:0%
+orthonormal
+okay how about
+
+ align:start position:0%
+okay how about
+ 
+
+ align:start position:0%
+okay how about
+re-normalizing so one of the things that
+
+ align:start position:0%
+re-normalizing so one of the things that
+ 
+
+ align:start position:0%
+re-normalizing so one of the things that
+happens suppose you have a graphic
+
+ align:start position:0%
+happens suppose you have a graphic
+ 
+
+ align:start position:0%
+happens suppose you have a graphic
+program that's trying to
+
+ align:start position:0%
+program that's trying to
+ 
+
+ align:start position:0%
+program that's trying to
+do some motion sequence and you're
+
+ align:start position:0%
+do some motion sequence and you're
+ 
+
+ align:start position:0%
+do some motion sequence and you're
+composing small incremental rotations
+
+ align:start position:0%
+composing small incremental rotations
+ 
+
+ align:start position:0%
+composing small incremental rotations
+and if you represent them let's say as
+
+ align:start position:0%
+and if you represent them let's say as
+ 
+
+ align:start position:0%
+and if you represent them let's say as
+orthogonal matrices you can imagine that
+
+ align:start position:0%
+orthogonal matrices you can imagine that
+ 
+
+ align:start position:0%
+orthogonal matrices you can imagine that
+because of the limitations of floating
+
+ align:start position:0%
+because of the limitations of floating
+ 
+
+ align:start position:0%
+because of the limitations of floating
+point arithmetic that errors will
+
+ align:start position:0%
+point arithmetic that errors will
+ 
+
+ align:start position:0%
+point arithmetic that errors will
+accumulate and after a while your three
+
+ align:start position:0%
+accumulate and after a while your three
+ 
+
+ align:start position:0%
+accumulate and after a while your three
+by three matrix is no longer orthonormal
+
+ align:start position:0%
+by three matrix is no longer orthonormal
+ 
+
+ align:start position:0%
+by three matrix is no longer orthonormal
+and so you'd want to sort of square it
+
+ align:start position:0%
+and so you'd want to sort of square it
+ 
+
+ align:start position:0%
+and so you'd want to sort of square it
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+and that can be done
+
+ align:start position:0%
+and that can be done
+ 
+
+ align:start position:0%
+and that can be done
+but it requires doing this you take your
+
+ align:start position:0%
+but it requires doing this you take your
+ 
+
+ align:start position:0%
+but it requires doing this you take your
+matrix m you multiply you take its
+
+ align:start position:0%
+matrix m you multiply you take its
+ 
+
+ align:start position:0%
+matrix m you multiply you take its
+transpose multiplied by m and you take
+
+ align:start position:0%
+transpose multiplied by m and you take
+ 
+
+ align:start position:0%
+transpose multiplied by m and you take
+the inverse of the square root of the
+
+ align:start position:0%
+the inverse of the square root of the
+ 
+
+ align:start position:0%
+the inverse of the square root of the
+matrix so you know right there you
+
+ align:start position:0%
+matrix so you know right there you
+ 
+
+ align:start position:0%
+matrix so you know right there you
+i'd imagine that you may not know how to
+
+ align:start position:0%
+i'd imagine that you may not know how to
+ 
+
+ align:start position:0%
+i'd imagine that you may not know how to
+do that but it can be done but that just
+
+ align:start position:0%
+do that but it can be done but that just
+ 
+
+ align:start position:0%
+do that but it can be done but that just
+suggests that this is not an operation
+
+ align:start position:0%
+suggests that this is not an operation
+ 
+
+ align:start position:0%
+suggests that this is not an operation
+that you'd normally want to do it's it's
+
+ align:start position:0%
+that you'd normally want to do it's it's
+ 
+
+ align:start position:0%
+that you'd normally want to do it's it's
+expensive
+
+ align:start position:0%
+expensive
+ 
+
+ align:start position:0%
+expensive
+with quaternions sure enough you take
+
+ align:start position:0%
+with quaternions sure enough you take
+ 
+
+ align:start position:0%
+with quaternions sure enough you take
+the unit quaternion you multiply it by
+
+ align:start position:0%
+the unit quaternion you multiply it by
+ 
+
+ align:start position:0%
+the unit quaternion you multiply it by
+another unit quaternion and so on and
+
+ align:start position:0%
+another unit quaternion and so on and
+ 
+
+ align:start position:0%
+another unit quaternion and so on and
+because of the limitations of floating
+
+ align:start position:0%
+because of the limitations of floating
+ 
+
+ align:start position:0%
+because of the limitations of floating
+point arithmetic after a while it isn't
+
+ align:start position:0%
+point arithmetic after a while it isn't
+ 
+
+ align:start position:0%
+point arithmetic after a while it isn't
+a unit quaternion how do you square it
+
+ align:start position:0%
+a unit quaternion how do you square it
+ 
+
+ align:start position:0%
+a unit quaternion how do you square it
+up well you know trivial so
+
+ align:start position:0%
+up well you know trivial so
+ 
+
+ align:start position:0%
+up well you know trivial so
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+one other small difference between them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh just about at the end so we talked
+
+ align:start position:0%
+uh just about at the end so we talked
+ 
+
+ align:start position:0%
+uh just about at the end so we talked
+about the space of rotation being uh
+
+ align:start position:0%
+about the space of rotation being uh
+ 
+
+ align:start position:0%
+about the space of rotation being uh
+this uh three three sphere
+
+ align:start position:0%
+this uh three three sphere
+ 
+
+ align:start position:0%
+this uh three three sphere
+unit sphere and four d with antipodal
+
+ align:start position:0%
+unit sphere and four d with antipodal
+ 
+
+ align:start position:0%
+unit sphere and four d with antipodal
+points identified and it also happens to
+
+ align:start position:0%
+points identified and it also happens to
+ 
+
+ align:start position:0%
+points identified and it also happens to
+be identical to the projective space p3
+
+ align:start position:0%
+be identical to the projective space p3
+ 
+
+ align:start position:0%
+be identical to the projective space p3
+although we don't use that and it's
+
+ align:start position:0%
+although we don't use that and it's
+ 
+
+ align:start position:0%
+although we don't use that and it's
+not as handy
+
+ align:start position:0%
+not as handy
+ 
+
+ align:start position:0%
+not as handy
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+sampling regular and random so how do we
+
+ align:start position:0%
+sampling regular and random so how do we
+ 
+
+ align:start position:0%
+sampling regular and random so how do we
+sample this space well you know in 3d we
+
+ align:start position:0%
+sample this space well you know in 3d we
+ 
+
+ align:start position:0%
+sample this space well you know in 3d we
+can easily come up with a regular
+
+ align:start position:0%
+can easily come up with a regular
+ 
+
+ align:start position:0%
+can easily come up with a regular
+sampling
+
+ align:start position:0%
+sampling
+ 
+
+ align:start position:0%
+sampling
+of space or even a random sampling but
+
+ align:start position:0%
+of space or even a random sampling but
+ 
+
+ align:start position:0%
+of space or even a random sampling but
+it's not so obvious how to do it here
+
+ align:start position:0%
+it's not so obvious how to do it here
+ 
+
+ align:start position:0%
+it's not so obvious how to do it here
+and one way
+
+ align:start position:0%
+and one way
+ 
+
+ align:start position:0%
+and one way
+is to
+
+ align:start position:0%
+is to
+ 
+
+ align:start position:0%
+is to
+find regular patterns
+
+ align:start position:0%
+find regular patterns
+ 
+
+ align:start position:0%
+find regular patterns
+you know if we're
+
+ align:start position:0%
+you know if we're
+ 
+
+ align:start position:0%
+you know if we're
+say we want to sample a sphere regularly
+
+ align:start position:0%
+say we want to sample a sphere regularly
+ 
+
+ align:start position:0%
+say we want to sample a sphere regularly
+that's not so easy either certainly
+
+ align:start position:0%
+that's not so easy either certainly
+ 
+
+ align:start position:0%
+that's not so easy either certainly
+latitude and longitude's not going to do
+
+ align:start position:0%
+latitude and longitude's not going to do
+ 
+
+ align:start position:0%
+latitude and longitude's not going to do
+it but one thing we can do is project
+
+ align:start position:0%
+it but one thing we can do is project
+ 
+
+ align:start position:0%
+it but one thing we can do is project
+polyhedra onto it because polyhedra are
+
+ align:start position:0%
+polyhedra onto it because polyhedra are
+ 
+
+ align:start position:0%
+polyhedra onto it because polyhedra are
+completely regular so if we project say
+
+ align:start position:0%
+completely regular so if we project say
+ 
+
+ align:start position:0%
+completely regular so if we project say
+a icosahedron
+
+ align:start position:0%
+a icosahedron
+ 
+
+ align:start position:0%
+a icosahedron
+or a dodeca icosahedron which is
+
+ align:start position:0%
+or a dodeca icosahedron which is
+ 
+
+ align:start position:0%
+or a dodeca icosahedron which is
+a soccer ball
+
+ align:start position:0%
+a soccer ball
+ 
+
+ align:start position:0%
+a soccer ball
+anyone here know about soccer uh
+
+ align:start position:0%
+anyone here know about soccer uh
+ 
+
+ align:start position:0%
+anyone here know about soccer uh
+then we end up with a pattern on the
+
+ align:start position:0%
+then we end up with a pattern on the
+ 
+
+ align:start position:0%
+then we end up with a pattern on the
+sphere that is regular but they're only
+
+ align:start position:0%
+sphere that is regular but they're only
+ 
+
+ align:start position:0%
+sphere that is regular but they're only
+some special ones like uh regular solids
+
+ align:start position:0%
+some special ones like uh regular solids
+ 
+
+ align:start position:0%
+some special ones like uh regular solids
+they're only a few of them well
+
+ align:start position:0%
+they're only a few of them well
+ 
+
+ align:start position:0%
+they're only a few of them well
+similarly here except now we're in 4d
+
+ align:start position:0%
+similarly here except now we're in 4d
+ 
+
+ align:start position:0%
+similarly here except now we're in 4d
+and the corresponding things are
+
+ align:start position:0%
+and the corresponding things are
+ 
+
+ align:start position:0%
+and the corresponding things are
+rotations rather than polyhedra and so
+
+ align:start position:0%
+rotations rather than polyhedra and so
+ 
+
+ align:start position:0%
+rotations rather than polyhedra and so
+it turns out that if you look at the
+
+ align:start position:0%
+it turns out that if you look at the
+ 
+
+ align:start position:0%
+it turns out that if you look at the
+rotations of polyhedra they will give
+
+ align:start position:0%
+rotations of polyhedra they will give
+ 
+
+ align:start position:0%
+rotations of polyhedra they will give
+you a nice even sampling of that space
+
+ align:start position:0%
+you a nice even sampling of that space
+ 
+
+ align:start position:0%
+you a nice even sampling of that space
+and the rotation groups are the so the
+
+ align:start position:0%
+and the rotation groups are the so the
+ 
+
+ align:start position:0%
+and the rotation groups are the so the
+tetrahedron
+
+ align:start position:0%
+tetrahedron
+ 
+
+ align:start position:0%
+tetrahedron
+has 12 rotations that will align it with
+
+ align:start position:0%
+has 12 rotations that will align it with
+ 
+
+ align:start position:0%
+has 12 rotations that will align it with
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+the cube and the octahedron have 24
+
+ align:start position:0%
+the cube and the octahedron have 24
+ 
+
+ align:start position:0%
+the cube and the octahedron have 24
+and the icosahedron and dodecahedron
+
+ align:start position:0%
+and the icosahedron and dodecahedron
+ 
+
+ align:start position:0%
+and the icosahedron and dodecahedron
+have 60. so these give you a perfectly
+
+ align:start position:0%
+have 60. so these give you a perfectly
+ 
+
+ align:start position:0%
+have 60. so these give you a perfectly
+uniform spaced uh
+
+ align:start position:0%
+uniform spaced uh
+ 
+
+ align:start position:0%
+uniform spaced uh
+sampling of that space
+
+ align:start position:0%
+sampling of that space
+ 
+
+ align:start position:0%
+sampling of that space
+unfortunately that's not a very fine
+
+ align:start position:0%
+unfortunately that's not a very fine
+ 
+
+ align:start position:0%
+unfortunately that's not a very fine
+sampling right because 60 in the four
+
+ align:start position:0%
+sampling right because 60 in the four
+ 
+
+ align:start position:0%
+sampling right because 60 in the four
+dimensional space
+
+ align:start position:0%
+dimensional space
+ 
+
+ align:start position:0%
+dimensional space
+so they're tricks to give you
+
+ align:start position:0%
+so they're tricks to give you
+ 
+
+ align:start position:0%
+so they're tricks to give you
+a finer sampling but they all start with
+
+ align:start position:0%
+a finer sampling but they all start with
+ 
+
+ align:start position:0%
+a finer sampling but they all start with
+those simple ones and just uh while i
+
+ align:start position:0%
+those simple ones and just uh while i
+ 
+
+ align:start position:0%
+those simple ones and just uh while i
+have the slides here
+
+ align:start position:0%
+have the slides here
+ 
+
+ align:start position:0%
+have the slides here
+if you pick the
+
+ align:start position:0%
+if you pick the
+ 
+
+ align:start position:0%
+if you pick the
+coordinate systems right you get very
+
+ align:start position:0%
+coordinate systems right you get very
+ 
+
+ align:start position:0%
+coordinate systems right you get very
+simple expressions for these rotation
+
+ align:start position:0%
+simple expressions for these rotation
+ 
+
+ align:start position:0%
+simple expressions for these rotation
+groups so each of these is a rotation
+
+ align:start position:0%
+groups so each of these is a rotation
+ 
+
+ align:start position:0%
+groups so each of these is a rotation
+this one of course is the identity
+
+ align:start position:0%
+this one of course is the identity
+ 
+
+ align:start position:0%
+this one of course is the identity
+rotation does nothing
+
+ align:start position:0%
+rotation does nothing
+ 
+
+ align:start position:0%
+rotation does nothing
+this is the rotation about the x-axis
+
+ align:start position:0%
+this is the rotation about the x-axis
+ 
+
+ align:start position:0%
+this is the rotation about the x-axis
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+180 degrees
+
+ align:start position:0%
+180 degrees
+ 
+
+ align:start position:0%
+180 degrees
+and this is about the y-axis and so on
+
+ align:start position:0%
+and this is about the y-axis and so on
+ 
+
+ align:start position:0%
+and this is about the y-axis and so on
+so this is the group for the tetrahedron
+
+ align:start position:0%
+so this is the group for the tetrahedron
+ 
+
+ align:start position:0%
+so this is the group for the tetrahedron
+they provide a regular space
+
+ align:start position:0%
+they provide a regular space
+ 
+
+ align:start position:0%
+they provide a regular space
+sampling of that space this is for the
+
+ align:start position:0%
+sampling of that space this is for the
+ 
+
+ align:start position:0%
+sampling of that space this is for the
+hexahedron and the octahedron and then
+
+ align:start position:0%
+hexahedron and the octahedron and then
+ 
+
+ align:start position:0%
+hexahedron and the octahedron and then
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the prize is this one this is the
+
+ align:start position:0%
+the prize is this one this is the
+ 
+
+ align:start position:0%
+the prize is this one this is the
+rotation group for the dodecahedron and
+
+ align:start position:0%
+rotation group for the dodecahedron and
+ 
+
+ align:start position:0%
+rotation group for the dodecahedron and
+icosahedron and where the you know
+
+ align:start position:0%
+icosahedron and where the you know
+ 
+
+ align:start position:0%
+icosahedron and where the you know
+these abcds are given by these
+
+ align:start position:0%
+these abcds are given by these
+ 
+
+ align:start position:0%
+these abcds are given by these
+expressions up there
+
+ align:start position:0%
+expressions up there
+ 
+
+ align:start position:0%
+expressions up there
+um these should look familiar
+
+ align:start position:0%
+um these should look familiar
+ 
+
+ align:start position:0%
+um these should look familiar
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this only works if you line it up nicely
+
+ align:start position:0%
+this only works if you line it up nicely
+ 
+
+ align:start position:0%
+this only works if you line it up nicely
+with the coordinate system anyway
+
+ align:start position:0%
+with the coordinate system anyway
+ 
+
+ align:start position:0%
+with the coordinate system anyway
+you this would be a sampling so you
+
+ align:start position:0%
+you this would be a sampling so you
+ 
+
+ align:start position:0%
+you this would be a sampling so you
+could try these 60
+
+ align:start position:0%
+could try these 60
+ 
+
+ align:start position:0%
+could try these 60
+orientations for
+
+ align:start position:0%
+orientations for
+ 
+
+ align:start position:0%
+orientations for
+your search or your averaging
+
+ align:start position:0%
+your search or your averaging
+ 
+
+ align:start position:0%
+your search or your averaging
+uh and then you can interpolate further
+
+ align:start position:0%
+uh and then you can interpolate further
+ 
+
+ align:start position:0%
+uh and then you can interpolate further
+okay well we've run out of time so
+
+ align:start position:0%
+okay well we've run out of time so
+ 
+
+ align:start position:0%
+okay well we've run out of time so
+that's it for today
\ No newline at end of file
diff --git a/v5jffYzm5pg.txt b/v5jffYzm5pg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1dc4da1ecf6e80bdbe4473eb20cfa3977f08e0c5
--- /dev/null
+++ b/v5jffYzm5pg.txt
@@ -0,0 +1,1571 @@
+align:start position:0%
+ 
+welcome back to 820 special relativity
+
+ align:start position:0%
+welcome back to 820 special relativity
+ 
+
+ align:start position:0%
+welcome back to 820 special relativity
+so in our quest
+
+ align:start position:0%
+so in our quest
+ 
+
+ align:start position:0%
+so in our quest
+to understand how we get to general
+
+ align:start position:0%
+to understand how we get to general
+ 
+
+ align:start position:0%
+to understand how we get to general
+relativity there's two things to
+
+ align:start position:0%
+relativity there's two things to
+ 
+
+ align:start position:0%
+relativity there's two things to
+consider the first one this lecture is
+
+ align:start position:0%
+consider the first one this lecture is
+ 
+
+ align:start position:0%
+consider the first one this lecture is
+not meant to give you a full description
+
+ align:start position:0%
+not meant to give you a full description
+ 
+
+ align:start position:0%
+not meant to give you a full description
+of general relativity but just a view
+
+ align:start position:0%
+of general relativity but just a view
+ 
+
+ align:start position:0%
+of general relativity but just a view
+into where this might lead where this
+
+ align:start position:0%
+into where this might lead where this
+ 
+
+ align:start position:0%
+into where this might lead where this
+discussion might lead
+
+ align:start position:0%
+discussion might lead
+ 
+
+ align:start position:0%
+discussion might lead
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in this quest
+
+ align:start position:0%
+in this quest
+ 
+
+ align:start position:0%
+in this quest
+we can understand the theory of
+
+ align:start position:0%
+we can understand the theory of
+ 
+
+ align:start position:0%
+we can understand the theory of
+general relativity as a theory on how to
+
+ align:start position:0%
+general relativity as a theory on how to
+ 
+
+ align:start position:0%
+general relativity as a theory on how to
+patch together the different reference
+
+ align:start position:0%
+patch together the different reference
+ 
+
+ align:start position:0%
+patch together the different reference
+frames which are each
+
+ align:start position:0%
+frames which are each
+ 
+
+ align:start position:0%
+frames which are each
+can be described in special relativity
+
+ align:start position:0%
+can be described in special relativity
+ 
+
+ align:start position:0%
+can be described in special relativity
+so in the framework we discussed up to
+
+ align:start position:0%
+so in the framework we discussed up to
+ 
+
+ align:start position:0%
+so in the framework we discussed up to
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+and is valid in short intervals in space
+
+ align:start position:0%
+and is valid in short intervals in space
+ 
+
+ align:start position:0%
+and is valid in short intervals in space
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+consequence of general relativity are
+
+ align:start position:0%
+consequence of general relativity are
+ 
+
+ align:start position:0%
+consequence of general relativity are
+that space time is curved so we have
+
+ align:start position:0%
+that space time is curved so we have
+ 
+
+ align:start position:0%
+that space time is curved so we have
+modified geometries
+
+ align:start position:0%
+modified geometries
+ 
+
+ align:start position:0%
+modified geometries
+um and we learned that because of
+
+ align:start position:0%
+um and we learned that because of
+ 
+
+ align:start position:0%
+um and we learned that because of
+gravitational effects matter curves
+
+ align:start position:0%
+gravitational effects matter curves
+ 
+
+ align:start position:0%
+gravitational effects matter curves
+space-time
+
+ align:start position:0%
+space-time
+ 
+
+ align:start position:0%
+space-time
+as a consequence of that you know there
+
+ align:start position:0%
+as a consequence of that you know there
+ 
+
+ align:start position:0%
+as a consequence of that you know there
+must be modification of of gravity based
+
+ align:start position:0%
+must be modification of of gravity based
+ 
+
+ align:start position:0%
+must be modification of of gravity based
+on meta distributions and so there must
+
+ align:start position:0%
+on meta distributions and so there must
+ 
+
+ align:start position:0%
+on meta distributions and so there must
+also be gravitational waves
+
+ align:start position:0%
+also be gravitational waves
+ 
+
+ align:start position:0%
+also be gravitational waves
+gravitational lenses which bend light
+
+ align:start position:0%
+gravitational lenses which bend light
+ 
+
+ align:start position:0%
+gravitational lenses which bend light
+black holes
+
+ align:start position:0%
+black holes
+ 
+
+ align:start position:0%
+black holes
+and there's cosmological predictions
+
+ align:start position:0%
+and there's cosmological predictions
+ 
+
+ align:start position:0%
+and there's cosmological predictions
+coming out of general relativity
+
+ align:start position:0%
+coming out of general relativity
+ 
+
+ align:start position:0%
+coming out of general relativity
+so let's have a discussion first
+
+ align:start position:0%
+so let's have a discussion first
+ 
+
+ align:start position:0%
+so let's have a discussion first
+what does it mean to have a changed or
+
+ align:start position:0%
+what does it mean to have a changed or
+ 
+
+ align:start position:0%
+what does it mean to have a changed or
+modified geometry
+
+ align:start position:0%
+modified geometry
+ 
+
+ align:start position:0%
+modified geometry
+what could that mean
+
+ align:start position:0%
+what could that mean
+ 
+
+ align:start position:0%
+what could that mean
+so you're all used to euclidean geometry
+
+ align:start position:0%
+so you're all used to euclidean geometry
+ 
+
+ align:start position:0%
+so you're all used to euclidean geometry
+where when you draw a
+
+ align:start position:0%
+where when you draw a
+ 
+
+ align:start position:0%
+where when you draw a
+triangle you add up all the angles to
+
+ align:start position:0%
+triangle you add up all the angles to
+ 
+
+ align:start position:0%
+triangle you add up all the angles to
+180 degrees if you draw two parallel
+
+ align:start position:0%
+180 degrees if you draw two parallel
+ 
+
+ align:start position:0%
+180 degrees if you draw two parallel
+lines they never cross they also don't
+
+ align:start position:0%
+lines they never cross they also don't
+ 
+
+ align:start position:0%
+lines they never cross they also don't
+diverge
+
+ align:start position:0%
+diverge
+ 
+
+ align:start position:0%
+diverge
+but if you have a modified geometry
+
+ align:start position:0%
+but if you have a modified geometry
+ 
+
+ align:start position:0%
+but if you have a modified geometry
+for example the geometry on the sphere
+
+ align:start position:0%
+for example the geometry on the sphere
+ 
+
+ align:start position:0%
+for example the geometry on the sphere
+like on our globe
+
+ align:start position:0%
+like on our globe
+ 
+
+ align:start position:0%
+like on our globe
+the angles do not add up to 180 degrees
+
+ align:start position:0%
+the angles do not add up to 180 degrees
+ 
+
+ align:start position:0%
+the angles do not add up to 180 degrees
+they actually the sum is larger than 180
+
+ align:start position:0%
+they actually the sum is larger than 180
+ 
+
+ align:start position:0%
+they actually the sum is larger than 180
+degrees and parallel lines will cross we
+
+ align:start position:0%
+degrees and parallel lines will cross we
+ 
+
+ align:start position:0%
+degrees and parallel lines will cross we
+would call this kind of space positively
+
+ align:start position:0%
+would call this kind of space positively
+ 
+
+ align:start position:0%
+would call this kind of space positively
+curved
+
+ align:start position:0%
+curved
+ 
+
+ align:start position:0%
+curved
+but you can have the opposite example
+
+ align:start position:0%
+but you can have the opposite example
+ 
+
+ align:start position:0%
+but you can have the opposite example
+like on a saddle
+
+ align:start position:0%
+like on a saddle
+ 
+
+ align:start position:0%
+like on a saddle
+so you can have other spaces and other
+
+ align:start position:0%
+so you can have other spaces and other
+ 
+
+ align:start position:0%
+so you can have other spaces and other
+curved spaces and they can be negatively
+
+ align:start position:0%
+curved spaces and they can be negatively
+ 
+
+ align:start position:0%
+curved spaces and they can be negatively
+skirved in this example if you add up
+
+ align:start position:0%
+skirved in this example if you add up
+ 
+
+ align:start position:0%
+skirved in this example if you add up
+all angles you find they add up to less
+
+ align:start position:0%
+all angles you find they add up to less
+ 
+
+ align:start position:0%
+all angles you find they add up to less
+than 180 degrees
+
+ align:start position:0%
+than 180 degrees
+ 
+
+ align:start position:0%
+than 180 degrees
+parallel lines will not cross but they
+
+ align:start position:0%
+parallel lines will not cross but they
+ 
+
+ align:start position:0%
+parallel lines will not cross but they
+will diverge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+mass has changed the geometry of
+
+ align:start position:0%
+mass has changed the geometry of
+ 
+
+ align:start position:0%
+mass has changed the geometry of
+spacecraft time you know we just talked
+
+ align:start position:0%
+spacecraft time you know we just talked
+ 
+
+ align:start position:0%
+spacecraft time you know we just talked
+about light bending
+
+ align:start position:0%
+about light bending
+ 
+
+ align:start position:0%
+about light bending
+and because of the change in geometry
+
+ align:start position:0%
+and because of the change in geometry
+ 
+
+ align:start position:0%
+and because of the change in geometry
+light will not go on a straight line
+
+ align:start position:0%
+light will not go on a straight line
+ 
+
+ align:start position:0%
+light will not go on a straight line
+anymore but will bend around massive
+
+ align:start position:0%
+anymore but will bend around massive
+ 
+
+ align:start position:0%
+anymore but will bend around massive
+object space time is
+
+ align:start position:0%
+object space time is
+ 
+
+ align:start position:0%
+object space time is
+curved geometry of space-time tells us
+
+ align:start position:0%
+curved geometry of space-time tells us
+ 
+
+ align:start position:0%
+curved geometry of space-time tells us
+how the masses move
+
+ align:start position:0%
+how the masses move
+ 
+
+ align:start position:0%
+how the masses move
+you can think about
+
+ align:start position:0%
+you can think about
+ 
+
+ align:start position:0%
+you can think about
+um a trampoline when you put a heavy
+
+ align:start position:0%
+um a trampoline when you put a heavy
+ 
+
+ align:start position:0%
+um a trampoline when you put a heavy
+object on a trampoline
+
+ align:start position:0%
+object on a trampoline
+ 
+
+ align:start position:0%
+object on a trampoline
+all the other objects on the trampoline
+
+ align:start position:0%
+all the other objects on the trampoline
+ 
+
+ align:start position:0%
+all the other objects on the trampoline
+will gravitate towards the heavier
+
+ align:start position:0%
+will gravitate towards the heavier
+ 
+
+ align:start position:0%
+will gravitate towards the heavier
+object and that's kind of a picture on
+
+ align:start position:0%
+object and that's kind of a picture on
+ 
+
+ align:start position:0%
+object and that's kind of a picture on
+how spacecraft spacetime actually looks
+
+ align:start position:0%
+how spacecraft spacetime actually looks
+ 
+
+ align:start position:0%
+how spacecraft spacetime actually looks
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+einstein
+
+ align:start position:0%
+einstein
+ 
+
+ align:start position:0%
+einstein
+used those finding in order to redefine
+
+ align:start position:0%
+used those finding in order to redefine
+ 
+
+ align:start position:0%
+used those finding in order to redefine
+newton's first law and found the
+
+ align:start position:0%
+newton's first law and found the
+ 
+
+ align:start position:0%
+newton's first law and found the
+so-called einstein field equation
+
+ align:start position:0%
+so-called einstein field equation
+ 
+
+ align:start position:0%
+so-called einstein field equation
+so there's on one side of the equation
+
+ align:start position:0%
+so there's on one side of the equation
+ 
+
+ align:start position:0%
+so there's on one side of the equation
+there's a description of space time and
+
+ align:start position:0%
+there's a description of space time and
+ 
+
+ align:start position:0%
+there's a description of space time and
+its curvature
+
+ align:start position:0%
+its curvature
+ 
+
+ align:start position:0%
+its curvature
+and on the other side of the equation is
+
+ align:start position:0%
+and on the other side of the equation is
+ 
+
+ align:start position:0%
+and on the other side of the equation is
+the energy momentum momentum tensor the
+
+ align:start position:0%
+the energy momentum momentum tensor the
+ 
+
+ align:start position:0%
+the energy momentum momentum tensor the
+description and how energy energy and
+
+ align:start position:0%
+description and how energy energy and
+ 
+
+ align:start position:0%
+description and how energy energy and
+momentum of object is distributed
+
+ align:start position:0%
+momentum of object is distributed
+ 
+
+ align:start position:0%
+momentum of object is distributed
+and those two things space time and
+
+ align:start position:0%
+and those two things space time and
+ 
+
+ align:start position:0%
+and those two things space time and
+energy and momentum they're kind of
+
+ align:start position:0%
+energy and momentum they're kind of
+ 
+
+ align:start position:0%
+energy and momentum they're kind of
+interlinked in this in this equation
+
+ align:start position:0%
+interlinked in this in this equation
+ 
+
+ align:start position:0%
+interlinked in this in this equation
+so if you read this description you can
+
+ align:start position:0%
+so if you read this description you can
+ 
+
+ align:start position:0%
+so if you read this description you can
+read it from one side to the next space
+
+ align:start position:0%
+read it from one side to the next space
+ 
+
+ align:start position:0%
+read it from one side to the next space
+time tells matter how to move
+
+ align:start position:0%
+time tells matter how to move
+ 
+
+ align:start position:0%
+time tells matter how to move
+or you read it from the other direction
+
+ align:start position:0%
+or you read it from the other direction
+ 
+
+ align:start position:0%
+or you read it from the other direction
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+meta tell space crime space time how to
+
+ align:start position:0%
+meta tell space crime space time how to
+ 
+
+ align:start position:0%
+meta tell space crime space time how to
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+there is an equation and you can just
+
+ align:start position:0%
+there is an equation and you can just
+ 
+
+ align:start position:0%
+there is an equation and you can just
+read it from the left to the right or
+
+ align:start position:0%
+read it from the left to the right or
+ 
+
+ align:start position:0%
+read it from the left to the right or
+from the right to the left so our
+
+ align:start position:0%
+from the right to the left so our
+ 
+
+ align:start position:0%
+from the right to the left so our
+understanding here
+
+ align:start position:0%
+understanding here
+ 
+
+ align:start position:0%
+understanding here
+it says space and time are not fixed
+
+ align:start position:0%
+it says space and time are not fixed
+ 
+
+ align:start position:0%
+it says space and time are not fixed
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+matter
+
+ align:start position:0%
+matter
+ 
+
+ align:start position:0%
+matter
+through which matter and energy moves
+
+ align:start position:0%
+through which matter and energy moves
+ 
+
+ align:start position:0%
+through which matter and energy moves
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+the matter and energy then itself
+
+ align:start position:0%
+the matter and energy then itself
+ 
+
+ align:start position:0%
+the matter and energy then itself
+defines space-time
+
+ align:start position:0%
+defines space-time
+ 
+
+ align:start position:0%
+defines space-time
+and matter because of that time sp
+
+ align:start position:0%
+and matter because of that time sp
+ 
+
+ align:start position:0%
+and matter because of that time sp
+space-time is dynamical it's changing
+
+ align:start position:0%
+space-time is dynamical it's changing
+ 
+
+ align:start position:0%
+space-time is dynamical it's changing
+it's interacting with the matter and
+
+ align:start position:0%
+it's interacting with the matter and
+ 
+
+ align:start position:0%
+it's interacting with the matter and
+with the energy
+
+ align:start position:0%
+with the energy
+ 
+
+ align:start position:0%
+with the energy
+this is a super exciting picture from
+
+ align:start position:0%
+this is a super exciting picture from
+ 
+
+ align:start position:0%
+this is a super exciting picture from
+hubble
+
+ align:start position:0%
+hubble
+ 
+
+ align:start position:0%
+hubble
+the hubble space telescope and you see
+
+ align:start position:0%
+the hubble space telescope and you see
+ 
+
+ align:start position:0%
+the hubble space telescope and you see
+galaxies um but what you also see
+
+ align:start position:0%
+galaxies um but what you also see
+ 
+
+ align:start position:0%
+galaxies um but what you also see
+is those structures which looked like
+
+ align:start position:0%
+is those structures which looked like
+ 
+
+ align:start position:0%
+is those structures which looked like
+something the light has gone through
+
+ align:start position:0%
+something the light has gone through
+ 
+
+ align:start position:0%
+something the light has gone through
+lenses those lenses are actually meta
+
+ align:start position:0%
+lenses those lenses are actually meta
+ 
+
+ align:start position:0%
+lenses those lenses are actually meta
+distributions galaxies themselves which
+
+ align:start position:0%
+distributions galaxies themselves which
+ 
+
+ align:start position:0%
+distributions galaxies themselves which
+actually lead to the bending of the
+
+ align:start position:0%
+actually lead to the bending of the
+ 
+
+ align:start position:0%
+actually lead to the bending of the
+light and those lensing effects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if you want to summarize um general
+
+ align:start position:0%
+okay if you want to summarize um general
+ 
+
+ align:start position:0%
+okay if you want to summarize um general
+relativity you can first say that space
+
+ align:start position:0%
+relativity you can first say that space
+ 
+
+ align:start position:0%
+relativity you can first say that space
+time is curved and it follows the pseudo
+
+ align:start position:0%
+time is curved and it follows the pseudo
+ 
+
+ align:start position:0%
+time is curved and it follows the pseudo
+romanian monifold with a specific metric
+
+ align:start position:0%
+romanian monifold with a specific metric
+ 
+
+ align:start position:0%
+romanian monifold with a specific metric
+we have seen the metric before with
+
+ align:start position:0%
+we have seen the metric before with
+ 
+
+ align:start position:0%
+we have seen the metric before with
+minus plus plus plus
+
+ align:start position:0%
+minus plus plus plus
+ 
+
+ align:start position:0%
+minus plus plus plus
+and the relationship between matter and
+
+ align:start position:0%
+and the relationship between matter and
+ 
+
+ align:start position:0%
+and the relationship between matter and
+curvature is given by the einstein
+
+ align:start position:0%
+curvature is given by the einstein
+ 
+
+ align:start position:0%
+curvature is given by the einstein
+equation and here i give you a slightly
+
+ align:start position:0%
+equation and here i give you a slightly
+ 
+
+ align:start position:0%
+equation and here i give you a slightly
+different form where there is the
+
+ align:start position:0%
+different form where there is the
+ 
+
+ align:start position:0%
+different form where there is the
+dynamics again on one side and the
+
+ align:start position:0%
+dynamics again on one side and the
+ 
+
+ align:start position:0%
+dynamics again on one side and the
+energy momentum on the other side
+
+ align:start position:0%
+energy momentum on the other side
+ 
+
+ align:start position:0%
+energy momentum on the other side
+let's just look at one
+
+ align:start position:0%
+let's just look at one
+ 
+
+ align:start position:0%
+let's just look at one
+example here so we discussed in special
+
+ align:start position:0%
+example here so we discussed in special
+ 
+
+ align:start position:0%
+example here so we discussed in special
+relativity invariant intervals right and
+
+ align:start position:0%
+relativity invariant intervals right and
+ 
+
+ align:start position:0%
+relativity invariant intervals right and
+we had this delta s squared or we had
+
+ align:start position:0%
+we had this delta s squared or we had
+ 
+
+ align:start position:0%
+we had this delta s squared or we had
+different name for i
+
+ align:start position:0%
+different name for i
+ 
+
+ align:start position:0%
+different name for i
+given by minus dt square plus dx square
+
+ align:start position:0%
+given by minus dt square plus dx square
+ 
+
+ align:start position:0%
+given by minus dt square plus dx square
+plus dy square plus dz squared we could
+
+ align:start position:0%
+plus dy square plus dz squared we could
+ 
+
+ align:start position:0%
+plus dy square plus dz squared we could
+have just written this in polar
+
+ align:start position:0%
+have just written this in polar
+ 
+
+ align:start position:0%
+have just written this in polar
+coordinates as well where you find the d
+
+ align:start position:0%
+coordinates as well where you find the d
+ 
+
+ align:start position:0%
+coordinates as well where you find the d
+r square and r square d theta square and
+
+ align:start position:0%
+r square and r square d theta square and
+ 
+
+ align:start position:0%
+r square and r square d theta square and
+then r square
+
+ align:start position:0%
+then r square
+ 
+
+ align:start position:0%
+then r square
+sine square theta d phi squared
+
+ align:start position:0%
+sine square theta d phi squared
+ 
+
+ align:start position:0%
+sine square theta d phi squared
+okay same thing it's just a different
+
+ align:start position:0%
+okay same thing it's just a different
+ 
+
+ align:start position:0%
+okay same thing it's just a different
+coordinate system
+
+ align:start position:0%
+coordinate system
+ 
+
+ align:start position:0%
+coordinate system
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+as a solution
+
+ align:start position:0%
+as a solution
+ 
+
+ align:start position:0%
+as a solution
+to einstein equation we find something
+
+ align:start position:0%
+to einstein equation we find something
+ 
+
+ align:start position:0%
+to einstein equation we find something
+which looks very very similar that's not
+
+ align:start position:0%
+which looks very very similar that's not
+ 
+
+ align:start position:0%
+which looks very very similar that's not
+a surprise as we
+
+ align:start position:0%
+a surprise as we
+ 
+
+ align:start position:0%
+a surprise as we
+find general relativity as a patchwork
+
+ align:start position:0%
+find general relativity as a patchwork
+ 
+
+ align:start position:0%
+find general relativity as a patchwork
+of small spaces of general special
+
+ align:start position:0%
+of small spaces of general special
+ 
+
+ align:start position:0%
+of small spaces of general special
+relativity
+
+ align:start position:0%
+relativity
+ 
+
+ align:start position:0%
+relativity
+so the solutions might be very similar
+
+ align:start position:0%
+so the solutions might be very similar
+ 
+
+ align:start position:0%
+so the solutions might be very similar
+okay in the solution found here by the
+
+ align:start position:0%
+okay in the solution found here by the
+ 
+
+ align:start position:0%
+okay in the solution found here by the
+so-called schwarzschild solution which
+
+ align:start position:0%
+so-called schwarzschild solution which
+ 
+
+ align:start position:0%
+so-called schwarzschild solution which
+are unique solution vacuum with
+
+ align:start position:0%
+are unique solution vacuum with
+ 
+
+ align:start position:0%
+are unique solution vacuum with
+spherical symmetry
+
+ align:start position:0%
+spherical symmetry
+ 
+
+ align:start position:0%
+spherical symmetry
+of a meta distribution so you have a
+
+ align:start position:0%
+of a meta distribution so you have a
+ 
+
+ align:start position:0%
+of a meta distribution so you have a
+spherical meta distribution like our sun
+
+ align:start position:0%
+spherical meta distribution like our sun
+ 
+
+ align:start position:0%
+spherical meta distribution like our sun
+right and this is solution which
+
+ align:start position:0%
+right and this is solution which
+ 
+
+ align:start position:0%
+right and this is solution which
+describes
+
+ align:start position:0%
+describes
+ 
+
+ align:start position:0%
+describes
+um space time around this you find this
+
+ align:start position:0%
+um space time around this you find this
+ 
+
+ align:start position:0%
+um space time around this you find this
+invariant interval here has two
+
+ align:start position:0%
+invariant interval here has two
+ 
+
+ align:start position:0%
+invariant interval here has two
+interesting features
+
+ align:start position:0%
+interesting features
+ 
+
+ align:start position:0%
+interesting features
+there's two
+
+ align:start position:0%
+there's two
+ 
+
+ align:start position:0%
+there's two
+singularities in here
+
+ align:start position:0%
+singularities in here
+ 
+
+ align:start position:0%
+singularities in here
+so you find this should be a minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you find those two singularities one is
+
+ align:start position:0%
+you find those two singularities one is
+ 
+
+ align:start position:0%
+you find those two singularities one is
+at r equals zero that's kind of expected
+
+ align:start position:0%
+at r equals zero that's kind of expected
+ 
+
+ align:start position:0%
+at r equals zero that's kind of expected
+in the middle of the mass distribution
+
+ align:start position:0%
+in the middle of the mass distribution
+ 
+
+ align:start position:0%
+in the middle of the mass distribution
+this thing is not defined anymore
+
+ align:start position:0%
+this thing is not defined anymore
+ 
+
+ align:start position:0%
+this thing is not defined anymore
+there's no mass left
+
+ align:start position:0%
+there's no mass left
+ 
+
+ align:start position:0%
+there's no mass left
+but there's also a second singularity at
+
+ align:start position:0%
+but there's also a second singularity at
+ 
+
+ align:start position:0%
+but there's also a second singularity at
+two gm
+
+ align:start position:0%
+two gm
+ 
+
+ align:start position:0%
+two gm
+this is called the so-called
+
+ align:start position:0%
+this is called the so-called
+ 
+
+ align:start position:0%
+this is called the so-called
+schwarzschild radius
+
+ align:start position:0%
+schwarzschild radius
+ 
+
+ align:start position:0%
+schwarzschild radius
+and it defines
+
+ align:start position:0%
+and it defines
+ 
+
+ align:start position:0%
+and it defines
+if you get to the singularity
+
+ align:start position:0%
+if you get to the singularity
+ 
+
+ align:start position:0%
+if you get to the singularity
+you basically don't define anymore this
+
+ align:start position:0%
+you basically don't define anymore this
+ 
+
+ align:start position:0%
+you basically don't define anymore this
+invariant interval
+
+ align:start position:0%
+invariant interval
+ 
+
+ align:start position:0%
+invariant interval
+you can think about the black hole the
+
+ align:start position:0%
+you can think about the black hole the
+ 
+
+ align:start position:0%
+you can think about the black hole the
+surface of a black hole as this
+
+ align:start position:0%
+surface of a black hole as this
+ 
+
+ align:start position:0%
+surface of a black hole as this
+singularity
+
+ align:start position:0%
+singularity
+ 
+
+ align:start position:0%
+singularity
+at this r values at those singularities
+
+ align:start position:0%
+at this r values at those singularities
+ 
+
+ align:start position:0%
+at this r values at those singularities
+everything becomes timeline time like or
+
+ align:start position:0%
+everything becomes timeline time like or
+ 
+
+ align:start position:0%
+everything becomes timeline time like or
+everything within the radius becomes
+
+ align:start position:0%
+everything within the radius becomes
+ 
+
+ align:start position:0%
+everything within the radius becomes
+time-like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/vICUY43i190.txt b/vICUY43i190.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0e6186de50ecf39cf5ff5327c7ce09ad97aff95c
--- /dev/null
+++ b/vICUY43i190.txt
@@ -0,0 +1,1939 @@
+align:start position:0%
+ 
+welcome back to 8701
+
+ align:start position:0%
+welcome back to 8701
+ 
+
+ align:start position:0%
+welcome back to 8701
+so in this lecture we look at the
+
+ align:start position:0%
+so in this lecture we look at the
+ 
+
+ align:start position:0%
+so in this lecture we look at the
+interaction of w
+
+ align:start position:0%
+interaction of w
+ 
+
+ align:start position:0%
+interaction of w
+codons with quarks so the charged weak
+
+ align:start position:0%
+codons with quarks so the charged weak
+ 
+
+ align:start position:0%
+codons with quarks so the charged weak
+interaction of quarks
+
+ align:start position:0%
+interaction of quarks
+ 
+
+ align:start position:0%
+interaction of quarks
+let's just make a number of observations
+
+ align:start position:0%
+let's just make a number of observations
+ 
+
+ align:start position:0%
+let's just make a number of observations
+so we observe that the weak interaction
+
+ align:start position:0%
+so we observe that the weak interaction
+ 
+
+ align:start position:0%
+so we observe that the weak interaction
+respects the lepton generation
+
+ align:start position:0%
+respects the lepton generation
+ 
+
+ align:start position:0%
+respects the lepton generation
+meaning that a w couples to an electron
+
+ align:start position:0%
+meaning that a w couples to an electron
+ 
+
+ align:start position:0%
+meaning that a w couples to an electron
+and an electro neutrino
+
+ align:start position:0%
+and an electro neutrino
+ 
+
+ align:start position:0%
+and an electro neutrino
+but not an electron in the mirena too
+
+ align:start position:0%
+but not an electron in the mirena too
+ 
+
+ align:start position:0%
+but not an electron in the mirena too
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+in the case of the quarks there is a
+
+ align:start position:0%
+in the case of the quarks there is a
+ 
+
+ align:start position:0%
+in the case of the quarks there is a
+violation of this
+
+ align:start position:0%
+violation of this
+ 
+
+ align:start position:0%
+violation of this
+so there is a disrespect of the clock
+
+ align:start position:0%
+so there is a disrespect of the clock
+ 
+
+ align:start position:0%
+so there is a disrespect of the clock
+generation
+
+ align:start position:0%
+generation
+ 
+
+ align:start position:0%
+generation
+when it comes to the interaction with ws
+
+ align:start position:0%
+when it comes to the interaction with ws
+ 
+
+ align:start position:0%
+when it comes to the interaction with ws
+so when you investigate these two
+
+ align:start position:0%
+so when you investigate these two
+ 
+
+ align:start position:0%
+so when you investigate these two
+diagrams here you find that the w
+
+ align:start position:0%
+diagrams here you find that the w
+ 
+
+ align:start position:0%
+diagrams here you find that the w
+couples couples to the u-quark but to
+
+ align:start position:0%
+couples couples to the u-quark but to
+ 
+
+ align:start position:0%
+couples couples to the u-quark but to
+the b quark and the u-quark but it also
+
+ align:start position:0%
+the b quark and the u-quark but it also
+ 
+
+ align:start position:0%
+the b quark and the u-quark but it also
+couples to the s-code
+
+ align:start position:0%
+couples to the s-code
+ 
+
+ align:start position:0%
+couples to the s-code
+s clock in the youth block all right
+
+ align:start position:0%
+s clock in the youth block all right
+ 
+
+ align:start position:0%
+s clock in the youth block all right
+um in order to encapsulate this we have
+
+ align:start position:0%
+um in order to encapsulate this we have
+ 
+
+ align:start position:0%
+um in order to encapsulate this we have
+to make a correction and the corrections
+
+ align:start position:0%
+to make a correction and the corrections
+ 
+
+ align:start position:0%
+to make a correction and the corrections
+are typically called
+
+ align:start position:0%
+are typically called
+ 
+
+ align:start position:0%
+are typically called
+cosine um theta c and sine theta c
+
+ align:start position:0%
+cosine um theta c and sine theta c
+ 
+
+ align:start position:0%
+cosine um theta c and sine theta c
+theta c is a cabinet angle so theta
+
+ align:start position:0%
+theta c is a cabinet angle so theta
+ 
+
+ align:start position:0%
+theta c is a cabinet angle so theta
+cable
+
+ align:start position:0%
+cable
+ 
+
+ align:start position:0%
+cable
+turns out this is rather small certain
+
+ align:start position:0%
+turns out this is rather small certain
+ 
+
+ align:start position:0%
+turns out this is rather small certain
+decrease so it is a correction of small
+
+ align:start position:0%
+decrease so it is a correction of small
+ 
+
+ align:start position:0%
+decrease so it is a correction of small
+correction when we study the
+
+ align:start position:0%
+correction when we study the
+ 
+
+ align:start position:0%
+correction when we study the
+partial decay with of the k on that in
+
+ align:start position:0%
+partial decay with of the k on that in
+ 
+
+ align:start position:0%
+partial decay with of the k on that in
+electronic decays
+
+ align:start position:0%
+electronic decays
+ 
+
+ align:start position:0%
+electronic decays
+um was a partial decays to the ion of
+
+ align:start position:0%
+um was a partial decays to the ion of
+ 
+
+ align:start position:0%
+um was a partial decays to the ion of
+the occupier in electronic decays
+
+ align:start position:0%
+the occupier in electronic decays
+ 
+
+ align:start position:0%
+the occupier in electronic decays
+we found that there is a set of forms
+
+ align:start position:0%
+we found that there is a set of forms
+ 
+
+ align:start position:0%
+we found that there is a set of forms
+that was a form factor for the pi and
+
+ align:start position:0%
+that was a form factor for the pi and
+ 
+
+ align:start position:0%
+that was a form factor for the pi and
+decay and a form factor for the k on
+
+ align:start position:0%
+decay and a form factor for the k on
+ 
+
+ align:start position:0%
+decay and a form factor for the k on
+decay
+
+ align:start position:0%
+decay
+ 
+
+ align:start position:0%
+decay
+it turns out that the form factors are
+
+ align:start position:0%
+it turns out that the form factors are
+ 
+
+ align:start position:0%
+it turns out that the form factors are
+due to
+
+ align:start position:0%
+due to
+ 
+
+ align:start position:0%
+due to
+this additional correction so you find
+
+ align:start position:0%
+this additional correction so you find
+ 
+
+ align:start position:0%
+this additional correction so you find
+the tangent square of the carbido angle
+
+ align:start position:0%
+the tangent square of the carbido angle
+ 
+
+ align:start position:0%
+the tangent square of the carbido angle
+as part of this correction good
+
+ align:start position:0%
+as part of this correction good
+ 
+
+ align:start position:0%
+as part of this correction good
+so far so good now we have made an
+
+ align:start position:0%
+so far so good now we have made an
+ 
+
+ align:start position:0%
+so far so good now we have made an
+observation we haven't explained
+
+ align:start position:0%
+observation we haven't explained
+ 
+
+ align:start position:0%
+observation we haven't explained
+anything yet
+
+ align:start position:0%
+anything yet
+ 
+
+ align:start position:0%
+anything yet
+you can make one more um observation or
+
+ align:start position:0%
+you can make one more um observation or
+ 
+
+ align:start position:0%
+you can make one more um observation or
+discuss
+
+ align:start position:0%
+discuss
+ 
+
+ align:start position:0%
+discuss
+one and that's the decay of neutral
+
+ align:start position:0%
+one and that's the decay of neutral
+ 
+
+ align:start position:0%
+one and that's the decay of neutral
+chaons to a pair of neurons it turns out
+
+ align:start position:0%
+chaons to a pair of neurons it turns out
+ 
+
+ align:start position:0%
+chaons to a pair of neurons it turns out
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+those are not very likely
+
+ align:start position:0%
+those are not very likely
+ 
+
+ align:start position:0%
+those are not very likely
+even so you would expect that the
+
+ align:start position:0%
+even so you would expect that the
+ 
+
+ align:start position:0%
+even so you would expect that the
+amplitude has a factor here
+
+ align:start position:0%
+amplitude has a factor here
+ 
+
+ align:start position:0%
+amplitude has a factor here
+of um sine and cosine tabito
+
+ align:start position:0%
+of um sine and cosine tabito
+ 
+
+ align:start position:0%
+of um sine and cosine tabito
+so the amplitude should be in the order
+
+ align:start position:0%
+so the amplitude should be in the order
+ 
+
+ align:start position:0%
+so the amplitude should be in the order
+of sine
+
+ align:start position:0%
+of sine
+ 
+
+ align:start position:0%
+of sine
+theta carbido times cosine theta
+
+ align:start position:0%
+theta carbido times cosine theta
+ 
+
+ align:start position:0%
+theta carbido times cosine theta
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um so when this was studied the charm
+
+ align:start position:0%
+um so when this was studied the charm
+ 
+
+ align:start position:0%
+um so when this was studied the charm
+clock hasn't been discovered
+
+ align:start position:0%
+clock hasn't been discovered
+ 
+
+ align:start position:0%
+clock hasn't been discovered
+um and the explanation to why
+
+ align:start position:0%
+um and the explanation to why
+ 
+
+ align:start position:0%
+um and the explanation to why
+uh this decay is suppressed comes from
+
+ align:start position:0%
+uh this decay is suppressed comes from
+ 
+
+ align:start position:0%
+uh this decay is suppressed comes from
+the fact that there is a second diagram
+
+ align:start position:0%
+the fact that there is a second diagram
+ 
+
+ align:start position:0%
+the fact that there is a second diagram
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+where we just replace the u chord in
+
+ align:start position:0%
+where we just replace the u chord in
+ 
+
+ align:start position:0%
+where we just replace the u chord in
+this loop as a c clock
+
+ align:start position:0%
+this loop as a c clock
+ 
+
+ align:start position:0%
+this loop as a c clock
+this diagram contributes as a minus sign
+
+ align:start position:0%
+this diagram contributes as a minus sign
+ 
+
+ align:start position:0%
+this diagram contributes as a minus sign
+to the amplitude and therefore those two
+
+ align:start position:0%
+to the amplitude and therefore those two
+ 
+
+ align:start position:0%
+to the amplitude and therefore those two
+diagrams they cancel
+
+ align:start position:0%
+diagrams they cancel
+ 
+
+ align:start position:0%
+diagrams they cancel
+right yeah they are the same magnitude
+
+ align:start position:0%
+right yeah they are the same magnitude
+ 
+
+ align:start position:0%
+right yeah they are the same magnitude
+about the same magnitude and we have an
+
+ align:start position:0%
+about the same magnitude and we have an
+ 
+
+ align:start position:0%
+about the same magnitude and we have an
+opposite side
+
+ align:start position:0%
+opposite side
+ 
+
+ align:start position:0%
+opposite side
+so this was the first indication that
+
+ align:start position:0%
+so this was the first indication that
+ 
+
+ align:start position:0%
+so this was the first indication that
+there must be a fourth quark
+
+ align:start position:0%
+there must be a fourth quark
+ 
+
+ align:start position:0%
+there must be a fourth quark
+contributing to this kind of processes
+
+ align:start position:0%
+contributing to this kind of processes
+ 
+
+ align:start position:0%
+contributing to this kind of processes
+the charm block
+
+ align:start position:0%
+the charm block
+ 
+
+ align:start position:0%
+the charm block
+um let me now try to understand what's
+
+ align:start position:0%
+um let me now try to understand what's
+ 
+
+ align:start position:0%
+um let me now try to understand what's
+going on here why is the w
+
+ align:start position:0%
+going on here why is the w
+ 
+
+ align:start position:0%
+going on here why is the w
+uh coupling modified um or why
+
+ align:start position:0%
+uh coupling modified um or why
+ 
+
+ align:start position:0%
+uh coupling modified um or why
+it's not the full down quark or
+
+ align:start position:0%
+it's not the full down quark or
+ 
+
+ align:start position:0%
+it's not the full down quark or
+a strange core participating in the weak
+
+ align:start position:0%
+a strange core participating in the weak
+ 
+
+ align:start position:0%
+a strange core participating in the weak
+interaction
+
+ align:start position:0%
+interaction
+ 
+
+ align:start position:0%
+interaction
+um we can do the following here we can
+
+ align:start position:0%
+um we can do the following here we can
+ 
+
+ align:start position:0%
+um we can do the following here we can
+rewrite
+
+ align:start position:0%
+rewrite
+ 
+
+ align:start position:0%
+rewrite
+or we note that the the weak interaction
+
+ align:start position:0%
+or we note that the the weak interaction
+ 
+
+ align:start position:0%
+or we note that the the weak interaction
+eigenstate the eigenstate which
+
+ align:start position:0%
+eigenstate the eigenstate which
+ 
+
+ align:start position:0%
+eigenstate the eigenstate which
+participate in the weak index is not the
+
+ align:start position:0%
+participate in the weak index is not the
+ 
+
+ align:start position:0%
+participate in the weak index is not the
+eigenstate of the particle itself the
+
+ align:start position:0%
+eigenstate of the particle itself the
+ 
+
+ align:start position:0%
+eigenstate of the particle itself the
+so-called mass eigenstate
+
+ align:start position:0%
+so-called mass eigenstate
+ 
+
+ align:start position:0%
+so-called mass eigenstate
+so we have to write the weak eigenstate
+
+ align:start position:0%
+so we have to write the weak eigenstate
+ 
+
+ align:start position:0%
+so we have to write the weak eigenstate
+with a linear combination of the
+
+ align:start position:0%
+with a linear combination of the
+ 
+
+ align:start position:0%
+with a linear combination of the
+the mass eigenstate or white version
+
+ align:start position:0%
+the mass eigenstate or white version
+ 
+
+ align:start position:0%
+the mass eigenstate or white version
+this can be done
+
+ align:start position:0%
+this can be done
+ 
+
+ align:start position:0%
+this can be done
+in this matrix form here where we simply
+
+ align:start position:0%
+in this matrix form here where we simply
+ 
+
+ align:start position:0%
+in this matrix form here where we simply
+modify
+
+ align:start position:0%
+modify
+ 
+
+ align:start position:0%
+modify
+multiply the weak eigenstates
+
+ align:start position:0%
+multiply the weak eigenstates
+ 
+
+ align:start position:0%
+multiply the weak eigenstates
+with the with a matrix and just
+
+ align:start position:0%
+with the with a matrix and just
+ 
+
+ align:start position:0%
+with the with a matrix and just
+basically rotate it
+
+ align:start position:0%
+basically rotate it
+ 
+
+ align:start position:0%
+basically rotate it
+into the mass eigenstate so this was
+
+ align:start position:0%
+into the mass eigenstate so this was
+ 
+
+ align:start position:0%
+into the mass eigenstate so this was
+proposed by gabibo and rather successful
+
+ align:start position:0%
+proposed by gabibo and rather successful
+ 
+
+ align:start position:0%
+proposed by gabibo and rather successful
+um but it didn't incorporate the search
+
+ align:start position:0%
+um but it didn't incorporate the search
+ 
+
+ align:start position:0%
+um but it didn't incorporate the search
+innovation articles and this was done by
+
+ align:start position:0%
+innovation articles and this was done by
+ 
+
+ align:start position:0%
+innovation articles and this was done by
+kobayashi and mascara who generalized
+
+ align:start position:0%
+kobayashi and mascara who generalized
+ 
+
+ align:start position:0%
+kobayashi and mascara who generalized
+the scheme
+
+ align:start position:0%
+the scheme
+ 
+
+ align:start position:0%
+the scheme
+and propose the so-called ckm matrix c
+
+ align:start position:0%
+and propose the so-called ckm matrix c
+ 
+
+ align:start position:0%
+and propose the so-called ckm matrix c
+is here for
+
+ align:start position:0%
+is here for
+ 
+
+ align:start position:0%
+is here for
+cabibo kobayashi and mascara
+
+ align:start position:0%
+cabibo kobayashi and mascara
+ 
+
+ align:start position:0%
+cabibo kobayashi and mascara
+because of constraints we'll discuss in
+
+ align:start position:0%
+because of constraints we'll discuss in
+ 
+
+ align:start position:0%
+because of constraints we'll discuss in
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+in one of the recitations um this matrix
+
+ align:start position:0%
+in one of the recitations um this matrix
+ 
+
+ align:start position:0%
+in one of the recitations um this matrix
+can be parameterized or has only
+
+ align:start position:0%
+can be parameterized or has only
+ 
+
+ align:start position:0%
+can be parameterized or has only
+three independent angles and one complex
+
+ align:start position:0%
+three independent angles and one complex
+ 
+
+ align:start position:0%
+three independent angles and one complex
+space as independent parameters
+
+ align:start position:0%
+space as independent parameters
+ 
+
+ align:start position:0%
+space as independent parameters
+so you can choose different
+
+ align:start position:0%
+so you can choose different
+ 
+
+ align:start position:0%
+so you can choose different
+parameterization to capture that there's
+
+ align:start position:0%
+parameterization to capture that there's
+ 
+
+ align:start position:0%
+parameterization to capture that there's
+only three
+
+ align:start position:0%
+only three
+ 
+
+ align:start position:0%
+only three
+four parameters in this matrix which has
+
+ align:start position:0%
+four parameters in this matrix which has
+ 
+
+ align:start position:0%
+four parameters in this matrix which has
+nine components um one is
+
+ align:start position:0%
+nine components um one is
+ 
+
+ align:start position:0%
+nine components um one is
+by uh thinking about this matrix as
+
+ align:start position:0%
+by uh thinking about this matrix as
+ 
+
+ align:start position:0%
+by uh thinking about this matrix as
+three independent rotations in this
+
+ align:start position:0%
+three independent rotations in this
+ 
+
+ align:start position:0%
+three independent rotations in this
+complex space here
+
+ align:start position:0%
+complex space here
+ 
+
+ align:start position:0%
+complex space here
+in terms of numerical values you see
+
+ align:start position:0%
+in terms of numerical values you see
+ 
+
+ align:start position:0%
+in terms of numerical values you see
+that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonal elements of this matrix are
+
+ align:start position:0%
+diagonal elements of this matrix are
+ 
+
+ align:start position:0%
+diagonal elements of this matrix are
+very close to one
+
+ align:start position:0%
+very close to one
+ 
+
+ align:start position:0%
+very close to one
+meaning that this this mixing is
+
+ align:start position:0%
+meaning that this this mixing is
+ 
+
+ align:start position:0%
+meaning that this this mixing is
+for in the dwark sector the wireless
+
+ align:start position:0%
+for in the dwark sector the wireless
+ 
+
+ align:start position:0%
+for in the dwark sector the wireless
+mount effect you find that those next
+
+ align:start position:0%
+mount effect you find that those next
+ 
+
+ align:start position:0%
+mount effect you find that those next
+nearest
+
+ align:start position:0%
+nearest
+ 
+
+ align:start position:0%
+nearest
+off diagonal elements and the order of
+
+ align:start position:0%
+off diagonal elements and the order of
+ 
+
+ align:start position:0%
+off diagonal elements and the order of
+20 percent
+
+ align:start position:0%
+20 percent
+ 
+
+ align:start position:0%
+20 percent
+and the next to next of elements are
+
+ align:start position:0%
+and the next to next of elements are
+ 
+
+ align:start position:0%
+and the next to next of elements are
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+smaller okay this leads us
+
+ align:start position:0%
+smaller okay this leads us
+ 
+
+ align:start position:0%
+smaller okay this leads us
+into the discussion that we can you know
+
+ align:start position:0%
+into the discussion that we can you know
+ 
+
+ align:start position:0%
+into the discussion that we can you know
+use different parameterization in order
+
+ align:start position:0%
+use different parameterization in order
+ 
+
+ align:start position:0%
+use different parameterization in order
+to capture
+
+ align:start position:0%
+to capture
+ 
+
+ align:start position:0%
+to capture
+we already discussed the standard
+
+ align:start position:0%
+we already discussed the standard
+ 
+
+ align:start position:0%
+we already discussed the standard
+parameterization which you can really
+
+ align:start position:0%
+parameterization which you can really
+ 
+
+ align:start position:0%
+parameterization which you can really
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+three different rotations um and the
+
+ align:start position:0%
+three different rotations um and the
+ 
+
+ align:start position:0%
+three different rotations um and the
+the values of this those angles are
+
+ align:start position:0%
+the values of this those angles are
+ 
+
+ align:start position:0%
+the values of this those angles are
+given here
+
+ align:start position:0%
+given here
+ 
+
+ align:start position:0%
+given here
+together with the value of this um
+
+ align:start position:0%
+together with the value of this um
+ 
+
+ align:start position:0%
+together with the value of this um
+additional phase
+
+ align:start position:0%
+additional phase
+ 
+
+ align:start position:0%
+additional phase
+another way to look at this is the
+
+ align:start position:0%
+another way to look at this is the
+ 
+
+ align:start position:0%
+another way to look at this is the
+so-called wolfenstein polarization and
+
+ align:start position:0%
+so-called wolfenstein polarization and
+ 
+
+ align:start position:0%
+so-called wolfenstein polarization and
+this captures the fact that it seems
+
+ align:start position:0%
+this captures the fact that it seems
+ 
+
+ align:start position:0%
+this captures the fact that it seems
+like that there is a
+
+ align:start position:0%
+like that there is a
+ 
+
+ align:start position:0%
+like that there is a
+correction being applied to the actual
+
+ align:start position:0%
+correction being applied to the actual
+ 
+
+ align:start position:0%
+correction being applied to the actual
+particle so you find
+
+ align:start position:0%
+particle so you find
+ 
+
+ align:start position:0%
+particle so you find
+elements the order of lambda lambda is
+
+ align:start position:0%
+elements the order of lambda lambda is
+ 
+
+ align:start position:0%
+elements the order of lambda lambda is
+about 22
+
+ align:start position:0%
+about 22
+ 
+
+ align:start position:0%
+about 22
+um then you find elements which are in
+
+ align:start position:0%
+um then you find elements which are in
+ 
+
+ align:start position:0%
+um then you find elements which are in
+the order of one minus
+
+ align:start position:0%
+the order of one minus
+ 
+
+ align:start position:0%
+the order of one minus
+the lambda square correction and then
+
+ align:start position:0%
+the lambda square correction and then
+ 
+
+ align:start position:0%
+the lambda square correction and then
+there's elements which are of lambda
+
+ align:start position:0%
+there's elements which are of lambda
+ 
+
+ align:start position:0%
+there's elements which are of lambda
+square and lambda
+
+ align:start position:0%
+square and lambda
+ 
+
+ align:start position:0%
+square and lambda
+third power so this captures
+
+ align:start position:0%
+third power so this captures
+ 
+
+ align:start position:0%
+third power so this captures
+the matrix and then there's higher order
+
+ align:start position:0%
+the matrix and then there's higher order
+ 
+
+ align:start position:0%
+the matrix and then there's higher order
+corrections to that
+
+ align:start position:0%
+corrections to that
+ 
+
+ align:start position:0%
+corrections to that
+which are of order lambda to the fourth
+
+ align:start position:0%
+which are of order lambda to the fourth
+ 
+
+ align:start position:0%
+which are of order lambda to the fourth
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um because there's constraints on this
+
+ align:start position:0%
+um because there's constraints on this
+ 
+
+ align:start position:0%
+um because there's constraints on this
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+specifically your unitarity constraints
+
+ align:start position:0%
+specifically your unitarity constraints
+ 
+
+ align:start position:0%
+specifically your unitarity constraints
+meaning that
+
+ align:start position:0%
+meaning that
+ 
+
+ align:start position:0%
+meaning that
+you know we have three generations if i
+
+ align:start position:0%
+you know we have three generations if i
+ 
+
+ align:start position:0%
+you know we have three generations if i
+make a mixing of those three
+
+ align:start position:0%
+make a mixing of those three
+ 
+
+ align:start position:0%
+make a mixing of those three
+uh mass eigenstate to a weak eigenstate
+
+ align:start position:0%
+uh mass eigenstate to a weak eigenstate
+ 
+
+ align:start position:0%
+uh mass eigenstate to a weak eigenstate
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+on you know unitarily the the total
+
+ align:start position:0%
+on you know unitarily the the total
+ 
+
+ align:start position:0%
+on you know unitarily the the total
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+particles in this discussion is
+
+ align:start position:0%
+particles in this discussion is
+ 
+
+ align:start position:0%
+particles in this discussion is
+conserved uh this will change if there
+
+ align:start position:0%
+conserved uh this will change if there
+ 
+
+ align:start position:0%
+conserved uh this will change if there
+would be for example a fourth generation
+
+ align:start position:0%
+would be for example a fourth generation
+ 
+
+ align:start position:0%
+would be for example a fourth generation
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+so the study of weak charge interaction
+
+ align:start position:0%
+so the study of weak charge interaction
+ 
+
+ align:start position:0%
+so the study of weak charge interaction
+with quark helps us to understand
+
+ align:start position:0%
+with quark helps us to understand
+ 
+
+ align:start position:0%
+with quark helps us to understand
+whether or not there might be a fourth
+
+ align:start position:0%
+whether or not there might be a fourth
+ 
+
+ align:start position:0%
+whether or not there might be a fourth
+generation
+
+ align:start position:0%
+generation
+ 
+
+ align:start position:0%
+generation
+um we'll not go into too much detail
+
+ align:start position:0%
+um we'll not go into too much detail
+ 
+
+ align:start position:0%
+um we'll not go into too much detail
+here but it also the the
+
+ align:start position:0%
+here but it also the the
+ 
+
+ align:start position:0%
+here but it also the the
+complex space um explains part of
+
+ align:start position:0%
+complex space um explains part of
+ 
+
+ align:start position:0%
+complex space um explains part of
+uh our understanding of cp violation
+
+ align:start position:0%
+uh our understanding of cp violation
+ 
+
+ align:start position:0%
+uh our understanding of cp violation
+and we might discuss it in a little bit
+
+ align:start position:0%
+and we might discuss it in a little bit
+ 
+
+ align:start position:0%
+and we might discuss it in a little bit
+of a later of a later lecture
+
+ align:start position:0%
+of a later of a later lecture
+ 
+
+ align:start position:0%
+of a later of a later lecture
+but nevertheless so what we can actually
+
+ align:start position:0%
+but nevertheless so what we can actually
+ 
+
+ align:start position:0%
+but nevertheless so what we can actually
+form here is those unitarity constraints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just simply summing over the matrix
+
+ align:start position:0%
+just simply summing over the matrix
+ 
+
+ align:start position:0%
+just simply summing over the matrix
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+the scalar product of matrix elements
+
+ align:start position:0%
+the scalar product of matrix elements
+ 
+
+ align:start position:0%
+the scalar product of matrix elements
+and those where
+
+ align:start position:0%
+and those where
+ 
+
+ align:start position:0%
+and those where
+the contribution vanishes vanishes so
+
+ align:start position:0%
+the contribution vanishes vanishes so
+ 
+
+ align:start position:0%
+the contribution vanishes vanishes so
+those where
+
+ align:start position:0%
+those where
+ 
+
+ align:start position:0%
+those where
+j and k are not equal those um
+
+ align:start position:0%
+j and k are not equal those um
+ 
+
+ align:start position:0%
+j and k are not equal those um
+can be represented as a triangle that's
+
+ align:start position:0%
+can be represented as a triangle that's
+ 
+
+ align:start position:0%
+can be represented as a triangle that's
+quite interesting you can just rewrite
+
+ align:start position:0%
+quite interesting you can just rewrite
+ 
+
+ align:start position:0%
+quite interesting you can just rewrite
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+you just say for those three elements of
+
+ align:start position:0%
+you just say for those three elements of
+ 
+
+ align:start position:0%
+you just say for those three elements of
+the sum are equal to zero
+
+ align:start position:0%
+the sum are equal to zero
+ 
+
+ align:start position:0%
+the sum are equal to zero
+then you normalize by one element in
+
+ align:start position:0%
+then you normalize by one element in
+ 
+
+ align:start position:0%
+then you normalize by one element in
+this case here
+
+ align:start position:0%
+this case here
+ 
+
+ align:start position:0%
+this case here
+normalized by uh vcd
+
+ align:start position:0%
+normalized by uh vcd
+ 
+
+ align:start position:0%
+normalized by uh vcd
+vcb and so then this makes this point
+
+ align:start position:0%
+vcb and so then this makes this point
+ 
+
+ align:start position:0%
+vcb and so then this makes this point
+being zero
+
+ align:start position:0%
+being zero
+ 
+
+ align:start position:0%
+being zero
+and so we have this nice triangle here
+
+ align:start position:0%
+and so we have this nice triangle here
+ 
+
+ align:start position:0%
+and so we have this nice triangle here
+which has
+
+ align:start position:0%
+which has
+ 
+
+ align:start position:0%
+which has
+three angles alpha data and gamma
+
+ align:start position:0%
+three angles alpha data and gamma
+ 
+
+ align:start position:0%
+three angles alpha data and gamma
+and this point here rho and eta
+
+ align:start position:0%
+and this point here rho and eta
+ 
+
+ align:start position:0%
+and this point here rho and eta
+and so this is a nice way to illustrate
+
+ align:start position:0%
+and so this is a nice way to illustrate
+ 
+
+ align:start position:0%
+and so this is a nice way to illustrate
+actual measurements of the elements
+
+ align:start position:0%
+actual measurements of the elements
+ 
+
+ align:start position:0%
+actual measurements of the elements
+of this ckm metric of the ckm matrix
+
+ align:start position:0%
+of this ckm metric of the ckm matrix
+ 
+
+ align:start position:0%
+of this ckm metric of the ckm matrix
+element
+
+ align:start position:0%
+element
+ 
+
+ align:start position:0%
+element
+and without actually explaining how we
+
+ align:start position:0%
+and without actually explaining how we
+ 
+
+ align:start position:0%
+and without actually explaining how we
+do this experiment you can assume that
+
+ align:start position:0%
+do this experiment you can assume that
+ 
+
+ align:start position:0%
+do this experiment you can assume that
+you know all measurements have or you
+
+ align:start position:0%
+you know all measurements have or you
+ 
+
+ align:start position:0%
+you know all measurements have or you
+can understand that all measurements
+
+ align:start position:0%
+can understand that all measurements
+ 
+
+ align:start position:0%
+can understand that all measurements
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+to do with the weak interaction with
+
+ align:start position:0%
+to do with the weak interaction with
+ 
+
+ align:start position:0%
+to do with the weak interaction with
+kwarf that's how we have access
+
+ align:start position:0%
+kwarf that's how we have access
+ 
+
+ align:start position:0%
+kwarf that's how we have access
+to the um speaker and matrix elements
+
+ align:start position:0%
+to the um speaker and matrix elements
+ 
+
+ align:start position:0%
+to the um speaker and matrix elements
+uh sometimes this results in
+
+ align:start position:0%
+uh sometimes this results in
+ 
+
+ align:start position:0%
+uh sometimes this results in
+modification of
+
+ align:start position:0%
+modification of
+ 
+
+ align:start position:0%
+modification of
+masses or splitting of mass states and
+
+ align:start position:0%
+masses or splitting of mass states and
+ 
+
+ align:start position:0%
+masses or splitting of mass states and
+sometimes the direct measurement
+
+ align:start position:0%
+sometimes the direct measurement
+ 
+
+ align:start position:0%
+sometimes the direct measurement
+of the coupling
+
+ align:start position:0%
+of the coupling
+ 
+
+ align:start position:0%
+of the coupling
+when you put all of those measurements
+
+ align:start position:0%
+when you put all of those measurements
+ 
+
+ align:start position:0%
+when you put all of those measurements
+back together you can
+
+ align:start position:0%
+back together you can
+ 
+
+ align:start position:0%
+back together you can
+look at this so we see on our triangle
+
+ align:start position:0%
+look at this so we see on our triangle
+ 
+
+ align:start position:0%
+look at this so we see on our triangle
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+we see this this point um
+
+ align:start position:0%
+we see this this point um
+ 
+
+ align:start position:0%
+we see this this point um
+etc and row which is given here in this
+
+ align:start position:0%
+etc and row which is given here in this
+ 
+
+ align:start position:0%
+etc and row which is given here in this
+plane and you see various number of
+
+ align:start position:0%
+plane and you see various number of
+ 
+
+ align:start position:0%
+plane and you see various number of
+measurements
+
+ align:start position:0%
+measurements
+ 
+
+ align:start position:0%
+measurements
+um which cause branch to um
+
+ align:start position:0%
+um which cause branch to um
+ 
+
+ align:start position:0%
+um which cause branch to um
+which corresponds to you know elements
+
+ align:start position:0%
+which corresponds to you know elements
+ 
+
+ align:start position:0%
+which corresponds to you know elements
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+of the cklm metrics
\ No newline at end of file
diff --git a/vIjmMUI2w4c.txt b/vIjmMUI2w4c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2f0eeadf8a44b1e9f2fae6dc20c0113673a4d49b
--- /dev/null
+++ b/vIjmMUI2w4c.txt
@@ -0,0 +1,12019 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu you know I didn't get to say
+
+ align:start position:0%
+ocw.mit.edu you know I didn't get to say
+ 
+
+ align:start position:0%
+ocw.mit.edu you know I didn't get to say
+in person to you how how fun this class
+
+ align:start position:0%
+in person to you how how fun this class
+ 
+
+ align:start position:0%
+in person to you how how fun this class
+is but this is the material itself is
+
+ align:start position:0%
+is but this is the material itself is
+ 
+
+ align:start position:0%
+is but this is the material itself is
+definitely the the uh
+
+ align:start position:0%
+definitely the the uh
+ 
+
+ align:start position:0%
+definitely the the uh
+the most exciting in all the tw3
+
+ align:start position:0%
+the most exciting in all the tw3
+ 
+
+ align:start position:0%
+the most exciting in all the tw3
+curriculum um I want to take a minute
+
+ align:start position:0%
+curriculum um I want to take a minute
+ 
+
+ align:start position:0%
+curriculum um I want to take a minute
+and just kind of reintroduce myself my
+
+ align:start position:0%
+and just kind of reintroduce myself my
+ 
+
+ align:start position:0%
+and just kind of reintroduce myself my
+name is Sanjay Sarma please call me
+
+ align:start position:0%
+name is Sanjay Sarma please call me
+ 
+
+ align:start position:0%
+name is Sanjay Sarma please call me
+Sanjay right I'm very informal I demand
+
+ align:start position:0%
+Sanjay right I'm very informal I demand
+ 
+
+ align:start position:0%
+Sanjay right I'm very informal I demand
+informality I will be informal to you as
+
+ align:start position:0%
+informality I will be informal to you as
+ 
+
+ align:start position:0%
+informality I will be informal to you as
+well I will learn all your names trust
+
+ align:start position:0%
+well I will learn all your names trust
+ 
+
+ align:start position:0%
+well I will learn all your names trust
+me how many people do we have in
+
+ align:start position:0%
+me how many people do we have in
+ 
+
+ align:start position:0%
+me how many people do we have in
+class 130 okay I'll learn half your
+
+ align:start position:0%
+class 130 okay I'll learn half your
+ 
+
+ align:start position:0%
+class 130 okay I'll learn half your
+names okay but we're going to have a lot
+
+ align:start position:0%
+names okay but we're going to have a lot
+ 
+
+ align:start position:0%
+names okay but we're going to have a lot
+of fun we the some of the classes are
+
+ align:start position:0%
+of fun we the some of the classes are
+ 
+
+ align:start position:0%
+of fun we the some of the classes are
+going to be videotaped uh because as
+
+ align:start position:0%
+going to be videotaped uh because as
+ 
+
+ align:start position:0%
+going to be videotaped uh because as
+we're doing it slightly differently this
+
+ align:start position:0%
+we're doing it slightly differently this
+ 
+
+ align:start position:0%
+we're doing it slightly differently this
+class is going to be a little
+
+ align:start position:0%
+class is going to be a little
+ 
+
+ align:start position:0%
+class is going to be a little
+more MIT than Harvard in other words
+
+ align:start position:0%
+more MIT than Harvard in other words
+ 
+
+ align:start position:0%
+more MIT than Harvard in other words
+we're going to do stuff um a little in a
+
+ align:start position:0%
+we're going to do stuff um a little in a
+ 
+
+ align:start position:0%
+we're going to do stuff um a little in a
+little more formal fundamental way um
+
+ align:start position:0%
+little more formal fundamental way um
+ 
+
+ align:start position:0%
+little more formal fundamental way um
+and it'll help us address and understand
+
+ align:start position:0%
+and it'll help us address and understand
+ 
+
+ align:start position:0%
+and it'll help us address and understand
+some of the uh Concepts especially in
+
+ align:start position:0%
+some of the uh Concepts especially in
+ 
+
+ align:start position:0%
+some of the uh Concepts especially in
+kinematics more intensely than if uh you
+
+ align:start position:0%
+kinematics more intensely than if uh you
+ 
+
+ align:start position:0%
+kinematics more intensely than if uh you
+took it the way that it's s in other
+
+ align:start position:0%
+took it the way that it's s in other
+ 
+
+ align:start position:0%
+took it the way that it's s in other
+classes um as I said my style is going
+
+ align:start position:0%
+classes um as I said my style is going
+ 
+
+ align:start position:0%
+classes um as I said my style is going
+to be very informal we're going to take
+
+ align:start position:0%
+to be very informal we're going to take
+ 
+
+ align:start position:0%
+to be very informal we're going to take
+Pi we're going to see who speaks we want
+
+ align:start position:0%
+Pi we're going to see who speaks we want
+ 
+
+ align:start position:0%
+Pi we're going to see who speaks we want
+you to speak up I'll ask questions uh
+
+ align:start position:0%
+you to speak up I'll ask questions uh
+ 
+
+ align:start position:0%
+you to speak up I'll ask questions uh
+you will never
+
+ align:start position:0%
+you will never
+ 
+
+ align:start position:0%
+you will never
+ever be uh penalized for seeing anything
+
+ align:start position:0%
+ever be uh penalized for seeing anything
+ 
+
+ align:start position:0%
+ever be uh penalized for seeing anything
+class you'll only get credit for it okay
+
+ align:start position:0%
+class you'll only get credit for it okay
+ 
+
+ align:start position:0%
+class you'll only get credit for it okay
+even if it's
+
+ align:start position:0%
+even if it's
+ 
+
+ align:start position:0%
+even if it's
+funny okay so in the last class we set
+
+ align:start position:0%
+funny okay so in the last class we set
+ 
+
+ align:start position:0%
+funny okay so in the last class we set
+up what we're going to do um I we
+
+ align:start position:0%
+up what we're going to do um I we
+ 
+
+ align:start position:0%
+up what we're going to do um I we
+explained that in the field of Dynamics
+
+ align:start position:0%
+explained that in the field of Dynamics
+ 
+
+ align:start position:0%
+explained that in the field of Dynamics
+there are actually two pieces there's
+
+ align:start position:0%
+there are actually two pieces there's
+ 
+
+ align:start position:0%
+there are actually two pieces there's
+kinematics and there's kinetics right
+
+ align:start position:0%
+kinematics and there's kinetics right
+ 
+
+ align:start position:0%
+kinematics and there's kinetics right
+and we said we would do kinematics in
+
+ align:start position:0%
+and we said we would do kinematics in
+ 
+
+ align:start position:0%
+and we said we would do kinematics in
+this class and we're going to do K
+
+ align:start position:0%
+this class and we're going to do K
+ 
+
+ align:start position:0%
+this class and we're going to do K
+kinetics afterwards kinematics is all
+
+ align:start position:0%
+kinetics afterwards kinematics is all
+ 
+
+ align:start position:0%
+kinetics afterwards kinematics is all
+about motion and as I said it's the most
+
+ align:start position:0%
+about motion and as I said it's the most
+ 
+
+ align:start position:0%
+about motion and as I said it's the most
+fun part of Dynamics so let me just
+
+ align:start position:0%
+fun part of Dynamics so let me just
+ 
+
+ align:start position:0%
+fun part of Dynamics so let me just
+lower this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh sorry sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's no better way to get get
+
+ align:start position:0%
+so there's no better way to get get
+ 
+
+ align:start position:0%
+so there's no better way to get get
+going than to Simply start by writing
+
+ align:start position:0%
+going than to Simply start by writing
+ 
+
+ align:start position:0%
+going than to Simply start by writing
+out a
+
+ align:start position:0%
+out a
+ 
+
+ align:start position:0%
+out a
+problem and trying to solve it in class
+
+ align:start position:0%
+problem and trying to solve it in class
+ 
+
+ align:start position:0%
+problem and trying to solve it in class
+and that's what we're going to do now
+
+ align:start position:0%
+and that's what we're going to do now
+ 
+
+ align:start position:0%
+and that's what we're going to do now
+get this all lined up focused
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the problem that we're going to
+
+ align:start position:0%
+okay so the problem that we're going to
+ 
+
+ align:start position:0%
+okay so the problem that we're going to
+start with is imagine that I'm standing
+
+ align:start position:0%
+start with is imagine that I'm standing
+ 
+
+ align:start position:0%
+start with is imagine that I'm standing
+here in the corner of this room okay I
+
+ align:start position:0%
+here in the corner of this room okay I
+ 
+
+ align:start position:0%
+here in the corner of this room okay I
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+Frisbee and I throw it across the room
+
+ align:start position:0%
+Frisbee and I throw it across the room
+ 
+
+ align:start position:0%
+Frisbee and I throw it across the room
+the Frisbee translates that as it moves
+
+ align:start position:0%
+the Frisbee translates that as it moves
+ 
+
+ align:start position:0%
+the Frisbee translates that as it moves
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+rotates and um let's make it more
+
+ align:start position:0%
+rotates and um let's make it more
+ 
+
+ align:start position:0%
+rotates and um let's make it more
+interesting there's an insect on the
+
+ align:start position:0%
+interesting there's an insect on the
+ 
+
+ align:start position:0%
+interesting there's an insect on the
+Frisbee okay and when the frisbee is
+
+ align:start position:0%
+Frisbee okay and when the frisbee is
+ 
+
+ align:start position:0%
+Frisbee okay and when the frisbee is
+moving across the room and rotating in
+
+ align:start position:0%
+moving across the room and rotating in
+ 
+
+ align:start position:0%
+moving across the room and rotating in
+insect starts
+
+ align:start position:0%
+insect starts
+ 
+
+ align:start position:0%
+insect starts
+running away from the
+
+ align:start position:0%
+running away from the
+ 
+
+ align:start position:0%
+running away from the
+center okay now this is a made of
+
+ align:start position:0%
+center okay now this is a made of
+ 
+
+ align:start position:0%
+center okay now this is a made of
+problem but this is the problem I'm
+
+ align:start position:0%
+problem but this is the problem I'm
+ 
+
+ align:start position:0%
+problem but this is the problem I'm
+going to solve today and what does
+
+ align:start position:0%
+going to solve today and what does
+ 
+
+ align:start position:0%
+going to solve today and what does
+solving a problem mean I'll solve a
+
+ align:start position:0%
+solving a problem mean I'll solve a
+ 
+
+ align:start position:0%
+solving a problem mean I'll solve a
+piece of it but let's let's examine what
+
+ align:start position:0%
+piece of it but let's let's examine what
+ 
+
+ align:start position:0%
+piece of it but let's let's examine what
+this could mean first of all this is
+
+ align:start position:0%
+this could mean first of all this is
+ 
+
+ align:start position:0%
+this could mean first of all this is
+obviously a silly you know exercise but
+
+ align:start position:0%
+obviously a silly you know exercise but
+ 
+
+ align:start position:0%
+obviously a silly you know exercise but
+um if you imagine an astronaut on the
+
+ align:start position:0%
+um if you imagine an astronaut on the
+ 
+
+ align:start position:0%
+um if you imagine an astronaut on the
+space shuttle hurtling through
+
+ align:start position:0%
+space shuttle hurtling through
+ 
+
+ align:start position:0%
+space shuttle hurtling through
+space um this is a similar problem and
+
+ align:start position:0%
+space um this is a similar problem and
+ 
+
+ align:start position:0%
+space um this is a similar problem and
+the question you might ask is the
+
+ align:start position:0%
+the question you might ask is the
+ 
+
+ align:start position:0%
+the question you might ask is the
+astronauts boots let's say the're
+
+ align:start position:0%
+astronauts boots let's say the're
+ 
+
+ align:start position:0%
+astronauts boots let's say the're
+magnetic exert a certain force on the
+
+ align:start position:0%
+magnetic exert a certain force on the
+ 
+
+ align:start position:0%
+magnetic exert a certain force on the
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+shuttle right now
+
+ align:start position:0%
+shuttle right now
+ 
+
+ align:start position:0%
+shuttle right now
+obviously uh there are certain
+
+ align:start position:0%
+obviously uh there are certain
+ 
+
+ align:start position:0%
+obviously uh there are certain
+conditions under which the astronaut
+
+ align:start position:0%
+conditions under which the astronaut
+ 
+
+ align:start position:0%
+conditions under which the astronaut
+would lose contact with the space
+
+ align:start position:0%
+would lose contact with the space
+ 
+
+ align:start position:0%
+would lose contact with the space
+shuttle assuming the surface actually
+
+ align:start position:0%
+shuttle assuming the surface actually
+ 
+
+ align:start position:0%
+shuttle assuming the surface actually
+the surface of the space shule isn't ion
+
+ align:start position:0%
+the surface of the space shule isn't ion
+ 
+
+ align:start position:0%
+the surface of the space shule isn't ion
+it's aluminum so my example doesn't
+
+ align:start position:0%
+it's aluminum so my example doesn't
+ 
+
+ align:start position:0%
+it's aluminum so my example doesn't
+really hold but that's okay okay so
+
+ align:start position:0%
+really hold but that's okay okay so
+ 
+
+ align:start position:0%
+really hold but that's okay okay so
+assuming it assume it's iron why isn't
+
+ align:start position:0%
+assuming it assume it's iron why isn't
+ 
+
+ align:start position:0%
+assuming it assume it's iron why isn't
+it Alum why isn't it iron because yeah
+
+ align:start position:0%
+it Alum why isn't it iron because yeah
+ 
+
+ align:start position:0%
+it Alum why isn't it iron because yeah
+it's heavy yeah we know all right but is
+
+ align:start position:0%
+it's heavy yeah we know all right but is
+ 
+
+ align:start position:0%
+it's heavy yeah we know all right but is
+assume it's iron right so let's assume
+
+ align:start position:0%
+assume it's iron right so let's assume
+ 
+
+ align:start position:0%
+assume it's iron right so let's assume
+that the astronaut's holding on to the
+
+ align:start position:0%
+that the astronaut's holding on to the
+ 
+
+ align:start position:0%
+that the astronaut's holding on to the
+space shut using a magnet using magnetic
+
+ align:start position:0%
+space shut using a magnet using magnetic
+ 
+
+ align:start position:0%
+space shut using a magnet using magnetic
+boots under what conditions would the
+
+ align:start position:0%
+boots under what conditions would the
+ 
+
+ align:start position:0%
+boots under what conditions would the
+astronaut stay in contact with the space
+
+ align:start position:0%
+astronaut stay in contact with the space
+ 
+
+ align:start position:0%
+astronaut stay in contact with the space
+shuttle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyone
+
+ align:start position:0%
+anyone
+ 
+
+ align:start position:0%
+anyone
+hi excuse
+
+ align:start position:0%
+hi excuse
+ 
+
+ align:start position:0%
+hi excuse
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+sorrys so under what conditions would
+
+ align:start position:0%
+sorrys so under what conditions would
+ 
+
+ align:start position:0%
+sorrys so under what conditions would
+the astronaut stay in contact with the
+
+ align:start position:0%
+the astronaut stay in contact with the
+ 
+
+ align:start position:0%
+the astronaut stay in contact with the
+space shuttle
+
+ align:start position:0%
+space shuttle
+ 
+
+ align:start position:0%
+space shuttle
+space shuttles swirling through space
+
+ align:start position:0%
+space shuttles swirling through space
+ 
+
+ align:start position:0%
+space shuttles swirling through space
+it's hot in here isn't it let's open the
+
+ align:start position:0%
+it's hot in here isn't it let's open the
+ 
+
+ align:start position:0%
+it's hot in here isn't it let's open the
+windows I don't know if there's a way to
+
+ align:start position:0%
+windows I don't know if there's a way to
+ 
+
+ align:start position:0%
+windows I don't know if there's a way to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+this go ahead how do how does the
+
+ align:start position:0%
+this go ahead how do how does the
+ 
+
+ align:start position:0%
+this go ahead how do how does the
+astronaut stay in touch with the space
+
+ align:start position:0%
+astronaut stay in touch with the space
+ 
+
+ align:start position:0%
+astronaut stay in touch with the space
+shuttle okay we'll figure this out it's
+
+ align:start position:0%
+shuttle okay we'll figure this out it's
+ 
+
+ align:start position:0%
+shuttle okay we'll figure this out it's
+broken anyone raise your hands
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes excellent magnetic force is strong
+
+ align:start position:0%
+yes excellent magnetic force is strong
+ 
+
+ align:start position:0%
+yes excellent magnetic force is strong
+enough to keep him or her in contact
+
+ align:start position:0%
+enough to keep him or her in contact
+ 
+
+ align:start position:0%
+enough to keep him or her in contact
+uh and able to overcome whatever force
+
+ align:start position:0%
+uh and able to overcome whatever force
+ 
+
+ align:start position:0%
+uh and able to overcome whatever force
+is pulling him or her away from the
+
+ align:start position:0%
+is pulling him or her away from the
+ 
+
+ align:start position:0%
+is pulling him or her away from the
+space shuttle what force is pulling him
+
+ align:start position:0%
+space shuttle what force is pulling him
+ 
+
+ align:start position:0%
+space shuttle what force is pulling him
+or her away from the space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shuttle what
+
+ align:start position:0%
+shuttle what
+ 
+
+ align:start position:0%
+shuttle what
+else inertial Force what's that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right look it's very simple right
+
+ align:start position:0%
+that's right look it's very simple right
+ 
+
+ align:start position:0%
+that's right look it's very simple right
+think of this astronaut forget the
+
+ align:start position:0%
+think of this astronaut forget the
+ 
+
+ align:start position:0%
+think of this astronaut forget the
+spaceship imagine you know just imagine
+
+ align:start position:0%
+spaceship imagine you know just imagine
+ 
+
+ align:start position:0%
+spaceship imagine you know just imagine
+the spaceship isn't there right if you
+
+ align:start position:0%
+the spaceship isn't there right if you
+ 
+
+ align:start position:0%
+the spaceship isn't there right if you
+just think of the astronaut this guy
+
+ align:start position:0%
+just think of the astronaut this guy
+ 
+
+ align:start position:0%
+just think of the astronaut this guy
+this woman is hurling through space
+
+ align:start position:0%
+this woman is hurling through space
+ 
+
+ align:start position:0%
+this woman is hurling through space
+right and it's he or she's doing it
+
+ align:start position:0%
+right and it's he or she's doing it
+ 
+
+ align:start position:0%
+right and it's he or she's doing it
+under the influence of a certain
+
+ align:start position:0%
+under the influence of a certain
+ 
+
+ align:start position:0%
+under the influence of a certain
+force and that Force had better be equal
+
+ align:start position:0%
+force and that Force had better be equal
+ 
+
+ align:start position:0%
+force and that Force had better be equal
+to mass times the acceleration of that
+
+ align:start position:0%
+to mass times the acceleration of that
+ 
+
+ align:start position:0%
+to mass times the acceleration of that
+astronaut
+
+ align:start position:0%
+astronaut
+ 
+
+ align:start position:0%
+astronaut
+right if the magnetic force cannot equal
+
+ align:start position:0%
+right if the magnetic force cannot equal
+ 
+
+ align:start position:0%
+right if the magnetic force cannot equal
+or exceed n * whatever the a
+
+ align:start position:0%
+or exceed n * whatever the a
+ 
+
+ align:start position:0%
+or exceed n * whatever the a
+is by by astronaut
+
+ align:start position:0%
+is by by astronaut
+ 
+
+ align:start position:0%
+is by by astronaut
+right get it because the magnetic force
+
+ align:start position:0%
+right get it because the magnetic force
+ 
+
+ align:start position:0%
+right get it because the magnetic force
+cannot
+
+ align:start position:0%
+cannot
+ 
+
+ align:start position:0%
+cannot
+provide the uh change cannot affect the
+
+ align:start position:0%
+provide the uh change cannot affect the
+ 
+
+ align:start position:0%
+provide the uh change cannot affect the
+change in momentum rate of change in
+
+ align:start position:0%
+change in momentum rate of change in
+ 
+
+ align:start position:0%
+change in momentum rate of change in
+momentum required to keep the astronaut
+
+ align:start position:0%
+momentum required to keep the astronaut
+ 
+
+ align:start position:0%
+momentum required to keep the astronaut
+in position get it so the magnetic force
+
+ align:start position:0%
+in position get it so the magnetic force
+ 
+
+ align:start position:0%
+in position get it so the magnetic force
+is weak and the space shuttle is kind of
+
+ align:start position:0%
+is weak and the space shuttle is kind of
+ 
+
+ align:start position:0%
+is weak and the space shuttle is kind of
+spinning away right it
+
+ align:start position:0%
+spinning away right it
+ 
+
+ align:start position:0%
+spinning away right it
+the if the force isn't enough to keep
+
+ align:start position:0%
+the if the force isn't enough to keep
+ 
+
+ align:start position:0%
+the if the force isn't enough to keep
+the astronaut spinning accelerating with
+
+ align:start position:0%
+the astronaut spinning accelerating with
+ 
+
+ align:start position:0%
+the astronaut spinning accelerating with
+the space shuttle so they're going to
+
+ align:start position:0%
+the space shuttle so they're going to
+ 
+
+ align:start position:0%
+the space shuttle so they're going to
+separate right so this problem of you
+
+ align:start position:0%
+separate right so this problem of you
+ 
+
+ align:start position:0%
+separate right so this problem of you
+know me throwing a uh a a frisbee across
+
+ align:start position:0%
+know me throwing a uh a a frisbee across
+ 
+
+ align:start position:0%
+know me throwing a uh a a frisbee across
+the room an insect on the Frisbee
+
+ align:start position:0%
+the room an insect on the Frisbee
+ 
+
+ align:start position:0%
+the room an insect on the Frisbee
+running away from the center of the
+
+ align:start position:0%
+running away from the center of the
+ 
+
+ align:start position:0%
+running away from the center of the
+Frisbee the the the practical
+
+ align:start position:0%
+Frisbee the the the practical
+ 
+
+ align:start position:0%
+Frisbee the the the practical
+application of the problem could be hey
+
+ align:start position:0%
+application of the problem could be hey
+ 
+
+ align:start position:0%
+application of the problem could be hey
+what is the attractive Force for example
+
+ align:start position:0%
+what is the attractive Force for example
+ 
+
+ align:start position:0%
+what is the attractive Force for example
+the you know spiders have adhesive pads
+
+ align:start position:0%
+the you know spiders have adhesive pads
+ 
+
+ align:start position:0%
+the you know spiders have adhesive pads
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so what is the kind of the adhesive
+
+ align:start position:0%
+so what is the kind of the adhesive
+ 
+
+ align:start position:0%
+so what is the kind of the adhesive
+force that the spider should be able to
+
+ align:start position:0%
+force that the spider should be able to
+ 
+
+ align:start position:0%
+force that the spider should be able to
+exert if it wants to stay on the Frisbee
+
+ align:start position:0%
+exert if it wants to stay on the Frisbee
+ 
+
+ align:start position:0%
+exert if it wants to stay on the Frisbee
+as I hle it across space and if it wants
+
+ align:start position:0%
+as I hle it across space and if it wants
+ 
+
+ align:start position:0%
+as I hle it across space and if it wants
+to kind of move on the Frisbee in some
+
+ align:start position:0%
+to kind of move on the Frisbee in some
+ 
+
+ align:start position:0%
+to kind of move on the Frisbee in some
+predetermined way get it now in order
+
+ align:start position:0%
+predetermined way get it now in order
+ 
+
+ align:start position:0%
+predetermined way get it now in order
+for me to answer this question what
+
+ align:start position:0%
+for me to answer this question what
+ 
+
+ align:start position:0%
+for me to answer this question what
+question do I need to answer
+
+ align:start position:0%
+question do I need to answer
+ 
+
+ align:start position:0%
+question do I need to answer
+first in order to answer the question
+
+ align:start position:0%
+first in order to answer the question
+ 
+
+ align:start position:0%
+first in order to answer the question
+what is the force required right let's
+
+ align:start position:0%
+what is the force required right let's
+ 
+
+ align:start position:0%
+what is the force required right let's
+say I know the mass of the the spider
+
+ align:start position:0%
+say I know the mass of the the spider
+ 
+
+ align:start position:0%
+say I know the mass of the the spider
+what is the one thing I need to figure
+
+ align:start position:0%
+what is the one thing I need to figure
+ 
+
+ align:start position:0%
+what is the one thing I need to figure
+out yep coordinate system you need yes
+
+ align:start position:0%
+out yep coordinate system you need yes
+ 
+
+ align:start position:0%
+out yep coordinate system you need yes
+that's how I start and then what do I
+
+ align:start position:0%
+that's how I start and then what do I
+ 
+
+ align:start position:0%
+that's how I start and then what do I
+need to
+
+ align:start position:0%
+need to
+ 
+
+ align:start position:0%
+need to
+do that's right all you need to do is
+
+ align:start position:0%
+do that's right all you need to do is
+ 
+
+ align:start position:0%
+do that's right all you need to do is
+find the
+
+ align:start position:0%
+find the
+ 
+
+ align:start position:0%
+find the
+acceleration of this dud the
+
+ align:start position:0%
+acceleration of this dud the
+ 
+
+ align:start position:0%
+acceleration of this dud the
+spider as it stays on the Frisbee and
+
+ align:start position:0%
+spider as it stays on the Frisbee and
+ 
+
+ align:start position:0%
+spider as it stays on the Frisbee and
+tries to move as it's hurling through
+
+ align:start position:0%
+tries to move as it's hurling through
+ 
+
+ align:start position:0%
+tries to move as it's hurling through
+space right that's all we need to do and
+
+ align:start position:0%
+space right that's all we need to do and
+ 
+
+ align:start position:0%
+space right that's all we need to do and
+answering that question is the subject
+
+ align:start position:0%
+answering that question is the subject
+ 
+
+ align:start position:0%
+answering that question is the subject
+of a topic which begins with k which is
+
+ align:start position:0%
+of a topic which begins with k which is
+ 
+
+ align:start position:0%
+of a topic which begins with k which is
+kinematics right okay all right so how
+
+ align:start position:0%
+kinematics right okay all right so how
+ 
+
+ align:start position:0%
+kinematics right okay all right so how
+do you do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how would you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it where do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start say it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again okay and then what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do very good right look if I'm sitting
+
+ align:start position:0%
+do very good right look if I'm sitting
+ 
+
+ align:start position:0%
+do very good right look if I'm sitting
+on the Frisby let's say I'm sitting on
+
+ align:start position:0%
+on the Frisby let's say I'm sitting on
+ 
+
+ align:start position:0%
+on the Frisby let's say I'm sitting on
+frisbee I'm the pilot of the Frisbee
+
+ align:start position:0%
+frisbee I'm the pilot of the Frisbee
+ 
+
+ align:start position:0%
+frisbee I'm the pilot of the Frisbee
+right and I see my buddy the astronaut
+
+ align:start position:0%
+right and I see my buddy the astronaut
+ 
+
+ align:start position:0%
+right and I see my buddy the astronaut
+trying to I move on the space shuttle
+
+ align:start position:0%
+trying to I move on the space shuttle
+ 
+
+ align:start position:0%
+trying to I move on the space shuttle
+right I'm or similarly I'm sitting on
+
+ align:start position:0%
+right I'm or similarly I'm sitting on
+ 
+
+ align:start position:0%
+right I'm or similarly I'm sitting on
+the Frisbee and I see this insect the
+
+ align:start position:0%
+the Frisbee and I see this insect the
+ 
+
+ align:start position:0%
+the Frisbee and I see this insect the
+spider running away from the center of
+
+ align:start position:0%
+spider running away from the center of
+ 
+
+ align:start position:0%
+spider running away from the center of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Frisbee with respect to myself what's a
+
+ align:start position:0%
+Frisbee with respect to myself what's a
+ 
+
+ align:start position:0%
+Frisbee with respect to myself what's a
+spider trying to
+
+ align:start position:0%
+spider trying to
+ 
+
+ align:start position:0%
+spider trying to
+do in a what what sort of path straight
+
+ align:start position:0%
+do in a what what sort of path straight
+ 
+
+ align:start position:0%
+do in a what what sort of path straight
+line right as far as I'm concerned just
+
+ align:start position:0%
+line right as far as I'm concerned just
+ 
+
+ align:start position:0%
+line right as far as I'm concerned just
+moving away in a straight line
+
+ align:start position:0%
+moving away in a straight line
+ 
+
+ align:start position:0%
+moving away in a straight line
+right what about with respect to the
+
+ align:start position:0%
+right what about with respect to the
+ 
+
+ align:start position:0%
+right what about with respect to the
+ground Observer of the Space Shuttle or
+
+ align:start position:0%
+ground Observer of the Space Shuttle or
+ 
+
+ align:start position:0%
+ground Observer of the Space Shuttle or
+with with respect to me what's the uh
+
+ align:start position:0%
+with with respect to me what's the uh
+ 
+
+ align:start position:0%
+with with respect to me what's the uh
+what's the uh Spider
+
+ align:start position:0%
+what's the uh Spider
+ 
+
+ align:start position:0%
+what's the uh Spider
+doing yeah it's kind of going like this
+
+ align:start position:0%
+doing yeah it's kind of going like this
+ 
+
+ align:start position:0%
+doing yeah it's kind of going like this
+right it's kind of bigger and bigger
+
+ align:start position:0%
+right it's kind of bigger and bigger
+ 
+
+ align:start position:0%
+right it's kind of bigger and bigger
+spiral kind of thing right so is the
+
+ align:start position:0%
+spiral kind of thing right so is the
+ 
+
+ align:start position:0%
+spiral kind of thing right so is the
+acceleration different depending on
+
+ align:start position:0%
+acceleration different depending on
+ 
+
+ align:start position:0%
+acceleration different depending on
+where I'm looking
+
+ align:start position:0%
+where I'm looking
+ 
+
+ align:start position:0%
+where I'm looking
+from yes okay which frame should I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pick where should I look at it from
+
+ align:start position:0%
+pick where should I look at it from
+ 
+
+ align:start position:0%
+pick where should I look at it from
+let's say I'm on Earth where do I look
+
+ align:start position:0%
+let's say I'm on Earth where do I look
+ 
+
+ align:start position:0%
+let's say I'm on Earth where do I look
+at it from should I should I pick the
+
+ align:start position:0%
+at it from should I should I pick the
+ 
+
+ align:start position:0%
+at it from should I should I pick the
+frame on Earth should I pick the frame
+
+ align:start position:0%
+frame on Earth should I pick the frame
+ 
+
+ align:start position:0%
+frame on Earth should I pick the frame
+attached to the spider I mean to the to
+
+ align:start position:0%
+attached to the spider I mean to the to
+ 
+
+ align:start position:0%
+attached to the spider I mean to the to
+the spider should I pick a frame
+
+ align:start position:0%
+the spider should I pick a frame
+ 
+
+ align:start position:0%
+the spider should I pick a frame
+attached to the Frisbee which one should
+
+ align:start position:0%
+attached to the Frisbee which one should
+ 
+
+ align:start position:0%
+attached to the Frisbee which one should
+I pick where should I be looking at it
+
+ align:start position:0%
+I pick where should I be looking at it
+ 
+
+ align:start position:0%
+I pick where should I be looking at it
+to do this F is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ma because obviously the accelerations
+
+ align:start position:0%
+ma because obviously the accelerations
+ 
+
+ align:start position:0%
+ma because obviously the accelerations
+are different right a frame attached to
+
+ align:start position:0%
+are different right a frame attached to
+ 
+
+ align:start position:0%
+are different right a frame attached to
+the spider sees no acceleration
+
+ align:start position:0%
+the spider sees no acceleration
+ 
+
+ align:start position:0%
+the spider sees no acceleration
+whatsoever
+
+ align:start position:0%
+whatsoever
+ 
+
+ align:start position:0%
+whatsoever
+right okay this is
+
+ align:start position:0%
+right okay this is
+ 
+
+ align:start position:0%
+right okay this is
+irritating so which frame should I
+
+ align:start position:0%
+irritating so which frame should I
+ 
+
+ align:start position:0%
+irritating so which frame should I
+pick come on let's warm up we have
+
+ align:start position:0%
+pick come on let's warm up we have
+ 
+
+ align:start position:0%
+pick come on let's warm up we have
+another 15 weeks to go we going to be
+
+ align:start position:0%
+another 15 weeks to go we going to be
+ 
+
+ align:start position:0%
+another 15 weeks to go we going to be
+doing a lot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talking that's excellent Insight so you
+
+ align:start position:0%
+talking that's excellent Insight so you
+ 
+
+ align:start position:0%
+talking that's excellent Insight so you
+got to pick some frame because if you
+
+ align:start position:0%
+got to pick some frame because if you
+ 
+
+ align:start position:0%
+got to pick some frame because if you
+pick the Frisbee then you're ignoring
+
+ align:start position:0%
+pick the Frisbee then you're ignoring
+ 
+
+ align:start position:0%
+pick the Frisbee then you're ignoring
+some things right so which frame should
+
+ align:start position:0%
+some things right so which frame should
+ 
+
+ align:start position:0%
+some things right so which frame should
+we pick that's exactly right but which
+
+ align:start position:0%
+we pick that's exactly right but which
+ 
+
+ align:start position:0%
+we pick that's exactly right but which
+one would you pick where you wouldn't
+
+ align:start position:0%
+one would you pick where you wouldn't
+ 
+
+ align:start position:0%
+one would you pick where you wouldn't
+have to add
+
+ align:start position:0%
+have to add
+ 
+
+ align:start position:0%
+have to add
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+H which one the
+
+ align:start position:0%
+H which one the
+ 
+
+ align:start position:0%
+H which one the
+Earth what do you think the Earth but
+
+ align:start position:0%
+Earth what do you think the Earth but
+ 
+
+ align:start position:0%
+Earth what do you think the Earth but
+isn't the Earth moving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what but that's true of any
+
+ align:start position:0%
+what but that's true of any
+ 
+
+ align:start position:0%
+what but that's true of any
+frame but you're actually on the right
+
+ align:start position:0%
+frame but you're actually on the right
+ 
+
+ align:start position:0%
+frame but you're actually on the right
+track should I tell you the answer the
+
+ align:start position:0%
+track should I tell you the answer the
+ 
+
+ align:start position:0%
+track should I tell you the answer the
+answer is actually you pick an inertial
+
+ align:start position:0%
+answer is actually you pick an inertial
+ 
+
+ align:start position:0%
+answer is actually you pick an inertial
+frame remember that word but there is no
+
+ align:start position:0%
+frame remember that word but there is no
+ 
+
+ align:start position:0%
+frame remember that word but there is no
+such thing as an inertial frame really
+
+ align:start position:0%
+such thing as an inertial frame really
+ 
+
+ align:start position:0%
+such thing as an inertial frame really
+okay what it means is it's a frame that
+
+ align:start position:0%
+okay what it means is it's a frame that
+ 
+
+ align:start position:0%
+okay what it means is it's a frame that
+is Motionless in space and the Earth
+
+ align:start position:0%
+is Motionless in space and the Earth
+ 
+
+ align:start position:0%
+is Motionless in space and the Earth
+moves with respect to that frame and the
+
+ align:start position:0%
+moves with respect to that frame and the
+ 
+
+ align:start position:0%
+moves with respect to that frame and the
+Frisbee or the space shuttle moves with
+
+ align:start position:0%
+Frisbee or the space shuttle moves with
+ 
+
+ align:start position:0%
+Frisbee or the space shuttle moves with
+respect to that frame and you need to
+
+ align:start position:0%
+respect to that frame and you need to
+ 
+
+ align:start position:0%
+respect to that frame and you need to
+calculate the acceleration with respect
+
+ align:start position:0%
+calculate the acceleration with respect
+ 
+
+ align:start position:0%
+calculate the acceleration with respect
+to that frame but it turns out that the
+
+ align:start position:0%
+to that frame but it turns out that the
+ 
+
+ align:start position:0%
+to that frame but it turns out that the
+relative velocity relative motion of the
+
+ align:start position:0%
+relative velocity relative motion of the
+ 
+
+ align:start position:0%
+relative velocity relative motion of the
+Earth with respect to inertial frame is
+
+ align:start position:0%
+Earth with respect to inertial frame is
+ 
+
+ align:start position:0%
+Earth with respect to inertial frame is
+much lower compared to the relative
+
+ align:start position:0%
+much lower compared to the relative
+ 
+
+ align:start position:0%
+much lower compared to the relative
+velocity of the Space Shuttle so we can
+
+ align:start position:0%
+velocity of the Space Shuttle so we can
+ 
+
+ align:start position:0%
+velocity of the Space Shuttle so we can
+just pick the Earth get it so it's
+
+ align:start position:0%
+just pick the Earth get it so it's
+ 
+
+ align:start position:0%
+just pick the Earth get it so it's
+actually an approximation so we're just
+
+ align:start position:0%
+actually an approximation so we're just
+ 
+
+ align:start position:0%
+actually an approximation so we're just
+going to pick the Earth right because
+
+ align:start position:0%
+going to pick the Earth right because
+ 
+
+ align:start position:0%
+going to pick the Earth right because
+space sh moves really fast on the earth
+
+ align:start position:0%
+space sh moves really fast on the earth
+ 
+
+ align:start position:0%
+space sh moves really fast on the earth
+so if you actually picked the inertial
+
+ align:start position:0%
+so if you actually picked the inertial
+ 
+
+ align:start position:0%
+so if you actually picked the inertial
+frame it would make such a big
+
+ align:start position:0%
+frame it would make such a big
+ 
+
+ align:start position:0%
+frame it would make such a big
+difference so from a Dynamics point of
+
+ align:start position:0%
+difference so from a Dynamics point of
+ 
+
+ align:start position:0%
+difference so from a Dynamics point of
+view we pick the Earth
+
+ align:start position:0%
+view we pick the Earth
+ 
+
+ align:start position:0%
+view we pick the Earth
+because it's an inertial frame or an
+
+ align:start position:0%
+because it's an inertial frame or an
+ 
+
+ align:start position:0%
+because it's an inertial frame or an
+approximation of inertial frame but from
+
+ align:start position:0%
+approximation of inertial frame but from
+ 
+
+ align:start position:0%
+approximation of inertial frame but from
+a kinematics point of view we don't care
+
+ align:start position:0%
+a kinematics point of view we don't care
+ 
+
+ align:start position:0%
+a kinematics point of view we don't care
+what an inertial frame is an inertial
+
+ align:start position:0%
+what an inertial frame is an inertial
+ 
+
+ align:start position:0%
+what an inertial frame is an inertial
+frame is simply the frame in which f is
+
+ align:start position:0%
+frame is simply the frame in which f is
+ 
+
+ align:start position:0%
+frame is simply the frame in which f is
+equal to ma right what we're going to
+
+ align:start position:0%
+equal to ma right what we're going to
+ 
+
+ align:start position:0%
+equal to ma right what we're going to
+concentrate on now is calculating the a
+
+ align:start position:0%
+concentrate on now is calculating the a
+ 
+
+ align:start position:0%
+concentrate on now is calculating the a
+in whichever frame you choose get it it
+
+ align:start position:0%
+in whichever frame you choose get it it
+ 
+
+ align:start position:0%
+in whichever frame you choose get it it
+just so happens then we start writing
+
+ align:start position:0%
+just so happens then we start writing
+ 
+
+ align:start position:0%
+just so happens then we start writing
+Dynamic equations by the way the word is
+
+ align:start position:0%
+Dynamic equations by the way the word is
+ 
+
+ align:start position:0%
+Dynamic equations by the way the word is
+the objective is dynamic or dynamical
+
+ align:start position:0%
+the objective is dynamic or dynamical
+ 
+
+ align:start position:0%
+the objective is dynamic or dynamical
+they're both correct okay it took me 20
+
+ align:start position:0%
+they're both correct okay it took me 20
+ 
+
+ align:start position:0%
+they're both correct okay it took me 20
+years to figure this out
+
+ align:start position:0%
+years to figure this out
+ 
+
+ align:start position:0%
+years to figure this out
+but anyway um if you from a kinematics
+
+ align:start position:0%
+but anyway um if you from a kinematics
+ 
+
+ align:start position:0%
+but anyway um if you from a kinematics
+point of view we should be able to
+
+ align:start position:0%
+point of view we should be able to
+ 
+
+ align:start position:0%
+point of view we should be able to
+figure out the velocity of anything with
+
+ align:start position:0%
+figure out the velocity of anything with
+ 
+
+ align:start position:0%
+figure out the velocity of anything with
+respect to any frame right and then when
+
+ align:start position:0%
+respect to any frame right and then when
+ 
+
+ align:start position:0%
+respect to any frame right and then when
+we come to Dynamics we'll make sure we
+
+ align:start position:0%
+we come to Dynamics we'll make sure we
+ 
+
+ align:start position:0%
+we come to Dynamics we'll make sure we
+do the Spectrum inertial frame and write
+
+ align:start position:0%
+do the Spectrum inertial frame and write
+ 
+
+ align:start position:0%
+do the Spectrum inertial frame and write
+f is equal to ma but right now our focus
+
+ align:start position:0%
+f is equal to ma but right now our focus
+ 
+
+ align:start position:0%
+f is equal to ma but right now our focus
+is on the a all right so let's figure
+
+ align:start position:0%
+is on the a all right so let's figure
+ 
+
+ align:start position:0%
+is on the a all right so let's figure
+out how to
+
+ align:start position:0%
+out how to
+ 
+
+ align:start position:0%
+out how to
+calculate um the velocity of and the
+
+ align:start position:0%
+calculate um the velocity of and the
+ 
+
+ align:start position:0%
+calculate um the velocity of and the
+acceleration of the spider with respect
+
+ align:start position:0%
+acceleration of the spider with respect
+ 
+
+ align:start position:0%
+acceleration of the spider with respect
+to different frames and We Know by the
+
+ align:start position:0%
+to different frames and We Know by the
+ 
+
+ align:start position:0%
+to different frames and We Know by the
+way that the Earth is the frame we
+
+ align:start position:0%
+way that the Earth is the frame we
+ 
+
+ align:start position:0%
+way that the Earth is the frame we
+really care about but we don't care in
+
+ align:start position:0%
+really care about but we don't care in
+ 
+
+ align:start position:0%
+really care about but we don't care in
+kinematics right because kinematics is
+
+ align:start position:0%
+kinematics right because kinematics is
+ 
+
+ align:start position:0%
+kinematics right because kinematics is
+all motion we don't care about okay so
+
+ align:start position:0%
+all motion we don't care about okay so
+ 
+
+ align:start position:0%
+all motion we don't care about okay so
+what's a frame let me start by asking
+
+ align:start position:0%
+what's a frame let me start by asking
+ 
+
+ align:start position:0%
+what's a frame let me start by asking
+you to guess and then I'll tell you what
+
+ align:start position:0%
+you to guess and then I'll tell you what
+ 
+
+ align:start position:0%
+you to guess and then I'll tell you what
+it is what's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frame
+
+ align:start position:0%
+frame
+ 
+
+ align:start position:0%
+frame
+perspective yeah it's a
+
+ align:start position:0%
+perspective yeah it's a
+ 
+
+ align:start position:0%
+perspective yeah it's a
+perspective any other words for it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm actually holding a frame here's what
+
+ align:start position:0%
+I'm actually holding a frame here's what
+ 
+
+ align:start position:0%
+I'm actually holding a frame here's what
+a frame is when in doubt imagine a frame
+
+ align:start position:0%
+a frame is when in doubt imagine a frame
+ 
+
+ align:start position:0%
+a frame is when in doubt imagine a frame
+to be some sort of three-dimensional
+
+ align:start position:0%
+to be some sort of three-dimensional
+ 
+
+ align:start position:0%
+to be some sort of three-dimensional
+transparency okay now let's limit
+
+ align:start position:0%
+transparency okay now let's limit
+ 
+
+ align:start position:0%
+transparency okay now let's limit
+ourselves to two- dimensional space a
+
+ align:start position:0%
+ourselves to two- dimensional space a
+ 
+
+ align:start position:0%
+ourselves to two- dimensional space a
+frame is a
+
+ align:start position:0%
+frame is a
+ 
+
+ align:start position:0%
+frame is a
+transparency that's all it is it is this
+
+ align:start position:0%
+transparency that's all it is it is this
+ 
+
+ align:start position:0%
+transparency that's all it is it is this
+imaginary set of points that are kind of
+
+ align:start position:0%
+imaginary set of points that are kind of
+ 
+
+ align:start position:0%
+imaginary set of points that are kind of
+rigid with respect to each other get it
+
+ align:start position:0%
+rigid with respect to each other get it
+ 
+
+ align:start position:0%
+rigid with respect to each other get it
+so here's a frame let us say that I say
+
+ align:start position:0%
+so here's a frame let us say that I say
+ 
+
+ align:start position:0%
+so here's a frame let us say that I say
+that draw it here
+
+ align:start position:0%
+that draw it here
+ 
+
+ align:start position:0%
+that draw it here
+this is the corner of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and this is the
+
+ align:start position:0%
+and this is the
+ 
+
+ align:start position:0%
+and this is the
+Frisbee now I can pick attach a frame to
+
+ align:start position:0%
+Frisbee now I can pick attach a frame to
+ 
+
+ align:start position:0%
+Frisbee now I can pick attach a frame to
+the Frisbee as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay now I'll call let me remove
+
+ align:start position:0%
+well okay now I'll call let me remove
+ 
+
+ align:start position:0%
+well okay now I'll call let me remove
+this I'm going to call this guy from
+
+ align:start position:0%
+this I'm going to call this guy from
+ 
+
+ align:start position:0%
+this I'm going to call this guy from
+name f for Frisbee for the time
+
+ align:start position:0%
+name f for Frisbee for the time
+ 
+
+ align:start position:0%
+name f for Frisbee for the time
+being and every point of the
+
+ align:start position:0%
+being and every point of the
+ 
+
+ align:start position:0%
+being and every point of the
+transparency moves kind of rigidly and
+
+ align:start position:0%
+transparency moves kind of rigidly and
+ 
+
+ align:start position:0%
+transparency moves kind of rigidly and
+that's that frame that's frame F get it
+
+ align:start position:0%
+that's that frame that's frame F get it
+ 
+
+ align:start position:0%
+that's that frame that's frame F get it
+I used a capital letter F I put a circle
+
+ align:start position:0%
+I used a capital letter F I put a circle
+ 
+
+ align:start position:0%
+I used a capital letter F I put a circle
+around it I put a squiggly line right
+
+ align:start position:0%
+around it I put a squiggly line right
+ 
+
+ align:start position:0%
+around it I put a squiggly line right
+and I called it a frame so this is the
+
+ align:start position:0%
+and I called it a frame so this is the
+ 
+
+ align:start position:0%
+and I called it a frame so this is the
+frame right and this is let's call it
+
+ align:start position:0%
+frame right and this is let's call it
+ 
+
+ align:start position:0%
+frame right and this is let's call it
+Earth e right so let's call this planet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Earth where most of us live
+
+ align:start position:0%
+Earth where most of us live
+ 
+
+ align:start position:0%
+Earth where most of us live
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh so this is the frame attached to this
+
+ align:start position:0%
+uh so this is the frame attached to this
+ 
+
+ align:start position:0%
+uh so this is the frame attached to this
+frisbee right it can turn it can move
+
+ align:start position:0%
+frisbee right it can turn it can move
+ 
+
+ align:start position:0%
+frisbee right it can turn it can move
+whatever right this is the frame
+
+ align:start position:0%
+whatever right this is the frame
+ 
+
+ align:start position:0%
+whatever right this is the frame
+attached to the Earth right now
+
+ align:start position:0%
+attached to the Earth right now
+ 
+
+ align:start position:0%
+attached to the Earth right now
+stationary and this guy's moving spect
+
+ align:start position:0%
+stationary and this guy's moving spect
+ 
+
+ align:start position:0%
+stationary and this guy's moving spect
+to this got
+
+ align:start position:0%
+to this got
+ 
+
+ align:start position:0%
+to this got
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so with respect to the Frisbee oh oh by
+
+ align:start position:0%
+so with respect to the Frisbee oh oh by
+ 
+
+ align:start position:0%
+so with respect to the Frisbee oh oh by
+the way now we have an insect here the
+
+ align:start position:0%
+the way now we have an insect here the
+ 
+
+ align:start position:0%
+the way now we have an insect here the
+spider let's call it
+
+ align:start position:0%
+spider let's call it
+ 
+
+ align:start position:0%
+spider let's call it
+s and it's kind of heading out in some
+
+ align:start position:0%
+s and it's kind of heading out in some
+ 
+
+ align:start position:0%
+s and it's kind of heading out in some
+Direction like this right so with
+
+ align:start position:0%
+Direction like this right so with
+ 
+
+ align:start position:0%
+Direction like this right so with
+respect to the frisbee
+
+ align:start position:0%
+respect to the frisbee
+ 
+
+ align:start position:0%
+respect to the frisbee
+if you're sitting on the Frisbee f is
+
+ align:start position:0%
+if you're sitting on the Frisbee f is
+ 
+
+ align:start position:0%
+if you're sitting on the Frisbee f is
+frozen
+
+ align:start position:0%
+frozen
+ 
+
+ align:start position:0%
+frozen
+right so all you see is the spider kind
+
+ align:start position:0%
+right so all you see is the spider kind
+ 
+
+ align:start position:0%
+right so all you see is the spider kind
+of walking away but respect to the
+
+ align:start position:0%
+of walking away but respect to the
+ 
+
+ align:start position:0%
+of walking away but respect to the
+ground or the Earth e right S is doing
+
+ align:start position:0%
+ground or the Earth e right S is doing
+ 
+
+ align:start position:0%
+ground or the Earth e right S is doing
+all sorts of funny things
+
+ align:start position:0%
+all sorts of funny things
+ 
+
+ align:start position:0%
+all sorts of funny things
+right so that's what a frame is so now
+
+ align:start position:0%
+right so that's what a frame is so now
+ 
+
+ align:start position:0%
+right so that's what a frame is so now
+with that let's jump in and get a little
+
+ align:start position:0%
+with that let's jump in and get a little
+ 
+
+ align:start position:0%
+with that let's jump in and get a little
+more detail I'll use transparencies once
+
+ align:start position:0%
+more detail I'll use transparencies once
+ 
+
+ align:start position:0%
+more detail I'll use transparencies once
+in a while but I really be doing chalk
+
+ align:start position:0%
+in a while but I really be doing chalk
+ 
+
+ align:start position:0%
+in a while but I really be doing chalk
+and talk right so you need to stop me
+
+ align:start position:0%
+and talk right so you need to stop me
+ 
+
+ align:start position:0%
+and talk right so you need to stop me
+I'll have my back turned towards you you
+
+ align:start position:0%
+I'll have my back turned towards you you
+ 
+
+ align:start position:0%
+I'll have my back turned towards you you
+need to stop me if you have any
+
+ align:start position:0%
+need to stop me if you have any
+ 
+
+ align:start position:0%
+need to stop me if you have any
+questions I'll put this away um in
+
+ align:start position:0%
+questions I'll put this away um in
+ 
+
+ align:start position:0%
+questions I'll put this away um in
+future by the way um if you don't mind
+
+ align:start position:0%
+future by the way um if you don't mind
+ 
+
+ align:start position:0%
+future by the way um if you don't mind
+what's your name I'm
+
+ align:start position:0%
+what's your name I'm
+ 
+
+ align:start position:0%
+what's your name I'm
+sorry kie if you don't mind you know
+
+ align:start position:0%
+sorry kie if you don't mind you know
+ 
+
+ align:start position:0%
+sorry kie if you don't mind you know
+this thing being right next to you it's
+
+ align:start position:0%
+this thing being right next to you it's
+ 
+
+ align:start position:0%
+this thing being right next to you it's
+hot um it's okay but if you do you know
+
+ align:start position:0%
+hot um it's okay but if you do you know
+ 
+
+ align:start position:0%
+hot um it's okay but if you do you know
+leave that chair unoccupied all right
+
+ align:start position:0%
+leave that chair unoccupied all right
+ 
+
+ align:start position:0%
+leave that chair unoccupied all right
+I've learned one name cly getting there
+
+ align:start position:0%
+I've learned one name cly getting there
+ 
+
+ align:start position:0%
+I've learned one name cly getting there
+another 129 to
+
+ align:start position:0%
+another 129 to
+ 
+
+ align:start position:0%
+another 129 to
+go okay so let's start the actual uh the
+
+ align:start position:0%
+go okay so let's start the actual uh the
+ 
+
+ align:start position:0%
+go okay so let's start the actual uh the
+serious portion of the class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I said a frame was basically a
+
+ align:start position:0%
+so I said a frame was basically a
+ 
+
+ align:start position:0%
+so I said a frame was basically a
+transparency okay and that's the best
+
+ align:start position:0%
+transparency okay and that's the best
+ 
+
+ align:start position:0%
+transparency okay and that's the best
+way to think about it um and a frame is
+
+ align:start position:0%
+way to think about it um and a frame is
+ 
+
+ align:start position:0%
+way to think about it um and a frame is
+essentially a in two dimensions a rigid
+
+ align:start position:0%
+essentially a in two dimensions a rigid
+ 
+
+ align:start position:0%
+essentially a in two dimensions a rigid
+imaginary set of points that are rigidly
+
+ align:start position:0%
+imaginary set of points that are rigidly
+ 
+
+ align:start position:0%
+imaginary set of points that are rigidly
+connected to each other okay like the
+
+ align:start position:0%
+connected to each other okay like the
+ 
+
+ align:start position:0%
+connected to each other okay like the
+transparency it doesn't mean there's any
+
+ align:start position:0%
+transparency it doesn't mean there's any
+ 
+
+ align:start position:0%
+transparency it doesn't mean there's any
+stuff there is an actual rigid body of
+
+ align:start position:0%
+stuff there is an actual rigid body of
+ 
+
+ align:start position:0%
+stuff there is an actual rigid body of
+frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody Yes No Maybe
+
+ align:start position:0%
+anybody Yes No Maybe
+ 
+
+ align:start position:0%
+anybody Yes No Maybe
+sometimes yes or no yes yes it is it
+
+ align:start position:0%
+sometimes yes or no yes yes it is it
+ 
+
+ align:start position:0%
+sometimes yes or no yes yes it is it
+just happens to be a a set of points
+
+ align:start position:0%
+just happens to be a a set of points
+ 
+
+ align:start position:0%
+just happens to be a a set of points
+where there's Mass on a frame get it
+
+ align:start position:0%
+where there's Mass on a frame get it
+ 
+
+ align:start position:0%
+where there's Mass on a frame get it
+that's all there is to it a rigid body
+
+ align:start position:0%
+that's all there is to it a rigid body
+ 
+
+ align:start position:0%
+that's all there is to it a rigid body
+is a set of points where there's Mass so
+
+ align:start position:0%
+is a set of points where there's Mass so
+ 
+
+ align:start position:0%
+is a set of points where there's Mass so
+a rigid body can also have a frame
+
+ align:start position:0%
+a rigid body can also have a frame
+ 
+
+ align:start position:0%
+a rigid body can also have a frame
+embedded in it and in fact it is kind of
+
+ align:start position:0%
+embedded in it and in fact it is kind of
+ 
+
+ align:start position:0%
+embedded in it and in fact it is kind of
+a frame it just has a mass right okay so
+
+ align:start position:0%
+a frame it just has a mass right okay so
+ 
+
+ align:start position:0%
+a frame it just has a mass right okay so
+let's start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frame is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rigidly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+connected continuum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imaginary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points right now one of the things I did
+
+ align:start position:0%
+points right now one of the things I did
+ 
+
+ align:start position:0%
+points right now one of the things I did
+was in that frame I put I picked a point
+
+ align:start position:0%
+was in that frame I put I picked a point
+ 
+
+ align:start position:0%
+was in that frame I put I picked a point
+I pied two little
+
+ align:start position:0%
+I pied two little
+ 
+
+ align:start position:0%
+I pied two little
+vectors right two vectors you know what
+
+ align:start position:0%
+vectors right two vectors you know what
+ 
+
+ align:start position:0%
+vectors right two vectors you know what
+those vectors are called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those little two vectors I put
+
+ align:start position:0%
+those little two vectors I put
+ 
+
+ align:start position:0%
+those little two vectors I put
+yeah yeah you could say axis you could
+
+ align:start position:0%
+yeah yeah you could say axis you could
+ 
+
+ align:start position:0%
+yeah yeah you could say axis you could
+even call them unit vectors right but
+
+ align:start position:0%
+even call them unit vectors right but
+ 
+
+ align:start position:0%
+even call them unit vectors right but
+the technical term is the're Basis
+
+ align:start position:0%
+the technical term is the're Basis
+ 
+
+ align:start position:0%
+the technical term is the're Basis
+vectors okay so I can identify a frame
+
+ align:start position:0%
+vectors okay so I can identify a frame
+ 
+
+ align:start position:0%
+vectors okay so I can identify a frame
+you know that transparency I could take
+
+ align:start position:0%
+you know that transparency I could take
+ 
+
+ align:start position:0%
+you know that transparency I could take
+the bottom left corner and take put two
+
+ align:start position:0%
+the bottom left corner and take put two
+ 
+
+ align:start position:0%
+the bottom left corner and take put two
+little unit length vectors at the bottom
+
+ align:start position:0%
+little unit length vectors at the bottom
+ 
+
+ align:start position:0%
+little unit length vectors at the bottom
+left corner right and that becomes the
+
+ align:start position:0%
+left corner right and that becomes the
+ 
+
+ align:start position:0%
+left corner right and that becomes the
+basis vectors of the frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I pick them once I can pick any two
+
+ align:start position:0%
+I pick them once I can pick any two
+ 
+
+ align:start position:0%
+I pick them once I can pick any two
+mutually perpendicular vectors I don't
+
+ align:start position:0%
+mutually perpendicular vectors I don't
+ 
+
+ align:start position:0%
+mutually perpendicular vectors I don't
+need them to be mutually perpendicular
+
+ align:start position:0%
+need them to be mutually perpendicular
+ 
+
+ align:start position:0%
+need them to be mutually perpendicular
+they just shouldn't be parallel right
+
+ align:start position:0%
+they just shouldn't be parallel right
+ 
+
+ align:start position:0%
+they just shouldn't be parallel right
+but for convenience we pick two mutually
+
+ align:start position:0%
+but for convenience we pick two mutually
+ 
+
+ align:start position:0%
+but for convenience we pick two mutually
+perpendicular little vectors unit length
+
+ align:start position:0%
+perpendicular little vectors unit length
+ 
+
+ align:start position:0%
+perpendicular little vectors unit length
+and we call them basis vectors right
+
+ align:start position:0%
+and we call them basis vectors right
+ 
+
+ align:start position:0%
+and we call them basis vectors right
+so we
+
+ align:start position:0%
+so we
+ 
+
+ align:start position:0%
+so we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+embed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two mutually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perpendicular unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors um which are frozen for that
+
+ align:start position:0%
+vectors um which are frozen for that
+ 
+
+ align:start position:0%
+vectors um which are frozen for that
+frame right
+
+ align:start position:0%
+frame right
+ 
+
+ align:start position:0%
+frame right
+once and for
+
+ align:start position:0%
+once and for
+ 
+
+ align:start position:0%
+once and for
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+and called them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors okay so what that means is that
+
+ align:start position:0%
+vectors okay so what that means is that
+ 
+
+ align:start position:0%
+vectors okay so what that means is that
+I could
+
+ align:start position:0%
+I could
+ 
+
+ align:start position:0%
+I could
+take uh I raised it you know what let me
+
+ align:start position:0%
+take uh I raised it you know what let me
+ 
+
+ align:start position:0%
+take uh I raised it you know what let me
+keep that down until I finish
+
+ align:start position:0%
+keep that down until I finish
+ 
+
+ align:start position:0%
+keep that down until I finish
+my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+demonstrations I could just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take in this case
+
+ align:start position:0%
+take in this case
+ 
+
+ align:start position:0%
+take in this case
+for this Frame right for this Frame the
+
+ align:start position:0%
+for this Frame right for this Frame the
+ 
+
+ align:start position:0%
+for this Frame right for this Frame the
+edge of the transparency is here can you
+
+ align:start position:0%
+edge of the transparency is here can you
+ 
+
+ align:start position:0%
+edge of the transparency is here can you
+see it let me see can you see that's the
+
+ align:start position:0%
+see it let me see can you see that's the
+ 
+
+ align:start position:0%
+see it let me see can you see that's the
+edge of the transparency I could have
+
+ align:start position:0%
+edge of the transparency I could have
+ 
+
+ align:start position:0%
+edge of the transparency I could have
+picked a little unit Vector along you
+
+ align:start position:0%
+picked a little unit Vector along you
+ 
+
+ align:start position:0%
+picked a little unit Vector along you
+know the horizontal a little one along
+
+ align:start position:0%
+know the horizontal a little one along
+ 
+
+ align:start position:0%
+know the horizontal a little one along
+the vertical and call them the two basis
+
+ align:start position:0%
+the vertical and call them the two basis
+ 
+
+ align:start position:0%
+the vertical and call them the two basis
+vectors of that frame does it matter
+
+ align:start position:0%
+vectors of that frame does it matter
+ 
+
+ align:start position:0%
+vectors of that frame does it matter
+where I pick
+
+ align:start position:0%
+where I pick
+ 
+
+ align:start position:0%
+where I pick
+them no I can pick any basis Vector
+
+ align:start position:0%
+them no I can pick any basis Vector
+ 
+
+ align:start position:0%
+them no I can pick any basis Vector
+right so I'm going to pick them here and
+
+ align:start position:0%
+right so I'm going to pick them here and
+ 
+
+ align:start position:0%
+right so I'm going to pick them here and
+I want to give you a little convention
+
+ align:start position:0%
+I want to give you a little convention
+ 
+
+ align:start position:0%
+I want to give you a little convention
+I'm going to refer to them as little
+
+ align:start position:0%
+I'm going to refer to them as little
+ 
+
+ align:start position:0%
+I'm going to refer to them as little
+F1 and little F2 the underscore
+
+ align:start position:0%
+F1 and little F2 the underscore
+ 
+
+ align:start position:0%
+F1 and little F2 the underscore
+indicates that it's a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector okay now I can
+
+ align:start position:0%
+Vector okay now I can
+ 
+
+ align:start position:0%
+Vector okay now I can
+similarly
+
+ align:start position:0%
+similarly
+ 
+
+ align:start position:0%
+similarly
+take Earth planet
+
+ align:start position:0%
+take Earth planet
+ 
+
+ align:start position:0%
+take Earth planet
+Earth where most of us
+
+ align:start position:0%
+Earth where most of us
+ 
+
+ align:start position:0%
+Earth where most of us
+live and call this
+
+ align:start position:0%
+live and call this
+ 
+
+ align:start position:0%
+live and call this
+E1 and E2 and this is my little
+
+ align:start position:0%
+E1 and E2 and this is my little
+ 
+
+ align:start position:0%
+E1 and E2 and this is my little
+convention right I'm going to limit my
+
+ align:start position:0%
+convention right I'm going to limit my
+ 
+
+ align:start position:0%
+convention right I'm going to limit my
+descriptions to two Dimensions but
+
+ align:start position:0%
+descriptions to two Dimensions but
+ 
+
+ align:start position:0%
+descriptions to two Dimensions but
+everything I tell you about in
+
+ align:start position:0%
+everything I tell you about in
+ 
+
+ align:start position:0%
+everything I tell you about in
+kinematics easily and seamlessly
+
+ align:start position:0%
+kinematics easily and seamlessly
+ 
+
+ align:start position:0%
+kinematics easily and seamlessly
+translates to three dimensions that's
+
+ align:start position:0%
+translates to three dimensions that's
+ 
+
+ align:start position:0%
+translates to three dimensions that's
+the beauty of the way we do it okay so
+
+ align:start position:0%
+the beauty of the way we do it okay so
+ 
+
+ align:start position:0%
+the beauty of the way we do it okay so
+we'll do everything in 2D but you just
+
+ align:start position:0%
+we'll do everything in 2D but you just
+ 
+
+ align:start position:0%
+we'll do everything in 2D but you just
+go to 3D everything's fine with cross
+
+ align:start position:0%
+go to 3D everything's fine with cross
+ 
+
+ align:start position:0%
+go to 3D everything's fine with cross
+products dot products everything will be
+
+ align:start position:0%
+products dot products everything will be
+ 
+
+ align:start position:0%
+products dot products everything will be
+the same okay so these are the basis
+
+ align:start position:0%
+the same okay so these are the basis
+ 
+
+ align:start position:0%
+the same okay so these are the basis
+vectors in the unit length and uh now so
+
+ align:start position:0%
+vectors in the unit length and uh now so
+ 
+
+ align:start position:0%
+vectors in the unit length and uh now so
+any Vector with respect to frame F can
+
+ align:start position:0%
+any Vector with respect to frame F can
+ 
+
+ align:start position:0%
+any Vector with respect to frame F can
+be using these basis vectors can be
+
+ align:start position:0%
+be using these basis vectors can be
+ 
+
+ align:start position:0%
+be using these basis vectors can be
+expressed as you know some something *
+
+ align:start position:0%
+expressed as you know some something *
+ 
+
+ align:start position:0%
+expressed as you know some something *
+FS1 plus something * FS2 right with
+
+ align:start position:0%
+FS1 plus something * FS2 right with
+ 
+
+ align:start position:0%
+FS1 plus something * FS2 right with
+respect to these basis vectors that be
+
+ align:start position:0%
+respect to these basis vectors that be
+ 
+
+ align:start position:0%
+respect to these basis vectors that be
+something * E1 something *
+
+ align:start position:0%
+something * E1 something *
+ 
+
+ align:start position:0%
+something * E1 something *
+E2
+
+ align:start position:0%
+E2
+ 
+
+ align:start position:0%
+E2
+right I might come back to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay let me ask you a question so
+
+ align:start position:0%
+this okay let me ask you a question so
+ 
+
+ align:start position:0%
+this okay let me ask you a question so
+let's say I pick a a frame f F1 oh sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F and I take a vector R it's a little
+
+ align:start position:0%
+F and I take a vector R it's a little
+ 
+
+ align:start position:0%
+F and I take a vector R it's a little
+unit it's a little you know vector and I
+
+ align:start position:0%
+unit it's a little you know vector and I
+ 
+
+ align:start position:0%
+unit it's a little you know vector and I
+freeze it in that transparency I draw it
+
+ align:start position:0%
+freeze it in that transparency I draw it
+ 
+
+ align:start position:0%
+freeze it in that transparency I draw it
+can it ever change within the F
+
+ align:start position:0%
+can it ever change within the F
+ 
+
+ align:start position:0%
+can it ever change within the F
+frame if I draw it there right and I'm
+
+ align:start position:0%
+frame if I draw it there right and I'm
+ 
+
+ align:start position:0%
+frame if I draw it there right and I'm
+sitting on FR frame will I ever see
+
+ align:start position:0%
+sitting on FR frame will I ever see
+ 
+
+ align:start position:0%
+sitting on FR frame will I ever see
+change in length or
+
+ align:start position:0%
+change in length or
+ 
+
+ align:start position:0%
+change in length or
+Direction no but that same Vector if I'm
+
+ align:start position:0%
+Direction no but that same Vector if I'm
+ 
+
+ align:start position:0%
+Direction no but that same Vector if I'm
+sitting in the E frame I'm using moving
+
+ align:start position:0%
+sitting in the E frame I'm using moving
+ 
+
+ align:start position:0%
+sitting in the E frame I'm using moving
+the transparency around will it
+
+ align:start position:0%
+the transparency around will it
+ 
+
+ align:start position:0%
+the transparency around will it
+change right will the length change no
+
+ align:start position:0%
+change right will the length change no
+ 
+
+ align:start position:0%
+change right will the length change no
+but what will change its direction will
+
+ align:start position:0%
+but what will change its direction will
+ 
+
+ align:start position:0%
+but what will change its direction will
+change right so that means that a vector
+
+ align:start position:0%
+change right so that means that a vector
+ 
+
+ align:start position:0%
+change right so that means that a vector
+embedded in a frame will not change in
+
+ align:start position:0%
+embedded in a frame will not change in
+ 
+
+ align:start position:0%
+embedded in a frame will not change in
+that frame but with respect to some
+
+ align:start position:0%
+that frame but with respect to some
+ 
+
+ align:start position:0%
+that frame but with respect to some
+other frame it might change okay all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so here's what I'm going to say
+
+ align:start position:0%
+right so here's what I'm going to say
+ 
+
+ align:start position:0%
+right so here's what I'm going to say
+and then I'll explain this more by the
+
+ align:start position:0%
+and then I'll explain this more by the
+ 
+
+ align:start position:0%
+and then I'll explain this more by the
+time we're done with today's class and
+
+ align:start position:0%
+time we're done with today's class and
+ 
+
+ align:start position:0%
+time we're done with today's class and
+next week's class you'll understand this
+
+ align:start position:0%
+next week's class you'll understand this
+ 
+
+ align:start position:0%
+next week's class you'll understand this
+completely because we're going to do
+
+ align:start position:0%
+completely because we're going to do
+ 
+
+ align:start position:0%
+completely because we're going to do
+this in gory detail okay but bear with
+
+ align:start position:0%
+this in gory detail okay but bear with
+ 
+
+ align:start position:0%
+this in gory detail okay but bear with
+me we're going to make some a a few
+
+ align:start position:0%
+me we're going to make some a a few
+ 
+
+ align:start position:0%
+me we're going to make some a a few
+leaps here but when when we're done
+
+ align:start position:0%
+leaps here but when when we're done
+ 
+
+ align:start position:0%
+leaps here but when when we're done
+you'll you'll be completely totally cop
+
+ align:start position:0%
+you'll you'll be completely totally cop
+ 
+
+ align:start position:0%
+you'll you'll be completely totally cop
+pathetic with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it oh sorry Miss Mis wrote
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by the way I haven't said anything
+
+ align:start position:0%
+by the way I haven't said anything
+ 
+
+ align:start position:0%
+by the way I haven't said anything
+profound yet everything is very
+
+ align:start position:0%
+profound yet everything is very
+ 
+
+ align:start position:0%
+profound yet everything is very
+intuitive right I haven't said anything
+
+ align:start position:0%
+intuitive right I haven't said anything
+ 
+
+ align:start position:0%
+intuitive right I haven't said anything
+special so you're not missing anything
+
+ align:start position:0%
+special so you're not missing anything
+ 
+
+ align:start position:0%
+special so you're not missing anything
+I'm just going slowly we'll gather speed
+
+ align:start position:0%
+I'm just going slowly we'll gather speed
+ 
+
+ align:start position:0%
+I'm just going slowly we'll gather speed
+in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minute and I'm going to say this in a
+
+ align:start position:0%
+minute and I'm going to say this in a
+ 
+
+ align:start position:0%
+minute and I'm going to say this in a
+I'm going to say what I just said in
+
+ align:start position:0%
+I'm going to say what I just said in
+ 
+
+ align:start position:0%
+I'm going to say what I just said in
+English in a slight more mathematical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way okay so so now I'm going to write
+
+ align:start position:0%
+way okay so so now I'm going to write
+ 
+
+ align:start position:0%
+way okay so so now I'm going to write
+something for you which might seem a
+
+ align:start position:0%
+something for you which might seem a
+ 
+
+ align:start position:0%
+something for you which might seem a
+little odd but this is the thing you
+
+ align:start position:0%
+little odd but this is the thing you
+ 
+
+ align:start position:0%
+little odd but this is the thing you
+need to get once you get this all of
+
+ align:start position:0%
+need to get once you get this all of
+ 
+
+ align:start position:0%
+need to get once you get this all of
+kinematics is is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Breeze d by DT
+
+ align:start position:0%
+Breeze d by DT
+ 
+
+ align:start position:0%
+Breeze d by DT
+of a vector fixed in a frame let's let's
+
+ align:start position:0%
+of a vector fixed in a frame let's let's
+ 
+
+ align:start position:0%
+of a vector fixed in a frame let's let's
+consider frame F which give me an
+
+ align:start position:0%
+consider frame F which give me an
+ 
+
+ align:start position:0%
+consider frame F which give me an
+example of a vector that's fixed in
+
+ align:start position:0%
+example of a vector that's fixed in
+ 
+
+ align:start position:0%
+example of a vector that's fixed in
+frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f um oh yeah actually give it to me in
+
+ align:start position:0%
+f um oh yeah actually give it to me in
+ 
+
+ align:start position:0%
+f um oh yeah actually give it to me in
+terms give me make up a vector that's
+
+ align:start position:0%
+terms give me make up a vector that's
+ 
+
+ align:start position:0%
+terms give me make up a vector that's
+fixed in terms of you know B1 B2 F1 F2
+
+ align:start position:0%
+fixed in terms of you know B1 B2 F1 F2
+ 
+
+ align:start position:0%
+fixed in terms of you know B1 B2 F1 F2
+in terms of frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F it's it's an odd question yeah huh vs
+
+ align:start position:0%
+F it's it's an odd question yeah huh vs
+ 
+
+ align:start position:0%
+F it's it's an odd question yeah huh vs
+vs is a velocity right it could be fixed
+
+ align:start position:0%
+vs is a velocity right it could be fixed
+ 
+
+ align:start position:0%
+vs is a velocity right it could be fixed
+let me actually let let me just tell you
+
+ align:start position:0%
+let me actually let let me just tell you
+ 
+
+ align:start position:0%
+let me actually let let me just tell you
+is this Vector fixed in frame this is f
+
+ align:start position:0%
+is this Vector fixed in frame this is f
+ 
+
+ align:start position:0%
+is this Vector fixed in frame this is f
+is Vector F1 fixed in frame F yeah what
+
+ align:start position:0%
+is Vector F1 fixed in frame F yeah what
+ 
+
+ align:start position:0%
+is Vector F1 fixed in frame F yeah what
+about this
+
+ align:start position:0%
+about this
+ 
+
+ align:start position:0%
+about this
+Vector is this fixed in frame
+
+ align:start position:0%
+Vector is this fixed in frame
+ 
+
+ align:start position:0%
+Vector is this fixed in frame
+one yes right so any Vector which can be
+
+ align:start position:0%
+one yes right so any Vector which can be
+ 
+
+ align:start position:0%
+one yes right so any Vector which can be
+written as in terms of the basis vectors
+
+ align:start position:0%
+written as in terms of the basis vectors
+ 
+
+ align:start position:0%
+written as in terms of the basis vectors
+and constant numbers is fixed in the
+
+ align:start position:0%
+and constant numbers is fixed in the
+ 
+
+ align:start position:0%
+and constant numbers is fixed in the
+frame F right so any Vector
+
+ align:start position:0%
+frame F right so any Vector
+ 
+
+ align:start position:0%
+frame F right so any Vector
+r that is fixed in frame M I'll just
+
+ align:start position:0%
+r that is fixed in frame M I'll just
+ 
+
+ align:start position:0%
+r that is fixed in frame M I'll just
+call it R right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+where R is
+
+ align:start position:0%
+where R is
+ 
+
+ align:start position:0%
+where R is
+fixed in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F here's what I'm going to say d by DT
+
+ align:start position:0%
+F here's what I'm going to say d by DT
+ 
+
+ align:start position:0%
+F here's what I'm going to say d by DT
+of that R is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to zero I haven't told you precisely
+
+ align:start position:0%
+to zero I haven't told you precisely
+ 
+
+ align:start position:0%
+to zero I haven't told you precisely
+what this D by DT is I'll explain it to
+
+ align:start position:0%
+what this D by DT is I'll explain it to
+ 
+
+ align:start position:0%
+what this D by DT is I'll explain it to
+you right but you know that that Vector
+
+ align:start position:0%
+you right but you know that that Vector
+ 
+
+ align:start position:0%
+you right but you know that that Vector
+if it's fixed in in frame F if I take
+
+ align:start position:0%
+if it's fixed in in frame F if I take
+ 
+
+ align:start position:0%
+if it's fixed in in frame F if I take
+the derivative it should be zero right
+
+ align:start position:0%
+the derivative it should be zero right
+ 
+
+ align:start position:0%
+the derivative it should be zero right
+it ain't changing isn't moving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now if I take this derivative of
+
+ align:start position:0%
+right now if I take this derivative of
+ 
+
+ align:start position:0%
+right now if I take this derivative of
+that same Vector not in the frame of the
+
+ align:start position:0%
+that same Vector not in the frame of the
+ 
+
+ align:start position:0%
+that same Vector not in the frame of the
+frisbe but in the frame of the earth is
+
+ align:start position:0%
+frisbe but in the frame of the earth is
+ 
+
+ align:start position:0%
+frisbe but in the frame of the earth is
+it going to be
+
+ align:start position:0%
+it going to be
+ 
+
+ align:start position:0%
+it going to be
+zero no so I need to have some way of
+
+ align:start position:0%
+zero no so I need to have some way of
+ 
+
+ align:start position:0%
+zero no so I need to have some way of
+saying listen I'm taking this derivative
+
+ align:start position:0%
+saying listen I'm taking this derivative
+ 
+
+ align:start position:0%
+saying listen I'm taking this derivative
+in frame F not in frame
+
+ align:start position:0%
+in frame F not in frame
+ 
+
+ align:start position:0%
+in frame F not in frame
+earth right how would I denote that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very good so for example I could put a
+
+ align:start position:0%
+very good so for example I could put a
+ 
+
+ align:start position:0%
+very good so for example I could put a
+parenthesis and a little F like this
+
+ align:start position:0%
+parenthesis and a little F like this
+ 
+
+ align:start position:0%
+parenthesis and a little F like this
+right to say listen I'm taking the
+
+ align:start position:0%
+right to say listen I'm taking the
+ 
+
+ align:start position:0%
+right to say listen I'm taking the
+derivative respect to frame F right I
+
+ align:start position:0%
+derivative respect to frame F right I
+ 
+
+ align:start position:0%
+derivative respect to frame F right I
+could do that but it turns out that
+
+ align:start position:0%
+could do that but it turns out that
+ 
+
+ align:start position:0%
+could do that but it turns out that
+a better convention is to Simply write
+
+ align:start position:0%
+a better convention is to Simply write
+ 
+
+ align:start position:0%
+a better convention is to Simply write
+the frame of reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so when you see something like
+
+ align:start position:0%
+here okay so when you see something like
+ 
+
+ align:start position:0%
+here okay so when you see something like
+that this is the way to read it in
+
+ align:start position:0%
+that this is the way to read it in
+ 
+
+ align:start position:0%
+that this is the way to read it in
+English the derivative of vector r with
+
+ align:start position:0%
+English the derivative of vector r with
+ 
+
+ align:start position:0%
+English the derivative of vector r with
+respect to frame F and if I tell you
+
+ align:start position:0%
+respect to frame F and if I tell you
+ 
+
+ align:start position:0%
+respect to frame F and if I tell you
+that derivative that R is fixed in F the
+
+ align:start position:0%
+that derivative that R is fixed in F the
+ 
+
+ align:start position:0%
+that derivative that R is fixed in F the
+statement I'm making is that derivative
+
+ align:start position:0%
+statement I'm making is that derivative
+ 
+
+ align:start position:0%
+statement I'm making is that derivative
+is zero got
+
+ align:start position:0%
+is zero got
+ 
+
+ align:start position:0%
+is zero got
+it makes sense any questions I insist on
+
+ align:start position:0%
+it makes sense any questions I insist on
+ 
+
+ align:start position:0%
+it makes sense any questions I insist on
+at least one question at this point I
+
+ align:start position:0%
+at least one question at this point I
+ 
+
+ align:start position:0%
+at least one question at this point I
+get tired I need you know I need a break
+
+ align:start position:0%
+get tired I need you know I need a break
+ 
+
+ align:start position:0%
+get tired I need you know I need a break
+anyone yes thank you what's your name
+
+ align:start position:0%
+anyone yes thank you what's your name
+ 
+
+ align:start position:0%
+anyone yes thank you what's your name
+Rachel Rachel
+
+ align:start position:0%
+Rachel Rachel
+ 
+
+ align:start position:0%
+Rachel Rachel
+two is that what two under the f it's
+
+ align:start position:0%
+two is that what two under the f it's
+ 
+
+ align:start position:0%
+two is that what two under the f it's
+actually just wasn't even meant to be a
+
+ align:start position:0%
+actually just wasn't even meant to be a
+ 
+
+ align:start position:0%
+actually just wasn't even meant to be a
+line it's not a vector it's just a frame
+
+ align:start position:0%
+line it's not a vector it's just a frame
+ 
+
+ align:start position:0%
+line it's not a vector it's just a frame
+so it's just a capital letter thank
+
+ align:start position:0%
+so it's just a capital letter thank
+ 
+
+ align:start position:0%
+so it's just a capital letter thank
+you right f is just the name of a frame
+
+ align:start position:0%
+you right f is just the name of a frame
+ 
+
+ align:start position:0%
+you right f is just the name of a frame
+I could call it Rachel right Rachel
+
+ align:start position:0%
+I could call it Rachel right Rachel
+ 
+
+ align:start position:0%
+I could call it Rachel right Rachel
+right yeah so I could call it Rachel I
+
+ align:start position:0%
+right yeah so I could call it Rachel I
+ 
+
+ align:start position:0%
+right yeah so I could call it Rachel I
+just call it f just a name okay any
+
+ align:start position:0%
+just call it f just a name okay any
+ 
+
+ align:start position:0%
+just call it f just a name okay any
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+questions anyone else it's oppressive
+
+ align:start position:0%
+questions anyone else it's oppressive
+ 
+
+ align:start position:0%
+questions anyone else it's oppressive
+and yeah we should call facilities and
+
+ align:start position:0%
+and yeah we should call facilities and
+ 
+
+ align:start position:0%
+and yeah we should call facilities and
+figure out how to turn the air
+
+ align:start position:0%
+figure out how to turn the air
+ 
+
+ align:start position:0%
+figure out how to turn the air
+conditioning or open the window or
+
+ align:start position:0%
+conditioning or open the window or
+ 
+
+ align:start position:0%
+conditioning or open the window or
+something so if you remind me I'll call
+
+ align:start position:0%
+something so if you remind me I'll call
+ 
+
+ align:start position:0%
+something so if you remind me I'll call
+them later thanks okay so that's all the
+
+ align:start position:0%
+them later thanks okay so that's all the
+ 
+
+ align:start position:0%
+them later thanks okay so that's all the
+RIS of frames when you look at one frame
+
+ align:start position:0%
+RIS of frames when you look at one frame
+ 
+
+ align:start position:0%
+RIS of frames when you look at one frame
+and now the fun starts because now we're
+
+ align:start position:0%
+and now the fun starts because now we're
+ 
+
+ align:start position:0%
+and now the fun starts because now we're
+going to start looking at taking
+
+ align:start position:0%
+going to start looking at taking
+ 
+
+ align:start position:0%
+going to start looking at taking
+derivatives and looking at stuff across
+
+ align:start position:0%
+derivatives and looking at stuff across
+ 
+
+ align:start position:0%
+derivatives and looking at stuff across
+frames all right and once I do that
+
+ align:start position:0%
+frames all right and once I do that
+ 
+
+ align:start position:0%
+frames all right and once I do that
+we'll jump into the Frisbee problem
+
+ align:start position:0%
+we'll jump into the Frisbee problem
+ 
+
+ align:start position:0%
+we'll jump into the Frisbee problem
+we'll nail it it's a 1010 about
+
+ align:start position:0%
+we'll nail it it's a 1010 about
+ 
+
+ align:start position:0%
+we'll nail it it's a 1010 about
+105 uh we might not finish the Frisbee
+
+ align:start position:0%
+105 uh we might not finish the Frisbee
+ 
+
+ align:start position:0%
+105 uh we might not finish the Frisbee
+problem we'll certainly set it up and
+
+ align:start position:0%
+problem we'll certainly set it up and
+ 
+
+ align:start position:0%
+problem we'll certainly set it up and
+start doing some of the math and U we'll
+
+ align:start position:0%
+start doing some of the math and U we'll
+ 
+
+ align:start position:0%
+start doing some of the math and U we'll
+finish it off worst case next class
+
+ align:start position:0%
+finish it off worst case next class
+ 
+
+ align:start position:0%
+finish it off worst case next class
+okay okay so now let's look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frames
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm going to call it multiple but
+
+ align:start position:0%
+so I'm going to call it multiple but
+ 
+
+ align:start position:0%
+so I'm going to call it multiple but
+we'll always look at pairs of frames two
+
+ align:start position:0%
+we'll always look at pairs of frames two
+ 
+
+ align:start position:0%
+we'll always look at pairs of frames two
+frames right and if you can do the math
+
+ align:start position:0%
+frames right and if you can do the math
+ 
+
+ align:start position:0%
+frames right and if you can do the math
+across two frames three frames is just a
+
+ align:start position:0%
+across two frames three frames is just a
+ 
+
+ align:start position:0%
+across two frames three frames is just a
+chain of two frames right so we'll just
+
+ align:start position:0%
+chain of two frames right so we'll just
+ 
+
+ align:start position:0%
+chain of two frames right so we'll just
+look at two frames but we'll call it
+
+ align:start position:0%
+look at two frames but we'll call it
+ 
+
+ align:start position:0%
+look at two frames but we'll call it
+multiple because it goes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so imagine one
+
+ align:start position:0%
+okay so imagine one
+ 
+
+ align:start position:0%
+okay so imagine one
+transparency or one frame which is
+
+ align:start position:0%
+transparency or one frame which is
+ 
+
+ align:start position:0%
+transparency or one frame which is
+planet Earth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's attach a basis Vector to it a
+
+ align:start position:0%
+let's attach a basis Vector to it a
+ 
+
+ align:start position:0%
+let's attach a basis Vector to it a
+basis or basis vectors to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+E1 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now let's think of another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frame frame B1 B I'm sorry actually we
+
+ align:start position:0%
+frame frame B1 B I'm sorry actually we
+ 
+
+ align:start position:0%
+frame frame B1 B I'm sorry actually we
+called it f for frisbe right so we call
+
+ align:start position:0%
+called it f for frisbe right so we call
+ 
+
+ align:start position:0%
+called it f for frisbe right so we call
+it f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are the basis vectors in
+
+ align:start position:0%
+what are the basis vectors in
+ 
+
+ align:start position:0%
+what are the basis vectors in
+f f and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F2
+
+ align:start position:0%
+F2
+ 
+
+ align:start position:0%
+F2
+okay first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question can you write E1 and E2 in
+
+ align:start position:0%
+question can you write E1 and E2 in
+ 
+
+ align:start position:0%
+question can you write E1 and E2 in
+terms of F1 and F2 or F1 and F2 in terms
+
+ align:start position:0%
+terms of F1 and F2 or F1 and F2 in terms
+ 
+
+ align:start position:0%
+terms of F1 and F2 or F1 and F2 in terms
+of E1 and E2 2 yes yes what do you need
+
+ align:start position:0%
+of E1 and E2 2 yes yes what do you need
+ 
+
+ align:start position:0%
+of E1 and E2 2 yes yes what do you need
+to tell me what E1 and E2 are in terms
+
+ align:start position:0%
+to tell me what E1 and E2 are in terms
+ 
+
+ align:start position:0%
+to tell me what E1 and E2 are in terms
+of F1 and
+
+ align:start position:0%
+of F1 and
+ 
+
+ align:start position:0%
+of F1 and
+F2 the starts with an A the angle right
+
+ align:start position:0%
+F2 the starts with an A the angle right
+ 
+
+ align:start position:0%
+F2 the starts with an A the angle right
+so now one of the things I'm going to do
+
+ align:start position:0%
+so now one of the things I'm going to do
+ 
+
+ align:start position:0%
+so now one of the things I'm going to do
+in this class especially because uh
+
+ align:start position:0%
+in this class especially because uh
+ 
+
+ align:start position:0%
+in this class especially because uh
+we're going to do a lot of stuff and I
+
+ align:start position:0%
+we're going to do a lot of stuff and I
+ 
+
+ align:start position:0%
+we're going to do a lot of stuff and I
+want to keep you guys engaged is I'm
+
+ align:start position:0%
+want to keep you guys engaged is I'm
+ 
+
+ align:start position:0%
+want to keep you guys engaged is I'm
+going to have these snap quizzes AJ may
+
+ align:start position:0%
+going to have these snap quizzes AJ may
+ 
+
+ align:start position:0%
+going to have these snap quizzes AJ may
+have explained the snap quiz to you but
+
+ align:start position:0%
+have explained the snap quiz to you but
+ 
+
+ align:start position:0%
+have explained the snap quiz to you but
+the way the snap quizes work is we look
+
+ align:start position:0%
+the way the snap quizes work is we look
+ 
+
+ align:start position:0%
+the way the snap quizes work is we look
+at them and we make sure you put in some
+
+ align:start position:0%
+at them and we make sure you put in some
+ 
+
+ align:start position:0%
+at them and we make sure you put in some
+effort
+
+ align:start position:0%
+effort
+ 
+
+ align:start position:0%
+effort
+and we absolutely don't penalize you for
+
+ align:start position:0%
+and we absolutely don't penalize you for
+ 
+
+ align:start position:0%
+and we absolutely don't penalize you for
+making any mistakes in fact we penalize
+
+ align:start position:0%
+making any mistakes in fact we penalize
+ 
+
+ align:start position:0%
+making any mistakes in fact we penalize
+ourselves we don't penalize ourselves
+
+ align:start position:0%
+ourselves we don't penalize ourselves
+ 
+
+ align:start position:0%
+ourselves we don't penalize ourselves
+but we you
+
+ align:start position:0%
+but we you
+ 
+
+ align:start position:0%
+but we you
+know we uh see what we succeeded in
+
+ align:start position:0%
+know we uh see what we succeeded in
+ 
+
+ align:start position:0%
+know we uh see what we succeeded in
+transmitting all right so here's what I
+
+ align:start position:0%
+transmitting all right so here's what I
+ 
+
+ align:start position:0%
+transmitting all right so here's what I
+want you to do and some of these snap
+
+ align:start position:0%
+want you to do and some of these snap
+ 
+
+ align:start position:0%
+want you to do and some of these snap
+goers are we haven't it's not like we're
+
+ align:start position:0%
+goers are we haven't it's not like we're
+ 
+
+ align:start position:0%
+goers are we haven't it's not like we're
+asking you to recall something we're
+
+ align:start position:0%
+asking you to recall something we're
+ 
+
+ align:start position:0%
+asking you to recall something we're
+actually asking you to look ahead here's
+
+ align:start position:0%
+actually asking you to look ahead here's
+ 
+
+ align:start position:0%
+actually asking you to look ahead here's
+a snap quiz I want you to write for me
+
+ align:start position:0%
+a snap quiz I want you to write for me
+ 
+
+ align:start position:0%
+a snap quiz I want you to write for me
+fub1 and F2 in terms of E1 and E2 is you
+
+ align:start position:0%
+fub1 and F2 in terms of E1 and E2 is you
+ 
+
+ align:start position:0%
+fub1 and F2 in terms of E1 and E2 is you
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+angle is Theta and this is basic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trigonometric yes pull out a sheet of
+
+ align:start position:0%
+trigonometric yes pull out a sheet of
+ 
+
+ align:start position:0%
+trigonometric yes pull out a sheet of
+paper write your name on top and have a
+
+ align:start position:0%
+paper write your name on top and have a
+ 
+
+ align:start position:0%
+paper write your name on top and have a
+go at it and we'll collect at the end of
+
+ align:start position:0%
+go at it and we'll collect at the end of
+ 
+
+ align:start position:0%
+go at it and we'll collect at the end of
+class yes
+
+ align:start position:0%
+class yes
+ 
+
+ align:start position:0%
+class yes
+sorry the angle is the very good so let
+
+ align:start position:0%
+sorry the angle is the very good so let
+ 
+
+ align:start position:0%
+sorry the angle is the very good so let
+me explain I have defined Theta I could
+
+ align:start position:0%
+me explain I have defined Theta I could
+ 
+
+ align:start position:0%
+me explain I have defined Theta I could
+have defined it any way I could you know
+
+ align:start position:0%
+have defined it any way I could you know
+ 
+
+ align:start position:0%
+have defined it any way I could you know
+because I'm the professor I can do what
+
+ align:start position:0%
+because I'm the professor I can do what
+ 
+
+ align:start position:0%
+because I'm the professor I can do what
+I want you know you know it works but
+
+ align:start position:0%
+I want you know you know it works but
+ 
+
+ align:start position:0%
+I want you know you know it works but
+anyway it's the angle between F1 and E1
+
+ align:start position:0%
+anyway it's the angle between F1 and E1
+ 
+
+ align:start position:0%
+anyway it's the angle between F1 and E1
+at a snapshot in time at an instant in
+
+ align:start position:0%
+at a snapshot in time at an instant in
+ 
+
+ align:start position:0%
+at a snapshot in time at an instant in
+time I'm calling it Theta and I want you
+
+ align:start position:0%
+time I'm calling it Theta and I want you
+ 
+
+ align:start position:0%
+time I'm calling it Theta and I want you
+to tell me what FS1 and F2 are in terms
+
+ align:start position:0%
+to tell me what FS1 and F2 are in terms
+ 
+
+ align:start position:0%
+to tell me what FS1 and F2 are in terms
+of E1 and E E2 as a function of
+
+ align:start position:0%
+of E1 and E E2 as a function of
+ 
+
+ align:start position:0%
+of E1 and E E2 as a function of
+theta
+
+ align:start position:0%
+theta
+ 
+
+ align:start position:0%
+theta
+y1 F1 and F2 are both unit vectors e and
+
+ align:start position:0%
+y1 F1 and F2 are both unit vectors e and
+ 
+
+ align:start position:0%
+y1 F1 and F2 are both unit vectors e and
+E2 unit vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I want you to write so I want you
+
+ align:start position:0%
+yeah I want you to write so I want you
+ 
+
+ align:start position:0%
+yeah I want you to write so I want you
+to write something like fub1 is equal
+
+ align:start position:0%
+to write something like fub1 is equal
+ 
+
+ align:start position:0%
+to write something like fub1 is equal
+to something E1 plus something E2 F2 is
+
+ align:start position:0%
+to something E1 plus something E2 F2 is
+ 
+
+ align:start position:0%
+to something E1 plus something E2 F2 is
+equal to something E1 plus something E2
+
+ align:start position:0%
+equal to something E1 plus something E2
+ 
+
+ align:start position:0%
+equal to something E1 plus something E2
+that's what it'll come out looking like
+
+ align:start position:0%
+that's what it'll come out looking like
+ 
+
+ align:start position:0%
+that's what it'll come out looking like
+and it might have a few SS and cosine
+
+ align:start position:0%
+and it might have a few SS and cosine
+ 
+
+ align:start position:0%
+and it might have a few SS and cosine
+thetas floating
+
+ align:start position:0%
+thetas floating
+ 
+
+ align:start position:0%
+thetas floating
+around in fact it better have some sin
+
+ align:start position:0%
+around in fact it better have some sin
+ 
+
+ align:start position:0%
+around in fact it better have some sin
+thetas and cosine thetas right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and by the way we will put up a handout
+
+ align:start position:0%
+and by the way we will put up a handout
+ 
+
+ align:start position:0%
+and by the way we will put up a handout
+um has it been put up yet AJ will the uh
+
+ align:start position:0%
+um has it been put up yet AJ will the uh
+ 
+
+ align:start position:0%
+um has it been put up yet AJ will the uh
+um kinematics PDF we'll put it up like
+
+ align:start position:0%
+um kinematics PDF we'll put it up like
+ 
+
+ align:start position:0%
+um kinematics PDF we'll put it up like
+today or tomorrow which explains all
+
+ align:start position:0%
+today or tomorrow which explains all
+ 
+
+ align:start position:0%
+today or tomorrow which explains all
+this all right I'll tell you about the
+
+ align:start position:0%
+this all right I'll tell you about the
+ 
+
+ align:start position:0%
+this all right I'll tell you about the
+book in a minute when you're done with
+
+ align:start position:0%
+book in a minute when you're done with
+ 
+
+ align:start position:0%
+book in a minute when you're done with
+the quiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep um it's just fub1 equals to cinea E1
+
+ align:start position:0%
+yep um it's just fub1 equals to cinea E1
+ 
+
+ align:start position:0%
+yep um it's just fub1 equals to cinea E1
+ah hold up up okay yeah good yeah I get
+
+ align:start position:0%
+ah hold up up okay yeah good yeah I get
+ 
+
+ align:start position:0%
+ah hold up up okay yeah good yeah I get
+it I know it's easy good I want you to
+
+ align:start position:0%
+it I know it's easy good I want you to
+ 
+
+ align:start position:0%
+it I know it's easy good I want you to
+know it's easy but I want everyone to
+
+ align:start position:0%
+know it's easy but I want everyone to
+ 
+
+ align:start position:0%
+know it's easy but I want everyone to
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+it good what's your
+
+ align:start position:0%
+it good what's your
+ 
+
+ align:start position:0%
+it good what's your
+name Joe what's your full name Joe
+
+ align:start position:0%
+name Joe what's your full name Joe
+ 
+
+ align:start position:0%
+name Joe what's your full name Joe
+kurri k h o u r y kurri
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excellent only because Joe is a common
+
+ align:start position:0%
+excellent only because Joe is a common
+ 
+
+ align:start position:0%
+excellent only because Joe is a common
+name so you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a Dean at MIT I think he's still
+
+ align:start position:0%
+there's a Dean at MIT I think he's still
+ 
+
+ align:start position:0%
+there's a Dean at MIT I think he's still
+a Dean right with your last name yeah
+
+ align:start position:0%
+a Dean right with your last name yeah
+ 
+
+ align:start position:0%
+a Dean right with your last name yeah
+Phil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cury okay everyone
+
+ align:start position:0%
+cury okay everyone
+ 
+
+ align:start position:0%
+cury okay everyone
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+another 90 seconds it doesn't matter if
+
+ align:start position:0%
+another 90 seconds it doesn't matter if
+ 
+
+ align:start position:0%
+another 90 seconds it doesn't matter if
+you don't get it once I write it down
+
+ align:start position:0%
+you don't get it once I write it down
+ 
+
+ align:start position:0%
+you don't get it once I write it down
+you'll get it I want you to put in the
+
+ align:start position:0%
+you'll get it I want you to put in the
+ 
+
+ align:start position:0%
+you'll get it I want you to put in the
+effort of trying that's all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll tell people that with things like
+
+ align:start position:0%
+I'll tell people that with things like
+ 
+
+ align:start position:0%
+I'll tell people that with things like
+this it really helps to grit your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+teeth doesn't really I'm just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conf got it got it
+
+ align:start position:0%
+conf got it got it
+ 
+
+ align:start position:0%
+conf got it got it
+okay 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds all righty we're done anyone Joe
+
+ align:start position:0%
+seconds all righty we're done anyone Joe
+ 
+
+ align:start position:0%
+seconds all righty we're done anyone Joe
+what's F1 and F2 in terms of E1 and E2
+
+ align:start position:0%
+what's F1 and F2 in terms of E1 and E2
+ 
+
+ align:start position:0%
+what's F1 and F2 in terms of E1 and E2
+F1 is uh cosine th E1 plus sin Theta E2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is um F2 =
+
+ align:start position:0%
+is um F2 =
+ 
+
+ align:start position:0%
+is um F2 =
+to- sin thet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus does did everyone get
+
+ align:start position:0%
+plus does did everyone get
+ 
+
+ align:start position:0%
+plus does did everyone get
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+yeah be
+
+ align:start position:0%
+yeah be
+ 
+
+ align:start position:0%
+yeah be
+normalized
+
+ align:start position:0%
+normalized
+ 
+
+ align:start position:0%
+normalized
+um they would automatically be yes they
+
+ align:start position:0%
+um they would automatically be yes they
+ 
+
+ align:start position:0%
+um they would automatically be yes they
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+think about it right no no think about
+
+ align:start position:0%
+think about it right no no think about
+ 
+
+ align:start position:0%
+think about it right no no think about
+it so the the question so first of all
+
+ align:start position:0%
+it so the the question so first of all
+ 
+
+ align:start position:0%
+it so the the question so first of all
+let me come back it's a great thought
+
+ align:start position:0%
+let me come back it's a great thought
+ 
+
+ align:start position:0%
+let me come back it's a great thought
+hold that thought all right does do
+
+ align:start position:0%
+hold that thought all right does do
+ 
+
+ align:start position:0%
+hold that thought all right does do
+people agree with this AJ is this
+
+ align:start position:0%
+people agree with this AJ is this
+ 
+
+ align:start position:0%
+people agree with this AJ is this
+correct a is a
+
+ align:start position:0%
+correct a is a
+ 
+
+ align:start position:0%
+correct a is a
+TA he wasn't looking okay that's fine
+
+ align:start position:0%
+TA he wasn't looking okay that's fine
+ 
+
+ align:start position:0%
+TA he wasn't looking okay that's fine
+let me look at my notes and confirm okay
+
+ align:start position:0%
+let me look at my notes and confirm okay
+ 
+
+ align:start position:0%
+let me look at my notes and confirm okay
+F1 and F2 that's correct excellent okay
+
+ align:start position:0%
+F1 and F2 that's correct excellent okay
+ 
+
+ align:start position:0%
+F1 and F2 that's correct excellent okay
+so what's your name r r how do you spell
+
+ align:start position:0%
+so what's your name r r how do you spell
+ 
+
+ align:start position:0%
+so what's your name r r how do you spell
+it r a n e
+
+ align:start position:0%
+it r a n e
+ 
+
+ align:start position:0%
+it r a n e
+R any excellent rain so the question
+
+ align:start position:0%
+R any excellent rain so the question
+ 
+
+ align:start position:0%
+R any excellent rain so the question
+rain is asking is look fub1 and F2 are
+
+ align:start position:0%
+rain is asking is look fub1 and F2 are
+ 
+
+ align:start position:0%
+rain is asking is look fub1 and F2 are
+unit
+
+ align:start position:0%
+unit
+ 
+
+ align:start position:0%
+unit
+vectors E1 and E2 are unit vectors I'm
+
+ align:start position:0%
+vectors E1 and E2 are unit vectors I'm
+ 
+
+ align:start position:0%
+vectors E1 and E2 are unit vectors I'm
+assuming this is what you're asking so
+
+ align:start position:0%
+assuming this is what you're asking so
+ 
+
+ align:start position:0%
+assuming this is what you're asking so
+obviously this better be a unit Vector
+
+ align:start position:0%
+obviously this better be a unit Vector
+ 
+
+ align:start position:0%
+obviously this better be a unit Vector
+right but as it turns out if you
+
+ align:start position:0%
+right but as it turns out if you
+ 
+
+ align:start position:0%
+right but as it turns out if you
+transform between unit vectors what
+
+ align:start position:0%
+transform between unit vectors what
+ 
+
+ align:start position:0%
+transform between unit vectors what
+comes out will end up being magnitude
+
+ align:start position:0%
+comes out will end up being magnitude
+ 
+
+ align:start position:0%
+comes out will end up being magnitude
+one and the reason is that if you take
+
+ align:start position:0%
+one and the reason is that if you take
+ 
+
+ align:start position:0%
+one and the reason is that if you take
+the magnitude of this you get cosine
+
+ align:start position:0%
+the magnitude of this you get cosine
+ 
+
+ align:start position:0%
+the magnitude of this you get cosine
+Square theta plus sin Square Theta which
+
+ align:start position:0%
+Square theta plus sin Square Theta which
+ 
+
+ align:start position:0%
+Square theta plus sin Square Theta which
+will be one so it'll kind of self
+
+ align:start position:0%
+will be one so it'll kind of self
+ 
+
+ align:start position:0%
+will be one so it'll kind of self
+normalize get it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did people understand what I just said
+
+ align:start position:0%
+did people understand what I just said
+ 
+
+ align:start position:0%
+did people understand what I just said
+right so this is correct any questions
+
+ align:start position:0%
+right so this is correct any questions
+ 
+
+ align:start position:0%
+right so this is correct any questions
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+this do you does anyone want to know how
+
+ align:start position:0%
+this do you does anyone want to know how
+ 
+
+ align:start position:0%
+this do you does anyone want to know how
+I got this it takes a lot of courage to
+
+ align:start position:0%
+I got this it takes a lot of courage to
+ 
+
+ align:start position:0%
+I got this it takes a lot of courage to
+say yes and I'll show you you want me to
+
+ align:start position:0%
+say yes and I'll show you you want me to
+ 
+
+ align:start position:0%
+say yes and I'll show you you want me to
+show you okay it's very simple right in
+
+ align:start position:0%
+show you okay it's very simple right in
+ 
+
+ align:start position:0%
+show you okay it's very simple right in
+the if you think of it the following way
+
+ align:start position:0%
+the if you think of it the following way
+ 
+
+ align:start position:0%
+the if you think of it the following way
+I'll I'll do it below all
+
+ align:start position:0%
+I'll I'll do it below all
+ 
+
+ align:start position:0%
+I'll I'll do it below all
+right I'll do it here by the way this is
+
+ align:start position:0%
+right I'll do it here by the way this is
+ 
+
+ align:start position:0%
+right I'll do it here by the way this is
+a terrible classroom I apologize so you
+
+ align:start position:0%
+a terrible classroom I apologize so you
+ 
+
+ align:start position:0%
+a terrible classroom I apologize so you
+can't see stuff from a distance just hey
+
+ align:start position:0%
+can't see stuff from a distance just hey
+ 
+
+ align:start position:0%
+can't see stuff from a distance just hey
+call me and I'll you know I'll try and
+
+ align:start position:0%
+call me and I'll you know I'll try and
+ 
+
+ align:start position:0%
+call me and I'll you know I'll try and
+make it bigger so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fub1
+
+ align:start position:0%
+fub1
+ 
+
+ align:start position:0%
+fub1
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+FS2 and we're trying to calculate F1 and
+
+ align:start position:0%
+FS2 and we're trying to calculate F1 and
+ 
+
+ align:start position:0%
+FS2 and we're trying to calculate F1 and
+F2 in terms
+
+ align:start position:0%
+F2 in terms
+ 
+
+ align:start position:0%
+F2 in terms
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E1 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E2 right so the way we would do it
+
+ align:start position:0%
+E2 right so the way we would do it
+ 
+
+ align:start position:0%
+E2 right so the way we would do it
+is there are a couple ways to do it one
+
+ align:start position:0%
+is there are a couple ways to do it one
+ 
+
+ align:start position:0%
+is there are a couple ways to do it one
+is you can just take components and add
+
+ align:start position:0%
+is you can just take components and add
+ 
+
+ align:start position:0%
+is you can just take components and add
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+up right so one of the things you could
+
+ align:start position:0%
+up right so one of the things you could
+ 
+
+ align:start position:0%
+up right so one of the things you could
+do is you could say listen um F1 is
+
+ align:start position:0%
+do is you could say listen um F1 is
+ 
+
+ align:start position:0%
+do is you could say listen um F1 is
+composed of this component of
+
+ align:start position:0%
+composed of this component of
+ 
+
+ align:start position:0%
+composed of this component of
+E2 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um how would I do it that's an easy way
+
+ align:start position:0%
+um how would I do it that's an easy way
+ 
+
+ align:start position:0%
+um how would I do it that's an easy way
+to say this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah or yeah I could do the other way
+
+ align:start position:0%
+yeah or yeah I could do the other way
+ 
+
+ align:start position:0%
+yeah or yeah I could do the other way
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+right so I can take the projection of F1
+
+ align:start position:0%
+right so I can take the projection of F1
+ 
+
+ align:start position:0%
+right so I can take the projection of F1
+on E1 and take the projection of F1 on
+
+ align:start position:0%
+on E1 and take the projection of F1 on
+ 
+
+ align:start position:0%
+on E1 and take the projection of F1 on
+E2 get it what's your name ER Erica
+
+ align:start position:0%
+E2 get it what's your name ER Erica
+ 
+
+ align:start position:0%
+E2 get it what's your name ER Erica
+right I can just take the projection of
+
+ align:start position:0%
+right I can just take the projection of
+ 
+
+ align:start position:0%
+right I can just take the projection of
+fub1 on E1 and E2 right and just use the
+
+ align:start position:0%
+fub1 on E1 and E2 right and just use the
+ 
+
+ align:start position:0%
+fub1 on E1 and E2 right and just use the
+these thetas right and then take the
+
+ align:start position:0%
+these thetas right and then take the
+ 
+
+ align:start position:0%
+these thetas right and then take the
+projection of F2 on E1 E2 and then write
+
+ align:start position:0%
+projection of F2 on E1 E2 and then write
+ 
+
+ align:start position:0%
+projection of F2 on E1 E2 and then write
+that's what you get okay I don't want to
+
+ align:start position:0%
+that's what you get okay I don't want to
+ 
+
+ align:start position:0%
+that's what you get okay I don't want to
+do it only because I uh I can show it
+
+ align:start position:0%
+do it only because I uh I can show it
+ 
+
+ align:start position:0%
+do it only because I uh I can show it
+you after class it's just very very
+
+ align:start position:0%
+you after class it's just very very
+ 
+
+ align:start position:0%
+you after class it's just very very
+basically just add the projections and
+
+ align:start position:0%
+basically just add the projections and
+ 
+
+ align:start position:0%
+basically just add the projections and
+you'll get that it's in the
+
+ align:start position:0%
+you'll get that it's in the
+ 
+
+ align:start position:0%
+you'll get that it's in the
+notes okay what is E1 and E2 in terms of
+
+ align:start position:0%
+notes okay what is E1 and E2 in terms of
+ 
+
+ align:start position:0%
+notes okay what is E1 and E2 in terms of
+F1 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F2 what's a quick way to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this H yeah you could solve it or
+
+ align:start position:0%
+this H yeah you could solve it or
+ 
+
+ align:start position:0%
+this H yeah you could solve it or
+there's another way to do it which is if
+
+ align:start position:0%
+there's another way to do it which is if
+ 
+
+ align:start position:0%
+there's another way to do it which is if
+you put yourself in F1 and f2s if you
+
+ align:start position:0%
+you put yourself in F1 and f2s if you
+ 
+
+ align:start position:0%
+you put yourself in F1 and f2s if you
+kind of turn it around if it's like
+
+ align:start position:0%
+kind of turn it around if it's like
+ 
+
+ align:start position:0%
+kind of turn it around if it's like
+replacing Theta with a minus
+
+ align:start position:0%
+replacing Theta with a minus
+ 
+
+ align:start position:0%
+replacing Theta with a minus
+Theta right so if you replace Theta with
+
+ align:start position:0%
+Theta right so if you replace Theta with
+ 
+
+ align:start position:0%
+Theta right so if you replace Theta with
+a minus Theta what you'll get is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got it so this is how you go back and
+
+ align:start position:0%
+got it so this is how you go back and
+ 
+
+ align:start position:0%
+got it so this is how you go back and
+forth between two frames and as long as
+
+ align:start position:0%
+forth between two frames and as long as
+ 
+
+ align:start position:0%
+forth between two frames and as long as
+you know the angle between the frames
+
+ align:start position:0%
+you know the angle between the frames
+ 
+
+ align:start position:0%
+you know the angle between the frames
+right now here's the deal if this
+
+ align:start position:0%
+right now here's the deal if this
+ 
+
+ align:start position:0%
+right now here's the deal if this
+Frame is rotating with respect to this
+
+ align:start position:0%
+Frame is rotating with respect to this
+ 
+
+ align:start position:0%
+Frame is rotating with respect to this
+Frame the Theta will change but at any
+
+ align:start position:0%
+Frame the Theta will change but at any
+ 
+
+ align:start position:0%
+Frame the Theta will change but at any
+given point in time if you know what the
+
+ align:start position:0%
+given point in time if you know what the
+ 
+
+ align:start position:0%
+given point in time if you know what the
+Theta is Binger you can calculate fub1
+
+ align:start position:0%
+Theta is Binger you can calculate fub1
+ 
+
+ align:start position:0%
+Theta is Binger you can calculate fub1
+from F1 and F2 in terms of E1 and E2 and
+
+ align:start position:0%
+from F1 and F2 in terms of E1 and E2 and
+ 
+
+ align:start position:0%
+from F1 and F2 in terms of E1 and E2 and
+vice
+
+ align:start position:0%
+vice
+ 
+
+ align:start position:0%
+vice
+ver okay any questions about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes you will but it's many more steps so
+
+ align:start position:0%
+yes you will but it's many more steps so
+ 
+
+ align:start position:0%
+yes you will but it's many more steps so
+we'll come to that we'll nail the spider
+
+ align:start position:0%
+we'll come to that we'll nail the spider
+ 
+
+ align:start position:0%
+we'll come to that we'll nail the spider
+now all right okay but this is how you
+
+ align:start position:0%
+now all right okay but this is how you
+ 
+
+ align:start position:0%
+now all right okay but this is how you
+trans transform between
+
+ align:start position:0%
+trans transform between
+ 
+
+ align:start position:0%
+trans transform between
+frames okay so now the notes go there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now I'm going to tell you something
+
+ align:start position:0%
+okay now I'm going to tell you something
+ 
+
+ align:start position:0%
+okay now I'm going to tell you something
+which will seem like an empty trick and
+
+ align:start position:0%
+which will seem like an empty trick and
+ 
+
+ align:start position:0%
+which will seem like an empty trick and
+then we'll do the spider problem and
+
+ align:start position:0%
+then we'll do the spider problem and
+ 
+
+ align:start position:0%
+then we'll do the spider problem and
+it'll make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense now let's assume that we have some
+
+ align:start position:0%
+sense now let's assume that we have some
+ 
+
+ align:start position:0%
+sense now let's assume that we have some
+Vector r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm trying to thread the needle here I'm
+
+ align:start position:0%
+I'm trying to thread the needle here I'm
+ 
+
+ align:start position:0%
+I'm trying to thread the needle here I'm
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thinking whether I should give you the
+
+ align:start position:0%
+thinking whether I should give you the
+ 
+
+ align:start position:0%
+thinking whether I should give you the
+conceptual Point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first okay let's just jump into the
+
+ align:start position:0%
+first okay let's just jump into the
+ 
+
+ align:start position:0%
+first okay let's just jump into the
+spider problem and then we'll because a
+
+ align:start position:0%
+spider problem and then we'll because a
+ 
+
+ align:start position:0%
+spider problem and then we'll because a
+lot of people asked about how solving
+
+ align:start position:0%
+lot of people asked about how solving
+ 
+
+ align:start position:0%
+lot of people asked about how solving
+that getting the velocity let's just do
+
+ align:start position:0%
+that getting the velocity let's just do
+ 
+
+ align:start position:0%
+that getting the velocity let's just do
+that now and then I'll make the final
+
+ align:start position:0%
+that now and then I'll make the final
+ 
+
+ align:start position:0%
+that now and then I'll make the final
+point I want to make after that okay so
+
+ align:start position:0%
+point I want to make after that okay so
+ 
+
+ align:start position:0%
+point I want to make after that okay so
+this is how you translate between frames
+
+ align:start position:0%
+this is how you translate between frames
+ 
+
+ align:start position:0%
+this is how you translate between frames
+this is how you transform between frames
+
+ align:start position:0%
+this is how you transform between frames
+ 
+
+ align:start position:0%
+this is how you transform between frames
+and we're all set so now we have all the
+
+ align:start position:0%
+and we're all set so now we have all the
+ 
+
+ align:start position:0%
+and we're all set so now we have all the
+math we need there's one little trick I
+
+ align:start position:0%
+math we need there's one little trick I
+ 
+
+ align:start position:0%
+math we need there's one little trick I
+want to tell you which I'll tell you now
+
+ align:start position:0%
+want to tell you which I'll tell you now
+ 
+
+ align:start position:0%
+want to tell you which I'll tell you now
+in the context of the spider problem and
+
+ align:start position:0%
+in the context of the spider problem and
+ 
+
+ align:start position:0%
+in the context of the spider problem and
+now what we're going to do is actually
+
+ align:start position:0%
+now what we're going to do is actually
+ 
+
+ align:start position:0%
+now what we're going to do is actually
+try and figure out what the velocity and
+
+ align:start position:0%
+try and figure out what the velocity and
+ 
+
+ align:start position:0%
+try and figure out what the velocity and
+acceleration of that spider are all
+
+ align:start position:0%
+acceleration of that spider are all
+ 
+
+ align:start position:0%
+acceleration of that spider are all
+right so let's do that okay so this is
+
+ align:start position:0%
+right so let's do that okay so this is
+ 
+
+ align:start position:0%
+right so let's do that okay so this is
+the corner of the
+
+ align:start position:0%
+the corner of the
+ 
+
+ align:start position:0%
+the corner of the
+room right this is the room and um in
+
+ align:start position:0%
+room right this is the room and um in
+ 
+
+ align:start position:0%
+room right this is the room and um in
+the in the corner of the room I have two
+
+ align:start position:0%
+the in the corner of the room I have two
+ 
+
+ align:start position:0%
+the in the corner of the room I have two
+two unit vectors let's make them a
+
+ align:start position:0%
+two unit vectors let's make them a
+ 
+
+ align:start position:0%
+two unit vectors let's make them a
+little shorter these are too
+
+ align:start position:0%
+little shorter these are too
+ 
+
+ align:start position:0%
+little shorter these are too
+long right uh we'll call them E and F
+
+ align:start position:0%
+long right uh we'll call them E and F
+ 
+
+ align:start position:0%
+long right uh we'll call them E and F
+just because we've been using that for
+
+ align:start position:0%
+just because we've been using that for
+ 
+
+ align:start position:0%
+just because we've been using that for
+Earth and
+
+ align:start position:0%
+Earth and
+ 
+
+ align:start position:0%
+Earth and
+frisbee right
+
+ align:start position:0%
+frisbee right
+ 
+
+ align:start position:0%
+frisbee right
+e and this is our
+
+ align:start position:0%
+e and this is our
+ 
+
+ align:start position:0%
+e and this is our
+frisbee we call that
+
+ align:start position:0%
+frisbee we call that
+ 
+
+ align:start position:0%
+frisbee we call that
+F and it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spinning we call these
+
+ align:start position:0%
+spinning we call these
+ 
+
+ align:start position:0%
+spinning we call these
+fub1 and FS2 so first question to your
+
+ align:start position:0%
+fub1 and FS2 so first question to your
+ 
+
+ align:start position:0%
+fub1 and FS2 so first question to your
+folks the first thing you need to do by
+
+ align:start position:0%
+folks the first thing you need to do by
+ 
+
+ align:start position:0%
+folks the first thing you need to do by
+the way actually as a comment is when
+
+ align:start position:0%
+the way actually as a comment is when
+ 
+
+ align:start position:0%
+the way actually as a comment is when
+you draw a picture like this you must
+
+ align:start position:0%
+you draw a picture like this you must
+ 
+
+ align:start position:0%
+you draw a picture like this you must
+always go out of your way to label
+
+ align:start position:0%
+always go out of your way to label
+ 
+
+ align:start position:0%
+always go out of your way to label
+points that are of importance so for
+
+ align:start position:0%
+points that are of importance so for
+ 
+
+ align:start position:0%
+points that are of importance so for
+example this point we'll call it
+
+ align:start position:0%
+example this point we'll call it
+ 
+
+ align:start position:0%
+example this point we'll call it
+P right it's just a point P I could have
+
+ align:start position:0%
+P right it's just a point P I could have
+ 
+
+ align:start position:0%
+P right it's just a point P I could have
+called it C center of the Frisbee let's
+
+ align:start position:0%
+called it C center of the Frisbee let's
+ 
+
+ align:start position:0%
+called it C center of the Frisbee let's
+call the position of the spider s now
+
+ align:start position:0%
+call the position of the spider s now
+ 
+
+ align:start position:0%
+call the position of the spider s now
+have I lost any generality in claiming
+
+ align:start position:0%
+have I lost any generality in claiming
+ 
+
+ align:start position:0%
+have I lost any generality in claiming
+that the spider is along this unit basis
+
+ align:start position:0%
+that the spider is along this unit basis
+ 
+
+ align:start position:0%
+that the spider is along this unit basis
+Vector have a lot I haven't right
+
+ align:start position:0%
+Vector have a lot I haven't right
+ 
+
+ align:start position:0%
+Vector have a lot I haven't right
+because I picked them arbitrarily so
+
+ align:start position:0%
+because I picked them arbitrarily so
+ 
+
+ align:start position:0%
+because I picked them arbitrarily so
+might as well just pick that okay let us
+
+ align:start position:0%
+might as well just pick that okay let us
+ 
+
+ align:start position:0%
+might as well just pick that okay let us
+call now actually even before that so
+
+ align:start position:0%
+call now actually even before that so
+ 
+
+ align:start position:0%
+call now actually even before that so
+here's the question to
+
+ align:start position:0%
+here's the question to
+ 
+
+ align:start position:0%
+here's the question to
+you how do I parameterize the position
+
+ align:start position:0%
+you how do I parameterize the position
+ 
+
+ align:start position:0%
+you how do I parameterize the position
+of the spider at any given moment in
+
+ align:start position:0%
+of the spider at any given moment in
+ 
+
+ align:start position:0%
+of the spider at any given moment in
+time what do I need to know to tell you
+
+ align:start position:0%
+time what do I need to know to tell you
+ 
+
+ align:start position:0%
+time what do I need to know to tell you
+where the spider is right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+loudly the relationship of F1 to
+
+ align:start position:0%
+loudly the relationship of F1 to
+ 
+
+ align:start position:0%
+loudly the relationship of F1 to
+reference frame e
+
+ align:start position:0%
+reference frame e
+ 
+
+ align:start position:0%
+reference frame e
+and what would that relationship
+
+ align:start position:0%
+and what would that relationship
+ 
+
+ align:start position:0%
+and what would that relationship
+be think about what do you need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know excellent okay so one parameter you
+
+ align:start position:0%
+know excellent okay so one parameter you
+ 
+
+ align:start position:0%
+know excellent okay so one parameter you
+need for sure is this angle
+
+ align:start position:0%
+need for sure is this angle
+ 
+
+ align:start position:0%
+need for sure is this angle
+right which is Theta which we just used
+
+ align:start position:0%
+right which is Theta which we just used
+ 
+
+ align:start position:0%
+right which is Theta which we just used
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+there what else do you need to
+
+ align:start position:0%
+there what else do you need to
+ 
+
+ align:start position:0%
+there what else do you need to
+parameterize if I want you you to give
+
+ align:start position:0%
+parameterize if I want you you to give
+ 
+
+ align:start position:0%
+parameterize if I want you you to give
+me the exact coordinates of the spider
+
+ align:start position:0%
+me the exact coordinates of the spider
+ 
+
+ align:start position:0%
+me the exact coordinates of the spider
+what are the numbers do I need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep now if I know the angle
+
+ align:start position:0%
+yep now if I know the angle
+ 
+
+ align:start position:0%
+yep now if I know the angle
+but I know it is a function of time then
+
+ align:start position:0%
+but I know it is a function of time then
+ 
+
+ align:start position:0%
+but I know it is a function of time then
+that's one parameter what are the other
+
+ align:start position:0%
+that's one parameter what are the other
+ 
+
+ align:start position:0%
+that's one parameter what are the other
+parameters I
+
+ align:start position:0%
+parameters I
+ 
+
+ align:start position:0%
+parameters I
+need don't think of motion yet just
+
+ align:start position:0%
+need don't think of motion yet just
+ 
+
+ align:start position:0%
+need don't think of motion yet just
+think of like a
+
+ align:start position:0%
+think of like a
+ 
+
+ align:start position:0%
+think of like a
+snapshot right just give me distances
+
+ align:start position:0%
+snapshot right just give me distances
+ 
+
+ align:start position:0%
+snapshot right just give me distances
+we'll get to Velocity right see this
+
+ align:start position:0%
+we'll get to Velocity right see this
+ 
+
+ align:start position:0%
+we'll get to Velocity right see this
+this is what I want you to think through
+
+ align:start position:0%
+this is what I want you to think through
+ 
+
+ align:start position:0%
+this is what I want you to think through
+velocities are derivatives of location
+
+ align:start position:0%
+velocities are derivatives of location
+ 
+
+ align:start position:0%
+velocities are derivatives of location
+so go ahead distance exactly so what
+
+ align:start position:0%
+so go ahead distance exactly so what
+ 
+
+ align:start position:0%
+so go ahead distance exactly so what
+else do we need we need the distance of
+
+ align:start position:0%
+else do we need we need the distance of
+ 
+
+ align:start position:0%
+else do we need we need the distance of
+this point P from some point embedded on
+
+ align:start position:0%
+this point P from some point embedded on
+ 
+
+ align:start position:0%
+this point P from some point embedded on
+the earth it doesn't matter which point
+
+ align:start position:0%
+the earth it doesn't matter which point
+ 
+
+ align:start position:0%
+the earth it doesn't matter which point
+we pick we need to pick one point that's
+
+ align:start position:0%
+we pick we need to pick one point that's
+ 
+
+ align:start position:0%
+we pick we need to pick one point that's
+embedded on the Earth right so I'm just
+
+ align:start position:0%
+embedded on the Earth right so I'm just
+ 
+
+ align:start position:0%
+embedded on the Earth right so I'm just
+going to pick one point at the corner of
+
+ align:start position:0%
+going to pick one point at the corner of
+ 
+
+ align:start position:0%
+going to pick one point at the corner of
+these two where I've drawn these axes it
+
+ align:start position:0%
+these two where I've drawn these axes it
+ 
+
+ align:start position:0%
+these two where I've drawn these axes it
+doesn't matter I got have picked it here
+
+ align:start position:0%
+doesn't matter I got have picked it here
+ 
+
+ align:start position:0%
+doesn't matter I got have picked it here
+uh I'll call that point O So this
+
+ align:start position:0%
+uh I'll call that point O So this
+ 
+
+ align:start position:0%
+uh I'll call that point O So this
+distance I'm going to call it
+
+ align:start position:0%
+distance I'm going to call it
+ 
+
+ align:start position:0%
+distance I'm going to call it
+U and what else do I
+
+ align:start position:0%
+U and what else do I
+ 
+
+ align:start position:0%
+U and what else do I
+need it's two
+
+ align:start position:0%
+need it's two
+ 
+
+ align:start position:0%
+need it's two
+Dimensions I need the vertical
+
+ align:start position:0%
+Dimensions I need the vertical
+ 
+
+ align:start position:0%
+Dimensions I need the vertical
+distance I'm going to call that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V what else do I need come on quick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excellent I need this
+
+ align:start position:0%
+excellent I need this
+ 
+
+ align:start position:0%
+excellent I need this
+distance and I'm making the making this
+
+ align:start position:0%
+distance and I'm making the making this
+ 
+
+ align:start position:0%
+distance and I'm making the making this
+up as I go I'll call that
+
+ align:start position:0%
+up as I go I'll call that
+ 
+
+ align:start position:0%
+up as I go I'll call that
+L
+
+ align:start position:0%
+L
+ 
+
+ align:start position:0%
+L
+okay now and this is something you
+
+ align:start position:0%
+okay now and this is something you
+ 
+
+ align:start position:0%
+okay now and this is something you
+should do every time you solve a problem
+
+ align:start position:0%
+should do every time you solve a problem
+ 
+
+ align:start position:0%
+should do every time you solve a problem
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this what is the position of the spider
+
+ align:start position:0%
+this what is the position of the spider
+ 
+
+ align:start position:0%
+this what is the position of the spider
+with respect to that point we picked on
+
+ align:start position:0%
+with respect to that point we picked on
+ 
+
+ align:start position:0%
+with respect to that point we picked on
+the surface of the Earth which we call O
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody okay this is so watch this I'm
+
+ align:start position:0%
+anybody okay this is so watch this I'm
+ 
+
+ align:start position:0%
+anybody okay this is so watch this I'm
+going to call it R all that thought okay
+
+ align:start position:0%
+going to call it R all that thought okay
+ 
+
+ align:start position:0%
+going to call it R all that thought okay
+I'm just going to write it out first the
+
+ align:start position:0%
+I'm just going to write it out first the
+ 
+
+ align:start position:0%
+I'm just going to write it out first the
+the position Vector from o to P which is
+
+ align:start position:0%
+the position Vector from o to P which is
+ 
+
+ align:start position:0%
+the position Vector from o to P which is
+the vector this
+
+ align:start position:0%
+the vector this
+ 
+
+ align:start position:0%
+the vector this
+Vector right that
+
+ align:start position:0%
+Vector right that
+ 
+
+ align:start position:0%
+Vector right that
+Vector get
+
+ align:start position:0%
+Vector get
+ 
+
+ align:start position:0%
+Vector get
+it right is equal to r o is equal to
+
+ align:start position:0%
+it right is equal to r o is equal to
+ 
+
+ align:start position:0%
+it right is equal to r o is equal to
+what go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead well no no you're no keep going U
+
+ align:start position:0%
+ahead well no no you're no keep going U
+ 
+
+ align:start position:0%
+ahead well no no you're no keep going U
+plus plus L cosine but don't do I need
+
+ align:start position:0%
+plus plus L cosine but don't do I need
+ 
+
+ align:start position:0%
+plus plus L cosine but don't do I need
+some uh L cosine Theta right yeah yeah
+
+ align:start position:0%
+some uh L cosine Theta right yeah yeah
+ 
+
+ align:start position:0%
+some uh L cosine Theta right yeah yeah
+yeah okay you going to write like this
+
+ align:start position:0%
+yeah okay you going to write like this
+ 
+
+ align:start position:0%
+yeah okay you going to write like this
+U plus L cosine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta E1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's perfectly correct
+
+ align:start position:0%
+okay that's perfectly correct
+ 
+
+ align:start position:0%
+okay that's perfectly correct
+yep I'm sorry that's s yeah a position
+
+ align:start position:0%
+yep I'm sorry that's s yeah a position
+ 
+
+ align:start position:0%
+yep I'm sorry that's s yeah a position
+of spider right that's what he wrote I
+
+ align:start position:0%
+of spider right that's what he wrote I
+ 
+
+ align:start position:0%
+of spider right that's what he wrote I
+beg you pardon right so that's exactly
+
+ align:start position:0%
+beg you pardon right so that's exactly
+ 
+
+ align:start position:0%
+beg you pardon right so that's exactly
+correct say it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again that should be V yeah okay so you
+
+ align:start position:0%
+again that should be V yeah okay so you
+ 
+
+ align:start position:0%
+again that should be V yeah okay so you
+actually that's perfectly correct you
+
+ align:start position:0%
+actually that's perfectly correct you
+ 
+
+ align:start position:0%
+actually that's perfectly correct you
+did it right but now I'm going to give
+
+ align:start position:0%
+did it right but now I'm going to give
+ 
+
+ align:start position:0%
+did it right but now I'm going to give
+you a slightly different way to think
+
+ align:start position:0%
+you a slightly different way to think
+ 
+
+ align:start position:0%
+you a slightly different way to think
+about it which will lead to the same
+
+ align:start position:0%
+about it which will lead to the same
+ 
+
+ align:start position:0%
+about it which will lead to the same
+answer you did a shortcut in your head
+
+ align:start position:0%
+answer you did a shortcut in your head
+ 
+
+ align:start position:0%
+answer you did a shortcut in your head
+which is brilliant right but I'm going
+
+ align:start position:0%
+which is brilliant right but I'm going
+ 
+
+ align:start position:0%
+which is brilliant right but I'm going
+to give you a different way to think
+
+ align:start position:0%
+to give you a different way to think
+ 
+
+ align:start position:0%
+to give you a different way to think
+about it which is a little more
+
+ align:start position:0%
+about it which is a little more
+ 
+
+ align:start position:0%
+about it which is a little more
+methodical but which also brings out the
+
+ align:start position:0%
+methodical but which also brings out the
+ 
+
+ align:start position:0%
+methodical but which also brings out the
+point I want to make to
+
+ align:start position:0%
+point I want to make to
+ 
+
+ align:start position:0%
+point I want to make to
+you I'm going to write this
+
+ align:start position:0%
+you I'm going to write this
+ 
+
+ align:start position:0%
+you I'm going to write this
+differently that was right I'm going to
+
+ align:start position:0%
+differently that was right I'm going to
+ 
+
+ align:start position:0%
+differently that was right I'm going to
+write it
+
+ align:start position:0%
+write it
+ 
+
+ align:start position:0%
+write it
+differently I'm going to write this
+
+ align:start position:0%
+differently I'm going to write this
+ 
+
+ align:start position:0%
+differently I'm going to write this
+Vector R
+
+ align:start position:0%
+Vector R
+ 
+
+ align:start position:0%
+Vector R
+oos as equal to
+
+ align:start position:0%
+oos as equal to
+ 
+
+ align:start position:0%
+oos as equal to
+because I'm not as
+
+ align:start position:0%
+because I'm not as
+ 
+
+ align:start position:0%
+because I'm not as
+smart r
+
+ align:start position:0%
+smart r
+ 
+
+ align:start position:0%
+smart r
+o plus r PS is this fair I can do that
+
+ align:start position:0%
+o plus r PS is this fair I can do that
+ 
+
+ align:start position:0%
+o plus r PS is this fair I can do that
+right break it them into two
+
+ align:start position:0%
+right break it them into two
+ 
+
+ align:start position:0%
+right break it them into two
+pieces now then I'm going to
+
+ align:start position:0%
+pieces now then I'm going to
+ 
+
+ align:start position:0%
+pieces now then I'm going to
+say r o p is
+
+ align:start position:0%
+say r o p is
+ 
+
+ align:start position:0%
+say r o p is
+simply U
+
+ align:start position:0%
+simply U
+ 
+
+ align:start position:0%
+simply U
+E1 plus v
+
+ align:start position:0%
+E1 plus v
+ 
+
+ align:start position:0%
+E1 plus v
+E2 that's this guy
+
+ align:start position:0%
+E2 that's this guy
+ 
+
+ align:start position:0%
+E2 that's this guy
+is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct am I going too fast do you see
+
+ align:start position:0%
+correct am I going too fast do you see
+ 
+
+ align:start position:0%
+correct am I going too fast do you see
+what I'm doing
+
+ align:start position:0%
+what I'm doing
+ 
+
+ align:start position:0%
+what I'm doing
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+everybody
+
+ align:start position:0%
+everybody
+ 
+
+ align:start position:0%
+everybody
+yeah and what is r PS and here's the rub
+
+ align:start position:0%
+yeah and what is r PS and here's the rub
+ 
+
+ align:start position:0%
+yeah and what is r PS and here's the rub
+I'm going to write it
+
+ align:start position:0%
+I'm going to write it
+ 
+
+ align:start position:0%
+I'm going to write it
+as get
+
+ align:start position:0%
+as get
+ 
+
+ align:start position:0%
+as get
+this l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does that make you
+
+ align:start position:0%
+does that make you
+ 
+
+ align:start position:0%
+does that make you
+queasy right makes you queasy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right it's like putting uh you know
+
+ align:start position:0%
+right it's like putting uh you know
+ 
+
+ align:start position:0%
+right it's like putting uh you know
+strawberry ice cream on a cheese
+
+ align:start position:0%
+strawberry ice cream on a cheese
+ 
+
+ align:start position:0%
+strawberry ice cream on a cheese
+sandwich
+
+ align:start position:0%
+sandwich
+ 
+
+ align:start position:0%
+sandwich
+yeah my daughter my daughter did that
+
+ align:start position:0%
+yeah my daughter my daughter did that
+ 
+
+ align:start position:0%
+yeah my daughter my daughter did that
+exra this morning so
+
+ align:start position:0%
+exra this morning so
+ 
+
+ align:start position:0%
+exra this morning so
+yeah oh I'm sorry that's probably what
+
+ align:start position:0%
+yeah oh I'm sorry that's probably what
+ 
+
+ align:start position:0%
+yeah oh I'm sorry that's probably what
+made you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squeasy and in this way now does this
+
+ align:start position:0%
+squeasy and in this way now does this
+ 
+
+ align:start position:0%
+squeasy and in this way now does this
+make you
+
+ align:start position:0%
+make you
+ 
+
+ align:start position:0%
+make you
+queasy no it doesn't make it that should
+
+ align:start position:0%
+queasy no it doesn't make it that should
+ 
+
+ align:start position:0%
+queasy no it doesn't make it that should
+still make you queasy think about it
+
+ align:start position:0%
+still make you queasy think about it
+ 
+
+ align:start position:0%
+still make you queasy think about it
+anti- mixing basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bases is that okay can iic
+
+ align:start position:0%
+bases is that okay can iic
+ 
+
+ align:start position:0%
+bases is that okay can iic
+bases yes no okay all in favor all
+
+ align:start position:0%
+bases yes no okay all in favor all
+ 
+
+ align:start position:0%
+bases yes no okay all in favor all
+against okay I set the all against up I
+
+ align:start position:0%
+against okay I set the all against up I
+ 
+
+ align:start position:0%
+against okay I set the all against up I
+I was misleading you it turns out no
+
+ align:start position:0%
+I was misleading you it turns out no
+ 
+
+ align:start position:0%
+I was misleading you it turns out no
+it's my fault buty you I wanted to
+
+ align:start position:0%
+it's my fault buty you I wanted to
+ 
+
+ align:start position:0%
+it's my fault buty you I wanted to
+wanted to kind of expose any hidden
+
+ align:start position:0%
+wanted to kind of expose any hidden
+ 
+
+ align:start position:0%
+wanted to kind of expose any hidden
+latent queasiness is
+
+ align:start position:0%
+latent queasiness is
+ 
+
+ align:start position:0%
+latent queasiness is
+right it's okay it's okay to mix bases
+
+ align:start position:0%
+right it's okay it's okay to mix bases
+ 
+
+ align:start position:0%
+right it's okay it's okay to mix bases
+absolutely okay
+
+ align:start position:0%
+absolutely okay
+ 
+
+ align:start position:0%
+absolutely okay
+yep find them up there in terms of each
+
+ align:start position:0%
+yep find them up there in terms of each
+ 
+
+ align:start position:0%
+yep find them up there in terms of each
+other yeah well it's okay because even
+
+ align:start position:0%
+other yeah well it's okay because even
+ 
+
+ align:start position:0%
+other yeah well it's okay because even
+if I didn't Define them it's a vector
+
+ align:start position:0%
+if I didn't Define them it's a vector
+ 
+
+ align:start position:0%
+if I didn't Define them it's a vector
+right I can add vectors it's perfectly
+
+ align:start position:0%
+right I can add vectors it's perfectly
+ 
+
+ align:start position:0%
+right I can add vectors it's perfectly
+okay even if they're different bases
+
+ align:start position:0%
+okay even if they're different bases
+ 
+
+ align:start position:0%
+okay even if they're different bases
+that's okay right so what you did was
+
+ align:start position:0%
+that's okay right so what you did was
+ 
+
+ align:start position:0%
+that's okay right so what you did was
+you can of downon converted everything
+
+ align:start position:0%
+you can of downon converted everything
+ 
+
+ align:start position:0%
+you can of downon converted everything
+to E1 and E2 right but I'm taking the
+
+ align:start position:0%
+to E1 and E2 right but I'm taking the
+ 
+
+ align:start position:0%
+to E1 and E2 right but I'm taking the
+lazy approach which is I'm going to
+
+ align:start position:0%
+lazy approach which is I'm going to
+ 
+
+ align:start position:0%
+lazy approach which is I'm going to
+write them like this just because you'll
+
+ align:start position:0%
+write them like this just because you'll
+ 
+
+ align:start position:0%
+write them like this just because you'll
+see in the class certain things come out
+
+ align:start position:0%
+see in the class certain things come out
+ 
+
+ align:start position:0%
+see in the class certain things come out
+if you write it this way but what you
+
+ align:start position:0%
+if you write it this way but what you
+ 
+
+ align:start position:0%
+if you write it this way but what you
+did was perfectly right in fact I'm
+
+ align:start position:0%
+did was perfectly right in fact I'm
+ 
+
+ align:start position:0%
+did was perfectly right in fact I'm
+going to do what you just said in a
+
+ align:start position:0%
+going to do what you just said in a
+ 
+
+ align:start position:0%
+going to do what you just said in a
+moment
+
+ align:start position:0%
+moment
+ 
+
+ align:start position:0%
+moment
+now here's the deal what is the
+
+ align:start position:0%
+now here's the deal what is the
+ 
+
+ align:start position:0%
+now here's the deal what is the
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+of the center of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Frisbee first of all that's an
+
+ align:start position:0%
+Frisbee first of all that's an
+ 
+
+ align:start position:0%
+Frisbee first of all that's an
+incomplete question I haven't asked I
+
+ align:start position:0%
+incomplete question I haven't asked I
+ 
+
+ align:start position:0%
+incomplete question I haven't asked I
+haven't told you everything you need to
+
+ align:start position:0%
+haven't told you everything you need to
+ 
+
+ align:start position:0%
+haven't told you everything you need to
+know but what's the velocity of the
+
+ align:start position:0%
+know but what's the velocity of the
+ 
+
+ align:start position:0%
+know but what's the velocity of the
+center of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Frisbee
+
+ align:start position:0%
+Frisbee
+ 
+
+ align:start position:0%
+Frisbee
+what I I can't hear
+
+ align:start position:0%
+what I I can't hear
+ 
+
+ align:start position:0%
+what I I can't hear
+you no no you might have said it right I
+
+ align:start position:0%
+you no no you might have said it right I
+ 
+
+ align:start position:0%
+you no no you might have said it right I
+really could everyone spoke I'm ten so
+
+ align:start position:0%
+really could everyone spoke I'm ten so
+ 
+
+ align:start position:0%
+really could everyone spoke I'm ten so
+you need to speak louder what what was
+
+ align:start position:0%
+you need to speak louder what what was
+ 
+
+ align:start position:0%
+you need to speak louder what what was
+incomplete about the question I just
+
+ align:start position:0%
+incomplete about the question I just
+ 
+
+ align:start position:0%
+incomplete about the question I just
+asked I said what's the velocity of the
+
+ align:start position:0%
+asked I said what's the velocity of the
+ 
+
+ align:start position:0%
+asked I said what's the velocity of the
+center of the Frisbee yep I didn't tell
+
+ align:start position:0%
+center of the Frisbee yep I didn't tell
+ 
+
+ align:start position:0%
+center of the Frisbee yep I didn't tell
+you a reference frame right so what's
+
+ align:start position:0%
+you a reference frame right so what's
+ 
+
+ align:start position:0%
+you a reference frame right so what's
+the velocity of the center of the frisbe
+
+ align:start position:0%
+the velocity of the center of the frisbe
+ 
+
+ align:start position:0%
+the velocity of the center of the frisbe
+with respect to planet
+
+ align:start position:0%
+with respect to planet
+ 
+
+ align:start position:0%
+with respect to planet
+Earth
+
+ align:start position:0%
+Earth
+ 
+
+ align:start position:0%
+Earth
+yes yeah so this is how I'm going to
+
+ align:start position:0%
+yes yeah so this is how I'm going to
+ 
+
+ align:start position:0%
+yes yeah so this is how I'm going to
+write
+
+ align:start position:0%
+write
+ 
+
+ align:start position:0%
+write
+velocity with respect to planet Earth a
+
+ align:start position:0%
+velocity with respect to planet Earth a
+ 
+
+ align:start position:0%
+velocity with respect to planet Earth a
+sorry sorry
+
+ align:start position:0%
+sorry sorry
+ 
+
+ align:start position:0%
+sorry sorry
+e right the velocity V of which point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P right this notation is very important
+
+ align:start position:0%
+P right this notation is very important
+ 
+
+ align:start position:0%
+P right this notation is very important
+if I just said the velocity of Point P
+
+ align:start position:0%
+if I just said the velocity of Point P
+ 
+
+ align:start position:0%
+if I just said the velocity of Point P
+it makes no sense because I could be
+
+ align:start position:0%
+it makes no sense because I could be
+ 
+
+ align:start position:0%
+it makes no sense because I could be
+asking the velocity of Point p with
+
+ align:start position:0%
+asking the velocity of Point p with
+ 
+
+ align:start position:0%
+asking the velocity of Point p with
+respect to the Frisbee which would be
+
+ align:start position:0%
+respect to the Frisbee which would be
+ 
+
+ align:start position:0%
+respect to the Frisbee which would be
+zero right right so the velocity of
+
+ align:start position:0%
+zero right right so the velocity of
+ 
+
+ align:start position:0%
+zero right right so the velocity of
+Point p with respect to
+
+ align:start position:0%
+Point p with respect to
+ 
+
+ align:start position:0%
+Point p with respect to
+Earth is equal to D by
+
+ align:start position:0%
+Earth is equal to D by
+ 
+
+ align:start position:0%
+Earth is equal to D by
+DT of r p is that complete or am I
+
+ align:start position:0%
+DT of r p is that complete or am I
+ 
+
+ align:start position:0%
+DT of r p is that complete or am I
+missing something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there any someone in the back someone on
+
+ align:start position:0%
+there any someone in the back someone on
+ 
+
+ align:start position:0%
+there any someone in the back someone on
+the that
+
+ align:start position:0%
+the that
+ 
+
+ align:start position:0%
+the that
+quadrant the way I wrote d by DTM I'm
+
+ align:start position:0%
+quadrant the way I wrote d by DTM I'm
+ 
+
+ align:start position:0%
+quadrant the way I wrote d by DTM I'm
+missing something
+
+ align:start position:0%
+missing something
+ 
+
+ align:start position:0%
+missing something
+here yeah I need to say from here on
+
+ align:start position:0%
+here yeah I need to say from here on
+ 
+
+ align:start position:0%
+here yeah I need to say from here on
+when you take a derivative which we
+
+ align:start position:0%
+when you take a derivative which we
+ 
+
+ align:start position:0%
+when you take a derivative which we
+still need to completely define I need
+
+ align:start position:0%
+still need to completely define I need
+ 
+
+ align:start position:0%
+still need to completely define I need
+to tell you which frame I'm taking the
+
+ align:start position:0%
+to tell you which frame I'm taking the
+ 
+
+ align:start position:0%
+to tell you which frame I'm taking the
+derivative with respect
+
+ align:start position:0%
+derivative with respect
+ 
+
+ align:start position:0%
+derivative with respect
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I should have written Ro I'm still a
+
+ align:start position:0%
+I I should have written Ro I'm still a
+ 
+
+ align:start position:0%
+I I should have written Ro I'm still a
+little rusty I've been gone for the
+
+ align:start position:0%
+little rusty I've been gone for the
+ 
+
+ align:start position:0%
+little rusty I've been gone for the
+summer so I'm making mistakes but you
+
+ align:start position:0%
+summer so I'm making mistakes but you
+ 
+
+ align:start position:0%
+summer so I'm making mistakes but you
+caught me that's good
+
+ align:start position:0%
+caught me that's good
+ 
+
+ align:start position:0%
+caught me that's good
+yep do you need the second with respect
+
+ align:start position:0%
+yep do you need the second with respect
+ 
+
+ align:start position:0%
+yep do you need the second with respect
+to why do I need the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second this one that's a beautiful
+
+ align:start position:0%
+second this one that's a beautiful
+ 
+
+ align:start position:0%
+second this one that's a beautiful
+question and hold that thought and
+
+ align:start position:0%
+question and hold that thought and
+ 
+
+ align:start position:0%
+question and hold that thought and
+remind me if I don't get back to it
+
+ align:start position:0%
+remind me if I don't get back to it
+ 
+
+ align:start position:0%
+remind me if I don't get back to it
+that's a great question okay but you can
+
+ align:start position:0%
+that's a great question okay but you can
+ 
+
+ align:start position:0%
+that's a great question okay but you can
+see that it doesn't hurt to write it
+
+ align:start position:0%
+see that it doesn't hurt to write it
+ 
+
+ align:start position:0%
+see that it doesn't hurt to write it
+it's complete it turns out that if I
+
+ align:start position:0%
+it's complete it turns out that if I
+ 
+
+ align:start position:0%
+it's complete it turns out that if I
+flip the frames it might look correct
+
+ align:start position:0%
+flip the frames it might look correct
+ 
+
+ align:start position:0%
+flip the frames it might look correct
+but it'll turn out to be wrong okay well
+
+ align:start position:0%
+but it'll turn out to be wrong okay well
+ 
+
+ align:start position:0%
+but it'll turn out to be wrong okay well
+what's your name Sam Sam all right I'll
+
+ align:start position:0%
+what's your name Sam Sam all right I'll
+ 
+
+ align:start position:0%
+what's your name Sam Sam all right I'll
+remember I'll remember that and we'll
+
+ align:start position:0%
+remember I'll remember that and we'll
+ 
+
+ align:start position:0%
+remember I'll remember that and we'll
+come back to that and what is the
+
+ align:start position:0%
+come back to that and what is the
+ 
+
+ align:start position:0%
+come back to that and what is the
+velocity of the spider how do I write
+
+ align:start position:0%
+velocity of the spider how do I write
+ 
+
+ align:start position:0%
+velocity of the spider how do I write
+the velocity of the spider with respect
+
+ align:start position:0%
+the velocity of the spider with respect
+ 
+
+ align:start position:0%
+the velocity of the spider with respect
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+Earth
+
+ align:start position:0%
+Earth
+ 
+
+ align:start position:0%
+Earth
+quick
+
+ align:start position:0%
+quick
+ 
+
+ align:start position:0%
+quick
+e v s is equal to
+
+ align:start position:0%
+e v s is equal to
+ 
+
+ align:start position:0%
+e v s is equal to
+come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on E DT let me raise this of r o
+
+ align:start position:0%
+on E DT let me raise this of r o
+ 
+
+ align:start position:0%
+on E DT let me raise this of r o
+p oh r
+
+ align:start position:0%
+p oh r
+ 
+
+ align:start position:0%
+p oh r
+s which is the same as e d by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT r
+
+ align:start position:0%
+DT r
+ 
+
+ align:start position:0%
+DT r
+o plus e d by
+
+ align:start position:0%
+o plus e d by
+ 
+
+ align:start position:0%
+o plus e d by
+DT r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PS
+
+ align:start position:0%
+PS
+ 
+
+ align:start position:0%
+PS
+right so I've done nothing differently
+
+ align:start position:0%
+right so I've done nothing differently
+ 
+
+ align:start position:0%
+right so I've done nothing differently
+than what Sam did but I'm just doing it
+
+ align:start position:0%
+than what Sam did but I'm just doing it
+ 
+
+ align:start position:0%
+than what Sam did but I'm just doing it
+in more painstaking way that's all
+
+ align:start position:0%
+in more painstaking way that's all
+ 
+
+ align:start position:0%
+in more painstaking way that's all
+nothing
+
+ align:start position:0%
+nothing
+ 
+
+ align:start position:0%
+nothing
+special okay I'm going to raise this up
+
+ align:start position:0%
+special okay I'm going to raise this up
+ 
+
+ align:start position:0%
+special okay I'm going to raise this up
+there and go to go back to these
+
+ align:start position:0%
+there and go to go back to these
+ 
+
+ align:start position:0%
+there and go to go back to these
+boards and finish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up this is very simple stuff so you're
+
+ align:start position:0%
+up this is very simple stuff so you're
+ 
+
+ align:start position:0%
+up this is very simple stuff so you're
+not missing anything if you if you're
+
+ align:start position:0%
+not missing anything if you if you're
+ 
+
+ align:start position:0%
+not missing anything if you if you're
+like what's it doing I know this it's
+
+ align:start position:0%
+like what's it doing I know this it's
+ 
+
+ align:start position:0%
+like what's it doing I know this it's
+okay I'm just doing it
+
+ align:start position:0%
+okay I'm just doing it
+ 
+
+ align:start position:0%
+okay I'm just doing it
+simply nothing
+
+ align:start position:0%
+simply nothing
+ 
+
+ align:start position:0%
+simply nothing
+profound okay so we're picking up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so let's go directly to this
+
+ align:start position:0%
+here okay so let's go directly to this
+ 
+
+ align:start position:0%
+here okay so let's go directly to this
+guy let's analyze this guy I just broke
+
+ align:start position:0%
+guy let's analyze this guy I just broke
+ 
+
+ align:start position:0%
+guy let's analyze this guy I just broke
+it out there for you just to kind of get
+
+ align:start position:0%
+it out there for you just to kind of get
+ 
+
+ align:start position:0%
+it out there for you just to kind of get
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+to walk through it with me I'm going to
+
+ align:start position:0%
+to walk through it with me I'm going to
+ 
+
+ align:start position:0%
+to walk through it with me I'm going to
+expand on that so I'm going to take
+
+ align:start position:0%
+expand on that so I'm going to take
+ 
+
+ align:start position:0%
+expand on that so I'm going to take
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay
+
+ align:start position:0%
+okay okay
+ 
+
+ align:start position:0%
+okay okay
+e d by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT R
+
+ align:start position:0%
+DT R
+ 
+
+ align:start position:0%
+DT R
+oos and what is r oos it's UE E1 sorry R
+
+ align:start position:0%
+oos and what is r oos it's UE E1 sorry R
+ 
+
+ align:start position:0%
+oos and what is r oos it's UE E1 sorry R
+I'm sorry r o p right this is r o it's U
+
+ align:start position:0%
+I'm sorry r o p right this is r o it's U
+ 
+
+ align:start position:0%
+I'm sorry r o p right this is r o it's U
+E1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yes what do I do now
+
+ align:start position:0%
+yes what do I do now
+ 
+
+ align:start position:0%
+yes what do I do now
+yes that's an equal to
+
+ align:start position:0%
+yes that's an equal to
+ 
+
+ align:start position:0%
+yes that's an equal to
+no that was a kind of a stroke I'm
+
+ align:start position:0%
+no that was a kind of a stroke I'm
+ 
+
+ align:start position:0%
+no that was a kind of a stroke I'm
+writing like this it's kind of hard I'm
+
+ align:start position:0%
+writing like this it's kind of hard I'm
+ 
+
+ align:start position:0%
+writing like this it's kind of hard I'm
+trying to say Blackboard but it wasn't a
+
+ align:start position:0%
+trying to say Blackboard but it wasn't a
+ 
+
+ align:start position:0%
+trying to say Blackboard but it wasn't a
+negative okay is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so what do I do now folks I'm
+
+ align:start position:0%
+good so what do I do now folks I'm
+ 
+
+ align:start position:0%
+good so what do I do now folks I'm
+simply trying to calculate this term
+
+ align:start position:0%
+simply trying to calculate this term
+ 
+
+ align:start position:0%
+simply trying to calculate this term
+what do I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do very painstakingly I'm doing very
+
+ align:start position:0%
+do very painstakingly I'm doing very
+ 
+
+ align:start position:0%
+do very painstakingly I'm doing very
+slowly and
+
+ align:start position:0%
+slowly and
+ 
+
+ align:start position:0%
+slowly and
+painstakingly how do I take the
+
+ align:start position:0%
+painstakingly how do I take the
+ 
+
+ align:start position:0%
+painstakingly how do I take the
+derivatives and the vectors what do I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here say it again you want constant so
+
+ align:start position:0%
+here say it again you want constant so
+ 
+
+ align:start position:0%
+here say it again you want constant so
+you can pull those out exactly and
+
+ align:start position:0%
+you can pull those out exactly and
+ 
+
+ align:start position:0%
+you can pull those out exactly and
+shouldn't be constant exactly nailed it
+
+ align:start position:0%
+shouldn't be constant exactly nailed it
+ 
+
+ align:start position:0%
+shouldn't be constant exactly nailed it
+all right so I could think of as two
+
+ align:start position:0%
+all right so I could think of as two
+ 
+
+ align:start position:0%
+all right so I could think of as two
+ways one is I can do it by parts right
+
+ align:start position:0%
+ways one is I can do it by parts right
+ 
+
+ align:start position:0%
+ways one is I can do it by parts right
+so I can go e d by DT U *
+
+ align:start position:0%
+so I can go e d by DT U *
+ 
+
+ align:start position:0%
+so I can go e d by DT U *
+E1 plus u e by DT of E1 what is e d e DT
+
+ align:start position:0%
+E1 plus u e by DT of E1 what is e d e DT
+ 
+
+ align:start position:0%
+E1 plus u e by DT of E1 what is e d e DT
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+E1 zero right it's what a constant is
+
+ align:start position:0%
+E1 zero right it's what a constant is
+ 
+
+ align:start position:0%
+E1 zero right it's what a constant is
+right so this corresponds to Simply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it anyone good with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this yes okay so that's that first term
+
+ align:start position:0%
+this yes okay so that's that first term
+ 
+
+ align:start position:0%
+this yes okay so that's that first term
+we just nailed this guy in excruciating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+detail now let's write this guy out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+what help me out you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what do I do here
+
+ align:start position:0%
+so what do I do here
+ 
+
+ align:start position:0%
+so what do I do here
+folks is F1 constant in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E yes no no right so strictly speaking
+
+ align:start position:0%
+E yes no no right so strictly speaking
+ 
+
+ align:start position:0%
+E yes no no right so strictly speaking
+I'm in a bit of trouble here so what do
+
+ align:start position:0%
+I'm in a bit of trouble here so what do
+ 
+
+ align:start position:0%
+I'm in a bit of trouble here so what do
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do Sam did that actually but he did it
+
+ align:start position:0%
+do Sam did that actually but he did it
+ 
+
+ align:start position:0%
+do Sam did that actually but he did it
+in he was right what should I
+
+ align:start position:0%
+in he was right what should I
+ 
+
+ align:start position:0%
+in he was right what should I
+do yeah yeah exactly so let's write it
+
+ align:start position:0%
+do yeah yeah exactly so let's write it
+ 
+
+ align:start position:0%
+do yeah yeah exactly so let's write it
+in terms of you know our wonderful trans
+
+ align:start position:0%
+in terms of you know our wonderful trans
+ 
+
+ align:start position:0%
+in terms of you know our wonderful trans
+transformation there those
+
+ align:start position:0%
+transformation there those
+ 
+
+ align:start position:0%
+transformation there those
+Transformations are very important by
+
+ align:start position:0%
+Transformations are very important by
+ 
+
+ align:start position:0%
+Transformations are very important by
+the way you need to nail them understand
+
+ align:start position:0%
+the way you need to nail them understand
+ 
+
+ align:start position:0%
+the way you need to nail them understand
+them okay and put them in your
+
+ align:start position:0%
+them okay and put them in your
+ 
+
+ align:start position:0%
+them okay and put them in your
+Sheets if if you know you in the exams
+
+ align:start position:0%
+Sheets if if you know you in the exams
+ 
+
+ align:start position:0%
+Sheets if if you know you in the exams
+we permit your sheets there are
+
+ align:start position:0%
+we permit your sheets there are
+ 
+
+ align:start position:0%
+we permit your sheets there are
+only tools we formulate that are
+
+ align:start position:0%
+only tools we formulate that are
+ 
+
+ align:start position:0%
+only tools we formulate that are
+important and that's that's kind of an
+
+ align:start position:0%
+important and that's that's kind of an
+ 
+
+ align:start position:0%
+important and that's that's kind of an
+important one these Transformations that
+
+ align:start position:0%
+important one these Transformations that
+ 
+
+ align:start position:0%
+important one these Transformations that
+we had down
+
+ align:start position:0%
+we had down
+ 
+
+ align:start position:0%
+we had down
+here those
+
+ align:start position:0%
+here those
+ 
+
+ align:start position:0%
+here those
+guys okay so these you should remember
+
+ align:start position:0%
+guys okay so these you should remember
+ 
+
+ align:start position:0%
+guys okay so these you should remember
+and understand them don't make mistakes
+
+ align:start position:0%
+and understand them don't make mistakes
+ 
+
+ align:start position:0%
+and understand them don't make mistakes
+there because they Cascade and screw
+
+ align:start position:0%
+there because they Cascade and screw
+ 
+
+ align:start position:0%
+there because they Cascade and screw
+everything else up okay so that is equal
+
+ align:start position:0%
+everything else up okay so that is equal
+ 
+
+ align:start position:0%
+everything else up okay so that is equal
+to expand it for me because I can't see
+
+ align:start position:0%
+to expand it for me because I can't see
+ 
+
+ align:start position:0%
+to expand it for me because I can't see
+it from here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry okay I'm going to raise that and
+
+ align:start position:0%
+sorry okay I'm going to raise that and
+ 
+
+ align:start position:0%
+sorry okay I'm going to raise that and
+finish it up here
+
+ align:start position:0%
+finish it up here
+ 
+
+ align:start position:0%
+finish it up here
+we're still calculating velocities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right what did I do
+
+ align:start position:0%
+right what did I do
+ 
+
+ align:start position:0%
+right what did I do
+wrong oh okay I
+
+ align:start position:0%
+wrong oh okay I
+ 
+
+ align:start position:0%
+wrong oh okay I
+thought let's see I can't see it from
+
+ align:start position:0%
+thought let's see I can't see it from
+ 
+
+ align:start position:0%
+thought let's see I can't see it from
+here so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I've F1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah they will backwards thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what do I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+H chain
+
+ align:start position:0%
+H chain
+ 
+
+ align:start position:0%
+H chain
+rule right so I just take the derivative
+
+ align:start position:0%
+rule right so I just take the derivative
+ 
+
+ align:start position:0%
+rule right so I just take the derivative
+that's and this is what it'll come out
+
+ align:start position:0%
+that's and this is what it'll come out
+ 
+
+ align:start position:0%
+that's and this is what it'll come out
+to be it'll
+
+ align:start position:0%
+to be it'll
+ 
+
+ align:start position:0%
+to be it'll
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+um is L constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the Theta
+
+ align:start position:0%
+is the Theta
+ 
+
+ align:start position:0%
+is the Theta
+constant is the E1 constant in
+
+ align:start position:0%
+constant is the E1 constant in
+ 
+
+ align:start position:0%
+constant is the E1 constant in
+E
+
+ align:start position:0%
+E
+ 
+
+ align:start position:0%
+E
+yeah that's going to be in parts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H actually I'll let you guys do it once
+
+ align:start position:0%
+H actually I'll let you guys do it once
+ 
+
+ align:start position:0%
+H actually I'll let you guys do it once
+you do it and read it out to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me do it in Parts like I was trying to
+
+ align:start position:0%
+me do it in Parts like I was trying to
+ 
+
+ align:start position:0%
+me do it in Parts like I was trying to
+do it there I don't want to just write
+
+ align:start position:0%
+do it there I don't want to just write
+ 
+
+ align:start position:0%
+do it there I don't want to just write
+it out and you know I want you to read
+
+ align:start position:0%
+it out and you know I want you to read
+ 
+
+ align:start position:0%
+it out and you know I want you to read
+it out to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me take this
+
+ align:start position:0%
+me take this
+ 
+
+ align:start position:0%
+me take this
+term Right Use the chain Rule and tell
+
+ align:start position:0%
+term Right Use the chain Rule and tell
+ 
+
+ align:start position:0%
+term Right Use the chain Rule and tell
+me what it's going to come out to be yes
+
+ align:start position:0%
+me what it's going to come out to be yes
+ 
+
+ align:start position:0%
+me what it's going to come out to be yes
+um E1 what's your name Amanda Amanda
+
+ align:start position:0%
+um E1 what's your name Amanda Amanda
+ 
+
+ align:start position:0%
+um E1 what's your name Amanda Amanda
+yeah yeah E1 uh in
+
+ align:start position:0%
+yeah yeah E1 uh in
+ 
+
+ align:start position:0%
+yeah yeah E1 uh in
+parentheses times uh L do cosine Theta
+
+ align:start position:0%
+parentheses times uh L do cosine Theta
+ 
+
+ align:start position:0%
+parentheses times uh L do cosine Theta
+minus L sin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta and then nothing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else L sin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta that's it yeah is there a theod
+
+ align:start position:0%
+Theta that's it yeah is there a theod
+ 
+
+ align:start position:0%
+Theta that's it yeah is there a theod
+DOT yes yes
+
+ align:start position:0%
+DOT yes yes
+ 
+
+ align:start position:0%
+DOT yes yes
+very good and then um plus
+
+ align:start position:0%
+very good and then um plus
+ 
+
+ align:start position:0%
+very good and then um plus
+E2 L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DOA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L make
+
+ align:start position:0%
+L make
+ 
+
+ align:start position:0%
+L make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+right so here's the trick you know when
+
+ align:start position:0%
+right so here's the trick you know when
+ 
+
+ align:start position:0%
+right so here's the trick you know when
+I write vectors like in this way it's
+
+ align:start position:0%
+I write vectors like in this way it's
+ 
+
+ align:start position:0%
+I write vectors like in this way it's
+perfectly reasonable to do this E1 E2
+
+ align:start position:0%
+perfectly reasonable to do this E1 E2
+ 
+
+ align:start position:0%
+perfectly reasonable to do this E1 E2
+and then I put an F1 here right and I
+
+ align:start position:0%
+and then I put an F1 here right and I
+ 
+
+ align:start position:0%
+and then I put an F1 here right and I
+said should make you feel queasy it
+
+ align:start position:0%
+said should make you feel queasy it
+ 
+
+ align:start position:0%
+said should make you feel queasy it
+shouldn't really that's okay it's okay
+
+ align:start position:0%
+shouldn't really that's okay it's okay
+ 
+
+ align:start position:0%
+shouldn't really that's okay it's okay
+but when you take the derivative of this
+
+ align:start position:0%
+but when you take the derivative of this
+ 
+
+ align:start position:0%
+but when you take the derivative of this
+guy with respect to a frame like e the
+
+ align:start position:0%
+guy with respect to a frame like e the
+ 
+
+ align:start position:0%
+guy with respect to a frame like e the
+first and cleanest way to do it is to
+
+ align:start position:0%
+first and cleanest way to do it is to
+ 
+
+ align:start position:0%
+first and cleanest way to do it is to
+downconvert all the uh kind of
+
+ align:start position:0%
+downconvert all the uh kind of
+ 
+
+ align:start position:0%
+downconvert all the uh kind of
+contaminating terms which are not E1 E2
+
+ align:start position:0%
+contaminating terms which are not E1 E2
+ 
+
+ align:start position:0%
+contaminating terms which are not E1 E2
+bases down to E1 E2 bases get it and
+
+ align:start position:0%
+bases down to E1 E2 bases get it and
+ 
+
+ align:start position:0%
+bases down to E1 E2 bases get it and
+then take the derivative because even in
+
+ align:start position:0%
+then take the derivative because even in
+ 
+
+ align:start position:0%
+then take the derivative because even in
+E2 bases the basis vectors are constant
+
+ align:start position:0%
+E2 bases the basis vectors are constant
+ 
+
+ align:start position:0%
+E2 bases the basis vectors are constant
+in E if you just do this you know if you
+
+ align:start position:0%
+in E if you just do this you know if you
+ 
+
+ align:start position:0%
+in E if you just do this you know if you
+take the derivative of F1 by itself then
+
+ align:start position:0%
+take the derivative of F1 by itself then
+ 
+
+ align:start position:0%
+take the derivative of F1 by itself then
+You' figure out what it is and you'll
+
+ align:start position:0%
+You' figure out what it is and you'll
+ 
+
+ align:start position:0%
+You' figure out what it is and you'll
+end up converting anyway get it so the
+
+ align:start position:0%
+end up converting anyway get it so the
+ 
+
+ align:start position:0%
+end up converting anyway get it so the
+bottom line is that we've just
+
+ align:start position:0%
+bottom line is that we've just
+ 
+
+ align:start position:0%
+bottom line is that we've just
+computed that R PS is this so the
+
+ align:start position:0%
+computed that R PS is this so the
+ 
+
+ align:start position:0%
+computed that R PS is this so the
+velocity of the spider when you put it
+
+ align:start position:0%
+velocity of the spider when you put it
+ 
+
+ align:start position:0%
+velocity of the spider when you put it
+all together with respect to the
+
+ align:start position:0%
+all together with respect to the
+ 
+
+ align:start position:0%
+all together with respect to the
+Earth right which we write
+
+ align:start position:0%
+Earth right which we write
+ 
+
+ align:start position:0%
+Earth right which we write
+as e spider with respect to the Earth is
+
+ align:start position:0%
+as e spider with respect to the Earth is
+ 
+
+ align:start position:0%
+as e spider with respect to the Earth is
+equal to now add it all up and tell me
+
+ align:start position:0%
+equal to now add it all up and tell me
+ 
+
+ align:start position:0%
+equal to now add it all up and tell me
+please
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what yeah that's d by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT right okay what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this what is the velocity of the spider
+
+ align:start position:0%
+this what is the velocity of the spider
+ 
+
+ align:start position:0%
+this what is the velocity of the spider
+with respect to the frame e the Earth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that my friends is the velocity of
+
+ align:start position:0%
+and that my friends is the velocity of
+ 
+
+ align:start position:0%
+and that my friends is the velocity of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+spider with respect to the Earth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and that's the cleanest way to do
+
+ align:start position:0%
+okay and that's the cleanest way to do
+ 
+
+ align:start position:0%
+okay and that's the cleanest way to do
+it and we use no magic right we use
+
+ align:start position:0%
+it and we use no magic right we use
+ 
+
+ align:start position:0%
+it and we use no magic right we use
+frames and a very basic geometric
+
+ align:start position:0%
+frames and a very basic geometric
+ 
+
+ align:start position:0%
+frames and a very basic geometric
+transformation between frames and we
+
+ align:start position:0%
+transformation between frames and we
+ 
+
+ align:start position:0%
+transformation between frames and we
+calculate the
+
+ align:start position:0%
+calculate the
+ 
+
+ align:start position:0%
+calculate the
+velocity that's it there's no magic to
+
+ align:start position:0%
+velocity that's it there's no magic to
+ 
+
+ align:start position:0%
+velocity that's it there's no magic to
+it it's painful and when we get an
+
+ align:start position:0%
+it it's painful and when we get an
+ 
+
+ align:start position:0%
+it it's painful and when we get an
+acceleration it's going to get even more
+
+ align:start position:0%
+acceleration it's going to get even more
+ 
+
+ align:start position:0%
+acceleration it's going to get even more
+painful trust me we're going to
+
+ align:start position:0%
+painful trust me we're going to
+ 
+
+ align:start position:0%
+painful trust me we're going to
+calculate the acceleration now right but
+
+ align:start position:0%
+calculate the acceleration now right but
+ 
+
+ align:start position:0%
+calculate the acceleration now right but
+that's what it
+
+ align:start position:0%
+that's what it
+ 
+
+ align:start position:0%
+that's what it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+so any questions about this and if if
+
+ align:start position:0%
+so any questions about this and if if
+ 
+
+ align:start position:0%
+so any questions about this and if if
+not we'll set up the next Point any
+
+ align:start position:0%
+not we'll set up the next Point any
+ 
+
+ align:start position:0%
+not we'll set up the next Point any
+questions I insist on at least one
+
+ align:start position:0%
+questions I insist on at least one
+ 
+
+ align:start position:0%
+questions I insist on at least one
+question at this point I'm out of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+breath anybody totally get it okay then
+
+ align:start position:0%
+breath anybody totally get it okay then
+ 
+
+ align:start position:0%
+breath anybody totally get it okay then
+I have a question for you how do you
+
+ align:start position:0%
+I have a question for you how do you
+ 
+
+ align:start position:0%
+I have a question for you how do you
+calculate the acceleration of the Spider
+
+ align:start position:0%
+calculate the acceleration of the Spider
+ 
+
+ align:start position:0%
+calculate the acceleration of the Spider
+by the way actually let's take a minute
+
+ align:start position:0%
+by the way actually let's take a minute
+ 
+
+ align:start position:0%
+by the way actually let's take a minute
+here and just appre appreciate what
+
+ align:start position:0%
+here and just appre appreciate what
+ 
+
+ align:start position:0%
+here and just appre appreciate what
+we've done
+
+ align:start position:0%
+we've done
+ 
+
+ align:start position:0%
+we've done
+here if this if the uh frisbee were not
+
+ align:start position:0%
+here if this if the uh frisbee were not
+ 
+
+ align:start position:0%
+here if this if the uh frisbee were not
+translating okay which terms would
+
+ align:start position:0%
+translating okay which terms would
+ 
+
+ align:start position:0%
+translating okay which terms would
+vanish so let's say I was spinning the
+
+ align:start position:0%
+vanish so let's say I was spinning the
+ 
+
+ align:start position:0%
+vanish so let's say I was spinning the
+frisbeer on my finger
+
+ align:start position:0%
+frisbeer on my finger
+ 
+
+ align:start position:0%
+frisbeer on my finger
+right this would go to
+
+ align:start position:0%
+right this would go to
+ 
+
+ align:start position:0%
+right this would go to
+zero and this would go to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero okay and you know what this turn
+
+ align:start position:0%
+zero okay and you know what this turn
+ 
+
+ align:start position:0%
+zero okay and you know what this turn
+the rest of it will turn
+
+ align:start position:0%
+the rest of it will turn
+ 
+
+ align:start position:0%
+the rest of it will turn
+into it'll be
+
+ align:start position:0%
+into it'll be
+ 
+
+ align:start position:0%
+into it'll be
+it'll be some sort of theta. L term
+
+ align:start position:0%
+it'll be some sort of theta. L term
+ 
+
+ align:start position:0%
+it'll be some sort of theta. L term
+theta. L does it make sense theta. L
+
+ align:start position:0%
+theta. L does it make sense theta. L
+ 
+
+ align:start position:0%
+theta. L does it make sense theta. L
+right this is the vector equivalent of
+
+ align:start position:0%
+right this is the vector equivalent of
+ 
+
+ align:start position:0%
+right this is the vector equivalent of
+theta. L get
+
+ align:start position:0%
+theta. L get
+ 
+
+ align:start position:0%
+theta. L get
+it right it's actually Omega cross R
+
+ align:start position:0%
+it right it's actually Omega cross R
+ 
+
+ align:start position:0%
+it right it's actually Omega cross R
+that's where it'll come down to be Omega
+
+ align:start position:0%
+that's where it'll come down to be Omega
+ 
+
+ align:start position:0%
+that's where it'll come down to be Omega
+cross the L Vector right we haven't done
+
+ align:start position:0%
+cross the L Vector right we haven't done
+ 
+
+ align:start position:0%
+cross the L Vector right we haven't done
+any cross products here by the way but
+
+ align:start position:0%
+any cross products here by the way but
+ 
+
+ align:start position:0%
+any cross products here by the way but
+you can see how it came out right does
+
+ align:start position:0%
+you can see how it came out right does
+ 
+
+ align:start position:0%
+you can see how it came out right does
+anyone understand what I just said to
+
+ align:start position:0%
+anyone understand what I just said to
+ 
+
+ align:start position:0%
+anyone understand what I just said to
+you right okay what if the if the SP if
+
+ align:start position:0%
+you right okay what if the if the SP if
+ 
+
+ align:start position:0%
+you right okay what if the if the SP if
+the spider were the center the Frisbee
+
+ align:start position:0%
+the spider were the center the Frisbee
+ 
+
+ align:start position:0%
+the spider were the center the Frisbee
+and not running
+
+ align:start position:0%
+and not running
+ 
+
+ align:start position:0%
+and not running
+away which terms would
+
+ align:start position:0%
+away which terms would
+ 
+
+ align:start position:0%
+away which terms would
+vanish l dot would go away what
+
+ align:start position:0%
+vanish l dot would go away what
+ 
+
+ align:start position:0%
+vanish l dot would go away what
+else and L would go
+
+ align:start position:0%
+else and L would go
+ 
+
+ align:start position:0%
+else and L would go
+zero right so what would the velocity be
+
+ align:start position:0%
+zero right so what would the velocity be
+ 
+
+ align:start position:0%
+zero right so what would the velocity be
+simply simply translation makes sense
+
+ align:start position:0%
+simply simply translation makes sense
+ 
+
+ align:start position:0%
+simply simply translation makes sense
+right right so this is a composition
+
+ align:start position:0%
+right right so this is a composition
+ 
+
+ align:start position:0%
+right right so this is a composition
+it's an addition of the translation
+
+ align:start position:0%
+it's an addition of the translation
+ 
+
+ align:start position:0%
+it's an addition of the translation
+velocity and the kind of the rotational
+
+ align:start position:0%
+velocity and the kind of the rotational
+ 
+
+ align:start position:0%
+velocity and the kind of the rotational
+aspect right so you know from basic
+
+ align:start position:0%
+aspect right so you know from basic
+ 
+
+ align:start position:0%
+aspect right so you know from basic
+physics you kind of see makes sense
+
+ align:start position:0%
+physics you kind of see makes sense
+ 
+
+ align:start position:0%
+physics you kind of see makes sense
+right yes okay now what we're going to
+
+ align:start position:0%
+right yes okay now what we're going to
+ 
+
+ align:start position:0%
+right yes okay now what we're going to
+do is calculate the
+
+ align:start position:0%
+do is calculate the
+ 
+
+ align:start position:0%
+do is calculate the
+acceleration and now we get into No
+
+ align:start position:0%
+acceleration and now we get into No
+ 
+
+ align:start position:0%
+acceleration and now we get into No
+Nonsense you know Vector derivatives
+
+ align:start position:0%
+Nonsense you know Vector derivatives
+ 
+
+ align:start position:0%
+Nonsense you know Vector derivatives
+here but there's no magic either it's
+
+ align:start position:0%
+here but there's no magic either it's
+ 
+
+ align:start position:0%
+here but there's no magic either it's
+just painstaking stuff we'll introduce
+
+ align:start position:0%
+just painstaking stuff we'll introduce
+ 
+
+ align:start position:0%
+just painstaking stuff we'll introduce
+the subtle stuff in a minute actually in
+
+ align:start position:0%
+the subtle stuff in a minute actually in
+ 
+
+ align:start position:0%
+the subtle stuff in a minute actually in
+the next class so how do you calculate
+
+ align:start position:0%
+the next class so how do you calculate
+ 
+
+ align:start position:0%
+the next class so how do you calculate
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration yep that's
+
+ align:start position:0%
+acceleration yep that's
+ 
+
+ align:start position:0%
+acceleration yep that's
+it no magic to it just take the
+
+ align:start position:0%
+it no magic to it just take the
+ 
+
+ align:start position:0%
+it no magic to it just take the
+derivative of the whole thing so let's
+
+ align:start position:0%
+derivative of the whole thing so let's
+ 
+
+ align:start position:0%
+derivative of the whole thing so let's
+do that because you know we right we
+
+ align:start position:0%
+do that because you know we right we
+ 
+
+ align:start position:0%
+do that because you know we right we
+don't do kind of stuff we do it all
+
+ align:start position:0%
+don't do kind of stuff we do it all
+ 
+
+ align:start position:0%
+don't do kind of stuff we do it all
+right let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so let's see e acceleration a of
+
+ align:start position:0%
+it so let's see e acceleration a of
+ 
+
+ align:start position:0%
+it so let's see e acceleration a of
+spider s is equal to D by DT I'm sorry
+
+ align:start position:0%
+spider s is equal to D by DT I'm sorry
+ 
+
+ align:start position:0%
+spider s is equal to D by DT I'm sorry
+I'm writing it small here of e velocity
+
+ align:start position:0%
+I'm writing it small here of e velocity
+ 
+
+ align:start position:0%
+I'm writing it small here of e velocity
+s is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to okay let's start at this term what
+
+ align:start position:0%
+to okay let's start at this term what
+ 
+
+ align:start position:0%
+to okay let's start at this term what
+does this term
+
+ align:start position:0%
+does this term
+ 
+
+ align:start position:0%
+does this term
+become so let's put an E1 here because
+
+ align:start position:0%
+become so let's put an E1 here because
+ 
+
+ align:start position:0%
+become so let's put an E1 here because
+E1 is constant u double dot yeah keep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going keep going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+keep going come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+huh did we miss a
+
+ align:start position:0%
+huh did we miss a
+ 
+
+ align:start position:0%
+huh did we miss a
+term is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct hold on that that should give us
+
+ align:start position:0%
+correct hold on that that should give us
+ 
+
+ align:start position:0%
+correct hold on that that should give us
+three terms right so it should give us
+
+ align:start position:0%
+three terms right so it should give us
+ 
+
+ align:start position:0%
+three terms right so it should give us
+the lble do term right the l dot
+
+ align:start position:0%
+the lble do term right the l dot
+ 
+
+ align:start position:0%
+the lble do term right the l dot
+um oh are we coming to this one now two
+
+ align:start position:0%
+um oh are we coming to this one now two
+ 
+
+ align:start position:0%
+um oh are we coming to this one now two
+terms I'm sorry okay yeah so go ahead
+
+ align:start position:0%
+terms I'm sorry okay yeah so go ahead
+ 
+
+ align:start position:0%
+terms I'm sorry okay yeah so go ahead
+sorry but I interrupted you go ahead
+
+ align:start position:0%
+sorry but I interrupted you go ahead
+ 
+
+ align:start position:0%
+sorry but I interrupted you go ahead
+yeah someone was reading out the next
+
+ align:start position:0%
+yeah someone was reading out the next
+ 
+
+ align:start position:0%
+yeah someone was reading out the next
+term to me go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh-huh see I don't have my notes in
+
+ align:start position:0%
+uh-huh see I don't have my notes in
+ 
+
+ align:start position:0%
+uh-huh see I don't have my notes in
+front of me I'm right next to the board
+
+ align:start position:0%
+front of me I'm right next to the board
+ 
+
+ align:start position:0%
+front of me I'm right next to the board
+so you need to help me out here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay is everyone in agreement with
+
+ align:start position:0%
+yeah okay is everyone in agreement with
+ 
+
+ align:start position:0%
+yeah okay is everyone in agreement with
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+huh
+
+ align:start position:0%
+huh
+ 
+
+ align:start position:0%
+huh
+okay everyone agreement with this you
+
+ align:start position:0%
+okay everyone agreement with this you
+ 
+
+ align:start position:0%
+okay everyone agreement with this you
+did it I didn't do it okay that's the
+
+ align:start position:0%
+did it I didn't do it okay that's the
+ 
+
+ align:start position:0%
+did it I didn't do it okay that's the
+first term
+
+ align:start position:0%
+first term
+ 
+
+ align:start position:0%
+first term
+right plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E2
+
+ align:start position:0%
+E2
+ 
+
+ align:start position:0%
+E2
+anybody someone else someone back
+
+ align:start position:0%
+anybody someone else someone back
+ 
+
+ align:start position:0%
+anybody someone else someone back
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+dot sin Theta okay try and keep it in
+
+ align:start position:0%
+dot sin Theta okay try and keep it in
+ 
+
+ align:start position:0%
+dot sin Theta okay try and keep it in
+the same pattern okay because I'm trying
+
+ align:start position:0%
+the same pattern okay because I'm trying
+ 
+
+ align:start position:0%
+the same pattern okay because I'm trying
+to pull out a pattern for you here yep
+
+ align:start position:0%
+to pull out a pattern for you here yep
+ 
+
+ align:start position:0%
+to pull out a pattern for you here yep
+keep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+uh-huh and then plus or minus next minus
+
+ align:start position:0%
+uh-huh and then plus or minus next minus
+ 
+
+ align:start position:0%
+uh-huh and then plus or minus next minus
+the double dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus okay Theta double
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot okay two more terms nearly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there plus Theta do L do cosine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta no magic was just pure hard work
+
+ align:start position:0%
+Theta no magic was just pure hard work
+ 
+
+ align:start position:0%
+Theta no magic was just pure hard work
+just took the derivative of that and we
+
+ align:start position:0%
+just took the derivative of that and we
+ 
+
+ align:start position:0%
+just took the derivative of that and we
+calculated the acceleration of the
+
+ align:start position:0%
+calculated the acceleration of the
+ 
+
+ align:start position:0%
+calculated the acceleration of the
+spider okay and what you just did
+
+ align:start position:0%
+spider okay and what you just did
+ 
+
+ align:start position:0%
+spider okay and what you just did
+encapsulates 300 years of physics
+
+ align:start position:0%
+encapsulates 300 years of physics
+ 
+
+ align:start position:0%
+encapsulates 300 years of physics
+believe it or not and there are famous
+
+ align:start position:0%
+believe it or not and there are famous
+ 
+
+ align:start position:0%
+believe it or not and there are famous
+names attached to some of these terms
+
+ align:start position:0%
+names attached to some of these terms
+ 
+
+ align:start position:0%
+names attached to some of these terms
+and I'm going to give you those names
+
+ align:start position:0%
+and I'm going to give you those names
+ 
+
+ align:start position:0%
+and I'm going to give you those names
+now and I said it to the last class and
+
+ align:start position:0%
+now and I said it to the last class and
+ 
+
+ align:start position:0%
+now and I said it to the last class and
+I make the pr same promise to you guys
+
+ align:start position:0%
+I make the pr same promise to you guys
+ 
+
+ align:start position:0%
+I make the pr same promise to you guys
+if he came up with a term here that the
+
+ align:start position:0%
+if he came up with a term here that the
+ 
+
+ align:start position:0%
+if he came up with a term here that the
+other physicist have missed we'll I'll
+
+ align:start position:0%
+other physicist have missed we'll I'll
+ 
+
+ align:start position:0%
+other physicist have missed we'll I'll
+name it after the guy the person in the
+
+ align:start position:0%
+name it after the guy the person in the
+ 
+
+ align:start position:0%
+name it after the guy the person in the
+class who came up with this right so for
+
+ align:start position:0%
+class who came up with this right so for
+ 
+
+ align:start position:0%
+class who came up with this right so for
+example some of these terms are called
+
+ align:start position:0%
+example some of these terms are called
+ 
+
+ align:start position:0%
+example some of these terms are called
+cholis terms so we'll call it the Rachel
+
+ align:start position:0%
+cholis terms so we'll call it the Rachel
+ 
+
+ align:start position:0%
+cholis terms so we'll call it the Rachel
+term if you came up with that okay all
+
+ align:start position:0%
+term if you came up with that okay all
+ 
+
+ align:start position:0%
+term if you came up with that okay all
+right right so let's examine this so
+
+ align:start position:0%
+right right so let's examine this so
+ 
+
+ align:start position:0%
+right right so let's examine this so
+this is the vector form of it right what
+
+ align:start position:0%
+this is the vector form of it right what
+ 
+
+ align:start position:0%
+this is the vector form of it right what
+is this kind of in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+English translation acceleration right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+translation
+
+ align:start position:0%
+translation
+ 
+
+ align:start position:0%
+translation
+okay of the Frisbee center of the
+
+ align:start position:0%
+okay of the Frisbee center of the
+ 
+
+ align:start position:0%
+okay of the Frisbee center of the
+Frisbee right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is um
+
+ align:start position:0%
+what is um
+ 
+
+ align:start position:0%
+what is um
+this capture kind of in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+English
+
+ align:start position:0%
+English
+ 
+
+ align:start position:0%
+English
+of with respect
+
+ align:start position:0%
+of with respect
+ 
+
+ align:start position:0%
+of with respect
+to yeah yeah in English that's kind of
+
+ align:start position:0%
+to yeah yeah in English that's kind of
+ 
+
+ align:start position:0%
+to yeah yeah in English that's kind of
+what this is this is a spider kind of
+
+ align:start position:0%
+what this is this is a spider kind of
+ 
+
+ align:start position:0%
+what this is this is a spider kind of
+right there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spider spider term okay these are kind
+
+ align:start position:0%
+spider spider term okay these are kind
+ 
+
+ align:start position:0%
+spider spider term okay these are kind
+of informal terms but I'll formalize
+
+ align:start position:0%
+of informal terms but I'll formalize
+ 
+
+ align:start position:0%
+of informal terms but I'll formalize
+them later
+
+ align:start position:0%
+them later
+ 
+
+ align:start position:0%
+them later
+on spider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+translation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um anyone recognize this term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and that's called
+
+ align:start position:0%
+yeah and that's called
+ 
+
+ align:start position:0%
+yeah and that's called
+the centripetal acceleration get it
+
+ align:start position:0%
+the centripetal acceleration get it
+ 
+
+ align:start position:0%
+the centripetal acceleration get it
+remember Theta do squ make ring a bell
+
+ align:start position:0%
+remember Theta do squ make ring a bell
+ 
+
+ align:start position:0%
+remember Theta do squ make ring a bell
+Theta dot squ right spin something kind
+
+ align:start position:0%
+Theta dot squ right spin something kind
+ 
+
+ align:start position:0%
+Theta dot squ right spin something kind
+of accelerates inwards right L Theta do
+
+ align:start position:0%
+of accelerates inwards right L Theta do
+ 
+
+ align:start position:0%
+of accelerates inwards right L Theta do
+squ hey there's an L Theta do squ sin
+
+ align:start position:0%
+squ hey there's an L Theta do squ sin
+ 
+
+ align:start position:0%
+squ hey there's an L Theta do squ sin
+Theta cos cosine Theta so that's the
+
+ align:start position:0%
+Theta cos cosine Theta so that's the
+ 
+
+ align:start position:0%
+Theta cos cosine Theta so that's the
+vector form of it right right so that's
+
+ align:start position:0%
+vector form of it right right so that's
+ 
+
+ align:start position:0%
+vector form of it right right so that's
+centripedal right it's named after a
+
+ align:start position:0%
+centripedal right it's named after a
+ 
+
+ align:start position:0%
+centripedal right it's named after a
+famous French engineer but the name is
+
+ align:start position:0%
+famous French engineer but the name is
+ 
+
+ align:start position:0%
+famous French engineer but the name is
+centripedal I'm kidding centripedal
+
+ align:start position:0%
+centripedal I'm kidding centripedal
+ 
+
+ align:start position:0%
+centripedal I'm kidding centripedal
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay anyone does this term kind of make
+
+ align:start position:0%
+okay anyone does this term kind of make
+ 
+
+ align:start position:0%
+okay anyone does this term kind of make
+sense what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah is the angular acceleration
+
+ align:start position:0%
+that yeah is the angular acceleration
+ 
+
+ align:start position:0%
+that yeah is the angular acceleration
+multipied by the force arm right but
+
+ align:start position:0%
+multipied by the force arm right but
+ 
+
+ align:start position:0%
+multipied by the force arm right but
+again written in vector vector form
+
+ align:start position:0%
+again written in vector vector form
+ 
+
+ align:start position:0%
+again written in vector vector form
+right does that make
+
+ align:start position:0%
+right does that make
+ 
+
+ align:start position:0%
+right does that make
+sense and that is actually for some
+
+ align:start position:0%
+sense and that is actually for some
+ 
+
+ align:start position:0%
+sense and that is actually for some
+reason coil the oiler
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration and then we have two guys
+
+ align:start position:0%
+acceleration and then we have two guys
+ 
+
+ align:start position:0%
+acceleration and then we have two guys
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+out anyone remember what those are
+
+ align:start position:0%
+out anyone remember what those are
+ 
+
+ align:start position:0%
+out anyone remember what those are
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+yep cholis here's the deal they're just
+
+ align:start position:0%
+yep cholis here's the deal they're just
+ 
+
+ align:start position:0%
+yep cholis here's the deal they're just
+two straight terms if you do the math
+
+ align:start position:0%
+two straight terms if you do the math
+ 
+
+ align:start position:0%
+two straight terms if you do the math
+right they show up we did the math right
+
+ align:start position:0%
+right they show up we did the math right
+ 
+
+ align:start position:0%
+right they show up we did the math right
+they showed up no
+
+ align:start position:0%
+they showed up no
+ 
+
+ align:start position:0%
+they showed up no
+surprise right now actually the funny
+
+ align:start position:0%
+surprise right now actually the funny
+ 
+
+ align:start position:0%
+surprise right now actually the funny
+thing is you see it's minus L do theta
+
+ align:start position:0%
+thing is you see it's minus L do theta
+ 
+
+ align:start position:0%
+thing is you see it's minus L do theta
+dot it's the same term twice right so I
+
+ align:start position:0%
+dot it's the same term twice right so I
+ 
+
+ align:start position:0%
+dot it's the same term twice right so I
+can actually make this
+
+ align:start position:0%
+can actually make this
+ 
+
+ align:start position:0%
+can actually make this
+two right and remove this and the same
+
+ align:start position:0%
+two right and remove this and the same
+ 
+
+ align:start position:0%
+two right and remove this and the same
+term twice here I can put a two here and
+
+ align:start position:0%
+term twice here I can put a two here and
+ 
+
+ align:start position:0%
+term twice here I can put a two here and
+remove this the same thing I just
+
+ align:start position:0%
+remove this the same thing I just
+ 
+
+ align:start position:0%
+remove this the same thing I just
+consolidating terms and there was this
+
+ align:start position:0%
+consolidating terms and there was this
+ 
+
+ align:start position:0%
+consolidating terms and there was this
+French engineer by the name of
+
+ align:start position:0%
+French engineer by the name of
+ 
+
+ align:start position:0%
+French engineer by the name of
+coris he found I think the history is
+
+ align:start position:0%
+coris he found I think the history is
+ 
+
+ align:start position:0%
+coris he found I think the history is
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+when you shoot a projectile from a ship
+
+ align:start position:0%
+when you shoot a projectile from a ship
+ 
+
+ align:start position:0%
+when you shoot a projectile from a ship
+or from any vehicle but usually ships in
+
+ align:start position:0%
+or from any vehicle but usually ships in
+ 
+
+ align:start position:0%
+or from any vehicle but usually ships in
+the northern hemisphere they I think
+
+ align:start position:0%
+the northern hemisphere they I think
+ 
+
+ align:start position:0%
+the northern hemisphere they I think
+Gunners found that they were missing to
+
+ align:start position:0%
+Gunners found that they were missing to
+ 
+
+ align:start position:0%
+Gunners found that they were missing to
+one side and there to kind of compensate
+
+ align:start position:0%
+one side and there to kind of compensate
+ 
+
+ align:start position:0%
+one side and there to kind of compensate
+and once the Gunners perfected the skill
+
+ align:start position:0%
+and once the Gunners perfected the skill
+ 
+
+ align:start position:0%
+and once the Gunners perfected the skill
+and they cross the Equator they found
+
+ align:start position:0%
+and they cross the Equator they found
+ 
+
+ align:start position:0%
+and they cross the Equator they found
+that their skill was useless because
+
+ align:start position:0%
+that their skill was useless because
+ 
+
+ align:start position:0%
+that their skill was useless because
+they would go to the other side and the
+
+ align:start position:0%
+they would go to the other side and the
+ 
+
+ align:start position:0%
+they would go to the other side and the
+straight term is referred to as the
+
+ align:start position:0%
+straight term is referred to as the
+ 
+
+ align:start position:0%
+straight term is referred to as the
+coris
+
+ align:start position:0%
+coris
+ 
+
+ align:start position:0%
+coris
+acceleration okay this is also the
+
+ align:start position:0%
+acceleration okay this is also the
+ 
+
+ align:start position:0%
+acceleration okay this is also the
+reason hurricanes spin one way in the
+
+ align:start position:0%
+reason hurricanes spin one way in the
+ 
+
+ align:start position:0%
+reason hurricanes spin one way in the
+northern Hemisphere and another way in
+
+ align:start position:0%
+northern Hemisphere and another way in
+ 
+
+ align:start position:0%
+northern Hemisphere and another way in
+the southern hemisphere we'll talk about
+
+ align:start position:0%
+the southern hemisphere we'll talk about
+ 
+
+ align:start position:0%
+the southern hemisphere we'll talk about
+all this the beginning of the next class
+
+ align:start position:0%
+all this the beginning of the next class
+ 
+
+ align:start position:0%
+all this the beginning of the next class
+but what you've just done with
+
+ align:start position:0%
+but what you've just done with
+ 
+
+ align:start position:0%
+but what you've just done with
+me is from Ground Zero using the most
+
+ align:start position:0%
+me is from Ground Zero using the most
+ 
+
+ align:start position:0%
+me is from Ground Zero using the most
+basic basic geometry you have derived
+
+ align:start position:0%
+basic basic geometry you have derived
+ 
+
+ align:start position:0%
+basic basic geometry you have derived
+terms that go back 300 years or took 300
+
+ align:start position:0%
+terms that go back 300 years or took 300
+ 
+
+ align:start position:0%
+terms that go back 300 years or took 300
+years to derive so this
+
+ align:start position:0%
+years to derive so this
+ 
+
+ align:start position:0%
+years to derive so this
+term this collection of terms is called
+
+ align:start position:0%
+term this collection of terms is called
+ 
+
+ align:start position:0%
+term this collection of terms is called
+coris and this is the most general
+
+ align:start position:0%
+coris and this is the most general
+ 
+
+ align:start position:0%
+coris and this is the most general
+statement of the calculation of
+
+ align:start position:0%
+statement of the calculation of
+ 
+
+ align:start position:0%
+statement of the calculation of
+acceleration that you will need in
+
+ align:start position:0%
+acceleration that you will need in
+ 
+
+ align:start position:0%
+acceleration that you will need in
+kinematics to
+
+ align:start position:0%
+kinematics to
+ 
+
+ align:start position:0%
+kinematics to
+compute the motion of complex systems
+
+ align:start position:0%
+compute the motion of complex systems
+ 
+
+ align:start position:0%
+compute the motion of complex systems
+and now if you have now look we can we
+
+ align:start position:0%
+and now if you have now look we can we
+ 
+
+ align:start position:0%
+and now if you have now look we can we
+can do frame e to F right let's say
+
+ align:start position:0%
+can do frame e to F right let's say
+ 
+
+ align:start position:0%
+can do frame e to F right let's say
+those let's say the Earth spinning and
+
+ align:start position:0%
+those let's say the Earth spinning and
+ 
+
+ align:start position:0%
+those let's say the Earth spinning and
+there's someone watching us from other
+
+ align:start position:0%
+there's someone watching us from other
+ 
+
+ align:start position:0%
+there's someone watching us from other
+another planet well no problem you can
+
+ align:start position:0%
+another planet well no problem you can
+ 
+
+ align:start position:0%
+another planet well no problem you can
+kind of compose it and you can you know
+
+ align:start position:0%
+kind of compose it and you can you know
+ 
+
+ align:start position:0%
+kind of compose it and you can you know
+compute the acceleration with respect to
+
+ align:start position:0%
+compute the acceleration with respect to
+ 
+
+ align:start position:0%
+compute the acceleration with respect to
+that planet the math will get hairy but
+
+ align:start position:0%
+that planet the math will get hairy but
+ 
+
+ align:start position:0%
+that planet the math will get hairy but
+there's nothing profound get it
+
+ align:start position:0%
+there's nothing profound get it
+ 
+
+ align:start position:0%
+there's nothing profound get it
+questions all right we'll see you next
+
+ align:start position:0%
+questions all right we'll see you next
+ 
+
+ align:start position:0%
+questions all right we'll see you next
+class
\ No newline at end of file
diff --git a/vyShGGc2X38.txt b/vyShGGc2X38.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7449f5658b6a719c894554a7b650af347429a128
--- /dev/null
+++ b/vyShGGc2X38.txt
@@ -0,0 +1,203 @@
+align:start position:0%
+ 
+hi everybody our first thing that we
+
+ align:start position:0%
+hi everybody our first thing that we
+ 
+
+ align:start position:0%
+hi everybody our first thing that we
+really want to think about is how are we
+
+ align:start position:0%
+really want to think about is how are we
+ 
+
+ align:start position:0%
+really want to think about is how are we
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+represent
+
+ align:start position:0%
+represent
+ 
+
+ align:start position:0%
+represent
+musical objects
+
+ align:start position:0%
+musical objects
+ 
+
+ align:start position:0%
+musical objects
+music on a computer so let's start with
+
+ align:start position:0%
+music on a computer so let's start with
+ 
+
+ align:start position:0%
+music on a computer so let's start with
+maybe one of the most fundamental things
+
+ align:start position:0%
+maybe one of the most fundamental things
+ 
+
+ align:start position:0%
+maybe one of the most fundamental things
+and that is pitch so
+
+ align:start position:0%
+and that is pitch so
+ 
+
+ align:start position:0%
+and that is pitch so
+in a score-based class we might
+
+ align:start position:0%
+in a score-based class we might
+ 
+
+ align:start position:0%
+in a score-based class we might
+represent pitch with a score and we
+
+ align:start position:0%
+represent pitch with a score and we
+ 
+
+ align:start position:0%
+represent pitch with a score and we
+write notes on
+
+ align:start position:0%
+write notes on
+ 
+
+ align:start position:0%
+write notes on
+it I guess then we assign it to a
+
+ align:start position:0%
+it I guess then we assign it to a
+ 
+
+ align:start position:0%
+it I guess then we assign it to a
+variable well that's not going to work
+
+ align:start position:0%
+variable well that's not going to work
+ 
+
+ align:start position:0%
+variable well that's not going to work
+um okay so we we take a a frequency and
+
+ align:start position:0%
+um okay so we we take a a frequency and
+ 
+
+ align:start position:0%
+um okay so we we take a a frequency and
+we assign that to a variable well I'm
+
+ align:start position:0%
+we assign that to a variable well I'm
+ 
+
+ align:start position:0%
+we assign that to a variable well I'm
+not exactly sure how to do that either
+
+ align:start position:0%
+not exactly sure how to do that either
+ 
+
+ align:start position:0%
+not exactly sure how to do that either
+um maybe we just assign a variable to a
+
+ align:start position:0%
+um maybe we just assign a variable to a
+ 
+
+ align:start position:0%
+um maybe we just assign a variable to a
+particular number representing a
+
+ align:start position:0%
+particular number representing a
+ 
+
+ align:start position:0%
+particular number representing a
+frequency or to a
+
+ align:start position:0%
+frequency or to a
+ 
+
+ align:start position:0%
+frequency or to a
+string representing a
+
+ align:start position:0%
+string representing a
+ 
+
+ align:start position:0%
+string representing a
+pitch
+
+ align:start position:0%
+pitch
+ 
+
+ align:start position:0%
+pitch
+okay first thing I want you to do is
+
+ align:start position:0%
+okay first thing I want you to do is
+ 
+
+ align:start position:0%
+okay first thing I want you to do is
+take five minutes no more than that and
+
+ align:start position:0%
+take five minutes no more than that and
+ 
+
+ align:start position:0%
+take five minutes no more than that and
+jot down some notes on how you like
+
+ align:start position:0%
+jot down some notes on how you like
+ 
+
+ align:start position:0%
+jot down some notes on how you like
+represent pitch on a computer very
+
+ align:start position:0%
+represent pitch on a computer very
+ 
+
+ align:start position:0%
+represent pitch on a computer very
+naively
\ No newline at end of file
diff --git a/wDLzLN1tArA.txt b/wDLzLN1tArA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d22818e0b2a837a2075e086282ea30d54e60c0da
--- /dev/null
+++ b/wDLzLN1tArA.txt
@@ -0,0 +1,11835 @@
+align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+topic for the classes interpretability
+
+ align:start position:0%
+topic for the classes interpretability
+ 
+
+ align:start position:0%
+topic for the classes interpretability
+as you know the modern machine learning
+
+ align:start position:0%
+as you know the modern machine learning
+ 
+
+ align:start position:0%
+as you know the modern machine learning
+models are justifiably reputed to be
+
+ align:start position:0%
+models are justifiably reputed to be
+ 
+
+ align:start position:0%
+models are justifiably reputed to be
+very difficult to understand so if I
+
+ align:start position:0%
+very difficult to understand so if I
+ 
+
+ align:start position:0%
+very difficult to understand so if I
+give you something like the GPT 2 model
+
+ align:start position:0%
+give you something like the GPT 2 model
+ 
+
+ align:start position:0%
+give you something like the GPT 2 model
+which we talked about a natural language
+
+ align:start position:0%
+which we talked about a natural language
+ 
+
+ align:start position:0%
+which we talked about a natural language
+processing and I tell you that it has
+
+ align:start position:0%
+processing and I tell you that it has
+ 
+
+ align:start position:0%
+processing and I tell you that it has
+1.5 billion parameters and then you say
+
+ align:start position:0%
+1.5 billion parameters and then you say
+ 
+
+ align:start position:0%
+1.5 billion parameters and then you say
+mm why is it working
+
+ align:start position:0%
+mm why is it working
+ 
+
+ align:start position:0%
+mm why is it working
+clearly the answer is not because these
+
+ align:start position:0%
+clearly the answer is not because these
+ 
+
+ align:start position:0%
+clearly the answer is not because these
+particular parameters have these
+
+ align:start position:0%
+particular parameters have these
+ 
+
+ align:start position:0%
+particular parameters have these
+particular values
+
+ align:start position:0%
+particular values
+ 
+
+ align:start position:0%
+particular values
+there's no way to understand that and so
+
+ align:start position:0%
+there's no way to understand that and so
+ 
+
+ align:start position:0%
+there's no way to understand that and so
+the topic today is something that we
+
+ align:start position:0%
+the topic today is something that we
+ 
+
+ align:start position:0%
+the topic today is something that we
+raised a little bit in the lecture on
+
+ align:start position:0%
+raised a little bit in the lecture on
+ 
+
+ align:start position:0%
+raised a little bit in the lecture on
+fairness where one of the issues there
+
+ align:start position:0%
+fairness where one of the issues there
+ 
+
+ align:start position:0%
+fairness where one of the issues there
+was also that if you can't understand
+
+ align:start position:0%
+was also that if you can't understand
+ 
+
+ align:start position:0%
+was also that if you can't understand
+the model you can't tell if the model
+
+ align:start position:0%
+the model you can't tell if the model
+ 
+
+ align:start position:0%
+the model you can't tell if the model
+has baked in prejudices by examining it
+
+ align:start position:0%
+has baked in prejudices by examining it
+ 
+
+ align:start position:0%
+has baked in prejudices by examining it
+and so today we're going to look at
+
+ align:start position:0%
+and so today we're going to look at
+ 
+
+ align:start position:0%
+and so today we're going to look at
+different methods that people have
+
+ align:start position:0%
+different methods that people have
+ 
+
+ align:start position:0%
+different methods that people have
+developed to try to overcome this
+
+ align:start position:0%
+developed to try to overcome this
+ 
+
+ align:start position:0%
+developed to try to overcome this
+problem of inscrutable models so there's
+
+ align:start position:0%
+problem of inscrutable models so there's
+ 
+
+ align:start position:0%
+problem of inscrutable models so there's
+a very interesting bit of history how
+
+ align:start position:0%
+a very interesting bit of history how
+ 
+
+ align:start position:0%
+a very interesting bit of history how
+many of you know of george miller 7 plus
+
+ align:start position:0%
+many of you know of george miller 7 plus
+ 
+
+ align:start position:0%
+many of you know of george miller 7 plus
+or minus 2 result only a few so miller
+
+ align:start position:0%
+or minus 2 result only a few so miller
+ 
+
+ align:start position:0%
+or minus 2 result only a few so miller
+was a psychologist at at harvard I think
+
+ align:start position:0%
+was a psychologist at at harvard I think
+ 
+
+ align:start position:0%
+was a psychologist at at harvard I think
+in the 1950s and he wrote this paper in
+
+ align:start position:0%
+in the 1950s and he wrote this paper in
+ 
+
+ align:start position:0%
+in the 1950s and he wrote this paper in
+1956 called the magical number 7 plus or
+
+ align:start position:0%
+1956 called the magical number 7 plus or
+ 
+
+ align:start position:0%
+1956 called the magical number 7 plus or
+minus 2 some limits on our capacity for
+
+ align:start position:0%
+minus 2 some limits on our capacity for
+ 
+
+ align:start position:0%
+minus 2 some limits on our capacity for
+processing information it's quite an
+
+ align:start position:0%
+processing information it's quite an
+ 
+
+ align:start position:0%
+processing information it's quite an
+interesting paper so he started off with
+
+ align:start position:0%
+interesting paper so he started off with
+ 
+
+ align:start position:0%
+interesting paper so he started off with
+something that I had forgotten I read
+
+ align:start position:0%
+something that I had forgotten I read
+ 
+
+ align:start position:0%
+something that I had forgotten I read
+this paper many many years ago and I had
+
+ align:start position:0%
+this paper many many years ago and I had
+ 
+
+ align:start position:0%
+this paper many many years ago and I had
+forgotten that he starts off with the
+
+ align:start position:0%
+forgotten that he starts off with the
+ 
+
+ align:start position:0%
+forgotten that he starts off with the
+question of how many different things
+
+ align:start position:0%
+question of how many different things
+ 
+
+ align:start position:0%
+question of how many different things
+can you sense how many different levels
+
+ align:start position:0%
+can you sense how many different levels
+ 
+
+ align:start position:0%
+can you sense how many different levels
+of things can you sense so if I put
+
+ align:start position:0%
+of things can you sense so if I put
+ 
+
+ align:start position:0%
+of things can you sense so if I put
+headphones on you and I ask you to tell
+
+ align:start position:0%
+headphones on you and I ask you to tell
+ 
+
+ align:start position:0%
+headphones on you and I ask you to tell
+me on a scale of 1 to n how loud is the
+
+ align:start position:0%
+me on a scale of 1 to n how loud is the
+ 
+
+ align:start position:0%
+me on a scale of 1 to n how loud is the
+sound
+
+ align:start position:0%
+sound
+ 
+
+ align:start position:0%
+sound
+that I'm playing in your headphone it
+
+ align:start position:0%
+that I'm playing in your headphone it
+ 
+
+ align:start position:0%
+that I'm playing in your headphone it
+turns out people get confused when you
+
+ align:start position:0%
+turns out people get confused when you
+ 
+
+ align:start position:0%
+turns out people get confused when you
+get beyond about five six seven
+
+ align:start position:0%
+get beyond about five six seven
+ 
+
+ align:start position:0%
+get beyond about five six seven
+different levels of intensity and
+
+ align:start position:0%
+different levels of intensity and
+ 
+
+ align:start position:0%
+different levels of intensity and
+similarly if I give you a bunch of
+
+ align:start position:0%
+similarly if I give you a bunch of
+ 
+
+ align:start position:0%
+similarly if I give you a bunch of
+colors and I ask you to tell me where
+
+ align:start position:0%
+colors and I ask you to tell me where
+ 
+
+ align:start position:0%
+colors and I ask you to tell me where
+the boundaries are between different
+
+ align:start position:0%
+the boundaries are between different
+ 
+
+ align:start position:0%
+the boundaries are between different
+colors people seem to come up with seven
+
+ align:start position:0%
+colors people seem to come up with seven
+ 
+
+ align:start position:0%
+colors people seem to come up with seven
+plus or minus two as the number of
+
+ align:start position:0%
+plus or minus two as the number of
+ 
+
+ align:start position:0%
+plus or minus two as the number of
+colors that they can distinguish and so
+
+ align:start position:0%
+colors that they can distinguish and so
+ 
+
+ align:start position:0%
+colors that they can distinguish and so
+there's a long psychological literature
+
+ align:start position:0%
+there's a long psychological literature
+ 
+
+ align:start position:0%
+there's a long psychological literature
+of this and then Miller went on to do
+
+ align:start position:0%
+of this and then Miller went on to do
+ 
+
+ align:start position:0%
+of this and then Miller went on to do
+experiments where he asked people to
+
+ align:start position:0%
+experiments where he asked people to
+ 
+
+ align:start position:0%
+experiments where he asked people to
+memorize lists of things and what he
+
+ align:start position:0%
+memorize lists of things and what he
+ 
+
+ align:start position:0%
+memorize lists of things and what he
+discovered is again that you could
+
+ align:start position:0%
+discovered is again that you could
+ 
+
+ align:start position:0%
+discovered is again that you could
+memorize a list of about seven plus or
+
+ align:start position:0%
+memorize a list of about seven plus or
+ 
+
+ align:start position:0%
+memorize a list of about seven plus or
+minus two things and beyond that you
+
+ align:start position:0%
+minus two things and beyond that you
+ 
+
+ align:start position:0%
+minus two things and beyond that you
+couldn't remember the list anymore so
+
+ align:start position:0%
+couldn't remember the list anymore so
+ 
+
+ align:start position:0%
+couldn't remember the list anymore so
+this tells us something about the
+
+ align:start position:0%
+this tells us something about the
+ 
+
+ align:start position:0%
+this tells us something about the
+cognitive capacity of the human mind and
+
+ align:start position:0%
+cognitive capacity of the human mind and
+ 
+
+ align:start position:0%
+cognitive capacity of the human mind and
+it suggests that if I give you an
+
+ align:start position:0%
+it suggests that if I give you an
+ 
+
+ align:start position:0%
+it suggests that if I give you an
+explanation that has 20 things in it
+
+ align:start position:0%
+explanation that has 20 things in it
+ 
+
+ align:start position:0%
+explanation that has 20 things in it
+you're unlikely to be able to fathom it
+
+ align:start position:0%
+you're unlikely to be able to fathom it
+ 
+
+ align:start position:0%
+you're unlikely to be able to fathom it
+because you can't keep all the moving
+
+ align:start position:0%
+because you can't keep all the moving
+ 
+
+ align:start position:0%
+because you can't keep all the moving
+parts in your mind at one time now it's
+
+ align:start position:0%
+parts in your mind at one time now it's
+ 
+
+ align:start position:0%
+parts in your mind at one time now it's
+a tricky result because he does point
+
+ align:start position:0%
+a tricky result because he does point
+ 
+
+ align:start position:0%
+a tricky result because he does point
+out even in 1956 that if you chunk
+
+ align:start position:0%
+out even in 1956 that if you chunk
+ 
+
+ align:start position:0%
+out even in 1956 that if you chunk
+things into bigger chunks you can
+
+ align:start position:0%
+things into bigger chunks you can
+ 
+
+ align:start position:0%
+things into bigger chunks you can
+remember seven of those even if they're
+
+ align:start position:0%
+remember seven of those even if they're
+ 
+
+ align:start position:0%
+remember seven of those even if they're
+much bigger and so people who are very
+
+ align:start position:0%
+much bigger and so people who are very
+ 
+
+ align:start position:0%
+much bigger and so people who are very
+good at memorizing things for example
+
+ align:start position:0%
+good at memorizing things for example
+ 
+
+ align:start position:0%
+good at memorizing things for example
+make up patterns and they remember those
+
+ align:start position:0%
+make up patterns and they remember those
+ 
+
+ align:start position:0%
+make up patterns and they remember those
+patterns which then allow them to
+
+ align:start position:0%
+patterns which then allow them to
+ 
+
+ align:start position:0%
+patterns which then allow them to
+actually remember more primitive objects
+
+ align:start position:0%
+actually remember more primitive objects
+ 
+
+ align:start position:0%
+actually remember more primitive objects
+so it you know and we still don't really
+
+ align:start position:0%
+so it you know and we still don't really
+ 
+
+ align:start position:0%
+so it you know and we still don't really
+understand how memory works but this is
+
+ align:start position:0%
+understand how memory works but this is
+ 
+
+ align:start position:0%
+understand how memory works but this is
+just an interesting observation and I
+
+ align:start position:0%
+just an interesting observation and I
+ 
+
+ align:start position:0%
+just an interesting observation and I
+think plays into the question of of how
+
+ align:start position:0%
+think plays into the question of of how
+ 
+
+ align:start position:0%
+think plays into the question of of how
+do you explain things in a complicated
+
+ align:start position:0%
+do you explain things in a complicated
+ 
+
+ align:start position:0%
+do you explain things in a complicated
+model because it suggests that you can't
+
+ align:start position:0%
+model because it suggests that you can't
+ 
+
+ align:start position:0%
+model because it suggests that you can't
+explain too many different things
+
+ align:start position:0%
+explain too many different things
+ 
+
+ align:start position:0%
+explain too many different things
+because people won't understand what
+
+ align:start position:0%
+because people won't understand what
+ 
+
+ align:start position:0%
+because people won't understand what
+you're talking about okay so what leads
+
+ align:start position:0%
+you're talking about okay so what leads
+ 
+
+ align:start position:0%
+you're talking about okay so what leads
+to complex models well as I say
+
+ align:start position:0%
+to complex models well as I say
+ 
+
+ align:start position:0%
+to complex models well as I say
+overfitting certainly lead
+
+ align:start position:0%
+overfitting certainly lead
+ 
+
+ align:start position:0%
+overfitting certainly lead
+two complex models I remember in the
+
+ align:start position:0%
+two complex models I remember in the
+ 
+
+ align:start position:0%
+two complex models I remember in the
+1970s when we started working on expert
+
+ align:start position:0%
+1970s when we started working on expert
+ 
+
+ align:start position:0%
+1970s when we started working on expert
+systems and in healthcare I I made a
+
+ align:start position:0%
+systems and in healthcare I I made a
+ 
+
+ align:start position:0%
+systems and in healthcare I I made a
+very bad faux pas I went to the first
+
+ align:start position:0%
+very bad faux pas I went to the first
+ 
+
+ align:start position:0%
+very bad faux pas I went to the first
+joint conference between statisticians
+
+ align:start position:0%
+joint conference between statisticians
+ 
+
+ align:start position:0%
+joint conference between statisticians
+and artificial intelligence researchers
+
+ align:start position:0%
+and artificial intelligence researchers
+ 
+
+ align:start position:0%
+and artificial intelligence researchers
+and the statisticians were all about you
+
+ align:start position:0%
+and the statisticians were all about you
+ 
+
+ align:start position:0%
+and the statisticians were all about you
+know understanding the variance and
+
+ align:start position:0%
+know understanding the variance and
+ 
+
+ align:start position:0%
+know understanding the variance and
+understanding statistical significance
+
+ align:start position:0%
+understanding statistical significance
+ 
+
+ align:start position:0%
+understanding statistical significance
+and so on and I was all about trying to
+
+ align:start position:0%
+and so on and I was all about trying to
+ 
+
+ align:start position:0%
+and so on and I was all about trying to
+model details of what was going on in an
+
+ align:start position:0%
+model details of what was going on in an
+ 
+
+ align:start position:0%
+model details of what was going on in an
+individual patient and in some
+
+ align:start position:0%
+individual patient and in some
+ 
+
+ align:start position:0%
+individual patient and in some
+discussion after my talk somebody
+
+ align:start position:0%
+discussion after my talk somebody
+ 
+
+ align:start position:0%
+discussion after my talk somebody
+challenged me and I said well what we a
+
+ align:start position:0%
+challenged me and I said well what we a
+ 
+
+ align:start position:0%
+challenged me and I said well what we a
+I people are really doing is fitting
+
+ align:start position:0%
+I people are really doing is fitting
+ 
+
+ align:start position:0%
+I people are really doing is fitting
+what you guys think is the noise right
+
+ align:start position:0%
+what you guys think is the noise right
+ 
+
+ align:start position:0%
+what you guys think is the noise right
+because we're trying to make a lot more
+
+ align:start position:0%
+because we're trying to make a lot more
+ 
+
+ align:start position:0%
+because we're trying to make a lot more
+detailed refinements in our theories in
+
+ align:start position:0%
+detailed refinements in our theories in
+ 
+
+ align:start position:0%
+detailed refinements in our theories in
+our models than what the typical
+
+ align:start position:0%
+our models than what the typical
+ 
+
+ align:start position:0%
+our models than what the typical
+statistical model does and of course I
+
+ align:start position:0%
+statistical model does and of course I
+ 
+
+ align:start position:0%
+statistical model does and of course I
+was roundly booed out of out of the hall
+
+ align:start position:0%
+was roundly booed out of out of the hall
+ 
+
+ align:start position:0%
+was roundly booed out of out of the hall
+and people shunned me for the rest of
+
+ align:start position:0%
+and people shunned me for the rest of
+ 
+
+ align:start position:0%
+and people shunned me for the rest of
+the conference because I had done
+
+ align:start position:0%
+the conference because I had done
+ 
+
+ align:start position:0%
+the conference because I had done
+something really stupid
+
+ align:start position:0%
+something really stupid
+ 
+
+ align:start position:0%
+something really stupid
+to admit that I was I was fitting noise
+
+ align:start position:0%
+to admit that I was I was fitting noise
+ 
+
+ align:start position:0%
+to admit that I was I was fitting noise
+and of course I didn't really believe
+
+ align:start position:0%
+and of course I didn't really believe
+ 
+
+ align:start position:0%
+and of course I didn't really believe
+that I was fitting noise I was believed
+
+ align:start position:0%
+that I was fitting noise I was believed
+ 
+
+ align:start position:0%
+that I was fitting noise I was believed
+that what I was fitting was what the
+
+ align:start position:0%
+that what I was fitting was what the
+ 
+
+ align:start position:0%
+that what I was fitting was what the
+average statistician just chalks up to
+
+ align:start position:0%
+average statistician just chalks up to
+ 
+
+ align:start position:0%
+average statistician just chalks up to
+noise and we're interested in more
+
+ align:start position:0%
+noise and we're interested in more
+ 
+
+ align:start position:0%
+noise and we're interested in more
+details of the mechanisms so overfitting
+
+ align:start position:0%
+details of the mechanisms so overfitting
+ 
+
+ align:start position:0%
+details of the mechanisms so overfitting
+we have a pretty good handle on by
+
+ align:start position:0%
+we have a pretty good handle on by
+ 
+
+ align:start position:0%
+we have a pretty good handle on by
+regularization so you can you know
+
+ align:start position:0%
+regularization so you can you know
+ 
+
+ align:start position:0%
+regularization so you can you know
+you've seen lots of examples of
+
+ align:start position:0%
+you've seen lots of examples of
+ 
+
+ align:start position:0%
+you've seen lots of examples of
+regularization throughout the course and
+
+ align:start position:0%
+regularization throughout the course and
+ 
+
+ align:start position:0%
+regularization throughout the course and
+people keep coming up with interesting
+
+ align:start position:0%
+people keep coming up with interesting
+ 
+
+ align:start position:0%
+people keep coming up with interesting
+ideas for how to apply regularization in
+
+ align:start position:0%
+ideas for how to apply regularization in
+ 
+
+ align:start position:0%
+ideas for how to apply regularization in
+order to simplify models or make them
+
+ align:start position:0%
+order to simplify models or make them
+ 
+
+ align:start position:0%
+order to simplify models or make them
+fit some preconception of what the model
+
+ align:start position:0%
+fit some preconception of what the model
+ 
+
+ align:start position:0%
+fit some preconception of what the model
+ought to look like before you start
+
+ align:start position:0%
+ought to look like before you start
+ 
+
+ align:start position:0%
+ought to look like before you start
+learning it from data but the problem is
+
+ align:start position:0%
+learning it from data but the problem is
+ 
+
+ align:start position:0%
+learning it from data but the problem is
+that there's there really is true
+
+ align:start position:0%
+that there's there really is true
+ 
+
+ align:start position:0%
+that there's there really is true
+complexity to these models whether or
+
+ align:start position:0%
+complexity to these models whether or
+ 
+
+ align:start position:0%
+complexity to these models whether or
+not you're fitting noise there's the
+
+ align:start position:0%
+not you're fitting noise there's the
+ 
+
+ align:start position:0%
+not you're fitting noise there's the
+world is a complicated place
+
+ align:start position:0%
+world is a complicated place
+ 
+
+ align:start position:0%
+world is a complicated place
+human beings were not designed they
+
+ align:start position:0%
+human beings were not designed they
+ 
+
+ align:start position:0%
+human beings were not designed they
+evolved and so there's all kinds of
+
+ align:start position:0%
+evolved and so there's all kinds of
+ 
+
+ align:start position:0%
+evolved and so there's all kinds of
+bizarre stuff left over from our
+
+ align:start position:0%
+bizarre stuff left over from our
+ 
+
+ align:start position:0%
+bizarre stuff left over from our
+evolutionary heritage and so it is just
+
+ align:start position:0%
+evolutionary heritage and so it is just
+ 
+
+ align:start position:0%
+evolutionary heritage and so it is just
+complex it's hard to understand in a
+
+ align:start position:0%
+complex it's hard to understand in a
+ 
+
+ align:start position:0%
+complex it's hard to understand in a
+simple way how to make predictions that
+
+ align:start position:0%
+simple way how to make predictions that
+ 
+
+ align:start position:0%
+simple way how to make predictions that
+are useful when the world really is
+
+ align:start position:0%
+are useful when the world really is
+ 
+
+ align:start position:0%
+are useful when the world really is
+complex so what do we do in order to try
+
+ align:start position:0%
+complex so what do we do in order to try
+ 
+
+ align:start position:0%
+complex so what do we do in order to try
+to deal with this well one approach is
+
+ align:start position:0%
+to deal with this well one approach is
+ 
+
+ align:start position:0%
+to deal with this well one approach is
+to make up what I call just so stories
+
+ align:start position:0%
+to make up what I call just so stories
+ 
+
+ align:start position:0%
+to make up what I call just so stories
+that give a simplified explanation of
+
+ align:start position:0%
+that give a simplified explanation of
+ 
+
+ align:start position:0%
+that give a simplified explanation of
+how a complicated thing actually works
+
+ align:start position:0%
+how a complicated thing actually works
+ 
+
+ align:start position:0%
+how a complicated thing actually works
+so how many of you have read these
+
+ align:start position:0%
+so how many of you have read these
+ 
+
+ align:start position:0%
+so how many of you have read these
+stories when you were a kid nobody my
+
+ align:start position:0%
+stories when you were a kid nobody my
+ 
+
+ align:start position:0%
+stories when you were a kid nobody my
+god okay must be a generational thing
+
+ align:start position:0%
+god okay must be a generational thing
+ 
+
+ align:start position:0%
+god okay must be a generational thing
+so Rudyard Kipling was a famous author
+
+ align:start position:0%
+so Rudyard Kipling was a famous author
+ 
+
+ align:start position:0%
+so Rudyard Kipling was a famous author
+and he wrote the series of just-so
+
+ align:start position:0%
+and he wrote the series of just-so
+ 
+
+ align:start position:0%
+and he wrote the series of just-so
+stories things like how the lion got his
+
+ align:start position:0%
+stories things like how the lion got his
+ 
+
+ align:start position:0%
+stories things like how the lion got his
+mane and how the camel got his hump and
+
+ align:start position:0%
+mane and how the camel got his hump and
+ 
+
+ align:start position:0%
+mane and how the camel got his hump and
+so on and of course they're all total
+
+ align:start position:0%
+so on and of course they're all total
+ 
+
+ align:start position:0%
+so on and of course they're all total
+bull right I mean it's not a Darwinian
+
+ align:start position:0%
+bull right I mean it's not a Darwinian
+ 
+
+ align:start position:0%
+bull right I mean it's not a Darwinian
+evolutionary explanation of why male
+
+ align:start position:0%
+evolutionary explanation of why male
+ 
+
+ align:start position:0%
+evolutionary explanation of why male
+lions have Mane's it's just some made-up
+
+ align:start position:0%
+lions have Mane's it's just some made-up
+ 
+
+ align:start position:0%
+lions have Mane's it's just some made-up
+story but they're really cute stories
+
+ align:start position:0%
+story but they're really cute stories
+ 
+
+ align:start position:0%
+story but they're really cute stories
+and and I enjoyed them as a kid and
+
+ align:start position:0%
+and and I enjoyed them as a kid and
+ 
+
+ align:start position:0%
+and and I enjoyed them as a kid and
+maybe you would have to if your parents
+
+ align:start position:0%
+maybe you would have to if your parents
+ 
+
+ align:start position:0%
+maybe you would have to if your parents
+had read them to you so I mean I use
+
+ align:start position:0%
+had read them to you so I mean I use
+ 
+
+ align:start position:0%
+had read them to you so I mean I use
+this as a kind of pejorative because
+
+ align:start position:0%
+this as a kind of pejorative because
+ 
+
+ align:start position:0%
+this as a kind of pejorative because
+what the people who follow this line of
+
+ align:start position:0%
+what the people who follow this line of
+ 
+
+ align:start position:0%
+what the people who follow this line of
+investigation do is they take some very
+
+ align:start position:0%
+investigation do is they take some very
+ 
+
+ align:start position:0%
+investigation do is they take some very
+complicated model they make a local
+
+ align:start position:0%
+complicated model they make a local
+ 
+
+ align:start position:0%
+complicated model they make a local
+approximation to it that says this is
+
+ align:start position:0%
+approximation to it that says this is
+ 
+
+ align:start position:0%
+approximation to it that says this is
+not an approximation to the entire model
+
+ align:start position:0%
+not an approximation to the entire model
+ 
+
+ align:start position:0%
+not an approximation to the entire model
+but it's an approximation to the model
+
+ align:start position:0%
+but it's an approximation to the model
+ 
+
+ align:start position:0%
+but it's an approximation to the model
+in the vicinity of a particular case and
+
+ align:start position:0%
+in the vicinity of a particular case and
+ 
+
+ align:start position:0%
+in the vicinity of a particular case and
+then they explain that simplified model
+
+ align:start position:0%
+then they explain that simplified model
+ 
+
+ align:start position:0%
+then they explain that simplified model
+and I'll show you some examples of that
+
+ align:start position:0%
+and I'll show you some examples of that
+ 
+
+ align:start position:0%
+and I'll show you some examples of that
+through the lecture today and the other
+
+ align:start position:0%
+through the lecture today and the other
+ 
+
+ align:start position:0%
+through the lecture today and the other
+approach which I'll also show you some
+
+ align:start position:0%
+approach which I'll also show you some
+ 
+
+ align:start position:0%
+approach which I'll also show you some
+examples of is that you simply trade off
+
+ align:start position:0%
+examples of is that you simply trade off
+ 
+
+ align:start position:0%
+examples of is that you simply trade off
+somewhat lower performance
+
+ align:start position:0%
+somewhat lower performance
+ 
+
+ align:start position:0%
+somewhat lower performance
+for simple model that's simple enough to
+
+ align:start position:0%
+for simple model that's simple enough to
+ 
+
+ align:start position:0%
+for simple model that's simple enough to
+be able to explain so things like
+
+ align:start position:0%
+be able to explain so things like
+ 
+
+ align:start position:0%
+be able to explain so things like
+decision trees and and logistic
+
+ align:start position:0%
+decision trees and and logistic
+ 
+
+ align:start position:0%
+decision trees and and logistic
+regression and so on typically don't
+
+ align:start position:0%
+regression and so on typically don't
+ 
+
+ align:start position:0%
+regression and so on typically don't
+perform quite as well as the best most
+
+ align:start position:0%
+perform quite as well as the best most
+ 
+
+ align:start position:0%
+perform quite as well as the best most
+sophisticated models although you've
+
+ align:start position:0%
+sophisticated models although you've
+ 
+
+ align:start position:0%
+sophisticated models although you've
+seen plenty of examples in this class
+
+ align:start position:0%
+seen plenty of examples in this class
+ 
+
+ align:start position:0%
+seen plenty of examples in this class
+where in fact they do perform quite well
+
+ align:start position:0%
+where in fact they do perform quite well
+ 
+
+ align:start position:0%
+where in fact they do perform quite well
+and where they're not outperformed by
+
+ align:start position:0%
+and where they're not outperformed by
+ 
+
+ align:start position:0%
+and where they're not outperformed by
+the fancy models but in general you can
+
+ align:start position:0%
+the fancy models but in general you can
+ 
+
+ align:start position:0%
+the fancy models but in general you can
+do a little better by tweaking a fancy
+
+ align:start position:0%
+do a little better by tweaking a fancy
+ 
+
+ align:start position:0%
+do a little better by tweaking a fancy
+model but then it becomes
+
+ align:start position:0%
+model but then it becomes
+ 
+
+ align:start position:0%
+model but then it becomes
+incomprehensible and so people are
+
+ align:start position:0%
+incomprehensible and so people are
+ 
+
+ align:start position:0%
+incomprehensible and so people are
+willing to say okay I'm gonna give up 1%
+
+ align:start position:0%
+willing to say okay I'm gonna give up 1%
+ 
+
+ align:start position:0%
+willing to say okay I'm gonna give up 1%
+or 2% in performance in order to have a
+
+ align:start position:0%
+or 2% in performance in order to have a
+ 
+
+ align:start position:0%
+or 2% in performance in order to have a
+model that I can really understand and
+
+ align:start position:0%
+model that I can really understand and
+ 
+
+ align:start position:0%
+model that I can really understand and
+the reason it makes sense is because
+
+ align:start position:0%
+the reason it makes sense is because
+ 
+
+ align:start position:0%
+the reason it makes sense is because
+these models are not self-executing
+
+ align:start position:0%
+these models are not self-executing
+ 
+
+ align:start position:0%
+these models are not self-executing
+they're typically used as advice for
+
+ align:start position:0%
+they're typically used as advice for
+ 
+
+ align:start position:0%
+they're typically used as advice for
+some human being who makes ultimate
+
+ align:start position:0%
+some human being who makes ultimate
+ 
+
+ align:start position:0%
+some human being who makes ultimate
+decisions your surgeon is not going to
+
+ align:start position:0%
+decisions your surgeon is not going to
+ 
+
+ align:start position:0%
+decisions your surgeon is not going to
+look at one of these models that says
+
+ align:start position:0%
+look at one of these models that says
+ 
+
+ align:start position:0%
+look at one of these models that says
+take out the guy's left kidney and say
+
+ align:start position:0%
+take out the guy's left kidney and say
+ 
+
+ align:start position:0%
+take out the guy's left kidney and say
+okay my guess they're gonna go well does
+
+ align:start position:0%
+okay my guess they're gonna go well does
+ 
+
+ align:start position:0%
+okay my guess they're gonna go well does
+that make sense and in order to answer
+
+ align:start position:0%
+that make sense and in order to answer
+ 
+
+ align:start position:0%
+that make sense and in order to answer
+the question of does that make sense it
+
+ align:start position:0%
+the question of does that make sense it
+ 
+
+ align:start position:0%
+the question of does that make sense it
+really helps to know what the model was
+
+ align:start position:0%
+really helps to know what the model was
+ 
+
+ align:start position:0%
+really helps to know what the model was
+what what the models recommendation is
+
+ align:start position:0%
+what what the models recommendation is
+ 
+
+ align:start position:0%
+what what the models recommendation is
+based on what is its internal logic and
+
+ align:start position:0%
+based on what is its internal logic and
+ 
+
+ align:start position:0%
+based on what is its internal logic and
+so even an approximation to that is
+
+ align:start position:0%
+so even an approximation to that is
+ 
+
+ align:start position:0%
+so even an approximation to that is
+useful so the need for trust clinical
+
+ align:start position:0%
+useful so the need for trust clinical
+ 
+
+ align:start position:0%
+useful so the need for trust clinical
+adoption of ML models there are two
+
+ align:start position:0%
+adoption of ML models there are two
+ 
+
+ align:start position:0%
+adoption of ML models there are two
+approaches in this paper that I'm going
+
+ align:start position:0%
+approaches in this paper that I'm going
+ 
+
+ align:start position:0%
+approaches in this paper that I'm going
+to talk about where they say okay what
+
+ align:start position:0%
+to talk about where they say okay what
+ 
+
+ align:start position:0%
+to talk about where they say okay what
+you'd like to do is to look at case
+
+ align:start position:0%
+you'd like to do is to look at case
+ 
+
+ align:start position:0%
+you'd like to do is to look at case
+specific predictions so there's a
+
+ align:start position:0%
+specific predictions so there's a
+ 
+
+ align:start position:0%
+specific predictions so there's a
+particular patient in a particular state
+
+ align:start position:0%
+particular patient in a particular state
+ 
+
+ align:start position:0%
+particular patient in a particular state
+and you want to understand what the
+
+ align:start position:0%
+and you want to understand what the
+ 
+
+ align:start position:0%
+and you want to understand what the
+model is saying about that patient and
+
+ align:start position:0%
+model is saying about that patient and
+ 
+
+ align:start position:0%
+model is saying about that patient and
+then you also want to have confidence in
+
+ align:start position:0%
+then you also want to have confidence in
+ 
+
+ align:start position:0%
+then you also want to have confidence in
+the model overall and so you'd like to
+
+ align:start position:0%
+the model overall and so you'd like to
+ 
+
+ align:start position:0%
+the model overall and so you'd like to
+be able to have an explanatory
+
+ align:start position:0%
+be able to have an explanatory
+ 
+
+ align:start position:0%
+be able to have an explanatory
+capability that says here are some
+
+ align:start position:0%
+capability that says here are some
+ 
+
+ align:start position:0%
+capability that says here are some
+interesting representative cases and
+
+ align:start position:0%
+interesting representative cases and
+ 
+
+ align:start position:0%
+interesting representative cases and
+here's how the model views them look
+
+ align:start position:0%
+here's how the model views them look
+ 
+
+ align:start position:0%
+here's how the model views them look
+through them and decide whether you
+
+ align:start position:0%
+through them and decide whether you
+ 
+
+ align:start position:0%
+through them and decide whether you
+agree with the approach that this model
+
+ align:start position:0%
+agree with the approach that this model
+ 
+
+ align:start position:0%
+agree with the approach that this model
+is take
+
+ align:start position:0%
+is take
+ 
+
+ align:start position:0%
+is take
+now remember my critique of randomized
+
+ align:start position:0%
+now remember my critique of randomized
+ 
+
+ align:start position:0%
+now remember my critique of randomized
+control trials that that people do these
+
+ align:start position:0%
+control trials that that people do these
+ 
+
+ align:start position:0%
+control trials that that people do these
+trials they choose the simplest cases
+
+ align:start position:0%
+trials they choose the simplest cases
+ 
+
+ align:start position:0%
+trials they choose the simplest cases
+the smallest number of patients that
+
+ align:start position:0%
+the smallest number of patients that
+ 
+
+ align:start position:0%
+the smallest number of patients that
+they need in order to reach statistical
+
+ align:start position:0%
+they need in order to reach statistical
+ 
+
+ align:start position:0%
+they need in order to reach statistical
+significance the shortest amount of
+
+ align:start position:0%
+significance the shortest amount of
+ 
+
+ align:start position:0%
+significance the shortest amount of
+follow-up time etc and then the results
+
+ align:start position:0%
+follow-up time etc and then the results
+ 
+
+ align:start position:0%
+follow-up time etc and then the results
+of those trials are applied to very
+
+ align:start position:0%
+of those trials are applied to very
+ 
+
+ align:start position:0%
+of those trials are applied to very
+different populations so david's talked
+
+ align:start position:0%
+different populations so david's talked
+ 
+
+ align:start position:0%
+different populations so david's talked
+about cohort shift as a generalization
+
+ align:start position:0%
+about cohort shift as a generalization
+ 
+
+ align:start position:0%
+about cohort shift as a generalization
+of that idea but the same thing happens
+
+ align:start position:0%
+of that idea but the same thing happens
+ 
+
+ align:start position:0%
+of that idea but the same thing happens
+in these machine learning models that
+
+ align:start position:0%
+in these machine learning models that
+ 
+
+ align:start position:0%
+in these machine learning models that
+you train on some set of data
+
+ align:start position:0%
+you train on some set of data
+ 
+
+ align:start position:0%
+you train on some set of data
+the typical publication will then test
+
+ align:start position:0%
+the typical publication will then test
+ 
+
+ align:start position:0%
+the typical publication will then test
+on some held out subset of the same data
+
+ align:start position:0%
+on some held out subset of the same data
+ 
+
+ align:start position:0%
+on some held out subset of the same data
+but that's not a very accurate
+
+ align:start position:0%
+but that's not a very accurate
+ 
+
+ align:start position:0%
+but that's not a very accurate
+representation of the real world if you
+
+ align:start position:0%
+representation of the real world if you
+ 
+
+ align:start position:0%
+representation of the real world if you
+then try to apply that model to data
+
+ align:start position:0%
+then try to apply that model to data
+ 
+
+ align:start position:0%
+then try to apply that model to data
+from a totally different source the
+
+ align:start position:0%
+from a totally different source the
+ 
+
+ align:start position:0%
+from a totally different source the
+chances are you will have specialized it
+
+ align:start position:0%
+chances are you will have specialized it
+ 
+
+ align:start position:0%
+chances are you will have specialized it
+in some way that you don't appreciate
+
+ align:start position:0%
+in some way that you don't appreciate
+ 
+
+ align:start position:0%
+in some way that you don't appreciate
+and the results that you get are not as
+
+ align:start position:0%
+and the results that you get are not as
+ 
+
+ align:start position:0%
+and the results that you get are not as
+good as what you got on the held-out
+
+ align:start position:0%
+good as what you got on the held-out
+ 
+
+ align:start position:0%
+good as what you got on the held-out
+test data because it's more
+
+ align:start position:0%
+test data because it's more
+ 
+
+ align:start position:0%
+test data because it's more
+heterogeneous I think I mentioned that
+
+ align:start position:0%
+heterogeneous I think I mentioned that
+ 
+
+ align:start position:0%
+heterogeneous I think I mentioned that
+Jeff Drazen the editor-in-chief of the
+
+ align:start position:0%
+Jeff Drazen the editor-in-chief of the
+ 
+
+ align:start position:0%
+Jeff Drazen the editor-in-chief of the
+New England Journal had a meeting about
+
+ align:start position:0%
+New England Journal had a meeting about
+ 
+
+ align:start position:0%
+New England Journal had a meeting about
+about a year ago in which he was arguing
+
+ align:start position:0%
+about a year ago in which he was arguing
+ 
+
+ align:start position:0%
+about a year ago in which he was arguing
+that the journal shouldn't ever publish
+
+ align:start position:0%
+that the journal shouldn't ever publish
+ 
+
+ align:start position:0%
+that the journal shouldn't ever publish
+a research study unless it's been
+
+ align:start position:0%
+a research study unless it's been
+ 
+
+ align:start position:0%
+a research study unless it's been
+validated on two independent data sets
+
+ align:start position:0%
+validated on two independent data sets
+ 
+
+ align:start position:0%
+validated on two independent data sets
+because he he's tired of publishing
+
+ align:start position:0%
+because he he's tired of publishing
+ 
+
+ align:start position:0%
+because he he's tired of publishing
+studies that wind up getting retracted
+
+ align:start position:0%
+studies that wind up getting retracted
+ 
+
+ align:start position:0%
+studies that wind up getting retracted
+because not because of any overt badness
+
+ align:start position:0%
+because not because of any overt badness
+ 
+
+ align:start position:0%
+because not because of any overt badness
+on the part of the investigators they've
+
+ align:start position:0%
+on the part of the investigators they've
+ 
+
+ align:start position:0%
+on the part of the investigators they've
+done exactly the kinds of things that
+
+ align:start position:0%
+done exactly the kinds of things that
+ 
+
+ align:start position:0%
+done exactly the kinds of things that
+you've learned how to do in this class
+
+ align:start position:0%
+you've learned how to do in this class
+ 
+
+ align:start position:0%
+you've learned how to do in this class
+but when they go to apply that model to
+
+ align:start position:0%
+but when they go to apply that model to
+ 
+
+ align:start position:0%
+but when they go to apply that model to
+a different population it just doesn't
+
+ align:start position:0%
+a different population it just doesn't
+ 
+
+ align:start position:0%
+a different population it just doesn't
+work nearly as well as it did in the
+
+ align:start position:0%
+work nearly as well as it did in the
+ 
+
+ align:start position:0%
+work nearly as well as it did in the
+published version and of course they're
+
+ align:start position:0%
+published version and of course they're
+ 
+
+ align:start position:0%
+published version and of course they're
+all the publication bias issues about
+
+ align:start position:0%
+all the publication bias issues about
+ 
+
+ align:start position:0%
+all the publication bias issues about
+you know if if 50 of us do the same
+
+ align:start position:0%
+you know if if 50 of us do the same
+ 
+
+ align:start position:0%
+you know if if 50 of us do the same
+experiment and by random chance some of
+
+ align:start position:0%
+experiment and by random chance some of
+ 
+
+ align:start position:0%
+experiment and by random chance some of
+us are going to get better results than
+
+ align:start position:0%
+us are going to get better results than
+ 
+
+ align:start position:0%
+us are going to get better results than
+others and those are the ones that
+
+ align:start position:0%
+others and those are the ones that
+ 
+
+ align:start position:0%
+others and those are the ones that
+I get published because the people who
+
+ align:start position:0%
+I get published because the people who
+ 
+
+ align:start position:0%
+I get published because the people who
+got poor results don't have anything
+
+ align:start position:0%
+got poor results don't have anything
+ 
+
+ align:start position:0%
+got poor results don't have anything
+interesting to report and so there's
+
+ align:start position:0%
+interesting to report and so there's
+ 
+
+ align:start position:0%
+interesting to report and so there's
+that whole issue of publication bias
+
+ align:start position:0%
+that whole issue of publication bias
+ 
+
+ align:start position:0%
+that whole issue of publication bias
+which is another serious one okay so I
+
+ align:start position:0%
+which is another serious one okay so I
+ 
+
+ align:start position:0%
+which is another serious one okay so I
+wanted to just spend a minute to say you
+
+ align:start position:0%
+wanted to just spend a minute to say you
+ 
+
+ align:start position:0%
+wanted to just spend a minute to say you
+know explanation is not a new idea so in
+
+ align:start position:0%
+know explanation is not a new idea so in
+ 
+
+ align:start position:0%
+know explanation is not a new idea so in
+the expert system zero that we talked
+
+ align:start position:0%
+the expert system zero that we talked
+ 
+
+ align:start position:0%
+the expert system zero that we talked
+about a little bit in one of one of our
+
+ align:start position:0%
+about a little bit in one of one of our
+ 
+
+ align:start position:0%
+about a little bit in one of one of our
+earlier classes we talked about the idea
+
+ align:start position:0%
+earlier classes we talked about the idea
+ 
+
+ align:start position:0%
+earlier classes we talked about the idea
+that we would take medical human medical
+
+ align:start position:0%
+that we would take medical human medical
+ 
+
+ align:start position:0%
+that we would take medical human medical
+experts and debrief them of what they
+
+ align:start position:0%
+experts and debrief them of what they
+ 
+
+ align:start position:0%
+experts and debrief them of what they
+knew and then try to encode those in
+
+ align:start position:0%
+knew and then try to encode those in
+ 
+
+ align:start position:0%
+knew and then try to encode those in
+patterns or in rules or in various ways
+
+ align:start position:0%
+patterns or in rules or in various ways
+ 
+
+ align:start position:0%
+patterns or in rules or in various ways
+in a computer program in order to
+
+ align:start position:0%
+in a computer program in order to
+ 
+
+ align:start position:0%
+in a computer program in order to
+reproduce their behavior so my son was
+
+ align:start position:0%
+reproduce their behavior so my son was
+ 
+
+ align:start position:0%
+reproduce their behavior so my son was
+one of those programs petroglyphs PhD
+
+ align:start position:0%
+one of those programs petroglyphs PhD
+ 
+
+ align:start position:0%
+one of those programs petroglyphs PhD
+thesis in 1975 and they published this
+
+ align:start position:0%
+thesis in 1975 and they published this
+ 
+
+ align:start position:0%
+thesis in 1975 and they published this
+nice paper that was about explanation
+
+ align:start position:0%
+nice paper that was about explanation
+ 
+
+ align:start position:0%
+nice paper that was about explanation
+and rule acquisition capabilities of the
+
+ align:start position:0%
+and rule acquisition capabilities of the
+ 
+
+ align:start position:0%
+and rule acquisition capabilities of the
+Meissen system and as an illustration
+
+ align:start position:0%
+Meissen system and as an illustration
+ 
+
+ align:start position:0%
+Meissen system and as an illustration
+they gave some examples of what you
+
+ align:start position:0%
+they gave some examples of what you
+ 
+
+ align:start position:0%
+they gave some examples of what you
+could do with the system so rules they
+
+ align:start position:0%
+could do with the system so rules they
+ 
+
+ align:start position:0%
+could do with the system so rules they
+argued were quite understandable because
+
+ align:start position:0%
+argued were quite understandable because
+ 
+
+ align:start position:0%
+argued were quite understandable because
+they say if a bunch of conditions then
+
+ align:start position:0%
+they say if a bunch of conditions then
+ 
+
+ align:start position:0%
+they say if a bunch of conditions then
+you can draw the following conclusion
+
+ align:start position:0%
+you can draw the following conclusion
+ 
+
+ align:start position:0%
+you can draw the following conclusion
+right so given that you can say well
+
+ align:start position:0%
+right so given that you can say well
+ 
+
+ align:start position:0%
+right so given that you can say well
+when the program comes back and says in
+
+ align:start position:0%
+when the program comes back and says in
+ 
+
+ align:start position:0%
+when the program comes back and says in
+light of the site from which the culture
+
+ align:start position:0%
+light of the site from which the culture
+ 
+
+ align:start position:0%
+light of the site from which the culture
+was obtained and the method of
+
+ align:start position:0%
+was obtained and the method of
+ 
+
+ align:start position:0%
+was obtained and the method of
+collection do you feel that a
+
+ align:start position:0%
+collection do you feel that a
+ 
+
+ align:start position:0%
+collection do you feel that a
+significant number of organism one were
+
+ align:start position:0%
+significant number of organism one were
+ 
+
+ align:start position:0%
+significant number of organism one were
+detected were obtained right in other
+
+ align:start position:0%
+detected were obtained right in other
+ 
+
+ align:start position:0%
+detected were obtained right in other
+words if you took a sample from
+
+ align:start position:0%
+words if you took a sample from
+ 
+
+ align:start position:0%
+words if you took a sample from
+somebody's body and you're looking for
+
+ align:start position:0%
+somebody's body and you're looking for
+ 
+
+ align:start position:0%
+somebody's body and you're looking for
+an infection do you think you got enough
+
+ align:start position:0%
+an infection do you think you got enough
+ 
+
+ align:start position:0%
+an infection do you think you got enough
+organisms in that sample and the user
+
+ align:start position:0%
+organisms in that sample and the user
+ 
+
+ align:start position:0%
+organisms in that sample and the user
+says well why are you asking that me
+
+ align:start position:0%
+says well why are you asking that me
+ 
+
+ align:start position:0%
+says well why are you asking that me
+this question and the answer in terms of
+
+ align:start position:0%
+this question and the answer in terms of
+ 
+
+ align:start position:0%
+this question and the answer in terms of
+the rules that the system works by is
+
+ align:start position:0%
+the rules that the system works by is
+ 
+
+ align:start position:0%
+the rules that the system works by is
+pretty good it says it's important to
+
+ align:start position:0%
+pretty good it says it's important to
+ 
+
+ align:start position:0%
+pretty good it says it's important to
+find out whether there's therapeutically
+
+ align:start position:0%
+find out whether there's therapeutically
+ 
+
+ align:start position:0%
+find out whether there's therapeutically
+significant disease associated with this
+
+ align:start position:0%
+significant disease associated with this
+ 
+
+ align:start position:0%
+significant disease associated with this
+occurrence of organism one we've already
+
+ align:start position:0%
+occurrence of organism one we've already
+ 
+
+ align:start position:0%
+occurrence of organism one we've already
+established that the culture
+
+ align:start position:0%
+established that the culture
+ 
+
+ align:start position:0%
+established that the culture
+is not one of those that are normally
+
+ align:start position:0%
+is not one of those that are normally
+ 
+
+ align:start position:0%
+is not one of those that are normally
+sterile and the method of collection is
+
+ align:start position:0%
+sterile and the method of collection is
+ 
+
+ align:start position:0%
+sterile and the method of collection is
+sterile
+
+ align:start position:0%
+sterile
+ 
+
+ align:start position:0%
+sterile
+therefore if the organism has been
+
+ align:start position:0%
+therefore if the organism has been
+ 
+
+ align:start position:0%
+therefore if the organism has been
+observed in significant numbers then
+
+ align:start position:0%
+observed in significant numbers then
+ 
+
+ align:start position:0%
+observed in significant numbers then
+they're strongly suggestive evidence
+
+ align:start position:0%
+they're strongly suggestive evidence
+ 
+
+ align:start position:0%
+they're strongly suggestive evidence
+that there's therapeutically significant
+
+ align:start position:0%
+that there's therapeutically significant
+ 
+
+ align:start position:0%
+that there's therapeutically significant
+disease associated with this occurrence
+
+ align:start position:0%
+disease associated with this occurrence
+ 
+
+ align:start position:0%
+disease associated with this occurrence
+of the organism okay
+
+ align:start position:0%
+of the organism okay
+ 
+
+ align:start position:0%
+of the organism okay
+so if you find bugs in a place carefully
+
+ align:start position:0%
+so if you find bugs in a place carefully
+ 
+
+ align:start position:0%
+so if you find bugs in a place carefully
+collected then that suggests that you
+
+ align:start position:0%
+collected then that suggests that you
+ 
+
+ align:start position:0%
+collected then that suggests that you
+ought to probably treat this patient if
+
+ align:start position:0%
+ought to probably treat this patient if
+ 
+
+ align:start position:0%
+ought to probably treat this patient if
+there are a bunch of enough enough bugs
+
+ align:start position:0%
+there are a bunch of enough enough bugs
+ 
+
+ align:start position:0%
+there are a bunch of enough enough bugs
+there and there's also strongly
+
+ align:start position:0%
+there and there's also strongly
+ 
+
+ align:start position:0%
+there and there's also strongly
+suggestive evidence that the organism is
+
+ align:start position:0%
+suggestive evidence that the organism is
+ 
+
+ align:start position:0%
+suggestive evidence that the organism is
+not a contaminant because the collection
+
+ align:start position:0%
+not a contaminant because the collection
+ 
+
+ align:start position:0%
+not a contaminant because the collection
+method was sterile and you can go on
+
+ align:start position:0%
+method was sterile and you can go on
+ 
+
+ align:start position:0%
+method was sterile and you can go on
+with this and you can say well why did
+
+ align:start position:0%
+with this and you can say well why did
+ 
+
+ align:start position:0%
+with this and you can say well why did
+why why that so why that that question
+
+ align:start position:0%
+why why that so why that that question
+ 
+
+ align:start position:0%
+why why that so why that that question
+and and and it traces back in its
+
+ align:start position:0%
+and and and it traces back in its
+ 
+
+ align:start position:0%
+and and and it traces back in its
+evolution of these rules and it says
+
+ align:start position:0%
+evolution of these rules and it says
+ 
+
+ align:start position:0%
+evolution of these rules and it says
+well in order to find out the locus of
+
+ align:start position:0%
+well in order to find out the locus of
+ 
+
+ align:start position:0%
+well in order to find out the locus of
+infection it's already been established
+
+ align:start position:0%
+infection it's already been established
+ 
+
+ align:start position:0%
+infection it's already been established
+that the site of the culture is known
+
+ align:start position:0%
+that the site of the culture is known
+ 
+
+ align:start position:0%
+that the site of the culture is known
+the number of days since the specimen
+
+ align:start position:0%
+the number of days since the specimen
+ 
+
+ align:start position:0%
+the number of days since the specimen
+was obtained is less than seven
+
+ align:start position:0%
+was obtained is less than seven
+ 
+
+ align:start position:0%
+was obtained is less than seven
+therefore there's therapeutically
+
+ align:start position:0%
+therefore there's therapeutically
+ 
+
+ align:start position:0%
+therefore there's therapeutically
+significant disease associated with this
+
+ align:start position:0%
+significant disease associated with this
+ 
+
+ align:start position:0%
+significant disease associated with this
+recurrence of the organism so there's
+
+ align:start position:0%
+recurrence of the organism so there's
+ 
+
+ align:start position:0%
+recurrence of the organism so there's
+some rule that says if you got bugs and
+
+ align:start position:0%
+some rule that says if you got bugs and
+ 
+
+ align:start position:0%
+some rule that says if you got bugs and
+it happened within the last seven days
+
+ align:start position:0%
+it happened within the last seven days
+ 
+
+ align:start position:0%
+it happened within the last seven days
+the patient probably really does have an
+
+ align:start position:0%
+the patient probably really does have an
+ 
+
+ align:start position:0%
+the patient probably really does have an
+infection right so and I mean I've got a
+
+ align:start position:0%
+infection right so and I mean I've got a
+ 
+
+ align:start position:0%
+infection right so and I mean I've got a
+lot of examples of this but you can keep
+
+ align:start position:0%
+lot of examples of this but you can keep
+ 
+
+ align:start position:0%
+lot of examples of this but you can keep
+going why you know this is the
+
+ align:start position:0%
+going why you know this is the
+ 
+
+ align:start position:0%
+going why you know this is the
+two-year-old but why daddy but why but
+
+ align:start position:0%
+two-year-old but why daddy but why but
+ 
+
+ align:start position:0%
+two-year-old but why daddy but why but
+why well why is it important to find out
+
+ align:start position:0%
+why well why is it important to find out
+ 
+
+ align:start position:0%
+why well why is it important to find out
+a locus of infection and well there's a
+
+ align:start position:0%
+a locus of infection and well there's a
+ 
+
+ align:start position:0%
+a locus of infection and well there's a
+reason which is that there's a rule that
+
+ align:start position:0%
+reason which is that there's a rule that
+ 
+
+ align:start position:0%
+reason which is that there's a rule that
+will conclude for example that the
+
+ align:start position:0%
+will conclude for example that the
+ 
+
+ align:start position:0%
+will conclude for example that the
+abdomen is a locus of infection or the
+
+ align:start position:0%
+abdomen is a locus of infection or the
+ 
+
+ align:start position:0%
+abdomen is a locus of infection or the
+pelvis as a locus of infection of the
+
+ align:start position:0%
+pelvis as a locus of infection of the
+ 
+
+ align:start position:0%
+pelvis as a locus of infection of the
+patient if you satisfy these these
+
+ align:start position:0%
+patient if you satisfy these these
+ 
+
+ align:start position:0%
+patient if you satisfy these these
+criteria and so this is a kind of
+
+ align:start position:0%
+criteria and so this is a kind of
+ 
+
+ align:start position:0%
+criteria and so this is a kind of
+rudimentary explanation that comes
+
+ align:start position:0%
+rudimentary explanation that comes
+ 
+
+ align:start position:0%
+rudimentary explanation that comes
+directly out of the fact that these are
+
+ align:start position:0%
+directly out of the fact that these are
+ 
+
+ align:start position:0%
+directly out of the fact that these are
+rule based system
+
+ align:start position:0%
+rule based system
+ 
+
+ align:start position:0%
+rule based system
+and so you can just play back the rules
+
+ align:start position:0%
+and so you can just play back the rules
+ 
+
+ align:start position:0%
+and so you can just play back the rules
+one of the things I like is you can also
+
+ align:start position:0%
+one of the things I like is you can also
+ 
+
+ align:start position:0%
+one of the things I like is you can also
+ask freeform questions 1975 the natural
+
+ align:start position:0%
+ask freeform questions 1975 the natural
+ 
+
+ align:start position:0%
+ask freeform questions 1975 the natural
+language processing was not so good and
+
+ align:start position:0%
+language processing was not so good and
+ 
+
+ align:start position:0%
+language processing was not so good and
+so this worked about one time in five
+
+ align:start position:0%
+so this worked about one time in five
+ 
+
+ align:start position:0%
+so this worked about one time in five
+but you could walk up to it and type
+
+ align:start position:0%
+but you could walk up to it and type
+ 
+
+ align:start position:0%
+but you could walk up to it and type
+some question and for example do you
+
+ align:start position:0%
+some question and for example do you
+ 
+
+ align:start position:0%
+some question and for example do you
+ever prescribe carbon a salon for
+
+ align:start position:0%
+ever prescribe carbon a salon for
+ 
+
+ align:start position:0%
+ever prescribe carbon a salon for
+Pseudomonas infections and it says well
+
+ align:start position:0%
+Pseudomonas infections and it says well
+ 
+
+ align:start position:0%
+Pseudomonas infections and it says well
+there are three rules in my database of
+
+ align:start position:0%
+there are three rules in my database of
+ 
+
+ align:start position:0%
+there are three rules in my database of
+rules that would conclude something
+
+ align:start position:0%
+rules that would conclude something
+ 
+
+ align:start position:0%
+rules that would conclude something
+relevant to that question so which one
+
+ align:start position:0%
+relevant to that question so which one
+ 
+
+ align:start position:0%
+relevant to that question so which one
+do you want to see and if you say I want
+
+ align:start position:0%
+do you want to see and if you say I want
+ 
+
+ align:start position:0%
+do you want to see and if you say I want
+to see rule 64 it says while that rule
+
+ align:start position:0%
+to see rule 64 it says while that rule
+ 
+
+ align:start position:0%
+to see rule 64 it says while that rule
+says if it's known with certainty that
+
+ align:start position:0%
+says if it's known with certainty that
+ 
+
+ align:start position:0%
+says if it's known with certainty that
+the organism is a pseudo Pseudomonas and
+
+ align:start position:0%
+the organism is a pseudo Pseudomonas and
+ 
+
+ align:start position:0%
+the organism is a pseudo Pseudomonas and
+the drug under consideration is
+
+ align:start position:0%
+the drug under consideration is
+ 
+
+ align:start position:0%
+the drug under consideration is
+gentamicin then a more appropriate
+
+ align:start position:0%
+gentamicin then a more appropriate
+ 
+
+ align:start position:0%
+gentamicin then a more appropriate
+therapy would be a combination of
+
+ align:start position:0%
+therapy would be a combination of
+ 
+
+ align:start position:0%
+therapy would be a combination of
+gentamicin and carvanha Siwan again this
+
+ align:start position:0%
+gentamicin and carvanha Siwan again this
+ 
+
+ align:start position:0%
+gentamicin and carvanha Siwan again this
+is medical knowledge as of 1975 but my
+
+ align:start position:0%
+is medical knowledge as of 1975 but my
+ 
+
+ align:start position:0%
+is medical knowledge as of 1975 but my
+guess is the real underlying reason is
+
+ align:start position:0%
+guess is the real underlying reason is
+ 
+
+ align:start position:0%
+guess is the real underlying reason is
+that there are probably worse
+
+ align:start position:0%
+that there are probably worse
+ 
+
+ align:start position:0%
+that there are probably worse
+Pseudomonas that were resistant by that
+
+ align:start position:0%
+Pseudomonas that were resistant by that
+ 
+
+ align:start position:0%
+Pseudomonas that were resistant by that
+point to gentamicin and so they used a
+
+ align:start position:0%
+point to gentamicin and so they used a
+ 
+
+ align:start position:0%
+point to gentamicin and so they used a
+combination therapy now notice by the
+
+ align:start position:0%
+combination therapy now notice by the
+ 
+
+ align:start position:0%
+combination therapy now notice by the
+way that this explanation capability
+
+ align:start position:0%
+way that this explanation capability
+ 
+
+ align:start position:0%
+way that this explanation capability
+does not tell you that right because it
+
+ align:start position:0%
+does not tell you that right because it
+ 
+
+ align:start position:0%
+does not tell you that right because it
+doesn't actually understand the
+
+ align:start position:0%
+doesn't actually understand the
+ 
+
+ align:start position:0%
+doesn't actually understand the
+rationale behind these individual rules
+
+ align:start position:0%
+rationale behind these individual rules
+ 
+
+ align:start position:0%
+rationale behind these individual rules
+and at the time there was also research
+
+ align:start position:0%
+and at the time there was also research
+ 
+
+ align:start position:0%
+and at the time there was also research
+for example by one of my students on how
+
+ align:start position:0%
+for example by one of my students on how
+ 
+
+ align:start position:0%
+for example by one of my students on how
+to do a better job of that by by
+
+ align:start position:0%
+to do a better job of that by by
+ 
+
+ align:start position:0%
+to do a better job of that by by
+encoding not only the rules or the
+
+ align:start position:0%
+encoding not only the rules or the
+ 
+
+ align:start position:0%
+encoding not only the rules or the
+patterns but also the rationale behind
+
+ align:start position:0%
+patterns but also the rationale behind
+ 
+
+ align:start position:0%
+patterns but also the rationale behind
+them so that the explanations could be
+
+ align:start position:0%
+them so that the explanations could be
+ 
+
+ align:start position:0%
+them so that the explanations could be
+more sensible
+
+ align:start position:0%
+more sensible
+ 
+
+ align:start position:0%
+more sensible
+okay well the granddaddy of the standard
+
+ align:start position:0%
+okay well the granddaddy of the standard
+ 
+
+ align:start position:0%
+okay well the granddaddy of the standard
+just so story approach to explanation of
+
+ align:start position:0%
+just so story approach to explanation of
+ 
+
+ align:start position:0%
+just so story approach to explanation of
+complex models today comes from this
+
+ align:start position:0%
+complex models today comes from this
+ 
+
+ align:start position:0%
+complex models today comes from this
+paper and a system called Lyme locally
+
+ align:start position:0%
+paper and a system called Lyme locally
+ 
+
+ align:start position:0%
+paper and a system called Lyme locally
+interpretable model agnostic
+
+ align:start position:0%
+interpretable model agnostic
+ 
+
+ align:start position:0%
+interpretable model agnostic
+explanations and just to give you an
+
+ align:start position:0%
+explanations and just to give you an
+ 
+
+ align:start position:0%
+explanations and just to give you an
+illustration you have some complicated
+
+ align:start position:0%
+illustration you have some complicated
+ 
+
+ align:start position:0%
+illustration you have some complicated
+model and it's trying to explain why the
+
+ align:start position:0%
+model and it's trying to explain why the
+ 
+
+ align:start position:0%
+model and it's trying to explain why the
+or human being made a certain decision
+
+ align:start position:0%
+or human being made a certain decision
+ 
+
+ align:start position:0%
+or human being made a certain decision
+or why the model made a certain decision
+
+ align:start position:0%
+or why the model made a certain decision
+ 
+
+ align:start position:0%
+or why the model made a certain decision
+and so it says well here are the data we
+
+ align:start position:0%
+and so it says well here are the data we
+ 
+
+ align:start position:0%
+and so it says well here are the data we
+have about the patient we know that the
+
+ align:start position:0%
+have about the patient we know that the
+ 
+
+ align:start position:0%
+have about the patient we know that the
+patient is sneezing and we know their
+
+ align:start position:0%
+patient is sneezing and we know their
+ 
+
+ align:start position:0%
+patient is sneezing and we know their
+weight and their headache and their age
+
+ align:start position:0%
+weight and their headache and their age
+ 
+
+ align:start position:0%
+weight and their headache and their age
+and the fact that they have no fatigue
+
+ align:start position:0%
+and the fact that they have no fatigue
+ 
+
+ align:start position:0%
+and the fact that they have no fatigue
+and so the explainer says well why did
+
+ align:start position:0%
+and so the explainer says well why did
+ 
+
+ align:start position:0%
+and so the explainer says well why did
+the model decide this patient has the
+
+ align:start position:0%
+the model decide this patient has the
+ 
+
+ align:start position:0%
+the model decide this patient has the
+flu
+
+ align:start position:0%
+flu
+ 
+
+ align:start position:0%
+flu
+well positives are sneeze and headache
+
+ align:start position:0%
+well positives are sneeze and headache
+ 
+
+ align:start position:0%
+well positives are sneeze and headache
+and a negative is no fatigue right so it
+
+ align:start position:0%
+and a negative is no fatigue right so it
+ 
+
+ align:start position:0%
+and a negative is no fatigue right so it
+goes into this complicated model and it
+
+ align:start position:0%
+goes into this complicated model and it
+ 
+
+ align:start position:0%
+goes into this complicated model and it
+says well I can't explain all the
+
+ align:start position:0%
+says well I can't explain all the
+ 
+
+ align:start position:0%
+says well I can't explain all the
+numerology that happens in that the role
+
+ align:start position:0%
+numerology that happens in that the role
+ 
+
+ align:start position:0%
+numerology that happens in that the role
+network or Bayesian network or whatever
+
+ align:start position:0%
+network or Bayesian network or whatever
+ 
+
+ align:start position:0%
+network or Bayesian network or whatever
+network it's being it's using but I can
+
+ align:start position:0%
+network it's being it's using but I can
+ 
+
+ align:start position:0%
+network it's being it's using but I can
+specify that it looks like these are the
+
+ align:start position:0%
+specify that it looks like these are the
+ 
+
+ align:start position:0%
+specify that it looks like these are the
+most important positive and negative
+
+ align:start position:0%
+most important positive and negative
+ 
+
+ align:start position:0%
+most important positive and negative
+contributors yeah I'll show you some
+
+ align:start position:0%
+contributors yeah I'll show you some
+ 
+
+ align:start position:0%
+contributors yeah I'll show you some
+other kind of data and in a minute I
+
+ align:start position:0%
+other kind of data and in a minute I
+ 
+
+ align:start position:0%
+other kind of data and in a minute I
+think they originally worked it out for
+
+ align:start position:0%
+think they originally worked it out for
+ 
+
+ align:start position:0%
+think they originally worked it out for
+notes but it was also used for images
+
+ align:start position:0%
+notes but it was also used for images
+ 
+
+ align:start position:0%
+notes but it was also used for images
+and other as well okay and the argument
+
+ align:start position:0%
+and other as well okay and the argument
+ 
+
+ align:start position:0%
+and other as well okay and the argument
+they make is that this approach also
+
+ align:start position:0%
+they make is that this approach also
+ 
+
+ align:start position:0%
+they make is that this approach also
+helps to detect data leakage for example
+
+ align:start position:0%
+helps to detect data leakage for example
+ 
+
+ align:start position:0%
+helps to detect data leakage for example
+in one of their experiments the the
+
+ align:start position:0%
+in one of their experiments the the
+ 
+
+ align:start position:0%
+in one of their experiments the the
+headers of the data had information in
+
+ align:start position:0%
+headers of the data had information in
+ 
+
+ align:start position:0%
+headers of the data had information in
+them that that correlated highly with
+
+ align:start position:0%
+them that that correlated highly with
+ 
+
+ align:start position:0%
+them that that correlated highly with
+the result I think they're I can't
+
+ align:start position:0%
+the result I think they're I can't
+ 
+
+ align:start position:0%
+the result I think they're I can't
+remember if it was these guys but
+
+ align:start position:0%
+remember if it was these guys but
+ 
+
+ align:start position:0%
+remember if it was these guys but
+somebody was assigning study IDs to each
+
+ align:start position:0%
+somebody was assigning study IDs to each
+ 
+
+ align:start position:0%
+somebody was assigning study IDs to each
+case and they did it in a stupid way so
+
+ align:start position:0%
+case and they did it in a stupid way so
+ 
+
+ align:start position:0%
+case and they did it in a stupid way so
+that all the small numbers correspond it
+
+ align:start position:0%
+that all the small numbers correspond it
+ 
+
+ align:start position:0%
+that all the small numbers correspond it
+to people who had the disease and the
+
+ align:start position:0%
+to people who had the disease and the
+ 
+
+ align:start position:0%
+to people who had the disease and the
+big numbers correspond it to the people
+
+ align:start position:0%
+big numbers correspond it to the people
+ 
+
+ align:start position:0%
+big numbers correspond it to the people
+who didn't and of course the most
+
+ align:start position:0%
+who didn't and of course the most
+ 
+
+ align:start position:0%
+who didn't and of course the most
+parsimonious predictive model just used
+
+ align:start position:0%
+parsimonious predictive model just used
+ 
+
+ align:start position:0%
+parsimonious predictive model just used
+the ID number and said okay I got it so
+
+ align:start position:0%
+the ID number and said okay I got it so
+ 
+
+ align:start position:0%
+the ID number and said okay I got it so
+this would help you identify that
+
+ align:start position:0%
+this would help you identify that
+ 
+
+ align:start position:0%
+this would help you identify that
+because if you see that the best
+
+ align:start position:0%
+because if you see that the best
+ 
+
+ align:start position:0%
+because if you see that the best
+predictor is the ID
+
+ align:start position:0%
+predictor is the ID
+ 
+
+ align:start position:0%
+predictor is the ID
+number then you would say there's
+
+ align:start position:0%
+number then you would say there's
+ 
+
+ align:start position:0%
+number then you would say there's
+something a little fishy going on here
+
+ align:start position:0%
+something a little fishy going on here
+ 
+
+ align:start position:0%
+something a little fishy going on here
+well so here's an example where this
+
+ align:start position:0%
+well so here's an example where this
+ 
+
+ align:start position:0%
+well so here's an example where this
+kind of capability is very useful so
+
+ align:start position:0%
+kind of capability is very useful so
+ 
+
+ align:start position:0%
+kind of capability is very useful so
+this was another this was from a news
+
+ align:start position:0%
+this was another this was from a news
+ 
+
+ align:start position:0%
+this was another this was from a news
+group and they were trying to decide
+
+ align:start position:0%
+group and they were trying to decide
+ 
+
+ align:start position:0%
+group and they were trying to decide
+whether a post was about christianity or
+
+ align:start position:0%
+whether a post was about christianity or
+ 
+
+ align:start position:0%
+whether a post was about christianity or
+atheism okay now look at these two
+
+ align:start position:0%
+atheism okay now look at these two
+ 
+
+ align:start position:0%
+atheism okay now look at these two
+models
+
+ align:start position:0%
+models
+ 
+
+ align:start position:0%
+models
+so there's algorithm one an algorithm -
+
+ align:start position:0%
+so there's algorithm one an algorithm -
+ 
+
+ align:start position:0%
+so there's algorithm one an algorithm -
+or model one and model two and when you
+
+ align:start position:0%
+or model one and model two and when you
+ 
+
+ align:start position:0%
+or model one and model two and when you
+explain a particular case about using
+
+ align:start position:0%
+explain a particular case about using
+ 
+
+ align:start position:0%
+explain a particular case about using
+model one it says well the words that I
+
+ align:start position:0%
+model one it says well the words that I
+ 
+
+ align:start position:0%
+model one it says well the words that I
+consider important are God mean anyone
+
+ align:start position:0%
+consider important are God mean anyone
+ 
+
+ align:start position:0%
+consider important are God mean anyone
+this Koresh and through does there
+
+ align:start position:0%
+this Koresh and through does there
+ 
+
+ align:start position:0%
+this Koresh and through does there
+anybody remember who David Koresh was he
+
+ align:start position:0%
+anybody remember who David Koresh was he
+ 
+
+ align:start position:0%
+anybody remember who David Koresh was he
+was some cult leader who I can't
+
+ align:start position:0%
+was some cult leader who I can't
+ 
+
+ align:start position:0%
+was some cult leader who I can't
+remember if if he killed a bunch of
+
+ align:start position:0%
+remember if if he killed a bunch of
+ 
+
+ align:start position:0%
+remember if if he killed a bunch of
+people or bad things happened oh I think
+
+ align:start position:0%
+people or bad things happened oh I think
+ 
+
+ align:start position:0%
+people or bad things happened oh I think
+he was the guy in Waco Texas that the
+
+ align:start position:0%
+he was the guy in Waco Texas that the
+ 
+
+ align:start position:0%
+he was the guy in Waco Texas that the
+FBI and the ATF went in and and set
+
+ align:start position:0%
+FBI and the ATF went in and and set
+ 
+
+ align:start position:0%
+FBI and the ATF went in and and set
+their place on fire and a whole bunch of
+
+ align:start position:0%
+their place on fire and a whole bunch of
+ 
+
+ align:start position:0%
+their place on fire and a whole bunch of
+people died so the prediction in this
+
+ align:start position:0%
+people died so the prediction in this
+ 
+
+ align:start position:0%
+people died so the prediction in this
+case is atheism and you notice that God
+
+ align:start position:0%
+case is atheism and you notice that God
+ 
+
+ align:start position:0%
+case is atheism and you notice that God
+and Koresh and mean are negatives and
+
+ align:start position:0%
+and Koresh and mean are negatives and
+ 
+
+ align:start position:0%
+and Koresh and mean are negatives and
+anyone this and through our positives
+
+ align:start position:0%
+anyone this and through our positives
+ 
+
+ align:start position:0%
+anyone this and through our positives
+and you go
+
+ align:start position:0%
+and you go
+ 
+
+ align:start position:0%
+and you go
+is that good but then you look at
+
+ align:start position:0%
+is that good but then you look at
+ 
+
+ align:start position:0%
+is that good but then you look at
+algorithm two and you say this also made
+
+ align:start position:0%
+algorithm two and you say this also made
+ 
+
+ align:start position:0%
+algorithm two and you say this also made
+the correct prediction which is that
+
+ align:start position:0%
+the correct prediction which is that
+ 
+
+ align:start position:0%
+the correct prediction which is that
+this particular article is about atheism
+
+ align:start position:0%
+this particular article is about atheism
+ 
+
+ align:start position:0%
+this particular article is about atheism
+but the positives were the word by and
+
+ align:start position:0%
+but the positives were the word by and
+ 
+
+ align:start position:0%
+but the positives were the word by and
+in not not terribly specific and the
+
+ align:start position:0%
+in not not terribly specific and the
+ 
+
+ align:start position:0%
+in not not terribly specific and the
+negatives were things like nntp you know
+
+ align:start position:0%
+negatives were things like nntp you know
+ 
+
+ align:start position:0%
+negatives were things like nntp you know
+what that is that's the network time
+
+ align:start position:0%
+what that is that's the network time
+ 
+
+ align:start position:0%
+what that is that's the network time
+protocol okay it's some technical thing
+
+ align:start position:0%
+protocol okay it's some technical thing
+ 
+
+ align:start position:0%
+protocol okay it's some technical thing
+and posting and host so this is probably
+
+ align:start position:0%
+and posting and host so this is probably
+ 
+
+ align:start position:0%
+and posting and host so this is probably
+like metadata that got into the header
+
+ align:start position:0%
+like metadata that got into the header
+ 
+
+ align:start position:0%
+like metadata that got into the header
+of the articles or something so
+
+ align:start position:0%
+of the articles or something so
+ 
+
+ align:start position:0%
+of the articles or something so
+it happened that in this case algorithm
+
+ align:start position:0%
+it happened that in this case algorithm
+ 
+
+ align:start position:0%
+it happened that in this case algorithm
+two turned out to be more accurate than
+
+ align:start position:0%
+two turned out to be more accurate than
+ 
+
+ align:start position:0%
+two turned out to be more accurate than
+algorithm one on their held-out test
+
+ align:start position:0%
+algorithm one on their held-out test
+ 
+
+ align:start position:0%
+algorithm one on their held-out test
+data but not for any good reason and so
+
+ align:start position:0%
+data but not for any good reason and so
+ 
+
+ align:start position:0%
+data but not for any good reason and so
+the explanation capability allows you to
+
+ align:start position:0%
+the explanation capability allows you to
+ 
+
+ align:start position:0%
+the explanation capability allows you to
+clue in on the fact that even though
+
+ align:start position:0%
+clue in on the fact that even though
+ 
+
+ align:start position:0%
+clue in on the fact that even though
+this thing is getting the right answers
+
+ align:start position:0%
+this thing is getting the right answers
+ 
+
+ align:start position:0%
+this thing is getting the right answers
+it's not for sensible reasons okay so
+
+ align:start position:0%
+it's not for sensible reasons okay so
+ 
+
+ align:start position:0%
+it's not for sensible reasons okay so
+what would you like from an explanation
+
+ align:start position:0%
+what would you like from an explanation
+ 
+
+ align:start position:0%
+what would you like from an explanation
+well they say you'd like it to be
+
+ align:start position:0%
+well they say you'd like it to be
+ 
+
+ align:start position:0%
+well they say you'd like it to be
+interpretable so it should provide
+
+ align:start position:0%
+interpretable so it should provide
+ 
+
+ align:start position:0%
+interpretable so it should provide
+qualitative understanding of the
+
+ align:start position:0%
+qualitative understanding of the
+ 
+
+ align:start position:0%
+qualitative understanding of the
+relationship between the input variables
+
+ align:start position:0%
+relationship between the input variables
+ 
+
+ align:start position:0%
+relationship between the input variables
+and the response but they also say that
+
+ align:start position:0%
+and the response but they also say that
+ 
+
+ align:start position:0%
+and the response but they also say that
+that's going to depend on the audience
+
+ align:start position:0%
+that's going to depend on the audience
+ 
+
+ align:start position:0%
+that's going to depend on the audience
+it requires sparsity for the george
+
+ align:start position:0%
+it requires sparsity for the george
+ 
+
+ align:start position:0%
+it requires sparsity for the george
+miller argument that i was making before
+
+ align:start position:0%
+miller argument that i was making before
+ 
+
+ align:start position:0%
+miller argument that i was making before
+you can't keep too many things in mind
+
+ align:start position:0%
+you can't keep too many things in mind
+ 
+
+ align:start position:0%
+you can't keep too many things in mind
+and the features themselves that you're
+
+ align:start position:0%
+and the features themselves that you're
+ 
+
+ align:start position:0%
+and the features themselves that you're
+explaining must make sense so for
+
+ align:start position:0%
+explaining must make sense so for
+ 
+
+ align:start position:0%
+explaining must make sense so for
+example if i say well the reason this
+
+ align:start position:0%
+example if i say well the reason this
+ 
+
+ align:start position:0%
+example if i say well the reason this
+decided that is because the eigenvector
+
+ align:start position:0%
+decided that is because the eigenvector
+ 
+
+ align:start position:0%
+decided that is because the eigenvector
+for the first principal component was
+
+ align:start position:0%
+for the first principal component was
+ 
+
+ align:start position:0%
+for the first principal component was
+the following
+
+ align:start position:0%
+the following
+ 
+
+ align:start position:0%
+the following
+that's not gonna mean much to most
+
+ align:start position:0%
+that's not gonna mean much to most
+ 
+
+ align:start position:0%
+that's not gonna mean much to most
+people and then they also say well it
+
+ align:start position:0%
+people and then they also say well it
+ 
+
+ align:start position:0%
+people and then they also say well it
+ought to have local fidelity so it must
+
+ align:start position:0%
+ought to have local fidelity so it must
+ 
+
+ align:start position:0%
+ought to have local fidelity so it must
+correspond to how the model behaves in
+
+ align:start position:0%
+correspond to how the model behaves in
+ 
+
+ align:start position:0%
+correspond to how the model behaves in
+the vicinity of the particular instance
+
+ align:start position:0%
+the vicinity of the particular instance
+ 
+
+ align:start position:0%
+the vicinity of the particular instance
+that you're trying to explain and their
+
+ align:start position:0%
+that you're trying to explain and their
+ 
+
+ align:start position:0%
+that you're trying to explain and their
+third criterion which i think is a
+
+ align:start position:0%
+third criterion which i think is a
+ 
+
+ align:start position:0%
+third criterion which i think is a
+little iffy er is that it must be model
+
+ align:start position:0%
+little iffy er is that it must be model
+ 
+
+ align:start position:0%
+little iffy er is that it must be model
+agnostic in other words you can't take
+
+ align:start position:0%
+agnostic in other words you can't take
+ 
+
+ align:start position:0%
+agnostic in other words you can't take
+advantage of anything you know that is
+
+ align:start position:0%
+advantage of anything you know that is
+ 
+
+ align:start position:0%
+advantage of anything you know that is
+specific about the structure of the
+
+ align:start position:0%
+specific about the structure of the
+ 
+
+ align:start position:0%
+specific about the structure of the
+model the way you trained it anything
+
+ align:start position:0%
+model the way you trained it anything
+ 
+
+ align:start position:0%
+model the way you trained it anything
+like that it has to be a general-purpose
+
+ align:start position:0%
+like that it has to be a general-purpose
+ 
+
+ align:start position:0%
+like that it has to be a general-purpose
+explainer that works on any kind of
+
+ align:start position:0%
+explainer that works on any kind of
+ 
+
+ align:start position:0%
+explainer that works on any kind of
+complicated model yeah I think their
+
+ align:start position:0%
+complicated model yeah I think their
+ 
+
+ align:start position:0%
+complicated model yeah I think their
+their reasoning for why they insist on
+
+ align:start position:0%
+their reasoning for why they insist on
+ 
+
+ align:start position:0%
+their reasoning for why they insist on
+this is because they don't want to have
+
+ align:start position:0%
+this is because they don't want to have
+ 
+
+ align:start position:0%
+this is because they don't want to have
+to write a separate explainer for each
+
+ align:start position:0%
+to write a separate explainer for each
+ 
+
+ align:start position:0%
+to write a separate explainer for each
+possible model so it's much more
+
+ align:start position:0%
+possible model so it's much more
+ 
+
+ align:start position:0%
+possible model so it's much more
+efficient if you can get this done but I
+
+ align:start position:0%
+efficient if you can get this done but I
+ 
+
+ align:start position:0%
+efficient if you can get this done but I
+actually questioned whether this is
+
+ align:start position:0%
+actually questioned whether this is
+ 
+
+ align:start position:0%
+actually questioned whether this is
+always a good idea or not but
+
+ align:start position:0%
+always a good idea or not but
+ 
+
+ align:start position:0%
+always a good idea or not but
+nevertheless this is one of their
+
+ align:start position:0%
+nevertheless this is one of their
+ 
+
+ align:start position:0%
+nevertheless this is one of their
+assumptions okay so here's the setup
+
+ align:start position:0%
+assumptions okay so here's the setup
+ 
+
+ align:start position:0%
+assumptions okay so here's the setup
+that they use they say all right X is a
+
+ align:start position:0%
+that they use they say all right X is a
+ 
+
+ align:start position:0%
+that they use they say all right X is a
+vector in some D dimensional space that
+
+ align:start position:0%
+vector in some D dimensional space that
+ 
+
+ align:start position:0%
+vector in some D dimensional space that
+defines your original data and what
+
+ align:start position:0%
+defines your original data and what
+ 
+
+ align:start position:0%
+defines your original data and what
+we're gonna do in order to make the data
+
+ align:start position:0%
+we're gonna do in order to make the data
+ 
+
+ align:start position:0%
+we're gonna do in order to make the data
+explainable in order to make the data
+
+ align:start position:0%
+explainable in order to make the data
+ 
+
+ align:start position:0%
+explainable in order to make the data
+not the model explainable is we're going
+
+ align:start position:0%
+not the model explainable is we're going
+ 
+
+ align:start position:0%
+not the model explainable is we're going
+to define a new set of variables X prime
+
+ align:start position:0%
+to define a new set of variables X prime
+ 
+
+ align:start position:0%
+to define a new set of variables X prime
+that are all binary and that are in some
+
+ align:start position:0%
+that are all binary and that are in some
+ 
+
+ align:start position:0%
+that are all binary and that are in some
+space of dimension D prime that is
+
+ align:start position:0%
+space of dimension D prime that is
+ 
+
+ align:start position:0%
+space of dimension D prime that is
+probably lower than D okay so it's we're
+
+ align:start position:0%
+probably lower than D okay so it's we're
+ 
+
+ align:start position:0%
+probably lower than D okay so it's we're
+simplifying the data that we're gonna
+
+ align:start position:0%
+simplifying the data that we're gonna
+ 
+
+ align:start position:0%
+simplifying the data that we're gonna
+explain about this model then they say
+
+ align:start position:0%
+explain about this model then they say
+ 
+
+ align:start position:0%
+explain about this model then they say
+okay we're going to build an explanation
+
+ align:start position:0%
+okay we're going to build an explanation
+ 
+
+ align:start position:0%
+okay we're going to build an explanation
+model G where G is the class of
+
+ align:start position:0%
+model G where G is the class of
+ 
+
+ align:start position:0%
+model G where G is the class of
+interpretable models so what's an
+
+ align:start position:0%
+interpretable models so what's an
+ 
+
+ align:start position:0%
+interpretable models so what's an
+interpretable model well they don't tell
+
+ align:start position:0%
+interpretable model well they don't tell
+ 
+
+ align:start position:0%
+interpretable model well they don't tell
+you but they say well examples might be
+
+ align:start position:0%
+you but they say well examples might be
+ 
+
+ align:start position:0%
+you but they say well examples might be
+linear models additive scores decision
+
+ align:start position:0%
+linear models additive scores decision
+ 
+
+ align:start position:0%
+linear models additive scores decision
+trees falling rule lists which
+
+ align:start position:0%
+trees falling rule lists which
+ 
+
+ align:start position:0%
+trees falling rule lists which
+see you later in the lecture and the
+
+ align:start position:0%
+see you later in the lecture and the
+ 
+
+ align:start position:0%
+see you later in the lecture and the
+domain of this is this input the
+
+ align:start position:0%
+domain of this is this input the
+ 
+
+ align:start position:0%
+domain of this is this input the
+simplified input data the binary
+
+ align:start position:0%
+simplified input data the binary
+ 
+
+ align:start position:0%
+simplified input data the binary
+variables in D prime dimensions and the
+
+ align:start position:0%
+variables in D prime dimensions and the
+ 
+
+ align:start position:0%
+variables in D prime dimensions and the
+model complexity is going to be some
+
+ align:start position:0%
+model complexity is going to be some
+ 
+
+ align:start position:0%
+model complexity is going to be some
+measure of the depths of the decision
+
+ align:start position:0%
+measure of the depths of the decision
+ 
+
+ align:start position:0%
+measure of the depths of the decision
+tree the number of nonzero weights and
+
+ align:start position:0%
+tree the number of nonzero weights and
+ 
+
+ align:start position:0%
+tree the number of nonzero weights and
+the logistic regression the number of
+
+ align:start position:0%
+the logistic regression the number of
+ 
+
+ align:start position:0%
+the logistic regression the number of
+clauses in a following rule list etc so
+
+ align:start position:0%
+clauses in a following rule list etc so
+ 
+
+ align:start position:0%
+clauses in a following rule list etc so
+it's some complexity measure and you
+
+ align:start position:0%
+it's some complexity measure and you
+ 
+
+ align:start position:0%
+it's some complexity measure and you
+want to minimize complexity so then they
+
+ align:start position:0%
+want to minimize complexity so then they
+ 
+
+ align:start position:0%
+want to minimize complexity so then they
+say alright the real model the the hairy
+
+ align:start position:0%
+say alright the real model the the hairy
+ 
+
+ align:start position:0%
+say alright the real model the the hairy
+complicated full Bohr model is F and
+
+ align:start position:0%
+complicated full Bohr model is F and
+ 
+
+ align:start position:0%
+complicated full Bohr model is F and
+that map's the original data space into
+
+ align:start position:0%
+that map's the original data space into
+ 
+
+ align:start position:0%
+that map's the original data space into
+some probability and for example for
+
+ align:start position:0%
+some probability and for example for
+ 
+
+ align:start position:0%
+some probability and for example for
+classification F is the probability that
+
+ align:start position:0%
+classification F is the probability that
+ 
+
+ align:start position:0%
+classification F is the probability that
+X belongs to a certain class and then
+
+ align:start position:0%
+X belongs to a certain class and then
+ 
+
+ align:start position:0%
+X belongs to a certain class and then
+they also need a proximity measure so
+
+ align:start position:0%
+they also need a proximity measure so
+ 
+
+ align:start position:0%
+they also need a proximity measure so
+they need to say we have to have a way
+
+ align:start position:0%
+they need to say we have to have a way
+ 
+
+ align:start position:0%
+they need to say we have to have a way
+of comparing two cases and saying how
+
+ align:start position:0%
+of comparing two cases and saying how
+ 
+
+ align:start position:0%
+of comparing two cases and saying how
+close are they to each other and the
+
+ align:start position:0%
+close are they to each other and the
+ 
+
+ align:start position:0%
+close are they to each other and the
+reason for that is because remember
+
+ align:start position:0%
+reason for that is because remember
+ 
+
+ align:start position:0%
+reason for that is because remember
+they're going to give you an explanation
+
+ align:start position:0%
+they're going to give you an explanation
+ 
+
+ align:start position:0%
+they're going to give you an explanation
+of a particular case and the most
+
+ align:start position:0%
+of a particular case and the most
+ 
+
+ align:start position:0%
+of a particular case and the most
+relevant things that will help with that
+
+ align:start position:0%
+relevant things that will help with that
+ 
+
+ align:start position:0%
+relevant things that will help with that
+explanation are the ones that are near
+
+ align:start position:0%
+explanation are the ones that are near
+ 
+
+ align:start position:0%
+explanation are the ones that are near
+it in this high dimensional input space
+
+ align:start position:0%
+it in this high dimensional input space
+ 
+
+ align:start position:0%
+it in this high dimensional input space
+okay so they then define their loss
+
+ align:start position:0%
+okay so they then define their loss
+ 
+
+ align:start position:0%
+okay so they then define their loss
+function based on the actual decision
+
+ align:start position:0%
+function based on the actual decision
+ 
+
+ align:start position:0%
+function based on the actual decision
+algorithm based on the simplified one
+
+ align:start position:0%
+algorithm based on the simplified one
+ 
+
+ align:start position:0%
+algorithm based on the simplified one
+and based on the proximity measure and
+
+ align:start position:0%
+and based on the proximity measure and
+ 
+
+ align:start position:0%
+and based on the proximity measure and
+they say well the best explanation is
+
+ align:start position:0%
+they say well the best explanation is
+ 
+
+ align:start position:0%
+they say well the best explanation is
+that G which minimizes this loss
+
+ align:start position:0%
+that G which minimizes this loss
+ 
+
+ align:start position:0%
+that G which minimizes this loss
+function plus the complexity of G pretty
+
+ align:start position:0%
+function plus the complexity of G pretty
+ 
+
+ align:start position:0%
+function plus the complexity of G pretty
+straightforward so that's our best best
+
+ align:start position:0%
+straightforward so that's our best best
+ 
+
+ align:start position:0%
+straightforward so that's our best best
+model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the clever idea here is to say
+
+ align:start position:0%
+now the clever idea here is to say
+ 
+
+ align:start position:0%
+now the clever idea here is to say
+instead of using all of the data that we
+
+ align:start position:0%
+instead of using all of the data that we
+ 
+
+ align:start position:0%
+instead of using all of the data that we
+started with what we're going to do is
+
+ align:start position:0%
+started with what we're going to do is
+ 
+
+ align:start position:0%
+started with what we're going to do is
+to sample the data so that we take more
+
+ align:start position:0%
+to sample the data so that we take more
+ 
+
+ align:start position:0%
+to sample the data so that we take more
+sample points near the point we're
+
+ align:start position:0%
+sample points near the point we're
+ 
+
+ align:start position:0%
+sample points near the point we're
+interested in exploit explaining we're
+
+ align:start position:0%
+interested in exploit explaining we're
+ 
+
+ align:start position:0%
+interested in exploit explaining we're
+going to sample in the simplified space
+
+ align:start position:0%
+going to sample in the simplified space
+ 
+
+ align:start position:0%
+going to sample in the simplified space
+that is explainable and then we'll build
+
+ align:start position:0%
+that is explainable and then we'll build
+ 
+
+ align:start position:0%
+that is explainable and then we'll build
+that G model the explanatory model from
+
+ align:start position:0%
+that G model the explanatory model from
+ 
+
+ align:start position:0%
+that G model the explanatory model from
+that sample of data where we wait by
+
+ align:start position:0%
+that sample of data where we wait by
+ 
+
+ align:start position:0%
+that sample of data where we wait by
+that proximity function so the things
+
+ align:start position:0%
+that proximity function so the things
+ 
+
+ align:start position:0%
+that proximity function so the things
+that are closer will have a larger
+
+ align:start position:0%
+that are closer will have a larger
+ 
+
+ align:start position:0%
+that are closer will have a larger
+influence on the model that we learn and
+
+ align:start position:0%
+influence on the model that we learn and
+ 
+
+ align:start position:0%
+influence on the model that we learn and
+then we recapture the sort of the
+
+ align:start position:0%
+then we recapture the sort of the
+ 
+
+ align:start position:0%
+then we recapture the sort of the
+closest point to this simplified
+
+ align:start position:0%
+closest point to this simplified
+ 
+
+ align:start position:0%
+closest point to this simplified
+representation we can calculate what its
+
+ align:start position:0%
+representation we can calculate what its
+ 
+
+ align:start position:0%
+representation we can calculate what its
+answer should be and that becomes the
+
+ align:start position:0%
+answer should be and that becomes the
+ 
+
+ align:start position:0%
+answer should be and that becomes the
+label for that point and so now we
+
+ align:start position:0%
+label for that point and so now we
+ 
+
+ align:start position:0%
+label for that point and so now we
+trained a simple model to predict the
+
+ align:start position:0%
+trained a simple model to predict the
+ 
+
+ align:start position:0%
+trained a simple model to predict the
+label that the complicated model would
+
+ align:start position:0%
+label that the complicated model would
+ 
+
+ align:start position:0%
+label that the complicated model would
+have predicted for the point that we've
+
+ align:start position:0%
+have predicted for the point that we've
+ 
+
+ align:start position:0%
+have predicted for the point that we've
+sampled okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a distance function of some sort
+
+ align:start position:0%
+it's a distance function of some sort
+ 
+
+ align:start position:0%
+it's a distance function of some sort
+and I'll say more about it in a minute
+
+ align:start position:0%
+and I'll say more about it in a minute
+ 
+
+ align:start position:0%
+and I'll say more about it in a minute
+because that's one of the critiques of
+
+ align:start position:0%
+because that's one of the critiques of
+ 
+
+ align:start position:0%
+because that's one of the critiques of
+this particular method has to do with
+
+ align:start position:0%
+this particular method has to do with
+ 
+
+ align:start position:0%
+this particular method has to do with
+how do you choose that distance function
+
+ align:start position:0%
+how do you choose that distance function
+ 
+
+ align:start position:0%
+how do you choose that distance function
+but it's basically a similarity so
+
+ align:start position:0%
+but it's basically a similarity so
+ 
+
+ align:start position:0%
+but it's basically a similarity so
+here's a nice graphical explanation of
+
+ align:start position:0%
+here's a nice graphical explanation of
+ 
+
+ align:start position:0%
+here's a nice graphical explanation of
+what's going on
+
+ align:start position:0%
+what's going on
+ 
+
+ align:start position:0%
+what's going on
+suppose that the actual model the
+
+ align:start position:0%
+suppose that the actual model the
+ 
+
+ align:start position:0%
+suppose that the actual model the
+decision boundary is between the blue
+
+ align:start position:0%
+decision boundary is between the blue
+ 
+
+ align:start position:0%
+decision boundary is between the blue
+and the pink regions okay
+
+ align:start position:0%
+and the pink regions okay
+ 
+
+ align:start position:0%
+and the pink regions okay
+so it's this god-awful hairy complicated
+
+ align:start position:0%
+so it's this god-awful hairy complicated
+ 
+
+ align:start position:0%
+so it's this god-awful hairy complicated
+decision model and we're trying to
+
+ align:start position:0%
+decision model and we're trying to
+ 
+
+ align:start position:0%
+decision model and we're trying to
+explain why this big red plus wound up
+
+ align:start position:0%
+explain why this big red plus wound up
+ 
+
+ align:start position:0%
+explain why this big red plus wound up
+in the pink rather than in the blue so
+
+ align:start position:0%
+in the pink rather than in the blue so
+ 
+
+ align:start position:0%
+in the pink rather than in the blue so
+the approach that they take is to say
+
+ align:start position:0%
+the approach that they take is to say
+ 
+
+ align:start position:0%
+the approach that they take is to say
+well let's sample a bunch of points
+
+ align:start position:0%
+well let's sample a bunch of points
+ 
+
+ align:start position:0%
+well let's sample a bunch of points
+weighted by shortest distance so we do
+
+ align:start position:0%
+weighted by shortest distance so we do
+ 
+
+ align:start position:0%
+weighted by shortest distance so we do
+sample a few points out here but mostly
+
+ align:start position:0%
+sample a few points out here but mostly
+ 
+
+ align:start position:0%
+sample a few points out here but mostly
+we're sampling points near the point
+
+ align:start position:0%
+we're sampling points near the point
+ 
+
+ align:start position:0%
+we're sampling points near the point
+that we're interested in we then learn a
+
+ align:start position:0%
+that we're interested in we then learn a
+ 
+
+ align:start position:0%
+that we're interested in we then learn a
+linear boundary between the positive and
+
+ align:start position:0%
+linear boundary between the positive and
+ 
+
+ align:start position:0%
+linear boundary between the positive and
+the negative cases and that boundary is
+
+ align:start position:0%
+the negative cases and that boundary is
+ 
+
+ align:start position:0%
+the negative cases and that boundary is
+an approximation to the actual boundary
+
+ align:start position:0%
+an approximation to the actual boundary
+ 
+
+ align:start position:0%
+an approximation to the actual boundary
+in the more complicated decision model
+
+ align:start position:0%
+in the more complicated decision model
+ 
+
+ align:start position:0%
+in the more complicated decision model
+okay so now we can give an explanation
+
+ align:start position:0%
+okay so now we can give an explanation
+ 
+
+ align:start position:0%
+okay so now we can give an explanation
+just like you saw before which says well
+
+ align:start position:0%
+just like you saw before which says well
+ 
+
+ align:start position:0%
+just like you saw before which says well
+this is some D prime dimensional space
+
+ align:start position:0%
+this is some D prime dimensional space
+ 
+
+ align:start position:0%
+this is some D prime dimensional space
+and so which variables in that the D
+
+ align:start position:0%
+and so which variables in that the D
+ 
+
+ align:start position:0%
+and so which variables in that the D
+prime dimensional space are the ones
+
+ align:start position:0%
+prime dimensional space are the ones
+ 
+
+ align:start position:0%
+prime dimensional space are the ones
+that influence where you are on one side
+
+ align:start position:0%
+that influence where you are on one side
+ 
+
+ align:start position:0%
+that influence where you are on one side
+or another of this newly computed
+
+ align:start position:0%
+or another of this newly computed
+ 
+
+ align:start position:0%
+or another of this newly computed
+decision boundary and to and to what
+
+ align:start position:0%
+decision boundary and to and to what
+ 
+
+ align:start position:0%
+decision boundary and to and to what
+extent and that becomes the explanation
+
+ align:start position:0%
+extent and that becomes the explanation
+ 
+
+ align:start position:0%
+extent and that becomes the explanation
+okay nice idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you apply this to text
+
+ align:start position:0%
+so if you apply this to text
+ 
+
+ align:start position:0%
+so if you apply this to text
+classification yes well that's why I
+
+ align:start position:0%
+classification yes well that's why I
+ 
+
+ align:start position:0%
+classification yes well that's why I
+called the called just so story right
+
+ align:start position:0%
+called the called just so story right
+ 
+
+ align:start position:0%
+called the called just so story right
+should you believe it well the
+
+ align:start position:0%
+should you believe it well the
+ 
+
+ align:start position:0%
+should you believe it well the
+engineering disciplines have a very long
+
+ align:start position:0%
+engineering disciplines have a very long
+ 
+
+ align:start position:0%
+engineering disciplines have a very long
+history of approximating extremely
+
+ align:start position:0%
+history of approximating extremely
+ 
+
+ align:start position:0%
+history of approximating extremely
+complicated phenomena with linear models
+
+ align:start position:0%
+complicated phenomena with linear models
+ 
+
+ align:start position:0%
+complicated phenomena with linear models
+right I mean I'm I'm in a Department of
+
+ align:start position:0%
+right I mean I'm I'm in a Department of
+ 
+
+ align:start position:0%
+right I mean I'm I'm in a Department of
+Electrical Engineering and computer
+
+ align:start position:0%
+Electrical Engineering and computer
+ 
+
+ align:start position:0%
+Electrical Engineering and computer
+science and if I talked to my electrical
+
+ align:start position:0%
+science and if I talked to my electrical
+ 
+
+ align:start position:0%
+science and if I talked to my electrical
+engineering colleagues they know that
+
+ align:start position:0%
+engineering colleagues they know that
+ 
+
+ align:start position:0%
+engineering colleagues they know that
+the world is insanely complicated
+
+ align:start position:0%
+the world is insanely complicated
+ 
+
+ align:start position:0%
+the world is insanely complicated
+nevertheless most models in electrical
+
+ align:start position:0%
+nevertheless most models in electrical
+ 
+
+ align:start position:0%
+nevertheless most models in electrical
+engineering or linear models and they
+
+ align:start position:0%
+engineering or linear models and they
+ 
+
+ align:start position:0%
+engineering or linear models and they
+work well enough that people are able to
+
+ align:start position:0%
+work well enough that people are able to
+ 
+
+ align:start position:0%
+work well enough that people are able to
+build really complicated things and have
+
+ align:start position:0%
+build really complicated things and have
+ 
+
+ align:start position:0%
+build really complicated things and have
+them work so I that's not a proof that
+
+ align:start position:0%
+them work so I that's not a proof that
+ 
+
+ align:start position:0%
+them work so I that's not a proof that
+that's an argument by by history or
+
+ align:start position:0%
+that's an argument by by history or
+ 
+
+ align:start position:0%
+that's an argument by by history or
+something but it's true linear models
+
+ align:start position:0%
+something but it's true linear models
+ 
+
+ align:start position:0%
+something but it's true linear models
+are very powerful especially when you
+
+ align:start position:0%
+are very powerful especially when you
+ 
+
+ align:start position:0%
+are very powerful especially when you
+limit them to giving explanations that
+
+ align:start position:0%
+limit them to giving explanations that
+ 
+
+ align:start position:0%
+limit them to giving explanations that
+are local notice that this model is a
+
+ align:start position:0%
+are local notice that this model is a
+ 
+
+ align:start position:0%
+are local notice that this model is a
+very poor approximation to this decision
+
+ align:start position:0%
+very poor approximation to this decision
+ 
+
+ align:start position:0%
+very poor approximation to this decision
+boundary or this one right and so it
+
+ align:start position:0%
+boundary or this one right and so it
+ 
+
+ align:start position:0%
+boundary or this one right and so it
+only works to explain in the
+
+ align:start position:0%
+only works to explain in the
+ 
+
+ align:start position:0%
+only works to explain in the
+neighborhood of the particular example
+
+ align:start position:0%
+neighborhood of the particular example
+ 
+
+ align:start position:0%
+neighborhood of the particular example
+that I've chosen all right but it does
+
+ align:start position:0%
+that I've chosen all right but it does
+ 
+
+ align:start position:0%
+that I've chosen all right but it does
+work okay there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the middle of the red space then
+
+ align:start position:0%
+in the middle of the red space then
+ 
+
+ align:start position:0%
+in the middle of the red space then
+well they did so they sample all over
+
+ align:start position:0%
+well they did so they sample all over
+ 
+
+ align:start position:0%
+well they did so they sample all over
+the place but remember that that
+
+ align:start position:0%
+the place but remember that that
+ 
+
+ align:start position:0%
+the place but remember that that
+proximity function says that this one is
+
+ align:start position:0%
+proximity function says that this one is
+ 
+
+ align:start position:0%
+proximity function says that this one is
+less relevant to predicting that that
+
+ align:start position:0%
+less relevant to predicting that that
+ 
+
+ align:start position:0%
+less relevant to predicting that that
+decision boundary because it's far away
+
+ align:start position:0%
+decision boundary because it's far away
+ 
+
+ align:start position:0%
+decision boundary because it's far away
+from the point that I'm interested in so
+
+ align:start position:0%
+from the point that I'm interested in so
+ 
+
+ align:start position:0%
+from the point that I'm interested in so
+that's the magic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well but but they they would I mean it's
+
+ align:start position:0%
+well but but they they would I mean it's
+ 
+
+ align:start position:0%
+well but but they they would I mean it's
+suppose they picked this point instead
+
+ align:start position:0%
+suppose they picked this point instead
+ 
+
+ align:start position:0%
+suppose they picked this point instead
+then they would sample around this point
+
+ align:start position:0%
+then they would sample around this point
+ 
+
+ align:start position:0%
+then they would sample around this point
+and and presumably they would find this
+
+ align:start position:0%
+and and presumably they would find this
+ 
+
+ align:start position:0%
+and and presumably they would find this
+decision boundary or this one or
+
+ align:start position:0%
+decision boundary or this one or
+ 
+
+ align:start position:0%
+decision boundary or this one or
+something like that and still still be
+
+ align:start position:0%
+something like that and still still be
+ 
+
+ align:start position:0%
+something like that and still still be
+able to come up with a coherent
+
+ align:start position:0%
+able to come up with a coherent
+ 
+
+ align:start position:0%
+able to come up with a coherent
+explanation okay so in the case of text
+
+ align:start position:0%
+explanation okay so in the case of text
+ 
+
+ align:start position:0%
+explanation okay so in the case of text
+you've seen this example already it's
+
+ align:start position:0%
+you've seen this example already it's
+ 
+
+ align:start position:0%
+you've seen this example already it's
+pretty simple they for their proximity
+
+ align:start position:0%
+pretty simple they for their proximity
+ 
+
+ align:start position:0%
+pretty simple they for their proximity
+function they use cosine distance so two
+
+ align:start position:0%
+function they use cosine distance so two
+ 
+
+ align:start position:0%
+function they use cosine distance so two
+bag of words model and they just
+
+ align:start position:0%
+bag of words model and they just
+ 
+
+ align:start position:0%
+bag of words model and they just
+calculate cosine distance between
+
+ align:start position:0%
+calculate cosine distance between
+ 
+
+ align:start position:0%
+calculate cosine distance between
+different examples by how much overlap
+
+ align:start position:0%
+different examples by how much overlap
+ 
+
+ align:start position:0%
+different examples by how much overlap
+there is between the words that they use
+
+ align:start position:0%
+there is between the words that they use
+ 
+
+ align:start position:0%
+there is between the words that they use
+and the frequency of words that they use
+
+ align:start position:0%
+and the frequency of words that they use
+ 
+
+ align:start position:0%
+and the frequency of words that they use
+and then they choose K with the number
+
+ align:start position:0%
+and then they choose K with the number
+ 
+
+ align:start position:0%
+and then they choose K with the number
+of words to show just as a preference so
+
+ align:start position:0%
+of words to show just as a preference so
+ 
+
+ align:start position:0%
+of words to show just as a preference so
+it's sort of a hyper parameter they say
+
+ align:start position:0%
+it's sort of a hyper parameter they say
+ 
+
+ align:start position:0%
+it's sort of a hyper parameter they say
+you know I'm interested in looking at
+
+ align:start position:0%
+you know I'm interested in looking at
+ 
+
+ align:start position:0%
+you know I'm interested in looking at
+the top five words or the top ten words
+
+ align:start position:0%
+the top five words or the top ten words
+ 
+
+ align:start position:0%
+the top five words or the top ten words
+that are either positively or negatively
+
+ align:start position:0%
+that are either positively or negatively
+ 
+
+ align:start position:0%
+that are either positively or negatively
+an influence on the decision but not the
+
+ align:start position:0%
+an influence on the decision but not the
+ 
+
+ align:start position:0%
+an influence on the decision but not the
+top 10,000 words because I don't know
+
+ align:start position:0%
+top 10,000 words because I don't know
+ 
+
+ align:start position:0%
+top 10,000 words because I don't know
+what to do with 10,000 words okay now
+
+ align:start position:0%
+what to do with 10,000 words okay now
+ 
+
+ align:start position:0%
+what to do with 10,000 words okay now
+what's interesting is you can also then
+
+ align:start position:0%
+what's interesting is you can also then
+ 
+
+ align:start position:0%
+what's interesting is you can also then
+apply the same idea to image
+
+ align:start position:0%
+apply the same idea to image
+ 
+
+ align:start position:0%
+apply the same idea to image
+interpretation so here's a dog playing a
+
+ align:start position:0%
+interpretation so here's a dog playing a
+ 
+
+ align:start position:0%
+interpretation so here's a dog playing a
+guitar and they say how do we interpret
+
+ align:start position:0%
+guitar and they say how do we interpret
+ 
+
+ align:start position:0%
+guitar and they say how do we interpret
+this and so this is one of these
+
+ align:start position:0%
+this and so this is one of these
+ 
+
+ align:start position:0%
+this and so this is one of these
+labeling tasks where you'd like to label
+
+ align:start position:0%
+labeling tasks where you'd like to label
+ 
+
+ align:start position:0%
+labeling tasks where you'd like to label
+this picture as a Labrador or maybe as
+
+ align:start position:0%
+this picture as a Labrador or maybe as
+ 
+
+ align:start position:0%
+this picture as a Labrador or maybe as
+an acoustic guitar but some some labels
+
+ align:start position:0%
+an acoustic guitar but some some labels
+ 
+
+ align:start position:0%
+an acoustic guitar but some some labels
+also decide that it's an electric guitar
+
+ align:start position:0%
+also decide that it's an electric guitar
+ 
+
+ align:start position:0%
+also decide that it's an electric guitar
+and so they say well what counts in
+
+ align:start position:0%
+and so they say well what counts in
+ 
+
+ align:start position:0%
+and so they say well what counts in
+favor of or against each of these and
+
+ align:start position:0%
+favor of or against each of these and
+ 
+
+ align:start position:0%
+favor of or against each of these and
+the approach they take is a relatively
+
+ align:start position:0%
+the approach they take is a relatively
+ 
+
+ align:start position:0%
+the approach they take is a relatively
+straightforward one they say let's
+
+ align:start position:0%
+straightforward one they say let's
+ 
+
+ align:start position:0%
+straightforward one they say let's
+define a super pixel as a region of
+
+ align:start position:0%
+define a super pixel as a region of
+ 
+
+ align:start position:0%
+define a super pixel as a region of
+pixels within it within an image that
+
+ align:start position:0%
+pixels within it within an image that
+ 
+
+ align:start position:0%
+pixels within it within an image that
+have roughly the same intensity so if
+
+ align:start position:0%
+have roughly the same intensity so if
+ 
+
+ align:start position:0%
+have roughly the same intensity so if
+you've ever used Photoshop the magic
+
+ align:start position:0%
+you've ever used Photoshop the magic
+ 
+
+ align:start position:0%
+you've ever used Photoshop the magic
+selection tool can be adjusted to say
+
+ align:start position:0%
+selection tool can be adjusted to say
+ 
+
+ align:start position:0%
+selection tool can be adjusted to say
+find the region around this point where
+
+ align:start position:0%
+find the region around this point where
+ 
+
+ align:start position:0%
+find the region around this point where
+all the intensities are within some
+
+ align:start position:0%
+all the intensities are within some
+ 
+
+ align:start position:0%
+all the intensities are within some
+Delta of the of the point that I've
+
+ align:start position:0%
+Delta of the of the point that I've
+ 
+
+ align:start position:0%
+Delta of the of the point that I've
+picked and so it will outline some
+
+ align:start position:0%
+picked and so it will outline some
+ 
+
+ align:start position:0%
+picked and so it will outline some
+region of the picture and what they do
+
+ align:start position:0%
+region of the picture and what they do
+ 
+
+ align:start position:0%
+region of the picture and what they do
+is they break up the entire image into
+
+ align:start position:0%
+is they break up the entire image into
+ 
+
+ align:start position:0%
+is they break up the entire image into
+these regions and then they treat those
+
+ align:start position:0%
+these regions and then they treat those
+ 
+
+ align:start position:0%
+these regions and then they treat those
+as if they were the words in the in the
+
+ align:start position:0%
+as if they were the words in the in the
+ 
+
+ align:start position:0%
+as if they were the words in the in the
+word style explanation okay so they say
+
+ align:start position:0%
+word style explanation okay so they say
+ 
+
+ align:start position:0%
+word style explanation okay so they say
+well this looks like an electric guitar
+
+ align:start position:0%
+well this looks like an electric guitar
+ 
+
+ align:start position:0%
+well this looks like an electric guitar
+to the algorithm and this looks like an
+
+ align:start position:0%
+to the algorithm and this looks like an
+ 
+
+ align:start position:0%
+to the algorithm and this looks like an
+acoustic guitar and this looks like a
+
+ align:start position:0%
+acoustic guitar and this looks like a
+ 
+
+ align:start position:0%
+acoustic guitar and this looks like a
+Labrador so some of that makes sense I
+
+ align:start position:0%
+Labrador so some of that makes sense I
+ 
+
+ align:start position:0%
+Labrador so some of that makes sense I
+mean you know that dog's face does kind
+
+ align:start position:0%
+mean you know that dog's face does kind
+ 
+
+ align:start position:0%
+mean you know that dog's face does kind
+of look like a lab this does look kind
+
+ align:start position:0%
+of look like a lab this does look kind
+ 
+
+ align:start position:0%
+of look like a lab this does look kind
+of like part of the body and part of the
+
+ align:start position:0%
+of like part of the body and part of the
+ 
+
+ align:start position:0%
+of like part of the body and part of the
+fret work of a guitar I have no idea
+
+ align:start position:0%
+fret work of a guitar I have no idea
+ 
+
+ align:start position:0%
+fret work of a guitar I have no idea
+what the stuff is or why this
+
+ align:start position:0%
+what the stuff is or why this
+ 
+
+ align:start position:0%
+what the stuff is or why this
+contributes to it being a dog but such
+
+ align:start position:0%
+contributes to it being a dog but such
+ 
+
+ align:start position:0%
+contributes to it being a dog but such
+as such as the nature of these models
+
+ align:start position:0%
+as such as the nature of these models
+ 
+
+ align:start position:0%
+as such as the nature of these models
+but at least it is telling you why it
+
+ align:start position:0%
+but at least it is telling you why it
+ 
+
+ align:start position:0%
+but at least it is telling you why it
+believes these various things so then
+
+ align:start position:0%
+believes these various things so then
+ 
+
+ align:start position:0%
+believes these various things so then
+the last thing they do is to say well
+
+ align:start position:0%
+the last thing they do is to say well
+ 
+
+ align:start position:0%
+the last thing they do is to say well
+okay that helps you understand the
+
+ align:start position:0%
+okay that helps you understand the
+ 
+
+ align:start position:0%
+okay that helps you understand the
+particular model but how do you convince
+
+ align:start position:0%
+particular model but how do you convince
+ 
+
+ align:start position:0%
+particular model but how do you convince
+yourself I mean a particular example
+
+ align:start position:0%
+yourself I mean a particular example
+ 
+
+ align:start position:0%
+yourself I mean a particular example
+where a model is applied to it but how
+
+ align:start position:0%
+where a model is applied to it but how
+ 
+
+ align:start position:0%
+where a model is applied to it but how
+do you convince yourself that the model
+
+ align:start position:0%
+do you convince yourself that the model
+ 
+
+ align:start position:0%
+do you convince yourself that the model
+itself is reasonable and so they say
+
+ align:start position:0%
+itself is reasonable and so they say
+ 
+
+ align:start position:0%
+itself is reasonable and so they say
+well the best technique we know is to
+
+ align:start position:0%
+well the best technique we know is to
+ 
+
+ align:start position:0%
+well the best technique we know is to
+show you a bunch of examples but we want
+
+ align:start position:0%
+show you a bunch of examples but we want
+ 
+
+ align:start position:0%
+show you a bunch of examples but we want
+those examples to kind of cover the
+
+ align:start position:0%
+those examples to kind of cover the
+ 
+
+ align:start position:0%
+those examples to kind of cover the
+gamut of places that you might be
+
+ align:start position:0%
+gamut of places that you might be
+ 
+
+ align:start position:0%
+gamut of places that you might be
+interested in and so they say let's
+
+ align:start position:0%
+interested in and so they say let's
+ 
+
+ align:start position:0%
+interested in and so they say let's
+create this matrix an explanation matrix
+
+ align:start position:0%
+create this matrix an explanation matrix
+ 
+
+ align:start position:0%
+create this matrix an explanation matrix
+where these are the cases and these are
+
+ align:start position:0%
+where these are the cases and these are
+ 
+
+ align:start position:0%
+where these are the cases and these are
+the various features you know the top
+
+ align:start position:0%
+the various features you know the top
+ 
+
+ align:start position:0%
+the various features you know the top
+words or the top pixel elements or
+
+ align:start position:0%
+words or the top pixel elements or
+ 
+
+ align:start position:0%
+words or the top pixel elements or
+something and then we'll fill in the
+
+ align:start position:0%
+something and then we'll fill in the
+ 
+
+ align:start position:0%
+something and then we'll fill in the
+element of the matrix that tells me how
+
+ align:start position:0%
+element of the matrix that tells me how
+ 
+
+ align:start position:0%
+element of the matrix that tells me how
+strongly the
+
+ align:start position:0%
+strongly the
+ 
+
+ align:start position:0%
+strongly the
+feature is correlated or anti-correlated
+
+ align:start position:0%
+feature is correlated or anti-correlated
+ 
+
+ align:start position:0%
+feature is correlated or anti-correlated
+with the classification for that model
+
+ align:start position:0%
+with the classification for that model
+ 
+
+ align:start position:0%
+with the classification for that model
+and then it becomes a kind of set
+
+ align:start position:0%
+and then it becomes a kind of set
+ 
+
+ align:start position:0%
+and then it becomes a kind of set
+covering issue find a set of models that
+
+ align:start position:0%
+covering issue find a set of models that
+ 
+
+ align:start position:0%
+covering issue find a set of models that
+gives me the best coverage of
+
+ align:start position:0%
+gives me the best coverage of
+ 
+
+ align:start position:0%
+gives me the best coverage of
+explanations across that set of features
+
+ align:start position:0%
+explanations across that set of features
+ 
+
+ align:start position:0%
+explanations across that set of features
+and then with that I can convince myself
+
+ align:start position:0%
+and then with that I can convince myself
+ 
+
+ align:start position:0%
+and then with that I can convince myself
+that the model is reasonable so they
+
+ align:start position:0%
+that the model is reasonable so they
+ 
+
+ align:start position:0%
+that the model is reasonable so they
+have this thing called the sub modular
+
+ align:start position:0%
+have this thing called the sub modular
+ 
+
+ align:start position:0%
+have this thing called the sub modular
+pick algorithm and you know probably if
+
+ align:start position:0%
+pick algorithm and you know probably if
+ 
+
+ align:start position:0%
+pick algorithm and you know probably if
+you're interested you should read the
+
+ align:start position:0%
+you're interested you should read the
+ 
+
+ align:start position:0%
+you're interested you should read the
+paper but what they're doing is this is
+
+ align:start position:0%
+paper but what they're doing is this is
+ 
+
+ align:start position:0%
+paper but what they're doing is this is
+essentially doing a kind of greedy
+
+ align:start position:0%
+essentially doing a kind of greedy
+ 
+
+ align:start position:0%
+essentially doing a kind of greedy
+search that says what feature should I
+
+ align:start position:0%
+search that says what feature should I
+ 
+
+ align:start position:0%
+search that says what feature should I
+add in order to get the best coverage in
+
+ align:start position:0%
+add in order to get the best coverage in
+ 
+
+ align:start position:0%
+add in order to get the best coverage in
+that space of features by documents and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then they did a bunch of experiments
+
+ align:start position:0%
+and then they did a bunch of experiments
+ 
+
+ align:start position:0%
+and then they did a bunch of experiments
+where they said okay let's compare the
+
+ align:start position:0%
+where they said okay let's compare the
+ 
+
+ align:start position:0%
+where they said okay let's compare the
+results of these explanations of these
+
+ align:start position:0%
+results of these explanations of these
+ 
+
+ align:start position:0%
+results of these explanations of these
+simplified models to two sentiment
+
+ align:start position:0%
+simplified models to two sentiment
+ 
+
+ align:start position:0%
+simplified models to two sentiment
+analysis tasks of two thousand instances
+
+ align:start position:0%
+analysis tasks of two thousand instances
+ 
+
+ align:start position:0%
+analysis tasks of two thousand instances
+each bag of words as features they
+
+ align:start position:0%
+each bag of words as features they
+ 
+
+ align:start position:0%
+each bag of words as features they
+compared it to decision trees logistic
+
+ align:start position:0%
+compared it to decision trees logistic
+ 
+
+ align:start position:0%
+compared it to decision trees logistic
+regression nearest neighbors SVM with a
+
+ align:start position:0%
+regression nearest neighbors SVM with a
+ 
+
+ align:start position:0%
+regression nearest neighbors SVM with a
+radial basis function kernel or random
+
+ align:start position:0%
+radial basis function kernel or random
+ 
+
+ align:start position:0%
+radial basis function kernel or random
+forests that use word to vacuum
+
+ align:start position:0%
+forests that use word to vacuum
+ 
+
+ align:start position:0%
+forests that use word to vacuum
+betting's
+
+ align:start position:0%
+betting's
+ 
+
+ align:start position:0%
+betting's
+highly non explainable with a thousand
+
+ align:start position:0%
+highly non explainable with a thousand
+ 
+
+ align:start position:0%
+highly non explainable with a thousand
+trees and k equal ten so they chose ten
+
+ align:start position:0%
+trees and k equal ten so they chose ten
+ 
+
+ align:start position:0%
+trees and k equal ten so they chose ten
+features to explain for each each of
+
+ align:start position:0%
+features to explain for each each of
+ 
+
+ align:start position:0%
+features to explain for each each of
+these models they then did a side
+
+ align:start position:0%
+these models they then did a side
+ 
+
+ align:start position:0%
+these models they then did a side
+calculation that said what are the ten
+
+ align:start position:0%
+calculation that said what are the ten
+ 
+
+ align:start position:0%
+calculation that said what are the ten
+most suggestive features for each case
+
+ align:start position:0%
+most suggestive features for each case
+ 
+
+ align:start position:0%
+most suggestive features for each case
+and then they said does that covering
+
+ align:start position:0%
+and then they said does that covering
+ 
+
+ align:start position:0%
+and then they said does that covering
+algorithm identify those features
+
+ align:start position:0%
+algorithm identify those features
+ 
+
+ align:start position:0%
+algorithm identify those features
+correctly and so what they show here is
+
+ align:start position:0%
+correctly and so what they show here is
+ 
+
+ align:start position:0%
+correctly and so what they show here is
+that they're their method line does
+
+ align:start position:0%
+that they're their method line does
+ 
+
+ align:start position:0%
+that they're their method line does
+better in every case than
+
+ align:start position:0%
+better in every case than
+ 
+
+ align:start position:0%
+better in every case than
+a random sampling that's not very
+
+ align:start position:0%
+a random sampling that's not very
+ 
+
+ align:start position:0%
+a random sampling that's not very
+surprising or a greedy sampling or a
+
+ align:start position:0%
+surprising or a greedy sampling or a
+ 
+
+ align:start position:0%
+surprising or a greedy sampling or a
+partisan sampling which I don't know the
+
+ align:start position:0%
+partisan sampling which I don't know the
+ 
+
+ align:start position:0%
+partisan sampling which I don't know the
+details of but in any case there's what
+
+ align:start position:0%
+details of but in any case there's what
+ 
+
+ align:start position:0%
+details of but in any case there's what
+this graph is showing is that of the
+
+ align:start position:0%
+this graph is showing is that of the
+ 
+
+ align:start position:0%
+this graph is showing is that of the
+features that they decided were
+
+ align:start position:0%
+features that they decided were
+ 
+
+ align:start position:0%
+features that they decided were
+important in each of these cases they're
+
+ align:start position:0%
+important in each of these cases they're
+ 
+
+ align:start position:0%
+important in each of these cases they're
+recovering so there recall is up around
+
+ align:start position:0%
+recovering so there recall is up around
+ 
+
+ align:start position:0%
+recovering so there recall is up around
+you know 90s 90 plus percent so in fact
+
+ align:start position:0%
+you know 90s 90 plus percent so in fact
+ 
+
+ align:start position:0%
+you know 90s 90 plus percent so in fact
+the algorithm is identifying the right
+
+ align:start position:0%
+the algorithm is identifying the right
+ 
+
+ align:start position:0%
+the algorithm is identifying the right
+cases to give you a broad coverage
+
+ align:start position:0%
+cases to give you a broad coverage
+ 
+
+ align:start position:0%
+cases to give you a broad coverage
+across all the important features that
+
+ align:start position:0%
+across all the important features that
+ 
+
+ align:start position:0%
+across all the important features that
+matter in classifying these cases they
+
+ align:start position:0%
+matter in classifying these cases they
+ 
+
+ align:start position:0%
+matter in classifying these cases they
+then also did a bunch of human
+
+ align:start position:0%
+then also did a bunch of human
+ 
+
+ align:start position:0%
+then also did a bunch of human
+experiments where they said okay we're
+
+ align:start position:0%
+experiments where they said okay we're
+ 
+
+ align:start position:0%
+experiments where they said okay we're
+going to ask users to choose which of
+
+ align:start position:0%
+going to ask users to choose which of
+ 
+
+ align:start position:0%
+going to ask users to choose which of
+two classifiers they think is going to
+
+ align:start position:0%
+two classifiers they think is going to
+ 
+
+ align:start position:0%
+two classifiers they think is going to
+generalize better so this is like the
+
+ align:start position:0%
+generalize better so this is like the
+ 
+
+ align:start position:0%
+generalize better so this is like the
+picture I showed you of the Christianity
+
+ align:start position:0%
+picture I showed you of the Christianity
+ 
+
+ align:start position:0%
+picture I showed you of the Christianity
+versus atheism algorithm where
+
+ align:start position:0%
+versus atheism algorithm where
+ 
+
+ align:start position:0%
+versus atheism algorithm where
+presumably if you were a Mechanical Turk
+
+ align:start position:0%
+presumably if you were a Mechanical Turk
+ 
+
+ align:start position:0%
+presumably if you were a Mechanical Turk
+er and somebody showed you an algorithm
+
+ align:start position:0%
+er and somebody showed you an algorithm
+ 
+
+ align:start position:0%
+er and somebody showed you an algorithm
+that has very high accuracy but that
+
+ align:start position:0%
+that has very high accuracy but that
+ 
+
+ align:start position:0%
+that has very high accuracy but that
+depends on things like finding the word
+
+ align:start position:0%
+depends on things like finding the word
+ 
+
+ align:start position:0%
+depends on things like finding the word
+and NTP in a classifier for atheism
+
+ align:start position:0%
+and NTP in a classifier for atheism
+ 
+
+ align:start position:0%
+and NTP in a classifier for atheism
+versus Christianity you would say well
+
+ align:start position:0%
+versus Christianity you would say well
+ 
+
+ align:start position:0%
+versus Christianity you would say well
+maybe that algorithm isn't going to
+
+ align:start position:0%
+maybe that algorithm isn't going to
+ 
+
+ align:start position:0%
+maybe that algorithm isn't going to
+generalize very well because it's
+
+ align:start position:0%
+generalize very well because it's
+ 
+
+ align:start position:0%
+generalize very well because it's
+depending on something random that may
+
+ align:start position:0%
+depending on something random that may
+ 
+
+ align:start position:0%
+depending on something random that may
+be correlated with this particular
+
+ align:start position:0%
+be correlated with this particular
+ 
+
+ align:start position:0%
+be correlated with this particular
+dataset but if I try it on a different
+
+ align:start position:0%
+dataset but if I try it on a different
+ 
+
+ align:start position:0%
+dataset but if I try it on a different
+data set it's unlikely to work so that
+
+ align:start position:0%
+data set it's unlikely to work so that
+ 
+
+ align:start position:0%
+data set it's unlikely to work so that
+was one of the tasks and then they asked
+
+ align:start position:0%
+was one of the tasks and then they asked
+ 
+
+ align:start position:0%
+was one of the tasks and then they asked
+them to identify features like that that
+
+ align:start position:0%
+them to identify features like that that
+ 
+
+ align:start position:0%
+them to identify features like that that
+looked bad they then ran this
+
+ align:start position:0%
+looked bad they then ran this
+ 
+
+ align:start position:0%
+looked bad they then ran this
+Christianity versus atheism test and had
+
+ align:start position:0%
+Christianity versus atheism test and had
+ 
+
+ align:start position:0%
+Christianity versus atheism test and had
+a separate test set of about 800
+
+ align:start position:0%
+a separate test set of about 800
+ 
+
+ align:start position:0%
+a separate test set of about 800
+additional webpages from this website
+
+ align:start position:0%
+additional webpages from this website
+ 
+
+ align:start position:0%
+additional webpages from this website
+they the underlying model was a support
+
+ align:start position:0%
+they the underlying model was a support
+ 
+
+ align:start position:0%
+they the underlying model was a support
+vector machine with RBF kernels trained
+
+ align:start position:0%
+vector machine with RBF kernels trained
+ 
+
+ align:start position:0%
+vector machine with RBF kernels trained
+on the 20 News group data I don't know
+
+ align:start position:0%
+on the 20 News group data I don't know
+ 
+
+ align:start position:0%
+on the 20 News group data I don't know
+if you know that
+
+ align:start position:0%
+if you know that
+ 
+
+ align:start position:0%
+if you know that
+dataset but it's it's a well known
+
+ align:start position:0%
+dataset but it's it's a well known
+ 
+
+ align:start position:0%
+dataset but it's it's a well known
+publicly available dataset they got a
+
+ align:start position:0%
+publicly available dataset they got a
+ 
+
+ align:start position:0%
+publicly available dataset they got a
+hundred Mechanical Turkish and they said
+
+ align:start position:0%
+hundred Mechanical Turkish and they said
+ 
+
+ align:start position:0%
+hundred Mechanical Turkish and they said
+okay we're gonna present each of them
+
+ align:start position:0%
+okay we're gonna present each of them
+ 
+
+ align:start position:0%
+okay we're gonna present each of them
+six documents and six features per
+
+ align:start position:0%
+six documents and six features per
+ 
+
+ align:start position:0%
+six documents and six features per
+document in order to ask them to make
+
+ align:start position:0%
+document in order to ask them to make
+ 
+
+ align:start position:0%
+document in order to ask them to make
+this and then they did an auxiliary
+
+ align:start position:0%
+this and then they did an auxiliary
+ 
+
+ align:start position:0%
+this and then they did an auxiliary
+experiment in which they said if you see
+
+ align:start position:0%
+experiment in which they said if you see
+ 
+
+ align:start position:0%
+experiment in which they said if you see
+words that are no good in this
+
+ align:start position:0%
+words that are no good in this
+ 
+
+ align:start position:0%
+words that are no good in this
+experiment just strike them out and that
+
+ align:start position:0%
+experiment just strike them out and that
+ 
+
+ align:start position:0%
+experiment just strike them out and that
+will tell us which of the features were
+
+ align:start position:0%
+will tell us which of the features were
+ 
+
+ align:start position:0%
+will tell us which of the features were
+bad in in this in this method and what
+
+ align:start position:0%
+bad in in this in this method and what
+ 
+
+ align:start position:0%
+bad in in this in this method and what
+they found was that the human subjects
+
+ align:start position:0%
+they found was that the human subjects
+ 
+
+ align:start position:0%
+they found was that the human subjects
+choosing between two classifiers were
+
+ align:start position:0%
+choosing between two classifiers were
+ 
+
+ align:start position:0%
+choosing between two classifiers were
+pretty good at figuring out which was
+
+ align:start position:0%
+pretty good at figuring out which was
+ 
+
+ align:start position:0%
+pretty good at figuring out which was
+the better classifier now this is better
+
+ align:start position:0%
+the better classifier now this is better
+ 
+
+ align:start position:0%
+the better classifier now this is better
+by their their judgment and so they said
+
+ align:start position:0%
+by their their judgment and so they said
+ 
+
+ align:start position:0%
+by their their judgment and so they said
+okay the the sub-module or pick
+
+ align:start position:0%
+okay the the sub-module or pick
+ 
+
+ align:start position:0%
+okay the the sub-module or pick
+algorithm which is the one that I didn't
+
+ align:start position:0%
+algorithm which is the one that I didn't
+ 
+
+ align:start position:0%
+algorithm which is the one that I didn't
+describe in detail but it's this set
+
+ align:start position:0%
+describe in detail but it's this set
+ 
+
+ align:start position:0%
+describe in detail but it's this set
+covering algorithm gives you better
+
+ align:start position:0%
+covering algorithm gives you better
+ 
+
+ align:start position:0%
+covering algorithm gives you better
+results than a random pick algorithm
+
+ align:start position:0%
+results than a random pick algorithm
+ 
+
+ align:start position:0%
+results than a random pick algorithm
+that just says pick random features
+
+ align:start position:0%
+that just says pick random features
+ 
+
+ align:start position:0%
+that just says pick random features
+again not totally surprising so and the
+
+ align:start position:0%
+again not totally surprising so and the
+ 
+
+ align:start position:0%
+again not totally surprising so and the
+other thing that's interesting is if you
+
+ align:start position:0%
+other thing that's interesting is if you
+ 
+
+ align:start position:0%
+other thing that's interesting is if you
+do the feature engineering experiment it
+
+ align:start position:0%
+do the feature engineering experiment it
+ 
+
+ align:start position:0%
+do the feature engineering experiment it
+shows that as the Turkish interacted
+
+ align:start position:0%
+shows that as the Turkish interacted
+ 
+
+ align:start position:0%
+shows that as the Turkish interacted
+with the system the system became better
+
+ align:start position:0%
+with the system the system became better
+ 
+
+ align:start position:0%
+with the system the system became better
+so they started off with real-world
+
+ align:start position:0%
+so they started off with real-world
+ 
+
+ align:start position:0%
+so they started off with real-world
+accuracy of just under 60 percent and
+
+ align:start position:0%
+accuracy of just under 60 percent and
+ 
+
+ align:start position:0%
+accuracy of just under 60 percent and
+using the better of their algorithms
+
+ align:start position:0%
+using the better of their algorithms
+ 
+
+ align:start position:0%
+using the better of their algorithms
+they reached about seventy five percent
+
+ align:start position:0%
+they reached about seventy five percent
+ 
+
+ align:start position:0%
+they reached about seventy five percent
+after three rounds of interaction so the
+
+ align:start position:0%
+after three rounds of interaction so the
+ 
+
+ align:start position:0%
+after three rounds of interaction so the
+users could say I don't like this
+
+ align:start position:0%
+users could say I don't like this
+ 
+
+ align:start position:0%
+users could say I don't like this
+feature and then the system would give
+
+ align:start position:0%
+feature and then the system would give
+ 
+
+ align:start position:0%
+feature and then the system would give
+them better features now they tried a
+
+ align:start position:0%
+them better features now they tried a
+ 
+
+ align:start position:0%
+them better features now they tried a
+similar thing with images and so they
+
+ align:start position:0%
+similar thing with images and so they
+ 
+
+ align:start position:0%
+similar thing with images and so they
+this one is a little funny
+
+ align:start position:0%
+this one is a little funny
+ 
+
+ align:start position:0%
+this one is a little funny
+so they trained a deliberately lousy
+
+ align:start position:0%
+so they trained a deliberately lousy
+ 
+
+ align:start position:0%
+so they trained a deliberately lousy
+classifier to classify between
+
+ align:start position:0%
+classifier to classify between
+ 
+
+ align:start position:0%
+classifier to classify between
+wolves and huskies right this is a
+
+ align:start position:0%
+wolves and huskies right this is a
+ 
+
+ align:start position:0%
+wolves and huskies right this is a
+famous example also it turns out that
+
+ align:start position:0%
+famous example also it turns out that
+ 
+
+ align:start position:0%
+famous example also it turns out that
+that Huskies live in Alaska and so and
+
+ align:start position:0%
+that Huskies live in Alaska and so and
+ 
+
+ align:start position:0%
+that Huskies live in Alaska and so and
+wolves I guess some wolves do but most
+
+ align:start position:0%
+wolves I guess some wolves do but most
+ 
+
+ align:start position:0%
+wolves I guess some wolves do but most
+wolves don't and so the data set on
+
+ align:start position:0%
+wolves don't and so the data set on
+ 
+
+ align:start position:0%
+wolves don't and so the data set on
+which that are written which was used in
+
+ align:start position:0%
+which that are written which was used in
+ 
+
+ align:start position:0%
+which that are written which was used in
+that original problem formulation there
+
+ align:start position:0%
+that original problem formulation there
+ 
+
+ align:start position:0%
+that original problem formulation there
+was an extremely accurate classifier
+
+ align:start position:0%
+was an extremely accurate classifier
+ 
+
+ align:start position:0%
+was an extremely accurate classifier
+that was trained and when they went to
+
+ align:start position:0%
+that was trained and when they went to
+ 
+
+ align:start position:0%
+that was trained and when they went to
+look to see what it had learned
+
+ align:start position:0%
+look to see what it had learned
+ 
+
+ align:start position:0%
+look to see what it had learned
+basically it had learned to look for
+
+ align:start position:0%
+basically it had learned to look for
+ 
+
+ align:start position:0%
+basically it had learned to look for
+snow and if it saw snow in the picture
+
+ align:start position:0%
+snow and if it saw snow in the picture
+ 
+
+ align:start position:0%
+snow and if it saw snow in the picture
+it said it's a husky and if it didn't
+
+ align:start position:0%
+it said it's a husky and if it didn't
+ 
+
+ align:start position:0%
+it said it's a husky and if it didn't
+see snow in the picture it said it's a
+
+ align:start position:0%
+see snow in the picture it said it's a
+ 
+
+ align:start position:0%
+see snow in the picture it said it's a
+wolf so that turns out to be pretty
+
+ align:start position:0%
+wolf so that turns out to be pretty
+ 
+
+ align:start position:0%
+wolf so that turns out to be pretty
+accurate for the sample that they had
+
+ align:start position:0%
+accurate for the sample that they had
+ 
+
+ align:start position:0%
+accurate for the sample that they had
+but of course it's not a very
+
+ align:start position:0%
+but of course it's not a very
+ 
+
+ align:start position:0%
+but of course it's not a very
+sophisticated classification algorithm
+
+ align:start position:0%
+sophisticated classification algorithm
+ 
+
+ align:start position:0%
+sophisticated classification algorithm
+because it's possible to put a wolf in a
+
+ align:start position:0%
+because it's possible to put a wolf in a
+ 
+
+ align:start position:0%
+because it's possible to put a wolf in a
+snowy picture and it's possible to have
+
+ align:start position:0%
+snowy picture and it's possible to have
+ 
+
+ align:start position:0%
+snowy picture and it's possible to have
+your husky indoors with no snow and then
+
+ align:start position:0%
+your husky indoors with no snow and then
+ 
+
+ align:start position:0%
+your husky indoors with no snow and then
+you're just missing the boat on this
+
+ align:start position:0%
+you're just missing the boat on this
+ 
+
+ align:start position:0%
+you're just missing the boat on this
+classification so these guys built a
+
+ align:start position:0%
+classification so these guys built a
+ 
+
+ align:start position:0%
+classification so these guys built a
+particularly bad classifier by having
+
+ align:start position:0%
+particularly bad classifier by having
+ 
+
+ align:start position:0%
+particularly bad classifier by having
+all wolves in the training set had snow
+
+ align:start position:0%
+all wolves in the training set had snow
+ 
+
+ align:start position:0%
+all wolves in the training set had snow
+in the picture and none of the Huskies
+
+ align:start position:0%
+in the picture and none of the Huskies
+ 
+
+ align:start position:0%
+in the picture and none of the Huskies
+did okay and then they presented cases
+
+ align:start position:0%
+did okay and then they presented cases
+ 
+
+ align:start position:0%
+did okay and then they presented cases
+to graduate students like you guys with
+
+ align:start position:0%
+to graduate students like you guys with
+ 
+
+ align:start position:0%
+to graduate students like you guys with
+math machine learning backgrounds ten
+
+ align:start position:0%
+math machine learning backgrounds ten
+ 
+
+ align:start position:0%
+math machine learning backgrounds ten
+balanced test predictions but they put
+
+ align:start position:0%
+balanced test predictions but they put
+ 
+
+ align:start position:0%
+balanced test predictions but they put
+one ringer in each category so they put
+
+ align:start position:0%
+one ringer in each category so they put
+ 
+
+ align:start position:0%
+one ringer in each category so they put
+in one husky in snow and one wolf who
+
+ align:start position:0%
+in one husky in snow and one wolf who
+ 
+
+ align:start position:0%
+in one husky in snow and one wolf who
+was not in snow and the comparison was
+
+ align:start position:0%
+was not in snow and the comparison was
+ 
+
+ align:start position:0%
+was not in snow and the comparison was
+between pre and post experiment trust
+
+ align:start position:0%
+between pre and post experiment trust
+ 
+
+ align:start position:0%
+between pre and post experiment trust
+and understanding and so before the
+
+ align:start position:0%
+and understanding and so before the
+ 
+
+ align:start position:0%
+and understanding and so before the
+experiment they said that 10 of the 27
+
+ align:start position:0%
+experiment they said that 10 of the 27
+ 
+
+ align:start position:0%
+experiment they said that 10 of the 27
+students said they trusted the bad mom
+
+ align:start position:0%
+students said they trusted the bad mom
+ 
+
+ align:start position:0%
+students said they trusted the bad mom
+this bad model that they trained and
+
+ align:start position:0%
+this bad model that they trained and
+ 
+
+ align:start position:0%
+this bad model that they trained and
+afterwards only 3 out of 27 trusted it
+
+ align:start position:0%
+afterwards only 3 out of 27 trusted it
+ 
+
+ align:start position:0%
+afterwards only 3 out of 27 trusted it
+so this is a kind of sociological
+
+ align:start position:0%
+so this is a kind of sociological
+ 
+
+ align:start position:0%
+so this is a kind of sociological
+experiment that says yes we can actually
+
+ align:start position:0%
+experiment that says yes we can actually
+ 
+
+ align:start position:0%
+experiment that says yes we can actually
+change people's minds about whether
+
+ align:start position:0%
+change people's minds about whether
+ 
+
+ align:start position:0%
+change people's minds about whether
+remodel is a good or a bad one
+
+ align:start position:0%
+remodel is a good or a bad one
+ 
+
+ align:start position:0%
+remodel is a good or a bad one
+an experiment before only 12 out of 27
+
+ align:start position:0%
+an experiment before only 12 out of 27
+ 
+
+ align:start position:0%
+an experiment before only 12 out of 27
+students mentioned snow as a potential
+
+ align:start position:0%
+students mentioned snow as a potential
+ 
+
+ align:start position:0%
+students mentioned snow as a potential
+feature in this classifier whereas
+
+ align:start position:0%
+feature in this classifier whereas
+ 
+
+ align:start position:0%
+feature in this classifier whereas
+afterwards almost everybody did so again
+
+ align:start position:0%
+afterwards almost everybody did so again
+ 
+
+ align:start position:0%
+afterwards almost everybody did so again
+this tells you that that the method is
+
+ align:start position:0%
+this tells you that that the method is
+ 
+
+ align:start position:0%
+this tells you that that the method is
+providing some useful information now
+
+ align:start position:0%
+providing some useful information now
+ 
+
+ align:start position:0%
+providing some useful information now
+this paper set off a lot of work
+
+ align:start position:0%
+this paper set off a lot of work
+ 
+
+ align:start position:0%
+this paper set off a lot of work
+including a lot of critiques of the work
+
+ align:start position:0%
+including a lot of critiques of the work
+ 
+
+ align:start position:0%
+including a lot of critiques of the work
+and so this is one particular one from
+
+ align:start position:0%
+and so this is one particular one from
+ 
+
+ align:start position:0%
+and so this is one particular one from
+just a few months ago the end of
+
+ align:start position:0%
+just a few months ago the end of
+ 
+
+ align:start position:0%
+just a few months ago the end of
+December and what these guys say is that
+
+ align:start position:0%
+December and what these guys say is that
+ 
+
+ align:start position:0%
+December and what these guys say is that
+that distance function which includes a
+
+ align:start position:0%
+that distance function which includes a
+ 
+
+ align:start position:0%
+that distance function which includes a
+Sigma which is sort of the scale of
+
+ align:start position:0%
+Sigma which is sort of the scale of
+ 
+
+ align:start position:0%
+Sigma which is sort of the scale of
+distance that you're willing to go is
+
+ align:start position:0%
+distance that you're willing to go is
+ 
+
+ align:start position:0%
+distance that you're willing to go is
+pretty arbitrary in the experiments that
+
+ align:start position:0%
+pretty arbitrary in the experiments that
+ 
+
+ align:start position:0%
+pretty arbitrary in the experiments that
+the original authors did they set that
+
+ align:start position:0%
+the original authors did they set that
+ 
+
+ align:start position:0%
+the original authors did they set that
+distance to 75 percent of the square
+
+ align:start position:0%
+distance to 75 percent of the square
+ 
+
+ align:start position:0%
+distance to 75 percent of the square
+root of the dimensionality of the data
+
+ align:start position:0%
+root of the dimensionality of the data
+ 
+
+ align:start position:0%
+root of the dimensionality of the data
+set and you know okay I mean that's a
+
+ align:start position:0%
+set and you know okay I mean that's a
+ 
+
+ align:start position:0%
+set and you know okay I mean that's a
+number but it's not obvious that that's
+
+ align:start position:0%
+number but it's not obvious that that's
+ 
+
+ align:start position:0%
+number but it's not obvious that that's
+the best number or the right number and
+
+ align:start position:0%
+the best number or the right number and
+ 
+
+ align:start position:0%
+the best number or the right number and
+so these guys argue that it's important
+
+ align:start position:0%
+so these guys argue that it's important
+ 
+
+ align:start position:0%
+so these guys argue that it's important
+to tune the size of the neighborhood
+
+ align:start position:0%
+to tune the size of the neighborhood
+ 
+
+ align:start position:0%
+to tune the size of the neighborhood
+according to how far Z the point that
+
+ align:start position:0%
+according to how far Z the point that
+ 
+
+ align:start position:0%
+according to how far Z the point that
+you're trying to explain is from a
+
+ align:start position:0%
+you're trying to explain is from a
+ 
+
+ align:start position:0%
+you're trying to explain is from a
+boundary so if it's close to the
+
+ align:start position:0%
+boundary so if it's close to the
+ 
+
+ align:start position:0%
+boundary so if it's close to the
+boundary then you ought to take a
+
+ align:start position:0%
+boundary then you ought to take a
+ 
+
+ align:start position:0%
+boundary then you ought to take a
+smaller region for your proximity
+
+ align:start position:0%
+smaller region for your proximity
+ 
+
+ align:start position:0%
+smaller region for your proximity
+measure and if it's far from the
+
+ align:start position:0%
+measure and if it's far from the
+ 
+
+ align:start position:0%
+measure and if it's far from the
+boundary this addresses the question you
+
+ align:start position:0%
+boundary this addresses the question you
+ 
+
+ align:start position:0%
+boundary this addresses the question you
+guys were asking about what happens if
+
+ align:start position:0%
+guys were asking about what happens if
+ 
+
+ align:start position:0%
+guys were asking about what happens if
+you pick a point in the middle and so
+
+ align:start position:0%
+you pick a point in the middle and so
+ 
+
+ align:start position:0%
+you pick a point in the middle and so
+they show some nice examples of places
+
+ align:start position:0%
+they show some nice examples of places
+ 
+
+ align:start position:0%
+they show some nice examples of places
+where for for instance if you compare
+
+ align:start position:0%
+where for for instance if you compare
+ 
+
+ align:start position:0%
+where for for instance if you compare
+this explaining this Green Point you get
+
+ align:start position:0%
+this explaining this Green Point you get
+ 
+
+ align:start position:0%
+this explaining this Green Point you get
+a nice green line that follows the local
+
+ align:start position:0%
+a nice green line that follows the local
+ 
+
+ align:start position:0%
+a nice green line that follows the local
+boundary but explaining the Blue Point
+
+ align:start position:0%
+boundary but explaining the Blue Point
+ 
+
+ align:start position:0%
+boundary but explaining the Blue Point
+which is close to a corner of the the
+
+ align:start position:0%
+which is close to a corner of the the
+ 
+
+ align:start position:0%
+which is close to a corner of the the
+actual decision boundary you get a line
+
+ align:start position:0%
+actual decision boundary you get a line
+ 
+
+ align:start position:0%
+actual decision boundary you get a line
+that's not very different from the green
+
+ align:start position:0%
+that's not very different from the green
+ 
+
+ align:start position:0%
+that's not very different from the green
+one and similarly for the red point and
+
+ align:start position:0%
+one and similarly for the red point and
+ 
+
+ align:start position:0%
+one and similarly for the red point and
+so they say well we really need to work
+
+ align:start position:0%
+so they say well we really need to work
+ 
+
+ align:start position:0%
+so they say well we really need to work
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+distance function and so they come up
+
+ align:start position:0%
+distance function and so they come up
+ 
+
+ align:start position:0%
+distance function and so they come up
+with a method that they call leaf äj--
+
+ align:start position:0%
+with a method that they call leaf äj--
+ 
+
+ align:start position:0%
+with a method that they call leaf äj--
+which basically says remember what lime
+
+ align:start position:0%
+which basically says remember what lime
+ 
+
+ align:start position:0%
+which basically says remember what lime
+did is it sampled nonexistent cases
+
+ align:start position:0%
+did is it sampled nonexistent cases
+ 
+
+ align:start position:0%
+did is it sampled nonexistent cases
+simplified non-existent cases but here
+
+ align:start position:0%
+simplified non-existent cases but here
+ 
+
+ align:start position:0%
+simplified non-existent cases but here
+they're gonna sample existing cases so
+
+ align:start position:0%
+they're gonna sample existing cases so
+ 
+
+ align:start position:0%
+they're gonna sample existing cases so
+they're going to learn from the
+
+ align:start position:0%
+they're going to learn from the
+ 
+
+ align:start position:0%
+they're going to learn from the
+trainings the original training set but
+
+ align:start position:0%
+trainings the original training set but
+ 
+
+ align:start position:0%
+trainings the original training set but
+they're going to sample it by proximity
+
+ align:start position:0%
+they're going to sample it by proximity
+ 
+
+ align:start position:0%
+they're going to sample it by proximity
+to the the example that they're trying
+
+ align:start position:0%
+to the the example that they're trying
+ 
+
+ align:start position:0%
+to the the example that they're trying
+to explain and they argue that this is a
+
+ align:start position:0%
+to explain and they argue that this is a
+ 
+
+ align:start position:0%
+to explain and they argue that this is a
+good idea because for example in law the
+
+ align:start position:0%
+good idea because for example in law the
+ 
+
+ align:start position:0%
+good idea because for example in law the
+notion of precedent is that you get to
+
+ align:start position:0%
+notion of precedent is that you get to
+ 
+
+ align:start position:0%
+notion of precedent is that you get to
+argue that this case is very similar to
+
+ align:start position:0%
+argue that this case is very similar to
+ 
+
+ align:start position:0%
+argue that this case is very similar to
+some previously decided case and
+
+ align:start position:0%
+some previously decided case and
+ 
+
+ align:start position:0%
+some previously decided case and
+therefore it should be decided the same
+
+ align:start position:0%
+therefore it should be decided the same
+ 
+
+ align:start position:0%
+therefore it should be decided the same
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+I mean Supreme Court arguments are
+
+ align:start position:0%
+I mean Supreme Court arguments are
+ 
+
+ align:start position:0%
+I mean Supreme Court arguments are
+always all about that lower court
+
+ align:start position:0%
+always all about that lower court
+ 
+
+ align:start position:0%
+always all about that lower court
+arguments are sometimes more driven by
+
+ align:start position:0%
+arguments are sometimes more driven by
+ 
+
+ align:start position:0%
+arguments are sometimes more driven by
+what the law actually says but case law
+
+ align:start position:0%
+what the law actually says but case law
+ 
+
+ align:start position:0%
+what the law actually says but case law
+has been well established in British law
+
+ align:start position:0%
+has been well established in British law
+ 
+
+ align:start position:0%
+has been well established in British law
+and then by by inheritance in American
+
+ align:start position:0%
+and then by by inheritance in American
+ 
+
+ align:start position:0%
+and then by by inheritance in American
+law for many many centuries so they say
+
+ align:start position:0%
+law for many many centuries so they say
+ 
+
+ align:start position:0%
+law for many many centuries so they say
+well case based reasoning normally
+
+ align:start position:0%
+well case based reasoning normally
+ 
+
+ align:start position:0%
+well case based reasoning normally
+involves retrieving a similar case
+
+ align:start position:0%
+involves retrieving a similar case
+ 
+
+ align:start position:0%
+involves retrieving a similar case
+adapting it and then learning at that as
+
+ align:start position:0%
+adapting it and then learning at that as
+ 
+
+ align:start position:0%
+adapting it and then learning at that as
+a new precedent and they also argue for
+
+ align:start position:0%
+a new precedent and they also argue for
+ 
+
+ align:start position:0%
+a new precedent and they also argue for
+contrastive justification which is not
+
+ align:start position:0%
+contrastive justification which is not
+ 
+
+ align:start position:0%
+contrastive justification which is not
+only why did you choose X but why did
+
+ align:start position:0%
+only why did you choose X but why did
+ 
+
+ align:start position:0%
+only why did you choose X but why did
+you choose X rather than Y as giving a
+
+ align:start position:0%
+you choose X rather than Y as giving a
+ 
+
+ align:start position:0%
+you choose X rather than Y as giving a
+more satisfying and a more insightful
+
+ align:start position:0%
+more satisfying and a more insightful
+ 
+
+ align:start position:0%
+more satisfying and a more insightful
+explanation of how some model is working
+
+ align:start position:0%
+explanation of how some model is working
+ 
+
+ align:start position:0%
+explanation of how some model is working
+so they say okay similar set up F solves
+
+ align:start position:0%
+so they say okay similar set up F solves
+ 
+
+ align:start position:0%
+so they say okay similar set up F solves
+the classification problem where X is
+
+ align:start position:0%
+the classification problem where X is
+ 
+
+ align:start position:0%
+the classification problem where X is
+the data and Y is some binary classifier
+
+ align:start position:0%
+the data and Y is some binary classifier
+ 
+
+ align:start position:0%
+the data and Y is some binary classifier
+you know 0 or 0 1 if you like the
+
+ align:start position:0%
+you know 0 or 0 1 if you like the
+ 
+
+ align:start position:0%
+you know 0 or 0 1 if you like the
+training set is a bunch of X's y sub
+
+ align:start position:0%
+training set is a bunch of X's y sub
+ 
+
+ align:start position:0%
+training set is a bunch of X's y sub
+true is the actual answer and Y
+
+ align:start position:0%
+true is the actual answer and Y
+ 
+
+ align:start position:0%
+true is the actual answer and Y
+predicted is what F predicts on that on
+
+ align:start position:0%
+predicted is what F predicts on that on
+ 
+
+ align:start position:0%
+predicted is what F predicts on that on
+that X and to explain f of Z equals some
+
+ align:start position:0%
+that X and to explain f of Z equals some
+ 
+
+ align:start position:0%
+that X and to explain f of Z equals some
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+or outcome you can define the allies of
+
+ align:start position:0%
+or outcome you can define the allies of
+ 
+
+ align:start position:0%
+or outcome you can define the allies of
+a case as ones that come up with the
+
+ align:start position:0%
+a case as ones that come up with the
+ 
+
+ align:start position:0%
+a case as ones that come up with the
+same answer and you can define the
+
+ align:start position:0%
+same answer and you can define the
+ 
+
+ align:start position:0%
+same answer and you can define the
+enemies as one that ones that come up
+
+ align:start position:0%
+enemies as one that ones that come up
+ 
+
+ align:start position:0%
+enemies as one that ones that come up
+with a different answer right so now
+
+ align:start position:0%
+with a different answer right so now
+ 
+
+ align:start position:0%
+with a different answer right so now
+you're gonna sample both the Allies and
+
+ align:start position:0%
+you're gonna sample both the Allies and
+ 
+
+ align:start position:0%
+you're gonna sample both the Allies and
+the enemies according to a new distance
+
+ align:start position:0%
+the enemies according to a new distance
+ 
+
+ align:start position:0%
+the enemies according to a new distance
+function and the intuition they had is
+
+ align:start position:0%
+function and the intuition they had is
+ 
+
+ align:start position:0%
+function and the intuition they had is
+that the reason that they're that the
+
+ align:start position:0%
+that the reason that they're that the
+ 
+
+ align:start position:0%
+that the reason that they're that the
+distance function in the original line
+
+ align:start position:0%
+distance function in the original line
+ 
+
+ align:start position:0%
+distance function in the original line
+work wasn't working very well is because
+
+ align:start position:0%
+work wasn't working very well is because
+ 
+
+ align:start position:0%
+work wasn't working very well is because
+it was a spherical distance function in
+
+ align:start position:0%
+it was a spherical distance function in
+ 
+
+ align:start position:0%
+it was a spherical distance function in
+n-dimensional space and so they're gonna
+
+ align:start position:0%
+n-dimensional space and so they're gonna
+ 
+
+ align:start position:0%
+n-dimensional space and so they're gonna
+bias it by saying that the distance this
+
+ align:start position:0%
+bias it by saying that the distance this
+ 
+
+ align:start position:0%
+bias it by saying that the distance this
+B is going to be some combination of the
+
+ align:start position:0%
+B is going to be some combination of the
+ 
+
+ align:start position:0%
+B is going to be some combination of the
+difference in in the linear predictions
+
+ align:start position:0%
+difference in in the linear predictions
+ 
+
+ align:start position:0%
+difference in in the linear predictions
+plus the difference in the two points
+
+ align:start position:0%
+plus the difference in the two points
+ 
+
+ align:start position:0%
+plus the difference in the two points
+and so the contour lines of the first
+
+ align:start position:0%
+and so the contour lines of the first
+ 
+
+ align:start position:0%
+and so the contour lines of the first
+term are these circular contour lines
+
+ align:start position:0%
+term are these circular contour lines
+ 
+
+ align:start position:0%
+term are these circular contour lines
+this is what lime was doing the contour
+
+ align:start position:0%
+this is what lime was doing the contour
+ 
+
+ align:start position:0%
+this is what lime was doing the contour
+lines of the second term are these
+
+ align:start position:0%
+lines of the second term are these
+ 
+
+ align:start position:0%
+lines of the second term are these
+linear gradients and they add them to
+
+ align:start position:0%
+linear gradients and they add them to
+ 
+
+ align:start position:0%
+linear gradients and they add them to
+get sort of oval shaped things and this
+
+ align:start position:0%
+get sort of oval shaped things and this
+ 
+
+ align:start position:0%
+get sort of oval shaped things and this
+is what gives you that desired feature
+
+ align:start position:0%
+is what gives you that desired feature
+ 
+
+ align:start position:0%
+is what gives you that desired feature
+of being more sensitive to how close
+
+ align:start position:0%
+of being more sensitive to how close
+ 
+
+ align:start position:0%
+of being more sensitive to how close
+this point is to the decision boundary
+
+ align:start position:0%
+this point is to the decision boundary
+ 
+
+ align:start position:0%
+this point is to the decision boundary
+okay again there are a lot of relatively
+
+ align:start position:0%
+okay again there are a lot of relatively
+ 
+
+ align:start position:0%
+okay again there are a lot of relatively
+hairy details which I'm going to elide
+
+ align:start position:0%
+hairy details which I'm going to elide
+ 
+
+ align:start position:0%
+hairy details which I'm going to elide
+in the in the class today but they're
+
+ align:start position:0%
+in the in the class today but they're
+ 
+
+ align:start position:0%
+in the in the class today but they're
+they're definitely in the paper so they
+
+ align:start position:0%
+they're definitely in the paper so they
+ 
+
+ align:start position:0%
+they're definitely in the paper so they
+also did a user study on some very
+
+ align:start position:0%
+also did a user study on some very
+ 
+
+ align:start position:0%
+also did a user study on some very
+simple prediction models so this was how
+
+ align:start position:0%
+simple prediction models so this was how
+ 
+
+ align:start position:0%
+simple prediction models so this was how
+much is your house worth based on things
+
+ align:start position:0%
+much is your house worth based on things
+ 
+
+ align:start position:0%
+much is your house worth based on things
+like how how big is it and what year was
+
+ align:start position:0%
+like how how big is it and what year was
+ 
+
+ align:start position:0%
+like how how big is it and what year was
+it built built in and what's some
+
+ align:start position:0%
+it built built in and what's some
+ 
+
+ align:start position:0%
+it built built in and what's some
+subjective quality judgment of it and so
+
+ align:start position:0%
+subjective quality judgment of it and so
+ 
+
+ align:start position:0%
+subjective quality judgment of it and so
+what they show is that you can find the
+
+ align:start position:0%
+what they show is that you can find the
+ 
+
+ align:start position:0%
+what they show is that you can find the
+examples that are the the allies and the
+
+ align:start position:0%
+examples that are the the allies and the
+ 
+
+ align:start position:0%
+examples that are the the allies and the
+enemies of this house in
+
+ align:start position:0%
+enemies of this house in
+ 
+
+ align:start position:0%
+enemies of this house in
+order to do the prediction so then they
+
+ align:start position:0%
+order to do the prediction so then they
+ 
+
+ align:start position:0%
+order to do the prediction so then they
+applied their algorithm and if it works
+
+ align:start position:0%
+applied their algorithm and if it works
+ 
+
+ align:start position:0%
+applied their algorithm and if it works
+it gives you better answers I'll have to
+
+ align:start position:0%
+it gives you better answers I'll have to
+ 
+
+ align:start position:0%
+it gives you better answers I'll have to
+go find that slide somewhere all right
+
+ align:start position:0%
+go find that slide somewhere all right
+ 
+
+ align:start position:0%
+go find that slide somewhere all right
+so that's that's all I'm gonna say about
+
+ align:start position:0%
+so that's that's all I'm gonna say about
+ 
+
+ align:start position:0%
+so that's that's all I'm gonna say about
+about this this idea of using simplified
+
+ align:start position:0%
+about this this idea of using simplified
+ 
+
+ align:start position:0%
+about this this idea of using simplified
+models in the local neighborhood of
+
+ align:start position:0%
+models in the local neighborhood of
+ 
+
+ align:start position:0%
+models in the local neighborhood of
+individual cases in order to explain
+
+ align:start position:0%
+individual cases in order to explain
+ 
+
+ align:start position:0%
+individual cases in order to explain
+something I wanted to talk about two
+
+ align:start position:0%
+something I wanted to talk about two
+ 
+
+ align:start position:0%
+something I wanted to talk about two
+other topics so this was a paper by some
+
+ align:start position:0%
+other topics so this was a paper by some
+ 
+
+ align:start position:0%
+other topics so this was a paper by some
+of my students recently in which they're
+
+ align:start position:0%
+of my students recently in which they're
+ 
+
+ align:start position:0%
+of my students recently in which they're
+looking at medical images and trying to
+
+ align:start position:0%
+looking at medical images and trying to
+ 
+
+ align:start position:0%
+looking at medical images and trying to
+generate radiology reports from those
+
+ align:start position:0%
+generate radiology reports from those
+ 
+
+ align:start position:0%
+generate radiology reports from those
+medical images right I mean you know
+
+ align:start position:0%
+medical images right I mean you know
+ 
+
+ align:start position:0%
+medical images right I mean you know
+machine learning can solve all problems
+
+ align:start position:0%
+machine learning can solve all problems
+ 
+
+ align:start position:0%
+machine learning can solve all problems
+I give you a collection of images and a
+
+ align:start position:0%
+I give you a collection of images and a
+ 
+
+ align:start position:0%
+I give you a collection of images and a
+collection of radiology reports should
+
+ align:start position:0%
+collection of radiology reports should
+ 
+
+ align:start position:0%
+collection of radiology reports should
+be straightforward to build a model that
+
+ align:start position:0%
+be straightforward to build a model that
+ 
+
+ align:start position:0%
+be straightforward to build a model that
+now takes new radiological images and
+
+ align:start position:0%
+now takes new radiological images and
+ 
+
+ align:start position:0%
+now takes new radiological images and
+produces new radiology reports that are
+
+ align:start position:0%
+produces new radiology reports that are
+ 
+
+ align:start position:0%
+produces new radiology reports that are
+understandable accurate etc I'm joking
+
+ align:start position:0%
+understandable accurate etc I'm joking
+ 
+
+ align:start position:0%
+understandable accurate etc I'm joking
+of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the the approach they took was kind
+
+ align:start position:0%
+but the the approach they took was kind
+ 
+
+ align:start position:0%
+but the the approach they took was kind
+of interesting so they taken a standard
+
+ align:start position:0%
+of interesting so they taken a standard
+ 
+
+ align:start position:0%
+of interesting so they taken a standard
+image decoder and then before the
+
+ align:start position:0%
+image decoder and then before the
+ 
+
+ align:start position:0%
+image decoder and then before the
+pooling layer they take essentially an
+
+ align:start position:0%
+pooling layer they take essentially an
+ 
+
+ align:start position:0%
+pooling layer they take essentially an
+image embedding from the next last layer
+
+ align:start position:0%
+image embedding from the next last layer
+ 
+
+ align:start position:0%
+image embedding from the next last layer
+of this imaging coding algorithm and
+
+ align:start position:0%
+of this imaging coding algorithm and
+ 
+
+ align:start position:0%
+of this imaging coding algorithm and
+then they feed that into a word decoder
+
+ align:start position:0%
+then they feed that into a word decoder
+ 
+
+ align:start position:0%
+then they feed that into a word decoder
+and word generator and the idea is to
+
+ align:start position:0%
+and word generator and the idea is to
+ 
+
+ align:start position:0%
+and word generator and the idea is to
+get things that appear in the image that
+
+ align:start position:0%
+get things that appear in the image that
+ 
+
+ align:start position:0%
+get things that appear in the image that
+correspond to words that appear in the
+
+ align:start position:0%
+correspond to words that appear in the
+ 
+
+ align:start position:0%
+correspond to words that appear in the
+report to wind up in the same place in
+
+ align:start position:0%
+report to wind up in the same place in
+ 
+
+ align:start position:0%
+report to wind up in the same place in
+the embedding space and so again there's
+
+ align:start position:0%
+the embedding space and so again there's
+ 
+
+ align:start position:0%
+the embedding space and so again there's
+a lot of hair it's a lsdm based encoder
+
+ align:start position:0%
+a lot of hair it's a lsdm based encoder
+ 
+
+ align:start position:0%
+a lot of hair it's a lsdm based encoder
+and it's modeled as a sentence decoder
+
+ align:start position:0%
+and it's modeled as a sentence decoder
+ 
+
+ align:start position:0%
+and it's modeled as a sentence decoder
+and within that there's a word decoder
+
+ align:start position:0%
+and within that there's a word decoder
+ 
+
+ align:start position:0%
+and within that there's a word decoder
+and then there's a generator
+
+ align:start position:0%
+and then there's a generator
+ 
+
+ align:start position:0%
+and then there's a generator
+that generates these reports and it uses
+
+ align:start position:0%
+that generates these reports and it uses
+ 
+
+ align:start position:0%
+that generates these reports and it uses
+reinforcement learning and it you know
+
+ align:start position:0%
+reinforcement learning and it you know
+ 
+
+ align:start position:0%
+reinforcement learning and it you know
+tons of hair but here's what I wanted to
+
+ align:start position:0%
+tons of hair but here's what I wanted to
+ 
+
+ align:start position:0%
+tons of hair but here's what I wanted to
+show you which is interesting so the
+
+ align:start position:0%
+show you which is interesting so the
+ 
+
+ align:start position:0%
+show you which is interesting so the
+encoder takes a bunch of spatial image
+
+ align:start position:0%
+encoder takes a bunch of spatial image
+ 
+
+ align:start position:0%
+encoder takes a bunch of spatial image
+features the sentence decoder uses these
+
+ align:start position:0%
+features the sentence decoder uses these
+ 
+
+ align:start position:0%
+features the sentence decoder uses these
+image features in addition to the the
+
+ align:start position:0%
+image features in addition to the the
+ 
+
+ align:start position:0%
+image features in addition to the the
+linguistic features the word embeddings
+
+ align:start position:0%
+linguistic features the word embeddings
+ 
+
+ align:start position:0%
+linguistic features the word embeddings
+that are fed into it and then for ground
+
+ align:start position:0%
+that are fed into it and then for ground
+ 
+
+ align:start position:0%
+that are fed into it and then for ground
+truth annotation they also use a remote
+
+ align:start position:0%
+truth annotation they also use a remote
+ 
+
+ align:start position:0%
+truth annotation they also use a remote
+annotation method which is this check
+
+ align:start position:0%
+annotation method which is this check
+ 
+
+ align:start position:0%
+annotation method which is this check
+spurt program which is a rule-based
+
+ align:start position:0%
+spurt program which is a rule-based
+ 
+
+ align:start position:0%
+spurt program which is a rule-based
+program out of stanford that reads
+
+ align:start position:0%
+program out of stanford that reads
+ 
+
+ align:start position:0%
+program out of stanford that reads
+radiology reports and identifies
+
+ align:start position:0%
+radiology reports and identifies
+ 
+
+ align:start position:0%
+radiology reports and identifies
+features in the report that it thinks
+
+ align:start position:0%
+features in the report that it thinks
+ 
+
+ align:start position:0%
+features in the report that it thinks
+are important and correct so it's not
+
+ align:start position:0%
+are important and correct so it's not
+ 
+
+ align:start position:0%
+are important and correct so it's not
+always correct of course but but that's
+
+ align:start position:0%
+always correct of course but but that's
+ 
+
+ align:start position:0%
+always correct of course but but that's
+used in order to guide the generator so
+
+ align:start position:0%
+used in order to guide the generator so
+ 
+
+ align:start position:0%
+used in order to guide the generator so
+here's an example so this is an image of
+
+ align:start position:0%
+here's an example so this is an image of
+ 
+
+ align:start position:0%
+here's an example so this is an image of
+a chest and the ground truth so this is
+
+ align:start position:0%
+a chest and the ground truth so this is
+ 
+
+ align:start position:0%
+a chest and the ground truth so this is
+the actual radiology report says
+
+ align:start position:0%
+the actual radiology report says
+ 
+
+ align:start position:0%
+the actual radiology report says
+cardiomegaly is moderate by basilar
+
+ align:start position:0%
+cardiomegaly is moderate by basilar
+ 
+
+ align:start position:0%
+cardiomegaly is moderate by basilar
+atelectasis is mild
+
+ align:start position:0%
+atelectasis is mild
+ 
+
+ align:start position:0%
+atelectasis is mild
+there's no pneumothorax a lower cervical
+
+ align:start position:0%
+there's no pneumothorax a lower cervical
+ 
+
+ align:start position:0%
+there's no pneumothorax a lower cervical
+spinal fusion is partially visualized
+
+ align:start position:0%
+spinal fusion is partially visualized
+ 
+
+ align:start position:0%
+spinal fusion is partially visualized
+healed right rib fractures are
+
+ align:start position:0%
+healed right rib fractures are
+ 
+
+ align:start position:0%
+healed right rib fractures are
+incidentally noted by the way I've
+
+ align:start position:0%
+incidentally noted by the way I've
+ 
+
+ align:start position:0%
+incidentally noted by the way I've
+stared at hundreds of radiological
+
+ align:start position:0%
+stared at hundreds of radiological
+ 
+
+ align:start position:0%
+stared at hundreds of radiological
+images like this I could never figure
+
+ align:start position:0%
+images like this I could never figure
+ 
+
+ align:start position:0%
+images like this I could never figure
+out that that this image says that but
+
+ align:start position:0%
+out that that this image says that but
+ 
+
+ align:start position:0%
+out that that this image says that but
+that's why radiologists trained for many
+
+ align:start position:0%
+that's why radiologists trained for many
+ 
+
+ align:start position:0%
+that's why radiologists trained for many
+many years to become good at this stuff
+
+ align:start position:0%
+many years to become good at this stuff
+ 
+
+ align:start position:0%
+many years to become good at this stuff
+so there was a previous program done by
+
+ align:start position:0%
+so there was a previous program done by
+ 
+
+ align:start position:0%
+so there was a previous program done by
+others called tie net which generates
+
+ align:start position:0%
+others called tie net which generates
+ 
+
+ align:start position:0%
+others called tie net which generates
+the following report it says ap portable
+
+ align:start position:0%
+the following report it says ap portable
+ 
+
+ align:start position:0%
+the following report it says ap portable
+upright view of the chest there's no
+
+ align:start position:0%
+upright view of the chest there's no
+ 
+
+ align:start position:0%
+upright view of the chest there's no
+pool no focal consolidation effusion or
+
+ align:start position:0%
+pool no focal consolidation effusion or
+ 
+
+ align:start position:0%
+pool no focal consolidation effusion or
+no pneumothorax the cardio meta
+
+ align:start position:0%
+no pneumothorax the cardio meta
+ 
+
+ align:start position:0%
+no pneumothorax the cardio meta
+mediastinal silhouette is normal imaged
+
+ align:start position:0%
+mediastinal silhouette is normal imaged
+ 
+
+ align:start position:0%
+mediastinal silhouette is normal imaged
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+structures are intact so if you compare
+
+ align:start position:0%
+structures are intact so if you compare
+ 
+
+ align:start position:0%
+structures are intact so if you compare
+this to that you say well if the cardio
+
+ align:start position:0%
+this to that you say well if the cardio
+ 
+
+ align:start position:0%
+this to that you say well if the cardio
+mediastinal silhouette is normal then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where would the the lower cervical
+
+ align:start position:0%
+where would the the lower cervical
+ 
+
+ align:start position:0%
+where would the the lower cervical
+spinal fusion being partially visualized
+
+ align:start position:0%
+spinal fusion being partially visualized
+ 
+
+ align:start position:0%
+spinal fusion being partially visualized
+because that's along the middle and so
+
+ align:start position:0%
+because that's along the middle and so
+ 
+
+ align:start position:0%
+because that's along the middle and so
+these are not quite consistent so the
+
+ align:start position:0%
+these are not quite consistent so the
+ 
+
+ align:start position:0%
+these are not quite consistent so the
+system that the students built says
+
+ align:start position:0%
+system that the students built says
+ 
+
+ align:start position:0%
+system that the students built says
+there's mild enlargement of the cardiac
+
+ align:start position:0%
+there's mild enlargement of the cardiac
+ 
+
+ align:start position:0%
+there's mild enlargement of the cardiac
+silhouette there's no pleural effusion
+
+ align:start position:0%
+silhouette there's no pleural effusion
+ 
+
+ align:start position:0%
+silhouette there's no pleural effusion
+or pneumothorax and there's no acute
+
+ align:start position:0%
+or pneumothorax and there's no acute
+ 
+
+ align:start position:0%
+or pneumothorax and there's no acute
+osseous abnormalities so it also missed
+
+ align:start position:0%
+osseous abnormalities so it also missed
+ 
+
+ align:start position:0%
+osseous abnormalities so it also missed
+the healed right rib fractures that were
+
+ align:start position:0%
+the healed right rib fractures that were
+ 
+
+ align:start position:0%
+the healed right rib fractures that were
+incidentally noted but anyway it's you
+
+ align:start position:0%
+incidentally noted but anyway it's you
+ 
+
+ align:start position:0%
+incidentally noted but anyway it's you
+know the remarkable thing about a
+
+ align:start position:0%
+know the remarkable thing about a
+ 
+
+ align:start position:0%
+know the remarkable thing about a
+singing dog is not how well it sings but
+
+ align:start position:0%
+singing dog is not how well it sings but
+ 
+
+ align:start position:0%
+singing dog is not how well it sings but
+the fact that it sings at all
+
+ align:start position:0%
+the fact that it sings at all
+ 
+
+ align:start position:0%
+the fact that it sings at all
+and the reason I included this work is
+
+ align:start position:0%
+and the reason I included this work is
+ 
+
+ align:start position:0%
+and the reason I included this work is
+not to convince you that this is gonna
+
+ align:start position:0%
+not to convince you that this is gonna
+ 
+
+ align:start position:0%
+not to convince you that this is gonna
+replace radiologists anytime soon but
+
+ align:start position:0%
+replace radiologists anytime soon but
+ 
+
+ align:start position:0%
+replace radiologists anytime soon but
+but that it had an interesting
+
+ align:start position:0%
+but that it had an interesting
+ 
+
+ align:start position:0%
+but that it had an interesting
+explanation facility and the explanation
+
+ align:start position:0%
+explanation facility and the explanation
+ 
+
+ align:start position:0%
+explanation facility and the explanation
+facility uses attention which is part of
+
+ align:start position:0%
+facility uses attention which is part of
+ 
+
+ align:start position:0%
+facility uses attention which is part of
+its model to say hey when we reach some
+
+ align:start position:0%
+its model to say hey when we reach some
+ 
+
+ align:start position:0%
+its model to say hey when we reach some
+conclusion we can point back into the
+
+ align:start position:0%
+conclusion we can point back into the
+ 
+
+ align:start position:0%
+conclusion we can point back into the
+image and say what part of the image
+
+ align:start position:0%
+image and say what part of the image
+ 
+
+ align:start position:0%
+image and say what part of the image
+corresponds to that part of the
+
+ align:start position:0%
+corresponds to that part of the
+ 
+
+ align:start position:0%
+corresponds to that part of the
+conclusion and so this is pretty
+
+ align:start position:0%
+conclusion and so this is pretty
+ 
+
+ align:start position:0%
+conclusion and so this is pretty
+interesting you say an upright and
+
+ align:start position:0%
+interesting you say an upright and
+ 
+
+ align:start position:0%
+interesting you say an upright and
+lateral views of the chest in red well
+
+ align:start position:0%
+lateral views of the chest in red well
+ 
+
+ align:start position:0%
+lateral views of the chest in red well
+that's kind of the chest in red
+
+ align:start position:0%
+that's kind of the chest in red
+ 
+
+ align:start position:0%
+that's kind of the chest in red
+there's moderate cardiomegaly so here
+
+ align:start position:0%
+there's moderate cardiomegaly so here
+ 
+
+ align:start position:0%
+there's moderate cardiomegaly so here
+the green certainly shows you where your
+
+ align:start position:0%
+the green certainly shows you where your
+ 
+
+ align:start position:0%
+the green certainly shows you where your
+heart is okay about there and a little
+
+ align:start position:0%
+heart is okay about there and a little
+ 
+
+ align:start position:0%
+heart is okay about there and a little
+bit to the left and there's no pleural
+
+ align:start position:0%
+bit to the left and there's no pleural
+ 
+
+ align:start position:0%
+bit to the left and there's no pleural
+effusion or pneumothorax this one is
+
+ align:start position:0%
+effusion or pneumothorax this one is
+ 
+
+ align:start position:0%
+effusion or pneumothorax this one is
+kind of funny that's the blue region so
+
+ align:start position:0%
+kind of funny that's the blue region so
+ 
+
+ align:start position:0%
+kind of funny that's the blue region so
+how do you show me that there isn't
+
+ align:start position:0%
+how do you show me that there isn't
+ 
+
+ align:start position:0%
+how do you show me that there isn't
+something and we were surprised actually
+
+ align:start position:0%
+something and we were surprised actually
+ 
+
+ align:start position:0%
+something and we were surprised actually
+when the way it showed us that there
+
+ align:start position:0%
+when the way it showed us that there
+ 
+
+ align:start position:0%
+when the way it showed us that there
+isn't something is to highlight
+
+ align:start position:0%
+isn't something is to highlight
+ 
+
+ align:start position:0%
+isn't something is to highlight
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+outside of anything that you might be
+
+ align:start position:0%
+outside of anything that you might be
+ 
+
+ align:start position:0%
+outside of anything that you might be
+interested in which is not exactly
+
+ align:start position:0%
+interested in which is not exactly
+ 
+
+ align:start position:0%
+interested in which is not exactly
+convincing that there's no no pleural
+
+ align:start position:0%
+convincing that there's no no pleural
+ 
+
+ align:start position:0%
+convincing that there's no no pleural
+effusion and here's another example
+
+ align:start position:0%
+effusion and here's another example
+ 
+
+ align:start position:0%
+effusion and here's another example
+there's no relevant change tracheostomy
+
+ align:start position:0%
+there's no relevant change tracheostomy
+ 
+
+ align:start position:0%
+there's no relevant change tracheostomy
+tube is in place so that roughly is
+
+ align:start position:0%
+tube is in place so that roughly is
+ 
+
+ align:start position:0%
+tube is in place so that roughly is
+showing a little too wide but it's
+
+ align:start position:0%
+showing a little too wide but it's
+ 
+
+ align:start position:0%
+showing a little too wide but it's
+showing roughly where a tracheostomy
+
+ align:start position:0%
+showing roughly where a tracheostomy
+ 
+
+ align:start position:0%
+showing roughly where a tracheostomy
+tube might be bilateral pleural effusion
+
+ align:start position:0%
+tube might be bilateral pleural effusion
+ 
+
+ align:start position:0%
+tube might be bilateral pleural effusion
+and compressive analytic ASIS and left
+
+ align:start position:0%
+and compressive analytic ASIS and left
+ 
+
+ align:start position:0%
+and compressive analytic ASIS and left
+ASIS is when your lung tissue stick
+
+ align:start position:0%
+ASIS is when your lung tissue stick
+ 
+
+ align:start position:0%
+ASIS is when your lung tissue stick
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+and so that does often happen in the
+
+ align:start position:0%
+and so that does often happen in the
+ 
+
+ align:start position:0%
+and so that does often happen in the
+lower part of the lung and again the
+
+ align:start position:0%
+lower part of the lung and again the
+ 
+
+ align:start position:0%
+lower part of the lung and again the
+negative shows you everything that's not
+
+ align:start position:0%
+negative shows you everything that's not
+ 
+
+ align:start position:0%
+negative shows you everything that's not
+sort of part of the action yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it's trying to predict the whole
+
+ align:start position:0%
+no it's trying to predict the whole
+ 
+
+ align:start position:0%
+no it's trying to predict the whole
+model the whole note yeah but these guys
+
+ align:start position:0%
+model the whole note yeah but these guys
+ 
+
+ align:start position:0%
+model the whole note yeah but these guys
+were ambitious you know what was it
+
+ align:start position:0%
+were ambitious you know what was it
+ 
+
+ align:start position:0%
+were ambitious you know what was it
+geoff hinton said a few years ago that
+
+ align:start position:0%
+geoff hinton said a few years ago that
+ 
+
+ align:start position:0%
+geoff hinton said a few years ago that
+he wouldn't want his children to become
+
+ align:start position:0%
+he wouldn't want his children to become
+ 
+
+ align:start position:0%
+he wouldn't want his children to become
+radiologists because that field is going
+
+ align:start position:0%
+radiologists because that field is going
+ 
+
+ align:start position:0%
+radiologists because that field is going
+to be replaced by by computers I think
+
+ align:start position:0%
+to be replaced by by computers I think
+ 
+
+ align:start position:0%
+to be replaced by by computers I think
+that was a stupid thing to say
+
+ align:start position:0%
+that was a stupid thing to say
+ 
+
+ align:start position:0%
+that was a stupid thing to say
+especially when you look at the state of
+
+ align:start position:0%
+especially when you look at the state of
+ 
+
+ align:start position:0%
+especially when you look at the state of
+the art of how well these things work
+
+ align:start position:0%
+the art of how well these things work
+ 
+
+ align:start position:0%
+the art of how well these things work
+but if that were true then you would in
+
+ align:start position:0%
+but if that were true then you would in
+ 
+
+ align:start position:0%
+but if that were true then you would in
+fact want something that is able to
+
+ align:start position:0%
+fact want something that is able to
+ 
+
+ align:start position:0%
+fact want something that is able to
+produce an entire radiology report so
+
+ align:start position:0%
+produce an entire radiology report so
+ 
+
+ align:start position:0%
+produce an entire radiology report so
+the motivation is there now after this
+
+ align:start position:0%
+the motivation is there now after this
+ 
+
+ align:start position:0%
+the motivation is there now after this
+work was done we ran into this
+
+ align:start position:0%
+work was done we ran into this
+ 
+
+ align:start position:0%
+work was done we ran into this
+interesting paper from Northeastern
+
+ align:start position:0%
+interesting paper from Northeastern
+ 
+
+ align:start position:0%
+interesting paper from Northeastern
+which says attempt but listen guys
+
+ align:start position:0%
+which says attempt but listen guys
+ 
+
+ align:start position:0%
+which says attempt but listen guys
+attention is not explanation okay
+
+ align:start position:0%
+attention is not explanation okay
+ 
+
+ align:start position:0%
+attention is not explanation okay
+so attention is clearly a mechanism
+
+ align:start position:0%
+so attention is clearly a mechanism
+ 
+
+ align:start position:0%
+so attention is clearly a mechanism
+that's very useful in all kinds of
+
+ align:start position:0%
+that's very useful in all kinds of
+ 
+
+ align:start position:0%
+that's very useful in all kinds of
+machine learning methods but you
+
+ align:start position:0%
+machine learning methods but you
+ 
+
+ align:start position:0%
+machine learning methods but you
+shouldn't confuse it with an explanation
+
+ align:start position:0%
+shouldn't confuse it with an explanation
+ 
+
+ align:start position:0%
+shouldn't confuse it with an explanation
+so they say well assumption it's the
+
+ align:start position:0%
+so they say well assumption it's the
+ 
+
+ align:start position:0%
+so they say well assumption it's the
+assumption that the input units are
+
+ align:start position:0%
+assumption that the input units are
+ 
+
+ align:start position:0%
+assumption that the input units are
+accorded high attention that are
+
+ align:start position:0%
+accorded high attention that are
+ 
+
+ align:start position:0%
+accorded high attention that are
+accorded high attention weights are
+
+ align:start position:0%
+accorded high attention weights are
+ 
+
+ align:start position:0%
+accorded high attention weights are
+responsible through the model outputs
+
+ align:start position:0%
+responsible through the model outputs
+ 
+
+ align:start position:0%
+responsible through the model outputs
+and that may not be true and so what
+
+ align:start position:0%
+and that may not be true and so what
+ 
+
+ align:start position:0%
+and that may not be true and so what
+they did is they did a bunch of
+
+ align:start position:0%
+they did is they did a bunch of
+ 
+
+ align:start position:0%
+they did is they did a bunch of
+experiments where they studied the
+
+ align:start position:0%
+experiments where they studied the
+ 
+
+ align:start position:0%
+experiments where they studied the
+correlation between the attention
+
+ align:start position:0%
+correlation between the attention
+ 
+
+ align:start position:0%
+correlation between the attention
+weights and the the gradients of the
+
+ align:start position:0%
+weights and the the gradients of the
+ 
+
+ align:start position:0%
+weights and the the gradients of the
+model parameters to see whether in fact
+
+ align:start position:0%
+model parameters to see whether in fact
+ 
+
+ align:start position:0%
+model parameters to see whether in fact
+the words that had high attention were
+
+ align:start position:0%
+the words that had high attention were
+ 
+
+ align:start position:0%
+the words that had high attention were
+the ones that were most decisive in
+
+ align:start position:0%
+the ones that were most decisive in
+ 
+
+ align:start position:0%
+the ones that were most decisive in
+making a decision in the model and they
+
+ align:start position:0%
+making a decision in the model and they
+ 
+
+ align:start position:0%
+making a decision in the model and they
+found that the evidence that correlation
+
+ align:start position:0%
+found that the evidence that correlation
+ 
+
+ align:start position:0%
+found that the evidence that correlation
+between intuitive feature importance
+
+ align:start position:0%
+between intuitive feature importance
+ 
+
+ align:start position:0%
+between intuitive feature importance
+measures including gradient and feature
+
+ align:start position:0%
+measures including gradient and feature
+ 
+
+ align:start position:0%
+measures including gradient and feature
+erasure approaches so this is ablation
+
+ align:start position:0%
+erasure approaches so this is ablation
+ 
+
+ align:start position:0%
+erasure approaches so this is ablation
+studies and learned attention weights is
+
+ align:start position:0%
+studies and learned attention weights is
+ 
+
+ align:start position:0%
+studies and learned attention weights is
+weak and so they did a bunch of
+
+ align:start position:0%
+weak and so they did a bunch of
+ 
+
+ align:start position:0%
+weak and so they did a bunch of
+experiments there are a lot of
+
+ align:start position:0%
+experiments there are a lot of
+ 
+
+ align:start position:0%
+experiments there are a lot of
+controversies about this particular
+
+ align:start position:0%
+controversies about this particular
+ 
+
+ align:start position:0%
+controversies about this particular
+study but what you find is that if you
+
+ align:start position:0%
+study but what you find is that if you
+ 
+
+ align:start position:0%
+study but what you find is that if you
+calculate we can
+
+ align:start position:0%
+calculate we can
+ 
+
+ align:start position:0%
+calculate we can
+Corden's you know between on different
+
+ align:start position:0%
+Corden's you know between on different
+ 
+
+ align:start position:0%
+Corden's you know between on different
+data sets using different models you see
+
+ align:start position:0%
+data sets using different models you see
+ 
+
+ align:start position:0%
+data sets using different models you see
+that for example the concordance is not
+
+ align:start position:0%
+that for example the concordance is not
+ 
+
+ align:start position:0%
+that for example the concordance is not
+very high it's less than a half for this
+
+ align:start position:0%
+very high it's less than a half for this
+ 
+
+ align:start position:0%
+very high it's less than a half for this
+data set and you know some of it below
+
+ align:start position:0%
+data set and you know some of it below
+ 
+
+ align:start position:0%
+data set and you know some of it below
+zero so the opposite for this data set
+
+ align:start position:0%
+zero so the opposite for this data set
+ 
+
+ align:start position:0%
+zero so the opposite for this data set
+the interestingly things like like
+
+ align:start position:0%
+the interestingly things like like
+ 
+
+ align:start position:0%
+the interestingly things like like
+diabetes which come from the mimic data
+
+ align:start position:0%
+diabetes which come from the mimic data
+ 
+
+ align:start position:0%
+diabetes which come from the mimic data
+have narrower bounds than some of the
+
+ align:start position:0%
+have narrower bounds than some of the
+ 
+
+ align:start position:0%
+have narrower bounds than some of the
+others so they seem to have a more
+
+ align:start position:0%
+others so they seem to have a more
+ 
+
+ align:start position:0%
+others so they seem to have a more
+definitive conclusion at least for this
+
+ align:start position:0%
+definitive conclusion at least for this
+ 
+
+ align:start position:0%
+definitive conclusion at least for this
+study okay let me finish off by talking
+
+ align:start position:0%
+study okay let me finish off by talking
+ 
+
+ align:start position:0%
+study okay let me finish off by talking
+about the opposite idea
+
+ align:start position:0%
+about the opposite idea
+ 
+
+ align:start position:0%
+about the opposite idea
+so rather than building a complicated
+
+ align:start position:0%
+so rather than building a complicated
+ 
+
+ align:start position:0%
+so rather than building a complicated
+model and then trying to explain it in
+
+ align:start position:0%
+model and then trying to explain it in
+ 
+
+ align:start position:0%
+model and then trying to explain it in
+simple ways what if we just built a
+
+ align:start position:0%
+simple ways what if we just built a
+ 
+
+ align:start position:0%
+simple ways what if we just built a
+simple model and Cynthia Rudin was now a
+
+ align:start position:0%
+simple model and Cynthia Rudin was now a
+ 
+
+ align:start position:0%
+simple model and Cynthia Rudin was now a
+Duke used to be at in the Sloan School
+
+ align:start position:0%
+Duke used to be at in the Sloan School
+ 
+
+ align:start position:0%
+Duke used to be at in the Sloan School
+at MIT has been championing this idea
+
+ align:start position:0%
+at MIT has been championing this idea
+ 
+
+ align:start position:0%
+at MIT has been championing this idea
+for many years and so she has come up
+
+ align:start position:0%
+for many years and so she has come up
+ 
+
+ align:start position:0%
+for many years and so she has come up
+with a bunch of different ideas for how
+
+ align:start position:0%
+with a bunch of different ideas for how
+ 
+
+ align:start position:0%
+with a bunch of different ideas for how
+to build simple models that trade-off
+
+ align:start position:0%
+to build simple models that trade-off
+ 
+
+ align:start position:0%
+to build simple models that trade-off
+maybe a little bit of accuracy in order
+
+ align:start position:0%
+maybe a little bit of accuracy in order
+ 
+
+ align:start position:0%
+maybe a little bit of accuracy in order
+to be explainable and one of her
+
+ align:start position:0%
+to be explainable and one of her
+ 
+
+ align:start position:0%
+to be explainable and one of her
+favorites is this thing called a falling
+
+ align:start position:0%
+favorites is this thing called a falling
+ 
+
+ align:start position:0%
+favorites is this thing called a falling
+rule list so this is an example for a
+
+ align:start position:0%
+rule list so this is an example for a
+ 
+
+ align:start position:0%
+rule list so this is an example for a
+mammographic mass data set so it says if
+
+ align:start position:0%
+mammographic mass data set so it says if
+ 
+
+ align:start position:0%
+mammographic mass data set so it says if
+the if some lump has an irregular shape
+
+ align:start position:0%
+the if some lump has an irregular shape
+ 
+
+ align:start position:0%
+the if some lump has an irregular shape
+and the patient is over 60 years old
+
+ align:start position:0%
+and the patient is over 60 years old
+ 
+
+ align:start position:0%
+and the patient is over 60 years old
+then there's an 85 percent chance of
+
+ align:start position:0%
+then there's an 85 percent chance of
+ 
+
+ align:start position:0%
+then there's an 85 percent chance of
+malignancy risk and there are 230 cases
+
+ align:start position:0%
+malignancy risk and there are 230 cases
+ 
+
+ align:start position:0%
+malignancy risk and there are 230 cases
+in which that happened okay if this is
+
+ align:start position:0%
+in which that happened okay if this is
+ 
+
+ align:start position:0%
+in which that happened okay if this is
+not the case then if the the lump has a
+
+ align:start position:0%
+not the case then if the the lump has a
+ 
+
+ align:start position:0%
+not the case then if the the lump has a
+speculated margin so it has little
+
+ align:start position:0%
+speculated margin so it has little
+ 
+
+ align:start position:0%
+speculated margin so it has little
+spikes coming out of it and the patient
+
+ align:start position:0%
+spikes coming out of it and the patient
+ 
+
+ align:start position:0%
+spikes coming out of it and the patient
+is over 45 then there's a 78% chance of
+
+ align:start position:0%
+is over 45 then there's a 78% chance of
+ 
+
+ align:start position:0%
+is over 45 then there's a 78% chance of
+malignancy and otherwise if the margin
+
+ align:start position:0%
+malignancy and otherwise if the margin
+ 
+
+ align:start position:0%
+malignancy and otherwise if the margin
+is kind of fuzzy the edge of it is kind
+
+ align:start position:0%
+is kind of fuzzy the edge of it is kind
+ 
+
+ align:start position:0%
+is kind of fuzzy the edge of it is kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+and the patient is over 60 then there's
+
+ align:start position:0%
+and the patient is over 60 then there's
+ 
+
+ align:start position:0%
+and the patient is over 60 then there's
+a 69% chance and if it has an irregular
+
+ align:start position:0%
+a 69% chance and if it has an irregular
+ 
+
+ align:start position:0%
+a 69% chance and if it has an irregular
+shape then there's a 63% chance and if
+
+ align:start position:0%
+shape then there's a 63% chance and if
+ 
+
+ align:start position:0%
+shape then there's a 63% chance and if
+it's lobular and the density is high
+
+ align:start position:0%
+it's lobular and the density is high
+ 
+
+ align:start position:0%
+it's lobular and the density is high
+then there's a 39% chance and if it's
+
+ align:start position:0%
+then there's a 39% chance and if it's
+ 
+
+ align:start position:0%
+then there's a 39% chance and if it's
+round and the patient is over 60 then
+
+ align:start position:0%
+round and the patient is over 60 then
+ 
+
+ align:start position:0%
+round and the patient is over 60 then
+there's a 26% chance otherwise there's a
+
+ align:start position:0%
+there's a 26% chance otherwise there's a
+ 
+
+ align:start position:0%
+there's a 26% chance otherwise there's a
+10% chance okay and the argument is that
+
+ align:start position:0%
+10% chance okay and the argument is that
+ 
+
+ align:start position:0%
+10% chance okay and the argument is that
+that description of the model the
+
+ align:start position:0%
+that description of the model the
+ 
+
+ align:start position:0%
+that description of the model the
+decision-making model is simple enough
+
+ align:start position:0%
+decision-making model is simple enough
+ 
+
+ align:start position:0%
+decision-making model is simple enough
+that even doctors can understand it he's
+
+ align:start position:0%
+that even doctors can understand it he's
+ 
+
+ align:start position:0%
+that even doctors can understand it he's
+supposed to laugh now there are still
+
+ align:start position:0%
+supposed to laugh now there are still
+ 
+
+ align:start position:0%
+supposed to laugh now there are still
+some problems so one of them is notice
+
+ align:start position:0%
+some problems so one of them is notice
+ 
+
+ align:start position:0%
+some problems so one of them is notice
+some of these are age greater than 60
+
+ align:start position:0%
+some of these are age greater than 60
+ 
+
+ align:start position:0%
+some of these are age greater than 60
+age greater than 45 age greater than 60
+
+ align:start position:0%
+age greater than 45 age greater than 60
+ 
+
+ align:start position:0%
+age greater than 45 age greater than 60
+it's not quite obvious what categories
+
+ align:start position:0%
+it's not quite obvious what categories
+ 
+
+ align:start position:0%
+it's not quite obvious what categories
+that's that's defining and in principle
+
+ align:start position:0%
+that's that's defining and in principle
+ 
+
+ align:start position:0%
+that's that's defining and in principle
+it could be different ages in in
+
+ align:start position:0%
+it could be different ages in in
+ 
+
+ align:start position:0%
+it could be different ages in in
+different ones but here's how they build
+
+ align:start position:0%
+different ones but here's how they build
+ 
+
+ align:start position:0%
+different ones but here's how they build
+it so this is a very simple model that's
+
+ align:start position:0%
+it so this is a very simple model that's
+ 
+
+ align:start position:0%
+it so this is a very simple model that's
+built by a very complicated process so
+
+ align:start position:0%
+built by a very complicated process so
+ 
+
+ align:start position:0%
+built by a very complicated process so
+the simple model is the one I've just
+
+ align:start position:0%
+the simple model is the one I've just
+ 
+
+ align:start position:0%
+the simple model is the one I've just
+showed you and there's a Bayesian
+
+ align:start position:0%
+showed you and there's a Bayesian
+ 
+
+ align:start position:0%
+showed you and there's a Bayesian
+approach a Bayesian generative approach
+
+ align:start position:0%
+approach a Bayesian generative approach
+ 
+
+ align:start position:0%
+approach a Bayesian generative approach
+where they have a bunch of hyper
+
+ align:start position:0%
+where they have a bunch of hyper
+ 
+
+ align:start position:0%
+where they have a bunch of hyper
+parameters falling rulest parameters
+
+ align:start position:0%
+parameters falling rulest parameters
+ 
+
+ align:start position:0%
+parameters falling rulest parameters
+theta they calculate a likelihood which
+
+ align:start position:0%
+theta they calculate a likelihood which
+ 
+
+ align:start position:0%
+theta they calculate a likelihood which
+is given a particular theta how likely
+
+ align:start position:0%
+is given a particular theta how likely
+ 
+
+ align:start position:0%
+is given a particular theta how likely
+are you to get the answers that are
+
+ align:start position:0%
+are you to get the answers that are
+ 
+
+ align:start position:0%
+are you to get the answers that are
+actually in your data given the model
+
+ align:start position:0%
+actually in your data given the model
+ 
+
+ align:start position:0%
+actually in your data given the model
+that you generate and they start with a
+
+ align:start position:0%
+that you generate and they start with a
+ 
+
+ align:start position:0%
+that you generate and they start with a
+possible set of if clauses so they do
+
+ align:start position:0%
+possible set of if clauses so they do
+ 
+
+ align:start position:0%
+possible set of if clauses so they do
+frequent Clause mining to say what
+
+ align:start position:0%
+frequent Clause mining to say what
+ 
+
+ align:start position:0%
+frequent Clause mining to say what
+conditions what binary conditions occur
+
+ align:start position:0%
+conditions what binary conditions occur
+ 
+
+ align:start position:0%
+conditions what binary conditions occur
+frequently together in the database and
+
+ align:start position:0%
+frequently together in the database and
+ 
+
+ align:start position:0%
+frequently together in the database and
+those are the only ones that are going
+
+ align:start position:0%
+those are the only ones that are going
+ 
+
+ align:start position:0%
+those are the only ones that are going
+to consider because of course the number
+
+ align:start position:0%
+to consider because of course the number
+ 
+
+ align:start position:0%
+to consider because of course the number
+of possible clauses is vast and they
+
+ align:start position:0%
+of possible clauses is vast and they
+ 
+
+ align:start position:0%
+of possible clauses is vast and they
+don't want to have to iterate through
+
+ align:start position:0%
+don't want to have to iterate through
+ 
+
+ align:start position:0%
+don't want to have to iterate through
+those and then for each setup for each
+
+ align:start position:0%
+those and then for each setup for each
+ 
+
+ align:start position:0%
+those and then for each setup for each
+Clause they they calculate a risk score
+
+ align:start position:0%
+Clause they they calculate a risk score
+ 
+
+ align:start position:0%
+Clause they they calculate a risk score
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+is generated by a by a probability
+
+ align:start position:0%
+is generated by a by a probability
+ 
+
+ align:start position:0%
+is generated by a by a probability
+distribution under the constraint that
+
+ align:start position:0%
+distribution under the constraint that
+ 
+
+ align:start position:0%
+distribution under the constraint that
+the risk score for the next Clause is
+
+ align:start position:0%
+the risk score for the next Clause is
+ 
+
+ align:start position:0%
+the risk score for the next Clause is
+lower or equal to the risk score for the
+
+ align:start position:0%
+lower or equal to the risk score for the
+ 
+
+ align:start position:0%
+lower or equal to the risk score for the
+previous Clause okay there are lots of
+
+ align:start position:0%
+previous Clause okay there are lots of
+ 
+
+ align:start position:0%
+previous Clause okay there are lots of
+details so there's this frequent
+
+ align:start position:0%
+details so there's this frequent
+ 
+
+ align:start position:0%
+details so there's this frequent
+itemsets mining algorithm it turns out
+
+ align:start position:0%
+itemsets mining algorithm it turns out
+ 
+
+ align:start position:0%
+itemsets mining algorithm it turns out
+that choosing our R sub L to be the logs
+
+ align:start position:0%
+that choosing our R sub L to be the logs
+ 
+
+ align:start position:0%
+that choosing our R sub L to be the logs
+of products of real numbers is an
+
+ align:start position:0%
+of products of real numbers is an
+ 
+
+ align:start position:0%
+of products of real numbers is an
+important step in order to guarantee
+
+ align:start position:0%
+important step in order to guarantee
+ 
+
+ align:start position:0%
+important step in order to guarantee
+that monotonicity constraint in a simple
+
+ align:start position:0%
+that monotonicity constraint in a simple
+ 
+
+ align:start position:0%
+that monotonicity constraint in a simple
+way L the number of clauses is drawn
+
+ align:start position:0%
+way L the number of clauses is drawn
+ 
+
+ align:start position:0%
+way L the number of clauses is drawn
+from a Poisson distribution and you give
+
+ align:start position:0%
+from a Poisson distribution and you give
+ 
+
+ align:start position:0%
+from a Poisson distribution and you give
+it a kind of scale that says roughly how
+
+ align:start position:0%
+it a kind of scale that says roughly how
+ 
+
+ align:start position:0%
+it a kind of scale that says roughly how
+many clauses would you be willing to
+
+ align:start position:0%
+many clauses would you be willing to
+ 
+
+ align:start position:0%
+many clauses would you be willing to
+tolerate in your in your following rule
+
+ align:start position:0%
+tolerate in your in your following rule
+ 
+
+ align:start position:0%
+tolerate in your in your following rule
+list and then there's a lot of
+
+ align:start position:0%
+list and then there's a lot of
+ 
+
+ align:start position:0%
+list and then there's a lot of
+computational hair where they do they
+
+ align:start position:0%
+computational hair where they do they
+ 
+
+ align:start position:0%
+computational hair where they do they
+get mean a posterior a probability
+
+ align:start position:0%
+get mean a posterior a probability
+ 
+
+ align:start position:0%
+get mean a posterior a probability
+estimation by using a simulated
+
+ align:start position:0%
+estimation by using a simulated
+ 
+
+ align:start position:0%
+estimation by using a simulated
+annealing algorithm so they basically
+
+ align:start position:0%
+annealing algorithm so they basically
+ 
+
+ align:start position:0%
+annealing algorithm so they basically
+generate some clauses and then they use
+
+ align:start position:0%
+generate some clauses and then they use
+ 
+
+ align:start position:0%
+generate some clauses and then they use
+swap replace add and delete operators in
+
+ align:start position:0%
+swap replace add and delete operators in
+ 
+
+ align:start position:0%
+swap replace add and delete operators in
+order to try different variations and
+
+ align:start position:0%
+order to try different variations and
+ 
+
+ align:start position:0%
+order to try different variations and
+they're doing hill climbing in that
+
+ align:start position:0%
+they're doing hill climbing in that
+ 
+
+ align:start position:0%
+they're doing hill climbing in that
+space there's also some Gibbs sampling
+
+ align:start position:0%
+space there's also some Gibbs sampling
+ 
+
+ align:start position:0%
+space there's also some Gibbs sampling
+because once you have one of these
+
+ align:start position:0%
+because once you have one of these
+ 
+
+ align:start position:0%
+because once you have one of these
+models simply calculating how accurate
+
+ align:start position:0%
+models simply calculating how accurate
+ 
+
+ align:start position:0%
+models simply calculating how accurate
+it is is not straightforward there's not
+
+ align:start position:0%
+it is is not straightforward there's not
+ 
+
+ align:start position:0%
+it is is not straightforward there's not
+a closed-form way of doing it and so
+
+ align:start position:0%
+a closed-form way of doing it and so
+ 
+
+ align:start position:0%
+a closed-form way of doing it and so
+they're doing sampling in order to try
+
+ align:start position:0%
+they're doing sampling in order to try
+ 
+
+ align:start position:0%
+they're doing sampling in order to try
+to generate that so it's a bunch of hair
+
+ align:start position:0%
+to generate that so it's a bunch of hair
+ 
+
+ align:start position:0%
+to generate that so it's a bunch of hair
+and again the paper describes it all
+
+ align:start position:0%
+and again the paper describes it all
+ 
+
+ align:start position:0%
+and again the paper describes it all
+well what's interesting is that on a 30
+
+ align:start position:0%
+well what's interesting is that on a 30
+ 
+
+ align:start position:0%
+well what's interesting is that on a 30
+day hospital readmission data set with
+
+ align:start position:0%
+day hospital readmission data set with
+ 
+
+ align:start position:0%
+day hospital readmission data set with
+about 8,000 patients they used about 34
+
+ align:start position:0%
+about 8,000 patients they used about 34
+ 
+
+ align:start position:0%
+about 8,000 patients they used about 34
+features like impaired Mental Status
+
+ align:start position:0%
+features like impaired Mental Status
+ 
+
+ align:start position:0%
+features like impaired Mental Status
+difficult behavior
+
+ align:start position:0%
+difficult behavior
+ 
+
+ align:start position:0%
+difficult behavior
+pain feels unsafe etc they mind rules or
+
+ align:start position:0%
+pain feels unsafe etc they mind rules or
+ 
+
+ align:start position:0%
+pain feels unsafe etc they mind rules or
+clauses with support more than 5% of the
+
+ align:start position:0%
+clauses with support more than 5% of the
+ 
+
+ align:start position:0%
+clauses with support more than 5% of the
+database and no more than two conditions
+
+ align:start position:0%
+database and no more than two conditions
+ 
+
+ align:start position:0%
+database and no more than two conditions
+they set the expected length of the
+
+ align:start position:0%
+they set the expected length of the
+ 
+
+ align:start position:0%
+they set the expected length of the
+decision list to be 8 clauses and then
+
+ align:start position:0%
+decision list to be 8 clauses and then
+ 
+
+ align:start position:0%
+decision list to be 8 clauses and then
+they compared the decision model they
+
+ align:start position:0%
+they compared the decision model they
+ 
+
+ align:start position:0%
+they compared the decision model they
+got to SVM's random forest logistic
+
+ align:start position:0%
+got to SVM's random forest logistic
+ 
+
+ align:start position:0%
+got to SVM's random forest logistic
+regression cart and an inductive logic
+
+ align:start position:0%
+regression cart and an inductive logic
+ 
+
+ align:start position:0%
+regression cart and an inductive logic
+programming approach and shockingly to
+
+ align:start position:0%
+programming approach and shockingly to
+ 
+
+ align:start position:0%
+programming approach and shockingly to
+me their method the falling rulest
+
+ align:start position:0%
+me their method the falling rulest
+ 
+
+ align:start position:0%
+me their method the falling rulest
+method got an a you see of about 0.8
+
+ align:start position:0%
+method got an a you see of about 0.8
+ 
+
+ align:start position:0%
+method got an a you see of about 0.8
+whereas all the others did like 0.7 9.75
+
+ align:start position:0%
+whereas all the others did like 0.7 9.75
+ 
+
+ align:start position:0%
+whereas all the others did like 0.7 9.75
+logistic regression as usual
+
+ align:start position:0%
+logistic regression as usual
+ 
+
+ align:start position:0%
+logistic regression as usual
+outperformed the one they got slightly
+
+ align:start position:0%
+outperformed the one they got slightly
+ 
+
+ align:start position:0%
+outperformed the one they got slightly
+right but this is interesting because
+
+ align:start position:0%
+right but this is interesting because
+ 
+
+ align:start position:0%
+right but this is interesting because
+their argument is that this
+
+ align:start position:0%
+their argument is that this
+ 
+
+ align:start position:0%
+their argument is that this
+representation of the model is much more
+
+ align:start position:0%
+representation of the model is much more
+ 
+
+ align:start position:0%
+representation of the model is much more
+easy to understand than even a logistic
+
+ align:start position:0%
+easy to understand than even a logistic
+ 
+
+ align:start position:0%
+easy to understand than even a logistic
+regression model for most human human
+
+ align:start position:0%
+regression model for most human human
+ 
+
+ align:start position:0%
+regression model for most human human
+users and also if you look at these are
+
+ align:start position:0%
+users and also if you look at these are
+ 
+
+ align:start position:0%
+users and also if you look at these are
+just various runs and the different
+
+ align:start position:0%
+just various runs and the different
+ 
+
+ align:start position:0%
+just various runs and the different
+models and their model has a pretty
+
+ align:start position:0%
+models and their model has a pretty
+ 
+
+ align:start position:0%
+models and their model has a pretty
+decent day you see up here I think the
+
+ align:start position:0%
+decent day you see up here I think the
+ 
+
+ align:start position:0%
+decent day you see up here I think the
+green one is the logistic regression one
+
+ align:start position:0%
+green one is the logistic regression one
+ 
+
+ align:start position:0%
+green one is the logistic regression one
+and it it's slightly better because it
+
+ align:start position:0%
+and it it's slightly better because it
+ 
+
+ align:start position:0%
+and it it's slightly better because it
+outperforms their best model in the
+
+ align:start position:0%
+outperforms their best model in the
+ 
+
+ align:start position:0%
+outperforms their best model in the
+region of low false positive rates which
+
+ align:start position:0%
+region of low false positive rates which
+ 
+
+ align:start position:0%
+region of low false positive rates which
+may be where you want to operate so that
+
+ align:start position:0%
+may be where you want to operate so that
+ 
+
+ align:start position:0%
+may be where you want to operate so that
+may actually be a better model so here's
+
+ align:start position:0%
+may actually be a better model so here's
+ 
+
+ align:start position:0%
+may actually be a better model so here's
+their readmission rule list and it says
+
+ align:start position:0%
+their readmission rule list and it says
+ 
+
+ align:start position:0%
+their readmission rule list and it says
+if the patient has bedsores and has a
+
+ align:start position:0%
+if the patient has bedsores and has a
+ 
+
+ align:start position:0%
+if the patient has bedsores and has a
+history of not showing up for
+
+ align:start position:0%
+history of not showing up for
+ 
+
+ align:start position:0%
+history of not showing up for
+appointments then there's a 33%
+
+ align:start position:0%
+appointments then there's a 33%
+ 
+
+ align:start position:0%
+appointments then there's a 33%
+probability that they'll be readmitted
+
+ align:start position:0%
+probability that they'll be readmitted
+ 
+
+ align:start position:0%
+probability that they'll be readmitted
+within 30 days if I think some note says
+
+ align:start position:0%
+within 30 days if I think some note says
+ 
+
+ align:start position:0%
+within 30 days if I think some note says
+poor prognosis and maximum care etc so
+
+ align:start position:0%
+poor prognosis and maximum care etc so
+ 
+
+ align:start position:0%
+poor prognosis and maximum care etc so
+this is the result that they came up
+
+ align:start position:0%
+this is the result that they came up
+ 
+
+ align:start position:0%
+this is the result that they came up
+with now by the way we've talked a
+
+ align:start position:0%
+with now by the way we've talked a
+ 
+
+ align:start position:0%
+with now by the way we've talked a
+little bit about a 30 day readmission
+
+ align:start position:0%
+little bit about a 30 day readmission
+ 
+
+ align:start position:0%
+little bit about a 30 day readmission
+predictions and getting over about 70%
+
+ align:start position:0%
+predictions and getting over about 70%
+ 
+
+ align:start position:0%
+predictions and getting over about 70%
+is not bad in that domain because it's
+
+ align:start position:0%
+is not bad in that domain because it's
+ 
+
+ align:start position:0%
+is not bad in that domain because it's
+just not that easily predictable who's
+
+ align:start position:0%
+just not that easily predictable who's
+ 
+
+ align:start position:0%
+just not that easily predictable who's
+gonna wind up back in the hospital
+
+ align:start position:0%
+gonna wind up back in the hospital
+ 
+
+ align:start position:0%
+gonna wind up back in the hospital
+within 30 days so these models are
+
+ align:start position:0%
+within 30 days so these models are
+ 
+
+ align:start position:0%
+within 30 days so these models are
+actually doing quite well and certainly
+
+ align:start position:0%
+actually doing quite well and certainly
+ 
+
+ align:start position:0%
+actually doing quite well and certainly
+understandable in these terms they also
+
+ align:start position:0%
+understandable in these terms they also
+ 
+
+ align:start position:0%
+understandable in these terms they also
+tried on a variety of University of
+
+ align:start position:0%
+tried on a variety of University of
+ 
+
+ align:start position:0%
+tried on a variety of University of
+california-irvine machine learning data
+
+ align:start position:0%
+california-irvine machine learning data
+ 
+
+ align:start position:0%
+california-irvine machine learning data
+sets these are just random public data
+
+ align:start position:0%
+sets these are just random public data
+ 
+
+ align:start position:0%
+sets these are just random public data
+sets and they tried building these
+
+ align:start position:0%
+sets and they tried building these
+ 
+
+ align:start position:0%
+sets and they tried building these
+falling rulest models to make
+
+ align:start position:0%
+falling rulest models to make
+ 
+
+ align:start position:0%
+falling rulest models to make
+predictions and what you see is that the
+
+ align:start position:0%
+predictions and what you see is that the
+ 
+
+ align:start position:0%
+predictions and what you see is that the
+au C's are pretty good so on the spam
+
+ align:start position:0%
+au C's are pretty good so on the spam
+ 
+
+ align:start position:0%
+au C's are pretty good so on the spam
+detection data set their system gets
+
+ align:start position:0%
+detection data set their system gets
+ 
+
+ align:start position:0%
+detection data set their system gets
+about 91 logistic regression again gets
+
+ align:start position:0%
+about 91 logistic regression again gets
+ 
+
+ align:start position:0%
+about 91 logistic regression again gets
+97 so you know part of the unfortunate
+
+ align:start position:0%
+97 so you know part of the unfortunate
+ 
+
+ align:start position:0%
+97 so you know part of the unfortunate
+lesson that we we teach in almost every
+
+ align:start position:0%
+lesson that we we teach in almost every
+ 
+
+ align:start position:0%
+lesson that we we teach in almost every
+example in this class is the simple
+
+ align:start position:0%
+example in this class is the simple
+ 
+
+ align:start position:0%
+example in this class is the simple
+models like logistic regression often do
+
+ align:start position:0%
+models like logistic regression often do
+ 
+
+ align:start position:0%
+models like logistic regression often do
+quite well but remember here they're
+
+ align:start position:0%
+quite well but remember here they're
+ 
+
+ align:start position:0%
+quite well but remember here they're
+optimizing for explained ability rather
+
+ align:start position:0%
+optimizing for explained ability rather
+ 
+
+ align:start position:0%
+optimizing for explained ability rather
+than for getting the right answer so
+
+ align:start position:0%
+than for getting the right answer so
+ 
+
+ align:start position:0%
+than for getting the right answer so
+they're willing to sacrifice some
+
+ align:start position:0%
+they're willing to sacrifice some
+ 
+
+ align:start position:0%
+they're willing to sacrifice some
+accuracy in their model in order to
+
+ align:start position:0%
+accuracy in their model in order to
+ 
+
+ align:start position:0%
+accuracy in their model in order to
+develop a result that is easy to explain
+
+ align:start position:0%
+develop a result that is easy to explain
+ 
+
+ align:start position:0%
+develop a result that is easy to explain
+to people so again there are many
+
+ align:start position:0%
+to people so again there are many
+ 
+
+ align:start position:0%
+to people so again there are many
+variations on this type of work where
+
+ align:start position:0%
+variations on this type of work where
+ 
+
+ align:start position:0%
+variations on this type of work where
+people have different notions of what
+
+ align:start position:0%
+people have different notions of what
+ 
+
+ align:start position:0%
+people have different notions of what
+counts as a simple explainable model but
+
+ align:start position:0%
+counts as a simple explainable model but
+ 
+
+ align:start position:0%
+counts as a simple explainable model but
+that's a very different approach than
+
+ align:start position:0%
+that's a very different approach than
+ 
+
+ align:start position:0%
+that's a very different approach than
+the Lyme approach which says build the
+
+ align:start position:0%
+the Lyme approach which says build the
+ 
+
+ align:start position:0%
+the Lyme approach which says build the
+Harry model and then produce local
+
+ align:start position:0%
+Harry model and then produce local
+ 
+
+ align:start position:0%
+Harry model and then produce local
+explanations for why it makes certain
+
+ align:start position:0%
+explanations for why it makes certain
+ 
+
+ align:start position:0%
+explanations for why it makes certain
+decisions on particular cases all right
+
+ align:start position:0%
+decisions on particular cases all right
+ 
+
+ align:start position:0%
+decisions on particular cases all right
+I think that's all I'm going to say
+
+ align:start position:0%
+I think that's all I'm going to say
+ 
+
+ align:start position:0%
+I think that's all I'm going to say
+about explain ability this is a very hot
+
+ align:start position:0%
+about explain ability this is a very hot
+ 
+
+ align:start position:0%
+about explain ability this is a very hot
+topic at the moment and so there are
+
+ align:start position:0%
+topic at the moment and so there are
+ 
+
+ align:start position:0%
+topic at the moment and so there are
+lots of papers
+
+ align:start position:0%
+lots of papers
+ 
+
+ align:start position:0%
+lots of papers
+I think there's I just saw a call for a
+
+ align:start position:0%
+I think there's I just saw a call for a
+ 
+
+ align:start position:0%
+I think there's I just saw a call for a
+conference on explainable machine
+
+ align:start position:0%
+conference on explainable machine
+ 
+
+ align:start position:0%
+conference on explainable machine
+learning models so there's more and more
+
+ align:start position:0%
+learning models so there's more and more
+ 
+
+ align:start position:0%
+learning models so there's more and more
+working in this area so with that we
+
+ align:start position:0%
+working in this area so with that we
+ 
+
+ align:start position:0%
+working in this area so with that we
+come to the end of our
+
+ align:start position:0%
+come to the end of our
+ 
+
+ align:start position:0%
+come to the end of our
+and I just wanted I just went through
+
+ align:start position:0%
+and I just wanted I just went through
+ 
+
+ align:start position:0%
+and I just wanted I just went through
+the the front page of the course website
+
+ align:start position:0%
+the the front page of the course website
+ 
+
+ align:start position:0%
+the the front page of the course website
+and listed all the topics so we've
+
+ align:start position:0%
+and listed all the topics so we've
+ 
+
+ align:start position:0%
+and listed all the topics so we've
+covered quite a lot of stuff right you
+
+ align:start position:0%
+covered quite a lot of stuff right you
+ 
+
+ align:start position:0%
+covered quite a lot of stuff right you
+know what what makes healthcare
+
+ align:start position:0%
+know what what makes healthcare
+ 
+
+ align:start position:0%
+know what what makes healthcare
+different and we talked about what
+
+ align:start position:0%
+different and we talked about what
+ 
+
+ align:start position:0%
+different and we talked about what
+clinical care is all about and what
+
+ align:start position:0%
+clinical care is all about and what
+ 
+
+ align:start position:0%
+clinical care is all about and what
+clinical data is like and risk
+
+ align:start position:0%
+clinical data is like and risk
+ 
+
+ align:start position:0%
+clinical data is like and risk
+stratification survival modeling
+
+ align:start position:0%
+stratification survival modeling
+ 
+
+ align:start position:0%
+stratification survival modeling
+physiological time-series how to
+
+ align:start position:0%
+physiological time-series how to
+ 
+
+ align:start position:0%
+physiological time-series how to
+interpret clinical text in a couple of
+
+ align:start position:0%
+interpret clinical text in a couple of
+ 
+
+ align:start position:0%
+interpret clinical text in a couple of
+lectures translating technology into the
+
+ align:start position:0%
+lectures translating technology into the
+ 
+
+ align:start position:0%
+lectures translating technology into the
+clinic the italicized ones were guest
+
+ align:start position:0%
+clinic the italicized ones were guest
+ 
+
+ align:start position:0%
+clinic the italicized ones were guest
+lecturers so machine learning for
+
+ align:start position:0%
+lecturers so machine learning for
+ 
+
+ align:start position:0%
+lecturers so machine learning for
+cardiology and machine learning for
+
+ align:start position:0%
+cardiology and machine learning for
+ 
+
+ align:start position:0%
+cardiology and machine learning for
+differential diagnosis machine learning
+
+ align:start position:0%
+differential diagnosis machine learning
+ 
+
+ align:start position:0%
+differential diagnosis machine learning
+for pathology for mammography David gave
+
+ align:start position:0%
+for pathology for mammography David gave
+ 
+
+ align:start position:0%
+for pathology for mammography David gave
+a couple of lectures on causal inference
+
+ align:start position:0%
+a couple of lectures on causal inference
+ 
+
+ align:start position:0%
+a couple of lectures on causal inference
+and reinforcement learning or David and
+
+ align:start position:0%
+and reinforcement learning or David and
+ 
+
+ align:start position:0%
+and reinforcement learning or David and
+a guest which I I didn't note here
+
+ align:start position:0%
+a guest which I I didn't note here
+ 
+
+ align:start position:0%
+a guest which I I didn't note here
+disease progression and subtyping we
+
+ align:start position:0%
+disease progression and subtyping we
+ 
+
+ align:start position:0%
+disease progression and subtyping we
+talked about precision medicine and the
+
+ align:start position:0%
+talked about precision medicine and the
+ 
+
+ align:start position:0%
+talked about precision medicine and the
+role of genetics automating clinical
+
+ align:start position:0%
+role of genetics automating clinical
+ 
+
+ align:start position:0%
+role of genetics automating clinical
+workflows the lecture on regulation and
+
+ align:start position:0%
+workflows the lecture on regulation and
+ 
+
+ align:start position:0%
+workflows the lecture on regulation and
+then recently fairness robustness the
+
+ align:start position:0%
+then recently fairness robustness the
+ 
+
+ align:start position:0%
+then recently fairness robustness the
+data set shift and interpretability
+
+ align:start position:0%
+data set shift and interpretability
+ 
+
+ align:start position:0%
+data set shift and interpretability
+so that's quite a lot we I think we're
+
+ align:start position:0%
+so that's quite a lot we I think we're
+ 
+
+ align:start position:0%
+so that's quite a lot we I think we're
+we the staff are pretty happy with how
+
+ align:start position:0%
+we the staff are pretty happy with how
+ 
+
+ align:start position:0%
+we the staff are pretty happy with how
+the class has gone it was our first time
+
+ align:start position:0%
+the class has gone it was our first time
+ 
+
+ align:start position:0%
+the class has gone it was our first time
+as this crew teaching it and we hope to
+
+ align:start position:0%
+as this crew teaching it and we hope to
+ 
+
+ align:start position:0%
+as this crew teaching it and we hope to
+do it again I can't stop without giving
+
+ align:start position:0%
+do it again I can't stop without giving
+ 
+
+ align:start position:0%
+do it again I can't stop without giving
+an immense vote of gratitude to Irene
+
+ align:start position:0%
+an immense vote of gratitude to Irene
+ 
+
+ align:start position:0%
+an immense vote of gratitude to Irene
+and Willi without whom we would have
+
+ align:start position:0%
+and Willi without whom we would have
+ 
+
+ align:start position:0%
+and Willi without whom we would have
+been totally sunk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I also want to acknowledge David's
+
+ align:start position:0%
+and I also want to acknowledge David's
+ 
+
+ align:start position:0%
+and I also want to acknowledge David's
+vision and putting this course together
+
+ align:start position:0%
+vision and putting this course together
+ 
+
+ align:start position:0%
+vision and putting this course together
+he taught a sort of half-size version of
+
+ align:start position:0%
+he taught a sort of half-size version of
+ 
+
+ align:start position:0%
+he taught a sort of half-size version of
+a class like this a couple of years ago
+
+ align:start position:0%
+a class like this a couple of years ago
+ 
+
+ align:start position:0%
+a class like this a couple of years ago
+and thought that it would be a good idea
+
+ align:start position:0%
+and thought that it would be a good idea
+ 
+
+ align:start position:0%
+and thought that it would be a good idea
+to expand it into a full semester a
+
+ align:start position:0%
+to expand it into a full semester a
+ 
+
+ align:start position:0%
+to expand it into a full semester a
+regular course and got me on board to
+
+ align:start position:0%
+regular course and got me on board to
+ 
+
+ align:start position:0%
+regular course and got me on board to
+work with them and I want to thank you
+
+ align:start position:0%
+work with them and I want to thank you
+ 
+
+ align:start position:0%
+work with them and I want to thank you
+all for your hard work and I and I'm
+
+ align:start position:0%
+all for your hard work and I and I'm
+ 
+
+ align:start position:0%
+all for your hard work and I and I'm
+looking forward to
\ No newline at end of file
diff --git a/wEyKvA_O-n4.txt b/wEyKvA_O-n4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b99ce344a3e5f58f4b31e3fd7feeb32a177a05bf
--- /dev/null
+++ b/wEyKvA_O-n4.txt
@@ -0,0 +1,619 @@
+align:start position:0%
+ 
+here I made the list of the ingredients
+
+ align:start position:0%
+here I made the list of the ingredients
+ 
+
+ align:start position:0%
+here I made the list of the ingredients
+with ingredients for the meatballs this
+
+ align:start position:0%
+with ingredients for the meatballs this
+ 
+
+ align:start position:0%
+with ingredients for the meatballs this
+is the ingredient tea for this
+
+ align:start position:0%
+is the ingredient tea for this
+ 
+
+ align:start position:0%
+is the ingredient tea for this
+and this is foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is the idea
+
+ align:start position:0%
+so what is the idea
+ 
+
+ align:start position:0%
+so what is the idea
+well you just have to mince chop ground
+
+ align:start position:0%
+well you just have to mince chop ground
+ 
+
+ align:start position:0%
+well you just have to mince chop ground
+everything make little balls you can
+
+ align:start position:0%
+everything make little balls you can
+ 
+
+ align:start position:0%
+everything make little balls you can
+make them smaller than
+
+ align:start position:0%
+make them smaller than
+ 
+
+ align:start position:0%
+make them smaller than
+if they cook faster and then what I was
+
+ align:start position:0%
+if they cook faster and then what I was
+ 
+
+ align:start position:0%
+if they cook faster and then what I was
+thinking is that we could cook the
+
+ align:start position:0%
+thinking is that we could cook the
+ 
+
+ align:start position:0%
+thinking is that we could cook the
+meatballs
+
+ align:start position:0%
+meatballs
+ 
+
+ align:start position:0%
+meatballs
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you take the salsicha you want to
+
+ align:start position:0%
+then you take the salsicha you want to
+ 
+
+ align:start position:0%
+then you take the salsicha you want to
+take the skin off so that and then you
+
+ align:start position:0%
+take the skin off so that and then you
+ 
+
+ align:start position:0%
+take the skin off so that and then you
+can use the sausage
+
+ align:start position:0%
+can use the sausage
+ 
+
+ align:start position:0%
+can use the sausage
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very very very small yes very small
+
+ align:start position:0%
+very very very small yes very small
+ 
+
+ align:start position:0%
+very very very small yes very small
+because then you're going to mix
+
+ align:start position:0%
+because then you're going to mix
+ 
+
+ align:start position:0%
+because then you're going to mix
+everything together and then wash the
+
+ align:start position:0%
+everything together and then wash the
+ 
+
+ align:start position:0%
+everything together and then wash the
+Brazil and you can use yes you chop it
+
+ align:start position:0%
+Brazil and you can use yes you chop it
+ 
+
+ align:start position:0%
+Brazil and you can use yes you chop it
+and you put it in there okay okay so
+
+ align:start position:0%
+and you put it in there okay okay so
+ 
+
+ align:start position:0%
+and you put it in there okay okay so
+it's a traditional
+
+ align:start position:0%
+it's a traditional
+ 
+
+ align:start position:0%
+it's a traditional
+we would also add the input
+
+ align:start position:0%
+we would also add the input
+ 
+
+ align:start position:0%
+we would also add the input
+but I thought we could make a version
+
+ align:start position:0%
+but I thought we could make a version
+ 
+
+ align:start position:0%
+but I thought we could make a version
+that's a little bit lighter okay so
+
+ align:start position:0%
+that's a little bit lighter okay so
+ 
+
+ align:start position:0%
+that's a little bit lighter okay so
+let's try without this okay but don't
+
+ align:start position:0%
+let's try without this okay but don't
+ 
+
+ align:start position:0%
+let's try without this okay but don't
+forget to add salad and then you will
+
+ align:start position:0%
+forget to add salad and then you will
+ 
+
+ align:start position:0%
+forget to add salad and then you will
+cook it in the pan
+
+ align:start position:0%
+cook it in the pan
+ 
+
+ align:start position:0%
+cook it in the pan
+you have different options you can um
+
+ align:start position:0%
+you have different options you can um
+ 
+
+ align:start position:0%
+you have different options you can um
+but I would avoid for frying yeah
+
+ align:start position:0%
+but I would avoid for frying yeah
+ 
+
+ align:start position:0%
+but I would avoid for frying yeah
+so what you can do maybe you can make a
+
+ align:start position:0%
+so what you can do maybe you can make a
+ 
+
+ align:start position:0%
+so what you can do maybe you can make a
+Sofrito
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you put a lot of Chipola
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know this one works better yeah
+
+ align:start position:0%
+you know this one works better yeah
+ 
+
+ align:start position:0%
+you know this one works better yeah
+this is the best so great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's gonna come out you will see a
+
+ align:start position:0%
+it's gonna come out you will see a
+ 
+
+ align:start position:0%
+it's gonna come out you will see a
+different consistency longer more fluffy
+
+ align:start position:0%
+different consistency longer more fluffy
+ 
+
+ align:start position:0%
+different consistency longer more fluffy
+yeah so it's really good then you want
+
+ align:start position:0%
+yeah so it's really good then you want
+ 
+
+ align:start position:0%
+yeah so it's really good then you want
+to mix everything together make little
+
+ align:start position:0%
+to mix everything together make little
+ 
+
+ align:start position:0%
+to mix everything together make little
+balls and then you cook them in the pan
+
+ align:start position:0%
+balls and then you cook them in the pan
+ 
+
+ align:start position:0%
+balls and then you cook them in the pan
+slow heat with a little bit of oil so
+
+ align:start position:0%
+slow heat with a little bit of oil so
+ 
+
+ align:start position:0%
+slow heat with a little bit of oil so
+wash the zucchini you're starting to
+
+ align:start position:0%
+wash the zucchini you're starting to
+ 
+
+ align:start position:0%
+wash the zucchini you're starting to
+chop them that's fine but it's fast
+
+ align:start position:0%
+chop them that's fine but it's fast
+ 
+
+ align:start position:0%
+chop them that's fine but it's fast
+sorry if you use the grater okay and
+
+ align:start position:0%
+sorry if you use the grater okay and
+ 
+
+ align:start position:0%
+sorry if you use the grater okay and
+they're they're not gonna come out too
+
+ align:start position:0%
+they're they're not gonna come out too
+ 
+
+ align:start position:0%
+they're they're not gonna come out too
+much thinner then you can use them
+
+ align:start position:0%
+much thinner then you can use them
+ 
+
+ align:start position:0%
+much thinner then you can use them
+directly as they are or I prefer to
+
+ align:start position:0%
+directly as they are or I prefer to
+ 
+
+ align:start position:0%
+directly as they are or I prefer to
+cook them with some Sofrito to add a
+
+ align:start position:0%
+cook them with some Sofrito to add a
+ 
+
+ align:start position:0%
+cook them with some Sofrito to add a
+little bit of taste so you can mix Frito
+
+ align:start position:0%
+little bit of taste so you can mix Frito
+ 
+
+ align:start position:0%
+little bit of taste so you can mix Frito
+with algae and your favorite space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spices and also in this way they're
+
+ align:start position:0%
+spices and also in this way they're
+ 
+
+ align:start position:0%
+spices and also in this way they're
+going to release some of the water
+
+ align:start position:0%
+going to release some of the water
+ 
+
+ align:start position:0%
+going to release some of the water
+otherwise they come out like very very
+
+ align:start position:0%
+otherwise they come out like very very
+ 
+
+ align:start position:0%
+otherwise they come out like very very
+watery okay then you let them cool you
+
+ align:start position:0%
+watery okay then you let them cool you
+ 
+
+ align:start position:0%
+watery okay then you let them cool you
+mix them with the rest of the
+
+ align:start position:0%
+mix them with the rest of the
+ 
+
+ align:start position:0%
+mix them with the rest of the
+ingredients make little balls and then
+
+ align:start position:0%
+ingredients make little balls and then
+ 
+
+ align:start position:0%
+ingredients make little balls and then
+you put them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very hungry yes and this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it goes so fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I find it a little bit more tasty
+
+ align:start position:0%
+I find it a little bit more tasty
+ 
+
+ align:start position:0%
+I find it a little bit more tasty
+but usually
+
+ align:start position:0%
+but usually
+ 
+
+ align:start position:0%
+but usually
+because it has been in the can it's not
+
+ align:start position:0%
+because it has been in the can it's not
+ 
+
+ align:start position:0%
+because it has been in the can it's not
+like the best quality so you want to
+
+ align:start position:0%
+like the best quality so you want to
+ 
+
+ align:start position:0%
+like the best quality so you want to
+drain it
+
+ align:start position:0%
+drain it
+ 
+
+ align:start position:0%
+drain it
+okay it's okay it's not a big deal if
+
+ align:start position:0%
+okay it's okay it's not a big deal if
+ 
+
+ align:start position:0%
+okay it's okay it's not a big deal if
+you added some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so right now we're making this mix into
+
+ align:start position:0%
+so right now we're making this mix into
+ 
+
+ align:start position:0%
+so right now we're making this mix into
+tiny little balls and then we're gonna
+
+ align:start position:0%
+tiny little balls and then we're gonna
+ 
+
+ align:start position:0%
+tiny little balls and then we're gonna
+cover them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then again it has kind of make sure
+
+ align:start position:0%
+so then again it has kind of make sure
+ 
+
+ align:start position:0%
+so then again it has kind of make sure
+yeah yeah when we fry them okay
+
+ align:start position:0%
+yeah yeah when we fry them okay
+ 
+
+ align:start position:0%
+yeah yeah when we fry them okay
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
\ No newline at end of file
diff --git a/wQBSalAFFC4.txt b/wQBSalAFFC4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9accbe22d7b7ae08142e35119c35f69c6b31d5ae
--- /dev/null
+++ b/wQBSalAFFC4.txt
@@ -0,0 +1,11882 @@
+align:start position:0%
+ 
+hello can people hear me in the
+
+ align:start position:0%
+hello can people hear me in the
+ 
+
+ align:start position:0%
+hello can people hear me in the
+back yeah thumbs up
+
+ align:start position:0%
+back yeah thumbs up
+ 
+
+ align:start position:0%
+back yeah thumbs up
+okay uh so today we're going to be
+
+ align:start position:0%
+okay uh so today we're going to be
+ 
+
+ align:start position:0%
+okay uh so today we're going to be
+continuing our discussion of uh
+
+ align:start position:0%
+continuing our discussion of uh
+ 
+
+ align:start position:0%
+continuing our discussion of uh
+probability uh in the last lecture we
+
+ align:start position:0%
+probability uh in the last lecture we
+ 
+
+ align:start position:0%
+probability uh in the last lecture we
+saw uh how to compute probabilities
+
+ align:start position:0%
+saw uh how to compute probabilities
+ 
+
+ align:start position:0%
+saw uh how to compute probabilities
+using the uh oh dear uh using the uh
+
+ align:start position:0%
+using the uh oh dear uh using the uh
+ 
+
+ align:start position:0%
+using the uh oh dear uh using the uh
+tree method and this lecture we are
+
+ align:start position:0%
+tree method and this lecture we are
+ 
+
+ align:start position:0%
+tree method and this lecture we are
+going to uh you know see how some of the
+
+ align:start position:0%
+going to uh you know see how some of the
+ 
+
+ align:start position:0%
+going to uh you know see how some of the
+tools that we learned in the last unit
+
+ align:start position:0%
+tools that we learned in the last unit
+ 
+
+ align:start position:0%
+tools that we learned in the last unit
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+counting uh for for reasoning about the
+
+ align:start position:0%
+counting uh for for reasoning about the
+ 
+
+ align:start position:0%
+counting uh for for reasoning about the
+sizes of sets and things like that can
+
+ align:start position:0%
+sizes of sets and things like that can
+ 
+
+ align:start position:0%
+sizes of sets and things like that can
+also carry over naturally into the uh
+
+ align:start position:0%
+also carry over naturally into the uh
+ 
+
+ align:start position:0%
+also carry over naturally into the uh
+into the realm of probability okay uh
+
+ align:start position:0%
+into the realm of probability okay uh
+ 
+
+ align:start position:0%
+into the realm of probability okay uh
+and we'll also learn how to express
+
+ align:start position:0%
+and we'll also learn how to express
+ 
+
+ align:start position:0%
+and we'll also learn how to express
+mathematically uh statements like uh if
+
+ align:start position:0%
+mathematically uh statements like uh if
+ 
+
+ align:start position:0%
+mathematically uh statements like uh if
+you recall I was saying things last time
+
+ align:start position:0%
+you recall I was saying things last time
+ 
+
+ align:start position:0%
+you recall I was saying things last time
+like you know if the prize is behind
+
+ align:start position:0%
+like you know if the prize is behind
+ 
+
+ align:start position:0%
+like you know if the prize is behind
+door a what is the probability that uh
+
+ align:start position:0%
+door a what is the probability that uh
+ 
+
+ align:start position:0%
+door a what is the probability that uh
+Marilyn selects door b or or something
+
+ align:start position:0%
+Marilyn selects door b or or something
+ 
+
+ align:start position:0%
+Marilyn selects door b or or something
+like that okay so we're going to uh you
+
+ align:start position:0%
+like that okay so we're going to uh you
+ 
+
+ align:start position:0%
+like that okay so we're going to uh you
+know see you know more formally what
+
+ align:start position:0%
+know see you know more formally what
+ 
+
+ align:start position:0%
+know see you know more formally what
+these statements are are trying to
+
+ align:start position:0%
+these statements are are trying to
+ 
+
+ align:start position:0%
+these statements are are trying to
+express and how to reason about them
+
+ align:start position:0%
+express and how to reason about them
+ 
+
+ align:start position:0%
+express and how to reason about them
+okay so uh recall how we Define the
+
+ align:start position:0%
+okay so uh recall how we Define the
+ 
+
+ align:start position:0%
+okay so uh recall how we Define the
+probability of an event a so an event is
+
+ align:start position:0%
+probability of an event a so an event is
+ 
+
+ align:start position:0%
+probability of an event a so an event is
+just a set of
+
+ align:start position:0%
+just a set of
+ 
+
+ align:start position:0%
+just a set of
+outcomes uh our probability function PR
+
+ align:start position:0%
+outcomes uh our probability function PR
+ 
+
+ align:start position:0%
+outcomes uh our probability function PR
+is a function from uh the set of
+
+ align:start position:0%
+is a function from uh the set of
+ 
+
+ align:start position:0%
+is a function from uh the set of
+outcomes the sample space uh to the
+
+ align:start position:0%
+outcomes the sample space uh to the
+ 
+
+ align:start position:0%
+outcomes the sample space uh to the
+interval 0 to 1 and we can can extend
+
+ align:start position:0%
+interval 0 to 1 and we can can extend
+ 
+
+ align:start position:0%
+interval 0 to 1 and we can can extend
+this naturally to events by saying that
+
+ align:start position:0%
+this naturally to events by saying that
+ 
+
+ align:start position:0%
+this naturally to events by saying that
+the probability of an event is just the
+
+ align:start position:0%
+the probability of an event is just the
+ 
+
+ align:start position:0%
+the probability of an event is just the
+sum of the probabilities of all of the
+
+ align:start position:0%
+sum of the probabilities of all of the
+ 
+
+ align:start position:0%
+sum of the probabilities of all of the
+outcomes in that event
+
+ align:start position:0%
+outcomes in that event
+ 
+
+ align:start position:0%
+outcomes in that event
+okay so an immediate consequence of this
+
+ align:start position:0%
+okay so an immediate consequence of this
+ 
+
+ align:start position:0%
+okay so an immediate consequence of this
+definition or several immediate
+
+ align:start position:0%
+definition or several immediate
+ 
+
+ align:start position:0%
+definition or several immediate
+consequences I suppose are the following
+
+ align:start position:0%
+consequences I suppose are the following
+ 
+
+ align:start position:0%
+consequences I suppose are the following
+so first we have the sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rule so if we have two events uh A and B
+
+ align:start position:0%
+rule so if we have two events uh A and B
+ 
+
+ align:start position:0%
+rule so if we have two events uh A and B
+and they're disjoint so A and B are
+
+ align:start position:0%
+and they're disjoint so A and B are
+ 
+
+ align:start position:0%
+and they're disjoint so A and B are
+disjoint of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+events this tells us that the
+
+ align:start position:0%
+events this tells us that the
+ 
+
+ align:start position:0%
+events this tells us that the
+probability of the Union of A and
+
+ align:start position:0%
+probability of the Union of A and
+ 
+
+ align:start position:0%
+probability of the Union of A and
+B is what what do we think that
+
+ align:start position:0%
+B is what what do we think that
+ 
+
+ align:start position:0%
+B is what what do we think that
+is any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideas
+
+ align:start position:0%
+ideas
+ 
+
+ align:start position:0%
+ideas
+yeah yeah the sum of the probabilities
+
+ align:start position:0%
+yeah yeah the sum of the probabilities
+ 
+
+ align:start position:0%
+yeah yeah the sum of the probabilities
+so probability of
+
+ align:start position:0%
+so probability of
+ 
+
+ align:start position:0%
+so probability of
+a plus the probability of B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so very similar to what we saw with
+
+ align:start position:0%
+okay so very similar to what we saw with
+ 
+
+ align:start position:0%
+okay so very similar to what we saw with
+sets if you have two disint sets the
+
+ align:start position:0%
+sets if you have two disint sets the
+ 
+
+ align:start position:0%
+sets if you have two disint sets the
+size of their Union is the same as as
+
+ align:start position:0%
+size of their Union is the same as as
+ 
+
+ align:start position:0%
+size of their Union is the same as as
+the uh sum of the individual sizes the
+
+ align:start position:0%
+the uh sum of the individual sizes the
+ 
+
+ align:start position:0%
+the uh sum of the individual sizes the
+same thing happens with
+
+ align:start position:0%
+same thing happens with
+ 
+
+ align:start position:0%
+same thing happens with
+probability okay uh we also have the
+
+ align:start position:0%
+probability okay uh we also have the
+ 
+
+ align:start position:0%
+probability okay uh we also have the
+complement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rule so if we have some event a what do
+
+ align:start position:0%
+rule so if we have some event a what do
+ 
+
+ align:start position:0%
+rule so if we have some event a what do
+we think the
+
+ align:start position:0%
+we think the
+ 
+
+ align:start position:0%
+we think the
+probability of the complement of a is so
+
+ align:start position:0%
+probability of the complement of a is so
+ 
+
+ align:start position:0%
+probability of the complement of a is so
+the probability that a does doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+occur oh I should
+
+ align:start position:0%
+occur oh I should
+ 
+
+ align:start position:0%
+occur oh I should
+probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah what's the probability of not
+
+ align:start position:0%
+yeah what's the probability of not
+ 
+
+ align:start position:0%
+yeah what's the probability of not
+a anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah one minus the probability of
+
+ align:start position:0%
+yeah yeah one minus the probability of
+ 
+
+ align:start position:0%
+yeah yeah one minus the probability of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+okay right because uh a and not a are
+
+ align:start position:0%
+okay right because uh a and not a are
+ 
+
+ align:start position:0%
+okay right because uh a and not a are
+disjoint and one of them must happen so
+
+ align:start position:0%
+disjoint and one of them must happen so
+ 
+
+ align:start position:0%
+disjoint and one of them must happen so
+you know with certainty uh one of a or
+
+ align:start position:0%
+you know with certainty uh one of a or
+ 
+
+ align:start position:0%
+you know with certainty uh one of a or
+not a happens so the probability of
+
+ align:start position:0%
+not a happens so the probability of
+ 
+
+ align:start position:0%
+not a happens so the probability of
+their Union is one so this kind of just
+
+ align:start position:0%
+their Union is one so this kind of just
+ 
+
+ align:start position:0%
+their Union is one so this kind of just
+follows from the sum rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what else do we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have uh the difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rule okay so in this case suppose we
+
+ align:start position:0%
+rule okay so in this case suppose we
+ 
+
+ align:start position:0%
+rule okay so in this case suppose we
+have uh again two events a and B and
+
+ align:start position:0%
+have uh again two events a and B and
+ 
+
+ align:start position:0%
+have uh again two events a and B and
+this time we'd like to look at the
+
+ align:start position:0%
+this time we'd like to look at the
+ 
+
+ align:start position:0%
+this time we'd like to look at the
+difference a set minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B what do we think that might be in
+
+ align:start position:0%
+B what do we think that might be in
+ 
+
+ align:start position:0%
+B what do we think that might be in
+terms of the probabilities of A and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly so the probability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a minus the
+
+ align:start position:0%
+a minus the
+ 
+
+ align:start position:0%
+a minus the
+probability of the
+
+ align:start position:0%
+probability of the
+ 
+
+ align:start position:0%
+probability of the
+intersection
+
+ align:start position:0%
+intersection
+ 
+
+ align:start position:0%
+intersection
+okay and why is that well a is just the
+
+ align:start position:0%
+okay and why is that well a is just the
+ 
+
+ align:start position:0%
+okay and why is that well a is just the
+disjoint Union of a minus b and a
+
+ align:start position:0%
+disjoint Union of a minus b and a
+ 
+
+ align:start position:0%
+disjoint Union of a minus b and a
+intercept B
+
+ align:start position:0%
+intercept B
+ 
+
+ align:start position:0%
+intercept B
+okay uh we also have an analog of
+
+ align:start position:0%
+okay uh we also have an analog of
+ 
+
+ align:start position:0%
+okay uh we also have an analog of
+principle of uh inclusion exclusion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the probability of
+
+ align:start position:0%
+so the probability of
+ 
+
+ align:start position:0%
+so the probability of
+uh a union B for more General A and B so
+
+ align:start position:0%
+uh a union B for more General A and B so
+ 
+
+ align:start position:0%
+uh a union B for more General A and B so
+you know they're not necessarily
+
+ align:start position:0%
+you know they're not necessarily
+ 
+
+ align:start position:0%
+you know they're not necessarily
+disjoint
+
+ align:start position:0%
+disjoint
+ 
+
+ align:start position:0%
+disjoint
+anymore just like we had with sets this
+
+ align:start position:0%
+anymore just like we had with sets this
+ 
+
+ align:start position:0%
+anymore just like we had with sets this
+is going to be the probability of
+
+ align:start position:0%
+is going to be the probability of
+ 
+
+ align:start position:0%
+is going to be the probability of
+a plus the probability of
+
+ align:start position:0%
+a plus the probability of
+ 
+
+ align:start position:0%
+a plus the probability of
+B minus the
+
+ align:start position:0%
+B minus the
+ 
+
+ align:start position:0%
+B minus the
+probability of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersection okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have a couple of um new uh rules
+
+ align:start position:0%
+and we have a couple of um new uh rules
+ 
+
+ align:start position:0%
+and we have a couple of um new uh rules
+that don't really have analoges in in
+
+ align:start position:0%
+that don't really have analoges in in
+ 
+
+ align:start position:0%
+that don't really have analoges in in
+the case of uh uh like in the case of
+
+ align:start position:0%
+the case of uh uh like in the case of
+ 
+
+ align:start position:0%
+the case of uh uh like in the case of
+counting
+
+ align:start position:0%
+counting
+ 
+
+ align:start position:0%
+counting
+sets so first we have the union
+
+ align:start position:0%
+sets so first we have the union
+ 
+
+ align:start position:0%
+sets so first we have the union
+Bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+so probability of a union B it's less
+
+ align:start position:0%
+so probability of a union B it's less
+ 
+
+ align:start position:0%
+so probability of a union B it's less
+than or equal to probability of
+
+ align:start position:0%
+than or equal to probability of
+ 
+
+ align:start position:0%
+than or equal to probability of
+a plus probability of b or I suppose I
+
+ align:start position:0%
+a plus probability of b or I suppose I
+ 
+
+ align:start position:0%
+a plus probability of b or I suppose I
+shouldn't say it doesn't really have an
+
+ align:start position:0%
+shouldn't say it doesn't really have an
+ 
+
+ align:start position:0%
+shouldn't say it doesn't really have an
+analog but we didn't really look at the
+
+ align:start position:0%
+analog but we didn't really look at the
+ 
+
+ align:start position:0%
+analog but we didn't really look at the
+analog
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and why might that be the
+
+ align:start position:0%
+okay and why might that be the
+ 
+
+ align:start position:0%
+okay and why might that be the
+case yeah oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh so uh the question is what's the
+
+ align:start position:0%
+yeah uh so uh the question is what's the
+ 
+
+ align:start position:0%
+yeah uh so uh the question is what's the
+difference between the sum Rule and Pi
+
+ align:start position:0%
+difference between the sum Rule and Pi
+ 
+
+ align:start position:0%
+difference between the sum Rule and Pi
+so so in the sum rule we assume that A
+
+ align:start position:0%
+so so in the sum rule we assume that A
+ 
+
+ align:start position:0%
+so so in the sum rule we assume that A
+and B are
+
+ align:start position:0%
+and B are
+ 
+
+ align:start position:0%
+and B are
+disjoint okay so if a and b are disjoint
+
+ align:start position:0%
+disjoint okay so if a and b are disjoint
+ 
+
+ align:start position:0%
+disjoint okay so if a and b are disjoint
+then their intersection is is empty so
+
+ align:start position:0%
+then their intersection is is empty so
+ 
+
+ align:start position:0%
+then their intersection is is empty so
+the intersection has zero probability so
+
+ align:start position:0%
+the intersection has zero probability so
+ 
+
+ align:start position:0%
+the intersection has zero probability so
+Pi is just a way to generalize uh the
+
+ align:start position:0%
+Pi is just a way to generalize uh the
+ 
+
+ align:start position:0%
+Pi is just a way to generalize uh the
+the sum rule okay to to the case where
+
+ align:start position:0%
+the sum rule okay to to the case where
+ 
+
+ align:start position:0%
+the sum rule okay to to the case where
+they're they're not necessarily disjoint
+
+ align:start position:0%
+they're they're not necessarily disjoint
+ 
+
+ align:start position:0%
+they're they're not necessarily disjoint
+anymore they may have a non-trivial
+
+ align:start position:0%
+anymore they may have a non-trivial
+ 
+
+ align:start position:0%
+anymore they may have a non-trivial
+intersection okay good question any
+
+ align:start position:0%
+intersection okay good question any
+ 
+
+ align:start position:0%
+intersection okay good question any
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions no okay so can anybody give a
+
+ align:start position:0%
+questions no okay so can anybody give a
+ 
+
+ align:start position:0%
+questions no okay so can anybody give a
+reason why the union bound might be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so the answer was the
+
+ align:start position:0%
+yeah yeah so the answer was the
+ 
+
+ align:start position:0%
+yeah yeah so the answer was the
+probability of the intersection is not
+
+ align:start position:0%
+probability of the intersection is not
+ 
+
+ align:start position:0%
+probability of the intersection is not
+negative right so uh you know if we just
+
+ align:start position:0%
+negative right so uh you know if we just
+ 
+
+ align:start position:0%
+negative right so uh you know if we just
+take PI right so this holds you know
+
+ align:start position:0%
+take PI right so this holds you know
+ 
+
+ align:start position:0%
+take PI right so this holds you know
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+equality and now if we just you know get
+
+ align:start position:0%
+equality and now if we just you know get
+ 
+
+ align:start position:0%
+equality and now if we just you know get
+rid of this negative term here we can
+
+ align:start position:0%
+rid of this negative term here we can
+ 
+
+ align:start position:0%
+rid of this negative term here we can
+only increase the uh the probability
+
+ align:start position:0%
+only increase the uh the probability
+ 
+
+ align:start position:0%
+only increase the uh the probability
+because all probabilities have to be
+
+ align:start position:0%
+because all probabilities have to be
+ 
+
+ align:start position:0%
+because all probabilities have to be
+between zero and one
+
+ align:start position:0%
+between zero and one
+ 
+
+ align:start position:0%
+between zero and one
+okay uh we also have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monotonicity again I don't think we uh
+
+ align:start position:0%
+monotonicity again I don't think we uh
+ 
+
+ align:start position:0%
+monotonicity again I don't think we uh
+you know saw an analogue of this with
+
+ align:start position:0%
+you know saw an analogue of this with
+ 
+
+ align:start position:0%
+you know saw an analogue of this with
+sets but uh you know
+
+ align:start position:0%
+sets but uh you know
+ 
+
+ align:start position:0%
+sets but uh you know
+if a is a subset of B what do you think
+
+ align:start position:0%
+if a is a subset of B what do you think
+ 
+
+ align:start position:0%
+if a is a subset of B what do you think
+that tells us about the uh probabilities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ites I'm I'm seeing some uh hand
+
+ align:start position:0%
+ites I'm I'm seeing some uh hand
+ 
+
+ align:start position:0%
+ites I'm I'm seeing some uh hand
+motions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so as you might expect from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+name if a is a subset of B then its
+
+ align:start position:0%
+name if a is a subset of B then its
+ 
+
+ align:start position:0%
+name if a is a subset of B then its
+probability should be smaller than the
+
+ align:start position:0%
+probability should be smaller than the
+ 
+
+ align:start position:0%
+probability should be smaller than the
+the probability of
+
+ align:start position:0%
+the probability of
+ 
+
+ align:start position:0%
+the probability of
+B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so do these make uh do these make
+
+ align:start position:0%
+okay so do these make uh do these make
+ 
+
+ align:start position:0%
+okay so do these make uh do these make
+sense to everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so just as we saw with uh with
+
+ align:start position:0%
+okay so just as we saw with uh with
+ 
+
+ align:start position:0%
+okay so just as we saw with uh with
+sets uh both the sum rule the union
+
+ align:start position:0%
+sets uh both the sum rule the union
+ 
+
+ align:start position:0%
+sets uh both the sum rule the union
+bound and uh principle of inclusion
+
+ align:start position:0%
+bound and uh principle of inclusion
+ 
+
+ align:start position:0%
+bound and uh principle of inclusion
+exclusion can all generalize to you know
+
+ align:start position:0%
+exclusion can all generalize to you know
+ 
+
+ align:start position:0%
+exclusion can all generalize to you know
+arbitrary numbers of of uh events uh or
+
+ align:start position:0%
+arbitrary numbers of of uh events uh or
+ 
+
+ align:start position:0%
+arbitrary numbers of of uh events uh or
+even you know countably many okay uh I
+
+ align:start position:0%
+even you know countably many okay uh I
+ 
+
+ align:start position:0%
+even you know countably many okay uh I
+suppose principle of inclusion exclusion
+
+ align:start position:0%
+suppose principle of inclusion exclusion
+ 
+
+ align:start position:0%
+suppose principle of inclusion exclusion
+you should probably only think about you
+
+ align:start position:0%
+you should probably only think about you
+ 
+
+ align:start position:0%
+you should probably only think about you
+know finite cases but the other two are
+
+ align:start position:0%
+know finite cases but the other two are
+ 
+
+ align:start position:0%
+know finite cases but the other two are
+you know they fairly naturally
+
+ align:start position:0%
+you know they fairly naturally
+ 
+
+ align:start position:0%
+you know they fairly naturally
+generalize to uh to countable sets of
+
+ align:start position:0%
+generalize to uh to countable sets of
+ 
+
+ align:start position:0%
+generalize to uh to countable sets of
+events okay so do these rules make sense
+
+ align:start position:0%
+events okay so do these rules make sense
+ 
+
+ align:start position:0%
+events okay so do these rules make sense
+to everybody he'll probably be using
+
+ align:start position:0%
+to everybody he'll probably be using
+ 
+
+ align:start position:0%
+to everybody he'll probably be using
+them quite a lot so uh you know make
+
+ align:start position:0%
+them quite a lot so uh you know make
+ 
+
+ align:start position:0%
+them quite a lot so uh you know make
+sure you're familiar with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay so in that case let us move on to
+
+ align:start position:0%
+okay so in that case let us move on to
+ 
+
+ align:start position:0%
+okay so in that case let us move on to
+the main topic of today's lecture
+
+ align:start position:0%
+the main topic of today's lecture
+ 
+
+ align:start position:0%
+the main topic of today's lecture
+conditional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability okay so if you recall on
+
+ align:start position:0%
+probability okay so if you recall on
+ 
+
+ align:start position:0%
+probability okay so if you recall on
+Tuesday when we were talking about the
+
+ align:start position:0%
+Tuesday when we were talking about the
+ 
+
+ align:start position:0%
+Tuesday when we were talking about the
+Monty Hall problem when we were drawing
+
+ align:start position:0%
+Monty Hall problem when we were drawing
+ 
+
+ align:start position:0%
+Monty Hall problem when we were drawing
+a tree diagram right um we were making
+
+ align:start position:0%
+a tree diagram right um we were making
+ 
+
+ align:start position:0%
+a tree diagram right um we were making
+statements such as you know if the car
+
+ align:start position:0%
+statements such as you know if the car
+ 
+
+ align:start position:0%
+statements such as you know if the car
+is behind door one what's the
+
+ align:start position:0%
+is behind door one what's the
+ 
+
+ align:start position:0%
+is behind door one what's the
+probability that we picked door two or I
+
+ align:start position:0%
+probability that we picked door two or I
+ 
+
+ align:start position:0%
+probability that we picked door two or I
+guess it was you purple gold and green
+
+ align:start position:0%
+guess it was you purple gold and green
+ 
+
+ align:start position:0%
+guess it was you purple gold and green
+uh purple gold silver silver
+
+ align:start position:0%
+uh purple gold silver silver
+ 
+
+ align:start position:0%
+uh purple gold silver silver
+yeah uh so how do we express this
+
+ align:start position:0%
+yeah uh so how do we express this
+ 
+
+ align:start position:0%
+yeah uh so how do we express this
+mathematically uh so that's where
+
+ align:start position:0%
+mathematically uh so that's where
+ 
+
+ align:start position:0%
+mathematically uh so that's where
+conditional probability comes
+
+ align:start position:0%
+conditional probability comes
+ 
+
+ align:start position:0%
+conditional probability comes
+in we're going to make use of the
+
+ align:start position:0%
+in we're going to make use of the
+ 
+
+ align:start position:0%
+in we're going to make use of the
+following definition okay so if we have
+
+ align:start position:0%
+following definition okay so if we have
+ 
+
+ align:start position:0%
+following definition okay so if we have
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+events A and
+
+ align:start position:0%
+events A and
+ 
+
+ align:start position:0%
+events A and
+B uh we Define the conditional
+
+ align:start position:0%
+B uh we Define the conditional
+ 
+
+ align:start position:0%
+B uh we Define the conditional
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+okay uh which we denote as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following so we' say uh you know a
+
+ align:start position:0%
+following so we' say uh you know a
+ 
+
+ align:start position:0%
+following so we' say uh you know a
+conditioned on B right we denote that
+
+ align:start position:0%
+conditioned on B right we denote that
+ 
+
+ align:start position:0%
+conditioned on B right we denote that
+with a vertical
+
+ align:start position:0%
+with a vertical
+ 
+
+ align:start position:0%
+with a vertical
+bar we Define this to be
+
+ align:start position:0%
+bar we Define this to be
+ 
+
+ align:start position:0%
+bar we Define this to be
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+probability of a intersect
+
+ align:start position:0%
+probability of a intersect
+ 
+
+ align:start position:0%
+probability of a intersect
+B divided by the probability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so intuitively you can kind of
+
+ align:start position:0%
+okay so intuitively you can kind of
+ 
+
+ align:start position:0%
+okay so intuitively you can kind of
+think of it a little bit as uh you know
+
+ align:start position:0%
+think of it a little bit as uh you know
+ 
+
+ align:start position:0%
+think of it a little bit as uh you know
+we're trying to scale our probability
+
+ align:start position:0%
+we're trying to scale our probability
+ 
+
+ align:start position:0%
+we're trying to scale our probability
+space so that you know B becomes our
+
+ align:start position:0%
+space so that you know B becomes our
+ 
+
+ align:start position:0%
+space so that you know B becomes our
+entire entire sample space okay so we
+
+ align:start position:0%
+entire entire sample space okay so we
+ 
+
+ align:start position:0%
+entire entire sample space okay so we
+kind of want to divide out this this
+
+ align:start position:0%
+kind of want to divide out this this
+ 
+
+ align:start position:0%
+kind of want to divide out this this
+probability of B uh so that you know we
+
+ align:start position:0%
+probability of B uh so that you know we
+ 
+
+ align:start position:0%
+probability of B uh so that you know we
+still get a a probability space all of
+
+ align:start position:0%
+still get a a probability space all of
+ 
+
+ align:start position:0%
+still get a a probability space all of
+the probabilities sum to one okay does
+
+ align:start position:0%
+the probabilities sum to one okay does
+ 
+
+ align:start position:0%
+the probabilities sum to one okay does
+that kind of make sense to
+
+ align:start position:0%
+that kind of make sense to
+ 
+
+ align:start position:0%
+that kind of make sense to
+everybody and then you know the analog
+
+ align:start position:0%
+everybody and then you know the analog
+ 
+
+ align:start position:0%
+everybody and then you know the analog
+of a right we're you know only looking
+
+ align:start position:0%
+of a right we're you know only looking
+ 
+
+ align:start position:0%
+of a right we're you know only looking
+at everything that that's already within
+
+ align:start position:0%
+at everything that that's already within
+ 
+
+ align:start position:0%
+at everything that that's already within
+B so we're looking at the intersection
+
+ align:start position:0%
+B so we're looking at the intersection
+ 
+
+ align:start position:0%
+B so we're looking at the intersection
+of A and
+
+ align:start position:0%
+of A and
+ 
+
+ align:start position:0%
+of A and
+B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now if we rewrite this we can get a
+
+ align:start position:0%
+okay now if we rewrite this we can get a
+ 
+
+ align:start position:0%
+okay now if we rewrite this we can get a
+product rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so if we want to know the
+
+ align:start position:0%
+right so if we want to know the
+ 
+
+ align:start position:0%
+right so if we want to know the
+probability of a intercept B we can kind
+
+ align:start position:0%
+probability of a intercept B we can kind
+ 
+
+ align:start position:0%
+probability of a intercept B we can kind
+of just move this probability of B over
+
+ align:start position:0%
+of just move this probability of B over
+ 
+
+ align:start position:0%
+of just move this probability of B over
+to the other
+
+ align:start position:0%
+to the other
+ 
+
+ align:start position:0%
+to the other
+side and we end up with probability of a
+
+ align:start position:0%
+side and we end up with probability of a
+ 
+
+ align:start position:0%
+side and we end up with probability of a
+intersect
+
+ align:start position:0%
+intersect
+ 
+
+ align:start position:0%
+intersect
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+equals probability of a given
+
+ align:start position:0%
+equals probability of a given
+ 
+
+ align:start position:0%
+equals probability of a given
+B times the
+
+ align:start position:0%
+B times the
+ 
+
+ align:start position:0%
+B times the
+probability of B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and as you might expect you can
+
+ align:start position:0%
+okay and as you might expect you can
+ 
+
+ align:start position:0%
+okay and as you might expect you can
+extend this to multiple
+
+ align:start position:0%
+extend this to multiple
+ 
+
+ align:start position:0%
+extend this to multiple
+events or I guess this is already kind
+
+ align:start position:0%
+events or I guess this is already kind
+ 
+
+ align:start position:0%
+events or I guess this is already kind
+of multiple events you can extend it to
+
+ align:start position:0%
+of multiple events you can extend it to
+ 
+
+ align:start position:0%
+of multiple events you can extend it to
+more than two
+
+ align:start position:0%
+more than two
+ 
+
+ align:start position:0%
+more than two
+events so you can also have
+
+ align:start position:0%
+events so you can also have
+ 
+
+ align:start position:0%
+events so you can also have
+EG the probability of a intercept B
+
+ align:start position:0%
+EG the probability of a intercept B
+ 
+
+ align:start position:0%
+EG the probability of a intercept B
+intercept
+
+ align:start position:0%
+intercept
+ 
+
+ align:start position:0%
+intercept
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+probability of a given being
+
+ align:start position:0%
+probability of a given being
+ 
+
+ align:start position:0%
+probability of a given being
+T times the
+
+ align:start position:0%
+T times the
+ 
+
+ align:start position:0%
+T times the
+probability of B uh or maybe I should
+
+ align:start position:0%
+probability of B uh or maybe I should
+ 
+
+ align:start position:0%
+probability of B uh or maybe I should
+write this out more
+
+ align:start position:0%
+write this out more
+ 
+
+ align:start position:0%
+write this out more
+explicitly B intercept C okay and then
+
+ align:start position:0%
+explicitly B intercept C okay and then
+ 
+
+ align:start position:0%
+explicitly B intercept C okay and then
+if we apply our uh apply our binary
+
+ align:start position:0%
+if we apply our uh apply our binary
+ 
+
+ align:start position:0%
+if we apply our uh apply our binary
+product rule again we can kind of expand
+
+ align:start position:0%
+product rule again we can kind of expand
+ 
+
+ align:start position:0%
+product rule again we can kind of expand
+out that uh this
+
+ align:start position:0%
+out that uh this
+ 
+
+ align:start position:0%
+out that uh this
+term as the probability of a given B and
+
+ align:start position:0%
+term as the probability of a given B and
+ 
+
+ align:start position:0%
+term as the probability of a given B and
+C probability of
+
+ align:start position:0%
+C probability of
+ 
+
+ align:start position:0%
+C probability of
+B given
+
+ align:start position:0%
+B given
+ 
+
+ align:start position:0%
+B given
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+probability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+okay so that's basically what we were
+
+ align:start position:0%
+okay so that's basically what we were
+ 
+
+ align:start position:0%
+okay so that's basically what we were
+doing on Tuesday you know written out
+
+ align:start position:0%
+doing on Tuesday you know written out
+ 
+
+ align:start position:0%
+doing on Tuesday you know written out
+more formally right so
+
+ align:start position:0%
+more formally right so
+ 
+
+ align:start position:0%
+more formally right so
+uh like probability of C corresponds to
+
+ align:start position:0%
+uh like probability of C corresponds to
+ 
+
+ align:start position:0%
+uh like probability of C corresponds to
+you know what is the first Edge we chose
+
+ align:start position:0%
+you know what is the first Edge we chose
+ 
+
+ align:start position:0%
+you know what is the first Edge we chose
+you know the the first Edge going away
+
+ align:start position:0%
+you know the the first Edge going away
+ 
+
+ align:start position:0%
+you know the the first Edge going away
+from the root okay and then conditioned
+
+ align:start position:0%
+from the root okay and then conditioned
+ 
+
+ align:start position:0%
+from the root okay and then conditioned
+on reaching a particular vertex like
+
+ align:start position:0%
+on reaching a particular vertex like
+ 
+
+ align:start position:0%
+on reaching a particular vertex like
+conditioned on you know Monty hiding the
+
+ align:start position:0%
+conditioned on you know Monty hiding the
+ 
+
+ align:start position:0%
+conditioned on you know Monty hiding the
+prize in the gold
+
+ align:start position:0%
+prize in the gold
+ 
+
+ align:start position:0%
+prize in the gold
+box you know what's the probability that
+
+ align:start position:0%
+box you know what's the probability that
+ 
+
+ align:start position:0%
+box you know what's the probability that
+Marilyn chooses the silver one okay so
+
+ align:start position:0%
+Marilyn chooses the silver one okay so
+ 
+
+ align:start position:0%
+Marilyn chooses the silver one okay so
+that's the conditional probability of
+
+ align:start position:0%
+that's the conditional probability of
+ 
+
+ align:start position:0%
+that's the conditional probability of
+choosing the Silver Box conditioned on
+
+ align:start position:0%
+choosing the Silver Box conditioned on
+ 
+
+ align:start position:0%
+choosing the Silver Box conditioned on
+the the prize being in the gold box okay
+
+ align:start position:0%
+the the prize being in the gold box okay
+ 
+
+ align:start position:0%
+the the prize being in the gold box okay
+and then you know as you continue along
+
+ align:start position:0%
+and then you know as you continue along
+ 
+
+ align:start position:0%
+and then you know as you continue along
+the uh uh along the path to a
+
+ align:start position:0%
+the uh uh along the path to a
+ 
+
+ align:start position:0%
+the uh uh along the path to a
+leaf uh all of the edge probabilities
+
+ align:start position:0%
+leaf uh all of the edge probabilities
+ 
+
+ align:start position:0%
+leaf uh all of the edge probabilities
+that you're looking at are secret like
+
+ align:start position:0%
+that you're looking at are secret like
+ 
+
+ align:start position:0%
+that you're looking at are secret like
+they were secretly just you know basic
+
+ align:start position:0%
+they were secretly just you know basic
+ 
+
+ align:start position:0%
+they were secretly just you know basic
+additional probabilities okay does that
+
+ align:start position:0%
+additional probabilities okay does that
+ 
+
+ align:start position:0%
+additional probabilities okay does that
+make sense to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay so another extension of this that
+
+ align:start position:0%
+okay so another extension of this that
+ 
+
+ align:start position:0%
+okay so another extension of this that
+you may find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useful is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following a intersect B
+
+ align:start position:0%
+following a intersect B
+ 
+
+ align:start position:0%
+following a intersect B
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+C is going to
+
+ align:start position:0%
+C is going to
+ 
+
+ align:start position:0%
+C is going to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+probability of a given B intercept
+
+ align:start position:0%
+probability of a given B intercept
+ 
+
+ align:start position:0%
+probability of a given B intercept
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+probability of B given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+okay so can anybody see why that might
+
+ align:start position:0%
+okay so can anybody see why that might
+ 
+
+ align:start position:0%
+okay so can anybody see why that might
+be the case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well first maybe we should look at you
+
+ align:start position:0%
+well first maybe we should look at you
+ 
+
+ align:start position:0%
+well first maybe we should look at you
+know what exactly is it saying okay so
+
+ align:start position:0%
+know what exactly is it saying okay so
+ 
+
+ align:start position:0%
+know what exactly is it saying okay so
+if you kind
+
+ align:start position:0%
+if you kind
+ 
+
+ align:start position:0%
+if you kind
+of squint a little bit and get rid of
+
+ align:start position:0%
+of squint a little bit and get rid of
+ 
+
+ align:start position:0%
+of squint a little bit and get rid of
+the C's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right it kind of looks a little
+
+ align:start position:0%
+right it kind of looks a little
+ 
+
+ align:start position:0%
+right it kind of looks a little
+bit like the product rule right a
+
+ align:start position:0%
+bit like the product rule right a
+ 
+
+ align:start position:0%
+bit like the product rule right a
+intercept B is
+
+ align:start position:0%
+intercept B is
+ 
+
+ align:start position:0%
+intercept B is
+probability a given
+
+ align:start position:0%
+probability a given
+ 
+
+ align:start position:0%
+probability a given
+B times probability of B
+
+ align:start position:0%
+B times probability of B
+ 
+
+ align:start position:0%
+B times probability of B
+okay it it looks kind of like that right
+
+ align:start position:0%
+okay it it looks kind of like that right
+ 
+
+ align:start position:0%
+okay it it looks kind of like that right
+but we've added a bunch of C's
+
+ align:start position:0%
+but we've added a bunch of C's
+ 
+
+ align:start position:0%
+but we've added a bunch of C's
+everywhere so basically what we're
+
+ align:start position:0%
+everywhere so basically what we're
+ 
+
+ align:start position:0%
+everywhere so basically what we're
+saying here is this is the product rule
+
+ align:start position:0%
+saying here is this is the product rule
+ 
+
+ align:start position:0%
+saying here is this is the product rule
+in the probability space where we're you
+
+ align:start position:0%
+in the probability space where we're you
+ 
+
+ align:start position:0%
+in the probability space where we're you
+know assuming C like it's it's the
+
+ align:start position:0%
+know assuming C like it's it's the
+ 
+
+ align:start position:0%
+know assuming C like it's it's the
+product rule conditioned on
+
+ align:start position:0%
+product rule conditioned on
+ 
+
+ align:start position:0%
+product rule conditioned on
+C okay does that make sense to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody and we can you know obtain it
+
+ align:start position:0%
+everybody and we can you know obtain it
+ 
+
+ align:start position:0%
+everybody and we can you know obtain it
+from the from the previous line just by
+
+ align:start position:0%
+from the from the previous line just by
+ 
+
+ align:start position:0%
+from the from the previous line just by
+dividing out by the probability of C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay do people have questions are we
+
+ align:start position:0%
+okay do people have questions are we
+ 
+
+ align:start position:0%
+okay do people have questions are we
+happy to move on to some examples yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry uh okay so the question was are we
+
+ align:start position:0%
+sorry uh okay so the question was are we
+ 
+
+ align:start position:0%
+sorry uh okay so the question was are we
+talking about sets or events uh yes uh
+
+ align:start position:0%
+talking about sets or events uh yes uh
+ 
+
+ align:start position:0%
+talking about sets or events uh yes uh
+so remember that uh events are defined
+
+ align:start position:0%
+so remember that uh events are defined
+ 
+
+ align:start position:0%
+so remember that uh events are defined
+to be sets of outcomes right so uh you
+
+ align:start position:0%
+to be sets of outcomes right so uh you
+ 
+
+ align:start position:0%
+to be sets of outcomes right so uh you
+know we're talking about events but you
+
+ align:start position:0%
+know we're talking about events but you
+ 
+
+ align:start position:0%
+know we're talking about events but you
+know events are sets and we can treat
+
+ align:start position:0%
+know events are sets and we can treat
+ 
+
+ align:start position:0%
+know events are sets and we can treat
+them as such so that's why we're using
+
+ align:start position:0%
+them as such so that's why we're using
+ 
+
+ align:start position:0%
+them as such so that's why we're using
+uh lots of notation here that you would
+
+ align:start position:0%
+uh lots of notation here that you would
+ 
+
+ align:start position:0%
+uh lots of notation here that you would
+typically associate with sets like Union
+
+ align:start position:0%
+typically associate with sets like Union
+ 
+
+ align:start position:0%
+typically associate with sets like Union
+intersection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Etc okay any other questions oh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah uh so these are not nodes in the tree
+
+ align:start position:0%
+ah uh so these are not nodes in the tree
+ 
+
+ align:start position:0%
+ah uh so these are not nodes in the tree
+um some of uh sorry question was if we
+
+ align:start position:0%
+um some of uh sorry question was if we
+ 
+
+ align:start position:0%
+um some of uh sorry question was if we
+have an event that's like a union B
+
+ align:start position:0%
+have an event that's like a union B
+ 
+
+ align:start position:0%
+have an event that's like a union B
+Union C or something uh are these
+
+ align:start position:0%
+Union C or something uh are these
+ 
+
+ align:start position:0%
+Union C or something uh are these
+General sets or are they nodes in in the
+
+ align:start position:0%
+General sets or are they nodes in in the
+ 
+
+ align:start position:0%
+General sets or are they nodes in in the
+tree um that is a good observation some
+
+ align:start position:0%
+tree um that is a good observation some
+ 
+
+ align:start position:0%
+tree um that is a good observation some
+of the nodes in the tree kind of
+
+ align:start position:0%
+of the nodes in the tree kind of
+ 
+
+ align:start position:0%
+of the nodes in the tree kind of
+naturally correspond to events right
+
+ align:start position:0%
+naturally correspond to events right
+ 
+
+ align:start position:0%
+naturally correspond to events right
+like uh you know if we draw out our tree
+
+ align:start position:0%
+like uh you know if we draw out our tree
+ 
+
+ align:start position:0%
+like uh you know if we draw out our tree
+diagram this node here fairly naturally
+
+ align:start position:0%
+diagram this node here fairly naturally
+ 
+
+ align:start position:0%
+diagram this node here fairly naturally
+corresponds to this set of events like
+
+ align:start position:0%
+corresponds to this set of events like
+ 
+
+ align:start position:0%
+corresponds to this set of events like
+or sorry this set of outcomes those
+
+ align:start position:0%
+or sorry this set of outcomes those
+ 
+
+ align:start position:0%
+or sorry this set of outcomes those
+those two uh leaves in its sub tree uh
+
+ align:start position:0%
+those two uh leaves in its sub tree uh
+ 
+
+ align:start position:0%
+those two uh leaves in its sub tree uh
+but not every event necessarily
+
+ align:start position:0%
+but not every event necessarily
+ 
+
+ align:start position:0%
+but not every event necessarily
+corresponds to an internal node of the
+
+ align:start position:0%
+corresponds to an internal node of the
+ 
+
+ align:start position:0%
+corresponds to an internal node of the
+tree like that like for instance you
+
+ align:start position:0%
+tree like that like for instance you
+ 
+
+ align:start position:0%
+tree like that like for instance you
+could
+
+ align:start position:0%
+could
+ 
+
+ align:start position:0%
+could
+have these two uh outcomes
+
+ align:start position:0%
+have these two uh outcomes
+ 
+
+ align:start position:0%
+have these two uh outcomes
+right uh if you you know consider the
+
+ align:start position:0%
+right uh if you you know consider the
+ 
+
+ align:start position:0%
+right uh if you you know consider the
+set of those two outcomes that's still a
+
+ align:start position:0%
+set of those two outcomes that's still a
+ 
+
+ align:start position:0%
+set of those two outcomes that's still a
+valid event but it doesn't really
+
+ align:start position:0%
+valid event but it doesn't really
+ 
+
+ align:start position:0%
+valid event but it doesn't really
+naturally correspond to a a a tree Noe
+
+ align:start position:0%
+naturally correspond to a a a tree Noe
+ 
+
+ align:start position:0%
+naturally correspond to a a a tree Noe
+in the same way
+
+ align:start position:0%
+in the same way
+ 
+
+ align:start position:0%
+in the same way
+does that make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense oh that that is quite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible okay um so asking about the
+
+ align:start position:0%
+possible okay um so asking about the
+ 
+
+ align:start position:0%
+possible okay um so asking about the
+conditional probabilities as they appear
+
+ align:start position:0%
+conditional probabilities as they appear
+ 
+
+ align:start position:0%
+conditional probabilities as they appear
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+tree uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes oh I see okay uh so I guess the the
+
+ align:start position:0%
+yes oh I see okay uh so I guess the the
+ 
+
+ align:start position:0%
+yes oh I see okay uh so I guess the the
+way that I like to think about uh a
+
+ align:start position:0%
+way that I like to think about uh a
+ 
+
+ align:start position:0%
+way that I like to think about uh a
+given B um it is an event in a different
+
+ align:start position:0%
+given B um it is an event in a different
+ 
+
+ align:start position:0%
+given B um it is an event in a different
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+space so you can kind of think of uh you
+
+ align:start position:0%
+space so you can kind of think of uh you
+ 
+
+ align:start position:0%
+space so you can kind of think of uh you
+know if you limit uh the scope rather
+
+ align:start position:0%
+know if you limit uh the scope rather
+ 
+
+ align:start position:0%
+know if you limit uh the scope rather
+rather than you know talking about your
+
+ align:start position:0%
+rather than you know talking about your
+ 
+
+ align:start position:0%
+rather than you know talking about your
+entire sample space s if you limit the
+
+ align:start position:0%
+entire sample space s if you limit the
+ 
+
+ align:start position:0%
+entire sample space s if you limit the
+the scope to just C so you like scale
+
+ align:start position:0%
+the scope to just C so you like scale
+ 
+
+ align:start position:0%
+the scope to just C so you like scale
+all of the probabilities down by by the
+
+ align:start position:0%
+all of the probabilities down by by the
+ 
+
+ align:start position:0%
+all of the probabilities down by by the
+probability of C you you end up with a
+
+ align:start position:0%
+probability of C you you end up with a
+ 
+
+ align:start position:0%
+probability of C you you end up with a
+different probability space so now the
+
+ align:start position:0%
+different probability space so now the
+ 
+
+ align:start position:0%
+different probability space so now the
+probability of or sorry the event you
+
+ align:start position:0%
+probability of or sorry the event you
+ 
+
+ align:start position:0%
+probability of or sorry the event you
+know be given C is an event in that
+
+ align:start position:0%
+know be given C is an event in that
+ 
+
+ align:start position:0%
+know be given C is an event in that
+probability space does that make
+
+ align:start position:0%
+probability space does that make
+ 
+
+ align:start position:0%
+probability space does that make
+sense okay yeah
+
+ align:start position:0%
+sense okay yeah
+ 
+
+ align:start position:0%
+sense okay yeah
+sorry thank you for the clarification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so why don't we move on to some
+
+ align:start position:0%
+okay so why don't we move on to some
+ 
+
+ align:start position:0%
+okay so why don't we move on to some
+examples then if uh if this makes you
+
+ align:start position:0%
+examples then if uh if this makes you
+ 
+
+ align:start position:0%
+examples then if uh if this makes you
+know reasonable amount of sense
+
+ align:start position:0%
+know reasonable amount of sense
+ 
+
+ align:start position:0%
+know reasonable amount of sense
+hopefully it'll make more sense after
+
+ align:start position:0%
+hopefully it'll make more sense after
+ 
+
+ align:start position:0%
+hopefully it'll make more sense after
+examples okay so uh you know suppose Ash
+
+ align:start position:0%
+examples okay so uh you know suppose Ash
+ 
+
+ align:start position:0%
+examples okay so uh you know suppose Ash
+and Gary are having a bunch of Pokemon
+
+ align:start position:0%
+and Gary are having a bunch of Pokemon
+ 
+
+ align:start position:0%
+and Gary are having a bunch of Pokemon
+battles against each other and you know
+
+ align:start position:0%
+battles against each other and you know
+ 
+
+ align:start position:0%
+battles against each other and you know
+they're doing like a tournament the the
+
+ align:start position:0%
+they're doing like a tournament the the
+ 
+
+ align:start position:0%
+they're doing like a tournament the the
+first to win two battles uh wins the uh
+
+ align:start position:0%
+first to win two battles uh wins the uh
+ 
+
+ align:start position:0%
+first to win two battles uh wins the uh
+the or I guess the series the first to
+
+ align:start position:0%
+the or I guess the series the first to
+ 
+
+ align:start position:0%
+the or I guess the series the first to
+win two battles wins the series okay and
+
+ align:start position:0%
+win two battles wins the series okay and
+ 
+
+ align:start position:0%
+win two battles wins the series okay and
+uh you know the the probability is of
+
+ align:start position:0%
+uh you know the the probability is of
+ 
+
+ align:start position:0%
+uh you know the the probability is of
+Victor are not you know entirely uniform
+
+ align:start position:0%
+Victor are not you know entirely uniform
+ 
+
+ align:start position:0%
+Victor are not you know entirely uniform
+so for the first match you know maybe
+
+ align:start position:0%
+so for the first match you know maybe
+ 
+
+ align:start position:0%
+so for the first match you know maybe
+it's a toss up okay Ash wins with
+
+ align:start position:0%
+it's a toss up okay Ash wins with
+ 
+
+ align:start position:0%
+it's a toss up okay Ash wins with
+probability one2 Gary wins with
+
+ align:start position:0%
+probability one2 Gary wins with
+ 
+
+ align:start position:0%
+probability one2 Gary wins with
+probability one half okay uh but after
+
+ align:start position:0%
+probability one half okay uh but after
+ 
+
+ align:start position:0%
+probability one half okay uh but after
+the first battle there's kind of an
+
+ align:start position:0%
+the first battle there's kind of an
+ 
+
+ align:start position:0%
+the first battle there's kind of an
+advantage to whoever won the last battle
+
+ align:start position:0%
+advantage to whoever won the last battle
+ 
+
+ align:start position:0%
+advantage to whoever won the last battle
+like you know their their their morale
+
+ align:start position:0%
+like you know their their their morale
+ 
+
+ align:start position:0%
+like you know their their their morale
+is high or something they they do better
+
+ align:start position:0%
+is high or something they they do better
+ 
+
+ align:start position:0%
+is high or something they they do better
+so they now have probability of 2/3 uh
+
+ align:start position:0%
+so they now have probability of 2/3 uh
+ 
+
+ align:start position:0%
+so they now have probability of 2/3 uh
+of winning the next battle
+
+ align:start position:0%
+of winning the next battle
+ 
+
+ align:start position:0%
+of winning the next battle
+okay and there aren't there aren't any
+
+ align:start position:0%
+okay and there aren't there aren't any
+ 
+
+ align:start position:0%
+okay and there aren't there aren't any
+draws uh they're bitter Rivals they will
+
+ align:start position:0%
+draws uh they're bitter Rivals they will
+ 
+
+ align:start position:0%
+draws uh they're bitter Rivals they will
+fight to the death
+
+ align:start position:0%
+fight to the death
+ 
+
+ align:start position:0%
+fight to the death
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so let's define a couple of events
+
+ align:start position:0%
+okay so let's define a couple of events
+ 
+
+ align:start position:0%
+okay so let's define a couple of events
+we'll say that a is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+event Ash
+
+ align:start position:0%
+event Ash
+ 
+
+ align:start position:0%
+event Ash
+wins oops the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+series and
+
+ align:start position:0%
+series and
+ 
+
+ align:start position:0%
+series and
+B is the event uh Ash wins
+
+ align:start position:0%
+B is the event uh Ash wins
+ 
+
+ align:start position:0%
+B is the event uh Ash wins
+the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+battal
+
+ align:start position:0%
+battal
+ 
+
+ align:start position:0%
+battal
+okay so now we can ask for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability of a given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+okay so does does the problem setup make
+
+ align:start position:0%
+okay so does does the problem setup make
+ 
+
+ align:start position:0%
+okay so does does the problem setup make
+sense yeah okay so how could we compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this any ideas where do we want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start should we just throw some numbers
+
+ align:start position:0%
+start should we just throw some numbers
+ 
+
+ align:start position:0%
+start should we just throw some numbers
+out there oh
+
+ align:start position:0%
+out there oh
+ 
+
+ align:start position:0%
+out there oh
+yeah yeah let's draw a tree diagram nice
+
+ align:start position:0%
+yeah yeah let's draw a tree diagram nice
+ 
+
+ align:start position:0%
+yeah yeah let's draw a tree diagram nice
+one okay
+
+ align:start position:0%
+one okay
+ 
+
+ align:start position:0%
+one okay
+so drawing a tree diagram what's the
+
+ align:start position:0%
+so drawing a tree diagram what's the
+ 
+
+ align:start position:0%
+so drawing a tree diagram what's the
+first you know random thing that happens
+
+ align:start position:0%
+first you know random thing that happens
+ 
+
+ align:start position:0%
+first you know random thing that happens
+what's the what's the first source of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Randomness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so F could win or lose the
+
+ align:start position:0%
+yeah yeah so F could win or lose the
+ 
+
+ align:start position:0%
+yeah yeah so F could win or lose the
+first battle so we can actually label
+
+ align:start position:0%
+first battle so we can actually label
+ 
+
+ align:start position:0%
+first battle so we can actually label
+these as
+
+ align:start position:0%
+these as
+ 
+
+ align:start position:0%
+these as
+B and not B
+
+ align:start position:0%
+B and not B
+ 
+
+ align:start position:0%
+B and not B
+okay what's the next random thing that
+
+ align:start position:0%
+okay what's the next random thing that
+ 
+
+ align:start position:0%
+okay what's the next random thing that
+could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah that's right so actually maybe
+
+ align:start position:0%
+yeah yeah that's right so actually maybe
+ 
+
+ align:start position:0%
+yeah yeah that's right so actually maybe
+it's better to call these just W and L
+
+ align:start position:0%
+it's better to call these just W and L
+ 
+
+ align:start position:0%
+it's better to call these just W and L
+so we can use the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everywhere so win lose win lose
+
+ align:start position:0%
+everywhere so win lose win lose
+ 
+
+ align:start position:0%
+everywhere so win lose win lose
+regardless of uh whether he wins or
+
+ align:start position:0%
+regardless of uh whether he wins or
+ 
+
+ align:start position:0%
+regardless of uh whether he wins or
+loses the first battle you can still
+
+ align:start position:0%
+loses the first battle you can still
+ 
+
+ align:start position:0%
+loses the first battle you can still
+either win or lose the second one Okay
+
+ align:start position:0%
+either win or lose the second one Okay
+ 
+
+ align:start position:0%
+either win or lose the second one Okay
+now what's the third layer going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+exactly yeah exactly okay so if he's one
+
+ align:start position:0%
+exactly yeah exactly okay so if he's one
+ 
+
+ align:start position:0%
+exactly yeah exactly okay so if he's one
+two or lost two those are just leaves
+
+ align:start position:0%
+two or lost two those are just leaves
+ 
+
+ align:start position:0%
+two or lost two those are just leaves
+now we don't do anything more the series
+
+ align:start position:0%
+now we don't do anything more the series
+ 
+
+ align:start position:0%
+now we don't do anything more the series
+is over okay but if he's won one and
+
+ align:start position:0%
+is over okay but if he's won one and
+ 
+
+ align:start position:0%
+is over okay but if he's won one and
+lost one in either order we can now
+
+ align:start position:0%
+lost one in either order we can now
+ 
+
+ align:start position:0%
+lost one in either order we can now
+split
+
+ align:start position:0%
+split
+ 
+
+ align:start position:0%
+split
+again oops that's a little bit long but
+
+ align:start position:0%
+again oops that's a little bit long but
+ 
+
+ align:start position:0%
+again oops that's a little bit long but
+oh well WL
+
+ align:start position:0%
+oh well WL
+ 
+
+ align:start position:0%
+oh well WL
+WL
+
+ align:start position:0%
+WL
+ 
+
+ align:start position:0%
+WL
+okay so now what are our outcomes again
+
+ align:start position:0%
+okay so now what are our outcomes again
+ 
+
+ align:start position:0%
+okay so now what are our outcomes again
+let's look at the uh uh paths from from
+
+ align:start position:0%
+let's look at the uh uh paths from from
+ 
+
+ align:start position:0%
+let's look at the uh uh paths from from
+root to leaves and just you know label
+
+ align:start position:0%
+root to leaves and just you know label
+ 
+
+ align:start position:0%
+root to leaves and just you know label
+with a uh a string of edge labels so
+
+ align:start position:0%
+with a uh a string of edge labels so
+ 
+
+ align:start position:0%
+with a uh a string of edge labels so
+this is going to be W comma w w l
+
+ align:start position:0%
+this is going to be W comma w w l
+ 
+
+ align:start position:0%
+this is going to be W comma w w l
+w w l
+
+ align:start position:0%
+w w l
+ 
+
+ align:start position:0%
+w w l
+l l w w l w l and l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+okay now what are the probabilities on
+
+ align:start position:0%
+okay now what are the probabilities on
+ 
+
+ align:start position:0%
+okay now what are the probabilities on
+each of the edges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the first layer what's the
+
+ align:start position:0%
+so in the first layer what's the
+ 
+
+ align:start position:0%
+so in the first layer what's the
+probability that Ash wins the first
+
+ align:start position:0%
+probability that Ash wins the first
+ 
+
+ align:start position:0%
+probability that Ash wins the first
+game first match
+
+ align:start position:0%
+game first match
+ 
+
+ align:start position:0%
+game first match
+yeah2 so each of these say probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one2 okay now the second layer we said
+
+ align:start position:0%
+one2 okay now the second layer we said
+ 
+
+ align:start position:0%
+one2 okay now the second layer we said
+are now conditional probabilities so
+
+ align:start position:0%
+are now conditional probabilities so
+ 
+
+ align:start position:0%
+are now conditional probabilities so
+conditioned on winning the first match
+
+ align:start position:0%
+conditioned on winning the first match
+ 
+
+ align:start position:0%
+conditioned on winning the first match
+what's the probability of winning the
+
+ align:start position:0%
+what's the probability of winning the
+ 
+
+ align:start position:0%
+what's the probability of winning the
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+match what's the probability on this
+
+ align:start position:0%
+match what's the probability on this
+ 
+
+ align:start position:0%
+match what's the probability on this
+edge here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do we
+
+ align:start position:0%
+do we
+ 
+
+ align:start position:0%
+do we
+remember 2/3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and so the other branch is going to
+
+ align:start position:0%
+yeah and so the other branch is going to
+ 
+
+ align:start position:0%
+yeah and so the other branch is going to
+be the complement of that so
+
+ align:start position:0%
+be the complement of that so
+ 
+
+ align:start position:0%
+be the complement of that so
+1/3 okay and then for the bottom Branch
+
+ align:start position:0%
+1/3 okay and then for the bottom Branch
+ 
+
+ align:start position:0%
+1/3 okay and then for the bottom Branch
+it's going to be exactly the opposite
+
+ align:start position:0%
+it's going to be exactly the opposite
+ 
+
+ align:start position:0%
+it's going to be exactly the opposite
+okay it's going to be one3 chance of
+
+ align:start position:0%
+okay it's going to be one3 chance of
+ 
+
+ align:start position:0%
+okay it's going to be one3 chance of
+winning 2/3 chance of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+losing okay
+
+ align:start position:0%
+losing okay
+ 
+
+ align:start position:0%
+losing okay
+now conditioned on winning the first
+
+ align:start position:0%
+now conditioned on winning the first
+ 
+
+ align:start position:0%
+now conditioned on winning the first
+match and losing the second match what's
+
+ align:start position:0%
+match and losing the second match what's
+ 
+
+ align:start position:0%
+match and losing the second match what's
+the probability of winning the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+third
+
+ align:start position:0%
+third
+ 
+
+ align:start position:0%
+third
+yeah one3
+
+ align:start position:0%
+yeah one3
+ 
+
+ align:start position:0%
+yeah one3
+yeah so 1/3 win 2/3 loss and uh this
+
+ align:start position:0%
+yeah so 1/3 win 2/3 loss and uh this
+ 
+
+ align:start position:0%
+yeah so 1/3 win 2/3 loss and uh this
+will be uh exactly the opposite so 2/3
+
+ align:start position:0%
+will be uh exactly the opposite so 2/3
+ 
+
+ align:start position:0%
+will be uh exactly the opposite so 2/3
+win 1/3 loss
+
+ align:start position:0%
+win 1/3 loss
+ 
+
+ align:start position:0%
+win 1/3 loss
+okay so now we can assign probabilities
+
+ align:start position:0%
+okay so now we can assign probabilities
+ 
+
+ align:start position:0%
+okay so now we can assign probabilities
+to all of the outcomes
+
+ align:start position:0%
+to all of the outcomes
+ 
+
+ align:start position:0%
+to all of the outcomes
+okay what's the probability of winning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+twice how do we compute these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probabilities anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh oh so that this was uh just you
+
+ align:start position:0%
+yeah uh oh so that this was uh just you
+ 
+
+ align:start position:0%
+yeah uh oh so that this was uh just you
+know what we assumed in the problem
+
+ align:start position:0%
+know what we assumed in the problem
+ 
+
+ align:start position:0%
+know what we assumed in the problem
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+if uh if it's not the first game uh you
+
+ align:start position:0%
+if uh if it's not the first game uh you
+ 
+
+ align:start position:0%
+if uh if it's not the first game uh you
+win with probability 2/3 if you won the
+
+ align:start position:0%
+win with probability 2/3 if you won the
+ 
+
+ align:start position:0%
+win with probability 2/3 if you won the
+last game or with probability 1/3 if you
+
+ align:start position:0%
+last game or with probability 1/3 if you
+ 
+
+ align:start position:0%
+last game or with probability 1/3 if you
+lost the last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+game okay so the the first branch is
+
+ align:start position:0%
+game okay so the the first branch is
+ 
+
+ align:start position:0%
+game okay so the the first branch is
+50/50 but the subsequent ones are going
+
+ align:start position:0%
+50/50 but the subsequent ones are going
+ 
+
+ align:start position:0%
+50/50 but the subsequent ones are going
+to be 2/3 1/3 in One Direction or the
+
+ align:start position:0%
+to be 2/3 1/3 in One Direction or the
+ 
+
+ align:start position:0%
+to be 2/3 1/3 in One Direction or the
+other depending on the outcome of the
+
+ align:start position:0%
+other depending on the outcome of the
+ 
+
+ align:start position:0%
+other depending on the outcome of the
+previous game maybe I shouldn't use
+
+ align:start position:0%
+previous game maybe I shouldn't use
+ 
+
+ align:start position:0%
+previous game maybe I shouldn't use
+outcome depending on the result of the
+
+ align:start position:0%
+outcome depending on the result of the
+ 
+
+ align:start position:0%
+outcome depending on the result of the
+previous
+
+ align:start position:0%
+previous
+ 
+
+ align:start position:0%
+previous
+game okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so how do we compute probabilities
+
+ align:start position:0%
+okay so how do we compute probabilities
+ 
+
+ align:start position:0%
+okay so how do we compute probabilities
+of outcomes does anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so you multiply probabilities
+
+ align:start position:0%
+yeah yeah so you multiply probabilities
+ 
+
+ align:start position:0%
+yeah yeah so you multiply probabilities
+along paths two outcomes okay so for
+
+ align:start position:0%
+along paths two outcomes okay so for
+ 
+
+ align:start position:0%
+along paths two outcomes okay so for
+this top outcome right we've got uh 1/2
+
+ align:start position:0%
+this top outcome right we've got uh 1/2
+ 
+
+ align:start position:0%
+this top outcome right we've got uh 1/2
+* 2/3 so this is probability
+
+ align:start position:0%
+* 2/3 so this is probability
+ 
+
+ align:start position:0%
+* 2/3 so this is probability
+1/3 uh win loss win has probability 1/3
+
+ align:start position:0%
+1/3 uh win loss win has probability 1/3
+ 
+
+ align:start position:0%
+1/3 uh win loss win has probability 1/3
+by/ 12 by 1/3 so that's
+
+ align:start position:0%
+by/ 12 by 1/3 so that's
+ 
+
+ align:start position:0%
+by/ 12 by 1/3 so that's
+118th uh when loss loss is probability
+
+ align:start position:0%
+118th uh when loss loss is probability
+ 
+
+ align:start position:0%
+118th uh when loss loss is probability
+1/2 * 1/3 * 2/3 so that's going to be 1
+
+ align:start position:0%
+1/2 * 1/3 * 2/3 so that's going to be 1
+ 
+
+ align:start position:0%
+1/2 * 1/3 * 2/3 so that's going to be 1
+nth uh and then these all
+
+ align:start position:0%
+nth uh and then these all
+ 
+
+ align:start position:0%
+nth uh and then these all
+reverse 11 18th and
+
+ align:start position:0%
+reverse 11 18th and
+ 
+
+ align:start position:0%
+reverse 11 18th and
+13 have I done that
+
+ align:start position:0%
+13 have I done that
+ 
+
+ align:start position:0%
+13 have I done that
+correctly yes that looks
+
+ align:start position:0%
+correctly yes that looks
+ 
+
+ align:start position:0%
+correctly yes that looks
+fine if I make an error please shout at
+
+ align:start position:0%
+fine if I make an error please shout at
+ 
+
+ align:start position:0%
+fine if I make an error please shout at
+me uh okay
+
+ align:start position:0%
+me uh okay
+ 
+
+ align:start position:0%
+me uh okay
+so we've got all of the uh we've got our
+
+ align:start position:0%
+so we've got all of the uh we've got our
+ 
+
+ align:start position:0%
+so we've got all of the uh we've got our
+tree diagram we've got our sample space
+
+ align:start position:0%
+tree diagram we've got our sample space
+ 
+
+ align:start position:0%
+tree diagram we've got our sample space
+we've got our our probability
+
+ align:start position:0%
+we've got our our probability
+ 
+
+ align:start position:0%
+we've got our our probability
+function uh what's the next thing we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need do we remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we've got step one the
+
+ align:start position:0%
+so we've got step one the
+ 
+
+ align:start position:0%
+so we've got step one the
+tree step two the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probabilities three right was the events
+
+ align:start position:0%
+probabilities three right was the events
+ 
+
+ align:start position:0%
+probabilities three right was the events
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what are the events we care
+
+ align:start position:0%
+okay so what are the events we care
+ 
+
+ align:start position:0%
+okay so what are the events we care
+about here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pardon okay winning the tournament and
+
+ align:start position:0%
+pardon okay winning the tournament and
+ 
+
+ align:start position:0%
+pardon okay winning the tournament and
+winning the first game okay
+
+ align:start position:0%
+winning the first game okay
+ 
+
+ align:start position:0%
+winning the first game okay
+so uh a was uh y a was winning the
+
+ align:start position:0%
+so uh a was uh y a was winning the
+ 
+
+ align:start position:0%
+so uh a was uh y a was winning the
+tournament B was winning the first
+
+ align:start position:0%
+tournament B was winning the first
+ 
+
+ align:start position:0%
+tournament B was winning the first
+game uh is that
+
+ align:start position:0%
+game uh is that
+ 
+
+ align:start position:0%
+game uh is that
+all are there any other events that we
+
+ align:start position:0%
+all are there any other events that we
+ 
+
+ align:start position:0%
+all are there any other events that we
+care about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes exactly so we also
+
+ align:start position:0%
+yeah yes exactly so we also
+ 
+
+ align:start position:0%
+yeah yes exactly so we also
+want a intersect B okay we also care
+
+ align:start position:0%
+want a intersect B okay we also care
+ 
+
+ align:start position:0%
+want a intersect B okay we also care
+about the event where you win the first
+
+ align:start position:0%
+about the event where you win the first
+ 
+
+ align:start position:0%
+about the event where you win the first
+battle and the series why is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that would you like to explain
+
+ align:start position:0%
+that would you like to explain
+ 
+
+ align:start position:0%
+that would you like to explain
+or yeah exactly so ultimately we want
+
+ align:start position:0%
+or yeah exactly so ultimately we want
+ 
+
+ align:start position:0%
+or yeah exactly so ultimately we want
+this conditional probability right the
+
+ align:start position:0%
+this conditional probability right the
+ 
+
+ align:start position:0%
+this conditional probability right the
+probability of a given B and if we go
+
+ align:start position:0%
+probability of a given B and if we go
+ 
+
+ align:start position:0%
+probability of a given B and if we go
+back to our definition right the
+
+ align:start position:0%
+back to our definition right the
+ 
+
+ align:start position:0%
+back to our definition right the
+probability of a given B is the
+
+ align:start position:0%
+probability of a given B is the
+ 
+
+ align:start position:0%
+probability of a given B is the
+probability of a intersect B divided by
+
+ align:start position:0%
+probability of a intersect B divided by
+ 
+
+ align:start position:0%
+probability of a intersect B divided by
+the probability of B okay so as it turns
+
+ align:start position:0%
+the probability of B okay so as it turns
+ 
+
+ align:start position:0%
+the probability of B okay so as it turns
+out we kind of don't really need a right
+
+ align:start position:0%
+out we kind of don't really need a right
+ 
+
+ align:start position:0%
+out we kind of don't really need a right
+the two probabilities we really need are
+
+ align:start position:0%
+the two probabilities we really need are
+ 
+
+ align:start position:0%
+the two probabilities we really need are
+these two or the two events I suppose
+
+ align:start position:0%
+these two or the two events I suppose
+ 
+
+ align:start position:0%
+these two or the two events I suppose
+okay so finally for answer
+
+ align:start position:0%
+okay so finally for answer
+ 
+
+ align:start position:0%
+okay so finally for answer
+what is our
+
+ align:start position:0%
+what is our
+ 
+
+ align:start position:0%
+what is our
+answer well probability of a given
+
+ align:start position:0%
+answer well probability of a given
+ 
+
+ align:start position:0%
+answer well probability of a given
+b as we just said is the probability of
+
+ align:start position:0%
+b as we just said is the probability of
+ 
+
+ align:start position:0%
+b as we just said is the probability of
+a intersect B divide by probability of
+
+ align:start position:0%
+a intersect B divide by probability of
+ 
+
+ align:start position:0%
+a intersect B divide by probability of
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+okay what are each of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probabilities well which events or sorry
+
+ align:start position:0%
+probabilities well which events or sorry
+ 
+
+ align:start position:0%
+probabilities well which events or sorry
+which outcomes are in the event a
+
+ align:start position:0%
+which outcomes are in the event a
+ 
+
+ align:start position:0%
+which outcomes are in the event a
+intersect B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's ww in a intercept
+
+ align:start position:0%
+it's ww in a intercept
+ 
+
+ align:start position:0%
+it's ww in a intercept
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+yeah win loss win also yes okay win loss
+
+ align:start position:0%
+yeah win loss win also yes okay win loss
+ 
+
+ align:start position:0%
+yeah win loss win also yes okay win loss
+loss nope and all of these he lost the
+
+ align:start position:0%
+loss nope and all of these he lost the
+ 
+
+ align:start position:0%
+loss nope and all of these he lost the
+first game so these are also not in it
+
+ align:start position:0%
+first game so these are also not in it
+ 
+
+ align:start position:0%
+first game so these are also not in it
+so we care about these two uh these two
+
+ align:start position:0%
+so we care about these two uh these two
+ 
+
+ align:start position:0%
+so we care about these two uh these two
+outcomes okay so this is going to be by
+
+ align:start position:0%
+outcomes okay so this is going to be by
+ 
+
+ align:start position:0%
+outcomes okay so this is going to be by
+the sum rule 1/3 +/ 18
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that doesn't look much like an
+
+ align:start position:0%
+that doesn't look much like an
+ 
+
+ align:start position:0%
+that doesn't look much like an
+eight oh well
+
+ align:start position:0%
+eight oh well
+ 
+
+ align:start position:0%
+eight oh well
+okay now what's the probability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B yeah yeah it's just one half right
+
+ align:start position:0%
+B yeah yeah it's just one half right
+ 
+
+ align:start position:0%
+B yeah yeah it's just one half right
+either by symmetry or you can actually
+
+ align:start position:0%
+either by symmetry or you can actually
+ 
+
+ align:start position:0%
+either by symmetry or you can actually
+look at what those outcomes are right
+
+ align:start position:0%
+look at what those outcomes are right
+ 
+
+ align:start position:0%
+look at what those outcomes are right
+it's these top uh these top three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and if we do this arithmetic we've
+
+ align:start position:0%
+okay and if we do this arithmetic we've
+ 
+
+ align:start position:0%
+okay and if we do this arithmetic we've
+got 7/8 divided 12 which is 7
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nths
+
+ align:start position:0%
+nths
+ 
+
+ align:start position:0%
+nths
+okay so the probability that Ash wins
+
+ align:start position:0%
+okay so the probability that Ash wins
+ 
+
+ align:start position:0%
+okay so the probability that Ash wins
+the entire series given that he won the
+
+ align:start position:0%
+the entire series given that he won the
+ 
+
+ align:start position:0%
+the entire series given that he won the
+first battle is going to be
+
+ align:start position:0%
+first battle is going to be
+ 
+
+ align:start position:0%
+first battle is going to be
+79ths okay so so far this is pretty
+
+ align:start position:0%
+79ths okay so so far this is pretty
+ 
+
+ align:start position:0%
+79ths okay so so far this is pretty
+straightforward right fairly routine uh
+
+ align:start position:0%
+straightforward right fairly routine uh
+ 
+
+ align:start position:0%
+straightforward right fairly routine uh
+mathemat well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arithmetic but what if
+
+ align:start position:0%
+arithmetic but what if
+ 
+
+ align:start position:0%
+arithmetic but what if
+instead we ask for the probability of B
+
+ align:start position:0%
+instead we ask for the probability of B
+ 
+
+ align:start position:0%
+instead we ask for the probability of B
+given a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability well numerically right we
+
+ align:start position:0%
+probability well numerically right we
+ 
+
+ align:start position:0%
+probability well numerically right we
+can compute it in exactly the same way
+
+ align:start position:0%
+can compute it in exactly the same way
+ 
+
+ align:start position:0%
+can compute it in exactly the same way
+right it's going to be the probability
+
+ align:start position:0%
+right it's going to be the probability
+ 
+
+ align:start position:0%
+right it's going to be the probability
+of the intersection divided by this time
+
+ align:start position:0%
+of the intersection divided by this time
+ 
+
+ align:start position:0%
+of the intersection divided by this time
+the probability of a rather than the
+
+ align:start position:0%
+the probability of a rather than the
+ 
+
+ align:start position:0%
+the probability of a rather than the
+probability of B but still by symmetry
+
+ align:start position:0%
+probability of B but still by symmetry
+ 
+
+ align:start position:0%
+probability of B but still by symmetry
+that probability is going to be2
+
+ align:start position:0%
+that probability is going to be2
+ 
+
+ align:start position:0%
+that probability is going to be2
+okay so this is also going to be 7
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9ths but what exactly does it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so the answer was you know
+
+ align:start position:0%
+yeah yeah so the answer was you know
+ 
+
+ align:start position:0%
+yeah yeah so the answer was you know
+given that you already won the series
+
+ align:start position:0%
+given that you already won the series
+ 
+
+ align:start position:0%
+given that you already won the series
+what's the probability that he won the
+
+ align:start position:0%
+what's the probability that he won the
+ 
+
+ align:start position:0%
+what's the probability that he won the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+battle okay now this might sound a
+
+ align:start position:0%
+battle okay now this might sound a
+ 
+
+ align:start position:0%
+battle okay now this might sound a
+little bit weird to some of you right
+
+ align:start position:0%
+little bit weird to some of you right
+ 
+
+ align:start position:0%
+little bit weird to some of you right
+like you know if we know that he's won
+
+ align:start position:0%
+like you know if we know that he's won
+ 
+
+ align:start position:0%
+like you know if we know that he's won
+the series right everything's already
+
+ align:start position:0%
+the series right everything's already
+ 
+
+ align:start position:0%
+the series right everything's already
+happened he either won the battle or he
+
+ align:start position:0%
+happened he either won the battle or he
+ 
+
+ align:start position:0%
+happened he either won the battle or he
+didn't right but uh you know when we're
+
+ align:start position:0%
+didn't right but uh you know when we're
+ 
+
+ align:start position:0%
+didn't right but uh you know when we're
+modeling probability questions you know
+
+ align:start position:0%
+modeling probability questions you know
+ 
+
+ align:start position:0%
+modeling probability questions you know
+we don't really care about any sort of
+
+ align:start position:0%
+we don't really care about any sort of
+ 
+
+ align:start position:0%
+we don't really care about any sort of
+temporal relations or anything like that
+
+ align:start position:0%
+temporal relations or anything like that
+ 
+
+ align:start position:0%
+temporal relations or anything like that
+or even causal ones right like uh you
+
+ align:start position:0%
+or even causal ones right like uh you
+ 
+
+ align:start position:0%
+or even causal ones right like uh you
+know we're just uh like it it's all just
+
+ align:start position:0%
+know we're just uh like it it's all just
+ 
+
+ align:start position:0%
+know we're just uh like it it's all just
+you know numerical right you can kind of
+
+ align:start position:0%
+you know numerical right you can kind of
+ 
+
+ align:start position:0%
+you know numerical right you can kind of
+think of it a bit like an inference
+
+ align:start position:0%
+think of it a bit like an inference
+ 
+
+ align:start position:0%
+think of it a bit like an inference
+right like you know you've got some
+
+ align:start position:0%
+right like you know you've got some
+ 
+
+ align:start position:0%
+right like you know you've got some
+uncertainty right like you know maybe
+
+ align:start position:0%
+uncertainty right like you know maybe
+ 
+
+ align:start position:0%
+uncertainty right like you know maybe
+you're told that he won the battle you
+
+ align:start position:0%
+you're told that he won the battle you
+ 
+
+ align:start position:0%
+you're told that he won the battle you
+want to or sorry you're told that he won
+
+ align:start position:0%
+want to or sorry you're told that he won
+ 
+
+ align:start position:0%
+want to or sorry you're told that he won
+the series you want to update your
+
+ align:start position:0%
+the series you want to update your
+ 
+
+ align:start position:0%
+the series you want to update your
+belief that you know maybe he won the
+
+ align:start position:0%
+belief that you know maybe he won the
+ 
+
+ align:start position:0%
+belief that you know maybe he won the
+the first battle maybe he didn't uh and
+
+ align:start position:0%
+the first battle maybe he didn't uh and
+ 
+
+ align:start position:0%
+the first battle maybe he didn't uh and
+maybe you're not entirely confident in
+
+ align:start position:0%
+maybe you're not entirely confident in
+ 
+
+ align:start position:0%
+maybe you're not entirely confident in
+it uh but you'd like to estimate you
+
+ align:start position:0%
+it uh but you'd like to estimate you
+ 
+
+ align:start position:0%
+it uh but you'd like to estimate you
+know how confident you should be uh that
+
+ align:start position:0%
+know how confident you should be uh that
+ 
+
+ align:start position:0%
+know how confident you should be uh that
+might be one way to think about
+
+ align:start position:0%
+might be one way to think about
+ 
+
+ align:start position:0%
+might be one way to think about
+it um
+
+ align:start position:0%
+it um
+ 
+
+ align:start position:0%
+it um
+so in a sense it's kind of like looking
+
+ align:start position:0%
+so in a sense it's kind of like looking
+ 
+
+ align:start position:0%
+so in a sense it's kind of like looking
+at a backwards probability that you know
+
+ align:start position:0%
+at a backwards probability that you know
+ 
+
+ align:start position:0%
+at a backwards probability that you know
+something in the past has happened given
+
+ align:start position:0%
+something in the past has happened given
+ 
+
+ align:start position:0%
+something in the past has happened given
+that we observed something in the
+
+ align:start position:0%
+that we observed something in the
+ 
+
+ align:start position:0%
+that we observed something in the
+future uh so you know in general you
+
+ align:start position:0%
+future uh so you know in general you
+ 
+
+ align:start position:0%
+future uh so you know in general you
+know they they won't always be the same
+
+ align:start position:0%
+know they they won't always be the same
+ 
+
+ align:start position:0%
+know they they won't always be the same
+like this like you can kind of relate
+
+ align:start position:0%
+like this like you can kind of relate
+ 
+
+ align:start position:0%
+like this like you can kind of relate
+the probability of B given a to the
+
+ align:start position:0%
+the probability of B given a to the
+ 
+
+ align:start position:0%
+the probability of B given a to the
+probability of a given B they won't
+
+ align:start position:0%
+probability of a given B they won't
+ 
+
+ align:start position:0%
+probability of a given B they won't
+always be equal okay let's see how to
+
+ align:start position:0%
+always be equal okay let's see how to
+ 
+
+ align:start position:0%
+always be equal okay let's see how to
+relate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them it just so happens that in this
+
+ align:start position:0%
+them it just so happens that in this
+ 
+
+ align:start position:0%
+them it just so happens that in this
+case right these two
+
+ align:start position:0%
+case right these two
+ 
+
+ align:start position:0%
+case right these two
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+oh these two things have the same
+
+ align:start position:0%
+oh these two things have the same
+ 
+
+ align:start position:0%
+oh these two things have the same
+probability okay so that's really the
+
+ align:start position:0%
+probability okay so that's really the
+ 
+
+ align:start position:0%
+probability okay so that's really the
+core reason why they were
+
+ align:start position:0%
+core reason why they were
+ 
+
+ align:start position:0%
+core reason why they were
+equal but more generally we have the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following okay this is called base
+
+ align:start position:0%
+following okay this is called base
+ 
+
+ align:start position:0%
+following okay this is called base
+rule
+
+ align:start position:0%
+rule
+ 
+
+ align:start position:0%
+rule
+okay uh you can kind of think of it is
+
+ align:start position:0%
+okay uh you can kind of think of it is
+ 
+
+ align:start position:0%
+okay uh you can kind of think of it is
+you know it's just the product rule in
+
+ align:start position:0%
+you know it's just the product rule in
+ 
+
+ align:start position:0%
+you know it's just the product rule in
+disguise right so the
+
+ align:start position:0%
+disguise right so the
+ 
+
+ align:start position:0%
+disguise right so the
+probability of B given
+
+ align:start position:0%
+probability of B given
+ 
+
+ align:start position:0%
+probability of B given
+a equals the probability Oops why don't
+
+ align:start position:0%
+a equals the probability Oops why don't
+ 
+
+ align:start position:0%
+a equals the probability Oops why don't
+I split this into two
+
+ align:start position:0%
+I split this into two
+ 
+
+ align:start position:0%
+I split this into two
+lines probability of a given
+
+ align:start position:0%
+lines probability of a given
+ 
+
+ align:start position:0%
+lines probability of a given
+B probability of
+
+ align:start position:0%
+B probability of
+ 
+
+ align:start position:0%
+B probability of
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+B divided by probability of
+
+ align:start position:0%
+B divided by probability of
+ 
+
+ align:start position:0%
+B divided by probability of
+a okay so in the example we just saw
+
+ align:start position:0%
+a okay so in the example we just saw
+ 
+
+ align:start position:0%
+a okay so in the example we just saw
+these two are the same so they just
+
+ align:start position:0%
+these two are the same so they just
+ 
+
+ align:start position:0%
+these two are the same so they just
+cancel uh but more generally you want to
+
+ align:start position:0%
+cancel uh but more generally you want to
+ 
+
+ align:start position:0%
+cancel uh but more generally you want to
+multiply by the quotient okay and you
+
+ align:start position:0%
+multiply by the quotient okay and you
+ 
+
+ align:start position:0%
+multiply by the quotient okay and you
+can kind of think of this as the product
+
+ align:start position:0%
+can kind of think of this as the product
+ 
+
+ align:start position:0%
+can kind of think of this as the product
+rule in disguise right like if you just
+
+ align:start position:0%
+rule in disguise right like if you just
+ 
+
+ align:start position:0%
+rule in disguise right like if you just
+move this probability of a over to this
+
+ align:start position:0%
+move this probability of a over to this
+ 
+
+ align:start position:0%
+move this probability of a over to this
+side right uh now you're just Computing
+
+ align:start position:0%
+side right uh now you're just Computing
+ 
+
+ align:start position:0%
+side right uh now you're just Computing
+the probability of the intersection of A
+
+ align:start position:0%
+the probability of the intersection of A
+ 
+
+ align:start position:0%
+the probability of the intersection of A
+and B on both sides does that make
+
+ align:start position:0%
+and B on both sides does that make
+ 
+
+ align:start position:0%
+and B on both sides does that make
+sense but uh it can often be useful uh
+
+ align:start position:0%
+sense but uh it can often be useful uh
+ 
+
+ align:start position:0%
+sense but uh it can often be useful uh
+you know even though it's not really
+
+ align:start position:0%
+you know even though it's not really
+ 
+
+ align:start position:0%
+you know even though it's not really
+saying anything new it can often be
+
+ align:start position:0%
+saying anything new it can often be
+ 
+
+ align:start position:0%
+saying anything new it can often be
+useful to think about it in this way
+
+ align:start position:0%
+useful to think about it in this way
+ 
+
+ align:start position:0%
+useful to think about it in this way
+okay if you kind of want to reverse the
+
+ align:start position:0%
+okay if you kind of want to reverse the
+ 
+
+ align:start position:0%
+okay if you kind of want to reverse the
+direction of an
+
+ align:start position:0%
+direction of an
+ 
+
+ align:start position:0%
+direction of an
+inference uh you want to multiply by the
+
+ align:start position:0%
+inference uh you want to multiply by the
+ 
+
+ align:start position:0%
+inference uh you want to multiply by the
+quotient of the two event the two
+
+ align:start position:0%
+quotient of the two event the two
+ 
+
+ align:start position:0%
+quotient of the two event the two
+probabilities of the events that you
+
+ align:start position:0%
+probabilities of the events that you
+ 
+
+ align:start position:0%
+probabilities of the events that you
+care about
+
+ align:start position:0%
+care about
+ 
+
+ align:start position:0%
+care about
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh and one particularly useful
+
+ align:start position:0%
+uh and one particularly useful
+ 
+
+ align:start position:0%
+uh and one particularly useful
+uh consequence of this is the following
+
+ align:start position:0%
+uh consequence of this is the following
+ 
+
+ align:start position:0%
+uh consequence of this is the following
+so suppose we have two events B and C
+
+ align:start position:0%
+so suppose we have two events B and C
+ 
+
+ align:start position:0%
+so suppose we have two events B and C
+and we're kind of trying to condition
+
+ align:start position:0%
+and we're kind of trying to condition
+ 
+
+ align:start position:0%
+and we're kind of trying to condition
+them both on the same
+
+ align:start position:0%
+them both on the same
+ 
+
+ align:start position:0%
+them both on the same
+event
+
+ align:start position:0%
+event
+ 
+
+ align:start position:0%
+event
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is the probability of C given
+
+ align:start position:0%
+so what is the probability of C given
+ 
+
+ align:start position:0%
+so what is the probability of C given
+a no B given a divided by the
+
+ align:start position:0%
+a no B given a divided by the
+ 
+
+ align:start position:0%
+a no B given a divided by the
+probability of C given
+
+ align:start position:0%
+probability of C given
+ 
+
+ align:start position:0%
+probability of C given
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and in particular often we would
+
+ align:start position:0%
+okay and in particular often we would
+ 
+
+ align:start position:0%
+okay and in particular often we would
+take C to be the complement of b or
+
+ align:start position:0%
+take C to be the complement of b or
+ 
+
+ align:start position:0%
+take C to be the complement of b or
+something like that and that will then
+
+ align:start position:0%
+something like that and that will then
+ 
+
+ align:start position:0%
+something like that and that will then
+help us to compute this probability of
+
+ align:start position:0%
+help us to compute this probability of
+ 
+
+ align:start position:0%
+help us to compute this probability of
+being given a
+
+ align:start position:0%
+being given a
+ 
+
+ align:start position:0%
+being given a
+okay so as it turns out this is going to
+
+ align:start position:0%
+okay so as it turns out this is going to
+ 
+
+ align:start position:0%
+okay so as it turns out this is going to
+be the probability of a given
+
+ align:start position:0%
+be the probability of a given
+ 
+
+ align:start position:0%
+be the probability of a given
+B times the probability of
+
+ align:start position:0%
+B times the probability of
+ 
+
+ align:start position:0%
+B times the probability of
+B divided
+
+ align:start position:0%
+B divided
+ 
+
+ align:start position:0%
+B divided
+by probability of a given
+
+ align:start position:0%
+by probability of a given
+ 
+
+ align:start position:0%
+by probability of a given
+C oops
+
+ align:start position:0%
+C oops
+ 
+
+ align:start position:0%
+C oops
+probability of C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so does that make sense to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody and the reason that this might
+
+ align:start position:0%
+everybody and the reason that this might
+ 
+
+ align:start position:0%
+everybody and the reason that this might
+you know this in particular might be
+
+ align:start position:0%
+you know this in particular might be
+ 
+
+ align:start position:0%
+you know this in particular might be
+useful uh in order to compute the
+
+ align:start position:0%
+useful uh in order to compute the
+ 
+
+ align:start position:0%
+useful uh in order to compute the
+probability of B you know if we uh use B
+
+ align:start position:0%
+probability of B you know if we uh use B
+ 
+
+ align:start position:0%
+probability of B you know if we uh use B
+complement to C
+
+ align:start position:0%
+complement to C
+ 
+
+ align:start position:0%
+complement to C
+right this right hand side here
+
+ align:start position:0%
+right this right hand side here
+ 
+
+ align:start position:0%
+right this right hand side here
+does not depend on the probability of a
+
+ align:start position:0%
+does not depend on the probability of a
+ 
+
+ align:start position:0%
+does not depend on the probability of a
+right like we don't have to compute the
+
+ align:start position:0%
+right like we don't have to compute the
+ 
+
+ align:start position:0%
+right like we don't have to compute the
+probability of a so maybe if a is some
+
+ align:start position:0%
+probability of a so maybe if a is some
+ 
+
+ align:start position:0%
+probability of a so maybe if a is some
+really nasty event right and we don't
+
+ align:start position:0%
+really nasty event right and we don't
+ 
+
+ align:start position:0%
+really nasty event right and we don't
+actually want to compute its probability
+
+ align:start position:0%
+actually want to compute its probability
+ 
+
+ align:start position:0%
+actually want to compute its probability
+but we can still condition on it we
+
+ align:start position:0%
+but we can still condition on it we
+ 
+
+ align:start position:0%
+but we can still condition on it we
+might still be able to use this formula
+
+ align:start position:0%
+might still be able to use this formula
+ 
+
+ align:start position:0%
+might still be able to use this formula
+more easily than we could use this
+
+ align:start position:0%
+more easily than we could use this
+ 
+
+ align:start position:0%
+more easily than we could use this
+one okay does that make sense to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody
+
+ align:start position:0%
+everybody
+ 
+
+ align:start position:0%
+everybody
+okay so let's take a look at a couple of
+
+ align:start position:0%
+okay so let's take a look at a couple of
+ 
+
+ align:start position:0%
+okay so let's take a look at a couple of
+applications of BAS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R uh or actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first first maybe I should uh give you a
+
+ align:start position:0%
+first first maybe I should uh give you a
+ 
+
+ align:start position:0%
+first first maybe I should uh give you a
+brief lesson in
+
+ align:start position:0%
+brief lesson in
+ 
+
+ align:start position:0%
+brief lesson in
+statistics uh so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terminology the probability of uh a
+
+ align:start position:0%
+terminology the probability of uh a
+ 
+
+ align:start position:0%
+terminology the probability of uh a
+given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B uh this would often be called the
+
+ align:start position:0%
+B uh this would often be called the
+ 
+
+ align:start position:0%
+B uh this would often be called the
+likelihood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B okay so if any of you have ever seen
+
+ align:start position:0%
+B okay so if any of you have ever seen
+ 
+
+ align:start position:0%
+B okay so if any of you have ever seen
+like maximum likelihood estimations or
+
+ align:start position:0%
+like maximum likelihood estimations or
+ 
+
+ align:start position:0%
+like maximum likelihood estimations or
+anything like that that's where this
+
+ align:start position:0%
+anything like that that's where this
+ 
+
+ align:start position:0%
+anything like that that's where this
+comes from or this is where that comes
+
+ align:start position:0%
+comes from or this is where that comes
+ 
+
+ align:start position:0%
+comes from or this is where that comes
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+sorry uh probability of B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we call the prior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B and the left hand side the probability
+
+ align:start position:0%
+B and the left hand side the probability
+ 
+
+ align:start position:0%
+B and the left hand side the probability
+of being given an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is the posterior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+B uh actually we don't usually specify a
+
+ align:start position:0%
+B uh actually we don't usually specify a
+ 
+
+ align:start position:0%
+B uh actually we don't usually specify a
+with that
+
+ align:start position:0%
+with that
+ 
+
+ align:start position:0%
+with that
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+okay so this is how you would normally
+
+ align:start position:0%
+okay so this is how you would normally
+ 
+
+ align:start position:0%
+okay so this is how you would normally
+talk about it like in statistics or
+
+ align:start position:0%
+talk about it like in statistics or
+ 
+
+ align:start position:0%
+talk about it like in statistics or
+something like that uh the the
+
+ align:start position:0%
+something like that uh the the
+ 
+
+ align:start position:0%
+something like that uh the the
+likelihood of a given B the prior
+
+ align:start position:0%
+likelihood of a given B the prior
+ 
+
+ align:start position:0%
+likelihood of a given B the prior
+probability and the posterior
+
+ align:start position:0%
+probability and the posterior
+ 
+
+ align:start position:0%
+probability and the posterior
+probability because basically what
+
+ align:start position:0%
+probability because basically what
+ 
+
+ align:start position:0%
+probability because basically what
+you're doing right is you're starting
+
+ align:start position:0%
+you're doing right is you're starting
+ 
+
+ align:start position:0%
+you're doing right is you're starting
+with some prior right if you don't know
+
+ align:start position:0%
+with some prior right if you don't know
+ 
+
+ align:start position:0%
+with some prior right if you don't know
+anything like this is kind of what you
+
+ align:start position:0%
+anything like this is kind of what you
+ 
+
+ align:start position:0%
+anything like this is kind of what you
+think the the probability of B should be
+
+ align:start position:0%
+think the the probability of B should be
+ 
+
+ align:start position:0%
+think the the probability of B should be
+and now you make some uh some
+
+ align:start position:0%
+and now you make some uh some
+ 
+
+ align:start position:0%
+and now you make some uh some
+observation a right and so now you
+
+ align:start position:0%
+observation a right and so now you
+ 
+
+ align:start position:0%
+observation a right and so now you
+update and you got a posterior
+
+ align:start position:0%
+update and you got a posterior
+ 
+
+ align:start position:0%
+update and you got a posterior
+probability of B you know condition on
+
+ align:start position:0%
+probability of B you know condition on
+ 
+
+ align:start position:0%
+probability of B you know condition on
+that that uh uh observation does that
+
+ align:start position:0%
+that that uh uh observation does that
+ 
+
+ align:start position:0%
+that that uh uh observation does that
+make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+okay so why don't we take a look at a
+
+ align:start position:0%
+okay so why don't we take a look at a
+ 
+
+ align:start position:0%
+okay so why don't we take a look at a
+couple of examples then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+here hopefully everybody is okay with
+
+ align:start position:0%
+here hopefully everybody is okay with
+ 
+
+ align:start position:0%
+here hopefully everybody is okay with
+those okay so first example suppose I've
+
+ align:start position:0%
+those okay so first example suppose I've
+ 
+
+ align:start position:0%
+those okay so first example suppose I've
+got two
+
+ align:start position:0%
+got two
+ 
+
+ align:start position:0%
+got two
+coins okay uh I've got one Fair coin
+
+ align:start position:0%
+coins okay uh I've got one Fair coin
+ 
+
+ align:start position:0%
+coins okay uh I've got one Fair coin
+right I toss this coin and it'll come up
+
+ align:start position:0%
+right I toss this coin and it'll come up
+ 
+
+ align:start position:0%
+right I toss this coin and it'll come up
+heads with 50% probability tails with
+
+ align:start position:0%
+heads with 50% probability tails with
+ 
+
+ align:start position:0%
+heads with 50% probability tails with
+50% probability okay and I've also got a
+
+ align:start position:0%
+50% probability okay and I've also got a
+ 
+
+ align:start position:0%
+50% probability okay and I've also got a
+trick coin right it's uh you know double
+
+ align:start position:0%
+trick coin right it's uh you know double
+ 
+
+ align:start position:0%
+trick coin right it's uh you know double
+heads I flip it I always get
+
+ align:start position:0%
+heads I flip it I always get
+ 
+
+ align:start position:0%
+heads I flip it I always get
+heads
+
+ align:start position:0%
+heads
+ 
+
+ align:start position:0%
+heads
+okay uh suppose I pick one of these
+
+ align:start position:0%
+okay uh suppose I pick one of these
+ 
+
+ align:start position:0%
+okay uh suppose I pick one of these
+coins uniformly at
+
+ align:start position:0%
+coins uniformly at
+ 
+
+ align:start position:0%
+coins uniformly at
+random I flip that
+
+ align:start position:0%
+random I flip that
+ 
+
+ align:start position:0%
+random I flip that
+coin and it comes up
+
+ align:start position:0%
+coin and it comes up
+ 
+
+ align:start position:0%
+coin and it comes up
+heads okay what is the probability that
+
+ align:start position:0%
+heads okay what is the probability that
+ 
+
+ align:start position:0%
+heads okay what is the probability that
+I picked the far coin to begin with as
+
+ align:start position:0%
+I picked the far coin to begin with as
+ 
+
+ align:start position:0%
+I picked the far coin to begin with as
+opposed to the biased one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any ideas does anybody have any guesses
+
+ align:start position:0%
+any ideas does anybody have any guesses
+ 
+
+ align:start position:0%
+any ideas does anybody have any guesses
+as to what the probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is who wants to just dra draw the tree
+
+ align:start position:0%
+is who wants to just dra draw the tree
+ 
+
+ align:start position:0%
+is who wants to just dra draw the tree
+diagram few people people aren't as
+
+ align:start position:0%
+diagram few people people aren't as
+ 
+
+ align:start position:0%
+diagram few people people aren't as
+enthusiastic about it as as they were on
+
+ align:start position:0%
+enthusiastic about it as as they were on
+ 
+
+ align:start position:0%
+enthusiastic about it as as they were on
+Tuesday that's uh that's slightly
+
+ align:start position:0%
+Tuesday that's uh that's slightly
+ 
+
+ align:start position:0%
+Tuesday that's uh that's slightly
+unfortunate let's do it anyway uh no
+
+ align:start position:0%
+unfortunate let's do it anyway uh no
+ 
+
+ align:start position:0%
+unfortunate let's do it anyway uh no
+let's let's first uh you know let's make
+
+ align:start position:0%
+let's let's first uh you know let's make
+ 
+
+ align:start position:0%
+let's let's first uh you know let's make
+precise the events that we care about
+
+ align:start position:0%
+precise the events that we care about
+ 
+
+ align:start position:0%
+precise the events that we care about
+okay um so let's let H be the event
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that we flipped
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heads uh and uh f is the
+
+ align:start position:0%
+heads uh and uh f is the
+ 
+
+ align:start position:0%
+heads uh and uh f is the
+event picked the fa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coin
+
+ align:start position:0%
+coin
+ 
+
+ align:start position:0%
+coin
+okay so what is the probability that
+
+ align:start position:0%
+okay so what is the probability that
+ 
+
+ align:start position:0%
+okay so what is the probability that
+we're trying to compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in terms of these two
+
+ align:start position:0%
+in terms of these two
+ 
+
+ align:start position:0%
+in terms of these two
+quantities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah probability of f given H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+okay so how might we compute
+
+ align:start position:0%
+okay so how might we compute
+ 
+
+ align:start position:0%
+okay so how might we compute
+this people didn't seem too enthusiastic
+
+ align:start position:0%
+this people didn't seem too enthusiastic
+ 
+
+ align:start position:0%
+this people didn't seem too enthusiastic
+about the tree diagram so what else
+
+ align:start position:0%
+about the tree diagram so what else
+ 
+
+ align:start position:0%
+about the tree diagram so what else
+could we do instead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does anybody see a way to use base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rule yeah or just a stretch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah the probability of H given f
+
+ align:start position:0%
+yeah yeah the probability of H given f
+ 
+
+ align:start position:0%
+yeah yeah the probability of H given f
+is easy right that's that's 50% okay so
+
+ align:start position:0%
+is easy right that's that's 50% okay so
+ 
+
+ align:start position:0%
+is easy right that's that's 50% okay so
+that's that's an easy known quantity so
+
+ align:start position:0%
+that's that's an easy known quantity so
+ 
+
+ align:start position:0%
+that's that's an easy known quantity so
+if we use base rule right that that
+
+ align:start position:0%
+if we use base rule right that that
+ 
+
+ align:start position:0%
+if we use base rule right that that
+might make it easier to uh to compute
+
+ align:start position:0%
+might make it easier to uh to compute
+ 
+
+ align:start position:0%
+might make it easier to uh to compute
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh actually why don't we use the uh
+
+ align:start position:0%
+so uh actually why don't we use the uh
+ 
+
+ align:start position:0%
+so uh actually why don't we use the uh
+you know slightly more complicated
+
+ align:start position:0%
+you know slightly more complicated
+ 
+
+ align:start position:0%
+you know slightly more complicated
+version of Base rule so let's compute
+
+ align:start position:0%
+version of Base rule so let's compute
+ 
+
+ align:start position:0%
+version of Base rule so let's compute
+the ratio of the probability that we
+
+ align:start position:0%
+the ratio of the probability that we
+ 
+
+ align:start position:0%
+the ratio of the probability that we
+picked the faircoin given that we
+
+ align:start position:0%
+picked the faircoin given that we
+ 
+
+ align:start position:0%
+picked the faircoin given that we
+observed a heads versus you know the the
+
+ align:start position:0%
+observed a heads versus you know the the
+ 
+
+ align:start position:0%
+observed a heads versus you know the the
+probability of the of picking the biased
+
+ align:start position:0%
+probability of the of picking the biased
+ 
+
+ align:start position:0%
+probability of the of picking the biased
+coin given that we observed a heads
+
+ align:start position:0%
+coin given that we observed a heads
+ 
+
+ align:start position:0%
+coin given that we observed a heads
+okay so the
+
+ align:start position:0%
+okay so the
+ 
+
+ align:start position:0%
+okay so the
+probability of f given
+
+ align:start position:0%
+probability of f given
+ 
+
+ align:start position:0%
+probability of f given
+H over probability of not F given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H so what was that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so right base rule is about you know
+
+ align:start position:0%
+so right base rule is about you know
+ 
+
+ align:start position:0%
+so right base rule is about you know
+flipping the uh flipping the order right
+
+ align:start position:0%
+flipping the uh flipping the order right
+ 
+
+ align:start position:0%
+flipping the uh flipping the order right
+so instead of f conditioned on H we want
+
+ align:start position:0%
+so instead of f conditioned on H we want
+ 
+
+ align:start position:0%
+so instead of f conditioned on H we want
+H conditioned on
+
+ align:start position:0%
+H conditioned on
+ 
+
+ align:start position:0%
+H conditioned on
+F multiplied by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what yeah yeah probability of f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and on the bottom we can do the
+
+ align:start position:0%
+okay and on the bottom we can do the
+ 
+
+ align:start position:0%
+okay and on the bottom we can do the
+same thing probability of H given not
+
+ align:start position:0%
+same thing probability of H given not
+ 
+
+ align:start position:0%
+same thing probability of H given not
+F times the probability of not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F
+
+ align:start position:0%
+F
+ 
+
+ align:start position:0%
+F
+okay so this expression is much easier
+
+ align:start position:0%
+okay so this expression is much easier
+ 
+
+ align:start position:0%
+okay so this expression is much easier
+to work with right what's the
+
+ align:start position:0%
+to work with right what's the
+ 
+
+ align:start position:0%
+to work with right what's the
+probability of H given f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay what about the probability of
+
+ align:start position:0%
+yeah okay what about the probability of
+ 
+
+ align:start position:0%
+yeah okay what about the probability of
+H given not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and probability of F and not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F those are each one half by assumption
+
+ align:start position:0%
+F those are each one half by assumption
+ 
+
+ align:start position:0%
+F those are each one half by assumption
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so those just cancel and we are
+
+ align:start position:0%
+okay so those just cancel and we are
+ 
+
+ align:start position:0%
+okay so those just cancel and we are
+left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with2
+
+ align:start position:0%
+with2
+ 
+
+ align:start position:0%
+with2
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+now what is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability we computed the ratio of
+
+ align:start position:0%
+probability we computed the ratio of
+ 
+
+ align:start position:0%
+probability we computed the ratio of
+this probability to its complement
+
+ align:start position:0%
+this probability to its complement
+ 
+
+ align:start position:0%
+this probability to its complement
+right so what does that tell us the uh
+
+ align:start position:0%
+right so what does that tell us the uh
+ 
+
+ align:start position:0%
+right so what does that tell us the uh
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is yeah one3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so OB serve here that uh if our
+
+ align:start position:0%
+okay so OB serve here that uh if our
+ 
+
+ align:start position:0%
+okay so OB serve here that uh if our
+prior changes right if the if the chance
+
+ align:start position:0%
+prior changes right if the if the chance
+ 
+
+ align:start position:0%
+prior changes right if the if the chance
+that we are you know picking the fa coin
+
+ align:start position:0%
+that we are you know picking the fa coin
+ 
+
+ align:start position:0%
+that we are you know picking the fa coin
+to begin with
+
+ align:start position:0%
+to begin with
+ 
+
+ align:start position:0%
+to begin with
+changes uh this posterior probability
+
+ align:start position:0%
+changes uh this posterior probability
+ 
+
+ align:start position:0%
+changes uh this posterior probability
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+changes okay
+
+ align:start position:0%
+changes okay
+ 
+
+ align:start position:0%
+changes okay
+so you know if if I if I originally
+
+ align:start position:0%
+so you know if if I if I originally
+ 
+
+ align:start position:0%
+so you know if if I if I originally
+picked the Fair coin with very high
+
+ align:start position:0%
+picked the Fair coin with very high
+ 
+
+ align:start position:0%
+picked the Fair coin with very high
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+right uh and then I observe a heads
+
+ align:start position:0%
+right uh and then I observe a heads
+ 
+
+ align:start position:0%
+right uh and then I observe a heads
+right do you think the uh probability
+
+ align:start position:0%
+right do you think the uh probability
+ 
+
+ align:start position:0%
+right do you think the uh probability
+that a the the posterior probability
+
+ align:start position:0%
+that a the the posterior probability
+ 
+
+ align:start position:0%
+that a the the posterior probability
+should be the same higher or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lower oh yeah how did we get a third oh
+
+ align:start position:0%
+lower oh yeah how did we get a third oh
+ 
+
+ align:start position:0%
+lower oh yeah how did we get a third oh
+question how did we get a
+
+ align:start position:0%
+question how did we get a
+ 
+
+ align:start position:0%
+question how did we get a
+third uh so the ratio of this to its
+
+ align:start position:0%
+third uh so the ratio of this to its
+ 
+
+ align:start position:0%
+third uh so the ratio of this to its
+complement is 12 right they sum to one
+
+ align:start position:0%
+complement is 12 right they sum to one
+ 
+
+ align:start position:0%
+complement is 12 right they sum to one
+right so they're 1/3 and 2/3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah the numerical values of h and
+
+ align:start position:0%
+yeah the numerical values of h and
+ 
+
+ align:start position:0%
+yeah the numerical values of h and
+f uh so h and f are events they're not
+
+ align:start position:0%
+f uh so h and f are events they're not
+ 
+
+ align:start position:0%
+f uh so h and f are events they're not
+uh they're not numbers
+
+ align:start position:0%
+uh they're not numbers
+ 
+
+ align:start position:0%
+uh they're not numbers
+exactly right so you know H is the event
+
+ align:start position:0%
+exactly right so you know H is the event
+ 
+
+ align:start position:0%
+exactly right so you know H is the event
+that you know whichever coin I flipped
+
+ align:start position:0%
+that you know whichever coin I flipped
+ 
+
+ align:start position:0%
+that you know whichever coin I flipped
+uh I got a heads on
+
+ align:start position:0%
+uh I got a heads on
+ 
+
+ align:start position:0%
+uh I got a heads on
+it right
+
+ align:start position:0%
+it right
+ 
+
+ align:start position:0%
+it right
+and F is the event that the the coin I
+
+ align:start position:0%
+and F is the event that the the coin I
+ 
+
+ align:start position:0%
+and F is the event that the the coin I
+picked was the Fair
+
+ align:start position:0%
+picked was the Fair
+ 
+
+ align:start position:0%
+picked was the Fair
+one okay so they're not really numbers
+
+ align:start position:0%
+one okay so they're not really numbers
+ 
+
+ align:start position:0%
+one okay so they're not really numbers
+they're just you know sets of outcomes
+
+ align:start position:0%
+they're just you know sets of outcomes
+ 
+
+ align:start position:0%
+they're just you know sets of outcomes
+that could have
+
+ align:start position:0%
+that could have
+ 
+
+ align:start position:0%
+that could have
+happened okay
+
+ align:start position:0%
+happened okay
+ 
+
+ align:start position:0%
+happened okay
+yeah oh the assumptions right so um you
+
+ align:start position:0%
+yeah oh the assumptions right so um you
+ 
+
+ align:start position:0%
+yeah oh the assumptions right so um you
+know pick uh
+
+ align:start position:0%
+know pick uh
+ 
+
+ align:start position:0%
+know pick uh
+fair or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+biased uh uniformly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then uh flip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so fair means it comes up with 5050
+
+ align:start position:0%
+it so fair means it comes up with 5050
+ 
+
+ align:start position:0%
+it so fair means it comes up with 5050
+you know heads or tails biased it's a
+
+ align:start position:0%
+you know heads or tails biased it's a
+ 
+
+ align:start position:0%
+you know heads or tails biased it's a
+two-headed
+
+ align:start position:0%
+two-headed
+ 
+
+ align:start position:0%
+two-headed
+coin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yeah uh explain where the one/ third
+
+ align:start position:0%
+yeah uh explain where the one/ third
+ 
+
+ align:start position:0%
+yeah uh explain where the one/ third
+came from again okay so uh the
+
+ align:start position:0%
+came from again okay so uh the
+ 
+
+ align:start position:0%
+came from again okay so uh the
+probability of f given H over not F
+
+ align:start position:0%
+probability of f given H over not F
+ 
+
+ align:start position:0%
+probability of f given H over not F
+given h
+
+ align:start position:0%
+given h
+ 
+
+ align:start position:0%
+given h
+right these are complimentary
+
+ align:start position:0%
+right these are complimentary
+ 
+
+ align:start position:0%
+right these are complimentary
+probabilities they should sum to one
+
+ align:start position:0%
+probabilities they should sum to one
+ 
+
+ align:start position:0%
+probabilities they should sum to one
+okay so we figured that the ratio right
+
+ align:start position:0%
+okay so we figured that the ratio right
+ 
+
+ align:start position:0%
+okay so we figured that the ratio right
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh2 okay so you know if we want them to
+
+ align:start position:0%
+uh2 okay so you know if we want them to
+ 
+
+ align:start position:0%
+uh2 okay so you know if we want them to
+to sum to one then then they should be
+
+ align:start position:0%
+to sum to one then then they should be
+ 
+
+ align:start position:0%
+to sum to one then then they should be
+1/3 and
+
+ align:start position:0%
+1/3 and
+ 
+
+ align:start position:0%
+1/3 and
+2/3 okay does does that make sense
+
+ align:start position:0%
+2/3 okay does does that make sense
+ 
+
+ align:start position:0%
+2/3 okay does does that make sense
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry oh question if it's biased do we
+
+ align:start position:0%
+sorry oh question if it's biased do we
+ 
+
+ align:start position:0%
+sorry oh question if it's biased do we
+care in which direction it's biased uh
+
+ align:start position:0%
+care in which direction it's biased uh
+ 
+
+ align:start position:0%
+care in which direction it's biased uh
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+absolutely so if it's you know a double
+
+ align:start position:0%
+absolutely so if it's you know a double
+ 
+
+ align:start position:0%
+absolutely so if it's you know a double
+tailed coin instead of a double heads
+
+ align:start position:0%
+tailed coin instead of a double heads
+ 
+
+ align:start position:0%
+tailed coin instead of a double heads
+coin right you know if I observe a heads
+
+ align:start position:0%
+coin right you know if I observe a heads
+ 
+
+ align:start position:0%
+coin right you know if I observe a heads
+it must be the Fair coin right because
+
+ align:start position:0%
+it must be the Fair coin right because
+ 
+
+ align:start position:0%
+it must be the Fair coin right because
+the the double Tales coin cannot get a
+
+ align:start position:0%
+the the double Tales coin cannot get a
+ 
+
+ align:start position:0%
+the the double Tales coin cannot get a
+heads right so then my probability is
+
+ align:start position:0%
+heads right so then my probability is
+ 
+
+ align:start position:0%
+heads right so then my probability is
+just one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay are people reasonably happy with
+
+ align:start position:0%
+okay are people reasonably happy with
+ 
+
+ align:start position:0%
+okay are people reasonably happy with
+this example shall we move on to a
+
+ align:start position:0%
+this example shall we move on to a
+ 
+
+ align:start position:0%
+this example shall we move on to a
+second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay second example Co testing woohoo
+
+ align:start position:0%
+okay second example Co testing woohoo
+ 
+
+ align:start position:0%
+okay second example Co testing woohoo
+everybody loves Co testing right oh I
+
+ align:start position:0%
+everybody loves Co testing right oh I
+ 
+
+ align:start position:0%
+everybody loves Co testing right oh I
+suppose you most of you probably weren't
+
+ align:start position:0%
+suppose you most of you probably weren't
+ 
+
+ align:start position:0%
+suppose you most of you probably weren't
+here when there were those like you know
+
+ align:start position:0%
+here when there were those like you know
+ 
+
+ align:start position:0%
+here when there were those like you know
+daily or near daily nasal swabs right
+
+ align:start position:0%
+daily or near daily nasal swabs right
+ 
+
+ align:start position:0%
+daily or near daily nasal swabs right
+well those those were fun times okay
+
+ align:start position:0%
+well those those were fun times okay
+ 
+
+ align:start position:0%
+well those those were fun times okay
+um so in the next next couple of
+
+ align:start position:0%
+um so in the next next couple of
+ 
+
+ align:start position:0%
+um so in the next next couple of
+examples we're going to see some you
+
+ align:start position:0%
+examples we're going to see some you
+ 
+
+ align:start position:0%
+examples we're going to see some you
+know rather counterintuitive behavior
+
+ align:start position:0%
+know rather counterintuitive behavior
+ 
+
+ align:start position:0%
+know rather counterintuitive behavior
+that uh arises from base rule okay
+
+ align:start position:0%
+that uh arises from base rule okay
+ 
+
+ align:start position:0%
+that uh arises from base rule okay
+so you know you just as we were
+
+ align:start position:0%
+so you know you just as we were
+ 
+
+ align:start position:0%
+so you know you just as we were
+discussing last time you kind of want to
+
+ align:start position:0%
+discussing last time you kind of want to
+ 
+
+ align:start position:0%
+discussing last time you kind of want to
+throw away uh intuitive reasoning and
+
+ align:start position:0%
+throw away uh intuitive reasoning and
+ 
+
+ align:start position:0%
+throw away uh intuitive reasoning and
+you know just go with the numbers okay
+
+ align:start position:0%
+you know just go with the numbers okay
+ 
+
+ align:start position:0%
+you know just go with the numbers okay
+so suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10% of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MIT has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Co
+
+ align:start position:0%
+Co
+ 
+
+ align:start position:0%
+Co
+okay uh and everybody has to take a
+
+ align:start position:0%
+okay uh and everybody has to take a
+ 
+
+ align:start position:0%
+okay uh and everybody has to take a
+covid test okay uh they have a false
+
+ align:start position:0%
+covid test okay uh they have a false
+ 
+
+ align:start position:0%
+covid test okay uh they have a false
+positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate uh uh of uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+30% and false negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate of
+
+ align:start position:0%
+rate of
+ 
+
+ align:start position:0%
+rate of
+10% okay so false positive rate means
+
+ align:start position:0%
+10% okay so false positive rate means
+ 
+
+ align:start position:0%
+10% okay so false positive rate means
+you know uh if I'm am healthy and I take
+
+ align:start position:0%
+you know uh if I'm am healthy and I take
+ 
+
+ align:start position:0%
+you know uh if I'm am healthy and I take
+a covid test there's a 30% chance that
+
+ align:start position:0%
+a covid test there's a 30% chance that
+ 
+
+ align:start position:0%
+a covid test there's a 30% chance that
+it's going to be wrong and it's going to
+
+ align:start position:0%
+it's going to be wrong and it's going to
+ 
+
+ align:start position:0%
+it's going to be wrong and it's going to
+say that I'm I have Co okay okay so it's
+
+ align:start position:0%
+say that I'm I have Co okay okay so it's
+ 
+
+ align:start position:0%
+say that I'm I have Co okay okay so it's
+it's falsely reporting a positive
+
+ align:start position:0%
+it's falsely reporting a positive
+ 
+
+ align:start position:0%
+it's falsely reporting a positive
+positive result uh and false negative is
+
+ align:start position:0%
+positive result uh and false negative is
+ 
+
+ align:start position:0%
+positive result uh and false negative is
+the opposite so if I'm sick and I take a
+
+ align:start position:0%
+the opposite so if I'm sick and I take a
+ 
+
+ align:start position:0%
+the opposite so if I'm sick and I take a
+covid test there is a 10% chance that it
+
+ align:start position:0%
+covid test there is a 10% chance that it
+ 
+
+ align:start position:0%
+covid test there is a 10% chance that it
+does not detect it and it reports that
+
+ align:start position:0%
+does not detect it and it reports that
+ 
+
+ align:start position:0%
+does not detect it and it reports that
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+healthy okay do does the setup make
+
+ align:start position:0%
+healthy okay do does the setup make
+ 
+
+ align:start position:0%
+healthy okay do does the setup make
+sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh uh question was are the false
+
+ align:start position:0%
+yeah oh uh question was are the false
+ 
+
+ align:start position:0%
+yeah oh uh question was are the false
+positives included in the 10% or is the
+
+ align:start position:0%
+positives included in the 10% or is the
+ 
+
+ align:start position:0%
+positives included in the 10% or is the
+10% when you actually have it uh so this
+
+ align:start position:0%
+10% when you actually have it uh so this
+ 
+
+ align:start position:0%
+10% when you actually have it uh so this
+10% is you know conditioned on being
+
+ align:start position:0%
+10% is you know conditioned on being
+ 
+
+ align:start position:0%
+10% is you know conditioned on being
+sick okay the conditional probability
+
+ align:start position:0%
+sick okay the conditional probability
+ 
+
+ align:start position:0%
+sick okay the conditional probability
+that it gets it wrong is
+
+ align:start position:0%
+that it gets it wrong is
+ 
+
+ align:start position:0%
+that it gets it wrong is
+10% and the false positive rate is
+
+ align:start position:0%
+10% and the false positive rate is
+ 
+
+ align:start position:0%
+10% and the false positive rate is
+conditioned on being oh sorry false
+
+ align:start position:0%
+conditioned on being oh sorry false
+ 
+
+ align:start position:0%
+conditioned on being oh sorry false
+negative is conditioned on being healthy
+
+ align:start position:0%
+negative is conditioned on being healthy
+ 
+
+ align:start position:0%
+negative is conditioned on being healthy
+false positive is conditioned on being
+
+ align:start position:0%
+false positive is conditioned on being
+ 
+
+ align:start position:0%
+false positive is conditioned on being
+sick
+
+ align:start position:0%
+sick
+ 
+
+ align:start position:0%
+sick
+no no positive positive is sick yeah it
+
+ align:start position:0%
+no no positive positive is sick yeah it
+ 
+
+ align:start position:0%
+no no positive positive is sick yeah it
+was right the first time sorry I'm I'm
+
+ align:start position:0%
+was right the first time sorry I'm I'm
+ 
+
+ align:start position:0%
+was right the first time sorry I'm I'm
+confused uh yeah so these are both
+
+ align:start position:0%
+confused uh yeah so these are both
+ 
+
+ align:start position:0%
+confused uh yeah so these are both
+talking about conditional probabilities
+
+ align:start position:0%
+talking about conditional probabilities
+ 
+
+ align:start position:0%
+talking about conditional probabilities
+okay conditioned on being healthy or
+
+ align:start position:0%
+okay conditioned on being healthy or
+ 
+
+ align:start position:0%
+okay conditioned on being healthy or
+sick what's the probability that the
+
+ align:start position:0%
+sick what's the probability that the
+ 
+
+ align:start position:0%
+sick what's the probability that the
+test is accurate or wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's define some
+
+ align:start position:0%
+okay so let's define some
+ 
+
+ align:start position:0%
+okay so let's define some
+events let's say that H is you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+healthy uh and S can be its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complement
+
+ align:start position:0%
+complement
+ 
+
+ align:start position:0%
+complement
+sick uh plus is going to be positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result and minus is going to be a
+
+ align:start position:0%
+result and minus is going to be a
+ 
+
+ align:start position:0%
+result and minus is going to be a
+negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so suppose I take this covid test
+
+ align:start position:0%
+okay so suppose I take this covid test
+ 
+
+ align:start position:0%
+okay so suppose I take this covid test
+and it comes out
+
+ align:start position:0%
+and it comes out
+ 
+
+ align:start position:0%
+and it comes out
+positive okay what's the probability
+
+ align:start position:0%
+positive okay what's the probability
+ 
+
+ align:start position:0%
+positive okay what's the probability
+that I have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+covid so first what is the probability
+
+ align:start position:0%
+covid so first what is the probability
+ 
+
+ align:start position:0%
+covid so first what is the probability
+that we're trying to compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah probability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unconditionally yeah so s given positive
+
+ align:start position:0%
+unconditionally yeah so s given positive
+ 
+
+ align:start position:0%
+unconditionally yeah so s given positive
+right the unconditional probability of s
+
+ align:start position:0%
+right the unconditional probability of s
+ 
+
+ align:start position:0%
+right the unconditional probability of s
+is just 10% by assumption okay what
+
+ align:start position:0%
+is just 10% by assumption okay what
+ 
+
+ align:start position:0%
+is just 10% by assumption okay what
+we're actually looking for is the
+
+ align:start position:0%
+we're actually looking for is the
+ 
+
+ align:start position:0%
+we're actually looking for is the
+probability of uh probability that I'm
+
+ align:start position:0%
+probability of uh probability that I'm
+ 
+
+ align:start position:0%
+probability of uh probability that I'm
+sick given that I tested positive okay
+
+ align:start position:0%
+sick given that I tested positive okay
+ 
+
+ align:start position:0%
+sick given that I tested positive okay
+because that's the observation that we
+
+ align:start position:0%
+because that's the observation that we
+ 
+
+ align:start position:0%
+because that's the observation that we
+made okay so how would we compute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this well let's do the same thing we
+
+ align:start position:0%
+this well let's do the same thing we
+ 
+
+ align:start position:0%
+this well let's do the same thing we
+just did over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here let's look at the ratio of this
+
+ align:start position:0%
+here let's look at the ratio of this
+ 
+
+ align:start position:0%
+here let's look at the ratio of this
+probability to its
+
+ align:start position:0%
+probability to its
+ 
+
+ align:start position:0%
+probability to its
+complement
+
+ align:start position:0%
+complement
+ 
+
+ align:start position:0%
+complement
+okay and and applies apply base
+
+ align:start position:0%
+okay and and applies apply base
+ 
+
+ align:start position:0%
+okay and and applies apply base
+rule so we're going to flip this uh
+
+ align:start position:0%
+rule so we're going to flip this uh
+ 
+
+ align:start position:0%
+rule so we're going to flip this uh
+conditional
+
+ align:start position:0%
+conditional
+ 
+
+ align:start position:0%
+conditional
+here positive given sick times
+
+ align:start position:0%
+here positive given sick times
+ 
+
+ align:start position:0%
+here positive given sick times
+probability of
+
+ align:start position:0%
+probability of
+ 
+
+ align:start position:0%
+probability of
+sick divided by probability of positive
+
+ align:start position:0%
+sick divided by probability of positive
+ 
+
+ align:start position:0%
+sick divided by probability of positive
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+healthy times probability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+healthy
+
+ align:start position:0%
+healthy
+ 
+
+ align:start position:0%
+healthy
+okay now those four probabilities are
+
+ align:start position:0%
+okay now those four probabilities are
+ 
+
+ align:start position:0%
+okay now those four probabilities are
+probab that we know okay what are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they what's the probability of plus
+
+ align:start position:0%
+they what's the probability of plus
+ 
+
+ align:start position:0%
+they what's the probability of plus
+given that I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sick
+
+ align:start position:0%
+sick
+ 
+
+ align:start position:0%
+sick
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+90% so let's write that as 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n what's the uh prior probability that
+
+ align:start position:0%
+n what's the uh prior probability that
+ 
+
+ align:start position:0%
+n what's the uh prior probability that
+I'm sick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10% and now what's the probability of a
+
+ align:start position:0%
+10% and now what's the probability of a
+ 
+
+ align:start position:0%
+10% and now what's the probability of a
+positive result condition on being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+healthy
+
+ align:start position:0%
+healthy
+ 
+
+ align:start position:0%
+healthy
+yeah yeah that's the false positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate3 times and what's the probability
+
+ align:start position:0%
+rate3 times and what's the probability
+ 
+
+ align:start position:0%
+rate3 times and what's the probability
+that I'm healthy the prior probility of
+
+ align:start position:0%
+that I'm healthy the prior probility of
+ 
+
+ align:start position:0%
+that I'm healthy the prior probility of
+I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+healthy well that's just going to be the
+
+ align:start position:0%
+healthy well that's just going to be the
+ 
+
+ align:start position:0%
+healthy well that's just going to be the
+complement of the uh the event that I'm
+
+ align:start position:0%
+complement of the uh the event that I'm
+ 
+
+ align:start position:0%
+complement of the uh the event that I'm
+sick so that's going to
+
+ align:start position:0%
+sick so that's going to
+ 
+
+ align:start position:0%
+sick so that's going to
+be.
+
+ align:start position:0%
+be.
+ 
+
+ align:start position:0%
+be.
+n okay so these NS
+
+ align:start position:0%
+n okay so these NS
+ 
+
+ align:start position:0%
+n okay so these NS
+cancel this is going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1/3 okay so I am 1/3 as likely to be
+
+ align:start position:0%
+1/3 okay so I am 1/3 as likely to be
+ 
+
+ align:start position:0%
+1/3 okay so I am 1/3 as likely to be
+sick as healthy so the probability that
+
+ align:start position:0%
+sick as healthy so the probability that
+ 
+
+ align:start position:0%
+sick as healthy so the probability that
+I'm sick condition on getting the
+
+ align:start position:0%
+I'm sick condition on getting the
+ 
+
+ align:start position:0%
+I'm sick condition on getting the
+positive result is actually only one and
+
+ align:start position:0%
+positive result is actually only one and
+ 
+
+ align:start position:0%
+positive result is actually only one and
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so probability s given
+
+ align:start position:0%
+so probability s given
+ 
+
+ align:start position:0%
+so probability s given
+plus equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1/4 does that make sense to
+
+ align:start position:0%
+1/4 does that make sense to
+ 
+
+ align:start position:0%
+1/4 does that make sense to
+everybody so it might seem a little bit
+
+ align:start position:0%
+everybody so it might seem a little bit
+ 
+
+ align:start position:0%
+everybody so it might seem a little bit
+weird right like uh uh you know this
+
+ align:start position:0%
+weird right like uh uh you know this
+ 
+
+ align:start position:0%
+weird right like uh uh you know this
+this test is a pretty good one right
+
+ align:start position:0%
+this test is a pretty good one right
+ 
+
+ align:start position:0%
+this test is a pretty good one right
+like it's usually giving the right
+
+ align:start position:0%
+like it's usually giving the right
+ 
+
+ align:start position:0%
+like it's usually giving the right
+answer but you know I took the test I
+
+ align:start position:0%
+answer but you know I took the test I
+ 
+
+ align:start position:0%
+answer but you know I took the test I
+got a positive result but I'm still
+
+ align:start position:0%
+got a positive result but I'm still
+ 
+
+ align:start position:0%
+got a positive result but I'm still
+probably healthy why is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that can anybody explain what's going on
+
+ align:start position:0%
+that can anybody explain what's going on
+ 
+
+ align:start position:0%
+that can anybody explain what's going on
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah exactly so that there's a very
+
+ align:start position:0%
+yeah yeah exactly so that there's a very
+ 
+
+ align:start position:0%
+yeah yeah exactly so that there's a very
+slim chance that I'd Co to begin with so
+
+ align:start position:0%
+slim chance that I'd Co to begin with so
+ 
+
+ align:start position:0%
+slim chance that I'd Co to begin with so
+it's actually much higher now that I've
+
+ align:start position:0%
+it's actually much higher now that I've
+ 
+
+ align:start position:0%
+it's actually much higher now that I've
+got a positive result but the uh the the
+
+ align:start position:0%
+got a positive result but the uh the the
+ 
+
+ align:start position:0%
+got a positive result but the uh the the
+prior was kind of overwhelmingly in
+
+ align:start position:0%
+prior was kind of overwhelmingly in
+ 
+
+ align:start position:0%
+prior was kind of overwhelmingly in
+favor of being healthy and so it's still
+
+ align:start position:0%
+favor of being healthy and so it's still
+ 
+
+ align:start position:0%
+favor of being healthy and so it's still
+you know very likely that I'm healthy
+
+ align:start position:0%
+you know very likely that I'm healthy
+ 
+
+ align:start position:0%
+you know very likely that I'm healthy
+just you know slightly less
+
+ align:start position:0%
+just you know slightly less
+ 
+
+ align:start position:0%
+just you know slightly less
+so okay so often people kind of
+
+ align:start position:0%
+so okay so often people kind of
+ 
+
+ align:start position:0%
+so okay so often people kind of
+underestimate the uh uh the impact of
+
+ align:start position:0%
+underestimate the uh uh the impact of
+ 
+
+ align:start position:0%
+underestimate the uh uh the impact of
+the prior in this way okay uh of course
+
+ align:start position:0%
+the prior in this way okay uh of course
+ 
+
+ align:start position:0%
+the prior in this way okay uh of course
+in the real world you generally don't uh
+
+ align:start position:0%
+in the real world you generally don't uh
+ 
+
+ align:start position:0%
+in the real world you generally don't uh
+do this so if you get a positive result
+
+ align:start position:0%
+do this so if you get a positive result
+ 
+
+ align:start position:0%
+do this so if you get a positive result
+uh you can be more confident in it
+
+ align:start position:0%
+uh you can be more confident in it
+ 
+
+ align:start position:0%
+uh you can be more confident in it
+because you know normally you only test
+
+ align:start position:0%
+because you know normally you only test
+ 
+
+ align:start position:0%
+because you know normally you only test
+when you have symptoms right so the
+
+ align:start position:0%
+when you have symptoms right so the
+ 
+
+ align:start position:0%
+when you have symptoms right so the
+probability that you uh uh that you're
+
+ align:start position:0%
+probability that you uh uh that you're
+ 
+
+ align:start position:0%
+probability that you uh uh that you're
+sick given that you tested positive and
+
+ align:start position:0%
+sick given that you tested positive and
+ 
+
+ align:start position:0%
+sick given that you tested positive and
+you have symptoms that's probably going
+
+ align:start position:0%
+you have symptoms that's probably going
+ 
+
+ align:start position:0%
+you have symptoms that's probably going
+to be much higher than
+
+ align:start position:0%
+to be much higher than
+ 
+
+ align:start position:0%
+to be much higher than
+1/4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay are people happy with
+
+ align:start position:0%
+okay are people happy with
+ 
+
+ align:start position:0%
+okay are people happy with
+that yeah
+
+ align:start position:0%
+that yeah
+ 
+
+ align:start position:0%
+that yeah
+okay why don't we look at another
+
+ align:start position:0%
+okay why don't we look at another
+ 
+
+ align:start position:0%
+okay why don't we look at another
+interesting application called Simpsons
+
+ align:start position:0%
+interesting application called Simpsons
+ 
+
+ align:start position:0%
+interesting application called Simpsons
+paradox
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there's actually kind of a funny
+
+ align:start position:0%
+okay so there's actually kind of a funny
+ 
+
+ align:start position:0%
+okay so there's actually kind of a funny
+story behind this one uh so about 50
+
+ align:start position:0%
+story behind this one uh so about 50
+ 
+
+ align:start position:0%
+story behind this one uh so about 50
+years ago uh Berkeley UC Berkeley got
+
+ align:start position:0%
+years ago uh Berkeley UC Berkeley got
+ 
+
+ align:start position:0%
+years ago uh Berkeley UC Berkeley got
+sued right because uh you know that it
+
+ align:start position:0%
+sued right because uh you know that it
+ 
+
+ align:start position:0%
+sued right because uh you know that it
+was claimed that they were being very
+
+ align:start position:0%
+was claimed that they were being very
+ 
+
+ align:start position:0%
+was claimed that they were being very
+sexist in their admissions
+
+ align:start position:0%
+sexist in their admissions
+ 
+
+ align:start position:0%
+sexist in their admissions
+policies um and
+
+ align:start position:0%
+policies um and
+ 
+
+ align:start position:0%
+policies um and
+uh you know the
+
+ align:start position:0%
+uh you know the
+ 
+
+ align:start position:0%
+uh you know the
+claim was that the admissions rate was
+
+ align:start position:0%
+claim was that the admissions rate was
+ 
+
+ align:start position:0%
+claim was that the admissions rate was
+much higher for men than it was for
+
+ align:start position:0%
+much higher for men than it was for
+ 
+
+ align:start position:0%
+much higher for men than it was for
+women right so you know that's that's
+
+ align:start position:0%
+women right so you know that's that's
+ 
+
+ align:start position:0%
+women right so you know that's that's
+clearly bad right but then Berkeley
+
+ align:start position:0%
+clearly bad right but then Berkeley
+ 
+
+ align:start position:0%
+clearly bad right but then Berkeley
+counter claimed by saying that if you
+
+ align:start position:0%
+counter claimed by saying that if you
+ 
+
+ align:start position:0%
+counter claimed by saying that if you
+look at each individual Department it's
+
+ align:start position:0%
+look at each individual Department it's
+ 
+
+ align:start position:0%
+look at each individual Department it's
+actually the opposite like women are
+
+ align:start position:0%
+actually the opposite like women are
+ 
+
+ align:start position:0%
+actually the opposite like women are
+being admitted uh with much higher rates
+
+ align:start position:0%
+being admitted uh with much higher rates
+ 
+
+ align:start position:0%
+being admitted uh with much higher rates
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+men right so
+
+ align:start position:0%
+men right so
+ 
+
+ align:start position:0%
+men right so
+um what's going on was somebody lying
+
+ align:start position:0%
+um what's going on was somebody lying
+ 
+
+ align:start position:0%
+um what's going on was somebody lying
+can these both be true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah exactly so the uh the the
+
+ align:start position:0%
+yeah yeah exactly so the uh the the
+ 
+
+ align:start position:0%
+yeah yeah exactly so the uh the the
+observation right was that the sizes of
+
+ align:start position:0%
+observation right was that the sizes of
+ 
+
+ align:start position:0%
+observation right was that the sizes of
+the Departments could be very different
+
+ align:start position:0%
+the Departments could be very different
+ 
+
+ align:start position:0%
+the Departments could be very different
+right and what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so the the the admissions
+
+ align:start position:0%
+yeah yeah so the the the admissions
+ 
+
+ align:start position:0%
+yeah yeah so the the the admissions
+rates like the the the overall
+
+ align:start position:0%
+rates like the the the overall
+ 
+
+ align:start position:0%
+rates like the the the overall
+admissions rates for the Departments can
+
+ align:start position:0%
+admissions rates for the Departments can
+ 
+
+ align:start position:0%
+admissions rates for the Departments can
+also be very different right and so you
+
+ align:start position:0%
+also be very different right and so you
+ 
+
+ align:start position:0%
+also be very different right and so you
+know maybe you know there's some
+
+ align:start position:0%
+know maybe you know there's some
+ 
+
+ align:start position:0%
+know maybe you know there's some
+departments like you know let's let's
+
+ align:start position:0%
+departments like you know let's let's
+ 
+
+ align:start position:0%
+departments like you know let's let's
+take a look at a very simple example
+
+ align:start position:0%
+take a look at a very simple example
+ 
+
+ align:start position:0%
+take a look at a very simple example
+okay so suppose we have two departments
+
+ align:start position:0%
+okay so suppose we have two departments
+ 
+
+ align:start position:0%
+okay so suppose we have two departments
+e and
+
+ align:start position:0%
+e and
+ 
+
+ align:start position:0%
+e and
+CS
+
+ align:start position:0%
+CS
+ 
+
+ align:start position:0%
+CS
+okay right uh and you
+
+ align:start position:0%
+okay right uh and you
+ 
+
+ align:start position:0%
+okay right uh and you
+know maybe both of them mildly favor
+
+ align:start position:0%
+know maybe both of them mildly favor
+ 
+
+ align:start position:0%
+know maybe both of them mildly favor
+women okay but uh uh you know one of
+
+ align:start position:0%
+women okay but uh uh you know one of
+ 
+
+ align:start position:0%
+women okay but uh uh you know one of
+them is much more popular with men one
+
+ align:start position:0%
+them is much more popular with men one
+ 
+
+ align:start position:0%
+them is much more popular with men one
+of them is much more popular with women
+
+ align:start position:0%
+of them is much more popular with women
+ 
+
+ align:start position:0%
+of them is much more popular with women
+and they have very different admissions
+
+ align:start position:0%
+and they have very different admissions
+ 
+
+ align:start position:0%
+and they have very different admissions
+rates you know
+
+ align:start position:0%
+rates you know
+ 
+
+ align:start position:0%
+rates you know
+generally
+
+ align:start position:0%
+generally
+ 
+
+ align:start position:0%
+generally
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+maybe uh we have a 100 men and 100 women
+
+ align:start position:0%
+maybe uh we have a 100 men and 100 women
+ 
+
+ align:start position:0%
+maybe uh we have a 100 men and 100 women
+applying to you know this two Department
+
+ align:start position:0%
+applying to you know this two Department
+ 
+
+ align:start position:0%
+applying to you know this two Department
+UC
+
+ align:start position:0%
+UC
+ 
+
+ align:start position:0%
+UC
+Berkeley
+
+ align:start position:0%
+Berkeley
+ 
+
+ align:start position:0%
+Berkeley
+okay and uh maybe we have
+
+ align:start position:0%
+okay and uh maybe we have
+ 
+
+ align:start position:0%
+okay and uh maybe we have
+99 uh women and one man apply to
+
+ align:start position:0%
+99 uh women and one man apply to
+ 
+
+ align:start position:0%
+99 uh women and one man apply to
+Cs and in we it's the opposite one woman
+
+ align:start position:0%
+Cs and in we it's the opposite one woman
+ 
+
+ align:start position:0%
+Cs and in we it's the opposite one woman
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+men
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+uh in CS we're a bunch of snobs right we
+
+ align:start position:0%
+uh in CS we're a bunch of snobs right we
+ 
+
+ align:start position:0%
+uh in CS we're a bunch of snobs right we
+we hate everybody we take one
+
+ align:start position:0%
+we hate everybody we take one
+ 
+
+ align:start position:0%
+we hate everybody we take one
+applicant okay so maybe we take you know
+
+ align:start position:0%
+applicant okay so maybe we take you know
+ 
+
+ align:start position:0%
+applicant okay so maybe we take you know
+one woman
+
+ align:start position:0%
+one woman
+ 
+
+ align:start position:0%
+one woman
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+accepted everybody else is rejected
+
+ align:start position:0%
+accepted everybody else is rejected
+ 
+
+ align:start position:0%
+accepted everybody else is rejected
+okay uh and dou on the other hand has no
+
+ align:start position:0%
+okay uh and dou on the other hand has no
+ 
+
+ align:start position:0%
+okay uh and dou on the other hand has no
+standards at all they'll just take
+
+ align:start position:0%
+standards at all they'll just take
+ 
+
+ align:start position:0%
+standards at all they'll just take
+anybody with a pulse uh but
+
+ align:start position:0%
+anybody with a pulse uh but
+ 
+
+ align:start position:0%
+anybody with a pulse uh but
+unfortunately one of these men is dead
+
+ align:start position:0%
+unfortunately one of these men is dead
+ 
+
+ align:start position:0%
+unfortunately one of these men is dead
+so uh you know they take one woman and
+
+ align:start position:0%
+so uh you know they take one woman and
+ 
+
+ align:start position:0%
+so uh you know they take one woman and
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+men
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now if you look at the
+
+ align:start position:0%
+okay so now if you look at the
+ 
+
+ align:start position:0%
+okay so now if you look at the
+individual Department's admissions rates
+
+ align:start position:0%
+individual Department's admissions rates
+ 
+
+ align:start position:0%
+individual Department's admissions rates
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+uh CS has accepted a woman right so
+
+ align:start position:0%
+uh CS has accepted a woman right so
+ 
+
+ align:start position:0%
+uh CS has accepted a woman right so
+their their admissions rate for women is
+
+ align:start position:0%
+their their admissions rate for women is
+ 
+
+ align:start position:0%
+their their admissions rate for women is
+you know nonzero they haven't accepted
+
+ align:start position:0%
+you know nonzero they haven't accepted
+ 
+
+ align:start position:0%
+you know nonzero they haven't accepted
+any men so they've got a zero admissions
+
+ align:start position:0%
+any men so they've got a zero admissions
+ 
+
+ align:start position:0%
+any men so they've got a zero admissions
+rate for
+
+ align:start position:0%
+rate for
+ 
+
+ align:start position:0%
+rate for
+men so it's higher for
+
+ align:start position:0%
+men so it's higher for
+ 
+
+ align:start position:0%
+men so it's higher for
+women right and in E they've accepted
+
+ align:start position:0%
+women right and in E they've accepted
+ 
+
+ align:start position:0%
+women right and in E they've accepted
+all of the women but not all of the men
+
+ align:start position:0%
+all of the women but not all of the men
+ 
+
+ align:start position:0%
+all of the women but not all of the men
+so again it's higher for women but if
+
+ align:start position:0%
+so again it's higher for women but if
+ 
+
+ align:start position:0%
+so again it's higher for women but if
+you look at what's happened overall
+
+ align:start position:0%
+you look at what's happened overall
+ 
+
+ align:start position:0%
+you look at what's happened overall
+right we've got two women being accepted
+
+ align:start position:0%
+right we've got two women being accepted
+ 
+
+ align:start position:0%
+right we've got two women being accepted
+and 98 men
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so you can kind of argue that you
+
+ align:start position:0%
+right so you can kind of argue that you
+ 
+
+ align:start position:0%
+right so you can kind of argue that you
+know rather than being a problem with
+
+ align:start position:0%
+know rather than being a problem with
+ 
+
+ align:start position:0%
+know rather than being a problem with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+university uh or or the Departments it's
+
+ align:start position:0%
+university uh or or the Departments it's
+ 
+
+ align:start position:0%
+university uh or or the Departments it's
+kind of more of a systemic problem like
+
+ align:start position:0%
+kind of more of a systemic problem like
+ 
+
+ align:start position:0%
+kind of more of a systemic problem like
+uh you know maybe they're you know
+
+ align:start position:0%
+uh you know maybe they're you know
+ 
+
+ align:start position:0%
+uh you know maybe they're you know
+encouraging men and women to apply to uh
+
+ align:start position:0%
+encouraging men and women to apply to uh
+ 
+
+ align:start position:0%
+encouraging men and women to apply to uh
+different departments at different rates
+
+ align:start position:0%
+different departments at different rates
+ 
+
+ align:start position:0%
+different departments at different rates
+and uh you know it's all a bit messy and
+
+ align:start position:0%
+and uh you know it's all a bit messy and
+ 
+
+ align:start position:0%
+and uh you know it's all a bit messy and
+uh you know also this is 50 years ago so
+
+ align:start position:0%
+uh you know also this is 50 years ago so
+ 
+
+ align:start position:0%
+uh you know also this is 50 years ago so
+you know they only really considered men
+
+ align:start position:0%
+you know they only really considered men
+ 
+
+ align:start position:0%
+you know they only really considered men
+and women women didn't really you know
+
+ align:start position:0%
+and women women didn't really you know
+ 
+
+ align:start position:0%
+and women women didn't really you know
+consider anybody who you know identified
+
+ align:start position:0%
+consider anybody who you know identified
+ 
+
+ align:start position:0%
+consider anybody who you know identified
+as anything else but you know we're not
+
+ align:start position:0%
+as anything else but you know we're not
+ 
+
+ align:start position:0%
+as anything else but you know we're not
+saying anything about that this is just
+
+ align:start position:0%
+saying anything about that this is just
+ 
+
+ align:start position:0%
+saying anything about that this is just
+kind of uh to illustrate the math so
+
+ align:start position:0%
+kind of uh to illustrate the math so
+ 
+
+ align:start position:0%
+kind of uh to illustrate the math so
+hopefully it's not terribly
+
+ align:start position:0%
+hopefully it's not terribly
+ 
+
+ align:start position:0%
+hopefully it's not terribly
+offensive but yeah uh even though for
+
+ align:start position:0%
+offensive but yeah uh even though for
+ 
+
+ align:start position:0%
+offensive but yeah uh even though for
+each department the the women are doing
+
+ align:start position:0%
+each department the the women are doing
+ 
+
+ align:start position:0%
+each department the the women are doing
+better than men the men are doing much
+
+ align:start position:0%
+better than men the men are doing much
+ 
+
+ align:start position:0%
+better than men the men are doing much
+better overall okay so that's what we
+
+ align:start position:0%
+better overall okay so that's what we
+ 
+
+ align:start position:0%
+better overall okay so that's what we
+call simp Simpsons
+
+ align:start position:0%
+call simp Simpsons
+ 
+
+ align:start position:0%
+call simp Simpsons
+Paradox does anybody have any question
+
+ align:start position:0%
+Paradox does anybody have any question
+ 
+
+ align:start position:0%
+Paradox does anybody have any question
+questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay so last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example has anybody seen the dragon
+
+ align:start position:0%
+example has anybody seen the dragon
+ 
+
+ align:start position:0%
+example has anybody seen the dragon
+prins couple of hands okay well so last
+
+ align:start position:0%
+prins couple of hands okay well so last
+ 
+
+ align:start position:0%
+prins couple of hands okay well so last
+example uh suppose a cake has gone
+
+ align:start position:0%
+example uh suppose a cake has gone
+ 
+
+ align:start position:0%
+example uh suppose a cake has gone
+missing from the bakery and and uh you
+
+ align:start position:0%
+missing from the bakery and and uh you
+ 
+
+ align:start position:0%
+missing from the bakery and and uh you
+know barus the baker has has a prime
+
+ align:start position:0%
+know barus the baker has has a prime
+ 
+
+ align:start position:0%
+know barus the baker has has a prime
+suspect right he thinks that Prince ezin
+
+ align:start position:0%
+suspect right he thinks that Prince ezin
+ 
+
+ align:start position:0%
+suspect right he thinks that Prince ezin
+stole the
+
+ align:start position:0%
+stole the
+ 
+
+ align:start position:0%
+stole the
+cake
+
+ align:start position:0%
+cake
+ 
+
+ align:start position:0%
+cake
+uh and you know he wants to present
+
+ align:start position:0%
+uh and you know he wants to present
+ 
+
+ align:start position:0%
+uh and you know he wants to present
+evidence to the
+
+ align:start position:0%
+evidence to the
+ 
+
+ align:start position:0%
+evidence to the
+king he would like to tell the king that
+
+ align:start position:0%
+king he would like to tell the king that
+ 
+
+ align:start position:0%
+king he would like to tell the king that
+you know this this uh this deviant is
+
+ align:start position:0%
+you know this this uh this deviant is
+ 
+
+ align:start position:0%
+you know this this uh this deviant is
+always stealing jelly Tarts from my
+
+ align:start position:0%
+always stealing jelly Tarts from my
+ 
+
+ align:start position:0%
+always stealing jelly Tarts from my
+bakery you know that makes it much more
+
+ align:start position:0%
+bakery you know that makes it much more
+ 
+
+ align:start position:0%
+bakery you know that makes it much more
+likely that he stole the cake right like
+
+ align:start position:0%
+likely that he stole the cake right like
+ 
+
+ align:start position:0%
+likely that he stole the cake right like
+jelly tart thieves are you know 10 times
+
+ align:start position:0%
+jelly tart thieves are you know 10 times
+ 
+
+ align:start position:0%
+jelly tart thieves are you know 10 times
+as likely as randos to to steal cakes
+
+ align:start position:0%
+as likely as randos to to steal cakes
+ 
+
+ align:start position:0%
+as likely as randos to to steal cakes
+okay it seems Seems fairly reasonable
+
+ align:start position:0%
+okay it seems Seems fairly reasonable
+ 
+
+ align:start position:0%
+okay it seems Seems fairly reasonable
+right does does anybody think that this
+
+ align:start position:0%
+right does does anybody think that this
+ 
+
+ align:start position:0%
+right does does anybody think that this
+is a good reason to uh admit the jelly
+
+ align:start position:0%
+is a good reason to uh admit the jelly
+ 
+
+ align:start position:0%
+is a good reason to uh admit the jelly
+tart thevery into uh into
+
+ align:start position:0%
+tart thevery into uh into
+ 
+
+ align:start position:0%
+tart thevery into uh into
+evidence who thinks that it's not a
+
+ align:start position:0%
+evidence who thinks that it's not a
+ 
+
+ align:start position:0%
+evidence who thinks that it's not a
+compelling
+
+ align:start position:0%
+compelling
+ 
+
+ align:start position:0%
+compelling
+reason well who has no
+
+ align:start position:0%
+reason well who has no
+ 
+
+ align:start position:0%
+reason well who has no
+idea morans okay so uh maybe Prince
+
+ align:start position:0%
+idea morans okay so uh maybe Prince
+ 
+
+ align:start position:0%
+idea morans okay so uh maybe Prince
+cen's counter claim
+
+ align:start position:0%
+cen's counter claim
+ 
+
+ align:start position:0%
+cen's counter claim
+is well if you look at you know all
+
+ align:start position:0%
+is well if you look at you know all
+ 
+
+ align:start position:0%
+is well if you look at you know all
+jelly tart thieves you know only one in
+
+ align:start position:0%
+jelly tart thieves you know only one in
+ 
+
+ align:start position:0%
+jelly tart thieves you know only one in
+say 2500 of them actually go on to Steel
+
+ align:start position:0%
+say 2500 of them actually go on to Steel
+ 
+
+ align:start position:0%
+say 2500 of them actually go on to Steel
+cakes so like you know even though the
+
+ align:start position:0%
+cakes so like you know even though the
+ 
+
+ align:start position:0%
+cakes so like you know even though the
+probability of you know being a cake
+
+ align:start position:0%
+probability of you know being a cake
+ 
+
+ align:start position:0%
+probability of you know being a cake
+thief has you know increased
+
+ align:start position:0%
+thief has you know increased
+ 
+
+ align:start position:0%
+thief has you know increased
+dramatically from from the the Baseline
+
+ align:start position:0%
+dramatically from from the the Baseline
+ 
+
+ align:start position:0%
+dramatically from from the the Baseline
+in terms of like a multiplicative Factor
+
+ align:start position:0%
+in terms of like a multiplicative Factor
+ 
+
+ align:start position:0%
+in terms of like a multiplicative Factor
+it can't actually have increased very
+
+ align:start position:0%
+it can't actually have increased very
+ 
+
+ align:start position:0%
+it can't actually have increased very
+much because you know it went from 1
+
+ align:start position:0%
+much because you know it went from 1
+ 
+
+ align:start position:0%
+much because you know it went from 1
+125,000 to 1
+
+ align:start position:0%
+125,000 to 1
+ 
+
+ align:start position:0%
+125,000 to 1
+12500 right so the uh the probative
+
+ align:start position:0%
+12500 right so the uh the probative
+ 
+
+ align:start position:0%
+12500 right so the uh the probative
+value here is you know essentially zero
+
+ align:start position:0%
+value here is you know essentially zero
+ 
+
+ align:start position:0%
+value here is you know essentially zero
+right you're you're trying to prove
+
+ align:start position:0%
+right you're you're trying to prove
+ 
+
+ align:start position:0%
+right you're you're trying to prove
+guilt Beyond A Reasonable Doubt
+
+ align:start position:0%
+guilt Beyond A Reasonable Doubt
+ 
+
+ align:start position:0%
+guilt Beyond A Reasonable Doubt
+right and so a 1 in 2500 chance increase
+
+ align:start position:0%
+right and so a 1 in 2500 chance increase
+ 
+
+ align:start position:0%
+right and so a 1 in 2500 chance increase
+is kind of negligible but on the other
+
+ align:start position:0%
+is kind of negligible but on the other
+ 
+
+ align:start position:0%
+is kind of negligible but on the other
+hand you know if you admit this into
+
+ align:start position:0%
+hand you know if you admit this into
+ 
+
+ align:start position:0%
+hand you know if you admit this into
+evidence the king is going to be biased
+
+ align:start position:0%
+evidence the king is going to be biased
+ 
+
+ align:start position:0%
+evidence the king is going to be biased
+against ezren right he's going to be
+
+ align:start position:0%
+against ezren right he's going to be
+ 
+
+ align:start position:0%
+against ezren right he's going to be
+like oh this kid's a thief this is
+
+ align:start position:0%
+like oh this kid's a thief this is
+ 
+
+ align:start position:0%
+like oh this kid's a thief this is
+terrible we got to punish him right
+
+ align:start position:0%
+terrible we got to punish him right
+ 
+
+ align:start position:0%
+terrible we got to punish him right
+regardless of whether he stole the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cake so uh so who's right is is the
+
+ align:start position:0%
+cake so uh so who's right is is the
+ 
+
+ align:start position:0%
+cake so uh so who's right is is the
+baker right or is the uh is the suspect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right who thinks Baker is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right who think suspect is
+
+ align:start position:0%
+right who think suspect is
+ 
+
+ align:start position:0%
+right who think suspect is
+right who thinks
+
+ align:start position:0%
+right who thinks
+ 
+
+ align:start position:0%
+right who thinks
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+neither yeah I've got a few HS
+
+ align:start position:0%
+neither yeah I've got a few HS
+ 
+
+ align:start position:0%
+neither yeah I've got a few HS
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um well both parties here are trying to
+
+ align:start position:0%
+um well both parties here are trying to
+ 
+
+ align:start position:0%
+um well both parties here are trying to
+reason
+
+ align:start position:0%
+reason
+ 
+
+ align:start position:0%
+reason
+about uh a conditional
+
+ align:start position:0%
+about uh a conditional
+ 
+
+ align:start position:0%
+about uh a conditional
+probability okay what is that
+
+ align:start position:0%
+probability okay what is that
+ 
+
+ align:start position:0%
+probability okay what is that
+conditional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anybody well maybe we should start by
+
+ align:start position:0%
+anybody well maybe we should start by
+ 
+
+ align:start position:0%
+anybody well maybe we should start by
+writing out some
+
+ align:start position:0%
+writing out some
+ 
+
+ align:start position:0%
+writing out some
+events
+
+ align:start position:0%
+events
+ 
+
+ align:start position:0%
+events
+so let's let J be the event
+
+ align:start position:0%
+so let's let J be the event
+ 
+
+ align:start position:0%
+so let's let J be the event
+suspect
+
+ align:start position:0%
+suspect
+ 
+
+ align:start position:0%
+suspect
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+steals jelly tarts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh C can be the event suspect steals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cake and X can be the event cake was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stolen
+
+ align:start position:0%
+stolen
+ 
+
+ align:start position:0%
+stolen
+okay so both the Baker and the suspect
+
+ align:start position:0%
+okay so both the Baker and the suspect
+ 
+
+ align:start position:0%
+okay so both the Baker and the suspect
+we making claims about conditional
+
+ align:start position:0%
+we making claims about conditional
+ 
+
+ align:start position:0%
+we making claims about conditional
+probabilities what specific conditional
+
+ align:start position:0%
+probabilities what specific conditional
+ 
+
+ align:start position:0%
+probabilities what specific conditional
+probability in terms of these events
+
+ align:start position:0%
+probability in terms of these events
+ 
+
+ align:start position:0%
+probability in terms of these events
+were they making claims
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+sorry uh repeat the assertions oh the
+
+ align:start position:0%
+sorry uh repeat the assertions oh the
+ 
+
+ align:start position:0%
+sorry uh repeat the assertions oh the
+assumptions uh so the assumptions were
+
+ align:start position:0%
+assumptions uh so the assumptions were
+ 
+
+ align:start position:0%
+assumptions uh so the assumptions were
+right that a cake has gone missing from
+
+ align:start position:0%
+right that a cake has gone missing from
+ 
+
+ align:start position:0%
+right that a cake has gone missing from
+the bakery the baker has a prime suspect
+
+ align:start position:0%
+the bakery the baker has a prime suspect
+ 
+
+ align:start position:0%
+the bakery the baker has a prime suspect
+okay and the the Baker wants to admit
+
+ align:start position:0%
+okay and the the Baker wants to admit
+ 
+
+ align:start position:0%
+okay and the the Baker wants to admit
+into evidence that this suspect is
+
+ align:start position:0%
+into evidence that this suspect is
+ 
+
+ align:start position:0%
+into evidence that this suspect is
+always stealing jelly Tarts okay and the
+
+ align:start position:0%
+always stealing jelly Tarts okay and the
+ 
+
+ align:start position:0%
+always stealing jelly Tarts okay and the
+reasoning is that uh you know jelly tart
+
+ align:start position:0%
+reasoning is that uh you know jelly tart
+ 
+
+ align:start position:0%
+reasoning is that uh you know jelly tart
+thieves are much more likely to steal
+
+ align:start position:0%
+thieves are much more likely to steal
+ 
+
+ align:start position:0%
+thieves are much more likely to steal
+cakes than you know random other
+
+ align:start position:0%
+cakes than you know random other
+ 
+
+ align:start position:0%
+cakes than you know random other
+people okay and the suspect counters by
+
+ align:start position:0%
+people okay and the suspect counters by
+ 
+
+ align:start position:0%
+people okay and the suspect counters by
+saying well sure but like only one in
+
+ align:start position:0%
+saying well sure but like only one in
+ 
+
+ align:start position:0%
+saying well sure but like only one in
+2500 jelly tart thieves is actually a
+
+ align:start position:0%
+2500 jelly tart thieves is actually a
+ 
+
+ align:start position:0%
+2500 jelly tart thieves is actually a
+cake thief right so you know the actual
+
+ align:start position:0%
+cake thief right so you know the actual
+ 
+
+ align:start position:0%
+cake thief right so you know the actual
+increase is less than 1 in
+
+ align:start position:0%
+increase is less than 1 in
+ 
+
+ align:start position:0%
+increase is less than 1 in
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay so what are the probabilities that
+
+ align:start position:0%
+okay so what are the probabilities that
+ 
+
+ align:start position:0%
+okay so what are the probabilities that
+they're reasoning about what are the
+
+ align:start position:0%
+they're reasoning about what are the
+ 
+
+ align:start position:0%
+they're reasoning about what are the
+conditional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probabilities yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah well you're both right sorry it's
+
+ align:start position:0%
+yeah well you're both right sorry it's
+ 
+
+ align:start position:0%
+yeah well you're both right sorry it's
+um geometry they're both trying to
+
+ align:start position:0%
+um geometry they're both trying to
+ 
+
+ align:start position:0%
+um geometry they're both trying to
+reason about probability of C given J
+
+ align:start position:0%
+reason about probability of C given J
+ 
+
+ align:start position:0%
+reason about probability of C given J
+right you know so we're conditioning on
+
+ align:start position:0%
+right you know so we're conditioning on
+ 
+
+ align:start position:0%
+right you know so we're conditioning on
+the suspect having stolen jelly Tarts
+
+ align:start position:0%
+the suspect having stolen jelly Tarts
+ 
+
+ align:start position:0%
+the suspect having stolen jelly Tarts
+and they're both trying to make claims
+
+ align:start position:0%
+and they're both trying to make claims
+ 
+
+ align:start position:0%
+and they're both trying to make claims
+about you know what is the probability
+
+ align:start position:0%
+about you know what is the probability
+ 
+
+ align:start position:0%
+about you know what is the probability
+of C conditioned on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay
+
+ align:start position:0%
+that okay
+ 
+
+ align:start position:0%
+that okay
+so well the baker is arguing that
+
+ align:start position:0%
+so well the baker is arguing that
+ 
+
+ align:start position:0%
+so well the baker is arguing that
+probability of C given J divided by
+
+ align:start position:0%
+probability of C given J divided by
+ 
+
+ align:start position:0%
+probability of C given J divided by
+probability of C given not
+
+ align:start position:0%
+probability of C given not
+ 
+
+ align:start position:0%
+probability of C given not
+J is
+
+ align:start position:0%
+J is
+ 
+
+ align:start position:0%
+J is
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+right so you know because this is you
+
+ align:start position:0%
+right so you know because this is you
+ 
+
+ align:start position:0%
+right so you know because this is you
+know about 10 J is very relevant to the
+
+ align:start position:0%
+know about 10 J is very relevant to the
+ 
+
+ align:start position:0%
+know about 10 J is very relevant to the
+case so it should be
+
+ align:start position:0%
+case so it should be
+ 
+
+ align:start position:0%
+case so it should be
+admitted okay uh the suspect is saying
+
+ align:start position:0%
+admitted okay uh the suspect is saying
+ 
+
+ align:start position:0%
+admitted okay uh the suspect is saying
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+probability of C given
+
+ align:start position:0%
+probability of C given
+ 
+
+ align:start position:0%
+probability of C given
+J is low
+
+ align:start position:0%
+J is low
+ 
+
+ align:start position:0%
+J is low
+right so J cannot actually uh
+
+ align:start position:0%
+right so J cannot actually uh
+ 
+
+ align:start position:0%
+right so J cannot actually uh
+dramatically increase the
+
+ align:start position:0%
+dramatically increase the
+ 
+
+ align:start position:0%
+dramatically increase the
+probability right the increase is going
+
+ align:start position:0%
+probability right the increase is going
+ 
+
+ align:start position:0%
+probability right the increase is going
+to be less than this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so that's a good point um so the
+
+ align:start position:0%
+yeah so that's a good point um so the
+ 
+
+ align:start position:0%
+yeah so that's a good point um so the
+the point was that we're we're talking
+
+ align:start position:0%
+the point was that we're we're talking
+ 
+
+ align:start position:0%
+the point was that we're we're talking
+about you know one individual suspect
+
+ align:start position:0%
+about you know one individual suspect
+ 
+
+ align:start position:0%
+about you know one individual suspect
+one individual cake one individual case
+
+ align:start position:0%
+one individual cake one individual case
+ 
+
+ align:start position:0%
+one individual cake one individual case
+right so kind of as we were saying
+
+ align:start position:0%
+right so kind of as we were saying
+ 
+
+ align:start position:0%
+right so kind of as we were saying
+before when we first uh started looking
+
+ align:start position:0%
+before when we first uh started looking
+ 
+
+ align:start position:0%
+before when we first uh started looking
+at rule like you know either it happened
+
+ align:start position:0%
+at rule like you know either it happened
+ 
+
+ align:start position:0%
+at rule like you know either it happened
+or it didn't right like you could say
+
+ align:start position:0%
+or it didn't right like you could say
+ 
+
+ align:start position:0%
+or it didn't right like you could say
+that it doesn't make a whole lot of
+
+ align:start position:0%
+that it doesn't make a whole lot of
+ 
+
+ align:start position:0%
+that it doesn't make a whole lot of
+sense to talk about probabilities right
+
+ align:start position:0%
+sense to talk about probabilities right
+ 
+
+ align:start position:0%
+sense to talk about probabilities right
+but you know you're trying to convince
+
+ align:start position:0%
+but you know you're trying to convince
+ 
+
+ align:start position:0%
+but you know you're trying to convince
+you know the king or a jury or somebody
+
+ align:start position:0%
+you know the king or a jury or somebody
+ 
+
+ align:start position:0%
+you know the king or a jury or somebody
+right um so this is kind of you know
+
+ align:start position:0%
+right um so this is kind of you know
+ 
+
+ align:start position:0%
+right um so this is kind of you know
+similar to when you present DNA evidence
+
+ align:start position:0%
+similar to when you present DNA evidence
+ 
+
+ align:start position:0%
+similar to when you present DNA evidence
+in court or something like that uh like
+
+ align:start position:0%
+in court or something like that uh like
+ 
+
+ align:start position:0%
+in court or something like that uh like
+the fact that there's a match means that
+
+ align:start position:0%
+the fact that there's a match means that
+ 
+
+ align:start position:0%
+the fact that there's a match means that
+there's you know overwhelming
+
+ align:start position:0%
+there's you know overwhelming
+ 
+
+ align:start position:0%
+there's you know overwhelming
+probability that the uh the suspect was
+
+ align:start position:0%
+probability that the uh the suspect was
+ 
+
+ align:start position:0%
+probability that the uh the suspect was
+at the crime scene or something like
+
+ align:start position:0%
+at the crime scene or something like
+ 
+
+ align:start position:0%
+at the crime scene or something like
+that right so like you you do kind of
+
+ align:start position:0%
+that right so like you you do kind of
+ 
+
+ align:start position:0%
+that right so like you you do kind of
+still talk about
+
+ align:start position:0%
+still talk about
+ 
+
+ align:start position:0%
+still talk about
+probabilities uh but you could think of
+
+ align:start position:0%
+probabilities uh but you could think of
+ 
+
+ align:start position:0%
+probabilities uh but you could think of
+it as like you know how confident are
+
+ align:start position:0%
+it as like you know how confident are
+ 
+
+ align:start position:0%
+it as like you know how confident are
+you in the inference that uh that the
+
+ align:start position:0%
+you in the inference that uh that the
+ 
+
+ align:start position:0%
+you in the inference that uh that the
+suspect did something does that make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so if you were the judge in this case
+
+ align:start position:0%
+so so if you were the judge in this case
+ 
+
+ align:start position:0%
+so so if you were the judge in this case
+determining what should be presented to
+
+ align:start position:0%
+determining what should be presented to
+ 
+
+ align:start position:0%
+determining what should be presented to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+king what would your verdict
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be do do we allow jelly tart thievery
+
+ align:start position:0%
+be do do we allow jelly tart thievery
+ 
+
+ align:start position:0%
+be do do we allow jelly tart thievery
+into evidence or
+
+ align:start position:0%
+into evidence or
+ 
+
+ align:start position:0%
+into evidence or
+no pardon draw a tree diagram draw a
+
+ align:start position:0%
+no pardon draw a tree diagram draw a
+ 
+
+ align:start position:0%
+no pardon draw a tree diagram draw a
+tree diagram uh well that's not actually
+
+ align:start position:0%
+tree diagram uh well that's not actually
+ 
+
+ align:start position:0%
+tree diagram uh well that's not actually
+necessary anymore we've already figured
+
+ align:start position:0%
+necessary anymore we've already figured
+ 
+
+ align:start position:0%
+necessary anymore we've already figured
+out what the uh probabilities are the uh
+
+ align:start position:0%
+out what the uh probabilities are the uh
+ 
+
+ align:start position:0%
+out what the uh probabilities are the uh
+question is um you know is the probative
+
+ align:start position:0%
+question is um you know is the probative
+ 
+
+ align:start position:0%
+question is um you know is the probative
+value good enough to justify you know
+
+ align:start position:0%
+value good enough to justify you know
+ 
+
+ align:start position:0%
+value good enough to justify you know
+putting it into evidence or is the
+
+ align:start position:0%
+putting it into evidence or is the
+ 
+
+ align:start position:0%
+putting it into evidence or is the
+probative value small enough that the uh
+
+ align:start position:0%
+probative value small enough that the uh
+ 
+
+ align:start position:0%
+probative value small enough that the uh
+bias is going to be more more of a
+
+ align:start position:0%
+bias is going to be more more of a
+ 
+
+ align:start position:0%
+bias is going to be more more of a
+factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so it it it will not you know
+
+ align:start position:0%
+yeah so it it it will not you know
+ 
+
+ align:start position:0%
+yeah so it it it will not you know
+generally capture the full story and
+
+ align:start position:0%
+generally capture the full story and
+ 
+
+ align:start position:0%
+generally capture the full story and
+this is why you know lawyers in a
+
+ align:start position:0%
+this is why you know lawyers in a
+ 
+
+ align:start position:0%
+this is why you know lawyers in a
+courtroom are you know trying to find
+
+ align:start position:0%
+courtroom are you know trying to find
+ 
+
+ align:start position:0%
+courtroom are you know trying to find
+all kinds of evidence to uh to bolster
+
+ align:start position:0%
+all kinds of evidence to uh to bolster
+ 
+
+ align:start position:0%
+all kinds of evidence to uh to bolster
+their cases so yeah like something like
+
+ align:start position:0%
+their cases so yeah like something like
+ 
+
+ align:start position:0%
+their cases so yeah like something like
+that might be something that the uh the
+
+ align:start position:0%
+that might be something that the uh the
+ 
+
+ align:start position:0%
+that might be something that the uh the
+defense would want to uh would want to
+
+ align:start position:0%
+defense would want to uh would want to
+ 
+
+ align:start position:0%
+defense would want to uh would want to
+present um or the prosecution might be
+
+ align:start position:0%
+present um or the prosecution might be
+ 
+
+ align:start position:0%
+present um or the prosecution might be
+like oh but even though it's an MIT
+
+ align:start position:0%
+like oh but even though it's an MIT
+ 
+
+ align:start position:0%
+like oh but even though it's an MIT
+student like it's an it eecs student who
+
+ align:start position:0%
+student like it's an it eecs student who
+ 
+
+ align:start position:0%
+student like it's an it eecs student who
+do steel cakes all the time
+
+ align:start position:0%
+do steel cakes all the time
+ 
+
+ align:start position:0%
+do steel cakes all the time
+so I'm getting some uh some nods That's
+
+ align:start position:0%
+so I'm getting some uh some nods That's
+ 
+
+ align:start position:0%
+so I'm getting some uh some nods That's
+mildly
+
+ align:start position:0%
+mildly
+ 
+
+ align:start position:0%
+mildly
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+concerning so uh you know like yeah it's
+
+ align:start position:0%
+concerning so uh you know like yeah it's
+ 
+
+ align:start position:0%
+concerning so uh you know like yeah it's
+going to be very difficult to capture
+
+ align:start position:0%
+going to be very difficult to capture
+ 
+
+ align:start position:0%
+going to be very difficult to capture
+the entire picture um for right now
+
+ align:start position:0%
+the entire picture um for right now
+ 
+
+ align:start position:0%
+the entire picture um for right now
+we're just trying to limit the scope to
+
+ align:start position:0%
+we're just trying to limit the scope to
+ 
+
+ align:start position:0%
+we're just trying to limit the scope to
+like these are these are the things that
+
+ align:start position:0%
+like these are these are the things that
+ 
+
+ align:start position:0%
+like these are these are the things that
+are known right we we know that a cake
+
+ align:start position:0%
+are known right we we know that a cake
+ 
+
+ align:start position:0%
+are known right we we know that a cake
+is stolen we know that this suspect
+
+ align:start position:0%
+is stolen we know that this suspect
+ 
+
+ align:start position:0%
+is stolen we know that this suspect
+steals jelly Tarts uh but that's it like
+
+ align:start position:0%
+steals jelly Tarts uh but that's it like
+ 
+
+ align:start position:0%
+steals jelly Tarts uh but that's it like
+we we want to try and figure out you
+
+ align:start position:0%
+we we want to try and figure out you
+ 
+
+ align:start position:0%
+we we want to try and figure out you
+know what the the probative value of
+
+ align:start position:0%
+know what the the probative value of
+ 
+
+ align:start position:0%
+know what the the probative value of
+this evidence is uh just based on
+
+ align:start position:0%
+this evidence is uh just based on
+ 
+
+ align:start position:0%
+this evidence is uh just based on
+those does that make
+
+ align:start position:0%
+those does that make
+ 
+
+ align:start position:0%
+those does that make
+sense so who thinks who thinks the jelly
+
+ align:start position:0%
+sense so who thinks who thinks the jelly
+ 
+
+ align:start position:0%
+sense so who thinks who thinks the jelly
+tart should be
+
+ align:start position:0%
+tart should be
+ 
+
+ align:start position:0%
+tart should be
+admitted who thinks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay I'm I'm I'm getting more hands
+
+ align:start position:0%
+no okay I'm I'm I'm getting more hands
+ 
+
+ align:start position:0%
+no okay I'm I'm I'm getting more hands
+this time less extensions okay does
+
+ align:start position:0%
+this time less extensions okay does
+ 
+
+ align:start position:0%
+this time less extensions okay does
+anybody want to say
+
+ align:start position:0%
+anybody want to say
+ 
+
+ align:start position:0%
+anybody want to say
+why yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mhm yeah so the the observation rate was
+
+ align:start position:0%
+mhm yeah so the the observation rate was
+ 
+
+ align:start position:0%
+mhm yeah so the the observation rate was
+uh you know the probability of C given
+
+ align:start position:0%
+uh you know the probability of C given
+ 
+
+ align:start position:0%
+uh you know the probability of C given
+not J is also very low right and in fact
+
+ align:start position:0%
+not J is also very low right and in fact
+ 
+
+ align:start position:0%
+not J is also very low right and in fact
+it is much lower than than C given J um
+
+ align:start position:0%
+it is much lower than than C given J um
+ 
+
+ align:start position:0%
+it is much lower than than C given J um
+so that's kind of where this this uh the
+
+ align:start position:0%
+so that's kind of where this this uh the
+ 
+
+ align:start position:0%
+so that's kind of where this this uh the
+the ratio there probability of C given J
+
+ align:start position:0%
+the ratio there probability of C given J
+ 
+
+ align:start position:0%
+the ratio there probability of C given J
+over C given not J is coming from right
+
+ align:start position:0%
+over C given not J is coming from right
+ 
+
+ align:start position:0%
+over C given not J is coming from right
+like uh probability of C given J is 1
+
+ align:start position:0%
+like uh probability of C given J is 1
+ 
+
+ align:start position:0%
+like uh probability of C given J is 1
+and 2500 probability of C given not J is
+
+ align:start position:0%
+and 2500 probability of C given not J is
+ 
+
+ align:start position:0%
+and 2500 probability of C given not J is
+1 and
+
+ align:start position:0%
+1 and
+ 
+
+ align:start position:0%
+1 and
+25,000 right so that's where you're
+
+ align:start position:0%
+25,000 right so that's where you're
+ 
+
+ align:start position:0%
+25,000 right so that's where you're
+getting this factor of
+
+ align:start position:0%
+getting this factor of
+ 
+
+ align:start position:0%
+getting this factor of
+10 so you you agree with the uh the
+
+ align:start position:0%
+10 so you you agree with the uh the
+ 
+
+ align:start position:0%
+10 so you you agree with the uh the
+defense that this should not be ad
+
+ align:start position:0%
+defense that this should not be ad
+ 
+
+ align:start position:0%
+defense that this should not be ad
+admitted into evidence okay does anybody
+
+ align:start position:0%
+admitted into evidence okay does anybody
+ 
+
+ align:start position:0%
+admitted into evidence okay does anybody
+have any Contra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claims
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so that's a good point we've
+
+ align:start position:0%
+yeah yeah so that's a good point we've
+ 
+
+ align:start position:0%
+yeah yeah so that's a good point we've
+uh we've kind of forgotten about
+
+ align:start position:0%
+uh we've kind of forgotten about
+ 
+
+ align:start position:0%
+uh we've kind of forgotten about
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right a cake was stolen right we don't
+
+ align:start position:0%
+right a cake was stolen right we don't
+ 
+
+ align:start position:0%
+right a cake was stolen right we don't
+care that the probability of cakes being
+
+ align:start position:0%
+care that the probability of cakes being
+ 
+
+ align:start position:0%
+care that the probability of cakes being
+stolen is low it it
+
+ align:start position:0%
+stolen is low it it
+ 
+
+ align:start position:0%
+stolen is low it it
+happened right
+
+ align:start position:0%
+happened right
+ 
+
+ align:start position:0%
+happened right
+so you know we we we don't really care
+
+ align:start position:0%
+so you know we we we don't really care
+ 
+
+ align:start position:0%
+so you know we we we don't really care
+about these probabilities at all what is
+
+ align:start position:0%
+about these probabilities at all what is
+ 
+
+ align:start position:0%
+about these probabilities at all what is
+the actual probability we care
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about what we really want is is
+
+ align:start position:0%
+about what we really want is is
+ 
+
+ align:start position:0%
+about what we really want is is
+probability of C given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah well not that they stole a cake but
+
+ align:start position:0%
+yeah well not that they stole a cake but
+ 
+
+ align:start position:0%
+yeah well not that they stole a cake but
+that a cake was stolen yeah so C given j
+
+ align:start position:0%
+that a cake was stolen yeah so C given j
+ 
+
+ align:start position:0%
+that a cake was stolen yeah so C given j
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+x okay so that's what we really care
+
+ align:start position:0%
+x okay so that's what we really care
+ 
+
+ align:start position:0%
+x okay so that's what we really care
+about right uh that the fact that the
+
+ align:start position:0%
+about right uh that the fact that the
+ 
+
+ align:start position:0%
+about right uh that the fact that the
+cake is stolen is really important right
+
+ align:start position:0%
+cake is stolen is really important right
+ 
+
+ align:start position:0%
+cake is stolen is really important right
+like if
+
+ align:start position:0%
+like if
+ 
+
+ align:start position:0%
+like if
+uh no if you don't know whether the cake
+
+ align:start position:0%
+uh no if you don't know whether the cake
+ 
+
+ align:start position:0%
+uh no if you don't know whether the cake
+is stolen right why are you even having
+
+ align:start position:0%
+is stolen right why are you even having
+ 
+
+ align:start position:0%
+is stolen right why are you even having
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trial and as it turns out this
+
+ align:start position:0%
+trial and as it turns out this
+ 
+
+ align:start position:0%
+trial and as it turns out this
+probability is something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+80% jelly tart thieves founded bakeries
+
+ align:start position:0%
+80% jelly tart thieves founded bakeries
+ 
+
+ align:start position:0%
+80% jelly tart thieves founded bakeries
+with missing cakes usually they're the
+
+ align:start position:0%
+with missing cakes usually they're the
+ 
+
+ align:start position:0%
+with missing cakes usually they're the
+guilty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+party um
+
+ align:start position:0%
+party um
+ 
+
+ align:start position:0%
+party um
+so yeah I've kind of made this a little
+
+ align:start position:0%
+so yeah I've kind of made this a little
+ 
+
+ align:start position:0%
+so yeah I've kind of made this a little
+bit more palatable but uh this is uh you
+
+ align:start position:0%
+bit more palatable but uh this is uh you
+ 
+
+ align:start position:0%
+bit more palatable but uh this is uh you
+know based on an actual courtroom case
+
+ align:start position:0%
+know based on an actual courtroom case
+ 
+
+ align:start position:0%
+know based on an actual courtroom case
+um like this this is the kind of thing
+
+ align:start position:0%
+um like this this is the kind of thing
+ 
+
+ align:start position:0%
+um like this this is the kind of thing
+that that people uh you know like people
+
+ align:start position:0%
+that that people uh you know like people
+ 
+
+ align:start position:0%
+that that people uh you know like people
+try and use and you know end up misusing
+
+ align:start position:0%
+try and use and you know end up misusing
+ 
+
+ align:start position:0%
+try and use and you know end up misusing
+probabilities and conditional
+
+ align:start position:0%
+probabilities and conditional
+ 
+
+ align:start position:0%
+probabilities and conditional
+probabilities all the time this was
+
+ align:start position:0%
+probabilities all the time this was
+ 
+
+ align:start position:0%
+probabilities all the time this was
+actually from a very high-profile case
+
+ align:start position:0%
+actually from a very high-profile case
+ 
+
+ align:start position:0%
+actually from a very high-profile case
+the OJ Simpson case um where both the
+
+ align:start position:0%
+the OJ Simpson case um where both the
+ 
+
+ align:start position:0%
+the OJ Simpson case um where both the
+defense and the prosecution attorneys
+
+ align:start position:0%
+defense and the prosecution attorneys
+ 
+
+ align:start position:0%
+defense and the prosecution attorneys
+like you know they're supposed to be
+
+ align:start position:0%
+like you know they're supposed to be
+ 
+
+ align:start position:0%
+like you know they're supposed to be
+experts uh but you know they were both
+
+ align:start position:0%
+experts uh but you know they were both
+ 
+
+ align:start position:0%
+experts uh but you know they were both
+making bogus claims about uh about
+
+ align:start position:0%
+making bogus claims about uh about
+ 
+
+ align:start position:0%
+making bogus claims about uh about
+conditional
+
+ align:start position:0%
+conditional
+ 
+
+ align:start position:0%
+conditional
+probabilities uh you know it's it's very
+
+ align:start position:0%
+probabilities uh you know it's it's very
+ 
+
+ align:start position:0%
+probabilities uh you know it's it's very
+easy to make these kinds of mistakes so
+
+ align:start position:0%
+easy to make these kinds of mistakes so
+ 
+
+ align:start position:0%
+easy to make these kinds of mistakes so
+you know fall back on fundamentals uh
+
+ align:start position:0%
+you know fall back on fundamentals uh
+ 
+
+ align:start position:0%
+you know fall back on fundamentals uh
+when you're an adult fall back on the
+
+ align:start position:0%
+when you're an adult fall back on the
+ 
+
+ align:start position:0%
+when you're an adult fall back on the
+fundamentals even if you're not it's
+
+ align:start position:0%
+fundamentals even if you're not it's
+ 
+
+ align:start position:0%
+fundamentals even if you're not it's
+probably a good idea anyway okay uh feel
+
+ align:start position:0%
+probably a good idea anyway okay uh feel
+ 
+
+ align:start position:0%
+probably a good idea anyway okay uh feel
+free to come up if you have any
+
+ align:start position:0%
+free to come up if you have any
+ 
+
+ align:start position:0%
+free to come up if you have any
+questions and uh otherwise we will see
+
+ align:start position:0%
+questions and uh otherwise we will see
+ 
+
+ align:start position:0%
+questions and uh otherwise we will see
+you next week
\ No newline at end of file
diff --git a/wrEcliDbXQk.txt b/wrEcliDbXQk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..53ee5aeabe292d37b4db76faa9da1f13945b8d3d
--- /dev/null
+++ b/wrEcliDbXQk.txt
@@ -0,0 +1,459 @@
+align:start position:0%
+ 
+the field of a square pair of coils can
+
+ align:start position:0%
+the field of a square pair of coils can
+ 
+
+ align:start position:0%
+the field of a square pair of coils can
+be found by using the biot-savart law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here are our square coils each with 50
+
+ align:start position:0%
+here are our square coils each with 50
+ 
+
+ align:start position:0%
+here are our square coils each with 50
+turns and sides of length 45 centimeters
+
+ align:start position:0%
+turns and sides of length 45 centimeters
+ 
+
+ align:start position:0%
+turns and sides of length 45 centimeters
+the axial magnetometer probe is mounted
+
+ align:start position:0%
+the axial magnetometer probe is mounted
+ 
+
+ align:start position:0%
+the axial magnetometer probe is mounted
+on this carriage to record the Z
+
+ align:start position:0%
+on this carriage to record the Z
+ 
+
+ align:start position:0%
+on this carriage to record the Z
+component of magnetic field before we
+
+ align:start position:0%
+component of magnetic field before we
+ 
+
+ align:start position:0%
+component of magnetic field before we
+apply current to the coils we have
+
+ align:start position:0%
+apply current to the coils we have
+ 
+
+ align:start position:0%
+apply current to the coils we have
+compensated for the small part of the
+
+ align:start position:0%
+compensated for the small part of the
+ 
+
+ align:start position:0%
+compensated for the small part of the
+Earth's magnetic field that is in the
+
+ align:start position:0%
+Earth's magnetic field that is in the
+ 
+
+ align:start position:0%
+Earth's magnetic field that is in the
+horizontal direction by zeroing the
+
+ align:start position:0%
+horizontal direction by zeroing the
+ 
+
+ align:start position:0%
+horizontal direction by zeroing the
+magnetometer the Earth's magnetic field
+
+ align:start position:0%
+magnetometer the Earth's magnetic field
+ 
+
+ align:start position:0%
+magnetometer the Earth's magnetic field
+is essentially vertical with the
+
+ align:start position:0%
+is essentially vertical with the
+ 
+
+ align:start position:0%
+is essentially vertical with the
+strength of about a half the Gauss and
+
+ align:start position:0%
+strength of about a half the Gauss and
+ 
+
+ align:start position:0%
+strength of about a half the Gauss and
+could contribute a slight error to the
+
+ align:start position:0%
+could contribute a slight error to the
+ 
+
+ align:start position:0%
+could contribute a slight error to the
+measurement if not accounted for a
+
+ align:start position:0%
+measurement if not accounted for a
+ 
+
+ align:start position:0%
+measurement if not accounted for a
+current of two and a half amperes is
+
+ align:start position:0%
+current of two and a half amperes is
+ 
+
+ align:start position:0%
+current of two and a half amperes is
+applied to the coils we have placed the
+
+ align:start position:0%
+applied to the coils we have placed the
+ 
+
+ align:start position:0%
+applied to the coils we have placed the
+theoretical variation of the magnetic
+
+ align:start position:0%
+theoretical variation of the magnetic
+ 
+
+ align:start position:0%
+theoretical variation of the magnetic
+field versus position Z as a solid line
+
+ align:start position:0%
+field versus position Z as a solid line
+ 
+
+ align:start position:0%
+field versus position Z as a solid line
+directly on the oscilloscope screen
+
+ align:start position:0%
+directly on the oscilloscope screen
+ 
+
+ align:start position:0%
+directly on the oscilloscope screen
+let's see if the scope trays follows
+
+ align:start position:0%
+let's see if the scope trays follows
+ 
+
+ align:start position:0%
+let's see if the scope trays follows
+this theoretical curve we have adjusted
+
+ align:start position:0%
+this theoretical curve we have adjusted
+ 
+
+ align:start position:0%
+this theoretical curve we have adjusted
+the scope vertical gain so that the
+
+ align:start position:0%
+the scope vertical gain so that the
+ 
+
+ align:start position:0%
+the scope vertical gain so that the
+display matches the theoretical waveform
+
+ align:start position:0%
+display matches the theoretical waveform
+ 
+
+ align:start position:0%
+display matches the theoretical waveform
+at one position we'll see if the scope
+
+ align:start position:0%
+at one position we'll see if the scope
+ 
+
+ align:start position:0%
+at one position we'll see if the scope
+trays follows the shape of this
+
+ align:start position:0%
+trays follows the shape of this
+ 
+
+ align:start position:0%
+trays follows the shape of this
+theoretical curve will check the field
+
+ align:start position:0%
+theoretical curve will check the field
+ 
+
+ align:start position:0%
+theoretical curve will check the field
+magnitude later the probe is initially
+
+ align:start position:0%
+magnitude later the probe is initially
+ 
+
+ align:start position:0%
+magnitude later the probe is initially
+here we now turn on the probe carriage
+
+ align:start position:0%
+here we now turn on the probe carriage
+ 
+
+ align:start position:0%
+here we now turn on the probe carriage
+the scope horizontal gain has been
+
+ align:start position:0%
+the scope horizontal gain has been
+ 
+
+ align:start position:0%
+the scope horizontal gain has been
+adjusted so that the horizontal
+
+ align:start position:0%
+adjusted so that the horizontal
+ 
+
+ align:start position:0%
+adjusted so that the horizontal
+deflection of the scope matches the Z
+
+ align:start position:0%
+deflection of the scope matches the Z
+ 
+
+ align:start position:0%
+deflection of the scope matches the Z
+position of the probe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the magnetic field is largest directly
+
+ align:start position:0%
+the magnetic field is largest directly
+ 
+
+ align:start position:0%
+the magnetic field is largest directly
+under a coil now the left one at Z equal
+
+ align:start position:0%
+under a coil now the left one at Z equal
+ 
+
+ align:start position:0%
+under a coil now the left one at Z equal
+minus D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and is fairly uniform in the central
+
+ align:start position:0%
+and is fairly uniform in the central
+ 
+
+ align:start position:0%
+and is fairly uniform in the central
+region between coils with a minimum at
+
+ align:start position:0%
+region between coils with a minimum at
+ 
+
+ align:start position:0%
+region between coils with a minimum at
+the center Z equals zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the field increases again to a maximum
+
+ align:start position:0%
+the field increases again to a maximum
+ 
+
+ align:start position:0%
+the field increases again to a maximum
+under the right coil at Z equal D and
+
+ align:start position:0%
+under the right coil at Z equal D and
+ 
+
+ align:start position:0%
+under the right coil at Z equal D and
+decreases in the region outside the
+
+ align:start position:0%
+decreases in the region outside the
+ 
+
+ align:start position:0%
+decreases in the region outside the
+coils now the magnetic field is an odd
+
+ align:start position:0%
+coils now the magnetic field is an odd
+ 
+
+ align:start position:0%
+coils now the magnetic field is an odd
+function around Z equals zero it is zero
+
+ align:start position:0%
+function around Z equals zero it is zero
+ 
+
+ align:start position:0%
+function around Z equals zero it is zero
+in the center is expected this reversing
+
+ align:start position:0%
+in the center is expected this reversing
+ 
+
+ align:start position:0%
+in the center is expected this reversing
+switch reverses the direction of current
+
+ align:start position:0%
+switch reverses the direction of current
+ 
+
+ align:start position:0%
+switch reverses the direction of current
+in the left coil let's see how the
+
+ align:start position:0%
+in the left coil let's see how the
+ 
+
+ align:start position:0%
+in the left coil let's see how the
+measured field compares with the
+
+ align:start position:0%
+measured field compares with the
+ 
+
+ align:start position:0%
+measured field compares with the
+prediction we have aligned the zero
+
+ align:start position:0%
+prediction we have aligned the zero
+ 
+
+ align:start position:0%
+prediction we have aligned the zero
+field lines and adjusted the vertical
+
+ align:start position:0%
+field lines and adjusted the vertical
+ 
+
+ align:start position:0%
+field lines and adjusted the vertical
+gain to match the waveform at one point
+
+ align:start position:0%
+gain to match the waveform at one point
+ 
+
+ align:start position:0%
+gain to match the waveform at one point
+we now turn on the probe carriage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the field is a negative maximum under
+
+ align:start position:0%
+the field is a negative maximum under
+ 
+
+ align:start position:0%
+the field is a negative maximum under
+the left coil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is zero at the center
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and reaches a positive maximum under the
+
+ align:start position:0%
+and reaches a positive maximum under the
+ 
+
+ align:start position:0%
+and reaches a positive maximum under the
+right coil
\ No newline at end of file
diff --git a/wsOoClvZmic.txt b/wsOoClvZmic.txt
new file mode 100644
index 0000000000000000000000000000000000000000..313fec30008e7a5e9faa6f6eff7b26c0a86e9bbc
--- /dev/null
+++ b/wsOoClvZmic.txt
@@ -0,0 +1,3475 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hi, welcome to calculus part two where
+
+ align:start position:0%
+Hi, welcome to calculus part two where
+ 
+
+ align:start position:0%
+Hi, welcome to calculus part two where
+our theme for the entire course will
+
+ align:start position:0%
+our theme for the entire course will
+ 
+
+ align:start position:0%
+our theme for the entire course will
+essentially be functions of several
+
+ align:start position:0%
+essentially be functions of several
+ 
+
+ align:start position:0%
+essentially be functions of several
+variables but a more underlying theme a
+
+ align:start position:0%
+variables but a more underlying theme a
+ 
+
+ align:start position:0%
+variables but a more underlying theme a
+theme which will not only permeate this
+
+ align:start position:0%
+theme which will not only permeate this
+ 
+
+ align:start position:0%
+theme which will not only permeate this
+course but virtually every course in the
+
+ align:start position:0%
+course but virtually every course in the
+ 
+
+ align:start position:0%
+course but virtually every course in the
+mathematics curriculum and perhaps other
+
+ align:start position:0%
+mathematics curriculum and perhaps other
+ 
+
+ align:start position:0%
+mathematics curriculum and perhaps other
+curricular as well is the idea of what
+
+ align:start position:0%
+curricular as well is the idea of what
+ 
+
+ align:start position:0%
+curricular as well is the idea of what
+we mean by a mathematical structure. And
+
+ align:start position:0%
+we mean by a mathematical structure. And
+ 
+
+ align:start position:0%
+we mean by a mathematical structure. And
+if this sounds a little bit ominous and
+
+ align:start position:0%
+if this sounds a little bit ominous and
+ 
+
+ align:start position:0%
+if this sounds a little bit ominous and
+frightening, the idea of a mathematical
+
+ align:start position:0%
+frightening, the idea of a mathematical
+ 
+
+ align:start position:0%
+frightening, the idea of a mathematical
+structure can be compared very nicely in
+
+ align:start position:0%
+structure can be compared very nicely in
+ 
+
+ align:start position:0%
+structure can be compared very nicely in
+terms of a game. And for this reason, I
+
+ align:start position:0%
+terms of a game. And for this reason, I
+ 
+
+ align:start position:0%
+terms of a game. And for this reason, I
+have chosen to entitle our first lesson,
+
+ align:start position:0%
+have chosen to entitle our first lesson,
+ 
+
+ align:start position:0%
+have chosen to entitle our first lesson,
+the game of mathematics. The game of
+
+ align:start position:0%
+the game of mathematics. The game of
+ 
+
+ align:start position:0%
+the game of mathematics. The game of
+mathematics. And let's emphasize the
+
+ align:start position:0%
+mathematics. And let's emphasize the
+ 
+
+ align:start position:0%
+mathematics. And let's emphasize the
+word game here. We do not mean game in a
+
+ align:start position:0%
+word game here. We do not mean game in a
+ 
+
+ align:start position:0%
+word game here. We do not mean game in a
+trivial sense where in elementary school
+
+ align:start position:0%
+trivial sense where in elementary school
+ 
+
+ align:start position:0%
+trivial sense where in elementary school
+the first row races the second row to
+
+ align:start position:0%
+the first row races the second row to
+ 
+
+ align:start position:0%
+the first row races the second row to
+see who finishes the addition problem
+
+ align:start position:0%
+see who finishes the addition problem
+ 
+
+ align:start position:0%
+see who finishes the addition problem
+first. The idea that we want to talk
+
+ align:start position:0%
+first. The idea that we want to talk
+ 
+
+ align:start position:0%
+first. The idea that we want to talk
+about is what is a game? And I remember
+
+ align:start position:0%
+about is what is a game? And I remember
+ 
+
+ align:start position:0%
+about is what is a game? And I remember
+an old riddle when I was in about the
+
+ align:start position:0%
+an old riddle when I was in about the
+ 
+
+ align:start position:0%
+an old riddle when I was in about the
+fourth or fifth grade when somebody said
+
+ align:start position:0%
+fourth or fifth grade when somebody said
+ 
+
+ align:start position:0%
+fourth or fifth grade when somebody said
+to me, "What is it that looks like a
+
+ align:start position:0%
+to me, "What is it that looks like a
+ 
+
+ align:start position:0%
+to me, "What is it that looks like a
+box, smells like cheese, and flies?" And
+
+ align:start position:0%
+box, smells like cheese, and flies?" And
+ 
+
+ align:start position:0%
+box, smells like cheese, and flies?" And
+the answer was a flying cheese box. And
+
+ align:start position:0%
+the answer was a flying cheese box. And
+ 
+
+ align:start position:0%
+the answer was a flying cheese box. And
+the interesting point is that this is
+
+ align:start position:0%
+the interesting point is that this is
+ 
+
+ align:start position:0%
+the interesting point is that this is
+how in the scientific world we often
+
+ align:start position:0%
+how in the scientific world we often
+ 
+
+ align:start position:0%
+how in the scientific world we often
+make up definitions. Namely, to define a
+
+ align:start position:0%
+make up definitions. Namely, to define a
+ 
+
+ align:start position:0%
+make up definitions. Namely, to define a
+game, we try to think of every single
+
+ align:start position:0%
+game, we try to think of every single
+ 
+
+ align:start position:0%
+game, we try to think of every single
+ingredient that is common to every game.
+
+ align:start position:0%
+ingredient that is common to every game.
+ 
+
+ align:start position:0%
+ingredient that is common to every game.
+And then we roll all of these
+
+ align:start position:0%
+And then we roll all of these
+ 
+
+ align:start position:0%
+And then we roll all of these
+ingredients into one long definition and
+
+ align:start position:0%
+ingredients into one long definition and
+ 
+
+ align:start position:0%
+ingredients into one long definition and
+that becomes our final definition. And
+
+ align:start position:0%
+that becomes our final definition. And
+ 
+
+ align:start position:0%
+that becomes our final definition. And
+with that in mind,
+
+ align:start position:0%
+with that in mind,
+ 
+
+ align:start position:0%
+with that in mind,
+let me take the following TAC. And again
+
+ align:start position:0%
+let me take the following TAC. And again
+ 
+
+ align:start position:0%
+let me take the following TAC. And again
+let me point out that I am going through
+
+ align:start position:0%
+let me point out that I am going through
+ 
+
+ align:start position:0%
+let me point out that I am going through
+this rather hurriedly because the main
+
+ align:start position:0%
+this rather hurriedly because the main
+ 
+
+ align:start position:0%
+this rather hurriedly because the main
+aim of the lesson is to give an overview
+
+ align:start position:0%
+aim of the lesson is to give an overview
+ 
+
+ align:start position:0%
+aim of the lesson is to give an overview
+with the idea that the supplementary
+
+ align:start position:0%
+with the idea that the supplementary
+ 
+
+ align:start position:0%
+with the idea that the supplementary
+notes and the exercises at the in the
+
+ align:start position:0%
+notes and the exercises at the in the
+ 
+
+ align:start position:0%
+notes and the exercises at the in the
+unit will give you the computational
+
+ align:start position:0%
+unit will give you the computational
+ 
+
+ align:start position:0%
+unit will give you the computational
+drill that you need. But for a first
+
+ align:start position:0%
+drill that you need. But for a first
+ 
+
+ align:start position:0%
+drill that you need. But for a first
+approximation let us say that in any
+
+ align:start position:0%
+approximation let us say that in any
+ 
+
+ align:start position:0%
+approximation let us say that in any
+game you must have definitions so that
+
+ align:start position:0%
+game you must have definitions so that
+ 
+
+ align:start position:0%
+game you must have definitions so that
+you know what terminology you have. Then
+
+ align:start position:0%
+you know what terminology you have. Then
+ 
+
+ align:start position:0%
+you know what terminology you have. Then
+you must have rules of the game and
+
+ align:start position:0%
+you must have rules of the game and
+ 
+
+ align:start position:0%
+you must have rules of the game and
+notice that the rules of the game are
+
+ align:start position:0%
+notice that the rules of the game are
+ 
+
+ align:start position:0%
+notice that the rules of the game are
+relationships between the terms or as a
+
+ align:start position:0%
+relationships between the terms or as a
+ 
+
+ align:start position:0%
+relationships between the terms or as a
+trivial example in playing cards. There
+
+ align:start position:0%
+trivial example in playing cards. There
+ 
+
+ align:start position:0%
+trivial example in playing cards. There
+are many different card games that can
+
+ align:start position:0%
+are many different card games that can
+ 
+
+ align:start position:0%
+are many different card games that can
+be played with the same deck of cards.
+
+ align:start position:0%
+be played with the same deck of cards.
+ 
+
+ align:start position:0%
+be played with the same deck of cards.
+What makes the game different is not
+
+ align:start position:0%
+What makes the game different is not
+ 
+
+ align:start position:0%
+What makes the game different is not
+diff different are not the definitions
+
+ align:start position:0%
+diff different are not the definitions
+ 
+
+ align:start position:0%
+diff different are not the definitions
+involved but the rules of the game. And
+
+ align:start position:0%
+involved but the rules of the game. And
+ 
+
+ align:start position:0%
+involved but the rules of the game. And
+finally, there are objectives. Well,
+
+ align:start position:0%
+finally, there are objectives. Well,
+ 
+
+ align:start position:0%
+finally, there are objectives. Well,
+obviously the objective of any game is
+
+ align:start position:0%
+obviously the objective of any game is
+ 
+
+ align:start position:0%
+obviously the objective of any game is
+to win. What we really mean by an
+
+ align:start position:0%
+to win. What we really mean by an
+ 
+
+ align:start position:0%
+to win. What we really mean by an
+objective is the art of carrying out a
+
+ align:start position:0%
+objective is the art of carrying out a
+ 
+
+ align:start position:0%
+objective is the art of carrying out a
+winning situation by successfully
+
+ align:start position:0%
+winning situation by successfully
+ 
+
+ align:start position:0%
+winning situation by successfully
+employing the definitions and the rules.
+
+ align:start position:0%
+employing the definitions and the rules.
+ 
+
+ align:start position:0%
+employing the definitions and the rules.
+All right? And the way we do that is
+
+ align:start position:0%
+All right? And the way we do that is
+ 
+
+ align:start position:0%
+All right? And the way we do that is
+usually called strategy. Strategy is the
+
+ align:start position:0%
+usually called strategy. Strategy is the
+ 
+
+ align:start position:0%
+usually called strategy. Strategy is the
+art of using the definitions and rules
+
+ align:start position:0%
+art of using the definitions and rules
+ 
+
+ align:start position:0%
+art of using the definitions and rules
+to carry out the objective in an
+
+ align:start position:0%
+to carry out the objective in an
+ 
+
+ align:start position:0%
+to carry out the objective in an
+inescapable manner. And the reason I
+
+ align:start position:0%
+inescapable manner. And the reason I
+ 
+
+ align:start position:0%
+inescapable manner. And the reason I
+like this particular little setup is it
+
+ align:start position:0%
+like this particular little setup is it
+ 
+
+ align:start position:0%
+like this particular little setup is it
+gives me a way to show you in
+
+ align:start position:0%
+gives me a way to show you in
+ 
+
+ align:start position:0%
+gives me a way to show you in
+juxtaposition the role of wrote versus
+
+ align:start position:0%
+juxtaposition the role of wrote versus
+ 
+
+ align:start position:0%
+juxtaposition the role of wrote versus
+reason, logic versus memory in any
+
+ align:start position:0%
+reason, logic versus memory in any
+ 
+
+ align:start position:0%
+reason, logic versus memory in any
+mathematical situation or real life
+
+ align:start position:0%
+mathematical situation or real life
+ 
+
+ align:start position:0%
+mathematical situation or real life
+situation. Namely, the strategy part of
+
+ align:start position:0%
+situation. Namely, the strategy part of
+ 
+
+ align:start position:0%
+situation. Namely, the strategy part of
+a game is logic and things like the
+
+ align:start position:0%
+a game is logic and things like the
+ 
+
+ align:start position:0%
+a game is logic and things like the
+definitions and the rules
+
+ align:start position:0%
+definitions and the rules
+ 
+
+ align:start position:0%
+definitions and the rules
+are things that we memorize.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Now the thing that we're going to
+
+ align:start position:0%
+Okay. Now the thing that we're going to
+ 
+
+ align:start position:0%
+Okay. Now the thing that we're going to
+do in our particular course is always
+
+ align:start position:0%
+do in our particular course is always
+ 
+
+ align:start position:0%
+do in our particular course is always
+come back to this particular structure.
+
+ align:start position:0%
+come back to this particular structure.
+ 
+
+ align:start position:0%
+come back to this particular structure.
+In other words, our definition of a game
+
+ align:start position:0%
+In other words, our definition of a game
+ 
+
+ align:start position:0%
+In other words, our definition of a game
+is any system which consists of
+
+ align:start position:0%
+is any system which consists of
+ 
+
+ align:start position:0%
+is any system which consists of
+definitions, rules and objectives where
+
+ align:start position:0%
+definitions, rules and objectives where
+ 
+
+ align:start position:0%
+definitions, rules and objectives where
+the objective is carried out as an
+
+ align:start position:0%
+the objective is carried out as an
+ 
+
+ align:start position:0%
+the objective is carried out as an
+inescapable consequence of the
+
+ align:start position:0%
+inescapable consequence of the
+ 
+
+ align:start position:0%
+inescapable consequence of the
+definitions and the rules by means of
+
+ align:start position:0%
+definitions and the rules by means of
+ 
+
+ align:start position:0%
+definitions and the rules by means of
+strategy. And by the way, don't take
+
+ align:start position:0%
+strategy. And by the way, don't take
+ 
+
+ align:start position:0%
+strategy. And by the way, don't take
+this lightly. This is a very serious
+
+ align:start position:0%
+this lightly. This is a very serious
+ 
+
+ align:start position:0%
+this lightly. This is a very serious
+topic. Later in the course, the
+
+ align:start position:0%
+topic. Later in the course, the
+ 
+
+ align:start position:0%
+topic. Later in the course, the
+computation will become sufficiently
+
+ align:start position:0%
+computation will become sufficiently
+ 
+
+ align:start position:0%
+computation will become sufficiently
+difficult that we may lose sight of the
+
+ align:start position:0%
+difficult that we may lose sight of the
+ 
+
+ align:start position:0%
+difficult that we may lose sight of the
+forest because of the trees. Right now,
+
+ align:start position:0%
+forest because of the trees. Right now,
+ 
+
+ align:start position:0%
+forest because of the trees. Right now,
+what I want to do is emphasize this to
+
+ align:start position:0%
+what I want to do is emphasize this to
+ 
+
+ align:start position:0%
+what I want to do is emphasize this to
+you in terms of topics that you're
+
+ align:start position:0%
+you in terms of topics that you're
+ 
+
+ align:start position:0%
+you in terms of topics that you're
+already familiar with so that you can
+
+ align:start position:0%
+already familiar with so that you can
+ 
+
+ align:start position:0%
+already familiar with so that you can
+see what the overall structure of
+
+ align:start position:0%
+see what the overall structure of
+ 
+
+ align:start position:0%
+see what the overall structure of
+mathematics is so that you will not be
+
+ align:start position:0%
+mathematics is so that you will not be
+ 
+
+ align:start position:0%
+mathematics is so that you will not be
+preoccupied with this when we're
+
+ align:start position:0%
+preoccupied with this when we're
+ 
+
+ align:start position:0%
+preoccupied with this when we're
+learning more computational things. Let
+
+ align:start position:0%
+learning more computational things. Let
+ 
+
+ align:start position:0%
+learning more computational things. Let
+me just take a look at well a relatively
+
+ align:start position:0%
+me just take a look at well a relatively
+ 
+
+ align:start position:0%
+me just take a look at well a relatively
+trivial example.
+
+ align:start position:0%
+trivial example.
+ 
+
+ align:start position:0%
+trivial example.
+I call this a new look at counting. We
+
+ align:start position:0%
+I call this a new look at counting. We
+ 
+
+ align:start position:0%
+I call this a new look at counting. We
+all know how to count. We start with a
+
+ align:start position:0%
+all know how to count. We start with a
+ 
+
+ align:start position:0%
+all know how to count. We start with a
+number called 1. And we have various
+
+ align:start position:0%
+number called 1. And we have various
+ 
+
+ align:start position:0%
+number called 1. And we have various
+definitions. 1 + 1 is 2. 2 + 1 is 3. 3 +
+
+ align:start position:0%
+definitions. 1 + 1 is 2. 2 + 1 is 3. 3 +
+ 
+
+ align:start position:0%
+definitions. 1 + 1 is 2. 2 + 1 is 3. 3 +
+1 is 4. 4 + 1 is 5. 5 + 1 is 6. 6 + 1 is
+
+ align:start position:0%
+1 is 4. 4 + 1 is 5. 5 + 1 is 6. 6 + 1 is
+ 
+
+ align:start position:0%
+1 is 4. 4 + 1 is 5. 5 + 1 is 6. 6 + 1 is
+7 etc. Okay. So far so good. Now we ask
+
+ align:start position:0%
+7 etc. Okay. So far so good. Now we ask
+ 
+
+ align:start position:0%
+7 etc. Okay. So far so good. Now we ask
+the question, how much is 4 + 3? Now
+
+ align:start position:0%
+the question, how much is 4 + 3? Now
+ 
+
+ align:start position:0%
+the question, how much is 4 + 3? Now
+obviously we all know that 4 + 3 is 7.
+
+ align:start position:0%
+obviously we all know that 4 + 3 is 7.
+ 
+
+ align:start position:0%
+obviously we all know that 4 + 3 is 7.
+We're not saying what are we looking at
+
+ align:start position:0%
+We're not saying what are we looking at
+ 
+
+ align:start position:0%
+We're not saying what are we looking at
+this problem for. What we're trying to
+
+ align:start position:0%
+this problem for. What we're trying to
+ 
+
+ align:start position:0%
+this problem for. What we're trying to
+show now is a very important aspect of
+
+ align:start position:0%
+show now is a very important aspect of
+ 
+
+ align:start position:0%
+show now is a very important aspect of
+the game of mathematics. You see notice
+
+ align:start position:0%
+the game of mathematics. You see notice
+ 
+
+ align:start position:0%
+the game of mathematics. You see notice
+that in our list of definitions, no
+
+ align:start position:0%
+that in our list of definitions, no
+ 
+
+ align:start position:0%
+that in our list of definitions, no
+place do we have the sum 4 + 3 defined.
+
+ align:start position:0%
+place do we have the sum 4 + 3 defined.
+ 
+
+ align:start position:0%
+place do we have the sum 4 + 3 defined.
+What we are interested in now is not so
+
+ align:start position:0%
+What we are interested in now is not so
+ 
+
+ align:start position:0%
+What we are interested in now is not so
+much the truthful statement that 4 plus
+
+ align:start position:0%
+much the truthful statement that 4 plus
+ 
+
+ align:start position:0%
+much the truthful statement that 4 plus
+3 is 7, but whether the result 4 + 3
+
+ align:start position:0%
+3 is 7, but whether the result 4 + 3
+ 
+
+ align:start position:0%
+3 is 7, but whether the result 4 + 3
+equals 7 follows inescapably from the
+
+ align:start position:0%
+equals 7 follows inescapably from the
+ 
+
+ align:start position:0%
+equals 7 follows inescapably from the
+definitions that we've listed. Now you
+
+ align:start position:0%
+definitions that we've listed. Now you
+ 
+
+ align:start position:0%
+definitions that we've listed. Now you
+see the point is all we've listed are
+
+ align:start position:0%
+see the point is all we've listed are
+ 
+
+ align:start position:0%
+see the point is all we've listed are
+definitions. We haven't told any
+
+ align:start position:0%
+definitions. We haven't told any
+ 
+
+ align:start position:0%
+definitions. We haven't told any
+particular rules of the game yet. Well,
+
+ align:start position:0%
+particular rules of the game yet. Well,
+ 
+
+ align:start position:0%
+particular rules of the game yet. Well,
+let's make up some rules as we go along.
+
+ align:start position:0%
+let's make up some rules as we go along.
+ 
+
+ align:start position:0%
+let's make up some rules as we go along.
+And as I say, we'll discuss these in
+
+ align:start position:0%
+And as I say, we'll discuss these in
+ 
+
+ align:start position:0%
+And as I say, we'll discuss these in
+more details in our notes and in the
+
+ align:start position:0%
+more details in our notes and in the
+ 
+
+ align:start position:0%
+more details in our notes and in the
+exercises. We essentially do something
+
+ align:start position:0%
+exercises. We essentially do something
+ 
+
+ align:start position:0%
+exercises. We essentially do something
+like this. We write down 4 + 3. Okay.
+
+ align:start position:0%
+like this. We write down 4 + 3. Okay.
+ 
+
+ align:start position:0%
+like this. We write down 4 + 3. Okay.
+Then we say, okay, we do know how to add
+
+ align:start position:0%
+Then we say, okay, we do know how to add
+ 
+
+ align:start position:0%
+Then we say, okay, we do know how to add
+by ones. That's what our definition
+
+ align:start position:0%
+by ones. That's what our definition
+ 
+
+ align:start position:0%
+by ones. That's what our definition
+says. So we rewrite three as 2 + 1. In
+
+ align:start position:0%
+says. So we rewrite three as 2 + 1. In
+ 
+
+ align:start position:0%
+says. So we rewrite three as 2 + 1. In
+other words, we substitute 2 + 1, which
+
+ align:start position:0%
+other words, we substitute 2 + 1, which
+ 
+
+ align:start position:0%
+other words, we substitute 2 + 1, which
+is equal to 3 by definition. Then we
+
+ align:start position:0%
+is equal to 3 by definition. Then we
+ 
+
+ align:start position:0%
+is equal to 3 by definition. Then we
+say, okay, 2 + 1 is the same as 1 + 2.
+
+ align:start position:0%
+say, okay, 2 + 1 is the same as 1 + 2.
+ 
+
+ align:start position:0%
+say, okay, 2 + 1 is the same as 1 + 2.
+Now, by the way, notice the tasted
+
+ align:start position:0%
+Now, by the way, notice the tasted
+ 
+
+ align:start position:0%
+Now, by the way, notice the tasted
+assumption that we're making. We're
+
+ align:start position:0%
+assumption that we're making. We're
+ 
+
+ align:start position:0%
+assumption that we're making. We're
+assuming that the order in which you add
+
+ align:start position:0%
+assuming that the order in which you add
+ 
+
+ align:start position:0%
+assuming that the order in which you add
+two numbers makes no difference.
+
+ align:start position:0%
+two numbers makes no difference.
+ 
+
+ align:start position:0%
+two numbers makes no difference.
+Obviously, this is not a rule in every
+
+ align:start position:0%
+Obviously, this is not a rule in every
+ 
+
+ align:start position:0%
+Obviously, this is not a rule in every
+game of life. In most things in life,
+
+ align:start position:0%
+game of life. In most things in life,
+ 
+
+ align:start position:0%
+game of life. In most things in life,
+order does make a difference. Consider,
+
+ align:start position:0%
+order does make a difference. Consider,
+ 
+
+ align:start position:0%
+order does make a difference. Consider,
+for example, the statements, first I
+
+ align:start position:0%
+for example, the statements, first I
+ 
+
+ align:start position:0%
+for example, the statements, first I
+undress and then I take a shower or
+
+ align:start position:0%
+undress and then I take a shower or
+ 
+
+ align:start position:0%
+undress and then I take a shower or
+first I shower and then I undress.
+
+ align:start position:0%
+first I shower and then I undress.
+ 
+
+ align:start position:0%
+first I shower and then I undress.
+Without meaning to pass judgment as to
+
+ align:start position:0%
+Without meaning to pass judgment as to
+ 
+
+ align:start position:0%
+Without meaning to pass judgment as to
+which is proper, at least notice there
+
+ align:start position:0%
+which is proper, at least notice there
+ 
+
+ align:start position:0%
+which is proper, at least notice there
+is a difference between the two. What
+
+ align:start position:0%
+is a difference between the two. What
+ 
+
+ align:start position:0%
+is a difference between the two. What
+we're saying is that somehow or other in
+
+ align:start position:0%
+we're saying is that somehow or other in
+ 
+
+ align:start position:0%
+we're saying is that somehow or other in
+the game of arithmetic we assume that
+
+ align:start position:0%
+the game of arithmetic we assume that
+ 
+
+ align:start position:0%
+the game of arithmetic we assume that
+addition has the property that the order
+
+ align:start position:0%
+addition has the property that the order
+ 
+
+ align:start position:0%
+addition has the property that the order
+in which you add makes no difference. So
+
+ align:start position:0%
+in which you add makes no difference. So
+ 
+
+ align:start position:0%
+in which you add makes no difference. So
+we say okay let's accept that as a rule
+
+ align:start position:0%
+we say okay let's accept that as a rule
+ 
+
+ align:start position:0%
+we say okay let's accept that as a rule
+of the game. If we accept that as a rule
+
+ align:start position:0%
+of the game. If we accept that as a rule
+ 
+
+ align:start position:0%
+of the game. If we accept that as a rule
+of a game 2 + 1 can then be substituted
+
+ align:start position:0%
+of a game 2 + 1 can then be substituted
+ 
+
+ align:start position:0%
+of a game 2 + 1 can then be substituted
+for by 1 + 2. We make the additional
+
+ align:start position:0%
+for by 1 + 2. We make the additional
+ 
+
+ align:start position:0%
+for by 1 + 2. We make the additional
+assumption that when you add three
+
+ align:start position:0%
+assumption that when you add three
+ 
+
+ align:start position:0%
+assumption that when you add three
+numbers the answer does not depend on
+
+ align:start position:0%
+numbers the answer does not depend on
+ 
+
+ align:start position:0%
+numbers the answer does not depend on
+voice inflection. In other words, that 4
+
+ align:start position:0%
+voice inflection. In other words, that 4
+ 
+
+ align:start position:0%
+voice inflection. In other words, that 4
++ 1 + 2 is equal to 4 + 1 + 2. And the
+
+ align:start position:0%
++ 1 + 2 is equal to 4 + 1 + 2. And the
+ 
+
+ align:start position:0%
++ 1 + 2 is equal to 4 + 1 + 2. And the
+strategy behind doing that is that we
+
+ align:start position:0%
+strategy behind doing that is that we
+ 
+
+ align:start position:0%
+strategy behind doing that is that we
+know that another name for 4 + 1 is
+
+ align:start position:0%
+know that another name for 4 + 1 is
+ 
+
+ align:start position:0%
+know that another name for 4 + 1 is
+five. In other words, we now arrive at
+
+ align:start position:0%
+five. In other words, we now arrive at
+ 
+
+ align:start position:0%
+five. In other words, we now arrive at
+the fact that 4 + 3 is equal to 5 + 2.
+
+ align:start position:0%
+the fact that 4 + 3 is equal to 5 + 2.
+ 
+
+ align:start position:0%
+the fact that 4 + 3 is equal to 5 + 2.
+We now rewrite two as 1 + 1. And we now
+
+ align:start position:0%
+We now rewrite two as 1 + 1. And we now
+ 
+
+ align:start position:0%
+We now rewrite two as 1 + 1. And we now
+have that 5 + 2 is the same as 5 + 1 +
+
+ align:start position:0%
+have that 5 + 2 is the same as 5 + 1 +
+ 
+
+ align:start position:0%
+have that 5 + 2 is the same as 5 + 1 +
+1. We now again use the fact that voice
+
+ align:start position:0%
+1. We now again use the fact that voice
+ 
+
+ align:start position:0%
+1. We now again use the fact that voice
+inflection makes no difference. And we
+
+ align:start position:0%
+inflection makes no difference. And we
+ 
+
+ align:start position:0%
+inflection makes no difference. And we
+rewrite this as 5 + 1 + 1.
+
+ align:start position:0%
+rewrite this as 5 + 1 + 1.
+ 
+
+ align:start position:0%
+rewrite this as 5 + 1 + 1.
+5 + 1 we know by definition is six. And
+
+ align:start position:0%
+5 + 1 we know by definition is six. And
+ 
+
+ align:start position:0%
+5 + 1 we know by definition is six. And
+6 + 1 we know by definition is seven. In
+
+ align:start position:0%
+6 + 1 we know by definition is seven. In
+ 
+
+ align:start position:0%
+6 + 1 we know by definition is seven. In
+other words, subject to the rules that
+
+ align:start position:0%
+other words, subject to the rules that
+ 
+
+ align:start position:0%
+other words, subject to the rules that
+we've talked about implicitly here but
+
+ align:start position:0%
+we've talked about implicitly here but
+ 
+
+ align:start position:0%
+we've talked about implicitly here but
+have not stated in our game format
+
+ align:start position:0%
+have not stated in our game format
+ 
+
+ align:start position:0%
+have not stated in our game format
+explicitly. What we have shown is that
+
+ align:start position:0%
+explicitly. What we have shown is that
+ 
+
+ align:start position:0%
+explicitly. What we have shown is that
+if we accept certain rules, it follows
+
+ align:start position:0%
+if we accept certain rules, it follows
+ 
+
+ align:start position:0%
+if we accept certain rules, it follows
+from our definitions that 4 + 3= 7 is an
+
+ align:start position:0%
+from our definitions that 4 + 3= 7 is an
+ 
+
+ align:start position:0%
+from our definitions that 4 + 3= 7 is an
+inescapable conclusion. Notice that the
+
+ align:start position:0%
+inescapable conclusion. Notice that the
+ 
+
+ align:start position:0%
+inescapable conclusion. Notice that the
+inescapability of the conclusion hinges
+
+ align:start position:0%
+inescapability of the conclusion hinges
+ 
+
+ align:start position:0%
+inescapability of the conclusion hinges
+on the fact
+
+ align:start position:0%
+on the fact
+ 
+
+ align:start position:0%
+on the fact
+that we've accepted certain rules. If we
+
+ align:start position:0%
+that we've accepted certain rules. If we
+ 
+
+ align:start position:0%
+that we've accepted certain rules. If we
+change the rules, we can change the
+
+ align:start position:0%
+change the rules, we can change the
+ 
+
+ align:start position:0%
+change the rules, we can change the
+conclusions. In other words, this thing
+
+ align:start position:0%
+conclusions. In other words, this thing
+ 
+
+ align:start position:0%
+conclusions. In other words, this thing
+called drawing inescapable conclusions
+
+ align:start position:0%
+called drawing inescapable conclusions
+ 
+
+ align:start position:0%
+called drawing inescapable conclusions
+is something called validity. And
+
+ align:start position:0%
+is something called validity. And
+ 
+
+ align:start position:0%
+is something called validity. And
+validity involves the art of drawing
+
+ align:start position:0%
+validity involves the art of drawing
+ 
+
+ align:start position:0%
+validity involves the art of drawing
+inescapable conclusions using given
+
+ align:start position:0%
+inescapable conclusions using given
+ 
+
+ align:start position:0%
+inescapable conclusions using given
+rules and given definitions. We'll talk
+
+ align:start position:0%
+rules and given definitions. We'll talk
+ 
+
+ align:start position:0%
+rules and given definitions. We'll talk
+about that in more detail. But for now,
+
+ align:start position:0%
+about that in more detail. But for now,
+ 
+
+ align:start position:0%
+about that in more detail. But for now,
+notice the difference here. Before we
+
+ align:start position:0%
+notice the difference here. Before we
+ 
+
+ align:start position:0%
+notice the difference here. Before we
+did this, we knew as a conjecture, a
+
+ align:start position:0%
+did this, we knew as a conjecture, a
+ 
+
+ align:start position:0%
+did this, we knew as a conjecture, a
+past experience thing that 4 + 3= 7 is a
+
+ align:start position:0%
+past experience thing that 4 + 3= 7 is a
+ 
+
+ align:start position:0%
+past experience thing that 4 + 3= 7 is a
+true statement. What we now know is in
+
+ align:start position:0%
+true statement. What we now know is in
+ 
+
+ align:start position:0%
+true statement. What we now know is in
+terms of certain rules of the game
+
+ align:start position:0%
+terms of certain rules of the game
+ 
+
+ align:start position:0%
+terms of certain rules of the game
+coupled with the definitions that we've
+
+ align:start position:0%
+coupled with the definitions that we've
+ 
+
+ align:start position:0%
+coupled with the definitions that we've
+accepted, 4 + 3= 7 is an inescapable
+
+ align:start position:0%
+accepted, 4 + 3= 7 is an inescapable
+ 
+
+ align:start position:0%
+accepted, 4 + 3= 7 is an inescapable
+conclusion. Henceforth to be called a
+
+ align:start position:0%
+conclusion. Henceforth to be called a
+ 
+
+ align:start position:0%
+conclusion. Henceforth to be called a
+theorem in our game. Let's see if we
+
+ align:start position:0%
+theorem in our game. Let's see if we
+ 
+
+ align:start position:0%
+theorem in our game. Let's see if we
+can't get away from this rather simple
+
+ align:start position:0%
+can't get away from this rather simple
+ 
+
+ align:start position:0%
+can't get away from this rather simple
+example. And again, let me emphasize
+
+ align:start position:0%
+example. And again, let me emphasize
+ 
+
+ align:start position:0%
+example. And again, let me emphasize
+that as simple as this example is,
+
+ align:start position:0%
+that as simple as this example is,
+ 
+
+ align:start position:0%
+that as simple as this example is,
+throughout our course, we will be using
+
+ align:start position:0%
+throughout our course, we will be using
+ 
+
+ align:start position:0%
+throughout our course, we will be using
+the same technique only at a more
+
+ align:start position:0%
+the same technique only at a more
+ 
+
+ align:start position:0%
+the same technique only at a more
+sophisticated level of computational
+
+ align:start position:0%
+sophisticated level of computational
+ 
+
+ align:start position:0%
+sophisticated level of computational
+skill. But let's take a look here and
+
+ align:start position:0%
+skill. But let's take a look here and
+ 
+
+ align:start position:0%
+skill. But let's take a look here and
+see what we're really saying.
+
+ align:start position:0%
+see what we're really saying.
+ 
+
+ align:start position:0%
+see what we're really saying.
+What mathematical structure really
+
+ align:start position:0%
+What mathematical structure really
+ 
+
+ align:start position:0%
+What mathematical structure really
+involves
+
+ align:start position:0%
+involves
+ 
+
+ align:start position:0%
+involves
+is a logic machine type of thing. We
+
+ align:start position:0%
+is a logic machine type of thing. We
+ 
+
+ align:start position:0%
+is a logic machine type of thing. We
+have a logic machine. A machine that
+
+ align:start position:0%
+have a logic machine. A machine that
+ 
+
+ align:start position:0%
+have a logic machine. A machine that
+being fed any kinds of definitions,
+
+ align:start position:0%
+being fed any kinds of definitions,
+ 
+
+ align:start position:0%
+being fed any kinds of definitions,
+rules, assumptions, etc. grinds these
+
+ align:start position:0%
+rules, assumptions, etc. grinds these
+ 
+
+ align:start position:0%
+rules, assumptions, etc. grinds these
+things through and has as the out as its
+
+ align:start position:0%
+things through and has as the out as its
+ 
+
+ align:start position:0%
+things through and has as the out as its
+output inescapable conclusions.
+
+ align:start position:0%
+output inescapable conclusions.
+ 
+
+ align:start position:0%
+output inescapable conclusions.
+Okay? In other words, you feed in
+
+ align:start position:0%
+Okay? In other words, you feed in
+ 
+
+ align:start position:0%
+Okay? In other words, you feed in
+definitions, rules, etc., which by the
+
+ align:start position:0%
+definitions, rules, etc., which by the
+ 
+
+ align:start position:0%
+definitions, rules, etc., which by the
+way don't really have to be true in the
+
+ align:start position:0%
+way don't really have to be true in the
+ 
+
+ align:start position:0%
+way don't really have to be true in the
+real life sense of being true. I mean
+
+ align:start position:0%
+real life sense of being true. I mean
+ 
+
+ align:start position:0%
+real life sense of being true. I mean
+for example in the baseball game to say
+
+ align:start position:0%
+for example in the baseball game to say
+ 
+
+ align:start position:0%
+for example in the baseball game to say
+the rule is three strikes is an out
+
+ align:start position:0%
+the rule is three strikes is an out
+ 
+
+ align:start position:0%
+the rule is three strikes is an out
+there is certainly no basic truth that
+
+ align:start position:0%
+there is certainly no basic truth that
+ 
+
+ align:start position:0%
+there is certainly no basic truth that
+said that that had to be the case. What
+
+ align:start position:0%
+said that that had to be the case. What
+ 
+
+ align:start position:0%
+said that that had to be the case. What
+is true is that in the world of science
+
+ align:start position:0%
+is true is that in the world of science
+ 
+
+ align:start position:0%
+is true is that in the world of science
+the scientist is the interpreter of
+
+ align:start position:0%
+the scientist is the interpreter of
+ 
+
+ align:start position:0%
+the scientist is the interpreter of
+nature. What happens in real life
+
+ align:start position:0%
+nature. What happens in real life
+ 
+
+ align:start position:0%
+nature. What happens in real life
+happens whether the scientist predicts
+
+ align:start position:0%
+happens whether the scientist predicts
+ 
+
+ align:start position:0%
+happens whether the scientist predicts
+it or not. What he tries to do is to
+
+ align:start position:0%
+it or not. What he tries to do is to
+ 
+
+ align:start position:0%
+it or not. What he tries to do is to
+make up definitions and rules which are
+
+ align:start position:0%
+make up definitions and rules which are
+ 
+
+ align:start position:0%
+make up definitions and rules which are
+compatible with his experience. Things
+
+ align:start position:0%
+compatible with his experience. Things
+ 
+
+ align:start position:0%
+compatible with his experience. Things
+which he calls truth. He feeds those
+
+ align:start position:0%
+which he calls truth. He feeds those
+ 
+
+ align:start position:0%
+which he calls truth. He feeds those
+through his logic machine, draws
+
+ align:start position:0%
+through his logic machine, draws
+ 
+
+ align:start position:0%
+through his logic machine, draws
+inescapable conclusions,
+
+ align:start position:0%
+inescapable conclusions,
+ 
+
+ align:start position:0%
+inescapable conclusions,
+and if the conclusions follow
+
+ align:start position:0%
+and if the conclusions follow
+ 
+
+ align:start position:0%
+and if the conclusions follow
+inescapably from the definitions and the
+
+ align:start position:0%
+inescapably from the definitions and the
+ 
+
+ align:start position:0%
+inescapably from the definitions and the
+rules, we call the resulting argument
+
+ align:start position:0%
+rules, we call the resulting argument
+ 
+
+ align:start position:0%
+rules, we call the resulting argument
+valid. In other words, truth is a value
+
+ align:start position:0%
+valid. In other words, truth is a value
+ 
+
+ align:start position:0%
+valid. In other words, truth is a value
+judgment that we make about a particular
+
+ align:start position:0%
+judgment that we make about a particular
+ 
+
+ align:start position:0%
+judgment that we make about a particular
+statement. Validity is a more objective
+
+ align:start position:0%
+statement. Validity is a more objective
+ 
+
+ align:start position:0%
+statement. Validity is a more objective
+thing that we attribute to an argument.
+
+ align:start position:0%
+thing that we attribute to an argument.
+ 
+
+ align:start position:0%
+thing that we attribute to an argument.
+In other words, a statement is either
+
+ align:start position:0%
+In other words, a statement is either
+ 
+
+ align:start position:0%
+In other words, a statement is either
+true or false. An argument is either
+
+ align:start position:0%
+true or false. An argument is either
+ 
+
+ align:start position:0%
+true or false. An argument is either
+valid or invalid. Meaning that we only
+
+ align:start position:0%
+valid or invalid. Meaning that we only
+ 
+
+ align:start position:0%
+valid or invalid. Meaning that we only
+judge whether the conclusion of the
+
+ align:start position:0%
+judge whether the conclusion of the
+ 
+
+ align:start position:0%
+judge whether the conclusion of the
+argument follows inescapably from the
+
+ align:start position:0%
+argument follows inescapably from the
+ 
+
+ align:start position:0%
+argument follows inescapably from the
+given assumptions independently of
+
+ align:start position:0%
+given assumptions independently of
+ 
+
+ align:start position:0%
+given assumptions independently of
+whether those assumptions happen to be
+
+ align:start position:0%
+whether those assumptions happen to be
+ 
+
+ align:start position:0%
+whether those assumptions happen to be
+true or not. By the way, as an aside,
+
+ align:start position:0%
+true or not. By the way, as an aside,
+ 
+
+ align:start position:0%
+true or not. By the way, as an aside,
+one of the reasons that the scientist
+
+ align:start position:0%
+one of the reasons that the scientist
+ 
+
+ align:start position:0%
+one of the reasons that the scientist
+prefers to dodge issues such as what is
+
+ align:start position:0%
+prefers to dodge issues such as what is
+ 
+
+ align:start position:0%
+prefers to dodge issues such as what is
+truth and leaves that to the philosopher
+
+ align:start position:0%
+truth and leaves that to the philosopher
+ 
+
+ align:start position:0%
+truth and leaves that to the philosopher
+is that truth in many cases is a
+
+ align:start position:0%
+is that truth in many cases is a
+ 
+
+ align:start position:0%
+is that truth in many cases is a
+relative thing. It's based on the
+
+ align:start position:0%
+relative thing. It's based on the
+ 
+
+ align:start position:0%
+relative thing. It's based on the
+available knowledge. It's also based on
+
+ align:start position:0%
+available knowledge. It's also based on
+ 
+
+ align:start position:0%
+available knowledge. It's also based on
+the situation that we want to handle. In
+
+ align:start position:0%
+the situation that we want to handle. In
+ 
+
+ align:start position:0%
+the situation that we want to handle. In
+other words, what is truth?
+
+ align:start position:0%
+other words, what is truth?
+ 
+
+ align:start position:0%
+other words, what is truth?
+And my claim is that the answer depends
+
+ align:start position:0%
+And my claim is that the answer depends
+ 
+
+ align:start position:0%
+And my claim is that the answer depends
+on the situation.
+
+ align:start position:0%
+on the situation.
+ 
+
+ align:start position:0%
+on the situation.
+Well, let me give you again a trivial
+
+ align:start position:0%
+Well, let me give you again a trivial
+ 
+
+ align:start position:0%
+Well, let me give you again a trivial
+arithmetic situation. Does 1/2 + 1/3= 56
+
+ align:start position:0%
+arithmetic situation. Does 1/2 + 1/3= 56
+ 
+
+ align:start position:0%
+arithmetic situation. Does 1/2 + 1/3= 56
+or does 1/2 + 1/3 equal two fifths? And
+
+ align:start position:0%
+or does 1/2 + 1/3 equal two fifths? And
+ 
+
+ align:start position:0%
+or does 1/2 + 1/3 equal two fifths? And
+again, the answer is it depends on what
+
+ align:start position:0%
+again, the answer is it depends on what
+ 
+
+ align:start position:0%
+again, the answer is it depends on what
+real life problem you're dealing with.
+
+ align:start position:0%
+real life problem you're dealing with.
+ 
+
+ align:start position:0%
+real life problem you're dealing with.
+For example, if a person is working for
+
+ align:start position:0%
+For example, if a person is working for
+ 
+
+ align:start position:0%
+For example, if a person is working for
+you by the hour and he works for you for
+
+ align:start position:0%
+you by the hour and he works for you for
+ 
+
+ align:start position:0%
+you by the hour and he works for you for
+a half hour one day and a third of an
+
+ align:start position:0%
+a half hour one day and a third of an
+ 
+
+ align:start position:0%
+a half hour one day and a third of an
+hour the next day, the total time he's
+
+ align:start position:0%
+hour the next day, the total time he's
+ 
+
+ align:start position:0%
+hour the next day, the total time he's
+worked is 56 of an hour. Why? Because
+
+ align:start position:0%
+worked is 56 of an hour. Why? Because
+ 
+
+ align:start position:0%
+worked is 56 of an hour. Why? Because
+this agrees with our real life
+
+ align:start position:0%
+this agrees with our real life
+ 
+
+ align:start position:0%
+this agrees with our real life
+experience that 30 minutes plus 20
+
+ align:start position:0%
+experience that 30 minutes plus 20
+ 
+
+ align:start position:0%
+experience that 30 minutes plus 20
+minutes is 50 minutes. On the other
+
+ align:start position:0%
+minutes is 50 minutes. On the other
+ 
+
+ align:start position:0%
+minutes is 50 minutes. On the other
+hand, if a baseball player goes one for
+
+ align:start position:0%
+hand, if a baseball player goes one for
+ 
+
+ align:start position:0%
+hand, if a baseball player goes one for
+two in the first game of a double header
+
+ align:start position:0%
+two in the first game of a double header
+ 
+
+ align:start position:0%
+two in the first game of a double header
+and one for three in the second game of
+
+ align:start position:0%
+and one for three in the second game of
+ 
+
+ align:start position:0%
+and one for three in the second game of
+a double header, he has batted two hits
+
+ align:start position:0%
+a double header, he has batted two hits
+ 
+
+ align:start position:0%
+a double header, he has batted two hits
+in five times at bat. In fact, if you
+
+ align:start position:0%
+in five times at bat. In fact, if you
+ 
+
+ align:start position:0%
+in five times at bat. In fact, if you
+could convince the public that he had
+
+ align:start position:0%
+could convince the public that he had
+ 
+
+ align:start position:0%
+could convince the public that he had
+five hits and six times at bat, you
+
+ align:start position:0%
+five hits and six times at bat, you
+ 
+
+ align:start position:0%
+five hits and six times at bat, you
+could become a director of any economy
+
+ align:start position:0%
+could become a director of any economy
+ 
+
+ align:start position:0%
+could become a director of any economy
+program in the nation. I guess the point
+
+ align:start position:0%
+program in the nation. I guess the point
+ 
+
+ align:start position:0%
+program in the nation. I guess the point
+however is this in most arithmetic
+
+ align:start position:0%
+however is this in most arithmetic
+ 
+
+ align:start position:0%
+however is this in most arithmetic
+questions that we deal with we are used
+
+ align:start position:0%
+questions that we deal with we are used
+ 
+
+ align:start position:0%
+questions that we deal with we are used
+to the physical interpretation in which
+
+ align:start position:0%
+to the physical interpretation in which
+ 
+
+ align:start position:0%
+to the physical interpretation in which
+1/2 + 1/3= 56 reflects the real life
+
+ align:start position:0%
+1/2 + 1/3= 56 reflects the real life
+ 
+
+ align:start position:0%
+1/2 + 1/3= 56 reflects the real life
+situation. Whereas this example here may
+
+ align:start position:0%
+situation. Whereas this example here may
+ 
+
+ align:start position:0%
+situation. Whereas this example here may
+seem trivial namely how often are you
+
+ align:start position:0%
+seem trivial namely how often are you
+ 
+
+ align:start position:0%
+seem trivial namely how often are you
+going to be involved with batting
+
+ align:start position:0%
+going to be involved with batting
+ 
+
+ align:start position:0%
+going to be involved with batting
+averages unless you're doing sixth grade
+
+ align:start position:0%
+averages unless you're doing sixth grade
+ 
+
+ align:start position:0%
+averages unless you're doing sixth grade
+arithmetic. The point remains ironically
+
+ align:start position:0%
+arithmetic. The point remains ironically
+ 
+
+ align:start position:0%
+arithmetic. The point remains ironically
+or whatever you want to call it that
+
+ align:start position:0%
+or whatever you want to call it that
+ 
+
+ align:start position:0%
+or whatever you want to call it that
+this little batting average problem is
+
+ align:start position:0%
+this little batting average problem is
+ 
+
+ align:start position:0%
+this little batting average problem is
+not trivial. In the world of
+
+ align:start position:0%
+not trivial. In the world of
+ 
+
+ align:start position:0%
+not trivial. In the world of
+engineering, we know this example as the
+
+ align:start position:0%
+engineering, we know this example as the
+ 
+
+ align:start position:0%
+engineering, we know this example as the
+weighted average problem. In other
+
+ align:start position:0%
+weighted average problem. In other
+ 
+
+ align:start position:0%
+weighted average problem. In other
+words, you'll notice that 2 over5 as a
+
+ align:start position:0%
+words, you'll notice that 2 over5 as a
+ 
+
+ align:start position:0%
+words, you'll notice that 2 over5 as a
+fraction is more nearly equal to 1/3
+
+ align:start position:0%
+fraction is more nearly equal to 1/3
+ 
+
+ align:start position:0%
+fraction is more nearly equal to 1/3
+than it is equal to 1/2. And the reason
+
+ align:start position:0%
+than it is equal to 1/2. And the reason
+ 
+
+ align:start position:0%
+than it is equal to 1/2. And the reason
+for that is that the player batted at
+
+ align:start position:0%
+for that is that the player batted at
+ 
+
+ align:start position:0%
+for that is that the player batted at
+the lower average one over three, one
+
+ align:start position:0%
+the lower average one over three, one
+ 
+
+ align:start position:0%
+the lower average one over three, one
+hit and three times at bat for more
+
+ align:start position:0%
+hit and three times at bat for more
+ 
+
+ align:start position:0%
+hit and three times at bat for more
+times at bat. In other words, the three
+
+ align:start position:0%
+times at bat. In other words, the three
+ 
+
+ align:start position:0%
+times at bat. In other words, the three
+has a heavier waiting factor than the
+
+ align:start position:0%
+has a heavier waiting factor than the
+ 
+
+ align:start position:0%
+has a heavier waiting factor than the
+two. And every time that you use a
+
+ align:start position:0%
+two. And every time that you use a
+ 
+
+ align:start position:0%
+two. And every time that you use a
+weighted average in a scientific
+
+ align:start position:0%
+weighted average in a scientific
+ 
+
+ align:start position:0%
+weighted average in a scientific
+engineering oriented investigation, this
+
+ align:start position:0%
+engineering oriented investigation, this
+ 
+
+ align:start position:0%
+engineering oriented investigation, this
+is the truth, not this. In other words,
+
+ align:start position:0%
+is the truth, not this. In other words,
+ 
+
+ align:start position:0%
+is the truth, not this. In other words,
+it is neither true nor false that 1/2 +
+
+ align:start position:0%
+it is neither true nor false that 1/2 +
+ 
+
+ align:start position:0%
+it is neither true nor false that 1/2 +
+1/3 equals 2- fifths or that 1/2 + 1/3=
+
+ align:start position:0%
+1/3 equals 2- fifths or that 1/2 + 1/3=
+ 
+
+ align:start position:0%
+1/3 equals 2- fifths or that 1/2 + 1/3=
+56. Which is true depends on the
+
+ align:start position:0%
+56. Which is true depends on the
+ 
+
+ align:start position:0%
+56. Which is true depends on the
+particular physical situation. You see a
+
+ align:start position:0%
+particular physical situation. You see a
+ 
+
+ align:start position:0%
+particular physical situation. You see a
+rather interesting point here that we
+
+ align:start position:0%
+rather interesting point here that we
+ 
+
+ align:start position:0%
+rather interesting point here that we
+sometimes allow truth to be based on
+
+ align:start position:0%
+sometimes allow truth to be based on
+ 
+
+ align:start position:0%
+sometimes allow truth to be based on
+what particular problem we're trying to
+
+ align:start position:0%
+what particular problem we're trying to
+ 
+
+ align:start position:0%
+what particular problem we're trying to
+solve. Another way that we manipulate
+
+ align:start position:0%
+solve. Another way that we manipulate
+ 
+
+ align:start position:0%
+solve. Another way that we manipulate
+truth is that we sometimes have a rule
+
+ align:start position:0%
+truth is that we sometimes have a rule
+ 
+
+ align:start position:0%
+truth is that we sometimes have a rule
+that we like to be true. In fact, I
+
+ align:start position:0%
+that we like to be true. In fact, I
+ 
+
+ align:start position:0%
+that we like to be true. In fact, I
+guess this is probably what happens with
+
+ align:start position:0%
+guess this is probably what happens with
+ 
+
+ align:start position:0%
+guess this is probably what happens with
+most political theories that one starts
+
+ align:start position:0%
+most political theories that one starts
+ 
+
+ align:start position:0%
+most political theories that one starts
+with the objectives, knows what it is
+
+ align:start position:0%
+with the objectives, knows what it is
+ 
+
+ align:start position:0%
+with the objectives, knows what it is
+that he wants to be true, and then
+
+ align:start position:0%
+that he wants to be true, and then
+ 
+
+ align:start position:0%
+that he wants to be true, and then
+invents the definitions and the rules to
+
+ align:start position:0%
+invents the definitions and the rules to
+ 
+
+ align:start position:0%
+invents the definitions and the rules to
+conform with this. In much the same way
+
+ align:start position:0%
+conform with this. In much the same way
+ 
+
+ align:start position:0%
+conform with this. In much the same way
+as around the fourth grade again, we
+
+ align:start position:0%
+as around the fourth grade again, we
+ 
+
+ align:start position:0%
+as around the fourth grade again, we
+learn such adages as look before you
+
+ align:start position:0%
+learn such adages as look before you
+ 
+
+ align:start position:0%
+learn such adages as look before you
+leap. And two minutes later, you learn
+
+ align:start position:0%
+leap. And two minutes later, you learn
+ 
+
+ align:start position:0%
+leap. And two minutes later, you learn
+he who hesitates is lost. and suddenly
+
+ align:start position:0%
+he who hesitates is lost. and suddenly
+ 
+
+ align:start position:0%
+he who hesitates is lost. and suddenly
+you come to the conclusion that you can
+
+ align:start position:0%
+you come to the conclusion that you can
+ 
+
+ align:start position:0%
+you come to the conclusion that you can
+make your assumptions validify any
+
+ align:start position:0%
+make your assumptions validify any
+ 
+
+ align:start position:0%
+make your assumptions validify any
+conclusion you want just by choosing
+
+ align:start position:0%
+conclusion you want just by choosing
+ 
+
+ align:start position:0%
+conclusion you want just by choosing
+your assumptions appropriately. Now if
+
+ align:start position:0%
+your assumptions appropriately. Now if
+ 
+
+ align:start position:0%
+your assumptions appropriately. Now if
+that sounds degrading let me show you
+
+ align:start position:0%
+that sounds degrading let me show you
+ 
+
+ align:start position:0%
+that sounds degrading let me show you
+how it's used effectively in
+
+ align:start position:0%
+how it's used effectively in
+ 
+
+ align:start position:0%
+how it's used effectively in
+mathematics.
+
+ align:start position:0%
+mathematics.
+ 
+
+ align:start position:0%
+mathematics.
+In other words, let me just say that
+
+ align:start position:0%
+In other words, let me just say that
+ 
+
+ align:start position:0%
+In other words, let me just say that
+predetermined rules may control truth.
+
+ align:start position:0%
+predetermined rules may control truth.
+ 
+
+ align:start position:0%
+predetermined rules may control truth.
+Let me give you an example. Going back
+
+ align:start position:0%
+Let me give you an example. Going back
+ 
+
+ align:start position:0%
+Let me give you an example. Going back
+to exponents, why does b to the 0 equal
+
+ align:start position:0%
+to exponents, why does b to the 0 equal
+ 
+
+ align:start position:0%
+to exponents, why does b to the 0 equal
+one?
+
+ align:start position:0%
+one?
+ 
+
+ align:start position:0%
+one?
+The answer is very simple that when we
+
+ align:start position:0%
+The answer is very simple that when we
+ 
+
+ align:start position:0%
+The answer is very simple that when we
+used positive exponents,
+
+ align:start position:0%
+used positive exponents,
+ 
+
+ align:start position:0%
+used positive exponents,
+positive whole number exponents, we
+
+ align:start position:0%
+positive whole number exponents, we
+ 
+
+ align:start position:0%
+positive whole number exponents, we
+talked about that many factors of B. And
+
+ align:start position:0%
+talked about that many factors of B. And
+ 
+
+ align:start position:0%
+talked about that many factors of B. And
+one of the interesting rules that we saw
+
+ align:start position:0%
+one of the interesting rules that we saw
+ 
+
+ align:start position:0%
+one of the interesting rules that we saw
+that was obeyed by whole number
+
+ align:start position:0%
+that was obeyed by whole number
+ 
+
+ align:start position:0%
+that was obeyed by whole number
+exponents was that if you multiplied B
+
+ align:start position:0%
+exponents was that if you multiplied B
+ 
+
+ align:start position:0%
+exponents was that if you multiplied B
+to the M power by B to the N power, you
+
+ align:start position:0%
+to the M power by B to the N power, you
+ 
+
+ align:start position:0%
+to the M power by B to the N power, you
+got as an answer B to the M + N power.
+
+ align:start position:0%
+got as an answer B to the M + N power.
+ 
+
+ align:start position:0%
+got as an answer B to the M + N power.
+Okay? B to the M plus N. Now, the
+
+ align:start position:0%
+Okay? B to the M plus N. Now, the
+ 
+
+ align:start position:0%
+Okay? B to the M plus N. Now, the
+interesting thing is
+
+ align:start position:0%
+interesting thing is
+ 
+
+ align:start position:0%
+interesting thing is
+that after a while, you never even paid
+
+ align:start position:0%
+that after a while, you never even paid
+ 
+
+ align:start position:0%
+that after a while, you never even paid
+attention to why this rule worked. What
+
+ align:start position:0%
+attention to why this rule worked. What
+ 
+
+ align:start position:0%
+attention to why this rule worked. What
+you did know was that this was a pretty
+
+ align:start position:0%
+you did know was that this was a pretty
+ 
+
+ align:start position:0%
+you did know was that this was a pretty
+darn convenient rule to use.
+
+ align:start position:0%
+darn convenient rule to use.
+ 
+
+ align:start position:0%
+darn convenient rule to use.
+Computationally, this rule simplified
+
+ align:start position:0%
+Computationally, this rule simplified
+ 
+
+ align:start position:0%
+Computationally, this rule simplified
+many particular combination uh uh
+
+ align:start position:0%
+many particular combination uh uh
+ 
+
+ align:start position:0%
+many particular combination uh uh
+computations that you were doing. In
+
+ align:start position:0%
+computations that you were doing. In
+ 
+
+ align:start position:0%
+computations that you were doing. In
+particular, then as soon as n is zero,
+
+ align:start position:0%
+particular, then as soon as n is zero,
+ 
+
+ align:start position:0%
+particular, then as soon as n is zero,
+you would still like to be able to use
+
+ align:start position:0%
+you would still like to be able to use
+ 
+
+ align:start position:0%
+you would still like to be able to use
+this rule. In other words, we want this
+
+ align:start position:0%
+this rule. In other words, we want this
+ 
+
+ align:start position:0%
+this rule. In other words, we want this
+nice rule to apply even when n equals z.
+
+ align:start position:0%
+nice rule to apply even when n equals z.
+ 
+
+ align:start position:0%
+nice rule to apply even when n equals z.
+Now, let's look at this from a
+
+ align:start position:0%
+Now, let's look at this from a
+ 
+
+ align:start position:0%
+Now, let's look at this from a
+computational point of view. If we want
+
+ align:start position:0%
+computational point of view. If we want
+ 
+
+ align:start position:0%
+computational point of view. If we want
+this rule
+
+ align:start position:0%
+this rule
+ 
+
+ align:start position:0%
+this rule
+to apply when n equals z, let's simply
+
+ align:start position:0%
+to apply when n equals z, let's simply
+ 
+
+ align:start position:0%
+to apply when n equals z, let's simply
+rewrite this exactly as it appears here
+
+ align:start position:0%
+rewrite this exactly as it appears here
+ 
+
+ align:start position:0%
+rewrite this exactly as it appears here
+with n equal to zero. All right, we then
+
+ align:start position:0%
+with n equal to zero. All right, we then
+ 
+
+ align:start position:0%
+with n equal to zero. All right, we then
+have what? We have B. We'll just repeat
+
+ align:start position:0%
+have what? We have B. We'll just repeat
+ 
+
+ align:start position:0%
+have what? We have B. We'll just repeat
+everything here. b to the M
+
+ align:start position:0%
+everything here. b to the M
+ 
+
+ align:start position:0%
+everything here. b to the M
+times B. Now we're replacing N by zero.
+
+ align:start position:0%
+times B. Now we're replacing N by zero.
+ 
+
+ align:start position:0%
+times B. Now we're replacing N by zero.
+So that's B to the 0. And that must
+
+ align:start position:0%
+So that's B to the 0. And that must
+ 
+
+ align:start position:0%
+So that's B to the 0. And that must
+equal B to the M + N. That's M + 0.
+
+ align:start position:0%
+equal B to the M + N. That's M + 0.
+ 
+
+ align:start position:0%
+equal B to the M + N. That's M + 0.
+But the interesting point is that we
+
+ align:start position:0%
+But the interesting point is that we
+ 
+
+ align:start position:0%
+But the interesting point is that we
+know how to add numbers. And for
+
+ align:start position:0%
+know how to add numbers. And for
+ 
+
+ align:start position:0%
+know how to add numbers. And for
+numbers, m + 0 is m. In other words,
+
+ align:start position:0%
+numbers, m + 0 is m. In other words,
+ 
+
+ align:start position:0%
+numbers, m + 0 is m. In other words,
+this is still b to the m. Now we look at
+
+ align:start position:0%
+this is still b to the m. Now we look at
+ 
+
+ align:start position:0%
+this is still b to the m. Now we look at
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+and what we're saying is if we want the
+
+ align:start position:0%
+and what we're saying is if we want the
+ 
+
+ align:start position:0%
+and what we're saying is if we want the
+rule b to the m * b to the n to equal b
+
+ align:start position:0%
+rule b to the m * b to the n to equal b
+ 
+
+ align:start position:0%
+rule b to the m * b to the n to equal b
+to the m + n to be true even when n is
+
+ align:start position:0%
+to the m + n to be true even when n is
+ 
+
+ align:start position:0%
+to the m + n to be true even when n is
+zero. This says that b to the 0 must be
+
+ align:start position:0%
+zero. This says that b to the 0 must be
+ 
+
+ align:start position:0%
+zero. This says that b to the 0 must be
+that number such that when we multiply
+
+ align:start position:0%
+that number such that when we multiply
+ 
+
+ align:start position:0%
+that number such that when we multiply
+it by b to the m we get b to the m. Now
+
+ align:start position:0%
+it by b to the m we get b to the m. Now
+ 
+
+ align:start position:0%
+it by b to the m we get b to the m. Now
+what number has the property that when
+
+ align:start position:0%
+what number has the property that when
+ 
+
+ align:start position:0%
+what number has the property that when
+you multiply it by b to the m you get b
+
+ align:start position:0%
+you multiply it by b to the m you get b
+ 
+
+ align:start position:0%
+you multiply it by b to the m you get b
+to the m? And if you're real quick, you
+
+ align:start position:0%
+to the m? And if you're real quick, you
+ 
+
+ align:start position:0%
+to the m? And if you're real quick, you
+say one. And if you're algebra oriented,
+
+ align:start position:0%
+say one. And if you're algebra oriented,
+ 
+
+ align:start position:0%
+say one. And if you're algebra oriented,
+you say b to the 0 is therefore equal b
+
+ align:start position:0%
+you say b to the 0 is therefore equal b
+ 
+
+ align:start position:0%
+you say b to the 0 is therefore equal b
+to the m / b to the m. And again, you
+
+ align:start position:0%
+to the m / b to the m. And again, you
+ 
+
+ align:start position:0%
+to the m / b to the m. And again, you
+say one,
+
+ align:start position:0%
+say one,
+ 
+
+ align:start position:0%
+say one,
+except of course that b must be unequal
+
+ align:start position:0%
+except of course that b must be unequal
+ 
+
+ align:start position:0%
+except of course that b must be unequal
+to zero because hopefully by this time
+
+ align:start position:0%
+to zero because hopefully by this time
+ 
+
+ align:start position:0%
+to zero because hopefully by this time
+we understand why we must never divide
+
+ align:start position:0%
+we understand why we must never divide
+ 
+
+ align:start position:0%
+we understand why we must never divide
+by zero. In other words, what we now
+
+ align:start position:0%
+by zero. In other words, what we now
+ 
+
+ align:start position:0%
+by zero. In other words, what we now
+have is the old high school rule that
+
+ align:start position:0%
+have is the old high school rule that
+ 
+
+ align:start position:0%
+have is the old high school rule that
+B to the 0 equals 1 provided B is
+
+ align:start position:0%
+B to the 0 equals 1 provided B is
+ 
+
+ align:start position:0%
+B to the 0 equals 1 provided B is
+unequal to zero. But here's the
+
+ align:start position:0%
+unequal to zero. But here's the
+ 
+
+ align:start position:0%
+unequal to zero. But here's the
+important point. If I have never defined
+
+ align:start position:0%
+important point. If I have never defined
+ 
+
+ align:start position:0%
+important point. If I have never defined
+B to the 0 and somebody says to me, make
+
+ align:start position:0%
+B to the 0 and somebody says to me, make
+ 
+
+ align:start position:0%
+B to the 0 and somebody says to me, make
+up a definition for B to the zero and I
+
+ align:start position:0%
+up a definition for B to the zero and I
+ 
+
+ align:start position:0%
+up a definition for B to the zero and I
+say okay B to the 0 is going to be 36. I
+
+ align:start position:0%
+say okay B to the 0 is going to be 36. I
+ 
+
+ align:start position:0%
+say okay B to the 0 is going to be 36. I
+have every right in the world to make up
+
+ align:start position:0%
+have every right in the world to make up
+ 
+
+ align:start position:0%
+have every right in the world to make up
+that definition. What I don't have a
+
+ align:start position:0%
+that definition. What I don't have a
+ 
+
+ align:start position:0%
+that definition. What I don't have a
+right to do is when I'm ever using an
+
+ align:start position:0%
+right to do is when I'm ever using an
+ 
+
+ align:start position:0%
+right to do is when I'm ever using an
+expression like B to the zero is to
+
+ align:start position:0%
+expression like B to the zero is to
+ 
+
+ align:start position:0%
+expression like B to the zero is to
+assume that I have the right to use this
+
+ align:start position:0%
+assume that I have the right to use this
+ 
+
+ align:start position:0%
+assume that I have the right to use this
+particular recipe. In other words, if I
+
+ align:start position:0%
+particular recipe. In other words, if I
+ 
+
+ align:start position:0%
+particular recipe. In other words, if I
+want to be able to use the nice recipe
+
+ align:start position:0%
+want to be able to use the nice recipe
+ 
+
+ align:start position:0%
+want to be able to use the nice recipe
+even when N is zero, I have no choice
+
+ align:start position:0%
+even when N is zero, I have no choice
+ 
+
+ align:start position:0%
+even when N is zero, I have no choice
+but to define B to the 0 to equal one.
+
+ align:start position:0%
+but to define B to the 0 to equal one.
+ 
+
+ align:start position:0%
+but to define B to the 0 to equal one.
+Therefore, we make up that definition
+
+ align:start position:0%
+Therefore, we make up that definition
+ 
+
+ align:start position:0%
+Therefore, we make up that definition
+because we want that recipe to apply.
+
+ align:start position:0%
+because we want that recipe to apply.
+ 
+
+ align:start position:0%
+because we want that recipe to apply.
+And that's exactly what we're going to
+
+ align:start position:0%
+And that's exactly what we're going to
+ 
+
+ align:start position:0%
+And that's exactly what we're going to
+be doing through most of this course. We
+
+ align:start position:0%
+be doing through most of this course. We
+ 
+
+ align:start position:0%
+be doing through most of this course. We
+are going to look at certain real life
+
+ align:start position:0%
+are going to look at certain real life
+ 
+
+ align:start position:0%
+are going to look at certain real life
+situations. We are going to look at
+
+ align:start position:0%
+situations. We are going to look at
+ 
+
+ align:start position:0%
+situations. We are going to look at
+certain recipes that we want to apply
+
+ align:start position:0%
+certain recipes that we want to apply
+ 
+
+ align:start position:0%
+certain recipes that we want to apply
+and we are going to make up definitions
+
+ align:start position:0%
+and we are going to make up definitions
+ 
+
+ align:start position:0%
+and we are going to make up definitions
+this way and then see how our
+
+ align:start position:0%
+this way and then see how our
+ 
+
+ align:start position:0%
+this way and then see how our
+inescapable conclusions follow from
+
+ align:start position:0%
+inescapable conclusions follow from
+ 
+
+ align:start position:0%
+inescapable conclusions follow from
+these definitions. More about that will
+
+ align:start position:0%
+these definitions. More about that will
+ 
+
+ align:start position:0%
+these definitions. More about that will
+be said in the remainder of this unit
+
+ align:start position:0%
+be said in the remainder of this unit
+ 
+
+ align:start position:0%
+be said in the remainder of this unit
+and our next lecture will pick up the
+
+ align:start position:0%
+and our next lecture will pick up the
+ 
+
+ align:start position:0%
+and our next lecture will pick up the
+game of mathematics in a different
+
+ align:start position:0%
+game of mathematics in a different
+ 
+
+ align:start position:0%
+game of mathematics in a different
+context. But until next time, goodbye.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Funding for the publication of this
+
+ align:start position:0%
+Funding for the publication of this
+ 
+
+ align:start position:0%
+Funding for the publication of this
+video was provided by the Gabriella and
+
+ align:start position:0%
+video was provided by the Gabriella and
+ 
+
+ align:start position:0%
+video was provided by the Gabriella and
+Paul Rosenbomb Foundation.
+
+ align:start position:0%
+Paul Rosenbomb Foundation.
+ 
+
+ align:start position:0%
+Paul Rosenbomb Foundation.
+Help OCW continue to provide free and
+
+ align:start position:0%
+Help OCW continue to provide free and
+ 
+
+ align:start position:0%
+Help OCW continue to provide free and
+open access to MIT courses by making a
+
+ align:start position:0%
+open access to MIT courses by making a
+ 
+
+ align:start position:0%
+open access to MIT courses by making a
+donation at ocw.mmit.edu/donate.
\ No newline at end of file
diff --git a/wvLUlPCbc5s.txt b/wvLUlPCbc5s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7d40550f14ca0b69f173d336ab0d832335590ec1
--- /dev/null
+++ b/wvLUlPCbc5s.txt
@@ -0,0 +1,12555 @@
+align:start position:0%
+ 
+Um, my name is Rob Clark. I'm from uh
+
+ align:start position:0%
+Um, my name is Rob Clark. I'm from uh
+ 
+
+ align:start position:0%
+Um, my name is Rob Clark. I'm from uh
+Michigan State University School of
+
+ align:start position:0%
+Michigan State University School of
+ 
+
+ align:start position:0%
+Michigan State University School of
+Packaging and I've been doing uh RFID
+
+ align:start position:0%
+Packaging and I've been doing uh RFID
+ 
+
+ align:start position:0%
+Packaging and I've been doing uh RFID
+research uh since 1999. Uh, we just are
+
+ align:start position:0%
+research uh since 1999. Uh, we just are
+ 
+
+ align:start position:0%
+research uh since 1999. Uh, we just are
+in the process of finalizing purchase of
+
+ align:start position:0%
+in the process of finalizing purchase of
+ 
+
+ align:start position:0%
+in the process of finalizing purchase of
+a 10,000 square foot facility to move uh
+
+ align:start position:0%
+a 10,000 square foot facility to move uh
+ 
+
+ align:start position:0%
+a 10,000 square foot facility to move uh
+a new lab uh that'll look at both active
+
+ align:start position:0%
+a new lab uh that'll look at both active
+ 
+
+ align:start position:0%
+a new lab uh that'll look at both active
+and passive. But um moving forward with
+
+ align:start position:0%
+and passive. But um moving forward with
+ 
+
+ align:start position:0%
+and passive. But um moving forward with
+this whole session now, uh a couple
+
+ align:start position:0%
+this whole session now, uh a couple
+ 
+
+ align:start position:0%
+this whole session now, uh a couple
+things that kind of bothered me about
+
+ align:start position:0%
+things that kind of bothered me about
+ 
+
+ align:start position:0%
+things that kind of bothered me about
+this. Um I keep walking in and on the
+
+ align:start position:0%
+this. Um I keep walking in and on the
+ 
+
+ align:start position:0%
+this. Um I keep walking in and on the
+bulletin boards right outside the door
+
+ align:start position:0%
+bulletin boards right outside the door
+ 
+
+ align:start position:0%
+bulletin boards right outside the door
+there is a big advertisement for urine
+
+ align:start position:0%
+there is a big advertisement for urine
+ 
+
+ align:start position:0%
+there is a big advertisement for urine
+town and I want to know who leaked
+
+ align:start position:0%
+town and I want to know who leaked
+ 
+
+ align:start position:0%
+town and I want to know who leaked
+information about this session.
+
+ align:start position:0%
+information about this session.
+ 
+
+ align:start position:0%
+information about this session.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Okay. Um from a packaging standpoint,
+
+ align:start position:0%
+Okay. Um from a packaging standpoint,
+ 
+
+ align:start position:0%
+Okay. Um from a packaging standpoint,
+how many people here are directly
+
+ align:start position:0%
+how many people here are directly
+ 
+
+ align:start position:0%
+how many people here are directly
+involved with packaging?
+
+ align:start position:0%
+involved with packaging?
+ 
+
+ align:start position:0%
+involved with packaging?
+Okay, a few uh you may or may not know
+
+ align:start position:0%
+Okay, a few uh you may or may not know
+ 
+
+ align:start position:0%
+Okay, a few uh you may or may not know
+Jim Goff, the name who founded the
+
+ align:start position:0%
+Jim Goff, the name who founded the
+ 
+
+ align:start position:0%
+Jim Goff, the name who founded the
+packaging discipline at Michigan State
+
+ align:start position:0%
+packaging discipline at Michigan State
+ 
+
+ align:start position:0%
+packaging discipline at Michigan State
+University, the first academic packaging
+
+ align:start position:0%
+University, the first academic packaging
+ 
+
+ align:start position:0%
+University, the first academic packaging
+uh facility in the world. Uh he just
+
+ align:start position:0%
+uh facility in the world. Uh he just
+ 
+
+ align:start position:0%
+uh facility in the world. Uh he just
+passed away last week and uh very
+
+ align:start position:0%
+passed away last week and uh very
+ 
+
+ align:start position:0%
+passed away last week and uh very
+unfortunate situation.
+
+ align:start position:0%
+unfortunate situation.
+ 
+
+ align:start position:0%
+unfortunate situation.
+Um, and for those of you that didn't
+
+ align:start position:0%
+Um, and for those of you that didn't
+ 
+
+ align:start position:0%
+Um, and for those of you that didn't
+know on the news this morning, Super
+
+ align:start position:0%
+know on the news this morning, Super
+ 
+
+ align:start position:0%
+know on the news this morning, Super
+Value just purchased Albertson's, and we
+
+ align:start position:0%
+Value just purchased Albertson's, and we
+ 
+
+ align:start position:0%
+Value just purchased Albertson's, and we
+don't know what that's going to do to
+
+ align:start position:0%
+don't know what that's going to do to
+ 
+
+ align:start position:0%
+don't know what that's going to do to
+their RFID
+
+ align:start position:0%
+their RFID
+ 
+
+ align:start position:0%
+their RFID
+uh, announcements.
+
+ align:start position:0%
+uh, announcements.
+ 
+
+ align:start position:0%
+uh, announcements.
+But, and I also want to thank the sound
+
+ align:start position:0%
+But, and I also want to thank the sound
+ 
+
+ align:start position:0%
+But, and I also want to thank the sound
+guy up there, uh, because he's been
+
+ align:start position:0%
+guy up there, uh, because he's been
+ 
+
+ align:start position:0%
+guy up there, uh, because he's been
+working his tail off for this entire
+
+ align:start position:0%
+working his tail off for this entire
+ 
+
+ align:start position:0%
+working his tail off for this entire
+conference.
+
+ align:start position:0%
+conference.
+ 
+
+ align:start position:0%
+conference.
+And the rest you'll wait for.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Special thanks to Steve Miles and the
+
+ align:start position:0%
+Special thanks to Steve Miles and the
+ 
+
+ align:start position:0%
+Special thanks to Steve Miles and the
+MIT crew, the conference committee for
+
+ align:start position:0%
+MIT crew, the conference committee for
+ 
+
+ align:start position:0%
+MIT crew, the conference committee for
+all the work and phone calls that we had
+
+ align:start position:0%
+all the work and phone calls that we had
+ 
+
+ align:start position:0%
+all the work and phone calls that we had
+back and forth, all the speakers, and of
+
+ align:start position:0%
+back and forth, all the speakers, and of
+ 
+
+ align:start position:0%
+back and forth, all the speakers, and of
+course all the attendees because without
+
+ align:start position:0%
+course all the attendees because without
+ 
+
+ align:start position:0%
+course all the attendees because without
+the interchange of our ideas and your
+
+ align:start position:0%
+the interchange of our ideas and your
+ 
+
+ align:start position:0%
+the interchange of our ideas and your
+input, this wouldn't move very far. And
+
+ align:start position:0%
+input, this wouldn't move very far. And
+ 
+
+ align:start position:0%
+input, this wouldn't move very far. And
+we can all say that we're part of the
+
+ align:start position:0%
+we can all say that we're part of the
+ 
+
+ align:start position:0%
+we can all say that we're part of the
+soers club now due to our walk yesterday
+
+ align:start position:0%
+soers club now due to our walk yesterday
+ 
+
+ align:start position:0%
+soers club now due to our walk yesterday
+uh crossing the puddles uh on the way
+
+ align:start position:0%
+uh crossing the puddles uh on the way
+ 
+
+ align:start position:0%
+uh crossing the puddles uh on the way
+there. We're we're we're bound for life.
+
+ align:start position:0%
+there. We're we're we're bound for life.
+ 
+
+ align:start position:0%
+there. We're we're we're bound for life.
+Why study packaging? What does packaging
+
+ align:start position:0%
+Why study packaging? What does packaging
+ 
+
+ align:start position:0%
+Why study packaging? What does packaging
+have to do with uh riffid or arid or
+
+ align:start position:0%
+have to do with uh riffid or arid or
+ 
+
+ align:start position:0%
+have to do with uh riffid or arid or
+anything else? Well, Throck Morton P.
+
+ align:start position:0%
+anything else? Well, Throck Morton P.
+ 
+
+ align:start position:0%
+anything else? Well, Throck Morton P.
+Ruddy III, one of my favorite people,
+
+ align:start position:0%
+Ruddy III, one of my favorite people,
+ 
+
+ align:start position:0%
+Ruddy III, one of my favorite people,
+once stated, "Packaging is a center of
+
+ align:start position:0%
+once stated, "Packaging is a center of
+ 
+
+ align:start position:0%
+once stated, "Packaging is a center of
+the universe. You might as well accept
+
+ align:start position:0%
+the universe. You might as well accept
+ 
+
+ align:start position:0%
+the universe. You might as well accept
+it now. All these other disciplines and
+
+ align:start position:0%
+it now. All these other disciplines and
+ 
+
+ align:start position:0%
+it now. All these other disciplines and
+fields just support packaging." And once
+
+ align:start position:0%
+fields just support packaging." And once
+ 
+
+ align:start position:0%
+fields just support packaging." And once
+you come to that agreement, you'll see
+
+ align:start position:0%
+you come to that agreement, you'll see
+ 
+
+ align:start position:0%
+you come to that agreement, you'll see
+why packaging is relevant to RFID.
+
+ align:start position:0%
+why packaging is relevant to RFID.
+ 
+
+ align:start position:0%
+why packaging is relevant to RFID.
+Our work is a ground level handson
+
+ align:start position:0%
+Our work is a ground level handson
+ 
+
+ align:start position:0%
+Our work is a ground level handson
+approach. A lot of the information that
+
+ align:start position:0%
+approach. A lot of the information that
+ 
+
+ align:start position:0%
+approach. A lot of the information that
+I hear is the 30,000 foot overview which
+
+ align:start position:0%
+I hear is the 30,000 foot overview which
+ 
+
+ align:start position:0%
+I hear is the 30,000 foot overview which
+is wonderful. It sets direction. It sets
+
+ align:start position:0%
+is wonderful. It sets direction. It sets
+ 
+
+ align:start position:0%
+is wonderful. It sets direction. It sets
+precedent and it doesn't mean if it
+
+ align:start position:0%
+precedent and it doesn't mean if it
+ 
+
+ align:start position:0%
+precedent and it doesn't mean if it
+doesn't work. You have to have the
+
+ align:start position:0%
+doesn't work. You have to have the
+ 
+
+ align:start position:0%
+doesn't work. You have to have the
+ground level hands-on approach to make
+
+ align:start position:0%
+ground level hands-on approach to make
+ 
+
+ align:start position:0%
+ground level hands-on approach to make
+sure it works. That's what packaging
+
+ align:start position:0%
+sure it works. That's what packaging
+ 
+
+ align:start position:0%
+sure it works. That's what packaging
+does.
+
+ align:start position:0%
+does.
+ 
+
+ align:start position:0%
+does.
+Now, why is this so?
+
+ align:start position:0%
+Now, why is this so?
+ 
+
+ align:start position:0%
+Now, why is this so?
+What is packaging? Real quickly, you're
+
+ align:start position:0%
+What is packaging? Real quickly, you're
+ 
+
+ align:start position:0%
+What is packaging? Real quickly, you're
+all going to be experts in 30 seconds or
+
+ align:start position:0%
+all going to be experts in 30 seconds or
+ 
+
+ align:start position:0%
+all going to be experts in 30 seconds or
+so. There are different levels of
+
+ align:start position:0%
+so. There are different levels of
+ 
+
+ align:start position:0%
+so. There are different levels of
+packaging. Primary, secondary, tertiary,
+
+ align:start position:0%
+packaging. Primary, secondary, tertiary,
+ 
+
+ align:start position:0%
+packaging. Primary, secondary, tertiary,
+all the way up through unitiz loads or
+
+ align:start position:0%
+all the way up through unitiz loads or
+ 
+
+ align:start position:0%
+all the way up through unitiz loads or
+cargo container loads, however you want
+
+ align:start position:0%
+cargo container loads, however you want
+ 
+
+ align:start position:0%
+cargo container loads, however you want
+to look at it. Primary physically holds
+
+ align:start position:0%
+to look at it. Primary physically holds
+ 
+
+ align:start position:0%
+to look at it. Primary physically holds
+the product. A bottle is a primary
+
+ align:start position:0%
+the product. A bottle is a primary
+ 
+
+ align:start position:0%
+the product. A bottle is a primary
+container. Secondary container, we're
+
+ align:start position:0%
+container. Secondary container, we're
+ 
+
+ align:start position:0%
+container. Secondary container, we're
+really brilliant, holds primary
+
+ align:start position:0%
+really brilliant, holds primary
+ 
+
+ align:start position:0%
+really brilliant, holds primary
+containers. So, a six-ack of your
+
+ align:start position:0%
+containers. So, a six-ack of your
+ 
+
+ align:start position:0%
+containers. So, a six-ack of your
+favorite Amber beverages would be a
+
+ align:start position:0%
+favorite Amber beverages would be a
+ 
+
+ align:start position:0%
+favorite Amber beverages would be a
+secondary container. Tertiary, I bet
+
+ align:start position:0%
+secondary container. Tertiary, I bet
+ 
+
+ align:start position:0%
+secondary container. Tertiary, I bet
+you're getting this now, holds the
+
+ align:start position:0%
+you're getting this now, holds the
+ 
+
+ align:start position:0%
+you're getting this now, holds the
+secondary. So, a shipping case would be
+
+ align:start position:0%
+secondary. So, a shipping case would be
+ 
+
+ align:start position:0%
+secondary. So, a shipping case would be
+the tertiary and on and on and on. Not
+
+ align:start position:0%
+the tertiary and on and on and on. Not
+ 
+
+ align:start position:0%
+the tertiary and on and on and on. Not
+all products have the same levels or
+
+ align:start position:0%
+all products have the same levels or
+ 
+
+ align:start position:0%
+all products have the same levels or
+requirements.
+
+ align:start position:0%
+requirements.
+ 
+
+ align:start position:0%
+requirements.
+You also have different requirements for
+
+ align:start position:0%
+You also have different requirements for
+ 
+
+ align:start position:0%
+You also have different requirements for
+different industries. You have the
+
+ align:start position:0%
+different industries. You have the
+ 
+
+ align:start position:0%
+different industries. You have the
+consumer sector, which we've heard a
+
+ align:start position:0%
+consumer sector, which we've heard a
+ 
+
+ align:start position:0%
+consumer sector, which we've heard a
+great deal about, retail outlets, these
+
+ align:start position:0%
+great deal about, retail outlets, these
+ 
+
+ align:start position:0%
+great deal about, retail outlets, these
+types of things. Industrial sector
+
+ align:start position:0%
+types of things. Industrial sector
+ 
+
+ align:start position:0%
+types of things. Industrial sector
+really hasn't gotten a lot of play here
+
+ align:start position:0%
+really hasn't gotten a lot of play here
+ 
+
+ align:start position:0%
+really hasn't gotten a lot of play here
+except some of the the DHL and larger
+
+ align:start position:0%
+except some of the the DHL and larger
+ 
+
+ align:start position:0%
+except some of the the DHL and larger
+volumes, but it's a huge market. When
+
+ align:start position:0%
+volumes, but it's a huge market. When
+ 
+
+ align:start position:0%
+volumes, but it's a huge market. When
+you think of all the trucks you see
+
+ align:start position:0%
+you think of all the trucks you see
+ 
+
+ align:start position:0%
+you think of all the trucks you see
+driving down the highways with the big
+
+ align:start position:0%
+driving down the highways with the big
+ 
+
+ align:start position:0%
+driving down the highways with the big
+boxes of materials or machinery, that's
+
+ align:start position:0%
+boxes of materials or machinery, that's
+ 
+
+ align:start position:0%
+boxes of materials or machinery, that's
+an a sector that is completely ignored.
+
+ align:start position:0%
+an a sector that is completely ignored.
+ 
+
+ align:start position:0%
+an a sector that is completely ignored.
+military.
+
+ align:start position:0%
+military.
+ 
+
+ align:start position:0%
+military.
+Think about packaging something that you
+
+ align:start position:0%
+Think about packaging something that you
+ 
+
+ align:start position:0%
+Think about packaging something that you
+don't know when it's going to be used,
+
+ align:start position:0%
+don't know when it's going to be used,
+ 
+
+ align:start position:0%
+don't know when it's going to be used,
+where it's going to be used, or what the
+
+ align:start position:0%
+where it's going to be used, or what the
+ 
+
+ align:start position:0%
+where it's going to be used, or what the
+evaluation is for once it is in use
+
+ align:start position:0%
+evaluation is for once it is in use
+ 
+
+ align:start position:0%
+evaluation is for once it is in use
+somewhere between now and 20 years from
+
+ align:start position:0%
+somewhere between now and 20 years from
+ 
+
+ align:start position:0%
+somewhere between now and 20 years from
+now. How do you package that? Real
+
+ align:start position:0%
+now. How do you package that? Real
+ 
+
+ align:start position:0%
+now. How do you package that? Real
+interesting dichotomy. And then of
+
+ align:start position:0%
+interesting dichotomy. And then of
+ 
+
+ align:start position:0%
+interesting dichotomy. And then of
+course medical pharmaceuticals, which
+
+ align:start position:0%
+course medical pharmaceuticals, which
+ 
+
+ align:start position:0%
+course medical pharmaceuticals, which
+we've heard a great deal about. How many
+
+ align:start position:0%
+we've heard a great deal about. How many
+ 
+
+ align:start position:0%
+we've heard a great deal about. How many
+of you want your packaging to fail
+
+ align:start position:0%
+of you want your packaging to fail
+ 
+
+ align:start position:0%
+of you want your packaging to fail
+prior to taking your medicine? Okay.
+
+ align:start position:0%
+prior to taking your medicine? Okay.
+ 
+
+ align:start position:0%
+prior to taking your medicine? Okay.
+Huge implications and what goes on for
+
+ align:start position:0%
+Huge implications and what goes on for
+ 
+
+ align:start position:0%
+Huge implications and what goes on for
+uh powdered soap for uh Mr. Proctor and
+
+ align:start position:0%
+uh powdered soap for uh Mr. Proctor and
+ 
+
+ align:start position:0%
+uh powdered soap for uh Mr. Proctor and
+Gamble Cascade. You brought that up
+
+ align:start position:0%
+Gamble Cascade. You brought that up
+ 
+
+ align:start position:0%
+Gamble Cascade. You brought that up
+earlier
+
+ align:start position:0%
+earlier
+ 
+
+ align:start position:0%
+earlier
+uh is a little different than what goes
+
+ align:start position:0%
+uh is a little different than what goes
+ 
+
+ align:start position:0%
+uh is a little different than what goes
+on for a uh life-saving medicine and
+
+ align:start position:0%
+on for a uh life-saving medicine and
+ 
+
+ align:start position:0%
+on for a uh life-saving medicine and
+there are different requirements. So
+
+ align:start position:0%
+there are different requirements. So
+ 
+
+ align:start position:0%
+there are different requirements. So
+packaging has to address those. It then
+
+ align:start position:0%
+packaging has to address those. It then
+ 
+
+ align:start position:0%
+packaging has to address those. It then
+has to do all of that with an eye
+
+ align:start position:0%
+has to do all of that with an eye
+ 
+
+ align:start position:0%
+has to do all of that with an eye
+towards cost. And for 10 seconds, cost
+
+ align:start position:0%
+towards cost. And for 10 seconds, cost
+ 
+
+ align:start position:0%
+towards cost. And for 10 seconds, cost
+and price are not equal. Period. You
+
+ align:start position:0%
+and price are not equal. Period. You
+ 
+
+ align:start position:0%
+and price are not equal. Period. You
+don't talk about the the uh adversion to
+
+ align:start position:0%
+don't talk about the the uh adversion to
+ 
+
+ align:start position:0%
+don't talk about the the uh adversion to
+moving into RFID because of the cost.
+
+ align:start position:0%
+moving into RFID because of the cost.
+ 
+
+ align:start position:0%
+moving into RFID because of the cost.
+It's actually the price that most people
+
+ align:start position:0%
+It's actually the price that most people
+ 
+
+ align:start position:0%
+It's actually the price that most people
+if they look at the cost you have
+
+ align:start position:0%
+if they look at the cost you have
+ 
+
+ align:start position:0%
+if they look at the cost you have
+insurance costs, liability costs,
+
+ align:start position:0%
+insurance costs, liability costs,
+ 
+
+ align:start position:0%
+insurance costs, liability costs,
+opportunity costs, uh goodwill costs and
+
+ align:start position:0%
+opportunity costs, uh goodwill costs and
+ 
+
+ align:start position:0%
+opportunity costs, uh goodwill costs and
+you have to balance the costs positive
+
+ align:start position:0%
+you have to balance the costs positive
+ 
+
+ align:start position:0%
+you have to balance the costs positive
+and negative before you can make a
+
+ align:start position:0%
+and negative before you can make a
+ 
+
+ align:start position:0%
+and negative before you can make a
+business case and that's more the
+
+ align:start position:0%
+business case and that's more the
+ 
+
+ align:start position:0%
+business case and that's more the
+business side coming out. Price is what
+
+ align:start position:0%
+business side coming out. Price is what
+ 
+
+ align:start position:0%
+business side coming out. Price is what
+you pay for something. Environmental
+
+ align:start position:0%
+you pay for something. Environmental
+ 
+
+ align:start position:0%
+you pay for something. Environmental
+issues.
+
+ align:start position:0%
+issues.
+ 
+
+ align:start position:0%
+issues.
+Simply put, your product plus your
+
+ align:start position:0%
+Simply put, your product plus your
+ 
+
+ align:start position:0%
+Simply put, your product plus your
+package
+
+ align:start position:0%
+package
+ 
+
+ align:start position:0%
+package
+at worst has to equal the environment
+
+ align:start position:0%
+at worst has to equal the environment
+ 
+
+ align:start position:0%
+at worst has to equal the environment
+that you're going to ship it through.
+
+ align:start position:0%
+that you're going to ship it through.
+ 
+
+ align:start position:0%
+that you're going to ship it through.
+Now you know everything you need to know
+
+ align:start position:0%
+Now you know everything you need to know
+ 
+
+ align:start position:0%
+Now you know everything you need to know
+about packaging pretty much. If a
+
+ align:start position:0%
+about packaging pretty much. If a
+ 
+
+ align:start position:0%
+about packaging pretty much. If a
+package doesn't do its job in that
+
+ align:start position:0%
+package doesn't do its job in that
+ 
+
+ align:start position:0%
+package doesn't do its job in that
+environment, it breaks down, product
+
+ align:start position:0%
+environment, it breaks down, product
+ 
+
+ align:start position:0%
+environment, it breaks down, product
+spills, breaks, no good. If it's too
+
+ align:start position:0%
+spills, breaks, no good. If it's too
+ 
+
+ align:start position:0%
+spills, breaks, no good. If it's too
+good and your product all gets there in
+
+ align:start position:0%
+good and your product all gets there in
+ 
+
+ align:start position:0%
+good and your product all gets there in
+perfect shape, you're losing money.
+
+ align:start position:0%
+perfect shape, you're losing money.
+ 
+
+ align:start position:0%
+perfect shape, you're losing money.
+So, there's a a fine balance and
+
+ align:start position:0%
+So, there's a a fine balance and
+ 
+
+ align:start position:0%
+So, there's a a fine balance and
+trade-off there that you have to look
+
+ align:start position:0%
+trade-off there that you have to look
+ 
+
+ align:start position:0%
+trade-off there that you have to look
+at.
+
+ align:start position:0%
+at.
+ 
+
+ align:start position:0%
+at.
+Four main functions of packaging, any
+
+ align:start position:0%
+Four main functions of packaging, any
+ 
+
+ align:start position:0%
+Four main functions of packaging, any
+one of which can be considered a package
+
+ align:start position:0%
+one of which can be considered a package
+ 
+
+ align:start position:0%
+one of which can be considered a package
+by itself, but ideally most of the
+
+ align:start position:0%
+by itself, but ideally most of the
+ 
+
+ align:start position:0%
+by itself, but ideally most of the
+packages we're talking about have all
+
+ align:start position:0%
+packages we're talking about have all
+ 
+
+ align:start position:0%
+packages we're talking about have all
+four. Containment, physical holding.
+
+ align:start position:0%
+four. Containment, physical holding.
+ 
+
+ align:start position:0%
+four. Containment, physical holding.
+You'll see my little no sign up there.
+
+ align:start position:0%
+You'll see my little no sign up there.
+ 
+
+ align:start position:0%
+You'll see my little no sign up there.
+Why? Because the containment function of
+
+ align:start position:0%
+Why? Because the containment function of
+ 
+
+ align:start position:0%
+Why? Because the containment function of
+packaging really doesn't mean anything
+
+ align:start position:0%
+packaging really doesn't mean anything
+ 
+
+ align:start position:0%
+packaging really doesn't mean anything
+with respect to RFID implementation,
+
+ align:start position:0%
+with respect to RFID implementation,
+ 
+
+ align:start position:0%
+with respect to RFID implementation,
+convenience and utility, easy opening
+
+ align:start position:0%
+convenience and utility, easy opening
+ 
+
+ align:start position:0%
+convenience and utility, easy opening
+features, uh reclosability,
+
+ align:start position:0%
+features, uh reclosability,
+ 
+
+ align:start position:0%
+features, uh reclosability,
+secondary uses, these types of things in
+
+ align:start position:0%
+secondary uses, these types of things in
+ 
+
+ align:start position:0%
+secondary uses, these types of things in
+packages maybe, maybe not
+
+ align:start position:0%
+packages maybe, maybe not
+ 
+
+ align:start position:0%
+packages maybe, maybe not
+uh have uh an opportunity with RF. If
+
+ align:start position:0%
+uh have uh an opportunity with RF. If
+ 
+
+ align:start position:0%
+uh have uh an opportunity with RF. If
+you're looking at material sorting in a
+
+ align:start position:0%
+you're looking at material sorting in a
+ 
+
+ align:start position:0%
+you're looking at material sorting in a
+recycling center, maybe that's a
+
+ align:start position:0%
+recycling center, maybe that's a
+ 
+
+ align:start position:0%
+recycling center, maybe that's a
+possibility. Now, communication and
+
+ align:start position:0%
+possibility. Now, communication and
+ 
+
+ align:start position:0%
+possibility. Now, communication and
+protection. A package should communicate
+
+ align:start position:0%
+protection. A package should communicate
+ 
+
+ align:start position:0%
+protection. A package should communicate
+to the users how to open it, how to
+
+ align:start position:0%
+to the users how to open it, how to
+ 
+
+ align:start position:0%
+to the users how to open it, how to
+close it. Safety. Don't try ripping the
+
+ align:start position:0%
+close it. Safety. Don't try ripping the
+ 
+
+ align:start position:0%
+close it. Safety. Don't try ripping the
+damn plastic clamshells apart with your
+
+ align:start position:0%
+damn plastic clamshells apart with your
+ 
+
+ align:start position:0%
+damn plastic clamshells apart with your
+hands cuz you'll cut your fingers up.
+
+ align:start position:0%
+hands cuz you'll cut your fingers up.
+ 
+
+ align:start position:0%
+hands cuz you'll cut your fingers up.
+That's the number one hated package in
+
+ align:start position:0%
+That's the number one hated package in
+ 
+
+ align:start position:0%
+That's the number one hated package in
+the world. Doesn't matter what country
+
+ align:start position:0%
+the world. Doesn't matter what country
+ 
+
+ align:start position:0%
+the world. Doesn't matter what country
+you're from. People hate it. But
+
+ align:start position:0%
+you're from. People hate it. But
+ 
+
+ align:start position:0%
+you're from. People hate it. But
+protection is a really key one for
+
+ align:start position:0%
+protection is a really key one for
+ 
+
+ align:start position:0%
+protection is a really key one for
+almost every package system. You have to
+
+ align:start position:0%
+almost every package system. You have to
+ 
+
+ align:start position:0%
+almost every package system. You have to
+protect the contents from the
+
+ align:start position:0%
+protect the contents from the
+ 
+
+ align:start position:0%
+protect the contents from the
+environment. Be it a physical
+
+ align:start position:0%
+environment. Be it a physical
+ 
+
+ align:start position:0%
+environment. Be it a physical
+environment uh shock, vibration,
+
+ align:start position:0%
+environment uh shock, vibration,
+ 
+
+ align:start position:0%
+environment uh shock, vibration,
+compression during distribution and
+
+ align:start position:0%
+compression during distribution and
+ 
+
+ align:start position:0%
+compression during distribution and
+handling. Be it uh environmental in uh
+
+ align:start position:0%
+handling. Be it uh environmental in uh
+ 
+
+ align:start position:0%
+handling. Be it uh environmental in uh
+temperature, humidity, uh uh salt spray
+
+ align:start position:0%
+temperature, humidity, uh uh salt spray
+ 
+
+ align:start position:0%
+temperature, humidity, uh uh salt spray
+we had uh conference to these types of
+
+ align:start position:0%
+we had uh conference to these types of
+ 
+
+ align:start position:0%
+we had uh conference to these types of
+things. You also in many cases need a
+
+ align:start position:0%
+things. You also in many cases need a
+ 
+
+ align:start position:0%
+things. You also in many cases need a
+package to protect the environment from
+
+ align:start position:0%
+package to protect the environment from
+ 
+
+ align:start position:0%
+package to protect the environment from
+the product
+
+ align:start position:0%
+the product
+ 
+
+ align:start position:0%
+the product
+nuclear waste. How many of you want
+
+ align:start position:0%
+nuclear waste. How many of you want
+ 
+
+ align:start position:0%
+nuclear waste. How many of you want
+those packages to fall apart and leak
+
+ align:start position:0%
+those packages to fall apart and leak
+ 
+
+ align:start position:0%
+those packages to fall apart and leak
+say anytime within the next 20,000
+
+ align:start position:0%
+say anytime within the next 20,000
+ 
+
+ align:start position:0%
+say anytime within the next 20,000
+years?
+
+ align:start position:0%
+years?
+ 
+
+ align:start position:0%
+years?
+So these are functions of packaging that
+
+ align:start position:0%
+So these are functions of packaging that
+ 
+
+ align:start position:0%
+So these are functions of packaging that
+you need to take into account. The
+
+ align:start position:0%
+you need to take into account. The
+ 
+
+ align:start position:0%
+you need to take into account. The
+impact of this, it's cool. Everything
+
+ align:start position:0%
+impact of this, it's cool. Everything
+ 
+
+ align:start position:0%
+impact of this, it's cool. Everything
+has to be packaged. It's the center of
+
+ align:start position:0%
+has to be packaged. It's the center of
+ 
+
+ align:start position:0%
+has to be packaged. It's the center of
+the universe. You can go into any field
+
+ align:start position:0%
+the universe. You can go into any field
+ 
+
+ align:start position:0%
+the universe. You can go into any field
+you want through packaging and students
+
+ align:start position:0%
+you want through packaging and students
+ 
+
+ align:start position:0%
+you want through packaging and students
+like that. All companies in industry use
+
+ align:start position:0%
+like that. All companies in industry use
+ 
+
+ align:start position:0%
+like that. All companies in industry use
+it at some level
+
+ align:start position:0%
+it at some level
+ 
+
+ align:start position:0%
+it at some level
+and it should withstand the rigors of
+
+ align:start position:0%
+and it should withstand the rigors of
+ 
+
+ align:start position:0%
+and it should withstand the rigors of
+distribution, manual and mechanical
+
+ align:start position:0%
+distribution, manual and mechanical
+ 
+
+ align:start position:0%
+distribution, manual and mechanical
+handlings, warehousing and storage, not
+
+ align:start position:0%
+handlings, warehousing and storage, not
+ 
+
+ align:start position:0%
+handlings, warehousing and storage, not
+create any problems and give the
+
+ align:start position:0%
+create any problems and give the
+ 
+
+ align:start position:0%
+create any problems and give the
+ultimate user a sense of value. What is
+
+ align:start position:0%
+ultimate user a sense of value. What is
+ 
+
+ align:start position:0%
+ultimate user a sense of value. What is
+value in this case? You ask somebody,
+
+ align:start position:0%
+value in this case? You ask somebody,
+ 
+
+ align:start position:0%
+value in this case? You ask somebody,
+"What is it that you want?" And then you
+
+ align:start position:0%
+"What is it that you want?" And then you
+ 
+
+ align:start position:0%
+"What is it that you want?" And then you
+give it to them. And if you really want
+
+ align:start position:0%
+give it to them. And if you really want
+ 
+
+ align:start position:0%
+give it to them. And if you really want
+customer satisfaction, give them
+
+ align:start position:0%
+customer satisfaction, give them
+ 
+
+ align:start position:0%
+customer satisfaction, give them
+something extra. What a bargain. What a
+
+ align:start position:0%
+something extra. What a bargain. What a
+ 
+
+ align:start position:0%
+something extra. What a bargain. What a
+value. Packaging can do this.
+
+ align:start position:0%
+value. Packaging can do this.
+ 
+
+ align:start position:0%
+value. Packaging can do this.
+Now, at the MSU School of Packaging, we
+
+ align:start position:0%
+Now, at the MSU School of Packaging, we
+ 
+
+ align:start position:0%
+Now, at the MSU School of Packaging, we
+focus on RFID applications for the
+
+ align:start position:0%
+focus on RFID applications for the
+ 
+
+ align:start position:0%
+focus on RFID applications for the
+supply chain because the item level is a
+
+ align:start position:0%
+supply chain because the item level is a
+ 
+
+ align:start position:0%
+supply chain because the item level is a
+great marketing thing, but it's a ways
+
+ align:start position:0%
+great marketing thing, but it's a ways
+ 
+
+ align:start position:0%
+great marketing thing, but it's a ways
+off. Um, supply chain has some real
+
+ align:start position:0%
+off. Um, supply chain has some real
+ 
+
+ align:start position:0%
+off. Um, supply chain has some real
+applications. You're using bulk
+
+ align:start position:0%
+applications. You're using bulk
+ 
+
+ align:start position:0%
+applications. You're using bulk
+quantities. You have fixed points that
+
+ align:start position:0%
+quantities. You have fixed points that
+ 
+
+ align:start position:0%
+quantities. You have fixed points that
+you're using, although they're nebulous
+
+ align:start position:0%
+you're using, although they're nebulous
+ 
+
+ align:start position:0%
+you're using, although they're nebulous
+depending on the company and everything
+
+ align:start position:0%
+depending on the company and everything
+ 
+
+ align:start position:0%
+depending on the company and everything
+else. And you want to ultimately define
+
+ align:start position:0%
+else. And you want to ultimately define
+ 
+
+ align:start position:0%
+else. And you want to ultimately define
+the perfect purchase order. So when a
+
+ align:start position:0%
+the perfect purchase order. So when a
+ 
+
+ align:start position:0%
+the perfect purchase order. So when a
+store or customer orders a product or a
+
+ align:start position:0%
+store or customer orders a product or a
+ 
+
+ align:start position:0%
+store or customer orders a product or a
+truckload of products, they get exactly
+
+ align:start position:0%
+truckload of products, they get exactly
+ 
+
+ align:start position:0%
+truckload of products, they get exactly
+what they want when they want it in the
+
+ align:start position:0%
+what they want when they want it in the
+ 
+
+ align:start position:0%
+what they want when they want it in the
+right count. And that's one of the
+
+ align:start position:0%
+right count. And that's one of the
+ 
+
+ align:start position:0%
+right count. And that's one of the
+things RFID can do.
+
+ align:start position:0%
+things RFID can do.
+ 
+
+ align:start position:0%
+things RFID can do.
+Um little aside, MSU School of
+
+ align:start position:0%
+Um little aside, MSU School of
+ 
+
+ align:start position:0%
+Um little aside, MSU School of
+Packaging, we have 600 undergraduates.
+
+ align:start position:0%
+Packaging, we have 600 undergraduates.
+ 
+
+ align:start position:0%
+Packaging, we have 600 undergraduates.
+We have just about a hundred master
+
+ align:start position:0%
+We have just about a hundred master
+ 
+
+ align:start position:0%
+We have just about a hundred master
+students and 20 PhDs.
+
+ align:start position:0%
+students and 20 PhDs.
+ 
+
+ align:start position:0%
+students and 20 PhDs.
+Who'd have thought packaging would be
+
+ align:start position:0%
+Who'd have thought packaging would be
+ 
+
+ align:start position:0%
+Who'd have thought packaging would be
+that big all in our own school.
+
+ align:start position:0%
+that big all in our own school.
+ 
+
+ align:start position:0%
+that big all in our own school.
+Now, we haven't spent a lot of time
+
+ align:start position:0%
+Now, we haven't spent a lot of time
+ 
+
+ align:start position:0%
+Now, we haven't spent a lot of time
+talking about active packaging a little
+
+ align:start position:0%
+talking about active packaging a little
+ 
+
+ align:start position:0%
+talking about active packaging a little
+bit yesterday, but there uh is a real
+
+ align:start position:0%
+bit yesterday, but there uh is a real
+ 
+
+ align:start position:0%
+bit yesterday, but there uh is a real
+opportunity for uh complimentary active
+
+ align:start position:0%
+opportunity for uh complimentary active
+ 
+
+ align:start position:0%
+opportunity for uh complimentary active
+and passive application. If you start
+
+ align:start position:0%
+and passive application. If you start
+ 
+
+ align:start position:0%
+and passive application. If you start
+down here with item levels going into a
+
+ align:start position:0%
+down here with item levels going into a
+ 
+
+ align:start position:0%
+down here with item levels going into a
+case, going into a pallet, ultimately
+
+ align:start position:0%
+case, going into a pallet, ultimately
+ 
+
+ align:start position:0%
+case, going into a pallet, ultimately
+going into a container, you can track
+
+ align:start position:0%
+going into a container, you can track
+ 
+
+ align:start position:0%
+going into a container, you can track
+those. And if you note, some of those
+
+ align:start position:0%
+those. And if you note, some of those
+ 
+
+ align:start position:0%
+those. And if you note, some of those
+require passive tags, meaning the tags
+
+ align:start position:0%
+require passive tags, meaning the tags
+ 
+
+ align:start position:0%
+require passive tags, meaning the tags
+don't have any internal energy source.
+
+ align:start position:0%
+don't have any internal energy source.
+ 
+
+ align:start position:0%
+don't have any internal energy source.
+They collect it from the readers at read
+
+ align:start position:0%
+They collect it from the readers at read
+ 
+
+ align:start position:0%
+They collect it from the readers at read
+points versus an active tag, which may
+
+ align:start position:0%
+points versus an active tag, which may
+ 
+
+ align:start position:0%
+points versus an active tag, which may
+go on the container. And you'll see if
+
+ align:start position:0%
+go on the container. And you'll see if
+ 
+
+ align:start position:0%
+go on the container. And you'll see if
+you look in the bottom corner, I stole
+
+ align:start position:0%
+you look in the bottom corner, I stole
+ 
+
+ align:start position:0%
+you look in the bottom corner, I stole
+this from the Department of Defense. Uh
+
+ align:start position:0%
+this from the Department of Defense. Uh
+ 
+
+ align:start position:0%
+this from the Department of Defense. Uh
+because this is how they ship things
+
+ align:start position:0%
+because this is how they ship things
+ 
+
+ align:start position:0%
+because this is how they ship things
+over to uh uh the Middle East for the uh
+
+ align:start position:0%
+over to uh uh the Middle East for the uh
+ 
+
+ align:start position:0%
+over to uh uh the Middle East for the uh
+uh Iraqi and Afghanistan or uh uh
+
+ align:start position:0%
+uh Iraqi and Afghanistan or uh uh
+ 
+
+ align:start position:0%
+uh Iraqi and Afghanistan or uh uh
+wherever the hell they are over there,
+
+ align:start position:0%
+wherever the hell they are over there,
+ 
+
+ align:start position:0%
+wherever the hell they are over there,
+Pakistan having problems. Um and I like
+
+ align:start position:0%
+Pakistan having problems. Um and I like
+ 
+
+ align:start position:0%
+Pakistan having problems. Um and I like
+it because it shows that you have
+
+ align:start position:0%
+it because it shows that you have
+ 
+
+ align:start position:0%
+it because it shows that you have
+different responsibilities at different
+
+ align:start position:0%
+different responsibilities at different
+ 
+
+ align:start position:0%
+different responsibilities at different
+parts of the supply chain. And there's a
+
+ align:start position:0%
+parts of the supply chain. And there's a
+ 
+
+ align:start position:0%
+parts of the supply chain. And there's a
+lot more to this, but I want you to
+
+ align:start position:0%
+lot more to this, but I want you to
+ 
+
+ align:start position:0%
+lot more to this, but I want you to
+realize that because here's the key.
+
+ align:start position:0%
+realize that because here's the key.
+ 
+
+ align:start position:0%
+realize that because here's the key.
+There's nothing that says some of those
+
+ align:start position:0%
+There's nothing that says some of those
+ 
+
+ align:start position:0%
+There's nothing that says some of those
+applications have to be RFID.
+
+ align:start position:0%
+applications have to be RFID.
+ 
+
+ align:start position:0%
+applications have to be RFID.
+I love RFID. I live and breathe RFID,
+
+ align:start position:0%
+I love RFID. I live and breathe RFID,
+ 
+
+ align:start position:0%
+I love RFID. I live and breathe RFID,
+but it's just a technology and there are
+
+ align:start position:0%
+but it's just a technology and there are
+ 
+
+ align:start position:0%
+but it's just a technology and there are
+a lot of different frequencies and
+
+ align:start position:0%
+a lot of different frequencies and
+ 
+
+ align:start position:0%
+a lot of different frequencies and
+applications, some of which are better
+
+ align:start position:0%
+applications, some of which are better
+ 
+
+ align:start position:0%
+applications, some of which are better
+suited by other technologies. There are
+
+ align:start position:0%
+suited by other technologies. There are
+ 
+
+ align:start position:0%
+suited by other technologies. There are
+different frequencies than 915.
+
+ align:start position:0%
+different frequencies than 915.
+ 
+
+ align:start position:0%
+different frequencies than 915.
+I think the uh opportunities presented
+
+ align:start position:0%
+I think the uh opportunities presented
+ 
+
+ align:start position:0%
+I think the uh opportunities presented
+by EPC for bringing a lot of positive
+
+ align:start position:0%
+by EPC for bringing a lot of positive
+ 
+
+ align:start position:0%
+by EPC for bringing a lot of positive
+things to the world is a strong
+
+ align:start position:0%
+things to the world is a strong
+ 
+
+ align:start position:0%
+things to the world is a strong
+well-defined
+
+ align:start position:0%
+well-defined
+ 
+
+ align:start position:0%
+well-defined
+uh uh forwardthinking
+
+ align:start position:0%
+uh uh forwardthinking
+ 
+
+ align:start position:0%
+uh uh forwardthinking
+process. But it's not the only RFID
+
+ align:start position:0%
+process. But it's not the only RFID
+ 
+
+ align:start position:0%
+process. But it's not the only RFID
+process out there. They cover 1356 915.
+
+ align:start position:0%
+process out there. They cover 1356 915.
+ 
+
+ align:start position:0%
+process out there. They cover 1356 915.
+Those are key elements, but there's a
+
+ align:start position:0%
+Those are key elements, but there's a
+ 
+
+ align:start position:0%
+Those are key elements, but there's a
+lot of other applications that don't use
+
+ align:start position:0%
+lot of other applications that don't use
+ 
+
+ align:start position:0%
+lot of other applications that don't use
+those frequencies, that don't use the
+
+ align:start position:0%
+those frequencies, that don't use the
+ 
+
+ align:start position:0%
+those frequencies, that don't use the
+same type of applications, and we have
+
+ align:start position:0%
+same type of applications, and we have
+ 
+
+ align:start position:0%
+same type of applications, and we have
+to be careful not to exclude those and
+
+ align:start position:0%
+to be careful not to exclude those and
+ 
+
+ align:start position:0%
+to be careful not to exclude those and
+focus only on certain areas.
+
+ align:start position:0%
+focus only on certain areas.
+ 
+
+ align:start position:0%
+focus only on certain areas.
+Now, why look to a university? Well, I
+
+ align:start position:0%
+Now, why look to a university? Well, I
+ 
+
+ align:start position:0%
+Now, why look to a university? Well, I
+made this one up because it looks cool.
+
+ align:start position:0%
+made this one up because it looks cool.
+ 
+
+ align:start position:0%
+made this one up because it looks cool.
+And of course, packaging's in the center
+
+ align:start position:0%
+And of course, packaging's in the center
+ 
+
+ align:start position:0%
+And of course, packaging's in the center
+of that universe, as we all know it
+
+ align:start position:0%
+of that universe, as we all know it
+ 
+
+ align:start position:0%
+of that universe, as we all know it
+should be by now. But we interact with
+
+ align:start position:0%
+should be by now. But we interact with
+ 
+
+ align:start position:0%
+should be by now. But we interact with
+users. We interact with institutional
+
+ align:start position:0%
+users. We interact with institutional
+ 
+
+ align:start position:0%
+users. We interact with institutional
+players and we interact with suppliers.
+
+ align:start position:0%
+players and we interact with suppliers.
+ 
+
+ align:start position:0%
+players and we interact with suppliers.
+We have nothing to sell except our work
+
+ align:start position:0%
+We have nothing to sell except our work
+ 
+
+ align:start position:0%
+We have nothing to sell except our work
+and our research. And if we don't do a
+
+ align:start position:0%
+and our research. And if we don't do a
+ 
+
+ align:start position:0%
+and our research. And if we don't do a
+good job, we don't sell it very well. So
+
+ align:start position:0%
+good job, we don't sell it very well. So
+ 
+
+ align:start position:0%
+good job, we don't sell it very well. So
+these are some of the areas that I would
+
+ align:start position:0%
+these are some of the areas that I would
+ 
+
+ align:start position:0%
+these are some of the areas that I would
+encourage you to look at, think about
+
+ align:start position:0%
+encourage you to look at, think about
+ 
+
+ align:start position:0%
+encourage you to look at, think about
+and if it makes sense for you to develop
+
+ align:start position:0%
+and if it makes sense for you to develop
+ 
+
+ align:start position:0%
+and if it makes sense for you to develop
+some of the work with the university,
+
+ align:start position:0%
+some of the work with the university,
+ 
+
+ align:start position:0%
+some of the work with the university,
+hey, we encourage it.
+
+ align:start position:0%
+hey, we encourage it.
+ 
+
+ align:start position:0%
+hey, we encourage it.
+Packaging materials. This is where I was
+
+ align:start position:0%
+Packaging materials. This is where I was
+ 
+
+ align:start position:0%
+Packaging materials. This is where I was
+afraid you were going to fall asleep, so
+
+ align:start position:0%
+afraid you were going to fall asleep, so
+ 
+
+ align:start position:0%
+afraid you were going to fall asleep, so
+I put in a moving picture for you. What
+
+ align:start position:0%
+I put in a moving picture for you. What
+ 
+
+ align:start position:0%
+I put in a moving picture for you. What
+are the materials, major materials of
+
+ align:start position:0%
+are the materials, major materials of
+ 
+
+ align:start position:0%
+are the materials, major materials of
+packaging? Well, in somewhat of an order
+
+ align:start position:0%
+packaging? Well, in somewhat of an order
+ 
+
+ align:start position:0%
+packaging? Well, in somewhat of an order
+here, wood, huge area. Very few people
+
+ align:start position:0%
+here, wood, huge area. Very few people
+ 
+
+ align:start position:0%
+here, wood, huge area. Very few people
+talk about it. They think wood, pallets,
+
+ align:start position:0%
+talk about it. They think wood, pallets,
+ 
+
+ align:start position:0%
+talk about it. They think wood, pallets,
+that's it. But there are so many wooden
+
+ align:start position:0%
+that's it. But there are so many wooden
+ 
+
+ align:start position:0%
+that's it. But there are so many wooden
+packages out there
+
+ align:start position:0%
+packages out there
+ 
+
+ align:start position:0%
+packages out there
+that you lose sight of them because
+
+ align:start position:0%
+that you lose sight of them because
+ 
+
+ align:start position:0%
+that you lose sight of them because
+they're a tree in the forest. paper,
+
+ align:start position:0%
+they're a tree in the forest. paper,
+ 
+
+ align:start position:0%
+they're a tree in the forest. paper,
+which is slightly different than that.
+
+ align:start position:0%
+which is slightly different than that.
+ 
+
+ align:start position:0%
+which is slightly different than that.
+Uh, and there are a lot of different
+
+ align:start position:0%
+Uh, and there are a lot of different
+ 
+
+ align:start position:0%
+Uh, and there are a lot of different
+types of paper. There is not one type of
+
+ align:start position:0%
+types of paper. There is not one type of
+ 
+
+ align:start position:0%
+types of paper. There is not one type of
+paper. So, you say it reads through
+
+ align:start position:0%
+paper. So, you say it reads through
+ 
+
+ align:start position:0%
+paper. So, you say it reads through
+paper. If you say that, you don't know
+
+ align:start position:0%
+paper. If you say that, you don't know
+ 
+
+ align:start position:0%
+paper. If you say that, you don't know
+what the hell you're talking about
+
+ align:start position:0%
+what the hell you're talking about
+ 
+
+ align:start position:0%
+what the hell you're talking about
+because papers are treated, coated,
+
+ align:start position:0%
+because papers are treated, coated,
+ 
+
+ align:start position:0%
+because papers are treated, coated,
+laminated, different processing issues
+
+ align:start position:0%
+laminated, different processing issues
+ 
+
+ align:start position:0%
+laminated, different processing issues
+that go on. And all of those can affect
+
+ align:start position:0%
+that go on. And all of those can affect
+ 
+
+ align:start position:0%
+that go on. And all of those can affect
+their characteristics and either lend
+
+ align:start position:0%
+their characteristics and either lend
+ 
+
+ align:start position:0%
+their characteristics and either lend
+themselves to benefit RFID or on the
+
+ align:start position:0%
+themselves to benefit RFID or on the
+ 
+
+ align:start position:0%
+themselves to benefit RFID or on the
+other side block it. Then we have
+
+ align:start position:0%
+other side block it. Then we have
+ 
+
+ align:start position:0%
+other side block it. Then we have
+problems. Plastics and these are things
+
+ align:start position:0%
+problems. Plastics and these are things
+ 
+
+ align:start position:0%
+problems. Plastics and these are things
+that I'll spend a little more time with.
+
+ align:start position:0%
+that I'll spend a little more time with.
+ 
+
+ align:start position:0%
+that I'll spend a little more time with.
+Name me the plastic. You can't. There's
+
+ align:start position:0%
+Name me the plastic. You can't. There's
+ 
+
+ align:start position:0%
+Name me the plastic. You can't. There's
+like a billion of them. It's the beauty
+
+ align:start position:0%
+like a billion of them. It's the beauty
+ 
+
+ align:start position:0%
+like a billion of them. It's the beauty
+of plastics. You can build in the
+
+ align:start position:0%
+of plastics. You can build in the
+ 
+
+ align:start position:0%
+of plastics. You can build in the
+requirements that you want. You add a
+
+ align:start position:0%
+requirements that you want. You add a
+ 
+
+ align:start position:0%
+requirements that you want. You add a
+little bit of this, a little bit of
+
+ align:start position:0%
+little bit of this, a little bit of
+ 
+
+ align:start position:0%
+little bit of this, a little bit of
+that, and you have a a gas barrier, a
+
+ align:start position:0%
+that, and you have a a gas barrier, a
+ 
+
+ align:start position:0%
+that, and you have a a gas barrier, a
+light barrier, a moisture barrier, all
+
+ align:start position:0%
+light barrier, a moisture barrier, all
+ 
+
+ align:start position:0%
+light barrier, a moisture barrier, all
+these things. And you can you can mix
+
+ align:start position:0%
+these things. And you can you can mix
+ 
+
+ align:start position:0%
+these things. And you can you can mix
+and match. So, you can design any
+
+ align:start position:0%
+and match. So, you can design any
+ 
+
+ align:start position:0%
+and match. So, you can design any
+plastic you want. Um, metals,
+
+ align:start position:0%
+plastic you want. Um, metals,
+ 
+
+ align:start position:0%
+plastic you want. Um, metals,
+huge opportunity. A lot of metal
+
+ align:start position:0%
+huge opportunity. A lot of metal
+ 
+
+ align:start position:0%
+huge opportunity. A lot of metal
+packaging still available. Um, and glass
+
+ align:start position:0%
+packaging still available. Um, and glass
+ 
+
+ align:start position:0%
+packaging still available. Um, and glass
+of course. Um, now the interesting thing
+
+ align:start position:0%
+of course. Um, now the interesting thing
+ 
+
+ align:start position:0%
+of course. Um, now the interesting thing
+about glass, well, I'll skip that. Now,
+
+ align:start position:0%
+about glass, well, I'll skip that. Now,
+ 
+
+ align:start position:0%
+about glass, well, I'll skip that. Now,
+from a packaging standpoint,
+
+ align:start position:0%
+from a packaging standpoint,
+ 
+
+ align:start position:0%
+from a packaging standpoint,
+there is no cardboard. All right. And
+
+ align:start position:0%
+there is no cardboard. All right. And
+ 
+
+ align:start position:0%
+there is no cardboard. All right. And
+I've heard several people make reference
+
+ align:start position:0%
+I've heard several people make reference
+ 
+
+ align:start position:0%
+I've heard several people make reference
+and it's okay because you hadn't had
+
+ align:start position:0%
+and it's okay because you hadn't had
+ 
+
+ align:start position:0%
+and it's okay because you hadn't had
+this class before. All right. But
+
+ align:start position:0%
+this class before. All right. But
+ 
+
+ align:start position:0%
+this class before. All right. But
+cardboard is not a technical term. And
+
+ align:start position:0%
+cardboard is not a technical term. And
+ 
+
+ align:start position:0%
+cardboard is not a technical term. And
+if you'll notice in some of the
+
+ align:start position:0%
+if you'll notice in some of the
+ 
+
+ align:start position:0%
+if you'll notice in some of the
+presentations, cardboard in one
+
+ align:start position:0%
+presentations, cardboard in one
+ 
+
+ align:start position:0%
+presentations, cardboard in one
+presentation referred to rolled paper.
+
+ align:start position:0%
+presentation referred to rolled paper.
+ 
+
+ align:start position:0%
+presentation referred to rolled paper.
+Cardboard in another referred to
+
+ align:start position:0%
+Cardboard in another referred to
+ 
+
+ align:start position:0%
+Cardboard in another referred to
+corrugated. And in another refer
+
+ align:start position:0%
+corrugated. And in another refer
+ 
+
+ align:start position:0%
+corrugated. And in another refer
+referred to paper board, which is like
+
+ align:start position:0%
+referred to paper board, which is like
+ 
+
+ align:start position:0%
+referred to paper board, which is like
+what's on the back of your uh uh writing
+
+ align:start position:0%
+what's on the back of your uh uh writing
+ 
+
+ align:start position:0%
+what's on the back of your uh uh writing
+tablets. And so from that standpoint,
+
+ align:start position:0%
+tablets. And so from that standpoint,
+ 
+
+ align:start position:0%
+tablets. And so from that standpoint,
+there are different terms. Solid fiber
+
+ align:start position:0%
+there are different terms. Solid fiber
+ 
+
+ align:start position:0%
+there are different terms. Solid fiber
+board would be the your your cardboard,
+
+ align:start position:0%
+board would be the your your cardboard,
+ 
+
+ align:start position:0%
+board would be the your your cardboard,
+if you'll use that on the back of your
+
+ align:start position:0%
+if you'll use that on the back of your
+ 
+
+ align:start position:0%
+if you'll use that on the back of your
+writing. Corrugated board, your
+
+ align:start position:0%
+writing. Corrugated board, your
+ 
+
+ align:start position:0%
+writing. Corrugated board, your
+cardboard box. And I'm going to put this
+
+ align:start position:0%
+cardboard box. And I'm going to put this
+ 
+
+ align:start position:0%
+cardboard box. And I'm going to put this
+up, not because you're idiots, but I
+
+ align:start position:0%
+up, not because you're idiots, but I
+ 
+
+ align:start position:0%
+up, not because you're idiots, but I
+just like to draw on the board.
+
+ align:start position:0%
+just like to draw on the board.
+ 
+
+ align:start position:0%
+just like to draw on the board.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+that's a cross-section of a corrugated
+
+ align:start position:0%
+that's a cross-section of a corrugated
+ 
+
+ align:start position:0%
+that's a cross-section of a corrugated
+box. And I have it there for a reason
+
+ align:start position:0%
+box. And I have it there for a reason
+ 
+
+ align:start position:0%
+box. And I have it there for a reason
+that I'll get to in a little bit.
+
+ align:start position:0%
+that I'll get to in a little bit.
+ 
+
+ align:start position:0%
+that I'll get to in a little bit.
+Now the impact of these materials on
+
+ align:start position:0%
+Now the impact of these materials on
+ 
+
+ align:start position:0%
+Now the impact of these materials on
+RFID
+
+ align:start position:0%
+RFID
+ 
+
+ align:start position:0%
+RFID
+different frequencies exhibit different
+
+ align:start position:0%
+different frequencies exhibit different
+ 
+
+ align:start position:0%
+different frequencies exhibit different
+behaviors around different materials in
+
+ align:start position:0%
+behaviors around different materials in
+ 
+
+ align:start position:0%
+behaviors around different materials in
+applications.
+
+ align:start position:0%
+applications.
+ 
+
+ align:start position:0%
+applications.
+Period. That's the nature of the world.
+
+ align:start position:0%
+Period. That's the nature of the world.
+ 
+
+ align:start position:0%
+Period. That's the nature of the world.
+Can't change it. You need to find the
+
+ align:start position:0%
+Can't change it. You need to find the
+ 
+
+ align:start position:0%
+Can't change it. You need to find the
+one that works. Metal has a large effect
+
+ align:start position:0%
+one that works. Metal has a large effect
+ 
+
+ align:start position:0%
+one that works. Metal has a large effect
+on most RF systems
+
+ align:start position:0%
+on most RF systems
+ 
+
+ align:start position:0%
+on most RF systems
+and particularly true at the UHF.
+
+ align:start position:0%
+and particularly true at the UHF.
+ 
+
+ align:start position:0%
+and particularly true at the UHF.
+it blocks it. It It reraiates it. It It
+
+ align:start position:0%
+it blocks it. It It reraiates it. It It
+ 
+
+ align:start position:0%
+it blocks it. It It reraiates it. It It
+uh sends it off elsewhere. Now,
+
+ align:start position:0%
+uh sends it off elsewhere. Now,
+ 
+
+ align:start position:0%
+uh sends it off elsewhere. Now,
+interestingly, if you know that, you can
+
+ align:start position:0%
+interestingly, if you know that, you can
+ 
+
+ align:start position:0%
+interestingly, if you know that, you can
+use that to your benefit. And in our
+
+ align:start position:0%
+use that to your benefit. And in our
+ 
+
+ align:start position:0%
+use that to your benefit. And in our
+facility, we've been able to double our
+
+ align:start position:0%
+facility, we've been able to double our
+ 
+
+ align:start position:0%
+facility, we've been able to double our
+read range by directing things at a an
+
+ align:start position:0%
+read range by directing things at a an
+ 
+
+ align:start position:0%
+read range by directing things at a an
+angle off of large metal structures. And
+
+ align:start position:0%
+angle off of large metal structures. And
+ 
+
+ align:start position:0%
+angle off of large metal structures. And
+it works wonderfully if you can control
+
+ align:start position:0%
+it works wonderfully if you can control
+ 
+
+ align:start position:0%
+it works wonderfully if you can control
+the environment. Now, in the supply
+
+ align:start position:0%
+the environment. Now, in the supply
+ 
+
+ align:start position:0%
+the environment. Now, in the supply
+chain, good luck. But in certain
+
+ align:start position:0%
+chain, good luck. But in certain
+ 
+
+ align:start position:0%
+chain, good luck. But in certain
+situations, you can do that.
+
+ align:start position:0%
+situations, you can do that.
+ 
+
+ align:start position:0%
+situations, you can do that.
+plastics. Now, plastics because there
+
+ align:start position:0%
+plastics. Now, plastics because there
+ 
+
+ align:start position:0%
+plastics. Now, plastics because there
+are so many different ones, they vary
+
+ align:start position:0%
+are so many different ones, they vary
+ 
+
+ align:start position:0%
+are so many different ones, they vary
+all over the map. Some plastics are RF
+
+ align:start position:0%
+all over the map. Some plastics are RF
+ 
+
+ align:start position:0%
+all over the map. Some plastics are RF
+friendly, some hate it. Common ones,
+
+ align:start position:0%
+friendly, some hate it. Common ones,
+ 
+
+ align:start position:0%
+friendly, some hate it. Common ones,
+your PETs, your polyethylene teralates,
+
+ align:start position:0%
+your PETs, your polyethylene teralates,
+ 
+
+ align:start position:0%
+your PETs, your polyethylene teralates,
+your coke bottles, um your
+
+ align:start position:0%
+your coke bottles, um your
+ 
+
+ align:start position:0%
+your coke bottles, um your
+polyethylines, your polyropylines,
+
+ align:start position:0%
+polyethylines, your polyropylines,
+ 
+
+ align:start position:0%
+polyethylines, your polyropylines,
+all of those are pretty RF friendly and
+
+ align:start position:0%
+all of those are pretty RF friendly and
+ 
+
+ align:start position:0%
+all of those are pretty RF friendly and
+can be utilized. But not all plastics
+
+ align:start position:0%
+can be utilized. But not all plastics
+ 
+
+ align:start position:0%
+can be utilized. But not all plastics
+react the same. Now, interestingly,
+
+ align:start position:0%
+react the same. Now, interestingly,
+ 
+
+ align:start position:0%
+react the same. Now, interestingly,
+glass can be claimed to have little to
+
+ align:start position:0%
+glass can be claimed to have little to
+ 
+
+ align:start position:0%
+glass can be claimed to have little to
+no effect on RF. That can be true, but
+
+ align:start position:0%
+no effect on RF. That can be true, but
+ 
+
+ align:start position:0%
+no effect on RF. That can be true, but
+you keep in mind that glass is not
+
+ align:start position:0%
+you keep in mind that glass is not
+ 
+
+ align:start position:0%
+you keep in mind that glass is not
+glass.
+
+ align:start position:0%
+glass.
+ 
+
+ align:start position:0%
+glass.
+All right, this is metaphysical already.
+
+ align:start position:0%
+All right, this is metaphysical already.
+ 
+
+ align:start position:0%
+All right, this is metaphysical already.
+All right, glass is like plastics. It's
+
+ align:start position:0%
+All right, glass is like plastics. It's
+ 
+
+ align:start position:0%
+All right, glass is like plastics. It's
+like paper. You order the type of glass
+
+ align:start position:0%
+like paper. You order the type of glass
+ 
+
+ align:start position:0%
+like paper. You order the type of glass
+you want to use. There are different
+
+ align:start position:0%
+you want to use. There are different
+ 
+
+ align:start position:0%
+you want to use. There are different
+classes of glass. Those of you in the
+
+ align:start position:0%
+classes of glass. Those of you in the
+ 
+
+ align:start position:0%
+classes of glass. Those of you in the
+pharmaceutical industry know that you
+
+ align:start position:0%
+pharmaceutical industry know that you
+ 
+
+ align:start position:0%
+pharmaceutical industry know that you
+can have class one, class 2, class 3,
+
+ align:start position:0%
+can have class one, class 2, class 3,
+ 
+
+ align:start position:0%
+can have class one, class 2, class 3,
+class 4. And in changing that, when
+
+ align:start position:0%
+class 4. And in changing that, when
+ 
+
+ align:start position:0%
+class 4. And in changing that, when
+you're making your glass, you add a
+
+ align:start position:0%
+you're making your glass, you add a
+ 
+
+ align:start position:0%
+you're making your glass, you add a
+little bit of this, a little bit of that
+
+ align:start position:0%
+little bit of this, a little bit of that
+ 
+
+ align:start position:0%
+little bit of this, a little bit of that
+to get different properties. Think about
+
+ align:start position:0%
+to get different properties. Think about
+ 
+
+ align:start position:0%
+to get different properties. Think about
+in your kitchen, those of you that have
+
+ align:start position:0%
+in your kitchen, those of you that have
+ 
+
+ align:start position:0%
+in your kitchen, those of you that have
+Pyrex cookware, if you drop it, it
+
+ align:start position:0%
+Pyrex cookware, if you drop it, it
+ 
+
+ align:start position:0%
+Pyrex cookware, if you drop it, it
+bounces. Okay? That's not the same as
+
+ align:start position:0%
+bounces. Okay? That's not the same as
+ 
+
+ align:start position:0%
+bounces. Okay? That's not the same as
+your light bulb. Glass is not always
+
+ align:start position:0%
+your light bulb. Glass is not always
+ 
+
+ align:start position:0%
+your light bulb. Glass is not always
+glass. and the composition of glass can
+
+ align:start position:0%
+glass. and the composition of glass can
+ 
+
+ align:start position:0%
+glass. and the composition of glass can
+impact the properties. Now, I didn't
+
+ align:start position:0%
+impact the properties. Now, I didn't
+ 
+
+ align:start position:0%
+impact the properties. Now, I didn't
+have time to put in a slide of this, but
+
+ align:start position:0%
+have time to put in a slide of this, but
+ 
+
+ align:start position:0%
+have time to put in a slide of this, but
+here's some testing we did. We took
+
+ align:start position:0%
+here's some testing we did. We took
+ 
+
+ align:start position:0%
+here's some testing we did. We took
+panes of glass, and it was class two, if
+
+ align:start position:0%
+panes of glass, and it was class two, if
+ 
+
+ align:start position:0%
+panes of glass, and it was class two, if
+anybody cares, like your window pane,
+
+ align:start position:0%
+anybody cares, like your window pane,
+ 
+
+ align:start position:0%
+anybody cares, like your window pane,
+clear, amber, and uh green.
+
+ align:start position:0%
+clear, amber, and uh green.
+ 
+
+ align:start position:0%
+clear, amber, and uh green.
+We took an RF tag read, got our read
+
+ align:start position:0%
+We took an RF tag read, got our read
+ 
+
+ align:start position:0%
+We took an RF tag read, got our read
+range, and then we put the tag behind
+
+ align:start position:0%
+range, and then we put the tag behind
+ 
+
+ align:start position:0%
+range, and then we put the tag behind
+glass.
+
+ align:start position:0%
+glass.
+ 
+
+ align:start position:0%
+glass.
+Our read range dropped. We sandwich the
+
+ align:start position:0%
+Our read range dropped. We sandwich the
+ 
+
+ align:start position:0%
+Our read range dropped. We sandwich the
+tag between glass. Our read range
+
+ align:start position:0%
+tag between glass. Our read range
+ 
+
+ align:start position:0%
+tag between glass. Our read range
+dropped.
+
+ align:start position:0%
+dropped.
+ 
+
+ align:start position:0%
+dropped.
+Huh? Shouldn't happen that way. But it
+
+ align:start position:0%
+Huh? Shouldn't happen that way. But it
+ 
+
+ align:start position:0%
+Huh? Shouldn't happen that way. But it
+depends on what's added. You need to
+
+ align:start position:0%
+depends on what's added. You need to
+ 
+
+ align:start position:0%
+depends on what's added. You need to
+think about that. Paper, little or no
+
+ align:start position:0%
+think about that. Paper, little or no
+ 
+
+ align:start position:0%
+think about that. Paper, little or no
+effect. And for the reasons I stated
+
+ align:start position:0%
+effect. And for the reasons I stated
+ 
+
+ align:start position:0%
+effect. And for the reasons I stated
+earlier, that's not always the case.
+
+ align:start position:0%
+earlier, that's not always the case.
+ 
+
+ align:start position:0%
+earlier, that's not always the case.
+Paper has some real unique properties,
+
+ align:start position:0%
+Paper has some real unique properties,
+ 
+
+ align:start position:0%
+Paper has some real unique properties,
+even if it's just plain brown paper like
+
+ align:start position:0%
+even if it's just plain brown paper like
+ 
+
+ align:start position:0%
+even if it's just plain brown paper like
+you get in grocery bags. Uh, we're going
+
+ align:start position:0%
+you get in grocery bags. Uh, we're going
+ 
+
+ align:start position:0%
+you get in grocery bags. Uh, we're going
+to look at that. composits. They're all
+
+ align:start position:0%
+to look at that. composits. They're all
+ 
+
+ align:start position:0%
+to look at that. composits. They're all
+over the map. Uh the only real composite
+
+ align:start position:0%
+over the map. Uh the only real composite
+ 
+
+ align:start position:0%
+over the map. Uh the only real composite
+I saw here was the bubble pack with
+
+ align:start position:0%
+I saw here was the bubble pack with
+ 
+
+ align:start position:0%
+I saw here was the bubble pack with
+myar. So it was a foilized plastic. And
+
+ align:start position:0%
+myar. So it was a foilized plastic. And
+ 
+
+ align:start position:0%
+myar. So it was a foilized plastic. And
+I'll tell you right now, that one
+
+ align:start position:0%
+I'll tell you right now, that one
+ 
+
+ align:start position:0%
+I'll tell you right now, that one
+doesn't read. It's a good insulator for
+
+ align:start position:0%
+doesn't read. It's a good insulator for
+ 
+
+ align:start position:0%
+doesn't read. It's a good insulator for
+RF energy.
+
+ align:start position:0%
+RF energy.
+ 
+
+ align:start position:0%
+RF energy.
+Problematic matchings come up because
+
+ align:start position:0%
+Problematic matchings come up because
+ 
+
+ align:start position:0%
+Problematic matchings come up because
+sometimes you have packaging and
+
+ align:start position:0%
+sometimes you have packaging and
+ 
+
+ align:start position:0%
+sometimes you have packaging and
+waterbased products. Water is
+
+ align:start position:0%
+waterbased products. Water is
+ 
+
+ align:start position:0%
+waterbased products. Water is
+particularly problematic with UHF.
+
+ align:start position:0%
+particularly problematic with UHF.
+ 
+
+ align:start position:0%
+particularly problematic with UHF.
+If you move to a different frequency,
+
+ align:start position:0%
+If you move to a different frequency,
+ 
+
+ align:start position:0%
+If you move to a different frequency,
+the water issue can decrease. All right?
+
+ align:start position:0%
+the water issue can decrease. All right?
+ 
+
+ align:start position:0%
+the water issue can decrease. All right?
+So that it becomes more friendly.
+
+ align:start position:0%
+So that it becomes more friendly.
+ 
+
+ align:start position:0%
+So that it becomes more friendly.
+They use energy through the earth to
+
+ align:start position:0%
+They use energy through the earth to
+ 
+
+ align:start position:0%
+They use energy through the earth to
+communicate with submarines. We got a
+
+ align:start position:0%
+communicate with submarines. We got a
+ 
+
+ align:start position:0%
+communicate with submarines. We got a
+500 mile long antenna buried in the
+
+ align:start position:0%
+500 mile long antenna buried in the
+ 
+
+ align:start position:0%
+500 mile long antenna buried in the
+upper peninsula of Michigan so that they
+
+ align:start position:0%
+upper peninsula of Michigan so that they
+ 
+
+ align:start position:0%
+upper peninsula of Michigan so that they
+can use frequencies through water to
+
+ align:start position:0%
+can use frequencies through water to
+ 
+
+ align:start position:0%
+can use frequencies through water to
+communicate with submarines. can use it,
+
+ align:start position:0%
+communicate with submarines. can use it,
+ 
+
+ align:start position:0%
+communicate with submarines. can use it,
+but it has to be really low in that
+
+ align:start position:0%
+but it has to be really low in that
+ 
+
+ align:start position:0%
+but it has to be really low in that
+particular case. The lower you go, the
+
+ align:start position:0%
+particular case. The lower you go, the
+ 
+
+ align:start position:0%
+particular case. The lower you go, the
+better it works. But not all liquids are
+
+ align:start position:0%
+better it works. But not all liquids are
+ 
+
+ align:start position:0%
+better it works. But not all liquids are
+water.
+
+ align:start position:0%
+water.
+ 
+
+ align:start position:0%
+water.
+If you think about it, how many of you
+
+ align:start position:0%
+If you think about it, how many of you
+ 
+
+ align:start position:0%
+If you think about it, how many of you
+put water in your car?
+
+ align:start position:0%
+put water in your car?
+ 
+
+ align:start position:0%
+put water in your car?
+I hope it goes, you know, into your
+
+ align:start position:0%
+I hope it goes, you know, into your
+ 
+
+ align:start position:0%
+I hope it goes, you know, into your
+washers rather than your fuel tank
+
+ align:start position:0%
+washers rather than your fuel tank
+ 
+
+ align:start position:0%
+washers rather than your fuel tank
+because they're different. Gasoline
+
+ align:start position:0%
+because they're different. Gasoline
+ 
+
+ align:start position:0%
+because they're different. Gasoline
+doesn't have water in it. Your gas
+
+ align:start position:0%
+doesn't have water in it. Your gas
+ 
+
+ align:start position:0%
+doesn't have water in it. Your gas
+engine doesn't like it. Um, motor oil
+
+ align:start position:0%
+engine doesn't like it. Um, motor oil
+ 
+
+ align:start position:0%
+engine doesn't like it. Um, motor oil
+does not have water in it. And so if you
+
+ align:start position:0%
+does not have water in it. And so if you
+ 
+
+ align:start position:0%
+does not have water in it. And so if you
+take those liquids, RF can go through
+
+ align:start position:0%
+take those liquids, RF can go through
+ 
+
+ align:start position:0%
+take those liquids, RF can go through
+those.
+
+ align:start position:0%
+those.
+ 
+
+ align:start position:0%
+those.
+So water-based problems is any product
+
+ align:start position:0%
+So water-based problems is any product
+ 
+
+ align:start position:0%
+So water-based problems is any product
+put in metal packaging. So your product
+
+ align:start position:0%
+put in metal packaging. So your product
+ 
+
+ align:start position:0%
+put in metal packaging. So your product
+can be perfectly red and if it goes into
+
+ align:start position:0%
+can be perfectly red and if it goes into
+ 
+
+ align:start position:0%
+can be perfectly red and if it goes into
+a package that doesn't work, you have
+
+ align:start position:0%
+a package that doesn't work, you have
+ 
+
+ align:start position:0%
+a package that doesn't work, you have
+problems. Now the uh the Cascade
+
+ align:start position:0%
+problems. Now the uh the Cascade
+ 
+
+ align:start position:0%
+problems. Now the uh the Cascade
+powdered soap that I'd mentioned earlier
+
+ align:start position:0%
+powdered soap that I'd mentioned earlier
+ 
+
+ align:start position:0%
+powdered soap that I'd mentioned earlier
+is a good example of a dry granular
+
+ align:start position:0%
+is a good example of a dry granular
+ 
+
+ align:start position:0%
+is a good example of a dry granular
+product. All right, let's put it in a
+
+ align:start position:0%
+product. All right, let's put it in a
+ 
+
+ align:start position:0%
+product. All right, let's put it in a
+standard corrugated box. Will it read or
+
+ align:start position:0%
+standard corrugated box. Will it read or
+ 
+
+ align:start position:0%
+standard corrugated box. Will it read or
+not read? What do you think? Read.
+
+ align:start position:0%
+not read? What do you think? Read.
+ 
+
+ align:start position:0%
+not read? What do you think? Read.
+Not read.
+
+ align:start position:0%
+Not read.
+ 
+
+ align:start position:0%
+Not read.
+Doesn't read. Why? It's not the water.
+
+ align:start position:0%
+Doesn't read. Why? It's not the water.
+ 
+
+ align:start position:0%
+Doesn't read. Why? It's not the water.
+One of the things you don't think about
+
+ align:start position:0%
+One of the things you don't think about
+ 
+
+ align:start position:0%
+One of the things you don't think about
+heavy iron content in the soap and hence
+
+ align:start position:0%
+heavy iron content in the soap and hence
+ 
+
+ align:start position:0%
+heavy iron content in the soap and hence
+it scatters the RF all over the place.
+
+ align:start position:0%
+it scatters the RF all over the place.
+ 
+
+ align:start position:0%
+it scatters the RF all over the place.
+So, you can't generally read through a
+
+ align:start position:0%
+So, you can't generally read through a
+ 
+
+ align:start position:0%
+So, you can't generally read through a
+uh a powdered soap. Who to think? Just
+
+ align:start position:0%
+uh a powdered soap. Who to think? Just
+ 
+
+ align:start position:0%
+uh a powdered soap. Who to think? Just
+looking up here. We have meats. We've
+
+ align:start position:0%
+looking up here. We have meats. We've
+ 
+
+ align:start position:0%
+looking up here. We have meats. We've
+been testing meats.
+
+ align:start position:0%
+been testing meats.
+ 
+
+ align:start position:0%
+been testing meats.
+Silly thing. Water-based. I talked about
+
+ align:start position:0%
+Silly thing. Water-based. I talked about
+ 
+
+ align:start position:0%
+Silly thing. Water-based. I talked about
+this is a uh TI. That's a 13.56 tag. We
+
+ align:start position:0%
+this is a uh TI. That's a 13.56 tag. We
+ 
+
+ align:start position:0%
+this is a uh TI. That's a 13.56 tag. We
+also tested it with 915 single cut of
+
+ align:start position:0%
+also tested it with 915 single cut of
+ 
+
+ align:start position:0%
+also tested it with 915 single cut of
+beef. And by the way, it was steak and
+
+ align:start position:0%
+beef. And by the way, it was steak and
+ 
+
+ align:start position:0%
+beef. And by the way, it was steak and
+damn good when we were done testing. Um
+
+ align:start position:0%
+damn good when we were done testing. Um
+ 
+
+ align:start position:0%
+damn good when we were done testing. Um
+we ran them at chilled temperatures and
+
+ align:start position:0%
+we ran them at chilled temperatures and
+ 
+
+ align:start position:0%
+we ran them at chilled temperatures and
+we ran them at frozen temperatures. 1356
+
+ align:start position:0%
+we ran them at frozen temperatures. 1356
+ 
+
+ align:start position:0%
+we ran them at frozen temperatures. 1356
+you could read two or three stacked in a
+
+ align:start position:0%
+you could read two or three stacked in a
+ 
+
+ align:start position:0%
+you could read two or three stacked in a
+in a column and still be able to read
+
+ align:start position:0%
+in a column and still be able to read
+ 
+
+ align:start position:0%
+in a column and still be able to read
+through uh UHF. You could read the top
+
+ align:start position:0%
+through uh UHF. You could read the top
+ 
+
+ align:start position:0%
+through uh UHF. You could read the top
+one and that was it. wouldn't penetrate
+
+ align:start position:0%
+one and that was it. wouldn't penetrate
+ 
+
+ align:start position:0%
+one and that was it. wouldn't penetrate
+to the bottom. When we froze those same
+
+ align:start position:0%
+to the bottom. When we froze those same
+ 
+
+ align:start position:0%
+to the bottom. When we froze those same
+cuts of meats with the same tags, we
+
+ align:start position:0%
+cuts of meats with the same tags, we
+ 
+
+ align:start position:0%
+cuts of meats with the same tags, we
+could read five and six deep
+
+ align:start position:0%
+could read five and six deep
+ 
+
+ align:start position:0%
+could read five and six deep
+because the uh water molecules get bound
+
+ align:start position:0%
+because the uh water molecules get bound
+ 
+
+ align:start position:0%
+because the uh water molecules get bound
+up as ice crystals and they leave gaps
+
+ align:start position:0%
+up as ice crystals and they leave gaps
+ 
+
+ align:start position:0%
+up as ice crystals and they leave gaps
+for RF to go through. So you can read
+
+ align:start position:0%
+for RF to go through. So you can read
+ 
+
+ align:start position:0%
+for RF to go through. So you can read
+frozen a lot of times with water. And
+
+ align:start position:0%
+frozen a lot of times with water. And
+ 
+
+ align:start position:0%
+frozen a lot of times with water. And
+for those of you that care, it's
+
+ align:start position:0%
+for those of you that care, it's
+ 
+
+ align:start position:0%
+for those of you that care, it's
+dialectric constant. If you look at
+
+ align:start position:0%
+dialectric constant. If you look at
+ 
+
+ align:start position:0%
+dialectric constant. If you look at
+dialectric constant of water, it's 70 to
+
+ align:start position:0%
+dialectric constant of water, it's 70 to
+ 
+
+ align:start position:0%
+dialectric constant of water, it's 70 to
+80 depending on the properties involved.
+
+ align:start position:0%
+80 depending on the properties involved.
+ 
+
+ align:start position:0%
+80 depending on the properties involved.
+If you look at the dialectric constant
+
+ align:start position:0%
+If you look at the dialectric constant
+ 
+
+ align:start position:0%
+If you look at the dialectric constant
+of ice 3.5
+
+ align:start position:0%
+of ice 3.5
+ 
+
+ align:start position:0%
+of ice 3.5
+right through it. So pretty good stuff.
+
+ align:start position:0%
+right through it. So pretty good stuff.
+ 
+
+ align:start position:0%
+right through it. So pretty good stuff.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+some of the research I just want to
+
+ align:start position:0%
+some of the research I just want to
+ 
+
+ align:start position:0%
+some of the research I just want to
+touch on these real briefly.
+
+ align:start position:0%
+touch on these real briefly.
+ 
+
+ align:start position:0%
+touch on these real briefly.
+Somebody give me a five minute sign when
+
+ align:start position:0%
+Somebody give me a five minute sign when
+ 
+
+ align:start position:0%
+Somebody give me a five minute sign when
+it's five minutes.
+
+ align:start position:0%
+it's five minutes.
+ 
+
+ align:start position:0%
+it's five minutes.
+Uh warehouse environment. This was
+
+ align:start position:0%
+Uh warehouse environment. This was
+ 
+
+ align:start position:0%
+Uh warehouse environment. This was
+starting way back when when we first
+
+ align:start position:0%
+starting way back when when we first
+ 
+
+ align:start position:0%
+starting way back when when we first
+where in the heck do you use this stuff?
+
+ align:start position:0%
+where in the heck do you use this stuff?
+ 
+
+ align:start position:0%
+where in the heck do you use this stuff?
+And so back in 99 we started this
+
+ align:start position:0%
+And so back in 99 we started this
+ 
+
+ align:start position:0%
+And so back in 99 we started this
+research. Well let's see if we can use
+
+ align:start position:0%
+research. Well let's see if we can use
+ 
+
+ align:start position:0%
+research. Well let's see if we can use
+it in a warehouse and developing a model
+
+ align:start position:0%
+it in a warehouse and developing a model
+ 
+
+ align:start position:0%
+it in a warehouse and developing a model
+for it. um transponder effects on bloom
+
+ align:start position:0%
+for it. um transponder effects on bloom
+ 
+
+ align:start position:0%
+for it. um transponder effects on bloom
+time. That meat study, the first one we
+
+ align:start position:0%
+time. That meat study, the first one we
+ 
+
+ align:start position:0%
+time. That meat study, the first one we
+looked at, because the uh inlay was
+
+ align:start position:0%
+looked at, because the uh inlay was
+ 
+
+ align:start position:0%
+looked at, because the uh inlay was
+printed on PET, if you put that on the
+
+ align:start position:0%
+printed on PET, if you put that on the
+ 
+
+ align:start position:0%
+printed on PET, if you put that on the
+surface over the meat, even though it
+
+ align:start position:0%
+surface over the meat, even though it
+ 
+
+ align:start position:0%
+surface over the meat, even though it
+was on the plastic over the meat, it
+
+ align:start position:0%
+was on the plastic over the meat, it
+ 
+
+ align:start position:0%
+was on the plastic over the meat, it
+created a double barrier. And when you
+
+ align:start position:0%
+created a double barrier. And when you
+ 
+
+ align:start position:0%
+created a double barrier. And when you
+peeled the plastic off of the meat, you
+
+ align:start position:0%
+peeled the plastic off of the meat, you
+ 
+
+ align:start position:0%
+peeled the plastic off of the meat, you
+had a big purple spot there because meat
+
+ align:start position:0%
+had a big purple spot there because meat
+ 
+
+ align:start position:0%
+had a big purple spot there because meat
+turns red during oxygenation. All right?
+
+ align:start position:0%
+turns red during oxygenation. All right?
+ 
+
+ align:start position:0%
+turns red during oxygenation. All right?
+And so when you peel the tag off,
+
+ align:start position:0%
+And so when you peel the tag off,
+ 
+
+ align:start position:0%
+And so when you peel the tag off,
+because you have an oxygen barrier on
+
+ align:start position:0%
+because you have an oxygen barrier on
+ 
+
+ align:start position:0%
+because you have an oxygen barrier on
+top, you left a big purple splotch. And
+
+ align:start position:0%
+top, you left a big purple splotch. And
+ 
+
+ align:start position:0%
+top, you left a big purple splotch. And
+people were returning meats to the store
+
+ align:start position:0%
+people were returning meats to the store
+ 
+
+ align:start position:0%
+people were returning meats to the store
+saying, "This crap spoiled." And yet if
+
+ align:start position:0%
+saying, "This crap spoiled." And yet if
+ 
+
+ align:start position:0%
+saying, "This crap spoiled." And yet if
+they waited 20 minutes, it would
+
+ align:start position:0%
+they waited 20 minutes, it would
+ 
+
+ align:start position:0%
+they waited 20 minutes, it would
+disappear
+
+ align:start position:0%
+disappear
+ 
+
+ align:start position:0%
+disappear
+because the meat becomes oxygenated.
+
+ align:start position:0%
+because the meat becomes oxygenated.
+ 
+
+ align:start position:0%
+because the meat becomes oxygenated.
+Um frozen and refrigerated temperatures,
+
+ align:start position:0%
+Um frozen and refrigerated temperatures,
+ 
+
+ align:start position:0%
+Um frozen and refrigerated temperatures,
+I just gave you that. That's Johno. He's
+
+ align:start position:0%
+I just gave you that. That's Johno. He's
+ 
+
+ align:start position:0%
+I just gave you that. That's Johno. He's
+now at uh Kimberly Clark and APC uh
+
+ align:start position:0%
+now at uh Kimberly Clark and APC uh
+ 
+
+ align:start position:0%
+now at uh Kimberly Clark and APC uh
+member and task group on something.
+
+ align:start position:0%
+member and task group on something.
+ 
+
+ align:start position:0%
+member and task group on something.
+Um Jeff Tazzlar now with Simon wherever
+
+ align:start position:0%
+Um Jeff Tazzlar now with Simon wherever
+ 
+
+ align:start position:0%
+Um Jeff Tazzlar now with Simon wherever
+Simon went um effects of tag orientation
+
+ align:start position:0%
+Simon went um effects of tag orientation
+ 
+
+ align:start position:0%
+Simon went um effects of tag orientation
+and package content on readability. I
+
+ align:start position:0%
+and package content on readability. I
+ 
+
+ align:start position:0%
+and package content on readability. I
+have a slide on this that I'll share
+
+ align:start position:0%
+have a slide on this that I'll share
+ 
+
+ align:start position:0%
+have a slide on this that I'll share
+with you shortly. Um failure modes of
+
+ align:start position:0%
+with you shortly. Um failure modes of
+ 
+
+ align:start position:0%
+with you shortly. Um failure modes of
+class zero in the lab. When you look at
+
+ align:start position:0%
+class zero in the lab. When you look at
+ 
+
+ align:start position:0%
+class zero in the lab. When you look at
+ISTA, the uh institute um
+
+ align:start position:0%
+ISTA, the uh institute um
+ 
+
+ align:start position:0%
+ISTA, the uh institute um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+international safe transit association,
+
+ align:start position:0%
+international safe transit association,
+ 
+
+ align:start position:0%
+international safe transit association,
+excuse me, mental uh burp.
+
+ align:start position:0%
+excuse me, mental uh burp.
+ 
+
+ align:start position:0%
+excuse me, mental uh burp.
+Um, they run a series of dynamic tests
+
+ align:start position:0%
+Um, they run a series of dynamic tests
+ 
+
+ align:start position:0%
+Um, they run a series of dynamic tests
+uh that UPS, FedEx, uh, DHL may use for
+
+ align:start position:0%
+uh that UPS, FedEx, uh, DHL may use for
+ 
+
+ align:start position:0%
+uh that UPS, FedEx, uh, DHL may use for
+uh, liability issues. If something goes
+
+ align:start position:0%
+uh, liability issues. If something goes
+ 
+
+ align:start position:0%
+uh, liability issues. If something goes
+wrong with your package, they beat the
+
+ align:start position:0%
+wrong with your package, they beat the
+ 
+
+ align:start position:0%
+wrong with your package, they beat the
+hell out of it and the product has to
+
+ align:start position:0%
+hell out of it and the product has to
+ 
+
+ align:start position:0%
+hell out of it and the product has to
+survive. That's their test in a in a
+
+ align:start position:0%
+survive. That's their test in a in a
+ 
+
+ align:start position:0%
+survive. That's their test in a in a
+nutshell. Now, American Society of
+
+ align:start position:0%
+nutshell. Now, American Society of
+ 
+
+ align:start position:0%
+nutshell. Now, American Society of
+Testing Materials, ASM, also has a
+
+ align:start position:0%
+Testing Materials, ASM, also has a
+ 
+
+ align:start position:0%
+Testing Materials, ASM, also has a
+series of tests, shock, vibration,
+
+ align:start position:0%
+series of tests, shock, vibration,
+ 
+
+ align:start position:0%
+series of tests, shock, vibration,
+compression, and you can build your own
+
+ align:start position:0%
+compression, and you can build your own
+ 
+
+ align:start position:0%
+compression, and you can build your own
+distribution to fine-tune so you don't
+
+ align:start position:0%
+distribution to fine-tune so you don't
+ 
+
+ align:start position:0%
+distribution to fine-tune so you don't
+overpackage. We did both tests side by
+
+ align:start position:0%
+overpackage. We did both tests side by
+ 
+
+ align:start position:0%
+overpackage. We did both tests side by
+side with the same tags. And uh one of
+
+ align:start position:0%
+side with the same tags. And uh one of
+ 
+
+ align:start position:0%
+side with the same tags. And uh one of
+the interesting things we found was that
+
+ align:start position:0%
+the interesting things we found was that
+ 
+
+ align:start position:0%
+the interesting things we found was that
+it was really hard to kill them in
+
+ align:start position:0%
+it was really hard to kill them in
+ 
+
+ align:start position:0%
+it was really hard to kill them in
+transit unless there is a direct impact
+
+ align:start position:0%
+transit unless there is a direct impact
+ 
+
+ align:start position:0%
+transit unless there is a direct impact
+to the chip. The chips were not affected
+
+ align:start position:0%
+to the chip. The chips were not affected
+ 
+
+ align:start position:0%
+to the chip. The chips were not affected
+by vibration which surprised me. They
+
+ align:start position:0%
+by vibration which surprised me. They
+ 
+
+ align:start position:0%
+by vibration which surprised me. They
+were not affected by shock unless the
+
+ align:start position:0%
+were not affected by shock unless the
+ 
+
+ align:start position:0%
+were not affected by shock unless the
+shock was directly over the chip. And
+
+ align:start position:0%
+shock was directly over the chip. And
+ 
+
+ align:start position:0%
+shock was directly over the chip. And
+it's a brittle piece of silicon glass so
+
+ align:start position:0%
+it's a brittle piece of silicon glass so
+ 
+
+ align:start position:0%
+it's a brittle piece of silicon glass so
+it breaks. And here's why I did this
+
+ align:start position:0%
+it breaks. And here's why I did this
+ 
+
+ align:start position:0%
+it breaks. And here's why I did this
+earlier. Little trivia for you. It makes
+
+ align:start position:0%
+earlier. Little trivia for you. It makes
+ 
+
+ align:start position:0%
+earlier. Little trivia for you. It makes
+a difference for survivability
+
+ align:start position:0%
+a difference for survivability
+ 
+
+ align:start position:0%
+a difference for survivability
+whether the chip on a tag is over the
+
+ align:start position:0%
+whether the chip on a tag is over the
+ 
+
+ align:start position:0%
+whether the chip on a tag is over the
+peak,
+
+ align:start position:0%
+peak,
+ 
+
+ align:start position:0%
+peak,
+over the slope,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or over the valley.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Try and plan that into your automated uh
+
+ align:start position:0%
+Try and plan that into your automated uh
+ 
+
+ align:start position:0%
+Try and plan that into your automated uh
+system.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll tell you later.
+
+ align:start position:0%
+I'll tell you later.
+ 
+
+ align:start position:0%
+I'll tell you later.
+Um, and we just finished one uh antenna
+
+ align:start position:0%
+Um, and we just finished one uh antenna
+ 
+
+ align:start position:0%
+Um, and we just finished one uh antenna
+configurations uh looking at product and
+
+ align:start position:0%
+configurations uh looking at product and
+ 
+
+ align:start position:0%
+configurations uh looking at product and
+tag types and we evaluated uh with the
+
+ align:start position:0%
+tag types and we evaluated uh with the
+ 
+
+ align:start position:0%
+tag types and we evaluated uh with the
+same readers and we looked at multiple
+
+ align:start position:0%
+same readers and we looked at multiple
+ 
+
+ align:start position:0%
+same readers and we looked at multiple
+readers. We looked at multiple classes
+
+ align:start position:0%
+readers. We looked at multiple classes
+ 
+
+ align:start position:0%
+readers. We looked at multiple classes
+of tags whether one antenna, two
+
+ align:start position:0%
+of tags whether one antenna, two
+ 
+
+ align:start position:0%
+of tags whether one antenna, two
+antenna, three antenna or four antenna
+
+ align:start position:0%
+antenna, three antenna or four antenna
+ 
+
+ align:start position:0%
+antenna, three antenna or four antenna
+gave better results and we looked at
+
+ align:start position:0%
+gave better results and we looked at
+ 
+
+ align:start position:0%
+gave better results and we looked at
+both uh linear and circular for
+
+ align:start position:0%
+both uh linear and circular for
+ 
+
+ align:start position:0%
+both uh linear and circular for
+different product mixes. So uh real
+
+ align:start position:0%
+different product mixes. So uh real
+ 
+
+ align:start position:0%
+different product mixes. So uh real
+interesting we hope to have that one
+
+ align:start position:0%
+interesting we hope to have that one
+ 
+
+ align:start position:0%
+interesting we hope to have that one
+published uh shortly because it's a
+
+ align:start position:0%
+published uh shortly because it's a
+ 
+
+ align:start position:0%
+published uh shortly because it's a
+fascinating study uh one that going on
+
+ align:start position:0%
+fascinating study uh one that going on
+ 
+
+ align:start position:0%
+fascinating study uh one that going on
+right now and uh Richard
+
+ align:start position:0%
+right now and uh Richard
+ 
+
+ align:start position:0%
+right now and uh Richard
+he disappeared. This is one I wanted to
+
+ align:start position:0%
+he disappeared. This is one I wanted to
+ 
+
+ align:start position:0%
+he disappeared. This is one I wanted to
+talk to him about. Electromagnetic
+
+ align:start position:0%
+talk to him about. Electromagnetic
+ 
+
+ align:start position:0%
+talk to him about. Electromagnetic
+property measurement and RF signal
+
+ align:start position:0%
+property measurement and RF signal
+ 
+
+ align:start position:0%
+property measurement and RF signal
+absorption evaluation for product
+
+ align:start position:0%
+absorption evaluation for product
+ 
+
+ align:start position:0%
+absorption evaluation for product
+simulant.
+
+ align:start position:0%
+simulant.
+ 
+
+ align:start position:0%
+simulant.
+I love these titles because they don't
+
+ align:start position:0%
+I love these titles because they don't
+ 
+
+ align:start position:0%
+I love these titles because they don't
+mean anything. But um we are evaluating
+
+ align:start position:0%
+mean anything. But um we are evaluating
+ 
+
+ align:start position:0%
+mean anything. But um we are evaluating
+how much the materials
+
+ align:start position:0%
+how much the materials
+ 
+
+ align:start position:0%
+how much the materials
+uh downgrade moving through various
+
+ align:start position:0%
+uh downgrade moving through various
+ 
+
+ align:start position:0%
+uh downgrade moving through various
+materials because they all have a
+
+ align:start position:0%
+materials because they all have a
+ 
+
+ align:start position:0%
+materials because they all have a
+different if you look at a freeze
+
+ align:start position:0%
+different if you look at a freeze
+ 
+
+ align:start position:0%
+different if you look at a freeze
+equation for those of you that know what
+
+ align:start position:0%
+equation for those of you that know what
+ 
+
+ align:start position:0%
+equation for those of you that know what
+I'm talking about. you have a signal
+
+ align:start position:0%
+I'm talking about. you have a signal
+ 
+
+ align:start position:0%
+I'm talking about. you have a signal
+strength and when it reaches a barrier
+
+ align:start position:0%
+strength and when it reaches a barrier
+ 
+
+ align:start position:0%
+strength and when it reaches a barrier
+if it's a packaging material you'll get
+
+ align:start position:0%
+if it's a packaging material you'll get
+ 
+
+ align:start position:0%
+if it's a packaging material you'll get
+a lessening as it crosses that barrier
+
+ align:start position:0%
+a lessening as it crosses that barrier
+ 
+
+ align:start position:0%
+a lessening as it crosses that barrier
+and you can actually measure these and
+
+ align:start position:0%
+and you can actually measure these and
+ 
+
+ align:start position:0%
+and you can actually measure these and
+we developed some new equipment to do
+
+ align:start position:0%
+we developed some new equipment to do
+ 
+
+ align:start position:0%
+we developed some new equipment to do
+that and it's coming out pretty
+
+ align:start position:0%
+that and it's coming out pretty
+ 
+
+ align:start position:0%
+that and it's coming out pretty
+interesting and then uh we did one on
+
+ align:start position:0%
+interesting and then uh we did one on
+ 
+
+ align:start position:0%
+interesting and then uh we did one on
+department of defense's RFID mandates
+
+ align:start position:0%
+department of defense's RFID mandates
+ 
+
+ align:start position:0%
+department of defense's RFID mandates
+blah blah blah this is the uh the chart
+
+ align:start position:0%
+blah blah blah this is the uh the chart
+ 
+
+ align:start position:0%
+blah blah blah this is the uh the chart
+that's kind of interesting on the one
+
+ align:start position:0%
+that's kind of interesting on the one
+ 
+
+ align:start position:0%
+that's kind of interesting on the one
+side here with the product
+
+ align:start position:0%
+side here with the product
+ 
+
+ align:start position:0%
+side here with the product
+you'll see that I have empty foam foam,
+
+ align:start position:0%
+you'll see that I have empty foam foam,
+ 
+
+ align:start position:0%
+you'll see that I have empty foam foam,
+empty bottles, rice and water bottles.
+
+ align:start position:0%
+empty bottles, rice and water bottles.
+ 
+
+ align:start position:0%
+empty bottles, rice and water bottles.
+Those are 12 by 12x 12 in cases, cubic
+
+ align:start position:0%
+Those are 12 by 12x 12 in cases, cubic
+ 
+
+ align:start position:0%
+Those are 12 by 12x 12 in cases, cubic
+foot with nothing in them, foam in them
+
+ align:start position:0%
+foot with nothing in them, foam in them
+ 
+
+ align:start position:0%
+foot with nothing in them, foam in them
+only because we were looking at some of
+
+ align:start position:0%
+only because we were looking at some of
+ 
+
+ align:start position:0%
+only because we were looking at some of
+the shipping uses. Empty PET bottles,
+
+ align:start position:0%
+the shipping uses. Empty PET bottles,
+ 
+
+ align:start position:0%
+the shipping uses. Empty PET bottles,
+rice in PET bottles, and filled water
+
+ align:start position:0%
+rice in PET bottles, and filled water
+ 
+
+ align:start position:0%
+rice in PET bottles, and filled water
+bottles, the same PET. And if you start
+
+ align:start position:0%
+bottles, the same PET. And if you start
+ 
+
+ align:start position:0%
+bottles, the same PET. And if you start
+going across the tag orientation at the
+
+ align:start position:0%
+going across the tag orientation at the
+ 
+
+ align:start position:0%
+going across the tag orientation at the
+top says outward-facing tags where we
+
+ align:start position:0%
+top says outward-facing tags where we
+ 
+
+ align:start position:0%
+top says outward-facing tags where we
+had as many tags facing outward as we
+
+ align:start position:0%
+had as many tags facing outward as we
+ 
+
+ align:start position:0%
+had as many tags facing outward as we
+could, inward facing tags, you'll see
+
+ align:start position:0%
+could, inward facing tags, you'll see
+ 
+
+ align:start position:0%
+could, inward facing tags, you'll see
+problems there. Forward-facing tags on
+
+ align:start position:0%
+problems there. Forward-facing tags on
+ 
+
+ align:start position:0%
+problems there. Forward-facing tags on
+the pallet, upward-facing tags on the
+
+ align:start position:0%
+the pallet, upward-facing tags on the
+ 
+
+ align:start position:0%
+the pallet, upward-facing tags on the
+pallet, and bottom base tags on the
+
+ align:start position:0%
+pallet, and bottom base tags on the
+ 
+
+ align:start position:0%
+pallet, and bottom base tags on the
+pallet. Um, one of the DHL uh uh movies,
+
+ align:start position:0%
+pallet. Um, one of the DHL uh uh movies,
+ 
+
+ align:start position:0%
+pallet. Um, one of the DHL uh uh movies,
+which I thought was interesting, when
+
+ align:start position:0%
+which I thought was interesting, when
+ 
+
+ align:start position:0%
+which I thought was interesting, when
+they left the tag on the product in the
+
+ align:start position:0%
+they left the tag on the product in the
+ 
+
+ align:start position:0%
+they left the tag on the product in the
+loading dock and the guy had to stop and
+
+ align:start position:0%
+loading dock and the guy had to stop and
+ 
+
+ align:start position:0%
+loading dock and the guy had to stop and
+run back and get it, the tag was sitting
+
+ align:start position:0%
+run back and get it, the tag was sitting
+ 
+
+ align:start position:0%
+run back and get it, the tag was sitting
+on the side so the reader could pick it
+
+ align:start position:0%
+on the side so the reader could pick it
+ 
+
+ align:start position:0%
+on the side so the reader could pick it
+up. If you took that same package and
+
+ align:start position:0%
+up. If you took that same package and
+ 
+
+ align:start position:0%
+up. If you took that same package and
+turn that tag down on the floor, chances
+
+ align:start position:0%
+turn that tag down on the floor, chances
+ 
+
+ align:start position:0%
+turn that tag down on the floor, chances
+are the reader wouldn't get it. Why?
+
+ align:start position:0%
+are the reader wouldn't get it. Why?
+ 
+
+ align:start position:0%
+are the reader wouldn't get it. Why?
+There's metal in the floor. Because when
+
+ align:start position:0%
+There's metal in the floor. Because when
+ 
+
+ align:start position:0%
+There's metal in the floor. Because when
+you build facilities, you put rebar down
+
+ align:start position:0%
+you build facilities, you put rebar down
+ 
+
+ align:start position:0%
+you build facilities, you put rebar down
+there and it scatters waves all over
+
+ align:start position:0%
+there and it scatters waves all over
+ 
+
+ align:start position:0%
+there and it scatters waves all over
+hell. So anyway, this just shows that
+
+ align:start position:0%
+hell. So anyway, this just shows that
+ 
+
+ align:start position:0%
+hell. So anyway, this just shows that
+the white are good reads. This is 1,200
+
+ align:start position:0%
+the white are good reads. This is 1,200
+ 
+
+ align:start position:0%
+the white are good reads. This is 1,200
+reads in for each test. Each box is
+
+ align:start position:0%
+reads in for each test. Each box is
+ 
+
+ align:start position:0%
+reads in for each test. Each box is
+1,200 reads and uh percentages of reads.
+
+ align:start position:0%
+1,200 reads and uh percentages of reads.
+ 
+
+ align:start position:0%
+1,200 reads and uh percentages of reads.
+And you can see that the white to the
+
+ align:start position:0%
+And you can see that the white to the
+ 
+
+ align:start position:0%
+And you can see that the white to the
+red you had orientation issues, not a
+
+ align:start position:0%
+red you had orientation issues, not a
+ 
+
+ align:start position:0%
+red you had orientation issues, not a
+lot but statistically significant. And
+
+ align:start position:0%
+lot but statistically significant. And
+ 
+
+ align:start position:0%
+lot but statistically significant. And
+in the uh product categories as you
+
+ align:start position:0%
+in the uh product categories as you
+ 
+
+ align:start position:0%
+in the uh product categories as you
+moved across, you had certain
+
+ align:start position:0%
+moved across, you had certain
+ 
+
+ align:start position:0%
+moved across, you had certain
+orientations of the tags on cases that
+
+ align:start position:0%
+orientations of the tags on cases that
+ 
+
+ align:start position:0%
+orientations of the tags on cases that
+were problematic. And when you looked at
+
+ align:start position:0%
+were problematic. And when you looked at
+ 
+
+ align:start position:0%
+were problematic. And when you looked at
+both of those areas, the orange squares
+
+ align:start position:0%
+both of those areas, the orange squares
+ 
+
+ align:start position:0%
+both of those areas, the orange squares
+up there did come out orange.
+
+ align:start position:0%
+up there did come out orange.
+ 
+
+ align:start position:0%
+up there did come out orange.
+Real problems, packaging and product
+
+ align:start position:0%
+Real problems, packaging and product
+ 
+
+ align:start position:0%
+Real problems, packaging and product
+issues that affect RFID, readability,
+
+ align:start position:0%
+issues that affect RFID, readability,
+ 
+
+ align:start position:0%
+issues that affect RFID, readability,
+transmission, any number of words you
+
+ align:start position:0%
+transmission, any number of words you
+ 
+
+ align:start position:0%
+transmission, any number of words you
+want to put in there. Now again, this is
+
+ align:start position:0%
+want to put in there. Now again, this is
+ 
+
+ align:start position:0%
+want to put in there. Now again, this is
+Richard's and I won't this is some of
+
+ align:start position:0%
+Richard's and I won't this is some of
+ 
+
+ align:start position:0%
+Richard's and I won't this is some of
+the stuff we're doing on the
+
+ align:start position:0%
+the stuff we're doing on the
+ 
+
+ align:start position:0%
+the stuff we're doing on the
+electromagnetic properties and being
+
+ align:start position:0%
+electromagnetic properties and being
+ 
+
+ align:start position:0%
+electromagnetic properties and being
+able to measure energy that gets through
+
+ align:start position:0%
+able to measure energy that gets through
+ 
+
+ align:start position:0%
+able to measure energy that gets through
+packaging to a tag and uh being able to
+
+ align:start position:0%
+packaging to a tag and uh being able to
+ 
+
+ align:start position:0%
+packaging to a tag and uh being able to
+measure how much energy it takes to
+
+ align:start position:0%
+measure how much energy it takes to
+ 
+
+ align:start position:0%
+measure how much energy it takes to
+breach the threshold for a passive tag
+
+ align:start position:0%
+breach the threshold for a passive tag
+ 
+
+ align:start position:0%
+breach the threshold for a passive tag
+to send a signal back and uh it's a it's
+
+ align:start position:0%
+to send a signal back and uh it's a it's
+ 
+
+ align:start position:0%
+to send a signal back and uh it's a it's
+a neat um we can talk about that later.
+
+ align:start position:0%
+a neat um we can talk about that later.
+ 
+
+ align:start position:0%
+a neat um we can talk about that later.
+Now, corrugated board. All right.
+
+ align:start position:0%
+Now, corrugated board. All right.
+ 
+
+ align:start position:0%
+Now, corrugated board. All right.
+When you add humidity to paper, it's a
+
+ align:start position:0%
+When you add humidity to paper, it's a
+ 
+
+ align:start position:0%
+When you add humidity to paper, it's a
+hyroscopic paper. It absorbs moisture to
+
+ align:start position:0%
+hyroscopic paper. It absorbs moisture to
+ 
+
+ align:start position:0%
+hyroscopic paper. It absorbs moisture to
+some level. It changes the moisture
+
+ align:start position:0%
+some level. It changes the moisture
+ 
+
+ align:start position:0%
+some level. It changes the moisture
+content. And if you see here, we have
+
+ align:start position:0%
+content. And if you see here, we have
+ 
+
+ align:start position:0%
+content. And if you see here, we have
+storage conditions, three different
+
+ align:start position:0%
+storage conditions, three different
+ 
+
+ align:start position:0%
+storage conditions, three different
+storage conditions, three different
+
+ align:start position:0%
+storage conditions, three different
+ 
+
+ align:start position:0%
+storage conditions, three different
+moisture contents associated with that.
+
+ align:start position:0%
+moisture contents associated with that.
+ 
+
+ align:start position:0%
+moisture contents associated with that.
+And guess what happens? As you go up in
+
+ align:start position:0%
+And guess what happens? As you go up in
+ 
+
+ align:start position:0%
+And guess what happens? As you go up in
+moisture content, you start having an
+
+ align:start position:0%
+moisture content, you start having an
+ 
+
+ align:start position:0%
+moisture content, you start having an
+effect on the paper.
+
+ align:start position:0%
+effect on the paper.
+ 
+
+ align:start position:0%
+effect on the paper.
+Now,
+
+ align:start position:0%
+Now,
+ 
+
+ align:start position:0%
+Now,
+doesn't look like much, but what it
+
+ align:start position:0%
+doesn't look like much, but what it
+ 
+
+ align:start position:0%
+doesn't look like much, but what it
+boils down to is corrugated board or any
+
+ align:start position:0%
+boils down to is corrugated board or any
+ 
+
+ align:start position:0%
+boils down to is corrugated board or any
+other paper, all right, can affect RFID.
+
+ align:start position:0%
+other paper, all right, can affect RFID.
+ 
+
+ align:start position:0%
+other paper, all right, can affect RFID.
+It does not say it will. It does not say
+
+ align:start position:0%
+It does not say it will. It does not say
+ 
+
+ align:start position:0%
+It does not say it will. It does not say
+it has to. It can when you have high
+
+ align:start position:0%
+it has to. It can when you have high
+ 
+
+ align:start position:0%
+it has to. It can when you have high
+humidity.
+
+ align:start position:0%
+humidity.
+ 
+
+ align:start position:0%
+humidity.
+If you have low to medium humidity, but
+
+ align:start position:0%
+If you have low to medium humidity, but
+ 
+
+ align:start position:0%
+If you have low to medium humidity, but
+the paper has already been exposed to
+
+ align:start position:0%
+the paper has already been exposed to
+ 
+
+ align:start position:0%
+the paper has already been exposed to
+high humidity. Hysteresus is a saying
+
+ align:start position:0%
+high humidity. Hysteresus is a saying
+ 
+
+ align:start position:0%
+high humidity. Hysteresus is a saying
+Mark and I had a conference in Tokyo
+
+ align:start position:0%
+Mark and I had a conference in Tokyo
+ 
+
+ align:start position:0%
+Mark and I had a conference in Tokyo
+where we discussed this very topic. When
+
+ align:start position:0%
+where we discussed this very topic. When
+ 
+
+ align:start position:0%
+where we discussed this very topic. When
+you uh change a paper's uh u uh
+
+ align:start position:0%
+you uh change a paper's uh u uh
+ 
+
+ align:start position:0%
+you uh change a paper's uh u uh
+chemistry by adding moisture and then
+
+ align:start position:0%
+chemistry by adding moisture and then
+ 
+
+ align:start position:0%
+chemistry by adding moisture and then
+dry it out, it never goes back to the
+
+ align:start position:0%
+dry it out, it never goes back to the
+ 
+
+ align:start position:0%
+dry it out, it never goes back to the
+same static condition. There's always a
+
+ align:start position:0%
+same static condition. There's always a
+ 
+
+ align:start position:0%
+same static condition. There's always a
+residual there. So, it's easier to pick
+
+ align:start position:0%
+residual there. So, it's easier to pick
+ 
+
+ align:start position:0%
+residual there. So, it's easier to pick
+up moisture the second time around. Uh
+
+ align:start position:0%
+up moisture the second time around. Uh
+ 
+
+ align:start position:0%
+up moisture the second time around. Uh
+so, with leakage or condensation, that's
+
+ align:start position:0%
+so, with leakage or condensation, that's
+ 
+
+ align:start position:0%
+so, with leakage or condensation, that's
+an issue. If you guys are trying to ship
+
+ align:start position:0%
+an issue. If you guys are trying to ship
+ 
+
+ align:start position:0%
+an issue. If you guys are trying to ship
+down to uh help Katrina in the uh uh
+
+ align:start position:0%
+down to uh help Katrina in the uh uh
+ 
+
+ align:start position:0%
+down to uh help Katrina in the uh uh
+southern coast where it literally rains
+
+ align:start position:0%
+southern coast where it literally rains
+ 
+
+ align:start position:0%
+southern coast where it literally rains
+inside of warehouses in the summer, this
+
+ align:start position:0%
+inside of warehouses in the summer, this
+ 
+
+ align:start position:0%
+inside of warehouses in the summer, this
+could be an issue.
+
+ align:start position:0%
+could be an issue.
+ 
+
+ align:start position:0%
+could be an issue.
+However, and here's an interesting
+
+ align:start position:0%
+However, and here's an interesting
+ 
+
+ align:start position:0%
+However, and here's an interesting
+point. I hear this a lot in my
+
+ align:start position:0%
+point. I hear this a lot in my
+ 
+
+ align:start position:0%
+point. I hear this a lot in my
+presentations. That means we should go
+
+ align:start position:0%
+presentations. That means we should go
+ 
+
+ align:start position:0%
+presentations. That means we should go
+to RPCs, returnable plastic containers,
+
+ align:start position:0%
+to RPCs, returnable plastic containers,
+ 
+
+ align:start position:0%
+to RPCs, returnable plastic containers,
+or actually there's about five acronyms
+
+ align:start position:0%
+or actually there's about five acronyms
+ 
+
+ align:start position:0%
+or actually there's about five acronyms
+for RPCs depending on the industry
+
+ align:start position:0%
+for RPCs depending on the industry
+ 
+
+ align:start position:0%
+for RPCs depending on the industry
+you're talking to. And here's one of the
+
+ align:start position:0%
+you're talking to. And here's one of the
+ 
+
+ align:start position:0%
+you're talking to. And here's one of the
+things that I find with that. If you do,
+
+ align:start position:0%
+things that I find with that. If you do,
+ 
+
+ align:start position:0%
+things that I find with that. If you do,
+and you can, they'll go, you can embed
+
+ align:start position:0%
+and you can, they'll go, you can embed
+ 
+
+ align:start position:0%
+and you can, they'll go, you can embed
+the tag. Absolutely right. No question.
+
+ align:start position:0%
+the tag. Absolutely right. No question.
+ 
+
+ align:start position:0%
+the tag. Absolutely right. No question.
+You can embed the tag and it's
+
+ align:start position:0%
+You can embed the tag and it's
+ 
+
+ align:start position:0%
+You can embed the tag and it's
+protected. Those are good things. You
+
+ align:start position:0%
+protected. Those are good things. You
+ 
+
+ align:start position:0%
+protected. Those are good things. You
+can embed the tag in corrugated, too.
+
+ align:start position:0%
+can embed the tag in corrugated, too.
+ 
+
+ align:start position:0%
+can embed the tag in corrugated, too.
+Um, I don't I have to look ahead. Don't
+
+ align:start position:0%
+Um, I don't I have to look ahead. Don't
+ 
+
+ align:start position:0%
+Um, I don't I have to look ahead. Don't
+look. Okay, good. Um, if you embed the
+
+ align:start position:0%
+look. Okay, good. Um, if you embed the
+ 
+
+ align:start position:0%
+look. Okay, good. Um, if you embed the
+tag in corrugated, there's a problem
+
+ align:start position:0%
+tag in corrugated, there's a problem
+ 
+
+ align:start position:0%
+tag in corrugated, there's a problem
+with that inherently from an operation
+
+ align:start position:0%
+with that inherently from an operation
+ 
+
+ align:start position:0%
+with that inherently from an operation
+standpoint because you embed it and
+
+ align:start position:0%
+standpoint because you embed it and
+ 
+
+ align:start position:0%
+standpoint because you embed it and
+those of you that have been in a
+
+ align:start position:0%
+those of you that have been in a
+ 
+
+ align:start position:0%
+those of you that have been in a
+corrugated plant, you see this stuff
+
+ align:start position:0%
+corrugated plant, you see this stuff
+ 
+
+ align:start position:0%
+corrugated plant, you see this stuff
+whipping off and you place tags every so
+
+ align:start position:0%
+whipping off and you place tags every so
+ 
+
+ align:start position:0%
+whipping off and you place tags every so
+often. You then have to die cut to get
+
+ align:start position:0%
+often. You then have to die cut to get
+ 
+
+ align:start position:0%
+often. You then have to die cut to get
+that box blank. And if you're changing
+
+ align:start position:0%
+that box blank. And if you're changing
+ 
+
+ align:start position:0%
+that box blank. And if you're changing
+the die,
+
+ align:start position:0%
+the die,
+ 
+
+ align:start position:0%
+the die,
+you don't know what's going to happen to
+
+ align:start position:0%
+you don't know what's going to happen to
+ 
+
+ align:start position:0%
+you don't know what's going to happen to
+that tag. So, that's really problematic.
+
+ align:start position:0%
+that tag. So, that's really problematic.
+ 
+
+ align:start position:0%
+that tag. So, that's really problematic.
+That means you end up having to
+
+ align:start position:0%
+That means you end up having to
+ 
+
+ align:start position:0%
+That means you end up having to
+inventory 8-ft sheets of board rather
+
+ align:start position:0%
+inventory 8-ft sheets of board rather
+ 
+
+ align:start position:0%
+inventory 8-ft sheets of board rather
+than diecut blanks or diecut uh boxes.
+
+ align:start position:0%
+than diecut blanks or diecut uh boxes.
+ 
+
+ align:start position:0%
+than diecut blanks or diecut uh boxes.
+That's a huge amount of space increase.
+
+ align:start position:0%
+That's a huge amount of space increase.
+ 
+
+ align:start position:0%
+That's a huge amount of space increase.
+All right. Now, the other thing that
+
+ align:start position:0%
+All right. Now, the other thing that
+ 
+
+ align:start position:0%
+All right. Now, the other thing that
+well, okay, with RPCs, I'll I'll cover
+
+ align:start position:0%
+well, okay, with RPCs, I'll I'll cover
+ 
+
+ align:start position:0%
+well, okay, with RPCs, I'll I'll cover
+that in a second. Uh don't let me
+
+ align:start position:0%
+that in a second. Uh don't let me
+ 
+
+ align:start position:0%
+that in a second. Uh don't let me
+forget. These are just some of our test
+
+ align:start position:0%
+forget. These are just some of our test
+ 
+
+ align:start position:0%
+forget. These are just some of our test
+conditions. We have loading docks at the
+
+ align:start position:0%
+conditions. We have loading docks at the
+ 
+
+ align:start position:0%
+conditions. We have loading docks at the
+school. Um and in the bottom corner over
+
+ align:start position:0%
+school. Um and in the bottom corner over
+ 
+
+ align:start position:0%
+school. Um and in the bottom corner over
+here, you'll see uh one of my labs. And
+
+ align:start position:0%
+here, you'll see uh one of my labs. And
+ 
+
+ align:start position:0%
+here, you'll see uh one of my labs. And
+uh I run that. I just put the corugated
+
+ align:start position:0%
+uh I run that. I just put the corugated
+ 
+
+ align:start position:0%
+uh I run that. I just put the corugated
+up to make it look clean because it's a
+
+ align:start position:0%
+up to make it look clean because it's a
+ 
+
+ align:start position:0%
+up to make it look clean because it's a
+dirty lab, if you will, literally and
+
+ align:start position:0%
+dirty lab, if you will, literally and
+ 
+
+ align:start position:0%
+dirty lab, if you will, literally and
+figuratively. Um, but we'll turn on all
+
+ align:start position:0%
+figuratively. Um, but we'll turn on all
+ 
+
+ align:start position:0%
+figuratively. Um, but we'll turn on all
+the equipment and see what
+
+ align:start position:0%
+the equipment and see what
+ 
+
+ align:start position:0%
+the equipment and see what
+electromagnetic interference uh does
+
+ align:start position:0%
+electromagnetic interference uh does
+ 
+
+ align:start position:0%
+electromagnetic interference uh does
+with respect to different tag and reader
+
+ align:start position:0%
+with respect to different tag and reader
+ 
+
+ align:start position:0%
+with respect to different tag and reader
+combinations.
+
+ align:start position:0%
+combinations.
+ 
+
+ align:start position:0%
+combinations.
+We did shock testing. Okay, so we're
+
+ align:start position:0%
+We did shock testing. Okay, so we're
+ 
+
+ align:start position:0%
+We did shock testing. Okay, so we're
+doing drops on here. Here's a vibration
+
+ align:start position:0%
+doing drops on here. Here's a vibration
+ 
+
+ align:start position:0%
+doing drops on here. Here's a vibration
+test unit load as well as column stack
+
+ align:start position:0%
+test unit load as well as column stack
+ 
+
+ align:start position:0%
+test unit load as well as column stack
+where we're trying to get the columns
+
+ align:start position:0%
+where we're trying to get the columns
+ 
+
+ align:start position:0%
+where we're trying to get the columns
+rubbing against each other to see if we
+
+ align:start position:0%
+rubbing against each other to see if we
+ 
+
+ align:start position:0%
+rubbing against each other to see if we
+could araid through to destroy the chip.
+
+ align:start position:0%
+could araid through to destroy the chip.
+ 
+
+ align:start position:0%
+could araid through to destroy the chip.
+compression tests. You can do these all
+
+ align:start position:0%
+compression tests. You can do these all
+ 
+
+ align:start position:0%
+compression tests. You can do these all
+day long. Nothing ever happens, but
+
+ align:start position:0%
+day long. Nothing ever happens, but
+ 
+
+ align:start position:0%
+day long. Nothing ever happens, but
+they're cool to look at. Um, now here's
+
+ align:start position:0%
+they're cool to look at. Um, now here's
+ 
+
+ align:start position:0%
+they're cool to look at. Um, now here's
+some issues that we also found in
+
+ align:start position:0%
+some issues that we also found in
+ 
+
+ align:start position:0%
+some issues that we also found in
+looking at a lot of product package
+
+ align:start position:0%
+looking at a lot of product package
+ 
+
+ align:start position:0%
+looking at a lot of product package
+combinations. This is a seven down
+
+ align:start position:0%
+combinations. This is a seven down
+ 
+
+ align:start position:0%
+combinations. This is a seven down
+footprint, four and three cases. And the
+
+ align:start position:0%
+footprint, four and three cases. And the
+ 
+
+ align:start position:0%
+footprint, four and three cases. And the
+white means you got 100% reads in um
+
+ align:start position:0%
+white means you got 100% reads in um
+ 
+
+ align:start position:0%
+white means you got 100% reads in um
+25 trials going through a portal. And
+
+ align:start position:0%
+25 trials going through a portal. And
+ 
+
+ align:start position:0%
+25 trials going through a portal. And
+you have the red with various
+
+ align:start position:0%
+you have the red with various
+ 
+
+ align:start position:0%
+you have the red with various
+percentages up there. Those tags didn't
+
+ align:start position:0%
+percentages up there. Those tags didn't
+ 
+
+ align:start position:0%
+percentages up there. Those tags didn't
+read, but they're all perimeter tags,
+
+ align:start position:0%
+read, but they're all perimeter tags,
+ 
+
+ align:start position:0%
+read, but they're all perimeter tags,
+and they didn't read because
+
+ align:start position:0%
+and they didn't read because
+ 
+
+ align:start position:0%
+and they didn't read because
+metal forklift blocked the RF from
+
+ align:start position:0%
+metal forklift blocked the RF from
+ 
+
+ align:start position:0%
+metal forklift blocked the RF from
+getting to them. I don't have it in
+
+ align:start position:0%
+getting to them. I don't have it in
+ 
+
+ align:start position:0%
+getting to them. I don't have it in
+here. We did a lot of studies on how
+
+ align:start position:0%
+here. We did a lot of studies on how
+ 
+
+ align:start position:0%
+here. We did a lot of studies on how
+much room do you need to measure in that
+
+ align:start position:0%
+much room do you need to measure in that
+ 
+
+ align:start position:0%
+much room do you need to measure in that
+gap and reflect off, but it's a
+
+ align:start position:0%
+gap and reflect off, but it's a
+ 
+
+ align:start position:0%
+gap and reflect off, but it's a
+different. Now, on the bottom is the
+
+ align:start position:0%
+different. Now, on the bottom is the
+ 
+
+ align:start position:0%
+different. Now, on the bottom is the
+exact same product, the exact same cases
+
+ align:start position:0%
+exact same product, the exact same cases
+ 
+
+ align:start position:0%
+exact same product, the exact same cases
+and tags, but I changed the stacking
+
+ align:start position:0%
+and tags, but I changed the stacking
+ 
+
+ align:start position:0%
+and tags, but I changed the stacking
+pattern.
+
+ align:start position:0%
+pattern.
+ 
+
+ align:start position:0%
+pattern.
+I agree. It is a stacking pattern that
+
+ align:start position:0%
+I agree. It is a stacking pattern that
+ 
+
+ align:start position:0%
+I agree. It is a stacking pattern that
+rhymes with It's a terrible
+
+ align:start position:0%
+rhymes with It's a terrible
+ 
+
+ align:start position:0%
+rhymes with It's a terrible
+pattern. You'd never use this. However,
+
+ align:start position:0%
+pattern. You'd never use this. However,
+ 
+
+ align:start position:0%
+pattern. You'd never use this. However,
+my point was to demonstrate that if you
+
+ align:start position:0%
+my point was to demonstrate that if you
+ 
+
+ align:start position:0%
+my point was to demonstrate that if you
+change stacking patterns, it can impact
+
+ align:start position:0%
+change stacking patterns, it can impact
+ 
+
+ align:start position:0%
+change stacking patterns, it can impact
+readability. That's all I wanted to
+
+ align:start position:0%
+readability. That's all I wanted to
+ 
+
+ align:start position:0%
+readability. That's all I wanted to
+prove.
+
+ align:start position:0%
+prove.
+ 
+
+ align:start position:0%
+prove.
+Now, here's one where the green is the
+
+ align:start position:0%
+Now, here's one where the green is the
+ 
+
+ align:start position:0%
+Now, here's one where the green is the
+tag location on these cases. And we have
+
+ align:start position:0%
+tag location on these cases. And we have
+ 
+
+ align:start position:0%
+tag location on these cases. And we have
+the same orientation, the same patterns.
+
+ align:start position:0%
+the same orientation, the same patterns.
+ 
+
+ align:start position:0%
+the same orientation, the same patterns.
+And I just turned the tags inward rather
+
+ align:start position:0%
+And I just turned the tags inward rather
+ 
+
+ align:start position:0%
+And I just turned the tags inward rather
+than leaving them at the perimeter. And
+
+ align:start position:0%
+than leaving them at the perimeter. And
+ 
+
+ align:start position:0%
+than leaving them at the perimeter. And
+those red reads, 25 trials, not a single
+
+ align:start position:0%
+those red reads, 25 trials, not a single
+ 
+
+ align:start position:0%
+those red reads, 25 trials, not a single
+time that case read. These are
+
+ align:start position:0%
+time that case read. These are
+ 
+
+ align:start position:0%
+time that case read. These are
+individual uh tiers stacked on top of
+
+ align:start position:0%
+individual uh tiers stacked on top of
+ 
+
+ align:start position:0%
+individual uh tiers stacked on top of
+each other. Same with the bottom ones,
+
+ align:start position:0%
+each other. Same with the bottom ones,
+ 
+
+ align:start position:0%
+each other. Same with the bottom ones,
+even though you have the channels into
+
+ align:start position:0%
+even though you have the channels into
+ 
+
+ align:start position:0%
+even though you have the channels into
+the tags.
+
+ align:start position:0%
+the tags.
+ 
+
+ align:start position:0%
+the tags.
+Okay. Now, here's just kind of a
+
+ align:start position:0%
+Okay. Now, here's just kind of a
+ 
+
+ align:start position:0%
+Okay. Now, here's just kind of a
+reversed all perimeter tags on the top
+
+ align:start position:0%
+reversed all perimeter tags on the top
+ 
+
+ align:start position:0%
+reversed all perimeter tags on the top
+one. good readability like no failures
+
+ align:start position:0%
+one. good readability like no failures
+ 
+
+ align:start position:0%
+one. good readability like no failures
+that's real handy inward-f facing tags
+
+ align:start position:0%
+that's real handy inward-f facing tags
+ 
+
+ align:start position:0%
+that's real handy inward-f facing tags
+death except on the top where there was
+
+ align:start position:0%
+death except on the top where there was
+ 
+
+ align:start position:0%
+death except on the top where there was
+no case surrounding it now what this
+
+ align:start position:0%
+no case surrounding it now what this
+ 
+
+ align:start position:0%
+no case surrounding it now what this
+means and you know we've done a lot of
+
+ align:start position:0%
+means and you know we've done a lot of
+ 
+
+ align:start position:0%
+means and you know we've done a lot of
+talking on processes here one of the
+
+ align:start position:0%
+talking on processes here one of the
+ 
+
+ align:start position:0%
+talking on processes here one of the
+processes that may have to occur before
+
+ align:start position:0%
+processes that may have to occur before
+ 
+
+ align:start position:0%
+processes that may have to occur before
+RFID enables all the benefits we're
+
+ align:start position:0%
+RFID enables all the benefits we're
+ 
+
+ align:start position:0%
+RFID enables all the benefits we're
+talking about in the supply chain is to
+
+ align:start position:0%
+talking about in the supply chain is to
+ 
+
+ align:start position:0%
+talking about in the supply chain is to
+look at changing the pallet patterns or
+
+ align:start position:0%
+look at changing the pallet patterns or
+ 
+
+ align:start position:0%
+look at changing the pallet patterns or
+case counts to match maximize perimeter
+
+ align:start position:0%
+case counts to match maximize perimeter
+ 
+
+ align:start position:0%
+case counts to match maximize perimeter
+tagging. In the video that DHL showed,
+
+ align:start position:0%
+tagging. In the video that DHL showed,
+ 
+
+ align:start position:0%
+tagging. In the video that DHL showed,
+did anybody notice that that pallet was
+
+ align:start position:0%
+did anybody notice that that pallet was
+ 
+
+ align:start position:0%
+did anybody notice that that pallet was
+a half pallet? It wasn't a typical uh
+
+ align:start position:0%
+a half pallet? It wasn't a typical uh
+ 
+
+ align:start position:0%
+a half pallet? It wasn't a typical uh
+GMA pallet like we use here in the
+
+ align:start position:0%
+GMA pallet like we use here in the
+ 
+
+ align:start position:0%
+GMA pallet like we use here in the
+United States, Grocery Manufacturers
+
+ align:start position:0%
+United States, Grocery Manufacturers
+ 
+
+ align:start position:0%
+United States, Grocery Manufacturers
+Association, a 40x 48 inch pallet. It
+
+ align:start position:0%
+Association, a 40x 48 inch pallet. It
+ 
+
+ align:start position:0%
+Association, a 40x 48 inch pallet. It
+was a half pallet. And if you go through
+
+ align:start position:0%
+was a half pallet. And if you go through
+ 
+
+ align:start position:0%
+was a half pallet. And if you go through
+Europe, you'll also see quarter pallets.
+
+ align:start position:0%
+Europe, you'll also see quarter pallets.
+ 
+
+ align:start position:0%
+Europe, you'll also see quarter pallets.
+And one of the benefits of that system
+
+ align:start position:0%
+And one of the benefits of that system
+ 
+
+ align:start position:0%
+And one of the benefits of that system
+is you always almost always pretty much
+
+ align:start position:0%
+is you always almost always pretty much
+ 
+
+ align:start position:0%
+is you always almost always pretty much
+always get that perimeter tagging
+
+ align:start position:0%
+always get that perimeter tagging
+ 
+
+ align:start position:0%
+always get that perimeter tagging
+opportunity and therefore better
+
+ align:start position:0%
+opportunity and therefore better
+ 
+
+ align:start position:0%
+opportunity and therefore better
+readability.
+
+ align:start position:0%
+readability.
+ 
+
+ align:start position:0%
+readability.
+Now product impact water we tested some
+
+ align:start position:0%
+Now product impact water we tested some
+ 
+
+ align:start position:0%
+Now product impact water we tested some
+and we found a case that would be
+
+ align:start position:0%
+and we found a case that would be
+ 
+
+ align:start position:0%
+and we found a case that would be
+readable non-readable readable
+
+ align:start position:0%
+readable non-readable readable
+ 
+
+ align:start position:0%
+readable non-readable readable
+non-readable nothing changed. What the
+
+ align:start position:0%
+non-readable nothing changed. What the
+ 
+
+ align:start position:0%
+non-readable nothing changed. What the
+hell's going on? I'm going crazy here.
+
+ align:start position:0%
+hell's going on? I'm going crazy here.
+ 
+
+ align:start position:0%
+hell's going on? I'm going crazy here.
+All right. What we found was we had
+
+ align:start position:0%
+All right. What we found was we had
+ 
+
+ align:start position:0%
+All right. What we found was we had
+heads of lettuce and a head of lettuce
+
+ align:start position:0%
+heads of lettuce and a head of lettuce
+ 
+
+ align:start position:0%
+heads of lettuce and a head of lettuce
+would rotate and put a flat portion of
+
+ align:start position:0%
+would rotate and put a flat portion of
+ 
+
+ align:start position:0%
+would rotate and put a flat portion of
+the head on the back side of the case
+
+ align:start position:0%
+the head on the back side of the case
+ 
+
+ align:start position:0%
+the head on the back side of the case
+where the tag was. And if that hunk of
+
+ align:start position:0%
+where the tag was. And if that hunk of
+ 
+
+ align:start position:0%
+where the tag was. And if that hunk of
+water in a lettuce was up against the
+
+ align:start position:0%
+water in a lettuce was up against the
+ 
+
+ align:start position:0%
+water in a lettuce was up against the
+corrugated behind the tag, you can't
+
+ align:start position:0%
+corrugated behind the tag, you can't
+ 
+
+ align:start position:0%
+corrugated behind the tag, you can't
+read the tag. And that was demonstrated
+
+ align:start position:0%
+read the tag. And that was demonstrated
+ 
+
+ align:start position:0%
+read the tag. And that was demonstrated
+last night with the different
+
+ align:start position:0%
+last night with the different
+ 
+
+ align:start position:0%
+last night with the different
+thicknesses on the uh water with Dan.
+
+ align:start position:0%
+thicknesses on the uh water with Dan.
+ 
+
+ align:start position:0%
+thicknesses on the uh water with Dan.
+When you rotated the uh uh tray full of
+
+ align:start position:0%
+When you rotated the uh uh tray full of
+ 
+
+ align:start position:0%
+When you rotated the uh uh tray full of
+water, you needed additional thicknesses
+
+ align:start position:0%
+water, you needed additional thicknesses
+ 
+
+ align:start position:0%
+water, you needed additional thicknesses
+because you need to separate the tag
+
+ align:start position:0%
+because you need to separate the tag
+ 
+
+ align:start position:0%
+because you need to separate the tag
+from the water to allow the signal to
+
+ align:start position:0%
+from the water to allow the signal to
+ 
+
+ align:start position:0%
+from the water to allow the signal to
+get in and energize the uh antenna. And
+
+ align:start position:0%
+get in and energize the uh antenna. And
+ 
+
+ align:start position:0%
+get in and energize the uh antenna. And
+here's a perfect example. We found it in
+
+ align:start position:0%
+here's a perfect example. We found it in
+ 
+
+ align:start position:0%
+here's a perfect example. We found it in
+lettuce. We found it in peaches. We
+
+ align:start position:0%
+lettuce. We found it in peaches. We
+ 
+
+ align:start position:0%
+lettuce. We found it in peaches. We
+found it in a couple different products.
+
+ align:start position:0%
+found it in a couple different products.
+ 
+
+ align:start position:0%
+found it in a couple different products.
+We started looking at uh reading on
+
+ align:start position:0%
+We started looking at uh reading on
+ 
+
+ align:start position:0%
+We started looking at uh reading on
+shrink wrap uh situations, stretch wrap,
+
+ align:start position:0%
+shrink wrap uh situations, stretch wrap,
+ 
+
+ align:start position:0%
+shrink wrap uh situations, stretch wrap,
+excuse me. And this is a portal that has
+
+ align:start position:0%
+excuse me. And this is a portal that has
+ 
+
+ align:start position:0%
+excuse me. And this is a portal that has
+four antenna. This is part of the uh
+
+ align:start position:0%
+four antenna. This is part of the uh
+ 
+
+ align:start position:0%
+four antenna. This is part of the uh
+antenna configuration and and
+
+ align:start position:0%
+antenna configuration and and
+ 
+
+ align:start position:0%
+antenna configuration and and
+readability and uh reading while it's
+
+ align:start position:0%
+readability and uh reading while it's
+ 
+
+ align:start position:0%
+readability and uh reading while it's
+because it's on there for roughly uh 30
+
+ align:start position:0%
+because it's on there for roughly uh 30
+ 
+
+ align:start position:0%
+because it's on there for roughly uh 30
+seconds while the uh uh uh stretch wrap
+
+ align:start position:0%
+seconds while the uh uh uh stretch wrap
+ 
+
+ align:start position:0%
+seconds while the uh uh uh stretch wrap
+is being put on. And uh we found some
+
+ align:start position:0%
+is being put on. And uh we found some
+ 
+
+ align:start position:0%
+is being put on. And uh we found some
+some fun results, but that'll be out
+
+ align:start position:0%
+some fun results, but that'll be out
+ 
+
+ align:start position:0%
+some fun results, but that'll be out
+shortly and I'll I'll tease you all with
+
+ align:start position:0%
+shortly and I'll I'll tease you all with
+ 
+
+ align:start position:0%
+shortly and I'll I'll tease you all with
+that. One of the things we're currently
+
+ align:start position:0%
+that. One of the things we're currently
+ 
+
+ align:start position:0%
+that. One of the things we're currently
+doing now is looking at water on
+
+ align:start position:0%
+doing now is looking at water on
+ 
+
+ align:start position:0%
+doing now is looking at water on
+corrugated. Corrugated has huge markets
+
+ align:start position:0%
+corrugated. Corrugated has huge markets
+ 
+
+ align:start position:0%
+corrugated. Corrugated has huge markets
+and opportunities within produce. No
+
+ align:start position:0%
+and opportunities within produce. No
+ 
+
+ align:start position:0%
+and opportunities within produce. No
+question about it. And here we've
+
+ align:start position:0%
+question about it. And here we've
+ 
+
+ align:start position:0%
+question about it. And here we've
+started a series of tests on these. We
+
+ align:start position:0%
+started a series of tests on these. We
+ 
+
+ align:start position:0%
+started a series of tests on these. We
+have produce trays. And in the top we
+
+ align:start position:0%
+have produce trays. And in the top we
+ 
+
+ align:start position:0%
+have produce trays. And in the top we
+just have a squeeze bottle. Real
+
+ align:start position:0%
+just have a squeeze bottle. Real
+ 
+
+ align:start position:0%
+just have a squeeze bottle. Real
+scientific. Cost me I think 89 cents to
+
+ align:start position:0%
+scientific. Cost me I think 89 cents to
+ 
+
+ align:start position:0%
+scientific. Cost me I think 89 cents to
+empty and fill up with water. And we
+
+ align:start position:0%
+empty and fill up with water. And we
+ 
+
+ align:start position:0%
+empty and fill up with water. And we
+spray on the tag. Okay. And the one
+
+ align:start position:0%
+spray on the tag. Okay. And the one
+ 
+
+ align:start position:0%
+spray on the tag. Okay. And the one
+below that we got a squeeze bottle. That
+
+ align:start position:0%
+below that we got a squeeze bottle. That
+ 
+
+ align:start position:0%
+below that we got a squeeze bottle. That
+was cheaper. That was like 39 cents. and
+
+ align:start position:0%
+was cheaper. That was like 39 cents. and
+ 
+
+ align:start position:0%
+was cheaper. That was like 39 cents. and
+we just squeeze a stream on it. Now, on
+
+ align:start position:0%
+we just squeeze a stream on it. Now, on
+ 
+
+ align:start position:0%
+we just squeeze a stream on it. Now, on
+the top, we run a tap and we have a
+
+ align:start position:0%
+the top, we run a tap and we have a
+ 
+
+ align:start position:0%
+the top, we run a tap and we have a
+calibrated hand splashing water across
+
+ align:start position:0%
+calibrated hand splashing water across
+ 
+
+ align:start position:0%
+calibrated hand splashing water across
+the tag, looking at different levels of
+
+ align:start position:0%
+the tag, looking at different levels of
+ 
+
+ align:start position:0%
+the tag, looking at different levels of
+moisture on the tag. And here's one of
+
+ align:start position:0%
+moisture on the tag. And here's one of
+ 
+
+ align:start position:0%
+moisture on the tag. And here's one of
+the interesting things that we found. If
+
+ align:start position:0%
+the interesting things that we found. If
+ 
+
+ align:start position:0%
+the interesting things that we found. If
+you have untreated board, any water on
+
+ align:start position:0%
+you have untreated board, any water on
+ 
+
+ align:start position:0%
+you have untreated board, any water on
+the tag, the tag disappears. You can't
+
+ align:start position:0%
+the tag, the tag disappears. You can't
+ 
+
+ align:start position:0%
+the tag, the tag disappears. You can't
+read it. Okay? And in the bottom
+
+ align:start position:0%
+read it. Okay? And in the bottom
+ 
+
+ align:start position:0%
+read it. Okay? And in the bottom
+picture, you see how the water has
+
+ align:start position:0%
+picture, you see how the water has
+ 
+
+ align:start position:0%
+picture, you see how the water has
+worked its way into some of the holes of
+
+ align:start position:0%
+worked its way into some of the holes of
+ 
+
+ align:start position:0%
+worked its way into some of the holes of
+the case.
+
+ align:start position:0%
+the case.
+ 
+
+ align:start position:0%
+the case.
+it holds moisture, you still have
+
+ align:start position:0%
+it holds moisture, you still have
+ 
+
+ align:start position:0%
+it holds moisture, you still have
+problems and you can't always read those
+
+ align:start position:0%
+problems and you can't always read those
+ 
+
+ align:start position:0%
+problems and you can't always read those
+after the water application stops.
+
+ align:start position:0%
+after the water application stops.
+ 
+
+ align:start position:0%
+after the water application stops.
+However, if you have treated board and
+
+ align:start position:0%
+However, if you have treated board and
+ 
+
+ align:start position:0%
+However, if you have treated board and
+you do this exact test, as soon as you
+
+ align:start position:0%
+you do this exact test, as soon as you
+ 
+
+ align:start position:0%
+you do this exact test, as soon as you
+stop the water, whether it's a spray, a
+
+ align:start position:0%
+stop the water, whether it's a spray, a
+ 
+
+ align:start position:0%
+stop the water, whether it's a spray, a
+squeeze bottle, or a flood of water, the
+
+ align:start position:0%
+squeeze bottle, or a flood of water, the
+ 
+
+ align:start position:0%
+squeeze bottle, or a flood of water, the
+second you stop that water and it
+
+ align:start position:0%
+second you stop that water and it
+ 
+
+ align:start position:0%
+second you stop that water and it
+drains, that tag reads again. That is no
+
+ align:start position:0%
+drains, that tag reads again. That is no
+ 
+
+ align:start position:0%
+drains, that tag reads again. That is no
+different than a tag embedded in a
+
+ align:start position:0%
+different than a tag embedded in a
+ 
+
+ align:start position:0%
+different than a tag embedded in a
+returnable plastic container. If you run
+
+ align:start position:0%
+returnable plastic container. If you run
+ 
+
+ align:start position:0%
+returnable plastic container. If you run
+water over those, the tag still
+
+ align:start position:0%
+water over those, the tag still
+ 
+
+ align:start position:0%
+water over those, the tag still
+disappears.
+
+ align:start position:0%
+disappears.
+ 
+
+ align:start position:0%
+disappears.
+There's no magic that if you bury a tag
+
+ align:start position:0%
+There's no magic that if you bury a tag
+ 
+
+ align:start position:0%
+There's no magic that if you bury a tag
+in plastic, you can still spray it with
+
+ align:start position:0%
+in plastic, you can still spray it with
+ 
+
+ align:start position:0%
+in plastic, you can still spray it with
+water and get the tag to read. You can
+
+ align:start position:0%
+water and get the tag to read. You can
+ 
+
+ align:start position:0%
+water and get the tag to read. You can
+spray it with water for cleaning. But
+
+ align:start position:0%
+spray it with water for cleaning. But
+ 
+
+ align:start position:0%
+spray it with water for cleaning. But
+here was an interesting thing. My wife
+
+ align:start position:0%
+here was an interesting thing. My wife
+ 
+
+ align:start position:0%
+here was an interesting thing. My wife
+is here with me and I was talking to her
+
+ align:start position:0%
+is here with me and I was talking to her
+ 
+
+ align:start position:0%
+is here with me and I was talking to her
+about returnable containers and she
+
+ align:start position:0%
+about returnable containers and she
+ 
+
+ align:start position:0%
+about returnable containers and she
+worked for a company in Dallas.
+
+ align:start position:0%
+worked for a company in Dallas.
+ 
+
+ align:start position:0%
+worked for a company in Dallas.
+We made a one-way container for a
+
+ align:start position:0%
+We made a one-way container for a
+ 
+
+ align:start position:0%
+We made a one-way container for a
+company and it was electronic company in
+
+ align:start position:0%
+company and it was electronic company in
+ 
+
+ align:start position:0%
+company and it was electronic company in
+Dallas. They came back a year later and
+
+ align:start position:0%
+Dallas. They came back a year later and
+ 
+
+ align:start position:0%
+Dallas. They came back a year later and
+wanted us to rebuild this corrugated box
+
+ align:start position:0%
+wanted us to rebuild this corrugated box
+ 
+
+ align:start position:0%
+wanted us to rebuild this corrugated box
+and it was about the length and width of
+
+ align:start position:0%
+and it was about the length and width of
+ 
+
+ align:start position:0%
+and it was about the length and width of
+this table about this deep. They had
+
+ align:start position:0%
+this table about this deep. They had
+ 
+
+ align:start position:0%
+this table about this deep. They had
+used it every week for a shipment to a
+
+ align:start position:0%
+used it every week for a shipment to a
+ 
+
+ align:start position:0%
+used it every week for a shipment to a
+plant and back for a year and then they
+
+ align:start position:0%
+plant and back for a year and then they
+ 
+
+ align:start position:0%
+plant and back for a year and then they
+asked them to rebuild it rather than a
+
+ align:start position:0%
+asked them to rebuild it rather than a
+ 
+
+ align:start position:0%
+asked them to rebuild it rather than a
+new one out of corrugated. Now, it was
+
+ align:start position:0%
+new one out of corrugated. Now, it was
+ 
+
+ align:start position:0%
+new one out of corrugated. Now, it was
+triple wall, but there is a good
+
+ align:start position:0%
+triple wall, but there is a good
+ 
+
+ align:start position:0%
+triple wall, but there is a good
+reusable. Fredo Lelay uses returnable uh
+
+ align:start position:0%
+reusable. Fredo Lelay uses returnable uh
+ 
+
+ align:start position:0%
+reusable. Fredo Lelay uses returnable uh
+corrugated boxes for all of their chips
+
+ align:start position:0%
+corrugated boxes for all of their chips
+ 
+
+ align:start position:0%
+corrugated boxes for all of their chips
+because they control the placement on
+
+ align:start position:0%
+because they control the placement on
+ 
+
+ align:start position:0%
+because they control the placement on
+the shelves and then they take the boxes
+
+ align:start position:0%
+the shelves and then they take the boxes
+ 
+
+ align:start position:0%
+the shelves and then they take the boxes
+back and they reuse them and they can
+
+ align:start position:0%
+back and they reuse them and they can
+ 
+
+ align:start position:0%
+back and they reuse them and they can
+reuse them for months at a time because
+
+ align:start position:0%
+reuse them for months at a time because
+ 
+
+ align:start position:0%
+reuse them for months at a time because
+they don't get beat up. Some good
+
+ align:start position:0%
+they don't get beat up. Some good
+ 
+
+ align:start position:0%
+they don't get beat up. Some good
+opportunities. Now, there's what we
+
+ align:start position:0%
+opportunities. Now, there's what we
+ 
+
+ align:start position:0%
+opportunities. Now, there's what we
+talked about. Reads stop drinking water.
+
+ align:start position:0%
+talked about. Reads stop drinking water.
+ 
+
+ align:start position:0%
+talked about. Reads stop drinking water.
+They'll continue to fail if it becomes
+
+ align:start position:0%
+They'll continue to fail if it becomes
+ 
+
+ align:start position:0%
+They'll continue to fail if it becomes
+saturated, but they resume failing if
+
+ align:start position:0%
+saturated, but they resume failing if
+ 
+
+ align:start position:0%
+saturated, but they resume failing if
+it's treated. And uh with that,
+
+ align:start position:0%
+it's treated. And uh with that,
+ 
+
+ align:start position:0%
+it's treated. And uh with that,
+I'm going to sit down and start
+
+ align:start position:0%
+I'm going to sit down and start
+ 
+
+ align:start position:0%
+I'm going to sit down and start
+drinking. And uh I'm going to turn this
+
+ align:start position:0%
+drinking. And uh I'm going to turn this
+ 
+
+ align:start position:0%
+drinking. And uh I'm going to turn this
+over to uh Dr. Aman from uh Florida. I
+
+ align:start position:0%
+over to uh Dr. Aman from uh Florida. I
+ 
+
+ align:start position:0%
+over to uh Dr. Aman from uh Florida. I
+appreciate your time and attention.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want everything. Yeah,
+
+ align:start position:0%
+want everything. Yeah,
+ 
+
+ align:start position:0%
+want everything. Yeah,
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+I'm very sorry for some of you that were
+
+ align:start position:0%
+I'm very sorry for some of you that were
+ 
+
+ align:start position:0%
+I'm very sorry for some of you that were
+done with me yesterday. Um, I'm always
+
+ align:start position:0%
+done with me yesterday. Um, I'm always
+ 
+
+ align:start position:0%
+done with me yesterday. Um, I'm always
+back. It's like a bad cold. I was coming
+
+ align:start position:0%
+back. It's like a bad cold. I was coming
+ 
+
+ align:start position:0%
+back. It's like a bad cold. I was coming
+back. Um, I'm going to go fast because
+
+ align:start position:0%
+back. Um, I'm going to go fast because
+ 
+
+ align:start position:0%
+back. Um, I'm going to go fast because
+we have lunch and uh so uh I'm sorry I
+
+ align:start position:0%
+we have lunch and uh so uh I'm sorry I
+ 
+
+ align:start position:0%
+we have lunch and uh so uh I'm sorry I
+had bad uh finger on this thing. Okay.
+
+ align:start position:0%
+had bad uh finger on this thing. Okay.
+ 
+
+ align:start position:0%
+had bad uh finger on this thing. Okay.
+Well, thank you again and uh well I'm
+
+ align:start position:0%
+Well, thank you again and uh well I'm
+ 
+
+ align:start position:0%
+Well, thank you again and uh well I'm
+going to talk about packaging and a few
+
+ align:start position:0%
+going to talk about packaging and a few
+ 
+
+ align:start position:0%
+going to talk about packaging and a few
+of the thing that uh Rob discussed a
+
+ align:start position:0%
+of the thing that uh Rob discussed a
+ 
+
+ align:start position:0%
+of the thing that uh Rob discussed a
+little bit earlier is uh I'm going to
+
+ align:start position:0%
+little bit earlier is uh I'm going to
+ 
+
+ align:start position:0%
+little bit earlier is uh I'm going to
+address that and that's really
+
+ align:start position:0%
+address that and that's really
+ 
+
+ align:start position:0%
+address that and that's really
+interesting uh very quick you know it's
+
+ align:start position:0%
+interesting uh very quick you know it's
+ 
+
+ align:start position:0%
+interesting uh very quick you know it's
+um and I explained about the center for
+
+ align:start position:0%
+um and I explained about the center for
+ 
+
+ align:start position:0%
+um and I explained about the center for
+food retailing yesterday and uh we are
+
+ align:start position:0%
+food retailing yesterday and uh we are
+ 
+
+ align:start position:0%
+food retailing yesterday and uh we are
+trying to develop smart packaging for
+
+ align:start position:0%
+trying to develop smart packaging for
+ 
+
+ align:start position:0%
+trying to develop smart packaging for
+the food industry in the pharmaceutical
+
+ align:start position:0%
+the food industry in the pharmaceutical
+ 
+
+ align:start position:0%
+the food industry in the pharmaceutical
+industry and uh one thing that uh we
+
+ align:start position:0%
+industry and uh one thing that uh we
+ 
+
+ align:start position:0%
+industry and uh one thing that uh we
+started as well in this area of RFID
+
+ align:start position:0%
+started as well in this area of RFID
+ 
+
+ align:start position:0%
+started as well in this area of RFID
+this is what happened in 2003 when uh
+
+ align:start position:0%
+this is what happened in 2003 when uh
+ 
+
+ align:start position:0%
+this is what happened in 2003 when uh
+friendwell a company based in plan city
+
+ align:start position:0%
+friendwell a company based in plan city
+ 
+
+ align:start position:0%
+friendwell a company based in plan city
+Florida came to us and said we're going
+
+ align:start position:0%
+Florida came to us and said we're going
+ 
+
+ align:start position:0%
+Florida came to us and said we're going
+to give you RFID lab and start to play
+
+ align:start position:0%
+to give you RFID lab and start to play
+ 
+
+ align:start position:0%
+to give you RFID lab and start to play
+with this thing. And the reason why it
+
+ align:start position:0%
+with this thing. And the reason why it
+ 
+
+ align:start position:0%
+with this thing. And the reason why it
+was a good match for the food industry
+
+ align:start position:0%
+was a good match for the food industry
+ 
+
+ align:start position:0%
+was a good match for the food industry
+is because we have already
+
+ align:start position:0%
+is because we have already
+ 
+
+ align:start position:0%
+is because we have already
+infrastructure. We have 14 cold room uh
+
+ align:start position:0%
+infrastructure. We have 14 cold room uh
+ 
+
+ align:start position:0%
+infrastructure. We have 14 cold room uh
+temperature humidity programmable and we
+
+ align:start position:0%
+temperature humidity programmable and we
+ 
+
+ align:start position:0%
+temperature humidity programmable and we
+have two freezer, we have two C
+
+ align:start position:0%
+have two freezer, we have two C
+ 
+
+ align:start position:0%
+have two freezer, we have two C
+container, uh one refrigerated trailer
+
+ align:start position:0%
+container, uh one refrigerated trailer
+ 
+
+ align:start position:0%
+container, uh one refrigerated trailer
+and even a 727 frider uh that they don't
+
+ align:start position:0%
+and even a 727 frider uh that they don't
+ 
+
+ align:start position:0%
+and even a 727 frider uh that they don't
+allow me to fly luckily for everybody.
+
+ align:start position:0%
+allow me to fly luckily for everybody.
+ 
+
+ align:start position:0%
+allow me to fly luckily for everybody.
+But the the goal was to um from that
+
+ align:start position:0%
+But the the goal was to um from that
+ 
+
+ align:start position:0%
+But the the goal was to um from that
+time is that to to get the uh all the
+
+ align:start position:0%
+time is that to to get the uh all the
+ 
+
+ align:start position:0%
+time is that to to get the uh all the
+RFID hardware software manufacturer to
+
+ align:start position:0%
+RFID hardware software manufacturer to
+ 
+
+ align:start position:0%
+RFID hardware software manufacturer to
+have a start there and since then every
+
+ align:start position:0%
+have a start there and since then every
+ 
+
+ align:start position:0%
+have a start there and since then every
+three months they come and they upgrade
+
+ align:start position:0%
+three months they come and they upgrade
+ 
+
+ align:start position:0%
+three months they come and they upgrade
+our our equipment software hardware. So
+
+ align:start position:0%
+our our equipment software hardware. So
+ 
+
+ align:start position:0%
+our our equipment software hardware. So
+that's pretty neat for that. We always
+
+ align:start position:0%
+that's pretty neat for that. We always
+ 
+
+ align:start position:0%
+that's pretty neat for that. We always
+uh pretty get the uh the new stuff
+
+ align:start position:0%
+uh pretty get the uh the new stuff
+ 
+
+ align:start position:0%
+uh pretty get the uh the new stuff
+pretty ahead. So our lab is designed
+
+ align:start position:0%
+pretty ahead. So our lab is designed
+ 
+
+ align:start position:0%
+pretty ahead. So our lab is designed
+like Rob, you know, we have uh for
+
+ align:start position:0%
+like Rob, you know, we have uh for
+ 
+
+ align:start position:0%
+like Rob, you know, we have uh for
+everything to measure, you know, the
+
+ align:start position:0%
+everything to measure, you know, the
+ 
+
+ align:start position:0%
+everything to measure, you know, the
+impact of packaging and things like
+
+ align:start position:0%
+impact of packaging and things like
+ 
+
+ align:start position:0%
+impact of packaging and things like
+that. You see, Rob, I I use a drawing so
+
+ align:start position:0%
+that. You see, Rob, I I use a drawing so
+ 
+
+ align:start position:0%
+that. You see, Rob, I I use a drawing so
+I don't have to put the boards to uh
+
+ align:start position:0%
+I don't have to put the boards to uh
+ 
+
+ align:start position:0%
+I don't have to put the boards to uh
+hide my dirt in this thing. Okay. So,
+
+ align:start position:0%
+hide my dirt in this thing. Okay. So,
+ 
+
+ align:start position:0%
+hide my dirt in this thing. Okay. So,
+well, very quick, you know, uh the first
+
+ align:start position:0%
+well, very quick, you know, uh the first
+ 
+
+ align:start position:0%
+well, very quick, you know, uh the first
+thing that we did was with the TNA and
+
+ align:start position:0%
+thing that we did was with the TNA and
+ 
+
+ align:start position:0%
+thing that we did was with the TNA and
+the Fresh Express, you know, prepare
+
+ align:start position:0%
+the Fresh Express, you know, prepare
+ 
+
+ align:start position:0%
+the Fresh Express, you know, prepare
+salad and the head of lettuce and we did
+
+ align:start position:0%
+salad and the head of lettuce and we did
+ 
+
+ align:start position:0%
+salad and the head of lettuce and we did
+shipment from coast to coast, study the
+
+ align:start position:0%
+shipment from coast to coast, study the
+ 
+
+ align:start position:0%
+shipment from coast to coast, study the
+tag location on the speed of the load,
+
+ align:start position:0%
+tag location on the speed of the load,
+ 
+
+ align:start position:0%
+tag location on the speed of the load,
+and I'm going to go fast on that. The
+
+ align:start position:0%
+and I'm going to go fast on that. The
+ 
+
+ align:start position:0%
+and I'm going to go fast on that. The
+idea was to map a pallet and see where
+
+ align:start position:0%
+idea was to map a pallet and see where
+ 
+
+ align:start position:0%
+idea was to map a pallet and see where
+are the uh the good place to put a tag
+
+ align:start position:0%
+are the uh the good place to put a tag
+ 
+
+ align:start position:0%
+are the uh the good place to put a tag
+and the other place that were critical
+
+ align:start position:0%
+and the other place that were critical
+ 
+
+ align:start position:0%
+and the other place that were critical
+not put a tag because we couldn't read
+
+ align:start position:0%
+not put a tag because we couldn't read
+ 
+
+ align:start position:0%
+not put a tag because we couldn't read
+it because the effect of the old pallet.
+
+ align:start position:0%
+it because the effect of the old pallet.
+ 
+
+ align:start position:0%
+it because the effect of the old pallet.
+So we played for with that for a while
+
+ align:start position:0%
+So we played for with that for a while
+ 
+
+ align:start position:0%
+So we played for with that for a while
+until we decided that it was we have to
+
+ align:start position:0%
+until we decided that it was we have to
+ 
+
+ align:start position:0%
+until we decided that it was we have to
+go further with that. So we started to
+
+ align:start position:0%
+go further with that. So we started to
+ 
+
+ align:start position:0%
+go further with that. So we started to
+compare different material plastic wire
+
+ align:start position:0%
+compare different material plastic wire
+ 
+
+ align:start position:0%
+compare different material plastic wire
+bound wooden crate and uh and corrugated
+
+ align:start position:0%
+bound wooden crate and uh and corrugated
+ 
+
+ align:start position:0%
+bound wooden crate and uh and corrugated
+boxes and the I apologize for the wood
+
+ align:start position:0%
+boxes and the I apologize for the wood
+ 
+
+ align:start position:0%
+boxes and the I apologize for the wood
+crate. Uh I was still learning how to
+
+ align:start position:0%
+crate. Uh I was still learning how to
+ 
+
+ align:start position:0%
+crate. Uh I was still learning how to
+drive the uh Publix forklift and the
+
+ align:start position:0%
+drive the uh Publix forklift and the
+ 
+
+ align:start position:0%
+drive the uh Publix forklift and the
+corner were pretty uh stiff on this
+
+ align:start position:0%
+corner were pretty uh stiff on this
+ 
+
+ align:start position:0%
+corner were pretty uh stiff on this
+thing. But the idea was to compare what
+
+ align:start position:0%
+thing. But the idea was to compare what
+ 
+
+ align:start position:0%
+thing. But the idea was to compare what
+was the effect if you're using because
+
+ align:start position:0%
+was the effect if you're using because
+ 
+
+ align:start position:0%
+was the effect if you're using because
+these are coming from the same grower
+
+ align:start position:0%
+these are coming from the same grower
+ 
+
+ align:start position:0%
+these are coming from the same grower
+and they have different kind of
+
+ align:start position:0%
+and they have different kind of
+ 
+
+ align:start position:0%
+and they have different kind of
+packaging and things like that. So we
+
+ align:start position:0%
+packaging and things like that. So we
+ 
+
+ align:start position:0%
+packaging and things like that. So we
+wanted to study that and we came with a
+
+ align:start position:0%
+wanted to study that and we came with a
+ 
+
+ align:start position:0%
+wanted to study that and we came with a
+different thing but the problem that we
+
+ align:start position:0%
+different thing but the problem that we
+ 
+
+ align:start position:0%
+different thing but the problem that we
+dis we discover is that when people were
+
+ align:start position:0%
+dis we discover is that when people were
+ 
+
+ align:start position:0%
+dis we discover is that when people were
+looking for um readability read rate
+
+ align:start position:0%
+looking for um readability read rate
+ 
+
+ align:start position:0%
+looking for um readability read rate
+were having pretty low number and they
+
+ align:start position:0%
+were having pretty low number and they
+ 
+
+ align:start position:0%
+were having pretty low number and they
+were like oh man you know that's awful
+
+ align:start position:0%
+were like oh man you know that's awful
+ 
+
+ align:start position:0%
+were like oh man you know that's awful
+but I said well because we're losing the
+
+ align:start position:0%
+but I said well because we're losing the
+ 
+
+ align:start position:0%
+but I said well because we're losing the
+tag you know we cannot read them if
+
+ align:start position:0%
+tag you know we cannot read them if
+ 
+
+ align:start position:0%
+tag you know we cannot read them if
+they're not there anymore and uh we
+
+ align:start position:0%
+they're not there anymore and uh we
+ 
+
+ align:start position:0%
+they're not there anymore and uh we
+started to discover a lot of falling
+
+ align:start position:0%
+started to discover a lot of falling
+ 
+
+ align:start position:0%
+started to discover a lot of falling
+tags everywhere and that was a big issue
+
+ align:start position:0%
+tags everywhere and that was a big issue
+ 
+
+ align:start position:0%
+tags everywhere and that was a big issue
+one thing that we decided is that why we
+
+ align:start position:0%
+one thing that we decided is that why we
+ 
+
+ align:start position:0%
+one thing that we decided is that why we
+don't look a little bit further and and
+
+ align:start position:0%
+don't look a little bit further and and
+ 
+
+ align:start position:0%
+don't look a little bit further and and
+say when you pack something in a package
+
+ align:start position:0%
+say when you pack something in a package
+ 
+
+ align:start position:0%
+say when you pack something in a package
+uh it should stay you know with the
+
+ align:start position:0%
+uh it should stay you know with the
+ 
+
+ align:start position:0%
+uh it should stay you know with the
+package the RFID tag all the time at
+
+ align:start position:0%
+package the RFID tag all the time at
+ 
+
+ align:start position:0%
+package the RFID tag all the time at
+least identification and this is where
+
+ align:start position:0%
+least identification and this is where
+ 
+
+ align:start position:0%
+least identification and this is where
+it's started to trigger that we should
+
+ align:start position:0%
+it's started to trigger that we should
+ 
+
+ align:start position:0%
+it's started to trigger that we should
+always try to improve uh the way of of
+
+ align:start position:0%
+always try to improve uh the way of of
+ 
+
+ align:start position:0%
+always try to improve uh the way of of
+mixing tag RFID tag with packaging by
+
+ align:start position:0%
+mixing tag RFID tag with packaging by
+ 
+
+ align:start position:0%
+mixing tag RFID tag with packaging by
+trying to know if we cannot in the
+
+ align:start position:0%
+trying to know if we cannot in the
+ 
+
+ align:start position:0%
+trying to know if we cannot in the
+process of making the package just get
+
+ align:start position:0%
+process of making the package just get
+ 
+
+ align:start position:0%
+process of making the package just get
+the RFID tag inside and uh make it one
+
+ align:start position:0%
+the RFID tag inside and uh make it one
+ 
+
+ align:start position:0%
+the RFID tag inside and uh make it one
+step rather than many step so we started
+
+ align:start position:0%
+step rather than many step so we started
+ 
+
+ align:start position:0%
+step rather than many step so we started
+to investigate that so what we did is
+
+ align:start position:0%
+to investigate that so what we did is
+ 
+
+ align:start position:0%
+to investigate that so what we did is
+that we started to embed RFID tag
+
+ align:start position:0%
+that we started to embed RFID tag
+ 
+
+ align:start position:0%
+that we started to embed RFID tag
+reusable blessing container of course to
+
+ align:start position:0%
+reusable blessing container of course to
+ 
+
+ align:start position:0%
+reusable blessing container of course to
+reduce the use uh the cost per use. So
+
+ align:start position:0%
+reduce the use uh the cost per use. So
+ 
+
+ align:start position:0%
+reduce the use uh the cost per use. So
+this tag is there you cannot see it but
+
+ align:start position:0%
+this tag is there you cannot see it but
+ 
+
+ align:start position:0%
+this tag is there you cannot see it but
+it's there uh and that was doing with
+
+ align:start position:0%
+it's there uh and that was doing with
+ 
+
+ align:start position:0%
+it's there uh and that was doing with
+the PL injection molding plastic that we
+
+ align:start position:0%
+the PL injection molding plastic that we
+ 
+
+ align:start position:0%
+the PL injection molding plastic that we
+did that. So we can always track the
+
+ align:start position:0%
+did that. So we can always track the
+ 
+
+ align:start position:0%
+did that. So we can always track the
+base you know because the wall you can
+
+ align:start position:0%
+base you know because the wall you can
+ 
+
+ align:start position:0%
+base you know because the wall you can
+change them because you can if you break
+
+ align:start position:0%
+change them because you can if you break
+ 
+
+ align:start position:0%
+change them because you can if you break
+one wall you can change it but the base
+
+ align:start position:0%
+one wall you can change it but the base
+ 
+
+ align:start position:0%
+one wall you can change it but the base
+is always the base and uh so we can
+
+ align:start position:0%
+is always the base and uh so we can
+ 
+
+ align:start position:0%
+is always the base and uh so we can
+always track the life of these RPC
+
+ align:start position:0%
+always track the life of these RPC
+ 
+
+ align:start position:0%
+always track the life of these RPC
+because sometime they're used in
+
+ align:start position:0%
+because sometime they're used in
+ 
+
+ align:start position:0%
+because sometime they're used in
+different industry where you're trying
+
+ align:start position:0%
+different industry where you're trying
+ 
+
+ align:start position:0%
+different industry where you're trying
+to use them for different uh use and u
+
+ align:start position:0%
+to use them for different uh use and u
+ 
+
+ align:start position:0%
+to use them for different uh use and u
+so what we did we did we did during
+
+ align:start position:0%
+so what we did we did we did during
+ 
+
+ align:start position:0%
+so what we did we did we did during
+injection molding process and it cannot
+
+ align:start position:0%
+injection molding process and it cannot
+ 
+
+ align:start position:0%
+injection molding process and it cannot
+be removed but the the interesting is
+
+ align:start position:0%
+be removed but the the interesting is
+ 
+
+ align:start position:0%
+be removed but the the interesting is
+that we were always wondering when you
+
+ align:start position:0%
+that we were always wondering when you
+ 
+
+ align:start position:0%
+that we were always wondering when you
+inject plastic it's very high
+
+ align:start position:0%
+inject plastic it's very high
+ 
+
+ align:start position:0%
+inject plastic it's very high
+temperature and a lot of friction in the
+
+ align:start position:0%
+temperature and a lot of friction in the
+ 
+
+ align:start position:0%
+temperature and a lot of friction in the
+the mold and is a tag can survive that
+
+ align:start position:0%
+the mold and is a tag can survive that
+ 
+
+ align:start position:0%
+the mold and is a tag can survive that
+and can we locate the tag at the right
+
+ align:start position:0%
+and can we locate the tag at the right
+ 
+
+ align:start position:0%
+and can we locate the tag at the right
+place and it happened and you know it it
+
+ align:start position:0%
+place and it happened and you know it it
+ 
+
+ align:start position:0%
+place and it happened and you know it it
+was easier than we expected they were
+
+ align:start position:0%
+was easier than we expected they were
+ 
+
+ align:start position:0%
+was easier than we expected they were
+very tough and what is interesting is
+
+ align:start position:0%
+very tough and what is interesting is
+ 
+
+ align:start position:0%
+very tough and what is interesting is
+that I I can cut pretty much the price
+
+ align:start position:0%
+that I I can cut pretty much the price
+ 
+
+ align:start position:0%
+that I I can cut pretty much the price
+of that by uh skipping few steps so I
+
+ align:start position:0%
+of that by uh skipping few steps so I
+ 
+
+ align:start position:0%
+of that by uh skipping few steps so I
+don't need a fancy RFID tag in this
+
+ align:start position:0%
+don't need a fancy RFID tag in this
+ 
+
+ align:start position:0%
+don't need a fancy RFID tag in this
+thing you know I don't need very much in
+
+ align:start position:0%
+thing you know I don't need very much in
+ 
+
+ align:start position:0%
+thing you know I don't need very much in
+fact you know uh we're going to see
+
+ align:start position:0%
+fact you know uh we're going to see
+ 
+
+ align:start position:0%
+fact you know uh we're going to see
+later I only need the chips once in a
+
+ align:start position:0%
+later I only need the chips once in a
+ 
+
+ align:start position:0%
+later I only need the chips once in a
+while so the price of the old process is
+
+ align:start position:0%
+while so the price of the old process is
+ 
+
+ align:start position:0%
+while so the price of the old process is
+made and this thing doesn't require any
+
+ align:start position:0%
+made and this thing doesn't require any
+ 
+
+ align:start position:0%
+made and this thing doesn't require any
+new equipment for the injection molding
+
+ align:start position:0%
+new equipment for the injection molding
+ 
+
+ align:start position:0%
+new equipment for the injection molding
+company any company can do that. So what
+
+ align:start position:0%
+company any company can do that. So what
+ 
+
+ align:start position:0%
+company any company can do that. So what
+we did also is we started to embed on
+
+ align:start position:0%
+we did also is we started to embed on
+ 
+
+ align:start position:0%
+we did also is we started to embed on
+smaller container. It was more
+
+ align:start position:0%
+smaller container. It was more
+ 
+
+ align:start position:0%
+smaller container. It was more
+challenging because the thickness of the
+
+ align:start position:0%
+challenging because the thickness of the
+ 
+
+ align:start position:0%
+challenging because the thickness of the
+uh the chip is what is limit the the
+
+ align:start position:0%
+uh the chip is what is limit the the
+ 
+
+ align:start position:0%
+uh the chip is what is limit the the
+thickness of my wall but you can always
+
+ align:start position:0%
+thickness of my wall but you can always
+ 
+
+ align:start position:0%
+thickness of my wall but you can always
+find a place to put it. So as I said we
+
+ align:start position:0%
+find a place to put it. So as I said we
+ 
+
+ align:start position:0%
+find a place to put it. So as I said we
+don't need these fancy label we need a
+
+ align:start position:0%
+don't need these fancy label we need a
+ 
+
+ align:start position:0%
+don't need these fancy label we need a
+chip and that's it and everybody can do
+
+ align:start position:0%
+chip and that's it and everybody can do
+ 
+
+ align:start position:0%
+chip and that's it and everybody can do
+it. So that's pretty cheap at what
+
+ align:start position:0%
+it. So that's pretty cheap at what
+ 
+
+ align:start position:0%
+it. So that's pretty cheap at what
+point. Okay. So um injection bolding
+
+ align:start position:0%
+point. Okay. So um injection bolding
+ 
+
+ align:start position:0%
+point. Okay. So um injection bolding
+company can run a batch of regular
+
+ align:start position:0%
+company can run a batch of regular
+ 
+
+ align:start position:0%
+company can run a batch of regular
+container and just switch in a matter of
+
+ align:start position:0%
+container and just switch in a matter of
+ 
+
+ align:start position:0%
+container and just switch in a matter of
+few seconds to uh with one with embedded
+
+ align:start position:0%
+few seconds to uh with one with embedded
+ 
+
+ align:start position:0%
+few seconds to uh with one with embedded
+RFID tag and this is what we are doing
+
+ align:start position:0%
+RFID tag and this is what we are doing
+ 
+
+ align:start position:0%
+RFID tag and this is what we are doing
+right now. Of course you know
+
+ align:start position:0%
+right now. Of course you know
+ 
+
+ align:start position:0%
+right now. Of course you know
+everybody's like oh item level Jeep it's
+
+ align:start position:0%
+everybody's like oh item level Jeep it's
+ 
+
+ align:start position:0%
+everybody's like oh item level Jeep it's
+way too ahead you know but it just
+
+ align:start position:0%
+way too ahead you know but it just
+ 
+
+ align:start position:0%
+way too ahead you know but it just
+proved that you know I can take RFID tag
+
+ align:start position:0%
+proved that you know I can take RFID tag
+ 
+
+ align:start position:0%
+proved that you know I can take RFID tag
+container and put that in this container
+
+ align:start position:0%
+container and put that in this container
+ 
+
+ align:start position:0%
+container and put that in this container
+and drive the price to very very cheap
+
+ align:start position:0%
+and drive the price to very very cheap
+ 
+
+ align:start position:0%
+and drive the price to very very cheap
+to the price almost of the chips only.
+
+ align:start position:0%
+to the price almost of the chips only.
+ 
+
+ align:start position:0%
+to the price almost of the chips only.
+So that's very interesting on that. Well
+
+ align:start position:0%
+So that's very interesting on that. Well
+ 
+
+ align:start position:0%
+So that's very interesting on that. Well
+and also we started to uh do uh with
+
+ align:start position:0%
+and also we started to uh do uh with
+ 
+
+ align:start position:0%
+and also we started to uh do uh with
+project with different nature of product
+
+ align:start position:0%
+project with different nature of product
+ 
+
+ align:start position:0%
+project with different nature of product
+and of course you know because of the
+
+ align:start position:0%
+and of course you know because of the
+ 
+
+ align:start position:0%
+and of course you know because of the
+water and what we said uh one of the big
+
+ align:start position:0%
+water and what we said uh one of the big
+ 
+
+ align:start position:0%
+water and what we said uh one of the big
+issues that if I have my tag and with
+
+ align:start position:0%
+issues that if I have my tag and with
+ 
+
+ align:start position:0%
+issues that if I have my tag and with
+water I cannot read it. So we sometime
+
+ align:start position:0%
+water I cannot read it. So we sometime
+ 
+
+ align:start position:0%
+water I cannot read it. So we sometime
+we have to redesign the package not very
+
+ align:start position:0%
+we have to redesign the package not very
+ 
+
+ align:start position:0%
+we have to redesign the package not very
+much but slight change that I can
+
+ align:start position:0%
+much but slight change that I can
+ 
+
+ align:start position:0%
+much but slight change that I can
+position my RFID tag to a location that
+
+ align:start position:0%
+position my RFID tag to a location that
+ 
+
+ align:start position:0%
+position my RFID tag to a location that
+it will not interfere with the been
+
+ align:start position:0%
+it will not interfere with the been
+ 
+
+ align:start position:0%
+it will not interfere with the been
+interfere by the the food that I put
+
+ align:start position:0%
+interfere by the the food that I put
+ 
+
+ align:start position:0%
+interfere by the the food that I put
+inside. So we were able to pinpoint
+
+ align:start position:0%
+inside. So we were able to pinpoint
+ 
+
+ align:start position:0%
+inside. So we were able to pinpoint
+location and redesign slightly some of
+
+ align:start position:0%
+location and redesign slightly some of
+ 
+
+ align:start position:0%
+location and redesign slightly some of
+these container and and get these good
+
+ align:start position:0%
+these container and and get these good
+ 
+
+ align:start position:0%
+these container and and get these good
+read. In fact, and I'm going to tell you
+
+ align:start position:0%
+read. In fact, and I'm going to tell you
+ 
+
+ align:start position:0%
+read. In fact, and I'm going to tell you
+something interesting. We did a thousand
+
+ align:start position:0%
+something interesting. We did a thousand
+ 
+
+ align:start position:0%
+something interesting. We did a thousand
+uh container with uh tags embedded and
+
+ align:start position:0%
+uh container with uh tags embedded and
+ 
+
+ align:start position:0%
+uh container with uh tags embedded and
+only one of them fail. All of them were
+
+ align:start position:0%
+only one of them fail. All of them were
+ 
+
+ align:start position:0%
+only one of them fail. All of them were
+good. So that was pretty interesting on
+
+ align:start position:0%
+good. So that was pretty interesting on
+ 
+
+ align:start position:0%
+good. So that was pretty interesting on
+that. What we are doing also in 2000
+
+ align:start position:0%
+that. What we are doing also in 2000
+ 
+
+ align:start position:0%
+that. What we are doing also in 2000
+right now is that we are looking for
+
+ align:start position:0%
+right now is that we are looking for
+ 
+
+ align:start position:0%
+right now is that we are looking for
+smaller antenna design. We don't some of
+
+ align:start position:0%
+smaller antenna design. We don't some of
+ 
+
+ align:start position:0%
+smaller antenna design. We don't some of
+them we just want to reach six to 12
+
+ align:start position:0%
+them we just want to reach six to 12
+ 
+
+ align:start position:0%
+them we just want to reach six to 12
+inches. So, we're going to need some
+
+ align:start position:0%
+inches. So, we're going to need some
+ 
+
+ align:start position:0%
+inches. So, we're going to need some
+help on the design, antenna design on
+
+ align:start position:0%
+help on the design, antenna design on
+ 
+
+ align:start position:0%
+help on the design, antenna design on
+this thing. So, I'm just uh asking you
+
+ align:start position:0%
+this thing. So, I'm just uh asking you
+ 
+
+ align:start position:0%
+this thing. So, I'm just uh asking you
+everybody, you know, help. Okay. On the
+
+ align:start position:0%
+everybody, you know, help. Okay. On the
+ 
+
+ align:start position:0%
+everybody, you know, help. Okay. On the
+firm industry, well, this is something
+
+ align:start position:0%
+firm industry, well, this is something
+ 
+
+ align:start position:0%
+firm industry, well, this is something
+interesting because um your container if
+
+ align:start position:0%
+interesting because um your container if
+ 
+
+ align:start position:0%
+interesting because um your container if
+you put pills in it and you want to
+
+ align:start position:0%
+you put pills in it and you want to
+ 
+
+ align:start position:0%
+you put pills in it and you want to
+follow that, I can remove a label. Okay?
+
+ align:start position:0%
+follow that, I can remove a label. Okay?
+ 
+
+ align:start position:0%
+follow that, I can remove a label. Okay?
+But if it's inside the container, I
+
+ align:start position:0%
+But if it's inside the container, I
+ 
+
+ align:start position:0%
+But if it's inside the container, I
+cannot remove the label. It's inside the
+
+ align:start position:0%
+cannot remove the label. It's inside the
+ 
+
+ align:start position:0%
+cannot remove the label. It's inside the
+container. I can stack up with the tons
+
+ align:start position:0%
+container. I can stack up with the tons
+ 
+
+ align:start position:0%
+container. I can stack up with the tons
+of label. Well, it's still part of the
+
+ align:start position:0%
+of label. Well, it's still part of the
+ 
+
+ align:start position:0%
+of label. Well, it's still part of the
+container. And we did that and so of the
+
+ align:start position:0%
+container. And we did that and so of the
+ 
+
+ align:start position:0%
+container. And we did that and so of the
+thing is that prescription drug using
+
+ align:start position:0%
+thing is that prescription drug using
+ 
+
+ align:start position:0%
+thing is that prescription drug using
+blow mold and count container uh has
+
+ align:start position:0%
+blow mold and count container uh has
+ 
+
+ align:start position:0%
+blow mold and count container uh has
+been something that we're working in
+
+ align:start position:0%
+been something that we're working in
+ 
+
+ align:start position:0%
+been something that we're working in
+pretty close to the to be successful on
+
+ align:start position:0%
+pretty close to the to be successful on
+ 
+
+ align:start position:0%
+pretty close to the to be successful on
+this one and also we work on the blood
+
+ align:start position:0%
+this one and also we work on the blood
+ 
+
+ align:start position:0%
+this one and also we work on the blood
+product right now and packaging
+
+ align:start position:0%
+product right now and packaging
+ 
+
+ align:start position:0%
+product right now and packaging
+component that you put in the when you
+
+ align:start position:0%
+component that you put in the when you
+ 
+
+ align:start position:0%
+component that you put in the when you
+ship
+
+ align:start position:0%
+ship
+ 
+
+ align:start position:0%
+ship
+perform product on this thing. That was
+
+ align:start position:0%
+perform product on this thing. That was
+ 
+
+ align:start position:0%
+perform product on this thing. That was
+a fast uh presentation but I'm going to
+
+ align:start position:0%
+a fast uh presentation but I'm going to
+ 
+
+ align:start position:0%
+a fast uh presentation but I'm going to
+let you after that just doing that. Hey
+
+ align:start position:0%
+let you after that just doing that. Hey
+ 
+
+ align:start position:0%
+let you after that just doing that. Hey
+we are uh we are there we are working
+
+ align:start position:0%
+we are uh we are there we are working
+ 
+
+ align:start position:0%
+we are uh we are there we are working
+very much but we need some collaboration
+
+ align:start position:0%
+very much but we need some collaboration
+ 
+
+ align:start position:0%
+very much but we need some collaboration
+also. So, thank you very much.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Was it fast?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Thank you. I'm going to Well, I
+
+ align:start position:0%
+Okay. Thank you. I'm going to Well, I
+ 
+
+ align:start position:0%
+Okay. Thank you. I'm going to Well, I
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+Well,
+
+ align:start position:0%
+Well,
+ 
+
+ align:start position:0%
+Well,
+we'll do the Laurel Hardy thing.
+
+ align:start position:0%
+we'll do the Laurel Hardy thing.
+ 
+
+ align:start position:0%
+we'll do the Laurel Hardy thing.
+John Pierre and I were talking. We're
+
+ align:start position:0%
+John Pierre and I were talking. We're
+ 
+
+ align:start position:0%
+John Pierre and I were talking. We're
+going to have a race. See who could do
+
+ align:start position:0%
+going to have a race. See who could do
+ 
+
+ align:start position:0%
+going to have a race. See who could do
+their presentation the fastest. So, I'm
+
+ align:start position:0%
+their presentation the fastest. So, I'm
+ 
+
+ align:start position:0%
+their presentation the fastest. So, I'm
+going to win on this one. But, all
+
+ align:start position:0%
+going to win on this one. But, all
+ 
+
+ align:start position:0%
+going to win on this one. But, all
+right. I'm first going to tell you guys
+
+ align:start position:0%
+right. I'm first going to tell you guys
+ 
+
+ align:start position:0%
+right. I'm first going to tell you guys
+who we are and why you should care.
+
+ align:start position:0%
+who we are and why you should care.
+ 
+
+ align:start position:0%
+who we are and why you should care.
+Then, I'm going to tell you about what
+
+ align:start position:0%
+Then, I'm going to tell you about what
+ 
+
+ align:start position:0%
+Then, I'm going to tell you about what
+we're looking for out there as far as
+
+ align:start position:0%
+we're looking for out there as far as
+ 
+
+ align:start position:0%
+we're looking for out there as far as
+technology and why we want that. So,
+
+ align:start position:0%
+technology and why we want that. So,
+ 
+
+ align:start position:0%
+technology and why we want that. So,
+we'll flip through. Um, we're once I
+
+ align:start position:0%
+we'll flip through. Um, we're once I
+ 
+
+ align:start position:0%
+we'll flip through. Um, we're once I
+figure out how to work this Midwest
+
+ align:start position:0%
+figure out how to work this Midwest
+ 
+
+ align:start position:0%
+figure out how to work this Midwest
+Feco. We're into consumer packaging. Um,
+
+ align:start position:0%
+Feco. We're into consumer packaging. Um,
+ 
+
+ align:start position:0%
+Feco. We're into consumer packaging. Um,
+we're into three principal areas. And if
+
+ align:start position:0%
+we're into three principal areas. And if
+ 
+
+ align:start position:0%
+we're into three principal areas. And if
+you look at these three principal areas
+
+ align:start position:0%
+you look at these three principal areas
+ 
+
+ align:start position:0%
+you look at these three principal areas
+and you think about RFID and ubiquitous
+
+ align:start position:0%
+and you think about RFID and ubiquitous
+ 
+
+ align:start position:0%
+and you think about RFID and ubiquitous
+tagging, these are are three areas where
+
+ align:start position:0%
+tagging, these are are three areas where
+ 
+
+ align:start position:0%
+tagging, these are are three areas where
+they're prime candidates for RFID. The
+
+ align:start position:0%
+they're prime candidates for RFID. The
+ 
+
+ align:start position:0%
+they're prime candidates for RFID. The
+media and entertainment. Here you have
+
+ align:start position:0%
+media and entertainment. Here you have
+ 
+
+ align:start position:0%
+media and entertainment. Here you have
+these high value items in small
+
+ align:start position:0%
+these high value items in small
+ 
+
+ align:start position:0%
+these high value items in small
+packages. You're ending up with high
+
+ align:start position:0%
+packages. You're ending up with high
+ 
+
+ align:start position:0%
+packages. You're ending up with high
+shrinkage. you have the um the area
+
+ align:start position:0%
+shrinkage. you have the um the area
+ 
+
+ align:start position:0%
+shrinkage. you have the um the area
+where an out of stock is a big issue
+
+ align:start position:0%
+where an out of stock is a big issue
+ 
+
+ align:start position:0%
+where an out of stock is a big issue
+because if somebody walks in there and
+
+ align:start position:0%
+because if somebody walks in there and
+ 
+
+ align:start position:0%
+because if somebody walks in there and
+they don't find the title they want,
+
+ align:start position:0%
+they don't find the title they want,
+ 
+
+ align:start position:0%
+they don't find the title they want,
+they're not going to buy some other
+
+ align:start position:0%
+they're not going to buy some other
+ 
+
+ align:start position:0%
+they're not going to buy some other
+title. They're going to go to some other
+
+ align:start position:0%
+title. They're going to go to some other
+ 
+
+ align:start position:0%
+title. They're going to go to some other
+store with all the money in their pocket
+
+ align:start position:0%
+store with all the money in their pocket
+ 
+
+ align:start position:0%
+store with all the money in their pocket
+and they're going to buy everything else
+
+ align:start position:0%
+and they're going to buy everything else
+ 
+
+ align:start position:0%
+and they're going to buy everything else
+they needed at that other store. Also,
+
+ align:start position:0%
+they needed at that other store. Also,
+ 
+
+ align:start position:0%
+they needed at that other store. Also,
+we're into the consumer products. We um
+
+ align:start position:0%
+we're into the consumer products. We um
+ 
+
+ align:start position:0%
+we're into the consumer products. We um
+heard about Simply uh white earlier on
+
+ align:start position:0%
+heard about Simply uh white earlier on
+ 
+
+ align:start position:0%
+heard about Simply uh white earlier on
+here. That's uh another you know
+
+ align:start position:0%
+here. That's uh another you know
+ 
+
+ align:start position:0%
+here. That's uh another you know
+interesting thing for tracking and out
+
+ align:start position:0%
+interesting thing for tracking and out
+ 
+
+ align:start position:0%
+interesting thing for tracking and out
+of stocks. And then we have the healthc
+
+ align:start position:0%
+of stocks. And then we have the healthc
+ 
+
+ align:start position:0%
+of stocks. And then we have the healthc
+care industry where you have the the
+
+ align:start position:0%
+care industry where you have the the
+ 
+
+ align:start position:0%
+care industry where you have the the
+huge issue of counterfeits. The FDA's um
+
+ align:start position:0%
+huge issue of counterfeits. The FDA's um
+ 
+
+ align:start position:0%
+huge issue of counterfeits. The FDA's um
+edict that has come down that basically
+
+ align:start position:0%
+edict that has come down that basically
+ 
+
+ align:start position:0%
+edict that has come down that basically
+strongly suggests uh RFID in the um in
+
+ align:start position:0%
+strongly suggests uh RFID in the um in
+ 
+
+ align:start position:0%
+strongly suggests uh RFID in the um in
+the packaging there.
+
+ align:start position:0%
+the packaging there.
+ 
+
+ align:start position:0%
+the packaging there.
+The other um area that you're probably
+
+ align:start position:0%
+The other um area that you're probably
+ 
+
+ align:start position:0%
+The other um area that you're probably
+more familiar with, ME West, or at least
+
+ align:start position:0%
+more familiar with, ME West, or at least
+ 
+
+ align:start position:0%
+more familiar with, ME West, or at least
+the MEED name, is in the consumer and
+
+ align:start position:0%
+the MEED name, is in the consumer and
+ 
+
+ align:start position:0%
+the MEED name, is in the consumer and
+office products area. And we're into
+
+ align:start position:0%
+office products area. And we're into
+ 
+
+ align:start position:0%
+office products area. And we're into
+RFID in that area thanks to Walmart. Uh
+
+ align:start position:0%
+RFID in that area thanks to Walmart. Uh
+ 
+
+ align:start position:0%
+RFID in that area thanks to Walmart. Uh
+we're at the uh pallet level in shipping
+
+ align:start position:0%
+we're at the uh pallet level in shipping
+ 
+
+ align:start position:0%
+we're at the uh pallet level in shipping
+our our goods on that uh in that product
+
+ align:start position:0%
+our our goods on that uh in that product
+ 
+
+ align:start position:0%
+our our goods on that uh in that product
+line. Now our um we've been in looking
+
+ align:start position:0%
+line. Now our um we've been in looking
+ 
+
+ align:start position:0%
+line. Now our um we've been in looking
+at RFID participating in this area for
+
+ align:start position:0%
+at RFID participating in this area for
+ 
+
+ align:start position:0%
+at RFID participating in this area for
+um about six years now. We were um one
+
+ align:start position:0%
+um about six years now. We were um one
+ 
+
+ align:start position:0%
+um about six years now. We were um one
+of the early members of the AutoID
+
+ align:start position:0%
+of the early members of the AutoID
+ 
+
+ align:start position:0%
+of the early members of the AutoID
+center up here at MIT. We also founded a
+
+ align:start position:0%
+center up here at MIT. We also founded a
+ 
+
+ align:start position:0%
+center up here at MIT. We also founded a
+um a group in our company called
+
+ align:start position:0%
+um a group in our company called
+ 
+
+ align:start position:0%
+um a group in our company called
+Intelligence Systems and I'm not sure if
+
+ align:start position:0%
+Intelligence Systems and I'm not sure if
+ 
+
+ align:start position:0%
+Intelligence Systems and I'm not sure if
+any of you had um read about them. They
+
+ align:start position:0%
+any of you had um read about them. They
+ 
+
+ align:start position:0%
+any of you had um read about them. They
+were in the news for uh quite some time
+
+ align:start position:0%
+were in the news for uh quite some time
+ 
+
+ align:start position:0%
+were in the news for uh quite some time
+now here. Basically that uh that group
+
+ align:start position:0%
+now here. Basically that uh that group
+ 
+
+ align:start position:0%
+now here. Basically that uh that group
+came up with a um an intelligent shelf
+
+ align:start position:0%
+came up with a um an intelligent shelf
+ 
+
+ align:start position:0%
+came up with a um an intelligent shelf
+system where uh unlike some of the other
+
+ align:start position:0%
+system where uh unlike some of the other
+ 
+
+ align:start position:0%
+system where uh unlike some of the other
+ones that were out there where people
+
+ align:start position:0%
+ones that were out there where people
+ 
+
+ align:start position:0%
+ones that were out there where people
+had sent multiple wires to each of the
+
+ align:start position:0%
+had sent multiple wires to each of the
+ 
+
+ align:start position:0%
+had sent multiple wires to each of the
+antennas trying to reduce the cost, we
+
+ align:start position:0%
+antennas trying to reduce the cost, we
+ 
+
+ align:start position:0%
+antennas trying to reduce the cost, we
+found a way of taking one reader and
+
+ align:start position:0%
+found a way of taking one reader and
+ 
+
+ align:start position:0%
+found a way of taking one reader and
+basically using that reader to read a
+
+ align:start position:0%
+basically using that reader to read a
+ 
+
+ align:start position:0%
+basically using that reader to read a
+100 antennas and having a single wire
+
+ align:start position:0%
+100 antennas and having a single wire
+ 
+
+ align:start position:0%
+100 antennas and having a single wire
+running down the line of a 100 antennas
+
+ align:start position:0%
+running down the line of a 100 antennas
+ 
+
+ align:start position:0%
+running down the line of a 100 antennas
+and uh bringing
+
+ align:start position:0%
+and uh bringing
+ 
+
+ align:start position:0%
+and uh bringing
+it back. Um, this as you can think about
+
+ align:start position:0%
+it back. Um, this as you can think about
+ 
+
+ align:start position:0%
+it back. Um, this as you can think about
+this is a really unique way of reducing
+
+ align:start position:0%
+this is a really unique way of reducing
+ 
+
+ align:start position:0%
+this is a really unique way of reducing
+the cost of the infrastructure by
+
+ align:start position:0%
+the cost of the infrastructure by
+ 
+
+ align:start position:0%
+the cost of the infrastructure by
+several orders of magnitude. And that
+
+ align:start position:0%
+several orders of magnitude. And that
+ 
+
+ align:start position:0%
+several orders of magnitude. And that
+was essentially our goal here as we got
+
+ align:start position:0%
+was essentially our goal here as we got
+ 
+
+ align:start position:0%
+was essentially our goal here as we got
+into this. We had we had looked at the
+
+ align:start position:0%
+into this. We had we had looked at the
+ 
+
+ align:start position:0%
+into this. We had we had looked at the
+field and realized that for tags to be
+
+ align:start position:0%
+field and realized that for tags to be
+ 
+
+ align:start position:0%
+field and realized that for tags to be
+ubiquitous, the tags were going to have
+
+ align:start position:0%
+ubiquitous, the tags were going to have
+ 
+
+ align:start position:0%
+ubiquitous, the tags were going to have
+to be commodity type items. And there
+
+ align:start position:0%
+to be commodity type items. And there
+ 
+
+ align:start position:0%
+to be commodity type items. And there
+were plenty of players out there like
+
+ align:start position:0%
+were plenty of players out there like
+ 
+
+ align:start position:0%
+were plenty of players out there like
+Alien. We were in discussions with them
+
+ align:start position:0%
+Alien. We were in discussions with them
+ 
+
+ align:start position:0%
+Alien. We were in discussions with them
+who were doing a very good job of that.
+
+ align:start position:0%
+who were doing a very good job of that.
+ 
+
+ align:start position:0%
+who were doing a very good job of that.
+But people weren't really addressing the
+
+ align:start position:0%
+But people weren't really addressing the
+ 
+
+ align:start position:0%
+But people weren't really addressing the
+infrastructure successfully. So um now
+
+ align:start position:0%
+infrastructure successfully. So um now
+ 
+
+ align:start position:0%
+infrastructure successfully. So um now
+this last year we uh sold the
+
+ align:start position:0%
+this last year we uh sold the
+ 
+
+ align:start position:0%
+this last year we uh sold the
+intelligence systems or most of the
+
+ align:start position:0%
+intelligence systems or most of the
+ 
+
+ align:start position:0%
+intelligence systems or most of the
+intelligence systems to an outside group
+
+ align:start position:0%
+intelligence systems to an outside group
+ 
+
+ align:start position:0%
+intelligence systems to an outside group
+so that they could um really concentrate
+
+ align:start position:0%
+so that they could um really concentrate
+ 
+
+ align:start position:0%
+so that they could um really concentrate
+on it uh full force. We still have a
+
+ align:start position:0%
+on it uh full force. We still have a
+ 
+
+ align:start position:0%
+on it uh full force. We still have a
+residual interest and are following it
+
+ align:start position:0%
+residual interest and are following it
+ 
+
+ align:start position:0%
+residual interest and are following it
+because we do think that that it's very
+
+ align:start position:0%
+because we do think that that it's very
+ 
+
+ align:start position:0%
+because we do think that that it's very
+important for success in this uh in this
+
+ align:start position:0%
+important for success in this uh in this
+ 
+
+ align:start position:0%
+important for success in this uh in this
+field for that company to be successful.
+
+ align:start position:0%
+field for that company to be successful.
+ 
+
+ align:start position:0%
+field for that company to be successful.
+our capabilities at this point in time.
+
+ align:start position:0%
+our capabilities at this point in time.
+ 
+
+ align:start position:0%
+our capabilities at this point in time.
+We do have production capabilities for
+
+ align:start position:0%
+We do have production capabilities for
+ 
+
+ align:start position:0%
+We do have production capabilities for
+uh doing um item level coding of tags of
+
+ align:start position:0%
+uh doing um item level coding of tags of
+ 
+
+ align:start position:0%
+uh doing um item level coding of tags of
+uh testing those tags in line and uh
+
+ align:start position:0%
+uh testing those tags in line and uh
+ 
+
+ align:start position:0%
+uh testing those tags in line and uh
+tagging boxes. Uh we have not seen the
+
+ align:start position:0%
+tagging boxes. Uh we have not seen the
+ 
+
+ align:start position:0%
+tagging boxes. Uh we have not seen the
+the pull from the customer base, but
+
+ align:start position:0%
+the pull from the customer base, but
+ 
+
+ align:start position:0%
+the pull from the customer base, but
+we're positioned and we're trying to um
+
+ align:start position:0%
+we're positioned and we're trying to um
+ 
+
+ align:start position:0%
+we're positioned and we're trying to um
+improve that position daily so that
+
+ align:start position:0%
+improve that position daily so that
+ 
+
+ align:start position:0%
+improve that position daily so that
+we're ready when the the market pull
+
+ align:start position:0%
+we're ready when the the market pull
+ 
+
+ align:start position:0%
+we're ready when the the market pull
+comes along. Uh that's basically our
+
+ align:start position:0%
+comes along. Uh that's basically our
+ 
+
+ align:start position:0%
+comes along. Uh that's basically our
+ability to tag is anything we can put an
+
+ align:start position:0%
+ability to tag is anything we can put an
+ 
+
+ align:start position:0%
+ability to tag is anything we can put an
+EAS tag on today we can uh switch over
+
+ align:start position:0%
+EAS tag on today we can uh switch over
+ 
+
+ align:start position:0%
+EAS tag on today we can uh switch over
+and do an RFID tag. Now, uh what we need
+
+ align:start position:0%
+and do an RFID tag. Now, uh what we need
+ 
+
+ align:start position:0%
+and do an RFID tag. Now, uh what we need
+as far as technology, we're looking for
+
+ align:start position:0%
+as far as technology, we're looking for
+ 
+
+ align:start position:0%
+as far as technology, we're looking for
+the things that are going to make our
+
+ align:start position:0%
+the things that are going to make our
+ 
+
+ align:start position:0%
+the things that are going to make our
+our customers successful and um probably
+
+ align:start position:0%
+our customers successful and um probably
+ 
+
+ align:start position:0%
+our customers successful and um probably
+the primary thing there would be item
+
+ align:start position:0%
+the primary thing there would be item
+ 
+
+ align:start position:0%
+the primary thing there would be item
+level tracking at low cost. And we've
+
+ align:start position:0%
+level tracking at low cost. And we've
+ 
+
+ align:start position:0%
+level tracking at low cost. And we've
+been hearing uh discussions uh yesterday
+
+ align:start position:0%
+been hearing uh discussions uh yesterday
+ 
+
+ align:start position:0%
+been hearing uh discussions uh yesterday
+and today on some of the things that
+
+ align:start position:0%
+and today on some of the things that
+ 
+
+ align:start position:0%
+and today on some of the things that
+would um go into reducing the cost of
+
+ align:start position:0%
+would um go into reducing the cost of
+ 
+
+ align:start position:0%
+would um go into reducing the cost of
+the tag and such. But uh also want to
+
+ align:start position:0%
+the tag and such. But uh also want to
+ 
+
+ align:start position:0%
+the tag and such. But uh also want to
+remind everyone that this doesn't
+
+ align:start position:0%
+remind everyone that this doesn't
+ 
+
+ align:start position:0%
+remind everyone that this doesn't
+necessarily mean 96bit RFID. There's a
+
+ align:start position:0%
+necessarily mean 96bit RFID. There's a
+ 
+
+ align:start position:0%
+necessarily mean 96bit RFID. There's a
+lot of attention out there to chipless
+
+ align:start position:0%
+lot of attention out there to chipless
+ 
+
+ align:start position:0%
+lot of attention out there to chipless
+tags to um organic RFID. Uh and these
+
+ align:start position:0%
+tags to um organic RFID. Uh and these
+ 
+
+ align:start position:0%
+tags to um organic RFID. Uh and these
+are areas that we're we're exploring and
+
+ align:start position:0%
+are areas that we're we're exploring and
+ 
+
+ align:start position:0%
+are areas that we're we're exploring and
+and discussions with various companies
+
+ align:start position:0%
+and discussions with various companies
+ 
+
+ align:start position:0%
+and discussions with various companies
+on. But uh if you are going forward
+
+ align:start position:0%
+on. But uh if you are going forward
+ 
+
+ align:start position:0%
+on. But uh if you are going forward
+looking into the field, one of the
+
+ align:start position:0%
+looking into the field, one of the
+ 
+
+ align:start position:0%
+looking into the field, one of the
+things that I want to caution everyone
+
+ align:start position:0%
+things that I want to caution everyone
+ 
+
+ align:start position:0%
+things that I want to caution everyone
+on is that uh these things cannot sit
+
+ align:start position:0%
+on is that uh these things cannot sit
+ 
+
+ align:start position:0%
+on is that uh these things cannot sit
+there and expect to come in and require
+
+ align:start position:0%
+there and expect to come in and require
+ 
+
+ align:start position:0%
+there and expect to come in and require
+a whole new infrastructure through the
+
+ align:start position:0%
+a whole new infrastructure through the
+ 
+
+ align:start position:0%
+a whole new infrastructure through the
+whole supply chain. I mean the the 96
+
+ align:start position:0%
+whole supply chain. I mean the the 96
+ 
+
+ align:start position:0%
+whole supply chain. I mean the the 96
+bit is a juggernaut going down that road
+
+ align:start position:0%
+bit is a juggernaut going down that road
+ 
+
+ align:start position:0%
+bit is a juggernaut going down that road
+there. we're going to see those that
+
+ align:start position:0%
+there. we're going to see those that
+ 
+
+ align:start position:0%
+there. we're going to see those that
+infrastructure go in there. If the or
+
+ align:start position:0%
+infrastructure go in there. If the or
+ 
+
+ align:start position:0%
+infrastructure go in there. If the or
+the organic RFID can only read at 125 um
+
+ align:start position:0%
+the organic RFID can only read at 125 um
+ 
+
+ align:start position:0%
+the organic RFID can only read at 125 um
+K megahertz or hertz, then um and you
+
+ align:start position:0%
+K megahertz or hertz, then um and you
+ 
+
+ align:start position:0%
+K megahertz or hertz, then um and you
+don't have an agile reader that can read
+
+ align:start position:0%
+don't have an agile reader that can read
+ 
+
+ align:start position:0%
+don't have an agile reader that can read
+at both points, you're going to have a
+
+ align:start position:0%
+at both points, you're going to have a
+ 
+
+ align:start position:0%
+at both points, you're going to have a
+hard time selling those that organic
+
+ align:start position:0%
+hard time selling those that organic
+ 
+
+ align:start position:0%
+hard time selling those that organic
+RFID in there. The same with the uh the
+
+ align:start position:0%
+RFID in there. The same with the uh the
+ 
+
+ align:start position:0%
+RFID in there. The same with the uh the
+chipless tags. Uh if you've looked at
+
+ align:start position:0%
+chipless tags. Uh if you've looked at
+ 
+
+ align:start position:0%
+chipless tags. Uh if you've looked at
+the chip various chipless technologies,
+
+ align:start position:0%
+the chip various chipless technologies,
+ 
+
+ align:start position:0%
+the chip various chipless technologies,
+it's very interesting. That's very
+
+ align:start position:0%
+it's very interesting. That's very
+ 
+
+ align:start position:0%
+it's very interesting. That's very
+appealing to us because our desire is to
+
+ align:start position:0%
+appealing to us because our desire is to
+ 
+
+ align:start position:0%
+appealing to us because our desire is to
+be able to just print the RFID on there.
+
+ align:start position:0%
+be able to just print the RFID on there.
+ 
+
+ align:start position:0%
+be able to just print the RFID on there.
+That's the way we're going to reduce it
+
+ align:start position:0%
+That's the way we're going to reduce it
+ 
+
+ align:start position:0%
+That's the way we're going to reduce it
+down the cost down for our customers.
+
+ align:start position:0%
+down the cost down for our customers.
+ 
+
+ align:start position:0%
+down the cost down for our customers.
+But uh again, what are you looking at
+
+ align:start position:0%
+But uh again, what are you looking at
+ 
+
+ align:start position:0%
+But uh again, what are you looking at
+when you get a chipless tag? You're
+
+ align:start position:0%
+when you get a chipless tag? You're
+ 
+
+ align:start position:0%
+when you get a chipless tag? You're
+probably not looking at 96 bits and
+
+ align:start position:0%
+probably not looking at 96 bits and
+ 
+
+ align:start position:0%
+probably not looking at 96 bits and
+you're definitely not looking at the
+
+ align:start position:0%
+you're definitely not looking at the
+ 
+
+ align:start position:0%
+you're definitely not looking at the
+same reader that you're using for using
+
+ align:start position:0%
+same reader that you're using for using
+ 
+
+ align:start position:0%
+same reader that you're using for using
+uh for reading your silicon based tag.
+
+ align:start position:0%
+uh for reading your silicon based tag.
+ 
+
+ align:start position:0%
+uh for reading your silicon based tag.
+Now there are value propositions out
+
+ align:start position:0%
+Now there are value propositions out
+ 
+
+ align:start position:0%
+Now there are value propositions out
+there that would would draw towards
+
+ align:start position:0%
+there that would would draw towards
+ 
+
+ align:start position:0%
+there that would would draw towards
+things these uh technologies. If you can
+
+ align:start position:0%
+things these uh technologies. If you can
+ 
+
+ align:start position:0%
+things these uh technologies. If you can
+if you can identify the niche market
+
+ align:start position:0%
+if you can identify the niche market
+ 
+
+ align:start position:0%
+if you can identify the niche market
+that you're going after um we have
+
+ align:start position:0%
+that you're going after um we have
+ 
+
+ align:start position:0%
+that you're going after um we have
+something to talk about.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. The other thing is uh we have
+
+ align:start position:0%
+All right. The other thing is uh we have
+ 
+
+ align:start position:0%
+All right. The other thing is uh we have
+to look at the total cost of the tag
+
+ align:start position:0%
+to look at the total cost of the tag
+ 
+
+ align:start position:0%
+to look at the total cost of the tag
+over the lifetime. It's not just the
+
+ align:start position:0%
+over the lifetime. It's not just the
+ 
+
+ align:start position:0%
+over the lifetime. It's not just the
+cost of the chip and I think we've heard
+
+ align:start position:0%
+cost of the chip and I think we've heard
+ 
+
+ align:start position:0%
+cost of the chip and I think we've heard
+that before. What's the cost of how how
+
+ align:start position:0%
+that before. What's the cost of how how
+ 
+
+ align:start position:0%
+that before. What's the cost of how how
+much does it cost to actually put it on
+
+ align:start position:0%
+much does it cost to actually put it on
+ 
+
+ align:start position:0%
+much does it cost to actually put it on
+the package? What's the antenna cost?
+
+ align:start position:0%
+the package? What's the antenna cost?
+ 
+
+ align:start position:0%
+the package? What's the antenna cost?
+What's the crossover uh cost there? Um
+
+ align:start position:0%
+What's the crossover uh cost there? Um
+ 
+
+ align:start position:0%
+What's the crossover uh cost there? Um
+what's going to happen um as far as
+
+ align:start position:0%
+what's going to happen um as far as
+ 
+
+ align:start position:0%
+what's going to happen um as far as
+testing? How do you handle the rejects?
+
+ align:start position:0%
+testing? How do you handle the rejects?
+ 
+
+ align:start position:0%
+testing? How do you handle the rejects?
+Uh when you get failed reads in the
+
+ align:start position:0%
+Uh when you get failed reads in the
+ 
+
+ align:start position:0%
+Uh when you get failed reads in the
+supply chain, how are you going to
+
+ align:start position:0%
+supply chain, how are you going to
+ 
+
+ align:start position:0%
+supply chain, how are you going to
+handle those? Those represent costs. Uh
+
+ align:start position:0%
+handle those? Those represent costs. Uh
+ 
+
+ align:start position:0%
+handle those? Those represent costs. Uh
+and then finally, and we've heard that
+
+ align:start position:0%
+and then finally, and we've heard that
+ 
+
+ align:start position:0%
+and then finally, and we've heard that
+alerted to before, uh this disposal
+
+ align:start position:0%
+alerted to before, uh this disposal
+ 
+
+ align:start position:0%
+alerted to before, uh this disposal
+issue is going to come and catch up to
+
+ align:start position:0%
+issue is going to come and catch up to
+ 
+
+ align:start position:0%
+issue is going to come and catch up to
+us at some point in time here. What is
+
+ align:start position:0%
+us at some point in time here. What is
+ 
+
+ align:start position:0%
+us at some point in time here. What is
+in your antenna? Um,
+
+ align:start position:0%
+in your antenna? Um,
+ 
+
+ align:start position:0%
+in your antenna? Um,
+look at Europe. Look at there's places
+
+ align:start position:0%
+look at Europe. Look at there's places
+ 
+
+ align:start position:0%
+look at Europe. Look at there's places
+in New England that are starting to look
+
+ align:start position:0%
+in New England that are starting to look
+ 
+
+ align:start position:0%
+in New England that are starting to look
+at the uh metals in the in the
+
+ align:start position:0%
+at the uh metals in the in the
+ 
+
+ align:start position:0%
+at the uh metals in the in the
+landfills.
+
+ align:start position:0%
+landfills.
+ 
+
+ align:start position:0%
+landfills.
+And then the last area is one that's
+
+ align:start position:0%
+And then the last area is one that's
+ 
+
+ align:start position:0%
+And then the last area is one that's
+gotten a lot of attention here and I'm
+
+ align:start position:0%
+gotten a lot of attention here and I'm
+ 
+
+ align:start position:0%
+gotten a lot of attention here and I'm
+glad to see it. And that's in the uh the
+
+ align:start position:0%
+glad to see it. And that's in the uh the
+ 
+
+ align:start position:0%
+glad to see it. And that's in the uh the
+whole area of track and trace. Track and
+
+ align:start position:0%
+whole area of track and trace. Track and
+ 
+
+ align:start position:0%
+whole area of track and trace. Track and
+trace is a very very um valuable um
+
+ align:start position:0%
+trace is a very very um valuable um
+ 
+
+ align:start position:0%
+trace is a very very um valuable um
+thing to look at especially when we're
+
+ align:start position:0%
+thing to look at especially when we're
+ 
+
+ align:start position:0%
+thing to look at especially when we're
+looking at the uh pharmaceutical
+
+ align:start position:0%
+looking at the uh pharmaceutical
+ 
+
+ align:start position:0%
+looking at the uh pharmaceutical
+industries. But what's what's going to
+
+ align:start position:0%
+industries. But what's what's going to
+ 
+
+ align:start position:0%
+industries. But what's what's going to
+be out there in the data data management
+
+ align:start position:0%
+be out there in the data data management
+ 
+
+ align:start position:0%
+be out there in the data data management
+infrastructure? Uh who's going to come
+
+ align:start position:0%
+infrastructure? Uh who's going to come
+ 
+
+ align:start position:0%
+infrastructure? Uh who's going to come
+up with that? How are we going to handle
+
+ align:start position:0%
+up with that? How are we going to handle
+ 
+
+ align:start position:0%
+up with that? How are we going to handle
+this data? Uh pass it from um various
+
+ align:start position:0%
+this data? Uh pass it from um various
+ 
+
+ align:start position:0%
+this data? Uh pass it from um various
+entities in the supply chain.
+
+ align:start position:0%
+entities in the supply chain.
+ 
+
+ align:start position:0%
+entities in the supply chain.
+That's it. I beat John Pierre.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess we're going to run this
+
+ align:start position:0%
+I guess we're going to run this
+ 
+
+ align:start position:0%
+I guess we're going to run this
+ourselves. So, if you have any
+
+ align:start position:0%
+ourselves. So, if you have any
+ 
+
+ align:start position:0%
+ourselves. So, if you have any
+questions, come on down. We Sorry, we
+
+ align:start position:0%
+questions, come on down. We Sorry, we
+ 
+
+ align:start position:0%
+questions, come on down. We Sorry, we
+felt like Miles Davis there with our
+
+ align:start position:0%
+felt like Miles Davis there with our
+ 
+
+ align:start position:0%
+felt like Miles Davis there with our
+back to the audience, but uh we wanted
+
+ align:start position:0%
+back to the audience, but uh we wanted
+ 
+
+ align:start position:0%
+back to the audience, but uh we wanted
+to learn something new at the same time
+
+ align:start position:0%
+to learn something new at the same time
+ 
+
+ align:start position:0%
+to learn something new at the same time
+and it's hard to do it that way. So,
+
+ align:start position:0%
+and it's hard to do it that way. So,
+ 
+
+ align:start position:0%
+and it's hard to do it that way. So,
+excuse us. It hurts. Yeah. Okay. Just
+
+ align:start position:0%
+excuse us. It hurts. Yeah. Okay. Just
+ 
+
+ align:start position:0%
+excuse us. It hurts. Yeah. Okay. Just
+one question again for what changes are
+
+ align:start position:0%
+one question again for what changes are
+ 
+
+ align:start position:0%
+one question again for what changes are
+you seeing to the metrics
+
+ align:start position:0%
+you seeing to the metrics
+ 
+
+ align:start position:0%
+you seeing to the metrics
+as you experiment with this technology
+
+ align:start position:0%
+as you experiment with this technology
+ 
+
+ align:start position:0%
+as you experiment with this technology
+in your packaging design? What do you
+
+ align:start position:0%
+in your packaging design? What do you
+ 
+
+ align:start position:0%
+in your packaging design? What do you
+measure measure performances that may be
+
+ align:start position:0%
+measure measure performances that may be
+ 
+
+ align:start position:0%
+measure measure performances that may be
+changing units that you measure may be
+
+ align:start position:0%
+changing units that you measure may be
+ 
+
+ align:start position:0%
+changing units that you measure may be
+changing? What have you experienced with
+
+ align:start position:0%
+changing? What have you experienced with
+ 
+
+ align:start position:0%
+changing? What have you experienced with
+all your testing or what you might see
+
+ align:start position:0%
+all your testing or what you might see
+ 
+
+ align:start position:0%
+all your testing or what you might see
+in the future?
+
+ align:start position:0%
+in the future?
+ 
+
+ align:start position:0%
+in the future?
+Um, I'm not sure this is the same
+
+ align:start position:0%
+Um, I'm not sure this is the same
+ 
+
+ align:start position:0%
+Um, I'm not sure this is the same
+answer, but uh I don't see much new at
+
+ align:start position:0%
+answer, but uh I don't see much new at
+ 
+
+ align:start position:0%
+answer, but uh I don't see much new at
+all, honestly. Um,
+
+ align:start position:0%
+all, honestly. Um,
+ 
+
+ align:start position:0%
+all, honestly. Um,
+units are the same that I used in my
+
+ align:start position:0%
+units are the same that I used in my
+ 
+
+ align:start position:0%
+units are the same that I used in my
+graduate work uh studying random
+
+ align:start position:0%
+graduate work uh studying random
+ 
+
+ align:start position:0%
+graduate work uh studying random
+vibration as an energy source. Um,
+
+ align:start position:0%
+vibration as an energy source. Um,
+ 
+
+ align:start position:0%
+vibration as an energy source. Um,
+RF is a great area and I'm I'm not here
+
+ align:start position:0%
+RF is a great area and I'm I'm not here
+ 
+
+ align:start position:0%
+RF is a great area and I'm I'm not here
+to uh disavow it in any way,
+
+ align:start position:0%
+to uh disavow it in any way,
+ 
+
+ align:start position:0%
+to uh disavow it in any way,
+but it's a technology. It's not a
+
+ align:start position:0%
+but it's a technology. It's not a
+ 
+
+ align:start position:0%
+but it's a technology. It's not a
+panacea. Uh I, you know, with all due
+
+ align:start position:0%
+panacea. Uh I, you know, with all due
+ 
+
+ align:start position:0%
+panacea. Uh I, you know, with all due
+deference to uh previous speakers, I
+
+ align:start position:0%
+deference to uh previous speakers, I
+ 
+
+ align:start position:0%
+deference to uh previous speakers, I
+don't think it's worthy of a discipline.
+
+ align:start position:0%
+don't think it's worthy of a discipline.
+ 
+
+ align:start position:0%
+don't think it's worthy of a discipline.
+Uh I did, uh get caught short here
+
+ align:start position:0%
+Uh I did, uh get caught short here
+ 
+
+ align:start position:0%
+Uh I did, uh get caught short here
+briefly by asking the uh gentleman from
+
+ align:start position:0%
+briefly by asking the uh gentleman from
+ 
+
+ align:start position:0%
+briefly by asking the uh gentleman from
+IBM if they still had barcode
+
+ align:start position:0%
+IBM if they still had barcode
+ 
+
+ align:start position:0%
+IBM if they still had barcode
+specialists on staff and he said, "Yes,
+
+ align:start position:0%
+specialists on staff and he said, "Yes,
+ 
+
+ align:start position:0%
+specialists on staff and he said, "Yes,
+we do." Although he might not have been
+
+ align:start position:0%
+we do." Although he might not have been
+ 
+
+ align:start position:0%
+we do." Although he might not have been
+sure what they did, but I know in
+
+ align:start position:0%
+sure what they did, but I know in
+ 
+
+ align:start position:0%
+sure what they did, but I know in
+Michigan we've gotten rid of barcode
+
+ align:start position:0%
+Michigan we've gotten rid of barcode
+ 
+
+ align:start position:0%
+Michigan we've gotten rid of barcode
+specialists. And you know uh one of my
+
+ align:start position:0%
+specialists. And you know uh one of my
+ 
+
+ align:start position:0%
+specialists. And you know uh one of my
+grad students is working with uh uh
+
+ align:start position:0%
+grad students is working with uh uh
+ 
+
+ align:start position:0%
+grad students is working with uh uh
+Simon Langford at Walmart running their
+
+ align:start position:0%
+Simon Langford at Walmart running their
+ 
+
+ align:start position:0%
+Simon Langford at Walmart running their
+lab. And uh when he was hired uh the
+
+ align:start position:0%
+lab. And uh when he was hired uh the
+ 
+
+ align:start position:0%
+lab. And uh when he was hired uh the
+comment Simon made was that we hope in 3
+
+ align:start position:0%
+comment Simon made was that we hope in 3
+ 
+
+ align:start position:0%
+comment Simon made was that we hope in 3
+years you don't have a job because the
+
+ align:start position:0%
+years you don't have a job because the
+ 
+
+ align:start position:0%
+years you don't have a job because the
+intent was to make this so broadly based
+
+ align:start position:0%
+intent was to make this so broadly based
+ 
+
+ align:start position:0%
+intent was to make this so broadly based
+across the company that it becomes as
+
+ align:start position:0%
+across the company that it becomes as
+ 
+
+ align:start position:0%
+across the company that it becomes as
+common as UPC and you don't need
+
+ align:start position:0%
+common as UPC and you don't need
+ 
+
+ align:start position:0%
+common as UPC and you don't need
+anything special. It's just an adaptive
+
+ align:start position:0%
+anything special. It's just an adaptive
+ 
+
+ align:start position:0%
+anything special. It's just an adaptive
+technology that helps.
+
+ align:start position:0%
+technology that helps.
+ 
+
+ align:start position:0%
+technology that helps.
+Thank you.
+
+ align:start position:0%
+Thank you.
+ 
+
+ align:start position:0%
+Thank you.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Hi uh Patrick Mone from Georgetown
+
+ align:start position:0%
+Hi uh Patrick Mone from Georgetown
+ 
+
+ align:start position:0%
+Hi uh Patrick Mone from Georgetown
+University and want to thank you guys
+
+ align:start position:0%
+University and want to thank you guys
+ 
+
+ align:start position:0%
+University and want to thank you guys
+first for this presentation. I think it
+
+ align:start position:0%
+first for this presentation. I think it
+ 
+
+ align:start position:0%
+first for this presentation. I think it
+outlined a lot of the shortcomings in
+
+ align:start position:0%
+outlined a lot of the shortcomings in
+ 
+
+ align:start position:0%
+outlined a lot of the shortcomings in
+this technology. I sat in on uh
+
+ align:start position:0%
+this technology. I sat in on uh
+ 
+
+ align:start position:0%
+this technology. I sat in on uh
+opportunities opportunities. Yes,
+
+ align:start position:0%
+opportunities opportunities. Yes,
+ 
+
+ align:start position:0%
+opportunities opportunities. Yes,
+absolutely. And I've sat in on on
+
+ align:start position:0%
+absolutely. And I've sat in on on
+ 
+
+ align:start position:0%
+absolutely. And I've sat in on on
+several government meetings on uh
+
+ align:start position:0%
+several government meetings on uh
+ 
+
+ align:start position:0%
+several government meetings on uh
+launching uh RFID for identity
+
+ align:start position:0%
+launching uh RFID for identity
+ 
+
+ align:start position:0%
+launching uh RFID for identity
+management. And the shortcomings that
+
+ align:start position:0%
+management. And the shortcomings that
+ 
+
+ align:start position:0%
+management. And the shortcomings that
+I'm seeing time and time again are the
+
+ align:start position:0%
+I'm seeing time and time again are the
+ 
+
+ align:start position:0%
+I'm seeing time and time again are the
+lack of understanding from I don't want
+
+ align:start position:0%
+lack of understanding from I don't want
+ 
+
+ align:start position:0%
+lack of understanding from I don't want
+to name names but these consulting
+
+ align:start position:0%
+to name names but these consulting
+ 
+
+ align:start position:0%
+to name names but these consulting
+companies that kind of promise RF
+
+ align:start position:0%
+companies that kind of promise RF
+ 
+
+ align:start position:0%
+companies that kind of promise RF
+fighting in a box and passive allowing
+
+ align:start position:0%
+fighting in a box and passive allowing
+ 
+
+ align:start position:0%
+fighting in a box and passive allowing
+you to drive through at 55 miles an hour
+
+ align:start position:0%
+you to drive through at 55 miles an hour
+ 
+
+ align:start position:0%
+you to drive through at 55 miles an hour
+and things like that and it's just not
+
+ align:start position:0%
+and things like that and it's just not
+ 
+
+ align:start position:0%
+and things like that and it's just not
+being answered. So I think research like
+
+ align:start position:0%
+being answered. So I think research like
+ 
+
+ align:start position:0%
+being answered. So I think research like
+this would be very advantageous uh to be
+
+ align:start position:0%
+this would be very advantageous uh to be
+ 
+
+ align:start position:0%
+this would be very advantageous uh to be
+out there in the public for the
+
+ align:start position:0%
+out there in the public for the
+ 
+
+ align:start position:0%
+out there in the public for the
+industry. My question is on
+
+ align:start position:0%
+industry. My question is on
+ 
+
+ align:start position:0%
+industry. My question is on
+pharmaceutical. Uh the FDA has asked to
+
+ align:start position:0%
+pharmaceutical. Uh the FDA has asked to
+ 
+
+ align:start position:0%
+pharmaceutical. Uh the FDA has asked to
+secure around counterfeiting that
+
+ align:start position:0%
+secure around counterfeiting that
+ 
+
+ align:start position:0%
+secure around counterfeiting that
+there's overt, covert, and forensic. And
+
+ align:start position:0%
+there's overt, covert, and forensic. And
+ 
+
+ align:start position:0%
+there's overt, covert, and forensic. And
+in the launches that are out there now,
+
+ align:start position:0%
+in the launches that are out there now,
+ 
+
+ align:start position:0%
+in the launches that are out there now,
+you're seeing overt and covert. You're
+
+ align:start position:0%
+you're seeing overt and covert. You're
+ 
+
+ align:start position:0%
+you're seeing overt and covert. You're
+not seeing forensic. And I'm and I'm
+
+ align:start position:0%
+not seeing forensic. And I'm and I'm
+ 
+
+ align:start position:0%
+not seeing forensic. And I'm and I'm
+curious if anyone can uh answer that.
+
+ align:start position:0%
+curious if anyone can uh answer that.
+ 
+
+ align:start position:0%
+curious if anyone can uh answer that.
+And then my last is a potential wag of
+
+ align:start position:0%
+And then my last is a potential wag of
+ 
+
+ align:start position:0%
+And then my last is a potential wag of
+the finger. I hope none of you are
+
+ align:start position:0%
+the finger. I hope none of you are
+ 
+
+ align:start position:0%
+the finger. I hope none of you are
+responsible for those damn huge plastic
+
+ align:start position:0%
+responsible for those damn huge plastic
+ 
+
+ align:start position:0%
+responsible for those damn huge plastic
+containers for my small microchip that
+
+ align:start position:0%
+containers for my small microchip that
+ 
+
+ align:start position:0%
+containers for my small microchip that
+are frustratingly impossible to open. So
+
+ align:start position:0%
+are frustratingly impossible to open. So
+ 
+
+ align:start position:0%
+are frustratingly impossible to open. So
+that uh thanks again.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't have a really good answer I
+
+ align:start position:0%
+I don't have a really good answer I
+ 
+
+ align:start position:0%
+I don't have a really good answer I
+guess on the uh uh forensic. Um, we have
+
+ align:start position:0%
+guess on the uh uh forensic. Um, we have
+ 
+
+ align:start position:0%
+guess on the uh uh forensic. Um, we have
+done work with both overt and covert and
+
+ align:start position:0%
+done work with both overt and covert and
+ 
+
+ align:start position:0%
+done work with both overt and covert and
+uh there are much better experts than uh
+
+ align:start position:0%
+uh there are much better experts than uh
+ 
+
+ align:start position:0%
+uh there are much better experts than uh
+at least the three of us on that. It's
+
+ align:start position:0%
+at least the three of us on that. It's
+ 
+
+ align:start position:0%
+at least the three of us on that. It's
+kind of interesting if you guys, you
+
+ align:start position:0%
+kind of interesting if you guys, you
+ 
+
+ align:start position:0%
+kind of interesting if you guys, you
+know, pull out a $100 bill and just pass
+
+ align:start position:0%
+know, pull out a $100 bill and just pass
+ 
+
+ align:start position:0%
+know, pull out a $100 bill and just pass
+them forward. I'll show you how they
+
+ align:start position:0%
+them forward. I'll show you how they
+ 
+
+ align:start position:0%
+them forward. I'll show you how they
+have all of these security or
+
+ align:start position:0%
+have all of these security or
+ 
+
+ align:start position:0%
+have all of these security or
+anti-counterfeiting
+
+ align:start position:0%
+anti-counterfeiting
+ 
+
+ align:start position:0%
+anti-counterfeiting
+uh techniques involved. And for those of
+
+ align:start position:0%
+uh techniques involved. And for those of
+ 
+
+ align:start position:0%
+uh techniques involved. And for those of
+you visiting from different countries,
+
+ align:start position:0%
+you visiting from different countries,
+ 
+
+ align:start position:0%
+you visiting from different countries,
+our our currency now has 20 uh overt uh
+
+ align:start position:0%
+our our currency now has 20 uh overt uh
+ 
+
+ align:start position:0%
+our our currency now has 20 uh overt uh
+or covert anti-counterfeiting
+
+ align:start position:0%
+or covert anti-counterfeiting
+ 
+
+ align:start position:0%
+or covert anti-counterfeiting
+uh detection devices built into it and
+
+ align:start position:0%
+uh detection devices built into it and
+ 
+
+ align:start position:0%
+uh detection devices built into it and
+at least 10 others that they won't talk
+
+ align:start position:0%
+at least 10 others that they won't talk
+ 
+
+ align:start position:0%
+at least 10 others that they won't talk
+about. Uh but there's roughly 30
+
+ align:start position:0%
+about. Uh but there's roughly 30
+ 
+
+ align:start position:0%
+about. Uh but there's roughly 30
+anti-counterfeiting features in in an
+
+ align:start position:0%
+anti-counterfeiting features in in an
+ 
+
+ align:start position:0%
+anti-counterfeiting features in in an
+individual bill. And those are the
+
+ align:start position:0%
+individual bill. And those are the
+ 
+
+ align:start position:0%
+individual bill. And those are the
+people you really need to uh bring into
+
+ align:start position:0%
+people you really need to uh bring into
+ 
+
+ align:start position:0%
+people you really need to uh bring into
+this discussion because I'm certainly
+
+ align:start position:0%
+this discussion because I'm certainly
+ 
+
+ align:start position:0%
+this discussion because I'm certainly
+not a specialist in that. All right.
+
+ align:start position:0%
+not a specialist in that. All right.
+ 
+
+ align:start position:0%
+not a specialist in that. All right.
+to answer that. Like to answer that, but
+
+ align:start position:0%
+to answer that. Like to answer that, but
+ 
+
+ align:start position:0%
+to answer that. Like to answer that, but
+we're on it. Uh we can't tell you what
+
+ align:start position:0%
+we're on it. Uh we can't tell you what
+ 
+
+ align:start position:0%
+we're on it. Uh we can't tell you what
+we're doing, but uh we're on it. We have
+
+ align:start position:0%
+we're doing, but uh we're on it. We have
+ 
+
+ align:start position:0%
+we're doing, but uh we're on it. We have
+those three areas covered. Excellent.
+
+ align:start position:0%
+those three areas covered. Excellent.
+ 
+
+ align:start position:0%
+those three areas covered. Excellent.
+Very quick. You know, the uh also on the
+
+ align:start position:0%
+Very quick. You know, the uh also on the
+ 
+
+ align:start position:0%
+Very quick. You know, the uh also on the
+other area that we never discussed is
+
+ align:start position:0%
+other area that we never discussed is
+ 
+
+ align:start position:0%
+other area that we never discussed is
+temporary evidence, you know, and um
+
+ align:start position:0%
+temporary evidence, you know, and um
+ 
+
+ align:start position:0%
+temporary evidence, you know, and um
+have you seen that sometime you have
+
+ align:start position:0%
+have you seen that sometime you have
+ 
+
+ align:start position:0%
+have you seen that sometime you have
+something a plastic it said if it's not
+
+ align:start position:0%
+something a plastic it said if it's not
+ 
+
+ align:start position:0%
+something a plastic it said if it's not
+there don't use it, but if it's not
+
+ align:start position:0%
+there don't use it, but if it's not
+ 
+
+ align:start position:0%
+there don't use it, but if it's not
+there, you cannot read it anymore. Okay.
+
+ align:start position:0%
+there, you cannot read it anymore. Okay.
+ 
+
+ align:start position:0%
+there, you cannot read it anymore. Okay.
+And uh so that we were discussing and
+
+ align:start position:0%
+And uh so that we were discussing and
+ 
+
+ align:start position:0%
+And uh so that we were discussing and
+the best protection for temporary vision
+
+ align:start position:0%
+the best protection for temporary vision
+ 
+
+ align:start position:0%
+the best protection for temporary vision
+is that nobody can see it and this is
+
+ align:start position:0%
+is that nobody can see it and this is
+ 
+
+ align:start position:0%
+is that nobody can see it and this is
+what we're working on.
+
+ align:start position:0%
+what we're working on.
+ 
+
+ align:start position:0%
+what we're working on.
+Thank you. Good presentation. Thank you.
+
+ align:start position:0%
+Thank you. Good presentation. Thank you.
+ 
+
+ align:start position:0%
+Thank you. Good presentation. Thank you.
+Yeah, John Hitchford from Mars. My
+
+ align:start position:0%
+Yeah, John Hitchford from Mars. My
+ 
+
+ align:start position:0%
+Yeah, John Hitchford from Mars. My
+question is how is RFID starting to work
+
+ align:start position:0%
+question is how is RFID starting to work
+ 
+
+ align:start position:0%
+question is how is RFID starting to work
+its way into the curriculum particularly
+
+ align:start position:0%
+its way into the curriculum particularly
+ 
+
+ align:start position:0%
+its way into the curriculum particularly
+undergraduate because it's important
+
+ align:start position:0%
+undergraduate because it's important
+ 
+
+ align:start position:0%
+undergraduate because it's important
+that they know and also how are you
+
+ align:start position:0%
+that they know and also how are you
+ 
+
+ align:start position:0%
+that they know and also how are you
+training the guys that aren't in school
+
+ align:start position:0%
+training the guys that aren't in school
+ 
+
+ align:start position:0%
+training the guys that aren't in school
+anymore about the utilization of
+
+ align:start position:0%
+anymore about the utilization of
+ 
+
+ align:start position:0%
+anymore about the utilization of
+technology in a supplier base? I'd be
+
+ align:start position:0%
+technology in a supplier base? I'd be
+ 
+
+ align:start position:0%
+technology in a supplier base? I'd be
+interested in that question.
+
+ align:start position:0%
+interested in that question.
+ 
+
+ align:start position:0%
+interested in that question.
+um from a Michigan State standpoint at
+
+ align:start position:0%
+um from a Michigan State standpoint at
+ 
+
+ align:start position:0%
+um from a Michigan State standpoint at
+least um I started teaching a class on
+
+ align:start position:0%
+least um I started teaching a class on
+ 
+
+ align:start position:0%
+least um I started teaching a class on
+RFID and packaging two years ago and uh
+
+ align:start position:0%
+RFID and packaging two years ago and uh
+ 
+
+ align:start position:0%
+RFID and packaging two years ago and uh
+it's been uh an elective class but I've
+
+ align:start position:0%
+it's been uh an elective class but I've
+ 
+
+ align:start position:0%
+it's been uh an elective class but I've
+had really good uh turnouts not only
+
+ align:start position:0%
+had really good uh turnouts not only
+ 
+
+ align:start position:0%
+had really good uh turnouts not only
+from packaging but uh from uh uh
+
+ align:start position:0%
+from packaging but uh from uh uh
+ 
+
+ align:start position:0%
+from packaging but uh from uh uh
+engineering from uh supply chain
+
+ align:start position:0%
+engineering from uh supply chain
+ 
+
+ align:start position:0%
+engineering from uh supply chain
+management logistics um and because all
+
+ align:start position:0%
+management logistics um and because all
+ 
+
+ align:start position:0%
+management logistics um and because all
+of these cross over these areas and we
+
+ align:start position:0%
+of these cross over these areas and we
+ 
+
+ align:start position:0%
+of these cross over these areas and we
+now have um uh companies coming in to
+
+ align:start position:0%
+now have um uh companies coming in to
+ 
+
+ align:start position:0%
+now have um uh companies coming in to
+hire our undergraduates and even our
+
+ align:start position:0%
+hire our undergraduates and even our
+ 
+
+ align:start position:0%
+hire our undergraduates and even our
+graduate students that will not even
+
+ align:start position:0%
+graduate students that will not even
+ 
+
+ align:start position:0%
+graduate students that will not even
+interview them if they haven't had the
+
+ align:start position:0%
+interview them if they haven't had the
+ 
+
+ align:start position:0%
+interview them if they haven't had the
+class because this is an area that
+
+ align:start position:0%
+class because this is an area that
+ 
+
+ align:start position:0%
+class because this is an area that
+companies are trying to find those
+
+ align:start position:0%
+companies are trying to find those
+ 
+
+ align:start position:0%
+companies are trying to find those
+answers and they're trying to find
+
+ align:start position:0%
+answers and they're trying to find
+ 
+
+ align:start position:0%
+answers and they're trying to find
+people that have hands-on
+
+ align:start position:0%
+people that have hands-on
+ 
+
+ align:start position:0%
+people that have hands-on
+work and and feel so that they come in
+
+ align:start position:0%
+work and and feel so that they come in
+ 
+
+ align:start position:0%
+work and and feel so that they come in
+hitting the ground running uh as opposed
+
+ align:start position:0%
+hitting the ground running uh as opposed
+ 
+
+ align:start position:0%
+hitting the ground running uh as opposed
+to having to be trained. Uh there are
+
+ align:start position:0%
+to having to be trained. Uh there are
+ 
+
+ align:start position:0%
+to having to be trained. Uh there are
+also just like yourself uh conferences
+
+ align:start position:0%
+also just like yourself uh conferences
+ 
+
+ align:start position:0%
+also just like yourself uh conferences
+up the wazoo. Um, you know, JP and I
+
+ align:start position:0%
+up the wazoo. Um, you know, JP and I
+ 
+
+ align:start position:0%
+up the wazoo. Um, you know, JP and I
+have talked uh repeatedly about we could
+
+ align:start position:0%
+have talked uh repeatedly about we could
+ 
+
+ align:start position:0%
+have talked uh repeatedly about we could
+be at a conference every week of the
+
+ align:start position:0%
+be at a conference every week of the
+ 
+
+ align:start position:0%
+be at a conference every week of the
+year and uh if you could get more of
+
+ align:start position:0%
+year and uh if you could get more of
+ 
+
+ align:start position:0%
+year and uh if you could get more of
+them in Hawaii, we might. Um, but uh
+
+ align:start position:0%
+them in Hawaii, we might. Um, but uh
+ 
+
+ align:start position:0%
+them in Hawaii, we might. Um, but uh
+that's really what you're almost limited
+
+ align:start position:0%
+that's really what you're almost limited
+ 
+
+ align:start position:0%
+that's really what you're almost limited
+to. But we are developing an uh online
+
+ align:start position:0%
+to. But we are developing an uh online
+ 
+
+ align:start position:0%
+to. But we are developing an uh online
+uh web-based program for uh uh recent
+
+ align:start position:0%
+uh web-based program for uh uh recent
+ 
+
+ align:start position:0%
+uh web-based program for uh uh recent
+graduates like yourself.
+
+ align:start position:0%
+graduates like yourself.
+ 
+
+ align:start position:0%
+graduates like yourself.
+Yeah. very quick and univers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+almost every courses where you can have
+
+ align:start position:0%
+almost every courses where you can have
+ 
+
+ align:start position:0%
+almost every courses where you can have
+RFID topic in it are is already there.
+
+ align:start position:0%
+RFID topic in it are is already there.
+ 
+
+ align:start position:0%
+RFID topic in it are is already there.
+So we have chapter in transportation
+
+ align:start position:0%
+So we have chapter in transportation
+ 
+
+ align:start position:0%
+So we have chapter in transportation
+distribution food uh packaging we have
+
+ align:start position:0%
+distribution food uh packaging we have
+ 
+
+ align:start position:0%
+distribution food uh packaging we have
+uh consumer product all these packaging
+
+ align:start position:0%
+uh consumer product all these packaging
+ 
+
+ align:start position:0%
+uh consumer product all these packaging
+courses we they all have chapter where
+
+ align:start position:0%
+courses we they all have chapter where
+ 
+
+ align:start position:0%
+courses we they all have chapter where
+it's suitable to to put it inside
+
+ align:start position:0%
+it's suitable to to put it inside
+ 
+
+ align:start position:0%
+it's suitable to to put it inside
+and uh well basically we've been talking
+
+ align:start position:0%
+and uh well basically we've been talking
+ 
+
+ align:start position:0%
+and uh well basically we've been talking
+to our senior management about it for
+
+ align:start position:0%
+to our senior management about it for
+ 
+
+ align:start position:0%
+to our senior management about it for
+probably six years now and um I think
+
+ align:start position:0%
+probably six years now and um I think
+ 
+
+ align:start position:0%
+probably six years now and um I think
+they get it now um we're way past the uh
+
+ align:start position:0%
+they get it now um we're way past the uh
+ 
+
+ align:start position:0%
+they get it now um we're way past the uh
+the early days when people thought RFID
+
+ align:start position:0%
+the early days when people thought RFID
+ 
+
+ align:start position:0%
+the early days when people thought RFID
+meant you'd read them from satellites.
+
+ align:start position:0%
+meant you'd read them from satellites.
+ 
+
+ align:start position:0%
+meant you'd read them from satellites.
+Um, I think if you if you cornered
+
+ align:start position:0%
+Um, I think if you if you cornered
+ 
+
+ align:start position:0%
+Um, I think if you if you cornered
+anyone in our senior management team,
+
+ align:start position:0%
+anyone in our senior management team,
+ 
+
+ align:start position:0%
+anyone in our senior management team,
+you'd have a pretty good conversation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Last question. Hi, my name is James Shed
+
+ align:start position:0%
+Last question. Hi, my name is James Shed
+ 
+
+ align:start position:0%
+Last question. Hi, my name is James Shed
+Dubage from Gillette PNG. Um,
+
+ align:start position:0%
+Dubage from Gillette PNG. Um,
+ 
+
+ align:start position:0%
+Dubage from Gillette PNG. Um,
+as part of EPC Global, there's a strong
+
+ align:start position:0%
+as part of EPC Global, there's a strong
+ 
+
+ align:start position:0%
+as part of EPC Global, there's a strong
+effort to try and standardize on
+
+ align:start position:0%
+effort to try and standardize on
+ 
+
+ align:start position:0%
+effort to try and standardize on
+measures and metrics and like you
+
+ align:start position:0%
+measures and metrics and like you
+ 
+
+ align:start position:0%
+measures and metrics and like you
+mentioned, John Anduro and both Jeff
+
+ align:start position:0%
+mentioned, John Anduro and both Jeff
+ 
+
+ align:start position:0%
+mentioned, John Anduro and both Jeff
+Talazar are co-chairs. I'm on I'm the
+
+ align:start position:0%
+Talazar are co-chairs. I'm on I'm the
+ 
+
+ align:start position:0%
+Talazar are co-chairs. I'm on I'm the
+third co-chair of that group. Uh we'd
+
+ align:start position:0%
+third co-chair of that group. Uh we'd
+ 
+
+ align:start position:0%
+third co-chair of that group. Uh we'd
+like to get more academic involvement
+
+ align:start position:0%
+like to get more academic involvement
+ 
+
+ align:start position:0%
+like to get more academic involvement
+into that group. How do how do we make
+
+ align:start position:0%
+into that group. How do how do we make
+ 
+
+ align:start position:0%
+into that group. How do how do we make
+that happen so that you're not going off
+
+ align:start position:0%
+that happen so that you're not going off
+ 
+
+ align:start position:0%
+that happen so that you're not going off
+and doing these tests that are very
+
+ align:start position:0%
+and doing these tests that are very
+ 
+
+ align:start position:0%
+and doing these tests that are very
+interesting, but if we can try and
+
+ align:start position:0%
+interesting, but if we can try and
+ 
+
+ align:start position:0%
+interesting, but if we can try and
+synergize on those, I'd like to hear
+
+ align:start position:0%
+synergize on those, I'd like to hear
+ 
+
+ align:start position:0%
+synergize on those, I'd like to hear
+your thoughts on that. Great issue. I
+
+ align:start position:0%
+your thoughts on that. Great issue. I
+ 
+
+ align:start position:0%
+your thoughts on that. Great issue. I
+actually had a conversation with uh some
+
+ align:start position:0%
+actually had a conversation with uh some
+ 
+
+ align:start position:0%
+actually had a conversation with uh some
+people from EPC Global yesterday to uh
+
+ align:start position:0%
+people from EPC Global yesterday to uh
+ 
+
+ align:start position:0%
+people from EPC Global yesterday to uh
+try and uh synthesize some of the work
+
+ align:start position:0%
+try and uh synthesize some of the work
+ 
+
+ align:start position:0%
+try and uh synthesize some of the work
+we're doing. I'm a uh uh co-chair
+
+ align:start position:0%
+we're doing. I'm a uh uh co-chair
+ 
+
+ align:start position:0%
+we're doing. I'm a uh uh co-chair
+actually a chair of a new task group
+
+ align:start position:0%
+actually a chair of a new task group
+ 
+
+ align:start position:0%
+actually a chair of a new task group
+within uh ASM the American Society of
+
+ align:start position:0%
+within uh ASM the American Society of
+ 
+
+ align:start position:0%
+within uh ASM the American Society of
+Testing and Materials uh where we are uh
+
+ align:start position:0%
+Testing and Materials uh where we are uh
+ 
+
+ align:start position:0%
+Testing and Materials uh where we are uh
+developing procedures and reporting on
+
+ align:start position:0%
+developing procedures and reporting on
+ 
+
+ align:start position:0%
+developing procedures and reporting on
+how you test case loads, pallet loads,
+
+ align:start position:0%
+how you test case loads, pallet loads,
+ 
+
+ align:start position:0%
+how you test case loads, pallet loads,
+uh military applications, pharmaceutical
+
+ align:start position:0%
+uh military applications, pharmaceutical
+ 
+
+ align:start position:0%
+uh military applications, pharmaceutical
+applications, etc. Um, we want to work
+
+ align:start position:0%
+applications, etc. Um, we want to work
+ 
+
+ align:start position:0%
+applications, etc. Um, we want to work
+in conjunction with you on developing
+
+ align:start position:0%
+in conjunction with you on developing
+ 
+
+ align:start position:0%
+in conjunction with you on developing
+these and and share all the data uh
+
+ align:start position:0%
+these and and share all the data uh
+ 
+
+ align:start position:0%
+these and and share all the data uh
+where we're different from EPC because
+
+ align:start position:0%
+where we're different from EPC because
+ 
+
+ align:start position:0%
+where we're different from EPC because
+that always comes up is that we are uh
+
+ align:start position:0%
+that always comes up is that we are uh
+ 
+
+ align:start position:0%
+that always comes up is that we are uh
+uh reader tag frequency agnostic. We
+
+ align:start position:0%
+uh reader tag frequency agnostic. We
+ 
+
+ align:start position:0%
+uh reader tag frequency agnostic. We
+don't care what you use. Here is a
+
+ align:start position:0%
+don't care what you use. Here is a
+ 
+
+ align:start position:0%
+don't care what you use. Here is a
+standard procedure for measuring
+
+ align:start position:0%
+standard procedure for measuring
+ 
+
+ align:start position:0%
+standard procedure for measuring
+readability
+
+ align:start position:0%
+readability
+ 
+
+ align:start position:0%
+readability
+of a case, readability of an item, read
+
+ align:start position:0%
+of a case, readability of an item, read
+ 
+
+ align:start position:0%
+of a case, readability of an item, read
+distance, read fields, uh, military,
+
+ align:start position:0%
+distance, read fields, uh, military,
+ 
+
+ align:start position:0%
+distance, read fields, uh, military,
+whatever it is. And so if it's if it
+
+ align:start position:0%
+whatever it is. And so if it's if it
+ 
+
+ align:start position:0%
+whatever it is. And so if it's if it
+fits into EPC through 1356, 915, they
+
+ align:start position:0%
+fits into EPC through 1356, 915, they
+ 
+
+ align:start position:0%
+fits into EPC through 1356, 915, they
+might be identical, but if you have a
+
+ align:start position:0%
+might be identical, but if you have a
+ 
+
+ align:start position:0%
+might be identical, but if you have a
+closed loop system and are looking at at
+
+ align:start position:0%
+closed loop system and are looking at at
+ 
+
+ align:start position:0%
+closed loop system and are looking at at
+134 or 2.4, 5.8, 8 uh and even different
+
+ align:start position:0%
+134 or 2.4, 5.8, 8 uh and even different
+ 
+
+ align:start position:0%
+134 or 2.4, 5.8, 8 uh and even different
+frequencies from that. Uh there's so
+
+ align:start position:0%
+frequencies from that. Uh there's so
+ 
+
+ align:start position:0%
+frequencies from that. Uh there's so
+much in military at 433 right now that
+
+ align:start position:0%
+much in military at 433 right now that
+ 
+
+ align:start position:0%
+much in military at 433 right now that
+um we just want to set up what that is
+
+ align:start position:0%
+um we just want to set up what that is
+ 
+
+ align:start position:0%
+um we just want to set up what that is
+and if anybody contacts me I'll be happy
+
+ align:start position:0%
+and if anybody contacts me I'll be happy
+ 
+
+ align:start position:0%
+and if anybody contacts me I'll be happy
+to respond.
+
+ align:start position:0%
+to respond.
+ 
+
+ align:start position:0%
+to respond.
+Maybe I can say something about it um
+
+ align:start position:0%
+Maybe I can say something about it um
+ 
+
+ align:start position:0%
+Maybe I can say something about it um
+about APC and u the standardization.
+
+ align:start position:0%
+about APC and u the standardization.
+ 
+
+ align:start position:0%
+about APC and u the standardization.
+I would say that in our lab you know we
+
+ align:start position:0%
+I would say that in our lab you know we
+ 
+
+ align:start position:0%
+I would say that in our lab you know we
+touch many many area some of them will
+
+ align:start position:0%
+touch many many area some of them will
+ 
+
+ align:start position:0%
+touch many many area some of them will
+fall under APC what you're looking for
+
+ align:start position:0%
+fall under APC what you're looking for
+ 
+
+ align:start position:0%
+fall under APC what you're looking for
+and uh that's going to be good but we
+
+ align:start position:0%
+and uh that's going to be good but we
+ 
+
+ align:start position:0%
+and uh that's going to be good but we
+still going to keep doing other area
+
+ align:start position:0%
+still going to keep doing other area
+ 
+
+ align:start position:0%
+still going to keep doing other area
+because the request of other application
+
+ align:start position:0%
+because the request of other application
+ 
+
+ align:start position:0%
+because the request of other application
+is pretty big and so if some of the
+
+ align:start position:0%
+is pretty big and so if some of the
+ 
+
+ align:start position:0%
+is pretty big and so if some of the
+thing that we do will fall under APC
+
+ align:start position:0%
+thing that we do will fall under APC
+ 
+
+ align:start position:0%
+thing that we do will fall under APC
+what you're looking for this is great
+
+ align:start position:0%
+what you're looking for this is great
+ 
+
+ align:start position:0%
+what you're looking for this is great
+okay but we still going to have a lot of
+
+ align:start position:0%
+okay but we still going to have a lot of
+ 
+
+ align:start position:0%
+okay but we still going to have a lot of
+thing that we want to keep uh running
+
+ align:start position:0%
+thing that we want to keep uh running
+ 
+
+ align:start position:0%
+thing that we want to keep uh running
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+thank you if we could on that note thank
\ No newline at end of file
diff --git a/wwQu2_u8jeo.txt b/wwQu2_u8jeo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cd95571054adcba46db267f2f49fd9171a05a5c5
--- /dev/null
+++ b/wwQu2_u8jeo.txt
@@ -0,0 +1,243 @@
+align:start position:0%
+ 
+so during the semester we have a few
+
+ align:start position:0%
+so during the semester we have a few
+ 
+
+ align:start position:0%
+so during the semester we have a few
+recitation instructors they help with
+
+ align:start position:0%
+recitation instructors they help with
+ 
+
+ align:start position:0%
+recitation instructors they help with
+the students during the recitation
+
+ align:start position:0%
+the students during the recitation
+ 
+
+ align:start position:0%
+the students during the recitation
+section so during those sections your
+
+ align:start position:0%
+section so during those sections your
+ 
+
+ align:start position:0%
+section so during those sections your
+the the instructor will solve a similar
+
+ align:start position:0%
+the the instructor will solve a similar
+ 
+
+ align:start position:0%
+the the instructor will solve a similar
+problem like what is actually covered
+
+ align:start position:0%
+problem like what is actually covered
+ 
+
+ align:start position:0%
+problem like what is actually covered
+during the same during the lecture and
+
+ align:start position:0%
+during the same during the lecture and
+ 
+
+ align:start position:0%
+during the same during the lecture and
+that give the students another chance to
+
+ align:start position:0%
+that give the students another chance to
+ 
+
+ align:start position:0%
+that give the students another chance to
+look at more example and to get for
+
+ align:start position:0%
+look at more example and to get for
+ 
+
+ align:start position:0%
+look at more example and to get for
+media will get used to the calculation
+
+ align:start position:0%
+media will get used to the calculation
+ 
+
+ align:start position:0%
+media will get used to the calculation
+which we carry how for the first time
+
+ align:start position:0%
+which we carry how for the first time
+ 
+
+ align:start position:0%
+which we carry how for the first time
+during the the lecture so also the
+
+ align:start position:0%
+during the the lecture so also the
+ 
+
+ align:start position:0%
+during the the lecture so also the
+recitation section and during the
+
+ align:start position:0%
+recitation section and during the
+ 
+
+ align:start position:0%
+recitation section and during the
+recitation section the instructors help
+
+ align:start position:0%
+recitation section the instructors help
+ 
+
+ align:start position:0%
+recitation section the instructors help
+the students they can actually ask more
+
+ align:start position:0%
+the students they can actually ask more
+ 
+
+ align:start position:0%
+the students they can actually ask more
+questions during the recitation sections
+
+ align:start position:0%
+questions during the recitation sections
+ 
+
+ align:start position:0%
+questions during the recitation sections
+including the questions they have the
+
+ align:start position:0%
+including the questions they have the
+ 
+
+ align:start position:0%
+including the questions they have the
+pset or any additional questions they
+
+ align:start position:0%
+pset or any additional questions they
+ 
+
+ align:start position:0%
+pset or any additional questions they
+they thought about after the lecture ok
+
+ align:start position:0%
+they thought about after the lecture ok
+ 
+
+ align:start position:0%
+they thought about after the lecture ok
+so that they get some chance another
+
+ align:start position:0%
+so that they get some chance another
+ 
+
+ align:start position:0%
+so that they get some chance another
+chance to clear some of the concept
+
+ align:start position:0%
+chance to clear some of the concept
+ 
+
+ align:start position:0%
+chance to clear some of the concept
+which they don't really understand
+
+ align:start position:0%
+which they don't really understand
+ 
+
+ align:start position:0%
+which they don't really understand
+during the during the lecture so we did
+
+ align:start position:0%
+during the during the lecture so we did
+ 
+
+ align:start position:0%
+during the during the lecture so we did
+not record the recitation sections
+
+ align:start position:0%
+not record the recitation sections
+ 
+
+ align:start position:0%
+not record the recitation sections
+during the fall semester in 2016 on the
+
+ align:start position:0%
+during the fall semester in 2016 on the
+ 
+
+ align:start position:0%
+during the fall semester in 2016 on the
+other hand we included problem-solving
+
+ align:start position:0%
+other hand we included problem-solving
+ 
+
+ align:start position:0%
+other hand we included problem-solving
+videos from Professor with Busha which
+
+ align:start position:0%
+videos from Professor with Busha which
+ 
+
+ align:start position:0%
+videos from Professor with Busha which
+is similar to what we do during the
+
+ align:start position:0%
+is similar to what we do during the
+ 
+
+ align:start position:0%
+is similar to what we do during the
+recitation sections from previous years
+
+ align:start position:0%
+recitation sections from previous years
+ 
+
+ align:start position:0%
+recitation sections from previous years
+to to go with the lecture videos done
+
+ align:start position:0%
+to to go with the lecture videos done
+ 
+
+ align:start position:0%
+to to go with the lecture videos done
+during the semester
\ No newline at end of file
diff --git a/xE9IGS-_6zo.txt b/xE9IGS-_6zo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..48f65850b6a3314ae29b4b20be0d78bb8e24fa91
--- /dev/null
+++ b/xE9IGS-_6zo.txt
@@ -0,0 +1,7771 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright let's get started so today we're
+
+ align:start position:0%
+alright let's get started so today we're
+ 
+
+ align:start position:0%
+alright let's get started so today we're
+going to talk about boundary value
+
+ align:start position:0%
+going to talk about boundary value
+ 
+
+ align:start position:0%
+going to talk about boundary value
+problems but I'm going to try to start
+
+ align:start position:0%
+problems but I'm going to try to start
+ 
+
+ align:start position:0%
+problems but I'm going to try to start
+back with a motivating example so like
+
+ align:start position:0%
+back with a motivating example so like
+ 
+
+ align:start position:0%
+back with a motivating example so like
+unfortunately like most technologies the
+
+ align:start position:0%
+unfortunately like most technologies the
+ 
+
+ align:start position:0%
+unfortunately like most technologies the
+biggest driver for differential equation
+
+ align:start position:0%
+biggest driver for differential equation
+ 
+
+ align:start position:0%
+biggest driver for differential equation
+solutions was from military technology
+
+ align:start position:0%
+solutions was from military technology
+ 
+
+ align:start position:0%
+solutions was from military technology
+and the military problem I'll tell you
+
+ align:start position:0%
+and the military problem I'll tell you
+ 
+
+ align:start position:0%
+and the military problem I'll tell you
+in a second let me the first will remind
+
+ align:start position:0%
+in a second let me the first will remind
+ 
+
+ align:start position:0%
+in a second let me the first will remind
+you so we have OD e IV P's and they are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so that's that the OD IV piece we
+
+ align:start position:0%
+right so that's that the OD IV piece we
+ 
+
+ align:start position:0%
+right so that's that the OD IV piece we
+have in differential equations and we
+
+ align:start position:0%
+have in differential equations and we
+ 
+
+ align:start position:0%
+have in differential equations and we
+have n initial conditions all right and
+
+ align:start position:0%
+have n initial conditions all right and
+ 
+
+ align:start position:0%
+have n initial conditions all right and
+you guys are really good at these now a
+
+ align:start position:0%
+you guys are really good at these now a
+ 
+
+ align:start position:0%
+you guys are really good at these now a
+lot of practice but you can have
+
+ align:start position:0%
+lot of practice but you can have
+ 
+
+ align:start position:0%
+lot of practice but you can have
+problems where some of the conditions
+
+ align:start position:0%
+problems where some of the conditions
+ 
+
+ align:start position:0%
+problems where some of the conditions
+are not specified at the at T naught are
+
+ align:start position:0%
+are not specified at the at T naught are
+ 
+
+ align:start position:0%
+are not specified at the at T naught are
+specified somewhere else so if all of
+
+ align:start position:0%
+specified somewhere else so if all of
+ 
+
+ align:start position:0%
+specified somewhere else so if all of
+them are specified T naught we call it
+
+ align:start position:0%
+them are specified T naught we call it
+ 
+
+ align:start position:0%
+them are specified T naught we call it
+an IVP and it we call it a be VP is if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the conditions are like this and not all
+
+ align:start position:0%
+the conditions are like this and not all
+ 
+
+ align:start position:0%
+the conditions are like this and not all
+the TMS are the same if all the teams
+
+ align:start position:0%
+the TMS are the same if all the teams
+ 
+
+ align:start position:0%
+the TMS are the same if all the teams
+are the same would call it t naught and
+
+ align:start position:0%
+are the same would call it t naught and
+ 
+
+ align:start position:0%
+are the same would call it t naught and
+we're back to IVP so IV feels like a
+
+ align:start position:0%
+we're back to IVP so IV feels like a
+ 
+
+ align:start position:0%
+we're back to IVP so IV feels like a
+special case of the OD BDD problem okay
+
+ align:start position:0%
+special case of the OD BDD problem okay
+ 
+
+ align:start position:0%
+special case of the OD BDD problem okay
+and here and write them as if
+
+ align:start position:0%
+and here and write them as if
+ 
+
+ align:start position:0%
+and here and write them as if
+everything's explicit so we know an
+
+ align:start position:0%
+everything's explicit so we know an
+ 
+
+ align:start position:0%
+everything's explicit so we know an
+explicit equation for dy DT we have an
+
+ align:start position:0%
+explicit equation for dy DT we have an
+ 
+
+ align:start position:0%
+explicit equation for dy DT we have an
+explicit equation for the boundary
+
+ align:start position:0%
+explicit equation for the boundary
+ 
+
+ align:start position:0%
+explicit equation for the boundary
+conditions in fact often we actually
+
+ align:start position:0%
+conditions in fact often we actually
+ 
+
+ align:start position:0%
+conditions in fact often we actually
+only have implicit equations so I'll
+
+ align:start position:0%
+only have implicit equations so I'll
+ 
+
+ align:start position:0%
+only have implicit equations so I'll
+show you an example in a minute
+
+ align:start position:0%
+show you an example in a minute
+ 
+
+ align:start position:0%
+show you an example in a minute
+all right that's it we still need to
+
+ align:start position:0%
+all right that's it we still need to
+ 
+
+ align:start position:0%
+all right that's it we still need to
+have n n equations well guess I can do
+
+ align:start position:0%
+have n n equations well guess I can do
+ 
+
+ align:start position:0%
+have n n equations well guess I can do
+this take this back I guess I call this
+
+ align:start position:0%
+this take this back I guess I call this
+ 
+
+ align:start position:0%
+this take this back I guess I call this
+n just be just be careful he's answered
+
+ align:start position:0%
+n just be just be careful he's answered
+ 
+
+ align:start position:0%
+n just be just be careful he's answered
+there's the same number of them
+
+ align:start position:0%
+there's the same number of them
+ 
+
+ align:start position:0%
+there's the same number of them
+there's sanitary conditions this is okay
+
+ align:start position:0%
+there's sanitary conditions this is okay
+ 
+
+ align:start position:0%
+there's sanitary conditions this is okay
+to write it this way but just be careful
+
+ align:start position:0%
+to write it this way but just be careful
+ 
+
+ align:start position:0%
+to write it this way but just be careful
+all right that's okay just to make it
+
+ align:start position:0%
+all right that's okay just to make it
+ 
+
+ align:start position:0%
+all right that's okay just to make it
+confusing all right that comes I guess
+
+ align:start position:0%
+confusing all right that comes I guess
+ 
+
+ align:start position:0%
+confusing all right that comes I guess
+think oh it's not now it's even though
+
+ align:start position:0%
+think oh it's not now it's even though
+ 
+
+ align:start position:0%
+think oh it's not now it's even though
+it's not really not right it's really
+
+ align:start position:0%
+it's not really not right it's really
+ 
+
+ align:start position:0%
+it's not really not right it's really
+maybe cold start at the boundary there's
+
+ align:start position:0%
+maybe cold start at the boundary there's
+ 
+
+ align:start position:0%
+maybe cold start at the boundary there's
+some special that some special place
+
+ align:start position:0%
+some special that some special place
+ 
+
+ align:start position:0%
+some special that some special place
+where you know the value of that Y okay
+
+ align:start position:0%
+where you know the value of that Y okay
+ 
+
+ align:start position:0%
+where you know the value of that Y okay
+all right so let's do the motivating
+
+ align:start position:0%
+all right so let's do the motivating
+ 
+
+ align:start position:0%
+all right so let's do the motivating
+example which comes from military
+
+ align:start position:0%
+example which comes from military
+ 
+
+ align:start position:0%
+example which comes from military
+technology and this is quite an old
+
+ align:start position:0%
+technology and this is quite an old
+ 
+
+ align:start position:0%
+technology and this is quite an old
+problem so because in the old days
+
+ align:start position:0%
+problem so because in the old days
+ 
+
+ align:start position:0%
+problem so because in the old days
+people didn't have motor vehicles and
+
+ align:start position:0%
+people didn't have motor vehicles and
+ 
+
+ align:start position:0%
+people didn't have motor vehicles and
+basically the roads were no good and
+
+ align:start position:0%
+basically the roads were no good and
+ 
+
+ align:start position:0%
+basically the roads were no good and
+there were a lot of bandits out on the
+
+ align:start position:0%
+there were a lot of bandits out on the
+ 
+
+ align:start position:0%
+there were a lot of bandits out on the
+roads people like to ship everything by
+
+ align:start position:0%
+roads people like to ship everything by
+ 
+
+ align:start position:0%
+roads people like to ship everything by
+water transportation and so all the
+
+ align:start position:0%
+water transportation and so all the
+ 
+
+ align:start position:0%
+water transportation and so all the
+towns grew up on rivers or on ports on
+
+ align:start position:0%
+towns grew up on rivers or on ports on
+ 
+
+ align:start position:0%
+towns grew up on rivers or on ports on
+the ocean and so if you lived in a nice
+
+ align:start position:0%
+the ocean and so if you lived in a nice
+ 
+
+ align:start position:0%
+the ocean and so if you lived in a nice
+little town you know there's up in the
+
+ align:start position:0%
+little town you know there's up in the
+ 
+
+ align:start position:0%
+little town you know there's up in the
+hills there and then the base of the
+
+ align:start position:0%
+hills there and then the base of the
+ 
+
+ align:start position:0%
+hills there and then the base of the
+hills
+
+ align:start position:0%
+hills
+ 
+
+ align:start position:0%
+hills
+you have your cute little town you have
+
+ align:start position:0%
+you have your cute little town you have
+ 
+
+ align:start position:0%
+you have your cute little town you have
+your house yeah some you know warehouses
+
+ align:start position:0%
+your house yeah some you know warehouses
+ 
+
+ align:start position:0%
+your house yeah some you know warehouses
+where you keep all your nice goods you
+
+ align:start position:0%
+where you keep all your nice goods you
+ 
+
+ align:start position:0%
+where you keep all your nice goods you
+have a dock that goes out onto the water
+
+ align:start position:0%
+have a dock that goes out onto the water
+ 
+
+ align:start position:0%
+have a dock that goes out onto the water
+here's the land here these nice ships
+
+ align:start position:0%
+here's the land here these nice ships
+ 
+
+ align:start position:0%
+here's the land here these nice ships
+come and park at the dock they unload
+
+ align:start position:0%
+come and park at the dock they unload
+ 
+
+ align:start position:0%
+come and park at the dock they unload
+nice good you trade your stuff to them
+
+ align:start position:0%
+nice good you trade your stuff to them
+ 
+
+ align:start position:0%
+nice good you trade your stuff to them
+you make a lot of money you're
+
+ align:start position:0%
+you make a lot of money you're
+ 
+
+ align:start position:0%
+you make a lot of money you're
+everyone's happy and prosperous and
+
+ align:start position:0%
+everyone's happy and prosperous and
+ 
+
+ align:start position:0%
+everyone's happy and prosperous and
+having a great time living those like
+
+ align:start position:0%
+having a great time living those like
+ 
+
+ align:start position:0%
+having a great time living those like
+poor city but then you look out on the
+
+ align:start position:0%
+poor city but then you look out on the
+ 
+
+ align:start position:0%
+poor city but then you look out on the
+horizon in the water and you see a ship
+
+ align:start position:0%
+horizon in the water and you see a ship
+ 
+
+ align:start position:0%
+horizon in the water and you see a ship
+is coming and sometimes the ship is
+
+ align:start position:0%
+is coming and sometimes the ship is
+ 
+
+ align:start position:0%
+is coming and sometimes the ship is
+coming is really good news for you but
+
+ align:start position:0%
+coming is really good news for you but
+ 
+
+ align:start position:0%
+coming is really good news for you but
+sometimes the ship coming is not good
+
+ align:start position:0%
+sometimes the ship coming is not good
+ 
+
+ align:start position:0%
+sometimes the ship coming is not good
+because on the back it has a flag and on
+
+ align:start position:0%
+because on the back it has a flag and on
+ 
+
+ align:start position:0%
+because on the back it has a flag and on
+the flag you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+skull and crossbones and your eyes the
+
+ align:start position:0%
+skull and crossbones and your eyes the
+ 
+
+ align:start position:0%
+skull and crossbones and your eyes the
+Pirates are coming and now you're in
+
+ align:start position:0%
+Pirates are coming and now you're in
+ 
+
+ align:start position:0%
+Pirates are coming and now you're in
+serious trouble because you're really
+
+ align:start position:0%
+serious trouble because you're really
+ 
+
+ align:start position:0%
+serious trouble because you're really
+done with the Pirates to come to your
+
+ align:start position:0%
+done with the Pirates to come to your
+ 
+
+ align:start position:0%
+done with the Pirates to come to your
+nice little town because who knows what
+
+ align:start position:0%
+nice little town because who knows what
+ 
+
+ align:start position:0%
+nice little town because who knows what
+they'll do there but it won't be good
+
+ align:start position:0%
+they'll do there but it won't be good
+ 
+
+ align:start position:0%
+they'll do there but it won't be good
+all right so the people who live in this
+
+ align:start position:0%
+all right so the people who live in this
+ 
+
+ align:start position:0%
+all right so the people who live in this
+town after this happens to you a few
+
+ align:start position:0%
+town after this happens to you a few
+ 
+
+ align:start position:0%
+town after this happens to you a few
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+you're really alarmed and you're really
+
+ align:start position:0%
+you're really alarmed and you're really
+ 
+
+ align:start position:0%
+you're really alarmed and you're really
+unhappy and you don't want to rebuild
+
+ align:start position:0%
+unhappy and you don't want to rebuild
+ 
+
+ align:start position:0%
+unhappy and you don't want to rebuild
+your town encounters it just got burned
+
+ align:start position:0%
+your town encounters it just got burned
+ 
+
+ align:start position:0%
+your town encounters it just got burned
+down the last time when the Pirates came
+
+ align:start position:0%
+down the last time when the Pirates came
+ 
+
+ align:start position:0%
+down the last time when the Pirates came
+to pillaged and took everything and you
+
+ align:start position:0%
+to pillaged and took everything and you
+ 
+
+ align:start position:0%
+to pillaged and took everything and you
+guys all had to run away into the hills
+
+ align:start position:0%
+guys all had to run away into the hills
+ 
+
+ align:start position:0%
+guys all had to run away into the hills
+so instead they've been in cannons or
+
+ align:start position:0%
+so instead they've been in cannons or
+ 
+
+ align:start position:0%
+so instead they've been in cannons or
+catapults and you put one of the cannons
+
+ align:start position:0%
+catapults and you put one of the cannons
+ 
+
+ align:start position:0%
+catapults and you put one of the cannons
+say at the top of the hill above your
+
+ align:start position:0%
+say at the top of the hill above your
+ 
+
+ align:start position:0%
+say at the top of the hill above your
+town and then you say the next time the
+
+ align:start position:0%
+town and then you say the next time the
+ 
+
+ align:start position:0%
+town and then you say the next time the
+Pirates come I'm ready for them okay
+
+ align:start position:0%
+Pirates come I'm ready for them okay
+ 
+
+ align:start position:0%
+Pirates come I'm ready for them okay
+drawing the cannon
+
+ align:start position:0%
+drawing the cannon
+ 
+
+ align:start position:0%
+drawing the cannon
+alright and so the question is you want
+
+ align:start position:0%
+alright and so the question is you want
+ 
+
+ align:start position:0%
+alright and so the question is you want
+to shoot the Cannonball so it hits the
+
+ align:start position:0%
+to shoot the Cannonball so it hits the
+ 
+
+ align:start position:0%
+to shoot the Cannonball so it hits the
+pirate ship at the waterline when the
+
+ align:start position:0%
+pirate ship at the waterline when the
+ 
+
+ align:start position:0%
+pirate ship at the waterline when the
+pirate is a distance L from the shore
+
+ align:start position:0%
+pirate is a distance L from the shore
+ 
+
+ align:start position:0%
+pirate is a distance L from the shore
+hopefully pretty far so they're not
+
+ align:start position:0%
+hopefully pretty far so they're not
+ 
+
+ align:start position:0%
+hopefully pretty far so they're not
+going to shoot at you first and you're
+
+ align:start position:0%
+going to shoot at you first and you're
+ 
+
+ align:start position:0%
+going to shoot at you first and you're
+shooting for up to the top of the hill
+
+ align:start position:0%
+shooting for up to the top of the hill
+ 
+
+ align:start position:0%
+shooting for up to the top of the hill
+so you can shoot further than they can
+
+ align:start position:0%
+so you can shoot further than they can
+ 
+
+ align:start position:0%
+so you can shoot further than they can
+so you're gonna shoot distance L and
+
+ align:start position:0%
+so you're gonna shoot distance L and
+ 
+
+ align:start position:0%
+so you're gonna shoot distance L and
+your sheep on top from a elevation H
+
+ align:start position:0%
+your sheep on top from a elevation H
+ 
+
+ align:start position:0%
+your sheep on top from a elevation H
+okay and you want to make sure your
+
+ align:start position:0%
+okay and you want to make sure your
+ 
+
+ align:start position:0%
+okay and you want to make sure your
+cannonball hits them ideally right at
+
+ align:start position:0%
+cannonball hits them ideally right at
+ 
+
+ align:start position:0%
+cannonball hits them ideally right at
+the waterline boom makes a nice hole in
+
+ align:start position:0%
+the waterline boom makes a nice hole in
+ 
+
+ align:start position:0%
+the waterline boom makes a nice hole in
+their ship and they sinks okay so that's
+
+ align:start position:0%
+their ship and they sinks okay so that's
+ 
+
+ align:start position:0%
+their ship and they sinks okay so that's
+the plan now the the problem is she's
+
+ align:start position:0%
+the plan now the the problem is she's
+ 
+
+ align:start position:0%
+the plan now the the problem is she's
+getting the cannonball to go from here
+
+ align:start position:0%
+getting the cannonball to go from here
+ 
+
+ align:start position:0%
+getting the cannonball to go from here
+to there it's not so easy it's a big
+
+ align:start position:0%
+to there it's not so easy it's a big
+ 
+
+ align:start position:0%
+to there it's not so easy it's a big
+ocean there's a lot of place your cannon
+
+ align:start position:0%
+ocean there's a lot of place your cannon
+ 
+
+ align:start position:0%
+ocean there's a lot of place your cannon
+balls can fall into the ocean and it
+
+ align:start position:0%
+balls can fall into the ocean and it
+ 
+
+ align:start position:0%
+balls can fall into the ocean and it
+might not be with the pirate ship is and
+
+ align:start position:0%
+might not be with the pirate ship is and
+ 
+
+ align:start position:0%
+might not be with the pirate ship is and
+reloading a cannon is pretty slow and
+
+ align:start position:0%
+reloading a cannon is pretty slow and
+ 
+
+ align:start position:0%
+reloading a cannon is pretty slow and
+you guys live in this prosperous port
+
+ align:start position:0%
+you guys live in this prosperous port
+ 
+
+ align:start position:0%
+you guys live in this prosperous port
+you're not military guys and say you
+
+ align:start position:0%
+you're not military guys and say you
+ 
+
+ align:start position:0%
+you're not military guys and say you
+don't know how that much practice doing
+
+ align:start position:0%
+don't know how that much practice doing
+ 
+
+ align:start position:0%
+don't know how that much practice doing
+it anyway and you're cheap because
+
+ align:start position:0%
+it anyway and you're cheap because
+ 
+
+ align:start position:0%
+it anyway and you're cheap because
+you're merchants you don't want to spend
+
+ align:start position:0%
+you're merchants you don't want to spend
+ 
+
+ align:start position:0%
+you're merchants you don't want to spend
+your money buying lots of cannonballs
+
+ align:start position:0%
+your money buying lots of cannonballs
+ 
+
+ align:start position:0%
+your money buying lots of cannonballs
+anyway so you only have a few
+
+ align:start position:0%
+anyway so you only have a few
+ 
+
+ align:start position:0%
+anyway so you only have a few
+cannonballs up here there's a little
+
+ align:start position:0%
+cannonballs up here there's a little
+ 
+
+ align:start position:0%
+cannonballs up here there's a little
+pile cannonball next to the cannon and
+
+ align:start position:0%
+pile cannonball next to the cannon and
+ 
+
+ align:start position:0%
+pile cannonball next to the cannon and
+then when you see the pirate ship coming
+
+ align:start position:0%
+then when you see the pirate ship coming
+ 
+
+ align:start position:0%
+then when you see the pirate ship coming
+you guys run up the hill quick and you
+
+ align:start position:0%
+you guys run up the hill quick and you
+ 
+
+ align:start position:0%
+you guys run up the hill quick and you
+get to take you know a couple of shots
+
+ align:start position:0%
+get to take you know a couple of shots
+ 
+
+ align:start position:0%
+get to take you know a couple of shots
+and that's it and if you hit them then
+
+ align:start position:0%
+and that's it and if you hit them then
+ 
+
+ align:start position:0%
+and that's it and if you hit them then
+your town is safe and otherwise
+
+ align:start position:0%
+your town is safe and otherwise
+ 
+
+ align:start position:0%
+your town is safe and otherwise
+everything you love and know in your
+
+ align:start position:0%
+everything you love and know in your
+ 
+
+ align:start position:0%
+everything you love and know in your
+world is to be destroyed by the parts
+
+ align:start position:0%
+world is to be destroyed by the parts
+ 
+
+ align:start position:0%
+world is to be destroyed by the parts
+okay so this was the motivating example
+
+ align:start position:0%
+okay so this was the motivating example
+ 
+
+ align:start position:0%
+okay so this was the motivating example
+for the development of differential
+
+ align:start position:0%
+for the development of differential
+ 
+
+ align:start position:0%
+for the development of differential
+equation solvers okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's see if we can write down the
+
+ align:start position:0%
+so let's see if we can write down the
+ 
+
+ align:start position:0%
+so let's see if we can write down the
+equations that correspond to this
+
+ align:start position:0%
+equations that correspond to this
+ 
+
+ align:start position:0%
+equations that correspond to this
+example so it's gonna be Newton's laws F
+
+ align:start position:0%
+example so it's gonna be Newton's laws F
+ 
+
+ align:start position:0%
+example so it's gonna be Newton's laws F
+equals MA on the cannonball is it
+
+ align:start position:0%
+equals MA on the cannonball is it
+ 
+
+ align:start position:0%
+equals MA on the cannonball is it
+travels right so where we can write that
+
+ align:start position:0%
+travels right so where we can write that
+ 
+
+ align:start position:0%
+travels right so where we can write that
+also as equals well what's what's the DF
+
+ align:start position:0%
+also as equals well what's what's the DF
+ 
+
+ align:start position:0%
+also as equals well what's what's the DF
+so f is going to be negative mg mg in
+
+ align:start position:0%
+so f is going to be negative mg mg in
+ 
+
+ align:start position:0%
+so f is going to be negative mg mg in
+the Z direction all right
+
+ align:start position:0%
+the Z direction all right
+ 
+
+ align:start position:0%
+the Z direction all right
+that's gravity's pulling the Cannonball
+
+ align:start position:0%
+that's gravity's pulling the Cannonball
+ 
+
+ align:start position:0%
+that's gravity's pulling the Cannonball
+down and then they'll have some air
+
+ align:start position:0%
+down and then they'll have some air
+ 
+
+ align:start position:0%
+down and then they'll have some air
+friction on the Cannonball and I'm going
+
+ align:start position:0%
+friction on the Cannonball and I'm going
+ 
+
+ align:start position:0%
+friction on the Cannonball and I'm going
+to call the air friction coefficient
+
+ align:start position:0%
+to call the air friction coefficient
+ 
+
+ align:start position:0%
+to call the air friction coefficient
+gamma M times V okay so that's the
+
+ align:start position:0%
+gamma M times V okay so that's the
+ 
+
+ align:start position:0%
+gamma M times V okay so that's the
+simplest model for what the forces are
+
+ align:start position:0%
+simplest model for what the forces are
+ 
+
+ align:start position:0%
+simplest model for what the forces are
+unaccountable is this flying for my
+
+ align:start position:0%
+unaccountable is this flying for my
+ 
+
+ align:start position:0%
+unaccountable is this flying for my
+cannon
+
+ align:start position:0%
+cannon
+ 
+
+ align:start position:0%
+cannon
+hopefully did the pirate ship and I can
+
+ align:start position:0%
+hopefully did the pirate ship and I can
+ 
+
+ align:start position:0%
+hopefully did the pirate ship and I can
+rearrange this by dividing through by M
+
+ align:start position:0%
+rearrange this by dividing through by M
+ 
+
+ align:start position:0%
+rearrange this by dividing through by M
+so D net acceleration velocity said DV
+
+ align:start position:0%
+so D net acceleration velocity said DV
+ 
+
+ align:start position:0%
+so D net acceleration velocity said DV
+DT is equal to negative G okay sorry
+
+ align:start position:0%
+DT is equal to negative G okay sorry
+ 
+
+ align:start position:0%
+DT is equal to negative G okay sorry
+patience not so good okay everybody
+
+ align:start position:0%
+patience not so good okay everybody
+ 
+
+ align:start position:0%
+patience not so good okay everybody
+right with us yeah so then we can write
+
+ align:start position:0%
+right with us yeah so then we can write
+ 
+
+ align:start position:0%
+right with us yeah so then we can write
+the whole differential equation system c
+
+ align:start position:0%
+the whole differential equation system c
+ 
+
+ align:start position:0%
+the whole differential equation system c
+dt x e DX DZ equals DX dt is DX DZ DT is
+
+ align:start position:0%
+dt x e DX DZ equals DX dt is DX DZ DT is
+ 
+
+ align:start position:0%
+dt x e DX DZ equals DX dt is DX DZ DT is
+VZ d DX DT is negative gamma D X D DZ DT
+
+ align:start position:0%
+VZ d DX DT is negative gamma D X D DZ DT
+ 
+
+ align:start position:0%
+VZ d DX DT is negative gamma D X D DZ DT
+is negative G minus
+
+ align:start position:0%
+is negative G minus
+ 
+
+ align:start position:0%
+is negative G minus
+easy all right so that's a fine Eau de
+
+ align:start position:0%
+easy all right so that's a fine Eau de
+ 
+
+ align:start position:0%
+easy all right so that's a fine Eau de
+system it's not too hard to solve it's
+
+ align:start position:0%
+system it's not too hard to solve it's
+ 
+
+ align:start position:0%
+system it's not too hard to solve it's
+actually linear piece of cake
+
+ align:start position:0%
+actually linear piece of cake
+ 
+
+ align:start position:0%
+actually linear piece of cake
+right you guys probably do this already
+
+ align:start position:0%
+right you guys probably do this already
+ 
+
+ align:start position:0%
+right you guys probably do this already
+when you're in high school or college
+
+ align:start position:0%
+when you're in high school or college
+ 
+
+ align:start position:0%
+when you're in high school or college
+anyway for sure
+
+ align:start position:0%
+anyway for sure
+ 
+
+ align:start position:0%
+anyway for sure
+and let's write down the initial
+
+ align:start position:0%
+and let's write down the initial
+ 
+
+ align:start position:0%
+and let's write down the initial
+conditions so we know X of 0 is equal to
+
+ align:start position:0%
+conditions so we know X of 0 is equal to
+ 
+
+ align:start position:0%
+conditions so we know X of 0 is equal to
+0 Z of 0 is equal to H the height of the
+
+ align:start position:0%
+0 Z of 0 is equal to H the height of the
+ 
+
+ align:start position:0%
+0 Z of 0 is equal to H the height of the
+of the cannon the X of 0 oh it's that
+
+ align:start position:0%
+of the cannon the X of 0 oh it's that
+ 
+
+ align:start position:0%
+of the cannon the X of 0 oh it's that
+equal to we don't know V Z of 0 we don't
+
+ align:start position:0%
+equal to we don't know V Z of 0 we don't
+ 
+
+ align:start position:0%
+equal to we don't know V Z of 0 we don't
+know that either but we bought this
+
+ align:start position:0%
+know that either but we bought this
+ 
+
+ align:start position:0%
+know that either but we bought this
+cannon with a certified muzzle velocity
+
+ align:start position:0%
+cannon with a certified muzzle velocity
+ 
+
+ align:start position:0%
+cannon with a certified muzzle velocity
+B naught so we actually know that V X of
+
+ align:start position:0%
+B naught so we actually know that V X of
+ 
+
+ align:start position:0%
+B naught so we actually know that V X of
+0 squared plus V Z of 0 squared is equal
+
+ align:start position:0%
+0 squared plus V Z of 0 squared is equal
+ 
+
+ align:start position:0%
+0 squared plus V Z of 0 squared is equal
+to V naught squared whereas my my when I
+
+ align:start position:0%
+to V naught squared whereas my my when I
+ 
+
+ align:start position:0%
+to V naught squared whereas my my when I
+bought the cannon the merchants went out
+
+ align:start position:0%
+bought the cannon the merchants went out
+ 
+
+ align:start position:0%
+bought the cannon the merchants went out
+to the local cannon dealer and buy
+
+ align:start position:0%
+to the local cannon dealer and buy
+ 
+
+ align:start position:0%
+to the local cannon dealer and buy
+cannon and the guy said you put this
+
+ align:start position:0%
+cannon and the guy said you put this
+ 
+
+ align:start position:0%
+cannon and the guy said you put this
+much gunpowder in it you'll get a muzzle
+
+ align:start position:0%
+much gunpowder in it you'll get a muzzle
+ 
+
+ align:start position:0%
+much gunpowder in it you'll get a muzzle
+velocity of you know I said they know
+
+ align:start position:0%
+velocity of you know I said they know
+ 
+
+ align:start position:0%
+velocity of you know I said they know
+that that numbers so we have a condition
+
+ align:start position:0%
+that that numbers so we have a condition
+ 
+
+ align:start position:0%
+that that numbers so we have a condition
+that's not really the way we expect it
+
+ align:start position:0%
+that's not really the way we expect it
+ 
+
+ align:start position:0%
+that's not really the way we expect it
+to be and we don't have enough
+
+ align:start position:0%
+to be and we don't have enough
+ 
+
+ align:start position:0%
+to be and we don't have enough
+conditions we need four conditions but
+
+ align:start position:0%
+conditions we need four conditions but
+ 
+
+ align:start position:0%
+conditions we need four conditions but
+of course the most important condition
+
+ align:start position:0%
+of course the most important condition
+ 
+
+ align:start position:0%
+of course the most important condition
+is what happens at L we really want to
+
+ align:start position:0%
+is what happens at L we really want to
+ 
+
+ align:start position:0%
+is what happens at L we really want to
+know that X of T final is equal to L and
+
+ align:start position:0%
+know that X of T final is equal to L and
+ 
+
+ align:start position:0%
+know that X of T final is equal to L and
+y of T final is equal to zero sea level
+
+ align:start position:0%
+y of T final is equal to zero sea level
+ 
+
+ align:start position:0%
+y of T final is equal to zero sea level
+so that's that we are cannibals get in
+
+ align:start position:0%
+so that's that we are cannibals get in
+ 
+
+ align:start position:0%
+so that's that we are cannibals get in
+to the right location at T final so we
+
+ align:start position:0%
+to the right location at T final so we
+ 
+
+ align:start position:0%
+to the right location at T final so we
+have two conditions specified way way
+
+ align:start position:0%
+have two conditions specified way way
+ 
+
+ align:start position:0%
+have two conditions specified way way
+away from where we are and we have two
+
+ align:start position:0%
+away from where we are and we have two
+ 
+
+ align:start position:0%
+away from where we are and we have two
+conditions specified initially I know
+
+ align:start position:0%
+conditions specified initially I know
+ 
+
+ align:start position:0%
+conditions specified initially I know
+you have some oddball thing in here
+
+ align:start position:0%
+you have some oddball thing in here
+ 
+
+ align:start position:0%
+you have some oddball thing in here
+let's let my own behind ball v condition
+
+ align:start position:0%
+let's let my own behind ball v condition
+ 
+
+ align:start position:0%
+let's let my own behind ball v condition
+now okay one problem here is we don't
+
+ align:start position:0%
+now okay one problem here is we don't
+ 
+
+ align:start position:0%
+now okay one problem here is we don't
+actually know what T final is right
+
+ align:start position:0%
+actually know what T final is right
+ 
+
+ align:start position:0%
+actually know what T final is right
+because before we shoot we really don't
+
+ align:start position:0%
+because before we shoot we really don't
+ 
+
+ align:start position:0%
+because before we shoot we really don't
+know how long it takes the Cannonball to
+
+ align:start position:0%
+know how long it takes the Cannonball to
+ 
+
+ align:start position:0%
+know how long it takes the Cannonball to
+get out there so this is a kind of weird
+
+ align:start position:0%
+get out there so this is a kind of weird
+ 
+
+ align:start position:0%
+get out there so this is a kind of weird
+condition where T finals unknown where
+
+ align:start position:0%
+condition where T finals unknown where
+ 
+
+ align:start position:0%
+condition where T finals unknown where
+so once you're done before I think
+
+ align:start position:0%
+so once you're done before I think
+ 
+
+ align:start position:0%
+so once you're done before I think
+you've always known T final so right so
+
+ align:start position:0%
+you've always known T final so right so
+ 
+
+ align:start position:0%
+you've always known T final so right so
+let's talk about how to deal with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one problem one one way to deal with
+
+ align:start position:0%
+so one problem one one way to deal with
+ 
+
+ align:start position:0%
+so one problem one one way to deal with
+us is to notice that if we have a
+
+ align:start position:0%
+us is to notice that if we have a
+ 
+
+ align:start position:0%
+us is to notice that if we have a
+equation system dy DT equals F of Y we
+
+ align:start position:0%
+equation system dy DT equals F of Y we
+ 
+
+ align:start position:0%
+equation system dy DT equals F of Y we
+could change variables instead of using
+
+ align:start position:0%
+could change variables instead of using
+ 
+
+ align:start position:0%
+could change variables instead of using
+T since we really don't know much about
+
+ align:start position:0%
+T since we really don't know much about
+ 
+
+ align:start position:0%
+T since we really don't know much about
+time in this problem T is not the best
+
+ align:start position:0%
+time in this problem T is not the best
+ 
+
+ align:start position:0%
+time in this problem T is not the best
+variable for us so we want to change it
+
+ align:start position:0%
+variable for us so we want to change it
+ 
+
+ align:start position:0%
+variable for us so we want to change it
+to some new variable U so suppose that
+
+ align:start position:0%
+to some new variable U so suppose that
+ 
+
+ align:start position:0%
+to some new variable U so suppose that
+we know what we want to change to you
+
+ align:start position:0%
+we know what we want to change to you
+ 
+
+ align:start position:0%
+we know what we want to change to you
+and if we change to you will have we can
+
+ align:start position:0%
+and if we change to you will have we can
+ 
+
+ align:start position:0%
+and if we change to you will have we can
+write something like this D why do you
+
+ align:start position:0%
+write something like this D why do you
+ 
+
+ align:start position:0%
+write something like this D why do you
+do you DT equals f of Y can you see that
+
+ align:start position:0%
+do you DT equals f of Y can you see that
+ 
+
+ align:start position:0%
+do you DT equals f of Y can you see that
+right so if I change I could try to get
+
+ align:start position:0%
+right so if I change I could try to get
+ 
+
+ align:start position:0%
+right so if I change I could try to get
+the differential is returned to you and
+
+ align:start position:0%
+the differential is returned to you and
+ 
+
+ align:start position:0%
+the differential is returned to you and
+I just have to know what my Dutt is and
+
+ align:start position:0%
+I just have to know what my Dutt is and
+ 
+
+ align:start position:0%
+I just have to know what my Dutt is and
+you guys might have been change the
+
+ align:start position:0%
+you guys might have been change the
+ 
+
+ align:start position:0%
+you guys might have been change the
+variable variables before in calculus
+
+ align:start position:0%
+variable variables before in calculus
+ 
+
+ align:start position:0%
+variable variables before in calculus
+some time you probably did this a long
+
+ align:start position:0%
+some time you probably did this a long
+ 
+
+ align:start position:0%
+some time you probably did this a long
+time ago and chain rule and stuff like
+
+ align:start position:0%
+time ago and chain rule and stuff like
+ 
+
+ align:start position:0%
+time ago and chain rule and stuff like
+that yeah all right so we can sort of
+
+ align:start position:0%
+that yeah all right so we can sort of
+ 
+
+ align:start position:0%
+that yeah all right so we can sort of
+pick whatever I do we want and as long
+
+ align:start position:0%
+pick whatever I do we want and as long
+ 
+
+ align:start position:0%
+pick whatever I do we want and as long
+as we put in the the Dutt in the
+
+ align:start position:0%
+as we put in the the Dutt in the
+ 
+
+ align:start position:0%
+as we put in the the Dutt in the
+equation it will be okay so let's let's
+
+ align:start position:0%
+equation it will be okay so let's let's
+ 
+
+ align:start position:0%
+equation it will be okay so let's let's
+just choose that U is equal to ax
+
+ align:start position:0%
+just choose that U is equal to ax
+ 
+
+ align:start position:0%
+just choose that U is equal to ax
+because we know Dutt would then be DX
+
+ align:start position:0%
+because we know Dutt would then be DX
+ 
+
+ align:start position:0%
+because we know Dutt would then be DX
+right so we could we could write this
+
+ align:start position:0%
+right so we could we could write this
+ 
+
+ align:start position:0%
+right so we could we could write this
+out this way we could write D I'll keep
+
+ align:start position:0%
+out this way we could write D I'll keep
+ 
+
+ align:start position:0%
+out this way we could write D I'll keep
+it as you for a minute so but the
+
+ align:start position:0%
+it as you for a minute so but the
+ 
+
+ align:start position:0%
+it as you for a minute so but the
+notation won't be so confusing so d we
+
+ align:start position:0%
+notation won't be so confusing so d we
+ 
+
+ align:start position:0%
+notation won't be so confusing so d we
+UDT py e edu is equal to f of y over u
+
+ align:start position:0%
+UDT py e edu is equal to f of y over u
+ 
+
+ align:start position:0%
+UDT py e edu is equal to f of y over u
+dt and as long as t du DT is never zero
+
+ align:start position:0%
+dt and as long as t du DT is never zero
+ 
+
+ align:start position:0%
+dt and as long as t du DT is never zero
+we're good so we could do any any we
+
+ align:start position:0%
+we're good so we could do any any we
+ 
+
+ align:start position:0%
+we're good so we could do any any we
+want as long as DT is never zero then we
+
+ align:start position:0%
+want as long as DT is never zero then we
+ 
+
+ align:start position:0%
+want as long as DT is never zero then we
+have we're still gonna have a nice
+
+ align:start position:0%
+have we're still gonna have a nice
+ 
+
+ align:start position:0%
+have we're still gonna have a nice
+simple equation here and so I'm gonna
+
+ align:start position:0%
+simple equation here and so I'm gonna
+ 
+
+ align:start position:0%
+simple equation here and so I'm gonna
+choose U is equal to X it's goes to UDC
+
+ align:start position:0%
+choose U is equal to X it's goes to UDC
+ 
+
+ align:start position:0%
+choose U is equal to X it's goes to UDC
+is VX and I know that VX is never zero
+
+ align:start position:0%
+is VX and I know that VX is never zero
+ 
+
+ align:start position:0%
+is VX and I know that VX is never zero
+the ball is always moving to the right
+
+ align:start position:0%
+the ball is always moving to the right
+ 
+
+ align:start position:0%
+the ball is always moving to the right
+okay so I'm gonna divide by something is
+
+ align:start position:0%
+okay so I'm gonna divide by something is
+ 
+
+ align:start position:0%
+okay so I'm gonna divide by something is
+not never zero so I can write it this
+
+ align:start position:0%
+not never zero so I can write it this
+ 
+
+ align:start position:0%
+not never zero so I can write it this
+way dy
+
+ align:start position:0%
+way dy
+ 
+
+ align:start position:0%
+way dy
+equal to thank you velvet list and
+
+ align:start position:0%
+equal to thank you velvet list and
+ 
+
+ align:start position:0%
+equal to thank you velvet list and
+divide each of these things by VX so
+
+ align:start position:0%
+divide each of these things by VX so
+ 
+
+ align:start position:0%
+divide each of these things by VX so
+it's one easy over B X negative gamma
+
+ align:start position:0%
+it's one easy over B X negative gamma
+ 
+
+ align:start position:0%
+it's one easy over B X negative gamma
+negative G over B X minus gamma easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's my new okay is everybody okay
+
+ align:start position:0%
+that's my new okay is everybody okay
+ 
+
+ align:start position:0%
+that's my new okay is everybody okay
+with this so far energetic nodding yeah
+
+ align:start position:0%
+with this so far energetic nodding yeah
+ 
+
+ align:start position:0%
+with this so far energetic nodding yeah
+yeah sure keep going faster did you go
+
+ align:start position:0%
+yeah sure keep going faster did you go
+ 
+
+ align:start position:0%
+yeah sure keep going faster did you go
+you wait you slept that's what I want
+
+ align:start position:0%
+you wait you slept that's what I want
+ 
+
+ align:start position:0%
+you wait you slept that's what I want
+you to say yeah apparently not okay all
+
+ align:start position:0%
+you to say yeah apparently not okay all
+ 
+
+ align:start position:0%
+you to say yeah apparently not okay all
+right so the the advantage to changing
+
+ align:start position:0%
+right so the the advantage to changing
+ 
+
+ align:start position:0%
+right so the the advantage to changing
+here is that now I can write the initial
+
+ align:start position:0%
+here is that now I can write the initial
+ 
+
+ align:start position:0%
+here is that now I can write the initial
+conditions and that the all these
+
+ align:start position:0%
+conditions and that the all these
+ 
+
+ align:start position:0%
+conditions and that the all these
+conditions in terms of U which is X so I
+
+ align:start position:0%
+conditions in terms of U which is X so I
+ 
+
+ align:start position:0%
+conditions in terms of U which is X so I
+really I want to go from U is equal to 0
+
+ align:start position:0%
+really I want to go from U is equal to 0
+ 
+
+ align:start position:0%
+really I want to go from U is equal to 0
+ie X equal to 0 to U is equal to L right
+
+ align:start position:0%
+ie X equal to 0 to U is equal to L right
+ 
+
+ align:start position:0%
+ie X equal to 0 to U is equal to L right
+so now I could also look at this and say
+
+ align:start position:0%
+so now I could also look at this and say
+ 
+
+ align:start position:0%
+so now I could also look at this and say
+this is kind of stupid dy to you the
+
+ align:start position:0%
+this is kind of stupid dy to you the
+ 
+
+ align:start position:0%
+this is kind of stupid dy to you the
+first component of Y is just do you want
+
+ align:start position:0%
+first component of Y is just do you want
+ 
+
+ align:start position:0%
+first component of Y is just do you want
+to U is equal to 1 and that first
+
+ align:start position:0%
+to U is equal to 1 and that first
+ 
+
+ align:start position:0%
+to U is equal to 1 and that first
+component of Y never appears and the
+
+ align:start position:0%
+component of Y never appears and the
+ 
+
+ align:start position:0%
+component of Y never appears and the
+rest of these equations so that's kind
+
+ align:start position:0%
+rest of these equations so that's kind
+ 
+
+ align:start position:0%
+rest of these equations so that's kind
+of not a very useful one so I can change
+
+ align:start position:0%
+of not a very useful one so I can change
+ 
+
+ align:start position:0%
+of not a very useful one so I can change
+and I could write a simpler equation do
+
+ align:start position:0%
+and I could write a simpler equation do
+ 
+
+ align:start position:0%
+and I could write a simpler equation do
+u Y tilde do u is equal to VZ over V X
+
+ align:start position:0%
+u Y tilde do u is equal to VZ over V X
+ 
+
+ align:start position:0%
+u Y tilde do u is equal to VZ over V X
+negative gamma negative G over B minus
+
+ align:start position:0%
+negative gamma negative G over B minus
+ 
+
+ align:start position:0%
+negative gamma negative G over B minus
+gamma V over V X where my Y tilde is
+
+ align:start position:0%
+gamma V over V X where my Y tilde is
+ 
+
+ align:start position:0%
+gamma V over V X where my Y tilde is
+just equal to the last three variables
+
+ align:start position:0%
+just equal to the last three variables
+ 
+
+ align:start position:0%
+just equal to the last three variables
+be sorry Z the X so right so I did a lot
+
+ align:start position:0%
+be sorry Z the X so right so I did a lot
+ 
+
+ align:start position:0%
+be sorry Z the X so right so I did a lot
+of algebra but I end up simplifying my
+
+ align:start position:0%
+of algebra but I end up simplifying my
+ 
+
+ align:start position:0%
+of algebra but I end up simplifying my
+life because I only have three different
+
+ align:start position:0%
+life because I only have three different
+ 
+
+ align:start position:0%
+life because I only have three different
+equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I can write that y tilde 0 of the
+
+ align:start position:0%
+and I can write that y tilde 0 of the
+ 
+
+ align:start position:0%
+and I can write that y tilde 0 of the
+first element of Y tilde which is Z is
+
+ align:start position:0%
+first element of Y tilde which is Z is
+ 
+
+ align:start position:0%
+first element of Y tilde which is Z is
+equal to H so that's a condition I know
+
+ align:start position:0%
+equal to H so that's a condition I know
+ 
+
+ align:start position:0%
+equal to H so that's a condition I know
+for sure and I know that I really want
+
+ align:start position:0%
+for sure and I know that I really want
+ 
+
+ align:start position:0%
+for sure and I know that I really want
+this kind of ball to hit the pirate ship
+
+ align:start position:0%
+this kind of ball to hit the pirate ship
+ 
+
+ align:start position:0%
+this kind of ball to hit the pirate ship
+so I want Y 1 tilde of L to be 0
+
+ align:start position:0%
+so I want Y 1 tilde of L to be 0
+ 
+
+ align:start position:0%
+so I want Y 1 tilde of L to be 0
+that's why 1 tilde is Z and I want C to
+
+ align:start position:0%
+that's why 1 tilde is Z and I want C to
+ 
+
+ align:start position:0%
+that's why 1 tilde is Z and I want C to
+be 0 at when the when X is equal to L
+
+ align:start position:0%
+be 0 at when the when X is equal to L
+ 
+
+ align:start position:0%
+be 0 at when the when X is equal to L
+all right that's the point where the
+
+ align:start position:0%
+all right that's the point where the
+ 
+
+ align:start position:0%
+all right that's the point where the
+kind of ball sitting the ship at the
+
+ align:start position:0%
+kind of ball sitting the ship at the
+ 
+
+ align:start position:0%
+kind of ball sitting the ship at the
+waterline over there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so those are two two definitely two
+
+ align:start position:0%
+so those are two two definitely two
+ 
+
+ align:start position:0%
+so those are two two definitely two
+conditions I have and then I need a
+
+ align:start position:0%
+conditions I have and then I need a
+ 
+
+ align:start position:0%
+conditions I have and then I need a
+third condition and my third condition
+
+ align:start position:0%
+third condition and my third condition
+ 
+
+ align:start position:0%
+third condition and my third condition
+is this crazy equation here ok all right
+
+ align:start position:0%
+is this crazy equation here ok all right
+ 
+
+ align:start position:0%
+is this crazy equation here ok all right
+so now I have three conditions for three
+
+ align:start position:0%
+so now I have three conditions for three
+ 
+
+ align:start position:0%
+so now I have three conditions for three
+different equations and one of them is
+
+ align:start position:0%
+different equations and one of them is
+ 
+
+ align:start position:0%
+different equations and one of them is
+an oddball looking thing these two look
+
+ align:start position:0%
+an oddball looking thing these two look
+ 
+
+ align:start position:0%
+an oddball looking thing these two look
+kind of normal however this one's this
+
+ align:start position:0%
+kind of normal however this one's this
+ 
+
+ align:start position:0%
+kind of normal however this one's this
+one's a t naught and this one's it some
+
+ align:start position:0%
+one's a t naught and this one's it some
+ 
+
+ align:start position:0%
+one's a t naught and this one's it some
+goofball value but at least I know the
+
+ align:start position:0%
+goofball value but at least I know the
+ 
+
+ align:start position:0%
+goofball value but at least I know the
+value I know one else so now how far
+
+ align:start position:0%
+value I know one else so now how far
+ 
+
+ align:start position:0%
+value I know one else so now how far
+away the prior to this okay so far so
+
+ align:start position:0%
+away the prior to this okay so far so
+ 
+
+ align:start position:0%
+away the prior to this okay so far so
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+yeah all right so but how am I going to
+
+ align:start position:0%
+yeah all right so but how am I going to
+ 
+
+ align:start position:0%
+yeah all right so but how am I going to
+solve this so one you know how do we
+
+ align:start position:0%
+solve this so one you know how do we
+ 
+
+ align:start position:0%
+solve this so one you know how do we
+know how to solve differential equations
+
+ align:start position:0%
+know how to solve differential equations
+ 
+
+ align:start position:0%
+know how to solve differential equations
+right now is we know how to do initial
+
+ align:start position:0%
+right now is we know how to do initial
+ 
+
+ align:start position:0%
+right now is we know how to do initial
+value problems we have these nice
+
+ align:start position:0%
+value problems we have these nice
+ 
+
+ align:start position:0%
+value problems we have these nice
+programs like go to you for five that
+
+ align:start position:0%
+programs like go to you for five that
+ 
+
+ align:start position:0%
+programs like go to you for five that
+work great integrate differential
+
+ align:start position:0%
+work great integrate differential
+ 
+
+ align:start position:0%
+work great integrate differential
+equations so we should be able to use
+
+ align:start position:0%
+equations so we should be able to use
+ 
+
+ align:start position:0%
+equations so we should be able to use
+that somehow to solve this but we don't
+
+ align:start position:0%
+that somehow to solve this but we don't
+ 
+
+ align:start position:0%
+that somehow to solve this but we don't
+have all the inputs because ode45 would
+
+ align:start position:0%
+have all the inputs because ode45 would
+ 
+
+ align:start position:0%
+have all the inputs because ode45 would
+expect us to give values of all three of
+
+ align:start position:0%
+expect us to give values of all three of
+ 
+
+ align:start position:0%
+expect us to give values of all three of
+the Y tilde values at zero I only know
+
+ align:start position:0%
+the Y tilde values at zero I only know
+ 
+
+ align:start position:0%
+the Y tilde values at zero I only know
+one of them okay so how can I approach
+
+ align:start position:0%
+one of them okay so how can I approach
+ 
+
+ align:start position:0%
+one of them okay so how can I approach
+it I'm sorry I put my beautiful drawing
+
+ align:start position:0%
+it I'm sorry I put my beautiful drawing
+ 
+
+ align:start position:0%
+it I'm sorry I put my beautiful drawing
+down below
+
+ align:start position:0%
+down below
+ 
+
+ align:start position:0%
+down below
+we'll save us for posterity you can look
+
+ align:start position:0%
+we'll save us for posterity you can look
+ 
+
+ align:start position:0%
+we'll save us for posterity you can look
+at it later all right so I could
+
+ align:start position:0%
+at it later all right so I could
+ 
+
+ align:start position:0%
+at it later all right so I could
+approach it by saying well I don't know
+
+ align:start position:0%
+approach it by saying well I don't know
+ 
+
+ align:start position:0%
+approach it by saying well I don't know
+what these two initial conditions should
+
+ align:start position:0%
+what these two initial conditions should
+ 
+
+ align:start position:0%
+what these two initial conditions should
+be what V X and B Z should be at zero
+
+ align:start position:0%
+be what V X and B Z should be at zero
+ 
+
+ align:start position:0%
+be what V X and B Z should be at zero
+I'll treat them as unknowns I want to
+
+ align:start position:0%
+I'll treat them as unknowns I want to
+ 
+
+ align:start position:0%
+I'll treat them as unknowns I want to
+figure out what they should be in and so
+
+ align:start position:0%
+figure out what they should be in and so
+ 
+
+ align:start position:0%
+figure out what they should be in and so
+I'm going to vary those unknowns and
+
+ align:start position:0%
+I'm going to vary those unknowns and
+ 
+
+ align:start position:0%
+I'm going to vary those unknowns and
+then for each value I choose then I can
+
+ align:start position:0%
+then for each value I choose then I can
+ 
+
+ align:start position:0%
+then for each value I choose then I can
+shoot the cannon with those V's and I
+
+ align:start position:0%
+shoot the cannon with those V's and I
+ 
+
+ align:start position:0%
+shoot the cannon with those V's and I
+can see where the cannonball went and if
+
+ align:start position:0%
+can see where the cannonball went and if
+ 
+
+ align:start position:0%
+can see where the cannonball went and if
+it didn't go to the right location I can
+
+ align:start position:0%
+it didn't go to the right location I can
+ 
+
+ align:start position:0%
+it didn't go to the right location I can
+readjust those bees and then try again
+
+ align:start position:0%
+readjust those bees and then try again
+ 
+
+ align:start position:0%
+readjust those bees and then try again
+right just like if you were running the
+
+ align:start position:0%
+right just like if you were running the
+ 
+
+ align:start position:0%
+right just like if you were running the
+cannon you might add you know shoot the
+
+ align:start position:0%
+cannon you might add you know shoot the
+ 
+
+ align:start position:0%
+cannon you might add you know shoot the
+certain angle and then adjust the angle
+
+ align:start position:0%
+certain angle and then adjust the angle
+ 
+
+ align:start position:0%
+certain angle and then adjust the angle
+to Canada and shoot again and that when
+
+ align:start position:0%
+to Canada and shoot again and that when
+ 
+
+ align:start position:0%
+to Canada and shoot again and that when
+you change the angle you'll change the
+
+ align:start position:0%
+you change the angle you'll change the
+ 
+
+ align:start position:0%
+you change the angle you'll change the
+ratio of v x wy initially right so
+
+ align:start position:0%
+ratio of v x wy initially right so
+ 
+
+ align:start position:0%
+ratio of v x wy initially right so
+that's called the shooting method for
+
+ align:start position:0%
+that's called the shooting method for
+ 
+
+ align:start position:0%
+that's called the shooting method for
+good reason okay so this in the shooting
+
+ align:start position:0%
+good reason okay so this in the shooting
+ 
+
+ align:start position:0%
+good reason okay so this in the shooting
+method that's what we do is we guess the
+
+ align:start position:0%
+method that's what we do is we guess the
+ 
+
+ align:start position:0%
+method that's what we do is we guess the
+missing initial conditions then you
+
+ align:start position:0%
+missing initial conditions then you
+ 
+
+ align:start position:0%
+missing initial conditions then you
+solve using the gas saw the dod iv-e
+
+ align:start position:0%
+solve using the gas saw the dod iv-e
+ 
+
+ align:start position:0%
+solve using the gas saw the dod iv-e
+problem and then you see where what it
+
+ align:start position:0%
+problem and then you see where what it
+ 
+
+ align:start position:0%
+problem and then you see where what it
+computes and if if the solution you get
+
+ align:start position:0%
+computes and if if the solution you get
+ 
+
+ align:start position:0%
+computes and if if the solution you get
+doesn't satisfy the conditions you
+
+ align:start position:0%
+doesn't satisfy the conditions you
+ 
+
+ align:start position:0%
+doesn't satisfy the conditions you
+demand you go back and adjust your guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you loop around okay so that's the
+
+ align:start position:0%
+and you loop around okay so that's the
+ 
+
+ align:start position:0%
+and you loop around okay so that's the
+idea now this thing of adjusting some
+
+ align:start position:0%
+idea now this thing of adjusting some
+ 
+
+ align:start position:0%
+idea now this thing of adjusting some
+parameter values some initial conditions
+
+ align:start position:0%
+parameter values some initial conditions
+ 
+
+ align:start position:0%
+parameter values some initial conditions
+to try to satisfy some condition that's
+
+ align:start position:0%
+to try to satisfy some condition that's
+ 
+
+ align:start position:0%
+to try to satisfy some condition that's
+like an F solve problem right that's a
+
+ align:start position:0%
+like an F solve problem right that's a
+ 
+
+ align:start position:0%
+like an F solve problem right that's a
+nonlinear system of nonlinear equations
+
+ align:start position:0%
+nonlinear system of nonlinear equations
+ 
+
+ align:start position:0%
+nonlinear system of nonlinear equations
+kind of problem so we're going to have F
+
+ align:start position:0%
+kind of problem so we're going to have F
+ 
+
+ align:start position:0%
+kind of problem so we're going to have F
+solve as the outside loop and that's
+
+ align:start position:0%
+solve as the outside loop and that's
+ 
+
+ align:start position:0%
+solve as the outside loop and that's
+gonna adjust some parameters and then
+
+ align:start position:0%
+gonna adjust some parameters and then
+ 
+
+ align:start position:0%
+gonna adjust some parameters and then
+what self self do so f self tries to
+
+ align:start position:0%
+what self self do so f self tries to
+ 
+
+ align:start position:0%
+what self self do so f self tries to
+solve problems the form G of usually
+
+ align:start position:0%
+solve problems the form G of usually
+ 
+
+ align:start position:0%
+solve problems the form G of usually
+right acts but cold be here
+
+ align:start position:0%
+right acts but cold be here
+ 
+
+ align:start position:0%
+right acts but cold be here
+no these not good either what letter
+
+ align:start position:0%
+no these not good either what letter
+ 
+
+ align:start position:0%
+no these not good either what letter
+have we have and not used yet any a
+
+ align:start position:0%
+have we have and not used yet any a
+ 
+
+ align:start position:0%
+have we have and not used yet any a
+letter Jeep W here we go G of W equals
+
+ align:start position:0%
+letter Jeep W here we go G of W equals
+ 
+
+ align:start position:0%
+letter Jeep W here we go G of W equals
+zero I want to figure out what W is I
+
+ align:start position:0%
+zero I want to figure out what W is I
+ 
+
+ align:start position:0%
+zero I want to figure out what W is I
+need to use okay and actually we can be
+
+ align:start position:0%
+need to use okay and actually we can be
+ 
+
+ align:start position:0%
+need to use okay and actually we can be
+is right we're trying to just the
+
+ align:start position:0%
+is right we're trying to just the
+ 
+
+ align:start position:0%
+is right we're trying to just the
+velocities right let's do sorry I'm
+
+ align:start position:0%
+velocities right let's do sorry I'm
+ 
+
+ align:start position:0%
+velocities right let's do sorry I'm
+messing up here it's good to use a racer
+
+ align:start position:0%
+messing up here it's good to use a racer
+ 
+
+ align:start position:0%
+messing up here it's good to use a racer
+in this class especially this nice big
+
+ align:start position:0%
+in this class especially this nice big
+ 
+
+ align:start position:0%
+in this class especially this nice big
+eraser all right all right so G V we're
+
+ align:start position:0%
+eraser all right all right so G V we're
+ 
+
+ align:start position:0%
+eraser all right all right so G V we're
+trying to adjust the velocities and to
+
+ align:start position:0%
+trying to adjust the velocities and to
+ 
+
+ align:start position:0%
+trying to adjust the velocities and to
+make something zero so what's our G that
+
+ align:start position:0%
+make something zero so what's our G that
+ 
+
+ align:start position:0%
+make something zero so what's our G that
+we're trying to we want we really want
+
+ align:start position:0%
+we're trying to we want we really want
+ 
+
+ align:start position:0%
+we're trying to we want we really want
+that the Z value at L we want that which
+
+ align:start position:0%
+that the Z value at L we want that which
+ 
+
+ align:start position:0%
+that the Z value at L we want that which
+this is we want that to be equal zero
+
+ align:start position:0%
+this is we want that to be equal zero
+ 
+
+ align:start position:0%
+this is we want that to be equal zero
+and this thing is like implicitly a
+
+ align:start position:0%
+and this thing is like implicitly a
+ 
+
+ align:start position:0%
+and this thing is like implicitly a
+function of the V's the V naught value
+
+ align:start position:0%
+function of the V's the V naught value
+ 
+
+ align:start position:0%
+function of the V's the V naught value
+so we get right if you put some if you
+
+ align:start position:0%
+so we get right if you put some if you
+ 
+
+ align:start position:0%
+so we get right if you put some if you
+put the right V naught values in then Z
+
+ align:start position:0%
+put the right V naught values in then Z
+ 
+
+ align:start position:0%
+put the right V naught values in then Z
+Adele would be zero okay so this is what
+
+ align:start position:0%
+Adele would be zero okay so this is what
+ 
+
+ align:start position:0%
+Adele would be zero okay so this is what
+we're really trying to solve now this is
+
+ align:start position:0%
+we're really trying to solve now this is
+ 
+
+ align:start position:0%
+we're really trying to solve now this is
+to get see eval we have to solve this
+
+ align:start position:0%
+to get see eval we have to solve this
+ 
+
+ align:start position:0%
+to get see eval we have to solve this
+system differential equations so it's a
+
+ align:start position:0%
+system differential equations so it's a
+ 
+
+ align:start position:0%
+system differential equations so it's a
+little complicated to go from V naught
+
+ align:start position:0%
+little complicated to go from V naught
+ 
+
+ align:start position:0%
+little complicated to go from V naught
+to Z all but we can do it as we have OD
+
+ align:start position:0%
+to Z all but we can do it as we have OD
+ 
+
+ align:start position:0%
+to Z all but we can do it as we have OD
+4 5 so we can write up a function to do
+
+ align:start position:0%
+4 5 so we can write up a function to do
+ 
+
+ align:start position:0%
+4 5 so we can write up a function to do
+this running out words
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let's try to write the
+
+ align:start position:0%
+all right so let's try to write the
+ 
+
+ align:start position:0%
+all right so let's try to write the
+program so we want to front write the
+
+ align:start position:0%
+program so we want to front write the
+ 
+
+ align:start position:0%
+program so we want to front write the
+program G right so we want to write Z
+
+ align:start position:0%
+program G right so we want to write Z
+ 
+
+ align:start position:0%
+program G right so we want to write Z
+Val is equal to G you know okay
+
+ align:start position:0%
+Val is equal to G you know okay
+ 
+
+ align:start position:0%
+Val is equal to G you know okay
+and that's striking what this function
+
+ align:start position:0%
+and that's striking what this function
+ 
+
+ align:start position:0%
+and that's striking what this function
+is so we're going to the meat of this is
+
+ align:start position:0%
+is so we're going to the meat of this is
+ 
+
+ align:start position:0%
+is so we're going to the meat of this is
+we answer to solve a differential
+
+ align:start position:0%
+we answer to solve a differential
+ 
+
+ align:start position:0%
+we answer to solve a differential
+equation at IVP so somewhere here we
+
+ align:start position:0%
+equation at IVP so somewhere here we
+ 
+
+ align:start position:0%
+equation at IVP so somewhere here we
+have to go to you for five call what is
+
+ align:start position:0%
+have to go to you for five call what is
+ 
+
+ align:start position:0%
+have to go to you for five call what is
+OD or five computing it's computing the
+
+ align:start position:0%
+OD or five computing it's computing the
+ 
+
+ align:start position:0%
+OD or five computing it's computing the
+position the expositions and the C
+
+ align:start position:0%
+position the expositions and the C
+ 
+
+ align:start position:0%
+position the expositions and the C
+prediction C positions right and it's
+
+ align:start position:0%
+prediction C positions right and it's
+ 
+
+ align:start position:0%
+prediction C positions right and it's
+gonna use some function f which was lost
+
+ align:start position:0%
+gonna use some function f which was lost
+ 
+
+ align:start position:0%
+gonna use some function f which was lost
+in here nope
+
+ align:start position:0%
+in here nope
+ 
+
+ align:start position:0%
+in here nope
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+sorry it's under the bow here I'm
+
+ align:start position:0%
+sorry it's under the bow here I'm
+ 
+
+ align:start position:0%
+sorry it's under the bow here I'm
+terrible board worker so this is our
+
+ align:start position:0%
+terrible board worker so this is our
+ 
+
+ align:start position:0%
+terrible board worker so this is our
+function f that's my right yeah so it's
+
+ align:start position:0%
+function f that's my right yeah so it's
+ 
+
+ align:start position:0%
+function f that's my right yeah so it's
+really F tilde slide that's the function
+
+ align:start position:0%
+really F tilde slide that's the function
+ 
+
+ align:start position:0%
+really F tilde slide that's the function
+that I'm gonna integrate and I can't
+
+ align:start position:0%
+that I'm gonna integrate and I can't
+ 
+
+ align:start position:0%
+that I'm gonna integrate and I can't
+remember that what are the arguments but
+
+ align:start position:0%
+remember that what are the arguments but
+ 
+
+ align:start position:0%
+remember that what are the arguments but
+it's me something like from zero to L
+
+ align:start position:0%
+it's me something like from zero to L
+ 
+
+ align:start position:0%
+it's me something like from zero to L
+and then I have to give it a why not and
+
+ align:start position:0%
+and then I have to give it a why not and
+ 
+
+ align:start position:0%
+and then I have to give it a why not and
+then we did some other stuff out there
+
+ align:start position:0%
+then we did some other stuff out there
+ 
+
+ align:start position:0%
+then we did some other stuff out there
+all right do you guys remember the ODU
+
+ align:start position:0%
+all right do you guys remember the ODU
+ 
+
+ align:start position:0%
+all right do you guys remember the ODU
+for five his diet is very water remember
+
+ align:start position:0%
+for five his diet is very water remember
+ 
+
+ align:start position:0%
+for five his diet is very water remember
+okay so I need to specify the why not
+
+ align:start position:0%
+okay so I need to specify the why not
+ 
+
+ align:start position:0%
+okay so I need to specify the why not
+so why not it's gonna be equal to the
+
+ align:start position:0%
+so why not it's gonna be equal to the
+ 
+
+ align:start position:0%
+so why not it's gonna be equal to the
+initial value of Z altitude so it's
+
+ align:start position:0%
+initial value of Z altitude so it's
+ 
+
+ align:start position:0%
+initial value of Z altitude so it's
+gonna be H and then it's the initial
+
+ align:start position:0%
+gonna be H and then it's the initial
+ 
+
+ align:start position:0%
+gonna be H and then it's the initial
+value of BX so I don't know what that is
+
+ align:start position:0%
+value of BX so I don't know what that is
+ 
+
+ align:start position:0%
+value of BX so I don't know what that is
+but it's funny it's maybe that's what
+
+ align:start position:0%
+but it's funny it's maybe that's what
+ 
+
+ align:start position:0%
+but it's funny it's maybe that's what
+called you not and then I haven't I do
+
+ align:start position:0%
+called you not and then I haven't I do
+ 
+
+ align:start position:0%
+called you not and then I haven't I do
+have one more condition here that V Z is
+
+ align:start position:0%
+have one more condition here that V Z is
+ 
+
+ align:start position:0%
+have one more condition here that V Z is
+related to V X so I can use that so I
+
+ align:start position:0%
+related to V X so I can use that so I
+ 
+
+ align:start position:0%
+related to V X so I can use that so I
+can have the last one be the square root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's that's the line for what y
+
+ align:start position:0%
+so that's that's the line for what y
+ 
+
+ align:start position:0%
+so that's that's the line for what y
+know it is and then I saw this and then
+
+ align:start position:0%
+know it is and then I saw this and then
+ 
+
+ align:start position:0%
+know it is and then I saw this and then
+I write the number of steps and the time
+
+ align:start position:0%
+I write the number of steps and the time
+ 
+
+ align:start position:0%
+I write the number of steps and the time
+stepping program that did in order to
+
+ align:start position:0%
+stepping program that did in order to
+ 
+
+ align:start position:0%
+stepping program that did in order to
+get here was X 2x stepping in this case
+
+ align:start position:0%
+get here was X 2x stepping in this case
+ 
+
+ align:start position:0%
+get here was X 2x stepping in this case
+I'm steps is equal to the land x and z
+
+ align:start position:0%
+I'm steps is equal to the land x and z
+ 
+
+ align:start position:0%
+I'm steps is equal to the land x and z
+Val is equal to z vac
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the function that you would
+
+ align:start position:0%
+so that's the function that you would
+ 
+
+ align:start position:0%
+so that's the function that you would
+feed to f solve and your correct value
+
+ align:start position:0%
+feed to f solve and your correct value
+ 
+
+ align:start position:0%
+feed to f solve and your correct value
+of VX 0 is the one that makes CL 0 which
+
+ align:start position:0%
+of VX 0 is the one that makes CL 0 which
+ 
+
+ align:start position:0%
+of VX 0 is the one that makes CL 0 which
+is what f stuff tries to do yeah you can
+
+ align:start position:0%
+is what f stuff tries to do yeah you can
+ 
+
+ align:start position:0%
+is what f stuff tries to do yeah you can
+but in the physical problem yeah usually
+
+ align:start position:0%
+but in the physical problem yeah usually
+ 
+
+ align:start position:0%
+but in the physical problem yeah usually
+canons always shoot upwards so what is
+
+ align:start position:0%
+canons always shoot upwards so what is
+ 
+
+ align:start position:0%
+canons always shoot upwards so what is
+the shippers oh yeah it could be either
+
+ align:start position:0%
+the shippers oh yeah it could be either
+ 
+
+ align:start position:0%
+the shippers oh yeah it could be either
+way yeah and in fact in this problem you
+
+ align:start position:0%
+way yeah and in fact in this problem you
+ 
+
+ align:start position:0%
+way yeah and in fact in this problem you
+might do better to change instead of
+
+ align:start position:0%
+might do better to change instead of
+ 
+
+ align:start position:0%
+might do better to change instead of
+using VX not as your unknown you might
+
+ align:start position:0%
+using VX not as your unknown you might
+ 
+
+ align:start position:0%
+using VX not as your unknown you might
+have a change to theta the angle the
+
+ align:start position:0%
+have a change to theta the angle the
+ 
+
+ align:start position:0%
+have a change to theta the angle the
+elevation angle the Canon and that would
+
+ align:start position:0%
+elevation angle the Canon and that would
+ 
+
+ align:start position:0%
+elevation angle the Canon and that would
+be more physical of what the actual user
+
+ align:start position:0%
+be more physical of what the actual user
+ 
+
+ align:start position:0%
+be more physical of what the actual user
+of the cannon is using their adjusting
+
+ align:start position:0%
+of the cannon is using their adjusting
+ 
+
+ align:start position:0%
+of the cannon is using their adjusting
+theta and not adjusting to the X here
+
+ align:start position:0%
+theta and not adjusting to the X here
+ 
+
+ align:start position:0%
+theta and not adjusting to the X here
+okay it's no problem actually right from
+
+ align:start position:0%
+okay it's no problem actually right from
+ 
+
+ align:start position:0%
+okay it's no problem actually right from
+the point of view of the F solve you can
+
+ align:start position:0%
+the point of view of the F solve you can
+ 
+
+ align:start position:0%
+the point of view of the F solve you can
+make this theta instead and then you'd
+
+ align:start position:0%
+make this theta instead and then you'd
+ 
+
+ align:start position:0%
+make this theta instead and then you'd
+have this be V naught times cosine theta
+
+ align:start position:0%
+have this be V naught times cosine theta
+ 
+
+ align:start position:0%
+have this be V naught times cosine theta
+and this VV v naught times sine of theta
+
+ align:start position:0%
+and this VV v naught times sine of theta
+ 
+
+ align:start position:0%
+and this VV v naught times sine of theta
+and then would work just as well do you
+
+ align:start position:0%
+and then would work just as well do you
+ 
+
+ align:start position:0%
+and then would work just as well do you
+the solution all right so that's the
+
+ align:start position:0%
+the solution all right so that's the
+ 
+
+ align:start position:0%
+the solution all right so that's the
+shooting method so this thing all this
+
+ align:start position:0%
+shooting method so this thing all this
+ 
+
+ align:start position:0%
+shooting method so this thing all this
+function G is the G that's going to be
+
+ align:start position:0%
+function G is the G that's going to be
+ 
+
+ align:start position:0%
+function G is the G that's going to be
+you'll have F solve so it's gonna say
+
+ align:start position:0%
+you'll have F solve so it's gonna say
+ 
+
+ align:start position:0%
+you'll have F solve so it's gonna say
+the X X naught is equal to F solve of G
+
+ align:start position:0%
+the X X naught is equal to F solve of G
+ 
+
+ align:start position:0%
+the X X naught is equal to F solve of G
+and then you have to have a guess all
+
+ align:start position:0%
+and then you have to have a guess all
+ 
+
+ align:start position:0%
+and then you have to have a guess all
+right for ourselves so that's how you
+
+ align:start position:0%
+right for ourselves so that's how you
+ 
+
+ align:start position:0%
+right for ourselves so that's how you
+would invoke this function all right and
+
+ align:start position:0%
+would invoke this function all right and
+ 
+
+ align:start position:0%
+would invoke this function all right and
+and so if we want to figure operation
+
+ align:start position:0%
+and so if we want to figure operation
+ 
+
+ align:start position:0%
+and so if we want to figure operation
+count of how many operations this is to
+
+ align:start position:0%
+count of how many operations this is to
+ 
+
+ align:start position:0%
+count of how many operations this is to
+find the solution this way how's it
+
+ align:start position:0%
+find the solution this way how's it
+ 
+
+ align:start position:0%
+find the solution this way how's it
+going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the ideas okay about how many
+
+ align:start position:0%
+and the ideas okay about how many
+ 
+
+ align:start position:0%
+and the ideas okay about how many
+iterations is to say to solve an eau de
+
+ align:start position:0%
+iterations is to say to solve an eau de
+ 
+
+ align:start position:0%
+iterations is to say to solve an eau de
+ivb that depends on the step size right
+
+ align:start position:0%
+ivb that depends on the step size right
+ 
+
+ align:start position:0%
+ivb that depends on the step size right
+it's adaptive usually dr. stepping so
+
+ align:start position:0%
+it's adaptive usually dr. stepping so
+ 
+
+ align:start position:0%
+it's adaptive usually dr. stepping so
+you you have some experience to that
+
+ align:start position:0%
+you you have some experience to that
+ 
+
+ align:start position:0%
+you you have some experience to that
+maybe 100 steps something like that this
+
+ align:start position:0%
+maybe 100 steps something like that this
+ 
+
+ align:start position:0%
+maybe 100 steps something like that this
+is usually enough maybe maybe thousand
+
+ align:start position:0%
+is usually enough maybe maybe thousand
+ 
+
+ align:start position:0%
+is usually enough maybe maybe thousand
+if it's not stiff and then how how many
+
+ align:start position:0%
+if it's not stiff and then how how many
+ 
+
+ align:start position:0%
+if it's not stiff and then how how many
+iterations does it take F solve this
+
+ align:start position:0%
+iterations does it take F solve this
+ 
+
+ align:start position:0%
+iterations does it take F solve this
+solve something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tenth
+
+ align:start position:0%
+tenth
+ 
+
+ align:start position:0%
+tenth
+okay so you have maybe a thousand time
+
+ align:start position:0%
+okay so you have maybe a thousand time
+ 
+
+ align:start position:0%
+okay so you have maybe a thousand time
+steps maybe ten ten iterations means ten
+
+ align:start position:0%
+steps maybe ten ten iterations means ten
+ 
+
+ align:start position:0%
+steps maybe ten ten iterations means ten
+different value initial values that you
+
+ align:start position:0%
+different value initial values that you
+ 
+
+ align:start position:0%
+different value initial values that you
+try before you before you converts the
+
+ align:start position:0%
+try before you before you converts the
+ 
+
+ align:start position:0%
+try before you before you converts the
+solution and then you may have to
+
+ align:start position:0%
+solution and then you may have to
+ 
+
+ align:start position:0%
+solution and then you may have to
+actually compute the Jacobian of G right
+
+ align:start position:0%
+actually compute the Jacobian of G right
+ 
+
+ align:start position:0%
+actually compute the Jacobian of G right
+inside F soffits gonna use the Newton
+
+ align:start position:0%
+inside F soffits gonna use the Newton
+ 
+
+ align:start position:0%
+inside F soffits gonna use the Newton
+newton raphson step it's going to need
+
+ align:start position:0%
+newton raphson step it's going to need
+ 
+
+ align:start position:0%
+newton raphson step it's going to need
+the Jacobian of G the Jacobian of G
+
+ align:start position:0%
+the Jacobian of G the Jacobian of G
+ 
+
+ align:start position:0%
+the Jacobian of G the Jacobian of G
+takes the number of unknowns times
+
+ align:start position:0%
+takes the number of unknowns times
+ 
+
+ align:start position:0%
+takes the number of unknowns times
+number of function evaluations right it
+
+ align:start position:0%
+number of function evaluations right it
+ 
+
+ align:start position:0%
+number of function evaluations right it
+took computed by finite differences
+
+ align:start position:0%
+took computed by finite differences
+ 
+
+ align:start position:0%
+took computed by finite differences
+maybe two times that number so it's
+
+ align:start position:0%
+maybe two times that number so it's
+ 
+
+ align:start position:0%
+maybe two times that number so it's
+gonna be something like n squared will
+
+ align:start position:0%
+gonna be something like n squared will
+ 
+
+ align:start position:0%
+gonna be something like n squared will
+be and N squared to evaluate the
+
+ align:start position:0%
+be and N squared to evaluate the
+ 
+
+ align:start position:0%
+be and N squared to evaluate the
+Jacobian takes n operations to evaluate
+
+ align:start position:0%
+Jacobian takes n operations to evaluate
+ 
+
+ align:start position:0%
+Jacobian takes n operations to evaluate
+half so it would have been where n is
+
+ align:start position:0%
+half so it would have been where n is
+ 
+
+ align:start position:0%
+half so it would have been where n is
+number variables and times that to the
+
+ align:start position:0%
+number variables and times that to the
+ 
+
+ align:start position:0%
+number variables and times that to the
+Jacobian so if you like order number
+
+ align:start position:0%
+Jacobian so if you like order number
+ 
+
+ align:start position:0%
+Jacobian so if you like order number
+variables squared times ten times a
+
+ align:start position:0%
+variables squared times ten times a
+ 
+
+ align:start position:0%
+variables squared times ten times a
+thousand it's kind of order of the cost
+
+ align:start position:0%
+thousand it's kind of order of the cost
+ 
+
+ align:start position:0%
+thousand it's kind of order of the cost
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and that's and it's only a thousand
+
+ align:start position:0%
+and that's and it's only a thousand
+ 
+
+ align:start position:0%
+and that's and it's only a thousand
+because it's only that cost because we
+
+ align:start position:0%
+because it's only that cost because we
+ 
+
+ align:start position:0%
+because it's only that cost because we
+can do explicit solver if you had to do
+
+ align:start position:0%
+can do explicit solver if you had to do
+ 
+
+ align:start position:0%
+can do explicit solver if you had to do
+an implicit OD solution to be a lot more
+
+ align:start position:0%
+an implicit OD solution to be a lot more
+ 
+
+ align:start position:0%
+an implicit OD solution to be a lot more
+right because you'd have to compute a
+
+ align:start position:0%
+right because you'd have to compute a
+ 
+
+ align:start position:0%
+right because you'd have to compute a
+jacobians more often alright so it's fun
+
+ align:start position:0%
+jacobians more often alright so it's fun
+ 
+
+ align:start position:0%
+jacobians more often alright so it's fun
+okay so this is a shooting method you
+
+ align:start position:0%
+okay so this is a shooting method you
+ 
+
+ align:start position:0%
+okay so this is a shooting method you
+guys should all do this no trouble
+
+ align:start position:0%
+guys should all do this no trouble
+ 
+
+ align:start position:0%
+guys should all do this no trouble
+conceptually this is not so different
+
+ align:start position:0%
+conceptually this is not so different
+ 
+
+ align:start position:0%
+conceptually this is not so different
+than the homework problem you did where
+
+ align:start position:0%
+than the homework problem you did where
+ 
+
+ align:start position:0%
+than the homework problem you did where
+you did an optimization of the parameter
+
+ align:start position:0%
+you did an optimization of the parameter
+ 
+
+ align:start position:0%
+you did an optimization of the parameter
+values remember she had some
+
+ align:start position:0%
+values remember she had some
+ 
+
+ align:start position:0%
+values remember she had some
+differential equations and you have to
+
+ align:start position:0%
+differential equations and you have to
+ 
+
+ align:start position:0%
+differential equations and you have to
+devise the parameters to try to find the
+
+ align:start position:0%
+devise the parameters to try to find the
+ 
+
+ align:start position:0%
+devise the parameters to try to find the
+best solutions here it's instead of
+
+ align:start position:0%
+best solutions here it's instead of
+ 
+
+ align:start position:0%
+best solutions here it's instead of
+optimizing them you're doing F solve
+
+ align:start position:0%
+optimizing them you're doing F solve
+ 
+
+ align:start position:0%
+optimizing them you're doing F solve
+you're trying to solve them to make
+
+ align:start position:0%
+you're trying to solve them to make
+ 
+
+ align:start position:0%
+you're trying to solve them to make
+something happen
+
+ align:start position:0%
+something happen
+ 
+
+ align:start position:0%
+something happen
+okay now how can this run into troubles
+
+ align:start position:0%
+okay now how can this run into troubles
+ 
+
+ align:start position:0%
+okay now how can this run into troubles
+why would the shooting problem not a
+
+ align:start position:0%
+why would the shooting problem not a
+ 
+
+ align:start position:0%
+why would the shooting problem not a
+cheesy method not always work everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so in a common case where that
+
+ align:start position:0%
+okay so in a common case where that
+ 
+
+ align:start position:0%
+okay so in a common case where that
+might happen be if your OD system was
+
+ align:start position:0%
+might happen be if your OD system was
+ 
+
+ align:start position:0%
+might happen be if your OD system was
+unstable right or your your OD solution
+
+ align:start position:0%
+unstable right or your your OD solution
+ 
+
+ align:start position:0%
+unstable right or your your OD solution
+method was not numerically unstable in
+
+ align:start position:0%
+method was not numerically unstable in
+ 
+
+ align:start position:0%
+method was not numerically unstable in
+either of those cases who knows what
+
+ align:start position:0%
+either of those cases who knows what
+ 
+
+ align:start position:0%
+either of those cases who knows what
+you're getting and actually don't know
+
+ align:start position:0%
+you're getting and actually don't know
+ 
+
+ align:start position:0%
+you're getting and actually don't know
+the solutions even real
+
+ align:start position:0%
+the solutions even real
+ 
+
+ align:start position:0%
+the solutions even real
+you don't know if the computed final
+
+ align:start position:0%
+you don't know if the computed final
+ 
+
+ align:start position:0%
+you don't know if the computed final
+value ZL is really what corresponds to
+
+ align:start position:0%
+value ZL is really what corresponds to
+ 
+
+ align:start position:0%
+value ZL is really what corresponds to
+that input value of VX 0 because if you
+
+ align:start position:0%
+that input value of VX 0 because if you
+ 
+
+ align:start position:0%
+that input value of VX 0 because if you
+have a big kind of numerical sensitivity
+
+ align:start position:0%
+have a big kind of numerical sensitivity
+ 
+
+ align:start position:0%
+have a big kind of numerical sensitivity
+and instability so that's one kind of
+
+ align:start position:0%
+and instability so that's one kind of
+ 
+
+ align:start position:0%
+and instability so that's one kind of
+problem so this is just like all the OD
+
+ align:start position:0%
+problem so this is just like all the OD
+ 
+
+ align:start position:0%
+problem so this is just like all the OD
+IBP problems if the Odie's problem
+
+ align:start position:0%
+IBP problems if the Odie's problem
+ 
+
+ align:start position:0%
+IBP problems if the Odie's problem
+intrinsically is unstable in a big way
+
+ align:start position:0%
+intrinsically is unstable in a big way
+ 
+
+ align:start position:0%
+intrinsically is unstable in a big way
+you're in trouble because your ears are
+
+ align:start position:0%
+you're in trouble because your ears are
+ 
+
+ align:start position:0%
+you're in trouble because your ears are
+going to amplify and then also if you
+
+ align:start position:0%
+going to amplify and then also if you
+ 
+
+ align:start position:0%
+going to amplify and then also if you
+use if you have a problem where the
+
+ align:start position:0%
+use if you have a problem where the
+ 
+
+ align:start position:0%
+use if you have a problem where the
+Delta T's are too large compared to the
+
+ align:start position:0%
+Delta T's are too large compared to the
+ 
+
+ align:start position:0%
+Delta T's are too large compared to the
+two this numerical stability of the
+
+ align:start position:0%
+two this numerical stability of the
+ 
+
+ align:start position:0%
+two this numerical stability of the
+solver you also have a problem right so
+
+ align:start position:0%
+solver you also have a problem right so
+ 
+
+ align:start position:0%
+solver you also have a problem right so
+those are two kinds of problem so we
+
+ align:start position:0%
+those are two kinds of problem so we
+ 
+
+ align:start position:0%
+those are two kinds of problem so we
+always have an OD each solutions and so
+
+ align:start position:0%
+always have an OD each solutions and so
+ 
+
+ align:start position:0%
+always have an OD each solutions and so
+you might actually want to use this
+
+ align:start position:0%
+you might actually want to use this
+ 
+
+ align:start position:0%
+you might actually want to use this
+method for some regular Oh de vie Biv
+
+ align:start position:0%
+method for some regular Oh de vie Biv
+ 
+
+ align:start position:0%
+method for some regular Oh de vie Biv
+problems so for example if you had a
+
+ align:start position:0%
+problems so for example if you had a
+ 
+
+ align:start position:0%
+problems so for example if you had a
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+I don't want to wreck my beautiful
+
+ align:start position:0%
+I don't want to wreck my beautiful
+ 
+
+ align:start position:0%
+I don't want to wreck my beautiful
+artwork okay you guys did this if you
+
+ align:start position:0%
+artwork okay you guys did this if you
+ 
+
+ align:start position:0%
+artwork okay you guys did this if you
+had a problem that said dy DT is equal
+
+ align:start position:0%
+had a problem that said dy DT is equal
+ 
+
+ align:start position:0%
+had a problem that said dy DT is equal
+to 10 to the sixth times y yes yes well
+
+ align:start position:0%
+to 10 to the sixth times y yes yes well
+ 
+
+ align:start position:0%
+to 10 to the sixth times y yes yes well
+two ways so you could either solve it
+
+ align:start position:0%
+two ways so you could either solve it
+ 
+
+ align:start position:0%
+two ways so you could either solve it
+for repeated values different initial
+
+ align:start position:0%
+for repeated values different initial
+ 
+
+ align:start position:0%
+for repeated values different initial
+values of V naught and by find a
+
+ align:start position:0%
+values of V naught and by find a
+ 
+
+ align:start position:0%
+values of V naught and by find a
+difference get the Jacobian or you could
+
+ align:start position:0%
+difference get the Jacobian or you could
+ 
+
+ align:start position:0%
+difference get the Jacobian or you could
+use the sensitivity method that we did
+
+ align:start position:0%
+use the sensitivity method that we did
+ 
+
+ align:start position:0%
+use the sensitivity method that we did
+in the second problem a problem set it
+
+ align:start position:0%
+in the second problem a problem set it
+ 
+
+ align:start position:0%
+in the second problem a problem set it
+go and get analytically got the
+
+ align:start position:0%
+go and get analytically got the
+ 
+
+ align:start position:0%
+go and get analytically got the
+derivatives are respect to the
+
+ align:start position:0%
+derivatives are respect to the
+ 
+
+ align:start position:0%
+derivatives are respect to the
+parameters either way but either way
+
+ align:start position:0%
+parameters either way but either way
+ 
+
+ align:start position:0%
+parameters either way but either way
+it's a lot of work yeah so the the
+
+ align:start position:0%
+it's a lot of work yeah so the the
+ 
+
+ align:start position:0%
+it's a lot of work yeah so the the
+supposed a problem like this this is a
+
+ align:start position:0%
+supposed a problem like this this is a
+ 
+
+ align:start position:0%
+supposed a problem like this this is a
+pretty simple problem right and you want
+
+ align:start position:0%
+pretty simple problem right and you want
+ 
+
+ align:start position:0%
+pretty simple problem right and you want
+to suppose you wanted to go all the way
+
+ align:start position:0%
+to suppose you wanted to go all the way
+ 
+
+ align:start position:0%
+to suppose you wanted to go all the way
+out to T equals one now the problem is
+
+ align:start position:0%
+out to T equals one now the problem is
+ 
+
+ align:start position:0%
+out to T equals one now the problem is
+that this is a solution of this is a e
+
+ align:start position:0%
+that this is a solution of this is a e
+ 
+
+ align:start position:0%
+that this is a solution of this is a e
+to attend to this x times T something
+
+ align:start position:0%
+to attend to this x times T something
+ 
+
+ align:start position:0%
+to attend to this x times T something
+right so this is really not looking so
+
+ align:start position:0%
+right so this is really not looking so
+ 
+
+ align:start position:0%
+right so this is really not looking so
+great as a as a problem to solve this is
+
+ align:start position:0%
+great as a as a problem to solve this is
+ 
+
+ align:start position:0%
+great as a as a problem to solve this is
+about as unstable as you can get the
+
+ align:start position:0%
+about as unstable as you can get the
+ 
+
+ align:start position:0%
+about as unstable as you can get the
+tiniest little deviation anywhere along
+
+ align:start position:0%
+tiniest little deviation anywhere along
+ 
+
+ align:start position:0%
+tiniest little deviation anywhere along
+the way it's going to make the thing
+
+ align:start position:0%
+the way it's going to make the thing
+ 
+
+ align:start position:0%
+the way it's going to make the thing
+blow up and so this this is not so great
+
+ align:start position:0%
+blow up and so this this is not so great
+ 
+
+ align:start position:0%
+blow up and so this this is not so great
+and so even if the initial condition is
+
+ align:start position:0%
+and so even if the initial condition is
+ 
+
+ align:start position:0%
+and so even if the initial condition is
+that Y of T naught is equal ten to minus
+
+ align:start position:0%
+that Y of T naught is equal ten to minus
+ 
+
+ align:start position:0%
+that Y of T naught is equal ten to minus
+twelve so actually this is not so bad
+
+ align:start position:0%
+twelve so actually this is not so bad
+ 
+
+ align:start position:0%
+twelve so actually this is not so bad
+this is still a hard to solve
+
+ align:start position:0%
+this is still a hard to solve
+ 
+
+ align:start position:0%
+this is still a hard to solve
+numerically but you could flip it around
+
+ align:start position:0%
+numerically but you could flip it around
+ 
+
+ align:start position:0%
+numerically but you could flip it around
+and treat it as a shooting problem and
+
+ align:start position:0%
+and treat it as a shooting problem and
+ 
+
+ align:start position:0%
+and treat it as a shooting problem and
+solve it reverse so you could change
+
+ align:start position:0%
+solve it reverse so you could change
+ 
+
+ align:start position:0%
+solve it reverse so you could change
+variables that U is equal to negative T
+
+ align:start position:0%
+variables that U is equal to negative T
+ 
+
+ align:start position:0%
+variables that U is equal to negative T
+and then you'd have dy D you
+
+ align:start position:0%
+and then you'd have dy D you
+ 
+
+ align:start position:0%
+and then you'd have dy D you
+is equal to negative 10 to the 6 times y
+
+ align:start position:0%
+is equal to negative 10 to the 6 times y
+ 
+
+ align:start position:0%
+is equal to negative 10 to the 6 times y
+and now this is really stable and now
+
+ align:start position:0%
+and now this is really stable and now
+ 
+
+ align:start position:0%
+and now this is really stable and now
+you might want to integrate in so from
+
+ align:start position:0%
+you might want to integrate in so from
+ 
+
+ align:start position:0%
+you might want to integrate in so from
+its so the original question was what is
+
+ align:start position:0%
+its so the original question was what is
+ 
+
+ align:start position:0%
+its so the original question was what is
+why I want from the in the differential
+
+ align:start position:0%
+why I want from the in the differential
+ 
+
+ align:start position:0%
+why I want from the in the differential
+equations you could do the same you
+
+ align:start position:0%
+equations you could do the same you
+ 
+
+ align:start position:0%
+equations you could do the same you
+could do a reverse and say I'm gonna
+
+ align:start position:0%
+could do a reverse and say I'm gonna
+ 
+
+ align:start position:0%
+could do a reverse and say I'm gonna
+guess Y of 1 is equal to Y gasps and I'm
+
+ align:start position:0%
+guess Y of 1 is equal to Y gasps and I'm
+ 
+
+ align:start position:0%
+guess Y of 1 is equal to Y gasps and I'm
+gonna integrate it and demand that this
+
+ align:start position:0%
+gonna integrate it and demand that this
+ 
+
+ align:start position:0%
+gonna integrate it and demand that this
+is my final condition so now it's
+
+ align:start position:0%
+is my final condition so now it's
+ 
+
+ align:start position:0%
+is my final condition so now it's
+actually why I choose dumb confusing
+
+ align:start position:0%
+actually why I choose dumb confusing
+ 
+
+ align:start position:0%
+actually why I choose dumb confusing
+myself if I have negative 1 I guess I
+
+ align:start position:0%
+myself if I have negative 1 I guess I
+ 
+
+ align:start position:0%
+myself if I have negative 1 I guess I
+just put the sine T and hmm they only
+
+ align:start position:0%
+just put the sine T and hmm they only
+ 
+
+ align:start position:0%
+just put the sine T and hmm they only
+had just failed make it easier this way
+
+ align:start position:0%
+had just failed make it easier this way
+ 
+
+ align:start position:0%
+had just failed make it easier this way
+I'm minus T says the same derivative so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y 0 2 I guess and y 1 is too much so
+
+ align:start position:0%
+y 0 2 I guess and y 1 is too much so
+ 
+
+ align:start position:0%
+y 0 2 I guess and y 1 is too much so
+this is my final condition that I'm
+
+ align:start position:0%
+this is my final condition that I'm
+ 
+
+ align:start position:0%
+this is my final condition that I'm
+trying to shoot to and I'll bury the Y
+
+ align:start position:0%
+trying to shoot to and I'll bury the Y
+ 
+
+ align:start position:0%
+trying to shoot to and I'll bury the Y
+guests integrate and now I have a
+
+ align:start position:0%
+guests integrate and now I have a
+ 
+
+ align:start position:0%
+guests integrate and now I have a
+perfectly stable differential equation I
+
+ align:start position:0%
+perfectly stable differential equation I
+ 
+
+ align:start position:0%
+perfectly stable differential equation I
+can solve it okay so this the same idea
+
+ align:start position:0%
+can solve it okay so this the same idea
+ 
+
+ align:start position:0%
+can solve it okay so this the same idea
+of shooting it comes up in mobile
+
+ align:start position:0%
+of shooting it comes up in mobile
+ 
+
+ align:start position:0%
+of shooting it comes up in mobile
+applications and this whole thing about
+
+ align:start position:0%
+applications and this whole thing about
+ 
+
+ align:start position:0%
+applications and this whole thing about
+flipping the changes of variables is
+
+ align:start position:0%
+flipping the changes of variables is
+ 
+
+ align:start position:0%
+flipping the changes of variables is
+often extremely useful trick to just
+
+ align:start position:0%
+often extremely useful trick to just
+ 
+
+ align:start position:0%
+often extremely useful trick to just
+recast equations in a way this more
+
+ align:start position:0%
+recast equations in a way this more
+ 
+
+ align:start position:0%
+recast equations in a way this more
+numerically stable to solve as fewer
+
+ align:start position:0%
+numerically stable to solve as fewer
+ 
+
+ align:start position:0%
+numerically stable to solve as fewer
+number equations you can write
+
+ align:start position:0%
+number equations you can write
+ 
+
+ align:start position:0%
+number equations you can write
+explicitly what you want but this takes
+
+ align:start position:0%
+explicitly what you want but this takes
+ 
+
+ align:start position:0%
+explicitly what you want but this takes
+some cleverness to know how to to recast
+
+ align:start position:0%
+some cleverness to know how to to recast
+ 
+
+ align:start position:0%
+some cleverness to know how to to recast
+them all right so so this this motivate
+
+ align:start position:0%
+them all right so so this this motivate
+ 
+
+ align:start position:0%
+them all right so so this this motivate
+example is is a good one yeah you could
+
+ align:start position:0%
+example is is a good one yeah you could
+ 
+
+ align:start position:0%
+example is is a good one yeah you could
+I was just trying to get back in the
+
+ align:start position:0%
+I was just trying to get back in the
+ 
+
+ align:start position:0%
+I was just trying to get back in the
+form of T naught equals 0 I guess I
+
+ align:start position:0%
+form of T naught equals 0 I guess I
+ 
+
+ align:start position:0%
+form of T naught equals 0 I guess I
+could have T naught equals negative 1
+
+ align:start position:0%
+could have T naught equals negative 1
+ 
+
+ align:start position:0%
+could have T naught equals negative 1
+and do it I just can do the arithmetic
+
+ align:start position:0%
+and do it I just can do the arithmetic
+ 
+
+ align:start position:0%
+and do it I just can do the arithmetic
+on the work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why of zeros know but that just start
+
+ align:start position:0%
+why of zeros know but that just start
+ 
+
+ align:start position:0%
+why of zeros know but that just start
+from T naught equals negative one so I
+
+ align:start position:0%
+from T naught equals negative one so I
+ 
+
+ align:start position:0%
+from T naught equals negative one so I
+could do sorry so suppose I did u equals
+
+ align:start position:0%
+could do sorry so suppose I did u equals
+ 
+
+ align:start position:0%
+could do sorry so suppose I did u equals
+negative T dy D u is equal to theta 1006
+
+ align:start position:0%
+negative T dy D u is equal to theta 1006
+ 
+
+ align:start position:0%
+negative T dy D u is equal to theta 1006
+why and I know Y of Y of 0 is equal to
+
+ align:start position:0%
+why and I know Y of Y of 0 is equal to
+ 
+
+ align:start position:0%
+why and I know Y of Y of 0 is equal to
+know what do I know yeah Y of 0 is equal
+
+ align:start position:0%
+know what do I know yeah Y of 0 is equal
+ 
+
+ align:start position:0%
+know what do I know yeah Y of 0 is equal
+to 10 to the minus 12 and y of negative
+
+ align:start position:0%
+to 10 to the minus 12 and y of negative
+ 
+
+ align:start position:0%
+to 10 to the minus 12 and y of negative
+1 is equal to I guess and I can
+
+ align:start position:0%
+1 is equal to I guess and I can
+ 
+
+ align:start position:0%
+1 is equal to I guess and I can
+integrate from negative 1 over so this
+
+ align:start position:0%
+integrate from negative 1 over so this
+ 
+
+ align:start position:0%
+integrate from negative 1 over so this
+would be Tino on if I was using a
+
+ align:start position:0%
+would be Tino on if I was using a
+ 
+
+ align:start position:0%
+would be Tino on if I was using a
+shooting method and this would be T
+
+ align:start position:0%
+shooting method and this would be T
+ 
+
+ align:start position:0%
+shooting method and this would be T
+final yeah or you could shift it over by
+
+ align:start position:0%
+final yeah or you could shift it over by
+ 
+
+ align:start position:0%
+final yeah or you could shift it over by
+1 if you want to do the way I did you
+
+ align:start position:0%
+1 if you want to do the way I did you
+ 
+
+ align:start position:0%
+1 if you want to do the way I did you
+know what's all right sorry tell you if
+
+ align:start position:0%
+know what's all right sorry tell you if
+ 
+
+ align:start position:0%
+know what's all right sorry tell you if
+she's all the arithmetic guys getting
+
+ align:start position:0%
+she's all the arithmetic guys getting
+ 
+
+ align:start position:0%
+she's all the arithmetic guys getting
+confused - all right now I wrote this ok
+
+ align:start position:0%
+confused - all right now I wrote this ok
+ 
+
+ align:start position:0%
+confused - all right now I wrote this ok
+another another situation where this
+
+ align:start position:0%
+another another situation where this
+ 
+
+ align:start position:0%
+another another situation where this
+will not work is you can have systems
+
+ align:start position:0%
+will not work is you can have systems
+ 
+
+ align:start position:0%
+will not work is you can have systems
+where you have both positive and
+
+ align:start position:0%
+where you have both positive and
+ 
+
+ align:start position:0%
+where you have both positive and
+negative eigen values of the Jacobian
+
+ align:start position:0%
+negative eigen values of the Jacobian
+ 
+
+ align:start position:0%
+negative eigen values of the Jacobian
+and that means that either way you
+
+ align:start position:0%
+and that means that either way you
+ 
+
+ align:start position:0%
+and that means that either way you
+integrate from plus in the plus T
+
+ align:start position:0%
+integrate from plus in the plus T
+ 
+
+ align:start position:0%
+integrate from plus in the plus T
+direction or the negative T direction
+
+ align:start position:0%
+direction or the negative T direction
+ 
+
+ align:start position:0%
+direction or the negative T direction
+either way it's always unstable right so
+
+ align:start position:0%
+either way it's always unstable right so
+ 
+
+ align:start position:0%
+either way it's always unstable right so
+no matter what you do you're doomed
+
+ align:start position:0%
+no matter what you do you're doomed
+ 
+
+ align:start position:0%
+no matter what you do you're doomed
+right the IBP method is not going to
+
+ align:start position:0%
+right the IBP method is not going to
+ 
+
+ align:start position:0%
+right the IBP method is not going to
+work cuz you're numerically unstable in
+
+ align:start position:0%
+work cuz you're numerically unstable in
+ 
+
+ align:start position:0%
+work cuz you're numerically unstable in
+both directions and so that's kind of a
+
+ align:start position:0%
+both directions and so that's kind of a
+ 
+
+ align:start position:0%
+both directions and so that's kind of a
+really a bummer and it means are all our
+
+ align:start position:0%
+really a bummer and it means are all our
+ 
+
+ align:start position:0%
+really a bummer and it means are all our
+you know our div P methods not going to
+
+ align:start position:0%
+you know our div P methods not going to
+ 
+
+ align:start position:0%
+you know our div P methods not going to
+work for us and so then we have to find
+
+ align:start position:0%
+work for us and so then we have to find
+ 
+
+ align:start position:0%
+work for us and so then we have to find
+a different method but before before I
+
+ align:start position:0%
+a different method but before before I
+ 
+
+ align:start position:0%
+a different method but before before I
+go into that let's just write the more
+
+ align:start position:0%
+go into that let's just write the more
+ 
+
+ align:start position:0%
+go into that let's just write the more
+general version of this ok so this is I
+
+ align:start position:0%
+general version of this ok so this is I
+ 
+
+ align:start position:0%
+general version of this ok so this is I
+think you guys all know this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's write a more general version of
+
+ align:start position:0%
+so let's write a more general version of
+ 
+
+ align:start position:0%
+so let's write a more general version of
+the ODB beefy problem and now will allow
+
+ align:start position:0%
+the ODB beefy problem and now will allow
+ 
+
+ align:start position:0%
+the ODB beefy problem and now will allow
+for the fact that things don't have to
+
+ align:start position:0%
+for the fact that things don't have to
+ 
+
+ align:start position:0%
+for the fact that things don't have to
+be explicit and don't have to be as
+
+ align:start position:0%
+be explicit and don't have to be as
+ 
+
+ align:start position:0%
+be explicit and don't have to be as
+simple as we thought and you could see
+
+ align:start position:0%
+simple as we thought and you could see
+ 
+
+ align:start position:0%
+simple as we thought and you could see
+even in the problem I just did we had a
+
+ align:start position:0%
+even in the problem I just did we had a
+ 
+
+ align:start position:0%
+even in the problem I just did we had a
+V x squared V 2 X square plus B Square
+
+ align:start position:0%
+V x squared V 2 X square plus B Square
+ 
+
+ align:start position:0%
+V x squared V 2 X square plus B Square
+and had to be equal something and so
+
+ align:start position:0%
+and had to be equal something and so
+ 
+
+ align:start position:0%
+and had to be equal something and so
+that's not a simple boundary condition
+
+ align:start position:0%
+that's not a simple boundary condition
+ 
+
+ align:start position:0%
+that's not a simple boundary condition
+like we saw it before so you know more
+
+ align:start position:0%
+like we saw it before so you know more
+ 
+
+ align:start position:0%
+like we saw it before so you know more
+complicated conditions and what you
+
+ align:start position:0%
+complicated conditions and what you
+ 
+
+ align:start position:0%
+complicated conditions and what you
+really can have is a set of equations GN
+
+ align:start position:0%
+really can have is a set of equations GN
+ 
+
+ align:start position:0%
+really can have is a set of equations GN
+of dy DT Y T is equal to 0 and
+
+ align:start position:0%
+of dy DT Y T is equal to 0 and
+ 
+
+ align:start position:0%
+of dy DT Y T is equal to 0 and
+corresponding sort of Q n of dy DT
+
+ align:start position:0%
+corresponding sort of Q n of dy DT
+ 
+
+ align:start position:0%
+corresponding sort of Q n of dy DT
+evaluated at TN y of TN TN is equal to 0
+
+ align:start position:0%
+evaluated at TN y of TN TN is equal to 0
+ 
+
+ align:start position:0%
+evaluated at TN y of TN TN is equal to 0
+says this is the general Oh de system
+
+ align:start position:0%
+says this is the general Oh de system
+ 
+
+ align:start position:0%
+says this is the general Oh de system
+that's written in an implicit form and
+
+ align:start position:0%
+that's written in an implicit form and
+ 
+
+ align:start position:0%
+that's written in an implicit form and
+this has to be true for for all T in the
+
+ align:start position:0%
+this has to be true for for all T in the
+ 
+
+ align:start position:0%
+this has to be true for for all T in the
+domain
+
+ align:start position:0%
+domain
+ 
+
+ align:start position:0%
+domain
+I'll te that are a member of T naught to
+
+ align:start position:0%
+I'll te that are a member of T naught to
+ 
+
+ align:start position:0%
+I'll te that are a member of T naught to
+TF right so all the T's are inside this
+
+ align:start position:0%
+TF right so all the T's are inside this
+ 
+
+ align:start position:0%
+TF right so all the T's are inside this
+interval that we domain we care about
+
+ align:start position:0%
+interval that we domain we care about
+ 
+
+ align:start position:0%
+interval that we domain we care about
+this is the differential equation
+
+ align:start position:0%
+this is the differential equation
+ 
+
+ align:start position:0%
+this is the differential equation
+written is just as general as can be and
+
+ align:start position:0%
+written is just as general as can be and
+ 
+
+ align:start position:0%
+written is just as general as can be and
+n is equal to 1 there's n of these
+
+ align:start position:0%
+n is equal to 1 there's n of these
+ 
+
+ align:start position:0%
+n is equal to 1 there's n of these
+equations yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I just want to make it clear that this
+
+ align:start position:0%
+I just want to make it clear that this
+ 
+
+ align:start position:0%
+I just want to make it clear that this
+is the conditions and this is the
+
+ align:start position:0%
+is the conditions and this is the
+ 
+
+ align:start position:0%
+is the conditions and this is the
+general equation I don't know you can
+
+ align:start position:0%
+general equation I don't know you can
+ 
+
+ align:start position:0%
+general equation I don't know you can
+write it any way you want
+
+ align:start position:0%
+write it any way you want
+ 
+
+ align:start position:0%
+write it any way you want
+so just like some variable letters
+
+ align:start position:0%
+so just like some variable letters
+ 
+
+ align:start position:0%
+so just like some variable letters
+instead of Q I can change this make them
+
+ align:start position:0%
+instead of Q I can change this make them
+ 
+
+ align:start position:0%
+instead of Q I can change this make them
+images yeah and this was this one I'm
+
+ align:start position:0%
+images yeah and this was this one I'm
+ 
+
+ align:start position:0%
+images yeah and this was this one I'm
+just trying to emphasize this one is
+
+ align:start position:0%
+just trying to emphasize this one is
+ 
+
+ align:start position:0%
+just trying to emphasize this one is
+only true at TN only this equation of
+
+ align:start position:0%
+only true at TN only this equation of
+ 
+
+ align:start position:0%
+only true at TN only this equation of
+this equation this is the condition at
+
+ align:start position:0%
+this equation this is the condition at
+ 
+
+ align:start position:0%
+this equation this is the condition at
+one particular time I demand something
+
+ align:start position:0%
+one particular time I demand something
+ 
+
+ align:start position:0%
+one particular time I demand something
+to be true and this is the general
+
+ align:start position:0%
+to be true and this is the general
+ 
+
+ align:start position:0%
+to be true and this is the general
+differential equation has to be true at
+
+ align:start position:0%
+differential equation has to be true at
+ 
+
+ align:start position:0%
+differential equation has to be true at
+all times
+
+ align:start position:0%
+all times
+ 
+
+ align:start position:0%
+all times
+and I need and if if I have n
+
+ align:start position:0%
+and I need and if if I have n
+ 
+
+ align:start position:0%
+and I need and if if I have n
+differentials I need in differential
+
+ align:start position:0%
+differentials I need in differential
+ 
+
+ align:start position:0%
+differentials I need in differential
+equations and in initial conditions by
+
+ align:start position:0%
+equations and in initial conditions by
+ 
+
+ align:start position:0%
+equations and in initial conditions by
+the way you can write the DA EES this
+
+ align:start position:0%
+the way you can write the DA EES this
+ 
+
+ align:start position:0%
+the way you can write the DA EES this
+way as well the differential algebraic
+
+ align:start position:0%
+way as well the differential algebraic
+ 
+
+ align:start position:0%
+way as well the differential algebraic
+equations and then he dos won't have as
+
+ align:start position:0%
+equations and then he dos won't have as
+ 
+
+ align:start position:0%
+equations and then he dos won't have as
+many initial conditions because every
+
+ align:start position:0%
+many initial conditions because every
+ 
+
+ align:start position:0%
+many initial conditions because every
+time you have an algebraic equation
+
+ align:start position:0%
+time you have an algebraic equation
+ 
+
+ align:start position:0%
+time you have an algebraic equation
+instead of a differential equation then
+
+ align:start position:0%
+instead of a differential equation then
+ 
+
+ align:start position:0%
+instead of a differential equation then
+you don't need an initial condition
+
+ align:start position:0%
+you don't need an initial condition
+ 
+
+ align:start position:0%
+you don't need an initial condition
+because the algebraic equation has its
+
+ align:start position:0%
+because the algebraic equation has its
+ 
+
+ align:start position:0%
+because the algebraic equation has its
+own its own condition
+
+ align:start position:0%
+own its own condition
+ 
+
+ align:start position:0%
+own its own condition
+so make sense alright so you can write
+
+ align:start position:0%
+so make sense alright so you can write
+ 
+
+ align:start position:0%
+so make sense alright so you can write
+this kind of in general and just by
+
+ align:start position:0%
+this kind of in general and just by
+ 
+
+ align:start position:0%
+this kind of in general and just by
+depending on how many differentials you
+
+ align:start position:0%
+depending on how many differentials you
+ 
+
+ align:start position:0%
+depending on how many differentials you
+have that's how many conditions you need
+
+ align:start position:0%
+have that's how many conditions you need
+ 
+
+ align:start position:0%
+have that's how many conditions you need
+and you know a lot of times you can
+
+ align:start position:0%
+and you know a lot of times you can
+ 
+
+ align:start position:0%
+and you know a lot of times you can
+write them explicit so you you this
+
+ align:start position:0%
+write them explicit so you you this
+ 
+
+ align:start position:0%
+write them explicit so you you this
+thing is equivalent to dy DT is equal to
+
+ align:start position:0%
+thing is equivalent to dy DT is equal to
+ 
+
+ align:start position:0%
+thing is equivalent to dy DT is equal to
+f of T y you know a lot many times you
+
+ align:start position:0%
+f of T y you know a lot many times you
+ 
+
+ align:start position:0%
+f of T y you know a lot many times you
+can solve for dy DT and write this way
+
+ align:start position:0%
+can solve for dy DT and write this way
+ 
+
+ align:start position:0%
+can solve for dy DT and write this way
+but not always okay all right and the
+
+ align:start position:0%
+but not always okay all right and the
+ 
+
+ align:start position:0%
+but not always okay all right and the
+reason why we need to have n conditions
+
+ align:start position:0%
+reason why we need to have n conditions
+ 
+
+ align:start position:0%
+reason why we need to have n conditions
+is just like when you're doing integrals
+
+ align:start position:0%
+is just like when you're doing integrals
+ 
+
+ align:start position:0%
+is just like when you're doing integrals
+you have n constants of integration
+
+ align:start position:0%
+you have n constants of integration
+ 
+
+ align:start position:0%
+you have n constants of integration
+every time you do an integral you get
+
+ align:start position:0%
+every time you do an integral you get
+ 
+
+ align:start position:0%
+every time you do an integral you get
+one now we have like three and we have n
+
+ align:start position:0%
+one now we have like three and we have n
+ 
+
+ align:start position:0%
+one now we have like three and we have n
+differential equations we'll have any
+
+ align:start position:0%
+differential equations we'll have any
+ 
+
+ align:start position:0%
+differential equations we'll have any
+conditions all right now a bad thing
+
+ align:start position:0%
+conditions all right now a bad thing
+ 
+
+ align:start position:0%
+conditions all right now a bad thing
+about these problems in general is that
+
+ align:start position:0%
+about these problems in general is that
+ 
+
+ align:start position:0%
+about these problems in general is that
+the solutions depend a lot on the
+
+ align:start position:0%
+the solutions depend a lot on the
+ 
+
+ align:start position:0%
+the solutions depend a lot on the
+boundary conditions and in fact you can
+
+ align:start position:0%
+boundary conditions and in fact you can
+ 
+
+ align:start position:0%
+boundary conditions and in fact you can
+write down boundary conditions that are
+
+ align:start position:0%
+write down boundary conditions that are
+ 
+
+ align:start position:0%
+write down boundary conditions that are
+not achievable which means there's no
+
+ align:start position:0%
+not achievable which means there's no
+ 
+
+ align:start position:0%
+not achievable which means there's no
+solution so this is really a bummer if
+
+ align:start position:0%
+solution so this is really a bummer if
+ 
+
+ align:start position:0%
+solution so this is really a bummer if
+you don't realize you did it because you
+
+ align:start position:0%
+you don't realize you did it because you
+ 
+
+ align:start position:0%
+you don't realize you did it because you
+can try solve it all day and you'll
+
+ align:start position:0%
+can try solve it all day and you'll
+ 
+
+ align:start position:0%
+can try solve it all day and you'll
+never solve it because it doesn't have a
+
+ align:start position:0%
+never solve it because it doesn't have a
+ 
+
+ align:start position:0%
+never solve it because it doesn't have a
+solution okay so for example in this
+
+ align:start position:0%
+solution okay so for example in this
+ 
+
+ align:start position:0%
+solution okay so for example in this
+problem if I set L to be too large the
+
+ align:start position:0%
+problem if I set L to be too large the
+ 
+
+ align:start position:0%
+problem if I set L to be too large the
+cannibal can't go that far I can't set L
+
+ align:start position:0%
+cannibal can't go that far I can't set L
+ 
+
+ align:start position:0%
+cannibal can't go that far I can't set L
+to be 3,000 kilometers and get a
+
+ align:start position:0%
+to be 3,000 kilometers and get a
+ 
+
+ align:start position:0%
+to be 3,000 kilometers and get a
+solution because the muzzle velocity is
+
+ align:start position:0%
+solution because the muzzle velocity is
+ 
+
+ align:start position:0%
+solution because the muzzle velocity is
+not high enough that the kind of ball is
+
+ align:start position:0%
+not high enough that the kind of ball is
+ 
+
+ align:start position:0%
+not high enough that the kind of ball is
+going to travel 3,000 kilometers but
+
+ align:start position:0%
+going to travel 3,000 kilometers but
+ 
+
+ align:start position:0%
+going to travel 3,000 kilometers but
+when I wrote the problem you didn't see
+
+ align:start position:0%
+when I wrote the problem you didn't see
+ 
+
+ align:start position:0%
+when I wrote the problem you didn't see
+that right you didn't come and tell me
+
+ align:start position:0%
+that right you didn't come and tell me
+ 
+
+ align:start position:0%
+that right you didn't come and tell me
+whoa watch out
+
+ align:start position:0%
+whoa watch out
+ 
+
+ align:start position:0%
+whoa watch out
+you know there's no way all could be
+
+ align:start position:0%
+you know there's no way all could be
+ 
+
+ align:start position:0%
+you know there's no way all could be
+bigger than such a touch okay and so you
+
+ align:start position:0%
+bigger than such a touch okay and so you
+ 
+
+ align:start position:0%
+bigger than such a touch okay and so you
+might not know it you might just you
+
+ align:start position:0%
+might not know it you might just you
+ 
+
+ align:start position:0%
+might not know it you might just you
+might specify a condition that's just
+
+ align:start position:0%
+might specify a condition that's just
+ 
+
+ align:start position:0%
+might specify a condition that's just
+not achievable I used to work an
+
+ align:start position:0%
+not achievable I used to work an
+ 
+
+ align:start position:0%
+not achievable I used to work an
+industry that's happened a lot manager
+
+ align:start position:0%
+industry that's happened a lot manager
+ 
+
+ align:start position:0%
+industry that's happened a lot manager
+would specify boundary conditions which
+
+ align:start position:0%
+would specify boundary conditions which
+ 
+
+ align:start position:0%
+would specify boundary conditions which
+were not achievable you know I want 99%
+
+ align:start position:0%
+were not achievable you know I want 99%
+ 
+
+ align:start position:0%
+were not achievable you know I want 99%
+yield and a 10% cost reduction go and
+
+ align:start position:0%
+yield and a 10% cost reduction go and
+ 
+
+ align:start position:0%
+yield and a 10% cost reduction go and
+now I'm the engineer I'm trying to work
+
+ align:start position:0%
+now I'm the engineer I'm trying to work
+ 
+
+ align:start position:0%
+now I'm the engineer I'm trying to work
+it out and then sometimes it didn't yeah
+
+ align:start position:0%
+it out and then sometimes it didn't yeah
+ 
+
+ align:start position:0%
+it out and then sometimes it didn't yeah
+so in some ways it's a lot better to
+
+ align:start position:0%
+so in some ways it's a lot better to
+ 
+
+ align:start position:0%
+so in some ways it's a lot better to
+just say max you know please maximize
+
+ align:start position:0%
+just say max you know please maximize
+ 
+
+ align:start position:0%
+just say max you know please maximize
+this as best you can subject to your
+
+ align:start position:0%
+this as best you can subject to your
+ 
+
+ align:start position:0%
+this as best you can subject to your
+constraints instead of specifying this
+
+ align:start position:0%
+constraints instead of specifying this
+ 
+
+ align:start position:0%
+constraints instead of specifying this
+but of course I don't know why there's a
+
+ align:start position:0%
+but of course I don't know why there's a
+ 
+
+ align:start position:0%
+but of course I don't know why there's a
+school management that says like we want
+
+ align:start position:0%
+school management that says like we want
+ 
+
+ align:start position:0%
+school management that says like we want
+definite targets we don't we don't want
+
+ align:start position:0%
+definite targets we don't we don't want
+ 
+
+ align:start position:0%
+definite targets we don't we don't want
+to be just the best we want to be
+
+ align:start position:0%
+to be just the best we want to be
+ 
+
+ align:start position:0%
+to be just the best we want to be
+perfect you know right so the No Child
+
+ align:start position:0%
+perfect you know right so the No Child
+ 
+
+ align:start position:0%
+perfect you know right so the No Child
+Left Behind every single student in this
+
+ align:start position:0%
+Left Behind every single student in this
+ 
+
+ align:start position:0%
+Left Behind every single student in this
+class is gonna really achieve that's it
+
+ align:start position:0%
+class is gonna really achieve that's it
+ 
+
+ align:start position:0%
+class is gonna really achieve that's it
+anyway that's that's that's the way
+
+ align:start position:0%
+anyway that's that's that's the way
+ 
+
+ align:start position:0%
+anyway that's that's that's the way
+targets get set but you know it's
+
+ align:start position:0%
+targets get set but you know it's
+ 
+
+ align:start position:0%
+targets get set but you know it's
+doesn't have to be achievable and it's
+
+ align:start position:0%
+doesn't have to be achievable and it's
+ 
+
+ align:start position:0%
+doesn't have to be achievable and it's
+actually a big branch of mathematics
+
+ align:start position:0%
+actually a big branch of mathematics
+ 
+
+ align:start position:0%
+actually a big branch of mathematics
+about trying to detect if the boundary
+
+ align:start position:0%
+about trying to detect if the boundary
+ 
+
+ align:start position:0%
+about trying to detect if the boundary
+conditions are indeed consistent so that
+
+ align:start position:0%
+conditions are indeed consistent so that
+ 
+
+ align:start position:0%
+conditions are indeed consistent so that
+they could be achieved and it's not so
+
+ align:start position:0%
+they could be achieved and it's not so
+ 
+
+ align:start position:0%
+they could be achieved and it's not so
+obvious to do it so I'm not gonna I'm
+
+ align:start position:0%
+obvious to do it so I'm not gonna I'm
+ 
+
+ align:start position:0%
+obvious to do it so I'm not gonna I'm
+not gonna get into that at all you could
+
+ align:start position:0%
+not gonna get into that at all you could
+ 
+
+ align:start position:0%
+not gonna get into that at all you could
+take a like a PDE class there's in the
+
+ align:start position:0%
+take a like a PDE class there's in the
+ 
+
+ align:start position:0%
+take a like a PDE class there's in the
+math department and that's all they talk
+
+ align:start position:0%
+math department and that's all they talk
+ 
+
+ align:start position:0%
+math department and that's all they talk
+about all day is about how to figure out
+
+ align:start position:0%
+about all day is about how to figure out
+ 
+
+ align:start position:0%
+about all day is about how to figure out
+you know are these boundary conditions
+
+ align:start position:0%
+you know are these boundary conditions
+ 
+
+ align:start position:0%
+you know are these boundary conditions
+consistent or not consistent you can
+
+ align:start position:0%
+consistent or not consistent you can
+ 
+
+ align:start position:0%
+consistent or not consistent you can
+also have boundary conditions are
+
+ align:start position:0%
+also have boundary conditions are
+ 
+
+ align:start position:0%
+also have boundary conditions are
+repetitive and don't have enough
+
+ align:start position:0%
+repetitive and don't have enough
+ 
+
+ align:start position:0%
+repetitive and don't have enough
+information in those cases you might
+
+ align:start position:0%
+information in those cases you might
+ 
+
+ align:start position:0%
+information in those cases you might
+have an infinite number of solutions and
+
+ align:start position:0%
+have an infinite number of solutions and
+ 
+
+ align:start position:0%
+have an infinite number of solutions and
+I think you can also have cases where
+
+ align:start position:0%
+I think you can also have cases where
+ 
+
+ align:start position:0%
+I think you can also have cases where
+you have multiple solutions so like in
+
+ align:start position:0%
+you have multiple solutions so like in
+ 
+
+ align:start position:0%
+you have multiple solutions so like in
+the Cannonball problem if you could have
+
+ align:start position:0%
+the Cannonball problem if you could have
+ 
+
+ align:start position:0%
+the Cannonball problem if you could have
+a negative UI and that the ship was
+
+ align:start position:0%
+a negative UI and that the ship was
+ 
+
+ align:start position:0%
+a negative UI and that the ship was
+close enough you might be able to shoot
+
+ align:start position:0%
+close enough you might be able to shoot
+ 
+
+ align:start position:0%
+close enough you might be able to shoot
+it two ways you could shoot shooting
+
+ align:start position:0%
+it two ways you could shoot shooting
+ 
+
+ align:start position:0%
+it two ways you could shoot shooting
+down at it or you could just follow up
+
+ align:start position:0%
+down at it or you could just follow up
+ 
+
+ align:start position:0%
+down at it or you could just follow up
+ahead up by and come down and they're
+
+ align:start position:0%
+ahead up by and come down and they're
+ 
+
+ align:start position:0%
+ahead up by and come down and they're
+both be solutions that satisfy all the
+
+ align:start position:0%
+both be solutions that satisfy all the
+ 
+
+ align:start position:0%
+both be solutions that satisfy all the
+conditions so is this is like general
+
+ align:start position:0%
+conditions so is this is like general
+ 
+
+ align:start position:0%
+conditions so is this is like general
+nonlinear equation problems that you
+
+ align:start position:0%
+nonlinear equation problems that you
+ 
+
+ align:start position:0%
+nonlinear equation problems that you
+don't know how many solutions you got
+
+ align:start position:0%
+don't know how many solutions you got
+ 
+
+ align:start position:0%
+don't know how many solutions you got
+you don't know if you have a solution
+
+ align:start position:0%
+you don't know if you have a solution
+ 
+
+ align:start position:0%
+you don't know if you have a solution
+you might have an infinite number of
+
+ align:start position:0%
+you might have an infinite number of
+ 
+
+ align:start position:0%
+you might have an infinite number of
+solutions you might have some finite
+
+ align:start position:0%
+solutions you might have some finite
+ 
+
+ align:start position:0%
+solutions you might have some finite
+number of solutions you don't know how
+
+ align:start position:0%
+number of solutions you don't know how
+ 
+
+ align:start position:0%
+number of solutions you don't know how
+many and it's just that's the way life
+
+ align:start position:0%
+many and it's just that's the way life
+ 
+
+ align:start position:0%
+many and it's just that's the way life
+is and you have to live with it but
+
+ align:start position:0%
+is and you have to live with it but
+ 
+
+ align:start position:0%
+is and you have to live with it but
+kind of annoying sometimes for now let's
+
+ align:start position:0%
+kind of annoying sometimes for now let's
+ 
+
+ align:start position:0%
+kind of annoying sometimes for now let's
+just assume that we somehow know that we
+
+ align:start position:0%
+just assume that we somehow know that we
+ 
+
+ align:start position:0%
+just assume that we somehow know that we
+have a unique solution there's a unique
+
+ align:start position:0%
+have a unique solution there's a unique
+ 
+
+ align:start position:0%
+have a unique solution there's a unique
+physical solution and we're just gonna
+
+ align:start position:0%
+physical solution and we're just gonna
+ 
+
+ align:start position:0%
+physical solution and we're just gonna
+try to find that and we're not gonna
+
+ align:start position:0%
+try to find that and we're not gonna
+ 
+
+ align:start position:0%
+try to find that and we're not gonna
+worry about this other problem about the
+
+ align:start position:0%
+worry about this other problem about the
+ 
+
+ align:start position:0%
+worry about this other problem about the
+fact that could actually be multiple
+
+ align:start position:0%
+fact that could actually be multiple
+ 
+
+ align:start position:0%
+fact that could actually be multiple
+solutions or no solution or whatever
+
+ align:start position:0%
+solutions or no solution or whatever
+ 
+
+ align:start position:0%
+solutions or no solution or whatever
+which you know when you actually run
+
+ align:start position:0%
+which you know when you actually run
+ 
+
+ align:start position:0%
+which you know when you actually run
+into a case like that then you'll really
+
+ align:start position:0%
+into a case like that then you'll really
+ 
+
+ align:start position:0%
+into a case like that then you'll really
+worry about it a lot good question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we had it we had an example
+
+ align:start position:0%
+all right so we had it we had an example
+ 
+
+ align:start position:0%
+all right so we had it we had an example
+in the actually the zeroth homework the
+
+ align:start position:0%
+in the actually the zeroth homework the
+ 
+
+ align:start position:0%
+in the actually the zeroth homework the
+very beginning that had a problem like
+
+ align:start position:0%
+very beginning that had a problem like
+ 
+
+ align:start position:0%
+very beginning that had a problem like
+this the homework 0p1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we had a problem where it was it gave
+
+ align:start position:0%
+we had a problem where it was it gave
+ 
+
+ align:start position:0%
+we had a problem where it was it gave
+you remember this it was like cylinder
+
+ align:start position:0%
+you remember this it was like cylinder
+ 
+
+ align:start position:0%
+you remember this it was like cylinder
+and you're trying to compute T of R or
+
+ align:start position:0%
+and you're trying to compute T of R or
+ 
+
+ align:start position:0%
+and you're trying to compute T of R or
+this and and it gave you some conditions
+
+ align:start position:0%
+this and and it gave you some conditions
+ 
+
+ align:start position:0%
+this and and it gave you some conditions
+about here so it gave you give you t
+
+ align:start position:0%
+about here so it gave you give you t
+ 
+
+ align:start position:0%
+about here so it gave you give you t
+when R was equal to R and it gave you
+
+ align:start position:0%
+when R was equal to R and it gave you
+ 
+
+ align:start position:0%
+when R was equal to R and it gave you
+DTD are actually give you some Quetta
+
+ align:start position:0%
+DTD are actually give you some Quetta
+ 
+
+ align:start position:0%
+DTD are actually give you some Quetta
+quai ssin it was a it was actually a
+
+ align:start position:0%
+quai ssin it was a it was actually a
+ 
+
+ align:start position:0%
+quai ssin it was a it was actually a
+function of this and T all of a
+
+ align:start position:0%
+function of this and T all of a
+ 
+
+ align:start position:0%
+function of this and T all of a
+evaluated at R was equal to something
+
+ align:start position:0%
+evaluated at R was equal to something
+ 
+
+ align:start position:0%
+evaluated at R was equal to something
+you remember this yeah so we gave you
+
+ align:start position:0%
+you remember this yeah so we gave you
+ 
+
+ align:start position:0%
+you remember this yeah so we gave you
+those two but then we also told you in
+
+ align:start position:0%
+those two but then we also told you in
+ 
+
+ align:start position:0%
+those two but then we also told you in
+the most recent homework oh by the way
+
+ align:start position:0%
+the most recent homework oh by the way
+ 
+
+ align:start position:0%
+the most recent homework oh by the way
+DTD are it's got to be equal to 0 at R
+
+ align:start position:0%
+DTD are it's got to be equal to 0 at R
+ 
+
+ align:start position:0%
+DTD are it's got to be equal to 0 at R
+equals 0 so this is one of these ones
+
+ align:start position:0%
+equals 0 so this is one of these ones
+ 
+
+ align:start position:0%
+equals 0 so this is one of these ones
+where we only have we should only have
+
+ align:start position:0%
+where we only have we should only have
+ 
+
+ align:start position:0%
+where we only have we should only have
+two conditions but we told you three
+
+ align:start position:0%
+two conditions but we told you three
+ 
+
+ align:start position:0%
+two conditions but we told you three
+conditions so then where it was any of
+
+ align:start position:0%
+conditions so then where it was any of
+ 
+
+ align:start position:0%
+conditions so then where it was any of
+you are able to achieve all three
+
+ align:start position:0%
+you are able to achieve all three
+ 
+
+ align:start position:0%
+you are able to achieve all three
+conditions no ok so this is this is
+
+ align:start position:0%
+conditions no ok so this is this is
+ 
+
+ align:start position:0%
+conditions no ok so this is this is
+highlighting the problem right so we
+
+ align:start position:0%
+highlighting the problem right so we
+ 
+
+ align:start position:0%
+highlighting the problem right so we
+gave you three boundary conditions are
+
+ align:start position:0%
+gave you three boundary conditions are
+ 
+
+ align:start position:0%
+gave you three boundary conditions are
+apparently incompatible that you
+
+ align:start position:0%
+apparently incompatible that you
+ 
+
+ align:start position:0%
+apparently incompatible that you
+couldn't actually solve them all at the
+
+ align:start position:0%
+couldn't actually solve them all at the
+ 
+
+ align:start position:0%
+couldn't actually solve them all at the
+same time so beware I guess now in that
+
+ align:start position:0%
+same time so beware I guess now in that
+ 
+
+ align:start position:0%
+same time so beware I guess now in that
+problem it might have been more natural
+
+ align:start position:0%
+problem it might have been more natural
+ 
+
+ align:start position:0%
+problem it might have been more natural
+to give you this equation which we are
+
+ align:start position:0%
+to give you this equation which we are
+ 
+
+ align:start position:0%
+to give you this equation which we are
+sure is exactly true
+
+ align:start position:0%
+sure is exactly true
+ 
+
+ align:start position:0%
+sure is exactly true
+by the symmetry situation as one of the
+
+ align:start position:0%
+by the symmetry situation as one of the
+ 
+
+ align:start position:0%
+by the symmetry situation as one of the
+conditions and then only one of these
+
+ align:start position:0%
+conditions and then only one of these
+ 
+
+ align:start position:0%
+conditions and then only one of these
+other conditions out
+
+ align:start position:0%
+other conditions out
+ 
+
+ align:start position:0%
+other conditions out
+that whichever one we were more sure was
+
+ align:start position:0%
+that whichever one we were more sure was
+ 
+
+ align:start position:0%
+that whichever one we were more sure was
+correct might be the thing to do and so
+
+ align:start position:0%
+correct might be the thing to do and so
+ 
+
+ align:start position:0%
+correct might be the thing to do and so
+we kind of you know gave you some
+
+ align:start position:0%
+we kind of you know gave you some
+ 
+
+ align:start position:0%
+we kind of you know gave you some
+goofball conditions I guess in some ways
+
+ align:start position:0%
+goofball conditions I guess in some ways
+ 
+
+ align:start position:0%
+goofball conditions I guess in some ways
+right yeah they could all be true and if
+
+ align:start position:0%
+right yeah they could all be true and if
+ 
+
+ align:start position:0%
+right yeah they could all be true and if
+they were all true then then if you saw
+
+ align:start position:0%
+they were all true then then if you saw
+ 
+
+ align:start position:0%
+they were all true then then if you saw
+the numerically exactly you should you
+
+ align:start position:0%
+the numerically exactly you should you
+ 
+
+ align:start position:0%
+the numerically exactly you should you
+should get the real solution it should
+
+ align:start position:0%
+should get the real solution it should
+ 
+
+ align:start position:0%
+should get the real solution it should
+satisfy all of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I think that I think one wasn't
+
+ align:start position:0%
+yeah I think that I think one wasn't
+ 
+
+ align:start position:0%
+yeah I think that I think one wasn't
+true and I think it's maybe due to
+
+ align:start position:0%
+true and I think it's maybe due to
+ 
+
+ align:start position:0%
+true and I think it's maybe due to
+roundoff yeah so but it's highlights a
+
+ align:start position:0%
+roundoff yeah so but it's highlights a
+ 
+
+ align:start position:0%
+roundoff yeah so but it's highlights a
+problem if you have three conditions
+
+ align:start position:0%
+problem if you have three conditions
+ 
+
+ align:start position:0%
+problem if you have three conditions
+that should be true but they evolved
+
+ align:start position:0%
+that should be true but they evolved
+ 
+
+ align:start position:0%
+that should be true but they evolved
+numbers in them then often they won't
+
+ align:start position:0%
+numbers in them then often they won't
+ 
+
+ align:start position:0%
+numbers in them then often they won't
+all be exactly consistent with each
+
+ align:start position:0%
+all be exactly consistent with each
+ 
+
+ align:start position:0%
+all be exactly consistent with each
+other but those are actually worse kind
+
+ align:start position:0%
+other but those are actually worse kind
+ 
+
+ align:start position:0%
+other but those are actually worse kind
+of problem right because it's like it's
+
+ align:start position:0%
+of problem right because it's like it's
+ 
+
+ align:start position:0%
+of problem right because it's like it's
+close to being consistent to all those
+
+ align:start position:0%
+close to being consistent to all those
+ 
+
+ align:start position:0%
+close to being consistent to all those
+conditions but you're not exactly
+
+ align:start position:0%
+conditions but you're not exactly
+ 
+
+ align:start position:0%
+conditions but you're not exactly
+conditioning consistent but then if you
+
+ align:start position:0%
+conditioning consistent but then if you
+ 
+
+ align:start position:0%
+conditioning consistent but then if you
+get into it trying to figure out what's
+
+ align:start position:0%
+get into it trying to figure out what's
+ 
+
+ align:start position:0%
+get into it trying to figure out what's
+going on a lot of times you'll get like
+
+ align:start position:0%
+going on a lot of times you'll get like
+ 
+
+ align:start position:0%
+going on a lot of times you'll get like
+new your singular matrices and stuff
+
+ align:start position:0%
+new your singular matrices and stuff
+ 
+
+ align:start position:0%
+new your singular matrices and stuff
+because you have things that are nearly
+
+ align:start position:0%
+because you have things that are nearly
+ 
+
+ align:start position:0%
+because you have things that are nearly
+linearly dependent in some way so really
+
+ align:start position:0%
+linearly dependent in some way so really
+ 
+
+ align:start position:0%
+linearly dependent in some way so really
+it's better if you just have the right
+
+ align:start position:0%
+it's better if you just have the right
+ 
+
+ align:start position:0%
+it's better if you just have the right
+number of conditions that you're really
+
+ align:start position:0%
+number of conditions that you're really
+ 
+
+ align:start position:0%
+number of conditions that you're really
+sure really specify everything correctly
+
+ align:start position:0%
+sure really specify everything correctly
+ 
+
+ align:start position:0%
+sure really specify everything correctly
+and just go with those and treat the
+
+ align:start position:0%
+and just go with those and treat the
+ 
+
+ align:start position:0%
+and just go with those and treat the
+ones that you think would be nice if
+
+ align:start position:0%
+ones that you think would be nice if
+ 
+
+ align:start position:0%
+ones that you think would be nice if
+they were true as like approximate
+
+ align:start position:0%
+they were true as like approximate
+ 
+
+ align:start position:0%
+they were true as like approximate
+things that are sort of physical checks
+
+ align:start position:0%
+things that are sort of physical checks
+ 
+
+ align:start position:0%
+things that are sort of physical checks
+to see what your solutions reasonable
+
+ align:start position:0%
+to see what your solutions reasonable
+ 
+
+ align:start position:0%
+to see what your solutions reasonable
+and we did it sort of like that in the
+
+ align:start position:0%
+and we did it sort of like that in the
+ 
+
+ align:start position:0%
+and we did it sort of like that in the
+problem you did we said well you know
+
+ align:start position:0%
+problem you did we said well you know
+ 
+
+ align:start position:0%
+problem you did we said well you know
+DTD r should really be equal to zero but
+
+ align:start position:0%
+DTD r should really be equal to zero but
+ 
+
+ align:start position:0%
+DTD r should really be equal to zero but
+we didn't demand that in your solution
+
+ align:start position:0%
+we didn't demand that in your solution
+ 
+
+ align:start position:0%
+we didn't demand that in your solution
+your solution didn't actually satisfy
+
+ align:start position:0%
+your solution didn't actually satisfy
+ 
+
+ align:start position:0%
+your solution didn't actually satisfy
+that and you we use that as a measure of
+
+ align:start position:0%
+that and you we use that as a measure of
+ 
+
+ align:start position:0%
+that and you we use that as a measure of
+how far off your solution is that's
+
+ align:start position:0%
+how far off your solution is that's
+ 
+
+ align:start position:0%
+how far off your solution is that's
+actually pretty useful in practice you
+
+ align:start position:0%
+actually pretty useful in practice you
+ 
+
+ align:start position:0%
+actually pretty useful in practice you
+get a solution it's good to have some
+
+ align:start position:0%
+get a solution it's good to have some
+ 
+
+ align:start position:0%
+get a solution it's good to have some
+additional condition that you can test
+
+ align:start position:0%
+additional condition that you can test
+ 
+
+ align:start position:0%
+additional condition that you can test
+for like physical reasonableness of the
+
+ align:start position:0%
+for like physical reasonableness of the
+ 
+
+ align:start position:0%
+for like physical reasonableness of the
+solution and particularly cuz this
+
+ align:start position:0%
+solution and particularly cuz this
+ 
+
+ align:start position:0%
+solution and particularly cuz this
+problem that you might have multiple
+
+ align:start position:0%
+problem that you might have multiple
+ 
+
+ align:start position:0%
+problem that you might have multiple
+solutions and maybe one of them is a
+
+ align:start position:0%
+solutions and maybe one of them is a
+ 
+
+ align:start position:0%
+solutions and maybe one of them is a
+physical solution and one is some other
+
+ align:start position:0%
+physical solution and one is some other
+ 
+
+ align:start position:0%
+physical solution and one is some other
+crazy solution and so you you need to
+
+ align:start position:0%
+crazy solution and so you you need to
+ 
+
+ align:start position:0%
+crazy solution and so you you need to
+have some way to detect the crazy
+
+ align:start position:0%
+have some way to detect the crazy
+ 
+
+ align:start position:0%
+have some way to detect the crazy
+solution by some other condition you can
+
+ align:start position:0%
+solution by some other condition you can
+ 
+
+ align:start position:0%
+solution by some other condition you can
+test does it make sense yeah all right
+
+ align:start position:0%
+test does it make sense yeah all right
+ 
+
+ align:start position:0%
+test does it make sense yeah all right
+so I said I said you know you could have
+
+ align:start position:0%
+so I said I said you know you could have
+ 
+
+ align:start position:0%
+so I said I said you know you could have
+cases where the Jacobian of
+
+ align:start position:0%
+cases where the Jacobian of
+ 
+
+ align:start position:0%
+cases where the Jacobian of
+your equation yeah so you can be trying
+
+ align:start position:0%
+your equation yeah so you can be trying
+ 
+
+ align:start position:0%
+your equation yeah so you can be trying
+to solve this and it could be for some
+
+ align:start position:0%
+to solve this and it could be for some
+ 
+
+ align:start position:0%
+to solve this and it could be for some
+problems that Jacobian always has both
+
+ align:start position:0%
+problems that Jacobian always has both
+ 
+
+ align:start position:0%
+problems that Jacobian always has both
+positive and negative eigenvalues
+
+ align:start position:0%
+positive and negative eigenvalues
+ 
+
+ align:start position:0%
+positive and negative eigenvalues
+together and in that case using I VPS
+
+ align:start position:0%
+together and in that case using I VPS
+ 
+
+ align:start position:0%
+together and in that case using I VPS
+it's not going to be a smart idea
+
+ align:start position:0%
+it's not going to be a smart idea
+ 
+
+ align:start position:0%
+it's not going to be a smart idea
+because you no matter which direction
+
+ align:start position:0%
+because you no matter which direction
+ 
+
+ align:start position:0%
+because you no matter which direction
+you integrate in you're gonna have a
+
+ align:start position:0%
+you integrate in you're gonna have a
+ 
+
+ align:start position:0%
+you integrate in you're gonna have a
+positive eigenvalue and so then the the
+
+ align:start position:0%
+positive eigenvalue and so then the the
+ 
+
+ align:start position:0%
+positive eigenvalue and so then the the
+ivv is not good and so instead we're
+
+ align:start position:0%
+ivv is not good and so instead we're
+ 
+
+ align:start position:0%
+ivv is not good and so instead we're
+gonna use a different methods and we'll
+
+ align:start position:0%
+gonna use a different methods and we'll
+ 
+
+ align:start position:0%
+gonna use a different methods and we'll
+talk about that next time and those are
+
+ align:start position:0%
+talk about that next time and those are
+ 
+
+ align:start position:0%
+talk about that next time and those are
+called relaxation methods and the
+
+ align:start position:0%
+called relaxation methods and the
+ 
+
+ align:start position:0%
+called relaxation methods and the
+concept of these is different than it
+
+ align:start position:0%
+concept of these is different than it
+ 
+
+ align:start position:0%
+concept of these is different than it
+was for shooting so the relaxation
+
+ align:start position:0%
+was for shooting so the relaxation
+ 
+
+ align:start position:0%
+was for shooting so the relaxation
+methods is you have a white gas that
+
+ align:start position:0%
+methods is you have a white gas that
+ 
+
+ align:start position:0%
+methods is you have a white gas that
+you're gonna have the whole guess for
+
+ align:start position:0%
+you're gonna have the whole guess for
+ 
+
+ align:start position:0%
+you're gonna have the whole guess for
+the entire Y throughout the whole domain
+
+ align:start position:0%
+the entire Y throughout the whole domain
+ 
+
+ align:start position:0%
+the entire Y throughout the whole domain
+and actually a lot of times you might
+
+ align:start position:0%
+and actually a lot of times you might
+ 
+
+ align:start position:0%
+and actually a lot of times you might
+you might set this up so that why I
+
+ align:start position:0%
+you might set this up so that why I
+ 
+
+ align:start position:0%
+you might set this up so that why I
+guess actually exactly satisfies the
+
+ align:start position:0%
+guess actually exactly satisfies the
+ 
+
+ align:start position:0%
+guess actually exactly satisfies the
+boundary conditions so you know it
+
+ align:start position:0%
+boundary conditions so you know it
+ 
+
+ align:start position:0%
+boundary conditions so you know it
+satisfies those equations right from the
+
+ align:start position:0%
+satisfies those equations right from the
+ 
+
+ align:start position:0%
+satisfies those equations right from the
+beginning just from the way you set up I
+
+ align:start position:0%
+beginning just from the way you set up I
+ 
+
+ align:start position:0%
+beginning just from the way you set up I
+guess but it won't satisfy the
+
+ align:start position:0%
+guess but it won't satisfy the
+ 
+
+ align:start position:0%
+guess but it won't satisfy the
+differential equation and then what
+
+ align:start position:0%
+differential equation and then what
+ 
+
+ align:start position:0%
+differential equation and then what
+you'll do is you'll say you know how
+
+ align:start position:0%
+you'll do is you'll say you know how
+ 
+
+ align:start position:0%
+you'll do is you'll say you know how
+badly does it fail to satisfy G and
+
+ align:start position:0%
+badly does it fail to satisfy G and
+ 
+
+ align:start position:0%
+badly does it fail to satisfy G and
+equals you know the G is equal zero all
+
+ align:start position:0%
+equals you know the G is equal zero all
+ 
+
+ align:start position:0%
+equals you know the G is equal zero all
+right because who really wants G's equal
+
+ align:start position:0%
+right because who really wants G's equal
+ 
+
+ align:start position:0%
+right because who really wants G's equal
+to zero for the true solution and we'll
+
+ align:start position:0%
+to zero for the true solution and we'll
+ 
+
+ align:start position:0%
+to zero for the true solution and we'll
+call this this failure of our Y guest to
+
+ align:start position:0%
+call this this failure of our Y guest to
+ 
+
+ align:start position:0%
+call this this failure of our Y guest to
+solve this we'll call that the residual
+
+ align:start position:0%
+solve this we'll call that the residual
+ 
+
+ align:start position:0%
+solve this we'll call that the residual
+so we can actually plug in y guess in
+
+ align:start position:0%
+so we can actually plug in y guess in
+ 
+
+ align:start position:0%
+so we can actually plug in y guess in
+here and y guess in here and evaluate
+
+ align:start position:0%
+here and y guess in here and evaluate
+ 
+
+ align:start position:0%
+here and y guess in here and evaluate
+this and normally it will not be 0
+
+ align:start position:0%
+this and normally it will not be 0
+ 
+
+ align:start position:0%
+this and normally it will not be 0
+because our y guess there's not perfect
+
+ align:start position:0%
+because our y guess there's not perfect
+ 
+
+ align:start position:0%
+because our y guess there's not perfect
+and so it's going to deviate from zero
+
+ align:start position:0%
+and so it's going to deviate from zero
+ 
+
+ align:start position:0%
+and so it's going to deviate from zero
+but how big a deviates from zero is
+
+ align:start position:0%
+but how big a deviates from zero is
+ 
+
+ align:start position:0%
+but how big a deviates from zero is
+going to be our measure of how bad that
+
+ align:start position:0%
+going to be our measure of how bad that
+ 
+
+ align:start position:0%
+going to be our measure of how bad that
+that guess was and then we're going to
+
+ align:start position:0%
+that guess was and then we're going to
+ 
+
+ align:start position:0%
+that guess was and then we're going to
+try to change Y gas to try to make it
+
+ align:start position:0%
+try to change Y gas to try to make it
+ 
+
+ align:start position:0%
+try to change Y gas to try to make it
+closer and closer to zero so the idea is
+
+ align:start position:0%
+closer and closer to zero so the idea is
+ 
+
+ align:start position:0%
+closer and closer to zero so the idea is
+relax it you get a incorrect solution
+
+ align:start position:0%
+relax it you get a incorrect solution
+ 
+
+ align:start position:0%
+relax it you get a incorrect solution
+and you adjust it to relax it to make it
+
+ align:start position:0%
+and you adjust it to relax it to make it
+ 
+
+ align:start position:0%
+and you adjust it to relax it to make it
+become the correct solution alright and
+
+ align:start position:0%
+become the correct solution alright and
+ 
+
+ align:start position:0%
+become the correct solution alright and
+so that's the the general idea of the
+
+ align:start position:0%
+so that's the the general idea of the
+ 
+
+ align:start position:0%
+so that's the the general idea of the
+relaxation methods and we'll talk about
+
+ align:start position:0%
+relaxation methods and we'll talk about
+ 
+
+ align:start position:0%
+relaxation methods and we'll talk about
+several different forms of that normally
+
+ align:start position:0%
+several different forms of that normally
+ 
+
+ align:start position:0%
+several different forms of that normally
+what we have to do is you have to write
+
+ align:start position:0%
+what we have to do is you have to write
+ 
+
+ align:start position:0%
+what we have to do is you have to write
+why guess and some in terms of some
+
+ align:start position:0%
+why guess and some in terms of some
+ 
+
+ align:start position:0%
+why guess and some in terms of some
+parameters so why guess T depends on
+
+ align:start position:0%
+parameters so why guess T depends on
+ 
+
+ align:start position:0%
+parameters so why guess T depends on
+some parameters and we're gonna adjust
+
+ align:start position:0%
+some parameters and we're gonna adjust
+ 
+
+ align:start position:0%
+some parameters and we're gonna adjust
+the parameters and that's going to
+
+ align:start position:0%
+the parameters and that's going to
+ 
+
+ align:start position:0%
+the parameters and that's going to
+change what Y guesses and so for example
+
+ align:start position:0%
+change what Y guesses and so for example
+ 
+
+ align:start position:0%
+change what Y guesses and so for example
+we could do a basis set expansion as we
+
+ align:start position:0%
+we could do a basis set expansion as we
+ 
+
+ align:start position:0%
+we could do a basis set expansion as we
+did one of the earlier classes we talked
+
+ align:start position:0%
+did one of the earlier classes we talked
+ 
+
+ align:start position:0%
+did one of the earlier classes we talked
+about how you could expand Y guests as a
+
+ align:start position:0%
+about how you could expand Y guests as a
+ 
+
+ align:start position:0%
+about how you could expand Y guests as a
+sum of some basis functions weighted by
+
+ align:start position:0%
+sum of some basis functions weighted by
+ 
+
+ align:start position:0%
+sum of some basis functions weighted by
+peas and then you can adjust the peas
+
+ align:start position:0%
+peas and then you can adjust the peas
+ 
+
+ align:start position:0%
+peas and then you can adjust the peas
+and find the best possible set of peas
+
+ align:start position:0%
+and find the best possible set of peas
+ 
+
+ align:start position:0%
+and find the best possible set of peas
+to get them to make this G as close to
+
+ align:start position:0%
+to get them to make this G as close to
+ 
+
+ align:start position:0%
+to get them to make this G as close to
+zero as possible for example but we'll
+
+ align:start position:0%
+zero as possible for example but we'll
+ 
+
+ align:start position:0%
+zero as possible for example but we'll
+give examples of that next time and talk
+
+ align:start position:0%
+give examples of that next time and talk
+ 
+
+ align:start position:0%
+give examples of that next time and talk
+about there's a several choices about
+
+ align:start position:0%
+about there's a several choices about
+ 
+
+ align:start position:0%
+about there's a several choices about
+that all right
\ No newline at end of file
diff --git a/xEnYH0KNkfA.txt b/xEnYH0KNkfA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3683202ea6a6e6e26780c4f5318838e5451fea49
--- /dev/null
+++ b/xEnYH0KNkfA.txt
@@ -0,0 +1,2915 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional material from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: All right.
+
+So today we're going to start
+the last section.
+
+We're going to do three lectures
+on phase diagrams.
+
+And I've given this the label
+here of Stability, Sustaining
+
+the Solid State.
+
+We've talked a lot about the
+solid state in 3.091 as the
+
+vehicle for teaching the
+rudiments of chemistry.
+
+One of the things we have not
+talked about, is what are the
+
+conditions that sustain
+the solid state?
+
+How do I know whether
+something's going to be a
+
+solid, or a liquid, or a gas?
+
+This is very important.
+
+For example, if you're in a
+foundry, you're running
+
+places, making auto parts,
+you have to know what the
+
+solidification temperature is of
+the alloys, so you can get
+
+the parts out quickly and
+keep productivity high.
+
+It's even important in
+failure analysis.
+
+You know, when they were looking
+at things like the
+
+rubble from the World Trade
+Center by understanding phase
+
+stability, the thermal history
+was imprinted in the metal.
+
+It's possible to determine
+what temperatures were
+
+achieved, and therefore, what
+the chain of events was that
+
+led to the collapse of
+those buildings.
+
+Now you might say, well, isn't
+this straightforward?
+
+I mean, for example, you just
+look up the melting point or
+
+boiling point.
+
+Water, 0 degrees C. Melting
+point, boiling point, 100
+
+degrees C.
+
+Well, suppose you decide to
+realize your life's ambition.
+
+You're going to go and
+scale Mount Everest.
+
+So you pay the $10,000, you
+get a license from the
+
+Nepalese Government,
+and you're at base
+
+camp at 20,000 feet.
+
+You're sitting there, you've
+got your campfire going,
+
+you've got a hankering for
+a hard-boiled egg.
+
+And you start, you put the eggs
+into boiling water and
+
+you cook them 10 minutes, you
+take them out, and they're
+
+still runny.
+
+You say, I must've lost
+track of time.
+
+So you cook them 20 minutes,
+and they're still runny.
+
+And you cook them 30 minutes,
+and they're still runny.
+
+And you eventually come to the
+realization that at 20,000
+
+feet, the boiling point of water
+is below the denaturing
+
+temperature of egg yolk.
+
+So now the boiling point is
+a function of pressure.
+
+So you know, we could have one
+of these Iron Chef cookoffs,
+
+only the dish is souffle, only
+we'll have the contest at
+
+Flagstaff, Arizona, where the
+altitude is so high that the
+
+classical recipes won't work,
+because the boiling point, the
+
+atmospheric pressure, and
+everything conspire so that
+
+you're not going to be able
+to support the souffle.
+
+So you're going to have to
+understand phase diagrams.
+
+In fact, if you understand phase
+diagrams, that's your
+
+ticket to being a four-star
+chef in the kitchen.
+
+Well, here's another place we
+can look at, where pressure
+
+has an important role.
+
+Let's look under the
+hood of a car.
+
+You're running an internal
+combustion engine.
+
+So this is the engine
+block, and there's
+
+combustion going on inside.
+
+We've got to keep this thing
+from overeating.
+
+It could damage the metal.
+
+In extreme, you could
+melt the metal.
+
+So we've got cooling channels
+in here with water flow.
+
+But then the water's going
+to heat up, and the
+
+water's going to boil.
+
+So we've got, over here,
+the radiator.
+
+So it's really a double
+cooling system.
+
+The water cools the block,
+and then the
+
+radiator cools the water.
+
+So how's that going to work?
+
+Well, here, the temperature is
+on the order of about 90
+
+degrees C, and here the
+temperature inside the engine
+
+block is much greater than 90
+degrees C. It's several
+
+hundred degrees C inside that
+engine block, and we've got
+
+water going like this.
+
+So we've got cooling water
+flow in this manner.
+
+And now cold water goes in and
+hot water comes out, and then
+
+we get into the radiator, and
+we've got channels here, and
+
+we've either got a fan or
+some kind of air flow.
+
+And so now, what's
+the gambit here?
+
+I want to see what's going
+on inside this radiator.
+
+So if this is the wall of the
+radiator, and in here I've got
+
+water, and over here I've got
+air, the idea is to have a
+
+high heat flux to get the energy
+out of the water and
+
+cool it down.
+
+Now, if things get really,
+really hot in here-- let's say
+
+you're zooming along down the
+highway at about 90, I mean,
+
+about 65 miles an hour, and all
+of a sudden you come upon
+
+a collision, and you have to
+go to a dead stop, all that
+
+energy in the engine
+is now dumped, and
+
+the water could overheat.
+
+And in the extreme, if it
+overheats, it can actually go
+
+into a boil.
+
+And this is bad.
+
+Because heat transfer is really
+good between a liquid
+
+and a solid, and it's
+really poor
+
+between a gas and a solid.
+
+This is a low heat flux,
+and this is bad.
+
+High heat flux, that's good.
+
+This is the bubbles.
+
+This is boiling.
+
+And why?
+
+Because what transfers energy?
+
+It's the atoms.
+
+And what's the atom density in
+a liquid versus the atom
+
+density in a gas?
+
+You just have really crummy
+heat transfer.
+
+That's why insulation involves
+dead airspace.
+
+Because you have very
+poor atom density.
+
+So what can we do in
+order to try to
+
+repress the bubble formation?
+
+Well, we said if we went up
+Mount Everest, we went to high
+
+altitude, the boiling
+point went down.
+
+And why did it go down?
+
+Because the atmospheric
+pressure is lower.
+
+So why don't we go the inverse
+here, and we'll put a pressure
+
+cap on the radiator, and make
+the pressure go up, and when
+
+the pressure goes up, it exerts
+a back pressure and
+
+represses bubble formation?
+
+So by increasing pressure, we
+can increase the temperature,
+
+and get the temperature up.
+
+So let's say p equals-- if you
+look on the top of the
+
+pressure cap, it will
+say 15 psi.
+
+And 15 psi is almost 14.7 psi,
+which is exactly 1 atmosphere,
+
+which in SI units is, and I know
+this to six significant
+
+figures, 101325 Pascals.
+
+Or, you know, from Torricelli,
+760 millimeters of mercury,
+
+that's the column that's
+supported.
+
+So we're at 2 atmospheres
+pressure in there, and with
+
+two atmospheres of pressure, we
+can raise the boiling point
+
+to 106 degrees C. And then what
+we can do, is now change
+
+the composition.
+
+So we change the pressure, and
+I change the boiling point.
+
+I change the composition.
+
+add 50% ethylene glycol.
+
+So now I've got a
+one-to-one mix,
+
+ethylene glycol and water.
+
+And that takes the boiling point
+up to 130 degrees C, or
+
+265 degrees Fahrenheit.
+
+So another example of how
+we can manage systems.
+
+So when I'm showing you by these
+several examples, is
+
+that the boiling point is a
+function of pressure and
+
+composition.
+
+So we can tune the
+boiling point.
+
+See we were tuning materials
+properties before.
+
+Now we're tuning physical
+chemical properties, because
+
+that's what chemistry
+is all about.
+
+It's about control.
+
+It's about management.
+
+Management to advantage.
+
+So how do we know
+what to do here?
+
+Can we predict this from
+first principles?
+
+No.
+
+Systems are still
+too complicated.
+
+Our models aren't
+robust enough.
+
+So instead, we turn
+to an archive.
+
+So we have phase diagrams.
+
+And the phase diagrams guide
+us in our search for better
+
+management of material
+systems.
+
+And these are stability maps.
+
+They tell us which phases are
+stable under which conditions
+
+of pressure, temperature,
+composition.
+
+You can consider them
+as archives.
+
+So that's what I want to talk
+about, because it's really
+
+important to know this stuff.
+
+OK.
+
+So what are we going to do?
+
+So first of all, let's--
+
+I don't want to write
+on that one.
+
+This is interesting.
+
+This could be a work of art.
+
+I'd hate to desecrate it.
+
+You like?
+
+This is really good!
+
+So I'm just going
+to leave that.
+
+That's very good.
+
+That's excellent.
+
+OK.
+
+So I've been talking
+about phase.
+
+What is a phase?
+
+Let's get the right
+definition here.
+
+What is a phase?
+
+It's a region uniform chemical
+composition.
+
+Just to get it down.
+
+it's a region in a material,
+region of uniform chemical
+
+composition, and it has these
+other properties.
+
+Uniform chemical composition.
+
+It's physically distinct.
+
+And I'll show you by examples,
+but let's just get the
+
+definition down.
+
+It's physically distinct, and
+in the extreme case--
+
+so that means it's bounded.
+
+It's physically distinct.
+
+That's a fancy way of saying
+that you can put a
+
+boundary around it.
+
+It's bounded.
+
+And then the other property that
+it has, it's mechanically
+
+separable in the extreme.
+
+And so that's in the
+case where you have
+
+a multi-phase system.
+
+You can point to the
+different p.
+
+So what I'm going to
+do, is I'm going to
+
+give you some examples.
+
+And so I'm going to let circle
+p equal number of phases.
+
+I'll give you some examples.
+
+Why am I using circle p?
+
+Because just plain old p
+is already pressure.
+
+So pressure, so this is kind of
+a Western motif, you know?
+
+Like a Circle Bar Ranch
+or something.
+
+So it's a p with a circle.
+
+That's my font.
+
+That's how I say number
+of phases.
+
+So let's take a look
+at some examples.
+
+So here's some examples
+of p equals 1.
+
+So simple one is pure water.
+
+Pure H2O liquid.
+
+It has all of this.
+
+Wherever I have the water, all
+right, here's some water, it's
+
+all of the same chemical
+composition.
+
+It is physically distinct.
+
+I can put a boundary
+around it.
+
+And in this case, there's
+nothing to separate, because
+
+it's just a one-phase system.
+
+White gold.
+
+White gold is one phase.
+
+Because we have gold.
+
+Obviously we have gold.
+
+If you market something as white
+gold, it has no gold,
+
+you'll go to prison.
+
+And how do we make white gold go
+to its white color from the
+
+normal yellow?
+
+We add silver and
+we add nickel.
+
+And these are all FCC metals,
+and they substitute for one
+
+another on the lattice, and if
+you sample anywhere in the
+
+white gold, you get
+the same chemical
+
+composition, and so on.
+
+Air is an example of
+a one-phase system.
+
+It's a gas, and in decreasing
+order, we
+
+have nitrogen, oxygen.
+
+So it's a solution.
+
+We're breathing a solution.
+
+Nitrogen, oxygen, argon are
+the main constituents.
+
+There's some CO2, some sulfur
+dioxide if you live near a
+
+power plant, NOx if you're
+near a tailpipe, and
+
+so on and so forth.
+
+And then the last one I'll
+give as an example is
+
+calcia-zirconia.
+
+Or cubic zirconia.
+
+Let's just call it
+cubic zirconia.
+
+The holidays are coming,
+so we better get
+
+cubic zirconia up here.
+
+That's the poor man's diamond.
+
+Cubic zirconia, which consists
+of a solid solution of calcium
+
+oxide in zirconium oxide.
+
+This is a solid solution, so
+it's continuous and chemical
+
+composition identical.
+
+Now, contrast that with
+two-phase system.
+
+So p equals 2 looks like this.
+
+So let's look at, instead of
+simple water liquid, if I have
+
+ice cubes in water.
+
+So now I have two different
+phases, and they're separated
+
+by state of matter.
+
+State of matter is
+the issue here.
+
+Because I have a solid--
+
+this is solid--
+
+and I'm going to put the
+boundary around them.
+
+The composition of the solid
+is different from the
+
+composition of liquid.
+
+They're both the same water,
+but you can tell it's a
+
+different crystal structure
+and so on.
+
+And I can put boundaries
+around, and it's
+
+mechanically separable.
+
+You can pull the ice cubes
+out of the mix.
+
+Milk is two-phase.
+
+Milk has a fatty phase and
+it has an aqueous phase.
+
+The aqueous phase contains
+the minerals.
+
+That's why you can drink skim
+milk and still get your
+
+calcium, because calcium, even
+the general public knows
+
+calcium is a mineral.
+
+It's not elemental calcium,
+it's a calcium compound.
+
+But it's ionic, it's soluble in
+water, and the fat contains
+
+the other parts.
+
+You know from last day, this
+is one of the lipids.
+
+And so you have fat globules
+that are mechanically
+
+separable and distinct
+from aqueous.
+
+So they actually have
+a different chemical
+
+composition, different
+type of bonding.
+
+Right?
+
+This is largely nonpolar, and
+nonpolar doesn't like to
+
+dissolve in something that is
+polar and hydrogen-bonded.
+
+So they phase separate.
+
+I've been saying phase
+separate all along.
+
+Now you know what we mean
+by phase separate.
+
+Here's a third one.
+
+This is really cool, because
+you won't get this in any
+
+other chemistry class,
+because only 3.091
+
+talks about such things.
+
+David, can we cut to the
+document camera?
+
+I want to show you a piece
+of snowflake obsidian.
+
+Obsidian is a volcanic glass.
+
+So here's the piece
+of obsidian.
+
+And what you're looking at is,
+the black area is the glassy
+
+part, and the white is actually
+some of the obsidian
+
+that has decided to devitrify.
+
+And it is turning crystalline.
+
+And so those are islands of
+obsidian crystal sitting in a
+
+matrix of obsidian glass.
+
+If we go back to the--
+
+I picked that up in
+Yellowstone Park.
+
+It's fantastic.
+
+There's a wall, just a wall of
+obsidian that comes down.
+
+And I think I've got
+an image here.
+
+There it is.
+
+This one I pulled off
+the internet.
+
+So this is crystalline
+phase, and this is
+
+the amorphous phase.
+
+And the overall composition,
+it's a glass, it's a silicate.
+
+And why isn't it transparent
+to visible light?
+
+Because it's got iron in it.
+
+The iron gives it the absorption
+and capabilities.
+
+The band gap is invisible,
+so it's black.
+
+But then when this crystallizes,
+it's got a
+
+different index, and
+it's mainly SiO2.
+
+It's really the cristobalite
+phase of the obsidian.
+
+So that's cool.
+
+So this is actually
+differentiated on the basis of
+
+amorphous and crystalline of
+something that's virtually the
+
+same chemical composition.
+
+So this could give you an idea
+of what happens in the area of
+
+phase separation.
+
+OK.
+
+Now the second thing that
+I have to bring to your
+
+attention, is that these phase
+diagrams treat systems at
+
+equilibrium.
+
+They're stability maps, and
+they treat systems at
+
+equilibrium.
+
+So what is equilibrium?
+
+Let's just get one time up
+here a definition of
+
+equilibrium.
+
+Equilibrium is a condition which
+there is no net reaction
+
+taking place.
+
+The system could be reacting.
+
+If you're looking at the ice
+cubes in water, the ice could
+
+be dissolving, and some of the
+water could be freezing, but
+
+overall, with time, there's
+no net reaction.
+
+It's a dynamic system with
+no net reaction.
+
+And it's characterized as
+the lowest energy state.
+
+Systems strive towards
+equilibrium.
+
+If it's the lowest energy state,
+no net reaction then.
+
+If a system is truly at
+equilibrium, the properties
+
+should be invariant
+over time, because
+
+there's no net reaction.
+
+You can't prove equilibrium.
+
+You can only demonstrate the
+absence of equilibrium.
+
+Because at equilibrium, there's
+nothing, there's no
+
+net reaction.
+
+And it could be attainable
+by multiple paths.
+
+So in other words, if I have ice
+as the equilibrium phase,
+
+I can make it by freezing water,
+and get to the same ice
+
+at the given temperature
+and pressure.
+
+Or I could sublime.
+
+But if I specify the pressure
+and the composition, I should
+
+always end up with
+the same system.
+
+So attainable by
+multiple paths.
+
+Because it's a stable
+state, so it doesn't
+
+matter how you got there.
+
+It's a state function.
+
+And you know from your physics,
+a state function has
+
+the same value, regardless
+of how you arrived there.
+
+And then the last thing is,
+I want to differentiate.
+
+See, these are all single phase,
+but some of them are
+
+just one element, some of them
+are just one compound, and
+
+some of them have a whole mix.
+
+So we have a way of quantifying
+the degree of
+
+chemical complexity by using
+the term called component.
+
+It's a measure of chemical
+complexity.
+
+It's the number of chemically
+distinguishable constituents.
+
+And again, these are
+definitions.
+
+I'll give you some examples
+so then the
+
+definition comes to life.
+
+I like to think of it as the
+number of bottles you've got
+
+to pull off the shelf to
+make the final product.
+
+The building blocks.
+
+So for example, water
+is just water.
+
+You could say, but it's
+hydrogen and oxygen.
+
+But if you take 560 or some
+other thermal class, you'll
+
+learn that they're bound
+by mole ratio.
+
+You don't have freedom of
+hydrogen and oxygen.
+
+So it's just one bottle, whereas
+to make white gold,
+
+you need three bottles.
+
+You need a bottle of gold,
+a bottle of silver,
+
+and a bottle of nickel.
+
+So that's a three component
+system.
+
+And I'm going to designate the
+components by c with a
+
+circle around it.
+
+Because c without a circle
+is already composition,
+
+concentration.
+
+OK.
+
+So now we can put all of this
+together, and we'll show the
+
+difference between
+multicomponent and multiphase.
+
+So we'll make a little table
+here, and here I'm going to
+
+talk about one-phase systems,
+and distinguish on the basis
+
+of components.
+
+So if it's single phase single
+component, that's just water.
+
+One phase, one component.
+
+Simple liquid.
+
+If it's two components one
+phase, that could be
+
+calcia-zirconia.
+
+I need a bottle of calcia and a
+bottle of zirconia in order
+
+to make this two component
+single-phase system.
+
+And then to have three
+components,
+
+that's the white gold.
+
+It's still single phase, but I
+need the gold, silver, and the
+
+nickel, whereas if I come over
+here, I've got two phases.
+
+That could be slush.
+
+Slush, that's ice water.
+
+It's just one component.
+
+I just start with water, and
+drop it down to 0 Centigrade,
+
+and I'm going to end up with
+ice crystals in the water.
+
+So that's one component.
+
+I just needed one bottle.
+
+Literally, one bottle.
+
+All right.
+
+Now what about two components,
+two phases?
+
+Well, we saw earlier when we
+started thinking about
+
+solubility, we did the
+bilayer with carbon
+
+tetrachloride and water.
+
+Remember, we dropped potassium
+permanganate and iodine, and
+
+the potassium permanganate
+dissolved in the water, and
+
+the iodine dissolved in the
+carbon tetrachloride?
+
+Two different components.
+
+I need a bottle of carbon tet
+and a bottle of water.
+
+And they'll phase separate.
+
+They don't dissolve in one
+another, because this is a
+
+nonpolar liquid, and this is
+polar hydrogen bonded.
+
+That's the origin of
+phase separation.
+
+It's all about bonding, and
+bonding is all about
+
+electronic structure, and that
+sounds like a good topic for a
+
+class in chemistry.
+
+And then the last one
+here is obsidian.
+
+The snowflake obsidian,
+in which the
+
+components are SiO2--
+
+so I'm going to have three
+components and
+
+end up with two phases.
+
+SiO2, there's some magnesia, and
+then the black comes from
+
+the magnetite.
+
+Fe304.
+
+So I've got three bottles off
+the shelf, and I end up with
+
+something that is crystalline
+and amorphous.
+
+So that's where I get
+the two phases.
+
+Three components, two phases.
+
+It's great.
+
+So now I want to look at
+some stability maps.
+
+And I'm going to start with the
+simplest of all, which is
+
+the one we know best from human
+
+experience, and that's water.
+
+So we're going to look
+at the one--
+
+so it's a one component.
+
+So for water, we start with c
+equals 1, and the example is
+
+going to be water.
+
+One component phase diagram.
+
+So we don't have a composition
+axis, because the only thing
+
+we can vary is pressure
+and temperature.
+
+If we change composition,
+we've lost water.
+
+So it has to be axiomatically,
+no variation composition.
+
+All we have is that
+the coordinates of
+
+temperature and pressure.
+
+So there it is out of the book,
+and I'm going to draw it
+
+a little bit differently, just
+to emphasize three of my
+
+favorite words.
+
+Not to scale.
+
+Otherwise you can't see some
+of the subtle features.
+
+So overall, it's a
+y-shaped diagram.
+
+And this is pressure.
+
+Let's make it pressure
+in atmospheres.
+
+Then our human experiences
+is at 1 atmosphere.
+
+So at the highest temperatures,
+we expect to
+
+have vapor, and at the lowest
+temperatures, we expect solid.
+
+And in between, we
+expect liquid.
+
+And then if we look at the 1
+atmosphere isobar, what's
+
+happening on this line?
+
+On the one side of line it's
+liquid, and the other side of
+
+line, it's vapor.
+
+At this temperature, liquid
+and vapor coexist.
+
+I call that the boiling point.
+
+So I'm going to put 100 here.
+
+And we already learned from our
+little example of Mount
+
+Everest that this locust here,
+this line, is the liquid
+
+equals vapor two phase
+equilibrium.
+
+And you see how it changes?
+
+If I go to the top of Mount
+Everest, the pressure is less
+
+than 1 atmosphere.
+
+which means the boiling point
+of water is below the
+
+denaturing point.
+
+So this actually gives
+you the map.
+
+Or if I put the pressure
+cap on, I go up here.
+
+And you can use this in
+the kitchen again.
+
+If you love wild rice, and you
+can't wait 45 minutes when you
+
+get home, use a pressure
+cooker.
+
+What the pressure cooker does,
+is it allows you to have
+
+liquid up to 130 degrees
+Celsius.
+
+See, you can't steam it.
+
+You've got to soak
+it in water.
+
+And you know the
+Arrhenius Law.
+
+If you can get the temperature
+up by 30 degrees, you'll cut
+
+the cooking time in half.
+
+So how do you get water,
+liquid, at 130 degrees?
+
+Then you can cook quicker!
+
+Pressure.
+
+Seal it.
+
+And then you've got liquid
+water way, way up here.
+
+Now over here, this is
+solid goes to liquid.
+
+So this is the freezing
+point line.
+
+At 1 atmosphere, that's 0.
+
+0 Celsius.
+
+And you know, if you
+go skating--
+
+so let's say the ice
+is minus 5 Celsius.
+
+And you're here, but you put
+your weight on the blades, and
+
+the blades have small area.
+
+So pressure is force per area.
+
+So that puts you up here, and
+now you cross, and now you
+
+glide on water.
+
+Film of water.
+
+You ever watch a hockey game?
+
+I grew up in Canada.
+
+We used to say, well,
+the ice is fast.
+
+Why is the ice fast?
+
+Because you get down to
+temperatures where you just
+
+get the right slickness
+of water.
+
+If the ice is slow, the
+temperature is so close that,
+
+you know, you get these big,
+bruising hockey players, and
+
+they're moving up into
+here, and it's
+
+like they're dragging.
+
+And if you ever come from
+Minnesota or North Dakota, if
+
+you've ever skated when the
+temperature gets down about
+
+minus 20, minus 30?
+
+It's a different experience,
+because you never
+
+get across this line.
+
+Your blades are just, they
+can't get a good grip.
+
+See?
+
+Everything you need
+to know is here.
+
+This is four-star chef, this is
+
+prize-winning hockey player.
+
+We haven't got off the 1
+atmosphere line yet.
+
+OK.
+
+So now I'm going to say, this
+is single phase, right?
+
+It's just vapor.
+
+This is single phase, and
+this is single phase.
+
+It's all solid.
+
+And along this line, it's
+two phase, isn't it?
+
+Solid-liquid.
+
+This is ice cubes, isn't it.
+
+Anywhere along this line
+is ice cubes in water.
+
+Look at this one.
+
+This is liquid vapor.
+
+This is solid, liquid--
+
+all three of them
+coexist here.
+
+This is p equals 3, which means,
+ice cubes floating in
+
+boiling water.
+
+And this happens at
+only one point.
+
+It's called the triple point,
+and its coordinates are--
+
+this is not to scale.
+
+So this is 0.01 degrees
+C. It's a
+
+1/100 of a degree higher.
+
+And the pressure here is 4.58
+millimeters of mercury, which
+
+then you can convert using
+the 760 as 1 atmosphere.
+
+Oh, and this is solid-vapor.
+
+You can go directly from solid
+to vapor down here.
+
+If you hang up your clothes on
+a line and it's minus 20
+
+degrees outside, first
+thing that
+
+happens, the clothes freeze.
+
+You come back five
+hours later, and
+
+the clothes are dry.
+
+Well, what happened?
+
+Did somebody take them in?
+
+Run them around the clothes
+dryer, then
+
+hang them up for you?
+
+No.
+
+You're going directly from solid
+to vapor, down in here.
+
+So here's the whole story
+of the phase diagram.
+
+One last thing I want
+to point out.
+
+Here, you're at a given
+temperature and it's vapor.
+
+And then you squeeze, squeeze,
+squeeze, and now things get
+
+closer together, and you go
+from paper to liquid at
+
+constant temperature.
+
+That makes sense, right?
+
+I start from vapor, constant
+temperature.
+
+I squeeze it, I get liquid,
+I keep squeezing,
+
+I should make solid.
+
+Here's vapor.
+
+I squeeze, I get solid,
+and I squeeze
+
+harder, and I get liquid.
+
+That makes no sense at all,
+but that's what happens.
+
+What does this tell me?
+
+It tells me that the number of
+nearest neighbors in the solid
+
+is greater than the vapor.
+
+Yeah, I get that.
+
+But the number of nearest
+neighbors in the liquid must
+
+be greater than the
+number of nearest
+
+neighbors in the solid.
+
+This is an exception.
+
+When I see this negative slope,
+it means that ice cubes
+
+are going to float on water.
+
+That's what I learn from
+this negative slope.
+
+So let's put that down.
+
+dp by dt when dp by dt
+is less than zero.
+
+This is for solid
+equals liquid.
+
+That means that the density of
+the solid is less than the
+
+density of the liquid.
+
+All from here.
+
+OK.
+
+Good.
+
+So let's look at a few
+other phase diagrams.
+
+I think I've got a few
+things up here.
+
+Here's silicon.
+
+Pressure versus temperature.
+
+Its normal melting
+point is about--
+
+see, now I said normal
+melting point.
+
+After today's lecture, if
+somebody says, what's the
+
+boiling point of water?
+
+You don't go, 100 degrees.
+
+You say, at what pressure?
+
+And they go, oh, I hate you.
+
+I hated you before.
+
+I'm going to use
+an adverb here.
+
+Now I really hate you.
+
+OK.
+
+So this is the normal melting
+point of silicon.
+
+It's about 1430 degrees
+Centigrade, or a 1700
+
+something Kelvin.
+
+And it also has this
+negative slope.
+
+And what does that tell you?
+
+That liquid silicon is denser
+than solid silicon, and it's a
+
+good thing it is, because
+we wouldn't have the
+
+microelectronics age if
+it weren't for that.
+
+We couldn't have Teukolsky
+crystal growth and everything
+
+else that makes silicon
+dirt cheap.
+
+You know why it's dirt cheap?
+
+Because it's made from dirt.
+
+That's why it's dirt cheap.
+
+It's true.
+
+Here's aluminum.
+
+This is normal.
+
+This is the normal solid-liquid
+equilibrium.
+
+This is FCC metal, which
+is the closest packed.
+
+Axiomatically, the liquid must
+be less well-packed.
+
+All right?
+
+So this is dog bites man,
+this is man bites dog.
+
+This is the unusual one.
+
+OK.
+
+What else do we have?
+
+Nitrogen!
+
+Here's nitrogen.
+
+I drew this.
+
+So there's the 1 atmosphere
+line.
+
+Nitrogen boils at 77
+Kelvin, and it
+
+freezes at about 63 Kelvin.
+
+And it's got the positive slope
+that you'd expect, and
+
+so solid nitrogen is denser
+then liquid nitrogen.
+
+And you can remember
+77 Kelvin.
+
+You want to remember a
+few of these things.
+
+I wanted to point out to
+you that at atmospheric
+
+temperature, ambient
+temperature, you
+
+can remember 20-20.
+
+20-20 vision.
+
+So at 20 degrees C, it's roughly
+20 millimeters of
+
+mercury, is the vapor
+pressure of water.
+
+It's not exactly true, but
+it's close enough.
+
+I think it's really 24.
+
+But 20-20 is nice to know.
+
+And what's the street
+address for MIT?
+
+77 Mass Ave. That's the boiling
+point of liquid
+
+nitrogen, 77 Kelvin.
+
+So I thought we'd do
+a few things here.
+
+And I'm going to show you a
+little bit of fun and games
+
+with liquid nitrogen.
+
+But first, I've been instructed
+I have to practice
+
+safe laboratory--
+
+So I'm going to put
+on my lab coat.
+
+Yes.
+
+It's a nice lab coat.
+
+Mm-hm!
+
+Yeah, look.
+
+You want to know--
+
+let's go back to this.
+
+They have to know where
+the-- this is not
+
+just any old lab coat.
+
+This is a nice lab coat.
+
+This is from France.
+
+It's from MAISON DUTECH.
+
+See?
+
+Notice the collar.
+
+It's not that typical,
+you know.
+
+MAISON DUTECH.
+
+OK.
+
+Let's go back to the
+phase diagram.
+
+So Dave Broderick is going
+to help us here.
+
+So we're going to
+have some fun.
+
+I'm going to put on
+a face shield so
+
+I don't blind myself.
+
+All right.
+
+Here we go.
+
+All right.
+
+So let's get some
+liquid nitrogen.
+
+Sounds different, huh?
+
+Sounds terrible for me.
+
+All right.
+
+So we've got some liquid
+nitrogen here, and I'll pour
+
+it into a Dewar.
+
+So what happens when you wet a
+sheet of paper with ink with
+
+liquid nitrogen?
+
+What kind of bonding is there
+in liquid nitrogen?
+
+Look.
+
+No running, no running.
+
+If it's liquid nitrogen.
+
+I tell you, everything you
+learn here is so valuable
+
+compared all the other stuff
+you learn here--
+
+All right.
+
+So there's a couple of things.
+
+So let's look at glass
+transition temperature.
+
+So this is a latex glove.
+
+You can see it's above its glass
+transition temperature,
+
+and the cross-links are
+snapping it back.
+
+What I'm going to do, is take
+it down below its glass
+
+transition temperature, and turn
+it glassy and brittle.
+
+So that it's below the TG.
+
+Here's some paraffin.
+
+Paraffin, which is also
+a polymer here.
+
+Take the paper off.
+
+OK.
+
+So here's paraffin.
+
+Look.
+
+Look at the van der
+Waals bond.
+
+All right?
+
+This is van der Waals bond.
+
+Now we're going to
+go below the TG.
+
+It's liquid nitrogen!
+
+It doesn't matter.
+
+OK, you can hear it already.
+
+So it's now below the glass
+transition temperature.
+
+So what else have we got?
+
+Oh, you've heard of the glass
+flowers at Harvard?
+
+Well, we've got glass
+flowers here, so.
+
+Here's a rose.
+
+See, in the proteins, you know,
+it's above the-- you
+
+know, it's soft.
+
+But now, we're going
+to put the--
+
+mm-hm.
+
+Here we go.
+
+You ready?
+
+Oh, come on.
+
+It's not a kitten.
+
+What's the matter?
+
+It's still burbling here.
+
+We have to wait until
+it's dead.
+
+This is for science.
+
+OK.
+
+Now it's below its glass
+transition temperature.
+
+Oh, I'm sorry, David.
+
+I should put this over
+on the other side.
+
+But maybe it's the red,
+or maybe it's
+
+because it's a rose.
+
+So here's the chrysanthemum.
+
+Today is your day.
+
+Let's go.
+
+Get this thing moving!
+
+Yeah.
+
+So there you have it.
+
+There you have it.
+
+I think that's--
+
+oh, there's one, may we
+go back to the slide?
+
+Better put the gloves
+on for this.
+
+I'll have to write
+apology letters.
+
+OK.
+
+So we're going to do next, is
+we're going to look at phase
+
+equilibriums.
+
+There's the melting points and
+boiling point of oxygen,
+
+argon, and nitrogen.
+
+And what you notice is that
+nitrogen boils at a lower
+
+temperature then oxygen
+and argon.
+
+So what I'm going to do, is I'm
+going to pour some liquid
+
+nitrogen into this beaker.
+
+And then inside the graduated
+cylinder, I'm going to let it
+
+sit here, and we're going
+to condense air.
+
+And the result will be that
+we're going to start
+
+condensing liquid oxygen, and
+they'll be little bits of
+
+argon ice floating
+in liquid oxygen.
+
+And liquid oxygen is faintly
+blue, and it's paramagnetic,
+
+as you know, because it's got
+the unpaired electrons, which
+
+means that it will levitate
+in a magnetic field.
+
+I couldn't bring a big magnet
+in here, but we'll see if we
+
+can make some blue stuff.
+
+And it's foaming, because this
+would be like pouring water
+
+into something that's--
+
+I don't know.
+
+300 degrees Centigrade.
+
+But eventually, the heat
+transfer gets low enough that
+
+you have stability here, and--
+
+yeah.
+
+OK.
+
+Oh, that's terrific.
+
+OK.
+
+What else have we got?
+
+Let's go back to the slide.
+
+God, I hate this thing.
+
+OK.
+
+So you've been looking
+at that nitrogen.
+
+Let's look at what's next.
+
+Ah.
+
+Now if you solidify nitrogen
+here, you get a whole bunch of
+
+different polymorphs.
+
+Different crystal structures.
+
+So there are about five or six
+different crystallographic
+
+forms of solid nitrogen.
+
+For that, we'd have to
+bring liquid helium.
+
+4.2 Kelvin.
+
+Very cool stuff.
+
+Here's carbon dioxide.
+
+Now, it also has the positive
+slope, so solid
+
+will sink in liquid.
+
+But look, the interesting
+point here.
+
+The triple point is
+5 atmospheres.
+
+At atmospheric pressure, you go
+directly from solid to gas.
+
+It sublimes.
+
+And that's advantageous.
+
+When we use carbon dioxide as
+a coolant, when it gives up
+
+its enthalpy to cool, it doesn't
+then turn into liquid.
+
+If you chill something with ice,
+with water ice, when it
+
+gives up its enthalpy,
+the object is
+
+now swimming in water.
+
+And that's no good.
+
+So hence we have the term dry
+ice, because we go directly
+
+from solid to vapor.
+
+And we want to prove this.
+
+So what we've got here is
+a big block of dry ice.
+
+So this is at minus 78 degrees
+Celsius, and it's
+
+still stable here.
+
+Well, it's subliming
+before your eyes.
+
+It's smaller than it was when
+we started the lecture.
+
+So what I'm going to do now--
+
+oh, I'm not wearing
+that stuff.
+
+I guess I'd better.
+
+They're going to write
+me up on some log,
+
+teaching you bad practice.
+
+But anyways.
+
+All right.
+
+So what we're going to do, is
+we're going to test the
+
+proposal that this actually
+goes-- so I've got some water.
+
+Here, David, let's go
+out to the video.
+
+So let's take some water.
+
+I think we got water
+from France.
+
+Goes with the lab coat.
+
+This is Evian, OK?
+
+So I pour the Evian into
+the Florence flask.
+
+This is Florence.
+
+Florence is round, and the
+Erlenmeyer is the flat one.
+
+So let's move this guy.
+
+You're going in the backstage
+for a while.
+
+You just keep
+
+condensing All right.
+
+So now, this is here.
+
+Now what we're going to do, is
+we're going to put some dry
+
+ice in there, and see
+if we go directly
+
+from solid to a vapor.
+
+Take a chip off the
+old block, here.
+
+OK.
+
+So now you can see that
+it's going directly
+
+from solid to vapor.
+
+So that's carbon dioxide
+bubbles.
+
+And we assume that the phase
+diagrams is correct.
+
+I mean, another thing
+we could do, is--
+
+I mean, I know what club
+soda tastes like.
+
+I could just test it, right?
+
+Yeah.
+
+It's carbon dioxide.
+
+Now!
+
+Here's the other thing.
+
+You know, Schweppes likes to
+pride itself on tiny bubbles.
+
+They have a tagline,
+Tiny Bubbles.
+
+Right?
+
+So here's Schweppes.
+
+And you can see Schweppes,
+with their
+
+wimpy little tiny bubbles.
+
+Can you get that, David?
+
+But we have, we have
+big bubbles.
+
+I mean, this is pure.
+
+You can't get any better
+than that.
+
+I got Evian water, and I got
+a block of carbon dioxide.
+
+I like making my own
+carbonated water.
+
+I've taken it to a new level.
+
+OK.
+
+What else do we have?
+
+Well, let's see if we made
+any liquid oxygen here.
+
+Try this.
+
+I don't know if we got
+anything here.
+
+Oh yeah!
+
+Oh, wow.
+
+Look.
+
+OK.
+
+So that liquid in there--
+oh, I see.
+
+You've got a separate thing.
+
+I don't know if you can see.
+
+It's condensing.
+
+That liquid in there, that's
+liquid oxygen.
+
+I won't drink this.
+
+But I can inhale it.
+
+Pure oxygen.
+
+I could have a cigarette,
+and just put the
+
+cigarette in there.
+
+What happens if I put the lit
+cigarette into the oxygen?
+
+All that happens is that it
+burns quickly, that's all.
+
+There's no explosion.
+
+It burns quickly.
+
+If you walk into a room full of
+oxygen, all that happens is
+
+you'll singe your nose,
+that's all.
+
+There's no explosion.
+
+It's just oxygen.
+
+There's no fuel.
+
+The fuel is just in tobacco,
+and there's not much.
+
+It's not a problem.
+
+A room full of oxygen?
+
+Pfft!
+
+OK.
+
+Let's go back to the slides.
+
+What have we got here?
+
+We've got some examples of
+other phase diagrams.
+
+All right.
+
+Yeah.
+
+[MUSIC PLAYBACK: FROM 'PHANTOM
+OF THE OPERA']
+
+PROFESSOR: Actually,
+it's quite tasty.
+
+All right.
+
+So.
+
+Now, here's zirconia.
+
+Now, here's the thing to
+know about zirconia.
+
+Look at all the different
+phases.
+
+And cubic zirconia is the one
+that has a high index of
+
+refraction, but it's stable only
+at temperatures exceeding
+
+2000 degrees C. So
+that's no good.
+
+So what I'm going to show you
+next day is that by changing
+
+the composition, and adding
+calcium oxide, we open up this
+
+zone here that's labeled cubic,
+and we get it stable
+
+all the way down to
+room temperature.
+
+It's an example of changing
+composition to get the
+
+stability of a phase
+that we want.
+
+This is carbon.
+
+So down here, the normal form,
+as we've learned earlier, the
+
+normal form is graphite.
+
+Diamond is formed at elevated
+temperatures and pressures.
+
+And this is liquid carbon.
+
+All right?
+
+Now, to make artificial diamond,
+you can try putting
+
+graphite in an anvil, and
+squeezing, and squeezing, and
+
+squeezing, and coming
+up into here.
+
+And then it becomes metastable,
+and then maybe,
+
+because the activation energy
+to jump from that sp3
+
+hybridized state to sp2 is so
+high, the diamond is stable.
+
+So you don't have to go running
+home to see if your
+
+diamond studs are now turning
+into graphite.
+
+They won't.
+
+Once you get into this
+zone, they'll stay.
+
+The activation energy
+is too high.
+
+You need more than 1/40 eV
+to do it, is necessary.
+
+But in the 1950s, General
+Electric, its Schenectady
+
+research labs, reasoned that
+because carbon is so soluble
+
+in iron, they could dissolve
+carbon in liquid iron, and
+
+then raise the pressure and
+temperature, and then change
+
+to exsolve and cause carbon
+to precipitate
+
+out of molten iron.
+
+That's the birth of artificial
+diamond.
+
+That's how they did it.
+
+Using this concept, but then
+dissolving it in molten iron.
+
+[MUSIC PLAYBACK: 'DIAMONDS ARE
+A GIRL'S BEST FRIEND']
+
+PROFESSOR: I don't know
+how that got in there.
+
+All right.
+
+Here's one for mercury.
+
+I looked it up, using the tools
+that you've been taught
+
+here in 3.091.
+
+So this is a paper phase
+diagram for mercury.
+
+And physicists drive me nuts,
+because they plot temperature
+
+versus pressure.
+
+I want pressure versus
+temperature.
+
+So I just turned it around.
+
+And so here's the liquid line.
+
+So you know that liquid mercury
+is going to float on
+
+solid mercury, and there's a
+plurality of solid phases.
+
+And these are all different
+crystal structures.
+
+Now I've got a treat for you.
+
+I was in Barcelona several
+years ago, and I saw the
+
+mercury fountain that was made
+by Joan Miro in collaboration
+
+with Calder.
+
+Calder has the big sail outside
+of East Campus.
+
+So Calder collaborated
+with Miro, back in
+
+the '30s and '40s.
+
+And this is in honor of the
+miners of Almaden, where there
+
+are cinnabar mines.
+
+And the miners fought bravely
+against the Fascist forces of
+
+Franco, and Miro wanted
+to honor them.
+
+So here's their museum.
+
+It's a beautiful place
+up on top of an
+
+escarpment over Barcelona.
+
+And what I'm going to show you
+is a mercury fountain.
+
+[MUSIC PLAYBACK]
+
+This is liquid mercury.
+
+The speed has not
+been altered.
+
+This is a liquid at room
+temperature, density 13.5,
+
+metallic bonds.
+
+Look at it.
+
+Very high surface tension.
+
+Look at the way it shimmers.
+
+Look at this shot.
+
+This has not been altered.
+
+That's the way it pours
+into gravity field.
+
+It's really fantastic.
+
+And of course, mercury vapor
+is toxic, so the
+
+whole thing is in a--
+
+[END MUSIC PLAYBACK]
+
+PROFESSOR: Oh, that's the--
+
+I cut that snippet out
+of the documentary.
+
+OK, we don't want to see that.
+
+So they have the whole
+thing inside of a
+
+polymethylmethacrylate cage, to
+keep the mercury vapor from
+
+affecting the people that
+work in the museum.
+
+Here are some phase diagrams
+from hell.
+
+This is bismuth.
+
+And look at bismuth.
+
+Bismuth is like water,
+and like silicon.
+
+So the solid is less dense
+than the liquid.
+
+But look at all of these
+different phases.
+
+Here's sulfur.
+
+Sulfur is crazy.
+
+Look, phases in the solid phase,
+there's even phases in
+
+the liquid!
+
+Different phases.
+
+They're allotropes.
+
+Here's sulfur.
+
+Elemental sulfur, the disulfide,
+hexasulfide.
+
+It makes rings, it makes
+long chains.
+
+And these are called
+allotropes.
+
+They're different forms
+of the same element.
+
+So oxygen is O. There's
+the diatomic molecule.
+
+And the triatomic molecule,
+which is ozone, these are all
+
+allotropes of oxygen.
+
+What else do we have?
+
+OK.
+
+This is polymorphs.
+
+So this is alpha goes to beta.
+
+See, different crystal
+structures.
+
+You could see with your naked
+eye what's going on here.
+
+Different crystal structures.
+
+And then this goes to lambda,
+and then finally, they're
+
+pouring here.
+
+And if you get a very high
+cooling rate, and you've got
+
+those long chains,
+what happens?
+
+You don't form the crystal.
+
+You form the amorphous form.
+
+So they'll call this forming
+plastic sulfur.
+
+We know better.
+
+It's amorphous sulfur.
+
+It's not plastic sulfur.
+
+Here's water, a complete
+diagram.
+
+Now, this is in kilobars.
+
+So there's all the different
+phases of water.
+
+There's the negative line.
+
+That's the thing here.
+
+But at very, very high.
+
+Look at all the different
+phases of water.
+
+And they have numbers on them.
+
+If you read Kurt Vonnegut's
+Cat's
+
+Cradle, there's ice nine.
+
+You get that going, it freezes
+the whole world, right?
+
+But here's, I draw your
+attention on this one.
+
+You see this point here?
+
+This is ice seven.
+
+At 100 degrees C, it's solid.
+
+You need 25 kilobars.
+
+So we could go over to the lab,
+take some water, put 25
+
+kilobars on it, make solid
+ice at 100 degrees C.
+
+And it'll be stable.
+
+Look!
+
+This is minus 78.
+
+It's been here for
+a long time.
+
+So now I come into a cocktail
+party with this, I drop this
+
+ice cube into a glass of aqueous
+beverage, it sinks to
+
+the bottom, and the beverage
+heats up to the boiling point.
+
+That's what this
+is telling you!
+
+That'll get you popularity
+instantly.
+
+How did you do that?
+
+How did you do that?
+
+And up here is the supercritical
+fluid, the last
+
+thing we haven't said
+anything about.
+
+Look.
+
+If you take a gas, and you
+keep squeezing it and
+
+squeezing it, eventually the gas
+molecules are close enough
+
+together that they're
+indistinguishable from the
+
+liquid phase.
+
+Or if you start here, with the
+liquid, and you keep raising
+
+the temperature, the density
+goes lower and lower until the
+
+molecules are far enough apart
+that you can't tell this zone,
+
+whether it's a rarefied liquid
+or a highly compressed gas.
+
+The properties criss-cross.
+
+This is supercritical.
+
+It has liquid-like transport
+properties, and vapor-like
+
+chemical properties.
+
+So you can end up doing things
+that are very, very different.
+
+Now, I'm going to give you an
+example of decaffeinating
+
+coffee by taking the coffee,
+going up into the
+
+supercritical regime, which
+allows you to extract the
+
+caffeine, and not
+brew the coffee.
+
+So you want to just get the--
+well, if you just heat it up,
+
+you'll make the coffee.
+
+So here's an example.
+
+It's called solvent
+extraction.
+
+Historically, this solvent was
+methylene chloride, which is
+
+also used as paint stripper.
+
+We don't do that anymore
+to coffee.
+
+They did in the '60s!
+
+They did.
+
+They also used
+trichloroethylene.
+
+It works really well to leech
+out the caffeine.
+
+How much is left in there for
+you to taste in your coffee?
+
+I don't know.
+
+Maybe that's why people were
+so excited in the '60s to
+
+drink their decaffeinated
+Sanka.
+
+I don't know.
+
+But anyway, so you take the
+green beans in carbon dioxide
+
+as supercritical, and drop the
+caffeine level, and then you
+
+play with temperature and
+pressure to go over the KSP.
+
+The caffeine salts out, and
+then you recycle the CO2.
+
+OK.
+
+I hope I've given you some
+
+introduction to phase diagrams.
+
+And we'll see you on Monday.
\ No newline at end of file
diff --git a/xdewLsXI_UQ.txt b/xdewLsXI_UQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..942c147703b93eaca4bde4318bb6c5a740482515
--- /dev/null
+++ b/xdewLsXI_UQ.txt
@@ -0,0 +1,1067 @@
+align:start position:0%
+ 
+we now study a model that involves the
+
+ align:start position:0%
+we now study a model that involves the
+ 
+
+ align:start position:0%
+we now study a model that involves the
+sum of independent random variables but
+
+ align:start position:0%
+sum of independent random variables but
+ 
+
+ align:start position:0%
+sum of independent random variables but
+with a twist it's going to be the sum of
+
+ align:start position:0%
+with a twist it's going to be the sum of
+ 
+
+ align:start position:0%
+with a twist it's going to be the sum of
+a random number of independent random
+
+ align:start position:0%
+a random number of independent random
+ 
+
+ align:start position:0%
+a random number of independent random
+variables as opposed to a fixed number
+
+ align:start position:0%
+variables as opposed to a fixed number
+ 
+
+ align:start position:0%
+variables as opposed to a fixed number
+this is a model that shows up in a
+
+ align:start position:0%
+this is a model that shows up in a
+ 
+
+ align:start position:0%
+this is a model that shows up in a
+variety of applications but it will also
+
+ align:start position:0%
+variety of applications but it will also
+ 
+
+ align:start position:0%
+variety of applications but it will also
+help us fine tune our command of the law
+
+ align:start position:0%
+help us fine tune our command of the law
+ 
+
+ align:start position:0%
+help us fine tune our command of the law
+of iterated expectations and the law of
+
+ align:start position:0%
+of iterated expectations and the law of
+ 
+
+ align:start position:0%
+of iterated expectations and the law of
+total variance the story goes as follows
+
+ align:start position:0%
+total variance the story goes as follows
+ 
+
+ align:start position:0%
+total variance the story goes as follows
+you go shopping and you visit a number
+
+ align:start position:0%
+you go shopping and you visit a number
+ 
+
+ align:start position:0%
+you go shopping and you visit a number
+of stores except that the number of
+
+ align:start position:0%
+of stores except that the number of
+ 
+
+ align:start position:0%
+of stores except that the number of
+stores that you will visit is itself a
+
+ align:start position:0%
+stores that you will visit is itself a
+ 
+
+ align:start position:0%
+stores that you will visit is itself a
+random variable at each one of the
+
+ align:start position:0%
+random variable at each one of the
+ 
+
+ align:start position:0%
+random variable at each one of the
+stores you spend a certain amount of
+
+ align:start position:0%
+stores you spend a certain amount of
+ 
+
+ align:start position:0%
+stores you spend a certain amount of
+money we denoted by X I and we make the
+
+ align:start position:0%
+money we denoted by X I and we make the
+ 
+
+ align:start position:0%
+money we denoted by X I and we make the
+assumption that the x i's are drawn from
+
+ align:start position:0%
+assumption that the x i's are drawn from
+ 
+
+ align:start position:0%
+assumption that the x i's are drawn from
+a certain distribution they're
+
+ align:start position:0%
+a certain distribution they're
+ 
+
+ align:start position:0%
+a certain distribution they're
+identically distributed and they're
+
+ align:start position:0%
+identically distributed and they're
+ 
+
+ align:start position:0%
+identically distributed and they're
+independent of each other
+
+ align:start position:0%
+independent of each other
+ 
+
+ align:start position:0%
+independent of each other
+we also make the assumption that the x
+
+ align:start position:0%
+we also make the assumption that the x
+ 
+
+ align:start position:0%
+we also make the assumption that the x
+i's are independent of capital and this
+
+ align:start position:0%
+i's are independent of capital and this
+ 
+
+ align:start position:0%
+i's are independent of capital and this
+means that no matter how many stores you
+
+ align:start position:0%
+means that no matter how many stores you
+ 
+
+ align:start position:0%
+means that no matter how many stores you
+visit the X I the amount of money you
+
+ align:start position:0%
+visit the X I the amount of money you
+ 
+
+ align:start position:0%
+visit the X I the amount of money you
+spend in each one of the stores that you
+
+ align:start position:0%
+spend in each one of the stores that you
+ 
+
+ align:start position:0%
+spend in each one of the stores that you
+visit is a random variable that's drawn
+
+ align:start position:0%
+visit is a random variable that's drawn
+ 
+
+ align:start position:0%
+visit is a random variable that's drawn
+from a common distribution which does
+
+ align:start position:0%
+from a common distribution which does
+ 
+
+ align:start position:0%
+from a common distribution which does
+not change no matter what capital n is
+
+ align:start position:0%
+not change no matter what capital n is
+ 
+
+ align:start position:0%
+not change no matter what capital n is
+with these assumptions in place let us
+
+ align:start position:0%
+with these assumptions in place let us
+ 
+
+ align:start position:0%
+with these assumptions in place let us
+now focus on the total amount of money
+
+ align:start position:0%
+now focus on the total amount of money
+ 
+
+ align:start position:0%
+now focus on the total amount of money
+that you are spending this is the sum of
+
+ align:start position:0%
+that you are spending this is the sum of
+ 
+
+ align:start position:0%
+that you are spending this is the sum of
+random variables but with the extra
+
+ align:start position:0%
+random variables but with the extra
+ 
+
+ align:start position:0%
+random variables but with the extra
+twist that the index goes up to capital
+
+ align:start position:0%
+twist that the index goes up to capital
+ 
+
+ align:start position:0%
+twist that the index goes up to capital
+n which is itself a random variable how
+
+ align:start position:0%
+n which is itself a random variable how
+ 
+
+ align:start position:0%
+n which is itself a random variable how
+do we deal with this situation
+
+ align:start position:0%
+do we deal with this situation
+ 
+
+ align:start position:0%
+do we deal with this situation
+one approach that's always worth trying
+
+ align:start position:0%
+one approach that's always worth trying
+ 
+
+ align:start position:0%
+one approach that's always worth trying
+when faced with a complicated problem is
+
+ align:start position:0%
+when faced with a complicated problem is
+ 
+
+ align:start position:0%
+when faced with a complicated problem is
+to try to condition on some information
+
+ align:start position:0%
+to try to condition on some information
+ 
+
+ align:start position:0%
+to try to condition on some information
+that will make the problem easier in
+
+ align:start position:0%
+that will make the problem easier in
+ 
+
+ align:start position:0%
+that will make the problem easier in
+this case we can condition on the value
+
+ align:start position:0%
+this case we can condition on the value
+ 
+
+ align:start position:0%
+this case we can condition on the value
+of capital n taking a fixed specific
+
+ align:start position:0%
+of capital n taking a fixed specific
+ 
+
+ align:start position:0%
+of capital n taking a fixed specific
+value because in that case we will be
+
+ align:start position:0%
+value because in that case we will be
+ 
+
+ align:start position:0%
+value because in that case we will be
+dealing with the sum of a finite number
+
+ align:start position:0%
+dealing with the sum of a finite number
+ 
+
+ align:start position:0%
+dealing with the sum of a finite number
+of random variables where that number is
+
+ align:start position:0%
+of random variables where that number is
+ 
+
+ align:start position:0%
+of random variables where that number is
+a fixed specific number and this is a
+
+ align:start position:0%
+a fixed specific number and this is a
+ 
+
+ align:start position:0%
+a fixed specific number and this is a
+situation we have encountered before and
+
+ align:start position:0%
+situation we have encountered before and
+ 
+
+ align:start position:0%
+situation we have encountered before and
+know how to deal with it
+
+ align:start position:0%
+know how to deal with it
+ 
+
+ align:start position:0%
+know how to deal with it
+so let us get started let us calculate
+
+ align:start position:0%
+so let us get started let us calculate
+ 
+
+ align:start position:0%
+so let us get started let us calculate
+the expected value of y if we condition
+
+ align:start position:0%
+the expected value of y if we condition
+ 
+
+ align:start position:0%
+the expected value of y if we condition
+on the number of stars let's say for
+
+ align:start position:0%
+on the number of stars let's say for
+ 
+
+ align:start position:0%
+on the number of stars let's say for
+example someone tells us that we visited
+
+ align:start position:0%
+example someone tells us that we visited
+ 
+
+ align:start position:0%
+example someone tells us that we visited
+five stars then the expected value of y
+
+ align:start position:0%
+five stars then the expected value of y
+ 
+
+ align:start position:0%
+five stars then the expected value of y
+is going to be the expected value of the
+
+ align:start position:0%
+is going to be the expected value of the
+ 
+
+ align:start position:0%
+is going to be the expected value of the
+sum of the amount of money you spend in
+
+ align:start position:0%
+sum of the amount of money you spend in
+ 
+
+ align:start position:0%
+sum of the amount of money you spend in
+each one of those five stores in our
+
+ align:start position:0%
+each one of those five stores in our
+ 
+
+ align:start position:0%
+each one of those five stores in our
+instance it's that random variable
+
+ align:start position:0%
+instance it's that random variable
+ 
+
+ align:start position:0%
+instance it's that random variable
+capital n but since I told you that
+
+ align:start position:0%
+capital n but since I told you that
+ 
+
+ align:start position:0%
+capital n but since I told you that
+capital n takes a specific numerical
+
+ align:start position:0%
+capital n takes a specific numerical
+ 
+
+ align:start position:0%
+capital n takes a specific numerical
+value this means that this instance of
+
+ align:start position:0%
+value this means that this instance of
+ 
+
+ align:start position:0%
+value this means that this instance of
+capital n in the index of the summation
+
+ align:start position:0%
+capital n in the index of the summation
+ 
+
+ align:start position:0%
+capital n in the index of the summation
+can be replaced by little n if I tell
+
+ align:start position:0%
+can be replaced by little n if I tell
+ 
+
+ align:start position:0%
+can be replaced by little n if I tell
+you that capital n is equal to little n
+
+ align:start position:0%
+you that capital n is equal to little n
+ 
+
+ align:start position:0%
+you that capital n is equal to little n
+then this number here capital n becomes
+
+ align:start position:0%
+then this number here capital n becomes
+ 
+
+ align:start position:0%
+then this number here capital n becomes
+the same as little n here we use now the
+
+ align:start position:0%
+the same as little n here we use now the
+ 
+
+ align:start position:0%
+the same as little n here we use now the
+assumption that capital n is independent
+
+ align:start position:0%
+assumption that capital n is independent
+ 
+
+ align:start position:0%
+assumption that capital n is independent
+from the excise here we have the sum of
+
+ align:start position:0%
+from the excise here we have the sum of
+ 
+
+ align:start position:0%
+from the excise here we have the sum of
+a fixed number of random variables all
+
+ align:start position:0%
+a fixed number of random variables all
+ 
+
+ align:start position:0%
+a fixed number of random variables all
+of them are independent of capital n if
+
+ align:start position:0%
+of them are independent of capital n if
+ 
+
+ align:start position:0%
+of them are independent of capital n if
+I give you some information on capital n
+
+ align:start position:0%
+I give you some information on capital n
+ 
+
+ align:start position:0%
+I give you some information on capital n
+this does not change the distribution of
+
+ align:start position:0%
+this does not change the distribution of
+ 
+
+ align:start position:0%
+this does not change the distribution of
+the x i's so the conditioning does not
+
+ align:start position:0%
+the x i's so the conditioning does not
+ 
+
+ align:start position:0%
+the x i's so the conditioning does not
+affect the answer the conditional
+
+ align:start position:0%
+affect the answer the conditional
+ 
+
+ align:start position:0%
+affect the answer the conditional
+expectation is going to be the same as
+
+ align:start position:0%
+expectation is going to be the same as
+ 
+
+ align:start position:0%
+expectation is going to be the same as
+the unconditional expectation and now we
+
+ align:start position:0%
+the unconditional expectation and now we
+ 
+
+ align:start position:0%
+the unconditional expectation and now we
+have the expected value of a sum of
+
+ align:start position:0%
+have the expected value of a sum of
+ 
+
+ align:start position:0%
+have the expected value of a sum of
+random variables each one of them has a
+
+ align:start position:0%
+random variables each one of them has a
+ 
+
+ align:start position:0%
+random variables each one of them has a
+common expectation let's denote it with
+
+ align:start position:0%
+common expectation let's denote it with
+ 
+
+ align:start position:0%
+common expectation let's denote it with
+this notation this is the common
+
+ align:start position:0%
+this notation this is the common
+ 
+
+ align:start position:0%
+this notation this is the common
+expected value of all the x i's and
+
+ align:start position:0%
+expected value of all the x i's and
+ 
+
+ align:start position:0%
+expected value of all the x i's and
+we're adding n of them so we obtain n
+
+ align:start position:0%
+we're adding n of them so we obtain n
+ 
+
+ align:start position:0%
+we're adding n of them so we obtain n
+times this expectation now let us apply
+
+ align:start position:0%
+times this expectation now let us apply
+ 
+
+ align:start position:0%
+times this expectation now let us apply
+the total expectation theorem do we take
+
+ align:start position:0%
+the total expectation theorem do we take
+ 
+
+ align:start position:0%
+the total expectation theorem do we take
+the familiar form of the total
+
+ align:start position:0%
+the familiar form of the total
+ 
+
+ align:start position:0%
+the familiar form of the total
+expectation theorem and in here we can
+
+ align:start position:0%
+expectation theorem and in here we can
+ 
+
+ align:start position:0%
+expectation theorem and in here we can
+plug in the expression that we have just
+
+ align:start position:0%
+plug in the expression that we have just
+ 
+
+ align:start position:0%
+plug in the expression that we have just
+found which is n times expected value of
+
+ align:start position:0%
+found which is n times expected value of
+ 
+
+ align:start position:0%
+found which is n times expected value of
+x now the expected value of x is just a
+
+ align:start position:0%
+x now the expected value of x is just a
+ 
+
+ align:start position:0%
+x now the expected value of x is just a
+number and then we have this summation
+
+ align:start position:0%
+number and then we have this summation
+ 
+
+ align:start position:0%
+number and then we have this summation
+here which we recognize to be just the
+
+ align:start position:0%
+here which we recognize to be just the
+ 
+
+ align:start position:0%
+here which we recognize to be just the
+definition of the expected value of N
+
+ align:start position:0%
+definition of the expected value of N
+ 
+
+ align:start position:0%
+definition of the expected value of N
+and so we come to the conclusion that
+
+ align:start position:0%
+and so we come to the conclusion that
+ 
+
+ align:start position:0%
+and so we come to the conclusion that
+the expected amount of money that you
+
+ align:start position:0%
+the expected amount of money that you
+ 
+
+ align:start position:0%
+the expected amount of money that you
+will be spending is equal to the
+
+ align:start position:0%
+will be spending is equal to the
+ 
+
+ align:start position:0%
+will be spending is equal to the
+following product the expected number of
+
+ align:start position:0%
+following product the expected number of
+ 
+
+ align:start position:0%
+following product the expected number of
+stores that you visit times the expected
+
+ align:start position:0%
+stores that you visit times the expected
+ 
+
+ align:start position:0%
+stores that you visit times the expected
+amount of money that you will be
+
+ align:start position:0%
+amount of money that you will be
+ 
+
+ align:start position:0%
+amount of money that you will be
+spending at each store this is a quite
+
+ align:start position:0%
+spending at each store this is a quite
+ 
+
+ align:start position:0%
+spending at each store this is a quite
+plausible answer it makes sense on the
+
+ align:start position:0%
+plausible answer it makes sense on the
+ 
+
+ align:start position:0%
+plausible answer it makes sense on the
+average the amount of money you spend is
+
+ align:start position:0%
+average the amount of money you spend is
+ 
+
+ align:start position:0%
+average the amount of money you spend is
+equal to the average number of stores
+
+ align:start position:0%
+equal to the average number of stores
+ 
+
+ align:start position:0%
+equal to the average number of stores
+times the average amount of money in
+
+ align:start position:0%
+times the average amount of money in
+ 
+
+ align:start position:0%
+times the average amount of money in
+each store so it is intuitively what you
+
+ align:start position:0%
+each store so it is intuitively what you
+ 
+
+ align:start position:0%
+each store so it is intuitively what you
+might expect on the other hand we know
+
+ align:start position:0%
+might expect on the other hand we know
+ 
+
+ align:start position:0%
+might expect on the other hand we know
+that reasoning on the average does not
+
+ align:start position:0%
+that reasoning on the average does not
+ 
+
+ align:start position:0%
+that reasoning on the average does not
+always give us the right answers so it's
+
+ align:start position:0%
+always give us the right answers so it's
+ 
+
+ align:start position:0%
+always give us the right answers so it's
+important to corroborate this particular
+
+ align:start position:0%
+important to corroborate this particular
+ 
+
+ align:start position:0%
+important to corroborate this particular
+formula by working out a mathematical
+
+ align:start position:0%
+formula by working out a mathematical
+ 
+
+ align:start position:0%
+formula by working out a mathematical
+derivation now let us carry out the
+
+ align:start position:0%
+derivation now let us carry out the
+ 
+
+ align:start position:0%
+derivation now let us carry out the
+second mathematical derivation using the
+
+ align:start position:0%
+second mathematical derivation using the
+ 
+
+ align:start position:0%
+second mathematical derivation using the
+law of iterated expectations to use the
+
+ align:start position:0%
+law of iterated expectations to use the
+ 
+
+ align:start position:0%
+law of iterated expectations to use the
+law of iterated expectations we need to
+
+ align:start position:0%
+law of iterated expectations we need to
+ 
+
+ align:start position:0%
+law of iterated expectations we need to
+put our hands on this random variable
+
+ align:start position:0%
+put our hands on this random variable
+ 
+
+ align:start position:0%
+put our hands on this random variable
+the abstract conditional expectation
+
+ align:start position:0%
+the abstract conditional expectation
+ 
+
+ align:start position:0%
+the abstract conditional expectation
+what is this object it's a random
+
+ align:start position:0%
+what is this object it's a random
+ 
+
+ align:start position:0%
+what is this object it's a random
+variable that takes this value whenever
+
+ align:start position:0%
+variable that takes this value whenever
+ 
+
+ align:start position:0%
+variable that takes this value whenever
+capital n is equal to little n so it's
+
+ align:start position:0%
+capital n is equal to little n so it's
+ 
+
+ align:start position:0%
+capital n is equal to little n so it's
+an object that takes this value whenever
+
+ align:start position:0%
+an object that takes this value whenever
+ 
+
+ align:start position:0%
+an object that takes this value whenever
+capital n is equal to little n but that
+
+ align:start position:0%
+capital n is equal to little n but that
+ 
+
+ align:start position:0%
+capital n is equal to little n but that
+object is the same as this random
+
+ align:start position:0%
+object is the same as this random
+ 
+
+ align:start position:0%
+object is the same as this random
+variable because this is the random
+
+ align:start position:0%
+variable because this is the random
+ 
+
+ align:start position:0%
+variable because this is the random
+variable that takes the value here when
+
+ align:start position:0%
+variable that takes the value here when
+ 
+
+ align:start position:0%
+variable that takes the value here when
+capital n is equal to little n therefore
+
+ align:start position:0%
+capital n is equal to little n therefore
+ 
+
+ align:start position:0%
+capital n is equal to little n therefore
+the abstract conditional expectation
+
+ align:start position:0%
+the abstract conditional expectation
+ 
+
+ align:start position:0%
+the abstract conditional expectation
+takes this particular form here which we
+
+ align:start position:0%
+takes this particular form here which we
+ 
+
+ align:start position:0%
+takes this particular form here which we
+can substitute inside this expectation
+
+ align:start position:0%
+can substitute inside this expectation
+ 
+
+ align:start position:0%
+can substitute inside this expectation
+here and now notice that the expected
+
+ align:start position:0%
+here and now notice that the expected
+ 
+
+ align:start position:0%
+here and now notice that the expected
+value of X is a constant so it can be
+
+ align:start position:0%
+value of X is a constant so it can be
+ 
+
+ align:start position:0%
+value of X is a constant so it can be
+pulled outside this expectation and
+
+ align:start position:0%
+pulled outside this expectation and
+ 
+
+ align:start position:0%
+pulled outside this expectation and
+we're left with the product of the
+
+ align:start position:0%
+we're left with the product of the
+ 
+
+ align:start position:0%
+we're left with the product of the
+expected value of n times the expected
+
+ align:start position:0%
+expected value of n times the expected
+ 
+
+ align:start position:0%
+expected value of n times the expected
+value of X so this completes the
+
+ align:start position:0%
+value of X so this completes the
+ 
+
+ align:start position:0%
+value of X so this completes the
+derivation of the expected value of the
+
+ align:start position:0%
+derivation of the expected value of the
+ 
+
+ align:start position:0%
+derivation of the expected value of the
+sum of a random number of random
+
+ align:start position:0%
+sum of a random number of random
+ 
+
+ align:start position:0%
+sum of a random number of random
+variables
\ No newline at end of file
diff --git a/yBOmyxg0sVM.txt b/yBOmyxg0sVM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f77d764eb353c5e4022750feeb2b4e349fce1ee4
--- /dev/null
+++ b/yBOmyxg0sVM.txt
@@ -0,0 +1,16323 @@
+align:start position:0%
+ 
+Let's uh let's start a so first the
+
+ align:start position:0%
+Let's uh let's start a so first the
+ 
+
+ align:start position:0%
+Let's uh let's start a so first the
+homework assignment is out as I
+
+ align:start position:0%
+homework assignment is out as I
+ 
+
+ align:start position:0%
+homework assignment is out as I
+said uh it's due right before
+
+ align:start position:0%
+said uh it's due right before
+ 
+
+ align:start position:0%
+said uh it's due right before
+Thanksgiving if anybody needs an
+
+ align:start position:0%
+Thanksgiving if anybody needs an
+ 
+
+ align:start position:0%
+Thanksgiving if anybody needs an
+extension just let me
+
+ align:start position:0%
+extension just let me
+ 
+
+ align:start position:0%
+extension just let me
+know a and
+
+ align:start position:0%
+know a and
+ 
+
+ align:start position:0%
+know a and
+uh the instructions are on the on the
+
+ align:start position:0%
+uh the instructions are on the on the
+ 
+
+ align:start position:0%
+uh the instructions are on the on the
+site essentially uh each one should
+
+ align:start position:0%
+site essentially uh each one should
+ 
+
+ align:start position:0%
+site essentially uh each one should
+write like their own solution to make
+
+ align:start position:0%
+write like their own solution to make
+ 
+
+ align:start position:0%
+write like their own solution to make
+sure you understand it's okay if you
+
+ align:start position:0%
+sure you understand it's okay if you
+ 
+
+ align:start position:0%
+sure you understand it's okay if you
+talk among one among one another as long
+
+ align:start position:0%
+talk among one among one another as long
+ 
+
+ align:start position:0%
+talk among one among one another as long
+as it's fruitful and please type it up
+
+ align:start position:0%
+as it's fruitful and please type it up
+ 
+
+ align:start position:0%
+as it's fruitful and please type it up
+in latch and submit it through great
+
+ align:start position:0%
+in latch and submit it through great
+ 
+
+ align:start position:0%
+in latch and submit it through great
+scope questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh you what why can't you do don't you
+
+ align:start position:0%
+oh you what why can't you do don't you
+ 
+
+ align:start position:0%
+oh you what why can't you do don't you
+use grade scope for other classes yeah
+
+ align:start position:0%
+use grade scope for other classes yeah
+ 
+
+ align:start position:0%
+use grade scope for other classes yeah
+but I have not seen this class oh no it
+
+ align:start position:0%
+but I have not seen this class oh no it
+ 
+
+ align:start position:0%
+but I have not seen this class oh no it
+is it is now when did you check
+
+ align:start position:0%
+is it is now when did you check
+ 
+
+ align:start position:0%
+is it is now when did you check
+oh yeah it's recently uh yeah if there's
+
+ align:start position:0%
+oh yeah it's recently uh yeah if there's
+ 
+
+ align:start position:0%
+oh yeah it's recently uh yeah if there's
+issues let me know yeah this class is
+
+ align:start position:0%
+issues let me know yeah this class is
+ 
+
+ align:start position:0%
+issues let me know yeah this class is
+assigned to there is a great scope site
+
+ align:start position:0%
+assigned to there is a great scope site
+ 
+
+ align:start position:0%
+assigned to there is a great scope site
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+this uh any any other questions before
+
+ align:start position:0%
+this uh any any other questions before
+ 
+
+ align:start position:0%
+this uh any any other questions before
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start okay so uh just a quick a quick
+
+ align:start position:0%
+start okay so uh just a quick a quick
+ 
+
+ align:start position:0%
+start okay so uh just a quick a quick
+recap uh so last time we talked Al about
+
+ align:start position:0%
+recap uh so last time we talked Al about
+ 
+
+ align:start position:0%
+recap uh so last time we talked Al about
+the kilan mikali protocol it's an
+
+ align:start position:0%
+the kilan mikali protocol it's an
+ 
+
+ align:start position:0%
+the kilan mikali protocol it's an
+interactive argument it's a succinct
+
+ align:start position:0%
+interactive argument it's a succinct
+ 
+
+ align:start position:0%
+interactive argument it's a succinct
+interactive argument that which you can
+
+ align:start position:0%
+interactive argument that which you can
+ 
+
+ align:start position:0%
+interactive argument that which you can
+use to prove uh membership in any NP
+
+ align:start position:0%
+use to prove uh membership in any NP
+ 
+
+ align:start position:0%
+use to prove uh membership in any NP
+language okay if you recall the idea was
+
+ align:start position:0%
+language okay if you recall the idea was
+ 
+
+ align:start position:0%
+language okay if you recall the idea was
+we started before that was kind of our
+
+ align:start position:0%
+we started before that was kind of our
+ 
+
+ align:start position:0%
+we started before that was kind of our
+entrance to to cryptography so we said
+
+ align:start position:0%
+entrance to to cryptography so we said
+ 
+
+ align:start position:0%
+entrance to to cryptography so we said
+the idea of the K mic protocol is that
+
+ align:start position:0%
+the idea of the K mic protocol is that
+ 
+
+ align:start position:0%
+the idea of the K mic protocol is that
+you take any PCP which is very very
+
+ align:start position:0%
+you take any PCP which is very very
+ 
+
+ align:start position:0%
+you take any PCP which is very very
+large but very efficiently if you just
+
+ align:start position:0%
+large but very efficiently if you just
+ 
+
+ align:start position:0%
+large but very efficiently if you just
+have Ram access to it you can verify it
+
+ align:start position:0%
+have Ram access to it you can verify it
+ 
+
+ align:start position:0%
+have Ram access to it you can verify it
+very efficiently
+
+ align:start position:0%
+very efficiently
+ 
+
+ align:start position:0%
+very efficiently
+and the idea is you take this very very
+
+ align:start position:0%
+and the idea is you take this very very
+ 
+
+ align:start position:0%
+and the idea is you take this very very
+large PCP and you kind of shrink it to
+
+ align:start position:0%
+large PCP and you kind of shrink it to
+ 
+
+ align:start position:0%
+large PCP and you kind of shrink it to
+kind of a you uh you know uh digest it
+
+ align:start position:0%
+kind of a you uh you know uh digest it
+ 
+
+ align:start position:0%
+kind of a you uh you know uh digest it
+down uh using cryptography to this kind
+
+ align:start position:0%
+down uh using cryptography to this kind
+ 
+
+ align:start position:0%
+down uh using cryptography to this kind
+of suing digest this is done using
+
+ align:start position:0%
+of suing digest this is done using
+ 
+
+ align:start position:0%
+of suing digest this is done using
+what's called using hash function but in
+
+ align:start position:0%
+what's called using hash function but in
+ 
+
+ align:start position:0%
+what's called using hash function but in
+particular mirle hash or hash function
+
+ align:start position:0%
+particular mirle hash or hash function
+ 
+
+ align:start position:0%
+particular mirle hash or hash function
+that are sixing but can be opened
+
+ align:start position:0%
+that are sixing but can be opened
+ 
+
+ align:start position:0%
+that are sixing but can be opened
+locally so I'll recall what this is in a
+
+ align:start position:0%
+locally so I'll recall what this is in a
+ 
+
+ align:start position:0%
+locally so I'll recall what this is in a
+second and once the prover sends over
+
+ align:start position:0%
+second and once the prover sends over
+ 
+
+ align:start position:0%
+second and once the prover sends over
+kind of a uh squished form of the PC
+
+ align:start position:0%
+kind of a uh squished form of the PC
+ 
+
+ align:start position:0%
+kind of a uh squished form of the PC
+then the verifier now behav like he's a
+
+ align:start position:0%
+then the verifier now behav like he's a
+ 
+
+ align:start position:0%
+then the verifier now behav like he's a
+PCP verifier he tells the Prov open this
+
+ align:start position:0%
+PCP verifier he tells the Prov open this
+ 
+
+ align:start position:0%
+PCP verifier he tells the Prov open this
+PCP and the location that the PCP
+
+ align:start position:0%
+PCP and the location that the PCP
+ 
+
+ align:start position:0%
+PCP and the location that the PCP
+verifier would want to open and he gets
+
+ align:start position:0%
+verifier would want to open and he gets
+ 
+
+ align:start position:0%
+verifier would want to open and he gets
+back the openings so uh so that's kind
+
+ align:start position:0%
+back the openings so uh so that's kind
+ 
+
+ align:start position:0%
+back the openings so uh so that's kind
+of what the Kil mikali protocol is but
+
+ align:start position:0%
+of what the Kil mikali protocol is but
+ 
+
+ align:start position:0%
+of what the Kil mikali protocol is but
+in order to to uh when I said you know
+
+ align:start position:0%
+in order to to uh when I said you know
+ 
+
+ align:start position:0%
+in order to to uh when I said you know
+it squishes down and then there's
+
+ align:start position:0%
+it squishes down and then there's
+ 
+
+ align:start position:0%
+it squishes down and then there's
+opening really what we need is a we want
+
+ align:start position:0%
+opening really what we need is a we want
+ 
+
+ align:start position:0%
+opening really what we need is a we want
+to take a hash function so if you
+
+ align:start position:0%
+to take a hash function so if you
+ 
+
+ align:start position:0%
+to take a hash function so if you
+remember a hash hash function is kind of
+
+ align:start position:0%
+remember a hash hash function is kind of
+ 
+
+ align:start position:0%
+remember a hash hash function is kind of
+consists of a key generation algorithm
+
+ align:start position:0%
+consists of a key generation algorithm
+ 
+
+ align:start position:0%
+consists of a key generation algorithm
+that generates a hash key and an eval
+
+ align:start position:0%
+that generates a hash key and an eval
+ 
+
+ align:start position:0%
+that generates a hash key and an eval
+algorithm that take a hash and an input
+
+ align:start position:0%
+algorithm that take a hash and an input
+ 
+
+ align:start position:0%
+algorithm that take a hash and an input
+and generates kind of a digest or a hash
+
+ align:start position:0%
+and generates kind of a digest or a hash
+ 
+
+ align:start position:0%
+and generates kind of a digest or a hash
+value a last time we uh we talk we
+
+ align:start position:0%
+value a last time we uh we talk we
+ 
+
+ align:start position:0%
+value a last time we uh we talk we
+showed how to get a a hash value uh how
+
+ align:start position:0%
+showed how to get a a hash value uh how
+ 
+
+ align:start position:0%
+showed how to get a a hash value uh how
+to construct from uh the discrete log we
+
+ align:start position:0%
+to construct from uh the discrete log we
+ 
+
+ align:start position:0%
+to construct from uh the discrete log we
+showed how to construct a hash function
+
+ align:start position:0%
+showed how to construct a hash function
+ 
+
+ align:start position:0%
+showed how to construct a hash function
+uh uh from two Lambda to Lambda it takes
+
+ align:start position:0%
+uh uh from two Lambda to Lambda it takes
+ 
+
+ align:start position:0%
+uh uh from two Lambda to Lambda it takes
+2 Lambda bit Lambda B actually was z p
+
+ align:start position:0%
+2 Lambda bit Lambda B actually was z p
+ 
+
+ align:start position:0%
+2 Lambda bit Lambda B actually was z p
+to the 2 Lambda to zp to Lambda but
+
+ align:start position:0%
+to the 2 Lambda to zp to Lambda but
+ 
+
+ align:start position:0%
+to the 2 Lambda to zp to Lambda but
+anyway one can encoded to have to be 01
+
+ align:start position:0%
+anyway one can encoded to have to be 01
+ 
+
+ align:start position:0%
+anyway one can encoded to have to be 01
+to the 2 Lambda to 0 1 to the
+
+ align:start position:0%
+to the 2 Lambda to 0 1 to the
+ 
+
+ align:start position:0%
+to the 2 Lambda to 0 1 to the
+Lambda but this is actually not enough
+
+ align:start position:0%
+Lambda but this is actually not enough
+ 
+
+ align:start position:0%
+Lambda but this is actually not enough
+for the Kil M protocol what we actually
+
+ align:start position:0%
+for the Kil M protocol what we actually
+ 
+
+ align:start position:0%
+for the Kil M protocol what we actually
+need is a collision hash function first
+
+ align:start position:0%
+need is a collision hash function first
+ 
+
+ align:start position:0%
+need is a collision hash function first
+it needs to be much bigger because we're
+
+ align:start position:0%
+it needs to be much bigger because we're
+ 
+
+ align:start position:0%
+it needs to be much bigger because we're
+taking a gigantic PCP we want to squish
+
+ align:start position:0%
+taking a gigantic PCP we want to squish
+ 
+
+ align:start position:0%
+taking a gigantic PCP we want to squish
+it way more than like half this takes
+
+ align:start position:0%
+it way more than like half this takes
+ 
+
+ align:start position:0%
+it way more than like half this takes
+you know make squishes the size reduces
+
+ align:start position:0%
+you know make squishes the size reduces
+ 
+
+ align:start position:0%
+you know make squishes the size reduces
+the size from two Lambda to Lambda so it
+
+ align:start position:0%
+the size from two Lambda to Lambda so it
+ 
+
+ align:start position:0%
+the size from two Lambda to Lambda so it
+squishes it by factor of two we actually
+
+ align:start position:0%
+squishes it by factor of two we actually
+ 
+
+ align:start position:0%
+squishes it by factor of two we actually
+want to squish it to much bigger Factor
+
+ align:start position:0%
+want to squish it to much bigger Factor
+ 
+
+ align:start position:0%
+want to squish it to much bigger Factor
+okay so we want to take kind of eval
+
+ align:start position:0%
+okay so we want to take kind of eval
+ 
+
+ align:start position:0%
+okay so we want to take kind of eval
+what we what we use actually is an eval
+
+ align:start position:0%
+what we what we use actually is an eval
+ 
+
+ align:start position:0%
+what we what we use actually is an eval
+algorithm that takes strings of size two
+
+ align:start position:0%
+algorithm that takes strings of size two
+ 
+
+ align:start position:0%
+algorithm that takes strings of size two
+to the Lambda to Lambda so note here the
+
+ align:start position:0%
+to the Lambda to Lambda so note here the
+ 
+
+ align:start position:0%
+to the Lambda to Lambda so note here the
+Lambda is upstairs it's very different
+
+ align:start position:0%
+Lambda is upstairs it's very different
+ 
+
+ align:start position:0%
+Lambda is upstairs it's very different
+than two Lambda it's exponential
+
+ align:start position:0%
+than two Lambda it's exponential
+ 
+
+ align:start position:0%
+than two Lambda it's exponential
+difference a so we take a a hash
+
+ align:start position:0%
+difference a so we take a a hash
+ 
+
+ align:start position:0%
+difference a so we take a a hash
+function that goes takes gigantic
+
+ align:start position:0%
+function that goes takes gigantic
+ 
+
+ align:start position:0%
+function that goes takes gigantic
+strings to lamb
+
+ align:start position:0%
+strings to lamb
+ 
+
+ align:start position:0%
+strings to lamb
+and moreover another property that we
+
+ align:start position:0%
+and moreover another property that we
+ 
+
+ align:start position:0%
+and moreover another property that we
+want is we can open locally remember we
+
+ align:start position:0%
+want is we can open locally remember we
+ 
+
+ align:start position:0%
+want is we can open locally remember we
+said the way the mikali protocol works
+
+ align:start position:0%
+said the way the mikali protocol works
+ 
+
+ align:start position:0%
+said the way the mikali protocol works
+is that the verifier asks okay you
+
+ align:start position:0%
+is that the verifier asks okay you
+ 
+
+ align:start position:0%
+is that the verifier asks okay you
+committed to the gigantic PCP open it in
+
+ align:start position:0%
+committed to the gigantic PCP open it in
+ 
+
+ align:start position:0%
+committed to the gigantic PCP open it in
+location you know 37 and 15 now how do
+
+ align:start position:0%
+location you know 37 and 15 now how do
+ 
+
+ align:start position:0%
+location you know 37 and 15 now how do
+you open it so we also want kind of a a
+
+ align:start position:0%
+you open it so we also want kind of a a
+ 
+
+ align:start position:0%
+you open it so we also want kind of a a
+opening algorithm so really what we
+
+ align:start position:0%
+opening algorithm so really what we
+ 
+
+ align:start position:0%
+opening algorithm so really what we
+needed when we talked about Miracle hash
+
+ align:start position:0%
+needed when we talked about Miracle hash
+ 
+
+ align:start position:0%
+needed when we talked about Miracle hash
+or hash hashes with local opening in
+
+ align:start position:0%
+or hash hashes with local opening in
+ 
+
+ align:start position:0%
+or hash hashes with local opening in
+addition to having a key generation and
+
+ align:start position:0%
+addition to having a key generation and
+ 
+
+ align:start position:0%
+addition to having a key generation and
+eval algorithm we also have a open
+
+ align:start position:0%
+eval algorithm we also have a open
+ 
+
+ align:start position:0%
+eval algorithm we also have a open
+algorithm that generates kind of a
+
+ align:start position:0%
+algorithm that generates kind of a
+ 
+
+ align:start position:0%
+algorithm that generates kind of a
+succinct
+
+ align:start position:0%
+succinct
+ 
+
+ align:start position:0%
+succinct
+opening and you which can be verified in
+
+ align:start position:0%
+opening and you which can be verified in
+ 
+
+ align:start position:0%
+opening and you which can be verified in
+a verification algorithm that verifies
+
+ align:start position:0%
+a verification algorithm that verifies
+ 
+
+ align:start position:0%
+a verification algorithm that verifies
+it so last time we we kind of
+
+ align:start position:0%
+it so last time we we kind of
+ 
+
+ align:start position:0%
+it so last time we we kind of
+constructed this morle hatch I'll recall
+
+ align:start position:0%
+constructed this morle hatch I'll recall
+ 
+
+ align:start position:0%
+constructed this morle hatch I'll recall
+it today quickly and we ended without
+
+ align:start position:0%
+it today quickly and we ended without
+ 
+
+ align:start position:0%
+it today quickly and we ended without
+kind of proving that it's collagen
+
+ align:start position:0%
+kind of proving that it's collagen
+ 
+
+ align:start position:0%
+kind of proving that it's collagen
+resistant so that's where we're going to
+
+ align:start position:0%
+resistant so that's where we're going to
+ 
+
+ align:start position:0%
+resistant so that's where we're going to
+start today we're going to just wrap up
+
+ align:start position:0%
+start today we're going to just wrap up
+ 
+
+ align:start position:0%
+start today we're going to just wrap up
+the K mikali
+
+ align:start position:0%
+the K mikali
+ 
+
+ align:start position:0%
+the K mikali
+protocol by explaining the thing that
+
+ align:start position:0%
+protocol by explaining the thing that
+ 
+
+ align:start position:0%
+protocol by explaining the thing that
+was left is kind of to argue that this
+
+ align:start position:0%
+was left is kind of to argue that this
+ 
+
+ align:start position:0%
+was left is kind of to argue that this
+Merkel hash
+
+ align:start position:0%
+Merkel hash
+ 
+
+ align:start position:0%
+Merkel hash
+construction is indeed Collision
+
+ align:start position:0%
+construction is indeed Collision
+ 
+
+ align:start position:0%
+construction is indeed Collision
+resistance so that's where we're going
+
+ align:start position:0%
+resistance so that's where we're going
+ 
+
+ align:start position:0%
+resistance so that's where we're going
+to start today but then uh so once we do
+
+ align:start position:0%
+to start today but then uh so once we do
+ 
+
+ align:start position:0%
+to start today but then uh so once we do
+that once we argue that the we have this
+
+ align:start position:0%
+that once we argue that the we have this
+ 
+
+ align:start position:0%
+that once we argue that the we have this
+Merkel hash we put that it's Collision
+
+ align:start position:0%
+Merkel hash we put that it's Collision
+ 
+
+ align:start position:0%
+Merkel hash we put that it's Collision
+resistant then we're done with the kill
+
+ align:start position:0%
+resistant then we're done with the kill
+ 
+
+ align:start position:0%
+resistant then we're done with the kill
+M you actually proved that it sound
+
+ align:start position:0%
+M you actually proved that it sound
+ 
+
+ align:start position:0%
+M you actually proved that it sound
+under this
+
+ align:start position:0%
+under this
+ 
+
+ align:start position:0%
+under this
+assumption so so okay so where are we
+
+ align:start position:0%
+assumption so so okay so where are we
+ 
+
+ align:start position:0%
+assumption so so okay so where are we
+heading today after we finished the
+
+ align:start position:0%
+heading today after we finished the
+ 
+
+ align:start position:0%
+heading today after we finished the
+Merkel hash now we we actually showed a
+
+ align:start position:0%
+Merkel hash now we we actually showed a
+ 
+
+ align:start position:0%
+Merkel hash now we we actually showed a
+succinct argument for all of NP this is
+
+ align:start position:0%
+succinct argument for all of NP this is
+ 
+
+ align:start position:0%
+succinct argument for all of NP this is
+great however it's
+
+ align:start position:0%
+great however it's
+ 
+
+ align:start position:0%
+great however it's
+interactive and interactive proofs or
+
+ align:start position:0%
+interactive and interactive proofs or
+ 
+
+ align:start position:0%
+interactive and interactive proofs or
+arguments are really they're not very
+
+ align:start position:0%
+arguments are really they're not very
+ 
+
+ align:start position:0%
+arguments are really they're not very
+useful and the reason they're not very
+
+ align:start position:0%
+useful and the reason they're not very
+ 
+
+ align:start position:0%
+useful and the reason they're not very
+useful is for many reasons a there's
+
+ align:start position:0%
+useful is for many reasons a there's
+ 
+
+ align:start position:0%
+useful is for many reasons a there's
+latency to talk back forth back forth
+
+ align:start position:0%
+latency to talk back forth back forth
+ 
+
+ align:start position:0%
+latency to talk back forth back forth
+but another reason perhaps much more
+
+ align:start position:0%
+but another reason perhaps much more
+ 
+
+ align:start position:0%
+but another reason perhaps much more
+important is that it's per per verifier
+
+ align:start position:0%
+important is that it's per per verifier
+ 
+
+ align:start position:0%
+important is that it's per per verifier
+so if I want to just prove to the world
+
+ align:start position:0%
+so if I want to just prove to the world
+ 
+
+ align:start position:0%
+so if I want to just prove to the world
+some statement I can't prove it using I
+
+ align:start position:0%
+some statement I can't prove it using I
+ 
+
+ align:start position:0%
+some statement I can't prove it using I
+I'm not gonna go to each person in the
+
+ align:start position:0%
+I'm not gonna go to each person in the
+ 
+
+ align:start position:0%
+I'm not gonna go to each person in the
+world and give him an an interactive
+
+ align:start position:0%
+world and give him an an interactive
+ 
+
+ align:start position:0%
+world and give him an an interactive
+proof so it's really verifier specific
+
+ align:start position:0%
+proof so it's really verifier specific
+ 
+
+ align:start position:0%
+proof so it's really verifier specific
+interactive proofs are verifier specific
+
+ align:start position:0%
+interactive proofs are verifier specific
+ 
+
+ align:start position:0%
+interactive proofs are verifier specific
+it convinces the specific verifier you
+
+ align:start position:0%
+it convinces the specific verifier you
+ 
+
+ align:start position:0%
+it convinces the specific verifier you
+talk
+
+ align:start position:0%
+talk
+ 
+
+ align:start position:0%
+talk
+with okay and we want to prove that
+
+ align:start position:0%
+with okay and we want to prove that
+ 
+
+ align:start position:0%
+with okay and we want to prove that
+convinces
+
+ align:start position:0%
+convinces
+ 
+
+ align:start position:0%
+convinces
+everyone so that's kind of where the
+
+ align:start position:0%
+everyone so that's kind of where the
+ 
+
+ align:start position:0%
+everyone so that's kind of where the
+segue we're taking today how do we
+
+ align:start position:0%
+segue we're taking today how do we
+ 
+
+ align:start position:0%
+segue we're taking today how do we
+construct actually
+
+ align:start position:0%
+construct actually
+ 
+
+ align:start position:0%
+construct actually
+non-interactive R now to reduce
+
+ align:start position:0%
+non-interactive R now to reduce
+ 
+
+ align:start position:0%
+non-interactive R now to reduce
+interraction okay so what we're going to
+
+ align:start position:0%
+interraction okay so what we're going to
+ 
+
+ align:start position:0%
+interraction okay so what we're going to
+show is how to eliminate interaction and
+
+ align:start position:0%
+show is how to eliminate interaction and
+ 
+
+ align:start position:0%
+show is how to eliminate interaction and
+this is going to be done using a really
+
+ align:start position:0%
+this is going to be done using a really
+ 
+
+ align:start position:0%
+this is going to be done using a really
+beautiful Paradigm called the F Paradigm
+
+ align:start position:0%
+beautiful Paradigm called the F Paradigm
+ 
+
+ align:start position:0%
+beautiful Paradigm called the F Paradigm
+so I'm going to explain what it is it's
+
+ align:start position:0%
+so I'm going to explain what it is it's
+ 
+
+ align:start position:0%
+so I'm going to explain what it is it's
+very very simple and then we're going to
+
+ align:start position:0%
+very very simple and then we're going to
+ 
+
+ align:start position:0%
+very very simple and then we're going to
+introduce the random Oracle model which
+
+ align:start position:0%
+introduce the random Oracle model which
+ 
+
+ align:start position:0%
+introduce the random Oracle model which
+is a model that was invented in order to
+
+ align:start position:0%
+is a model that was invented in order to
+ 
+
+ align:start position:0%
+is a model that was invented in order to
+an attempt to analyze or to understand
+
+ align:start position:0%
+an attempt to analyze or to understand
+ 
+
+ align:start position:0%
+an attempt to analyze or to understand
+the security of this F Paradigm uh it's
+
+ align:start position:0%
+the security of this F Paradigm uh it's
+ 
+
+ align:start position:0%
+the security of this F Paradigm uh it's
+an ideal model okay we're gonna prove
+
+ align:start position:0%
+an ideal model okay we're gonna prove
+ 
+
+ align:start position:0%
+an ideal model okay we're gonna prove
+the soundness of the Kil mikali protocol
+
+ align:start position:0%
+the soundness of the Kil mikali protocol
+ 
+
+ align:start position:0%
+the soundness of the Kil mikali protocol
+that we we saw last time we're going to
+
+ align:start position:0%
+that we we saw last time we're going to
+ 
+
+ align:start position:0%
+that we we saw last time we're going to
+actually show that it sound uh even if
+
+ align:start position:0%
+actually show that it sound uh even if
+ 
+
+ align:start position:0%
+actually show that it sound uh even if
+you apply the F Paradigm to it as long
+
+ align:start position:0%
+you apply the F Paradigm to it as long
+ 
+
+ align:start position:0%
+you apply the F Paradigm to it as long
+as you rign this random Oracle model and
+
+ align:start position:0%
+as you rign this random Oracle model and
+ 
+
+ align:start position:0%
+as you rign this random Oracle model and
+this ideal
+
+ align:start position:0%
+this ideal
+ 
+
+ align:start position:0%
+this ideal
+model and then we're going to probably
+
+ align:start position:0%
+model and then we're going to probably
+ 
+
+ align:start position:0%
+model and then we're going to probably
+this we're going to only get till next
+
+ align:start position:0%
+this we're going to only get till next
+ 
+
+ align:start position:0%
+this we're going to only get till next
+time but we're going to try to we're
+
+ align:start position:0%
+time but we're going to try to we're
+ 
+
+ align:start position:0%
+time but we're going to try to we're
+talk about the soundness uh of the F and
+
+ align:start position:0%
+talk about the soundness uh of the F and
+ 
+
+ align:start position:0%
+talk about the soundness uh of the F and
+the standard model okay so again we're
+
+ align:start position:0%
+the standard model okay so again we're
+ 
+
+ align:start position:0%
+the standard model okay so again we're
+going to talk about eliminating
+
+ align:start position:0%
+going to talk about eliminating
+ 
+
+ align:start position:0%
+going to talk about eliminating
+interaction using F talk about the
+
+ align:start position:0%
+interaction using F talk about the
+ 
+
+ align:start position:0%
+interaction using F talk about the
+random orical model show that actually
+
+ align:start position:0%
+random orical model show that actually
+ 
+
+ align:start position:0%
+random orical model show that actually
+the random oral model of this Paradigm
+
+ align:start position:0%
+the random oral model of this Paradigm
+ 
+
+ align:start position:0%
+the random oral model of this Paradigm
+works well often uh we'll see exactly
+
+ align:start position:0%
+works well often uh we'll see exactly
+ 
+
+ align:start position:0%
+works well often uh we'll see exactly
+when it works well when it doesn't and
+
+ align:start position:0%
+when it works well when it doesn't and
+ 
+
+ align:start position:0%
+when it works well when it doesn't and
+then we're going to talk about if we
+
+ align:start position:0%
+then we're going to talk about if we
+ 
+
+ align:start position:0%
+then we're going to talk about if we
+have time maybe start talking about uh
+
+ align:start position:0%
+have time maybe start talking about uh
+ 
+
+ align:start position:0%
+have time maybe start talking about uh
+about Security in that standard model
+
+ align:start position:0%
+about Security in that standard model
+ 
+
+ align:start position:0%
+about Security in that standard model
+because the random work model is not
+
+ align:start position:0%
+because the random work model is not
+ 
+
+ align:start position:0%
+because the random work model is not
+it's a it's an ideal model so is it
+
+ align:start position:0%
+it's a it's an ideal model so is it
+ 
+
+ align:start position:0%
+it's a it's an ideal model so is it
+secure is it sound like in when used in
+
+ align:start position:0%
+secure is it sound like in when used in
+ 
+
+ align:start position:0%
+secure is it sound like in when used in
+actual
+
+ align:start position:0%
+actual
+ 
+
+ align:start position:0%
+actual
+reality that's the plan questions yes
+
+ align:start position:0%
+reality that's the plan questions yes
+ 
+
+ align:start position:0%
+reality that's the plan questions yes
+you shouldn't be able to do two of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+land you're something that long you find
+
+ align:start position:0%
+land you're something that long you find
+ 
+
+ align:start position:0%
+land you're something that long you find
+a oh okay so um uh okay uh of course of
+
+ align:start position:0%
+a oh okay so um uh okay uh of course of
+ 
+
+ align:start position:0%
+a oh okay so um uh okay uh of course of
+course you can find the Collision the qu
+
+ align:start position:0%
+course you can find the Collision the qu
+ 
+
+ align:start position:0%
+course you can find the Collision the qu
+okay so I we Define it okay so the
+
+ align:start position:0%
+okay so I we Define it okay so the
+ 
+
+ align:start position:0%
+okay so I we Define it okay so the
+question was about this two two to the
+
+ align:start position:0%
+question was about this two two to the
+ 
+
+ align:start position:0%
+question was about this two two to the
+Lambda let me get let me now we'll see
+
+ align:start position:0%
+Lambda let me get let me now we'll see
+ 
+
+ align:start position:0%
+Lambda let me get let me now we'll see
+the definition the construction I'll
+
+ align:start position:0%
+the definition the construction I'll
+ 
+
+ align:start position:0%
+the definition the construction I'll
+explain but the the we get we get
+
+ align:start position:0%
+explain but the the we get we get
+ 
+
+ align:start position:0%
+explain but the the we get we get
+completeness for two to the Lambda now
+
+ align:start position:0%
+completeness for two to the Lambda now
+ 
+
+ align:start position:0%
+completeness for two to the Lambda now
+you're talking about soundness okay
+
+ align:start position:0%
+you're talking about soundness okay
+ 
+
+ align:start position:0%
+you're talking about soundness okay
+soundness says that any poly adversary
+
+ align:start position:0%
+soundness says that any poly adversary
+ 
+
+ align:start position:0%
+soundness says that any poly adversary
+or t time adversary yeah poly Lambda
+
+ align:start position:0%
+or t time adversary yeah poly Lambda
+ 
+
+ align:start position:0%
+or t time adversary yeah poly Lambda
+adversary or po or t poly in t Lambda
+
+ align:start position:0%
+adversary or po or t poly in t Lambda
+ 
+
+ align:start position:0%
+adversary or po or t poly in t Lambda
+adversary
+
+ align:start position:0%
+adversary
+ 
+
+ align:start position:0%
+adversary
+cannot find a collision now if this T is
+
+ align:start position:0%
+cannot find a collision now if this T is
+ 
+
+ align:start position:0%
+cannot find a collision now if this T is
+two to the Lambda then you're not going
+
+ align:start position:0%
+two to the Lambda then you're not going
+ 
+
+ align:start position:0%
+two to the Lambda then you're not going
+to be secure so that I mean the
+
+ align:start position:0%
+to be secure so that I mean the
+ 
+
+ align:start position:0%
+to be secure so that I mean the
+Assumption R so there's this is for
+
+ align:start position:0%
+Assumption R so there's this is for
+ 
+
+ align:start position:0%
+Assumption R so there's this is for
+completeness for soundness the
+
+ align:start position:0%
+completeness for soundness the
+ 
+
+ align:start position:0%
+completeness for soundness the
+assumption is for Collision resistance
+
+ align:start position:0%
+assumption is for Collision resistance
+ 
+
+ align:start position:0%
+assumption is for Collision resistance
+the the definition is that no poly
+
+ align:start position:0%
+the the definition is that no poly
+ 
+
+ align:start position:0%
+the the definition is that no poly
+Lambda time or poly T Lambda depending
+
+ align:start position:0%
+Lambda time or poly T Lambda depending
+ 
+
+ align:start position:0%
+Lambda time or poly T Lambda depending
+on if you want standard Collision
+
+ align:start position:0%
+on if you want standard Collision
+ 
+
+ align:start position:0%
+on if you want standard Collision
+resistant or T Collision resistant which
+
+ align:start position:0%
+resistant or T Collision resistant which
+ 
+
+ align:start position:0%
+resistant or T Collision resistant which
+is slightly stronger assumption cannot
+
+ align:start position:0%
+is slightly stronger assumption cannot
+ 
+
+ align:start position:0%
+is slightly stronger assumption cannot
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+collisions great thank thanks for the
+
+ align:start position:0%
+collisions great thank thanks for the
+ 
+
+ align:start position:0%
+collisions great thank thanks for the
+question any any other
+
+ align:start position:0%
+question any any other
+ 
+
+ align:start position:0%
+question any any other
+questions I like questions just
+
+ align:start position:0%
+questions I like questions just
+ 
+
+ align:start position:0%
+questions I like questions just
+reminding you
+
+ align:start position:0%
+reminding you
+ 
+
+ align:start position:0%
+reminding you
+guys okay yeah so during this whole
+
+ align:start position:0%
+guys okay yeah so during this whole
+ 
+
+ align:start position:0%
+guys okay yeah so during this whole
+thing I'm trying to imagine like how big
+
+ align:start position:0%
+thing I'm trying to imagine like how big
+ 
+
+ align:start position:0%
+thing I'm trying to imagine like how big
+are the parameters so n like inside of
+
+ align:start position:0%
+are the parameters so n like inside of
+ 
+
+ align:start position:0%
+are the parameters so n like inside of
+the input is something that's like like
+
+ align:start position:0%
+the input is something that's like like
+ 
+
+ align:start position:0%
+the input is something that's like like
+normal people can read right yeah yeah
+
+ align:start position:0%
+normal people can read right yeah yeah
+ 
+
+ align:start position:0%
+normal people can read right yeah yeah
+yeah yeah yeah yeah exactly okay so let
+
+ align:start position:0%
+yeah yeah yeah yeah exactly okay so let
+ 
+
+ align:start position:0%
+yeah yeah yeah yeah exactly okay so let
+me yeah let me talk a little bit about
+
+ align:start position:0%
+me yeah let me talk a little bit about
+ 
+
+ align:start position:0%
+me yeah let me talk a little bit about
+the parameters that's a great question
+
+ align:start position:0%
+the parameters that's a great question
+ 
+
+ align:start position:0%
+the parameters that's a great question
+that's a good good thing to start with
+
+ align:start position:0%
+that's a good good thing to start with
+ 
+
+ align:start position:0%
+that's a good good thing to start with
+so we want succinctness okay now when we
+
+ align:start position:0%
+so we want succinctness okay now when we
+ 
+
+ align:start position:0%
+so we want succinctness okay now when we
+say succinct really what we want is so
+
+ align:start position:0%
+say succinct really what we want is so
+ 
+
+ align:start position:0%
+say succinct really what we want is so
+we that's the things by using
+
+ align:start position:0%
+we that's the things by using
+ 
+
+ align:start position:0%
+we that's the things by using
+cryptography once we use cryptography
+
+ align:start position:0%
+cryptography once we use cryptography
+ 
+
+ align:start position:0%
+cryptography once we use cryptography
+things grow with the security of the
+
+ align:start position:0%
+things grow with the security of the
+ 
+
+ align:start position:0%
+things grow with the security of the
+that we want so things will grow with
+
+ align:start position:0%
+that we want so things will grow with
+ 
+
+ align:start position:0%
+that we want so things will grow with
+Lambda which is the security parameter
+
+ align:start position:0%
+Lambda which is the security parameter
+ 
+
+ align:start position:0%
+Lambda which is the security parameter
+what the security parameter is depends
+
+ align:start position:0%
+what the security parameter is depends
+ 
+
+ align:start position:0%
+what the security parameter is depends
+kind of how paranoid we are in the world
+
+ align:start position:0%
+kind of how paranoid we are in the world
+ 
+
+ align:start position:0%
+kind of how paranoid we are in the world
+okay you can think about it is 256 bits
+
+ align:start position:0%
+okay you can think about it is 256 bits
+ 
+
+ align:start position:0%
+okay you can think about it is 256 bits
+sometimes it's more depending on also
+
+ align:start position:0%
+sometimes it's more depending on also
+ 
+
+ align:start position:0%
+sometimes it's more depending on also
+which crypto systems you use but that's
+
+ align:start position:0%
+which crypto systems you use but that's
+ 
+
+ align:start position:0%
+which crypto systems you use but that's
+a good it's kind of independent of the
+
+ align:start position:0%
+a good it's kind of independent of the
+ 
+
+ align:start position:0%
+a good it's kind of independent of the
+input okay just you want as succinct as
+
+ align:start position:0%
+input okay just you want as succinct as
+ 
+
+ align:start position:0%
+input okay just you want as succinct as
+you can get and you know if you want to
+
+ align:start position:0%
+you can get and you know if you want to
+ 
+
+ align:start position:0%
+you can get and you know if you want to
+use cryptography it's it's like security
+
+ align:start position:0%
+use cryptography it's it's like security
+ 
+
+ align:start position:0%
+use cryptography it's it's like security
+parameter now the input it should in
+
+ align:start position:0%
+parameter now the input it should in
+ 
+
+ align:start position:0%
+parameter now the input it should in
+some sense it should not depend on the
+
+ align:start position:0%
+some sense it should not depend on the
+ 
+
+ align:start position:0%
+some sense it should not depend on the
+input but of course the input is not
+
+ align:start position:0%
+input but of course the input is not
+ 
+
+ align:start position:0%
+input but of course the input is not
+going to be like more than two to the
+
+ align:start position:0%
+going to be like more than two to the
+ 
+
+ align:start position:0%
+going to be like more than two to the
+Lambda because you think of Lambda is
+
+ align:start position:0%
+Lambda because you think of Lambda is
+ 
+
+ align:start position:0%
+Lambda because you think of Lambda is
+such that two to the Lambda is like more
+
+ align:start position:0%
+such that two to the Lambda is like more
+ 
+
+ align:start position:0%
+such that two to the Lambda is like more
+than the number of of molecules in the
+
+ align:start position:0%
+than the number of of molecules in the
+ 
+
+ align:start position:0%
+than the number of of molecules in the
+universe so nothing is that big in our
+
+ align:start position:0%
+universe so nothing is that big in our
+ 
+
+ align:start position:0%
+universe so nothing is that big in our
+world okay so you think of the X can be
+
+ align:start position:0%
+world okay so you think of the X can be
+ 
+
+ align:start position:0%
+world okay so you think of the X can be
+bigger actually the input can also be
+
+ align:start position:0%
+bigger actually the input can also be
+ 
+
+ align:start position:0%
+bigger actually the input can also be
+small you know but then sometimes you
+
+ align:start position:0%
+small you know but then sometimes you
+ 
+
+ align:start position:0%
+small you know but then sometimes you
+don't need cryptography so so tiny it's
+
+ align:start position:0%
+don't need cryptography so so tiny it's
+ 
+
+ align:start position:0%
+don't need cryptography so so tiny it's
+like phography is useless uh you can
+
+ align:start position:0%
+like phography is useless uh you can
+ 
+
+ align:start position:0%
+like phography is useless uh you can
+just give the witness um so usually we
+
+ align:start position:0%
+just give the witness um so usually we
+ 
+
+ align:start position:0%
+just give the witness um so usually we
+think think in our head of the input as
+
+ align:start position:0%
+think think in our head of the input as
+ 
+
+ align:start position:0%
+think think in our head of the input as
+being can be much bigger than Lambda can
+
+ align:start position:0%
+being can be much bigger than Lambda can
+ 
+
+ align:start position:0%
+being can be much bigger than Lambda can
+be poly Lambda and maybe even be like
+
+ align:start position:0%
+be poly Lambda and maybe even be like
+ 
+
+ align:start position:0%
+be poly Lambda and maybe even be like
+Lambda to the log Lambda it can be you
+
+ align:start position:0%
+Lambda to the log Lambda it can be you
+ 
+
+ align:start position:0%
+Lambda to the log Lambda it can be you
+know but it's not as big as two to the
+
+ align:start position:0%
+know but it's not as big as two to the
+ 
+
+ align:start position:0%
+know but it's not as big as two to the
+Lambda that's doesn't exist okay but it
+
+ align:start position:0%
+Lambda that's doesn't exist okay but it
+ 
+
+ align:start position:0%
+Lambda that's doesn't exist okay but it
+can be kind of anything that's kind of
+
+ align:start position:0%
+can be kind of anything that's kind of
+ 
+
+ align:start position:0%
+can be kind of anything that's kind of
+real world number in in the sense um and
+
+ align:start position:0%
+real world number in in the sense um and
+ 
+
+ align:start position:0%
+real world number in in the sense um and
+so that's kind of what what we should
+
+ align:start position:0%
+so that's kind of what what we should
+ 
+
+ align:start position:0%
+so that's kind of what what we should
+think of okay does
+
+ align:start position:0%
+think of okay does
+ 
+
+ align:start position:0%
+think of okay does
+that okay so when we do we're trying to
+
+ align:start position:0%
+that okay so when we do we're trying to
+ 
+
+ align:start position:0%
+that okay so when we do we're trying to
+reduce the amount of the side of the pro
+
+ align:start position:0%
+reduce the amount of the side of the pro
+ 
+
+ align:start position:0%
+reduce the amount of the side of the pro
+from like still a reasonable polze thing
+
+ align:start position:0%
+from like still a reasonable polze thing
+ 
+
+ align:start position:0%
+from like still a reasonable polze thing
+but just like a 26 exactly exactly or or
+
+ align:start position:0%
+but just like a 26 exactly exactly or or
+ 
+
+ align:start position:0%
+but just like a 26 exactly exactly or or
+right so you can think of it you're
+
+ align:start position:0%
+right so you can think of it you're
+ 
+
+ align:start position:0%
+right so you can think of it you're
+trying to when when you do and let me
+
+ align:start position:0%
+trying to when when you do and let me
+ 
+
+ align:start position:0%
+trying to when when you do and let me
+just repeat it also for the mic uh when
+
+ align:start position:0%
+just repeat it also for the mic uh when
+ 
+
+ align:start position:0%
+just repeat it also for the mic uh when
+you're trying uh when you do this
+
+ align:start position:0%
+you're trying uh when you do this
+ 
+
+ align:start position:0%
+you're trying uh when you do this
+interactive argument you think of you
+
+ align:start position:0%
+interactive argument you think of you
+ 
+
+ align:start position:0%
+interactive argument you think of you
+take an X that's still real world you
+
+ align:start position:0%
+take an X that's still real world you
+ 
+
+ align:start position:0%
+take an X that's still real world you
+can think of it polom l but it can be
+
+ align:start position:0%
+can think of it polom l but it can be
+ 
+
+ align:start position:0%
+can think of it polom l but it can be
+more but as long as a kind of real world
+
+ align:start position:0%
+more but as long as a kind of real world
+ 
+
+ align:start position:0%
+more but as long as a kind of real world
+thing and you reduce it to kind of 256
+
+ align:start position:0%
+thing and you reduce it to kind of 256
+ 
+
+ align:start position:0%
+thing and you reduce it to kind of 256
+bits okay that's kind of the um the
+
+ align:start position:0%
+bits okay that's kind of the um the
+ 
+
+ align:start position:0%
+bits okay that's kind of the um the
+Practical idea you should think of and
+
+ align:start position:0%
+Practical idea you should think of and
+ 
+
+ align:start position:0%
+Practical idea you should think of and
+the more theoretical idea is to say you
+
+ align:start position:0%
+the more theoretical idea is to say you
+ 
+
+ align:start position:0%
+the more theoretical idea is to say you
+can take any input X but not more than
+
+ align:start position:0%
+can take any input X but not more than
+ 
+
+ align:start position:0%
+can take any input X but not more than
+two to the Lambda because that's like
+
+ align:start position:0%
+two to the Lambda because that's like
+ 
+
+ align:start position:0%
+two to the Lambda because that's like
+you know but something anything less and
+
+ align:start position:0%
+you know but something anything less and
+ 
+
+ align:start position:0%
+you know but something anything less and
+we make it as small as as po
+
+ align:start position:0%
+we make it as small as as po
+ 
+
+ align:start position:0%
+we make it as small as as po
+Lambda okay great any any other
+
+ align:start position:0%
+Lambda okay great any any other
+ 
+
+ align:start position:0%
+Lambda okay great any any other
+questions yeah and verify that row is
+
+ align:start position:0%
+questions yeah and verify that row is
+ 
+
+ align:start position:0%
+questions yeah and verify that row is
+like the opening is that what it
+
+ align:start position:0%
+like the opening is that what it
+ 
+
+ align:start position:0%
+like the opening is that what it
+is yes yes yes yeah yeah sorry yes this
+
+ align:start position:0%
+is yes yes yes yeah yeah sorry yes this
+ 
+
+ align:start position:0%
+is yes yes yes yeah yeah sorry yes this
+is yeah I'll I'll go to it now yeah yeah
+
+ align:start position:0%
+is yeah I'll I'll go to it now yeah yeah
+ 
+
+ align:start position:0%
+is yeah I'll I'll go to it now yeah yeah
+yeah yeah yeah yeah let me let me okay
+
+ align:start position:0%
+yeah yeah yeah yeah let me let me okay
+ 
+
+ align:start position:0%
+yeah yeah yeah yeah let me let me okay
+so good so let me uh just finish wrap up
+
+ align:start position:0%
+so good so let me uh just finish wrap up
+ 
+
+ align:start position:0%
+so good so let me uh just finish wrap up
+what we where we left last time which is
+
+ align:start position:0%
+what we where we left last time which is
+ 
+
+ align:start position:0%
+what we where we left last time which is
+the Merle hash so we use ml hash in the
+
+ align:start position:0%
+the Merle hash so we use ml hash in the
+ 
+
+ align:start position:0%
+the Merle hash so we use ml hash in the
+kilan mikali protocol actually we don't
+
+ align:start position:0%
+kilan mikali protocol actually we don't
+ 
+
+ align:start position:0%
+kilan mikali protocol actually we don't
+need to really remember the kilan mikali
+
+ align:start position:0%
+need to really remember the kilan mikali
+ 
+
+ align:start position:0%
+need to really remember the kilan mikali
+protocol for today we're not going to
+
+ align:start position:0%
+protocol for today we're not going to
+ 
+
+ align:start position:0%
+protocol for today we're not going to
+actually really use it but let me still
+
+ align:start position:0%
+actually really use it but let me still
+ 
+
+ align:start position:0%
+actually really use it but let me still
+finish the Merle hash because it's a
+
+ align:start position:0%
+finish the Merle hash because it's a
+ 
+
+ align:start position:0%
+finish the Merle hash because it's a
+very important primitive it's kind of
+
+ align:start position:0%
+very important primitive it's kind of
+ 
+
+ align:start position:0%
+very important primitive it's kind of
+used everywhere in cryptography so it's
+
+ align:start position:0%
+used everywhere in cryptography so it's
+ 
+
+ align:start position:0%
+used everywhere in cryptography so it's
+very important to know so uh so what is
+
+ align:start position:0%
+very important to know so uh so what is
+ 
+
+ align:start position:0%
+very important to know so uh so what is
+the miracle hash it takes any hash
+
+ align:start position:0%
+the miracle hash it takes any hash
+ 
+
+ align:start position:0%
+the miracle hash it takes any hash
+function not local opening just a
+
+ align:start position:0%
+function not local opening just a
+ 
+
+ align:start position:0%
+function not local opening just a
+regular hash function that generates a
+
+ align:start position:0%
+regular hash function that generates a
+ 
+
+ align:start position:0%
+regular hash function that generates a
+hash key and has an eval algorithm
+
+ align:start position:0%
+hash key and has an eval algorithm
+ 
+
+ align:start position:0%
+hash key and has an eval algorithm
+evaluates just generates hash value such
+
+ align:start position:0%
+evaluates just generates hash value such
+ 
+
+ align:start position:0%
+evaluates just generates hash value such
+that it takes two Lambda bits to Lambda
+
+ align:start position:0%
+that it takes two Lambda bits to Lambda
+ 
+
+ align:start position:0%
+that it takes two Lambda bits to Lambda
+bits okay you can actually you can make
+
+ align:start position:0%
+bits okay you can actually you can make
+ 
+
+ align:start position:0%
+bits okay you can actually you can make
+it more you can be even one plus Epsilon
+
+ align:start position:0%
+it more you can be even one plus Epsilon
+ 
+
+ align:start position:0%
+it more you can be even one plus Epsilon
+Lambda bits to lamb you can play with it
+
+ align:start position:0%
+Lambda bits to lamb you can play with it
+ 
+
+ align:start position:0%
+Lambda bits to lamb you can play with it
+but let's say two Lambda to Lambda
+
+ align:start position:0%
+but let's say two Lambda to Lambda
+ 
+
+ align:start position:0%
+but let's say two Lambda to Lambda
+bits and we construct from it a hash
+
+ align:start position:0%
+bits and we construct from it a hash
+ 
+
+ align:start position:0%
+bits and we construct from it a hash
+function with local opening so let me
+
+ align:start position:0%
+function with local opening so let me
+ 
+
+ align:start position:0%
+function with local opening so let me
+tell you exactly what this hash function
+
+ align:start position:0%
+tell you exactly what this hash function
+ 
+
+ align:start position:0%
+tell you exactly what this hash function
+with local opening what it looks like so
+
+ align:start position:0%
+with local opening what it looks like so
+ 
+
+ align:start position:0%
+with local opening what it looks like so
+that then the hash key is exactly the
+
+ align:start position:0%
+that then the hash key is exactly the
+ 
+
+ align:start position:0%
+that then the hash key is exactly the
+same as before we take the same hash key
+
+ align:start position:0%
+same as before we take the same hash key
+ 
+
+ align:start position:0%
+same as before we take the same hash key
+as our underlying so first we started
+
+ align:start position:0%
+as our underlying so first we started
+ 
+
+ align:start position:0%
+as our underlying so first we started
+with a hash we started with this hash
+
+ align:start position:0%
+with a hash we started with this hash
+ 
+
+ align:start position:0%
+with a hash we started with this hash
+family what is it last time we saw we
+
+ align:start position:0%
+family what is it last time we saw we
+ 
+
+ align:start position:0%
+family what is it last time we saw we
+can take for example I gave an example
+
+ align:start position:0%
+can take for example I gave an example
+ 
+
+ align:start position:0%
+can take for example I gave an example
+with this discrete log but you can even
+
+ align:start position:0%
+with this discrete log but you can even
+ 
+
+ align:start position:0%
+with this discrete log but you can even
+if you don't remember it doesn't matter
+
+ align:start position:0%
+if you don't remember it doesn't matter
+ 
+
+ align:start position:0%
+if you don't remember it doesn't matter
+take think of it someone gave you a hash
+
+ align:start position:0%
+take think of it someone gave you a hash
+ 
+
+ align:start position:0%
+take think of it someone gave you a hash
+family with this domain and range okay
+
+ align:start position:0%
+family with this domain and range okay
+ 
+
+ align:start position:0%
+family with this domain and range okay
+now I'm gonna do a domain extension I'm
+
+ align:start position:0%
+now I'm gonna do a domain extension I'm
+ 
+
+ align:start position:0%
+now I'm gonna do a domain extension I'm
+going to make the domain much bigger and
+
+ align:start position:0%
+going to make the domain much bigger and
+ 
+
+ align:start position:0%
+going to make the domain much bigger and
+get local opening how do I do it so this
+
+ align:start position:0%
+get local opening how do I do it so this
+ 
+
+ align:start position:0%
+get local opening how do I do it so this
+is the miracle hash
+
+ align:start position:0%
+is the miracle hash
+ 
+
+ align:start position:0%
+is the miracle hash
+construction the idea is so the Gen is
+
+ align:start position:0%
+construction the idea is so the Gen is
+ 
+
+ align:start position:0%
+construction the idea is so the Gen is
+as I said just generate the same hash
+
+ align:start position:0%
+as I said just generate the same hash
+ 
+
+ align:start position:0%
+as I said just generate the same hash
+key as the original gen no change to the
+
+ align:start position:0%
+key as the original gen no change to the
+ 
+
+ align:start position:0%
+key as the original gen no change to the
+Gen algorithm the eval algorithm on the
+
+ align:start position:0%
+Gen algorithm the eval algorithm on the
+ 
+
+ align:start position:0%
+Gen algorithm the eval algorithm on the
+other end of course changes because the
+
+ align:start position:0%
+other end of course changes because the
+ 
+
+ align:start position:0%
+other end of course changes because the
+domain is much bigger okay it takes
+
+ align:start position:0%
+domain is much bigger okay it takes
+ 
+
+ align:start position:0%
+domain is much bigger okay it takes
+strings of size at most two to the L
+
+ align:start position:0%
+strings of size at most two to the L
+ 
+
+ align:start position:0%
+strings of size at most two to the L
+bits and what does it do so what it does
+
+ align:start position:0%
+bits and what does it do so what it does
+ 
+
+ align:start position:0%
+bits and what does it do so what it does
+is the following it takes his input X
+
+ align:start position:0%
+is the following it takes his input X
+ 
+
+ align:start position:0%
+is the following it takes his input X
+let's suppose for Simplicity that X is
+
+ align:start position:0%
+let's suppose for Simplicity that X is
+ 
+
+ align:start position:0%
+let's suppose for Simplicity that X is
+exactly kind of 2 the L time Lambda
+
+ align:start position:0%
+exactly kind of 2 the L time Lambda
+ 
+
+ align:start position:0%
+exactly kind of 2 the L time Lambda
+bits
+
+ align:start position:0%
+bits
+ 
+
+ align:start position:0%
+bits
+okay a so it's uh you don't have to
+
+ align:start position:0%
+okay a so it's uh you don't have to
+ 
+
+ align:start position:0%
+okay a so it's uh you don't have to
+assume this this is just easy to assume
+
+ align:start position:0%
+assume this this is just easy to assume
+ 
+
+ align:start position:0%
+assume this this is just easy to assume
+and you can always get it with padding
+
+ align:start position:0%
+and you can always get it with padding
+ 
+
+ align:start position:0%
+and you can always get it with padding
+kind of take any input and Pad it so
+
+ align:start position:0%
+kind of take any input and Pad it so
+ 
+
+ align:start position:0%
+kind of take any input and Pad it so
+it'll be of this form and I'll hash it
+
+ align:start position:0%
+it'll be of this form and I'll hash it
+ 
+
+ align:start position:0%
+it'll be of this form and I'll hash it
+okay I I'll say a word if it's not of
+
+ align:start position:0%
+okay I I'll say a word if it's not of
+ 
+
+ align:start position:0%
+okay I I'll say a word if it's not of
+this form uh but if it is of this form
+
+ align:start position:0%
+this form uh but if it is of this form
+ 
+
+ align:start position:0%
+this form uh but if it is of this form
+what do you do you take your input X
+
+ align:start position:0%
+what do you do you take your input X
+ 
+
+ align:start position:0%
+what do you do you take your input X
+just partition it to blocks each of
+
+ align:start position:0%
+just partition it to blocks each of
+ 
+
+ align:start position:0%
+just partition it to blocks each of
+length Lambda so you have two to the L
+
+ align:start position:0%
+length Lambda so you have two to the L
+ 
+
+ align:start position:0%
+length Lambda so you have two to the L
+blocks okay you have an input X of
+
+ align:start position:0%
+blocks okay you have an input X of
+ 
+
+ align:start position:0%
+blocks okay you have an input X of
+length two to the L * Lambda you
+
+ align:start position:0%
+length two to the L * Lambda you
+ 
+
+ align:start position:0%
+length two to the L * Lambda you
+partition it to chunks each of length
+
+ align:start position:0%
+partition it to chunks each of length
+ 
+
+ align:start position:0%
+partition it to chunks each of length
+Lambda so you have two to the L chunks
+
+ align:start position:0%
+Lambda so you have two to the L chunks
+ 
+
+ align:start position:0%
+Lambda so you have two to the L chunks
+let's call the chunks X1 X2 X3 X4 and so
+
+ align:start position:0%
+let's call the chunks X1 X2 X3 X4 and so
+ 
+
+ align:start position:0%
+let's call the chunks X1 X2 X3 X4 and so
+on up to X2 to the Lambda each of them
+
+ align:start position:0%
+on up to X2 to the Lambda each of them
+ 
+
+ align:start position:0%
+on up to X2 to the Lambda each of them
+up to X2 to the L
+
+ align:start position:0%
+up to X2 to the L
+ 
+
+ align:start position:0%
+up to X2 to the L
+sorry each of them of length Lambda and
+
+ align:start position:0%
+sorry each of them of length Lambda and
+ 
+
+ align:start position:0%
+sorry each of them of length Lambda and
+now what you do you take two blocks this
+
+ align:start position:0%
+now what you do you take two blocks this
+ 
+
+ align:start position:0%
+now what you do you take two blocks this
+is two Lambda bits and hash it using our
+
+ align:start position:0%
+is two Lambda bits and hash it using our
+ 
+
+ align:start position:0%
+is two Lambda bits and hash it using our
+building block hash that takes 2 Lambda
+
+ align:start position:0%
+building block hash that takes 2 Lambda
+ 
+
+ align:start position:0%
+building block hash that takes 2 Lambda
+to Lambda you take the to Lambda you
+
+ align:start position:0%
+to Lambda you take the to Lambda you
+ 
+
+ align:start position:0%
+to Lambda you take the to Lambda you
+hash you take these two you hash so in
+
+ align:start position:0%
+hash you take these two you hash so in
+ 
+
+ align:start position:0%
+hash you take these two you hash so in
+other words you take the two to the L
+
+ align:start position:0%
+other words you take the two to the L
+ 
+
+ align:start position:0%
+other words you take the two to the L
+blocks to two to the L minus one blocks
+
+ align:start position:0%
+blocks to two to the L minus one blocks
+ 
+
+ align:start position:0%
+blocks to two to the L minus one blocks
+you hash every every pair you hash every
+
+ align:start position:0%
+you hash every every pair you hash every
+ 
+
+ align:start position:0%
+you hash every every pair you hash every
+pair you hash every pair you hash every
+
+ align:start position:0%
+pair you hash every pair you hash every
+ 
+
+ align:start position:0%
+pair you hash every pair you hash every
+pair you hash you got two to the L minus
+
+ align:start position:0%
+pair you hash you got two to the L minus
+ 
+
+ align:start position:0%
+pair you hash you got two to the L minus
+one blocks then you take these blocks
+
+ align:start position:0%
+one blocks then you take these blocks
+ 
+
+ align:start position:0%
+one blocks then you take these blocks
+and again every pair you hash every pair
+
+ align:start position:0%
+and again every pair you hash every pair
+ 
+
+ align:start position:0%
+and again every pair you hash every pair
+you hash every pair two to the L minus
+
+ align:start position:0%
+you hash every pair two to the L minus
+ 
+
+ align:start position:0%
+you hash every pair two to the L minus
+two blocks and so on for so forth until
+
+ align:start position:0%
+two blocks and so on for so forth until
+ 
+
+ align:start position:0%
+two blocks and so on for so forth until
+you arrive to one block at the end
+
+ align:start position:0%
+you arrive to one block at the end
+ 
+
+ align:start position:0%
+you arrive to one block at the end
+what do you output you output the top
+
+ align:start position:0%
+what do you output you output the top
+ 
+
+ align:start position:0%
+what do you output you output the top
+the final I guess it's going to be
+
+ align:start position:0%
+the final I guess it's going to be
+ 
+
+ align:start position:0%
+the final I guess it's going to be
+somewhere
+
+ align:start position:0%
+somewhere
+ 
+
+ align:start position:0%
+somewhere
+here uh block which is often called a
+
+ align:start position:0%
+here uh block which is often called a
+ 
+
+ align:start position:0%
+here uh block which is often called a
+root you output the root and you output
+
+ align:start position:0%
+root you output the root and you output
+ 
+
+ align:start position:0%
+root you output the root and you output
+the depth of the
+
+ align:start position:0%
+the depth of the
+ 
+
+ align:start position:0%
+the depth of the
+tree okay that's the output of the hash
+
+ align:start position:0%
+tree okay that's the output of the hash
+ 
+
+ align:start position:0%
+tree okay that's the output of the hash
+so the output is the root the hash value
+
+ align:start position:0%
+so the output is the root the hash value
+ 
+
+ align:start position:0%
+so the output is the root the hash value
+here it's Lambda
+
+ align:start position:0%
+here it's Lambda
+ 
+
+ align:start position:0%
+here it's Lambda
+bits and D which you also think of it as
+
+ align:start position:0%
+bits and D which you also think of it as
+ 
+
+ align:start position:0%
+bits and D which you also think of it as
+being Lambda bits even if it's less just
+
+ align:start position:0%
+being Lambda bits even if it's less just
+ 
+
+ align:start position:0%
+being Lambda bits even if it's less just
+encoded using Lambda bits so if you're
+
+ align:start position:0%
+encoded using Lambda bits so if you're
+ 
+
+ align:start position:0%
+encoded using Lambda bits so if you're
+mad now at me because I promise you
+
+ align:start position:0%
+mad now at me because I promise you
+ 
+
+ align:start position:0%
+mad now at me because I promise you
+Lambda bits and you see here two Lambda
+
+ align:start position:0%
+Lambda bits and you see here two Lambda
+ 
+
+ align:start position:0%
+Lambda bits and you see here two Lambda
+bits apply this hash one more time and
+
+ align:start position:0%
+bits apply this hash one more time and
+ 
+
+ align:start position:0%
+bits apply this hash one more time and
+you'll get your Lambda
+
+ align:start position:0%
+you'll get your Lambda
+ 
+
+ align:start position:0%
+you'll get your Lambda
+bits okay but how two Lambda bits is
+
+ align:start position:0%
+bits okay but how two Lambda bits is
+ 
+
+ align:start position:0%
+bits okay but how two Lambda bits is
+also fine yeah um why are we Bing the
+
+ align:start position:0%
+also fine yeah um why are we Bing the
+ 
+
+ align:start position:0%
+also fine yeah um why are we Bing the
+input L to two to the Lambda instead of
+
+ align:start position:0%
+input L to two to the Lambda instead of
+ 
+
+ align:start position:0%
+input L to two to the Lambda instead of
+just arbitrary good good good good good
+
+ align:start position:0%
+just arbitrary good good good good good
+ 
+
+ align:start position:0%
+just arbitrary good good good good good
+great because last time great question
+
+ align:start position:0%
+great because last time great question
+ 
+
+ align:start position:0%
+great because last time great question
+so last time when I mention I said oh
+
+ align:start position:0%
+so last time when I mention I said oh
+ 
+
+ align:start position:0%
+so last time when I mention I said oh
+just take STAR here anything so why am I
+
+ align:start position:0%
+just take STAR here anything so why am I
+ 
+
+ align:start position:0%
+just take STAR here anything so why am I
+why am I bounding out to to the Lambda
+
+ align:start position:0%
+why am I bounding out to to the Lambda
+ 
+
+ align:start position:0%
+why am I bounding out to to the Lambda
+so this construction bounds two to the
+
+ align:start position:0%
+so this construction bounds two to the
+ 
+
+ align:start position:0%
+so this construction bounds two to the
+Lambda because as you I take every
+
+ align:start position:0%
+Lambda because as you I take every
+ 
+
+ align:start position:0%
+Lambda because as you I take every
+Lambda I can't take that's all it gives
+
+ align:start position:0%
+Lambda I can't take that's all it gives
+ 
+
+ align:start position:0%
+Lambda I can't take that's all it gives
+me so that's all I get now you can say
+
+ align:start position:0%
+me so that's all I get now you can say
+ 
+
+ align:start position:0%
+me so that's all I get now you can say
+wait what if I want more maybe I more
+
+ align:start position:0%
+wait what if I want more maybe I more
+ 
+
+ align:start position:0%
+wait what if I want more maybe I more
+than two Lambda you can actually get
+
+ align:start position:0%
+than two Lambda you can actually get
+ 
+
+ align:start position:0%
+than two Lambda you can actually get
+more than two to the Lambda for example
+
+ align:start position:0%
+more than two to the Lambda for example
+ 
+
+ align:start position:0%
+more than two to the Lambda for example
+you can bootstrap this so now you can
+
+ align:start position:0%
+you can bootstrap this so now you can
+ 
+
+ align:start position:0%
+you can bootstrap this so now you can
+take two to the Lambda to Lambda you can
+
+ align:start position:0%
+take two to the Lambda to Lambda you can
+ 
+
+ align:start position:0%
+take two to the Lambda to Lambda you can
+kind of create a Merkel hash of this
+
+ align:start position:0%
+kind of create a Merkel hash of this
+ 
+
+ align:start position:0%
+kind of create a Merkel hash of this
+Merkel hash you know you can kind of uh
+
+ align:start position:0%
+Merkel hash you know you can kind of uh
+ 
+
+ align:start position:0%
+Merkel hash you know you can kind of uh
+uh but actually you never it doesn't
+
+ align:start position:0%
+uh but actually you never it doesn't
+ 
+
+ align:start position:0%
+uh but actually you never it doesn't
+come up because you never need to two to
+
+ align:start position:0%
+come up because you never need to two to
+ 
+
+ align:start position:0%
+come up because you never need to two to
+Lambda is like nothing is more than two
+
+ align:start position:0%
+Lambda is like nothing is more than two
+ 
+
+ align:start position:0%
+Lambda is like nothing is more than two
+to we choose Lambda to in our world
+
+ align:start position:0%
+to we choose Lambda to in our world
+ 
+
+ align:start position:0%
+to we choose Lambda to in our world
+nothing is more than size two to the
+
+ align:start position:0%
+nothing is more than size two to the
+ 
+
+ align:start position:0%
+nothing is more than size two to the
+Lambda but you can think of like um you
+
+ align:start position:0%
+Lambda but you can think of like um you
+ 
+
+ align:start position:0%
+Lambda but you can think of like um you
+you can get if you just as a kind of
+
+ align:start position:0%
+you can get if you just as a kind of
+ 
+
+ align:start position:0%
+you can get if you just as a kind of
+mathematical curiosity you can uh apply
+
+ align:start position:0%
+mathematical curiosity you can uh apply
+ 
+
+ align:start position:0%
+mathematical curiosity you can uh apply
+it you know so once you have from two to
+
+ align:start position:0%
+it you know so once you have from two to
+ 
+
+ align:start position:0%
+it you know so once you have from two to
+the Lambda to Lambda you
+
+ align:start position:0%
+the Lambda to Lambda you
+ 
+
+ align:start position:0%
+the Lambda to Lambda you
+can chop your things to two to the
+
+ align:start position:0%
+can chop your things to two to the
+ 
+
+ align:start position:0%
+can chop your things to two to the
+Lambda and and do this kind of use this
+
+ align:start position:0%
+Lambda and and do this kind of use this
+ 
+
+ align:start position:0%
+Lambda and and do this kind of use this
+as a building block to a bigger morle
+
+ align:start position:0%
+as a building block to a bigger morle
+ 
+
+ align:start position:0%
+as a building block to a bigger morle
+high so you can kind of amplify it you
+
+ align:start position:0%
+high so you can kind of amplify it you
+ 
+
+ align:start position:0%
+high so you can kind of amplify it you
+know uh but we're not for us 2 to the
+
+ align:start position:0%
+know uh but we're not for us 2 to the
+ 
+
+ align:start position:0%
+know uh but we're not for us 2 to the
+Lambda to Lambda is good enough great
+
+ align:start position:0%
+Lambda to Lambda is good enough great
+ 
+
+ align:start position:0%
+Lambda to Lambda is good enough great
+great question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any any other question yes why does the
+
+ align:start position:0%
+any any other question yes why does the
+ 
+
+ align:start position:0%
+any any other question yes why does the
+need to be included in the like should
+
+ align:start position:0%
+need to be included in the like should
+ 
+
+ align:start position:0%
+need to be included in the like should
+it not just be a function of the left of
+
+ align:start position:0%
+it not just be a function of the left of
+ 
+
+ align:start position:0%
+it not just be a function of the left of
+X ah good great great question why do
+
+ align:start position:0%
+X ah good great great question why do
+ 
+
+ align:start position:0%
+X ah good great great question why do
+why do I insist on including D is it not
+
+ align:start position:0%
+why do I insist on including D is it not
+ 
+
+ align:start position:0%
+why do I insist on including D is it not
+a function of X it is a function of X
+
+ align:start position:0%
+a function of X it is a function of X
+ 
+
+ align:start position:0%
+a function of X it is a function of X
+it's a deterministic function of the L
+
+ align:start position:0%
+it's a deterministic function of the L
+ 
+
+ align:start position:0%
+it's a deterministic function of the L
+not even X of the length of X yes
+
+ align:start position:0%
+not even X of the length of X yes
+ 
+
+ align:start position:0%
+not even X of the length of X yes
+however nobody knows what x is so you
+
+ align:start position:0%
+however nobody knows what x is so you
+ 
+
+ align:start position:0%
+however nobody knows what x is so you
+know at the end of the day I want
+
+ align:start position:0%
+know at the end of the day I want
+ 
+
+ align:start position:0%
+know at the end of the day I want
+Collision resistance and so the property
+
+ align:start position:0%
+Collision resistance and so the property
+ 
+
+ align:start position:0%
+Collision resistance and so the property
+we want from this hash is that it's
+
+ align:start position:0%
+we want from this hash is that it's
+ 
+
+ align:start position:0%
+we want from this hash is that it's
+Collision resistance what does Collision
+
+ align:start position:0%
+Collision resistance what does Collision
+ 
+
+ align:start position:0%
+Collision resistance what does Collision
+resistant means it means that you cannot
+
+ align:start position:0%
+resistant means it means that you cannot
+ 
+
+ align:start position:0%
+resistant means it means that you cannot
+output a hash value with two different
+
+ align:start position:0%
+output a hash value with two different
+ 
+
+ align:start position:0%
+output a hash value with two different
+openings now when you outut a has value
+
+ align:start position:0%
+openings now when you outut a has value
+ 
+
+ align:start position:0%
+openings now when you outut a has value
+nobody knows what the x is actually you
+
+ align:start position:0%
+nobody knows what the x is actually you
+ 
+
+ align:start position:0%
+nobody knows what the x is actually you
+may not even know well if
+
+ align:start position:0%
+may not even know well if
+ 
+
+ align:start position:0%
+may not even know well if
+you um okay when you open you know but
+
+ align:start position:0%
+you um okay when you open you know but
+ 
+
+ align:start position:0%
+you um okay when you open you know but
+uh you know when you give someone a hash
+
+ align:start position:0%
+uh you know when you give someone a hash
+ 
+
+ align:start position:0%
+uh you know when you give someone a hash
+value there's no X
+
+ align:start position:0%
+value there's no X
+ 
+
+ align:start position:0%
+value there's no X
+inherently a part of it if you don't
+
+ align:start position:0%
+inherently a part of it if you don't
+ 
+
+ align:start position:0%
+inherently a part of it if you don't
+include the dep actually there's an
+
+ align:start position:0%
+include the dep actually there's an
+ 
+
+ align:start position:0%
+include the dep actually there's an
+attack it's not collig resistance it's
+
+ align:start position:0%
+attack it's not collig resistance it's
+ 
+
+ align:start position:0%
+attack it's not collig resistance it's
+really not it's not just a why is it not
+
+ align:start position:0%
+really not it's not just a why is it not
+ 
+
+ align:start position:0%
+really not it's not just a why is it not
+Collision resistance for example just as
+
+ align:start position:0%
+Collision resistance for example just as
+ 
+
+ align:start position:0%
+Collision resistance for example just as
+an attack let's say I publish this route
+
+ align:start position:0%
+an attack let's say I publish this route
+ 
+
+ align:start position:0%
+an attack let's say I publish this route
+even this is my root okay this is my
+
+ align:start position:0%
+even this is my root okay this is my
+ 
+
+ align:start position:0%
+even this is my root okay this is my
+input my input is X1 X2 X3 X4 and the
+
+ align:start position:0%
+input my input is X1 X2 X3 X4 and the
+ 
+
+ align:start position:0%
+input my input is X1 X2 X3 X4 and the
+output is root now let me break the
+
+ align:start position:0%
+output is root now let me break the
+ 
+
+ align:start position:0%
+output is root now let me break the
+Collision resistance I'll give you two
+
+ align:start position:0%
+Collision resistance I'll give you two
+ 
+
+ align:start position:0%
+Collision resistance I'll give you two
+different openings one is X1 X2 X3 X4
+
+ align:start position:0%
+different openings one is X1 X2 X3 X4
+ 
+
+ align:start position:0%
+different openings one is X1 X2 X3 X4
+you do the hash you see yeah you're
+
+ align:start position:0%
+you do the hash you see yeah you're
+ 
+
+ align:start position:0%
+you do the hash you see yeah you're
+happy it's a good opening now let me
+
+ align:start position:0%
+happy it's a good opening now let me
+ 
+
+ align:start position:0%
+happy it's a good opening now let me
+give you another opening just this and
+
+ align:start position:0%
+give you another opening just this and
+ 
+
+ align:start position:0%
+give you another opening just this and
+this that's also a good open opening so
+
+ align:start position:0%
+this that's also a good open opening so
+ 
+
+ align:start position:0%
+this that's also a good open opening so
+I open it in two different
+
+ align:start position:0%
+I open it in two different
+ 
+
+ align:start position:0%
+I open it in two different
+ways that's not okay that's a collision
+
+ align:start position:0%
+ways that's not okay that's a collision
+ 
+
+ align:start position:0%
+ways that's not okay that's a collision
+if you include D however then so that's
+
+ align:start position:0%
+if you include D however then so that's
+ 
+
+ align:start position:0%
+if you include D however then so that's
+exactly what will allow me to argue
+
+ align:start position:0%
+exactly what will allow me to argue
+ 
+
+ align:start position:0%
+exactly what will allow me to argue
+Collision resistance it's this D great
+
+ align:start position:0%
+Collision resistance it's this D great
+ 
+
+ align:start position:0%
+Collision resistance it's this D great
+question thank you any so so this is the
+
+ align:start position:0%
+question thank you any so so this is the
+ 
+
+ align:start position:0%
+question thank you any so so this is the
+construction
+
+ align:start position:0%
+construction
+ 
+
+ align:start position:0%
+construction
+questions okay let's see how do we open
+
+ align:start position:0%
+questions okay let's see how do we open
+ 
+
+ align:start position:0%
+questions okay let's see how do we open
+so now this is this is just so far great
+
+ align:start position:0%
+so now this is this is just so far great
+ 
+
+ align:start position:0%
+so now this is this is just so far great
+we managed to go from two to the Lambda
+
+ align:start position:0%
+we managed to go from two to the Lambda
+ 
+
+ align:start position:0%
+we managed to go from two to the Lambda
+to Lambda I didn't argue Collision resen
+
+ align:start position:0%
+to Lambda I didn't argue Collision resen
+ 
+
+ align:start position:0%
+to Lambda I didn't argue Collision resen
+but at least we did domain extension so
+
+ align:start position:0%
+but at least we did domain extension so
+ 
+
+ align:start position:0%
+but at least we did domain extension so
+we extended the domain but I also want
+
+ align:start position:0%
+we extended the domain but I also want
+ 
+
+ align:start position:0%
+we extended the domain but I also want
+especially I need it for the killan M
+
+ align:start position:0%
+especially I need it for the killan M
+ 
+
+ align:start position:0%
+especially I need it for the killan M
+protocol and for many many other uses in
+
+ align:start position:0%
+protocol and for many many other uses in
+ 
+
+ align:start position:0%
+protocol and for many many other uses in
+cryptography I want to be able to do
+
+ align:start position:0%
+cryptography I want to be able to do
+ 
+
+ align:start position:0%
+cryptography I want to be able to do
+local opening so remember what does
+
+ align:start position:0%
+local opening so remember what does
+ 
+
+ align:start position:0%
+local opening so remember what does
+local opening mean I may not want to
+
+ align:start position:0%
+local opening mean I may not want to
+ 
+
+ align:start position:0%
+local opening mean I may not want to
+open when with I may not want to give
+
+ align:start position:0%
+open when with I may not want to give
+ 
+
+ align:start position:0%
+open when with I may not want to give
+you my entire
+
+ align:start position:0%
+you my entire
+ 
+
+ align:start position:0%
+you my entire
+input I may just want to give you to
+
+ align:start position:0%
+input I may just want to give you to
+ 
+
+ align:start position:0%
+input I may just want to give you to
+convince you that this hash value in
+
+ align:start position:0%
+convince you that this hash value in
+ 
+
+ align:start position:0%
+convince you that this hash value in
+some location I of the of the of the
+
+ align:start position:0%
+some location I of the of the of the
+ 
+
+ align:start position:0%
+some location I of the of the of the
+input the value is some bit B but I
+
+ align:start position:0%
+input the value is some bit B but I
+ 
+
+ align:start position:0%
+input the value is some bit B but I
+don't want to give you the entire
+
+ align:start position:0%
+don't want to give you the entire
+ 
+
+ align:start position:0%
+don't want to give you the entire
+because the entire input is gigantic you
+
+ align:start position:0%
+because the entire input is gigantic you
+ 
+
+ align:start position:0%
+because the entire input is gigantic you
+can't even hold it so I want kind of a
+
+ align:start position:0%
+can't even hold it so I want kind of a
+ 
+
+ align:start position:0%
+can't even hold it so I want kind of a
+succinct opener I want to convince you
+
+ align:start position:0%
+succinct opener I want to convince you
+ 
+
+ align:start position:0%
+succinct opener I want to convince you
+in a kind of a very succinct way that
+
+ align:start position:0%
+in a kind of a very succinct way that
+ 
+
+ align:start position:0%
+in a kind of a very succinct way that
+what's sitting here in this bit is zero
+
+ align:start position:0%
+what's sitting here in this bit is zero
+ 
+
+ align:start position:0%
+what's sitting here in this bit is zero
+or it's one so how do I do it so this um
+
+ align:start position:0%
+or it's one so how do I do it so this um
+ 
+
+ align:start position:0%
+or it's one so how do I do it so this um
+a uh construction is actually really
+
+ align:start position:0%
+a uh construction is actually really
+ 
+
+ align:start position:0%
+a uh construction is actually really
+nice it gives you a local opening in a
+
+ align:start position:0%
+nice it gives you a local opening in a
+ 
+
+ align:start position:0%
+nice it gives you a local opening in a
+very nice way so what's the local
+
+ align:start position:0%
+very nice way so what's the local
+ 
+
+ align:start position:0%
+very nice way so what's the local
+opening suppose I want to open this kind
+
+ align:start position:0%
+opening suppose I want to open this kind
+ 
+
+ align:start position:0%
+opening suppose I want to open this kind
+of the bit here sitting here what I'm
+
+ align:start position:0%
+of the bit here sitting here what I'm
+ 
+
+ align:start position:0%
+of the bit here sitting here what I'm
+going to do I'm going to actually give
+
+ align:start position:0%
+going to do I'm going to actually give
+ 
+
+ align:start position:0%
+going to do I'm going to actually give
+you this entire Block it's only L the
+
+ align:start position:0%
+you this entire Block it's only L the
+ 
+
+ align:start position:0%
+you this entire Block it's only L the
+bit so it's not that big okay I give you
+
+ align:start position:0%
+bit so it's not that big okay I give you
+ 
+
+ align:start position:0%
+bit so it's not that big okay I give you
+this block what do you do with it so let
+
+ align:start position:0%
+this block what do you do with it so let
+ 
+
+ align:start position:0%
+this block what do you do with it so let
+me help you convince you that this block
+
+ align:start position:0%
+me help you convince you that this block
+ 
+
+ align:start position:0%
+me help you convince you that this block
+is indeed the block related to the root
+
+ align:start position:0%
+is indeed the block related to the root
+ 
+
+ align:start position:0%
+is indeed the block related to the root
+namely it's the it's the block that
+
+ align:start position:0%
+namely it's the it's the block that
+ 
+
+ align:start position:0%
+namely it's the it's the block that
+indeed sits here next to how do I
+
+ align:start position:0%
+indeed sits here next to how do I
+ 
+
+ align:start position:0%
+indeed sits here next to how do I
+convince
+
+ align:start position:0%
+convince
+ 
+
+ align:start position:0%
+convince
+you I give you the sibling so this block
+
+ align:start position:0%
+you I give you the sibling so this block
+ 
+
+ align:start position:0%
+you I give you the sibling so this block
+has a parent I give you the sibling and
+
+ align:start position:0%
+has a parent I give you the sibling and
+ 
+
+ align:start position:0%
+has a parent I give you the sibling and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+parent this parent has a parent I give
+
+ align:start position:0%
+parent this parent has a parent I give
+ 
+
+ align:start position:0%
+parent this parent has a parent I give
+you the sibling and the parent and so on
+
+ align:start position:0%
+you the sibling and the parent and so on
+ 
+
+ align:start position:0%
+you the sibling and the parent and so on
+so forth until you get to the root I
+
+ align:start position:0%
+so forth until you get to the root I
+ 
+
+ align:start position:0%
+so forth until you get to the root I
+give you all these blocks so in each
+
+ align:start position:0%
+give you all these blocks so in each
+ 
+
+ align:start position:0%
+give you all these blocks so in each
+layer I open two blocks which are the
+
+ align:start position:0%
+layer I open two blocks which are the
+ 
+
+ align:start position:0%
+layer I open two blocks which are the
+two siblings so I open two siblings you
+
+ align:start position:0%
+two siblings so I open two siblings you
+ 
+
+ align:start position:0%
+two siblings so I open two siblings you
+get this I open the two siblings you get
+
+ align:start position:0%
+get this I open the two siblings you get
+ 
+
+ align:start position:0%
+get this I open the two siblings you get
+this I open the twoing and so on
+
+ align:start position:0%
+this I open the twoing and so on
+ 
+
+ align:start position:0%
+this I open the twoing and so on
+yes so I don't know if it matters but
+
+ align:start position:0%
+yes so I don't know if it matters but
+ 
+
+ align:start position:0%
+yes so I don't know if it matters but
+you strictly you to return the ancestors
+
+ align:start position:0%
+you strictly you to return the ancestors
+ 
+
+ align:start position:0%
+you strictly you to return the ancestors
+you can only return the sit ons right
+
+ align:start position:0%
+you can only return the sit ons right
+ 
+
+ align:start position:0%
+you can only return the sit ons right
+good good good right right right you're
+
+ align:start position:0%
+good good good right right right you're
+ 
+
+ align:start position:0%
+good good good right right right you're
+totally right you're saying well if you
+
+ align:start position:0%
+totally right you're saying well if you
+ 
+
+ align:start position:0%
+totally right you're saying well if you
+really want to be what you're saying
+
+ align:start position:0%
+really want to be what you're saying
+ 
+
+ align:start position:0%
+really want to be what you're saying
+which is completely right thing this is
+
+ align:start position:0%
+which is completely right thing this is
+ 
+
+ align:start position:0%
+which is completely right thing this is
+wasteful because actually all I need to
+
+ align:start position:0%
+wasteful because actually all I need to
+ 
+
+ align:start position:0%
+wasteful because actually all I need to
+give you is the sibling so why waste
+
+ align:start position:0%
+give you is the sibling so why waste
+ 
+
+ align:start position:0%
+give you is the sibling so why waste
+communication I if I want to open this
+
+ align:start position:0%
+communication I if I want to open this
+ 
+
+ align:start position:0%
+communication I if I want to open this
+I'll give you this and this sibling I
+
+ align:start position:0%
+I'll give you this and this sibling I
+ 
+
+ align:start position:0%
+I'll give you this and this sibling I
+don't need to give you this you can
+
+ align:start position:0%
+don't need to give you this you can
+ 
+
+ align:start position:0%
+don't need to give you this you can
+compute this on your own so compute this
+
+ align:start position:0%
+compute this on your own so compute this
+ 
+
+ align:start position:0%
+compute this on your own so compute this
+on your own I'll give you this I don't
+
+ align:start position:0%
+on your own I'll give you this I don't
+ 
+
+ align:start position:0%
+on your own I'll give you this I don't
+need to give you this you have these two
+
+ align:start position:0%
+need to give you this you have these two
+ 
+
+ align:start position:0%
+need to give you this you have these two
+so complet it on this on your own and
+
+ align:start position:0%
+so complet it on this on your own and
+ 
+
+ align:start position:0%
+so complet it on this on your own and
+then I'll only give you this and then
+
+ align:start position:0%
+then I'll only give you this and then
+ 
+
+ align:start position:0%
+then I'll only give you this and then
+and so on you're 100% correct I actually
+
+ align:start position:0%
+and so on you're 100% correct I actually
+ 
+
+ align:start position:0%
+and so on you're 100% correct I actually
+just need to give you
+
+ align:start position:0%
+just need to give you
+ 
+
+ align:start position:0%
+just need to give you
+one okay I wrote two because it's just
+
+ align:start position:0%
+one okay I wrote two because it's just
+ 
+
+ align:start position:0%
+one okay I wrote two because it's just
+easier to say something but yes exactly
+
+ align:start position:0%
+easier to say something but yes exactly
+ 
+
+ align:start position:0%
+easier to say something but yes exactly
+one is enough and you can compute the
+
+ align:start position:0%
+one is enough and you can compute the
+ 
+
+ align:start position:0%
+one is enough and you can compute the
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+fantastic uh so that's the so I I I
+
+ align:start position:0%
+fantastic uh so that's the so I I I
+ 
+
+ align:start position:0%
+fantastic uh so that's the so I I I
+denoted by so what does the open do it
+
+ align:start position:0%
+denoted by so what does the open do it
+ 
+
+ align:start position:0%
+denoted by so what does the open do it
+gives you for each layer it gives you
+
+ align:start position:0%
+gives you for each layer it gives you
+ 
+
+ align:start position:0%
+gives you for each layer it gives you
+two blocks for layer J denoted by ZJ so
+
+ align:start position:0%
+two blocks for layer J denoted by ZJ so
+ 
+
+ align:start position:0%
+two blocks for layer J denoted by ZJ so
+ZJ is two blocks okay there's on the
+
+ align:start position:0%
+ZJ is two blocks okay there's on the
+ 
+
+ align:start position:0%
+ZJ is two blocks okay there's on the
+leaves it's two blocks J equal zero it's
+
+ align:start position:0%
+leaves it's two blocks J equal zero it's
+ 
+
+ align:start position:0%
+leaves it's two blocks J equal zero it's
+on the leaf layer one layer two up to
+
+ align:start position:0%
+on the leaf layer one layer two up to
+ 
+
+ align:start position:0%
+on the leaf layer one layer two up to
+layer D it's actually just the root so
+
+ align:start position:0%
+layer D it's actually just the root so
+ 
+
+ align:start position:0%
+layer D it's actually just the root so
+you don't you can actually go to D minus
+
+ align:start position:0%
+you don't you can actually go to D minus
+ 
+
+ align:start position:0%
+you don't you can actually go to D minus
+one if you want okay but I I'll just in
+
+ align:start position:0%
+one if you want okay but I I'll just in
+ 
+
+ align:start position:0%
+one if you want okay but I I'll just in
+in my mind I want to include the root
+
+ align:start position:0%
+in my mind I want to include the root
+ 
+
+ align:start position:0%
+in my mind I want to include the root
+it's just you'll the reason I include
+
+ align:start position:0%
+it's just you'll the reason I include
+ 
+
+ align:start position:0%
+it's just you'll the reason I include
+both and the root is now when I analyze
+
+ align:start position:0%
+both and the root is now when I analyze
+ 
+
+ align:start position:0%
+both and the root is now when I analyze
+it it's notation wise it's just very
+
+ align:start position:0%
+it it's notation wise it's just very
+ 
+
+ align:start position:0%
+it it's notation wise it's just very
+very easy but really it's enough like
+
+ align:start position:0%
+very easy but really it's enough like
+ 
+
+ align:start position:0%
+very easy but really it's enough like
+you said to have the sibling and the
+
+ align:start position:0%
+you said to have the sibling and the
+ 
+
+ align:start position:0%
+you said to have the sibling and the
+roots of course you don't need to
+
+ align:start position:0%
+roots of course you don't need to
+ 
+
+ align:start position:0%
+roots of course you don't need to
+give okay but let's just think this is
+
+ align:start position:0%
+give okay but let's just think this is
+ 
+
+ align:start position:0%
+give okay but let's just think this is
+how I open and now how do I
+
+ align:start position:0%
+how I open and now how do I
+ 
+
+ align:start position:0%
+how I open and now how do I
+verify I just take each two sibling
+
+ align:start position:0%
+verify I just take each two sibling
+ 
+
+ align:start position:0%
+verify I just take each two sibling
+compute the hash and make sure it
+
+ align:start position:0%
+compute the hash and make sure it
+ 
+
+ align:start position:0%
+compute the hash and make sure it
+corresponds to the relevant the relevant
+
+ align:start position:0%
+corresponds to the relevant the relevant
+ 
+
+ align:start position:0%
+corresponds to the relevant the relevant
+Z is indeed uh the parent so again you
+
+ align:start position:0%
+Z is indeed uh the parent so again you
+ 
+
+ align:start position:0%
+Z is indeed uh the parent so again you
+gave me all these things I compute these
+
+ align:start position:0%
+gave me all these things I compute these
+ 
+
+ align:start position:0%
+gave me all these things I compute these
+two I check that it's consistent with
+
+ align:start position:0%
+two I check that it's consistent with
+ 
+
+ align:start position:0%
+two I check that it's consistent with
+the what you gave you if you didn't give
+
+ align:start position:0%
+the what you gave you if you didn't give
+ 
+
+ align:start position:0%
+the what you gave you if you didn't give
+me fine I'll compute on my own I get
+
+ align:start position:0%
+me fine I'll compute on my own I get
+ 
+
+ align:start position:0%
+me fine I'll compute on my own I get
+this I'll compute this and give and then
+
+ align:start position:0%
+this I'll compute this and give and then
+ 
+
+ align:start position:0%
+this I'll compute this and give and then
+they'll check that all I need to check
+
+ align:start position:0%
+they'll check that all I need to check
+ 
+
+ align:start position:0%
+they'll check that all I need to check
+it then is consistency with the
+
+ align:start position:0%
+it then is consistency with the
+ 
+
+ align:start position:0%
+it then is consistency with the
+root okay that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+verification question about the design
+
+ align:start position:0%
+verification question about the design
+ 
+
+ align:start position:0%
+verification question about the design
+the the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithms okay so this is kind of where
+
+ align:start position:0%
+algorithms okay so this is kind of where
+ 
+
+ align:start position:0%
+algorithms okay so this is kind of where
+we left off actually last time and what
+
+ align:start position:0%
+we left off actually last time and what
+ 
+
+ align:start position:0%
+we left off actually last time and what
+I want to do now is do the Collision
+
+ align:start position:0%
+I want to do now is do the Collision
+ 
+
+ align:start position:0%
+I want to do now is do the Collision
+resistance I'm happy that actually we
+
+ align:start position:0%
+resistance I'm happy that actually we
+ 
+
+ align:start position:0%
+resistance I'm happy that actually we
+got a chance to do it again because it's
+
+ align:start position:0%
+got a chance to do it again because it's
+ 
+
+ align:start position:0%
+got a chance to do it again because it's
+a very important primitive so it's worth
+
+ align:start position:0%
+a very important primitive so it's worth
+ 
+
+ align:start position:0%
+a very important primitive so it's worth
+kind of having it ingrained in your mind
+
+ align:start position:0%
+kind of having it ingrained in your mind
+ 
+
+ align:start position:0%
+kind of having it ingrained in your mind
+a okay so why why is it collagen
+
+ align:start position:0%
+a okay so why why is it collagen
+ 
+
+ align:start position:0%
+a okay so why why is it collagen
+resistant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to prove Collision resistance what do
+
+ align:start position:0%
+so to prove Collision resistance what do
+ 
+
+ align:start position:0%
+so to prove Collision resistance what do
+we want to argue that an adversary
+
+ align:start position:0%
+we want to argue that an adversary
+ 
+
+ align:start position:0%
+we want to argue that an adversary
+that's given a hash key cannot produce a
+
+ align:start position:0%
+that's given a hash key cannot produce a
+ 
+
+ align:start position:0%
+that's given a hash key cannot produce a
+hash value namely root and D with two
+
+ align:start position:0%
+hash value namely root and D with two
+ 
+
+ align:start position:0%
+hash value namely root and D with two
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+openings okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Suppose there
+
+ align:start position:0%
+Suppose there
+ 
+
+ align:start position:0%
+Suppose there
+exists a poly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size adversary that does find the
+
+ align:start position:0%
+size adversary that does find the
+ 
+
+ align:start position:0%
+size adversary that does find the
+Collision okay such that the probability
+
+ align:start position:0%
+Collision okay such that the probability
+ 
+
+ align:start position:0%
+Collision okay such that the probability
+that a he gets a hash key hash key is
+
+ align:start position:0%
+that a he gets a hash key hash key is
+ 
+
+ align:start position:0%
+that a he gets a hash key hash key is
+from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gen and somehow he manages to Output a
+
+ align:start position:0%
+gen and somehow he manages to Output a
+ 
+
+ align:start position:0%
+gen and somehow he manages to Output a
+hash value which is root and D that's
+
+ align:start position:0%
+hash value which is root and D that's
+ 
+
+ align:start position:0%
+hash value which is root and D that's
+just a hash
+
+ align:start position:0%
+just a hash
+ 
+
+ align:start position:0%
+just a hash
+value and he gives me some
+
+ align:start position:0%
+value and he gives me some
+ 
+
+ align:start position:0%
+value and he gives me some
+index uh I and he managed to open it in
+
+ align:start position:0%
+index uh I and he managed to open it in
+ 
+
+ align:start position:0%
+index uh I and he managed to open it in
+two different way he gives me an open
+
+ align:start position:0%
+two different way he gives me an open
+ 
+
+ align:start position:0%
+two different way he gives me an open
+opening that says oh I is zero and it
+
+ align:start position:0%
+opening that says oh I is zero and it
+ 
+
+ align:start position:0%
+opening that says oh I is zero and it
+gives me another opening that says the I
+
+ align:start position:0%
+gives me another opening that says the I
+ 
+
+ align:start position:0%
+gives me another opening that says the I
+bit is one and such that for both of
+
+ align:start position:0%
+bit is one and such that for both of
+ 
+
+ align:start position:0%
+bit is one and such that for both of
+them such that for every B for both zero
+
+ align:start position:0%
+them such that for every B for both zero
+ 
+
+ align:start position:0%
+them such that for every B for both zero
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+one there will accept there and hash
+
+ align:start position:0%
+one there will accept there and hash
+ 
+
+ align:start position:0%
+one there will accept there and hash
+key uh root and d i and row b outputs
+
+ align:start position:0%
+key uh root and d i and row b outputs
+ 
+
+ align:start position:0%
+key uh root and d i and row b outputs
+one so suppose I have an algorithm
+
+ align:start position:0%
+one so suppose I have an algorithm
+ 
+
+ align:start position:0%
+one so suppose I have an algorithm
+that gives me a hash value an index and
+
+ align:start position:0%
+that gives me a hash value an index and
+ 
+
+ align:start position:0%
+that gives me a hash value an index and
+a valid opening both to zero and to one
+
+ align:start position:0%
+a valid opening both to zero and to one
+ 
+
+ align:start position:0%
+a valid opening both to zero and to one
+valid I mean that the ver will accept
+
+ align:start position:0%
+valid I mean that the ver will accept
+ 
+
+ align:start position:0%
+valid I mean that the ver will accept
+both of them oh sorry
+
+ align:start position:0%
+both of them oh sorry
+ 
+
+ align:start position:0%
+both of them oh sorry
+B so ver takes hash key a value an index
+
+ align:start position:0%
+B so ver takes hash key a value an index
+ 
+
+ align:start position:0%
+B so ver takes hash key a value an index
+I and a b bit B saying whether index I
+
+ align:start position:0%
+I and a b bit B saying whether index I
+ 
+
+ align:start position:0%
+I and a b bit B saying whether index I
+is zero or one and a proof an
+
+ align:start position:0%
+is zero or one and a proof an
+ 
+
+ align:start position:0%
+is zero or one and a proof an
+opening and suppose he accepts
+
+ align:start position:0%
+opening and suppose he accepts
+ 
+
+ align:start position:0%
+opening and suppose he accepts
+both suppose he accepts both with
+
+ align:start position:0%
+both suppose he accepts both with
+ 
+
+ align:start position:0%
+both suppose he accepts both with
+probability at least I know
+
+ align:start position:0%
+probability at least I know
+ 
+
+ align:start position:0%
+probability at least I know
+Epsilon okay so Suppose there exist an
+
+ align:start position:0%
+Epsilon okay so Suppose there exist an
+ 
+
+ align:start position:0%
+Epsilon okay so Suppose there exist an
+exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon so Suppose there exist epon so
+
+ align:start position:0%
+Epsilon so Suppose there exist epon so
+ 
+
+ align:start position:0%
+Epsilon so Suppose there exist epon so
+that for any L that the probability that
+
+ align:start position:0%
+that for any L that the probability that
+ 
+
+ align:start position:0%
+that for any L that the probability that
+a managed to find the Collision like
+
+ align:start position:0%
+a managed to find the Collision like
+ 
+
+ align:start position:0%
+a managed to find the Collision like
+this is at least Epsilon I'm going to
+
+ align:start position:0%
+this is at least Epsilon I'm going to
+ 
+
+ align:start position:0%
+this is at least Epsilon I'm going to
+argue then then you can find a collision
+
+ align:start position:0%
+argue then then you can find a collision
+ 
+
+ align:start position:0%
+argue then then you can find a collision
+in the underlying H in the small H with
+
+ align:start position:0%
+in the underlying H in the small H with
+ 
+
+ align:start position:0%
+in the underlying H in the small H with
+probability Epsilon
+
+ align:start position:0%
+probability Epsilon
+ 
+
+ align:start position:0%
+probability Epsilon
+okay so if you you if you have an
+
+ align:start position:0%
+okay so if you you if you have an
+ 
+
+ align:start position:0%
+okay so if you you if you have an
+algorithm like this
+
+ align:start position:0%
+algorithm like this
+ 
+
+ align:start position:0%
+algorithm like this
+then there exists an algorithm uh uh
+
+ align:start position:0%
+then there exists an algorithm uh uh
+ 
+
+ align:start position:0%
+then there exists an algorithm uh uh
+poly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size such that
+
+ align:start position:0%
+size such that
+ 
+
+ align:start position:0%
+size such that
+b such that the
+
+ align:start position:0%
+b such that the
+ 
+
+ align:start position:0%
+b such that the
+probability that b he gets hash key the
+
+ align:start position:0%
+probability that b he gets hash key the
+ 
+
+ align:start position:0%
+probability that b he gets hash key the
+probability that he outputs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a I don't know x0 x and x Prime such
+
+ align:start position:0%
+a I don't know x0 x and x Prime such
+ 
+
+ align:start position:0%
+a I don't know x0 x and x Prime such
+that the original eval HK x equals
+
+ align:start position:0%
+that the original eval HK x equals
+ 
+
+ align:start position:0%
+that the original eval HK x equals
+eval hkx Prime and X is different than x
+
+ align:start position:0%
+eval hkx Prime and X is different than x
+ 
+
+ align:start position:0%
+eval hkx Prime and X is different than x
+Prime is at least
+
+ align:start position:0%
+Prime is at least
+ 
+
+ align:start position:0%
+Prime is at least
+Epsilon but we assume that this is
+
+ align:start position:0%
+Epsilon but we assume that this is
+ 
+
+ align:start position:0%
+Epsilon but we assume that this is
+Collision resistance we started with an
+
+ align:start position:0%
+Collision resistance we started with an
+ 
+
+ align:start position:0%
+Collision resistance we started with an
+underlying hash function that's
+
+ align:start position:0%
+underlying hash function that's
+ 
+
+ align:start position:0%
+underlying hash function that's
+Collision resistance so the Epsilon has
+
+ align:start position:0%
+Collision resistance so the Epsilon has
+ 
+
+ align:start position:0%
+Collision resistance so the Epsilon has
+to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negligible okay that's what we're going
+
+ align:start position:0%
+negligible okay that's what we're going
+ 
+
+ align:start position:0%
+negligible okay that's what we're going
+to show so we're going to use if an
+
+ align:start position:0%
+to show so we're going to use if an
+ 
+
+ align:start position:0%
+to show so we're going to use if an
+adversary can find a coll a local
+
+ align:start position:0%
+adversary can find a coll a local
+ 
+
+ align:start position:0%
+adversary can find a coll a local
+opening that collides for the Merkel
+
+ align:start position:0%
+opening that collides for the Merkel
+ 
+
+ align:start position:0%
+opening that collides for the Merkel
+hash we can use them to actually
+
+ align:start position:0%
+hash we can use them to actually
+ 
+
+ align:start position:0%
+hash we can use them to actually
+break the to find collisions in the
+
+ align:start position:0%
+break the to find collisions in the
+ 
+
+ align:start position:0%
+break the to find collisions in the
+underlying kind of two Lambda to L to
+
+ align:start position:0%
+underlying kind of two Lambda to L to
+ 
+
+ align:start position:0%
+underlying kind of two Lambda to L to
+Lambda uh hash function in the little
+
+ align:start position:0%
+Lambda uh hash function in the little
+ 
+
+ align:start position:0%
+Lambda uh hash function in the little
+hash
+
+ align:start position:0%
+hash
+ 
+
+ align:start position:0%
+hash
+function so how does B work what does B
+
+ align:start position:0%
+function so how does B work what does B
+ 
+
+ align:start position:0%
+function so how does B work what does B
+do B takes it a hash key he just run a
+
+ align:start position:0%
+do B takes it a hash key he just run a
+ 
+
+ align:start position:0%
+do B takes it a hash key he just run a
+so let me so we claim that there exists
+
+ align:start position:0%
+so let me so we claim that there exists
+ 
+
+ align:start position:0%
+so let me so we claim that there exists
+a b so let's see
+
+ align:start position:0%
+a b so let's see
+ 
+
+ align:start position:0%
+a b so let's see
+B an input hash key what does it do just
+
+ align:start position:0%
+B an input hash key what does it do just
+ 
+
+ align:start position:0%
+B an input hash key what does it do just
+run a so get root d i row0 Row
+
+ align:start position:0%
+run a so get root d i row0 Row
+ 
+
+ align:start position:0%
+run a so get root d i row0 Row
+one which is just a and hash
+
+ align:start position:0%
+one which is just a and hash
+ 
+
+ align:start position:0%
+one which is just a and hash
+key now
+
+ align:start position:0%
+key now
+ 
+
+ align:start position:0%
+key now
+he got row zero and Row one what are row
+
+ align:start position:0%
+he got row zero and Row one what are row
+ 
+
+ align:start position:0%
+he got row zero and Row one what are row
+zero Row one each row is this kind of
+
+ align:start position:0%
+zero Row one each row is this kind of
+ 
+
+ align:start position:0%
+zero Row one each row is this kind of
+two uh pairs of siblings I'm going to
+
+ align:start position:0%
+two uh pairs of siblings I'm going to
+ 
+
+ align:start position:0%
+two uh pairs of siblings I'm going to
+assume that both exist because it's just
+
+ align:start position:0%
+assume that both exist because it's just
+ 
+
+ align:start position:0%
+assume that both exist because it's just
+easier for me that's why I wrote both of
+
+ align:start position:0%
+easier for me that's why I wrote both of
+ 
+
+ align:start position:0%
+easier for me that's why I wrote both of
+them so each
+
+ align:start position:0%
+them so each
+ 
+
+ align:start position:0%
+them so each
+opening so row zero is for each level
+
+ align:start position:0%
+opening so row zero is for each level
+ 
+
+ align:start position:0%
+opening so row zero is for each level
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+z0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J from zero to D and Row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one is let's call it z uh one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J now what do we know in the leaves so
+
+ align:start position:0%
+J now what do we know in the leaves so
+ 
+
+ align:start position:0%
+J now what do we know in the leaves so
+we know that
+
+ align:start position:0%
+we know that
+ 
+
+ align:start position:0%
+we know that
+z0 Z is different than Z One Z the two
+
+ align:start position:0%
+z0 Z is different than Z One Z the two
+ 
+
+ align:start position:0%
+z0 Z is different than Z One Z the two
+leaves are different because in one
+
+ align:start position:0%
+leaves are different because in one
+ 
+
+ align:start position:0%
+leaves are different because in one
+leaf okay suppose suppose verify access
+
+ align:start position:0%
+leaf okay suppose suppose verify access
+ 
+
+ align:start position:0%
+leaf okay suppose suppose verify access
+to both of them in the case that these
+
+ align:start position:0%
+to both of them in the case that these
+ 
+
+ align:start position:0%
+to both of them in the case that these
+are both accepted I'm going to argue
+
+ align:start position:0%
+are both accepted I'm going to argue
+ 
+
+ align:start position:0%
+are both accepted I'm going to argue
+that I found
+
+ align:start position:0%
+that I found
+ 
+
+ align:start position:0%
+that I found
+collisions okay so now suppose row Z and
+
+ align:start position:0%
+collisions okay so now suppose row Z and
+ 
+
+ align:start position:0%
+collisions okay so now suppose row Z and
+Row one are accepted so
+
+ align:start position:0%
+Row one are accepted so
+ 
+
+ align:start position:0%
+Row one are accepted so
+ver ver accepts both of
+
+ align:start position:0%
+ver ver accepts both of
+ 
+
+ align:start position:0%
+ver ver accepts both of
+them now if there accepts both of them
+
+ align:start position:0%
+them now if there accepts both of them
+ 
+
+ align:start position:0%
+them now if there accepts both of them
+so we know that the leaves are different
+
+ align:start position:0%
+so we know that the leaves are different
+ 
+
+ align:start position:0%
+so we know that the leaves are different
+because in the leaves in one case I have
+
+ align:start position:0%
+because in the leaves in one case I have
+ 
+
+ align:start position:0%
+because in the leaves in one case I have
+here one and the other case I have zero
+
+ align:start position:0%
+here one and the other case I have zero
+ 
+
+ align:start position:0%
+here one and the other case I have zero
+so they have to be different so I know
+
+ align:start position:0%
+so they have to be different so I know
+ 
+
+ align:start position:0%
+so they have to be different so I know
+the leaves are different I also know
+
+ align:start position:0%
+the leaves are different I also know
+ 
+
+ align:start position:0%
+the leaves are different I also know
+that z0
+
+ align:start position:0%
+that z0
+ 
+
+ align:start position:0%
+that z0
+D equals z1d these are both a
+
+ align:start position:0%
+D equals z1d these are both a
+ 
+
+ align:start position:0%
+D equals z1d these are both a
+root now of course I said we don't need
+
+ align:start position:0%
+root now of course I said we don't need
+ 
+
+ align:start position:0%
+root now of course I said we don't need
+to include it because but I'm just
+
+ align:start position:0%
+to include it because but I'm just
+ 
+
+ align:start position:0%
+to include it because but I'm just
+putting here because I want what the
+
+ align:start position:0%
+putting here because I want what the
+ 
+
+ align:start position:0%
+putting here because I want what the
+reason I want to include it is just for
+
+ align:start position:0%
+reason I want to include it is just for
+ 
+
+ align:start position:0%
+reason I want to include it is just for
+clarity to say look we have kind of D
+
+ align:start position:0%
+clarity to say look we have kind of D
+ 
+
+ align:start position:0%
+clarity to say look we have kind of D
+layers of information on each
+
+ align:start position:0%
+layers of information on each
+ 
+
+ align:start position:0%
+layers of information on each
+opening the leaves they must be
+
+ align:start position:0%
+opening the leaves they must be
+ 
+
+ align:start position:0%
+opening the leaves they must be
+different because one opens to zero one
+
+ align:start position:0%
+different because one opens to zero one
+ 
+
+ align:start position:0%
+different because one opens to zero one
+opens to one the root the last one must
+
+ align:start position:0%
+opens to one the root the last one must
+ 
+
+ align:start position:0%
+opens to one the root the last one must
+be the same it's the root
+
+ align:start position:0%
+be the same it's the root
+ 
+
+ align:start position:0%
+be the same it's the root
+it means that there must be some kind of
+
+ align:start position:0%
+it means that there must be some kind of
+ 
+
+ align:start position:0%
+it means that there must be some kind of
+two adjacent layers on which one of
+
+ align:start position:0%
+two adjacent layers on which one of
+ 
+
+ align:start position:0%
+two adjacent layers on which one of
+below they disagree and above they agree
+
+ align:start position:0%
+below they disagree and above they agree
+ 
+
+ align:start position:0%
+below they disagree and above they agree
+okay we know here they disagree here
+
+ align:start position:0%
+okay we know here they disagree here
+ 
+
+ align:start position:0%
+okay we know here they disagree here
+they agree okay they disagree do they
+
+ align:start position:0%
+they agree okay they disagree do they
+ 
+
+ align:start position:0%
+they agree okay they disagree do they
+disagree here disagree here at some
+
+ align:start position:0%
+disagree here disagree here at some
+ 
+
+ align:start position:0%
+disagree here disagree here at some
+point they're going to agree so we say
+
+ align:start position:0%
+point they're going to agree so we say
+ 
+
+ align:start position:0%
+point they're going to agree so we say
+there must
+
+ align:start position:0%
+there must
+ 
+
+ align:start position:0%
+there must
+be a layer J such that zj0 is different
+
+ align:start position:0%
+be a layer J such that zj0 is different
+ 
+
+ align:start position:0%
+be a layer J such that zj0 is different
+than zj1 but ZJ + one 0 is equal to
+
+ align:start position:0%
+than zj1 but ZJ + one 0 is equal to
+ 
+
+ align:start position:0%
+than zj1 but ZJ + one 0 is equal to
+ZJ + 1
+
+ align:start position:0%
+ZJ + 1
+ 
+
+ align:start position:0%
+ZJ + 1
+1 yeah okay they disagree here how about
+
+ align:start position:0%
+1 yeah okay they disagree here how about
+ 
+
+ align:start position:0%
+1 yeah okay they disagree here how about
+one layer above do they agree if they
+
+ align:start position:0%
+one layer above do they agree if they
+ 
+
+ align:start position:0%
+one layer above do they agree if they
+agree great then that's going to be our
+
+ align:start position:0%
+agree great then that's going to be our
+ 
+
+ align:start position:0%
+agree great then that's going to be our
+J plus one they disagree let's go up
+
+ align:start position:0%
+J plus one they disagree let's go up
+ 
+
+ align:start position:0%
+J plus one they disagree let's go up
+until at some point they'll agree
+
+ align:start position:0%
+until at some point they'll agree
+ 
+
+ align:start position:0%
+until at some point they'll agree
+because they agree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh thank you very much thank you uh
+
+ align:start position:0%
+yeah oh thank you very much thank you uh
+ 
+
+ align:start position:0%
+yeah oh thank you very much thank you uh
+great thank you yeah it's not just for
+
+ align:start position:0%
+great thank you yeah it's not just for
+ 
+
+ align:start position:0%
+great thank you yeah it's not just for
+the video it's also for you guys so I
+
+ align:start position:0%
+the video it's also for you guys so I
+ 
+
+ align:start position:0%
+the video it's also for you guys so I
+won't uh confuse you more than it thank
+
+ align:start position:0%
+won't uh confuse you more than it thank
+ 
+
+ align:start position:0%
+won't uh confuse you more than it thank
+you a one J One J + one thank
+
+ align:start position:0%
+you a one J One J + one thank
+ 
+
+ align:start position:0%
+you a one J One J + one thank
+you okay yes I I is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I did I miss
+
+ align:start position:0%
+it I did I miss
+ 
+
+ align:start position:0%
+it I did I miss
+I yes
+
+ align:start position:0%
+I yes
+ 
+
+ align:start position:0%
+I yes
+my God okay no there zero one
+
+ align:start position:0%
+my God okay no there zero one
+ 
+
+ align:start position:0%
+my God okay no there zero one
+ah okay did I get it right yes okay so
+
+ align:start position:0%
+ah okay did I get it right yes okay so
+ 
+
+ align:start position:0%
+ah okay did I get it right yes okay so
+there's a layer J said that in layer J
+
+ align:start position:0%
+there's a layer J said that in layer J
+ 
+
+ align:start position:0%
+there's a layer J said that in layer J
+they disagree in layer j+ one they
+
+ align:start position:0%
+they disagree in layer j+ one they
+ 
+
+ align:start position:0%
+they disagree in layer j+ one they
+agree that's it this is a collision why
+
+ align:start position:0%
+agree that's it this is a collision why
+ 
+
+ align:start position:0%
+agree that's it this is a collision why
+what is layer J + one one of them is the
+
+ align:start position:0%
+what is layer J + one one of them is the
+ 
+
+ align:start position:0%
+what is layer J + one one of them is the
+father is the
+
+ align:start position:0%
+father is the
+ 
+
+ align:start position:0%
+father is the
+parent so we have two that they
+
+ align:start position:0%
+parent so we have two that they
+ 
+
+ align:start position:0%
+parent so we have two that they
+disagree but both of these they agree
+
+ align:start position:0%
+disagree but both of these they agree
+ 
+
+ align:start position:0%
+disagree but both of these they agree
+on in particular they agree on this so
+
+ align:start position:0%
+on in particular they agree on this so
+ 
+
+ align:start position:0%
+on in particular they agree on this so
+done so we found a collision this must
+
+ align:start position:0%
+done so we found a collision this must
+ 
+
+ align:start position:0%
+done so we found a collision this must
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the hash
+
+ align:start position:0%
+that the hash
+ 
+
+ align:start position:0%
+that the hash
+eval hash key of
+
+ align:start position:0%
+eval hash key of
+ 
+
+ align:start position:0%
+eval hash key of
+z0j is equal to
+
+ align:start position:0%
+z0j is equal to
+ 
+
+ align:start position:0%
+z0j is equal to
+eval H key of z1j because this value is
+
+ align:start position:0%
+eval H key of z1j because this value is
+ 
+
+ align:start position:0%
+eval H key of z1j because this value is
+one of the it's you know one of this and
+
+ align:start position:0%
+one of the it's you know one of this and
+ 
+
+ align:start position:0%
+one of the it's you know one of this and
+one one of this and one of this
+
+ align:start position:0%
+one one of this and one of this
+ 
+
+ align:start position:0%
+one one of this and one of this
+depending if it's the left or the right
+
+ align:start position:0%
+depending if it's the left or the right
+ 
+
+ align:start position:0%
+depending if it's the left or the right
+depending on the tree but and they're
+
+ align:start position:0%
+depending on the tree but and they're
+ 
+
+ align:start position:0%
+depending on the tree but and they're
+both equal so done I found a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collision okay with the same exact
+
+ align:start position:0%
+collision okay with the same exact
+ 
+
+ align:start position:0%
+collision okay with the same exact
+probability so it's
+
+ align:start position:0%
+probability so it's
+ 
+
+ align:start position:0%
+probability so it's
+uh now as I said this I wrote here
+
+ align:start position:0%
+uh now as I said this I wrote here
+ 
+
+ align:start position:0%
+uh now as I said this I wrote here
+supposed to exist P Lambda I could have
+
+ align:start position:0%
+supposed to exist P Lambda I could have
+ 
+
+ align:start position:0%
+supposed to exist P Lambda I could have
+if we assumed that the underlying hash
+
+ align:start position:0%
+if we assumed that the underlying hash
+ 
+
+ align:start position:0%
+if we assumed that the underlying hash
+function is t- secure namely you can't
+
+ align:start position:0%
+function is t- secure namely you can't
+ 
+
+ align:start position:0%
+function is t- secure namely you can't
+find collisions even if you run time
+
+ align:start position:0%
+find collisions even if you run time
+ 
+
+ align:start position:0%
+find collisions even if you run time
+poly T of Lambda then we get that the
+
+ align:start position:0%
+poly T of Lambda then we get that the
+ 
+
+ align:start position:0%
+poly T of Lambda then we get that the
+Merle hash is POL secure because B all
+
+ align:start position:0%
+Merle hash is POL secure because B all
+ 
+
+ align:start position:0%
+Merle hash is POL secure because B all
+it does really is just run a it doesn't
+
+ align:start position:0%
+it does really is just run a it doesn't
+ 
+
+ align:start position:0%
+it does really is just run a it doesn't
+run much more than a it just runs a and
+
+ align:start position:0%
+run much more than a it just runs a and
+ 
+
+ align:start position:0%
+run much more than a it just runs a and
+then it does something very trivial so
+
+ align:start position:0%
+then it does something very trivial so
+ 
+
+ align:start position:0%
+then it does something very trivial so
+the complexity of breaking the miracle
+
+ align:start position:0%
+the complexity of breaking the miracle
+ 
+
+ align:start position:0%
+the complexity of breaking the miracle
+hash is really the same as the
+
+ align:start position:0%
+hash is really the same as the
+ 
+
+ align:start position:0%
+hash is really the same as the
+complexity of breaking the underlying
+
+ align:start position:0%
+complexity of breaking the underlying
+ 
+
+ align:start position:0%
+complexity of breaking the underlying
+hash so if the underlying hash is tsec
+
+ align:start position:0%
+hash so if the underlying hash is tsec
+ 
+
+ align:start position:0%
+hash so if the underlying hash is tsec
+Miracle hash is TC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+secure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay so where are we so we
+
+ align:start position:0%
+questions okay so where are we so we
+ 
+
+ align:start position:0%
+questions okay so where are we so we
+prove the Merkel hash as we saw the
+
+ align:start position:0%
+prove the Merkel hash as we saw the
+ 
+
+ align:start position:0%
+prove the Merkel hash as we saw the
+Merkel hash was used to give an
+
+ align:start position:0%
+Merkel hash was used to give an
+ 
+
+ align:start position:0%
+Merkel hash was used to give an
+interactive a succinct interactive
+
+ align:start position:0%
+interactive a succinct interactive
+ 
+
+ align:start position:0%
+interactive a succinct interactive
+argument for all of
+
+ align:start position:0%
+argument for all of
+ 
+
+ align:start position:0%
+argument for all of
+NP so now if you're willing to you know
+
+ align:start position:0%
+NP so now if you're willing to you know
+ 
+
+ align:start position:0%
+NP so now if you're willing to you know
+to you're happy with intrac
+
+ align:start position:0%
+to you're happy with intrac
+ 
+
+ align:start position:0%
+to you're happy with intrac
+protocols thank you very much I hope you
+
+ align:start position:0%
+protocols thank you very much I hope you
+ 
+
+ align:start position:0%
+protocols thank you very much I hope you
+enjoyed the semester and we're
+
+ align:start position:0%
+enjoyed the semester and we're
+ 
+
+ align:start position:0%
+enjoyed the semester and we're
+done if you're not though but as I said
+
+ align:start position:0%
+done if you're not though but as I said
+ 
+
+ align:start position:0%
+done if you're not though but as I said
+we're actually we're not happy with
+
+ align:start position:0%
+we're actually we're not happy with
+ 
+
+ align:start position:0%
+we're actually we're not happy with
+interactive protocols it's really
+
+ align:start position:0%
+interactive protocols it's really
+ 
+
+ align:start position:0%
+interactive protocols it's really
+interesting actually to think of the
+
+ align:start position:0%
+interesting actually to think of the
+ 
+
+ align:start position:0%
+interesting actually to think of the
+evolution of of this because you know it
+
+ align:start position:0%
+evolution of of this because you know it
+ 
+
+ align:start position:0%
+evolution of of this because you know it
+before all this interactive proofs and
+
+ align:start position:0%
+before all this interactive proofs and
+ 
+
+ align:start position:0%
+before all this interactive proofs and
+arguments and so on we had just
+
+ align:start position:0%
+arguments and so on we had just
+ 
+
+ align:start position:0%
+arguments and so on we had just
+mathematical proofs which were not
+
+ align:start position:0%
+mathematical proofs which were not
+ 
+
+ align:start position:0%
+mathematical proofs which were not
+interactive but they were very very
+
+ align:start position:0%
+interactive but they were very very
+ 
+
+ align:start position:0%
+interactive but they were very very
+long and people were not happy like kid
+
+ align:start position:0%
+long and people were not happy like kid
+ 
+
+ align:start position:0%
+long and people were not happy like kid
+like oh they're so long and then
+
+ align:start position:0%
+like oh they're so long and then
+ 
+
+ align:start position:0%
+like oh they're so long and then
+interactive proofs were defined I think
+
+ align:start position:0%
+interactive proofs were defined I think
+ 
+
+ align:start position:0%
+interactive proofs were defined I think
+they were defined only for the sake of
+
+ align:start position:0%
+they were defined only for the sake of
+ 
+
+ align:start position:0%
+they were defined only for the sake of
+zero knowledge they were defined just to
+
+ align:start position:0%
+zero knowledge they were defined just to
+ 
+
+ align:start position:0%
+zero knowledge they were defined just to
+get zero knowledge proofs I'm GNA
+
+ align:start position:0%
+get zero knowledge proofs I'm GNA
+ 
+
+ align:start position:0%
+get zero knowledge proofs I'm GNA
+actually mention we're going to talk
+
+ align:start position:0%
+actually mention we're going to talk
+ 
+
+ align:start position:0%
+actually mention we're going to talk
+about zero knowledge later
+
+ align:start position:0%
+about zero knowledge later
+ 
+
+ align:start position:0%
+about zero knowledge later
+today and this motivated kind of the int
+
+ align:start position:0%
+today and this motivated kind of the int
+ 
+
+ align:start position:0%
+today and this motivated kind of the int
+to introduce
+
+ align:start position:0%
+to introduce
+ 
+
+ align:start position:0%
+to introduce
+interraction and then people like wow
+
+ align:start position:0%
+interraction and then people like wow
+ 
+
+ align:start position:0%
+interraction and then people like wow
+you oh what a great forget about zero
+
+ align:start position:0%
+you oh what a great forget about zero
+ 
+
+ align:start position:0%
+you oh what a great forget about zero
+knowledge forget about cryptography this
+
+ align:start position:0%
+knowledge forget about cryptography this
+ 
+
+ align:start position:0%
+knowledge forget about cryptography this
+is such a great model using intraction
+
+ align:start position:0%
+is such a great model using intraction
+ 
+
+ align:start position:0%
+is such a great model using intraction
+we can prove a lot more right and we saw
+
+ align:start position:0%
+we can prove a lot more right and we saw
+ 
+
+ align:start position:0%
+we can prove a lot more right and we saw
+the Gare protocol you can can do like uh
+
+ align:start position:0%
+the Gare protocol you can can do like uh
+ 
+
+ align:start position:0%
+the Gare protocol you can can do like uh
+you can prove actually any any circuits
+
+ align:start position:0%
+you can prove actually any any circuits
+ 
+
+ align:start position:0%
+you can prove actually any any circuits
+that are really really huge as long as
+
+ align:start position:0%
+that are really really huge as long as
+ 
+
+ align:start position:0%
+that are really really huge as long as
+they're kind of have dep you can do PE
+
+ align:start position:0%
+they're kind of have dep you can do PE
+ 
+
+ align:start position:0%
+they're kind of have dep you can do PE
+space or any computation that has poly
+
+ align:start position:0%
+space or any computation that has poly
+ 
+
+ align:start position:0%
+space or any computation that has poly
+depth you verify can be any depth V you
+
+ align:start position:0%
+depth you verify can be any depth V you
+ 
+
+ align:start position:0%
+depth you verify can be any depth V you
+can the verify runs in time deep great
+
+ align:start position:0%
+can the verify runs in time deep great
+ 
+
+ align:start position:0%
+can the verify runs in time deep great
+not it doesn't run in the sign so it's
+
+ align:start position:0%
+not it doesn't run in the sign so it's
+ 
+
+ align:start position:0%
+not it doesn't run in the sign so it's
+much much more powerful wow wow wow and
+
+ align:start position:0%
+much much more powerful wow wow wow and
+ 
+
+ align:start position:0%
+much much more powerful wow wow wow and
+then people like actually with
+
+ align:start position:0%
+then people like actually with
+ 
+
+ align:start position:0%
+then people like actually with
+cryptographer can do much more great but
+
+ align:start position:0%
+cryptographer can do much more great but
+ 
+
+ align:start position:0%
+cryptographer can do much more great but
+now like but wait there was a big price
+
+ align:start position:0%
+now like but wait there was a big price
+ 
+
+ align:start position:0%
+now like but wait there was a big price
+we actually don't want ction so where
+
+ align:start position:0%
+we actually don't want ction so where
+ 
+
+ align:start position:0%
+we actually don't want ction so where
+are we are we back at
+
+ align:start position:0%
+are we are we back at
+ 
+
+ align:start position:0%
+are we are we back at
+NP NP is very we're back in the
+
+ align:start position:0%
+NP NP is very we're back in the
+ 
+
+ align:start position:0%
+NP NP is very we're back in the
+mathematical proof that are way way too
+
+ align:start position:0%
+mathematical proof that are way way too
+ 
+
+ align:start position:0%
+mathematical proof that are way way too
+long so I said
+
+ align:start position:0%
+long so I said
+ 
+
+ align:start position:0%
+long so I said
+no we're actually going to circle back
+
+ align:start position:0%
+no we're actually going to circle back
+ 
+
+ align:start position:0%
+no we're actually going to circle back
+in a very interesting way and get suin
+
+ align:start position:0%
+in a very interesting way and get suin
+ 
+
+ align:start position:0%
+in a very interesting way and get suin
+non-interactive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proofs so how do we Circle back okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this idea of how to Circle back
+
+ align:start position:0%
+so so this idea of how to Circle back
+ 
+
+ align:start position:0%
+so so this idea of how to Circle back
+actually was
+
+ align:start position:0%
+actually was
+ 
+
+ align:start position:0%
+actually was
+um put forth by fat Cham this is in the
+
+ align:start position:0%
+um put forth by fat Cham this is in the
+ 
+
+ align:start position:0%
+um put forth by fat Cham this is in the
+mid 80s and
+
+ align:start position:0%
+mid 80s and
+ 
+
+ align:start position:0%
+mid 80s and
+86 they proposed a really really nice
+
+ align:start position:0%
+86 they proposed a really really nice
+ 
+
+ align:start position:0%
+86 they proposed a really really nice
+Paradigm actually they didn't think
+
+ align:start position:0%
+Paradigm actually they didn't think
+ 
+
+ align:start position:0%
+Paradigm actually they didn't think
+about this is this is 86 this is kind of
+
+ align:start position:0%
+about this is this is 86 this is kind of
+ 
+
+ align:start position:0%
+about this is this is 86 this is kind of
+before intractive proofs it was just
+
+ align:start position:0%
+before intractive proofs it was just
+ 
+
+ align:start position:0%
+before intractive proofs it was just
+when zonal was introduced um interactive
+
+ align:start position:0%
+when zonal was introduced um interactive
+ 
+
+ align:start position:0%
+when zonal was introduced um interactive
+proofs just came about but no you know
+
+ align:start position:0%
+proofs just came about but no you know
+ 
+
+ align:start position:0%
+proofs just came about but no you know
+there was no PCP no interactive argument
+
+ align:start position:0%
+there was no PCP no interactive argument
+ 
+
+ align:start position:0%
+there was no PCP no interactive argument
+none of that okay this is an 86
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F they proposed the method
+
+ align:start position:0%
+F they proposed the method
+ 
+
+ align:start position:0%
+F they proposed the method
+of actually reducing interaction of
+
+ align:start position:0%
+of actually reducing interaction of
+ 
+
+ align:start position:0%
+of actually reducing interaction of
+constructing signature schemes now I I
+
+ align:start position:0%
+constructing signature schemes now I I
+ 
+
+ align:start position:0%
+constructing signature schemes now I I
+stand behind what I said that this class
+
+ align:start position:0%
+stand behind what I said that this class
+ 
+
+ align:start position:0%
+stand behind what I said that this class
+will not require a lot of cryptog crypto
+
+ align:start position:0%
+will not require a lot of cryptog crypto
+ 
+
+ align:start position:0%
+will not require a lot of cryptog crypto
+background you don't need to know what
+
+ align:start position:0%
+background you don't need to know what
+ 
+
+ align:start position:0%
+background you don't need to know what
+signature schemes are but the what they
+
+ align:start position:0%
+signature schemes are but the what they
+ 
+
+ align:start position:0%
+signature schemes are but the what they
+did their idea is there was there's a
+
+ align:start position:0%
+did their idea is there was there's a
+ 
+
+ align:start position:0%
+did their idea is there was there's a
+primitive called identification scheme I
+
+ align:start position:0%
+primitive called identification scheme I
+ 
+
+ align:start position:0%
+primitive called identification scheme I
+want to prove to you that I'm y okay how
+
+ align:start position:0%
+want to prove to you that I'm y okay how
+ 
+
+ align:start position:0%
+want to prove to you that I'm y okay how
+do I prove that I'm y I have a public
+
+ align:start position:0%
+do I prove that I'm y I have a public
+ 
+
+ align:start position:0%
+do I prove that I'm y I have a public
+key corresponding to my name and I'm
+
+ align:start position:0%
+key corresponding to my name and I'm
+ 
+
+ align:start position:0%
+key corresponding to my name and I'm
+going to prove to that I know the secret
+
+ align:start position:0%
+going to prove to that I know the secret
+ 
+
+ align:start position:0%
+going to prove to that I know the secret
+key
+
+ align:start position:0%
+key
+ 
+
+ align:start position:0%
+key
+me knowing whoever knows the secret key
+
+ align:start position:0%
+me knowing whoever knows the secret key
+ 
+
+ align:start position:0%
+me knowing whoever knows the secret key
+has my identity essentially that's how
+
+ align:start position:0%
+has my identity essentially that's how
+ 
+
+ align:start position:0%
+has my identity essentially that's how
+things work in the digital world so I'm
+
+ align:start position:0%
+things work in the digital world so I'm
+ 
+
+ align:start position:0%
+things work in the digital world so I'm
+going to prove to you that I know the
+
+ align:start position:0%
+going to prove to you that I know the
+ 
+
+ align:start position:0%
+going to prove to you that I know the
+secret key this proves that I'm me okay
+
+ align:start position:0%
+secret key this proves that I'm me okay
+ 
+
+ align:start position:0%
+secret key this proves that I'm me okay
+this proof was interactive okay
+
+ align:start position:0%
+this proof was interactive okay
+ 
+
+ align:start position:0%
+this proof was interactive okay
+identification Protocols are like three
+
+ align:start position:0%
+identification Protocols are like three
+ 
+
+ align:start position:0%
+identification Protocols are like three
+round protocols I give you a message
+
+ align:start position:0%
+round protocols I give you a message
+ 
+
+ align:start position:0%
+round protocols I give you a message
+Alpha you send me a question beta I give
+
+ align:start position:0%
+Alpha you send me a question beta I give
+ 
+
+ align:start position:0%
+Alpha you send me a question beta I give
+you an answer gamma you verify that's
+
+ align:start position:0%
+you an answer gamma you verify that's
+ 
+
+ align:start position:0%
+you an answer gamma you verify that's
+how it
+
+ align:start position:0%
+how it
+ 
+
+ align:start position:0%
+how it
+works now they said let's convert this
+
+ align:start position:0%
+works now they said let's convert this
+ 
+
+ align:start position:0%
+works now they said let's convert this
+identification scheme into a signature
+
+ align:start position:0%
+identification scheme into a signature
+ 
+
+ align:start position:0%
+identification scheme into a signature
+scheme instead of kind of interacting to
+
+ align:start position:0%
+scheme instead of kind of interacting to
+ 
+
+ align:start position:0%
+scheme instead of kind of interacting to
+make sure it's you every time you sign a
+
+ align:start position:0%
+make sure it's you every time you sign a
+ 
+
+ align:start position:0%
+make sure it's you every time you sign a
+you want to send a message kind of use
+
+ align:start position:0%
+you want to send a message kind of use
+ 
+
+ align:start position:0%
+you want to send a message kind of use
+this use this message take this
+
+ align:start position:0%
+this use this message take this
+ 
+
+ align:start position:0%
+this use this message take this
+identification protocol together with
+
+ align:start position:0%
+identification protocol together with
+ 
+
+ align:start position:0%
+identification protocol together with
+some message and kind of eliminate the
+
+ align:start position:0%
+some message and kind of eliminate the
+ 
+
+ align:start position:0%
+some message and kind of eliminate the
+interaction I'll explain exactly how
+
+ align:start position:0%
+interaction I'll explain exactly how
+ 
+
+ align:start position:0%
+interaction I'll explain exactly how
+they do it but but they do it in a way
+
+ align:start position:0%
+they do it but but they do it in a way
+ 
+
+ align:start position:0%
+they do it but but they do it in a way
+to construct signature scheme that was
+
+ align:start position:0%
+to construct signature scheme that was
+ 
+
+ align:start position:0%
+to construct signature scheme that was
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+goal but now after several years after
+
+ align:start position:0%
+goal but now after several years after
+ 
+
+ align:start position:0%
+goal but now after several years after
+we use it all the time to actually
+
+ align:start position:0%
+we use it all the time to actually
+ 
+
+ align:start position:0%
+we use it all the time to actually
+forget about just the specific
+
+ align:start position:0%
+forget about just the specific
+ 
+
+ align:start position:0%
+forget about just the specific
+application of identification skin to
+
+ align:start position:0%
+application of identification skin to
+ 
+
+ align:start position:0%
+application of identification skin to
+signature that's one application
+
+ align:start position:0%
+signature that's one application
+ 
+
+ align:start position:0%
+signature that's one application
+but actually we can show we can use it
+
+ align:start position:0%
+but actually we can show we can use it
+ 
+
+ align:start position:0%
+but actually we can show we can use it
+to reduce to eliminate intraction not
+
+ align:start position:0%
+to reduce to eliminate intraction not
+ 
+
+ align:start position:0%
+to reduce to eliminate intraction not
+only from identification scheme but from
+
+ align:start position:0%
+only from identification scheme but from
+ 
+
+ align:start position:0%
+only from identification scheme but from
+any interactive protocol that is public
+
+ align:start position:0%
+any interactive protocol that is public
+ 
+
+ align:start position:0%
+any interactive protocol that is public
+coin so let me explain so now take any
+
+ align:start position:0%
+coin so let me explain so now take any
+ 
+
+ align:start position:0%
+coin so let me explain so now take any
+protocol uh so so this is a this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paradigm for eliminating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+interaction
+
+ align:start position:0%
+interaction
+ 
+
+ align:start position:0%
+interaction
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+interactive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protocols that are public
+
+ align:start position:0%
+protocols that are public
+ 
+
+ align:start position:0%
+protocols that are public
+coin so not all protocol but ones that
+
+ align:start position:0%
+coin so not all protocol but ones that
+ 
+
+ align:start position:0%
+coin so not all protocol but ones that
+are public coin so what is a public coin
+
+ align:start position:0%
+are public coin so what is a public coin
+ 
+
+ align:start position:0%
+are public coin so what is a public coin
+protocol take any protocol let say a
+
+ align:start position:0%
+protocol take any protocol let say a
+ 
+
+ align:start position:0%
+protocol take any protocol let say a
+proof so I have aover and a VAR
+
+ align:start position:0%
+proof so I have aover and a VAR
+ 
+
+ align:start position:0%
+proof so I have aover and a VAR
+verifier and suppose for a second it's
+
+ align:start position:0%
+verifier and suppose for a second it's
+ 
+
+ align:start position:0%
+verifier and suppose for a second it's
+so the suppose for Simplicity that it's
+
+ align:start position:0%
+so the suppose for Simplicity that it's
+ 
+
+ align:start position:0%
+so the suppose for Simplicity that it's
+three messages okay so the verify the
+
+ align:start position:0%
+three messages okay so the verify the
+ 
+
+ align:start position:0%
+three messages okay so the verify the
+prover sends a message Alpha the
+
+ align:start position:0%
+prover sends a message Alpha the
+ 
+
+ align:start position:0%
+prover sends a message Alpha the
+verifier sends beta which is random okay
+
+ align:start position:0%
+verifier sends beta which is random okay
+ 
+
+ align:start position:0%
+verifier sends beta which is random okay
+that's public CO mean the message of the
+
+ align:start position:0%
+that's public CO mean the message of the
+ 
+
+ align:start position:0%
+that's public CO mean the message of the
+ver far is completely random okay let's
+
+ align:start position:0%
+ver far is completely random okay let's
+ 
+
+ align:start position:0%
+ver far is completely random okay let's
+say it's kind of Lambda bits if it's
+
+ align:start position:0%
+say it's kind of Lambda bits if it's
+ 
+
+ align:start position:0%
+say it's kind of Lambda bits if it's
+less then just P it to be Lambda okay
+
+ align:start position:0%
+less then just P it to be Lambda okay
+ 
+
+ align:start position:0%
+less then just P it to be Lambda okay
+and if it's more just call that Lambda
+
+ align:start position:0%
+and if it's more just call that Lambda
+ 
+
+ align:start position:0%
+and if it's more just call that Lambda
+make that the security parameter just
+
+ align:start position:0%
+make that the security parameter just
+ 
+
+ align:start position:0%
+make that the security parameter just
+increase the security parameter
+
+ align:start position:0%
+increase the security parameter
+ 
+
+ align:start position:0%
+increase the security parameter
+okay now you send
+
+ align:start position:0%
+okay now you send
+ 
+
+ align:start position:0%
+okay now you send
+gamma and maybe it's more round so maybe
+
+ align:start position:0%
+gamma and maybe it's more round so maybe
+ 
+
+ align:start position:0%
+gamma and maybe it's more round so maybe
+then he sends
+
+ align:start position:0%
+then he sends
+ 
+
+ align:start position:0%
+then he sends
+Delta let's say random bits and then you
+
+ align:start position:0%
+Delta let's say random bits and then you
+ 
+
+ align:start position:0%
+Delta let's say random bits and then you
+say epsilon and you can continue okay
+
+ align:start position:0%
+say epsilon and you can continue okay
+ 
+
+ align:start position:0%
+say epsilon and you can continue okay
+let me stop here for the sake
+
+ align:start position:0%
+let me stop here for the sake
+ 
+
+ align:start position:0%
+let me stop here for the sake
+of okay now I'm going to eliminate
+
+ align:start position:0%
+of okay now I'm going to eliminate
+ 
+
+ align:start position:0%
+of okay now I'm going to eliminate
+intraction how do we eliminate
+
+ align:start position:0%
+intraction how do we eliminate
+ 
+
+ align:start position:0%
+intraction how do we eliminate
+intraction it seem like intraction is
+
+ align:start position:0%
+intraction it seem like intraction is
+ 
+
+ align:start position:0%
+intraction it seem like intraction is
+very important I mean the entire kind of
+
+ align:start position:0%
+very important I mean the entire kind of
+ 
+
+ align:start position:0%
+very important I mean the entire kind of
+if you remember the surack and G
+
+ align:start position:0%
+if you remember the surack and G
+ 
+
+ align:start position:0%
+if you remember the surack and G
+I mean it's tempting maybe to say oh
+
+ align:start position:0%
+I mean it's tempting maybe to say oh
+ 
+
+ align:start position:0%
+I mean it's tempting maybe to say oh
+tell the prover compute Alpha Beta GMA
+
+ align:start position:0%
+tell the prover compute Alpha Beta GMA
+ 
+
+ align:start position:0%
+tell the prover compute Alpha Beta GMA
+just compute the transcript on your own
+
+ align:start position:0%
+just compute the transcript on your own
+ 
+
+ align:start position:0%
+just compute the transcript on your own
+you simulate the verifi messages then
+
+ align:start position:0%
+you simulate the verifi messages then
+ 
+
+ align:start position:0%
+you simulate the verifi messages then
+he'll
+
+ align:start position:0%
+he'll
+ 
+
+ align:start position:0%
+he'll
+cheat so how do you get rid of the
+
+ align:start position:0%
+cheat so how do you get rid of the
+ 
+
+ align:start position:0%
+cheat so how do you get rid of the
+interaction seems
+
+ align:start position:0%
+interaction seems
+ 
+
+ align:start position:0%
+interaction seems
+really really hard actually it's so easy
+
+ align:start position:0%
+really really hard actually it's so easy
+ 
+
+ align:start position:0%
+really really hard actually it's so easy
+I mean there idea is Trivial so what is
+
+ align:start position:0%
+I mean there idea is Trivial so what is
+ 
+
+ align:start position:0%
+I mean there idea is Trivial so what is
+their idea they said they say the
+
+ align:start position:0%
+their idea they said they say the
+ 
+
+ align:start position:0%
+their idea they said they say the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+how does the verifier how does the Prov
+
+ align:start position:0%
+how does the verifier how does the Prov
+ 
+
+ align:start position:0%
+how does the verifier how does the Prov
+get this
+
+ align:start position:0%
+get this
+ 
+
+ align:start position:0%
+get this
+beta the verifier chose it so you know
+
+ align:start position:0%
+beta the verifier chose it so you know
+ 
+
+ align:start position:0%
+beta the verifier chose it so you know
+what let's comp let not have the ver now
+
+ align:start position:0%
+what let's comp let not have the ver now
+ 
+
+ align:start position:0%
+what let's comp let not have the ver now
+we don't have a verifier it's not
+
+ align:start position:0%
+we don't have a verifier it's not
+ 
+
+ align:start position:0%
+we don't have a verifier it's not
+interactive there's no verifier so how
+
+ align:start position:0%
+interactive there's no verifier so how
+ 
+
+ align:start position:0%
+interactive there's no verifier so how
+to compute this beta let's compute it as
+
+ align:start position:0%
+to compute this beta let's compute it as
+ 
+
+ align:start position:0%
+to compute this beta let's compute it as
+kind of a hash function applied to the
+
+ align:start position:0%
+kind of a hash function applied to the
+ 
+
+ align:start position:0%
+kind of a hash function applied to the
+transcript so
+
+ align:start position:0%
+transcript so
+ 
+
+ align:start position:0%
+transcript so
+far so let me explain so
+
+ align:start position:0%
+far so let me explain so
+ 
+
+ align:start position:0%
+far so let me explain so
+how here's how you convert it
+
+ align:start position:0%
+how here's how you convert it
+ 
+
+ align:start position:0%
+how here's how you convert it
+to p f CH
+
+ align:start position:0%
+to p f CH
+ 
+
+ align:start position:0%
+to p f CH
+V this is associated with some hash
+
+ align:start position:0%
+V this is associated with some hash
+ 
+
+ align:start position:0%
+V this is associated with some hash
+family okay there's some It's associated
+
+ align:start position:0%
+family okay there's some It's associated
+ 
+
+ align:start position:0%
+family okay there's some It's associated
+with a hash family so the F Paradigm you
+
+ align:start position:0%
+with a hash family so the F Paradigm you
+ 
+
+ align:start position:0%
+with a hash family so the F Paradigm you
+can take any hash family and use that to
+
+ align:start position:0%
+can take any hash family and use that to
+ 
+
+ align:start position:0%
+can take any hash family and use that to
+reduce interraction how do you use it to
+
+ align:start position:0%
+reduce interraction how do you use it to
+ 
+
+ align:start position:0%
+reduce interraction how do you use it to
+reduce intraction now there's some hash
+
+ align:start position:0%
+reduce intraction now there's some hash
+ 
+
+ align:start position:0%
+reduce intraction now there's some hash
+key that's chosen once and for all
+
+ align:start position:0%
+key that's chosen once and for all
+ 
+
+ align:start position:0%
+key that's chosen once and for all
+everybody knows it either the verifier
+
+ align:start position:0%
+everybody knows it either the verifier
+ 
+
+ align:start position:0%
+everybody knows it either the verifier
+sends it once or if you think about
+
+ align:start position:0%
+sends it once or if you think about
+ 
+
+ align:start position:0%
+sends it once or if you think about
+public like everybody can verify I don't
+
+ align:start position:0%
+public like everybody can verify I don't
+ 
+
+ align:start position:0%
+public like everybody can verify I don't
+know the
+
+ align:start position:0%
+know the
+ 
+
+ align:start position:0%
+know the
+the US government publishes this hash
+
+ align:start position:0%
+the US government publishes this hash
+ 
+
+ align:start position:0%
+the US government publishes this hash
+key everybody uses this hash key okay
+
+ align:start position:0%
+key everybody uses this hash key okay
+ 
+
+ align:start position:0%
+key everybody uses this hash key okay
+there's some fixed hash key everybody
+
+ align:start position:0%
+there's some fixed hash key everybody
+ 
+
+ align:start position:0%
+there's some fixed hash key everybody
+uses it now once we agree on a hash key
+
+ align:start position:0%
+uses it now once we agree on a hash key
+ 
+
+ align:start position:0%
+uses it now once we agree on a hash key
+what does the prover
+
+ align:start position:0%
+what does the prover
+ 
+
+ align:start position:0%
+what does the prover
+do he computes Alpha that's let's say he
+
+ align:start position:0%
+do he computes Alpha that's let's say he
+ 
+
+ align:start position:0%
+do he computes Alpha that's let's say he
+wants to prove that X is in some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+language so he let's say he want he's
+
+ align:start position:0%
+language so he let's say he want he's
+ 
+
+ align:start position:0%
+language so he let's say he want he's
+telling okay I'm going to prove to you
+
+ align:start position:0%
+telling okay I'm going to prove to you
+ 
+
+ align:start position:0%
+telling okay I'm going to prove to you
+that X is in the language let me prove
+
+ align:start position:0%
+that X is in the language let me prove
+ 
+
+ align:start position:0%
+that X is in the language let me prove
+it to you okay I compute the
+
+ align:start position:0%
+it to you okay I compute the
+ 
+
+ align:start position:0%
+it to you okay I compute the
+alpha now I'm waiting for a beta but
+
+ align:start position:0%
+alpha now I'm waiting for a beta but
+ 
+
+ align:start position:0%
+alpha now I'm waiting for a beta but
+there's no verifier fine the I'll tell
+
+ align:start position:0%
+there's no verifier fine the I'll tell
+ 
+
+ align:start position:0%
+there's no verifier fine the I'll tell
+you what the beta is beta is just has is
+
+ align:start position:0%
+you what the beta is beta is just has is
+ 
+
+ align:start position:0%
+you what the beta is beta is just has is
+going to be EV Val of hash key on the
+
+ align:start position:0%
+going to be EV Val of hash key on the
+ 
+
+ align:start position:0%
+going to be EV Val of hash key on the
+transcript so far X in Alpha that's
+
+ align:start position:0%
+transcript so far X in Alpha that's
+ 
+
+ align:start position:0%
+transcript so far X in Alpha that's
+currently what's in the transcript the
+
+ align:start position:0%
+currently what's in the transcript the
+ 
+
+ align:start position:0%
+currently what's in the transcript the
+the statement and the first message
+
+ align:start position:0%
+the statement and the first message
+ 
+
+ align:start position:0%
+the statement and the first message
+Alpha now the proof is like okay this is
+
+ align:start position:0%
+Alpha now the proof is like okay this is
+ 
+
+ align:start position:0%
+Alpha now the proof is like okay this is
+the beta I got from the verifier he's
+
+ align:start position:0%
+the beta I got from the verifier he's
+ 
+
+ align:start position:0%
+the beta I got from the verifier he's
+interpreting this as the beta he got
+
+ align:start position:0%
+interpreting this as the beta he got
+ 
+
+ align:start position:0%
+interpreting this as the beta he got
+from the verifier and now he computes
+
+ align:start position:0%
+from the verifier and now he computes
+ 
+
+ align:start position:0%
+from the verifier and now he computes
+gamma my answer
+
+ align:start position:0%
+gamma my answer
+ 
+
+ align:start position:0%
+gamma my answer
+the Pro's answer now he's waiting for a
+
+ align:start position:0%
+the Pro's answer now he's waiting for a
+ 
+
+ align:start position:0%
+the Pro's answer now he's waiting for a
+message a query from the verifier some
+
+ align:start position:0%
+message a query from the verifier some
+ 
+
+ align:start position:0%
+message a query from the verifier some
+Delta but there is no verifier so he's
+
+ align:start position:0%
+Delta but there is no verifier so he's
+ 
+
+ align:start position:0%
+Delta but there is no verifier so he's
+going to compute
+
+ align:start position:0%
+going to compute
+ 
+
+ align:start position:0%
+going to compute
+Delta as eval of the hash key using the
+
+ align:start position:0%
+Delta as eval of the hash key using the
+ 
+
+ align:start position:0%
+Delta as eval of the hash key using the
+transcript so far so X Alpha Beta
+
+ align:start position:0%
+transcript so far so X Alpha Beta
+ 
+
+ align:start position:0%
+transcript so far so X Alpha Beta
+gamma once he has Delta he's going to go
+
+ align:start position:0%
+gamma once he has Delta he's going to go
+ 
+
+ align:start position:0%
+gamma once he has Delta he's going to go
+back to being aover and
+
+ align:start position:0%
+back to being aover and
+ 
+
+ align:start position:0%
+back to being aover and
+compute Epsilon
+
+ align:start position:0%
+compute Epsilon
+ 
+
+ align:start position:0%
+compute Epsilon
+and then you can continue next message
+
+ align:start position:0%
+and then you can continue next message
+ 
+
+ align:start position:0%
+and then you can continue next message
+he goes computes a hash value of all the
+
+ align:start position:0%
+he goes computes a hash value of all the
+ 
+
+ align:start position:0%
+he goes computes a hash value of all the
+transends of so far compute the next
+
+ align:start position:0%
+transends of so far compute the next
+ 
+
+ align:start position:0%
+transends of so far compute the next
+Pro's
+
+ align:start position:0%
+Pro's
+ 
+
+ align:start position:0%
+Pro's
+message another ver and we go that's how
+
+ align:start position:0%
+message another ver and we go that's how
+ 
+
+ align:start position:0%
+message another ver and we go that's how
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+continue any questions about so what
+
+ align:start position:0%
+continue any questions about so what
+ 
+
+ align:start position:0%
+continue any questions about so what
+what did we go we got we started from an
+
+ align:start position:0%
+what did we go we got we started from an
+ 
+
+ align:start position:0%
+what did we go we got we started from an
+interactive
+
+ align:start position:0%
+interactive
+ 
+
+ align:start position:0%
+interactive
+protocol can have many rounds and now
+
+ align:start position:0%
+protocol can have many rounds and now
+ 
+
+ align:start position:0%
+protocol can have many rounds and now
+all we need is to agree on a
+
+ align:start position:0%
+all we need is to agree on a
+ 
+
+ align:start position:0%
+all we need is to agree on a
+haski and once we agree on Hashi the pro
+
+ align:start position:0%
+haski and once we agree on Hashi the pro
+ 
+
+ align:start position:0%
+haski and once we agree on Hashi the pro
+just gives you this is one message
+
+ align:start position:0%
+just gives you this is one message
+ 
+
+ align:start position:0%
+just gives you this is one message
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah good great question is it important
+
+ align:start position:0%
+yeah good great question is it important
+ 
+
+ align:start position:0%
+yeah good great question is it important
+to include beta actually you don't need
+
+ align:start position:0%
+to include beta actually you don't need
+ 
+
+ align:start position:0%
+to include beta actually you don't need
+to include beta at all because the
+
+ align:start position:0%
+to include beta at all because the
+ 
+
+ align:start position:0%
+to include beta at all because the
+verifier can compute beta so we you only
+
+ align:start position:0%
+verifier can compute beta so we you only
+ 
+
+ align:start position:0%
+verifier can compute beta so we you only
+need to know beta so you can compute
+
+ align:start position:0%
+need to know beta so you can compute
+ 
+
+ align:start position:0%
+need to know beta so you can compute
+gamma you actually don't need to include
+
+ align:start position:0%
+gamma you actually don't need to include
+ 
+
+ align:start position:0%
+gamma you actually don't need to include
+it great question great great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question so note for example if you
+
+ align:start position:0%
+question so note for example if you
+ 
+
+ align:start position:0%
+question so note for example if you
+think about kilan mikali protocol you
+
+ align:start position:0%
+think about kilan mikali protocol you
+ 
+
+ align:start position:0%
+think about kilan mikali protocol you
+may not remembered but let me just write
+
+ align:start position:0%
+may not remembered but let me just write
+ 
+
+ align:start position:0%
+may not remembered but let me just write
+it here just to refresh your memory why
+
+ align:start position:0%
+it here just to refresh your memory why
+ 
+
+ align:start position:0%
+it here just to refresh your memory why
+not you don't need to actually to
+
+ align:start position:0%
+not you don't need to actually to
+ 
+
+ align:start position:0%
+not you don't need to actually to
+understand this but uh since it's such a
+
+ align:start position:0%
+understand this but uh since it's such a
+ 
+
+ align:start position:0%
+understand this but uh since it's such a
+nice protocol and so how does it go
+
+ align:start position:0%
+nice protocol and so how does it go
+ 
+
+ align:start position:0%
+nice protocol and so how does it go
+there's a prover and a verifier the
+
+ align:start position:0%
+there's a prover and a verifier the
+ 
+
+ align:start position:0%
+there's a prover and a verifier the
+verifier sends a hash key so he wants to
+
+ align:start position:0%
+verifier sends a hash key so he wants to
+ 
+
+ align:start position:0%
+verifier sends a hash key so he wants to
+prove that X is an
+
+ align:start position:0%
+prove that X is an
+ 
+
+ align:start position:0%
+prove that X is an
+L he does a Merkle
+
+ align:start position:0%
+L he does a Merkle
+ 
+
+ align:start position:0%
+L he does a Merkle
+hash of the PCP so he computes a PCP Pi
+
+ align:start position:0%
+hash of the PCP so he computes a PCP Pi
+ 
+
+ align:start position:0%
+hash of the PCP so he computes a PCP Pi
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+PCP for x and
+
+ align:start position:0%
+PCP for x and
+ 
+
+ align:start position:0%
+PCP for x and
+L and he sends you the Merkel hash so he
+
+ align:start position:0%
+L and he sends you the Merkel hash so he
+ 
+
+ align:start position:0%
+L and he sends you the Merkel hash so he
+sends you root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the and the depth
+
+ align:start position:0%
+and the and the depth
+ 
+
+ align:start position:0%
+and the and the depth
+that's that's just the so he takes the
+
+ align:start position:0%
+that's that's just the so he takes the
+ 
+
+ align:start position:0%
+that's that's just the so he takes the
+PCP and he does a hatch with local
+
+ align:start position:0%
+PCP and he does a hatch with local
+ 
+
+ align:start position:0%
+PCP and he does a hatch with local
+opening for example mer hatch actually
+
+ align:start position:0%
+opening for example mer hatch actually
+ 
+
+ align:start position:0%
+opening for example mer hatch actually
+can do any hatch with local opening that
+
+ align:start position:0%
+can do any hatch with local opening that
+ 
+
+ align:start position:0%
+can do any hatch with local opening that
+you want this is the most common one and
+
+ align:start position:0%
+you want this is the most common one and
+ 
+
+ align:start position:0%
+you want this is the most common one and
+then he gets kind of the randomness from
+
+ align:start position:0%
+then he gets kind of the randomness from
+ 
+
+ align:start position:0%
+then he gets kind of the randomness from
+the PCP verifier so this is R from our
+
+ align:start position:0%
+the PCP verifier so this is R from our
+ 
+
+ align:start position:0%
+the PCP verifier so this is R from our
+correspond to the PCP
+
+ align:start position:0%
+correspond to the PCP
+ 
+
+ align:start position:0%
+correspond to the PCP
+verifier this determines a few locations
+
+ align:start position:0%
+verifier this determines a few locations
+ 
+
+ align:start position:0%
+verifier this determines a few locations
+to open so now he opens so he gives so
+
+ align:start position:0%
+to open so now he opens so he gives so
+ 
+
+ align:start position:0%
+to open so now he opens so he gives so
+this may this you know this Randomness
+
+ align:start position:0%
+this may this you know this Randomness
+ 
+
+ align:start position:0%
+this may this you know this Randomness
+corresponds to like some locations i1 up
+
+ align:start position:0%
+corresponds to like some locations i1 up
+ 
+
+ align:start position:0%
+corresponds to like some locations i1 up
+to I L and then you just Open PI i1 with
+
+ align:start position:0%
+to I L and then you just Open PI i1 with
+ 
+
+ align:start position:0%
+to I L and then you just Open PI i1 with
+open one up to Pi i l with open
+
+ align:start position:0%
+open one up to Pi i l with open
+ 
+
+ align:start position:0%
+open one up to Pi i l with open
+L that's the protocol note this is
+
+ align:start position:0%
+L that's the protocol note this is
+ 
+
+ align:start position:0%
+L that's the protocol note this is
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+random it's the randomness of the PCP
+
+ align:start position:0%
+random it's the randomness of the PCP
+ 
+
+ align:start position:0%
+random it's the randomness of the PCP
+verifier so we can uh eliminate
+
+ align:start position:0%
+verifier so we can uh eliminate
+ 
+
+ align:start position:0%
+verifier so we can uh eliminate
+intraction this you if you think of it
+
+ align:start position:0%
+intraction this you if you think of it
+ 
+
+ align:start position:0%
+intraction this you if you think of it
+this is just kind of a protocol where
+
+ align:start position:0%
+this is just kind of a protocol where
+ 
+
+ align:start position:0%
+this is just kind of a protocol where
+you send a hash key and then you have
+
+ align:start position:0%
+you send a hash key and then you have
+ 
+
+ align:start position:0%
+you send a hash key and then you have
+kind of Alpha Beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gamma okay so let's eliminate
+
+ align:start position:0%
+gamma okay so let's eliminate
+ 
+
+ align:start position:0%
+gamma okay so let's eliminate
+interaction so how do we eliminate
+
+ align:start position:0%
+interaction so how do we eliminate
+ 
+
+ align:start position:0%
+interaction so how do we eliminate
+interaction well there's this hash key
+
+ align:start position:0%
+interaction well there's this hash key
+ 
+
+ align:start position:0%
+interaction well there's this hash key
+let's we can use this hash key to do but
+
+ align:start position:0%
+let's we can use this hash key to do but
+ 
+
+ align:start position:0%
+let's we can use this hash key to do but
+we can also use another hash key hash
+
+ align:start position:0%
+we can also use another hash key hash
+ 
+
+ align:start position:0%
+we can also use another hash key hash
+key and
+
+ align:start position:0%
+key and
+ 
+
+ align:start position:0%
+key and
+now the well this can be now you give
+
+ align:start position:0%
+now the well this can be now you give
+ 
+
+ align:start position:0%
+now the well this can be now you give
+Alpha beta is going to be simply you
+
+ align:start position:0%
+Alpha beta is going to be simply you
+ 
+
+ align:start position:0%
+Alpha beta is going to be simply you
+don't have to include it but it's going
+
+ align:start position:0%
+don't have to include it but it's going
+ 
+
+ align:start position:0%
+don't have to include it but it's going
+to be in your in our head it's going to
+
+ align:start position:0%
+to be in your in our head it's going to
+ 
+
+ align:start position:0%
+to be in your in our head it's going to
+be eval of hash
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hash of X in
+
+ align:start position:0%
+hash of X in
+ 
+
+ align:start position:0%
+hash of X in
+Alpha and then maybe hash key is also
+
+ align:start position:0%
+Alpha and then maybe hash key is also
+ 
+
+ align:start position:0%
+Alpha and then maybe hash key is also
+part of the
+
+ align:start position:0%
+part of the
+ 
+
+ align:start position:0%
+part of the
+transcript and and uh this gives bit and
+
+ align:start position:0%
+transcript and and uh this gives bit and
+ 
+
+ align:start position:0%
+transcript and and uh this gives bit and
+now you compute the GMA which is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+opening okay so you can
+
+ align:start position:0%
+opening okay so you can
+ 
+
+ align:start position:0%
+opening okay so you can
+you can take any so now if what does the
+
+ align:start position:0%
+you can take any so now if what does the
+ 
+
+ align:start position:0%
+you can take any so now if what does the
+F give you it gives us a away remember K
+
+ align:start position:0%
+F give you it gives us a away remember K
+ 
+
+ align:start position:0%
+F give you it gives us a away remember K
+mikali was very succinct right you can
+
+ align:start position:0%
+mikali was very succinct right you can
+ 
+
+ align:start position:0%
+mikali was very succinct right you can
+take X any let's say NP
+
+ align:start position:0%
+take X any let's say NP
+ 
+
+ align:start position:0%
+take X any let's say NP
+language n can be very large it can be
+
+ align:start position:0%
+language n can be very large it can be
+ 
+
+ align:start position:0%
+language n can be very large it can be
+Lambda to that thousand I know it can be
+
+ align:start position:0%
+Lambda to that thousand I know it can be
+ 
+
+ align:start position:0%
+Lambda to that thousand I know it can be
+what it can be even super poom Lambda it
+
+ align:start position:0%
+what it can be even super poom Lambda it
+ 
+
+ align:start position:0%
+what it can be even super poom Lambda it
+can be almost as l two to the
+
+ align:start position:0%
+can be almost as l two to the
+ 
+
+ align:start position:0%
+can be almost as l two to the
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+okay and look how sucing the protocol is
+
+ align:start position:0%
+okay and look how sucing the protocol is
+ 
+
+ align:start position:0%
+okay and look how sucing the protocol is
+you just send a hash key the root which
+
+ align:start position:0%
+you just send a hash key the root which
+ 
+
+ align:start position:0%
+you just send a hash key the root which
+is Lambda bits and the opening and this
+
+ align:start position:0%
+is Lambda bits and the opening and this
+ 
+
+ align:start position:0%
+is Lambda bits and the opening and this
+the PCP is all L the bits poly L the
+
+ align:start position:0%
+the PCP is all L the bits poly L the
+ 
+
+ align:start position:0%
+the PCP is all L the bits poly L the
+bits so very very succinct and now you
+
+ align:start position:0%
+bits so very very succinct and now you
+ 
+
+ align:start position:0%
+bits so very very succinct and now you
+can even just make it
+
+ align:start position:0%
+can even just make it
+ 
+
+ align:start position:0%
+can even just make it
+so what is this you can all send it all
+
+ align:start position:0%
+so what is this you can all send it all
+ 
+
+ align:start position:0%
+so what is this you can all send it all
+in one round so what what does it give
+
+ align:start position:0%
+in one round so what what does it give
+ 
+
+ align:start position:0%
+in one round so what what does it give
+you what does it tell us that you we can
+
+ align:start position:0%
+you what does it tell us that you we can
+ 
+
+ align:start position:0%
+you what does it tell us that you we can
+take any NP
+
+ align:start position:0%
+take any NP
+ 
+
+ align:start position:0%
+take any NP
+statement and give a proof of size poly
+
+ align:start position:0%
+statement and give a proof of size poly
+ 
+
+ align:start position:0%
+statement and give a proof of size poly
+Lambda doesn't matter what size X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that's
+
+ align:start position:0%
+is that's
+ 
+
+ align:start position:0%
+is that's
+amazing without cryptography we need po
+
+ align:start position:0%
+amazing without cryptography we need po
+ 
+
+ align:start position:0%
+amazing without cryptography we need po
+you know these G Witnesses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+prob imagine ofd hash family where there
+
+ align:start position:0%
+prob imagine ofd hash family where there
+ 
+
+ align:start position:0%
+prob imagine ofd hash family where there
+exist hash keys that are really bad okay
+
+ align:start position:0%
+exist hash keys that are really bad okay
+ 
+
+ align:start position:0%
+exist hash keys that are really bad okay
+and so I guess here it's fine because
+
+ align:start position:0%
+and so I guess here it's fine because
+ 
+
+ align:start position:0%
+and so I guess here it's fine because
+the verifier chooses the hash key but
+
+ align:start position:0%
+the verifier chooses the hash key but
+ 
+
+ align:start position:0%
+the verifier chooses the hash key but
+you might imagine if the US publishes a
+
+ align:start position:0%
+you might imagine if the US publishes a
+ 
+
+ align:start position:0%
+you might imagine if the US publishes a
+anything else what if it happens to be a
+
+ align:start position:0%
+anything else what if it happens to be a
+ 
+
+ align:start position:0%
+anything else what if it happens to be a
+bad one or to be a bad one okay you two
+
+ align:start position:0%
+bad one or to be a bad one okay you two
+ 
+
+ align:start position:0%
+bad one or to be a bad one okay you two
+things first you're saying who chooses
+
+ align:start position:0%
+things first you're saying who chooses
+ 
+
+ align:start position:0%
+things first you're saying who chooses
+this hash key of the F how do we know
+
+ align:start position:0%
+this hash key of the F how do we know
+ 
+
+ align:start position:0%
+this hash key of the F how do we know
+that we trusted but you know it's much
+
+ align:start position:0%
+that we trusted but you know it's much
+ 
+
+ align:start position:0%
+that we trusted but you know it's much
+worse than that is it secure let's say
+
+ align:start position:0%
+worse than that is it secure let's say
+ 
+
+ align:start position:0%
+worse than that is it secure let's say
+let's say it's chosen randomly from the
+
+ align:start position:0%
+let's say it's chosen randomly from the
+ 
+
+ align:start position:0%
+let's say it's chosen randomly from the
+hash
+
+ align:start position:0%
+hash
+ 
+
+ align:start position:0%
+hash
+family is this
+
+ align:start position:0%
+family is this
+ 
+
+ align:start position:0%
+family is this
+sound it's so again what did we do here
+
+ align:start position:0%
+sound it's so again what did we do here
+ 
+
+ align:start position:0%
+sound it's so again what did we do here
+we started with an interactive protocol
+
+ align:start position:0%
+we started with an interactive protocol
+ 
+
+ align:start position:0%
+we started with an interactive protocol
+we proved it sound let's say k m sound
+
+ align:start position:0%
+we proved it sound let's say k m sound
+ 
+
+ align:start position:0%
+we proved it sound let's say k m sound
+we proved it ass we have Collision in
+
+ align:start position:0%
+we proved it ass we have Collision in
+ 
+
+ align:start position:0%
+we proved it ass we have Collision in
+hash we prove that it
+
+ align:start position:0%
+hash we prove that it
+ 
+
+ align:start position:0%
+hash we prove that it
+sound it sound assuming the prover gets
+
+ align:start position:0%
+sound it sound assuming the prover gets
+ 
+
+ align:start position:0%
+sound it sound assuming the prover gets
+the ver the messages of the verify
+
+ align:start position:0%
+the ver the messages of the verify
+ 
+
+ align:start position:0%
+the ver the messages of the verify
+randomly that's one 20 it sounds that's
+
+ align:start position:0%
+randomly that's one 20 it sounds that's
+ 
+
+ align:start position:0%
+randomly that's one 20 it sounds that's
+we used it to Pro Sound is
+
+ align:start position:0%
+we used it to Pro Sound is
+ 
+
+ align:start position:0%
+we used it to Pro Sound is
+now what am I saying what are we doing
+
+ align:start position:0%
+now what am I saying what are we doing
+ 
+
+ align:start position:0%
+now what am I saying what are we doing
+now I'm saying oh forget about it it's
+
+ align:start position:0%
+now I'm saying oh forget about it it's
+ 
+
+ align:start position:0%
+now I'm saying oh forget about it it's
+not random actually you comput it on
+
+ align:start position:0%
+not random actually you comput it on
+ 
+
+ align:start position:0%
+not random actually you comput it on
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+own from some hash key that someone
+
+ align:start position:0%
+own from some hash key that someone
+ 
+
+ align:start position:0%
+own from some hash key that someone
+chooses even honestly from let's say we
+
+ align:start position:0%
+chooses even honestly from let's say we
+ 
+
+ align:start position:0%
+chooses even honestly from let's say we
+agree we all agreed on some hash family
+
+ align:start position:0%
+agree we all agreed on some hash family
+ 
+
+ align:start position:0%
+agree we all agreed on some hash family
+and someone honestly chose a hash key
+
+ align:start position:0%
+and someone honestly chose a hash key
+ 
+
+ align:start position:0%
+and someone honestly chose a hash key
+but now you know this hash key now you
+
+ align:start position:0%
+but now you know this hash key now you
+ 
+
+ align:start position:0%
+but now you know this hash key now you
+compute who says it sound I mean is it
+
+ align:start position:0%
+compute who says it sound I mean is it
+ 
+
+ align:start position:0%
+compute who says it sound I mean is it
+still sound maybe it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sound okay so
+
+ align:start position:0%
+sound okay so
+ 
+
+ align:start position:0%
+sound okay so
+first of all okay so first of all of
+
+ align:start position:0%
+first of all okay so first of all of
+ 
+
+ align:start position:0%
+first of all okay so first of all of
+course there's one can think
+
+ align:start position:0%
+course there's one can think
+ 
+
+ align:start position:0%
+course there's one can think
+of this hash this hash functions need to
+
+ align:start position:0%
+of this hash this hash functions need to
+ 
+
+ align:start position:0%
+of this hash this hash functions need to
+have some property okay Collision
+
+ align:start position:0%
+have some property okay Collision
+ 
+
+ align:start position:0%
+have some property okay Collision
+resistance like at the minimum if if you
+
+ align:start position:0%
+resistance like at the minimum if if you
+ 
+
+ align:start position:0%
+resistance like at the minimum if if you
+can find collisions for example here
+
+ align:start position:0%
+can find collisions for example here
+ 
+
+ align:start position:0%
+can find collisions for example here
+you're screwed it can be it can be ID it
+
+ align:start position:0%
+you're screwed it can be it can be ID it
+ 
+
+ align:start position:0%
+you're screwed it can be it can be ID it
+can be trivial okay so you need some
+
+ align:start position:0%
+can be trivial okay so you need some
+ 
+
+ align:start position:0%
+can be trivial okay so you need some
+property now the question is what
+
+ align:start position:0%
+property now the question is what
+ 
+
+ align:start position:0%
+property now the question is what
+property do you need what property do
+
+ align:start position:0%
+property do you need what property do
+ 
+
+ align:start position:0%
+property do you need what property do
+you need from this hash family to argue
+
+ align:start position:0%
+you need from this hash family to argue
+ 
+
+ align:start position:0%
+you need from this hash family to argue
+soundness yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very very okay good so it seems like
+
+ align:start position:0%
+very very okay good so it seems like
+ 
+
+ align:start position:0%
+very very okay good so it seems like
+well what do you need it need to be
+
+ align:start position:0%
+well what do you need it need to be
+ 
+
+ align:start position:0%
+well what do you need it need to be
+random like in the protocol like okay we
+
+ align:start position:0%
+random like in the protocol like okay we
+ 
+
+ align:start position:0%
+random like in the protocol like okay we
+we want to say take any what is our goal
+
+ align:start position:0%
+we want to say take any what is our goal
+ 
+
+ align:start position:0%
+we want to say take any what is our goal
+our goal is to say take any
+
+ align:start position:0%
+our goal is to say take any
+ 
+
+ align:start position:0%
+our goal is to say take any
+protocol that is sound public coin and
+
+ align:start position:0%
+protocol that is sound public coin and
+ 
+
+ align:start position:0%
+protocol that is sound public coin and
+we want to convert it to non-interactive
+
+ align:start position:0%
+we want to convert it to non-interactive
+ 
+
+ align:start position:0%
+we want to convert it to non-interactive
+that's what we're trying to do now I'm
+
+ align:start position:0%
+that's what we're trying to do now I'm
+ 
+
+ align:start position:0%
+that's what we're trying to do now I'm
+saying what property do you need well
+
+ align:start position:0%
+saying what property do you need well
+ 
+
+ align:start position:0%
+saying what property do you need well
+look here the our guarantee was that it
+
+ align:start position:0%
+look here the our guarantee was that it
+ 
+
+ align:start position:0%
+look here the our guarantee was that it
+sound if this was random so need this
+
+ align:start position:0%
+sound if this was random so need this
+ 
+
+ align:start position:0%
+sound if this was random so need this
+has to be somehow
+
+ align:start position:0%
+has to be somehow
+ 
+
+ align:start position:0%
+has to be somehow
+random stand for reason so this is okay
+
+ align:start position:0%
+random stand for reason so this is okay
+ 
+
+ align:start position:0%
+random stand for reason so this is okay
+but look hash functions are not random
+
+ align:start position:0%
+but look hash functions are not random
+ 
+
+ align:start position:0%
+but look hash functions are not random
+it's a hash function by the way let me
+
+ align:start position:0%
+it's a hash function by the way let me
+ 
+
+ align:start position:0%
+it's a hash function by the way let me
+say this Paradigm is used all over the
+
+ align:start position:0%
+say this Paradigm is used all over the
+ 
+
+ align:start position:0%
+say this Paradigm is used all over the
+place it's a very popular Paradigm it's
+
+ align:start position:0%
+place it's a very popular Paradigm it's
+ 
+
+ align:start position:0%
+place it's a very popular Paradigm it's
+used a lot in in signature schemes and
+
+ align:start position:0%
+used a lot in in signature schemes and
+ 
+
+ align:start position:0%
+used a lot in in signature schemes and
+also in in uh um proof systems it's used
+
+ align:start position:0%
+also in in uh um proof systems it's used
+ 
+
+ align:start position:0%
+also in in uh um proof systems it's used
+all over the place and which hash
+
+ align:start position:0%
+all over the place and which hash
+ 
+
+ align:start position:0%
+all over the place and which hash
+function is used some of the Shelf hash
+
+ align:start position:0%
+function is used some of the Shelf hash
+ 
+
+ align:start position:0%
+function is used some of the Shelf hash
+function sh 250 six like
+
+ align:start position:0%
+function sh 250 six like
+ 
+
+ align:start position:0%
+function sh 250 six like
+these engineered type you know hash
+
+ align:start position:0%
+these engineered type you know hash
+ 
+
+ align:start position:0%
+these engineered type you know hash
+function that are
+
+ align:start position:0%
+function that are
+ 
+
+ align:start position:0%
+function that are
+optimized so is it secure with shot
+
+ align:start position:0%
+optimized so is it secure with shot
+ 
+
+ align:start position:0%
+optimized so is it secure with shot
+256 it's definitely not random
+
+ align:start position:0%
+256 it's definitely not random
+ 
+
+ align:start position:0%
+256 it's definitely not random
+it's so we actually don't know that so
+
+ align:start position:0%
+it's so we actually don't know that so
+ 
+
+ align:start position:0%
+it's so we actually don't know that so
+let me be honest that is it
+
+ align:start position:0%
+let me be honest that is it
+ 
+
+ align:start position:0%
+let me be honest that is it
+secure I don't
+
+ align:start position:0%
+secure I don't
+ 
+
+ align:start position:0%
+secure I don't
+know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah extension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah right yeah you right right right
+
+ align:start position:0%
+yeah right yeah you right right right
+ 
+
+ align:start position:0%
+yeah right yeah you right right right
+right right so actually let me good so
+
+ align:start position:0%
+right right so actually let me good so
+ 
+
+ align:start position:0%
+right right so actually let me good so
+let me just say a few
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things okay maybe I'll cut to just to
+
+ align:start position:0%
+things okay maybe I'll cut to just to
+ 
+
+ align:start position:0%
+things okay maybe I'll cut to just to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+chase I do know let me tell you it's not
+
+ align:start position:0%
+chase I do know let me tell you it's not
+ 
+
+ align:start position:0%
+chase I do know let me tell you it's not
+necessarily secure actually
+
+ align:start position:0%
+necessarily secure actually
+ 
+
+ align:start position:0%
+necessarily secure actually
+unfortunately we have counter examples
+
+ align:start position:0%
+unfortunately we have counter examples
+ 
+
+ align:start position:0%
+unfortunately we have counter examples
+so I said this is used in practice all
+
+ align:start position:0%
+so I said this is used in practice all
+ 
+
+ align:start position:0%
+so I said this is used in practice all
+the time you know it's uh one of the
+
+ align:start position:0%
+the time you know it's uh one of the
+ 
+
+ align:start position:0%
+the time you know it's uh one of the
+great inventions of cryptography is it
+
+ align:start position:0%
+great inventions of cryptography is it
+ 
+
+ align:start position:0%
+great inventions of cryptography is it
+secure
+
+ align:start position:0%
+secure
+ 
+
+ align:start position:0%
+secure
+no okay so what do I mean by no okay let
+
+ align:start position:0%
+no okay so what do I mean by no okay let
+ 
+
+ align:start position:0%
+no okay so what do I mean by no okay let
+me is it always secure no so yeah let me
+
+ align:start position:0%
+me is it always secure no so yeah let me
+ 
+
+ align:start position:0%
+me is it always secure no so yeah let me
+say let me take back my know thing is it
+
+ align:start position:0%
+say let me take back my know thing is it
+ 
+
+ align:start position:0%
+say let me take back my know thing is it
+always secure is it always the case that
+
+ align:start position:0%
+always secure is it always the case that
+ 
+
+ align:start position:0%
+always secure is it always the case that
+when you start with an
+
+ align:start position:0%
+when you start with an
+ 
+
+ align:start position:0%
+when you start with an
+interactive protocol and convert public
+
+ align:start position:0%
+interactive protocol and convert public
+ 
+
+ align:start position:0%
+interactive protocol and convert public
+coin and you apply is it always secure
+
+ align:start position:0%
+coin and you apply is it always secure
+ 
+
+ align:start position:0%
+coin and you apply is it always secure
+no moreover let me tell you we have
+
+ align:start position:0%
+no moreover let me tell you we have
+ 
+
+ align:start position:0%
+no moreover let me tell you we have
+protocols so that no matter which has
+
+ align:start position:0%
+protocols so that no matter which has
+ 
+
+ align:start position:0%
+protocols so that no matter which has
+family you use for for all half families
+
+ align:start position:0%
+family you use for for all half families
+ 
+
+ align:start position:0%
+family you use for for all half families
+the protocol becomes
+
+ align:start position:0%
+the protocol becomes
+ 
+
+ align:start position:0%
+the protocol becomes
+insecure hey let me tell you even more
+
+ align:start position:0%
+insecure hey let me tell you even more
+ 
+
+ align:start position:0%
+insecure hey let me tell you even more
+than that that will kind of really
+
+ align:start position:0%
+than that that will kind of really
+ 
+
+ align:start position:0%
+than that that will kind of really
+you'll be
+
+ align:start position:0%
+you'll be
+ 
+
+ align:start position:0%
+you'll be
+mad you know the K mikali
+
+ align:start position:0%
+mad you know the K mikali
+ 
+
+ align:start position:0%
+mad you know the K mikali
+protocol that we kind of built
+
+ align:start position:0%
+protocol that we kind of built
+ 
+
+ align:start position:0%
+protocol that we kind of built
+up even that's not secure the the F
+
+ align:start position:0%
+up even that's not secure the the F
+ 
+
+ align:start position:0%
+up even that's not secure the the F
+won't be secure on it but this let me
+
+ align:start position:0%
+won't be secure on it but this let me
+ 
+
+ align:start position:0%
+won't be secure on it but this let me
+actually put an Asters
+
+ align:start position:0%
+actually put an Asters
+ 
+
+ align:start position:0%
+actually put an Asters
+there it's what okay so let me let me
+
+ align:start position:0%
+there it's what okay so let me let me
+ 
+
+ align:start position:0%
+there it's what okay so let me let me
+tell you what's known about the
+
+ align:start position:0%
+tell you what's known about the
+ 
+
+ align:start position:0%
+tell you what's known about the
+insecurity
+
+ align:start position:0%
+insecurity
+ 
+
+ align:start position:0%
+insecurity
+of the F Paradigm for this protocol what
+
+ align:start position:0%
+of the F Paradigm for this protocol what
+ 
+
+ align:start position:0%
+of the F Paradigm for this protocol what
+is known is there are some contrived so
+
+ align:start position:0%
+is known is there are some contrived so
+ 
+
+ align:start position:0%
+is known is there are some contrived so
+the F the KE mikali protocol says take
+
+ align:start position:0%
+the F the KE mikali protocol says take
+ 
+
+ align:start position:0%
+the F the KE mikali protocol says take
+any hash function that's Collision
+
+ align:start position:0%
+any hash function that's Collision
+ 
+
+ align:start position:0%
+any hash function that's Collision
+resistance and uh and take any
+
+ align:start position:0%
+resistance and uh and take any
+ 
+
+ align:start position:0%
+resistance and uh and take any
+PCP we get
+
+ align:start position:0%
+PCP we get
+ 
+
+ align:start position:0%
+PCP we get
+tness there are examples of specific
+
+ align:start position:0%
+tness there are examples of specific
+ 
+
+ align:start position:0%
+tness there are examples of specific
+hash functions or specific pcps that are
+
+ align:start position:0%
+hash functions or specific pcps that are
+ 
+
+ align:start position:0%
+hash functions or specific pcps that are
+sound of course because it's so I mean
+
+ align:start position:0%
+sound of course because it's so I mean
+ 
+
+ align:start position:0%
+sound of course because it's so I mean
+there are example of collision resistant
+
+ align:start position:0%
+there are example of collision resistant
+ 
+
+ align:start position:0%
+there are example of collision resistant
+hash functions and pcps such that this
+
+ align:start position:0%
+hash functions and pcps such that this
+ 
+
+ align:start position:0%
+hash functions and pcps such that this
+of course it sound it sounds for any
+
+ align:start position:0%
+of course it sound it sounds for any
+ 
+
+ align:start position:0%
+of course it sound it sounds for any
+Collision hash function PCP but such
+
+ align:start position:0%
+Collision hash function PCP but such
+ 
+
+ align:start position:0%
+Collision hash function PCP but such
+that no matter which hash function you
+
+ align:start position:0%
+that no matter which hash function you
+ 
+
+ align:start position:0%
+that no matter which hash function you
+use for the phia this will be insecure
+
+ align:start position:0%
+use for the phia this will be insecure
+ 
+
+ align:start position:0%
+use for the phia this will be insecure
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+sound no matter what you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+yeah what break yeah I I'll say a little
+
+ align:start position:0%
+yeah what break yeah I I'll say a little
+ 
+
+ align:start position:0%
+yeah what break yeah I I'll say a little
+bit what break
+
+ align:start position:0%
+bit what break
+ 
+
+ align:start position:0%
+bit what break
+in a second yeah example or okay good
+
+ align:start position:0%
+in a second yeah example or okay good
+ 
+
+ align:start position:0%
+in a second yeah example or okay good
+good good same question so the example
+
+ align:start position:0%
+good good same question so the example
+ 
+
+ align:start position:0%
+good good same question so the example
+for why it so why it breaks the example
+
+ align:start position:0%
+for why it so why it breaks the example
+ 
+
+ align:start position:0%
+for why it so why it breaks the example
+for why it break is very contrived
+
+ align:start position:0%
+for why it break is very contrived
+ 
+
+ align:start position:0%
+for why it break is very contrived
+actually so that's why am is the message
+
+ align:start position:0%
+actually so that's why am is the message
+ 
+
+ align:start position:0%
+actually so that's why am is the message
+here don't use f CH we have a break no
+
+ align:start position:0%
+here don't use f CH we have a break no
+ 
+
+ align:start position:0%
+here don't use f CH we have a break no
+that's not the message you should use f
+
+ align:start position:0%
+that's not the message you should use f
+ 
+
+ align:start position:0%
+that's not the message you should use f
+because in practice it works very well I
+
+ align:start position:0%
+because in practice it works very well I
+ 
+
+ align:start position:0%
+because in practice it works very well I
+don't have a single instance that people
+
+ align:start position:0%
+don't have a single instance that people
+ 
+
+ align:start position:0%
+don't have a single instance that people
+used F practice and it broke so it's a
+
+ align:start position:0%
+used F practice and it broke so it's a
+ 
+
+ align:start position:0%
+used F practice and it broke so it's a
+great paradigm use
+
+ align:start position:0%
+great paradigm use
+ 
+
+ align:start position:0%
+great paradigm use
+it can we come up with a general proof
+
+ align:start position:0%
+it can we come up with a general proof
+ 
+
+ align:start position:0%
+it can we come up with a general proof
+of security no because we have counter
+
+ align:start position:0%
+of security no because we have counter
+ 
+
+ align:start position:0%
+of security no because we have counter
+examples so what did we learn okay so
+
+ align:start position:0%
+examples so what did we learn okay so
+ 
+
+ align:start position:0%
+examples so what did we learn okay so
+maybe I'll start by saying I'll say very
+
+ align:start position:0%
+maybe I'll start by saying I'll say very
+ 
+
+ align:start position:0%
+maybe I'll start by saying I'll say very
+very high level not in detail but about
+
+ align:start position:0%
+very high level not in detail but about
+ 
+
+ align:start position:0%
+very high level not in detail but about
+the counter examples okay how can we
+
+ align:start position:0%
+the counter examples okay how can we
+ 
+
+ align:start position:0%
+the counter examples okay how can we
+build counter examples and as opposed to
+
+ align:start position:0%
+build counter examples and as opposed to
+ 
+
+ align:start position:0%
+build counter examples and as opposed to
+going to the K mikali protocol because
+
+ align:start position:0%
+going to the K mikali protocol because
+ 
+
+ align:start position:0%
+going to the K mikali protocol because
+there you need to work a little harder
+
+ align:start position:0%
+there you need to work a little harder
+ 
+
+ align:start position:0%
+there you need to work a little harder
+to fit it in uh I'll say a word how you
+
+ align:start position:0%
+to fit it in uh I'll say a word how you
+ 
+
+ align:start position:0%
+to fit it in uh I'll say a word how you
+fit it in there too but the idea is the
+
+ align:start position:0%
+fit it in there too but the idea is the
+ 
+
+ align:start position:0%
+fit it in there too but the idea is the
+foll let me try to give you a a proof
+
+ align:start position:0%
+foll let me try to give you a a proof
+ 
+
+ align:start position:0%
+foll let me try to give you a a proof
+that is or an interactive protocol that
+
+ align:start position:0%
+that is or an interactive protocol that
+ 
+
+ align:start position:0%
+that is or an interactive protocol that
+is sound but when you convert it to uh
+
+ align:start position:0%
+is sound but when you convert it to uh
+ 
+
+ align:start position:0%
+is sound but when you convert it to uh
+when you apply F soundness
+
+ align:start position:0%
+when you apply F soundness
+ 
+
+ align:start position:0%
+when you apply F soundness
+breaks so the idea is the following it's
+
+ align:start position:0%
+breaks so the idea is the following it's
+ 
+
+ align:start position:0%
+breaks so the idea is the following it's
+going to be a very contrived protocol
+
+ align:start position:0%
+going to be a very contrived protocol
+ 
+
+ align:start position:0%
+going to be a very contrived protocol
+okay so my what I want to do is
+
+ align:start position:0%
+okay so my what I want to do is
+ 
+
+ align:start position:0%
+okay so my what I want to do is
+construct a contrived
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protocol that is sound
+
+ align:start position:0%
+protocol that is sound
+ 
+
+ align:start position:0%
+protocol that is sound
+but when you apply F no matter which
+
+ align:start position:0%
+but when you apply F no matter which
+ 
+
+ align:start position:0%
+but when you apply F no matter which
+hash function you use it will
+
+ align:start position:0%
+hash function you use it will
+ 
+
+ align:start position:0%
+hash function you use it will
+break and intuitively the contri
+
+ align:start position:0%
+break and intuitively the contri
+ 
+
+ align:start position:0%
+break and intuitively the contri
+protocol is the following take any sound
+
+ align:start position:0%
+protocol is the following take any sound
+ 
+
+ align:start position:0%
+protocol is the following take any sound
+protocol for example f for example kilan
+
+ align:start position:0%
+protocol for example f for example kilan
+ 
+
+ align:start position:0%
+protocol for example f for example kilan
+mikali whatever or gkr whatever sound
+
+ align:start position:0%
+mikali whatever or gkr whatever sound
+ 
+
+ align:start position:0%
+mikali whatever or gkr whatever sound
+protocol you like and I'm going to
+
+ align:start position:0%
+protocol you like and I'm going to
+ 
+
+ align:start position:0%
+protocol you like and I'm going to
+change it I'm going to tweak a little
+
+ align:start position:0%
+change it I'm going to tweak a little
+ 
+
+ align:start position:0%
+change it I'm going to tweak a little
+bit that the sound will still remain I'm
+
+ align:start position:0%
+bit that the sound will still remain I'm
+ 
+
+ align:start position:0%
+bit that the sound will still remain I'm
+I'm going to tweak it so that I the
+
+ align:start position:0%
+I'm going to tweak it so that I the
+ 
+
+ align:start position:0%
+I'm going to tweak it so that I the
+soundness will still
+
+ align:start position:0%
+soundness will still
+ 
+
+ align:start position:0%
+soundness will still
+hold but on the twick protocol when you
+
+ align:start position:0%
+hold but on the twick protocol when you
+ 
+
+ align:start position:0%
+hold but on the twick protocol when you
+apply for will
+
+ align:start position:0%
+apply for will
+ 
+
+ align:start position:0%
+apply for will
+fail okay so start with PV for example
+
+ align:start position:0%
+fail okay so start with PV for example
+ 
+
+ align:start position:0%
+fail okay so start with PV for example
+gkr for example k m whatever you like
+
+ align:start position:0%
+gkr for example k m whatever you like
+ 
+
+ align:start position:0%
+gkr for example k m whatever you like
+and I'm gonna kind of tweak it a little
+
+ align:start position:0%
+and I'm gonna kind of tweak it a little
+ 
+
+ align:start position:0%
+and I'm gonna kind of tweak it a little
+bit how am I going to tweak it I'm gonna
+
+ align:start position:0%
+bit how am I going to tweak it I'm gonna
+ 
+
+ align:start position:0%
+bit how am I going to tweak it I'm gonna
+say tell the tell the verifier you know
+
+ align:start position:0%
+say tell the tell the verifier you know
+ 
+
+ align:start position:0%
+say tell the tell the verifier you know
+what accept if you accept it before but
+
+ align:start position:0%
+what accept if you accept it before but
+ 
+
+ align:start position:0%
+what accept if you accept it before but
+accept also if something very weird
+
+ align:start position:0%
+accept also if something very weird
+ 
+
+ align:start position:0%
+accept also if something very weird
+happens but don't worry it will never
+
+ align:start position:0%
+happens but don't worry it will never
+ 
+
+ align:start position:0%
+happens but don't worry it will never
+happen Okay when else are we going to
+
+ align:start position:0%
+happen Okay when else are we going to
+ 
+
+ align:start position:0%
+happen Okay when else are we going to
+accept so remember the verifier let's
+
+ align:start position:0%
+accept so remember the verifier let's
+ 
+
+ align:start position:0%
+accept so remember the verifier let's
+say he sends kind of a random beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if the prover let's say ahead of time
+
+ align:start position:0%
+if the prover let's say ahead of time
+ 
+
+ align:start position:0%
+if the prover let's say ahead of time
+guessed your beta he told you I know how
+
+ align:start position:0%
+guessed your beta he told you I know how
+ 
+
+ align:start position:0%
+guessed your beta he told you I know how
+you're going Compu your beta so if the
+
+ align:start position:0%
+you're going Compu your beta so if the
+ 
+
+ align:start position:0%
+you're going Compu your beta so if the
+pro ahead of time sent you kind of um
+
+ align:start position:0%
+pro ahead of time sent you kind of um
+ 
+
+ align:start position:0%
+pro ahead of time sent you kind of um
+sent you a message that will kind of
+
+ align:start position:0%
+sent you a message that will kind of
+ 
+
+ align:start position:0%
+sent you a message that will kind of
+tell say kind of I can
+
+ align:start position:0%
+tell say kind of I can
+ 
+
+ align:start position:0%
+tell say kind of I can
+predict beta and kind of will predict
+
+ align:start position:0%
+predict beta and kind of will predict
+ 
+
+ align:start position:0%
+predict beta and kind of will predict
+bet ahead of time then you accept him
+
+ align:start position:0%
+bet ahead of time then you accept him
+ 
+
+ align:start position:0%
+bet ahead of time then you accept him
+this is random what's the property that
+
+ align:start position:0%
+this is random what's the property that
+ 
+
+ align:start position:0%
+this is random what's the property that
+you can prct my bet
+
+ align:start position:0%
+you can prct my bet
+ 
+
+ align:start position:0%
+you can prct my bet
+if beta is like random and 0 one to the
+
+ align:start position:0%
+if beta is like random and 0 one to the
+ 
+
+ align:start position:0%
+if beta is like random and 0 one to the
+Lambda there's no way you can predict it
+
+ align:start position:0%
+Lambda there's no way you can predict it
+ 
+
+ align:start position:0%
+Lambda there's no way you can predict it
+so if by any chance you predict I'm
+
+ align:start position:0%
+so if by any chance you predict I'm
+ 
+
+ align:start position:0%
+so if by any chance you predict I'm
+going to you know you can won the
+
+ align:start position:0%
+going to you know you can won the
+ 
+
+ align:start position:0%
+going to you know you can won the
+lottery I'll accept you no matter I
+
+ align:start position:0%
+lottery I'll accept you no matter I
+ 
+
+ align:start position:0%
+lottery I'll accept you no matter I
+don't care if that's in the language or
+
+ align:start position:0%
+don't care if that's in the language or
+ 
+
+ align:start position:0%
+don't care if that's in the language or
+not it only adds like a negligable
+
+ align:start position:0%
+not it only adds like a negligable
+ 
+
+ align:start position:0%
+not it only adds like a negligable
+probability of you know because the
+
+ align:start position:0%
+probability of you know because the
+ 
+
+ align:start position:0%
+probability of you know because the
+probability that you can predict beta is
+
+ align:start position:0%
+probability that you can predict beta is
+ 
+
+ align:start position:0%
+probability that you can predict beta is
+one over two to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta now what happens in the F meal
+
+ align:start position:0%
+beta now what happens in the F meal
+ 
+
+ align:start position:0%
+beta now what happens in the F meal
+Paradigm oh I can tell you oh I know bet
+
+ align:start position:0%
+Paradigm oh I can tell you oh I know bet
+ 
+
+ align:start position:0%
+Paradigm oh I can tell you oh I know bet
+I'm I can predict it I'm going to tell
+
+ align:start position:0%
+I'm I can predict it I'm going to tell
+ 
+
+ align:start position:0%
+I'm I can predict it I'm going to tell
+you exactly how I predict it beta is
+
+ align:start position:0%
+you exactly how I predict it beta is
+ 
+
+ align:start position:0%
+you exactly how I predict it beta is
+going to be eval hash key and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+message that's the idea now to implement
+
+ align:start position:0%
+message that's the idea now to implement
+ 
+
+ align:start position:0%
+message that's the idea now to implement
+this idea it's harder it requires some
+
+ align:start position:0%
+this idea it's harder it requires some
+ 
+
+ align:start position:0%
+this idea it's harder it requires some
+work I'll tell you why this idea is not
+
+ align:start position:0%
+work I'll tell you why this idea is not
+ 
+
+ align:start position:0%
+work I'll tell you why this idea is not
+trivially
+
+ align:start position:0%
+trivially
+ 
+
+ align:start position:0%
+trivially
+implemented
+
+ align:start position:0%
+implemented
+ 
+
+ align:start position:0%
+implemented
+because when we do F we say we
+
+ align:start position:0%
+because when we do F we say we
+ 
+
+ align:start position:0%
+because when we do F we say we
+start with a protocol and now the
+
+ align:start position:0%
+start with a protocol and now the
+ 
+
+ align:start position:0%
+start with a protocol and now the
+question question is does there exist a
+
+ align:start position:0%
+question question is does there exist a
+ 
+
+ align:start position:0%
+question question is does there exist a
+hash a f has family for which it's
+
+ align:start position:0%
+hash a f has family for which it's
+ 
+
+ align:start position:0%
+hash a f has family for which it's
+secure now we start with a protocol this
+
+ align:start position:0%
+secure now we start with a protocol this
+ 
+
+ align:start position:0%
+secure now we start with a protocol this
+protocol can say can say Okay Alpha is
+
+ align:start position:0%
+protocol can say can say Okay Alpha is
+ 
+
+ align:start position:0%
+protocol can say can say Okay Alpha is
+Hash key for
+
+ align:start position:0%
+Hash key for
+ 
+
+ align:start position:0%
+Hash key for
+example and then you accept if you
+
+ align:start position:0%
+example and then you accept if you
+ 
+
+ align:start position:0%
+example and then you accept if you
+originally accepted or if eval of hash
+
+ align:start position:0%
+originally accepted or if eval of hash
+ 
+
+ align:start position:0%
+originally accepted or if eval of hash
+key of alpha which is also hash key is
+
+ align:start position:0%
+key of alpha which is also hash key is
+ 
+
+ align:start position:0%
+key of alpha which is also hash key is
+equal to Beta now this will not happen
+
+ align:start position:0%
+equal to Beta now this will not happen
+ 
+
+ align:start position:0%
+equal to Beta now this will not happen
+but in the future me it will happen
+
+ align:start position:0%
+but in the future me it will happen
+ 
+
+ align:start position:0%
+but in the future me it will happen
+I'm going to just send the F in haski
+
+ align:start position:0%
+I'm going to just send the F in haski
+ 
+
+ align:start position:0%
+I'm going to just send the F in haski
+that's what I
+
+ align:start position:0%
+that's what I
+ 
+
+ align:start position:0%
+that's what I
+do okay but then someone will say okay
+
+ align:start position:0%
+do okay but then someone will say okay
+ 
+
+ align:start position:0%
+do okay but then someone will say okay
+so you give me a protocol what is the
+
+ align:start position:0%
+so you give me a protocol what is the
+ 
+
+ align:start position:0%
+so you give me a protocol what is the
+length of your Alpha it's Lambda bits
+
+ align:start position:0%
+length of your Alpha it's Lambda bits
+ 
+
+ align:start position:0%
+length of your Alpha it's Lambda bits
+I'm going to use a hash function that
+
+ align:start position:0%
+I'm going to use a hash function that
+ 
+
+ align:start position:0%
+I'm going to use a hash function that
+the hash key is longer and now you can't
+
+ align:start position:0%
+the hash key is longer and now you can't
+ 
+
+ align:start position:0%
+the hash key is longer and now you can't
+send it because here I'm like I'll send
+
+ align:start position:0%
+send it because here I'm like I'll send
+ 
+
+ align:start position:0%
+send it because here I'm like I'll send
+the hash
+
+ align:start position:0%
+the hash
+ 
+
+ align:start position:0%
+the hash
+key so then you need to use a hash to
+
+ align:start position:0%
+key so then you need to use a hash to
+ 
+
+ align:start position:0%
+key so then you need to use a hash to
+kind of Squish this hash key it it's
+
+ align:start position:0%
+kind of Squish this hash key it it's
+ 
+
+ align:start position:0%
+kind of Squish this hash key it it's
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+complicated but the the basic idea
+
+ align:start position:0%
+complicated but the the basic idea
+ 
+
+ align:start position:0%
+complicated but the the basic idea
+is this does not work if somehow the
+
+ align:start position:0%
+is this does not work if somehow the
+ 
+
+ align:start position:0%
+is this does not work if somehow the
+verifier accepts you if you kind of
+
+ align:start position:0%
+verifier accepts you if you kind of
+ 
+
+ align:start position:0%
+verifier accepts you if you kind of
+convinced him that you can kind of
+
+ align:start position:0%
+convinced him that you can kind of
+ 
+
+ align:start position:0%
+convinced him that you can kind of
+predict his his beta that's really
+
+ align:start position:0%
+predict his his beta that's really
+ 
+
+ align:start position:0%
+predict his his beta that's really
+and so we can construct kind of
+
+ align:start position:0%
+and so we can construct kind of
+ 
+
+ align:start position:0%
+and so we can construct kind of
+contrived um protocols that achieve this
+
+ align:start position:0%
+contrived um protocols that achieve this
+ 
+
+ align:start position:0%
+contrived um protocols that achieve this
+or we can cont construct very contrived
+
+ align:start position:0%
+or we can cont construct very contrived
+ 
+
+ align:start position:0%
+or we can cont construct very contrived
+hash function that do this weird game
+
+ align:start position:0%
+hash function that do this weird game
+ 
+
+ align:start position:0%
+hash function that do this weird game
+inside the hash function like the hash
+
+ align:start position:0%
+inside the hash function like the hash
+ 
+
+ align:start position:0%
+inside the hash function like the hash
+function becomes trivial if you feed it
+
+ align:start position:0%
+function becomes trivial if you feed it
+ 
+
+ align:start position:0%
+function becomes trivial if you feed it
+something that kind of so so it requires
+
+ align:start position:0%
+something that kind of so so it requires
+ 
+
+ align:start position:0%
+something that kind of so so it requires
+more work but it's all very
+
+ align:start position:0%
+more work but it's all very
+ 
+
+ align:start position:0%
+more work but it's all very
+contrived okay so I hope I convinced you
+
+ align:start position:0%
+contrived okay so I hope I convinced you
+ 
+
+ align:start position:0%
+contrived okay so I hope I convinced you
+by with these examples the counter
+
+ align:start position:0%
+by with these examples the counter
+ 
+
+ align:start position:0%
+by with these examples the counter
+examples are so contrived so when you
+
+ align:start position:0%
+examples are so contrived so when you
+ 
+
+ align:start position:0%
+examples are so contrived so when you
+when you say oh we found the p is not
+
+ align:start position:0%
+when you say oh we found the p is not
+ 
+
+ align:start position:0%
+when you say oh we found the p is not
+secure and you show these example the
+
+ align:start position:0%
+secure and you show these example the
+ 
+
+ align:start position:0%
+secure and you show these example the
+reaction should be come on okay nobody
+
+ align:start position:0%
+reaction should be come on okay nobody
+ 
+
+ align:start position:0%
+reaction should be come on okay nobody
+uses these
+
+ align:start position:0%
+uses these
+ 
+
+ align:start position:0%
+uses these
+protocols but what it does tell us you
+
+ align:start position:0%
+protocols but what it does tell us you
+ 
+
+ align:start position:0%
+protocols but what it does tell us you
+can't apply F blind you can't okay what
+
+ align:start position:0%
+can't apply F blind you can't okay what
+ 
+
+ align:start position:0%
+can't apply F blind you can't okay what
+it does tell us is for all of us who are
+
+ align:start position:0%
+it does tell us is for all of us who are
+ 
+
+ align:start position:0%
+it does tell us is for all of us who are
+upset with trying to prove the Paradigm
+
+ align:start position:0%
+upset with trying to prove the Paradigm
+ 
+
+ align:start position:0%
+upset with trying to prove the Paradigm
+there's no General proof because we have
+
+ align:start position:0%
+there's no General proof because we have
+ 
+
+ align:start position:0%
+there's no General proof because we have
+counter examples at least
+
+ align:start position:0%
+counter examples at least
+ 
+
+ align:start position:0%
+counter examples at least
+that question you need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start great great question okay I that's
+
+ align:start position:0%
+start great great question okay I that's
+ 
+
+ align:start position:0%
+start great great question okay I that's
+my next so I I'll I'll uh
+
+ align:start position:0%
+my next so I I'll I'll uh
+ 
+
+ align:start position:0%
+my next so I I'll I'll uh
+yeah I'll the answer is yes but I'll
+
+ align:start position:0%
+yeah I'll the answer is yes but I'll
+ 
+
+ align:start position:0%
+yeah I'll the answer is yes but I'll
+I'll I'll talk about that next the
+
+ align:start position:0%
+I'll I'll talk about that next the
+ 
+
+ align:start position:0%
+I'll I'll talk about that next the
+question was about negligible soundness
+
+ align:start position:0%
+question was about negligible soundness
+ 
+
+ align:start position:0%
+question was about negligible soundness
+but we'll get to that next so any
+
+ align:start position:0%
+but we'll get to that next so any
+ 
+
+ align:start position:0%
+but we'll get to that next so any
+question though
+
+ align:start position:0%
+question though
+ 
+
+ align:start position:0%
+question though
+before okay so but you know still people
+
+ align:start position:0%
+before okay so but you know still people
+ 
+
+ align:start position:0%
+before okay so but you know still people
+use the F Paradigm and there's a
+
+ align:start position:0%
+use the F Paradigm and there's a
+ 
+
+ align:start position:0%
+use the F Paradigm and there's a
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+of is it sound for natural protocols is
+
+ align:start position:0%
+of is it sound for natural protocols is
+ 
+
+ align:start position:0%
+of is it sound for natural protocols is
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+sound and the answer is actually it
+
+ align:start position:0%
+sound and the answer is actually it
+ 
+
+ align:start position:0%
+sound and the answer is actually it
+would have been nice if we can come up
+
+ align:start position:0%
+would have been nice if we can come up
+ 
+
+ align:start position:0%
+would have been nice if we can come up
+with Pro nice protocols and say at least
+
+ align:start position:0%
+with Pro nice protocols and say at least
+ 
+
+ align:start position:0%
+with Pro nice protocols and say at least
+a large class of protocols and say yeah
+
+ align:start position:0%
+a large class of protocols and say yeah
+ 
+
+ align:start position:0%
+a large class of protocols and say yeah
+if you use this hash function this
+
+ align:start position:0%
+if you use this hash function this
+ 
+
+ align:start position:0%
+if you use this hash function this
+specific hash function which we know is
+
+ align:start position:0%
+specific hash function which we know is
+ 
+
+ align:start position:0%
+specific hash function which we know is
+Collision resistant under discret log or
+
+ align:start position:0%
+Collision resistant under discret log or
+ 
+
+ align:start position:0%
+Collision resistant under discret log or
+under some other
+
+ align:start position:0%
+under some other
+ 
+
+ align:start position:0%
+under some other
+then your scheme is sound that would be
+
+ align:start position:0%
+then your scheme is sound that would be
+ 
+
+ align:start position:0%
+then your scheme is sound that would be
+very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nice we're still not there yet but we
+
+ align:start position:0%
+nice we're still not there yet but we
+ 
+
+ align:start position:0%
+nice we're still not there yet but we
+made a lot of progress in recent years
+
+ align:start position:0%
+made a lot of progress in recent years
+ 
+
+ align:start position:0%
+made a lot of progress in recent years
+and I want to tell you about the
+
+ align:start position:0%
+and I want to tell you about the
+ 
+
+ align:start position:0%
+and I want to tell you about the
+progress but before that the first way
+
+ align:start position:0%
+progress but before that the first way
+ 
+
+ align:start position:0%
+progress but before that the first way
+the first a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a uh kind of way we try to analyze so
+
+ align:start position:0%
+a uh kind of way we try to analyze so
+ 
+
+ align:start position:0%
+a uh kind of way we try to analyze so
+the F gained popularity very quickly
+
+ align:start position:0%
+the F gained popularity very quickly
+ 
+
+ align:start position:0%
+the F gained popularity very quickly
+okay uh and because it's so simple and
+
+ align:start position:0%
+okay uh and because it's so simple and
+ 
+
+ align:start position:0%
+okay uh and because it's so simple and
+so efficient uh it became very very
+
+ align:start position:0%
+so efficient uh it became very very
+ 
+
+ align:start position:0%
+so efficient uh it became very very
+popular
+
+ align:start position:0%
+popular
+ 
+
+ align:start position:0%
+popular
+and people really wanted to understand
+
+ align:start position:0%
+and people really wanted to understand
+ 
+
+ align:start position:0%
+and people really wanted to understand
+its uh security is it sound is it not
+
+ align:start position:0%
+its uh security is it sound is it not
+ 
+
+ align:start position:0%
+its uh security is it sound is it not
+sound and then in
+
+ align:start position:0%
+sound and then in
+ 
+
+ align:start position:0%
+sound and then in
+93 Bela and rway introduced kind of an
+
+ align:start position:0%
+93 Bela and rway introduced kind of an
+ 
+
+ align:start position:0%
+93 Bela and rway introduced kind of an
+ideal model called the random Oracle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model and this model said you know
+
+ align:start position:0%
+model and this model said you know
+ 
+
+ align:start position:0%
+model and this model said you know
+what by the way this was before we had
+
+ align:start position:0%
+what by the way this was before we had
+ 
+
+ align:start position:0%
+what by the way this was before we had
+any counter examples okay this model was
+
+ align:start position:0%
+any counter examples okay this model was
+ 
+
+ align:start position:0%
+any counter examples okay this model was
+introduced by Bel and rway in I believe
+
+ align:start position:0%
+introduced by Bel and rway in I believe
+ 
+
+ align:start position:0%
+introduced by Bel and rway in I believe
+80 uh
+
+ align:start position:0%
+80 uh
+ 
+
+ align:start position:0%
+80 uh
+93 this was before we knew any counter
+
+ align:start position:0%
+93 this was before we knew any counter
+ 
+
+ align:start position:0%
+93 this was before we knew any counter
+examples for the Paradigm and they I
+
+ align:start position:0%
+examples for the Paradigm and they I
+ 
+
+ align:start position:0%
+examples for the Paradigm and they I
+mean except for some which goes through
+
+ align:start position:0%
+mean except for some which goes through
+ 
+
+ align:start position:0%
+mean except for some which goes through
+your question Leo but I'm going to get
+
+ align:start position:0%
+your question Leo but I'm going to get
+ 
+
+ align:start position:0%
+your question Leo but I'm going to get
+to it and they wanted to ask can we
+
+ align:start position:0%
+to it and they wanted to ask can we
+ 
+
+ align:start position:0%
+to it and they wanted to ask can we
+prove security of of
+
+ align:start position:0%
+prove security of of
+ 
+
+ align:start position:0%
+prove security of of
+the uh what do we need about the hash
+
+ align:start position:0%
+the uh what do we need about the hash
+ 
+
+ align:start position:0%
+the uh what do we need about the hash
+function what properties do we need
+
+ align:start position:0%
+function what properties do we need
+ 
+
+ align:start position:0%
+function what properties do we need
+about the hash function to prove
+
+ align:start position:0%
+about the hash function to prove
+ 
+
+ align:start position:0%
+about the hash function to prove
+security and the first property they
+
+ align:start position:0%
+security and the first property they
+ 
+
+ align:start position:0%
+security and the first property they
+said you know what what if the hash
+
+ align:start position:0%
+said you know what what if the hash
+ 
+
+ align:start position:0%
+said you know what what if the hash
+function was completely
+
+ align:start position:0%
+function was completely
+ 
+
+ align:start position:0%
+function was completely
+random so when you use we use a specific
+
+ align:start position:0%
+random so when you use we use a specific
+ 
+
+ align:start position:0%
+random so when you use we use a specific
+there's a circuit that computes the hash
+
+ align:start position:0%
+there's a circuit that computes the hash
+ 
+
+ align:start position:0%
+there's a circuit that computes the hash
+function it's like a touring machine a
+
+ align:start position:0%
+function it's like a touring machine a
+ 
+
+ align:start position:0%
+function it's like a touring machine a
+polinomial Time touring machine or a
+
+ align:start position:0%
+polinomial Time touring machine or a
+ 
+
+ align:start position:0%
+polinomial Time touring machine or a
+polinomial size circuit takes a hash key
+
+ align:start position:0%
+polinomial size circuit takes a hash key
+ 
+
+ align:start position:0%
+polinomial size circuit takes a hash key
+and okay they say you know what what if
+
+ align:start position:0%
+and okay they say you know what what if
+ 
+
+ align:start position:0%
+and okay they say you know what what if
+the hash function is completely
+
+ align:start position:0%
+the hash function is completely
+ 
+
+ align:start position:0%
+the hash function is completely
+random Okay so the r welome model says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose we
+
+ align:start position:0%
+suppose we
+ 
+
+ align:start position:0%
+suppose we
+apply Fe to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Paradigm with
+
+ align:start position:0%
+Paradigm with
+ 
+
+ align:start position:0%
+Paradigm with
+truly
+
+ align:start position:0%
+truly
+ 
+
+ align:start position:0%
+truly
+random function
+
+ align:start position:0%
+random function
+ 
+
+ align:start position:0%
+random function
+H so this is completely completely
+
+ align:start position:0%
+H so this is completely completely
+ 
+
+ align:start position:0%
+H so this is completely completely
+random so what do I mean by completely
+
+ align:start position:0%
+random so what do I mean by completely
+ 
+
+ align:start position:0%
+random so what do I mean by completely
+random so now I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guess let me
+
+ align:start position:0%
+guess let me
+ 
+
+ align:start position:0%
+guess let me
+instead of
+
+ align:start position:0%
+instead of
+ 
+
+ align:start position:0%
+instead of
+choosing a function from a
+
+ align:start position:0%
+choosing a function from a
+ 
+
+ align:start position:0%
+choosing a function from a
+family we don't choose a function and we
+
+ align:start position:0%
+family we don't choose a function and we
+ 
+
+ align:start position:0%
+family we don't choose a function and we
+just say suppose they have a truly
+
+ align:start position:0%
+just say suppose they have a truly
+ 
+
+ align:start position:0%
+just say suppose they have a truly
+random they have access to both of them
+
+ align:start position:0%
+random they have access to both of them
+ 
+
+ align:start position:0%
+random they have access to both of them
+to a truly truly random function and
+
+ align:start position:0%
+to a truly truly random function and
+ 
+
+ align:start position:0%
+to a truly truly random function and
+they can ask so when the prover computes
+
+ align:start position:0%
+they can ask so when the prover computes
+ 
+
+ align:start position:0%
+they can ask so when the prover computes
+Alpha he asks he has Oracle this
+
+ align:start position:0%
+Alpha he asks he has Oracle this
+ 
+
+ align:start position:0%
+Alpha he asks he has Oracle this
+function and he tells the function give
+
+ align:start position:0%
+function and he tells the function give
+ 
+
+ align:start position:0%
+function and he tells the function give
+me the function apply 2 x and Alpha and
+
+ align:start position:0%
+me the function apply 2 x and Alpha and
+ 
+
+ align:start position:0%
+me the function apply 2 x and Alpha and
+he gets back a beta and every time this
+
+ align:start position:0%
+he gets back a beta and every time this
+ 
+
+ align:start position:0%
+he gets back a beta and every time this
+hash this Oracle he gets a query he
+
+ align:start position:0%
+hash this Oracle he gets a query he
+ 
+
+ align:start position:0%
+hash this Oracle he gets a query he
+chooses a completely random so think of
+
+ align:start position:0%
+chooses a completely random so think of
+ 
+
+ align:start position:0%
+chooses a completely random so think of
+this as like a database of all like size
+
+ align:start position:0%
+this as like a database of all like size
+ 
+
+ align:start position:0%
+this as like a database of all like size
+two to the Lambda of all like just
+
+ align:start position:0%
+two to the Lambda of all like just
+ 
+
+ align:start position:0%
+two to the Lambda of all like just
+random random random elements a really
+
+ align:start position:0%
+random random random elements a really
+ 
+
+ align:start position:0%
+random random random elements a really
+really truly random
+
+ align:start position:0%
+really truly random
+ 
+
+ align:start position:0%
+really truly random
+function so now the question was okay if
+
+ align:start position:0%
+function so now the question was okay if
+ 
+
+ align:start position:0%
+function so now the question was okay if
+this is truly random now can we get
+
+ align:start position:0%
+this is truly random now can we get
+ 
+
+ align:start position:0%
+this is truly random now can we get
+security at least like that's the
+
+ align:start position:0%
+security at least like that's the
+ 
+
+ align:start position:0%
+security at least like that's the
+minimum and moreover it seem like the
+
+ align:start position:0%
+minimum and moreover it seem like the
+ 
+
+ align:start position:0%
+minimum and moreover it seem like the
+answer should be yes because in some
+
+ align:start position:0%
+answer should be yes because in some
+ 
+
+ align:start position:0%
+answer should be yes because in some
+sense what was their what was their
+
+ align:start position:0%
+sense what was their what was their
+ 
+
+ align:start position:0%
+sense what was their what was their
+intuition the intuition is what does it
+
+ align:start position:0%
+intuition the intuition is what does it
+ 
+
+ align:start position:0%
+intuition the intuition is what does it
+matter if you're talking to a verifier
+
+ align:start position:0%
+matter if you're talking to a verifier
+ 
+
+ align:start position:0%
+matter if you're talking to a verifier
+that gives you random queries or you're
+
+ align:start position:0%
+that gives you random queries or you're
+ 
+
+ align:start position:0%
+that gives you random queries or you're
+talking to in terms of the prover so the
+
+ align:start position:0%
+talking to in terms of the prover so the
+ 
+
+ align:start position:0%
+talking to in terms of the prover so the
+prover is trying to cheat what does it
+
+ align:start position:0%
+prover is trying to cheat what does it
+ 
+
+ align:start position:0%
+prover is trying to cheat what does it
+matter if he's talking to a verifier
+
+ align:start position:0%
+matter if he's talking to a verifier
+ 
+
+ align:start position:0%
+matter if he's talking to a verifier
+that give him kind of random vas or he's
+
+ align:start position:0%
+that give him kind of random vas or he's
+ 
+
+ align:start position:0%
+that give him kind of random vas or he's
+talking to a random function that gives
+
+ align:start position:0%
+talking to a random function that gives
+ 
+
+ align:start position:0%
+talking to a random function that gives
+them random betas both of them do random
+
+ align:start position:0%
+them random betas both of them do random
+ 
+
+ align:start position:0%
+them random betas both of them do random
+betas what's the
+
+ align:start position:0%
+betas what's the
+ 
+
+ align:start position:0%
+betas what's the
+difference so it should at least be
+
+ align:start position:0%
+difference so it should at least be
+ 
+
+ align:start position:0%
+difference so it should at least be
+secure in the random Oracle model let's
+
+ align:start position:0%
+secure in the random Oracle model let's
+ 
+
+ align:start position:0%
+secure in the random Oracle model let's
+first establish
+
+ align:start position:0%
+first establish
+ 
+
+ align:start position:0%
+first establish
+that so is it secure in the random
+
+ align:start position:0%
+that so is it secure in the random
+ 
+
+ align:start position:0%
+that so is it secure in the random
+Oracle model
+
+ align:start position:0%
+Oracle model
+ 
+
+ align:start position:0%
+Oracle model
+no and this goes to Leo's
+
+ align:start position:0%
+no and this goes to Leo's
+ 
+
+ align:start position:0%
+no and this goes to Leo's
+question and I'm going to tell you why
+
+ align:start position:0%
+question and I'm going to tell you why
+ 
+
+ align:start position:0%
+question and I'm going to tell you why
+it's not secured the random oracal model
+
+ align:start position:0%
+it's not secured the random oracal model
+ 
+
+ align:start position:0%
+it's not secured the random oracal model
+and actually let me take a little
+
+ align:start position:0%
+and actually let me take a little
+ 
+
+ align:start position:0%
+and actually let me take a little
+detour and uh tell you I'll I'll show
+
+ align:start position:0%
+detour and uh tell you I'll I'll show
+ 
+
+ align:start position:0%
+detour and uh tell you I'll I'll show
+why it's not secure in the random oracal
+
+ align:start position:0%
+why it's not secure in the random oracal
+ 
+
+ align:start position:0%
+why it's not secure in the random oracal
+model via a little protocol
+
+ align:start position:0%
+model via a little protocol
+ 
+
+ align:start position:0%
+model via a little protocol
+this protocol actually is going to be
+
+ align:start position:0%
+this protocol actually is going to be
+ 
+
+ align:start position:0%
+this protocol actually is going to be
+useful because actually later we will
+
+ align:start position:0%
+useful because actually later we will
+ 
+
+ align:start position:0%
+useful because actually later we will
+show that the f is sound for this
+
+ align:start position:0%
+show that the f is sound for this
+ 
+
+ align:start position:0%
+show that the f is sound for this
+protocol it's kind of weird but let's
+
+ align:start position:0%
+protocol it's kind of weird but let's
+ 
+
+ align:start position:0%
+protocol it's kind of weird but let's
+this protocol by the way is very
+
+ align:start position:0%
+this protocol by the way is very
+ 
+
+ align:start position:0%
+this protocol by the way is very
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+protocol so so let me quickly do let me
+
+ align:start position:0%
+protocol so so let me quickly do let me
+ 
+
+ align:start position:0%
+protocol so so let me quickly do let me
+do a little detour I think it's a really
+
+ align:start position:0%
+do a little detour I think it's a really
+ 
+
+ align:start position:0%
+do a little detour I think it's a really
+interesting detour so I hope you enjoy
+
+ align:start position:0%
+interesting detour so I hope you enjoy
+ 
+
+ align:start position:0%
+interesting detour so I hope you enjoy
+it um it takes us a little bit into the
+
+ align:start position:0%
+it um it takes us a little bit into the
+ 
+
+ align:start position:0%
+it um it takes us a little bit into the
+land of
+
+ align:start position:0%
+land of
+ 
+
+ align:start position:0%
+land of
+cryptography but not too bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little further than we went so far so
+
+ align:start position:0%
+a little further than we went so far so
+ 
+
+ align:start position:0%
+a little further than we went so far so
+far we just talked about hash
+
+ align:start position:0%
+far we just talked about hash
+ 
+
+ align:start position:0%
+far we just talked about hash
+functions okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I'm going to say now is going to
+
+ align:start position:0%
+so what I'm going to say now is going to
+ 
+
+ align:start position:0%
+so what I'm going to say now is going to
+be a little bit of a high level
+
+ align:start position:0%
+be a little bit of a high level
+ 
+
+ align:start position:0%
+be a little bit of a high level
+a so a protocol that I want
+
+ align:start position:0%
+a so a protocol that I want
+ 
+
+ align:start position:0%
+a so a protocol that I want
+to talk about is actually a zero
+
+ align:start position:0%
+to talk about is actually a zero
+ 
+
+ align:start position:0%
+to talk about is actually a zero
+knowledge protocol so you know so far we
+
+ align:start position:0%
+knowledge protocol so you know so far we
+ 
+
+ align:start position:0%
+knowledge protocol so you know so far we
+just talked about verification
+
+ align:start position:0%
+just talked about verification
+ 
+
+ align:start position:0%
+just talked about verification
+verification you know synness and
+
+ align:start position:0%
+verification you know synness and
+ 
+
+ align:start position:0%
+verification you know synness and
+efficiency but uh as I mentioned
+
+ align:start position:0%
+efficiency but uh as I mentioned
+ 
+
+ align:start position:0%
+efficiency but uh as I mentioned
+interactive protocols were actually
+
+ align:start position:0%
+interactive protocols were actually
+ 
+
+ align:start position:0%
+interactive protocols were actually
+invented for the sake of zero
+
+ align:start position:0%
+invented for the sake of zero
+ 
+
+ align:start position:0%
+invented for the sake of zero
+knowledge so what was the goal the goal
+
+ align:start position:0%
+knowledge so what was the goal the goal
+ 
+
+ align:start position:0%
+knowledge so what was the goal the goal
+was forget about sness now it was not at
+
+ align:start position:0%
+was forget about sness now it was not at
+ 
+
+ align:start position:0%
+was forget about sness now it was not at
+all about sness all we wanted is a
+
+ align:start position:0%
+all about sness all we wanted is a
+ 
+
+ align:start position:0%
+all about sness all we wanted is a
+prover that has let's say a witness for
+
+ align:start position:0%
+prover that has let's say a witness for
+ 
+
+ align:start position:0%
+prover that has let's say a witness for
+some there's some there's some language
+
+ align:start position:0%
+some there's some there's some language
+ 
+
+ align:start position:0%
+some there's some there's some language
+and let's say the language we're going
+
+ align:start position:0%
+and let's say the language we're going
+ 
+
+ align:start position:0%
+and let's say the language we're going
+to be interested for today just as an
+
+ align:start position:0%
+to be interested for today just as an
+ 
+
+ align:start position:0%
+to be interested for today just as an
+example is the language of hamiltonian
+
+ align:start position:0%
+example is the language of hamiltonian
+ 
+
+ align:start position:0%
+example is the language of hamiltonian
+cycle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's just an example so this language
+
+ align:start position:0%
+that's just an example so this language
+ 
+
+ align:start position:0%
+that's just an example so this language
+consists of
+
+ align:start position:0%
+consists of
+ 
+
+ align:start position:0%
+consists of
+graphs so this is the language that
+
+ align:start position:0%
+graphs so this is the language that
+ 
+
+ align:start position:0%
+graphs so this is the language that
+consists of all graphs graph is just
+
+ align:start position:0%
+consists of all graphs graph is just
+ 
+
+ align:start position:0%
+consists of all graphs graph is just
+consists of nodes and
+
+ align:start position:0%
+consists of nodes and
+ 
+
+ align:start position:0%
+consists of nodes and
+edges such that this graph has a
+
+ align:start position:0%
+edges such that this graph has a
+ 
+
+ align:start position:0%
+edges such that this graph has a
+hamiltonian cycle so that g
+
+ align:start position:0%
+hamiltonian cycle so that g
+ 
+
+ align:start position:0%
+hamiltonian cycle so that g
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+hamiltonian cycle what this means is
+
+ align:start position:0%
+hamiltonian cycle what this means is
+ 
+
+ align:start position:0%
+hamiltonian cycle what this means is
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can just there's a kind of a a cycle
+
+ align:start position:0%
+you can just there's a kind of a a cycle
+ 
+
+ align:start position:0%
+you can just there's a kind of a a cycle
+of all the nodes so it means that
+
+ align:start position:0%
+of all the nodes so it means that
+ 
+
+ align:start position:0%
+of all the nodes so it means that
+there's a cycle of all the nodes so
+
+ align:start position:0%
+there's a cycle of all the nodes so
+ 
+
+ align:start position:0%
+there's a cycle of all the nodes so
+let's say you start with node i1
+
+ align:start position:0%
+let's say you start with node i1
+ 
+
+ align:start position:0%
+let's say you start with node i1
+I2 up to i n and then go up to I in said
+
+ align:start position:0%
+I2 up to i n and then go up to I in said
+ 
+
+ align:start position:0%
+I2 up to i n and then go up to I in said
+that there's an edge here Edge Edge Edge
+
+ align:start position:0%
+that there's an edge here Edge Edge Edge
+ 
+
+ align:start position:0%
+that there's an edge here Edge Edge Edge
+Edge Edge an edge all the way back
+
+ align:start position:0%
+Edge Edge an edge all the way back
+ 
+
+ align:start position:0%
+Edge Edge an edge all the way back
+that's that means it if if you can if
+
+ align:start position:0%
+that's that means it if if you can if
+ 
+
+ align:start position:0%
+that's that means it if if you can if
+there's some such um uh uh a setting of
+
+ align:start position:0%
+there's some such um uh uh a setting of
+ 
+
+ align:start position:0%
+there's some such um uh uh a setting of
+The nodes for which you can kind of set
+
+ align:start position:0%
+The nodes for which you can kind of set
+ 
+
+ align:start position:0%
+The nodes for which you can kind of set
+them in a way that there's edges that
+
+ align:start position:0%
+them in a way that there's edges that
+ 
+
+ align:start position:0%
+them in a way that there's edges that
+kind of complete a cycle then we say the
+
+ align:start position:0%
+kind of complete a cycle then we say the
+ 
+
+ align:start position:0%
+kind of complete a cycle then we say the
+graph has the hamiltonian cycle okay
+
+ align:start position:0%
+graph has the hamiltonian cycle okay
+ 
+
+ align:start position:0%
+graph has the hamiltonian cycle okay
+this language is NP complete okay now so
+
+ align:start position:0%
+this language is NP complete okay now so
+ 
+
+ align:start position:0%
+this language is NP complete okay now so
+now going back what is a zero knowledge
+
+ align:start position:0%
+now going back what is a zero knowledge
+ 
+
+ align:start position:0%
+now going back what is a zero knowledge
+proof a zero knowledge proof is a way I
+
+ align:start position:0%
+proof a zero knowledge proof is a way I
+ 
+
+ align:start position:0%
+proof a zero knowledge proof is a way I
+want to convince you that a graph G has
+
+ align:start position:0%
+want to convince you that a graph G has
+ 
+
+ align:start position:0%
+want to convince you that a graph G has
+aonian cycle now I can give you the
+
+ align:start position:0%
+aonian cycle now I can give you the
+ 
+
+ align:start position:0%
+aonian cycle now I can give you the
+cycle I can give you see here's the node
+
+ align:start position:0%
+cycle I can give you see here's the node
+ 
+
+ align:start position:0%
+cycle I can give you see here's the node
+you can look there's a cycle there but I
+
+ align:start position:0%
+you can look there's a cycle there but I
+ 
+
+ align:start position:0%
+you can look there's a cycle there but I
+don't want to give you any information I
+
+ align:start position:0%
+don't want to give you any information I
+ 
+
+ align:start position:0%
+don't want to give you any information I
+don't want you to learn anything I don't
+
+ align:start position:0%
+don't want you to learn anything I don't
+ 
+
+ align:start position:0%
+don't want you to learn anything I don't
+want you to to find the cycle I don't
+
+ align:start position:0%
+want you to to find the cycle I don't
+ 
+
+ align:start position:0%
+want you to to find the cycle I don't
+want to reveal any information but I
+
+ align:start position:0%
+want to reveal any information but I
+ 
+
+ align:start position:0%
+want to reveal any information but I
+want to convince you that it has a
+
+ align:start position:0%
+want to convince you that it has a
+ 
+
+ align:start position:0%
+want to convince you that it has a
+hamiltonian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cycle how do I do that so this kind of
+
+ align:start position:0%
+cycle how do I do that so this kind of
+ 
+
+ align:start position:0%
+cycle how do I do that so this kind of
+so there's a a celebrated result it
+
+ align:start position:0%
+so there's a a celebrated result it
+ 
+
+ align:start position:0%
+so there's a a celebrated result it
+started with gasali and ROV in mid 80s
+
+ align:start position:0%
+started with gasali and ROV in mid 80s
+ 
+
+ align:start position:0%
+started with gasali and ROV in mid 80s
+and uh where they defined this notion of
+
+ align:start position:0%
+and uh where they defined this notion of
+ 
+
+ align:start position:0%
+and uh where they defined this notion of
+zero knowledge uh and constructed some
+
+ align:start position:0%
+zero knowledge uh and constructed some
+ 
+
+ align:start position:0%
+zero knowledge uh and constructed some
+protocols but later very shortly later
+
+ align:start position:0%
+protocols but later very shortly later
+ 
+
+ align:start position:0%
+protocols but later very shortly later
+uh uh by gold gold mikali and vigone
+
+ align:start position:0%
+uh uh by gold gold mikali and vigone
+ 
+
+ align:start position:0%
+uh uh by gold gold mikali and vigone
+showed that actually any NP language has
+
+ align:start position:0%
+showed that actually any NP language has
+ 
+
+ align:start position:0%
+showed that actually any NP language has
+a zero knowledge
+
+ align:start position:0%
+a zero knowledge
+ 
+
+ align:start position:0%
+a zero knowledge
+proof okay let me give you one specific
+
+ align:start position:0%
+proof okay let me give you one specific
+ 
+
+ align:start position:0%
+proof okay let me give you one specific
+zero knowledge proof for the aonian uh
+
+ align:start position:0%
+zero knowledge proof for the aonian uh
+ 
+
+ align:start position:0%
+zero knowledge proof for the aonian uh
+cycle language uh and this is Du to blam
+
+ align:start position:0%
+cycle language uh and this is Du to blam
+ 
+
+ align:start position:0%
+cycle language uh and this is Du to blam
+okay so I'll show you the the proof it's
+
+ align:start position:0%
+okay so I'll show you the the proof it's
+ 
+
+ align:start position:0%
+okay so I'll show you the the proof it's
+very very nice okay and it's going to be
+
+ align:start position:0%
+very very nice okay and it's going to be
+ 
+
+ align:start position:0%
+very very nice okay and it's going to be
+useful for us uh to show NE to show why
+
+ align:start position:0%
+useful for us uh to show NE to show why
+ 
+
+ align:start position:0%
+useful for us uh to show NE to show why
+the random oral model fails and then
+
+ align:start position:0%
+the random oral model fails and then
+ 
+
+ align:start position:0%
+the random oral model fails and then
+also to show the security of the F so
+
+ align:start position:0%
+also to show the security of the F so
+ 
+
+ align:start position:0%
+also to show the security of the F so
+this is actually we'll get back to this
+
+ align:start position:0%
+this is actually we'll get back to this
+ 
+
+ align:start position:0%
+this is actually we'll get back to this
+protocol okay so what is this protocol
+
+ align:start position:0%
+protocol okay so what is this protocol
+ 
+
+ align:start position:0%
+protocol okay so what is this protocol
+there's a prover in a
+
+ align:start position:0%
+there's a prover in a
+ 
+
+ align:start position:0%
+there's a prover in a
+verifier the idea is the following the
+
+ align:start position:0%
+verifier the idea is the following the
+ 
+
+ align:start position:0%
+verifier the idea is the following the
+prover will he knows he will first he
+
+ align:start position:0%
+prover will he knows he will first he
+ 
+
+ align:start position:0%
+prover will he knows he will first he
+has a
+
+ align:start position:0%
+has a
+ 
+
+ align:start position:0%
+has a
+g the first thing he's going to permute
+
+ align:start position:0%
+g the first thing he's going to permute
+ 
+
+ align:start position:0%
+g the first thing he's going to permute
+completely permute that the nodes okay
+
+ align:start position:0%
+completely permute that the nodes okay
+ 
+
+ align:start position:0%
+completely permute that the nodes okay
+so he's going to choose a random
+
+ align:start position:0%
+so he's going to choose a random
+ 
+
+ align:start position:0%
+so he's going to choose a random
+permutation Pi let's say n is the number
+
+ align:start position:0%
+permutation Pi let's say n is the number
+ 
+
+ align:start position:0%
+permutation Pi let's say n is the number
+denoted by
+
+ align:start position:0%
+denoted by
+ 
+
+ align:start position:0%
+denoted by
+n the number of vertices in G he's going
+
+ align:start position:0%
+n the number of vertices in G he's going
+ 
+
+ align:start position:0%
+n the number of vertices in G he's going
+to to choose a a random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+permutation of the
+
+ align:start position:0%
+permutation of the
+ 
+
+ align:start position:0%
+permutation of the
+nodes now he has kind of the permuted
+
+ align:start position:0%
+nodes now he has kind of the permuted
+ 
+
+ align:start position:0%
+nodes now he has kind of the permuted
+graph in his head so he has pi of G in
+
+ align:start position:0%
+graph in his head so he has pi of G in
+ 
+
+ align:start position:0%
+graph in his head so he has pi of G in
+his
+
+ align:start position:0%
+his
+ 
+
+ align:start position:0%
+his
+head now this it has this P of G has a
+
+ align:start position:0%
+head now this it has this P of G has a
+ 
+
+ align:start position:0%
+head now this it has this P of G has a
+hamiltonian cycle because G has and I
+
+ align:start position:0%
+hamiltonian cycle because G has and I
+ 
+
+ align:start position:0%
+hamiltonian cycle because G has and I
+just renamed the nodes now I'm going to
+
+ align:start position:0%
+just renamed the nodes now I'm going to
+ 
+
+ align:start position:0%
+just renamed the nodes now I'm going to
+I want to give you I want to give you
+
+ align:start position:0%
+I want to give you I want to give you
+ 
+
+ align:start position:0%
+I want to give you I want to give you
+just this hamiltonian cycle so I want to
+
+ align:start position:0%
+just this hamiltonian cycle so I want to
+ 
+
+ align:start position:0%
+just this hamiltonian cycle so I want to
+give you the nodes here that form
+
+ align:start position:0%
+give you the nodes here that form
+ 
+
+ align:start position:0%
+give you the nodes here that form
+Hamilton so I want to give you H I would
+
+ align:start position:0%
+Hamilton so I want to give you H I would
+ 
+
+ align:start position:0%
+Hamilton so I want to give you H I would
+like to give you the nodes that form the
+
+ align:start position:0%
+like to give you the nodes that form the
+ 
+
+ align:start position:0%
+like to give you the nodes that form the
+ham just the hamiltonian cycle but I
+
+ align:start position:0%
+ham just the hamiltonian cycle but I
+ 
+
+ align:start position:0%
+ham just the hamiltonian cycle but I
+can't give you that will reveal
+
+ align:start position:0%
+can't give you that will reveal
+ 
+
+ align:start position:0%
+can't give you that will reveal
+information okay so I don't want to do
+
+ align:start position:0%
+information okay so I don't want to do
+ 
+
+ align:start position:0%
+information okay so I don't want to do
+that instead I'm going to give it to you
+
+ align:start position:0%
+that instead I'm going to give it to you
+ 
+
+ align:start position:0%
+that instead I'm going to give it to you
+kind of in a safe okay hidden this is
+
+ align:start position:0%
+kind of in a safe okay hidden this is
+ 
+
+ align:start position:0%
+kind of in a safe okay hidden this is
+what called in cryptography call this
+
+ align:start position:0%
+what called in cryptography call this
+ 
+
+ align:start position:0%
+what called in cryptography call this
+commitment scheme so I'm going to give
+
+ align:start position:0%
+commitment scheme so I'm going to give
+ 
+
+ align:start position:0%
+commitment scheme so I'm going to give
+you a
+
+ align:start position:0%
+you a
+ 
+
+ align:start position:0%
+you a
+commitment of the cycle C
+
+ align:start position:0%
+commitment of the cycle C
+ 
+
+ align:start position:0%
+commitment of the cycle C
+so think of this I'm for all the
+
+ align:start position:0%
+so think of this I'm for all the
+ 
+
+ align:start position:0%
+so think of this I'm for all the
+possible edges I'm put 0 0 0 0 only in
+
+ align:start position:0%
+possible edges I'm put 0 0 0 0 only in
+ 
+
+ align:start position:0%
+possible edges I'm put 0 0 0 0 only in
+the cycle I'm going to put one that's
+
+ align:start position:0%
+the cycle I'm going to put one that's
+ 
+
+ align:start position:0%
+the cycle I'm going to put one that's
+what I mean here because this so this is
+
+ align:start position:0%
+what I mean here because this so this is
+ 
+
+ align:start position:0%
+what I mean here because this so this is
+like think of it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix uh of n byn uh
+
+ align:start position:0%
+matrix uh of n byn uh
+ 
+
+ align:start position:0%
+matrix uh of n byn uh
+sorry yeah n
+
+ align:start position:0%
+sorry yeah n
+ 
+
+ align:start position:0%
+sorry yeah n
+byn for any possible Edge for any
+
+ align:start position:0%
+byn for any possible Edge for any
+ 
+
+ align:start position:0%
+byn for any possible Edge for any
+possible node I and J I'm going to put
+
+ align:start position:0%
+possible node I and J I'm going to put
+ 
+
+ align:start position:0%
+possible node I and J I'm going to put
+zero like there's no Edge only if it's
+
+ align:start position:0%
+zero like there's no Edge only if it's
+ 
+
+ align:start position:0%
+zero like there's no Edge only if it's
+in the cycle I'm going to put an edge
+
+ align:start position:0%
+in the cycle I'm going to put an edge
+ 
+
+ align:start position:0%
+in the cycle I'm going to put an edge
+there yeah is on the label of the like
+
+ align:start position:0%
+there yeah is on the label of the like
+ 
+
+ align:start position:0%
+there yeah is on the label of the like
+permuted gra exactly on the permuted
+
+ align:start position:0%
+permuted gra exactly on the permuted
+ 
+
+ align:start position:0%
+permuted gra exactly on the permuted
+graph okay this the reason I permute the
+
+ align:start position:0%
+graph okay this the reason I permute the
+ 
+
+ align:start position:0%
+graph okay this the reason I permute the
+graph is to ensure zero knowledg this
+
+ align:start position:0%
+graph is to ensure zero knowledg this
+ 
+
+ align:start position:0%
+graph is to ensure zero knowledg this
+even though when I send the commitment
+
+ align:start position:0%
+even though when I send the commitment
+ 
+
+ align:start position:0%
+even though when I send the commitment
+really think of it I'm we're going to
+
+ align:start position:0%
+really think of it I'm we're going to
+ 
+
+ align:start position:0%
+really think of it I'm we're going to
+later talk about how to do this
+
+ align:start position:0%
+later talk about how to do this
+ 
+
+ align:start position:0%
+later talk about how to do this
+commitment but for now think of it
+
+ align:start position:0%
+commitment but for now think of it
+ 
+
+ align:start position:0%
+commitment but for now think of it
+there's a safe I'm putting my commitment
+
+ align:start position:0%
+there's a safe I'm putting my commitment
+ 
+
+ align:start position:0%
+there's a safe I'm putting my commitment
+inside the safe I leave the key to
+
+ align:start position:0%
+inside the safe I leave the key to
+ 
+
+ align:start position:0%
+inside the safe I leave the key to
+myself and I give you this box so you
+
+ align:start position:0%
+myself and I give you this box so you
+ 
+
+ align:start position:0%
+myself and I give you this box so you
+learn
+
+ align:start position:0%
+learn
+ 
+
+ align:start position:0%
+learn
+nothing okay so here really you learn
+
+ align:start position:0%
+nothing okay so here really you learn
+ 
+
+ align:start position:0%
+nothing okay so here really you learn
+nothing but now but you but you're not
+
+ align:start position:0%
+nothing but now but you but you're not
+ 
+
+ align:start position:0%
+nothing but now but you but you're not
+convinced either because you just got a
+
+ align:start position:0%
+convinced either because you just got a
+ 
+
+ align:start position:0%
+convinced either because you just got a
+safe what are you going to do with it so
+
+ align:start position:0%
+safe what are you going to do with it so
+ 
+
+ align:start position:0%
+safe what are you going to do with it so
+now here's how I'm going to convince you
+
+ align:start position:0%
+now here's how I'm going to convince you
+ 
+
+ align:start position:0%
+now here's how I'm going to convince you
+that actually this graph is is has a
+
+ align:start position:0%
+that actually this graph is is has a
+ 
+
+ align:start position:0%
+that actually this graph is is has a
+hamiltonian cycle without leaking any
+
+ align:start position:0%
+hamiltonian cycle without leaking any
+ 
+
+ align:start position:0%
+hamiltonian cycle without leaking any
+information so you the verifier you're
+
+ align:start position:0%
+information so you the verifier you're
+ 
+
+ align:start position:0%
+information so you the verifier you're
+going to give me a random bid
+
+ align:start position:0%
+going to give me a random bid
+ 
+
+ align:start position:0%
+going to give me a random bid
+B this is going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+random random bit now
+
+ align:start position:0%
+random random bit now
+ 
+
+ align:start position:0%
+random random bit now
+if B is
+
+ align:start position:0%
+if B is
+ 
+
+ align:start position:0%
+if B is
+zero I'm just going to open this so if B
+
+ align:start position:0%
+zero I'm just going to open this so if B
+ 
+
+ align:start position:0%
+zero I'm just going to open this so if B
+zero if B is zero open I'm going to open
+
+ align:start position:0%
+zero if B is zero open I'm going to open
+ 
+
+ align:start position:0%
+zero if B is zero open I'm going to open
+the safe and now you can see that what's
+
+ align:start position:0%
+the safe and now you can see that what's
+ 
+
+ align:start position:0%
+the safe and now you can see that what's
+sitting there is a hamiltonian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cycle okay now what did you
+
+ align:start position:0%
+cycle okay now what did you
+ 
+
+ align:start position:0%
+cycle okay now what did you
+learn well because I permuted it's just
+
+ align:start position:0%
+learn well because I permuted it's just
+ 
+
+ align:start position:0%
+learn well because I permuted it's just
+a random cycle actually it has nothing
+
+ align:start position:0%
+a random cycle actually it has nothing
+ 
+
+ align:start position:0%
+a random cycle actually it has nothing
+to do with the graph I can even first
+
+ align:start position:0%
+to do with the graph I can even first
+ 
+
+ align:start position:0%
+to do with the graph I can even first
+just choose a random cycle commit to it
+
+ align:start position:0%
+just choose a random cycle commit to it
+ 
+
+ align:start position:0%
+just choose a random cycle commit to it
+and then kind of post kind of choose
+
+ align:start position:0%
+and then kind of post kind of choose
+ 
+
+ align:start position:0%
+and then kind of post kind of choose
+this permutation to align with this uh
+
+ align:start position:0%
+this permutation to align with this uh
+ 
+
+ align:start position:0%
+this permutation to align with this uh
+with this cycle so really because I G I
+
+ align:start position:0%
+with this cycle so really because I G I
+ 
+
+ align:start position:0%
+with this cycle so really because I G I
+chose you a random permutation it's just
+
+ align:start position:0%
+chose you a random permutation it's just
+ 
+
+ align:start position:0%
+chose you a random permutation it's just
+a random cycle so you didn't learn
+
+ align:start position:0%
+a random cycle so you didn't learn
+ 
+
+ align:start position:0%
+a random cycle so you didn't learn
+anything it's just a random cycle you
+
+ align:start position:0%
+anything it's just a random cycle you
+ 
+
+ align:start position:0%
+anything it's just a random cycle you
+and yourself can put a random cycle in a
+
+ align:start position:0%
+and yourself can put a random cycle in a
+ 
+
+ align:start position:0%
+and yourself can put a random cycle in a
+safe so really no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+information what if B equals
+
+ align:start position:0%
+information what if B equals
+ 
+
+ align:start position:0%
+information what if B equals
+1 if B equals 1
+
+ align:start position:0%
+1 if B equals 1
+ 
+
+ align:start position:0%
+1 if B equals 1
+I want to first I want to give you Pi
+
+ align:start position:0%
+I want to first I want to give you Pi
+ 
+
+ align:start position:0%
+I want to first I want to give you Pi
+okay so I give you Pi but now I can't
+
+ align:start position:0%
+okay so I give you Pi but now I can't
+ 
+
+ align:start position:0%
+okay so I give you Pi but now I can't
+open this because now if you know pi and
+
+ align:start position:0%
+open this because now if you know pi and
+ 
+
+ align:start position:0%
+open this because now if you know pi and
+you see the cycle you know where my
+
+ align:start position:0%
+you see the cycle you know where my
+ 
+
+ align:start position:0%
+you see the cycle you know where my
+hamiltonian cycle
+
+ align:start position:0%
+hamiltonian cycle
+ 
+
+ align:start position:0%
+hamiltonian cycle
+is so what I'm going to do I just want
+
+ align:start position:0%
+is so what I'm going to do I just want
+ 
+
+ align:start position:0%
+is so what I'm going to do I just want
+to convince
+
+ align:start position:0%
+to convince
+ 
+
+ align:start position:0%
+to convince
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+that this cycle only
+
+ align:start position:0%
+that this cycle only
+ 
+
+ align:start position:0%
+that this cycle only
+has edges that were in this
+
+ align:start position:0%
+has edges that were in this
+ 
+
+ align:start position:0%
+has edges that were in this
+graph so I'm G to open only the non
+
+ align:start position:0%
+graph so I'm G to open only the non
+ 
+
+ align:start position:0%
+graph so I'm G to open only the non
+edges so instead of opening everything
+
+ align:start position:0%
+edges so instead of opening everything
+ 
+
+ align:start position:0%
+edges so instead of opening everything
+I'm going to
+
+ align:start position:0%
+I'm going to
+ 
+
+ align:start position:0%
+I'm going to
+open non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges
+
+ align:start position:0%
+edges
+ 
+
+ align:start position:0%
+edges
+in the the permuted
+
+ align:start position:0%
+in the the permuted
+ 
+
+ align:start position:0%
+in the the permuted
+graph so note here we have so I have
+
+ align:start position:0%
+graph so note here we have so I have
+ 
+
+ align:start position:0%
+graph so note here we have so I have
+here like okay so there's a question how
+
+ align:start position:0%
+here like okay so there's a question how
+ 
+
+ align:start position:0%
+here like okay so there's a question how
+do I how do I open so think of
+
+ align:start position:0%
+do I how do I open so think of
+ 
+
+ align:start position:0%
+do I how do I open so think of
+it I I commit to N squared bits okay for
+
+ align:start position:0%
+it I I commit to N squared bits okay for
+ 
+
+ align:start position:0%
+it I I commit to N squared bits okay for
+any possible IG I have a bit saying is
+
+ align:start position:0%
+any possible IG I have a bit saying is
+ 
+
+ align:start position:0%
+any possible IG I have a bit saying is
+it zero or is it one is there an edge or
+
+ align:start position:0%
+it zero or is it one is there an edge or
+ 
+
+ align:start position:0%
+it zero or is it one is there an edge or
+is it not an edge think of it as I'm
+
+ align:start position:0%
+is it not an edge think of it as I'm
+ 
+
+ align:start position:0%
+is it not an edge think of it as I'm
+giving you N squared safes okay like now
+
+ align:start position:0%
+giving you N squared safes okay like now
+ 
+
+ align:start position:0%
+giving you N squared safes okay like now
+if B is zero I open all the safes I open
+
+ align:start position:0%
+if B is zero I open all the safes I open
+ 
+
+ align:start position:0%
+if B is zero I open all the safes I open
+all the safes and you see oh there's
+
+ align:start position:0%
+all the safes and you see oh there's
+ 
+
+ align:start position:0%
+all the safes and you see oh there's
+only there's just a cycle you know
+
+ align:start position:0%
+only there's just a cycle you know
+ 
+
+ align:start position:0%
+only there's just a cycle you know
+there's everything is zero except for
+
+ align:start position:0%
+there's everything is zero except for
+ 
+
+ align:start position:0%
+there's everything is zero except for
+you know i1 and I2 are there's one and
+
+ align:start position:0%
+you know i1 and I2 are there's one and
+ 
+
+ align:start position:0%
+you know i1 and I2 are there's one and
+then I2 I3 that's it everything else is
+
+ align:start position:0%
+then I2 I3 that's it everything else is
+ 
+
+ align:start position:0%
+then I2 I3 that's it everything else is
+zero if you send me a one then I open
+
+ align:start position:0%
+zero if you send me a one then I open
+ 
+
+ align:start position:0%
+zero if you send me a one then I open
+something else I don't open everything
+
+ align:start position:0%
+something else I don't open everything
+ 
+
+ align:start position:0%
+something else I don't open everything
+now opposite what I do is I give you
+
+ align:start position:0%
+now opposite what I do is I give you
+ 
+
+ align:start position:0%
+now opposite what I do is I give you
+pi and for every nonedge in pi I open
+
+ align:start position:0%
+pi and for every nonedge in pi I open
+ 
+
+ align:start position:0%
+pi and for every nonedge in pi I open
+the nonedge safe and I show you see
+
+ align:start position:0%
+the nonedge safe and I show you see
+ 
+
+ align:start position:0%
+the nonedge safe and I show you see
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+zero so all the all the safes I opened
+
+ align:start position:0%
+zero so all the all the safes I opened
+ 
+
+ align:start position:0%
+zero so all the all the safes I opened
+are just going to be
+
+ align:start position:0%
+are just going to be
+ 
+
+ align:start position:0%
+are just going to be
+zero so you really didn't learn anything
+
+ align:start position:0%
+zero so you really didn't learn anything
+ 
+
+ align:start position:0%
+zero so you really didn't learn anything
+I just opened zeros you can simulate
+
+ align:start position:0%
+I just opened zeros you can simulate
+ 
+
+ align:start position:0%
+I just opened zeros you can simulate
+that in your head what do you learn in
+
+ align:start position:0%
+that in your head what do you learn in
+ 
+
+ align:start position:0%
+that in your head what do you learn in
+some sense you know if if you you know
+
+ align:start position:0%
+some sense you know if if you you know
+ 
+
+ align:start position:0%
+some sense you know if if you you know
+that if you accept me oh I'm going to
+
+ align:start position:0%
+that if you accept me oh I'm going to
+ 
+
+ align:start position:0%
+that if you accept me oh I'm going to
+open to do zeros
+
+ align:start position:0%
+open to do zeros
+ 
+
+ align:start position:0%
+open to do zeros
+there and the pi doesn't reveal anything
+
+ align:start position:0%
+there and the pi doesn't reveal anything
+ 
+
+ align:start position:0%
+there and the pi doesn't reveal anything
+it's just random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+permutation so note you the verifier
+
+ align:start position:0%
+permutation so note you the verifier
+ 
+
+ align:start position:0%
+permutation so note you the verifier
+didn't learn anything if you open to
+
+ align:start position:0%
+didn't learn anything if you open to
+ 
+
+ align:start position:0%
+didn't learn anything if you open to
+zero if you send me zero I just open
+
+ align:start position:0%
+zero if you send me zero I just open
+ 
+
+ align:start position:0%
+zero if you send me zero I just open
+random cycle has nothing to do with the
+
+ align:start position:0%
+random cycle has nothing to do with the
+ 
+
+ align:start position:0%
+random cycle has nothing to do with the
+graph nothing just random cycle okay
+
+ align:start position:0%
+graph nothing just random cycle okay
+ 
+
+ align:start position:0%
+graph nothing just random cycle okay
+that doesn't get that that's not helpful
+
+ align:start position:0%
+that doesn't get that that's not helpful
+ 
+
+ align:start position:0%
+that doesn't get that that's not helpful
+for you if you open one I gave you
+
+ align:start position:0%
+for you if you open one I gave you
+ 
+
+ align:start position:0%
+for you if you open one I gave you
+completely random permutation
+
+ align:start position:0%
+completely random permutation
+ 
+
+ align:start position:0%
+completely random permutation
+you know p on your own and I open to
+
+ align:start position:0%
+you know p on your own and I open to
+ 
+
+ align:start position:0%
+you know p on your own and I open to
+zeros all the n edes i open to zero you
+
+ align:start position:0%
+zeros all the n edes i open to zero you
+ 
+
+ align:start position:0%
+zeros all the n edes i open to zero you
+learn
+
+ align:start position:0%
+learn
+ 
+
+ align:start position:0%
+learn
+nothing
+
+ align:start position:0%
+nothing
+ 
+
+ align:start position:0%
+nothing
+still you are somewhat
+
+ align:start position:0%
+still you are somewhat
+ 
+
+ align:start position:0%
+still you are somewhat
+convinced that this protocol that that
+
+ align:start position:0%
+convinced that this protocol that that
+ 
+
+ align:start position:0%
+convinced that this protocol that that
+the graph is hamiltonian why are you
+
+ align:start position:0%
+the graph is hamiltonian why are you
+ 
+
+ align:start position:0%
+the graph is hamiltonian why are you
+somewhat convinced that the that there's
+
+ align:start position:0%
+somewhat convinced that the that there's
+ 
+
+ align:start position:0%
+somewhat convinced that the that there's
+a hamiltonian cycle why are you someone
+
+ align:start position:0%
+a hamiltonian cycle why are you someone
+ 
+
+ align:start position:0%
+a hamiltonian cycle why are you someone
+convinced because if there is no
+
+ align:start position:0%
+convinced because if there is no
+ 
+
+ align:start position:0%
+convinced because if there is no
+hamiltonian cycle in G I cannot open to
+
+ align:start position:0%
+hamiltonian cycle in G I cannot open to
+ 
+
+ align:start position:0%
+hamiltonian cycle in G I cannot open to
+both zero and
+
+ align:start position:0%
+both zero and
+ 
+
+ align:start position:0%
+both zero and
+one why why is it the case that I cannot
+
+ align:start position:0%
+one why why is it the case that I cannot
+ 
+
+ align:start position:0%
+one why why is it the case that I cannot
+open let's
+
+ align:start position:0%
+open let's
+ 
+
+ align:start position:0%
+open let's
+see I'm a cheating let's say the graph
+
+ align:start position:0%
+see I'm a cheating let's say the graph
+ 
+
+ align:start position:0%
+see I'm a cheating let's say the graph
+is there's no hamiltonian
+
+ align:start position:0%
+is there's no hamiltonian
+ 
+
+ align:start position:0%
+is there's no hamiltonian
+cycle now I sent you these N squared
+
+ align:start position:0%
+cycle now I sent you these N squared
+ 
+
+ align:start position:0%
+cycle now I sent you these N squared
+safes case one there's indeed only a
+
+ align:start position:0%
+safes case one there's indeed only a
+ 
+
+ align:start position:0%
+safes case one there's indeed only a
+hamiltonian cycle there like indeed when
+
+ align:start position:0%
+hamiltonian cycle there like indeed when
+ 
+
+ align:start position:0%
+hamiltonian cycle there like indeed when
+you open all these end saves what you
+
+ align:start position:0%
+you open all these end saves what you
+ 
+
+ align:start position:0%
+you open all these end saves what you
+see is everything is zero except for
+
+ align:start position:0%
+see is everything is zero except for
+ 
+
+ align:start position:0%
+see is everything is zero except for
+hamiltonian cycle
+
+ align:start position:0%
+hamiltonian cycle
+ 
+
+ align:start position:0%
+hamiltonian cycle
+if that's not the case I cannot open to
+
+ align:start position:0%
+if that's not the case I cannot open to
+ 
+
+ align:start position:0%
+if that's not the case I cannot open to
+zero if I open to zero you catch
+
+ align:start position:0%
+zero if I open to zero you catch
+ 
+
+ align:start position:0%
+zero if I open to zero you catch
+me now suppose I did succeed in opening
+
+ align:start position:0%
+me now suppose I did succeed in opening
+ 
+
+ align:start position:0%
+me now suppose I did succeed in opening
+to zero namely there's just aonian cycle
+
+ align:start position:0%
+to zero namely there's just aonian cycle
+ 
+
+ align:start position:0%
+to zero namely there's just aonian cycle
+there that's
+
+ align:start position:0%
+there that's
+ 
+
+ align:start position:0%
+there that's
+it then I claim there's no way I can
+
+ align:start position:0%
+it then I claim there's no way I can
+ 
+
+ align:start position:0%
+it then I claim there's no way I can
+open to one why if there is a
+
+ align:start position:0%
+open to one why if there is a
+ 
+
+ align:start position:0%
+open to one why if there is a
+hamiltonian cycle there I know the
+
+ align:start position:0%
+hamiltonian cycle there I know the
+ 
+
+ align:start position:0%
+hamiltonian cycle there I know the
+hamiltonian cycle is not on the
+
+ align:start position:0%
+hamiltonian cycle is not on the
+ 
+
+ align:start position:0%
+hamiltonian cycle is not on the
+non-edges because the non-edges are zero
+
+ align:start position:0%
+non-edges because the non-edges are zero
+ 
+
+ align:start position:0%
+non-edges because the non-edges are zero
+if I open on one the non-edges are zero
+
+ align:start position:0%
+if I open on one the non-edges are zero
+ 
+
+ align:start position:0%
+if I open on one the non-edges are zero
+so Theon CLE is on the edges but there
+
+ align:start position:0%
+so Theon CLE is on the edges but there
+ 
+
+ align:start position:0%
+so Theon CLE is on the edges but there
+is noonian cycle it can be on the
+
+ align:start position:0%
+is noonian cycle it can be on the
+ 
+
+ align:start position:0%
+is noonian cycle it can be on the
+edges so either I'm a chover either I
+
+ align:start position:0%
+edges so either I'm a chover either I
+ 
+
+ align:start position:0%
+edges so either I'm a chover either I
+can I I may be able to open to zero I
+
+ align:start position:0%
+can I I may be able to open to zero I
+ 
+
+ align:start position:0%
+can I I may be able to open to zero I
+may be able to open to one but I can't
+
+ align:start position:0%
+may be able to open to one but I can't
+ 
+
+ align:start position:0%
+may be able to open to one but I can't
+open to
+
+ align:start position:0%
+open to
+ 
+
+ align:start position:0%
+open to
+both so with probability half you'll
+
+ align:start position:0%
+both so with probability half you'll
+ 
+
+ align:start position:0%
+both so with probability half you'll
+reject
+
+ align:start position:0%
+reject
+ 
+
+ align:start position:0%
+reject
+me half is not that great but it's
+
+ align:start position:0%
+me half is not that great but it's
+ 
+
+ align:start position:0%
+me half is not that great but it's
+something okay so at least now we know
+
+ align:start position:0%
+something okay so at least now we know
+ 
+
+ align:start position:0%
+something okay so at least now we know
+with probability half I'm going to be
+
+ align:start position:0%
+with probability half I'm going to be
+ 
+
+ align:start position:0%
+with probability half I'm going to be
+rejected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you like The
+
+ align:start position:0%
+okay you like The
+ 
+
+ align:start position:0%
+okay you like The
+Detour okay let's go back to the random
+
+ align:start position:0%
+Detour okay let's go back to the random
+ 
+
+ align:start position:0%
+Detour okay let's go back to the random
+or but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I so what no what I commit to is
+
+ align:start position:0%
+yeah I so what no what I commit to is
+ 
+
+ align:start position:0%
+yeah I so what no what I commit to is
+actually I have N squared commitments
+
+ align:start position:0%
+actually I have N squared commitments
+ 
+
+ align:start position:0%
+actually I have N squared commitments
+everything is zero except for a random
+
+ align:start position:0%
+everything is zero except for a random
+ 
+
+ align:start position:0%
+everything is zero except for a random
+cycle I don't I only commit to zeros why
+
+ align:start position:0%
+cycle I don't I only commit to zeros why
+ 
+
+ align:start position:0%
+cycle I don't I only commit to zeros why
+is it important that I only commit to
+
+ align:start position:0%
+is it important that I only commit to
+ 
+
+ align:start position:0%
+is it important that I only commit to
+zeros because
+
+ align:start position:0%
+zeros because
+ 
+
+ align:start position:0%
+zeros because
+when I open okay I want to make sure
+
+ align:start position:0%
+when I open okay I want to make sure
+ 
+
+ align:start position:0%
+when I open okay I want to make sure
+that there's a cycle
+
+ align:start position:0%
+that there's a cycle
+ 
+
+ align:start position:0%
+that there's a cycle
+here but when I open to one I don't want
+
+ align:start position:0%
+here but when I open to one I don't want
+ 
+
+ align:start position:0%
+here but when I open to one I don't want
+to reveal anything and the way I don't
+
+ align:start position:0%
+to reveal anything and the way I don't
+ 
+
+ align:start position:0%
+to reveal anything and the way I don't
+reveal anything is I show that all the
+
+ align:start position:0%
+reveal anything is I show that all the
+ 
+
+ align:start position:0%
+reveal anything is I show that all the
+non edges in pi in pi of G if you open
+
+ align:start position:0%
+non edges in pi in pi of G if you open
+ 
+
+ align:start position:0%
+non edges in pi in pi of G if you open
+them here you'll get a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero just with the cyle like outline
+
+ align:start position:0%
+zero just with the cyle like outline
+ 
+
+ align:start position:0%
+zero just with the cyle like outline
+exactly exactly what I commit is a
+
+ align:start position:0%
+exactly exactly what I commit is a
+ 
+
+ align:start position:0%
+exactly exactly what I commit is a
+matrix what I commit to is like a matrix
+
+ align:start position:0%
+matrix what I commit to is like a matrix
+ 
+
+ align:start position:0%
+matrix what I commit to is like a matrix
+that only has like a hamiltonian cycle
+
+ align:start position:0%
+that only has like a hamiltonian cycle
+ 
+
+ align:start position:0%
+that only has like a hamiltonian cycle
+and that's it everything else is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero yeah so in the second case the
+
+ align:start position:0%
+zero yeah so in the second case the
+ 
+
+ align:start position:0%
+zero yeah so in the second case the
+verifi cannot use the permutation to
+
+ align:start position:0%
+verifi cannot use the permutation to
+ 
+
+ align:start position:0%
+verifi cannot use the permutation to
+figure out what edges are not in the hon
+
+ align:start position:0%
+figure out what edges are not in the hon
+ 
+
+ align:start position:0%
+figure out what edges are not in the hon
+ccle for the original right so in the in
+
+ align:start position:0%
+ccle for the original right so in the in
+ 
+
+ align:start position:0%
+ccle for the original right so in the in
+in the b equals one case you're talking
+
+ align:start position:0%
+in the b equals one case you're talking
+ 
+
+ align:start position:0%
+in the b equals one case you're talking
+about yeah in the b equals one case the
+
+ align:start position:0%
+about yeah in the b equals one case the
+ 
+
+ align:start position:0%
+about yeah in the b equals one case the
+verifier what does he learn he learns Pi
+
+ align:start position:0%
+verifier what does he learn he learns Pi
+ 
+
+ align:start position:0%
+verifier what does he learn he learns Pi
+the permutation that's just a random
+
+ align:start position:0%
+the permutation that's just a random
+ 
+
+ align:start position:0%
+the permutation that's just a random
+permutation
+
+ align:start position:0%
+permutation
+ 
+
+ align:start position:0%
+permutation
+and then I'm just telling you I'm
+
+ align:start position:0%
+and then I'm just telling you I'm
+ 
+
+ align:start position:0%
+and then I'm just telling you I'm
+reassuring you that I didn't lie what do
+
+ align:start position:0%
+reassuring you that I didn't lie what do
+ 
+
+ align:start position:0%
+reassuring you that I didn't lie what do
+I mean by reassure you I open everybody
+
+ align:start position:0%
+I mean by reassure you I open everybody
+ 
+
+ align:start position:0%
+I mean by reassure you I open everybody
+you can compute Pi G on your own that's
+
+ align:start position:0%
+you can compute Pi G on your own that's
+ 
+
+ align:start position:0%
+you can compute Pi G on your own that's
+not a secret G's given Pi is given you
+
+ align:start position:0%
+not a secret G's given Pi is given you
+ 
+
+ align:start position:0%
+not a secret G's given Pi is given you
+can Pi G you see all the non edges
+
+ align:start position:0%
+can Pi G you see all the non edges
+ 
+
+ align:start position:0%
+can Pi G you see all the non edges
+that's not a that's not and all the N
+
+ align:start position:0%
+that's not a that's not and all the N
+ 
+
+ align:start position:0%
+that's not a that's not and all the N
+edges I'm going to open only the N edges
+
+ align:start position:0%
+edges I'm going to open only the N edges
+ 
+
+ align:start position:0%
+edges I'm going to open only the N edges
+and show you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zeros okay because the point is if I was
+
+ align:start position:0%
+zeros okay because the point is if I was
+ 
+
+ align:start position:0%
+zeros okay because the point is if I was
+honest what I should do is put on only
+
+ align:start position:0%
+honest what I should do is put on only
+ 
+
+ align:start position:0%
+honest what I should do is put on only
+on edges and not only on edges only on
+
+ align:start position:0%
+on edges and not only on edges only on
+ 
+
+ align:start position:0%
+on edges and not only on edges only on
+hamiltonian and the edes that former
+
+ align:start position:0%
+hamiltonian and the edes that former
+ 
+
+ align:start position:0%
+hamiltonian and the edes that former
+hamiltonian cycle that's what I should
+
+ align:start position:0%
+hamiltonian cycle that's what I should
+ 
+
+ align:start position:0%
+hamiltonian cycle that's what I should
+do if I'm honest and what I show you I
+
+ align:start position:0%
+do if I'm honest and what I show you I
+ 
+
+ align:start position:0%
+do if I'm honest and what I show you I
+don't show you that because that will
+
+ align:start position:0%
+don't show you that because that will
+ 
+
+ align:start position:0%
+don't show you that because that will
+give information but at least what I
+
+ align:start position:0%
+give information but at least what I
+ 
+
+ align:start position:0%
+give information but at least what I
+show you then all the non-edges here I
+
+ align:start position:0%
+show you then all the non-edges here I
+ 
+
+ align:start position:0%
+show you then all the non-edges here I
+committed to
+
+ align:start position:0%
+committed to
+ 
+
+ align:start position:0%
+committed to
+zero and that gives you no
+
+ align:start position:0%
+zero and that gives you no
+ 
+
+ align:start position:0%
+zero and that gives you no
+information but if indeed I the
+
+ align:start position:0%
+information but if indeed I the
+ 
+
+ align:start position:0%
+information but if indeed I the
+non-edges are zero and there's
+
+ align:start position:0%
+non-edges are zero and there's
+ 
+
+ align:start position:0%
+non-edges are zero and there's
+hamiltonian cycle then it means Honan
+
+ align:start position:0%
+hamiltonian cycle then it means Honan
+ 
+
+ align:start position:0%
+hamiltonian cycle then it means Honan
+must must be edges and then it means
+
+ align:start position:0%
+must must be edges and then it means
+ 
+
+ align:start position:0%
+must must be edges and then it means
+that P G has a hon cycle and that can't
+
+ align:start position:0%
+that P G has a hon cycle and that can't
+ 
+
+ align:start position:0%
+that P G has a hon cycle and that can't
+be if G doesn't have a hilon cycle 5G
+
+ align:start position:0%
+be if G doesn't have a hilon cycle 5G
+ 
+
+ align:start position:0%
+be if G doesn't have a hilon cycle 5G
+doesn't have a honi cycle and that's why
+
+ align:start position:0%
+doesn't have a honi cycle and that's why
+ 
+
+ align:start position:0%
+doesn't have a honi cycle and that's why
+I can't succeed in convincing
+
+ align:start position:0%
+I can't succeed in convincing
+ 
+
+ align:start position:0%
+I can't succeed in convincing
+you in answering both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions yeah is there a formal way to
+
+ align:start position:0%
+questions yeah is there a formal way to
+ 
+
+ align:start position:0%
+questions yeah is there a formal way to
+say what it means to be zero knowledge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like good good good good good so the
+
+ align:start position:0%
+like good good good good good so the
+ 
+
+ align:start position:0%
+like good good good good good so the
+question yeah actually I plan not to go
+
+ align:start position:0%
+question yeah actually I plan not to go
+ 
+
+ align:start position:0%
+question yeah actually I plan not to go
+into the the but it's so beautiful so I
+
+ align:start position:0%
+into the the but it's so beautiful so I
+ 
+
+ align:start position:0%
+into the the but it's so beautiful so I
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+a yeah so the question was uh what is
+
+ align:start position:0%
+a yeah so the question was uh what is
+ 
+
+ align:start position:0%
+a yeah so the question was uh what is
+the definition actually of zero
+
+ align:start position:0%
+the definition actually of zero
+ 
+
+ align:start position:0%
+the definition actually of zero
+knowledge and the definition of zero
+
+ align:start position:0%
+knowledge and the definition of zero
+ 
+
+ align:start position:0%
+knowledge and the definition of zero
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+says that what does it mean you don't
+
+ align:start position:0%
+says that what does it mean you don't
+ 
+
+ align:start position:0%
+says that what does it mean you don't
+learn anything so the definition says
+
+ align:start position:0%
+learn anything so the definition says
+ 
+
+ align:start position:0%
+learn anything so the definition says
+that so this is the definition of zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knowledge what it says
+
+ align:start position:0%
+knowledge what it says
+ 
+
+ align:start position:0%
+knowledge what it says
+is the verifier actually it's it says
+
+ align:start position:0%
+is the verifier actually it's it says
+ 
+
+ align:start position:0%
+is the verifier actually it's it says
+it's stronger it says for every verifier
+
+ align:start position:0%
+it's stronger it says for every verifier
+ 
+
+ align:start position:0%
+it's stronger it says for every verifier
+not just the honest verifier even
+
+ align:start position:0%
+not just the honest verifier even
+ 
+
+ align:start position:0%
+not just the honest verifier even
+malicious ver there's you can talk about
+
+ align:start position:0%
+malicious ver there's you can talk about
+ 
+
+ align:start position:0%
+malicious ver there's you can talk about
+honest verifier you an object the honest
+
+ align:start position:0%
+honest verifier you an object the honest
+ 
+
+ align:start position:0%
+honest verifier you an object the honest
+verifier who just does what it should do
+
+ align:start position:0%
+verifier who just does what it should do
+ 
+
+ align:start position:0%
+verifier who just does what it should do
+and just listens doesn't learn anything
+
+ align:start position:0%
+and just listens doesn't learn anything
+ 
+
+ align:start position:0%
+and just listens doesn't learn anything
+but actually there's a stronger notion
+
+ align:start position:0%
+but actually there's a stronger notion
+ 
+
+ align:start position:0%
+but actually there's a stronger notion
+of malicious so I say even for malicious
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+verifier you want to say what he learned
+
+ align:start position:0%
+verifier you want to say what he learned
+ 
+
+ align:start position:0%
+verifier you want to say what he learned
+he could have simulated on his
+
+ align:start position:0%
+he could have simulated on his
+ 
+
+ align:start position:0%
+he could have simulated on his
+own so the definition says for every uh
+
+ align:start position:0%
+own so the definition says for every uh
+ 
+
+ align:start position:0%
+own so the definition says for every uh
+so you okay for every verifier if you
+
+ align:start position:0%
+so you okay for every verifier if you
+ 
+
+ align:start position:0%
+so you okay for every verifier if you
+look the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transcript of and and for every X and
+
+ align:start position:0%
+transcript of and and for every X and
+ 
+
+ align:start position:0%
+transcript of and and for every X and
+L for every X if you look at the
+
+ align:start position:0%
+L for every X if you look at the
+ 
+
+ align:start position:0%
+L for every X if you look at the
+transcript between the honest prover and
+
+ align:start position:0%
+transcript between the honest prover and
+ 
+
+ align:start position:0%
+transcript between the honest prover and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+verifier the prover has a witness but
+
+ align:start position:0%
+verifier the prover has a witness but
+ 
+
+ align:start position:0%
+verifier the prover has a witness but
+the verifier
+
+ align:start position:0%
+the verifier
+ 
+
+ align:start position:0%
+the verifier
+doesn't what he learned from this
+
+ align:start position:0%
+doesn't what he learned from this
+ 
+
+ align:start position:0%
+doesn't what he learned from this
+transcript or what the verify maybe
+
+ align:start position:0%
+transcript or what the verify maybe
+ 
+
+ align:start position:0%
+transcript or what the verify maybe
+sorry let me write it differently let me
+
+ align:start position:0%
+sorry let me write it differently let me
+ 
+
+ align:start position:0%
+sorry let me write it differently let me
+say The View
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of V Star while interacting with
+
+ align:start position:0%
+of V Star while interacting with
+ 
+
+ align:start position:0%
+of V Star while interacting with
+P an input
+
+ align:start position:0%
+P an input
+ 
+
+ align:start position:0%
+P an input
+X so whatever varar
+
+ align:start position:0%
+X so whatever varar
+ 
+
+ align:start position:0%
+X so whatever varar
+learned he could have simulated on his
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+own so it says there
+
+ align:start position:0%
+own so it says there
+ 
+
+ align:start position:0%
+own so it says there
+exists a
+
+ align:start position:0%
+exists a
+ 
+
+ align:start position:0%
+exists a
+simulator and this is efficient and
+
+ align:start position:0%
+simulator and this is efficient and
+ 
+
+ align:start position:0%
+simulator and this is efficient and
+efficient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simulator such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the simulator efficiently can
+
+ align:start position:0%
+that the simulator efficiently can
+ 
+
+ align:start position:0%
+that the simulator efficiently can
+generate this transcript on his
+
+ align:start position:0%
+generate this transcript on his
+ 
+
+ align:start position:0%
+generate this transcript on his
+own if he has v he needs varar because
+
+ align:start position:0%
+own if he has v he needs varar because
+ 
+
+ align:start position:0%
+own if he has v he needs varar because
+of course varar depends what he sends
+
+ align:start position:0%
+of course varar depends what he sends
+ 
+
+ align:start position:0%
+of course varar depends what he sends
+and so on but he could generate it on
+
+ align:start position:0%
+and so on but he could generate it on
+ 
+
+ align:start position:0%
+and so on but he could generate it on
+his
+
+ align:start position:0%
+his
+ 
+
+ align:start position:0%
+his
+own
+
+ align:start position:0%
+own
+ 
+
+ align:start position:0%
+own
+yeah on
+
+ align:start position:0%
+yeah on
+ 
+
+ align:start position:0%
+yeah on
+than is it the same SIM for every oh my
+
+ align:start position:0%
+than is it the same SIM for every oh my
+ 
+
+ align:start position:0%
+than is it the same SIM for every oh my
+God there's so many okay there's so so
+
+ align:start position:0%
+God there's so many okay there's so so
+ 
+
+ align:start position:0%
+God there's so many okay there's so so
+many Notions of zero knowledge so for
+
+ align:start position:0%
+many Notions of zero knowledge so for
+ 
+
+ align:start position:0%
+many Notions of zero knowledge so for
+example first of all it I'll answer your
+
+ align:start position:0%
+example first of all it I'll answer your
+ 
+
+ align:start position:0%
+example first of all it I'll answer your
+question the question was is the
+
+ align:start position:0%
+question the question was is the
+ 
+
+ align:start position:0%
+question the question was is the
+simulator only gets V Star as Oracle AIS
+
+ align:start position:0%
+simulator only gets V Star as Oracle AIS
+ 
+
+ align:start position:0%
+simulator only gets V Star as Oracle AIS
+does it get as an input is it Universal
+
+ align:start position:0%
+does it get as an input is it Universal
+ 
+
+ align:start position:0%
+does it get as an input is it Universal
+is it for there exist for every V is it
+
+ align:start position:0%
+is it for there exist for every V is it
+ 
+
+ align:start position:0%
+is it for there exist for every V is it
+for every V there's a simulator moreover
+
+ align:start position:0%
+for every V there's a simulator moreover
+ 
+
+ align:start position:0%
+for every V there's a simulator moreover
+let me continue is V all powerful is V
+
+ align:start position:0%
+let me continue is V all powerful is V
+ 
+
+ align:start position:0%
+let me continue is V all powerful is V
+supposed to be PPT or poly siiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the answers there's many definitions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but yeah so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um originally all the protocols we had
+
+ align:start position:0%
+um originally all the protocols we had
+ 
+
+ align:start position:0%
+um originally all the protocols we had
+used the verifiers of
+
+ align:start position:0%
+used the verifiers of
+ 
+
+ align:start position:0%
+used the verifiers of
+blackbox uh however in 2001 I think was
+
+ align:start position:0%
+blackbox uh however in 2001 I think was
+ 
+
+ align:start position:0%
+blackbox uh however in 2001 I think was
+it h BOS Barak was the first kind of
+
+ align:start position:0%
+it h BOS Barak was the first kind of
+ 
+
+ align:start position:0%
+it h BOS Barak was the first kind of
+construct non blackbox Z knowledge where
+
+ align:start position:0%
+construct non blackbox Z knowledge where
+ 
+
+ align:start position:0%
+construct non blackbox Z knowledge where
+the simulator used verifire as a non
+
+ align:start position:0%
+the simulator used verifire as a non
+ 
+
+ align:start position:0%
+the simulator used verifire as a non
+blackbox and it was a really
+
+ align:start position:0%
+blackbox and it was a really
+ 
+
+ align:start position:0%
+blackbox and it was a really
+breakthrough result because what he
+
+ align:start position:0%
+breakthrough result because what he
+ 
+
+ align:start position:0%
+breakthrough result because what he
+managed to to get is a new Zer knowledge
+
+ align:start position:0%
+managed to to get is a new Zer knowledge
+ 
+
+ align:start position:0%
+managed to to get is a new Zer knowledge
+proof that we didn't know of before it
+
+ align:start position:0%
+proof that we didn't know of before it
+ 
+
+ align:start position:0%
+proof that we didn't know of before it
+was kind of constant round now you you
+
+ align:start position:0%
+was kind of constant round now you you
+ 
+
+ align:start position:0%
+was kind of constant round now you you
+can say wait this is also constant round
+
+ align:start position:0%
+can say wait this is also constant round
+ 
+
+ align:start position:0%
+can say wait this is also constant round
+what do you mean we didn't know before
+
+ align:start position:0%
+what do you mean we didn't know before
+ 
+
+ align:start position:0%
+what do you mean we didn't know before
+but this is only sound as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half turns out if you want NE sound this
+
+ align:start position:0%
+half turns out if you want NE sound this
+ 
+
+ align:start position:0%
+half turns out if you want NE sound this
+you need to repeat this protocol
+
+ align:start position:0%
+you need to repeat this protocol
+ 
+
+ align:start position:0%
+you need to repeat this protocol
+sequentially you can if you repeat it in
+
+ align:start position:0%
+sequentially you can if you repeat it in
+ 
+
+ align:start position:0%
+sequentially you can if you repeat it in
+parallel
+
+ align:start position:0%
+parallel
+ 
+
+ align:start position:0%
+parallel
+it's it's not necessarily zero knowledge
+
+ align:start position:0%
+it's it's not necessarily zero knowledge
+ 
+
+ align:start position:0%
+it's it's not necessarily zero knowledge
+actually yeah this one actually is not
+
+ align:start position:0%
+actually yeah this one actually is not
+ 
+
+ align:start position:0%
+actually yeah this one actually is not
+zero knowledge if you're you're
+
+ align:start position:0%
+zero knowledge if you're you're
+ 
+
+ align:start position:0%
+zero knowledge if you're you're
+repeating in parallel we we'll talk
+
+ align:start position:0%
+repeating in parallel we we'll talk
+ 
+
+ align:start position:0%
+repeating in parallel we we'll talk
+about that and so using non blackbox
+
+ align:start position:0%
+about that and so using non blackbox
+ 
+
+ align:start position:0%
+about that and so using non blackbox
+technique he managed to show the first
+
+ align:start position:0%
+technique he managed to show the first
+ 
+
+ align:start position:0%
+technique he managed to show the first
+kind of Conant round zero knowledge
+
+ align:start position:0%
+kind of Conant round zero knowledge
+ 
+
+ align:start position:0%
+kind of Conant round zero knowledge
+public coin zero knowledge proof so
+
+ align:start position:0%
+public coin zero knowledge proof so
+ 
+
+ align:start position:0%
+public coin zero knowledge proof so
+there's there's many many variants okay
+
+ align:start position:0%
+there's there's many many variants okay
+ 
+
+ align:start position:0%
+there's there's many many variants okay
+is is the
+
+ align:start position:0%
+is is the
+ 
+
+ align:start position:0%
+is is the
+a the the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point okay but this is kind of a common
+
+ align:start position:0%
+point okay but this is kind of a common
+ 
+
+ align:start position:0%
+point okay but this is kind of a common
+variant to think
+
+ align:start position:0%
+variant to think
+ 
+
+ align:start position:0%
+variant to think
+about and also um so this is kind of
+
+ align:start position:0%
+about and also um so this is kind of
+ 
+
+ align:start position:0%
+about and also um so this is kind of
+poly size or or V can have auxiliary
+
+ align:start position:0%
+poly size or or V can have auxiliary
+ 
+
+ align:start position:0%
+poly size or or V can have auxiliary
+input so for every X and A or V Star is
+
+ align:start position:0%
+input so for every X and A or V Star is
+ 
+
+ align:start position:0%
+input so for every X and A or V Star is
+poly size so we can have like auxilary
+
+ align:start position:0%
+poly size so we can have like auxilary
+ 
+
+ align:start position:0%
+poly size so we can have like auxilary
+information about X even if he has ail
+
+ align:start position:0%
+information about X even if he has ail
+ 
+
+ align:start position:0%
+information about X even if he has ail
+information about X still so V Star is
+
+ align:start position:0%
+information about X still so V Star is
+ 
+
+ align:start position:0%
+information about X still so V Star is
+kind of has may have ex information
+
+ align:start position:0%
+kind of has may have ex information
+ 
+
+ align:start position:0%
+kind of has may have ex information
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+X still the two are
+
+ align:start position:0%
+X still the two are
+ 
+
+ align:start position:0%
+X still the two are
+indistinguishable
+
+ align:start position:0%
+indistinguishable
+ 
+
+ align:start position:0%
+indistinguishable
+yeah what if
+
+ align:start position:0%
+yeah what if
+ 
+
+ align:start position:0%
+yeah what if
+the follow with
+
+ align:start position:0%
+the follow with
+ 
+
+ align:start position:0%
+the follow with
+commitment where he create that matrices
+
+ align:start position:0%
+commitment where he create that matrices
+ 
+
+ align:start position:0%
+commitment where he create that matrices
+that cycle in that matri Comm that wait
+
+ align:start position:0%
+that cycle in that matri Comm that wait
+ 
+
+ align:start position:0%
+that cycle in that matri Comm that wait
+again what if the commit approver
+
+ align:start position:0%
+again what if the commit approver
+ 
+
+ align:start position:0%
+again what if the commit approver
+commits to a cycle or no he commits to a
+
+ align:start position:0%
+commits to a cycle or no he commits to a
+ 
+
+ align:start position:0%
+commits to a cycle or no he commits to a
+cycle but the cycle is not necessarily
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it has nothing to do with G just commits
+
+ align:start position:0%
+it has nothing to do with G just commits
+ 
+
+ align:start position:0%
+it has nothing to do with G just commits
+to any cycle he to CC that then able
+
+ align:start position:0%
+to any cycle he to CC that then able
+ 
+
+ align:start position:0%
+to any cycle he to CC that then able
+to it's zero right yeah he'll be able to
+
+ align:start position:0%
+to it's zero right yeah he'll be able to
+ 
+
+ align:start position:0%
+to it's zero right yeah he'll be able to
+exactly he'll be able to answer zero but
+
+ align:start position:0%
+exactly he'll be able to answer zero but
+ 
+
+ align:start position:0%
+exactly he'll be able to answer zero but
+he won't be able to answer
+
+ align:start position:0%
+he won't be able to answer
+ 
+
+ align:start position:0%
+he won't be able to answer
+one because that cycle must touch an
+
+ align:start position:0%
+one because that cycle must touch an
+ 
+
+ align:start position:0%
+one because that cycle must touch an
+edge
+
+ align:start position:0%
+edge
+ 
+
+ align:start position:0%
+edge
+because sorry that cycle must touch a
+
+ align:start position:0%
+because sorry that cycle must touch a
+ 
+
+ align:start position:0%
+because sorry that cycle must touch a
+non-edge because if it only touched
+
+ align:start position:0%
+non-edge because if it only touched
+ 
+
+ align:start position:0%
+non-edge because if it only touched
+edges
+
+ align:start position:0%
+edges
+ 
+
+ align:start position:0%
+edges
+there is no cycle so that cycle you give
+
+ align:start position:0%
+there is no cycle so that cycle you give
+ 
+
+ align:start position:0%
+there is no cycle so that cycle you give
+here Pi now the prover can the cheating
+
+ align:start position:0%
+here Pi now the prover can the cheating
+ 
+
+ align:start position:0%
+here Pi now the prover can the cheating
+prover can give whatever Pi he wants but
+
+ align:start position:0%
+prover can give whatever Pi he wants but
+ 
+
+ align:start position:0%
+prover can give whatever Pi he wants but
+the point is that the graph the permuted
+
+ align:start position:0%
+the point is that the graph the permuted
+ 
+
+ align:start position:0%
+the point is that the graph the permuted
+graph doesn't have a hamiltonian cycle
+
+ align:start position:0%
+graph doesn't have a hamiltonian cycle
+ 
+
+ align:start position:0%
+graph doesn't have a hamiltonian cycle
+because if G doesn't have a hamiltonian
+
+ align:start position:0%
+because if G doesn't have a hamiltonian
+ 
+
+ align:start position:0%
+because if G doesn't have a hamiltonian
+cyle the permuted G also doesn't have a
+
+ align:start position:0%
+cyle the permuted G also doesn't have a
+ 
+
+ align:start position:0%
+cyle the permuted G also doesn't have a
+hamiltonian cycle so this graph doesn't
+
+ align:start position:0%
+hamiltonian cycle so this graph doesn't
+ 
+
+ align:start position:0%
+hamiltonian cycle so this graph doesn't
+have a hamiltonian cycle and that means
+
+ align:start position:0%
+have a hamiltonian cycle and that means
+ 
+
+ align:start position:0%
+have a hamiltonian cycle and that means
+that the cycle that's here I don't care
+
+ align:start position:0%
+that the cycle that's here I don't care
+ 
+
+ align:start position:0%
+that the cycle that's here I don't care
+how you generate whatever the cycle was
+
+ align:start position:0%
+how you generate whatever the cycle was
+ 
+
+ align:start position:0%
+how you generate whatever the cycle was
+it must touch such a non
+
+ align:start position:0%
+it must touch such a non
+ 
+
+ align:start position:0%
+it must touch such a non
+Edge so so the hamiltonan CLE says you
+
+ align:start position:0%
+Edge so so the hamiltonan CLE says you
+ 
+
+ align:start position:0%
+Edge so so the hamiltonan CLE says you
+know there's an edge between i1 I2
+
+ align:start position:0%
+know there's an edge between i1 I2
+ 
+
+ align:start position:0%
+know there's an edge between i1 I2
+there's an edge between I2 I3 there one
+
+ align:start position:0%
+there's an edge between I2 I3 there one
+ 
+
+ align:start position:0%
+there's an edge between I2 I3 there one
+of them cannot be edge here it can't be
+
+ align:start position:0%
+of them cannot be edge here it can't be
+ 
+
+ align:start position:0%
+of them cannot be edge here it can't be
+that all of them are edges here because
+
+ align:start position:0%
+that all of them are edges here because
+ 
+
+ align:start position:0%
+that all of them are edges here because
+they're so because it doesn't have an
+
+ align:start position:0%
+they're so because it doesn't have an
+ 
+
+ align:start position:0%
+they're so because it doesn't have an
+malonian cycle so one of them cannot be
+
+ align:start position:0%
+malonian cycle so one of them cannot be
+ 
+
+ align:start position:0%
+malonian cycle so one of them cannot be
+an edge here and now what the what the
+
+ align:start position:0%
+an edge here and now what the what the
+ 
+
+ align:start position:0%
+an edge here and now what the what the
+verifier is asking from the prover he
+
+ align:start position:0%
+verifier is asking from the prover he
+ 
+
+ align:start position:0%
+verifier is asking from the prover he
+looks at all the I i1 and I all the I
+
+ align:start position:0%
+looks at all the I i1 and I all the I
+ 
+
+ align:start position:0%
+looks at all the I i1 and I all the I
+and J that do not have an edge and he
+
+ align:start position:0%
+and J that do not have an edge and he
+ 
+
+ align:start position:0%
+and J that do not have an edge and he
+open that edge I want to see that it's
+
+ align:start position:0%
+open that edge I want to see that it's
+ 
+
+ align:start position:0%
+open that edge I want to see that it's
+zero I want I want you I want to see
+
+ align:start position:0%
+zero I want I want you I want to see
+ 
+
+ align:start position:0%
+zero I want I want you I want to see
+that I gave you n squar safes so for
+
+ align:start position:0%
+that I gave you n squar safes so for
+ 
+
+ align:start position:0%
+that I gave you n squar safes so for
+every inj there's a safe and it should
+
+ align:start position:0%
+every inj there's a safe and it should
+ 
+
+ align:start position:0%
+every inj there's a safe and it should
+be one if there's an edge and zero other
+
+ align:start position:0%
+be one if there's an edge and zero other
+ 
+
+ align:start position:0%
+be one if there's an edge and zero other
+I mean if there's an edge in the
+
+ align:start position:0%
+I mean if there's an edge in the
+ 
+
+ align:start position:0%
+I mean if there's an edge in the
+hamiltonian cycle and zero otherwise now
+
+ align:start position:0%
+hamiltonian cycle and zero otherwise now
+ 
+
+ align:start position:0%
+hamiltonian cycle and zero otherwise now
+with the with the verifier is asking the
+
+ align:start position:0%
+with the with the verifier is asking the
+ 
+
+ align:start position:0%
+with the with the verifier is asking the
+prover for every J here that does not
+
+ align:start position:0%
+prover for every J here that does not
+ 
+
+ align:start position:0%
+prover for every J here that does not
+have an edge I want you to open the safe
+
+ align:start position:0%
+have an edge I want you to open the safe
+ 
+
+ align:start position:0%
+have an edge I want you to open the safe
+corresponding to that edge and I want to
+
+ align:start position:0%
+corresponding to that edge and I want to
+ 
+
+ align:start position:0%
+corresponding to that edge and I want to
+see a zero there if there's a one there
+
+ align:start position:0%
+see a zero there if there's a one there
+ 
+
+ align:start position:0%
+see a zero there if there's a one there
+I'm not happy I'm going to reject you
+
+ align:start position:0%
+I'm not happy I'm going to reject you
+ 
+
+ align:start position:0%
+I'm not happy I'm going to reject you
+because this there should be on only on
+
+ align:start position:0%
+because this there should be on only on
+ 
+
+ align:start position:0%
+because this there should be on only on
+the hamiltonian cycle and these are only
+
+ align:start position:0%
+the hamiltonian cycle and these are only
+ 
+
+ align:start position:0%
+the hamiltonian cycle and these are only
+places that have an edge on your
+
+ align:start position:0%
+places that have an edge on your
+ 
+
+ align:start position:0%
+places that have an edge on your
+graph but the problem
+
+ align:start position:0%
+graph but the problem
+ 
+
+ align:start position:0%
+graph but the problem
+is on one of these I that don't have an
+
+ align:start position:0%
+is on one of these I that don't have an
+ 
+
+ align:start position:0%
+is on one of these I that don't have an
+edge you'll see an edge because the
+
+ align:start position:0%
+edge you'll see an edge because the
+ 
+
+ align:start position:0%
+edge you'll see an edge because the
+aonian tyo is not all on edges and then
+
+ align:start position:0%
+aonian tyo is not all on edges and then
+ 
+
+ align:start position:0%
+aonian tyo is not all on edges and then
+I'm going to catch
+
+ align:start position:0%
+I'm going to catch
+ 
+
+ align:start position:0%
+I'm going to catch
+you yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great any more questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah slightly stronger that requires the
+
+ align:start position:0%
+yeah slightly stronger that requires the
+ 
+
+ align:start position:0%
+yeah slightly stronger that requires the
+pro to actually
+
+ align:start position:0%
+pro to actually
+ 
+
+ align:start position:0%
+pro to actually
+know the hamiltonian cycle right so here
+
+ align:start position:0%
+know the hamiltonian cycle right so here
+ 
+
+ align:start position:0%
+know the hamiltonian cycle right so here
+the proof like with the second part say
+
+ align:start position:0%
+the proof like with the second part say
+ 
+
+ align:start position:0%
+the proof like with the second part say
+that only guarante that if G is not
+
+ align:start position:0%
+that only guarante that if G is not
+ 
+
+ align:start position:0%
+that only guarante that if G is not
+doesn't have a
+
+ align:start position:0%
+doesn't have a
+ 
+
+ align:start position:0%
+doesn't have a
+hon proof
+
+ align:start position:0%
+hon proof
+ 
+
+ align:start position:0%
+hon proof
+the cannot but do necess like Converse
+
+ align:start position:0%
+the cannot but do necess like Converse
+ 
+
+ align:start position:0%
+the cannot but do necess like Converse
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+is it possible for G to not know cyle
+
+ align:start position:0%
+is it possible for G to not know cyle
+ 
+
+ align:start position:0%
+is it possible for G to not know cyle
+but still ver good G good good good
+
+ align:start position:0%
+but still ver good G good good good
+ 
+
+ align:start position:0%
+but still ver good G good good good
+great question great question so the
+
+ align:start position:0%
+great question great question so the
+ 
+
+ align:start position:0%
+great question great question so the
+question was or let me just answer the
+
+ align:start position:0%
+question was or let me just answer the
+ 
+
+ align:start position:0%
+question was or let me just answer the
+question is the qu the question was wait
+
+ align:start position:0%
+question is the qu the question was wait
+ 
+
+ align:start position:0%
+question is the qu the question was wait
+we just proved your soundness that if x
+
+ align:start position:0%
+we just proved your soundness that if x
+ 
+
+ align:start position:0%
+we just proved your soundness that if x
+is an non the language on one of the
+
+ align:start position:0%
+is an non the language on one of the
+ 
+
+ align:start position:0%
+is an non the language on one of the
+answers you'll fail but actually doesn't
+
+ align:start position:0%
+answers you'll fail but actually doesn't
+ 
+
+ align:start position:0%
+answers you'll fail but actually doesn't
+this protocol give you something
+
+ align:start position:0%
+this protocol give you something
+ 
+
+ align:start position:0%
+this protocol give you something
+stronger was the question and the answer
+
+ align:start position:0%
+stronger was the question and the answer
+ 
+
+ align:start position:0%
+stronger was the question and the answer
+is yes so what what do we mean by some
+
+ align:start position:0%
+is yes so what what do we mean by some
+ 
+
+ align:start position:0%
+is yes so what what do we mean by some
+something stronger let's say G is does
+
+ align:start position:0%
+something stronger let's say G is does
+ 
+
+ align:start position:0%
+something stronger let's say G is does
+have a hamiltonian
+
+ align:start position:0%
+have a hamiltonian
+ 
+
+ align:start position:0%
+have a hamiltonian
+cycle doesn't this protocol tell us not
+
+ align:start position:0%
+cycle doesn't this protocol tell us not
+ 
+
+ align:start position:0%
+cycle doesn't this protocol tell us not
+only that g has a hamiltonian cycle if
+
+ align:start position:0%
+only that g has a hamiltonian cycle if
+ 
+
+ align:start position:0%
+only that g has a hamiltonian cycle if
+you succeed let's say you succeed
+
+ align:start position:0%
+you succeed let's say you succeed
+ 
+
+ align:start position:0%
+you succeed let's say you succeed
+probability one or you know with h more
+
+ align:start position:0%
+probability one or you know with h more
+ 
+
+ align:start position:0%
+probability one or you know with h more
+more than
+
+ align:start position:0%
+more than
+ 
+
+ align:start position:0%
+more than
+half this protocol tells us not only
+
+ align:start position:0%
+half this protocol tells us not only
+ 
+
+ align:start position:0%
+half this protocol tells us not only
+that g has a hamiltonian cycle it means
+
+ align:start position:0%
+that g has a hamiltonian cycle it means
+ 
+
+ align:start position:0%
+that g has a hamiltonian cycle it means
+that P must know the
+
+ align:start position:0%
+that P must know the
+ 
+
+ align:start position:0%
+that P must know the
+cycle you can actually find you can
+
+ align:start position:0%
+cycle you can actually find you can
+ 
+
+ align:start position:0%
+cycle you can actually find you can
+extract the cycle from from from p and
+
+ align:start position:0%
+extract the cycle from from from p and
+ 
+
+ align:start position:0%
+extract the cycle from from from p and
+the answer is yes yes you can you can
+
+ align:start position:0%
+the answer is yes yes you can you can
+ 
+
+ align:start position:0%
+the answer is yes yes you can you can
+actually this is what's called proof of
+
+ align:start position:0%
+actually this is what's called proof of
+ 
+
+ align:start position:0%
+actually this is what's called proof of
+knowledge it means that P knows now I
+
+ align:start position:0%
+knowledge it means that P knows now I
+ 
+
+ align:start position:0%
+knowledge it means that P knows now I
+can say what does it mean that P knows
+
+ align:start position:0%
+can say what does it mean that P knows
+ 
+
+ align:start position:0%
+can say what does it mean that P knows
+what do we this is this is a theory
+
+ align:start position:0%
+what do we this is this is a theory
+ 
+
+ align:start position:0%
+what do we this is this is a theory
+class mathematics what does no mean you
+
+ align:start position:0%
+class mathematics what does no mean you
+ 
+
+ align:start position:0%
+class mathematics what does no mean you
+know so what what what we mean by P NOS
+
+ align:start position:0%
+know so what what what we mean by P NOS
+ 
+
+ align:start position:0%
+know so what what what we mean by P NOS
+what we mean is that we can actually
+
+ align:start position:0%
+what we mean is that we can actually
+ 
+
+ align:start position:0%
+what we mean is that we can actually
+efficiently extract the cycle from p and
+
+ align:start position:0%
+efficiently extract the cycle from p and
+ 
+
+ align:start position:0%
+efficiently extract the cycle from p and
+how do we extract the cycle it's
+
+ align:start position:0%
+how do we extract the cycle it's
+ 
+
+ align:start position:0%
+how do we extract the cycle it's
+actually very
+
+ align:start position:0%
+actually very
+ 
+
+ align:start position:0%
+actually very
+easy we ask him he committed to
+
+ align:start position:0%
+easy we ask him he committed to
+ 
+
+ align:start position:0%
+easy we ask him he committed to
+something he knows how to open both
+
+ align:start position:0%
+something he knows how to open both
+ 
+
+ align:start position:0%
+something he knows how to open both
+that's assumption so first we'll ask him
+
+ align:start position:0%
+that's assumption so first we'll ask him
+ 
+
+ align:start position:0%
+that's assumption so first we'll ask him
+okay open only the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cycle and
+
+ align:start position:0%
+cycle and
+ 
+
+ align:start position:0%
+cycle and
+then give me the
+
+ align:start position:0%
+then give me the
+ 
+
+ align:start position:0%
+then give me the
+pi once I know the pi and the cycle I
+
+ align:start position:0%
+pi once I know the pi and the cycle I
+ 
+
+ align:start position:0%
+pi once I know the pi and the cycle I
+can I can undo I can I know what py gen
+
+ align:start position:0%
+can I can undo I can I know what py gen
+ 
+
+ align:start position:0%
+can I can undo I can I know what py gen
+I can see I can actually find the aonian
+
+ align:start position:0%
+I can see I can actually find the aonian
+ 
+
+ align:start position:0%
+I can see I can actually find the aonian
+cycle so it's it's more than just a
+
+ align:start position:0%
+cycle so it's it's more than just a
+ 
+
+ align:start position:0%
+cycle so it's it's more than just a
+soundness it's a proof of knowledge he
+
+ align:start position:0%
+soundness it's a proof of knowledge he
+ 
+
+ align:start position:0%
+soundness it's a proof of knowledge he
+must no I can actually use him to kind
+
+ align:start position:0%
+must no I can actually use him to kind
+ 
+
+ align:start position:0%
+must no I can actually use him to kind
+of extract the the antonian cycle from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+him any any other
+
+ align:start position:0%
+him any any other
+ 
+
+ align:start position:0%
+him any any other
+questions okay so let's take a five
+
+ align:start position:0%
+questions okay so let's take a five
+ 
+
+ align:start position:0%
+questions okay so let's take a five
+minute break and then after the break
+
+ align:start position:0%
+minute break and then after the break
+ 
+
+ align:start position:0%
+minute break and then after the break
+I'm going to show you why this protocol
+
+ align:start position:0%
+I'm going to show you why this protocol
+ 
+
+ align:start position:0%
+I'm going to show you why this protocol
+is not secure in the roral model but
+
+ align:start position:0%
+is not secure in the roral model but
+ 
+
+ align:start position:0%
+is not secure in the roral model but
+we'll fix it don't worry okay I'll take
+
+ align:start position:0%
+we'll fix it don't worry okay I'll take
+ 
+
+ align:start position:0%
+we'll fix it don't worry okay I'll take
+a break
\ No newline at end of file
diff --git a/yIjTCMlIgpU.txt b/yIjTCMlIgpU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a039a7151b1fa95929429485076091fc66cfafa5
--- /dev/null
+++ b/yIjTCMlIgpU.txt
@@ -0,0 +1,2774 @@
+PROFESSOR: OK,
+welcome back to 6849.
+
+So last lecture,
+lecture three, we
+
+were talking about
+local foldability
+
+and some complicated flat
+folding, like a flapping bird
+
+here.
+
+We were looking at a
+single vertex and locally
+
+around that vertex
+what properties
+
+it would have to have.
+
+And we saw Kawasaki's theorem
+which characterized the angles.
+
+And without a mountain
+valley assignment
+
+Kawasaki was all you needed.
+
+The alternating sum
+of angles should be 0.
+
+And given a mountain
+valley pattern, locally
+
+we characterize things
+as a sequence, anything
+
+you can do by a
+sequence of crimps.
+
+So sort of a similar
+version to lecture
+
+two, which was about
+1D flat foldability.
+
+There we needed
+crimps and end folds.
+
+Here we needed just
+crimps, which is easier.
+
+So I'm going to
+jump into questions.
+
+And in particular, this
+is an opportunity for me
+
+to talk about the main
+thing that I skipped
+
+last class, class two,
+because it relates again
+
+to this lecture, which is how
+do we do this algorithmically?
+
+So it's one thing
+to say, oh, just
+
+do crimps and end folds
+till you can't anymore,
+
+and then when you run out of
+stuff to do, if you're done,
+
+you're done, otherwise
+it's not flat foldable.
+
+That's true.
+
+But the obvious way to
+implement that algorithm
+
+is to sweep over
+the crease pattern,
+
+look for any crimps
+or end folds.
+
+If you find one, do it, and
+then repeat and keep sweeping.
+
+And that would take
+quadratic time,
+
+because in the worst
+case every scan
+
+you have to look through
+the whole pattern
+
+and at the very end you
+find what you need to do.
+
+So after about n
+operations-- n is
+
+the number of creases
+in your pattern--
+
+you find what you need to
+do, you do the operation,
+
+and then you repeat.
+
+So n plus n plus n, n
+times, is n squared.
+
+But you can do
+better and it's been
+
+alluded to in the lectures,
+but it wasn't covered.
+
+And so I wanted to cover
+it, because there's actually
+
+a really simple way to do it.
+
+There's one version
+in the textbook,
+
+but there is a simpler way.
+
+So I want to talk about that.
+
+This is a new way we
+just invented last week?
+
+This week?
+
+I forget.
+
+So I'm going to first talk
+about it in the 1D scenario,
+
+but it's pretty much
+the same for both.
+
+1D's a little bit easier
+to think about, though.
+
+So 1D mountain valley
+pattern something like this.
+
+So I'm going to follow
+the same approach, which
+
+is sweep left to right
+until I find either an end
+
+fold or a crimp that I can do.
+
+So in this case, maybe this
+would be the first thing
+
+that I find sweeping
+left to right.
+
+That's a crimpable pair--
+or crimpable segment,
+
+I'm going to call it-- is just
+one that is locally smallest.
+
+It's less than or equal to
+its two neighbors in length,
+
+and it has two different
+assignments, M/V or V/M.
+
+So that's a crimpable
+pair, because it's
+
+shorter than those two guys.
+
+So that's the basic
+algorithm, but what
+
+I do after that is going to
+be a little bit different.
+
+So I want to search left to
+right for a segment that's
+
+either crimpable
+or end foldable.
+
+And there's two situations.
+
+If I don't find any operations
+to do, then we stop.
+
+And if there are
+any creases left
+
+we know that the
+resulting thing is not
+
+flat foldable from what
+we proved in lecture two.
+
+If there's no crimp or end
+fold, you're not flat foldable.
+
+But if you do find
+something, then do the fold.
+
+This is so far pretty obvious.
+
+I'm going to draw the picture
+for a crimp situation.
+
+So in the crimp
+situation-- these
+
+are the previous
+and next creases--
+
+we have these
+lengths x, y, and z.
+
+We know that y is less than
+or equal to z and is less than
+
+or equal to x.
+
+And after we do the
+crimp, it looks like this.
+
+So we have x, y, and
+z here, but we're
+
+then going to fuse
+this material together,
+
+because these creases
+are done with.
+
+We don't really care about them.
+
+The new length that we
+get is x minus y plus z.
+
+OK.
+
+So that's what I
+mean by do the fold.
+
+And we'll also call this
+sort of merging the segments,
+
+meaning replace-- so normally
+we have a sequence of lengths--
+
+replace x, y, z with
+x minus y plus z,
+
+remove these two creases
+which were, say, M and V.
+
+Now we want to continue.
+
+And the realization
+is that we don't
+
+have to start over our
+search in searching
+
+left to right for
+a crimpable thing.
+
+If we went all the way
+through the pattern
+
+and then finally found
+a crimp at the end,
+
+should we start way back here?
+
+No.
+
+There's no point.
+
+You might as well start
+basically where you just were.
+
+Not quite.
+
+You have to go back one step.
+
+So the next step in this
+algorithm is go back one step,
+
+and then continue the search.
+
+Back means left.
+
+And the search is this line.
+
+OK.
+
+So that's an algorithm,
+a little loop there.
+
+So in this example we-- the
+point of what's going on
+
+and the reason this
+algorithm is correct
+
+is we just modified
+these three segments.
+
+And we replaced
+these three segments
+
+with a single segment which
+looks something like that.
+
+And the rest, the parts to
+the left and to the right
+
+are the same.
+
+I still claim we need
+to back up one segment
+
+and look at this one again,
+because now potentially
+
+this one might be crimpable
+whereas it wasn't before.
+
+Because we changed
+this length, it
+
+may have gotten
+longer potentially.
+
+Or shorter.
+
+It could have changed.
+
+So this pair may be crimpable
+whereas it wasn't before.
+
+So just to make sure,
+we'll go left one step,
+
+and then we'll check, is
+that segment crimpable?
+
+Is this one?
+
+Is this one?
+
+And just keep going.
+
+And I'm guessing
+this pattern is not
+
+is not flat foldable
+because of these two.
+
+We could check.
+
+Did I miss one?
+
+V, M, M. M is the little thing.
+
+So I think this
+is going to crimp.
+
+And then this will
+get end folded.
+
+But still this is a problem
+because of the two M's.
+
+So this will not flat fold.
+
+We'll be left with
+something like this,
+
+which is the two M's
+and then we say, oh.
+
+We'll reach the stop case.
+
+Can't find a crimp
+or and end fold
+
+and there are
+still creases left.
+
+And so we know that
+we're not flat foldable.
+
+But the reason I'm doing this
+fast resume of the search,
+
+continuing the search
+from one step to the left,
+
+is because we get a
+good running time.
+
+I'm going to use running
+time notation of order n.
+
+This means some
+constant times n.
+
+We don't really care what the
+constant is, but the growth is
+
+linear in the number
+of creases that's n.
+
+And the reason it's
+linear is that the number
+
+of rightward steps
+that we make is
+
+going to be equal to n plus
+the number of leftward steps.
+
+Why is that?
+
+Because overall the search
+is going left to right,
+
+and if it doesn't find
+anything it just takes n steps.
+
+You look at all the creases
+or all the segments.
+
+It's basically n,
+n plus 1, whatever.
+
+For each one, you check is
+it crimpable, end foldable.
+
+That takes constant time.
+
+You're just comparing
+a couple of numbers.
+
+So I'm counting the
+number of rightward steps.
+
+The trouble with the
+search is that every time I
+
+find a fold to do
+I go back one step
+
+and so I'm kind
+of losing progress
+
+because I go backwards.
+
+There's actually two
+reasons why that's OK.
+
+One is you're also decreasing
+n at the same time,
+
+because you're replacing
+3 things with 1 thing,
+
+so n goes down by 2.
+
+But also, in order to
+make a rightward step
+
+either it's in the
+full search or it's
+
+because you went back one and
+you have to go right again.
+
+So this is true.
+
+And the point is the number
+of leftward steps is also
+
+at most n, because
+every time you
+
+do a leftward step
+you did a fold,
+
+and there's only
+n folds to make.
+
+So-- it's actually less,
+because crimps do two at a time.
+
+But the point is
+this is at most 2n.
+
+And so the number of rightward
+steps we make is linear.
+
+And so the overall
+running time is linear.
+
+For the algorithms people, this
+is a very simple amortization
+
+argument.
+
+We're charging the
+leftward steps to the folds
+
+that we're doing.
+
+So that's an easy way to
+do 1D flat foldability
+
+testing for mountain
+valley patterns.
+
+Yes?
+
+AUDIENCE: Why do you
+need to go back a step?
+
+So, the segment
+that you labelled x,
+
+its new length is x plus
+the quantity z minus y,
+
+and z is greater than y.
+
+So it's x plus a
+positive number, right?
+
+So it's only increasing
+in length, not decreasing.
+
+PROFESSOR: Only increasing.
+
+But that's of interest, right?
+
+Because if you had something
+that wasn't crimpable
+
+because this was too short, and
+then-- OK, here's an example.
+
+Good question.
+
+I hadn't thoroughly checked.
+
+So we scan.
+
+This guy's not crimpable
+because this guy's too short.
+
+Then we reach-- suppose
+then we jump to this guy.
+
+I'll do valley mountain to make
+this definitely not crimpable.
+
+We look at this guy.
+
+We do the crimp.
+
+And now suddenly we have
+this nice big length.
+
+And so now this
+pair is crimpable.
+
+Good.
+
+So that's why we need
+to go back a step.
+
+After we crimp
+this guy, this one
+
+becomes crimpable
+if it wasn't before.
+
+Yeah.
+
+I could have easily believed
+that this step wasn't
+
+necessary, but it
+definitely doesn't hurt
+
+and it is indeed necessary.
+
+The key is that we don't have
+to back up more than one step,
+
+because we're only changing
+our neighbors, basically.
+
+Other questions
+about this algorithm?
+
+OK, well once we have this for--
+this is really for lecture two
+
+material, we can adapt it to
+lecture three material, which
+
+is the circular case.
+
+Instead of having a line
+we have a circle of paper.
+
+In that case, we only
+need to look for crimps,
+
+and so we do the same
+thing for crimps.
+
+I don't think I really need to
+write this down, but algorithm
+
+for a single vertex
+mountain valley pattern.
+
+It's basically the
+same algorithm.
+
+Instead of wherever
+you see left and right
+
+you replace it with clockwise
+and counterclockwise
+
+going around in a circle.
+
+There's no obvious
+starting point
+
+you just start at an arbitrary
+segment, which in this case
+
+is an angle of the
+crease pattern.
+
+Maybe I should draw a
+little crease pattern, just
+
+for a picture.
+
+So you start, let's
+say, at this segment.
+
+You see is this pair crimpable.
+
+If not continue,
+let's say, clockwise.
+
+Keep going.
+
+If you ever find a crimpable
+pair, like these two guys--
+
+maybe this is
+mountain and valley
+
+and this is a locally
+smallest angle--
+
+you do the crimp, meaning
+you replace this angle x y
+
+and z with x minus y
+plus z, just as before.
+
+And then you step
+counterclockwise one step.
+
+And the point is
+the invariant you're
+
+maintaining at all times during
+this algorithm, the interval
+
+of the segments from the very
+first segment you went to,
+
+up to but not
+including the segment
+
+you're currently
+looking at, those
+
+are all guaranteed not
+crimpable at the moment.
+
+And so when you do a crimp,
+that may invalidate this one,
+
+and so you have to step
+backwards because you're not
+
+sure whether that one's
+crimpable anymore.
+
+But you maintain that invariant.
+
+And so when if you ever get
+back to the original angle
+
+that you were considering,
+the original segment,
+
+then you know that in fact
+everything is not crimpable,
+
+and then you're in trouble.
+
+Maybe.
+
+Except for this issue
+which I also forgot about
+
+in lecture three-- I mean, I
+didn't forget about this time,
+
+but I forgot about it then--
+which is in the base case.
+
+You can never actually do
+everything by crimping,
+
+because at the
+very end your hope
+
+is that you have a cone
+with two creases that
+
+are both the same orientation.
+
+That is your goal.
+
+You know that there's two more
+mountains or two more valleys
+
+and crimps pair them up.
+
+So you hope that you end
+up with the situation.
+
+If you do, and these
+two angles are equal,
+
+then you're flat foldable.
+
+You have that one
+last fold to make.
+
+Otherwise, if you have anything
+else, you're not flat foldable.
+
+That's what we proved
+in lecture three,
+
+is that crimps are enough to
+get down to this situation
+
+where you have only
+two creases left,
+
+and that's what's foldable
+when you only have two creases.
+
+OK so this is becoming a cone
+as soon as you do operations.
+
+It's just like the
+analysis we did.
+
+But this algorithm
+will run in linear time
+
+for the same reason.
+
+The number of clockwise
+steps equals at most n
+
+plus the number of
+counterclockwise steps.
+
+And so I guess I should
+maybe write "at most."
+
+And so this is
+linear time as well.
+
+Any questions about
+those algorithms?
+
+Yeah.
+
+AUDIENCE: For the
+simple one, could you
+
+run into some edge case
+where the very last crimp
+
+you considered makes the
+very first one, which
+
+wasn't crimpable,
+crimpable and then you
+
+have to go around
+the circle again?
+
+PROFESSOR: Ah.
+
+OK.
+
+Good question.
+
+Right.
+
+So we said, OK, this is
+guaranteed not crimpable,
+
+but if you then crimp
+the very last segment
+
+this one may become crimpable,
+and then that may propagate
+
+and force you to go
+around a second time.
+
+AUDIENCE: So if that happens
+at each step, then at each step
+
+you go all the way around,
+and it could become quadratic.
+
+PROFESSOR: Ooh, interesting.
+
+AUDIENCE: But I'm
+not sure if it's
+
+possible for that to
+happen every step.
+
+PROFESSOR: Good.
+
+Well, this is the nature
+of new algorithms.
+
+Yeah.
+
+AUDIENCE: The set of
+possibly crimpable things
+
+increases by at most 1 every
+time-- or at most 2 every time
+
+you make a crimp.
+
+PROFESSOR: Yeah.
+
+So certainly you will only have
+to go around at most n times,
+
+but a quadratic bound
+overall is not very exciting.
+
+AUDIENCE: So it stays linear.
+
+The interval in which things
+are possibly crimpable
+
+expands by at most 2 every
+time you make a crimp.
+
+PROFESSOR: I see.
+
+OK.
+
+So this is a different
+algorithm, unfortunately.
+
+But you maintain the
+interval of things
+
+that are guaranteed
+not crimpable
+
+and you can look at
+both ends whether you
+
+can crimp something.
+
+If you can, fine, you do it.
+
+You shrink the
+interval a little bit.
+
+So in general your interval
+is-- I have colored chalk,
+
+I should use it-- your
+interval is an interval.
+
+It starts somewhere,
+ends somewhere.
+
+And you're checking
+is this guy crimpable.
+
+If it's not crimpable
+you can extend
+
+the interval a little bit.
+
+If it is crimpable
+you do the fold
+
+and you actually shrink
+the interval a little bit.
+
+But every time you shrink
+the interval, you did a fold,
+
+and that only happens n times.
+
+Every time you grow the
+interval, you grew the interval
+
+and you can only grow n times.
+
+Good.
+
+So that will clean
+up this situation.
+
+If this ends up being
+crimpable, you just
+
+shrink the interval
+from the other side.
+
+So I guess if I
+wanted to just tweak
+
+this algorithm I would
+change the notion of first.
+
+So I said, oh, this guy is
+the first one that I visited.
+
+But if I end up
+crimping this guy,
+
+I have to advance the first
+to be the very next interval.
+
+Good.
+
+Thank you.
+
+All right.
+
+I'll correct that in
+the notes as well.
+
+It was almost correct.
+
+Think now that
+should be correct.
+
+Thanks for checking.
+
+And now we can do
+it in linear time.
+
+There's a different
+algorithm in the textbook,
+
+which uses more data structures.
+
+This I like because
+it's very simple.
+
+It's just, like, storing
+two pointers and that's it.
+
+Other questions?
+
+OK.
+
+That does algorithms.
+
+That was the new material
+I wanted to cover.
+
+Then there is the other--
+the actual algorithm that
+
+was briefly described in class
+is this local foldability
+
+algorithm.
+
+So you have now not
+just a single vertex,
+
+but you have a whole
+crease pattern.
+
+You'd like to assign a mountain
+valley assignment to it that
+
+is at least locally
+good, that when
+
+you run this algorithm
+at each vertex it gives
+
+the right answer, it
+says that, yeah, it's
+
+locally foldable
+for each vertex.
+
+It doesn't mean the whole
+thing will fold flat,
+
+but it's a start, at least.
+
+It's a necessary
+condition for that.
+
+So I just want to give
+you a few examples
+
+of this algorithm,
+because it is confusing.
+
+I didn't do any
+examples in lecture.
+
+It's always been the most
+confusing part to me,
+
+and especially this notion
+of merging cycles and paths.
+
+So for starters, these are
+the examples in the textbook.
+
+They're pretty simple, but at
+least they'll get us warmed up.
+
+So the crease pattern
+is the bold black lines.
+
+It's two of them.
+
+And in this case it's
+the generic case,
+
+so there's a unique
+pairing here.
+
+There's only one crimpable
+pair, which are these two guys.
+
+This is the only
+locally smallest angle.
+
+So those two have
+to be crimped first.
+
+One's going to be a mountain,
+one's going to be a valley.
+
+So we would write not
+equals in this blue thing
+
+to represent that constraint.
+
+This will be all that's left.
+
+And so these two guys
+have to be equal.
+
+It's symmetric, so it looks
+the same all the way around.
+
+And so when you see, OK, these
+two guys have to be not equal,
+
+but also these two guys
+have to be not equal,
+
+but also these two guys
+have to be not equal,
+
+this is what we call a
+cycle of constraints.
+
+In general, you get paths.
+
+Like, this one starts
+and ends at infinity,
+
+so these two guys
+have to be equal,
+
+these two guys have to be equal.
+
+They could both be mountain,
+both be valley, doesn't matter.
+
+These are the only constraints.
+
+But this cycle--
+cycles can be problems,
+
+and here because it's
+an odd cycle of not
+
+equals there's no
+way to assign it.
+
+If you say mountain,
+valley, mountain,
+
+then these two guys
+are both mountains,
+
+which violates that constraint.
+
+In general, the
+number of not equals
+
+should be even in each cycle.
+
+If it's ever an odd number of
+not equals, you're in trouble.
+
+Here's an example where
+the cycle is even,
+
+but we end up with
+an equals here,
+
+and so the number of
+not equals is still odd,
+
+so this is also bad.
+
+I mean, it's just replacing this
+segment with two equal creases.
+
+Still can't assign a
+mountain or valley.
+
+But these are kind
+of simple examples.
+
+These are cycles and everything
+was uniquely determined here.
+
+You had to crimp this guy first.
+
+You had to crimp this guy first.
+
+There was no choice.
+
+And the tricky part
+of the algorithm
+
+is when you have choice, when
+you have multiple equal angles,
+
+you don't know what
+to crimp first.
+
+The algorithm just
+crimps one of them first,
+
+but then it might
+have to fix things.
+
+So I came up with
+a simple example
+
+where you have to do that.
+
+I think it will help clarify
+how this merging really happens.
+
+So the example is-- it's hard
+to draw an equilateral triangle
+
+with accurate angles,
+but I'll do my best--
+
+and then these are supposed
+to be right angles.
+
+OK.
+
+So that's my crease pattern.
+
+And some of this is forced.
+
+This guy-- at this vertex, this
+is the only locally smallest
+
+angle.
+
+It's only 60 degrees,
+these are 90.
+
+This is bigger than 90.
+
+So this has to be crimped
+first, and it's not equal.
+
+That means these guys are equal.
+
+We don't really
+care about those.
+
+And it's symmetric,
+so not equal, equal.
+
+OK.
+
+But here we have a choice.
+
+There's two 60 degree angles.
+
+This does not look
+very flat foldable.
+
+I think I'd better add
+some more creases there.
+
+Got to have to even
+parity at every vertex.
+
+So now we have a choice.
+
+Do we crimp this one first or
+do we crimp the other one first?
+
+At this point, it's symmetric,
+so I'll do this one first.
+
+This'll be my pairing.
+
+And there are two
+possibilities here.
+
+Either I crimp this one first
+or crimp this one first.
+
+The algorithm doesn't care.
+
+So let's suppose it does
+this one, because this
+
+is the bad one.
+
+OK.
+
+Now we have a cycle with
+an odd number not equals.
+
+So this is not
+possible to satisfy.
+
+The algorithm
+doesn't stop there.
+
+It says, OK, I have these paths.
+
+There's a cycle here
+that's a problem,
+
+then I also have a path up here.
+
+How does it go?
+
+There's a path that goes
+here, here, here, here.
+
+And there's a path
+that goes here.
+
+But really it looks at the
+vertices that had choice.
+
+It says, look, at
+this moment I had
+
+a choice between whether to
+fold this angle or this angle.
+
+In general, it might have
+been a bunch of equal angles.
+
+We see here that there's a cycle
+that the other choice would've
+
+involved a path.
+
+And so we merge.
+
+In general, if there's
+two different things--
+
+one could be a cycle,
+one could be a path,
+
+they could both be cycles,
+they could both be paths,
+
+whatever-- if I ever
+have the opportunity
+
+to join those two parts
+together I'll do it.
+
+So in other words, I do
+the other crease first.
+
+Let me draw that.
+
+What that means will become
+clear once we actually do one.
+
+So I want to do this first.
+
+The rest is the same.
+
+OK.
+
+So in that situation, what do
+my paths and cycle look like?
+
+Well, there was this path
+that started over here.
+
+It used to go like this, but
+now this vertex has changed.
+
+So it's going to do something
+different at that vertex.
+
+Now it goes over this way.
+
+I'm just following
+the constraints.
+
+Now those two guys are
+constrained to be different.
+
+And these are
+constrained to be equal.
+
+So lo and behold we merged
+a path and the cycle
+
+and we got a single path.
+
+The other paths remain the same.
+
+Just these two guys
+got interchanged.
+
+What we're doing is basically
+turning here and turning here
+
+instead of going that
+way and going that way.
+
+And whenever you have two pieces
+like this, and one of which
+
+is a cycle, you will do a merge.
+
+Merging can only help
+us, because they'll
+
+get bigger and
+bigger and bigger.
+
+The bigger these
+sets of constraints
+
+are, essentially,
+the better chance
+
+that you'll get
+the parity right.
+
+I can never-- and this
+is argued in the notes,
+
+but few-- it never hurts to
+merge something, is the point.
+
+And if you're lucky-- if you,
+say, merge two odd cycles--
+
+they will become even.
+
+If you merge with a path,
+you'll become a path.
+
+And so you're golden.
+
+Paths are always good.
+
+And so this thing becomes
+flat foldable, or at least
+
+locally flat foldable.
+
+And we can mark in a
+crease pattern, I guess.
+
+You could make this-- that's
+going to be hard to see,
+
+I think-- mountain, valley,
+mountain, valley, mountain--
+
+oh, sorry-- equals, not equals,
+this is not equals, not equals,
+
+not equals, equals.
+
+These guys are free.
+
+So you can make one
+of them mountain,
+
+one of--- you can make them
+all mountains, I guess.
+
+Or not.
+
+OK.
+
+This is a locally
+valid flat folding.
+
+And it's hard to tell
+whether it actually works
+
+except by folding it.
+
+So here I made one.
+
+That's the top side, I think.
+
+Ideally I got the same
+crease pattern as here.
+
+The reds are mountains.
+
+Looks the same.
+
+And then--
+
+It's clear that this pattern
+is flat foldable, right?
+
+You just simple fold
+here, and then you've
+
+got a single vertex and that
+single vertex is flat foldable.
+
+But this does not do that.
+
+It does a kind of twist.
+
+It's kind of a fun mountain
+valley assignment for it.
+
+So in this case it works.
+
+In general, you might get
+some weird mountain valley
+
+assignment that doesn't work.
+
+But something simple
+like this pattern,
+
+which has four
+vertices, always will.
+
+Any more questions
+about local foldability?
+
+That gives you at least an idea
+of what the merges look like.
+
+It's hard to draw a huge
+example, but-- Yeah.
+
+AUDIENCE: So the
+generic case, you
+
+don't really have
+a choice at any--
+
+PROFESSOR: In the generic
+case you have no choices,
+
+and so you've got to-- you
+just check, does it work.
+
+And if it--
+
+AUDIENCE: If you have
+an odd number of faces,
+
+odd number of sides, then
+it's not going to work?
+
+PROFESSOR: If you have a face
+with an odd number of sides,
+
+that might be fine.
+
+It depends on these
+assignments, whether they're
+
+not equal or equals.
+
+Like if this were an equal
+sign, then you'd be happy.
+
+And that would
+happen, for example,
+
+if you move these
+creases to be very small.
+
+I'd have to also make this
+one proportionally big, which
+
+is possible if I move
+this vertex way over here.
+
+I'll have a triangle.
+
+This will have a big angle.
+
+Then I can have a
+small angle here
+
+and these two guys
+will be made not equal
+
+and these two will
+be made equal,
+
+and then the parity's fine.
+
+So if you have a cycle with
+an odd number of not equals,
+
+then you're screwed.
+
+In the generic case
+there's nothing you can do.
+
+When you have equal angles,
+when you had a choice,
+
+you go back and check whether
+the choices would do merges.
+
+If you do, you do them.
+
+Overall, this turns out
+to take a linear time
+
+if you're careful, because you
+can only merge so many times.
+
+You have at most n parts and
+each merge-- with some care.
+
+You need fancy data structures
+to get this to work.
+
+You need find stuff,
+but then you'll
+
+get linear time over all.
+
+Other questions?
+
+AUDIENCE: So what's the
+definition of merging, again?
+
+PROFESSOR: So the
+definition of merging
+
+is you look at every time
+you had a choice in running
+
+this algorithm-- which you have
+to not just run this algorithm
+
+but you have to maintain all
+the choices that you had made.
+
+So whenever you had two
+equal angles-- in general,
+
+the algorithm is you look at
+a sequence of equal angles.
+
+The algorithm maybe
+chooses the first one,
+
+but you could have chosen any.
+
+You see for each of the
+other possibilities,
+
+would that end up combining
+two of the components.
+
+So the constraints sort of join
+together either into cycles
+
+or into paths, like this guy.
+
+And we just check, if
+I do this other change,
+
+does it end up combining
+two of those components?
+
+Before I had 1, 2,
+3, 4 components.
+
+Now I only have 3 components.
+
+So just see what happens.
+
+If that decreases the number
+of components I do it.
+
+And you can guarantee
+this never hurts you.
+
+Keep merging components
+until you can't anymore.
+
+And then either it
+works and you've
+
+got no parity problems or no
+cycles, or it doesn't work.
+
+If it doesn't work, there is
+no local foldable assignment.
+
+Yeah.
+
+AUDIENCE: When you
+say it's linear,
+
+are you counting
+vertices or edges?
+
+PROFESSOR: Let's say number
+of vertices plus edges.
+
+That's the safe way to define
+n and then linear in that.
+
+Or if you count
+the endpoints here
+
+it doesn't matter whether you
+just count vertices or edges.
+
+The sum of the two
+is always safe.
+
+So n usually just means
+the size of the input,
+
+and those vertices and edges,
+so why not just count them both.
+
+Other questions?
+
+Cool.
+
+So that's local foldability.
+
+I just have a few
+more little things
+
+and then you can
+ask more questions.
+
+Oh, sorry.
+
+I have one more example.
+
+I forgot.
+
+This is an example where
+everything works fine.
+
+You don't get any cycles.
+
+But it's kind of a fun example.
+
+The crane.
+
+I'd never analyzed it
+before, so I spent the time
+
+to draw one of these pictures.
+
+So first I just put a
+bunch of circles down,
+
+and I look for things that
+are forced, just because that
+
+is more interesting.
+
+I tried to make it
+as bad as possible.
+
+It turns out I couldn't
+make it that bad.
+
+But this guy's
+forced, because it's
+
+the only locally smallest angle.
+
+And then it's
+symmetrical around.
+
+So this guy's forced.
+
+Four of them should be forced.
+
+If I advance, yeah.
+
+This one, this one.
+
+Those are all forced
+to be not equal.
+
+The rest are equal.
+
+The other guys have ambiguity.
+
+And I tried.
+
+I thought this would be a
+great place to find the cycle
+
+and then we could resolve
+the cycle, because I know
+
+this should work in the end,
+but I couldn't make a cycle.
+
+It's not possible, because
+there's sort of this cut point
+
+here.
+
+And you once you go to
+one side of the pattern,
+
+you can't come back
+to the other side.
+
+I could make a really
+long path though.
+
+So I chose-- there's
+a lot of choices here,
+
+but the algorithm
+just chooses one.
+
+I tried to make the
+longest path I could.
+
+It's kind of a fun puzzle.
+
+Not that hard to solve.
+
+It gets a little hard
+to draw these pairings.
+
+Here these two guys are
+paired together as not equal.
+
+We crimp that first.
+
+Then let's say we
+crimp these two.
+
+Then we've got two
+angles here, each
+
+of which I think is 90 degrees
+after you do the crimps.
+
+And so these two guys
+have to be equal.
+
+That's what this notation means.
+
+So here there were, I think
+four different possibilities.
+
+And if you trace all the
+paths, you get these guys.
+
+So there's some simple paths
+out here, but then there's
+
+this purple path in the
+middle, which starts here,
+
+goes up here, over here,
+over here, along this crease,
+
+over here, here, here, here, up
+there, here, here, there, back,
+
+forth, and then it
+escapes in the corner.
+
+So you get a mountain valley
+assignment out of this.
+
+I didn't test whether
+it was possible.
+
+Probably not.
+
+Anyway, you get something,
+and it might be possible.
+
+Exercise for you to try at home.
+
+All right.
+
+That took some time to draw.
+
+Cool.
+
+That's local foldability.
+
+Now with the
+Kawasaki condition, I
+
+mentioned briefly
+in lecture three
+
+that-- We were talking
+about convex cones, where
+
+the amount of material is
+less than or equal to 360.
+
+Someone pointed out and
+said, oh, out of paper
+
+you can't make
+something more than 360.
+
+And it's true if you start
+from one sheet of paper.
+
+But if you start with
+multiple sheets of material
+
+and join them together, like
+sew them up, like in a T-shirt,
+
+you can get non-convex
+cones, meaning
+
+more than 360 degrees
+of material here.
+
+This is, let's say,
+270, let's call it?
+
+So you double that,
+because there's
+
+a front side and the
+back side of the T-shirt.
+
+Easier to see in a 3D one.
+
+You've got more than 360 degrees
+of material in the armpits.
+
+So, yes, it's true.
+
+And what happens, as I mentioned
+briefly, is there's a new case.
+
+There's sort of
+two situations when
+
+you have a kind of a mess
+of material like this,
+
+more than 360
+degrees of material.
+
+There are two possibilities.
+
+Either you end up folding it to
+lie in less than a full circle,
+
+in terms of the boundary,
+and then it's just like here.
+
+The alternating sum
+should be equal to 0.
+
+Or you end up folding it
+so that it encompasses
+
+an entire circle,
+and then you end up
+
+with this alternating sum of
+angles being plus or minus 360.
+
+And it's in the textbook.
+
+It's not so easy to prove
+that that's all that happens,
+
+but you-- Basically, you
+can't twist multiple times,
+
+because then you'd end
+up with a crossing.
+
+So it's not that much
+harder to analyze
+
+these kinds of situations.
+
+You can do it.
+
+But this is a
+great excuse for me
+
+to show cool ways
+to fold T-shirts.
+
+How many people seen this video?
+
+most.
+
+It's like six years old.
+
+Have you ever tried it?
+
+[LAUGHTER]
+
+I brought an extra
+little T-shirt here.
+
+This is totally for fun.
+
+You pinch here and here.
+
+Bring this side over here.
+
+You pinch.
+
+You do a nice
+flourish, and then you
+
+get your perfectly
+folded-- I didn't
+
+do it perfectly--
+T-shirt in one motion.
+
+As they say, in two seconds,
+and it works for us.
+
+So it's a great T-shirts.
+
+And for fun, here's the--
+this is like the high tech way
+
+to do it.
+
+There's actually a whole bunch
+of T-shirt folding machines.
+
+You push the button.
+
+It's a bunch of simple
+folds, actually.
+
+So it's a nice little
+simple folding machine.
+
+[LAUGHTER]
+
+It's kind of fun to watch.
+
+Seems like a lot of set up time.
+
+You have set up time with
+the fast method also.
+
+So It's kind of fun.
+
+The same machine. you can also
+wrap them directly into bags.
+
+Question?
+
+AUDIENCE: Have you
+in clothing stores
+
+they have non-mechanical
+versions of those
+
+that are just plastic boards.
+
+PROFESSOR: And you just--
+
+AUDIENCE: That you can flop over
+so that all your T-shirts are
+
+folded the same.
+
+PROFESSOR: It's not automated.
+
+Yes.
+
+You can actually buy-- I've
+only seen them in stores rarely.
+
+They're usually
+in the back room.
+
+But you can actually buy
+this folding machine.
+
+It's like a giant piece of
+plastic with exactly-- maybe
+
+only three creases,
+I think typically.
+
+And then you just do them
+in some order manually
+
+with simple folds,
+and it does make
+
+really nicely folded T-shirts.
+
+Nicer than I could
+fold by hand, anyway.
+
+All right.
+
+That was just for fun.
+
+While we're on the
+topic of T-shirts.
+
+Next question is about
+higher dimensions.
+
+So I mentioned
+briefly, yeah, you
+
+can do higher
+dimensional origami.
+
+Not much is known about it.
+
+So a natural thing to ask
+about is flat foldability
+
+for higher dimensions.
+
+And there are exactly
+two papers about this.
+
+Well, maybe even just one.
+
+The old one is this paper
+by Kawasaki-- same guy
+
+as Kawasaki's condition--
+and this is in this book.
+
+This the first--
+this is a hard book
+
+to get a copy of,
+First International
+
+Meeting of Origami
+Science and Technology.
+
+These days it's called
+Origami Science, Math,
+
+and Education, OSME.
+
+And this T-shirt is from
+the latest one, which
+
+was in Singapore two
+years ago, I think, 2010.
+
+Next one is in a
+year or two in Japan.
+
+So this is the very first one.
+
+This is before my time.
+
+And there's this paper.
+
+It's a translated Japanese
+paper, so it has a few typos.
+
+We also have the
+Japanese original
+
+if you're interested in
+reading this some time.
+
+You see, for example,
+here is folding
+
+a regular piece
+of paper in half.
+
+Here's folding a 3D
+solid of paper in half.
+
+A little harder to
+imagine, but there it is.
+
+And let's see,
+what's in this paper?
+
+There's a definition,
+although I would really
+
+call it a necessary condition.
+
+I think this is not
+a good definition
+
+of flat origami in 3D.
+
+But there it is.
+
+This is the definition.
+
+What it says is basically,
+locally everything works out.
+
+When you do a fold,
+it's like a reflection.
+
+If you do it
+instantaneously, this
+
+is like reflecting this
+piece through the line
+
+for flat folding.
+
+This is like reflecting this
+piece through the plane.
+
+And so one condition you
+have is that if you-- it's
+
+easier to look at one of
+the examples in the paper.
+
+So you have this
+crease pattern, which
+
+you can draw by a bunch
+of planes, let's say.
+
+If you kind of walk
+around and say, OK, I
+
+go through this
+crease, which means
+
+I reflect through
+that plane, then
+
+I reflect through this plane,
+this plane, this plane,
+
+you can take any sort of path,
+any cycle through this world.
+
+In the end I should end
+up back where I started.
+
+Otherwise I'm ripping.
+
+And what that condition
+says is that if you
+
+take the sequence of reflections
+and you compose them,
+
+you end up with no reflection
+at all, that nothing moved.
+
+And so that's a necessary
+condition for flat foldability.
+
+I wouldn't call it a definition,
+although this paper did.
+
+Natural definition
+is more like what
+
+we draw in 2D for
+flat folding, where
+
+we add another layer,
+another dimension,
+
+and then guarantee no
+collisions in that dimension.
+
+So same thing in 3D.
+
+It's just harder to imagine
+stacking up copies of 3D.
+
+Question?
+
+AUDIENCE: Doesn't the
+reflection analogy
+
+only apply to
+simple folds, where
+
+the plane goes all the way?
+
+PROFESSOR: OK.
+
+Good question.
+
+The reflection
+analogy definitely
+
+applies to simple folds.
+
+It also applies to
+non-simple folds.
+
+But it does require
+straight folds,
+
+which here mean flat
+folds, like planar folds.
+
+For curve creases,
+you're not really
+
+reflecting, because
+you can't fold
+
+a curve crease all the way.
+
+You can't fold it flat.
+
+But whenever you fold
+something all the way-- so even
+
+in something like this, which is
+not a simple fold in the end--
+
+you can check.
+
+Essentially, this is what we--
+on the circle, when we said,
+
+OK, you walk this way and then
+you just change direction.
+
+That's essentially
+the reflection
+
+that's happening on the circle.
+
+If you live on the circle
+you're reflecting in
+
+that you're immediately
+bouncing back at that crease.
+
+It turns out to
+hold in 2D as well.
+
+So if you look at the
+effect of this crease,
+
+it is that you're reflecting
+this part over that crease.
+
+I guess you can see
+it in the folding too.
+
+I mean, you go over this
+crease, then you hit this line,
+
+and then you immediately
+bounce back at the line.
+
+That is actually a
+reflection through the line.
+
+Good question.
+
+It's obvious for simple
+folds, but reflection actually
+
+works here as well.
+
+We'll talk more about that in
+the next lecture, I believe.
+
+OK.
+
+I was looking up reference,
+any papers that cited that one,
+
+and there's basically
+one paper, which
+
+is this kind of a
+graphics/art/math paper talking
+
+about four-dimensional origami.
+
+It's basically some
+simulations and some examples.
+
+Here's the not folding
+all the way picture.
+
+A little harder to imagine.
+
+Here they're doing, I think, the
+4D analog of a rabbit ear fold.
+
+Little hard to
+tell, but first they
+
+do a simple fold
+along a bisector.
+
+That I can understand.
+
+And then they do an
+inside reverse fold.
+
+And then you end up with
+1/4 of the tetrahedron.
+
+So if you divide, this is the
+centroid of the tetrahedron.
+
+It's really hard to
+draw these pictures.
+
+In the paper, they
+actually showed two images,
+
+and if you align
+them with your eyes
+
+then you'll see
+a 3D image, which
+
+is of course a projection
+of the 4D thing.
+
+They also have this one.
+
+Anyone have red-blue
+glasses with them?
+
+Then you'll see this in 3D.
+
+Here you can watch that later.
+
+This is their 4D analog of
+a flapping bird, I guess.
+
+It's pretty hard to see
+these pictures, though
+
+But this is the state of the art
+in 4D origami as far as I know.
+
+It's kind of neat to find.
+
+This is a pretty recent paper.
+
+Questions about
+higher dimensions?
+
+Lots of things are open.
+
+For example, single
+vertex flat foldability
+
+could be a neat problem.
+
+I don't think-- It may be
+that Kawasaki's condition
+
+from that paper is enough.
+
+I don't know.
+
+Maybe not.
+
+OK.
+
+Last question, just kind
+of a nice place to end
+
+is, why are we spending all
+this time on flat foldability.
+
+Flat origami's kind of boring.
+
+And so why do we spend
+all this time with it?
+
+It's good to check
+why are we doing this.
+
+One answer of course is that
+there's interesting mathematics
+
+here.
+
+It's kind of a natural question.
+
+Why not?
+
+That's the math cop-out answer.
+
+But there are actually a
+lot of good answers as well.
+
+One answer is that flat origami
+actually is pretty cool.
+
+There's a whole world of
+flat tessellations, where
+
+you fold a repeating
+pattern in your sheet.
+
+This is from a
+rectangle of paper.
+
+What you're seeing here
+is a shadow pattern.
+
+It's held up to a window, and
+so you see this shadow pattern,
+
+which looks an awful lot like
+a 6 by 6 by 6 Rubik's cube.
+
+That's the design here.
+
+You could make it even
+larger if you want.
+
+Another answer is, well,
+maybe I need to store stuff.
+
+And while I can
+unfold things, it's
+
+kind of big when it's unfolded.
+
+If I could fold it
+all the way flat--
+
+maybe I care about the 3D
+shape, but if I could fold it
+
+all the way flat, then it
+would be easier to store.
+
+It's going to be smaller, more
+compact, I can roll it up,
+
+I can do lots of things.
+
+Airbag folding is one example.
+
+Here you actually
+start with a 3D shape.
+
+There's no sort of unfold.
+
+It's been sewn into a 3D shape.
+
+And then you want to collapse
+it into some nice flat shape
+
+for storage in your steering
+wheel, or the side of your car,
+
+or whatever.
+
+And this is an example of
+folding using flat origami
+
+designs.
+
+This crease pattern is
+based on the tree method,
+
+and other stuff we haven't
+covered yet, fold and cut.
+
+So that's another.
+
+That's sort of the
+practical answer.
+
+And then there's more
+mathematical answers,
+
+deeper things.
+
+Even if you don't care about
+flat folding by itself,
+
+it turns out to relate
+to 3D folding as well.
+
+This is a paper
+that's very cool.
+
+We have a guest lecture by
+Tomohiro Tachi coming up.
+
+I haven't scheduled
+exactly when it will be,
+
+because it's in the in the box.
+
+It's on tape.
+
+So we'll be watching
+that at some point.
+
+He was actually just
+visiting a couple weeks ago.
+
+And he has this
+cool theorem which
+
+says that if you
+have a plane or quad
+
+mesh-- so a particular kind of
+crease pattern, every vertex
+
+has four incident increases,
+every face is a quadrilateral--
+
+and it's flat foldable--
+so you may not
+
+care about flat
+foldability, but you
+
+need this Kawasaki
+condition to guarantee
+
+that this will work-- then it
+has a rigid folding motion, if
+
+and only if it has a 3D state.
+
+Let me show you some examples.
+
+So this a kind of a classic
+origami called miura-ori.
+
+And it has this cool property
+that even if these panels are
+
+made up out of rigid material
+like sheet metal or plastic
+
+or whatever, if these are
+hinges you can still fold it.
+
+And this is an
+animation of it folding.
+
+And indeed it folds flat.
+
+And what the
+theorem is saying is
+
+if you can build a 3D picture
+like this, any one of these,
+
+that guarantees that there's
+this folding motion-- not
+
+necessarily all the way to flat,
+but at least part way to flat.
+
+And often you can get
+it all the way to flat.
+
+And so Tomohiro's
+developed software
+
+that lets you start
+with something
+
+you know works-- so this
+is a miura-ori that's
+
+been folded partly--
+and then just start
+
+pulling on the vertices and
+messing it up and just changing
+
+the shapes.
+
+So this is not a folding.
+
+You're changing how the
+paper fits together.
+
+You're changing
+the crease pattern.
+
+As you do that, he keeps
+track of the crease pattern
+
+and he adds constraints
+to make sure
+
+that it stays flat foldable.
+
+The result is you end up with
+a 3D embedding, a 3D folding,
+
+and you have a flat
+foldable crease
+
+pattern that goes with it.
+
+And that guarantees
+that you get a motion.
+
+Those two things.
+
+So this technique of
+having flat foldability
+
+lets him design crazy
+crease patterns that
+
+fold into whatever
+shape he wants
+
+with a nice rigid motion where
+all these panels stay rigid.
+
+So that's another motivation
+for flat foldability.
+
+It's probably used
+elsewhere as well,
+
+but this is kind of the
+coolest, newest example I know,
+
+where it's just a
+condition in the theorem,
+
+and in order to check
+that condition you
+
+need to understand
+flat foldability.
+
+Other questions?
+
+That's all I have for slides.
+
+Cool.
+
+That's the end of class.
\ No newline at end of file
diff --git a/ywl3pq6yc54.txt b/ywl3pq6yc54.txt
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--- /dev/null
+++ b/ywl3pq6yc54.txt
@@ -0,0 +1,13195 @@
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+ 
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+of MIT courses visit MIT opencourseware
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+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu well today's today's topic
+
+ align:start position:0%
+ocw.mit.edu well today's today's topic
+ 
+
+ align:start position:0%
+ocw.mit.edu well today's today's topic
+is portfolio Theory and it's uh really
+
+ align:start position:0%
+is portfolio Theory and it's uh really
+ 
+
+ align:start position:0%
+is portfolio Theory and it's uh really
+one of the most important topics in
+
+ align:start position:0%
+one of the most important topics in
+ 
+
+ align:start position:0%
+one of the most important topics in
+finance
+
+ align:start position:0%
+finance
+ 
+
+ align:start position:0%
+finance
+um we're going to go through the uh
+
+ align:start position:0%
+um we're going to go through the uh
+ 
+
+ align:start position:0%
+um we're going to go through the uh
+historical theory of
+
+ align:start position:0%
+historical theory of
+ 
+
+ align:start position:0%
+historical theory of
+portfolio uh optimization uh beginning
+
+ align:start position:0%
+portfolio uh optimization uh beginning
+ 
+
+ align:start position:0%
+portfolio uh optimization uh beginning
+with marwitz mean variance
+
+ align:start position:0%
+with marwitz mean variance
+ 
+
+ align:start position:0%
+with marwitz mean variance
+optimization uh where we look at
+
+ align:start position:0%
+optimization uh where we look at
+ 
+
+ align:start position:0%
+optimization uh where we look at
+portfolios in terms of their performance
+
+ align:start position:0%
+portfolios in terms of their performance
+ 
+
+ align:start position:0%
+portfolios in terms of their performance
+characteristics as determined by their
+
+ align:start position:0%
+characteristics as determined by their
+ 
+
+ align:start position:0%
+characteristics as determined by their
+mean return and the volatility of
+
+ align:start position:0%
+mean return and the volatility of
+ 
+
+ align:start position:0%
+mean return and the volatility of
+returns uh this analysis uh gets
+
+ align:start position:0%
+returns uh this analysis uh gets
+ 
+
+ align:start position:0%
+returns uh this analysis uh gets
+extended by looking at also investing
+
+ align:start position:0%
+extended by looking at also investing
+ 
+
+ align:start position:0%
+extended by looking at also investing
+with a risk-free asset uh the initial
+
+ align:start position:0%
+with a risk-free asset uh the initial
+ 
+
+ align:start position:0%
+with a risk-free asset uh the initial
+Theory on folio analysis didn't consider
+
+ align:start position:0%
+Theory on folio analysis didn't consider
+ 
+
+ align:start position:0%
+Theory on folio analysis didn't consider
+investing in cash but just investing in
+
+ align:start position:0%
+investing in cash but just investing in
+ 
+
+ align:start position:0%
+investing in cash but just investing in
+Risky assets uh the problem changes
+
+ align:start position:0%
+Risky assets uh the problem changes
+ 
+
+ align:start position:0%
+Risky assets uh the problem changes
+quite dramatically when we add the
+
+ align:start position:0%
+quite dramatically when we add the
+ 
+
+ align:start position:0%
+quite dramatically when we add the
+risk-free
+
+ align:start position:0%
+risk-free
+ 
+
+ align:start position:0%
+risk-free
+asset uh then the topic of utility
+
+ align:start position:0%
+asset uh then the topic of utility
+ 
+
+ align:start position:0%
+asset uh then the topic of utility
+Theory uh vanoyan Morganstern utility
+
+ align:start position:0%
+Theory uh vanoyan Morganstern utility
+ 
+
+ align:start position:0%
+Theory uh vanoyan Morganstern utility
+Theory uh in uh statistical decision
+
+ align:start position:0%
+Theory uh in uh statistical decision
+ 
+
+ align:start position:0%
+Theory uh in uh statistical decision
+Theory uh we are trying to make
+
+ align:start position:0%
+Theory uh we are trying to make
+ 
+
+ align:start position:0%
+Theory uh we are trying to make
+decisions under uncertainty in a
+
+ align:start position:0%
+decisions under uncertainty in a
+ 
+
+ align:start position:0%
+decisions under uncertainty in a
+rational way and Von noyman and uh
+
+ align:start position:0%
+rational way and Von noyman and uh
+ 
+
+ align:start position:0%
+rational way and Von noyman and uh
+Morgan Stern uh developed a UT expected
+
+ align:start position:0%
+Morgan Stern uh developed a UT expected
+ 
+
+ align:start position:0%
+Morgan Stern uh developed a UT expected
+utility hypothesis for rational
+
+ align:start position:0%
+utility hypothesis for rational
+ 
+
+ align:start position:0%
+utility hypothesis for rational
+decision- making and that's really very
+
+ align:start position:0%
+decision- making and that's really very
+ 
+
+ align:start position:0%
+decision- making and that's really very
+important motivator for uh decision
+
+ align:start position:0%
+important motivator for uh decision
+ 
+
+ align:start position:0%
+important motivator for uh decision
+analysis generally and portfolio
+
+ align:start position:0%
+analysis generally and portfolio
+ 
+
+ align:start position:0%
+analysis generally and portfolio
+selection in particular so we'll go
+
+ align:start position:0%
+selection in particular so we'll go
+ 
+
+ align:start position:0%
+selection in particular so we'll go
+through that uh then we'll turn to
+
+ align:start position:0%
+through that uh then we'll turn to
+ 
+
+ align:start position:0%
+through that uh then we'll turn to
+portfolio optimization constraints there
+
+ align:start position:0%
+portfolio optimization constraints there
+ 
+
+ align:start position:0%
+portfolio optimization constraints there
+are realistic issues when you have well
+
+ align:start position:0%
+are realistic issues when you have well
+ 
+
+ align:start position:0%
+are realistic issues when you have well
+there's how much money you have to
+
+ align:start position:0%
+there's how much money you have to
+ 
+
+ align:start position:0%
+there's how much money you have to
+invest or how much Capital you have to
+
+ align:start position:0%
+invest or how much Capital you have to
+ 
+
+ align:start position:0%
+invest or how much Capital you have to
+invest whether you can short Securities
+
+ align:start position:0%
+invest whether you can short Securities
+ 
+
+ align:start position:0%
+invest whether you can short Securities
+or not uh whether there are uh sort of
+
+ align:start position:0%
+or not uh whether there are uh sort of
+ 
+
+ align:start position:0%
+or not uh whether there are uh sort of
+limits in capacity of different assets
+
+ align:start position:0%
+limits in capacity of different assets
+ 
+
+ align:start position:0%
+limits in capacity of different assets
+you might want to trade those can come
+
+ align:start position:0%
+you might want to trade those can come
+ 
+
+ align:start position:0%
+you might want to trade those can come
+into play and affect the
+
+ align:start position:0%
+into play and affect the
+ 
+
+ align:start position:0%
+into play and affect the
+solutions um all of these methods are
+
+ align:start position:0%
+solutions um all of these methods are
+ 
+
+ align:start position:0%
+solutions um all of these methods are
+driven by estimates of how well we
+
+ align:start position:0%
+driven by estimates of how well we
+ 
+
+ align:start position:0%
+driven by estimates of how well we
+expect assets to do so estimating
+
+ align:start position:0%
+expect assets to do so estimating
+ 
+
+ align:start position:0%
+expect assets to do so estimating
+returns are estimating
+
+ align:start position:0%
+returns are estimating
+ 
+
+ align:start position:0%
+returns are estimating
+Alphas uh and also estimating the
+
+ align:start position:0%
+Alphas uh and also estimating the
+ 
+
+ align:start position:0%
+Alphas uh and also estimating the
+volatilities and correlations amongst
+
+ align:start position:0%
+volatilities and correlations amongst
+ 
+
+ align:start position:0%
+volatilities and correlations amongst
+the assets we're trading in uh most of
+
+ align:start position:0%
+the assets we're trading in uh most of
+ 
+
+ align:start position:0%
+the assets we're trading in uh most of
+the theory we'll talk about today deals
+
+ align:start position:0%
+the theory we'll talk about today deals
+ 
+
+ align:start position:0%
+the theory we'll talk about today deals
+with uh estimates well with the problem
+
+ align:start position:0%
+with uh estimates well with the problem
+ 
+
+ align:start position:0%
+with uh estimates well with the problem
+where we're assuming basically uh
+
+ align:start position:0%
+where we're assuming basically uh
+ 
+
+ align:start position:0%
+where we're assuming basically uh
+certainty in terms of understanding
+
+ align:start position:0%
+certainty in terms of understanding
+ 
+
+ align:start position:0%
+certainty in terms of understanding
+those uh underlying uh return
+
+ align:start position:0%
+those uh underlying uh return
+ 
+
+ align:start position:0%
+those uh underlying uh return
+characteristics the means variances and
+
+ align:start position:0%
+characteristics the means variances and
+ 
+
+ align:start position:0%
+characteristics the means variances and
+correlations but when we have to
+
+ align:start position:0%
+correlations but when we have to
+ 
+
+ align:start position:0%
+correlations but when we have to
+estimate those that that raises new
+
+ align:start position:0%
+estimate those that that raises new
+ 
+
+ align:start position:0%
+estimate those that that raises new
+problems and finally we'll finish up
+
+ align:start position:0%
+problems and finally we'll finish up
+ 
+
+ align:start position:0%
+problems and finally we'll finish up
+talking about some alternative risk
+
+ align:start position:0%
+talking about some alternative risk
+ 
+
+ align:start position:0%
+talking about some alternative risk
+measures which extend the
+
+ align:start position:0%
+measures which extend the
+ 
+
+ align:start position:0%
+measures which extend the
+straightforward mean or simple mean
+
+ align:start position:0%
+straightforward mean or simple mean
+ 
+
+ align:start position:0%
+straightforward mean or simple mean
+variance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis now now the mean variance
+
+ align:start position:0%
+analysis now now the mean variance
+ 
+
+ align:start position:0%
+analysis now now the mean variance
+analysis is a single period analysis uh
+
+ align:start position:0%
+analysis is a single period analysis uh
+ 
+
+ align:start position:0%
+analysis is a single period analysis uh
+what we want to do is consider investing
+
+ align:start position:0%
+what we want to do is consider investing
+ 
+
+ align:start position:0%
+what we want to do is consider investing
+our capital in some assets and we want
+
+ align:start position:0%
+our capital in some assets and we want
+ 
+
+ align:start position:0%
+our capital in some assets and we want
+to do so for just a single period and do
+
+ align:start position:0%
+to do so for just a single period and do
+ 
+
+ align:start position:0%
+to do so for just a single period and do
+so optimally um so in terms of notation
+
+ align:start position:0%
+so optimally um so in terms of notation
+ 
+
+ align:start position:0%
+so optimally um so in terms of notation
+we'll consider risky assets indexed by I
+
+ align:start position:0%
+we'll consider risky assets indexed by I
+ 
+
+ align:start position:0%
+we'll consider risky assets indexed by I
+1 through M single period returns will
+
+ align:start position:0%
+1 through M single period returns will
+ 
+
+ align:start position:0%
+1 through M single period returns will
+be a multivariant vector
+
+ align:start position:0%
+be a multivariant vector
+ 
+
+ align:start position:0%
+be a multivariant vector
+of those
+
+ align:start position:0%
+of those
+ 
+
+ align:start position:0%
+of those
+Returns the mean and covariance of this
+
+ align:start position:0%
+Returns the mean and covariance of this
+ 
+
+ align:start position:0%
+Returns the mean and covariance of this
+uh of these assets are represented in a
+
+ align:start position:0%
+uh of these assets are represented in a
+ 
+
+ align:start position:0%
+uh of these assets are represented in a
+vector of returns and a cence matrix of
+
+ align:start position:0%
+vector of returns and a cence matrix of
+ 
+
+ align:start position:0%
+vector of returns and a cence matrix of
+squared volatilities the variances of
+
+ align:start position:0%
+squared volatilities the variances of
+ 
+
+ align:start position:0%
+squared volatilities the variances of
+the assets along the diagonals and the
+
+ align:start position:0%
+the assets along the diagonals and the
+ 
+
+ align:start position:0%
+the assets along the diagonals and the
+co-variances on the off
+
+ align:start position:0%
+co-variances on the off
+ 
+
+ align:start position:0%
+co-variances on the off
+diagonals uh a portfolio will be
+
+ align:start position:0%
+diagonals uh a portfolio will be
+ 
+
+ align:start position:0%
+diagonals uh a portfolio will be
+represented as basically a waiting in of
+
+ align:start position:0%
+represented as basically a waiting in of
+ 
+
+ align:start position:0%
+represented as basically a waiting in of
+our investment in these M assets
+
+ align:start position:0%
+our investment in these M assets
+ 
+
+ align:start position:0%
+our investment in these M assets
+so we'll have a vector W consisting of
+
+ align:start position:0%
+so we'll have a vector W consisting of
+ 
+
+ align:start position:0%
+so we'll have a vector W consisting of
+W1 up to W1 giving the relative weights
+
+ align:start position:0%
+W1 up to W1 giving the relative weights
+ 
+
+ align:start position:0%
+W1 up to W1 giving the relative weights
+an absolute weights of those uh
+
+ align:start position:0%
+an absolute weights of those uh
+ 
+
+ align:start position:0%
+an absolute weights of those uh
+Investments uh we'll assume that we have
+
+ align:start position:0%
+Investments uh we'll assume that we have
+ 
+
+ align:start position:0%
+Investments uh we'll assume that we have
+one unit of capital to invest so the sum
+
+ align:start position:0%
+one unit of capital to invest so the sum
+ 
+
+ align:start position:0%
+one unit of capital to invest so the sum
+of these weights equals one and the
+
+ align:start position:0%
+of these weights equals one and the
+ 
+
+ align:start position:0%
+of these weights equals one and the
+portfolio return has uh expected return
+
+ align:start position:0%
+portfolio return has uh expected return
+ 
+
+ align:start position:0%
+portfolio return has uh expected return
+given by the expectation of this linear
+
+ align:start position:0%
+given by the expectation of this linear
+ 
+
+ align:start position:0%
+given by the expectation of this linear
+combination of the returns which is
+
+ align:start position:0%
+combination of the returns which is
+ 
+
+ align:start position:0%
+combination of the returns which is
+simply the the same linear combination
+
+ align:start position:0%
+simply the the same linear combination
+ 
+
+ align:start position:0%
+simply the the same linear combination
+of the underlying expectations and the
+
+ align:start position:0%
+of the underlying expectations and the
+ 
+
+ align:start position:0%
+of the underlying expectations and the
+co the variance of the portfolio is
+
+ align:start position:0%
+co the variance of the portfolio is
+ 
+
+ align:start position:0%
+co the variance of the portfolio is
+given by the variance of the weighted
+
+ align:start position:0%
+given by the variance of the weighted
+ 
+
+ align:start position:0%
+given by the variance of the weighted
+average of the individual returns which
+
+ align:start position:0%
+average of the individual returns which
+ 
+
+ align:start position:0%
+average of the individual returns which
+is given by this quadratic form in The
+
+ align:start position:0%
+is given by this quadratic form in The
+ 
+
+ align:start position:0%
+is given by this quadratic form in The
+covariance Matrix so uh you know we've
+
+ align:start position:0%
+covariance Matrix so uh you know we've
+ 
+
+ align:start position:0%
+covariance Matrix so uh you know we've
+gone through this uh or you understand I
+
+ align:start position:0%
+gone through this uh or you understand I
+ 
+
+ align:start position:0%
+gone through this uh or you understand I
+think these calculations from our
+
+ align:start position:0%
+think these calculations from our
+ 
+
+ align:start position:0%
+think these calculations from our
+discussion in Time series and that
+
+ align:start position:0%
+discussion in Time series and that
+ 
+
+ align:start position:0%
+discussion in Time series and that
+that's quite quite simple now let's
+
+ align:start position:0%
+that's quite quite simple now let's
+ 
+
+ align:start position:0%
+that's quite quite simple now let's
+before going into the theory for this
+
+ align:start position:0%
+before going into the theory for this
+ 
+
+ align:start position:0%
+before going into the theory for this
+let's look at the
+
+ align:start position:0%
+let's look at the
+ 
+
+ align:start position:0%
+let's look at the
+problem let's look at the portfolio
+
+ align:start position:0%
+problem let's look at the portfolio
+ 
+
+ align:start position:0%
+problem let's look at the portfolio
+analysis problem in a very simplified
+
+ align:start position:0%
+analysis problem in a very simplified
+ 
+
+ align:start position:0%
+analysis problem in a very simplified
+setting uh we're just going to consider
+
+ align:start position:0%
+setting uh we're just going to consider
+ 
+
+ align:start position:0%
+setting uh we're just going to consider
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+assets and talk about optimal portfoli
+
+ align:start position:0%
+assets and talk about optimal portfoli
+ 
+
+ align:start position:0%
+assets and talk about optimal portfoli
+is investing in these two assets so m
+
+ align:start position:0%
+is investing in these two assets so m
+ 
+
+ align:start position:0%
+is investing in these two assets so m
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+2 the first asset uh has return R1 with
+
+ align:start position:0%
+2 the first asset uh has return R1 with
+ 
+
+ align:start position:0%
+2 the first asset uh has return R1 with
+mean .15 now I'm going to think of this
+
+ align:start position:0%
+mean .15 now I'm going to think of this
+ 
+
+ align:start position:0%
+mean .15 now I'm going to think of this
+as annualized returns so a 15%
+
+ align:start position:0%
+as annualized returns so a 15%
+ 
+
+ align:start position:0%
+as annualized returns so a 15%
+annualized return and a volatility of
+
+ align:start position:0%
+annualized return and a volatility of
+ 
+
+ align:start position:0%
+annualized return and a volatility of
+25% the second asset has expected return
+
+ align:start position:0%
+25% the second asset has expected return
+ 
+
+ align:start position:0%
+25% the second asset has expected return
+of 20% and a volatility of
+
+ align:start position:0%
+of 20% and a volatility of
+ 
+
+ align:start position:0%
+of 20% and a volatility of
+30% Sigma
+
+ align:start position:0%
+30% Sigma
+ 
+
+ align:start position:0%
+30% Sigma
+2 these assets are possibly correlated
+
+ align:start position:0%
+2 these assets are possibly correlated
+ 
+
+ align:start position:0%
+2 these assets are possibly correlated
+we'll let row denote the correlation
+
+ align:start position:0%
+we'll let row denote the correlation
+ 
+
+ align:start position:0%
+we'll let row denote the correlation
+between the two and a
+
+ align:start position:0%
+between the two and a
+ 
+
+ align:start position:0%
+between the two and a
+portfolio uh basically all the
+
+ align:start position:0%
+portfolio uh basically all the
+ 
+
+ align:start position:0%
+portfolio uh basically all the
+portfolios we can invest in uh so long
+
+ align:start position:0%
+portfolios we can invest in uh so long
+ 
+
+ align:start position:0%
+portfolios we can invest in uh so long
+as we are you know limited to a unit of
+
+ align:start position:0%
+as we are you know limited to a unit of
+ 
+
+ align:start position:0%
+as we are you know limited to a unit of
+capital and no shorting um are given by
+
+ align:start position:0%
+capital and no shorting um are given by
+ 
+
+ align:start position:0%
+capital and no shorting um are given by
+portfolios indexed by W basically the
+
+ align:start position:0%
+portfolios indexed by W basically the
+ 
+
+ align:start position:0%
+portfolios indexed by W basically the
+amount of money we invest in the second
+
+ align:start position:0%
+amount of money we invest in the second
+ 
+
+ align:start position:0%
+amount of money we invest in the second
+asset so RW is WR wr2 plus 1 minus WR
+
+ align:start position:0%
+asset so RW is WR wr2 plus 1 minus WR
+ 
+
+ align:start position:0%
+asset so RW is WR wr2 plus 1 minus WR
+wr1 that's the return on the portfolio
+
+ align:start position:0%
+wr1 that's the return on the portfolio
+ 
+
+ align:start position:0%
+wr1 that's the return on the portfolio
+that invests in that proport those
+
+ align:start position:0%
+that invests in that proport those
+ 
+
+ align:start position:0%
+that invests in that proport those
+proportions in the two assets the
+
+ align:start position:0%
+proportions in the two assets the
+ 
+
+ align:start position:0%
+proportions in the two assets the
+expected return is this linear
+
+ align:start position:0%
+expected return is this linear
+ 
+
+ align:start position:0%
+expected return is this linear
+combination which is given in Matrix
+
+ align:start position:0%
+combination which is given in Matrix
+ 
+
+ align:start position:0%
+combination which is given in Matrix
+form in the previous page or the pre on
+
+ align:start position:0%
+form in the previous page or the pre on
+ 
+
+ align:start position:0%
+form in the previous page or the pre on
+the lecture notes and the variance are
+
+ align:start position:0%
+the lecture notes and the variance are
+ 
+
+ align:start position:0%
+the lecture notes and the variance are
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+volatility is what it's 1 - Omega 2 time
+
+ align:start position:0%
+volatility is what it's 1 - Omega 2 time
+ 
+
+ align:start position:0%
+volatility is what it's 1 - Omega 2 time
+the variance of R1 plus W ^2 times the
+
+ align:start position:0%
+the variance of R1 plus W ^2 times the
+ 
+
+ align:start position:0%
+the variance of R1 plus W ^2 times the
+variance of R2 then we have a cross uh a
+
+ align:start position:0%
+variance of R2 then we have a cross uh a
+ 
+
+ align:start position:0%
+variance of R2 then we have a cross uh a
+a covariance term that comes into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+play now the mean variance analysis that
+
+ align:start position:0%
+play now the mean variance analysis that
+ 
+
+ align:start position:0%
+play now the mean variance analysis that
+markwitz
+
+ align:start position:0%
+markwitz
+ 
+
+ align:start position:0%
+markwitz
+addressed basically looks at the
+
+ align:start position:0%
+addressed basically looks at the
+ 
+
+ align:start position:0%
+addressed basically looks at the
+feasible portfolio set
+
+ align:start position:0%
+feasible portfolio set
+ 
+
+ align:start position:0%
+feasible portfolio set
+okay we we simplify things by saying
+
+ align:start position:0%
+okay we we simplify things by saying
+ 
+
+ align:start position:0%
+okay we we simplify things by saying
+let's ju Focus just on the volatility or
+
+ align:start position:0%
+let's ju Focus just on the volatility or
+ 
+
+ align:start position:0%
+let's ju Focus just on the volatility or
+variance and the expected return of our
+
+ align:start position:0%
+variance and the expected return of our
+ 
+
+ align:start position:0%
+variance and the expected return of our
+portfolio so we can Define the uh
+
+ align:start position:0%
+portfolio so we can Define the uh
+ 
+
+ align:start position:0%
+portfolio so we can Define the uh
+feasible portfolio set as the collection
+
+ align:start position:0%
+feasible portfolio set as the collection
+ 
+
+ align:start position:0%
+feasible portfolio set as the collection
+of volatility return pairs for all the
+
+ align:start position:0%
+of volatility return pairs for all the
+ 
+
+ align:start position:0%
+of volatility return pairs for all the
+assets or for all the
+
+ align:start position:0%
+assets or for all the
+ 
+
+ align:start position:0%
+assets or for all the
+portfolios and uh so you know well what
+
+ align:start position:0%
+portfolios and uh so you know well what
+ 
+
+ align:start position:0%
+portfolios and uh so you know well what
+is piar that collection basically what's
+
+ align:start position:0%
+is piar that collection basically what's
+ 
+
+ align:start position:0%
+is piar that collection basically what's
+the universe of possible portfolios we
+
+ align:start position:0%
+the universe of possible portfolios we
+ 
+
+ align:start position:0%
+the universe of possible portfolios we
+could construct in this two-dimensional
+
+ align:start position:0%
+could construct in this two-dimensional
+ 
+
+ align:start position:0%
+could construct in this two-dimensional
+case it's going to be very simple in
+
+ align:start position:0%
+case it's going to be very simple in
+ 
+
+ align:start position:0%
+case it's going to be very simple in
+multi-dimensional cases it's more
+
+ align:start position:0%
+multi-dimensional cases it's more
+ 
+
+ align:start position:0%
+multi-dimensional cases it's more
+complicated but what portfolios are
+
+ align:start position:0%
+complicated but what portfolios are
+ 
+
+ align:start position:0%
+complicated but what portfolios are
+optimal
+
+ align:start position:0%
+optimal
+ 
+
+ align:start position:0%
+optimal
+suboptimal how do we choose or identify
+
+ align:start position:0%
+suboptimal how do we choose or identify
+ 
+
+ align:start position:0%
+suboptimal how do we choose or identify
+a particular portfolio to invest in how
+
+ align:start position:0%
+a particular portfolio to invest in how
+ 
+
+ align:start position:0%
+a particular portfolio to invest in how
+is that choice made and is there any
+
+ align:start position:0%
+is that choice made and is there any
+ 
+
+ align:start position:0%
+is that choice made and is there any
+special structure to these
+
+ align:start position:0%
+special structure to these
+ 
+
+ align:start position:0%
+special structure to these
+portfolios um what you'll see in the
+
+ align:start position:0%
+portfolios um what you'll see in the
+ 
+
+ align:start position:0%
+portfolios um what you'll see in the
+lecture today is that the uh marwitz
+
+ align:start position:0%
+lecture today is that the uh marwitz
+ 
+
+ align:start position:0%
+lecture today is that the uh marwitz
+Theory and extensions of that provide
+
+ align:start position:0%
+Theory and extensions of that provide
+ 
+
+ align:start position:0%
+Theory and extensions of that provide
+really elegant answers to these uh
+
+ align:start position:0%
+really elegant answers to these uh
+ 
+
+ align:start position:0%
+really elegant answers to these uh
+questions and but let's understand
+
+ align:start position:0%
+questions and but let's understand
+ 
+
+ align:start position:0%
+questions and but let's understand
+basically what's going on just with this
+
+ align:start position:0%
+basically what's going on just with this
+ 
+
+ align:start position:0%
+basically what's going on just with this
+two asset
+
+ align:start position:0%
+two asset
+ 
+
+ align:start position:0%
+two asset
+case and what I'm going to do here is uh
+
+ align:start position:0%
+case and what I'm going to do here is uh
+ 
+
+ align:start position:0%
+case and what I'm going to do here is uh
+just simulate 500 weekly
+
+ align:start position:0%
+just simulate 500 weekly
+ 
+
+ align:start position:0%
+just simulate 500 weekly
+returns with different values of the
+
+ align:start position:0%
+returns with different values of the
+ 
+
+ align:start position:0%
+returns with different values of the
+correlation between the two
+
+ align:start position:0%
+correlation between the two
+ 
+
+ align:start position:0%
+correlation between the two
+assets and we want to examine the
+
+ align:start position:0%
+assets and we want to examine the
+ 
+
+ align:start position:0%
+assets and we want to examine the
+cumulative returns of each
+
+ align:start position:0%
+cumulative returns of each
+ 
+
+ align:start position:0%
+cumulative returns of each
+asset the asset returns in terms of
+
+ align:start position:0%
+asset the asset returns in terms of
+ 
+
+ align:start position:0%
+asset the asset returns in terms of
+their means volatilities and
+
+ align:start position:0%
+their means volatilities and
+ 
+
+ align:start position:0%
+their means volatilities and
+correlations a plot of piar and the uh
+
+ align:start position:0%
+correlations a plot of piar and the uh
+ 
+
+ align:start position:0%
+correlations a plot of piar and the uh
+cumulative returns of each asset uh with
+
+ align:start position:0%
+cumulative returns of each asset uh with
+ 
+
+ align:start position:0%
+cumulative returns of each asset uh with
+the minimum variance portfolio so um let
+
+ align:start position:0%
+the minimum variance portfolio so um let
+ 
+
+ align:start position:0%
+the minimum variance portfolio so um let
+me just highlight here that what we want
+
+ align:start position:0%
+me just highlight here that what we want
+ 
+
+ align:start position:0%
+me just highlight here that what we want
+here is to be plotting Sigma Omega
+
+ align:start position:0%
+here is to be plotting Sigma Omega
+ 
+
+ align:start position:0%
+here is to be plotting Sigma Omega
+versus Alpha
+
+ align:start position:0%
+versus Alpha
+ 
+
+ align:start position:0%
+versus Alpha
+Omega um and we have two assets
+
+ align:start position:0%
+Omega um and we have two assets
+ 
+
+ align:start position:0%
+Omega um and we have two assets
+We
+
+ align:start position:0%
+We
+ 
+
+ align:start position:0%
+We
+have basically
+
+ align:start position:0%
+have basically
+ 
+
+ align:start position:0%
+have basically
+um Sigma 1 and Alpha 1 corresponds to
+
+ align:start position:0%
+um Sigma 1 and Alpha 1 corresponds to
+ 
+
+ align:start position:0%
+um Sigma 1 and Alpha 1 corresponds to
+our first asset Sigma 2 and Alpha
+
+ align:start position:0%
+our first asset Sigma 2 and Alpha
+ 
+
+ align:start position:0%
+our first asset Sigma 2 and Alpha
+2 corresponds to our second asset so
+
+ align:start position:0%
+2 corresponds to our second asset so
+ 
+
+ align:start position:0%
+2 corresponds to our second asset so
+this point here corresponds to
+
+ align:start position:0%
+this point here corresponds to
+ 
+
+ align:start position:0%
+this point here corresponds to
+W
+
+ align:start position:0%
+W
+ 
+
+ align:start position:0%
+W
+equals W equals uh
+
+ align:start position:0%
+equals W equals uh
+ 
+
+ align:start position:0%
+equals W equals uh
+zero and U the other corresponds to W
+
+ align:start position:0%
+zero and U the other corresponds to W
+ 
+
+ align:start position:0%
+zero and U the other corresponds to W
+equals 1 so uh R1 and
+
+ align:start position:0%
+equals 1 so uh R1 and
+ 
+
+ align:start position:0%
+equals 1 so uh R1 and
+R2 now what's going to happen when we
+
+ align:start position:0%
+R2 now what's going to happen when we
+ 
+
+ align:start position:0%
+R2 now what's going to happen when we
+combine the Assets in a
+
+ align:start position:0%
+combine the Assets in a
+ 
+
+ align:start position:0%
+combine the Assets in a
+portfolio well
+
+ align:start position:0%
+portfolio well
+ 
+
+ align:start position:0%
+portfolio well
+um let's take a
+
+ align:start position:0%
+um let's take a
+ 
+
+ align:start position:0%
+um let's take a
+look at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simulation and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here is a
+
+ align:start position:0%
+okay here is a
+ 
+
+ align:start position:0%
+okay here is a
+graph of the
+
+ align:start position:0%
+graph of the
+ 
+
+ align:start position:0%
+graph of the
+simulated asset
+
+ align:start position:0%
+simulated asset
+ 
+
+ align:start position:0%
+simulated asset
+returns
+
+ align:start position:0%
+returns
+ 
+
+ align:start position:0%
+returns
+with basically a uh the mean returns
+
+ align:start position:0%
+with basically a uh the mean returns
+ 
+
+ align:start position:0%
+with basically a uh the mean returns
+given by 15% 25% volatility is 20 and 30
+
+ align:start position:0%
+given by 15% 25% volatility is 20 and 30
+ 
+
+ align:start position:0%
+given by 15% 25% volatility is 20 and 30
+and with an asset correlation of zero so
+
+ align:start position:0%
+and with an asset correlation of zero so
+ 
+
+ align:start position:0%
+and with an asset correlation of zero so
+here's just a scatter plot of the weekly
+
+ align:start position:0%
+here's just a scatter plot of the weekly
+ 
+
+ align:start position:0%
+here's just a scatter plot of the weekly
+returns there's basically no apparent
+
+ align:start position:0%
+returns there's basically no apparent
+ 
+
+ align:start position:0%
+returns there's basically no apparent
+correlation there there actually is a
+
+ align:start position:0%
+correlation there there actually is a
+ 
+
+ align:start position:0%
+correlation there there actually is a
+sample correlation because the a sample
+
+ align:start position:0%
+sample correlation because the a sample
+ 
+
+ align:start position:0%
+sample correlation because the a sample
+from this uh these distributions does
+
+ align:start position:0%
+from this uh these distributions does
+ 
+
+ align:start position:0%
+from this uh these distributions does
+you know won't have perfectly zero
+
+ align:start position:0%
+you know won't have perfectly zero
+ 
+
+ align:start position:0%
+you know won't have perfectly zero
+correlation on top we have graphs of the
+
+ align:start position:0%
+correlation on top we have graphs of the
+ 
+
+ align:start position:0%
+correlation on top we have graphs of the
+cumulative returns of the two ass
+
+ align:start position:0%
+cumulative returns of the two ass
+ 
+
+ align:start position:0%
+cumulative returns of the two ass
+individual
+
+ align:start position:0%
+individual
+ 
+
+ align:start position:0%
+individual
+assets uh rather obviously the higher
+
+ align:start position:0%
+assets uh rather obviously the higher
+ 
+
+ align:start position:0%
+assets uh rather obviously the higher
+graph corresponds to the asset with
+
+ align:start position:0%
+graph corresponds to the asset with
+ 
+
+ align:start position:0%
+graph corresponds to the asset with
+higher return um the lower which is
+
+ align:start position:0%
+higher return um the lower which is
+ 
+
+ align:start position:0%
+higher return um the lower which is
+asset two and the green corresponds to
+
+ align:start position:0%
+asset two and the green corresponds to
+ 
+
+ align:start position:0%
+asset two and the green corresponds to
+asset
+
+ align:start position:0%
+asset
+ 
+
+ align:start position:0%
+asset
+one the graph on the right top right is
+
+ align:start position:0%
+one the graph on the right top right is
+ 
+
+ align:start position:0%
+one the graph on the right top right is
+the graph of the feasible set as we
+
+ align:start position:0%
+the graph of the feasible set as we
+ 
+
+ align:start position:0%
+the graph of the feasible set as we
+allocate between asset one and asset
+
+ align:start position:0%
+allocate between asset one and asset
+ 
+
+ align:start position:0%
+allocate between asset one and asset
+two and so by the simulation
+
+ align:start position:0%
+two and so by the simulation
+ 
+
+ align:start position:0%
+two and so by the simulation
+this you
+
+ align:start position:0%
+this you
+ 
+
+ align:start position:0%
+this you
+know this curve corresponds to the
+
+ align:start position:0%
+know this curve corresponds to the
+ 
+
+ align:start position:0%
+know this curve corresponds to the
+feasible set of
+
+ align:start position:0%
+feasible set of
+ 
+
+ align:start position:0%
+feasible set of
+portfolios and what's uh really
+
+ align:start position:0%
+portfolios and what's uh really
+ 
+
+ align:start position:0%
+portfolios and what's uh really
+remarkable um is that we can get uh
+
+ align:start position:0%
+remarkable um is that we can get uh
+ 
+
+ align:start position:0%
+remarkable um is that we can get uh
+basically a reduction in the volatility
+
+ align:start position:0%
+basically a reduction in the volatility
+ 
+
+ align:start position:0%
+basically a reduction in the volatility
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+portfolio without compromising and in
+
+ align:start position:0%
+portfolio without compromising and in
+ 
+
+ align:start position:0%
+portfolio without compromising and in
+fact improving the return of the
+
+ align:start position:0%
+fact improving the return of the
+ 
+
+ align:start position:0%
+fact improving the return of the
+portfolio so if we invest fully in asset
+
+ align:start position:0%
+portfolio so if we invest fully in asset
+ 
+
+ align:start position:0%
+portfolio so if we invest fully in asset
+one we're at this point as we
+
+ align:start position:0%
+one we're at this point as we
+ 
+
+ align:start position:0%
+one we're at this point as we
+increase as we start allocating towards
+
+ align:start position:0%
+increase as we start allocating towards
+ 
+
+ align:start position:0%
+increase as we start allocating towards
+asset
+
+ align:start position:0%
+asset
+ 
+
+ align:start position:0%
+asset
+2 not only does the return of asset of
+
+ align:start position:0%
+2 not only does the return of asset of
+ 
+
+ align:start position:0%
+2 not only does the return of asset of
+the portfolio go up but the volatility
+
+ align:start position:0%
+the portfolio go up but the volatility
+ 
+
+ align:start position:0%
+the portfolio go up but the volatility
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+down and uh let's see on
+
+ align:start position:0%
+down and uh let's see on
+ 
+
+ align:start position:0%
+down and uh let's see on
+the in this simulation what I've done is
+
+ align:start position:0%
+the in this simulation what I've done is
+ 
+
+ align:start position:0%
+the in this simulation what I've done is
+also plotted the uh Return of the
+
+ align:start position:0%
+also plotted the uh Return of the
+ 
+
+ align:start position:0%
+also plotted the uh Return of the
+portfolio corresponding to the minimum
+
+ align:start position:0%
+portfolio corresponding to the minimum
+ 
+
+ align:start position:0%
+portfolio corresponding to the minimum
+variance
+
+ align:start position:0%
+variance
+ 
+
+ align:start position:0%
+variance
+um so let's uh just look at the minimum
+
+ align:start position:0%
+um so let's uh just look at the minimum
+ 
+
+ align:start position:0%
+um so let's uh just look at the minimum
+variance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+portfolio
+
+ align:start position:0%
+portfolio
+ 
+
+ align:start position:0%
+portfolio
+um for a minute we have Sigma squar
+
+ align:start position:0%
+um for a minute we have Sigma squar
+ 
+
+ align:start position:0%
+um for a minute we have Sigma squar
+W is equal to 1 -
+
+ align:start position:0%
+W is equal to 1 -
+ 
+
+ align:start position:0%
+W is equal to 1 -
+w^2 +
+
+ align:start position:0%
+w^2 +
+ 
+
+ align:start position:0%
+w^2 +
+w^2 Sigma 2^ 2 this is Sigma 1^
+
+ align:start position:0%
+w^2 Sigma 2^ 2 this is Sigma 1^
+ 
+
+ align:start position:0%
+w^2 Sigma 2^ 2 this is Sigma 1^
+2 and then plus Z in the case that
+
+ align:start position:0%
+2 and then plus Z in the case that
+ 
+
+ align:start position:0%
+2 and then plus Z in the case that
+there's no correlation between the two
+
+ align:start position:0%
+there's no correlation between the two
+ 
+
+ align:start position:0%
+there's no correlation between the two
+assets if we want to minimize this uh
+
+ align:start position:0%
+assets if we want to minimize this uh
+ 
+
+ align:start position:0%
+assets if we want to minimize this uh
+portfolio uh
+
+ align:start position:0%
+portfolio uh
+ 
+
+ align:start position:0%
+portfolio uh
+volatility we
+
+ align:start position:0%
+volatility we
+ 
+
+ align:start position:0%
+volatility we
+can take the derivative of that with
+
+ align:start position:0%
+can take the derivative of that with
+ 
+
+ align:start position:0%
+can take the derivative of that with
+respect to the weight and uh set that
+
+ align:start position:0%
+respect to the weight and uh set that
+ 
+
+ align:start position:0%
+respect to the weight and uh set that
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+zero so what's that equal to well it's
+
+ align:start position:0%
+zero so what's that equal to well it's
+ 
+
+ align:start position:0%
+zero so what's that equal to well it's
+uh let's see did I do this
+
+ align:start position:0%
+uh let's see did I do this
+ 
+
+ align:start position:0%
+uh let's see did I do this
+right actually just with the uh previous
+
+ align:start position:0%
+right actually just with the uh previous
+ 
+
+ align:start position:0%
+right actually just with the uh previous
+notes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah sorry R1 is equal to zero okay
+
+ align:start position:0%
+so yeah sorry R1 is equal to zero okay
+ 
+
+ align:start position:0%
+so yeah sorry R1 is equal to zero okay
+right okay so we have 2 1 minus W Sig 1^
+
+ align:start position:0%
+right okay so we have 2 1 minus W Sig 1^
+ 
+
+ align:start position:0%
+right okay so we have 2 1 minus W Sig 1^
+2 * -1 + 2 W Sigma 2^ 2 is equal to
+
+ align:start position:0%
+2 * -1 + 2 W Sigma 2^ 2 is equal to
+ 
+
+ align:start position:0%
+2 * -1 + 2 W Sigma 2^ 2 is equal to
+Z and so the uh solving this we get w
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to let's see you get one over Sigma 1^
+
+ align:start position:0%
+to let's see you get one over Sigma 1^
+ 
+
+ align:start position:0%
+to let's see you get one over Sigma 1^
+2 sorry 1/ Sigma 2^ 2 / 1 over Sigma 1^
+
+ align:start position:0%
+2 sorry 1/ Sigma 2^ 2 / 1 over Sigma 1^
+ 
+
+ align:start position:0%
+2 sorry 1/ Sigma 2^ 2 / 1 over Sigma 1^
+2 + 1 over Sigma 2^ 2 if you solve this
+
+ align:start position:0%
+2 + 1 over Sigma 2^ 2 if you solve this
+ 
+
+ align:start position:0%
+2 + 1 over Sigma 2^ 2 if you solve this
+out you basically get a
+
+ align:start position:0%
+out you basically get a
+ 
+
+ align:start position:0%
+out you basically get a
+waiting on the different assets which
+
+ align:start position:0%
+waiting on the different assets which
+ 
+
+ align:start position:0%
+waiting on the different assets which
+weights inversely proportional to their
+
+ align:start position:0%
+weights inversely proportional to their
+ 
+
+ align:start position:0%
+weights inversely proportional to their
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+volatility and with
+
+ align:start position:0%
+volatility and with
+ 
+
+ align:start position:0%
+volatility and with
+this graph here you can see that it is
+
+ align:start position:0%
+this graph here you can see that it is
+ 
+
+ align:start position:0%
+this graph here you can see that it is
+the blue graph is a bit closer to asset
+
+ align:start position:0%
+the blue graph is a bit closer to asset
+ 
+
+ align:start position:0%
+the blue graph is a bit closer to asset
+one than to asset 2's cumulative return
+
+ align:start position:0%
+one than to asset 2's cumulative return
+ 
+
+ align:start position:0%
+one than to asset 2's cumulative return
+that corresponds to giving a slightly
+
+ align:start position:0%
+that corresponds to giving a slightly
+ 
+
+ align:start position:0%
+that corresponds to giving a slightly
+higher weight to asset one
+
+ align:start position:0%
+higher weight to asset one
+ 
+
+ align:start position:0%
+higher weight to asset one
+because whatever Sigma 1^ 2 is bigger
+
+ align:start position:0%
+because whatever Sigma 1^ 2 is bigger
+ 
+
+ align:start position:0%
+because whatever Sigma 1^ 2 is bigger
+than 1/ Sigma 2^
+
+ align:start position:0%
+than 1/ Sigma 2^
+ 
+
+ align:start position:0%
+than 1/ Sigma 2^
+squ well let's look at what happen
+
+ align:start position:0%
+squ well let's look at what happen
+ 
+
+ align:start position:0%
+squ well let's look at what happen
+happens if
+
+ align:start position:0%
+happens if
+ 
+
+ align:start position:0%
+happens if
+we consider negative correlations
+
+ align:start position:0%
+we consider negative correlations
+ 
+
+ align:start position:0%
+we consider negative correlations
+between the two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assets well actually okay before we do
+
+ align:start position:0%
+assets well actually okay before we do
+ 
+
+ align:start position:0%
+assets well actually okay before we do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um you know if you were going to choose
+
+ align:start position:0%
+um you know if you were going to choose
+ 
+
+ align:start position:0%
+um you know if you were going to choose
+one of these portfolios
+
+ align:start position:0%
+one of these portfolios
+ 
+
+ align:start position:0%
+one of these portfolios
+for uh investing you know are there any
+
+ align:start position:0%
+for uh investing you know are there any
+ 
+
+ align:start position:0%
+for uh investing you know are there any
+portfolios that you wouldn't invest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in and are any of these portfolios
+
+ align:start position:0%
+in and are any of these portfolios
+ 
+
+ align:start position:0%
+in and are any of these portfolios
+suboptimal in terms of mean variance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W well W1 is certainly
+
+ align:start position:0%
+W well W1 is certainly
+ 
+
+ align:start position:0%
+W well W1 is certainly
+infeasible in terms of because we can
+
+ align:start position:0%
+infeasible in terms of because we can
+ 
+
+ align:start position:0%
+infeasible in terms of because we can
+all we can increase its mean and we can
+
+ align:start position:0%
+all we can increase its mean and we can
+ 
+
+ align:start position:0%
+all we can increase its mean and we can
+increase its uh and decrease its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volatility so actually all of these
+
+ align:start position:0%
+volatility so actually all of these
+ 
+
+ align:start position:0%
+volatility so actually all of these
+points here are really suboptimal
+
+ align:start position:0%
+points here are really suboptimal
+ 
+
+ align:start position:0%
+points here are really suboptimal
+portfolios and from the minimum variance
+
+ align:start position:0%
+portfolios and from the minimum variance
+ 
+
+ align:start position:0%
+portfolios and from the minimum variance
+portfolio which is basically getting us
+
+ align:start position:0%
+portfolio which is basically getting us
+ 
+
+ align:start position:0%
+portfolio which is basically getting us
+you know the vertical tangent all the
+
+ align:start position:0%
+you know the vertical tangent all the
+ 
+
+ align:start position:0%
+you know the vertical tangent all the
+points from here up to the uh asset to
+
+ align:start position:0%
+points from here up to the uh asset to
+ 
+
+ align:start position:0%
+points from here up to the uh asset to
+fully investing in asset 2 are are are
+
+ align:start position:0%
+fully investing in asset 2 are are are
+ 
+
+ align:start position:0%
+fully investing in asset 2 are are are
+uh feasible and none of these portfolios
+
+ align:start position:0%
+uh feasible and none of these portfolios
+ 
+
+ align:start position:0%
+uh feasible and none of these portfolios
+is dominates the other basically it's a
+
+ align:start position:0%
+is dominates the other basically it's a
+ 
+
+ align:start position:0%
+is dominates the other basically it's a
+trade-off between return and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volatility okay so so that's a really
+
+ align:start position:0%
+volatility okay so so that's a really
+ 
+
+ align:start position:0%
+volatility okay so so that's a really
+important point that uh you know there
+
+ align:start position:0%
+important point that uh you know there
+ 
+
+ align:start position:0%
+important point that uh you know there
+really are portfolios that you can just
+
+ align:start position:0%
+really are portfolios that you can just
+ 
+
+ align:start position:0%
+really are portfolios that you can just
+disregard um considering um the uh there
+
+ align:start position:0%
+disregard um considering um the uh there
+ 
+
+ align:start position:0%
+disregard um considering um the uh there
+are definite well when there's zero
+
+ align:start position:0%
+are definite well when there's zero
+ 
+
+ align:start position:0%
+are definite well when there's zero
+correlation there is a benefit to
+
+ align:start position:0%
+correlation there is a benefit to
+ 
+
+ align:start position:0%
+correlation there is a benefit to
+diversifying across these two assets so
+
+ align:start position:0%
+diversifying across these two assets so
+ 
+
+ align:start position:0%
+diversifying across these two assets so
+with if if you have an asset and you are
+
+ align:start position:0%
+with if if you have an asset and you are
+ 
+
+ align:start position:0%
+with if if you have an asset and you are
+considering uh pulling that asset with
+
+ align:start position:0%
+considering uh pulling that asset with
+ 
+
+ align:start position:0%
+considering uh pulling that asset with
+another in your portfolio if those are
+
+ align:start position:0%
+another in your portfolio if those are
+ 
+
+ align:start position:0%
+another in your portfolio if those are
+fully
+
+ align:start position:0%
+fully
+ 
+
+ align:start position:0%
+fully
+uncorrelated then you should be able to
+
+ align:start position:0%
+uncorrelated then you should be able to
+ 
+
+ align:start position:0%
+uncorrelated then you should be able to
+improve your portfolio by adding some
+
+ align:start position:0%
+improve your portfolio by adding some
+ 
+
+ align:start position:0%
+improve your portfolio by adding some
+allocation to that second asset let's
+
+ align:start position:0%
+allocation to that second asset let's
+ 
+
+ align:start position:0%
+allocation to that second asset let's
+look at the
+
+ align:start position:0%
+look at the
+ 
+
+ align:start position:0%
+look at the
+considering a negative a more negative
+
+ align:start position:0%
+considering a negative a more negative
+ 
+
+ align:start position:0%
+considering a negative a more negative
+autocorrelation or a more negative
+
+ align:start position:0%
+autocorrelation or a more negative
+ 
+
+ align:start position:0%
+autocorrelation or a more negative
+correlation between the two assets of
+
+ align:start position:0%
+correlation between the two assets of
+ 
+
+ align:start position:0%
+correlation between the two assets of
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+point4 here you'll see that
+
+ align:start position:0%
+point4 here you'll see that
+ 
+
+ align:start position:0%
+point4 here you'll see that
+there's a basically a tilt a negative
+
+ align:start position:0%
+there's a basically a tilt a negative
+ 
+
+ align:start position:0%
+there's a basically a tilt a negative
+tilt to the scatter plot of
+
+ align:start position:0%
+tilt to the scatter plot of
+ 
+
+ align:start position:0%
+tilt to the scatter plot of
+returns and with the portfolios of two
+
+ align:start position:0%
+returns and with the portfolios of two
+ 
+
+ align:start position:0%
+returns and with the portfolios of two
+assets based of the feasible set that
+
+ align:start position:0%
+assets based of the feasible set that
+ 
+
+ align:start position:0%
+assets based of the feasible set that
+feasible
+
+ align:start position:0%
+feasible
+ 
+
+ align:start position:0%
+feasible
+set is actually stretching further to
+
+ align:start position:0%
+set is actually stretching further to
+ 
+
+ align:start position:0%
+set is actually stretching further to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+left so with a negative correlation
+
+ align:start position:0%
+left so with a negative correlation
+ 
+
+ align:start position:0%
+left so with a negative correlation
+between the assets we're actually able
+
+ align:start position:0%
+between the assets we're actually able
+ 
+
+ align:start position:0%
+between the assets we're actually able
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+reduce the volatility even more if
+
+ align:start position:0%
+reduce the volatility even more if
+ 
+
+ align:start position:0%
+reduce the volatility even more if
+that's what you know is is our
+
+ align:start position:0%
+that's what you know is is our
+ 
+
+ align:start position:0%
+that's what you know is is our
+preference if we go up here to
+
+ align:start position:0%
+preference if we go up here to
+ 
+
+ align:start position:0%
+preference if we go up here to
+minus8 you it gets even more
+
+ align:start position:0%
+minus8 you it gets even more
+ 
+
+ align:start position:0%
+minus8 you it gets even more
+exaggerated now what's going to happen
+
+ align:start position:0%
+exaggerated now what's going to happen
+ 
+
+ align:start position:0%
+exaggerated now what's going to happen
+if we have a correlation of negative-1
+
+ align:start position:0%
+if we have a correlation of negative-1
+ 
+
+ align:start position:0%
+if we have a correlation of negative-1
+between these two as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assets yes then a portfolio the two
+
+ align:start position:0%
+assets yes then a portfolio the two
+ 
+
+ align:start position:0%
+assets yes then a portfolio the two
+assets can have zero variability so um
+
+ align:start position:0%
+assets can have zero variability so um
+ 
+
+ align:start position:0%
+assets can have zero variability so um
+in indeed with the
+
+ align:start position:0%
+in indeed with the
+ 
+
+ align:start position:0%
+in indeed with the
+hedging uh
+
+ align:start position:0%
+hedging uh
+ 
+
+ align:start position:0%
+hedging uh
+strategies um one often is considering
+
+ align:start position:0%
+strategies um one often is considering
+ 
+
+ align:start position:0%
+strategies um one often is considering
+you know investing in assets consisting
+
+ align:start position:0%
+you know investing in assets consisting
+ 
+
+ align:start position:0%
+you know investing in assets consisting
+of uh perhaps you know an underlying
+
+ align:start position:0%
+of uh perhaps you know an underlying
+ 
+
+ align:start position:0%
+of uh perhaps you know an underlying
+security and some derivative on that and
+
+ align:start position:0%
+security and some derivative on that and
+ 
+
+ align:start position:0%
+security and some derivative on that and
+that derivative you know if it's a
+
+ align:start position:0%
+that derivative you know if it's a
+ 
+
+ align:start position:0%
+that derivative you know if it's a
+future say you know could have basically
+
+ align:start position:0%
+future say you know could have basically
+ 
+
+ align:start position:0%
+future say you know could have basically
+a negative one correlation so you could
+
+ align:start position:0%
+a negative one correlation so you could
+ 
+
+ align:start position:0%
+a negative one correlation so you could
+essentially hedge out the the volatility
+
+ align:start position:0%
+essentially hedge out the the volatility
+ 
+
+ align:start position:0%
+essentially hedge out the the volatility
+almost perfectly so so that special case
+
+ align:start position:0%
+almost perfectly so so that special case
+ 
+
+ align:start position:0%
+almost perfectly so so that special case
+actually does exist uh quite frequently
+
+ align:start position:0%
+actually does exist uh quite frequently
+ 
+
+ align:start position:0%
+actually does exist uh quite frequently
+and is exploited um but it falls out
+
+ align:start position:0%
+and is exploited um but it falls out
+ 
+
+ align:start position:0%
+and is exploited um but it falls out
+just from this simple analysis of this
+
+ align:start position:0%
+just from this simple analysis of this
+ 
+
+ align:start position:0%
+just from this simple analysis of this
+uh this simple
+
+ align:start position:0%
+uh this simple
+ 
+
+ align:start position:0%
+uh this simple
+simulation okay let's also look at the
+
+ align:start position:0%
+simulation okay let's also look at the
+ 
+
+ align:start position:0%
+simulation okay let's also look at the
+uh going to increase in the
+
+ align:start position:0%
+uh going to increase in the
+ 
+
+ align:start position:0%
+uh going to increase in the
+correlation
+
+ align:start position:0%
+correlation
+ 
+
+ align:start position:0%
+correlation
+yes of the whole portfolio is zero does
+
+ align:start position:0%
+yes of the whole portfolio is zero does
+ 
+
+ align:start position:0%
+yes of the whole portfolio is zero does
+that mean it's valuable always mean
+
+ align:start position:0%
+that mean it's valuable always mean
+ 
+
+ align:start position:0%
+that mean it's valuable always mean
+constant equal to does that mean what so
+
+ align:start position:0%
+constant equal to does that mean what so
+ 
+
+ align:start position:0%
+constant equal to does that mean what so
+would that mean since it has zero
+
+ align:start position:0%
+would that mean since it has zero
+ 
+
+ align:start position:0%
+would that mean since it has zero
+variance so it will actually be constant
+
+ align:start position:0%
+variance so it will actually be constant
+ 
+
+ align:start position:0%
+variance so it will actually be constant
+over time the whole okay um I mean if it
+
+ align:start position:0%
+over time the whole okay um I mean if it
+ 
+
+ align:start position:0%
+over time the whole okay um I mean if it
+has zero variance then it should be
+
+ align:start position:0%
+has zero variance then it should be
+ 
+
+ align:start position:0%
+has zero variance then it should be
+constant over time yeah and zero
+
+ align:start position:0%
+constant over time yeah and zero
+ 
+
+ align:start position:0%
+constant over time yeah and zero
+variance means that over that that that
+
+ align:start position:0%
+variance means that over that that that
+ 
+
+ align:start position:0%
+variance means that over that that that
+it's its value is a
+
+ align:start position:0%
+it's its value is a
+ 
+
+ align:start position:0%
+it's its value is a
+constant um and so
+
+ align:start position:0%
+constant um and so
+ 
+
+ align:start position:0%
+constant um and so
+aide well it in terms of uh uh I
+
+ align:start position:0%
+aide well it in terms of uh uh I
+ 
+
+ align:start position:0%
+aide well it in terms of uh uh I
+and in in the markets nothing has zero
+
+ align:start position:0%
+and in in the markets nothing has zero
+ 
+
+ align:start position:0%
+and in in the markets nothing has zero
+or almost nothing has zero zero
+
+ align:start position:0%
+or almost nothing has zero zero
+ 
+
+ align:start position:0%
+or almost nothing has zero zero
+volatility um and uh so you know indeed
+
+ align:start position:0%
+volatility um and uh so you know indeed
+ 
+
+ align:start position:0%
+volatility um and uh so you know indeed
+but but the IDE but in in the pricing
+
+ align:start position:0%
+but but the IDE but in in the pricing
+ 
+
+ align:start position:0%
+but but the IDE but in in the pricing
+theory that uh chungong will be
+
+ align:start position:0%
+theory that uh chungong will be
+ 
+
+ align:start position:0%
+theory that uh chungong will be
+discussing uh in subsequent lectures if
+
+ align:start position:0%
+discussing uh in subsequent lectures if
+ 
+
+ align:start position:0%
+discussing uh in subsequent lectures if
+we have basically a portfolio which has
+
+ align:start position:0%
+we have basically a portfolio which has
+ 
+
+ align:start position:0%
+we have basically a portfolio which has
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+volatility then its return should be
+
+ align:start position:0%
+volatility then its return should be
+ 
+
+ align:start position:0%
+volatility then its return should be
+equal to whatever a risk free rate ought
+
+ align:start position:0%
+equal to whatever a risk free rate ought
+ 
+
+ align:start position:0%
+equal to whatever a risk free rate ought
+to be and so you know this particular
+
+ align:start position:0%
+to be and so you know this particular
+ 
+
+ align:start position:0%
+to be and so you know this particular
+portfolio ought to be structured so that
+
+ align:start position:0%
+portfolio ought to be structured so that
+ 
+
+ align:start position:0%
+portfolio ought to be structured so that
+it achieves a return equal to a
+
+ align:start position:0%
+it achieves a return equal to a
+ 
+
+ align:start position:0%
+it achieves a return equal to a
+risk-free rate barring transaction costs
+
+ align:start position:0%
+risk-free rate barring transaction costs
+ 
+
+ align:start position:0%
+risk-free rate barring transaction costs
+and frictions and all that kind of thing
+
+ align:start position:0%
+and frictions and all that kind of thing
+ 
+
+ align:start position:0%
+and frictions and all that kind of thing
+but um yeah okay uh so if we increase
+
+ align:start position:0%
+but um yeah okay uh so if we increase
+ 
+
+ align:start position:0%
+but um yeah okay uh so if we increase
+the correlation from from uh from
+
+ align:start position:0%
+the correlation from from uh from
+ 
+
+ align:start position:0%
+the correlation from from uh from
+zero uh to
+
+ align:start position:0%
+zero uh to
+ 
+
+ align:start position:0%
+zero uh to
+point4 well we still get a benefit of
+
+ align:start position:0%
+point4 well we still get a benefit of
+ 
+
+ align:start position:0%
+point4 well we still get a benefit of
+diversification but
+
+ align:start position:0%
+diversification but
+ 
+
+ align:start position:0%
+diversification but
+less um we're basically not able to
+
+ align:start position:0%
+less um we're basically not able to
+ 
+
+ align:start position:0%
+less um we're basically not able to
+lower the variance as much
+
+ align:start position:0%
+lower the variance as much
+ 
+
+ align:start position:0%
+lower the variance as much
+um and it's even more exaggerated with a
+
+ align:start position:0%
+um and it's even more exaggerated with a
+ 
+
+ align:start position:0%
+um and it's even more exaggerated with a
+correlation
+
+ align:start position:0%
+correlation
+ 
+
+ align:start position:0%
+correlation
+of8
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um now in looking
+
+ align:start position:0%
+um now in looking
+ 
+
+ align:start position:0%
+um now in looking
+at these or the simulation I one thing I
+
+ align:start position:0%
+at these or the simulation I one thing I
+ 
+
+ align:start position:0%
+at these or the simulation I one thing I
+want to highlight to you now which will
+
+ align:start position:0%
+want to highlight to you now which will
+ 
+
+ align:start position:0%
+want to highlight to you now which will
+come up later is you know here I've
+
+ align:start position:0%
+come up later is you know here I've
+ 
+
+ align:start position:0%
+come up later is you know here I've
+simulated returns according to gaussing
+
+ align:start position:0%
+simulated returns according to gaussing
+ 
+
+ align:start position:0%
+simulated returns according to gaussing
+distributions with these means
+
+ align:start position:0%
+distributions with these means
+ 
+
+ align:start position:0%
+distributions with these means
+volatilities and
+
+ align:start position:0%
+volatilities and
+ 
+
+ align:start position:0%
+volatilities and
+correlations and in the
+
+ align:start position:0%
+correlations and in the
+ 
+
+ align:start position:0%
+correlations and in the
+the lower left panel I give the sample
+
+ align:start position:0%
+the lower left panel I give the sample
+ 
+
+ align:start position:0%
+the lower left panel I give the sample
+statistics basically the maximum
+
+ align:start position:0%
+statistics basically the maximum
+ 
+
+ align:start position:0%
+statistics basically the maximum
+likelihood estimates for all the
+
+ align:start position:0%
+likelihood estimates for all the
+ 
+
+ align:start position:0%
+likelihood estimates for all the
+parameters and what you'll see is that
+
+ align:start position:0%
+parameters and what you'll see is that
+ 
+
+ align:start position:0%
+parameters and what you'll see is that
+these sample estimates differ quite a
+
+ align:start position:0%
+these sample estimates differ quite a
+ 
+
+ align:start position:0%
+these sample estimates differ quite a
+bit from well they differ from the the
+
+ align:start position:0%
+bit from well they differ from the the
+ 
+
+ align:start position:0%
+bit from well they differ from the the
+theoretical parameters okay in this
+
+ align:start position:0%
+theoretical parameters okay in this
+ 
+
+ align:start position:0%
+theoretical parameters okay in this
+case uh the sample volatility is almost
+
+ align:start position:0%
+case uh the sample volatility is almost
+ 
+
+ align:start position:0%
+case uh the sample volatility is almost
+you know exactly on point for the first
+
+ align:start position:0%
+you know exactly on point for the first
+ 
+
+ align:start position:0%
+you know exactly on point for the first
+asset it's a bit below 0 287 for the
+
+ align:start position:0%
+asset it's a bit below 0 287 for the
+ 
+
+ align:start position:0%
+asset it's a bit below 0 287 for the
+second the sample mean is 0. 21 which is
+
+ align:start position:0%
+second the sample mean is 0. 21 which is
+ 
+
+ align:start position:0%
+second the sample mean is 0. 21 which is
+a bit high for the first and it's 321
+
+ align:start position:0%
+a bit high for the first and it's 321
+ 
+
+ align:start position:0%
+a bit high for the first and it's 321
+which is also a bit high for the second
+
+ align:start position:0%
+which is also a bit high for the second
+ 
+
+ align:start position:0%
+which is also a bit high for the second
+let's just go back and look at a couple
+
+ align:start position:0%
+let's just go back and look at a couple
+ 
+
+ align:start position:0%
+let's just go back and look at a couple
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+others because it can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get okay well here's one
+
+ align:start position:0%
+get okay well here's one
+ 
+
+ align:start position:0%
+get okay well here's one
+where the sample means are 0.144 and
+
+ align:start position:0%
+where the sample means are 0.144 and
+ 
+
+ align:start position:0%
+where the sample means are 0.144 and
+343 um and so those are actually quite
+
+ align:start position:0%
+343 um and so those are actually quite
+ 
+
+ align:start position:0%
+343 um and so those are actually quite
+different from the the uh population
+
+ align:start position:0%
+different from the the uh population
+ 
+
+ align:start position:0%
+different from the the uh population
+parameters um and uh at least the the
+
+ align:start position:0%
+parameters um and uh at least the the
+ 
+
+ align:start position:0%
+parameters um and uh at least the the
+second asset has has a much higher
+
+ align:start position:0%
+second asset has has a much higher
+ 
+
+ align:start position:0%
+second asset has has a much higher
+sample mean so so it's important to note
+
+ align:start position:0%
+sample mean so so it's important to note
+ 
+
+ align:start position:0%
+sample mean so so it's important to note
+that uh sample estimates can have a
+
+ align:start position:0%
+that uh sample estimates can have a
+ 
+
+ align:start position:0%
+that uh sample estimates can have a
+certain amount of variability turns out
+
+ align:start position:0%
+certain amount of variability turns out
+ 
+
+ align:start position:0%
+certain amount of variability turns out
+that there's less variability in
+
+ align:start position:0%
+that there's less variability in
+ 
+
+ align:start position:0%
+that there's less variability in
+estimating covariances and correlations
+
+ align:start position:0%
+estimating covariances and correlations
+ 
+
+ align:start position:0%
+estimating covariances and correlations
+if the assumptions hold and greater uh
+
+ align:start position:0%
+if the assumptions hold and greater uh
+ 
+
+ align:start position:0%
+if the assumptions hold and greater uh
+variability in the sample means so uh at
+
+ align:start position:0%
+variability in the sample means so uh at
+ 
+
+ align:start position:0%
+variability in the sample means so uh at
+the end of the day we really need to be
+
+ align:start position:0%
+the end of the day we really need to be
+ 
+
+ align:start position:0%
+the end of the day we really need to be
+very sensitive to what estimates
+
+ align:start position:0%
+very sensitive to what estimates
+ 
+
+ align:start position:0%
+very sensitive to what estimates
+we use and how much uncertainty there is
+
+ align:start position:0%
+we use and how much uncertainty there is
+ 
+
+ align:start position:0%
+we use and how much uncertainty there is
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+let's go back to the lecture notes now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+view full screen all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right all right so we've just gone
+
+ align:start position:0%
+right all right so we've just gone
+ 
+
+ align:start position:0%
+right all right so we've just gone
+through how we are evaluating different
+
+ align:start position:0%
+through how we are evaluating different
+ 
+
+ align:start position:0%
+through how we are evaluating different
+portfolios in terms of the the pair of
+
+ align:start position:0%
+portfolios in terms of the the pair of
+ 
+
+ align:start position:0%
+portfolios in terms of the the pair of
+the uh basically the mean of the
+
+ align:start position:0%
+the uh basically the mean of the
+ 
+
+ align:start position:0%
+the uh basically the mean of the
+portfolio and the volatility squared
+
+ align:start position:0%
+portfolio and the volatility squared
+ 
+
+ align:start position:0%
+portfolio and the volatility squared
+volatility of the portfolio higher
+
+ align:start position:0%
+volatility of the portfolio higher
+ 
+
+ align:start position:0%
+volatility of the portfolio higher
+expected returns are obviously desirable
+
+ align:start position:0%
+expected returns are obviously desirable
+ 
+
+ align:start position:0%
+expected returns are obviously desirable
+lower volatility is desirable and so
+
+ align:start position:0%
+lower volatility is desirable and so
+ 
+
+ align:start position:0%
+lower volatility is desirable and so
+what uh markwitz did was to uh basically
+
+ align:start position:0%
+what uh markwitz did was to uh basically
+ 
+
+ align:start position:0%
+what uh markwitz did was to uh basically
+pose this as a uh quadratic programming
+
+ align:start position:0%
+pose this as a uh quadratic programming
+ 
+
+ align:start position:0%
+pose this as a uh quadratic programming
+problem where what we want to do is
+
+ align:start position:0%
+problem where what we want to do is
+ 
+
+ align:start position:0%
+problem where what we want to do is
+minimize the
+
+ align:start position:0%
+minimize the
+ 
+
+ align:start position:0%
+minimize the
+volatility of the or the squared
+
+ align:start position:0%
+volatility of the or the squared
+ 
+
+ align:start position:0%
+volatility of the or the squared
+volatility of the portfolio subject to a
+
+ align:start position:0%
+volatility of the portfolio subject to a
+ 
+
+ align:start position:0%
+volatility of the portfolio subject to a
+constraint on the mean of the portfolio
+
+ align:start position:0%
+constraint on the mean of the portfolio
+ 
+
+ align:start position:0%
+constraint on the mean of the portfolio
+and considering that we're fully
+
+ align:start position:0%
+and considering that we're fully
+ 
+
+ align:start position:0%
+and considering that we're fully
+invested so this mathematical problem is
+
+ align:start position:0%
+invested so this mathematical problem is
+ 
+
+ align:start position:0%
+invested so this mathematical problem is
+you know a standard you know convex
+
+ align:start position:0%
+you know a standard you know convex
+ 
+
+ align:start position:0%
+you know a standard you know convex
+optimization problem a quadratic
+
+ align:start position:0%
+optimization problem a quadratic
+ 
+
+ align:start position:0%
+optimization problem a quadratic
+programming problem which is very simple
+
+ align:start position:0%
+programming problem which is very simple
+ 
+
+ align:start position:0%
+programming problem which is very simple
+and we solve it by defining a
+
+ align:start position:0%
+and we solve it by defining a
+ 
+
+ align:start position:0%
+and we solve it by defining a
+lran basically we take our objective
+
+ align:start position:0%
+lran basically we take our objective
+ 
+
+ align:start position:0%
+lran basically we take our objective
+function the
+
+ align:start position:0%
+function the
+ 
+
+ align:start position:0%
+function the
+volatility and we want to minimize that
+
+ align:start position:0%
+volatility and we want to minimize that
+ 
+
+ align:start position:0%
+volatility and we want to minimize that
+we're going to use a half Factor just to
+
+ align:start position:0%
+we're going to use a half Factor just to
+ 
+
+ align:start position:0%
+we're going to use a half Factor just to
+simplify the computations and then we
+
+ align:start position:0%
+simplify the computations and then we
+ 
+
+ align:start position:0%
+simplify the computations and then we
+add lran for the different constraints
+
+ align:start position:0%
+add lran for the different constraints
+ 
+
+ align:start position:0%
+add lran for the different constraints
+of the problem so we add Lambda 1 *
+
+ align:start position:0%
+of the problem so we add Lambda 1 *
+ 
+
+ align:start position:0%
+of the problem so we add Lambda 1 *
+Alpha us W Prime Alpha we want the mean
+
+ align:start position:0%
+Alpha us W Prime Alpha we want the mean
+ 
+
+ align:start position:0%
+Alpha us W Prime Alpha we want the mean
+return WP Prime Alpha to be constrained
+
+ align:start position:0%
+return WP Prime Alpha to be constrained
+ 
+
+ align:start position:0%
+return WP Prime Alpha to be constrained
+to equal Alpha not and we also want the
+
+ align:start position:0%
+to equal Alpha not and we also want the
+ 
+
+ align:start position:0%
+to equal Alpha not and we also want the
+sum of the weights W Prime 1M to equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 and the first order conditions of the
+
+ align:start position:0%
+1 and the first order conditions of the
+ 
+
+ align:start position:0%
+1 and the first order conditions of the
+Gran basically give us those two
+
+ align:start position:0%
+Gran basically give us those two
+ 
+
+ align:start position:0%
+Gran basically give us those two
+constraints for differentiating with
+
+ align:start position:0%
+constraints for differentiating with
+ 
+
+ align:start position:0%
+constraints for differentiating with
+respect to Lambda one and
+
+ align:start position:0%
+respect to Lambda one and
+ 
+
+ align:start position:0%
+respect to Lambda one and
+lamb2 uh the the the initial first order
+
+ align:start position:0%
+lamb2 uh the the the initial first order
+ 
+
+ align:start position:0%
+lamb2 uh the the the initial first order
+condition with respect to the port folio
+
+ align:start position:0%
+condition with respect to the port folio
+ 
+
+ align:start position:0%
+condition with respect to the port folio
+weights uh basically allows us to solve
+
+ align:start position:0%
+weights uh basically allows us to solve
+ 
+
+ align:start position:0%
+weights uh basically allows us to solve
+for for those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weights now this first order condition
+
+ align:start position:0%
+weights now this first order condition
+ 
+
+ align:start position:0%
+weights now this first order condition
+is going to solve our problem
+
+ align:start position:0%
+is going to solve our problem
+ 
+
+ align:start position:0%
+is going to solve our problem
+because this uh if we take the second
+
+ align:start position:0%
+because this uh if we take the second
+ 
+
+ align:start position:0%
+because this uh if we take the second
+order derivative of this
+
+ align:start position:0%
+order derivative of this
+ 
+
+ align:start position:0%
+order derivative of this
+lran it's going to
+
+ align:start position:0%
+lran it's going to
+ 
+
+ align:start position:0%
+lran it's going to
+be Sigma so um let me just point out
+
+ align:start position:0%
+be Sigma so um let me just point out
+ 
+
+ align:start position:0%
+be Sigma so um let me just point out
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if we take d^2 L by DW DW Prime that's
+
+ align:start position:0%
+if we take d^2 L by DW DW Prime that's
+ 
+
+ align:start position:0%
+if we take d^2 L by DW DW Prime that's
+equal to our covariance Matrix
+
+ align:start position:0%
+equal to our covariance Matrix
+ 
+
+ align:start position:0%
+equal to our covariance Matrix
+Sigma and that is a positive definite or
+
+ align:start position:0%
+Sigma and that is a positive definite or
+ 
+
+ align:start position:0%
+Sigma and that is a positive definite or
+positive semi-finite Matrix so so we
+
+ align:start position:0%
+positive semi-finite Matrix so so we
+ 
+
+ align:start position:0%
+positive semi-finite Matrix so so we
+indeed are minimizing the problem so
+
+ align:start position:0%
+indeed are minimizing the problem so
+ 
+
+ align:start position:0%
+indeed are minimizing the problem so
+this is just a
+
+ align:start position:0%
+this is just a
+ 
+
+ align:start position:0%
+this is just a
+generalization of uh basically a a
+
+ align:start position:0%
+generalization of uh basically a a
+ 
+
+ align:start position:0%
+generalization of uh basically a a
+parabola in multi-dimensions and we're
+
+ align:start position:0%
+parabola in multi-dimensions and we're
+ 
+
+ align:start position:0%
+parabola in multi-dimensions and we're
+trying to to minimize that well what's
+
+ align:start position:0%
+trying to to minimize that well what's
+ 
+
+ align:start position:0%
+trying to to minimize that well what's
+the solution to
+
+ align:start position:0%
+the solution to
+ 
+
+ align:start position:0%
+the solution to
+this well first we can solve for w the
+
+ align:start position:0%
+this well first we can solve for w the
+ 
+
+ align:start position:0%
+this well first we can solve for w the
+weights in terms of Lambda 1 and Lambda
+
+ align:start position:0%
+weights in terms of Lambda 1 and Lambda
+ 
+
+ align:start position:0%
+weights in terms of Lambda 1 and Lambda
+2 so we take the first order the first
+
+ align:start position:0%
+2 so we take the first order the first
+ 
+
+ align:start position:0%
+2 so we take the first order the first
+equation of the first order conditions
+
+ align:start position:0%
+equation of the first order conditions
+ 
+
+ align:start position:0%
+equation of the first order conditions
+and basically premultiply by Sigma
+
+ align:start position:0%
+and basically premultiply by Sigma
+ 
+
+ align:start position:0%
+and basically premultiply by Sigma
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+across and we get W is equal to Lambda 1
+
+ align:start position:0%
+across and we get W is equal to Lambda 1
+ 
+
+ align:start position:0%
+across and we get W is equal to Lambda 1
+Sigma inverse Alpha plus Lambda 2 Sigma
+
+ align:start position:0%
+Sigma inverse Alpha plus Lambda 2 Sigma
+ 
+
+ align:start position:0%
+Sigma inverse Alpha plus Lambda 2 Sigma
+inverse the unit Vector our Vector of
+
+ align:start position:0%
+inverse the unit Vector our Vector of
+ 
+
+ align:start position:0%
+inverse the unit Vector our Vector of
+units
+
+ align:start position:0%
+units
+ 
+
+ align:start position:0%
+units
+and then we can just solve for Lambda 1
+
+ align:start position:0%
+and then we can just solve for Lambda 1
+ 
+
+ align:start position:0%
+and then we can just solve for Lambda 1
+and Lambda 2 by plugging this W
+
+ align:start position:0%
+and Lambda 2 by plugging this W
+ 
+
+ align:start position:0%
+and Lambda 2 by plugging this W
+KN solution into the second two
+
+ align:start position:0%
+KN solution into the second two
+ 
+
+ align:start position:0%
+KN solution into the second two
+equations and this these two equations
+
+ align:start position:0%
+equations and this these two equations
+ 
+
+ align:start position:0%
+equations and this these two equations
+for the second and third first order
+
+ align:start position:0%
+for the second and third first order
+ 
+
+ align:start position:0%
+for the second and third first order
+conditions is just a very simple linear
+
+ align:start position:0%
+conditions is just a very simple linear
+ 
+
+ align:start position:0%
+conditions is just a very simple linear
+set of linear
+
+ align:start position:0%
+set of linear
+ 
+
+ align:start position:0%
+set of linear
+equations um we basically
+
+ align:start position:0%
+equations um we basically
+ 
+
+ align:start position:0%
+equations um we basically
+have you know Alpha not alpha alpha not
+
+ align:start position:0%
+have you know Alpha not alpha alpha not
+ 
+
+ align:start position:0%
+have you know Alpha not alpha alpha not
+one is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Su Matrix times Lambda 1 Lambda 2 and
+
+ align:start position:0%
+Su Matrix times Lambda 1 Lambda 2 and
+ 
+
+ align:start position:0%
+Su Matrix times Lambda 1 Lambda 2 and
+that Matrix AB b c is given by Alpha
+
+ align:start position:0%
+that Matrix AB b c is given by Alpha
+ 
+
+ align:start position:0%
+that Matrix AB b c is given by Alpha
+Prime Sigma inverse Alpha for the a
+
+ align:start position:0%
+Prime Sigma inverse Alpha for the a
+ 
+
+ align:start position:0%
+Prime Sigma inverse Alpha for the a
+element and the B and C elements are
+
+ align:start position:0%
+element and the B and C elements are
+ 
+
+ align:start position:0%
+element and the B and C elements are
+those corresponding elements so this
+
+ align:start position:0%
+those corresponding elements so this
+ 
+
+ align:start position:0%
+those corresponding elements so this
+solves the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem and the variance of the optimal
+
+ align:start position:0%
+problem and the variance of the optimal
+ 
+
+ align:start position:0%
+problem and the variance of the optimal
+portfolio with a given return can
+
+ align:start position:0%
+portfolio with a given return can
+ 
+
+ align:start position:0%
+portfolio with a given return can
+also be solved by just substituting in
+
+ align:start position:0%
+also be solved by just substituting in
+ 
+
+ align:start position:0%
+also be solved by just substituting in
+these Solutions so we get that uh for a
+
+ align:start position:0%
+these Solutions so we get that uh for a
+ 
+
+ align:start position:0%
+these Solutions so we get that uh for a
+given Alpha not our Target
+
+ align:start position:0%
+given Alpha not our Target
+ 
+
+ align:start position:0%
+given Alpha not our Target
+return the squared volatility of that
+
+ align:start position:0%
+return the squared volatility of that
+ 
+
+ align:start position:0%
+return the squared volatility of that
+optimal
+
+ align:start position:0%
+optimal
+ 
+
+ align:start position:0%
+optimal
+portfolio is this has that form now
+
+ align:start position:0%
+portfolio is this has that form now
+ 
+
+ align:start position:0%
+portfolio is this has that form now
+what's that
+
+ align:start position:0%
+what's that
+ 
+
+ align:start position:0%
+what's that
+form it's essentially a parabola in
+
+ align:start position:0%
+form it's essentially a parabola in
+ 
+
+ align:start position:0%
+form it's essentially a parabola in
+Alpha
+
+ align:start position:0%
+Alpha
+ 
+
+ align:start position:0%
+Alpha
+notot Okay so when we're looking
+
+ align:start position:0%
+notot Okay so when we're looking
+ 
+
+ align:start position:0%
+notot Okay so when we're looking
+at when we're looking let's see is there
+
+ align:start position:0%
+at when we're looking let's see is there
+ 
+
+ align:start position:0%
+at when we're looking let's see is there
+an eraser here it is when we're looking
+
+ align:start position:0%
+an eraser here it is when we're looking
+ 
+
+ align:start position:0%
+an eraser here it is when we're looking
+at this
+
+ align:start position:0%
+at this
+ 
+
+ align:start position:0%
+at this
+graph here in the two-dimensional case
+
+ align:start position:0%
+graph here in the two-dimensional case
+ 
+
+ align:start position:0%
+graph here in the two-dimensional case
+then there's basically a
+
+ align:start position:0%
+then there's basically a
+ 
+
+ align:start position:0%
+then there's basically a
+parabola I can't draw parabas very well
+
+ align:start position:0%
+parabola I can't draw parabas very well
+ 
+
+ align:start position:0%
+parabola I can't draw parabas very well
+but there's a parabola between those two
+
+ align:start position:0%
+but there's a parabola between those two
+ 
+
+ align:start position:0%
+but there's a parabola between those two
+points that uh characterizes the thing
+
+ align:start position:0%
+points that uh characterizes the thing
+ 
+
+ align:start position:0%
+points that uh characterizes the thing
+and in multi-dimension with you know
+
+ align:start position:0%
+and in multi-dimension with you know
+ 
+
+ align:start position:0%
+and in multi-dimension with you know
+multiple assets it's just a you know a
+
+ align:start position:0%
+multiple assets it's just a you know a
+ 
+
+ align:start position:0%
+multiple assets it's just a you know a
+multivar extension of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um all right this particular problem uh
+
+ align:start position:0%
+um all right this particular problem uh
+ 
+
+ align:start position:0%
+um all right this particular problem uh
+can also be looked at in many in two
+
+ align:start position:0%
+can also be looked at in many in two
+ 
+
+ align:start position:0%
+can also be looked at in many in two
+other ways I before we're looking at
+
+ align:start position:0%
+other ways I before we're looking at
+ 
+
+ align:start position:0%
+other ways I before we're looking at
+minimizing the variant subject to a
+
+ align:start position:0%
+minimizing the variant subject to a
+ 
+
+ align:start position:0%
+minimizing the variant subject to a
+constraint on the expected return we can
+
+ align:start position:0%
+constraint on the expected return we can
+ 
+
+ align:start position:0%
+constraint on the expected return we can
+also say well let's maximize the return
+
+ align:start position:0%
+also say well let's maximize the return
+ 
+
+ align:start position:0%
+also say well let's maximize the return
+subject to a constraint on the
+
+ align:start position:0%
+subject to a constraint on the
+ 
+
+ align:start position:0%
+subject to a constraint on the
+volatility and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+problem is basically has the same lran
+
+ align:start position:0%
+problem is basically has the same lran
+ 
+
+ align:start position:0%
+problem is basically has the same lran
+and we can also consider just
+
+ align:start position:0%
+and we can also consider just
+ 
+
+ align:start position:0%
+and we can also consider just
+maximizing a weighted average of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return and have a negative multiple on
+
+ align:start position:0%
+return and have a negative multiple on
+ 
+
+ align:start position:0%
+return and have a negative multiple on
+the variance and consider maximizing
+
+ align:start position:0%
+the variance and consider maximizing
+ 
+
+ align:start position:0%
+the variance and consider maximizing
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+expression um this turns out it to be
+
+ align:start position:0%
+expression um this turns out it to be
+ 
+
+ align:start position:0%
+expression um this turns out it to be
+the risk aversion
+
+ align:start position:0%
+the risk aversion
+ 
+
+ align:start position:0%
+the risk aversion
+optimization um where we basically are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+penalizing portfolios
+
+ align:start position:0%
+penalizing portfolios
+ 
+
+ align:start position:0%
+penalizing portfolios
+W for how
+
+ align:start position:0%
+W for how
+ 
+
+ align:start position:0%
+W for how
+much variance they have and the Lambda
+
+ align:start position:0%
+much variance they have and the Lambda
+ 
+
+ align:start position:0%
+much variance they have and the Lambda
+Factor tells us how much penalty to
+
+ align:start position:0%
+Factor tells us how much penalty to
+ 
+
+ align:start position:0%
+Factor tells us how much penalty to
+associate per variance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unit and these are all equivalent uh
+
+ align:start position:0%
+unit and these are all equivalent uh
+ 
+
+ align:start position:0%
+unit and these are all equivalent uh
+problems uh being solved by the same
+
+ align:start position:0%
+problems uh being solved by the same
+ 
+
+ align:start position:0%
+problems uh being solved by the same
+lren and from these problems we can
+
+ align:start position:0%
+lren and from these problems we can
+ 
+
+ align:start position:0%
+lren and from these problems we can
+Define the efficient Frontier which is
+
+ align:start position:0%
+Define the efficient Frontier which is
+ 
+
+ align:start position:0%
+Define the efficient Frontier which is
+the collection of all possible
+
+ align:start position:0%
+the collection of all possible
+ 
+
+ align:start position:0%
+the collection of all possible
+solutions where we
+
+ align:start position:0%
+solutions where we
+ 
+
+ align:start position:0%
+solutions where we
+range the target return amongst values
+
+ align:start position:0%
+range the target return amongst values
+ 
+
+ align:start position:0%
+range the target return amongst values
+that are feasible and the volatility
+
+ align:start position:0%
+that are feasible and the volatility
+ 
+
+ align:start position:0%
+that are feasible and the volatility
+amongst values that are feasible as
+
+ align:start position:0%
+amongst values that are feasible as
+ 
+
+ align:start position:0%
+amongst values that are feasible as
+well so the efficient Frontier will just
+
+ align:start position:0%
+well so the efficient Frontier will just
+ 
+
+ align:start position:0%
+well so the efficient Frontier will just
+Trace these
+
+ align:start position:0%
+Trace these
+ 
+
+ align:start position:0%
+Trace these
+out um and in our two variable case our
+
+ align:start position:0%
+out um and in our two variable case our
+ 
+
+ align:start position:0%
+out um and in our two variable case our
+two asset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case okay we have Sigma and Alpha we
+
+ align:start position:0%
+case okay we have Sigma and Alpha we
+ 
+
+ align:start position:0%
+case okay we have Sigma and Alpha we
+have two assets is basically a parabola
+
+ align:start position:0%
+have two assets is basically a parabola
+ 
+
+ align:start position:0%
+have two assets is basically a parabola
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that if we have another two assets that
+
+ align:start position:0%
+that if we have another two assets that
+ 
+
+ align:start position:0%
+that if we have another two assets that
+we're investing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with then if we consider the two asset
+
+ align:start position:0%
+with then if we consider the two asset
+ 
+
+ align:start position:0%
+with then if we consider the two asset
+combinate portfolios of just these two
+
+ align:start position:0%
+combinate portfolios of just these two
+ 
+
+ align:start position:0%
+combinate portfolios of just these two
+assets there's basically another
+
+ align:start position:0%
+assets there's basically another
+ 
+
+ align:start position:0%
+assets there's basically another
+Parabola there and as we consider
+
+ align:start position:0%
+Parabola there and as we consider
+ 
+
+ align:start position:0%
+Parabola there and as we consider
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+other Assets in the mix we basically get
+
+ align:start position:0%
+other Assets in the mix we basically get
+ 
+
+ align:start position:0%
+other Assets in the mix we basically get
+all these parabas of two asset
+
+ align:start position:0%
+all these parabas of two asset
+ 
+
+ align:start position:0%
+all these parabas of two asset
+portfolios and then combinations of
+
+ align:start position:0%
+portfolios and then combinations of
+ 
+
+ align:start position:0%
+portfolios and then combinations of
+those two asset portfolios gives us
+
+ align:start position:0%
+those two asset portfolios gives us
+ 
+
+ align:start position:0%
+those two asset portfolios gives us
+our uh feasible set and so at the end of
+
+ align:start position:0%
+our uh feasible set and so at the end of
+ 
+
+ align:start position:0%
+our uh feasible set and so at the end of
+the day we basically have a convex
+
+ align:start position:0%
+the day we basically have a convex
+ 
+
+ align:start position:0%
+the day we basically have a convex
+set of all Fe feasible assets which uh
+
+ align:start position:0%
+set of all Fe feasible assets which uh
+ 
+
+ align:start position:0%
+set of all Fe feasible assets which uh
+Define the efficient Frontier and the
+
+ align:start position:0%
+Define the efficient Frontier and the
+ 
+
+ align:start position:0%
+Define the efficient Frontier and the
+efficient Frontier is always going to
+
+ align:start position:0%
+efficient Frontier is always going to
+ 
+
+ align:start position:0%
+efficient Frontier is always going to
+be basically the top side of that
+
+ align:start position:0%
+be basically the top side of that
+ 
+
+ align:start position:0%
+be basically the top side of that
+curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with let's see the next topic considers
+
+ align:start position:0%
+with let's see the next topic considers
+ 
+
+ align:start position:0%
+with let's see the next topic considers
+adding basically a risk-free asset to
+
+ align:start position:0%
+adding basically a risk-free asset to
+ 
+
+ align:start position:0%
+adding basically a risk-free asset to
+invest in the problem as it's been
+
+ align:start position:0%
+invest in the problem as it's been
+ 
+
+ align:start position:0%
+invest in the problem as it's been
+stated so far says we want to be fully
+
+ align:start position:0%
+stated so far says we want to be fully
+ 
+
+ align:start position:0%
+stated so far says we want to be fully
+invested across our M assets and what
+
+ align:start position:0%
+invested across our M assets and what
+ 
+
+ align:start position:0%
+invested across our M assets and what
+are the optimal
+
+ align:start position:0%
+are the optimal
+ 
+
+ align:start position:0%
+are the optimal
+portfolios well what if
+
+ align:start position:0%
+portfolios well what if
+ 
+
+ align:start position:0%
+portfolios well what if
+we don't what if we want to invest some
+
+ align:start position:0%
+we don't what if we want to invest some
+ 
+
+ align:start position:0%
+we don't what if we want to invest some
+of our money our Capital just in cash or
+
+ align:start position:0%
+of our money our Capital just in cash or
+ 
+
+ align:start position:0%
+of our money our Capital just in cash or
+not invest our full capital and and
+
+ align:start position:0%
+not invest our full capital and and
+ 
+
+ align:start position:0%
+not invest our full capital and and
+invest the rest in in the in the
+
+ align:start position:0%
+invest the rest in in the in the
+ 
+
+ align:start position:0%
+invest the rest in in the in the
+portfolios so
+
+ align:start position:0%
+portfolios so
+ 
+
+ align:start position:0%
+portfolios so
+um if we consider adding a risk-free
+
+ align:start position:0%
+um if we consider adding a risk-free
+ 
+
+ align:start position:0%
+um if we consider adding a risk-free
+asset uh then this is an asset we'll
+
+ align:start position:0%
+asset uh then this is an asset we'll
+ 
+
+ align:start position:0%
+asset uh then this is an asset we'll
+call it the zeroth
+
+ align:start position:0%
+call it the zeroth
+ 
+
+ align:start position:0%
+call it the zeroth
+asset it has say some expected return
+
+ align:start position:0%
+asset it has say some expected return
+ 
+
+ align:start position:0%
+asset it has say some expected return
+are not it's risk-free so that's a
+
+ align:start position:0%
+are not it's risk-free so that's a
+ 
+
+ align:start position:0%
+are not it's risk-free so that's a
+constant it has zero
+
+ align:start position:0%
+constant it has zero
+ 
+
+ align:start position:0%
+constant it has zero
+variance and if we're investing as well
+
+ align:start position:0%
+variance and if we're investing as well
+ 
+
+ align:start position:0%
+variance and if we're investing as well
+in that possible risky asset then we can
+
+ align:start position:0%
+in that possible risky asset then we can
+ 
+
+ align:start position:0%
+in that possible risky asset then we can
+basically consider investing W weights
+
+ align:start position:0%
+basically consider investing W weights
+ 
+
+ align:start position:0%
+basically consider investing W weights
+in the risky assets and one minus W
+
+ align:start position:0%
+in the risky assets and one minus W
+ 
+
+ align:start position:0%
+in the risky assets and one minus W
+Times the unit Vector in in in the
+
+ align:start position:0%
+Times the unit Vector in in in the
+ 
+
+ align:start position:0%
+Times the unit Vector in in in the
+risk-free
+
+ align:start position:0%
+risk-free
+ 
+
+ align:start position:0%
+risk-free
+asset um and let's see I want to draw
+
+ align:start position:0%
+asset um and let's see I want to draw
+ 
+
+ align:start position:0%
+asset um and let's see I want to draw
+this graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see okay
+
+ align:start position:0%
+see okay
+ 
+
+ align:start position:0%
+see okay
+um okay suppose we have two assets where
+
+ align:start position:0%
+um okay suppose we have two assets where
+ 
+
+ align:start position:0%
+um okay suppose we have two assets where
+this is the efficient
+
+ align:start position:0%
+this is the efficient
+ 
+
+ align:start position:0%
+this is the efficient
+set and we consider now allowing for for
+
+ align:start position:0%
+set and we consider now allowing for for
+ 
+
+ align:start position:0%
+set and we consider now allowing for for
+a risk-free asset to be invested in as
+
+ align:start position:0%
+a risk-free asset to be invested in as
+ 
+
+ align:start position:0%
+a risk-free asset to be invested in as
+well well that risk-free asset is
+
+ align:start position:0%
+well well that risk-free asset is
+ 
+
+ align:start position:0%
+well well that risk-free asset is
+basically this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and it has mean r KN and variance
+
+ align:start position:0%
+here and it has mean r KN and variance
+ 
+
+ align:start position:0%
+here and it has mean r KN and variance
+zero now if we combine this asset with
+
+ align:start position:0%
+zero now if we combine this asset with
+ 
+
+ align:start position:0%
+zero now if we combine this asset with
+any of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+portfolios what's the feasible set going
+
+ align:start position:0%
+portfolios what's the feasible set going
+ 
+
+ align:start position:0%
+portfolios what's the feasible set going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+well we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically invest in some money in the
+
+ align:start position:0%
+basically invest in some money in the
+ 
+
+ align:start position:0%
+basically invest in some money in the
+risk-free asset and some in asset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two so we can get any point along this
+
+ align:start position:0%
+two so we can get any point along this
+ 
+
+ align:start position:0%
+two so we can get any point along this
+line basically if we invest in the
+
+ align:start position:0%
+line basically if we invest in the
+ 
+
+ align:start position:0%
+line basically if we invest in the
+risk-free
+
+ align:start position:0%
+risk-free
+ 
+
+ align:start position:0%
+risk-free
+asset um if we invest uh some fraction
+
+ align:start position:0%
+asset um if we invest uh some fraction
+ 
+
+ align:start position:0%
+asset um if we invest uh some fraction
+in asset two and the remainder in the
+
+ align:start position:0%
+in asset two and the remainder in the
+ 
+
+ align:start position:0%
+in asset two and the remainder in the
+risk-free asset then our expected return
+
+ align:start position:0%
+risk-free asset then our expected return
+ 
+
+ align:start position:0%
+risk-free asset then our expected return
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+linear U line between R KN and Alpha
+
+ align:start position:0%
+linear U line between R KN and Alpha
+ 
+
+ align:start position:0%
+linear U line between R KN and Alpha
+2 and the volatility of a weighted
+
+ align:start position:0%
+2 and the volatility of a weighted
+ 
+
+ align:start position:0%
+2 and the volatility of a weighted
+average or of a fraction of asset
+
+ align:start position:0%
+average or of a fraction of asset
+ 
+
+ align:start position:0%
+average or of a fraction of asset
+to uh is has volatility given by
+
+ align:start position:0%
+to uh is has volatility given by
+ 
+
+ align:start position:0%
+to uh is has volatility given by
+whatever that weight is times the
+
+ align:start position:0%
+whatever that weight is times the
+ 
+
+ align:start position:0%
+whatever that weight is times the
+volatility so um so this point here
+
+ align:start position:0%
+volatility so um so this point here
+ 
+
+ align:start position:0%
+volatility so um so this point here
+corresponds to
+
+ align:start position:0%
+corresponds to
+ 
+
+ align:start position:0%
+corresponds to
+uh say w * Sigma
+
+ align:start position:0%
+uh say w * Sigma
+ 
+
+ align:start position:0%
+uh say w * Sigma
+2 for its
+
+ align:start position:0%
+2 for its
+ 
+
+ align:start position:0%
+2 for its
+volatility
+
+ align:start position:0%
+volatility
+ 
+
+ align:start position:0%
+volatility
+and R KN plus W * Alpha 2 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r now the dramatic thing is that U we
+
+ align:start position:0%
+r now the dramatic thing is that U we
+ 
+
+ align:start position:0%
+r now the dramatic thing is that U we
+actually are able to achieve
+
+ align:start position:0%
+actually are able to achieve
+ 
+
+ align:start position:0%
+actually are able to achieve
+an improvement
+
+ align:start position:0%
+an improvement
+ 
+
+ align:start position:0%
+an improvement
+over points on the efficient
+
+ align:start position:0%
+over points on the efficient
+ 
+
+ align:start position:0%
+over points on the efficient
+Frontier such as say the minimum
+
+ align:start position:0%
+Frontier such as say the minimum
+ 
+
+ align:start position:0%
+Frontier such as say the minimum
+variance
+
+ align:start position:0%
+variance
+ 
+
+ align:start position:0%
+variance
+portfolio um and if we consider the
+
+ align:start position:0%
+portfolio um and if we consider the
+ 
+
+ align:start position:0%
+portfolio um and if we consider the
+fraction up here we actually have a
+
+ align:start position:0%
+fraction up here we actually have a
+ 
+
+ align:start position:0%
+fraction up here we actually have a
+higher
+
+ align:start position:0%
+higher
+ 
+
+ align:start position:0%
+higher
+return and a lower variance than the
+
+ align:start position:0%
+return and a lower variance than the
+ 
+
+ align:start position:0%
+return and a lower variance than the
+minimum variance portfolio that we
+
+ align:start position:0%
+minimum variance portfolio that we
+ 
+
+ align:start position:0%
+minimum variance portfolio that we
+considered
+
+ align:start position:0%
+considered
+ 
+
+ align:start position:0%
+considered
+before and so investing in the risk free
+
+ align:start position:0%
+before and so investing in the risk free
+ 
+
+ align:start position:0%
+before and so investing in the risk free
+asset does sort of enlarge our
+
+ align:start position:0%
+asset does sort of enlarge our
+ 
+
+ align:start position:0%
+asset does sort of enlarge our
+opportunity space quite dramatically and
+
+ align:start position:0%
+opportunity space quite dramatically and
+ 
+
+ align:start position:0%
+opportunity space quite dramatically and
+uh there are some very special results
+
+ align:start position:0%
+uh there are some very special results
+ 
+
+ align:start position:0%
+uh there are some very special results
+that come from this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so let's go through the mathematics
+
+ align:start position:0%
+um so let's go through the mathematics
+ 
+
+ align:start position:0%
+um so let's go through the mathematics
+for solving this problem and in the
+
+ align:start position:0%
+for solving this problem and in the
+ 
+
+ align:start position:0%
+for solving this problem and in the
+lecture notes I'm going to go over this
+
+ align:start position:0%
+lecture notes I'm going to go over this
+ 
+
+ align:start position:0%
+lecture notes I'm going to go over this
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+quickly I it's really when you go
+
+ align:start position:0%
+quickly I it's really when you go
+ 
+
+ align:start position:0%
+quickly I it's really when you go
+through it slowly you'll say oh this is
+
+ align:start position:0%
+through it slowly you'll say oh this is
+ 
+
+ align:start position:0%
+through it slowly you'll say oh this is
+very straightforward logical
+
+ align:start position:0%
+very straightforward logical
+ 
+
+ align:start position:0%
+very straightforward logical
+um so we're basically going to minimize
+
+ align:start position:0%
+um so we're basically going to minimize
+ 
+
+ align:start position:0%
+um so we're basically going to minimize
+the volatility subject to the constraint
+
+ align:start position:0%
+the volatility subject to the constraint
+ 
+
+ align:start position:0%
+the volatility subject to the constraint
+that the return is equal to Alpha not we
+
+ align:start position:0%
+that the return is equal to Alpha not we
+ 
+
+ align:start position:0%
+that the return is equal to Alpha not we
+Define the
+
+ align:start position:0%
+Define the
+ 
+
+ align:start position:0%
+Define the
+lonian and do the first order conditions
+
+ align:start position:0%
+lonian and do the first order conditions
+ 
+
+ align:start position:0%
+lonian and do the first order conditions
+solve those and if we solve those we get
+
+ align:start position:0%
+solve those and if we solve those we get
+ 
+
+ align:start position:0%
+solve those and if we solve those we get
+basically uh Lambda 1 has this nice form
+
+ align:start position:0%
+basically uh Lambda 1 has this nice form
+ 
+
+ align:start position:0%
+basically uh Lambda 1 has this nice form
+here and this is obtained by just very
+
+ align:start position:0%
+here and this is obtained by just very
+ 
+
+ align:start position:0%
+here and this is obtained by just very
+simple equation solving of those two
+
+ align:start position:0%
+simple equation solving of those two
+ 
+
+ align:start position:0%
+simple equation solving of those two
+first order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions and if we have M assets
+
+ align:start position:0%
+conditions and if we have M assets
+ 
+
+ align:start position:0%
+conditions and if we have M assets
+uh available um when we look at the
+
+ align:start position:0%
+uh available um when we look at the
+ 
+
+ align:start position:0%
+uh available um when we look at the
+solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we get an optimal
+
+ align:start position:0%
+then we get an optimal
+ 
+
+ align:start position:0%
+then we get an optimal
+portfolio that has a w Vector given by
+
+ align:start position:0%
+portfolio that has a w Vector given by
+ 
+
+ align:start position:0%
+portfolio that has a w Vector given by
+this solution and Lambda one given by
+
+ align:start position:0%
+this solution and Lambda one given by
+ 
+
+ align:start position:0%
+this solution and Lambda one given by
+this solution now W is the proportion uh
+
+ align:start position:0%
+this solution now W is the proportion uh
+ 
+
+ align:start position:0%
+this solution now W is the proportion uh
+is the allocation to the risky
+
+ align:start position:0%
+is the allocation to the risky
+ 
+
+ align:start position:0%
+is the allocation to the risky
+assets what is what
+
+ align:start position:0%
+assets what is what
+ 
+
+ align:start position:0%
+assets what is what
+varies depending on our Target return
+
+ align:start position:0%
+varies depending on our Target return
+ 
+
+ align:start position:0%
+varies depending on our Target return
+Alpha KN is simply
+
+ align:start position:0%
+Alpha KN is simply
+ 
+
+ align:start position:0%
+Alpha KN is simply
+this uh Lambda 1 uh lran multiplier
+
+ align:start position:0%
+this uh Lambda 1 uh lran multiplier
+ 
+
+ align:start position:0%
+this uh Lambda 1 uh lran multiplier
+basically Alpha not our Target
+
+ align:start position:0%
+basically Alpha not our Target
+ 
+
+ align:start position:0%
+basically Alpha not our Target
+return only affects the value of Lambda
+
+ align:start position:0%
+return only affects the value of Lambda
+ 
+
+ align:start position:0%
+return only affects the value of Lambda
+1 and our weights across the risky
+
+ align:start position:0%
+1 and our weights across the risky
+ 
+
+ align:start position:0%
+1 and our weights across the risky
+assets is a simple multiple of of a
+
+ align:start position:0%
+assets is a simple multiple of of a
+ 
+
+ align:start position:0%
+assets is a simple multiple of of a
+fixed
+
+ align:start position:0%
+fixed
+ 
+
+ align:start position:0%
+fixed
+Vector of relative
+
+ align:start position:0%
+Vector of relative
+ 
+
+ align:start position:0%
+Vector of relative
+weights and and this fixed Vector of
+
+ align:start position:0%
+weights and and this fixed Vector of
+ 
+
+ align:start position:0%
+weights and and this fixed Vector of
+relative
+
+ align:start position:0%
+relative
+ 
+
+ align:start position:0%
+relative
+weights is the inverse of the covariance
+
+ align:start position:0%
+weights is the inverse of the covariance
+ 
+
+ align:start position:0%
+weights is the inverse of the covariance
+Matrix across the assets times Alpha
+
+ align:start position:0%
+Matrix across the assets times Alpha
+ 
+
+ align:start position:0%
+Matrix across the assets times Alpha
+minus 1 M
+
+ align:start position:0%
+minus 1 M
+ 
+
+ align:start position:0%
+minus 1 M
+r0 and uh so what we have is a
+
+ align:start position:0%
+r0 and uh so what we have is a
+ 
+
+ align:start position:0%
+r0 and uh so what we have is a
+portfolio
+
+ align:start position:0%
+portfolio
+ 
+
+ align:start position:0%
+portfolio
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh basically in invests in the risky
+
+ align:start position:0%
+uh basically in invests in the risky
+ 
+
+ align:start position:0%
+uh basically in invests in the risky
+Assets in the same way the only thing
+
+ align:start position:0%
+Assets in the same way the only thing
+ 
+
+ align:start position:0%
+Assets in the same way the only thing
+that differs is how much weight we give
+
+ align:start position:0%
+that differs is how much weight we give
+ 
+
+ align:start position:0%
+that differs is how much weight we give
+to that particular portfolio as we
+
+ align:start position:0%
+to that particular portfolio as we
+ 
+
+ align:start position:0%
+to that particular portfolio as we
+increase Lambda 1 then we give more
+
+ align:start position:0%
+increase Lambda 1 then we give more
+ 
+
+ align:start position:0%
+increase Lambda 1 then we give more
+allocation to this fixed Vector of
+
+ align:start position:0%
+allocation to this fixed Vector of
+ 
+
+ align:start position:0%
+allocation to this fixed Vector of
+weight so we invest proportionally in
+
+ align:start position:0%
+weight so we invest proportionally in
+ 
+
+ align:start position:0%
+weight so we invest proportionally in
+the assets and we just scale how much
+
+ align:start position:0%
+the assets and we just scale how much
+ 
+
+ align:start position:0%
+the assets and we just scale how much
+that uh overall factor is uh to achieve
+
+ align:start position:0%
+that uh overall factor is uh to achieve
+ 
+
+ align:start position:0%
+that uh overall factor is uh to achieve
+different levels of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return okay we can get nice closed form
+
+ align:start position:0%
+return okay we can get nice closed form
+ 
+
+ align:start position:0%
+return okay we can get nice closed form
+expressions for the portfolio
+
+ align:start position:0%
+expressions for the portfolio
+ 
+
+ align:start position:0%
+expressions for the portfolio
+variance um just you know as an
+
+ align:start position:0%
+variance um just you know as an
+ 
+
+ align:start position:0%
+variance um just you know as an
+extension of the sort of two asset case
+
+ align:start position:0%
+extension of the sort of two asset case
+ 
+
+ align:start position:0%
+extension of the sort of two asset case
+basically the portfolio variance is a
+
+ align:start position:0%
+basically the portfolio variance is a
+ 
+
+ align:start position:0%
+basically the portfolio variance is a
+parabola in the Target
+
+ align:start position:0%
+parabola in the Target
+ 
+
+ align:start position:0%
+parabola in the Target
+return um and so as we increase our
+
+ align:start position:0%
+return um and so as we increase our
+ 
+
+ align:start position:0%
+return um and so as we increase our
+Target return we have to increase our
+
+ align:start position:0%
+Target return we have to increase our
+ 
+
+ align:start position:0%
+Target return we have to increase our
+portfolio variability there's there is
+
+ align:start position:0%
+portfolio variability there's there is
+ 
+
+ align:start position:0%
+portfolio variability there's there is
+that tradeoff with these optimal
+
+ align:start position:0%
+that tradeoff with these optimal
+ 
+
+ align:start position:0%
+that tradeoff with these optimal
+portfolio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we consider the fully invested
+
+ align:start position:0%
+and if we consider the fully invested
+ 
+
+ align:start position:0%
+and if we consider the fully invested
+optimal
+
+ align:start position:0%
+optimal
+ 
+
+ align:start position:0%
+optimal
+portfolio well
+
+ align:start position:0%
+portfolio well
+ 
+
+ align:start position:0%
+portfolio well
+um the fully invested Mark uh uh the
+
+ align:start position:0%
+um the fully invested Mark uh uh the
+ 
+
+ align:start position:0%
+um the fully invested Mark uh uh the
+fully invested portfolio invests nothing
+
+ align:start position:0%
+fully invested portfolio invests nothing
+ 
+
+ align:start position:0%
+fully invested portfolio invests nothing
+in cash invests everything in the risky
+
+ align:start position:0%
+in cash invests everything in the risky
+ 
+
+ align:start position:0%
+in cash invests everything in the risky
+assets um we actually are going to call
+
+ align:start position:0%
+assets um we actually are going to call
+ 
+
+ align:start position:0%
+assets um we actually are going to call
+that the market
+
+ align:start position:0%
+that the market
+ 
+
+ align:start position:0%
+that the market
+portfolio um um and the Expressions here
+
+ align:start position:0%
+portfolio um um and the Expressions here
+ 
+
+ align:start position:0%
+portfolio um um and the Expressions here
+give us the weights for that uh Market
+
+ align:start position:0%
+give us the weights for that uh Market
+ 
+
+ align:start position:0%
+give us the weights for that uh Market
+portfolio and
+
+ align:start position:0%
+portfolio and
+ 
+
+ align:start position:0%
+portfolio and
+uh and this may look a little
+
+ align:start position:0%
+uh and this may look a little
+ 
+
+ align:start position:0%
+uh and this may look a little
+complicated um in terms of the
+
+ align:start position:0%
+complicated um in terms of the
+ 
+
+ align:start position:0%
+complicated um in terms of the
+Expressions but it's actually simple
+
+ align:start position:0%
+Expressions but it's actually simple
+ 
+
+ align:start position:0%
+Expressions but it's actually simple
+closed form expressions
+
+ align:start position:0%
+closed form expressions
+ 
+
+ align:start position:0%
+closed form expressions
+for uh the expected return and the
+
+ align:start position:0%
+for uh the expected return and the
+ 
+
+ align:start position:0%
+for uh the expected return and the
+variance of the market
+
+ align:start position:0%
+variance of the market
+ 
+
+ align:start position:0%
+variance of the market
+portfolio um and and what's
+
+ align:start position:0%
+portfolio um and and what's
+ 
+
+ align:start position:0%
+portfolio um and and what's
+happening with this is We
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have basically for the risky assets we
+
+ align:start position:0%
+have basically for the risky assets we
+ 
+
+ align:start position:0%
+have basically for the risky assets we
+have some
+
+ align:start position:0%
+have some
+ 
+
+ align:start position:0%
+have some
+efficient uh or set of feasible
+
+ align:start position:0%
+efficient uh or set of feasible
+ 
+
+ align:start position:0%
+efficient uh or set of feasible
+portfolios which is all in this range
+
+ align:start position:0%
+portfolios which is all in this range
+ 
+
+ align:start position:0%
+portfolios which is all in this range
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then with our risky
+
+ align:start position:0%
+then with our risky
+ 
+
+ align:start position:0%
+then with our risky
+asset we could be investing here and so
+
+ align:start position:0%
+asset we could be investing here and so
+ 
+
+ align:start position:0%
+asset we could be investing here and so
+the optimal
+
+ align:start position:0%
+the optimal
+ 
+
+ align:start position:0%
+the optimal
+portfolio the optimal portfolio is in in
+
+ align:start position:0%
+portfolio the optimal portfolio is in in
+ 
+
+ align:start position:0%
+portfolio the optimal portfolio is in in
+in the case where we can invest in in
+
+ align:start position:0%
+in the case where we can invest in in
+ 
+
+ align:start position:0%
+in the case where we can invest in in
+the uh risk-free
+
+ align:start position:0%
+the uh risk-free
+ 
+
+ align:start position:0%
+the uh risk-free
+asset will basically correspond to sort
+
+ align:start position:0%
+asset will basically correspond to sort
+ 
+
+ align:start position:0%
+asset will basically correspond to sort
+of maximizing the return the mean return
+
+ align:start position:0%
+of maximizing the return the mean return
+ 
+
+ align:start position:0%
+of maximizing the return the mean return
+for across all portfolio so it's
+
+ align:start position:0%
+for across all portfolio so it's
+ 
+
+ align:start position:0%
+for across all portfolio so it's
+actually going to correspond to the
+
+ align:start position:0%
+actually going to correspond to the
+ 
+
+ align:start position:0%
+actually going to correspond to the
+simple tangent
+
+ align:start position:0%
+simple tangent
+ 
+
+ align:start position:0%
+simple tangent
+line which
+
+ align:start position:0%
+line which
+ 
+
+ align:start position:0%
+line which
+basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crosses the uh Market
+
+ align:start position:0%
+crosses the uh Market
+ 
+
+ align:start position:0%
+crosses the uh Market
+portfolio which is the fully invested
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+portfolio Okay now
+
+ align:start position:0%
+portfolio Okay now
+ 
+
+ align:start position:0%
+portfolio Okay now
+um this structure of the problem is is
+
+ align:start position:0%
+um this structure of the problem is is
+ 
+
+ align:start position:0%
+um this structure of the problem is is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+incredibly powerful and there's an
+
+ align:start position:0%
+incredibly powerful and there's an
+ 
+
+ align:start position:0%
+incredibly powerful and there's an
+important paper by Tobin
+
+ align:start position:0%
+important paper by Tobin
+ 
+
+ align:start position:0%
+important paper by Tobin
+which uh states that basically every
+
+ align:start position:0%
+which uh states that basically every
+ 
+
+ align:start position:0%
+which uh states that basically every
+portfolio is going to under these
+
+ align:start position:0%
+portfolio is going to under these
+ 
+
+ align:start position:0%
+portfolio is going to under these
+assumptions for the investment uh
+
+ align:start position:0%
+assumptions for the investment uh
+ 
+
+ align:start position:0%
+assumptions for the investment uh
+problem every optimal portfolio invests
+
+ align:start position:0%
+problem every optimal portfolio invests
+ 
+
+ align:start position:0%
+problem every optimal portfolio invests
+in a combination of the risk-free asset
+
+ align:start position:0%
+in a combination of the risk-free asset
+ 
+
+ align:start position:0%
+in a combination of the risk-free asset
+and the market
+
+ align:start position:0%
+and the market
+ 
+
+ align:start position:0%
+and the market
+portfolio
+
+ align:start position:0%
+portfolio
+ 
+
+ align:start position:0%
+portfolio
+so regardless of what of how you want of
+
+ align:start position:0%
+so regardless of what of how you want of
+ 
+
+ align:start position:0%
+so regardless of what of how you want of
+regardless of uh how much risk you want
+
+ align:start position:0%
+regardless of uh how much risk you want
+ 
+
+ align:start position:0%
+regardless of uh how much risk you want
+to take the optimal portfolio
+
+ align:start position:0%
+to take the optimal portfolio
+ 
+
+ align:start position:0%
+to take the optimal portfolio
+is essentially the same it just depends
+
+ align:start position:0%
+is essentially the same it just depends
+ 
+
+ align:start position:0%
+is essentially the same it just depends
+on how much Capital you're going to put
+
+ align:start position:0%
+on how much Capital you're going to put
+ 
+
+ align:start position:0%
+on how much Capital you're going to put
+into that optimal
+
+ align:start position:0%
+into that optimal
+ 
+
+ align:start position:0%
+into that optimal
+portfolio and so uh all the optimal
+
+ align:start position:0%
+portfolio and so uh all the optimal
+ 
+
+ align:start position:0%
+portfolio and so uh all the optimal
+portfolios will invest in the same risky
+
+ align:start position:0%
+portfolios will invest in the same risky
+ 
+
+ align:start position:0%
+portfolios will invest in the same risky
+assets as the market portfolio and the
+
+ align:start position:0%
+assets as the market portfolio and the
+ 
+
+ align:start position:0%
+assets as the market portfolio and the
+same proportions and the only difference
+
+ align:start position:0%
+same proportions and the only difference
+ 
+
+ align:start position:0%
+same proportions and the only difference
+is is their total
+
+ align:start position:0%
+is is their total
+ 
+
+ align:start position:0%
+is is their total
+weight now plugging in the expressions
+
+ align:start position:0%
+weight now plugging in the expressions
+ 
+
+ align:start position:0%
+weight now plugging in the expressions
+for the different uh lrange multipliers
+
+ align:start position:0%
+for the different uh lrange multipliers
+ 
+
+ align:start position:0%
+for the different uh lrange multipliers
+for a given
+
+ align:start position:0%
+for a given
+ 
+
+ align:start position:0%
+for a given
+portfolio p with
+
+ align:start position:0%
+portfolio p with
+ 
+
+ align:start position:0%
+portfolio p with
+return and we get that expression so let
+
+ align:start position:0%
+return and we get that expression so let
+ 
+
+ align:start position:0%
+return and we get that expression so let
+me just summarize that so suppose we
+
+ align:start position:0%
+me just summarize that so suppose we
+ 
+
+ align:start position:0%
+me just summarize that so suppose we
+want the portfolio P such that the
+
+ align:start position:0%
+want the portfolio P such that the
+ 
+
+ align:start position:0%
+want the portfolio P such that the
+expectation of RP is equal to Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then this uh this portfolio RP
+
+ align:start position:0%
+then this uh this portfolio RP
+ 
+
+ align:start position:0%
+then this uh this portfolio RP
+is going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal it's going to equal um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically what uh it's going to invest
+
+ align:start position:0%
+basically what uh it's going to invest
+ 
+
+ align:start position:0%
+basically what uh it's going to invest
+in the risk-free asset with one minus
+
+ align:start position:0%
+in the risk-free asset with one minus
+ 
+
+ align:start position:0%
+in the risk-free asset with one minus
+one transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+WM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus WM transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm sorry WM
+
+ align:start position:0%
+I'm sorry WM
+ 
+
+ align:start position:0%
+I'm sorry WM
+times the return of the
+
+ align:start position:0%
+times the return of the
+ 
+
+ align:start position:0%
+times the return of the
+market and uh the actual weights are
+
+ align:start position:0%
+market and uh the actual weights are
+ 
+
+ align:start position:0%
+market and uh the actual weights are
+given by this expression here
+
+ align:start position:0%
+given by this expression here
+ 
+
+ align:start position:0%
+given by this expression here
+which gives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us okay the expression that I'm just
+
+ align:start position:0%
+us okay the expression that I'm just
+ 
+
+ align:start position:0%
+us okay the expression that I'm just
+writing up from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+board we have that the expected return
+
+ align:start position:0%
+board we have that the expected return
+ 
+
+ align:start position:0%
+board we have that the expected return
+is R plus WM * the market return minus r
+
+ align:start position:0%
+is R plus WM * the market return minus r
+ 
+
+ align:start position:0%
+is R plus WM * the market return minus r
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+volatility Sigma 2 p is simply the
+
+ align:start position:0%
+volatility Sigma 2 p is simply the
+ 
+
+ align:start position:0%
+volatility Sigma 2 p is simply the
+square of the weight in the market times
+
+ align:start position:0%
+square of the weight in the market times
+ 
+
+ align:start position:0%
+square of the weight in the market times
+the market
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volatility okay this uh leads to the
+
+ align:start position:0%
+volatility okay this uh leads to the
+ 
+
+ align:start position:0%
+volatility okay this uh leads to the
+definition of basically the Capital
+
+ align:start position:0%
+definition of basically the Capital
+ 
+
+ align:start position:0%
+definition of basically the Capital
+Market
+
+ align:start position:0%
+Market
+ 
+
+ align:start position:0%
+Market
+line which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is which is essentially this line here
+
+ align:start position:0%
+is which is essentially this line here
+ 
+
+ align:start position:0%
+is which is essentially this line here
+this is our Capital Market line
+
+ align:start position:0%
+this is our Capital Market line
+ 
+
+ align:start position:0%
+this is our Capital Market line
+for the portfolio
+
+ align:start position:0%
+for the portfolio
+ 
+
+ align:start position:0%
+for the portfolio
+optimization and the structure of this
+
+ align:start position:0%
+optimization and the structure of this
+ 
+
+ align:start position:0%
+optimization and the structure of this
+line is such that this point for the
+
+ align:start position:0%
+line is such that this point for the
+ 
+
+ align:start position:0%
+line is such that this point for the
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+portfolio that has volatility given by
+
+ align:start position:0%
+portfolio that has volatility given by
+ 
+
+ align:start position:0%
+portfolio that has volatility given by
+the market portfolios volatility Sigma M
+
+ align:start position:0%
+the market portfolios volatility Sigma M
+ 
+
+ align:start position:0%
+the market portfolios volatility Sigma M
+and the return on the market alpha M or
+
+ align:start position:0%
+and the return on the market alpha M or
+ 
+
+ align:start position:0%
+and the return on the market alpha M or
+expected value of M of
+
+ align:start position:0%
+expected value of M of
+ 
+
+ align:start position:0%
+expected value of M of
+RM
+
+ align:start position:0%
+RM
+ 
+
+ align:start position:0%
+RM
+and the slope of this
+
+ align:start position:0%
+and the slope of this
+ 
+
+ align:start position:0%
+and the slope of this
+line is given
+
+ align:start position:0%
+line is given
+ 
+
+ align:start position:0%
+line is given
+by Alpha
+
+ align:start position:0%
+by Alpha
+ 
+
+ align:start position:0%
+by Alpha
+M minus r KN over Sigma
+
+ align:start position:0%
+M minus r KN over Sigma
+ 
+
+ align:start position:0%
+M minus r KN over Sigma
+M and points along the line are given by
+
+ align:start position:0%
+M and points along the line are given by
+ 
+
+ align:start position:0%
+M and points along the line are given by
+R
+
+ align:start position:0%
+R
+ 
+
+ align:start position:0%
+R
+KN Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sigma P times this Factor so this is the
+
+ align:start position:0%
+Sigma P times this Factor so this is the
+ 
+
+ align:start position:0%
+Sigma P times this Factor so this is the
+uh expected value of
+
+ align:start position:0%
+uh expected value of
+ 
+
+ align:start position:0%
+uh expected value of
+RP is any optimal portfolio has return
+
+ align:start position:0%
+RP is any optimal portfolio has return
+ 
+
+ align:start position:0%
+RP is any optimal portfolio has return
+equal to the risk-free
+
+ align:start position:0%
+equal to the risk-free
+ 
+
+ align:start position:0%
+equal to the risk-free
+rate plus a
+
+ align:start position:0%
+rate plus a
+ 
+
+ align:start position:0%
+rate plus a
+multiple of the return per risk of the
+
+ align:start position:0%
+multiple of the return per risk of the
+ 
+
+ align:start position:0%
+multiple of the return per risk of the
+market
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+portfolio This this term here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is called the price of Market
+
+ align:start position:0%
+is called the price of Market
+ 
+
+ align:start position:0%
+is called the price of Market
+risk yes is that the same as the sharp
+
+ align:start position:0%
+risk yes is that the same as the sharp
+ 
+
+ align:start position:0%
+risk yes is that the same as the sharp
+ratio I it's
+
+ align:start position:0%
+ratio I it's
+ 
+
+ align:start position:0%
+ratio I it's
+uh close to the sharp ratio and the
+
+ align:start position:0%
+uh close to the sharp ratio and the
+ 
+
+ align:start position:0%
+uh close to the sharp ratio and the
+sharp ratio is
+
+ align:start position:0%
+sharp ratio is
+ 
+
+ align:start position:0%
+sharp ratio is
+is yes and this is is the sharp ratio
+
+ align:start position:0%
+is yes and this is is the sharp ratio
+ 
+
+ align:start position:0%
+is yes and this is is the sharp ratio
+for the uh for the market portfolio
+
+ align:start position:0%
+for the uh for the market portfolio
+ 
+
+ align:start position:0%
+for the uh for the market portfolio
+yeah and so um if we want to invest in
+
+ align:start position:0%
+yeah and so um if we want to invest in
+ 
+
+ align:start position:0%
+yeah and so um if we want to invest in
+uh in the market our decision is reduced
+
+ align:start position:0%
+uh in the market our decision is reduced
+ 
+
+ align:start position:0%
+uh in the market our decision is reduced
+then to how much risk are we willing to
+
+ align:start position:0%
+then to how much risk are we willing to
+ 
+
+ align:start position:0%
+then to how much risk are we willing to
+take and the compensation for taking
+
+ align:start position:0%
+take and the compensation for taking
+ 
+
+ align:start position:0%
+take and the compensation for taking
+extra risk is extra return and we
+
+ align:start position:0%
+extra risk is extra return and we
+ 
+
+ align:start position:0%
+extra risk is extra return and we
+achieve that by essentially investing in
+
+ align:start position:0%
+achieve that by essentially investing in
+ 
+
+ align:start position:0%
+achieve that by essentially investing in
+the same portfolio only we change the
+
+ align:start position:0%
+the same portfolio only we change the
+ 
+
+ align:start position:0%
+the same portfolio only we change the
+scale at which we're investing in that
+
+ align:start position:0%
+scale at which we're investing in that
+ 
+
+ align:start position:0%
+scale at which we're investing in that
+portfolio so
+
+ align:start position:0%
+portfolio so
+ 
+
+ align:start position:0%
+portfolio so
+uh now
+
+ align:start position:0%
+uh now
+ 
+
+ align:start position:0%
+uh now
+if right now so far we've been been
+
+ align:start position:0%
+if right now so far we've been been
+ 
+
+ align:start position:0%
+if right now so far we've been been
+considering sort of points so between uh
+
+ align:start position:0%
+considering sort of points so between uh
+ 
+
+ align:start position:0%
+considering sort of points so between uh
+being fully invested in the market or
+
+ align:start position:0%
+being fully invested in the market or
+ 
+
+ align:start position:0%
+being fully invested in the market or
+fully invested in cash if we are able to
+
+ align:start position:0%
+fully invested in cash if we are able to
+ 
+
+ align:start position:0%
+fully invested in cash if we are able to
+borrow
+
+ align:start position:0%
+borrow
+ 
+
+ align:start position:0%
+borrow
+money at the risk-free
+
+ align:start position:0%
+money at the risk-free
+ 
+
+ align:start position:0%
+money at the risk-free
+rate then we can basically allocate
+
+ align:start position:0%
+rate then we can basically allocate
+ 
+
+ align:start position:0%
+rate then we can basically allocate
+additional weights to the market
+
+ align:start position:0%
+additional weights to the market
+ 
+
+ align:start position:0%
+additional weights to the market
+portfolio and Achieve
+
+ align:start position:0%
+portfolio and Achieve
+ 
+
+ align:start position:0%
+portfolio and Achieve
+points that are
+
+ align:start position:0%
+points that are
+ 
+
+ align:start position:0%
+points that are
+Beyond you know have higher return
+
+ align:start position:0%
+Beyond you know have higher return
+ 
+
+ align:start position:0%
+Beyond you know have higher return
+higher volatility than the market
+
+ align:start position:0%
+higher volatility than the market
+ 
+
+ align:start position:0%
+higher volatility than the market
+portfolio we can basically lever the
+
+ align:start position:0%
+portfolio we can basically lever the
+ 
+
+ align:start position:0%
+portfolio we can basically lever the
+strategy by borrowing money and
+
+ align:start position:0%
+strategy by borrowing money and
+ 
+
+ align:start position:0%
+strategy by borrowing money and
+investing that in in in this market
+
+ align:start position:0%
+investing that in in in this market
+ 
+
+ align:start position:0%
+investing that in in in this market
+portfolio so so this
+
+ align:start position:0%
+portfolio so so this
+ 
+
+ align:start position:0%
+portfolio so so this
+uh efficient
+
+ align:start position:0%
+uh efficient
+ 
+
+ align:start position:0%
+uh efficient
+Frontier uh if we can borrow riskless
+
+ align:start position:0%
+Frontier uh if we can borrow riskless
+ 
+
+ align:start position:0%
+Frontier uh if we can borrow riskless
+you know would it just be the Capital
+
+ align:start position:0%
+you know would it just be the Capital
+ 
+
+ align:start position:0%
+you know would it just be the Capital
+Market line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extended um here's a listing of of the
+
+ align:start position:0%
+extended um here's a listing of of the
+ 
+
+ align:start position:0%
+extended um here's a listing of of the
+papers that go through sort of the
+
+ align:start position:0%
+papers that go through sort of the
+ 
+
+ align:start position:0%
+papers that go through sort of the
+classical foundations for the and I
+
+ align:start position:0%
+classical foundations for the and I
+ 
+
+ align:start position:0%
+classical foundations for the and I
+these are all accessible on the web and
+
+ align:start position:0%
+these are all accessible on the web and
+ 
+
+ align:start position:0%
+these are all accessible on the web and
+I encourage you to actually look at
+
+ align:start position:0%
+I encourage you to actually look at
+ 
+
+ align:start position:0%
+I encourage you to actually look at
+these papers because uh the arguments
+
+ align:start position:0%
+these papers because uh the arguments
+ 
+
+ align:start position:0%
+these papers because uh the arguments
+are very straightforward the motivation
+
+ align:start position:0%
+are very straightforward the motivation
+ 
+
+ align:start position:0%
+are very straightforward the motivation
+and uh background is is is interesting
+
+ align:start position:0%
+and uh background is is is interesting
+ 
+
+ align:start position:0%
+and uh background is is is interesting
+to read um I virtually everyone on this
+
+ align:start position:0%
+to read um I virtually everyone on this
+ 
+
+ align:start position:0%
+to read um I virtually everyone on this
+page actually has a Nobel Prize except
+
+ align:start position:0%
+page actually has a Nobel Prize except
+ 
+
+ align:start position:0%
+page actually has a Nobel Prize except
+lintner I think he died before they gave
+
+ align:start position:0%
+lintner I think he died before they gave
+ 
+
+ align:start position:0%
+lintner I think he died before they gave
+the Nobel Prize to Mark witz and sharp
+
+ align:start position:0%
+the Nobel Prize to Mark witz and sharp
+ 
+
+ align:start position:0%
+the Nobel Prize to Mark witz and sharp
+uh but he would certainly would have
+
+ align:start position:0%
+uh but he would certainly would have
+ 
+
+ align:start position:0%
+uh but he would certainly would have
+been included in this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pardon me the latest and the latest one
+
+ align:start position:0%
+pardon me the latest and the latest one
+ 
+
+ align:start position:0%
+pardon me the latest and the latest one
+yes yes F was just awarded what two
+
+ align:start position:0%
+yes yes F was just awarded what two
+ 
+
+ align:start position:0%
+yes yes F was just awarded what two
+weeks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ago all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's okay let's move on to uh Von
+
+ align:start position:0%
+let's okay let's move on to uh Von
+ 
+
+ align:start position:0%
+let's okay let's move on to uh Von
+noyman Morganstern utility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory now in in the markwitz mean
+
+ align:start position:0%
+Theory now in in the markwitz mean
+ 
+
+ align:start position:0%
+Theory now in in the markwitz mean
+variance analysis we sort of reduced all
+
+ align:start position:0%
+variance analysis we sort of reduced all
+ 
+
+ align:start position:0%
+variance analysis we sort of reduced all
+portfolios to the properties of what's
+
+ align:start position:0%
+portfolios to the properties of what's
+ 
+
+ align:start position:0%
+portfolios to the properties of what's
+their expected return and what's their
+
+ align:start position:0%
+their expected return and what's their
+ 
+
+ align:start position:0%
+their expected return and what's their
+the variance or volatility of the
+
+ align:start position:0%
+the variance or volatility of the
+ 
+
+ align:start position:0%
+the variance or volatility of the
+returns
+
+ align:start position:0%
+returns
+ 
+
+ align:start position:0%
+returns
+um why under what circumstances would
+
+ align:start position:0%
+um why under what circumstances would
+ 
+
+ align:start position:0%
+um why under what circumstances would
+that be a really good decision to be
+
+ align:start position:0%
+that be a really good decision to be
+ 
+
+ align:start position:0%
+that be a really good decision to be
+making for how to do
+
+ align:start position:0%
+making for how to do
+ 
+
+ align:start position:0%
+making for how to do
+portfolio uh optimization portfolio
+
+ align:start position:0%
+portfolio uh optimization portfolio
+ 
+
+ align:start position:0%
+portfolio uh optimization portfolio
+allocations well uh V noyman the V
+
+ align:start position:0%
+allocations well uh V noyman the V
+ 
+
+ align:start position:0%
+allocations well uh V noyman the V
+noyman Morganstern theory is a theory
+
+ align:start position:0%
+noyman Morganstern theory is a theory
+ 
+
+ align:start position:0%
+noyman Morganstern theory is a theory
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+motivates making decisions under
+
+ align:start position:0%
+motivates making decisions under
+ 
+
+ align:start position:0%
+motivates making decisions under
+uncertainty
+
+ align:start position:0%
+uncertainty
+ 
+
+ align:start position:0%
+uncertainty
+where you should specify a utility
+
+ align:start position:0%
+where you should specify a utility
+ 
+
+ align:start position:0%
+where you should specify a utility
+function for your
+
+ align:start position:0%
+function for your
+ 
+
+ align:start position:0%
+function for your
+wealth and you should engage in
+
+ align:start position:0%
+wealth and you should engage in
+ 
+
+ align:start position:0%
+wealth and you should engage in
+decisions that maximize the expected
+
+ align:start position:0%
+decisions that maximize the expected
+ 
+
+ align:start position:0%
+decisions that maximize the expected
+utility of your wealth and uh the theory
+
+ align:start position:0%
+utility of your wealth and uh the theory
+ 
+
+ align:start position:0%
+utility of your wealth and uh the theory
+is is really very uh powerful um in that
+
+ align:start position:0%
+is is really very uh powerful um in that
+ 
+
+ align:start position:0%
+is is really very uh powerful um in that
+uh the
+
+ align:start position:0%
+uh the
+ 
+
+ align:start position:0%
+uh the
+uh when you're making decisions under
+
+ align:start position:0%
+uh when you're making decisions under
+ 
+
+ align:start position:0%
+uh when you're making decisions under
+uncertainty that there are there's are
+
+ align:start position:0%
+uncertainty that there are there's are
+ 
+
+ align:start position:0%
+uncertainty that there are there's are
+rational things you should do um you
+
+ align:start position:0%
+rational things you should do um you
+ 
+
+ align:start position:0%
+rational things you should do um you
+know you basically um like you if you
+
+ align:start position:0%
+know you basically um like you if you
+ 
+
+ align:start position:0%
+know you basically um like you if you
+like higher return you know you the
+
+ align:start position:0%
+like higher return you know you the
+ 
+
+ align:start position:0%
+like higher return you know you the
+decision should be consistent with
+
+ align:start position:0%
+decision should be consistent with
+ 
+
+ align:start position:0%
+decision should be consistent with
+preferring uh outcomes with higher
+
+ align:start position:0%
+preferring uh outcomes with higher
+ 
+
+ align:start position:0%
+preferring uh outcomes with higher
+returns if you don't like variability
+
+ align:start position:0%
+returns if you don't like variability
+ 
+
+ align:start position:0%
+returns if you don't like variability
+then you should be preferring returns
+
+ align:start position:0%
+then you should be preferring returns
+ 
+
+ align:start position:0%
+then you should be preferring returns
+that have the same expected return that
+
+ align:start position:0%
+that have the same expected return that
+ 
+
+ align:start position:0%
+that have the same expected return that
+have lower volatility um but depending
+
+ align:start position:0%
+have lower volatility um but depending
+ 
+
+ align:start position:0%
+have lower volatility um but depending
+on how your utility function is defined
+
+ align:start position:0%
+on how your utility function is defined
+ 
+
+ align:start position:0%
+on how your utility function is defined
+you may get different different outcomes
+
+ align:start position:0%
+you may get different different outcomes
+ 
+
+ align:start position:0%
+you may get different different outcomes
+and uh the uh so so to set up this
+
+ align:start position:0%
+and uh the uh so so to set up this
+ 
+
+ align:start position:0%
+and uh the uh so so to set up this
+problem let's just consider you know the
+
+ align:start position:0%
+problem let's just consider you know the
+ 
+
+ align:start position:0%
+problem let's just consider you know the
+the problem that Mark was addressed you
+
+ align:start position:0%
+the problem that Mark was addressed you
+ 
+
+ align:start position:0%
+the problem that Mark was addressed you
+have a one period investment you start
+
+ align:start position:0%
+have a one period investment you start
+ 
+
+ align:start position:0%
+have a one period investment you start
+with initial wealth w0 you're going to
+
+ align:start position:0%
+with initial wealth w0 you're going to
+ 
+
+ align:start position:0%
+with initial wealth w0 you're going to
+choose a portfolio p and uh the wealth
+
+ align:start position:0%
+choose a portfolio p and uh the wealth
+ 
+
+ align:start position:0%
+choose a portfolio p and uh the wealth
+after one period is simply going to be
+
+ align:start position:0%
+after one period is simply going to be
+ 
+
+ align:start position:0%
+after one period is simply going to be
+one plus the return on that portfolio
+
+ align:start position:0%
+one plus the return on that portfolio
+ 
+
+ align:start position:0%
+one plus the return on that portfolio
+given uh terminal wealth W and our
+
+ align:start position:0%
+given uh terminal wealth W and our
+ 
+
+ align:start position:0%
+given uh terminal wealth W and our
+utility function is going to be some
+
+ align:start position:0%
+utility function is going to be some
+ 
+
+ align:start position:0%
+utility function is going to be some
+quantitative measure of the outcome
+
+ align:start position:0%
+quantitative measure of the outcome
+ 
+
+ align:start position:0%
+quantitative measure of the outcome
+what's the value to the investor and we
+
+ align:start position:0%
+what's the value to the investor and we
+ 
+
+ align:start position:0%
+what's the value to the investor and we
+simply want to uh compute the expected
+
+ align:start position:0%
+simply want to uh compute the expected
+ 
+
+ align:start position:0%
+simply want to uh compute the expected
+volatility of different strategies and
+
+ align:start position:0%
+volatility of different strategies and
+ 
+
+ align:start position:0%
+volatility of different strategies and
+find the strategy that maximizes the
+
+ align:start position:0%
+find the strategy that maximizes the
+ 
+
+ align:start position:0%
+find the strategy that maximizes the
+expected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+utility what kind what would or what are
+
+ align:start position:0%
+utility what kind what would or what are
+ 
+
+ align:start position:0%
+utility what kind what would or what are
+the basic properties of utility
+
+ align:start position:0%
+the basic properties of utility
+ 
+
+ align:start position:0%
+the basic properties of utility
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+well you know if we
+
+ align:start position:0%
+well you know if we
+ 
+
+ align:start position:0%
+well you know if we
+graph over wealth
+
+ align:start position:0%
+graph over wealth
+ 
+
+ align:start position:0%
+graph over wealth
+our utility of
+
+ align:start position:0%
+our utility of
+ 
+
+ align:start position:0%
+our utility of
+wealth starting at w0 our initial
+
+ align:start position:0%
+wealth starting at w0 our initial
+ 
+
+ align:start position:0%
+wealth starting at w0 our initial
+wealth if
+
+ align:start position:0%
+wealth if
+ 
+
+ align:start position:0%
+wealth if
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+uh have greater wealth
+
+ align:start position:0%
+uh have greater wealth
+ 
+
+ align:start position:0%
+uh have greater wealth
+presumably uh will have greater utility
+
+ align:start position:0%
+presumably uh will have greater utility
+ 
+
+ align:start position:0%
+presumably uh will have greater utility
+so the slope of the utility function
+
+ align:start position:0%
+so the slope of the utility function
+ 
+
+ align:start position:0%
+so the slope of the utility function
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+increasing perhaps as we get more and
+
+ align:start position:0%
+increasing perhaps as we get more and
+ 
+
+ align:start position:0%
+increasing perhaps as we get more and
+more wealthy the mark marginal benefit
+
+ align:start position:0%
+more wealthy the mark marginal benefit
+ 
+
+ align:start position:0%
+more wealthy the mark marginal benefit
+of additional wealth isn't quite as much
+
+ align:start position:0%
+of additional wealth isn't quite as much
+ 
+
+ align:start position:0%
+of additional wealth isn't quite as much
+as it was when we were poor and so
+
+ align:start position:0%
+as it was when we were poor and so
+ 
+
+ align:start position:0%
+as it was when we were poor and so
+perhaps the curve for the utility
+
+ align:start position:0%
+perhaps the curve for the utility
+ 
+
+ align:start position:0%
+perhaps the curve for the utility
+function should taper off a bit okay
+
+ align:start position:0%
+function should taper off a bit okay
+ 
+
+ align:start position:0%
+function should taper off a bit okay
+these conditions um would correspond to
+
+ align:start position:0%
+these conditions um would correspond to
+ 
+
+ align:start position:0%
+these conditions um would correspond to
+the first derivative being increasing
+
+ align:start position:0%
+the first derivative being increasing
+ 
+
+ align:start position:0%
+the first derivative being increasing
+always and the second derivative being
+
+ align:start position:0%
+always and the second derivative being
+ 
+
+ align:start position:0%
+always and the second derivative being
+less than zero
+
+ align:start position:0%
+less than zero
+ 
+
+ align:start position:0%
+less than zero
+perhaps
+
+ align:start position:0%
+perhaps
+ 
+
+ align:start position:0%
+perhaps
+um there are definitions in the
+
+ align:start position:0%
+um there are definitions in the
+ 
+
+ align:start position:0%
+um there are definitions in the
+literature of risk aversion absolute
+
+ align:start position:0%
+literature of risk aversion absolute
+ 
+
+ align:start position:0%
+literature of risk aversion absolute
+risk aversion and relative risk
+
+ align:start position:0%
+risk aversion and relative risk
+ 
+
+ align:start position:0%
+risk aversion and relative risk
+aversion um and these are simple
+
+ align:start position:0%
+aversion um and these are simple
+ 
+
+ align:start position:0%
+aversion um and these are simple
+functions of the first and second
+
+ align:start position:0%
+functions of the first and second
+ 
+
+ align:start position:0%
+functions of the first and second
+derivatives of the utility function to
+
+ align:start position:0%
+derivatives of the utility function to
+ 
+
+ align:start position:0%
+derivatives of the utility function to
+see where these come into play Let's
+
+ align:start position:0%
+see where these come into play Let's
+ 
+
+ align:start position:0%
+see where these come into play Let's
+just look at let's assume that the
+
+ align:start position:0%
+just look at let's assume that the
+ 
+
+ align:start position:0%
+just look at let's assume that the
+utility function is a smooth function
+
+ align:start position:0%
+utility function is a smooth function
+ 
+
+ align:start position:0%
+utility function is a smooth function
+and uh consider a tailor series
+
+ align:start position:0%
+and uh consider a tailor series
+ 
+
+ align:start position:0%
+and uh consider a tailor series
+approximation of that so if we consider
+
+ align:start position:0%
+approximation of that so if we consider
+ 
+
+ align:start position:0%
+approximation of that so if we consider
+expanding the utility function about
+
+ align:start position:0%
+expanding the utility function about
+ 
+
+ align:start position:0%
+expanding the utility function about
+some base wealth
+
+ align:start position:0%
+some base wealth
+ 
+
+ align:start position:0%
+some base wealth
+wstar then it's simply equal to to you
+
+ align:start position:0%
+wstar then it's simply equal to to you
+ 
+
+ align:start position:0%
+wstar then it's simply equal to to you
+know that value at w Star Plus the first
+
+ align:start position:0%
+know that value at w Star Plus the first
+ 
+
+ align:start position:0%
+know that value at w Star Plus the first
+derivative time wus W Star Plus uh 1
+
+ align:start position:0%
+derivative time wus W Star Plus uh 1
+ 
+
+ align:start position:0%
+derivative time wus W Star Plus uh 1
+half the second derivative times the
+
+ align:start position:0%
+half the second derivative times the
+ 
+
+ align:start position:0%
+half the second derivative times the
+squar deviation of the wealth from W
+
+ align:start position:0%
+squar deviation of the wealth from W
+ 
+
+ align:start position:0%
+squar deviation of the wealth from W
+star and if we take expectations of
+
+ align:start position:0%
+star and if we take expectations of
+ 
+
+ align:start position:0%
+star and if we take expectations of
+this and if W star is the actual
+
+ align:start position:0%
+this and if W star is the actual
+ 
+
+ align:start position:0%
+this and if W star is the actual
+expected wealth of the random variable
+
+ align:start position:0%
+expected wealth of the random variable
+ 
+
+ align:start position:0%
+expected wealth of the random variable
+then the this expected utility is
+
+ align:start position:0%
+then the this expected utility is
+ 
+
+ align:start position:0%
+then the this expected utility is
+actually proportional to
+
+ align:start position:0%
+actually proportional to
+ 
+
+ align:start position:0%
+actually proportional to
+the expected wealth minus a half Lambda
+
+ align:start position:0%
+the expected wealth minus a half Lambda
+ 
+
+ align:start position:0%
+the expected wealth minus a half Lambda
+times the variance of the wealth so sort
+
+ align:start position:0%
+times the variance of the wealth so sort
+ 
+
+ align:start position:0%
+times the variance of the wealth so sort
+of to a whatever second order
+
+ align:start position:0%
+of to a whatever second order
+ 
+
+ align:start position:0%
+of to a whatever second order
+approximation this expected utility
+
+ align:start position:0%
+approximation this expected utility
+ 
+
+ align:start position:0%
+approximation this expected utility
+is a function which is looking at
+
+ align:start position:0%
+is a function which is looking at
+ 
+
+ align:start position:0%
+is a function which is looking at
+expected return minus a multiple of the
+
+ align:start position:0%
+expected return minus a multiple of the
+ 
+
+ align:start position:0%
+expected return minus a multiple of the
+volatility of that return or the wealth
+
+ align:start position:0%
+volatility of that return or the wealth
+ 
+
+ align:start position:0%
+volatility of that return or the wealth
+if we're considering it on that
+
+ align:start position:0%
+if we're considering it on that
+ 
+
+ align:start position:0%
+if we're considering it on that
+scale um so
+
+ align:start position:0%
+scale um so
+ 
+
+ align:start position:0%
+scale um so
+well there are various different utility
+
+ align:start position:0%
+well there are various different utility
+ 
+
+ align:start position:0%
+well there are various different utility
+functions that economists have uh worked
+
+ align:start position:0%
+functions that economists have uh worked
+ 
+
+ align:start position:0%
+functions that economists have uh worked
+with and you know
+
+ align:start position:0%
+with and you know
+ 
+
+ align:start position:0%
+with and you know
+basically the kinds of functions they
+
+ align:start position:0%
+basically the kinds of functions they
+ 
+
+ align:start position:0%
+basically the kinds of functions they
+work with are all the simple functions
+
+ align:start position:0%
+work with are all the simple functions
+ 
+
+ align:start position:0%
+work with are all the simple functions
+we as mathematicians know about linear
+
+ align:start position:0%
+we as mathematicians know about linear
+ 
+
+ align:start position:0%
+we as mathematicians know about linear
+functions quadratic functions
+
+ align:start position:0%
+functions quadratic functions
+ 
+
+ align:start position:0%
+functions quadratic functions
+exponential functions power functions
+
+ align:start position:0%
+exponential functions power functions
+ 
+
+ align:start position:0%
+exponential functions power functions
+right and log functions so you know
+
+ align:start position:0%
+right and log functions so you know
+ 
+
+ align:start position:0%
+right and log functions so you know
+these are just uh you know the first
+
+ align:start position:0%
+these are just uh you know the first
+ 
+
+ align:start position:0%
+these are just uh you know the first
+ones uh that come to mind perhaps to
+
+ align:start position:0%
+ones uh that come to mind perhaps to
+ 
+
+ align:start position:0%
+ones uh that come to mind perhaps to
+economists but um there's actually a a
+
+ align:start position:0%
+economists but um there's actually a a
+ 
+
+ align:start position:0%
+economists but um there's actually a a
+some rich theory in terms terms of uh
+
+ align:start position:0%
+some rich theory in terms terms of uh
+ 
+
+ align:start position:0%
+some rich theory in terms terms of uh
+sort of portfolio or investment Choice
+
+ align:start position:0%
+sort of portfolio or investment Choice
+ 
+
+ align:start position:0%
+sort of portfolio or investment Choice
+with different utility functions of of
+
+ align:start position:0%
+with different utility functions of of
+ 
+
+ align:start position:0%
+with different utility functions of of
+these types and uh uh you know there's
+
+ align:start position:0%
+these types and uh uh you know there's
+ 
+
+ align:start position:0%
+these types and uh uh you know there's
+there's there there is some interesting
+
+ align:start position:0%
+there's there there is some interesting
+ 
+
+ align:start position:0%
+there's there there is some interesting
+work work there in the economics
+
+ align:start position:0%
+work work there in the economics
+ 
+
+ align:start position:0%
+work work there in the economics
+literature um one thing that is
+
+ align:start position:0%
+literature um one thing that is
+ 
+
+ align:start position:0%
+literature um one thing that is
+uh uh to be pointed out is that with
+
+ align:start position:0%
+uh uh to be pointed out is that with
+ 
+
+ align:start position:0%
+uh uh to be pointed out is that with
+quadratic
+
+ align:start position:0%
+quadratic
+ 
+
+ align:start position:0%
+quadratic
+utility then if we consider the expected
+
+ align:start position:0%
+utility then if we consider the expected
+ 
+
+ align:start position:0%
+utility then if we consider the expected
+utility under quadratic utility that is
+
+ align:start position:0%
+utility under quadratic utility that is
+ 
+
+ align:start position:0%
+utility under quadratic utility that is
+a expected utility function that only
+
+ align:start position:0%
+a expected utility function that only
+ 
+
+ align:start position:0%
+a expected utility function that only
+only depends on the expected wealth and
+
+ align:start position:0%
+only depends on the expected wealth and
+ 
+
+ align:start position:0%
+only depends on the expected wealth and
+the variance of the wealth which depends
+
+ align:start position:0%
+the variance of the wealth which depends
+ 
+
+ align:start position:0%
+the variance of the wealth which depends
+only on the expected return and the
+
+ align:start position:0%
+only on the expected return and the
+ 
+
+ align:start position:0%
+only on the expected return and the
+variance of the return of the portfolio
+
+ align:start position:0%
+variance of the return of the portfolio
+ 
+
+ align:start position:0%
+variance of the return of the portfolio
+so if we are working with a quadratic
+
+ align:start position:0%
+so if we are working with a quadratic
+ 
+
+ align:start position:0%
+so if we are working with a quadratic
+utility
+
+ align:start position:0%
+utility
+ 
+
+ align:start position:0%
+utility
+function then this mean variance
+
+ align:start position:0%
+function then this mean variance
+ 
+
+ align:start position:0%
+function then this mean variance
+analysis is the right thing to be doing
+
+ align:start position:0%
+analysis is the right thing to be doing
+ 
+
+ align:start position:0%
+analysis is the right thing to be doing
+under the Von no and Morganstern
+
+ align:start position:0%
+under the Von no and Morganstern
+ 
+
+ align:start position:0%
+under the Von no and Morganstern
+expected utility
+
+ align:start position:0%
+expected utility
+ 
+
+ align:start position:0%
+expected utility
+Theory so uh so doing that is
+
+ align:start position:0%
+Theory so uh so doing that is
+ 
+
+ align:start position:0%
+Theory so uh so doing that is
+is a good a good decision under under
+
+ align:start position:0%
+is a good a good decision under under
+ 
+
+ align:start position:0%
+is a good a good decision under under
+that if that's the utility function now
+
+ align:start position:0%
+that if that's the utility function now
+ 
+
+ align:start position:0%
+that if that's the utility function now
+when is that solution not to be
+
+ align:start position:0%
+when is that solution not to be
+ 
+
+ align:start position:0%
+when is that solution not to be
+preferred well really it's not to be
+
+ align:start position:0%
+preferred well really it's not to be
+ 
+
+ align:start position:0%
+preferred well really it's not to be
+preferred if you have a different
+
+ align:start position:0%
+preferred if you have a different
+ 
+
+ align:start position:0%
+preferred if you have a different
+utility function possibly and maybe the
+
+ align:start position:0%
+utility function possibly and maybe the
+ 
+
+ align:start position:0%
+utility function possibly and maybe the
+uh utility function should be adding
+
+ align:start position:0%
+uh utility function should be adding
+ 
+
+ align:start position:0%
+uh utility function should be adding
+some penalties for skewness or
+
+ align:start position:0%
+some penalties for skewness or
+ 
+
+ align:start position:0%
+some penalties for skewness or
+curtosis and that's being ignored here
+
+ align:start position:0%
+curtosis and that's being ignored here
+ 
+
+ align:start position:0%
+curtosis and that's being ignored here
+so extensions can can can be uh looked
+
+ align:start position:0%
+so extensions can can can be uh looked
+ 
+
+ align:start position:0%
+so extensions can can can be uh looked
+at uh an interesting mathematical fact
+
+ align:start position:0%
+at uh an interesting mathematical fact
+ 
+
+ align:start position:0%
+at uh an interesting mathematical fact
+is that you know under the
+
+ align:start position:0%
+is that you know under the
+ 
+
+ align:start position:0%
+is that you know under the
+assumption or should I say the
+
+ align:start position:0%
+assumption or should I say the
+ 
+
+ align:start position:0%
+assumption or should I say the
+imagination that returns are gaussian
+
+ align:start position:0%
+imagination that returns are gaussian
+ 
+
+ align:start position:0%
+imagination that returns are gaussian
+distributed um then the sort of means
+
+ align:start position:0%
+distributed um then the sort of means
+ 
+
+ align:start position:0%
+distributed um then the sort of means
+and variances of portfolios completely
+
+ align:start position:0%
+and variances of portfolios completely
+ 
+
+ align:start position:0%
+and variances of portfolios completely
+characterize all the distributions of of
+
+ align:start position:0%
+characterize all the distributions of of
+ 
+
+ align:start position:0%
+characterize all the distributions of of
+portfolios of assets if the underlying
+
+ align:start position:0%
+portfolios of assets if the underlying
+ 
+
+ align:start position:0%
+portfolios of assets if the underlying
+assets are gaussing distributions so a
+
+ align:start position:0%
+assets are gaussing distributions so a
+ 
+
+ align:start position:0%
+assets are gaussing distributions so a
+mean variance analysis is actually
+
+ align:start position:0%
+mean variance analysis is actually
+ 
+
+ align:start position:0%
+mean variance analysis is actually
+optimal under non-quadratic
+
+ align:start position:0%
+optimal under non-quadratic
+ 
+
+ align:start position:0%
+optimal under non-quadratic
+uh utility
+
+ align:start position:0%
+uh utility
+ 
+
+ align:start position:0%
+uh utility
+functions if the underlying assets are
+
+ align:start position:0%
+functions if the underlying assets are
+ 
+
+ align:start position:0%
+functions if the underlying assets are
+have gaussin distributions because
+
+ align:start position:0%
+have gaussin distributions because
+ 
+
+ align:start position:0%
+have gaussin distributions because
+basically only the means and variances
+
+ align:start position:0%
+basically only the means and variances
+ 
+
+ align:start position:0%
+basically only the means and variances
+are going to characterize the optimal
+
+ align:start position:0%
+are going to characterize the optimal
+ 
+
+ align:start position:0%
+are going to characterize the optimal
+portfolios and properties of those and
+
+ align:start position:0%
+portfolios and properties of those and
+ 
+
+ align:start position:0%
+portfolios and properties of those and
+uh uh basally stochastic dominance of
+
+ align:start position:0%
+uh uh basally stochastic dominance of
+ 
+
+ align:start position:0%
+uh uh basally stochastic dominance of
+functions of these variables will
+
+ align:start position:0%
+functions of these variables will
+ 
+
+ align:start position:0%
+functions of these variables will
+generally apply when the uh there's that
+
+ align:start position:0%
+generally apply when the uh there's that
+ 
+
+ align:start position:0%
+generally apply when the uh there's that
+corresponding stochastic dominance in
+
+ align:start position:0%
+corresponding stochastic dominance in
+ 
+
+ align:start position:0%
+corresponding stochastic dominance in
+terms of their means and variances
+
+ align:start position:0%
+terms of their means and variances
+ 
+
+ align:start position:0%
+terms of their means and variances
+anyway that this kind of theory can can
+
+ align:start position:0%
+anyway that this kind of theory can can
+ 
+
+ align:start position:0%
+anyway that this kind of theory can can
+uh can get involved but allows us to
+
+ align:start position:0%
+uh can get involved but allows us to
+ 
+
+ align:start position:0%
+uh can get involved but allows us to
+extend the the basic model that we
+
+ align:start position:0%
+extend the the basic model that we
+ 
+
+ align:start position:0%
+extend the the basic model that we
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+here let's turn to then to the topic of
+
+ align:start position:0%
+here let's turn to then to the topic of
+ 
+
+ align:start position:0%
+here let's turn to then to the topic of
+uh portfolio constraints so far in
+
+ align:start position:0%
+uh portfolio constraints so far in
+ 
+
+ align:start position:0%
+uh portfolio constraints so far in
+looking at this problem we haven't made
+
+ align:start position:0%
+looking at this problem we haven't made
+ 
+
+ align:start position:0%
+looking at this problem we haven't made
+any constraints on the problem we just
+
+ align:start position:0%
+any constraints on the problem we just
+ 
+
+ align:start position:0%
+any constraints on the problem we just
+want to maximize return minimize
+
+ align:start position:0%
+want to maximize return minimize
+ 
+
+ align:start position:0%
+want to maximize return minimize
+variance and uh consider trade-offs
+
+ align:start position:0%
+variance and uh consider trade-offs
+ 
+
+ align:start position:0%
+variance and uh consider trade-offs
+between those um with uh pract with
+
+ align:start position:0%
+between those um with uh pract with
+ 
+
+ align:start position:0%
+between those um with uh pract with
+practical uh portfolio optimization
+
+ align:start position:0%
+practical uh portfolio optimization
+ 
+
+ align:start position:0%
+practical uh portfolio optimization
+problems there there are different
+
+ align:start position:0%
+problems there there are different
+ 
+
+ align:start position:0%
+problems there there are different
+constraints that come into play
+
+ align:start position:0%
+constraints that come into play
+ 
+
+ align:start position:0%
+constraints that come into play
+um portfolios that are long only
+
+ align:start position:0%
+um portfolios that are long only
+ 
+
+ align:start position:0%
+um portfolios that are long only
+constrain the weights to only be
+
+ align:start position:0%
+constrain the weights to only be
+ 
+
+ align:start position:0%
+constrain the weights to only be
+positive there can be holding
+
+ align:start position:0%
+positive there can be holding
+ 
+
+ align:start position:0%
+positive there can be holding
+constraints which uh and it may be that
+
+ align:start position:0%
+constraints which uh and it may be that
+ 
+
+ align:start position:0%
+constraints which uh and it may be that
+we don't want the amount of a given
+
+ align:start position:0%
+we don't want the amount of a given
+ 
+
+ align:start position:0%
+we don't want the amount of a given
+asset to be too too big um in uh
+
+ align:start position:0%
+asset to be too too big um in uh
+ 
+
+ align:start position:0%
+asset to be too too big um in uh
+basically Equity strategies you you
+
+ align:start position:0%
+basically Equity strategies you you
+ 
+
+ align:start position:0%
+basically Equity strategies you you
+don't want to be holding uh if you have
+
+ align:start position:0%
+don't want to be holding uh if you have
+ 
+
+ align:start position:0%
+don't want to be holding uh if you have
+a sort of a medium frequency trading
+
+ align:start position:0%
+a sort of a medium frequency trading
+ 
+
+ align:start position:0%
+a sort of a medium frequency trading
+strategy and equities you don't want to
+
+ align:start position:0%
+strategy and equities you don't want to
+ 
+
+ align:start position:0%
+strategy and equities you don't want to
+be holding uh much more than the trading
+
+ align:start position:0%
+be holding uh much more than the trading
+ 
+
+ align:start position:0%
+be holding uh much more than the trading
+volume of a few hours or maybe a day in
+
+ align:start position:0%
+volume of a few hours or maybe a day in
+ 
+
+ align:start position:0%
+volume of a few hours or maybe a day in
+in the asset because if you're have
+
+ align:start position:0%
+in the asset because if you're have
+ 
+
+ align:start position:0%
+in the asset because if you're have
+having to sell it uh you know there
+
+ align:start position:0%
+having to sell it uh you know there
+ 
+
+ align:start position:0%
+having to sell it uh you know there
+really won't be the liquidity to trade
+
+ align:start position:0%
+really won't be the liquidity to trade
+ 
+
+ align:start position:0%
+really won't be the liquidity to trade
+that um but uh we can
+
+ align:start position:0%
+that um but uh we can
+ 
+
+ align:start position:0%
+that um but uh we can
+add basically simple linear constraints
+
+ align:start position:0%
+add basically simple linear constraints
+ 
+
+ align:start position:0%
+add basically simple linear constraints
+on the Holdings there can be turnover
+
+ align:start position:0%
+on the Holdings there can be turnover
+ 
+
+ align:start position:0%
+on the Holdings there can be turnover
+constraints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we're
+
+ align:start position:0%
+if we're
+ 
+
+ align:start position:0%
+if we're
+considering um changing our or basically
+
+ align:start position:0%
+considering um changing our or basically
+ 
+
+ align:start position:0%
+considering um changing our or basically
+adjusting our portfolio uh from one
+
+ align:start position:0%
+adjusting our portfolio uh from one
+ 
+
+ align:start position:0%
+adjusting our portfolio uh from one
+period to the next uh we may not or
+
+ align:start position:0%
+period to the next uh we may not or
+ 
+
+ align:start position:0%
+period to the next uh we may not or
+there are limits in terms of how much we
+
+ align:start position:0%
+there are limits in terms of how much we
+ 
+
+ align:start position:0%
+there are limits in terms of how much we
+can actually trade of the different
+
+ align:start position:0%
+can actually trade of the different
+ 
+
+ align:start position:0%
+can actually trade of the different
+assets um there can be a benchmark
+
+ align:start position:0%
+assets um there can be a benchmark
+ 
+
+ align:start position:0%
+assets um there can be a benchmark
+exposure constraints um suppose we want
+
+ align:start position:0%
+exposure constraints um suppose we want
+ 
+
+ align:start position:0%
+exposure constraints um suppose we want
+to invest in a portfolio that's very
+
+ align:start position:0%
+to invest in a portfolio that's very
+ 
+
+ align:start position:0%
+to invest in a portfolio that's very
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+like um but basically a market index say
+
+ align:start position:0%
+like um but basically a market index say
+ 
+
+ align:start position:0%
+like um but basically a market index say
+the S&P
+
+ align:start position:0%
+the S&P
+ 
+
+ align:start position:0%
+the S&P
+500 um but we want to try and do better
+
+ align:start position:0%
+500 um but we want to try and do better
+ 
+
+ align:start position:0%
+500 um but we want to try and do better
+than the S&P 500 but um but at the but
+
+ align:start position:0%
+than the S&P 500 but um but at the but
+ 
+
+ align:start position:0%
+than the S&P 500 but um but at the but
+we don't but we want to protect
+
+ align:start position:0%
+we don't but we want to protect
+ 
+
+ align:start position:0%
+we don't but we want to protect
+ourselves from uh basically not being
+
+ align:start position:0%
+ourselves from uh basically not being
+ 
+
+ align:start position:0%
+ourselves from uh basically not being
+very close to the Benchmark if our bets
+
+ align:start position:0%
+very close to the Benchmark if our bets
+ 
+
+ align:start position:0%
+very close to the Benchmark if our bets
+basically on allocation are wrong then
+
+ align:start position:0%
+basically on allocation are wrong then
+ 
+
+ align:start position:0%
+basically on allocation are wrong then
+uh one can basically attempt one can
+
+ align:start position:0%
+uh one can basically attempt one can
+ 
+
+ align:start position:0%
+uh one can basically attempt one can
+control how different from the Benchmark
+
+ align:start position:0%
+control how different from the Benchmark
+ 
+
+ align:start position:0%
+control how different from the Benchmark
+allocation we are and and limit that uh
+
+ align:start position:0%
+allocation we are and and limit that uh
+ 
+
+ align:start position:0%
+allocation we are and and limit that uh
+that departure so we can uh basically
+
+ align:start position:0%
+that departure so we can uh basically
+ 
+
+ align:start position:0%
+that departure so we can uh basically
+limit how far from The Benchmark weights
+
+ align:start position:0%
+limit how far from The Benchmark weights
+ 
+
+ align:start position:0%
+limit how far from The Benchmark weights
+we want our portfolio to be and and and
+
+ align:start position:0%
+we want our portfolio to be and and and
+ 
+
+ align:start position:0%
+we want our portfolio to be and and and
+this is useful basically for considering
+
+ align:start position:0%
+this is useful basically for considering
+ 
+
+ align:start position:0%
+this is useful basically for considering
+strategies that uh do as well or better
+
+ align:start position:0%
+strategies that uh do as well or better
+ 
+
+ align:start position:0%
+strategies that uh do as well or better
+than particular Benchmark
+
+ align:start position:0%
+than particular Benchmark
+ 
+
+ align:start position:0%
+than particular Benchmark
+indices um related to this our tracking
+
+ align:start position:0%
+indices um related to this our tracking
+ 
+
+ align:start position:0%
+indices um related to this our tracking
+error
+
+ align:start position:0%
+error
+ 
+
+ align:start position:0%
+error
+constraints
+
+ align:start position:0%
+constraints
+ 
+
+ align:start position:0%
+constraints
+um you know in addition to to um
+
+ align:start position:0%
+um you know in addition to to um
+ 
+
+ align:start position:0%
+um you know in addition to to um
+basically not
+
+ align:start position:0%
+basically not
+ 
+
+ align:start position:0%
+basically not
+having allocation weights that depart
+
+ align:start position:0%
+having allocation weights that depart
+ 
+
+ align:start position:0%
+having allocation weights that depart
+much from The Benchmark weights uh we
+
+ align:start position:0%
+much from The Benchmark weights uh we
+ 
+
+ align:start position:0%
+much from The Benchmark weights uh we
+can consider how much variation is there
+
+ align:start position:0%
+can consider how much variation is there
+ 
+
+ align:start position:0%
+can consider how much variation is there
+in our
+
+ align:start position:0%
+in our
+ 
+
+ align:start position:0%
+in our
+portfolio uh compared with an underlying
+
+ align:start position:0%
+portfolio uh compared with an underlying
+ 
+
+ align:start position:0%
+portfolio uh compared with an underlying
+uh Benchmark and we can consider the
+
+ align:start position:0%
+uh Benchmark and we can consider the
+ 
+
+ align:start position:0%
+uh Benchmark and we can consider the
+tracking error between our portfolio p
+
+ align:start position:0%
+tracking error between our portfolio p
+ 
+
+ align:start position:0%
+tracking error between our portfolio p
+and the underlying Benchmark and measure
+
+ align:start position:0%
+and the underlying Benchmark and measure
+ 
+
+ align:start position:0%
+and the underlying Benchmark and measure
+that tracking error in terms of the
+
+ align:start position:0%
+that tracking error in terms of the
+ 
+
+ align:start position:0%
+that tracking error in terms of the
+variability of that difference and want
+
+ align:start position:0%
+variability of that difference and want
+ 
+
+ align:start position:0%
+variability of that difference and want
+to control that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are also risk factor constraints
+
+ align:start position:0%
+there are also risk factor constraints
+ 
+
+ align:start position:0%
+there are also risk factor constraints
+and in and in equity markets there are
+
+ align:start position:0%
+and in and in equity markets there are
+ 
+
+ align:start position:0%
+and in and in equity markets there are
+many different factors that uh affect uh
+
+ align:start position:0%
+many different factors that uh affect uh
+ 
+
+ align:start position:0%
+many different factors that uh affect uh
+returns um and uh these factors can be
+
+ align:start position:0%
+returns um and uh these factors can be
+ 
+
+ align:start position:0%
+returns um and uh these factors can be
+identified
+
+ align:start position:0%
+identified
+ 
+
+ align:start position:0%
+identified
+empirically uh and controlled for by
+
+ align:start position:0%
+empirically uh and controlled for by
+ 
+
+ align:start position:0%
+empirically uh and controlled for by
+basically limiting the exposure to
+
+ align:start position:0%
+basically limiting the exposure to
+ 
+
+ align:start position:0%
+basically limiting the exposure to
+different factors in in the portfolio I
+
+ align:start position:0%
+different factors in in the portfolio I
+ 
+
+ align:start position:0%
+different factors in in the portfolio I
+we'll see this in our uh uh next lecture
+
+ align:start position:0%
+we'll see this in our uh uh next lecture
+ 
+
+ align:start position:0%
+we'll see this in our uh uh next lecture
+some but uh basically if they're
+
+ align:start position:0%
+some but uh basically if they're
+ 
+
+ align:start position:0%
+some but uh basically if they're
+underlying factors F which
+
+ align:start position:0%
+underlying factors F which
+ 
+
+ align:start position:0%
+underlying factors F which
+uh basically a return on asset I can be
+
+ align:start position:0%
+uh basically a return on asset I can be
+ 
+
+ align:start position:0%
+uh basically a return on asset I can be
+explained by sort of an idios
+
+ align:start position:0%
+explained by sort of an idios
+ 
+
+ align:start position:0%
+explained by sort of an idios
+idiosyncratic Alpha for that asset
+
+ align:start position:0%
+idiosyncratic Alpha for that asset
+ 
+
+ align:start position:0%
+idiosyncratic Alpha for that asset
+plus certain correlations with Market
+
+ align:start position:0%
+plus certain correlations with Market
+ 
+
+ align:start position:0%
+plus certain correlations with Market
+factors F and and then a residual uh
+
+ align:start position:0%
+factors F and and then a residual uh
+ 
+
+ align:start position:0%
+factors F and and then a residual uh
+Innovation Epsilon um and
+
+ align:start position:0%
+Innovation Epsilon um and
+ 
+
+ align:start position:0%
+Innovation Epsilon um and
+so the Returns on these assets can uh be
+
+ align:start position:0%
+so the Returns on these assets can uh be
+ 
+
+ align:start position:0%
+so the Returns on these assets can uh be
+explained perhaps 50% by underlying
+
+ align:start position:0%
+explained perhaps 50% by underlying
+ 
+
+ align:start position:0%
+explained perhaps 50% by underlying
+Market
+
+ align:start position:0%
+Market
+ 
+
+ align:start position:0%
+Market
+forces and um given by the underlying
+
+ align:start position:0%
+forces and um given by the underlying
+ 
+
+ align:start position:0%
+forces and um given by the underlying
+factors fjt which are uh constant across
+
+ align:start position:0%
+factors fjt which are uh constant across
+ 
+
+ align:start position:0%
+factors fjt which are uh constant across
+ey so these are affecting all the stocks
+
+ align:start position:0%
+ey so these are affecting all the stocks
+ 
+
+ align:start position:0%
+ey so these are affecting all the stocks
+with different coefficients beta
+
+ align:start position:0%
+with different coefficients beta
+ 
+
+ align:start position:0%
+with different coefficients beta
+ik and uh in a portfolio
+
+ align:start position:0%
+ik and uh in a portfolio
+ 
+
+ align:start position:0%
+ik and uh in a portfolio
+we may want to limit the exposure to a
+
+ align:start position:0%
+we may want to limit the exposure to a
+ 
+
+ align:start position:0%
+we may want to limit the exposure to a
+given factor and with many strategies
+
+ align:start position:0%
+given factor and with many strategies
+ 
+
+ align:start position:0%
+given factor and with many strategies
+you actually want to neutralize the
+
+ align:start position:0%
+you actually want to neutralize the
+ 
+
+ align:start position:0%
+you actually want to neutralize the
+portfolio to those Market risk factors
+
+ align:start position:0%
+portfolio to those Market risk factors
+ 
+
+ align:start position:0%
+portfolio to those Market risk factors
+so we can actually constrain our weights
+
+ align:start position:0%
+so we can actually constrain our weights
+ 
+
+ align:start position:0%
+so we can actually constrain our weights
+to have zero exposure across these
+
+ align:start position:0%
+to have zero exposure across these
+ 
+
+ align:start position:0%
+to have zero exposure across these
+different uh Market
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+factors U there are other other
+
+ align:start position:0%
+factors U there are other other
+ 
+
+ align:start position:0%
+factors U there are other other
+constraints minimum transaction size
+
+ align:start position:0%
+constraints minimum transaction size
+ 
+
+ align:start position:0%
+constraints minimum transaction size
+um you know It generally is the case
+
+ align:start position:0%
+um you know It generally is the case
+ 
+
+ align:start position:0%
+um you know It generally is the case
+that uh know trades and equities are in
+
+ align:start position:0%
+that uh know trades and equities are in
+ 
+
+ align:start position:0%
+that uh know trades and equities are in
+in a 100 share units although that's
+
+ align:start position:0%
+in a 100 share units although that's
+ 
+
+ align:start position:0%
+in a 100 share units although that's
+changing um there can be minimum uh
+
+ align:start position:0%
+changing um there can be minimum uh
+ 
+
+ align:start position:0%
+changing um there can be minimum uh
+holding sizes and uh there's also
+
+ align:start position:0%
+holding sizes and uh there's also
+ 
+
+ align:start position:0%
+holding sizes and uh there's also
+integer constraints that that can be
+
+ align:start position:0%
+integer constraints that that can be
+ 
+
+ align:start position:0%
+integer constraints that that can be
+applied
+
+ align:start position:0%
+applied
+ 
+
+ align:start position:0%
+applied
+um if you're trading
+
+ align:start position:0%
+um if you're trading
+ 
+
+ align:start position:0%
+um if you're trading
+uh assets that have sort of large values
+
+ align:start position:0%
+uh assets that have sort of large values
+ 
+
+ align:start position:0%
+uh assets that have sort of large values
+then uh these integer constraints
+
+ align:start position:0%
+then uh these integer constraints
+ 
+
+ align:start position:0%
+then uh these integer constraints
+actually come into play I if you're
+
+ align:start position:0%
+actually come into play I if you're
+ 
+
+ align:start position:0%
+actually come into play I if you're
+trading Google stock and how much is
+
+ align:start position:0%
+trading Google stock and how much is
+ 
+
+ align:start position:0%
+trading Google stock and how much is
+Google stock worth now
+
+ align:start position:0%
+Google stock worth now
+ 
+
+ align:start position:0%
+Google stock worth now
+800 something like that so you know
+
+ align:start position:0%
+800 something like that so you know
+ 
+
+ align:start position:0%
+800 something like that so you know
+compare that with h Ford you know which
+
+ align:start position:0%
+compare that with h Ford you know which
+ 
+
+ align:start position:0%
+compare that with h Ford you know which
+is like $50 or I don't know but you know
+
+ align:start position:0%
+is like $50 or I don't know but you know
+ 
+
+ align:start position:0%
+is like $50 or I don't know but you know
+the orders of magnitude different so so
+
+ align:start position:0%
+the orders of magnitude different so so
+ 
+
+ align:start position:0%
+the orders of magnitude different so so
+integer constraints can come into play
+
+ align:start position:0%
+integer constraints can come into play
+ 
+
+ align:start position:0%
+integer constraints can come into play
+um if you're dealing in very large size
+
+ align:start position:0%
+um if you're dealing in very large size
+ 
+
+ align:start position:0%
+um if you're dealing in very large size
+then these things don't really have much
+
+ align:start position:0%
+then these things don't really have much
+ 
+
+ align:start position:0%
+then these things don't really have much
+of an impact but uh uh they can uh with
+
+ align:start position:0%
+of an impact but uh uh they can uh with
+ 
+
+ align:start position:0%
+of an impact but uh uh they can uh with
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+portfolios now all of these different
+
+ align:start position:0%
+portfolios now all of these different
+ 
+
+ align:start position:0%
+portfolios now all of these different
+constraints can be expressed as linear
+
+ align:start position:0%
+constraints can be expressed as linear
+ 
+
+ align:start position:0%
+constraints can be expressed as linear
+and quadratic constraints on the weights
+
+ align:start position:0%
+and quadratic constraints on the weights
+ 
+
+ align:start position:0%
+and quadratic constraints on the weights
+and uh so so the setup for uh the
+
+ align:start position:0%
+and uh so so the setup for uh the
+ 
+
+ align:start position:0%
+and uh so so the setup for uh the
+portfolio optimization problem can be
+
+ align:start position:0%
+portfolio optimization problem can be
+ 
+
+ align:start position:0%
+portfolio optimization problem can be
+the same as before except we add in
+
+ align:start position:0%
+the same as before except we add in
+ 
+
+ align:start position:0%
+the same as before except we add in
+these additional constraints so we add
+
+ align:start position:0%
+these additional constraints so we add
+ 
+
+ align:start position:0%
+these additional constraints so we add
+basically add in additional lrange
+
+ align:start position:0%
+basically add in additional lrange
+ 
+
+ align:start position:0%
+basically add in additional lrange
+multipliers times these particular
+
+ align:start position:0%
+multipliers times these particular
+ 
+
+ align:start position:0%
+multipliers times these particular
+constraints with their linear quadratic
+
+ align:start position:0%
+constraints with their linear quadratic
+ 
+
+ align:start position:0%
+constraints with their linear quadratic
+and we can implement the portfolio
+
+ align:start position:0%
+and we can implement the portfolio
+ 
+
+ align:start position:0%
+and we can implement the portfolio
+optimization problem that
+
+ align:start position:0%
+optimization problem that
+ 
+
+ align:start position:0%
+optimization problem that
+way let me uh turn to an
+
+ align:start position:0%
+way let me uh turn to an
+ 
+
+ align:start position:0%
+way let me uh turn to an
+example let's go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see is
+
+ align:start position:0%
+see is
+ 
+
+ align:start position:0%
+see is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay let me magnify this
+
+ align:start position:0%
+okay let me magnify this
+ 
+
+ align:start position:0%
+okay let me magnify this
+here okay I want
+
+ align:start position:0%
+here okay I want
+ 
+
+ align:start position:0%
+here okay I want
+to go through an
+
+ align:start position:0%
+to go through an
+ 
+
+ align:start position:0%
+to go through an
+example of uh
+
+ align:start position:0%
+example of uh
+ 
+
+ align:start position:0%
+example of uh
+uh I'll use the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mouse okay I want to
+
+ align:start position:0%
+mouse okay I want to
+ 
+
+ align:start position:0%
+mouse okay I want to
+consider um us sector exchange traded
+
+ align:start position:0%
+consider um us sector exchange traded
+ 
+
+ align:start position:0%
+consider um us sector exchange traded
+funds between 2009 and last week um the
+
+ align:start position:0%
+funds between 2009 and last week um the
+ 
+
+ align:start position:0%
+funds between 2009 and last week um the
+uh basically there are uh you exchange
+
+ align:start position:0%
+uh basically there are uh you exchange
+ 
+
+ align:start position:0%
+uh basically there are uh you exchange
+trade FS allow you to
+
+ align:start position:0%
+trade FS allow you to
+ 
+
+ align:start position:0%
+trade FS allow you to
+invest in equity markets with sort of
+
+ align:start position:0%
+invest in equity markets with sort of
+ 
+
+ align:start position:0%
+invest in equity markets with sort of
+single assets that represent different
+
+ align:start position:0%
+single assets that represent different
+ 
+
+ align:start position:0%
+single assets that represent different
+sectors um the ones that are considered
+
+ align:start position:0%
+sectors um the ones that are considered
+ 
+
+ align:start position:0%
+sectors um the ones that are considered
+here are basically spider traded funds
+
+ align:start position:0%
+here are basically spider traded funds
+ 
+
+ align:start position:0%
+here are basically spider traded funds
+uh which invest in the different major
+
+ align:start position:0%
+uh which invest in the different major
+ 
+
+ align:start position:0%
+uh which invest in the different major
+industrial sectors of the US market uh
+
+ align:start position:0%
+industrial sectors of the US market uh
+ 
+
+ align:start position:0%
+industrial sectors of the US market uh
+ranging from materials Health Care
+
+ align:start position:0%
+ranging from materials Health Care
+ 
+
+ align:start position:0%
+ranging from materials Health Care
+Consumer Staples down to technology and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+utilities here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a graph of the cumulative returns of
+
+ align:start position:0%
+is a graph of the cumulative returns of
+ 
+
+ align:start position:0%
+is a graph of the cumulative returns of
+these nine different exchange traded
+
+ align:start position:0%
+these nine different exchange traded
+ 
+
+ align:start position:0%
+these nine different exchange traded
+funds and uh over the period uh from
+
+ align:start position:0%
+funds and uh over the period uh from
+ 
+
+ align:start position:0%
+funds and uh over the period uh from
+2009 up through uh last week and what
+
+ align:start position:0%
+2009 up through uh last week and what
+ 
+
+ align:start position:0%
+2009 up through uh last week and what
+one can see is uh basically they perform
+
+ align:start position:0%
+one can see is uh basically they perform
+ 
+
+ align:start position:0%
+one can see is uh basically they perform
+differently um and what I'd like to do
+
+ align:start position:0%
+differently um and what I'd like to do
+ 
+
+ align:start position:0%
+differently um and what I'd like to do
+is just examine of what would have
+
+ align:start position:0%
+is just examine of what would have
+ 
+
+ align:start position:0%
+is just examine of what would have
+been an optimal allocation across these
+
+ align:start position:0%
+been an optimal allocation across these
+ 
+
+ align:start position:0%
+been an optimal allocation across these
+exchange traded funds over this period
+
+ align:start position:0%
+exchange traded funds over this period
+ 
+
+ align:start position:0%
+exchange traded funds over this period
+so basically looking back at the data
+
+ align:start position:0%
+so basically looking back at the data
+ 
+
+ align:start position:0%
+so basically looking back at the data
+and seeing how our
+
+ align:start position:0%
+and seeing how our
+ 
+
+ align:start position:0%
+and seeing how our
+portfolio
+
+ align:start position:0%
+portfolio
+ 
+
+ align:start position:0%
+portfolio
+uh analysis uh tools um would would
+
+ align:start position:0%
+uh analysis uh tools um would would
+ 
+
+ align:start position:0%
+uh analysis uh tools um would would
+result in particular application
+
+ align:start position:0%
+result in particular application
+ 
+
+ align:start position:0%
+result in particular application
+allocations so um so we can look at the
+
+ align:start position:0%
+allocations so um so we can look at the
+ 
+
+ align:start position:0%
+allocations so um so we can look at the
+risk versus return annualized of these
+
+ align:start position:0%
+risk versus return annualized of these
+ 
+
+ align:start position:0%
+risk versus return annualized of these
+let's see
+
+ align:start position:0%
+let's see
+ 
+
+ align:start position:0%
+let's see
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is I don't know if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's I guess that's good enough anyway
+
+ align:start position:0%
+that's I guess that's good enough anyway
+ 
+
+ align:start position:0%
+that's I guess that's good enough anyway
+what you can see is you know basically
+
+ align:start position:0%
+what you can see is you know basically
+ 
+
+ align:start position:0%
+what you can see is you know basically
+with volatility range between 0 and 30
+
+ align:start position:0%
+with volatility range between 0 and 30
+ 
+
+ align:start position:0%
+with volatility range between 0 and 30
+OD annual ex return between 0 and
+
+ align:start position:0%
+OD annual ex return between 0 and
+ 
+
+ align:start position:0%
+OD annual ex return between 0 and
+25 um we have the different sectors in
+
+ align:start position:0%
+25 um we have the different sectors in
+ 
+
+ align:start position:0%
+25 um we have the different sectors in
+this uh in this plot so this is our
+
+ align:start position:0%
+this uh in this plot so this is our
+ 
+
+ align:start position:0%
+this uh in this plot so this is our
+feasible set
+
+ align:start position:0%
+feasible set
+ 
+
+ align:start position:0%
+feasible set
+of uh or this is the plot of return
+
+ align:start position:0%
+of uh or this is the plot of return
+ 
+
+ align:start position:0%
+of uh or this is the plot of return
+versus volatility for these nine
+
+ align:start position:0%
+versus volatility for these nine
+ 
+
+ align:start position:0%
+versus volatility for these nine
+exchange traded funds um this happens to
+
+ align:start position:0%
+exchange traded funds um this happens to
+ 
+
+ align:start position:0%
+exchange traded funds um this happens to
+be utilities there's financials over
+
+ align:start position:0%
+be utilities there's financials over
+ 
+
+ align:start position:0%
+be utilities there's financials over
+there here's Consumer Staples the very
+
+ align:start position:0%
+there here's Consumer Staples the very
+ 
+
+ align:start position:0%
+there here's Consumer Staples the very
+top is consumer uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discretionary let's see I applied a uh
+
+ align:start position:0%
+discretionary let's see I applied a uh
+ 
+
+ align:start position:0%
+discretionary let's see I applied a uh
+mean variance optimization to this
+
+ align:start position:0%
+mean variance optimization to this
+ 
+
+ align:start position:0%
+mean variance optimization to this
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh assuming that There's a
+
+ align:start position:0%
+uh assuming that There's a
+ 
+
+ align:start position:0%
+uh assuming that There's a
+constraint of
+
+ align:start position:0%
+constraint of
+ 
+
+ align:start position:0%
+constraint of
+30% of the capital per asset so we don't
+
+ align:start position:0%
+30% of the capital per asset so we don't
+ 
+
+ align:start position:0%
+30% of the capital per asset so we don't
+want to invest more than 30% of the
+
+ align:start position:0%
+want to invest more than 30% of the
+ 
+
+ align:start position:0%
+want to invest more than 30% of the
+capital in any single exchange traded
+
+ align:start position:0%
+capital in any single exchange traded
+ 
+
+ align:start position:0%
+capital in any single exchange traded
+fund and this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh graph here shows how as we vary our
+
+ align:start position:0%
+uh graph here shows how as we vary our
+ 
+
+ align:start position:0%
+uh graph here shows how as we vary our
+Target return from sort of the minimum
+
+ align:start position:0%
+Target return from sort of the minimum
+ 
+
+ align:start position:0%
+Target return from sort of the minimum
+value up to the maximum value for being
+
+ align:start position:0%
+value up to the maximum value for being
+ 
+
+ align:start position:0%
+value up to the maximum value for being
+fully
+
+ align:start position:0%
+fully
+ 
+
+ align:start position:0%
+fully
+invested how much of the capital we're
+
+ align:start position:0%
+invested how much of the capital we're
+ 
+
+ align:start position:0%
+invested how much of the capital we're
+going to invest in the different sector
+
+ align:start position:0%
+going to invest in the different sector
+ 
+
+ align:start position:0%
+going to invest in the different sector
+funds so what you can see is this yellow
+
+ align:start position:0%
+funds so what you can see is this yellow
+ 
+
+ align:start position:0%
+funds so what you can see is this yellow
+one which is consumer staples is coming
+
+ align:start position:0%
+one which is consumer staples is coming
+ 
+
+ align:start position:0%
+one which is consumer staples is coming
+in with a really high weight and the
+
+ align:start position:0%
+in with a really high weight and the
+ 
+
+ align:start position:0%
+in with a really high weight and the
+green is
+
+ align:start position:0%
+green is
+ 
+
+ align:start position:0%
+green is
+energy um let's see I think it's energy
+
+ align:start position:0%
+energy um let's see I think it's energy
+ 
+
+ align:start position:0%
+energy um let's see I think it's energy
+that is is the next one then in Orange
+
+ align:start position:0%
+that is is the next one then in Orange
+ 
+
+ align:start position:0%
+that is is the next one then in Orange
+is is
+
+ align:start position:0%
+is is
+ 
+
+ align:start position:0%
+is is
+health and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's what's important to see is that
+
+ align:start position:0%
+what's what's important to see is that
+ 
+
+ align:start position:0%
+what's what's important to see is that
+when when we're looking sort of at the
+
+ align:start position:0%
+when when we're looking sort of at the
+ 
+
+ align:start position:0%
+when when we're looking sort of at the
+lower range of the returns basically
+
+ align:start position:0%
+lower range of the returns basically
+ 
+
+ align:start position:0%
+lower range of the returns basically
+expecting returns above the risk-free
+
+ align:start position:0%
+expecting returns above the risk-free
+ 
+
+ align:start position:0%
+expecting returns above the risk-free
+rate that's very low
+
+ align:start position:0%
+rate that's very low
+ 
+
+ align:start position:0%
+rate that's very low
+then the relative proportion invested in
+
+ align:start position:0%
+then the relative proportion invested in
+ 
+
+ align:start position:0%
+then the relative proportion invested in
+the different assets is the same
+
+ align:start position:0%
+the different assets is the same
+ 
+
+ align:start position:0%
+the different assets is the same
+basically these allocations are slowly
+
+ align:start position:0%
+basically these allocations are slowly
+ 
+
+ align:start position:0%
+basically these allocations are slowly
+scaling up just linearly and that
+
+ align:start position:0%
+scaling up just linearly and that
+ 
+
+ align:start position:0%
+scaling up just linearly and that
+corresponds to basically investing in
+
+ align:start position:0%
+corresponds to basically investing in
+ 
+
+ align:start position:0%
+corresponds to basically investing in
+the optimal port folio without
+
+ align:start position:0%
+the optimal port folio without
+ 
+
+ align:start position:0%
+the optimal port folio without
+constraints with a fixed
+
+ align:start position:0%
+constraints with a fixed
+ 
+
+ align:start position:0%
+constraints with a fixed
+value but once we hit the 30% level then
+
+ align:start position:0%
+value but once we hit the 30% level then
+ 
+
+ align:start position:0%
+value but once we hit the 30% level then
+that constraint starts to be active and
+
+ align:start position:0%
+that constraint starts to be active and
+ 
+
+ align:start position:0%
+that constraint starts to be active and
+we can't invest any more in that so we
+
+ align:start position:0%
+we can't invest any more in that so we
+ 
+
+ align:start position:0%
+we can't invest any more in that so we
+have to add more to other Securities and
+
+ align:start position:0%
+have to add more to other Securities and
+ 
+
+ align:start position:0%
+have to add more to other Securities and
+so basically more is given to uh the uh
+
+ align:start position:0%
+so basically more is given to uh the uh
+ 
+
+ align:start position:0%
+so basically more is given to uh the uh
+I think it's consumer
+
+ align:start position:0%
+I think it's consumer
+ 
+
+ align:start position:0%
+I think it's consumer
+discretionary and and the other now this
+
+ align:start position:0%
+discretionary and and the other now this
+ 
+
+ align:start position:0%
+discretionary and and the other now this
+graph actually here's another graph of
+
+ align:start position:0%
+graph actually here's another graph of
+ 
+
+ align:start position:0%
+graph actually here's another graph of
+the same data just stacking the
+
+ align:start position:0%
+the same data just stacking the
+ 
+
+ align:start position:0%
+the same data just stacking the
+allocation
+
+ align:start position:0%
+allocation
+ 
+
+ align:start position:0%
+allocation
+the allocation so we consider ranging
+
+ align:start position:0%
+the allocation so we consider ranging
+ 
+
+ align:start position:0%
+the allocation so we consider ranging
+from basically how are we investing all
+
+ align:start position:0%
+from basically how are we investing all
+ 
+
+ align:start position:0%
+from basically how are we investing all
+of our Capital the this dark red is how
+
+ align:start position:0%
+of our Capital the this dark red is how
+ 
+
+ align:start position:0%
+of our Capital the this dark red is how
+much money we invest in
+
+ align:start position:0%
+much money we invest in
+ 
+
+ align:start position:0%
+much money we invest in
+cash and then these colored lines
+
+ align:start position:0%
+cash and then these colored lines
+ 
+
+ align:start position:0%
+cash and then these colored lines
+indicate by their vertical length how
+
+ align:start position:0%
+indicate by their vertical length how
+ 
+
+ align:start position:0%
+indicate by their vertical length how
+much we're investing in the different
+
+ align:start position:0%
+much we're investing in the different
+ 
+
+ align:start position:0%
+much we're investing in the different
+exchange traded
+
+ align:start position:0%
+exchange traded
+ 
+
+ align:start position:0%
+exchange traded
+funds so so basically
+
+ align:start position:0%
+funds so so basically
+ 
+
+ align:start position:0%
+funds so so basically
+as the constraints get hit we basically
+
+ align:start position:0%
+as the constraints get hit we basically
+ 
+
+ align:start position:0%
+as the constraints get hit we basically
+the portfolio sort of change in terms of
+
+ align:start position:0%
+the portfolio sort of change in terms of
+ 
+
+ align:start position:0%
+the portfolio sort of change in terms of
+their overall structure
+
+ align:start position:0%
+their overall structure
+ 
+
+ align:start position:0%
+their overall structure
+and what can
+
+ align:start position:0%
+and what can
+ 
+
+ align:start position:0%
+and what can
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+is um actually as we're trying to
+
+ align:start position:0%
+is um actually as we're trying to
+ 
+
+ align:start position:0%
+is um actually as we're trying to
+achieve more and more
+
+ align:start position:0%
+achieve more and more
+ 
+
+ align:start position:0%
+achieve more and more
+return well there may not be assets that
+
+ align:start position:0%
+return well there may not be assets that
+ 
+
+ align:start position:0%
+return well there may not be assets that
+provide that additional return or there
+
+ align:start position:0%
+provide that additional return or there
+ 
+
+ align:start position:0%
+provide that additional return or there
+may be a very few assets that provide
+
+ align:start position:0%
+may be a very few assets that provide
+ 
+
+ align:start position:0%
+may be a very few assets that provide
+that return and so that um in this case
+
+ align:start position:0%
+that return and so that um in this case
+ 
+
+ align:start position:0%
+that return and so that um in this case
+uh technology stocks are coming in as
+
+ align:start position:0%
+uh technology stocks are coming in as
+ 
+
+ align:start position:0%
+uh technology stocks are coming in as
+we're trying to get really high levels
+
+ align:start position:0%
+we're trying to get really high levels
+ 
+
+ align:start position:0%
+we're trying to get really high levels
+of return in our optimal
+
+ align:start position:0%
+of return in our optimal
+ 
+
+ align:start position:0%
+of return in our optimal
+portfolios and um so if we really want
+
+ align:start position:0%
+portfolios and um so if we really want
+ 
+
+ align:start position:0%
+portfolios and um so if we really want
+that higher return that's going to come
+
+ align:start position:0%
+that higher return that's going to come
+ 
+
+ align:start position:0%
+that higher return that's going to come
+at higher
+
+ align:start position:0%
+at higher
+ 
+
+ align:start position:0%
+at higher
+risk uh and we actually are deallocating
+
+ align:start position:0%
+risk uh and we actually are deallocating
+ 
+
+ align:start position:0%
+risk uh and we actually are deallocating
+some from uh the consumer staples and uh
+
+ align:start position:0%
+some from uh the consumer staples and uh
+ 
+
+ align:start position:0%
+some from uh the consumer staples and uh
+the consumer discretionary at that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point okay this um okay here's a graph
+
+ align:start position:0%
+point okay this um okay here's a graph
+ 
+
+ align:start position:0%
+point okay this um okay here's a graph
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+uh efficient Frontier
+
+ align:start position:0%
+uh efficient Frontier
+ 
+
+ align:start position:0%
+uh efficient Frontier
+as estimated with the with the data um
+
+ align:start position:0%
+as estimated with the with the data um
+ 
+
+ align:start position:0%
+as estimated with the with the data um
+and what you can see is that uh
+
+ align:start position:0%
+and what you can see is that uh
+ 
+
+ align:start position:0%
+and what you can see is that uh
+basically these portfolios optimal
+
+ align:start position:0%
+basically these portfolios optimal
+ 
+
+ align:start position:0%
+basically these portfolios optimal
+portfolios yield improvements over each
+
+ align:start position:0%
+portfolios yield improvements over each
+ 
+
+ align:start position:0%
+portfolios yield improvements over each
+of the individual exchange traded funds
+
+ align:start position:0%
+of the individual exchange traded funds
+ 
+
+ align:start position:0%
+of the individual exchange traded funds
+in terms of having higher return with
+
+ align:start position:0%
+in terms of having higher return with
+ 
+
+ align:start position:0%
+in terms of having higher return with
+lower
+
+ align:start position:0%
+lower
+ 
+
+ align:start position:0%
+lower
+risk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and as see if we consider just a
+
+ align:start position:0%
+um and as see if we consider just a
+ 
+
+ align:start position:0%
+um and as see if we consider just a
+Target return of 10% okay there's the
+
+ align:start position:0%
+Target return of 10% okay there's the
+ 
+
+ align:start position:0%
+Target return of 10% okay there's the
+optimal portfolio I've graft here sort
+
+ align:start position:0%
+optimal portfolio I've graft here sort
+ 
+
+ align:start position:0%
+optimal portfolio I've graft here sort
+of in solid blue what the uh optimal
+
+ align:start position:0%
+of in solid blue what the uh optimal
+ 
+
+ align:start position:0%
+of in solid blue what the uh optimal
+portfolio with a 10% uh volatility is
+
+ align:start position:0%
+portfolio with a 10% uh volatility is
+ 
+
+ align:start position:0%
+portfolio with a 10% uh volatility is
+that's the solid Blue Line there so this
+
+ align:start position:0%
+that's the solid Blue Line there so this
+ 
+
+ align:start position:0%
+that's the solid Blue Line there so this
+is the these are the results
+
+ align:start position:0%
+is the these are the results
+ 
+
+ align:start position:0%
+is the these are the results
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+uh this 30% Capital constraint now how
+
+ align:start position:0%
+uh this 30% Capital constraint now how
+ 
+
+ align:start position:0%
+uh this 30% Capital constraint now how
+is this problem going to change if we uh
+
+ align:start position:0%
+is this problem going to change if we uh
+ 
+
+ align:start position:0%
+is this problem going to change if we uh
+reduce the capital constraint from 30%
+
+ align:start position:0%
+reduce the capital constraint from 30%
+ 
+
+ align:start position:0%
+reduce the capital constraint from 30%
+per asset to 15%
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who can comment on what what will
+
+ align:start position:0%
+who can comment on what what will
+ 
+
+ align:start position:0%
+who can comment on what what will
+change Dan I'm a little confused why
+
+ align:start position:0%
+change Dan I'm a little confused why
+ 
+
+ align:start position:0%
+change Dan I'm a little confused why
+wouldn't you put a constraint on the
+
+ align:start position:0%
+wouldn't you put a constraint on the
+ 
+
+ align:start position:0%
+wouldn't you put a constraint on the
+risk free asset could you do that as
+
+ align:start position:0%
+risk free asset could you do that as
+ 
+
+ align:start position:0%
+risk free asset could you do that as
+well or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+well the risk- free asset has no
+
+ align:start position:0%
+well the risk- free asset has no
+ 
+
+ align:start position:0%
+well the risk- free asset has no
+risk and so
+
+ align:start position:0%
+risk and so
+ 
+
+ align:start position:0%
+risk and so
+um putting a constraint well you could
+
+ align:start position:0%
+um putting a constraint well you could
+ 
+
+ align:start position:0%
+um putting a constraint well you could
+put a constraint on it in terms of it
+
+ align:start position:0%
+put a constraint on it in terms of it
+ 
+
+ align:start position:0%
+put a constraint on it in terms of it
+not going negative and it not being
+
+ align:start position:0%
+not going negative and it not being
+ 
+
+ align:start position:0%
+not going negative and it not being
+greater than one so in fact that is a
+
+ align:start position:0%
+greater than one so in fact that is a
+ 
+
+ align:start position:0%
+greater than one so in fact that is a
+constraint those are constraints that
+
+ align:start position:0%
+constraint those are constraints that
+ 
+
+ align:start position:0%
+constraint those are constraints that
+are imposed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here but um but and I guess in some well
+
+ align:start position:0%
+here but um but and I guess in some well
+ 
+
+ align:start position:0%
+here but um but and I guess in some well
+there are like uh I guess endowments say
+
+ align:start position:0%
+there are like uh I guess endowments say
+ 
+
+ align:start position:0%
+there are like uh I guess endowments say
+that have investment policies that say
+
+ align:start position:0%
+that have investment policies that say
+ 
+
+ align:start position:0%
+that have investment policies that say
+that they want a certain fraction of
+
+ align:start position:0%
+that they want a certain fraction of
+ 
+
+ align:start position:0%
+that they want a certain fraction of
+their assets invested in Risky assets
+
+ align:start position:0%
+their assets invested in Risky assets
+ 
+
+ align:start position:0%
+their assets invested in Risky assets
+and not in cash and so that you know is
+
+ align:start position:0%
+and not in cash and so that you know is
+ 
+
+ align:start position:0%
+and not in cash and so that you know is
+is uh is a realistic constraint in
+
+ align:start position:0%
+is uh is a realistic constraint in
+ 
+
+ align:start position:0%
+is uh is a realistic constraint in
+certain circumstances and this is just
+
+ align:start position:0%
+certain circumstances and this is just
+ 
+
+ align:start position:0%
+certain circumstances and this is just
+highlighting you
+
+ align:start position:0%
+highlighting you
+ 
+
+ align:start position:0%
+highlighting you
+know the how the allocations vary across
+
+ align:start position:0%
+know the how the allocations vary across
+ 
+
+ align:start position:0%
+know the how the allocations vary across
+the risky assets if if we only have very
+
+ align:start position:0%
+the risky assets if if we only have very
+ 
+
+ align:start position:0%
+the risky assets if if we only have very
+simple constraints on on the cash
+
+ align:start position:0%
+simple constraints on on the cash
+ 
+
+ align:start position:0%
+simple constraints on on the cash
+investment
+
+ align:start position:0%
+investment
+ 
+
+ align:start position:0%
+investment
+well the question I want to focus on is
+
+ align:start position:0%
+well the question I want to focus on is
+ 
+
+ align:start position:0%
+well the question I want to focus on is
+what happens if we make these the
+
+ align:start position:0%
+what happens if we make these the
+ 
+
+ align:start position:0%
+what happens if we make these the
+maximum allocation constraint more
+
+ align:start position:0%
+maximum allocation constraint more
+ 
+
+ align:start position:0%
+maximum allocation constraint more
+severe so it's 15% instead of 30 then
+
+ align:start position:0%
+severe so it's 15% instead of 30 then
+ 
+
+ align:start position:0%
+severe so it's 15% instead of 30 then
+what's going to happen
+
+ align:start position:0%
+what's going to happen
+ 
+
+ align:start position:0%
+what's going to happen
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the these these Capital constraints are
+
+ align:start position:0%
+the these these Capital constraints are
+ 
+
+ align:start position:0%
+the these these Capital constraints are
+going going to start hitting sooner so
+
+ align:start position:0%
+going going to start hitting sooner so
+ 
+
+ align:start position:0%
+going going to start hitting sooner so
+we have to allocate to
+
+ align:start position:0%
+we have to allocate to
+ 
+
+ align:start position:0%
+we have to allocate to
+more uh to the other exchange traded
+
+ align:start position:0%
+more uh to the other exchange traded
+ 
+
+ align:start position:0%
+more uh to the other exchange traded
+funds so let me show you how that works
+
+ align:start position:0%
+funds so let me show you how that works
+ 
+
+ align:start position:0%
+funds so let me show you how that works
+out with the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay let me just close that and
+
+ align:start position:0%
+right okay let me just close that and
+ 
+
+ align:start position:0%
+right okay let me just close that and
+then me go here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this shows let see with a 50%
+
+ align:start position:0%
+okay this shows let see with a 50%
+ 
+
+ align:start position:0%
+okay this shows let see with a 50%
+allocation how how the allocations
+
+ align:start position:0%
+allocation how how the allocations
+ 
+
+ align:start position:0%
+allocation how how the allocations
+vary and uh I'll I'll be posting this on
+
+ align:start position:0%
+vary and uh I'll I'll be posting this on
+ 
+
+ align:start position:0%
+vary and uh I'll I'll be posting this on
+the course website um but uh turns out
+
+ align:start position:0%
+the course website um but uh turns out
+ 
+
+ align:start position:0%
+the course website um but uh turns out
+the efficient Frontier is actually lower
+
+ align:start position:0%
+the efficient Frontier is actually lower
+ 
+
+ align:start position:0%
+the efficient Frontier is actually lower
+basically we you know for higher returns
+
+ align:start position:0%
+basically we you know for higher returns
+ 
+
+ align:start position:0%
+basically we you know for higher returns
+we actually can't get those higher
+
+ align:start position:0%
+we actually can't get those higher
+ 
+
+ align:start position:0%
+we actually can't get those higher
+returns from by giving the getting the
+
+ align:start position:0%
+returns from by giving the getting the
+ 
+
+ align:start position:0%
+returns from by giving the getting the
+biggest bang for the buck we don't want
+
+ align:start position:0%
+biggest bang for the buck we don't want
+ 
+
+ align:start position:0%
+biggest bang for the buck we don't want
+to allocate too much to those higher
+
+ align:start position:0%
+to allocate too much to those higher
+ 
+
+ align:start position:0%
+to allocate too much to those higher
+return higher risk Securities and so the
+
+ align:start position:0%
+return higher risk Securities and so the
+ 
+
+ align:start position:0%
+return higher risk Securities and so the
+uh optimal uh the efficient Frontier as
+
+ align:start position:0%
+uh optimal uh the efficient Frontier as
+ 
+
+ align:start position:0%
+uh optimal uh the efficient Frontier as
+estimated uh basically slopes down um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now just uh okay as an ex okay with with
+
+ align:start position:0%
+now just uh okay as an ex okay with with
+ 
+
+ align:start position:0%
+now just uh okay as an ex okay with with
+this particular example of these uh
+
+ align:start position:0%
+this particular example of these uh
+ 
+
+ align:start position:0%
+this particular example of these uh
+exchange traded funds and how You'
+
+ align:start position:0%
+exchange traded funds and how You'
+ 
+
+ align:start position:0%
+exchange traded funds and how You'
+allocate across those um you know this
+
+ align:start position:0%
+allocate across those um you know this
+ 
+
+ align:start position:0%
+allocate across those um you know this
+provides some insight into portfolio IO
+
+ align:start position:0%
+provides some insight into portfolio IO
+ 
+
+ align:start position:0%
+provides some insight into portfolio IO
+optimization it's not really a realistic
+
+ align:start position:0%
+optimization it's not really a realistic
+ 
+
+ align:start position:0%
+optimization it's not really a realistic
+setting because we're looking over the
+
+ align:start position:0%
+setting because we're looking over the
+ 
+
+ align:start position:0%
+setting because we're looking over the
+past and using the actual sample
+
+ align:start position:0%
+past and using the actual sample
+ 
+
+ align:start position:0%
+past and using the actual sample
+performance to Define these
+
+ align:start position:0%
+performance to Define these
+ 
+
+ align:start position:0%
+performance to Define these
+portfolios um let me just highlight a an
+
+ align:start position:0%
+portfolios um let me just highlight a an
+ 
+
+ align:start position:0%
+portfolios um let me just highlight a an
+example of applying these kinds of
+
+ align:start position:0%
+example of applying these kinds of
+ 
+
+ align:start position:0%
+example of applying these kinds of
+methods with
+
+ align:start position:0%
+methods with
+ 
+
+ align:start position:0%
+methods with
+um let's see is it
+
+ align:start position:0%
+um let's see is it
+ 
+
+ align:start position:0%
+um let's see is it
+here yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see is that the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph yeah okay okay suppose we
+
+ align:start position:0%
+graph yeah okay okay suppose we
+ 
+
+ align:start position:0%
+graph yeah okay okay suppose we
+uh consider not investing in exchange
+
+ align:start position:0%
+uh consider not investing in exchange
+ 
+
+ align:start position:0%
+uh consider not investing in exchange
+traded funds but we are a a hedge fund
+
+ align:start position:0%
+traded funds but we are a a hedge fund
+ 
+
+ align:start position:0%
+traded funds but we are a a hedge fund
+and we have uh sector pricing models
+
+ align:start position:0%
+and we have uh sector pricing models
+ 
+
+ align:start position:0%
+and we have uh sector pricing models
+across all all these different sectors
+
+ align:start position:0%
+across all all these different sectors
+ 
+
+ align:start position:0%
+across all all these different sectors
+and what we can do is consider in going
+
+ align:start position:0%
+and what we can do is consider in going
+ 
+
+ align:start position:0%
+and what we can do is consider in going
+long short in these
+
+ align:start position:0%
+long short in these
+ 
+
+ align:start position:0%
+long short in these
+sectors and in fact we consider sort of
+
+ align:start position:0%
+sectors and in fact we consider sort of
+ 
+
+ align:start position:0%
+sectors and in fact we consider sort of
+a sort of a a market neutral strategy
+
+ align:start position:0%
+a sort of a a market neutral strategy
+ 
+
+ align:start position:0%
+a sort of a a market neutral strategy
+sector by sector and consider
+
+ align:start position:0%
+sector by sector and consider
+ 
+
+ align:start position:0%
+sector by sector and consider
+investing uh in in the sector by sector
+
+ align:start position:0%
+investing uh in in the sector by sector
+ 
+
+ align:start position:0%
+investing uh in in the sector by sector
+in these different sector-based models
+
+ align:start position:0%
+in these different sector-based models
+ 
+
+ align:start position:0%
+in these different sector-based models
+okay here's a graph of different
+
+ align:start position:0%
+okay here's a graph of different
+ 
+
+ align:start position:0%
+okay here's a graph of different
+multiactor pricing models for trading
+
+ align:start position:0%
+multiactor pricing models for trading
+ 
+
+ align:start position:0%
+multiactor pricing models for trading
+Market neutral programs within each of
+
+ align:start position:0%
+Market neutral programs within each of
+ 
+
+ align:start position:0%
+Market neutral programs within each of
+uh nine industrial sectors the same ones
+
+ align:start position:0%
+uh nine industrial sectors the same ones
+ 
+
+ align:start position:0%
+uh nine industrial sectors the same ones
+corresponding to the exchange traded
+
+ align:start position:0%
+corresponding to the exchange traded
+ 
+
+ align:start position:0%
+corresponding to the exchange traded
+funds and uh okay because the these
+
+ align:start position:0%
+funds and uh okay because the these
+ 
+
+ align:start position:0%
+funds and uh okay because the these
+strategies are Market neutral the sort
+
+ align:start position:0%
+strategies are Market neutral the sort
+ 
+
+ align:start position:0%
+strategies are Market neutral the sort
+of total returns over this is a 5-year
+
+ align:start position:0%
+of total returns over this is a 5-year
+ 
+
+ align:start position:0%
+of total returns over this is a 5-year
+period um are rather
+
+ align:start position:0%
+period um are rather
+ 
+
+ align:start position:0%
+period um are rather
+modest namely uh you know sort of 60%
+
+ align:start position:0%
+modest namely uh you know sort of 60%
+ 
+
+ align:start position:0%
+modest namely uh you know sort of 60%
+for some of the models 20% for other
+
+ align:start position:0%
+for some of the models 20% for other
+ 
+
+ align:start position:0%
+for some of the models 20% for other
+models
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's particularly uh relevant with
+
+ align:start position:0%
+what's particularly uh relevant with
+ 
+
+ align:start position:0%
+what's particularly uh relevant with
+these models though is that they tend to
+
+ align:start position:0%
+these models though is that they tend to
+ 
+
+ align:start position:0%
+these models though is that they tend to
+be less correlated and um the
+
+ align:start position:0%
+be less correlated and um the
+ 
+
+ align:start position:0%
+be less correlated and um the
+diversification benefits can be rather
+
+ align:start position:0%
+diversification benefits can be rather
+ 
+
+ align:start position:0%
+diversification benefits can be rather
+dramatic and so here is a graph of the
+
+ align:start position:0%
+dramatic and so here is a graph of the
+ 
+
+ align:start position:0%
+dramatic and so here is a graph of the
+optimal allocations across these
+
+ align:start position:0%
+optimal allocations across these
+ 
+
+ align:start position:0%
+optimal allocations across these
+different sector uh Market neutral
+
+ align:start position:0%
+different sector uh Market neutral
+ 
+
+ align:start position:0%
+different sector uh Market neutral
+models and we can see that this red
+
+ align:start position:0%
+models and we can see that this red
+ 
+
+ align:start position:0%
+models and we can see that this red
+model is getting a lot lot of weight
+
+ align:start position:0%
+model is getting a lot lot of weight
+ 
+
+ align:start position:0%
+model is getting a lot lot of weight
+that actually is uh the utility sector
+
+ align:start position:0%
+that actually is uh the utility sector
+ 
+
+ align:start position:0%
+that actually is uh the utility sector
+and then these other models are uh
+
+ align:start position:0%
+and then these other models are uh
+ 
+
+ align:start position:0%
+and then these other models are uh
+Industrials and
+
+ align:start position:0%
+Industrials and
+ 
+
+ align:start position:0%
+Industrials and
+uh let's see Industrials and
+
+ align:start position:0%
+uh let's see Industrials and
+ 
+
+ align:start position:0%
+uh let's see Industrials and
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+um and so if we
+
+ align:start position:0%
+um and so if we
+ 
+
+ align:start position:0%
+um and so if we
+consider investing in these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can actually
+
+ align:start position:0%
+we can actually
+ 
+
+ align:start position:0%
+we can actually
+achieve uh with a Target volatility of
+
+ align:start position:0%
+achieve uh with a Target volatility of
+ 
+
+ align:start position:0%
+achieve uh with a Target volatility of
+10% we're can achieve this solid blue
+
+ align:start position:0%
+10% we're can achieve this solid blue
+ 
+
+ align:start position:0%
+10% we're can achieve this solid blue
+line as as the portfolio strategy and
+
+ align:start position:0%
+line as as the portfolio strategy and
+ 
+
+ align:start position:0%
+line as as the portfolio strategy and
+one can see how by combining these
+
+ align:start position:0%
+one can see how by combining these
+ 
+
+ align:start position:0%
+one can see how by combining these
+assets together these assets are
+
+ align:start position:0%
+assets together these assets are
+ 
+
+ align:start position:0%
+assets together these assets are
+different uh uh Market neutral trading
+
+ align:start position:0%
+different uh uh Market neutral trading
+ 
+
+ align:start position:0%
+different uh uh Market neutral trading
+models um we actually get uh quite a bit
+
+ align:start position:0%
+models um we actually get uh quite a bit
+ 
+
+ align:start position:0%
+models um we actually get uh quite a bit
+of benefit from the portfolio
+
+ align:start position:0%
+of benefit from the portfolio
+ 
+
+ align:start position:0%
+of benefit from the portfolio
+optimization and the greater benefit and
+
+ align:start position:0%
+optimization and the greater benefit and
+ 
+
+ align:start position:0%
+optimization and the greater benefit and
+the portfolio optimization is because
+
+ align:start position:0%
+the portfolio optimization is because
+ 
+
+ align:start position:0%
+the portfolio optimization is because
+these uh strategies tend to be uh have
+
+ align:start position:0%
+these uh strategies tend to be uh have
+ 
+
+ align:start position:0%
+these uh strategies tend to be uh have
+much lower correlations with each other
+
+ align:start position:0%
+much lower correlations with each other
+ 
+
+ align:start position:0%
+much lower correlations with each other
+and uh it's adding value let's go back
+
+ align:start position:0%
+and uh it's adding value let's go back
+ 
+
+ align:start position:0%
+and uh it's adding value let's go back
+now finish up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with how do we how do we go back here
+
+ align:start position:0%
+with how do we how do we go back here
+ 
+
+ align:start position:0%
+with how do we how do we go back here
+where's my Red
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dot okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay just to finish up the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discussion um with these methods um it's
+
+ align:start position:0%
+discussion um with these methods um it's
+ 
+
+ align:start position:0%
+discussion um with these methods um it's
+important to highlight that you know
+
+ align:start position:0%
+important to highlight that you know
+ 
+
+ align:start position:0%
+important to highlight that you know
+what we've been using we're estimated
+
+ align:start position:0%
+what we've been using we're estimated
+ 
+
+ align:start position:0%
+what we've been using we're estimated
+returns estimated volatilities and
+
+ align:start position:0%
+returns estimated volatilities and
+ 
+
+ align:start position:0%
+returns estimated volatilities and
+correlations and these estimates can
+
+ align:start position:0%
+correlations and these estimates can
+ 
+
+ align:start position:0%
+correlations and these estimates can
+have a huge impact on on the results um
+
+ align:start position:0%
+have a huge impact on on the results um
+ 
+
+ align:start position:0%
+have a huge impact on on the results um
+there's basically choices of estimation
+
+ align:start position:0%
+there's basically choices of estimation
+ 
+
+ align:start position:0%
+there's basically choices of estimation
+period there's estimation error uh
+
+ align:start position:0%
+period there's estimation error uh
+ 
+
+ align:start position:0%
+period there's estimation error uh
+different techniques can uh modulate
+
+ align:start position:0%
+different techniques can uh modulate
+ 
+
+ align:start position:0%
+different techniques can uh modulate
+these these issues uh exponential moving
+
+ align:start position:0%
+these these issues uh exponential moving
+ 
+
+ align:start position:0%
+these these issues uh exponential moving
+average are often applied having Dynamic
+
+ align:start position:0%
+average are often applied having Dynamic
+ 
+
+ align:start position:0%
+average are often applied having Dynamic
+Factor models is is used um basically
+
+ align:start position:0%
+Factor models is is used um basically
+ 
+
+ align:start position:0%
+Factor models is is used um basically
+rather than using sample estimates of
+
+ align:start position:0%
+rather than using sample estimates of
+ 
+
+ align:start position:0%
+rather than using sample estimates of
+the variance co-variance Matrix using
+
+ align:start position:0%
+the variance co-variance Matrix using
+ 
+
+ align:start position:0%
+the variance co-variance Matrix using
+Factor models to estimate the variance
+
+ align:start position:0%
+Factor models to estimate the variance
+ 
+
+ align:start position:0%
+Factor models to estimate the variance
+co-variance Matrix um results in uh more
+
+ align:start position:0%
+co-variance Matrix um results in uh more
+ 
+
+ align:start position:0%
+co-variance Matrix um results in uh more
+precise
+
+ align:start position:0%
+precise
+ 
+
+ align:start position:0%
+precise
+uh inputs to to the
+
+ align:start position:0%
+uh inputs to to the
+ 
+
+ align:start position:0%
+uh inputs to to the
+optimization um and finally just with uh
+
+ align:start position:0%
+optimization um and finally just with uh
+ 
+
+ align:start position:0%
+optimization um and finally just with uh
+different risk measures we've been
+
+ align:start position:0%
+different risk measures we've been
+ 
+
+ align:start position:0%
+different risk measures we've been
+focusing on portfolio volatility and
+
+ align:start position:0%
+focusing on portfolio volatility and
+ 
+
+ align:start position:0%
+focusing on portfolio volatility and
+minimizing that the methodologies can be
+
+ align:start position:0%
+minimizing that the methodologies can be
+ 
+
+ align:start position:0%
+minimizing that the methodologies can be
+extended to have different measures of
+
+ align:start position:0%
+extended to have different measures of
+ 
+
+ align:start position:0%
+extended to have different measures of
+risk mean absolute deviation for example
+
+ align:start position:0%
+risk mean absolute deviation for example
+ 
+
+ align:start position:0%
+risk mean absolute deviation for example
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+semivariance um in terms of you know the
+
+ align:start position:0%
+semivariance um in terms of you know the
+ 
+
+ align:start position:0%
+semivariance um in terms of you know the
+motivation for squared volatility
+
+ align:start position:0%
+motivation for squared volatility
+ 
+
+ align:start position:0%
+motivation for squared volatility
+minimizing that you'll recall that in
+
+ align:start position:0%
+minimizing that you'll recall that in
+ 
+
+ align:start position:0%
+minimizing that you'll recall that in
+likelihood analysis of gaussing
+
+ align:start position:0%
+likelihood analysis of gaussing
+ 
+
+ align:start position:0%
+likelihood analysis of gaussing
+distributions the sort of square
+
+ align:start position:0%
+distributions the sort of square
+ 
+
+ align:start position:0%
+distributions the sort of square
+deviations from the means are
+
+ align:start position:0%
+deviations from the means are
+ 
+
+ align:start position:0%
+deviations from the means are
+characterizing variability well if we
+
+ align:start position:0%
+characterizing variability well if we
+ 
+
+ align:start position:0%
+characterizing variability well if we
+focus on mean absolute deviation then
+
+ align:start position:0%
+focus on mean absolute deviation then
+ 
+
+ align:start position:0%
+focus on mean absolute deviation then
+probability distributions that where the
+
+ align:start position:0%
+probability distributions that where the
+ 
+
+ align:start position:0%
+probability distributions that where the
+distributions relate to the absolute
+
+ align:start position:0%
+distributions relate to the absolute
+ 
+
+ align:start position:0%
+distributions relate to the absolute
+deviation from the mean characterizing
+
+ align:start position:0%
+deviation from the mean characterizing
+ 
+
+ align:start position:0%
+deviation from the mean characterizing
+the distribution might be appropriate
+
+ align:start position:0%
+the distribution might be appropriate
+ 
+
+ align:start position:0%
+the distribution might be appropriate
+and indeed uh distributions with heavier
+
+ align:start position:0%
+and indeed uh distributions with heavier
+ 
+
+ align:start position:0%
+and indeed uh distributions with heavier
+Tails like exponential
+
+ align:start position:0%
+Tails like exponential
+ 
+
+ align:start position:0%
+Tails like exponential
+distributions uh basically are
+
+ align:start position:0%
+distributions uh basically are
+ 
+
+ align:start position:0%
+distributions uh basically are
+appropriate when we consider mean
+
+ align:start position:0%
+appropriate when we consider mean
+ 
+
+ align:start position:0%
+appropriate when we consider mean
+absolute deviation so um some alternate
+
+ align:start position:0%
+absolute deviation so um some alternate
+ 
+
+ align:start position:0%
+absolute deviation so um some alternate
+risk measures are appropriate when the
+
+ align:start position:0%
+risk measures are appropriate when the
+ 
+
+ align:start position:0%
+risk measures are appropriate when the
+volatility measure itself isn't um
+
+ align:start position:0%
+volatility measure itself isn't um
+ 
+
+ align:start position:0%
+volatility measure itself isn't um
+necessarily appropriate because of the
+
+ align:start position:0%
+necessarily appropriate because of the
+ 
+
+ align:start position:0%
+necessarily appropriate because of the
+the distributional assumptions uh
+
+ align:start position:0%
+the distributional assumptions uh
+ 
+
+ align:start position:0%
+the distributional assumptions uh
+semivariance was introduced actually by
+
+ align:start position:0%
+semivariance was introduced actually by
+ 
+
+ align:start position:0%
+semivariance was introduced actually by
+marwitz uh where you're interested in
+
+ align:start position:0%
+marwitz uh where you're interested in
+ 
+
+ align:start position:0%
+marwitz uh where you're interested in
+controlling the downside risk as opposed
+
+ align:start position:0%
+controlling the downside risk as opposed
+ 
+
+ align:start position:0%
+controlling the downside risk as opposed
+to the upside risk um and uh there's
+
+ align:start position:0%
+to the upside risk um and uh there's
+ 
+
+ align:start position:0%
+to the upside risk um and uh there's
+value at risk meas measures which are
+
+ align:start position:0%
+value at risk meas measures which are
+ 
+
+ align:start position:0%
+value at risk meas measures which are
+now completely standard in uh portfolio
+
+ align:start position:0%
+now completely standard in uh portfolio
+ 
+
+ align:start position:0%
+now completely standard in uh portfolio
+management and uh management of uh risky
+
+ align:start position:0%
+management and uh management of uh risky
+ 
+
+ align:start position:0%
+management and uh management of uh risky
+assets um
+
+ align:start position:0%
+assets um
+ 
+
+ align:start position:0%
+assets um
+where one is actually well this was
+
+ align:start position:0%
+where one is actually well this was
+ 
+
+ align:start position:0%
+where one is actually well this was
+introduced by Ken Abbott in one of the
+
+ align:start position:0%
+introduced by Ken Abbott in one of the
+ 
+
+ align:start position:0%
+introduced by Ken Abbott in one of the
+first few lectures uh value at risk is
+
+ align:start position:0%
+first few lectures uh value at risk is
+ 
+
+ align:start position:0%
+first few lectures uh value at risk is
+basically a very simple idea of
+
+ align:start position:0%
+basically a very simple idea of
+ 
+
+ align:start position:0%
+basically a very simple idea of
+characterizing what outcome is uh sort
+
+ align:start position:0%
+characterizing what outcome is uh sort
+ 
+
+ align:start position:0%
+characterizing what outcome is uh sort
+of the threshold of extreme at say the
+
+ align:start position:0%
+of the threshold of extreme at say the
+ 
+
+ align:start position:0%
+of the threshold of extreme at say the
+5% level or the 1% level and to
+
+ align:start position:0%
+5% level or the 1% level and to
+ 
+
+ align:start position:0%
+5% level or the 1% level and to
+basically keep a monitor of that the
+
+ align:start position:0%
+basically keep a monitor of that the
+ 
+
+ align:start position:0%
+basically keep a monitor of that the
+value at risk so if we had a risk that
+
+ align:start position:0%
+value at risk so if we had a risk that
+ 
+
+ align:start position:0%
+value at risk so if we had a risk that
+was you know basically in the worst 5%
+
+ align:start position:0%
+was you know basically in the worst 5%
+ 
+
+ align:start position:0%
+was you know basically in the worst 5%
+or 1% of the time what is that level
+
+ align:start position:0%
+or 1% of the time what is that level
+ 
+
+ align:start position:0%
+or 1% of the time what is that level
+that's the value at risk um that as a
+
+ align:start position:0%
+that's the value at risk um that as a
+ 
+
+ align:start position:0%
+that's the value at risk um that as a
+nice risk measure is um simple to Define
+
+ align:start position:0%
+nice risk measure is um simple to Define
+ 
+
+ align:start position:0%
+nice risk measure is um simple to Define
+but and and reasonably simple to to
+
+ align:start position:0%
+but and and reasonably simple to to
+ 
+
+ align:start position:0%
+but and and reasonably simple to to
+estimate but um it doesn't characterize
+
+ align:start position:0%
+estimate but um it doesn't characterize
+ 
+
+ align:start position:0%
+estimate but um it doesn't characterize
+sort of what the potential exposure is
+
+ align:start position:0%
+sort of what the potential exposure is
+ 
+
+ align:start position:0%
+sort of what the potential exposure is
+if you exceed that and there are
+
+ align:start position:0%
+if you exceed that and there are
+ 
+
+ align:start position:0%
+if you exceed that and there are
+extensions of that the conditional value
+
+ align:start position:0%
+extensions of that the conditional value
+ 
+
+ align:start position:0%
+extensions of that the conditional value
+at risk which is looking at the expected
+
+ align:start position:0%
+at risk which is looking at the expected
+ 
+
+ align:start position:0%
+at risk which is looking at the expected
+loss given that you exceed the value
+
+ align:start position:0%
+loss given that you exceed the value
+ 
+
+ align:start position:0%
+loss given that you exceed the value
+risk threshold and uh this method is now
+
+ align:start position:0%
+risk threshold and uh this method is now
+ 
+
+ align:start position:0%
+risk threshold and uh this method is now
+uh I I think it's being going to be
+
+ align:start position:0%
+uh I I think it's being going to be
+ 
+
+ align:start position:0%
+uh I I think it's being going to be
+incorporated into uh regulatory uh uh
+
+ align:start position:0%
+incorporated into uh regulatory uh uh
+ 
+
+ align:start position:0%
+incorporated into uh regulatory uh uh
+requirements for for banks in terms of
+
+ align:start position:0%
+requirements for for banks in terms of
+ 
+
+ align:start position:0%
+requirements for for banks in terms of
+how they measure risk right now I
+
+ align:start position:0%
+how they measure risk right now I
+ 
+
+ align:start position:0%
+how they measure risk right now I
+believe it's almost all value at risk uh
+
+ align:start position:0%
+believe it's almost all value at risk uh
+ 
+
+ align:start position:0%
+believe it's almost all value at risk uh
+extensions but this uh conditional value
+
+ align:start position:0%
+extensions but this uh conditional value
+ 
+
+ align:start position:0%
+extensions but this uh conditional value
+risk is is definitely going to be uh
+
+ align:start position:0%
+risk is is definitely going to be uh
+ 
+
+ align:start position:0%
+risk is is definitely going to be uh
+applied um and in the discussion of
+
+ align:start position:0%
+applied um and in the discussion of
+ 
+
+ align:start position:0%
+applied um and in the discussion of
+different risk measures there's
+
+ align:start position:0%
+different risk measures there's
+ 
+
+ align:start position:0%
+different risk measures there's
+literature talking about what are
+
+ align:start position:0%
+literature talking about what are
+ 
+
+ align:start position:0%
+literature talking about what are
+appropriate risk measures and how how do
+
+ align:start position:0%
+appropriate risk measures and how how do
+ 
+
+ align:start position:0%
+appropriate risk measures and how how do
+we Define those
+
+ align:start position:0%
+we Define those
+ 
+
+ align:start position:0%
+we Define those
+well you know it really depends on what
+
+ align:start position:0%
+well you know it really depends on what
+ 
+
+ align:start position:0%
+well you know it really depends on what
+your assets are and if you your assets
+
+ align:start position:0%
+your assets are and if you your assets
+ 
+
+ align:start position:0%
+your assets are and if you your assets
+are simply
+
+ align:start position:0%
+are simply
+ 
+
+ align:start position:0%
+are simply
+simple investments in stocks or bonds
+
+ align:start position:0%
+simple investments in stocks or bonds
+ 
+
+ align:start position:0%
+simple investments in stocks or bonds
+sort of cash assets or you know uh cash
+
+ align:start position:0%
+sort of cash assets or you know uh cash
+ 
+
+ align:start position:0%
+sort of cash assets or you know uh cash
+cash instruments then uh value at risk
+
+ align:start position:0%
+cash instruments then uh value at risk
+ 
+
+ align:start position:0%
+cash instruments then uh value at risk
+is quite reasonable if you're investing
+
+ align:start position:0%
+is quite reasonable if you're investing
+ 
+
+ align:start position:0%
+is quite reasonable if you're investing
+in derivatives which have nonlinear
+
+ align:start position:0%
+in derivatives which have nonlinear
+ 
+
+ align:start position:0%
+in derivatives which have nonlinear
+payoffs then things get complicated and
+
+ align:start position:0%
+payoffs then things get complicated and
+ 
+
+ align:start position:0%
+payoffs then things get complicated and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um things basically need to be handled
+
+ align:start position:0%
+um things basically need to be handled
+ 
+
+ align:start position:0%
+um things basically need to be handled
+on on a case-by Case basis there but uh
+
+ align:start position:0%
+on on a case-by Case basis there but uh
+ 
+
+ align:start position:0%
+on on a case-by Case basis there but uh
+but if you're interested in in Risk
+
+ align:start position:0%
+but if you're interested in in Risk
+ 
+
+ align:start position:0%
+but if you're interested in in Risk
+analysis there's a whole discussion on
+
+ align:start position:0%
+analysis there's a whole discussion on
+ 
+
+ align:start position:0%
+analysis there's a whole discussion on
+coherent risk measures that uh uh you
+
+ align:start position:0%
+coherent risk measures that uh uh you
+ 
+
+ align:start position:0%
+coherent risk measures that uh uh you
+you can you can look into that's quite
+
+ align:start position:0%
+you can you can look into that's quite
+ 
+
+ align:start position:0%
+you can you can look into that's quite
+interesting all right let's stop there
+
+ align:start position:0%
+interesting all right let's stop there
+ 
+
+ align:start position:0%
+interesting all right let's stop there
+thank you
\ No newline at end of file
diff --git a/z6kTOFSZZmQ.txt b/z6kTOFSZZmQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0e3917f0fbeb1eec5712364984ada5fab863f9b2
--- /dev/null
+++ b/z6kTOFSZZmQ.txt
@@ -0,0 +1,163 @@
+align:start position:0%
+ 
+my name is Michel de Graaff and I've
+
+ align:start position:0%
+my name is Michel de Graaff and I've
+ 
+
+ align:start position:0%
+my name is Michel de Graaff and I've
+been teaching in linguistics at MIT for
+
+ align:start position:0%
+been teaching in linguistics at MIT for
+ 
+
+ align:start position:0%
+been teaching in linguistics at MIT for
+the past 21 years already and I'm the
+
+ align:start position:0%
+the past 21 years already and I'm the
+ 
+
+ align:start position:0%
+the past 21 years already and I'm the
+faculty instructor for the course on
+
+ align:start position:0%
+faculty instructor for the course on
+ 
+
+ align:start position:0%
+faculty instructor for the course on
+clear languages and Caribbean identities
+
+ align:start position:0%
+clear languages and Caribbean identities
+ 
+
+ align:start position:0%
+clear languages and Caribbean identities
+so my research is about trying to
+
+ align:start position:0%
+so my research is about trying to
+ 
+
+ align:start position:0%
+so my research is about trying to
+understand how languages evolve over
+
+ align:start position:0%
+understand how languages evolve over
+ 
+
+ align:start position:0%
+understand how languages evolve over
+time and what happens when new languages
+
+ align:start position:0%
+time and what happens when new languages
+ 
+
+ align:start position:0%
+time and what happens when new languages
+are created say for example the
+
+ align:start position:0%
+are created say for example the
+ 
+
+ align:start position:0%
+are created say for example the
+Caribbean in magnitude Haiti where
+
+ align:start position:0%
+Caribbean in magnitude Haiti where
+ 
+
+ align:start position:0%
+Caribbean in magnitude Haiti where
+Haitian Creole emerged in the seventeen
+
+ align:start position:0%
+Haitian Creole emerged in the seventeen
+ 
+
+ align:start position:0%
+Haitian Creole emerged in the seventeen
+eighteenth century so we try to
+
+ align:start position:0%
+eighteenth century so we try to
+ 
+
+ align:start position:0%
+eighteenth century so we try to
+understand the patterns of development
+
+ align:start position:0%
+understand the patterns of development
+ 
+
+ align:start position:0%
+understand the patterns of development
+of the things that we call Creole
+
+ align:start position:0%
+of the things that we call Creole
+ 
+
+ align:start position:0%
+of the things that we call Creole
+languages and in terms of the structure
+
+ align:start position:0%
+languages and in terms of the structure
+ 
+
+ align:start position:0%
+languages and in terms of the structure
+but also have an applied side to my work
+
+ align:start position:0%
+but also have an applied side to my work
+ 
+
+ align:start position:0%
+but also have an applied side to my work
+where I try to understand how best to
+
+ align:start position:0%
+where I try to understand how best to
+ 
+
+ align:start position:0%
+where I try to understand how best to
+use say Haitian Creole and other local
+
+ align:start position:0%
+use say Haitian Creole and other local
+ 
+
+ align:start position:0%
+use say Haitian Creole and other local
+languages in education and how that's
+
+ align:start position:0%
+languages in education and how that's
+ 
+
+ align:start position:0%
+languages in education and how that's
+crucial for development of countries
+
+ align:start position:0%
+crucial for development of countries
+ 
+
+ align:start position:0%
+crucial for development of countries
+like Haiti
\ No newline at end of file
diff --git a/zB9aY8tzd74.txt b/zB9aY8tzd74.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8191145680dd4790b20980f5fe3d88021f29fff5
--- /dev/null
+++ b/zB9aY8tzd74.txt
@@ -0,0 +1,3693 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+OCW.MIT.edu.
+
+PROFESSOR: OK.
+
+We are talking about jointly
+Gaussian random variables.
+
+One comment through all of this
+and through all of the
+
+notes is that you can add a
+mean to Gaussian random
+
+variables, or you
+can talk about
+
+zero-mean random variables.
+
+Here we're using random
+variables mostly
+
+to talk about noise.
+
+When we're talking about noise,
+you really should be
+
+talking about zero-mean random
+variables, because you can
+
+always take the mean out.
+
+And because of that, I don't
+like to state everything twice
+
+once for variables of processes
+without a mean, and
+
+once for variables of processes
+with a mean.
+
+And after looking at the notes,
+I think I've been a
+
+little inconsistent
+about that.
+
+I think the point is you can
+keep yourself straight by just
+
+saying the only thing
+important is the
+
+case without a mean.
+
+Putting the mean in is something
+unfortunately done
+
+by people who like complexity.
+
+And they have unfortunately
+got in the
+
+notation on their side.
+
+So anytime you want
+to talk about a
+
+zero-mean random variable.
+
+You have to say zero-mean
+random variable.
+
+And if you say random variable,
+it means it could
+
+have a mean or not
+have a mean.
+
+And of course the way the
+notation should be stated is
+
+you talk about random variables
+as things which
+
+don't have means.
+
+And then you can talk about
+random variables plus means as
+
+things which do have means,
+which would make life easier
+
+but unfortunately it's
+not that way.
+
+So anytime you see something
+and are wondering about
+
+whether I've been careful about
+the mean or not, the
+
+answer is I well might
+not have been.
+
+And two, it's not
+very important.
+
+So anyway.
+
+Here I'll be talking all
+about zero-mean things.
+
+A k-tuple of zero-mean random
+variables is said to be
+
+jointly Gaussian if you can
+express them in this way here.
+
+Namely as a linear combination
+of IID normal Gaussian again
+
+random variables.
+
+OK.
+
+In your homework, those of you
+who've done it already, have
+
+realized that just having two
+Gaussian random variables is
+
+not enough to make
+those two random
+
+variables be jointly Gaussian.
+
+They can be individually
+Gaussian
+
+but not jointly Gaussian.
+
+This is sort of important
+because when you start
+
+manipulating things as we will
+do when we're generating
+
+signals to send and things like
+this, you can very easily
+
+wind up with things which look
+Gaussian and are appropriately
+
+modeled as Gaussian, but which
+are not jointly Gaussian.
+
+Things which are jointly
+Gaussian are
+
+defined in this way.
+
+We will come up with
+a couple of other
+
+definitions of them later.
+
+But you've undoubtedly been
+taught that any old Gaussian
+
+random variables are
+jointly Gaussian.
+
+You've probably seen joint
+densities for them
+
+and things like this.
+
+Those joint densities only apply
+when you have jointly
+
+Gaussian random variables.
+
+And the fundamental definition
+is this.
+
+This fundamental definition
+makes sense, because the way
+
+that you generate these noise
+random variables is usually
+
+from some very large underlying
+set of very, very
+
+small random variables.
+
+And the Law of Large Numbers
+says that when you add up a
+
+very, very large number of
+small underlying random
+
+variables, you normalize the sum
+so it has some reasonable
+
+variance then that random
+variable is going to be
+
+appropriately modeled
+as being Gaussian.
+
+If you at the same time look
+at linear combinations of
+
+those things for the same
+reason, it's appropriate to
+
+model each of the random
+variables you're looking at as
+
+a linear combination of some
+underlying set of noise
+
+variables which is
+very, very large.
+
+Probably not Gaussian.
+
+But here when we're trying to
+do this, because of the
+
+central limit theorem, we just
+model these as normal Gaussian
+
+random variables
+to start with.
+
+So that's where that definition
+comes from.
+
+It's why when you're looking at
+noise processes in the real
+
+world, and trying to model them
+in a sensible way this
+
+jointly Gaussian is the
+thing you almost
+
+always come up with.
+
+OK.
+
+So one important point here, and
+the notes point this out.
+
+If each of these random
+variables Z sub i is
+
+independent of each of the
+others, and they have
+
+arbitrary variances, then
+because of this formula, the
+
+set of Z i's are going to
+be jointly Gaussian.
+
+Why is that?
+
+Well you simply make a matrix
+here A, which is diagonal.
+
+And the elements of this
+diagonal matrix are sigma 1
+
+squared, sigma 2 squared, sigma
+3 squared, and so forth.
+
+If you have a vector Z, which
+is then sigma 1 squared down
+
+to sigma k squared times a noise
+vector N1 to N sub k.
+
+What you wind up with is Z sub
+i is going to be equal to --
+
+I guess I don't want those
+squares in there.
+
+Sigma 1 up to sigma k --
+
+Z sub i is going to be equal to
+sigma i, N sub i; N sub i
+
+is a Gaussian random variable
+with variance one and
+
+therefore Z sub i as Gaussian
+random variable with variance
+
+sigma sub i squared.
+
+OK.
+
+So anyway, one special case of
+this formula is anytime that
+
+you want to deal with a set of
+independent Gaussian random
+
+variables with arbitrary
+variances, they are always
+
+going to be jointly Gaussian.
+
+Saying that they're
+uncorrelated is
+
+not enough for that.
+
+You really need the statement
+that they're independent of
+
+each other.
+
+OK.
+
+That's sort of where
+we were last time.
+
+When you look at this formula,
+you can look at it in terms of
+
+sample values.
+
+And if we look at a sample value
+what's happening is that
+
+the sample value of the random
+vector Z, namely little z, is
+
+going to be defined as some
+matrix A times this sample
+
+value for the normal
+vector N. OK.
+
+And what we want to look
+at is geometrically
+
+what happens there.
+
+Well this matrix a is going to
+map a unit vector, E sub i
+
+into the i'th column
+of A. Why is that?
+
+Well you look at A, which is
+whatever it is, A sub 1, 1,
+
+blah, blah, blah up
+to A sub k, k.
+
+And you look at multiplying it
+by a vector which is zero only
+
+in the i'th position.
+
+And what's this matrix
+multiplication going to do?
+
+It's going to simply pick
+out the i'th column
+
+of this matrix here.
+
+OK.
+
+So a is going to map e sub i
+into the i'th column of A. OK.
+
+So then the question is what is
+this matrix A going to do
+
+to some small cube
+in the n plane?
+
+OK.
+
+If you take a small cube in the
+n plane from 0 to delta
+
+along the n1 line is going to
+map into 0 to this point here,
+
+which is A e sub 1.
+
+This point here is going to
+map into A times e sub 2.
+
+This is just drawing for two
+dimensions of course.
+
+So in fact all the points in
+this cube are going to get map
+
+into this little
+rectangle here.
+
+OK.
+
+Namely, that's what a matrix
+times a vector is going to do.
+
+Anybody awake out there?
+
+You're all looking at me as
+if I'm totally insane.
+
+OK.
+
+Every everyone following this?
+
+OK.
+
+So perhaps this is
+just too trivial.
+
+I hope not.
+
+OK.
+
+So unit cubes get mapped
+into rectangles here.
+
+If I take a unit cube up here,
+it's going to get mapped into
+
+the same kind of unit
+rectangle here.
+
+If I visualize tiling this plane
+here with little tiny
+
+cubes, delta on a side, what's
+going to happen?
+
+Each of these little cubes
+is going to map into a
+
+parallelogram over here, and
+these parallelograms going to
+
+tile this space here.
+
+OK.
+
+Which means that each little
+cube here maps into one of
+
+these rectangles.
+
+Each rectangle here maps back
+into a little cube here.
+
+Which means that I'm
+looking at a very
+
+special case of a here.
+
+I'm looking at a case where
+a is non-singular.
+
+In other words, I can get the
+any point in this plane by
+
+starting with some point
+in this plane.
+
+Which means for any point here,
+I can go back here also.
+
+In other words, I can also write
+n is equal to A to the
+
+minus 1 times Z. And this
+matrix has to exist.
+
+OK.
+
+That's what you mean
+geometrically by a
+
+non-singular matrix.
+
+It means that all points in
+this plane get mapped into
+
+points in this plane.
+
+And get mapped into only one
+point in this plane, and get
+
+mapped into only one point
+in this plane.
+
+Where every point in this
+plane is the map
+
+of some point here.
+
+In other words you can go
+from here to there.
+
+You can also go back again.
+
+OK.
+
+The volume of a parallelepiped
+here, and this is in an
+
+arbitrary number of dimensions
+is going to be the determinant
+
+of A. And you all know how
+to find determinants.
+
+Namely you program a computer
+to do it, and the
+
+computer does it.
+
+I mean it used to be we had to
+do this by an enormous amount
+
+of calculation.
+
+And of course nobody
+does that anymore.
+
+OK.
+
+So we can find the volume of
+this parallelepiped, it's this
+
+determinant.
+
+And what does all
+of that mean?
+
+Well first let me ask
+you the question.
+
+What's going to happen if
+the determinant of a
+
+is equaled to zero?
+
+What does that mean
+geometrically?
+
+What does that mean here
+in terms of this
+
+two dimensional diagram?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: What?
+
+AUDIENCE: Projection
+onto a line.
+
+PROFESSOR: Yeah.
+
+This little cube here is simply
+going to get projected
+
+onto some line here.
+
+Like for example that.
+
+In other words it means that
+this matrix is not invertible
+
+for one thing, but it also means
+everything here gets
+
+mapped onto some lower
+dimensional
+
+sub-space here in general.
+
+OK.
+
+Now remember that for a minute,
+and we'll come back to
+
+that when we start talking about
+probability densities.
+
+OK because of the picture we
+were just looking at, the
+
+density of the random variables
+Z at A times N,
+
+namely the density of Z at this
+particular value here is
+
+just the density that we get
+corresponding to the density
+
+of some point here mapped
+over into here.
+
+And what's going to happen when
+we take a point here and
+
+map it over into here?
+
+If you have a certain amount
+of density here, which is
+
+probability per unit volume.
+
+Now when you map it into here,
+and the determinant is bigger
+
+than zero, what you're doing
+is mapping a little volume
+
+into a big volume.
+
+And if you're doing that over
+small enough region where the
+
+probability density is of such
+essentially fixed, what's
+
+going to happen to the
+probability density over here?
+
+It's going to get scaled down,
+and it's going to get scaled
+
+down precisely by that
+determinant.
+
+OK.
+
+So what this is saying is the
+probability density of the
+
+random variable z, which is
+linear combination of these
+
+normal random variables, is in
+fact the probability density
+
+of this normal vector N, and we
+know what that probability
+
+density is, divided by this
+determinant of a.
+
+In fact this is a general
+formula for any old
+
+probability density at all.
+
+You can start out with anything
+which you call a
+
+random vector N and you can
+derive the probability density
+
+of any linear combination
+of those elements in
+
+precisely this way.
+
+So long as this volume element
+is non-zero, which means
+
+you're not mapping an entire
+space into a sub-space.
+
+When you're mapping an entire
+space into a sub-space and you
+
+define density as being density
+per unit volume, of
+
+course the density in this map
+space doesn't exist anymore.
+
+Which is exactly what
+this formula says.
+
+If this determinant is zero, it
+means this density here is
+
+going to be infinite in the
+regions where this z exists at
+
+all, which is just in this
+linear sub-space, and what do
+
+you do about that?
+
+I mean do you get all
+frustrated about it?
+
+Or do you say what's going
+on and treat it in
+
+some sensible way?
+
+I mean the thing is
+happening here.
+
+And this talks about
+it a little bit.
+
+If a is singular, then
+A is going to map Rk
+
+into a proper sub-space.
+
+Determinant A is going
+to be equal to 0.
+
+The density doesn't exist.
+
+So what do you do about it?
+
+I mean what does this mean
+if you're mapping
+
+into a smaller sub-space.
+
+What does it mean in terms
+of this diagram here?
+
+Well in the diagram here
+it's pretty clear.
+
+Because these little cubes here
+are getting mapped into
+
+straight lines here.
+
+Yeah?
+
+What?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Some linear
+combinations of this are being
+
+mapped into 0.
+
+Namely if this straight line
+is this way any Z which is
+
+going in this direction is
+being mapped into 0.
+
+Any vector Z which is going in
+this direction has to be
+
+identically equaled to 0.
+
+In other words some linear
+combination of n1 and n2 is a
+
+random variable which takes on
+the value 0 identically.
+
+Why do you try to represent that
+in a probabilistic sense?
+
+Why don't you just take it out
+of consideration altogether?
+
+Here what it means is that z1
+and z2 are simply linear
+
+combinations of each other.
+
+OK.
+
+In other words once you know
+what the sample value of z1
+
+is, you can find the
+sample values z2.
+
+In other words z2 is a linear
+combination of z1.
+
+It's linearly dependent on z1,
+which means that you can
+
+identify it exactly once
+you know what z1 is.
+
+Which means you might as
+well not call it a
+
+random variable at all.
+
+Which means you might as well
+view this situation where the
+
+determinant is 0 as where the
+vector Z is really just one
+
+random variable, and everything
+else is determined.
+
+So you throw out these extra
+random variables,
+
+pseudo-random variables, which
+are really just linear
+
+combinations of the others.
+
+So you deal with a smaller
+dimensional set.
+
+You find the probability
+density of the smaller
+
+dimensional set, and you don't
+worry about all of these
+
+mathematical peculiarities that
+would arise otherwise.
+
+OK.
+
+So once we do that, A is going
+to be non-singular.
+
+Because we're going to be left
+with a set of random
+
+variables, which are
+not linearly
+
+dependent on each other.
+
+They can be statistically
+dependent on each other, but
+
+not linearly dependent, OK.
+
+So for all z then, since
+determinant A is not 0, the
+
+probability density at some
+arbitrary vector Z is going to
+
+be the normal joint density
+evaluated at a to the minus 1z
+
+divided by the determinant
+of A. OK.
+
+In other words we're just
+working the map backwards.
+
+This formula is the same as this
+formula, except instead
+
+of writing An here, we're
+writing z here.
+
+And when An is equal to z then
+little n has to be equal to A
+
+to the minus 1z.
+
+And what does that say?
+
+It says that the joint
+probability density has to be
+
+equal to this quantity here.
+
+Which in matrix terms looks
+rather simple, it
+
+looks rather nice.
+
+You can rewrite this.
+
+This is a norm here,
+so it's this vector
+
+there times this vector.
+
+Where in fact when you want to
+multiply vectors in this way,
+
+you're taking inner product of
+the vector with this cell.
+
+These are real vectors
+we're looking at.
+
+Because we're trying to model
+real noise, because we're
+
+modeling the noise on
+communication channels.
+
+So this is going to be the
+inner product of A to the
+
+minus 1z with itself, which
+means you want to look at the
+
+transform of a to
+the minus 1z.
+
+Now what's the transform
+of a to the minus 1z?
+
+It's z transform times a to
+the minus 1 transform.
+
+So we wind up with a to the
+minus 1 transform times a to
+
+the minus 1 times z.
+
+So we have some kind of peculiar
+bilinear form here.
+
+So for any sample value of the
+random vector Z we can find
+
+the probability density in terms
+of this quantity here.
+
+Which looks a little bit
+peculiar, but it
+
+doesn't look too bad.
+
+OK.
+
+Now we want to simplify
+that a little bit.
+
+Anytime you're dealing with
+zero-mean random variables --
+
+now remember I'm going to forget
+to say zero-mean half
+
+the time because everything is
+concerned with zero-mean
+
+random variables.
+
+The covariance of Z1 and Z2 is
+expected value of Z1 times Z2.
+
+So if you have a k-tuple Z,
+the covariance is a matrix
+
+whose i,j element is expected
+value of Zi times Zj.
+
+And what that means is that the
+covariance matrix, this is
+
+a matrix now, it's going to be
+the expected value of z times
+
+z transpose.
+
+Z is a random vector, which is
+a column random vector, Z
+
+transpose is a row-random
+vector, which is this simply
+
+turned upside down, turned
+by 90 degrees.
+
+Now when you multiply the
+components of this vector
+
+together, you can see that what
+you get is the elements
+
+of this covariance matrix.
+
+In other words this is just
+standard matrix manipulation,
+
+which I hope most of you or at
+least partly familiar with.
+
+OK.
+
+When we then talk about the
+expected values Z times Z
+
+transpose we can write this as
+the expected value of A times
+
+N, which is what z is.
+
+N transpose times A transpose,
+which is what Z transpose is.
+
+And miraculously here the N and
+the N transpose are in the
+
+middle here, where it's easy
+to deal with them, because
+
+these are normal Gaussian
+random variables.
+
+And when you look at this column
+times this row, since
+
+all diagonal elements are
+independent of each other, and
+
+all of them have variance one,
+the expected value of N times
+
+N transpose is simply
+the identity matrix.
+
+All the randomness goes out of
+this which it obviously has to
+
+because we're looking at a
+covariance which is just a
+
+matrix and not something
+random.
+
+So you wind up with this
+covariance matrix is equal to
+
+a rather arbitrary matrix A,
+but not singular, times the
+
+transpose of that matrix.
+
+OK.
+
+We've assumed that A is
+non-singular and therefore
+
+it's not too hard to see the k
+sub Z is non-singular also.
+
+And explicitly case of Z mainly
+its co-variance matrix,
+
+the inverse of it, is A to the
+minus 1 transpose times A to
+
+the minus 1.
+
+Namely you take the inverse and
+you start flipping things
+
+and you do all of these
+neat matrix things
+
+that you always do.
+
+And you should review them
+if you've forgotten that.
+
+So that when we write our
+probability density, which was
+
+this in terms of this
+transformation here, what we
+
+get is the density of Z is
+equal to, in place of
+
+determinant of A, we get the
+square root of the determinant
+
+in the k sub Z. You probably
+don't remember that, but is
+
+what you get.
+
+And it's sort of a blah.
+
+Here this is more interesting.
+
+This is minus 1/2 z transpose
+times Kz to the
+
+minus 1 times z.
+
+What does this tell you?
+
+Look at this formula.
+
+Is it just a big formula or
+what does it say to you?
+
+You got to look at these things
+and see what they say.
+
+I mean we've gone through
+a lot of work to derive
+
+something here.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Well it
+is Gaussian.
+
+Yes.
+
+I mean that's the way we define
+jointly Gaussian.
+
+But what's the funny
+thing about
+
+this probability density?
+
+What does it depend on?
+
+What do I have to tell you in
+order for you to calculate
+
+this probability density
+for every z you
+
+want to plug in here?
+
+I have to tell you what this
+covariance matrix is.
+
+And once I tell you what the
+covariance matrix is, there is
+
+nothing more to be specified.
+
+In other words, a jointly
+Gaussian random vector is
+
+completely specified by
+its covariance matrix.
+
+And it's specified exactly
+this way by
+
+its covariance matrix.
+
+OK.
+
+There's nothing more there.
+
+So this says anytime you're
+dealing with jointly Gaussian,
+
+the only thing you have to
+be interested in is this
+
+covariance here.
+
+Namely all you need to have
+jointly Gaussian is somebody
+
+has to tell you what the
+covariance is, and somebody
+
+has to tell you also that
+it's jointly Gaussian.
+
+Jointly Gaussian plus a given
+covariance specifies the
+
+probability density.
+
+OK.
+
+What does that tell you?
+
+Well let's look at an example
+where we just have two random
+
+variables, Z1 and Z2.
+
+then expected value of Z1
+squared is the upper.
+
+Left hand element of that
+covariance matrix, which we'll
+
+call sigma 1 squared.
+
+The lower, right hand side of
+the matrix is K22, which we'll
+
+call sigma 2 squared.
+
+And we're going to let rho be
+the normalize covariance.
+
+We're just defining a bunch of
+things here, because this is
+
+the way people usually
+define this.
+
+So rho will be the normalized
+cross covariance.
+
+Then the determinant of the
+Kz is this mess here.
+
+For A to be non-singular, we
+have to have rho less than 1.
+
+If rho is equal to 1 then this
+determinant is going to be
+
+equal to 0, and we're back in
+this awful case that we don't
+
+want to think about.
+
+So then if we go through the
+trouble of finding out what
+
+the inverse of K sub z is, we
+find this 1 over 1 minus row
+
+square times this matrix here.
+
+The probability density plugging
+this in is this big
+
+thing here.
+
+OK what does that tell you?
+
+Well the thing that it tells
+me is that I never want to
+
+deal with this, and I
+particularly don't want to
+
+deal with it if I'm dealing with
+three or more variables.
+
+OK.
+
+In other words the interesting
+thing here is the simple
+
+formula we had before, which
+is this formula.
+
+OK.
+
+And we have computers these
+days which say given nice
+
+formulas like this, their
+standard computer routines to
+
+calculate things like this.
+
+And you never want to look at
+some awful mess like this.
+
+OK.
+
+And if you put a mean into here,
+which you will see in
+
+every textbook on random
+variables and probability you
+
+ever look at, this thing becomes
+so ugly that you were
+
+probably convinced before you
+took this class that jointly
+
+Gaussian random variables were
+things you wanted to avoid
+
+like the plague.
+
+And if you really have to deal
+with explicit formulas like
+
+this, you're absolutely right.
+
+You do want to avoid them like
+the plague, because you can't
+
+get any insight from what that
+says, or at least I can't.
+
+So I say OK, we have
+to deal with this.
+
+But yet we like to get a little
+more insight about what
+
+this means.
+
+And to do this, we like to find
+a little bit more about
+
+what these bilinear forms
+are all about.
+
+Those of you who have taken any
+course on linear algebra
+
+have dealt with these
+bilinear forms.
+
+And played with them forever.
+
+And those of you who haven't are
+probably puzzled about how
+
+to deal with them.
+
+The notes have an appendix,
+which is about two pages long
+
+which tells you what you have to
+know about these matrices.
+
+And I will just sort of quote
+those results as we go.
+
+Incidentally those results
+are not hard to derive.
+
+And not hard to find
+out about.
+
+You can simply derive them on
+your own, or you can look at
+
+Strang's book on linear algebra,
+which is about the
+
+simplest way to get them.
+
+And that's all you need to do.
+
+OK.
+
+We've said the probability
+density depends on this
+
+bilinear form z transpose
+times Kz to the
+
+minus 1 time z.
+
+What is this?
+
+Is this a matrix or
+a vector or what?
+
+How many people think
+it's a matrix?
+
+How many people think
+it's a vector?
+
+You think it's a vector?
+
+OK.
+
+Well in a very peculiar
+sense it is.
+
+How many people think
+it's a number?
+
+Good.
+
+OK.
+
+It is a number, and it's
+a number because
+
+this is a row vector.
+
+This is a matrix.
+
+This is a column vector.
+
+And if you think of multiplying
+a matrix times a
+
+column vector, you get
+a column vector.
+
+And if you take a row vector
+times a column
+
+vector, you got a number.
+
+OK.
+
+So this is just a number which
+depends on little z.
+
+OK.
+
+Kz is called a positive
+definite matrix.
+
+And it's called a positive
+definite matrix, because this
+
+thing is always non-negative.
+
+And it always has to be
+non-negative because this
+
+refers to the --
+
+if I put capital Z in here,
+namely if I put the random
+
+vector in here Z, then what this
+is, is the variance of a
+
+particular random variable.
+
+So it has to be greater
+than or equal to zero.
+
+So anyway K sub z is always
+non-negative definite.
+
+Here it's going to be positive
+definite, because we've
+
+already assumed that the matrix
+A was non-singular, and
+
+therefore the matrix Kz has
+to be non-singular.
+
+So this has to be positive
+definite.
+
+So it has an inverse, K sub
+z minus 1 is also positive
+
+definite which means this
+quantity is always greater
+
+than zero, if z is non-zero.
+
+You can take these positive
+definite matrices and you can
+
+find eigenvectors and
+eigenvalues for them.
+
+Do you ever actually calculate
+these eigenvectors and
+
+eigenvalues?
+
+I hope not.
+
+It's a mess to do it.
+
+I mean it's just as bad as
+writing that awful formula we
+
+had before.
+
+So you don't want to actually do
+this, but it's nice to know
+
+that these things exist.
+
+And because these vectors exist,
+and in fact if you have
+
+a matrix which is k by k, little
+k by little k, then
+
+there are k such eigenvectors
+and they can be chosen
+
+orthonormal.
+
+OK.
+
+In other words each of these Q
+sub i are orthogonal to each
+
+of the others.
+
+You can clearly scale them,
+because you scale this and
+
+scale this together.
+
+And it's going to maintain
+equality.
+
+So you just scale them down so
+you can make them normalize.
+
+If you have a bunch of
+eigenvectors with the same
+
+eigenvalue, then the whole
+linear sub-space formed by
+
+that set of eigenvectors all
+have the same eigenvalue
+
+lambda sub i.
+
+Namely you take any linear
+combination of these things
+
+which satisfy this equation
+for a particular lambda.
+
+And any linear combination
+will satisfy the
+
+same the same equation.
+
+So you can simply choose an
+orthonormal set among them to
+
+satisfy this.
+
+And if you look at Q sub i and
+Q sub j, which have different
+
+eigenvalues, then it's pretty
+easy to show that in fact they
+
+have to be orthogonal
+to each other.
+
+So anyway when you do this you
+wind up with this form becomes
+
+just the sum over i of lambda
+sub i to the minus 1.
+
+Namely these eigenvalues
+to the minus 1.
+
+These eigenvalues are
+all positive.
+
+Times the inner product
+of z with Q sub i.
+
+In other words, you take
+whatever vector Z you're
+
+interested in here, you
+project it on these k
+
+orthonormal vectors Q sub i.
+
+You get those k values.
+
+And then this form here is
+just that sum there.
+
+So when you write
+the probability
+
+density in that way --
+
+we still have this here
+we'll get rid of that
+
+in the minute --
+
+you have e to the minus sum over
+i, these inner product
+
+terms squared divided by
+2 times lambda sub i.
+
+That's just because this
+is equal to this.
+
+It's just substituting this for
+this in the formula for
+
+the probability density.
+
+OK.
+
+What does that say
+pictorially?
+
+Let me show you a picture
+of it first.
+
+It says that for any positive
+definite matrix and therefore
+
+for any covariance matrix,
+you can always find these
+
+orthonormal vectors.
+
+I've drawn them here
+for two dimensions.
+
+They're just some arbitrary
+vector q1; q2 has to be
+
+orthogonal to it.
+
+And if you look at the square
+root of lambda 1 times q1, you
+
+got a point here.
+
+You look at the square root of
+lambda 2 times q2, you got a
+
+point here.
+
+If you then look at this
+probability density here, you
+
+see that all the points on this
+ellipse here have to have
+
+the same sum of z
+times Q sub i.
+
+OK.
+
+It looked a little
+better over here.
+
+Yes.
+
+OK.
+
+Namely the points little z for
+which this is constant are the
+
+points which form
+this ellipse.
+
+And it's the ellipse which has
+the axes square root of lambda
+
+i times Q sub i.
+
+And then you just imagine it
+if it's lined up this way.
+
+And think of what you would get
+if you were looking at the
+
+lines of equal probability
+density for independent
+
+Gaussian random variables with
+different variances.
+
+I mean we already pointed out
+if the variances are all the
+
+same, these equal probability
+contours are spheres.
+
+If you now expand on some of
+the axes, you get ellipses.
+
+And now we've taken these
+arbitrary vectors, so these
+
+are not in the directions we
+started out with, but in some
+
+arbitrary directions.
+
+We have q1 and q2 are
+orthornormal to each other,
+
+because that's the way
+we've chosen them.
+
+And then the probability
+density has this form
+
+which is this form.
+
+And the other thing we can do is
+to take this form here and
+
+say gee this is just a
+probability density for a
+
+bunch of independent random
+variables, where the
+
+independent random variables are
+the inner product of the
+
+random vector Z with Q sub 1 up
+to the inner product of z
+
+with Q sub k.
+
+So these are independent
+Gaussian random variables.
+
+They have variances
+lambda sub i.
+
+And this is the nicest formula
+for the probability density of
+
+an arbitrary set of jointly
+density of jointly Gaussian
+
+random variables.
+
+OK.
+
+In other words what this says
+is in general if you have a
+
+set of jointly Gaussian random
+variables and I have this
+
+messy form here, all you're
+doing is looking at them in a
+
+wrong coordinate system.
+
+If you switch them around, you
+look at them this way instead
+
+of this way, you're going to
+have independent Gaussian
+
+random variables.
+
+And the way to look at them
+is found by solving this
+
+eigenvector eigenvalue equation,
+which will tell you
+
+what these orthogonal
+directions are.
+
+And then it'll tell you how to
+get this nice picture that
+
+looks this way.
+
+OK.
+
+OK so that tells us what we
+need to know, maybe even a
+
+little more than we have to
+know, about jointly Gaussian
+
+random variables.
+
+But there's one more
+bonus we get.
+
+And the bonus is
+the following.
+
+If you create a matrix here B
+where the i'th row of B is
+
+this vector Q sub i divided by
+the square root of lambda sub
+
+i, then what this is going to
+do is the corresponding
+
+element here is going to be a
+normalized Gaussian random
+
+variable with variance one and
+all of these are going to be
+
+independent of each other.
+
+OK.
+
+That's essentially what
+we were saying before.
+
+This is just another way of
+saying the same thing.
+
+That when you squish this
+probability density around and
+
+look at it in a different frame
+of reference, and then
+
+you scale the random variables
+down or up, what you wind up
+
+with is IID normal Gaussian
+random variables.
+
+OK.
+
+But that says that Z is
+equal to B to the
+
+minus 1 times N prime.
+
+Well so what?
+
+Here's the reason for so what.
+
+We started out with a definition
+of jointly
+
+Gaussian, which is probably not
+the definition of jointly
+
+Gaussian you've ever seen if
+you've seen this before.
+
+Then what we did was to say,
+OK if you have jointly
+
+Gaussian random variables
+and they're not linearly
+
+independent and none of them are
+linearly dependent on the
+
+others, then this matrix
+A is invertible.
+
+From that we derive the
+probability density.
+
+From the probability density
+we derive this.
+
+OK.
+
+The only thing you need
+to get this is
+
+the probability density.
+
+And this says that anytime you
+have a random vector Z with
+
+this probability density that
+we just wrote down.
+
+Then you have the property that
+N prime is equal to BZ,
+
+and Z is equal to B to
+the minus 1 N prime.
+
+Which says that if you have this
+probability density, then
+
+you have jointly Gaussian
+random variables.
+
+So we have an alternate
+
+definition of jointly Gaussian.
+
+Random variables are jointly
+Gaussian if they have this
+
+probability density.
+
+You can somehow represent them
+as linear combinations of
+
+normal random variables.
+
+OK.
+
+Then there's something
+even simpler.
+
+It says that if all linear
+combinations of a random
+
+vector Z are Gaussian, then
+Z is jointly Gaussian.
+
+Why is that?
+
+well If you look at this formula
+here, it says take any
+
+old random vector at all that
+has a covariance matrix.
+
+From that covariance matrix, we
+can solve for all of these
+
+eigenvectors.
+
+If I find the appropriate random
+variables here from
+
+this transformation, those
+random variables are then
+
+uncorrelated from each other,
+they are all statistically
+
+independent of each other, And
+it follows from that, that if
+
+all these linear combinations
+are Gaussian then Z has to be
+
+jointly Gaussian.
+
+OK.
+
+So we now have three
+definitions.
+
+This one is the simplest
+one to state.
+
+It's the hardest one
+to work with.
+
+That's life you know.
+
+This one is probably the most
+straightforward, because you
+
+don't have to know anything to
+understand this definition.
+
+This original definition is
+physically the most appealing
+
+because it shows why noise
+vectors actually
+
+do have this property.
+
+OK.
+
+So here's a summary
+of all of this.
+
+It says if Kz is singular, you
+want to remove the linearly
+
+independent random variables.
+
+You just take them away because
+they're uniquely
+
+specified in terms of
+the other variables.
+
+And then you take the resulting
+non-singular matrix,
+
+and Z is going to be jointly
+Gaussian if and only if Z is
+
+equal to AN for some normal
+random variable N. If Z has
+
+jointly Gaussian density or if
+all linear combinations of Z
+
+are Gaussian all of this for 0
+mean would mean it applies to
+
+fluctuation.
+
+OK.
+
+So why do we have to know all of
+that about jointly Gaussian
+
+random variables?
+
+Well because everything about
+Gaussian processes depends on
+
+jointly Gaussian random
+variables.
+
+You can't do anything with
+Gaussian processes without
+
+being able to look
+at these jointly
+
+Gaussian random variables.
+
+And the reason is that we said
+that Z of t is a Gaussian
+
+process if for every k and every
+set of time instance,
+
+every set of e, that's
+t1 to t sub k.
+
+If Z of t1 up to Z of
+tk is a jointly
+
+Gaussian random vector.
+
+OK.
+
+So that directly links the
+definition of a Gaussian
+
+process to Gaussian
+random vectors.
+
+OK.
+
+Supposed the sample functions
+of Z of t or L2 with
+
+probability one.
+
+I want to say a little bit about
+this because otherwise
+
+you can't sort out any of these
+things about how L2
+
+theory connects with
+random processes.
+
+OK.
+
+So I'm going to start out by
+just assuming that all these
+
+sample functions are going
+to be L2 functions with
+
+probability 1.
+
+One way to ensure this is to
+look only at processes of the
+
+form Z of t equals some sum
+of Z sub i times ti of t.
+
+OK remember at the beginning
+we started looking at this
+
+process the sum of a set of
+normalized Gaussian random
+
+variables times sinc
+functions times
+
+displaced sinc functions.
+
+You can also do the same
+thing with Fourier
+
+coefficients or anything.
+
+You got a fairly general set
+of processes that way.
+
+unfortunately they don't quite
+work, because if you look at
+
+the sinc functions and you
+look at noise, which is
+
+independent and identically
+distributed in time, then the
+
+sample functions are going
+to have infinite energy.
+
+I mean that kind of process
+just runs on forever.
+
+It runs on with finite
+power forever.
+
+And therefore it has
+infinite energy.
+
+And therefore the simplest
+process to look at, the sample
+
+functions are non-L2 with
+probability one, which is sort
+
+of unfortunate.
+
+So we say OK we don't care about
+that, because if you
+
+want to look at that process
+a sum of Z sub i times sinc
+
+functions, what do
+you care about?
+
+I mean you only care about the
+terms in that expansion, which
+
+run from the big bang until
+the next big bang.
+
+OK.
+
+We certainly don't care about it
+before that or after that.
+
+And if we look within those
+finite time limits, then all
+
+these functions are
+going to be L2.
+
+Because they just last for
+a finite amount of time.
+
+So all we need to do is to
+truncate these things somehow.
+
+And we're going to diddle around
+a little bit with a
+
+question of how to truncate
+these series.
+
+But for the time being we
+just say we can do that.
+
+And we will do it.
+
+So we can look at any processes
+the form sum of Zi
+
+times phi i of t, where the Zi
+are independent and the phi i
+
+of t are orthonormal.
+
+And to make things L2, we're
+going to assume that the sum
+
+over i of Zi squared bar
+is less than infinity.
+
+OK.
+
+In other words we only take a
+finite number of these things,
+
+or if we want to take infinite
+a number of them, the
+
+variances are going
+to go off to zero.
+
+And I don't know whether you're
+proving it in the
+
+homework this time or you will
+prove it in the homework next
+
+time, I forget, but you're going
+to look at the question
+
+of why this finite variance
+condition makes these sample
+
+functions be L2 with
+probability one.
+
+OK.
+
+So if you had this condition,
+then all your sample functions
+
+are going to be L2.
+
+I'm going to get off
+all of this L2
+
+business relatively shortly.
+
+I want to do a little bit
+of it to start with.
+
+Because if any of you have start
+doing any research in
+
+this area, at some point you're
+going to be merrily
+
+working away calculating
+all sorts of things.
+
+And suddenly you're going to
+find that none of it exists,
+
+because of these problems
+of infinite energy.
+
+And you're going to
+get very puzzled.
+
+So one of the things I tried to
+do in the notes is to write
+
+them in way that you can
+understand them at a first
+
+reading without worrying
+about any of this.
+
+And then when you go back for a
+second reading, you can pick
+
+up all the mathematics
+that you need.
+
+So that in fact you won't have
+the problem of suddenly
+
+finding out that three-quarters
+of your thesis
+
+has to be thrown away, because
+you've been dealing with
+
+things that don't
+make any sense.
+
+OK.
+
+So, we're going to define linear
+functionals in the
+
+following way.
+
+We're going to first look at the
+sample functions of this
+
+random process Z. OK.
+
+Now we talked about
+this last time.
+
+If you have a random process Z
+than really what you have is a
+
+set of functions defined
+on some samples space.
+
+So the quantities you're
+interested in is what is the
+
+value of the random process at
+time t for sample point omega.
+
+OK.
+
+If we look at that and make it
+for a given omega, this thing
+
+becomes a function of t.
+
+In fact for a given omega, this
+is just what we've been
+
+calling a sample element
+of the random process.
+
+So if we take this sample
+element, look at the inner
+
+product of that with some
+function g of t.
+
+In other words we look at the
+integral of Z of t omega times
+
+g of t, dt.
+
+And if all these sample
+functions are L2 and if g of t
+
+is L2, what happens when you
+take the integral of an L2
+
+function times an L2 function,
+which is the inner product of
+
+something L2 with something L2
+which says something with
+
+finite energy inner
+product with
+
+something with finite energy.
+
+Well the Schwarz inequality
+tells you that if this has
+
+finite energy and this has
+finite energy, the inner
+
+product exists.
+
+That's the reason why we went
+through the Schwarz
+
+inequality.
+
+It's the main reason
+for doing that.
+
+So these things have
+finite value.
+
+So V of omega the results of
+doing this namely V as a
+
+function of the sample space
+is a real number.
+
+And it's a real number for the
+sample points of omega with
+
+probability one, which means
+we can talk about V as a
+
+random variable.
+
+OK.
+
+And now V is a random variable
+which is defined in this way.
+
+And from now on we will call
+these things linear
+
+functionals which are in fact
+the integral of a random
+
+process times a function.
+
+And we can take that
+kind of integral.
+
+It sort of looks like the linear
+combinations of things
+
+we were doing before when we
+were talking about matrices
+
+and random vectors.
+
+OK.
+
+If we restrict the random
+process to have the following
+
+form, where these are
+independent and these are
+
+orthonormal, then one of these
+linear functionals is given by
+
+the random variable V is going
+to be the integral of Z of t
+
+times g of t, but
+Z of t is this.
+
+And at this point we're not
+going to fuss about
+
+interchanging integrals
+with summations.
+
+You have the machinery to do it,
+because we're now dealing
+
+with an L2 space.
+
+We're not going to
+fuss about it.
+
+And I advise you not
+to fuss about it.
+
+So we have a sum of these random
+variables here times
+
+these integrals here.
+
+These integrals here are just
+projections of g of t on this
+
+space of orthonormal
+functions.
+
+So whatever space of orthonormal
+functions gives
+
+you your jollies, use it talk
+about the inner products on
+
+that space.
+
+This gives you a nice inner
+products space of
+
+sequences of numbers.
+
+And then if the z i are jointly
+Gaussian, then V is
+
+going to be Gaussian.
+
+And then to generalize this one
+little bit further, if you
+
+take a whole bunch of L2
+functions, g1 of t g2 of t and
+
+so forth, you can talk about
+a whole bunch of random
+
+variables V1 up to V sub j, 0.
+
+And V sub j is going to be
+the integral of Z of
+
+t times gj of tdt.
+
+Remember this thing
+looks very simple.
+
+It looks like the --
+
+like the convolutions you've
+been doing all your life.
+
+It's not.
+
+It's really a rather
+peculiar quantity.
+
+This in fact is what we call a
+linear functional, and is the
+
+integral of a random
+process times this.
+
+Which we have defined in terms
+of the sample functions of the
+
+random process.
+
+And now we said OK now that we
+understand what it is, we will
+
+just write this all the time.
+
+But I just caution
+you not to let
+
+familiarity breed contempt.
+
+Because this is a rather
+peculiar notion.
+
+And a rather powerful notion.
+
+OK.
+
+So these things are
+jointly Gaussian.
+
+We want to take the expected
+value of V sub i times V sub
+
+j, and now we're going to do
+this without worrying about
+
+being careful at all.
+
+We have the expected value of
+the integral of Z of t, gi of
+
+t, td times the integral of
+Z tau gj of tau, d tau.
+
+And now we're going to slide
+this expected value inside of
+
+both of these integrals.
+
+And not worry about it.
+
+And therefore what we're going
+to have is a double integral
+
+of gi of t expected value of z
+of t time z of tau times gj of
+
+tau dt, d tau, which
+is this thing here.
+
+Which you should compare with
+what we've been dealing with
+
+most of the lecture today.
+
+This is the same kind of form
+for a covariance function as
+
+we've been dealing with for
+covariance matrices.
+
+It has very similar effects.
+
+I mean before you were just
+talking about finite
+
+dimensional matrices, which is
+all simple mathematically in
+
+eigenfunctions and
+eigenvalues.
+
+You have eigenfunctions
+and eigenvalues of
+
+these things also.
+
+And so long as these are defined
+nicely by these L2
+
+properties we've been
+talking about.
+
+In fact you can deal with these
+in virtually the same
+
+way that you can deal with
+the matrices we were
+
+dealing with before.
+
+If you just remember what the
+results are from matrices, you
+
+can guess what they are for
+these covariance functions.
+
+OK.
+
+But anyway you can find the
+expected value of Vi times Vj
+
+by this formula.
+
+Again we're dealing with
+zero-mean and therefore we
+
+don't have to worry about the
+mean, put that in later.
+
+And that all exists.
+
+OK.
+
+So the next thing we want
+to deal with, hitting
+
+you with a lot today.
+
+But I mean the trouble is a lot
+of this is half familiar
+
+to most of you.
+
+People who have taken various
+communication courses at
+
+various places have all been
+exposed to random processes in
+
+some highly trivialized sense.
+
+But the major results are the
+same as the results we're
+
+going through here.
+
+And all we're doing here is
+adding a little bit of
+
+carefulness about what works
+and what doesn't work.
+
+Incidentally in the notes which
+is towards the end of
+
+lectures 14 and 15, we give
+three examples which let you
+
+know why in fact we want to
+look primarily at random
+
+processes which are defined in
+terms of a sum of independent
+
+Gaussian random variables time
+orthonormal functions.
+
+And if you look at those
+three examples, some
+
+of them have problems.
+
+Because of the fact that
+everything you're dealing with
+
+has infinite energy.
+
+And therefore it doesn't
+really make any sense.
+
+And one of them I should
+talk about this just a
+
+little bit in class.
+
+And I think I still have a
+couple of minutes, is a very
+
+strange process where
+Z of t is IID.
+
+In fact just let it be normal.
+
+And independent for all t.
+
+OK.
+
+In other words you generate a
+random process by looking at
+
+an uncountably infinite
+collection of
+
+normal random variables.
+
+How do you deal with
+such a process?
+
+I don't know how to
+deal with it.
+
+I mean it sounds like
+it's simple.
+
+If I put this on a quiz,
+three-quarters of you would
+
+say oh that's very simple.
+
+What we're dealing with is a
+family of impulse functions.
+
+Spaced arbitrarily
+closely together.
+
+This is not impulse function.
+
+Impulse functions are even worse
+than this, but this is
+
+bad enough.
+
+When we start talking about
+spectral density, we can
+
+explain this a little bit better
+by thinking this kind
+
+of process it doesn't
+make any sense.
+
+But this kind of process, if
+you look at its spectral
+
+density, it's going to have a
+spectral density which is zero
+
+everywhere, but whose integral
+over all frequencies is one.
+
+OK.
+
+In other words it's not
+something you want to wish on
+
+your on your worse friend.
+
+It makes a certain amount of
+sense as a limit of things.
+
+You can look at a very broadband
+process where in
+
+fact you spread the process
+out enormously.
+
+You can make pseudo noise which
+looks sort of like this.
+
+And you make the process broader
+and broader and lower
+
+and lower intensity
+everywhere.
+
+But it still has this
+energy of one.
+
+It still has a power
+of one everywhere.
+
+And it just is ugly.
+
+OK.
+
+Now if you never worried about
+these questions of L2, you
+
+would look at a process like
+that and say, gee there must
+
+be some easy way to handle that
+because it's probably the
+
+easiest process you
+can define.
+
+I mean everything is normal.
+
+If you look at any set at
+different times, you get a set
+
+of IID normal Gaussian
+variables.
+
+You try to put it together, and
+it doesn't mean anything.
+
+If you pass it through a filter,
+the filter is going to
+
+cancel it all out.
+
+So anyway, that's one reason
+why we want to look at this
+
+restricted class of random
+processes we're looking at.
+
+OK.
+
+What we're interested in now is
+we want to take a Gaussian
+
+random process really, but you
+can take any random process.
+
+We want to pass it through a
+filter, and we want to look at
+
+the random process
+that comes out.
+
+OK.
+
+And that certainly is a very
+physical kind of operation.
+
+I mean any kind of communication
+system that you
+
+build is going to have
+noise on the channel.
+
+And one of the first things
+you're going to do is you're
+
+going to filter what
+you've received.
+
+So you have to have some way
+of dealing with this.
+
+OK.
+
+And the way we sort of been
+dealing with it all along in
+
+terms of the transmitted way
+forms we've been dealing with
+
+is to say OK.
+
+What we're going to do is to
+first look what happens when
+
+we take sample functions of
+this, pass them through the
+
+filter, and then what comes
+out is going to be some
+
+function again.
+
+And then we're back into
+what you studied as an
+
+undergraduate talking about
+functions through filters.
+
+We're going to jazz it up a
+little bit by saying these
+
+functions are going to
+be L2 the filters
+
+are going to be L2.
+
+So that in fact you know
+you'd get something
+
+out that make sense.
+
+So what we're doing is looking
+at these sample functions V
+
+the output at time tau for
+sample point omega is going to
+
+be the convolution of the input
+at time t and sample
+
+point omega.
+
+Remember this one sample point
+exists for all time.
+
+That's why these sample points
+and sample spaces are so damn
+
+complicated.
+
+Because they have everything
+in them.
+
+OK.
+
+So there's one sample point
+which exists for all of them.
+
+This is a sample function.
+
+You're passing the sample
+function through a filter,
+
+which is just normal
+convolution.
+
+What comes out then.
+
+If in fact we express this
+random process in terms of
+
+this orthonormal sum the way
+we've been doing before.
+
+Is you get the sum over j of
+this, which is a sample value
+
+of the j'th random variable
+coming out times the integral
+
+of pj of t, h of tau
+minus t, d tau.
+
+OK.
+
+For each tau that you look at,
+this is just a sample value of
+
+a linear functional.
+
+OK.
+
+If I want to look at this at one
+value of tau, I have this
+
+integral here which is
+a random process.
+
+A sample value of a
+random process at
+
+omega time a function.
+
+This is just a function
+of t for given tau.
+
+OK.
+
+So this is a linear
+functional.
+
+As a type we've been
+talking about.
+
+And that linear functional
+is then given by
+
+this for each tau.
+
+This is a sample value
+of a linear
+
+functional we can talk about.
+
+OK.
+
+These things are then, if you
+look over the whole sample
+
+space omega, V of tau becomes
+a random variable.
+
+OK.
+
+V of tau is the random variable
+whose sample values
+
+are V of t omega, and they're
+given by this.
+
+So if z of t is Gaussian
+process, you get jointly
+
+Gaussian linear functionals at
+each of any set of times tau
+
+1, tau 2 up to tau sub k.
+
+So this just gives you a whole
+set of linear functionals.
+
+And if z of t is a Gaussian
+process, then all these linear
+
+functionals are going to be
+jointly Gaussian also.
+
+And bingo.
+
+What we have then is an
+alternate way to generate
+
+Gaussian processes.
+
+OK.
+
+In other words you can generate
+a Gaussian process by
+
+specifying at each set of k
+times, you have jointly
+
+Gaussian random variables.
+
+But once you do that, once you
+understand one Gaussian
+
+process, you're off
+and running.
+
+Because then you can pass
+it through any L2 filter
+
+that you want to.
+
+And you generate another
+Gaussian process.
+
+So for example, if you start
+out with this sinc type
+
+process, I mean we'll see that
+that has a spectral density,
+
+which is flat over
+all frequencies.
+
+And we'll talk about spectral
+density tomorrow.
+
+But then you pass it through a
+linear filter, and you can
+
+give it any spectral density
+that you want.
+
+So at this point, we really
+have enough to talk about
+
+arbitrary covariance functions
+just by starting out with
+
+random processes, which are
+defined in terms of some
+
+sequence of orthonormal
+random variables.
+
+OK.
+
+Now we can get to covariance
+function of a filter process
+
+in the same way as we got the
+matrix for linear functionals.
+
+OK.
+
+And this is just computation.
+
+OK.
+
+So what is it?
+
+The covariance function of
+this output process V
+
+evaluated at one time
+r another time s.
+
+One of the nasty things about
+notation when you start
+
+dealing with a covariance
+function of the input and the
+
+output to a linear filter is
+you suddenly need to worry
+
+about two times at the
+input and two other
+
+times at the output.
+
+OK.
+
+Because this thing is then
+expected value of V sub r
+
+times the expected
+value of V subs.
+
+OK.
+
+This is a random variable, which
+is the process V of r
+
+evaluated at time r.
+
+This is the random variable,
+which is the process V of t
+
+evaluated at a particular
+time s.
+
+This is going to be the expected
+value of what this
+
+random variable now is the
+integral of the random process
+
+z of t times this function
+here, which is now
+
+a function of t.
+
+Because we're looking at
+a fixed value of r.
+
+So this is a linear functional,
+
+which is a random variable.
+
+This is another linear
+functional.
+
+This is evaluated at some time
+s, which is the output of the
+
+filter at time s.
+
+Then we will throw caution to
+the wind interchange integrals
+
+with expectation
+and everything.
+
+And then in the middle we'll
+have expected value of z of t
+
+times z of tau, which is the
+covariance function of z.
+
+OK.
+
+So the covariance function of
+z then specifies what the
+
+covariance function
+of the output is.
+
+OK.
+
+So whenever you pass a random
+process through a filter if
+
+you know what the covariance
+function of input to the
+
+filter is, you can find the
+covariance function of the
+
+output of the filter.
+
+That's a kind of a nasty
+formula, it's not very nice.
+
+But anyway the thing that it
+tells you is that whether this
+
+random process is
+Gaussian or not.
+
+The only thing that determines
+the covariance function of the
+
+output of the filter is the
+covariance function of the
+
+input to the filter plus of
+course the filter response,
+
+which is needed OK.
+
+And this is just the same kind
+of bilinear form that we were
+
+dealing with before.
+
+Next time we will talk a little
+bit about the fact that
+
+when you're dealing with a
+bilinear form like this, you
+
+can take these covariance
+functions and they have the
+
+same kind of eigenvalues and
+eigenvectors that we had
+
+before for a matrix.
+
+Namely this is again going to
+be positive definite as a
+
+function, and we will be able
+to find its eigenvectors and
+
+its eigenvalues.
+
+We can't calculate them.
+
+Computers can calculate them.
+
+People who've spend their
+lives doing this
+
+can calculate them.
+
+I wouldn't suggest that you
+spend your life doing this.
+
+Because again you would be
+setting yourself up as a
+
+second class computer, and
+you don't make any
+
+profit out of that.
+
+But anyway, we can find this
+in principle from this.
+
+OK.
+
+One of the things that we
+haven't talked about at all
+
+yet, and which we will start
+talking about next time in
+
+which the next set of lecture
+notes, lecture 16, we'll deal
+
+with is the question
+of stationarity.
+
+Let me say just a little bit
+about that to get into it.
+
+And then we'll talk a lot
+more about it next time.
+
+The notes will probably be on
+the web some time tomorrow.
+
+I hope before noon if you
+want to look at them.
+
+Physically if you look at a
+stochastic process, and you
+
+want to model it.
+
+I mean suppose you want to
+model a noise process.
+
+How do you model a
+noise process?
+
+Well you look at it over
+a long period of time.
+
+You start taking statistics
+about it over a
+
+long period of time.
+
+And somehow you want to model
+it in such a way, I mean the
+
+only thing you can look at
+is statistics over a
+
+long period of time.
+
+So if you're only looking at one
+process, you can look at
+
+it for a year and then you can
+model it, and then you can use
+
+that model for the
+next 10 years.
+
+And what that's assuming is that
+the noise process looks
+
+the same way this year
+as it does next year.
+
+You can go further than that
+and say, OK I'm going to
+
+manufacture cell phones or some
+other kind of widget.
+
+And what I'm interested in then
+is what these noise wave
+
+forms are to the whole
+collection of my widgets.
+
+Namely different people
+will buy my widgets.
+
+They will use them in
+different places.
+
+So I'm interested in modeling
+the noise over this whole set
+
+of widgets.
+
+But still if you're doing that
+you're still almost forced to
+
+deal with models which have the
+same statistics over at
+
+least a broad range of times.
+
+Sometimes when we're dealing
+with wireless communication we
+
+say, no the channel keeps
+changing in time. and the
+
+channel keeps changing
+slowly in time.
+
+And therefore you don't have
+the same statistics
+
+now as you have then.
+
+If you want to understands that,
+believe me, the only way
+
+you're going to understand it is
+to first understand how to
+
+deal with statistics for
+the channel which
+
+stay the same forever.
+
+And once you understand those
+statistics, you will then be
+
+in a position to start to
+understand what happens when
+
+these statistics
+change slowly.
+
+OK.
+
+In other words, what our
+modeling assumption is in this
+
+course, and I believe it's the
+right modeling assumption for
+
+all engineers, is that you never
+start with some physical
+
+phenomena and say, I want to
+test the hell out of this
+
+until I find an appropriate
+statistical model for it.
+
+You do that only after
+you know enough
+
+about random processes.
+
+That you know how to deal with
+an enormous variety of
+
+different home cooked
+random processes.
+
+OK.
+
+So what we do in a course like
+this is we deal with lots of
+
+different home cooked random
+processes, which is in fact
+
+why we've done rather peculiar
+things like saying, let's look
+
+at a random process which
+comes from a sum of
+
+independent random variables
+multiplied
+
+by orthonormal functions.
+
+And you see what we've
+accomplished by that already.
+
+Namely by starting out that way
+we've been able to define
+
+Gaussian processes.
+
+We've been able to define what
+happens when one of those
+
+Gaussian processes goes
+through a filter.
+
+And in fact, that gives a way
+of generating a lot more
+
+random processes.
+
+And next time what we're going
+to do is not to say how is it
+
+that we know that processes
+are stationary.
+
+How do you test whether
+processes are
+
+stationary or not.
+
+But we're just going to assume
+that they're stationary.
+
+In other words if they had the
+same statistics now as they're
+
+going to have next year.
+
+And those statistics stay
+the same forever.
+
+And then see what we
+can say about it.
+
+To give you a clue as to how
+to start looking at this,
+
+remember what we said quite
+a long time ago
+
+about Markov chains.
+
+OK.
+
+And now when you look at Markov
+chains, remember that
+
+what happens at one time is
+statistically a function of
+
+what happened at the unit
+of time before it.
+
+OK.
+
+But we can still model those
+Markov change as being
+
+stationary.
+
+Because the dependents at this
+time on the previous sample of
+
+time is the same now as it will
+be five years from now.
+
+OK.
+
+In other words you can't just
+look at the process at one
+
+instant of time and say
+this is independent
+
+of all other times.
+
+That's not what stationary
+means.
+
+What stationary means is the way
+the process depends on the
+
+past at time t is the same is
+the way it depends on the past
+
+at some later time tau.
+
+And that in fact is the way
+we're going to define
+
+stationarity.
+
+It's at these joint sample times
+that we're going to be
+
+looking at.
+
+Which I had a better
+word for that.
+
+Join sets of epochs that
+we'll be looking at.
+
+The joint statistics over a set
+of epics is going to be
+
+the same now as it will be at
+sometime in the future.
+
+And that's the way we're going
+to define stationarity.
+
+A prelude of what we're going
+to find when we do that is
+
+that this covariance function,
+if the covariance function at
+
+time t and time tau is the same
+if you translate it up to
+
+t plus t1 and tau plus t1, then
+in fact this function is
+
+going to be a function only if
+the difference t minus tau.
+
+It's going to be a function
+of one variable
+
+instead of two variables.
+
+OK.
+
+So as soon as we get this
+function being a function of
+
+one variable instead of two
+variables, first thing we're
+
+going to do is to take the
+Fourier transform of this.
+
+Because then we'll be taking
+the Fourier transform of a
+
+function of a single variable.
+
+We're going to call
+that the spectral
+
+density of the process.
+
+And we're going to find that for
+stationary processes the
+
+spectrum densities tell you
+
+everything if they're Gaussian.
+
+Why is that?
+
+Well the inverse Fourier
+transform is
+
+this covariance function.
+
+And we've now seen that the
+covariance function tells you
+
+everything about a
+Gaussian process.
+
+So if you know the spectral
+density for a stationary
+
+process, it will tell
+you everything.
+
+We will also have to fiddle
+around a little bit about how
+
+we define stationarity.
+
+But at the same time
+don't have this
+
+infinite energy problem.
+
+And the way we're going
+to do it is the way
+
+we've done it all along.
+
+We're going to take something
+that looked stationary, we're
+
+going to truncate it over some
+long period of time, and we're
+
+going to have our cake and
+eat it too that way.
+
+OK.
+
+So we'll do that next time.
\ No newline at end of file
diff --git a/zM5MW5NKZJg.txt b/zM5MW5NKZJg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eb094b23e955a8410410946a21b9ade8039e91b4
--- /dev/null
+++ b/zM5MW5NKZJg.txt
@@ -0,0 +1,5955 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So today
+
+ align:start position:0%
+So today
+ 
+
+ align:start position:0%
+So today
+we're going to look at approximation
+
+ align:start position:0%
+we're going to look at approximation
+ 
+
+ align:start position:0%
+we're going to look at approximation
+algorithms for the traveling salesman
+
+ align:start position:0%
+algorithms for the traveling salesman
+ 
+
+ align:start position:0%
+algorithms for the traveling salesman
+problem. So you should so I hope
+
+ align:start position:0%
+problem. So you should so I hope
+ 
+
+ align:start position:0%
+problem. So you should so I hope
+everyone knows what the trouble and
+
+ align:start position:0%
+everyone knows what the trouble and
+ 
+
+ align:start position:0%
+everyone knows what the trouble and
+salesman problem is. You have a graph
+
+ align:start position:0%
+salesman problem is. You have a graph
+ 
+
+ align:start position:0%
+salesman problem is. You have a graph
+you're trying to visit every vertex and
+
+ align:start position:0%
+you're trying to visit every vertex and
+ 
+
+ align:start position:0%
+you're trying to visit every vertex and
+you want to do this. So you start at a
+
+ align:start position:0%
+you want to do this. So you start at a
+ 
+
+ align:start position:0%
+you want to do this. So you start at a
+vertex you visit every single one and
+
+ align:start position:0%
+vertex you visit every single one and
+ 
+
+ align:start position:0%
+vertex you visit every single one and
+you end at the starting vertex and you
+
+ align:start position:0%
+you end at the starting vertex and you
+ 
+
+ align:start position:0%
+you end at the starting vertex and you
+want to do that in the shortest possible
+
+ align:start position:0%
+want to do that in the shortest possible
+ 
+
+ align:start position:0%
+want to do that in the shortest possible
+time or distance or whatever the metric
+
+ align:start position:0%
+time or distance or whatever the metric
+ 
+
+ align:start position:0%
+time or distance or whatever the metric
+is. So unfortunately this is np hard
+
+ align:start position:0%
+is. So unfortunately this is np hard
+ 
+
+ align:start position:0%
+is. So unfortunately this is np hard
+also the approximation algorithms for
+
+ align:start position:0%
+also the approximation algorithms for
+ 
+
+ align:start position:0%
+also the approximation algorithms for
+any constant approximation is also known
+
+ align:start position:0%
+any constant approximation is also known
+ 
+
+ align:start position:0%
+any constant approximation is also known
+to be np hard. Um so you should have
+
+ align:start position:0%
+to be np hard. Um so you should have
+ 
+
+ align:start position:0%
+to be np hard. Um so you should have
+gone over approximation algorithms in
+
+ align:start position:0%
+gone over approximation algorithms in
+ 
+
+ align:start position:0%
+gone over approximation algorithms in
+lecture. So basically uh let's say the
+
+ align:start position:0%
+lecture. So basically uh let's say the
+ 
+
+ align:start position:0%
+lecture. So basically uh let's say the
+optimal solution has some value v and if
+
+ align:start position:0%
+optimal solution has some value v and if
+ 
+
+ align:start position:0%
+optimal solution has some value v and if
+you want to calc if you want to
+
+ align:start position:0%
+you want to calc if you want to
+ 
+
+ align:start position:0%
+you want to calc if you want to
+guarantee that your algorithm will end
+
+ align:start position:0%
+guarantee that your algorithm will end
+ 
+
+ align:start position:0%
+guarantee that your algorithm will end
+up with a value which is within a
+
+ align:start position:0%
+up with a value which is within a
+ 
+
+ align:start position:0%
+up with a value which is within a
+constant factor of v so less than cv
+
+ align:start position:0%
+constant factor of v so less than cv
+ 
+
+ align:start position:0%
+constant factor of v so less than cv
+that that is an approximation algorithm
+
+ align:start position:0%
+that that is an approximation algorithm
+ 
+
+ align:start position:0%
+that that is an approximation algorithm
+but for the traveling salesman problem
+
+ align:start position:0%
+but for the traveling salesman problem
+ 
+
+ align:start position:0%
+but for the traveling salesman problem
+the approx constant approximation
+
+ align:start position:0%
+the approx constant approximation
+ 
+
+ align:start position:0%
+the approx constant approximation
+algorithms are also np hard so instead
+
+ align:start position:0%
+algorithms are also np hard so instead
+ 
+
+ align:start position:0%
+algorithms are also np hard so instead
+we we modify it slightly so on the
+
+ align:start position:0%
+we we modify it slightly so on the
+ 
+
+ align:start position:0%
+we we modify it slightly so on the
+traveling salesman problem we impose
+
+ align:start position:0%
+traveling salesman problem we impose
+ 
+
+ align:start position:0%
+traveling salesman problem we impose
+something called a metric so the
+
+ align:start position:0%
+something called a metric so the
+ 
+
+ align:start position:0%
+something called a metric so the
+important relation here is this one so
+
+ align:start position:0%
+important relation here is this one so
+ 
+
+ align:start position:0%
+important relation here is this one so
+first of all Let's go through this. So
+
+ align:start position:0%
+first of all Let's go through this. So
+ 
+
+ align:start position:0%
+first of all Let's go through this. So
+you have a distance metric for so if X Y
+
+ align:start position:0%
+you have a distance metric for so if X Y
+ 
+
+ align:start position:0%
+you have a distance metric for so if X Y
+are vertices your distance is always
+
+ align:start position:0%
+are vertices your distance is always
+ 
+
+ align:start position:0%
+are vertices your distance is always
+greater than zero which is reasonable.
+
+ align:start position:0%
+greater than zero which is reasonable.
+ 
+
+ align:start position:0%
+greater than zero which is reasonable.
+Your this undirected which is this
+
+ align:start position:0%
+Your this undirected which is this
+ 
+
+ align:start position:0%
+Your this undirected which is this
+relation and you have the triangle
+
+ align:start position:0%
+relation and you have the triangle
+ 
+
+ align:start position:0%
+relation and you have the triangle
+inequality which means that if you have
+
+ align:start position:0%
+inequality which means that if you have
+ 
+
+ align:start position:0%
+inequality which means that if you have
+three vert vertices
+
+ align:start position:0%
+three vert vertices
+ 
+
+ align:start position:0%
+three vert vertices
+and you have distances like this
+
+ align:start position:0%
+and you have distances like this
+ 
+
+ align:start position:0%
+and you have distances like this
+distance is always smaller than the sum
+
+ align:start position:0%
+distance is always smaller than the sum
+ 
+
+ align:start position:0%
+distance is always smaller than the sum
+of these two distances which is at least
+
+ align:start position:0%
+of these two distances which is at least
+ 
+
+ align:start position:0%
+of these two distances which is at least
+like real worldish things that make
+
+ align:start position:0%
+like real worldish things that make
+ 
+
+ align:start position:0%
+like real worldish things that make
+sense right if if this system was longer
+
+ align:start position:0%
+sense right if if this system was longer
+ 
+
+ align:start position:0%
+sense right if if this system was longer
+you would just take this path instead.
+
+ align:start position:0%
+you would just take this path instead.
+ 
+
+ align:start position:0%
+you would just take this path instead.
+So the distance by taking another node
+
+ align:start position:0%
+So the distance by taking another node
+ 
+
+ align:start position:0%
+So the distance by taking another node
+is always greater than equal to the
+
+ align:start position:0%
+is always greater than equal to the
+ 
+
+ align:start position:0%
+is always greater than equal to the
+direct distance.
+
+ align:start position:0%
+direct distance.
+ 
+
+ align:start position:0%
+direct distance.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+turns out the metric ts problem is also
+
+ align:start position:0%
+turns out the metric ts problem is also
+ 
+
+ align:start position:0%
+turns out the metric ts problem is also
+np hard. So not nothing very great
+
+ align:start position:0%
+np hard. So not nothing very great
+ 
+
+ align:start position:0%
+np hard. So not nothing very great
+there. But but you can do a constant
+
+ align:start position:0%
+there. But but you can do a constant
+ 
+
+ align:start position:0%
+there. But but you can do a constant
+approximation here and we'll go through
+
+ align:start position:0%
+approximation here and we'll go through
+ 
+
+ align:start position:0%
+approximation here and we'll go through
+two approximations today. The first the
+
+ align:start position:0%
+two approximations today. The first the
+ 
+
+ align:start position:0%
+two approximations today. The first the
+simpler one is a two approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we'll improve this to 3 over2.
+
+ align:start position:0%
+and then we'll improve this to 3 over2.
+ 
+
+ align:start position:0%
+and then we'll improve this to 3 over2.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+let's start with the first one. So
+
+ align:start position:0%
+let's start with the first one. So
+ 
+
+ align:start position:0%
+let's start with the first one. So
+before we begin, let's uh define a
+
+ align:start position:0%
+before we begin, let's uh define a
+ 
+
+ align:start position:0%
+before we begin, let's uh define a
+couple of terms. Let's define
+
+ align:start position:0%
+couple of terms. Let's define
+ 
+
+ align:start position:0%
+couple of terms. Let's define
+C of S. So let's so what is S? So let S
+
+ align:start position:0%
+C of S. So let's so what is S? So let S
+ 
+
+ align:start position:0%
+C of S. So let's so what is S? So let S
+be a path
+
+ align:start position:0%
+be a path
+ 
+
+ align:start position:0%
+be a path
+or rather let's say S
+
+ align:start position:0%
+or rather let's say S
+ 
+
+ align:start position:0%
+or rather let's say S
+is a set of edges.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if you have your graph here,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your set of edges could be something
+
+ align:start position:0%
+your set of edges could be something
+ 
+
+ align:start position:0%
+your set of edges could be something
+like this, this, this, this. So that
+
+ align:start position:0%
+like this, this, this, this. So that
+ 
+
+ align:start position:0%
+like this, this, this, this. So that
+that's set of edges. And C of S is
+
+ align:start position:0%
+that's set of edges. And C of S is
+ 
+
+ align:start position:0%
+that's set of edges. And C of S is
+defined as the sum of the sum of the
+
+ align:start position:0%
+defined as the sum of the sum of the
+ 
+
+ align:start position:0%
+defined as the sum of the sum of the
+weights of all the edges. And this
+
+ align:start position:0%
+weights of all the edges. And this
+ 
+
+ align:start position:0%
+weights of all the edges. And this
+actually should be a multi set because
+
+ align:start position:0%
+actually should be a multi set because
+ 
+
+ align:start position:0%
+actually should be a multi set because
+you can have you can count the same edge
+
+ align:start position:0%
+you can have you can count the same edge
+ 
+
+ align:start position:0%
+you can have you can count the same edge
+twice. So you can count this edge three
+
+ align:start position:0%
+twice. So you can count this edge three
+ 
+
+ align:start position:0%
+twice. So you can count this edge three
+times or whatever you want, how many
+
+ align:start position:0%
+times or whatever you want, how many
+ 
+
+ align:start position:0%
+times or whatever you want, how many
+however many times you want. So that's
+
+ align:start position:0%
+however many times you want. So that's
+ 
+
+ align:start position:0%
+however many times you want. So that's
+the definition. So now we want to find a
+
+ align:start position:0%
+the definition. So now we want to find a
+ 
+
+ align:start position:0%
+the definition. So now we want to find a
+cycle which goes through all the
+
+ align:start position:0%
+cycle which goes through all the
+ 
+
+ align:start position:0%
+cycle which goes through all the
+vertices and we want to minimize the
+
+ align:start position:0%
+vertices and we want to minimize the
+ 
+
+ align:start position:0%
+vertices and we want to minimize the
+cost of that cycle. So let's say your
+
+ align:start position:0%
+cost of that cycle. So let's say your
+ 
+
+ align:start position:0%
+cost of that cycle. So let's say your
+optimal so this is this should remind
+
+ align:start position:0%
+optimal so this is this should remind
+ 
+
+ align:start position:0%
+optimal so this is this should remind
+you of the Hamiltonian cycle problem. So
+
+ align:start position:0%
+you of the Hamiltonian cycle problem. So
+ 
+
+ align:start position:0%
+you of the Hamiltonian cycle problem. So
+this is essentially finding a
+
+ align:start position:0%
+this is essentially finding a
+ 
+
+ align:start position:0%
+this is essentially finding a
+Hamiltonian cycle in the graph of
+
+ align:start position:0%
+Hamiltonian cycle in the graph of
+ 
+
+ align:start position:0%
+Hamiltonian cycle in the graph of
+minimum weight. So this is worse than
+
+ align:start position:0%
+minimum weight. So this is worse than
+ 
+
+ align:start position:0%
+minimum weight. So this is worse than
+the Hamiltonian cycle problem. This is
+
+ align:start position:0%
+the Hamiltonian cycle problem. This is
+ 
+
+ align:start position:0%
+the Hamiltonian cycle problem. This is
+finding the minimum weight Hamiltonian
+
+ align:start position:0%
+finding the minimum weight Hamiltonian
+ 
+
+ align:start position:0%
+finding the minimum weight Hamiltonian
+cycle. Okay. So let's say there exists
+
+ align:start position:0%
+cycle. Okay. So let's say there exists
+ 
+
+ align:start position:0%
+cycle. Okay. So let's say there exists
+this beautiful Hamiltonian cycle which
+
+ align:start position:0%
+this beautiful Hamiltonian cycle which
+ 
+
+ align:start position:0%
+this beautiful Hamiltonian cycle which
+is min you know of is of minimum weight.
+
+ align:start position:0%
+is min you know of is of minimum weight.
+ 
+
+ align:start position:0%
+is min you know of is of minimum weight.
+Let's call that h star g. So it's the
+
+ align:start position:0%
+Let's call that h star g. So it's the
+ 
+
+ align:start position:0%
+Let's call that h star g. So it's the
+best Hamiltonian cycle on this graph and
+
+ align:start position:0%
+best Hamiltonian cycle on this graph and
+ 
+
+ align:start position:0%
+best Hamiltonian cycle on this graph and
+that's the shortest path that your
+
+ align:start position:0%
+that's the shortest path that your
+ 
+
+ align:start position:0%
+that's the shortest path that your
+traveling salesman can take. And so the
+
+ align:start position:0%
+traveling salesman can take. And so the
+ 
+
+ align:start position:0%
+traveling salesman can take. And so the
+cost of that is given by cf sg. Okay. So
+
+ align:start position:0%
+cost of that is given by cf sg. Okay. So
+ 
+
+ align:start position:0%
+cost of that is given by cf sg. Okay. So
+how do we go about trying to approximate
+
+ align:start position:0%
+how do we go about trying to approximate
+ 
+
+ align:start position:0%
+how do we go about trying to approximate
+this problem? So think about what
+
+ align:start position:0%
+this problem? So think about what
+ 
+
+ align:start position:0%
+this problem? So think about what
+algorithms you've seen that can that
+
+ align:start position:0%
+algorithms you've seen that can that
+ 
+
+ align:start position:0%
+algorithms you've seen that can that
+sort of connect all the vertices of a
+
+ align:start position:0%
+sort of connect all the vertices of a
+ 
+
+ align:start position:0%
+sort of connect all the vertices of a
+graph and minimize costs of edges.
+
+ align:start position:0%
+graph and minimize costs of edges.
+ 
+
+ align:start position:0%
+graph and minimize costs of edges.
+Remind you of anything polomial that
+
+ align:start position:0%
+Remind you of anything polomial that
+ 
+
+ align:start position:0%
+Remind you of anything polomial that
+you've seen in the class that connects
+
+ align:start position:0%
+you've seen in the class that connects
+ 
+
+ align:start position:0%
+you've seen in the class that connects
+all the vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spans all the vertices.
+
+ align:start position:0%
+spans all the vertices.
+ 
+
+ align:start position:0%
+spans all the vertices.
+Exactly. So Chris call min spanning
+
+ align:start position:0%
+Exactly. So Chris call min spanning
+ 
+
+ align:start position:0%
+Exactly. So Chris call min spanning
+tree. So min spanning tree is polomial
+
+ align:start position:0%
+tree. So min spanning tree is polomial
+ 
+
+ align:start position:0%
+tree. So min spanning tree is polomial
+time and it connects all the vertex
+
+ align:start position:0%
+time and it connects all the vertex
+ 
+
+ align:start position:0%
+time and it connects all the vertex
+vert. So let's let's take some graph.
+
+ align:start position:0%
+vert. So let's let's take some graph.
+ 
+
+ align:start position:0%
+vert. So let's let's take some graph.
+Let's just go with this one. So you have
+
+ align:start position:0%
+Let's just go with this one. So you have
+ 
+
+ align:start position:0%
+Let's just go with this one. So you have
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+vertices and you connect you make a
+
+ align:start position:0%
+vertices and you connect you make a
+ 
+
+ align:start position:0%
+vertices and you connect you make a
+minimum spanning tree out of them.
+
+ align:start position:0%
+minimum spanning tree out of them.
+ 
+
+ align:start position:0%
+minimum spanning tree out of them.
+Now clearly this is not a cycle yet. But
+
+ align:start position:0%
+Now clearly this is not a cycle yet. But
+ 
+
+ align:start position:0%
+Now clearly this is not a cycle yet. But
+let's try to construct a path out of
+
+ align:start position:0%
+let's try to construct a path out of
+ 
+
+ align:start position:0%
+let's try to construct a path out of
+this minimum spanning tree.
+
+ align:start position:0%
+this minimum spanning tree.
+ 
+
+ align:start position:0%
+this minimum spanning tree.
+So first let's root it. So let's say we
+
+ align:start position:0%
+So first let's root it. So let's say we
+ 
+
+ align:start position:0%
+So first let's root it. So let's say we
+have rooted minimum spanning tree.
+
+ align:start position:0%
+have rooted minimum spanning tree.
+ 
+
+ align:start position:0%
+have rooted minimum spanning tree.
+Let's say this is the root. So you have
+
+ align:start position:0%
+Let's say this is the root. So you have
+ 
+
+ align:start position:0%
+Let's say this is the root. So you have
+three things coming out of there. I
+
+ align:start position:0%
+three things coming out of there. I
+ 
+
+ align:start position:0%
+three things coming out of there. I
+think that's it. Okay. So let's give
+
+ align:start position:0%
+think that's it. Okay. So let's give
+ 
+
+ align:start position:0%
+think that's it. Okay. So let's give
+these labels.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now what we're going to do is the way
+
+ align:start position:0%
+So now what we're going to do is the way
+ 
+
+ align:start position:0%
+So now what we're going to do is the way
+we're going to traverse all the
+
+ align:start position:0%
+we're going to traverse all the
+ 
+
+ align:start position:0%
+we're going to traverse all the
+vertices. Let's just do a DFS. So in DFS
+
+ align:start position:0%
+vertices. Let's just do a DFS. So in DFS
+ 
+
+ align:start position:0%
+vertices. Let's just do a DFS. So in DFS
+traversal you'll first C1
+
+ align:start position:0%
+traversal you'll first C1
+ 
+
+ align:start position:0%
+traversal you'll first C1
+then you'll go down in C2
+
+ align:start position:0%
+then you'll go down in C2
+ 
+
+ align:start position:0%
+then you'll go down in C2
+then go down in C3
+
+ align:start position:0%
+then go down in C3
+ 
+
+ align:start position:0%
+then go down in C3
+then you'll go back up C2 again then go
+
+ align:start position:0%
+then you'll go back up C2 again then go
+ 
+
+ align:start position:0%
+then you'll go back up C2 again then go
+back down C4 go back up C2 one 5 1 6 so
+
+ align:start position:0%
+back down C4 go back up C2 one 5 1 6 so
+ 
+
+ align:start position:0%
+back down C4 go back up C2 one 5 1 6 so
+basically you're ignoring the rest of
+
+ align:start position:0%
+basically you're ignoring the rest of
+ 
+
+ align:start position:0%
+basically you're ignoring the rest of
+the graph you find your minimum spanning
+
+ align:start position:0%
+the graph you find your minimum spanning
+ 
+
+ align:start position:0%
+the graph you find your minimum spanning
+tree and you follow all the paths follow
+
+ align:start position:0%
+tree and you follow all the paths follow
+ 
+
+ align:start position:0%
+tree and you follow all the paths follow
+them back up and just do a DFS reversal
+
+ align:start position:0%
+them back up and just do a DFS reversal
+ 
+
+ align:start position:0%
+them back up and just do a DFS reversal
+and that is and then you go reach back
+
+ align:start position:0%
+and that is and then you go reach back
+ 
+
+ align:start position:0%
+and that is and then you go reach back
+to one I think And then you have this
+
+ align:start position:0%
+to one I think And then you have this
+ 
+
+ align:start position:0%
+to one I think And then you have this
+well it visits all the vertices. It
+
+ align:start position:0%
+well it visits all the vertices. It
+ 
+
+ align:start position:0%
+well it visits all the vertices. It
+visits some of them more than once which
+
+ align:start position:0%
+visits some of them more than once which
+ 
+
+ align:start position:0%
+visits some of them more than once which
+is a problem which we'll deal with
+
+ align:start position:0%
+is a problem which we'll deal with
+ 
+
+ align:start position:0%
+is a problem which we'll deal with
+shortly. But it visits all the vertices
+
+ align:start position:0%
+shortly. But it visits all the vertices
+ 
+
+ align:start position:0%
+shortly. But it visits all the vertices
+and it's a cycle. So now the problem is
+
+ align:start position:0%
+and it's a cycle. So now the problem is
+ 
+
+ align:start position:0%
+and it's a cycle. So now the problem is
+the travel and salesman problem does not
+
+ align:start position:0%
+the travel and salesman problem does not
+ 
+
+ align:start position:0%
+the travel and salesman problem does not
+allow you to visit vertices more than
+
+ align:start position:0%
+allow you to visit vertices more than
+ 
+
+ align:start position:0%
+allow you to visit vertices more than
+once because if you did not have this
+
+ align:start position:0%
+once because if you did not have this
+ 
+
+ align:start position:0%
+once because if you did not have this
+restriction you could shorten your path
+
+ align:start position:0%
+restriction you could shorten your path
+ 
+
+ align:start position:0%
+restriction you could shorten your path
+length by going to a separate vertex and
+
+ align:start position:0%
+length by going to a separate vertex and
+ 
+
+ align:start position:0%
+length by going to a separate vertex and
+coming back or something like that. So
+
+ align:start position:0%
+coming back or something like that. So
+ 
+
+ align:start position:0%
+coming back or something like that. So
+let's make that more concrete. So at
+
+ align:start position:0%
+let's make that more concrete. So at
+ 
+
+ align:start position:0%
+let's make that more concrete. So at
+least so in this case given this
+
+ align:start position:0%
+least so in this case given this
+ 
+
+ align:start position:0%
+least so in this case given this
+triangle inequality I claim that
+
+ align:start position:0%
+triangle inequality I claim that
+ 
+
+ align:start position:0%
+triangle inequality I claim that
+you can just delete the duplicate
+
+ align:start position:0%
+you can just delete the duplicate
+ 
+
+ align:start position:0%
+you can just delete the duplicate
+vertices. So let's look at the duplicate
+
+ align:start position:0%
+vertices. So let's look at the duplicate
+ 
+
+ align:start position:0%
+vertices. So let's look at the duplicate
+ones. You have 1 2 3 this repeats. So
+
+ align:start position:0%
+ones. You have 1 2 3 this repeats. So
+ 
+
+ align:start position:0%
+ones. You have 1 2 3 this repeats. So
+you delete that repeats repeats repeats
+
+ align:start position:0%
+you delete that repeats repeats repeats
+ 
+
+ align:start position:0%
+you delete that repeats repeats repeats
+and that's cycling back. So how do you
+
+ align:start position:0%
+and that's cycling back. So how do you
+ 
+
+ align:start position:0%
+and that's cycling back. So how do you
+delete things? So in this case you had a
+
+ align:start position:0%
+delete things? So in this case you had a
+ 
+
+ align:start position:0%
+delete things? So in this case you had a
+path right? You were going to one to two
+
+ align:start position:0%
+path right? You were going to one to two
+ 
+
+ align:start position:0%
+path right? You were going to one to two
+and two to three
+
+ align:start position:0%
+and two to three
+ 
+
+ align:start position:0%
+and two to three
+to two and so on. So
+
+ align:start position:0%
+to two and so on. So
+ 
+
+ align:start position:0%
+to two and so on. So
+let's draw the four in. So this is
+
+ align:start position:0%
+let's draw the four in. So this is
+ 
+
+ align:start position:0%
+let's draw the four in. So this is
+following only the tree edges. So how
+
+ align:start position:0%
+following only the tree edges. So how
+ 
+
+ align:start position:0%
+following only the tree edges. So how
+would you delete this? So let's say you
+
+ align:start position:0%
+would you delete this? So let's say you
+ 
+
+ align:start position:0%
+would you delete this? So let's say you
+find the first duplicate vertex and you
+
+ align:start position:0%
+find the first duplicate vertex and you
+ 
+
+ align:start position:0%
+find the first duplicate vertex and you
+don't want that. That's not allowed. So
+
+ align:start position:0%
+don't want that. That's not allowed. So
+ 
+
+ align:start position:0%
+don't want that. That's not allowed. So
+all you do is simply you follow the path
+
+ align:start position:0%
+all you do is simply you follow the path
+ 
+
+ align:start position:0%
+all you do is simply you follow the path
+and you bypass it. And by the triangle
+
+ align:start position:0%
+and you bypass it. And by the triangle
+ 
+
+ align:start position:0%
+and you bypass it. And by the triangle
+inequality, you know that bypassing it
+
+ align:start position:0%
+inequality, you know that bypassing it
+ 
+
+ align:start position:0%
+inequality, you know that bypassing it
+will will never increase your cost.
+
+ align:start position:0%
+will will never increase your cost.
+ 
+
+ align:start position:0%
+will will never increase your cost.
+It'll decrease it or like keep it the
+
+ align:start position:0%
+It'll decrease it or like keep it the
+ 
+
+ align:start position:0%
+It'll decrease it or like keep it the
+same. So you can remove the duplicate
+
+ align:start position:0%
+same. So you can remove the duplicate
+ 
+
+ align:start position:0%
+same. So you can remove the duplicate
+vertex in this path just bypassing it
+
+ align:start position:0%
+vertex in this path just bypassing it
+ 
+
+ align:start position:0%
+vertex in this path just bypassing it
+with also remember that this is a
+
+ align:start position:0%
+with also remember that this is a
+ 
+
+ align:start position:0%
+with also remember that this is a
+complete graph. So a metric is defined
+
+ align:start position:0%
+complete graph. So a metric is defined
+ 
+
+ align:start position:0%
+complete graph. So a metric is defined
+on all pairs of vertices. So every edge
+
+ align:start position:0%
+on all pairs of vertices. So every edge
+ 
+
+ align:start position:0%
+on all pairs of vertices. So every edge
+exists with some value.
+
+ align:start position:0%
+exists with some value.
+ 
+
+ align:start position:0%
+exists with some value.
+So that also follows by the triangle
+
+ align:start position:0%
+So that also follows by the triangle
+ 
+
+ align:start position:0%
+So that also follows by the triangle
+inequality. So if an edge does not
+
+ align:start position:0%
+inequality. So if an edge does not
+ 
+
+ align:start position:0%
+inequality. So if an edge does not
+exist, just make it the sum of the So if
+
+ align:start position:0%
+exist, just make it the sum of the So if
+ 
+
+ align:start position:0%
+exist, just make it the sum of the So if
+XZ is not an edge, just make it the sum
+
+ align:start position:0%
+XZ is not an edge, just make it the sum
+ 
+
+ align:start position:0%
+XZ is not an edge, just make it the sum
+of XY plus YZ.
+
+ align:start position:0%
+of XY plus YZ.
+ 
+
+ align:start position:0%
+of XY plus YZ.
+So in any case, so so you construct the
+
+ align:start position:0%
+So in any case, so so you construct the
+ 
+
+ align:start position:0%
+So in any case, so so you construct the
+an initial path just by going down the
+
+ align:start position:0%
+an initial path just by going down the
+ 
+
+ align:start position:0%
+an initial path just by going down the
+tree and doing a naive DFS reversal and
+
+ align:start position:0%
+tree and doing a naive DFS reversal and
+ 
+
+ align:start position:0%
+tree and doing a naive DFS reversal and
+then you correct that path by skipping
+
+ align:start position:0%
+then you correct that path by skipping
+ 
+
+ align:start position:0%
+then you correct that path by skipping
+over the duplicates. So finally you'll
+
+ align:start position:0%
+over the duplicates. So finally you'll
+ 
+
+ align:start position:0%
+over the duplicates. So finally you'll
+end up with after skipping over the
+
+ align:start position:0%
+end up with after skipping over the
+ 
+
+ align:start position:0%
+end up with after skipping over the
+duplicates you get a 1 2 3 4 5 6 1 and
+
+ align:start position:0%
+duplicates you get a 1 2 3 4 5 6 1 and
+ 
+
+ align:start position:0%
+duplicates you get a 1 2 3 4 5 6 1 and
+that's a valid cycle right. So so let's
+
+ align:start position:0%
+that's a valid cycle right. So so let's
+ 
+
+ align:start position:0%
+that's a valid cycle right. So so let's
+call this minimum spanning tree t.
+
+ align:start position:0%
+call this minimum spanning tree t.
+ 
+
+ align:start position:0%
+call this minimum spanning tree t.
+So that's your mst
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you are removing duplicate edges and
+
+ align:start position:0%
+and you are removing duplicate edges and
+ 
+
+ align:start position:0%
+and you are removing duplicate edges and
+getting a cycle c let's say.
+
+ align:start position:0%
+getting a cycle c let's say.
+ 
+
+ align:start position:0%
+getting a cycle c let's say.
+So now you know that um actually let's
+
+ align:start position:0%
+So now you know that um actually let's
+ 
+
+ align:start position:0%
+So now you know that um actually let's
+take another step back. Let's say okay
+
+ align:start position:0%
+take another step back. Let's say okay
+ 
+
+ align:start position:0%
+take another step back. Let's say okay
+let's say let's define
+
+ align:start position:0%
+let's say let's define
+ 
+
+ align:start position:0%
+let's say let's define
+let's define a cycle first which is so
+
+ align:start position:0%
+let's define a cycle first which is so
+ 
+
+ align:start position:0%
+let's define a cycle first which is so
+let's say let's call this cycle
+
+ align:start position:0%
+let's say let's call this cycle
+ 
+
+ align:start position:0%
+let's say let's call this cycle
+this guy is C
+
+ align:start position:0%
+this guy is C
+ 
+
+ align:start position:0%
+this guy is C
+and then you're going from C and you're
+
+ align:start position:0%
+and then you're going from C and you're
+ 
+
+ align:start position:0%
+and then you're going from C and you're
+deleting the duplicates and you're
+
+ align:start position:0%
+deleting the duplicates and you're
+ 
+
+ align:start position:0%
+deleting the duplicates and you're
+getting C dash
+
+ align:start position:0%
+getting C dash
+ 
+
+ align:start position:0%
+getting C dash
+so now what you have is
+
+ align:start position:0%
+so now what you have is
+ 
+
+ align:start position:0%
+so now what you have is
+cost of
+
+ align:start position:0%
+cost of
+ 
+
+ align:start position:0%
+cost of
+C dash it's a valation but anyway Okay,
+
+ align:start position:0%
+C dash it's a valation but anyway Okay,
+ 
+
+ align:start position:0%
+C dash it's a valation but anyway Okay,
+the cost of C dash is less than equal to
+
+ align:start position:0%
+the cost of C dash is less than equal to
+ 
+
+ align:start position:0%
+the cost of C dash is less than equal to
+cost of C. And what is the cost of C?
+
+ align:start position:0%
+cost of C. And what is the cost of C?
+ 
+
+ align:start position:0%
+cost of C. And what is the cost of C?
+If you know the weight of your minimum
+
+ align:start position:0%
+If you know the weight of your minimum
+ 
+
+ align:start position:0%
+If you know the weight of your minimum
+spanning tree, what is the cost of C? C
+
+ align:start position:0%
+spanning tree, what is the cost of C? C
+ 
+
+ align:start position:0%
+spanning tree, what is the cost of C? C
+is just doing a GFS reversal. So what is
+
+ align:start position:0%
+is just doing a GFS reversal. So what is
+ 
+
+ align:start position:0%
+is just doing a GFS reversal. So what is
+the cost of C?
+
+ align:start position:0%
+the cost of C?
+ 
+
+ align:start position:0%
+the cost of C?
+If you have if you know your minimum
+
+ align:start position:0%
+If you have if you know your minimum
+ 
+
+ align:start position:0%
+If you have if you know your minimum
+spanning tree,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no. So you're traversing every edge on
+
+ align:start position:0%
+no. So you're traversing every edge on
+ 
+
+ align:start position:0%
+no. So you're traversing every edge on
+the minimum spanning tree twice. So
+
+ align:start position:0%
+the minimum spanning tree twice. So
+ 
+
+ align:start position:0%
+the minimum spanning tree twice. So
+you're doing a DFS travers, right? So
+
+ align:start position:0%
+you're doing a DFS travers, right? So
+ 
+
+ align:start position:0%
+you're doing a DFS travers, right? So
+you're going down, you're coming back
+
+ align:start position:0%
+you're going down, you're coming back
+ 
+
+ align:start position:0%
+you're going down, you're coming back
+up. It's like you're going down, coming
+
+ align:start position:0%
+up. It's like you're going down, coming
+ 
+
+ align:start position:0%
+up. It's like you're going down, coming
+back up, backtracking, going back down.
+
+ align:start position:0%
+back up, backtracking, going back down.
+ 
+
+ align:start position:0%
+back up, backtracking, going back down.
+So every edge is reversed twice. So it's
+
+ align:start position:0%
+So every edge is reversed twice. So it's
+ 
+
+ align:start position:0%
+So every edge is reversed twice. So it's
+exactly twice D. So let's bring up a
+
+ align:start position:0%
+exactly twice D. So let's bring up a
+ 
+
+ align:start position:0%
+exactly twice D. So let's bring up a
+different board.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you know that cost of C is twice the
+
+ align:start position:0%
+So you know that cost of C is twice the
+ 
+
+ align:start position:0%
+So you know that cost of C is twice the
+cost of T. Does that make sense? Why the
+
+ align:start position:0%
+cost of T. Does that make sense? Why the
+ 
+
+ align:start position:0%
+cost of T. Does that make sense? Why the
+traversal implies that you have every
+
+ align:start position:0%
+traversal implies that you have every
+ 
+
+ align:start position:0%
+traversal implies that you have every
+edge being visited twice, right? Okay.
+
+ align:start position:0%
+edge being visited twice, right? Okay.
+ 
+
+ align:start position:0%
+edge being visited twice, right? Okay.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+now our claim is that the C dash cycle
+
+ align:start position:0%
+now our claim is that the C dash cycle
+ 
+
+ align:start position:0%
+now our claim is that the C dash cycle
+is uh two approximation of the actual
+
+ align:start position:0%
+is uh two approximation of the actual
+ 
+
+ align:start position:0%
+is uh two approximation of the actual
+Hamilton actual cycle. So why is that?
+
+ align:start position:0%
+Hamilton actual cycle. So why is that?
+ 
+
+ align:start position:0%
+Hamilton actual cycle. So why is that?
+So we already proved. So this impli also
+
+ align:start position:0%
+So we already proved. So this impli also
+ 
+
+ align:start position:0%
+So we already proved. So this impli also
+implies that C of C dash is less than
+
+ align:start position:0%
+implies that C of C dash is less than
+ 
+
+ align:start position:0%
+implies that C of C dash is less than
+equal to 2 of CT.
+
+ align:start position:0%
+equal to 2 of CT.
+ 
+
+ align:start position:0%
+equal to 2 of CT.
+Realize that this is not a valid cycle
+
+ align:start position:0%
+Realize that this is not a valid cycle
+ 
+
+ align:start position:0%
+Realize that this is not a valid cycle
+but this is a valid cycle. Okay. So now
+
+ align:start position:0%
+but this is a valid cycle. Okay. So now
+ 
+
+ align:start position:0%
+but this is a valid cycle. Okay. So now
+we need to show that this is somehow
+
+ align:start position:0%
+we need to show that this is somehow
+ 
+
+ align:start position:0%
+we need to show that this is somehow
+bounded by H star G. So how do you do
+
+ align:start position:0%
+bounded by H star G. So how do you do
+ 
+
+ align:start position:0%
+bounded by H star G. So how do you do
+that? Well, look at HRG. What is HRG?
+
+ align:start position:0%
+that? Well, look at HRG. What is HRG?
+ 
+
+ align:start position:0%
+that? Well, look at HRG. What is HRG?
+HRG is just a cycle which goes the
+
+ align:start position:0%
+HRG is just a cycle which goes the
+ 
+
+ align:start position:0%
+HRG is just a cycle which goes the
+optimal cycle which goes through all the
+
+ align:start position:0%
+optimal cycle which goes through all the
+ 
+
+ align:start position:0%
+optimal cycle which goes through all the
+vertices and comes back to the parent
+
+ align:start position:0%
+vertices and comes back to the parent
+ 
+
+ align:start position:0%
+vertices and comes back to the parent
+vertex. So what you can do? So this is a
+
+ align:start position:0%
+vertex. So what you can do? So this is a
+ 
+
+ align:start position:0%
+vertex. So what you can do? So this is a
+star of G. This is the optimal thing.
+
+ align:start position:0%
+star of G. This is the optimal thing.
+ 
+
+ align:start position:0%
+star of G. This is the optimal thing.
+Now you can take an edge E here and
+
+ align:start position:0%
+Now you can take an edge E here and
+ 
+
+ align:start position:0%
+Now you can take an edge E here and
+delete it and then you will get a
+
+ align:start position:0%
+delete it and then you will get a
+ 
+
+ align:start position:0%
+delete it and then you will get a
+spanning tree because this is your
+
+ align:start position:0%
+spanning tree because this is your
+ 
+
+ align:start position:0%
+spanning tree because this is your
+optimal cycle. Remove one edge and you
+
+ align:start position:0%
+optimal cycle. Remove one edge and you
+ 
+
+ align:start position:0%
+optimal cycle. Remove one edge and you
+get a spanning tree. So let's call that
+
+ align:start position:0%
+get a spanning tree. So let's call that
+ 
+
+ align:start position:0%
+get a spanning tree. So let's call that
+t ddash.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Does that make sense why that is a
+
+ align:start position:0%
+Does that make sense why that is a
+ 
+
+ align:start position:0%
+Does that make sense why that is a
+spanning tree? Because you had a cycle
+
+ align:start position:0%
+spanning tree? Because you had a cycle
+ 
+
+ align:start position:0%
+spanning tree? Because you had a cycle
+and you move one edge. So it's touches
+
+ align:start position:0%
+and you move one edge. So it's touches
+ 
+
+ align:start position:0%
+and you move one edge. So it's touches
+all the vertices and has and it's a
+
+ align:start position:0%
+all the vertices and has and it's a
+ 
+
+ align:start position:0%
+all the vertices and has and it's a
+tree. So it's a spanning tree but it's
+
+ align:start position:0%
+tree. So it's a spanning tree but it's
+ 
+
+ align:start position:0%
+tree. So it's a spanning tree but it's
+not the minimum spanning tree. So you
+
+ align:start position:0%
+not the minimum spanning tree. So you
+ 
+
+ align:start position:0%
+not the minimum spanning tree. So you
+know that
+
+ align:start position:0%
+know that
+ 
+
+ align:start position:0%
+know that
+H star G the cost of H star of G
+
+ align:start position:0%
+H star G the cost of H star of G
+ 
+
+ align:start position:0%
+H star G the cost of H star of G
+is greater than equal to the cost of H
+
+ align:start position:0%
+is greater than equal to the cost of H
+ 
+
+ align:start position:0%
+is greater than equal to the cost of H
+star of G minus the edge we removed
+
+ align:start position:0%
+star of G minus the edge we removed
+ 
+
+ align:start position:0%
+star of G minus the edge we removed
+is greater than equal to the cost of T.
+
+ align:start position:0%
+is greater than equal to the cost of T.
+ 
+
+ align:start position:0%
+is greater than equal to the cost of T.
+Make sense? So you removed one edge and
+
+ align:start position:0%
+Make sense? So you removed one edge and
+ 
+
+ align:start position:0%
+Make sense? So you removed one edge and
+then that that is still greater than the
+
+ align:start position:0%
+then that that is still greater than the
+ 
+
+ align:start position:0%
+then that that is still greater than the
+minimum spanning tree. So now combining
+
+ align:start position:0%
+minimum spanning tree. So now combining
+ 
+
+ align:start position:0%
+minimum spanning tree. So now combining
+this guy and this guy you get cost of C
+
+ align:start position:0%
+this guy and this guy you get cost of C
+ 
+
+ align:start position:0%
+this guy and this guy you get cost of C
+dash is less than equal to 2 * cost of
+
+ align:start position:0%
+dash is less than equal to 2 * cost of
+ 
+
+ align:start position:0%
+dash is less than equal to 2 * cost of
+C. But you know cost of C is less than
+
+ align:start position:0%
+C. But you know cost of C is less than
+ 
+
+ align:start position:0%
+C. But you know cost of C is less than
+cost of H of G. So you get a two
+
+ align:start position:0%
+cost of H of G. So you get a two
+ 
+
+ align:start position:0%
+cost of H of G. So you get a two
+approximation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So does that make sense?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Okay. So that was a true
+
+ align:start position:0%
+Okay. Okay. So that was a true
+ 
+
+ align:start position:0%
+Okay. Okay. So that was a true
+approximation. That was pretty
+
+ align:start position:0%
+approximation. That was pretty
+ 
+
+ align:start position:0%
+approximation. That was pretty
+straightforward. You just constructed a
+
+ align:start position:0%
+straightforward. You just constructed a
+ 
+
+ align:start position:0%
+straightforward. You just constructed a
+spanning tree. You did a DFS reversal,
+
+ align:start position:0%
+spanning tree. You did a DFS reversal,
+ 
+
+ align:start position:0%
+spanning tree. You did a DFS reversal,
+remove duplicates, and you have a nice
+
+ align:start position:0%
+remove duplicates, and you have a nice
+ 
+
+ align:start position:0%
+remove duplicates, and you have a nice
+path.
+
+ align:start position:0%
+path.
+ 
+
+ align:start position:0%
+path.
+But okay, let's just leave it down.
+
+ align:start position:0%
+But okay, let's just leave it down.
+ 
+
+ align:start position:0%
+But okay, let's just leave it down.
+But here's the thing. It seems kind of
+
+ align:start position:0%
+But here's the thing. It seems kind of
+ 
+
+ align:start position:0%
+But here's the thing. It seems kind of
+wasteful to go through all the edges
+
+ align:start position:0%
+wasteful to go through all the edges
+ 
+
+ align:start position:0%
+wasteful to go through all the edges
+when you don't need to. So you're
+
+ align:start position:0%
+when you don't need to. So you're
+ 
+
+ align:start position:0%
+when you don't need to. So you're
+traveling down the tree, you're going
+
+ align:start position:0%
+traveling down the tree, you're going
+ 
+
+ align:start position:0%
+traveling down the tree, you're going
+back up, and you're you're traversing
+
+ align:start position:0%
+back up, and you're you're traversing
+ 
+
+ align:start position:0%
+back up, and you're you're traversing
+every edge twice. So it seems kind of
+
+ align:start position:0%
+every edge twice. So it seems kind of
+ 
+
+ align:start position:0%
+every edge twice. So it seems kind of
+ridiculous that you would be doing every
+
+ align:start position:0%
+ridiculous that you would be doing every
+ 
+
+ align:start position:0%
+ridiculous that you would be doing every
+edge twice. Doesn't So what could you do
+
+ align:start position:0%
+edge twice. Doesn't So what could you do
+ 
+
+ align:start position:0%
+edge twice. Doesn't So what could you do
+better? Well,
+
+ align:start position:0%
+better? Well,
+ 
+
+ align:start position:0%
+better? Well,
+before we introduce that, let's prove a
+
+ align:start position:0%
+before we introduce that, let's prove a
+ 
+
+ align:start position:0%
+before we introduce that, let's prove a
+couple of lemmas,
+
+ align:start position:0%
+couple of lemmas,
+ 
+
+ align:start position:0%
+couple of lemmas,
+let's so first
+
+ align:start position:0%
+let's so first
+ 
+
+ align:start position:0%
+let's so first
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+we start with this. So let's say S is a
+
+ align:start position:0%
+we start with this. So let's say S is a
+ 
+
+ align:start position:0%
+we start with this. So let's say S is a
+subset of V. So you have a graph
+
+ align:start position:0%
+subset of V. So you have a graph
+ 
+
+ align:start position:0%
+subset of V. So you have a graph
+and you take make a subgraph. So you so
+
+ align:start position:0%
+and you take make a subgraph. So you so
+ 
+
+ align:start position:0%
+and you take make a subgraph. So you so
+you pick out some vertices. So pick out
+
+ align:start position:0%
+you pick out some vertices. So pick out
+ 
+
+ align:start position:0%
+you pick out some vertices. So pick out
+this one and this one and this one and
+
+ align:start position:0%
+this one and this one and this one and
+ 
+
+ align:start position:0%
+this one and this one and this one and
+this one and that is your S.
+
+ align:start position:0%
+this one and that is your S.
+ 
+
+ align:start position:0%
+this one and that is your S.
+And so you get a new graph which
+
+ align:start position:0%
+And so you get a new graph which
+ 
+
+ align:start position:0%
+And so you get a new graph which
+contains just those vertices
+
+ align:start position:0%
+contains just those vertices
+ 
+
+ align:start position:0%
+contains just those vertices
+and whatever edges connect them.
+
+ align:start position:0%
+and whatever edges connect them.
+ 
+
+ align:start position:0%
+and whatever edges connect them.
+So the claim is that that that graph
+
+ align:start position:0%
+So the claim is that that that graph
+ 
+
+ align:start position:0%
+So the claim is that that that graph
+also has a Hamiltonian cycle the minimum
+
+ align:start position:0%
+also has a Hamiltonian cycle the minimum
+ 
+
+ align:start position:0%
+also has a Hamiltonian cycle the minimum
+cost Hamiltonian cycle which is also the
+
+ align:start position:0%
+cost Hamiltonian cycle which is also the
+ 
+
+ align:start position:0%
+cost Hamiltonian cycle which is also the
+traveling salesman solution. So let's
+
+ align:start position:0%
+traveling salesman solution. So let's
+ 
+
+ align:start position:0%
+traveling salesman solution. So let's
+call that h star of s. So is some cycle
+
+ align:start position:0%
+call that h star of s. So is some cycle
+ 
+
+ align:start position:0%
+call that h star of s. So is some cycle
+which looks like this I guess here. So h
+
+ align:start position:0%
+which looks like this I guess here. So h
+ 
+
+ align:start position:0%
+which looks like this I guess here. So h
+star of s. Now the claim is that the
+
+ align:start position:0%
+star of s. Now the claim is that the
+ 
+
+ align:start position:0%
+star of s. Now the claim is that the
+cost of h star of s is less than equal
+
+ align:start position:0%
+cost of h star of s is less than equal
+ 
+
+ align:start position:0%
+cost of h star of s is less than equal
+to cost of h star of g. That should make
+
+ align:start position:0%
+to cost of h star of g. That should make
+ 
+
+ align:start position:0%
+to cost of h star of g. That should make
+intuitive sense because you're taking
+
+ align:start position:0%
+intuitive sense because you're taking
+ 
+
+ align:start position:0%
+intuitive sense because you're taking
+only some of the vertices and trying to
+
+ align:start position:0%
+only some of the vertices and trying to
+ 
+
+ align:start position:0%
+only some of the vertices and trying to
+traverse them. And in this case you're
+
+ align:start position:0%
+traverse them. And in this case you're
+ 
+
+ align:start position:0%
+traverse them. And in this case you're
+trying to traverse all the vertices.
+
+ align:start position:0%
+trying to traverse all the vertices.
+ 
+
+ align:start position:0%
+trying to traverse all the vertices.
+However, this is not this is not this is
+
+ align:start position:0%
+However, this is not this is not this is
+ 
+
+ align:start position:0%
+However, this is not this is not this is
+only true because of the triangle
+
+ align:start position:0%
+only true because of the triangle
+ 
+
+ align:start position:0%
+only true because of the triangle
+inequality. And let's see why that is
+
+ align:start position:0%
+inequality. And let's see why that is
+ 
+
+ align:start position:0%
+inequality. And let's see why that is
+the case.
+
+ align:start position:0%
+the case.
+ 
+
+ align:start position:0%
+the case.
+So let's say let's so proof by
+
+ align:start position:0%
+So let's say let's so proof by
+ 
+
+ align:start position:0%
+So let's say let's so proof by
+contradiction.
+
+ align:start position:0%
+contradiction.
+ 
+
+ align:start position:0%
+contradiction.
+Say
+
+ align:start position:0%
+Say
+ 
+
+ align:start position:0%
+Say
+cost of
+
+ align:start position:0%
+cost of
+ 
+
+ align:start position:0%
+cost of
+har of s is actually greater than cost
+
+ align:start position:0%
+har of s is actually greater than cost
+ 
+
+ align:start position:0%
+har of s is actually greater than cost
+of h star of g.
+
+ align:start position:0%
+of h star of g.
+ 
+
+ align:start position:0%
+of h star of g.
+Okay. So look at h star of g. It's a
+
+ align:start position:0%
+Okay. So look at h star of g. It's a
+ 
+
+ align:start position:0%
+Okay. So look at h star of g. It's a
+cycle, right? So you have something that
+
+ align:start position:0%
+cycle, right? So you have something that
+ 
+
+ align:start position:0%
+cycle, right? So you have something that
+your cycle and in this cycle you have
+
+ align:start position:0%
+your cycle and in this cycle you have
+ 
+
+ align:start position:0%
+your cycle and in this cycle you have
+all the vertices of s. So pick them out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now so you have a cycle which has
+
+ align:start position:0%
+And now so you have a cycle which has
+ 
+
+ align:start position:0%
+And now so you have a cycle which has
+cost less than the optimal cycle in S
+
+ align:start position:0%
+cost less than the optimal cycle in S
+ 
+
+ align:start position:0%
+cost less than the optimal cycle in S
+but it contains all the vertices in S.
+
+ align:start position:0%
+but it contains all the vertices in S.
+ 
+
+ align:start position:0%
+but it contains all the vertices in S.
+So what you can do is now you can use
+
+ align:start position:0%
+So what you can do is now you can use
+ 
+
+ align:start position:0%
+So what you can do is now you can use
+the skipping lema from before. So
+
+ align:start position:0%
+the skipping lema from before. So
+ 
+
+ align:start position:0%
+the skipping lema from before. So
+instead of so last time you remove
+
+ align:start position:0%
+instead of so last time you remove
+ 
+
+ align:start position:0%
+instead of so last time you remove
+duplicate vertices but this time what
+
+ align:start position:0%
+duplicate vertices but this time what
+ 
+
+ align:start position:0%
+duplicate vertices but this time what
+you'll do is instead you'll just skip
+
+ align:start position:0%
+you'll do is instead you'll just skip
+ 
+
+ align:start position:0%
+you'll do is instead you'll just skip
+over this vertex and you'll skip over
+
+ align:start position:0%
+over this vertex and you'll skip over
+ 
+
+ align:start position:0%
+over this vertex and you'll skip over
+this vertex and so every vertex that's
+
+ align:start position:0%
+this vertex and so every vertex that's
+ 
+
+ align:start position:0%
+this vertex and so every vertex that's
+not an S skip over it and that can only
+
+ align:start position:0%
+not an S skip over it and that can only
+ 
+
+ align:start position:0%
+not an S skip over it and that can only
+decrease the cost. So now you've
+
+ align:start position:0%
+decrease the cost. So now you've
+ 
+
+ align:start position:0%
+decrease the cost. So now you've
+constructed another cycle which contains
+
+ align:start position:0%
+constructed another cycle which contains
+ 
+
+ align:start position:0%
+constructed another cycle which contains
+only the vertices of S. So it's a
+
+ align:start position:0%
+only the vertices of S. So it's a
+ 
+
+ align:start position:0%
+only the vertices of S. So it's a
+Hamiltonian cycle for S but it has cost
+
+ align:start position:0%
+Hamiltonian cycle for S but it has cost
+ 
+
+ align:start position:0%
+Hamiltonian cycle for S but it has cost
+less than equals H star G which means
+
+ align:start position:0%
+less than equals H star G which means
+ 
+
+ align:start position:0%
+less than equals H star G which means
+that this this can never be true. So
+
+ align:start position:0%
+that this this can never be true. So
+ 
+
+ align:start position:0%
+that this this can never be true. So
+that is the reason so so the important
+
+ align:start position:0%
+that is the reason so so the important
+ 
+
+ align:start position:0%
+that is the reason so so the important
+fact is there that if you have a subset
+
+ align:start position:0%
+fact is there that if you have a subset
+ 
+
+ align:start position:0%
+fact is there that if you have a subset
+of vertices making the the restricted
+
+ align:start position:0%
+of vertices making the the restricted
+ 
+
+ align:start position:0%
+of vertices making the the restricted
+graph the Hamiltonian cycle is always
+
+ align:start position:0%
+graph the Hamiltonian cycle is always
+ 
+
+ align:start position:0%
+graph the Hamiltonian cycle is always
+less than equal to the cost of the
+
+ align:start position:0%
+less than equal to the cost of the
+ 
+
+ align:start position:0%
+less than equal to the cost of the
+Hamilton minimum Hamiltonian cycle is
+
+ align:start position:0%
+Hamilton minimum Hamiltonian cycle is
+ 
+
+ align:start position:0%
+Hamilton minimum Hamiltonian cycle is
+always less than equal to the one in the
+
+ align:start position:0%
+always less than equal to the one in the
+ 
+
+ align:start position:0%
+always less than equal to the one in the
+original graph. So intuitively that
+
+ align:start position:0%
+original graph. So intuitively that
+ 
+
+ align:start position:0%
+original graph. So intuitively that
+should make sense. That's the proof.
+
+ align:start position:0%
+should make sense. That's the proof.
+ 
+
+ align:start position:0%
+should make sense. That's the proof.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+next thing is something which might seem
+
+ align:start position:0%
+next thing is something which might seem
+ 
+
+ align:start position:0%
+next thing is something which might seem
+unrelated right now. Uh
+
+ align:start position:0%
+unrelated right now. Uh
+ 
+
+ align:start position:0%
+unrelated right now. Uh
+perfect matchings.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, so we've seen perfect matchings in
+
+ align:start position:0%
+So, so we've seen perfect matchings in
+ 
+
+ align:start position:0%
+So, so we've seen perfect matchings in
+the context of bipartite graphs, right?
+
+ align:start position:0%
+the context of bipartite graphs, right?
+ 
+
+ align:start position:0%
+the context of bipartite graphs, right?
+So, you find the minimum cost perfect
+
+ align:start position:0%
+So, you find the minimum cost perfect
+ 
+
+ align:start position:0%
+So, you find the minimum cost perfect
+matching. You do this flow thing. You
+
+ align:start position:0%
+matching. You do this flow thing. You
+ 
+
+ align:start position:0%
+matching. You do this flow thing. You
+send all the flow in and then you
+
+ align:start position:0%
+send all the flow in and then you
+ 
+
+ align:start position:0%
+send all the flow in and then you
+connect the vertices with the capacities
+
+ align:start position:0%
+connect the vertices with the capacities
+ 
+
+ align:start position:0%
+connect the vertices with the capacities
+and whatever. So turns out in a complete
+
+ align:start position:0%
+and whatever. So turns out in a complete
+ 
+
+ align:start position:0%
+and whatever. So turns out in a complete
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+uh you can still do perfect matching. So
+
+ align:start position:0%
+uh you can still do perfect matching. So
+ 
+
+ align:start position:0%
+uh you can still do perfect matching. So
+perfect matching is you have a bunch of
+
+ align:start position:0%
+perfect matching is you have a bunch of
+ 
+
+ align:start position:0%
+perfect matching is you have a bunch of
+so let's say you need to have an even
+
+ align:start position:0%
+so let's say you need to have an even
+ 
+
+ align:start position:0%
+so let's say you need to have an even
+number of vertices right have perfect
+
+ align:start position:0%
+number of vertices right have perfect
+ 
+
+ align:start position:0%
+number of vertices right have perfect
+matching. So let's say you have these
+
+ align:start position:0%
+matching. So let's say you have these
+ 
+
+ align:start position:0%
+matching. So let's say you have these
+vertices and so this is the perfect
+
+ align:start position:0%
+vertices and so this is the perfect
+ 
+
+ align:start position:0%
+vertices and so this is the perfect
+matching. So every vertex has one edge
+
+ align:start position:0%
+matching. So every vertex has one edge
+ 
+
+ align:start position:0%
+matching. So every vertex has one edge
+coming out of it uh exactly one edge
+
+ align:start position:0%
+coming out of it uh exactly one edge
+ 
+
+ align:start position:0%
+coming out of it uh exactly one edge
+coming out of it and it needs to be even
+
+ align:start position:0%
+coming out of it and it needs to be even
+ 
+
+ align:start position:0%
+coming out of it and it needs to be even
+because otherwise it doesn't work out.
+
+ align:start position:0%
+because otherwise it doesn't work out.
+ 
+
+ align:start position:0%
+because otherwise it doesn't work out.
+So that's perfect matching and the
+
+ align:start position:0%
+So that's perfect matching and the
+ 
+
+ align:start position:0%
+So that's perfect matching and the
+minimum cost perfect matching is the
+
+ align:start position:0%
+minimum cost perfect matching is the
+ 
+
+ align:start position:0%
+minimum cost perfect matching is the
+minimum among among all all such things
+
+ align:start position:0%
+minimum among among all all such things
+ 
+
+ align:start position:0%
+minimum among among all all such things
+and you did this for bipartite graphs.
+
+ align:start position:0%
+and you did this for bipartite graphs.
+ 
+
+ align:start position:0%
+and you did this for bipartite graphs.
+It's fine with flow networks. You can so
+
+ align:start position:0%
+It's fine with flow networks. You can so
+ 
+
+ align:start position:0%
+It's fine with flow networks. You can so
+I'm not going to go into the algorithm
+
+ align:start position:0%
+I'm not going to go into the algorithm
+ 
+
+ align:start position:0%
+I'm not going to go into the algorithm
+for this. It's kind of complicated but
+
+ align:start position:0%
+for this. It's kind of complicated but
+ 
+
+ align:start position:0%
+for this. It's kind of complicated but
+it uses linear programming and you can
+
+ align:start position:0%
+it uses linear programming and you can
+ 
+
+ align:start position:0%
+it uses linear programming and you can
+find this for complete graph and it's
+
+ align:start position:0%
+find this for complete graph and it's
+ 
+
+ align:start position:0%
+find this for complete graph and it's
+polinomial. That's good. So given a
+
+ align:start position:0%
+polinomial. That's good. So given a
+ 
+
+ align:start position:0%
+polinomial. That's good. So given a
+complete graph you can find the perfect
+
+ align:start position:0%
+complete graph you can find the perfect
+ 
+
+ align:start position:0%
+complete graph you can find the perfect
+matching is what you should assume for
+
+ align:start position:0%
+matching is what you should assume for
+ 
+
+ align:start position:0%
+matching is what you should assume for
+now. Okay. One last thing we want to
+
+ align:start position:0%
+now. Okay. One last thing we want to
+ 
+
+ align:start position:0%
+now. Okay. One last thing we want to
+introduce
+
+ align:start position:0%
+introduce
+ 
+
+ align:start position:0%
+introduce
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+so that's called it's oiler circuits. So
+
+ align:start position:0%
+so that's called it's oiler circuits. So
+ 
+
+ align:start position:0%
+so that's called it's oiler circuits. So
+who who has heard of oiler circuits
+
+ align:start position:0%
+who who has heard of oiler circuits
+ 
+
+ align:start position:0%
+who who has heard of oiler circuits
+before?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the reason we're So, okay, let's go
+
+ align:start position:0%
+so the reason we're So, okay, let's go
+ 
+
+ align:start position:0%
+so the reason we're So, okay, let's go
+back to the what we did before. We had a
+
+ align:start position:0%
+back to the what we did before. We had a
+ 
+
+ align:start position:0%
+back to the what we did before. We had a
+tree and we were the best way found to
+
+ align:start position:0%
+tree and we were the best way found to
+ 
+
+ align:start position:0%
+tree and we were the best way found to
+traverse it was just going down and
+
+ align:start position:0%
+traverse it was just going down and
+ 
+
+ align:start position:0%
+traverse it was just going down and
+going back up and going down and sort of
+
+ align:start position:0%
+going back up and going down and sort of
+ 
+
+ align:start position:0%
+going back up and going down and sort of
+messy. So, what we would rather want to
+
+ align:start position:0%
+messy. So, what we would rather want to
+ 
+
+ align:start position:0%
+messy. So, what we would rather want to
+do is sort of traverse the thing without
+
+ align:start position:0%
+do is sort of traverse the thing without
+ 
+
+ align:start position:0%
+do is sort of traverse the thing without
+repeating edges. So I don't know if
+
+ align:start position:0%
+repeating edges. So I don't know if
+ 
+
+ align:start position:0%
+repeating edges. So I don't know if
+you've probably seen this puzzle before.
+
+ align:start position:0%
+you've probably seen this puzzle before.
+ 
+
+ align:start position:0%
+you've probably seen this puzzle before.
+So you you have you have this graph
+
+ align:start position:0%
+So you you have you have this graph
+ 
+
+ align:start position:0%
+So you you have you have this graph
+given to you and the task is to draw
+
+ align:start position:0%
+given to you and the task is to draw
+ 
+
+ align:start position:0%
+given to you and the task is to draw
+this graph without lifting your pen off
+
+ align:start position:0%
+this graph without lifting your pen off
+ 
+
+ align:start position:0%
+this graph without lifting your pen off
+the paper. So for for example in this
+
+ align:start position:0%
+the paper. So for for example in this
+ 
+
+ align:start position:0%
+the paper. So for for example in this
+graph you could start here go here go
+
+ align:start position:0%
+graph you could start here go here go
+ 
+
+ align:start position:0%
+graph you could start here go here go
+here and come back and something and
+
+ align:start position:0%
+here and come back and something and
+ 
+
+ align:start position:0%
+here and come back and something and
+there you go. So you can do that then if
+
+ align:start position:0%
+there you go. So you can do that then if
+ 
+
+ align:start position:0%
+there you go. So you can do that then if
+you but if you add on like another thing
+
+ align:start position:0%
+you but if you add on like another thing
+ 
+
+ align:start position:0%
+you but if you add on like another thing
+another lobe here then you can't make a
+
+ align:start position:0%
+another lobe here then you can't make a
+ 
+
+ align:start position:0%
+another lobe here then you can't make a
+circuit. You can still make a path I
+
+ align:start position:0%
+circuit. You can still make a path I
+ 
+
+ align:start position:0%
+circuit. You can still make a path I
+believe if you add another one you can't
+
+ align:start position:0%
+believe if you add another one you can't
+ 
+
+ align:start position:0%
+believe if you add another one you can't
+even make a path. So how does this work?
+
+ align:start position:0%
+even make a path. So how does this work?
+ 
+
+ align:start position:0%
+even make a path. So how does this work?
+Let's see. So um
+
+ align:start position:0%
+Let's see. So um
+ 
+
+ align:start position:0%
+Let's see. So um
+let's say forget about the graph for
+
+ align:start position:0%
+let's say forget about the graph for
+ 
+
+ align:start position:0%
+let's say forget about the graph for
+now. Let's say you're just drawing. So
+
+ align:start position:0%
+now. Let's say you're just drawing. So
+ 
+
+ align:start position:0%
+now. Let's say you're just drawing. So
+you start somewhere. You go to a vertex.
+
+ align:start position:0%
+you start somewhere. You go to a vertex.
+ 
+
+ align:start position:0%
+you start somewhere. You go to a vertex.
+Go to another vertex. Come back. Go to
+
+ align:start position:0%
+Go to another vertex. Come back. Go to
+ 
+
+ align:start position:0%
+Go to another vertex. Come back. Go to
+this vertex. Leave it. come back. And so
+
+ align:start position:0%
+this vertex. Leave it. come back. And so
+ 
+
+ align:start position:0%
+this vertex. Leave it. come back. And so
+observe that whenever you're making this
+
+ align:start position:0%
+observe that whenever you're making this
+ 
+
+ align:start position:0%
+observe that whenever you're making this
+drawing, you go to a vertex and you
+
+ align:start position:0%
+drawing, you go to a vertex and you
+ 
+
+ align:start position:0%
+drawing, you go to a vertex and you
+leave it. Every time you hit a vertex,
+
+ align:start position:0%
+leave it. Every time you hit a vertex,
+ 
+
+ align:start position:0%
+leave it. Every time you hit a vertex,
+you leave it. Since this is a circuit,
+
+ align:start position:0%
+you leave it. Since this is a circuit,
+ 
+
+ align:start position:0%
+you leave it. Since this is a circuit,
+you just loop around and every time you
+
+ align:start position:0%
+you just loop around and every time you
+ 
+
+ align:start position:0%
+you just loop around and every time you
+enter a vertex, you have to leave it.
+
+ align:start position:0%
+enter a vertex, you have to leave it.
+ 
+
+ align:start position:0%
+enter a vertex, you have to leave it.
+What that means is that even though this
+
+ align:start position:0%
+What that means is that even though this
+ 
+
+ align:start position:0%
+What that means is that even though this
+is not directed, if you like drew out
+
+ align:start position:0%
+is not directed, if you like drew out
+ 
+
+ align:start position:0%
+is not directed, if you like drew out
+the actual path, you would see the
+
+ align:start position:0%
+the actual path, you would see the
+ 
+
+ align:start position:0%
+the actual path, you would see the
+number of vertices go number of edges
+
+ align:start position:0%
+number of vertices go number of edges
+ 
+
+ align:start position:0%
+number of vertices go number of edges
+going into a vertex is equal number of
+
+ align:start position:0%
+going into a vertex is equal number of
+ 
+
+ align:start position:0%
+going into a vertex is equal number of
+ones leaving. Which means that every
+
+ align:start position:0%
+ones leaving. Which means that every
+ 
+
+ align:start position:0%
+ones leaving. Which means that every
+degree has to be even.
+
+ align:start position:0%
+degree has to be even.
+ 
+
+ align:start position:0%
+degree has to be even.
+So if you go and look at this graph
+
+ align:start position:0%
+So if you go and look at this graph
+ 
+
+ align:start position:0%
+So if you go and look at this graph
+which is with added loes, this degree is
+
+ align:start position:0%
+which is with added loes, this degree is
+ 
+
+ align:start position:0%
+which is with added loes, this degree is
+not even. Neither is this, neither is
+
+ align:start position:0%
+not even. Neither is this, neither is
+ 
+
+ align:start position:0%
+not even. Neither is this, neither is
+this, neither is this. They're all five,
+
+ align:start position:0%
+this, neither is this. They're all five,
+ 
+
+ align:start position:0%
+this, neither is this. They're all five,
+I think. Yeah, they're all five. Which
+
+ align:start position:0%
+I think. Yeah, they're all five. Which
+ 
+
+ align:start position:0%
+I think. Yeah, they're all five. Which
+means that this this can never have
+
+ align:start position:0%
+means that this this can never have
+ 
+
+ align:start position:0%
+means that this this can never have
+oiler circuit. So a graph can only have
+
+ align:start position:0%
+oiler circuit. So a graph can only have
+ 
+
+ align:start position:0%
+oiler circuit. So a graph can only have
+an oiler circuit if it has even degrees
+
+ align:start position:0%
+an oiler circuit if it has even degrees
+ 
+
+ align:start position:0%
+an oiler circuit if it has even degrees
+for every vertex.
+
+ align:start position:0%
+for every vertex.
+ 
+
+ align:start position:0%
+for every vertex.
+And the other way is also true. If a
+
+ align:start position:0%
+And the other way is also true. If a
+ 
+
+ align:start position:0%
+And the other way is also true. If a
+graph has even degrees on every vertex,
+
+ align:start position:0%
+graph has even degrees on every vertex,
+ 
+
+ align:start position:0%
+graph has even degrees on every vertex,
+then it must have an oiler circuit.
+
+ align:start position:0%
+then it must have an oiler circuit.
+ 
+
+ align:start position:0%
+then it must have an oiler circuit.
+That's not harder to prove, but like
+
+ align:start position:0%
+That's not harder to prove, but like
+ 
+
+ align:start position:0%
+That's not harder to prove, but like
+there's a constructive algorithm you can
+
+ align:start position:0%
+there's a constructive algorithm you can
+ 
+
+ align:start position:0%
+there's a constructive algorithm you can
+use. So let's say you're given this
+
+ align:start position:0%
+use. So let's say you're given this
+ 
+
+ align:start position:0%
+use. So let's say you're given this
+graph for instance. You would just you
+
+ align:start position:0%
+graph for instance. You would just you
+ 
+
+ align:start position:0%
+graph for instance. You would just you
+would simply go through the graph just
+
+ align:start position:0%
+would simply go through the graph just
+ 
+
+ align:start position:0%
+would simply go through the graph just
+like start at some random node and then
+
+ align:start position:0%
+like start at some random node and then
+ 
+
+ align:start position:0%
+like start at some random node and then
+like go through can keep following edges
+
+ align:start position:0%
+like go through can keep following edges
+ 
+
+ align:start position:0%
+like go through can keep following edges
+till you can no longer follow edges. So
+
+ align:start position:0%
+till you can no longer follow edges. So
+ 
+
+ align:start position:0%
+till you can no longer follow edges. So
+let's say you stop here then you pick
+
+ align:start position:0%
+let's say you stop here then you pick
+ 
+
+ align:start position:0%
+let's say you stop here then you pick
+another edge and start and so on and
+
+ align:start position:0%
+another edge and start and so on and
+ 
+
+ align:start position:0%
+another edge and start and so on and
+then you can like splice these cycles
+
+ align:start position:0%
+then you can like splice these cycles
+ 
+
+ align:start position:0%
+then you can like splice these cycles
+together at some point. So it's kind of
+
+ align:start position:0%
+together at some point. So it's kind of
+ 
+
+ align:start position:0%
+together at some point. So it's kind of
+a hand wavy argument but it should be
+
+ align:start position:0%
+a hand wavy argument but it should be
+ 
+
+ align:start position:0%
+a hand wavy argument but it should be
+sort of intuitive why you can construct
+
+ align:start position:0%
+sort of intuitive why you can construct
+ 
+
+ align:start position:0%
+sort of intuitive why you can construct
+another path given an even degree.
+
+ align:start position:0%
+another path given an even degree.
+ 
+
+ align:start position:0%
+another path given an even degree.
+You just perform searches. You just
+
+ align:start position:0%
+You just perform searches. You just
+ 
+
+ align:start position:0%
+You just perform searches. You just
+create cycles and you splice them
+
+ align:start position:0%
+create cycles and you splice them
+ 
+
+ align:start position:0%
+create cycles and you splice them
+together. But for now, I just take it as
+
+ align:start position:0%
+together. But for now, I just take it as
+ 
+
+ align:start position:0%
+together. But for now, I just take it as
+fact that give a graph as an oiler
+
+ align:start position:0%
+fact that give a graph as an oiler
+ 
+
+ align:start position:0%
+fact that give a graph as an oiler
+circuit as in you can draw it without
+
+ align:start position:0%
+circuit as in you can draw it without
+ 
+
+ align:start position:0%
+circuit as in you can draw it without
+lifting your pen off if and only if
+
+ align:start position:0%
+lifting your pen off if and only if
+ 
+
+ align:start position:0%
+lifting your pen off if and only if
+every vertex has even degree. So why is
+
+ align:start position:0%
+every vertex has even degree. So why is
+ 
+
+ align:start position:0%
+every vertex has even degree. So why is
+that interesting? So let's say we could
+
+ align:start position:0%
+that interesting? So let's say we could
+ 
+
+ align:start position:0%
+that interesting? So let's say we could
+add some edges to our tree and turn it
+
+ align:start position:0%
+add some edges to our tree and turn it
+ 
+
+ align:start position:0%
+add some edges to our tree and turn it
+into turn it into one of those nice
+
+ align:start position:0%
+into turn it into one of those nice
+ 
+
+ align:start position:0%
+into turn it into one of those nice
+graphs. Right? Now this is not right.
+
+ align:start position:0%
+graphs. Right? Now this is not right.
+ 
+
+ align:start position:0%
+graphs. Right? Now this is not right.
+This is vertic degree 1 degree 1 degree
+
+ align:start position:0%
+This is vertic degree 1 degree 1 degree
+ 
+
+ align:start position:0%
+This is vertic degree 1 degree 1 degree
+3 degree 1 degree 1 degree three. All of
+
+ align:start position:0%
+3 degree 1 degree 1 degree three. All of
+ 
+
+ align:start position:0%
+3 degree 1 degree 1 degree three. All of
+them are odd but that's not good. But
+
+ align:start position:0%
+them are odd but that's not good. But
+ 
+
+ align:start position:0%
+them are odd but that's not good. But
+let's say you could add some edges in,
+
+ align:start position:0%
+let's say you could add some edges in,
+ 
+
+ align:start position:0%
+let's say you could add some edges in,
+turn it to an oiler circuit and then you
+
+ align:start position:0%
+turn it to an oiler circuit and then you
+ 
+
+ align:start position:0%
+turn it to an oiler circuit and then you
+could do a nice reversal of it and maybe
+
+ align:start position:0%
+could do a nice reversal of it and maybe
+ 
+
+ align:start position:0%
+could do a nice reversal of it and maybe
+that'll give you a better approximation.
+
+ align:start position:0%
+that'll give you a better approximation.
+ 
+
+ align:start position:0%
+that'll give you a better approximation.
+So with that hope, let's look at the
+
+ align:start position:0%
+So with that hope, let's look at the
+ 
+
+ align:start position:0%
+So with that hope, let's look at the
+algorithm.
+
+ align:start position:0%
+algorithm.
+ 
+
+ align:start position:0%
+algorithm.
+So what you do is you go back to your
+
+ align:start position:0%
+So what you do is you go back to your
+ 
+
+ align:start position:0%
+So what you do is you go back to your
+tree.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's just leave it at that. So
+
+ align:start position:0%
+Let's just leave it at that. So
+ 
+
+ align:start position:0%
+Let's just leave it at that. So
+now let's see. So this is degree two.
+
+ align:start position:0%
+now let's see. So this is degree two.
+ 
+
+ align:start position:0%
+now let's see. So this is degree two.
+That's good. This is degree three.
+
+ align:start position:0%
+That's good. This is degree three.
+ 
+
+ align:start position:0%
+That's good. This is degree three.
+That's not good. Degree one. This is
+
+ align:start position:0%
+That's not good. Degree one. This is
+ 
+
+ align:start position:0%
+That's not good. Degree one. This is
+fine. This is degree one. This also has
+
+ align:start position:0%
+fine. This is degree one. This also has
+ 
+
+ align:start position:0%
+fine. This is degree one. This also has
+degree one. This is degree three.
+
+ align:start position:0%
+degree one. This is degree three.
+ 
+
+ align:start position:0%
+degree one. This is degree three.
+Actually, let's let's get rid of this.
+
+ align:start position:0%
+Actually, let's let's get rid of this.
+ 
+
+ align:start position:0%
+Actually, let's let's get rid of this.
+It does not have degree three. That's a
+
+ align:start position:0%
+It does not have degree three. That's a
+ 
+
+ align:start position:0%
+It does not have degree three. That's a
+lot of vertices. Okay, there we go.
+
+ align:start position:0%
+lot of vertices. Okay, there we go.
+ 
+
+ align:start position:0%
+lot of vertices. Okay, there we go.
+So in this graph, you see that you have
+
+ align:start position:0%
+So in this graph, you see that you have
+ 
+
+ align:start position:0%
+So in this graph, you see that you have
+1 2 3 4 five vertices which have degree
+
+ align:start position:0%
+1 2 3 4 five vertices which have degree
+ 
+
+ align:start position:0%
+1 2 3 4 five vertices which have degree
+odd. So now we would like to add some
+
+ align:start position:0%
+odd. So now we would like to add some
+ 
+
+ align:start position:0%
+odd. So now we would like to add some
+edges to make to turn this set of turn
+
+ align:start position:0%
+edges to make to turn this set of turn
+ 
+
+ align:start position:0%
+edges to make to turn this set of turn
+this into another circuitable graph. So
+
+ align:start position:0%
+this into another circuitable graph. So
+ 
+
+ align:start position:0%
+this into another circuitable graph. So
+how do we do that? So let's call the set
+
+ align:start position:0%
+how do we do that? So let's call the set
+ 
+
+ align:start position:0%
+how do we do that? So let's call the set
+of odd edges S.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's odd vertices. Sorry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you take the set of odd degree
+
+ align:start position:0%
+So you take the set of odd degree
+ 
+
+ align:start position:0%
+So you take the set of odd degree
+vertices. Now
+
+ align:start position:0%
+vertices. Now
+ 
+
+ align:start position:0%
+vertices. Now
+go back to perfect matchings. So what
+
+ align:start position:0%
+go back to perfect matchings. So what
+ 
+
+ align:start position:0%
+go back to perfect matchings. So what
+does a perfect matching do? It adds
+
+ align:start position:0%
+does a perfect matching do? It adds
+ 
+
+ align:start position:0%
+does a perfect matching do? It adds
+edges to that graph so that everything
+
+ align:start position:0%
+edges to that graph so that everything
+ 
+
+ align:start position:0%
+edges to that graph so that everything
+gets degree increased by one.
+
+ align:start position:0%
+gets degree increased by one.
+ 
+
+ align:start position:0%
+gets degree increased by one.
+So if you increase the degree of all the
+
+ align:start position:0%
+So if you increase the degree of all the
+ 
+
+ align:start position:0%
+So if you increase the degree of all the
+odd vertices by one, everything turns
+
+ align:start position:0%
+odd vertices by one, everything turns
+ 
+
+ align:start position:0%
+odd vertices by one, everything turns
+even. Right?
+
+ align:start position:0%
+even. Right?
+ 
+
+ align:start position:0%
+even. Right?
+So you take the set of odd vertices.
+
+ align:start position:0%
+So you take the set of odd vertices.
+ 
+
+ align:start position:0%
+So you take the set of odd vertices.
+Okay. Another thing to observe, realize
+
+ align:start position:0%
+Okay. Another thing to observe, realize
+ 
+
+ align:start position:0%
+Okay. Another thing to observe, realize
+that how many odd verses can you have?
+
+ align:start position:0%
+that how many odd verses can you have?
+ 
+
+ align:start position:0%
+that how many odd verses can you have?
+Can you have an odd number of odd
+
+ align:start position:0%
+Can you have an odd number of odd
+ 
+
+ align:start position:0%
+Can you have an odd number of odd
+vertices? Because that would that would
+
+ align:start position:0%
+vertices? Because that would that would
+ 
+
+ align:start position:0%
+vertices? Because that would that would
+that would screw up the whole thing
+
+ align:start position:0%
+that would screw up the whole thing
+ 
+
+ align:start position:0%
+that would screw up the whole thing
+where we needed an even number of
+
+ align:start position:0%
+where we needed an even number of
+ 
+
+ align:start position:0%
+where we needed an even number of
+things.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, so why why could can you why why is
+
+ align:start position:0%
+So, so why why could can you why why is
+ 
+
+ align:start position:0%
+So, so why why could can you why why is
+that not possible? Why can you not have
+
+ align:start position:0%
+that not possible? Why can you not have
+ 
+
+ align:start position:0%
+that not possible? Why can you not have
+an odd number of odd vertices?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, the thing is that
+
+ align:start position:0%
+So, the thing is that
+ 
+
+ align:start position:0%
+So, the thing is that
+let's say let's say you have some graph
+
+ align:start position:0%
+let's say let's say you have some graph
+ 
+
+ align:start position:0%
+let's say let's say you have some graph
+and what is the sum of the degrees of
+
+ align:start position:0%
+and what is the sum of the degrees of
+ 
+
+ align:start position:0%
+and what is the sum of the degrees of
+the graph? Let's move to a different
+
+ align:start position:0%
+the graph? Let's move to a different
+ 
+
+ align:start position:0%
+the graph? Let's move to a different
+board for this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you have a graph G and you want the
+
+ align:start position:0%
+So you have a graph G and you want the
+ 
+
+ align:start position:0%
+So you have a graph G and you want the
+sum of degrees. So DI is the degree for
+
+ align:start position:0%
+sum of degrees. So DI is the degree for
+ 
+
+ align:start position:0%
+sum of degrees. So DI is the degree for
+all V. So what is this equal to? So
+
+ align:start position:0%
+all V. So what is this equal to? So
+ 
+
+ align:start position:0%
+all V. So what is this equal to? So
+let's say you have this graph.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So now if you count the degrees of every
+
+ align:start position:0%
+So now if you count the degrees of every
+ 
+
+ align:start position:0%
+So now if you count the degrees of every
+vertex,
+
+ align:start position:0%
+vertex,
+ 
+
+ align:start position:0%
+vertex,
+you're basically counting the number of
+
+ align:start position:0%
+you're basically counting the number of
+ 
+
+ align:start position:0%
+you're basically counting the number of
+edges coming out, which means that every
+
+ align:start position:0%
+edges coming out, which means that every
+ 
+
+ align:start position:0%
+edges coming out, which means that every
+edge is counted twice. Once for its this
+
+ align:start position:0%
+edge is counted twice. Once for its this
+ 
+
+ align:start position:0%
+edge is counted twice. Once for its this
+end point, once for this end point. This
+
+ align:start position:0%
+end point, once for this end point. This
+ 
+
+ align:start position:0%
+end point, once for this end point. This
+edge is counted twice for here and here.
+
+ align:start position:0%
+edge is counted twice for here and here.
+ 
+
+ align:start position:0%
+edge is counted twice for here and here.
+This edge is also counted twice. So
+
+ align:start position:0%
+This edge is also counted twice. So
+ 
+
+ align:start position:0%
+This edge is also counted twice. So
+basically the sum of the degrees is
+
+ align:start position:0%
+basically the sum of the degrees is
+ 
+
+ align:start position:0%
+basically the sum of the degrees is
+nothing but 2 * mod of e. Does that make
+
+ align:start position:0%
+nothing but 2 * mod of e. Does that make
+ 
+
+ align:start position:0%
+nothing but 2 * mod of e. Does that make
+sense? Right?
+
+ align:start position:0%
+sense? Right?
+ 
+
+ align:start position:0%
+sense? Right?
+So this is even. Now let's say you take
+
+ align:start position:0%
+So this is even. Now let's say you take
+ 
+
+ align:start position:0%
+So this is even. Now let's say you take
+only the odd vertices out. So you the
+
+ align:start position:0%
+only the odd vertices out. So you the
+ 
+
+ align:start position:0%
+only the odd vertices out. So you the
+even vertices are good. This is good.
+
+ align:start position:0%
+even vertices are good. This is good.
+ 
+
+ align:start position:0%
+even vertices are good. This is good.
+This is good. This is not good. This is
+
+ align:start position:0%
+This is good. This is not good. This is
+ 
+
+ align:start position:0%
+This is good. This is not good. This is
+also not good. This is Yeah. So these
+
+ align:start position:0%
+also not good. This is Yeah. So these
+ 
+
+ align:start position:0%
+also not good. This is Yeah. So these
+are the odd vertices.
+
+ align:start position:0%
+are the odd vertices.
+ 
+
+ align:start position:0%
+are the odd vertices.
+So the sum of the degrees of the even
+
+ align:start position:0%
+So the sum of the degrees of the even
+ 
+
+ align:start position:0%
+So the sum of the degrees of the even
+vertices are by definition even even. So
+
+ align:start position:0%
+vertices are by definition even even. So
+ 
+
+ align:start position:0%
+vertices are by definition even even. So
+if you remove them the sum of the odd
+
+ align:start position:0%
+if you remove them the sum of the odd
+ 
+
+ align:start position:0%
+if you remove them the sum of the odd
+vertices should also remain even.
+
+ align:start position:0%
+vertices should also remain even.
+ 
+
+ align:start position:0%
+vertices should also remain even.
+And so you have the sum of odd degrees
+
+ align:start position:0%
+And so you have the sum of odd degrees
+ 
+
+ align:start position:0%
+And so you have the sum of odd degrees
+becoming even which means that you need
+
+ align:start position:0%
+becoming even which means that you need
+ 
+
+ align:start position:0%
+becoming even which means that you need
+to have an even number of them. Make
+
+ align:start position:0%
+to have an even number of them. Make
+ 
+
+ align:start position:0%
+to have an even number of them. Make
+sense?
+
+ align:start position:0%
+sense?
+ 
+
+ align:start position:0%
+sense?
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+going back to this, so there's a lot of
+
+ align:start position:0%
+going back to this, so there's a lot of
+ 
+
+ align:start position:0%
+going back to this, so there's a lot of
+lot of branching off here, but going
+
+ align:start position:0%
+lot of branching off here, but going
+ 
+
+ align:start position:0%
+lot of branching off here, but going
+back to the main point here is that you
+
+ align:start position:0%
+back to the main point here is that you
+ 
+
+ align:start position:0%
+back to the main point here is that you
+have an even number of odd vertices. So
+
+ align:start position:0%
+have an even number of odd vertices. So
+ 
+
+ align:start position:0%
+have an even number of odd vertices. So
+consider the restriction of the original
+
+ align:start position:0%
+consider the restriction of the original
+ 
+
+ align:start position:0%
+consider the restriction of the original
+graph G to this set S. So now we're
+
+ align:start position:0%
+graph G to this set S. So now we're
+ 
+
+ align:start position:0%
+graph G to this set S. So now we're
+going to the first thing we did there
+
+ align:start position:0%
+going to the first thing we did there
+ 
+
+ align:start position:0%
+going to the first thing we did there
+where we considered a restriction of the
+
+ align:start position:0%
+where we considered a restriction of the
+ 
+
+ align:start position:0%
+where we considered a restriction of the
+graph to a certain set of vertices. So
+
+ align:start position:0%
+graph to a certain set of vertices. So
+ 
+
+ align:start position:0%
+graph to a certain set of vertices. So
+you take the set. So 1 2 3 4 5. So you
+
+ align:start position:0%
+you take the set. So 1 2 3 4 5. So you
+ 
+
+ align:start position:0%
+you take the set. So 1 2 3 4 5. So you
+take these five vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you consider the graph that is
+
+ align:start position:0%
+and you consider the graph that is
+ 
+
+ align:start position:0%
+and you consider the graph that is
+restricted to these five vertices. Oh
+
+ align:start position:0%
+restricted to these five vertices. Oh
+ 
+
+ align:start position:0%
+restricted to these five vertices. Oh
+sorry there should be six.
+
+ align:start position:0%
+sorry there should be six.
+ 
+
+ align:start position:0%
+sorry there should be six.
+Oh there's there we go. That's the other
+
+ align:start position:0%
+Oh there's there we go. That's the other
+ 
+
+ align:start position:0%
+Oh there's there we go. That's the other
+one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So those are your six vertices which
+
+ align:start position:0%
+So those are your six vertices which
+ 
+
+ align:start position:0%
+So those are your six vertices which
+have odd degrees. Now you find a perfect
+
+ align:start position:0%
+have odd degrees. Now you find a perfect
+ 
+
+ align:start position:0%
+have odd degrees. Now you find a perfect
+matching with your polinomal sign
+
+ align:start position:0%
+matching with your polinomal sign
+ 
+
+ align:start position:0%
+matching with your polinomal sign
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+and you get something. So you can now
+
+ align:start position:0%
+and you get something. So you can now
+ 
+
+ align:start position:0%
+and you get something. So you can now
+add those edges back in here. So these
+
+ align:start position:0%
+add those edges back in here. So these
+ 
+
+ align:start position:0%
+add those edges back in here. So these
+are your new edges and let's say
+
+ align:start position:0%
+are your new edges and let's say
+ 
+
+ align:start position:0%
+are your new edges and let's say
+and something
+
+ align:start position:0%
+and something
+ 
+
+ align:start position:0%
+and something
+this one. Okay. So you get three new
+
+ align:start position:0%
+this one. Okay. So you get three new
+ 
+
+ align:start position:0%
+this one. Okay. So you get three new
+edges and now realize that all the
+
+ align:start position:0%
+edges and now realize that all the
+ 
+
+ align:start position:0%
+edges and now realize that all the
+degrees are now even. So now you can do
+
+ align:start position:0%
+degrees are now even. So now you can do
+ 
+
+ align:start position:0%
+degrees are now even. So now you can do
+your circuit also. So let's call this
+
+ align:start position:0%
+your circuit also. So let's call this
+ 
+
+ align:start position:0%
+your circuit also. So let's call this
+matching M. So this is a set of edges M.
+
+ align:start position:0%
+matching M. So this is a set of edges M.
+ 
+
+ align:start position:0%
+matching M. So this is a set of edges M.
+Let's call the original tree T and the
+
+ align:start position:0%
+Let's call the original tree T and the
+ 
+
+ align:start position:0%
+Let's call the original tree T and the
+new thing that is formed is T union M.
+
+ align:start position:0%
+new thing that is formed is T union M.
+ 
+
+ align:start position:0%
+new thing that is formed is T union M.
+So you're taking all the edges from T
+
+ align:start position:0%
+So you're taking all the edges from T
+ 
+
+ align:start position:0%
+So you're taking all the edges from T
+and you're adding all the edges from M.
+
+ align:start position:0%
+and you're adding all the edges from M.
+ 
+
+ align:start position:0%
+and you're adding all the edges from M.
+So realize that you can have multiple
+
+ align:start position:0%
+So realize that you can have multiple
+ 
+
+ align:start position:0%
+So realize that you can have multiple
+edges, but that's fine because oiler
+
+ align:start position:0%
+edges, but that's fine because oiler
+ 
+
+ align:start position:0%
+edges, but that's fine because oiler
+circuits allow you to have multiple
+
+ align:start position:0%
+circuits allow you to have multiple
+ 
+
+ align:start position:0%
+circuits allow you to have multiple
+edges. So now you take this graph and
+
+ align:start position:0%
+edges. So now you take this graph and
+ 
+
+ align:start position:0%
+edges. So now you take this graph and
+you find this oiler circuit.
+
+ align:start position:0%
+you find this oiler circuit.
+ 
+
+ align:start position:0%
+you find this oiler circuit.
+So that is basically this thing. So the
+
+ align:start position:0%
+So that is basically this thing. So the
+ 
+
+ align:start position:0%
+So that is basically this thing. So the
+set of edges in some order and that
+
+ align:start position:0%
+set of edges in some order and that
+ 
+
+ align:start position:0%
+set of edges in some order and that
+order exists. So the cost of the oiler
+
+ align:start position:0%
+order exists. So the cost of the oiler
+ 
+
+ align:start position:0%
+order exists. So the cost of the oiler
+circuit let's call it C is equal to the
+
+ align:start position:0%
+circuit let's call it C is equal to the
+ 
+
+ align:start position:0%
+circuit let's call it C is equal to the
+cost of T plus the cost of M right
+
+ align:start position:0%
+cost of T plus the cost of M right
+ 
+
+ align:start position:0%
+cost of T plus the cost of M right
+because you're traversing all the edges
+
+ align:start position:0%
+because you're traversing all the edges
+ 
+
+ align:start position:0%
+because you're traversing all the edges
+in your graph. So that is the cost
+
+ align:start position:0%
+in your graph. So that is the cost
+ 
+
+ align:start position:0%
+in your graph. So that is the cost
+circuit. Now my claim is that so this
+
+ align:start position:0%
+circuit. Now my claim is that so this
+ 
+
+ align:start position:0%
+circuit. Now my claim is that so this
+this is visiting all the nodes in the
+
+ align:start position:0%
+this is visiting all the nodes in the
+ 
+
+ align:start position:0%
+this is visiting all the nodes in the
+graph and remember you can do the whole
+
+ align:start position:0%
+graph and remember you can do the whole
+ 
+
+ align:start position:0%
+graph and remember you can do the whole
+dup duplication argument from before
+
+ align:start position:0%
+dup duplication argument from before
+ 
+
+ align:start position:0%
+dup duplication argument from before
+where so where was that ah there so you
+
+ align:start position:0%
+where so where was that ah there so you
+ 
+
+ align:start position:0%
+where so where was that ah there so you
+can do the duplication argument so
+
+ align:start position:0%
+can do the duplication argument so
+ 
+
+ align:start position:0%
+can do the duplication argument so
+you're visiting all the edges in the
+
+ align:start position:0%
+you're visiting all the edges in the
+ 
+
+ align:start position:0%
+you're visiting all the edges in the
+graph all the vertices in the graph you
+
+ align:start position:0%
+graph all the vertices in the graph you
+ 
+
+ align:start position:0%
+graph all the vertices in the graph you
+remove the duplicates and you have a
+
+ align:start position:0%
+remove the duplicates and you have a
+ 
+
+ align:start position:0%
+remove the duplicates and you have a
+valid path now let's see if this valid
+
+ align:start position:0%
+valid path now let's see if this valid
+ 
+
+ align:start position:0%
+valid path now let's see if this valid
+path is actually
+
+ align:start position:0%
+path is actually
+ 
+
+ align:start position:0%
+path is actually
+uh a better approximation
+
+ align:start position:0%
+uh a better approximation
+ 
+
+ align:start position:0%
+uh a better approximation
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again you will go from C. So this C
+
+ align:start position:0%
+so again you will go from C. So this C
+ 
+
+ align:start position:0%
+so again you will go from C. So this C
+will go to C dash
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this will give you as before uh cost
+
+ align:start position:0%
+and this will give you as before uh cost
+ 
+
+ align:start position:0%
+and this will give you as before uh cost
+of C dash is less than equal to cost of
+
+ align:start position:0%
+of C dash is less than equal to cost of
+ 
+
+ align:start position:0%
+of C dash is less than equal to cost of
+C. So now you're only interested in cost
+
+ align:start position:0%
+C. So now you're only interested in cost
+ 
+
+ align:start position:0%
+C. So now you're only interested in cost
+of C. So what are we doing there? So we
+
+ align:start position:0%
+of C. So what are we doing there? So we
+ 
+
+ align:start position:0%
+of C. So what are we doing there? So we
+know that the cost of
+
+ align:start position:0%
+know that the cost of
+ 
+
+ align:start position:0%
+know that the cost of
+C is equal to cost of T plus the cost of
+
+ align:start position:0%
+C is equal to cost of T plus the cost of
+ 
+
+ align:start position:0%
+C is equal to cost of T plus the cost of
+M.
+
+ align:start position:0%
+M.
+ 
+
+ align:start position:0%
+M.
+So from the previous problem we know
+
+ align:start position:0%
+So from the previous problem we know
+ 
+
+ align:start position:0%
+So from the previous problem we know
+that the cost of t is less than equal to
+
+ align:start position:0%
+that the cost of t is less than equal to
+ 
+
+ align:start position:0%
+that the cost of t is less than equal to
+the cost of h star of g right. So this
+
+ align:start position:0%
+the cost of h star of g right. So this
+ 
+
+ align:start position:0%
+the cost of h star of g right. So this
+is less than equal to cost of
+
+ align:start position:0%
+is less than equal to cost of
+ 
+
+ align:start position:0%
+is less than equal to cost of
+h star g.
+
+ align:start position:0%
+h star g.
+ 
+
+ align:start position:0%
+h star g.
+So this guy is less than the optimal
+
+ align:start position:0%
+So this guy is less than the optimal
+ 
+
+ align:start position:0%
+So this guy is less than the optimal
+hamiltonian path. What about this guy?
+
+ align:start position:0%
+hamiltonian path. What about this guy?
+ 
+
+ align:start position:0%
+hamiltonian path. What about this guy?
+Well, so let's take let's look at the
+
+ align:start position:0%
+Well, so let's take let's look at the
+ 
+
+ align:start position:0%
+Well, so let's take let's look at the
+actual H star G again.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So actually let's look at H star S.
+
+ align:start position:0%
+So actually let's look at H star S.
+ 
+
+ align:start position:0%
+So actually let's look at H star S.
+So S remember that S is the set of odd
+
+ align:start position:0%
+So S remember that S is the set of odd
+ 
+
+ align:start position:0%
+So S remember that S is the set of odd
+vertices and that is where this matching
+
+ align:start position:0%
+vertices and that is where this matching
+ 
+
+ align:start position:0%
+vertices and that is where this matching
+is done. So H star S is nothing but the
+
+ align:start position:0%
+is done. So H star S is nothing but the
+ 
+
+ align:start position:0%
+is done. So H star S is nothing but the
+optimal Hamiltonian cycle on that
+
+ align:start position:0%
+optimal Hamiltonian cycle on that
+ 
+
+ align:start position:0%
+optimal Hamiltonian cycle on that
+restricted graph. Okay, from our
+
+ align:start position:0%
+restricted graph. Okay, from our
+ 
+
+ align:start position:0%
+restricted graph. Okay, from our
+previous lema which I which is down
+
+ align:start position:0%
+previous lema which I which is down
+ 
+
+ align:start position:0%
+previous lema which I which is down
+here, we know that H star of S is less
+
+ align:start position:0%
+here, we know that H star of S is less
+ 
+
+ align:start position:0%
+here, we know that H star of S is less
+than H star of G.
+
+ align:start position:0%
+than H star of G.
+ 
+
+ align:start position:0%
+than H star of G.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+we know that cost of
+
+ align:start position:0%
+we know that cost of
+ 
+
+ align:start position:0%
+we know that cost of
+is less than equal to cost of whatever
+
+ align:start position:0%
+is less than equal to cost of whatever
+ 
+
+ align:start position:0%
+is less than equal to cost of whatever
+G.
+
+ align:start position:0%
+G.
+ 
+
+ align:start position:0%
+G.
+So now let's look at just look at HR.
+
+ align:start position:0%
+So now let's look at just look at HR.
+ 
+
+ align:start position:0%
+So now let's look at just look at HR.
+Now we construct a matching.
+
+ align:start position:0%
+Now we construct a matching.
+ 
+
+ align:start position:0%
+Now we construct a matching.
+We take every other edge. You take this
+
+ align:start position:0%
+We take every other edge. You take this
+ 
+
+ align:start position:0%
+We take every other edge. You take this
+one, you would take this one, you take
+
+ align:start position:0%
+one, you would take this one, you take
+ 
+
+ align:start position:0%
+one, you would take this one, you take
+this one and
+
+ align:start position:0%
+this one and
+ 
+
+ align:start position:0%
+this one and
+and look at the alternate set also. So
+
+ align:start position:0%
+and look at the alternate set also. So
+ 
+
+ align:start position:0%
+and look at the alternate set also. So
+take this one and this one and this one.
+
+ align:start position:0%
+take this one and this one and this one.
+ 
+
+ align:start position:0%
+take this one and this one and this one.
+So look at the blue set and the red set.
+
+ align:start position:0%
+So look at the blue set and the red set.
+ 
+
+ align:start position:0%
+So look at the blue set and the red set.
+Since it's part of a Hamiltonian cycle,
+
+ align:start position:0%
+Since it's part of a Hamiltonian cycle,
+ 
+
+ align:start position:0%
+Since it's part of a Hamiltonian cycle,
+they're both matchings, right?
+
+ align:start position:0%
+they're both matchings, right?
+ 
+
+ align:start position:0%
+they're both matchings, right?
+So let's call the red one M1 and the
+
+ align:start position:0%
+So let's call the red one M1 and the
+ 
+
+ align:start position:0%
+So let's call the red one M1 and the
+blue one M2.
+
+ align:start position:0%
+blue one M2.
+ 
+
+ align:start position:0%
+blue one M2.
+So I'm not saying they're perfect
+
+ align:start position:0%
+So I'm not saying they're perfect
+ 
+
+ align:start position:0%
+So I'm not saying they're perfect
+matchings. They're they're not the min
+
+ align:start position:0%
+matchings. They're they're not the min
+ 
+
+ align:start position:0%
+matchings. They're they're not the min
+minimum matchings, but they're
+
+ align:start position:0%
+minimum matchings, but they're
+ 
+
+ align:start position:0%
+minimum matchings, but they're
+definitely perfect matchings. And
+
+ align:start position:0%
+definitely perfect matchings. And
+ 
+
+ align:start position:0%
+definitely perfect matchings. And
+because they're because we know the
+
+ align:start position:0%
+because they're because we know the
+ 
+
+ align:start position:0%
+because they're because we know the
+perfect matching is M
+
+ align:start position:0%
+perfect matching is M
+ 
+
+ align:start position:0%
+perfect matching is M
+or the minimum matching is M. Cost of M
+
+ align:start position:0%
+or the minimum matching is M. Cost of M
+ 
+
+ align:start position:0%
+or the minimum matching is M. Cost of M
+is less than equal to
+
+ align:start position:0%
+is less than equal to
+ 
+
+ align:start position:0%
+is less than equal to
+cost of M1.
+
+ align:start position:0%
+cost of M1.
+ 
+
+ align:start position:0%
+cost of M1.
+And also the cost of M is less than
+
+ align:start position:0%
+And also the cost of M is less than
+ 
+
+ align:start position:0%
+And also the cost of M is less than
+equal to the cost of
+
+ align:start position:0%
+equal to the cost of
+ 
+
+ align:start position:0%
+equal to the cost of
+M2.
+
+ align:start position:0%
+M2.
+ 
+
+ align:start position:0%
+M2.
+Make sense? Because M was the minimum
+
+ align:start position:0%
+Make sense? Because M was the minimum
+ 
+
+ align:start position:0%
+Make sense? Because M was the minimum
+cost matching. you have cost of M is
+
+ align:start position:0%
+cost matching. you have cost of M is
+ 
+
+ align:start position:0%
+cost matching. you have cost of M is
+less than any other matching which is
+
+ align:start position:0%
+less than any other matching which is
+ 
+
+ align:start position:0%
+less than any other matching which is
+constructed from this again. So this
+
+ align:start position:0%
+constructed from this again. So this
+ 
+
+ align:start position:0%
+constructed from this again. So this
+implies that the cost of M
+
+ align:start position:0%
+implies that the cost of M
+ 
+
+ align:start position:0%
+implies that the cost of M
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+less than equal to
+
+ align:start position:0%
+less than equal to
+ 
+
+ align:start position:0%
+less than equal to
+half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cost of okay let's not let's not write
+
+ align:start position:0%
+cost of okay let's not let's not write
+ 
+
+ align:start position:0%
+cost of okay let's not let's not write
+this here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's get a different board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this here so cost of H that's less than
+
+ align:start position:0%
+this here so cost of H that's less than
+ 
+
+ align:start position:0%
+this here so cost of H that's less than
+equal to half
+
+ align:start position:0%
+equal to half
+ 
+
+ align:start position:0%
+equal to half
+cost of M1
+
+ align:start position:0%
+cost of M1
+ 
+
+ align:start position:0%
+cost of M1
+plus cost of M2.
+
+ align:start position:0%
+plus cost of M2.
+ 
+
+ align:start position:0%
+plus cost of M2.
+Since both of these guys are larger than
+
+ align:start position:0%
+Since both of these guys are larger than
+ 
+
+ align:start position:0%
+Since both of these guys are larger than
+this, their average is also larger than
+
+ align:start position:0%
+this, their average is also larger than
+ 
+
+ align:start position:0%
+this, their average is also larger than
+this. Right? But what is cost of M1 plus
+
+ align:start position:0%
+this. Right? But what is cost of M1 plus
+ 
+
+ align:start position:0%
+this. Right? But what is cost of M1 plus
+of M2? This is nothing but half
+
+ align:start position:0%
+of M2? This is nothing but half
+ 
+
+ align:start position:0%
+of M2? This is nothing but half
+cost of H star of S. Right? Because the
+
+ align:start position:0%
+cost of H star of S. Right? Because the
+ 
+
+ align:start position:0%
+cost of H star of S. Right? Because the
+Hamiltonian cycle is constructed from M1
+
+ align:start position:0%
+Hamiltonian cycle is constructed from M1
+ 
+
+ align:start position:0%
+Hamiltonian cycle is constructed from M1
+and M2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So and by our lema this is less than
+
+ align:start position:0%
+So and by our lema this is less than
+ 
+
+ align:start position:0%
+So and by our lema this is less than
+equal to half cost of h star of g.
+
+ align:start position:0%
+equal to half cost of h star of g.
+ 
+
+ align:start position:0%
+equal to half cost of h star of g.
+Right? So now we have all we need. This
+
+ align:start position:0%
+Right? So now we have all we need. This
+ 
+
+ align:start position:0%
+Right? So now we have all we need. This
+is less than equal to half cost of
+
+ align:start position:0%
+is less than equal to half cost of
+ 
+
+ align:start position:0%
+is less than equal to half cost of
+h star of g. And then add them together
+
+ align:start position:0%
+h star of g. And then add them together
+ 
+
+ align:start position:0%
+h star of g. And then add them together
+you get cost of C dash is less than
+
+ align:start position:0%
+you get cost of C dash is less than
+ 
+
+ align:start position:0%
+you get cost of C dash is less than
+equal to cost of C is less than equal to
+
+ align:start position:0%
+equal to cost of C is less than equal to
+ 
+
+ align:start position:0%
+equal to cost of C is less than equal to
+the sum which is equal to three cost of
+
+ align:start position:0%
+the sum which is equal to three cost of
+ 
+
+ align:start position:0%
+the sum which is equal to three cost of
+H star of G.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's the proof. So there's a lot of
+
+ align:start position:0%
+So that's the proof. So there's a lot of
+ 
+
+ align:start position:0%
+So that's the proof. So there's a lot of
+lot lot of things going on here. Let's
+
+ align:start position:0%
+lot lot of things going on here. Let's
+ 
+
+ align:start position:0%
+lot lot of things going on here. Let's
+try to go back and see what we did. So
+
+ align:start position:0%
+try to go back and see what we did. So
+ 
+
+ align:start position:0%
+try to go back and see what we did. So
+we took a minimum spanning tree and then
+
+ align:start position:0%
+we took a minimum spanning tree and then
+ 
+
+ align:start position:0%
+we took a minimum spanning tree and then
+we tried to remove all the odd odd
+
+ align:start position:0%
+we tried to remove all the odd odd
+ 
+
+ align:start position:0%
+we tried to remove all the odd odd
+degree vertices. So we took all the odd
+
+ align:start position:0%
+degree vertices. So we took all the odd
+ 
+
+ align:start position:0%
+degree vertices. So we took all the odd
+degree vertices and made a perfect
+
+ align:start position:0%
+degree vertices and made a perfect
+ 
+
+ align:start position:0%
+degree vertices and made a perfect
+matching the minimum cost perfect
+
+ align:start position:0%
+matching the minimum cost perfect
+ 
+
+ align:start position:0%
+matching the minimum cost perfect
+matching. So we added edges just to make
+
+ align:start position:0%
+matching. So we added edges just to make
+ 
+
+ align:start position:0%
+matching. So we added edges just to make
+everything even degree.
+
+ align:start position:0%
+everything even degree.
+ 
+
+ align:start position:0%
+everything even degree.
+Then we took the oiler circuit on that
+
+ align:start position:0%
+Then we took the oiler circuit on that
+ 
+
+ align:start position:0%
+Then we took the oiler circuit on that
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+and we removed duplicates. So that's
+
+ align:start position:0%
+and we removed duplicates. So that's
+ 
+
+ align:start position:0%
+and we removed duplicates. So that's
+fine. That's the easy part. But you took
+
+ align:start position:0%
+fine. That's the easy part. But you took
+ 
+
+ align:start position:0%
+fine. That's the easy part. But you took
+the oiler circuit on that graph. And
+
+ align:start position:0%
+the oiler circuit on that graph. And
+ 
+
+ align:start position:0%
+the oiler circuit on that graph. And
+then you argued that because all the
+
+ align:start position:0%
+then you argued that because all the
+ 
+
+ align:start position:0%
+then you argued that because all the
+circuit in that graph is just the sum of
+
+ align:start position:0%
+circuit in that graph is just the sum of
+ 
+
+ align:start position:0%
+circuit in that graph is just the sum of
+the edges in the spanning tree plus the
+
+ align:start position:0%
+the edges in the spanning tree plus the
+ 
+
+ align:start position:0%
+the edges in the spanning tree plus the
+sum of the edges in the matching which
+
+ align:start position:0%
+sum of the edges in the matching which
+ 
+
+ align:start position:0%
+sum of the edges in the matching which
+you added later. So the spanning tree
+
+ align:start position:0%
+you added later. So the spanning tree
+ 
+
+ align:start position:0%
+you added later. So the spanning tree
+had already bounded in the previous
+
+ align:start position:0%
+had already bounded in the previous
+ 
+
+ align:start position:0%
+had already bounded in the previous
+argument. The matching was bounded by
+
+ align:start position:0%
+argument. The matching was bounded by
+ 
+
+ align:start position:0%
+argument. The matching was bounded by
+taking the optimal Hamiltonian cycle
+
+ align:start position:0%
+taking the optimal Hamiltonian cycle
+ 
+
+ align:start position:0%
+taking the optimal Hamiltonian cycle
+decomposing it into two matchings
+
+ align:start position:0%
+decomposing it into two matchings
+ 
+
+ align:start position:0%
+decomposing it into two matchings
+arguing that those two matchings are not
+
+ align:start position:0%
+arguing that those two matchings are not
+ 
+
+ align:start position:0%
+arguing that those two matchings are not
+the optimal matching. So not necessarily
+
+ align:start position:0%
+the optimal matching. So not necessarily
+ 
+
+ align:start position:0%
+the optimal matching. So not necessarily
+the optimal matchings but they're at
+
+ align:start position:0%
+the optimal matchings but they're at
+ 
+
+ align:start position:0%
+the optimal matchings but they're at
+least they're less than equal to the
+
+ align:start position:0%
+least they're less than equal to the
+ 
+
+ align:start position:0%
+least they're less than equal to the
+optimal. So there he went there. And so
+
+ align:start position:0%
+optimal. So there he went there. And so
+ 
+
+ align:start position:0%
+optimal. So there he went there. And so
+the cost of the optimal matching which
+
+ align:start position:0%
+the cost of the optimal matching which
+ 
+
+ align:start position:0%
+the cost of the optimal matching which
+you're using in our constructed path
+
+ align:start position:0%
+you're using in our constructed path
+ 
+
+ align:start position:0%
+you're using in our constructed path
+constructed Hamiltonian cycle is less
+
+ align:start position:0%
+constructed Hamiltonian cycle is less
+ 
+
+ align:start position:0%
+constructed Hamiltonian cycle is less
+than equal to both of these matchings.
+
+ align:start position:0%
+than equal to both of these matchings.
+ 
+
+ align:start position:0%
+than equal to both of these matchings.
+You add them up you get that bound and
+
+ align:start position:0%
+You add them up you get that bound and
+ 
+
+ align:start position:0%
+You add them up you get that bound and
+works. So questions on any of the steps.
+
+ align:start position:0%
+works. So questions on any of the steps.
+ 
+
+ align:start position:0%
+works. So questions on any of the steps.
+This is a lot of branching off and then
+
+ align:start position:0%
+This is a lot of branching off and then
+ 
+
+ align:start position:0%
+This is a lot of branching off and then
+coming back together but yeah
+
+ align:start position:0%
+coming back together but yeah
+ 
+
+ align:start position:0%
+coming back together but yeah
+yes that is not 3x3 that that would be P
+
+ align:start position:0%
+yes that is not 3x3 that that would be P
+ 
+
+ align:start position:0%
+yes that is not 3x3 that that would be P
+equals NP.
+
+ align:start position:0%
+equals NP.
+ 
+
+ align:start position:0%
+equals NP.
+Yeah. Anything else?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, you're free to go or ask questions
+
+ align:start position:0%
+Okay, you're free to go or ask questions
+ 
+
+ align:start position:0%
+Okay, you're free to go or ask questions
+or whatever.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh,
\ No newline at end of file
diff --git a/zPGh2bBeIgM.txt b/zPGh2bBeIgM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c8f6430e5cf156b823fa2771f413ee7f77672e52
--- /dev/null
+++ b/zPGh2bBeIgM.txt
@@ -0,0 +1,14368 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
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+ align:start position:0%
+opencourseware under a creative commons
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+
+ align:start position:0%
+opencourseware under a creative commons
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+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
+additional information about our license
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+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
+
+ align:start position:0%
+and mit opencourseware in general is
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+
+ align:start position:0%
+and mit opencourseware in general is
+available at ocw.mit.edu
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+ align:start position:0%
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+ align:start position:0%
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+okay uh then what we'll do today is
+
+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+music sharing like no one predicted that
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+
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+ align:start position:0%
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+sort of fuel this huge music sharing
+
+ align:start position:0%
+sort of fuel this huge music sharing
+ 
+
+ align:start position:0%
+sort of fuel this huge music sharing
+problem whether or not to enable
+
+ align:start position:0%
+problem whether or not to enable
+ 
+
+ align:start position:0%
+problem whether or not to enable
+encryption over the internet for a long
+
+ align:start position:0%
+encryption over the internet for a long
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+encryption to be enabled because then
+
+ align:start position:0%
+encryption to be enabled because then
+ 
+
+ align:start position:0%
+encryption to be enabled because then
+spies could use the internet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very recently what google
+
+ align:start position:0%
+very recently what google
+ 
+
+ align:start position:0%
+very recently what google
+is doing in china to make search engines
+
+ align:start position:0%
+is doing in china to make search engines
+ 
+
+ align:start position:0%
+is doing in china to make search engines
+tailored to the
+
+ align:start position:0%
+tailored to the
+ 
+
+ align:start position:0%
+tailored to the
+laws or practices of a specific country
+
+ align:start position:0%
+laws or practices of a specific country
+ 
+
+ align:start position:0%
+laws or practices of a specific country
+he says
+
+ align:start position:0%
+he says
+ 
+
+ align:start position:0%
+he says
+what we have isn't is technology that is
+
+ align:start position:0%
+what we have isn't is technology that is
+ 
+
+ align:start position:0%
+what we have isn't is technology that is
+the same everywhere but policies and
+
+ align:start position:0%
+the same everywhere but policies and
+ 
+
+ align:start position:0%
+the same everywhere but policies and
+cultures that are very different
+
+ align:start position:0%
+cultures that are very different
+ 
+
+ align:start position:0%
+cultures that are very different
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+are used to designing technology for
+
+ align:start position:0%
+are used to designing technology for
+ 
+
+ align:start position:0%
+are used to designing technology for
+specific cultures we don't know how to
+
+ align:start position:0%
+specific cultures we don't know how to
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+
+ align:start position:0%
+specific cultures we don't know how to
+design technology
+
+ align:start position:0%
+design technology
+ 
+
+ align:start position:0%
+design technology
+in many different cultures at once
+
+ align:start position:0%
+in many different cultures at once
+ 
+
+ align:start position:0%
+in many different cultures at once
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in conclusion
+
+ align:start position:0%
+in conclusion
+ 
+
+ align:start position:0%
+in conclusion
+he says part of predicting tussle is to
+
+ align:start position:0%
+he says part of predicting tussle is to
+ 
+
+ align:start position:0%
+he says part of predicting tussle is to
+think about the values that were
+
+ align:start position:0%
+think about the values that were
+ 
+
+ align:start position:0%
+think about the values that were
+embedded in the creation of the internet
+
+ align:start position:0%
+embedded in the creation of the internet
+ 
+
+ align:start position:0%
+embedded in the creation of the internet
+the the computer scientists who wrote
+
+ align:start position:0%
+the the computer scientists who wrote
+ 
+
+ align:start position:0%
+the the computer scientists who wrote
+the initial code and protocol
+
+ align:start position:0%
+the initial code and protocol
+ 
+
+ align:start position:0%
+the initial code and protocol
+did embed values user empowerment
+
+ align:start position:0%
+did embed values user empowerment
+ 
+
+ align:start position:0%
+did embed values user empowerment
+ability to be anonymous
+
+ align:start position:0%
+ability to be anonymous
+ 
+
+ align:start position:0%
+ability to be anonymous
+distrust of losing control
+
+ align:start position:0%
+distrust of losing control
+ 
+
+ align:start position:0%
+distrust of losing control
+and the idea that what is not forbidden
+
+ align:start position:0%
+and the idea that what is not forbidden
+ 
+
+ align:start position:0%
+and the idea that what is not forbidden
+is permitted so
+
+ align:start position:0%
+is permitted so
+ 
+
+ align:start position:0%
+is permitted so
+whether we like it or not they embedded
+
+ align:start position:0%
+whether we like it or not they embedded
+ 
+
+ align:start position:0%
+whether we like it or not they embedded
+those values in the way they wrote the
+
+ align:start position:0%
+those values in the way they wrote the
+ 
+
+ align:start position:0%
+those values in the way they wrote the
+performance
+
+ align:start position:0%
+performance
+ 
+
+ align:start position:0%
+performance
+so there's that and one set and then
+
+ align:start position:0%
+so there's that and one set and then
+ 
+
+ align:start position:0%
+so there's that and one set and then
+there's values that we sort of expect
+
+ align:start position:0%
+there's values that we sort of expect
+ 
+
+ align:start position:0%
+there's values that we sort of expect
+that users expect freedom from attack
+
+ align:start position:0%
+that users expect freedom from attack
+ 
+
+ align:start position:0%
+that users expect freedom from attack
+stability
+
+ align:start position:0%
+stability
+ 
+
+ align:start position:0%
+stability
+freedom of speech access to information
+
+ align:start position:0%
+freedom of speech access to information
+ 
+
+ align:start position:0%
+freedom of speech access to information
+so those values that the creators
+
+ align:start position:0%
+so those values that the creators
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+
+ align:start position:0%
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+embedded the values that users expect
+
+ align:start position:0%
+embedded the values that users expect
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+
+ align:start position:0%
+embedded the values that users expect
+are in conflict and then there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there were some good questions from the
+
+ align:start position:0%
+there were some good questions from the
+ 
+
+ align:start position:0%
+there were some good questions from the
+floor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me see how did he frame that
+
+ align:start position:0%
+let me see how did he frame that
+ 
+
+ align:start position:0%
+let me see how did he frame that
+question about happiness
+
+ align:start position:0%
+ 
+ 
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+ align:start position:0%
+ 
+someone asked if
+
+ align:start position:0%
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+
+ align:start position:0%
+in thinking about
+ 
+
+ align:start position:0%
+in thinking about
+what the internet should enable
+
+ align:start position:0%
+what the internet should enable
+ 
+
+ align:start position:0%
+what the internet should enable
+or what its value should be do you ever
+
+ align:start position:0%
+or what its value should be do you ever
+ 
+
+ align:start position:0%
+or what its value should be do you ever
+consider one of its purposes to be
+
+ align:start position:0%
+consider one of its purposes to be
+ 
+
+ align:start position:0%
+consider one of its purposes to be
+enabling the pursuit of happiness
+
+ align:start position:0%
+enabling the pursuit of happiness
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+
+ align:start position:0%
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+that's kind of what the person asked yes
+
+ align:start position:0%
+that's kind of what the person asked yes
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+
+ align:start position:0%
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+uh the way he asked
+
+ align:start position:0%
+uh the way he asked
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+
+ align:start position:0%
+uh the way he asked
+was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a question in political science
+
+ align:start position:0%
+a question in political science
+ 
+
+ align:start position:0%
+a question in political science
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the notion here in the united states
+
+ align:start position:0%
+the notion here in the united states
+ 
+
+ align:start position:0%
+the notion here in the united states
+that one should be free
+
+ align:start position:0%
+that one should be free
+ 
+
+ align:start position:0%
+that one should be free
+to pursue happiness
+
+ align:start position:0%
+to pursue happiness
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+
+ align:start position:0%
+to pursue happiness
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+we all know that that
+
+ align:start position:0%
+we all know that that
+ 
+
+ align:start position:0%
+we all know that that
+pursuit of happiness concept comes from
+
+ align:start position:0%
+pursuit of happiness concept comes from
+ 
+
+ align:start position:0%
+pursuit of happiness concept comes from
+the happiness principle in ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that you have
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+ align:start position:0%
+that you have
+ 
+
+ align:start position:0%
+that you have
+you should be free to pursue
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+ align:start position:0%
+you should be free to pursue
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+ align:start position:0%
+you should be free to pursue
+happiness
+
+ align:start position:0%
+happiness
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+
+ align:start position:0%
+happiness
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i think dave clark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+took it the way that it was put
+
+ align:start position:0%
+took it the way that it was put
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+
+ align:start position:0%
+took it the way that it was put
+as a question of political science
+
+ align:start position:0%
+as a question of political science
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+
+ align:start position:0%
+as a question of political science
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh didn't have
+
+ align:start position:0%
+uh didn't have
+ 
+
+ align:start position:0%
+uh didn't have
+much to say about it i'm sure that i
+
+ align:start position:0%
+much to say about it i'm sure that i
+ 
+
+ align:start position:0%
+much to say about it i'm sure that i
+wouldn't have had anything to say about
+
+ align:start position:0%
+wouldn't have had anything to say about
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+
+ align:start position:0%
+wouldn't have had anything to say about
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+but the question
+
+ align:start position:0%
+but the question
+ 
+
+ align:start position:0%
+but the question
+when you look at it from the standpoint
+
+ align:start position:0%
+when you look at it from the standpoint
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+
+ align:start position:0%
+when you look at it from the standpoint
+of the happiness principle now that's a
+
+ align:start position:0%
+of the happiness principle now that's a
+ 
+
+ align:start position:0%
+of the happiness principle now that's a
+that is um
+
+ align:start position:0%
+that is um
+ 
+
+ align:start position:0%
+that is um
+an intriguing question does the internet
+
+ align:start position:0%
+an intriguing question does the internet
+ 
+
+ align:start position:0%
+an intriguing question does the internet
+make people happy
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll tell you one way that
+
+ align:start position:0%
+i'll tell you one way that
+ 
+
+ align:start position:0%
+i'll tell you one way that
+we i think we shouldn't answer the
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+ align:start position:0%
+we i think we shouldn't answer the
+ 
+
+ align:start position:0%
+we i think we shouldn't answer the
+question what would life be like if we
+
+ align:start position:0%
+question what would life be like if we
+ 
+
+ align:start position:0%
+question what would life be like if we
+didn't have it
+
+ align:start position:0%
+didn't have it
+ 
+
+ align:start position:0%
+didn't have it
+all right the reason i say that that's
+
+ align:start position:0%
+all right the reason i say that that's
+ 
+
+ align:start position:0%
+all right the reason i say that that's
+not a good way to answer the question is
+
+ align:start position:0%
+not a good way to answer the question is
+ 
+
+ align:start position:0%
+not a good way to answer the question is
+that a drug addict
+
+ align:start position:0%
+that a drug addict
+ 
+
+ align:start position:0%
+that a drug addict
+says the same thing
+
+ align:start position:0%
+says the same thing
+ 
+
+ align:start position:0%
+says the same thing
+what would it be like if i didn't have
+
+ align:start position:0%
+what would it be like if i didn't have
+ 
+
+ align:start position:0%
+what would it be like if i didn't have
+my drugs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we might be addicted to this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called the internet
+
+ align:start position:0%
+called the internet
+ 
+
+ align:start position:0%
+called the internet
+and if we are addicted to it then i
+
+ align:start position:0%
+and if we are addicted to it then i
+ 
+
+ align:start position:0%
+and if we are addicted to it then i
+don't think that that kind of happiness
+
+ align:start position:0%
+don't think that that kind of happiness
+ 
+
+ align:start position:0%
+don't think that that kind of happiness
+is what john stuart mills talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh let's let's let let's not leave
+
+ align:start position:0%
+so uh let's let's let let's not leave
+ 
+
+ align:start position:0%
+so uh let's let's let let's not leave
+that as a rhetorical question does this
+
+ align:start position:0%
+that as a rhetorical question does this
+ 
+
+ align:start position:0%
+that as a rhetorical question does this
+does
+
+ align:start position:0%
+does
+ 
+
+ align:start position:0%
+does
+let's pursue that for a second does the
+
+ align:start position:0%
+let's pursue that for a second does the
+ 
+
+ align:start position:0%
+let's pursue that for a second does the
+internet make anybody happy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right how would you break it down
+
+ align:start position:0%
+all right how would you break it down
+ 
+
+ align:start position:0%
+all right how would you break it down
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm asking does it make people happy
+
+ align:start position:0%
+i'm asking does it make people happy
+ 
+
+ align:start position:0%
+i'm asking does it make people happy
+is it good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's for everybody is it good i mean
+
+ align:start position:0%
+that's for everybody is it good i mean
+ 
+
+ align:start position:0%
+that's for everybody is it good i mean
+do we really like the internet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um so you're saying that everything
+
+ align:start position:0%
+okay um so you're saying that everything
+ 
+
+ align:start position:0%
+okay um so you're saying that everything
+has a price tag attached to it the price
+
+ align:start position:0%
+has a price tag attached to it the price
+ 
+
+ align:start position:0%
+has a price tag attached to it the price
+to pay for everything and you're willing
+
+ align:start position:0%
+to pay for everything and you're willing
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+
+ align:start position:0%
+to pay for everything and you're willing
+to pay the price for this thing
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+keep talking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
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+if
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+ align:start position:0%
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+ 
+
+ align:start position:0%
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+i have one advantage
+
+ align:start position:0%
+i have one advantage
+ 
+
+ align:start position:0%
+i have one advantage
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i'm 63 years old
+
+ align:start position:0%
+i'm 63 years old
+ 
+
+ align:start position:0%
+i'm 63 years old
+i can remember when there was
+
+ align:start position:0%
+i can remember when there was
+ 
+
+ align:start position:0%
+i can remember when there was
+no internet or if if there was an
+
+ align:start position:0%
+no internet or if if there was an
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+
+ align:start position:0%
+no internet or if if there was an
+internet nobody knew about it except the
+
+ align:start position:0%
+internet nobody knew about it except the
+ 
+
+ align:start position:0%
+internet nobody knew about it except the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+specialists
+
+ align:start position:0%
+specialists
+ 
+
+ align:start position:0%
+specialists
+and i can put myself in a position of
+
+ align:start position:0%
+and i can put myself in a position of
+ 
+
+ align:start position:0%
+and i can put myself in a position of
+asking myself
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+ align:start position:0%
+asking myself
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+
+ align:start position:0%
+asking myself
+if somebody brought an idea for the
+
+ align:start position:0%
+if somebody brought an idea for the
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+
+ align:start position:0%
+if somebody brought an idea for the
+internet before me and showed me the
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+ align:start position:0%
+internet before me and showed me the
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+
+ align:start position:0%
+internet before me and showed me the
+price
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+ align:start position:0%
+price
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+
+ align:start position:0%
+price
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+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would i have bought it in 19.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the only thing that i can think that
+
+ align:start position:0%
+uh the only thing that i can think that
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+
+ align:start position:0%
+uh the only thing that i can think that
+would have given me pause about that
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+ align:start position:0%
+would have given me pause about that
+ 
+
+ align:start position:0%
+would have given me pause about that
+whole thing was privacy
+
+ align:start position:0%
+whole thing was privacy
+ 
+
+ align:start position:0%
+whole thing was privacy
+that a private that a a a cost that i
+
+ align:start position:0%
+that a private that a a a cost that i
+ 
+
+ align:start position:0%
+that a private that a a a cost that i
+might have to pay for for this whole
+
+ align:start position:0%
+might have to pay for for this whole
+ 
+
+ align:start position:0%
+might have to pay for for this whole
+thing is that my social security number
+
+ align:start position:0%
+thing is that my social security number
+ 
+
+ align:start position:0%
+thing is that my social security number
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+gets right out for anybody to use
+
+ align:start position:0%
+gets right out for anybody to use
+ 
+
+ align:start position:0%
+gets right out for anybody to use
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i'm i'm putting aside
+
+ align:start position:0%
+i'm i'm putting aside
+ 
+
+ align:start position:0%
+i'm i'm putting aside
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+
+ align:start position:0%
+i'm not putting aside but i'm not
+ 
+
+ align:start position:0%
+i'm not putting aside but i'm not
+focusing on the fact
+
+ align:start position:0%
+focusing on the fact
+ 
+
+ align:start position:0%
+focusing on the fact
+that they can get in my bank account
+
+ align:start position:0%
+that they can get in my bank account
+ 
+
+ align:start position:0%
+that they can get in my bank account
+transfer funds
+
+ align:start position:0%
+transfer funds
+ 
+
+ align:start position:0%
+transfer funds
+i'm really talking about how they can do
+
+ align:start position:0%
+i'm really talking about how they can do
+ 
+
+ align:start position:0%
+i'm really talking about how they can do
+all sorts of other things with things
+
+ align:start position:0%
+all sorts of other things with things
+ 
+
+ align:start position:0%
+all sorts of other things with things
+that are very private to me
+
+ align:start position:0%
+that are very private to me
+ 
+
+ align:start position:0%
+that are very private to me
+and things that i have a legitimate
+
+ align:start position:0%
+and things that i have a legitimate
+ 
+
+ align:start position:0%
+and things that i have a legitimate
+right not to tell you or anybody else
+
+ align:start position:0%
+right not to tell you or anybody else
+ 
+
+ align:start position:0%
+right not to tell you or anybody else
+now i'm
+
+ align:start position:0%
+now i'm
+ 
+
+ align:start position:0%
+now i'm
+i'm still in 1960 i still have this
+
+ align:start position:0%
+i'm still in 1960 i still have this
+ 
+
+ align:start position:0%
+i'm still in 1960 i still have this
+thing in my mind before me what i want
+
+ align:start position:0%
+thing in my mind before me what i want
+ 
+
+ align:start position:0%
+thing in my mind before me what i want
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+tell me all of the uses all of the bad
+
+ align:start position:0%
+tell me all of the uses all of the bad
+ 
+
+ align:start position:0%
+tell me all of the uses all of the bad
+things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm i'm not so sure what i would say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i am not so sure about what i would say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that being unsure makes a statement
+
+ align:start position:0%
+that being unsure makes a statement
+ 
+
+ align:start position:0%
+that being unsure makes a statement
+uh is you know given that i was in that
+
+ align:start position:0%
+uh is you know given that i was in that
+ 
+
+ align:start position:0%
+uh is you know given that i was in that
+position and had all of these big
+
+ align:start position:0%
+position and had all of these big
+ 
+
+ align:start position:0%
+position and had all of these big
+choices and understood them
+
+ align:start position:0%
+choices and understood them
+ 
+
+ align:start position:0%
+choices and understood them
+like i do now
+
+ align:start position:0%
+like i do now
+ 
+
+ align:start position:0%
+like i do now
+would i take this thing and i probably
+
+ align:start position:0%
+would i take this thing and i probably
+ 
+
+ align:start position:0%
+would i take this thing and i probably
+would have a big difficulty with it i
+
+ align:start position:0%
+would have a big difficulty with it i
+ 
+
+ align:start position:0%
+would have a big difficulty with it i
+would say well uh uh thinking right now
+
+ align:start position:0%
+would say well uh uh thinking right now
+ 
+
+ align:start position:0%
+would say well uh uh thinking right now
+i would probably say something like well
+
+ align:start position:0%
+i would probably say something like well
+ 
+
+ align:start position:0%
+i would probably say something like well
+let's see if we can't work out the
+
+ align:start position:0%
+let's see if we can't work out the
+ 
+
+ align:start position:0%
+let's see if we can't work out the
+privacy issue then bring it back
+
+ align:start position:0%
+privacy issue then bring it back
+ 
+
+ align:start position:0%
+privacy issue then bring it back
+well we might not be able to work that
+
+ align:start position:0%
+well we might not be able to work that
+ 
+
+ align:start position:0%
+well we might not be able to work that
+out for two or three years four or five
+
+ align:start position:0%
+out for two or three years four or five
+ 
+
+ align:start position:0%
+out for two or three years four or five
+years well hopefully i'll still be able
+
+ align:start position:0%
+years well hopefully i'll still be able
+ 
+
+ align:start position:0%
+years well hopefully i'll still be able
+to bring it back then i probably
+
+ align:start position:0%
+to bring it back then i probably
+ 
+
+ align:start position:0%
+to bring it back then i probably
+wouldn't want to do it without that
+
+ align:start position:0%
+wouldn't want to do it without that
+ 
+
+ align:start position:0%
+wouldn't want to do it without that
+issue solved i probably wouldn't want to
+
+ align:start position:0%
+issue solved i probably wouldn't want to
+ 
+
+ align:start position:0%
+issue solved i probably wouldn't want to
+go into it
+
+ align:start position:0%
+go into it
+ 
+
+ align:start position:0%
+go into it
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they never saw it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right then let's ask another
+
+ align:start position:0%
+all right then let's ask another
+ 
+
+ align:start position:0%
+all right then let's ask another
+question for this class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can we find where any human being did
+
+ align:start position:0%
+can we find where any human being did
+ 
+
+ align:start position:0%
+can we find where any human being did
+anything wrong in terms of uh
+
+ align:start position:0%
+anything wrong in terms of uh
+ 
+
+ align:start position:0%
+anything wrong in terms of uh
+the internet or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right any uh questions of con
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no i i remember now what i was going to
+
+ align:start position:0%
+no i i remember now what i was going to
+ 
+
+ align:start position:0%
+no i i remember now what i was going to
+say uh what you had to say was more
+
+ align:start position:0%
+say uh what you had to say was more
+ 
+
+ align:start position:0%
+say uh what you had to say was more
+intriguing but i was going to ask um
+
+ align:start position:0%
+intriguing but i was going to ask um
+ 
+
+ align:start position:0%
+intriguing but i was going to ask um
+is the internet can we talk about the
+
+ align:start position:0%
+is the internet can we talk about the
+ 
+
+ align:start position:0%
+is the internet can we talk about the
+internet
+
+ align:start position:0%
+internet
+ 
+
+ align:start position:0%
+internet
+as being
+
+ align:start position:0%
+as being
+ 
+
+ align:start position:0%
+as being
+a um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moral agent is the can is that is the
+
+ align:start position:0%
+moral agent is the can is that is the
+ 
+
+ align:start position:0%
+moral agent is the can is that is the
+internet itself bad
+
+ align:start position:0%
+internet itself bad
+ 
+
+ align:start position:0%
+internet itself bad
+now now the internet becomes becomes a
+
+ align:start position:0%
+now now the internet becomes becomes a
+ 
+
+ align:start position:0%
+now now the internet becomes becomes a
+very interesting question about a
+
+ align:start position:0%
+very interesting question about a
+ 
+
+ align:start position:0%
+very interesting question about a
+technology being bad because the
+
+ align:start position:0%
+technology being bad because the
+ 
+
+ align:start position:0%
+technology being bad because the
+technology is activated
+
+ align:start position:0%
+technology is activated
+ 
+
+ align:start position:0%
+technology is activated
+uh by human beings all the time it's
+
+ align:start position:0%
+uh by human beings all the time it's
+ 
+
+ align:start position:0%
+uh by human beings all the time it's
+what human beings are doing
+
+ align:start position:0%
+what human beings are doing
+ 
+
+ align:start position:0%
+what human beings are doing
+but now
+
+ align:start position:0%
+but now
+ 
+
+ align:start position:0%
+but now
+dave clark comes in and says
+
+ align:start position:0%
+dave clark comes in and says
+ 
+
+ align:start position:0%
+dave clark comes in and says
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+it's fair to think about the internet as
+
+ align:start position:0%
+it's fair to think about the internet as
+ 
+
+ align:start position:0%
+it's fair to think about the internet as
+an object that has a life of its own
+
+ align:start position:0%
+an object that has a life of its own
+ 
+
+ align:start position:0%
+an object that has a life of its own
+that the rest of us
+
+ align:start position:0%
+that the rest of us
+ 
+
+ align:start position:0%
+that the rest of us
+do not control this thing totally
+
+ align:start position:0%
+do not control this thing totally
+ 
+
+ align:start position:0%
+do not control this thing totally
+so can we think about it in moral terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's leave that as a rhetorical
+
+ align:start position:0%
+uh let's leave that as a rhetorical
+ 
+
+ align:start position:0%
+uh let's leave that as a rhetorical
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+for right now we'll come back at the end
+
+ align:start position:0%
+for right now we'll come back at the end
+ 
+
+ align:start position:0%
+for right now we'll come back at the end
+of class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that question's still on the floor but i
+
+ align:start position:0%
+that question's still on the floor but i
+ 
+
+ align:start position:0%
+that question's still on the floor but i
+want to give a recapitulation of a talk
+
+ align:start position:0%
+want to give a recapitulation of a talk
+ 
+
+ align:start position:0%
+want to give a recapitulation of a talk
+that i gave yesterday which i wrote for
+
+ align:start position:0%
+that i gave yesterday which i wrote for
+ 
+
+ align:start position:0%
+that i gave yesterday which i wrote for
+this class as well it's a recapitulation
+
+ align:start position:0%
+this class as well it's a recapitulation
+ 
+
+ align:start position:0%
+this class as well it's a recapitulation
+of the course
+
+ align:start position:0%
+of the course
+ 
+
+ align:start position:0%
+of the course
+and the class that i gave yesterday was
+
+ align:start position:0%
+and the class that i gave yesterday was
+ 
+
+ align:start position:0%
+and the class that i gave yesterday was
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+this course
+
+ align:start position:0%
+this course
+ 
+
+ align:start position:0%
+this course
+called managing nuclear technology
+
+ align:start position:0%
+called managing nuclear technology
+ 
+
+ align:start position:0%
+called managing nuclear technology
+out of the nuclear engineering program
+
+ align:start position:0%
+out of the nuclear engineering program
+ 
+
+ align:start position:0%
+out of the nuclear engineering program
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it was a graduate class
+
+ align:start position:0%
+it was a graduate class
+ 
+
+ align:start position:0%
+it was a graduate class
+but not everybody in the class was a
+
+ align:start position:0%
+but not everybody in the class was a
+ 
+
+ align:start position:0%
+but not everybody in the class was a
+nuclear engineer some of them were tpp
+
+ align:start position:0%
+nuclear engineer some of them were tpp
+ 
+
+ align:start position:0%
+nuclear engineer some of them were tpp
+uh majors uh well another thing that
+
+ align:start position:0%
+uh majors uh well another thing that
+ 
+
+ align:start position:0%
+uh majors uh well another thing that
+made the class very interesting was that
+
+ align:start position:0%
+made the class very interesting was that
+ 
+
+ align:start position:0%
+made the class very interesting was that
+there were two students in there from
+
+ align:start position:0%
+there were two students in there from
+ 
+
+ align:start position:0%
+there were two students in there from
+france
+
+ align:start position:0%
+france
+ 
+
+ align:start position:0%
+france
+that was interesting to me because
+
+ align:start position:0%
+that was interesting to me because
+ 
+
+ align:start position:0%
+that was interesting to me because
+france has embraced
+
+ align:start position:0%
+france has embraced
+ 
+
+ align:start position:0%
+france has embraced
+nuclear power whereas the united states
+
+ align:start position:0%
+nuclear power whereas the united states
+ 
+
+ align:start position:0%
+nuclear power whereas the united states
+has had problems with it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the outline of the talk uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is as follows we want to talk about what
+
+ align:start position:0%
+is as follows we want to talk about what
+ 
+
+ align:start position:0%
+is as follows we want to talk about what
+were the times like
+
+ align:start position:0%
+were the times like
+ 
+
+ align:start position:0%
+were the times like
+and i'm talking about mainly in the
+
+ align:start position:0%
+and i'm talking about mainly in the
+ 
+
+ align:start position:0%
+and i'm talking about mainly in the
+united states
+
+ align:start position:0%
+united states
+ 
+
+ align:start position:0%
+united states
+but not because the united states is
+
+ align:start position:0%
+but not because the united states is
+ 
+
+ align:start position:0%
+but not because the united states is
+more important than anything else
+
+ align:start position:0%
+more important than anything else
+ 
+
+ align:start position:0%
+more important than anything else
+but because we're here in the united
+
+ align:start position:0%
+but because we're here in the united
+ 
+
+ align:start position:0%
+but because we're here in the united
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and that brought about what we call the
+
+ align:start position:0%
+and that brought about what we call the
+ 
+
+ align:start position:0%
+and that brought about what we call the
+sts movement
+
+ align:start position:0%
+sts movement
+ 
+
+ align:start position:0%
+sts movement
+science technology and society
+
+ align:start position:0%
+science technology and society
+ 
+
+ align:start position:0%
+science technology and society
+you know we have an sts department here
+
+ align:start position:0%
+you know we have an sts department here
+ 
+
+ align:start position:0%
+you know we have an sts department here
+uh our sts department
+
+ align:start position:0%
+uh our sts department
+ 
+
+ align:start position:0%
+uh our sts department
+does have a focus and
+
+ align:start position:0%
+does have a focus and
+ 
+
+ align:start position:0%
+does have a focus and
+not to the exclusion of everything else
+
+ align:start position:0%
+not to the exclusion of everything else
+ 
+
+ align:start position:0%
+not to the exclusion of everything else
+but it focuses on
+
+ align:start position:0%
+but it focuses on
+ 
+
+ align:start position:0%
+but it focuses on
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+history of technology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but sts in the beginning uh
+
+ align:start position:0%
+but sts in the beginning uh
+ 
+
+ align:start position:0%
+but sts in the beginning uh
+was a response to many issues in
+
+ align:start position:0%
+was a response to many issues in
+ 
+
+ align:start position:0%
+was a response to many issues in
+the american life and i'll talk about
+
+ align:start position:0%
+the american life and i'll talk about
+ 
+
+ align:start position:0%
+the american life and i'll talk about
+those in which i call the times and out
+
+ align:start position:0%
+those in which i call the times and out
+ 
+
+ align:start position:0%
+those in which i call the times and out
+of it came
+
+ align:start position:0%
+of it came
+ 
+
+ align:start position:0%
+of it came
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+an engagement of two learning
+
+ align:start position:0%
+an engagement of two learning
+ 
+
+ align:start position:0%
+an engagement of two learning
+disciplines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the engagements that we're talking
+
+ align:start position:0%
+but the engagements that we're talking
+ 
+
+ align:start position:0%
+but the engagements that we're talking
+about mostly are going to be with ethics
+
+ align:start position:0%
+about mostly are going to be with ethics
+ 
+
+ align:start position:0%
+about mostly are going to be with ethics
+and with engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which gives rise to engineering ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll look at a particular case
+
+ align:start position:0%
+and we'll look at a particular case
+ 
+
+ align:start position:0%
+and we'll look at a particular case
+study of tmi the which is three mile
+
+ align:start position:0%
+study of tmi the which is three mile
+ 
+
+ align:start position:0%
+study of tmi the which is three mile
+island nuclear they call it an accident
+
+ align:start position:0%
+island nuclear they call it an accident
+ 
+
+ align:start position:0%
+island nuclear they call it an accident
+that's the official term
+
+ align:start position:0%
+that's the official term
+ 
+
+ align:start position:0%
+that's the official term
+uh 1979. we'll look at a case study of
+
+ align:start position:0%
+uh 1979. we'll look at a case study of
+ 
+
+ align:start position:0%
+uh 1979. we'll look at a case study of
+that we did look at it a little bit in
+
+ align:start position:0%
+that we did look at it a little bit in
+ 
+
+ align:start position:0%
+that we did look at it a little bit in
+class we read a little bit about that
+
+ align:start position:0%
+class we read a little bit about that
+ 
+
+ align:start position:0%
+class we read a little bit about that
+but i would like to go a little bit
+
+ align:start position:0%
+but i would like to go a little bit
+ 
+
+ align:start position:0%
+but i would like to go a little bit
+deeper into it today
+
+ align:start position:0%
+deeper into it today
+ 
+
+ align:start position:0%
+deeper into it today
+and then let's talk about
+
+ align:start position:0%
+and then let's talk about
+ 
+
+ align:start position:0%
+and then let's talk about
+whether or not we're making a
+
+ align:start position:0%
+whether or not we're making a
+ 
+
+ align:start position:0%
+whether or not we're making a
+a world for ourselves that we want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and i'm asking the question about is
+
+ align:start position:0%
+uh and i'm asking the question about is
+ 
+
+ align:start position:0%
+uh and i'm asking the question about is
+or do we really have a brave new world
+
+ align:start position:0%
+or do we really have a brave new world
+ 
+
+ align:start position:0%
+or do we really have a brave new world
+and if that's good
+
+ align:start position:0%
+and if that's good
+ 
+
+ align:start position:0%
+and if that's good
+if you read aldous huxley's brave new
+
+ align:start position:0%
+if you read aldous huxley's brave new
+ 
+
+ align:start position:0%
+if you read aldous huxley's brave new
+world that was not a place that we would
+
+ align:start position:0%
+world that was not a place that we would
+ 
+
+ align:start position:0%
+world that was not a place that we would
+really want
+
+ align:start position:0%
+really want
+ 
+
+ align:start position:0%
+really want
+human beings grown in
+
+ align:start position:0%
+human beings grown in
+ 
+
+ align:start position:0%
+human beings grown in
+hatcheries they call them
+
+ align:start position:0%
+hatcheries they call them
+ 
+
+ align:start position:0%
+hatcheries they call them
+okay but nevertheless this is a good
+
+ align:start position:0%
+okay but nevertheless this is a good
+ 
+
+ align:start position:0%
+okay but nevertheless this is a good
+term to raise the question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the outline these are the
+
+ align:start position:0%
+so this is the outline these are the
+ 
+
+ align:start position:0%
+so this is the outline these are the
+main sections of this talk
+
+ align:start position:0%
+main sections of this talk
+ 
+
+ align:start position:0%
+main sections of this talk
+and when it comes to engineering ethics
+
+ align:start position:0%
+and when it comes to engineering ethics
+ 
+
+ align:start position:0%
+and when it comes to engineering ethics
+there were a number of issues that
+
+ align:start position:0%
+there were a number of issues that
+ 
+
+ align:start position:0%
+there were a number of issues that
+motivated the whole thing um
+
+ align:start position:0%
+motivated the whole thing um
+ 
+
+ align:start position:0%
+motivated the whole thing um
+one was in 1974 spiro t agnews
+
+ align:start position:0%
+one was in 1974 spiro t agnews
+ 
+
+ align:start position:0%
+one was in 1974 spiro t agnews
+i was about to say as you recall
+
+ align:start position:0%
+i was about to say as you recall
+ 
+
+ align:start position:0%
+i was about to say as you recall
+spiro t agnew was vice president of the
+
+ align:start position:0%
+spiro t agnew was vice president of the
+ 
+
+ align:start position:0%
+spiro t agnew was vice president of the
+united states
+
+ align:start position:0%
+united states
+ 
+
+ align:start position:0%
+united states
+he was accused
+
+ align:start position:0%
+he was accused
+ 
+
+ align:start position:0%
+he was accused
+and resigned as a result of the scandal
+
+ align:start position:0%
+and resigned as a result of the scandal
+ 
+
+ align:start position:0%
+and resigned as a result of the scandal
+those are two for terms of art for this
+
+ align:start position:0%
+those are two for terms of art for this
+ 
+
+ align:start position:0%
+those are two for terms of art for this
+particular case
+
+ align:start position:0%
+particular case
+ 
+
+ align:start position:0%
+particular case
+a accusation and scandal not conviction
+
+ align:start position:0%
+a accusation and scandal not conviction
+ 
+
+ align:start position:0%
+a accusation and scandal not conviction
+he was accused of taking bribes
+
+ align:start position:0%
+he was accused of taking bribes
+ 
+
+ align:start position:0%
+he was accused of taking bribes
+from engineers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the scandal that broke out over it
+
+ align:start position:0%
+and the scandal that broke out over it
+ 
+
+ align:start position:0%
+and the scandal that broke out over it
+prompted his resignation
+
+ align:start position:0%
+prompted his resignation
+ 
+
+ align:start position:0%
+prompted his resignation
+and gave motivation
+
+ align:start position:0%
+and gave motivation
+ 
+
+ align:start position:0%
+and gave motivation
+for this thing called engineering ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the challenger accident
+
+ align:start position:0%
+uh the challenger accident
+ 
+
+ align:start position:0%
+uh the challenger accident
+uh was one that um
+
+ align:start position:0%
+uh was one that um
+ 
+
+ align:start position:0%
+uh was one that um
+we have looked at
+
+ align:start position:0%
+we have looked at
+ 
+
+ align:start position:0%
+we have looked at
+and in the challenger accident uh we
+
+ align:start position:0%
+and in the challenger accident uh we
+ 
+
+ align:start position:0%
+and in the challenger accident uh we
+looked at the
+
+ align:start position:0%
+looked at the
+ 
+
+ align:start position:0%
+looked at the
+issue of whistleblowing
+
+ align:start position:0%
+issue of whistleblowing
+ 
+
+ align:start position:0%
+issue of whistleblowing
+we looked at the question of what
+
+ align:start position:0%
+we looked at the question of what
+ 
+
+ align:start position:0%
+we looked at the question of what
+engineering really is are we as
+
+ align:start position:0%
+engineering really is are we as
+ 
+
+ align:start position:0%
+engineering really is are we as
+engineering
+
+ align:start position:0%
+engineering
+ 
+
+ align:start position:0%
+engineering
+inherently lethal
+
+ align:start position:0%
+inherently lethal
+ 
+
+ align:start position:0%
+inherently lethal
+and this particular one
+
+ align:start position:0%
+and this particular one
+ 
+
+ align:start position:0%
+and this particular one
+uh was interesting to us from a number
+
+ align:start position:0%
+uh was interesting to us from a number
+ 
+
+ align:start position:0%
+uh was interesting to us from a number
+of reasons but not the least of which
+
+ align:start position:0%
+of reasons but not the least of which
+ 
+
+ align:start position:0%
+of reasons but not the least of which
+was that this was the first
+
+ align:start position:0%
+was that this was the first
+ 
+
+ align:start position:0%
+was that this was the first
+massive flight with a
+
+ align:start position:0%
+massive flight with a
+ 
+
+ align:start position:0%
+massive flight with a
+shuttle that had a person on board
+
+ align:start position:0%
+shuttle that had a person on board
+ 
+
+ align:start position:0%
+shuttle that had a person on board
+who was neither an employee of nasa nor
+
+ align:start position:0%
+who was neither an employee of nasa nor
+ 
+
+ align:start position:0%
+who was neither an employee of nasa nor
+of the military
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which meant that that person was not an
+
+ align:start position:0%
+which meant that that person was not an
+ 
+
+ align:start position:0%
+which meant that that person was not an
+expert
+
+ align:start position:0%
+expert
+ 
+
+ align:start position:0%
+expert
+on this
+
+ align:start position:0%
+on this
+ 
+
+ align:start position:0%
+on this
+that was mcauliffe who was a school
+
+ align:start position:0%
+that was mcauliffe who was a school
+ 
+
+ align:start position:0%
+that was mcauliffe who was a school
+teacher
+
+ align:start position:0%
+teacher
+ 
+
+ align:start position:0%
+teacher
+and they were trying to make the case
+
+ align:start position:0%
+and they were trying to make the case
+ 
+
+ align:start position:0%
+and they were trying to make the case
+that space travel
+
+ align:start position:0%
+that space travel
+ 
+
+ align:start position:0%
+that space travel
+could be for the for ordinary people
+
+ align:start position:0%
+could be for the for ordinary people
+ 
+
+ align:start position:0%
+could be for the for ordinary people
+just like getting on an airplane is for
+
+ align:start position:0%
+just like getting on an airplane is for
+ 
+
+ align:start position:0%
+just like getting on an airplane is for
+ordinary people now
+
+ align:start position:0%
+ordinary people now
+ 
+
+ align:start position:0%
+ordinary people now
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+bo paul introduced
+
+ align:start position:0%
+bo paul introduced
+ 
+
+ align:start position:0%
+bo paul introduced
+the issue of safety standards across
+
+ align:start position:0%
+the issue of safety standards across
+ 
+
+ align:start position:0%
+the issue of safety standards across
+cultures
+
+ align:start position:0%
+cultures
+ 
+
+ align:start position:0%
+cultures
+that in the united states we had union
+
+ align:start position:0%
+that in the united states we had union
+ 
+
+ align:start position:0%
+that in the united states we had union
+carbide had some safety standards for
+
+ align:start position:0%
+carbide had some safety standards for
+ 
+
+ align:start position:0%
+carbide had some safety standards for
+its chemical plants
+
+ align:start position:0%
+its chemical plants
+ 
+
+ align:start position:0%
+its chemical plants
+they went to india there were different
+
+ align:start position:0%
+they went to india there were different
+ 
+
+ align:start position:0%
+they went to india there were different
+standards
+
+ align:start position:0%
+standards
+ 
+
+ align:start position:0%
+standards
+an accident occurred killed 3 000 people
+
+ align:start position:0%
+an accident occurred killed 3 000 people
+ 
+
+ align:start position:0%
+an accident occurred killed 3 000 people
+children included
+
+ align:start position:0%
+children included
+ 
+
+ align:start position:0%
+children included
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the question is as you just raised the
+
+ align:start position:0%
+the question is as you just raised the
+ 
+
+ align:start position:0%
+the question is as you just raised the
+question about google
+
+ align:start position:0%
+question about google
+ 
+
+ align:start position:0%
+question about google
+in china what do we do about
+
+ align:start position:0%
+in china what do we do about
+ 
+
+ align:start position:0%
+in china what do we do about
+ethical standards i'm not talking about
+
+ align:start position:0%
+ethical standards i'm not talking about
+ 
+
+ align:start position:0%
+ethical standards i'm not talking about
+legal standards ethical standards
+
+ align:start position:0%
+legal standards ethical standards
+ 
+
+ align:start position:0%
+legal standards ethical standards
+are across cultures
+
+ align:start position:0%
+are across cultures
+ 
+
+ align:start position:0%
+are across cultures
+raises that issue
+
+ align:start position:0%
+raises that issue
+ 
+
+ align:start position:0%
+raises that issue
+and three mile allen is something i'll
+
+ align:start position:0%
+and three mile allen is something i'll
+ 
+
+ align:start position:0%
+and three mile allen is something i'll
+talk about a little in a little bit of
+
+ align:start position:0%
+talk about a little in a little bit of
+ 
+
+ align:start position:0%
+talk about a little in a little bit of
+detail because we haven't talked about
+
+ align:start position:0%
+detail because we haven't talked about
+ 
+
+ align:start position:0%
+detail because we haven't talked about
+it in detail
+
+ align:start position:0%
+it in detail
+ 
+
+ align:start position:0%
+it in detail
+in the class yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sds movement did not include was not
+
+ align:start position:0%
+the sds movement did not include was not
+ 
+
+ align:start position:0%
+the sds movement did not include was not
+restricted engineering ethics
+
+ align:start position:0%
+restricted engineering ethics
+ 
+
+ align:start position:0%
+restricted engineering ethics
+there's a discipline called
+
+ align:start position:0%
+there's a discipline called
+ 
+
+ align:start position:0%
+there's a discipline called
+environmental ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a discipline and when i say
+
+ align:start position:0%
+there's a discipline and when i say
+ 
+
+ align:start position:0%
+there's a discipline and when i say
+discipline i'm talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a world view
+
+ align:start position:0%
+a world view
+ 
+
+ align:start position:0%
+a world view
+a way of looking at the world we talked
+
+ align:start position:0%
+a way of looking at the world we talked
+ 
+
+ align:start position:0%
+a way of looking at the world we talked
+about that already how it is that a
+
+ align:start position:0%
+about that already how it is that a
+ 
+
+ align:start position:0%
+about that already how it is that a
+scientist looks at the world in one way
+
+ align:start position:0%
+scientist looks at the world in one way
+ 
+
+ align:start position:0%
+scientist looks at the world in one way
+an engineer can look at the world
+
+ align:start position:0%
+an engineer can look at the world
+ 
+
+ align:start position:0%
+an engineer can look at the world
+another way that it has a body of
+
+ align:start position:0%
+another way that it has a body of
+ 
+
+ align:start position:0%
+another way that it has a body of
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+that it has a community of scholars that
+
+ align:start position:0%
+that it has a community of scholars that
+ 
+
+ align:start position:0%
+that it has a community of scholars that
+cultivate that body
+
+ align:start position:0%
+cultivate that body
+ 
+
+ align:start position:0%
+cultivate that body
+that cultivates that body of learning
+
+ align:start position:0%
+that cultivates that body of learning
+ 
+
+ align:start position:0%
+that cultivates that body of learning
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+university degree granting programs
+
+ align:start position:0%
+university degree granting programs
+ 
+
+ align:start position:0%
+university degree granting programs
+so if you do not get a degree in
+
+ align:start position:0%
+so if you do not get a degree in
+ 
+
+ align:start position:0%
+so if you do not get a degree in
+business ethics
+
+ align:start position:0%
+business ethics
+ 
+
+ align:start position:0%
+business ethics
+you can certainly get a degree in sts
+
+ align:start position:0%
+you can certainly get a degree in sts
+ 
+
+ align:start position:0%
+you can certainly get a degree in sts
+even the phd
+
+ align:start position:0%
+even the phd
+ 
+
+ align:start position:0%
+even the phd
+with a major in
+
+ align:start position:0%
+with a major in
+ 
+
+ align:start position:0%
+with a major in
+engineering ethics
+
+ align:start position:0%
+engineering ethics
+ 
+
+ align:start position:0%
+engineering ethics
+or business ethics
+
+ align:start position:0%
+or business ethics
+ 
+
+ align:start position:0%
+or business ethics
+that's what my master's degree is my
+
+ align:start position:0%
+that's what my master's degree is my
+ 
+
+ align:start position:0%
+that's what my master's degree is my
+master's degree is an sts
+
+ align:start position:0%
+master's degree is an sts
+ 
+
+ align:start position:0%
+master's degree is an sts
+the major is in engineering ethics
+
+ align:start position:0%
+the major is in engineering ethics
+ 
+
+ align:start position:0%
+the major is in engineering ethics
+bioethics
+
+ align:start position:0%
+bioethics
+ 
+
+ align:start position:0%
+bioethics
+medical ethics academic ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the class yesterday that uh this
+
+ align:start position:0%
+in the class yesterday that uh this
+ 
+
+ align:start position:0%
+in the class yesterday that uh this
+issue here raised some questions
+
+ align:start position:0%
+issue here raised some questions
+ 
+
+ align:start position:0%
+issue here raised some questions
+the students wanted to know how
+
+ align:start position:0%
+the students wanted to know how
+ 
+
+ align:start position:0%
+the students wanted to know how
+the student phrased the question
+
+ align:start position:0%
+the student phrased the question
+ 
+
+ align:start position:0%
+the student phrased the question
+what ethical problems do faculty have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i said well if even if we put aside
+
+ align:start position:0%
+i said well if even if we put aside
+ 
+
+ align:start position:0%
+i said well if even if we put aside
+questions that
+
+ align:start position:0%
+questions that
+ 
+
+ align:start position:0%
+questions that
+ethical issues that faculty have with
+
+ align:start position:0%
+ethical issues that faculty have with
+ 
+
+ align:start position:0%
+ethical issues that faculty have with
+students
+
+ align:start position:0%
+students
+ 
+
+ align:start position:0%
+students
+we have a lot of ethical issues among
+
+ align:start position:0%
+we have a lot of ethical issues among
+ 
+
+ align:start position:0%
+we have a lot of ethical issues among
+ourselves and the biggest one probably i
+
+ align:start position:0%
+ourselves and the biggest one probably i
+ 
+
+ align:start position:0%
+ourselves and the biggest one probably i
+don't know what you think about it
+
+ align:start position:0%
+don't know what you think about it
+ 
+
+ align:start position:0%
+don't know what you think about it
+our faculty members here but it's
+
+ align:start position:0%
+our faculty members here but it's
+ 
+
+ align:start position:0%
+our faculty members here but it's
+plagiarism
+
+ align:start position:0%
+plagiarism
+ 
+
+ align:start position:0%
+plagiarism
+that is the nightmare for us for one
+
+ align:start position:0%
+that is the nightmare for us for one
+ 
+
+ align:start position:0%
+that is the nightmare for us for one
+faculty member to plagiarize another one
+
+ align:start position:0%
+faculty member to plagiarize another one
+ 
+
+ align:start position:0%
+faculty member to plagiarize another one
+and that becomes uh a matter of
+
+ align:start position:0%
+and that becomes uh a matter of
+ 
+
+ align:start position:0%
+and that becomes uh a matter of
+irritation for students too
+
+ align:start position:0%
+irritation for students too
+ 
+
+ align:start position:0%
+irritation for students too
+but i think the big issue for students
+
+ align:start position:0%
+but i think the big issue for students
+ 
+
+ align:start position:0%
+but i think the big issue for students
+in plagiarism
+
+ align:start position:0%
+in plagiarism
+ 
+
+ align:start position:0%
+in plagiarism
+is after the plagiarism has occurred
+
+ align:start position:0%
+is after the plagiarism has occurred
+ 
+
+ align:start position:0%
+is after the plagiarism has occurred
+actually it's not so much plagiarism is
+
+ align:start position:0%
+actually it's not so much plagiarism is
+ 
+
+ align:start position:0%
+actually it's not so much plagiarism is
+falsification of data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because you get this paper you're going
+
+ align:start position:0%
+because you get this paper you're going
+ 
+
+ align:start position:0%
+because you get this paper you're going
+to build your master's thesis on this
+
+ align:start position:0%
+to build your master's thesis on this
+ 
+
+ align:start position:0%
+to build your master's thesis on this
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+and you just before you go in for your
+
+ align:start position:0%
+and you just before you go in for your
+ 
+
+ align:start position:0%
+and you just before you go in for your
+defense you find out that the data is
+
+ align:start position:0%
+defense you find out that the data is
+ 
+
+ align:start position:0%
+defense you find out that the data is
+corrupt
+
+ align:start position:0%
+corrupt
+ 
+
+ align:start position:0%
+corrupt
+what would you do in this situation the
+
+ align:start position:0%
+what would you do in this situation the
+ 
+
+ align:start position:0%
+what would you do in this situation the
+committee's sitting there saying well
+
+ align:start position:0%
+committee's sitting there saying well
+ 
+
+ align:start position:0%
+committee's sitting there saying well
+look we know it wasn't your fault
+
+ align:start position:0%
+look we know it wasn't your fault
+ 
+
+ align:start position:0%
+look we know it wasn't your fault
+we can't pass this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that can that can be pretty
+
+ align:start position:0%
+all right so that can that can be pretty
+ 
+
+ align:start position:0%
+all right so that can that can be pretty
+bad uh
+
+ align:start position:0%
+bad uh
+ 
+
+ align:start position:0%
+bad uh
+and tpp
+
+ align:start position:0%
+and tpp
+ 
+
+ align:start position:0%
+and tpp
+part of sts movement
+
+ align:start position:0%
+part of sts movement
+ 
+
+ align:start position:0%
+part of sts movement
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this picture up here
+
+ align:start position:0%
+this picture up here
+ 
+
+ align:start position:0%
+this picture up here
+i think best describes what
+
+ align:start position:0%
+i think best describes what
+ 
+
+ align:start position:0%
+i think best describes what
+the people the scholars in the is of the
+
+ align:start position:0%
+the people the scholars in the is of the
+ 
+
+ align:start position:0%
+the people the scholars in the is of the
+sts movement
+
+ align:start position:0%
+sts movement
+ 
+
+ align:start position:0%
+sts movement
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+how we looked at ourselves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in relationship to
+
+ align:start position:0%
+in relationship to
+ 
+
+ align:start position:0%
+in relationship to
+big business and big government
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh and there were big hopes back in
+
+ align:start position:0%
+uh and there were big hopes back in
+ 
+
+ align:start position:0%
+uh and there were big hopes back in
+those days
+
+ align:start position:0%
+those days
+ 
+
+ align:start position:0%
+those days
+uh for uh us i say us i was one of the
+
+ align:start position:0%
+uh for uh us i say us i was one of the
+ 
+
+ align:start position:0%
+uh for uh us i say us i was one of the
+young people in those i was
+
+ align:start position:0%
+young people in those i was
+ 
+
+ align:start position:0%
+young people in those i was
+i was just being brought along and
+
+ align:start position:0%
+i was just being brought along and
+ 
+
+ align:start position:0%
+i was just being brought along and
+learning this is 1972
+
+ align:start position:0%
+learning this is 1972
+ 
+
+ align:start position:0%
+learning this is 1972
+73 i was just being brought up brought
+
+ align:start position:0%
+73 i was just being brought up brought
+ 
+
+ align:start position:0%
+73 i was just being brought up brought
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+me
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ 
+
+ align:start position:0%
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+to put their names uh in the history of
+
+ align:start position:0%
+to put their names uh in the history of
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+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
+because now we have the opportunity to
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+ align:start position:0%
+because now we have the opportunity to
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+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
+so now we can write things and be
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+
+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
+equated with emmanuel kant
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+
+ align:start position:0%
+and we can be equated
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+
+ align:start position:0%
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+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
+what i'm trying to describe to you the
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+ align:start position:0%
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+nice word for it
+
+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
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+ align:start position:0%
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+on this whole notion of you know
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+and we and we wanted to be able to write
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+
+ align:start position:0%
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+ 
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+who is a friend of mine
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+
+ align:start position:0%
+in these roman uh vaulted ceilings
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+
+ align:start position:0%
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+
+ align:start position:0%
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+in 1509
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+
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+
+ align:start position:0%
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+ align:start position:0%
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+
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+tradition
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+and that is based as i said on reason
+
+ align:start position:0%
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+and out of that tradition we get two
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+other traditions
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+an ethical situ an ethical problem can
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+ align:start position:0%
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+ align:start position:0%
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+and for him first principles were
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+
+ align:start position:0%
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+
+ align:start position:0%
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+
+ align:start position:0%
+and
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+
+ align:start position:0%
+and
+that gives us one great tradition that
+
+ align:start position:0%
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+
+ align:start position:0%
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+still holds with us today
+
+ align:start position:0%
+still holds with us today
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+
+ align:start position:0%
+still holds with us today
+the other one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is empirical
+
+ align:start position:0%
+is empirical
+ 
+
+ align:start position:0%
+is empirical
+and it says that if an action can be
+
+ align:start position:0%
+and it says that if an action can be
+ 
+
+ align:start position:0%
+and it says that if an action can be
+judged good or bad right or wrong
+
+ align:start position:0%
+judged good or bad right or wrong
+ 
+
+ align:start position:0%
+judged good or bad right or wrong
+depending on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the happiness that it tends
+
+ align:start position:0%
+the happiness that it tends
+ 
+
+ align:start position:0%
+the happiness that it tends
+to either give people or take from
+
+ align:start position:0%
+to either give people or take from
+ 
+
+ align:start position:0%
+to either give people or take from
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+as a result of the action
+
+ align:start position:0%
+as a result of the action
+ 
+
+ align:start position:0%
+as a result of the action
+so it's factual
+
+ align:start position:0%
+so it's factual
+ 
+
+ align:start position:0%
+so it's factual
+and we have
+
+ align:start position:0%
+and we have
+ 
+
+ align:start position:0%
+and we have
+probably john stuart mill
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not who originated this point of view
+
+ align:start position:0%
+not who originated this point of view
+ 
+
+ align:start position:0%
+not who originated this point of view
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+who
+
+ align:start position:0%
+who
+ 
+
+ align:start position:0%
+who
+pretty much did more than anybody else i
+
+ align:start position:0%
+pretty much did more than anybody else i
+ 
+
+ align:start position:0%
+pretty much did more than anybody else i
+think to perfect it
+
+ align:start position:0%
+think to perfect it
+ 
+
+ align:start position:0%
+think to perfect it
+frankly i think that jeremy bentham is
+
+ align:start position:0%
+frankly i think that jeremy bentham is
+ 
+
+ align:start position:0%
+frankly i think that jeremy bentham is
+the person
+
+ align:start position:0%
+the person
+ 
+
+ align:start position:0%
+the person
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+made the greatest contribution because
+
+ align:start position:0%
+made the greatest contribution because
+ 
+
+ align:start position:0%
+made the greatest contribution because
+he saw it as a solution to a political
+
+ align:start position:0%
+he saw it as a solution to a political
+ 
+
+ align:start position:0%
+he saw it as a solution to a political
+problem not so much a political problem
+
+ align:start position:0%
+problem not so much a political problem
+ 
+
+ align:start position:0%
+problem not so much a political problem
+but a problem of political science he
+
+ align:start position:0%
+but a problem of political science he
+ 
+
+ align:start position:0%
+but a problem of political science he
+was trying to really
+
+ align:start position:0%
+was trying to really
+ 
+
+ align:start position:0%
+was trying to really
+organize um
+
+ align:start position:0%
+organize um
+ 
+
+ align:start position:0%
+organize um
+thinking about how to build a british
+
+ align:start position:0%
+thinking about how to build a british
+ 
+
+ align:start position:0%
+thinking about how to build a british
+society but nevertheless mill got worked
+
+ align:start position:0%
+society but nevertheless mill got worked
+ 
+
+ align:start position:0%
+society but nevertheless mill got worked
+out all of the kinks
+
+ align:start position:0%
+out all of the kinks
+ 
+
+ align:start position:0%
+out all of the kinks
+and when i say all of the kinks you know
+
+ align:start position:0%
+and when i say all of the kinks you know
+ 
+
+ align:start position:0%
+and when i say all of the kinks you know
+what i mean by that the major ones we
+
+ align:start position:0%
+what i mean by that the major ones we
+ 
+
+ align:start position:0%
+what i mean by that the major ones we
+can still write a dissertation on on
+
+ align:start position:0%
+can still write a dissertation on on
+ 
+
+ align:start position:0%
+can still write a dissertation on on
+this stuff
+
+ align:start position:0%
+this stuff
+ 
+
+ align:start position:0%
+this stuff
+but uh he's the one that's gonna that's
+
+ align:start position:0%
+but uh he's the one that's gonna that's
+ 
+
+ align:start position:0%
+but uh he's the one that's gonna that's
+been remembered mostly for that
+
+ align:start position:0%
+been remembered mostly for that
+ 
+
+ align:start position:0%
+been remembered mostly for that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+there is another tradition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in so far as greek antiquity is
+
+ align:start position:0%
+in so far as greek antiquity is
+ 
+
+ align:start position:0%
+in so far as greek antiquity is
+concerned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh has given us to uh given to us
+
+ align:start position:0%
+that uh has given us to uh given to us
+ 
+
+ align:start position:0%
+that uh has given us to uh given to us
+by plato
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+plato's tradition is
+
+ align:start position:0%
+plato's tradition is
+ 
+
+ align:start position:0%
+plato's tradition is
+that really what good what is good and
+
+ align:start position:0%
+that really what good what is good and
+ 
+
+ align:start position:0%
+that really what good what is good and
+bad what is right and wrong is
+
+ align:start position:0%
+bad what is right and wrong is
+ 
+
+ align:start position:0%
+bad what is right and wrong is
+determined by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+character
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are certain people who are good
+
+ align:start position:0%
+there are certain people who are good
+ 
+
+ align:start position:0%
+there are certain people who are good
+people there are certain people he would
+
+ align:start position:0%
+people there are certain people he would
+ 
+
+ align:start position:0%
+people there are certain people he would
+say are bad people
+
+ align:start position:0%
+say are bad people
+ 
+
+ align:start position:0%
+say are bad people
+and what he would say makes the
+
+ align:start position:0%
+and what he would say makes the
+ 
+
+ align:start position:0%
+and what he would say makes the
+difference between a good person
+
+ align:start position:0%
+difference between a good person
+ 
+
+ align:start position:0%
+difference between a good person
+a bad person and an ordinary person or
+
+ align:start position:0%
+a bad person and an ordinary person or
+ 
+
+ align:start position:0%
+a bad person and an ordinary person or
+what he calls the possession of virtues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he cannot articulate those virtues
+
+ align:start position:0%
+and he cannot articulate those virtues
+ 
+
+ align:start position:0%
+and he cannot articulate those virtues
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+which means that as we come into
+
+ align:start position:0%
+which means that as we come into
+ 
+
+ align:start position:0%
+which means that as we come into
+different cultures we can articulate
+
+ align:start position:0%
+different cultures we can articulate
+ 
+
+ align:start position:0%
+different cultures we can articulate
+different virtues but nevertheless
+
+ align:start position:0%
+different virtues but nevertheless
+ 
+
+ align:start position:0%
+different virtues but nevertheless
+it's the notion that we're talking about
+
+ align:start position:0%
+it's the notion that we're talking about
+ 
+
+ align:start position:0%
+it's the notion that we're talking about
+good character
+
+ align:start position:0%
+good character
+ 
+
+ align:start position:0%
+good character
+and he got his virtues from
+
+ align:start position:0%
+and he got his virtues from
+ 
+
+ align:start position:0%
+and he got his virtues from
+uh the kind of society that he came from
+
+ align:start position:0%
+uh the kind of society that he came from
+ 
+
+ align:start position:0%
+uh the kind of society that he came from
+and though that side it was a warrior
+
+ align:start position:0%
+and though that side it was a warrior
+ 
+
+ align:start position:0%
+and though that side it was a warrior
+society basically and so good virtues
+
+ align:start position:0%
+society basically and so good virtues
+ 
+
+ align:start position:0%
+society basically and so good virtues
+meant good
+
+ align:start position:0%
+meant good
+ 
+
+ align:start position:0%
+meant good
+warrior virgins heroic
+
+ align:start position:0%
+warrior virgins heroic
+ 
+
+ align:start position:0%
+warrior virgins heroic
+virtues
+
+ align:start position:0%
+virtues
+ 
+
+ align:start position:0%
+virtues
+now out of that in the united states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here's a point that we have not
+
+ align:start position:0%
+and here's a point that we have not
+ 
+
+ align:start position:0%
+and here's a point that we have not
+covered in class but it's an opportunity
+
+ align:start position:0%
+covered in class but it's an opportunity
+ 
+
+ align:start position:0%
+covered in class but it's an opportunity
+for me to cover to cover it in class
+
+ align:start position:0%
+for me to cover to cover it in class
+ 
+
+ align:start position:0%
+for me to cover to cover it in class
+uh in the united states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me put down a number you see tell me
+
+ align:start position:0%
+let me put down a number you see tell me
+ 
+
+ align:start position:0%
+let me put down a number you see tell me
+if you can correct this number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the united states since about 1650
+
+ align:start position:0%
+in the united states since about 1650
+ 
+
+ align:start position:0%
+in the united states since about 1650
+there was
+
+ align:start position:0%
+there was
+ 
+
+ align:start position:0%
+there was
+in the universities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a concept called classical education do
+
+ align:start position:0%
+a concept called classical education do
+ 
+
+ align:start position:0%
+a concept called classical education do
+you know what number i'm looking for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when the first university united states
+
+ align:start position:0%
+when the first university united states
+ 
+
+ align:start position:0%
+when the first university united states
+was founded well first of all do you
+
+ align:start position:0%
+was founded well first of all do you
+ 
+
+ align:start position:0%
+was founded well first of all do you
+know which university that was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+harvard
+
+ align:start position:0%
+harvard
+ 
+
+ align:start position:0%
+harvard
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+right down the street
+
+ align:start position:0%
+right down the street
+ 
+
+ align:start position:0%
+right down the street
+it was 16 something
+
+ align:start position:0%
+it was 16 something
+ 
+
+ align:start position:0%
+it was 16 something
+you remember
+
+ align:start position:0%
+you remember
+ 
+
+ align:start position:0%
+you remember
+i don't remember the exact date but it
+
+ align:start position:0%
+i don't remember the exact date but it
+ 
+
+ align:start position:0%
+i don't remember the exact date but it
+was after i remember this much it was
+
+ align:start position:0%
+was after i remember this much it was
+ 
+
+ align:start position:0%
+was after i remember this much it was
+after 1620 when the pilgrims landed
+
+ align:start position:0%
+after 1620 when the pilgrims landed
+ 
+
+ align:start position:0%
+after 1620 when the pilgrims landed
+and i remember it was 16 something okay
+
+ align:start position:0%
+and i remember it was 16 something okay
+ 
+
+ align:start position:0%
+and i remember it was 16 something okay
+now classical education
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was education for
+
+ align:start position:0%
+was education for
+ 
+
+ align:start position:0%
+was education for
+the clergy
+
+ align:start position:0%
+the clergy
+ 
+
+ align:start position:0%
+the clergy
+and for
+
+ align:start position:0%
+and for
+ 
+
+ align:start position:0%
+and for
+the aristocratic class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the idea was
+
+ align:start position:0%
+and the idea was
+ 
+
+ align:start position:0%
+and the idea was
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+what a person needed from a college
+
+ align:start position:0%
+what a person needed from a college
+ 
+
+ align:start position:0%
+what a person needed from a college
+education what these people needed from
+
+ align:start position:0%
+education what these people needed from
+ 
+
+ align:start position:0%
+education what these people needed from
+a college education
+
+ align:start position:0%
+a college education
+ 
+
+ align:start position:0%
+a college education
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+good character
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that the virtues of good character were
+
+ align:start position:0%
+that the virtues of good character were
+ 
+
+ align:start position:0%
+that the virtues of good character were
+spelled out in christian religion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that the textbooks the curriculum
+
+ align:start position:0%
+and that the textbooks the curriculum
+ 
+
+ align:start position:0%
+and that the textbooks the curriculum
+was taken from greek antiquity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trivium quadrillion
+
+ align:start position:0%
+trivium quadrillion
+ 
+
+ align:start position:0%
+trivium quadrillion
+classical studies in philosophy
+
+ align:start position:0%
+classical studies in philosophy
+ 
+
+ align:start position:0%
+classical studies in philosophy
+mathematics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+rhetoric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+dialectic
+
+ align:start position:0%
+dialectic
+ 
+
+ align:start position:0%
+dialectic
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+literature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i have some mem some numbers i've
+
+ align:start position:0%
+now i have some mem some numbers i've
+ 
+
+ align:start position:0%
+now i have some mem some numbers i've
+committed to memory i uh trust my num my
+
+ align:start position:0%
+committed to memory i uh trust my num my
+ 
+
+ align:start position:0%
+committed to memory i uh trust my num my
+my my memory on these numbers
+
+ align:start position:0%
+my my memory on these numbers
+ 
+
+ align:start position:0%
+my my memory on these numbers
+but that doesn't mean i'm going to ask
+
+ align:start position:0%
+but that doesn't mean i'm going to ask
+ 
+
+ align:start position:0%
+but that doesn't mean i'm going to ask
+you to trust these numbers
+
+ align:start position:0%
+you to trust these numbers
+ 
+
+ align:start position:0%
+you to trust these numbers
+so as a matter of fact i'm going to ask
+
+ align:start position:0%
+so as a matter of fact i'm going to ask
+ 
+
+ align:start position:0%
+so as a matter of fact i'm going to ask
+you to look them up but i have some
+
+ align:start position:0%
+you to look them up but i have some
+ 
+
+ align:start position:0%
+you to look them up but i have some
+other figures some other numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before the civil war before 1861
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there were 350 universities in the
+
+ align:start position:0%
+there were 350 universities in the
+ 
+
+ align:start position:0%
+there were 350 universities in the
+united states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it got up to about 350.
+
+ align:start position:0%
+it got up to about 350.
+ 
+
+ align:start position:0%
+it got up to about 350.
+now some
+
+ align:start position:0%
+now some
+ 
+
+ align:start position:0%
+now some
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+closed their doors there were new ones
+
+ align:start position:0%
+closed their doors there were new ones
+ 
+
+ align:start position:0%
+closed their doors there were new ones
+that came in but there were about 350 of
+
+ align:start position:0%
+that came in but there were about 350 of
+ 
+
+ align:start position:0%
+that came in but there were about 350 of
+them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+11 out of 12 of those universities
+
+ align:start position:0%
+11 out of 12 of those universities
+ 
+
+ align:start position:0%
+11 out of 12 of those universities
+over the entire periods of their
+
+ align:start position:0%
+over the entire periods of their
+ 
+
+ align:start position:0%
+over the entire periods of their
+existence
+
+ align:start position:0%
+existence
+ 
+
+ align:start position:0%
+existence
+up until
+
+ align:start position:0%
+up until
+ 
+
+ align:start position:0%
+up until
+the civil war
+
+ align:start position:0%
+the civil war
+ 
+
+ align:start position:0%
+the civil war
+11 out of 12 presidents were
+
+ align:start position:0%
+11 out of 12 presidents were
+ 
+
+ align:start position:0%
+11 out of 12 presidents were
+clergymen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and many of the ones who were not clergy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+had studied for the ministry but decided
+
+ align:start position:0%
+had studied for the ministry but decided
+ 
+
+ align:start position:0%
+had studied for the ministry but decided
+either to go to law or otherwise not get
+
+ align:start position:0%
+either to go to law or otherwise not get
+ 
+
+ align:start position:0%
+either to go to law or otherwise not get
+ordained
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in 1833
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a man by the name of john quincy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not to be confused with john quincy
+
+ align:start position:0%
+not to be confused with john quincy
+ 
+
+ align:start position:0%
+not to be confused with john quincy
+adams
+
+ align:start position:0%
+adams
+ 
+
+ align:start position:0%
+adams
+but i think was a relative of john
+
+ align:start position:0%
+but i think was a relative of john
+ 
+
+ align:start position:0%
+but i think was a relative of john
+quincy adams
+
+ align:start position:0%
+quincy adams
+ 
+
+ align:start position:0%
+quincy adams
+a man by the name of john quincy became
+
+ align:start position:0%
+a man by the name of john quincy became
+ 
+
+ align:start position:0%
+a man by the name of john quincy became
+pres became president of harvard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and john quincy said
+
+ align:start position:0%
+and john quincy said
+ 
+
+ align:start position:0%
+and john quincy said
+his program is to get rid of classical
+
+ align:start position:0%
+his program is to get rid of classical
+ 
+
+ align:start position:0%
+his program is to get rid of classical
+education
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he was not
+
+ align:start position:0%
+he was not
+ 
+
+ align:start position:0%
+he was not
+a clergyman
+
+ align:start position:0%
+a clergyman
+ 
+
+ align:start position:0%
+a clergyman
+he was one of the first clergyman to
+
+ align:start position:0%
+he was one of the first clergyman to
+ 
+
+ align:start position:0%
+he was one of the first clergyman to
+become president of the university of
+
+ align:start position:0%
+become president of the university of
+ 
+
+ align:start position:0%
+become president of the university of
+the united states
+
+ align:start position:0%
+the united states
+ 
+
+ align:start position:0%
+the united states
+who was not a clergyman at all
+
+ align:start position:0%
+who was not a clergyman at all
+ 
+
+ align:start position:0%
+who was not a clergyman at all
+and i mean at all in any of his training
+
+ align:start position:0%
+and i mean at all in any of his training
+ 
+
+ align:start position:0%
+and i mean at all in any of his training
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now why did he want to get rid of
+
+ align:start position:0%
+now why did he want to get rid of
+ 
+
+ align:start position:0%
+now why did he want to get rid of
+classical education and what did he want
+
+ align:start position:0%
+classical education and what did he want
+ 
+
+ align:start position:0%
+classical education and what did he want
+to want to want to replace it with and
+
+ align:start position:0%
+to want to want to replace it with and
+ 
+
+ align:start position:0%
+to want to want to replace it with and
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+um if you don't know
+
+ align:start position:0%
+um if you don't know
+ 
+
+ align:start position:0%
+um if you don't know
+your speculation is invited because you
+
+ align:start position:0%
+your speculation is invited because you
+ 
+
+ align:start position:0%
+your speculation is invited because you
+will probably be right
+
+ align:start position:0%
+will probably be right
+ 
+
+ align:start position:0%
+will probably be right
+we're talking about 1833
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very beginning of the industrial
+
+ align:start position:0%
+very beginning of the industrial
+ 
+
+ align:start position:0%
+very beginning of the industrial
+revolution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is classical education going to help you
+
+ align:start position:0%
+is classical education going to help you
+ 
+
+ align:start position:0%
+is classical education going to help you
+make a
+
+ align:start position:0%
+make a
+ 
+
+ align:start position:0%
+make a
+a plant
+
+ align:start position:0%
+a plant
+ 
+
+ align:start position:0%
+a plant
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+at least in his mind and apparently he
+
+ align:start position:0%
+at least in his mind and apparently he
+ 
+
+ align:start position:0%
+at least in his mind and apparently he
+was not alone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what would
+
+ align:start position:0%
+so what would
+ 
+
+ align:start position:0%
+so what would
+get the united states into the
+
+ align:start position:0%
+get the united states into the
+ 
+
+ align:start position:0%
+get the united states into the
+industrial revolution
+
+ align:start position:0%
+industrial revolution
+ 
+
+ align:start position:0%
+industrial revolution
+which had already started in in britain
+
+ align:start position:0%
+which had already started in in britain
+ 
+
+ align:start position:0%
+which had already started in in britain
+at that time
+
+ align:start position:0%
+at that time
+ 
+
+ align:start position:0%
+at that time
+when did it get on the continent
+
+ align:start position:0%
+when did it get on the continent
+ 
+
+ align:start position:0%
+when did it get on the continent
+before us i'm sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around that time turn this okay
+
+ align:start position:0%
+around that time turn this okay
+ 
+
+ align:start position:0%
+around that time turn this okay
+john quincy now here's where you have to
+
+ align:start position:0%
+john quincy now here's where you have to
+ 
+
+ align:start position:0%
+john quincy now here's where you have to
+when you read any of this stuff you have
+
+ align:start position:0%
+when you read any of this stuff you have
+ 
+
+ align:start position:0%
+when you read any of this stuff you have
+to you have to read between the lines on
+
+ align:start position:0%
+to you have to read between the lines on
+ 
+
+ align:start position:0%
+to you have to read between the lines on
+on some of the
+
+ align:start position:0%
+on some of the
+ 
+
+ align:start position:0%
+on some of the
+the words they use john quincy said
+
+ align:start position:0%
+the words they use john quincy said
+ 
+
+ align:start position:0%
+the words they use john quincy said
+science and mathematics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you can say well science and
+
+ align:start position:0%
+okay so you can say well science and
+ 
+
+ align:start position:0%
+okay so you can say well science and
+mathematics is already here
+
+ align:start position:0%
+mathematics is already here
+ 
+
+ align:start position:0%
+mathematics is already here
+john quincy meant applied science
+
+ align:start position:0%
+john quincy meant applied science
+ 
+
+ align:start position:0%
+john quincy meant applied science
+and applied mathematics
+
+ align:start position:0%
+and applied mathematics
+ 
+
+ align:start position:0%
+and applied mathematics
+and he did not
+
+ align:start position:0%
+and he did not
+ 
+
+ align:start position:0%
+and he did not
+use the word engineering at the
+
+ align:start position:0%
+use the word engineering at the
+ 
+
+ align:start position:0%
+use the word engineering at the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+but that's who these people were they
+
+ align:start position:0%
+but that's who these people were they
+ 
+
+ align:start position:0%
+but that's who these people were they
+were engineers
+
+ align:start position:0%
+were engineers
+ 
+
+ align:start position:0%
+were engineers
+uh applied scientists and applied
+
+ align:start position:0%
+uh applied scientists and applied
+ 
+
+ align:start position:0%
+uh applied scientists and applied
+mathematicians that's what he thought we
+
+ align:start position:0%
+mathematicians that's what he thought we
+ 
+
+ align:start position:0%
+mathematicians that's what he thought we
+needed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a struggle
+
+ align:start position:0%
+so a struggle
+ 
+
+ align:start position:0%
+so a struggle
+ensued at that point
+
+ align:start position:0%
+ensued at that point
+ 
+
+ align:start position:0%
+ensued at that point
+that has not been
+
+ align:start position:0%
+that has not been
+ 
+
+ align:start position:0%
+that has not been
+resolved
+
+ align:start position:0%
+resolved
+ 
+
+ align:start position:0%
+resolved
+in the united states
+
+ align:start position:0%
+in the united states
+ 
+
+ align:start position:0%
+in the united states
+john quincy introduced
+
+ align:start position:0%
+john quincy introduced
+ 
+
+ align:start position:0%
+john quincy introduced
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+new curriculum
+
+ align:start position:0%
+new curriculum
+ 
+
+ align:start position:0%
+new curriculum
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+got a name
+
+ align:start position:0%
+got a name
+ 
+
+ align:start position:0%
+got a name
+a hundred years later
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay i'll tell you what the name of it
+
+ align:start position:0%
+okay i'll tell you what the name of it
+ 
+
+ align:start position:0%
+okay i'll tell you what the name of it
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pragmatism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it had went by different names it's
+
+ align:start position:0%
+so it had went by different names it's
+ 
+
+ align:start position:0%
+so it had went by different names it's
+still you can talk about
+
+ align:start position:0%
+still you can talk about
+ 
+
+ align:start position:0%
+still you can talk about
+the alternative to classical education
+
+ align:start position:0%
+the alternative to classical education
+ 
+
+ align:start position:0%
+the alternative to classical education
+being pragmatic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+scholars of education have different
+
+ align:start position:0%
+scholars of education have different
+ 
+
+ align:start position:0%
+scholars of education have different
+names but it's good for us in this class
+
+ align:start position:0%
+names but it's good for us in this class
+ 
+
+ align:start position:0%
+names but it's good for us in this class
+to use the philosophical name because we
+
+ align:start position:0%
+to use the philosophical name because we
+ 
+
+ align:start position:0%
+to use the philosophical name because we
+can now associate that with a person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+john dewey
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now what was the nature of this
+
+ align:start position:0%
+okay now what was the nature of this
+ 
+
+ align:start position:0%
+okay now what was the nature of this
+why do you think people would do battle
+
+ align:start position:0%
+why do you think people would do battle
+ 
+
+ align:start position:0%
+why do you think people would do battle
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+replacing the curriculum
+
+ align:start position:0%
+replacing the curriculum
+ 
+
+ align:start position:0%
+replacing the curriculum
+replacing classical education
+
+ align:start position:0%
+replacing classical education
+ 
+
+ align:start position:0%
+replacing classical education
+let's think of all of the reasons well
+
+ align:start position:0%
+let's think of all of the reasons well
+ 
+
+ align:start position:0%
+let's think of all of the reasons well
+one of them starts out means that
+
+ align:start position:0%
+one of them starts out means that
+ 
+
+ align:start position:0%
+one of them starts out means that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+religious institutions have funded a
+
+ align:start position:0%
+religious institutions have funded a
+ 
+
+ align:start position:0%
+religious institutions have funded a
+whole lot of colleges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+and if not anti-religious dir definitely
+
+ align:start position:0%
+and if not anti-religious dir definitely
+ 
+
+ align:start position:0%
+and if not anti-religious dir definitely
+anti-religious people
+
+ align:start position:0%
+anti-religious people
+ 
+
+ align:start position:0%
+anti-religious people
+or better stated
+
+ align:start position:0%
+or better stated
+ 
+
+ align:start position:0%
+or better stated
+anti-religious control
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you go to the midwest today
+
+ align:start position:0%
+and if you go to the midwest today
+ 
+
+ align:start position:0%
+and if you go to the midwest today
+you see much of the same arguments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about schools
+
+ align:start position:0%
+about schools
+ 
+
+ align:start position:0%
+about schools
+today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what happened was the the main
+
+ align:start position:0%
+well what happened was the the main
+ 
+
+ align:start position:0%
+well what happened was the the main
+reason i'm bringing this up and i'm
+
+ align:start position:0%
+reason i'm bringing this up and i'm
+ 
+
+ align:start position:0%
+reason i'm bringing this up and i'm
+still going to go back and do some more
+
+ align:start position:0%
+still going to go back and do some more
+ 
+
+ align:start position:0%
+still going to go back and do some more
+history i'm still going to require you
+
+ align:start position:0%
+history i'm still going to require you
+ 
+
+ align:start position:0%
+history i'm still going to require you
+to get these numbers right i'm still
+
+ align:start position:0%
+to get these numbers right i'm still
+ 
+
+ align:start position:0%
+to get these numbers right i'm still
+going to require you to say when you've
+
+ align:start position:0%
+going to require you to say when you've
+ 
+
+ align:start position:0%
+going to require you to say when you've
+got the numbers right to bring the right
+
+ align:start position:0%
+got the numbers right to bring the right
+ 
+
+ align:start position:0%
+got the numbers right to bring the right
+numbers back to class
+
+ align:start position:0%
+numbers back to class
+ 
+
+ align:start position:0%
+numbers back to class
+okay but nevertheless uh i'm gonna trust
+
+ align:start position:0%
+okay but nevertheless uh i'm gonna trust
+ 
+
+ align:start position:0%
+okay but nevertheless uh i'm gonna trust
+my memory um for right now um
+
+ align:start position:0%
+my memory um for right now um
+ 
+
+ align:start position:0%
+my memory um for right now um
+no the main reason for bringing this up
+
+ align:start position:0%
+no the main reason for bringing this up
+ 
+
+ align:start position:0%
+no the main reason for bringing this up
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+character
+
+ align:start position:0%
+character
+ 
+
+ align:start position:0%
+character
+this whole platonic tradition
+
+ align:start position:0%
+this whole platonic tradition
+ 
+
+ align:start position:0%
+this whole platonic tradition
+got wiped out in the united states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we never replaced it if we had religious
+
+ align:start position:0%
+we never replaced it if we had religious
+ 
+
+ align:start position:0%
+we never replaced it if we had religious
+character at first could we have another
+
+ align:start position:0%
+character at first could we have another
+ 
+
+ align:start position:0%
+character at first could we have another
+kind of character
+
+ align:start position:0%
+kind of character
+ 
+
+ align:start position:0%
+kind of character
+it never was replaced
+
+ align:start position:0%
+it never was replaced
+ 
+
+ align:start position:0%
+it never was replaced
+okay now that's the reason i'm bringing
+
+ align:start position:0%
+okay now that's the reason i'm bringing
+ 
+
+ align:start position:0%
+okay now that's the reason i'm bringing
+it up
+
+ align:start position:0%
+it up
+ 
+
+ align:start position:0%
+it up
+that plato got wiped out
+
+ align:start position:0%
+that plato got wiped out
+ 
+
+ align:start position:0%
+that plato got wiped out
+and in the end i'm going to say plato's
+
+ align:start position:0%
+and in the end i'm going to say plato's
+ 
+
+ align:start position:0%
+and in the end i'm going to say plato's
+got to be brought back
+
+ align:start position:0%
+got to be brought back
+ 
+
+ align:start position:0%
+got to be brought back
+all right so i'm going to give you my
+
+ align:start position:0%
+all right so i'm going to give you my
+ 
+
+ align:start position:0%
+all right so i'm going to give you my
+thesis on it you don't have to
+
+ align:start position:0%
+thesis on it you don't have to
+ 
+
+ align:start position:0%
+thesis on it you don't have to
+adopt my thesis on it
+
+ align:start position:0%
+adopt my thesis on it
+ 
+
+ align:start position:0%
+adopt my thesis on it
+but if you don't adopt my thesis on it
+
+ align:start position:0%
+but if you don't adopt my thesis on it
+ 
+
+ align:start position:0%
+but if you don't adopt my thesis on it
+you've got two responsibilities number
+
+ align:start position:0%
+you've got two responsibilities number
+ 
+
+ align:start position:0%
+you've got two responsibilities number
+one tell me what
+
+ align:start position:0%
+one tell me what
+ 
+
+ align:start position:0%
+one tell me what
+thesis you do adopt and number two
+
+ align:start position:0%
+thesis you do adopt and number two
+ 
+
+ align:start position:0%
+thesis you do adopt and number two
+give me your justification
+
+ align:start position:0%
+give me your justification
+ 
+
+ align:start position:0%
+give me your justification
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+but the but the fact is that we just
+
+ align:start position:0%
+but the but the fact is that we just
+ 
+
+ align:start position:0%
+but the but the fact is that we just
+won't see this tradition
+
+ align:start position:0%
+won't see this tradition
+ 
+
+ align:start position:0%
+won't see this tradition
+in the united states after the civil war
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh we have what's called the scopes
+
+ align:start position:0%
+uh we have what's called the scopes
+ 
+
+ align:start position:0%
+uh we have what's called the scopes
+trial
+
+ align:start position:0%
+trial
+ 
+
+ align:start position:0%
+trial
+in the united states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where a school teacher this was in the
+
+ align:start position:0%
+where a school teacher this was in the
+ 
+
+ align:start position:0%
+where a school teacher this was in the
+1920s
+
+ align:start position:0%
+1920s
+ 
+
+ align:start position:0%
+1920s
+was put on trial
+
+ align:start position:0%
+was put on trial
+ 
+
+ align:start position:0%
+was put on trial
+for teaching creationism in the class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it had
+
+ align:start position:0%
+and it had
+ 
+
+ align:start position:0%
+and it had
+evolution
+
+ align:start position:0%
+evolution
+ 
+
+ align:start position:0%
+evolution
+i said creationism i didn't mean to
+
+ align:start position:0%
+i said creationism i didn't mean to
+ 
+
+ align:start position:0%
+i said creationism i didn't mean to
+sacrifice i meant to say evolution it
+
+ align:start position:0%
+sacrifice i meant to say evolution it
+ 
+
+ align:start position:0%
+sacrifice i meant to say evolution it
+was against creationism
+
+ align:start position:0%
+was against creationism
+ 
+
+ align:start position:0%
+was against creationism
+uh in the in the classroom it became
+
+ align:start position:0%
+uh in the in the classroom it became
+ 
+
+ align:start position:0%
+uh in the in the classroom it became
+national news and became a big they made
+
+ align:start position:0%
+national news and became a big they made
+ 
+
+ align:start position:0%
+national news and became a big they made
+movies out of it
+
+ align:start position:0%
+movies out of it
+ 
+
+ align:start position:0%
+movies out of it
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so uh this this battle continues can you
+
+ align:start position:0%
+so uh this this battle continues can you
+ 
+
+ align:start position:0%
+so uh this this battle continues can you
+think of any other reasons
+
+ align:start position:0%
+think of any other reasons
+ 
+
+ align:start position:0%
+think of any other reasons
+that people would want to fight over
+
+ align:start position:0%
+that people would want to fight over
+ 
+
+ align:start position:0%
+that people would want to fight over
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clearly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+john dewey said why have
+
+ align:start position:0%
+john dewey said why have
+ 
+
+ align:start position:0%
+john dewey said why have
+john dewey said why i have education
+
+ align:start position:0%
+john dewey said why i have education
+ 
+
+ align:start position:0%
+john dewey said why i have education
+just for the aristocrats and the
+
+ align:start position:0%
+just for the aristocrats and the
+ 
+
+ align:start position:0%
+just for the aristocrats and the
+preachers
+
+ align:start position:0%
+preachers
+ 
+
+ align:start position:0%
+preachers
+why not the poor people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+it was threatening to them in many ways
+
+ align:start position:0%
+it was threatening to them in many ways
+ 
+
+ align:start position:0%
+it was threatening to them in many ways
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh can you imagine yourself an
+
+ align:start position:0%
+uh can you imagine yourself an
+ 
+
+ align:start position:0%
+uh can you imagine yourself an
+aristocrat in 1850
+
+ align:start position:0%
+aristocrat in 1850
+ 
+
+ align:start position:0%
+aristocrat in 1850
+at harvard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's some kid just coming off a farm
+
+ align:start position:0%
+there's some kid just coming off a farm
+ 
+
+ align:start position:0%
+there's some kid just coming off a farm
+from iowa
+
+ align:start position:0%
+from iowa
+ 
+
+ align:start position:0%
+from iowa
+coming to harvard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not a fit
+
+ align:start position:0%
+not a fit
+ 
+
+ align:start position:0%
+not a fit
+you can see where somebody would object
+
+ align:start position:0%
+you can see where somebody would object
+ 
+
+ align:start position:0%
+you can see where somebody would object
+to that teachers students everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that there was a class issue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this whole thing filtered all the
+
+ align:start position:0%
+and this whole thing filtered all the
+ 
+
+ align:start position:0%
+and this whole thing filtered all the
+way down to first grade not just the
+
+ align:start position:0%
+way down to first grade not just the
+ 
+
+ align:start position:0%
+way down to first grade not just the
+colleges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right can you think of another issue
+
+ align:start position:0%
+all right can you think of another issue
+ 
+
+ align:start position:0%
+all right can you think of another issue
+any other issue i'll tell you one that's
+
+ align:start position:0%
+any other issue i'll tell you one that's
+ 
+
+ align:start position:0%
+any other issue i'll tell you one that's
+not that that actually it's sort of like
+
+ align:start position:0%
+not that that actually it's sort of like
+ 
+
+ align:start position:0%
+not that that actually it's sort of like
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+it's actually one that's sort of obvious
+
+ align:start position:0%
+it's actually one that's sort of obvious
+ 
+
+ align:start position:0%
+it's actually one that's sort of obvious
+when you think about it but you might
+
+ align:start position:0%
+when you think about it but you might
+ 
+
+ align:start position:0%
+when you think about it but you might
+not be motivated to think about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's to me what turned out to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+battleground in the united states over
+
+ align:start position:0%
+battleground in the united states over
+ 
+
+ align:start position:0%
+battleground in the united states over
+these two forms of education
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think was paramount
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that was
+
+ align:start position:0%
+and that was
+ 
+
+ align:start position:0%
+and that was
+here's the question
+
+ align:start position:0%
+here's the question
+ 
+
+ align:start position:0%
+here's the question
+here is the question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've talked about means and ends
+
+ align:start position:0%
+we've talked about means and ends
+ 
+
+ align:start position:0%
+we've talked about means and ends
+we gave a name to it called teleology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the question is what is the end of
+
+ align:start position:0%
+and the question is what is the end of
+ 
+
+ align:start position:0%
+and the question is what is the end of
+education
+
+ align:start position:0%
+education
+ 
+
+ align:start position:0%
+education
+the state or the individual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+john dewey's end was the state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+classical education is the individual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i see what you're saying this was a
+
+ align:start position:0%
+i see what you're saying this was a
+ 
+
+ align:start position:0%
+i see what you're saying this was a
+matter of open debate and it was a
+
+ align:start position:0%
+matter of open debate and it was a
+ 
+
+ align:start position:0%
+matter of open debate and it was a
+matter that dewey was charged with
+
+ align:start position:0%
+matter that dewey was charged with
+ 
+
+ align:start position:0%
+matter that dewey was charged with
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+dewey and i think it's fair to say that
+
+ align:start position:0%
+dewey and i think it's fair to say that
+ 
+
+ align:start position:0%
+dewey and i think it's fair to say that
+in his mind
+
+ align:start position:0%
+in his mind
+ 
+
+ align:start position:0%
+in his mind
+his greatest work
+
+ align:start position:0%
+his greatest work
+ 
+
+ align:start position:0%
+his greatest work
+was one of his later works we got plenty
+
+ align:start position:0%
+was one of his later works we got plenty
+ 
+
+ align:start position:0%
+was one of his later works we got plenty
+of time
+
+ align:start position:0%
+of time
+ 
+
+ align:start position:0%
+of time
+was one of his later works called
+
+ align:start position:0%
+was one of his later works called
+ 
+
+ align:start position:0%
+was one of his later works called
+democracy and education
+
+ align:start position:0%
+democracy and education
+ 
+
+ align:start position:0%
+democracy and education
+so dewey tried to defend himself
+
+ align:start position:0%
+so dewey tried to defend himself
+ 
+
+ align:start position:0%
+so dewey tried to defend himself
+against these claims of education for
+
+ align:start position:0%
+against these claims of education for
+ 
+
+ align:start position:0%
+against these claims of education for
+the state as a very as opposed to the
+
+ align:start position:0%
+the state as a very as opposed to the
+ 
+
+ align:start position:0%
+the state as a very as opposed to the
+individual
+
+ align:start position:0%
+individual
+ 
+
+ align:start position:0%
+individual
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+i happen to take the position that that
+
+ align:start position:0%
+i happen to take the position that that
+ 
+
+ align:start position:0%
+i happen to take the position that that
+defense is not strong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but i'm not but the point the point that
+
+ align:start position:0%
+but i'm not but the point the point that
+ 
+
+ align:start position:0%
+but i'm not but the point the point that
+i want to make that i think uh we all
+
+ align:start position:0%
+i want to make that i think uh we all
+ 
+
+ align:start position:0%
+i want to make that i think uh we all
+will agree on it and be able to see the
+
+ align:start position:0%
+will agree on it and be able to see the
+ 
+
+ align:start position:0%
+will agree on it and be able to see the
+justification that this was a
+
+ align:start position:0%
+justification that this was a
+ 
+
+ align:start position:0%
+justification that this was a
+point of debate
+
+ align:start position:0%
+point of debate
+ 
+
+ align:start position:0%
+point of debate
+there was a major point of debate and it
+
+ align:start position:0%
+there was a major point of debate and it
+ 
+
+ align:start position:0%
+there was a major point of debate and it
+continues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+the classicist the cl the religious
+
+ align:start position:0%
+the classicist the cl the religious
+ 
+
+ align:start position:0%
+the classicist the cl the religious
+classes would say
+
+ align:start position:0%
+classes would say
+ 
+
+ align:start position:0%
+classes would say
+that the ideal for the state is in
+
+ align:start position:0%
+that the ideal for the state is in
+ 
+
+ align:start position:0%
+that the ideal for the state is in
+heaven
+
+ align:start position:0%
+heaven
+ 
+
+ align:start position:0%
+heaven
+more precisely that if you're if you're
+
+ align:start position:0%
+more precisely that if you're if you're
+ 
+
+ align:start position:0%
+more precisely that if you're if you're
+christian you're talking about the
+
+ align:start position:0%
+christian you're talking about the
+ 
+
+ align:start position:0%
+christian you're talking about the
+trinity
+
+ align:start position:0%
+trinity
+ 
+
+ align:start position:0%
+trinity
+that the relationship of god the father
+
+ align:start position:0%
+that the relationship of god the father
+ 
+
+ align:start position:0%
+that the relationship of god the father
+god the son god the holy spirit is the
+
+ align:start position:0%
+god the son god the holy spirit is the
+ 
+
+ align:start position:0%
+god the son god the holy spirit is the
+model for the family
+
+ align:start position:0%
+model for the family
+ 
+
+ align:start position:0%
+model for the family
+for government
+
+ align:start position:0%
+for government
+ 
+
+ align:start position:0%
+for government
+for the community for business
+
+ align:start position:0%
+for the community for business
+ 
+
+ align:start position:0%
+for the community for business
+all right that's what they would say
+
+ align:start position:0%
+all right that's what they would say
+ 
+
+ align:start position:0%
+all right that's what they would say
+so they said so they would say yes we
+
+ align:start position:0%
+so they said so they would say yes we
+ 
+
+ align:start position:0%
+so they said so they would say yes we
+are not just for the individual but
+
+ align:start position:0%
+are not just for the individual but
+ 
+
+ align:start position:0%
+are not just for the individual but
+we're for the state
+
+ align:start position:0%
+we're for the state
+ 
+
+ align:start position:0%
+we're for the state
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+john dewey and the others will say
+
+ align:start position:0%
+john dewey and the others will say
+ 
+
+ align:start position:0%
+john dewey and the others will say
+that argument doesn't sound strong
+
+ align:start position:0%
+that argument doesn't sound strong
+ 
+
+ align:start position:0%
+that argument doesn't sound strong
+coming from you all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+democracy is by definition as the greeks
+
+ align:start position:0%
+democracy is by definition as the greeks
+ 
+
+ align:start position:0%
+democracy is by definition as the greeks
+put it a community of free individuals
+
+ align:start position:0%
+put it a community of free individuals
+ 
+
+ align:start position:0%
+put it a community of free individuals
+the individual is the primacy in
+
+ align:start position:0%
+the individual is the primacy in
+ 
+
+ align:start position:0%
+the individual is the primacy in
+democracy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh they so everybody said we're
+
+ align:start position:0%
+so uh they so everybody said we're
+ 
+
+ align:start position:0%
+so uh they so everybody said we're
+covering both bases and each side said
+
+ align:start position:0%
+covering both bases and each side said
+ 
+
+ align:start position:0%
+covering both bases and each side said
+you really aren't sincere about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in 1945
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a very important book was published it
+
+ align:start position:0%
+a very important book was published it
+ 
+
+ align:start position:0%
+a very important book was published it
+was called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general education in a free society
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this book came out in 1945 that's
+
+ align:start position:0%
+now this book came out in 1945 that's
+ 
+
+ align:start position:0%
+now this book came out in 1945 that's
+auspicious
+
+ align:start position:0%
+auspicious
+ 
+
+ align:start position:0%
+auspicious
+second world world war ended
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the national science foundation was
+
+ align:start position:0%
+the national science foundation was
+ 
+
+ align:start position:0%
+the national science foundation was
+founded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it attempted
+
+ align:start position:0%
+and it attempted
+ 
+
+ align:start position:0%
+and it attempted
+general education and free society this
+
+ align:start position:0%
+general education and free society this
+ 
+
+ align:start position:0%
+general education and free society this
+book
+
+ align:start position:0%
+book
+ 
+
+ align:start position:0%
+book
+to make sense out of this debate
+
+ align:start position:0%
+to make sense out of this debate
+ 
+
+ align:start position:0%
+to make sense out of this debate
+classical versus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pragmatic education
+
+ align:start position:0%
+pragmatic education
+ 
+
+ align:start position:0%
+pragmatic education
+tried to find a compromise
+
+ align:start position:0%
+tried to find a compromise
+ 
+
+ align:start position:0%
+tried to find a compromise
+now who wrote it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right you ready for this if you
+
+ align:start position:0%
+all right you ready for this if you
+ 
+
+ align:start position:0%
+all right you ready for this if you
+haven't heard of haven't heard of this
+
+ align:start position:0%
+haven't heard of haven't heard of this
+ 
+
+ align:start position:0%
+haven't heard of haven't heard of this
+book you'd never guess who wrote it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll tell you why you'd never get it was
+
+ align:start position:0%
+i'll tell you why you'd never get it was
+ 
+
+ align:start position:0%
+i'll tell you why you'd never get it was
+a committee that wrote it
+
+ align:start position:0%
+a committee that wrote it
+ 
+
+ align:start position:0%
+a committee that wrote it
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+it was a faculty committee at harvard
+
+ align:start position:0%
+it was a faculty committee at harvard
+ 
+
+ align:start position:0%
+it was a faculty committee at harvard
+believe it i mentioned harvard three
+
+ align:start position:0%
+believe it i mentioned harvard three
+ 
+
+ align:start position:0%
+believe it i mentioned harvard three
+times already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it was a faculty committee at harvard uh
+
+ align:start position:0%
+it was a faculty committee at harvard uh
+ 
+
+ align:start position:0%
+it was a faculty committee at harvard uh
+commissioned by james by a very famous
+
+ align:start position:0%
+commissioned by james by a very famous
+ 
+
+ align:start position:0%
+commissioned by james by a very famous
+college president a lot of you can name
+
+ align:start position:0%
+college president a lot of you can name
+ 
+
+ align:start position:0%
+college president a lot of you can name
+a lot of nobel prize winning faculty
+
+ align:start position:0%
+a lot of nobel prize winning faculty
+ 
+
+ align:start position:0%
+a lot of nobel prize winning faculty
+members but it's hard to name college
+
+ align:start position:0%
+members but it's hard to name college
+ 
+
+ align:start position:0%
+members but it's hard to name college
+presidents
+
+ align:start position:0%
+presidents
+ 
+
+ align:start position:0%
+presidents
+but there's one that you ought to
+
+ align:start position:0%
+but there's one that you ought to
+ 
+
+ align:start position:0%
+but there's one that you ought to
+remember james bryant conant c-o-n-a-n-t
+
+ align:start position:0%
+remember james bryant conant c-o-n-a-n-t
+ 
+
+ align:start position:0%
+remember james bryant conant c-o-n-a-n-t
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and uh he commissioned this uh committee
+
+ align:start position:0%
+and uh he commissioned this uh committee
+ 
+
+ align:start position:0%
+and uh he commissioned this uh committee
+and the committee came back with this
+
+ align:start position:0%
+and the committee came back with this
+ 
+
+ align:start position:0%
+and the committee came back with this
+report and the report
+
+ align:start position:0%
+report and the report
+ 
+
+ align:start position:0%
+report and the report
+uh actually tried to make a compromise
+
+ align:start position:0%
+uh actually tried to make a compromise
+ 
+
+ align:start position:0%
+uh actually tried to make a compromise
+out of all of this uh we can go through
+
+ align:start position:0%
+out of all of this uh we can go through
+ 
+
+ align:start position:0%
+out of all of this uh we can go through
+what the compromise meant
+
+ align:start position:0%
+what the compromise meant
+ 
+
+ align:start position:0%
+what the compromise meant
+uh i'd like to take a minute or two to
+
+ align:start position:0%
+uh i'd like to take a minute or two to
+ 
+
+ align:start position:0%
+uh i'd like to take a minute or two to
+say what the compromise meant but the
+
+ align:start position:0%
+say what the compromise meant but the
+ 
+
+ align:start position:0%
+say what the compromise meant but the
+compromise never stuck and i'll tell you
+
+ align:start position:0%
+compromise never stuck and i'll tell you
+ 
+
+ align:start position:0%
+compromise never stuck and i'll tell you
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+let's see let's see what what
+
+ align:start position:0%
+let's see let's see what what
+ 
+
+ align:start position:0%
+let's see let's see what what
+what this very important book is about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it's a book that's hard to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to my knowledge you might be able to get
+
+ align:start position:0%
+to my knowledge you might be able to get
+ 
+
+ align:start position:0%
+to my knowledge you might be able to get
+it on ebay you won't be able to get it
+
+ align:start position:0%
+it on ebay you won't be able to get it
+ 
+
+ align:start position:0%
+it on ebay you won't be able to get it
+on amazon.com
+
+ align:start position:0%
+on amazon.com
+ 
+
+ align:start position:0%
+on amazon.com
+i tell you where else you will not be
+
+ align:start position:0%
+i tell you where else you will not be
+ 
+
+ align:start position:0%
+i tell you where else you will not be
+able to get it
+
+ align:start position:0%
+able to get it
+ 
+
+ align:start position:0%
+able to get it
+harvard's bookstore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh my copy was a gift
+
+ align:start position:0%
+um uh my copy was a gift
+ 
+
+ align:start position:0%
+um uh my copy was a gift
+from an older faculty member when i was
+
+ align:start position:0%
+from an older faculty member when i was
+ 
+
+ align:start position:0%
+from an older faculty member when i was
+a young faculty member
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here's what they tried to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general education in the free society
+
+ align:start position:0%
+general education in the free society
+ 
+
+ align:start position:0%
+general education in the free society
+then i'll go back to these slides and
+
+ align:start position:0%
+then i'll go back to these slides and
+ 
+
+ align:start position:0%
+then i'll go back to these slides and
+then we'll get on and we'll finish up
+
+ align:start position:0%
+then we'll get on and we'll finish up
+ 
+
+ align:start position:0%
+then we'll get on and we'll finish up
+the class
+
+ align:start position:0%
+the class
+ 
+
+ align:start position:0%
+the class
+general education in a free society said
+
+ align:start position:0%
+general education in a free society said
+ 
+
+ align:start position:0%
+general education in a free society said
+that education has got to have two parts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one part
+
+ align:start position:0%
+one part
+ 
+
+ align:start position:0%
+one part
+is pus is for the individual and the
+
+ align:start position:0%
+is pus is for the individual and the
+ 
+
+ align:start position:0%
+is pus is for the individual and the
+other part is for the state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the part that's for the individual is
+
+ align:start position:0%
+the part that's for the individual is
+ 
+
+ align:start position:0%
+the part that's for the individual is
+called general education
+
+ align:start position:0%
+called general education
+ 
+
+ align:start position:0%
+called general education
+and you take many classical studies
+
+ align:start position:0%
+and you take many classical studies
+ 
+
+ align:start position:0%
+and you take many classical studies
+and it's supposed to be um to bring back
+
+ align:start position:0%
+and it's supposed to be um to bring back
+ 
+
+ align:start position:0%
+and it's supposed to be um to bring back
+character i'm gonna tell you why it
+
+ align:start position:0%
+character i'm gonna tell you why it
+ 
+
+ align:start position:0%
+character i'm gonna tell you why it
+never came back but that's
+
+ align:start position:0%
+never came back but that's
+ 
+
+ align:start position:0%
+never came back but that's
+that's what the argument was
+
+ align:start position:0%
+that's what the argument was
+ 
+
+ align:start position:0%
+that's what the argument was
+and that special education was the other
+
+ align:start position:0%
+and that special education was the other
+ 
+
+ align:start position:0%
+and that special education was the other
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and special education was to um
+
+ align:start position:0%
+and special education was to um
+ 
+
+ align:start position:0%
+and special education was to um
+help you find a job in a career
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and given that the state
+
+ align:start position:0%
+and given that the state
+ 
+
+ align:start position:0%
+and given that the state
+uh pretty much determines
+
+ align:start position:0%
+uh pretty much determines
+ 
+
+ align:start position:0%
+uh pretty much determines
+what jobs are available
+
+ align:start position:0%
+what jobs are available
+ 
+
+ align:start position:0%
+what jobs are available
+and where your career is going that's
+
+ align:start position:0%
+and where your career is going that's
+ 
+
+ align:start position:0%
+and where your career is going that's
+indirectly how you satisfy
+
+ align:start position:0%
+indirectly how you satisfy
+ 
+
+ align:start position:0%
+indirectly how you satisfy
+the people who say
+
+ align:start position:0%
+the people who say
+ 
+
+ align:start position:0%
+the people who say
+we need to have education for the state
+
+ align:start position:0%
+we need to have education for the state
+ 
+
+ align:start position:0%
+we need to have education for the state
+and at first to get in the industrial
+
+ align:start position:0%
+and at first to get in the industrial
+ 
+
+ align:start position:0%
+and at first to get in the industrial
+revolution
+
+ align:start position:0%
+revolution
+ 
+
+ align:start position:0%
+revolution
+secondly to defend ourselves against
+
+ align:start position:0%
+secondly to defend ourselves against
+ 
+
+ align:start position:0%
+secondly to defend ourselves against
+guess what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+communism
+
+ align:start position:0%
+communism
+ 
+
+ align:start position:0%
+communism
+why were we afraid of communism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we were afraid of communism because we
+
+ align:start position:0%
+we were afraid of communism because we
+ 
+
+ align:start position:0%
+we were afraid of communism because we
+were afraid of the russians
+
+ align:start position:0%
+were afraid of the russians
+ 
+
+ align:start position:0%
+were afraid of the russians
+we were afraid of the russians because
+
+ align:start position:0%
+we were afraid of the russians because
+ 
+
+ align:start position:0%
+we were afraid of the russians because
+the russians had a formula that said if
+
+ align:start position:0%
+the russians had a formula that said if
+ 
+
+ align:start position:0%
+the russians had a formula that said if
+we need three million engineers we will
+
+ align:start position:0%
+we need three million engineers we will
+ 
+
+ align:start position:0%
+we need three million engineers we will
+command that we shall have three million
+
+ align:start position:0%
+command that we shall have three million
+ 
+
+ align:start position:0%
+command that we shall have three million
+engineers in the united states if we
+
+ align:start position:0%
+engineers in the united states if we
+ 
+
+ align:start position:0%
+engineers in the united states if we
+need three million engineers we say well
+
+ align:start position:0%
+need three million engineers we say well
+ 
+
+ align:start position:0%
+need three million engineers we say well
+we've got some scholarships
+
+ align:start position:0%
+we've got some scholarships
+ 
+
+ align:start position:0%
+we've got some scholarships
+you know in other words could we compete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with a culture like that
+
+ align:start position:0%
+with a culture like that
+ 
+
+ align:start position:0%
+with a culture like that
+that was the question
+
+ align:start position:0%
+that was the question
+ 
+
+ align:start position:0%
+that was the question
+all right so a lot of people who wanted
+
+ align:start position:0%
+all right so a lot of people who wanted
+ 
+
+ align:start position:0%
+all right so a lot of people who wanted
+education for the state wanted us to be
+
+ align:start position:0%
+education for the state wanted us to be
+ 
+
+ align:start position:0%
+education for the state wanted us to be
+competitive
+
+ align:start position:0%
+competitive
+ 
+
+ align:start position:0%
+competitive
+all of this free choice did not promise
+
+ align:start position:0%
+all of this free choice did not promise
+ 
+
+ align:start position:0%
+all of this free choice did not promise
+to be competitive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh so general this general
+
+ align:start position:0%
+okay uh so general this general
+ 
+
+ align:start position:0%
+okay uh so general this general
+education and free society said we
+
+ align:start position:0%
+education and free society said we
+ 
+
+ align:start position:0%
+education and free society said we
+should have
+
+ align:start position:0%
+should have
+ 
+
+ align:start position:0%
+should have
+two kinds general education and special
+
+ align:start position:0%
+two kinds general education and special
+ 
+
+ align:start position:0%
+two kinds general education and special
+education
+
+ align:start position:0%
+education
+ 
+
+ align:start position:0%
+education
+general education was what they put in
+
+ align:start position:0%
+general education was what they put in
+ 
+
+ align:start position:0%
+general education was what they put in
+the part of the curriculum we call the
+
+ align:start position:0%
+the part of the curriculum we call the
+ 
+
+ align:start position:0%
+the part of the curriculum we call the
+core curriculum that is the courses that
+
+ align:start position:0%
+core curriculum that is the courses that
+ 
+
+ align:start position:0%
+core curriculum that is the courses that
+everybody takes
+
+ align:start position:0%
+everybody takes
+ 
+
+ align:start position:0%
+everybody takes
+special education is what they call the
+
+ align:start position:0%
+special education is what they call the
+ 
+
+ align:start position:0%
+special education is what they call the
+major
+
+ align:start position:0%
+major
+ 
+
+ align:start position:0%
+major
+you want to be an engineer an economist
+
+ align:start position:0%
+you want to be an engineer an economist
+ 
+
+ align:start position:0%
+you want to be an engineer an economist
+or whatever that's what you specialize
+
+ align:start position:0%
+or whatever that's what you specialize
+ 
+
+ align:start position:0%
+or whatever that's what you specialize
+in and get your special education so you
+
+ align:start position:0%
+in and get your special education so you
+ 
+
+ align:start position:0%
+in and get your special education so you
+see this this book did have
+
+ align:start position:0%
+see this this book did have
+ 
+
+ align:start position:0%
+see this this book did have
+a formula that a lot of which that we
+
+ align:start position:0%
+a formula that a lot of which that we
+ 
+
+ align:start position:0%
+a formula that a lot of which that we
+live by at least in the united states
+
+ align:start position:0%
+live by at least in the united states
+ 
+
+ align:start position:0%
+live by at least in the united states
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+then the book comes out in its early
+
+ align:start position:0%
+then the book comes out in its early
+ 
+
+ align:start position:0%
+then the book comes out in its early
+pages we're talking about before you get
+
+ align:start position:0%
+pages we're talking about before you get
+ 
+
+ align:start position:0%
+pages we're talking about before you get
+to think to page
+
+ align:start position:0%
+to think to page
+ 
+
+ align:start position:0%
+to think to page
+uh we have another we have until five
+
+ align:start position:0%
+uh we have another we have until five
+ 
+
+ align:start position:0%
+uh we have another we have until five
+minutes of
+
+ align:start position:0%
+minutes of
+ 
+
+ align:start position:0%
+minutes of
+and this is the class so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so what at uh 55
+
+ align:start position:0%
+yeah so what at uh 55
+ 
+
+ align:start position:0%
+yeah so what at uh 55
+10 55 uh yeah we'll be out of here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i could have said that we could dispose
+
+ align:start position:0%
+i could have said that we could dispose
+ 
+
+ align:start position:0%
+i could have said that we could dispose
+of those pizzas
+
+ align:start position:0%
+of those pizzas
+ 
+
+ align:start position:0%
+of those pizzas
+that might not be ethical
+
+ align:start position:0%
+that might not be ethical
+ 
+
+ align:start position:0%
+that might not be ethical
+all right uh let's finish up this
+
+ align:start position:0%
+all right uh let's finish up this
+ 
+
+ align:start position:0%
+all right uh let's finish up this
+thing here
+
+ align:start position:0%
+thing here
+ 
+
+ align:start position:0%
+thing here
+that ethics was included
+
+ align:start position:0%
+that ethics was included
+ 
+
+ align:start position:0%
+that ethics was included
+in uh the i forgot to mention ethics
+
+ align:start position:0%
+in uh the i forgot to mention ethics
+ 
+
+ align:start position:0%
+in uh the i forgot to mention ethics
+when i was mentioning these courses
+
+ align:start position:0%
+when i was mentioning these courses
+ 
+
+ align:start position:0%
+when i was mentioning these courses
+uh that i don't know why i forgot to
+
+ align:start position:0%
+uh that i don't know why i forgot to
+ 
+
+ align:start position:0%
+uh that i don't know why i forgot to
+mention that
+
+ align:start position:0%
+mention that
+ 
+
+ align:start position:0%
+mention that
+but ethics was included in all of this
+
+ align:start position:0%
+but ethics was included in all of this
+ 
+
+ align:start position:0%
+but ethics was included in all of this
+and what the what the what the uh
+
+ align:start position:0%
+and what the what the what the uh
+ 
+
+ align:start position:0%
+and what the what the what the uh
+general education and free society said
+
+ align:start position:0%
+general education and free society said
+ 
+
+ align:start position:0%
+general education and free society said
+was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the big challenge to
+
+ align:start position:0%
+the big challenge to
+ 
+
+ align:start position:0%
+the big challenge to
+general education there were two
+
+ align:start position:0%
+general education there were two
+ 
+
+ align:start position:0%
+general education there were two
+challenges to general education
+
+ align:start position:0%
+challenges to general education
+ 
+
+ align:start position:0%
+challenges to general education
+it said this in 1945 i'm sure that you
+
+ align:start position:0%
+it said this in 1945 i'm sure that you
+ 
+
+ align:start position:0%
+it said this in 1945 i'm sure that you
+it sounds like it's been it was said in
+
+ align:start position:0%
+it sounds like it's been it was said in
+ 
+
+ align:start position:0%
+it sounds like it's been it was said in
+2005.
+
+ align:start position:0%
+2005.
+ 
+
+ align:start position:0%
+2005.
+they said there were two big challenges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the challenges was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they call it the proliferation of
+
+ align:start position:0%
+they call it the proliferation of
+ 
+
+ align:start position:0%
+they call it the proliferation of
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+there's just too many things too much
+
+ align:start position:0%
+there's just too many things too much
+ 
+
+ align:start position:0%
+there's just too many things too much
+too many books being written
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+out of all of these things
+
+ align:start position:0%
+out of all of these things
+ 
+
+ align:start position:0%
+out of all of these things
+which ones do you choose
+
+ align:start position:0%
+which ones do you choose
+ 
+
+ align:start position:0%
+which ones do you choose
+to teach to everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the second one was
+
+ align:start position:0%
+the second one was
+ 
+
+ align:start position:0%
+the second one was
+diversification of culture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the united states population between
+
+ align:start position:0%
+the united states population between
+ 
+
+ align:start position:0%
+the united states population between
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and 1950 uh
+
+ align:start position:0%
+and 1950 uh
+ 
+
+ align:start position:0%
+and 1950 uh
+i think increased by a pro
+
+ align:start position:0%
+i think increased by a pro
+ 
+
+ align:start position:0%
+i think increased by a pro
+of kids in school increased by something
+
+ align:start position:0%
+of kids in school increased by something
+ 
+
+ align:start position:0%
+of kids in school increased by something
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+20 times
+
+ align:start position:0%
+20 times
+ 
+
+ align:start position:0%
+20 times
+that's another number for you to verify
+
+ align:start position:0%
+that's another number for you to verify
+ 
+
+ align:start position:0%
+that's another number for you to verify
+but it's a big number
+
+ align:start position:0%
+but it's a big number
+ 
+
+ align:start position:0%
+but it's a big number
+and uh the question then is how do you
+
+ align:start position:0%
+and uh the question then is how do you
+ 
+
+ align:start position:0%
+and uh the question then is how do you
+teach
+
+ align:start position:0%
+teach
+ 
+
+ align:start position:0%
+teach
+once you've decided what to teach how do
+
+ align:start position:0%
+once you've decided what to teach how do
+ 
+
+ align:start position:0%
+once you've decided what to teach how do
+you teach it to each individual given
+
+ align:start position:0%
+you teach it to each individual given
+ 
+
+ align:start position:0%
+you teach it to each individual given
+different tastes and abilities and all
+
+ align:start position:0%
+different tastes and abilities and all
+ 
+
+ align:start position:0%
+different tastes and abilities and all
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+that okay
+
+ align:start position:0%
+that okay
+ 
+
+ align:start position:0%
+that okay
+so they said that
+
+ align:start position:0%
+so they said that
+ 
+
+ align:start position:0%
+so they said that
+what they needed was what was called a
+
+ align:start position:0%
+what they needed was what was called a
+ 
+
+ align:start position:0%
+what they needed was what was called a
+unity principle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is that after you have
+
+ align:start position:0%
+and that is that after you have
+ 
+
+ align:start position:0%
+and that is that after you have
+chosen all from all of this wealth of
+
+ align:start position:0%
+chosen all from all of this wealth of
+ 
+
+ align:start position:0%
+chosen all from all of this wealth of
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+and learning better stated learning
+
+ align:start position:0%
+and learning better stated learning
+ 
+
+ align:start position:0%
+and learning better stated learning
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+few things you're going to teach to
+
+ align:start position:0%
+few things you're going to teach to
+ 
+
+ align:start position:0%
+few things you're going to teach to
+everybody
+
+ align:start position:0%
+everybody
+ 
+
+ align:start position:0%
+everybody
+and after you've decided
+
+ align:start position:0%
+and after you've decided
+ 
+
+ align:start position:0%
+and after you've decided
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that you you know how to teach it to
+
+ align:start position:0%
+that you you know how to teach it to
+ 
+
+ align:start position:0%
+that you you know how to teach it to
+each individual
+
+ align:start position:0%
+each individual
+ 
+
+ align:start position:0%
+each individual
+what you've got to do is to say that
+
+ align:start position:0%
+what you've got to do is to say that
+ 
+
+ align:start position:0%
+what you've got to do is to say that
+what a person has learned
+
+ align:start position:0%
+what a person has learned
+ 
+
+ align:start position:0%
+what a person has learned
+in school
+
+ align:start position:0%
+in school
+ 
+
+ align:start position:0%
+in school
+has got to help them learn more when
+
+ align:start position:0%
+has got to help them learn more when
+ 
+
+ align:start position:0%
+has got to help them learn more when
+they get out of school
+
+ align:start position:0%
+they get out of school
+ 
+
+ align:start position:0%
+they get out of school
+so it's got all of this stuff has to fit
+
+ align:start position:0%
+so it's got all of this stuff has to fit
+ 
+
+ align:start position:0%
+so it's got all of this stuff has to fit
+into some kind of pattern
+
+ align:start position:0%
+into some kind of pattern
+ 
+
+ align:start position:0%
+into some kind of pattern
+now we did that in this course we were
+
+ align:start position:0%
+now we did that in this course we were
+ 
+
+ align:start position:0%
+now we did that in this course we were
+very to be able to show the diff show a
+
+ align:start position:0%
+very to be able to show the diff show a
+ 
+
+ align:start position:0%
+very to be able to show the diff show a
+pattern between the structure
+
+ align:start position:0%
+pattern between the structure
+ 
+
+ align:start position:0%
+pattern between the structure
+of ethics and the structure of science
+
+ align:start position:0%
+of ethics and the structure of science
+ 
+
+ align:start position:0%
+of ethics and the structure of science
+when we said talk about the empirical
+
+ align:start position:0%
+when we said talk about the empirical
+ 
+
+ align:start position:0%
+when we said talk about the empirical
+the rational and now
+
+ align:start position:0%
+the rational and now
+ 
+
+ align:start position:0%
+the rational and now
+uh which i haven't gone into any detail
+
+ align:start position:0%
+uh which i haven't gone into any detail
+ 
+
+ align:start position:0%
+uh which i haven't gone into any detail
+on because i'm waiting for the
+
+ align:start position:0%
+on because i'm waiting for the
+ 
+
+ align:start position:0%
+on because i'm waiting for the
+believe it or not three mile island
+
+ align:start position:0%
+believe it or not three mile island
+ 
+
+ align:start position:0%
+believe it or not three mile island
+piece to do it
+
+ align:start position:0%
+piece to do it
+ 
+
+ align:start position:0%
+piece to do it
+but uh the question is how do you take
+
+ align:start position:0%
+but uh the question is how do you take
+ 
+
+ align:start position:0%
+but uh the question is how do you take
+learning from music
+
+ align:start position:0%
+learning from music
+ 
+
+ align:start position:0%
+learning from music
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+mathematics
+
+ align:start position:0%
+mathematics
+ 
+
+ align:start position:0%
+mathematics
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+art
+
+ align:start position:0%
+art
+ 
+
+ align:start position:0%
+art
+and physics
+
+ align:start position:0%
+and physics
+ 
+
+ align:start position:0%
+and physics
+how do you make sense of all of that
+
+ align:start position:0%
+how do you make sense of all of that
+ 
+
+ align:start position:0%
+how do you make sense of all of that
+and what they went through was with some
+
+ align:start position:0%
+and what they went through was with some
+ 
+
+ align:start position:0%
+and what they went through was with some
+formulas
+
+ align:start position:0%
+formulas
+ 
+
+ align:start position:0%
+formulas
+and many proposals have come in but
+
+ align:start position:0%
+and many proposals have come in but
+ 
+
+ align:start position:0%
+and many proposals have come in but
+nobody has accepted any of them
+
+ align:start position:0%
+nobody has accepted any of them
+ 
+
+ align:start position:0%
+nobody has accepted any of them
+as a principal for general education
+
+ align:start position:0%
+as a principal for general education
+ 
+
+ align:start position:0%
+as a principal for general education
+let's name some the first one that came
+
+ align:start position:0%
+let's name some the first one that came
+ 
+
+ align:start position:0%
+let's name some the first one that came
+in was christianity
+
+ align:start position:0%
+in was christianity
+ 
+
+ align:start position:0%
+in was christianity
+well not everybody's a christian
+
+ align:start position:0%
+well not everybody's a christian
+ 
+
+ align:start position:0%
+well not everybody's a christian
+so they threw that out
+
+ align:start position:0%
+so they threw that out
+ 
+
+ align:start position:0%
+so they threw that out
+uh i'll name one or two
+
+ align:start position:0%
+uh i'll name one or two
+ 
+
+ align:start position:0%
+uh i'll name one or two
+cut me off this is a good place to cut
+
+ align:start position:0%
+cut me off this is a good place to cut
+ 
+
+ align:start position:0%
+cut me off this is a good place to cut
+me off if you think of some others that
+
+ align:start position:0%
+me off if you think of some others that
+ 
+
+ align:start position:0%
+me off if you think of some others that
+some other proposals and why they if
+
+ align:start position:0%
+some other proposals and why they if
+ 
+
+ align:start position:0%
+some other proposals and why they if
+they came up and why they were slashed
+
+ align:start position:0%
+they came up and why they were slashed
+ 
+
+ align:start position:0%
+they came up and why they were slashed
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+uh one of them was um
+
+ align:start position:0%
+uh one of them was um
+ 
+
+ align:start position:0%
+uh one of them was um
+cultural literacy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back in the 50s it was called the
+
+ align:start position:0%
+back in the 50s it was called the
+ 
+
+ align:start position:0%
+back in the 50s it was called the
+chicago school they dedicated themselves
+
+ align:start position:0%
+chicago school they dedicated themselves
+ 
+
+ align:start position:0%
+chicago school they dedicated themselves
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+that's been thrown out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nobody just seems to benefit from a
+
+ align:start position:0%
+nobody just seems to benefit from a
+ 
+
+ align:start position:0%
+nobody just seems to benefit from a
+vocabulary
+
+ align:start position:0%
+vocabulary
+ 
+
+ align:start position:0%
+vocabulary
+you don't get meaning you don't get
+
+ align:start position:0%
+you don't get meaning you don't get
+ 
+
+ align:start position:0%
+you don't get meaning you don't get
+context too much of it if it's
+
+ align:start position:0%
+context too much of it if it's
+ 
+
+ align:start position:0%
+context too much of it if it's
+technological it changes too fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+critical thinking
+
+ align:start position:0%
+critical thinking
+ 
+
+ align:start position:0%
+critical thinking
+actually that was the chicago school
+
+ align:start position:0%
+actually that was the chicago school
+ 
+
+ align:start position:0%
+actually that was the chicago school
+critical thinking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that got thrown out can anybody
+
+ align:start position:0%
+okay that got thrown out can anybody
+ 
+
+ align:start position:0%
+okay that got thrown out can anybody
+name any others a whole bunch of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the book said that it did not have
+
+ align:start position:0%
+the book said that it did not have
+ 
+
+ align:start position:0%
+the book said that it did not have
+a solution to this problem of a unity
+
+ align:start position:0%
+a solution to this problem of a unity
+ 
+
+ align:start position:0%
+a solution to this problem of a unity
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+it had the faith that somebody was going
+
+ align:start position:0%
+it had the faith that somebody was going
+ 
+
+ align:start position:0%
+it had the faith that somebody was going
+to find one nobody's found one to this
+
+ align:start position:0%
+to find one nobody's found one to this
+ 
+
+ align:start position:0%
+to find one nobody's found one to this
+day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means we're struggling along with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what was left out of this piece
+
+ align:start position:0%
+what was left out of this piece
+ 
+
+ align:start position:0%
+what was left out of this piece
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+one of the big casualties of it
+
+ align:start position:0%
+one of the big casualties of it
+ 
+
+ align:start position:0%
+one of the big casualties of it
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+character
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is engineering ah let's see now
+
+ align:start position:0%
+what is engineering ah let's see now
+ 
+
+ align:start position:0%
+what is engineering ah let's see now
+i really wanted this to be a good
+
+ align:start position:0%
+i really wanted this to be a good
+ 
+
+ align:start position:0%
+i really wanted this to be a good
+picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can anybody tell what this picture is of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can it's a nighttime view
+
+ align:start position:0%
+you can it's a nighttime view
+ 
+
+ align:start position:0%
+you can it's a nighttime view
+of the status center
+
+ align:start position:0%
+of the status center
+ 
+
+ align:start position:0%
+of the status center
+and this building is right up here on
+
+ align:start position:0%
+and this building is right up here on
+ 
+
+ align:start position:0%
+and this building is right up here on
+campus
+
+ align:start position:0%
+campus
+ 
+
+ align:start position:0%
+campus
+okay now we did discuss some ideas about
+
+ align:start position:0%
+okay now we did discuss some ideas about
+ 
+
+ align:start position:0%
+okay now we did discuss some ideas about
+what is what really is engineering
+
+ align:start position:0%
+what is what really is engineering
+ 
+
+ align:start position:0%
+what is what really is engineering
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+joel moses dr moses came in and he said
+
+ align:start position:0%
+joel moses dr moses came in and he said
+ 
+
+ align:start position:0%
+joel moses dr moses came in and he said
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+plato and aristotle gave us two ways of
+
+ align:start position:0%
+plato and aristotle gave us two ways of
+ 
+
+ align:start position:0%
+plato and aristotle gave us two ways of
+thinking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aristotle gave us
+
+ align:start position:0%
+aristotle gave us
+ 
+
+ align:start position:0%
+aristotle gave us
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+systematic way of thinking
+
+ align:start position:0%
+systematic way of thinking
+ 
+
+ align:start position:0%
+systematic way of thinking
+that was what we call analytic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is if you want to understand
+
+ align:start position:0%
+and that is if you want to understand
+ 
+
+ align:start position:0%
+and that is if you want to understand
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you break it up into its parts
+
+ align:start position:0%
+you break it up into its parts
+ 
+
+ align:start position:0%
+you break it up into its parts
+and you understand the parts
+
+ align:start position:0%
+and you understand the parts
+ 
+
+ align:start position:0%
+and you understand the parts
+and then you put the parts back together
+
+ align:start position:0%
+and then you put the parts back together
+ 
+
+ align:start position:0%
+and then you put the parts back together
+and maybe you can understand the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plato said was
+
+ align:start position:0%
+plato said was
+ 
+
+ align:start position:0%
+plato said was
+synthetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plato said
+
+ align:start position:0%
+plato said
+ 
+
+ align:start position:0%
+plato said
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+if we want to understand a thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we first say what it is
+
+ align:start position:0%
+we first say what it is
+ 
+
+ align:start position:0%
+we first say what it is
+and then we say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what it is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then somehow out of a synthetic
+
+ align:start position:0%
+and then somehow out of a synthetic
+ 
+
+ align:start position:0%
+and then somehow out of a synthetic
+approach we're able to understand better
+
+ align:start position:0%
+approach we're able to understand better
+ 
+
+ align:start position:0%
+approach we're able to understand better
+what this thing is that we're talking
+
+ align:start position:0%
+what this thing is that we're talking
+ 
+
+ align:start position:0%
+what this thing is that we're talking
+about as a whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when you bring these two
+
+ align:start position:0%
+and when you bring these two
+ 
+
+ align:start position:0%
+and when you bring these two
+approaches or traditions together into
+
+ align:start position:0%
+approaches or traditions together into
+ 
+
+ align:start position:0%
+approaches or traditions together into
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you get something different from the two
+
+ align:start position:0%
+you get something different from the two
+ 
+
+ align:start position:0%
+you get something different from the two
+and we call it engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+uh the reason that we are going to take
+
+ align:start position:0%
+uh the reason that we are going to take
+ 
+
+ align:start position:0%
+uh the reason that we are going to take
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+idea very seriously is not
+
+ align:start position:0%
+idea very seriously is not
+ 
+
+ align:start position:0%
+idea very seriously is not
+because simply because somebody's here
+
+ align:start position:0%
+because simply because somebody's here
+ 
+
+ align:start position:0%
+because simply because somebody's here
+to say it
+
+ align:start position:0%
+to say it
+ 
+
+ align:start position:0%
+to say it
+not because it is compelling
+
+ align:start position:0%
+not because it is compelling
+ 
+
+ align:start position:0%
+not because it is compelling
+but because there really isn't a
+
+ align:start position:0%
+but because there really isn't a
+ 
+
+ align:start position:0%
+but because there really isn't a
+philosophy of engineering out here it
+
+ align:start position:0%
+philosophy of engineering out here it
+ 
+
+ align:start position:0%
+philosophy of engineering out here it
+really isn't
+
+ align:start position:0%
+really isn't
+ 
+
+ align:start position:0%
+really isn't
+i'm writing a book on it so i have my
+
+ align:start position:0%
+i'm writing a book on it so i have my
+ 
+
+ align:start position:0%
+i'm writing a book on it so i have my
+views about it
+
+ align:start position:0%
+views about it
+ 
+
+ align:start position:0%
+views about it
+and and there will be a time towards the
+
+ align:start position:0%
+and and there will be a time towards the
+ 
+
+ align:start position:0%
+and and there will be a time towards the
+end of the class when i will share my
+
+ align:start position:0%
+end of the class when i will share my
+ 
+
+ align:start position:0%
+end of the class when i will share my
+views which you will find very
+
+ align:start position:0%
+views which you will find very
+ 
+
+ align:start position:0%
+views which you will find very
+interesting it doesn't really conflict
+
+ align:start position:0%
+interesting it doesn't really conflict
+ 
+
+ align:start position:0%
+interesting it doesn't really conflict
+with all this it comes it
+
+ align:start position:0%
+with all this it comes it
+ 
+
+ align:start position:0%
+with all this it comes it
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+subsumes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and what i will say is that
+
+ align:start position:0%
+it and what i will say is that
+ 
+
+ align:start position:0%
+it and what i will say is that
+engineering uh began
+
+ align:start position:0%
+engineering uh began
+ 
+
+ align:start position:0%
+engineering uh began
+when what used to be called
+
+ align:start position:0%
+when what used to be called
+ 
+
+ align:start position:0%
+when what used to be called
+uh the practical arts
+
+ align:start position:0%
+uh the practical arts
+ 
+
+ align:start position:0%
+uh the practical arts
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+road building things like that came
+
+ align:start position:0%
+road building things like that came
+ 
+
+ align:start position:0%
+road building things like that came
+together with the science of mathematics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we put those two together
+
+ align:start position:0%
+okay we put those two together
+ 
+
+ align:start position:0%
+okay we put those two together
+and we're just about done we had talked
+
+ align:start position:0%
+and we're just about done we had talked
+ 
+
+ align:start position:0%
+and we're just about done we had talked
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did i do no i didn't it's just very
+
+ align:start position:0%
+did i do no i didn't it's just very
+ 
+
+ align:start position:0%
+did i do no i didn't it's just very
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+is she okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+we talked about how engineering and
+
+ align:start position:0%
+we talked about how engineering and
+ 
+
+ align:start position:0%
+we talked about how engineering and
+ethics can engage each other sometimes
+
+ align:start position:0%
+ethics can engage each other sometimes
+ 
+
+ align:start position:0%
+ethics can engage each other sometimes
+you don't really have to be an engineer
+
+ align:start position:0%
+you don't really have to be an engineer
+ 
+
+ align:start position:0%
+you don't really have to be an engineer
+you really don't need to know the
+
+ align:start position:0%
+you really don't need to know the
+ 
+
+ align:start position:0%
+you really don't need to know the
+technological system
+
+ align:start position:0%
+technological system
+ 
+
+ align:start position:0%
+technological system
+what you do then if this is if this is
+
+ align:start position:0%
+what you do then if this is if this is
+ 
+
+ align:start position:0%
+what you do then if this is if this is
+technology and if these are people then
+
+ align:start position:0%
+technology and if these are people then
+ 
+
+ align:start position:0%
+technology and if these are people then
+you study their interactions
+
+ align:start position:0%
+you study their interactions
+ 
+
+ align:start position:0%
+you study their interactions
+and how they relate themselves to
+
+ align:start position:0%
+and how they relate themselves to
+ 
+
+ align:start position:0%
+and how they relate themselves to
+technology and you make a decision we
+
+ align:start position:0%
+technology and you make a decision we
+ 
+
+ align:start position:0%
+technology and you make a decision we
+did that already in class
+
+ align:start position:0%
+did that already in class
+ 
+
+ align:start position:0%
+did that already in class
+uh particularly when we analyzed the a7d
+
+ align:start position:0%
+uh particularly when we analyzed the a7d
+ 
+
+ align:start position:0%
+uh particularly when we analyzed the a7d
+case you really didn't have to know a
+
+ align:start position:0%
+case you really didn't have to know a
+ 
+
+ align:start position:0%
+case you really didn't have to know a
+whole lot about airplanes and ever and
+
+ align:start position:0%
+whole lot about airplanes and ever and
+ 
+
+ align:start position:0%
+whole lot about airplanes and ever and
+brakes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this case and when we talk about uh
+
+ align:start position:0%
+in this case and when we talk about uh
+ 
+
+ align:start position:0%
+in this case and when we talk about uh
+like for three mile island you really
+
+ align:start position:0%
+like for three mile island you really
+ 
+
+ align:start position:0%
+like for three mile island you really
+have to know what a nuclear plant is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to understand uh about how uh to make an
+
+ align:start position:0%
+to understand uh about how uh to make an
+ 
+
+ align:start position:0%
+to understand uh about how uh to make an
+ethical judgment about the situation
+
+ align:start position:0%
+ethical judgment about the situation
+ 
+
+ align:start position:0%
+ethical judgment about the situation
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is this interdisciplinary mode now
+
+ align:start position:0%
+there is this interdisciplinary mode now
+ 
+
+ align:start position:0%
+there is this interdisciplinary mode now
+i want to take a minute to say something
+
+ align:start position:0%
+i want to take a minute to say something
+ 
+
+ align:start position:0%
+i want to take a minute to say something
+about that and according to my watch
+
+ align:start position:0%
+about that and according to my watch
+ 
+
+ align:start position:0%
+about that and according to my watch
+we've got six minutes and we're out of
+
+ align:start position:0%
+we've got six minutes and we're out of
+ 
+
+ align:start position:0%
+we've got six minutes and we're out of
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this slide here provoked
+
+ align:start position:0%
+this slide here provoked
+ 
+
+ align:start position:0%
+this slide here provoked
+a long and in-depth discussion yesterday
+
+ align:start position:0%
+a long and in-depth discussion yesterday
+ 
+
+ align:start position:0%
+a long and in-depth discussion yesterday
+you know both in the class and outside
+
+ align:start position:0%
+you know both in the class and outside
+ 
+
+ align:start position:0%
+you know both in the class and outside
+of it i went to
+
+ align:start position:0%
+of it i went to
+ 
+
+ align:start position:0%
+of it i went to
+dick lester's office which is actually
+
+ align:start position:0%
+dick lester's office which is actually
+ 
+
+ align:start position:0%
+dick lester's office which is actually
+in the same suite that i'm in
+
+ align:start position:0%
+in the same suite that i'm in
+ 
+
+ align:start position:0%
+in the same suite that i'm in
+went down and we talked for about i
+
+ align:start position:0%
+went down and we talked for about i
+ 
+
+ align:start position:0%
+went down and we talked for about i
+think we had lunch together in his
+
+ align:start position:0%
+think we had lunch together in his
+ 
+
+ align:start position:0%
+think we had lunch together in his
+office and we talked about almost an
+
+ align:start position:0%
+office and we talked about almost an
+ 
+
+ align:start position:0%
+office and we talked about almost an
+hour
+
+ align:start position:0%
+hour
+ 
+
+ align:start position:0%
+hour
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this one is
+
+ align:start position:0%
+this one is
+ 
+
+ align:start position:0%
+this one is
+the big issue here because what it says
+
+ align:start position:0%
+the big issue here because what it says
+ 
+
+ align:start position:0%
+the big issue here because what it says
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+that there's a possibility when you
+
+ align:start position:0%
+that there's a possibility when you
+ 
+
+ align:start position:0%
+that there's a possibility when you
+engage two learned disciplines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that in order to solve the problem
+
+ align:start position:0%
+that in order to solve the problem
+ 
+
+ align:start position:0%
+that in order to solve the problem
+you have to throw out one of the
+
+ align:start position:0%
+you have to throw out one of the
+ 
+
+ align:start position:0%
+you have to throw out one of the
+fundamental principles of one of those
+
+ align:start position:0%
+fundamental principles of one of those
+ 
+
+ align:start position:0%
+fundamental principles of one of those
+disciplines
+
+ align:start position:0%
+disciplines
+ 
+
+ align:start position:0%
+disciplines
+now let's see how that happens in ethics
+
+ align:start position:0%
+now let's see how that happens in ethics
+ 
+
+ align:start position:0%
+now let's see how that happens in ethics
+is what i did with this paper
+
+ align:start position:0%
+is what i did with this paper
+ 
+
+ align:start position:0%
+is what i did with this paper
+when i said
+
+ align:start position:0%
+when i said
+ 
+
+ align:start position:0%
+when i said
+let's put a person
+
+ align:start position:0%
+let's put a person
+ 
+
+ align:start position:0%
+let's put a person
+in a situation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this case was my uncle roy
+
+ align:start position:0%
+and this case was my uncle roy
+ 
+
+ align:start position:0%
+and this case was my uncle roy
+and other cases we call them
+
+ align:start position:0%
+and other cases we call them
+ 
+
+ align:start position:0%
+and other cases we call them
+uh matum and kirky
+
+ align:start position:0%
+uh matum and kirky
+ 
+
+ align:start position:0%
+uh matum and kirky
+uh the the nigerians call it
+
+ align:start position:0%
+uh the the nigerians call it
+ 
+
+ align:start position:0%
+uh the the nigerians call it
+character
+
+ align:start position:0%
+character
+ 
+
+ align:start position:0%
+character
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jews call it the hasid the number names
+
+ align:start position:0%
+jews call it the hasid the number names
+ 
+
+ align:start position:0%
+jews call it the hasid the number names
+you put a person into a situation
+
+ align:start position:0%
+you put a person into a situation
+ 
+
+ align:start position:0%
+you put a person into a situation
+who is not a virtuous person now once
+
+ align:start position:0%
+who is not a virtuous person now once
+ 
+
+ align:start position:0%
+who is not a virtuous person now once
+you do that you're outside of the realm
+
+ align:start position:0%
+you do that you're outside of the realm
+ 
+
+ align:start position:0%
+you do that you're outside of the realm
+of everything that western ethics has to
+
+ align:start position:0%
+of everything that western ethics has to
+ 
+
+ align:start position:0%
+of everything that western ethics has to
+say you're outside of the realm
+
+ align:start position:0%
+say you're outside of the realm
+ 
+
+ align:start position:0%
+say you're outside of the realm
+because we're not looking to do the
+
+ align:start position:0%
+because we're not looking to do the
+ 
+
+ align:start position:0%
+because we're not looking to do the
+right thing
+
+ align:start position:0%
+right thing
+ 
+
+ align:start position:0%
+right thing
+we're talking about a situation that is
+
+ align:start position:0%
+we're talking about a situation that is
+ 
+
+ align:start position:0%
+we're talking about a situation that is
+that is exigent you have to make a
+
+ align:start position:0%
+that is exigent you have to make a
+ 
+
+ align:start position:0%
+that is exigent you have to make a
+decision right away potentially lethal
+
+ align:start position:0%
+decision right away potentially lethal
+ 
+
+ align:start position:0%
+decision right away potentially lethal
+so you have to make a decision
+
+ align:start position:0%
+so you have to make a decision
+ 
+
+ align:start position:0%
+so you have to make a decision
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and the question is after you've done it
+
+ align:start position:0%
+and the question is after you've done it
+ 
+
+ align:start position:0%
+and the question is after you've done it
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and even if you've done the wrong thing
+
+ align:start position:0%
+and even if you've done the wrong thing
+ 
+
+ align:start position:0%
+and even if you've done the wrong thing
+will the rest of the society forgive you
+
+ align:start position:0%
+will the rest of the society forgive you
+ 
+
+ align:start position:0%
+will the rest of the society forgive you
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+when i brought this thing up with
+
+ align:start position:0%
+when i brought this thing up with
+ 
+
+ align:start position:0%
+when i brought this thing up with
+philosophers
+
+ align:start position:0%
+philosophers
+ 
+
+ align:start position:0%
+philosophers
+the first time
+
+ align:start position:0%
+the first time
+ 
+
+ align:start position:0%
+the first time
+they were of one mind in total agreement
+
+ align:start position:0%
+they were of one mind in total agreement
+ 
+
+ align:start position:0%
+they were of one mind in total agreement
+total agreement that this was outside of
+
+ align:start position:0%
+total agreement that this was outside of
+ 
+
+ align:start position:0%
+total agreement that this was outside of
+the realm of anything we call ethics
+
+ align:start position:0%
+the realm of anything we call ethics
+ 
+
+ align:start position:0%
+the realm of anything we call ethics
+or moral philosophy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+they finally accepted it
+
+ align:start position:0%
+they finally accepted it
+ 
+
+ align:start position:0%
+they finally accepted it
+but it's outside the realm
+
+ align:start position:0%
+but it's outside the realm
+ 
+
+ align:start position:0%
+but it's outside the realm
+now here's what i want you to try to do
+
+ align:start position:0%
+now here's what i want you to try to do
+ 
+
+ align:start position:0%
+now here's what i want you to try to do
+i want you to try to do two things
+
+ align:start position:0%
+i want you to try to do two things
+ 
+
+ align:start position:0%
+i want you to try to do two things
+first of all i want you to try to
+
+ align:start position:0%
+first of all i want you to try to
+ 
+
+ align:start position:0%
+first of all i want you to try to
+imagine
+
+ align:start position:0%
+imagine
+ 
+
+ align:start position:0%
+imagine
+that you were
+
+ align:start position:0%
+that you were
+ 
+
+ align:start position:0%
+that you were
+that you were doing
+
+ align:start position:0%
+that you were doing
+ 
+
+ align:start position:0%
+that you were doing
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+but you're doing it for your
+
+ align:start position:0%
+but you're doing it for your
+ 
+
+ align:start position:0%
+but you're doing it for your
+dissertation
+
+ align:start position:0%
+dissertation
+ 
+
+ align:start position:0%
+dissertation
+your committee is going to say no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say that you're a faculty member
+
+ align:start position:0%
+let's say that you're a faculty member
+ 
+
+ align:start position:0%
+let's say that you're a faculty member
+and you want to do this
+
+ align:start position:0%
+and you want to do this
+ 
+
+ align:start position:0%
+and you want to do this
+and you want to go out for tenure
+
+ align:start position:0%
+and you want to go out for tenure
+ 
+
+ align:start position:0%
+and you want to go out for tenure
+the committee's going to say no all
+
+ align:start position:0%
+the committee's going to say no all
+ 
+
+ align:start position:0%
+the committee's going to say no all
+right so so there is a i
+
+ align:start position:0%
+right so so there is a i
+ 
+
+ align:start position:0%
+right so so there is a i
+argue and i'm not alone in this that um
+
+ align:start position:0%
+argue and i'm not alone in this that um
+ 
+
+ align:start position:0%
+argue and i'm not alone in this that um
+and lester is a guy who uh
+
+ align:start position:0%
+and lester is a guy who uh
+ 
+
+ align:start position:0%
+and lester is a guy who uh
+does um public policy
+
+ align:start position:0%
+does um public policy
+ 
+
+ align:start position:0%
+does um public policy
+and had been doing it uh when he became
+
+ align:start position:0%
+and had been doing it uh when he became
+ 
+
+ align:start position:0%
+and had been doing it uh when he became
+when he came here
+
+ align:start position:0%
+when he came here
+ 
+
+ align:start position:0%
+when he came here
+uh along with nuclear engineering
+
+ align:start position:0%
+uh along with nuclear engineering
+ 
+
+ align:start position:0%
+uh along with nuclear engineering
+and he had to deal with this problem in
+
+ align:start position:0%
+and he had to deal with this problem in
+ 
+
+ align:start position:0%
+and he had to deal with this problem in
+terms of getting rank continued
+
+ align:start position:0%
+terms of getting rank continued
+ 
+
+ align:start position:0%
+terms of getting rank continued
+so the question is when you're when
+
+ align:start position:0%
+so the question is when you're when
+ 
+
+ align:start position:0%
+so the question is when you're when
+you're engaging two or more learned
+
+ align:start position:0%
+you're engaging two or more learned
+ 
+
+ align:start position:0%
+you're engaging two or more learned
+disciplines
+
+ align:start position:0%
+disciplines
+ 
+
+ align:start position:0%
+disciplines
+what do you do if you encounter a
+
+ align:start position:0%
+what do you do if you encounter a
+ 
+
+ align:start position:0%
+what do you do if you encounter a
+problem that you can solve but at the
+
+ align:start position:0%
+problem that you can solve but at the
+ 
+
+ align:start position:0%
+problem that you can solve but at the
+expense
+
+ align:start position:0%
+expense
+ 
+
+ align:start position:0%
+expense
+of a first principle in one of the
+
+ align:start position:0%
+of a first principle in one of the
+ 
+
+ align:start position:0%
+of a first principle in one of the
+disciplines that you're bringing
+
+ align:start position:0%
+disciplines that you're bringing
+ 
+
+ align:start position:0%
+disciplines that you're bringing
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+what normally happens out of that is
+
+ align:start position:0%
+what normally happens out of that is
+ 
+
+ align:start position:0%
+what normally happens out of that is
+that you spawn a brand new distance
+
+ align:start position:0%
+that you spawn a brand new distance
+ 
+
+ align:start position:0%
+that you spawn a brand new distance
+what happens when you spawn a brand new
+
+ align:start position:0%
+what happens when you spawn a brand new
+ 
+
+ align:start position:0%
+what happens when you spawn a brand new
+discipline is that you're the only
+
+ align:start position:0%
+discipline is that you're the only
+ 
+
+ align:start position:0%
+discipline is that you're the only
+expert on the planet
+
+ align:start position:0%
+expert on the planet
+ 
+
+ align:start position:0%
+expert on the planet
+on that new discipline
+
+ align:start position:0%
+on that new discipline
+ 
+
+ align:start position:0%
+on that new discipline
+and anybody who's going to make a
+
+ align:start position:0%
+and anybody who's going to make a
+ 
+
+ align:start position:0%
+and anybody who's going to make a
+judgment about it is outside the realm
+
+ align:start position:0%
+judgment about it is outside the realm
+ 
+
+ align:start position:0%
+judgment about it is outside the realm
+it takes time
+
+ align:start position:0%
+it takes time
+ 
+
+ align:start position:0%
+it takes time
+this is a cultural issue
+
+ align:start position:0%
+this is a cultural issue
+ 
+
+ align:start position:0%
+this is a cultural issue
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+i'm just going to conclude go and just
+
+ align:start position:0%
+i'm just going to conclude go and just
+ 
+
+ align:start position:0%
+i'm just going to conclude go and just
+show you some of these other slides
+
+ align:start position:0%
+show you some of these other slides
+ 
+
+ align:start position:0%
+show you some of these other slides
+actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh the uh
+
+ align:start position:0%
+that uh the uh
+ 
+
+ align:start position:0%
+that uh the uh
+three mile allen case was aggravated by
+
+ align:start position:0%
+three mile allen case was aggravated by
+ 
+
+ align:start position:0%
+three mile allen case was aggravated by
+some real events and and movies that
+
+ align:start position:0%
+some real events and and movies that
+ 
+
+ align:start position:0%
+some real events and and movies that
+were made of real events
+
+ align:start position:0%
+were made of real events
+ 
+
+ align:start position:0%
+were made of real events
+and this particular case occurred
+
+ align:start position:0%
+and this particular case occurred
+ 
+
+ align:start position:0%
+and this particular case occurred
+this particular movie came out two weeks
+
+ align:start position:0%
+this particular movie came out two weeks
+ 
+
+ align:start position:0%
+this particular movie came out two weeks
+before three mile island actually
+
+ align:start position:0%
+before three mile island actually
+ 
+
+ align:start position:0%
+before three mile island actually
+happened it was almost as though it
+
+ align:start position:0%
+happened it was almost as though it
+ 
+
+ align:start position:0%
+happened it was almost as though it
+predicted
+
+ align:start position:0%
+predicted
+ 
+
+ align:start position:0%
+predicted
+the three-mile island case and what that
+
+ align:start position:0%
+the three-mile island case and what that
+ 
+
+ align:start position:0%
+the three-mile island case and what that
+meant was that people couldn't make good
+
+ align:start position:0%
+meant was that people couldn't make good
+ 
+
+ align:start position:0%
+meant was that people couldn't make good
+rational decisions about nuclear power
+
+ align:start position:0%
+rational decisions about nuclear power
+ 
+
+ align:start position:0%
+rational decisions about nuclear power
+in the united states
+
+ align:start position:0%
+in the united states
+ 
+
+ align:start position:0%
+in the united states
+those movies scared us to death
+
+ align:start position:0%
+those movies scared us to death
+ 
+
+ align:start position:0%
+those movies scared us to death
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+what happened here
+
+ align:start position:0%
+what happened here
+ 
+
+ align:start position:0%
+what happened here
+that is very important for an ethical
+
+ align:start position:0%
+that is very important for an ethical
+ 
+
+ align:start position:0%
+that is very important for an ethical
+class a class in ethics
+
+ align:start position:0%
+class a class in ethics
+ 
+
+ align:start position:0%
+class a class in ethics
+which is also an ethical class
+
+ align:start position:0%
+which is also an ethical class
+ 
+
+ align:start position:0%
+which is also an ethical class
+i hope
+
+ align:start position:0%
+i hope
+ 
+
+ align:start position:0%
+i hope
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+when this pump went bad
+
+ align:start position:0%
+when this pump went bad
+ 
+
+ align:start position:0%
+when this pump went bad
+it was just a mechanical it was just a
+
+ align:start position:0%
+it was just a mechanical it was just a
+ 
+
+ align:start position:0%
+it was just a mechanical it was just a
+technological failure it just went bad
+
+ align:start position:0%
+technological failure it just went bad
+ 
+
+ align:start position:0%
+technological failure it just went bad
+did not pump and when it did not pump it
+
+ align:start position:0%
+did not pump and when it did not pump it
+ 
+
+ align:start position:0%
+did not pump and when it did not pump it
+caused readings to be made in the uh
+
+ align:start position:0%
+caused readings to be made in the uh
+ 
+
+ align:start position:0%
+caused readings to be made in the uh
+control room
+
+ align:start position:0%
+control room
+ 
+
+ align:start position:0%
+control room
+that were deceptive it did not say that
+
+ align:start position:0%
+that were deceptive it did not say that
+ 
+
+ align:start position:0%
+that were deceptive it did not say that
+the pumps were working it said that
+
+ align:start position:0%
+the pumps were working it said that
+ 
+
+ align:start position:0%
+the pumps were working it said that
+something was overheating
+
+ align:start position:0%
+something was overheating
+ 
+
+ align:start position:0%
+something was overheating
+and when they tried to compensate they
+
+ align:start position:0%
+and when they tried to compensate they
+ 
+
+ align:start position:0%
+and when they tried to compensate they
+did the wrong thing
+
+ align:start position:0%
+did the wrong thing
+ 
+
+ align:start position:0%
+did the wrong thing
+and this almost
+
+ align:start position:0%
+and this almost
+ 
+
+ align:start position:0%
+and this almost
+could have this could have been
+
+ align:start position:0%
+could have this could have been
+ 
+
+ align:start position:0%
+could have this could have been
+the real scare of nuclear power could
+
+ align:start position:0%
+the real scare of nuclear power could
+ 
+
+ align:start position:0%
+the real scare of nuclear power could
+have been a militant
+
+ align:start position:0%
+have been a militant
+ 
+
+ align:start position:0%
+have been a militant
+the important thing for ethics is
+
+ align:start position:0%
+the important thing for ethics is
+ 
+
+ align:start position:0%
+the important thing for ethics is
+that we could never
+
+ align:start position:0%
+that we could never
+ 
+
+ align:start position:0%
+that we could never
+assigned
+
+ align:start position:0%
+assigned
+ 
+
+ align:start position:0%
+assigned
+moral responsibility to any individual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the question is is there something
+
+ align:start position:0%
+so the question is is there something
+ 
+
+ align:start position:0%
+so the question is is there something
+about the way we as a culture look at
+
+ align:start position:0%
+about the way we as a culture look at
+ 
+
+ align:start position:0%
+about the way we as a culture look at
+nuclear power that is wrong and maybe
+
+ align:start position:0%
+nuclear power that is wrong and maybe
+ 
+
+ align:start position:0%
+nuclear power that is wrong and maybe
+bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i would argue that that's true um i
+
+ align:start position:0%
+and i would argue that that's true um i
+ 
+
+ align:start position:0%
+and i would argue that that's true um i
+went to work for the nuclear regulatory
+
+ align:start position:0%
+went to work for the nuclear regulatory
+ 
+
+ align:start position:0%
+went to work for the nuclear regulatory
+commission june 1st
+
+ align:start position:0%
+commission june 1st
+ 
+
+ align:start position:0%
+commission june 1st
+of 1979 that was march april may june
+
+ align:start position:0%
+of 1979 that was march april may june
+ 
+
+ align:start position:0%
+of 1979 that was march april may june
+that was three months right after three
+
+ align:start position:0%
+that was three months right after three
+ 
+
+ align:start position:0%
+that was three months right after three
+mile
+
+ align:start position:0%
+mile
+ 
+
+ align:start position:0%
+mile
+hour and this is the nuclear power plant
+
+ align:start position:0%
+hour and this is the nuclear power plant
+ 
+
+ align:start position:0%
+hour and this is the nuclear power plant
+my job
+
+ align:start position:0%
+my job
+ 
+
+ align:start position:0%
+my job
+was to analyze what happens
+
+ align:start position:0%
+was to analyze what happens
+ 
+
+ align:start position:0%
+was to analyze what happens
+if a small aircraft
+
+ align:start position:0%
+if a small aircraft
+ 
+
+ align:start position:0%
+if a small aircraft
+crashes into
+
+ align:start position:0%
+crashes into
+ 
+
+ align:start position:0%
+crashes into
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+containment
+
+ align:start position:0%
+containment
+ 
+
+ align:start position:0%
+containment
+structure that was in 1979
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh i wound up being on a consultant list
+
+ align:start position:0%
+uh i wound up being on a consultant list
+ 
+
+ align:start position:0%
+uh i wound up being on a consultant list
+at the cia
+
+ align:start position:0%
+at the cia
+ 
+
+ align:start position:0%
+at the cia
+for this kind of problem
+
+ align:start position:0%
+for this kind of problem
+ 
+
+ align:start position:0%
+for this kind of problem
+looks a lot like
+
+ align:start position:0%
+looks a lot like
+ 
+
+ align:start position:0%
+looks a lot like
+9-1-1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so with that then i conclude that we got
+
+ align:start position:0%
+so with that then i conclude that we got
+ 
+
+ align:start position:0%
+so with that then i conclude that we got
+some things to do
+
+ align:start position:0%
+some things to do
+ 
+
+ align:start position:0%
+some things to do
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+those conclusions there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've made all along i need i think we
+
+ align:start position:0%
+we've made all along i need i think we
+ 
+
+ align:start position:0%
+we've made all along i need i think we
+need character development back
+
+ align:start position:0%
+need character development back
+ 
+
+ align:start position:0%
+need character development back
+i think we need to define competency
+
+ align:start position:0%
+i think we need to define competency
+ 
+
+ align:start position:0%
+i think we need to define competency
+with good character
+
+ align:start position:0%
+with good character
+ 
+
+ align:start position:0%
+with good character
+and the last part of it is that i think
+
+ align:start position:0%
+and the last part of it is that i think
+ 
+
+ align:start position:0%
+and the last part of it is that i think
+that more organizations have moral
+
+ align:start position:0%
+that more organizations have moral
+ 
+
+ align:start position:0%
+that more organizations have moral
+agency and i will prove it before this
+
+ align:start position:0%
+agency and i will prove it before this
+ 
+
+ align:start position:0%
+agency and i will prove it before this
+class is over
+
+ align:start position:0%
+class is over
+ 
+
+ align:start position:0%
+class is over
+that you've convinced me when you first
+
+ align:start position:0%
+that you've convinced me when you first
+ 
+
+ align:start position:0%
+that you've convinced me when you first
+started the class that really had a
+
+ align:start position:0%
+started the class that really had a
+ 
+
+ align:start position:0%
+started the class that really had a
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of the things was just talking
+
+ align:start position:0%
+and one of the things was just talking
+ 
+
+ align:start position:0%
+and one of the things was just talking
+about the internet is whether these
+
+ align:start position:0%
+about the internet is whether these
+ 
+
+ align:start position:0%
+about the internet is whether these
+complex systems of engineering design
+
+ align:start position:0%
+complex systems of engineering design
+ 
+
+ align:start position:0%
+complex systems of engineering design
+can have general agencies i've been
+
+ align:start position:0%
+can have general agencies i've been
+ 
+
+ align:start position:0%
+can have general agencies i've been
+reading a lot of stuff on network
+
+ align:start position:0%
+reading a lot of stuff on network
+ 
+
+ align:start position:0%
+reading a lot of stuff on network
+neutrality you probably know a lot more
+
+ align:start position:0%
+neutrality you probably know a lot more
+ 
+
+ align:start position:0%
+neutrality you probably know a lot more
+about it and i understand a lot more
+
+ align:start position:0%
+about it and i understand a lot more
+ 
+
+ align:start position:0%
+about it and i understand a lot more
+than i do and so it kind of made me play
+
+ align:start position:0%
+than i do and so it kind of made me play
+ 
+
+ align:start position:0%
+than i do and so it kind of made me play
+with this idea of the internet being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well two of us will help yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions comments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little bit outside of the
+
+ align:start position:0%
+a little bit outside of the
+ 
+
+ align:start position:0%
+a little bit outside of the
+presentation
+
+ align:start position:0%
+presentation
+ 
+
+ align:start position:0%
+presentation
+when you mention the term
+
+ align:start position:0%
+when you mention the term
+ 
+
+ align:start position:0%
+when you mention the term
+interdisciplinary
+
+ align:start position:0%
+interdisciplinary
+ 
+
+ align:start position:0%
+interdisciplinary
+this is a discussion that i've been
+
+ align:start position:0%
+this is a discussion that i've been
+ 
+
+ align:start position:0%
+this is a discussion that i've been
+having with a lot of people
+
+ align:start position:0%
+having with a lot of people
+ 
+
+ align:start position:0%
+having with a lot of people
+how would you define the difference
+
+ align:start position:0%
+how would you define the difference
+ 
+
+ align:start position:0%
+how would you define the difference
+between a multi-disciplinary
+
+ align:start position:0%
+between a multi-disciplinary
+ 
+
+ align:start position:0%
+between a multi-disciplinary
+interdisciplinary or cross-disciplinary
+
+ align:start position:0%
+interdisciplinary or cross-disciplinary
+ 
+
+ align:start position:0%
+interdisciplinary or cross-disciplinary
+yeah and transdisciplinary is a new one
+
+ align:start position:0%
+yeah and transdisciplinary is a new one
+ 
+
+ align:start position:0%
+yeah and transdisciplinary is a new one
+that i read right yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah cross-disciplinary is when you use
+
+ align:start position:0%
+yeah cross-disciplinary is when you use
+ 
+
+ align:start position:0%
+yeah cross-disciplinary is when you use
+the tools and methods of one discipline
+
+ align:start position:0%
+the tools and methods of one discipline
+ 
+
+ align:start position:0%
+the tools and methods of one discipline
+to study the other one
+
+ align:start position:0%
+to study the other one
+ 
+
+ align:start position:0%
+to study the other one
+multidisciplinary is when you want to
+
+ align:start position:0%
+multidisciplinary is when you want to
+ 
+
+ align:start position:0%
+multidisciplinary is when you want to
+study a problem with both of the
+
+ align:start position:0%
+study a problem with both of the
+ 
+
+ align:start position:0%
+study a problem with both of the
+disciplines interact together
+
+ align:start position:0%
+disciplines interact together
+ 
+
+ align:start position:0%
+disciplines interact together
+to give you the solution
+
+ align:start position:0%
+to give you the solution
+ 
+
+ align:start position:0%
+to give you the solution
+and interdisciplinary is when
+
+ align:start position:0%
+and interdisciplinary is when
+ 
+
+ align:start position:0%
+and interdisciplinary is when
+the two interact but one has to give up
+
+ align:start position:0%
+the two interact but one has to give up
+ 
+
+ align:start position:0%
+the two interact but one has to give up
+a fundamental principle of itself in
+
+ align:start position:0%
+a fundamental principle of itself in
+ 
+
+ align:start position:0%
+a fundamental principle of itself in
+order to solve the problem in other
+
+ align:start position:0%
+order to solve the problem in other
+ 
+
+ align:start position:0%
+order to solve the problem in other
+words the two disciplines do not remain
+
+ align:start position:0%
+words the two disciplines do not remain
+ 
+
+ align:start position:0%
+words the two disciplines do not remain
+intact one of them loses something
+
+ align:start position:0%
+intact one of them loses something
+ 
+
+ align:start position:0%
+intact one of them loses something
+or is replaced by something else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i have not talked about
+
+ align:start position:0%
+so i have not talked about
+ 
+
+ align:start position:0%
+so i have not talked about
+transdisciplinary but only those three
+
+ align:start position:0%
+transdisciplinary but only those three
+ 
+
+ align:start position:0%
+transdisciplinary but only those three
+and that's where i define
\ No newline at end of file
diff --git a/zRslv221V9c.txt b/zRslv221V9c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6be5a9aff80692cfa6e36f2b37c29566ac0e7715
--- /dev/null
+++ b/zRslv221V9c.txt
@@ -0,0 +1,1899 @@
+align:start position:0%
+ 
+how did MIT undergraduates design a
+
+ align:start position:0%
+how did MIT undergraduates design a
+ 
+
+ align:start position:0%
+how did MIT undergraduates design a
+robot to lift a small model police car
+
+ align:start position:0%
+robot to lift a small model police car
+ 
+
+ align:start position:0%
+robot to lift a small model police car
+and place it on top of a model of mi
+
+ align:start position:0%
+and place it on top of a model of mi
+ 
+
+ align:start position:0%
+and place it on top of a model of mi
+t--'s great dome calculus in this video
+
+ align:start position:0%
+t--'s great dome calculus in this video
+ 
+
+ align:start position:0%
+t--'s great dome calculus in this video
+we'll use calculus to describe the
+
+ align:start position:0%
+we'll use calculus to describe the
+ 
+
+ align:start position:0%
+we'll use calculus to describe the
+motion of rigid bodies and see how these
+
+ align:start position:0%
+motion of rigid bodies and see how these
+ 
+
+ align:start position:0%
+motion of rigid bodies and see how these
+concepts are used in the field of
+
+ align:start position:0%
+concepts are used in the field of
+ 
+
+ align:start position:0%
+concepts are used in the field of
+robotics
+
+ align:start position:0%
+robotics
+ 
+
+ align:start position:0%
+robotics
+this video is part of the derivatives
+
+ align:start position:0%
+this video is part of the derivatives
+ 
+
+ align:start position:0%
+this video is part of the derivatives
+and integrals video series derivatives
+
+ align:start position:0%
+and integrals video series derivatives
+ 
+
+ align:start position:0%
+and integrals video series derivatives
+and integrals are used to analyze the
+
+ align:start position:0%
+and integrals are used to analyze the
+ 
+
+ align:start position:0%
+and integrals are used to analyze the
+properties of a system derivatives
+
+ align:start position:0%
+properties of a system derivatives
+ 
+
+ align:start position:0%
+properties of a system derivatives
+describe local properties of systems and
+
+ align:start position:0%
+describe local properties of systems and
+ 
+
+ align:start position:0%
+describe local properties of systems and
+integrals quantify their cumulative
+
+ align:start position:0%
+integrals quantify their cumulative
+ 
+
+ align:start position:0%
+integrals quantify their cumulative
+properties hello my name is Dan Frey I'm
+
+ align:start position:0%
+properties hello my name is Dan Frey I'm
+ 
+
+ align:start position:0%
+properties hello my name is Dan Frey I'm
+a professor in the mechanical
+
+ align:start position:0%
+a professor in the mechanical
+ 
+
+ align:start position:0%
+a professor in the mechanical
+engineering department at MIT and today
+
+ align:start position:0%
+engineering department at MIT and today
+ 
+
+ align:start position:0%
+engineering department at MIT and today
+I'll be talking with you about the
+
+ align:start position:0%
+I'll be talking with you about the
+ 
+
+ align:start position:0%
+I'll be talking with you about the
+motion of rigid bodies both translation
+
+ align:start position:0%
+motion of rigid bodies both translation
+ 
+
+ align:start position:0%
+motion of rigid bodies both translation
+and rotation in order to understand this
+
+ align:start position:0%
+and rotation in order to understand this
+ 
+
+ align:start position:0%
+and rotation in order to understand this
+video you should be very comfortable
+
+ align:start position:0%
+video you should be very comfortable
+ 
+
+ align:start position:0%
+video you should be very comfortable
+with linear motion including position
+
+ align:start position:0%
+with linear motion including position
+ 
+
+ align:start position:0%
+with linear motion including position
+velocity and acceleration you'll want to
+
+ align:start position:0%
+velocity and acceleration you'll want to
+ 
+
+ align:start position:0%
+velocity and acceleration you'll want to
+know how to turn measurements in polar
+
+ align:start position:0%
+know how to turn measurements in polar
+ 
+
+ align:start position:0%
+know how to turn measurements in polar
+coordinates into measurements in
+
+ align:start position:0%
+coordinates into measurements in
+ 
+
+ align:start position:0%
+coordinates into measurements in
+Cartesian coordinates you should also
+
+ align:start position:0%
+Cartesian coordinates you should also
+ 
+
+ align:start position:0%
+Cartesian coordinates you should also
+know enough introductory calculus to
+
+ align:start position:0%
+know enough introductory calculus to
+ 
+
+ align:start position:0%
+know enough introductory calculus to
+apply the chain rule after watching this
+
+ align:start position:0%
+apply the chain rule after watching this
+ 
+
+ align:start position:0%
+apply the chain rule after watching this
+video you should be able to explain what
+
+ align:start position:0%
+video you should be able to explain what
+ 
+
+ align:start position:0%
+video you should be able to explain what
+is meant by the phrase rigid body you
+
+ align:start position:0%
+is meant by the phrase rigid body you
+ 
+
+ align:start position:0%
+is meant by the phrase rigid body you
+should also be able to describe
+
+ align:start position:0%
+should also be able to describe
+ 
+
+ align:start position:0%
+should also be able to describe
+restrictions on the motion of an object
+
+ align:start position:0%
+restrictions on the motion of an object
+ 
+
+ align:start position:0%
+restrictions on the motion of an object
+by using constraint equations finally
+
+ align:start position:0%
+by using constraint equations finally
+ 
+
+ align:start position:0%
+by using constraint equations finally
+you should be able to use derivatives
+
+ align:start position:0%
+you should be able to use derivatives
+ 
+
+ align:start position:0%
+you should be able to use derivatives
+and integrals to connect different
+
+ align:start position:0%
+and integrals to connect different
+ 
+
+ align:start position:0%
+and integrals to connect different
+mathematical descriptions of rigid body
+
+ align:start position:0%
+mathematical descriptions of rigid body
+ 
+
+ align:start position:0%
+mathematical descriptions of rigid body
+motion our primary examples today will
+
+ align:start position:0%
+motion our primary examples today will
+ 
+
+ align:start position:0%
+motion our primary examples today will
+be robots let's look at how basic ideas
+
+ align:start position:0%
+be robots let's look at how basic ideas
+ 
+
+ align:start position:0%
+be robots let's look at how basic ideas
+of motion are used in the field of
+
+ align:start position:0%
+of motion are used in the field of
+ 
+
+ align:start position:0%
+of motion are used in the field of
+Robotics here you can see some footage
+
+ align:start position:0%
+Robotics here you can see some footage
+ 
+
+ align:start position:0%
+Robotics here you can see some footage
+from a Robotics Competition at MIT the
+
+ align:start position:0%
+from a Robotics Competition at MIT the
+ 
+
+ align:start position:0%
+from a Robotics Competition at MIT the
+competition is part of a mechanical
+
+ align:start position:0%
+competition is part of a mechanical
+ 
+
+ align:start position:0%
+competition is part of a mechanical
+engineering course number two
+
+ align:start position:0%
+engineering course number two
+ 
+
+ align:start position:0%
+engineering course number two
+double-oh-seven
+
+ align:start position:0%
+double-oh-seven
+ 
+
+ align:start position:0%
+double-oh-seven
+one typical task that robots perform is
+
+ align:start position:0%
+one typical task that robots perform is
+ 
+
+ align:start position:0%
+one typical task that robots perform is
+to grab something pick it up and move it
+
+ align:start position:0%
+to grab something pick it up and move it
+ 
+
+ align:start position:0%
+to grab something pick it up and move it
+this robot uses a gripper at the end of
+
+ align:start position:0%
+this robot uses a gripper at the end of
+ 
+
+ align:start position:0%
+this robot uses a gripper at the end of
+the arm to pick up objects one of the
+
+ align:start position:0%
+the arm to pick up objects one of the
+ 
+
+ align:start position:0%
+the arm to pick up objects one of the
+difficulties in programming a robot arm
+
+ align:start position:0%
+difficulties in programming a robot arm
+ 
+
+ align:start position:0%
+difficulties in programming a robot arm
+is that we typically have no direct
+
+ align:start position:0%
+is that we typically have no direct
+ 
+
+ align:start position:0%
+is that we typically have no direct
+measurement of where that gripper is
+
+ align:start position:0%
+measurement of where that gripper is
+ 
+
+ align:start position:0%
+measurement of where that gripper is
+there's usually no convenient sort of
+
+ align:start position:0%
+there's usually no convenient sort of
+ 
+
+ align:start position:0%
+there's usually no convenient sort of
+position meter that could tell its
+
+ align:start position:0%
+position meter that could tell its
+ 
+
+ align:start position:0%
+position meter that could tell its
+location instead we might determine the
+
+ align:start position:0%
+location instead we might determine the
+ 
+
+ align:start position:0%
+location instead we might determine the
+location for the base of the arm and we
+
+ align:start position:0%
+location for the base of the arm and we
+ 
+
+ align:start position:0%
+location for the base of the arm and we
+can measure the angles for different
+
+ align:start position:0%
+can measure the angles for different
+ 
+
+ align:start position:0%
+can measure the angles for different
+parts of the arm we need to use the
+
+ align:start position:0%
+parts of the arm we need to use the
+ 
+
+ align:start position:0%
+parts of the arm we need to use the
+measurements that we can make in order
+
+ align:start position:0%
+measurements that we can make in order
+ 
+
+ align:start position:0%
+measurements that we can make in order
+to determine the location of the gripper
+
+ align:start position:0%
+to determine the location of the gripper
+ 
+
+ align:start position:0%
+to determine the location of the gripper
+he's got to let go of the police car
+
+ align:start position:0%
+he's got to let go of the police car
+ 
+
+ align:start position:0%
+he's got to let go of the police car
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+or to score is it balanced properly
+
+ align:start position:0%
+or to score is it balanced properly
+ 
+
+ align:start position:0%
+or to score is it balanced properly
+still six seconds five four he did like
+
+ align:start position:0%
+still six seconds five four he did like
+ 
+
+ align:start position:0%
+still six seconds five four he did like
+oh he did like oh he did it fifteen will
+
+ align:start position:0%
+oh he did like oh he did it fifteen will
+ 
+
+ align:start position:0%
+oh he did like oh he did it fifteen will
+gone gram this is made easier by the
+
+ align:start position:0%
+gone gram this is made easier by the
+ 
+
+ align:start position:0%
+gone gram this is made easier by the
+concept of a rigid body rigid bodies can
+
+ align:start position:0%
+concept of a rigid body rigid bodies can
+ 
+
+ align:start position:0%
+concept of a rigid body rigid bodies can
+translate and rotate but they do not
+
+ align:start position:0%
+translate and rotate but they do not
+ 
+
+ align:start position:0%
+translate and rotate but they do not
+Bend stretch or twist in mathematical
+
+ align:start position:0%
+Bend stretch or twist in mathematical
+ 
+
+ align:start position:0%
+Bend stretch or twist in mathematical
+terms the distance between any two
+
+ align:start position:0%
+terms the distance between any two
+ 
+
+ align:start position:0%
+terms the distance between any two
+points in the object does not change
+
+ align:start position:0%
+points in the object does not change
+ 
+
+ align:start position:0%
+points in the object does not change
+rigid bodies are idealization to
+
+ align:start position:0%
+rigid bodies are idealization to
+ 
+
+ align:start position:0%
+rigid bodies are idealization to
+simplify our work we imagine that we are
+
+ align:start position:0%
+simplify our work we imagine that we are
+ 
+
+ align:start position:0%
+simplify our work we imagine that we are
+working with objects that do not deform
+
+ align:start position:0%
+working with objects that do not deform
+ 
+
+ align:start position:0%
+working with objects that do not deform
+this idealization works best when the
+
+ align:start position:0%
+this idealization works best when the
+ 
+
+ align:start position:0%
+this idealization works best when the
+object only experiences low amounts of
+
+ align:start position:0%
+object only experiences low amounts of
+ 
+
+ align:start position:0%
+object only experiences low amounts of
+force higher amounts of force can lead
+
+ align:start position:0%
+force higher amounts of force can lead
+ 
+
+ align:start position:0%
+force higher amounts of force can lead
+to objects deforming or breaking
+
+ align:start position:0%
+to objects deforming or breaking
+ 
+
+ align:start position:0%
+to objects deforming or breaking
+depending on the object the robot we saw
+
+ align:start position:0%
+depending on the object the robot we saw
+ 
+
+ align:start position:0%
+depending on the object the robot we saw
+earlier is a good example of a rigid
+
+ align:start position:0%
+earlier is a good example of a rigid
+ 
+
+ align:start position:0%
+earlier is a good example of a rigid
+body you can see in this video that as
+
+ align:start position:0%
+body you can see in this video that as
+ 
+
+ align:start position:0%
+body you can see in this video that as
+our robot moves its pieces do not bend
+
+ align:start position:0%
+our robot moves its pieces do not bend
+ 
+
+ align:start position:0%
+our robot moves its pieces do not bend
+or distort noticeably so we can treat
+
+ align:start position:0%
+or distort noticeably so we can treat
+ 
+
+ align:start position:0%
+or distort noticeably so we can treat
+each piece as a rigid body we could use
+
+ align:start position:0%
+each piece as a rigid body we could use
+ 
+
+ align:start position:0%
+each piece as a rigid body we could use
+the definition of a rigid body to help
+
+ align:start position:0%
+the definition of a rigid body to help
+ 
+
+ align:start position:0%
+the definition of a rigid body to help
+us determine the location of points on
+
+ align:start position:0%
+us determine the location of points on
+ 
+
+ align:start position:0%
+us determine the location of points on
+that robot this robot on the other hand
+
+ align:start position:0%
+that robot this robot on the other hand
+ 
+
+ align:start position:0%
+that robot this robot on the other hand
+has a less sturdy frame you can see the
+
+ align:start position:0%
+has a less sturdy frame you can see the
+ 
+
+ align:start position:0%
+has a less sturdy frame you can see the
+arm flex as the robot moves we might not
+
+ align:start position:0%
+arm flex as the robot moves we might not
+ 
+
+ align:start position:0%
+arm flex as the robot moves we might not
+want to treat this arm as a rigid body
+
+ align:start position:0%
+want to treat this arm as a rigid body
+ 
+
+ align:start position:0%
+want to treat this arm as a rigid body
+let's try to solve a problem involving a
+
+ align:start position:0%
+let's try to solve a problem involving a
+ 
+
+ align:start position:0%
+let's try to solve a problem involving a
+rigid body here is a very simple robot
+
+ align:start position:0%
+rigid body here is a very simple robot
+ 
+
+ align:start position:0%
+rigid body here is a very simple robot
+arm it has a joint on the left that can
+
+ align:start position:0%
+arm it has a joint on the left that can
+ 
+
+ align:start position:0%
+arm it has a joint on the left that can
+tilt up and down and a piston that can
+
+ align:start position:0%
+tilt up and down and a piston that can
+ 
+
+ align:start position:0%
+tilt up and down and a piston that can
+extend its arm in addition this part of
+
+ align:start position:0%
+extend its arm in addition this part of
+ 
+
+ align:start position:0%
+extend its arm in addition this part of
+the piston can be considered a rigid
+
+ align:start position:0%
+the piston can be considered a rigid
+ 
+
+ align:start position:0%
+the piston can be considered a rigid
+body so its length will be a constant
+
+ align:start position:0%
+body so its length will be a constant
+ 
+
+ align:start position:0%
+body so its length will be a constant
+here is a task for you describe the
+
+ align:start position:0%
+here is a task for you describe the
+ 
+
+ align:start position:0%
+here is a task for you describe the
+acceleration of the gripper at the end
+
+ align:start position:0%
+acceleration of the gripper at the end
+ 
+
+ align:start position:0%
+acceleration of the gripper at the end
+of the arm first set the origin for your
+
+ align:start position:0%
+of the arm first set the origin for your
+ 
+
+ align:start position:0%
+of the arm first set the origin for your
+coordinate system then write an
+
+ align:start position:0%
+coordinate system then write an
+ 
+
+ align:start position:0%
+coordinate system then write an
+expression for the X&Y position of the
+
+ align:start position:0%
+expression for the X&Y position of the
+ 
+
+ align:start position:0%
+expression for the X&Y position of the
+gripper in terms of the quantities shown
+
+ align:start position:0%
+gripper in terms of the quantities shown
+ 
+
+ align:start position:0%
+gripper in terms of the quantities shown
+here once you have that position use
+
+ align:start position:0%
+here once you have that position use
+ 
+
+ align:start position:0%
+here once you have that position use
+derivatives to find the velocity and the
+
+ align:start position:0%
+derivatives to find the velocity and the
+ 
+
+ align:start position:0%
+derivatives to find the velocity and the
+acceleration of the gripper
+
+ align:start position:0%
+acceleration of the gripper
+ 
+
+ align:start position:0%
+acceleration of the gripper
+pause the video here to carry out your
+
+ align:start position:0%
+pause the video here to carry out your
+ 
+
+ align:start position:0%
+pause the video here to carry out your
+calculations let's take a look at the
+
+ align:start position:0%
+calculations let's take a look at the
+ 
+
+ align:start position:0%
+calculations let's take a look at the
+answer first we need to choose an origin
+
+ align:start position:0%
+answer first we need to choose an origin
+ 
+
+ align:start position:0%
+answer first we need to choose an origin
+let's choose an arbitrary location as
+
+ align:start position:0%
+let's choose an arbitrary location as
+ 
+
+ align:start position:0%
+let's choose an arbitrary location as
+the origin of our coordinate system our
+
+ align:start position:0%
+the origin of our coordinate system our
+ 
+
+ align:start position:0%
+the origin of our coordinate system our
+robots joint may be moving so we will
+
+ align:start position:0%
+robots joint may be moving so we will
+ 
+
+ align:start position:0%
+robots joint may be moving so we will
+use a pair of functions X sub J of time
+
+ align:start position:0%
+use a pair of functions X sub J of time
+ 
+
+ align:start position:0%
+use a pair of functions X sub J of time
+and y sub J of time to describe its
+
+ align:start position:0%
+and y sub J of time to describe its
+ 
+
+ align:start position:0%
+and y sub J of time to describe its
+location X sub J will be the horizontal
+
+ align:start position:0%
+location X sub J will be the horizontal
+ 
+
+ align:start position:0%
+location X sub J will be the horizontal
+distance from our origin to the joint
+
+ align:start position:0%
+distance from our origin to the joint
+ 
+
+ align:start position:0%
+distance from our origin to the joint
+and Y sub J will be the vertical
+
+ align:start position:0%
+and Y sub J will be the vertical
+ 
+
+ align:start position:0%
+and Y sub J will be the vertical
+distance we can use derivatives of these
+
+ align:start position:0%
+distance we can use derivatives of these
+ 
+
+ align:start position:0%
+distance we can use derivatives of these
+functions to describe any relative
+
+ align:start position:0%
+functions to describe any relative
+ 
+
+ align:start position:0%
+functions to describe any relative
+movement that the joint has when
+
+ align:start position:0%
+movement that the joint has when
+ 
+
+ align:start position:0%
+movement that the joint has when
+compared with our coordinate system such
+
+ align:start position:0%
+compared with our coordinate system such
+ 
+
+ align:start position:0%
+compared with our coordinate system such
+as velocity or acceleration
+
+ align:start position:0%
+as velocity or acceleration
+ 
+
+ align:start position:0%
+as velocity or acceleration
+this slide shows just the X components
+
+ align:start position:0%
+this slide shows just the X components
+ 
+
+ align:start position:0%
+this slide shows just the X components
+of the answer with the value X sub J
+
+ align:start position:0%
+of the answer with the value X sub J
+ 
+
+ align:start position:0%
+of the answer with the value X sub J
+indicating the location of the joint you
+
+ align:start position:0%
+indicating the location of the joint you
+ 
+
+ align:start position:0%
+indicating the location of the joint you
+can see that the expressions can easily
+
+ align:start position:0%
+can see that the expressions can easily
+ 
+
+ align:start position:0%
+can see that the expressions can easily
+become complicated
+
+ align:start position:0%
+become complicated
+ 
+
+ align:start position:0%
+become complicated
+if both s and theta change at the same
+
+ align:start position:0%
+if both s and theta change at the same
+ 
+
+ align:start position:0%
+if both s and theta change at the same
+time one reason that we want to know the
+
+ align:start position:0%
+time one reason that we want to know the
+ 
+
+ align:start position:0%
+time one reason that we want to know the
+acceleration is because some objects
+
+ align:start position:0%
+acceleration is because some objects
+ 
+
+ align:start position:0%
+acceleration is because some objects
+respond poorly to a high acceleration
+
+ align:start position:0%
+respond poorly to a high acceleration
+ 
+
+ align:start position:0%
+respond poorly to a high acceleration
+here you can see a different sort of
+
+ align:start position:0%
+here you can see a different sort of
+ 
+
+ align:start position:0%
+here you can see a different sort of
+robot arm lifting a car instead of a
+
+ align:start position:0%
+robot arm lifting a car instead of a
+ 
+
+ align:start position:0%
+robot arm lifting a car instead of a
+gripper these two robots use a forklift
+
+ align:start position:0%
+gripper these two robots use a forklift
+ 
+
+ align:start position:0%
+gripper these two robots use a forklift
+design their arms must move very gently
+
+ align:start position:0%
+design their arms must move very gently
+ 
+
+ align:start position:0%
+design their arms must move very gently
+especially as they slow down or the car
+
+ align:start position:0%
+especially as they slow down or the car
+ 
+
+ align:start position:0%
+especially as they slow down or the car
+will fall off the arms are capable of
+
+ align:start position:0%
+will fall off the arms are capable of
+ 
+
+ align:start position:0%
+will fall off the arms are capable of
+moving more quickly but the robots
+
+ align:start position:0%
+moving more quickly but the robots
+ 
+
+ align:start position:0%
+moving more quickly but the robots
+designers have programmed it to use a
+
+ align:start position:0%
+designers have programmed it to use a
+ 
+
+ align:start position:0%
+designers have programmed it to use a
+lower acceleration this leads us to a
+
+ align:start position:0%
+lower acceleration this leads us to a
+ 
+
+ align:start position:0%
+lower acceleration this leads us to a
+discussion of constraints this section
+
+ align:start position:0%
+discussion of constraints this section
+ 
+
+ align:start position:0%
+discussion of constraints this section
+will have a few examples as well as
+
+ align:start position:0%
+will have a few examples as well as
+ 
+
+ align:start position:0%
+will have a few examples as well as
+several opportunities for you to
+
+ align:start position:0%
+several opportunities for you to
+ 
+
+ align:start position:0%
+several opportunities for you to
+practice be ready to pause the video
+
+ align:start position:0%
+practice be ready to pause the video
+ 
+
+ align:start position:0%
+practice be ready to pause the video
+constraints are any sort of restriction
+
+ align:start position:0%
+constraints are any sort of restriction
+ 
+
+ align:start position:0%
+constraints are any sort of restriction
+on a situation when they can be
+
+ align:start position:0%
+on a situation when they can be
+ 
+
+ align:start position:0%
+on a situation when they can be
+expressed mathematically we refer to
+
+ align:start position:0%
+expressed mathematically we refer to
+ 
+
+ align:start position:0%
+expressed mathematically we refer to
+equations of constraint these describe
+
+ align:start position:0%
+equations of constraint these describe
+ 
+
+ align:start position:0%
+equations of constraint these describe
+the physical connection between two or
+
+ align:start position:0%
+the physical connection between two or
+ 
+
+ align:start position:0%
+the physical connection between two or
+more rigid bodies constraint equations
+
+ align:start position:0%
+more rigid bodies constraint equations
+ 
+
+ align:start position:0%
+more rigid bodies constraint equations
+are useful because they link one
+
+ align:start position:0%
+are useful because they link one
+ 
+
+ align:start position:0%
+are useful because they link one
+variable to another in a way that
+
+ align:start position:0%
+variable to another in a way that
+ 
+
+ align:start position:0%
+variable to another in a way that
+reduces the total number of variables in
+
+ align:start position:0%
+reduces the total number of variables in
+ 
+
+ align:start position:0%
+reduces the total number of variables in
+a problem this helps to make otherwise
+
+ align:start position:0%
+a problem this helps to make otherwise
+ 
+
+ align:start position:0%
+a problem this helps to make otherwise
+impossible problems solvable constraint
+
+ align:start position:0%
+impossible problems solvable constraint
+ 
+
+ align:start position:0%
+impossible problems solvable constraint
+equations are used throughout physics
+
+ align:start position:0%
+equations are used throughout physics
+ 
+
+ align:start position:0%
+equations are used throughout physics
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+engineering some fields refer to a
+
+ align:start position:0%
+engineering some fields refer to a
+ 
+
+ align:start position:0%
+engineering some fields refer to a
+similar idea called degree of freedom
+
+ align:start position:0%
+similar idea called degree of freedom
+ 
+
+ align:start position:0%
+similar idea called degree of freedom
+analysis here is a classic example of a
+
+ align:start position:0%
+analysis here is a classic example of a
+ 
+
+ align:start position:0%
+analysis here is a classic example of a
+situation with a constraint the car on
+
+ align:start position:0%
+situation with a constraint the car on
+ 
+
+ align:start position:0%
+situation with a constraint the car on
+this rollercoaster
+
+ align:start position:0%
+this rollercoaster
+ 
+
+ align:start position:0%
+this rollercoaster
+cannot leave the tracks if the track is
+
+ align:start position:0%
+cannot leave the tracks if the track is
+ 
+
+ align:start position:0%
+cannot leave the tracks if the track is
+circular we can use the equation for a
+
+ align:start position:0%
+circular we can use the equation for a
+ 
+
+ align:start position:0%
+circular we can use the equation for a
+circle to constrain our movement we can
+
+ align:start position:0%
+circle to constrain our movement we can
+ 
+
+ align:start position:0%
+circle to constrain our movement we can
+use this to reduce the number of
+
+ align:start position:0%
+use this to reduce the number of
+ 
+
+ align:start position:0%
+use this to reduce the number of
+variables in our equations for the
+
+ align:start position:0%
+variables in our equations for the
+ 
+
+ align:start position:0%
+variables in our equations for the
+position of the roller-coaster rather
+
+ align:start position:0%
+position of the roller-coaster rather
+ 
+
+ align:start position:0%
+position of the roller-coaster rather
+than an equation in X and y we could
+
+ align:start position:0%
+than an equation in X and y we could
+ 
+
+ align:start position:0%
+than an equation in X and y we could
+have equations in just X or just Y we
+
+ align:start position:0%
+have equations in just X or just Y we
+ 
+
+ align:start position:0%
+have equations in just X or just Y we
+could also use constraints that involve
+
+ align:start position:0%
+could also use constraints that involve
+ 
+
+ align:start position:0%
+could also use constraints that involve
+the distance along the track or another
+
+ align:start position:0%
+the distance along the track or another
+ 
+
+ align:start position:0%
+the distance along the track or another
+sensible measurement for the situation
+
+ align:start position:0%
+sensible measurement for the situation
+ 
+
+ align:start position:0%
+sensible measurement for the situation
+we're investigating it's important to
+
+ align:start position:0%
+we're investigating it's important to
+ 
+
+ align:start position:0%
+we're investigating it's important to
+note that constraints being giving up
+
+ align:start position:0%
+note that constraints being giving up
+ 
+
+ align:start position:0%
+note that constraints being giving up
+some freedom in our variables in our
+
+ align:start position:0%
+some freedom in our variables in our
+ 
+
+ align:start position:0%
+some freedom in our variables in our
+example we can only specify X or Y not
+
+ align:start position:0%
+example we can only specify X or Y not
+ 
+
+ align:start position:0%
+example we can only specify X or Y not
+both once we choose a value for X there
+
+ align:start position:0%
+both once we choose a value for X there
+ 
+
+ align:start position:0%
+both once we choose a value for X there
+are only two values of Y that will work
+
+ align:start position:0%
+are only two values of Y that will work
+ 
+
+ align:start position:0%
+are only two values of Y that will work
+here's a situation where you can find
+
+ align:start position:0%
+here's a situation where you can find
+ 
+
+ align:start position:0%
+here's a situation where you can find
+the equation of constraint a cart is
+
+ align:start position:0%
+the equation of constraint a cart is
+ 
+
+ align:start position:0%
+the equation of constraint a cart is
+being pulled across a flat surface and
+
+ align:start position:0%
+being pulled across a flat surface and
+ 
+
+ align:start position:0%
+being pulled across a flat surface and
+the wheels turn without slipping
+
+ align:start position:0%
+the wheels turn without slipping
+ 
+
+ align:start position:0%
+the wheels turn without slipping
+effectively the wheel is constrained to
+
+ align:start position:0%
+effectively the wheel is constrained to
+ 
+
+ align:start position:0%
+effectively the wheel is constrained to
+move only by rolling and not in any
+
+ align:start position:0%
+move only by rolling and not in any
+ 
+
+ align:start position:0%
+move only by rolling and not in any
+other way no lifting up no sliding no
+
+ align:start position:0%
+other way no lifting up no sliding no
+ 
+
+ align:start position:0%
+other way no lifting up no sliding no
+peeling out can you find an equation
+
+ align:start position:0%
+peeling out can you find an equation
+ 
+
+ align:start position:0%
+peeling out can you find an equation
+that connects X the distance the cart
+
+ align:start position:0%
+that connects X the distance the cart
+ 
+
+ align:start position:0%
+that connects X the distance the cart
+has moved to theta the amount that the
+
+ align:start position:0%
+has moved to theta the amount that the
+ 
+
+ align:start position:0%
+has moved to theta the amount that the
+wheels have turned pause the video here
+
+ align:start position:0%
+wheels have turned pause the video here
+ 
+
+ align:start position:0%
+wheels have turned pause the video here
+to discuss this in class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is an arm that is fairly complex it
+
+ align:start position:0%
+here is an arm that is fairly complex it
+ 
+
+ align:start position:0%
+here is an arm that is fairly complex it
+has many joints pause the video and
+
+ align:start position:0%
+has many joints pause the video and
+ 
+
+ align:start position:0%
+has many joints pause the video and
+write down the variables and constants
+
+ align:start position:0%
+write down the variables and constants
+ 
+
+ align:start position:0%
+write down the variables and constants
+you would use for this robot there are
+
+ align:start position:0%
+you would use for this robot there are
+ 
+
+ align:start position:0%
+you would use for this robot there are
+three separate angles that must be
+
+ align:start position:0%
+three separate angles that must be
+ 
+
+ align:start position:0%
+three separate angles that must be
+recorded as well as the extension of the
+
+ align:start position:0%
+recorded as well as the extension of the
+ 
+
+ align:start position:0%
+recorded as well as the extension of the
+arm
+
+ align:start position:0%
+arm
+ 
+
+ align:start position:0%
+arm
+there are also three pieces of constant
+
+ align:start position:0%
+there are also three pieces of constant
+ 
+
+ align:start position:0%
+there are also three pieces of constant
+length now we have an opportunity to
+
+ align:start position:0%
+length now we have an opportunity to
+ 
+
+ align:start position:0%
+length now we have an opportunity to
+describe a constraint in a complex
+
+ align:start position:0%
+describe a constraint in a complex
+ 
+
+ align:start position:0%
+describe a constraint in a complex
+situation we could choose for example to
+
+ align:start position:0%
+situation we could choose for example to
+ 
+
+ align:start position:0%
+situation we could choose for example to
+constrain the motion of the arm to just
+
+ align:start position:0%
+constrain the motion of the arm to just
+ 
+
+ align:start position:0%
+constrain the motion of the arm to just
+the horizontal direction because there
+
+ align:start position:0%
+the horizontal direction because there
+ 
+
+ align:start position:0%
+the horizontal direction because there
+are so many variables in this situation
+
+ align:start position:0%
+are so many variables in this situation
+ 
+
+ align:start position:0%
+are so many variables in this situation
+there are many possible ways to satisfy
+
+ align:start position:0%
+there are many possible ways to satisfy
+ 
+
+ align:start position:0%
+there are many possible ways to satisfy
+the constraint write an expression for
+
+ align:start position:0%
+the constraint write an expression for
+ 
+
+ align:start position:0%
+the constraint write an expression for
+just the vertical position in the
+
+ align:start position:0%
+just the vertical position in the
+ 
+
+ align:start position:0%
+just the vertical position in the
+gripper in terms of the quantities shown
+
+ align:start position:0%
+gripper in terms of the quantities shown
+ 
+
+ align:start position:0%
+gripper in terms of the quantities shown
+once you have done that answer this
+
+ align:start position:0%
+once you have done that answer this
+ 
+
+ align:start position:0%
+once you have done that answer this
+question how might we move the gripper
+
+ align:start position:0%
+question how might we move the gripper
+ 
+
+ align:start position:0%
+question how might we move the gripper
+in just the horizontal direction you
+
+ align:start position:0%
+in just the horizontal direction you
+ 
+
+ align:start position:0%
+in just the horizontal direction you
+should come up with at least two ways
+
+ align:start position:0%
+should come up with at least two ways
+ 
+
+ align:start position:0%
+should come up with at least two ways
+that we could do this and describe them
+
+ align:start position:0%
+that we could do this and describe them
+ 
+
+ align:start position:0%
+that we could do this and describe them
+mathematically your teacher will then
+
+ align:start position:0%
+mathematically your teacher will then
+ 
+
+ align:start position:0%
+mathematically your teacher will then
+lead the class in a discussion of your
+
+ align:start position:0%
+lead the class in a discussion of your
+ 
+
+ align:start position:0%
+lead the class in a discussion of your
+answers pause the video here to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is a simulation of a Hydra bot
+
+ align:start position:0%
+here is a simulation of a Hydra bot
+ 
+
+ align:start position:0%
+here is a simulation of a Hydra bot
+doing exactly what you just calculated
+
+ align:start position:0%
+doing exactly what you just calculated
+ 
+
+ align:start position:0%
+doing exactly what you just calculated
+moving one end horizontally you can see
+
+ align:start position:0%
+moving one end horizontally you can see
+ 
+
+ align:start position:0%
+moving one end horizontally you can see
+that it matches up quite well with our
+
+ align:start position:0%
+that it matches up quite well with our
+ 
+
+ align:start position:0%
+that it matches up quite well with our
+hypothetical robot examine its motion
+
+ align:start position:0%
+hypothetical robot examine its motion
+ 
+
+ align:start position:0%
+hypothetical robot examine its motion
+closely is this one of the motions you
+
+ align:start position:0%
+closely is this one of the motions you
+ 
+
+ align:start position:0%
+closely is this one of the motions you
+described are there extra constraints
+
+ align:start position:0%
+described are there extra constraints
+ 
+
+ align:start position:0%
+described are there extra constraints
+present here what freedom of motion did
+
+ align:start position:0%
+present here what freedom of motion did
+ 
+
+ align:start position:0%
+present here what freedom of motion did
+we give up by making our choice let's
+
+ align:start position:0%
+we give up by making our choice let's
+ 
+
+ align:start position:0%
+we give up by making our choice let's
+review today you use derivatives to find
+
+ align:start position:0%
+review today you use derivatives to find
+ 
+
+ align:start position:0%
+review today you use derivatives to find
+the velocity and acceleration of an
+
+ align:start position:0%
+the velocity and acceleration of an
+ 
+
+ align:start position:0%
+the velocity and acceleration of an
+object based on its position you also
+
+ align:start position:0%
+object based on its position you also
+ 
+
+ align:start position:0%
+object based on its position you also
+learned the definition of a rigid body
+
+ align:start position:0%
+learned the definition of a rigid body
+ 
+
+ align:start position:0%
+learned the definition of a rigid body
+that it does not bend or stretch when
+
+ align:start position:0%
+that it does not bend or stretch when
+ 
+
+ align:start position:0%
+that it does not bend or stretch when
+forces applied finally you saw the
+
+ align:start position:0%
+forces applied finally you saw the
+ 
+
+ align:start position:0%
+forces applied finally you saw the
+constraint equations can reduce the
+
+ align:start position:0%
+constraint equations can reduce the
+ 
+
+ align:start position:0%
+constraint equations can reduce the
+total number of equations in a system
+
+ align:start position:0%
+total number of equations in a system
+ 
+
+ align:start position:0%
+total number of equations in a system
+thus making the problems easier to solve
+
+ align:start position:0%
+thus making the problems easier to solve
+ 
+
+ align:start position:0%
+thus making the problems easier to solve
+I hope you enjoyed seeing some
+
+ align:start position:0%
+I hope you enjoyed seeing some
+ 
+
+ align:start position:0%
+I hope you enjoyed seeing some
+applications of basic motion concepts
+
+ align:start position:0%
+applications of basic motion concepts
+ 
+
+ align:start position:0%
+applications of basic motion concepts
+good luck in your further investigations
+
+ align:start position:0%
+good luck in your further investigations
+ 
+
+ align:start position:0%
+good luck in your further investigations
+of physics and engineering
\ No newline at end of file
diff --git a/zVzixXOtq7Y.txt b/zVzixXOtq7Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..83aef0c4549705770b18d00ebf1d73ba83cb0d6e
--- /dev/null
+++ b/zVzixXOtq7Y.txt
@@ -0,0 +1,1283 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free to make a donation or view
+
+ align:start position:0%
+for free to make a donation or view
+ 
+
+ align:start position:0%
+for free to make a donation or view
+additional materials from hundreds of
+
+ align:start position:0%
+additional materials from hundreds of
+ 
+
+ align:start position:0%
+additional materials from hundreds of
+MIT courses visit MIT opencourseware at
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ 
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first thing we're going to do is
+
+ align:start position:0%
+so the first thing we're going to do is
+ 
+
+ align:start position:0%
+so the first thing we're going to do is
+a power module and it's important that
+
+ align:start position:0%
+a power module and it's important that
+ 
+
+ align:start position:0%
+a power module and it's important that
+when you're trying to get draw power
+
+ align:start position:0%
+when you're trying to get draw power
+ 
+
+ align:start position:0%
+when you're trying to get draw power
+from any source even a battery or
+
+ align:start position:0%
+from any source even a battery or
+ 
+
+ align:start position:0%
+from any source even a battery or
+anything like that that you try to match
+
+ align:start position:0%
+anything like that that you try to match
+ 
+
+ align:start position:0%
+anything like that that you try to match
+or you want to Matt draw the maximum
+
+ align:start position:0%
+or you want to Matt draw the maximum
+ 
+
+ align:start position:0%
+or you want to Matt draw the maximum
+amount of power you need to have the
+
+ align:start position:0%
+amount of power you need to have the
+ 
+
+ align:start position:0%
+amount of power you need to have the
+right load on it so we're going to try
+
+ align:start position:0%
+right load on it so we're going to try
+ 
+
+ align:start position:0%
+right load on it so we're going to try
+to figure out experimentally what the
+
+ align:start position:0%
+to figure out experimentally what the
+ 
+
+ align:start position:0%
+to figure out experimentally what the
+right load is for this solar panel and
+
+ align:start position:0%
+right load is for this solar panel and
+ 
+
+ align:start position:0%
+right load is for this solar panel and
+the way you do that is you you hook up a
+
+ align:start position:0%
+the way you do that is you you hook up a
+ 
+
+ align:start position:0%
+the way you do that is you you hook up a
+resistor or a potentiometer to a in a
+
+ align:start position:0%
+resistor or a potentiometer to a in a
+ 
+
+ align:start position:0%
+resistor or a potentiometer to a in a
+closed circuit around this and first to
+
+ align:start position:0%
+closed circuit around this and first to
+ 
+
+ align:start position:0%
+closed circuit around this and first to
+measure the resistance of it then you
+
+ align:start position:0%
+measure the resistance of it then you
+ 
+
+ align:start position:0%
+measure the resistance of it then you
+hook a hook this up in a closed circuit
+
+ align:start position:0%
+hook a hook this up in a closed circuit
+ 
+
+ align:start position:0%
+hook a hook this up in a closed circuit
+and measure the voltage drop across it
+
+ align:start position:0%
+and measure the voltage drop across it
+ 
+
+ align:start position:0%
+and measure the voltage drop across it
+and you can calculate power from a V
+
+ align:start position:0%
+and you can calculate power from a V
+ 
+
+ align:start position:0%
+and you can calculate power from a V
+squared over R and so you just do that
+
+ align:start position:0%
+squared over R and so you just do that
+ 
+
+ align:start position:0%
+squared over R and so you just do that
+for a bunch of different resistances
+
+ align:start position:0%
+for a bunch of different resistances
+ 
+
+ align:start position:0%
+for a bunch of different resistances
+just changing this and you should be
+
+ align:start position:0%
+just changing this and you should be
+ 
+
+ align:start position:0%
+just changing this and you should be
+able to get a graph that goes up and
+
+ align:start position:0%
+able to get a graph that goes up and
+ 
+
+ align:start position:0%
+able to get a graph that goes up and
+then down and if your graph power versus
+
+ align:start position:0%
+then down and if your graph power versus
+ 
+
+ align:start position:0%
+then down and if your graph power versus
+resistance and based off of that you can
+
+ align:start position:0%
+resistance and based off of that you can
+ 
+
+ align:start position:0%
+resistance and based off of that you can
+figure out what the appropriate load to
+
+ align:start position:0%
+figure out what the appropriate load to
+ 
+
+ align:start position:0%
+figure out what the appropriate load to
+place on it is and still generate a
+
+ align:start position:0%
+place on it is and still generate a
+ 
+
+ align:start position:0%
+place on it is and still generate a
+power curve for that again make sure you
+
+ align:start position:0%
+power curve for that again make sure you
+ 
+
+ align:start position:0%
+power curve for that again make sure you
+don't measure the resistance when it's
+
+ align:start position:0%
+don't measure the resistance when it's
+ 
+
+ align:start position:0%
+don't measure the resistance when it's
+hooked up because you're going to fry
+
+ align:start position:0%
+hooked up because you're going to fry
+ 
+
+ align:start position:0%
+hooked up because you're going to fry
+the voltmeter and then the second thing
+
+ align:start position:0%
+the voltmeter and then the second thing
+ 
+
+ align:start position:0%
+the voltmeter and then the second thing
+we're going to have you do is optimize
+
+ align:start position:0%
+we're going to have you do is optimize
+ 
+
+ align:start position:0%
+we're going to have you do is optimize
+the angle so you want to put the solar
+
+ align:start position:0%
+the angle so you want to put the solar
+ 
+
+ align:start position:0%
+the angle so you want to put the solar
+panel at different angles both in this
+
+ align:start position:0%
+panel at different angles both in this
+ 
+
+ align:start position:0%
+panel at different angles both in this
+direction and in this direction and
+
+ align:start position:0%
+direction and in this direction and
+ 
+
+ align:start position:0%
+direction and in this direction and
+measure for a variety of angles what the
+
+ align:start position:0%
+measure for a variety of angles what the
+ 
+
+ align:start position:0%
+measure for a variety of angles what the
+power output it is and so for that you
+
+ align:start position:0%
+power output it is and so for that you
+ 
+
+ align:start position:0%
+power output it is and so for that you
+can just have choose a resistance with
+
+ align:start position:0%
+can just have choose a resistance with
+ 
+
+ align:start position:0%
+can just have choose a resistance with
+the potentiometer and then measure
+
+ align:start position:0%
+the potentiometer and then measure
+ 
+
+ align:start position:0%
+the potentiometer and then measure
+voltage and get power that way and then
+
+ align:start position:0%
+voltage and get power that way and then
+ 
+
+ align:start position:0%
+voltage and get power that way and then
+I have protractor somewhere yeah or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what close enough yeah and so you can
+
+ align:start position:0%
+what close enough yeah and so you can
+ 
+
+ align:start position:0%
+what close enough yeah and so you can
+use that to measure the angle of the
+
+ align:start position:0%
+use that to measure the angle of the
+ 
+
+ align:start position:0%
+use that to measure the angle of the
+solar panel and when you're doing this I
+
+ align:start position:0%
+solar panel and when you're doing this I
+ 
+
+ align:start position:0%
+solar panel and when you're doing this I
+want you to take for the two for the
+
+ align:start position:0%
+want you to take for the two for the
+ 
+
+ align:start position:0%
+want you to take for the two for the
+angle ones and the shading once I want
+
+ align:start position:0%
+angle ones and the shading once I want
+ 
+
+ align:start position:0%
+angle ones and the shading once I want
+you to take at least 10 data points and
+
+ align:start position:0%
+you to take at least 10 data points and
+ 
+
+ align:start position:0%
+you to take at least 10 data points and
+for the voltage one I want you to take
+
+ align:start position:0%
+for the voltage one I want you to take
+ 
+
+ align:start position:0%
+for the voltage one I want you to take
+at least 15 data points for different
+
+ align:start position:0%
+at least 15 data points for different
+ 
+
+ align:start position:0%
+at least 15 data points for different
+resistances empowers and then the last
+
+ align:start position:0%
+resistances empowers and then the last
+ 
+
+ align:start position:0%
+resistances empowers and then the last
+thing we're going to look at is how
+
+ align:start position:0%
+thing we're going to look at is how
+ 
+
+ align:start position:0%
+thing we're going to look at is how
+shading the solar panel affects the
+
+ align:start position:0%
+shading the solar panel affects the
+ 
+
+ align:start position:0%
+shading the solar panel affects the
+energy being outputted by it and in this
+
+ align:start position:0%
+energy being outputted by it and in this
+ 
+
+ align:start position:0%
+energy being outputted by it and in this
+case I want you to if you look at these
+
+ align:start position:0%
+case I want you to if you look at these
+ 
+
+ align:start position:0%
+case I want you to if you look at these
+solar panels each of these long things
+
+ align:start position:0%
+solar panels each of these long things
+ 
+
+ align:start position:0%
+solar panels each of these long things
+is an individual cell and they're wired
+
+ align:start position:0%
+is an individual cell and they're wired
+ 
+
+ align:start position:0%
+is an individual cell and they're wired
+in series so I want you to shade the
+
+ align:start position:0%
+in series so I want you to shade the
+ 
+
+ align:start position:0%
+in series so I want you to shade the
+solar panel going down this way and then
+
+ align:start position:0%
+solar panel going down this way and then
+ 
+
+ align:start position:0%
+solar panel going down this way and then
+going across this way and just measure
+
+ align:start position:0%
+going across this way and just measure
+ 
+
+ align:start position:0%
+going across this way and just measure
+the surface area of the exposed solar
+
+ align:start position:0%
+the surface area of the exposed solar
+ 
+
+ align:start position:0%
+the surface area of the exposed solar
+panel and then food for that one just
+
+ align:start position:0%
+panel and then food for that one just
+ 
+
+ align:start position:0%
+panel and then food for that one just
+choose the angle that you like and
+
+ align:start position:0%
+choose the angle that you like and
+ 
+
+ align:start position:0%
+choose the angle that you like and
+choose a resistance that you like and
+
+ align:start position:0%
+choose a resistance that you like and
+ 
+
+ align:start position:0%
+choose a resistance that you like and
+then measure power being outputted by
+
+ align:start position:0%
+then measure power being outputted by
+ 
+
+ align:start position:0%
+then measure power being outputted by
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as you can see it's kind of annoying
+
+ align:start position:0%
+and as you can see it's kind of annoying
+ 
+
+ align:start position:0%
+and as you can see it's kind of annoying
+to attach wires to other wires in the
+
+ align:start position:0%
+to attach wires to other wires in the
+ 
+
+ align:start position:0%
+to attach wires to other wires in the
+developing world especially if you don't
+
+ align:start position:0%
+developing world especially if you don't
+ 
+
+ align:start position:0%
+developing world especially if you don't
+have solder in techniques or anything
+
+ align:start position:0%
+have solder in techniques or anything
+ 
+
+ align:start position:0%
+have solder in techniques or anything
+like that easily available so there are
+
+ align:start position:0%
+like that easily available so there are
+ 
+
+ align:start position:0%
+like that easily available so there are
+a lot of different ways of attaching
+
+ align:start position:0%
+a lot of different ways of attaching
+ 
+
+ align:start position:0%
+a lot of different ways of attaching
+them together a lot of times you the way
+
+ align:start position:0%
+them together a lot of times you the way
+ 
+
+ align:start position:0%
+them together a lot of times you the way
+you'll see people wire things it's just
+
+ align:start position:0%
+you'll see people wire things it's just
+ 
+
+ align:start position:0%
+you'll see people wire things it's just
+taking two wires and twisting them
+
+ align:start position:0%
+taking two wires and twisting them
+ 
+
+ align:start position:0%
+taking two wires and twisting them
+together and I neither works as a short
+
+ align:start position:0%
+together and I neither works as a short
+ 
+
+ align:start position:0%
+together and I neither works as a short
+term solution but you'll see entire
+
+ align:start position:0%
+term solution but you'll see entire
+ 
+
+ align:start position:0%
+term solution but you'll see entire
+system's rigged up that way and yeah
+
+ align:start position:0%
+system's rigged up that way and yeah
+ 
+
+ align:start position:0%
+system's rigged up that way and yeah
+it's not particularly good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you are you're comfortable
+
+ align:start position:0%
+so you are you're comfortable
+ 
+
+ align:start position:0%
+so you are you're comfortable
+calculating power given this we just do
+
+ align:start position:0%
+calculating power given this we just do
+ 
+
+ align:start position:0%
+calculating power given this we just do
+this right over our 19
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're not i'm not going seven yeah right
+
+ align:start position:0%
+we're not i'm not going seven yeah right
+ 
+
+ align:start position:0%
+we're not i'm not going seven yeah right
+so go to Twitter go about 20 yeah it's
+
+ align:start position:0%
+so go to Twitter go about 20 yeah it's
+ 
+
+ align:start position:0%
+so go to Twitter go about 20 yeah it's
+gonna
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they saw our panel outputs 15 watts and
+
+ align:start position:0%
+they saw our panel outputs 15 watts and
+ 
+
+ align:start position:0%
+they saw our panel outputs 15 watts and
+most of like the tiny resistors you see
+
+ align:start position:0%
+most of like the tiny resistors you see
+ 
+
+ align:start position:0%
+most of like the tiny resistors you see
+are rated for underwater have one so if
+
+ align:start position:0%
+are rated for underwater have one so if
+ 
+
+ align:start position:0%
+are rated for underwater have one so if
+you hook them up to this they were just
+
+ align:start position:0%
+you hook them up to this they were just
+ 
+
+ align:start position:0%
+you hook them up to this they were just
+thrown out or get like super hot burning
+
+ align:start position:0%
+thrown out or get like super hot burning
+ 
+
+ align:start position:0%
+thrown out or get like super hot burning
+so this one's rated for nothing like
+
+ align:start position:0%
+so this one's rated for nothing like
+ 
+
+ align:start position:0%
+so this one's rated for nothing like
+point where point for ya and so change
+
+ align:start position:0%
+point where point for ya and so change
+ 
+
+ align:start position:0%
+point where point for ya and so change
+your angle relative to Point into the
+
+ align:start position:0%
+your angle relative to Point into the
+ 
+
+ align:start position:0%
+your angle relative to Point into the
+Sun would that make sense you be like
+
+ align:start position:0%
+Sun would that make sense you be like
+ 
+
+ align:start position:0%
+Sun would that make sense you be like
+yes you just like your son is there then
+
+ align:start position:0%
+yes you just like your son is there then
+ 
+
+ align:start position:0%
+yes you just like your son is there then
+like kind of tilt your panel here and an
+
+ align:start position:0%
+like kind of tilt your panel here and an
+ 
+
+ align:start position:0%
+like kind of tilt your panel here and an
+angle towards the Sun like kind of like
+
+ align:start position:0%
+angle towards the Sun like kind of like
+ 
+
+ align:start position:0%
+angle towards the Sun like kind of like
+that that make sense like the Sun is
+
+ align:start position:0%
+that that make sense like the Sun is
+ 
+
+ align:start position:0%
+that that make sense like the Sun is
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+understand accord and I want to really
+
+ align:start position:0%
+understand accord and I want to really
+ 
+
+ align:start position:0%
+understand accord and I want to really
+battery out of the way too because I
+
+ align:start position:0%
+battery out of the way too because I
+ 
+
+ align:start position:0%
+battery out of the way too because I
+think it might officiating so we're
+
+ align:start position:0%
+think it might officiating so we're
+ 
+
+ align:start position:0%
+think it might officiating so we're
+gonna use it kind of our thang sounds
+
+ align:start position:0%
+gonna use it kind of our thang sounds
+ 
+
+ align:start position:0%
+gonna use it kind of our thang sounds
+really yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you move it
+
+ align:start position:0%
+can you move it
+ 
+
+ align:start position:0%
+can you move it
+the manger scenes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so now we flip it 90 degrees
+
+ align:start position:0%
+okay and so now we flip it 90 degrees
+ 
+
+ align:start position:0%
+okay and so now we flip it 90 degrees
+and then do the exact same thing a
+
+ align:start position:0%
+and then do the exact same thing a
+ 
+
+ align:start position:0%
+and then do the exact same thing a
+figure on political metric say it's 95
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this lab is just for fun so I gave
+
+ align:start position:0%
+this lab is just for fun so I gave
+ 
+
+ align:start position:0%
+this lab is just for fun so I gave
+people the option of either making
+
+ align:start position:0%
+people the option of either making
+ 
+
+ align:start position:0%
+people the option of either making
+something cool if you're feeling
+
+ align:start position:0%
+something cool if you're feeling
+ 
+
+ align:start position:0%
+something cool if you're feeling
+creative or just doing each operation
+
+ align:start position:0%
+creative or just doing each operation
+ 
+
+ align:start position:0%
+creative or just doing each operation
+with no intent other than learning the
+
+ align:start position:0%
+with no intent other than learning the
+ 
+
+ align:start position:0%
+with no intent other than learning the
+operation if you're not feeling creative
+
+ align:start position:0%
+operation if you're not feeling creative
+ 
+
+ align:start position:0%
+operation if you're not feeling creative
+it's up to you so some people made
+
+ align:start position:0%
+it's up to you so some people made
+ 
+
+ align:start position:0%
+it's up to you so some people made
+really cool stuff and some people just
+
+ align:start position:0%
+really cool stuff and some people just
+ 
+
+ align:start position:0%
+really cool stuff and some people just
+have fun and anything is fine thing so
+
+ align:start position:0%
+have fun and anything is fine thing so
+ 
+
+ align:start position:0%
+have fun and anything is fine thing so
+we're going to go through a bunch of
+
+ align:start position:0%
+we're going to go through a bunch of
+ 
+
+ align:start position:0%
+we're going to go through a bunch of
+things so one is drilling holes and
+
+ align:start position:0%
+things so one is drilling holes and
+ 
+
+ align:start position:0%
+things so one is drilling holes and
+sheet metal and you also want to cut pc
+
+ align:start position:0%
+sheet metal and you also want to cut pc
+ 
+
+ align:start position:0%
+sheet metal and you also want to cut pc
+pipe and if you you could cut this on
+
+ align:start position:0%
+pipe and if you you could cut this on
+ 
+
+ align:start position:0%
+pipe and if you you could cut this on
+the bandsaw but it's probably going to
+
+ align:start position:0%
+the bandsaw but it's probably going to
+ 
+
+ align:start position:0%
+the bandsaw but it's probably going to
+be a little and even and this is
+
+ align:start position:0%
+be a little and even and this is
+ 
+
+ align:start position:0%
+be a little and even and this is
+actually faster and really successful so
+
+ align:start position:0%
+actually faster and really successful so
+ 
+
+ align:start position:0%
+actually faster and really successful so
+what you do with this PVC cutter is you
+
+ align:start position:0%
+what you do with this PVC cutter is you
+ 
+
+ align:start position:0%
+what you do with this PVC cutter is you
+just open it all the way up and then
+
+ align:start position:0%
+just open it all the way up and then
+ 
+
+ align:start position:0%
+just open it all the way up and then
+just tonight you really quickly cut a
+
+ align:start position:0%
+just tonight you really quickly cut a
+ 
+
+ align:start position:0%
+just tonight you really quickly cut a
+ring very handy you couldn't use that
+
+ align:start position:0%
+ring very handy you couldn't use that
+ 
+
+ align:start position:0%
+ring very handy you couldn't use that
+tool on metal unfortunately so we have
+
+ align:start position:0%
+tool on metal unfortunately so we have
+ 
+
+ align:start position:0%
+tool on metal unfortunately so we have
+this tool for cutting pipe this is the
+
+ align:start position:0%
+this tool for cutting pipe this is the
+ 
+
+ align:start position:0%
+this tool for cutting pipe this is the
+sharp bit and these are just bearings
+
+ align:start position:0%
+sharp bit and these are just bearings
+ 
+
+ align:start position:0%
+sharp bit and these are just bearings
+that allow the pipe to spin around and
+
+ align:start position:0%
+that allow the pipe to spin around and
+ 
+
+ align:start position:0%
+that allow the pipe to spin around and
+around so what you do is you open it up
+
+ align:start position:0%
+around so what you do is you open it up
+ 
+
+ align:start position:0%
+around so what you do is you open it up
+you load the copper in you tighten it
+
+ align:start position:0%
+you load the copper in you tighten it
+ 
+
+ align:start position:0%
+you load the copper in you tighten it
+and then you spin it around a few times
+
+ align:start position:0%
+and then you spin it around a few times
+ 
+
+ align:start position:0%
+and then you spin it around a few times
+tight Nets band tight and spend the more
+
+ align:start position:0%
+tight Nets band tight and spend the more
+ 
+
+ align:start position:0%
+tight Nets band tight and spend the more
+times you tighten and spin then the
+
+ align:start position:0%
+times you tighten and spin then the
+ 
+
+ align:start position:0%
+times you tighten and spin then the
+cleaner edge you'll get if you really
+
+ align:start position:0%
+cleaner edge you'll get if you really
+ 
+
+ align:start position:0%
+cleaner edge you'll get if you really
+just use a lot of course of course it'll
+
+ align:start position:0%
+just use a lot of course of course it'll
+ 
+
+ align:start position:0%
+just use a lot of course of course it'll
+work but it'll be ugly so this is copper
+
+ align:start position:0%
+work but it'll be ugly so this is copper
+ 
+
+ align:start position:0%
+work but it'll be ugly so this is copper
+which is expensive and we don't have
+
+ align:start position:0%
+which is expensive and we don't have
+ 
+
+ align:start position:0%
+which is expensive and we don't have
+that much so this is the one area where
+
+ align:start position:0%
+that much so this is the one area where
+ 
+
+ align:start position:0%
+that much so this is the one area where
+you need to just cut a little ring don't
+
+ align:start position:0%
+you need to just cut a little ring don't
+ 
+
+ align:start position:0%
+you need to just cut a little ring don't
+cut after yourself we also are going to
+
+ align:start position:0%
+cut after yourself we also are going to
+ 
+
+ align:start position:0%
+cut after yourself we also are going to
+cut rebar so the hacksaw is ready here
+
+ align:start position:0%
+cut rebar so the hacksaw is ready here
+ 
+
+ align:start position:0%
+cut rebar so the hacksaw is ready here
+for cutting leave our well you could
+
+ align:start position:0%
+for cutting leave our well you could
+ 
+
+ align:start position:0%
+for cutting leave our well you could
+just hold the rebar in one hand and use
+
+ align:start position:0%
+just hold the rebar in one hand and use
+ 
+
+ align:start position:0%
+just hold the rebar in one hand and use
+the hex on the other it's going to be
+
+ align:start position:0%
+the hex on the other it's going to be
+ 
+
+ align:start position:0%
+the hex on the other it's going to be
+really miserable and your possible to do
+
+ align:start position:0%
+really miserable and your possible to do
+ 
+
+ align:start position:0%
+really miserable and your possible to do
+successfully so we have advice so you
+
+ align:start position:0%
+successfully so we have advice so you
+ 
+
+ align:start position:0%
+successfully so we have advice so you
+can load the rebar in and then cut so
+
+ align:start position:0%
+can load the rebar in and then cut so
+ 
+
+ align:start position:0%
+can load the rebar in and then cut so
+you too long maybe there's a bigger
+
+ align:start position:0%
+you too long maybe there's a bigger
+ 
+
+ align:start position:0%
+you too long maybe there's a bigger
+fight
+
+ align:start position:0%
+fight
+ 
+
+ align:start position:0%
+fight
+Oh
\ No newline at end of file
diff --git a/zdotUAxiPGM.txt b/zdotUAxiPGM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..78f4694e6a3264afb62def3d000af9ebe5bfcbd6
--- /dev/null
+++ b/zdotUAxiPGM.txt
@@ -0,0 +1,9259 @@
+align:start position:0%
+ 
+a three-part lecture today still
+
+ align:start position:0%
+a three-part lecture today still
+ 
+
+ align:start position:0%
+a three-part lecture today still
+continuing on the theme of reinforcement
+
+ align:start position:0%
+continuing on the theme of reinforcement
+ 
+
+ align:start position:0%
+continuing on the theme of reinforcement
+learning part one I'm going to be
+
+ align:start position:0%
+learning part one I'm going to be
+ 
+
+ align:start position:0%
+learning part one I'm going to be
+speaking and I will be following up on
+
+ align:start position:0%
+speaking and I will be following up on
+ 
+
+ align:start position:0%
+speaking and I will be following up on
+last week's discussion about causal
+
+ align:start position:0%
+last week's discussion about causal
+ 
+
+ align:start position:0%
+last week's discussion about causal
+inference and Tuesday's discussion on
+
+ align:start position:0%
+inference and Tuesday's discussion on
+ 
+
+ align:start position:0%
+inference and Tuesday's discussion on
+reinforcement learning and I'll be going
+
+ align:start position:0%
+reinforcement learning and I'll be going
+ 
+
+ align:start position:0%
+reinforcement learning and I'll be going
+into sort of one one more subtlety that
+
+ align:start position:0%
+into sort of one one more subtlety that
+ 
+
+ align:start position:0%
+into sort of one one more subtlety that
+that arises there and where we can
+
+ align:start position:0%
+that arises there and where we can
+ 
+
+ align:start position:0%
+that arises there and where we can
+develop some nice mathematical methods
+
+ align:start position:0%
+develop some nice mathematical methods
+ 
+
+ align:start position:0%
+develop some nice mathematical methods
+to help with and then I'm going to turn
+
+ align:start position:0%
+to help with and then I'm going to turn
+ 
+
+ align:start position:0%
+to help with and then I'm going to turn
+over the show to to Barbara who will
+
+ align:start position:0%
+over the show to to Barbara who will
+ 
+
+ align:start position:0%
+over the show to to Barbara who will
+formally introduce when the time comes
+
+ align:start position:0%
+formally introduce when the time comes
+ 
+
+ align:start position:0%
+formally introduce when the time comes
+and she's going to both talk about some
+
+ align:start position:0%
+and she's going to both talk about some
+ 
+
+ align:start position:0%
+and she's going to both talk about some
+of her work on developing on evaluating
+
+ align:start position:0%
+of her work on developing on evaluating
+ 
+
+ align:start position:0%
+of her work on developing on evaluating
+dynamics treatment regimes and
+
+ align:start position:0%
+dynamics treatment regimes and
+ 
+
+ align:start position:0%
+dynamics treatment regimes and
+eventually lead a discussion on the
+
+ align:start position:0%
+eventually lead a discussion on the
+ 
+
+ align:start position:0%
+eventually lead a discussion on the
+sepsis paper which was required reading
+
+ align:start position:0%
+sepsis paper which was required reading
+ 
+
+ align:start position:0%
+sepsis paper which was required reading
+from today's class so those are the
+
+ align:start position:0%
+from today's class so those are the
+ 
+
+ align:start position:0%
+from today's class so those are the
+three parts today's today's lecture so I
+
+ align:start position:0%
+three parts today's today's lecture so I
+ 
+
+ align:start position:0%
+three parts today's today's lecture so I
+want you to return back put your back in
+
+ align:start position:0%
+want you to return back put your back in
+ 
+
+ align:start position:0%
+want you to return back put your back in
+your self back in the mindset of
+
+ align:start position:0%
+your self back in the mindset of
+ 
+
+ align:start position:0%
+your self back in the mindset of
+Tuesday's lecture where we talk about
+
+ align:start position:0%
+Tuesday's lecture where we talk about
+ 
+
+ align:start position:0%
+Tuesday's lecture where we talk about
+reinforcement learning I remember that
+
+ align:start position:0%
+reinforcement learning I remember that
+ 
+
+ align:start position:0%
+reinforcement learning I remember that
+the goal of reinforcement learning was
+
+ align:start position:0%
+the goal of reinforcement learning was
+ 
+
+ align:start position:0%
+the goal of reinforcement learning was
+to optimize some reward specifically our
+
+ align:start position:0%
+to optimize some reward specifically our
+ 
+
+ align:start position:0%
+to optimize some reward specifically our
+goal was to find some policy which I'm
+
+ align:start position:0%
+goal was to find some policy which I'm
+ 
+
+ align:start position:0%
+goal was to find some policy which I'm
+going to go to spy star which is the Arg
+
+ align:start position:0%
+going to go to spy star which is the Arg
+ 
+
+ align:start position:0%
+going to go to spy star which is the Arg
+max over all possible policies PI of V
+
+ align:start position:0%
+max over all possible policies PI of V
+ 
+
+ align:start position:0%
+max over all possible policies PI of V
+of Pi where just remind you V if pi is
+
+ align:start position:0%
+of Pi where just remind you V if pi is
+ 
+
+ align:start position:0%
+of Pi where just remind you V if pi is
+the value of the policy PI formally it's
+
+ align:start position:0%
+the value of the policy PI formally it's
+ 
+
+ align:start position:0%
+the value of the policy PI formally it's
+defined as the expectation of the sum of
+
+ align:start position:0%
+defined as the expectation of the sum of
+ 
+
+ align:start position:0%
+defined as the expectation of the sum of
+the rewards across time okay so the
+
+ align:start position:0%
+the rewards across time okay so the
+ 
+
+ align:start position:0%
+the rewards across time okay so the
+reason why I'm calling this an
+
+ align:start position:0%
+reason why I'm calling this an
+ 
+
+ align:start position:0%
+reason why I'm calling this an
+expectation is like the PI is because
+
+ align:start position:0%
+expectation is like the PI is because
+ 
+
+ align:start position:0%
+expectation is like the PI is because
+there's stochasticity both in the
+
+ align:start position:0%
+there's stochasticity both in the
+ 
+
+ align:start position:0%
+there's stochasticity both in the
+environment and possibly pi e is going
+
+ align:start position:0%
+environment and possibly pi e is going
+ 
+
+ align:start position:0%
+environment and possibly pi e is going
+to be a stochastic policy and this is
+
+ align:start position:0%
+to be a stochastic policy and this is
+ 
+
+ align:start position:0%
+to be a stochastic policy and this is
+summing over the time steps because this
+
+ align:start position:0%
+summing over the time steps because this
+ 
+
+ align:start position:0%
+summing over the time steps because this
+is a this is not just a single time step
+
+ align:start position:0%
+is a this is not just a single time step
+ 
+
+ align:start position:0%
+is a this is not just a single time step
+problem but we're going to be
+
+ align:start position:0%
+problem but we're going to be
+ 
+
+ align:start position:0%
+problem but we're going to be
+considering interventions across time of
+
+ align:start position:0%
+considering interventions across time of
+ 
+
+ align:start position:0%
+considering interventions across time of
+the reward at each point in time and the
+
+ align:start position:0%
+the reward at each point in time and the
+ 
+
+ align:start position:0%
+the reward at each point in time and the
+reward function could either be at each
+
+ align:start position:0%
+reward function could either be at each
+ 
+
+ align:start position:0%
+reward function could either be at each
+point in time or you might imagine that
+
+ align:start position:0%
+point in time or you might imagine that
+ 
+
+ align:start position:0%
+point in time or you might imagine that
+this is zero for all time steps except
+
+ align:start position:0%
+this is zero for all time steps except
+ 
+
+ align:start position:0%
+this is zero for all time steps except
+the last time step so the first question
+
+ align:start position:0%
+the last time step so the first question
+ 
+
+ align:start position:0%
+the last time step so the first question
+I want to think about is well what are
+
+ align:start position:0%
+I want to think about is well what are
+ 
+
+ align:start position:0%
+I want to think about is well what are
+the implications of this as a learning
+
+ align:start position:0%
+the implications of this as a learning
+ 
+
+ align:start position:0%
+the implications of this as a learning
+paradigm if we look what's going on over
+
+ align:start position:0%
+paradigm if we look what's going on over
+ 
+
+ align:start position:0%
+paradigm if we look what's going on over
+here hidden in my story is also an
+
+ align:start position:0%
+here hidden in my story is also an
+ 
+
+ align:start position:0%
+here hidden in my story is also an
+expectation over acts the in the patient
+
+ align:start position:0%
+expectation over acts the in the patient
+ 
+
+ align:start position:0%
+expectation over acts the in the patient
+for example or the initial state and so
+
+ align:start position:0%
+for example or the initial state and so
+ 
+
+ align:start position:0%
+for example or the initial state and so
+this intuitively is saying let's try to
+
+ align:start position:0%
+this intuitively is saying let's try to
+ 
+
+ align:start position:0%
+this intuitively is saying let's try to
+find a policy that has high expected
+
+ align:start position:0%
+find a policy that has high expected
+ 
+
+ align:start position:0%
+find a policy that has high expected
+reward average nessing's over all
+
+ align:start position:0%
+reward average nessing's over all
+ 
+
+ align:start position:0%
+reward average nessing's over all
+patients and I just want to you think
+
+ align:start position:0%
+patients and I just want to you think
+ 
+
+ align:start position:0%
+patients and I just want to you think
+about whether that isn't indeed the
+
+ align:start position:0%
+about whether that isn't indeed the
+ 
+
+ align:start position:0%
+about whether that isn't indeed the
+right goal okay can anyone think about a
+
+ align:start position:0%
+right goal okay can anyone think about a
+ 
+
+ align:start position:0%
+right goal okay can anyone think about a
+setting where that might not be
+
+ align:start position:0%
+setting where that might not be
+ 
+
+ align:start position:0%
+setting where that might not be
+desirable yep
+
+ align:start position:0%
+desirable yep
+ 
+
+ align:start position:0%
+desirable yep
+what if the reward is the patient living
+
+ align:start position:0%
+what if the reward is the patient living
+ 
+
+ align:start position:0%
+what if the reward is the patient living
+or dying you don't want it doing have
+
+ align:start position:0%
+or dying you don't want it doing have
+ 
+
+ align:start position:0%
+or dying you don't want it doing have
+high ratings like saving to patients and
+
+ align:start position:0%
+high ratings like saving to patients and
+ 
+
+ align:start position:0%
+high ratings like saving to patients and
+see what they expected since panics all
+
+ align:start position:0%
+see what they expected since panics all
+ 
+
+ align:start position:0%
+see what they expected since panics all
+right so what happens this word is
+
+ align:start position:0%
+right so what happens this word is
+ 
+
+ align:start position:0%
+right so what happens this word is
+something mission critical like patient
+
+ align:start position:0%
+something mission critical like patient
+ 
+
+ align:start position:0%
+something mission critical like patient
+patient dying you really want to try to
+
+ align:start position:0%
+patient dying you really want to try to
+ 
+
+ align:start position:0%
+patient dying you really want to try to
+avoid that from happening as much as
+
+ align:start position:0%
+avoid that from happening as much as
+ 
+
+ align:start position:0%
+avoid that from happening as much as
+possible of course there are other
+
+ align:start position:0%
+possible of course there are other
+ 
+
+ align:start position:0%
+possible of course there are other
+criteria that we might be interested in
+
+ align:start position:0%
+criteria that we might be interested in
+ 
+
+ align:start position:0%
+criteria that we might be interested in
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+and both in Fredericks lecture on
+
+ align:start position:0%
+and both in Fredericks lecture on
+ 
+
+ align:start position:0%
+and both in Fredericks lecture on
+Tuesday and in the readings we talked
+
+ align:start position:0%
+Tuesday and in the readings we talked
+ 
+
+ align:start position:0%
+Tuesday and in the readings we talked
+about how there might be other aspects
+
+ align:start position:0%
+about how there might be other aspects
+ 
+
+ align:start position:0%
+about how there might be other aspects
+about making sure that a patient is just
+
+ align:start position:0%
+about making sure that a patient is just
+ 
+
+ align:start position:0%
+about making sure that a patient is just
+not just alive but also healthy which
+
+ align:start position:0%
+not just alive but also healthy which
+ 
+
+ align:start position:0%
+not just alive but also healthy which
+might play into reward function so there
+
+ align:start position:0%
+might play into reward function so there
+ 
+
+ align:start position:0%
+might play into reward function so there
+might be rewards to rate those and if
+
+ align:start position:0%
+might be rewards to rate those and if
+ 
+
+ align:start position:0%
+might be rewards to rate those and if
+you were to just for example put a
+
+ align:start position:0%
+you were to just for example put a
+ 
+
+ align:start position:0%
+you were to just for example put a
+positive or negative infinity for
+
+ align:start position:0%
+positive or negative infinity for
+ 
+
+ align:start position:0%
+positive or negative infinity for
+patient dying that's a non-starter right
+
+ align:start position:0%
+patient dying that's a non-starter right
+ 
+
+ align:start position:0%
+patient dying that's a non-starter right
+because if you did that unfortunately in
+
+ align:start position:0%
+because if you did that unfortunately in
+ 
+
+ align:start position:0%
+because if you did that unfortunately in
+this situation in this world we're not
+
+ align:start position:0%
+this situation in this world we're not
+ 
+
+ align:start position:0%
+this situation in this world we're not
+always going to be able to keep patients
+
+ align:start position:0%
+always going to be able to keep patients
+ 
+
+ align:start position:0%
+always going to be able to keep patients
+alive and so you're going to get into an
+
+ align:start position:0%
+alive and so you're going to get into an
+ 
+
+ align:start position:0%
+alive and so you're going to get into an
+infeasible optimization problem so minus
+
+ align:start position:0%
+infeasible optimization problem so minus
+ 
+
+ align:start position:0%
+infeasible optimization problem so minus
+infinity is not an option we're going to
+
+ align:start position:0%
+infinity is not an option we're going to
+ 
+
+ align:start position:0%
+infinity is not an option we're going to
+have to put some number to it in this
+
+ align:start position:0%
+have to put some number to it in this
+ 
+
+ align:start position:0%
+have to put some number to it in this
+type of approach but then you're going
+
+ align:start position:0%
+type of approach but then you're going
+ 
+
+ align:start position:0%
+type of approach but then you're going
+to start trading off between patients
+
+ align:start position:0%
+to start trading off between patients
+ 
+
+ align:start position:0%
+to start trading off between patients
+you know in some cases you might you
+
+ align:start position:0%
+you know in some cases you might you
+ 
+
+ align:start position:0%
+you know in some cases you might you
+might have a very high reward for you
+
+ align:start position:0%
+might have a very high reward for you
+ 
+
+ align:start position:0%
+might have a very high reward for you
+might you there are two different
+
+ align:start position:0%
+might you there are two different
+ 
+
+ align:start position:0%
+might you there are two different
+equations that you can might imagine one
+
+ align:start position:0%
+equations that you can might imagine one
+ 
+
+ align:start position:0%
+equations that you can might imagine one
+solution where the reward is somewhat
+
+ align:start position:0%
+solution where the reward is somewhat
+ 
+
+ align:start position:0%
+solution where the reward is somewhat
+balanced across patients and another
+
+ align:start position:0%
+balanced across patients and another
+ 
+
+ align:start position:0%
+balanced across patients and another
+situation where you have really small
+
+ align:start position:0%
+situation where you have really small
+ 
+
+ align:start position:0%
+situation where you have really small
+values of
+
+ align:start position:0%
+values of
+ 
+
+ align:start position:0%
+values of
+for some patience and a few patients
+
+ align:start position:0%
+for some patience and a few patients
+ 
+
+ align:start position:0%
+for some patience and a few patients
+with very large values and rewards and
+
+ align:start position:0%
+with very large values and rewards and
+ 
+
+ align:start position:0%
+with very large values and rewards and
+both would give you the same average
+
+ align:start position:0%
+both would give you the same average
+ 
+
+ align:start position:0%
+both would give you the same average
+obviously but not both but both are not
+
+ align:start position:0%
+obviously but not both but both are not
+ 
+
+ align:start position:0%
+obviously but not both but both are not
+necessarily equally useful right we
+
+ align:start position:0%
+necessarily equally useful right we
+ 
+
+ align:start position:0%
+necessarily equally useful right we
+might want to say that we prefer to
+
+ align:start position:0%
+might want to say that we prefer to
+ 
+
+ align:start position:0%
+might want to say that we prefer to
+avoid that worst case situation so one
+
+ align:start position:0%
+avoid that worst case situation so one
+ 
+
+ align:start position:0%
+avoid that worst case situation so one
+could imagine other ways of formulating
+
+ align:start position:0%
+could imagine other ways of formulating
+ 
+
+ align:start position:0%
+could imagine other ways of formulating
+this optimization problem like maybe you
+
+ align:start position:0%
+this optimization problem like maybe you
+ 
+
+ align:start position:0%
+this optimization problem like maybe you
+want to maybe you want to control the
+
+ align:start position:0%
+want to maybe you want to control the
+ 
+
+ align:start position:0%
+want to maybe you want to control the
+worst case reward instead of the average
+
+ align:start position:0%
+worst case reward instead of the average
+ 
+
+ align:start position:0%
+worst case reward instead of the average
+case reward or maybe you want to say
+
+ align:start position:0%
+case reward or maybe you want to say
+ 
+
+ align:start position:0%
+case reward or maybe you want to say
+something about different quartiles I
+
+ align:start position:0%
+something about different quartiles I
+ 
+
+ align:start position:0%
+something about different quartiles I
+just wanted to point that out because
+
+ align:start position:0%
+just wanted to point that out because
+ 
+
+ align:start position:0%
+just wanted to point that out because
+really that's the starting place for a
+
+ align:start position:0%
+really that's the starting place for a
+ 
+
+ align:start position:0%
+really that's the starting place for a
+lot of the work that we're doing here so
+
+ align:start position:0%
+lot of the work that we're doing here so
+ 
+
+ align:start position:0%
+lot of the work that we're doing here so
+now that wants to think they're okay
+
+ align:start position:0%
+now that wants to think they're okay
+ 
+
+ align:start position:0%
+now that wants to think they're okay
+returning back to this goal we've done
+
+ align:start position:0%
+returning back to this goal we've done
+ 
+
+ align:start position:0%
+returning back to this goal we've done
+our policy iteration and/or we've done
+
+ align:start position:0%
+our policy iteration and/or we've done
+ 
+
+ align:start position:0%
+our policy iteration and/or we've done
+our cue learning that is and we get a
+
+ align:start position:0%
+our cue learning that is and we get a
+ 
+
+ align:start position:0%
+our cue learning that is and we get a
+policy out and when might now want to
+
+ align:start position:0%
+policy out and when might now want to
+ 
+
+ align:start position:0%
+policy out and when might now want to
+know well what is the value of that
+
+ align:start position:0%
+know well what is the value of that
+ 
+
+ align:start position:0%
+know well what is the value of that
+policy right so what is our estimate of
+
+ align:start position:0%
+policy right so what is our estimate of
+ 
+
+ align:start position:0%
+policy right so what is our estimate of
+that quantity well to get that one could
+
+ align:start position:0%
+that quantity well to get that one could
+ 
+
+ align:start position:0%
+that quantity well to get that one could
+just try to read it off from the results
+
+ align:start position:0%
+just try to read it off from the results
+ 
+
+ align:start position:0%
+just try to read it off from the results
+of Q learning
+
+ align:start position:0%
+of Q learning
+ 
+
+ align:start position:0%
+of Q learning
+by just computing that V PI well V PI
+
+ align:start position:0%
+by just computing that V PI well V PI
+ 
+
+ align:start position:0%
+by just computing that V PI well V PI
+hat the estimate is just equal to now a
+
+ align:start position:0%
+hat the estimate is just equal to now a
+ 
+
+ align:start position:0%
+hat the estimate is just equal to now a
+maximum over actions a of your Q
+
+ align:start position:0%
+maximum over actions a of your Q
+ 
+
+ align:start position:0%
+maximum over actions a of your Q
+function evaluated at whatever your
+
+ align:start position:0%
+function evaluated at whatever your
+ 
+
+ align:start position:0%
+function evaluated at whatever your
+initial state is and your and the
+
+ align:start position:0%
+initial state is and your and the
+ 
+
+ align:start position:0%
+initial state is and your and the
+optimal choice of action a all right so
+
+ align:start position:0%
+optimal choice of action a all right so
+ 
+
+ align:start position:0%
+optimal choice of action a all right so
+this is all I'm saying here is that the
+
+ align:start position:0%
+this is all I'm saying here is that the
+ 
+
+ align:start position:0%
+this is all I'm saying here is that the
+last step of that will be that might be
+
+ align:start position:0%
+last step of that will be that might be
+ 
+
+ align:start position:0%
+last step of that will be that might be
+to ask well what is the expected reward
+
+ align:start position:0%
+to ask well what is the expected reward
+ 
+
+ align:start position:0%
+to ask well what is the expected reward
+of this policy and if remember the Q
+
+ align:start position:0%
+of this policy and if remember the Q
+ 
+
+ align:start position:0%
+of this policy and if remember the Q
+learning algorithm is essence that
+
+ align:start position:0%
+learning algorithm is essence that
+ 
+
+ align:start position:0%
+learning algorithm is essence that
+dynamic programming algorithm working
+
+ align:start position:0%
+dynamic programming algorithm working
+ 
+
+ align:start position:0%
+dynamic programming algorithm working
+its way from the you know sort of large
+
+ align:start position:0%
+its way from the you know sort of large
+ 
+
+ align:start position:0%
+its way from the you know sort of large
+values of time up to the up to the
+
+ align:start position:0%
+values of time up to the up to the
+ 
+
+ align:start position:0%
+values of time up to the up to the
+present and it is indeed actually
+
+ align:start position:0%
+present and it is indeed actually
+ 
+
+ align:start position:0%
+present and it is indeed actually
+computing this expected value that
+
+ align:start position:0%
+computing this expected value that
+ 
+
+ align:start position:0%
+computing this expected value that
+you're interested in so you could just
+
+ align:start position:0%
+you're interested in so you could just
+ 
+
+ align:start position:0%
+you're interested in so you could just
+read it off from the Q values at the
+
+ align:start position:0%
+read it off from the Q values at the
+ 
+
+ align:start position:0%
+read it off from the Q values at the
+very end but I want to point out that
+
+ align:start position:0%
+very end but I want to point out that
+ 
+
+ align:start position:0%
+very end but I want to point out that
+here there's an implicit policy built-in
+
+ align:start position:0%
+here there's an implicit policy built-in
+ 
+
+ align:start position:0%
+here there's an implicit policy built-in
+right so I'm gonna compare this in just
+
+ align:start position:0%
+right so I'm gonna compare this in just
+ 
+
+ align:start position:0%
+right so I'm gonna compare this in just
+a second to what happens under the
+
+ align:start position:0%
+a second to what happens under the
+ 
+
+ align:start position:0%
+a second to what happens under the
+causal inference scenarios or just a
+
+ align:start position:0%
+causal inference scenarios or just a
+ 
+
+ align:start position:0%
+causal inference scenarios or just a
+single time step and potential outcomes
+
+ align:start position:0%
+single time step and potential outcomes
+ 
+
+ align:start position:0%
+single time step and potential outcomes
+framework that were used to notice that
+
+ align:start position:0%
+framework that were used to notice that
+ 
+
+ align:start position:0%
+framework that were used to notice that
+the value of this policy it's the reason
+
+ align:start position:0%
+the value of this policy it's the reason
+ 
+
+ align:start position:0%
+the value of this policy it's the reason
+why it's a function of of Pi is because
+
+ align:start position:0%
+why it's a function of of Pi is because
+ 
+
+ align:start position:0%
+why it's a function of of Pi is because
+the values of
+
+ align:start position:0%
+the values of
+ 
+
+ align:start position:0%
+the values of
+is a function of every subsequent action
+
+ align:start position:0%
+is a function of every subsequent action
+ 
+
+ align:start position:0%
+is a function of every subsequent action
+that you're taking as well and so now
+
+ align:start position:0%
+that you're taking as well and so now
+ 
+
+ align:start position:0%
+that you're taking as well and so now
+let's just compare that for a second to
+
+ align:start position:0%
+let's just compare that for a second to
+ 
+
+ align:start position:0%
+let's just compare that for a second to
+what happens within the potential
+
+ align:start position:0%
+what happens within the potential
+ 
+
+ align:start position:0%
+what happens within the potential
+outcomes framework so there are starting
+
+ align:start position:0%
+outcomes framework so there are starting
+ 
+
+ align:start position:0%
+outcomes framework so there are starting
+place so now I'm going to I'm going to
+
+ align:start position:0%
+place so now I'm going to I'm going to
+ 
+
+ align:start position:0%
+place so now I'm going to I'm going to
+turn our attention for one just one
+
+ align:start position:0%
+turn our attention for one just one
+ 
+
+ align:start position:0%
+turn our attention for one just one
+moment from reinforcement learning now
+
+ align:start position:0%
+moment from reinforcement learning now
+ 
+
+ align:start position:0%
+moment from reinforcement learning now
+back to just causal inference and
+
+ align:start position:0%
+back to just causal inference and
+ 
+
+ align:start position:0%
+back to just causal inference and
+reinforcement learning we talked about
+
+ align:start position:0%
+reinforcement learning we talked about
+ 
+
+ align:start position:0%
+reinforcement learning we talked about
+policies how do we find policies to do
+
+ align:start position:0%
+policies how do we find policies to do
+ 
+
+ align:start position:0%
+policies how do we find policies to do
+well in terms of some expected reward of
+
+ align:start position:0%
+well in terms of some expected reward of
+ 
+
+ align:start position:0%
+well in terms of some expected reward of
+this policy but yet when we were talking
+
+ align:start position:0%
+this policy but yet when we were talking
+ 
+
+ align:start position:0%
+this policy but yet when we were talking
+about causal inference we only used
+
+ align:start position:0%
+about causal inference we only used
+ 
+
+ align:start position:0%
+about causal inference we only used
+words like average treatment effect or
+
+ align:start position:0%
+words like average treatment effect or
+ 
+
+ align:start position:0%
+words like average treatment effect or
+conditional average treatment effect
+
+ align:start position:0%
+conditional average treatment effect
+ 
+
+ align:start position:0%
+conditional average treatment effect
+where for example to estimate the
+
+ align:start position:0%
+where for example to estimate the
+ 
+
+ align:start position:0%
+where for example to estimate the
+conditional average treatment effect
+
+ align:start position:0%
+conditional average treatment effect
+ 
+
+ align:start position:0%
+conditional average treatment effect
+what we said is we're going to first
+
+ align:start position:0%
+what we said is we're going to first
+ 
+
+ align:start position:0%
+what we said is we're going to first
+learn if we use if you we use a
+
+ align:start position:0%
+learn if we use if you we use a
+ 
+
+ align:start position:0%
+learn if we use if you we use a
+covariate judgment approach we learn
+
+ align:start position:0%
+covariate judgment approach we learn
+ 
+
+ align:start position:0%
+covariate judgment approach we learn
+some function f of X comma T which is
+
+ align:start position:0%
+some function f of X comma T which is
+ 
+
+ align:start position:0%
+some function f of X comma T which is
+intended to be an approximation of the
+
+ align:start position:0%
+intended to be an approximation of the
+ 
+
+ align:start position:0%
+intended to be an approximation of the
+expected value of your outcome Y given X
+
+ align:start position:0%
+expected value of your outcome Y given X
+ 
+
+ align:start position:0%
+expected value of your outcome Y given X
+comma comma o say I'll say Y of T there
+
+ align:start position:0%
+comma comma o say I'll say Y of T there
+ 
+
+ align:start position:0%
+comma comma o say I'll say Y of T there
+so that notation so the goal of Kaveri
+
+ align:start position:0%
+so that notation so the goal of Kaveri
+ 
+
+ align:start position:0%
+so that notation so the goal of Kaveri
+adjustment was to estimate this quantity
+
+ align:start position:0%
+adjustment was to estimate this quantity
+ 
+
+ align:start position:0%
+adjustment was to estimate this quantity
+and we could use that then to try to
+
+ align:start position:0%
+and we could use that then to try to
+ 
+
+ align:start position:0%
+and we could use that then to try to
+construct a policy for example you could
+
+ align:start position:0%
+construct a policy for example you could
+ 
+
+ align:start position:0%
+construct a policy for example you could
+continue could think about the policy PI
+
+ align:start position:0%
+continue could think about the policy PI
+ 
+
+ align:start position:0%
+continue could think about the policy PI
+of X which simply looks to see is it
+
+ align:start position:0%
+of X which simply looks to see is it
+ 
+
+ align:start position:0%
+of X which simply looks to see is it
+will say it's 1 if Kate or your estimate
+
+ align:start position:0%
+will say it's 1 if Kate or your estimate
+ 
+
+ align:start position:0%
+will say it's 1 if Kate or your estimate
+of Kate for X is positive and 0
+
+ align:start position:0%
+of Kate for X is positive and 0
+ 
+
+ align:start position:0%
+of Kate for X is positive and 0
+otherwise just remind you the way that
+
+ align:start position:0%
+otherwise just remind you the way that
+ 
+
+ align:start position:0%
+otherwise just remind you the way that
+we got the estimate of Kate for an
+
+ align:start position:0%
+we got the estimate of Kate for an
+ 
+
+ align:start position:0%
+we got the estimate of Kate for an
+individual acts was just by looking at f
+
+ align:start position:0%
+individual acts was just by looking at f
+ 
+
+ align:start position:0%
+individual acts was just by looking at f
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+X comma 1 minus f of X comma 0 ok so if
+
+ align:start position:0%
+X comma 1 minus f of X comma 0 ok so if
+ 
+
+ align:start position:0%
+X comma 1 minus f of X comma 0 ok so if
+we have a policy so now we're gonna
+
+ align:start position:0%
+we have a policy so now we're gonna
+ 
+
+ align:start position:0%
+we have a policy so now we're gonna
+start thinking about policies in the
+
+ align:start position:0%
+start thinking about policies in the
+ 
+
+ align:start position:0%
+start thinking about policies in the
+context of causal inference just like we
+
+ align:start position:0%
+context of causal inference just like we
+ 
+
+ align:start position:0%
+context of causal inference just like we
+were doing in reinforcement learning and
+
+ align:start position:0%
+were doing in reinforcement learning and
+ 
+
+ align:start position:0%
+were doing in reinforcement learning and
+I want us to think through what would
+
+ align:start position:0%
+I want us to think through what would
+ 
+
+ align:start position:0%
+I want us to think through what would
+the analogous value of the policy be
+
+ align:start position:0%
+the analogous value of the policy be
+ 
+
+ align:start position:0%
+the analogous value of the policy be
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+how good is is that policy it could be
+
+ align:start position:0%
+how good is is that policy it could be
+ 
+
+ align:start position:0%
+how good is is that policy it could be
+another policy but right now I'm
+
+ align:start position:0%
+another policy but right now I'm
+ 
+
+ align:start position:0%
+another policy but right now I'm
+assuming I'm just going to focus on this
+
+ align:start position:0%
+assuming I'm just going to focus on this
+ 
+
+ align:start position:0%
+assuming I'm just going to focus on this
+policy that show up here well one
+
+ align:start position:0%
+policy that show up here well one
+ 
+
+ align:start position:0%
+policy that show up here well one
+approach to try to evaluate how good
+
+ align:start position:0%
+approach to try to evaluate how good
+ 
+
+ align:start position:0%
+approach to try to evaluate how good
+that policy would is is exactly
+
+ align:start position:0%
+that policy would is is exactly
+ 
+
+ align:start position:0%
+that policy would is is exactly
+analogous to what we did in
+
+ align:start position:0%
+analogous to what we did in
+ 
+
+ align:start position:0%
+analogous to what we did in
+reinforcement learning in essence what
+
+ align:start position:0%
+reinforcement learning in essence what
+ 
+
+ align:start position:0%
+reinforcement learning in essence what
+we're gonna say is we evaluate the quote
+
+ align:start position:0%
+we're gonna say is we evaluate the quote
+ 
+
+ align:start position:0%
+we're gonna say is we evaluate the quote
+of the policy by summing over your
+
+ align:start position:0%
+of the policy by summing over your
+ 
+
+ align:start position:0%
+of the policy by summing over your
+empirical data of PI of X I so this is
+
+ align:start position:0%
+empirical data of PI of X I so this is
+ 
+
+ align:start position:0%
+empirical data of PI of X I so this is
+going to be 1 if the policy says to give
+
+ align:start position:0%
+going to be 1 if the policy says to give
+ 
+
+ align:start position:0%
+going to be 1 if the policy says to give
+treatment 1 to individual X I that in
+
+ align:start position:0%
+treatment 1 to individual X I that in
+ 
+
+ align:start position:0%
+treatment 1 to individual X I that in
+that case we say that the value is f of
+
+ align:start position:0%
+that case we say that the value is f of
+ 
+
+ align:start position:0%
+that case we say that the value is f of
+X comma 1 or if you gave the second if
+
+ align:start position:0%
+X comma 1 or if you gave the second if
+ 
+
+ align:start position:0%
+X comma 1 or if you gave the second if
+the policy would would give treatment 0
+
+ align:start position:0%
+the policy would would give treatment 0
+ 
+
+ align:start position:0%
+the policy would would give treatment 0
+the value of the policy on that
+
+ align:start position:0%
+the value of the policy on that
+ 
+
+ align:start position:0%
+the value of the policy on that
+individual is 1 minus PI of X times f of
+
+ align:start position:0%
+individual is 1 minus PI of X times f of
+ 
+
+ align:start position:0%
+individual is 1 minus PI of X times f of
+X comma 0 so I'm going to call this an X
+
+ align:start position:0%
+X comma 0 so I'm going to call this an X
+ 
+
+ align:start position:0%
+X comma 0 so I'm going to call this an X
+sort of an empirical estimate of the
+
+ align:start position:0%
+sort of an empirical estimate of the
+ 
+
+ align:start position:0%
+sort of an empirical estimate of the
+what you should think about as the
+
+ align:start position:0%
+what you should think about as the
+ 
+
+ align:start position:0%
+what you should think about as the
+reward for a policy PI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and an a yes to the estimate of a V of
+
+ align:start position:0%
+and an a yes to the estimate of a V of
+ 
+
+ align:start position:0%
+and an a yes to the estimate of a V of
+Pi that you would get from a
+
+ align:start position:0%
+Pi that you would get from a
+ 
+
+ align:start position:0%
+Pi that you would get from a
+reinforcement learning context but now
+
+ align:start position:0%
+reinforcement learning context but now
+ 
+
+ align:start position:0%
+reinforcement learning context but now
+we're talking about policy that
+
+ align:start position:0%
+we're talking about policy that
+ 
+
+ align:start position:0%
+we're talking about policy that
+explicitly so let's try to dig down a
+
+ align:start position:0%
+explicitly so let's try to dig down a
+ 
+
+ align:start position:0%
+explicitly so let's try to dig down a
+little bit deeper and think about what
+
+ align:start position:0%
+little bit deeper and think about what
+ 
+
+ align:start position:0%
+little bit deeper and think about what
+this is actually saying imagine the
+
+ align:start position:0%
+this is actually saying imagine the
+ 
+
+ align:start position:0%
+this is actually saying imagine the
+story where you just have a single
+
+ align:start position:0%
+story where you just have a single
+ 
+
+ align:start position:0%
+story where you just have a single
+covariant X we'll think about access
+
+ align:start position:0%
+covariant X we'll think about access
+ 
+
+ align:start position:0%
+covariant X we'll think about access
+being let's say the patient's age and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fortunately there's just one color here
+
+ align:start position:0%
+fortunately there's just one color here
+ 
+
+ align:start position:0%
+fortunately there's just one color here
+but I'll do my best with that and
+
+ align:start position:0%
+but I'll do my best with that and
+ 
+
+ align:start position:0%
+but I'll do my best with that and
+imagine that the potential outcome Y is
+
+ align:start position:0%
+imagine that the potential outcome Y is
+ 
+
+ align:start position:0%
+imagine that the potential outcome Y is
+zero as a function of the patient's age
+
+ align:start position:0%
+zero as a function of the patient's age
+ 
+
+ align:start position:0%
+zero as a function of the patient's age
+axe looks like this now imagine that the
+
+ align:start position:0%
+axe looks like this now imagine that the
+ 
+
+ align:start position:0%
+axe looks like this now imagine that the
+other potential outcome y1 look like
+
+ align:start position:0%
+other potential outcome y1 look like
+ 
+
+ align:start position:0%
+other potential outcome y1 look like
+that all right so I'll call this the Y
+
+ align:start position:0%
+that all right so I'll call this the Y
+ 
+
+ align:start position:0%
+that all right so I'll call this the Y
+one potential outcome suppose now that
+
+ align:start position:0%
+one potential outcome suppose now that
+ 
+
+ align:start position:0%
+one potential outcome suppose now that
+the policy that we're defining is this
+
+ align:start position:0%
+the policy that we're defining is this
+ 
+
+ align:start position:0%
+the policy that we're defining is this
+so we're going to give treatment 1 if
+
+ align:start position:0%
+so we're going to give treatment 1 if
+ 
+
+ align:start position:0%
+so we're going to give treatment 1 if
+the conditional average treatment effect
+
+ align:start position:0%
+the conditional average treatment effect
+ 
+
+ align:start position:0%
+the conditional average treatment effect
+is positive and 0 otherwise I want
+
+ align:start position:0%
+is positive and 0 otherwise I want
+ 
+
+ align:start position:0%
+is positive and 0 otherwise I want
+everyone to draw what the value of that
+
+ align:start position:0%
+everyone to draw what the value of that
+ 
+
+ align:start position:0%
+everyone to draw what the value of that
+policy is on a piece of paper it's going
+
+ align:start position:0%
+policy is on a piece of paper it's going
+ 
+
+ align:start position:0%
+policy is on a piece of paper it's going
+to be I'm sorry I want everyone to write
+
+ align:start position:0%
+to be I'm sorry I want everyone to write
+ 
+
+ align:start position:0%
+to be I'm sorry I want everyone to write
+on a piece of paper what the value of
+
+ align:start position:0%
+on a piece of paper what the value of
+ 
+
+ align:start position:0%
+on a piece of paper what the value of
+the policy would be for each individual
+
+ align:start position:0%
+the policy would be for each individual
+ 
+
+ align:start position:0%
+the policy would be for each individual
+so it's going to be a function of X and
+
+ align:start position:0%
+so it's going to be a function of X and
+ 
+
+ align:start position:0%
+so it's going to be a function of X and
+now I want it to be I'm looking for y of
+
+ align:start position:0%
+now I want it to be I'm looking for y of
+ 
+
+ align:start position:0%
+now I want it to be I'm looking for y of
+PI of X ok
+
+ align:start position:0%
+PI of X ok
+ 
+
+ align:start position:0%
+PI of X ok
+so I'm looking for you to draw that plot
+
+ align:start position:0%
+so I'm looking for you to draw that plot
+ 
+
+ align:start position:0%
+so I'm looking for you to draw that plot
+and feel free to talk to your neighbor
+
+ align:start position:0%
+and feel free to talk to your neighbor
+ 
+
+ align:start position:0%
+and feel free to talk to your neighbor
+in fact I encourage you to talk to your
+
+ align:start position:0%
+in fact I encourage you to talk to your
+ 
+
+ align:start position:0%
+in fact I encourage you to talk to your
+neighbor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just to try to connect this a little bit
+
+ align:start position:0%
+just to try to connect this a little bit
+ 
+
+ align:start position:0%
+just to try to connect this a little bit
+better to what I have up here I'm gonna
+
+ align:start position:0%
+better to what I have up here I'm gonna
+ 
+
+ align:start position:0%
+better to what I have up here I'm gonna
+assume that F this is f of X 1 and this
+
+ align:start position:0%
+assume that F this is f of X 1 and this
+ 
+
+ align:start position:0%
+assume that F this is f of X 1 and this
+is f of X 0 all right any any guesses
+
+ align:start position:0%
+is f of X 0 all right any any guesses
+ 
+
+ align:start position:0%
+is f of X 0 all right any any guesses
+what does this pot look like someone who
+
+ align:start position:0%
+what does this pot look like someone who
+ 
+
+ align:start position:0%
+what does this pot look like someone who
+hasn't spoken in the last one week and a
+
+ align:start position:0%
+hasn't spoken in the last one week and a
+ 
+
+ align:start position:0%
+hasn't spoken in the last one week and a
+half if possible so something like this
+
+ align:start position:0%
+half if possible so something like this
+ 
+
+ align:start position:0%
+half if possible so something like this
+until the intersection point and then
+
+ align:start position:0%
+until the intersection point and then
+ 
+
+ align:start position:0%
+until the intersection point and then
+like that outdoors yeah this exact what
+
+ align:start position:0%
+like that outdoors yeah this exact what
+ 
+
+ align:start position:0%
+like that outdoors yeah this exact what
+I'm going for and let's try to think
+
+ align:start position:0%
+I'm going for and let's try to think
+ 
+
+ align:start position:0%
+I'm going for and let's try to think
+through why is that the value of the
+
+ align:start position:0%
+through why is that the value of the
+ 
+
+ align:start position:0%
+through why is that the value of the
+policy well here the Kate which is
+
+ align:start position:0%
+policy well here the Kate which is
+ 
+
+ align:start position:0%
+policy well here the Kate which is
+looking at the difference between these
+
+ align:start position:0%
+looking at the difference between these
+ 
+
+ align:start position:0%
+looking at the difference between these
+two lines is negative right so for every
+
+ align:start position:0%
+two lines is negative right so for every
+ 
+
+ align:start position:0%
+two lines is negative right so for every
+X up to this crossing point the policy
+
+ align:start position:0%
+X up to this crossing point the policy
+ 
+
+ align:start position:0%
+X up to this crossing point the policy
+that we've defined over there is going
+
+ align:start position:0%
+that we've defined over there is going
+ 
+
+ align:start position:0%
+that we've defined over there is going
+to perform action action do to do wait
+
+ align:start position:0%
+to perform action action do to do wait
+ 
+
+ align:start position:0%
+to perform action action do to do wait
+am i drawing this correctly
+
+ align:start position:0%
+am i drawing this correctly
+ 
+
+ align:start position:0%
+am i drawing this correctly
+maybe it's actually opposite right you
+
+ align:start position:0%
+maybe it's actually opposite right you
+ 
+
+ align:start position:0%
+maybe it's actually opposite right you
+should be doing action one okay so here
+
+ align:start position:0%
+should be doing action one okay so here
+ 
+
+ align:start position:0%
+should be doing action one okay so here
+okay so here the Kate is negative and so
+
+ align:start position:0%
+okay so here the Kate is negative and so
+ 
+
+ align:start position:0%
+okay so here the Kate is negative and so
+by my definition the action perform is
+
+ align:start position:0%
+by my definition the action perform is
+ 
+
+ align:start position:0%
+by my definition the action perform is
+action zero and so the the value of the
+
+ align:start position:0%
+action zero and so the the value of the
+ 
+
+ align:start position:0%
+action zero and so the the value of the
+policy is actually this one right wait
+
+ align:start position:0%
+policy is actually this one right wait
+ 
+
+ align:start position:0%
+policy is actually this one right wait
+oh wait oh good you Lou knows what wanna
+
+ align:start position:0%
+oh wait oh good you Lou knows what wanna
+ 
+
+ align:start position:0%
+oh wait oh good you Lou knows what wanna
+get you cuz this is the graph I have in
+
+ align:start position:0%
+get you cuz this is the graph I have in
+ 
+
+ align:start position:0%
+get you cuz this is the graph I have in
+my notes oh good okay
+
+ align:start position:0%
+my notes oh good okay
+ 
+
+ align:start position:0%
+my notes oh good okay
+I was getting I was getting worried okay
+
+ align:start position:0%
+I was getting I was getting worried okay
+ 
+
+ align:start position:0%
+I was getting I was getting worried okay
+so to this action right all the way up
+
+ align:start position:0%
+so to this action right all the way up
+ 
+
+ align:start position:0%
+so to this action right all the way up
+until you get over here
+
+ align:start position:0%
+until you get over here
+ 
+
+ align:start position:0%
+until you get over here
+and then over here now the Kate suddenly
+
+ align:start position:0%
+and then over here now the Kate suddenly
+ 
+
+ align:start position:0%
+and then over here now the Kate suddenly
+becomes positive and so the action
+
+ align:start position:0%
+becomes positive and so the action
+ 
+
+ align:start position:0%
+becomes positive and so the action
+chosen is is one and so and so the value
+
+ align:start position:0%
+chosen is is one and so and so the value
+ 
+
+ align:start position:0%
+chosen is is one and so and so the value
+of that policy is y one okay and so one
+
+ align:start position:0%
+of that policy is y one okay and so one
+ 
+
+ align:start position:0%
+of that policy is y one okay and so one
+could write this a little bit
+
+ align:start position:0%
+could write this a little bit
+ 
+
+ align:start position:0%
+could write this a little bit
+differently for and in the case of just
+
+ align:start position:0%
+differently for and in the case of just
+ 
+
+ align:start position:0%
+differently for and in the case of just
+in the case of just two policies and now
+
+ align:start position:0%
+in the case of just two policies and now
+ 
+
+ align:start position:0%
+in the case of just two policies and now
+I'm going to write this in a way that
+
+ align:start position:0%
+I'm going to write this in a way that
+ 
+
+ align:start position:0%
+I'm going to write this in a way that
+some that it's really clear in the case
+
+ align:start position:0%
+some that it's really clear in the case
+ 
+
+ align:start position:0%
+some that it's really clear in the case
+of just just two actions one could write
+
+ align:start position:0%
+of just just two actions one could write
+ 
+
+ align:start position:0%
+of just just two actions one could write
+this equivalently as an average over the
+
+ align:start position:0%
+this equivalently as an average over the
+ 
+
+ align:start position:0%
+this equivalently as an average over the
+data points of the maximum of F X comma
+
+ align:start position:0%
+data points of the maximum of F X comma
+ 
+
+ align:start position:0%
+data points of the maximum of F X comma
+zero and f of X comma one okay and this
+
+ align:start position:0%
+zero and f of X comma one okay and this
+ 
+
+ align:start position:0%
+zero and f of X comma one okay and this
+this simplification turning this formula
+
+ align:start position:0%
+this simplification turning this formula
+ 
+
+ align:start position:0%
+this simplification turning this formula
+into into this formula is making the
+
+ align:start position:0%
+into into this formula is making the
+ 
+
+ align:start position:0%
+into into this formula is making the
+assumption that the pie that were being
+
+ align:start position:0%
+assumption that the pie that were being
+ 
+
+ align:start position:0%
+assumption that the pie that were being
+evaluated on is precisely this pie right
+
+ align:start position:0%
+evaluated on is precisely this pie right
+ 
+
+ align:start position:0%
+evaluated on is precisely this pie right
+so this implication is only for that pie
+
+ align:start position:0%
+so this implication is only for that pie
+ 
+
+ align:start position:0%
+so this implication is only for that pie
+for another policy which is not looking
+
+ align:start position:0%
+for another policy which is not looking
+ 
+
+ align:start position:0%
+for another policy which is not looking
+at Kate or for example she might
+
+ align:start position:0%
+at Kate or for example she might
+ 
+
+ align:start position:0%
+at Kate or for example she might
+threshold Kate at a gamma it wouldn't
+
+ align:start position:0%
+threshold Kate at a gamma it wouldn't
+ 
+
+ align:start position:0%
+threshold Kate at a gamma it wouldn't
+quite be this will be something else
+
+ align:start position:0%
+quite be this will be something else
+ 
+
+ align:start position:0%
+quite be this will be something else
+okay so but I've gone a step further
+
+ align:start position:0%
+okay so but I've gone a step further
+ 
+
+ align:start position:0%
+okay so but I've gone a step further
+here right so what are what I've shown
+
+ align:start position:0%
+here right so what are what I've shown
+ 
+
+ align:start position:0%
+here right so what are what I've shown
+you right here is not the average value
+
+ align:start position:0%
+you right here is not the average value
+ 
+
+ align:start position:0%
+you right here is not the average value
+but sort of individual values where I've
+
+ align:start position:0%
+but sort of individual values where I've
+ 
+
+ align:start position:0%
+but sort of individual values where I've
+shown you the max function but what this
+
+ align:start position:0%
+shown you the max function but what this
+ 
+
+ align:start position:0%
+shown you the max function but what this
+is actually looking at is the expected
+
+ align:start position:0%
+is actually looking at is the expected
+ 
+
+ align:start position:0%
+is actually looking at is the expected
+reward which is now averaging across all
+
+ align:start position:0%
+reward which is now averaging across all
+ 
+
+ align:start position:0%
+reward which is now averaging across all
+X so to truly draw a connection between
+
+ align:start position:0%
+X so to truly draw a connection between
+ 
+
+ align:start position:0%
+X so to truly draw a connection between
+this plot we're drawing and the and the
+
+ align:start position:0%
+this plot we're drawing and the and the
+ 
+
+ align:start position:0%
+this plot we're drawing and the and the
+average reward of that policy what we
+
+ align:start position:0%
+average reward of that policy what we
+ 
+
+ align:start position:0%
+average reward of that policy what we
+should be looking at is the average of
+
+ align:start position:0%
+should be looking at is the average of
+ 
+
+ align:start position:0%
+should be looking at is the average of
+these two functions which is we'll say
+
+ align:start position:0%
+these two functions which is we'll say
+ 
+
+ align:start position:0%
+these two functions which is we'll say
+you know something something like that
+
+ align:start position:0%
+you know something something like that
+ 
+
+ align:start position:0%
+you know something something like that
+okay and that value is the expected
+
+ align:start position:0%
+okay and that value is the expected
+ 
+
+ align:start position:0%
+okay and that value is the expected
+reward now this all goes to show that
+
+ align:start position:0%
+reward now this all goes to show that
+ 
+
+ align:start position:0%
+reward now this all goes to show that
+the expected reward of this policy is
+
+ align:start position:0%
+the expected reward of this policy is
+ 
+
+ align:start position:0%
+the expected reward of this policy is
+not a quantity that we've considered in
+
+ align:start position:0%
+not a quantity that we've considered in
+ 
+
+ align:start position:0%
+not a quantity that we've considered in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+previous lectures these not the previous
+
+ align:start position:0%
+previous lectures these not the previous
+ 
+
+ align:start position:0%
+previous lectures these not the previous
+lectures and causal inference right this
+
+ align:start position:0%
+lectures and causal inference right this
+ 
+
+ align:start position:0%
+lectures and causal inference right this
+is not the same as the average treatment
+
+ align:start position:0%
+is not the same as the average treatment
+ 
+
+ align:start position:0%
+is not the same as the average treatment
+effect for example so I'm just giving
+
+ align:start position:0%
+effect for example so I'm just giving
+ 
+
+ align:start position:0%
+effect for example so I'm just giving
+you one way to think through number one
+
+ align:start position:0%
+you one way to think through number one
+ 
+
+ align:start position:0%
+you one way to think through number one
+what is the policy that you might want
+
+ align:start position:0%
+what is the policy that you might want
+ 
+
+ align:start position:0%
+what is the policy that you might want
+to derive when you're doing causal
+
+ align:start position:0%
+to derive when you're doing causal
+ 
+
+ align:start position:0%
+to derive when you're doing causal
+inference and number two what is one way
+
+ align:start position:0%
+inference and number two what is one way
+ 
+
+ align:start position:0%
+inference and number two what is one way
+to estimate the value of that policy
+
+ align:start position:0%
+to estimate the value of that policy
+ 
+
+ align:start position:0%
+to estimate the value of that policy
+which goes through the process of
+
+ align:start position:0%
+which goes through the process of
+ 
+
+ align:start position:0%
+which goes through the process of
+estimating potential outcomes via covary
+
+ align:start position:0%
+estimating potential outcomes via covary
+ 
+
+ align:start position:0%
+estimating potential outcomes via covary
+adjustment but we might wonder just like
+
+ align:start position:0%
+adjustment but we might wonder just like
+ 
+
+ align:start position:0%
+adjustment but we might wonder just like
+when we talked about and causal
+
+ align:start position:0%
+when we talked about and causal
+ 
+
+ align:start position:0%
+when we talked about and causal
+inference where I said there are two
+
+ align:start position:0%
+inference where I said there are two
+ 
+
+ align:start position:0%
+inference where I said there are two
+approaches or these or more than two but
+
+ align:start position:0%
+approaches or these or more than two but
+ 
+
+ align:start position:0%
+approaches or these or more than two but
+we focused on two using Coverity
+
+ align:start position:0%
+we focused on two using Coverity
+ 
+
+ align:start position:0%
+we focused on two using Coverity
+adjustment and doing propensity inverse
+
+ align:start position:0%
+adjustment and doing propensity inverse
+ 
+
+ align:start position:0%
+adjustment and doing propensity inverse
+propensity score waiting you might
+
+ align:start position:0%
+propensity score waiting you might
+ 
+
+ align:start position:0%
+propensity score waiting you might
+wonder is there another approach to this
+
+ align:start position:0%
+wonder is there another approach to this
+ 
+
+ align:start position:0%
+wonder is there another approach to this
+problem altogether is there approach
+
+ align:start position:0%
+problem altogether is there approach
+ 
+
+ align:start position:0%
+problem altogether is there approach
+which wouldn't have had to go through
+
+ align:start position:0%
+which wouldn't have had to go through
+ 
+
+ align:start position:0%
+which wouldn't have had to go through
+estimating the potential outcomes and
+
+ align:start position:0%
+estimating the potential outcomes and
+ 
+
+ align:start position:0%
+estimating the potential outcomes and
+that's what I'll spend the rest of the
+
+ align:start position:0%
+that's what I'll spend the rest of the
+ 
+
+ align:start position:0%
+that's what I'll spend the rest of the
+this third of the lecture focused
+
+ align:start position:0%
+this third of the lecture focused
+ 
+
+ align:start position:0%
+this third of the lecture focused
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+and so to help you page this back in
+
+ align:start position:0%
+and so to help you page this back in
+ 
+
+ align:start position:0%
+and so to help you page this back in
+remember that we derived in last
+
+ align:start position:0%
+remember that we derived in last
+ 
+
+ align:start position:0%
+remember that we derived in last
+Thursday's lecture an estimator for the
+
+ align:start position:0%
+Thursday's lecture an estimator for the
+ 
+
+ align:start position:0%
+Thursday's lecture an estimator for the
+average treatment effect which was 1
+
+ align:start position:0%
+average treatment effect which was 1
+ 
+
+ align:start position:0%
+average treatment effect which was 1
+over N times the sum over data points
+
+ align:start position:0%
+over N times the sum over data points
+ 
+
+ align:start position:0%
+over N times the sum over data points
+that got treatment one of why I the
+
+ align:start position:0%
+that got treatment one of why I the
+ 
+
+ align:start position:0%
+that got treatment one of why I the
+observed outcome for that data point
+
+ align:start position:0%
+observed outcome for that data point
+ 
+
+ align:start position:0%
+observed outcome for that data point
+divided by the propensity score which
+
+ align:start position:0%
+divided by the propensity score which
+ 
+
+ align:start position:0%
+divided by the propensity score which
+I'm just going to write as e I so AI is
+
+ align:start position:0%
+I'm just going to write as e I so AI is
+ 
+
+ align:start position:0%
+I'm just going to write as e I so AI is
+equal to the probability of of observing
+
+ align:start position:0%
+equal to the probability of of observing
+ 
+
+ align:start position:0%
+equal to the probability of of observing
+treat T equals T equals 1 given the data
+
+ align:start position:0%
+treat T equals T equals 1 given the data
+ 
+
+ align:start position:0%
+treat T equals T equals 1 given the data
+point X I plus sorry minus a sum over
+
+ align:start position:0%
+point X I plus sorry minus a sum over
+ 
+
+ align:start position:0%
+point X I plus sorry minus a sum over
+data points I such that T I equals 0 of
+
+ align:start position:0%
+data points I such that T I equals 0 of
+ 
+
+ align:start position:0%
+data points I such that T I equals 0 of
+Y I
+
+ align:start position:0%
+Y I
+ 
+
+ align:start position:0%
+Y I
+/ 1 - e I and by the way there was a lot
+
+ align:start position:0%
+/ 1 - e I and by the way there was a lot
+ 
+
+ align:start position:0%
+/ 1 - e I and by the way there was a lot
+of confusion in class why do I have why
+
+ align:start position:0%
+of confusion in class why do I have why
+ 
+
+ align:start position:0%
+of confusion in class why do I have why
+do they have a 1 / n here one of our n
+
+ align:start position:0%
+do they have a 1 / n here one of our n
+ 
+
+ align:start position:0%
+do they have a 1 / n here one of our n
+here but right now I just took it out
+
+ align:start position:0%
+here but right now I just took it out
+ 
+
+ align:start position:0%
+here but right now I just took it out
+all together and not one over the number
+
+ align:start position:0%
+all together and not one over the number
+ 
+
+ align:start position:0%
+all together and not one over the number
+of positive data points and one over the
+
+ align:start position:0%
+of positive data points and one over the
+ 
+
+ align:start position:0%
+of positive data points and one over the
+number of negative or zero data points
+
+ align:start position:0%
+number of negative or zero data points
+ 
+
+ align:start position:0%
+number of negative or zero data points
+and I expanded the derivation that I
+
+ align:start position:0%
+and I expanded the derivation that I
+ 
+
+ align:start position:0%
+and I expanded the derivation that I
+gave in class I posted new slides online
+
+ align:start position:0%
+gave in class I posted new slides online
+ 
+
+ align:start position:0%
+gave in class I posted new slides online
+after class so if you're curious about
+
+ align:start position:0%
+after class so if you're curious about
+ 
+
+ align:start position:0%
+after class so if you're curious about
+that go to those slides and look at the
+
+ align:start position:0%
+that go to those slides and look at the
+ 
+
+ align:start position:0%
+that go to those slides and look at the
+derivation so in a very analogous way
+
+ align:start position:0%
+derivation so in a very analogous way
+ 
+
+ align:start position:0%
+derivation so in a very analogous way
+now I'm going to give you a new
+
+ align:start position:0%
+now I'm going to give you a new
+ 
+
+ align:start position:0%
+now I'm going to give you a new
+estimator for this same quantity that I
+
+ align:start position:0%
+estimator for this same quantity that I
+ 
+
+ align:start position:0%
+estimator for this same quantity that I
+had over here the expected reward of a
+
+ align:start position:0%
+had over here the expected reward of a
+ 
+
+ align:start position:0%
+had over here the expected reward of a
+policy
+
+ align:start position:0%
+policy
+ 
+
+ align:start position:0%
+policy
+notice that this estimator here it made
+
+ align:start position:0%
+notice that this estimator here it made
+ 
+
+ align:start position:0%
+notice that this estimator here it made
+sense for any policy didn't have to be
+
+ align:start position:0%
+sense for any policy didn't have to be
+ 
+
+ align:start position:0%
+sense for any policy didn't have to be
+the policy which looked at is Kate's
+
+ align:start position:0%
+the policy which looked at is Kate's
+ 
+
+ align:start position:0%
+the policy which looked at is Kate's
+just greater than 0 or not this held for
+
+ align:start position:0%
+just greater than 0 or not this held for
+ 
+
+ align:start position:0%
+just greater than 0 or not this held for
+any policy that simplification I gave
+
+ align:start position:0%
+any policy that simplification I gave
+ 
+
+ align:start position:0%
+any policy that simplification I gave
+was only in this particular setting I'm
+
+ align:start position:0%
+was only in this particular setting I'm
+ 
+
+ align:start position:0%
+was only in this particular setting I'm
+gonna give you now another estimator for
+
+ align:start position:0%
+gonna give you now another estimator for
+ 
+
+ align:start position:0%
+gonna give you now another estimator for
+the average value of a policy which
+
+ align:start position:0%
+the average value of a policy which
+ 
+
+ align:start position:0%
+the average value of a policy which
+doesn't go through estimating potential
+
+ align:start position:0%
+doesn't go through estimating potential
+ 
+
+ align:start position:0%
+doesn't go through estimating potential
+outcomes at all and analogous to this is
+
+ align:start position:0%
+outcomes at all and analogous to this is
+ 
+
+ align:start position:0%
+outcomes at all and analogous to this is
+just going to make use of the propensity
+
+ align:start position:0%
+just going to make use of the propensity
+ 
+
+ align:start position:0%
+just going to make use of the propensity
+scores and I'll call that the I'll call
+
+ align:start position:0%
+scores and I'll call that the I'll call
+ 
+
+ align:start position:0%
+scores and I'll call that the I'll call
+it R hat now I'm going to put a
+
+ align:start position:0%
+it R hat now I'm going to put a
+ 
+
+ align:start position:0%
+it R hat now I'm going to put a
+superscript ipw for inverse propensity
+
+ align:start position:0%
+superscript ipw for inverse propensity
+ 
+
+ align:start position:0%
+superscript ipw for inverse propensity
+weighted and it's a function of Pi and
+
+ align:start position:0%
+weighted and it's a function of Pi and
+ 
+
+ align:start position:0%
+weighted and it's a function of Pi and
+it's given to you by the following
+
+ align:start position:0%
+it's given to you by the following
+ 
+
+ align:start position:0%
+it's given to you by the following
+formula 1 over n sum over the data
+
+ align:start position:0%
+formula 1 over n sum over the data
+ 
+
+ align:start position:0%
+formula 1 over n sum over the data
+points of an indicator function for if
+
+ align:start position:0%
+points of an indicator function for if
+ 
+
+ align:start position:0%
+points of an indicator function for if
+the treatment which was actually given
+
+ align:start position:0%
+the treatment which was actually given
+ 
+
+ align:start position:0%
+the treatment which was actually given
+to the eigth patient is equal to what
+
+ align:start position:0%
+to the eigth patient is equal to what
+ 
+
+ align:start position:0%
+to the eigth patient is equal to what
+the policy would have done for the ice
+
+ align:start position:0%
+the policy would have done for the ice
+ 
+
+ align:start position:0%
+the policy would have done for the ice
+patient and by the way here i'm assuming
+
+ align:start position:0%
+patient and by the way here i'm assuming
+ 
+
+ align:start position:0%
+patient and by the way here i'm assuming
+that pi is a deterministic function so
+
+ align:start position:0%
+that pi is a deterministic function so
+ 
+
+ align:start position:0%
+that pi is a deterministic function so
+it so the policy says for this patient
+
+ align:start position:0%
+it so the policy says for this patient
+ 
+
+ align:start position:0%
+it so the policy says for this patient
+you should do this treatment all right
+
+ align:start position:0%
+you should do this treatment all right
+ 
+
+ align:start position:0%
+you should do this treatment all right
+so we're gonna look at just the data
+
+ align:start position:0%
+so we're gonna look at just the data
+ 
+
+ align:start position:0%
+so we're gonna look at just the data
+points for which the observed treatment
+
+ align:start position:0%
+points for which the observed treatment
+ 
+
+ align:start position:0%
+points for which the observed treatment
+is consistent with the observed unfor
+
+ align:start position:0%
+is consistent with the observed unfor
+ 
+
+ align:start position:0%
+is consistent with the observed unfor
+that patient and this indicator function
+
+ align:start position:0%
+that patient and this indicator function
+ 
+
+ align:start position:0%
+that patient and this indicator function
+is 0 otherwise and we're going to divide
+
+ align:start position:0%
+is 0 otherwise and we're going to divide
+ 
+
+ align:start position:0%
+is 0 otherwise and we're going to divide
+it by by the probability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of TI given x i so the way i'm writing
+
+ align:start position:0%
+of TI given x i so the way i'm writing
+ 
+
+ align:start position:0%
+of TI given x i so the way i'm writing
+this by the way is already is very
+
+ align:start position:0%
+this by the way is already is very
+ 
+
+ align:start position:0%
+this by the way is already is very
+general so this formula will hold for
+
+ align:start position:0%
+general so this formula will hold for
+ 
+
+ align:start position:0%
+general so this formula will hold for
+for non-binary treatments as well and
+
+ align:start position:0%
+for non-binary treatments as well and
+ 
+
+ align:start position:0%
+for non-binary treatments as well and
+that's one of the really nice things
+
+ align:start position:0%
+that's one of the really nice things
+ 
+
+ align:start position:0%
+that's one of the really nice things
+about thinking about policies which is
+
+ align:start position:0%
+about thinking about policies which is
+ 
+
+ align:start position:0%
+about thinking about policies which is
+whereas when thinking about when talking
+
+ align:start position:0%
+whereas when thinking about when talking
+ 
+
+ align:start position:0%
+whereas when thinking about when talking
+about average treatment effect average
+
+ align:start position:0%
+about average treatment effect average
+ 
+
+ align:start position:0%
+about average treatment effect average
+treatment effect is sort of makes sense
+
+ align:start position:0%
+treatment effect is sort of makes sense
+ 
+
+ align:start position:0%
+treatment effect is sort of makes sense
+in the comparative sentence right
+
+ align:start position:0%
+in the comparative sentence right
+ 
+
+ align:start position:0%
+in the comparative sentence right
+comparing one to another but when we
+
+ align:start position:0%
+comparing one to another but when we
+ 
+
+ align:start position:0%
+comparing one to another but when we
+talk about how good is a policy it's
+
+ align:start position:0%
+talk about how good is a policy it's
+ 
+
+ align:start position:0%
+talk about how good is a policy it's
+it's not a comparative statement at all
+
+ align:start position:0%
+it's not a comparative statement at all
+ 
+
+ align:start position:0%
+it's not a comparative statement at all
+the policy does something for everyone
+
+ align:start position:0%
+the policy does something for everyone
+ 
+
+ align:start position:0%
+the policy does something for everyone
+you could ask well what is the average
+
+ align:start position:0%
+you could ask well what is the average
+ 
+
+ align:start position:0%
+you could ask well what is the average
+value of the outcomes that you get for
+
+ align:start position:0%
+value of the outcomes that you get for
+ 
+
+ align:start position:0%
+value of the outcomes that you get for
+those actions that we're taking for
+
+ align:start position:0%
+those actions that we're taking for
+ 
+
+ align:start position:0%
+those actions that we're taking for
+those individuals um so that's why i'm
+
+ align:start position:0%
+those individuals um so that's why i'm
+ 
+
+ align:start position:0%
+those individuals um so that's why i'm
+writing in a slightly more general
+
+ align:start position:0%
+writing in a slightly more general
+ 
+
+ align:start position:0%
+writing in a slightly more general
+fashion already here x why i obviously
+
+ align:start position:0%
+fashion already here x why i obviously
+ 
+
+ align:start position:0%
+fashion already here x why i obviously
+okay so this is now a new estimator i'm
+
+ align:start position:0%
+okay so this is now a new estimator i'm
+ 
+
+ align:start position:0%
+okay so this is now a new estimator i'm
+not going to derive it for you in class
+
+ align:start position:0%
+not going to derive it for you in class
+ 
+
+ align:start position:0%
+not going to derive it for you in class
+but the derivation is very similar to
+
+ align:start position:0%
+but the derivation is very similar to
+ 
+
+ align:start position:0%
+but the derivation is very similar to
+what we did last week when we tried to
+
+ align:start position:0%
+what we did last week when we tried to
+ 
+
+ align:start position:0%
+what we did last week when we tried to
+drive the average treatment effect and
+
+ align:start position:0%
+drive the average treatment effect and
+ 
+
+ align:start position:0%
+drive the average treatment effect and
+the critical point is were dividing by
+
+ align:start position:0%
+the critical point is were dividing by
+ 
+
+ align:start position:0%
+the critical point is were dividing by
+that propensity score just like we did
+
+ align:start position:0%
+that propensity score just like we did
+ 
+
+ align:start position:0%
+that propensity score just like we did
+over there so this if all of the
+
+ align:start position:0%
+over there so this if all of the
+ 
+
+ align:start position:0%
+over there so this if all of the
+sumption x' made sense to an infinite
+
+ align:start position:0%
+sumption x' made sense to an infinite
+ 
+
+ align:start position:0%
+sumption x' made sense to an infinite
+data should give you exactly the same
+
+ align:start position:0%
+data should give you exactly the same
+ 
+
+ align:start position:0%
+data should give you exactly the same
+estimates as this but here you're not
+
+ align:start position:0%
+estimates as this but here you're not
+ 
+
+ align:start position:0%
+estimates as this but here you're not
+estimating potential outcomes at all
+
+ align:start position:0%
+estimating potential outcomes at all
+ 
+
+ align:start position:0%
+estimating potential outcomes at all
+right so you never have to try to impute
+
+ align:start position:0%
+right so you never have to try to impute
+ 
+
+ align:start position:0%
+right so you never have to try to impute
+the the counterfactuals here all it
+
+ align:start position:0%
+the the counterfactuals here all it
+ 
+
+ align:start position:0%
+the the counterfactuals here all it
+relies on knowing is that you have the
+
+ align:start position:0%
+relies on knowing is that you have the
+ 
+
+ align:start position:0%
+relies on knowing is that you have the
+propensity scores for each of the data
+
+ align:start position:0%
+propensity scores for each of the data
+ 
+
+ align:start position:0%
+propensity scores for each of the data
+points in your training set or in a data
+
+ align:start position:0%
+points in your training set or in a data
+ 
+
+ align:start position:0%
+points in your training set or in a data
+set so for example this opens the door
+
+ align:start position:0%
+set so for example this opens the door
+ 
+
+ align:start position:0%
+set so for example this opens the door
+to tons of new exciting directions
+
+ align:start position:0%
+to tons of new exciting directions
+ 
+
+ align:start position:0%
+to tons of new exciting directions
+imagine that you had a very large
+
+ align:start position:0%
+imagine that you had a very large
+ 
+
+ align:start position:0%
+imagine that you had a very large
+observers observational data set and you
+
+ align:start position:0%
+observers observational data set and you
+ 
+
+ align:start position:0%
+observers observational data set and you
+learned a policy from it for example you
+
+ align:start position:0%
+learned a policy from it for example you
+ 
+
+ align:start position:0%
+learned a policy from it for example you
+might have done covariant adjustment and
+
+ align:start position:0%
+might have done covariant adjustment and
+ 
+
+ align:start position:0%
+might have done covariant adjustment and
+then said okay based on coverity
+
+ align:start position:0%
+then said okay based on coverity
+ 
+
+ align:start position:0%
+then said okay based on coverity
+adjustment this is my new policy so you
+
+ align:start position:0%
+adjustment this is my new policy so you
+ 
+
+ align:start position:0%
+adjustment this is my new policy so you
+might have gotten it via that approach
+
+ align:start position:0%
+might have gotten it via that approach
+ 
+
+ align:start position:0%
+might have gotten it via that approach
+and now you want to know how good is
+
+ align:start position:0%
+and now you want to know how good is
+ 
+
+ align:start position:0%
+and now you want to know how good is
+that well suppose that you then run a
+
+ align:start position:0%
+that well suppose that you then run a
+ 
+
+ align:start position:0%
+that well suppose that you then run a
+randomized control trial and then your
+
+ align:start position:0%
+randomized control trial and then your
+ 
+
+ align:start position:0%
+randomized control trial and then your
+demise control trial you have
+
+ align:start position:0%
+demise control trial you have
+ 
+
+ align:start position:0%
+demise control trial you have
+100 people maybe 200 people so not that
+
+ align:start position:0%
+100 people maybe 200 people so not that
+ 
+
+ align:start position:0%
+100 people maybe 200 people so not that
+many so not nearly enough people to have
+
+ align:start position:0%
+many so not nearly enough people to have
+ 
+
+ align:start position:0%
+many so not nearly enough people to have
+actually estimated your your policy
+
+ align:start position:0%
+actually estimated your your policy
+ 
+
+ align:start position:0%
+actually estimated your your policy
+alone right you might have needed
+
+ align:start position:0%
+alone right you might have needed
+ 
+
+ align:start position:0%
+alone right you might have needed
+thousands or millions of individuals to
+
+ align:start position:0%
+thousands or millions of individuals to
+ 
+
+ align:start position:0%
+thousands or millions of individuals to
+estimate your policy now you're only
+
+ align:start position:0%
+estimate your policy now you're only
+ 
+
+ align:start position:0%
+estimate your policy now you're only
+gonna have a couple hundred individuals
+
+ align:start position:0%
+gonna have a couple hundred individuals
+ 
+
+ align:start position:0%
+gonna have a couple hundred individuals
+that you could actually afford to do a
+
+ align:start position:0%
+that you could actually afford to do a
+ 
+
+ align:start position:0%
+that you could actually afford to do a
+randomized control trial on for those
+
+ align:start position:0%
+randomized control trial on for those
+ 
+
+ align:start position:0%
+randomized control trial on for those
+people because you're flipping a coin
+
+ align:start position:0%
+people because you're flipping a coin
+ 
+
+ align:start position:0%
+people because you're flipping a coin
+for for which cheat me they're going to
+
+ align:start position:0%
+for for which cheat me they're going to
+ 
+
+ align:start position:0%
+for for which cheat me they're going to
+get suppose that we're in a binary
+
+ align:start position:0%
+get suppose that we're in a binary
+ 
+
+ align:start position:0%
+get suppose that we're in a binary
+setting with only two treatments then
+
+ align:start position:0%
+setting with only two treatments then
+ 
+
+ align:start position:0%
+setting with only two treatments then
+this value is always one-half one-half
+
+ align:start position:0%
+this value is always one-half one-half
+ 
+
+ align:start position:0%
+this value is always one-half one-half
+and what I'm giving you here is going to
+
+ align:start position:0%
+and what I'm giving you here is going to
+ 
+
+ align:start position:0%
+and what I'm giving you here is going to
+be an unbiased estimate of how good that
+
+ align:start position:0%
+be an unbiased estimate of how good that
+ 
+
+ align:start position:0%
+be an unbiased estimate of how good that
+policy is which one can now estimate
+
+ align:start position:0%
+policy is which one can now estimate
+ 
+
+ align:start position:0%
+policy is which one can now estimate
+using that randomized control trial now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this also might lead you to think
+
+ align:start position:0%
+this also might lead you to think
+ 
+
+ align:start position:0%
+this also might lead you to think
+through the question of well rather than
+
+ align:start position:0%
+through the question of well rather than
+ 
+
+ align:start position:0%
+through the question of well rather than
+estimating the policy through rather
+
+ align:start position:0%
+estimating the policy through rather
+ 
+
+ align:start position:0%
+estimating the policy through rather
+than obtaining a policy through the lens
+
+ align:start position:0%
+than obtaining a policy through the lens
+ 
+
+ align:start position:0%
+than obtaining a policy through the lens
+of of optimizing Kate of figuring how to
+
+ align:start position:0%
+of of optimizing Kate of figuring how to
+ 
+
+ align:start position:0%
+of of optimizing Kate of figuring how to
+estimate Kate maybe we could have
+
+ align:start position:0%
+estimate Kate maybe we could have
+ 
+
+ align:start position:0%
+estimate Kate maybe we could have
+skipped that altogether for example I
+
+ align:start position:0%
+skipped that altogether for example I
+ 
+
+ align:start position:0%
+skipped that altogether for example I
+suppose that we had that randomized
+
+ align:start position:0%
+suppose that we had that randomized
+ 
+
+ align:start position:0%
+suppose that we had that randomized
+control trial data
+
+ align:start position:0%
+control trial data
+ 
+
+ align:start position:0%
+control trial data
+now imagine that rather than 20 other
+
+ align:start position:0%
+now imagine that rather than 20 other
+ 
+
+ align:start position:0%
+now imagine that rather than 20 other
+than 100 individuals you had a really
+
+ align:start position:0%
+than 100 individuals you had a really
+ 
+
+ align:start position:0%
+than 100 individuals you had a really
+large randomized control trial with
+
+ align:start position:0%
+large randomized control trial with
+ 
+
+ align:start position:0%
+large randomized control trial with
+10,000 individuals in it this now opens
+
+ align:start position:0%
+10,000 individuals in it this now opens
+ 
+
+ align:start position:0%
+10,000 individuals in it this now opens
+the door to thinking about directly
+
+ align:start position:0%
+the door to thinking about directly
+ 
+
+ align:start position:0%
+the door to thinking about directly
+meant maximizing or minimizing depending
+
+ align:start position:0%
+meant maximizing or minimizing depending
+ 
+
+ align:start position:0%
+meant maximizing or minimizing depending
+what of what they want this to be large
+
+ align:start position:0%
+what of what they want this to be large
+ 
+
+ align:start position:0%
+what of what they want this to be large
+or small pie with respect to this
+
+ align:start position:0%
+or small pie with respect to this
+ 
+
+ align:start position:0%
+or small pie with respect to this
+quantity right which completely bypasses
+
+ align:start position:0%
+quantity right which completely bypasses
+ 
+
+ align:start position:0%
+quantity right which completely bypasses
+the goal of estimating the condition the
+
+ align:start position:0%
+the goal of estimating the condition the
+ 
+
+ align:start position:0%
+the goal of estimating the condition the
+the conditional average treatment effect
+
+ align:start position:0%
+the conditional average treatment effect
+ 
+
+ align:start position:0%
+the conditional average treatment effect
+and you'll notice how this looks exactly
+
+ align:start position:0%
+and you'll notice how this looks exactly
+ 
+
+ align:start position:0%
+and you'll notice how this looks exactly
+like a classification problem right this
+
+ align:start position:0%
+like a classification problem right this
+ 
+
+ align:start position:0%
+like a classification problem right this
+quantity here looks exactly like a 0 1
+
+ align:start position:0%
+quantity here looks exactly like a 0 1
+ 
+
+ align:start position:0%
+quantity here looks exactly like a 0 1
+loss and the only difference is that
+
+ align:start position:0%
+loss and the only difference is that
+ 
+
+ align:start position:0%
+loss and the only difference is that
+you're waiting each of the data points
+
+ align:start position:0%
+you're waiting each of the data points
+ 
+
+ align:start position:0%
+you're waiting each of the data points
+by this inverse propensity so one can
+
+ align:start position:0%
+by this inverse propensity so one can
+ 
+
+ align:start position:0%
+by this inverse propensity so one can
+reduce the problem of actually finding
+
+ align:start position:0%
+reduce the problem of actually finding
+ 
+
+ align:start position:0%
+reduce the problem of actually finding
+an optimal policy here to that of a
+
+ align:start position:0%
+an optimal policy here to that of a
+ 
+
+ align:start position:0%
+an optimal policy here to that of a
+weighted classification problem in the
+
+ align:start position:0%
+weighted classification problem in the
+ 
+
+ align:start position:0%
+weighted classification problem in the
+case of a discrete set of treatments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like big cat there are two big caveats
+
+ align:start position:0%
+like big cat there are two big caveats
+ 
+
+ align:start position:0%
+like big cat there are two big caveats
+to that line of thinking
+
+ align:start position:0%
+to that line of thinking
+ 
+
+ align:start position:0%
+to that line of thinking
+the first major caveat is that you you
+
+ align:start position:0%
+the first major caveat is that you you
+ 
+
+ align:start position:0%
+the first major caveat is that you you
+have to know these propensity scores and
+
+ align:start position:0%
+have to know these propensity scores and
+ 
+
+ align:start position:0%
+have to know these propensity scores and
+so if you have data coming from
+
+ align:start position:0%
+so if you have data coming from
+ 
+
+ align:start position:0%
+so if you have data coming from
+randomized controlled trial you will
+
+ align:start position:0%
+randomized controlled trial you will
+ 
+
+ align:start position:0%
+randomized controlled trial you will
+know those propensity scores so or or if
+
+ align:start position:0%
+know those propensity scores so or or if
+ 
+
+ align:start position:0%
+know those propensity scores so or or if
+you have for example some control over
+
+ align:start position:0%
+you have for example some control over
+ 
+
+ align:start position:0%
+you have for example some control over
+the data generation process right for
+
+ align:start position:0%
+the data generation process right for
+ 
+
+ align:start position:0%
+the data generation process right for
+example if you are a company and you're
+
+ align:start position:0%
+example if you are a company and you're
+ 
+
+ align:start position:0%
+example if you are a company and you're
+showing you get it shoes which ads to
+
+ align:start position:0%
+showing you get it shoes which ads to
+ 
+
+ align:start position:0%
+showing you get it shoes which ads to
+show to your customers then you look to
+
+ align:start position:0%
+show to your customers then you look to
+ 
+
+ align:start position:0%
+show to your customers then you look to
+see who clicks on what you might know
+
+ align:start position:0%
+see who clicks on what you might know
+ 
+
+ align:start position:0%
+see who clicks on what you might know
+what that policy was that was showing
+
+ align:start position:0%
+what that policy was that was showing
+ 
+
+ align:start position:0%
+what that policy was that was showing
+things it's right in that case you might
+
+ align:start position:0%
+things it's right in that case you might
+ 
+
+ align:start position:0%
+things it's right in that case you might
+exactly know the propensity scores in
+
+ align:start position:0%
+exactly know the propensity scores in
+ 
+
+ align:start position:0%
+exactly know the propensity scores in
+healthcare we other than in randomized
+
+ align:start position:0%
+healthcare we other than in randomized
+ 
+
+ align:start position:0%
+healthcare we other than in randomized
+control trials we typically don't know
+
+ align:start position:0%
+control trials we typically don't know
+ 
+
+ align:start position:0%
+control trials we typically don't know
+this value so we either have to have a
+
+ align:start position:0%
+this value so we either have to have a
+ 
+
+ align:start position:0%
+this value so we either have to have a
+large enough randomized control trial
+
+ align:start position:0%
+large enough randomized control trial
+ 
+
+ align:start position:0%
+large enough randomized control trial
+that we won't over fit by trying to
+
+ align:start position:0%
+that we won't over fit by trying to
+ 
+
+ align:start position:0%
+that we won't over fit by trying to
+directly minimize this or we have to
+
+ align:start position:0%
+directly minimize this or we have to
+ 
+
+ align:start position:0%
+directly minimize this or we have to
+work within an observational data
+
+ align:start position:0%
+work within an observational data
+ 
+
+ align:start position:0%
+work within an observational data
+setting but we have to estimate the
+
+ align:start position:0%
+setting but we have to estimate the
+ 
+
+ align:start position:0%
+setting but we have to estimate the
+propensity scores directly alright so
+
+ align:start position:0%
+propensity scores directly alright so
+ 
+
+ align:start position:0%
+propensity scores directly alright so
+you would then have a two-step procedure
+
+ align:start position:0%
+you would then have a two-step procedure
+ 
+
+ align:start position:0%
+you would then have a two-step procedure
+where first you estimate the propensity
+
+ align:start position:0%
+where first you estimate the propensity
+ 
+
+ align:start position:0%
+where first you estimate the propensity
+scores for example by doing logistic
+
+ align:start position:0%
+scores for example by doing logistic
+ 
+
+ align:start position:0%
+scores for example by doing logistic
+regression and then you attempt to
+
+ align:start position:0%
+regression and then you attempt to
+ 
+
+ align:start position:0%
+regression and then you attempt to
+maximize or minimize this quantity in
+
+ align:start position:0%
+maximize or minimize this quantity in
+ 
+
+ align:start position:0%
+maximize or minimize this quantity in
+order to find the optimal policy and
+
+ align:start position:0%
+order to find the optimal policy and
+ 
+
+ align:start position:0%
+order to find the optimal policy and
+that has a lot of challenges because
+
+ align:start position:0%
+that has a lot of challenges because
+ 
+
+ align:start position:0%
+that has a lot of challenges because
+this quantity shown in the very bottom
+
+ align:start position:0%
+this quantity shown in the very bottom
+ 
+
+ align:start position:0%
+this quantity shown in the very bottom
+here could be really smaller really
+
+ align:start position:0%
+here could be really smaller really
+ 
+
+ align:start position:0%
+here could be really smaller really
+large in observational data set and due
+
+ align:start position:0%
+large in observational data set and due
+ 
+
+ align:start position:0%
+large in observational data set and due
+to these issues of of having very small
+
+ align:start position:0%
+to these issues of of having very small
+ 
+
+ align:start position:0%
+to these issues of of having very small
+overlap between your treatments and this
+
+ align:start position:0%
+overlap between your treatments and this
+ 
+
+ align:start position:0%
+overlap between your treatments and this
+being very small implies then that the
+
+ align:start position:0%
+being very small implies then that the
+ 
+
+ align:start position:0%
+being very small implies then that the
+variance of this estimator is very very
+
+ align:start position:0%
+variance of this estimator is very very
+ 
+
+ align:start position:0%
+variance of this estimator is very very
+large and and so when one wants to use
+
+ align:start position:0%
+large and and so when one wants to use
+ 
+
+ align:start position:0%
+large and and so when one wants to use
+an approach like this similar to when
+
+ align:start position:0%
+an approach like this similar to when
+ 
+
+ align:start position:0%
+an approach like this similar to when
+one wants to use an average treatment
+
+ align:start position:0%
+one wants to use an average treatment
+ 
+
+ align:start position:0%
+one wants to use an average treatment
+effect estimator and when you're
+
+ align:start position:0%
+effect estimator and when you're
+ 
+
+ align:start position:0%
+effect estimator and when you're
+estimating these two propensity is often
+
+ align:start position:0%
+estimating these two propensity is often
+ 
+
+ align:start position:0%
+estimating these two propensity is often
+you might need to do things like
+
+ align:start position:0%
+you might need to do things like
+ 
+
+ align:start position:0%
+you might need to do things like
+clipping of the propensity scores in
+
+ align:start position:0%
+clipping of the propensity scores in
+ 
+
+ align:start position:0%
+clipping of the propensity scores in
+order to prevent the variance from being
+
+ align:start position:0%
+order to prevent the variance from being
+ 
+
+ align:start position:0%
+order to prevent the variance from being
+too large that then however leads to a
+
+ align:start position:0%
+too large that then however leads to a
+ 
+
+ align:start position:0%
+too large that then however leads to a
+biased estimator typically and I wanted
+
+ align:start position:0%
+biased estimator typically and I wanted
+ 
+
+ align:start position:0%
+biased estimator typically and I wanted
+to give you a couple of references here
+
+ align:start position:0%
+to give you a couple of references here
+ 
+
+ align:start position:0%
+to give you a couple of references here
+so one is Swami
+
+ align:start position:0%
+so one is Swami
+ 
+
+ align:start position:0%
+so one is Swami
+nothin and jokey-joke UM's J Oh a CH IMS
+
+ align:start position:0%
+nothin and jokey-joke UM's J Oh a CH IMS
+ 
+
+ align:start position:0%
+nothin and jokey-joke UM's J Oh a CH IMS
+ICML 2015 in that paper they tackle this
+
+ align:start position:0%
+ICML 2015 in that paper they tackle this
+ 
+
+ align:start position:0%
+ICML 2015 in that paper they tackle this
+question they focus on the setting where
+
+ align:start position:0%
+question they focus on the setting where
+ 
+
+ align:start position:0%
+question they focus on the setting where
+the propensity scores are known such as
+
+ align:start position:0%
+the propensity scores are known such as
+ 
+
+ align:start position:0%
+the propensity scores are known such as
+you would have from a randomized control
+
+ align:start position:0%
+you would have from a randomized control
+ 
+
+ align:start position:0%
+you would have from a randomized control
+trial and they recognize that you might
+
+ align:start position:0%
+trial and they recognize that you might
+ 
+
+ align:start position:0%
+trial and they recognize that you might
+decide that you want you prefer it
+
+ align:start position:0%
+decide that you want you prefer it
+ 
+
+ align:start position:0%
+decide that you want you prefer it
+something like a biased estimator
+
+ align:start position:0%
+something like a biased estimator
+ 
+
+ align:start position:0%
+something like a biased estimator
+because of the fact that these
+
+ align:start position:0%
+because of the fact that these
+ 
+
+ align:start position:0%
+because of the fact that these
+propensity scores could be really small
+
+ align:start position:0%
+propensity scores could be really small
+ 
+
+ align:start position:0%
+propensity scores could be really small
+and so they use some generalization
+
+ align:start position:0%
+and so they use some generalization
+ 
+
+ align:start position:0%
+and so they use some generalization
+results from the machine learning theory
+
+ align:start position:0%
+results from the machine learning theory
+ 
+
+ align:start position:0%
+results from the machine learning theory
+community in order to try to control the
+
+ align:start position:0%
+community in order to try to control the
+ 
+
+ align:start position:0%
+community in order to try to control the
+variance of the estimator as a function
+
+ align:start position:0%
+variance of the estimator as a function
+ 
+
+ align:start position:0%
+variance of the estimator as a function
+of these propensity scores and then they
+
+ align:start position:0%
+of these propensity scores and then they
+ 
+
+ align:start position:0%
+of these propensity scores and then they
+then learn directly minimise the policy
+
+ align:start position:0%
+then learn directly minimise the policy
+ 
+
+ align:start position:0%
+then learn directly minimise the policy
+which is what they call counterfactual
+
+ align:start position:0%
+which is what they call counterfactual
+ 
+
+ align:start position:0%
+which is what they call counterfactual
+regrettin minimization in order to in
+
+ align:start position:0%
+regrettin minimization in order to in
+ 
+
+ align:start position:0%
+regrettin minimization in order to in
+order to allow one to generalize as best
+
+ align:start position:0%
+order to allow one to generalize as best
+ 
+
+ align:start position:0%
+order to allow one to generalize as best
+as possible from sort of the small
+
+ align:start position:0%
+as possible from sort of the small
+ 
+
+ align:start position:0%
+as possible from sort of the small
+amount of data you might have available
+
+ align:start position:0%
+amount of data you might have available
+ 
+
+ align:start position:0%
+amount of data you might have available
+the second reference that I want to give
+
+ align:start position:0%
+the second reference that I want to give
+ 
+
+ align:start position:0%
+the second reference that I want to give
+just to point you into this literature
+
+ align:start position:0%
+just to point you into this literature
+ 
+
+ align:start position:0%
+just to point you into this literature
+if you're interested is by Nathan
+
+ align:start position:0%
+if you're interested is by Nathan
+ 
+
+ align:start position:0%
+if you're interested is by Nathan
+callous and his student I believe Angela
+
+ align:start position:0%
+callous and his student I believe Angela
+ 
+
+ align:start position:0%
+callous and his student I believe Angela
+Zhu from Europe's 2018 and that was a
+
+ align:start position:0%
+Zhu from Europe's 2018 and that was a
+ 
+
+ align:start position:0%
+Zhu from Europe's 2018 and that was a
+paper which was one of the optional
+
+ align:start position:0%
+paper which was one of the optional
+ 
+
+ align:start position:0%
+paper which was one of the optional
+readings for last Thursday's class now
+
+ align:start position:0%
+readings for last Thursday's class now
+ 
+
+ align:start position:0%
+readings for last Thursday's class now
+that paper they also start from
+
+ align:start position:0%
+that paper they also start from
+ 
+
+ align:start position:0%
+that paper they also start from
+something like this from this
+
+ align:start position:0%
+something like this from this
+ 
+
+ align:start position:0%
+something like this from this
+perspective and they say that oh now
+
+ align:start position:0%
+perspective and they say that oh now
+ 
+
+ align:start position:0%
+perspective and they say that oh now
+that you have we're working in this
+
+ align:start position:0%
+that you have we're working in this
+ 
+
+ align:start position:0%
+that you have we're working in this
+framework one could think about what
+
+ align:start position:0%
+framework one could think about what
+ 
+
+ align:start position:0%
+framework one could think about what
+happens if you have actually unobserved
+
+ align:start position:0%
+happens if you have actually unobserved
+ 
+
+ align:start position:0%
+happens if you have actually unobserved
+confounding so there you might not
+
+ align:start position:0%
+confounding so there you might not
+ 
+
+ align:start position:0%
+confounding so there you might not
+actually know the true propensity scores
+
+ align:start position:0%
+actually know the true propensity scores
+ 
+
+ align:start position:0%
+actually know the true propensity scores
+because there are unobserved confounders
+
+ align:start position:0%
+because there are unobserved confounders
+ 
+
+ align:start position:0%
+because there are unobserved confounders
+that you don't observe and that you can
+
+ align:start position:0%
+that you don't observe and that you can
+ 
+
+ align:start position:0%
+that you don't observe and that you can
+think about trying to bound how how
+
+ align:start position:0%
+think about trying to bound how how
+ 
+
+ align:start position:0%
+think about trying to bound how how
+wrong your estimator can be as a
+
+ align:start position:0%
+wrong your estimator can be as a
+ 
+
+ align:start position:0%
+wrong your estimator can be as a
+function of how much you don't know this
+
+ align:start position:0%
+function of how much you don't know this
+ 
+
+ align:start position:0%
+function of how much you don't know this
+quantity and they show that when you try
+
+ align:start position:0%
+quantity and they show that when you try
+ 
+
+ align:start position:0%
+quantity and they show that when you try
+to if you think about having some backup
+
+ align:start position:0%
+to if you think about having some backup
+ 
+
+ align:start position:0%
+to if you think about having some backup
+strategy like if your goal is to find a
+
+ align:start position:0%
+strategy like if your goal is to find a
+ 
+
+ align:start position:0%
+strategy like if your goal is to find a
+new policy which performs as best as
+
+ align:start position:0%
+new policy which performs as best as
+ 
+
+ align:start position:0%
+new policy which performs as best as
+possible with respect to an old policy
+
+ align:start position:0%
+possible with respect to an old policy
+ 
+
+ align:start position:0%
+possible with respect to an old policy
+then it gives you a really elegant
+
+ align:start position:0%
+then it gives you a really elegant
+ 
+
+ align:start position:0%
+then it gives you a really elegant
+framework for trying to think about a
+
+ align:start position:0%
+framework for trying to think about a
+ 
+
+ align:start position:0%
+framework for trying to think about a
+robust optimization of this even taking
+
+ align:start position:0%
+robust optimization of this even taking
+ 
+
+ align:start position:0%
+robust optimization of this even taking
+the fact that there might be an observed
+
+ align:start position:0%
+the fact that there might be an observed
+ 
+
+ align:start position:0%
+the fact that there might be an observed
+confounding and that worked oh so in
+
+ align:start position:0%
+confounding and that worked oh so in
+ 
+
+ align:start position:0%
+confounding and that worked oh so in
+this in this framework so I'm nearly
+
+ align:start position:0%
+this in this framework so I'm nearly
+ 
+
+ align:start position:0%
+this in this framework so I'm nearly
+done now
+
+ align:start position:0%
+done now
+ 
+
+ align:start position:0%
+done now
+I just want to now finish with the
+
+ align:start position:0%
+I just want to now finish with the
+ 
+
+ align:start position:0%
+I just want to now finish with the
+thought can we do the same thing for
+
+ align:start position:0%
+thought can we do the same thing for
+ 
+
+ align:start position:0%
+thought can we do the same thing for
+policies learned by reinforcement
+
+ align:start position:0%
+policies learned by reinforcement
+ 
+
+ align:start position:0%
+policies learned by reinforcement
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+so now let's now that we've sort of
+
+ align:start position:0%
+so now let's now that we've sort of
+ 
+
+ align:start position:0%
+so now let's now that we've sort of
+built up this language let's return to
+
+ align:start position:0%
+built up this language let's return to
+ 
+
+ align:start position:0%
+built up this language let's return to
+the RL setting and there one can show
+
+ align:start position:0%
+the RL setting and there one can show
+ 
+
+ align:start position:0%
+the RL setting and there one can show
+that you can get a similar estimate for
+
+ align:start position:0%
+that you can get a similar estimate for
+ 
+
+ align:start position:0%
+that you can get a similar estimate for
+the value of a policy by summing over
+
+ align:start position:0%
+the value of a policy by summing over
+ 
+
+ align:start position:0%
+the value of a policy by summing over
+your observed sequences summing over the
+
+ align:start position:0%
+your observed sequences summing over the
+ 
+
+ align:start position:0%
+your observed sequences summing over the
+time steps of that sequence of the
+
+ align:start position:0%
+time steps of that sequence of the
+ 
+
+ align:start position:0%
+time steps of that sequence of the
+reward observed at that time step times
+
+ align:start position:0%
+reward observed at that time step times
+ 
+
+ align:start position:0%
+reward observed at that time step times
+a ratio of probabilities which is going
+
+ align:start position:0%
+a ratio of probabilities which is going
+ 
+
+ align:start position:0%
+a ratio of probabilities which is going
+from the first time step up to time
+
+ align:start position:0%
+from the first time step up to time
+ 
+
+ align:start position:0%
+from the first time step up to time
+little T of the probability that you
+
+ align:start position:0%
+little T of the probability that you
+ 
+
+ align:start position:0%
+little T of the probability that you
+would actually take the observed action
+
+ align:start position:0%
+would actually take the observed action
+ 
+
+ align:start position:0%
+would actually take the observed action
+T prime given that you were in the
+
+ align:start position:0%
+T prime given that you were in the
+ 
+
+ align:start position:0%
+T prime given that you were in the
+observe state T prime divided by the
+
+ align:start position:0%
+observe state T prime divided by the
+ 
+
+ align:start position:0%
+observe state T prime divided by the
+probability this is where this is the
+
+ align:start position:0%
+probability this is where this is the
+ 
+
+ align:start position:0%
+probability this is where this is the
+knowledge of the propensity score the
+
+ align:start position:0%
+knowledge of the propensity score the
+ 
+
+ align:start position:0%
+knowledge of the propensity score the
+probability under the data generating
+
+ align:start position:0%
+probability under the data generating
+ 
+
+ align:start position:0%
+probability under the data generating
+process of of seeing action a given that
+
+ align:start position:0%
+process of of seeing action a given that
+ 
+
+ align:start position:0%
+process of of seeing action a given that
+you're in state T prime so if as we
+
+ align:start position:0%
+you're in state T prime so if as we
+ 
+
+ align:start position:0%
+you're in state T prime so if as we
+discussed there you had a deterministic
+
+ align:start position:0%
+discussed there you had a deterministic
+ 
+
+ align:start position:0%
+discussed there you had a deterministic
+policy then this PI would it would just
+
+ align:start position:0%
+policy then this PI would it would just
+ 
+
+ align:start position:0%
+policy then this PI would it would just
+be a delta function and so this would
+
+ align:start position:0%
+be a delta function and so this would
+ 
+
+ align:start position:0%
+be a delta function and so this would
+just be looking at what this would this
+
+ align:start position:0%
+just be looking at what this would this
+ 
+
+ align:start position:0%
+just be looking at what this would this
+estimator would only be looking at
+
+ align:start position:0%
+estimator would only be looking at
+ 
+
+ align:start position:0%
+estimator would only be looking at
+sequences where the precise sequence of
+
+ align:start position:0%
+sequences where the precise sequence of
+ 
+
+ align:start position:0%
+sequences where the precise sequence of
+actions taken are identical to the
+
+ align:start position:0%
+actions taken are identical to the
+ 
+
+ align:start position:0%
+actions taken are identical to the
+precise sequence of actions that the
+
+ align:start position:0%
+precise sequence of actions that the
+ 
+
+ align:start position:0%
+precise sequence of actions that the
+policy would have taken and the
+
+ align:start position:0%
+policy would have taken and the
+ 
+
+ align:start position:0%
+policy would have taken and the
+difference here is that now instead of
+
+ align:start position:0%
+difference here is that now instead of
+ 
+
+ align:start position:0%
+difference here is that now instead of
+having a single propensity score one has
+
+ align:start position:0%
+having a single propensity score one has
+ 
+
+ align:start position:0%
+having a single propensity score one has
+a product of these propensity scores
+
+ align:start position:0%
+a product of these propensity scores
+ 
+
+ align:start position:0%
+a product of these propensity scores
+corresponding to the propensity of
+
+ align:start position:0%
+corresponding to the propensity of
+ 
+
+ align:start position:0%
+corresponding to the propensity of
+observing that action given the
+
+ align:start position:0%
+observing that action given the
+ 
+
+ align:start position:0%
+observing that action given the
+corresponding state at each point along
+
+ align:start position:0%
+corresponding state at each point along
+ 
+
+ align:start position:0%
+corresponding state at each point along
+the sequence and so this is nice because
+
+ align:start position:0%
+the sequence and so this is nice because
+ 
+
+ align:start position:0%
+the sequence and so this is nice because
+this gives you one way to do what's
+
+ align:start position:0%
+this gives you one way to do what's
+ 
+
+ align:start position:0%
+this gives you one way to do what's
+called off policy evaluation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is an estimator which is I
+
+ align:start position:0%
+and this is an estimator which is I
+ 
+
+ align:start position:0%
+and this is an estimator which is I
+which is a completely analogous to the
+
+ align:start position:0%
+which is a completely analogous to the
+ 
+
+ align:start position:0%
+which is a completely analogous to the
+estimator that we got from q-learning
+
+ align:start position:0%
+estimator that we got from q-learning
+ 
+
+ align:start position:0%
+estimator that we got from q-learning
+so if all assumptions were correct and
+
+ align:start position:0%
+so if all assumptions were correct and
+ 
+
+ align:start position:0%
+so if all assumptions were correct and
+you had a lot of data then those two
+
+ align:start position:0%
+you had a lot of data then those two
+ 
+
+ align:start position:0%
+you had a lot of data then those two
+should give you precisely the same
+
+ align:start position:0%
+should give you precisely the same
+ 
+
+ align:start position:0%
+should give you precisely the same
+answer but here like in the causal
+
+ align:start position:0%
+answer but here like in the causal
+ 
+
+ align:start position:0%
+answer but here like in the causal
+inference setting we are not making the
+
+ align:start position:0%
+inference setting we are not making the
+ 
+
+ align:start position:0%
+inference setting we are not making the
+assumption that we can do Co very two
+
+ align:start position:0%
+assumption that we can do Co very two
+ 
+
+ align:start position:0%
+assumption that we can do Co very two
+adjustment well or said differently
+
+ align:start position:0%
+adjustment well or said differently
+ 
+
+ align:start position:0%
+adjustment well or said differently
+we're not assuming that we can fit the Q
+
+ align:start position:0%
+we're not assuming that we can fit the Q
+ 
+
+ align:start position:0%
+we're not assuming that we can fit the Q
+function well and this is now just just
+
+ align:start position:0%
+function well and this is now just just
+ 
+
+ align:start position:0%
+function well and this is now just just
+like they're based on the assumption
+
+ align:start position:0%
+like they're based on the assumption
+ 
+
+ align:start position:0%
+like they're based on the assumption
+that we have the ability to really
+
+ align:start position:0%
+that we have the ability to really
+ 
+
+ align:start position:0%
+that we have the ability to really
+accurately know what the propensity
+
+ align:start position:0%
+accurately know what the propensity
+ 
+
+ align:start position:0%
+accurately know what the propensity
+scores are so it now gives you an
+
+ align:start position:0%
+scores are so it now gives you an
+ 
+
+ align:start position:0%
+scores are so it now gives you an
+alternative approach to do evaluation
+
+ align:start position:0%
+alternative approach to do evaluation
+ 
+
+ align:start position:0%
+alternative approach to do evaluation
+and you could think about looking for
+
+ align:start position:0%
+and you could think about looking for
+ 
+
+ align:start position:0%
+and you could think about looking for
+the robustness of your estimates from
+
+ align:start position:0%
+the robustness of your estimates from
+ 
+
+ align:start position:0%
+the robustness of your estimates from
+these two different different estimators
+
+ align:start position:0%
+these two different different estimators
+ 
+
+ align:start position:0%
+these two different different estimators
+and here if you're and there this is the
+
+ align:start position:0%
+and here if you're and there this is the
+ 
+
+ align:start position:0%
+and here if you're and there this is the
+most naive of des tomaters there are
+
+ align:start position:0%
+most naive of des tomaters there are
+ 
+
+ align:start position:0%
+most naive of des tomaters there are
+many ways to try to try to make this
+
+ align:start position:0%
+many ways to try to try to make this
+ 
+
+ align:start position:0%
+many ways to try to try to make this
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+such as by by doing wo bust estimators
+
+ align:start position:0%
+such as by by doing wo bust estimators
+ 
+
+ align:start position:0%
+such as by by doing wo bust estimators
+and if you want to learn more I
+
+ align:start position:0%
+and if you want to learn more I
+ 
+
+ align:start position:0%
+and if you want to learn more I
+recommend reading this paper by Thomas
+
+ align:start position:0%
+recommend reading this paper by Thomas
+ 
+
+ align:start position:0%
+recommend reading this paper by Thomas
+and I'm a Brun skill and I CML 2016 and
+
+ align:start position:0%
+and I'm a Brun skill and I CML 2016 and
+ 
+
+ align:start position:0%
+and I'm a Brun skill and I CML 2016 and
+with that I want Barbara to come up and
+
+ align:start position:0%
+with that I want Barbara to come up and
+ 
+
+ align:start position:0%
+with that I want Barbara to come up and
+get set up and we're going to transition
+
+ align:start position:0%
+get set up and we're going to transition
+ 
+
+ align:start position:0%
+get set up and we're going to transition
+to the next part of the lecture yes one
+
+ align:start position:0%
+to the next part of the lecture yes one
+ 
+
+ align:start position:0%
+to the next part of the lecture yes one
+easy way to think about this is suppose
+
+ align:start position:0%
+easy way to think about this is suppose
+ 
+
+ align:start position:0%
+easy way to think about this is suppose
+that you only had a reward at the last
+
+ align:start position:0%
+that you only had a reward at the last
+ 
+
+ align:start position:0%
+that you only had a reward at the last
+time step if you only had a reward of
+
+ align:start position:0%
+time step if you only had a reward of
+ 
+
+ align:start position:0%
+time step if you only had a reward of
+the last time step then you wouldn't
+
+ align:start position:0%
+the last time step then you wouldn't
+ 
+
+ align:start position:0%
+the last time step then you wouldn't
+have this sum over T because the rewards
+
+ align:start position:0%
+have this sum over T because the rewards
+ 
+
+ align:start position:0%
+have this sum over T because the rewards
+in the earlier steps would be zero
+
+ align:start position:0%
+in the earlier steps would be zero
+ 
+
+ align:start position:0%
+in the earlier steps would be zero
+you would just have that product going
+
+ align:start position:0%
+you would just have that product going
+ 
+
+ align:start position:0%
+you would just have that product going
+from zero up to capital T the last time
+
+ align:start position:0%
+from zero up to capital T the last time
+ 
+
+ align:start position:0%
+from zero up to capital T the last time
+step the reason why you have it up to at
+
+ align:start position:0%
+step the reason why you have it up to at
+ 
+
+ align:start position:0%
+step the reason why you have it up to at
+each time step is because one wants to
+
+ align:start position:0%
+each time step is because one wants to
+ 
+
+ align:start position:0%
+each time step is because one wants to
+be able to appropriately way the likely
+
+ align:start position:0%
+be able to appropriately way the likely
+ 
+
+ align:start position:0%
+be able to appropriately way the likely
+in essence the likelihood of seeing that
+
+ align:start position:0%
+in essence the likelihood of seeing that
+ 
+
+ align:start position:0%
+in essence the likelihood of seeing that
+reward at that point in time one could
+
+ align:start position:0%
+reward at that point in time one could
+ 
+
+ align:start position:0%
+reward at that point in time one could
+rewrite this in other ways I want to
+
+ align:start position:0%
+rewrite this in other ways I want to
+ 
+
+ align:start position:0%
+rewrite this in other ways I want to
+hold other questions because this part
+
+ align:start position:0%
+hold other questions because this part
+ 
+
+ align:start position:0%
+hold other questions because this part
+of lecture is gonna be much more
+
+ align:start position:0%
+of lecture is gonna be much more
+ 
+
+ align:start position:0%
+of lecture is gonna be much more
+interesting than my part of lecture
+
+ align:start position:0%
+interesting than my part of lecture
+ 
+
+ align:start position:0%
+interesting than my part of lecture
+and with that I want to introduce
+
+ align:start position:0%
+and with that I want to introduce
+ 
+
+ align:start position:0%
+and with that I want to introduce
+Barbara Barbara I first met her when she
+
+ align:start position:0%
+Barbara Barbara I first met her when she
+ 
+
+ align:start position:0%
+Barbara Barbara I first met her when she
+invited me to give a talk in her class
+
+ align:start position:0%
+invited me to give a talk in her class
+ 
+
+ align:start position:0%
+invited me to give a talk in her class
+last year she is an instructor at at
+
+ align:start position:0%
+last year she is an instructor at at
+ 
+
+ align:start position:0%
+last year she is an instructor at at
+harvard medical school or School of
+
+ align:start position:0%
+harvard medical school or School of
+ 
+
+ align:start position:0%
+harvard medical school or School of
+Public Health and she recently finished
+
+ align:start position:0%
+Public Health and she recently finished
+ 
+
+ align:start position:0%
+Public Health and she recently finished
+her PhD in 2018
+
+ align:start position:0%
+her PhD in 2018
+ 
+
+ align:start position:0%
+her PhD in 2018
+and her PhD looked at many questions
+
+ align:start position:0%
+and her PhD looked at many questions
+ 
+
+ align:start position:0%
+and her PhD looked at many questions
+related to the themes of the last couple
+
+ align:start position:0%
+related to the themes of the last couple
+ 
+
+ align:start position:0%
+related to the themes of the last couple
+of weeks since that time in addition to
+
+ align:start position:0%
+of weeks since that time in addition to
+ 
+
+ align:start position:0%
+of weeks since that time in addition to
+continue her research
+
+ align:start position:0%
+continue her research
+ 
+
+ align:start position:0%
+continue her research
+she's been really leading the way in
+
+ align:start position:0%
+she's been really leading the way in
+ 
+
+ align:start position:0%
+she's been really leading the way in
+creating data science curriculum over at
+
+ align:start position:0%
+creating data science curriculum over at
+ 
+
+ align:start position:0%
+creating data science curriculum over at
+Harvard so please take away thank you so
+
+ align:start position:0%
+Harvard so please take away thank you so
+ 
+
+ align:start position:0%
+Harvard so please take away thank you so
+much for the introduction David I'm very
+
+ align:start position:0%
+much for the introduction David I'm very
+ 
+
+ align:start position:0%
+much for the introduction David I'm very
+happy to be here to share some of my
+
+ align:start position:0%
+happy to be here to share some of my
+ 
+
+ align:start position:0%
+happy to be here to share some of my
+work on evaluating dynamic treatment
+
+ align:start position:0%
+work on evaluating dynamic treatment
+ 
+
+ align:start position:0%
+work on evaluating dynamic treatment
+strategies which you've been talking
+
+ align:start position:0%
+strategies which you've been talking
+ 
+
+ align:start position:0%
+strategies which you've been talking
+about over the past few lectures so my
+
+ align:start position:0%
+about over the past few lectures so my
+ 
+
+ align:start position:0%
+about over the past few lectures so my
+goals for today I'm just gonna breeze
+
+ align:start position:0%
+goals for today I'm just gonna breeze
+ 
+
+ align:start position:0%
+goals for today I'm just gonna breeze
+over defining dynamic treatment
+
+ align:start position:0%
+over defining dynamic treatment
+ 
+
+ align:start position:0%
+over defining dynamic treatment
+strategies as you're already familiar
+
+ align:start position:0%
+strategies as you're already familiar
+ 
+
+ align:start position:0%
+strategies as you're already familiar
+with it but I would like to touch on
+
+ align:start position:0%
+with it but I would like to touch on
+ 
+
+ align:start position:0%
+with it but I would like to touch on
+when we need a special class of methods
+
+ align:start position:0%
+when we need a special class of methods
+ 
+
+ align:start position:0%
+when we need a special class of methods
+called G methods and then we'll talk
+
+ align:start position:0%
+called G methods and then we'll talk
+ 
+
+ align:start position:0%
+called G methods and then we'll talk
+about two different applications
+
+ align:start position:0%
+about two different applications
+ 
+
+ align:start position:0%
+about two different applications
+different analyses that have focused on
+
+ align:start position:0%
+different analyses that have focused on
+ 
+
+ align:start position:0%
+different analyses that have focused on
+evaluating dynamic treatment strategies
+
+ align:start position:0%
+evaluating dynamic treatment strategies
+ 
+
+ align:start position:0%
+evaluating dynamic treatment strategies
+so the first will be an application of
+
+ align:start position:0%
+so the first will be an application of
+ 
+
+ align:start position:0%
+so the first will be an application of
+the parametric G formula which is a
+
+ align:start position:0%
+the parametric G formula which is a
+ 
+
+ align:start position:0%
+the parametric G formula which is a
+powerful G method to cancer research and
+
+ align:start position:0%
+powerful G method to cancer research and
+ 
+
+ align:start position:0%
+powerful G method to cancer research and
+so the goal here is to give you my
+
+ align:start position:0%
+so the goal here is to give you my
+ 
+
+ align:start position:0%
+so the goal here is to give you my
+causal inference perspective on how we
+
+ align:start position:0%
+causal inference perspective on how we
+ 
+
+ align:start position:0%
+causal inference perspective on how we
+think about this task of sequential
+
+ align:start position:0%
+think about this task of sequential
+ 
+
+ align:start position:0%
+think about this task of sequential
+decision making and then with whatever
+
+ align:start position:0%
+decision making and then with whatever
+ 
+
+ align:start position:0%
+decision making and then with whatever
+time remains will be discussing a recent
+
+ align:start position:0%
+time remains will be discussing a recent
+ 
+
+ align:start position:0%
+time remains will be discussing a recent
+publication on the AI clinician to talk
+
+ align:start position:0%
+publication on the AI clinician to talk
+ 
+
+ align:start position:0%
+publication on the AI clinician to talk
+through the reinforcement learning
+
+ align:start position:0%
+through the reinforcement learning
+ 
+
+ align:start position:0%
+through the reinforcement learning
+perspective so I think it'll be a really
+
+ align:start position:0%
+perspective so I think it'll be a really
+ 
+
+ align:start position:0%
+perspective so I think it'll be a really
+interesting discussion where we can
+
+ align:start position:0%
+interesting discussion where we can
+ 
+
+ align:start position:0%
+interesting discussion where we can
+share these perspectives talk about the
+
+ align:start position:0%
+share these perspectives talk about the
+ 
+
+ align:start position:0%
+share these perspectives talk about the
+relative strengths and limitations as
+
+ align:start position:0%
+relative strengths and limitations as
+ 
+
+ align:start position:0%
+relative strengths and limitations as
+well and please stop me if you have any
+
+ align:start position:0%
+well and please stop me if you have any
+ 
+
+ align:start position:0%
+well and please stop me if you have any
+questions so you already know this when
+
+ align:start position:0%
+questions so you already know this when
+ 
+
+ align:start position:0%
+questions so you already know this when
+it comes to treatment strategies there's
+
+ align:start position:0%
+it comes to treatment strategies there's
+ 
+
+ align:start position:0%
+it comes to treatment strategies there's
+three main types there's point
+
+ align:start position:0%
+three main types there's point
+ 
+
+ align:start position:0%
+three main types there's point
+interventions happening at a single
+
+ align:start position:0%
+interventions happening at a single
+ 
+
+ align:start position:0%
+interventions happening at a single
+point in time there's sustained
+
+ align:start position:0%
+point in time there's sustained
+ 
+
+ align:start position:0%
+point in time there's sustained
+interventions happening over time when
+
+ align:start position:0%
+interventions happening over time when
+ 
+
+ align:start position:0%
+interventions happening over time when
+it comes to clinical care this is often
+
+ align:start position:0%
+it comes to clinical care this is often
+ 
+
+ align:start position:0%
+it comes to clinical care this is often
+what we're most interested in within
+
+ align:start position:0%
+what we're most interested in within
+ 
+
+ align:start position:0%
+what we're most interested in within
+that there's static strategies which are
+
+ align:start position:0%
+that there's static strategies which are
+ 
+
+ align:start position:0%
+that there's static strategies which are
+constant over time and then there's
+
+ align:start position:0%
+constant over time and then there's
+ 
+
+ align:start position:0%
+constant over time and then there's
+dynamic strategies which we're going to
+
+ align:start position:0%
+dynamic strategies which we're going to
+ 
+
+ align:start position:0%
+dynamic strategies which we're going to
+focus on
+
+ align:start position:0%
+focus on
+ 
+
+ align:start position:0%
+focus on
+and these differ in that the
+
+ align:start position:0%
+and these differ in that the
+ 
+
+ align:start position:0%
+and these differ in that the
+intervention over time depends on
+
+ align:start position:0%
+intervention over time depends on
+ 
+
+ align:start position:0%
+intervention over time depends on
+evolving characteristics so for example
+
+ align:start position:0%
+evolving characteristics so for example
+ 
+
+ align:start position:0%
+evolving characteristics so for example
+initiate treatment at baseline and
+
+ align:start position:0%
+initiate treatment at baseline and
+ 
+
+ align:start position:0%
+initiate treatment at baseline and
+continue it over follow-up until a
+
+ align:start position:0%
+continue it over follow-up until a
+ 
+
+ align:start position:0%
+continue it over follow-up until a
+contraindication occurs at which point
+
+ align:start position:0%
+contraindication occurs at which point
+ 
+
+ align:start position:0%
+contraindication occurs at which point
+you may stop treatment and decide with
+
+ align:start position:0%
+you may stop treatment and decide with
+ 
+
+ align:start position:0%
+you may stop treatment and decide with
+your doctor whether you're going to
+
+ align:start position:0%
+your doctor whether you're going to
+ 
+
+ align:start position:0%
+your doctor whether you're going to
+switch to an alternate treatment you
+
+ align:start position:0%
+switch to an alternate treatment you
+ 
+
+ align:start position:0%
+switch to an alternate treatment you
+would still be adhering to that strategy
+
+ align:start position:0%
+would still be adhering to that strategy
+ 
+
+ align:start position:0%
+would still be adhering to that strategy
+even though you quit the comparison here
+
+ align:start position:0%
+even though you quit the comparison here
+ 
+
+ align:start position:0%
+even though you quit the comparison here
+being do not initiate treatment over
+
+ align:start position:0%
+being do not initiate treatment over
+ 
+
+ align:start position:0%
+being do not initiate treatment over
+follow-up
+
+ align:start position:0%
+follow-up
+ 
+
+ align:start position:0%
+follow-up
+likewise unless an indication occurs at
+
+ align:start position:0%
+likewise unless an indication occurs at
+ 
+
+ align:start position:0%
+likewise unless an indication occurs at
+which point you may start treatment and
+
+ align:start position:0%
+which point you may start treatment and
+ 
+
+ align:start position:0%
+which point you may start treatment and
+still be adhering to the strategy so
+
+ align:start position:0%
+still be adhering to the strategy so
+ 
+
+ align:start position:0%
+still be adhering to the strategy so
+we're focusing on these because they're
+
+ align:start position:0%
+we're focusing on these because they're
+ 
+
+ align:start position:0%
+we're focusing on these because they're
+the most clinically relevant and so
+
+ align:start position:0%
+the most clinically relevant and so
+ 
+
+ align:start position:0%
+the most clinically relevant and so
+clinicians encounter these every day in
+
+ align:start position:0%
+clinicians encounter these every day in
+ 
+
+ align:start position:0%
+clinicians encounter these every day in
+practice so when they're making a
+
+ align:start position:0%
+practice so when they're making a
+ 
+
+ align:start position:0%
+practice so when they're making a
+recommendation to their patient about a
+
+ align:start position:0%
+recommendation to their patient about a
+ 
+
+ align:start position:0%
+recommendation to their patient about a
+prevention intervention they're going to
+
+ align:start position:0%
+prevention intervention they're going to
+ 
+
+ align:start position:0%
+prevention intervention they're going to
+be taking into consideration the
+
+ align:start position:0%
+be taking into consideration the
+ 
+
+ align:start position:0%
+be taking into consideration the
+patient's evolving comorbidities or when
+
+ align:start position:0%
+patient's evolving comorbidities or when
+ 
+
+ align:start position:0%
+patient's evolving comorbidities or when
+they're deciding the next screening
+
+ align:start position:0%
+they're deciding the next screening
+ 
+
+ align:start position:0%
+they're deciding the next screening
+interval they'll consider the previous
+
+ align:start position:0%
+interval they'll consider the previous
+ 
+
+ align:start position:0%
+interval they'll consider the previous
+result from the last screening test when
+
+ align:start position:0%
+result from the last screening test when
+ 
+
+ align:start position:0%
+result from the last screening test when
+deciding that likewise for treatment
+
+ align:start position:0%
+deciding that likewise for treatment
+ 
+
+ align:start position:0%
+deciding that likewise for treatment
+deciding whether to keep the patient on
+
+ align:start position:0%
+deciding whether to keep the patient on
+ 
+
+ align:start position:0%
+deciding whether to keep the patient on
+treatment or not is the patient having
+
+ align:start position:0%
+treatment or not is the patient having
+ 
+
+ align:start position:0%
+treatment or not is the patient having
+any changes in symptoms or lab values
+
+ align:start position:0%
+any changes in symptoms or lab values
+ 
+
+ align:start position:0%
+any changes in symptoms or lab values
+that may reflect toxicity so one thing
+
+ align:start position:0%
+that may reflect toxicity so one thing
+ 
+
+ align:start position:0%
+that may reflect toxicity so one thing
+to note is that while many of the
+
+ align:start position:0%
+to note is that while many of the
+ 
+
+ align:start position:0%
+to note is that while many of the
+strategies that you may see in clinical
+
+ align:start position:0%
+strategies that you may see in clinical
+ 
+
+ align:start position:0%
+strategies that you may see in clinical
+guidelines and in clinical practice our
+
+ align:start position:0%
+guidelines and in clinical practice our
+ 
+
+ align:start position:0%
+guidelines and in clinical practice our
+dynamic strategies these may not be the
+
+ align:start position:0%
+dynamic strategies these may not be the
+ 
+
+ align:start position:0%
+dynamic strategies these may not be the
+optimal strategies so maybe what we're
+
+ align:start position:0%
+optimal strategies so maybe what we're
+ 
+
+ align:start position:0%
+optimal strategies so maybe what we're
+recommending and doing is not optimal
+
+ align:start position:0%
+recommending and doing is not optimal
+ 
+
+ align:start position:0%
+recommending and doing is not optimal
+for patients however the optimal
+
+ align:start position:0%
+for patients however the optimal
+ 
+
+ align:start position:0%
+for patients however the optimal
+strategies will be dynamic in some way
+
+ align:start position:0%
+strategies will be dynamic in some way
+ 
+
+ align:start position:0%
+strategies will be dynamic in some way
+in that they will be adapting to
+
+ align:start position:0%
+in that they will be adapting to
+ 
+
+ align:start position:0%
+in that they will be adapting to
+individuals unique and evolving
+
+ align:start position:0%
+individuals unique and evolving
+ 
+
+ align:start position:0%
+individuals unique and evolving
+characteristics so that's why we care
+
+ align:start position:0%
+characteristics so that's why we care
+ 
+
+ align:start position:0%
+characteristics so that's why we care
+about them so what's the problem so one
+
+ align:start position:0%
+about them so what's the problem so one
+ 
+
+ align:start position:0%
+about them so what's the problem so one
+problem deals with something called
+
+ align:start position:0%
+problem deals with something called
+ 
+
+ align:start position:0%
+problem deals with something called
+treatment confounder feedback which you
+
+ align:start position:0%
+treatment confounder feedback which you
+ 
+
+ align:start position:0%
+treatment confounder feedback which you
+may have spoken about in this class so
+
+ align:start position:0%
+may have spoken about in this class so
+ 
+
+ align:start position:0%
+may have spoken about in this class so
+conventional statistical methods cannot
+
+ align:start position:0%
+conventional statistical methods cannot
+ 
+
+ align:start position:0%
+conventional statistical methods cannot
+appropriately compare dynamic treatment
+
+ align:start position:0%
+appropriately compare dynamic treatment
+ 
+
+ align:start position:0%
+appropriately compare dynamic treatment
+strategies in the presence of treatment
+
+ align:start position:0%
+strategies in the presence of treatment
+ 
+
+ align:start position:0%
+strategies in the presence of treatment
+confounder feedback so this is when time
+
+ align:start position:0%
+confounder feedback so this is when time
+ 
+
+ align:start position:0%
+confounder feedback so this is when time
+varying confounders are affected by
+
+ align:start position:0%
+varying confounders are affected by
+ 
+
+ align:start position:0%
+varying confounders are affected by
+previous treatment so if we kind of
+
+ align:start position:0%
+previous treatment so if we kind of
+ 
+
+ align:start position:0%
+previous treatment so if we kind of
+ground this in a concrete example with
+
+ align:start position:0%
+ground this in a concrete example with
+ 
+
+ align:start position:0%
+ground this in a concrete example with
+this causal diagram let's say we're
+
+ align:start position:0%
+this causal diagram let's say we're
+ 
+
+ align:start position:0%
+this causal diagram let's say we're
+interested in s2
+
+ align:start position:0%
+interested in s2
+ 
+
+ align:start position:0%
+interested in s2
+the effect of some intervention a
+
+ align:start position:0%
+the effect of some intervention a
+ 
+
+ align:start position:0%
+the effect of some intervention a
+vasopressors or it could be IV fluids on
+
+ align:start position:0%
+vasopressors or it could be IV fluids on
+ 
+
+ align:start position:0%
+vasopressors or it could be IV fluids on
+some outcome y which we'll call survival
+
+ align:start position:0%
+some outcome y which we'll call survival
+ 
+
+ align:start position:0%
+some outcome y which we'll call survival
+here we know that vasopressors affect
+
+ align:start position:0%
+here we know that vasopressors affect
+ 
+
+ align:start position:0%
+here we know that vasopressors affect
+blood pressure and blood pressure will
+
+ align:start position:0%
+blood pressure and blood pressure will
+ 
+
+ align:start position:0%
+blood pressure and blood pressure will
+affect subsequent decisions to treat
+
+ align:start position:0%
+affect subsequent decisions to treat
+ 
+
+ align:start position:0%
+affect subsequent decisions to treat
+with vasopressors we also know that
+
+ align:start position:0%
+with vasopressors we also know that
+ 
+
+ align:start position:0%
+with vasopressors we also know that
+hypotension so again blood pressure l1
+
+ align:start position:0%
+hypotension so again blood pressure l1
+ 
+
+ align:start position:0%
+hypotension so again blood pressure l1
+affects survival based on our clinical
+
+ align:start position:0%
+affects survival based on our clinical
+ 
+
+ align:start position:0%
+affects survival based on our clinical
+knowledge and then in this dag we also
+
+ align:start position:0%
+knowledge and then in this dag we also
+ 
+
+ align:start position:0%
+knowledge and then in this dag we also
+have the node U which represents disease
+
+ align:start position:0%
+have the node U which represents disease
+ 
+
+ align:start position:0%
+have the node U which represents disease
+severity so these could be potentially
+
+ align:start position:0%
+severity so these could be potentially
+ 
+
+ align:start position:0%
+severity so these could be potentially
+unmeasured markers of disease severity
+
+ align:start position:0%
+unmeasured markers of disease severity
+ 
+
+ align:start position:0%
+unmeasured markers of disease severity
+that are affecting your blood pressure
+
+ align:start position:0%
+that are affecting your blood pressure
+ 
+
+ align:start position:0%
+that are affecting your blood pressure
+and also affecting your probability of
+
+ align:start position:0%
+and also affecting your probability of
+ 
+
+ align:start position:0%
+and also affecting your probability of
+survival so if we're interested in
+
+ align:start position:0%
+survival so if we're interested in
+ 
+
+ align:start position:0%
+survival so if we're interested in
+estimating the effect of a sustained
+
+ align:start position:0%
+estimating the effect of a sustained
+ 
+
+ align:start position:0%
+estimating the effect of a sustained
+treatment strategy then we want to know
+
+ align:start position:0%
+treatment strategy then we want to know
+ 
+
+ align:start position:0%
+treatment strategy then we want to know
+something about the total effective
+
+ align:start position:0%
+something about the total effective
+ 
+
+ align:start position:0%
+something about the total effective
+treatment at all time points we can see
+
+ align:start position:0%
+treatment at all time points we can see
+ 
+
+ align:start position:0%
+treatment at all time points we can see
+that l1 here is a confounder for the
+
+ align:start position:0%
+that l1 here is a confounder for the
+ 
+
+ align:start position:0%
+that l1 here is a confounder for the
+effect of a1 on Y so we have to do
+
+ align:start position:0%
+effect of a1 on Y so we have to do
+ 
+
+ align:start position:0%
+effect of a1 on Y so we have to do
+something to adjust for that and if we
+
+ align:start position:0%
+something to adjust for that and if we
+ 
+
+ align:start position:0%
+something to adjust for that and if we
+were to apply a conventional statistical
+
+ align:start position:0%
+were to apply a conventional statistical
+ 
+
+ align:start position:0%
+were to apply a conventional statistical
+method we would essentially be
+
+ align:start position:0%
+method we would essentially be
+ 
+
+ align:start position:0%
+method we would essentially be
+conditioning on a Collider and inducing
+
+ align:start position:0%
+conditioning on a Collider and inducing
+ 
+
+ align:start position:0%
+conditioning on a Collider and inducing
+a selection bias so an open path from a
+
+ align:start position:0%
+a selection bias so an open path from a
+ 
+
+ align:start position:0%
+a selection bias so an open path from a
+0 to L 1 to u 2 y what's the consequence
+
+ align:start position:0%
+0 to L 1 to u 2 y what's the consequence
+ 
+
+ align:start position:0%
+0 to L 1 to u 2 y what's the consequence
+of this if we look in our data set we
+
+ align:start position:0%
+of this if we look in our data set we
+ 
+
+ align:start position:0%
+of this if we look in our data set we
+may see an association between a and Y
+
+ align:start position:0%
+may see an association between a and Y
+ 
+
+ align:start position:0%
+may see an association between a and Y
+but that Association is not because
+
+ align:start position:0%
+but that Association is not because
+ 
+
+ align:start position:0%
+but that Association is not because
+there's necessarily an effective a on Y
+
+ align:start position:0%
+there's necessarily an effective a on Y
+ 
+
+ align:start position:0%
+there's necessarily an effective a on Y
+it might not be causal it may be due to
+
+ align:start position:0%
+it might not be causal it may be due to
+ 
+
+ align:start position:0%
+it might not be causal it may be due to
+this selection bias that we created so
+
+ align:start position:0%
+this selection bias that we created so
+ 
+
+ align:start position:0%
+this selection bias that we created so
+this is the problem and so in these
+
+ align:start position:0%
+this is the problem and so in these
+ 
+
+ align:start position:0%
+this is the problem and so in these
+cases we need a special type of method
+
+ align:start position:0%
+cases we need a special type of method
+ 
+
+ align:start position:0%
+cases we need a special type of method
+that can handle these settings and so a
+
+ align:start position:0%
+that can handle these settings and so a
+ 
+
+ align:start position:0%
+that can handle these settings and so a
+class of methods that was designed
+
+ align:start position:0%
+class of methods that was designed
+ 
+
+ align:start position:0%
+class of methods that was designed
+specifically to handle this is G methods
+
+ align:start position:0%
+specifically to handle this is G methods
+ 
+
+ align:start position:0%
+specifically to handle this is G methods
+and so these are sometimes referred to
+
+ align:start position:0%
+and so these are sometimes referred to
+ 
+
+ align:start position:0%
+and so these are sometimes referred to
+as causal methods they've been developed
+
+ align:start position:0%
+as causal methods they've been developed
+ 
+
+ align:start position:0%
+as causal methods they've been developed
+by Jamie Robbins and colleagues and
+
+ align:start position:0%
+by Jamie Robbins and colleagues and
+ 
+
+ align:start position:0%
+by Jamie Robbins and colleagues and
+collaborators since 1986 and they
+
+ align:start position:0%
+collaborators since 1986 and they
+ 
+
+ align:start position:0%
+collaborators since 1986 and they
+include the parametric G formula G
+
+ align:start position:0%
+include the parametric G formula G
+ 
+
+ align:start position:0%
+include the parametric G formula G
+estimation of structural nested models
+
+ align:start position:0%
+estimation of structural nested models
+ 
+
+ align:start position:0%
+estimation of structural nested models
+and inverse probability weighting of
+
+ align:start position:0%
+and inverse probability weighting of
+ 
+
+ align:start position:0%
+and inverse probability weighting of
+marginal structural models
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in my research what I do is I combine
+
+ align:start position:0%
+so in my research what I do is I combine
+ 
+
+ align:start position:0%
+so in my research what I do is I combine
+G methods with large longitudinal
+
+ align:start position:0%
+G methods with large longitudinal
+ 
+
+ align:start position:0%
+G methods with large longitudinal
+databases to try to evaluate dynamic
+
+ align:start position:0%
+databases to try to evaluate dynamic
+ 
+
+ align:start position:0%
+databases to try to evaluate dynamic
+treatment strategies so I'm particularly
+
+ align:start position:0%
+treatment strategies so I'm particularly
+ 
+
+ align:start position:0%
+treatment strategies so I'm particularly
+interested in bringing these methods to
+
+ align:start position:0%
+interested in bringing these methods to
+ 
+
+ align:start position:0%
+interested in bringing these methods to
+cancer research because they haven't
+
+ align:start position:0%
+cancer research because they haven't
+ 
+
+ align:start position:0%
+cancer research because they haven't
+been applied much there so a lot of my
+
+ align:start position:0%
+been applied much there so a lot of my
+ 
+
+ align:start position:0%
+been applied much there so a lot of my
+research questions are focused on
+
+ align:start position:0%
+research questions are focused on
+ 
+
+ align:start position:0%
+research questions are focused on
+answering questions like how and when
+
+ align:start position:0%
+answering questions like how and when
+ 
+
+ align:start position:0%
+answering questions like how and when
+can we intervene to best prevent detect
+
+ align:start position:0%
+can we intervene to best prevent detect
+ 
+
+ align:start position:0%
+can we intervene to best prevent detect
+and treat cancer and so I'd like to
+
+ align:start position:0%
+and treat cancer and so I'd like to
+ 
+
+ align:start position:0%
+and treat cancer and so I'd like to
+share one example with you which focused
+
+ align:start position:0%
+share one example with you which focused
+ 
+
+ align:start position:0%
+share one example with you which focused
+on evaluating the effect of adhering to
+
+ align:start position:0%
+on evaluating the effect of adhering to
+ 
+
+ align:start position:0%
+on evaluating the effect of adhering to
+guideline based physical activity
+
+ align:start position:0%
+guideline based physical activity
+ 
+
+ align:start position:0%
+guideline based physical activity
+interventions on survival among men with
+
+ align:start position:0%
+interventions on survival among men with
+ 
+
+ align:start position:0%
+interventions on survival among men with
+prostate cancer so the motivation for
+
+ align:start position:0%
+prostate cancer so the motivation for
+ 
+
+ align:start position:0%
+prostate cancer so the motivation for
+this study there's a large clinical
+
+ align:start position:0%
+this study there's a large clinical
+ 
+
+ align:start position:0%
+this study there's a large clinical
+organization ASCO the American Society
+
+ align:start position:0%
+organization ASCO the American Society
+ 
+
+ align:start position:0%
+organization ASCO the American Society
+of Clinical Oncology but it actually
+
+ align:start position:0%
+of Clinical Oncology but it actually
+ 
+
+ align:start position:0%
+of Clinical Oncology but it actually
+called for randomized trials to generate
+
+ align:start position:0%
+called for randomized trials to generate
+ 
+
+ align:start position:0%
+called for randomized trials to generate
+these estimates for several cancers
+
+ align:start position:0%
+these estimates for several cancers
+ 
+
+ align:start position:0%
+these estimates for several cancers
+thinking with prostate cancer is it's a
+
+ align:start position:0%
+thinking with prostate cancer is it's a
+ 
+
+ align:start position:0%
+thinking with prostate cancer is it's a
+very slowly progressing disease so the
+
+ align:start position:0%
+very slowly progressing disease so the
+ 
+
+ align:start position:0%
+very slowly progressing disease so the
+feasibility of doing a trial to evaluate
+
+ align:start position:0%
+feasibility of doing a trial to evaluate
+ 
+
+ align:start position:0%
+feasibility of doing a trial to evaluate
+this is very limited the trial would
+
+ align:start position:0%
+this is very limited the trial would
+ 
+
+ align:start position:0%
+this is very limited the trial would
+have to be ten years long probably so
+
+ align:start position:0%
+have to be ten years long probably so
+ 
+
+ align:start position:0%
+have to be ten years long probably so
+given that given the absence of this
+
+ align:start position:0%
+given that given the absence of this
+ 
+
+ align:start position:0%
+given that given the absence of this
+randomized evidence we did the next best
+
+ align:start position:0%
+randomized evidence we did the next best
+ 
+
+ align:start position:0%
+randomized evidence we did the next best
+thing that we could do to generate this
+
+ align:start position:0%
+thing that we could do to generate this
+ 
+
+ align:start position:0%
+thing that we could do to generate this
+estimate which was combine high-quality
+
+ align:start position:0%
+estimate which was combine high-quality
+ 
+
+ align:start position:0%
+estimate which was combine high-quality
+observational data with you know
+
+ align:start position:0%
+observational data with you know
+ 
+
+ align:start position:0%
+observational data with you know
+advanced epi methods in this case the
+
+ align:start position:0%
+advanced epi methods in this case the
+ 
+
+ align:start position:0%
+advanced epi methods in this case the
+parametric G formula and so we leveraged
+
+ align:start position:0%
+parametric G formula and so we leveraged
+ 
+
+ align:start position:0%
+parametric G formula and so we leveraged
+data from the health professionals
+
+ align:start position:0%
+data from the health professionals
+ 
+
+ align:start position:0%
+data from the health professionals
+follow-up study which is a well
+
+ align:start position:0%
+follow-up study which is a well
+ 
+
+ align:start position:0%
+follow-up study which is a well
+characterized prospective cohort study
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in these cases there's a three step
+
+ align:start position:0%
+so in these cases there's a three step
+ 
+
+ align:start position:0%
+so in these cases there's a three step
+process that we take to extract the most
+
+ align:start position:0%
+process that we take to extract the most
+ 
+
+ align:start position:0%
+process that we take to extract the most
+meaningful and actionable insights from
+
+ align:start position:0%
+meaningful and actionable insights from
+ 
+
+ align:start position:0%
+meaningful and actionable insights from
+observational data so the first thing
+
+ align:start position:0%
+observational data so the first thing
+ 
+
+ align:start position:0%
+observational data so the first thing
+that we do is we specify the protocol of
+
+ align:start position:0%
+that we do is we specify the protocol of
+ 
+
+ align:start position:0%
+that we do is we specify the protocol of
+the target trial that we would have
+
+ align:start position:0%
+the target trial that we would have
+ 
+
+ align:start position:0%
+the target trial that we would have
+liked to conduct had it been feasible
+
+ align:start position:0%
+liked to conduct had it been feasible
+ 
+
+ align:start position:0%
+liked to conduct had it been feasible
+the second thing we do is we make sure
+
+ align:start position:0%
+the second thing we do is we make sure
+ 
+
+ align:start position:0%
+the second thing we do is we make sure
+that we measure enough covariance to
+
+ align:start position:0%
+that we measure enough covariance to
+ 
+
+ align:start position:0%
+that we measure enough covariance to
+approximately adjust for confounding and
+
+ align:start position:0%
+approximately adjust for confounding and
+ 
+
+ align:start position:0%
+approximately adjust for confounding and
+achieve conditional exchangeability and
+
+ align:start position:0%
+achieve conditional exchangeability and
+ 
+
+ align:start position:0%
+achieve conditional exchangeability and
+then the third thing we do is we apply
+
+ align:start position:0%
+then the third thing we do is we apply
+ 
+
+ align:start position:0%
+then the third thing we do is we apply
+an appropriate method to compare the
+
+ align:start position:0%
+an appropriate method to compare the
+ 
+
+ align:start position:0%
+an appropriate method to compare the
+specified treatment strategies under
+
+ align:start position:0%
+specified treatment strategies under
+ 
+
+ align:start position:0%
+specified treatment strategies under
+this assumption
+
+ align:start position:0%
+this assumption
+ 
+
+ align:start position:0%
+this assumption
+conditional exchangeability and so in
+
+ align:start position:0%
+conditional exchangeability and so in
+ 
+
+ align:start position:0%
+conditional exchangeability and so in
+this case eligible men for this study
+
+ align:start position:0%
+this case eligible men for this study
+ 
+
+ align:start position:0%
+this case eligible men for this study
+had been diagnosed with non metastatic
+
+ align:start position:0%
+had been diagnosed with non metastatic
+ 
+
+ align:start position:0%
+had been diagnosed with non metastatic
+prostate cancer and a baseline they were
+
+ align:start position:0%
+prostate cancer and a baseline they were
+ 
+
+ align:start position:0%
+prostate cancer and a baseline they were
+free of cardiovascular and neurologic
+
+ align:start position:0%
+free of cardiovascular and neurologic
+ 
+
+ align:start position:0%
+free of cardiovascular and neurologic
+conditions that may limit physical
+
+ align:start position:0%
+conditions that may limit physical
+ 
+
+ align:start position:0%
+conditions that may limit physical
+ability for the treatment strategies men
+
+ align:start position:0%
+ability for the treatment strategies men
+ 
+
+ align:start position:0%
+ability for the treatment strategies men
+were to initiate one of six physical
+
+ align:start position:0%
+were to initiate one of six physical
+ 
+
+ align:start position:0%
+were to initiate one of six physical
+activity strategies at diagnosis and
+
+ align:start position:0%
+activity strategies at diagnosis and
+ 
+
+ align:start position:0%
+activity strategies at diagnosis and
+continue it over follow-up until the
+
+ align:start position:0%
+continue it over follow-up until the
+ 
+
+ align:start position:0%
+continue it over follow-up until the
+development of a condition limiting
+
+ align:start position:0%
+development of a condition limiting
+ 
+
+ align:start position:0%
+development of a condition limiting
+physical activity so this is what made
+
+ align:start position:0%
+physical activity so this is what made
+ 
+
+ align:start position:0%
+physical activity so this is what made
+the strategies dynamic the intervention
+
+ align:start position:0%
+the strategies dynamic the intervention
+ 
+
+ align:start position:0%
+the strategies dynamic the intervention
+over time depended on these evolving
+
+ align:start position:0%
+over time depended on these evolving
+ 
+
+ align:start position:0%
+over time depended on these evolving
+conditions and so just to note we pre
+
+ align:start position:0%
+conditions and so just to note we pre
+ 
+
+ align:start position:0%
+conditions and so just to note we pre
+specified these strategies that we were
+
+ align:start position:0%
+specified these strategies that we were
+ 
+
+ align:start position:0%
+specified these strategies that we were
+evaluating as well as the conditions men
+
+ align:start position:0%
+evaluating as well as the conditions men
+ 
+
+ align:start position:0%
+evaluating as well as the conditions men
+were followed until diagnosis until
+
+ align:start position:0%
+were followed until diagnosis until
+ 
+
+ align:start position:0%
+were followed until diagnosis until
+death and to follow-up ten years after
+
+ align:start position:0%
+death and to follow-up ten years after
+ 
+
+ align:start position:0%
+death and to follow-up ten years after
+diagnosis or administrative end to
+
+ align:start position:0%
+diagnosis or administrative end to
+ 
+
+ align:start position:0%
+diagnosis or administrative end to
+follow-up which ever happened first our
+
+ align:start position:0%
+follow-up which ever happened first our
+ 
+
+ align:start position:0%
+follow-up which ever happened first our
+outcome of interest was all cause
+
+ align:start position:0%
+outcome of interest was all cause
+ 
+
+ align:start position:0%
+outcome of interest was all cause
+mortality within ten years and we were
+
+ align:start position:0%
+mortality within ten years and we were
+ 
+
+ align:start position:0%
+mortality within ten years and we were
+interested in estimating the per
+
+ align:start position:0%
+interested in estimating the per
+ 
+
+ align:start position:0%
+interested in estimating the per
+protocol effect of not just initiating
+
+ align:start position:0%
+protocol effect of not just initiating
+ 
+
+ align:start position:0%
+protocol effect of not just initiating
+these strategies but adhering to them
+
+ align:start position:0%
+these strategies but adhering to them
+ 
+
+ align:start position:0%
+these strategies but adhering to them
+over follow-up and again we applied the
+
+ align:start position:0%
+over follow-up and again we applied the
+ 
+
+ align:start position:0%
+over follow-up and again we applied the
+parametric G formula so I think you've
+
+ align:start position:0%
+parametric G formula so I think you've
+ 
+
+ align:start position:0%
+parametric G formula so I think you've
+already heard about the G formula in a
+
+ align:start position:0%
+already heard about the G formula in a
+ 
+
+ align:start position:0%
+already heard about the G formula in a
+previous lecture possibly in a slightly
+
+ align:start position:0%
+previous lecture possibly in a slightly
+ 
+
+ align:start position:0%
+previous lecture possibly in a slightly
+different way so I'll I won't spend too
+
+ align:start position:0%
+different way so I'll I won't spend too
+ 
+
+ align:start position:0%
+different way so I'll I won't spend too
+much time on this so the G formula
+
+ align:start position:0%
+much time on this so the G formula
+ 
+
+ align:start position:0%
+much time on this so the G formula
+essentially the way I think about it is
+
+ align:start position:0%
+essentially the way I think about it is
+ 
+
+ align:start position:0%
+essentially the way I think about it is
+a generalization of standardization to
+
+ align:start position:0%
+a generalization of standardization to
+ 
+
+ align:start position:0%
+a generalization of standardization to
+time varying exposures and confounders
+
+ align:start position:0%
+time varying exposures and confounders
+ 
+
+ align:start position:0%
+time varying exposures and confounders
+so it's basically a weighted average of
+
+ align:start position:0%
+so it's basically a weighted average of
+ 
+
+ align:start position:0%
+so it's basically a weighted average of
+risks where you can think of the weights
+
+ align:start position:0%
+risks where you can think of the weights
+ 
+
+ align:start position:0%
+risks where you can think of the weights
+being the probability density functions
+
+ align:start position:0%
+being the probability density functions
+ 
+
+ align:start position:0%
+being the probability density functions
+of the time varying confounders which we
+
+ align:start position:0%
+of the time varying confounders which we
+ 
+
+ align:start position:0%
+of the time varying confounders which we
+estimate using parametric regression
+
+ align:start position:0%
+estimate using parametric regression
+ 
+
+ align:start position:0%
+estimate using parametric regression
+models and we approximate the weighted
+
+ align:start position:0%
+models and we approximate the weighted
+ 
+
+ align:start position:0%
+models and we approximate the weighted
+average using Monte Carlo simulation so
+
+ align:start position:0%
+average using Monte Carlo simulation so
+ 
+
+ align:start position:0%
+average using Monte Carlo simulation so
+practically how do we do this so the
+
+ align:start position:0%
+practically how do we do this so the
+ 
+
+ align:start position:0%
+practically how do we do this so the
+first thing we do is we fit parametric
+
+ align:start position:0%
+first thing we do is we fit parametric
+ 
+
+ align:start position:0%
+first thing we do is we fit parametric
+regression models for all of the
+
+ align:start position:0%
+regression models for all of the
+ 
+
+ align:start position:0%
+regression models for all of the
+variables that we're going to be
+
+ align:start position:0%
+variables that we're going to be
+ 
+
+ align:start position:0%
+variables that we're going to be
+studying so for treatment confounders
+
+ align:start position:0%
+studying so for treatment confounders
+ 
+
+ align:start position:0%
+studying so for treatment confounders
+and death at each follow-up time the
+
+ align:start position:0%
+and death at each follow-up time the
+ 
+
+ align:start position:0%
+and death at each follow-up time the
+next thing we do is Monte Carlo
+
+ align:start position:0%
+next thing we do is Monte Carlo
+ 
+
+ align:start position:0%
+next thing we do is Monte Carlo
+simulation where essentially what we
+
+ align:start position:0%
+simulation where essentially what we
+ 
+
+ align:start position:0%
+simulation where essentially what we
+want to do is simulate the outcome
+
+ align:start position:0%
+want to do is simulate the outcome
+ 
+
+ align:start position:0%
+want to do is simulate the outcome
+distribution under each treatment
+
+ align:start position:0%
+distribution under each treatment
+ 
+
+ align:start position:0%
+distribution under each treatment
+strategy that we're interested in
+
+ align:start position:0%
+strategy that we're interested in
+ 
+
+ align:start position:0%
+strategy that we're interested in
+and then we bootstrap the confidence
+
+ align:start position:0%
+and then we bootstrap the confidence
+ 
+
+ align:start position:0%
+and then we bootstrap the confidence
+intervals so I'd like to show you kind
+
+ align:start position:0%
+intervals so I'd like to show you kind
+ 
+
+ align:start position:0%
+intervals so I'd like to show you kind
+of in a schematic what this looks like
+
+ align:start position:0%
+of in a schematic what this looks like
+ 
+
+ align:start position:0%
+of in a schematic what this looks like
+because it might be a little bit easier
+
+ align:start position:0%
+because it might be a little bit easier
+ 
+
+ align:start position:0%
+because it might be a little bit easier
+to see so again the idea is we're gonna
+
+ align:start position:0%
+to see so again the idea is we're gonna
+ 
+
+ align:start position:0%
+to see so again the idea is we're gonna
+make copies of our data set where in
+
+ align:start position:0%
+make copies of our data set where in
+ 
+
+ align:start position:0%
+make copies of our data set where in
+each copy everyone is adhering to the
+
+ align:start position:0%
+each copy everyone is adhering to the
+ 
+
+ align:start position:0%
+each copy everyone is adhering to the
+strategy that we're focusing on in that
+
+ align:start position:0%
+strategy that we're focusing on in that
+ 
+
+ align:start position:0%
+strategy that we're focusing on in that
+copy so how do we construct each of
+
+ align:start position:0%
+copy so how do we construct each of
+ 
+
+ align:start position:0%
+copy so how do we construct each of
+these copies of the data set we have to
+
+ align:start position:0%
+these copies of the data set we have to
+ 
+
+ align:start position:0%
+these copies of the data set we have to
+build them each from the ground up
+
+ align:start position:0%
+build them each from the ground up
+ 
+
+ align:start position:0%
+build them each from the ground up
+starting with time zero so the values of
+
+ align:start position:0%
+starting with time zero so the values of
+ 
+
+ align:start position:0%
+starting with time zero so the values of
+all of the time varying covariates at
+
+ align:start position:0%
+all of the time varying covariates at
+ 
+
+ align:start position:0%
+all of the time varying covariates at
+time zero are sampled from their
+
+ align:start position:0%
+time zero are sampled from their
+ 
+
+ align:start position:0%
+time zero are sampled from their
+empirical distribution so these are
+
+ align:start position:0%
+empirical distribution so these are
+ 
+
+ align:start position:0%
+empirical distribution so these are
+actually observed values of the
+
+ align:start position:0%
+actually observed values of the
+ 
+
+ align:start position:0%
+actually observed values of the
+covariance how do we get the values at
+
+ align:start position:0%
+covariance how do we get the values at
+ 
+
+ align:start position:0%
+covariance how do we get the values at
+the next time point we use the
+
+ align:start position:0%
+the next time point we use the
+ 
+
+ align:start position:0%
+the next time point we use the
+parametric regression models that I
+
+ align:start position:0%
+parametric regression models that I
+ 
+
+ align:start position:0%
+parametric regression models that I
+mentioned that we fit in step one then
+
+ align:start position:0%
+mentioned that we fit in step one then
+ 
+
+ align:start position:0%
+mentioned that we fit in step one then
+what we do is we force the level of the
+
+ align:start position:0%
+what we do is we force the level of the
+ 
+
+ align:start position:0%
+what we do is we force the level of the
+intervention variable to be whatever was
+
+ align:start position:0%
+intervention variable to be whatever was
+ 
+
+ align:start position:0%
+intervention variable to be whatever was
+specified by that intervention strategy
+
+ align:start position:0%
+specified by that intervention strategy
+ 
+
+ align:start position:0%
+specified by that intervention strategy
+and then we estimate the risk of the
+
+ align:start position:0%
+and then we estimate the risk of the
+ 
+
+ align:start position:0%
+and then we estimate the risk of the
+outcome at each time period given these
+
+ align:start position:0%
+outcome at each time period given these
+ 
+
+ align:start position:0%
+outcome at each time period given these
+variables again using the parametric
+
+ align:start position:0%
+variables again using the parametric
+ 
+
+ align:start position:0%
+variables again using the parametric
+regression model for the outcome now and
+
+ align:start position:0%
+regression model for the outcome now and
+ 
+
+ align:start position:0%
+regression model for the outcome now and
+so we repeat this over all time periods
+
+ align:start position:0%
+so we repeat this over all time periods
+ 
+
+ align:start position:0%
+so we repeat this over all time periods
+to estimate a cumulative risk under that
+
+ align:start position:0%
+to estimate a cumulative risk under that
+ 
+
+ align:start position:0%
+to estimate a cumulative risk under that
+strategy which is taken as the average
+
+ align:start position:0%
+strategy which is taken as the average
+ 
+
+ align:start position:0%
+strategy which is taken as the average
+of the subject specific risks so this is
+
+ align:start position:0%
+of the subject specific risks so this is
+ 
+
+ align:start position:0%
+of the subject specific risks so this is
+what I'm doing this is kind of under the
+
+ align:start position:0%
+what I'm doing this is kind of under the
+ 
+
+ align:start position:0%
+what I'm doing this is kind of under the
+hood what's going on with this with this
+
+ align:start position:0%
+hood what's going on with this with this
+ 
+
+ align:start position:0%
+hood what's going on with this with this
+method so you first estimate the Markov
+
+ align:start position:0%
+method so you first estimate the Markov
+ 
+
+ align:start position:0%
+method so you first estimate the Markov
+decision process mm-hmm which allows you
+
+ align:start position:0%
+decision process mm-hmm which allows you
+ 
+
+ align:start position:0%
+decision process mm-hmm which allows you
+in essence to simulate from the
+
+ align:start position:0%
+in essence to simulate from the
+ 
+
+ align:start position:0%
+in essence to simulate from the
+underlying data distribution so you know
+
+ align:start position:0%
+underlying data distribution so you know
+ 
+
+ align:start position:0%
+underlying data distribution so you know
+that probability of the sort of next
+
+ align:start position:0%
+that probability of the sort of next
+ 
+
+ align:start position:0%
+that probability of the sort of next
+sequence of observations given the
+
+ align:start position:0%
+sequence of observations given the
+ 
+
+ align:start position:0%
+sequence of observations given the
+previous sequence and action and
+
+ align:start position:0%
+previous sequence and action and
+ 
+
+ align:start position:0%
+previous sequence and action and
+previous actions and then with that then
+
+ align:start position:0%
+previous actions and then with that then
+ 
+
+ align:start position:0%
+previous actions and then with that then
+you could sort of you could you could
+
+ align:start position:0%
+you could sort of you could you could
+ 
+
+ align:start position:0%
+you could sort of you could you could
+then intervene and simulate for so that
+
+ align:start position:0%
+then intervene and simulate for so that
+ 
+
+ align:start position:0%
+then intervene and simulate for so that
+was if you remember graduate gave you
+
+ align:start position:0%
+was if you remember graduate gave you
+ 
+
+ align:start position:0%
+was if you remember graduate gave you
+three different buckets of approaches
+
+ align:start position:0%
+three different buckets of approaches
+ 
+
+ align:start position:0%
+three different buckets of approaches
+and then he focused on the middle one
+
+ align:start position:0%
+and then he focused on the middle one
+ 
+
+ align:start position:0%
+and then he focused on the middle one
+this is the leftmost problem
+
+ align:start position:0%
+this is the leftmost problem
+ 
+
+ align:start position:0%
+this is the leftmost problem
+I have that right so we didn't talk
+
+ align:start position:0%
+I have that right so we didn't talk
+ 
+
+ align:start position:0%
+I have that right so we didn't talk
+about yes but it's very sensible what
+
+ align:start position:0%
+about yes but it's very sensible what
+ 
+
+ align:start position:0%
+about yes but it's very sensible what
+side oh it seems very hard yeah so that
+
+ align:start position:0%
+side oh it seems very hard yeah so that
+ 
+
+ align:start position:0%
+side oh it seems very hard yeah so that
+is a challenge that is the hardest part
+
+ align:start position:0%
+is a challenge that is the hardest part
+ 
+
+ align:start position:0%
+is a challenge that is the hardest part
+about this mm-hm and it's relying on a
+
+ align:start position:0%
+about this mm-hm and it's relying on a
+ 
+
+ align:start position:0%
+about this mm-hm and it's relying on a
+lot of assumptions yeah so the primary
+
+ align:start position:0%
+lot of assumptions yeah so the primary
+ 
+
+ align:start position:0%
+lot of assumptions yeah so the primary
+results that kind of come out after we
+
+ align:start position:0%
+results that kind of come out after we
+ 
+
+ align:start position:0%
+results that kind of come out after we
+do all of this so this is the estimated
+
+ align:start position:0%
+do all of this so this is the estimated
+ 
+
+ align:start position:0%
+do all of this so this is the estimated
+risk of all-cause mortality under
+
+ align:start position:0%
+risk of all-cause mortality under
+ 
+
+ align:start position:0%
+risk of all-cause mortality under
+several physical activity interventions
+
+ align:start position:0%
+several physical activity interventions
+ 
+
+ align:start position:0%
+several physical activity interventions
+so I'm not gonna focus too much on the
+
+ align:start position:0%
+so I'm not gonna focus too much on the
+ 
+
+ align:start position:0%
+so I'm not gonna focus too much on the
+results I want to focus on two main kind
+
+ align:start position:0%
+results I want to focus on two main kind
+ 
+
+ align:start position:0%
+results I want to focus on two main kind
+of takeaways from this slide one thing
+
+ align:start position:0%
+of takeaways from this slide one thing
+ 
+
+ align:start position:0%
+of takeaways from this slide one thing
+to emphasize is we pre specified the
+
+ align:start position:0%
+to emphasize is we pre specified the
+ 
+
+ align:start position:0%
+to emphasize is we pre specified the
+weekly duration of physical activity or
+
+ align:start position:0%
+weekly duration of physical activity or
+ 
+
+ align:start position:0%
+weekly duration of physical activity or
+you can think of this like the dose of
+
+ align:start position:0%
+you can think of this like the dose of
+ 
+
+ align:start position:0%
+you can think of this like the dose of
+the intervention we pre specified that
+
+ align:start position:0%
+the intervention we pre specified that
+ 
+
+ align:start position:0%
+the intervention we pre specified that
+and this was based on current guidelines
+
+ align:start position:0%
+and this was based on current guidelines
+ 
+
+ align:start position:0%
+and this was based on current guidelines
+so the third row of each band we did
+
+ align:start position:0%
+so the third row of each band we did
+ 
+
+ align:start position:0%
+so the third row of each band we did
+look at some dose or level beyond the
+
+ align:start position:0%
+look at some dose or level beyond the
+ 
+
+ align:start position:0%
+look at some dose or level beyond the
+guidelines to see if there might be
+
+ align:start position:0%
+guidelines to see if there might be
+ 
+
+ align:start position:0%
+guidelines to see if there might be
+additional survival benefits but these
+
+ align:start position:0%
+additional survival benefits but these
+ 
+
+ align:start position:0%
+additional survival benefits but these
+were all pre specified we also pre
+
+ align:start position:0%
+were all pre specified we also pre
+ 
+
+ align:start position:0%
+were all pre specified we also pre
+specified all of the time varying
+
+ align:start position:0%
+specified all of the time varying
+ 
+
+ align:start position:0%
+specified all of the time varying
+covariates that made these strategies
+
+ align:start position:0%
+covariates that made these strategies
+ 
+
+ align:start position:0%
+covariates that made these strategies
+dynamic so I mentioned that men were
+
+ align:start position:0%
+dynamic so I mentioned that men were
+ 
+
+ align:start position:0%
+dynamic so I mentioned that men were
+excused from following the recommended
+
+ align:start position:0%
+excused from following the recommended
+ 
+
+ align:start position:0%
+excused from following the recommended
+physical activity levels if they
+
+ align:start position:0%
+physical activity levels if they
+ 
+
+ align:start position:0%
+physical activity levels if they
+developed one of these listed conditions
+
+ align:start position:0%
+developed one of these listed conditions
+ 
+
+ align:start position:0%
+developed one of these listed conditions
+metastasis and my stroke etc we pre
+
+ align:start position:0%
+metastasis and my stroke etc we pre
+ 
+
+ align:start position:0%
+metastasis and my stroke etc we pre
+specified all of those it's possible
+
+ align:start position:0%
+specified all of those it's possible
+ 
+
+ align:start position:0%
+specified all of those it's possible
+that maybe you know a different
+
+ align:start position:0%
+that maybe you know a different
+ 
+
+ align:start position:0%
+that maybe you know a different
+dependence on a different time varying
+
+ align:start position:0%
+dependence on a different time varying
+ 
+
+ align:start position:0%
+dependence on a different time varying
+ovarian may have led to a more optimal
+
+ align:start position:0%
+ovarian may have led to a more optimal
+ 
+
+ align:start position:0%
+ovarian may have led to a more optimal
+strategy there was a lot that remained
+
+ align:start position:0%
+strategy there was a lot that remained
+ 
+
+ align:start position:0%
+strategy there was a lot that remained
+unexplored so we did a lot of
+
+ align:start position:0%
+unexplored so we did a lot of
+ 
+
+ align:start position:0%
+unexplored so we did a lot of
+sensitivity analyses as part of this
+
+ align:start position:0%
+sensitivity analyses as part of this
+ 
+
+ align:start position:0%
+sensitivity analyses as part of this
+project I'd like to focus though on the
+
+ align:start position:0%
+project I'd like to focus though on the
+ 
+
+ align:start position:0%
+project I'd like to focus though on the
+sensitivity analyses that we did for
+
+ align:start position:0%
+sensitivity analyses that we did for
+ 
+
+ align:start position:0%
+sensitivity analyses that we did for
+potential unmeasured confounding by
+
+ align:start position:0%
+potential unmeasured confounding by
+ 
+
+ align:start position:0%
+potential unmeasured confounding by
+chronic disease that may be severe
+
+ align:start position:0%
+chronic disease that may be severe
+ 
+
+ align:start position:0%
+chronic disease that may be severe
+enough to affect both physical activity
+
+ align:start position:0%
+enough to affect both physical activity
+ 
+
+ align:start position:0%
+enough to affect both physical activity
+and survival and so the G formula is
+
+ align:start position:0%
+and survival and so the G formula is
+ 
+
+ align:start position:0%
+and survival and so the G formula is
+actually providing a natural way to at
+
+ align:start position:0%
+actually providing a natural way to at
+ 
+
+ align:start position:0%
+actually providing a natural way to at
+least partly address this by estimating
+
+ align:start position:0%
+least partly address this by estimating
+ 
+
+ align:start position:0%
+least partly address this by estimating
+the risk of these physical activity
+
+ align:start position:0%
+the risk of these physical activity
+ 
+
+ align:start position:0%
+the risk of these physical activity
+interventions
+
+ align:start position:0%
+interventions
+ 
+
+ align:start position:0%
+interventions
+that are at each time point t only
+
+ align:start position:0%
+that are at each time point t only
+ 
+
+ align:start position:0%
+that are at each time point t only
+applied to men who are healthy enough to
+
+ align:start position:0%
+applied to men who are healthy enough to
+ 
+
+ align:start position:0%
+applied to men who are healthy enough to
+maintain the physical activity level at
+
+ align:start position:0%
+maintain the physical activity level at
+ 
+
+ align:start position:0%
+maintain the physical activity level at
+that time and so again in the main
+
+ align:start position:0%
+that time and so again in the main
+ 
+
+ align:start position:0%
+that time and so again in the main
+analysis we excused men from following
+
+ align:start position:0%
+analysis we excused men from following
+ 
+
+ align:start position:0%
+analysis we excused men from following
+the recommended levels if they developed
+
+ align:start position:0%
+the recommended levels if they developed
+ 
+
+ align:start position:0%
+the recommended levels if they developed
+one of these serious conditions so in
+
+ align:start position:0%
+one of these serious conditions so in
+ 
+
+ align:start position:0%
+one of these serious conditions so in
+sensitivity analyses we then expanded
+
+ align:start position:0%
+sensitivity analyses we then expanded
+ 
+
+ align:start position:0%
+sensitivity analyses we then expanded
+this list of serious conditions to also
+
+ align:start position:0%
+this list of serious conditions to also
+ 
+
+ align:start position:0%
+this list of serious conditions to also
+include the conditions that are shown in
+
+ align:start position:0%
+include the conditions that are shown in
+ 
+
+ align:start position:0%
+include the conditions that are shown in
+blue text and so this attenuated our
+
+ align:start position:0%
+blue text and so this attenuated our
+ 
+
+ align:start position:0%
+blue text and so this attenuated our
+estimates but didn't change our
+
+ align:start position:0%
+estimates but didn't change our
+ 
+
+ align:start position:0%
+estimates but didn't change our
+conclusions one thing to point out is
+
+ align:start position:0%
+conclusions one thing to point out is
+ 
+
+ align:start position:0%
+conclusions one thing to point out is
+that the validity of this approach rests
+
+ align:start position:0%
+that the validity of this approach rests
+ 
+
+ align:start position:0%
+that the validity of this approach rests
+on the assumption that at each time T we
+
+ align:start position:0%
+on the assumption that at each time T we
+ 
+
+ align:start position:0%
+on the assumption that at each time T we
+had available data needed to identify
+
+ align:start position:0%
+had available data needed to identify
+ 
+
+ align:start position:0%
+had available data needed to identify
+which men were healthy at that time
+
+ align:start position:0%
+which men were healthy at that time
+ 
+
+ align:start position:0%
+which men were healthy at that time
+enough to do the physical activity yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great question
+
+ align:start position:0%
+great question
+ 
+
+ align:start position:0%
+great question
+so because the strategy was pre
+
+ align:start position:0%
+so because the strategy was pre
+ 
+
+ align:start position:0%
+so because the strategy was pre
+specified to say that if you develop one
+
+ align:start position:0%
+specified to say that if you develop one
+ 
+
+ align:start position:0%
+specified to say that if you develop one
+of these conditions you may essentially
+
+ align:start position:0%
+of these conditions you may essentially
+ 
+
+ align:start position:0%
+of these conditions you may essentially
+do whatever level of physical activity
+
+ align:start position:0%
+do whatever level of physical activity
+ 
+
+ align:start position:0%
+do whatever level of physical activity
+you're able to do so importantly I'm
+
+ align:start position:0%
+you're able to do so importantly I'm
+ 
+
+ align:start position:0%
+you're able to do so importantly I'm
+glad you brought this up we did not
+
+ align:start position:0%
+glad you brought this up we did not
+ 
+
+ align:start position:0%
+glad you brought this up we did not
+censor men at that time they were still
+
+ align:start position:0%
+censor men at that time they were still
+ 
+
+ align:start position:0%
+censor men at that time they were still
+followed because they were still
+
+ align:start position:0%
+followed because they were still
+ 
+
+ align:start position:0%
+followed because they were still
+adhering to the strategy as defined
+
+ align:start position:0%
+adhering to the strategy as defined
+ 
+
+ align:start position:0%
+adhering to the strategy as defined
+mm-hm
+
+ align:start position:0%
+mm-hm
+ 
+
+ align:start position:0%
+mm-hm
+thanks for asking and so given that we
+
+ align:start position:0%
+thanks for asking and so given that we
+ 
+
+ align:start position:0%
+thanks for asking and so given that we
+don't know whether the data contain at
+
+ align:start position:0%
+don't know whether the data contain at
+ 
+
+ align:start position:0%
+don't know whether the data contain at
+each time T the information necessary to
+
+ align:start position:0%
+each time T the information necessary to
+ 
+
+ align:start position:0%
+each time T the information necessary to
+know are these men healthy enough at
+
+ align:start position:0%
+know are these men healthy enough at
+ 
+
+ align:start position:0%
+know are these men healthy enough at
+that time we therefore conducted a few
+
+ align:start position:0%
+that time we therefore conducted a few
+ 
+
+ align:start position:0%
+that time we therefore conducted a few
+alternate analyses in which we lagged
+
+ align:start position:0%
+alternate analyses in which we lagged
+ 
+
+ align:start position:0%
+alternate analyses in which we lagged
+physical activity and covariate data by
+
+ align:start position:0%
+physical activity and covariate data by
+ 
+
+ align:start position:0%
+physical activity and covariate data by
+two years and we also used a negative
+
+ align:start position:0%
+two years and we also used a negative
+ 
+
+ align:start position:0%
+two years and we also used a negative
+outcome control to explore potential
+
+ align:start position:0%
+outcome control to explore potential
+ 
+
+ align:start position:0%
+outcome control to explore potential
+unmeasured confounding by clinical
+
+ align:start position:0%
+unmeasured confounding by clinical
+ 
+
+ align:start position:0%
+unmeasured confounding by clinical
+disease or disease severity so what's
+
+ align:start position:0%
+disease or disease severity so what's
+ 
+
+ align:start position:0%
+disease or disease severity so what's
+the rationale behind this so in the DAGs
+
+ align:start position:0%
+the rationale behind this so in the DAGs
+ 
+
+ align:start position:0%
+the rationale behind this so in the DAGs
+below for the original analysis we have
+
+ align:start position:0%
+below for the original analysis we have
+ 
+
+ align:start position:0%
+below for the original analysis we have
+physical activity a we have survival Y
+
+ align:start position:0%
+physical activity a we have survival Y
+ 
+
+ align:start position:0%
+physical activity a we have survival Y
+and this may be confounded by disease
+
+ align:start position:0%
+and this may be confounded by disease
+ 
+
+ align:start position:0%
+and this may be confounded by disease
+severity you so when we see an
+
+ align:start position:0%
+severity you so when we see an
+ 
+
+ align:start position:0%
+severity you so when we see an
+association between a and Y in our data
+
+ align:start position:0%
+association between a and Y in our data
+ 
+
+ align:start position:0%
+association between a and Y in our data
+we want to make sure that it's causal
+
+ align:start position:0%
+we want to make sure that it's causal
+ 
+
+ align:start position:0%
+we want to make sure that it's causal
+that is because of the blue arrow and
+
+ align:start position:0%
+that is because of the blue arrow and
+ 
+
+ align:start position:0%
+that is because of the blue arrow and
+not because of this confounding bias the
+
+ align:start position:0%
+not because of this confounding bias the
+ 
+
+ align:start position:0%
+not because of this confounding bias the
+red arrow so how can we
+
+ align:start position:0%
+red arrow so how can we
+ 
+
+ align:start position:0%
+red arrow so how can we
+potentially provide evidence for whether
+
+ align:start position:0%
+potentially provide evidence for whether
+ 
+
+ align:start position:0%
+potentially provide evidence for whether
+that red pathway is there we selected
+
+ align:start position:0%
+that red pathway is there we selected
+ 
+
+ align:start position:0%
+that red pathway is there we selected
+questionnaire non-response as an
+
+ align:start position:0%
+questionnaire non-response as an
+ 
+
+ align:start position:0%
+questionnaire non-response as an
+alternate outcome instead of survival
+
+ align:start position:0%
+alternate outcome instead of survival
+ 
+
+ align:start position:0%
+alternate outcome instead of survival
+that we assumed was not directly
+
+ align:start position:0%
+that we assumed was not directly
+ 
+
+ align:start position:0%
+that we assumed was not directly
+affected by physical activity but that
+
+ align:start position:0%
+affected by physical activity but that
+ 
+
+ align:start position:0%
+affected by physical activity but that
+we thought would be similarly confounded
+
+ align:start position:0%
+we thought would be similarly confounded
+ 
+
+ align:start position:0%
+we thought would be similarly confounded
+by disease severity and so when we
+
+ align:start position:0%
+by disease severity and so when we
+ 
+
+ align:start position:0%
+by disease severity and so when we
+repeated the analysis with a negative
+
+ align:start position:0%
+repeated the analysis with a negative
+ 
+
+ align:start position:0%
+repeated the analysis with a negative
+outcome control
+
+ align:start position:0%
+outcome control
+ 
+
+ align:start position:0%
+outcome control
+we found that physical activity had a
+
+ align:start position:0%
+we found that physical activity had a
+ 
+
+ align:start position:0%
+we found that physical activity had a
+nearly null effect on questionnaire
+
+ align:start position:0%
+nearly null effect on questionnaire
+ 
+
+ align:start position:0%
+nearly null effect on questionnaire
+non-response as we would expect which
+
+ align:start position:0%
+non-response as we would expect which
+ 
+
+ align:start position:0%
+non-response as we would expect which
+provide some support that in our
+
+ align:start position:0%
+provide some support that in our
+ 
+
+ align:start position:0%
+provide some support that in our
+original analysis physical activity the
+
+ align:start position:0%
+original analysis physical activity the
+ 
+
+ align:start position:0%
+original analysis physical activity the
+effect of physical activity on death was
+
+ align:start position:0%
+effect of physical activity on death was
+ 
+
+ align:start position:0%
+effect of physical activity on death was
+not confounded through the pathways
+
+ align:start position:0%
+not confounded through the pathways
+ 
+
+ align:start position:0%
+not confounded through the pathways
+explored through the negative control so
+
+ align:start position:0%
+explored through the negative control so
+ 
+
+ align:start position:0%
+explored through the negative control so
+one thing to highlight here is the
+
+ align:start position:0%
+one thing to highlight here is the
+ 
+
+ align:start position:0%
+one thing to highlight here is the
+sensitivity analyses were driven by our
+
+ align:start position:0%
+sensitivity analyses were driven by our
+ 
+
+ align:start position:0%
+sensitivity analyses were driven by our
+subject matter knowledge and there's
+
+ align:start position:0%
+subject matter knowledge and there's
+ 
+
+ align:start position:0%
+subject matter knowledge and there's
+nothing in the data that kind of drove
+
+ align:start position:0%
+nothing in the data that kind of drove
+ 
+
+ align:start position:0%
+nothing in the data that kind of drove
+this and so just to recap this portion
+
+ align:start position:0%
+this and so just to recap this portion
+ 
+
+ align:start position:0%
+this and so just to recap this portion
+shoji methods are useful tool because
+
+ align:start position:0%
+shoji methods are useful tool because
+ 
+
+ align:start position:0%
+shoji methods are useful tool because
+they let us validly estimate the effect
+
+ align:start position:0%
+they let us validly estimate the effect
+ 
+
+ align:start position:0%
+they let us validly estimate the effect
+of pre-specified dynamic strategies an
+
+ align:start position:0%
+of pre-specified dynamic strategies an
+ 
+
+ align:start position:0%
+of pre-specified dynamic strategies an
+estimate adjusted absolute risks which
+
+ align:start position:0%
+estimate adjusted absolute risks which
+ 
+
+ align:start position:0%
+estimate adjusted absolute risks which
+are clinically meaningful to us and
+
+ align:start position:0%
+are clinically meaningful to us and
+ 
+
+ align:start position:0%
+are clinically meaningful to us and
+appropriately adjusted survival curves
+
+ align:start position:0%
+appropriately adjusted survival curves
+ 
+
+ align:start position:0%
+appropriately adjusted survival curves
+even in the presence of treatment
+
+ align:start position:0%
+even in the presence of treatment
+ 
+
+ align:start position:0%
+even in the presence of treatment
+confounder feedback which occurs often
+
+ align:start position:0%
+confounder feedback which occurs often
+ 
+
+ align:start position:0%
+confounder feedback which occurs often
+in clinical questions and of course this
+
+ align:start position:0%
+in clinical questions and of course this
+ 
+
+ align:start position:0%
+in clinical questions and of course this
+is under our typical identifiability
+
+ align:start position:0%
+is under our typical identifiability
+ 
+
+ align:start position:0%
+is under our typical identifiability
+assumptions so this makes it a powerful
+
+ align:start position:0%
+assumptions so this makes it a powerful
+ 
+
+ align:start position:0%
+assumptions so this makes it a powerful
+approach to estimate the effects of
+
+ align:start position:0%
+approach to estimate the effects of
+ 
+
+ align:start position:0%
+approach to estimate the effects of
+currently recommended or proposed
+
+ align:start position:0%
+currently recommended or proposed
+ 
+
+ align:start position:0%
+currently recommended or proposed
+strategies that therefore we can specify
+
+ align:start position:0%
+strategies that therefore we can specify
+ 
+
+ align:start position:0%
+strategies that therefore we can specify
+and write out precisely as we did here
+
+ align:start position:0%
+and write out precisely as we did here
+ 
+
+ align:start position:0%
+and write out precisely as we did here
+however these pre specified strategies
+
+ align:start position:0%
+however these pre specified strategies
+ 
+
+ align:start position:0%
+however these pre specified strategies
+may not be the optimal strategies so
+
+ align:start position:0%
+may not be the optimal strategies so
+ 
+
+ align:start position:0%
+may not be the optimal strategies so
+again when I was doing this analysis I
+
+ align:start position:0%
+again when I was doing this analysis I
+ 
+
+ align:start position:0%
+again when I was doing this analysis I
+was thinking there's so many different
+
+ align:start position:0%
+was thinking there's so many different
+ 
+
+ align:start position:0%
+was thinking there's so many different
+weekly durations of physical activity
+
+ align:start position:0%
+weekly durations of physical activity
+ 
+
+ align:start position:0%
+weekly durations of physical activity
+that we're not looking at there's so
+
+ align:start position:0%
+that we're not looking at there's so
+ 
+
+ align:start position:0%
+that we're not looking at there's so
+many different time varying covariates
+
+ align:start position:0%
+many different time varying covariates
+ 
+
+ align:start position:0%
+many different time varying covariates
+where we could have different
+
+ align:start position:0%
+where we could have different
+ 
+
+ align:start position:0%
+where we could have different
+dependencies on those for these
+
+ align:start position:0%
+dependencies on those for these
+ 
+
+ align:start position:0%
+dependencies on those for these
+strategies over the time and maybe those
+
+ align:start position:0%
+strategies over the time and maybe those
+ 
+
+ align:start position:0%
+strategies over the time and maybe those
+would have led to better survival
+
+ align:start position:0%
+would have led to better survival
+ 
+
+ align:start position:0%
+would have led to better survival
+outcomes among these men but all of that
+
+ align:start position:0%
+outcomes among these men but all of that
+ 
+
+ align:start position:0%
+outcomes among these men but all of that
+was unexplored
\ No newline at end of file
diff --git a/zlmokDj0DaU.txt b/zlmokDj0DaU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..945df5bc9f6dc1aa838149b3fc27f1c88acf9be1
--- /dev/null
+++ b/zlmokDj0DaU.txt
@@ -0,0 +1,16355 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free to make a donation or view
+
+ align:start position:0%
+for free to make a donation or view
+ 
+
+ align:start position:0%
+for free to make a donation or view
+additional materials from hundreds of
+
+ align:start position:0%
+additional materials from hundreds of
+ 
+
+ align:start position:0%
+additional materials from hundreds of
+MIT courses visit MIT opencourseware at
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ 
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so today I promised I would play through
+
+ align:start position:0%
+so today I promised I would play through
+ 
+
+ align:start position:0%
+so today I promised I would play through
+the second half of the tournament that I
+
+ align:start position:0%
+the second half of the tournament that I
+ 
+
+ align:start position:0%
+the second half of the tournament that I
+started last time so two times ago but
+
+ align:start position:0%
+started last time so two times ago but
+ 
+
+ align:start position:0%
+started last time so two times ago but
+before Jennifer Shahi days guest lecture
+
+ align:start position:0%
+before Jennifer Shahi days guest lecture
+ 
+
+ align:start position:0%
+before Jennifer Shahi days guest lecture
+but before I start so so remember last
+
+ align:start position:0%
+but before I start so so remember last
+ 
+
+ align:start position:0%
+but before I start so so remember last
+time we got to the final table this is
+
+ align:start position:0%
+time we got to the final table this is
+ 
+
+ align:start position:0%
+time we got to the final table this is
+essentially the start of the final table
+
+ align:start position:0%
+essentially the start of the final table
+ 
+
+ align:start position:0%
+essentially the start of the final table
+and but before I get into the hands I
+
+ align:start position:0%
+and but before I get into the hands I
+ 
+
+ align:start position:0%
+and but before I get into the hands I
+want to do a bit of Theory first that
+
+ align:start position:0%
+want to do a bit of Theory first that
+ 
+
+ align:start position:0%
+want to do a bit of Theory first that
+I've sort of been for going so far in
+
+ align:start position:0%
+I've sort of been for going so far in
+ 
+
+ align:start position:0%
+I've sort of been for going so far in
+this class and it's essentially is what
+
+ align:start position:0%
+this class and it's essentially is what
+ 
+
+ align:start position:0%
+this class and it's essentially is what
+what's called the independent chip model
+
+ align:start position:0%
+what's called the independent chip model
+ 
+
+ align:start position:0%
+what's called the independent chip model
+or ICM theory and essentially what it's
+
+ align:start position:0%
+or ICM theory and essentially what it's
+ 
+
+ align:start position:0%
+or ICM theory and essentially what it's
+used for is in
+
+ align:start position:0%
+used for is in
+ 
+
+ align:start position:0%
+used for is in
+tournaments essentially the the value of
+
+ align:start position:0%
+tournaments essentially the the value of
+ 
+
+ align:start position:0%
+tournaments essentially the the value of
+chips is essentially nonlinear because
+
+ align:start position:0%
+chips is essentially nonlinear because
+ 
+
+ align:start position:0%
+chips is essentially nonlinear because
+you're not really trying to just get out
+
+ align:start position:0%
+you're not really trying to just get out
+ 
+
+ align:start position:0%
+you're not really trying to just get out
+the chips you're trying to last as long
+
+ align:start position:0%
+the chips you're trying to last as long
+ 
+
+ align:start position:0%
+the chips you're trying to last as long
+as possible and move up the pants so I
+
+ align:start position:0%
+as possible and move up the pants so I
+ 
+
+ align:start position:0%
+as possible and move up the pants so I
+want to sort of now formally quantify
+
+ align:start position:0%
+want to sort of now formally quantify
+ 
+
+ align:start position:0%
+want to sort of now formally quantify
+what this means and how we calculate the
+
+ align:start position:0%
+what this means and how we calculate the
+ 
+
+ align:start position:0%
+what this means and how we calculate the
+DV of your Gamble's so
+
+ align:start position:0%
+DV of your Gamble's so
+ 
+
+ align:start position:0%
+DV of your Gamble's so
+far I think I've just told you you know
+
+ align:start position:0%
+far I think I've just told you you know
+ 
+
+ align:start position:0%
+far I think I've just told you you know
+everything I've done so far in this
+
+ align:start position:0%
+everything I've done so far in this
+ 
+
+ align:start position:0%
+everything I've done so far in this
+class has been shifty B and that told
+
+ align:start position:0%
+class has been shifty B and that told
+ 
+
+ align:start position:0%
+class has been shifty B and that told
+you you know just play you maximize chip
+
+ align:start position:0%
+you you know just play you maximize chip
+ 
+
+ align:start position:0%
+you you know just play you maximize chip
+evey maximize your expected number of
+
+ align:start position:0%
+evey maximize your expected number of
+ 
+
+ align:start position:0%
+evey maximize your expected number of
+chips and that's a pretty reasonable way
+
+ align:start position:0%
+chips and that's a pretty reasonable way
+ 
+
+ align:start position:0%
+chips and that's a pretty reasonable way
+to play and cash games is what you want
+
+ align:start position:0%
+to play and cash games is what you want
+ 
+
+ align:start position:0%
+to play and cash games is what you want
+to do and in tournaments it's it's not a
+
+ align:start position:0%
+to do and in tournaments it's it's not a
+ 
+
+ align:start position:0%
+to do and in tournaments it's it's not a
+bad approximation so I don't want
+
+ align:start position:0%
+bad approximation so I don't want
+ 
+
+ align:start position:0%
+bad approximation so I don't want
+everyone after this I see I'm not sure
+
+ align:start position:0%
+everyone after this I see I'm not sure
+ 
+
+ align:start position:0%
+everyone after this I see I'm not sure
+do you think you know I got a completely
+
+ align:start position:0%
+do you think you know I got a completely
+ 
+
+ align:start position:0%
+do you think you know I got a completely
+change by playing in tournaments because
+
+ align:start position:0%
+change by playing in tournaments because
+ 
+
+ align:start position:0%
+change by playing in tournaments because
+that's not the case essentially playing
+
+ align:start position:0%
+that's not the case essentially playing
+ 
+
+ align:start position:0%
+that's not the case essentially playing
+you're maximized expected number of
+
+ align:start position:0%
+you're maximized expected number of
+ 
+
+ align:start position:0%
+you're maximized expected number of
+chips is a pretty good approximation of
+
+ align:start position:0%
+chips is a pretty good approximation of
+ 
+
+ align:start position:0%
+chips is a pretty good approximation of
+how you actually should be playing but
+
+ align:start position:0%
+how you actually should be playing but
+ 
+
+ align:start position:0%
+how you actually should be playing but
+there are some small differences and
+
+ align:start position:0%
+there are some small differences and
+ 
+
+ align:start position:0%
+there are some small differences and
+extreme situations and I'd like to
+
+ align:start position:0%
+extreme situations and I'd like to
+ 
+
+ align:start position:0%
+extreme situations and I'd like to
+highlight some of that today so okay
+
+ align:start position:0%
+highlight some of that today so okay
+ 
+
+ align:start position:0%
+highlight some of that today so okay
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so this is essentially yes so it's this
+
+ align:start position:0%
+so this is essentially yes so it's this
+ 
+
+ align:start position:0%
+so this is essentially yes so it's this
+idea of minimizing risks you stay alive
+
+ align:start position:0%
+idea of minimizing risks you stay alive
+ 
+
+ align:start position:0%
+idea of minimizing risks you stay alive
+and move up to escalating payouts so I
+
+ align:start position:0%
+and move up to escalating payouts so I
+ 
+
+ align:start position:0%
+and move up to escalating payouts so I
+want to make an important distinction
+
+ align:start position:0%
+want to make an important distinction
+ 
+
+ align:start position:0%
+want to make an important distinction
+though what I'm saying we're still
+
+ align:start position:0%
+though what I'm saying we're still
+ 
+
+ align:start position:0%
+though what I'm saying we're still
+trading maximize our expected amount of
+
+ align:start position:0%
+trading maximize our expected amount of
+ 
+
+ align:start position:0%
+trading maximize our expected amount of
+money what I'm saying you should be
+
+ align:start position:0%
+money what I'm saying you should be
+ 
+
+ align:start position:0%
+money what I'm saying you should be
+minimizing your risk in a tournament so
+
+ align:start position:0%
+minimizing your risk in a tournament so
+ 
+
+ align:start position:0%
+minimizing your risk in a tournament so
+that you can move up the payouts that is
+
+ align:start position:0%
+that you can move up the payouts that is
+ 
+
+ align:start position:0%
+that you can move up the payouts that is
+that's different than saying you should
+
+ align:start position:0%
+that's different than saying you should
+ 
+
+ align:start position:0%
+that's different than saying you should
+you should minimize your monetary risk
+
+ align:start position:0%
+you should minimize your monetary risk
+ 
+
+ align:start position:0%
+you should minimize your monetary risk
+because I'm still assuming returning
+
+ align:start position:0%
+because I'm still assuming returning
+ 
+
+ align:start position:0%
+because I'm still assuming returning
+maximize our expected money without
+
+ align:start position:0%
+maximize our expected money without
+ 
+
+ align:start position:0%
+maximize our expected money without
+worrying about risk but I'm only
+
+ align:start position:0%
+worrying about risk but I'm only
+ 
+
+ align:start position:0%
+worrying about risk but I'm only
+minimizing tournament risk to maximize
+
+ align:start position:0%
+minimizing tournament risk to maximize
+ 
+
+ align:start position:0%
+minimizing tournament risk to maximize
+our expected amount of money but I'm not
+
+ align:start position:0%
+our expected amount of money but I'm not
+ 
+
+ align:start position:0%
+our expected amount of money but I'm not
+saying we should be overly conservative
+
+ align:start position:0%
+saying we should be overly conservative
+ 
+
+ align:start position:0%
+saying we should be overly conservative
+in tournament and just trying to move up
+
+ align:start position:0%
+in tournament and just trying to move up
+ 
+
+ align:start position:0%
+in tournament and just trying to move up
+the money ladder slowly when you should
+
+ align:start position:0%
+the money ladder slowly when you should
+ 
+
+ align:start position:0%
+the money ladder slowly when you should
+be gambling because it's positive money
+
+ align:start position:0%
+be gambling because it's positive money
+ 
+
+ align:start position:0%
+be gambling because it's positive money
+expectation if you find yourself in this
+
+ align:start position:0%
+expectation if you find yourself in this
+ 
+
+ align:start position:0%
+expectation if you find yourself in this
+situation then you know if you're trying
+
+ align:start position:0%
+situation then you know if you're trying
+ 
+
+ align:start position:0%
+situation then you know if you're trying
+to play like professionally and just
+
+ align:start position:0%
+to play like professionally and just
+ 
+
+ align:start position:0%
+to play like professionally and just
+maximize your expected amount of money
+
+ align:start position:0%
+maximize your expected amount of money
+ 
+
+ align:start position:0%
+maximize your expected amount of money
+in every situation then you should
+
+ align:start position:0%
+in every situation then you should
+ 
+
+ align:start position:0%
+in every situation then you should
+probably play smaller tournaments where
+
+ align:start position:0%
+probably play smaller tournaments where
+ 
+
+ align:start position:0%
+probably play smaller tournaments where
+this is not really the key what if this
+
+ align:start position:0%
+this is not really the key what if this
+ 
+
+ align:start position:0%
+this is not really the key what if this
+doesn't occur to you often you know I
+
+ align:start position:0%
+doesn't occur to you often you know I
+ 
+
+ align:start position:0%
+doesn't occur to you often you know I
+can understand in practice like if you
+
+ align:start position:0%
+can understand in practice like if you
+ 
+
+ align:start position:0%
+can understand in practice like if you
+play poker for fun and you made it farm
+
+ align:start position:0%
+play poker for fun and you made it farm
+ 
+
+ align:start position:0%
+play poker for fun and you made it farm
+in front of it and you know it's like
+
+ align:start position:0%
+in front of it and you know it's like
+ 
+
+ align:start position:0%
+in front of it and you know it's like
+the top like let's say 50k and there's
+
+ align:start position:0%
+the top like let's say 50k and there's
+ 
+
+ align:start position:0%
+the top like let's say 50k and there's
+like 55 left you know I can understand
+
+ align:start position:0%
+like 55 left you know I can understand
+ 
+
+ align:start position:0%
+like 55 left you know I can understand
+why you might not want to make a
+
+ align:start position:0%
+why you might not want to make a
+ 
+
+ align:start position:0%
+why you might not want to make a
+positive money X a positive money
+
+ align:start position:0%
+positive money X a positive money
+ 
+
+ align:start position:0%
+positive money X a positive money
+expectation play because you know you've
+
+ align:start position:0%
+expectation play because you know you've
+ 
+
+ align:start position:0%
+expectation play because you know you've
+knew you've played this tournament
+
+ align:start position:0%
+knew you've played this tournament
+ 
+
+ align:start position:0%
+knew you've played this tournament
+you're probably not going to be in the
+
+ align:start position:0%
+you're probably not going to be in the
+ 
+
+ align:start position:0%
+you're probably not going to be in the
+situation that many times in your
+
+ align:start position:0%
+situation that many times in your
+ 
+
+ align:start position:0%
+situation that many times in your
+lifetime and you just really want to
+
+ align:start position:0%
+lifetime and you just really want to
+ 
+
+ align:start position:0%
+lifetime and you just really want to
+cash like the World Series of Poker Main
+
+ align:start position:0%
+cash like the World Series of Poker Main
+ 
+
+ align:start position:0%
+cash like the World Series of Poker Main
+Event or something and I think you know
+
+ align:start position:0%
+Event or something and I think you know
+ 
+
+ align:start position:0%
+Event or something and I think you know
+that's that's a reasonable life decision
+
+ align:start position:0%
+that's that's a reasonable life decision
+ 
+
+ align:start position:0%
+that's that's a reasonable life decision
+I'm not criticizing that decision but
+
+ align:start position:0%
+I'm not criticizing that decision but
+ 
+
+ align:start position:0%
+I'm not criticizing that decision but
+I'm just saying but I'm gonna talk about
+
+ align:start position:0%
+I'm just saying but I'm gonna talk about
+ 
+
+ align:start position:0%
+I'm just saying but I'm gonna talk about
+all these decisions assuming work we
+
+ align:start position:0%
+all these decisions assuming work we
+ 
+
+ align:start position:0%
+all these decisions assuming work we
+don't care about that we're still trying
+
+ align:start position:0%
+don't care about that we're still trying
+ 
+
+ align:start position:0%
+don't care about that we're still trying
+to maximize expected amount of money and
+
+ align:start position:0%
+to maximize expected amount of money and
+ 
+
+ align:start position:0%
+to maximize expected amount of money and
+if you aren't playing like
+
+ align:start position:0%
+if you aren't playing like
+ 
+
+ align:start position:0%
+if you aren't playing like
+professionally where you're getting into
+
+ align:start position:0%
+professionally where you're getting into
+ 
+
+ align:start position:0%
+professionally where you're getting into
+that situation very frequently then it
+
+ align:start position:0%
+that situation very frequently then it
+ 
+
+ align:start position:0%
+that situation very frequently then it
+is very important to maximize risk in
+
+ align:start position:0%
+is very important to maximize risk in
+ 
+
+ align:start position:0%
+is very important to maximize risk in
+some cases and to maximize your doll or
+
+ align:start position:0%
+some cases and to maximize your doll or
+ 
+
+ align:start position:0%
+some cases and to maximize your doll or
+evey because you know in tournaments
+
+ align:start position:0%
+evey because you know in tournaments
+ 
+
+ align:start position:0%
+evey because you know in tournaments
+you're losing most of the time you
+
+ align:start position:0%
+you're losing most of the time you
+ 
+
+ align:start position:0%
+you're losing most of the time you
+really have to win a lot the times that
+
+ align:start position:0%
+really have to win a lot the times that
+ 
+
+ align:start position:0%
+really have to win a lot the times that
+we do win you can't be content like you
+
+ align:start position:0%
+we do win you can't be content like you
+ 
+
+ align:start position:0%
+we do win you can't be content like you
+can't be content because we made like
+
+ align:start position:0%
+can't be content because we made like
+ 
+
+ align:start position:0%
+can't be content because we made like
+$30,000
+
+ align:start position:0%
+$30,000
+ 
+
+ align:start position:0%
+$30,000
+that we could have made like fifty
+
+ align:start position:0%
+that we could have made like fifty
+ 
+
+ align:start position:0%
+that we could have made like fifty
+thousand dollars so okay so what is the
+
+ align:start position:0%
+thousand dollars so okay so what is the
+ 
+
+ align:start position:0%
+thousand dollars so okay so what is the
+exact formula from ICM so I'm just going
+
+ align:start position:0%
+exact formula from ICM so I'm just going
+ 
+
+ align:start position:0%
+exact formula from ICM so I'm just going
+to sort of demonstrate how to calculate
+
+ align:start position:0%
+to sort of demonstrate how to calculate
+ 
+
+ align:start position:0%
+to sort of demonstrate how to calculate
+the value chips in a tournament with an
+
+ align:start position:0%
+the value chips in a tournament with an
+ 
+
+ align:start position:0%
+the value chips in a tournament with an
+example so ICM is essentially a formula
+
+ align:start position:0%
+example so ICM is essentially a formula
+ 
+
+ align:start position:0%
+example so ICM is essentially a formula
+to calculate how much your stack is
+
+ align:start position:0%
+to calculate how much your stack is
+ 
+
+ align:start position:0%
+to calculate how much your stack is
+worth in a tournament so let's suppose
+
+ align:start position:0%
+worth in a tournament so let's suppose
+ 
+
+ align:start position:0%
+worth in a tournament so let's suppose
+there's three players left and the
+
+ align:start position:0%
+there's three players left and the
+ 
+
+ align:start position:0%
+there's three players left and the
+payoffs are five three two this is a
+
+ align:start position:0%
+payoffs are five three two this is a
+ 
+
+ align:start position:0%
+payoffs are five three two this is a
+common structure and likes it and goes
+
+ align:start position:0%
+common structure and likes it and goes
+ 
+
+ align:start position:0%
+common structure and likes it and goes
+if you play those which are like ten
+
+ align:start position:0%
+if you play those which are like ten
+ 
+
+ align:start position:0%
+if you play those which are like ten
+player tournaments so the statement is
+
+ align:start position:0%
+player tournaments so the statement is
+ 
+
+ align:start position:0%
+player tournaments so the statement is
+essentially your chances of winning the
+
+ align:start position:0%
+essentially your chances of winning the
+ 
+
+ align:start position:0%
+essentially your chances of winning the
+tournament is proportional to your
+
+ align:start position:0%
+tournament is proportional to your
+ 
+
+ align:start position:0%
+tournament is proportional to your
+percent of the total chips and
+
+ align:start position:0%
+percent of the total chips and
+ 
+
+ align:start position:0%
+percent of the total chips and
+essentially we're assuming this champion
+
+ align:start position:0%
+essentially we're assuming this champion
+ 
+
+ align:start position:0%
+essentially we're assuming this champion
+is true and we're going to derive from
+
+ align:start position:0%
+is true and we're going to derive from
+ 
+
+ align:start position:0%
+is true and we're going to derive from
+it all the formulas
+
+ align:start position:0%
+it all the formulas
+ 
+
+ align:start position:0%
+it all the formulas
+and this thing that is a proximal nature
+
+ align:start position:0%
+and this thing that is a proximal nature
+ 
+
+ align:start position:0%
+and this thing that is a proximal nature
+you know there are more advanced ICM
+
+ align:start position:0%
+you know there are more advanced ICM
+ 
+
+ align:start position:0%
+you know there are more advanced ICM
+calculators that also take into account
+
+ align:start position:0%
+calculators that also take into account
+ 
+
+ align:start position:0%
+calculators that also take into account
+your position if the stack sizes are
+
+ align:start position:0%
+your position if the stack sizes are
+ 
+
+ align:start position:0%
+your position if the stack sizes are
+rather shallow because there are some
+
+ align:start position:0%
+rather shallow because there are some
+ 
+
+ align:start position:0%
+rather shallow because there are some
+inaccuracies because this statement it
+
+ align:start position:0%
+inaccuracies because this statement it
+ 
+
+ align:start position:0%
+inaccuracies because this statement it
+calculates only based on chips but you
+
+ align:start position:0%
+calculates only based on chips but you
+ 
+
+ align:start position:0%
+calculates only based on chips but you
+know if you're folding and then you're
+
+ align:start position:0%
+know if you're folding and then you're
+ 
+
+ align:start position:0%
+know if you're folding and then you're
+the button the next hand which is the
+
+ align:start position:0%
+the button the next hand which is the
+ 
+
+ align:start position:0%
+the button the next hand which is the
+best position then that's actually sort
+
+ align:start position:0%
+best position then that's actually sort
+ 
+
+ align:start position:0%
+best position then that's actually sort
+of an entire big blind better almost
+
+ align:start position:0%
+of an entire big blind better almost
+ 
+
+ align:start position:0%
+of an entire big blind better almost
+then being under together the next but
+
+ align:start position:0%
+then being under together the next but
+ 
+
+ align:start position:0%
+then being under together the next but
+look more we're not going to worry about
+
+ align:start position:0%
+look more we're not going to worry about
+ 
+
+ align:start position:0%
+look more we're not going to worry about
+that we're just going to assume you're
+
+ align:start position:0%
+that we're just going to assume you're
+ 
+
+ align:start position:0%
+that we're just going to assume you're
+aware of chances of winning the
+
+ align:start position:0%
+aware of chances of winning the
+ 
+
+ align:start position:0%
+aware of chances of winning the
+tournament is proportional to your
+
+ align:start position:0%
+tournament is proportional to your
+ 
+
+ align:start position:0%
+tournament is proportional to your
+percentage chips so how do we calculate
+
+ align:start position:0%
+percentage chips so how do we calculate
+ 
+
+ align:start position:0%
+percentage chips so how do we calculate
+this so I sent it so okay so you can't
+
+ align:start position:0%
+this so I sent it so okay so you can't
+ 
+
+ align:start position:0%
+this so I sent it so okay so you can't
+really do it by hand in practice but for
+
+ align:start position:0%
+really do it by hand in practice but for
+ 
+
+ align:start position:0%
+really do it by hand in practice but for
+this example with three people I'll show
+
+ align:start position:0%
+this example with three people I'll show
+ 
+
+ align:start position:0%
+this example with three people I'll show
+you how to do it by hand so let's
+
+ align:start position:0%
+you how to do it by hand so let's
+ 
+
+ align:start position:0%
+you how to do it by hand so let's
+suppose the chip stamps are also five
+
+ align:start position:0%
+suppose the chip stamps are also five
+ 
+
+ align:start position:0%
+suppose the chip stamps are also five
+three two okay so the payouts are five
+
+ align:start position:0%
+three two okay so the payouts are five
+ 
+
+ align:start position:0%
+three two okay so the payouts are five
+three two and the chip stacks are also
+
+ align:start position:0%
+three two and the chip stacks are also
+ 
+
+ align:start position:0%
+three two and the chip stacks are also
+five three two ratio so you know if
+
+ align:start position:0%
+five three two ratio so you know if
+ 
+
+ align:start position:0%
+five three two ratio so you know if
+should be the equals money evie then the
+
+ align:start position:0%
+should be the equals money evie then the
+ 
+
+ align:start position:0%
+should be the equals money evie then the
+guy with five thousand their equity from
+
+ align:start position:0%
+guy with five thousand their equity from
+ 
+
+ align:start position:0%
+guy with five thousand their equity from
+the tournament should be five dollars
+
+ align:start position:0%
+the tournament should be five dollars
+ 
+
+ align:start position:0%
+the tournament should be five dollars
+and the guy in third place their equity
+
+ align:start position:0%
+and the guy in third place their equity
+ 
+
+ align:start position:0%
+and the guy in third place their equity
+should be two dollars right but this is
+
+ align:start position:0%
+should be two dollars right but this is
+ 
+
+ align:start position:0%
+should be two dollars right but this is
+clearly not correct right because the
+
+ align:start position:0%
+clearly not correct right because the
+ 
+
+ align:start position:0%
+clearly not correct right because the
+guy in third place is guaranteed two
+
+ align:start position:0%
+guy in third place is guaranteed two
+ 
+
+ align:start position:0%
+guy in third place is guaranteed two
+dollars and clearly there's a nonzero
+
+ align:start position:0%
+dollars and clearly there's a nonzero
+ 
+
+ align:start position:0%
+dollars and clearly there's a nonzero
+chance of them laying the tournament so
+
+ align:start position:0%
+chance of them laying the tournament so
+ 
+
+ align:start position:0%
+chance of them laying the tournament so
+clearly their equity is actually more
+
+ align:start position:0%
+clearly their equity is actually more
+ 
+
+ align:start position:0%
+clearly their equity is actually more
+than two dollars right and then
+
+ align:start position:0%
+than two dollars right and then
+ 
+
+ align:start position:0%
+than two dollars right and then
+similarly if your player a your equity
+
+ align:start position:0%
+similarly if your player a your equity
+ 
+
+ align:start position:0%
+similarly if your player a your equity
+is clearly not five dollars because
+
+ align:start position:0%
+is clearly not five dollars because
+ 
+
+ align:start position:0%
+is clearly not five dollars because
+you're not guaranteed to win they turn
+
+ align:start position:0%
+you're not guaranteed to win they turn
+ 
+
+ align:start position:0%
+you're not guaranteed to win they turn
+up right so it's clear from this example
+
+ align:start position:0%
+up right so it's clear from this example
+ 
+
+ align:start position:0%
+up right so it's clear from this example
+why if you just do chippy be equal
+
+ align:start position:0%
+why if you just do chippy be equal
+ 
+
+ align:start position:0%
+why if you just do chippy be equal
+people's money easy that's clearly wrong
+
+ align:start position:0%
+people's money easy that's clearly wrong
+ 
+
+ align:start position:0%
+people's money easy that's clearly wrong
+raise equity everyone so
+
+ align:start position:0%
+raise equity everyone so
+ 
+
+ align:start position:0%
+raise equity everyone so
+how do we calculate it it's okay so this
+
+ align:start position:0%
+how do we calculate it it's okay so this
+ 
+
+ align:start position:0%
+how do we calculate it it's okay so this
+is so let's calculate it for player to
+
+ align:start position:0%
+is so let's calculate it for player to
+ 
+
+ align:start position:0%
+is so let's calculate it for player to
+see so essentially what it's saying your
+
+ align:start position:0%
+see so essentially what it's saying your
+ 
+
+ align:start position:0%
+see so essentially what it's saying your
+chances of winning your chances are
+
+ align:start position:0%
+chances of winning your chances are
+ 
+
+ align:start position:0%
+chances of winning your chances are
+coming first is 2,000
+
+ align:start position:0%
+coming first is 2,000
+ 
+
+ align:start position:0%
+coming first is 2,000
+over 10,000 which is 20% and then you
+
+ align:start position:0%
+over 10,000 which is 20% and then you
+ 
+
+ align:start position:0%
+over 10,000 which is 20% and then you
+calculate their chances of coming second
+
+ align:start position:0%
+calculate their chances of coming second
+ 
+
+ align:start position:0%
+calculate their chances of coming second
+you just condition on each of the other
+
+ align:start position:0%
+you just condition on each of the other
+ 
+
+ align:start position:0%
+you just condition on each of the other
+players way so conditioned on a winning
+
+ align:start position:0%
+players way so conditioned on a winning
+ 
+
+ align:start position:0%
+players way so conditioned on a winning
+which will happen 50% of the time we
+
+ align:start position:0%
+which will happen 50% of the time we
+ 
+
+ align:start position:0%
+which will happen 50% of the time we
+assume that our chances of coming second
+
+ align:start position:0%
+assume that our chances of coming second
+ 
+
+ align:start position:0%
+assume that our chances of coming second
+is 2,000 divided by 5,000 which is the
+
+ align:start position:0%
+is 2,000 divided by 5,000 which is the
+ 
+
+ align:start position:0%
+is 2,000 divided by 5,000 which is the
+remaining number of chips besides
+
+ align:start position:0%
+remaining number of chips besides
+ 
+
+ align:start position:0%
+remaining number of chips besides
+clutter a does that make sense so player
+
+ align:start position:0%
+clutter a does that make sense so player
+ 
+
+ align:start position:0%
+clutter a does that make sense so player
+a has 5,000 chips so between between use
+
+ align:start position:0%
+a has 5,000 chips so between between use
+ 
+
+ align:start position:0%
+a has 5,000 chips so between between use
+player C and player D you've got five
+
+ align:start position:0%
+player C and player D you've got five
+ 
+
+ align:start position:0%
+player C and player D you've got five
+deuce 5,000 ships in total and you've
+
+ align:start position:0%
+deuce 5,000 ships in total and you've
+ 
+
+ align:start position:0%
+deuce 5,000 ships in total and you've
+got 2,000 of those so it's 2,000 over
+
+ align:start position:0%
+got 2,000 of those so it's 2,000 over
+ 
+
+ align:start position:0%
+got 2,000 of those so it's 2,000 over
+5,000 so it's point four and then if
+
+ align:start position:0%
+5,000 so it's point four and then if
+ 
+
+ align:start position:0%
+5,000 so it's point four and then if
+player B wins then your chances of
+
+ align:start position:0%
+player B wins then your chances of
+ 
+
+ align:start position:0%
+player B wins then your chances of
+coming second is 2,000 over 7,000 so
+
+ align:start position:0%
+coming second is 2,000 over 7,000 so
+ 
+
+ align:start position:0%
+coming second is 2,000 over 7,000 so
+overall your chances are coming second
+
+ align:start position:0%
+overall your chances are coming second
+ 
+
+ align:start position:0%
+overall your chances are coming second
+is 0.42
+
+ align:start position:0%
+is 0.42
+ 
+
+ align:start position:0%
+is 0.42
+so point is so yeah so it's just 50%
+
+ align:start position:0%
+so point is so yeah so it's just 50%
+ 
+
+ align:start position:0%
+so point is so yeah so it's just 50%
+times 0.4 plus 30% times 2/7 which
+
+ align:start position:0%
+times 0.4 plus 30% times 2/7 which
+ 
+
+ align:start position:0%
+times 0.4 plus 30% times 2/7 which
+equals 2/7 so then you can calculate
+
+ align:start position:0%
+equals 2/7 so then you can calculate
+ 
+
+ align:start position:0%
+equals 2/7 so then you can calculate
+your equity is they're guaranteed to
+
+ align:start position:0%
+your equity is they're guaranteed to
+ 
+
+ align:start position:0%
+your equity is they're guaranteed to
+bucks and you have a 20% chance of
+
+ align:start position:0%
+bucks and you have a 20% chance of
+ 
+
+ align:start position:0%
+bucks and you have a 20% chance of
+winning which will give you three
+
+ align:start position:0%
+winning which will give you three
+ 
+
+ align:start position:0%
+winning which will give you three
+additional dollars and then a 29% chance
+
+ align:start position:0%
+additional dollars and then a 29% chance
+ 
+
+ align:start position:0%
+additional dollars and then a 29% chance
+of coming second which will give you an
+
+ align:start position:0%
+of coming second which will give you an
+ 
+
+ align:start position:0%
+of coming second which will give you an
+additional dollar so your equity is
+
+ align:start position:0%
+additional dollar so your equity is
+ 
+
+ align:start position:0%
+additional dollar so your equity is
+actually 289 this displace this case
+
+ align:start position:0%
+actually 289 this displace this case
+ 
+
+ align:start position:0%
+actually 289 this displace this case
+it's actually closer to second place
+
+ align:start position:0%
+it's actually closer to second place
+ 
+
+ align:start position:0%
+it's actually closer to second place
+then third place does I have a place you
+
+ align:start position:0%
+then third place does I have a place you
+ 
+
+ align:start position:0%
+then third place does I have a place you
+make sense to everyone so if there is
+
+ align:start position:0%
+make sense to everyone so if there is
+ 
+
+ align:start position:0%
+make sense to everyone so if there is
+like five players you know you just have
+
+ align:start position:0%
+like five players you know you just have
+ 
+
+ align:start position:0%
+like five players you know you just have
+to recursively condition you have to
+
+ align:start position:0%
+to recursively condition you have to
+ 
+
+ align:start position:0%
+to recursively condition you have to
+condition on play a winning and then go
+
+ align:start position:0%
+condition on play a winning and then go
+ 
+
+ align:start position:0%
+condition on play a winning and then go
+through all the possibilities if you
+
+ align:start position:0%
+through all the possibilities if you
+ 
+
+ align:start position:0%
+through all the possibilities if you
+becomes second then go through all the
+
+ align:start position:0%
+becomes second then go through all the
+ 
+
+ align:start position:0%
+becomes second then go through all the
+possibilities if you becomes third etc
+
+ align:start position:0%
+possibilities if you becomes third etc
+ 
+
+ align:start position:0%
+possibilities if you becomes third etc
+etc so it's not a completion make them
+
+ align:start position:0%
+etc so it's not a completion make them
+ 
+
+ align:start position:0%
+etc so it's not a completion make them
+really do in your head it's but there
+
+ align:start position:0%
+really do in your head it's but there
+ 
+
+ align:start position:0%
+really do in your head it's but there
+that it's quite easy to find a
+
+ align:start position:0%
+that it's quite easy to find a
+ 
+
+ align:start position:0%
+that it's quite easy to find a
+calculator to do it for you on you just
+
+ align:start position:0%
+calculator to do it for you on you just
+ 
+
+ align:start position:0%
+calculator to do it for you on you just
+Google ICM calculator and you punch it
+
+ align:start position:0%
+Google ICM calculator and you punch it
+ 
+
+ align:start position:0%
+Google ICM calculator and you punch it
+in and and even though you know it's not
+
+ align:start position:0%
+in and and even though you know it's not
+ 
+
+ align:start position:0%
+in and and even though you know it's not
+like like your grows exponentially but
+
+ align:start position:0%
+like like your grows exponentially but
+ 
+
+ align:start position:0%
+like like your grows exponentially but
+you know there's only going to be like
+
+ align:start position:0%
+you know there's only going to be like
+ 
+
+ align:start position:0%
+you know there's only going to be like
+nine players so it's still fine and
+
+ align:start position:0%
+nine players so it's still fine and
+ 
+
+ align:start position:0%
+nine players so it's still fine and
+we'll take that though the computer can
+
+ align:start position:0%
+we'll take that though the computer can
+ 
+
+ align:start position:0%
+we'll take that though the computer can
+do it instantly even for nine ten
+
+ align:start position:0%
+do it instantly even for nine ten
+ 
+
+ align:start position:0%
+do it instantly even for nine ten
+players okay
+
+ align:start position:0%
+players okay
+ 
+
+ align:start position:0%
+players okay
+so what are some cases where ICM is easy
+
+ align:start position:0%
+so what are some cases where ICM is easy
+ 
+
+ align:start position:0%
+so what are some cases where ICM is easy
+to calculate so
+
+ align:start position:0%
+to calculate so
+ 
+
+ align:start position:0%
+to calculate so
+like I said in cash games there is no
+
+ align:start position:0%
+like I said in cash games there is no
+ 
+
+ align:start position:0%
+like I said in cash games there is no
+such thing as I see em you're just
+
+ align:start position:0%
+such thing as I see em you're just
+ 
+
+ align:start position:0%
+such thing as I see em you're just
+playing to maximize expected number of
+
+ align:start position:0%
+playing to maximize expected number of
+ 
+
+ align:start position:0%
+playing to maximize expected number of
+chips and your goal is essentially
+
+ align:start position:0%
+chips and your goal is essentially
+ 
+
+ align:start position:0%
+chips and your goal is essentially
+you're sitting down at the cash game
+
+ align:start position:0%
+you're sitting down at the cash game
+ 
+
+ align:start position:0%
+you're sitting down at the cash game
+looking to get into all and looking to
+
+ align:start position:0%
+looking to get into all and looking to
+ 
+
+ align:start position:0%
+looking to get into all and looking to
+get into favorable and hopefully winning
+
+ align:start position:0%
+get into favorable and hopefully winning
+ 
+
+ align:start position:0%
+get into favorable and hopefully winning
+the the person who you're targeting is
+
+ align:start position:0%
+the the person who you're targeting is
+ 
+
+ align:start position:0%
+the the person who you're targeting is
+light and turn and and winner takes all
+
+ align:start position:0%
+light and turn and and winner takes all
+ 
+
+ align:start position:0%
+light and turn and and winner takes all
+tournaments it's also the same the yours
+
+ align:start position:0%
+tournaments it's also the same the yours
+ 
+
+ align:start position:0%
+tournaments it's also the same the yours
+because you're just looking at your
+
+ align:start position:0%
+because you're just looking at your
+ 
+
+ align:start position:0%
+because you're just looking at your
+chances of winning the tournament and
+
+ align:start position:0%
+chances of winning the tournament and
+ 
+
+ align:start position:0%
+chances of winning the tournament and
+that's always just your number of chips
+
+ align:start position:0%
+that's always just your number of chips
+ 
+
+ align:start position:0%
+that's always just your number of chips
+so you're just trying to maximize
+
+ align:start position:0%
+so you're just trying to maximize
+ 
+
+ align:start position:0%
+so you're just trying to maximize
+expected number of chips so as a
+
+ align:start position:0%
+expected number of chips so as a
+ 
+
+ align:start position:0%
+expected number of chips so as a
+corollary once it gets down to two
+
+ align:start position:0%
+corollary once it gets down to two
+ 
+
+ align:start position:0%
+corollary once it gets down to two
+players there's no knows more such thing
+
+ align:start position:0%
+players there's no knows more such thing
+ 
+
+ align:start position:0%
+players there's no knows more such thing
+as I see em so sort of three is the
+
+ align:start position:0%
+as I see em so sort of three is the
+ 
+
+ align:start position:0%
+as I see em so sort of three is the
+minimum number of players you need for
+
+ align:start position:0%
+minimum number of players you need for
+ 
+
+ align:start position:0%
+minimum number of players you need for
+ICM to be relevant once it's two players
+
+ align:start position:0%
+ICM to be relevant once it's two players
+ 
+
+ align:start position:0%
+ICM to be relevant once it's two players
+it doesn't maximize your chip maybe
+
+ align:start position:0%
+it doesn't maximize your chip maybe
+ 
+
+ align:start position:0%
+it doesn't maximize your chip maybe
+because there's there's no sense of you
+
+ align:start position:0%
+because there's there's no sense of you
+ 
+
+ align:start position:0%
+because there's there's no sense of you
+know trying to survive who said someone
+
+ align:start position:0%
+know trying to survive who said someone
+ 
+
+ align:start position:0%
+know trying to survive who said someone
+else busts first because with only two
+
+ align:start position:0%
+else busts first because with only two
+ 
+
+ align:start position:0%
+else busts first because with only two
+people for the other guy bus do you have
+
+ align:start position:0%
+people for the other guy bus do you have
+ 
+
+ align:start position:0%
+people for the other guy bus do you have
+to you have to take all their chips okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what are some mathematical qualities
+
+ align:start position:0%
+so what are some mathematical qualities
+ 
+
+ align:start position:0%
+so what are some mathematical qualities
+of the LCM formula so big sacks have
+
+ align:start position:0%
+of the LCM formula so big sacks have
+ 
+
+ align:start position:0%
+of the LCM formula so big sacks have
+money easy less than ship TV small
+
+ align:start position:0%
+money easy less than ship TV small
+ 
+
+ align:start position:0%
+money easy less than ship TV small
+snacks have money you need greater than
+
+ align:start position:0%
+snacks have money you need greater than
+ 
+
+ align:start position:0%
+snacks have money you need greater than
+ship TV small
+
+ align:start position:0%
+ship TV small
+ 
+
+ align:start position:0%
+ship TV small
+sex also tend to have positive shitty B
+
+ align:start position:0%
+sex also tend to have positive shitty B
+ 
+
+ align:start position:0%
+sex also tend to have positive shitty B
+in general this is something I didn't
+
+ align:start position:0%
+in general this is something I didn't
+ 
+
+ align:start position:0%
+in general this is something I didn't
+mention too much but in general so you
+
+ align:start position:0%
+mention too much but in general so you
+ 
+
+ align:start position:0%
+mention too much but in general so you
+might have seen this if you guys have
+
+ align:start position:0%
+might have seen this if you guys have
+ 
+
+ align:start position:0%
+might have seen this if you guys have
+like Bindu casino and play cash games so
+
+ align:start position:0%
+like Bindu casino and play cash games so
+ 
+
+ align:start position:0%
+like Bindu casino and play cash games so
+like let's say you sit down at a table
+
+ align:start position:0%
+like let's say you sit down at a table
+ 
+
+ align:start position:0%
+like let's say you sit down at a table
+with in a cash game and evarin buys it
+
+ align:start position:0%
+with in a cash game and evarin buys it
+ 
+
+ align:start position:0%
+with in a cash game and evarin buys it
+for like a hundred big blinds at some
+
+ align:start position:0%
+for like a hundred big blinds at some
+ 
+
+ align:start position:0%
+for like a hundred big blinds at some
+tables usually they'll allow you to buy
+
+ align:start position:0%
+tables usually they'll allow you to buy
+ 
+
+ align:start position:0%
+tables usually they'll allow you to buy
+in for as low as like 20 big blinds and
+
+ align:start position:0%
+in for as low as like 20 big blinds and
+ 
+
+ align:start position:0%
+in for as low as like 20 big blinds and
+if you do this in general that's gonna
+
+ align:start position:0%
+if you do this in general that's gonna
+ 
+
+ align:start position:0%
+if you do this in general that's gonna
+be positive evie for the guy with 20 big
+
+ align:start position:0%
+be positive evie for the guy with 20 big
+ 
+
+ align:start position:0%
+be positive evie for the guy with 20 big
+blinds because there's situations where
+
+ align:start position:0%
+blinds because there's situations where
+ 
+
+ align:start position:0%
+blinds because there's situations where
+they have to wear like let's say they
+
+ align:start position:0%
+they have to wear like let's say they
+ 
+
+ align:start position:0%
+they have to wear like let's say they
+have to essentially sometimes one guy
+
+ align:start position:0%
+have to essentially sometimes one guy
+ 
+
+ align:start position:0%
+have to essentially sometimes one guy
+will raise one guy will call and then
+
+ align:start position:0%
+will raise one guy will call and then
+ 
+
+ align:start position:0%
+will raise one guy will call and then
+you can go on and then one guy will like
+
+ align:start position:0%
+you can go on and then one guy will like
+ 
+
+ align:start position:0%
+you can go on and then one guy will like
+go all in on top of you and the other
+
+ align:start position:0%
+go all in on top of you and the other
+ 
+
+ align:start position:0%
+go all in on top of you and the other
+guy will fold and then you'll have like
+
+ align:start position:0%
+guy will fold and then you'll have like
+ 
+
+ align:start position:0%
+guy will fold and then you'll have like
+good money so
+
+ align:start position:0%
+good money so
+ 
+
+ align:start position:0%
+good money so
+another thing is early on in the
+
+ align:start position:0%
+another thing is early on in the
+ 
+
+ align:start position:0%
+another thing is early on in the
+tournament ICM is irrelevant you just
+
+ align:start position:0%
+tournament ICM is irrelevant you just
+ 
+
+ align:start position:0%
+tournament ICM is irrelevant you just
+want to can relate chips so like if you
+
+ align:start position:0%
+want to can relate chips so like if you
+ 
+
+ align:start position:0%
+want to can relate chips so like if you
+you know if you try to do this formula
+
+ align:start position:0%
+you know if you try to do this formula
+ 
+
+ align:start position:0%
+you know if you try to do this formula
+early on in a tournament what you'll
+
+ align:start position:0%
+early on in a tournament what you'll
+ 
+
+ align:start position:0%
+early on in a tournament what you'll
+find is essentially the
+
+ align:start position:0%
+find is essentially the
+ 
+
+ align:start position:0%
+find is essentially the
+essentially you're so far away from the
+
+ align:start position:0%
+essentially you're so far away from the
+ 
+
+ align:start position:0%
+essentially you're so far away from the
+money that none of the things really
+
+ align:start position:0%
+money that none of the things really
+ 
+
+ align:start position:0%
+money that none of the things really
+matter to maximize your chances of even
+
+ align:start position:0%
+matter to maximize your chances of even
+ 
+
+ align:start position:0%
+matter to maximize your chances of even
+getting through the money you just wanna
+
+ align:start position:0%
+getting through the money you just wanna
+ 
+
+ align:start position:0%
+getting through the money you just wanna
+maximize your number of chairs so
+
+ align:start position:0%
+maximize your number of chairs so
+ 
+
+ align:start position:0%
+maximize your number of chairs so
+where does I see a most relevant it's
+
+ align:start position:0%
+where does I see a most relevant it's
+ 
+
+ align:start position:0%
+where does I see a most relevant it's
+most relevant on the exact pay level and
+
+ align:start position:0%
+most relevant on the exact pay level and
+ 
+
+ align:start position:0%
+most relevant on the exact pay level and
+on the final table so let me so roughly
+
+ align:start position:0%
+on the final table so let me so roughly
+ 
+
+ align:start position:0%
+on the final table so let me so roughly
+speaking in every took poker tournament
+
+ align:start position:0%
+speaking in every took poker tournament
+ 
+
+ align:start position:0%
+speaking in every took poker tournament
+I've seen other than like strange ones
+
+ align:start position:0%
+I've seen other than like strange ones
+ 
+
+ align:start position:0%
+I've seen other than like strange ones
+that are like winter takes all our
+
+ align:start position:0%
+that are like winter takes all our
+ 
+
+ align:start position:0%
+that are like winter takes all our
+satellites the pay looks roughly like
+
+ align:start position:0%
+satellites the pay looks roughly like
+ 
+
+ align:start position:0%
+satellites the pay looks roughly like
+this so so it's zero you go in and once
+
+ align:start position:0%
+this so so it's zero you go in and once
+ 
+
+ align:start position:0%
+this so so it's zero you go in and once
+you hit about top twenty percent is the
+
+ align:start position:0%
+you hit about top twenty percent is the
+ 
+
+ align:start position:0%
+you hit about top twenty percent is the
+bubble and then there's like a jump here
+
+ align:start position:0%
+bubble and then there's like a jump here
+ 
+
+ align:start position:0%
+bubble and then there's like a jump here
+or suddenly you get paid so this is
+
+ align:start position:0%
+or suddenly you get paid so this is
+ 
+
+ align:start position:0%
+or suddenly you get paid so this is
+about this is about 80 percent get zero
+
+ align:start position:0%
+about this is about 80 percent get zero
+ 
+
+ align:start position:0%
+about this is about 80 percent get zero
+and then so here there's a jump and then
+
+ align:start position:0%
+and then so here there's a jump and then
+ 
+
+ align:start position:0%
+and then so here there's a jump and then
+it escalates slowly until you get to the
+
+ align:start position:0%
+it escalates slowly until you get to the
+ 
+
+ align:start position:0%
+it escalates slowly until you get to the
+final table
+
+ align:start position:0%
+final table
+ 
+
+ align:start position:0%
+final table
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+final survey is my sister she's color
+
+ align:start position:0%
+final survey is my sister she's color
+ 
+
+ align:start position:0%
+final survey is my sister she's color
+I know table and then it escalates
+
+ align:start position:0%
+I know table and then it escalates
+ 
+
+ align:start position:0%
+I know table and then it escalates
+really fast so essentially basically I
+
+ align:start position:0%
+really fast so essentially basically I
+ 
+
+ align:start position:0%
+really fast so essentially basically I
+see them as most relevant at the points
+
+ align:start position:0%
+see them as most relevant at the points
+ 
+
+ align:start position:0%
+see them as most relevant at the points
+where like essentially the derivative or
+
+ align:start position:0%
+where like essentially the derivative or
+ 
+
+ align:start position:0%
+where like essentially the derivative or
+the rate of change of the payout is
+
+ align:start position:0%
+the rate of change of the payout is
+ 
+
+ align:start position:0%
+the rate of change of the payout is
+highest and those points as you can see
+
+ align:start position:0%
+highest and those points as you can see
+ 
+
+ align:start position:0%
+highest and those points as you can see
+are here and here so essentially it
+
+ align:start position:0%
+are here and here so essentially it
+ 
+
+ align:start position:0%
+are here and here so essentially it
+matters most at the exact money bubble
+
+ align:start position:0%
+matters most at the exact money bubble
+ 
+
+ align:start position:0%
+matters most at the exact money bubble
+and in the final table okay
+
+ align:start position:0%
+and in the final table okay
+ 
+
+ align:start position:0%
+and in the final table okay
+let me clear this okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah so some more extreme examples of
+
+ align:start position:0%
+so yeah so some more extreme examples of
+ 
+
+ align:start position:0%
+so yeah so some more extreme examples of
+ICM is you have one ship let left late
+
+ align:start position:0%
+ICM is you have one ship let left late
+ 
+
+ align:start position:0%
+ICM is you have one ship let left late
+in a tournament when everyone else has
+
+ align:start position:0%
+in a tournament when everyone else has
+ 
+
+ align:start position:0%
+in a tournament when everyone else has
+thousands of chips so clearly this ship
+
+ align:start position:0%
+thousands of chips so clearly this ship
+ 
+
+ align:start position:0%
+thousands of chips so clearly this ship
+is worth a lot more than its value as a
+
+ align:start position:0%
+is worth a lot more than its value as a
+ 
+
+ align:start position:0%
+is worth a lot more than its value as a
+fraction of the chips and your is trying
+
+ align:start position:0%
+fraction of the chips and your is trying
+ 
+
+ align:start position:0%
+fraction of the chips and your is trying
+to survive with this one chip
+
+ align:start position:0%
+to survive with this one chip
+ 
+
+ align:start position:0%
+to survive with this one chip
+essentially instead of trying to win
+
+ align:start position:0%
+essentially instead of trying to win
+ 
+
+ align:start position:0%
+essentially instead of trying to win
+more chips and and so maybe maybe I was
+
+ align:start position:0%
+more chips and and so maybe maybe I was
+ 
+
+ align:start position:0%
+more chips and and so maybe maybe I was
+talking about this in a bit so in
+
+ align:start position:0%
+talking about this in a bit so in
+ 
+
+ align:start position:0%
+talking about this in a bit so in
+satellites so sad what satellites are
+
+ align:start position:0%
+satellites so sad what satellites are
+ 
+
+ align:start position:0%
+satellites so sad what satellites are
+there tournaments where you're trying to
+
+ align:start position:0%
+there tournaments where you're trying to
+ 
+
+ align:start position:0%
+there tournaments where you're trying to
+qualify for a bigger tournament so
+
+ align:start position:0%
+qualify for a bigger tournament so
+ 
+
+ align:start position:0%
+qualify for a bigger tournament so
+essentially the important thing is so
+
+ align:start position:0%
+essentially the important thing is so
+ 
+
+ align:start position:0%
+essentially the important thing is so
+you know there will be maybe like a
+
+ align:start position:0%
+you know there will be maybe like a
+ 
+
+ align:start position:0%
+you know there will be maybe like a
+hundred players and there will be ten
+
+ align:start position:0%
+hundred players and there will be ten
+ 
+
+ align:start position:0%
+hundred players and there will be ten
+seats which means the top ten get an
+
+ align:start position:0%
+seats which means the top ten get an
+ 
+
+ align:start position:0%
+seats which means the top ten get an
+invite to the bigger tournament and then
+
+ align:start position:0%
+invite to the bigger tournament and then
+ 
+
+ align:start position:0%
+invite to the bigger tournament and then
+everyone else gets nothing so answer the
+
+ align:start position:0%
+everyone else gets nothing so answer the
+ 
+
+ align:start position:0%
+everyone else gets nothing so answer the
+qualifiers for the MIT Series of Poker
+
+ align:start position:0%
+qualifiers for the MIT Series of Poker
+ 
+
+ align:start position:0%
+qualifiers for the MIT Series of Poker
+Main Event are kind of like this right
+
+ align:start position:0%
+Main Event are kind of like this right
+ 
+
+ align:start position:0%
+Main Event are kind of like this right
+it says your eternity I guess there's
+
+ align:start position:0%
+it says your eternity I guess there's
+ 
+
+ align:start position:0%
+it says your eternity I guess there's
+other prizes too but you're essentially
+
+ align:start position:0%
+other prizes too but you're essentially
+ 
+
+ align:start position:0%
+other prizes too but you're essentially
+trying to come to Talk 10 so this is how
+
+ align:start position:0%
+trying to come to Talk 10 so this is how
+ 
+
+ align:start position:0%
+trying to come to Talk 10 so this is how
+that works and in that case right the
+
+ align:start position:0%
+that works and in that case right the
+ 
+
+ align:start position:0%
+that works and in that case right the
+pay though is the payout is essentially
+
+ align:start position:0%
+pay though is the payout is essentially
+ 
+
+ align:start position:0%
+pay though is the payout is essentially
+this so there's not really much
+
+ align:start position:0%
+this so there's not really much
+ 
+
+ align:start position:0%
+this so there's not really much
+incentive to win you're just trying to
+
+ align:start position:0%
+incentive to win you're just trying to
+ 
+
+ align:start position:0%
+incentive to win you're just trying to
+be one of this top 10% that gets paid so
+
+ align:start position:0%
+be one of this top 10% that gets paid so
+ 
+
+ align:start position:0%
+be one of this top 10% that gets paid so
+that's another case where ICM has
+
+ align:start position:0%
+that's another case where ICM has
+ 
+
+ align:start position:0%
+that's another case where ICM has
+extreme importance and you often find
+
+ align:start position:0%
+extreme importance and you often find
+ 
+
+ align:start position:0%
+extreme importance and you often find
+you are not often but you can often make
+
+ align:start position:0%
+you are not often but you can often make
+ 
+
+ align:start position:0%
+you are not often but you can often make
+a case for folding pocket aces pretty
+
+ align:start position:0%
+a case for folding pocket aces pretty
+ 
+
+ align:start position:0%
+a case for folding pocket aces pretty
+fun even though it's even though you
+
+ align:start position:0%
+fun even though it's even though you
+ 
+
+ align:start position:0%
+fun even though it's even though you
+know it's gonna have positive chip TV if
+
+ align:start position:0%
+know it's gonna have positive chip TV if
+ 
+
+ align:start position:0%
+know it's gonna have positive chip TV if
+you call because it's the best possible
+
+ align:start position:0%
+you call because it's the best possible
+ 
+
+ align:start position:0%
+you call because it's the best possible
+hand but because you just really don't
+
+ align:start position:0%
+hand but because you just really don't
+ 
+
+ align:start position:0%
+hand but because you just really don't
+want to bust then you actually want to
+
+ align:start position:0%
+want to bust then you actually want to
+ 
+
+ align:start position:0%
+want to bust then you actually want to
+fold theses okay we'll talk about this a
+
+ align:start position:0%
+fold theses okay we'll talk about this a
+ 
+
+ align:start position:0%
+fold theses okay we'll talk about this a
+bit more later later or less get to okay
+
+ align:start position:0%
+bit more later later or less get to okay
+ 
+
+ align:start position:0%
+bit more later later or less get to okay
+so let's get back to the tournament so
+
+ align:start position:0%
+so let's get back to the tournament so
+ 
+
+ align:start position:0%
+so let's get back to the tournament so
+this is the final table so
+
+ align:start position:0%
+this is the final table so
+ 
+
+ align:start position:0%
+this is the final table so
+ICM is going to be quite relevant here
+
+ align:start position:0%
+ICM is going to be quite relevant here
+ 
+
+ align:start position:0%
+ICM is going to be quite relevant here
+and so I as I'm talking through my
+
+ align:start position:0%
+and so I as I'm talking through my
+ 
+
+ align:start position:0%
+and so I as I'm talking through my
+decisions in the hands I'll talk about
+
+ align:start position:0%
+decisions in the hands I'll talk about
+ 
+
+ align:start position:0%
+decisions in the hands I'll talk about
+sort of the ICM decisions as well okay
+
+ align:start position:0%
+sort of the ICM decisions as well okay
+ 
+
+ align:start position:0%
+sort of the ICM decisions as well okay
+so this is a
+
+ align:start position:0%
+so this is a
+ 
+
+ align:start position:0%
+so this is a
+this is the first hand or I think might
+
+ align:start position:0%
+this is the first hand or I think might
+ 
+
+ align:start position:0%
+this is the first hand or I think might
+have maybe one orbit past but so we're
+
+ align:start position:0%
+have maybe one orbit past but so we're
+ 
+
+ align:start position:0%
+have maybe one orbit past but so we're
+at the final table we're right now we're
+
+ align:start position:0%
+at the final table we're right now we're
+ 
+
+ align:start position:0%
+at the final table we're right now we're
+the second biggest stack and so yeah we
+
+ align:start position:0%
+the second biggest stack and so yeah we
+ 
+
+ align:start position:0%
+the second biggest stack and so yeah we
+should maybe look at the stack sizes so
+
+ align:start position:0%
+should maybe look at the stack sizes so
+ 
+
+ align:start position:0%
+should maybe look at the stack sizes so
+we look around at the stack sizes so so
+
+ align:start position:0%
+we look around at the stack sizes so so
+ 
+
+ align:start position:0%
+we look around at the stack sizes so so
+what do you notice about this access or
+
+ align:start position:0%
+what do you notice about this access or
+ 
+
+ align:start position:0%
+what do you notice about this access or
+like specifically like how are we doing
+
+ align:start position:0%
+like specifically like how are we doing
+ 
+
+ align:start position:0%
+like specifically like how are we doing
+how many just how many chips we have
+
+ align:start position:0%
+how many just how many chips we have
+ 
+
+ align:start position:0%
+how many just how many chips we have
+we'll
+
+ align:start position:0%
+we'll
+ 
+
+ align:start position:0%
+we'll
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+we have quite a lot right we have quite
+
+ align:start position:0%
+we have quite a lot right we have quite
+ 
+
+ align:start position:0%
+we have quite a lot right we have quite
+a lot but we're not in the first place
+
+ align:start position:0%
+a lot but we're not in the first place
+ 
+
+ align:start position:0%
+a lot but we're not in the first place
+there's this one guy who covers us so
+
+ align:start position:0%
+there's this one guy who covers us so
+ 
+
+ align:start position:0%
+there's this one guy who covers us so
+this pen hand Krissy guy uh if you
+
+ align:start position:0%
+this pen hand Krissy guy uh if you
+ 
+
+ align:start position:0%
+this pen hand Krissy guy uh if you
+covers us so specifically
+
+ align:start position:0%
+covers us so specifically
+ 
+
+ align:start position:0%
+covers us so specifically
+the thing I'm trying to avoid is getting
+
+ align:start position:0%
+the thing I'm trying to avoid is getting
+ 
+
+ align:start position:0%
+the thing I'm trying to avoid is getting
+in a big pot with Pam and Chrissy like I
+
+ align:start position:0%
+in a big pot with Pam and Chrissy like I
+ 
+
+ align:start position:0%
+in a big pot with Pam and Chrissy like I
+mean let's say she goes all in and I
+
+ align:start position:0%
+mean let's say she goes all in and I
+ 
+
+ align:start position:0%
+mean let's say she goes all in and I
+have pocket kings I'm gonna call but I'm
+
+ align:start position:0%
+have pocket kings I'm gonna call but I'm
+ 
+
+ align:start position:0%
+have pocket kings I'm gonna call but I'm
+not going to be that happy about calling
+
+ align:start position:0%
+not going to be that happy about calling
+ 
+
+ align:start position:0%
+not going to be that happy about calling
+in a situation where otherwise I should
+
+ align:start position:0%
+in a situation where otherwise I should
+ 
+
+ align:start position:0%
+in a situation where otherwise I should
+be very happy just because you know
+
+ align:start position:0%
+be very happy just because you know
+ 
+
+ align:start position:0%
+be very happy just because you know
+chances are he's gonna have an ace he's
+
+ align:start position:0%
+chances are he's gonna have an ace he's
+ 
+
+ align:start position:0%
+chances are he's gonna have an ace he's
+gonna have 30% equity I mean it's no
+
+ align:start position:0%
+gonna have 30% equity I mean it's no
+ 
+
+ align:start position:0%
+gonna have 30% equity I mean it's no
+gonna be positive money you need to call
+
+ align:start position:0%
+gonna be positive money you need to call
+ 
+
+ align:start position:0%
+gonna be positive money you need to call
+but it's so bad if I basically bust
+
+ align:start position:0%
+but it's so bad if I basically bust
+ 
+
+ align:start position:0%
+but it's so bad if I basically bust
+right now in eighth place against the
+
+ align:start position:0%
+right now in eighth place against the
+ 
+
+ align:start position:0%
+right now in eighth place against the
+damn hangers so essentially I'm really
+
+ align:start position:0%
+damn hangers so essentially I'm really
+ 
+
+ align:start position:0%
+damn hangers so essentially I'm really
+incentivized to avoid like getting in
+
+ align:start position:0%
+incentivized to avoid like getting in
+ 
+
+ align:start position:0%
+incentivized to avoid like getting in
+big pots of them and I'm essentially
+
+ align:start position:0%
+big pots of them and I'm essentially
+ 
+
+ align:start position:0%
+big pots of them and I'm essentially
+hoping for some of these smaller stacks
+
+ align:start position:0%
+hoping for some of these smaller stacks
+ 
+
+ align:start position:0%
+hoping for some of these smaller stacks
+to bust so that then even if I lose a
+
+ align:start position:0%
+to bust so that then even if I lose a
+ 
+
+ align:start position:0%
+to bust so that then even if I lose a
+big pot to him I don't get the low
+
+ align:start position:0%
+big pot to him I don't get the low
+ 
+
+ align:start position:0%
+big pot to him I don't get the low
+eighth place payoff so okay so it's
+
+ align:start position:0%
+eighth place payoff so okay so it's
+ 
+
+ align:start position:0%
+eighth place payoff so okay so it's
+folded to us we raise here I think this
+
+ align:start position:0%
+folded to us we raise here I think this
+ 
+
+ align:start position:0%
+folded to us we raise here I think this
+is one of the weakest hands I I'm
+
+ align:start position:0%
+is one of the weakest hands I I'm
+ 
+
+ align:start position:0%
+is one of the weakest hands I I'm
+raising from the button but so far
+
+ align:start position:0%
+raising from the button but so far
+ 
+
+ align:start position:0%
+raising from the button but so far
+players have seemed to be reasonably
+
+ align:start position:0%
+players have seemed to be reasonably
+ 
+
+ align:start position:0%
+players have seemed to be reasonably
+tight so I'm gonna raise and then I get
+
+ align:start position:0%
+tight so I'm gonna raise and then I get
+ 
+
+ align:start position:0%
+tight so I'm gonna raise and then I get
+the blinds okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'll supposed to give some hands at
+
+ align:start position:0%
+so I'll supposed to give some hands at
+ 
+
+ align:start position:0%
+so I'll supposed to give some hands at
+the beginning near the end they'll apply
+
+ align:start position:0%
+the beginning near the end they'll apply
+ 
+
+ align:start position:0%
+the beginning near the end they'll apply
+every hand this thing we don't play but
+
+ align:start position:0%
+every hand this thing we don't play but
+ 
+
+ align:start position:0%
+every hand this thing we don't play but
+I'll try to show the hands were someone
+
+ align:start position:0%
+I'll try to show the hands were someone
+ 
+
+ align:start position:0%
+I'll try to show the hands were someone
+busts so this hand small one goes all in
+
+ align:start position:0%
+busts so this hand small one goes all in
+ 
+
+ align:start position:0%
+busts so this hand small one goes all in
+big blind calls and so
+
+ align:start position:0%
+big blind calls and so
+ 
+
+ align:start position:0%
+big blind calls and so
+small mine wins with ten to suited
+
+ align:start position:0%
+small mine wins with ten to suited
+ 
+
+ align:start position:0%
+small mine wins with ten to suited
+against ace 4 which is basically great
+
+ align:start position:0%
+against ace 4 which is basically great
+ 
+
+ align:start position:0%
+against ace 4 which is basically great
+for everyone because someone busted
+
+ align:start position:0%
+for everyone because someone busted
+ 
+
+ align:start position:0%
+for everyone because someone busted
+you're always cheering for people to
+
+ align:start position:0%
+you're always cheering for people to
+ 
+
+ align:start position:0%
+you're always cheering for people to
+bust especially and
+
+ align:start position:0%
+bust especially and
+ 
+
+ align:start position:0%
+bust especially and
+I think also both of their plays are
+
+ align:start position:0%
+I think also both of their plays are
+ 
+
+ align:start position:0%
+I think also both of their plays are
+fine so I think small with small minds
+
+ align:start position:0%
+fine so I think small with small minds
+ 
+
+ align:start position:0%
+fine so I think small with small minds
+play it looks a bit silly but
+
+ align:start position:0%
+play it looks a bit silly but
+ 
+
+ align:start position:0%
+play it looks a bit silly but
+realistically not
+
+ align:start position:0%
+realistically not
+ 
+
+ align:start position:0%
+realistically not
+only does 10 - reasonable equity when
+
+ align:start position:0%
+only does 10 - reasonable equity when
+ 
+
+ align:start position:0%
+only does 10 - reasonable equity when
+you're called it's also the ICM is very
+
+ align:start position:0%
+you're called it's also the ICM is very
+ 
+
+ align:start position:0%
+you're called it's also the ICM is very
+very very developed like this Gerard ox
+
+ align:start position:0%
+very very developed like this Gerard ox
+ 
+
+ align:start position:0%
+very very developed like this Gerard ox
+died he's
+
+ align:start position:0%
+died he's
+ 
+
+ align:start position:0%
+died he's
+not the shortest I mean he is one of the
+
+ align:start position:0%
+not the shortest I mean he is one of the
+ 
+
+ align:start position:0%
+not the shortest I mean he is one of the
+shortest so he does need to take some
+
+ align:start position:0%
+shortest so he does need to take some
+ 
+
+ align:start position:0%
+shortest so he does need to take some
+risk but he's still really very much
+
+ align:start position:0%
+risk but he's still really very much
+ 
+
+ align:start position:0%
+risk but he's still really very much
+would like to bust after I show to hit
+
+ align:start position:0%
+would like to bust after I show to hit
+ 
+
+ align:start position:0%
+would like to bust after I show to hit
+78 so he so he can't call with anything
+
+ align:start position:0%
+78 so he so he can't call with anything
+ 
+
+ align:start position:0%
+78 so he so he can't call with anything
+I mean with ace floor I think that's
+
+ align:start position:0%
+I mean with ace floor I think that's
+ 
+
+ align:start position:0%
+I mean with ace floor I think that's
+definitely good enough to call but let's
+
+ align:start position:0%
+definitely good enough to call but let's
+ 
+
+ align:start position:0%
+definitely good enough to call but let's
+say they have like king two officers I
+
+ align:start position:0%
+say they have like king two officers I
+ 
+
+ align:start position:0%
+say they have like king two officers I
+think that's a situation I do normally
+
+ align:start position:0%
+think that's a situation I do normally
+ 
+
+ align:start position:0%
+think that's a situation I do normally
+call if it was like not a final table
+
+ align:start position:0%
+call if it was like not a final table
+ 
+
+ align:start position:0%
+call if it was like not a final table
+under tournament but I had a final table
+
+ align:start position:0%
+under tournament but I had a final table
+ 
+
+ align:start position:0%
+under tournament but I had a final table
+where I'm not the shortest and there's
+
+ align:start position:0%
+where I'm not the shortest and there's
+ 
+
+ align:start position:0%
+where I'm not the shortest and there's
+someone shorter than me I would consider
+
+ align:start position:0%
+someone shorter than me I would consider
+ 
+
+ align:start position:0%
+someone shorter than me I would consider
+folding tend to cert King to offsuit
+
+ align:start position:0%
+folding tend to cert King to offsuit
+ 
+
+ align:start position:0%
+folding tend to cert King to offsuit
+here just because um just because of ICM
+
+ align:start position:0%
+here just because um just because of ICM
+ 
+
+ align:start position:0%
+here just because um just because of ICM
+essentially all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the next hand so so the so the
+
+ align:start position:0%
+right so the next hand so so the so the
+ 
+
+ align:start position:0%
+right so the next hand so so the so the
+big blind busts and then there's no
+
+ align:start position:0%
+big blind busts and then there's no
+ 
+
+ align:start position:0%
+big blind busts and then there's no
+small line this sandwich is great
+
+ align:start position:0%
+small line this sandwich is great
+ 
+
+ align:start position:0%
+small line this sandwich is great
+because where people are less than sent
+
+ align:start position:0%
+because where people are less than sent
+ 
+
+ align:start position:0%
+because where people are less than sent
+device of steel and indeed we get our
+
+ align:start position:0%
+device of steel and indeed we get our
+ 
+
+ align:start position:0%
+device of steel and indeed we get our
+nice
+
+ align:start position:0%
+nice
+ 
+
+ align:start position:0%
+nice
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+not much happens here I'll skip forward
+
+ align:start position:0%
+not much happens here I'll skip forward
+ 
+
+ align:start position:0%
+not much happens here I'll skip forward
+a bit okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this hand I guess it's quite convenient
+
+ align:start position:0%
+this hand I guess it's quite convenient
+ 
+
+ align:start position:0%
+this hand I guess it's quite convenient
+for us but this'll illustrate the points
+
+ align:start position:0%
+for us but this'll illustrate the points
+ 
+
+ align:start position:0%
+for us but this'll illustrate the points
+so okay so so this guy who doesn't love
+
+ align:start position:0%
+so okay so so this guy who doesn't love
+ 
+
+ align:start position:0%
+so okay so so this guy who doesn't love
+a bit earlier right now he goes on and
+
+ align:start position:0%
+a bit earlier right now he goes on and
+ 
+
+ align:start position:0%
+a bit earlier right now he goes on and
+for quite a lot right this is quite a
+
+ align:start position:0%
+for quite a lot right this is quite a
+ 
+
+ align:start position:0%
+for quite a lot right this is quite a
+big shove and if you plenty by my
+
+ align:start position:0%
+big shove and if you plenty by my
+ 
+
+ align:start position:0%
+big shove and if you plenty by my
+recommendations I would never recommend
+
+ align:start position:0%
+recommendations I would never recommend
+ 
+
+ align:start position:0%
+recommendations I would never recommend
+shoving like this this many bets I mean
+
+ align:start position:0%
+shoving like this this many bets I mean
+ 
+
+ align:start position:0%
+shoving like this this many bets I mean
+it's not it's like 24 it's quite great
+
+ align:start position:0%
+it's not it's like 24 it's quite great
+ 
+
+ align:start position:0%
+it's not it's like 24 it's quite great
+actually 23 it says 23 23 big blinds
+
+ align:start position:0%
+actually 23 it says 23 23 big blinds
+ 
+
+ align:start position:0%
+actually 23 it says 23 23 big blinds
+which is like wage you watch the show
+
+ align:start position:0%
+which is like wage you watch the show
+ 
+
+ align:start position:0%
+which is like wage you watch the show
+right there's no need you can't risk
+
+ align:start position:0%
+right there's no need you can't risk
+ 
+
+ align:start position:0%
+right there's no need you can't risk
+this much but once again I think his
+
+ align:start position:0%
+this much but once again I think his
+ 
+
+ align:start position:0%
+this much but once again I think his
+play is justifiable because of ICM you
+
+ align:start position:0%
+play is justifiable because of ICM you
+ 
+
+ align:start position:0%
+play is justifiable because of ICM you
+know he doesn't and so ok so let's see
+
+ align:start position:0%
+know he doesn't and so ok so let's see
+ 
+
+ align:start position:0%
+know he doesn't and so ok so let's see
+what he had so we call I mean here it's
+
+ align:start position:0%
+what he had so we call I mean here it's
+ 
+
+ align:start position:0%
+what he had so we call I mean here it's
+a bit different because even if I call
+
+ align:start position:0%
+a bit different because even if I call
+ 
+
+ align:start position:0%
+a bit different because even if I call
+and lose I'm not out of the tournament
+
+ align:start position:0%
+and lose I'm not out of the tournament
+ 
+
+ align:start position:0%
+and lose I'm not out of the tournament
+and I mean even if I even if I'm what
+
+ align:start position:0%
+and I mean even if I even if I'm what
+ 
+
+ align:start position:0%
+and I mean even if I even if I'm what
+would be out like even if you have to mm
+
+ align:start position:0%
+would be out like even if you have to mm
+ 
+
+ align:start position:0%
+would be out like even if you have to mm
+I'd probably still call with Queens mr.
+
+ align:start position:0%
+I'd probably still call with Queens mr.
+ 
+
+ align:start position:0%
+I'd probably still call with Queens mr.
+beautiful so
+
+ align:start position:0%
+beautiful so
+ 
+
+ align:start position:0%
+beautiful so
+we need a screen here which is great for
+
+ align:start position:0%
+we need a screen here which is great for
+ 
+
+ align:start position:0%
+we need a screen here which is great for
+us but if you look at the play from his
+
+ align:start position:0%
+us but if you look at the play from his
+ 
+
+ align:start position:0%
+us but if you look at the play from his
+perspective again it actually seems
+
+ align:start position:0%
+perspective again it actually seems
+ 
+
+ align:start position:0%
+perspective again it actually seems
+quite reasonable if you think about it
+
+ align:start position:0%
+quite reasonable if you think about it
+ 
+
+ align:start position:0%
+quite reasonable if you think about it
+because you know for him ace queen is a
+
+ align:start position:0%
+because you know for him ace queen is a
+ 
+
+ align:start position:0%
+because you know for him ace queen is a
+great hand from this position it's
+
+ align:start position:0%
+great hand from this position it's
+ 
+
+ align:start position:0%
+great hand from this position it's
+definitely good enough where you know if
+
+ align:start position:0%
+definitely good enough where you know if
+ 
+
+ align:start position:0%
+definitely good enough where you know if
+it was between folding and shoving for
+
+ align:start position:0%
+it was between folding and shoving for
+ 
+
+ align:start position:0%
+it was between folding and shoving for
+23 big blinds you would definitely
+
+ align:start position:0%
+23 big blinds you would definitely
+ 
+
+ align:start position:0%
+23 big blinds you would definitely
+rather rather show for 23 big blinds so
+
+ align:start position:0%
+rather rather show for 23 big blinds so
+ 
+
+ align:start position:0%
+rather rather show for 23 big blinds so
+you know the main reason why normally
+
+ align:start position:0%
+you know the main reason why normally
+ 
+
+ align:start position:0%
+you know the main reason why normally
+one would criticize his play is because
+
+ align:start position:0%
+one would criticize his play is because
+ 
+
+ align:start position:0%
+one would criticize his play is because
+you know why that wasn't he just made a
+
+ align:start position:0%
+you know why that wasn't he just made a
+ 
+
+ align:start position:0%
+you know why that wasn't he just made a
+small with ace Queen well understandably
+
+ align:start position:0%
+small with ace Queen well understandably
+ 
+
+ align:start position:0%
+small with ace Queen well understandably
+he doesn't really want you want to
+
+ align:start position:0%
+he doesn't really want you want to
+ 
+
+ align:start position:0%
+he doesn't really want you want to
+incentivize me to like rebates or panca
+
+ align:start position:0%
+incentivize me to like rebates or panca
+ 
+
+ align:start position:0%
+incentivize me to like rebates or panca
+see to make a tree raise he actually
+
+ align:start position:0%
+see to make a tree raise he actually
+ 
+
+ align:start position:0%
+see to make a tree raise he actually
+wants to minimize the chances that he
+
+ align:start position:0%
+wants to minimize the chances that he
+ 
+
+ align:start position:0%
+wants to minimize the chances that he
+actually played for his stack in this
+
+ align:start position:0%
+actually played for his stack in this
+ 
+
+ align:start position:0%
+actually played for his stack in this
+hand and the way he does that is
+
+ align:start position:0%
+hand and the way he does that is
+ 
+
+ align:start position:0%
+hand and the way he does that is
+essentially by going all-in so if so you
+
+ align:start position:0%
+essentially by going all-in so if so you
+ 
+
+ align:start position:0%
+essentially by going all-in so if so you
+know looking looking at back at it I
+
+ align:start position:0%
+know looking looking at back at it I
+ 
+
+ align:start position:0%
+know looking looking at back at it I
+think his play is fine the only weakness
+
+ align:start position:0%
+think his play is fine the only weakness
+ 
+
+ align:start position:0%
+think his play is fine the only weakness
+of his play I think is it is a bit sort
+
+ align:start position:0%
+of his play I think is it is a bit sort
+ 
+
+ align:start position:0%
+of his play I think is it is a bit sort
+of predictable what his hand is in this
+
+ align:start position:0%
+of predictable what his hand is in this
+ 
+
+ align:start position:0%
+of predictable what his hand is in this
+situation because I think like if he had
+
+ align:start position:0%
+situation because I think like if he had
+ 
+
+ align:start position:0%
+situation because I think like if he had
+a hand as good as pocket aces then he
+
+ align:start position:0%
+a hand as good as pocket aces then he
+ 
+
+ align:start position:0%
+a hand as good as pocket aces then he
+shouldn't be doing this he should just
+
+ align:start position:0%
+shouldn't be doing this he should just
+ 
+
+ align:start position:0%
+shouldn't be doing this he should just
+be raising small because it's good
+
+ align:start position:0%
+be raising small because it's good
+ 
+
+ align:start position:0%
+be raising small because it's good
+enough where he's happy getting it in
+
+ align:start position:0%
+enough where he's happy getting it in
+ 
+
+ align:start position:0%
+enough where he's happy getting it in
+against me or pan-pan chrissie where is
+
+ align:start position:0%
+against me or pan-pan chrissie where is
+ 
+
+ align:start position:0%
+against me or pan-pan chrissie where is
+you know also if his hand was slightly
+
+ align:start position:0%
+you know also if his hand was slightly
+ 
+
+ align:start position:0%
+you know also if his hand was slightly
+worse like East Jack offsuit I think is
+
+ align:start position:0%
+worse like East Jack offsuit I think is
+ 
+
+ align:start position:0%
+worse like East Jack offsuit I think is
+a good example I think ace Jack offsuit
+
+ align:start position:0%
+a good example I think ace Jack offsuit
+ 
+
+ align:start position:0%
+a good example I think ace Jack offsuit
+is is not strong enough to make this all
+
+ align:start position:0%
+is is not strong enough to make this all
+ 
+
+ align:start position:0%
+is is not strong enough to make this all
+and play with but you still want to be
+
+ align:start position:0%
+and play with but you still want to be
+ 
+
+ align:start position:0%
+and play with but you still want to be
+raising so I think there's a small range
+
+ align:start position:0%
+raising so I think there's a small range
+ 
+
+ align:start position:0%
+raising so I think there's a small range
+of hands that you want to be making this
+
+ align:start position:0%
+of hands that you want to be making this
+ 
+
+ align:start position:0%
+of hands that you want to be making this
+on plays like I think that's basically
+
+ align:start position:0%
+on plays like I think that's basically
+ 
+
+ align:start position:0%
+on plays like I think that's basically
+exactly ace Queen off suit maybe Ace
+
+ align:start position:0%
+exactly ace Queen off suit maybe Ace
+ 
+
+ align:start position:0%
+exactly ace Queen off suit maybe Ace
+King maybe ace Queen Ace King and then
+
+ align:start position:0%
+King maybe ace Queen Ace King and then
+ 
+
+ align:start position:0%
+King maybe ace Queen Ace King and then
+like middle pairs let's say like between
+
+ align:start position:0%
+like middle pairs let's say like between
+ 
+
+ align:start position:0%
+like middle pairs let's say like between
+like pockets eights and pocket tennis or
+
+ align:start position:0%
+like pockets eights and pocket tennis or
+ 
+
+ align:start position:0%
+like pockets eights and pocket tennis or
+something so so like the only downside
+
+ align:start position:0%
+something so so like the only downside
+ 
+
+ align:start position:0%
+something so so like the only downside
+of this play I think is essentially his
+
+ align:start position:0%
+of this play I think is essentially his
+ 
+
+ align:start position:0%
+of this play I think is essentially his
+range here is very predictable it's
+
+ align:start position:0%
+range here is very predictable it's
+ 
+
+ align:start position:0%
+range here is very predictable it's
+gonna be like ace Jack suited plus ace
+
+ align:start position:0%
+gonna be like ace Jack suited plus ace
+ 
+
+ align:start position:0%
+gonna be like ace Jack suited plus ace
+queen and pocket eights three times or
+
+ align:start position:0%
+queen and pocket eights three times or
+ 
+
+ align:start position:0%
+queen and pocket eights three times or
+something like that so but nonetheless I
+
+ align:start position:0%
+something like that so but nonetheless I
+ 
+
+ align:start position:0%
+something like that so but nonetheless I
+mean I think because it's a final table
+
+ align:start position:0%
+mean I think because it's a final table
+ 
+
+ align:start position:0%
+mean I think because it's a final table
+because if I see em it's fine he
+
+ align:start position:0%
+because if I see em it's fine he
+ 
+
+ align:start position:0%
+because if I see em it's fine he
+gets unlucky nobody runs into Queens
+
+ align:start position:0%
+gets unlucky nobody runs into Queens
+ 
+
+ align:start position:0%
+gets unlucky nobody runs into Queens
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+we get a walk okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's see this hand so I show two
+
+ align:start position:0%
+so let's see this hand so I show two
+ 
+
+ align:start position:0%
+so let's see this hand so I show two
+raises goes all-in so we call here we're
+
+ align:start position:0%
+raises goes all-in so we call here we're
+ 
+
+ align:start position:0%
+raises goes all-in so we call here we're
+kind of deep where I want to give myself
+
+ align:start position:0%
+kind of deep where I want to give myself
+ 
+
+ align:start position:0%
+kind of deep where I want to give myself
+the opportunity to fold if ten pain
+
+ align:start position:0%
+the opportunity to fold if ten pain
+ 
+
+ align:start position:0%
+the opportunity to fold if ten pain
+Chrissy goes on and we
+
+ align:start position:0%
+Chrissy goes on and we
+ 
+
+ align:start position:0%
+Chrissy goes on and we
+call and he and we went so okay so I
+
+ align:start position:0%
+call and he and we went so okay so I
+ 
+
+ align:start position:0%
+call and he and we went so okay so I
+guess I've been running pretty good in
+
+ align:start position:0%
+guess I've been running pretty good in
+ 
+
+ align:start position:0%
+guess I've been running pretty good in
+this tournament there
+
+ align:start position:0%
+this tournament there
+ 
+
+ align:start position:0%
+this tournament there
+is a lot of selection bias here right
+
+ align:start position:0%
+is a lot of selection bias here right
+ 
+
+ align:start position:0%
+is a lot of selection bias here right
+because I'm gonna I'm not going to like
+
+ align:start position:0%
+because I'm gonna I'm not going to like
+ 
+
+ align:start position:0%
+because I'm gonna I'm not going to like
+place your tournament where I get all
+
+ align:start position:0%
+place your tournament where I get all
+ 
+
+ align:start position:0%
+place your tournament where I get all
+another standards right so I mean so
+
+ align:start position:0%
+another standards right so I mean so
+ 
+
+ align:start position:0%
+another standards right so I mean so
+it's in some sense not the best
+
+ align:start position:0%
+it's in some sense not the best
+ 
+
+ align:start position:0%
+it's in some sense not the best
+pedagogical example to use there is a
+
+ align:start position:0%
+pedagogical example to use there is a
+ 
+
+ align:start position:0%
+pedagogical example to use there is a
+lot of like selection bias you know that
+
+ align:start position:0%
+lot of like selection bias you know that
+ 
+
+ align:start position:0%
+lot of like selection bias you know that
+I'm gonna run very good in the
+
+ align:start position:0%
+I'm gonna run very good in the
+ 
+
+ align:start position:0%
+I'm gonna run very good in the
+tournament I choose to show you guys but
+
+ align:start position:0%
+tournament I choose to show you guys but
+ 
+
+ align:start position:0%
+tournament I choose to show you guys but
+I mean if it's between that and you know
+
+ align:start position:0%
+I mean if it's between that and you know
+ 
+
+ align:start position:0%
+I mean if it's between that and you know
+having the class be over five minutes is
+
+ align:start position:0%
+having the class be over five minutes is
+ 
+
+ align:start position:0%
+having the class be over five minutes is
+a classic this
+
+ align:start position:0%
+a classic this
+ 
+
+ align:start position:0%
+a classic this
+is this is the lesser of two evils all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so so here yeah so once again this
+
+ align:start position:0%
+right so so here yeah so once again this
+ 
+
+ align:start position:0%
+right so so here yeah so once again this
+isn't pretty it's not that big but it's
+
+ align:start position:0%
+isn't pretty it's not that big but it's
+ 
+
+ align:start position:0%
+isn't pretty it's not that big but it's
+a it's a 17 big blind shove and once
+
+ align:start position:0%
+a it's a 17 big blind shove and once
+ 
+
+ align:start position:0%
+a it's a 17 big blind shove and once
+again it's justified by ICM maybe fold
+
+ align:start position:0%
+again it's justified by ICM maybe fold
+ 
+
+ align:start position:0%
+again it's justified by ICM maybe fold
+get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here Queen seven off yeah I shove I mean
+
+ align:start position:0%
+here Queen seven off yeah I shove I mean
+ 
+
+ align:start position:0%
+here Queen seven off yeah I shove I mean
+I think it's it's probably barely a pull
+
+ align:start position:0%
+I think it's it's probably barely a pull
+ 
+
+ align:start position:0%
+I think it's it's probably barely a pull
+I think it's pretty close it should be
+
+ align:start position:0%
+I think it's pretty close it should be
+ 
+
+ align:start position:0%
+I think it's pretty close it should be
+be equals money evey it would be a
+
+ align:start position:0%
+be equals money evey it would be a
+ 
+
+ align:start position:0%
+be equals money evey it would be a
+borderline show with these smallish
+
+ align:start position:0%
+borderline show with these smallish
+ 
+
+ align:start position:0%
+borderline show with these smallish
+entities but given ICM I know he's less
+
+ align:start position:0%
+entities but given ICM I know he's less
+ 
+
+ align:start position:0%
+entities but given ICM I know he's less
+incentivized to call than usual so all
+
+ align:start position:0%
+incentivized to call than usual so all
+ 
+
+ align:start position:0%
+incentivized to call than usual so all
+borderline hands I'm going to be shoving
+
+ align:start position:0%
+borderline hands I'm going to be shoving
+ 
+
+ align:start position:0%
+borderline hands I'm going to be shoving
+so I do okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this hand we get King 10 so once
+
+ align:start position:0%
+so this hand we get King 10 so once
+ 
+
+ align:start position:0%
+so this hand we get King 10 so once
+again I just shove um well once again
+
+ align:start position:0%
+again I just shove um well once again
+ 
+
+ align:start position:0%
+again I just shove um well once again
+it's I think I basically
+
+ align:start position:0%
+it's I think I basically
+ 
+
+ align:start position:0%
+it's I think I basically
+it's hard for them to call if I just
+
+ align:start position:0%
+it's hard for them to call if I just
+ 
+
+ align:start position:0%
+it's hard for them to call if I just
+shoved and I am because if I see a so
+
+ align:start position:0%
+shoved and I am because if I see a so
+ 
+
+ align:start position:0%
+shoved and I am because if I see a so
+I'm essentially bullying him bullying
+
+ align:start position:0%
+I'm essentially bullying him bullying
+ 
+
+ align:start position:0%
+I'm essentially bullying him bullying
+them so when you're the big stack you
+
+ align:start position:0%
+them so when you're the big stack you
+ 
+
+ align:start position:0%
+them so when you're the big stack you
+can sort of bully people at the final
+
+ align:start position:0%
+can sort of bully people at the final
+ 
+
+ align:start position:0%
+can sort of bully people at the final
+table because because if I see him would
+
+ align:start position:0%
+table because because if I see him would
+ 
+
+ align:start position:0%
+table because because if I see him would
+you get it looked up here though and we
+
+ align:start position:0%
+you get it looked up here though and we
+ 
+
+ align:start position:0%
+you get it looked up here though and we
+have looked at by a say and so he he
+
+ align:start position:0%
+have looked at by a say and so he he
+ 
+
+ align:start position:0%
+have looked at by a say and so he he
+wins I think I'm
+
+ align:start position:0%
+wins I think I'm
+ 
+
+ align:start position:0%
+wins I think I'm
+not gonna do an exact calculation
+
+ align:start position:0%
+not gonna do an exact calculation
+ 
+
+ align:start position:0%
+not gonna do an exact calculation
+because I'm gonna do an exact ICM
+
+ align:start position:0%
+because I'm gonna do an exact ICM
+ 
+
+ align:start position:0%
+because I'm gonna do an exact ICM
+calculation later but I would guess his
+
+ align:start position:0%
+calculation later but I would guess his
+ 
+
+ align:start position:0%
+calculation later but I would guess his
+call I would guess his calls very
+
+ align:start position:0%
+call I would guess his calls very
+ 
+
+ align:start position:0%
+call I would guess his calls very
+borderline I mean it's definitely it's
+
+ align:start position:0%
+borderline I mean it's definitely it's
+ 
+
+ align:start position:0%
+borderline I mean it's definitely it's
+definitely positive ship expectancy but
+
+ align:start position:0%
+definitely positive ship expectancy but
+ 
+
+ align:start position:0%
+definitely positive ship expectancy but
+the fact that there's this guy 150 7,000
+
+ align:start position:0%
+the fact that there's this guy 150 7,000
+ 
+
+ align:start position:0%
+the fact that there's this guy 150 7,000
+in this time of 70,000 I think I think
+
+ align:start position:0%
+in this time of 70,000 I think I think
+ 
+
+ align:start position:0%
+in this time of 70,000 I think I think
+it's a call but I think like a six is
+
+ align:start position:0%
+it's a call but I think like a six is
+ 
+
+ align:start position:0%
+it's a call but I think like a six is
+definitely full so I think it's probably
+
+ align:start position:0%
+definitely full so I think it's probably
+ 
+
+ align:start position:0%
+definitely full so I think it's probably
+one of the weakest hands you should be
+
+ align:start position:0%
+one of the weakest hands you should be
+ 
+
+ align:start position:0%
+one of the weakest hands you should be
+calling what I think a state is probably
+
+ align:start position:0%
+calling what I think a state is probably
+ 
+
+ align:start position:0%
+calling what I think a state is probably
+too good he has to call but I think it's
+
+ align:start position:0%
+too good he has to call but I think it's
+ 
+
+ align:start position:0%
+too good he has to call but I think it's
+very borderline in either case because
+
+ align:start position:0%
+very borderline in either case because
+ 
+
+ align:start position:0%
+very borderline in either case because
+if I see him so
+
+ align:start position:0%
+if I see him so
+ 
+
+ align:start position:0%
+if I see him so
+he does hold though so now so now I see
+
+ align:start position:0%
+he does hold though so now so now I see
+ 
+
+ align:start position:0%
+he does hold though so now so now I see
+em is a bit trickier because now we're
+
+ align:start position:0%
+em is a bit trickier because now we're
+ 
+
+ align:start position:0%
+em is a bit trickier because now we're
+smaller we're getting it all in with any
+
+ align:start position:0%
+smaller we're getting it all in with any
+ 
+
+ align:start position:0%
+smaller we're getting it all in with any
+of these guys can really damage us and
+
+ align:start position:0%
+of these guys can really damage us and
+ 
+
+ align:start position:0%
+of these guys can really damage us and
+there's still like two short stacks that
+
+ align:start position:0%
+there's still like two short stacks that
+ 
+
+ align:start position:0%
+there's still like two short stacks that
+were kind of everyone is hoping a little
+
+ align:start position:0%
+were kind of everyone is hoping a little
+ 
+
+ align:start position:0%
+were kind of everyone is hoping a little
+bust soon so
+
+ align:start position:0%
+bust soon so
+ 
+
+ align:start position:0%
+bust soon so
+you know so in this situation you know I
+
+ align:start position:0%
+you know so in this situation you know I
+ 
+
+ align:start position:0%
+you know so in this situation you know I
+could like go all in and believe this
+
+ align:start position:0%
+could like go all in and believe this
+ 
+
+ align:start position:0%
+could like go all in and believe this
+pimp accuracy guy but I see him isn't
+
+ align:start position:0%
+pimp accuracy guy but I see him isn't
+ 
+
+ align:start position:0%
+pimp accuracy guy but I see him isn't
+that relevant like I can't he's not
+
+ align:start position:0%
+that relevant like I can't he's not
+ 
+
+ align:start position:0%
+that relevant like I can't he's not
+gonna fold like East Queen if I go all
+
+ align:start position:0%
+gonna fold like East Queen if I go all
+ 
+
+ align:start position:0%
+gonna fold like East Queen if I go all
+in so I just give this one to them
+
+ align:start position:0%
+in so I just give this one to them
+ 
+
+ align:start position:0%
+in so I just give this one to them
+yeah like calling calling is probably
+
+ align:start position:0%
+yeah like calling calling is probably
+ 
+
+ align:start position:0%
+yeah like calling calling is probably
+bad anyway but calling I think is
+
+ align:start position:0%
+bad anyway but calling I think is
+ 
+
+ align:start position:0%
+bad anyway but calling I think is
+especially bad because it just increases
+
+ align:start position:0%
+especially bad because it just increases
+ 
+
+ align:start position:0%
+especially bad because it just increases
+the chances of lutely getting in a
+
+ align:start position:0%
+the chances of lutely getting in a
+ 
+
+ align:start position:0%
+the chances of lutely getting in a
+bigger pot okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well skip forward a bit let's see this
+
+ align:start position:0%
+well skip forward a bit let's see this
+ 
+
+ align:start position:0%
+well skip forward a bit let's see this
+hand so East
+
+ align:start position:0%
+hand so East
+ 
+
+ align:start position:0%
+hand so East
+10 okay so he's 10 off here so this guy
+
+ align:start position:0%
+10 okay so he's 10 off here so this guy
+ 
+
+ align:start position:0%
+10 okay so he's 10 off here so this guy
+makes it twelve thousand and I guess I
+
+ align:start position:0%
+makes it twelve thousand and I guess I
+ 
+
+ align:start position:0%
+makes it twelve thousand and I guess I
+just skipped a bunch of hands but so
+
+ align:start position:0%
+just skipped a bunch of hands but so
+ 
+
+ align:start position:0%
+just skipped a bunch of hands but so
+Nicholas Brody I think has been very
+
+ align:start position:0%
+Nicholas Brody I think has been very
+ 
+
+ align:start position:0%
+Nicholas Brody I think has been very
+active and overall I think people have
+
+ align:start position:0%
+active and overall I think people have
+ 
+
+ align:start position:0%
+active and overall I think people have
+become very active everyone's playing a
+
+ align:start position:0%
+become very active everyone's playing a
+ 
+
+ align:start position:0%
+become very active everyone's playing a
+lot of pots so overall I'm gonna put
+
+ align:start position:0%
+lot of pots so overall I'm gonna put
+ 
+
+ align:start position:0%
+lot of pots so overall I'm gonna put
+people on wider ranges than I normally
+
+ align:start position:0%
+people on wider ranges than I normally
+ 
+
+ align:start position:0%
+people on wider ranges than I normally
+do but nonetheless here I still full
+
+ align:start position:0%
+do but nonetheless here I still full
+ 
+
+ align:start position:0%
+do but nonetheless here I still full
+day's 10 I think it's I think it's East
+
+ align:start position:0%
+day's 10 I think it's I think it's East
+ 
+
+ align:start position:0%
+day's 10 I think it's I think it's East
+Jack I would probably get it in and each
+
+ align:start position:0%
+Jack I would probably get it in and each
+ 
+
+ align:start position:0%
+Jack I would probably get it in and each
+ten suited I think I would get it in
+
+ align:start position:0%
+ten suited I think I would get it in
+ 
+
+ align:start position:0%
+ten suited I think I would get it in
+it's ten suited is sort of borderline
+
+ align:start position:0%
+it's ten suited is sort of borderline
+ 
+
+ align:start position:0%
+it's ten suited is sort of borderline
+and once again you know once again
+
+ align:start position:0%
+and once again you know once again
+ 
+
+ align:start position:0%
+and once again you know once again
+whatever there's sort of when you're
+
+ align:start position:0%
+whatever there's sort of when you're
+ 
+
+ align:start position:0%
+whatever there's sort of when you're
+tied between getting in a smaller pot
+
+ align:start position:0%
+tied between getting in a smaller pot
+ 
+
+ align:start position:0%
+tied between getting in a smaller pot
+and getting in a bigger pot you kind of
+
+ align:start position:0%
+and getting in a bigger pot you kind of
+ 
+
+ align:start position:0%
+and getting in a bigger pot you kind of
+want to be you want to be folding so
+
+ align:start position:0%
+want to be you want to be folding so
+ 
+
+ align:start position:0%
+want to be you want to be folding so
+yeah so I guess in the final table I
+
+ align:start position:0%
+yeah so I guess in the final table I
+ 
+
+ align:start position:0%
+yeah so I guess in the final table I
+should make this clear it's not like you
+
+ align:start position:0%
+should make this clear it's not like you
+ 
+
+ align:start position:0%
+should make this clear it's not like you
+want to fold more it's sort of you want
+
+ align:start position:0%
+want to fold more it's sort of you want
+ 
+
+ align:start position:0%
+want to fold more it's sort of you want
+to go all-in more when you're first to
+
+ align:start position:0%
+to go all-in more when you're first to
+ 
+
+ align:start position:0%
+to go all-in more when you're first to
+act but call other people as all-in is
+
+ align:start position:0%
+act but call other people as all-in is
+ 
+
+ align:start position:0%
+act but call other people as all-in is
+less so that's exactly what's going on
+
+ align:start position:0%
+less so that's exactly what's going on
+ 
+
+ align:start position:0%
+less so that's exactly what's going on
+here he's already moved all in and I'm
+
+ align:start position:0%
+here he's already moved all in and I'm
+ 
+
+ align:start position:0%
+here he's already moved all in and I'm
+gonna fold to his all in more often then
+
+ align:start position:0%
+gonna fold to his all in more often then
+ 
+
+ align:start position:0%
+gonna fold to his all in more often then
+normal game but as you can see I'm I
+
+ align:start position:0%
+normal game but as you can see I'm I
+ 
+
+ align:start position:0%
+normal game but as you can see I'm I
+haven't really been tighter in every
+
+ align:start position:0%
+haven't really been tighter in every
+ 
+
+ align:start position:0%
+haven't really been tighter in every
+sense because when I have to go first
+
+ align:start position:0%
+sense because when I have to go first
+ 
+
+ align:start position:0%
+sense because when I have to go first
+I've been actually going all any more
+
+ align:start position:0%
+I've been actually going all any more
+ 
+
+ align:start position:0%
+I've been actually going all any more
+often and risking it more often because
+
+ align:start position:0%
+often and risking it more often because
+ 
+
+ align:start position:0%
+often and risking it more often because
+I know my opponents are highly
+
+ align:start position:0%
+I know my opponents are highly
+ 
+
+ align:start position:0%
+I know my opponents are highly
+incentivized people so anyway so it's so
+
+ align:start position:0%
+incentivized people so anyway so it's so
+ 
+
+ align:start position:0%
+incentivized people so anyway so it's so
+they go on and I fold here so Nicholas
+
+ align:start position:0%
+they go on and I fold here so Nicholas
+ 
+
+ align:start position:0%
+they go on and I fold here so Nicholas
+Brody also folds which I guess is fine
+
+ align:start position:0%
+Brody also folds which I guess is fine
+ 
+
+ align:start position:0%
+Brody also folds which I guess is fine
+but it's it's definitely a pretty good
+
+ align:start position:0%
+but it's it's definitely a pretty good
+ 
+
+ align:start position:0%
+but it's it's definitely a pretty good
+Odyssey call there but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once again yeah like I see em just makes
+
+ align:start position:0%
+once again yeah like I see em just makes
+ 
+
+ align:start position:0%
+once again yeah like I see em just makes
+it changes things up a bit Jack 7 suited
+
+ align:start position:0%
+it changes things up a bit Jack 7 suited
+ 
+
+ align:start position:0%
+it changes things up a bit Jack 7 suited
+once again it's a pretty big shove but
+
+ align:start position:0%
+once again it's a pretty big shove but
+ 
+
+ align:start position:0%
+once again it's a pretty big shove but
+Jack sevens you did plenty good enough
+
+ align:start position:0%
+Jack sevens you did plenty good enough
+ 
+
+ align:start position:0%
+Jack sevens you did plenty good enough
+it I see em relevant pocket
+
+ align:start position:0%
+it I see em relevant pocket
+ 
+
+ align:start position:0%
+it I see em relevant pocket
+nines here we make it twelve thousand on
+
+ align:start position:0%
+nines here we make it twelve thousand on
+ 
+
+ align:start position:0%
+nines here we make it twelve thousand on
+the on the button so here I think pocket
+
+ align:start position:0%
+the on the button so here I think pocket
+ 
+
+ align:start position:0%
+the on the button so here I think pocket
+nines is sort of good enough where I'm
+
+ align:start position:0%
+nines is sort of good enough where I'm
+ 
+
+ align:start position:0%
+nines is sort of good enough where I'm
+happy at one of them three bases all in
+
+ align:start position:0%
+happy at one of them three bases all in
+ 
+
+ align:start position:0%
+happy at one of them three bases all in
+there I call so essentially my strategy
+
+ align:start position:0%
+there I call so essentially my strategy
+ 
+
+ align:start position:0%
+there I call so essentially my strategy
+here is I'm going to show like all my
+
+ align:start position:0%
+here is I'm going to show like all my
+ 
+
+ align:start position:0%
+here is I'm going to show like all my
+sort of medium strength hands and
+
+ align:start position:0%
+sort of medium strength hands and
+ 
+
+ align:start position:0%
+sort of medium strength hands and
+especially hands that don't play well
+
+ align:start position:0%
+especially hands that don't play well
+ 
+
+ align:start position:0%
+especially hands that don't play well
+post off like east to offsuit and then
+
+ align:start position:0%
+post off like east to offsuit and then
+ 
+
+ align:start position:0%
+post off like east to offsuit and then
+I'm gonna raise small with some of my
+
+ align:start position:0%
+I'm gonna raise small with some of my
+ 
+
+ align:start position:0%
+I'm gonna raise small with some of my
+hands
+
+ align:start position:0%
+hands
+ 
+
+ align:start position:0%
+hands
+that are less good preflop the better
+
+ align:start position:0%
+that are less good preflop the better
+ 
+
+ align:start position:0%
+that are less good preflop the better
+post flop let's say like ten eight
+
+ align:start position:0%
+post flop let's say like ten eight
+ 
+
+ align:start position:0%
+post flop let's say like ten eight
+suited and also my monster hands like
+
+ align:start position:0%
+suited and also my monster hands like
+ 
+
+ align:start position:0%
+suited and also my monster hands like
+pocket nines that are also reasonable to
+
+ align:start position:0%
+pocket nines that are also reasonable to
+ 
+
+ align:start position:0%
+pocket nines that are also reasonable to
+play post flop so so
+
+ align:start position:0%
+play post flop so so
+ 
+
+ align:start position:0%
+play post flop so so
+Nicolas nobody calls here and the flop
+
+ align:start position:0%
+Nicolas nobody calls here and the flop
+ 
+
+ align:start position:0%
+Nicolas nobody calls here and the flop
+is East Jack seven with regards so it's
+
+ align:start position:0%
+is East Jack seven with regards so it's
+ 
+
+ align:start position:0%
+is East Jack seven with regards so it's
+a bad fall for a hand but it's a good
+
+ align:start position:0%
+a bad fall for a hand but it's a good
+ 
+
+ align:start position:0%
+a bad fall for a hand but it's a good
+flop for our range because
+
+ align:start position:0%
+flop for our range because
+ 
+
+ align:start position:0%
+flop for our range because
+I I think given the way the table was
+
+ align:start position:0%
+I I think given the way the table was
+ 
+
+ align:start position:0%
+I I think given the way the table was
+going I was opening a lot and Nicholas
+
+ align:start position:0%
+going I was opening a lot and Nicholas
+ 
+
+ align:start position:0%
+going I was opening a lot and Nicholas
+Brody is very aggressive I would guess
+
+ align:start position:0%
+Brody is very aggressive I would guess
+ 
+
+ align:start position:0%
+Brody is very aggressive I would guess
+unless he had like pocket he says where
+
+ align:start position:0%
+unless he had like pocket he says where
+ 
+
+ align:start position:0%
+unless he had like pocket he says where
+she might slow play he would rebase most
+
+ align:start position:0%
+she might slow play he would rebase most
+ 
+
+ align:start position:0%
+she might slow play he would rebase most
+I was I wasn't like a hundred percent
+
+ align:start position:0%
+I was I wasn't like a hundred percent
+ 
+
+ align:start position:0%
+I was I wasn't like a hundred percent
+sure confident but I was reasonably I'd
+
+ align:start position:0%
+sure confident but I was reasonably I'd
+ 
+
+ align:start position:0%
+sure confident but I was reasonably I'd
+say like maybe eighty-five percent
+
+ align:start position:0%
+say like maybe eighty-five percent
+ 
+
+ align:start position:0%
+say like maybe eighty-five percent
+confident that if he had an ace preflop
+
+ align:start position:0%
+confident that if he had an ace preflop
+ 
+
+ align:start position:0%
+confident that if he had an ace preflop
+he would have just went all-in pretty
+
+ align:start position:0%
+he would have just went all-in pretty
+ 
+
+ align:start position:0%
+he would have just went all-in pretty
+flop so overall I still say it's a very
+
+ align:start position:0%
+flop so overall I still say it's a very
+ 
+
+ align:start position:0%
+flop so overall I still say it's a very
+good flop for my range cuz I think he's
+
+ align:start position:0%
+good flop for my range cuz I think he's
+ 
+
+ align:start position:0%
+good flop for my range cuz I think he's
+way less likely to have an ace to me
+
+ align:start position:0%
+way less likely to have an ace to me
+ 
+
+ align:start position:0%
+way less likely to have an ace to me
+there's a small chance maybe he he would
+
+ align:start position:0%
+there's a small chance maybe he he would
+ 
+
+ align:start position:0%
+there's a small chance maybe he he would
+chicken out with like east to officers
+
+ align:start position:0%
+chicken out with like east to officers
+ 
+
+ align:start position:0%
+chicken out with like east to officers
+and just call but I but given how
+
+ align:start position:0%
+and just call but I but given how
+ 
+
+ align:start position:0%
+and just call but I but given how
+aggressive he's been I would be
+
+ align:start position:0%
+aggressive he's been I would be
+ 
+
+ align:start position:0%
+aggressive he's been I would be
+surprised if he did that so so I decided
+
+ align:start position:0%
+surprised if he did that so so I decided
+ 
+
+ align:start position:0%
+surprised if he did that so so I decided
+you've been here and I'm still not sure
+
+ align:start position:0%
+you've been here and I'm still not sure
+ 
+
+ align:start position:0%
+you've been here and I'm still not sure
+how good this bed is so I think at the
+
+ align:start position:0%
+how good this bed is so I think at the
+ 
+
+ align:start position:0%
+how good this bed is so I think at the
+time that because of my logic that he
+
+ align:start position:0%
+time that because of my logic that he
+ 
+
+ align:start position:0%
+time that because of my logic that he
+can't it's really hard forever you have
+
+ align:start position:0%
+can't it's really hard forever you have
+ 
+
+ align:start position:0%
+can't it's really hard forever you have
+a nice and so I think the best strategy
+
+ align:start position:0%
+a nice and so I think the best strategy
+ 
+
+ align:start position:0%
+a nice and so I think the best strategy
+for me on this flop and in this
+
+ align:start position:0%
+for me on this flop and in this
+ 
+
+ align:start position:0%
+for me on this flop and in this
+situation is just been a hundred percent
+
+ align:start position:0%
+situation is just been a hundred percent
+ 
+
+ align:start position:0%
+situation is just been a hundred percent
+of my hands and he's kind of just forced
+
+ align:start position:0%
+of my hands and he's kind of just forced
+ 
+
+ align:start position:0%
+of my hands and he's kind of just forced
+to fold basically very often because she
+
+ align:start position:0%
+to fold basically very often because she
+ 
+
+ align:start position:0%
+to fold basically very often because she
+can't really keep up with an a second
+
+ align:start position:0%
+can't really keep up with an a second
+ 
+
+ align:start position:0%
+can't really keep up with an a second
+discontinue betting that being said
+
+ align:start position:0%
+discontinue betting that being said
+ 
+
+ align:start position:0%
+discontinue betting that being said
+though I do think you know if I do
+
+ align:start position:0%
+though I do think you know if I do
+ 
+
+ align:start position:0%
+though I do think you know if I do
+decide as part of my strategy to check
+
+ align:start position:0%
+decide as part of my strategy to check
+ 
+
+ align:start position:0%
+decide as part of my strategy to check
+any part of my range here party lines
+
+ align:start position:0%
+any part of my range here party lines
+ 
+
+ align:start position:0%
+any part of my range here party lines
+and light actually be one of the best
+
+ align:start position:0%
+and light actually be one of the best
+ 
+
+ align:start position:0%
+and light actually be one of the best
+possible hands to check back so I think
+
+ align:start position:0%
+possible hands to check back so I think
+ 
+
+ align:start position:0%
+possible hands to check back so I think
+checking back would have been fine I
+
+ align:start position:0%
+checking back would have been fine I
+ 
+
+ align:start position:0%
+checking back would have been fine I
+guess I've been here because I told
+
+ align:start position:0%
+guess I've been here because I told
+ 
+
+ align:start position:0%
+guess I've been here because I told
+myself I want my strategy to be bet a
+
+ align:start position:0%
+myself I want my strategy to be bet a
+ 
+
+ align:start position:0%
+myself I want my strategy to be bet a
+hundred percent of my hands which I did
+
+ align:start position:0%
+hundred percent of my hands which I did
+ 
+
+ align:start position:0%
+hundred percent of my hands which I did
+and he fold which
+
+ align:start position:0%
+and he fold which
+ 
+
+ align:start position:0%
+and he fold which
+is yet which is reasonably smart because
+
+ align:start position:0%
+is yet which is reasonably smart because
+ 
+
+ align:start position:0%
+is yet which is reasonably smart because
+he knows that you know I can bet again
+
+ align:start position:0%
+he knows that you know I can bet again
+ 
+
+ align:start position:0%
+he knows that you know I can bet again
+and he's gonna have to make a decision
+
+ align:start position:0%
+and he's gonna have to make a decision
+ 
+
+ align:start position:0%
+and he's gonna have to make a decision
+for all his chips probably and it's just
+
+ align:start position:0%
+for all his chips probably and it's just
+ 
+
+ align:start position:0%
+for all his chips probably and it's just
+gonna be tough okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this hand be my sponsor goes all-in gets
+
+ align:start position:0%
+this hand be my sponsor goes all-in gets
+ 
+
+ align:start position:0%
+this hand be my sponsor goes all-in gets
+the vines oh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry why why don't you say oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I think it's basically it's the I
+
+ align:start position:0%
+um I think it's basically it's the I
+ 
+
+ align:start position:0%
+um I think it's basically it's the I
+think I very rarely get called by worse
+
+ align:start position:0%
+think I very rarely get called by worse
+ 
+
+ align:start position:0%
+think I very rarely get called by worse
+and I get called by everything better
+
+ align:start position:0%
+and I get called by everything better
+ 
+
+ align:start position:0%
+and I get called by everything better
+like I think she's always calling a jack
+
+ align:start position:0%
+like I think she's always calling a jack
+ 
+
+ align:start position:0%
+like I think she's always calling a jack
+and usually folding a seven like maybe
+
+ align:start position:0%
+and usually folding a seven like maybe
+ 
+
+ align:start position:0%
+and usually folding a seven like maybe
+he won't fold seven eight with some back
+
+ align:start position:0%
+he won't fold seven eight with some back
+ 
+
+ align:start position:0%
+he won't fold seven eight with some back
+door drums but I think he'll usually
+
+ align:start position:0%
+door drums but I think he'll usually
+ 
+
+ align:start position:0%
+door drums but I think he'll usually
+call a jacket maybe they'll call seven
+
+ align:start position:0%
+call a jacket maybe they'll call seven
+ 
+
+ align:start position:0%
+call a jacket maybe they'll call seven
+sometimes but I still think mostly it's
+
+ align:start position:0%
+sometimes but I still think mostly it's
+ 
+
+ align:start position:0%
+sometimes but I still think mostly it's
+just he'll basically fold everything
+
+ align:start position:0%
+just he'll basically fold everything
+ 
+
+ align:start position:0%
+just he'll basically fold everything
+that beats me and call everything that
+
+ align:start position:0%
+that beats me and call everything that
+ 
+
+ align:start position:0%
+that beats me and call everything that
+it's just sorry he'll fold everything
+
+ align:start position:0%
+it's just sorry he'll fold everything
+ 
+
+ align:start position:0%
+it's just sorry he'll fold everything
+that I beat and call everything that
+
+ align:start position:0%
+that I beat and call everything that
+ 
+
+ align:start position:0%
+that I beat and call everything that
+needs me basically yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I saw the side to bed nonetheless
+
+ align:start position:0%
+but I saw the side to bed nonetheless
+ 
+
+ align:start position:0%
+but I saw the side to bed nonetheless
+just to win the pot there and not give
+
+ align:start position:0%
+just to win the pot there and not give
+ 
+
+ align:start position:0%
+just to win the pot there and not give
+him extra outs if he happens you have
+
+ align:start position:0%
+him extra outs if he happens you have
+ 
+
+ align:start position:0%
+him extra outs if he happens you have
+like ten or something so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we'll go through this hand so
+
+ align:start position:0%
+okay so we'll go through this hand so
+ 
+
+ align:start position:0%
+okay so we'll go through this hand so
+I'm Hank receive raises he doesn't go
+
+ align:start position:0%
+I'm Hank receive raises he doesn't go
+ 
+
+ align:start position:0%
+I'm Hank receive raises he doesn't go
+all-in which is kind of curious but um
+
+ align:start position:0%
+all-in which is kind of curious but um
+ 
+
+ align:start position:0%
+all-in which is kind of curious but um
+LP box calls he calls again it's checked
+
+ align:start position:0%
+LP box calls he calls again it's checked
+ 
+
+ align:start position:0%
+LP box calls he calls again it's checked
+and then LP Marx goes all-in on the
+
+ align:start position:0%
+and then LP Marx goes all-in on the
+ 
+
+ align:start position:0%
+and then LP Marx goes all-in on the
+river gym sit down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you Jack stuff in here yes I guess
+
+ align:start position:0%
+can you Jack stuff in here yes I guess
+ 
+
+ align:start position:0%
+can you Jack stuff in here yes I guess
+so once again Nicholas Brady braces and
+
+ align:start position:0%
+so once again Nicholas Brady braces and
+ 
+
+ align:start position:0%
+so once again Nicholas Brady braces and
+then LT marks goes on over him wins
+
+ align:start position:0%
+then LT marks goes on over him wins
+ 
+
+ align:start position:0%
+then LT marks goes on over him wins
+a big pot so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess I do the same for Nicholas Brady
+
+ align:start position:0%
+I guess I do the same for Nicholas Brady
+ 
+
+ align:start position:0%
+I guess I do the same for Nicholas Brady
+he's been he's been grazing a lot so
+
+ align:start position:0%
+he's been he's been grazing a lot so
+ 
+
+ align:start position:0%
+he's been he's been grazing a lot so
+pocket sixes definitely good enough to
+
+ align:start position:0%
+pocket sixes definitely good enough to
+ 
+
+ align:start position:0%
+pocket sixes definitely good enough to
+risk going all in there okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this hand if so we get ace Jack suited
+
+ align:start position:0%
+this hand if so we get ace Jack suited
+ 
+
+ align:start position:0%
+this hand if so we get ace Jack suited
+and I raised from cut off so
+
+ align:start position:0%
+and I raised from cut off so
+ 
+
+ align:start position:0%
+and I raised from cut off so
+I've been raising fairly to a fairly
+
+ align:start position:0%
+I've been raising fairly to a fairly
+ 
+
+ align:start position:0%
+I've been raising fairly to a fairly
+small size because the antes are smaller
+
+ align:start position:0%
+small size because the antes are smaller
+ 
+
+ align:start position:0%
+small size because the antes are smaller
+so that's one thing to remember at a
+
+ align:start position:0%
+so that's one thing to remember at a
+ 
+
+ align:start position:0%
+so that's one thing to remember at a
+final table is the pots are actually a
+
+ align:start position:0%
+final table is the pots are actually a
+ 
+
+ align:start position:0%
+final table is the pots are actually a
+bit smaller because with only five
+
+ align:start position:0%
+bit smaller because with only five
+ 
+
+ align:start position:0%
+bit smaller because with only five
+players the ante the ante the some of
+
+ align:start position:0%
+players the ante the ante the some of
+ 
+
+ align:start position:0%
+players the ante the ante the some of
+the antes instead of normally being six
+
+ align:start position:0%
+the antes instead of normally being six
+ 
+
+ align:start position:0%
+the antes instead of normally being six
+thousand is only three thousand in this
+
+ align:start position:0%
+thousand is only three thousand in this
+ 
+
+ align:start position:0%
+thousand is only three thousand in this
+case so the big blind has a response to
+
+ align:start position:0%
+case so the big blind has a response to
+ 
+
+ align:start position:0%
+case so the big blind has a response to
+call so
+
+ align:start position:0%
+call so
+ 
+
+ align:start position:0%
+call so
+Nicholas Brody goes all-in I look them
+
+ align:start position:0%
+Nicholas Brody goes all-in I look them
+ 
+
+ align:start position:0%
+Nicholas Brody goes all-in I look them
+up with ace Jack suited definitely good
+
+ align:start position:0%
+up with ace Jack suited definitely good
+ 
+
+ align:start position:0%
+up with ace Jack suited definitely good
+enough I mean also at this point is
+
+ align:start position:0%
+enough I mean also at this point is
+ 
+
+ align:start position:0%
+enough I mean also at this point is
+because a number of pots have gotten my
+
+ align:start position:0%
+because a number of pots have gotten my
+ 
+
+ align:start position:0%
+because a number of pots have gotten my
+way I'm sort of big enough where even if
+
+ align:start position:0%
+way I'm sort of big enough where even if
+ 
+
+ align:start position:0%
+way I'm sort of big enough where even if
+I call and lose this I'm still I won't
+
+ align:start position:0%
+I call and lose this I'm still I won't
+ 
+
+ align:start position:0%
+I call and lose this I'm still I won't
+be chip leader but I'll still have a
+
+ align:start position:0%
+be chip leader but I'll still have a
+ 
+
+ align:start position:0%
+be chip leader but I'll still have a
+decent amount of chips so
+
+ align:start position:0%
+decent amount of chips so
+ 
+
+ align:start position:0%
+decent amount of chips so
+unfortunately we lose the AC here so now
+
+ align:start position:0%
+unfortunately we lose the AC here so now
+ 
+
+ align:start position:0%
+unfortunately we lose the AC here so now
+we're a second place but we're still
+
+ align:start position:0%
+we're a second place but we're still
+ 
+
+ align:start position:0%
+we're a second place but we're still
+doing reasonably well yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know like I could have I could
+
+ align:start position:0%
+so you know like I could have I could
+ 
+
+ align:start position:0%
+so you know like I could have I could
+have just maybe gone all in here I mean
+
+ align:start position:0%
+have just maybe gone all in here I mean
+ 
+
+ align:start position:0%
+have just maybe gone all in here I mean
+I guess this guy has a lot of chips but
+
+ align:start position:0%
+I guess this guy has a lot of chips but
+ 
+
+ align:start position:0%
+I guess this guy has a lot of chips but
+I could have like raised to a bigger
+
+ align:start position:0%
+I could have like raised to a bigger
+ 
+
+ align:start position:0%
+I could have like raised to a bigger
+size you disincentivize nicolas from me
+
+ align:start position:0%
+size you disincentivize nicolas from me
+ 
+
+ align:start position:0%
+size you disincentivize nicolas from me
+from doing this with the right wide
+
+ align:start position:0%
+from doing this with the right wide
+ 
+
+ align:start position:0%
+from doing this with the right wide
+range of hands and then sort of like
+
+ align:start position:0%
+range of hands and then sort of like
+ 
+
+ align:start position:0%
+range of hands and then sort of like
+protecting my stack more from an ICM
+
+ align:start position:0%
+protecting my stack more from an ICM
+ 
+
+ align:start position:0%
+protecting my stack more from an ICM
+point of view but I mean I'm happy with
+
+ align:start position:0%
+point of view but I mean I'm happy with
+ 
+
+ align:start position:0%
+point of view but I mean I'm happy with
+I think ace Jack suited is just good
+
+ align:start position:0%
+I think ace Jack suited is just good
+ 
+
+ align:start position:0%
+I think ace Jack suited is just good
+enough where I'm happy calling his his
+
+ align:start position:0%
+enough where I'm happy calling his his
+ 
+
+ align:start position:0%
+enough where I'm happy calling his his
+all in which I should have been in this
+
+ align:start position:0%
+all in which I should have been in this
+ 
+
+ align:start position:0%
+all in which I should have been in this
+case I guess yet he sings but yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Jack ten suited here so yeah here I
+
+ align:start position:0%
+so Jack ten suited here so yeah here I
+ 
+
+ align:start position:0%
+so Jack ten suited here so yeah here I
+just decided to fold weak I mean we
+
+ align:start position:0%
+just decided to fold weak I mean we
+ 
+
+ align:start position:0%
+just decided to fold weak I mean we
+could consider doing a crazy Bluff
+
+ align:start position:0%
+could consider doing a crazy Bluff
+ 
+
+ align:start position:0%
+could consider doing a crazy Bluff
+all-in but I don't think this guy's
+
+ align:start position:0%
+all-in but I don't think this guy's
+ 
+
+ align:start position:0%
+all-in but I don't think this guy's
+folding that often they made a rather
+
+ align:start position:0%
+folding that often they made a rather
+ 
+
+ align:start position:0%
+folding that often they made a rather
+big rebase
+
+ align:start position:0%
+big rebase
+ 
+
+ align:start position:0%
+big rebase
+preflop from going three times the
+
+ align:start position:0%
+preflop from going three times the
+ 
+
+ align:start position:0%
+preflop from going three times the
+initial opening so Nicholas Brody goes
+
+ align:start position:0%
+initial opening so Nicholas Brody goes
+ 
+
+ align:start position:0%
+initial opening so Nicholas Brody goes
+on here and they beautiful so Nicholas
+
+ align:start position:0%
+on here and they beautiful so Nicholas
+ 
+
+ align:start position:0%
+on here and they beautiful so Nicholas
+Brody you picking up a bunch of chips so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he just takes it down again he's been
+
+ align:start position:0%
+he just takes it down again he's been
+ 
+
+ align:start position:0%
+he just takes it down again he's been
+raising quite a lot so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again a raise and a call so ok lol p.m.
+
+ align:start position:0%
+again a raise and a call so ok lol p.m.
+ 
+
+ align:start position:0%
+again a raise and a call so ok lol p.m.
+box has been raising over to other
+
+ align:start position:0%
+box has been raising over to other
+ 
+
+ align:start position:0%
+box has been raising over to other
+people's Oh
+
+ align:start position:0%
+people's Oh
+ 
+
+ align:start position:0%
+people's Oh
+opens quite a lot so he gets called here
+
+ align:start position:0%
+opens quite a lot so he gets called here
+ 
+
+ align:start position:0%
+opens quite a lot so he gets called here
+but he holds and wins which is
+
+ align:start position:0%
+but he holds and wins which is
+ 
+
+ align:start position:0%
+but he holds and wins which is
+definitely bad news for everyone like
+
+ align:start position:0%
+definitely bad news for everyone like
+ 
+
+ align:start position:0%
+definitely bad news for everyone like
+you know if I could have if I would pay
+
+ align:start position:0%
+you know if I could have if I would pay
+ 
+
+ align:start position:0%
+you know if I could have if I would pay
+ten thousand chips into the pot you have
+
+ align:start position:0%
+ten thousand chips into the pot you have
+ 
+
+ align:start position:0%
+ten thousand chips into the pot you have
+this all and build the other way it
+
+ align:start position:0%
+this all and build the other way it
+ 
+
+ align:start position:0%
+this all and build the other way it
+almost certainly would be profitable
+
+ align:start position:0%
+almost certainly would be profitable
+ 
+
+ align:start position:0%
+almost certainly would be profitable
+like the amount I should be willing to
+
+ align:start position:0%
+like the amount I should be willing to
+ 
+
+ align:start position:0%
+like the amount I should be willing to
+pay to make this all and build the other
+
+ align:start position:0%
+pay to make this all and build the other
+ 
+
+ align:start position:0%
+pay to make this all and build the other
+way is probably like twenty five
+
+ align:start position:0%
+way is probably like twenty five
+ 
+
+ align:start position:0%
+way is probably like twenty five
+thousand like it's a ridiculous enough
+
+ align:start position:0%
+thousand like it's a ridiculous enough
+ 
+
+ align:start position:0%
+thousand like it's a ridiculous enough
+because the just the value of having
+
+ align:start position:0%
+because the just the value of having
+ 
+
+ align:start position:0%
+because the just the value of having
+people bust and moving up the payouts is
+
+ align:start position:0%
+people bust and moving up the payouts is
+ 
+
+ align:start position:0%
+people bust and moving up the payouts is
+so significant especially when I'm not
+
+ align:start position:0%
+so significant especially when I'm not
+ 
+
+ align:start position:0%
+so significant especially when I'm not
+such a big stack anymore okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now this guy he just doubled up so
+
+ align:start position:0%
+so now this guy he just doubled up so
+ 
+
+ align:start position:0%
+so now this guy he just doubled up so
+yeah so forth so I guess that we were
+
+ align:start position:0%
+yeah so forth so I guess that we were
+ 
+
+ align:start position:0%
+yeah so forth so I guess that we were
+running pretty good but I say in the
+
+ align:start position:0%
+running pretty good but I say in the
+ 
+
+ align:start position:0%
+running pretty good but I say in the
+last two or three orbits as you can seen
+
+ align:start position:0%
+last two or three orbits as you can seen
+ 
+
+ align:start position:0%
+last two or three orbits as you can seen
+a lot of things haven't been that
+
+ align:start position:0%
+a lot of things haven't been that
+ 
+
+ align:start position:0%
+a lot of things haven't been that
+favorable we've lost some all ends and
+
+ align:start position:0%
+favorable we've lost some all ends and
+ 
+
+ align:start position:0%
+favorable we've lost some all ends and
+also people haven't really busted the
+
+ align:start position:0%
+also people haven't really busted the
+ 
+
+ align:start position:0%
+also people haven't really busted the
+chips are sort of just being passed
+
+ align:start position:0%
+chips are sort of just being passed
+ 
+
+ align:start position:0%
+chips are sort of just being passed
+around the table which is basically not
+
+ align:start position:0%
+around the table which is basically not
+ 
+
+ align:start position:0%
+around the table which is basically not
+what you're hoping for so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+king 10 off suit we got to walk we
+
+ align:start position:0%
+king 10 off suit we got to walk we
+ 
+
+ align:start position:0%
+king 10 off suit we got to walk we
+actually go there so walk just means
+
+ align:start position:0%
+actually go there so walk just means
+ 
+
+ align:start position:0%
+actually go there so walk just means
+everyone folds to do in the big blind I
+
+ align:start position:0%
+everyone folds to do in the big blind I
+ 
+
+ align:start position:0%
+everyone folds to do in the big blind I
+think we've actually gotten quite a lot
+
+ align:start position:0%
+think we've actually gotten quite a lot
+ 
+
+ align:start position:0%
+think we've actually gotten quite a lot
+of walks at this final table so
+
+ align:start position:0%
+of walks at this final table so
+ 
+
+ align:start position:0%
+of walks at this final table so
+something we can keep in mind if we're
+
+ align:start position:0%
+something we can keep in mind if we're
+ 
+
+ align:start position:0%
+something we can keep in mind if we're
+trying to play exploitative Lee later
+
+ align:start position:0%
+trying to play exploitative Lee later
+ 
+
+ align:start position:0%
+trying to play exploitative Lee later
+Queen Jack go all in few folds so at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+8/7 I guess LPL p.m. box after winning
+
+ align:start position:0%
+8/7 I guess LPL p.m. box after winning
+ 
+
+ align:start position:0%
+8/7 I guess LPL p.m. box after winning
+that so as I sort of noticed the big
+
+ align:start position:0%
+that so as I sort of noticed the big
+ 
+
+ align:start position:0%
+that so as I sort of noticed the big
+stacks are sort of the ones who win most
+
+ align:start position:0%
+stacks are sort of the ones who win most
+ 
+
+ align:start position:0%
+stacks are sort of the ones who win most
+of the pots and this is sort of expected
+
+ align:start position:0%
+of the pots and this is sort of expected
+ 
+
+ align:start position:0%
+of the pots and this is sort of expected
+so whenever I see em is relevant you
+
+ align:start position:0%
+so whenever I see em is relevant you
+ 
+
+ align:start position:0%
+so whenever I see em is relevant you
+would expect that so although the small
+
+ align:start position:0%
+would expect that so although the small
+ 
+
+ align:start position:0%
+would expect that so although the small
+stacks have a hired chef EB then so I
+
+ align:start position:0%
+stacks have a hired chef EB then so I
+ 
+
+ align:start position:0%
+stacks have a hired chef EB then so I
+have a higher money eg than chef EB
+
+ align:start position:0%
+have a higher money eg than chef EB
+ 
+
+ align:start position:0%
+have a higher money eg than chef EB
+usually this the ships get transferred
+
+ align:start position:0%
+usually this the ships get transferred
+ 
+
+ align:start position:0%
+usually this the ships get transferred
+from the small stacks to the big stacks
+
+ align:start position:0%
+from the small stacks to the big stacks
+ 
+
+ align:start position:0%
+from the small stacks to the big stacks
+because the big stacks have more since
+
+ align:start position:0%
+because the big stacks have more since
+ 
+
+ align:start position:0%
+because the big stacks have more since
+to you know go all in first and sort of
+
+ align:start position:0%
+to you know go all in first and sort of
+ 
+
+ align:start position:0%
+to you know go all in first and sort of
+bully people around so
+
+ align:start position:0%
+bully people around so
+ 
+
+ align:start position:0%
+bully people around so
+he takes this one down next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time we get jacks here so pimp and
+
+ align:start position:0%
+time we get jacks here so pimp and
+ 
+
+ align:start position:0%
+time we get jacks here so pimp and
+Christy is actually kind of short now
+
+ align:start position:0%
+Christy is actually kind of short now
+ 
+
+ align:start position:0%
+Christy is actually kind of short now
+even though he started the final table
+
+ align:start position:0%
+even though he started the final table
+ 
+
+ align:start position:0%
+even though he started the final table
+as the chick later because he's lost a
+
+ align:start position:0%
+as the chick later because he's lost a
+ 
+
+ align:start position:0%
+as the chick later because he's lost a
+bunch of all ins he gets it all in here
+
+ align:start position:0%
+bunch of all ins he gets it all in here
+ 
+
+ align:start position:0%
+bunch of all ins he gets it all in here
+and we hold we hold against a six so
+
+ align:start position:0%
+and we hold we hold against a six so
+ 
+
+ align:start position:0%
+and we hold we hold against a six so
+there's actually an interesting play
+
+ align:start position:0%
+there's actually an interesting play
+ 
+
+ align:start position:0%
+there's actually an interesting play
+here I I don't think he should have done
+
+ align:start position:0%
+here I I don't think he should have done
+ 
+
+ align:start position:0%
+here I I don't think he should have done
+it but this is actually often a good ICM
+
+ align:start position:0%
+it but this is actually often a good ICM
+ 
+
+ align:start position:0%
+it but this is actually often a good ICM
+play so normally I would say in this
+
+ align:start position:0%
+play so normally I would say in this
+ 
+
+ align:start position:0%
+play so normally I would say in this
+situation if you have a good hand just
+
+ align:start position:0%
+situation if you have a good hand just
+ 
+
+ align:start position:0%
+situation if you have a good hand just
+go all-in because he knows I'm gonna
+
+ align:start position:0%
+go all-in because he knows I'm gonna
+ 
+
+ align:start position:0%
+go all-in because he knows I'm gonna
+call so with a sixty just went all-in
+
+ align:start position:0%
+call so with a sixty just went all-in
+ 
+
+ align:start position:0%
+call so with a sixty just went all-in
+but often um there's this play called
+
+ align:start position:0%
+but often um there's this play called
+ 
+
+ align:start position:0%
+but often um there's this play called
+the stop-and-go which is in fact it's
+
+ align:start position:0%
+the stop-and-go which is in fact it's
+ 
+
+ align:start position:0%
+the stop-and-go which is in fact it's
+not very good like I don't think it
+
+ align:start position:0%
+not very good like I don't think it
+ 
+
+ align:start position:0%
+not very good like I don't think it
+would have been here but it's an
+
+ align:start position:0%
+would have been here but it's an
+ 
+
+ align:start position:0%
+would have been here but it's an
+interesting theoretical concept which is
+
+ align:start position:0%
+interesting theoretical concept which is
+ 
+
+ align:start position:0%
+interesting theoretical concept which is
+instead of going on he just called okay
+
+ align:start position:0%
+instead of going on he just called okay
+ 
+
+ align:start position:0%
+instead of going on he just called okay
+he calls and then he basically blindly
+
+ align:start position:0%
+he calls and then he basically blindly
+ 
+
+ align:start position:0%
+he calls and then he basically blindly
+goes all-in on the flop like he I mean
+
+ align:start position:0%
+goes all-in on the flop like he I mean
+ 
+
+ align:start position:0%
+goes all-in on the flop like he I mean
+she doesn't actually have to but this is
+
+ align:start position:0%
+she doesn't actually have to but this is
+ 
+
+ align:start position:0%
+she doesn't actually have to but this is
+what players used to do and you can do
+
+ align:start position:0%
+what players used to do and you can do
+ 
+
+ align:start position:0%
+what players used to do and you can do
+this in live poker what you would do in
+
+ align:start position:0%
+this in live poker what you would do in
+ 
+
+ align:start position:0%
+this in live poker what you would do in
+this situation is you would say call and
+
+ align:start position:0%
+this situation is you would say call and
+ 
+
+ align:start position:0%
+this situation is you would say call and
+then before the dealer even deals the
+
+ align:start position:0%
+then before the dealer even deals the
+ 
+
+ align:start position:0%
+then before the dealer even deals the
+floppy would you say all-in and this is
+
+ align:start position:0%
+floppy would you say all-in and this is
+ 
+
+ align:start position:0%
+floppy would you say all-in and this is
+a legal play and is
+
+ align:start position:0%
+a legal play and is
+ 
+
+ align:start position:0%
+a legal play and is
+essentially to the point is essentially
+
+ align:start position:0%
+essentially to the point is essentially
+ 
+
+ align:start position:0%
+essentially to the point is essentially
+it's an ICM they'll be the justification
+
+ align:start position:0%
+it's an ICM they'll be the justification
+ 
+
+ align:start position:0%
+it's an ICM they'll be the justification
+which i think is mostly wrong but still
+
+ align:start position:0%
+which i think is mostly wrong but still
+ 
+
+ align:start position:0%
+which i think is mostly wrong but still
+interesting is he
+
+ align:start position:0%
+interesting is he
+ 
+
+ align:start position:0%
+interesting is he
+sort of wants to maximize the chances
+
+ align:start position:0%
+sort of wants to maximize the chances
+ 
+
+ align:start position:0%
+sort of wants to maximize the chances
+that I fold so essentially okay this is
+
+ align:start position:0%
+that I fold so essentially okay this is
+ 
+
+ align:start position:0%
+that I fold so essentially okay this is
+strictly better right sorry the fact
+
+ align:start position:0%
+strictly better right sorry the fact
+ 
+
+ align:start position:0%
+strictly better right sorry the fact
+that the fact that he would call let me
+
+ align:start position:0%
+that the fact that he would call let me
+ 
+
+ align:start position:0%
+that the fact that he would call let me
+see the flop and then I get to decide
+
+ align:start position:0%
+see the flop and then I get to decide
+ 
+
+ align:start position:0%
+see the flop and then I get to decide
+whether to put the remaining chips in
+
+ align:start position:0%
+whether to put the remaining chips in
+ 
+
+ align:start position:0%
+whether to put the remaining chips in
+sounds like it should be better for me
+
+ align:start position:0%
+sounds like it should be better for me
+ 
+
+ align:start position:0%
+sounds like it should be better for me
+than me having to put all the chips in
+
+ align:start position:0%
+than me having to put all the chips in
+ 
+
+ align:start position:0%
+than me having to put all the chips in
+preflop but the main reason why he does
+
+ align:start position:0%
+preflop but the main reason why he does
+ 
+
+ align:start position:0%
+preflop but the main reason why he does
+this is because he doesn't he wants me
+
+ align:start position:0%
+this is because he doesn't he wants me
+ 
+
+ align:start position:0%
+this is because he doesn't he wants me
+to have an opportunity to fold my cards
+
+ align:start position:0%
+to have an opportunity to fold my cards
+ 
+
+ align:start position:0%
+to have an opportunity to fold my cards
+and avoid getting in a situation where
+
+ align:start position:0%
+and avoid getting in a situation where
+ 
+
+ align:start position:0%
+and avoid getting in a situation where
+both of us are playing for all our
+
+ align:start position:0%
+both of us are playing for all our
+ 
+
+ align:start position:0%
+both of us are playing for all our
+entire stack so this was sort of the
+
+ align:start position:0%
+entire stack so this was sort of the
+ 
+
+ align:start position:0%
+entire stack so this was sort of the
+justification for it so even though
+
+ align:start position:0%
+justification for it so even though
+ 
+
+ align:start position:0%
+justification for it so even though
+you're you're giving your opponent more
+
+ align:start position:0%
+you're you're giving your opponent more
+ 
+
+ align:start position:0%
+you're you're giving your opponent more
+information you're also decreasing the
+
+ align:start position:0%
+information you're also decreasing the
+ 
+
+ align:start position:0%
+information you're also decreasing the
+chances that they decide to call to the
+
+ align:start position:0%
+chances that they decide to call to the
+ 
+
+ align:start position:0%
+chances that they decide to call to the
+river card and have more chances of
+
+ align:start position:0%
+river card and have more chances of
+ 
+
+ align:start position:0%
+river card and have more chances of
+beating you so I mean that justification
+
+ align:start position:0%
+beating you so I mean that justification
+ 
+
+ align:start position:0%
+beating you so I mean that justification
+is correct but it's just that if you
+
+ align:start position:0%
+is correct but it's just that if you
+ 
+
+ align:start position:0%
+is correct but it's just that if you
+crunch the numbers usually this
+
+ align:start position:0%
+crunch the numbers usually this
+ 
+
+ align:start position:0%
+crunch the numbers usually this
+situation won't be favorable enough and
+
+ align:start position:0%
+situation won't be favorable enough and
+ 
+
+ align:start position:0%
+situation won't be favorable enough and
+usually don't want to be giving your
+
+ align:start position:0%
+usually don't want to be giving your
+ 
+
+ align:start position:0%
+usually don't want to be giving your
+opponent that extra information okay
+
+ align:start position:0%
+opponent that extra information okay
+ 
+
+ align:start position:0%
+opponent that extra information okay
+so so finally someone busts we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get Jackson off again so he normally I
+
+ align:start position:0%
+get Jackson off again so he normally I
+ 
+
+ align:start position:0%
+get Jackson off again so he normally I
+think I would often consider calling
+
+ align:start position:0%
+think I would often consider calling
+ 
+
+ align:start position:0%
+think I would often consider calling
+this but I think just a voice so now
+
+ align:start position:0%
+this but I think just a voice so now
+ 
+
+ align:start position:0%
+this but I think just a voice so now
+this extra sort of even before the chip
+
+ align:start position:0%
+this extra sort of even before the chip
+ 
+
+ align:start position:0%
+this extra sort of even before the chip
+leader but not by a time and I don't
+
+ align:start position:0%
+leader but not by a time and I don't
+ 
+
+ align:start position:0%
+leader but not by a time and I don't
+really want to get in a big pot here so
+
+ align:start position:0%
+really want to get in a big pot here so
+ 
+
+ align:start position:0%
+really want to get in a big pot here so
+I decided to just give it to him even
+
+ align:start position:0%
+I decided to just give it to him even
+ 
+
+ align:start position:0%
+I decided to just give it to him even
+though normally I would definitely call
+
+ align:start position:0%
+though normally I would definitely call
+ 
+
+ align:start position:0%
+though normally I would definitely call
+this King
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seven suited I make a pretty big line
+
+ align:start position:0%
+seven suited I make a pretty big line
+ 
+
+ align:start position:0%
+seven suited I make a pretty big line
+for 21 and a half bets from the small
+
+ align:start position:0%
+for 21 and a half bets from the small
+ 
+
+ align:start position:0%
+for 21 and a half bets from the small
+blind and take it down all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right wasn't we'll see if we'll see all
+
+ align:start position:0%
+right wasn't we'll see if we'll see all
+ 
+
+ align:start position:0%
+right wasn't we'll see if we'll see all
+means um so we we full of six three
+
+ align:start position:0%
+means um so we we full of six three
+ 
+
+ align:start position:0%
+means um so we we full of six three
+suited here be my sponsor decided to
+
+ align:start position:0%
+suited here be my sponsor decided to
+ 
+
+ align:start position:0%
+suited here be my sponsor decided to
+raise small which is once again a bit
+
+ align:start position:0%
+raise small which is once again a bit
+ 
+
+ align:start position:0%
+raise small which is once again a bit
+unusual it usually just want to go all
+
+ align:start position:0%
+unusual it usually just want to go all
+ 
+
+ align:start position:0%
+unusual it usually just want to go all
+in a situation where ICM is so relevant
+
+ align:start position:0%
+in a situation where ICM is so relevant
+ 
+
+ align:start position:0%
+in a situation where ICM is so relevant
+and then Nicolas goes on and he folds
+
+ align:start position:0%
+and then Nicolas goes on and he folds
+ 
+
+ align:start position:0%
+and then Nicolas goes on and he folds
+Jack
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five offsuit here do we fold so once
+
+ align:start position:0%
+five offsuit here do we fold so once
+ 
+
+ align:start position:0%
+five offsuit here do we fold so once
+again this guy raises small so maybe he
+
+ align:start position:0%
+again this guy raises small so maybe he
+ 
+
+ align:start position:0%
+again this guy raises small so maybe he
+doesn't really want to do this ICM thing
+
+ align:start position:0%
+doesn't really want to do this ICM thing
+ 
+
+ align:start position:0%
+doesn't really want to do this ICM thing
+and just he wants to play box he
+
+ align:start position:0%
+and just he wants to play box he
+ 
+
+ align:start position:0%
+and just he wants to play box he
+takes that one down though Nicholas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Brody so as you can see it's it's a bit
+
+ align:start position:0%
+Brody so as you can see it's it's a bit
+ 
+
+ align:start position:0%
+Brody so as you can see it's it's a bit
+boring there's not too many hands I I
+
+ align:start position:0%
+boring there's not too many hands I I
+ 
+
+ align:start position:0%
+boring there's not too many hands I I
+mean that's sort of what happens when
+
+ align:start position:0%
+mean that's sort of what happens when
+ 
+
+ align:start position:0%
+mean that's sort of what happens when
+there's ICM because you people don't you
+
+ align:start position:0%
+there's ICM because you people don't you
+ 
+
+ align:start position:0%
+there's ICM because you people don't you
+don't really want to splash around you
+
+ align:start position:0%
+don't really want to splash around you
+ 
+
+ align:start position:0%
+don't really want to splash around you
+kind of just want to survive in the
+
+ align:start position:0%
+kind of just want to survive in the
+ 
+
+ align:start position:0%
+kind of just want to survive in the
+tournament by risking all your chips
+
+ align:start position:0%
+tournament by risking all your chips
+ 
+
+ align:start position:0%
+tournament by risking all your chips
+once in a while instead of like slowly
+
+ align:start position:0%
+once in a while instead of like slowly
+ 
+
+ align:start position:0%
+once in a while instead of like slowly
+bleeding your tips in a variety of pots
+
+ align:start position:0%
+bleeding your tips in a variety of pots
+ 
+
+ align:start position:0%
+bleeding your tips in a variety of pots
+so once again we nine suited big all and
+
+ align:start position:0%
+so once again we nine suited big all and
+ 
+
+ align:start position:0%
+so once again we nine suited big all and
+hungie good enough Queen seven suited I
+
+ align:start position:0%
+hungie good enough Queen seven suited I
+ 
+
+ align:start position:0%
+hungie good enough Queen seven suited I
+decided to open it raised it up but
+
+ align:start position:0%
+decided to open it raised it up but
+ 
+
+ align:start position:0%
+decided to open it raised it up but
+unfortunately I guess I mean even if
+
+ align:start position:0%
+unfortunately I guess I mean even if
+ 
+
+ align:start position:0%
+unfortunately I guess I mean even if
+just one guy went on and I'm clearly
+
+ align:start position:0%
+just one guy went on and I'm clearly
+ 
+
+ align:start position:0%
+just one guy went on and I'm clearly
+folding so they both go all-in and Ace
+
+ align:start position:0%
+folding so they both go all-in and Ace
+ 
+
+ align:start position:0%
+folding so they both go all-in and Ace
+King meets Kings which is really bad
+
+ align:start position:0%
+King meets Kings which is really bad
+ 
+
+ align:start position:0%
+King meets Kings which is really bad
+news for everyone essentially because if
+
+ align:start position:0%
+news for everyone essentially because if
+ 
+
+ align:start position:0%
+news for everyone essentially because if
+Kings held then he would have busted but
+
+ align:start position:0%
+Kings held then he would have busted but
+ 
+
+ align:start position:0%
+Kings held then he would have busted but
+unfortunately he doesn't so
+
+ align:start position:0%
+unfortunately he doesn't so
+ 
+
+ align:start position:0%
+unfortunately he doesn't so
+pocket eights I'm racing here this
+
+ align:start position:0%
+pocket eights I'm racing here this
+ 
+
+ align:start position:0%
+pocket eights I'm racing here this
+would have been a gross spot by the way
+
+ align:start position:0%
+would have been a gross spot by the way
+ 
+
+ align:start position:0%
+would have been a gross spot by the way
+I think if
+
+ align:start position:0%
+I think if
+ 
+
+ align:start position:0%
+I think if
+it'd be my song sir went on here I don't
+
+ align:start position:0%
+it'd be my song sir went on here I don't
+ 
+
+ align:start position:0%
+it'd be my song sir went on here I don't
+know what would have that it would it
+
+ align:start position:0%
+know what would have that it would it
+ 
+
+ align:start position:0%
+know what would have that it would it
+would have been very gross because on
+
+ align:start position:0%
+would have been very gross because on
+ 
+
+ align:start position:0%
+would have been very gross because on
+one hand I definitely don't want to be
+
+ align:start position:0%
+one hand I definitely don't want to be
+ 
+
+ align:start position:0%
+one hand I definitely don't want to be
+old folding and hand as good as pocket
+
+ align:start position:0%
+old folding and hand as good as pocket
+ 
+
+ align:start position:0%
+old folding and hand as good as pocket
+eights but on the other hand I see him
+
+ align:start position:0%
+eights but on the other hand I see him
+ 
+
+ align:start position:0%
+eights but on the other hand I see him
+is just so relevant I think I probably
+
+ align:start position:0%
+is just so relevant I think I probably
+ 
+
+ align:start position:0%
+is just so relevant I think I probably
+have to fold so yeah this is a case
+
+ align:start position:0%
+have to fold so yeah this is a case
+ 
+
+ align:start position:0%
+have to fold so yeah this is a case
+where I could have made an extreme like
+
+ align:start position:0%
+where I could have made an extreme like
+ 
+
+ align:start position:0%
+where I could have made an extreme like
+a very a hero fold essentially a fold in
+
+ align:start position:0%
+a very a hero fold essentially a fold in
+ 
+
+ align:start position:0%
+a very a hero fold essentially a fold in
+a very good hand if be my sponsor right
+
+ align:start position:0%
+a very good hand if be my sponsor right
+ 
+
+ align:start position:0%
+a very good hand if be my sponsor right
+all in so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+King jack off we get another lock okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Jack I Jack 10 off um okay this I'll
+
+ align:start position:0%
+Jack I Jack 10 off um okay this I'll
+ 
+
+ align:start position:0%
+Jack I Jack 10 off um okay this I'll
+tell you what happened and then we'll
+
+ align:start position:0%
+tell you what happened and then we'll
+ 
+
+ align:start position:0%
+tell you what happened and then we'll
+take a break and then I'll analyze it
+
+ align:start position:0%
+take a break and then I'll analyze it
+ 
+
+ align:start position:0%
+take a break and then I'll analyze it
+after you listen I want to analyze in a
+
+ align:start position:0%
+after you listen I want to analyze in a
+ 
+
+ align:start position:0%
+after you listen I want to analyze in a
+bit more depth because I was actually
+
+ align:start position:0%
+bit more depth because I was actually
+ 
+
+ align:start position:0%
+bit more depth because I was actually
+surprised going through the replays
+
+ align:start position:0%
+surprised going through the replays
+ 
+
+ align:start position:0%
+surprised going through the replays
+looking at how I played this so LPM
+
+ align:start position:0%
+looking at how I played this so LPM
+ 
+
+ align:start position:0%
+looking at how I played this so LPM
+box makes it 16,000
+
+ align:start position:0%
+box makes it 16,000
+ 
+
+ align:start position:0%
+box makes it 16,000
+and I rearranged to 44 for 44 um
+
+ align:start position:0%
+and I rearranged to 44 for 44 um
+ 
+
+ align:start position:0%
+and I rearranged to 44 for 44 um
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+I think this onion I'm not I don't have
+
+ align:start position:0%
+I think this onion I'm not I don't have
+ 
+
+ align:start position:0%
+I think this onion I'm not I don't have
+a great hand but I think this is one of
+
+ align:start position:0%
+a great hand but I think this is one of
+ 
+
+ align:start position:0%
+a great hand but I think this is one of
+the this hand is too good not to make a
+
+ align:start position:0%
+the this hand is too good not to make a
+ 
+
+ align:start position:0%
+the this hand is too good not to make a
+bluff with so that I do that and then he
+
+ align:start position:0%
+bluff with so that I do that and then he
+ 
+
+ align:start position:0%
+bluff with so that I do that and then he
+goes all-in and then I think this is
+
+ align:start position:0%
+goes all-in and then I think this is
+ 
+
+ align:start position:0%
+goes all-in and then I think this is
+this is a very tough spot because my
+
+ align:start position:0%
+this is a very tough spot because my
+ 
+
+ align:start position:0%
+this is a very tough spot because my
+hand isn't good but when i really is i
+
+ align:start position:0%
+hand isn't good but when i really is i
+ 
+
+ align:start position:0%
+hand isn't good but when i really is i
+definitely had the you know if this guy
+
+ align:start position:0%
+definitely had the you know if this guy
+ 
+
+ align:start position:0%
+definitely had the you know if this guy
+had fewer chips i would have just went
+
+ align:start position:0%
+had fewer chips i would have just went
+ 
+
+ align:start position:0%
+had fewer chips i would have just went
+all-in myself I definitely didn't
+
+ align:start position:0%
+all-in myself I definitely didn't
+ 
+
+ align:start position:0%
+all-in myself I definitely didn't
+rearrange the size thinking I would even
+
+ align:start position:0%
+rearrange the size thinking I would even
+ 
+
+ align:start position:0%
+rearrange the size thinking I would even
+consider folding if he moved on but
+
+ align:start position:0%
+consider folding if he moved on but
+ 
+
+ align:start position:0%
+consider folding if he moved on but
+so yeah the reason I made this size it
+
+ align:start position:0%
+so yeah the reason I made this size it
+ 
+
+ align:start position:0%
+so yeah the reason I made this size it
+so that if this guy went all-in I could
+
+ align:start position:0%
+so that if this guy went all-in I could
+ 
+
+ align:start position:0%
+so that if this guy went all-in I could
+fold but as it turns out heating people
+
+ align:start position:0%
+fold but as it turns out heating people
+ 
+
+ align:start position:0%
+fold but as it turns out heating people
+then he went all-in and then so let's
+
+ align:start position:0%
+then he went all-in and then so let's
+ 
+
+ align:start position:0%
+then he went all-in and then so let's
+analyze this hand after the break we'll
+
+ align:start position:0%
+analyze this hand after the break we'll
+ 
+
+ align:start position:0%
+analyze this hand after the break we'll
+take like a short to three minute break
+
+ align:start position:0%
+take like a short to three minute break
+ 
+
+ align:start position:0%
+take like a short to three minute break
+okay oh yeah I'll get started again so
+
+ align:start position:0%
+okay oh yeah I'll get started again so
+ 
+
+ align:start position:0%
+okay oh yeah I'll get started again so
+get so let's calculate this hand so I
+
+ align:start position:0%
+get so let's calculate this hand so I
+ 
+
+ align:start position:0%
+get so let's calculate this hand so I
+actually decided to go back and
+
+ align:start position:0%
+actually decided to go back and
+ 
+
+ align:start position:0%
+actually decided to go back and
+calculate this hand from an ICM
+
+ align:start position:0%
+calculate this hand from an ICM
+ 
+
+ align:start position:0%
+calculate this hand from an ICM
+perspective because ICM is basically
+
+ align:start position:0%
+perspective because ICM is basically
+ 
+
+ align:start position:0%
+perspective because ICM is basically
+very relevant here okay so let's see
+
+ align:start position:0%
+very relevant here okay so let's see
+ 
+
+ align:start position:0%
+very relevant here okay so let's see
+exactly how to do this in practice okay
+
+ align:start position:0%
+exactly how to do this in practice okay
+ 
+
+ align:start position:0%
+exactly how to do this in practice okay
+so okay
+
+ align:start position:0%
+so okay
+ 
+
+ align:start position:0%
+so okay
+so so okay so let's first see the chip
+
+ align:start position:0%
+so so okay so let's first see the chip
+ 
+
+ align:start position:0%
+so so okay so let's first see the chip
+be be kept the play shape okay let me
+
+ align:start position:0%
+be be kept the play shape okay let me
+ 
+
+ align:start position:0%
+be be kept the play shape okay let me
+pursue that ship TV calculation so I
+
+ align:start position:0%
+pursue that ship TV calculation so I
+ 
+
+ align:start position:0%
+pursue that ship TV calculation so I
+have okay so uh you can trust that I
+
+ align:start position:0%
+have okay so uh you can trust that I
+ 
+
+ align:start position:0%
+have okay so uh you can trust that I
+copied the numbers correctly so it's
+
+ align:start position:0%
+copied the numbers correctly so it's
+ 
+
+ align:start position:0%
+copied the numbers correctly so it's
+actually there's three possibilities
+
+ align:start position:0%
+actually there's three possibilities
+ 
+
+ align:start position:0%
+actually there's three possibilities
+okay there's um if I fold this is the Oh
+
+ align:start position:0%
+okay there's um if I fold this is the Oh
+ 
+
+ align:start position:0%
+okay there's um if I fold this is the Oh
+chips this is the amount of chips I'll
+
+ align:start position:0%
+chips this is the amount of chips I'll
+ 
+
+ align:start position:0%
+chips this is the amount of chips I'll
+have ok so right now I'm only carrying
+
+ align:start position:0%
+have ok so right now I'm only carrying
+ 
+
+ align:start position:0%
+have ok so right now I'm only carrying
+about chips so if I fold this is the
+
+ align:start position:0%
+about chips so if I fold this is the
+ 
+
+ align:start position:0%
+about chips so if I fold this is the
+amount of chips I'll have if I call in
+
+ align:start position:0%
+amount of chips I'll have if I call in
+ 
+
+ align:start position:0%
+amount of chips I'll have if I call in
+wins this is the amount of chips I'll
+
+ align:start position:0%
+wins this is the amount of chips I'll
+ 
+
+ align:start position:0%
+wins this is the amount of chips I'll
+have and if I call and lose this is the
+
+ align:start position:0%
+have and if I call and lose this is the
+ 
+
+ align:start position:0%
+have and if I call and lose this is the
+amount of chips I'll have so we could
+
+ align:start position:0%
+amount of chips I'll have so we could
+ 
+
+ align:start position:0%
+amount of chips I'll have so we could
+basically do a calculation here where I
+
+ align:start position:0%
+basically do a calculation here where I
+ 
+
+ align:start position:0%
+basically do a calculation here where I
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+it's- so let's say my chances of winning
+
+ align:start position:0%
+it's- so let's say my chances of winning
+ 
+
+ align:start position:0%
+it's- so let's say my chances of winning
+as X so it's x times so
+
+ align:start position:0%
+as X so it's x times so
+ 
+
+ align:start position:0%
+as X so it's x times so
+it's x times how many chips I have if i
+
+ align:start position:0%
+it's x times how many chips I have if i
+ 
+
+ align:start position:0%
+it's x times how many chips I have if i
+if i call them lose which is 107 I'm
+
+ align:start position:0%
+if i call them lose which is 107 I'm
+ 
+
+ align:start position:0%
+if i call them lose which is 107 I'm
+gonna not write the last three zeroes
+
+ align:start position:0%
+gonna not write the last three zeroes
+ 
+
+ align:start position:0%
+gonna not write the last three zeroes
+plus one minus x times 402
+
+ align:start position:0%
+plus one minus x times 402
+ 
+
+ align:start position:0%
+plus one minus x times 402
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+I did this in Reverse ok X is my chances
+
+ align:start position:0%
+I did this in Reverse ok X is my chances
+ 
+
+ align:start position:0%
+I did this in Reverse ok X is my chances
+of losing so again I'm basically
+
+ align:start position:0%
+of losing so again I'm basically
+ 
+
+ align:start position:0%
+of losing so again I'm basically
+comparing this number this is how many
+
+ align:start position:0%
+comparing this number this is how many
+ 
+
+ align:start position:0%
+comparing this number this is how many
+chips I have this by full okay and then
+
+ align:start position:0%
+chips I have this by full okay and then
+ 
+
+ align:start position:0%
+chips I have this by full okay and then
+essentially I'm just solving for x right
+
+ align:start position:0%
+essentially I'm just solving for x right
+ 
+
+ align:start position:0%
+essentially I'm just solving for x right
+so you so the way I do it is I set these
+
+ align:start position:0%
+so you so the way I do it is I set these
+ 
+
+ align:start position:0%
+so you so the way I do it is I set these
+to be equal and then I calculate X and
+
+ align:start position:0%
+to be equal and then I calculate X and
+ 
+
+ align:start position:0%
+to be equal and then I calculate X and
+that's sort of the break-even X which
+
+ align:start position:0%
+that's sort of the break-even X which
+ 
+
+ align:start position:0%
+that's sort of the break-even X which
+tells me what's the minimum equity I
+
+ align:start position:0%
+tells me what's the minimum equity I
+ 
+
+ align:start position:0%
+tells me what's the minimum equity I
+need against his range to call so a so
+
+ align:start position:0%
+need against his range to call so a so
+ 
+
+ align:start position:0%
+need against his range to call so a so
+we can do that so I think it turns out
+
+ align:start position:0%
+we can do that so I think it turns out
+ 
+
+ align:start position:0%
+we can do that so I think it turns out
+to be so this formula is equal to the
+
+ align:start position:0%
+to be so this formula is equal to the
+ 
+
+ align:start position:0%
+to be so this formula is equal to the
+fold - call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+/
+
+ align:start position:0%
+/
+ 
+
+ align:start position:0%
+/
+I'm just gonna I did it okay so okay
+
+ align:start position:0%
+I'm just gonna I did it okay so okay
+ 
+
+ align:start position:0%
+I'm just gonna I did it okay so okay
+so I can show these so it's so
+
+ align:start position:0%
+so I can show these so it's so
+ 
+
+ align:start position:0%
+so I can show these so it's so
+essentially it's I had to do one else
+
+ align:start position:0%
+essentially it's I had to do one else
+ 
+
+ align:start position:0%
+essentially it's I had to do one else
+right I to do one odds so it makes sense
+
+ align:start position:0%
+right I to do one odds so it makes sense
+ 
+
+ align:start position:0%
+right I to do one odds so it makes sense
+that I needed a 33% equity you call okay
+
+ align:start position:0%
+that I needed a 33% equity you call okay
+ 
+
+ align:start position:0%
+that I needed a 33% equity you call okay
+so how do we give this side so this is
+
+ align:start position:0%
+so how do we give this side so this is
+ 
+
+ align:start position:0%
+so how do we give this side so this is
+these are essentially the ICM numbers so
+
+ align:start position:0%
+these are essentially the ICM numbers so
+ 
+
+ align:start position:0%
+these are essentially the ICM numbers so
+essentially the way you complete this is
+
+ align:start position:0%
+essentially the way you complete this is
+ 
+
+ align:start position:0%
+essentially the way you complete this is
+you Google ICM
+
+ align:start position:0%
+you Google ICM
+ 
+
+ align:start position:0%
+you Google ICM
+calculator and then you just go to the
+
+ align:start position:0%
+calculator and then you just go to the
+ 
+
+ align:start position:0%
+calculator and then you just go to the
+first one it's usually quite easy to
+
+ align:start position:0%
+first one it's usually quite easy to
+ 
+
+ align:start position:0%
+first one it's usually quite easy to
+find okay so it's a bit tricky because
+
+ align:start position:0%
+find okay so it's a bit tricky because
+ 
+
+ align:start position:0%
+find okay so it's a bit tricky because
+you have to put in the exact payouts so
+
+ align:start position:0%
+you have to put in the exact payouts so
+ 
+
+ align:start position:0%
+you have to put in the exact payouts so
+I think at the time they were like
+
+ align:start position:0%
+I think at the time they were like
+ 
+
+ align:start position:0%
+I think at the time they were like
+eighteen point five this this is all as
+
+ align:start position:0%
+eighteen point five this this is all as
+ 
+
+ align:start position:0%
+eighteen point five this this is all as
+a percentage of the total pot so I
+
+ align:start position:0%
+a percentage of the total pot so I
+ 
+
+ align:start position:0%
+a percentage of the total pot so I
+forget exactly the numbers but it was
+
+ align:start position:0%
+forget exactly the numbers but it was
+ 
+
+ align:start position:0%
+forget exactly the numbers but it was
+something like this okay and then you
+
+ align:start position:0%
+something like this okay and then you
+ 
+
+ align:start position:0%
+something like this okay and then you
+type in the force you type in the stack
+
+ align:start position:0%
+type in the force you type in the stack
+ 
+
+ align:start position:0%
+type in the force you type in the stack
+sizes so it takes a bit of time and you
+
+ align:start position:0%
+sizes so it takes a bit of time and you
+ 
+
+ align:start position:0%
+sizes so it takes a bit of time and you
+know even if you're fast at this if you
+
+ align:start position:0%
+know even if you're fast at this if you
+ 
+
+ align:start position:0%
+know even if you're fast at this if you
+conserve your entire time bank from the
+
+ align:start position:0%
+conserve your entire time bank from the
+ 
+
+ align:start position:0%
+conserve your entire time bank from the
+whole tournament for this one population
+
+ align:start position:0%
+whole tournament for this one population
+ 
+
+ align:start position:0%
+whole tournament for this one population
+you probably have enough time to do it
+
+ align:start position:0%
+you probably have enough time to do it
+ 
+
+ align:start position:0%
+you probably have enough time to do it
+because you're gonna have like you'll
+
+ align:start position:0%
+because you're gonna have like you'll
+ 
+
+ align:start position:0%
+because you're gonna have like you'll
+probably have like two or three minutes
+
+ align:start position:0%
+probably have like two or three minutes
+ 
+
+ align:start position:0%
+probably have like two or three minutes
+of time back saved up so you can you
+
+ align:start position:0%
+of time back saved up so you can you
+ 
+
+ align:start position:0%
+of time back saved up so you can you
+probably can do it you have to
+
+ align:start position:0%
+probably can do it you have to
+ 
+
+ align:start position:0%
+probably can do it you have to
+essentially right so there's three
+
+ align:start position:0%
+essentially right so there's three
+ 
+
+ align:start position:0%
+essentially right so there's three
+possibilities I have to calculate if I
+
+ align:start position:0%
+possibilities I have to calculate if I
+ 
+
+ align:start position:0%
+possibilities I have to calculate if I
+fold not only how many chips I have but
+
+ align:start position:0%
+fold not only how many chips I have but
+ 
+
+ align:start position:0%
+fold not only how many chips I have but
+how many chips everyone else has and
+
+ align:start position:0%
+how many chips everyone else has and
+ 
+
+ align:start position:0%
+how many chips everyone else has and
+then I take them in and then I think
+
+ align:start position:0%
+then I take them in and then I think
+ 
+
+ align:start position:0%
+then I take them in and then I think
+that's actually calculate the value of
+
+ align:start position:0%
+that's actually calculate the value of
+ 
+
+ align:start position:0%
+that's actually calculate the value of
+my stack in terms of as a fraction of
+
+ align:start position:0%
+my stack in terms of as a fraction of
+ 
+
+ align:start position:0%
+my stack in terms of as a fraction of
+the total money in a pot and then
+
+ align:start position:0%
+the total money in a pot and then
+ 
+
+ align:start position:0%
+the total money in a pot and then
+similarly I do it for the other two
+
+ align:start position:0%
+similarly I do it for the other two
+ 
+
+ align:start position:0%
+similarly I do it for the other two
+cases and then I calculate the ICM
+
+ align:start position:0%
+cases and then I calculate the ICM
+ 
+
+ align:start position:0%
+cases and then I calculate the ICM
+numbers and roughly speaking this is my
+
+ align:start position:0%
+numbers and roughly speaking this is my
+ 
+
+ align:start position:0%
+numbers and roughly speaking this is my
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+these are all this is all normalized but
+
+ align:start position:0%
+these are all this is all normalized but
+ 
+
+ align:start position:0%
+these are all this is all normalized but
+these are rough this is roughly midol or
+
+ align:start position:0%
+these are rough this is roughly midol or
+ 
+
+ align:start position:0%
+these are rough this is roughly midol or
+EB in each of these three scenarios and
+
+ align:start position:0%
+EB in each of these three scenarios and
+ 
+
+ align:start position:0%
+EB in each of these three scenarios and
+if I do the same if I do the same
+
+ align:start position:0%
+if I do the same if I do the same
+ 
+
+ align:start position:0%
+if I do the same if I do the same
+calculation I'll find that I actually
+
+ align:start position:0%
+calculation I'll find that I actually
+ 
+
+ align:start position:0%
+calculation I'll find that I actually
+39.6
+
+ align:start position:0%
+39.6
+ 
+
+ align:start position:0%
+39.6
+equity okay so so far does the
+
+ align:start position:0%
+equity okay so so far does the
+ 
+
+ align:start position:0%
+equity okay so so far does the
+calculation make sense to everyone I
+
+ align:start position:0%
+calculation make sense to everyone I
+ 
+
+ align:start position:0%
+calculation make sense to everyone I
+didn't do all the steps in practice but
+
+ align:start position:0%
+didn't do all the steps in practice but
+ 
+
+ align:start position:0%
+didn't do all the steps in practice but
+I explain how to do all the steps so
+
+ align:start position:0%
+I explain how to do all the steps so
+ 
+
+ align:start position:0%
+I explain how to do all the steps so
+this yeah if you're fast it takes it
+
+ align:start position:0%
+this yeah if you're fast it takes it
+ 
+
+ align:start position:0%
+this yeah if you're fast it takes it
+still takes like a minute a minute and a
+
+ align:start position:0%
+still takes like a minute a minute and a
+ 
+
+ align:start position:0%
+still takes like a minute a minute and a
+half but the last part is now we have to
+
+ align:start position:0%
+half but the last part is now we have to
+ 
+
+ align:start position:0%
+half but the last part is now we have to
+open poker state now we have to take
+
+ align:start position:0%
+open poker state now we have to take
+ 
+
+ align:start position:0%
+open poker state now we have to take
+them to Jack ten off C and then we have
+
+ align:start position:0%
+them to Jack ten off C and then we have
+ 
+
+ align:start position:0%
+them to Jack ten off C and then we have
+to put him on the range so so okay let's
+
+ align:start position:0%
+to put him on the range so so okay let's
+ 
+
+ align:start position:0%
+to put him on the range so so okay let's
+just put him on a Sookie I suspect that
+
+ align:start position:0%
+just put him on a Sookie I suspect that
+ 
+
+ align:start position:0%
+just put him on a Sookie I suspect that
+I'm probably gonna have to fold because
+
+ align:start position:0%
+I'm probably gonna have to fold because
+ 
+
+ align:start position:0%
+I'm probably gonna have to fold because
+39.6% is quite a lot so I'm gonna put
+
+ align:start position:0%
+39.6% is quite a lot so I'm gonna put
+ 
+
+ align:start position:0%
+39.6% is quite a lot so I'm gonna put
+him on the loosest I'm gonna put him on
+
+ align:start position:0%
+him on the loosest I'm gonna put him on
+ 
+
+ align:start position:0%
+him on the loosest I'm gonna put him on
+the loosest range and see if I have
+
+ align:start position:0%
+the loosest range and see if I have
+ 
+
+ align:start position:0%
+the loosest range and see if I have
+thirty nine point six so
+
+ align:start position:0%
+thirty nine point six so
+ 
+
+ align:start position:0%
+thirty nine point six so
+let's say he's pretty loose so he's
+
+ align:start position:0%
+let's say he's pretty loose so he's
+ 
+
+ align:start position:0%
+let's say he's pretty loose so he's
+going to gamble with let's say pocket
+
+ align:start position:0%
+going to gamble with let's say pocket
+ 
+
+ align:start position:0%
+going to gamble with let's say pocket
+fours plus I mean this another thing to
+
+ align:start position:0%
+fours plus I mean this another thing to
+ 
+
+ align:start position:0%
+fours plus I mean this another thing to
+be that's relevant here is I think it
+
+ align:start position:0%
+be that's relevant here is I think it
+ 
+
+ align:start position:0%
+be that's relevant here is I think it
+looks like he doesn't have full equity
+
+ align:start position:0%
+looks like he doesn't have full equity
+ 
+
+ align:start position:0%
+looks like he doesn't have full equity
+like I don't think Wendy's going on here
+
+ align:start position:0%
+like I don't think Wendy's going on here
+ 
+
+ align:start position:0%
+like I don't think Wendy's going on here
+he suspects that I'm ever folding or at
+
+ align:start position:0%
+he suspects that I'm ever folding or at
+ 
+
+ align:start position:0%
+he suspects that I'm ever folding or at
+least he probably thinks I'm calling him
+
+ align:start position:0%
+least he probably thinks I'm calling him
+ 
+
+ align:start position:0%
+least he probably thinks I'm calling him
+the overwhelming majority of the time so
+
+ align:start position:0%
+the overwhelming majority of the time so
+ 
+
+ align:start position:0%
+the overwhelming majority of the time so
+I think he's really gonna turn up a
+
+ align:start position:0%
+I think he's really gonna turn up a
+ 
+
+ align:start position:0%
+I think he's really gonna turn up a
+stone bluff like eight seven suited
+
+ align:start position:0%
+stone bluff like eight seven suited
+ 
+
+ align:start position:0%
+stone bluff like eight seven suited
+because of this so I would I would I
+
+ align:start position:0%
+because of this so I would I would I
+ 
+
+ align:start position:0%
+because of this so I would I would I
+would be very surprised if he ever had
+
+ align:start position:0%
+would be very surprised if he ever had
+ 
+
+ align:start position:0%
+would be very surprised if he ever had
+eight seven suited unless he would
+
+ align:start position:0%
+eight seven suited unless he would
+ 
+
+ align:start position:0%
+eight seven suited unless he would
+somehow unless he read into this and
+
+ align:start position:0%
+somehow unless he read into this and
+ 
+
+ align:start position:0%
+somehow unless he read into this and
+realized that I could actually fold some
+
+ align:start position:0%
+realized that I could actually fold some
+ 
+
+ align:start position:0%
+realized that I could actually fold some
+hands here which maybe he did I do you
+
+ align:start position:0%
+hands here which maybe he did I do you
+ 
+
+ align:start position:0%
+hands here which maybe he did I do you
+shouldn't give them enough credit so um
+
+ align:start position:0%
+shouldn't give them enough credit so um
+ 
+
+ align:start position:0%
+shouldn't give them enough credit so um
+okay let just do something somewhat
+
+ align:start position:0%
+okay let just do something somewhat
+ 
+
+ align:start position:0%
+okay let just do something somewhat
+quick let's say he called the he gets it
+
+ align:start position:0%
+quick let's say he called the he gets it
+ 
+
+ align:start position:0%
+quick let's say he called the he gets it
+in with he stayed off suit a spy suited
+
+ align:start position:0%
+in with he stayed off suit a spy suited
+ 
+
+ align:start position:0%
+in with he stayed off suit a spy suited
+plus King Jack suited King Queen off and
+
+ align:start position:0%
+plus King Jack suited King Queen off and
+ 
+
+ align:start position:0%
+plus King Jack suited King Queen off and
+pocket fours plus so that's like 14.6%
+
+ align:start position:0%
+pocket fours plus so that's like 14.6%
+ 
+
+ align:start position:0%
+pocket fours plus so that's like 14.6%
+of hands so let's do this so against
+
+ align:start position:0%
+of hands so let's do this so against
+ 
+
+ align:start position:0%
+of hands so let's do this so against
+this we have we have thirty six percent
+
+ align:start position:0%
+this we have we have thirty six percent
+ 
+
+ align:start position:0%
+this we have we have thirty six percent
+equity so that's not enough we need
+
+ align:start position:0%
+equity so that's not enough we need
+ 
+
+ align:start position:0%
+equity so that's not enough we need
+thirty nine let's see how wide this
+
+ align:start position:0%
+thirty nine let's see how wide this
+ 
+
+ align:start position:0%
+thirty nine let's see how wide this
+range has to be for us we have 39 all
+
+ align:start position:0%
+range has to be for us we have 39 all
+ 
+
+ align:start position:0%
+range has to be for us we have 39 all
+right let's say he gets in um there's
+
+ align:start position:0%
+right let's say he gets in um there's
+ 
+
+ align:start position:0%
+right let's say he gets in um there's
+20% of hands which is quite a lot which
+
+ align:start position:0%
+20% of hands which is quite a lot which
+ 
+
+ align:start position:0%
+20% of hands which is quite a lot which
+is I think way too much 18.6%
+
+ align:start position:0%
+is I think way too much 18.6%
+ 
+
+ align:start position:0%
+is I think way too much 18.6%
+of hands oh we
+
+ align:start position:0%
+of hands oh we
+ 
+
+ align:start position:0%
+of hands oh we
+actually haven't worse against this
+
+ align:start position:0%
+actually haven't worse against this
+ 
+
+ align:start position:0%
+actually haven't worse against this
+range because her suppose these it has
+
+ align:start position:0%
+range because her suppose these it has
+ 
+
+ align:start position:0%
+range because her suppose these it has
+more hands than dominate us because I
+
+ align:start position:0%
+more hands than dominate us because I
+ 
+
+ align:start position:0%
+more hands than dominate us because I
+put in a lot of hands like King 10 and
+
+ align:start position:0%
+put in a lot of hands like King 10 and
+ 
+
+ align:start position:0%
+put in a lot of hands like King 10 and
+removed a lot of the hands like a sports
+
+ align:start position:0%
+removed a lot of the hands like a sports
+ 
+
+ align:start position:0%
+removed a lot of the hands like a sports
+so basically
+
+ align:start position:0%
+so basically
+ 
+
+ align:start position:0%
+so basically
+okay you could play with it however you
+
+ align:start position:0%
+okay you could play with it however you
+ 
+
+ align:start position:0%
+okay you could play with it however you
+want but I think it's hard to play with
+
+ align:start position:0%
+want but I think it's hard to play with
+ 
+
+ align:start position:0%
+want but I think it's hard to play with
+it in the way to give yourself 39
+
+ align:start position:0%
+it in the way to give yourself 39
+ 
+
+ align:start position:0%
+it in the way to give yourself 39
+percent equity yeah see we're very
+
+ align:start position:0%
+percent equity yeah see we're very
+ 
+
+ align:start position:0%
+percent equity yeah see we're very
+optimistic about how wide his range was
+
+ align:start position:0%
+optimistic about how wide his range was
+ 
+
+ align:start position:0%
+optimistic about how wide his range was
+so any other case so so at the time I
+
+ align:start position:0%
+so any other case so so at the time I
+ 
+
+ align:start position:0%
+so any other case so so at the time I
+did fold and it looked weird to me at
+
+ align:start position:0%
+did fold and it looked weird to me at
+ 
+
+ align:start position:0%
+did fold and it looked weird to me at
+first but after analyzing it I think
+
+ align:start position:0%
+first but after analyzing it I think
+ 
+
+ align:start position:0%
+first but after analyzing it I think
+this is kept playing the right play if
+
+ align:start position:0%
+this is kept playing the right play if
+ 
+
+ align:start position:0%
+this is kept playing the right play if
+you take into account ICM so I think
+
+ align:start position:0%
+you take into account ICM so I think
+ 
+
+ align:start position:0%
+you take into account ICM so I think
+it's a good example of ICM because if
+
+ align:start position:0%
+it's a good example of ICM because if
+ 
+
+ align:start position:0%
+it's a good example of ICM because if
+you remember like the one we were
+
+ align:start position:0%
+you remember like the one we were
+ 
+
+ align:start position:0%
+you remember like the one we were
+playing with it our equity was always
+
+ align:start position:0%
+playing with it our equity was always
+ 
+
+ align:start position:0%
+playing with it our equity was always
+essentially between 33 and 39 like if we
+
+ align:start position:0%
+essentially between 33 and 39 like if we
+ 
+
+ align:start position:0%
+essentially between 33 and 39 like if we
+put them on a looser range our equity
+
+ align:start position:0%
+put them on a looser range our equity
+ 
+
+ align:start position:0%
+put them on a looser range our equity
+would be like 37 and if we put them on a
+
+ align:start position:0%
+would be like 37 and if we put them on a
+ 
+
+ align:start position:0%
+would be like 37 and if we put them on a
+tighter range our equity would be like
+
+ align:start position:0%
+tighter range our equity would be like
+ 
+
+ align:start position:0%
+tighter range our equity would be like
+34 but basically it's all it's a
+
+ align:start position:0%
+34 but basically it's all it's a
+ 
+
+ align:start position:0%
+34 but basically it's all it's a
+situation where I would always call if I
+
+ align:start position:0%
+situation where I would always call if I
+ 
+
+ align:start position:0%
+situation where I would always call if I
+see him was not relevant and always fold
+
+ align:start position:0%
+see him was not relevant and always fold
+ 
+
+ align:start position:0%
+see him was not relevant and always fold
+if I see him was relevant and and
+
+ align:start position:0%
+if I see him was relevant and and
+ 
+
+ align:start position:0%
+if I see him was relevant and and
+this isn't even the case where it looks
+
+ align:start position:0%
+this isn't even the case where it looks
+ 
+
+ align:start position:0%
+this isn't even the case where it looks
+like I see em should be that relevant
+
+ align:start position:0%
+like I see em should be that relevant
+ 
+
+ align:start position:0%
+like I see em should be that relevant
+but I guess yeah so we do fold so so you
+
+ align:start position:0%
+but I guess yeah so we do fold so so you
+ 
+
+ align:start position:0%
+but I guess yeah so we do fold so so you
+know with hindsight maybe my initial
+
+ align:start position:0%
+know with hindsight maybe my initial
+ 
+
+ align:start position:0%
+know with hindsight maybe my initial
+strategy was wrongly maybe I should have
+
+ align:start position:0%
+strategy was wrongly maybe I should have
+ 
+
+ align:start position:0%
+strategy was wrongly maybe I should have
+should not have even plus two maybe I
+
+ align:start position:0%
+should not have even plus two maybe I
+ 
+
+ align:start position:0%
+should not have even plus two maybe I
+should have just fold it in the first
+
+ align:start position:0%
+should have just fold it in the first
+ 
+
+ align:start position:0%
+should have just fold it in the first
+place that's that's a different story
+
+ align:start position:0%
+place that's that's a different story
+ 
+
+ align:start position:0%
+place that's that's a different story
+but given that I did Bluff I think the
+
+ align:start position:0%
+but given that I did Bluff I think the
+ 
+
+ align:start position:0%
+but given that I did Bluff I think the
+best thing I can do your response okay
+
+ align:start position:0%
+best thing I can do your response okay
+ 
+
+ align:start position:0%
+best thing I can do your response okay
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+let me just jump jump back to the
+
+ align:start position:0%
+let me just jump jump back to the
+ 
+
+ align:start position:0%
+let me just jump jump back to the
+PowerPoint for so I just want to talk
+
+ align:start position:0%
+PowerPoint for so I just want to talk
+ 
+
+ align:start position:0%
+PowerPoint for so I just want to talk
+about a bit more about this theory of
+
+ align:start position:0%
+about a bit more about this theory of
+ 
+
+ align:start position:0%
+about a bit more about this theory of
+sort of satellites and going all in the
+
+ align:start position:0%
+sort of satellites and going all in the
+ 
+
+ align:start position:0%
+sort of satellites and going all in the
+first so if in game theory this is sort
+
+ align:start position:0%
+first so if in game theory this is sort
+ 
+
+ align:start position:0%
+first so if in game theory this is sort
+of called the traffic intersection game
+
+ align:start position:0%
+of called the traffic intersection game
+ 
+
+ align:start position:0%
+of called the traffic intersection game
+so ICM does not say play tighter it
+
+ align:start position:0%
+so ICM does not say play tighter it
+ 
+
+ align:start position:0%
+so ICM does not say play tighter it
+allows you to play looser if you can go
+
+ align:start position:0%
+allows you to play looser if you can go
+ 
+
+ align:start position:0%
+allows you to play looser if you can go
+all in first so this is where it's I
+
+ align:start position:0%
+all in first so this is where it's I
+ 
+
+ align:start position:0%
+all in first so this is where it's I
+actually think it's very interesting
+
+ align:start position:0%
+actually think it's very interesting
+ 
+
+ align:start position:0%
+actually think it's very interesting
+because in satellites you want to be
+
+ align:start position:0%
+because in satellites you want to be
+ 
+
+ align:start position:0%
+because in satellites you want to be
+under the gun right so normally in poker
+
+ align:start position:0%
+under the gun right so normally in poker
+ 
+
+ align:start position:0%
+under the gun right so normally in poker
+that's sort of the worst position
+
+ align:start position:0%
+that's sort of the worst position
+ 
+
+ align:start position:0%
+that's sort of the worst position
+because you gotta act first everyone
+
+ align:start position:0%
+because you gotta act first everyone
+ 
+
+ align:start position:0%
+because you gotta act first everyone
+else gets to act act after you but in
+
+ align:start position:0%
+else gets to act act after you but in
+ 
+
+ align:start position:0%
+else gets to act act after you but in
+satellites basically you just want to be
+
+ align:start position:0%
+satellites basically you just want to be
+ 
+
+ align:start position:0%
+satellites basically you just want to be
+the first person to be able to threat
+
+ align:start position:0%
+the first person to be able to threat
+ 
+
+ align:start position:0%
+the first person to be able to threat
+and say look I'm putting all my chips in
+
+ align:start position:0%
+and say look I'm putting all my chips in
+ 
+
+ align:start position:0%
+and say look I'm putting all my chips in
+you pretty much have to fold and that's
+
+ align:start position:0%
+you pretty much have to fold and that's
+ 
+
+ align:start position:0%
+you pretty much have to fold and that's
+so and satellites let's say there's 11
+
+ align:start position:0%
+so and satellites let's say there's 11
+ 
+
+ align:start position:0%
+so and satellites let's say there's 11
+people left and 10 people get a seat if
+
+ align:start position:0%
+people left and 10 people get a seat if
+ 
+
+ align:start position:0%
+people left and 10 people get a seat if
+you go on no one can call you even if
+
+ align:start position:0%
+you go on no one can call you even if
+ 
+
+ align:start position:0%
+you go on no one can call you even if
+they have aces because if you because
+
+ align:start position:0%
+they have aces because if you because
+ 
+
+ align:start position:0%
+they have aces because if you because
+you call you they essentially need to be
+
+ align:start position:0%
+you call you they essentially need to be
+ 
+
+ align:start position:0%
+you call you they essentially need to be
+more than 10 11 sure that they're gonna
+
+ align:start position:0%
+more than 10 11 sure that they're gonna
+ 
+
+ align:start position:0%
+more than 10 11 sure that they're gonna
+win the hand and even if they have
+
+ align:start position:0%
+win the hand and even if they have
+ 
+
+ align:start position:0%
+win the hand and even if they have
+populations they're not going to be 10
+
+ align:start position:0%
+populations they're not going to be 10
+ 
+
+ align:start position:0%
+populations they're not going to be 10
+11 sir that they they're gonna win the
+
+ align:start position:0%
+11 sir that they they're gonna win the
+ 
+
+ align:start position:0%
+11 sir that they they're gonna win the
+hand so basically
+
+ align:start position:0%
+hand so basically
+ 
+
+ align:start position:0%
+hand so basically
+going Owens first is very very good it's
+
+ align:start position:0%
+going Owens first is very very good it's
+ 
+
+ align:start position:0%
+going Owens first is very very good it's
+essentially like it so it's called the
+
+ align:start position:0%
+essentially like it so it's called the
+ 
+
+ align:start position:0%
+essentially like it so it's called the
+traffic intersection game because you
+
+ align:start position:0%
+traffic intersection game because you
+ 
+
+ align:start position:0%
+traffic intersection game because you
+can imagine the situation where there's
+
+ align:start position:0%
+can imagine the situation where there's
+ 
+
+ align:start position:0%
+can imagine the situation where there's
+like two cards trying to pass each other
+
+ align:start position:0%
+like two cards trying to pass each other
+ 
+
+ align:start position:0%
+like two cards trying to pass each other
+at an intersection and you sort of want
+
+ align:start position:0%
+at an intersection and you sort of want
+ 
+
+ align:start position:0%
+at an intersection and you sort of want
+to save time you pass get there first
+
+ align:start position:0%
+to save time you pass get there first
+ 
+
+ align:start position:0%
+to save time you pass get there first
+but you're worried that the other guy
+
+ align:start position:0%
+but you're worried that the other guy
+ 
+
+ align:start position:0%
+but you're worried that the other guy
+might crash right you don't yet both
+
+ align:start position:0%
+might crash right you don't yet both
+ 
+
+ align:start position:0%
+might crash right you don't yet both
+players really want to avoid an accident
+
+ align:start position:0%
+players really want to avoid an accident
+ 
+
+ align:start position:0%
+players really want to avoid an accident
+but both those players really want to be
+
+ align:start position:0%
+but both those players really want to be
+ 
+
+ align:start position:0%
+but both those players really want to be
+the guy to get through first well if you
+
+ align:start position:0%
+the guy to get through first well if you
+ 
+
+ align:start position:0%
+the guy to get through first well if you
+can act first and if you just tell the
+
+ align:start position:0%
+can act first and if you just tell the
+ 
+
+ align:start position:0%
+can act first and if you just tell the
+guy look I'm like closing my eyes and
+
+ align:start position:0%
+guy look I'm like closing my eyes and
+ 
+
+ align:start position:0%
+guy look I'm like closing my eyes and
+tie up my hands I cannot stop my car
+
+ align:start position:0%
+tie up my hands I cannot stop my car
+ 
+
+ align:start position:0%
+tie up my hands I cannot stop my car
+okay I'm just gonna go through the
+
+ align:start position:0%
+okay I'm just gonna go through the
+ 
+
+ align:start position:0%
+okay I'm just gonna go through the
+intersection no matter what right if
+
+ align:start position:0%
+intersection no matter what right if
+ 
+
+ align:start position:0%
+intersection no matter what right if
+you're the first person to be able to do
+
+ align:start position:0%
+you're the first person to be able to do
+ 
+
+ align:start position:0%
+you're the first person to be able to do
+this then the other guy he's like okay I
+
+ align:start position:0%
+this then the other guy he's like okay I
+ 
+
+ align:start position:0%
+this then the other guy he's like okay I
+guess I got to stop my car now I'm glad
+
+ align:start position:0%
+guess I got to stop my car now I'm glad
+ 
+
+ align:start position:0%
+guess I got to stop my car now I'm glad
+you go first all right that's
+
+ align:start position:0%
+you go first all right that's
+ 
+
+ align:start position:0%
+you go first all right that's
+essentially what it's like if you're the
+
+ align:start position:0%
+essentially what it's like if you're the
+ 
+
+ align:start position:0%
+essentially what it's like if you're the
+first person to go all-in and you
+
+ align:start position:0%
+first person to go all-in and you
+ 
+
+ align:start position:0%
+first person to go all-in and you
+already said look I'm all-in and there's
+
+ align:start position:0%
+already said look I'm all-in and there's
+ 
+
+ align:start position:0%
+already said look I'm all-in and there's
+nothing I can do to take my chips back
+
+ align:start position:0%
+nothing I can do to take my chips back
+ 
+
+ align:start position:0%
+nothing I can do to take my chips back
+then the other guys like all right I
+
+ align:start position:0%
+then the other guys like all right I
+ 
+
+ align:start position:0%
+then the other guys like all right I
+guess I'll fold and you can win the
+
+ align:start position:0%
+guess I'll fold and you can win the
+ 
+
+ align:start position:0%
+guess I'll fold and you can win the
+blinds so it's sort of how it works I
+
+ align:start position:0%
+blinds so it's sort of how it works I
+ 
+
+ align:start position:0%
+blinds so it's sort of how it works I
+mean of course some opponents are not
+
+ align:start position:0%
+mean of course some opponents are not
+ 
+
+ align:start position:0%
+mean of course some opponents are not
+rational right if you do this enough
+
+ align:start position:0%
+rational right if you do this enough
+ 
+
+ align:start position:0%
+rational right if you do this enough
+times he might fly okay screw this I'm
+
+ align:start position:0%
+times he might fly okay screw this I'm
+ 
+
+ align:start position:0%
+times he might fly okay screw this I'm
+just gonna kill this guy right so it's a
+
+ align:start position:0%
+just gonna kill this guy right so it's a
+ 
+
+ align:start position:0%
+just gonna kill this guy right so it's a
+bit weird and you know in practice this
+
+ align:start position:0%
+bit weird and you know in practice this
+ 
+
+ align:start position:0%
+bit weird and you know in practice this
+happens a lot too I definitely had very
+
+ align:start position:0%
+happens a lot too I definitely had very
+ 
+
+ align:start position:0%
+happens a lot too I definitely had very
+bad situations where you know I'm going
+
+ align:start position:0%
+bad situations where you know I'm going
+ 
+
+ align:start position:0%
+bad situations where you know I'm going
+on with any two cards and I know this is
+
+ align:start position:0%
+on with any two cards and I know this is
+ 
+
+ align:start position:0%
+on with any two cards and I know this is
+a game theoretically optimal strategy
+
+ align:start position:0%
+a game theoretically optimal strategy
+ 
+
+ align:start position:0%
+a game theoretically optimal strategy
+but my opponent is fed up and then he
+
+ align:start position:0%
+but my opponent is fed up and then he
+ 
+
+ align:start position:0%
+but my opponent is fed up and then he
+calls me with like ace Jack or something
+
+ align:start position:0%
+calls me with like ace Jack or something
+ 
+
+ align:start position:0%
+calls me with like ace Jack or something
+and then I have like Jack to off Susan
+
+ align:start position:0%
+and then I have like Jack to off Susan
+ 
+
+ align:start position:0%
+and then I have like Jack to off Susan
+he looks like a genius and he beats me
+
+ align:start position:0%
+he looks like a genius and he beats me
+ 
+
+ align:start position:0%
+he looks like a genius and he beats me
+when his plays just like terrible
+
+ align:start position:0%
+when his plays just like terrible
+ 
+
+ align:start position:0%
+when his plays just like terrible
+basically oh yeah right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the snack size doesn't matter yet so
+
+ align:start position:0%
+so the snack size doesn't matter yet so
+ 
+
+ align:start position:0%
+so the snack size doesn't matter yet so
+I'm assuming if everyone had the same
+
+ align:start position:0%
+I'm assuming if everyone had the same
+ 
+
+ align:start position:0%
+I'm assuming if everyone had the same
+snack size in that extreme example where
+
+ align:start position:0%
+snack size in that extreme example where
+ 
+
+ align:start position:0%
+snack size in that extreme example where
+I said other people should fold aces I'm
+
+ align:start position:0%
+I said other people should fold aces I'm
+ 
+
+ align:start position:0%
+I said other people should fold aces I'm
+assuming everyone has the same success I
+
+ align:start position:0%
+assuming everyone has the same success I
+ 
+
+ align:start position:0%
+assuming everyone has the same success I
+guess where's the balance between
+
+ align:start position:0%
+guess where's the balance between
+ 
+
+ align:start position:0%
+guess where's the balance between
+knocking
+
+ align:start position:0%
+knocking
+ 
+
+ align:start position:0%
+knocking
+you out versus the chip stack I like the
+
+ align:start position:0%
+you out versus the chip stack I like the
+ 
+
+ align:start position:0%
+you out versus the chip stack I like the
+chips differential right right exactly
+
+ align:start position:0%
+chips differential right right exactly
+ 
+
+ align:start position:0%
+chips differential right right exactly
+so so the reason in that case where it's
+
+ align:start position:0%
+so so the reason in that case where it's
+ 
+
+ align:start position:0%
+so so the reason in that case where it's
+correctable aces is because like let's
+
+ align:start position:0%
+correctable aces is because like let's
+ 
+
+ align:start position:0%
+correctable aces is because like let's
+say they call and knock me out it
+
+ align:start position:0%
+say they call and knock me out it
+ 
+
+ align:start position:0%
+say they call and knock me out it
+doesn't help them that much because
+
+ align:start position:0%
+doesn't help them that much because
+ 
+
+ align:start position:0%
+doesn't help them that much because
+first place in a satellite does not get
+
+ align:start position:0%
+first place in a satellite does not get
+ 
+
+ align:start position:0%
+first place in a satellite does not get
+paid anymore than intense plus but in
+
+ align:start position:0%
+paid anymore than intense plus but in
+ 
+
+ align:start position:0%
+paid anymore than intense plus but in
+real tournaments you'd basically never
+
+ align:start position:0%
+real tournaments you'd basically never
+ 
+
+ align:start position:0%
+real tournaments you'd basically never
+hold aces because even if you're risking
+
+ align:start position:0%
+hold aces because even if you're risking
+ 
+
+ align:start position:0%
+hold aces because even if you're risking
+losing all your money just first place
+
+ align:start position:0%
+losing all your money just first place
+ 
+
+ align:start position:0%
+losing all your money just first place
+will be higher than second place buy it
+
+ align:start position:0%
+will be higher than second place buy it
+ 
+
+ align:start position:0%
+will be higher than second place buy it
+up and winning with those aces will
+
+ align:start position:0%
+up and winning with those aces will
+ 
+
+ align:start position:0%
+up and winning with those aces will
+increases your chances of coming first
+
+ align:start position:0%
+increases your chances of coming first
+ 
+
+ align:start position:0%
+increases your chances of coming first
+by so much that you should just gamble
+
+ align:start position:0%
+by so much that you should just gamble
+ 
+
+ align:start position:0%
+by so much that you should just gamble
+anyway but so this is only in semblance
+
+ align:start position:0%
+anyway but so this is only in semblance
+ 
+
+ align:start position:0%
+anyway but so this is only in semblance
+yeah please don't hold aces in like a
+
+ align:start position:0%
+yeah please don't hold aces in like a
+ 
+
+ align:start position:0%
+yeah please don't hold aces in like a
+normal person
+
+ align:start position:0%
+normal person
+ 
+
+ align:start position:0%
+normal person
+yeah if your shorts back in a sack viola
+
+ align:start position:0%
+yeah if your shorts back in a sack viola
+ 
+
+ align:start position:0%
+yeah if your shorts back in a sack viola
+wanna show two steps and this is going
+
+ align:start position:0%
+wanna show two steps and this is going
+ 
+
+ align:start position:0%
+wanna show two steps and this is going
+all-in still makes sense because people
+
+ align:start position:0%
+all-in still makes sense because people
+ 
+
+ align:start position:0%
+all-in still makes sense because people
+can call you without risking a
+
+ align:start position:0%
+can call you without risking a
+ 
+
+ align:start position:0%
+can call you without risking a
+tournament right exactly so in that case
+
+ align:start position:0%
+tournament right exactly so in that case
+ 
+
+ align:start position:0%
+tournament right exactly so in that case
+you actually need a goodie and you go
+
+ align:start position:0%
+you actually need a goodie and you go
+ 
+
+ align:start position:0%
+you actually need a goodie and you go
+online like you actually need to have
+
+ align:start position:0%
+online like you actually need to have
+ 
+
+ align:start position:0%
+online like you actually need to have
+positive chip EP as well to go on yeah
+
+ align:start position:0%
+positive chip EP as well to go on yeah
+ 
+
+ align:start position:0%
+positive chip EP as well to go on yeah
+so that's why when I see em is relevant
+
+ align:start position:0%
+so that's why when I see em is relevant
+ 
+
+ align:start position:0%
+so that's why when I see em is relevant
+the small stack swing and the big story
+
+ align:start position:0%
+the small stack swing and the big story
+ 
+
+ align:start position:0%
+the small stack swing and the big story
+the small stacks lose and the big stack
+
+ align:start position:0%
+the small stacks lose and the big stack
+ 
+
+ align:start position:0%
+the small stacks lose and the big stack
+swing because the big stacks have more
+
+ align:start position:0%
+swing because the big stacks have more
+ 
+
+ align:start position:0%
+swing because the big stacks have more
+license to bully the small sacks around
+
+ align:start position:0%
+license to bully the small sacks around
+ 
+
+ align:start position:0%
+license to bully the small sacks around
+where is the sauce tax can't ya because
+
+ align:start position:0%
+where is the sauce tax can't ya because
+ 
+
+ align:start position:0%
+where is the sauce tax can't ya because
+the big stacks and call them more often
+
+ align:start position:0%
+the big stacks and call them more often
+ 
+
+ align:start position:0%
+the big stacks and call them more often
+and and also does it matter if other
+
+ align:start position:0%
+and and also does it matter if other
+ 
+
+ align:start position:0%
+and and also does it matter if other
+people have like raised behind you it
+
+ align:start position:0%
+people have like raised behind you it
+ 
+
+ align:start position:0%
+people have like raised behind you it
+doesn't just matter who goes all in
+
+ align:start position:0%
+doesn't just matter who goes all in
+ 
+
+ align:start position:0%
+doesn't just matter who goes all in
+first so
+
+ align:start position:0%
+first so
+ 
+
+ align:start position:0%
+first so
+if someone's already raised then it's
+
+ align:start position:0%
+if someone's already raised then it's
+ 
+
+ align:start position:0%
+if someone's already raised then it's
+like more likely you going all-in like
+
+ align:start position:0%
+like more likely you going all-in like
+ 
+
+ align:start position:0%
+like more likely you going all-in like
+it's more likely they're already
+
+ align:start position:0%
+it's more likely they're already
+ 
+
+ align:start position:0%
+it's more likely they're already
+committed so that if you go on they
+
+ align:start position:0%
+committed so that if you go on they
+ 
+
+ align:start position:0%
+committed so that if you go on they
+won't fold so so that is relevant yeah
+
+ align:start position:0%
+won't fold so so that is relevant yeah
+ 
+
+ align:start position:0%
+won't fold so so that is relevant yeah
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+so so exactly so like in practice it's
+
+ align:start position:0%
+so so exactly so like in practice it's
+ 
+
+ align:start position:0%
+so so exactly so like in practice it's
+very tricky and in fact it can be
+
+ align:start position:0%
+very tricky and in fact it can be
+ 
+
+ align:start position:0%
+very tricky and in fact it can be
+beneficial if you can somehow convince
+
+ align:start position:0%
+beneficial if you can somehow convince
+ 
+
+ align:start position:0%
+beneficial if you can somehow convince
+your opponents that you're not rational
+
+ align:start position:0%
+your opponents that you're not rational
+ 
+
+ align:start position:0%
+your opponents that you're not rational
+I've never personally done this but I've
+
+ align:start position:0%
+I've never personally done this but I've
+ 
+
+ align:start position:0%
+I've never personally done this but I've
+heard of people like making a bad call
+
+ align:start position:0%
+heard of people like making a bad call
+ 
+
+ align:start position:0%
+heard of people like making a bad call
+sometimes in assembly just so people
+
+ align:start position:0%
+sometimes in assembly just so people
+ 
+
+ align:start position:0%
+sometimes in assembly just so people
+know inoculate mess of them essentially
+
+ align:start position:0%
+know inoculate mess of them essentially
+ 
+
+ align:start position:0%
+know inoculate mess of them essentially
+good I mean it's it's a bit weird so it
+
+ align:start position:0%
+good I mean it's it's a bit weird so it
+ 
+
+ align:start position:0%
+good I mean it's it's a bit weird so it
+is there's this weird meta game with
+
+ align:start position:0%
+is there's this weird meta game with
+ 
+
+ align:start position:0%
+is there's this weird meta game with
+this traffic intersection type game
+
+ align:start position:0%
+this traffic intersection type game
+ 
+
+ align:start position:0%
+this traffic intersection type game
+although this is only relevant in like
+
+ align:start position:0%
+although this is only relevant in like
+ 
+
+ align:start position:0%
+although this is only relevant in like
+the most extreme ICL situations which
+
+ align:start position:0%
+the most extreme ICL situations which
+ 
+
+ align:start position:0%
+the most extreme ICL situations which
+are like satellites um so
+
+ align:start position:0%
+are like satellites um so
+ 
+
+ align:start position:0%
+are like satellites um so
+I mean I should say one scenario where I
+
+ align:start position:0%
+I mean I should say one scenario where I
+ 
+
+ align:start position:0%
+I mean I should say one scenario where I
+think you could consider folding aces
+
+ align:start position:0%
+think you could consider folding aces
+ 
+
+ align:start position:0%
+think you could consider folding aces
+preflop in a normal tournament is
+
+ align:start position:0%
+preflop in a normal tournament is
+ 
+
+ align:start position:0%
+preflop in a normal tournament is
+actually this so let's say let's say
+
+ align:start position:0%
+actually this so let's say let's say
+ 
+
+ align:start position:0%
+actually this so let's say let's say
+there's 55 and Tilden let's say 54 get
+
+ align:start position:0%
+there's 55 and Tilden let's say 54 get
+ 
+
+ align:start position:0%
+there's 55 and Tilden let's say 54 get
+paid and there's 55 left and you got one
+
+ align:start position:0%
+paid and there's 55 left and you got one
+ 
+
+ align:start position:0%
+paid and there's 55 left and you got one
+chip and everyone else as thousands of
+
+ align:start position:0%
+chip and everyone else as thousands of
+ 
+
+ align:start position:0%
+chip and everyone else as thousands of
+chips and you know that like someone
+
+ align:start position:0%
+chips and you know that like someone
+ 
+
+ align:start position:0%
+chips and you know that like someone
+else has already gotten eliminated that
+
+ align:start position:0%
+else has already gotten eliminated that
+ 
+
+ align:start position:0%
+else has already gotten eliminated that
+hand so like if you fold it guarantee to
+
+ align:start position:0%
+hand so like if you fold it guarantee to
+ 
+
+ align:start position:0%
+hand so like if you fold it guarantee to
+get in the money then I would definitely
+
+ align:start position:0%
+get in the money then I would definitely
+ 
+
+ align:start position:0%
+get in the money then I would definitely
+fold aces because even if you win and
+
+ align:start position:0%
+fold aces because even if you win and
+ 
+
+ align:start position:0%
+fold aces because even if you win and
+double up congratulations you don't have
+
+ align:start position:0%
+double up congratulations you don't have
+ 
+
+ align:start position:0%
+double up congratulations you don't have
+ten chips instead of one chip you
+
+ align:start position:0%
+ten chips instead of one chip you
+ 
+
+ align:start position:0%
+ten chips instead of one chip you
+everyone still has thousands of chips so
+
+ align:start position:0%
+everyone still has thousands of chips so
+ 
+
+ align:start position:0%
+everyone still has thousands of chips so
+and so there are cases where you could
+
+ align:start position:0%
+and so there are cases where you could
+ 
+
+ align:start position:0%
+and so there are cases where you could
+construct an extreme case where you
+
+ align:start position:0%
+construct an extreme case where you
+ 
+
+ align:start position:0%
+construct an extreme case where you
+should fold aces preflop in a tournament
+
+ align:start position:0%
+should fold aces preflop in a tournament
+ 
+
+ align:start position:0%
+should fold aces preflop in a tournament
+in a normal tournament as well okay
+
+ align:start position:0%
+in a normal tournament as well okay
+ 
+
+ align:start position:0%
+in a normal tournament as well okay
+so let's get back to the tournament now
+
+ align:start position:0%
+so let's get back to the tournament now
+ 
+
+ align:start position:0%
+so let's get back to the tournament now
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+where were we so okay so yeah so we lost
+
+ align:start position:0%
+where were we so okay so yeah so we lost
+ 
+
+ align:start position:0%
+where were we so okay so yeah so we lost
+a bunch of chips here but so the next
+
+ align:start position:0%
+a bunch of chips here but so the next
+ 
+
+ align:start position:0%
+a bunch of chips here but so the next
+hand we get we get a king a dog suit I
+
+ align:start position:0%
+hand we get we get a king a dog suit I
+ 
+
+ align:start position:0%
+hand we get we get a king a dog suit I
+raise from the button so we are
+
+ align:start position:0%
+raise from the button so we are
+ 
+
+ align:start position:0%
+raise from the button so we are
+committed here I mean it sucks because
+
+ align:start position:0%
+committed here I mean it sucks because
+ 
+
+ align:start position:0%
+committed here I mean it sucks because
+our hand sucks but it's way too good
+
+ align:start position:0%
+our hand sucks but it's way too good
+ 
+
+ align:start position:0%
+our hand sucks but it's way too good
+odds to call and I and I see him is
+
+ align:start position:0%
+odds to call and I and I see him is
+ 
+
+ align:start position:0%
+odds to call and I and I see him is
+nowhere near that relevant when it's
+
+ align:start position:0%
+nowhere near that relevant when it's
+ 
+
+ align:start position:0%
+nowhere near that relevant when it's
+against the small stack it's the guy
+
+ align:start position:0%
+against the small stack it's the guy
+ 
+
+ align:start position:0%
+against the small stack it's the guy
+you're trying to eliminate so we call we
+
+ align:start position:0%
+you're trying to eliminate so we call we
+ 
+
+ align:start position:0%
+you're trying to eliminate so we call we
+get pretty lucky here good
+
+ align:start position:0%
+get pretty lucky here good
+ 
+
+ align:start position:0%
+get pretty lucky here good
+good redemption for that a terrible Jack
+
+ align:start position:0%
+good redemption for that a terrible Jack
+ 
+
+ align:start position:0%
+good redemption for that a terrible Jack
+tenkan played by me okay so there's
+
+ align:start position:0%
+tenkan played by me okay so there's
+ 
+
+ align:start position:0%
+tenkan played by me okay so there's
+three players left so I see him is still
+
+ align:start position:0%
+three players left so I see him is still
+ 
+
+ align:start position:0%
+three players left so I see him is still
+very relevant we're the second stack so
+
+ align:start position:0%
+very relevant we're the second stack so
+ 
+
+ align:start position:0%
+very relevant we're the second stack so
+I were trying not to get in big on with
+
+ align:start position:0%
+I were trying not to get in big on with
+ 
+
+ align:start position:0%
+I were trying not to get in big on with
+this guy although it's less significant
+
+ align:start position:0%
+this guy although it's less significant
+ 
+
+ align:start position:0%
+this guy although it's less significant
+because this guy has still has a decent
+
+ align:start position:0%
+because this guy has still has a decent
+ 
+
+ align:start position:0%
+because this guy has still has a decent
+amount of chips like if this guy only
+
+ align:start position:0%
+amount of chips like if this guy only
+ 
+
+ align:start position:0%
+amount of chips like if this guy only
+had 50,000 chips then I would try a lot
+
+ align:start position:0%
+had 50,000 chips then I would try a lot
+ 
+
+ align:start position:0%
+had 50,000 chips then I would try a lot
+harder to avoid getting in a big pot
+
+ align:start position:0%
+harder to avoid getting in a big pot
+ 
+
+ align:start position:0%
+harder to avoid getting in a big pot
+with me my sponsor
+
+ align:start position:0%
+with me my sponsor
+ 
+
+ align:start position:0%
+with me my sponsor
+so oops so yeah so he bases and LP and
+
+ align:start position:0%
+so oops so yeah so he bases and LP and
+ 
+
+ align:start position:0%
+so oops so yeah so he bases and LP and
+bucks goes on and takes it down so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this hand he makes it 3x and I decided I
+
+ align:start position:0%
+this hand he makes it 3x and I decided I
+ 
+
+ align:start position:0%
+this hand he makes it 3x and I decided I
+could call here with Queen six suited
+
+ align:start position:0%
+could call here with Queen six suited
+ 
+
+ align:start position:0%
+could call here with Queen six suited
+which is which is sort of gutsy I think
+
+ align:start position:0%
+which is which is sort of gutsy I think
+ 
+
+ align:start position:0%
+which is which is sort of gutsy I think
+but I think it's in position and it's
+
+ align:start position:0%
+but I think it's in position and it's
+ 
+
+ align:start position:0%
+but I think it's in position and it's
+fairly deep and being able to click ICM
+
+ align:start position:0%
+fairly deep and being able to click ICM
+ 
+
+ align:start position:0%
+fairly deep and being able to click ICM
+pressure on him is reasonable I think it
+
+ align:start position:0%
+pressure on him is reasonable I think it
+ 
+
+ align:start position:0%
+pressure on him is reasonable I think it
+could have gone either way I think
+
+ align:start position:0%
+could have gone either way I think
+ 
+
+ align:start position:0%
+could have gone either way I think
+folding is folding as a holding as I
+
+ align:start position:0%
+folding is folding as a holding as I
+ 
+
+ align:start position:0%
+folding is folding as a holding as I
+play the safer play but Queen six dude
+
+ align:start position:0%
+play the safer play but Queen six dude
+ 
+
+ align:start position:0%
+play the safer play but Queen six dude
+it is is plenty good enough here so I
+
+ align:start position:0%
+it is is plenty good enough here so I
+ 
+
+ align:start position:0%
+it is is plenty good enough here so I
+call he just checks um he might just be
+
+ align:start position:0%
+call he just checks um he might just be
+ 
+
+ align:start position:0%
+call he just checks um he might just be
+giving up on this board where there's a
+
+ align:start position:0%
+giving up on this board where there's a
+ 
+
+ align:start position:0%
+giving up on this board where there's a
+decent amount of it's fairly variety
+
+ align:start position:0%
+decent amount of it's fairly variety
+ 
+
+ align:start position:0%
+decent amount of it's fairly variety
+right so from what I said last class if
+
+ align:start position:0%
+right so from what I said last class if
+ 
+
+ align:start position:0%
+right so from what I said last class if
+the board is fairly drawing where like
+
+ align:start position:0%
+the board is fairly drawing where like
+ 
+
+ align:start position:0%
+the board is fairly drawing where like
+every hand has something if you've got
+
+ align:start position:0%
+every hand has something if you've got
+ 
+
+ align:start position:0%
+every hand has something if you've got
+absolutely nothing then there's not even
+
+ align:start position:0%
+absolutely nothing then there's not even
+ 
+
+ align:start position:0%
+absolutely nothing then there's not even
+much point to make it Bluff like if he's
+
+ align:start position:0%
+much point to make it Bluff like if he's
+ 
+
+ align:start position:0%
+much point to make it Bluff like if he's
+got east to offsuit here so he just
+
+ align:start position:0%
+got east to offsuit here so he just
+ 
+
+ align:start position:0%
+got east to offsuit here so he just
+checks in I bet if he folds so he
+
+ align:start position:0%
+checks in I bet if he folds so he
+ 
+
+ align:start position:0%
+checks in I bet if he folds so he
+probably had like east to officer some
+
+ align:start position:0%
+probably had like east to officer some
+ 
+
+ align:start position:0%
+probably had like east to officer some
+hand like that next
+
+ align:start position:0%
+hand like that next
+ 
+
+ align:start position:0%
+hand like that next
+time we get a skank um I decided to race
+
+ align:start position:0%
+time we get a skank um I decided to race
+ 
+
+ align:start position:0%
+time we get a skank um I decided to race
+small here once again so I guess this
+
+ align:start position:0%
+small here once again so I guess this
+ 
+
+ align:start position:0%
+small here once again so I guess this
+sort of protects that Jack 10 him so I
+
+ align:start position:0%
+sort of protects that Jack 10 him so I
+ 
+
+ align:start position:0%
+sort of protects that Jack 10 him so I
+mean you know if I'm doing this with
+
+ align:start position:0%
+mean you know if I'm doing this with
+ 
+
+ align:start position:0%
+mean you know if I'm doing this with
+Jack 10 I do need to get it with do it
+
+ align:start position:0%
+Jack 10 I do need to get it with do it
+ 
+
+ align:start position:0%
+Jack 10 I do need to get it with do it
+with good hands as well to protect the
+
+ align:start position:0%
+with good hands as well to protect the
+ 
+
+ align:start position:0%
+with good hands as well to protect the
+times that you have Jackson
+
+ align:start position:0%
+times that you have Jackson
+ 
+
+ align:start position:0%
+times that you have Jackson
+unfortunately he gets his correctly he
+
+ align:start position:0%
+unfortunately he gets his correctly he
+ 
+
+ align:start position:0%
+unfortunately he gets his correctly he
+he doesn't hold on I have Jack 10 in
+
+ align:start position:0%
+he doesn't hold on I have Jack 10 in
+ 
+
+ align:start position:0%
+he doesn't hold on I have Jack 10 in
+Folsom have a skink so
+
+ align:start position:0%
+Folsom have a skink so
+ 
+
+ align:start position:0%
+Folsom have a skink so
+we still take that one down and we win
+
+ align:start position:0%
+we still take that one down and we win
+ 
+
+ align:start position:0%
+we still take that one down and we win
+the blinds the next hand again so
+
+ align:start position:0%
+the blinds the next hand again so
+ 
+
+ align:start position:0%
+the blinds the next hand again so
+suddenly were were chipped leader by a
+
+ align:start position:0%
+suddenly were were chipped leader by a
+ 
+
+ align:start position:0%
+suddenly were were chipped leader by a
+decent margin after those three hands 94
+
+ align:start position:0%
+decent margin after those three hands 94
+ 
+
+ align:start position:0%
+decent margin after those three hands 94
+off I'm not gonna call so sold him so
+
+ align:start position:0%
+off I'm not gonna call so sold him so
+ 
+
+ align:start position:0%
+off I'm not gonna call so sold him so
+Jackson and so once again because if I
+
+ align:start position:0%
+Jackson and so once again because if I
+ 
+
+ align:start position:0%
+Jackson and so once again because if I
+see him this guy just goes all-in
+
+ align:start position:0%
+see him this guy just goes all-in
+ 
+
+ align:start position:0%
+see him this guy just goes all-in
+knowing we can't call that much Jake sit
+
+ align:start position:0%
+knowing we can't call that much Jake sit
+ 
+
+ align:start position:0%
+knowing we can't call that much Jake sit
+down seven
+
+ align:start position:0%
+down seven
+ 
+
+ align:start position:0%
+down seven
+six offices I decided fold I think
+
+ align:start position:0%
+six offices I decided fold I think
+ 
+
+ align:start position:0%
+six offices I decided fold I think
+that's very reasonable considering they
+
+ align:start position:0%
+that's very reasonable considering they
+ 
+
+ align:start position:0%
+that's very reasonable considering they
+can just go all-in on top of that Queen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nine Queen I've gotta walk so one thing
+
+ align:start position:0%
+nine Queen I've gotta walk so one thing
+ 
+
+ align:start position:0%
+nine Queen I've gotta walk so one thing
+I should pay attention is I do think
+
+ align:start position:0%
+I should pay attention is I do think
+ 
+
+ align:start position:0%
+I should pay attention is I do think
+these guys but the by now I've sort of
+
+ align:start position:0%
+these guys but the by now I've sort of
+ 
+
+ align:start position:0%
+these guys but the by now I've sort of
+collected enough data points of getting
+
+ align:start position:0%
+collected enough data points of getting
+ 
+
+ align:start position:0%
+collected enough data points of getting
+a lot way more often than I should or I
+
+ align:start position:0%
+a lot way more often than I should or I
+ 
+
+ align:start position:0%
+a lot way more often than I should or I
+think these it's not just a coincidence
+
+ align:start position:0%
+think these it's not just a coincidence
+ 
+
+ align:start position:0%
+think these it's not just a coincidence
+like I'm constantly confident enough
+
+ align:start position:0%
+like I'm constantly confident enough
+ 
+
+ align:start position:0%
+like I'm constantly confident enough
+that they're actually just giving me too
+
+ align:start position:0%
+that they're actually just giving me too
+ 
+
+ align:start position:0%
+that they're actually just giving me too
+many walks so when they don't give me a
+
+ align:start position:0%
+many walks so when they don't give me a
+ 
+
+ align:start position:0%
+many walks so when they don't give me a
+walk I should be I should put them on a
+
+ align:start position:0%
+walk I should be I should put them on a
+ 
+
+ align:start position:0%
+walk I should be I should put them on a
+stronger range of hands than I normally
+
+ align:start position:0%
+stronger range of hands than I normally
+ 
+
+ align:start position:0%
+stronger range of hands than I normally
+do pocket
+
+ align:start position:0%
+do pocket
+ 
+
+ align:start position:0%
+do pocket
+tens we three bet this guy again he gets
+
+ align:start position:0%
+tens we three bet this guy again he gets
+ 
+
+ align:start position:0%
+tens we three bet this guy again he gets
+away again so sixty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off see so we've begun built good cards
+
+ align:start position:0%
+off see so we've begun built good cards
+ 
+
+ align:start position:0%
+off see so we've begun built good cards
+even though we haven't gotten too much
+
+ align:start position:0%
+even though we haven't gotten too much
+ 
+
+ align:start position:0%
+even though we haven't gotten too much
+action from them we're still won a bunch
+
+ align:start position:0%
+action from them we're still won a bunch
+ 
+
+ align:start position:0%
+action from them we're still won a bunch
+of chips from getting good cards so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Jeff for off I'm gonna fold you this guy
+
+ align:start position:0%
+Jeff for off I'm gonna fold you this guy
+ 
+
+ align:start position:0%
+Jeff for off I'm gonna fold you this guy
+so as you can see it's fairly boring but
+
+ align:start position:0%
+so as you can see it's fairly boring but
+ 
+
+ align:start position:0%
+so as you can see it's fairly boring but
+I think this is this is how essentially
+
+ align:start position:0%
+I think this is this is how essentially
+ 
+
+ align:start position:0%
+I think this is this is how essentially
+what you essentially should happen in
+
+ align:start position:0%
+what you essentially should happen in
+ 
+
+ align:start position:0%
+what you essentially should happen in
+the final final a couple of people left
+
+ align:start position:0%
+the final final a couple of people left
+ 
+
+ align:start position:0%
+the final final a couple of people left
+in the tournament a spin-off so I decide
+
+ align:start position:0%
+in the tournament a spin-off so I decide
+ 
+
+ align:start position:0%
+in the tournament a spin-off so I decide
+to so I decided you to not go all in
+
+ align:start position:0%
+to so I decided you to not go all in
+ 
+
+ align:start position:0%
+to so I decided you to not go all in
+here I guess that would be 27 big 26 and
+
+ align:start position:0%
+here I guess that would be 27 big 26 and
+ 
+
+ align:start position:0%
+here I guess that would be 27 big 26 and
+a half big blinds which is a bit much so
+
+ align:start position:0%
+a half big blinds which is a bit much so
+ 
+
+ align:start position:0%
+a half big blinds which is a bit much so
+I decide to just raise small if he three
+
+ align:start position:0%
+I decide to just raise small if he three
+ 
+
+ align:start position:0%
+I decide to just raise small if he three
+bets if he realizes to say like 60,000
+
+ align:start position:0%
+bets if he realizes to say like 60,000
+ 
+
+ align:start position:0%
+bets if he realizes to say like 60,000
+I'm always going on here and he goes
+
+ align:start position:0%
+I'm always going on here and he goes
+ 
+
+ align:start position:0%
+I'm always going on here and he goes
+all-in himself I'm probably I'm
+
+ align:start position:0%
+all-in himself I'm probably I'm
+ 
+
+ align:start position:0%
+all-in himself I'm probably I'm
+basically not folding even though it
+
+ align:start position:0%
+basically not folding even though it
+ 
+
+ align:start position:0%
+basically not folding even though it
+kind of sucks from an ICM point of view
+
+ align:start position:0%
+kind of sucks from an ICM point of view
+ 
+
+ align:start position:0%
+kind of sucks from an ICM point of view
+think he's 10 off suit is just way too
+
+ align:start position:0%
+think he's 10 off suit is just way too
+ 
+
+ align:start position:0%
+think he's 10 off suit is just way too
+good so I'm essentially just raising
+
+ align:start position:0%
+good so I'm essentially just raising
+ 
+
+ align:start position:0%
+good so I'm essentially just raising
+small looking for an action here that he
+
+ align:start position:0%
+small looking for an action here that he
+ 
+
+ align:start position:0%
+small looking for an action here that he
+folds 72
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off suit we raise enough so
+
+ align:start position:0%
+off suit we raise enough so
+ 
+
+ align:start position:0%
+off suit we raise enough so
+OPM bucks gets a lot Queen
+
+ align:start position:0%
+OPM bucks gets a lot Queen
+ 
+
+ align:start position:0%
+OPM bucks gets a lot Queen
+3 off we get another walk which is nice
+
+ align:start position:0%
+3 off we get another walk which is nice
+ 
+
+ align:start position:0%
+3 off we get another walk which is nice
+Jack
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five off I I raise here which is
+
+ align:start position:0%
+five off I I raise here which is
+ 
+
+ align:start position:0%
+five off I I raise here which is
+definitely like an exploitative play
+
+ align:start position:0%
+definitely like an exploitative play
+ 
+
+ align:start position:0%
+definitely like an exploitative play
+it's definitely not you know like
+
+ align:start position:0%
+it's definitely not you know like
+ 
+
+ align:start position:0%
+it's definitely not you know like
+definitely from a Nash equilibrium
+
+ align:start position:0%
+definitely from a Nash equilibrium
+ 
+
+ align:start position:0%
+definitely from a Nash equilibrium
+optimal play point of view this is
+
+ align:start position:0%
+optimal play point of view this is
+ 
+
+ align:start position:0%
+optimal play point of view this is
+there's no way the optimal strategy is
+
+ align:start position:0%
+there's no way the optimal strategy is
+ 
+
+ align:start position:0%
+there's no way the optimal strategy is
+to raise a fraction of hands so big that
+
+ align:start position:0%
+to raise a fraction of hands so big that
+ 
+
+ align:start position:0%
+to raise a fraction of hands so big that
+includes jack by bob suit but I think at
+
+ align:start position:0%
+includes jack by bob suit but I think at
+ 
+
+ align:start position:0%
+includes jack by bob suit but I think at
+the time I probably told myself this guy
+
+ align:start position:0%
+the time I probably told myself this guy
+ 
+
+ align:start position:0%
+the time I probably told myself this guy
+was being overly scared even though he
+
+ align:start position:0%
+was being overly scared even though he
+ 
+
+ align:start position:0%
+was being overly scared even though he
+was playing somewhat aggressive earlier
+
+ align:start position:0%
+was playing somewhat aggressive earlier
+ 
+
+ align:start position:0%
+was playing somewhat aggressive earlier
+I'm she's maybe is over adjusting for I
+
+ align:start position:0%
+I'm she's maybe is over adjusting for I
+ 
+
+ align:start position:0%
+I'm she's maybe is over adjusting for I
+see em as being and is respecting me too
+
+ align:start position:0%
+see em as being and is respecting me too
+ 
+
+ align:start position:0%
+see em as being and is respecting me too
+much in the presence of this short step
+
+ align:start position:0%
+much in the presence of this short step
+ 
+
+ align:start position:0%
+much in the presence of this short step
+I can look at the HUD stats at the time
+
+ align:start position:0%
+I can look at the HUD stats at the time
+ 
+
+ align:start position:0%
+I can look at the HUD stats at the time
+although they won't be that accurate
+
+ align:start position:0%
+although they won't be that accurate
+ 
+
+ align:start position:0%
+although they won't be that accurate
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+they're gonna include all the hands so
+
+ align:start position:0%
+they're gonna include all the hands so
+ 
+
+ align:start position:0%
+they're gonna include all the hands so
+so that so normally I do play with all
+
+ align:start position:0%
+so that so normally I do play with all
+ 
+
+ align:start position:0%
+so that so normally I do play with all
+these numbers on so we can see that his
+
+ align:start position:0%
+these numbers on so we can see that his
+ 
+
+ align:start position:0%
+these numbers on so we can see that his
+yeah but this is it's gonna be biased
+
+ align:start position:0%
+yeah but this is it's gonna be biased
+ 
+
+ align:start position:0%
+yeah but this is it's gonna be biased
+because this includes the hands with
+
+ align:start position:0%
+because this includes the hands with
+ 
+
+ align:start position:0%
+because this includes the hands with
+with like six or seven people at the
+
+ align:start position:0%
+with like six or seven people at the
+ 
+
+ align:start position:0%
+with like six or seven people at the
+table but it says that he he
+
+ align:start position:0%
+table but it says that he he
+ 
+
+ align:start position:0%
+table but it says that he he
+calls from the big blind like only 20%
+
+ align:start position:0%
+calls from the big blind like only 20%
+ 
+
+ align:start position:0%
+calls from the big blind like only 20%
+of time but but I mean that's not a
+
+ align:start position:0%
+of time but but I mean that's not a
+ 
+
+ align:start position:0%
+of time but but I mean that's not a
+great that's not that's yeah that's
+
+ align:start position:0%
+great that's not that's yeah that's
+ 
+
+ align:start position:0%
+great that's not that's yeah that's
+gonna be biased so it doesn't it doesn't
+
+ align:start position:0%
+gonna be biased so it doesn't it doesn't
+ 
+
+ align:start position:0%
+gonna be biased so it doesn't it doesn't
+tell this too much um but
+
+ align:start position:0%
+tell this too much um but
+ 
+
+ align:start position:0%
+tell this too much um but
+I guess at the time I must have told
+
+ align:start position:0%
+I guess at the time I must have told
+ 
+
+ align:start position:0%
+I guess at the time I must have told
+myself I'm gonna try to exploit this guy
+
+ align:start position:0%
+myself I'm gonna try to exploit this guy
+ 
+
+ align:start position:0%
+myself I'm gonna try to exploit this guy
+that's the only way I can see why I
+
+ align:start position:0%
+that's the only way I can see why I
+ 
+
+ align:start position:0%
+that's the only way I can see why I
+decided to raise Jack fight off suit
+
+ align:start position:0%
+decided to raise Jack fight off suit
+ 
+
+ align:start position:0%
+decided to raise Jack fight off suit
+here so we got a call but I mean I'm
+
+ align:start position:0%
+here so we got a call but I mean I'm
+ 
+
+ align:start position:0%
+here so we got a call but I mean I'm
+gonna continuation that we do have a
+
+ align:start position:0%
+gonna continuation that we do have a
+ 
+
+ align:start position:0%
+gonna continuation that we do have a
+backdoor hard draw and this is our best
+
+ align:start position:0%
+backdoor hard draw and this is our best
+ 
+
+ align:start position:0%
+backdoor hard draw and this is our best
+chance of just winning the pot and I
+
+ align:start position:0%
+chance of just winning the pot and I
+ 
+
+ align:start position:0%
+chance of just winning the pot and I
+could I could maybe barrel on by barrel
+
+ align:start position:0%
+could I could maybe barrel on by barrel
+ 
+
+ align:start position:0%
+could I could maybe barrel on by barrel
+I mean bet again as if left on a bunch
+
+ align:start position:0%
+I mean bet again as if left on a bunch
+ 
+
+ align:start position:0%
+I mean bet again as if left on a bunch
+of turns so I just bet here he does fold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+time with Queen 9 we open the button but
+
+ align:start position:0%
+time with Queen 9 we open the button but
+ 
+
+ align:start position:0%
+time with Queen 9 we open the button but
+we get shoved on and I guess we have to
+
+ align:start position:0%
+we get shoved on and I guess we have to
+ 
+
+ align:start position:0%
+we get shoved on and I guess we have to
+fold clean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4 we get another block yeah so this is a
+
+ align:start position:0%
+4 we get another block yeah so this is a
+ 
+
+ align:start position:0%
+4 we get another block yeah so this is a
+feeling ridiculous it seems like we we
+
+ align:start position:0%
+feeling ridiculous it seems like we we
+ 
+
+ align:start position:0%
+feeling ridiculous it seems like we we
+literally gotten like five or six blocks
+
+ align:start position:0%
+literally gotten like five or six blocks
+ 
+
+ align:start position:0%
+literally gotten like five or six blocks
+in a row and I would guess probably we
+
+ align:start position:0%
+in a row and I would guess probably we
+ 
+
+ align:start position:0%
+in a row and I would guess probably we
+should be getting a walk like less than
+
+ align:start position:0%
+should be getting a walk like less than
+ 
+
+ align:start position:0%
+should be getting a walk like less than
+less I guess at a three and a table it's
+
+ align:start position:0%
+less I guess at a three and a table it's
+ 
+
+ align:start position:0%
+less I guess at a three and a table it's
+more often but still less than like
+
+ align:start position:0%
+more often but still less than like
+ 
+
+ align:start position:0%
+more often but still less than like
+thirty percent of the times yeah maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have been fairly active and but I did
+
+ align:start position:0%
+I have been fairly active and but I did
+ 
+
+ align:start position:0%
+I have been fairly active and but I did
+fold a bunch of I didn't fold some water
+
+ align:start position:0%
+fold a bunch of I didn't fold some water
+ 
+
+ align:start position:0%
+fold a bunch of I didn't fold some water
+line situations though like this like
+
+ align:start position:0%
+line situations though like this like
+ 
+
+ align:start position:0%
+line situations though like this like
+this Jack I think it was a different
+
+ align:start position:0%
+this Jack I think it was a different
+ 
+
+ align:start position:0%
+this Jack I think it was a different
+Jack seven times yeah maybe that's
+
+ align:start position:0%
+Jack seven times yeah maybe that's
+ 
+
+ align:start position:0%
+Jack seven times yeah maybe that's
+possible yeah good point yeah that's
+
+ align:start position:0%
+possible yeah good point yeah that's
+ 
+
+ align:start position:0%
+possible yeah good point yeah that's
+good it's good that word like I'm not
+
+ align:start position:0%
+good it's good that word like I'm not
+ 
+
+ align:start position:0%
+good it's good that word like I'm not
+complaining that we're getting a lot and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and we are the big stack so in
+
+ align:start position:0%
+yeah and we are the big stack so in
+ 
+
+ align:start position:0%
+yeah and we are the big stack so in
+general you know it is it is harder for
+
+ align:start position:0%
+general you know it is it is harder for
+ 
+
+ align:start position:0%
+general you know it is it is harder for
+them to bully us surrounded us to bully
+
+ align:start position:0%
+them to bully us surrounded us to bully
+ 
+
+ align:start position:0%
+them to bully us surrounded us to bully
+them around so it does make sense from
+
+ align:start position:0%
+them around so it does make sense from
+ 
+
+ align:start position:0%
+them around so it does make sense from
+that point of view to I still thought it
+
+ align:start position:0%
+that point of view to I still thought it
+ 
+
+ align:start position:0%
+that point of view to I still thought it
+was this kind of too many so anyway so I
+
+ align:start position:0%
+was this kind of too many so anyway so I
+ 
+
+ align:start position:0%
+was this kind of too many so anyway so I
+just continue trying to raise a lot
+
+ align:start position:0%
+just continue trying to raise a lot
+ 
+
+ align:start position:0%
+just continue trying to raise a lot
+especially against this guy so Jackie it
+
+ align:start position:0%
+especially against this guy so Jackie it
+ 
+
+ align:start position:0%
+especially against this guy so Jackie it
+offsuit we take it down jack - maybe we
+
+ align:start position:0%
+offsuit we take it down jack - maybe we
+ 
+
+ align:start position:0%
+offsuit we take it down jack - maybe we
+could have folded but by now this guy
+
+ align:start position:0%
+could have folded but by now this guy
+ 
+
+ align:start position:0%
+could have folded but by now this guy
+was getting short enough like he's
+
+ align:start position:0%
+was getting short enough like he's
+ 
+
+ align:start position:0%
+was getting short enough like he's
+blinded down from 15 and a half big
+
+ align:start position:0%
+blinded down from 15 and a half big
+ 
+
+ align:start position:0%
+blinded down from 15 and a half big
+blinds I think just 15 and a half he
+
+ align:start position:0%
+blinds I think just 15 and a half he
+ 
+
+ align:start position:0%
+blinds I think just 15 and a half he
+might have had even more before like 17
+
+ align:start position:0%
+might have had even more before like 17
+ 
+
+ align:start position:0%
+might have had even more before like 17
+so he might be looking for a spot to
+
+ align:start position:0%
+so he might be looking for a spot to
+ 
+
+ align:start position:0%
+so he might be looking for a spot to
+shut down the
+
+ align:start position:0%
+shut down the
+ 
+
+ align:start position:0%
+shut down the
+unites monster actually bases small here
+
+ align:start position:0%
+unites monster actually bases small here
+ 
+
+ align:start position:0%
+unites monster actually bases small here
+and get some beef old Jack
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sticks off here we got another walk I
+
+ align:start position:0%
+sticks off here we got another walk I
+ 
+
+ align:start position:0%
+sticks off here we got another walk I
+just skipped the hands on big blinds
+
+ align:start position:0%
+just skipped the hands on big blinds
+ 
+
+ align:start position:0%
+just skipped the hands on big blinds
+nothing ever happens this way just great
+
+ align:start position:0%
+nothing ever happens this way just great
+ 
+
+ align:start position:0%
+nothing ever happens this way just great
+for us
+
+ align:start position:0%
+for us
+ 
+
+ align:start position:0%
+for us
+so pocket threes here I just go all-in
+
+ align:start position:0%
+so pocket threes here I just go all-in
+ 
+
+ align:start position:0%
+so pocket threes here I just go all-in
+so I talked about this before but what
+
+ align:start position:0%
+so I talked about this before but what
+ 
+
+ align:start position:0%
+so I talked about this before but what
+is like what's sort of them okay what's
+
+ align:start position:0%
+is like what's sort of them okay what's
+ 
+
+ align:start position:0%
+is like what's sort of them okay what's
+a problem with my what this play in some
+
+ align:start position:0%
+a problem with my what this play in some
+ 
+
+ align:start position:0%
+a problem with my what this play in some
+sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+employ dogs right good so say so if I
+
+ align:start position:0%
+employ dogs right good so say so if I
+ 
+
+ align:start position:0%
+employ dogs right good so say so if I
+don't do this if I just raise small I
+
+ align:start position:0%
+don't do this if I just raise small I
+ 
+
+ align:start position:0%
+don't do this if I just raise small I
+have bad reversal five dots right but
+
+ align:start position:0%
+have bad reversal five dots right but
+ 
+
+ align:start position:0%
+have bad reversal five dots right but
+the one particular issue sort of is
+
+ align:start position:0%
+the one particular issue sort of is
+ 
+
+ align:start position:0%
+the one particular issue sort of is
+every other time we've made it twenty
+
+ align:start position:0%
+every other time we've made it twenty
+ 
+
+ align:start position:0%
+every other time we've made it twenty
+five thousand and really nothing's
+
+ align:start position:0%
+five thousand and really nothing's
+ 
+
+ align:start position:0%
+five thousand and really nothing's
+changed and suddenly we could we go all
+
+ align:start position:0%
+changed and suddenly we could we go all
+ 
+
+ align:start position:0%
+changed and suddenly we could we go all
+in so it is you know it is a bit
+
+ align:start position:0%
+in so it is you know it is a bit
+ 
+
+ align:start position:0%
+in so it is you know it is a bit
+suspicious where he came she basically
+
+ align:start position:0%
+suspicious where he came she basically
+ 
+
+ align:start position:0%
+suspicious where he came she basically
+knows we have a hand that has very bad
+
+ align:start position:0%
+knows we have a hand that has very bad
+ 
+
+ align:start position:0%
+knows we have a hand that has very bad
+reverse implied odds he basically knows
+
+ align:start position:0%
+reverse implied odds he basically knows
+ 
+
+ align:start position:0%
+reverse implied odds he basically knows
+we have like pocket threes or a spore
+
+ align:start position:0%
+we have like pocket threes or a spore
+ 
+
+ align:start position:0%
+we have like pocket threes or a spore
+offsuit or something like that but it's
+
+ align:start position:0%
+offsuit or something like that but it's
+ 
+
+ align:start position:0%
+offsuit or something like that but it's
+still sort of hard for him to exploit
+
+ align:start position:0%
+still sort of hard for him to exploit
+ 
+
+ align:start position:0%
+still sort of hard for him to exploit
+like you know I mean sure you can call
+
+ align:start position:0%
+like you know I mean sure you can call
+ 
+
+ align:start position:0%
+like you know I mean sure you can call
+like ace nine and exploit us but I mean
+
+ align:start position:0%
+like ace nine and exploit us but I mean
+ 
+
+ align:start position:0%
+like ace nine and exploit us but I mean
+ace nine is already a great hand or you
+
+ align:start position:0%
+ace nine is already a great hand or you
+ 
+
+ align:start position:0%
+ace nine is already a great hand or you
+know you can call the pocket for is an
+
+ align:start position:0%
+know you can call the pocket for is an
+ 
+
+ align:start position:0%
+know you can call the pocket for is an
+exploit us but it's not that easy to get
+
+ align:start position:0%
+exploit us but it's not that easy to get
+ 
+
+ align:start position:0%
+exploit us but it's not that easy to get
+dealt pocket phones order a bit or a
+
+ align:start position:0%
+dealt pocket phones order a bit or a
+ 
+
+ align:start position:0%
+dealt pocket phones order a bit or a
+better pair of the pocket fours so so
+
+ align:start position:0%
+better pair of the pocket fours so so
+ 
+
+ align:start position:0%
+better pair of the pocket fours so so
+here yeah even though you know against a
+
+ align:start position:0%
+here yeah even though you know against a
+ 
+
+ align:start position:0%
+here yeah even though you know against a
+good player he sort of knows my range is
+
+ align:start position:0%
+good player he sort of knows my range is
+ 
+
+ align:start position:0%
+good player he sort of knows my range is
+a very small specific number of hands
+
+ align:start position:0%
+a very small specific number of hands
+ 
+
+ align:start position:0%
+a very small specific number of hands
+it's still hard for him do like you
+
+ align:start position:0%
+it's still hard for him do like you
+ 
+
+ align:start position:0%
+it's still hard for him do like you
+can't really just call Jack ten suited
+
+ align:start position:0%
+can't really just call Jack ten suited
+ 
+
+ align:start position:0%
+can't really just call Jack ten suited
+here maybe he can but probably like Jack
+
+ align:start position:0%
+here maybe he can but probably like Jack
+ 
+
+ align:start position:0%
+here maybe he can but probably like Jack
+nine suited or queen seven suited you
+
+ align:start position:0%
+nine suited or queen seven suited you
+ 
+
+ align:start position:0%
+nine suited or queen seven suited you
+can't call because it's there's there's
+
+ align:start position:0%
+can't call because it's there's there's
+ 
+
+ align:start position:0%
+can't call because it's there's there's
+still an off chance we have like three 9
+
+ align:start position:0%
+still an off chance we have like three 9
+ 
+
+ align:start position:0%
+still an off chance we have like three 9
+offsuit or something so uh so
+
+ align:start position:0%
+offsuit or something so uh so
+ 
+
+ align:start position:0%
+offsuit or something so uh so
+anyway so he does fold but it definitely
+
+ align:start position:0%
+anyway so he does fold but it definitely
+ 
+
+ align:start position:0%
+anyway so he does fold but it definitely
+raises suspicion Jack ten off so Jack's
+
+ align:start position:0%
+raises suspicion Jack ten off so Jack's
+ 
+
+ align:start position:0%
+raises suspicion Jack ten off so Jack's
+enough we just go all in here so I think
+
+ align:start position:0%
+enough we just go all in here so I think
+ 
+
+ align:start position:0%
+enough we just go all in here so I think
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is actually important so but so
+
+ align:start position:0%
+this is actually important so but so
+ 
+
+ align:start position:0%
+this is actually important so but so
+normally how you just raise from the
+
+ align:start position:0%
+normally how you just raise from the
+ 
+
+ align:start position:0%
+normally how you just raise from the
+button but by now the big blind has
+
+ align:start position:0%
+button but by now the big blind has
+ 
+
+ align:start position:0%
+button but by now the big blind has
+gotten so sort that I'm willing to just
+
+ align:start position:0%
+gotten so sort that I'm willing to just
+ 
+
+ align:start position:0%
+gotten so sort that I'm willing to just
+go all in because the big blind is sort
+
+ align:start position:0%
+go all in because the big blind is sort
+ 
+
+ align:start position:0%
+go all in because the big blind is sort
+of sort enough for even if he picks up a
+
+ align:start position:0%
+of sort enough for even if he picks up a
+ 
+
+ align:start position:0%
+of sort enough for even if he picks up a
+hand and calls and beats me I'm still
+
+ align:start position:0%
+hand and calls and beats me I'm still
+ 
+
+ align:start position:0%
+hand and calls and beats me I'm still
+the chip leader even if that happens so
+
+ align:start position:0%
+the chip leader even if that happens so
+ 
+
+ align:start position:0%
+the chip leader even if that happens so
+the ICM is doesn't hurt me that much
+
+ align:start position:0%
+the ICM is doesn't hurt me that much
+ 
+
+ align:start position:0%
+the ICM is doesn't hurt me that much
+because yeah and also just the fact that
+
+ align:start position:0%
+because yeah and also just the fact that
+ 
+
+ align:start position:0%
+because yeah and also just the fact that
+I'm risking less and also not the other
+
+ align:start position:0%
+I'm risking less and also not the other
+ 
+
+ align:start position:0%
+I'm risking less and also not the other
+important thing of the big blind getting
+
+ align:start position:0%
+important thing of the big blind getting
+ 
+
+ align:start position:0%
+important thing of the big blind getting
+short is now the small blind is much
+
+ align:start position:0%
+short is now the small blind is much
+ 
+
+ align:start position:0%
+short is now the small blind is much
+less incentivized to gamble than before
+
+ align:start position:0%
+less incentivized to gamble than before
+ 
+
+ align:start position:0%
+less incentivized to gamble than before
+like before it when the big blank had
+
+ align:start position:0%
+like before it when the big blank had
+ 
+
+ align:start position:0%
+like before it when the big blank had
+180 K you know he he was in symptom isin
+
+ align:start position:0%
+180 K you know he he was in symptom isin
+ 
+
+ align:start position:0%
+180 K you know he he was in symptom isin
+gamble against me because it's
+
+ align:start position:0%
+gamble against me because it's
+ 
+
+ align:start position:0%
+gamble against me because it's
+not that easy to wait for the big blind
+
+ align:start position:0%
+not that easy to wait for the big blind
+ 
+
+ align:start position:0%
+not that easy to wait for the big blind
+you bust but now that the big mine only
+
+ align:start position:0%
+you bust but now that the big mine only
+ 
+
+ align:start position:0%
+you bust but now that the big mine only
+has ten K it's easier to sort of just
+
+ align:start position:0%
+has ten K it's easier to sort of just
+ 
+
+ align:start position:0%
+has ten K it's easier to sort of just
+wait and hope that he busts so basically
+
+ align:start position:0%
+wait and hope that he busts so basically
+ 
+
+ align:start position:0%
+wait and hope that he busts so basically
+I see M becomes more favorable in both
+
+ align:start position:0%
+I see M becomes more favorable in both
+ 
+
+ align:start position:0%
+I see M becomes more favorable in both
+cases and something I think is very good
+
+ align:start position:0%
+cases and something I think is very good
+ 
+
+ align:start position:0%
+cases and something I think is very good
+now with the Saxons so we do shove and
+
+ align:start position:0%
+now with the Saxons so we do shove and
+ 
+
+ align:start position:0%
+now with the Saxons so we do shove and
+we take it down 92
+
+ align:start position:0%
+we take it down 92
+ 
+
+ align:start position:0%
+we take it down 92
+off so no one usually wants our blinds
+
+ align:start position:0%
+off so no one usually wants our blinds
+ 
+
+ align:start position:0%
+off so no one usually wants our blinds
+but then they both want our blinds I'll
+
+ align:start position:0%
+but then they both want our blinds I'll
+ 
+
+ align:start position:0%
+but then they both want our blinds I'll
+be unboxing stem so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+East to I just go all in here basically
+
+ align:start position:0%
+East to I just go all in here basically
+ 
+
+ align:start position:0%
+East to I just go all in here basically
+same justification as the pocket threes
+
+ align:start position:0%
+same justification as the pocket threes
+ 
+
+ align:start position:0%
+same justification as the pocket threes
+eats
+
+ align:start position:0%
+eats
+ 
+
+ align:start position:0%
+eats
+of it off I think I probably should have
+
+ align:start position:0%
+of it off I think I probably should have
+ 
+
+ align:start position:0%
+of it off I think I probably should have
+raised this we
+
+ align:start position:0%
+raised this we
+ 
+
+ align:start position:0%
+raised this we
+all in honesty might not be that bad I'd
+
+ align:start position:0%
+all in honesty might not be that bad I'd
+ 
+
+ align:start position:0%
+all in honesty might not be that bad I'd
+have to do an exact calculation but I
+
+ align:start position:0%
+have to do an exact calculation but I
+ 
+
+ align:start position:0%
+have to do an exact calculation but I
+think probably I mean it's not it's a
+
+ align:start position:0%
+think probably I mean it's not it's a
+ 
+
+ align:start position:0%
+think probably I mean it's not it's a
+pretty bad hand but I think probably I
+
+ align:start position:0%
+pretty bad hand but I think probably I
+ 
+
+ align:start position:0%
+pretty bad hand but I think probably I
+shouldn't be folding given that I'm the
+
+ align:start position:0%
+shouldn't be folding given that I'm the
+ 
+
+ align:start position:0%
+shouldn't be folding given that I'm the
+big stack and given that they both been
+
+ align:start position:0%
+big stack and given that they both been
+ 
+
+ align:start position:0%
+big stack and given that they both been
+giving me lots of respect but I fold
+
+ align:start position:0%
+giving me lots of respect but I fold
+ 
+
+ align:start position:0%
+giving me lots of respect but I fold
+which can't be a big mistake but I think
+
+ align:start position:0%
+which can't be a big mistake but I think
+ 
+
+ align:start position:0%
+which can't be a big mistake but I think
+probably I shouldn't have folded the
+
+ align:start position:0%
+probably I shouldn't have folded the
+ 
+
+ align:start position:0%
+probably I shouldn't have folded the
+next handout the mbox goes on and we
+
+ align:start position:0%
+next handout the mbox goes on and we
+ 
+
+ align:start position:0%
+next handout the mbox goes on and we
+fold next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing we get 8 7 suited so by now this
+
+ align:start position:0%
+thing we get 8 7 suited so by now this
+ 
+
+ align:start position:0%
+thing we get 8 7 suited so by now this
+guy be my sponsor so we've just won
+
+ align:start position:0%
+guy be my sponsor so we've just won
+ 
+
+ align:start position:0%
+guy be my sponsor so we've just won
+enough pots where this guy is also sort
+
+ align:start position:0%
+enough pots where this guy is also sort
+ 
+
+ align:start position:0%
+enough pots where this guy is also sort
+of short now so it's a pretty good
+
+ align:start position:0%
+of short now so it's a pretty good
+ 
+
+ align:start position:0%
+of short now so it's a pretty good
+situation for us from an ICM perspective
+
+ align:start position:0%
+situation for us from an ICM perspective
+ 
+
+ align:start position:0%
+situation for us from an ICM perspective
+they're both kind of short enough where
+
+ align:start position:0%
+they're both kind of short enough where
+ 
+
+ align:start position:0%
+they're both kind of short enough where
+we can just go all-in preflop very often
+
+ align:start position:0%
+we can just go all-in preflop very often
+ 
+
+ align:start position:0%
+we can just go all-in preflop very often
+and they have to fold quite often tens
+
+ align:start position:0%
+and they have to fold quite often tens
+ 
+
+ align:start position:0%
+and they have to fold quite often tens
+evanov is a bit too weak but I decided
+
+ align:start position:0%
+evanov is a bit too weak but I decided
+ 
+
+ align:start position:0%
+evanov is a bit too weak but I decided
+raise but yeah this is a bit
+
+ align:start position:0%
+raise but yeah this is a bit
+ 
+
+ align:start position:0%
+raise but yeah this is a bit
+inconsistent play for my part because I
+
+ align:start position:0%
+inconsistent play for my part because I
+ 
+
+ align:start position:0%
+inconsistent play for my part because I
+think for most purposes 8:7 off is a
+
+ align:start position:0%
+think for most purposes 8:7 off is a
+ 
+
+ align:start position:0%
+think for most purposes 8:7 off is a
+better hand than 10 7 off but for some
+
+ align:start position:0%
+better hand than 10 7 off but for some
+ 
+
+ align:start position:0%
+better hand than 10 7 off but for some
+reason I raise 10 7 off and fold 8 7 off
+
+ align:start position:0%
+reason I raise 10 7 off and fold 8 7 off
+ 
+
+ align:start position:0%
+reason I raise 10 7 off and fold 8 7 off
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+5 suited we get a walk again Queen 5 off
+
+ align:start position:0%
+5 suited we get a walk again Queen 5 off
+ 
+
+ align:start position:0%
+5 suited we get a walk again Queen 5 off
+yeah so I just go all in here I mean
+
+ align:start position:0%
+yeah so I just go all in here I mean
+ 
+
+ align:start position:0%
+yeah so I just go all in here I mean
+yeah this is so this is definitely not a
+
+ align:start position:0%
+yeah this is so this is definitely not a
+ 
+
+ align:start position:0%
+yeah this is so this is definitely not a
+plus ship EVD all in but once again I
+
+ align:start position:0%
+plus ship EVD all in but once again I
+ 
+
+ align:start position:0%
+plus ship EVD all in but once again I
+think I see him by now is relevant
+
+ align:start position:0%
+think I see him by now is relevant
+ 
+
+ align:start position:0%
+think I see him by now is relevant
+enough where um it's fine because he
+
+ align:start position:0%
+enough where um it's fine because he
+ 
+
+ align:start position:0%
+enough where um it's fine because he
+just have to fold we
+
+ align:start position:0%
+just have to fold we
+ 
+
+ align:start position:0%
+just have to fold we
+see it down 10 6 off I decided fold big
+
+ align:start position:0%
+see it down 10 6 off I decided fold big
+ 
+
+ align:start position:0%
+see it down 10 6 off I decided fold big
+blank gets a walk get
+
+ align:start position:0%
+blank gets a walk get
+ 
+
+ align:start position:0%
+blank gets a walk get
+a walk with six deuce pretty good ace
+
+ align:start position:0%
+a walk with six deuce pretty good ace
+ 
+
+ align:start position:0%
+a walk with six deuce pretty good ace
+two off once again we just go on they
+
+ align:start position:0%
+two off once again we just go on they
+ 
+
+ align:start position:0%
+two off once again we just go on they
+fold pocket kings Sybase I yeah so this
+
+ align:start position:0%
+fold pocket kings Sybase I yeah so this
+ 
+
+ align:start position:0%
+fold pocket kings Sybase I yeah so this
+is a bit suspicious again normally I've
+
+ align:start position:0%
+is a bit suspicious again normally I've
+ 
+
+ align:start position:0%
+is a bit suspicious again normally I've
+been going all in you know he raises
+
+ align:start position:0%
+been going all in you know he raises
+ 
+
+ align:start position:0%
+been going all in you know he raises
+small obviously yes five kings so
+
+ align:start position:0%
+small obviously yes five kings so
+ 
+
+ align:start position:0%
+small obviously yes five kings so
+yeah I mean that's basically true but I
+
+ align:start position:0%
+yeah I mean that's basically true but I
+ 
+
+ align:start position:0%
+yeah I mean that's basically true but I
+mean also I think I will do this with
+
+ align:start position:0%
+mean also I think I will do this with
+ 
+
+ align:start position:0%
+mean also I think I will do this with
+some of the weakest hands that I'm not
+
+ align:start position:0%
+some of the weakest hands that I'm not
+ 
+
+ align:start position:0%
+some of the weakest hands that I'm not
+willing to gamble and with but still
+
+ align:start position:0%
+willing to gamble and with but still
+ 
+
+ align:start position:0%
+willing to gamble and with but still
+want to raise like maybe like something
+
+ align:start position:0%
+want to raise like maybe like something
+ 
+
+ align:start position:0%
+want to raise like maybe like something
+like nine seven offsuit maybe but
+
+ align:start position:0%
+like nine seven offsuit maybe but
+ 
+
+ align:start position:0%
+like nine seven offsuit maybe but
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take it down so if he goes on we fold
+
+ align:start position:0%
+take it down so if he goes on we fold
+ 
+
+ align:start position:0%
+take it down so if he goes on we fold
+Jack to off suit Queens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pursued and go all-in so I'm gonna go
+
+ align:start position:0%
+pursued and go all-in so I'm gonna go
+ 
+
+ align:start position:0%
+pursued and go all-in so I'm gonna go
+through this fairly faster there's a lot
+
+ align:start position:0%
+through this fairly faster there's a lot
+ 
+
+ align:start position:0%
+through this fairly faster there's a lot
+of the same same stuff six five off we
+
+ align:start position:0%
+of the same same stuff six five off we
+ 
+
+ align:start position:0%
+of the same same stuff six five off we
+we fold these yeah by now they're sort
+
+ align:start position:0%
+we fold these yeah by now they're sort
+ 
+
+ align:start position:0%
+we fold these yeah by now they're sort
+of short enough where they might
+
+ align:start position:0%
+of short enough where they might
+ 
+
+ align:start position:0%
+of short enough where they might
+actually just call us pretty often so
+
+ align:start position:0%
+actually just call us pretty often so
+ 
+
+ align:start position:0%
+actually just call us pretty often so
+iPhone six five off so here pocket
+
+ align:start position:0%
+iPhone six five off so here pocket
+ 
+
+ align:start position:0%
+iPhone six five off so here pocket
+threes holds against Queen Jack so that
+
+ align:start position:0%
+threes holds against Queen Jack so that
+ 
+
+ align:start position:0%
+threes holds against Queen Jack so that
+so this isn't so this is an extreme ICM
+
+ align:start position:0%
+so this isn't so this is an extreme ICM
+ 
+
+ align:start position:0%
+so this isn't so this is an extreme ICM
+spot so he calls here and he does double
+
+ align:start position:0%
+spot so he calls here and he does double
+ 
+
+ align:start position:0%
+spot so he calls here and he does double
+up so the next hand we are we do have an
+
+ align:start position:0%
+up so the next hand we are we do have an
+ 
+
+ align:start position:0%
+up so the next hand we are we do have an
+extreme ICM spot because this guy only
+
+ align:start position:0%
+extreme ICM spot because this guy only
+ 
+
+ align:start position:0%
+extreme ICM spot because this guy only
+has one big blind so essentially the
+
+ align:start position:0%
+has one big blind so essentially the
+ 
+
+ align:start position:0%
+has one big blind so essentially the
+correct strategy is going to be hein
+
+ align:start position:0%
+correct strategy is going to be hein
+ 
+
+ align:start position:0%
+correct strategy is going to be hein
+socially shove any two cards and he's
+
+ align:start position:0%
+socially shove any two cards and he's
+ 
+
+ align:start position:0%
+socially shove any two cards and he's
+only socially call I would guess like
+
+ align:start position:0%
+only socially call I would guess like
+ 
+
+ align:start position:0%
+only socially call I would guess like
+maybe like the top top seminary percent
+
+ align:start position:0%
+maybe like the top top seminary percent
+ 
+
+ align:start position:0%
+maybe like the top top seminary percent
+of hands in the situation he normally
+
+ align:start position:0%
+of hands in the situation he normally
+ 
+
+ align:start position:0%
+of hands in the situation he normally
+shouldn't be calling like tops thirty or
+
+ align:start position:0%
+shouldn't be calling like tops thirty or
+ 
+
+ align:start position:0%
+shouldn't be calling like tops thirty or
+something so I just go all-in and like
+
+ align:start position:0%
+something so I just go all-in and like
+ 
+
+ align:start position:0%
+something so I just go all-in and like
+the FES East to off suit I'm certain es
+
+ align:start position:0%
+the FES East to off suit I'm certain es
+ 
+
+ align:start position:0%
+the FES East to off suit I'm certain es
+people like even if he has like say king
+
+ align:start position:0%
+people like even if he has like say king
+ 
+
+ align:start position:0%
+people like even if he has like say king
+queen and I turn up my hand and show him
+
+ align:start position:0%
+queen and I turn up my hand and show him
+ 
+
+ align:start position:0%
+queen and I turn up my hand and show him
+Jack seven he probably still has to fold
+
+ align:start position:0%
+Jack seven he probably still has to fold
+ 
+
+ align:start position:0%
+Jack seven he probably still has to fold
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+because he really can't bust lady yeah I
+
+ align:start position:0%
+because he really can't bust lady yeah I
+ 
+
+ align:start position:0%
+because he really can't bust lady yeah I
+haven't done the exact math but you know
+
+ align:start position:0%
+haven't done the exact math but you know
+ 
+
+ align:start position:0%
+haven't done the exact math but you know
+I wouldn't be that surprised if he told
+
+ align:start position:0%
+I wouldn't be that surprised if he told
+ 
+
+ align:start position:0%
+I wouldn't be that surprised if he told
+me like pocket nines is a fold for him I
+
+ align:start position:0%
+me like pocket nines is a fold for him I
+ 
+
+ align:start position:0%
+me like pocket nines is a fold for him I
+wouldn't be that surprised so
+
+ align:start position:0%
+wouldn't be that surprised so
+ 
+
+ align:start position:0%
+wouldn't be that surprised so
+yeah so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so once again I go all-in because this
+
+ align:start position:0%
+so once again I go all-in because this
+ 
+
+ align:start position:0%
+so once again I go all-in because this
+guy probably can't call so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you do okay so yeah we went we
+
+ align:start position:0%
+so you do okay so yeah we went we
+ 
+
+ align:start position:0%
+so you do okay so yeah we went we
+waiting at ASIC we know we're just quite
+
+ align:start position:0%
+waiting at ASIC we know we're just quite
+ 
+
+ align:start position:0%
+waiting at ASIC we know we're just quite
+it's kind of crazy that he picked up a
+
+ align:start position:0%
+it's kind of crazy that he picked up a
+ 
+
+ align:start position:0%
+it's kind of crazy that he picked up a
+nice clean with one big blinds
+
+ align:start position:0%
+nice clean with one big blinds
+ 
+
+ align:start position:0%
+nice clean with one big blinds
+some some players like to do do this
+
+ align:start position:0%
+some some players like to do do this
+ 
+
+ align:start position:0%
+some some players like to do do this
+thing called like cooperative play to
+
+ align:start position:0%
+thing called like cooperative play to
+ 
+
+ align:start position:0%
+thing called like cooperative play to
+get the big blind to bust so this is in
+
+ align:start position:0%
+get the big blind to bust so this is in
+ 
+
+ align:start position:0%
+get the big blind to bust so this is in
+the history of poker
+
+ align:start position:0%
+the history of poker
+ 
+
+ align:start position:0%
+the history of poker
+it's sort of what was almost customary
+
+ align:start position:0%
+it's sort of what was almost customary
+ 
+
+ align:start position:0%
+it's sort of what was almost customary
+for the players in if you have chips in
+
+ align:start position:0%
+for the players in if you have chips in
+ 
+
+ align:start position:0%
+for the players in if you have chips in
+here to basically just all agree to just
+
+ align:start position:0%
+here to basically just all agree to just
+ 
+
+ align:start position:0%
+here to basically just all agree to just
+call and not raise each other and to
+
+ align:start position:0%
+call and not raise each other and to
+ 
+
+ align:start position:0%
+call and not raise each other and to
+maximize their chances of busting the
+
+ align:start position:0%
+maximize their chances of busting the
+ 
+
+ align:start position:0%
+maximize their chances of busting the
+big blind it's sort of a form of
+
+ align:start position:0%
+big blind it's sort of a form of
+ 
+
+ align:start position:0%
+big blind it's sort of a form of
+cheating in some sense it's like
+
+ align:start position:0%
+cheating in some sense it's like
+ 
+
+ align:start position:0%
+cheating in some sense it's like
+collusion in some sense but it's
+
+ align:start position:0%
+collusion in some sense but it's
+ 
+
+ align:start position:0%
+collusion in some sense but it's
+customary maybe like five six years ago
+
+ align:start position:0%
+customary maybe like five six years ago
+ 
+
+ align:start position:0%
+customary maybe like five six years ago
+we're never going to do this because it
+
+ align:start position:0%
+we're never going to do this because it
+ 
+
+ align:start position:0%
+we're never going to do this because it
+sort of benefits everyone else it sort
+
+ align:start position:0%
+sort of benefits everyone else it sort
+ 
+
+ align:start position:0%
+sort of benefits everyone else it sort
+of benefits all of these guys if they
+
+ align:start position:0%
+of benefits all of these guys if they
+ 
+
+ align:start position:0%
+of benefits all of these guys if they
+all agree to do this and it
+
+ align:start position:0%
+all agree to do this and it
+ 
+
+ align:start position:0%
+all agree to do this and it
+just maximizes the chances that the big
+
+ align:start position:0%
+just maximizes the chances that the big
+ 
+
+ align:start position:0%
+just maximizes the chances that the big
+blind is eliminated but the issue with
+
+ align:start position:0%
+blind is eliminated but the issue with
+ 
+
+ align:start position:0%
+blind is eliminated but the issue with
+this is unfortunately
+
+ align:start position:0%
+this is unfortunately
+ 
+
+ align:start position:0%
+this is unfortunately
+unfortunately
+
+ align:start position:0%
+unfortunately
+ 
+
+ align:start position:0%
+unfortunately
+there is an option to be selfish right
+
+ align:start position:0%
+there is an option to be selfish right
+ 
+
+ align:start position:0%
+there is an option to be selfish right
+unfortunately if you know if we both
+
+ align:start position:0%
+unfortunately if you know if we both
+ 
+
+ align:start position:0%
+unfortunately if you know if we both
+trusted each other completely we could
+
+ align:start position:0%
+trusted each other completely we could
+ 
+
+ align:start position:0%
+trusted each other completely we could
+pollute and be like okay we're just
+
+ align:start position:0%
+pollute and be like okay we're just
+ 
+
+ align:start position:0%
+pollute and be like okay we're just
+gonna call check down every flop turn
+
+ align:start position:0%
+gonna call check down every flop turn
+ 
+
+ align:start position:0%
+gonna call check down every flop turn
+and River no matter what to match so
+
+ align:start position:0%
+and River no matter what to match so
+ 
+
+ align:start position:0%
+and River no matter what to match so
+that we can both see the river with any
+
+ align:start position:0%
+that we can both see the river with any
+ 
+
+ align:start position:0%
+that we can both see the river with any
+two cards and maximize the chances of
+
+ align:start position:0%
+two cards and maximize the chances of
+ 
+
+ align:start position:0%
+two cards and maximize the chances of
+busting this guy the issue with this is
+
+ align:start position:0%
+busting this guy the issue with this is
+ 
+
+ align:start position:0%
+busting this guy the issue with this is
+you know players when you play a game
+
+ align:start position:0%
+you know players when you play a game
+ 
+
+ align:start position:0%
+you know players when you play a game
+you're selfish right and you want to you
+
+ align:start position:0%
+you're selfish right and you want to you
+ 
+
+ align:start position:0%
+you're selfish right and you want to you
+know if there is an opportunity to bet
+
+ align:start position:0%
+know if there is an opportunity to bet
+ 
+
+ align:start position:0%
+know if there is an opportunity to bet
+because you have a good hand you're
+
+ align:start position:0%
+because you have a good hand you're
+ 
+
+ align:start position:0%
+because you have a good hand you're
+gonna want to bet more like you know if
+
+ align:start position:0%
+gonna want to bet more like you know if
+ 
+
+ align:start position:0%
+gonna want to bet more like you know if
+there's a draw and you have a good hand
+
+ align:start position:0%
+there's a draw and you have a good hand
+ 
+
+ align:start position:0%
+there's a draw and you have a good hand
+you wanna bet you get the other guy to
+
+ align:start position:0%
+you wanna bet you get the other guy to
+ 
+
+ align:start position:0%
+you wanna bet you get the other guy to
+fold and basically from a game theoretic
+
+ align:start position:0%
+fold and basically from a game theoretic
+ 
+
+ align:start position:0%
+fold and basically from a game theoretic
+perspective since we have these options
+
+ align:start position:0%
+perspective since we have these options
+ 
+
+ align:start position:0%
+perspective since we have these options
+there's no way for us to essentially
+
+ align:start position:0%
+there's no way for us to essentially
+ 
+
+ align:start position:0%
+there's no way for us to essentially
+agree that we're gonna just check down
+
+ align:start position:0%
+agree that we're gonna just check down
+ 
+
+ align:start position:0%
+agree that we're gonna just check down
+and see the river which is why I
+
+ align:start position:0%
+and see the river which is why I
+ 
+
+ align:start position:0%
+and see the river which is why I
+consider a collision if players actually
+
+ align:start position:0%
+consider a collision if players actually
+ 
+
+ align:start position:0%
+consider a collision if players actually
+use um so
+
+ align:start position:0%
+use um so
+ 
+
+ align:start position:0%
+use um so
+nonetheless I do the I do the most
+
+ align:start position:0%
+nonetheless I do the I do the most
+ 
+
+ align:start position:0%
+nonetheless I do the I do the most
+selfish line which is just go all-in
+
+ align:start position:0%
+selfish line which is just go all-in
+ 
+
+ align:start position:0%
+selfish line which is just go all-in
+but yeah this guy was my best friend and
+
+ align:start position:0%
+but yeah this guy was my best friend and
+ 
+
+ align:start position:0%
+but yeah this guy was my best friend and
+I wanted to do cheat then I could just
+
+ align:start position:0%
+I wanted to do cheat then I could just
+ 
+
+ align:start position:0%
+I wanted to do cheat then I could just
+call and let him call and then just
+
+ align:start position:0%
+call and let him call and then just
+ 
+
+ align:start position:0%
+call and let him call and then just
+check it down even if I flop the nut
+
+ align:start position:0%
+check it down even if I flop the nut
+ 
+
+ align:start position:0%
+check it down even if I flop the nut
+flush but
+
+ align:start position:0%
+flush but
+ 
+
+ align:start position:0%
+flush but
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now it's heads up and so
+
+ align:start position:0%
+so now it's heads up and so
+ 
+
+ align:start position:0%
+so now it's heads up and so
+I'll try to show every hand okay
+
+ align:start position:0%
+I'll try to show every hand okay
+ 
+
+ align:start position:0%
+I'll try to show every hand okay
+so now I see him doesn't matter but it
+
+ align:start position:0%
+so now I see him doesn't matter but it
+ 
+
+ align:start position:0%
+so now I see him doesn't matter but it
+would be good to show a bit of heads-up
+
+ align:start position:0%
+would be good to show a bit of heads-up
+ 
+
+ align:start position:0%
+would be good to show a bit of heads-up
+play because I don't think we've done
+
+ align:start position:0%
+play because I don't think we've done
+ 
+
+ align:start position:0%
+play because I don't think we've done
+too much heads-up play in this class so
+
+ align:start position:0%
+too much heads-up play in this class so
+ 
+
+ align:start position:0%
+too much heads-up play in this class so
+we call here and we
+
+ align:start position:0%
+we call here and we
+ 
+
+ align:start position:0%
+we call here and we
+check he makes it 32 and I decided check
+
+ align:start position:0%
+check he makes it 32 and I decided check
+ 
+
+ align:start position:0%
+check he makes it 32 and I decided check
+raise check raise bluff this flop I
+
+ align:start position:0%
+raise check raise bluff this flop I
+ 
+
+ align:start position:0%
+raise check raise bluff this flop I
+think I think it's close I mean I think
+
+ align:start position:0%
+think I think it's close I mean I think
+ 
+
+ align:start position:0%
+think I think it's close I mean I think
+I probably shouldn't be folding I think
+
+ align:start position:0%
+I probably shouldn't be folding I think
+ 
+
+ align:start position:0%
+I probably shouldn't be folding I think
+Jack's exuded it just has too many
+
+ align:start position:0%
+Jack's exuded it just has too many
+ 
+
+ align:start position:0%
+Jack's exuded it just has too many
+backdoor draws on this spot to ever fold
+
+ align:start position:0%
+backdoor draws on this spot to ever fold
+ 
+
+ align:start position:0%
+backdoor draws on this spot to ever fold
+just as part of us part of my strategy I
+
+ align:start position:0%
+just as part of us part of my strategy I
+ 
+
+ align:start position:0%
+just as part of us part of my strategy I
+think I decided that I wanted my
+
+ align:start position:0%
+think I decided that I wanted my
+ 
+
+ align:start position:0%
+think I decided that I wanted my
+strategy to to be I'm gonna raise good
+
+ align:start position:0%
+strategy to to be I'm gonna raise good
+ 
+
+ align:start position:0%
+strategy to to be I'm gonna raise good
+hands like eights and fours and then I'm
+
+ align:start position:0%
+hands like eights and fours and then I'm
+ 
+
+ align:start position:0%
+hands like eights and fours and then I'm
+gonna also raise hands with lots of
+
+ align:start position:0%
+gonna also raise hands with lots of
+ 
+
+ align:start position:0%
+gonna also raise hands with lots of
+backdrops like Jack's six cards so I
+
+ align:start position:0%
+backdrops like Jack's six cards so I
+ 
+
+ align:start position:0%
+backdrops like Jack's six cards so I
+decided to do this so
+
+ align:start position:0%
+decided to do this so
+ 
+
+ align:start position:0%
+decided to do this so
+unfortunately he goes all and so we fold
+
+ align:start position:0%
+unfortunately he goes all and so we fold
+ 
+
+ align:start position:0%
+unfortunately he goes all and so we fold
+it doesn't quite work so we
+
+ align:start position:0%
+it doesn't quite work so we
+ 
+
+ align:start position:0%
+it doesn't quite work so we
+turn off me raise Oh so
+
+ align:start position:0%
+turn off me raise Oh so
+ 
+
+ align:start position:0%
+turn off me raise Oh so
+one thing I should say is I think most
+
+ align:start position:0%
+one thing I should say is I think most
+ 
+
+ align:start position:0%
+one thing I should say is I think most
+of you know this but once a tournament
+
+ align:start position:0%
+of you know this but once a tournament
+ 
+
+ align:start position:0%
+of you know this but once a tournament
+gets heads up and it's just the small
+
+ align:start position:0%
+gets heads up and it's just the small
+ 
+
+ align:start position:0%
+gets heads up and it's just the small
+wine and the big blind the small blind
+
+ align:start position:0%
+wine and the big blind the small blind
+ 
+
+ align:start position:0%
+wine and the big blind the small blind
+is actually has position so normally
+
+ align:start position:0%
+is actually has position so normally
+ 
+
+ align:start position:0%
+is actually has position so normally
+when it's small line against big blind a
+
+ align:start position:0%
+when it's small line against big blind a
+ 
+
+ align:start position:0%
+when it's small line against big blind a
+big volume has position post-flop but
+
+ align:start position:0%
+big volume has position post-flop but
+ 
+
+ align:start position:0%
+big volume has position post-flop but
+when it ends up at a small line you
+
+ align:start position:0%
+when it ends up at a small line you
+ 
+
+ align:start position:0%
+when it ends up at a small line you
+actually have position so you're very
+
+ align:start position:0%
+actually have position so you're very
+ 
+
+ align:start position:0%
+actually have position so you're very
+strongly incentivized to play in the
+
+ align:start position:0%
+strongly incentivized to play in the
+ 
+
+ align:start position:0%
+strongly incentivized to play in the
+spotlight it's just by far the better
+
+ align:start position:0%
+spotlight it's just by far the better
+ 
+
+ align:start position:0%
+spotlight it's just by far the better
+position because um because you have
+
+ align:start position:0%
+position because um because you have
+ 
+
+ align:start position:0%
+position because um because you have
+position and you'll be put in less of a
+
+ align:start position:0%
+position and you'll be put in less of a
+ 
+
+ align:start position:0%
+position and you'll be put in less of a
+blind so
+
+ align:start position:0%
+blind so
+ 
+
+ align:start position:0%
+blind so
+another cheat that so I'm teaching you
+
+ align:start position:0%
+another cheat that so I'm teaching you
+ 
+
+ align:start position:0%
+another cheat that so I'm teaching you
+guys all these different sheets another
+
+ align:start position:0%
+guys all these different sheets another
+ 
+
+ align:start position:0%
+guys all these different sheets another
+cheat that people used to do it's not
+
+ align:start position:0%
+cheat that people used to do it's not
+ 
+
+ align:start position:0%
+cheat that people used to do it's not
+really a cheat but another sort of angle
+
+ align:start position:0%
+really a cheat but another sort of angle
+ 
+
+ align:start position:0%
+really a cheat but another sort of angle
+shootin people used to do back in the
+
+ align:start position:0%
+shootin people used to do back in the
+ 
+
+ align:start position:0%
+shootin people used to do back in the
+day is there would be people who like
+
+ align:start position:0%
+day is there would be people who like
+ 
+
+ align:start position:0%
+day is there would be people who like
+normally play pretty low stakes let's
+
+ align:start position:0%
+normally play pretty low stakes let's
+ 
+
+ align:start position:0%
+normally play pretty low stakes let's
+say like 25 cent 50 cent and then they
+
+ align:start position:0%
+say like 25 cent 50 cent and then they
+ 
+
+ align:start position:0%
+say like 25 cent 50 cent and then they
+would play they would sit at these $25
+
+ align:start position:0%
+would play they would sit at these $25
+ 
+
+ align:start position:0%
+would play they would sit at these $25
+$50 tables so like where the blinds are
+
+ align:start position:0%
+$50 tables so like where the blinds are
+ 
+
+ align:start position:0%
+$50 tables so like where the blinds are
+play five bucks 50 bucks which is pretty
+
+ align:start position:0%
+play five bucks 50 bucks which is pretty
+ 
+
+ align:start position:0%
+play five bucks 50 bucks which is pretty
+which is really high stakes for them and
+
+ align:start position:0%
+which is really high stakes for them and
+ 
+
+ align:start position:0%
+which is really high stakes for them and
+you know like that it's something they
+
+ align:start position:0%
+you know like that it's something they
+ 
+
+ align:start position:0%
+you know like that it's something they
+really don't have the bankroll to gamble
+
+ align:start position:0%
+really don't have the bankroll to gamble
+ 
+
+ align:start position:0%
+really don't have the bankroll to gamble
+all that but their strategy basically is
+
+ align:start position:0%
+all that but their strategy basically is
+ 
+
+ align:start position:0%
+all that but their strategy basically is
+if you're the first to sit down you get
+
+ align:start position:0%
+if you're the first to sit down you get
+ 
+
+ align:start position:0%
+if you're the first to sit down you get
+to be the dealer on the first hand so
+
+ align:start position:0%
+to be the dealer on the first hand so
+ 
+
+ align:start position:0%
+to be the dealer on the first hand so
+the strategy is basically just um sit
+
+ align:start position:0%
+the strategy is basically just um sit
+ 
+
+ align:start position:0%
+the strategy is basically just um sit
+there and then wait for someone else to
+
+ align:start position:0%
+there and then wait for someone else to
+ 
+
+ align:start position:0%
+there and then wait for someone else to
+sit down and then play the first hand as
+
+ align:start position:0%
+sit down and then play the first hand as
+ 
+
+ align:start position:0%
+sit down and then play the first hand as
+the dealer or they have a huge advantage
+
+ align:start position:0%
+the dealer or they have a huge advantage
+ 
+
+ align:start position:0%
+the dealer or they have a huge advantage
+they ain't just raised and usually the
+
+ align:start position:0%
+they ain't just raised and usually the
+ 
+
+ align:start position:0%
+they ain't just raised and usually the
+other guy will fold and they'll wait
+
+ align:start position:0%
+other guy will fold and they'll wait
+ 
+
+ align:start position:0%
+other guy will fold and they'll wait
+fifty bucks is a huge deal to them and
+
+ align:start position:0%
+fifty bucks is a huge deal to them and
+ 
+
+ align:start position:0%
+fifty bucks is a huge deal to them and
+another's leave after my first hand so
+
+ align:start position:0%
+another's leave after my first hand so
+ 
+
+ align:start position:0%
+another's leave after my first hand so
+this is something that happened quite a
+
+ align:start position:0%
+this is something that happened quite a
+ 
+
+ align:start position:0%
+this is something that happened quite a
+lot and then so you know my friends and
+
+ align:start position:0%
+lot and then so you know my friends and
+ 
+
+ align:start position:0%
+lot and then so you know my friends and
+I we talked about playing a crazy
+
+ align:start position:0%
+I we talked about playing a crazy
+ 
+
+ align:start position:0%
+I we talked about playing a crazy
+strategy where you would sit down
+
+ align:start position:0%
+strategy where you would sit down
+ 
+
+ align:start position:0%
+strategy where you would sit down
+knowing this is what the other guy's
+
+ align:start position:0%
+knowing this is what the other guy's
+ 
+
+ align:start position:0%
+knowing this is what the other guy's
+gonna do and then sit down with them and
+
+ align:start position:0%
+gonna do and then sit down with them and
+ 
+
+ align:start position:0%
+gonna do and then sit down with them and
+you know we would have the capital to
+
+ align:start position:0%
+you know we would have the capital to
+ 
+
+ align:start position:0%
+you know we would have the capital to
+take on risk and then we would basically
+
+ align:start position:0%
+take on risk and then we would basically
+ 
+
+ align:start position:0%
+take on risk and then we would basically
+just play the first name extremely
+
+ align:start position:0%
+just play the first name extremely
+ 
+
+ align:start position:0%
+just play the first name extremely
+aggressively yeah you don't worry about
+
+ align:start position:0%
+aggressively yeah you don't worry about
+ 
+
+ align:start position:0%
+aggressively yeah you don't worry about
+the guy has to pull those of the time
+
+ align:start position:0%
+the guy has to pull those of the time
+ 
+
+ align:start position:0%
+the guy has to pull those of the time
+because if he calls that's all his money
+
+ align:start position:0%
+because if he calls that's all his money
+ 
+
+ align:start position:0%
+because if he calls that's all his money
+up site so so yeah it lets do a lot of
+
+ align:start position:0%
+up site so so yeah it lets do a lot of
+ 
+
+ align:start position:0%
+up site so so yeah it lets do a lot of
+weird dynamics but
+
+ align:start position:0%
+weird dynamics but
+ 
+
+ align:start position:0%
+weird dynamics but
+okay so here we have but this is a turn
+
+ align:start position:0%
+okay so here we have but this is a turn
+ 
+
+ align:start position:0%
+okay so here we have but this is a turn
+this is I chose tournaments not cash
+
+ align:start position:0%
+this is I chose tournaments not cash
+ 
+
+ align:start position:0%
+this is I chose tournaments not cash
+gangsters there's fewer ways to do these
+
+ align:start position:0%
+gangsters there's fewer ways to do these
+ 
+
+ align:start position:0%
+gangsters there's fewer ways to do these
+commuters cheats so Queen ten we raise
+
+ align:start position:0%
+commuters cheats so Queen ten we raise
+ 
+
+ align:start position:0%
+commuters cheats so Queen ten we raise
+we take it down next
+
+ align:start position:0%
+we take it down next
+ 
+
+ align:start position:0%
+we take it down next
+time we get East Queen certain so
+
+ align:start position:0%
+time we get East Queen certain so
+ 
+
+ align:start position:0%
+time we get East Queen certain so
+unfortunately we go to lock so
+
+ align:start position:0%
+unfortunately we go to lock so
+ 
+
+ align:start position:0%
+unfortunately we go to lock so
+create we raise we take it down I
+
+ align:start position:0%
+create we raise we take it down I
+ 
+
+ align:start position:0%
+create we raise we take it down I
+started he calls um and then it's
+
+ align:start position:0%
+started he calls um and then it's
+ 
+
+ align:start position:0%
+started he calls um and then it's
+checked to us we continuation bed and he
+
+ align:start position:0%
+checked to us we continuation bed and he
+ 
+
+ align:start position:0%
+checked to us we continuation bed and he
+raises which is weird because it's a
+
+ align:start position:0%
+raises which is weird because it's a
+ 
+
+ align:start position:0%
+raises which is weird because it's a
+flop that's a lot better for my range
+
+ align:start position:0%
+flop that's a lot better for my range
+ 
+
+ align:start position:0%
+flop that's a lot better for my range
+than his because I can have ace king and
+
+ align:start position:0%
+than his because I can have ace king and
+ 
+
+ align:start position:0%
+than his because I can have ace king and
+his queen and even ace Jack I think if
+
+ align:start position:0%
+his queen and even ace Jack I think if
+ 
+
+ align:start position:0%
+his queen and even ace Jack I think if
+he had a strategy would it be raised
+
+ align:start position:0%
+he had a strategy would it be raised
+ 
+
+ align:start position:0%
+he had a strategy would it be raised
+preflop so in some sense it's weird
+
+ align:start position:0%
+preflop so in some sense it's weird
+ 
+
+ align:start position:0%
+preflop so in some sense it's weird
+because the like it's really hard for
+
+ align:start position:0%
+because the like it's really hard for
+ 
+
+ align:start position:0%
+because the like it's really hard for
+him to have I think pocket aces or
+
+ align:start position:0%
+him to have I think pocket aces or
+ 
+
+ align:start position:0%
+him to have I think pocket aces or
+pocket eights or like even pocket threes
+
+ align:start position:0%
+pocket eights or like even pocket threes
+ 
+
+ align:start position:0%
+pocket eights or like even pocket threes
+he probably would have rebase all-in
+
+ align:start position:0%
+he probably would have rebase all-in
+ 
+
+ align:start position:0%
+he probably would have rebase all-in
+preflop so really it's like what do you
+
+ align:start position:0%
+preflop so really it's like what do you
+ 
+
+ align:start position:0%
+preflop so really it's like what do you
+have right it's like I don't have much
+
+ align:start position:0%
+have right it's like I don't have much
+ 
+
+ align:start position:0%
+have right it's like I don't have much
+but really the court it's like what do
+
+ align:start position:0%
+but really the court it's like what do
+ 
+
+ align:start position:0%
+but really the court it's like what do
+you have so it's kind of weird because
+
+ align:start position:0%
+you have so it's kind of weird because
+ 
+
+ align:start position:0%
+you have so it's kind of weird because
+you know good I expect him to check
+
+ align:start position:0%
+you know good I expect him to check
+ 
+
+ align:start position:0%
+you know good I expect him to check
+raises flop so really that what he does
+
+ align:start position:0%
+raises flop so really that what he does
+ 
+
+ align:start position:0%
+raises flop so really that what he does
+on the one hand is just strange but on
+
+ align:start position:0%
+on the one hand is just strange but on
+ 
+
+ align:start position:0%
+on the one hand is just strange but on
+the other hand he must know that so it's
+
+ align:start position:0%
+the other hand he must know that so it's
+ 
+
+ align:start position:0%
+the other hand he must know that so it's
+you know I'm assuming it's somewhat
+
+ align:start position:0%
+you know I'm assuming it's somewhat
+ 
+
+ align:start position:0%
+you know I'm assuming it's somewhat
+balanced and he will occasionally turn
+
+ align:start position:0%
+balanced and he will occasionally turn
+ 
+
+ align:start position:0%
+balanced and he will occasionally turn
+up like h3 or something here so I decide
+
+ align:start position:0%
+up like h3 or something here so I decide
+ 
+
+ align:start position:0%
+up like h3 or something here so I decide
+to call and see one more card I don't
+
+ align:start position:0%
+to call and see one more card I don't
+ 
+
+ align:start position:0%
+to call and see one more card I don't
+know if that's that's great like maybe I
+
+ align:start position:0%
+know if that's that's great like maybe I
+ 
+
+ align:start position:0%
+know if that's that's great like maybe I
+should have just folded and just
+
+ align:start position:0%
+should have just folded and just
+ 
+
+ align:start position:0%
+should have just folded and just
+believed him or just like really raised
+
+ align:start position:0%
+believed him or just like really raised
+ 
+
+ align:start position:0%
+believed him or just like really raised
+if I didn't believe him
+
+ align:start position:0%
+if I didn't believe him
+ 
+
+ align:start position:0%
+if I didn't believe him
+re-raise essentially as a bluff like
+
+ align:start position:0%
+re-raise essentially as a bluff like
+ 
+
+ align:start position:0%
+re-raise essentially as a bluff like
+make it like a hundred thousand and two
+
+ align:start position:0%
+make it like a hundred thousand and two
+ 
+
+ align:start position:0%
+make it like a hundred thousand and two
+so he folds but I decide to call the
+
+ align:start position:0%
+so he folds but I decide to call the
+ 
+
+ align:start position:0%
+so he folds but I decide to call the
+turn is a nine putting out some straight
+
+ align:start position:0%
+turn is a nine putting out some straight
+ 
+
+ align:start position:0%
+turn is a nine putting out some straight
+draws but no flush draws and he that's
+
+ align:start position:0%
+draws but no flush draws and he that's
+ 
+
+ align:start position:0%
+draws but no flush draws and he that's
+fairly big and I fold I don't really
+
+ align:start position:0%
+fairly big and I fold I don't really
+ 
+
+ align:start position:0%
+fairly big and I fold I don't really
+know how I feel about how he played that
+
+ align:start position:0%
+know how I feel about how he played that
+ 
+
+ align:start position:0%
+know how I feel about how he played that
+hand I think I mostly played
+
+ align:start position:0%
+hand I think I mostly played
+ 
+
+ align:start position:0%
+hand I think I mostly played
+exploitative li-like I just called the
+
+ align:start position:0%
+exploitative li-like I just called the
+ 
+
+ align:start position:0%
+exploitative li-like I just called the
+flop because I wanted to see what he did
+
+ align:start position:0%
+flop because I wanted to see what he did
+ 
+
+ align:start position:0%
+flop because I wanted to see what he did
+and I folded the term because maybe
+
+ align:start position:0%
+and I folded the term because maybe
+ 
+
+ align:start position:0%
+and I folded the term because maybe
+based based on his bets sizing or his
+
+ align:start position:0%
+based based on his bets sizing or his
+ 
+
+ align:start position:0%
+based based on his bets sizing or his
+bad timing I just felt like he had it so
+
+ align:start position:0%
+bad timing I just felt like he had it so
+ 
+
+ align:start position:0%
+bad timing I just felt like he had it so
+I I'm not sure I'm extremely happy with
+
+ align:start position:0%
+I I'm not sure I'm extremely happy with
+ 
+
+ align:start position:0%
+I I'm not sure I'm extremely happy with
+how I played that hand but probably just
+
+ align:start position:0%
+how I played that hand but probably just
+ 
+
+ align:start position:0%
+how I played that hand but probably just
+at the time I decided to play
+
+ align:start position:0%
+at the time I decided to play
+ 
+
+ align:start position:0%
+at the time I decided to play
+exploitative Lee and try to play best
+
+ align:start position:0%
+exploitative Lee and try to play best
+ 
+
+ align:start position:0%
+exploitative Lee and try to play best
+against how I expected him to act so
+
+ align:start position:0%
+against how I expected him to act so
+ 
+
+ align:start position:0%
+against how I expected him to act so
+here with ten seven with ten seven off I
+
+ align:start position:0%
+here with ten seven with ten seven off I
+ 
+
+ align:start position:0%
+here with ten seven with ten seven off I
+decide you'd be base so
+
+ align:start position:0%
+decide you'd be base so
+ 
+
+ align:start position:0%
+decide you'd be base so
+this is so the reason I IV raise a hand
+
+ align:start position:0%
+this is so the reason I IV raise a hand
+ 
+
+ align:start position:0%
+this is so the reason I IV raise a hand
+as bad as ten send an officer I talked a
+
+ align:start position:0%
+as bad as ten send an officer I talked a
+ 
+
+ align:start position:0%
+as bad as ten send an officer I talked a
+bit about this lap two classes ago about
+
+ align:start position:0%
+bit about this lap two classes ago about
+ 
+
+ align:start position:0%
+bit about this lap two classes ago about
+like your preflop raising strategy so
+
+ align:start position:0%
+like your preflop raising strategy so
+ 
+
+ align:start position:0%
+like your preflop raising strategy so
+essentially what I'm doing is I want to
+
+ align:start position:0%
+essentially what I'm doing is I want to
+ 
+
+ align:start position:0%
+essentially what I'm doing is I want to
+be rebasing my good hands and also my
+
+ align:start position:0%
+be rebasing my good hands and also my
+ 
+
+ align:start position:0%
+be rebasing my good hands and also my
+hands that I'm not sad if he goes all in
+
+ align:start position:0%
+hands that I'm not sad if he goes all in
+ 
+
+ align:start position:0%
+hands that I'm not sad if he goes all in
+and I have to fold and then don't get to
+
+ align:start position:0%
+and I have to fold and then don't get to
+ 
+
+ align:start position:0%
+and I have to fold and then don't get to
+see a flop with so like if I had ten
+
+ align:start position:0%
+see a flop with so like if I had ten
+ 
+
+ align:start position:0%
+see a flop with so like if I had ten
+seven suited that's sort of like too
+
+ align:start position:0%
+seven suited that's sort of like too
+ 
+
+ align:start position:0%
+seven suited that's sort of like too
+good of a hand and I really don't want
+
+ align:start position:0%
+good of a hand and I really don't want
+ 
+
+ align:start position:0%
+good of a hand and I really don't want
+to rebase and then if he goes all-in
+
+ align:start position:0%
+to rebase and then if he goes all-in
+ 
+
+ align:start position:0%
+to rebase and then if he goes all-in
+fold by pretty ten seven suited and not
+
+ align:start position:0%
+fold by pretty ten seven suited and not
+ 
+
+ align:start position:0%
+fold by pretty ten seven suited and not
+even get to see a flop with it but ten
+
+ align:start position:0%
+even get to see a flop with it but ten
+ 
+
+ align:start position:0%
+even get to see a flop with it but ten
+seven offsuit is a bad enough hand where
+
+ align:start position:0%
+seven offsuit is a bad enough hand where
+ 
+
+ align:start position:0%
+seven offsuit is a bad enough hand where
+I'm not that sad if he just goes on and
+
+ align:start position:0%
+I'm not that sad if he just goes on and
+ 
+
+ align:start position:0%
+I'm not that sad if he just goes on and
+I have to fold so that's why I'm raising
+
+ align:start position:0%
+I have to fold so that's why I'm raising
+ 
+
+ align:start position:0%
+I have to fold so that's why I'm raising
+like my good hands and also my sort of
+
+ align:start position:0%
+like my good hands and also my sort of
+ 
+
+ align:start position:0%
+like my good hands and also my sort of
+weakest possible hands that I that I'm
+
+ align:start position:0%
+weakest possible hands that I that I'm
+ 
+
+ align:start position:0%
+weakest possible hands that I that I'm
+okay if I don't get to see a flop with
+
+ align:start position:0%
+okay if I don't get to see a flop with
+ 
+
+ align:start position:0%
+okay if I don't get to see a flop with
+she
+
+ align:start position:0%
+she
+ 
+
+ align:start position:0%
+she
+does call unfortunately but we do hit a
+
+ align:start position:0%
+does call unfortunately but we do hit a
+ 
+
+ align:start position:0%
+does call unfortunately but we do hit a
+pretty good swap so I'm just going to
+
+ align:start position:0%
+pretty good swap so I'm just going to
+ 
+
+ align:start position:0%
+pretty good swap so I'm just going to
+bet and get it all in heads up basically
+
+ align:start position:0%
+bet and get it all in heads up basically
+ 
+
+ align:start position:0%
+bet and get it all in heads up basically
+any kind of top pair is in general just
+
+ align:start position:0%
+any kind of top pair is in general just
+ 
+
+ align:start position:0%
+any kind of top pair is in general just
+way more than good enough to put all
+
+ align:start position:0%
+way more than good enough to put all
+ 
+
+ align:start position:0%
+way more than good enough to put all
+your money in like people and stuff so
+
+ align:start position:0%
+your money in like people and stuff so
+ 
+
+ align:start position:0%
+your money in like people and stuff so
+he sips we raise I'm you know fairly
+
+ align:start position:0%
+he sips we raise I'm you know fairly
+ 
+
+ align:start position:0%
+he sips we raise I'm you know fairly
+quickly because I'm running a bit short
+
+ align:start position:0%
+quickly because I'm running a bit short
+ 
+
+ align:start position:0%
+quickly because I'm running a bit short
+of time we continuation bet the flop
+
+ align:start position:0%
+of time we continuation bet the flop
+ 
+
+ align:start position:0%
+of time we continuation bet the flop
+engine down he
+
+ align:start position:0%
+engine down he
+ 
+
+ align:start position:0%
+engine down he
+raises here I call with King six which
+
+ align:start position:0%
+raises here I call with King six which
+ 
+
+ align:start position:0%
+raises here I call with King six which
+is pretty borderline not prime how could
+
+ align:start position:0%
+is pretty borderline not prime how could
+ 
+
+ align:start position:0%
+is pretty borderline not prime how could
+I go I mean I think fold it's too good a
+
+ align:start position:0%
+I go I mean I think fold it's too good a
+ 
+
+ align:start position:0%
+I go I mean I think fold it's too good a
+hindi fold but probably it's too bad a
+
+ align:start position:0%
+hindi fold but probably it's too bad a
+ 
+
+ align:start position:0%
+hindi fold but probably it's too bad a
+hand you call probably I should have
+
+ align:start position:0%
+hand you call probably I should have
+ 
+
+ align:start position:0%
+hand you call probably I should have
+just raised by the same logic as before
+
+ align:start position:0%
+just raised by the same logic as before
+ 
+
+ align:start position:0%
+just raised by the same logic as before
+but we call and I decided to donk out on
+
+ align:start position:0%
+but we call and I decided to donk out on
+ 
+
+ align:start position:0%
+but we call and I decided to donk out on
+the spot because I figured there's I
+
+ align:start position:0%
+the spot because I figured there's I
+ 
+
+ align:start position:0%
+the spot because I figured there's I
+mean there's a number of draws I can
+
+ align:start position:0%
+mean there's a number of draws I can
+ 
+
+ align:start position:0%
+mean there's a number of draws I can
+have so and here I do sort of have a
+
+ align:start position:0%
+have so and here I do sort of have a
+ 
+
+ align:start position:0%
+have so and here I do sort of have a
+weak drawn like a seven gives me a bad
+
+ align:start position:0%
+weak drawn like a seven gives me a bad
+ 
+
+ align:start position:0%
+weak drawn like a seven gives me a bad
+straight but still a very good hand in
+
+ align:start position:0%
+straight but still a very good hand in
+ 
+
+ align:start position:0%
+straight but still a very good hand in
+that you play clock he calls and the
+
+ align:start position:0%
+that you play clock he calls and the
+ 
+
+ align:start position:0%
+that you play clock he calls and the
+turn is a jock which I still have a
+
+ align:start position:0%
+turn is a jock which I still have a
+ 
+
+ align:start position:0%
+turn is a jock which I still have a
+straight job because now a queen gives
+
+ align:start position:0%
+straight job because now a queen gives
+ 
+
+ align:start position:0%
+straight job because now a queen gives
+Street so I continued bluffing
+
+ align:start position:0%
+Street so I continued bluffing
+ 
+
+ align:start position:0%
+Street so I continued bluffing
+it's a hit Gold's just good 62
+
+ align:start position:0%
+it's a hit Gold's just good 62
+ 
+
+ align:start position:0%
+it's a hit Gold's just good 62
+offsuit I just give one to them so yeah
+
+ align:start position:0%
+offsuit I just give one to them so yeah
+ 
+
+ align:start position:0%
+offsuit I just give one to them so yeah
+I think you should be playing like 90 90
+
+ align:start position:0%
+I think you should be playing like 90 90
+ 
+
+ align:start position:0%
+I think you should be playing like 90 90
+95 percent of buttons and maybe not that
+
+ align:start position:0%
+95 percent of buttons and maybe not that
+ 
+
+ align:start position:0%
+95 percent of buttons and maybe not that
+high when it's getting shallower but
+
+ align:start position:0%
+high when it's getting shallower but
+ 
+
+ align:start position:0%
+high when it's getting shallower but
+like at least 80% of buttons but 2/3 off
+
+ align:start position:0%
+like at least 80% of buttons but 2/3 off
+ 
+
+ align:start position:0%
+like at least 80% of buttons but 2/3 off
+suit is one of the hands I'm ok with
+
+ align:start position:0%
+suit is one of the hands I'm ok with
+ 
+
+ align:start position:0%
+suit is one of the hands I'm ok with
+folding 8 5 suited I just check raising
+
+ align:start position:0%
+folding 8 5 suited I just check raising
+ 
+
+ align:start position:0%
+folding 8 5 suited I just check raising
+the swapping getting it in field so yeah
+
+ align:start position:0%
+the swapping getting it in field so yeah
+ 
+
+ align:start position:0%
+the swapping getting it in field so yeah
+the same has up you of it you had an
+
+ align:start position:0%
+the same has up you of it you had an
+ 
+
+ align:start position:0%
+the same has up you of it you had an
+opponent that like from the big blind
+
+ align:start position:0%
+opponent that like from the big blind
+ 
+
+ align:start position:0%
+opponent that like from the big blind
+was very likely to three bet you yeah
+
+ align:start position:0%
+was very likely to three bet you yeah
+ 
+
+ align:start position:0%
+was very likely to three bet you yeah
+like how would you adjust your range
+
+ align:start position:0%
+like how would you adjust your range
+ 
+
+ align:start position:0%
+like how would you adjust your range
+like opening from the button or the
+
+ align:start position:0%
+like opening from the button or the
+ 
+
+ align:start position:0%
+like opening from the button or the
+small one okay so I mean if they're if
+
+ align:start position:0%
+small one okay so I mean if they're if
+ 
+
+ align:start position:0%
+small one okay so I mean if they're if
+they're so if they're really loose you
+
+ align:start position:0%
+they're so if they're really loose you
+ 
+
+ align:start position:0%
+they're so if they're really loose you
+would basically raise only or like good
+
+ align:start position:0%
+would basically raise only or like good
+ 
+
+ align:start position:0%
+would basically raise only or like good
+hands that you're hoping they raise
+
+ align:start position:0%
+hands that you're hoping they raise
+ 
+
+ align:start position:0%
+hands that you're hoping they raise
+along with and so like maybe 60% of your
+
+ align:start position:0%
+along with and so like maybe 60% of your
+ 
+
+ align:start position:0%
+along with and so like maybe 60% of your
+hands like down maybe or oh yeah yeah
+
+ align:start position:0%
+hands like down maybe or oh yeah yeah
+ 
+
+ align:start position:0%
+hands like down maybe or oh yeah yeah
+yeah you would you would basically raise
+
+ align:start position:0%
+yeah you would you would basically raise
+ 
+
+ align:start position:0%
+yeah you would you would basically raise
+less they just have more value
+
+ align:start position:0%
+less they just have more value
+ 
+
+ align:start position:0%
+less they just have more value
+essentially yeah good
+
+ align:start position:0%
+essentially yeah good
+ 
+
+ align:start position:0%
+essentially yeah good
+yeah yeah and also another thing you can
+
+ align:start position:0%
+yeah yeah and also another thing you can
+ 
+
+ align:start position:0%
+yeah yeah and also another thing you can
+do is call more I don't think it gets
+
+ align:start position:0%
+do is call more I don't think it gets
+ 
+
+ align:start position:0%
+do is call more I don't think it gets
+relevant in this heads-up match but
+
+ align:start position:0%
+relevant in this heads-up match but
+ 
+
+ align:start position:0%
+relevant in this heads-up match but
+sometimes it gets shallow enough where
+
+ align:start position:0%
+sometimes it gets shallow enough where
+ 
+
+ align:start position:0%
+sometimes it gets shallow enough where
+you actually want to have a calling
+
+ align:start position:0%
+you actually want to have a calling
+ 
+
+ align:start position:0%
+you actually want to have a calling
+range pre-thought from the button okay
+
+ align:start position:0%
+range pre-thought from the button okay
+ 
+
+ align:start position:0%
+range pre-thought from the button okay
+so Kington so case it was okay so I do
+
+ align:start position:0%
+so Kington so case it was okay so I do
+ 
+
+ align:start position:0%
+so Kington so case it was okay so I do
+call here I think I essentially call
+
+ align:start position:0%
+call here I think I essentially call
+ 
+
+ align:start position:0%
+call here I think I essentially call
+thinking I would call if he went on but
+
+ align:start position:0%
+thinking I would call if he went on but
+ 
+
+ align:start position:0%
+thinking I would call if he went on but
+also just to make it so that I can also
+
+ align:start position:0%
+also just to make it so that I can also
+ 
+
+ align:start position:0%
+also just to make it so that I can also
+sometimes call a hand like 10-4 off suit
+
+ align:start position:0%
+sometimes call a hand like 10-4 off suit
+ 
+
+ align:start position:0%
+sometimes call a hand like 10-4 off suit
+and he can't just shove any to it expect
+
+ align:start position:0%
+and he can't just shove any to it expect
+ 
+
+ align:start position:0%
+and he can't just shove any to it expect
+beautiful so I said to Collier we got a
+
+ align:start position:0%
+beautiful so I said to Collier we got a
+ 
+
+ align:start position:0%
+beautiful so I said to Collier we got a
+great spot so I check it back as a slow
+
+ align:start position:0%
+great spot so I check it back as a slow
+ 
+
+ align:start position:0%
+great spot so I check it back as a slow
+play he
+
+ align:start position:0%
+play he
+ 
+
+ align:start position:0%
+play he
+checks again on the turn so I bet he
+
+ align:start position:0%
+checks again on the turn so I bet he
+ 
+
+ align:start position:0%
+checks again on the turn so I bet he
+calls the river he leads out quite big
+
+ align:start position:0%
+calls the river he leads out quite big
+ 
+
+ align:start position:0%
+calls the river he leads out quite big
+and I just call because I think raising
+
+ align:start position:0%
+and I just call because I think raising
+ 
+
+ align:start position:0%
+and I just call because I think raising
+I'll usually only get called by better
+
+ align:start position:0%
+I'll usually only get called by better
+ 
+
+ align:start position:0%
+I'll usually only get called by better
+and he actually turns up a fluster so
+
+ align:start position:0%
+and he actually turns up a fluster so
+ 
+
+ align:start position:0%
+and he actually turns up a fluster so
+it's a weird handle but I mean it seems
+
+ align:start position:0%
+it's a weird handle but I mean it seems
+ 
+
+ align:start position:0%
+it's a weird handle but I mean it seems
+like we could have lost a lot more but
+
+ align:start position:0%
+like we could have lost a lot more but
+ 
+
+ align:start position:0%
+like we could have lost a lot more but
+I'm not saying our opponent played the
+
+ align:start position:0%
+I'm not saying our opponent played the
+ 
+
+ align:start position:0%
+I'm not saying our opponent played the
+hand badly but we were very lucky to
+
+ align:start position:0%
+hand badly but we were very lucky to
+ 
+
+ align:start position:0%
+hand badly but we were very lucky to
+lose this little when we have you know
+
+ align:start position:0%
+lose this little when we have you know
+ 
+
+ align:start position:0%
+lose this little when we have you know
+two pair against a flush and we only
+
+ align:start position:0%
+two pair against a flush and we only
+ 
+
+ align:start position:0%
+two pair against a flush and we only
+lost essentially like four big blinds or
+
+ align:start position:0%
+lost essentially like four big blinds or
+ 
+
+ align:start position:0%
+lost essentially like four big blinds or
+something I guess I'll be happy to get
+
+ align:start position:0%
+something I guess I'll be happy to get
+ 
+
+ align:start position:0%
+something I guess I'll be happy to get
+away with that okay I'll probably I'll
+
+ align:start position:0%
+away with that okay I'll probably I'll
+ 
+
+ align:start position:0%
+away with that okay I'll probably I'll
+probably run like two or three minutes
+
+ align:start position:0%
+probably run like two or three minutes
+ 
+
+ align:start position:0%
+probably run like two or three minutes
+over time I'll try to bury but I don't
+
+ align:start position:0%
+over time I'll try to bury but I don't
+ 
+
+ align:start position:0%
+over time I'll try to bury but I don't
+want to not finish the tournament today
+
+ align:start position:0%
+want to not finish the tournament today
+ 
+
+ align:start position:0%
+want to not finish the tournament today
+so we fooled this maybe I'll skip
+
+ align:start position:0%
+so we fooled this maybe I'll skip
+ 
+
+ align:start position:0%
+so we fooled this maybe I'll skip
+forward a bit to some of the bigger pots
+
+ align:start position:0%
+forward a bit to some of the bigger pots
+ 
+
+ align:start position:0%
+forward a bit to some of the bigger pots
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what happened here so we based Jack
+
+ align:start position:0%
+what happened here so we based Jack
+ 
+
+ align:start position:0%
+what happened here so we based Jack
+sticks he goes all in we fold all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right let's go to this one okay so kings
+
+ align:start position:0%
+right let's go to this one okay so kings
+ 
+
+ align:start position:0%
+right let's go to this one okay so kings
+okay so the match has gone in for a bit
+
+ align:start position:0%
+okay so the match has gone in for a bit
+ 
+
+ align:start position:0%
+okay so the match has gone in for a bit
+if he's won a bunch of pots he's
+
+ align:start position:0%
+if he's won a bunch of pots he's
+ 
+
+ align:start position:0%
+if he's won a bunch of pots he's
+catching up he's catching up King three
+
+ align:start position:0%
+catching up he's catching up King three
+ 
+
+ align:start position:0%
+catching up he's catching up King three
+off rebates he calls so here the flop I
+
+ align:start position:0%
+off rebates he calls so here the flop I
+ 
+
+ align:start position:0%
+off rebates he calls so here the flop I
+think is so once again it's a situation
+
+ align:start position:0%
+think is so once again it's a situation
+ 
+
+ align:start position:0%
+think is so once again it's a situation
+where I don't think he ever has an ace
+
+ align:start position:0%
+where I don't think he ever has an ace
+ 
+
+ align:start position:0%
+where I don't think he ever has an ace
+so I'm basically betting a hundred
+
+ align:start position:0%
+so I'm basically betting a hundred
+ 
+
+ align:start position:0%
+so I'm basically betting a hundred
+percent he
+
+ align:start position:0%
+percent he
+ 
+
+ align:start position:0%
+percent he
+calls the turns another ace which is a
+
+ align:start position:0%
+calls the turns another ace which is a
+ 
+
+ align:start position:0%
+calls the turns another ace which is a
+bad card for us because now it's less
+
+ align:start position:0%
+bad card for us because now it's less
+ 
+
+ align:start position:0%
+bad card for us because now it's less
+likely we have an ace but so but
+
+ align:start position:0%
+likely we have an ace but so but
+ 
+
+ align:start position:0%
+likely we have an ace but so but
+normally it's I still think it's a fine
+
+ align:start position:0%
+normally it's I still think it's a fine
+ 
+
+ align:start position:0%
+normally it's I still think it's a fine
+spot to Bluff just because he it's he
+
+ align:start position:0%
+spot to Bluff just because he it's he
+ 
+
+ align:start position:0%
+spot to Bluff just because he it's he
+essentially can't have an ace and we can
+
+ align:start position:0%
+essentially can't have an ace and we can
+ 
+
+ align:start position:0%
+essentially can't have an ace and we can
+but I think King high is good enough
+
+ align:start position:0%
+but I think King high is good enough
+ 
+
+ align:start position:0%
+but I think King high is good enough
+here where I'm gonna win the pot by
+
+ align:start position:0%
+here where I'm gonna win the pot by
+ 
+
+ align:start position:0%
+here where I'm gonna win the pot by
+checking it down with my king high often
+
+ align:start position:0%
+checking it down with my king high often
+ 
+
+ align:start position:0%
+checking it down with my king high often
+enough that bluffing is superfluous so I
+
+ align:start position:0%
+enough that bluffing is superfluous so I
+ 
+
+ align:start position:0%
+enough that bluffing is superfluous so I
+just check and it struck down and he was
+
+ align:start position:0%
+just check and it struck down and he was
+ 
+
+ align:start position:0%
+just check and it struck down and he was
+actually trapping with King 9 here so he
+
+ align:start position:0%
+actually trapping with King 9 here so he
+ 
+
+ align:start position:0%
+actually trapping with King 9 here so he
+wins that one yeah
+
+ align:start position:0%
+wins that one yeah
+ 
+
+ align:start position:0%
+wins that one yeah
+and probably he wouldn't have folded
+
+ align:start position:0%
+and probably he wouldn't have folded
+ 
+
+ align:start position:0%
+and probably he wouldn't have folded
+like let's say I I bet the turn inch
+
+ align:start position:0%
+like let's say I I bet the turn inch
+ 
+
+ align:start position:0%
+like let's say I I bet the turn inch
+went all-in on the river probably he has
+
+ align:start position:0%
+went all-in on the river probably he has
+ 
+
+ align:start position:0%
+went all-in on the river probably he has
+to call just because it's like almost
+
+ align:start position:0%
+to call just because it's like almost
+ 
+
+ align:start position:0%
+to call just because it's like almost
+the best hand you can possibly have it
+
+ align:start position:0%
+the best hand you can possibly have it
+ 
+
+ align:start position:0%
+the best hand you can possibly have it
+pretty much is the best thing you can
+
+ align:start position:0%
+pretty much is the best thing you can
+ 
+
+ align:start position:0%
+pretty much is the best thing you can
+possibly have other than maybe like 76
+
+ align:start position:0%
+possibly have other than maybe like 76
+ 
+
+ align:start position:0%
+possibly have other than maybe like 76
+but I think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nothing happens there so let me see okay
+
+ align:start position:0%
+nothing happens there so let me see okay
+ 
+
+ align:start position:0%
+nothing happens there so let me see okay
+so yeah we lose a bunch of pots because
+
+ align:start position:0%
+so yeah we lose a bunch of pots because
+ 
+
+ align:start position:0%
+so yeah we lose a bunch of pots because
+we've raised and he goes he be raises
+
+ align:start position:0%
+we've raised and he goes he be raises
+ 
+
+ align:start position:0%
+we've raised and he goes he be raises
+and we fold so things aren't looking too
+
+ align:start position:0%
+and we fold so things aren't looking too
+ 
+
+ align:start position:0%
+and we fold so things aren't looking too
+good Oh so I actually made sort of a
+
+ align:start position:0%
+good Oh so I actually made sort of a
+ 
+
+ align:start position:0%
+good Oh so I actually made sort of a
+hero fold here umm I think once again
+
+ align:start position:0%
+hero fold here umm I think once again
+ 
+
+ align:start position:0%
+hero fold here umm I think once again
+this is an exploitative play I would
+
+ align:start position:0%
+this is an exploitative play I would
+ 
+
+ align:start position:0%
+this is an exploitative play I would
+probably never fold this like from an
+
+ align:start position:0%
+probably never fold this like from an
+ 
+
+ align:start position:0%
+probably never fold this like from an
+optimal strategy point of view I think
+
+ align:start position:0%
+optimal strategy point of view I think
+ 
+
+ align:start position:0%
+optimal strategy point of view I think
+an ace and heads up with only 20 big
+
+ align:start position:0%
+an ace and heads up with only 20 big
+ 
+
+ align:start position:0%
+an ace and heads up with only 20 big
+blinds is way too good but he did just
+
+ align:start position:0%
+blinds is way too good but he did just
+ 
+
+ align:start position:0%
+blinds is way too good but he did just
+rear ace me two hands ago and I don't
+
+ align:start position:0%
+rear ace me two hands ago and I don't
+ 
+
+ align:start position:0%
+rear ace me two hands ago and I don't
+know I think at the time I just felt
+
+ align:start position:0%
+know I think at the time I just felt
+ 
+
+ align:start position:0%
+know I think at the time I just felt
+like he almost only had it did this so I
+
+ align:start position:0%
+like he almost only had it did this so I
+ 
+
+ align:start position:0%
+like he almost only had it did this so I
+made it exploitative I made an
+
+ align:start position:0%
+made it exploitative I made an
+ 
+
+ align:start position:0%
+made it exploitative I made an
+exploitative fold I'm based on what I
+
+ align:start position:0%
+exploitative fold I'm based on what I
+ 
+
+ align:start position:0%
+exploitative fold I'm based on what I
+thought he had so the next hand he
+
+ align:start position:0%
+thought he had so the next hand he
+ 
+
+ align:start position:0%
+thought he had so the next hand he
+raised as we go along the pocket fives
+
+ align:start position:0%
+raised as we go along the pocket fives
+ 
+
+ align:start position:0%
+raised as we go along the pocket fives
+and we heard her a five yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I was very surprised I was basically
+
+ align:start position:0%
+I was very surprised I was basically
+ 
+
+ align:start position:0%
+I was very surprised I was basically
+ready to just leave it I was right in
+
+ align:start position:0%
+ready to just leave it I was right in
+ 
+
+ align:start position:0%
+ready to just leave it I was right in
+some other tournaments but I basically
+
+ align:start position:0%
+some other tournaments but I basically
+ 
+
+ align:start position:0%
+some other tournaments but I basically
+was ready to close the table and focus
+
+ align:start position:0%
+was ready to close the table and focus
+ 
+
+ align:start position:0%
+was ready to close the table and focus
+on the other tournaments but somehow we
+
+ align:start position:0%
+on the other tournaments but somehow we
+ 
+
+ align:start position:0%
+on the other tournaments but somehow we
+get there and
+
+ align:start position:0%
+get there and
+ 
+
+ align:start position:0%
+get there and
+then the tournament just is easy from
+
+ align:start position:0%
+then the tournament just is easy from
+ 
+
+ align:start position:0%
+then the tournament just is easy from
+there we get a sniper go online he folds
+
+ align:start position:0%
+there we get a sniper go online he folds
+ 
+
+ align:start position:0%
+there we get a sniper go online he folds
+and then he goes on into our pocket
+
+ align:start position:0%
+and then he goes on into our pocket
+ 
+
+ align:start position:0%
+and then he goes on into our pocket
+sixes and we hit a straight so we win
+
+ align:start position:0%
+sixes and we hit a straight so we win
+ 
+
+ align:start position:0%
+sixes and we hit a straight so we win
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right cool yeah so so okay so yeah so I
+
+ align:start position:0%
+right cool yeah so so okay so yeah so I
+ 
+
+ align:start position:0%
+right cool yeah so so okay so yeah so I
+played through all the hands in a
+
+ align:start position:0%
+played through all the hands in a
+ 
+
+ align:start position:0%
+played through all the hands in a
+tournament once again yeah there's a lot
+
+ align:start position:0%
+tournament once again yeah there's a lot
+ 
+
+ align:start position:0%
+tournament once again yeah there's a lot
+of selection bias there but hopefully
+
+ align:start position:0%
+of selection bias there but hopefully
+ 
+
+ align:start position:0%
+of selection bias there but hopefully
+you learn some stuff from that so
+
+ align:start position:0%
+you learn some stuff from that so
+ 
+
+ align:start position:0%
+you learn some stuff from that so
+there's two classes left next class all
+
+ align:start position:0%
+there's two classes left next class all
+ 
+
+ align:start position:0%
+there's two classes left next class all
+sort of wrap up the theory is the exact
+
+ align:start position:0%
+sort of wrap up the theory is the exact
+ 
+
+ align:start position:0%
+sort of wrap up the theory is the exact
+poker example so talk a bit more about
+
+ align:start position:0%
+poker example so talk a bit more about
+ 
+
+ align:start position:0%
+poker example so talk a bit more about
+cash games and show you how to play when
+
+ align:start position:0%
+cash games and show you how to play when
+ 
+
+ align:start position:0%
+cash games and show you how to play when
+you're like really deep and talk about
+
+ align:start position:0%
+you're like really deep and talk about
+ 
+
+ align:start position:0%
+you're like really deep and talk about
+like cool spot raising and then Friday
+
+ align:start position:0%
+like cool spot raising and then Friday
+ 
+
+ align:start position:0%
+like cool spot raising and then Friday
+we have a guest lecture from Bill Chang
+
+ align:start position:0%
+we have a guest lecture from Bill Chang
+ 
+
+ align:start position:0%
+we have a guest lecture from Bill Chang
+which should be really exciting he
+
+ align:start position:0%
+which should be really exciting he
+ 
+
+ align:start position:0%
+which should be really exciting he
+always have some very interesting stuff
+
+ align:start position:0%
+always have some very interesting stuff
+ 
+
+ align:start position:0%
+always have some very interesting stuff
+so I'll see you guys around
\ No newline at end of file